LMFDB - Embedded newform 69.7.f.a.10.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(7,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("69.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.f (of order $22$, degree $10$, 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:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			10.16
Character	$\chi$	$=$	69.10
Dual form			69.7.f.a.7.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.76160 + 4.34111i) q^{2} +(13.1138 + 8.42776i) q^{3} +(4.41249 - 30.6896i) q^{4} +(172.538 + 78.7957i) q^{5} +(12.7431 + 88.6305i) q^{6} +(43.8846 - 149.457i) q^{7} +(459.089 - 295.039i) q^{8} +(100.946 + 221.041i) q^{9} +O(q^{10})$	\(q+(3.76160 + 4.34111i) q^{2} +(13.1138 + 8.42776i) q^{3} +(4.41249 - 30.6896i) q^{4} +(172.538 + 78.7957i) q^{5} +(12.7431 + 88.6305i) q^{6} +(43.8846 - 149.457i) q^{7} +(459.089 - 295.039i) q^{8} +(100.946 + 221.041i) q^{9} +(306.959 + 1045.41i) q^{10} +(-1273.06 - 1103.11i) q^{11} +(316.509 - 365.271i) q^{12} +(2552.36 - 749.440i) q^{13} +(813.887 - 371.690i) q^{14} +(1598.57 + 2487.43i) q^{15} +(1103.75 + 324.092i) q^{16} +(-4036.43 + 580.350i) q^{17} +(-579.845 + 1269.68i) q^{18} +(11582.8 + 1665.36i) q^{19} +(3179.53 - 4947.44i) q^{20} +(1835.08 - 1590.11i) q^{21} -9675.95i q^{22} +(-9998.78 + 6932.55i) q^{23} +8506.94 q^{24} +(13328.6 + 15382.0i) q^{25} +(12854.3 + 8260.99i) q^{26} +(-539.088 + 3749.44i) q^{27} +(-4393.13 - 2006.28i) q^{28} +(6021.80 + 41882.6i) q^{29} +(-4785.02 + 16296.3i) q^{30} +(-25705.6 + 16520.0i) q^{31} +(-11763.9 - 25759.3i) q^{32} +(-7397.94 - 25195.1i) q^{33} +(-17702.8 - 15339.5i) q^{34} +(19348.4 - 22329.2i) q^{35} +(7229.06 - 2122.64i) q^{36} +(263.159 - 120.181i) q^{37} +(36340.3 + 56546.6i) q^{38} +(39787.3 + 11682.6i) q^{39} +(102458. - 14731.3i) q^{40} +(30308.7 - 66366.7i) q^{41} +(13805.7 + 1984.96i) q^{42} +(2580.99 - 4016.10i) q^{43} +(-39471.4 + 34202.1i) q^{44} +46092.1i q^{45} +(-67706.4 - 17328.4i) q^{46} -78549.2 q^{47} +(11743.1 + 13552.3i) q^{48} +(78561.0 + 50488.1i) q^{49} +(-16638.3 + 115722. i) q^{50} +(-57824.1 - 26407.4i) q^{51} +(-11737.7 - 81637.7i) q^{52} +(31846.1 - 108458. i) q^{53} +(-18304.6 + 11763.6i) q^{54} +(-132731. - 290641. i) q^{55} +(-23948.7 - 81561.9i) q^{56} +(137860. + 119456. i) q^{57} +(-159165. + 183687. i) q^{58} +(-302501. + 88822.3i) q^{59} +(83391.7 - 38083.7i) q^{60} +(-147029. - 228782. i) q^{61} +(-168409. - 49449.4i) q^{62} +(37466.1 - 5386.81i) q^{63} +(98156.9 - 214934. i) q^{64} +(499433. + 71807.6i) q^{65} +(81546.6 - 126889. i) q^{66} +(-371235. + 321677. i) q^{67} +126437. i q^{68} +(-189548. + 6645.09i) q^{69} +169714. q^{70} +(-347163. - 400647. i) q^{71} +(111559. + 71694.4i) q^{72} +(18276.5 - 127116. i) q^{73} +(1511.61 + 690.331i) q^{74} +(45153.1 + 314047. i) q^{75} +(102218. - 348123. i) q^{76} +(-220736. + 141858. i) q^{77} +(98948.3 + 216667. i) q^{78} +(-66572.3 - 226724. i) q^{79} +(164903. + 142889. i) q^{80} +(-38668.9 + 44626.3i) q^{81} +(402114. - 118071. i) q^{82} +(90831.3 - 41481.3i) q^{83} +(-40702.5 - 63334.3i) q^{84} +(-742168. - 217920. i) q^{85} +(27143.0 - 3902.57i) q^{86} +(-274007. + 599992. i) q^{87} +(-909909. - 130825. i) q^{88} +(-156195. + 243044. i) q^{89} +(-200091. + 173380. i) q^{90} -414357. i q^{91} +(168637. + 337448. i) q^{92} -476326. q^{93} +(-295470. - 340991. i) q^{94} +(1.86726e6 + 1.20001e6i) q^{95} +(62823.4 - 436946. i) q^{96} +(-657396. - 300223. i) q^{97} +(76340.3 + 530958. i) q^{98} +(115322. - 392752. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) $ 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{3}{22}\right)$	$1$

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 $

$2$	3.76160	+	4.34111i	0.470199	+	0.542639i	0.940467	−	0.339885i	$-0.110388\pi$
$2$	3.76160	+	4.34111i	0.470199	+	0.542639i	−0.470268	+	0.882524i	$0.655843\pi$
$3$	13.1138	+	8.42776i	0.485698	+	0.312139i
$3$	13.1138	+	8.42776i	0.485698	+	0.312139i
$4$	4.41249	−	30.6896i	0.0689452	−	0.479524i
$5$	172.538	+	78.7957i	1.38031	+	0.630365i	0.960763	−	0.277369i	$-0.0894625\pi$
$5$	172.538	+	78.7957i	1.38031	+	0.630365i	0.419545	+	0.907735i	$0.362190\pi$
$6$	12.7431	+	88.6305i	0.0589960	+	0.410326i
$7$	43.8846	−	149.457i	0.127943	−	0.435735i	−0.870459	−	0.492241i	$-0.836178\pi$
$7$	43.8846	−	149.457i	0.127943	−	0.435735i	0.998402	+	0.0565059i	$0.0179960\pi$
$8$	459.089	−	295.039i	0.896659	−	0.576248i
$9$	100.946	+	221.041i	0.138472	+	0.303211i
$10$	306.959	+	1045.41i	0.306959	+	1.04541i
$11$	−1273.06	−	1103.11i	−0.956468	−	0.828784i	0.0288376	−	0.999584i	$-0.490819\pi$
$11$	−1273.06	−	1103.11i	−0.956468	−	0.828784i	−0.985306	+	0.170800i	$0.945365\pi$
$12$	316.509	−	365.271i	0.183165	−	0.211383i
$13$	2552.36	−	749.440i	1.16175	−	0.341120i	0.356636	−	0.934243i	$-0.383924\pi$
$13$	2552.36	−	749.440i	1.16175	−	0.341120i	0.805111	+	0.593123i	$0.202105\pi$
$14$	813.887	−	371.690i	0.296606	−	0.135455i
$15$	1598.57	+	2487.43i	0.473651	+	0.737015i
$16$	1103.75	+	324.092i	0.269471	+	0.0791239i
$17$	−4036.43	+	580.350i	−0.821581	+	0.118125i	−0.540270	−	0.841491i	$-0.681678\pi$
$17$	−4036.43	+	580.350i	−0.821581	+	0.118125i	−0.281310	+	0.959617i	$0.590769\pi$
$18$	−579.845	+	1269.68i	−0.0994247	+	0.217710i
$19$	11582.8	+	1665.36i	1.68870	+	0.242799i	0.918619	−	0.395145i	$-0.129306\pi$
$19$	11582.8	+	1665.36i	1.68870	+	0.242799i	0.770083	+	0.637944i	$0.220215\pi$
$20$	3179.53	−	4947.44i	0.397441	−	0.618431i
$21$	1835.08	−	1590.11i	0.198152	−	0.171700i
$22$		−	9675.95i		−	0.908711i
$23$	−9998.78	+	6932.55i	−0.821795	+	0.569783i
$23$	−9998.78	+	6932.55i	−0.821795	+	0.569783i
$24$	8506.94			0.615375
$25$	13328.6	+	15382.0i	0.853028	+	0.984447i
$26$	12854.3	+	8260.99i	0.731358	+	0.470015i
$27$	−539.088	+	3749.44i	−0.0273885	+	0.190491i
$28$	−4393.13	−	2006.28i	−0.200125	−	0.0913938i
$29$	6021.80	+	41882.6i	0.246906	+	1.71727i	0.615886	+	0.787835i	$0.288798\pi$
$29$	6021.80	+	41882.6i	0.246906	+	1.71727i	−0.368980	+	0.929437i	$0.620293\pi$
$30$	−4785.02	+	16296.3i	−0.177223	+	0.603566i
$31$	−25705.6	+	16520.0i	−0.862865	+	0.554530i	−0.895563	−	0.444935i	$-0.853227\pi$
$31$	−25705.6	+	16520.0i	−0.862865	+	0.554530i	0.0326972	+	0.999465i	$0.489590\pi$
$32$	−11763.9	−	25759.3i	−0.359005	−	0.786111i
$33$	−7397.94	−	25195.1i	−0.205859	−	0.701090i
$34$	−17702.8	−	15339.5i	−0.450406	−	0.390279i
$35$	19348.4	−	22329.2i	0.451274	−	0.520798i
$36$	7229.06	−	2122.64i	0.154944	−	0.0454956i
$37$	263.159	−	120.181i	0.00519532	−	0.00237263i	−0.412816	−	0.910815i	$-0.635455\pi$
$37$	263.159	−	120.181i	0.00519532	−	0.00237263i	0.418011	+	0.908442i	$0.362727\pi$
$38$	36340.3	+	56546.6i	0.662274	+	1.03052i
$39$	39787.3	+	11682.6i	0.670735	+	0.196946i
$40$	102458.	−	14731.3i	1.60091	−	0.230176i
$41$	30308.7	−	66366.7i	0.439759	−	0.962939i	−0.551883	−	0.833921i	$-0.686091\pi$
$41$	30308.7	−	66366.7i	0.439759	−	0.962939i	0.991642	−	0.129017i	$-0.0411822\pi$
$42$	13805.7	+	1984.96i	0.186342	+	0.0267919i
$43$	2580.99	−	4016.10i	0.0324624	−	0.0505125i	−0.824643	−	0.565653i	$-0.808624\pi$
$43$	2580.99	−	4016.10i	0.0324624	−	0.0505125i	0.857106	+	0.515141i	$0.172260\pi$
$44$	−39471.4	+	34202.1i	−0.463366	+	0.401509i
$45$			46092.1i			0.505812i
$46$	−67706.4	−	17328.4i	−0.695594	−	0.178026i
$47$	−78549.2			−0.756568			−0.378284	−	0.925690i	$-0.623486\pi$
$47$	−78549.2			−0.756568			−0.378284	+	0.925690i	$0.623486\pi$
$48$	11743.1	+	13552.3i	0.106184	+	0.122543i
$49$	78561.0	+	50488.1i	0.667758	+	0.429142i
$50$	−16638.3	+	115722.i	−0.133106	+	0.925773i
$51$	−57824.1	−	26407.4i	−0.435912	−	0.199074i
$52$	−11737.7	−	81637.7i	−0.0834784	−	0.580605i
$53$	31846.1	−	108458.i	0.213909	−	0.728507i	−0.780709	−	0.624895i	$-0.785142\pi$
$53$	31846.1	−	108458.i	0.213909	−	0.728507i	0.994618	−	0.103612i	$-0.0330400\pi$
$54$	−18304.6	+	11763.6i	−0.116246	+	0.0747068i
$55$	−132731.	−	290641.i	−0.797783	−	1.74690i
$56$	−23948.7	−	81561.9i	−0.136370	−	0.464433i
$57$	137860.	+	119456.i	0.744412	+	0.645037i
$58$	−159165.	+	183687.i	−0.815764	+	0.941442i
$59$	−302501.	+	88822.3i	−1.47289	+	0.432480i	−0.917038	−	0.398800i	$-0.869427\pi$
$59$	−302501.	+	88822.3i	−1.47289	+	0.432480i	−0.555854	+	0.831280i	$0.687609\pi$
$60$	83391.7	−	38083.7i	0.386073	−	0.176313i
$61$	−147029.	−	228782.i	−0.647759	−	1.00793i	−0.997471	−	0.0710756i	$-0.977357\pi$
$61$	−147029.	−	228782.i	−0.647759	−	1.00793i	0.349712	−	0.936857i	$-0.386280\pi$
$62$	−168409.	−	49449.4i	−0.706628	−	0.207485i
$63$	37466.1	−	5386.81i	0.149836	−	0.0215432i
$64$	98156.9	−	214934.i	0.374439	−	0.819907i
$65$	499433.	+	71807.6i	1.81860	+	0.261475i
$66$	81546.6	−	126889.i	0.283644	−	0.441359i
$67$	−371235.	+	321677.i	−1.23431	+	1.06954i	−0.239180	+	0.970975i	$0.576879\pi$
$67$	−371235.	+	321677.i	−1.23431	+	1.06954i	−0.995131	+	0.0985614i	$0.968576\pi$
$68$			126437.i			0.402112i
$69$	−189548.	+	6645.09i	−0.576996	+	0.0202280i
$70$	169714.			0.494794
$71$	−347163.	−	400647.i	−0.969970	−	1.11940i	−0.992814	−	0.119666i	$-0.961818\pi$
$71$	−347163.	−	400647.i	−0.969970	−	1.11940i	0.0228445	−	0.999739i	$-0.492728\pi$
$72$	111559.	+	71694.4i	0.298886	+	0.192083i
$73$	18276.5	−	127116.i	0.0469811	−	0.326761i	−0.952754	−	0.303743i	$-0.901763\pi$
$73$	18276.5	−	127116.i	0.0469811	−	0.326761i	0.999735	−	0.0230178i	$-0.00732743\pi$
$74$	1511.61	+	690.331i	0.00373032	+	0.00170358i
$75$	45153.1	+	314047.i	0.107030	+	0.744408i
$76$	102218.	−	348123.i	0.232856	−	0.793033i
$77$	−220736.	+	141858.i	−0.483504	+	0.310729i
$78$	98948.3	+	216667.i	0.208509	+	0.456571i
$79$	−66572.3	−	226724.i	−0.135024	−	0.459851i	0.864025	−	0.503449i	$-0.167936\pi$
