LMFDB - Embedded newform 61.8.g.a.3.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,8,Mod(3,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("61.3");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	61.g (of order $10$, degree $4$, 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:	$19.0554865545$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$34$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			3.3
Character	$\chi$	$=$	61.3
Dual form			61.8.g.a.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-18.8795 - 6.13431i) q^{2} +(16.2847 - 50.1192i) q^{3} +(215.250 + 156.388i) q^{4} +(104.780 + 76.1270i) q^{5} +(-614.893 + 846.327i) q^{6} +(-701.080 + 227.795i) q^{7} +(-1610.95 - 2217.28i) q^{8} +(-477.419 - 346.865i) q^{9} +O(q^{10})$	\(q+(-18.8795 - 6.13431i) q^{2} +(16.2847 - 50.1192i) q^{3} +(215.250 + 156.388i) q^{4} +(104.780 + 76.1270i) q^{5} +(-614.893 + 846.327i) q^{6} +(-701.080 + 227.795i) q^{7} +(-1610.95 - 2217.28i) q^{8} +(-477.419 - 346.865i) q^{9} +(-1511.20 - 2079.99i) q^{10} +138.078i q^{11} +(11343.3 - 8241.42i) q^{12} +6609.11 q^{13} +14633.4 q^{14} +(5521.73 - 4011.77i) q^{15} +(6288.44 + 19353.8i) q^{16} +(8182.28 - 11261.9i) q^{17} +(6885.63 + 9477.26i) q^{18} +(3456.88 - 10639.2i) q^{19} +(10648.5 + 32772.7i) q^{20} +38847.1i q^{21} +(847.013 - 2606.84i) q^{22} +(15390.5 - 21183.2i) q^{23} +(-137362. + 44631.7i) q^{24} +(-18958.5 - 58348.2i) q^{25} +(-124777. - 40542.4i) q^{26} +(68081.2 - 49463.9i) q^{27} +(-186532. - 60608.0i) q^{28} -139973. i q^{29} +(-128857. + 41868.1i) q^{30} +(-185131. + 60152.8i) q^{31} -53153.9i q^{32} +(6920.35 + 2248.56i) q^{33} +(-223561. + 162427. i) q^{34} +(-90800.3 - 29502.8i) q^{35} +(-48518.8 - 149325. i) q^{36} +(-73125.9 + 23760.0i) q^{37} +(-130528. + 179657. i) q^{38} +(107627. - 331243. i) q^{39} -354963. i q^{40} +(88294.5 + 271743. i) q^{41} +(238300. - 733413. i) q^{42} +(-340111. - 468122. i) q^{43} +(-21593.8 + 29721.3i) q^{44} +(-23618.0 - 72688.9i) q^{45} +(-420508. + 305517. i) q^{46} +379031. q^{47} +1.07240e6 q^{48} +(-226637. + 164662. i) q^{49} +1.21788e6i q^{50} +(-431193. - 593486. i) q^{51} +(1.42261e6 + 1.03359e6i) q^{52} +(-128986. - 177535. i) q^{53} +(-1.58876e6 + 516220. i) q^{54} +(-10511.5 + 14467.8i) q^{55} +(1.63449e6 + 1.18753e6i) q^{56} +(-476933. - 346512. i) q^{57} +(-858636. + 2.64261e6i) q^{58} +(1.17834e6 + 382865. i) q^{59} +1.81595e6 q^{60} +(-1.59590e6 - 771915. i) q^{61} +3.86417e6 q^{62} +(413723. + 134427. i) q^{63} +(478858. - 1.47377e6i) q^{64} +(692502. + 503132. i) q^{65} +(-116859. - 84903.2i) q^{66} +(1.29202e6 - 1.77832e6i) q^{67} +(3.52248e6 - 1.14452e6i) q^{68} +(-811054. - 1.11632e6i) q^{69} +(1.53328e6 + 1.11399e6i) q^{70} +(-1.69844e6 - 2.33770e6i) q^{71} +1.61735e6i q^{72} +(543950. - 395203. i) q^{73} +1.52633e6 q^{74} -3.23309e6 q^{75} +(2.40794e6 - 1.74947e6i) q^{76} +(-31453.4 - 96803.7i) q^{77} +(-4.06390e6 + 5.59347e6i) q^{78} +(-4.30461e6 - 5.92479e6i) q^{79} +(-814447. + 2.50661e6i) q^{80} +(-1.76922e6 - 5.44510e6i) q^{81} -5.67198e6i q^{82} +(-1.38289e6 + 4.25609e6i) q^{83} +(-6.07524e6 + 8.36185e6i) q^{84} +(1.71468e6 - 557132. i) q^{85} +(3.54950e6 + 1.09242e7i) q^{86} +(-7.01532e6 - 2.27941e6i) q^{87} +(306158. - 222437. i) q^{88} +(-312767. - 101624. i) q^{89} +1.51721e6i q^{90} +(-4.63352e6 + 1.50552e6i) q^{91} +(6.62561e6 - 2.15279e6i) q^{92} +1.02582e7i q^{93} +(-7.15590e6 - 2.32509e6i) q^{94} +(1.17214e6 - 851610. i) q^{95} +(-2.66403e6 - 865596. i) q^{96} +(-2.13593e6 - 6.57373e6i) q^{97} +(5.28888e6 - 1.71846e6i) q^{98} +(47894.4 - 65921.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 5 q^{2} - 57 q^{3} + 1969 q^{4} + 414 q^{5} - 275 q^{6} - 2650 q^{7} - 5 q^{8} - 22677 q^{9}+O(q^{10}) $ 136 * q - 5 * q^2 - 57 * q^3 + 1969 * q^4 + 414 * q^5 - 275 * q^6 - 2650 * q^7 - 5 * q^8 - 22677 * q^9	\( 136 q - 5 q^{2} - 57 q^{3} + 1969 q^{4} + 414 q^{5} - 275 q^{6} - 2650 q^{7} - 5 q^{8} - 22677 q^{9} + 18405 q^{10} - 14698 q^{12} - 41840 q^{13} + 51126 q^{14} + 7203 q^{15} - 94007 q^{16} - 31920 q^{17} + 72980 q^{18} + 102795 q^{19} + 147581 q^{20} - 168127 q^{22} - 277935 q^{23} + 921540 q^{24} - 609554 q^{25} - 341870 q^{26} - 139608 q^{27} - 355845 q^{28} + 218815 q^{30} - 235615 q^{31} + 96625 q^{33} + 1996448 q^{34} - 821930 q^{35} + 1923233 q^{36} - 5 q^{37} + 164715 q^{38} - 55295 q^{39} - 2738004 q^{41} - 3935531 q^{42} - 124265 q^{43} + 496870 q^{44} - 1705580 q^{45} + 3949707 q^{46} - 6522690 q^{47} + 4081416 q^{48} + 4581948 q^{49} + 3506350 q^{51} - 4794960 q^{52} + 2288650 q^{53} + 13111480 q^{54} - 7615700 q^{55} - 8104924 q^{56} - 1851487 q^{57} + 2821869 q^{58} + 512285 q^{59} - 11303002 q^{60} + 4003165 q^{61} + 11267092 q^{62} - 3732265 q^{63} + 4089213 q^{64} + 14201480 q^{65} - 4750133 q^{66} - 2990255 q^{67} - 28116100 q^{68} + 6452165 q^{69} + 2929505 q^{70} - 20770790 q^{71} + 4931233 q^{73} - 2981520 q^{74} + 43273192 q^{75} + 6320137 q^{76} - 4357269 q^{77} + 32574470 q^{78} - 1203220 q^{79} - 64168363 q^{80} + 16681123 q^{81} + 20705839 q^{83} - 25806085 q^{84} - 36617415 q^{85} + 463139 q^{86} - 4611115 q^{87} + 52109661 q^{88} + 39392730 q^{89} - 31163475 q^{91} - 31104005 q^{92} + 15981295 q^{94} + 8937948 q^{95} + 91723305 q^{96} + 5094353 q^{97} - 84253670 q^{98} - 55470065 q^{99}+O(q^{100}) \) 136 * q - 5 * q^2 - 57 * q^3 + 1969 * q^4 + 414 * q^5 - 275 * q^6 - 2650 * q^7 - 5 * q^8 - 22677 * q^9 + 18405 * q^10 - 14698 * q^12 - 41840 * q^13 + 51126 * q^14 + 7203 * q^15 - 94007 * q^16 - 31920 * q^17 + 72980 * q^18 + 102795 * q^19 + 147581 * q^20 - 168127 * q^22 - 277935 * q^23 + 921540 * q^24 - 609554 * q^25 - 341870 * q^26 - 139608 * q^27 - 355845 * q^28 + 218815 * q^30 - 235615 * q^31 + 96625 * q^33 + 1996448 * q^34 - 821930 * q^35 + 1923233 * q^36 - 5 * q^37 + 164715 * q^38 - 55295 * q^39 - 2738004 * q^41 - 3935531 * q^42 - 124265 * q^43 + 496870 * q^44 - 1705580 * q^45 + 3949707 * q^46 - 6522690 * q^47 + 4081416 * q^48 + 4581948 * q^49 + 3506350 * q^51 - 4794960 * q^52 + 2288650 * q^53 + 13111480 * q^54 - 7615700 * q^55 - 8104924 * q^56 - 1851487 * q^57 + 2821869 * q^58 + 512285 * q^59 - 11303002 * q^60 + 4003165 * q^61 + 11267092 * q^62 - 3732265 * q^63 + 4089213 * q^64 + 14201480 * q^65 - 4750133 * q^66 - 2990255 * q^67 - 28116100 * q^68 + 6452165 * q^69 + 2929505 * q^70 - 20770790 * q^71 + 4931233 * q^73 - 2981520 * q^74 + 43273192 * q^75 + 6320137 * q^76 - 4357269 * q^77 + 32574470 * q^78 - 1203220 * q^79 - 64168363 * q^80 + 16681123 * q^81 + 20705839 * q^83 - 25806085 * q^84 - 36617415 * q^85 + 463139 * q^86 - 4611115 * q^87 + 52109661 * q^88 + 39392730 * q^89 - 31163475 * q^91 - 31104005 * q^92 + 15981295 * q^94 + 8937948 * q^95 + 91723305 * q^96 + 5094353 * q^97 - 84253670 * q^98 - 55470065 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−18.8795	−	6.13431i	−1.66872	−	0.542201i	−0.686052	−	0.727552i	$-0.740658\pi$
$2$	−18.8795	−	6.13431i	−1.66872	−	0.542201i	−0.982672	+	0.185351i	$0.940658\pi$
$3$	16.2847	−	50.1192i	0.348221	−	1.07172i	−0.611615	−	0.791155i	$-0.709480\pi$
$3$	16.2847	−	50.1192i	0.348221	−	1.07172i	0.959837	−	0.280560i	$-0.0905201\pi$
$4$	215.250	+	156.388i	1.68164	+	1.22178i
$5$	104.780	+	76.1270i	0.374872	+	0.272360i	0.759228	−	0.650825i	$-0.225577\pi$
$5$	104.780	+	76.1270i	0.374872	+	0.272360i	−0.384357	+	0.923185i	$0.625577\pi$
$6$	−614.893	+	846.327i	−1.16217	+	1.59959i
$7$	−701.080	+	227.795i	−0.772546	+	0.251015i	−0.668655	−	0.743573i	$-0.733130\pi$
$7$	−701.080	+	227.795i	−0.772546	+	0.251015i	−0.103892	+	0.994589i	$0.533130\pi$
$8$	−1610.95	−	2217.28i	−1.11242	−	1.53111i
$9$	−477.419	−	346.865i	−0.218298	−	0.158603i
$10$	−1511.20	−	2079.99i	−0.477883	−	0.657750i
$11$			138.078i			0.0312788i	0.999878	+	0.0156394i	$0.00497838\pi$
$11$			138.078i			0.0312788i	−0.999878	+	0.0156394i	$0.995022\pi$
