LMFDB - Embedded newform 76.7.l.a.23.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(23,76)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("76.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.l (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$58$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.14
Character	$\chi$	$=$	76.23
Dual form			76.7.l.a.43.14

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.92630 - 5.37392i) q^{2} +(27.6808 - 4.88087i) q^{3} +(6.24202 + 63.6949i) q^{4} +(-34.1068 + 28.6190i) q^{5} +(-190.274 - 119.829i) q^{6} +(83.9559 + 48.4720i) q^{7} +(305.299 - 411.019i) q^{8} +(57.3665 - 20.8797i) q^{9} +O(q^{10})$	\(q+(-5.92630 - 5.37392i) q^{2} +(27.6808 - 4.88087i) q^{3} +(6.24202 + 63.6949i) q^{4} +(-34.1068 + 28.6190i) q^{5} +(-190.274 - 119.829i) q^{6} +(83.9559 + 48.4720i) q^{7} +(305.299 - 411.019i) q^{8} +(57.3665 - 20.8797i) q^{9} +(355.923 + 13.6824i) q^{10} +(815.927 - 471.076i) q^{11} +(483.670 + 1732.66i) q^{12} +(-755.075 + 4282.24i) q^{13} +(-237.063 - 738.431i) q^{14} +(-804.416 + 958.666i) q^{15} +(-4018.07 + 795.170i) q^{16} +(-3638.63 - 1324.35i) q^{17} +(-452.177 - 184.544i) q^{18} +(6812.71 + 795.568i) q^{19} +(-2035.78 - 1993.79i) q^{20} +(2560.55 + 931.964i) q^{21} +(-7366.95 - 1592.99i) q^{22} +(-10416.9 + 12414.4i) q^{23} +(6444.78 - 12867.4i) q^{24} +(-2369.03 + 13435.4i) q^{25} +(27487.2 - 21320.1i) q^{26} +(-16259.3 + 9387.33i) q^{27} +(-2563.36 + 5650.12i) q^{28} +(36648.4 - 13338.9i) q^{29} +(9919.00 - 1358.47i) q^{30} +(40577.6 + 23427.5i) q^{31} +(28085.5 + 16880.4i) q^{32} +(20286.2 - 17022.2i) q^{33} +(14446.7 + 27402.2i) q^{34} +(-4250.68 + 749.510i) q^{35} +(1688.01 + 3523.62i) q^{36} +58049.8 q^{37} +(-36098.8 - 41325.7i) q^{38} +122221. i q^{39} +(1350.18 + 22755.9i) q^{40} +(2165.93 + 12283.6i) q^{41} +(-10166.3 - 19283.3i) q^{42} +(-11932.4 - 14220.4i) q^{43} +(35098.1 + 49029.9i) q^{44} +(-1359.03 + 2353.91i) q^{45} +(128448. - 17591.8i) q^{46} +(4562.85 + 12536.3i) q^{47} +(-107342. + 41622.6i) q^{48} +(-54125.4 - 93748.0i) q^{49} +(86240.4 - 66891.4i) q^{50} +(-107184. - 18899.5i) q^{51} +(-277470. - 21364.5i) q^{52} +(48900.6 + 41032.4i) q^{53} +(146804. + 31744.2i) q^{54} +(-14346.9 + 39417.9i) q^{55} +(45554.5 - 19709.0i) q^{56} +(192464. - 11230.0i) q^{57} +(-288872. - 117895. i) q^{58} +(-75569.9 + 207627. i) q^{59} +(-66083.3 - 45253.2i) q^{60} +(-165600. - 138955. i) q^{61} +(-114578. - 356899. i) q^{62} +(5828.34 + 1027.69i) q^{63} +(-75729.2 - 250967. i) q^{64} +(-96800.3 - 167663. i) q^{65} +(-211698. - 8138.08i) q^{66} +(-28802.8 - 79135.0i) q^{67} +(61642.1 - 240029. i) q^{68} +(-227756. + 394485. i) q^{69} +(29218.6 + 18401.0i) q^{70} +(-32265.4 - 38452.4i) q^{71} +(8931.98 - 29953.3i) q^{72} +(116889. + 662910. i) q^{73} +(-344020. - 311955. i) q^{74} +383466. i q^{75} +(-8148.51 + 438900. i) q^{76} +91335.9 q^{77} +(656807. - 724320. i) q^{78} +(-388719. + 68541.7i) q^{79} +(114287. - 142114. i) q^{80} +(-438345. + 367815. i) q^{81} +(53175.2 - 84435.9i) q^{82} +(564813. + 326095. i) q^{83} +(-43378.3 + 168911. i) q^{84} +(162004. - 58964.5i) q^{85} +(-5704.70 + 148398. i) q^{86} +(949351. - 548108. i) q^{87} +(55480.6 - 479180. i) q^{88} +(150198. - 851816. i) q^{89} +(20703.7 - 6646.66i) q^{90} +(-270962. + 322920. i) q^{91} +(-855758. - 586014. i) q^{92} +(1.23757e6 + 450437. i) q^{93} +(40328.3 - 98814.3i) q^{94} +(-255128. + 167838. i) q^{95} +(859819. + 330181. i) q^{96} +(-624554. - 227319. i) q^{97} +(-183031. + 846444. i) q^{98} +(36971.0 - 44060.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9}+O(q^{10}) $ 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9	\( 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9} + 2811 q^{10} - 3 q^{12} - 7572 q^{13} + 8217 q^{14} - 1392 q^{16} - 12 q^{17} - 12 q^{18} + 33618 q^{20} - 33546 q^{21} - 198 q^{22} - 7128 q^{24} - 12 q^{25} + 84453 q^{26} + 13464 q^{28} - 12 q^{29} + 75510 q^{30} + 9339 q^{32} - 366 q^{33} - 289248 q^{34} - 419349 q^{36} - 24 q^{37} + 158040 q^{38} + 264570 q^{40} + 27360 q^{41} + 206001 q^{42} - 525639 q^{44} - 6 q^{45} - 269328 q^{46} - 703179 q^{48} + 2319360 q^{49} + 264534 q^{50} + 130809 q^{52} - 182292 q^{53} + 607083 q^{54} - 705906 q^{56} - 12 q^{57} - 710004 q^{58} + 1060416 q^{60} - 325092 q^{61} - 1967868 q^{62} - 1611921 q^{64} + 398994 q^{65} - 2295684 q^{66} + 1125642 q^{68} - 1625190 q^{69} + 3496059 q^{70} + 4948626 q^{72} - 2224812 q^{73} + 2661159 q^{74} - 968262 q^{76} + 974412 q^{77} - 340743 q^{78} - 3996663 q^{80} + 4277754 q^{81} - 3214221 q^{82} - 872109 q^{84} - 3207900 q^{85} + 3189360 q^{86} + 827973 q^{88} - 2016084 q^{89} - 710406 q^{90} - 2545116 q^{92} + 4486254 q^{93} - 14322630 q^{94} + 2623530 q^{96} - 1223112 q^{97} + 10989009 q^{98}+O(q^{100}) \) 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9 + 2811 * q^10 - 3 * q^12 - 7572 * q^13 + 8217 * q^14 - 1392 * q^16 - 12 * q^17 - 12 * q^18 + 33618 * q^20 - 33546 * q^21 - 198 * q^22 - 7128 * q^24 - 12 * q^25 + 84453 * q^26 + 13464 * q^28 - 12 * q^29 + 75510 * q^30 + 9339 * q^32 - 366 * q^33 - 289248 * q^34 - 419349 * q^36 - 24 * q^37 + 158040 * q^38 + 264570 * q^40 + 27360 * q^41 + 206001 * q^42 - 525639 * q^44 - 6 * q^45 - 269328 * q^46 - 703179 * q^48 + 2319360 * q^49 + 264534 * q^50 + 130809 * q^52 - 182292 * q^53 + 607083 * q^54 - 705906 * q^56 - 12 * q^57 - 710004 * q^58 + 1060416 * q^60 - 325092 * q^61 - 1967868 * q^62 - 1611921 * q^64 + 398994 * q^65 - 2295684 * q^66 + 1125642 * q^68 - 1625190 * q^69 + 3496059 * q^70 + 4948626 * q^72 - 2224812 * q^73 + 2661159 * q^74 - 968262 * q^76 + 974412 * q^77 - 340743 * q^78 - 3996663 * q^80 + 4277754 * q^81 - 3214221 * q^82 - 872109 * q^84 - 3207900 * q^85 + 3189360 * q^86 + 827973 * q^88 - 2016084 * q^89 - 710406 * q^90 - 2545116 * q^92 + 4486254 * q^93 - 14322630 * q^94 + 2623530 * q^96 - 1223112 * q^97 + 10989009 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−5.92630	−	5.37392i	−0.740787	−	0.671740i
$2$	−5.92630	−	5.37392i	−0.740787	−	0.671740i
$3$	27.6808	−	4.88087i	1.02521	−	0.180773i	0.364337	−	0.931267i	$-0.381296\pi$
$3$	27.6808	−	4.88087i	1.02521	−	0.180773i	0.660877	+	0.750494i	$0.270185\pi$
$4$	6.24202	+	63.6949i	0.0975316	+	0.995232i
$5$	−34.1068	+	28.6190i	−0.272854	+	0.228952i	−0.768939	−	0.639322i	$-0.779215\pi$
$5$	−34.1068	+	28.6190i	−0.272854	+	0.228952i	0.496085	+	0.868274i	$0.334771\pi$
$6$	−190.274	−	119.829i	−0.880898	−	0.554763i
$7$	83.9559	+	48.4720i	0.244769	+	0.141318i	0.617367	−	0.786675i	$-0.288199\pi$
$7$	83.9559	+	48.4720i	0.244769	+	0.141318i	−0.372597	+	0.927993i	$0.621533\pi$
$8$	305.299	−	411.019i	0.596287	−	0.802771i
$9$	57.3665	−	20.8797i	0.0786921	−	0.0286416i
$10$	355.923	+	13.6824i	0.355923	+	0.0136824i
$11$	815.927	−	471.076i	0.613018	−	0.353926i	−0.161128	−	0.986934i	$-0.551513\pi$
$11$	815.927	−	471.076i	0.613018	−	0.353926i	0.774146	+	0.633007i	$0.218180\pi$
$12$	483.670	+	1732.66i	0.279902	+	1.00270i
$13$	−755.075	+	4282.24i	−0.343685	+	1.94913i	−0.0301859	+	0.999544i	$0.509610\pi$
$13$	−755.075	+	4282.24i	−0.343685	+	1.94913i	−0.313499	+	0.949589i	$0.601501\pi$
$14$	−237.063	−	738.431i	−0.0863934	−	0.269108i
$15$	−804.416	+	958.666i	−0.238346	+	0.284049i
$16$	−4018.07	+	795.170i	−0.980975	+	0.194133i
$17$	−3638.63	−	1324.35i	−0.740613	−	0.269561i	−0.0559630	−	0.998433i	$-0.517823\pi$
$17$	−3638.63	−	1324.35i	−0.740613	−	0.269561i	−0.684650	+	0.728872i	$0.740045\pi$
$18$	−452.177	−	184.544i	−0.0775338	−	0.0316433i
$19$	6812.71	+	795.568i	0.993251	+	0.115989i
$19$	6812.71	+	795.568i	0.993251	+	0.115989i
$20$	−2035.78	−	1993.79i	−0.254472	−	0.249223i
$21$	2560.55	+	931.964i	0.276487	+	0.100633i
$22$	−7366.95	−	1592.99i	−0.691862	−	0.149605i
$23$	−10416.9	+	12414.4i	−0.856163	+	1.02034i	0.143367	+	0.989670i	$0.454207\pi$
$23$	−10416.9	+	12414.4i	−0.856163	+	1.02034i	−0.999530	+	0.0306658i	$0.990237\pi$
$24$	6444.78	−	12867.4i	0.466202	−	0.930805i
$25$	−2369.03	+	13435.4i	−0.151618	+	0.859867i
$26$	27487.2	−	21320.1i	1.56391	−	1.21303i
$27$	−16259.3	+	9387.33i	−0.826059	+	0.476926i
$28$	−2563.36	+	5650.12i	−0.116771	+	0.257385i
$29$	36648.4	−	13338.9i	1.50266	−	0.546924i	0.545913	−	0.837842i	$-0.316183\pi$
$29$	36648.4	−	13338.9i	1.50266	−	0.546924i	0.956748	+	0.290918i	$0.0939607\pi$
$30$	9919.00	−	1358.47i	0.367370	−	0.0503139i
$31$	40577.6	+	23427.5i	1.36208	+	0.786395i	0.989900	−	0.141767i	$-0.0452785\pi$
$31$	40577.6	+	23427.5i	1.36208	+	0.786395i	0.372176	+	0.928162i	$0.378612\pi$
$32$	28085.5	+	16880.4i	0.857101	+	0.515148i
$33$	20286.2	−	17022.2i	0.564494	−	0.473667i
$34$	14446.7	+	27402.2i	0.367562	+	0.697187i
$35$	−4250.68	+	749.510i	−0.0991413	+	0.0174813i
$36$	1688.01	+	3523.62i	0.0361800	+	0.0755235i
$37$	58049.8			1.14603			0.573015	−	0.819545i	$-0.305774\pi$
$37$	58049.8			1.14603			0.573015	+	0.819545i	$0.305774\pi$
$38$	−36098.8	−	41325.7i	−0.657873	−	0.753129i
$39$			122221.i			2.06041i
$40$	1350.18	+	22755.9i	0.0210966	+	0.355560i
$41$	2165.93	+	12283.6i	0.0314263	+	0.178227i	0.996481	−	0.0838220i	$-0.0267127\pi$
$41$	2165.93	+	12283.6i	0.0314263	+	0.178227i	−0.965054	+	0.262050i	$0.915602\pi$
$42$	−10166.3	−	19283.3i	−0.137219	−	0.260275i
$43$	−11932.4	−	14220.4i	−0.150079	−	0.178858i	0.685767	−	0.727821i	$-0.259467\pi$
$43$	−11932.4	−	14220.4i	−0.150079	−	0.178858i	−0.835846	+	0.548964i	$0.815023\pi$
$44$	35098.1	+	49029.9i	0.412027	+	0.575576i
$45$	−1359.03	+	2353.91i	−0.0149139	+	0.0258317i
$46$	128448.	−	17591.8i	1.31963	−	0.180733i
$47$	4562.85	+	12536.3i	0.0439483	+	0.120747i	0.959725	−	0.280940i	$-0.0906462\pi$
$47$	4562.85	+	12536.3i	0.0439483	+	0.120747i	−0.915777	+	0.401687i	$0.868424\pi$
$48$	−107342.	+	41622.6i	−0.970615	+	0.376362i
$49$	−54125.4	−	93748.0i	−0.460059	−	0.796845i
$50$	86240.4	−	66891.4i	0.689923	−	0.535131i
$51$	−107184.	−	18899.5i	−0.808017	−	0.142475i
$52$	−277470.	−	21364.5i	−1.97336	−	0.151944i
$53$	48900.6	+	41032.4i	0.328463	+	0.275613i	0.792073	−	0.610426i	$-0.209002\pi$
$53$	48900.6	+	41032.4i	0.328463	+	0.275613i	−0.463610	+	0.886039i	$0.653446\pi$
$54$	146804.	+	31744.2i	0.932304	+	0.201596i
$55$	−14346.9	+	39417.9i	−0.0862325	+	0.236922i
$56$	45554.5	−	19709.0i	0.259399	−	0.112228i
$57$	192464.	−	11230.0i	1.03926	−	0.0606393i