$79$	−66572.3	−	226724.i	−0.135024	−	0.459851i	−0.999049	+	0.0435985i	$0.986118\pi$
$80$	164903.	+	142889.i	0.322076	+	0.279081i
$81$	−38668.9	+	44626.3i	−0.0727623	+	0.0839722i
$82$	402114.	−	118071.i	0.729303	−	0.214143i
$83$	90831.3	−	41481.3i	0.158855	−	0.0725467i	−0.334401	−	0.942431i	$-0.608534\pi$
$83$	90831.3	−	41481.3i	0.158855	−	0.0725467i	0.493256	+	0.869884i	$0.335807\pi$
$84$	−40702.5	−	63334.3i	−0.0686725	−	0.106857i
$85$	−742168.	−	217920.i	−1.20850	−	0.354847i
$86$	27143.0	−	3902.57i	0.0426739	−	0.00613557i
$87$	−274007.	+	599992.i	−0.416106	+	0.911145i
$88$	−909909.	−	130825.i	−1.33521	−	0.191974i
$89$	−156195.	+	243044.i	−0.221563	+	0.344759i	−0.934185	−	0.356790i	$-0.883871\pi$
$89$	−156195.	+	243044.i	−0.221563	+	0.344759i	0.712622	+	0.701548i	$0.247508\pi$
$90$	−200091.	+	173380.i	−0.274473	+	0.237832i
$91$		−	414357.i		−	0.549858i
$92$	168637.	+	337448.i	0.216566	+	0.433355i
$93$	−476326.			−0.592182
$94$	−295470.	−	340991.i	−0.355738	−	0.410543i
$95$	1.86726e6	+	1.20001e6i	2.17788	+	1.39964i
$96$	62823.4	−	436946.i	0.0710081	−	0.493872i
$97$	−657396.	−	300223.i	−0.720298	−	0.328949i	0.0213190	−	0.999773i	$-0.493213\pi$
$97$	−657396.	−	300223.i	−0.720298	−	0.328949i	−0.741617	+	0.670824i	$0.765941\pi$
$98$	76340.3	+	530958.i	0.0811102	+	0.564134i
$99$	115322.	−	392752.i	0.118853	−	0.404774i
$100$	530879.	−	341175.i	0.530879	−	0.341175i
$101$	753007.	+	1.64886e6i	0.730862	+	1.60036i	0.798027	+	0.602622i	$0.205877\pi$
$101$	753007.	+	1.64886e6i	0.730862	+	1.60036i	−0.0671656	+	0.997742i	$0.521396\pi$
$102$	−102873.	−	350355.i	−0.0969400	−	0.330147i
$103$	944007.	+	817987.i	0.863900	+	0.748574i	0.969306	−	0.245856i	$-0.0790689\pi$
$103$	944007.	+	817987.i	0.863900	+	0.748574i	−0.105406	+	0.994429i	$0.533614\pi$
$104$	950647.	−	1.09711e6i	0.845122	−	0.975322i
$105$	441917.	−	129758.i	0.381744	−	0.112090i
$106$	590620.	−	269727.i	0.495896	−	0.226468i
$107$	349282.	+	543493.i	0.285118	+	0.443652i	0.954040	−	0.299681i	$-0.0968802\pi$
$107$	349282.	+	543493.i	0.285118	+	0.443652i	−0.668922	+	0.743333i	$0.733244\pi$
$108$	112690.	+	33088.7i	0.0894569	+	0.0262669i
$109$	1.29063e6	−	185564.i	0.996601	−	0.143290i	0.375335	−	0.926889i	$-0.377528\pi$
$109$	1.29063e6	−	185564.i	0.996601	−	0.143290i	0.621266	+	0.783600i	$0.286619\pi$
$110$	762423.	−	1.66947e6i	0.572820	−	1.25430i
$111$	4463.88	+	641.809i	0.00326395	+	0.000469285i
$112$	96875.7	−	150741.i	0.0689542	−	0.107295i
$113$	−298036.	+	258249.i	−0.206554	+	0.178980i	−0.751994	−	0.659170i	$-0.770908\pi$
$113$	−298036.	+	258249.i	−0.206554	+	0.178980i	0.545440	+	0.838150i	$0.316362\pi$
$114$			1.04781e6i			0.707243i
$115$	−2.27143e6	+	408271.i	−1.49350	+	0.268445i
$116$	1.31193e6			0.840497
$117$	423307.	+	488522.i	0.264300	+	0.305019i
$118$	−1.52347e6	−	979078.i	−0.927234	−	0.595897i
$119$	−90399.4	+	628741.i	−0.0536444	+	0.373105i
$120$	1.46777e6	+	670310.i	0.849407	+	0.387911i
$121$	151704.	+	1.05512e6i	0.0856329	+	0.595590i
$122$	440103.	−	1.49885e6i	0.242368	−	0.825429i
$123$	956785.	−	614889.i	0.514161	−	0.330431i
$124$	393566.	+	861789.i	0.206420	+	0.451997i
$125$	252674.	+	860530.i	0.129369	+	0.440591i
$126$	164317.	+	142381.i	0.0821430	+	0.0711773i
$127$	2.14038e6	−	2.47013e6i	1.04491	−	1.20589i	0.0668087	−	0.997766i	$-0.478718\pi$
$127$	2.14038e6	−	2.47013e6i	1.04491	−	1.20589i	0.978102	−	0.208126i	$-0.0667363\pi$
$128$	−436683.	+	128222.i	−0.208227	+	0.0611409i
$129$	67693.4	−	30914.5i	0.0315338	−	0.0144010i
$130$	1.56694e6	+	2.43821e6i	0.713218	+	1.10979i
$131$	−4.03448e6	−	1.18463e6i	−1.79463	−	0.526950i	−0.797541	−	0.603264i	$-0.793866\pi$
$131$	−4.03448e6	−	1.18463e6i	−1.79463	−	0.526950i	−0.997084	+	0.0763146i	$0.975685\pi$
$132$	−805869.	+	115866.i	−0.350383	+	0.0503774i
$133$	757206.	−	1.65805e6i	0.321854	−	0.704762i
$134$	−2.79287e6	−	401554.i	−1.16074	−	0.166890i
$135$	−388453.	+	604445.i	−0.157884	+	0.245672i
$136$	−1.68185e6	+	1.45733e6i	−0.668608	+	0.579352i
$137$			1.46012e6i			0.567840i	0.958848	+	0.283920i	$0.0916350\pi$
$137$			1.46012e6i			0.567840i	−0.958848	+	0.283920i	$0.908365\pi$
$138$	−741851.	−	797854.i	−0.282280	−	0.303589i
$139$	−1.20336e6			−0.448074			−0.224037	−	0.974581i	$-0.571924\pi$
$139$	−1.20336e6			−0.448074			−0.224037	+	0.974581i	$0.571924\pi$
$140$	−599899.	−	692320.i	−0.218622	−	0.252303i
$141$	−1.03008e6	−	661993.i	−0.367464	−	0.236155i
$142$	433369.	−	3.01415e6i	0.151354	−	1.05269i
$143$	−4.07602e6	−	1.86146e6i	−1.39389	−	0.636568i
$144$	39782.1	+	276690.i	0.0133229	+	0.0926630i
$145$	−2.26117e6	+	7.70084e6i	−0.741702	+	2.52601i
$146$	620572.	−	398817.i	0.199404	−	0.128149i
$147$	604736.	+	1.32419e6i	0.190377	+	0.416867i
$148$	−2527.10	−	8606.52i	−0.000779539	−	0.00265487i
$149$	−184768.	−	160103.i	−0.0558559	−	0.0483994i	0.626486	−	0.779433i	$-0.284493\pi$
$149$	−184768.	−	160103.i	−0.0558559	−	0.0483994i	−0.682341	+	0.731034i	$0.739038\pi$
$150$	−1.19347e6	+	1.37733e6i	−0.353619	+	0.408099i
$151$	2.11938e6	−	622307.i	0.615572	−	0.180748i	0.0409418	−	0.999162i	$-0.486964\pi$
$151$	2.11938e6	−	622307.i	0.615572	−	0.180748i	0.574630	+	0.818413i	$0.305146\pi$
$152$	5.80888e6	−	2.65283e6i	1.65410	−	0.755403i
$153$	−535741.	−	833630.i	−0.149583	−	0.232755i
$154$	−1.44614e6	−	424625.i	−0.395957	−	0.116264i
$155$	−5.73691e6	+	824844.i	−1.54058	+	0.221501i
$156$	534096.	−	1.16951e6i	0.140684	−	0.308055i
$157$	−2.43616e6	−	350267.i	−0.629515	−	0.0905107i	−0.179830	−	0.983698i	$-0.557555\pi$
$157$	−2.43616e6	−	350267.i	−0.629515	−	0.0905107i	−0.449685	+	0.893187i	$0.648464\pi$
$158$	733818.	−	1.14184e6i	0.186045	−	0.289491i
$159$	1.33168e6	−	1.15391e6i	0.331291	−	0.287065i
$160$		−	5.37141e6i		−	1.31138i
$161$	597327.	+	1.79862e6i	0.143131	+	0.430985i
$162$	−339184.			−0.0797794
$163$	1.00536e6	+	1.16025e6i	0.232146	+	0.267910i	0.859856	−	0.510537i	$-0.170553\pi$
$163$	1.00536e6	+	1.16025e6i	0.232146	+	0.267910i	−0.627710	+	0.778447i	$0.716008\pi$
$164$	−1.90303e6	−	1.22300e6i	−0.431433	−	0.277265i
$165$	708833.	−	4.93005e6i	0.157795	−	1.09749i
$166$	521745.	+	238273.i	0.114060	+	0.0520896i
$167$	618873.	+	4.30436e6i	0.132878	+	0.924185i	0.941777	+	0.336238i	$0.109155\pi$
$167$	618873.	+	4.30436e6i	0.132878	+	0.924185i	−0.808899	+	0.587947i	$0.799936\pi$
$168$	373324.	−	1.27142e6i	0.0787332	−	0.268140i
$169$	1.89231e6	−	1.21611e6i	0.392041	−	0.251950i
$170$	−1.84572e6	−	4.04156e6i	−0.375681	−	0.822626i
$171$	801125.	+	2.72838e6i	0.160218	+	0.545653i
$172$	−111864.	−	96930.4i	−0.0219838	−	0.0190491i
$173$	−4.47207e6	+	5.16105e6i	−0.863715	+	0.996781i	0.136266	+	0.990672i	$0.456490\pi$
$173$	−4.47207e6	+	5.16105e6i	−0.863715	+	0.996781i	−0.999981	+	0.00610841i	$0.998056\pi$
$174$	−3.63533e6	+	1.06743e6i	−0.690076	+	0.202624i
$175$	2.88387e6	−	1.31702e6i	0.538098	−	0.245741i
$176$	−1.04764e6	−	1.63015e6i	−0.192164	−	0.299013i
$177$	−4.71553e6	−	1.38460e6i	−0.850375	−	0.249693i
$178$	−1.64262e6	+	236174.i	−0.291258	+	0.0418766i
$179$	−165644.	+	362711.i	−0.0288814	+	0.0632413i	−0.923523	−	0.383543i	$-0.874704\pi$
$179$	−165644.	+	362711.i	−0.0288814	+	0.0632413i	0.894642	+	0.446785i	$0.147431\pi$
$180$	1.41455e6	+	203381.i	0.242549	+	0.0348733i
$181$	2.90134e6	−	4.51458e6i	0.489286	−	0.761344i	−0.505554	−	0.862795i	$-0.668712\pi$
$181$	2.90134e6	−	4.51458e6i	0.489286	−	0.761344i	0.994841	+	0.101450i	$0.0323483\pi$
$182$	1.79877e6	−	1.55864e6i	0.298375	−	0.258543i
$183$		−	4.23933e6i		−	0.691742i
$184$	−2.54496e6	+	6.13269e6i	−0.408534	+	0.984458i
$185$	54874.7			0.00866677
$186$	−1.79175e6	−	2.06779e6i	−0.278444	−	0.321341i
$187$	5.77880e6	+	3.71381e6i	0.883716	+	0.567930i
$188$	−346598.	+	2.41064e6i	−0.0521617	+	0.362793i
$189$	536723.	+	245113.i	0.0794996	+	0.0363062i
$190$	1.81447e6	+	1.26199e7i	0.264539	+	1.83991i
$191$	2.79545e6	−	9.52044e6i	0.401192	−	1.36633i	−0.473132	−	0.880992i	$-0.656877\pi$
$191$	2.79545e6	−	9.52044e6i	0.401192	−	1.36633i	0.874324	−	0.485343i	$-0.161305\pi$
$192$	3.09862e6	−	1.99136e6i	0.437789	−	0.281350i
$193$	−209014.	−	457677.i	−0.0290739	−	0.0636630i	0.894538	−	0.446992i	$-0.147505\pi$
$193$	−209014.	−	457677.i	−0.0290739	−	0.0636630i	−0.923612	+	0.383329i	$0.874778\pi$
$194$	−1.16956e6	−	3.98315e6i	−0.160183	−	0.545533i
$195$	5.94431e6	+	5.15077e6i	0.801673	+	0.694654i
$196$	1.89611e6	−	2.18822e6i	0.251823	−	0.290619i
$197$	3.71255e6	−	1.09010e6i	0.485594	−	0.142583i	−0.0297661	−	0.999557i	$-0.509476\pi$
$197$	3.71255e6	−	1.09010e6i	0.485594	−	0.142583i	0.515360	+	0.856974i	$0.327658\pi$
$198$	2.13878e6	−	976747.i	0.275531	−	0.125831i
$199$	3.93723e6	+	6.12645e6i	0.499610	+	0.777409i	0.995872	−	0.0907641i	$-0.0289309\pi$
$199$	3.93723e6	+	6.12645e6i	0.499610	+	0.777409i	−0.496262	+	0.868173i	$0.665295\pi$
$200$	1.06573e7	+	3.12926e6i	1.33216	+	0.391158i
$201$	−7.57934e6	+	1.08974e6i	−0.933347	+	0.134195i
$202$	−4.32536e6	+	9.47122e6i	−0.524769	+	1.14908i
$203$	6.52391e6	+	937997.i	0.779866	+	0.112128i
$204$	−1.06558e6	+	1.65807e6i	−0.125515	+	0.195305i
$205$	1.04588e7	−	9.06262e6i	1.21401	−	1.05194i
$206$			7.17497e6i			0.820765i
$207$	−2.54171e6	−	1.51032e6i	−0.286560	−	0.170278i
$208$	3.06007e6			0.340048
$209$	−1.29085e7	−	1.48972e7i	−1.41396	−	1.63180i
$210$	2.22561e6	+	1.43031e6i	0.240320	+	0.154445i
$211$	−1.12616e6	+	7.83261e6i	−0.119882	+	0.833795i	0.837803	+	0.545973i	$0.183840\pi$
$211$	−1.12616e6	+	7.83261e6i	−0.119882	+	0.833795i	−0.957684	+	0.287821i	$0.907069\pi$
$212$	−3.18800e6	−	1.45591e6i	−0.334589	−	0.152802i
$213$	−1.17608e6	−	8.17983e6i	−0.121702	−	0.846458i
$214$	−1.04551e6	+	3.56067e6i	−0.106681	+	0.363321i