$12$	11343.3	−	8241.42i	1.89499	−	1.37679i
$13$	6609.11			0.834337			0.417169	−	0.908829i	$-0.363022\pi$
$13$	6609.11			0.834337			0.417169	+	0.908829i	$0.363022\pi$
$14$	14633.4			1.42527
$15$	5521.73	−	4011.77i	0.422431	−	0.306914i
$16$	6288.44	+	19353.8i	0.383816	+	1.18126i
$17$	8182.28	−	11261.9i	0.403927	−	0.555958i	−0.557797	−	0.829977i	$-0.688353\pi$
$17$	8182.28	−	11261.9i	0.403927	−	0.555958i	0.961724	+	0.274019i	$0.0883532\pi$
$18$	6885.63	+	9477.26i	0.278285	+	0.383027i
$19$	3456.88	−	10639.2i	0.115624	−	0.355853i	−0.876453	−	0.481488i	$-0.840097\pi$
$19$	3456.88	−	10639.2i	0.115624	−	0.355853i	0.992077	+	0.125634i	$0.0400966\pi$
$20$	10648.5	+	32772.7i	0.297634	+	0.916025i
$21$			38847.1i			0.915359i
$22$	847.013	−	2606.84i	0.0169594	−	0.0521957i
$23$	15390.5	−	21183.2i	0.263757	−	0.363031i	−0.656512	−	0.754315i	$-0.727969\pi$
$23$	15390.5	−	21183.2i	0.263757	−	0.363031i	0.920270	+	0.391284i	$0.127969\pi$
$24$	−137362.	+	44631.7i	−2.02828	+	0.659028i
$25$	−18958.5	−	58348.2i	−0.242668	−	0.746856i
$26$	−124777.	−	40542.4i	−1.39228	−	0.452379i
$27$	68081.2	−	49463.9i	0.665662	−	0.483632i
$28$	−186532.	−	60608.0i	−1.60583	−	0.521767i
$29$		−	139973.i		−	1.06574i	−0.846198	−	0.532869i	$-0.821114\pi$
$29$		−	139973.i		−	1.06574i	0.846198	−	0.532869i	$-0.178886\pi$
$30$	−128857.	+	41868.1i	−0.871330	+	0.283112i
$31$	−185131.	+	60152.8i	−1.11613	+	0.362652i	−0.808288	−	0.588787i	$-0.799606\pi$
$31$	−185131.	+	60152.8i	−1.11613	+	0.362652i	−0.307839	+	0.951438i	$0.599606\pi$
$32$		−	53153.9i		−	0.286755i
$33$	6920.35	+	2248.56i	0.0335220	+	0.0108919i
$34$	−223561.	+	162427.i	−0.975485	+	0.708731i
$35$	−90800.3	−	29502.8i	−0.357972	−	0.116312i
$36$	−48518.8	−	149325.i	−0.173321	−	0.533427i
$37$	−73125.9	+	23760.0i	−0.237337	+	0.0771154i	−0.425270	−	0.905066i	$-0.639821\pi$
$37$	−73125.9	+	23760.0i	−0.237337	+	0.0771154i	0.187934	+	0.982182i	$0.439821\pi$
$38$	−130528.	+	179657.i	−0.385888	+	0.531130i
$39$	107627.	−	331243.i	0.290534	−	0.894172i
$40$		−	354963.i		−	0.876947i
$41$	88294.5	+	271743.i	0.200074	+	0.615764i	0.999880	+	0.0155052i	$0.00493566\pi$
$41$	88294.5	+	271743.i	0.200074	+	0.615764i	−0.799806	+	0.600259i	$0.795064\pi$
$42$	238300.	−	733413.i	0.496309	−	1.52748i
$43$	−340111.	−	468122.i	−0.652350	−	0.897883i	0.346848	−	0.937921i	$-0.387252\pi$
$43$	−340111.	−	468122.i	−0.652350	−	0.897883i	−0.999198	+	0.0400386i	$0.987252\pi$
$44$	−21593.8	+	29721.3i	−0.0382159	+	0.0525997i
$45$	−23618.0	−	72688.9i	−0.0386367	−	0.118912i
$46$	−420508.	+	305517.i	−0.636975	+	0.462789i
$47$	379031.			0.532515			0.266258	−	0.963902i	$-0.414213\pi$
$47$	379031.			0.532515			0.266258	+	0.963902i	$0.414213\pi$
$48$	1.07240e6			1.39963
$49$	−226637.	+	164662.i	−0.275198	+	0.199943i
$50$			1.21788e6i			1.37787i
$51$	−431193.	−	593486.i	−0.455173	−	0.626492i
$52$	1.42261e6	+	1.03359e6i	1.40306	+	1.01938i
$53$	−128986.	−	177535.i	−0.119009	−	0.163801i	0.745356	−	0.666666i	$-0.232279\pi$
$53$	−128986.	−	177535.i	−0.119009	−	0.163801i	−0.864365	+	0.502865i	$0.832279\pi$
$54$	−1.58876e6	+	516220.i	−1.37303	+	0.446125i
$55$	−10511.5	+	14467.8i	−0.00851910	+	0.0117255i
$56$	1.63449e6	+	1.18753e6i	1.24372	+	0.903619i
$57$	−476933.	−	346512.i	−0.341111	−	0.247832i
$58$	−858636.	+	2.64261e6i	−0.577845	+	1.77842i
$59$	1.17834e6	+	382865.i	0.746943	+	0.242697i	0.657665	−	0.753310i	$-0.271544\pi$
$59$	1.17834e6	+	382865.i	0.746943	+	0.242697i	0.0892779	+	0.996007i	$0.471544\pi$
$60$	1.81595e6			1.08536
$61$	−1.59590e6	−	771915.i	−0.900224	−	0.435427i
$61$	−1.59590e6	−	771915.i	−0.900224	−	0.435427i
$62$	3.86417e6			2.05914
$63$	413723.	+	134427.i	0.208457	+	0.0677319i
$64$	478858.	−	1.47377e6i	0.228337	−	0.702749i
$65$	692502.	+	503132.i	0.312769	+	0.227240i
$66$	−116859.	−	84903.2i	−0.0500333	−	0.0363513i
$67$	1.29202e6	−	1.77832e6i	0.524818	−	0.722351i	−0.461511	−	0.887134i	$-0.652693\pi$
$67$	1.29202e6	−	1.77832e6i	0.524818	−	0.722351i	0.986330	+	0.164784i	$0.0526926\pi$
$68$	3.52248e6	−	1.14452e6i	1.35852	−	0.441411i
$69$	−811054.	−	1.11632e6i	−0.297220	−	0.409088i
$70$	1.53328e6	+	1.11399e6i	0.534292	+	0.388186i
$71$	−1.69844e6	−	2.33770e6i	−0.563178	−	0.775148i	0.428548	−	0.903519i	$-0.359025\pi$
$71$	−1.69844e6	−	2.33770e6i	−0.563178	−	0.775148i	−0.991726	+	0.128371i	$0.959025\pi$
$72$			1.61735e6i			0.510671i
$73$	543950.	−	395203.i	0.163655	−	0.118902i	−0.502943	−	0.864319i	$-0.667750\pi$
$73$	543950.	−	395203.i	0.163655	−	0.118902i	0.666598	+	0.745417i	$0.267750\pi$
$74$	1.52633e6			0.437862
$75$	−3.23309e6			−0.884920
$76$	2.40794e6	−	1.74947e6i	0.629214	−	0.457151i
$77$	−31453.4	−	96803.7i	−0.00785146	−	0.0241643i
$78$	−4.06390e6	+	5.59347e6i	−0.969642	+	1.33460i
$79$	−4.30461e6	−	5.92479e6i	−0.982288	−	1.35200i	−0.935587	−	0.353095i	$-0.885129\pi$
$79$	−4.30461e6	−	5.92479e6i	−0.982288	−	1.35200i	−0.0467009	−	0.998909i	$-0.514871\pi$
$80$	−814447.	+	2.50661e6i	−0.177847	+	0.547358i
$81$	−1.76922e6	−	5.44510e6i	−0.369900	−	1.13844i
$82$		−	5.67198e6i		−	1.13602i
$83$	−1.38289e6	+	4.25609e6i	−0.265469	+	0.817029i	0.726116	+	0.687572i	$0.241323\pi$
$83$	−1.38289e6	+	4.25609e6i	−0.265469	+	0.817029i	−0.991585	+	0.129457i	$0.958677\pi$
$84$	−6.07524e6	+	8.36185e6i	−1.11837	+	1.53931i
$85$	1.71468e6	−	557132.i	0.302842	−	0.0983992i
$86$	3.54950e6	+	1.09242e7i	0.601759	+	1.85202i
$87$	−7.01532e6	−	2.27941e6i	−1.14217	−	0.371113i
$88$	306158.	−	222437.i	0.0478912	−	0.0347950i
$89$	−312767.	−	101624.i	−0.0470279	−	0.0152803i	0.285409	−	0.958406i	$-0.407871\pi$
$89$	−312767.	−	101624.i	−0.0470279	−	0.0152803i	−0.332437	+	0.943126i	$0.607871\pi$
$90$			1.51721e6i			0.219379i
$91$	−4.63352e6	+	1.50552e6i	−0.644564	+	0.209432i
$92$	6.62561e6	−	2.15279e6i	0.887091	−	0.288233i
$93$			1.02582e7i			1.32245i
$94$	−7.15590e6	−	2.32509e6i	−0.888621	−	0.288730i
$95$	1.17214e6	−	851610.i	0.140264	−	0.101908i
$96$	−2.66403e6	−	865596.i	−0.307319	−	0.0998541i
$97$	−2.13593e6	−	6.57373e6i	−0.237622	−	0.731326i	−0.996763	−	0.0803990i	$-0.974381\pi$
$97$	−2.13593e6	−	6.57373e6i	−0.237622	−	0.731326i	0.759141	−	0.650927i	$-0.225619\pi$
$98$	5.28888e6	−	1.71846e6i	0.567639	−	0.184437i
$99$	47894.4	−	65921.0i	0.00496091	−	0.00682811i
$100$	5.04416e6	−	1.55243e7i	0.504416	−	1.55243i
$101$			3.37812e6i			0.326249i	0.986605	+	0.163125i	$0.0521573\pi$
$101$			3.37812e6i			0.326249i	−0.986605	+	0.163125i	$0.947843\pi$
$102$	4.50007e6	+	1.38498e7i	0.419873	+	1.29224i
$103$	2.13766e6	−	6.57903e6i	0.192756	−	0.593242i	−0.807239	−	0.590224i	$-0.799039\pi$
$103$	2.13766e6	−	6.57903e6i	0.192756	−	0.593242i	0.999995	−	0.00301785i	$-0.000960612\pi$
$104$	−1.06470e7	−	1.46543e7i	−0.928130	−	1.27746i
$105$	−2.95731e6	+	4.07039e6i	−0.249307	+	0.343142i
$106$	1.34614e6	+	4.14300e6i	0.109779	+	0.337866i
$107$	4.59415e6	−	3.33784e6i	0.362545	−	0.263404i	−0.391568	−	0.920149i	$-0.628067\pi$
$107$	4.59415e6	−	3.33784e6i	0.362545	−	0.263404i	0.754113	+	0.656745i	$0.228067\pi$
$108$	2.23901e7			1.71030
$109$	−4.74646e6			−0.351056			−0.175528	−	0.984474i	$-0.556163\pi$
$109$	−4.74646e6			−0.351056			−0.175528	+	0.984474i	$0.556163\pi$
$110$	287200.	−	208663.i	0.0205736	−	0.0149476i
$111$			4.05193e6i			0.281211i
$112$	−8.81740e6	−	1.21361e7i	−0.593031	−	0.816237i
$113$	2.00223e7	+	1.45470e7i	1.30539	+	0.948419i	0.999993	−	0.00380759i	$-0.00121200\pi$
$113$	2.00223e7	+	1.45470e7i	1.30539	+	0.948419i	0.305394	+	0.952226i	$0.401212\pi$
$114$	6.87863e6	+	9.46762e6i	0.434845	+	0.598513i
$115$	3.22522e6	−	1.04794e6i	0.197750	−	0.0642530i
$116$	2.18901e7	−	3.01292e7i	1.30210	−	1.79219i
$117$	−3.15531e6	−	2.29247e6i	−0.182134	−	0.132328i
$118$	−1.98978e7	−	1.44566e7i	−1.11485	−	0.809987i
$119$	−3.17102e6	+	9.75941e6i	−0.172498	+	0.530895i
$120$	−1.77905e7	−	5.78047e6i	−0.939837	−	0.305372i
$121$	1.94681e7			0.999022
$122$	2.53945e7	+	2.43631e7i	1.26614	+	1.21471i
