LMFDB - Embedded newform 27.7.f.a.2.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	27.f (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:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$102$
Relative dimension:	$17$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.13
Character	$\chi$	$=$	27.2
Dual form			27.7.f.a.14.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.40620 + 1.30591i) q^{2} +(20.7548 - 17.2696i) q^{3} +(-6.99392 - 2.54558i) q^{4} +(93.4519 + 111.372i) q^{5} +(176.267 - 100.798i) q^{6} +(468.870 - 170.655i) q^{7} +(-465.300 - 268.641i) q^{8} +(132.523 - 716.853i) q^{9} +O(q^{10})$	\(q+(7.40620 + 1.30591i) q^{2} +(20.7548 - 17.2696i) q^{3} +(-6.99392 - 2.54558i) q^{4} +(93.4519 + 111.372i) q^{5} +(176.267 - 100.798i) q^{6} +(468.870 - 170.655i) q^{7} +(-465.300 - 268.641i) q^{8} +(132.523 - 716.853i) q^{9} +(546.682 + 946.881i) q^{10} +(-224.091 + 267.061i) q^{11} +(-189.118 + 67.9491i) q^{12} +(134.825 + 764.633i) q^{13} +(3695.40 - 651.600i) q^{14} +(3862.92 + 697.619i) q^{15} +(-2730.39 - 2291.07i) q^{16} +(-5550.68 + 3204.68i) q^{17} +(1917.64 - 5136.10i) q^{18} +(-1943.92 + 3366.96i) q^{19} +(-370.090 - 1016.81i) q^{20} +(6784.16 - 11639.1i) q^{21} +(-2008.42 + 1685.26i) q^{22} +(-5229.60 + 14368.2i) q^{23} +(-14296.5 + 2459.95i) q^{24} +(-957.130 + 5428.15i) q^{25} +5839.09i q^{26} +(-9629.28 - 17166.8i) q^{27} -3713.65 q^{28} +(-1445.02 - 254.796i) q^{29} +(27698.5 + 10211.3i) q^{30} +(-31916.9 - 11616.8i) q^{31} +(4873.06 + 5807.49i) q^{32} +(-38.9246 + 9412.75i) q^{33} +(-45294.5 + 16485.8i) q^{34} +(62822.9 + 36270.8i) q^{35} +(-2751.66 + 4676.27i) q^{36} +(-45438.5 - 78701.8i) q^{37} +(-18794.0 + 22397.8i) q^{38} +(16003.2 + 13541.4i) q^{39} +(-13564.2 - 76926.2i) q^{40} +(123662. - 21805.0i) q^{41} +(65444.5 - 77341.9i) q^{42} +(103394. + 86758.2i) q^{43} +(2247.10 - 1297.36i) q^{44} +(92221.6 - 52232.0i) q^{45} +(-57495.1 + 99584.5i) q^{46} +(-7944.94 - 21828.6i) q^{47} +(-96234.4 - 397.959i) q^{48} +(100592. - 84406.3i) q^{49} +(-14177.4 + 38952.1i) q^{50} +(-59859.6 + 162370. i) q^{51} +(1003.47 - 5690.99i) q^{52} +92167.3i q^{53} +(-48898.1 - 139715. i) q^{54} -50684.7 q^{55} +(-264010. - 46552.1i) q^{56} +(17800.5 + 103451. i) q^{57} +(-10369.4 - 3774.14i) q^{58} +(-22456.1 - 26762.2i) q^{59} +(-25241.1 - 14712.4i) q^{60} +(-211010. + 76801.5i) q^{61} +(-221213. - 127717. i) q^{62} +(-60198.4 - 358727. i) q^{63} +(142563. + 246927. i) q^{64} +(-72558.7 + 86472.1i) q^{65} +(-12580.5 + 69661.9i) q^{66} +(-1201.29 - 6812.86i) q^{67} +(46978.7 - 8283.62i) q^{68} +(139594. + 388522. i) q^{69} +(417912. + 350670. i) q^{70} +(309301. - 178575. i) q^{71} +(-254239. + 297951. i) q^{72} +(384512. - 665995. i) q^{73} +(-233749. - 642220. i) q^{74} +(73876.9 + 129189. i) q^{75} +(22166.5 - 18599.9i) q^{76} +(-59494.2 + 163459. i) q^{77} +(100839. + 121189. i) q^{78} +(-53075.9 + 301008. i) q^{79} -518192. i q^{80} +(-496316. - 189999. i) q^{81} +944343. q^{82} +(-222841. - 39292.8i) q^{83} +(-77076.1 + 64133.2i) q^{84} +(-875632. - 318704. i) q^{85} +(652461. + 777572. i) q^{86} +(-34391.3 + 19666.7i) q^{87} +(176013. - 64063.5i) q^{88} +(86060.1 + 49686.8i) q^{89} +(751222. - 266407. i) q^{90} +(193704. + 335505. i) q^{91} +(73150.8 - 87177.7i) q^{92} +(-863046. + 310088. i) q^{93} +(-30335.7 - 172042. i) q^{94} +(-556647. + 98151.8i) q^{95} +(201432. + 36377.5i) q^{96} +(-713372. - 598591. i) q^{97} +(855229. - 493766. i) q^{98} +(161746. + 196032. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) $ 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	7.40620	+	1.30591i	0.925775	+	0.163239i	0.616158	−	0.787622i	$-0.288688\pi$
$2$	7.40620	+	1.30591i	0.925775	+	0.163239i	0.309617	+	0.950861i	$0.399799\pi$
$3$	20.7548	−	17.2696i	0.768696	−	0.639614i
$3$	20.7548	−	17.2696i	0.768696	−	0.639614i
$4$	−6.99392	−	2.54558i	−0.109280	−	0.0397747i
$5$	93.4519	+	111.372i	0.747615	+	0.890973i	0.996998	−	0.0774321i	$-0.0246721\pi$
$5$	93.4519	+	111.372i	0.747615	+	0.890973i	−0.249383	+	0.968405i	$0.580228\pi$
$6$	176.267	−	100.798i	0.816050	−	0.466658i
$7$	468.870	−	170.655i	1.36697	−	0.497535i	0.448766	−	0.893649i	$-0.351864\pi$
$7$	468.870	−	170.655i	1.36697	−	0.497535i	0.918201	+	0.396114i	$0.129641\pi$
$8$	−465.300	−	268.641i	−0.908789	−	0.524690i
$9$	132.523	−	716.853i	0.181787	−	0.983338i
$10$	546.682	+	946.881i	0.546682	+	0.946881i
$11$	−224.091	+	267.061i	−0.168363	+	0.200647i	−0.843628	−	0.536928i	$-0.819585\pi$
$11$	−224.091	+	267.061i	−0.168363	+	0.200647i	0.675265	+	0.737575i	$0.264029\pi$
$12$	−189.118	+	67.9491i	−0.109444	+	0.0393224i
$13$	134.825	+	764.633i	0.0613679	+	0.348035i	0.999995	+	0.00310171i	$0.000987307\pi$
$13$	134.825	+	764.633i	0.0613679	+	0.348035i	−0.938627	+	0.344933i	$0.887902\pi$
$14$	3695.40	−	651.600i	1.34672	−	0.237463i
$15$	3862.92	+	697.619i	1.14457	+	0.206702i
$16$	−2730.39	−	2291.07i	−0.666599	−	0.559343i
$17$	−5550.68	+	3204.68i	−1.12979	+	0.652287i	−0.943883	−	0.330280i	$-0.892857\pi$
$17$	−5550.68	+	3204.68i	−1.12979	+	0.652287i	−0.185911	+	0.982567i	$0.559523\pi$
$18$	1917.64	−	5136.10i	0.328813	−	0.880675i
$19$	−1943.92	+	3366.96i	−0.283411	+	0.490882i	−0.972223	−	0.234058i	$-0.924799\pi$
$19$	−1943.92	+	3366.96i	−0.283411	+	0.490882i	0.688812	+	0.724940i	$0.258133\pi$
$20$	−370.090	−	1016.81i	−0.0462612	−	0.127102i
$21$	6784.16	−	11639.1i	0.732552	−	1.25679i
$22$	−2008.42	+	1685.26i	−0.188619	+	0.158271i
$23$	−5229.60	+	14368.2i	−0.429818	+	1.18092i	0.516105	+	0.856526i	$0.327382\pi$
$23$	−5229.60	+	14368.2i	−0.429818	+	1.18092i	−0.945923	+	0.324391i	$0.894841\pi$
$24$	−14296.5	+	2459.95i	−1.03418	+	0.177948i
$25$	−957.130	+	5428.15i	−0.0612563	+	0.347402i
$26$			5839.09i			0.332220i
$27$	−9629.28	−	17166.8i	−0.489218	−	0.872162i
$28$	−3713.65			−0.169171
$29$	−1445.02	−	254.796i	−0.0592489	−	0.0104472i	0.143945	−	0.989586i	$-0.454021\pi$
$29$	−1445.02	−	254.796i	−0.0592489	−	0.0104472i	−0.203194	+	0.979138i	$0.565132\pi$
$30$	27698.5	+	10211.3i	1.02587	+	0.378198i
$31$	−31916.9	−	11616.8i	−1.07136	−	0.389944i	−0.254676	−	0.967027i	$-0.581969\pi$
$31$	−31916.9	−	11616.8i	−1.07136	−	0.389944i	−0.816685	+	0.577083i	$0.804191\pi$
$32$	4873.06	+	5807.49i	0.148714	+	0.177231i
$33$	−38.9246	+	9412.75i	−0.00108313	+	0.261924i
$34$	−45294.5	+	16485.8i	−1.15241	+	0.419444i
$35$	62822.9	+	36270.8i	1.46526	+	0.845966i
$36$	−2751.66	+	4676.27i	−0.0589776	+	0.100229i
$37$	−45438.5	−	78701.8i	−0.897054	−	1.55374i	−0.831242	−	0.555911i	$-0.812369\pi$
$37$	−45438.5	−	78701.8i	−0.897054	−	1.55374i	−0.0658126	−	0.997832i	$-0.520964\pi$
$38$	−18794.0	+	22397.8i	−0.342506	+	0.408183i
$39$	16003.2	+	13541.4i	0.269781	+	0.228281i
$40$	−13564.2	−	76926.2i	−0.211940	−	1.20197i
$41$	123662.	−	21805.0i	1.79426	−	0.316376i	0.825505	−	0.564395i	$-0.190890\pi$
$41$	123662.	−	21805.0i	1.79426	−	0.316376i	0.968755	+	0.248018i	$0.0797794\pi$
$42$	65444.5	−	77341.9i	0.883335	−	1.04392i
$43$	103394.	+	86758.2i	1.30044	+	1.09120i	0.990068	+	0.140587i	$0.0448991\pi$
$43$	103394.	+	86758.2i	1.30044	+	1.09120i	0.310375	+	0.950614i	$0.399545\pi$
$44$	2247.10	−	1297.36i	0.0263793	−	0.0152301i
$45$	92221.6	−	52232.0i	1.01203	−	0.573191i
$46$	−57495.1	+	99584.5i	−0.590687	+	1.02310i
$47$	−7944.94	−	21828.6i	−0.0765239	−	0.210248i	0.895532	−	0.444997i	$-0.146795\pi$
$47$	−7944.94	−	21828.6i	−0.0765239	−	0.210248i	−0.972056	+	0.234749i	$0.924573\pi$
$48$	−96234.4	−	397.959i	−0.870175	−	0.00359844i
$49$	100592.	−	84406.3i	0.855014	−	0.717442i
$50$	−14177.4	+	38952.1i	−0.113419	+	0.311617i