$215$	761771.	−	489560.i	0.0766494	−	0.0492596i
$216$	858740.	+	1.88038e6i	0.0852120	+	0.186588i
$217$	1.34095e6	+	4.56686e6i	0.131230	+	0.446929i
$218$	5.66037e6	+	4.90474e6i	0.546356	+	0.473420i
$219$	1.31097e6	−	1.51294e6i	0.124814	−	0.144043i
$220$	−9.50531e6	+	2.79101e6i	−0.892685	+	0.262116i
$221$	−9.86747e6	+	4.50632e6i	−0.914174	+	0.417489i
$222$	14005.1	+	21792.4i	0.00128005	+	0.00199180i
$223$	−97063.3	−	28500.4i	−0.00875267	−	0.00257002i	0.277353	−	0.960768i	$-0.410543\pi$
$223$	−97063.3	−	28500.4i	−0.00875267	−	0.00257002i	−0.286106	+	0.958198i	$0.592361\pi$
$224$	−4.36616e6	+	627759.i	−0.388469	+	0.0558534i
$225$	−2.05458e6	+	4.49890e6i	−0.180375	+	0.394965i
$226$	−2.24218e6	−	322377.i	−0.194243	−	0.0279279i
$227$	8.06682e6	−	1.25522e7i	0.689644	−	1.07311i	−0.303112	−	0.952955i	$-0.598026\pi$
$227$	8.06682e6	−	1.25522e7i	0.689644	−	1.07311i	0.992756	−	0.120151i	$-0.0383380\pi$
$228$	4.27436e6	−	3.70376e6i	0.360634	−	0.312491i
$229$		−	7.64318e6i		−	0.636455i	−0.948014	−	0.318228i	$-0.896912\pi$
$229$		−	7.64318e6i		−	0.636455i	0.948014	−	0.318228i	$-0.103088\pi$
$230$	−1.03165e7	−	8.32478e6i	−0.847912	−	0.684210i
$231$	−4.09024e6			−0.331828
$232$	1.51215e7	+	1.74512e7i	1.21096	+	1.39753i
$233$	1.47784e7	+	9.49753e6i	1.16832	+	0.750832i	0.973203	−	0.229948i	$-0.0738557\pi$
$233$	1.47784e7	+	9.49753e6i	1.16832	+	0.750832i	0.195115	+	0.980780i	$0.437492\pi$
$234$	−528420.	+	3.67525e6i	−0.0412413	+	0.286839i
$235$	−1.35528e7	−	6.18934e6i	−1.04430	−	0.476914i
$236$	1.39113e6	+	9.67555e6i	0.105836	+	0.736105i
$237$	1.03776e6	−	3.53428e6i	0.0779564	−	0.265495i
$238$	−3.06948e6	+	1.97264e6i	−0.227685	+	0.146324i
$239$	−3.10442e6	−	6.79774e6i	−0.227398	−	0.497933i	0.761199	−	0.648519i	$-0.224611\pi$
$239$	−3.10442e6	−	6.79774e6i	−0.227398	−	0.497933i	−0.988597	+	0.150586i	$0.951884\pi$
$240$	958277.	+	3.26359e6i	0.0693198	+	0.236082i
$241$	−1.14145e7	−	9.89068e6i	−0.815463	−	0.706603i	0.143649	−	0.989629i	$-0.454116\pi$
$241$	−1.14145e7	−	9.89068e6i	−0.815463	−	0.706603i	−0.959112	+	0.283026i	$0.908662\pi$
$242$	−4.00976e6	+	4.62751e6i	−0.282926	+	0.326514i
$243$	−883197.	+	259330.i	−0.0615515	+	0.0180732i
$244$	−7.66997e6	+	3.50276e6i	−0.527988	+	0.241124i
$245$	9.57656e6	+	1.49014e7i	0.651195	+	1.01328i
$246$	6.26834e6	+	1.84055e6i	0.421063	+	0.123635i
$247$	3.08116e7	−	4.43003e6i	2.04467	−	0.293979i
$248$	−6.92714e6	+	1.51683e7i	−0.454149	+	0.994448i
$249$	1.54074e6	+	221525.i	0.0998003	+	0.0143491i
$250$	−2.78520e6	+	4.33385e6i	−0.178253	+	0.277367i
$251$	4.45875e6	−	3.86353e6i	0.281963	−	0.244322i	−0.502384	−	0.864645i	$-0.667544\pi$
$251$	4.45875e6	−	3.86353e6i	0.281963	−	0.244322i	0.784347	+	0.620322i	$0.212998\pi$
$252$		−	1.17359e6i		−	0.0733354i
$253$	2.03764e7	+	2.20423e6i	1.25825	+	0.136112i
$254$	1.87743e7			1.14568
$255$	−7.89610e6	−	9.11258e6i	−0.476203	−	0.549567i
$256$	−1.49210e7	−	9.58912e6i	−0.889359	−	0.571556i
$257$	−2.07594e6	+	1.44385e7i	−0.122297	+	0.850595i	0.832646	+	0.553806i	$0.186825\pi$
$257$	−2.07594e6	+	1.44385e7i	−0.122297	+	0.850595i	−0.954943	+	0.296789i	$0.904084\pi$
$258$	388838.	+	177577.i	0.0226418	+	0.0103401i
$259$	−6413.24	−	44605.1i	−0.000369129	−	0.00256735i
$260$	4.40749e6	−	1.50105e7i	0.250767	−	0.854035i
$261$	−8.64987e6	+	5.55893e6i	−0.486506	+	0.312658i
$262$	−1.00335e7	−	2.19702e7i	−0.557888	−	1.22161i
$263$	−1.19180e6	−	4.05891e6i	−0.0655145	−	0.223122i	0.920228	−	0.391383i	$-0.128003\pi$
$263$	−1.19180e6	−	4.05891e6i	−0.0655145	−	0.223122i	−0.985743	+	0.168261i	$0.946185\pi$
$264$	−1.08298e7	−	9.38411e6i	−0.588586	−	0.510013i
$265$	1.40407e7	−	1.62038e7i	0.754486	−	0.870723i
$266$	1.00461e7	−	2.94980e6i	0.533767	−	0.156728i
$267$	−4.09663e6	+	1.87087e6i	−0.215225	+	0.0982901i
$268$	8.23405e6	+	1.28124e7i	0.427769	+	0.665622i
$269$	1.63603e7	+	4.80382e6i	0.840495	+	0.246792i	0.673519	−	0.739170i	$-0.264782\pi$
$269$	1.63603e7	+	4.80382e6i	0.840495	+	0.246792i	0.166975	+	0.985961i	$0.446600\pi$
$270$	−4.08517e6	+	587358.i	−0.207548	+	0.0298409i
$271$	−3.15175e6	+	6.90138e6i	−0.158360	+	0.346759i	−0.972136	−	0.234420i	$-0.924681\pi$
$271$	−3.15175e6	+	6.90138e6i	−0.158360	+	0.346759i	0.813776	+	0.581179i	$0.197408\pi$
$272$	−4.64331e6	−	667607.i	−0.230739	−	0.0331753i
$273$	3.49210e6	−	5.43382e6i	0.171632	−	0.267065i
$274$	−6.33853e6	+	5.49237e6i	−0.308132	+	0.266998i
$275$		−	3.42851e7i		−	1.64857i
$276$	−632445.	+	5.84647e6i	−0.0300812	+	0.278078i
$277$	−3.09242e7			−1.45499			−0.727493	−	0.686116i	$-0.759314\pi$
$277$	−3.09242e7			−1.45499			−0.727493	+	0.686116i	$0.759314\pi$
$278$	−4.52654e6	−	5.22390e6i	−0.210684	−	0.243142i
$279$	−6.24647e6	−	4.01436e6i	−0.287622	−	0.184843i
$280$	2.29465e6	−	1.59596e7i	0.104530	−	0.727023i
$281$	2.45134e7	+	1.11949e7i	1.10480	+	0.504545i	0.882443	−	0.470420i	$-0.155897\pi$
$281$	2.45134e7	+	1.11949e7i	1.10480	+	0.504545i	0.222358	+	0.974965i	$0.428625\pi$
$282$	−1.00096e6	−	6.96185e6i	−0.0446345	−	0.310440i
$283$	1.90063e6	−	6.47294e6i	0.0838566	−	0.285589i	−0.906880	−	0.421390i	$-0.861542\pi$
$283$	1.90063e6	−	6.47294e6i	0.0838566	−	0.285589i	0.990736	+	0.135800i	$0.0433606\pi$
$284$	−1.38275e7	+	8.88642e6i	−0.603657	+	0.387947i
$285$	1.43735e7	+	3.14736e7i	0.620909	+	1.35960i
$286$	−7.25155e6	−	2.46965e7i	−0.309979	−	1.05569i
$287$	−8.58890e6	−	7.44232e6i	−0.363322	−	0.314820i
$288$	4.50633e6	−	5.20059e6i	0.188645	−	0.217708i
$289$	−7.20390e6	+	2.11526e6i	−0.298452	+	0.0876334i
$290$	−4.19358e7	+	1.91515e7i	−1.71946	+	0.785250i
$291$	−6.09079e6	−	9.47745e6i	−0.247169	−	0.384603i
$292$	−3.82048e6	−	1.12179e6i	−0.153451	−	0.0450572i
$293$	−6.20737e6	+	892485.i	−0.246777	+	0.0354812i	−0.264593	−	0.964360i	$-0.585238\pi$
$293$	−6.20737e6	+	892485.i	−0.246777	+	0.0354812i	0.0178162	+	0.999841i	$0.494329\pi$
$294$	−3.47367e6	+	7.60628e6i	−0.136693	+	0.299316i
$295$	−5.91919e7	−	8.51051e6i	−2.30567	−	0.331505i
$296$	85355.4	−	132816.i	0.00329121	−	0.00512123i
$297$	4.82234e6	−	4.17858e6i	0.184072	−	0.159500i
$298$		−	1.40434e6i		−	0.0530669i
$299$	−2.03250e7	+	2.51879e7i	−0.760354	+	0.942275i
$300$	9.83720e6			0.364341
$301$	−486969.	−	561992.i	−0.0178567	−	0.0206078i
$302$	1.06738e7	+	6.85961e6i	0.387522	+	0.249046i
$303$	−4.02134e6	+	2.79690e7i	−0.144558	+	1.00542i
$304$	1.22448e7	+	5.59203e6i	0.435845	+	0.199044i
$305$	−7.34116e6	−	5.10589e7i	−0.258741	−	1.79958i
$306$	1.60364e6	−	5.46149e6i	0.0559683	−	0.190611i
$307$	−2.89794e7	+	1.86239e7i	−1.00155	+	0.643659i	−0.935193	−	0.354137i	$-0.884775\pi$
$307$	−2.89794e7	+	1.86239e7i	−1.00155	+	0.643659i	−0.0663589	+	0.997796i	$0.521138\pi$
$308$	3.37957e6	+	7.40023e6i	0.115667	+	0.253275i
$309$	5.48577e6	+	1.86828e7i	0.185935	+	0.633238i
$310$	−2.51607e7	−	2.18019e7i	−0.844574	−	0.731827i
$311$	3.58808e6	−	4.14086e6i	0.119284	−	0.137661i	−0.692967	−	0.720969i	$-0.743697\pi$
$311$	3.58808e6	−	4.14086e6i	0.119284	−	0.137661i	0.812250	+	0.583309i	$0.198242\pi$
$312$	2.17128e7	−	6.37544e6i	0.714910	−	0.209917i
$313$	4.57676e7	−	2.09014e7i	1.49254	−	0.681619i	0.508743	−	0.860918i	$-0.330110\pi$
$313$	4.57676e7	−	2.09014e7i	1.49254	−	0.681619i	0.983795	+	0.179299i	$0.0573830\pi$
$314$	−7.64329e6	−	1.18932e7i	−0.246883	−	0.384158i
$315$	6.88880e6	+	2.02273e6i	0.220400	+	0.0647153i
$316$	−7.25182e6	+	1.04265e6i	−0.229819	+	0.0330430i
$317$	−1.80135e7	+	3.94440e7i	−0.565483	+	1.23823i	0.383685	+	0.923464i	$0.374655\pi$
$317$	−1.80135e7	+	3.94440e7i	−0.565483	+	1.23823i	−0.949168	+	0.314771i	$0.898072\pi$
$318$	1.00185e7	+	1.44044e6i	0.311545	+	0.0447934i
$319$	3.85350e7	−	5.99617e7i	1.18709	−	1.84715i
$320$	3.38717e7	−	2.93500e7i	1.03368	−	0.895691i
$321$			1.00709e7i			0.304477i
$322$	−5.56112e6	+	9.35875e6i	−0.166569	+	0.280318i
$323$	−4.77196e7			−1.41608
$324$	1.19893e6	+	1.38364e6i	0.0352501	+	0.0406808i
$325$	4.55472e7	+	2.92714e7i	1.32682	+	0.852694i
$326$	−1.25501e6	+	8.72879e6i	−0.0362239	+	0.251942i
$327$	1.84890e7	+	8.44363e6i	0.528773	+	0.241483i
$328$	−5.66637e6	−	3.94105e7i	−0.160577	−	1.11684i
$329$	−3.44710e6	+	1.17397e7i	−0.0967979	+	0.329663i
$330$	2.40682e7	−	1.54677e7i	0.669734	−	0.430412i
$331$	2.71779e7	+	5.95112e7i	0.749431	+	1.64102i	0.767386	+	0.641185i	$0.221557\pi$
$331$	2.71779e7	+	5.95112e7i	0.749431	+	1.64102i	−0.0179553	+	0.999839i	$0.505716\pi$
$332$	−872249.	−	2.97061e6i	−0.0238356	−	0.0811766i
$333$	53129.6	+	46037.0i	0.00143881	+	0.00124674i
$334$	−1.63577e7	+	1.88778e7i	−0.439020	+	0.506656i
$335$	−8.93991e7	+	2.62499e7i	−2.37793	+	0.698223i
$336$	2.54082e6	−	1.16036e6i	0.0669818	−	0.0305896i
$337$	2.25445e6	+	3.50800e6i	0.0589049	+	0.0916579i	0.869457	−	0.494009i	$-0.164469\pi$
$337$	2.25445e6	+	3.50800e6i	0.0589049	+	0.0916579i	−0.810552	+	0.585667i	$0.800833\pi$
$338$	1.23974e7	+	3.64020e6i	0.321055	+	0.0942703i
$339$	−6.08486e6	+	874870.i	−0.156189	+	0.0224566i
$340$	−9.96268e6	+	2.18152e7i	−0.253478	+	0.555038i
$341$	5.09482e7	+	7.32524e6i	1.28489	+	0.184739i
$342$	−8.83070e6	+	1.37408e7i	−0.220758	+	0.343506i
$343$	2.48432e7	−	2.15267e7i	0.615637	−	0.533452i
$344$		−	2.60524e6i		−	0.0639989i
$345$	−3.32280e7	−	1.37891e7i	−0.809183	−	0.335797i
$346$	−3.92268e7			−0.947011
$347$	2.26830e7	+	2.61776e7i	0.542891	+	0.626529i	0.959212	−	0.282688i	$-0.0912262\pi$
$347$	2.26830e7	+	2.61776e7i	0.542891	+	0.626529i	−0.416321	+	0.909218i	$0.636681\pi$
$348$	1.72044e7	+	1.10566e7i	0.408228	+	0.262352i
$349$	−2.13070e6	+	1.48193e7i	−0.0501239	+	0.348620i	0.949290	+	0.314401i	$0.101803\pi$
$349$	−2.13070e6	+	1.48193e7i	−0.0501239	+	0.348620i	−0.999414	+	0.0342191i	$0.989106\pi$
$350$	1.65653e7	+	7.56511e6i	0.386362	+	0.176446i