$123$	1.50574e7			0.729593
$124$	−4.92567e7	−	1.60045e7i	−2.32001	−	0.753817i
$125$	5.58215e6	−	1.71801e7i	0.255633	−	0.786756i
$126$	−6.98625e6	−	5.07581e6i	−0.311134	−	0.226052i
$127$	−2.38630e7	−	1.73375e7i	−1.03374	−	0.751058i	−0.0646884	−	0.997906i	$-0.520605\pi$
$127$	−2.38630e7	−	1.73375e7i	−1.03374	−	0.751058i	−0.969054	+	0.246847i	$0.920605\pi$
$128$	−2.20803e7	+	3.03909e7i	−0.930614	+	1.28088i
$129$	−2.90005e7	+	9.42283e6i	−1.18944	+	0.386471i
$130$	−9.98769e6	−	1.37469e7i	−0.398716	−	0.548785i
$131$	−1.19397e7	−	8.67472e6i	−0.464029	−	0.337137i	0.331081	−	0.943602i	$-0.392587\pi$
$131$	−1.19397e7	−	8.67472e6i	−0.464029	−	0.337137i	−0.795110	+	0.606466i	$0.792587\pi$
$132$	1.13796e6	+	1.56627e6i	0.0430643	+	0.0592730i
$133$			8.24639e6i			0.303937i
$134$	−3.53015e7	+	2.56480e7i	−1.26744	+	0.920847i
$135$	1.08991e7			0.381260
$136$	−3.81522e7			−1.30057
$137$	1.93616e7	−	1.40670e7i	0.643307	−	0.467390i	−0.217678	−	0.976021i	$-0.569848\pi$
$137$	1.93616e7	−	1.40670e7i	0.643307	−	0.467390i	0.860985	+	0.508631i	$0.169848\pi$
$138$	8.46441e6	+	2.60508e7i	0.274170	+	0.843808i
$139$	−2.34715e7	+	3.23057e7i	−0.741291	+	1.02030i	0.257252	+	0.966344i	$0.417183\pi$
$139$	−2.34715e7	+	3.23057e7i	−0.741291	+	1.02030i	−0.998543	+	0.0539551i	$0.982817\pi$
$140$	−1.49309e7	−	2.05506e7i	−0.459873	−	0.632960i
$141$	6.17240e6	−	1.89967e7i	0.185433	−	0.570704i
$142$	1.77254e7	+	5.45533e7i	0.519503	+	1.59886i
$143$			912573.i			0.0260971i
$144$	3.71095e6	−	1.14211e7i	0.103566	−	0.318742i
$145$	1.06557e7	−	1.46663e7i	0.290265	−	0.399515i
$146$	−1.26938e7	+	4.12446e6i	−0.337564	+	0.109681i
$147$	4.56198e6	+	1.40403e7i	0.118452	+	0.364558i
$148$	−1.94562e7	−	6.32169e6i	−0.493334	−	0.160294i
$149$	6.39698e7	−	4.64767e7i	1.58425	−	1.15102i	0.672631	−	0.739978i	$-0.265164\pi$
$149$	6.39698e7	−	4.64767e7i	1.58425	−	1.15102i	0.911615	−	0.411044i	$-0.134836\pi$
$150$	6.10391e7	+	1.98328e7i	1.47669	+	0.479805i
$151$		−	7.28076e7i		−	1.72091i	−0.509530	−	0.860453i	$-0.670181\pi$
$151$		−	7.28076e7i		−	1.72091i	0.509530	−	0.860453i	$-0.329819\pi$
$152$	−2.91590e7	+	9.47432e6i	−0.673472	+	0.218824i
$153$	−7.81275e6	+	2.53852e6i	−0.176353	+	0.0573007i
$154$			2.02055e6i			0.0445807i
$155$	−2.39773e7	−	7.79068e6i	−0.517176	−	0.168041i
$156$	7.49694e7	−	5.44685e7i	1.58106	−	1.14871i
$157$	8.22980e7	+	2.67402e7i	1.69723	+	0.551463i	0.988126	−	0.153643i	$-0.0491005\pi$
$157$	8.22980e7	+	2.67402e7i	1.69723	+	0.551463i	0.709102	+	0.705106i	$0.249101\pi$
$158$	4.49242e7	+	1.38263e8i	0.906110	+	2.78872i
$159$	−1.09984e7	+	3.57359e6i	−0.216990	+	0.0705042i
$160$	4.04645e6	−	5.56945e6i	0.0781005	−	0.107496i
$161$	−5.96454e6	+	1.83570e7i	−0.112638	+	0.346665i
$162$			1.13654e8i			2.10030i
$163$	1.54596e7	+	4.75798e7i	0.279603	+	0.860530i	0.987965	+	0.154680i	$0.0494347\pi$
$163$	1.54596e7	+	4.75798e7i	0.279603	+	0.860530i	−0.708361	+	0.705850i	$0.750565\pi$
$164$	−2.34920e7	+	7.23009e7i	−0.415878	+	1.27994i
$165$	553937.	+	762429.i	0.00959990	+	0.0132131i
$166$	5.22163e7	−	7.18696e7i	0.885988	−	1.21946i
$167$	−1.63709e7	−	5.03845e7i	−0.271998	−	0.837122i	−0.989998	−	0.141080i	$-0.954943\pi$
$167$	−1.63709e7	−	5.03845e7i	−0.271998	−	0.837122i	0.718001	−	0.696042i	$-0.245057\pi$
$168$	8.61350e7	−	6.25808e7i	1.40151	−	1.01826i
$169$	−1.90681e7			−0.303882
$170$	−3.57898e7			−0.558712
$171$	−5.34074e6	+	3.88028e6i	−0.0816799	+	0.0593439i
$172$		−	1.53953e8i		−	2.30695i
$173$	−1.02924e7	−	1.41663e7i	−0.151132	−	0.208015i	0.726738	−	0.686915i	$-0.241036\pi$
$173$	−1.02924e7	−	1.41663e7i	−0.151132	−	0.208015i	−0.877869	+	0.478900i	$0.841036\pi$
$174$	1.18463e8	+	8.60683e7i	1.70475	+	1.23857i
$175$	2.65828e7	+	3.65881e7i	0.374945	+	0.516068i
$176$	−2.67234e6	+	868295.i	−0.0369485	+	0.0120053i
$177$	3.83777e7	−	5.28224e7i	0.520203	−	0.715998i
$178$	5.28148e6	+	3.83722e6i	0.0701917	+	0.0509972i
$179$	−1.04227e8	−	7.57251e7i	−1.35829	−	0.986858i	−0.998551	−	0.0538055i	$-0.982865\pi$
$179$	−1.04227e8	−	7.57251e7i	−1.35829	−	0.986858i	−0.359741	−	0.933052i	$-0.617135\pi$
$180$	6.28391e6	−	1.93399e7i	0.0803112	−	0.247172i
$181$	−6.68435e7	−	2.17188e7i	−0.837885	−	0.272245i	−0.141522	−	0.989935i	$-0.545200\pi$
$181$	−6.68435e7	−	2.17188e7i	−0.837885	−	0.272245i	−0.696363	+	0.717690i	$0.745200\pi$
$182$	9.67137e7			1.18915
$183$	−6.46765e7	+	6.74147e7i	−0.780131	+	0.813159i
$184$	−7.17624e7			−0.849248
$185$	−9.47089e6	−	3.07728e6i	−0.109974	−	0.0357327i
$186$	6.29269e7	−	1.93669e8i	0.717036	−	2.20681i
$187$	1.55503e6	+	1.12979e6i	0.0173897	+	0.0126344i
$188$	8.15864e7	+	5.92760e7i	0.895500	+	0.650619i
$189$	−3.64627e7	+	5.01867e7i	−0.392856	+	0.540719i
$190$	−2.73534e7	+	8.88767e6i	−0.289317	+	0.0940049i
$191$	3.41678e7	+	4.70279e7i	0.354814	+	0.488359i	0.948695	−	0.316194i	$-0.102405\pi$
$191$	3.41678e7	+	4.70279e7i	0.354814	+	0.488359i	−0.593881	+	0.804553i	$0.702405\pi$
$192$	−6.60662e7	−	4.79999e7i	−0.673635	−	0.489425i
$193$	5.67648e7	+	7.81301e7i	0.568367	+	0.782290i	0.992360	−	0.123375i	$-0.0393720\pi$
$193$	5.67648e7	+	7.81301e7i	0.568367	+	0.782290i	−0.423993	+	0.905665i	$0.639372\pi$
$194$			1.37211e8i			1.34922i
$195$	3.64937e7	−	2.65142e7i	0.352450	−	0.256070i
$196$	−7.45349e7			−0.707072
$197$	1.52165e7			0.141802			0.0709009	−	0.997483i	$-0.477413\pi$
$197$	1.52165e7			0.141802			0.0709009	+	0.997483i	$0.477413\pi$
$198$	−1.30860e6	+	950754.i	−0.0119806	+	0.00870442i
$199$	3.00049e7	+	9.23456e7i	0.269902	+	0.830673i	0.990523	+	0.137344i	$0.0438567\pi$
$199$	3.00049e7	+	9.23456e7i	0.269902	+	0.830673i	−0.720621	+	0.693329i	$0.756143\pi$
$200$	−9.88332e7	+	1.36032e8i	−0.873570	+	1.20237i
$201$	−6.80876e7	−	9.37146e7i	−0.591401	−	0.813994i
$202$	2.07224e7	−	6.37770e7i	0.176893	−	0.544421i
$203$	3.18851e7	+	9.81321e7i	0.267517	+	0.823332i
$204$		−	1.95182e8i		−	1.60966i
$205$	−1.14355e7	+	3.51947e7i	−0.0927075	+	0.285324i
$206$	−8.07157e7	+	1.11096e8i	−0.643313	+	0.885445i
$207$	−1.46954e7	+	4.77483e6i	−0.115156	+	0.0374163i
$208$	4.15610e7	+	1.27912e8i	0.320232	+	0.985572i
$209$	1.46904e6	+	477319.i	0.0111307	+	0.00361657i
$210$	8.08015e7	−	5.87057e7i	0.602077	−	0.437435i
$211$	−2.44456e8	−	7.94284e7i	−1.79148	−	0.582086i	−0.791886	−	0.610669i	$-0.790900\pi$
$211$	−2.44456e8	−	7.94284e7i	−1.79148	−	0.582086i	−0.999591	+	0.0285830i	$0.990900\pi$
$212$		−	5.83863e7i		−	0.420858i
$213$	−1.44822e8	+	4.70556e7i	−1.02685	+	0.333643i
$214$	−1.07210e8	+	3.48348e7i	−0.747806	+	0.242977i
$215$		−	7.49413e7i		−	0.514265i
$216$	−2.19351e8	−	7.12714e7i	−1.48099	−	0.481201i
$217$	1.16089e8	−	8.43438e7i	0.771229	−	0.560331i
$218$	8.96105e7	+	2.91162e7i	0.585816	+	0.190343i
$219$	−1.09492e7	−	3.36981e7i	−0.0704412	−	0.216796i
$220$	−4.52519e6	+	1.47032e6i	−0.0286521	+	0.00930964i
$221$	5.40776e7	−	7.44315e7i	0.337011	−	0.463857i
$222$	2.48558e7	−	7.64983e7i	0.152473	−	0.469263i
$223$		−	7.38226e7i		−	0.445782i	−0.974843	−	0.222891i	$-0.928451\pi$
$223$		−	7.38226e7i		−	0.445782i	0.974843	−	0.222891i	$-0.0715493\pi$
$224$	1.21082e7	+	3.72651e7i	0.0719798	+	0.221531i
$225$	−1.11878e7	+	3.44325e7i	−0.0654796	+	0.201525i
$226$	−2.88774e8	−	3.97463e8i	−1.66410	−	2.29043i
$227$	−5.47481e7	+	7.53543e7i	−0.310655	+	0.427580i	−0.935585	−	0.353101i	$-0.885127\pi$
$227$	−5.47481e7	+	7.53543e7i	−0.310655	+	0.427580i	0.624930	+	0.780681i	$0.285127\pi$
$228$	−4.84695e7	−	1.49174e8i	−0.270830	−	0.833528i
$229$	8.16855e7	−	5.93480e7i	0.449491	−	0.326574i	−0.339904	−	0.940460i	$-0.610394\pi$
$229$	8.16855e7	−	5.93480e7i	0.449491	−	0.326574i	0.789395	+	0.613886i	$0.210394\pi$
$230$	−6.73188e7			−0.364829
$231$	−5.36393e6			−0.0286313
$232$	−3.10359e8	+	2.25489e8i	−1.63176	+	1.18554i
$233$		−	2.48257e8i		−	1.28575i	−0.765972	−	0.642874i	$-0.777742\pi$
$233$		−	2.48257e8i		−	1.28575i	0.765972	−	0.642874i	$-0.222258\pi$
$234$	4.55079e7	+	6.26363e7i	0.232184	+	0.319573i