$51$	−59859.6	+	162370.i	−0.451256	+	1.22404i
$52$	1003.47	−	5690.99i	0.00713668	−	0.0404741i
$53$			92167.3i			0.619084i	0.950886	+	0.309542i	$0.100176\pi$
$53$			92167.3i			0.619084i	−0.950886	+	0.309542i	$0.899824\pi$
$54$	−48898.1	−	139715.i	−0.310535	−	0.887285i
$55$	−50684.7			−0.304641
$56$	−264010.	−	46552.1i	−1.50334	−	0.265079i
$57$	17800.5	+	103451.i	0.0961184	+	0.558613i
$58$	−10369.4	−	3774.14i	−0.0531457	−	0.0193435i
$59$	−22456.1	−	26762.2i	−0.109340	−	0.130306i	0.708599	−	0.705612i	$-0.249328\pi$
$59$	−22456.1	−	26762.2i	−0.109340	−	0.130306i	−0.817939	+	0.575305i	$0.804883\pi$
$60$	−25241.1	−	14712.4i	−0.116857	−	0.0681132i
$61$	−211010.	+	76801.5i	−0.929639	+	0.338361i	−0.762067	−	0.647499i	$-0.775815\pi$
$61$	−211010.	+	76801.5i	−0.929639	+	0.338361i	−0.167573	+	0.985860i	$0.553593\pi$
$62$	−221213.	−	127717.i	−0.928185	−	0.535888i
$63$	−60198.4	−	358727.i	−0.240748	−	1.43464i
$64$	142563.	+	246927.i	0.543836	+	0.941952i
$65$	−72558.7	+	86472.1i	−0.264210	+	0.314873i
$66$	−12580.5	+	69661.9i	−0.0437589	+	0.242306i
$67$	−1201.29	−	6812.86i	−0.00399414	−	0.0226519i	0.982746	−	0.184963i	$-0.0592164\pi$
$67$	−1201.29	−	6812.86i	−0.00399414	−	0.0226519i	−0.986740	+	0.162311i	$0.948105\pi$
$68$	46978.7	−	8283.62i	0.149408	−	0.0263447i
$69$	139594.	+	388522.i	0.424931	+	1.18268i
$70$	417912.	+	350670.i	1.21840	+	1.02236i
$71$	309301.	−	178575.i	0.864185	−	0.498937i	−0.00122661	−	0.999999i	$-0.500390\pi$
$71$	309301.	−	178575.i	0.864185	−	0.498937i	0.865411	+	0.501062i	$0.167057\pi$
$72$	−254239.	+	297951.i	−0.681153	+	0.798265i
$73$	384512.	−	665995.i	0.988420	−	1.71199i	0.362797	−	0.931868i	$-0.381822\pi$
$73$	384512.	−	665995.i	0.988420	−	1.71199i	0.625623	−	0.780125i	$-0.284845\pi$
$74$	−233749.	−	642220.i	−0.576839	−	1.58485i
$75$	73876.9	+	129189.i	0.175116	+	0.306227i
$76$	22166.5	−	18599.9i	0.0504958	−	0.0423710i
$77$	−59494.2	+	163459.i	−0.130317	+	0.358044i
$78$	100839.	+	121189.i	0.212492	+	0.255376i
$79$	−53075.9	+	301008.i	−0.107650	+	0.610516i	0.882478	+	0.470353i	$0.155874\pi$
$79$	−53075.9	+	301008.i	−0.107650	+	0.610516i	−0.990129	+	0.140162i	$0.955238\pi$
$80$		−	518192.i		−	1.01209i
$81$	−496316.	−	189999.i	−0.933907	−	0.357516i
$82$	944343.			1.71273
$83$	−222841.	−	39292.8i	−0.389727	−	0.0687194i	−0.0246485	−	0.999696i	$-0.507847\pi$
$83$	−222841.	−	39292.8i	−0.389727	−	0.0687194i	−0.365078	+	0.930977i	$0.618958\pi$
$84$	−77076.1	+	64133.2i	−0.130041	+	0.108204i
$85$	−875632.	−	318704.i	−1.42582	−	0.518956i
$86$	652461.	+	777572.i	1.02579	+	1.22249i
$87$	−34391.3	+	19666.7i	−0.0522265	+	0.0298657i
$88$	176013.	−	64063.5i	0.258284	−	0.0940075i
$89$	86060.1	+	49686.8i	0.122076	+	0.0704809i	0.559795	−	0.828631i	$-0.310880\pi$
$89$	86060.1	+	49686.8i	0.122076	+	0.0704809i	−0.437718	+	0.899112i	$0.644213\pi$
$90$	751222.	−	266407.i	1.03048	−	0.365442i
$91$	193704.	+	335505.i	0.257048	+	0.445220i
$92$	73150.8	−	87177.7i	0.0939411	−	0.111955i
$93$	−863046.	+	310088.i	−1.07296	+	0.385510i
$94$	−30335.7	−	172042.i	−0.0365233	−	0.207134i
$95$	−556647.	+	98151.8i	−0.649245	+	0.114479i
$96$	201432.	+	36377.5i	0.227675	+	0.0411168i
$97$	−713372.	−	598591.i	−0.781630	−	0.655865i	0.162029	−	0.986786i	$-0.448196\pi$
$97$	−713372.	−	598591.i	−0.781630	−	0.655865i	−0.943659	+	0.330921i	$0.892641\pi$
$98$	855229.	−	493766.i	0.908665	−	0.524618i
$99$	161746.	+	196032.i	0.166698	+	0.202032i
$100$	20511.9	−	35527.6i	0.0205119	−	0.0355276i
$101$	247654.	+	680425.i	0.240371	+	0.660414i	0.999950	+	0.00999887i	$0.00318279\pi$
$101$	247654.	+	680425.i	0.240371	+	0.660414i	−0.759579	+	0.650415i	$0.774595\pi$
$102$	−655374.	+	1.12438e6i	−0.617573	+	1.05953i
$103$	652512.	−	547522.i	0.597141	−	0.501060i	−0.293385	−	0.955995i	$-0.594782\pi$
$103$	652512.	−	547522.i	0.597141	−	0.501060i	0.890525	+	0.454934i	$0.150337\pi$
$104$	142677.	−	392003.i	0.126840	−	0.348489i
$105$	1.93026e6	−	332132.i	1.66743	−	0.286908i
$106$	−120362.	+	682610.i	−0.101059	+	0.573132i
$107$		−	1.18265e6i		−	0.965396i	−0.875787	−	0.482698i	$-0.839657\pi$
$107$		−	1.18265e6i		−	0.965396i	0.875787	−	0.482698i	$-0.160343\pi$
$108$	23647.1	+	144575.i	0.0187718	+	0.114768i
$109$	−73802.6			−0.0569891			−0.0284946	−	0.999594i	$-0.509071\pi$
$109$	−73802.6			−0.0569891			−0.0284946	+	0.999594i	$0.509071\pi$
$110$	−375381.	−	66189.9i	−0.282030	−	0.0497294i
$111$	−2.30221e6	−	848735.i	−1.68336	−	0.620588i
$112$	−1.67118e6	−	608259.i	−1.18951	−	0.432947i
$113$	814945.	+	971214.i	0.564798	+	0.673100i	0.970555	−	0.240881i	$-0.0774364\pi$
$113$	814945.	+	971214.i	0.564798	+	0.673100i	−0.405757	+	0.913981i	$0.632992\pi$
$114$	−3264.52	+	789427.i	−0.00220346	+	0.532840i
$115$	−2.08893e6	+	760307.i	−1.37350	+	0.499914i
$116$	9457.75	+	5460.44i	0.00605918	+	0.00349827i
$117$	565997.	+	4681.22i	0.353392	+	0.00292282i
$118$	−131366.	−	227532.i	−0.0799531	−	0.138483i
$119$	−2.05565e6	+	2.44983e6i	−1.21986	+	1.45377i
$120$	−1.61001e6	−	1.36234e6i	−0.931716	−	0.788391i
$121$	286523.	+	1.62496e6i	0.161735	+	0.917245i
$122$	−1.66308e6	+	293246.i	−0.915871	+	0.161493i
$123$	2.19002e6	−	2.58815e6i	1.17688	−	1.39083i
$124$	193653.	+	162494.i	0.101568	+	0.0852260i
$125$	1.27331e6	−	735149.i	0.651937	−	0.376396i
$126$	22623.9	−	2.73541e6i	0.0113098	−	1.36745i
$127$	615839.	−	1.06666e6i	0.300646	−	0.520735i	−0.675636	−	0.737235i	$-0.736131\pi$
$127$	615839.	−	1.06666e6i	0.300646	−	0.520735i	0.976283	+	0.216500i	$0.0694643\pi$
$128$	567442.	+	1.55903e6i	0.270577	+	0.743405i
$129$	3.64421e6	+	15069.9i	1.69759	+	0.00702007i
$130$	−650309.	+	545674.i	−0.295999	+	0.248372i
$131$	−1.28721e6	+	3.53658e6i	−0.572580	+	1.57315i	0.227832	+	0.973700i	$0.426836\pi$
$131$	−1.28721e6	+	3.53658e6i	−0.572580	+	1.57315i	−0.800412	+	0.599450i	$0.795386\pi$
$132$	24233.1	−	65732.9i	0.0105363	−	0.0285799i
$133$	−336856.	+	1.91041e6i	−0.143182	+	0.812027i
$134$		−	52026.2i		−	0.0216226i
$135$	1.01202e6	−	2.67669e6i	0.411326	−	1.08792i
$136$	3.44364e6			1.36899
$137$	−155845.	−	27479.7i	−0.0606082	−	0.0106869i	0.143262	−	0.989685i	$-0.454241\pi$
$137$	−155845.	−	27479.7i	−0.0606082	−	0.0106869i	−0.203870	+	0.978998i	$0.565352\pi$
$138$	526483.	+	3.05977e6i	0.200331	+	1.16426i
$139$	−3.24166e6	−	1.17987e6i	−1.20704	−	0.439328i	−0.341367	−	0.939930i	$-0.610890\pi$
$139$	−3.24166e6	−	1.17987e6i	−1.20704	−	0.439328i	−0.865678	+	0.500602i	$0.833112\pi$
$140$	−347048.	−	413595.i	−0.126475	−	0.150727i
$141$	−541866.	−	315841.i	−0.193301	−	0.112671i
$142$	2.52395e6	−	918643.i	0.881487	−	0.320835i
$143$	−234417.	−	135341.i	−0.0801642	−	0.0462828i
$144$	−2.00420e6	+	1.65367e6i	−0.671202	+	0.553810i
$145$	−106663.	−	184745.i	−0.0349872	−	0.0605996i
$146$	3.71751e6	−	4.43035e6i	1.19452	−	1.42357i
$147$	630094.	−	3.48901e6i	0.198360	−	1.09837i
$148$	117452.	+	666101.i	0.0362304	+	0.205473i
$149$	5.33368e6	−	940471.i	1.61238	−	0.284306i	0.706460	−	0.707753i	$-0.250291\pi$
$149$	5.33368e6	−	940471.i	1.61238	−	0.284306i	0.905921	+	0.423446i	$0.139180\pi$
$150$	378437.	+	1.05328e6i	0.112130	+	0.312083i
$151$	−2.87080e6	−	2.40888e6i	−0.833818	−	0.699656i	0.122346	−	0.992488i	$-0.460958\pi$
$151$	−2.87080e6	−	2.40888e6i	−0.833818	−	0.699656i	−0.956164	+	0.292831i	$0.905403\pi$
$152$	1.80901e6	−	1.04443e6i	0.515122	−	0.297406i
$153$	1.56170e6	+	4.40371e6i	0.436036	+	1.22955i
$154$	−654089.	+	1.13292e6i	−0.179091	+	0.310196i
$155$	−1.68891e6	−	4.64025e6i	−0.453537	−	1.24608i
$156$	−77454.1	−	135445.i	−0.0204019	−	0.0356770i
$157$	2.50682e6	−	2.10347e6i	0.647776	−	0.543548i	−0.258619	−	0.965979i	$-0.583268\pi$