$351$	1.43403e6	+	9.97393e6i	0.0331618	+	0.230645i
$352$	−1.34393e7	+	4.57700e7i	−0.308140	+	1.04943i
$353$	5.49561e7	−	3.53182e7i	1.24937	−	0.802923i	0.262580	−	0.964910i	$-0.415427\pi$
$353$	5.49561e7	−	3.53182e7i	1.24937	−	0.802923i	0.986793	+	0.161987i	$0.0517902\pi$
$354$	−1.17272e7	−	2.56789e7i	−0.264353	−	0.578852i
$355$	−2.83297e7	−	9.64820e7i	−0.633223	−	2.15656i
$356$	6.76971e6	+	5.86598e6i	0.150044	+	0.130014i
$357$	−6.48436e6	+	7.48335e6i	−0.142516	+	0.164472i
$358$	−2.19765e6	+	645290.i	−0.0478972	+	0.0140639i
$359$	−6.30676e6	+	2.88020e6i	−0.136309	+	0.0622500i	−0.482402	−	0.875950i	$-0.660235\pi$
$359$	−6.30676e6	+	2.88020e6i	−0.136309	+	0.0622500i	0.346093	+	0.938200i	$0.387508\pi$
$360$	1.35990e7	+	2.11604e7i	0.291473	+	0.453541i
$361$	8.62477e7	+	2.53246e7i	1.83327	+	0.538296i
$362$	3.05120e7	−	4.38696e6i	0.643197	−	0.0924778i
$363$	−6.90291e6	+	1.51153e7i	−0.144315	+	0.316006i
$364$	−1.27164e7	−	1.82835e6i	−0.263671	−	0.0379101i
$365$	1.31696e7	−	2.04922e7i	0.270827	−	0.421416i
$366$	1.84034e7	−	1.59467e7i	0.375366	−	0.325257i
$367$		−	8.58677e7i		−	1.73713i	−0.495578	−	0.868563i	$-0.665044\pi$
$367$		−	8.58677e7i		−	1.73713i	0.495578	−	0.868563i	$-0.334956\pi$
$368$	−1.32830e7	+	4.41131e6i	−0.266534	+	0.0885165i
$369$	1.77293e7			0.352867
$370$	206417.	+	238217.i	0.00407511	+	0.00470293i
$371$	−1.48123e7	−	9.51926e6i	−0.290068	−	0.186415i
$372$	−2.10179e6	+	1.46182e7i	−0.0408281	+	0.283966i
$373$	−8.15796e6	−	3.72562e6i	−0.157201	−	0.0717913i	0.335261	−	0.942125i	$-0.391176\pi$
$373$	−8.15796e6	−	3.72562e6i	−0.157201	−	0.0717913i	−0.492462	+	0.870334i	$0.663903\pi$
$374$	5.61544e6	+	3.90563e7i	0.107342	+	0.746579i
$375$	−3.93881e6	+	1.34143e7i	−0.0746914	+	0.254376i
$376$	−3.60611e7	+	2.31751e7i	−0.678383	+	0.435971i
$377$	4.67583e7	+	1.02386e8i	0.872639	+	1.91081i
$378$	954871.	+	3.25199e6i	0.0176795	+	0.0602107i
$379$	−4.08791e6	−	3.54220e6i	−0.0750903	−	0.0650661i	0.616507	−	0.787349i	$-0.288547\pi$
$379$	−4.08791e6	−	3.54220e6i	−0.0750903	−	0.0650661i	−0.691597	+	0.722283i	$0.743093\pi$
$380$	4.50671e7	−	5.20102e7i	0.821313	−	0.947846i
$381$	4.88862e7	−	1.43543e7i	0.883917	−	0.259541i
$382$	5.18447e7	−	2.36767e7i	0.930067	−	0.424747i
$383$	−3.54725e7	−	5.51962e7i	−0.631386	−	0.982456i	−0.998630	−	0.0523313i	$-0.983335\pi$
$383$	−3.54725e7	−	5.51962e7i	−0.631386	−	0.982456i	0.367244	−	0.930125i	$-0.380302\pi$
$384$	−6.80721e6	−	1.99878e6i	−0.120220	−	0.0352997i
$385$	−4.92632e7	+	7.08298e6i	−0.863258	+	0.124118i
$386$	1.20060e6	−	2.62895e6i	0.0208755	−	0.0457110i
$387$	1.14826e6	+	165095.i	0.0198111	+	0.00284840i
$388$	−1.21145e7	+	1.88505e7i	−0.207400	+	0.322721i
$389$	−1.14256e7	+	9.90035e6i	−0.194102	+	0.168191i	−0.746490	−	0.665397i	$-0.768262\pi$
$389$	−1.14256e7	+	9.90035e6i	−0.194102	+	0.168191i	0.552388	+	0.833587i	$0.313717\pi$
$390$			4.51800e7i			0.761645i
$391$	3.63360e7	−	3.37855e7i	0.607865	−	0.565198i
$392$	5.09625e7			0.846043
$393$	−4.29238e7	−	4.95367e7i	−0.707164	−	0.816111i
$394$	1.86974e7	+	1.20161e7i	0.305697	+	0.196460i
$395$	6.37862e6	−	4.43643e7i	0.103499	−	0.719850i
$396$	−1.15445e7	−	5.27221e6i	−0.185905	−	0.0848999i
$397$	1.22140e7	+	8.49506e7i	0.195204	+	1.35767i	0.817969	+	0.575263i	$0.195100\pi$
$397$	1.22140e7	+	8.49506e7i	0.195204	+	1.35767i	−0.622765	+	0.782409i	$0.713991\pi$
$398$	−1.17853e7	+	4.01372e7i	−0.186936	+	0.636645i
$399$	2.39035e7	−	1.53619e7i	0.376308	−	0.241838i
$400$	9.72630e6	+	2.12976e7i	0.151973	+	0.332775i
$401$	1.76088e7	+	5.99700e7i	0.273084	+	0.930039i	0.975818	+	0.218586i	$0.0701444\pi$
$401$	1.76088e7	+	5.99700e7i	0.273084	+	0.930039i	−0.702734	+	0.711453i	$0.748037\pi$
$402$	−3.32411e7	−	2.88036e7i	−0.511678	−	0.443372i
$403$	−5.32292e7	+	6.14298e7i	−0.813271	+	0.938564i
$404$	5.39253e7	−	1.58339e7i	0.817803	−	0.240128i
$405$	−1.01882e7	+	4.65281e6i	−0.153368	+	0.0700406i
$406$	2.04684e7	+	3.18494e7i	0.305848	+	0.475908i
$407$	−467589.	−	137297.i	−0.00693556	−	0.00203646i
$408$	−3.43376e7	+	4.93701e6i	−0.505580	+	0.0726914i
$409$	3.98443e6	−	8.72468e6i	0.0582366	−	0.127520i	−0.878276	−	0.478153i	$-0.841306\pi$
$409$	3.98443e6	−	8.72468e6i	0.0582366	−	0.127520i	0.936513	+	0.350633i	$0.114034\pi$
$410$	7.86837e7	+	1.13130e7i	1.14165	+	0.164145i
$411$	−1.23055e7	+	1.91478e7i	−0.177245	+	0.275799i
$412$	2.92691e7	−	2.53618e7i	0.418521	−	0.362651i
$413$			4.91089e7i			0.697124i
$414$	−3.00440e6	−	1.67151e7i	−0.0423406	−	0.235563i
$415$	1.89404e7			0.265000
$416$	−4.93307e7	−	5.69306e7i	−0.685231	−	0.790799i
$417$	−1.57806e7	−	1.01416e7i	−0.217628	−	0.139861i
$418$	1.61139e7	−	1.12075e8i	0.220634	−	1.53454i
$419$	−6.11524e7	−	2.79274e7i	−0.831326	−	0.379654i	−0.0461563	−	0.998934i	$-0.514697\pi$
$419$	−6.11524e7	−	2.79274e7i	−0.831326	−	0.379654i	−0.785170	+	0.619280i	$0.787424\pi$
$420$	−2.03227e6	−	1.41348e7i	−0.0274305	−	0.190784i
$421$	−2.59041e7	+	8.82213e7i	−0.347154	+	1.18230i	0.582180	+	0.813060i	$0.302200\pi$
$421$	−2.59041e7	+	8.82213e7i	−0.347154	+	1.18230i	−0.929335	+	0.369239i	$0.879618\pi$
$422$	−3.82384e7	+	2.45743e7i	−0.508818	+	0.326997i
$423$	−7.92921e6	−	1.73626e7i	−0.104763	−	0.229400i
$424$	−1.73791e7	−	5.91877e7i	−0.227997	−	0.776486i
$425$	−6.27267e7	−	5.43530e7i	−0.817120	−	0.708038i
$426$	3.10856e7	−	3.58747e7i	0.402097	−	0.464045i
$427$	−4.06454e7	+	1.19346e7i	−0.522069	+	0.153293i
$428$	1.82208e7	−	8.32114e6i	0.232400	−	0.106133i
$429$	−3.77644e7	−	5.87626e7i	−0.478311	−	0.744267i
$430$	4.99071e6	+	1.46541e6i	0.0627707	+	0.0184311i
$431$	6.75891e6	−	971785.i	0.0844199	−	0.0121378i	−0.0999754	−	0.994990i	$-0.531876\pi$
$431$	6.75891e6	−	971785.i	0.0844199	−	0.0121378i	0.184395	+	0.982852i	$0.440967\pi$
$432$	−1.81018e6	+	3.96375e6i	−0.0224528	+	0.0491648i
$433$	6.33753e7	+	9.11200e6i	0.780651	+	0.112241i	0.521108	−	0.853491i	$-0.325519\pi$
$433$	6.33753e7	+	9.11200e6i	0.780651	+	0.112241i	0.259543	+	0.965732i	$0.416428\pi$
$434$	−1.47812e7	+	2.29999e7i	−0.180817	+	0.281357i
$435$	−9.45535e7	+	8.19311e7i	−1.14871	+	0.995362i
$436$		−	4.04276e7i		−	0.487774i
$437$	−1.27359e8	+	6.36468e7i	−1.52611	+	0.762663i
$438$	1.14992e7			0.136850
$439$	−6.54658e7	−	7.55515e7i	−0.773786	−	0.892996i	0.222859	−	0.974851i	$-0.428461\pi$
$439$	−6.54658e7	−	7.55515e7i	−0.773786	−	0.892996i	−0.996644	+	0.0818545i	$0.973916\pi$
$440$	−1.46686e8	−	9.42692e7i	−1.72199	−	1.10665i
$441$	−3.22951e6	+	2.24617e7i	−0.0376549	+	0.261895i
$442$	−5.66799e7	−	2.58848e7i	−0.656390	−	0.299763i
$443$	1.22303e7	+	8.50638e7i	0.140678	+	0.978438i	0.930811	+	0.365502i	$0.119103\pi$
$443$	1.22303e7	+	8.50638e7i	0.140678	+	0.978438i	−0.790132	+	0.612936i	$0.789988\pi$
$444$	39393.6	−	134162.i	0.000450067	−	0.00153279i
$445$	−4.61005e7	+	2.96270e7i	−0.523149	+	0.336207i
$446$	−241390.	−	528570.i	−0.00272091	−	0.00595796i
$447$	−1.07372e6	−	3.65675e6i	−0.0120217	−	0.0409423i
$448$	−2.78158e7	−	2.41025e7i	−0.309355	−	0.268058i
$449$	5.86462e7	−	6.76813e7i	0.647889	−	0.747704i	−0.332860	−	0.942976i	$-0.608014\pi$
$449$	5.86462e7	−	6.76813e7i	0.647889	−	0.747704i	0.980749	+	0.195272i	$0.0625591\pi$
$450$	−2.72587e7	+	8.00389e6i	−0.299136	+	0.0878342i
$451$	−1.11795e8	+	5.10549e7i	−1.21868	+	0.556554i
$452$	6.61048e6	+	1.02861e7i	0.0715843	+	0.111387i
$453$	3.30379e7	+	9.70081e6i	0.355400	+	0.104355i
$454$	8.48347e7	−	1.21974e7i	0.906580	−	0.130346i
$455$	3.26496e7	−	7.14926e7i	0.346612	−	0.758974i
$456$	9.85342e7	+	1.41671e7i	1.03918	+	0.149412i
$457$	4.54632e7	−	7.07420e7i	0.476333	−	0.741189i	−0.517060	−	0.855949i	$-0.672974\pi$
$457$	4.54632e7	−	7.07420e7i	0.476333	−	0.741189i	0.993393	+	0.114760i	$0.0366099\pi$
$458$	3.31799e7	−	2.87506e7i	0.345365	−	0.299261i
$459$		−	1.54472e7i		−	0.159739i
$460$	2.50699e6	+	7.15107e7i	0.0257560	+	0.734678i
$461$	6.31981e7			0.645062			0.322531	−	0.946559i	$-0.395466\pi$
$461$	6.31981e7			0.645062			0.322531	+	0.946559i	$0.395466\pi$
$462$	−1.53858e7	−	1.77562e7i	−0.156025	−	0.180063i
$463$	9.67298e7	+	6.21644e7i	0.974579	+	0.626324i	0.927996	−	0.372590i	$-0.121530\pi$
$463$	9.67298e7	+	6.21644e7i	0.974579	+	0.626324i	0.0465834	+	0.998914i	$0.485167\pi$
$464$	−6.92719e6	+	4.81797e7i	−0.0693431	+	0.482292i
$465$	−8.21846e7	−	3.75324e7i	−0.817394	−	0.373291i
$466$	1.43607e7	+	9.98807e7i	0.141911	+	0.987016i
$467$	3.07404e7	−	1.04692e8i	0.301827	−	1.02793i	−0.659313	−	0.751869i	$-0.729153\pi$
$467$	3.07404e7	−	1.04692e8i	0.301827	−	1.02793i	0.961140	−	0.276061i	$-0.0890291\pi$
$468$	1.68604e7	−	1.08355e7i	0.164486	−	0.105709i
$469$	3.17855e7	+	6.96004e7i	0.308113	+	0.674673i
$470$	−2.41114e7	−	8.21158e7i	−0.232235	−	0.790921i
$471$	−2.89954e7	−	2.51247e7i	−0.277502	−	0.240457i
$472$	−1.12669e8	+	1.30027e8i	−1.07147	+	1.23654i
$473$	−7.71596e6	+	2.26561e6i	−0.0729132	+	0.0214093i
$474$	1.92464e7	−	8.78951e6i	0.180723	−	0.0825334i
$475$	1.28766e8	+	2.00363e8i	1.20149	+	1.86955i
$476$	1.88969e7	+	5.54863e6i	0.175214	+	0.0514476i
$477$	2.71883e7	−	3.90909e6i	0.250511	−	0.0360181i
$478$	1.78322e7	−	3.90470e7i	0.163275	−	0.357523i
$479$	−1.67503e8	−	2.40832e7i	−1.52411	−	0.219133i	−0.671231	−	0.741248i	$-0.734234\pi$
$479$	−1.67503e8	−	2.40832e7i	−1.52411	−	0.219133i	−0.852875	+	0.522115i	$0.825143\pi$
$480$	4.52689e7	−	7.04398e7i	0.409333	−	0.636934i
$481$	581608.	−	503966.i	0.00522631	−	0.00452862i
$482$		−	8.67562e7i		−	0.774746i
$483$	−7.32509e6	+	2.86210e7i	−0.0650088	+	0.254005i
$484$	3.30507e7			0.291504
$485$	−8.97699e7	−	1.03600e8i	−0.786875	−	0.908102i
$486$	−4.44801e6	−	2.85856e6i	−0.0387487	−	0.0249023i
$487$	1.83234e7	−	1.27442e8i	0.158642	−	1.10338i	−0.742496	−	0.669851i	$-0.766358\pi$