$58$	−288872.	−	117895.i	−1.48054	−	0.604243i
$59$	−75569.9	+	207627.i	−0.367953	+	1.01094i	0.608185	+	0.793795i	$0.291898\pi$
$59$	−75569.9	+	207627.i	−0.367953	+	1.01094i	−0.976139	+	0.217148i	$0.930325\pi$
$60$	−66083.3	−	45253.2i	−0.305941	−	0.209505i
$61$	−165600.	−	138955.i	−0.729575	−	0.612186i	0.200441	−	0.979706i	$-0.435763\pi$
$61$	−165600.	−	138955.i	−0.729575	−	0.612186i	−0.930016	+	0.367520i	$0.880207\pi$
$62$	−114578.	−	356899.i	−0.480756	−	1.49751i
$63$	5828.34	+	1027.69i	0.0233090	+	0.00411000i
$64$	−75729.2	−	250967.i	−0.288884	−	0.957364i
$65$	−96800.3	−	167663.i	−0.352482	−	0.610516i
$66$	−211698.	−	8138.08i	−0.736351	−	0.0283068i
$67$	−28802.8	−	79135.0i	−0.0957657	−	0.263114i	0.882555	−	0.470209i	$-0.155821\pi$
$67$	−28802.8	−	79135.0i	−0.0957657	−	0.263114i	−0.978321	+	0.207095i	$0.933599\pi$
$68$	61642.1	−	240029.i	0.196043	−	0.763373i
$69$	−227756.	+	394485.i	−0.693301	+	1.20083i
$70$	29218.6	+	18401.0i	0.0851855	+	0.0536472i
$71$	−32265.4	−	38452.4i	−0.0901491	−	0.107436i	0.719084	−	0.694923i	$-0.244562\pi$
$71$	−32265.4	−	38452.4i	−0.0901491	−	0.107436i	−0.809233	+	0.587487i	$0.800117\pi$
$72$	8931.98	−	29953.3i	0.0239304	−	0.0802504i
$73$	116889.	+	662910.i	0.300473	+	1.70406i	0.644086	+	0.764953i	$0.277238\pi$
$73$	116889.	+	662910.i	0.300473	+	1.70406i	−0.343613	+	0.939111i	$0.611651\pi$
$74$	−344020.	−	311955.i	−0.848964	−	0.769833i
$75$			383466.i			0.908956i
$76$	−8148.51	+	438900.i	−0.0185625	+	0.999828i
$77$	91335.9			0.200064
$78$	656807.	−	724320.i	1.38406	−	1.52632i
$79$	−388719.	+	68541.7i	−0.788415	+	0.139019i	−0.553337	−	0.832958i	$-0.686646\pi$
$79$	−388719.	+	68541.7i	−0.788415	+	0.139019i	−0.235078	+	0.971976i	$0.575535\pi$
$80$	114287.	−	142114.i	0.223216	−	0.277566i
$81$	−438345.	+	367815.i	−0.824823	+	0.692108i
$82$	53175.2	−	84435.9i	0.0964423	−	0.153139i
$83$	564813.	+	326095.i	0.987802	+	0.570308i	0.904617	−	0.426226i	$-0.140157\pi$
$83$	564813.	+	326095.i	0.987802	+	0.570308i	0.0831858	+	0.996534i	$0.473491\pi$
$84$	−43378.3	+	168911.i	−0.0731871	+	0.284984i
$85$	162004.	−	58964.5i	0.263796	−	0.0960139i
$86$	−5704.70	+	148398.i	−0.00896887	+	0.233310i
$87$	949351.	−	548108.i	1.44168	−	0.832354i
$88$	55480.6	−	479180.i	0.0814129	−	0.703155i
$89$	150198.	−	851816.i	0.213056	−	1.20830i	−0.671191	−	0.741284i	$-0.734217\pi$
$89$	150198.	−	851816.i	0.213056	−	1.20830i	0.884248	−	0.467018i	$-0.154672\pi$
$90$	20703.7	−	6646.66i	0.0284002	−	0.00911750i
$91$	−270962.	+	322920.i	−0.359570	+	0.428519i
$92$	−855758.	−	586014.i	−1.09897	−	0.752566i
$93$	1.23757e6	+	450437.i	1.53858	+	0.559997i
$94$	40328.3	−	98814.3i	0.0485542	−	0.118970i
$95$	−255128.	+	167838.i	−0.297568	+	0.195758i
$96$	859819.	+	330181.i	0.971837	+	0.373197i
$97$	−624554.	−	227319.i	−0.684313	−	0.249070i	−0.0236148	−	0.999721i	$-0.507518\pi$
$97$	−624554.	−	227319.i	−0.684313	−	0.249070i	−0.660698	+	0.750652i	$0.729740\pi$
$98$	−183031.	+	846444.i	−0.194467	+	0.899332i
$99$	36971.0	−	44060.3i	0.0381027	−	0.0454090i
$100$	−870555.	−	67030.7i	−0.870555	−	0.0670307i
$101$	258546.	−	1.46629e6i	0.250942	−	1.42316i	−0.555336	−	0.831626i	$-0.687410\pi$
$101$	258546.	−	1.46629e6i	0.250942	−	1.42316i	0.806278	−	0.591537i	$-0.201479\pi$
$102$	533641.	+	688003.i	0.502862	+	0.648321i
$103$	−1.37130e6	+	791721.i	−1.25493	+	0.724537i	−0.972085	−	0.234627i	$-0.924613\pi$
$103$	−1.37130e6	+	791721.i	−1.25493	+	0.724537i	−0.282850	+	0.959164i	$0.591280\pi$
$104$	1.52956e6	+	1.61771e6i	1.35977	+	1.43814i
$105$	−114004.	+	41494.0i	−0.0984809	+	0.0358441i
$106$	−69294.4	−	505958.i	−0.0581809	−	0.424812i
$107$	−896424.	−	517551.i	−0.731749	−	0.422475i	0.0873128	−	0.996181i	$-0.472172\pi$
$107$	−896424.	−	517551.i	−0.731749	−	0.422475i	−0.819062	+	0.573706i	$0.805505\pi$
$108$	−699416.	−	977040.i	−0.555219	−	0.775606i
$109$	−245244.	+	205784.i	−0.189373	+	0.158903i	−0.732545	−	0.680719i	$-0.761668\pi$
$109$	−245244.	+	205784.i	−0.189373	+	0.158903i	0.543172	+	0.839622i	$0.317223\pi$
$110$	296853.	−	156503.i	0.223030	−	0.117583i
$111$	1.60686e6	−	283333.i	1.17492	−	0.207171i
$112$	−375885.	−	128005.i	−0.267547	−	0.0911112i
$113$	853052.			0.591208			0.295604	−	0.955311i	$-0.404479\pi$
$113$	853052.			0.591208			0.295604	+	0.955311i	$0.404479\pi$
$114$	−1.20095e6	−	967734.i	−0.810606	−	0.653193i
$115$		−	721538.i		−	0.474423i
$116$	1.07838e6	+	2.25105e6i	0.690873	+	1.44215i
$117$	46096.0	+	261423.i	0.0287810	+	0.163225i
$118$	1.56362e6	−	824350.i	0.951666	−	0.501725i
$119$	−241291.	−	287559.i	−0.143186	−	0.170642i
$120$	148443.	+	623310.i	0.0859042	+	0.360712i
$121$	−441956.	+	765490.i	−0.249473	+	0.432099i
$122$	234662.	+	1.71340e6i	0.129230	+	0.943584i
$123$	119909.	+	329448.i	0.0644374	+	0.177040i
$124$	−1.23892e6	+	2.73082e6i	−0.649800	+	1.43228i
$125$	−651546.	−	1.12851e6i	−0.333591	−	0.577797i
$126$	−29017.7	−	37411.4i	−0.0145061	−	0.0187022i
$127$	134671.	+	23746.1i	0.0657449	+	0.0115926i	0.206424	−	0.978463i	$-0.433817\pi$
$127$	134671.	+	23746.1i	0.0657449	+	0.0115926i	−0.140679	+	0.990055i	$0.544929\pi$
$128$	−899884.	+	1.89427e6i	−0.429098	+	0.903258i
$129$	−399705.	−	335392.i	−0.186196	−	0.156237i
$130$	−327340.	+	1.51382e6i	−0.148994	+	0.689039i
$131$	915764.	−	2.51604e6i	0.407352	−	1.11919i	−0.551225	−	0.834357i	$-0.685839\pi$
$131$	915764.	−	2.51604e6i	0.407352	−	1.11919i	0.958577	−	0.284834i	$-0.0919384\pi$
$132$	1.21085e6	+	1.18588e6i	0.526465	+	0.515606i
$133$	533404.	+	397018.i	0.226726	+	0.168754i
$134$	−254571.	+	623761.i	−0.105802	+	0.259241i
$135$	285897.	−	785497.i	0.116201	−	0.319259i
$136$	−1.65521e6	+	1.09122e6i	−0.658014	+	0.433807i
$137$	−778809.	−	653499.i	−0.302879	−	0.254146i	0.478662	−	0.877999i	$-0.341122\pi$
$137$	−778809.	−	653499.i	−0.302879	−	0.254146i	−0.781541	+	0.623853i	$0.785566\pi$
$138$	3.46968e6	−	1.11389e6i	1.32024	−	0.423844i
$139$	158465.	+	27941.7i	0.0590051	+	0.0104042i	0.203073	−	0.979164i	$-0.434907\pi$
$139$	158465.	+	27941.7i	0.0590051	+	0.0104042i	−0.144068	+	0.989568i	$0.546018\pi$
$140$	−74272.8	−	266068.i	−0.0270674	−	0.0969636i
$141$	187491.	+	324744.i	0.0668842	+	0.115847i
$142$	−15425.7	+	401272.i	−0.00538739	+	0.140144i
$143$	1.40118e6	+	3.84970e6i	0.479164	+	1.31649i
$144$	−213900.	+	129512.i	−0.0716347	+	0.0433734i
$145$	−868212.	+	1.50379e6i	−0.284788	+	0.493267i
$146$	2.86971e6	−	4.55675e6i	0.922102	−	1.46419i
$147$	−1.95581e6	−	2.33084e6i	−0.615706	−	0.733770i
$148$	362348.	+	3.69748e6i	0.111774	+	1.14057i
$149$	155722.	+	883144.i	0.0470751	+	0.266976i	0.999256	−	0.0385573i	$-0.0122762\pi$
$149$	155722.	+	883144.i	0.0470751	+	0.266976i	−0.952181	+	0.305534i	$0.901165\pi$
$150$	2.06071e6	−	2.27253e6i	0.610582	−	0.673343i
$151$		−	5.64567e6i		−	1.63978i	−0.572524	−	0.819888i	$-0.694036\pi$
$151$		−	5.64567e6i		−	1.63978i	0.572524	−	0.819888i	$-0.305964\pi$
$152$	2.40690e6	−	2.55727e6i	0.685375	−	0.728190i
$153$	−236388.			−0.0660011
$154$	−541284.	−	490831.i	−0.148205	−	0.134391i
$155$	−2.05444e6	+	362253.i	−0.551695	+	0.0972786i
$156$	−7.78487e6	+	762908.i	−2.05058	+	0.200955i
$157$	2.82818e6	−	2.37312e6i	0.730816	−	0.613227i	−0.199538	−	0.979890i	$-0.563944\pi$
$157$	2.82818e6	−	2.37312e6i	0.730816	−	0.613227i	0.930354	+	0.366663i	$0.119500\pi$
$158$	2.67200e6	+	1.68275e6i	0.677432	+	0.426626i
$159$	1.55388e6	+	897133.i	0.386568	+	0.223185i
$160$	−1.44100e6	+	228042.i	−0.351808	+	0.0556744i
$161$	−1.47631e6	+	537335.i	−0.353754	+	0.128756i
$162$	4.57437e6	+	175847.i	1.07593	+	0.0413610i
$163$	3.22508e6	−	1.86200e6i	0.744693	−	0.429949i	−0.0790802	−	0.996868i	$-0.525198\pi$
$163$	3.22508e6	−	1.86200e6i	0.744693	−	0.429949i	0.823773	+	0.566920i	$0.191865\pi$
$164$	−768884.	+	214633.i	−0.174313	+	0.0486593i
$165$	−204741.	+	1.16114e6i	−0.0455777	+	0.258484i
$166$	−1.59484e6	−	4.96779e6i	−0.348653	−	1.08602i
$167$	4.89733e6	−	5.83641e6i	1.05150	−	1.25313i	0.0850243	−	0.996379i	$-0.472903\pi$
$167$	4.89733e6	−	5.83641e6i	1.05150	−	1.25313i	0.966477	−	0.256752i	$-0.0826524\pi$
$168$	1.16479e6	−	767907.i	0.245651	−	0.161950i
$169$	−1.32318e7	−	4.81597e6i	−2.74131	−	0.997754i
$170$	−1.27695e6	−	521153.i	−0.259913	−	0.106076i
$171$	407432.	−	96608.3i	0.0814831	−	0.0193209i
$172$	831286.	−	848794.i	0.163367	−	0.166808i
$173$	5.46995e6	+	1.99090e6i	1.05644	+	0.384513i	0.811090	−	0.584922i	$-0.198875\pi$
$173$	5.46995e6	+	1.99090e6i	1.05644	+	0.384513i	0.245351	+	0.969434i	$0.421097\pi$
$174$	−8.57162e6	−	1.85348e6i	−1.62710	−	0.351836i
$175$	−850135.	+	1.01315e6i	−0.158626	+	0.189043i
$176$	−2.90387e6	+	2.54162e6i	−0.532647	+	0.466200i
$177$	−1.07844e6	+	6.11611e6i	−0.194480	+	1.10295i
$178$	−5.46771e6	+	4.24096e6i	−0.969494	+	0.751977i
$179$	−1.99030e6	+	1.14910e6i	−0.347024	+	0.200355i	−0.663374	−	0.748288i	$-0.730876\pi$
$179$	−1.99030e6	+	1.14910e6i	−0.347024	+	0.200355i	0.316350	+	0.948643i	$0.397543\pi$
$180$	−158415.	−	71870.1i	−0.0271631	−	0.0123234i
$181$	1.57770e6	−	574237.i	0.266066	−	0.0968401i	−0.205542	−	0.978648i	$-0.565896\pi$
$181$	1.57770e6	−	574237.i	0.266066	−	0.0968401i	0.471608	+	0.881808i	$0.343674\pi$
$182$	3.34115e6	−	457592.i	0.554219	−	0.0759040i
$183$	−5.26214e6	−	3.03810e6i	−0.858637	−	0.495734i
$184$	1.92228e6	+	8.07167e6i	0.308577	+	1.29572i
$185$	−1.97989e6	+	1.66133e6i	−0.312699	+	0.262385i
$186$	−4.91357e6	−	9.32000e6i	−0.763587	−	1.44836i
$187$	−3.59273e6	+	633495.i	−0.549414	+	0.0968766i
$188$	−770018.	+	368882.i	−0.115885	+	0.0555154i
$189$	−1.82009e6			−0.269592
$190$	2.41391e6	+	376375.i	0.351934	+	0.0548731i
$191$			3.23808e6i			0.464716i	0.972630	+	0.232358i	$0.0746441\pi$
$191$			3.23808e6i			0.464716i	−0.972630	+	0.232358i	$0.925356\pi$
$192$	−3.32118e6	−	6.57734e6i	−0.469233	−	0.929281i
$193$	220758.	+	1.25198e6i	0.0307075	+	0.174151i	0.996304	−	0.0858925i	$-0.0273742\pi$
$193$	220758.	+	1.25198e6i	0.0307075	+	0.174151i	−0.965597	+	0.260044i	$0.916263\pi$
$194$	2.47970e6	+	4.70346e6i	0.339621	+	0.644188i
$195$	−3.49785e6	−	4.16857e6i	−0.471734	−	0.562191i
$196$	5.63342e6	−	4.03269e6i	0.748176	−	0.535583i
$197$	390604.	−	676546.i	0.0510902	−	0.0884909i	−0.839349	−	0.543592i	$-0.817064\pi$
$197$	390604.	−	676546.i	0.0510902	−	0.0884909i	0.890440	+	0.455102i	$0.150397\pi$
$198$	−455877.	+	62435.5i	−0.0587290	+	0.00804333i
$199$	1.75097e6	+	4.81076e6i	0.222188	+	0.610456i	0.999834	−	0.0182467i	$-0.00580843\pi$