$157$	2.50682e6	−	2.10347e6i	0.647776	−	0.543548i	0.906395	+	0.422431i	$0.138823\pi$
$158$	−786181.	+	2.16001e6i	−0.199320	+	0.547628i
$159$	1.59169e6	+	1.91291e6i	0.395975	+	0.475887i
$160$	−191393.	+	1.08544e6i	−0.0467267	+	0.265001i
$161$			7.62928e6i			1.82812i
$162$	−3.42770e6	−	2.05532e6i	−0.806227	−	0.483430i
$163$	−2.41459e6			−0.557546			−0.278773	−	0.960357i	$-0.589928\pi$
$163$	−2.41459e6			−0.557546			−0.278773	+	0.960357i	$0.589928\pi$
$164$	−920390.	−	162290.i	−0.208660	−	0.0367925i
$165$	−1.05195e6	+	875304.i	−0.234177	+	0.194853i
$166$	−1.59909e6	−	582021.i	−0.349582	−	0.127237i
$167$	−1.35342e6	−	1.61294e6i	−0.290592	−	0.346314i	0.600922	−	0.799308i	$-0.294800\pi$
$167$	−1.35342e6	−	1.61294e6i	−0.290592	−	0.346314i	−0.891514	+	0.452994i	$0.850356\pi$
$168$	−6.28341e6	+	3.59316e6i	−1.32516	+	0.757791i
$169$	3.96923e6	−	1.44468e6i	0.822330	−	0.299304i
$170$	−6.06891e6	−	3.50389e6i	−1.23528	−	0.713187i
$171$	2.15600e6	+	1.83970e6i	0.431183	+	0.367925i
$172$	−502282.	−	869978.i	−0.0987103	−	0.170971i
$173$	−2.84771e6	+	3.39377e6i	−0.549994	+	0.655457i	−0.967397	−	0.253264i	$-0.918496\pi$
$173$	−2.84771e6	+	3.39377e6i	−0.549994	+	0.655457i	0.417403	+	0.908721i	$0.362940\pi$
$174$	−280392.	+	100743.i	−0.0532253	+	0.0191235i
$175$	477570.	+	2.70844e6i	0.0891094	+	0.505364i
$176$	1.22371e6	−	215773.i	0.224461	−	0.0395785i
$177$	−928244.	−	167635.i	−0.167395	−	0.0302305i
$178$	572492.	+	480378.i	0.101510	+	0.0851771i
$179$	−907387.	+	523880.i	−0.158210	+	0.0913425i	−0.577015	−	0.816734i	$-0.695782\pi$
$179$	−907387.	+	523880.i	−0.158210	+	0.0913425i	0.418805	+	0.908076i	$0.362449\pi$
$180$	−777951.	+	130549.i	−0.133394	+	0.0223850i
$181$	−2.36930e6	+	4.10375e6i	−0.399563	+	0.692063i	−0.993672	−	0.112321i	$-0.964171\pi$
$181$	−2.36930e6	+	4.10375e6i	−0.399563	+	0.692063i	0.594109	+	0.804384i	$0.297505\pi$
$182$	996468.	+	2.73777e6i	0.165291	+	0.454133i
$183$	−3.05315e6	+	5.23806e6i	−0.498190	+	0.854708i
$184$	6.29322e6	−	5.28064e6i	1.01023	−	0.847683i
$185$	4.51883e6	−	1.24154e7i	0.713692	−	1.96085i
$186$	−6.79684e6	+	1.16951e6i	−1.05625	+	0.181746i
$187$	388009.	−	2.20051e6i	0.0593359	−	0.336510i
$188$			172892.i			0.0260196i
$189$	−7.44446e6	−	6.40569e6i	−1.10268	−	0.948813i
$190$	−4.25082e6			−0.619743
$191$	620235.	+	109364.i	0.0890136	+	0.0156955i	0.217978	−	0.975954i	$-0.430054\pi$
$191$	620235.	+	109364.i	0.0890136	+	0.0156955i	−0.128964	+	0.991649i	$0.541165\pi$
$192$	7.22320e6	+	2.66291e6i	1.02053	+	0.376229i
$193$	8.25190e6	+	3.00345e6i	1.14784	+	0.417780i	0.844740	−	0.535177i	$-0.179755\pi$
$193$	8.25190e6	+	3.00345e6i	1.14784	+	0.417780i	0.303103	+	0.952958i	$0.401977\pi$
$194$	−4.50167e6	−	5.36488e6i	−0.616551	−	0.734776i
$195$	−12603.5	+	3.04777e6i	−0.00169975	+	0.411034i
$196$	−918392.	+	334267.i	−0.121972	+	0.0443941i
$197$	−4.60178e6	−	2.65684e6i	−0.601904	−	0.347510i	0.167886	−	0.985806i	$-0.446306\pi$
$197$	−4.60178e6	−	2.65684e6i	−0.601904	−	0.347510i	−0.769790	+	0.638297i	$0.779639\pi$
$198$	941926.	+	1.66308e6i	0.121345	+	0.214248i
$199$	−1.07663e6	−	1.86477e6i	−0.136617	−	0.236628i	0.789597	−	0.613626i	$-0.210290\pi$
$199$	−1.07663e6	−	1.86477e6i	−0.136617	−	0.236628i	−0.926214	+	0.376998i	$0.876956\pi$
$200$	1.90358e6	−	2.26860e6i	0.237947	−	0.283574i
$201$	−142588.	−	120654.i	−0.0175588	−	0.0148577i
$202$	945603.	+	5.36278e6i	0.114724	+	0.650633i
$203$	−721009.	+	127133.i	−0.0861891	+	0.0151975i
$204$	831979.	−	983228.i	0.0979991	−	0.115815i
$205$	1.39849e7	+	1.17347e7i	1.62330	+	1.36211i
$206$	5.54765e6	−	3.20294e6i	0.634611	−	0.366393i
$207$	9.60686e6	+	5.65297e6i	1.08310	+	0.637332i
$208$	1.38370e6	−	2.39664e6i	0.153763	−	0.266325i
$209$	−463571.	−	1.27365e6i	−0.0507782	−	0.139512i
$210$	1.47296e7	+	60911.4i	1.59050	+	0.00657720i
$211$	9.37320e6	−	7.86505e6i	0.997793	−	0.837248i	0.0111160	−	0.999938i	$-0.496462\pi$
$211$	9.37320e6	−	7.86505e6i	0.997793	−	0.837248i	0.986677	+	0.162690i	$0.0520172\pi$
$212$	234619.	−	644611.i	0.0246238	−	0.0676534i
$213$	3.33556e6	−	9.04780e6i	0.345168	−	0.936276i
$214$	1.54444e6	−	8.75895e6i	0.157590	−	0.893740i
$215$			1.96229e7i			1.97446i
$216$	−131193.	+	1.05745e7i	−0.0130181	+	1.04930i
$217$	−1.69473e7			−1.65853
$218$	−546597.	−	96379.8i	−0.0527591	−	0.00930286i
$219$	−3.52098e6	−	2.04629e7i	−0.335221	−	1.94821i
$220$	354485.	+	129022.i	0.0332912	+	0.0121170i
$221$	−3.19878e6	−	3.81216e6i	−0.296352	−	0.353178i
$222$	−1.59423e7	−	9.29239e6i	−1.45711	−	0.849315i
$223$	−9.19176e6	+	3.34553e6i	−0.828865	+	0.301682i	−0.721393	−	0.692526i	$-0.756498\pi$
$223$	−9.19176e6	+	3.34553e6i	−0.828865	+	0.301682i	−0.107472	+	0.994208i	$0.534276\pi$
$224$	3.27591e6	+	1.89135e6i	0.291466	+	0.168278i
$225$	3.76435e6	+	1.40548e6i	0.330478	+	0.123389i
$226$	4.76733e6	+	8.25725e6i	0.413000	+	0.715336i
$227$	3.85892e6	−	4.59888e6i	0.329904	−	0.393165i	−0.575439	−	0.817845i	$-0.695169\pi$
$227$	3.85892e6	−	4.59888e6i	0.329904	−	0.393165i	0.905344	+	0.424680i	$0.139613\pi$
$228$	138848.	−	768842.i	0.0117148	−	0.0648683i
$229$	1.33245e6	+	7.55667e6i	0.110954	+	0.629251i	0.988674	+	0.150078i	$0.0479524\pi$
$229$	1.33245e6	+	7.55667e6i	0.110954	+	0.629251i	−0.877720	+	0.479174i	$0.840936\pi$
$230$	−1.64639e7	+	2.90303e6i	−1.35316	+	0.238599i
$231$	1.58808e6	+	4.42000e6i	0.128836	+	0.358580i
$232$	603919.	+	506748.i	0.0483632	+	0.0405815i
$233$	−8.15029e6	+	4.70557e6i	−0.644326	+	0.372002i	−0.786279	−	0.617872i	$-0.787995\pi$
$233$	−8.15029e6	+	4.70557e6i	−0.644326	+	0.372002i	0.141953	+	0.989873i	$0.454662\pi$
$234$	4.18577e6	+	773813.i	0.326684	+	0.0603932i
$235$	1.68861e6	−	2.92476e6i	0.130115	−	0.225365i
$236$	88931.2	+	244336.i	0.00676578	+	0.0185888i
$237$	4.09671e6	+	7.16396e6i	0.307744	+	0.538156i
$238$	−1.84238e7	+	1.54594e7i	−1.36662	+	1.14673i
$239$	3.04185e6	−	8.35741e6i	0.222815	−	0.612178i	−0.777036	−	0.629456i	$-0.783278\pi$
$239$	3.04185e6	−	8.35741e6i	0.222815	−	0.612178i	0.999851	+	0.0172777i	$0.00549994\pi$
$240$	−8.94897e6	−	1.07550e7i	−0.647350	−	0.777993i
$241$	3.68622e6	−	2.09056e7i	0.263348	−	1.49352i	−0.510350	−	0.859967i	$-0.670484\pi$
$241$	3.68622e6	−	2.09056e7i	0.263348	−	1.49352i	0.773698	−	0.633555i	$-0.218405\pi$
$242$			1.24089e7i			0.875564i
$243$	−1.35821e7	+	4.62779e6i	−0.946563	+	0.322519i
$244$	1.67129e6			0.115049
$245$	1.88009e7	+	3.31511e6i	1.27844	+	0.225424i
$246$	1.95996e7	−	1.63084e7i	1.31657	−	1.09548i
$247$	−2.83658e6	−	1.03243e6i	−0.188237	−	0.0685125i
$248$	1.17302e7	+	1.39795e7i	0.769042	+	0.916508i
$249$	−5.30358e6	+	3.03285e6i	−0.343535	+	0.196451i
$250$	1.03905e7	−	3.78182e6i	0.664990	−	0.242037i
$251$	−1.36443e7	−	7.87754e6i	−0.862840	−	0.498161i	0.00212263	−	0.999998i	$-0.499324\pi$
$251$	−1.36443e7	−	7.87754e6i	−0.862840	−	0.498161i	−0.864962	+	0.501837i	$0.832658\pi$
$252$	−492143.	+	2.66214e6i	−0.0307532	+	0.166353i
$253$	−2.66528e6	−	4.61641e6i	−0.164582	−	0.285064i
$254$	5.95400e6	−	7.09570e6i	0.363335	−	0.433006i
$255$	−2.36774e7	+	8.50717e6i	−1.42795	+	0.513056i
$256$	−1.00212e6	−	5.68333e6i	−0.0597313	−	0.338753i
$257$	6.88891e6	−	1.21470e6i	0.405836	−	0.0715599i	0.0329962	−	0.999455i	$-0.489495\pi$
$257$	6.88891e6	−	1.21470e6i	0.405836	−	0.0715599i	0.372840	+	0.927896i	$0.378384\pi$
$258$	2.69700e7	+	4.87063e6i	1.57044	+	0.283613i
$259$	−3.47356e7	−	2.91466e7i	−1.99929	−	1.67760i
$260$	727591.	−	420075.i	0.0413968	−	0.0239005i
$261$	−374150.	+	1.00210e6i	−0.0210438	+	0.0563625i
$262$	−1.41518e7	+	2.45117e7i	−0.786880	+	1.36292i
$263$	9.05082e6	+	2.48669e7i	0.497531	+	1.36696i	0.893653	+	0.448758i	$0.148134\pi$