$235$	3.97147e7	+	2.88545e7i	0.199625	+	0.145036i
$236$	1.93762e8	+	2.66690e8i	0.959568	+	1.32073i
$237$	−3.67045e8	+	1.19260e8i	−1.79102	+	0.581937i
$238$	1.19734e8	−	1.64800e8i	0.575705	−	0.792389i
$239$	4.87040e7	+	3.53855e7i	0.230766	+	0.167661i	0.697160	−	0.716916i	$-0.254447\pi$
$239$	4.87040e7	+	3.53855e7i	0.230766	+	0.167661i	−0.466393	+	0.884577i	$0.654447\pi$
$240$	1.12366e8	+	8.16388e7i	0.524682	+	0.381204i
$241$	−4.59973e7	+	1.41565e8i	−0.211677	+	0.651474i	0.787696	+	0.616064i	$0.211274\pi$
$241$	−4.59973e7	+	1.41565e8i	−0.211677	+	0.651474i	−0.999373	+	0.0354099i	$0.988726\pi$
$242$	−3.67547e8	−	1.19423e8i	−1.66709	−	0.541671i
$243$	−1.17673e8			−0.526083
$244$	−2.22799e8	−	4.15735e8i	−0.981857	−	1.83211i
$245$	−3.62822e7			−0.157620
$246$	−2.84275e8	−	9.23665e7i	−1.21749	−	0.395587i
$247$	2.28469e7	−	7.03156e7i	0.0964692	−	0.296902i
$248$	4.31613e8	+	3.13585e8i	1.79686	+	1.30549i
$249$	1.90792e8	+	1.38618e8i	0.783180	+	0.569014i
$250$	−2.10776e8	+	2.90108e8i	−0.853161	+	1.17428i
$251$	2.59845e8	−	8.44288e7i	1.03719	−	0.337002i	0.259558	−	0.965727i	$-0.416423\pi$
$251$	2.59845e8	−	8.44288e7i	1.03719	−	0.337002i	0.777627	+	0.628725i	$0.216423\pi$
$252$	6.80311e7	+	9.36368e7i	0.267797	+	0.368591i
$253$	2.92493e6	+	2.12509e6i	0.0113552	+	0.00825002i
$254$	3.44168e8	+	4.73706e8i	1.31781	+	1.81381i
$255$		−	9.50108e7i		−	0.358825i
$256$	4.42821e8	−	3.21729e8i	1.64964	−	1.19853i
$257$	4.97402e8			1.82785			0.913927	−	0.405877i	$-0.133034\pi$
$257$	4.97402e8			1.82785			0.913927	+	0.405877i	$0.133034\pi$
$258$	6.05316e8			2.19439
$259$	4.58547e7	−	3.33154e7i	0.163996	−	0.119150i
$260$	7.03771e7	+	2.16598e8i	0.248327	+	0.764273i
$261$	−4.85516e7	+	6.68256e7i	−0.169029	+	0.232649i
$262$	1.72202e8	+	2.37016e8i	0.591540	+	0.814186i
$263$	8.68165e7	−	2.67194e8i	0.294278	−	0.905694i	−0.689185	−	0.724585i	$-0.742031\pi$
$263$	8.68165e7	−	2.67194e8i	0.294278	−	0.905694i	0.983463	−	0.181109i	$-0.0579685\pi$
$264$	−6.16265e6	−	1.89667e7i	−0.0206136	−	0.0634421i
$265$		−	2.84214e7i		−	0.0938176i
$266$	5.05859e7	−	1.55687e8i	0.164795	−	0.507186i
$267$	−1.01866e7	+	1.40207e7i	−0.0327523	+	0.0450796i
$268$	5.56217e8	−	1.80726e8i	1.76511	−	0.573520i
$269$	1.91978e8	+	5.90848e8i	0.601338	+	1.85073i	0.520237	+	0.854022i	$0.325844\pi$
$269$	1.91978e8	+	5.90848e8i	0.601338	+	1.85073i	0.0811011	+	0.996706i	$0.474156\pi$
$270$	−2.05768e8	−	6.68582e7i	−0.636217	−	0.206720i
$271$	1.33494e8	−	9.69894e7i	0.407447	−	0.296027i	−0.365121	−	0.930960i	$-0.618972\pi$
$271$	1.33494e8	−	9.69894e7i	0.407447	−	0.296027i	0.772567	+	0.634933i	$0.218972\pi$
$272$	2.69415e8	+	8.75384e7i	0.811767	+	0.263759i
$273$			2.56745e8i			0.763718i
$274$	−4.51827e8	+	1.46808e8i	−1.32692	+	0.431143i
$275$	8.05659e6	−	2.61775e6i	0.0233608	−	0.00759037i
$276$		−	3.67128e8i		−	1.05108i
$277$	−6.01024e7	−	1.95284e7i	−0.169907	−	0.0552063i	0.222828	−	0.974858i	$-0.428471\pi$
$277$	−6.01024e7	−	1.95284e7i	−0.169907	−	0.0552063i	−0.392735	+	0.919652i	$0.628471\pi$
$278$	6.41302e8	−	4.65933e8i	1.79022	−	1.30067i
$279$	1.09250e8	+	3.54975e7i	0.301167	+	0.0978549i
$280$	8.08587e7	+	2.48858e8i	0.220127	+	0.677482i
$281$	−1.78752e8	+	5.80800e7i	−0.480594	+	0.156155i	−0.539288	−	0.842122i	$-0.681306\pi$
$281$	−1.78752e8	+	5.80800e7i	−0.480594	+	0.156155i	0.0586936	+	0.998276i	$0.481306\pi$
$282$	−2.33063e8	+	3.20784e8i	−0.618874	+	0.851806i
$283$	−6.97735e7	+	2.14741e8i	−0.182995	+	0.563199i	−0.999908	−	0.0135609i	$-0.995683\pi$
$283$	−6.97735e7	+	2.14741e8i	−0.182995	+	0.563199i	0.816913	+	0.576760i	$0.195683\pi$
$284$		−	7.68807e8i		−	1.99160i
$285$	−2.35940e7	−	7.26149e7i	−0.0603733	−	0.185810i
$286$	5.59801e6	−	1.72289e7i	0.0141499	−	0.0435488i
$287$	−1.23803e8	−	1.70400e8i	−0.309132	−	0.425484i
$288$	−1.84372e7	+	2.53767e7i	−0.0454801	+	0.0625980i
$289$	6.69200e7	+	2.05958e8i	0.163085	+	0.501923i
$290$	−2.91142e8	+	2.11527e8i	−0.700989	+	0.509298i
$291$	−3.64253e8			−0.866518
$292$	1.78891e8			0.420482
$293$	−5.53257e8	+	4.01965e8i	−1.28496	+	0.933579i	−0.999691	−	0.0248679i	$-0.992083\pi$
$293$	−5.53257e8	+	4.01965e8i	−1.28496	+	0.933579i	−0.285271	+	0.958447i	$0.592083\pi$
$294$		−	2.93059e8i		−	0.672572i
$295$	9.43196e7	+	1.29820e8i	0.213907	+	0.294418i
$296$	1.70485e8	+	1.23864e8i	0.382089	+	0.277604i
$297$	6.82987e6	+	9.40051e6i	0.0151274	+	0.0208211i
$298$	−1.49282e9	+	4.85046e8i	−3.26776	+	1.06176i
$299$	1.01717e8	−	1.40002e8i	0.220063	−	0.302890i
$300$	−6.95924e8	−	5.05618e8i	−1.48812	−	1.08118i
$301$	3.45081e8	+	2.50716e8i	0.729353	+	0.529906i
$302$	−4.46624e8	+	1.37457e9i	−0.933078	+	2.87172i
$303$	1.69308e8	+	5.50116e7i	0.349647	+	0.113607i
$304$	2.27647e8			0.464735
$305$	−1.08454e8	−	2.02372e8i	−0.218876	−	0.408414i
$306$	1.63072e8			0.325354
$307$	6.22020e8	+	2.02106e8i	1.22693	+	0.398654i	0.849601	−	0.527426i	$-0.176843\pi$
$307$	6.22020e8	+	2.02106e8i	1.22693	+	0.398654i	0.377329	+	0.926079i	$0.376843\pi$
$308$	8.36862e6	−	2.57560e7i	0.0163202	−	0.0502285i
$309$	−2.94925e8	−	2.14275e8i	−0.568665	−	0.413159i
$310$	4.04887e8	+	2.94168e8i	0.771913	+	0.560828i
$311$	−8.54407e7	+	1.17599e8i	−0.161066	+	0.221688i	−0.881921	−	0.471398i	$-0.843750\pi$
$311$	−8.54407e7	+	1.17599e8i	−0.161066	+	0.221688i	0.720855	+	0.693086i	$0.243750\pi$
$312$	−9.07842e8	+	2.94976e8i	−1.69227	+	0.549852i
$313$	5.85001e8	+	8.05185e8i	1.07833	+	1.48419i	0.861346	+	0.508019i	$0.169622\pi$
$313$	5.85001e8	+	8.05185e8i	1.07833	+	1.48419i	0.216984	+	0.976175i	$0.430378\pi$
$314$	−1.38971e9	−	1.00968e9i	−2.53320	−	1.84048i
$315$	3.31163e7	+	4.55806e7i	0.0596973	+	0.0821663i
$316$		−	1.94850e9i		−	3.47373i
$317$	1.87767e8	−	1.36421e8i	0.331064	−	0.240532i	−0.409818	−	0.912167i	$-0.634408\pi$
$317$	1.87767e8	−	1.36421e8i	0.331064	−	0.240532i	0.740882	+	0.671635i	$0.234408\pi$
$318$	2.29565e8			0.400323
$319$	1.93272e7			0.0333350
$320$	1.62368e8	−	1.17968e8i	0.276998	−	0.201251i
$321$	−9.24756e7	−	2.84611e8i	−0.156048	−	0.480268i
$322$	2.25215e8	−	3.09982e8i	0.375925	−	0.517416i
$323$	−9.15328e7	−	1.25984e8i	−0.151136	−	0.208021i
$324$	4.70726e8	−	1.44875e9i	0.768884	−	2.36638i
$325$	−1.25299e8	−	3.85630e8i	−0.202467	−	0.623130i
$326$		−	9.93115e8i		−	1.58759i
$327$	−7.72946e7	+	2.37888e8i	−0.122245	+	0.376232i
$328$	4.60292e8	−	6.33538e8i	0.720236	−	0.991320i
$329$	−2.65731e8	+	8.63412e7i	−0.411392	+	0.133670i
$330$	−5.78106e6	−	1.77923e7i	−0.00885541	−	0.0272541i
$331$	1.06985e9	+	3.47615e8i	1.62153	+	0.526866i	0.972302	−	0.233730i	$-0.0750932\pi$
$331$	1.06985e9	+	3.47615e8i	1.62153	+	0.526866i	0.649225	+	0.760596i	$0.275093\pi$
$332$	−9.63270e8	+	6.99856e8i	−1.44466	+	1.04960i
$333$	4.31532e7	+	1.40213e7i	0.0640410	+	0.0208082i
$334$			1.05166e9i			1.54440i
$335$	2.70756e8	−	8.79740e7i	0.393479	−	0.127849i
$336$	−7.51840e8	+	2.44288e8i	−1.08128	+	0.351329i
$337$			8.64526e8i			1.23048i	0.788341	+	0.615238i	$0.210940\pi$
$337$			8.64526e8i			1.23048i	−0.788341	+	0.615238i	$0.789060\pi$
$338$	3.59996e8	+	1.16970e8i	0.507095	+	0.164765i
$339$	1.05514e9	−	7.66606e8i	1.47100	−	1.06874i
$340$	4.56213e8	+	1.48233e8i	0.629494	+	0.204535i
$341$	−8.30577e6	−	2.55625e7i	−0.0113433	−	0.0349111i
$342$	1.24633e8	−	4.04958e7i	0.168478	−	0.0547417i
$343$	4.78216e8	−	6.58208e8i	0.639874	−	0.880711i
$344$	−4.90058e8	+	1.50824e9i	−0.649072	+	1.99764i
$345$		−	1.78711e8i		−	0.234306i
$346$	1.07415e8	+	3.30589e8i	0.139411	+	0.429064i
$347$	−3.96302e8	+	1.21969e9i	−0.509182	+	1.56710i	0.284443	+	0.958693i	$0.408191\pi$
$347$	−3.96302e8	+	1.21969e9i	−0.509182	+	1.56710i	−0.793625	+	0.608407i	$0.791809\pi$
$348$	−1.15357e9	−	1.58776e9i	−1.46730	−	2.01956i
$349$	−1.61064e8	+	2.21685e8i	−0.202819	+	0.279156i	−0.898295	−	0.439393i	$-0.855194\pi$
$349$	−1.61064e8	+	2.21685e8i	−0.202819	+	0.279156i	0.695476	+	0.718549i	$0.255194\pi$
$350$	−2.77426e8	−	8.53831e8i	−0.345867	−	1.06447i
$351$	4.49956e8	−	3.26912e8i	0.555386	−	0.403512i