$199$	1.75097e6	+	4.81076e6i	0.222188	+	0.610456i	−0.777646	+	0.628703i	$0.783586\pi$
$200$	4.79895e6	+	5.07553e6i	0.599869	+	0.634442i
$201$	−1.18353e6	−	2.04994e6i	−0.145744	−	0.252436i
$202$	−9.41193e6	+	7.30025e6i	−1.14189	+	0.885694i
$203$	3.72341e6	+	656538.i	0.445095	+	0.0784823i
$204$	534753.	−	6.94506e6i	0.0629887	−	0.818060i
$205$	−425418.	−	356968.i	−0.0493803	−	0.0414350i
$206$	1.23814e7	+	2.67728e6i	1.41634	+	0.306262i
$207$	−338374.	+	929675.i	−0.0381492	+	0.104814i
$208$	−371164.	−	1.78068e7i	−0.0412454	−	1.97877i
$209$	5.93344e6	−	2.56017e6i	0.649932	−	0.280434i
$210$	898607.	+	366742.i	0.0970313	+	0.0396007i
$211$	169690.	−	466221.i	0.0180638	−	0.0496300i	−0.930333	−	0.366716i	$-0.880482\pi$
$211$	169690.	−	466221.i	0.0180638	−	0.0496300i	0.948397	+	0.317086i	$0.102704\pi$
$212$	−2.30832e6	+	3.37084e6i	−0.242263	+	0.353778i
$213$	−1.08081e6	−	906908.i	−0.111844	−	0.0938479i
$214$	2.53120e6	+	7.88447e6i	0.258277	+	0.804509i
$215$	813948.	+	143521.i	0.0818995	+	0.0144411i
$216$	−1.10559e6	+	9.54883e6i	−0.109706	+	0.947521i
$217$	2.27115e6	+	3.93375e6i	0.222263	+	0.384971i
$218$	2.55925e6	+	98382.6i	0.247027	+	0.00949617i
$219$	6.47115e6	+	1.77793e7i	0.616097	+	1.69271i
$220$	−2.60027e6	−	667779.i	−0.244203	−	0.0627140i
$221$	8.41865e6	−	1.45815e7i	0.779948	−	1.35091i
$222$	−1.10454e7	−	6.95603e6i	−1.00953	−	0.635774i
$223$	−1.00649e7	−	1.19949e7i	−0.907603	−	1.08164i	−0.996331	−	0.0855830i	$-0.972725\pi$
$223$	−1.00649e7	−	1.19949e7i	−0.907603	−	1.08164i	0.0887282	−	0.996056i	$-0.471720\pi$
$224$	1.53972e6	+	2.77857e6i	0.136993	+	0.247216i
$225$	144625.	+	820208.i	0.0126968	+	0.0720073i
$226$	−5.05544e6	−	4.58423e6i	−0.437959	−	0.397138i
$227$			2.21790e7i			1.89611i	0.318101	+	0.948057i	$0.396955\pi$
$227$			2.21790e7i			1.89611i	−0.318101	+	0.948057i	$0.603045\pi$
$228$	1.91666e6	+	1.21889e7i	0.161711	+	1.02839i
$229$	1.52160e7			1.26705			0.633524	−	0.773723i	$-0.281608\pi$
$229$	1.52160e7			1.26705			0.633524	+	0.773723i	$0.281608\pi$
$230$	−3.87748e6	+	4.27605e6i	−0.318689	+	0.351446i
$231$	2.52825e6	−	445798.i	0.205109	−	0.0361662i
$232$	5.70616e6	−	1.91355e7i	0.456962	−	1.53242i
$233$	6.36996e6	−	5.34503e6i	0.503580	−	0.422554i	−0.355283	−	0.934759i	$-0.615616\pi$
$233$	6.36996e6	−	5.34503e6i	0.503580	−	0.422554i	0.858863	+	0.512205i	$0.171171\pi$
$234$	1.13169e6	−	1.79699e6i	0.0883241	−	0.140248i
$235$	−514400.	−	296989.i	−0.0396367	−	0.0228843i
$236$	−1.36965e7	−	3.51740e6i	−1.04201	−	0.267600i
$237$	−1.04255e7	+	3.79458e6i	−0.783163	+	0.285048i
$238$	−115358.	+	3.00084e6i	−0.00855690	+	0.222593i
$239$	−7.53006e6	+	4.34748e6i	−0.551575	+	0.318452i	−0.749757	−	0.661713i	$-0.769830\pi$
$239$	−7.53006e6	+	4.34748e6i	−0.551575	+	0.318452i	0.198182	+	0.980165i	$0.436496\pi$
$240$	2.46990e6	−	4.49164e6i	0.178668	−	0.324916i
$241$	1.05937e6	−	6.00800e6i	0.0756828	−	0.429219i	−0.923298	−	0.384084i	$-0.874517\pi$
$241$	1.05937e6	−	6.00800e6i	0.0756828	−	0.429219i	0.998981	−	0.0451345i	$-0.0143716\pi$
$242$	6.73284e6	−	2.16149e6i	0.475064	−	0.152513i
$243$	−1.54081e6	+	1.83626e6i	−0.107382	+	0.127972i
$244$	7.81702e6	−	1.14152e7i	0.538111	−	0.785804i
$245$	4.52902e6	+	1.64843e6i	0.307968	+	0.112091i
$246$	1.05981e6	−	2.59679e6i	0.0711906	−	0.174434i
$247$	−8.55092e6	+	2.85730e7i	−0.567443	+	1.89611i
$248$	2.20174e7	−	9.52578e6i	1.44348	−	0.624519i
$249$	1.72261e7	+	6.26978e6i	1.11581	+	0.406120i
$250$	−2.20327e6	+	1.01892e7i	−0.141009	+	0.652111i
$251$	−1.01292e7	+	1.20715e7i	−0.640549	+	0.763377i	−0.984457	−	0.175627i	$-0.943805\pi$
$251$	−1.01292e7	+	1.20715e7i	−0.640549	+	0.763377i	0.343907	+	0.939004i	$0.388249\pi$
$252$	−29078.2	+	377650.i	−0.00181704	+	0.0235987i
$253$	−2.65133e6	+	1.50364e7i	−0.163720	+	0.928503i
$254$	−670489.	−	864435.i	−0.0409157	−	0.0527511i
$255$	4.19659e6	−	2.42290e6i	0.253091	−	0.146122i
$256$	1.55126e7	−	6.39010e6i	0.924625	−	0.380880i
$257$	4.49976e6	−	1.63778e6i	0.265088	−	0.0964840i	−0.206057	−	0.978540i	$-0.566063\pi$
$257$	4.49976e6	−	1.63778e6i	0.265088	−	0.0964840i	0.471145	+	0.882056i	$0.343841\pi$
$258$	566400.	+	4.13561e6i	0.0329810	+	0.240814i
$259$	4.87362e6	+	2.81379e6i	0.280513	+	0.161954i
$260$	1.00750e7	−	7.21224e6i	0.573227	−	0.410346i
$261$	1.82388e6	−	1.53042e6i	0.102583	−	0.0860772i
$262$	−1.89481e7	+	9.98957e6i	−1.05357	+	0.555447i
$263$	3.27786e7	−	5.77975e6i	1.80187	−	0.317718i	0.830810	−	0.556556i	$-0.187878\pi$
$263$	3.27786e7	−	5.77975e6i	1.80187	−	0.317718i	0.971059	+	0.238838i	$0.0767666\pi$
$264$	−803071.	−	1.35349e7i	−0.0436457	−	0.735601i
$265$	−2.84215e6			−0.152725
$266$	−1.02757e6	−	5.21932e6i	−0.0545968	−	0.277312i
$267$		−	2.43120e7i		−	1.27728i
$268$	4.86071e6	−	2.32855e6i	0.252520	−	0.120971i
$269$	1.42001e6	+	8.05325e6i	0.0729513	+	0.413728i	0.999312	+	0.0370898i	$0.0118087\pi$
$269$	1.42001e6	+	8.05325e6i	0.0729513	+	0.413728i	−0.926361	+	0.376638i	$0.877080\pi$
$270$	−5.91551e6	+	3.11870e6i	−0.300539	+	0.158446i
$271$	1.33872e7	+	1.59543e7i	0.672640	+	0.801621i	0.989141	−	0.146971i	$-0.0469524\pi$
$271$	1.33872e7	+	1.59543e7i	0.672640	+	0.801621i	−0.316501	+	0.948592i	$0.602508\pi$
$272$	1.56734e7	+	2.42802e6i	0.778854	+	0.120655i
$273$	−5.92431e6	+	1.02612e7i	−0.291172	+	0.504325i
$274$	1.10361e6	+	8.05808e6i	0.0536492	+	0.391724i
$275$	4.39615e6	+	1.20783e7i	0.211385	+	0.580775i
$276$	−2.65483e7	−	1.20445e7i	−1.26273	−	0.572877i
$277$	4.93973e6	+	8.55586e6i	0.232415	+	0.402554i	0.958518	−	0.285031i	$-0.0920040\pi$
$277$	4.93973e6	+	8.55586e6i	0.232415	+	0.402554i	−0.726103	+	0.687585i	$0.758671\pi$
$278$	−788956.	−	1.01717e6i	−0.0367213	−	0.0473434i
$279$	2.81696e6	+	496705.i	0.129708	+	0.0228711i
$280$	−989666.	+	1.97594e6i	−0.0450832	+	0.0900116i
$281$	−6.34693e6	−	5.32571e6i	−0.286052	−	0.240026i	0.488459	−	0.872587i	$-0.337559\pi$
$281$	−6.34693e6	−	5.32571e6i	−0.286052	−	0.240026i	−0.774511	+	0.632561i	$0.782004\pi$
$282$	634020.	−	2.93209e6i	0.0282719	−	0.130747i
$283$	−4.87259e6	+	1.33873e7i	−0.214981	+	0.590656i	−0.999569	−	0.0293618i	$-0.990653\pi$
$283$	−4.87259e6	+	1.33873e7i	−0.214981	+	0.590656i	0.784588	+	0.620018i	$0.212875\pi$
$284$	2.24782e6	−	2.29516e6i	0.0981310	−	0.100198i
$285$	−6.24293e6	+	5.89114e6i	−0.269683	+	0.254487i
$286$	1.23842e7	−	3.03443e7i	0.529382	−	1.29711i
$287$	−413568.	+	1.13627e6i	−0.0174945	+	0.0480657i
$288$	1.96362e6	+	381952.i	0.0822017	+	0.0159894i
$289$	−7.00471e6	−	5.87765e6i	−0.290199	−	0.243506i
$290$	1.32265e7	−	4.24619e6i	0.542315	−	0.174103i
$291$	−1.83977e7	−	3.24400e6i	−0.746592	−	0.131644i
$292$	−4.14944e7	+	1.15831e7i	−1.66663	+	0.465240i
$293$	−1.53775e7	−	2.66346e7i	−0.611341	−	1.05887i	−0.991015	−	0.133753i	$-0.957297\pi$
$293$	−1.53775e7	−	2.66346e7i	−0.611341	−	1.05887i	0.379674	−	0.925120i	$-0.376036\pi$
$294$	−935045.	+	2.43236e7i	−0.0367951	+	0.957162i
$295$	−3.36461e6	−	9.24420e6i	−0.131060	−	0.360084i
$296$	1.77225e7	−	2.38596e7i	0.683362	−	0.919999i
$297$	−8.84428e6	+	1.53187e7i	−0.337593	+	0.584728i
$298$	3.82309e6	−	6.07062e6i	0.144466	−	0.229395i
$299$	−4.52960e7	−	5.39817e7i	−1.69452	−	2.01945i
$300$	−2.44248e7	+	2.39360e6i	−0.904622	+	0.0886520i
$301$	−312500.	−	1.77227e6i	−0.0114591	−	0.0649877i
$302$	−3.03394e7	+	3.34579e7i	−1.10150	+	1.21473i
$303$		−	4.18499e7i		−	1.50441i
$304$	−2.80066e7	+	2.22061e6i	−0.996871	+	0.0790408i
$305$	9.62480e6			0.339228
$306$	1.40091e6	+	1.27033e6i	0.0488928	+	0.0443355i
$307$	−1.97832e7	+	3.48831e6i	−0.683725	+	0.120559i	−0.504712	−	0.863288i	$-0.668401\pi$
$307$	−1.97832e7	+	3.48831e6i	−0.683725	+	0.120559i	−0.179013	+	0.983847i	$0.557290\pi$
$308$	570121.	+	5.81763e6i	0.0195126	+	0.199110i
$309$	−3.40944e7	+	2.86086e7i	−1.15560	+	0.969664i
$310$	1.41220e7	+	8.89358e6i	0.474034	+	0.298532i
$311$	3.49481e7	+	2.01773e7i	1.16183	+	0.670782i	0.951742	−	0.306901i	$-0.0992919\pi$
$311$	3.49481e7	+	2.01773e7i	1.16183	+	0.670782i	0.210087	+	0.977683i	$0.432625\pi$
$312$	5.02353e7	+	3.73140e7i	1.65404	+	1.22859i
$313$	1.22985e7	−	4.47628e6i	0.401068	−	0.145977i	−0.133607	−	0.991034i	$-0.542656\pi$
$313$	1.22985e7	−	4.47628e6i	0.401068	−	0.145977i	0.534675	+	0.845058i	$0.320434\pi$
$314$	−2.95136e7	−	1.13456e6i	−0.953308	−	0.0366470i
$315$	−228197.	+	131750.i	−0.00730094	+	0.00421520i
$316$	−6.79215e6	−	2.43316e7i	−0.215251	−	0.771097i
$317$	−636734.	+	3.61110e6i	−0.0199885	+	0.113360i	−0.993170	−	0.116680i	$-0.962775\pi$
$317$	−636734.	+	3.61110e6i	−0.0199885	+	0.113360i	0.973181	+	0.230041i	$0.0738859\pi$
$318$	−4.38764e6	−	1.36671e7i	−0.136442	−	0.425006i
$319$	2.36188e7	−	2.81478e7i	0.727588	−	0.867105i
$320$	9.76530e6	+	6.39239e6i	0.298013	+	0.195080i
$321$	−2.73398e7	−	9.95087e6i	−0.826571	−	0.300847i
$322$	1.16367e7	+	4.74919e6i	0.348547	+	0.142250i
$323$	−2.37353e7	−	1.19172e7i	−0.704349	−	0.353645i
$324$	−2.61641e7	−	2.56244e7i	−0.769255	−	0.753388i
$325$	−5.57450e7	−	2.02895e7i	−1.62389	−	0.591046i
$326$	−2.91190e7	−	6.29653e6i	−0.840473	−	0.181739i
$327$	−5.78413e6	+	6.89326e6i	−0.165423	+	0.197143i
$328$	5.71006e6	+	2.85994e6i	0.161815	+	0.0810466i
$329$	−224582.	+	1.27367e6i	−0.00630648	+	0.0357658i
$330$	7.45324e6	−	5.78102e6i	0.207397	−	0.160865i
$331$	3.89402e7	−	2.24821e7i	1.07378	−	0.619946i	0.144566	−	0.989495i	$-0.453821\pi$
$331$	3.89402e7	−	2.24821e7i	1.07378	−	0.619946i	0.929211	+	0.369549i	$0.120488\pi$
$332$	−1.72450e7	+	3.80112e7i	−0.471247	+	1.03872i
$333$	3.33012e6	−	1.21206e6i	0.0901834	−	0.0328241i
$334$	−6.03874e7	+	8.27046e6i	−1.62072	+	0.221968i
$335$	3.24713e6	+	1.87473e6i	0.0863705	+	0.0498661i
$336$	−1.10295e7	−	1.70863e6i	−0.290764	−	0.0450432i
$337$	2.94971e7	−	2.47510e7i	0.770708	−	0.646701i	−0.170182	−	0.985413i	$-0.554436\pi$
$337$	2.94971e7	−	2.47510e7i	0.770708	−	0.646701i	0.940890	+	0.338712i	$0.109991\pi$
$338$	5.25348e7	+	9.96473e7i	1.36049	+	2.58057i
$339$	2.36131e7	−	4.16363e6i	0.606114	−	0.106874i
$340$	4.76697e6	+	9.95075e6i	0.121285	+	0.253174i
$341$	4.41445e7			1.11330
$342$	−2.93373e6	−	1.61698e6i	−0.0733402	−	0.0404228i
$343$		−	2.18996e7i		−	0.542693i
$344$	−9.48780e6	+	562943.i	−0.233072	+	0.0138290i
$345$	−3.52173e6	−	1.99727e7i	−0.0857628	−	0.486385i
$346$	−2.17176e7	−	4.11937e7i	−0.524305	−	0.994495i
$347$	−2.25791e7	−	2.69088e7i	−0.540405	−	0.644029i	0.424874	−	0.905253i	$-0.360318\pi$