$263$	9.05082e6	+	2.48669e7i	0.497531	+	1.36696i	−0.396122	+	0.918198i	$0.629644\pi$
$264$	2.54676e6	−	4.36930e6i	0.138413	−	0.237465i
$265$	−1.02648e7	+	8.61321e6i	−0.551587	+	0.462836i
$266$	−4.98965e6	+	1.37089e7i	−0.265109	+	0.728382i
$267$	2.64423e6	−	454983.i	0.138920	−	0.0239035i
$268$	−8940.93	+	50706.5i	−0.000464492	+	0.00263427i
$269$		−	2.07069e6i		−	0.106379i	−0.998584	−	0.0531897i	$-0.983061\pi$
$269$		−	2.07069e6i		−	0.106379i	0.998584	−	0.0531897i	$-0.0169388\pi$
$270$	1.09907e7	−	1.85025e7i	0.558386	−	0.940026i
$271$	387902.			0.0194901			0.00974504	−	0.999953i	$-0.496898\pi$
$271$	387902.			0.0194901			0.00974504	+	0.999953i	$0.496898\pi$
$272$	2.24976e7	+	3.96694e6i	1.11797	+	0.197128i
$273$	9.81430e6	+	3.61815e6i	0.482360	+	0.177827i
$274$	−1.11833e6	−	407040.i	−0.0543651	−	0.0197873i
$275$	−1.23516e6	−	1.47201e6i	−0.0593918	−	0.0707804i
$276$	12706.3	−	3.07264e6i	0.000604355	−	0.146145i
$277$	−1.24346e7	+	4.52581e6i	−0.585048	+	0.212940i	−0.617550	−	0.786532i	$-0.711875\pi$
$277$	−1.24346e7	+	4.52581e6i	−0.585048	+	0.212940i	0.0325022	+	0.999472i	$0.489652\pi$
$278$	−2.24676e7	−	1.29717e7i	−1.04574	−	0.603756i
$279$	−1.25573e7	+	2.13403e7i	−0.578206	+	0.982623i
$280$	−1.94876e7	−	3.37536e7i	−0.887739	−	1.53761i
$281$	−1.15069e7	+	1.37134e7i	−0.518609	+	0.618055i	−0.960251	−	0.279137i	$-0.909952\pi$
$281$	−1.15069e7	+	1.37134e7i	−0.518609	+	0.618055i	0.441642	+	0.897191i	$0.354396\pi$
$282$	−3.60071e6	−	3.04681e6i	−0.160561	−	0.135862i
$283$	3.00492e6	+	1.70417e7i	0.132579	+	0.751891i	0.976515	+	0.215448i	$0.0691212\pi$
$283$	3.00492e6	+	1.70417e7i	0.132579	+	0.751891i	−0.843937	+	0.536443i	$0.819768\pi$
$284$	−2.61780e6	+	461590.i	−0.114283	+	0.0201512i
$285$	−9.85804e6	+	1.16502e7i	−0.425850	+	0.503266i
$286$	−1.55939e6	−	1.30849e6i	−0.0666589	−	0.0559334i
$287$	5.42604e7	−	3.13272e7i	2.29529	−	1.32518i
$288$	4.80891e6	−	2.72365e6i	0.201312	−	0.114018i
$289$	8.47122e6	−	1.46726e7i	0.350956	−	0.607873i
$290$	−548705.	−	1.50755e6i	−0.0224981	−	0.0618129i
$291$	−2.51433e7	−	103975.i	−1.02034	−	0.00421940i
$292$	−4.38459e6	+	3.67911e6i	−0.176108	+	0.147773i
$293$	6.41469e6	−	1.76242e7i	0.255019	−	0.700660i	−0.744437	−	0.667692i	$-0.767282\pi$
$293$	6.41469e6	−	1.76242e7i	0.255019	−	0.700660i	0.999456	−	0.0329671i	$-0.0104956\pi$
$294$	9.22295e6	−	2.50175e7i	0.362934	−	0.984467i
$295$	881979.	−	5.00195e6i	0.0343552	−	0.194838i
$296$			4.88266e7i			1.88270i
$297$	6.74240e6	+	1.27531e6i	0.257363	+	0.0486794i
$298$	4.07304e7			1.53911
$299$	−1.16915e7	−	2.06152e6i	−0.437377	−	0.0771214i
$300$	−187827.	−	1.09160e6i	−0.00695657	−	0.0404296i
$301$	6.32842e7	+	2.30336e7i	2.32058	+	0.844620i
$302$	−1.81159e7	−	2.15897e7i	−0.657717	−	0.783836i
$303$	1.68907e7	+	9.84519e6i	0.607182	+	0.353913i
$304$	1.30216e7	−	4.73947e6i	0.463493	−	0.168698i
$305$	−2.82728e7	−	1.63233e7i	−0.996483	−	0.575320i
$306$	5.81538e6	+	3.46542e7i	0.202962	+	1.20946i
$307$	2.63315e7	+	4.56075e7i	0.910040	+	1.57624i	0.814005	+	0.580857i	$0.197283\pi$
$307$	2.63315e7	+	4.56075e7i	0.910040	+	1.57624i	0.0960344	+	0.995378i	$0.469384\pi$
$308$	832195.	−	991772.i	0.0284822	−	0.0339437i
$309$	4.08726e6	−	2.26323e7i	0.138534	−	0.767103i
$310$	−6.44867e6	−	3.65722e7i	−0.216464	−	1.22763i
$311$	−2.62379e7	+	4.62644e6i	−0.872263	+	0.153803i	−0.591823	−	0.806068i	$-0.701591\pi$
$311$	−2.62379e7	+	4.62644e6i	−0.872263	+	0.153803i	−0.280440	+	0.959872i	$0.590480\pi$
$312$	−3.80849e6	−	1.05999e7i	−0.125398	−	0.349011i
$313$	2.52090e7	+	2.11529e7i	0.822096	+	0.689821i	0.953462	−	0.301513i	$-0.0974918\pi$
$313$	2.52090e7	+	2.11529e7i	0.822096	+	0.689821i	−0.131366	+	0.991334i	$0.541936\pi$
$314$	2.13130e7	−	1.23051e7i	0.688423	−	0.397461i
$315$	3.43263e7	−	4.02281e7i	1.09824	−	1.28706i
$316$	1.13745e6	−	1.97012e6i	0.0360471	−	0.0624354i
$317$	−3.45348e6	−	9.48835e6i	−0.108412	−	0.297860i	0.873610	−	0.486628i	$-0.161773\pi$
$317$	−3.45348e6	−	9.48835e6i	−0.108412	−	0.297860i	−0.982022	+	0.188767i	$0.939551\pi$
$318$	9.29029e6	+	1.62460e7i	0.288900	+	0.505203i
$319$	391862.	−	328811.i	0.0120715	−	0.0101292i
$320$	−1.41778e7	+	3.89533e7i	−0.432674	+	1.18876i
$321$	−2.04239e7	−	2.45457e7i	−0.617481	−	0.742096i
$322$	−9.96317e6	+	5.65040e7i	−0.298421	+	1.69243i
$323$		−	2.49186e7i		−	0.739461i
$324$	2.98754e6	+	2.59225e6i	0.0878372	+	0.0762152i
$325$	−4.27959e6			−0.124667
$326$	−1.78829e7	−	3.15325e6i	−0.516162	−	0.0910133i
$327$	−1.53176e6	+	1.27454e6i	−0.0438073	+	0.0364511i
$328$	−6.33977e7	−	2.30749e7i	−1.79660	−	0.653910i
$329$	−7.45029e6	−	8.87891e6i	−0.209211	−	0.249329i
$330$	−8.93403e6	+	5.10892e6i	−0.248603	+	0.142163i
$331$	2.27743e7	−	8.28916e6i	0.628001	−	0.228574i	−0.00835975	−	0.999965i	$-0.502661\pi$
$331$	2.27743e7	−	8.28916e6i	0.628001	−	0.228574i	0.636361	+	0.771391i	$0.280439\pi$
$332$	1.45851e6	+	842069.i	0.0398560	+	0.0230109i
$333$	−6.24393e7	+	2.21430e7i	−1.69093	+	0.599657i
$334$	−7.91734e6	−	1.37132e7i	−0.212491	−	0.368045i
$335$	646496.	−	770464.i	0.0171962	−	0.0204936i
$336$	−4.51893e7	+	1.62363e7i	−1.19129	+	0.428024i
$337$	−8.00076e6	−	4.53746e7i	−0.209046	−	1.18556i	−0.890945	−	0.454112i	$-0.849957\pi$
$337$	−8.00076e6	−	4.53746e7i	−0.209046	−	1.18556i	0.681899	−	0.731447i	$-0.261154\pi$
$338$	3.12836e7	−	5.51614e6i	0.810151	−	0.142852i
$339$	3.36865e7	+	6.08358e6i	0.864682	+	0.156156i
$340$	5.31281e6	+	4.45798e6i	0.135172	+	0.113423i
$341$	1.02547e7	−	5.92055e6i	0.258618	−	0.149313i
$342$	1.35653e7	+	1.64408e7i	0.339119	+	0.411002i
$343$	3.40888e6	−	5.90436e6i	0.0844753	−	0.146316i
$344$	−2.48026e7	−	6.81445e7i	−0.609287	−	1.67400i
$345$	−3.02251e7	+	5.18549e7i	−0.736054	+	1.26279i
$346$	−2.55227e7	+	2.14161e7i	−0.616167	+	0.517025i
$347$	−8.46370e6	+	2.32538e7i	−0.202568	+	0.556552i	−0.998828	−	0.0484031i	$-0.984587\pi$
$347$	−8.46370e6	+	2.32538e7i	−0.202568	+	0.556552i	0.796259	+	0.604955i	$0.206809\pi$
$348$	290593.	−	50001.3i	0.00689521	−	0.00118643i
$349$	−5.33348e6	+	3.02476e7i	−0.125468	+	0.711566i	0.855560	+	0.517703i	$0.173213\pi$
$349$	−5.33348e6	+	3.02476e7i	−0.125468	+	0.711566i	−0.981029	+	0.193863i	$0.937898\pi$
$350$			2.06829e7i			0.482400i
$351$	1.18280e7	−	9.67737e6i	0.273520	−	0.223788i
$352$	−2.64296e6			−0.0605987
$353$	−7.67559e7	−	1.35341e7i	−1.74497	−	0.307685i	−0.791947	−	0.610589i	$-0.790933\pi$
$353$	−7.67559e7	−	1.35341e7i	−1.74497	−	0.307685i	−0.953021	+	0.302904i	$0.902044\pi$
$354$	−6.65585e6	−	2.45375e6i	−0.150035	−	0.0553121i
$355$	4.87930e7	+	1.77592e7i	1.09062	+	0.396952i
$356$	−475416.	−	566578.i	−0.0105372	−	0.0125577i
$357$	−357067.	+	8.63459e7i	−0.00784774	+	1.89774i
$358$	−7.40444e6	+	2.69499e6i	−0.161377	+	0.0587366i
$359$	−5.88565e7	−	3.39808e7i	−1.27207	−	0.734430i	−0.296693	−	0.954973i	$-0.595884\pi$
$359$	−5.88565e7	−	3.39808e7i	−1.27207	−	0.734430i	−0.975377	+	0.220543i	$0.929217\pi$
$360$	−5.69424e7	−	470956.i	−1.22047	−	0.0100942i
$361$	1.59653e7	+	2.76527e7i	0.339356	+	0.587782i
$362$	−2.29067e7	+	2.72991e7i	−0.482877	+	0.575471i
$363$	3.40090e7	+	2.87775e7i	0.711008	+	0.601634i
$364$	−500694.	−	2.83958e6i	−0.0103817	−	0.0588776i
$365$	1.10106e8	−	1.94147e7i	2.26430	−	0.399257i
$366$	−2.94527e7	+	3.48070e7i	−0.600733	+	0.709943i
$367$	4.51765e6	+	3.79076e6i	0.0913933	+	0.0766881i	0.687340	−	0.726336i	$-0.258778\pi$
$367$	4.51765e6	+	3.79076e6i	0.0913933	+	0.0766881i	−0.595946	+	0.803024i	$0.703223\pi$
$368$	4.71974e7	−	2.72494e7i	0.947053	−	0.546781i
$369$	757083.	−	9.15373e7i	0.0150683	−	1.82188i
$370$	4.96808e7	−	8.60496e7i	0.980806	−	1.69881i
$371$	1.57288e7	+	4.32145e7i	0.308016	+	0.846267i