$487$	1.83234e7	−	1.27442e8i	0.158642	−	1.10338i	0.901138	−	0.433532i	$-0.142733\pi$
$488$	−1.34999e8	−	6.16519e7i	−1.16164	−	0.530502i
$489$	3.40587e6	+	2.36883e7i	0.0291273	+	0.202585i
$490$	−2.86656e7	+	9.76260e7i	−0.243653	+	0.829807i
$491$	9.31286e6	−	5.98501e6i	0.0786753	−	0.0505616i	−0.500712	−	0.865614i	$-0.666928\pi$
$491$	9.31286e6	−	5.98501e6i	0.0786753	−	0.0505616i	0.579387	+	0.815053i	$0.303292\pi$
$492$	−1.46488e7	−	3.20765e7i	−0.123001	−	0.269334i
$493$	−4.86131e7	−	1.65561e8i	−0.405707	−	1.38171i
$494$	1.35132e8	+	1.17092e8i	1.12093	+	0.971288i
$495$	5.08448e7	−	5.86780e7i	0.419209	−	0.483793i
$496$	−3.37267e7	+	9.90305e6i	−0.276394	+	0.0811566i
$497$	−7.51147e7	+	3.43037e7i	−0.611865	+	0.279430i
$498$	4.83398e6	+	7.52182e6i	0.0391396	+	0.0609025i
$499$	−1.44417e8	−	4.24047e7i	−1.16230	−	0.341281i	−0.356972	−	0.934115i	$-0.616191\pi$
$499$	−1.44417e8	−	4.24047e7i	−1.16230	−	0.341281i	−0.805325	+	0.592834i	$0.798009\pi$
$500$	2.75242e7	−	3.95738e6i	0.220194	−	0.0316591i
$501$	−2.81603e7	+	6.16624e7i	−0.223936	+	0.490351i
$502$	3.35440e7	+	4.82291e6i	0.265158	+	0.0381239i
$503$	7.57224e7	−	1.17826e8i	0.595005	−	0.925845i	−0.404929	−	0.914348i	$-0.632704\pi$
$503$	7.57224e7	−	1.17826e8i	0.595005	−	0.925845i	0.999934	−	0.0114972i	$-0.00365974\pi$
$504$	1.56110e7	−	1.35270e7i	0.121938	−	0.105660i
$505$			3.43825e8i			2.66970i
$506$	6.70790e7	+	9.67477e7i	0.517768	+	0.746774i
$507$	3.50645e7			0.269057
$508$	−6.63627e7	−	7.65866e7i	−0.506213	−	0.584201i
$509$	6.30387e7	+	4.05125e7i	0.478029	+	0.307210i	0.757375	−	0.652980i	$-0.226481\pi$
$509$	6.30387e7	+	4.05125e7i	0.478029	+	0.307210i	−0.279347	+	0.960190i	$0.590118\pi$
$510$	9.85682e6	−	6.85557e7i	0.0743064	−	0.516812i
$511$	−1.81963e7	−	8.30997e6i	−0.136370	−	0.0622783i
$512$	−1.03539e7	−	7.20129e7i	−0.0771425	−	0.536538i
$513$	−1.24883e7	+	4.25312e7i	−0.0925020	+	0.315033i
$514$	−7.04880e7	+	4.52999e7i	−0.519070	+	0.333586i
$515$	9.84237e7	+	2.15518e8i	0.720573	+	1.57783i
$516$	−650057.	−	2.21389e6i	−0.00473154	−	0.0161141i
$517$	9.99977e7	+	8.66485e7i	0.723633	+	0.627032i
$518$	169512.	−	195627.i	0.00121958	−	0.00140747i
$519$	−1.02142e8	+	2.99916e7i	−0.730639	+	0.214535i
$520$	2.50470e8	−	1.14386e8i	1.78134	−	0.813510i
$521$	−6.09403e6	−	9.48249e6i	−0.0430915	−	0.0670516i	0.819040	−	0.573737i	$-0.194507\pi$
$521$	−6.09403e6	−	9.48249e6i	−0.0430915	−	0.0670516i	−0.862131	+	0.506686i	$0.830871\pi$
$522$	−5.66693e7	−	1.66396e7i	−0.398415	−	0.116985i
$523$	1.77269e8	−	2.54874e7i	1.23916	−	0.178164i	0.508594	−	0.861007i	$-0.330166\pi$
$523$	1.77269e8	−	2.54874e7i	1.23916	−	0.178164i	0.730566	+	0.682842i	$0.239256\pi$
$524$	−5.41579e7	+	1.18589e8i	−0.376416	+	0.824236i
$525$	4.89181e7	+	7.03336e6i	0.338058	+	0.0486055i
$526$	1.31371e7	−	2.04417e7i	0.0902697	−	0.140462i
$527$	9.41715e7	−	8.16000e7i	0.643409	−	0.557517i
$528$		−	3.02068e7i		−	0.205212i
$529$	5.19154e7	−	1.38634e8i	0.350695	−	0.936490i
$530$	1.23158e8			0.827247
$531$	−5.01696e7	−	5.78988e7i	−0.335086	−	0.386710i
$532$	−4.75436e7	−	3.05544e7i	−0.315760	−	0.202927i
$533$	2.76207e7	−	1.92106e8i	0.182412	−	1.26870i
$534$	−2.35315e7	−	1.07465e7i	−0.154535	−	0.0705737i
$535$	1.74396e7	+	1.21295e8i	0.113888	+	0.792105i
$536$	−7.55229e7	+	2.57207e8i	−0.490438	+	1.67028i
$537$	−5.22907e6	+	3.36052e6i	−0.0337677	+	0.0217012i
$538$	4.06870e7	+	8.90920e7i	0.261281	+	0.572127i
$539$	−4.43188e7	−	1.50936e8i	−0.283023	−	0.963888i
$540$	1.68361e7	+	1.45886e7i	0.106920	+	0.0926469i
$541$	6.91218e7	−	7.97708e7i	0.436539	−	0.503793i	−0.494265	−	0.869311i	$-0.664563\pi$
$541$	6.91218e7	−	7.97708e7i	0.436539	−	0.503793i	0.930804	+	0.365518i	$0.119108\pi$
$542$	−4.18153e7	+	1.22781e7i	−0.262626	+	0.0771139i
$543$	7.60955e7	−	3.47516e7i	0.475291	−	0.217058i
$544$	6.24334e7	+	9.71483e7i	0.387811	+	0.603446i
$545$	2.37305e8	+	6.96789e7i	1.46594	+	0.430439i
$546$	3.67247e7	−	5.28021e6i	0.225621	−	0.0324395i
$547$	1.08761e8	−	2.38153e8i	0.664524	−	1.45511i	−0.213721	−	0.976895i	$-0.568558\pi$
$547$	1.08761e8	−	2.38153e8i	0.664524	−	1.45511i	0.878245	−	0.478211i	$-0.158714\pi$
$548$	4.48104e7	+	6.44276e6i	0.272293	+	0.0391498i
$549$	3.57281e7	−	5.55939e7i	0.215920	−	0.335978i
$550$	1.48835e8	−	1.28967e8i	0.894578	−	0.775156i
$551$			4.95146e8i			2.95991i
$552$	−8.50590e7	+	5.89748e7i	−0.505712	+	0.350630i
$553$	−3.68071e7			−0.217649
$554$	−1.16324e8	−	1.34245e8i	−0.684133	−	0.789532i
$555$	719619.	+	462471.i	0.00420943	+	0.00270524i
$556$	−5.30980e6	+	3.69304e7i	−0.0308925	+	0.214862i
$557$	1.47139e8	+	6.71961e7i	0.851456	+	0.388847i	0.792837	−	0.609434i	$-0.208603\pi$
$557$	1.47139e8	+	6.71961e7i	0.851456	+	0.388847i	0.0586186	+	0.998280i	$0.481330\pi$
$558$	−6.06989e6	−	4.22170e7i	−0.0349364	−	0.242988i
$559$	3.57779e6	−	1.21848e7i	0.0204823	−	0.0697563i
$560$	2.85926e7	−	1.83753e7i	0.162813	−	0.104634i
$561$	4.44832e7	+	9.74046e7i	0.251946	+	0.551685i
$562$	4.36111e7	+	1.48526e8i	0.245690	+	0.836745i
$563$	−1.31589e8	−	1.14022e8i	−0.737384	−	0.638947i	0.202954	−	0.979188i	$-0.434946\pi$
$563$	−1.31589e8	−	1.14022e8i	−0.737384	−	0.638947i	−0.940338	+	0.340241i	$0.889491\pi$
$564$	−2.48615e7	+	2.86917e7i	−0.138577	+	0.159926i
$565$	−7.17716e7	+	2.10740e7i	−0.397930	+	0.116843i
$566$	3.52491e7	−	1.60977e7i	0.194401	−	0.0887801i
$567$	4.97275e6	+	7.73775e6i	0.0272802	+	0.0424488i
$568$	−2.77585e8	−	8.15064e7i	−1.51479	−	0.444781i
$569$	−1.84463e8	+	2.65218e7i	−1.00132	+	0.143968i	−0.623427	−	0.781881i	$-0.714260\pi$
$569$	−1.84463e8	+	2.65218e7i	−1.00132	+	0.143968i	−0.377893	+	0.925849i	$0.623351\pi$
$570$	−8.25630e7	+	1.80788e8i	−0.445821	+	0.976213i
$571$	1.88980e8	+	2.71713e7i	1.01510	+	0.145949i	0.629731	−	0.776814i	$-0.283165\pi$
$571$	1.88980e8	+	2.71713e7i	1.01510	+	0.145949i	0.385368	+	0.922763i	$0.374074\pi$
$572$	−7.51127e7	+	1.16878e8i	−0.401352	+	0.624516i
$573$	1.16895e8	−	1.01290e8i	0.621345	−	0.538398i
$574$		−	6.52804e7i		−	0.345181i
$575$	−2.39906e8	−	6.14002e7i	−1.26194	−	0.322973i
$576$	5.74176e7			0.300454
$577$	−1.73300e7	−	1.99998e7i	−0.0902132	−	0.104112i	0.708848	−	0.705361i	$-0.249215\pi$
$577$	−1.73300e7	−	1.99998e7i	−0.0902132	−	0.104112i	−0.799061	+	0.601250i	$0.794670\pi$
$578$	−3.62807e7	−	2.33162e7i	−0.187885	−	0.120746i
$579$	1.11621e6	−	7.76343e6i	0.00575057	−	0.0399961i
$580$	2.26358e8	+	1.03374e8i	1.16014	+	0.529820i
$581$	−2.21358e6	−	1.53958e7i	−0.0112867	−	0.0785007i
$582$	1.82316e7	−	6.20911e7i	0.0924817	−	0.314964i
$583$	−1.60183e8	+	1.02943e8i	−0.808372	+	0.519509i
$584$	−2.91135e7	−	6.37497e7i	−0.146169	−	0.320066i
$585$	3.45433e7	+	1.17644e8i	0.172542	+	0.587626i
$586$	−2.72240e7	−	2.35897e7i	−0.135288	−	0.117228i
$587$	−5.11721e7	+	5.90557e7i	−0.252999	+	0.291976i	−0.868015	−	0.496539i	$-0.834604\pi$
$587$	−5.11721e7	+	5.90557e7i	−0.252999	+	0.291976i	0.615016	+	0.788515i	$0.289150\pi$
$588$	4.33071e7	−	1.27161e7i	0.213023	−	0.0625493i
$589$	−3.25255e8	+	1.48539e8i	−1.59176	+	0.726933i
$590$	−1.85711e8	−	2.88972e8i	−0.904235	−	1.40702i
$591$	5.78729e7	+	1.69930e7i	0.280358	+	0.0823205i
$592$	329412.	−	47362.3i	0.00158772	−	0.000228280i
$593$	4.92281e7	−	1.07795e8i	0.236075	−	0.516931i	−0.754101	−	0.656758i	$-0.771927\pi$
$593$	4.92281e7	−	1.07795e8i	0.236075	−	0.516931i	0.990176	+	0.139827i	$0.0446546\pi$
$594$	3.62794e7	+	5.21619e6i	0.173101	+	0.0248882i
$595$	−6.51395e7	+	1.01359e8i	−0.309238	+	0.481184i
$596$	−5.72877e6	+	4.96401e6i	−0.0270597	+	0.0234473i
$597$			1.13523e8i			0.533534i
$598$	−1.85798e8	+	6.51360e6i	−0.868833	+	0.0304591i
$599$	3.39543e8			1.57985			0.789923	−	0.613207i	$-0.210121\pi$
$599$	3.39543e8			1.57985			0.789923	+	0.613207i	$0.210121\pi$
$600$	1.13385e8	+	1.30854e8i	0.524932	+	0.605804i
$601$	−5.51135e7	−	3.54193e7i	−0.253884	−	0.163161i	0.407509	−	0.913201i	$-0.366398\pi$
$601$	−5.51135e7	−	3.54193e7i	−0.253884	−	0.163161i	−0.661392	+	0.750040i	$0.730034\pi$
$602$	607891.	−	4.22797e6i	0.00278635	−	0.0193795i
$603$	−1.08578e8	−	4.95861e7i	−0.495212	−	0.226156i
$604$	−9.74657e6	−	6.77888e7i	−0.0442324	−	0.307643i
$605$	−5.69645e7	+	1.94003e8i	−0.257240	+	0.876078i
$606$	−1.36543e8	+	8.77510e7i	−0.613553	+	0.394307i
$607$	2.84337e7	+	6.22610e7i	0.127135	+	0.278388i	0.962487	−	0.271329i	$-0.0874630\pi$
$607$	2.84337e7	+	6.22610e7i	0.127135	+	0.278388i	−0.835351	+	0.549716i	$0.814736\pi$
$608$	−9.33602e7	−	3.17956e8i	−0.415385	−	1.41467i
$609$	7.76484e7	+	6.72827e7i	0.343780	+	0.297887i
$610$	1.94038e8	−	2.23932e8i	0.854864	−	0.986566i
$611$	−2.00486e8	+	5.88679e7i	−0.878941	+	0.258080i
$612$	−2.79477e7	+	1.27633e7i	−0.121925	+	0.0556811i
$613$	−1.55564e8	−	2.42063e8i	−0.675349	−	1.05086i	−0.994659	−	0.103213i	$-0.967088\pi$
$613$	−1.55564e8	−	2.42063e8i	−0.675349	−	1.05086i	0.319310	−	0.947650i	$-0.396549\pi$
$614$	−1.89857e8	−	5.57471e7i	−0.820204	−	0.240834i
$615$	2.13533e8	−	3.07014e7i	0.917993	−	0.131987i
$616$	−5.94837e7	+	1.30251e8i	−0.254481	+	0.557236i
$617$	−4.00618e8	−	5.76001e7i	−1.70559	−	0.245227i	−0.780549	−	0.625094i	$-0.785061\pi$
$617$	−4.00618e8	−	5.76001e7i	−1.70559	−	0.245227i	−0.925041	+	0.379867i	$0.875970\pi$
$618$	−6.04689e7	+	9.40915e7i	−0.256193	+	0.398644i
$619$	5.07215e7	−	4.39505e7i	0.213855	−	0.185307i	−0.541345	−	0.840800i	$-0.682085\pi$
$619$	5.07215e7	−	4.39505e7i	0.213855	−	0.185307i	0.755201	+	0.655494i	$0.227539\pi$
$620$			1.79703e8i			0.754015i
$621$	−2.06030e7	−	4.12271e7i	−0.0860309	−	0.172150i
$622$	3.14729e7			0.130787
$623$	2.94701e7	+	3.40104e7i	0.121876	+	0.140652i
$624$	4.01292e7	+	2.57895e7i	0.165161	+	0.106142i
$625$	2.10490e7	−	1.46399e8i	0.0862167	−	0.599650i
$626$	2.62894e8	+	1.20060e8i	1.07166	+	0.489412i