$352$	7.33938e6			0.00896933
$353$	−2.52080e8			−0.305019			−0.152510	−	0.988302i	$-0.548736\pi$
$353$	−2.52080e8			−0.305019			−0.152510	+	0.988302i	$0.548736\pi$
$354$	−1.04858e9	+	7.61838e8i	−1.25629	+	0.912749i
$355$		−	3.74241e8i		−	0.443968i
$356$	−5.14303e7	−	7.07878e7i	−0.0604149	−	0.0831540i
$357$	4.37494e8	+	3.17858e8i	0.508901	+	0.369738i
$358$	1.50322e9	+	2.06901e9i	1.73154	+	2.38326i
$359$	−7.07482e8	+	2.29875e8i	−0.807021	+	0.262217i	−0.683336	−	0.730105i	$-0.739471\pi$
$359$	−7.07482e8	+	2.29875e8i	−0.807021	+	0.262217i	−0.123685	+	0.992321i	$0.539471\pi$
$360$	−1.23124e8	+	1.69466e8i	−0.139086	+	0.191436i
$361$	6.21915e8	+	4.51848e8i	0.695754	+	0.505495i
$362$	1.12874e9	+	8.20077e8i	1.25059	+	0.908604i
$363$	3.17032e8	−	9.75725e8i	0.347881	−	1.07067i
$364$	−1.23281e9	−	4.00565e8i	−1.33981	−	0.435329i
$365$	8.70806e7			0.0937338
$366$	1.63460e9	−	8.76007e8i	1.74272	−	0.933950i
$367$	−9.12127e8			−0.963217			−0.481608	−	0.876387i	$-0.659947\pi$
$367$	−9.12127e8			−0.963217			−0.481608	+	0.876387i	$0.659947\pi$
$368$	5.06758e8	+	1.64656e8i	0.530070	+	0.172230i
$369$	5.21045e7	−	1.60361e8i	0.0539862	−	0.166153i
$370$	1.59928e8	+	1.16195e8i	0.164142	+	0.119256i
$371$	1.30871e8	+	9.50835e7i	0.133056	+	0.0966710i
$372$	−1.60426e9	+	2.20808e9i	−1.61575	+	2.22389i
$373$	−1.15997e9	+	3.76899e8i	−1.15736	+	0.376048i	−0.823910	−	0.566720i	$-0.808212\pi$
$373$	−1.15997e9	+	3.76899e8i	−1.15736	+	0.376048i	−0.333447	+	0.942769i	$0.608212\pi$
$374$	−2.24276e7	−	3.08689e7i	−0.0221683	−	0.0305120i
$375$	−7.70148e8	−	5.59545e8i	−0.754162	−	0.547931i
$376$	−6.10600e8	−	8.40418e8i	−0.592378	−	0.815339i
$377$		−	9.25096e8i		−	0.889185i
$378$	9.96257e8	−	7.23823e8i	0.948747	−	0.689305i
$379$	−3.98444e8			−0.375950			−0.187975	−	0.982174i	$-0.560192\pi$
$379$	−3.98444e8			−0.375950			−0.187975	+	0.982174i	$0.560192\pi$
$380$	3.85486e8			0.360384
$381$	−1.25754e9	+	9.13659e8i	−1.16489	+	0.846343i
$382$	−3.56586e8	−	1.09746e9i	−0.327297	−	1.00732i
$383$	1.60759e8	−	2.21266e8i	0.146211	−	0.201242i	−0.729630	−	0.683842i	$-0.760308\pi$
$383$	1.60759e8	−	2.21266e8i	0.146211	−	0.201242i	0.875841	+	0.482600i	$0.160308\pi$
$384$	1.16359e9	+	1.60155e9i	1.04868	+	1.44338i
$385$	4.07369e6	−	1.25375e7i	0.00363811	−	0.0111969i
$386$	−5.92415e8	−	1.82327e9i	−0.524289	−	1.61360i
$387$			3.41463e8i			0.299471i
$388$	5.68295e8	−	1.74903e9i	0.493927	−	1.52015i
$389$	9.95047e7	−	1.36956e8i	0.0857077	−	0.117967i	−0.764010	−	0.645204i	$-0.776772\pi$
$389$	9.95047e7	−	1.36956e8i	0.0857077	−	0.117967i	0.849718	+	0.527238i	$0.176772\pi$
$390$	−8.51629e8	+	2.76711e8i	−0.726983	+	0.236211i
$391$	−1.12635e8	−	3.46653e8i	−0.0952912	−	0.293276i
$392$	7.30203e8	+	2.37257e8i	0.612269	+	0.198938i
$393$	−6.29205e8	+	4.57144e8i	−0.522899	+	0.379909i
$394$	−2.87279e8	−	9.33425e7i	−0.236628	−	0.0768852i
$395$		−	9.48495e8i		−	0.774364i
$396$	2.06186e7	−	6.69938e6i	0.0166850	−	0.00542127i
$397$	−3.27614e8	+	1.06448e8i	−0.262782	+	0.0853831i	−0.437445	−	0.899245i	$-0.644117\pi$
$397$	−3.27614e8	+	1.06448e8i	−0.262782	+	0.0853831i	0.174663	+	0.984628i	$0.444117\pi$
$398$		−	1.92749e9i		−	1.53251i
$399$	4.13302e8	+	1.34290e8i	0.325733	+	0.105837i
$400$	1.01004e9	−	7.33838e8i	0.789094	−	0.573311i
$401$	3.09303e8	+	1.00499e8i	0.239540	+	0.0778313i	0.426327	−	0.904569i	$-0.359807\pi$
$401$	3.09303e8	+	1.00499e8i	0.239540	+	0.0778313i	−0.186787	+	0.982400i	$0.559807\pi$
$402$	7.10584e8	+	2.18695e9i	0.545537	+	1.67899i
$403$	−1.22355e9	+	3.97557e8i	−0.931226	+	0.302574i
$404$	−5.28298e8	+	7.27140e8i	−0.398607	+	0.548635i
$405$	2.29141e8	−	7.05222e8i	0.171399	−	0.527513i
$406$		−	2.04827e9i		−	1.51896i
$407$	−3.28074e6	−	1.00971e7i	−0.00241208	−	0.00742361i
$408$	−6.21297e8	+	1.91215e9i	−0.452885	+	1.39384i
$409$	−9.80842e8	−	1.35001e9i	−0.708871	−	0.975677i	−0.999821	−	0.0189390i	$-0.993971\pi$
$409$	−9.80842e8	−	1.35001e9i	−0.708871	−	0.975677i	0.290949	−	0.956738i	$-0.406029\pi$
$410$	4.31791e8	−	5.94309e8i	0.309407	−	0.425862i
$411$	−3.89729e8	−	1.19946e9i	−0.276896	−	0.852197i
$412$	1.48902e9	−	1.08183e9i	1.04896	−	0.762114i
$413$	−9.13324e8			−0.637969
$414$	3.06732e8			0.212450
$415$	−4.68902e8	+	3.40677e8i	−0.322043	+	0.233978i
$416$		−	3.51300e8i		−	0.239250i
$417$	1.23691e9	+	1.70246e9i	0.835337	+	1.14974i
$418$	−2.48066e7	−	1.80231e7i	−0.0166131	−	0.0120701i
$419$	9.18332e8	+	1.26398e9i	0.609889	+	0.839440i	0.996568	−	0.0827742i	$-0.0263780\pi$
$419$	9.18332e8	+	1.26398e9i	0.609889	+	0.839440i	−0.386679	+	0.922214i	$0.626378\pi$
$420$	−1.27312e9	+	4.13663e8i	−0.838491	+	0.272442i
$421$	−5.08112e8	+	6.99356e8i	−0.331873	+	0.456784i	−0.942046	−	0.335484i	$-0.891100\pi$
$421$	−5.08112e8	+	6.99356e8i	−0.331873	+	0.456784i	0.610173	+	0.792268i	$0.291100\pi$
$422$	4.12795e9	+	2.99913e9i	2.67387	+	1.94268i
$423$	−1.80956e8	−	1.31472e8i	−0.116247	−	0.0844585i
$424$	−1.85854e8	+	5.71998e8i	−0.118411	+	0.364430i
$425$	−8.12237e8	−	2.63912e8i	−0.513241	−	0.166762i
$426$	3.02282e9			1.89443
$427$	1.29469e9	+	1.77637e8i	0.804764	+	0.110417i
$428$	1.51089e9			0.931494
$429$	4.57374e7	+	1.48610e7i	0.0279686	+	0.00908755i
$430$	−4.59713e8	+	1.41485e9i	−0.278835	+	0.858166i
$431$	1.34336e8	+	9.76005e7i	0.0808203	+	0.0587194i	0.627462	−	0.778647i	$-0.284094\pi$
$431$	1.34336e8	+	9.76005e7i	0.0808203	+	0.0587194i	−0.546641	+	0.837367i	$0.684094\pi$
$432$	1.38544e9	+	1.00658e9i	0.826788	+	0.600697i
$433$	−4.31914e8	+	5.94479e8i	−0.255676	+	0.351908i	−0.917489	−	0.397761i	$-0.869787\pi$
$433$	−4.31914e8	+	5.94479e8i	−0.255676	+	0.351908i	0.661813	+	0.749669i	$0.269787\pi$
$434$	−2.70910e9	+	8.80239e8i	−1.59078	+	0.516876i
$435$	−5.61538e8	−	7.72891e8i	−0.327090	−	0.450201i
$436$	−1.02168e9	−	7.42291e8i	−0.590351	−	0.428915i
$437$	−1.72169e8	−	2.36970e8i	−0.0986892	−	0.135834i
$438$			7.03367e8i			0.399966i
$439$	7.29503e8	−	5.30015e8i	0.411530	−	0.298994i	−0.362691	−	0.931909i	$-0.618142\pi$
$439$	7.29503e8	−	5.30015e8i	0.411530	−	0.298994i	0.774221	+	0.632916i	$0.218142\pi$
$440$	4.90126e7			0.0274298
$441$	1.65316e8			0.0917869
$442$	−1.47754e9	+	1.07350e9i	−0.813883	+	0.591321i
$443$	−1.12967e9	−	3.47677e9i	−0.617361	−	1.90004i	−0.353058	−	0.935601i	$-0.614858\pi$
$443$	−1.12967e9	−	3.47677e9i	−0.617361	−	1.90004i	−0.264303	−	0.964440i	$-0.585142\pi$
$444$	−6.33675e8	+	8.72179e8i	−0.343579	+	0.472896i
$445$	−2.50353e7	−	3.44582e7i	−0.0134677	−	0.0185367i
$446$	−4.52851e8	+	1.39373e9i	−0.241703	+	0.743887i
$447$	−1.28765e9	−	3.96297e9i	−0.681900	−	2.09867i
$448$			1.14231e9i			0.600223i
$449$	−2.69193e8	+	8.28492e8i	−0.140347	+	0.431943i	−0.996383	−	0.0849725i	$-0.972920\pi$
$449$	−2.69193e8	+	8.28492e8i	−0.140347	+	0.431943i	0.856037	+	0.516915i	$0.172920\pi$
$450$	4.22439e8	−	5.81438e8i	0.218535	−	0.300787i
$451$	−3.75217e7	+	1.21915e7i	−0.0192603	+	0.00625807i
$452$	2.03481e9	+	6.26251e9i	1.03643	+	3.18980i
$453$	−3.64905e9	−	1.18565e9i	−1.84432	−	0.599256i
$454$	1.49586e9	−	1.08681e9i	0.750232	−	0.545076i
$455$	−6.00110e8	−	1.94988e8i	−0.298669	−	0.0970436i
$456$			1.61571e9i			0.797970i
$457$	1.22767e9	−	3.98894e8i	0.601693	−	0.195502i	0.00769746	−	0.999970i	$-0.497550\pi$
$457$	1.22767e9	−	3.98894e8i	0.601693	−	0.195502i	0.593995	+	0.804469i	$0.297550\pi$
$458$	−1.90624e9	+	6.19374e8i	−0.927146	+	0.301248i
$459$		−	1.17145e9i		−	0.565432i
$460$	8.58115e8	+	2.78819e8i	0.411049	+	0.133558i
$461$	1.59894e9	−	1.16170e9i	0.760114	−	0.552255i	−0.138832	−	0.990316i	$-0.544335\pi$
$461$	1.59894e9	−	1.16170e9i	0.760114	−	0.552255i	0.898945	+	0.438061i	$0.144335\pi$
$462$	1.01268e8	+	3.29040e7i	0.0477778	+	0.0155239i
$463$	−2.54710e8	−	7.83918e8i	−0.119265	−	0.367060i	0.873548	−	0.486739i	$-0.161814\pi$
$463$	−2.54710e8	−	7.83918e8i	−0.119265	−	0.367060i	−0.992813	+	0.119679i	$0.961814\pi$
$464$	2.70901e9	−	8.80210e8i	1.25892	−	0.409047i