$372$	6.82543e6	+	28225.2i	0.132587	+	0.000548288i
$373$	1.57238e7	−	1.31939e7i	0.302993	−	0.254241i	−0.478596	−	0.878035i	$-0.658854\pi$
$373$	1.57238e7	−	1.31939e7i	0.302993	−	0.254241i	0.781589	+	0.623794i	$0.214410\pi$
$374$	5.74735e6	−	1.57907e7i	0.109863	−	0.301847i
$375$	1.37317e7	−	3.72475e7i	0.260393	−	0.706323i
$376$	−2.16726e6	+	1.22912e7i	−0.0407707	+	0.231222i
$377$		−	1.13926e6i		−	0.0212618i
$378$	−4.67699e7	−	5.71637e7i	−0.865947	−	1.05839i
$379$	5.78283e6			0.106224			0.0531120	−	0.998589i	$-0.483086\pi$
$379$	5.78283e6			0.106224			0.0531120	+	0.998589i	$0.483086\pi$
$380$	4.14299e6	+	730522.i	0.0755029	+	0.0133132i
$381$	−5.63924e6	−	3.27737e7i	−0.101964	−	0.592584i
$382$	4.45077e6	+	1.61995e6i	0.0798445	+	0.0290610i
$383$	4.90584e7	+	5.84656e7i	0.873207	+	1.04065i	0.998820	+	0.0485686i	$0.0154660\pi$
$383$	4.90584e7	+	5.84656e7i	0.873207	+	1.04065i	−0.125612	+	0.992079i	$0.540090\pi$
$384$	3.87010e7	+	2.25579e7i	0.683485	+	0.398388i
$385$	−2.37645e7	+	8.64959e6i	−0.416435	+	0.151570i
$386$	5.71930e7	+	3.30204e7i	0.994446	+	0.574144i
$387$	7.58950e7	−	6.26212e7i	1.30942	−	1.08041i
$388$	3.46551e6	+	6.00244e6i	0.0593297	+	0.102762i
$389$	3.04941e7	−	3.63415e7i	0.518044	−	0.617381i	−0.442073	−	0.896979i	$-0.645757\pi$
$389$	3.04941e7	−	3.63415e7i	0.518044	−	0.617381i	0.960117	+	0.279598i	$0.0902011\pi$
$390$	−4.07346e6	+	2.25559e7i	−0.0686705	+	0.380248i
$391$	−1.70178e7	−	9.65125e7i	−0.284690	−	1.61456i
$392$	−6.94802e7	+	1.22512e7i	−1.15346	+	0.203386i
$393$	3.43595e7	+	9.56307e7i	0.566070	+	1.57550i
$394$	−3.06121e7	−	2.56866e7i	−0.500501	−	0.419970i
$395$	−3.84838e7	+	2.22186e7i	−0.624434	+	0.360517i
$396$	−632227.	−	1.78277e6i	−0.0101809	−	0.0287084i
$397$	−5.27862e7	+	9.14284e7i	−0.843624	+	1.46120i	0.0431860	+	0.999067i	$0.486249\pi$
$397$	−5.27862e7	+	9.14284e7i	−0.843624	+	1.46120i	−0.886810	+	0.462133i	$0.847084\pi$
$398$	−5.53848e6	−	1.52168e7i	−0.0878499	−	0.241366i
$399$	2.60005e7	+	4.54674e7i	0.409321	+	0.715784i
$400$	1.50496e7	−	1.26281e7i	0.235150	−	0.197314i
$401$	8.83539e6	−	2.42750e7i	0.137023	−	0.376467i	−0.852135	−	0.523321i	$-0.824693\pi$
$401$	8.83539e6	−	2.42750e7i	0.137023	−	0.376467i	0.989158	+	0.146855i	$0.0469149\pi$
$402$	−898471.	−	1.07979e6i	−0.0138301	−	0.0166212i
$403$	4.57938e6	−	2.59710e7i	0.0699667	−	0.396801i
$404$		−	5.38926e6i		−	0.0817307i
$405$	−2.52212e7	−	7.30313e7i	−0.379666	−	1.09937i
$406$	−5.50596e6			−0.0822726
$407$	3.12005e7	+	5.50149e6i	0.462784	+	0.0816014i
$408$	7.14720e7	−	5.94702e7i	1.05234	−	0.875627i
$409$	−6.59311e7	−	2.39970e7i	−0.963652	−	0.350741i	−0.188189	−	0.982133i	$-0.560262\pi$
$409$	−6.59311e7	−	2.39970e7i	−0.963652	−	0.350741i	−0.775464	+	0.631392i	$0.782484\pi$
$410$	8.82506e7	+	1.05173e8i	1.28046	+	1.52599i
$411$	−3.70910e6	+	2.12104e6i	−0.0534248	+	0.0305509i
$412$	−5.95737e6	+	2.16831e6i	−0.0851850	+	0.0310048i
$413$	−1.50961e7	−	8.71573e6i	−0.214296	−	0.123724i
$414$	6.37680e7	+	5.44128e7i	0.898674	+	0.766831i
$415$	−1.64488e7	−	2.84901e7i	−0.230139	−	0.398612i
$416$	−3.78358e6	+	4.50910e6i	−0.0525561	+	0.0626340i
$417$	−8.76559e7	+	3.14942e7i	−1.20885	+	0.434333i
$418$	−1.77002e6	−	1.00383e7i	−0.0242354	−	0.137446i
$419$	−8.25085e6	+	1.45485e6i	−0.112165	+	0.0197777i	−0.229449	−	0.973321i	$-0.573692\pi$
$419$	−8.25085e6	+	1.45485e6i	−0.112165	+	0.0197777i	0.117284	+	0.993098i	$0.462581\pi$
$420$	−1.43455e7	−	2.59072e6i	−0.193628	−	0.0349681i
$421$	2.18574e7	+	1.83405e7i	0.292922	+	0.245791i	0.777391	−	0.629018i	$-0.216543\pi$
$421$	2.18574e7	+	1.83405e7i	0.292922	+	0.245791i	−0.484469	+	0.874809i	$0.660987\pi$
$422$	7.96909e7	−	4.60096e7i	1.06040	−	0.612224i
$423$	−1.67008e7	+	2.80258e6i	−0.220656	+	0.0370286i
$424$	2.47599e7	−	4.28854e7i	0.324827	−	0.562616i
$425$	−1.20828e7	−	3.31972e7i	−0.157399	−	0.432449i
$426$	3.65195e7	−	6.26538e7i	0.472385	−	0.810436i
$427$	−8.58299e7	+	7.20199e7i	−1.10244	+	0.925057i
$428$	−3.01053e6	+	8.27137e6i	−0.0383983	+	0.105498i
$429$	−7.20254e6	+	1.23931e6i	−0.0912250	+	0.0156967i
$430$	−2.56258e7	+	1.45331e8i	−0.322309	+	1.82790i
$431$			9.56182e7i			1.19429i	0.802134	+	0.597144i	$0.203698\pi$
$431$			9.56182e7i			1.19429i	−0.802134	+	0.597144i	$0.796302\pi$
$432$	−1.30385e7	+	6.89332e7i	−0.161725	+	0.855022i
$433$	−7.37401e6			−0.0908323			−0.0454161	−	0.998968i	$-0.514461\pi$
$433$	−7.37401e6			−0.0908323			−0.0454161	+	0.998968i	$0.514461\pi$
$434$	−1.25515e8	−	2.21318e7i	−1.53542	−	0.270736i
$435$	−5.40424e6	−	1.99233e6i	−0.0656549	−	0.0242044i
$436$	516169.	+	187870.i	0.00622777	+	0.00226672i
$437$	−3.82113e7	−	4.55385e7i	−0.457876	−	0.545675i
$438$	645731.	−	1.56151e8i	0.00768475	−	1.85833i
$439$	−5.65628e7	+	2.05872e7i	−0.668555	+	0.243334i	−0.653926	−	0.756559i	$-0.726879\pi$
$439$	−5.65628e7	+	2.05872e7i	−0.668555	+	0.243334i	−0.0146294	+	0.999893i	$0.504657\pi$
$440$	2.35836e7	+	1.36160e7i	0.276855	+	0.159842i
$441$	−4.71763e7	−	8.32951e7i	−0.550057	−	0.971189i
$442$	−1.87125e7	−	3.24109e7i	−0.216702	−	0.375340i
$443$	−9.07636e7	+	1.08168e8i	−1.04400	+	1.24419i	−0.0749862	+	0.997185i	$0.523891\pi$
$443$	−9.07636e7	+	1.08168e8i	−1.04400	+	1.24419i	−0.969014	+	0.247006i	$0.920553\pi$
$444$	1.39410e7	+	1.17964e7i	0.159274	+	0.134773i
$445$	2.50878e6	+	1.42280e7i	0.0284697	+	0.161459i
$446$	−7.24450e7	+	1.27740e7i	−0.816589	+	0.143987i
$447$	9.44578e7	−	1.11630e8i	1.05758	−	1.24985i
$448$	1.08983e8	+	9.14475e7i	1.21206	+	1.01704i
$449$	6.86153e6	−	3.96151e6i	0.0758023	−	0.0437645i	−0.461620	−	0.887078i	$-0.652732\pi$
$449$	6.86153e6	−	3.96151e6i	0.0758023	−	0.0437645i	0.537422	+	0.843313i	$0.319398\pi$
$450$	2.60441e7	+	1.53252e7i	0.285806	+	0.168177i
$451$	−2.18883e7	+	3.79117e7i	−0.238607	+	0.413279i
$452$	−3.22736e6	−	8.86710e6i	−0.0349488	−	0.0960210i
$453$	−1.01183e8	−	418423.i	−1.08846	−	0.00450113i
$454$	3.45857e7	−	2.90208e7i	0.369597	−	0.310129i
$455$	−1.92637e7	+	5.29266e7i	−0.204506	+	0.561875i
$456$	1.95087e7	−	5.29178e7i	0.205747	−	0.558094i
$457$	2.45002e7	−	1.38947e8i	0.256697	−	1.45580i	−0.534982	−	0.844863i	$-0.679682\pi$
$457$	2.45002e7	−	1.38947e8i	0.256697	−	1.45580i	0.791679	−	0.610937i	$-0.209207\pi$
$458$			5.77063e7i			0.600657i
$459$	1.08463e8	+	6.44283e7i	1.12161	+	0.666252i
$460$	1.65452e7			0.169980
$461$	6.00137e7	+	1.05820e7i	0.612558	+	0.108011i	0.471316	−	0.881965i	$-0.343779\pi$
$461$	6.00137e7	+	1.05820e7i	0.612558	+	0.108011i	0.141242	+	0.989975i	$0.454890\pi$
$462$	5.98950e6	+	3.48093e7i	0.0607386	+	0.352996i
$463$	−7.56770e7	−	2.75442e7i	−0.762467	−	0.277515i	−0.0686251	−	0.997643i	$-0.521861\pi$
$463$	−7.56770e7	−	2.75442e7i	−0.762467	−	0.277515i	−0.693842	+	0.720127i	$0.744083\pi$
$464$	3.36171e6	+	4.00633e6i	0.0336517	+	0.0401045i
$465$	−1.15188e8	−	6.71406e7i	−1.14564	−	0.667769i
$466$	−6.65078e7	+	2.42069e7i	−0.657226	+	0.239211i
$467$	−7.67709e7	−	4.43237e7i	−0.753782	−	0.435196i	0.0732766	−	0.997312i	$-0.476654\pi$
$467$	−7.67709e7	−	4.43237e7i	−0.753782	−	0.435196i	−0.827059	+	0.562115i	$0.809988\pi$
$468$	−3.94662e6	−	1.47353e6i	−0.0385024	−	0.0143754i
$469$	−1.72589e6	−	2.98934e6i	−0.0167300	−	0.0289772i
$470$	1.63257e7	−	1.94562e7i	0.157245	−	0.187398i
$471$	1.57025e7	−	8.69490e7i	0.150281	−	0.832150i
$472$	3.25942e6	+	1.84851e7i	0.0309966	+	0.175790i
$473$	−4.63395e7	+	8.17090e6i	−0.437892	+	0.0772123i
$474$	2.09855e7	+	5.84077e7i	0.197054	+	0.548447i
$475$	−1.64158e7	−	1.37745e7i	−0.153173	−	0.128527i
$476$	2.06133e7	−	1.19011e7i	0.191129	−	0.110348i
$477$	6.60704e7	+	1.22143e7i	0.608768	+	0.112541i
$478$	3.34426e7	−	5.79243e7i	0.306208	−	0.530368i