$347$	−2.25791e7	−	2.69088e7i	−0.540405	−	0.644029i	−0.965278	+	0.261223i	$0.915874\pi$
$348$	4.08375e7	+	5.70475e7i	0.968995	+	1.35363i
$349$	2.48944e7	−	4.31184e7i	0.585633	−	1.01435i	−0.409163	−	0.912461i	$-0.634179\pi$
$349$	2.48944e7	−	4.31184e7i	0.585633	−	1.01435i	0.994796	−	0.101885i	$-0.0324874\pi$
$350$	1.04827e7	−	1.43568e6i	0.244496	−	0.0334853i
$351$	−2.79218e7	−	7.67146e7i	−0.645687	−	1.77401i
$352$	3.08676e7	+	542773.i	0.707743	+	0.0124449i
$353$	−2.29711e7	−	3.97871e7i	−0.522225	−	0.904520i	−0.999666	−	0.0258558i	$-0.991769\pi$
$353$	−2.29711e7	−	3.97871e7i	−0.522225	−	0.904520i	0.477441	−	0.878664i	$-0.341564\pi$
$354$	3.92586e7	−	3.04505e7i	0.884963	−	0.686411i
$355$	2.20093e6	+	388084.i	0.0491951	+	0.00867443i
$356$	5.51939e7	+	4.24980e6i	1.22332	+	0.0941929i
$357$	−8.08265e6	−	6.78215e6i	−0.177643	−	0.149061i
$358$	1.79703e7	+	3.88580e6i	0.391657	+	0.0846899i
$359$	−1.81318e7	+	4.98168e7i	−0.391885	+	1.07670i	0.574255	+	0.818677i	$0.305292\pi$
$359$	−1.81318e7	+	4.98168e7i	−0.391885	+	1.07670i	−0.966140	+	0.258019i	$0.916930\pi$
$360$	552591.	+	1.27723e6i	0.0118439	+	0.0273756i
$361$	4.57800e7	+	1.08399e7i	0.973093	+	0.230412i
$362$	−1.24358e7	−	5.07534e6i	−0.262150	−	0.106989i
$363$	−8.49742e6	+	2.33465e7i	−0.177651	+	0.488092i
$364$	−2.22597e7	−	1.52432e7i	−0.461546	−	0.316062i
$365$	−2.29585e7	−	1.92645e7i	−0.472134	−	0.396167i
$366$	1.48585e7	+	4.62830e7i	0.303063	+	0.944014i
$367$	3.30606e7	+	5.82948e6i	0.668826	+	0.117932i	0.497743	−	0.867325i	$-0.334162\pi$
$367$	3.30606e7	+	5.82948e6i	0.668826	+	0.117932i	0.171083	+	0.985257i	$0.445273\pi$
$368$	3.19845e7	−	5.81653e7i	0.641794	−	1.16713i
$369$	380730.	+	659444.i	0.00757772	+	0.0131250i
$370$	2.06613e7	+	794258.i	0.407898	+	0.0156804i
$371$	2.11657e6	+	5.81522e6i	0.0414487	+	0.113879i
$372$	−2.09656e7	+	8.16382e7i	−0.407267	+	1.58586i
$373$	−1.99706e7	+	3.45901e7i	−0.384826	+	0.666538i	−0.991745	−	0.128226i	$-0.959072\pi$
$373$	−1.99706e7	+	3.45901e7i	−0.384826	+	0.666538i	0.606919	+	0.794764i	$0.292405\pi$
$374$	2.46959e7	+	1.55528e7i	0.472075	+	0.297298i
$375$	−2.35434e7	−	2.80579e7i	−0.446453	−	0.532062i
$376$	6.54570e6	+	1.95191e6i	0.123138	+	0.0367194i
$377$	2.94482e7	+	1.67009e8i	0.549586	+	3.11686i
$378$	1.07864e7	+	9.78101e6i	0.199710	+	0.181096i
$379$			6.02246e7i			1.10626i	0.833095	+	0.553129i	$0.186566\pi$
$379$			6.02246e7i			1.10626i	−0.833095	+	0.553129i	$0.813434\pi$
$380$	−1.22830e7	−	1.52027e7i	−0.223847	−	0.277057i
$381$	3.84369e6			0.0694982
$382$	1.74012e7	−	1.91898e7i	0.312168	−	0.344256i
$383$	1.07398e8	−	1.89371e7i	1.91161	−	0.337068i	0.913970	−	0.405782i	$-0.133001\pi$
$383$	1.07398e8	−	1.89371e7i	1.91161	−	0.337068i	0.997636	+	0.0687146i	$0.0218898\pi$
$384$	−1.56638e7	+	5.68271e7i	−0.276633	+	1.00360i
$385$	−3.11517e6	+	2.61394e6i	−0.0545883	+	0.0458050i
$386$	5.41977e6	−	8.60596e6i	0.0942365	−	0.149636i
$387$	−981436.	−	566632.i	−0.0169328	−	0.00977616i
$388$	1.05806e7	−	4.11998e7i	0.181140	−	0.705343i
$389$	−9.08694e7	+	3.30738e7i	−1.54372	+	0.561868i	−0.966934	−	0.255026i	$-0.917916\pi$
$389$	−9.08694e7	+	3.30738e7i	−1.54372	+	0.561868i	−0.576787	+	0.816895i	$0.695694\pi$
$390$	−1.67228e6	+	4.35014e7i	−0.0281912	+	0.733346i
$391$	5.43445e7	−	3.13758e7i	0.909129	−	0.524886i
$392$	−5.50566e7	−	6.37458e6i	−0.914011	−	0.105826i
$393$	1.30686e7	−	7.41157e7i	0.215304	−	1.22105i
$394$	−5.95054e6	+	1.91034e6i	−0.0972898	+	0.0312336i
$395$	1.12964e7	−	1.34625e7i	0.183294	−	0.218441i
$396$	3.03719e6	+	2.07984e6i	0.0489087	+	0.0334922i
$397$	6.40818e7	+	2.33239e7i	1.02415	+	0.372760i	0.798850	−	0.601530i	$-0.205442\pi$
$397$	6.40818e7	+	2.33239e7i	1.02415	+	0.372760i	0.225299	+	0.974290i	$0.427664\pi$
$398$	1.54758e7	−	3.79196e7i	0.245474	−	0.601470i
$399$	1.67028e7	+	8.38629e6i	0.262949	+	0.132023i
$400$	−1.16452e6	−	5.58683e7i	−0.0181956	−	0.872942i
$401$	1.81977e7	+	6.62341e6i	0.282217	+	0.102718i	0.479250	−	0.877678i	$-0.340909\pi$
$401$	1.81977e7	+	6.62341e6i	0.282217	+	0.102718i	−0.197034	+	0.980397i	$0.563131\pi$
$402$	−4.00223e6	+	1.85087e7i	−0.0616061	+	0.284904i
$403$	−1.30961e8	+	1.56074e8i	−2.00091	+	2.38459i
$404$	9.50088e7	+	7.31545e6i	1.44085	+	0.110942i
$405$	4.42403e6	−	2.50899e7i	0.0665968	−	0.377689i
$406$	−1.85379e7	−	2.39002e7i	−0.277001	−	0.357127i
$407$	4.73644e7	−	2.73459e7i	0.702537	−	0.405610i
$408$	−4.04913e7	+	3.82848e7i	−0.596185	+	0.563697i
$409$	−4.33522e7	+	1.57789e7i	−0.633638	+	0.230626i	−0.638814	−	0.769361i	$-0.720575\pi$
$409$	−4.33522e7	+	1.57789e7i	−0.633638	+	0.230626i	0.00517574	+	0.999987i	$0.498353\pi$
$410$	602836.	+	4.40166e6i	0.00874677	+	0.0638652i
$411$	−2.47477e7	−	1.42881e7i	−0.356459	−	0.205801i
$412$	−5.89883e7	−	8.24029e7i	−0.843479	−	1.17829i
$413$	−1.64086e7	+	1.37685e7i	−0.232928	+	0.195450i
$414$	7.00130e6	−	3.69114e6i	0.0986683	−	0.0520187i
$415$	−2.85964e7	+	5.04232e6i	−0.400099	+	0.0705483i
$416$	−9.34926e7	+	1.07523e8i	−1.29867	+	1.49356i
$417$	4.52282e6			0.0623737
$418$	−4.89215e7	−	1.67135e7i	−0.669840	−	0.228843i
$419$		−	5.30039e7i		−	0.720553i	−0.932846	−	0.360276i	$-0.882682\pi$
$419$		−	5.30039e7i		−	0.720553i	0.932846	−	0.360276i	$-0.117318\pi$
$420$	−3.35457e6	−	7.00246e6i	−0.0452782	−	0.0945154i
$421$	−6.67046e6	−	3.78300e7i	−0.0893942	−	0.506980i	−0.996322	−	0.0856928i	$-0.972690\pi$
$421$	−6.67046e6	−	3.78300e7i	−0.0893942	−	0.506980i	0.906927	−	0.421287i	$-0.138421\pi$
$422$	−3.51107e6	+	1.85106e6i	−0.0467199	+	0.0246311i
$423$	523509.	+	623894.i	0.00691677	+	0.00824308i
$424$	3.17944e7	−	7.57190e6i	0.417112	−	0.0993361i
$425$	2.64133e7	−	4.57491e7i	0.344077	−	0.595959i
$426$	1.53156e6	+	1.11828e7i	0.0198109	+	0.144651i
$427$	−7.16766e6	−	1.96930e7i	−0.0920649	−	0.252946i
$428$	2.73698e7	−	6.03282e7i	0.349093	−	0.769465i
$429$	5.75755e7	+	9.97237e7i	0.729232	+	1.26307i
$430$	−4.05243e6	−	5.22464e6i	−0.0509695	−	0.0657129i
$431$	7.22175e6	+	1.27339e6i	0.0902009	+	0.0159048i	0.218566	−	0.975822i	$-0.429862\pi$
$431$	7.22175e6	+	1.27339e6i	0.0902009	+	0.0159048i	−0.128366	+	0.991727i	$0.540973\pi$
$432$	5.78667e7	−	5.06479e7i	0.717757	−	0.628218i
$433$	−3.14065e7	−	2.63532e7i	−0.386862	−	0.324615i	0.428527	−	0.903529i	$-0.359033\pi$
$433$	−3.14065e7	−	2.63532e7i	−0.386862	−	0.324615i	−0.815389	+	0.578913i	$0.803477\pi$
$434$	7.68013e6	−	3.55176e7i	0.0939506	−	0.434484i
$435$	−1.66930e7	+	4.58636e7i	−0.202799	+	0.557186i
$436$	−1.46382e7	−	1.43363e7i	−0.176615	−	0.172972i
$437$	−8.08440e7	+	7.62884e7i	−0.968732	+	0.914143i
$438$	5.71948e7	−	1.40141e8i	0.680666	−	1.66780i
$439$	−3.35142e7	+	9.20795e7i	−0.396128	+	1.08835i	0.568026	+	0.823010i	$0.307707\pi$
$439$	−3.35142e7	+	9.20795e7i	−0.396128	+	1.08835i	−0.964154	+	0.265342i	$0.914515\pi$
$440$	1.18214e7	+	1.79311e7i	0.138775	+	0.210498i
$441$	−5.06242e6	−	4.24787e6i	−0.0590259	−	0.0495286i
$442$	−1.28251e8	+	4.11734e7i	−1.48524	+	0.476815i
$443$	−9.09025e7	−	1.60286e7i	−1.04560	−	0.184367i	−0.375640	−	0.926766i	$-0.622577\pi$
$443$	−9.09025e7	−	1.60286e7i	−1.04560	−	0.184367i	−0.669958	+	0.742399i	$0.733688\pi$
$444$	2.80770e7	+	1.00580e8i	0.320776	+	1.14912i
$445$	1.92553e7	+	3.33512e7i	0.218510	+	0.378470i
$446$	−4.81191e6	+	1.25173e8i	−0.0542391	+	1.41094i
$447$	8.62102e6	+	2.36861e7i	0.0965242	+	0.265198i
$448$	5.80697e6	−	2.47409e7i	0.0645826	−	0.275158i
$449$	7.98830e7	−	1.38361e8i	0.882502	−	1.52854i	0.0339512	−	0.999423i	$-0.489191\pi$
$449$	7.98830e7	−	1.38361e8i	0.882502	−	1.52854i	0.848551	−	0.529114i	$-0.177476\pi$
$450$	3.55064e6	−	5.63800e6i	0.0389645	−	0.0618710i
$451$	7.55376e6	+	9.00222e6i	0.0823443	+	0.0981341i
$452$	5.32477e6	+	5.43350e7i	0.0576615	+	0.588389i
$453$	−2.75558e7	−	1.56276e8i	−0.296427	−	1.68112i
$454$	1.19188e8	−	1.31439e8i	1.27369	−	1.40462i
$455$		−	1.87684e7i		−	0.199248i
$456$	5.41433e7	−	8.25349e7i	0.571019	−	0.870448i
$457$	1.71819e8			1.80021			0.900103	−	0.435677i	$-0.143491\pi$
$457$	1.71819e8			1.80021			0.900103	+	0.435677i	$0.143491\pi$
$458$	−9.01743e7	−	8.17693e7i	−0.938613	−	0.851126i
$459$	7.15939e7	−	1.26239e7i	0.740351	−	0.130544i
$460$	4.59583e7	−	4.50386e6i	0.472161	−	0.0462712i
$461$	1.75734e7	−	1.47458e7i	0.179371	−	0.150510i	−0.548682	−	0.836031i	$-0.684870\pi$
$461$	1.75734e7	−	1.47458e7i	0.179371	−	0.150510i	0.728053	+	0.685521i	$0.240426\pi$
$462$	−1.73788e7	−	1.09447e7i	−0.176236	−	0.110988i
$463$	1.21404e8	+	7.00929e7i	1.22318	+	0.706205i	0.965595	−	0.260050i	$-0.0837389\pi$
$463$	1.21404e8	+	7.00929e7i	1.22318	+	0.706205i	0.257588	+	0.966255i	$0.417072\pi$
$464$	−1.36649e8	+	8.27385e7i	−1.36790	+	0.828235i
$465$	−5.51004e7	+	2.00549e7i	−0.548020	+	0.199463i
$466$	−6.64740e7	−	2.55539e6i	−0.656892	−	0.0252522i
$467$	−4.18701e7	+	2.41737e7i	−0.411105	+	0.237352i	−0.691265	−	0.722602i	$-0.742946\pi$
$467$	−4.18701e7	+	2.41737e7i	−0.411105	+	0.237352i	0.280159	+	0.959954i	$0.409613\pi$
$468$	−1.63636e7	+	4.56789e6i	−0.159640	+	0.0445634i
$469$	1.41767e6	−	8.03998e6i	0.0137422	−	0.0779357i
$470$	1.45249e6	+	4.52439e6i	0.0139901	+	0.0435779i
$471$	6.67033e7	−	7.94939e7i	0.638388	−	0.760801i
$472$	6.22670e7	+	9.44488e7i	0.592151	+	0.898195i
$473$	−1.64348e7	−	5.98179e6i	−0.155304	−	0.0565259i
$474$	8.21764e7	+	3.35380e7i	0.771636	+	0.314922i
$475$	−2.68283e7	+	8.96468e7i	−0.250329	+	0.836477i
$476$	1.68099e7	−	1.71639e7i	0.155863	−	0.159146i
$477$	3.66200e6	+	1.33286e6i	0.0337414	+	0.0122809i
$478$	6.79884e7	+	1.47014e7i	0.622516	+	0.134610i
$479$	−8.53463e6	+	1.01712e7i	−0.0776566	+	0.0925475i	−0.803474	−	0.595340i	$-0.797017\pi$
$479$	−8.53463e6	+	1.01712e7i	−0.0776566	+	0.0925475i	0.725817	+	0.687888i	$0.241462\pi$
$480$	−3.87751e7	+	1.33457e7i	−0.350614	+	0.120675i
$481$	−4.38320e7	+	2.48583e8i	−0.393873	+	2.23376i
$482$	−3.85646e7	+	2.99122e7i	−0.344388	+	0.267121i
$483$	−3.82429e7	+	2.20795e7i	−0.339398	+	0.195951i
$484$	−5.15165e7	−	2.33721e7i	−0.454371	−	0.206140i
$485$	2.78072e7	−	1.01210e7i	0.243743	−	0.0887151i
$486$	1.89992e7	−	2.60207e6i	0.165511	−	0.0226678i
$487$	−7.97039e6	−	4.60171e6i	−0.0690070	−	0.0398412i	0.465100	−	0.885258i	$-0.346019\pi$
$487$	−7.97039e6	−	4.60171e6i	−0.0690070	−	0.0398412i	−0.534106	+	0.845417i	$0.679352\pi$
$488$	−1.07670e8	+	2.56419e7i	−0.926481	+	0.220643i
$489$	8.01844e7	−	6.72827e7i	0.685746	−	0.575410i