$627$	−4.37301e7	−	3.04150e8i	−0.177410	−	1.23391i
$628$	−2.14990e7	+	7.32190e7i	−0.0868041	+	0.295628i
$629$	−992474.	+	637824.i	−0.00398811	+	0.00256300i
$630$	1.71320e7	+	3.75137e7i	0.0685149	+	0.150027i
$631$	−5.07502e7	−	1.72839e8i	−0.201999	−	0.687947i	−0.996717	−	0.0809671i	$-0.974199\pi$
$631$	−5.07502e7	−	1.72839e8i	−0.201999	−	0.687947i	0.794717	−	0.606980i	$-0.207619\pi$
$632$	−9.74551e7	−	8.44453e7i	−0.386059	−	0.334522i
$633$	−8.07796e7	+	9.32246e7i	−0.318486	+	0.367553i
$634$	−2.38990e8	+	7.01738e7i	−0.937804	+	0.275364i
$635$	5.63933e8	−	2.57540e8i	2.20245	−	1.00583i
$636$	−2.95369e7	−	4.59603e7i	−0.114814	−	0.178654i
$637$	2.38354e8	+	6.99870e7i	0.922155	+	0.270769i
$638$	4.05254e8	−	5.82667e7i	1.56050	−	0.224367i
$639$	5.35147e7	−	1.17181e8i	0.205102	−	0.449111i
$640$	−8.54479e7	−	1.22856e7i	−0.325958	−	0.0468657i
$641$	4.26056e7	−	6.62956e7i	0.161768	−	0.251716i	−0.750902	−	0.660414i	$-0.770381\pi$
$641$	4.26056e7	−	6.62956e7i	0.161768	−	0.251716i	0.912670	+	0.408698i	$0.134017\pi$
$642$	−4.37191e7	+	3.78828e7i	−0.165221	+	0.143165i
$643$		−	4.14704e8i		−	1.55993i	−0.625823	−	0.779965i	$-0.715237\pi$
$643$		−	4.14704e8i		−	1.55993i	0.625823	−	0.779965i	$-0.284763\pi$
$644$	5.78346e7	−	1.03953e7i	0.216536	−	0.0389206i
$645$	1.41156e7			0.0526043
$646$	−1.79502e8	−	2.07156e8i	−0.665842	−	0.768423i
$647$	1.46813e8	+	9.43511e7i	0.542066	+	0.348365i	0.782846	−	0.622215i	$-0.213767\pi$
$647$	1.46813e8	+	9.43511e7i	0.542066	+	0.348365i	−0.240780	+	0.970580i	$0.577403\pi$
$648$	−4.58599e6	+	3.18963e7i	−0.0168542	+	0.117223i
$649$	4.83083e8	+	2.20617e8i	1.76721	+	0.807057i
$650$	4.42596e7	+	3.07833e8i	0.161164	+	1.12092i
$651$	−2.09034e7	+	7.11904e7i	−0.0757659	+	0.258035i
$652$	4.00438e7	−	2.57346e7i	0.144475	−	0.0928483i
$653$	−8.55719e7	−	1.87376e8i	−0.307321	−	0.672938i	0.691454	−	0.722420i	$-0.256970\pi$
$653$	−8.55719e7	−	1.87376e8i	−0.307321	−	0.672938i	−0.998775	+	0.0494818i	$0.984243\pi$
$654$	3.28933e7	+	1.12024e8i	0.117591	+	0.400478i
$655$	−6.02759e8	−	5.22294e8i	−2.14496	−	1.85862i
$656$	5.49622e7	−	6.34298e7i	0.194694	−	0.224689i
$657$	2.99426e7	−	8.79195e6i	0.105583	−	0.0310020i
$658$	−6.39301e7	+	2.91959e7i	−0.224403	+	0.102481i
$659$	1.48170e8	+	2.30557e8i	0.517731	+	0.805605i	0.997416	−	0.0718356i	$-0.0228857\pi$
$659$	1.48170e8	+	2.30557e8i	0.517731	+	0.805605i	−0.479686	+	0.877440i	$0.659249\pi$
$660$	−1.48173e8	−	4.35076e7i	−0.515392	−	0.151333i
$661$	3.39391e8	−	4.87970e7i	1.17516	−	0.168962i	0.473051	−	0.881035i	$-0.343153\pi$
$661$	3.39391e8	−	4.87970e7i	1.17516	−	0.168962i	0.702105	+	0.712073i	$0.252244\pi$
$662$	−1.56113e8	+	3.41839e8i	−0.538102	+	1.17828i
$663$	−1.67379e8	−	2.40654e7i	−0.574327	−	0.0825758i
$664$	2.94611e7	−	4.58424e7i	0.100634	−	0.156590i
$665$	2.61294e8	−	2.26413e8i	0.888516	−	0.769903i
$666$			403814.i			0.00136697i
$667$	−3.50564e8	−	3.77028e8i	−1.18138	−	1.27056i
$668$	1.34830e8			0.452330
$669$	−1.03268e6	−	1.19178e6i	−0.00344895	−	0.00398030i
$670$	−4.50237e8	−	2.89350e8i	−1.49698	−	0.962053i
$671$	−6.51951e7	+	4.53442e8i	−0.215798	+	1.50091i
$672$	−6.25478e7	−	2.85646e7i	−0.206112	−	0.0941284i
$673$	3.25298e6	+	2.26250e7i	0.0106718	+	0.0742237i	0.994461	−	0.105103i	$-0.0335172\pi$
$673$	3.25298e6	+	2.26250e7i	0.0106718	+	0.0742237i	−0.983790	+	0.179327i	$0.942608\pi$
$674$	−6.74827e6	+	2.29825e7i	−0.0220401	+	0.0750616i
$675$	−6.48591e7	+	4.16824e7i	−0.210892	+	0.135532i
$676$	−2.89722e7	−	6.34402e7i	−0.0937866	−	0.205364i
$677$	1.31672e8	+	4.48435e8i	0.424354	+	1.44522i	0.843416	+	0.537261i	$0.180541\pi$
$677$	1.31672e8	+	4.48435e8i	0.424354	+	1.44522i	−0.419062	+	0.907958i	$0.637641\pi$
$678$	−2.66867e7	−	2.31241e7i	−0.0856260	−	0.0741953i
$679$	−7.37200e7	+	8.50775e7i	−0.235492	+	0.271772i
$680$	−4.05016e8	+	1.18923e8i	−1.28809	+	0.378217i
$681$	2.11574e8	−	9.66226e7i	0.669917	−	0.305941i
$682$	1.59847e8	+	2.48726e8i	0.503907	+	0.784095i
$683$	1.45427e7	+	4.27011e6i	0.0456438	+	0.0134022i	0.304475	−	0.952520i	$-0.401519\pi$
$683$	1.45427e7	+	4.27011e6i	0.0456438	+	0.0134022i	−0.258831	+	0.965923i	$0.583337\pi$
$684$	8.72677e7	−	1.25472e7i	0.272700	−	0.0392084i
$685$	−1.15051e8	+	2.51926e8i	−0.357947	+	0.783794i
$686$	1.86900e8	+	2.68721e7i	0.578944	+	0.0832396i
$687$	6.44149e7	−	1.00232e8i	0.198663	−	0.309125i
$688$	4.15036e6	−	3.59631e6i	0.0127444	−	0.0110431i
$689$		−	3.00690e8i		−	0.919310i
$690$	−6.51304e7	−	1.96115e8i	−0.198261	−	0.596986i
$691$	−3.39907e8			−1.03021			−0.515105	−	0.857127i	$-0.672247\pi$
$691$	−3.39907e8			−1.03021			−0.515105	+	0.857127i	$0.672247\pi$
$692$	1.38657e8	+	1.60019e8i	0.418432	+	0.482896i
$693$	−5.36388e7	−	3.44716e7i	−0.161168	−	0.103576i
$694$	−2.83156e7	+	1.96939e8i	−0.0847124	+	0.589188i
$695$	−2.07625e8	−	9.48192e7i	−0.618480	−	0.282450i
$696$	5.12271e7	+	3.56292e8i	0.151940	+	1.05677i
$697$	−8.38227e7	+	2.85474e8i	−0.247550	+	0.843078i
$698$	−7.23471e7	+	4.64947e7i	−0.212743	+	0.136722i
$699$	1.13759e8	+	2.49098e8i	0.333085	+	0.729355i
$700$	−2.76937e7	−	9.43160e7i	−0.0807396	−	0.274974i
$701$	−3.79981e8	−	3.29256e8i	−1.10308	−	0.955827i	−0.103835	−	0.994595i	$-0.533111\pi$
$701$	−3.79981e8	−	3.29256e8i	−1.10308	−	0.955827i	−0.999248	+	0.0387676i	$0.987657\pi$
$702$	−3.79037e7	+	4.37432e7i	−0.109565	+	0.126444i
$703$	3.24826e6	−	953775.i	0.00934942	−	0.00274524i
$704$	−3.62055e8	+	1.65345e8i	−1.03766	+	0.473886i
$705$	−1.25567e8	−	1.95385e8i	−0.358349	−	0.557602i
$706$	3.60043e8	+	1.05718e8i	1.02315	+	0.300425i
$707$	2.79479e8	−	4.01830e7i	0.790844	−	0.113706i
$708$	−6.33001e7	+	1.38608e8i	−0.178363	+	0.390560i
$709$	−1.36362e8	−	1.96059e7i	−0.382608	−	0.0550107i	−0.0516723	−	0.998664i	$-0.516455\pi$
$709$	−1.36362e8	−	1.96059e7i	−0.382608	−	0.0550107i	−0.330935	+	0.943653i	$0.607364\pi$
$710$	3.12274e8	−	4.85909e8i	0.872492	−	1.35762i
$711$	4.33951e7	−	3.76021e7i	0.120735	−	0.104617i
$712$			1.57663e8i			0.436806i
$713$	1.42499e8	−	3.43385e8i	0.393137	−	0.947356i
$714$	−5.68776e7			−0.156260
$715$	−5.56596e8	−	6.42346e8i	−1.52273	−	1.75732i
$716$	1.04005e7	+	6.68401e6i	0.0283345	+	0.0182095i
$717$	1.65788e7	−	1.15308e8i	0.0449774	−	0.312825i
$718$	−3.62268e7	−	1.65442e7i	−0.0978715	−	0.0446964i
$719$	1.51247e7	+	1.05195e8i	0.0406912	+	0.283014i	1.00000		0.000653911i	$0.000208146\pi$
$719$	1.51247e7	+	1.05195e8i	0.0406912	+	0.283014i	−0.959309	+	0.282360i	$0.908883\pi$
$720$	−1.49381e7	+	5.08744e7i	−0.0400218	+	0.136302i
$721$	1.63681e8	−	1.05192e8i	0.436710	−	0.280657i
$722$	2.14492e8	+	4.69672e8i	0.569901	+	1.24791i
$723$	−6.63312e7	−	2.25903e8i	−0.175510	−	0.597733i
$724$	−1.25748e8	−	1.08961e8i	−0.331349	−	0.287116i
$725$	−5.63975e8	+	6.50862e8i	−1.47995	+	1.70795i
$726$	−9.15830e7	+	2.68912e7i	−0.239334	+	0.0702749i
$727$	−2.50375e8	+	1.14342e8i	−0.651609	+	0.297580i	−0.713659	−	0.700493i	$-0.752963\pi$
$727$	−2.50375e8	+	1.14342e8i	−0.651609	+	0.297580i	0.0620502	+	0.998073i	$0.480236\pi$
$728$	−1.22251e8	−	1.90227e8i	−0.316855	−	0.493035i
$729$	−1.37677e7	−	4.04255e6i	−0.0355368	−	0.0104345i
$730$	1.38498e8	−	1.99129e7i	0.356019	−	0.0511879i
$731$	−8.08723e6	+	1.77086e7i	−0.0207037	+	0.0453347i
$732$	−1.30103e8	−	1.87060e7i	−0.331707	−	0.0476923i
$733$	−4.80267e6	+	7.47309e6i	−0.0121947	+	0.0189753i	−0.847297	−	0.531119i	$-0.821772\pi$
$733$	−4.80267e6	+	7.47309e6i	−0.0121947	+	0.0189753i	0.835103	+	0.550094i	$0.185408\pi$
$734$	3.72761e8	−	3.22999e8i	0.942633	−	0.816796i
$735$			2.76124e8i			0.695411i
$736$	2.96202e8	+	1.76008e8i	0.742941	+	0.441467i
$737$	8.27450e8			2.06699
$738$	6.66903e7	+	7.69647e7i	0.165918	+	0.191480i
$739$	6.34456e8	+	4.07740e8i	1.57206	+	1.01030i	0.978684	+	0.205372i	$0.0658405\pi$
$739$	6.34456e8	+	4.07740e8i	1.57206	+	1.01030i	0.593373	+	0.804928i	$0.297796\pi$
$740$	242134.	−	1.68408e6i	0.000597532	−	0.00415593i
$741$	4.41393e8	+	2.01578e8i	1.08485	+	0.495436i
$742$	−1.43935e7	−	1.00109e8i	−0.0352335	−	0.245055i
$743$	−3.48871e7	+	1.18814e8i	−0.0850546	+	0.289669i	−0.991026	−	0.133670i	$-0.957324\pi$
$743$	−3.48871e7	+	1.18814e8i	−0.0850546	+	0.289669i	0.905971	+	0.423339i	$0.139142\pi$
$744$	−2.18676e8	+	1.40535e8i	−0.530986	+	0.341244i
$745$	−1.92643e7	−	4.21828e7i	−0.0465890	−	0.102016i
$746$	−1.45136e7	−	4.94289e7i	−0.0349590	−	0.119060i
$747$	1.83381e7	+	1.58900e7i	0.0439939	+	0.0381209i
$748$	1.39474e8	−	1.60962e8i	0.333264	−	0.384607i
$749$	9.65570e7	−	2.83517e7i	0.229794	−	0.0674736i
$750$	−7.30493e7	+	3.33605e7i	−0.173154	+	0.0790768i
$751$	−3.21349e7	−	5.00029e7i	−0.0758678	−	0.118053i	0.801246	−	0.598335i	$-0.204171\pi$
$751$	−3.21349e7	−	5.00029e7i	−0.0758678	−	0.118053i	−0.877114	+	0.480282i	$0.840534\pi$
$752$	−8.66990e7	−	2.54571e7i	−0.203873	−	0.0598626i
$753$	9.10323e7	−	1.30885e7i	0.213211	−	0.0306552i
$754$	−2.68585e8	+	5.88119e8i	−0.626567	+	1.37199i
$755$	4.14710e8	+	5.96263e7i	0.963616	+	0.138547i
$756$	9.89070e6	−	1.53902e7i	0.0228908	−	0.0356188i
$757$	5.41947e8	−	4.69600e8i	1.24931	−	1.08253i	0.256043	−	0.966665i	$-0.417581\pi$
$757$	5.41947e8	−	4.69600e8i	1.24931	−	1.08253i	0.993265	−	0.115866i	$-0.0369643\pi$
$758$		−	3.10704e7i		−	0.0713410i
$759$	2.48636e8	+	2.00633e8i	0.568643	+	0.458858i
$760$	1.21129e9			2.75935
$761$	2.25574e8	+	2.60327e8i	0.511842	+	0.590697i	0.951569	−	0.307435i	$-0.0994705\pi$
$761$	2.25574e8	+	2.60327e8i	0.511842	+	0.590697i	−0.439728	+	0.898131i	$0.644925\pi$
$762$	2.46204e8	+	1.58226e8i	0.556455	+	0.357612i
$763$	2.89048e7	−	2.01037e8i	0.0650722	−	0.452587i
$764$	−2.79843e8	−	1.27800e8i	−0.627530	−	0.286583i
$765$	−2.67496e7	−	1.86047e8i	−0.0597493	−	0.415565i