$479$	6.09968e7	+	1.67587e8i	0.555010	+	1.52488i	0.826786	+	0.562516i	$0.190166\pi$
$479$	6.09968e7	+	1.67587e8i	0.555010	+	1.52488i	−0.271777	+	0.962360i	$0.587611\pi$
$480$	1.47728e7	+	2.58334e7i	0.133579	+	0.233592i
$481$	5.40517e7	−	4.53547e7i	0.485707	−	0.407556i
$482$	5.46018e7	−	1.50017e8i	0.487602	−	1.33968i
$483$	1.31754e8	+	1.58344e8i	1.16929	+	1.40527i
$484$	2.13253e6	−	1.20942e7i	0.0188087	−	0.106669i
$485$		−	1.35389e8i		−	1.18675i
$486$	−1.06636e8	+	1.65373e7i	−0.928952	+	0.144064i
$487$	−3.83723e6			−0.0332224			−0.0166112	−	0.999862i	$-0.505288\pi$
$487$	−3.83723e6			−0.0332224			−0.0166112	+	0.999862i	$0.505288\pi$
$488$	1.18815e8	+	2.09503e7i	1.02238	+	0.180273i
$489$	−5.01143e7	+	4.16990e7i	−0.428583	+	0.356614i
$490$	1.34914e8	+	4.91048e7i	1.14675	+	0.417384i
$491$	−3.89588e6	−	4.64293e6i	−0.0329125	−	0.0392236i	0.749337	−	0.662189i	$-0.230372\pi$
$491$	−3.89588e6	−	4.64293e6i	−0.0329125	−	0.0392236i	−0.782250	+	0.622965i	$0.785928\pi$
$492$	−2.19052e7	+	1.25265e7i	−0.183929	+	0.105180i
$493$	8.83738e6	−	3.21654e6i	0.0737535	−	0.0268441i
$494$	−1.96600e7	−	1.13507e7i	−0.163081	−	0.0941547i
$495$	−6.71688e6	+	3.63335e7i	−0.0553799	+	0.299566i
$496$	6.05307e7	+	1.04842e8i	0.496056	+	0.859194i
$497$	1.14547e8	−	1.36512e8i	0.933074	−	1.11199i
$498$	−4.32401e7	+	1.55359e7i	−0.350105	+	0.125791i
$499$	3.10166e7	+	1.75904e8i	0.249628	+	1.41571i	0.809495	+	0.587126i	$0.199741\pi$
$499$	3.10166e7	+	1.75904e8i	0.249628	+	1.41571i	−0.559868	+	0.828582i	$0.689148\pi$
$500$	−1.07768e7	+	1.90025e6i	−0.0862147	+	0.0152020i
$501$	−5.59448e7	−	1.01033e7i	−0.444884	−	0.0803434i
$502$	−9.07650e7	−	7.61609e7i	−0.717476	−	0.602034i
$503$	−3.54035e7	+	2.04402e7i	−0.278191	+	0.160613i	−0.632604	−	0.774475i	$-0.718014\pi$
$503$	−3.54035e7	+	2.04402e7i	−0.278191	+	0.160613i	0.354413	+	0.935089i	$0.384681\pi$
$504$	−6.83583e7	+	1.83087e8i	−0.533949	+	1.43010i
$505$	−5.26363e7	+	9.11687e7i	−0.408706	+	0.707899i
$506$	−1.37110e7	−	3.76707e7i	−0.105832	−	0.290771i
$507$	5.74315e7	−	9.85311e7i	0.440683	−	0.756048i
$508$	−7.02240e6	+	5.89250e6i	−0.0535667	+	0.0449478i
$509$	−3.96572e7	+	1.08957e8i	−0.300724	+	0.826233i	0.693650	+	0.720312i	$0.256001\pi$
$509$	−3.96572e7	+	1.08957e8i	−0.300724	+	0.826233i	−0.994375	+	0.105921i	$0.966221\pi$
$510$	−1.86470e8	+	3.20851e7i	−1.40572	+	0.241876i
$511$	6.66311e7	−	3.77884e8i	0.499360	−	2.83201i
$512$		−	1.49582e8i		−	1.11448i
$513$	7.65183e7	+	949324.i	0.566779	+	0.00703173i
$514$	5.26069e7			0.387395
$515$	1.21957e8	+	2.15043e7i	0.892863	+	0.157436i
$516$	−2.54489e7	−	9.38201e6i	−0.185234	−	0.0682884i
$517$	7.60995e6	+	2.76979e6i	0.0550693	+	0.0200436i
$518$	−2.19196e8	−	2.61227e8i	−1.57704	−	1.87944i
$519$	−494648.	+	1.19616e8i	−0.00353830	+	0.855631i
$520$	5.69915e7	−	2.07432e7i	0.405322	−	0.147525i
$521$	5.03955e7	+	2.90958e7i	0.356351	+	0.205739i	0.667479	−	0.744629i	$-0.267373\pi$
$521$	5.03955e7	+	2.90958e7i	0.356351	+	0.205739i	−0.311128	+	0.950368i	$0.600707\pi$
$522$	−4.07968e6	+	6.93316e6i	−0.0286824	+	0.0487438i
$523$	−7.31377e7	−	1.26678e8i	−0.511254	−	0.885517i	−0.999915	−	0.0130438i	$-0.995848\pi$
$523$	−7.31377e7	−	1.26678e8i	−0.511254	−	0.885517i	0.488661	−	0.872474i	$-0.337485\pi$
$524$	1.80053e7	−	2.14579e7i	0.125143	−	0.149140i
$525$	5.66855e7	+	4.79656e7i	0.391736	+	0.331476i
$526$	3.45581e7	+	1.95989e8i	0.237461	+	1.34671i
$527$	2.14389e8	−	3.78025e7i	1.46477	−	0.258279i
$528$	2.16715e7	−	2.56113e7i	0.147227	−	0.173992i
$529$	−6.56947e7	−	5.51244e7i	−0.443775	−	0.372372i
$530$	−8.72714e7	+	5.03862e7i	−0.586198	+	0.338442i
$531$	−2.21605e7	+	1.25512e7i	−0.148012	+	0.0838301i
$532$	7.21903e6	−	1.25037e7i	0.0479451	−	0.0830433i
$533$	3.33456e7	+	9.16163e7i	0.220220	+	0.605050i
$534$	2.01779e7	+	83441.7i	0.132511	+	0.000547973i
$535$	1.31714e8	−	1.10521e8i	0.860142	−	0.721745i
$536$	−1.27125e6	+	3.49274e6i	−0.00825539	+	0.0226815i
$537$	−9.78544e6	+	2.65432e7i	−0.0631913	+	0.171408i
$538$	2.70414e6	−	1.53359e7i	0.0173653	−	0.0984834i
$539$			4.57788e7i			0.292346i
$540$	−1.38917e7	+	1.61444e7i	−0.0882213	+	0.102528i
$541$	1.88227e8			1.18875			0.594373	−	0.804189i	$-0.297400\pi$
$541$	1.88227e8			1.18875			0.594373	+	0.804189i	$0.297400\pi$
$542$	2.87288e6	+	506566.i	0.0180434	+	0.00318154i
$543$	2.16957e7	+	1.26089e8i	0.135511	+	0.787552i
$544$	−4.56600e7	−	1.66189e7i	−0.283621	−	0.103230i
$545$	−6.89699e6	−	8.21951e6i	−0.0426059	−	0.0507758i
$546$	6.79617e7	+	3.96133e7i	0.417529	+	0.243368i
$547$	4.38270e6	−	1.59517e6i	0.0267781	−	0.00974643i	−0.328596	−	0.944470i	$-0.606576\pi$
$547$	4.38270e6	−	1.59517e6i	0.0267781	−	0.00974643i	0.355374	+	0.934724i	$0.384353\pi$
$548$	1.02002e6	+	588907.i	0.00619820	+	0.00357853i
$549$	2.70917e7	+	1.61442e8i	0.163727	+	0.975659i
$550$	−7.22556e6	−	1.25150e7i	−0.0434293	−	0.0752218i
$551$	3.66689e6	−	4.37003e6i	0.0219201	−	0.0261234i
$552$	3.94201e7	−	2.18280e8i	0.234369	−	1.29777i
$553$	2.64828e7	+	1.50191e8i	0.156599	+	0.888115i
$554$	−9.80032e7	+	1.72806e7i	−0.576383	+	0.101632i
$555$	−1.20621e8	−	3.35717e8i	−0.705577	−	1.96379i
$556$	1.96685e7	+	1.65038e7i	0.114432	+	0.0960196i
$557$	−1.68576e8	+	9.73273e7i	−0.975506	+	0.563209i	−0.900910	−	0.434005i	$-0.857100\pi$
$557$	−1.68576e8	+	9.73273e7i	−0.975506	+	0.563209i	−0.0745956	+	0.997214i	$0.523767\pi$
$558$	−1.20870e8	+	1.41652e8i	−0.695691	+	0.815302i
$559$	−5.23979e7	+	9.07559e7i	−0.299971	+	0.519564i
$560$	−8.84319e7	−	2.42965e8i	−0.503553	−	1.38350i
$561$	−2.99488e7	−	5.23719e7i	−0.169626	−	0.296626i
$562$	−1.03131e8	+	8.65373e7i	−0.581006	+	0.487522i
$563$	−1.48600e7	+	4.08274e7i	−0.0832708	+	0.228785i	−0.974339	−	0.225084i	$-0.927734\pi$
$563$	−1.48600e7	+	4.08274e7i	−0.0832708	+	0.228785i	0.891069	+	0.453869i	$0.149957\pi$
$564$	2.98577e6	+	3.58833e6i	0.0166425	+	0.0200012i
$565$	−3.20075e7	+	1.81524e8i	−0.177462	+	1.00644i
$566$			1.30139e8i			0.717724i
$567$	−2.65132e8	−	4.38598e6i	−1.45450	−	0.0240612i
$568$	−1.91890e8			−1.04715
$569$	4.85439e7	+	8.55960e6i	0.263511	+	0.0464640i	0.303842	−	0.952722i	$-0.401730\pi$
$569$	4.85439e7	+	8.55960e6i	0.263511	+	0.0464640i	−0.0403318	+	0.999186i	$0.512841\pi$
$570$	−8.82248e7	+	7.34098e7i	−0.476394	+	0.396396i
$571$	−9.17986e7	−	3.34120e7i	−0.493092	−	0.179471i	0.0834924	−	0.996508i	$-0.473393\pi$
$571$	−9.17986e7	−	3.34120e7i	−0.493092	−	0.179471i	−0.576584	+	0.817038i	$0.695615\pi$
$572$	1.29497e6	+	1.54329e6i	0.00691946	+	0.00824629i
$573$	1.47615e7	−	8.44138e6i	0.0784635	−	0.0448693i
$574$	4.42774e8	−	1.61156e8i	2.34124	−	0.852142i
$575$	−7.29875e7	−	4.21393e7i	−0.383923	−	0.221658i
$576$	1.95903e8	−	6.94736e7i	1.02512	−	0.363540i
$577$	9.04646e7	+	1.56689e8i	0.470925	+	0.815665i	0.999447	−	0.0332541i	$-0.0105871\pi$
$577$	9.04646e7	+	1.56689e8i	0.470925	+	0.815665i	−0.528522	+	0.848919i	$0.677254\pi$
$578$	8.19007e7	−	9.76054e7i	0.424135	−	0.505464i
$579$	2.23135e8	−	8.01710e7i	1.14956	−	0.413030i
$580$	275707.	+	1.56361e6i	0.00141307	+	0.00801393i
$581$	−1.11189e8	+	1.96056e7i	−0.566934	+	0.0999658i
$582$	−1.86081e8	−	3.36050e7i	−0.943914	−	0.170465i
$583$	−2.46143e7	−	2.06538e7i	−0.124217	−	0.104231i
$584$	−3.57827e8	+	2.06592e8i	−1.79653	+	1.03723i
$585$	5.23721e7	+	6.34735e7i	0.261597	+	0.317048i
$586$	7.05242e7	−	1.22151e8i	0.350466	−	0.607024i
$587$	−1.75536e7	−	4.82280e7i	−0.0867863	−	0.238443i	0.888706	−	0.458478i	$-0.151605\pi$
$587$	−1.75536e7	−	4.82280e7i	−0.0867863	−	0.238443i	−0.975492	+	0.220035i	$0.929383\pi$
$588$	−1.32884e7	+	2.27979e7i	−0.0653642	+	0.112141i