$465$	−7.80925e8	+	1.07485e9i	−0.360184	+	0.495750i
$466$	−1.52289e9	+	4.68696e9i	−0.697135	+	2.14556i
$467$		−	1.55258e9i		−	0.705413i	−0.935734	−	0.352707i	$-0.885261\pi$
$467$		−	1.55258e9i		−	0.705413i	0.935734	−	0.352707i	$-0.114739\pi$
$468$	−3.20666e8	−	9.86909e8i	−0.144608	−	0.445058i
$469$	−5.00721e8	+	1.54106e9i	−0.224125	+	0.689787i
$470$	−5.72791e8	−	7.88379e8i	−0.254480	−	0.350262i
$471$	2.68040e9	−	3.68925e9i	1.18202	−	1.62691i
$472$	−1.04932e9	−	3.22948e9i	−0.459317	−	1.41363i
$473$	6.46373e7	−	4.69618e7i	0.0280847	−	0.0204047i
$474$	7.66118e9			3.30424
$475$	−6.86315e8			−0.293830
$476$	−2.20882e9	+	1.60480e9i	−0.938720	+	0.682020i
$477$			1.29499e8i			0.0546327i
$478$	−7.02440e8	−	9.66825e8i	−0.294179	−	0.404902i
$479$	1.47851e9	+	1.07420e9i	0.614683	+	0.446593i	0.851060	−	0.525068i	$-0.175960\pi$
$479$	1.47851e9	+	1.07420e9i	0.614683	+	0.446593i	−0.236377	+	0.971661i	$0.575960\pi$
$480$	−2.13241e8	−	2.93501e8i	−0.0880090	−	0.121134i
$481$	−4.83297e8	+	1.57033e8i	−0.198019	+	0.0643402i
$482$	1.73681e9	−	2.39051e9i	0.706460	−	0.972359i
$483$	8.22905e8	+	5.97876e8i	0.332304	+	0.241433i
$484$	4.19051e9	+	3.04459e9i	1.68000	+	1.22059i
$485$	2.76635e8	−	8.51396e8i	0.110106	−	0.338872i
$486$	2.22160e9	+	7.21842e8i	0.877888	+	0.285243i
$487$	3.47353e9			1.36276			0.681381	−	0.731929i	$-0.261380\pi$
$487$	3.47353e9			1.36276			0.681381	+	0.731929i	$0.261380\pi$
$488$	8.59358e8	+	4.78207e9i	0.334738	+	1.86272i
$489$	2.63642e9			1.01961
$490$	6.84989e8	+	2.22566e8i	0.263025	+	0.0854620i
$491$	6.41170e8	−	1.97332e9i	0.244449	−	0.752337i	−0.751278	−	0.659986i	$-0.770562\pi$
$491$	6.41170e8	−	1.97332e9i	0.244449	−	0.752337i	0.995727	−	0.0923503i	$-0.0294380\pi$
$492$	3.24110e9	+	2.35480e9i	1.22692	+	0.891406i
$493$	−1.57637e9	−	1.14530e9i	−0.592506	−	0.430481i
$494$	−8.62676e8	+	1.18737e9i	−0.321961	+	0.443141i
$495$	1.00367e7	−	3.26113e6i	0.00371941	−	0.00120851i
$496$	−2.32837e9	−	3.20473e9i	−0.856775	−	1.17925i
$497$	1.72326e9	+	1.25202e9i	0.629655	+	0.457471i
$498$	−2.75172e9	−	3.78741e9i	−0.998392	−	1.37417i
$499$			5.99528e8i			0.216002i	0.994151	+	0.108001i	$0.0344450\pi$
$499$			5.99528e8i			0.216002i	−0.994151	+	0.108001i	$0.965555\pi$
$500$	3.88832e9	−	2.82503e9i	1.39113	−	1.01071i
$501$	−2.79182e9			−0.991872
$502$	−5.42365e9			−1.91350
$503$	4.00629e8	−	2.91074e8i	0.140364	−	0.101980i	−0.515388	−	0.856957i	$-0.672352\pi$
$503$	4.00629e8	−	2.91074e8i	0.140364	−	0.101980i	0.655751	+	0.754977i	$0.272352\pi$
$504$	−3.68425e8	−	1.13389e9i	−0.128186	−	0.394517i
$505$	−2.57166e8	+	3.53958e8i	−0.0888573	+	0.122302i
$506$	−4.21852e7	−	5.80629e7i	−0.0144755	−	0.0199238i
$507$	−3.10519e8	+	9.55678e8i	−0.105818	+	0.325675i
$508$	−2.42514e9	−	7.46380e9i	−0.820754	−	2.52602i
$509$			1.67210e9i			0.562017i	0.959705	+	0.281008i	$0.0906689\pi$
$509$			1.67210e9i			0.562017i	−0.959705	+	0.281008i	$0.909331\pi$
$510$	−5.82826e8	+	1.79375e9i	−0.194555	+	0.598780i
$511$	−2.91327e8	+	4.00978e8i	−0.0965847	+	0.132937i
$512$	−5.76081e9	+	1.87180e9i	−1.89687	+	0.616332i
$513$	−2.90907e8	−	8.95319e8i	−0.0951356	−	0.292797i
$514$	−9.39069e9	−	3.05122e9i	−3.05019	−	0.991066i
$515$	7.24825e8	−	5.26616e8i	0.233834	−	0.169890i
$516$	−7.71598e9	−	2.50707e9i	−2.47239	−	0.803329i
$517$			5.23358e7i			0.0166564i
$518$	−1.07008e9	+	3.47690e8i	−0.338268	+	0.109910i
$519$	−8.77611e8	+	2.85153e8i	−0.275560	+	0.0895349i
$520$		−	2.34599e9i		−	0.731669i
$521$	3.72084e9	+	1.20897e9i	1.15268	+	0.374528i	0.822152	−	0.569268i	$-0.192773\pi$
$521$	3.72084e9	+	1.20897e9i	1.15268	+	0.374528i	0.330528	+	0.943796i	$0.392773\pi$
$522$	1.32656e9	−	9.63801e8i	0.408206	−	0.296579i
$523$	−4.16504e9	−	1.35330e9i	−1.27310	−	0.413656i	−0.406957	−	0.913448i	$-0.633410\pi$
$523$	−4.16504e9	−	1.35330e9i	−1.27310	−	0.413656i	−0.866146	+	0.499792i	$0.833410\pi$
$524$	−1.21340e9	−	3.73447e9i	−0.368422	−	1.13389i
$525$	2.26666e9	−	7.36482e8i	0.683641	−	0.222129i
$526$	−3.27810e9	+	4.51192e9i	−0.982137	+	1.35180i
$527$	−8.37359e8	+	2.57712e9i	−0.249215	+	0.767005i
$528$			1.48075e8i			0.0437788i
$529$	8.40289e8	+	2.58614e9i	0.246793	+	0.759552i
$530$	−1.74345e8	+	5.36580e8i	−0.0508681	+	0.156556i
$531$	−4.29758e8	−	5.91511e8i	−0.124564	−	0.171448i
$532$	−1.28964e9	+	1.77504e9i	−0.371345	+	0.511113i
$533$	5.83548e8	+	1.79598e9i	0.166929	+	0.513755i
$534$	2.78326e8	−	2.02215e8i	0.0790968	−	0.0574672i
$535$	7.35474e8			0.207649
$536$	−6.02442e9			−1.68981
$537$	−5.49258e9	+	3.99059e9i	−1.53062	+	1.11206i
$538$		−	1.23325e10i		−	3.41440i
$539$	−2.27362e7	−	3.12936e7i	−0.00625398	−	0.00860786i
$540$	2.34603e9	+	1.70449e9i	0.641142	+	0.465817i
$541$	−9.19703e8	−	1.26586e9i	−0.249722	−	0.343713i	0.665692	−	0.746227i	$-0.268137\pi$
$541$	−9.19703e8	−	1.26586e9i	−0.249722	−	0.343713i	−0.915414	+	0.402514i	$0.868137\pi$
$542$	−3.11527e9	+	1.01221e9i	−0.840423	+	0.273070i
$543$	−2.17705e9	+	2.99646e9i	−0.583539	+	0.803172i
$544$	−5.98616e8	−	4.34920e8i	−0.159424	−	0.115828i
$545$	−4.97333e8	−	3.61333e8i	−0.131601	−	0.0956137i
$546$	1.57495e9	−	4.84721e9i	0.414089	−	1.27443i
$547$	3.90967e9	+	1.27033e9i	1.02137	+	0.331864i	0.771374	−	0.636382i	$-0.219570\pi$
$547$	3.90967e9	+	1.27033e9i	1.02137	+	0.331864i	0.249998	+	0.968246i	$0.419570\pi$
$548$	6.36750e9			1.65286
$549$	4.94161e8	+	9.22088e8i	0.127457	+	0.237831i
$550$	−1.68162e8			−0.0430982
$551$	−1.48920e9	−	4.83870e8i	−0.379247	−	0.123225i
$552$	−1.16863e9	+	3.59667e9i	−0.295726	+	0.910152i
$553$	4.36751e9	+	3.17318e9i	1.09824	+	0.797916i
$554$	1.01491e9	+	7.37373e8i	0.253596	+	0.184248i
$555$	−3.08461e8	+	4.24560e8i	−0.0765905	+	0.105418i
$556$	−1.01045e10	+	3.28315e9i	−2.49317	+	0.810081i
$557$	2.67337e9	+	3.67958e9i	0.655489	+	0.902203i	0.999322	−	0.0368276i	$-0.0117252\pi$
$557$	2.67337e9	+	3.67958e9i	0.655489	+	0.902203i	−0.343832	+	0.939031i	$0.611725\pi$
$558$	−1.84483e9	−	1.34035e9i	−0.449507	−	0.326586i
$559$	−2.24783e9	−	3.09387e9i	−0.544280	−	0.749137i
$560$		−	1.94286e9i		−	0.467502i
$561$	8.19474e7	−	5.95383e7i	0.0195959	−	0.0142373i
$562$	3.73102e9			0.886647
$563$	−5.02280e9			−1.18622			−0.593112	−	0.805120i	$-0.702101\pi$
$563$	−5.02280e9			−1.18622			−0.593112	+	0.805120i	$0.702101\pi$
$564$	4.29947e9	−	3.12375e9i	1.00911	−	0.733161i
$565$	9.90508e8	+	3.04847e9i	0.231041	+	0.711070i
$566$	2.63457e9	−	3.62618e9i	0.610735	−	0.840605i
$567$	2.48073e9	+	3.41444e9i	0.571530	+	0.786644i
$568$	−2.44724e9	+	7.53184e9i	−0.560348	+	1.72457i
$569$	1.61496e8	+	4.97032e8i	0.0367509	+	0.113108i	0.967749	−	0.251916i	$-0.0810608\pi$
$569$	1.61496e8	+	4.97032e8i	0.0367509	+	0.113108i	−0.930998	+	0.365024i	$0.881061\pi$
$570$			1.51566e9i			0.342800i
$571$	−1.37375e9	+	4.22797e9i	−0.308803	+	0.950398i	0.669428	+	0.742877i	$0.266539\pi$
$571$	−1.37375e9	+	4.22797e9i	−0.308803	+	0.950398i	−0.978231	+	0.207520i	$0.933461\pi$
$572$	−1.42716e8	+	1.96432e8i	−0.0318850	+	0.0438859i
$573$	2.91341e9	−	9.46625e8i	0.646935	−	0.210202i
$574$	1.29205e9	+	3.97651e9i	0.285159	+	0.877628i
$575$	−1.52778e9	−	4.96406e8i	−0.335138	−	0.108893i
$576$	−7.39815e8	+	5.37507e8i	−0.161304	+	0.117194i
$577$	−3.61011e9	−	1.17299e9i	−0.782356	−	0.254203i	−0.109510	−	0.993986i	$-0.534928\pi$
$577$	−3.61011e9	−	1.17299e9i	−0.782356	−	0.254203i	−0.672846	+	0.739783i	$0.734928\pi$
$578$		−	4.29889e9i		−	0.925996i
$579$	4.84021e9	−	1.57268e9i	1.03631	−	0.336717i
$580$	4.58728e9	−	1.49050e9i	0.976242	−	0.317200i
$581$		−	3.29887e9i		−	0.697829i
$582$	6.87690e9	+	2.23444e9i	1.44598	+	0.469827i
$583$	2.45136e7	−	1.78102e7i	0.00512351	−	0.00372244i
$584$	−1.75255e9	−	5.69439e8i	−0.364105	−	0.118305i
$585$	−1.56094e8	−	4.80409e8i	−0.0322360	−	0.0992123i
$586$	1.29110e10	−	4.19503e9i	2.65043	−	0.861178i
$587$	−4.98779e9	+	6.86511e9i	−1.01783	+	1.40092i	−0.104115	+	0.994565i	$0.533201\pi$
$587$	−4.98779e9	+	6.86511e9i	−1.01783	+	1.40092i	−0.913715	+	0.406357i	$0.866799\pi$