$766$	1.06180e8	−	3.61616e8i	0.236242	−	0.804565i
$767$	−7.05525e8	+	4.53413e8i	−1.56360	+	1.00487i
$768$	−1.14856e8	−	2.51500e8i	−0.253555	−	0.555207i
$769$	2.48355e8	+	8.45819e8i	0.546127	+	1.85994i	0.509250	+	0.860619i	$0.329923\pi$
$769$	2.48355e8	+	8.45819e8i	0.546127	+	1.85994i	0.0368777	+	0.999320i	$0.488259\pi$
$770$	−2.16056e8	−	1.87214e8i	−0.473255	−	0.410077i
$771$	−1.48908e8	+	1.71849e8i	−0.324903	+	0.374959i
$772$	−1.49682e7	+	4.39505e6i	−0.0325325	+	0.00955240i
$773$	−3.24796e8	+	1.48329e8i	−0.703189	+	0.321136i	−0.734723	−	0.678367i	$-0.762688\pi$
$773$	−3.24796e8	+	1.48329e8i	−0.703189	+	0.321136i	0.0315343	+	0.999503i	$0.489961\pi$
$774$	3.60260e6	+	5.60575e6i	0.00776949	+	0.0120896i
$775$	−5.96730e8	−	1.75216e8i	−1.28195	−	0.376416i
$776$	−3.90381e8	+	5.61283e7i	−0.835417	+	0.120115i
$777$	291818.	−	638993.i	0.000622085	−	0.00136218i
$778$	−8.59571e7	−	1.23588e7i	−0.182534	−	0.0262444i
$779$	4.61583e8	−	7.18238e8i	0.976422	−	1.51934i
$780$	1.84304e8	−	1.59700e8i	0.388375	−	0.336529i
$781$			8.93007e8i			1.87457i
$782$	2.83348e8	+	3.06513e7i	0.592516	+	0.0640957i
$783$	−1.60282e8			−0.333888
$784$	7.03493e7	+	8.11875e7i	0.145986	+	0.168477i
$785$	−3.92731e8	−	2.52393e8i	−0.811870	−	0.521757i
$786$	5.35824e7	−	3.72674e8i	0.110346	−	0.767470i
$787$	4.47410e8	+	2.04325e8i	0.917871	+	0.419178i	0.817603	−	0.575783i	$-0.195303\pi$
$787$	4.47410e8	+	2.04325e8i	0.917871	+	0.419178i	0.100268	+	0.994960i	$0.468030\pi$
$788$	−1.70732e7	−	1.18747e8i	−0.0348928	−	0.242685i
$789$	1.85784e7	−	6.32721e7i	0.0378248	−	0.128819i
$790$	2.16584e8	−	1.39190e8i	0.439284	−	0.282311i
$791$	2.55181e7	+	5.58767e7i	0.0515606	+	0.112902i
$792$	−6.29338e7	−	2.14333e8i	−0.126680	−	0.431433i
$793$	−5.46729e8	−	4.73743e8i	−1.09636	−	0.950000i
$794$	−3.22836e8	+	3.72572e8i	−0.644941	+	0.744302i
$795$	3.20689e8	−	9.41629e7i	0.638239	−	0.187404i
$796$	2.05391e8	−	9.37989e7i	0.407232	−	0.185977i
$797$	−1.77392e8	−	2.76027e8i	−0.350395	−	0.545226i	0.620660	−	0.784080i	$-0.286865\pi$
$797$	−1.77392e8	−	2.76027e8i	−0.350395	−	0.545226i	−0.971056	+	0.238854i	$0.923228\pi$
$798$	1.56603e8	+	4.59828e7i	0.308171	+	0.0904871i
$799$	3.17058e8	−	4.55860e7i	0.621582	−	0.0893700i
$800$	2.39433e8	−	5.24286e8i	0.467643	−	1.02400i
$801$	−6.94898e7	−	9.99113e6i	−0.135215	−	0.0194409i
$802$	−1.94099e8	+	3.02025e8i	−0.376271	+	0.585490i
$803$	−1.63490e8	+	1.41665e8i	−0.315750	+	0.273599i
$804$			2.37415e8i			0.456814i
$805$	−3.86618e7	+	3.57398e8i	−0.0741129	+	0.685117i
$806$	−4.66901e8			−0.891701
$807$	1.74061e8	+	2.00877e8i	0.331193	+	0.382217i
$808$	8.32174e8	+	5.34806e8i	1.57754	+	1.01382i
$809$	9.40423e7	−	6.54078e8i	0.177614	−	1.23533i	−0.684649	−	0.728873i	$-0.740045\pi$
$809$	9.40423e7	−	6.54078e8i	0.177614	−	1.23533i	0.862263	−	0.506460i	$-0.169046\pi$
$810$	−5.85223e7	−	2.67263e7i	−0.110120	−	0.0502902i
$811$	4.20998e7	+	2.92810e8i	0.0789254	+	0.548939i	0.990469	+	0.137735i	$0.0439823\pi$
$811$	4.20998e7	+	2.92810e8i	0.0789254	+	0.548939i	−0.911544	+	0.411203i	$0.865109\pi$
$812$	5.75734e7	−	1.96077e8i	0.107536	−	0.366234i
$813$	−9.94948e7	+	6.39414e7i	−0.185152	+	0.118990i
$814$	−1.16286e6	−	2.54631e6i	−0.00215603	−	0.00472105i
$815$	8.20411e7	+	2.79406e8i	0.151551	+	0.516135i
$816$	−5.52652e7	−	4.78876e7i	−0.101714	−	0.0881358i
$817$	3.65833e7	−	4.22194e7i	0.0670837	−	0.0774187i
$818$	5.28626e7	−	1.55219e7i	0.0965803	−	0.0283585i
$819$	9.15898e7	−	4.18277e7i	0.166723	−	0.0761398i
$820$	−2.31978e8	−	3.60965e8i	−0.420732	−	0.654672i
$821$	−1.23256e8	−	3.61913e7i	−0.222731	−	0.0653996i	0.168463	−	0.985708i	$-0.446120\pi$
$821$	−1.23256e8	−	3.61913e7i	−0.222731	−	0.0653996i	−0.391194	+	0.920308i	$0.627938\pi$
$822$	−1.29411e8	+	1.86065e7i	−0.233000	+	0.0335003i
$823$	−1.16338e7	+	2.54744e7i	−0.0208699	+	0.0456987i	−0.919780	−	0.392435i	$-0.871633\pi$
$823$	−1.16338e7	+	2.54744e7i	−0.0208699	+	0.0456987i	0.898910	+	0.438133i	$0.144360\pi$
$824$	6.74721e8	+	9.70103e7i	1.20599	+	0.173395i
$825$	2.88946e8	−	4.49609e8i	0.514583	−	0.800707i
$826$	−2.13187e8	+	1.84728e8i	−0.378287	+	0.327787i
$827$			6.93208e7i			0.122559i	0.998121	+	0.0612797i	$0.0195182\pi$
$827$			6.93208e7i			0.122559i	−0.998121	+	0.0612797i	$0.980482\pi$
$828$	−5.75665e7	+	7.13397e7i	−0.101409	+	0.125672i
$829$	9.15779e8			1.60741			0.803705	−	0.595027i	$-0.202859\pi$
$829$	9.15779e8			1.60741			0.803705	+	0.595027i	$0.202859\pi$
$830$	7.12463e7	+	8.22226e7i	0.124603	+	0.143799i
$831$	−4.05535e8	−	2.60621e8i	−0.706683	−	0.454158i
$832$	8.94518e7	−	6.22151e8i	0.155317	−	1.08025i
$833$	−3.46407e8	−	1.58199e8i	−0.599309	−	0.273695i
$834$	−1.53345e7	−	1.06654e8i	−0.0264346	−	0.183856i
$835$	−2.32385e8	+	7.91432e8i	−0.399162	+	1.35942i
$836$	−5.14148e8	+	3.30423e8i	−0.879973	+	0.565524i
$837$	−4.80831e7	−	1.05287e8i	−0.0820005	−	0.179556i
$838$	−1.08795e8	−	3.70521e8i	−0.184874	−	0.629623i
$839$	−2.44242e8	−	2.11637e8i	−0.413556	−	0.358349i	0.423094	−	0.906086i	$-0.360944\pi$
$839$	−2.44242e8	−	2.11637e8i	−0.413556	−	0.358349i	−0.836650	+	0.547737i	$0.815489\pi$
$840$	1.64595e8	−	1.89953e8i	0.277703	−	0.320486i
$841$	−1.14716e9	+	3.36836e8i	−1.92857	+	0.566279i
$842$	−4.80419e8	+	2.19400e8i	−0.804793	+	0.367537i
$843$	2.27117e8	+	3.53400e8i	0.379111	+	0.589908i
$844$	2.35410e8	+	6.91226e7i	0.391559	+	0.114972i
$845$	4.22320e8	−	6.07205e7i	0.699958	−	0.100639i
$846$	4.55463e7	−	9.97325e7i	0.0752215	−	0.164712i
$847$	1.64353e8	+	2.36305e7i	0.270476	+	0.0388886i
$848$	7.03006e7	−	1.09390e8i	0.115285	−	0.179386i
$849$	7.94768e7	−	6.88671e7i	0.129873	−	0.112535i
$850$		−	4.76758e8i		−	0.776320i
$851$	−1.79811e6	+	3.02602e6i	−0.00291761	+	0.00491002i
$852$	−2.56225e8			−0.414288
$853$	−4.36216e8	−	5.03420e8i	−0.702837	−	0.811117i	0.286296	−	0.958141i	$-0.407576\pi$
$853$	−4.36216e8	−	5.03420e8i	−0.702837	−	0.811117i	−0.989133	+	0.147024i	$0.953030\pi$
$854$	−2.04701e8	−	1.31553e8i	−0.328659	−	0.211216i
$855$	−7.67597e7	+	5.33876e8i	−0.122810	+	0.854165i
$856$	3.20703e8	+	1.46460e8i	0.511307	+	0.233506i
$857$	7.97362e7	+	5.54577e8i	0.126681	+	0.881089i	0.949719	+	0.313102i	$0.101368\pi$
$857$	7.97362e7	+	5.54577e8i	0.126681	+	0.881089i	−0.823038	+	0.567986i	$0.807723\pi$
$858$	1.13040e8	−	3.84981e8i	0.178967	−	0.609504i
$859$	5.33387e8	−	3.42787e8i	0.841517	−	0.540810i	−0.0474014	−	0.998876i	$-0.515094\pi$
$859$	5.33387e8	−	3.42787e8i	0.841517	−	0.540810i	0.888918	+	0.458066i	$0.151458\pi$
$860$	−1.16631e7	−	2.55386e7i	−0.0183366	−	0.0401515i
$861$	−4.99114e7	−	1.69983e8i	−0.0781970	−	0.266315i
$862$	2.96429e7	+	2.56857e7i	0.0462806	+	0.0401024i
$863$	−2.87675e8	+	3.31995e8i	−0.447579	+	0.516534i	−0.934040	−	0.357168i	$-0.883742\pi$
$863$	−2.87675e8	+	3.31995e8i	−0.447579	+	0.516534i	0.486461	+	0.873703i	$0.338288\pi$
$864$	1.02925e8	−	3.02214e7i	0.159580	−	0.0468569i
$865$	−1.17827e9	+	5.38099e8i	−1.82053	+	0.831408i
$866$	1.98836e8	+	3.09395e8i	0.306155	+	0.476387i
$867$	−1.12298e8	−	3.29736e7i	−0.172311	−	0.0505952i
$868$	1.46072e8	−	2.10020e7i	0.223361	−	0.0321145i
$869$	−1.65352e8	+	3.62070e8i	−0.251971	+	0.551739i
$870$	−7.11344e8	−	1.02276e8i	−1.08024	−	0.155316i
$871$	−7.06448e8	+	1.09925e9i	−1.06912	+	1.66358i
$872$	5.37765e8	−	4.65976e8i	0.811041	−	0.702771i
$873$		−	1.75618e8i		−	0.263952i
$874$	−7.55371e8	−	3.13466e8i	−1.13143	−	0.469523i
$875$	1.39701e8			0.208533
$876$	−4.06469e7	−	4.69091e7i	−0.0604666	−	0.0697822i
$877$	3.97596e8	+	2.55519e8i	0.589445	+	0.378813i	0.801099	−	0.598531i	$-0.204249\pi$
$877$	3.97596e8	+	2.55519e8i	0.589445	+	0.378813i	−0.211655	+	0.977345i	$0.567885\pi$
$878$	8.17219e7	−	5.68388e8i	0.120741	−	0.839773i
$879$	−8.89241e7	−	4.06103e7i	−0.130934	−	0.0597956i
$880$	−5.23084e7	−	3.63813e8i	−0.0767580	−	0.533864i
$881$	2.97133e8	−	1.01194e9i	0.434533	−	1.47988i	−0.393564	−	0.919297i	$-0.628758\pi$
$881$	2.97133e8	−	1.01194e9i	0.434533	−	1.47988i	0.828097	−	0.560585i	$-0.189424\pi$
$882$	−1.09657e8	+	7.04723e7i	−0.159820	+	0.102710i
$883$	−2.16352e8	−	4.73745e8i	−0.314252	−	0.688117i	0.684927	−	0.728611i	$-0.259834\pi$
$883$	−2.16352e8	−	4.73745e8i	−0.314252	−	0.688117i	−0.999180	+	0.0404946i	$0.987107\pi$
$884$	9.47569e7	+	3.22712e8i	0.137168	+	0.467153i
$885$	−7.04509e8	−	6.10460e8i	−1.01638	−	0.880699i
$886$	−3.23266e8	+	3.73069e8i	−0.464792	+	0.536399i
$887$	2.09339e8	−	6.14675e7i	0.299971	−	0.0880794i	−0.128284	−	0.991738i	$-0.540947\pi$
$887$	2.09339e8	−	6.14675e7i	0.299971	−	0.0880794i	0.428255	+	0.903658i	$0.359129\pi$
$888$	2.23868e6	−	1.02237e6i	0.00319707	−	0.00146005i
$889$	−2.75249e8	−	4.28295e8i	−0.391760	−	0.609590i
$890$	−3.02025e8	−	8.86826e7i	−0.428424	−	0.125797i
$891$	9.84555e7	−	1.41558e7i	0.139190	−	0.0200125i
$892$	−1.30295e6	+	2.85307e6i	−0.00183584	+	0.00401993i
$893$	−9.09820e8	−	1.30812e8i	−1.27762	−	0.183694i
$894$	1.18355e7	−	1.84163e7i	0.0165643	−	0.0257745i
$895$	−5.71601e7	+	4.95295e7i	−0.0797303	+	0.0690867i
$896$			7.08924e7i			0.0985543i
$897$	−4.78815e8	+	1.59016e8i	−0.663423	+	0.220325i
$898$	5.14415e8			0.710370
$899$	−8.46694e8	−	9.77137e8i	−1.16533	−	1.34486i
$900$	1.29004e8	+	8.29055e7i	0.176960	+	0.113725i
$901$	−6.56009e7	+	4.56264e8i	−0.0896882	+	0.623795i
$902$	−6.42161e8	−	2.93265e8i	−0.875033	−	0.399614i
$903$	−1.64970e6	−	1.14739e7i	−0.00224049	−	0.0155829i
$904$	−6.06314e7	+	2.06492e8i	−0.0820715	+	0.279510i
$905$	8.56322e8	−	5.50325e8i	1.15529	−	0.742460i
$906$	8.21630e7	+	1.79912e8i	0.110482	+	0.241922i
$907$	1.19775e8	+	4.07917e8i	0.160526	+	0.546701i	0.999995	+	0.00329298i	$0.00104819\pi$
$907$	1.19775e8	+	4.07917e8i	0.160526	+	0.546701i	−0.839469	+	0.543408i	$0.817134\pi$