$589$	1.01157e8	−	8.48809e7i	0.495052	−	0.415398i
$590$	1.30642e7	−	3.58937e7i	0.0636103	−	0.174768i
$591$	−1.41392e8	+	2.43287e7i	−0.684954	+	0.117857i
$592$	−5.62464e7	+	3.18989e8i	−0.271100	+	1.53748i
$593$		−	2.89171e8i		−	1.38672i	−0.720589	−	0.693362i	$-0.756129\pi$
$593$		−	2.89171e8i		−	1.38672i	0.720589	−	0.693362i	$-0.243871\pi$
$594$	4.82702e7	+	1.82502e7i	0.230314	+	0.0870779i
$595$	−4.64946e8			−2.20725
$596$	−3.96973e7	−	6.99971e6i	−0.187509	−	0.0330629i
$597$	−5.45490e7	−	2.01100e7i	−0.256368	−	0.0945127i
$598$	−8.38973e7	−	3.05361e7i	−0.392324	−	0.142794i
$599$	−1.31785e8	−	1.57055e8i	−0.613175	−	0.730754i	0.366706	−	0.930337i	$-0.380486\pi$
$599$	−1.31785e8	−	1.57055e8i	−0.613175	−	0.730754i	−0.979881	+	0.199583i	$0.936041\pi$
$600$	330652.	−	7.99582e7i	0.00153080	−	0.370177i
$601$	1.69067e7	−	6.15352e6i	0.0778815	−	0.0283466i	−0.302786	−	0.953059i	$-0.597917\pi$
$601$	1.69067e7	−	6.15352e6i	0.0778815	−	0.0283466i	0.380667	+	0.924712i	$0.375694\pi$
$602$	4.38616e8	+	2.53235e8i	2.01046	+	1.16074i
$603$	−5.04302e6	−	41709.6i	−0.0230006	−	0.000190232i
$604$	1.39461e7	+	2.41554e7i	0.0632910	+	0.109623i
$605$	−1.54198e8	+	1.83766e8i	−0.696325	+	0.829848i
$606$	1.12239e8	+	9.49732e7i	0.504342	+	0.426760i
$607$	5.33230e6	+	3.02410e7i	0.0238423	+	0.135216i	0.994405	−	0.105630i	$-0.0336860\pi$
$607$	5.33230e6	+	3.02410e7i	0.0238423	+	0.135216i	−0.970563	+	0.240847i	$0.922575\pi$
$608$	−2.90264e7	+	5.11814e6i	−0.129147	+	0.0227720i
$609$	−1.27688e7	+	1.50901e7i	−0.0565327	+	0.0668100i
$610$	−1.88077e8	−	1.57816e8i	−0.828605	−	0.695282i
$611$	1.56196e7	−	9.01801e6i	0.0684774	−	0.0395355i
$612$	287613.	−	3.47746e7i	0.00125474	−	0.151708i
$613$	−4.37849e6	+	7.58376e6i	−0.0190083	+	0.0329233i	−0.875373	−	0.483448i	$-0.839384\pi$
$613$	−4.37849e6	+	7.58376e6i	−0.0190083	+	0.0329233i	0.856365	+	0.516371i	$0.172718\pi$
$614$	1.35457e8	+	3.72165e8i	0.585189	+	1.60779i
$615$	4.92908e8	+	2.03833e6i	2.11905	+	0.00876291i
$616$	7.15944e7	−	6.00749e7i	0.306293	−	0.257010i
$617$	9.24068e7	−	2.53886e8i	0.393413	−	1.08089i	−0.572020	−	0.820240i	$-0.693840\pi$
$617$	9.24068e7	−	2.53886e8i	0.393413	−	1.08089i	0.965433	−	0.260653i	$-0.0839378\pi$
$618$	5.98269e7	−	1.62282e8i	0.253473	−	0.687551i
$619$	2.10547e6	−	1.19407e7i	0.00887724	−	0.0503453i	−0.980047	−	0.198764i	$-0.936307\pi$
$619$	2.10547e6	−	1.19407e7i	0.00887724	−	0.0503453i	0.988925	+	0.148419i	$0.0474183\pi$
$620$			3.67528e7i			0.154211i
$621$	2.97013e8	−	4.85802e7i	1.24022	−	0.202854i
$622$	−2.00365e8			−0.832626
$623$	4.88303e7	+	8.61010e6i	0.201941	+	0.0356077i
$624$	−1.26705e7	−	7.36376e7i	−0.0521485	−	0.303072i
$625$	2.81798e8	+	1.02566e8i	1.15424	+	0.420110i
$626$	1.59079e8	+	1.89583e8i	0.648471	+	0.772817i
$627$	−3.16167e7	−	1.84287e7i	−0.128267	−	0.0747638i
$628$	−2.28871e7	+	8.33021e6i	−0.0924084	+	0.0336339i
$629$	5.04429e8	+	2.91232e8i	2.02697	+	1.17027i
$630$	3.06762e8	−	2.53110e8i	1.22682	−	1.01225i
$631$	−1.17821e8	−	2.04072e8i	−0.468959	−	0.812261i	0.530411	−	0.847741i	$-0.322038\pi$
$631$	−1.17821e8	−	2.04072e8i	−0.468959	−	0.812261i	−0.999370	+	0.0354793i	$0.988704\pi$
$632$	1.05559e8	−	1.25801e8i	0.418163	−	0.498347i
$633$	5.87127e7	−	3.25109e8i	0.231484	−	1.28179i
$634$	−1.31862e7	−	7.47826e7i	−0.0517430	−	0.293449i
$635$	1.76347e8	−	3.10948e7i	0.688728	−	0.121441i
$636$	−6.26269e6	−	1.74305e7i	−0.0243439	−	0.0677547i
$637$	7.81021e7	+	6.55355e7i	0.302165	+	0.253547i
$638$	3.33161e6	−	1.92350e6i	0.0128290	−	0.00740681i
$639$	−8.70227e7	−	2.45389e8i	−0.333526	−	0.940486i
$640$	−1.20604e8	+	2.08892e8i	−0.460066	+	0.796858i
$641$	−1.25610e7	−	3.45111e7i	−0.0476926	−	0.131034i	0.913560	−	0.406705i	$-0.133322\pi$
$641$	−1.25610e7	−	3.45111e7i	−0.0476926	−	0.131034i	−0.961252	+	0.275671i	$0.911100\pi$
$642$	−1.19209e8	−	2.08462e8i	−0.450509	−	0.787811i
$643$	3.51780e8	−	2.95178e8i	1.32324	−	1.11033i	0.337629	−	0.941279i	$-0.390375\pi$
$643$	3.51780e8	−	2.95178e8i	1.32324	−	1.11033i	0.985608	−	0.169049i	$-0.0540695\pi$
$644$	1.94209e7	−	5.33585e7i	0.0727130	−	0.199777i
$645$	3.38880e8	+	4.07269e8i	1.26289	+	1.51776i
$646$	3.25415e7	−	1.84552e8i	0.120709	−	0.684575i
$647$			3.08588e8i			1.13937i	0.821862	+	0.569687i	$0.192936\pi$
$647$			3.08588e8i			1.13937i	−0.821862	+	0.569687i	$0.807064\pi$
$648$	1.79895e8	+	2.21737e8i	0.661139	+	0.814918i
$649$	1.21793e7			0.0445543
$650$	−3.16955e7	−	5.58877e6i	−0.115414	−	0.0203506i
$651$	−3.51739e8	+	2.92674e8i	−1.27490	+	1.06082i
$652$	1.68874e7	+	6.14653e6i	0.0609286	+	0.0221762i
$653$	−4.26290e7	−	5.08033e7i	−0.153097	−	0.182454i	0.684045	−	0.729440i	$-0.260219\pi$
$653$	−4.26290e7	−	5.08033e7i	−0.153097	−	0.182454i	−0.837141	+	0.546987i	$0.815775\pi$
$654$	−1.30089e7	+	7.43916e6i	−0.0465060	+	0.0265944i
$655$	−5.14168e8	+	1.87142e8i	−1.82970	+	0.665958i
$656$	−3.87602e8	−	2.23782e8i	−1.37301	−	0.792710i
$657$	−4.26464e8	−	3.63898e8i	−1.50379	−	1.28317i
$658$	−4.35833e7	−	7.54884e7i	−0.152983	−	0.264974i
$659$	−2.56591e8	+	3.05793e8i	−0.896573	+	1.06849i	0.100717	+	0.994915i	$0.467886\pi$
$659$	−2.56591e8	+	3.05793e8i	−0.896573	+	1.06849i	−0.997289	+	0.0735785i	$0.976558\pi$
$660$	9.58541e6	−	3.44398e6i	0.0333410	−	0.0119792i
$661$	1.52381e7	+	8.64194e7i	0.0527625	+	0.299231i	0.999758	−	0.0220169i	$-0.00700877\pi$
$661$	1.52381e7	+	8.64194e7i	0.0527625	+	0.299231i	−0.946995	+	0.321248i	$0.895898\pi$
$662$	1.79496e8	−	3.16500e7i	0.618700	−	0.109094i
$663$	−1.32224e8	−	2.38789e7i	−0.453702	−	0.0819359i
$664$	9.31321e7	+	7.81471e7i	0.318123	+	0.266937i
$665$	−2.44245e8	+	1.41015e8i	−0.830540	+	0.479512i
$666$	−4.91354e8	+	8.24549e7i	−1.66331	+	0.279122i
$667$	1.12178e7	−	1.94299e7i	0.0378035	−	0.0654776i
$668$	5.35984e6	+	1.47260e7i	0.0179813	+	0.0494033i
$669$	−1.32997e8	+	2.28174e8i	−0.444185	+	0.762056i
$670$	5.79424e6	−	4.86194e6i	0.0192651	−	0.0161654i
$671$	2.67748e7	−	7.35632e7i	0.0886255	−	0.243497i
$672$	1.00654e8	−	1.73191e7i	0.331682	−	0.0570712i
$673$	2.82148e6	−	1.60014e7i	0.00925618	−	0.0524944i	−0.979830	−	0.199834i	$-0.935960\pi$
$673$	2.82148e6	−	1.60014e7i	0.00925618	−	0.0524944i	0.989086	+	0.147339i	$0.0470709\pi$
$674$		−	3.46502e8i		−	1.13169i
$675$	1.02400e8	−	3.58384e7i	0.332958	−	0.116530i
$676$	−3.14380e7			−0.101769
$677$	8.29921e7	+	1.46337e7i	0.267467	+	0.0471617i	0.305773	−	0.952104i	$-0.401085\pi$
$677$	8.29921e7	+	1.46337e7i	0.267467	+	0.0471617i	−0.0383060	+	0.999266i	$0.512196\pi$
$678$	2.41544e8	+	8.90478e7i	0.775011	+	0.285716i
$679$	−4.36631e8	−	1.58921e8i	−1.39478	−	0.507658i
$680$	3.21815e8	+	3.83524e8i	1.02348	+	1.21973i
$681$	670295.	−	1.62091e8i	0.00212239	−	0.513236i
$682$	8.36800e7	−	3.04570e7i	0.263796	−	0.0960139i
$683$	−2.94407e7	−	1.69976e7i	−0.0924031	−	0.0533489i	0.453086	−	0.891467i	$-0.350323\pi$
$683$	−2.94407e7	−	1.69976e7i	−0.0924031	−	0.0533489i	−0.545489	+	0.838118i	$0.683656\pi$
$684$	−1.03958e7	−	1.83550e7i	−0.0324856	−	0.0573570i
$685$	−1.15036e7	−	1.99247e7i	−0.0357899	−	0.0619899i
$686$	3.29575e7	−	3.92772e7i	0.102090	−	0.121666i
$687$	1.58155e8	+	1.33826e8i	0.487768	+	0.412735i
$688$	−8.35379e7	−	4.73767e8i	−0.256518	−	1.45479i
$689$	−7.04741e7	+	1.24265e7i	−0.215463	+	0.0379919i
$690$	−2.91571e8	+	3.44577e8i	−0.887558	+	1.04891i
$691$	2.23677e8	+	1.87687e8i	0.677934	+	0.568854i	0.915402	−	0.402541i	$-0.131873\pi$
$691$	2.23677e8	+	1.87687e8i	0.677934	+	0.568854i	−0.237468	+	0.971395i	$0.576317\pi$
$692$	2.85558e7	−	1.64867e7i	0.0861739	−	0.0497525i
$693$	1.09292e8	+	6.43107e7i	0.328388	+	0.193234i
$694$	−9.30513e7	+	1.61170e8i	−0.278384	+	0.482175i