$588$	−1.21378e9	+	3.73563e9i	−0.246218	+	0.757780i
$589$			2.17759e9i			0.439109i
$590$	−9.84348e8	−	3.02951e9i	−0.197318	−	0.607283i
$591$	2.47796e8	−	7.62636e8i	0.0493784	−	0.151971i
$592$	−9.19695e8	−	1.26585e9i	−0.182187	−	0.250759i
$593$	2.21331e9	−	3.04636e9i	0.435863	−	0.599914i	−0.533423	−	0.845848i	$-0.679095\pi$
$593$	2.21331e9	−	3.04636e9i	0.435863	−	0.599914i	0.969287	+	0.245934i	$0.0790947\pi$
$594$	−7.12786e7	−	2.19373e8i	−0.0139543	−	0.0429468i
$595$	−1.07521e9	+	7.81188e8i	−0.209259	+	0.152036i
$596$	2.10379e10			4.07044
$597$	5.11690e9			0.984231
$598$	−2.77919e9	+	2.01920e9i	−0.531451	+	0.386122i
$599$		−	6.41853e9i		−	1.22023i	−0.792313	−	0.610115i	$-0.791123\pi$
$599$		−	6.41853e9i		−	1.22023i	0.792313	−	0.610115i	$-0.208877\pi$
$600$	5.20835e9	+	7.16868e9i	0.984399	+	1.35491i
$601$	5.35610e9	+	3.89143e9i	1.00644	+	0.731222i	0.963459	−	0.267854i	$-0.0863145\pi$
$601$	5.35610e9	+	3.89143e9i	1.00644	+	0.731222i	0.0429810	+	0.999076i	$0.486315\pi$
$602$	−4.97697e9	−	6.85021e9i	−0.929773	−	1.27972i
$603$	−1.23367e9	+	4.00845e8i	−0.229134	+	0.0744502i
$604$	1.13863e10	−	1.56718e10i	2.10258	−	2.89395i
$605$	2.03986e9	+	1.48205e9i	0.374505	+	0.272094i
$606$	−2.85899e9	−	2.07718e9i	−0.521866	−	0.379158i
$607$	2.15012e9	−	6.61738e9i	0.390213	−	1.20095i	−0.542414	−	0.840111i	$-0.682490\pi$
$607$	2.15012e9	−	6.61738e9i	0.390213	−	1.20095i	0.932627	−	0.360841i	$-0.117510\pi$
$608$	−5.65515e8	−	1.83747e8i	−0.102043	−	0.0331556i
$609$	5.43754e9			0.975533
$610$	8.06146e8	+	4.48597e9i	0.143800	+	0.800206i
$611$	2.50506e9			0.444297
$612$	−2.07869e9	−	6.75407e8i	−0.366572	−	0.119107i
$613$	−5.84242e8	+	1.79811e9i	−0.102443	+	0.315286i	−0.989122	−	0.147099i	$-0.953006\pi$
$613$	−5.84242e8	+	1.79811e9i	−0.102443	+	0.315286i	0.886679	+	0.462385i	$0.153006\pi$
$614$	−1.05036e10	−	7.63132e9i	−1.83126	−	1.33049i
$615$	1.57771e9	+	1.14627e9i	0.273504	+	0.198712i
$616$	−1.63971e8	+	2.25687e8i	−0.0282641	+	0.0389022i
$617$	−2.81831e9	+	9.15726e8i	−0.483049	+	0.156952i	−0.540411	−	0.841401i	$-0.681731\pi$
$617$	−2.81831e9	+	9.15726e8i	−0.483049	+	0.156952i	0.0573616	+	0.998353i	$0.481731\pi$
$618$	4.25359e9	+	5.85456e9i	0.724929	+	0.997779i
$619$	2.84951e9	+	2.07029e9i	0.482896	+	0.350844i	0.802446	−	0.596725i	$-0.203532\pi$
$619$	2.84951e9	+	2.07029e9i	0.482896	+	0.350844i	−0.319550	+	0.947569i	$0.603532\pi$
$620$	−3.94274e9	−	5.42671e9i	−0.664396	−	0.914462i
$621$		−	2.20345e9i		−	0.369217i
$622$	2.33446e9	−	1.69609e9i	0.388974	−	0.282606i
$623$	2.42424e8			0.0401669
$624$	7.08763e9			1.16776
$625$	−1.98489e9	+	1.44210e9i	−0.325204	+	0.236274i
$626$	−6.10526e9	−	1.87900e10i	−0.994704	−	3.06138i
$627$	4.78457e7	−	6.58540e7i	0.00775187	−	0.0106695i
$628$	1.35328e10	+	1.86263e10i	2.18036	+	3.00101i
$629$	−3.30752e8	+	1.01795e9i	−0.0529938	+	0.163098i
$630$	−3.45612e8	−	1.06368e9i	−0.0550677	−	0.169481i
$631$			1.40343e9i			0.222376i	0.993799	+	0.111188i	$0.0354657\pi$
$631$			1.40343e9i			0.222376i	−0.993799	+	0.111188i	$0.964534\pi$
$632$	−6.20242e9	+	1.90891e10i	−0.977352	+	3.00798i
$633$	−7.96177e9	+	1.09584e10i	−1.24766	+	1.71726i
$634$	−4.38179e9	+	1.42373e9i	−0.682872	+	0.221879i
$635$	−1.18051e9	−	3.63324e9i	−0.182962	−	0.563101i
$636$	−2.92627e9	−	9.50804e8i	−0.451040	−	0.146552i
$637$	−1.49787e9	+	1.08827e9i	−0.229608	+	0.166820i
$638$	−3.64886e8	−	1.18559e8i	−0.0556269	−	0.0180743i
$639$			1.70519e9i			0.258535i
$640$	−4.62713e9	+	1.50345e9i	−0.697721	+	0.226703i
$641$	3.35610e9	−	1.09046e9i	0.503306	−	0.163534i	−0.0463500	−	0.998925i	$-0.514759\pi$
$641$	3.35610e9	−	1.09046e9i	0.503306	−	0.163534i	0.549656	+	0.835391i	$0.314759\pi$
$642$			5.94057e9i			0.886044i
$643$	9.12670e9	+	2.96545e9i	1.35387	+	0.439898i	0.893990	−	0.448086i	$-0.147894\pi$
$643$	9.12670e9	+	2.96545e9i	1.35387	+	0.439898i	0.459875	+	0.887984i	$0.347894\pi$
$644$	−4.15469e9	+	3.01856e9i	−0.612968	+	0.445347i
$645$	−3.75600e9	−	1.22040e9i	−0.551145	−	0.179078i
$646$	9.55265e8	+	2.94000e9i	0.139415	+	0.429076i
$647$	−4.72117e9	+	1.53400e9i	−0.685306	+	0.222669i	−0.630917	−	0.775851i	$-0.717321\pi$
$647$	−4.72117e9	+	1.53400e9i	−0.685306	+	0.222669i	−0.0543888	+	0.998520i	$0.517321\pi$
$648$	−9.22321e9	+	1.26947e10i	−1.33159	+	1.83277i
$649$	−5.28652e7	+	1.62702e8i	−0.00759126	+	0.0233635i
$650$			8.04910e9i			1.14961i
$651$	−2.33676e9	−	7.19181e9i	−0.331956	−	1.02166i
$652$	−4.11325e9	+	1.26593e10i	−0.581190	+	1.78872i
$653$	−1.67738e9	−	2.30872e9i	−0.235742	−	0.324471i	0.674712	−	0.738081i	$-0.264268\pi$
$653$	−1.67738e9	−	2.30872e9i	−0.235742	−	0.324471i	−0.910454	+	0.413610i	$0.864268\pi$
$654$	2.91856e9	−	4.01706e9i	0.407987	−	0.561547i
$655$	−5.90662e8	−	1.81787e9i	−0.0821286	−	0.252766i
$656$	−4.70402e9	+	3.41767e9i	−0.650588	+	0.472680i
$657$	−3.96774e8			−0.0545839
$658$	5.54650e9			0.758977
$659$	2.69630e9	−	1.95898e9i	0.367003	−	0.266643i	−0.388964	−	0.921253i	$-0.627167\pi$
$659$	2.69630e9	−	1.95898e9i	0.367003	−	0.266643i	0.755967	+	0.654610i	$0.227167\pi$
$660$			2.50742e8i			0.0339488i
$661$	−3.32733e9	−	4.57968e9i	−0.448117	−	0.616780i	0.523875	−	0.851795i	$-0.324486\pi$
$661$	−3.32733e9	−	4.57968e9i	−0.448117	−	0.616780i	−0.971992	+	0.235015i	$0.924486\pi$
$662$	−1.80658e10	−	1.31256e10i	−2.42021	−	1.75839i
$663$	−2.84980e9	−	3.92242e9i	−0.379767	−	0.522705i
$664$	1.16647e10	−	3.79009e9i	1.54627	−	0.502414i
$665$	−6.27772e8	+	8.64055e8i	−0.0827802	+	0.113937i
$666$	−7.28697e8	−	5.29430e8i	−0.0955845	−	0.0694462i
$667$	−2.96507e9	−	2.15425e9i	−0.386896	−	0.281096i
$668$	4.35571e9	−	1.34055e10i	0.565381	−	1.74006i
$669$	−3.69993e9	−	1.20218e9i	−0.477751	−	0.155231i
$670$	−5.65139e9			−0.725928
$671$	1.06584e8	−	2.20358e8i	0.0136196	−	0.0281579i
$672$	2.06488e9			0.262483
$673$	1.31996e10	+	4.28880e9i	1.66919	+	0.542354i	0.982768	−	0.184844i	$-0.0591781\pi$
$673$	1.31996e10	+	4.28880e9i	1.66919	+	0.542354i	0.686427	+	0.727199i	$0.259178\pi$
$674$	5.30327e9	−	1.63218e10i	0.667166	−	2.05333i
$675$	−4.17684e9	−	3.03465e9i	−0.522739	−	0.379792i
$676$	−4.10442e9	−	2.98203e9i	−0.511020	−	0.371278i
$677$	3.72979e9	−	5.13362e9i	0.461981	−	0.635862i	−0.512937	−	0.858426i	$-0.671443\pi$
$677$	3.72979e9	−	5.13362e9i	0.461981	−	0.635862i	0.974918	+	0.222564i	$0.0714426\pi$
$678$	−2.46231e10	+	8.00054e9i	−3.03416	+	0.985860i
$679$	2.99492e9	+	4.12216e9i	0.367148	+	0.505336i
$680$	−3.99757e9	−	2.90441e9i	−0.487546	−	0.354223i
$681$	2.88514e9	+	3.97105e9i	0.350067	+	0.481826i
$682$			5.33557e8i			0.0644074i
$683$	9.44341e9	−	6.86104e9i	1.13411	−	0.823981i	0.147825	−	0.989014i	$-0.452773\pi$
$683$	9.44341e9	−	6.86104e9i	1.13411	−	0.823981i	0.986288	+	0.165033i	$0.0527729\pi$
$684$	−1.75643e9			−0.209862
$685$	3.09958e9			0.368456
$686$	−1.30661e10	+	9.49309e9i	−1.54530	+	1.12272i
$687$	−1.64425e9	−	5.06048e9i	−0.193472	−	0.595447i
$688$	6.92119e9	−	9.52620e9i	0.810254	−	1.11522i
$689$	−8.52486e8	−	1.17335e9i	−0.0992933	−	0.136665i
$690$	−1.09627e9	+	3.37396e9i	−0.127041	+	0.390993i
$691$	2.00524e9	+	6.17150e9i	0.231203	+	0.711570i	0.997602	+	0.0692058i	$0.0220465\pi$
$691$	2.00524e9	+	6.17150e9i	0.231203	+	0.711570i	−0.766399	+	0.642365i	$0.777953\pi$
$692$		−	4.65891e9i		−	0.534457i
$693$	−1.85614e7	+	5.71260e7i	−0.00211857	+	0.00652030i
$694$	1.49639e10	−	2.05961e10i	1.69937	−	2.33898i
$695$	−4.91867e9	+	1.59817e9i	−0.555778	+	0.180583i
$696$	6.24722e9	+	1.92270e10i	0.702351	+	2.16162i
$697$	3.78280e9	+	1.22911e9i	0.423154	+	0.137491i
$698$	4.40068e9	−	3.19728e9i	0.489808	−	0.355866i
$699$	−1.24424e10	−	4.04279e9i	−1.37796	−	0.447725i
$700$			1.20328e10i			1.32594i
$701$	−2.25326e9	+	7.32128e8i	−0.247057	+	0.0802738i	−0.429928	−	0.902863i	$-0.641461\pi$
$701$	−2.25326e9	+	7.32128e8i	−0.247057	+	0.0802738i	0.182871	+	0.983137i	$0.441461\pi$
$702$	−1.05003e10	+	3.41176e9i	−1.14557	+	0.372219i
$703$			8.60136e8i			0.0933734i