$908$	−3.49627e8	−	3.02954e8i	−0.467033	−	0.404686i
$909$	−2.88451e8	+	3.32890e8i	−0.384044	+	0.443210i
$910$	4.33172e8	−	1.27191e8i	0.574826	−	0.168784i
$911$	7.07929e8	−	3.23300e8i	0.936342	−	0.427613i	0.112002	−	0.993708i	$-0.464274\pi$
$911$	7.07929e8	−	3.23300e8i	0.936342	−	0.427613i	0.824340	+	0.566095i	$0.191547\pi$
$912$	1.13449e8	+	1.76530e8i	0.149560	+	0.232720i
$913$	−1.61392e8	−	4.73890e7i	−0.212065	−	0.0622680i
$914$	4.78113e8	−	6.87423e7i	0.626170	−	0.0900296i
$915$	3.34041e8	−	7.31448e8i	0.436050	−	0.954817i
$916$	−2.34566e8	−	3.37255e7i	−0.305196	−	0.0438805i
$917$	−3.54103e8	+	5.50995e8i	−0.459221	+	0.714562i
$918$	6.70580e7	−	5.81061e7i	0.0866807	−	0.0751093i
$919$			8.78360e8i			1.13169i	0.824513	+	0.565843i	$0.191449\pi$
$919$			8.78360e8i			1.13169i	−0.824513	+	0.565843i	$0.808551\pi$
$920$	−9.22333e8	+	8.57593e8i	−1.18447	+	1.10133i
$921$	−5.36989e8			−0.687363
$922$	2.37726e8	+	2.74350e8i	0.303308	+	0.350036i
$923$	−1.18635e9	−	7.62418e8i	−1.50871	−	0.969590i
$924$	−1.80482e7	+	1.25528e8i	−0.0228779	+	0.159120i
$925$	5.35615e6	+	2.44607e6i	0.00676748	+	0.00309061i
$926$	9.39954e7	+	6.53752e8i	0.118379	+	0.823342i
$927$	−8.55147e7	+	2.91236e8i	−0.107350	+	0.365600i
$928$	1.00802e9	−	6.47818e8i	1.26133	−	0.810605i
$929$	3.05827e8	+	6.69667e8i	0.381442	+	0.835241i	0.998820	+	0.0485744i	$0.0154678\pi$
$929$	3.05827e8	+	6.69667e8i	0.381442	+	0.835241i	−0.617378	+	0.786667i	$0.711805\pi$
$930$	−1.46213e8	−	4.97954e8i	−0.181776	−	0.619071i
$931$	8.25876e8	+	7.15626e8i	1.02345	+	0.886823i
$932$	3.56685e8	−	4.11636e8i	0.440592	−	0.508470i
$933$	8.19517e7	−	2.40632e7i	0.100905	−	0.0296284i
$934$	5.70113e8	−	2.60362e8i	0.699714	−	0.319549i
$935$	7.04433e8	+	1.09612e9i	0.861797	+	1.34098i
$936$	3.38469e8	+	9.93833e7i	0.412754	+	0.121195i
$937$	−1.25617e9	+	1.80609e8i	−1.52696	+	0.219544i	−0.854055	−	0.520183i	$-0.825864\pi$
$937$	−1.25617e9	+	1.80609e8i	−1.52696	+	0.219544i	−0.672907	+	0.739727i	$0.734955\pi$
$938$	−1.82579e8	+	3.99793e8i	−0.221229	+	0.484425i
$939$	7.76341e8	+	1.11621e8i	0.937683	+	0.134818i
$940$	−2.49749e8	+	3.88618e8i	−0.300691	+	0.467885i
$941$	1.03568e9	−	8.97422e8i	1.24296	−	1.07703i	0.248862	−	0.968539i	$-0.419943\pi$
$941$	1.03568e9	−	8.97422e8i	1.24296	−	1.07703i	0.994097	−	0.108491i	$-0.0346020\pi$
$942$		−	2.20381e8i		−	0.263647i
$943$	1.57041e8	+	8.73702e8i	0.187274	+	1.04191i
$944$	−3.62674e8			−0.431122
$945$	7.32915e7	+	8.45829e7i	0.0868477	+	0.100228i
$946$	−3.88596e7	−	2.49735e7i	−0.0459013	−	0.0294989i
$947$	6.48273e7	−	4.50884e8i	0.0763323	−	0.530903i	−0.915397	−	0.402553i	$-0.868123\pi$
$947$	6.48273e7	−	4.50884e8i	0.0763323	−	0.530903i	0.991729	−	0.128350i	$-0.0409680\pi$
$948$	−1.03886e8	−	4.74434e7i	−0.121937	−	0.0556866i
$949$	−4.86175e7	−	3.38142e8i	−0.0568845	−	0.395640i
$950$	−3.85435e8	+	1.31267e9i	−0.449553	+	1.53104i
$951$	−5.68650e8	+	3.65449e8i	−0.661155	+	0.424899i
$952$	1.44002e8	+	3.15320e8i	0.166900	+	0.365460i
$953$	−1.17826e8	−	4.01278e8i	−0.136133	−	0.463625i	0.863003	−	0.505199i	$-0.168581\pi$
$953$	−1.17826e8	−	4.01278e8i	−0.136133	−	0.463625i	−0.999135	+	0.0415739i	$0.986763\pi$
$954$	1.19241e8	+	1.03323e8i	0.137335	+	0.119002i
$955$	1.23249e9	−	1.42237e9i	1.41506	−	1.63306i
$956$	−2.22318e8	+	6.52784e7i	−0.254449	+	0.0747130i
$957$	1.01069e9	−	4.61564e8i	1.15313	−	0.526619i
$958$	−5.25529e8	−	8.17739e8i	−0.597723	−	0.930076i
$959$	2.18225e8	+	6.40767e7i	0.247428	+	0.0726514i
$960$	6.91543e8	−	9.94288e7i	0.781637	−	0.112382i
$961$	1.91863e7	−	4.20122e7i	0.0216183	−	0.0473375i
$962$	4.37555e6	+	629108.i	0.00491481	+	0.000706643i
$963$	−8.48755e7	+	1.32069e8i	−0.0950393	+	0.147884i
$964$	−3.53907e8	+	3.06662e8i	−0.395055	+	0.342317i
$965$		−	9.54363e7i		−	0.106202i
$966$	−1.51801e8	+	7.58615e7i	−0.168400	+	0.0841569i
$967$	−1.58206e8			−0.174962			−0.0874809	−	0.996166i	$-0.527882\pi$
$967$	−1.58206e8			−0.174962			−0.0874809	+	0.996166i	$0.527882\pi$
$968$	3.80948e8	+	4.39638e8i	0.419991	+	0.484695i
$969$	−6.25788e8	−	4.02169e8i	−0.687790	−	0.442016i
$970$	1.12061e8	−	7.79403e8i	0.122783	−	0.853978i
$971$	7.27701e8	+	3.32330e8i	0.794868	+	0.363004i	0.771101	−	0.636713i	$-0.219707\pi$
$971$	7.27701e8	+	3.32330e8i	0.794868	+	0.363004i	0.0237676	+	0.999718i	$0.492434\pi$
$972$	4.06162e6	+	2.82492e7i	0.00442284	+	0.0307615i
$973$	−5.28088e7	+	1.79850e8i	−0.0573281	+	0.195242i
$974$	6.22166e8	−	3.99842e8i	0.673332	−	0.432724i
$975$	3.50607e8	+	7.67721e8i	0.378274	+	0.828304i
$976$	−8.81378e7	−	3.00170e8i	−0.0948009	−	0.322862i
$977$	2.00321e8	+	1.73579e8i	0.214805	+	0.186129i	0.755616	−	0.655014i	$-0.227337\pi$
$977$	2.00321e8	+	1.73579e8i	0.214805	+	0.186129i	−0.540812	+	0.841144i	$0.681883\pi$
$978$	−9.00222e7	+	1.03891e8i	−0.0962350	+	0.111061i
$979$	4.66950e8	−	1.37109e8i	0.497648	−	0.146123i
$980$	4.99574e8	−	2.28148e8i	0.530789	−	0.242403i
$981$	1.71301e8	+	2.66549e8i	0.181448	+	0.282339i
$982$	6.10128e7	+	1.79150e7i	0.0644298	+	0.0189183i
$983$	5.90956e8	−	8.49667e7i	0.622150	−	0.0894516i	0.175971	−	0.984395i	$-0.443694\pi$
$983$	5.90956e8	−	8.49667e7i	0.622150	−	0.0894516i	0.446179	+	0.894944i	$0.352785\pi$
$984$	2.57834e8	−	5.64577e8i	0.270617	−	0.592568i
$985$	7.26453e8	+	1.04448e8i	0.760149	+	0.109293i
$986$	5.35856e8	−	8.33809e8i	0.559007	−	0.869833i
$987$	−1.44144e8	+	1.24902e8i	−0.149915	+	0.129902i
$988$		−	9.65141e8i		−	1.00074i
$989$	2.03505e6	+	5.80489e7i	0.00210371	+	0.0600075i
$990$	4.45985e8			0.459637
$991$	−5.20528e8	−	6.00721e8i	−0.534839	−	0.617237i	0.422444	−	0.906389i	$-0.361172\pi$
$991$	−5.20528e8	−	6.00721e8i	−0.534839	−	0.617237i	−0.957283	+	0.289152i	$0.906627\pi$
$992$	7.27941e8	+	4.67819e8i	0.745695	+	0.479229i
$993$	−1.45140e8	+	1.00947e9i	−0.148231	+	1.03097i
$994$	−4.31468e8	−	1.97045e8i	−0.439328	−	0.200634i
$995$	1.96586e8	+	1.36728e9i	0.199564	+	1.38800i
$996$	1.35970e7	−	4.63072e7i	0.0137615	−	0.0468674i
$997$	−6.72573e8	+	4.32236e8i	−0.678663	+	0.436150i	−0.834039	−	0.551705i	$-0.813977\pi$
$997$	−6.72573e8	+	4.32236e8i	−0.678663	+	0.436150i	0.155377	+	0.987855i	$0.450341\pi$
$998$	−3.59155e8	−	7.86440e8i	−0.361319	−	0.791178i
$999$	308744.	+	1.05149e6i	0.000309672	+	0.00105465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.f.a.10.16	yes	240
23.7	odd	22	inner	69.7.f.a.7.16	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.f.a.7.16	✓	240	23.7	odd	22	inner
69.7.f.a.10.16	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(3.76160 + 4.34111i) q^{2} +(13.1138 + 8.42776i) q^{3} +(4.41249 - 30.6896i) q^{4} +(172.538 + 78.7957i) q^{5} +(12.7431 + 88.6305i) q^{6} +(43.8846 - 149.457i) q^{7} +(459.089 - 295.039i) q^{8} +(100.946 + 221.041i) q^{9} +O(q^{10})\)	\(q+(3.76160 + 4.34111i) q^{2} +(13.1138 + 8.42776i) q^{3} +(4.41249 - 30.6896i) q^{4} +(172.538 + 78.7957i) q^{5} +(12.7431 + 88.6305i) q^{6} +(43.8846 - 149.457i) q^{7} +(459.089 - 295.039i) q^{8} +(100.946 + 221.041i) q^{9} +(306.959 + 1045.41i) q^{10} +(-1273.06 - 1103.11i) q^{11} +(316.509 - 365.271i) q^{12} +(2552.36 - 749.440i) q^{13} +(813.887 - 371.690i) q^{14} +(1598.57 + 2487.43i) q^{15} +(1103.75 + 324.092i) q^{16} +(-4036.43 + 580.350i) q^{17} +(-579.845 + 1269.68i) q^{18} +(11582.8 + 1665.36i) q^{19} +(3179.53 - 4947.44i) q^{20} +(1835.08 - 1590.11i) q^{21} -9675.95i q^{22} +(-9998.78 + 6932.55i) q^{23} +8506.94 q^{24} +(13328.6 + 15382.0i) q^{25} +(12854.3 + 8260.99i) q^{26} +(-539.088 + 3749.44i) q^{27} +(-4393.13 - 2006.28i) q^{28} +(6021.80 + 41882.6i) q^{29} +(-4785.02 + 16296.3i) q^{30} +(-25705.6 + 16520.0i) q^{31} +(-11763.9 - 25759.3i) q^{32} +(-7397.94 - 25195.1i) q^{33} +(-17702.8 - 15339.5i) q^{34} +(19348.4 - 22329.2i) q^{35} +(7229.06 - 2122.64i) q^{36} +(263.159 - 120.181i) q^{37} +(36340.3 + 56546.6i) q^{38} +(39787.3 + 11682.6i) q^{39} +(102458. - 14731.3i) q^{40} +(30308.7 - 66366.7i) q^{41} +(13805.7 + 1984.96i) q^{42} +(2580.99 - 4016.10i) q^{43} +(-39471.4 + 34202.1i) q^{44} +46092.1i q^{45} +(-67706.4 - 17328.4i) q^{46} -78549.2 q^{47} +(11743.1 + 13552.3i) q^{48} +(78561.0 + 50488.1i) q^{49} +(-16638.3 + 115722. i) q^{50} +(-57824.1 - 26407.4i) q^{51} +(-11737.7 - 81637.7i) q^{52} +(31846.1 - 108458. i) q^{53} +(-18304.6 + 11763.6i) q^{54} +(-132731. - 290641. i) q^{55} +(-23948.7 - 81561.9i) q^{56} +(137860. + 119456. i) q^{57} +(-159165. + 183687. i) q^{58} +(-302501. + 88822.3i) q^{59} +(83391.7 - 38083.7i) q^{60} +(-147029. - 228782. i) q^{61} +(-168409. - 49449.4i) q^{62} +(37466.1 - 5386.81i) q^{63} +(98156.9 - 214934. i) q^{64} +(499433. + 71807.6i) q^{65} +(81546.6 - 126889. i) q^{66} +(-371235. + 321677. i) q^{67} +126437. i q^{68} +(-189548. + 6645.09i) q^{69} +169714. q^{70} +(-347163. - 400647. i) q^{71} +(111559. + 71694.4i) q^{72} +(18276.5 - 127116. i) q^{73} +(1511.61 + 690.331i) q^{74} +(45153.1 + 314047. i) q^{75} +(102218. - 348123. i) q^{76} +(-220736. + 141858. i) q^{77} +(98948.3 + 216667. i) q^{78} +(-66572.3 - 226724. i) q^{79} +(164903. + 142889. i) q^{80} +(-38668.9 + 44626.3i) q^{81} +(402114. - 118071. i) q^{82} +(90831.3 - 41481.3i) q^{83} +(-40702.5 - 63334.3i) q^{84} +(-742168. - 217920. i) q^{85} +(27143.0 - 3902.57i) q^{86} +(-274007. + 599992. i) q^{87} +(-909909. - 130825. i) q^{88} +(-156195. + 243044. i) q^{89} +(-200091. + 173380. i) q^{90} -414357. i q^{91} +(168637. + 337448. i) q^{92} -476326. q^{93} +(-295470. - 340991. i) q^{94} +(1.86726e6 + 1.20001e6i) q^{95} +(62823.4 - 436946. i) q^{96} +(-657396. - 300223. i) q^{97} +(76340.3 + 530958. i) q^{98} +(115322. - 392752. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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