$490$	−1.79818e7	−	3.41076e7i	−0.152843	−	0.289910i
$491$	−1.13195e6	+	199593.i	−0.00956273	+	0.00168617i	−0.178427	−	0.983953i	$-0.557101\pi$
$491$	−1.13195e6	+	199593.i	−0.00956273	+	0.00168617i	0.168865	+	0.985639i	$0.445990\pi$
$492$	−2.02357e7	+	9.69404e6i	−0.169912	+	0.0813972i
$493$	−1.51016e8			−1.26032
$494$	2.04224e8	−	1.23380e8i	1.69405	−	1.02344i
$495$			2.56083e6i			0.0211137i
$496$	−1.81673e8	−	6.18673e7i	−1.48883	−	0.507010i
$497$	−845006.	−	4.79227e6i	−0.00688321	−	0.0390366i
$498$	−6.83936e7	−	1.29728e8i	−0.553767	−	1.05038i
$499$	−4.14447e7	−	4.93918e7i	−0.333555	−	0.397515i	0.573033	−	0.819532i	$-0.305767\pi$
$499$	−4.14447e7	−	4.93918e7i	−0.333555	−	0.397515i	−0.906588	+	0.422017i	$0.861322\pi$
$500$	6.78134e7	−	4.85443e7i	0.542507	−	0.388355i
$501$	1.07075e8	−	1.85460e8i	0.851482	−	1.47481i
$502$	1.24900e8	−	1.71058e7i	0.987301	−	0.135218i
$503$	4.31101e7	+	1.18444e8i	0.338747	+	0.930699i	0.985751	+	0.168212i	$0.0537995\pi$
$503$	4.31101e7	+	1.18444e8i	0.338747	+	0.930699i	−0.647004	+	0.762487i	$0.723978\pi$
$504$	2.20179e6	−	2.08180e6i	0.0171982	−	0.0162610i
$505$	3.31455e7	+	5.74096e7i	0.257365	+	0.445770i
$506$	9.65171e7	−	7.48623e7i	0.744994	−	0.577846i
$507$	−3.89772e8	−	6.87273e7i	−2.99079	−	0.527358i
$508$	−671885.	+	8.72605e6i	−0.00512512	+	0.0665621i
$509$	5.56331e7	+	4.66817e7i	0.421872	+	0.353992i	0.828874	−	0.559435i	$-0.188982\pi$
$509$	5.56331e7	+	4.66817e7i	0.421872	+	0.353992i	−0.407003	+	0.913427i	$0.633426\pi$
$510$	−3.78907e7	−	8.19329e6i	−0.285642	−	0.0617657i
$511$	−2.23190e7	+	6.13211e7i	−0.167268	+	0.459565i
$512$	−1.26272e8	−	4.54939e7i	−0.940802	−	0.338956i
$513$	−1.18238e8	+	5.10177e7i	−0.875802	+	0.377893i
$514$	−3.54682e7	−	1.44754e7i	−0.261186	−	0.106596i
$515$	2.41124e7	−	6.62483e7i	0.176530	−	0.485013i
$516$	1.88678e7	−	2.75527e7i	0.137332	−	0.200546i
$517$	9.62850e6	+	8.07927e6i	0.0696766	+	0.0584656i
$518$	−1.37615e7	−	4.28658e7i	−0.0990093	−	0.308405i
$519$	1.61130e8	+	2.84115e7i	1.15259	+	0.203232i
$520$	−9.84657e7	−	1.14006e7i	−0.700285	−	0.0810806i
$521$	68636.4	+	118882.i	0.000485334	+	0.000840624i	0.866268	−	0.499580i	$-0.166512\pi$
$521$	68636.4	+	118882.i	0.000485334	+	0.000840624i	−0.865783	+	0.500420i	$0.833179\pi$
$522$	−1.90332e7	−	731672.i	−0.133813	−	0.00514405i
$523$	7.29630e7	+	2.00464e8i	0.510032	+	1.40130i	0.881203	+	0.472738i	$0.156734\pi$
$523$	7.29630e7	+	2.00464e8i	0.510032	+	1.40130i	−0.371171	+	0.928565i	$0.621044\pi$
$524$	1.65975e8	+	4.26243e7i	1.15358	+	0.296253i
$525$	−1.85873e7	+	3.21942e7i	−0.128452	+	0.222485i
$526$	−2.25316e8	−	1.41897e8i	−1.54823	−	0.975025i
$527$	−1.16621e8	−	1.38983e8i	−0.796790	−	0.949578i
$528$	−6.79761e7	+	8.45274e7i	−0.461800	+	0.574243i
$529$	−1.98991e7	−	1.12854e8i	−0.134421	−	0.762340i
$530$	1.68434e7	+	1.52735e7i	0.113136	+	0.102591i
$531$			1.34887e7i			0.0900920i
$532$	−2.19585e7	+	3.64533e7i	−0.145837	+	0.242104i
$533$	−5.42369e7			−0.358190
$534$	−1.30651e8	+	1.44080e8i	−0.858002	+	0.946195i
$535$	4.53859e7	−	8.00276e6i	0.296387	−	0.0522611i
$536$	−4.13194e7	−	1.23213e7i	−0.268324	−	0.0800135i
$537$	−4.94845e7	+	4.15224e7i	−0.319556	+	0.268139i
$538$	3.48621e7	−	5.53570e7i	0.223876	−	0.355488i
$539$	−8.83248e7	−	5.09944e7i	−0.564049	−	0.325654i
$540$	5.18167e7	+	1.33071e7i	0.329070	+	0.0845089i
$541$	8.77581e7	−	3.19413e7i	0.554237	−	0.201726i	−0.0496911	−	0.998765i	$-0.515824\pi$
$541$	8.77581e7	−	3.19413e7i	0.554237	−	0.201726i	0.603928	+	0.797039i	$0.293601\pi$
$542$	6.40026e6	−	1.66492e8i	0.0401976	−	1.04567i
$543$	4.08692e7	−	2.35959e7i	0.255268	−	0.147379i
$544$	−7.98372e7	−	9.86167e7i	−0.495916	−	0.612567i
$545$	2.47514e6	−	1.40372e7i	0.0152901	−	0.0867146i
$546$	9.02520e7	−	2.89742e7i	0.554471	−	0.178006i
$547$	5.97037e7	−	7.11521e7i	0.364787	−	0.434736i	−0.552164	−	0.833735i	$-0.686198\pi$
$547$	5.97037e7	−	7.11521e7i	0.364787	−	0.434736i	0.916951	+	0.398999i	$0.130642\pi$
$548$	3.67632e7	−	5.36853e7i	0.223394	−	0.326222i
$549$	−1.24012e7	−	4.51367e6i	−0.0749457	−	0.0272780i
$550$	3.88550e7	−	9.52042e7i	0.233539	−	0.572227i
$551$	2.60287e8	−	6.17179e7i	1.55596	−	0.368940i
$552$	9.26070e7	+	2.14048e8i	0.550588	+	1.27260i
$553$	−3.59576e7	−	1.30875e7i	−0.212626	−	0.0773894i
$554$	1.67042e7	−	7.72503e7i	0.0982417	−	0.454329i
$555$	−4.66962e7	+	5.56504e7i	−0.273151	+	0.325529i
$556$	−790599.	+	1.02678e7i	−0.00459973	+	0.0597385i
$557$	−3.45731e7	+	1.96074e8i	−0.200066	+	1.13463i	0.704952	+	0.709255i	$0.250969\pi$
$557$	−3.45731e7	+	1.96074e8i	−0.200066	+	1.13463i	−0.905017	+	0.425374i	$0.860142\pi$
$558$	−1.40249e7	−	1.80817e7i	−0.0807228	−	0.104073i
$559$	6.99052e7	−	4.03598e7i	0.400197	−	0.231054i
$560$	1.64836e7	−	6.39160e6i	0.0938614	−	0.0363953i
$561$	−9.63576e7	+	3.50713e7i	−0.545754	+	0.198638i
$562$	8.99390e6	+	6.56696e7i	0.0506686	+	0.369961i
$563$	7.49485e7	+	4.32716e7i	0.419989	+	0.242481i	0.695073	−	0.718940i	$-0.255372\pi$
$563$	7.49485e7	+	4.32716e7i	0.419989	+	0.242481i	−0.275084	+	0.961420i	$0.588706\pi$
$564$	−1.95142e7	+	1.39693e7i	−0.108771	+	0.0778641i
$565$	−2.90948e7	+	2.44135e7i	−0.161313	+	0.135358i
$566$	1.00819e8	−	5.31524e7i	0.556023	−	0.293139i
$567$	−5.46303e7	+	9.63280e6i	−0.299699	+	0.0528449i
$568$	−2.56552e7	+	1.52221e6i	−0.140001	+	0.00830673i
$569$	−5.10585e7			−0.277160			−0.138580	−	0.990351i	$-0.544254\pi$
$569$	−5.10585e7			−0.277160			−0.138580	+	0.990351i	$0.544254\pi$
$570$	6.86560e7	−	1.36365e6i	0.370727	−	0.00736338i
$571$			2.00473e8i			1.07683i	0.842679	+	0.538416i	$0.180977\pi$
$571$			2.00473e8i			1.07683i	−0.842679	+	0.538416i	$0.819023\pi$
$572$	−2.36460e8	+	1.13278e8i	−1.26348	+	0.605279i
$573$	1.58047e7	+	8.96326e7i	0.0840081	+	0.476433i
$574$	8.55715e6	−	4.51139e6i	0.0452474	−	0.0238547i
$575$	−1.42115e8	−	1.69366e8i	−0.747543	−	0.890887i
$576$	−9.58444e6	−	1.28159e7i	−0.0501533	−	0.0670629i
$577$	−3.10826e7	+	5.38367e7i	−0.161804	+	0.280253i	−0.935516	−	0.353285i	$-0.885065\pi$
$577$	−3.10826e7	+	5.38367e7i	−0.161804	+	0.280253i	0.773711	+	0.633538i	$0.218398\pi$
$578$	9.92600e6	+	7.24754e7i	0.0514032	+	0.375325i
$579$	1.22215e7	+	3.35783e7i	0.0629636	+	0.172991i
$580$	−1.01203e8	−	4.59140e7i	−0.518692	−	0.235321i
$581$	3.16129e7	+	5.47552e7i	0.161189	+	0.279188i
$582$	9.15970e7	+	1.18092e8i	0.464635	+	0.599036i
$583$	5.92287e7	+	1.04436e7i	0.298900	+	0.0527042i
$584$	3.08155e8	+	1.54342e8i	1.54714	+	0.774901i
$585$	−9.05385e6	−	7.59708e6i	−0.0452237	−	0.0379472i
$586$	−5.20006e7	+	2.40482e8i	−0.258414	+	1.19506i
$587$	−4.51651e6	+	1.24090e7i	−0.0223300	+	0.0613512i	−0.950357	−	0.311162i	$-0.899282\pi$
$587$	−4.51651e6	+	1.24090e7i	−0.0223300	+	0.0613512i	0.928027	+	0.372513i	$0.121504\pi$
$588$	1.36254e8	−	1.39124e8i	0.670221	−	0.684337i
$589$	2.57805e8	+	1.91887e8i	1.26167	+	0.939073i
$590$	−2.97379e7	+	7.28651e7i	−0.144795	+	0.354783i
$591$	7.51009e6	−	2.06338e7i	0.0363817	−	0.0999578i
$592$	−2.33248e8	+	4.61595e7i	−1.12423	+	0.222482i
$593$	−2.31207e8	−	1.94006e8i	−1.10876	−	0.930358i	−0.110775	−	0.993846i	$-0.535333\pi$
$593$	−2.31207e8	−	1.94006e8i	−1.10876	−	0.930358i	−0.997983	+	0.0634878i	$0.979778\pi$
$594$	1.34736e8	−	4.32550e7i	0.642870	−	0.206385i
$595$	1.64593e7	+	2.90222e6i	0.0781376	+	0.0137778i
$596$	−5.52798e7	+	1.54313e7i	−0.261112	+	0.0728894i
$597$	7.19490e7	+	1.24619e8i	0.338144	+	0.585683i
$598$	−2.16554e7	+	5.63329e8i	−0.101266	+	2.63426i
$599$	−9.35359e7	−	2.56988e8i	−0.435209	−	1.19573i	−0.942575	−	0.333996i	$-0.891603\pi$
$599$	−9.35359e7	−	2.56988e8i	−0.435209	−	1.19573i	0.507366	−	0.861731i	$-0.330619\pi$
$600$	1.57612e8	+	1.17072e8i	0.729684	+	0.541998i
$601$	3.05727e7	−	5.29534e7i	0.140835	−	0.243933i	−0.786976	−	0.616983i	$-0.788355\pi$
$601$	3.05727e7	−	5.29534e7i	0.140835	−	0.243933i	0.927811	+	0.373050i	$0.121688\pi$
$602$	−7.67208e6	+	1.21824e7i	−0.0351661	+	0.0558396i
$603$	−3.30463e6	−	3.93831e6i	−0.0150720	−	0.0179621i
$604$	3.59600e8	−	3.52404e7i	1.63196	−	0.159930i
$605$	−6.83385e6	−	3.87567e7i	−0.0308603	−	0.175017i
$606$	−2.24898e8	+	2.48015e8i	−1.01057	+	1.11445i
$607$			2.53022e8i			1.13134i	0.824633	+	0.565668i	$0.191382\pi$
$607$			2.53022e8i			1.13134i	−0.824633	+	0.565668i	$0.808618\pi$
$608$	1.77909e8	+	1.37345e8i	0.791564	+	0.611086i
$609$	1.06271e8			0.470506
$610$	−5.70395e7	−	5.17229e7i	−0.251296	−	0.227873i
$611$	−5.71289e7	+	1.00734e7i	−0.250456	+	0.0441622i
$612$	−1.47554e6	−	1.50567e7i	−0.00643719	−	0.0656864i
$613$	1.87006e8	−	1.56916e8i	0.811846	−	0.681219i	−0.139202	−	0.990264i	$-0.544454\pi$
$613$	1.87006e8	−	1.56916e8i	0.811846	−	0.681219i	0.951048	+	0.309045i	$0.100009\pi$
$614$	1.35987e8	+	8.56405e7i	0.587479	+	0.369977i
$615$	−1.35182e7	−	7.80474e6i	−0.0581157	−	0.0335531i
$616$	2.78847e7	−	3.75408e7i	0.119296	−	0.160606i
$617$	−3.98931e7	+	1.45199e7i	−0.169841	+	0.0618170i	−0.425541	−	0.904939i	$-0.639916\pi$
$617$	−3.98931e7	+	1.45199e7i	−0.169841	+	0.0618170i	0.255700	+	0.966756i	$0.417694\pi$
$618$	3.55794e8	+	1.36774e7i	1.50742	+	0.0579479i
$619$	3.38699e8	−	1.95548e8i	1.42805	−	0.824482i	0.431079	−	0.902314i	$-0.358133\pi$
$619$	3.38699e8	−	1.95548e8i	1.42805	−	0.824482i	0.996966	+	0.0778319i	$0.0247997\pi$
$620$	−3.58976e7	−	1.28596e8i	−0.150623	−	0.539577i
$621$	5.28341e7	−	2.99637e8i	0.220617	−	1.25118i
$622$	−9.86817e7	−	3.07385e8i	−0.410077	−	1.27735i
$623$	5.38992e7	−	6.42346e7i	0.222904	−	0.265647i
$624$	−9.71867e7	−	4.91094e8i	−0.399994	−	2.02121i
$625$	−1.45792e8	−	5.30641e7i	−0.597166	−	0.217351i
$626$	−9.69395e7	−	3.95632e7i	−0.395164	−	0.161275i
$627$	1.51746e8	−	9.98280e7i	0.615624	−	0.404995i
$628$	1.68809e8	+	1.65327e8i	0.681581	+	0.667522i
$629$	−2.11222e8	−	7.68785e7i	−0.848765	−	0.308925i
$630$	2.06038e6	+	445525.i	0.00823996	+	0.00178177i
$631$	7.07629e7	−	8.43319e7i	0.281655	−	0.335663i	−0.606606	−	0.795003i	$-0.707469\pi$
$631$	7.07629e7	−	8.43319e7i	0.281655	−	0.335663i	0.888261	+	0.459339i	$0.151914\pi$
$632$	−9.05037e7	+	1.80697e8i	−0.358521	+	0.715812i
$633$	2.42160e6	−	1.37336e7i	0.00954754	−	0.0541468i
$634$	2.31792e7	−	1.79787e7i	0.0909559	−	0.0705489i
$635$	−5.27277e6	+	3.04423e6i	−0.0205929	+	0.0118893i
$636$	−4.74434e7	+	1.04574e8i	−0.184418	+	0.406493i
$637$	4.42321e8	−	1.60992e8i	1.71127	−	0.622852i
$638$	−2.91236e8	+	3.98867e7i	−1.12146	+	0.153591i
$639$	−2.65383e6	−	1.53219e6i	−0.0101711	−	0.00587231i