$695$	−1.71536e8	−	4.71290e8i	−0.510975	−	1.40389i
$696$	2.12856e7	+	88022.3i	0.0631331	+	0.000261075i
$697$	−6.16531e8	+	5.17331e8i	−1.82078	+	1.52781i
$698$	−7.90016e7	+	2.17055e8i	−0.232311	+	0.638269i
$699$	−8.78943e7	+	2.38415e8i	−0.257353	+	0.698076i
$700$	3.55445e6	−	2.01583e7i	0.0103628	−	0.0587705i
$701$		−	2.39283e8i		−	0.694638i	−0.937747	−	0.347319i	$-0.887092\pi$
$701$		−	2.39283e8i		−	0.694638i	0.937747	−	0.347319i	$-0.112908\pi$
$702$	1.00238e8	−	5.62263e7i	0.289749	−	0.162528i
$703$	3.53314e8			1.01694
$704$	−9.78917e7	−	1.72610e7i	−0.280561	−	0.0494706i
$705$	−1.54626e7	−	8.98644e7i	−0.0441282	−	0.256460i
$706$	−5.50795e8	−	2.00473e8i	−1.56522	−	0.569694i
$707$	2.32235e8	+	2.76767e8i	0.657159	+	0.783171i
$708$	6.06533e6	+	3.53535e6i	0.0170905	+	0.00996167i
$709$	1.85616e8	−	6.75588e7i	0.520808	−	0.189558i	−0.0682216	−	0.997670i	$-0.521733\pi$
$709$	1.85616e8	−	6.75588e7i	0.520808	−	0.189558i	0.589029	+	0.808112i	$0.299510\pi$
$710$	3.38179e8	+	1.95248e8i	0.944868	+	0.545520i
$711$	2.08745e8	+	7.79380e7i	0.580774	+	0.216841i
$712$	−2.66958e7	−	4.62386e7i	−0.0739612	−	0.128105i
$713$	3.33825e8	−	3.97838e8i	0.920981	−	1.09758i
$714$	−1.15405e8	+	6.39029e8i	−0.317051	+	1.75560i
$715$	−6.83359e6	−	3.87552e7i	−0.0186952	−	0.106026i
$716$	7.67977e6	−	1.35415e6i	0.0209223	−	0.00368916i
$717$	−8.11961e7	−	2.25988e8i	−0.220281	−	0.613095i
$718$	−3.91527e8	−	3.28530e8i	−1.05776	−	0.887569i
$719$	−9.46559e7	+	5.46496e7i	−0.254660	+	0.147028i	−0.621896	−	0.783100i	$-0.713637\pi$
$719$	−9.46559e7	+	5.46496e7i	−0.254660	+	0.147028i	0.367236	+	0.930128i	$0.380304\pi$
$720$	−3.71468e8	−	6.86723e7i	−0.995231	−	0.183986i
$721$	2.12506e8	−	3.68071e8i	0.566976	−	0.982032i
$722$	8.21303e7	+	2.25651e8i	0.218219	+	0.599551i
$723$	−2.84524e8	−	4.97551e8i	−0.752843	−	1.31651i
$724$	2.70171e7	−	2.26701e7i	0.0711908	−	0.0597362i
$725$	2.76615e6	−	7.59992e6i	0.00725874	−	0.0199432i
$726$	2.14297e8	+	2.57545e8i	0.560023	+	0.673043i
$727$	−6.00966e7	+	3.40825e8i	−0.156404	+	0.887009i	0.801088	+	0.598547i	$0.204255\pi$
$727$	−6.00966e7	+	3.40825e8i	−0.156404	+	0.887009i	−0.957491	+	0.288462i	$0.906856\pi$
$728$		−	2.08147e8i		−	0.539481i
$729$	−2.01974e8	+	3.30607e8i	−0.521331	+	0.853354i
$730$	8.40823e8			2.16140
$731$	−8.51941e8	−	1.50220e8i	−2.18101	−	0.384571i
$732$	3.46874e7	−	2.88626e7i	0.0884378	−	0.0735871i
$733$	5.91331e8	+	2.15227e8i	1.50148	+	0.546493i	0.956442	−	0.291921i	$-0.0942946\pi$
$733$	5.91331e8	+	2.15227e8i	1.50148	+	0.546493i	0.545034	+	0.838414i	$0.316517\pi$
$734$	2.85082e7	+	3.39748e7i	0.0720912	+	0.0859149i
$735$	4.47460e8	−	2.55880e8i	1.12692	−	0.644428i
$736$	−1.08927e8	+	3.96463e7i	−0.273215	+	0.0994420i
$737$	2.08865e6	+	1.20588e6i	0.00521750	+	0.00301233i
$738$	1.25147e8	−	6.76955e8i	0.311352	−	1.68419i
$739$	5.36635e7	+	9.29479e7i	0.132967	+	0.230306i	0.924819	−	0.380407i	$-0.124216\pi$
$739$	5.36635e7	+	9.29479e7i	0.132967	+	0.230306i	−0.791852	+	0.610713i	$0.790883\pi$
$740$	−6.32087e7	+	7.53292e7i	−0.155985	+	0.185895i
$741$	−7.67022e7	+	2.75587e7i	−0.188518	+	0.0677335i
$742$	6.00562e7	+	3.40595e8i	0.147010	+	0.833733i
$743$	−6.67182e8	+	1.17642e8i	−1.62659	+	0.286811i	−0.911215	−	0.411931i	$-0.864854\pi$
$743$	−6.67182e8	+	1.17642e8i	−1.62659	+	0.286811i	−0.715373	+	0.698742i	$0.753743\pi$
$744$	4.84878e8	+	8.75660e7i	1.17737	+	0.212626i
$745$	6.03184e8	+	5.06131e8i	1.45875	+	1.22404i
$746$	1.33684e8	−	7.71825e7i	0.322005	−	0.185910i
$747$	−5.76987e7	+	1.54537e8i	−0.138422	+	0.370741i
$748$	−8.31527e6	+	1.44025e7i	−0.0198688	+	0.0344138i
$749$	−2.01825e8	−	5.54510e8i	−0.480319	−	1.31966i
$750$	1.50342e8	−	2.57930e8i	0.356365	−	0.611390i
$751$	1.15180e8	−	9.66475e7i	0.271930	−	0.228176i	−0.496617	−	0.867970i	$-0.665425\pi$
$751$	1.15180e8	−	9.66475e7i	0.271930	−	0.228176i	0.768547	+	0.639793i	$0.220980\pi$
$752$	−2.83179e7	+	7.78028e7i	−0.0665898	+	0.182954i
$753$	−4.19226e8	+	7.21347e7i	−0.981892	+	0.168950i
$754$	1.48778e6	−	8.43761e6i	0.00347076	−	0.0196836i
$755$		−	5.44840e8i		−	1.26598i
$756$	3.57598e7	+	6.37514e7i	0.0827617	+	0.147545i
$757$	7.40692e8			1.70746			0.853729	−	0.520717i	$-0.174335\pi$
$757$	7.40692e8			1.70746			0.853729	+	0.520717i	$0.174335\pi$
$758$	4.28288e7	+	7.55187e6i	0.0983395	+	0.0173399i
$759$	−1.35041e8	−	4.97842e7i	−0.308844

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(7.40620 + 1.30591i) q^{2} +(20.7548 - 17.2696i) q^{3} +(-6.99392 - 2.54558i) q^{4} +(93.4519 + 111.372i) q^{5} +(176.267 - 100.798i) q^{6} +(468.870 - 170.655i) q^{7} +(-465.300 - 268.641i) q^{8} +(132.523 - 716.853i) q^{9} +O(q^{10})\)	\(q+(7.40620 + 1.30591i) q^{2} +(20.7548 - 17.2696i) q^{3} +(-6.99392 - 2.54558i) q^{4} +(93.4519 + 111.372i) q^{5} +(176.267 - 100.798i) q^{6} +(468.870 - 170.655i) q^{7} +(-465.300 - 268.641i) q^{8} +(132.523 - 716.853i) q^{9} +(546.682 + 946.881i) q^{10} +(-224.091 + 267.061i) q^{11} +(-189.118 + 67.9491i) q^{12} +(134.825 + 764.633i) q^{13} +(3695.40 - 651.600i) q^{14} +(3862.92 + 697.619i) q^{15} +(-2730.39 - 2291.07i) q^{16} +(-5550.68 + 3204.68i) q^{17} +(1917.64 - 5136.10i) q^{18} +(-1943.92 + 3366.96i) q^{19} +(-370.090 - 1016.81i) q^{20} +(6784.16 - 11639.1i) q^{21} +(-2008.42 + 1685.26i) q^{22} +(-5229.60 + 14368.2i) q^{23} +(-14296.5 + 2459.95i) q^{24} +(-957.130 + 5428.15i) q^{25} +5839.09i q^{26} +(-9629.28 - 17166.8i) q^{27} -3713.65 q^{28} +(-1445.02 - 254.796i) q^{29} +(27698.5 + 10211.3i) q^{30} +(-31916.9 - 11616.8i) q^{31} +(4873.06 + 5807.49i) q^{32} +(-38.9246 + 9412.75i) q^{33} +(-45294.5 + 16485.8i) q^{34} +(62822.9 + 36270.8i) q^{35} +(-2751.66 + 4676.27i) q^{36} +(-45438.5 - 78701.8i) q^{37} +(-18794.0 + 22397.8i) q^{38} +(16003.2 + 13541.4i) q^{39} +(-13564.2 - 76926.2i) q^{40} +(123662. - 21805.0i) q^{41} +(65444.5 - 77341.9i) q^{42} +(103394. + 86758.2i) q^{43} +(2247.10 - 1297.36i) q^{44} +(92221.6 - 52232.0i) q^{45} +(-57495.1 + 99584.5i) q^{46} +(-7944.94 - 21828.6i) q^{47} +(-96234.4 - 397.959i) q^{48} +(100592. - 84406.3i) q^{49} +(-14177.4 + 38952.1i) q^{50} +(-59859.6 + 162370. i) q^{51} +(1003.47 - 5690.99i) q^{52} +92167.3i q^{53} +(-48898.1 - 139715. i) q^{54} -50684.7 q^{55} +(-264010. - 46552.1i) q^{56} +(17800.5 + 103451. i) q^{57} +(-10369.4 - 3774.14i) q^{58} +(-22456.1 - 26762.2i) q^{59} +(-25241.1 - 14712.4i) q^{60} +(-211010. + 76801.5i) q^{61} +(-221213. - 127717. i) q^{62} +(-60198.4 - 358727. i) q^{63} +(142563. + 246927. i) q^{64} +(-72558.7 + 86472.1i) q^{65} +(-12580.5 + 69661.9i) q^{66} +(-1201.29 - 6812.86i) q^{67} +(46978.7 - 8283.62i) q^{68} +(139594. + 388522. i) q^{69} +(417912. + 350670. i) q^{70} +(309301. - 178575. i) q^{71} +(-254239. + 297951. i) q^{72} +(384512. - 665995. i) q^{73} +(-233749. - 642220. i) q^{74} +(73876.9 + 129189. i) q^{75} +(22166.5 - 18599.9i) q^{76} +(-59494.2 + 163459. i) q^{77} +(100839. + 121189. i) q^{78} +(-53075.9 + 301008. i) q^{79} -518192. i q^{80} +(-496316. - 189999. i) q^{81} +944343. q^{82} +(-222841. - 39292.8i) q^{83} +(-77076.1 + 64133.2i) q^{84} +(-875632. - 318704. i) q^{85} +(652461. + 777572. i) q^{86} +(-34391.3 + 19666.7i) q^{87} +(176013. - 64063.5i) q^{88} +(86060.1 + 49686.8i) q^{89} +(751222. - 266407. i) q^{90} +(193704. + 335505. i) q^{91} +(73150.8 - 87177.7i) q^{92} +(-863046. + 310088. i) q^{93} +(-30335.7 - 172042. i) q^{94} +(-556647. + 98151.8i) q^{95} +(201432. + 36377.5i) q^{96} +(-713372. - 598591. i) q^{97} +(855229. - 493766. i) q^{98} +(161746. + 196032. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

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