$640$	−2.35199e7	−	9.03611e7i	−0.0897214	−	0.344700i
$641$	1.88736e8	−	1.58368e8i	0.716607	−	0.601304i	−0.209838	−	0.977736i	$-0.567294\pi$
$641$	1.88736e8	−	1.58368e8i	0.716607	−	0.601304i	0.926444	+	0.376432i	$0.122849\pi$
$642$	1.08549e8	+	2.05894e8i	0.410222	+	0.778105i
$643$	−3.45531e8	+	6.09265e7i	−1.29973	+	0.229178i	−0.780339	−	0.625357i	$-0.784953\pi$
$643$	−3.45531e8	+	6.09265e7i	−1.29973	+	0.229178i	−0.519394	+	0.854535i	$0.673842\pi$
$644$	−4.34407e7	−	9.06796e7i	−0.162644	−	0.339510i
$645$	2.32312e7			0.0865751
$646$	7.66205e7	+	1.98177e8i	0.284215	+	0.735114i
$647$		−	2.31151e8i		−	0.853460i	−0.904379	−	0.426730i	$-0.859666\pi$
$647$		−	2.31151e8i		−	0.853460i	0.904379	−	0.426730i	$-0.140334\pi$
$648$	1.73527e7	+	2.92461e8i	0.0637739	+	1.07484i
$649$	3.61483e7	+	2.05007e8i	0.132237	+	0.749955i
$650$	2.21327e8	+	4.19811e8i	0.805925	+	1.52867i
$651$	8.20674e7	+	9.78041e7i	0.297459	+	0.354498i
$652$	1.38731e8	+	1.93798e8i	0.500530	+	0.699209i
$653$	1.07959e8	−	1.86990e8i	0.387720	−	0.671551i	−0.604423	−	0.796664i	$-0.706596\pi$
$653$	1.07959e8	−	1.86990e8i	0.387720	−	0.671551i	0.992142	+	0.125113i	$0.0399295\pi$
$654$	7.13223e7	−	9.76807e6i	0.254972	−	0.0349201i
$655$	4.07728e7	+	1.12022e8i	0.145093	+	0.398640i
$656$	−1.84704e7	−	4.76342e7i	−0.0654283	−	0.168736i
$657$	2.05469e7	+	3.55882e7i	0.0724519	+	0.125490i
$658$	8.17553e6	−	6.34125e6i	0.0286971	−	0.0222586i
$659$	−3.81280e8	−	6.72300e7i	−1.33226	−	0.234913i	−0.538232	−	0.842797i	$-0.680908\pi$
$659$	−3.81280e8	−	6.72300e7i	−1.33226	−	0.234913i	−0.794026	+	0.607884i	$0.792019\pi$
$660$	−7.52368e7	−	5.79306e6i	−0.261697	−	0.0201500i
$661$	−1.60832e8	−	1.34954e8i	−0.556889	−	0.467285i	0.320377	−	0.947290i	$-0.396190\pi$
$661$	−1.60832e8	−	1.34954e8i	−0.556889	−	0.467285i	−0.877266	+	0.480005i	$0.840635\pi$
$662$	−3.51588e8	−	7.60256e7i	−1.21188	−	0.262051i
$663$	1.61864e8	−	4.44719e8i	0.555406	−	1.52597i
$664$	3.06468e8	−	1.32592e8i	1.04684	−	0.452912i
$665$	−2.95549e7	+	1.72449e6i	−0.100500	+	0.00586401i
$666$	−2.62488e7	−	1.07127e7i	−0.0888560	−	0.0362641i
$667$	−2.16169e8	+	5.93919e8i	−0.728477	+	2.00147i
$668$	4.02319e8	+	2.75504e8i	1.34971	+	0.924269i
$669$	−3.37150e8	−	2.82903e8i	−1.12602	−	0.944841i
$670$	−9.16882e6	−	2.85600e7i	−0.0304852	−	0.0949587i
$671$	−2.00575e8	−	3.53668e7i	−0.663911	−	0.117065i
$672$	5.61824e7	+	6.93977e7i	0.185137	+	0.228685i
$673$	−2.24263e8	−	3.88434e8i	−0.735718	−	1.27430i	−0.954407	−	0.298507i	$-0.903511\pi$
$673$	−2.24263e8	−	3.88434e8i	−0.735718	−	1.27430i	0.218689	−	0.975795i	$-0.429822\pi$
$674$	−3.07819e8	−	1.18331e7i	−1.00535	−	0.0386474i
$675$	−8.76039e7	−	2.40690e8i	−0.284847	−	0.782611i
$676$	2.24160e8	−	8.72857e8i	0.725633	−	2.82555i
$677$	−2.10207e8	+	3.64089e8i	−0.677456	+	1.17339i	0.298289	+	0.954476i	$0.403584\pi$
$677$	−2.10207e8	+	3.64089e8i	−0.677456	+	1.17339i	−0.975745	+	0.218912i	$0.929749\pi$
$678$	−1.62314e8	−	1.02220e8i	−0.520794	−	0.327980i
$679$	−4.14164e7	−	4.93581e7i	−0.132301	−	0.157670i
$680$	2.52240e7	−	8.45884e7i	0.0802209	−	0.269020i
$681$	1.08253e8	+	6.13932e8i	0.342766	+	1.94392i
$682$	−2.61613e8	−	2.37229e8i	−0.824721	−	0.747850i
$683$		−	2.66091e8i		−	0.835157i	−0.908641	−	0.417578i	$-0.862879\pi$
$683$		−	2.66091e8i		−	0.835157i	0.908641	−	0.417578i	$-0.137121\pi$
$684$	8.69666e6	+	2.53483e7i	0.0271759	+	0.0792102i
$685$	4.52651e7			0.140829
$686$	−1.17687e8	+	1.29784e8i	−0.364548	+	0.402020i
$687$	4.21190e8	−	7.42671e7i	1.29900	−	0.229048i
$688$	5.92527e7	+	4.76505e7i	0.181946	+	0.146319i
$689$	−2.12635e8	+	1.78422e8i	−0.650094	+	0.545494i
$690$	−8.64610e7	+	1.37290e8i	−0.263192	+	0.417918i
$691$	−4.39501e8	−	2.53746e8i	−1.33207	−	0.769069i	−0.346451	−	0.938068i	$-0.612613\pi$
$691$	−4.39501e8	−	2.53746e8i	−1.33207	−	0.769069i	−0.985616	+	0.168999i	$0.945947\pi$
$692$	−9.26665e7	+	3.60835e8i	−0.279643	+	1.08891i
$693$	5.23962e6	−	1.90707e6i	0.0157435	−	0.00573015i
$694$	−1.07948e7	+	2.80808e8i	−0.0322950	+	0.840100i
$695$	−6.20440e6	+	3.58211e6i	−0.0184818	+	0.0106705i
$696$	6.45530e7	−	5.57538e8i	0.191465	−	1.65366i
$697$	8.38683e6	−	4.75641e7i	0.0247685	−	0.140469i
$698$	−3.79246e8	+	1.21752e8i	−1.11521	+	0.358022i
$699$	1.50237e8	−	1.79045e8i	0.439891	−	0.524242i
$700$	−6.98391e7	−	4.78251e7i	−0.203613	−	0.139432i
$701$	−7.79272e7	−	2.83632e7i	−0.226222	−	0.0823381i	0.226422	−	0.974029i	$-0.427297\pi$
$701$	−7.79272e7	−	2.83632e7i	−0.226222	−	0.0823381i	−0.452644	+	0.891691i	$0.649519\pi$
$702$	−2.46785e8	+	6.04683e8i	−0.713357	+	1.74790i
$703$	3.95476e8	+	4.61826e7i	1.13829	+	0.132927i
$704$	−1.80014e8	−	1.69097e8i	−0.515927	−	0.484638i
$705$	−1.56886e7	−	5.71017e6i	−0.0447730	−	0.0162960i
$706$	−7.76790e7	+	3.59235e8i	−0.220744	+	1.02086i
$707$	9.27803e7	−	1.10571e8i	0.262541	−	0.312884i
$708$	−3.96296e8	−	3.05139e7i	−1.11666	−	0.0859800i
$709$	5.58796e7	−	3.16909e8i	0.156789	−	0.889193i	−0.800343	−	0.599542i	$-0.795350\pi$
$709$	5.58796e7	−	3.16909e8i	0.156789	−	0.889193i	0.957132	−	0.289651i	$-0.0935394\pi$
$710$	−1.09579e7	−	1.41275e7i	−0.0306162	−	0.0394722i
$711$	−2.08684e7	+	1.20483e7i	−0.0580603	+	0.0335211i
$712$	−3.04257e8	−	3.21793e8i	−0.842948	−	0.891531i
$713$	−7.13533e8	+	2.59705e8i	−1.96855	+	0.716492i
$714$	1.14535e7	+	8.36286e7i	0.0314661	+	0.229752i
$715$	−1.57964e8	−	9.12005e7i	−0.432155	−	0.249505i
$716$	−8.56154e7	−	1.19599e8i	−0.233245	−	0.325829i
$717$	−1.87218e8	+	1.57095e8i	−0.507915	+	0.426191i
$718$	3.75166e8	−	1.97790e8i	1.01356	−	0.534358i
$719$	2.83310e8	−	4.99552e7i	0.762211	−	0.134398i	0.220987	−	0.975277i	$-0.429072\pi$
$719$	2.83310e8	−	4.99552e7i	0.762211	−	0.134398i	0.541224	+	0.840878i	$0.317961\pi$
$720$	3.58893e6	−	1.05388e7i	0.00961540	−	0.0282355i
$721$	−1.53505e8			−0.409560
$722$	−2.13053e8	−	3.10259e8i	−0.566078	−	0.824352i
$723$		−	1.71477e8i		−	0.453722i
$724$	4.64240e7	+	9.69071e7i	0.122328	+	0.255352i
$725$	9.23930e7	+	5.23987e8i	0.242452	+	1.37501i
$726$	1.75820e8	−	9.26938e7i	0.459472	−	0.242237i
$727$	3.06132e8	+	3.64834e8i	0.796719	+	0.949493i	0.999558	−	0.0297192i	$-0.00946130\pi$
$727$	3.06132e8	+	3.64834e8i	0.796719	+	0.949493i	−0.202839	+	0.979212i	$0.565017\pi$
$728$	5.00018e7	+	2.09958e8i	0.129596	+	0.544173i
$729$	1.74885e8	−	3.02910e8i	0.451410	−	0.781864i
$730$	3.25333e7	+	2.37544e8i	0.0836294	+	0.610627i
$731$	2.45846e7	+	6.75456e7i	0.0629377	+	0.172920i
$732$	1.60665e8	−	3.54135e8i	0.409626	−	0.902893i
$733$	2.32593e8	+	4.02862e8i	0.590587	+	1.02293i	0.994153	+	0.107977i	$0.0344372\pi$
$733$	2.32593e8	+	4.02862e8i	0.590587	+	1.02293i	−0.403566	+	0.914950i	$0.632229\pi$
$734$	−1.64600e8	−	2.12212e8i	−0.416238	−	0.536640i
$735$	1.33412e8	+	2.35242e7i	0.335996	+	0.0592452i
$736$	−5.02125e8	+	1.72823e8i	−1.25944	+	0.433479i
$737$	−6.07796e7	−	5.10001e7i	−0.151829	−	0.127400i
$738$	1.28748e6	−	5.95408e6i	0.00320310	−	0.0148131i
$739$	−3.04297e7	+	8.36049e7i	−0.0753988	+	0.207156i	−0.971666	−	0.236358i	$-0.924046\pi$
$739$	−3.04297e7	+	8.36049e7i	−0.0753988	+	0.207156i	0.896267	+	0.443514i	$0.146268\pi$
$740$	−1.18176e8	−	1.15739e8i	−0.291632	−	0.285617i
$741$	−9.72353e7	+	8.32658e8i	−0.238984	+	2.04650i
$742$	1.87071e7	−	4.58370e7i	0.0457926	−	0.112203i
$743$	−4.13319e7	+	1.13558e8i	−0.100767	+	0.276855i	−0.979824	−	0.199861i	$-0.935951\pi$
$743$	−4.13319e7	+	1.13558e8i	−0.100767	+	0.276855i	0.879057	+	0.476716i	$0.158173\pi$
$744$	5.62966e8	−	3.71145e8i	1.36698	−	0.901208i
$745$	−3.05859e7	−	2.56646e7i	−0.0739694	−	0.0620677i
$746$	3.04236e8	−	9.76708e7i	0.732814	−	0.235260i
$747$	3.92101e7	+	6.91380e6i	0.0940668	+	0.0165865i
$748$	−6.27763e7	−	2.24884e8i	−0.150000	−	0.537346i
$749$	−5.01734e7	−	8.69029e7i	−0.119406	−	0.206818i
$750$	−1.12558e7	+	2.92800e8i	−0.0266804	+	0.694044i
$751$	4.02773e7	+	1.10661e8i	0.0950913	+	0.261261i	0.978114	−	0.208069i	$-0.0667177\pi$
$751$	4.02773e7	+	1.10661e8i	0.0950913	+	0.261261i	−0.883023	+	0.469330i	$0.844496\pi$
$752$	−2.83024e7	−	4.67436e7i	−0.0665532	−	0.109918i
$753$	−2.21464e8	+	3.83587e8i	−0.518702	+	0.898419i
$754$	7.22975e8	−	1.14800e9i	1.68659	−	2.67811i
$755$	1.61573e8	+	1.92556e8i	0.375430	+	0.447420i
$756$	−1.13610e7	−	1.15930e8i	−0.0262938	−	0.268307i
$757$	−5.53688e7	−	3.14012e8i	−0.127637	−	0.723867i	−0.979706	−	0.200438i	$-0.935764\pi$
$757$	−5.53688e7	−	3.14012e8i	−0.127637	−	0.723867i	0.852069	−	0.523429i	$-0.175348\pi$
$758$	3.23642e8	−	3.56909e8i	0.743118	−	0.819502i
$759$			4.29161e8i			0.981510i
$760$	−8.90543e6	+	1.56103e8i	−0.0202868	+	0.355608i
$761$	4.46350e8			1.01280			0.506398	−	0.862300i	$-0.330977\pi$
$761$	4.46350e8			1.01280			0.506398	+	0.862300i	$0.330977\pi$
$762$	−2.27788e7	−	2.06557e7i	−0.0514834	−	0.0466847i
$763$	−3.05644e7	+	5.38933e6i	−0.0688085	+	0.0121328i
$764$	−2.06249e8	+	2.02122e7i	−0.462501	+	0.0453245i
$765$	8.06243e6	−	6.76518e6i	0.0180087	−	0.0151111i
$766$	−7.38237e8	−	4.64919e8i	−1.64252	−	1.03441i
$767$	−8.32047e8	−	4.80382e8i	−1.84400	−	1.06464i
$768$	3.98212e8	−	2.52598e8i	0.879085	−	0.557630i
$769$	3.49074e8	−	1.27053e8i	0.767607	−	0.279386i	0.0716117	−	0.997433i	$-0.477186\pi$
$769$	3.49074e8	−	1.27053e8i	0.767607	−	0.279386i	0.695995	+	0.718047i	$0.254964\pi$
$770$	3.25085e7	+	1.24969e6i	0.0712074	+	0.00273735i
$771$	1.16563e8	−	6.72977e7i	0.254330	−	0.146837i
$772$	−7.83669e7	+	2.18761e7i	−0.170326	+	0.0475464i
$773$	1.54732e8	−	8.77531e8i	0.334999	−	1.89987i	−0.0922484	−	0.995736i	$-0.529405\pi$
$773$	1.54732e8	−	8.77531e8i	0.334999	−	1.89987i	0.427247	−	0.904135i	$-0.359483\pi$
$774$	2.77125e6	+	8.63219e6i	0.00597657	+	0.0186165i
$775$	−4.10888e8	+	4.89677e8i	−0.882710	+	1.05197i
$776$	−2.84108e8	+	1.87303e8i	−0.607993	+	0.400830i
$777$	1.48639e8	+	5.41003e7i	0.316863	+	0.115329i
$778$	7.16255e8	+	2.92320e8i	1.52100	+	0.620754i
$779$	4.98342e6	+	8.54078e7i	0.0105418	+	0.180670i
$780$	2.43683e8	−	2.48815e8i	0.513501	−	0.524316i
$781$	−4.44402e7	−	1.61749e7i	−0.0932873	−	0.0339538i
$782$	−4.90673e8	−	1.06100e8i	−1.02606	−	0.221869i
$783$	−4.70661e8	+	5.60912e8i	−0.980445	+	1.16845i
$784$	2.92026e8	+	3.33648e8i	0.606000	+	0.692372i
$785$	−2.85437e7	+	1.61879e8i	−0.0590066	+	0.334643i
$786$	−4.75740e8	+	3.69002e8i	−0.979720	+	0.759909i
$787$	−6.04619e8	+	3.49077e8i	−1.24039	+	0.716138i	−0.969173	−	0.246380i	$-0.920759\pi$
$787$	−6.04619e8	+	3.49077e8i	−1.24039	+	0.716138i	−0.271215	+	0.962519i	$0.587425\pi$
$788$	4.55307e7	+	2.06565e7i	0.0930519	+	0.0422160i
$789$	8.79127e8	−	3.19976e8i	1.78987	−	0.651458i
$790$	−1.39292e8	+	1.90770e7i	−0.282517	+	0.0386926i
$791$	7.16188e7	+	4.13491e7i	0.144710	+	0.0835481i
$792$	−6.82242e6	−	2.86473e7i	−0.0137329	−	0.0576645i
$793$	7.20078e8	−	6.04217e8i	1.44398	−	1.21164i
$794$	−2.54427e8	−	4.82595e8i	−0.508279	−	0.964098i
$795$	−7.86728e7	+	1.38721e7i	−0.156575	+	0.0276085i
$796$	−2.95491e8	+	1.41557e8i	−0.585875	+	0.280667i
$797$	−2.87770e8			−0.568422			−0.284211	−	0.958762i	$-0.591732\pi$
$797$	−2.87770e8			−0.568422			−0.284211	+	0.958762i	$0.591732\pi$
$798$	−5.39188e7	−	1.39459e8i	−0.106104	−	0.274435i
$799$		−	5.16579e7i		−	0.101274i
$800$	−2.93330e8	+	3.37350e8i	−0.572911	+	0.658887i
$801$	−9.16932e6	−	5.20018e7i	−0.0178418	−	0.101186i
$802$	−7.22512e7	−	1.37045e8i	−0.140062	−	0.265669i
$803$	4.07654e8	+	4.85823e8i	0.787308	+	0.938277i
$804$	1.23183e8	−	8.81806e7i	0.237018	−	0.169670i
$805$	3.49744e7	−	6.05774e7i	0.0670443	−	0.116124i
$806$	1.61484e9	−	2.21164e8i	3.08408	−	0.422385i
$807$	7.86137e7	+	2.15989e8i	0.149581	+	0.410972i
$808$	−5.23738e8	−	5.53923e8i	−0.992842	−	1.05006i
$809$	−1.39905e8	−	2.42322e8i	−0.264233	−	0.457664i	0.703130	−	0.711062i	$-0.251785\pi$
$809$	−1.39905e8	−	2.42322e8i	−0.264233	−	0.457664i	−0.967362	+	0.253397i	$0.918452\pi$
$810$	−1.61049e8	+	1.24916e8i	−0.303043	+	0.235052i
$811$	7.43419e8	+	1.31085e8i	1.39371	+	0.245748i	0.819554	−	0.573002i	$-0.194221\pi$
$811$	7.43419e8	+	1.31085e8i	1.39371	+	0.245748i	0.574151	+	0.818750i	$0.305332\pi$
$812$	−1.85765e7	+	2.41260e8i	−0.0346973	+	0.450628i
$813$	4.48440e8	+	3.76286e8i	0.834512	+	0.700238i
$814$	−4.27650e8	−	9.24727e7i	−0.792894	−	0.171451i
$815$	−5.67084e7	+	1.55805e8i	−0.104755	+	0.287812i
$816$	4.45702e8	−	9.29020e6i	0.820303	−	0.0170984i
$817$	−6.99783e7	−	1.06373e8i	−0.128321	−	0.195058i
$818$	3.41713e8	+	1.39461e8i	0.624312	+	0.254796i
$819$	−8.80167e6	+	2.41824e7i	−0.0160219	+	0.0440197i
$820$	2.00815e7	−	2.93251e7i	0.0364213	−	0.0531861i
$821$	−2.19183e8	−	1.83916e8i	−0.396075	−	0.332346i	0.422899	−	0.906177i	$-0.361012\pi$
$821$	−2.19183e8	−	1.83916e8i	−0.396075	−	0.332346i	−0.818974	+	0.573831i	$0.805457\pi$
$822$	6.98792e7	+	2.17667e8i	0.125815	+	0.391903i
$823$	9.57765e8	+	1.68880e8i	1.71814	+	0.302955i	0.943973	−	0.330022i	$-0.107056\pi$
$823$	9.57765e8	+	1.68880e8i	1.71814	+	0.302955i	0.774170	+	0.632977i	$0.218167\pi$
$824$	−9.32444e7	+	8.05342e8i	−0.166664	+	1.43946i
$825$	1.80641e8	+	3.12880e8i	0.321703	+	0.557206i
$826$	1.71233e8	+	6.58252e6i	0.303841	+	0.0116802i
$827$	−1.35041e8	−	3.71022e8i	−0.238753	−	0.655969i	−0.999972	−	0.00747417i	$-0.997621\pi$
$827$	−1.35041e8	−	3.71022e8i	−0.238753	−	0.655969i	0.761219	−	0.648495i	$-0.224601\pi$
$828$	−6.13277e7	−	1.57496e7i	−0.108035	−	0.0277447i
$829$	1.87637e7	−	3.24996e7i	0.0329347	−	0.0570447i	−0.849088	−	0.528251i	$-0.822848\pi$
$829$	1.87637e7	−	3.24996e7i	0.0329347	−	0.0570447i	0.882023	+	0.471206i	$0.156181\pi$
$830$	1.96568e8	+	1.23793e8i	0.343778	+	0.216501i
$831$	1.78495e8	+	2.12723e8i	0.311046	+	0.370690i
$832$	1.13188e9	−	1.34792e8i	1.96531	−	0.234042i
$833$	7.27871e7	+	4.12796e8i	0.125927	+	0.714168i
$834$	−2.68036e7	−	2.43053e7i	−0.0462056	−	0.0418989i
$835$			3.39218e8i			0.582665i
$836$	2.00107e8	+	3.61949e8i	0.342486	+	0.619482i
$837$	−8.79686e8			−1.50021
$838$	−2.84839e8	+	3.14117e8i	−0.484024	+	0.533776i
$839$	−6.94236e8	+	1.22412e8i	−1.17550	+	0.207272i	−0.727080	−	0.686553i	$-0.759123\pi$
$839$	−6.94236e8	+	1.22412e8i	−1.17550	+	0.207272i	−0.448416	+	0.893825i	$0.648012\pi$
$840$	−1.77504e7	+	5.95259e7i	−0.0299482	+	0.100431i
$841$	7.09517e8	−	5.95355e8i	1.19282	−	1.00089i
$842$	−1.63764e8	+	2.60039e8i	−0.274336	+	0.435614i
$843$	−2.01682e8	−	1.16441e8i	−0.336655	−	0.194368i
$844$	3.07551e7	+	7.89825e6i	0.0511552	+	0.0131372i
$845$	5.89121e8	−	2.14422e8i	0.976415	−	0.355386i
$846$	250283.	−	6.51068e6i	0.000413352	−	0.0107526i
$847$	−7.42096e7	+	4.28449e7i	−0.122126	+	0.0705098i
$848$	−2.29114e8	−	1.25987e8i	−0.375720	−	0.206604i
$849$	−6.95353e7	+	3.94354e8i	−0.113627	+	0.644412i
$850$	−4.02385e8	+	1.29180e8i	−0.655217	+	0.210349i
$851$	−6.04701e8	+	7.20655e8i	−0.981188	+	1.16933i
$852$	5.10190e7	−	7.45031e7i	0.0824922	−	0.120464i
$853$	−4.51735e8	−	1.64418e8i	−0.727841	−	0.264912i	−0.0485901	−	0.998819i	$-0.515473\pi$
$853$	−4.51735e8	−	1.64418e8i	−0.727841	−	0.264912i	−0.679251	+	0.733906i	$0.737695\pi$
$854$	−6.33508e7	+	1.55225e8i	−0.101713	+	0.249223i
$855$	−1.11314e7	+	1.49553e7i	−0.0178094	+	0.0239275i
$856$	−4.86400e8	+	2.10440e8i	−0.775483	+	0.335511i
$857$	9.87605e8	+	3.59459e8i	1.56906	+	0.571093i	0.972790	−	0.231688i	$-0.0744248\pi$
$857$	9.87605e8	+	3.59459e8i	1.56906	+	0.571093i	0.596274	+	0.802781i	$0.296647\pi$
$858$	1.94697e8	−	9.00398e8i	0.308246	−	1.42552i
$859$	1.39273e8	−	1.65979e8i	0.219730	−	0.261863i	−0.644907	−	0.764261i	$-0.723104\pi$
$859$	1.39273e8	−	1.65979e8i	0.219730	−	0.261863i	0.864637	+	0.502397i	$0.167549\pi$
$860$	−4.06087e6	+	5.27402e7i	−0.00638445	+	0.0829175i
$861$	−5.90191e6	+	3.34714e7i	−0.00924662	+	0.0524402i
$862$	−3.59552e7	−	4.63556e7i	−0.0561357	−	0.0723736i
$863$	4.05820e8	−	2.34300e8i	0.631394	−	0.364536i	−0.149898	−	0.988702i	$-0.547894\pi$
$863$	4.05820e8	−	2.34300e8i	0.631394	−	0.364536i	0.781292	+	0.624166i	$0.214561\pi$
$864$	−6.15113e8	−	1.08161e7i	−0.953704	−	0.0167698i
$865$	−2.43540e8	+	8.86412e7i	−0.376289	+	0.136958i
$866$	4.45045e7	+	3.24953e8i	0.0685251	+	0.500341i
$867$	−2.22584e8	−	1.28509e8i	−0.341536	−	0.197186i
$868$	−2.36383e8	+	1.69215e8i	−0.361458	+	0.258750i
$869$	−2.84878e8	+	2.39041e8i	−0.434110	+	0.364262i
$870$	3.45395e8	−	1.82095e8i	0.524515	−	0.276528i
$871$	3.60624e8	−	6.35877e7i	0.545758	−	0.0962318i
$872$	9.70845e6	+	1.63625e8i	0.0146420	+	0.246775i
$873$	−4.05749e7			−0.0609838
$874$	8.89074e8	−	1.76588e7i	1.33169	−	0.0264500i
$875$		−	1.26327e8i		−	0.188569i
$876$	−1.09206e9	+	5.23158e8i	−1.62455	+	0.778253i
$877$	1.80370e8	+	1.02293e9i	0.267403	+	1.51652i	0.762105	+	0.647454i	$0.224166\pi$
$877$	1.80370e8	+	1.02293e9i	0.267403	+	1.51652i	−0.494702	+	0.869063i	$0.664723\pi$
$878$	6.93443e8	−	3.65588e8i	1.02454	−	0.540143i
$879$	−5.55662e8	−	6.62212e8i	−0.818171	−	0.975058i
$880$	2.63031e7	−	1.69792e8i	0.0385975	−	0.249155i
$881$	3.50498e8	−	6.07080e8i	0.512575	−	0.887806i	−0.487319	−	0.873224i	$-0.662025\pi$
$881$	3.50498e8	−	6.07080e8i	0.512575	−	0.887806i	0.999894	−	0.0145819i	$-0.00464174\pi$
$882$	7.17368e6	+	5.23792e7i	0.0104553	+	0.0763402i
$883$	6.42534e7	+	1.76535e8i	0.0933285	+	0.256418i	0.977570	−	0.210613i	$-0.0675459\pi$
$883$	6.42534e7	+	1.76535e8i	0.0933285	+	0.256418i	−0.884241	+	0.467031i	$0.845324\pi$
$884$	9.81318e8	+	4.45207e8i	1.42054	+	0.644473i
$885$	−1.38255e8	−	2.39464e8i	−0.199458	−	0.345471i
$886$	4.52579e8	+	5.83493e8i	0.650719	+	0.838947i
$887$	−6.90726e8	−	1.21794e8i	−0.989772	−	0.174524i	−0.344756	−	0.938692i	$-0.612038\pi$
$887$	−6.90726e8	−	1.21794e8i	−0.989772	−	0.174524i	−0.645016	+	0.764169i	$0.723149\pi$
$888$	3.74118e8	−	7.46953e8i	0.534281	−	1.06673i
$889$	1.01554e7	+	8.52137e6i	0.0144541	+	0.0121284i
$890$	6.51138e7	−	3.01126e8i	0.0923641	−	0.427147i
$891$	−1.84389e8	+	5.06604e8i	−0.260676	+	0.716201i
$892$	7.01189e8	−	7.15956e8i	0.987962	−	1.00877i
$893$	2.11118e7	+	8.90363e7i	0.0296464	+	0.125030i
$894$	7.61962e7	−	1.86699e8i	0.106640	−	0.261294i
$895$	3.49967e7	−	9.61526e7i	0.0488155	−	0.134119i
$896$	−1.67370e8	+	1.15416e8i	−0.232676	+	0.160451i
$897$	−1.51731e9	−	1.27317e9i	−2.10231	−	1.76404i
$898$	−1.21695e9	+	3.90687e8i	−1.68053	+	0.539510i
$899$	1.79960e9	+	3.17318e8i	2.47684	+	0.436733i
$900$	−5.13403e7	+	1.43316e7i	−0.0704256	+	0.0196593i
$901$	−1.23590e8	−	2.14064e8i	−0.168969	−	0.292664i
$902$	3.61135e6	−	9.39431e7i	0.00492097	−	0.128010i
$903$	−1.73005e7	−	4.75326e7i	−0.0234960	−	0.0645548i
$904$	2.60436e8	−	3.50621e8i	0.352529	−	0.474605i
$905$	−3.73763e7	+	6.47376e7i	−0.0504255	+	0.0873395i
$906$	−6.76513e8	+	1.07422e9i	−0.909686	+	1.44448i
$907$	−3.28838e7	−	3.91894e7i	−0.0440718	−	0.0525227i	0.743558	−	0.668671i	$-0.233137\pi$
$907$	−3.28838e7	−	3.91894e7i	−0.0440718	−	0.0525227i	−0.787630	+	0.616148i	$0.788692\pi$
$908$	−1.41269e9	+	1.38442e8i	−1.88707	+	0.184931i
$909$	−1.57838e7	−	8.95142e7i	−0.0210145	−	0.119179i
$910$	−1.00860e8	+	1.11227e8i	−0.133843	+	0.147600i
$911$		−	6.69661e8i		−	0.885727i	−0.896589	−	0.442863i	$-0.853963\pi$
$911$		−	6.69661e8i		−	0.885727i	0.896589	−	0.442863i	$-0.146037\pi$
$912$	−7.64405e8	+	1.98165e8i	−1.00772	+	0.261241i
$913$	6.14461e8			0.807388
$914$	−1.01825e9	−	9.23340e8i	−1.33357	−	1.20927i
$915$	2.66422e8	−	4.69774e7i	0.347782	−	0.0613233i
$916$	9.49784e7	+	9.69179e8i	0.123577	+	1.26101i
$917$	1.98841e8	−	1.66848e8i	0.257869	−	0.216378i
$918$	−4.92127e8	−	3.09926e8i	−0.636134	−	0.400618i
$919$	−7.86336e8	−	4.53991e8i	−1.01312	−	0.584926i	−0.101017	−	0.994885i	$-0.532210\pi$
$919$	−7.86336e8	−	4.53991e8i	−1.01312	−	0.584926i	−0.912104	+	0.409959i	$0.865543\pi$
$920$	−2.96566e8	−	2.20285e8i	−0.380853	−	0.282892i
$921$	−5.30589e8	+	1.93118e8i	−0.679171	+	0.247198i
$922$	−1.83388e8	−	7.04977e6i	−0.233979	−	0.00899461i
$923$	1.89025e8	−	1.09134e8i	0.240389	−	0.138789i
$924$	4.41764e7	+	1.58254e8i	0.0559983	+	0.200603i
$925$	−1.37522e8	+	7.79924e8i	−0.173758	+	0.985432i
$926$	−3.42805e8	−	1.06781e9i	−0.431733	−	1.34481i
$927$	−6.21359e7	+	7.40507e7i	−0.0780016	+	0.0929586i
$928$	1.25445e9	+	2.44009e8i	1.56968	+	0.305324i
$929$	−1.77113e7	−	6.44638e6i	−0.0220904	−	0.00804023i	0.330951	−	0.943648i	$-0.392630\pi$
$929$	−1.77113e7	−	6.44638e6i	−0.0220904	−	0.00804023i	−0.353042	+	0.935608i	$0.614853\pi$
$930$	4.34315e8	+	1.77254e8i	0.539953	+	0.220367i
$931$	−2.94158e8	−	6.81738e8i	−0.364528	−	0.844828i
$932$	3.80212e8	+	3.72370e8i	0.469655	+	0.459967i
$933$	1.06587e9	+	3.87946e8i	1.31238	+	0.477668i
$934$	3.78042e8	+	8.17458e7i	0.463980	+	0.100329i
$935$	1.04406e8	−	1.24427e8i	0.127730	−	0.152223i
$936$	1.21523e8	+	6.08659e7i	0.148194	+	0.0742244i
$937$	−1.77872e8	+	1.00876e9i	−0.216217	+	1.22623i	0.662565	+	0.749004i	$0.269468\pi$
$937$	−1.77872e8	+	1.00876e9i	−0.216217	+	1.22623i	−0.878782	+	0.477223i	$0.841643\pi$
$938$	−5.16077e7	+	4.00289e7i	−0.0625325	+	0.0485026i
$939$	3.18583e8	−	1.83934e8i	0.384792	−	0.222160i
$940$	1.57058e7	−	3.46185e7i	0.0189093	−	0.0416797i
$941$	−1.09172e9	+	3.97355e8i	−1.31022	+	0.476881i	−0.900312	−	0.435246i	$-0.856661\pi$
$941$	−1.09172e9	+	3.97355e8i	−1.31022	+	0.476881i	−0.409908	+	0.912127i	$0.634439\pi$
$942$	−8.22497e8	+	1.12646e8i	−0.983969	+	0.134761i
$943$	−1.75056e8	−	1.01069e8i	−0.208758	−	0.120526i
$944$	1.38547e8	−	8.94350e8i	0.164695	−	1.06314i
$945$	6.20773e7	−	5.20891e7i	0.0735593	−	0.0617236i
$946$	6.52521e7	+	1.23769e8i	0.0770763	+	0.146197i
$947$	4.13944e8	−	7.29895e7i	0.487407	−	0.0859429i	0.0754561	−	0.997149i	$-0.475959\pi$
$947$	4.13944e8	−	7.29895e7i	0.487407	−	0.0859429i	0.411951	+	0.911206i	$0.364848\pi$
$948$	−3.06771e8	−	6.40366e8i	−0.360072	−	0.751628i
$949$	−2.92700e9			−3.42472
$950$	6.40747e8	−	3.87101e8i	0.747336	−	0.451496i
$951$			1.03066e8i			0.119832i
$952$	−1.91858e8	+	1.13836e7i	−0.222366	+	0.0131938i
$953$	−2.40217e7	−	1.36234e8i	−0.0277539	−	0.157400i	0.967781	−	0.251793i	$-0.0810202\pi$
$953$	−2.40217e7	−	1.36234e8i	−0.0277539	−	0.157400i	−0.995535	+	0.0943926i	$0.969909\pi$
$954$	−1.45394e7	−	2.75782e7i	−0.0167457	−	0.0317630i
$955$	−9.26706e7	−	1.10441e8i	−0.106398	−	0.126800i
$956$	−3.23915e8	−	4.52489e8i	−0.370730	−	0.517886i
$957$	5.16401e8	−	8.94432e8i	0.589184	−	1.02050i
$958$	1.05238e8	−	1.44130e7i	0.119695	−	0.0163930i
$959$	−3.37093e7	−	9.26155e7i	−0.0382203	−	0.105009i
$960$	3.01512e8	+	1.29283e8i	0.340793	+	0.146126i
$961$	6.53943e8	+	1.13266e9i	0.736834	+	1.27623i
$962$	1.59563e9	−	1.23763e9i	1.79228	−	1.39016i
$963$	−6.22310e7	−	1.09730e7i	−0.0696832	−	0.0122870i
$964$	3.89291e8	+	2.99745e7i	0.434554	+	0.0334596i
$965$	−4.33598e7	−	3.63832e7i	−0.0482509	−	0.0404873i
$966$	3.45292e8	+	7.46642e7i	0.383050	+	0.0828287i
$967$	2.45420e8	−	6.74285e8i	0.271413	−	0.745700i	−0.726851	−	0.686795i	$-0.759017\pi$
$967$	2.45420e8	−	6.74285e8i	0.271413	−	0.745700i	0.998264	−	0.0589048i	$-0.0187609\pi$
$968$	1.79702e8	+	4.15355e8i	0.198120	+	0.457924i
$969$	−7.15179e8	−	2.14029e8i	−0.786037	−	0.235234i
$970$	−2.19183e8	−	8.94534e7i	−0.240155	−	0.0980126i
$971$	5.27449e8	−	1.44915e9i	0.576133	−	1.58291i	−0.218510	−	0.975835i	$-0.570120\pi$
$971$	5.27449e8	−	1.44915e9i	0.576133	−	1.58291i	0.794643	−	0.607078i	$-0.207658\pi$
$972$	−1.26578e8	−	8.66796e7i	−0.137835	−	0.0943882i
$973$	1.19497e7	+	1.00270e7i	0.0129723	+	0.0108851i
$974$	2.25057e7	+	7.01033e7i	0.0243566	+	0.0758686i
$975$	−1.64209e9	−	2.89546e8i	−1.77168	−	0.312394i
$976$	7.75884e8	+	4.26650e8i	0.834540	+	0.458904i
$977$	−2.19626e8	−	3.80404e8i	−0.235505	−	0.407907i	0.723914	−	0.689890i	$-0.242341\pi$
$977$	−2.19626e8	−	3.80404e8i	−0.235505	−	0.407907i	−0.959419	+	0.281983i	$0.909008\pi$
$978$	−8.36769e8	−	3.21670e7i	−0.894518	−	0.0343870i
$979$	−2.78719e8	−	7.65774e8i	−0.297043	−	0.816118i
$980$	−7.67261e7	+	2.98765e8i	−0.0815201	+	0.317432i
$981$	−9.77207e6	+	1.69257e7i	−0.0103509	+	0.0179283i
$982$	7.78086e6	+	4.90015e6i	0.00821662	+	0.00517458i
$983$	8.41469e8	+	1.00282e9i	0.885886	+	1.05576i	0.998072	+	0.0620703i	$0.0197703\pi$
$983$	8.41469e8	+	1.00282e9i	0.885886	+	1.05576i	−0.112186	+	0.993687i	$0.535785\pi$
$984$	1.72018e8	+	5.12952e7i	0.180546	+	0.0538383i
$985$	6.03981e6	+	3.42535e7i	0.00631997	+	0.0358423i
$986$	8.94963e8	+	8.11545e8i	0.933629	+	0.846607i
$987$			3.63523e7i			0.0378077i
$988$	−1.87333e9	−	3.66297e8i	−1.94242	−	0.379806i
$989$	3.00837e8			0.310987
$990$	1.37617e7	−	1.51762e7i	0.0141829	−	0.0156408i
$991$	−2.18583e8	+	3.85421e7i	−0.224593	+	0.0396017i	−0.284812	−	0.958583i	$-0.591931\pi$
$991$	−2.18583e8	+	3.85421e7i	−0.224593	+	0.0396017i	0.0602192	+	0.998185i	$0.480820\pi$
$992$	7.44177e8	+	1.34294e9i	0.762326	+	1.37569i
$993$	9.68163e8	−	8.12385e8i	0.988782	−	0.829687i
$994$	−2.07455e7	+	3.29414e7i	−0.0211234	+	0.0335415i
$995$	−1.97399e8	−	1.13968e8i	−0.200390	−	0.115695i
$996$	−2.91827e8	+	1.13635e9i	−0.295357	+	1.15009i
$997$	−2.74726e8	+	9.99921e7i	−0.277214	+	0.100898i	−0.476886	−	0.878965i	$-0.658234\pi$
$997$	−2.74726e8	+	9.99921e7i	−0.277214	+	0.100898i	0.199672	+	0.979863i	$0.436012\pi$
$998$	−1.98142e7	+	5.15431e8i	−0.0199335	+	0.518536i
$999$	−9.43851e8	+	5.44933e8i	−0.946688	+	0.546571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.l.a.23.14	yes	348
4.3	odd	2	inner	76.7.l.a.23.1	✓	348
19.5	even	9	inner	76.7.l.a.43.1	yes	348
76.43	odd	18	inner	76.7.l.a.43.14	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.l.a.23.1	✓	348	4.3	odd	2	inner
76.7.l.a.23.14	yes	348	1.1	even	1	trivial
76.7.l.a.43.1	yes	348	19.5	even	9	inner
76.7.l.a.43.14	yes	348	76.43	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.92630 - 5.37392i) q^{2} +(27.6808 - 4.88087i) q^{3} +(6.24202 + 63.6949i) q^{4} +(-34.1068 + 28.6190i) q^{5} +(-190.274 - 119.829i) q^{6} +(83.9559 + 48.4720i) q^{7} +(305.299 - 411.019i) q^{8} +(57.3665 - 20.8797i) q^{9} +O(q^{10})\)	\(q+(-5.92630 - 5.37392i) q^{2} +(27.6808 - 4.88087i) q^{3} +(6.24202 + 63.6949i) q^{4} +(-34.1068 + 28.6190i) q^{5} +(-190.274 - 119.829i) q^{6} +(83.9559 + 48.4720i) q^{7} +(305.299 - 411.019i) q^{8} +(57.3665 - 20.8797i) q^{9} +(355.923 + 13.6824i) q^{10} +(815.927 - 471.076i) q^{11} +(483.670 + 1732.66i) q^{12} +(-755.075 + 4282.24i) q^{13} +(-237.063 - 738.431i) q^{14} +(-804.416 + 958.666i) q^{15} +(-4018.07 + 795.170i) q^{16} +(-3638.63 - 1324.35i) q^{17} +(-452.177 - 184.544i) q^{18} +(6812.71 + 795.568i) q^{19} +(-2035.78 - 1993.79i) q^{20} +(2560.55 + 931.964i) q^{21} +(-7366.95 - 1592.99i) q^{22} +(-10416.9 + 12414.4i) q^{23} +(6444.78 - 12867.4i) q^{24} +(-2369.03 + 13435.4i) q^{25} +(27487.2 - 21320.1i) q^{26} +(-16259.3 + 9387.33i) q^{27} +(-2563.36 + 5650.12i) q^{28} +(36648.4 - 13338.9i) q^{29} +(9919.00 - 1358.47i) q^{30} +(40577.6 + 23427.5i) q^{31} +(28085.5 + 16880.4i) q^{32} +(20286.2 - 17022.2i) q^{33} +(14446.7 + 27402.2i) q^{34} +(-4250.68 + 749.510i) q^{35} +(1688.01 + 3523.62i) q^{36} +58049.8 q^{37} +(-36098.8 - 41325.7i) q^{38} +122221. i q^{39} +(1350.18 + 22755.9i) q^{40} +(2165.93 + 12283.6i) q^{41} +(-10166.3 - 19283.3i) q^{42} +(-11932.4 - 14220.4i) q^{43} +(35098.1 + 49029.9i) q^{44} +(-1359.03 + 2353.91i) q^{45} +(128448. - 17591.8i) q^{46} +(4562.85 + 12536.3i) q^{47} +(-107342. + 41622.6i) q^{48} +(-54125.4 - 93748.0i) q^{49} +(86240.4 - 66891.4i) q^{50} +(-107184. - 18899.5i) q^{51} +(-277470. - 21364.5i) q^{52} +(48900.6 + 41032.4i) q^{53} +(146804. + 31744.2i) q^{54} +(-14346.9 + 39417.9i) q^{55} +(45554.5 - 19709.0i) q^{56} +(192464. - 11230.0i) q^{57} +(-288872. - 117895. i) q^{58} +(-75569.9 + 207627. i) q^{59} +(-66083.3 - 45253.2i) q^{60} +(-165600. - 138955. i) q^{61} +(-114578. - 356899. i) q^{62} +(5828.34 + 1027.69i) q^{63} +(-75729.2 - 250967. i) q^{64} +(-96800.3 - 167663. i) q^{65} +(-211698. - 8138.08i) q^{66} +(-28802.8 - 79135.0i) q^{67} +(61642.1 - 240029. i) q^{68} +(-227756. + 394485. i) q^{69} +(29218.6 + 18401.0i) q^{70} +(-32265.4 - 38452.4i) q^{71} +(8931.98 - 29953.3i) q^{72} +(116889. + 662910. i) q^{73} +(-344020. - 311955. i) q^{74} +383466. i q^{75} +(-8148.51 + 438900. i) q^{76} +91335.9 q^{77} +(656807. - 724320. i) q^{78} +(-388719. + 68541.7i) q^{79} +(114287. - 142114. i) q^{80} +(-438345. + 367815. i) q^{81} +(53175.2 - 84435.9i) q^{82} +(564813. + 326095. i) q^{83} +(-43378.3 + 168911. i) q^{84} +(162004. - 58964.5i) q^{85} +(-5704.70 + 148398. i) q^{86} +(949351. - 548108. i) q^{87} +(55480.6 - 479180. i) q^{88} +(150198. - 851816. i) q^{89} +(20703.7 - 6646.66i) q^{90} +(-270962. + 322920. i) q^{91} +(-855758. - 586014. i) q^{92} +(1.23757e6 + 450437. i) q^{93} +(40328.3 - 98814.3i) q^{94} +(-255128. + 167838. i) q^{95} +(859819. + 330181. i) q^{96} +(-624554. - 227319. i) q^{97} +(-183031. + 846444. i) q^{98} +(36971.0 - 44060.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9}+O(q^{10}) \) 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9	\( 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9} + 2811 q^{10} - 3 q^{12} - 7572 q^{13} + 8217 q^{14} - 1392 q^{16} - 12 q^{17} - 12 q^{18} + 33618 q^{20} - 33546 q^{21} - 198 q^{22} - 7128 q^{24} - 12 q^{25} + 84453 q^{26} + 13464 q^{28} - 12 q^{29} + 75510 q^{30} + 9339 q^{32} - 366 q^{33} - 289248 q^{34} - 419349 q^{36} - 24 q^{37} + 158040 q^{38} + 264570 q^{40} + 27360 q^{41} + 206001 q^{42} - 525639 q^{44} - 6 q^{45} - 269328 q^{46} - 703179 q^{48} + 2319360 q^{49} + 264534 q^{50} + 130809 q^{52} - 182292 q^{53} + 607083 q^{54} - 705906 q^{56} - 12 q^{57} - 710004 q^{58} + 1060416 q^{60} - 325092 q^{61} - 1967868 q^{62} - 1611921 q^{64} + 398994 q^{65} - 2295684 q^{66} + 1125642 q^{68} - 1625190 q^{69} + 3496059 q^{70} + 4948626 q^{72} - 2224812 q^{73} + 2661159 q^{74} - 968262 q^{76} + 974412 q^{77} - 340743 q^{78} - 3996663 q^{80} + 4277754 q^{81} - 3214221 q^{82} - 872109 q^{84} - 3207900 q^{85} + 3189360 q^{86} + 827973 q^{88} - 2016084 q^{89} - 710406 q^{90} - 2545116 q^{92} + 4486254 q^{93} - 14322630 q^{94} + 2623530 q^{96} - 1223112 q^{97} + 10989009 q^{98}+O(q^{100}) \) 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9 + 2811 * q^10 - 3 * q^12 - 7572 * q^13 + 8217 * q^14 - 1392 * q^16 - 12 * q^17 - 12 * q^18 + 33618 * q^20 - 33546 * q^21 - 198 * q^22 - 7128 * q^24 - 12 * q^25 + 84453 * q^26 + 13464 * q^28 - 12 * q^29 + 75510 * q^30 + 9339 * q^32 - 366 * q^33 - 289248 * q^34 - 419349 * q^36 - 24 * q^37 + 158040 * q^38 + 264570 * q^40 + 27360 * q^41 + 206001 * q^42 - 525639 * q^44 - 6 * q^45 - 269328 * q^46 - 703179 * q^48 + 2319360 * q^49 + 264534 * q^50 + 130809 * q^52 - 182292 * q^53 + 607083 * q^54 - 705906 * q^56 - 12 * q^57 - 710004 * q^58 + 1060416 * q^60 - 325092 * q^61 - 1967868 * q^62 - 1611921 * q^64 + 398994 * q^65 - 2295684 * q^66 + 1125642 * q^68 - 1625190 * q^69 + 3496059 * q^70 + 4948626 * q^72 - 2224812 * q^73 + 2661159 * q^74 - 968262 * q^76 + 974412 * q^77 - 340743 * q^78 - 3996663 * q^80 + 4277754 * q^81 - 3214221 * q^82 - 872109 * q^84 - 3207900 * q^85 + 3189360 * q^86 + 827973 * q^88 - 2016084 * q^89 - 710406 * q^90 - 2545116 * q^92 + 4486254 * q^93 - 14322630 * q^94 + 2623530 * q^96 - 1223112 * q^97 + 10989009 * q^98

Introduction

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