$704$	2.03495e8	+	6.61197e7i	0.0219812	+	0.00714211i
$705$	2.09290e9	−	1.52058e9i	0.224951	−	0.163436i
$706$	4.75914e9	+	1.54634e9i	0.508993	+	0.165382i
$707$	−7.69517e8	−	2.36833e9i	−0.0818937	−	0.252043i
$708$	1.65216e10	−	5.36821e9i	1.74959	−	0.568477i
$709$	−5.30578e9	+	7.30278e9i	−0.559097	+	0.769531i	−0.991211	−	0.132288i	$-0.957768\pi$
$709$	−5.30578e9	+	7.30278e9i	−0.559097	+	0.769531i	0.432114	+	0.901819i	$0.357768\pi$
$710$	−2.29571e9	+	7.06547e9i	−0.240720	+	0.740861i
$711$			4.32172e9i			0.450934i
$712$	2.78523e8	+	8.57204e8i	0.0289188	+	0.0890030i
$713$	−1.57503e9	+	4.84745e9i	−0.162733	+	0.500841i
$714$	−6.30981e9	−	8.68471e9i	−0.648743	−	0.892918i
$715$	−6.94714e7	+	9.56192e7i	−0.00710780	+	0.00978304i
$716$	−1.05923e10	−	3.25997e10i	−1.07844	−	3.31908i
$717$	2.56662e9	−	1.86476e9i	0.260043	−	0.188932i
$718$	1.47670e10			1.48887
$719$	−5.39175e9			−0.540977			−0.270488	−	0.962723i	$-0.587185\pi$
$719$	−5.39175e9			−0.540977			−0.270488	+	0.962723i	$0.587185\pi$
$720$	1.25829e9	−	9.14199e8i	0.125637	−	0.0912803i
$721$			5.09938e9i			0.506692i
$722$	−8.96965e9	−	1.23457e10i	−0.886942	−	1.22077i
$723$	6.34608e9	+	4.61069e9i	0.624484	+	0.453714i
$724$	−1.09915e10	−	1.51285e10i	−1.07640	−	1.48153i
$725$	−8.16715e9	+	2.65367e9i	−0.795953	+	0.258621i
$726$	−1.19708e10	+	1.64764e10i	−1.16103	+	1.59803i
$727$	3.06085e9	+	2.22384e9i	0.295442	+	0.214651i	0.725625	−	0.688091i	$-0.241551\pi$
$727$	3.06085e9	+	2.22384e9i	0.295442	+	0.214651i	−0.430183	+	0.902742i	$0.641551\pi$
$728$	1.08025e10	+	7.84850e9i	1.03769	+	0.753923i
$729$	1.95302e9	−	6.01078e9i	0.186707	−	0.574625i
$730$	−1.64403e9	−	5.34179e8i	−0.156416	−	0.0508226i
$731$	−8.05485e9			−0.762687
$732$	−2.44645e10	+	4.39637e9i	−2.30541	+	0.414291i
$733$	−9.57134e9			−0.897654			−0.448827	−	0.893619i	$-0.648158\pi$
$733$	−9.57134e9			−0.897654			−0.448827	+	0.893619i	$0.648158\pi$
$734$	1.72205e10	+	5.59527e9i	1.60734	+	0.522257i
$735$	−5.90845e8	+	1.81843e9i	−0.0548868	+	0.168924i
$736$	−1.12597e9	−	8.18064e8i	−0.104101	−	0.0756336i
$737$	2.45547e8	+	1.78400e8i	0.0225943	+	0.0164157i
$738$	−1.96741e9	+	2.70791e9i	−0.180176	+	0.247991i
$739$	−1.10298e10	+	3.58379e9i	−1.00533	+	0.326653i	−0.764995	−	0.644036i	$-0.777259\pi$
$739$	−1.10298e10	+	3.58379e9i	−1.00533	+	0.326653i	−0.240339	+	0.970689i	$0.577259\pi$
$740$	−1.55736e9	−	2.14352e9i	−0.141279	−	0.194454i
$741$	−3.15211e9	−	2.29014e9i	−0.284601	−	0.206775i
$742$	−1.88751e9	−	2.59793e9i	−0.169619	−	0.233461i
$743$		−	4.97671e9i		−	0.445125i	−0.974918	−	0.222562i	$-0.928558\pi$
$743$		−	4.97671e9i		−	0.445125i	0.974918	−	0.222562i	$-0.0714421\pi$
$744$	2.27453e10	−	1.65254e10i	2.02482	−	1.47112i
$745$	1.02409e10			0.907381
$746$	2.42117e10			2.13520
$747$	2.13650e9	−	1.55226e9i	0.187535	−	0.136252i
$748$	1.58033e8	+	4.86376e8i	0.0138068	+	0.0424929i
$749$	−2.46052e9	+	3.38662e9i	−0.213964	+	0.294496i
$750$	1.11076e10	+	1.52882e10i	0.961400	+	1.32325i
$751$	−1.19022e9	+	3.66312e9i	−0.102539	+	0.315582i	−0.989145	−	0.146943i	$-0.953056\pi$
$751$	−1.19022e9	+	3.66312e9i	−0.102539	+	0.315582i	0.886606	+	0.462525i	$0.153056\pi$
$752$	2.38351e9	+	7.33569e9i	0.204388	+	0.629041i
$753$		−	1.43981e10i		−	1.22892i
$754$	−5.67483e9	+	1.74653e10i	−0.482117	+	1.48380i
$755$	5.54262e9	−	7.62876e9i	0.468706	−	0.645119i
$756$	−1.56972e10	+	5.10034e9i	−1.32129	+	0.429312i
$757$	−4.96575e9	−	1.52830e10i	−0.416054	−	1.28048i	−0.911305	−	0.411732i	$-0.864924\pi$
$757$	−4.96575e9	−	1.52830e10i	−0.416054	−	1.28048i	0.495251	−	0.868750i	$-0.335076\pi$
$758$	7.52241e9	+	2.44418e9i	0.627357	+	0.203841i
$759$	1.54139e8	−	1.11989e8i	0.0127958	−	0.00929668i
$760$	−3.77652e9	−	1.22707e9i	−0.312065	−	0.101396i
$761$			9.71245e9i			0.798882i	0.916759	+	0.399441i	$0.130796\pi$
$761$			9.71245e9i			0.798882i	−0.916759	+	0.399441i	$0.869204\pi$
$762$	2.93464e10	−	9.53523e9i	2.40277	−	0.780708i
$763$	3.32765e9	−	1.08122e9i	0.271207	−	0.0881206i
$764$			1.54662e10i			1.25475i
$765$	−1.01187e9	−	3.28776e8i	−0.0817163	−	0.0265512i
$766$	−4.39236e9	+	3.19123e9i	−0.353099	+	0.256542i
$767$	7.78777e9	+	2.53040e9i	0.623202	+	0.202491i
$768$	−8.91355e9	−	2.74331e10i	−0.710046	−	2.18530i
$769$	2.92549e9	−	9.50550e8i	0.231983	−	0.0753760i	−0.190718	−	0.981645i	$-0.561082\pi$
$769$	2.92549e9	−	9.50550e8i	0.231983	−	0.0753760i	0.422702	+	0.906269i	$0.361082\pi$
$770$	−1.53818e8	+	2.11712e8i	−0.0121420	+	0.0167120i
$771$	8.10005e9	−	2.49294e10i	0.636498	−	1.95894i
$772$			2.56949e10i			2.00995i
$773$	3.08071e9	+	9.48146e9i	0.239896	+	0.738324i	0.996434	+	0.0843742i	$0.0268891\pi$
$773$	3.08071e9	+	9.48146e9i	0.239896	+	0.738324i	−0.756538	+	0.653949i	$0.773111\pi$
$774$	2.09464e9	−	6.44663e9i	0.162374	−	0.499735i
$775$	7.01961e9	+	9.66166e9i	0.541698	+	0.745583i
$776$	−1.11349e10	+	1.53259e10i	−0.855405	+	1.17736i
$777$	−9.23009e8	−	2.84073e9i	−0.0705882	−	0.217248i
$778$	−2.71873e9	+	1.97527e9i	−0.206984	+	0.150383i
$779$	3.19635e9			0.242255
$780$	1.20018e10			0.905556
$781$	3.22785e8	−	2.34517e8i	0.0242457	−	0.0176155i
$782$			7.23557e9i			0.541064i
$783$	−6.92359e9	−	9.52951e9i	−0.515425	−	0.709421i
$784$	−4.61203e9	−	3.35084e9i	−0.341811	−	0.248340i
$785$	6.58751e9	+	9.06693e9i	0.486046	+	0.668985i
$786$	1.46833e10	−	4.77090e9i	1.07856	−	0.350446i
$787$	4.04488e8	−	5.56730e8i	0.0295797	−	0.0407130i	−0.793971	−	0.607956i	$-0.791990\pi$
$787$	4.04488e8	−	5.56730e8i	0.0295797	−	0.0407130i	0.823551	+	0.567243i	$0.191990\pi$
$788$	3.27535e9	+	2.37968e9i	0.238460	+	0.173251i
$789$	−1.19777e10	−	8.70234e9i	−0.868172	−	0.630764i
$790$	−5.81836e9	+	1.79071e10i	−0.419861	+	1.29220i
$791$	−1.73510e10	−	5.63767e9i	−1.24654	−	0.405025i
$792$	−2.23321e8			−0.0159732
$793$	−1.05475e10	−	5.10168e9i	−0.751090	−	0.363293i
$794$	6.83817e9			0.484806
$795$	−1.42446e9	−	4.62833e8i	−0.100546	−	0.0326693i
$796$	−7.98322e9	+	2.45698e10i	−0.561025	+	1.72666i
$797$	−7.28983e9	−	5.29637e9i	−0.510050	−	0.370573i	0.302792	−	0.953057i	$-0.402081\pi$
$797$	−7.28983e9	−	5.29637e9i	−0.510050	−	0.370573i	−0.812843	+	0.582483i	$0.802081\pi$
$798$	−6.97914e9	−	5.07064e9i	−0.486174	−	0.353226i
$799$	3.10134e9	−	4.26862e9i	0.215097	−	0.296056i
$800$	−3.10143e9	+	1.00772e9i	−0.214164	+	0.0695862i
$801$	1.14071e8	+	1.57005e8i	0.00784262	+	0.0107944i
$802$	−5.22298e9	−	3.79472e9i	−0.357526	−	0.259758i
$803$	5.45688e7	+	7.51075e7i	0.00371912	+	0.00511893i
$804$		−	3.08202e10i		−	2.09141i
$805$	−2.02242e9	+	1.46938e9i	−0.136643	+	0.0992768i
$806$	2.55388e10			1.71802
$807$	3.27391e10			2.19285
$808$	7.49024e9	−	5.44198e9i	0.499524	−	0.362925i
$809$	1.07916e8	+	3.32131e8i	0.00716580	+	0.0220541i	0.954575	−	0.297969i	$-0.0963093\pi$
$809$	1.07916e8	+	3.32131e8i	0.00716580	+	0.0220541i	−0.947410	+	0.320023i	$0.896309\pi$
$810$	−8.65210e9	+	1.19086e10i	−0.572037	+	0.787341i
$811$	7.74285e9	+	1.06571e10i	0.509716	+	0.701563i	0.983871	−	0.178878i	$-0.0572466\pi$
$811$	7.74285e9	+	1.06571e10i	0.509716	+	0.701563i	−0.474156	+	0.880441i	$0.657247\pi$
$812$	−8.48346e9	+	2.61094e10i	−0.556067	+	1.71140i
$813$	−2.68711e9	−	8.27007e9i	−0.175375	−	0.539750i
$814$			2.10752e8i			0.0136958i
$815$	−2.00225e9	+	6.16230e9i	−0.129559	+	0.398741i
$816$	8.77470e9	−	1.20773e10i	0.565349	−	0.778136i
$817$	−6.15617e9	+	2.00026e9i	−0.394942	+	0.128324i
$818$	1.02364e10	+	3.15043e10i	0.653897	+	2.01249i
$819$	2.73434e9	+	8.88441e8i	0.173924	+	0.0565113i
$820$	−7.96553e9	+	5.78730e9i	−0.504506	+	0.366545i
$821$	9.69357e9	+	3.14963e9i	0.611340	+	0.198636i	0.598291	−	0.801279i	$-0.295847\pi$
$821$	9.69357e9	+	3.14963e9i	0.611340	+	0.198636i	0.0130482	+	0.999915i	$0.495847\pi$
$822$			2.50359e10i			1.57222i
$823$	−1.73116e10	+	5.62488e9i	−1.08252	+	0.351734i	−0.795354	−	0.606146i	$-0.792715\pi$
$823$	−1.73116e10	+	5.62488e9i	−1.08252	+	0.351734i	−0.287171	+	0.957879i	$0.592715\pi$
$824$	−1.80312e10	+	5.85870e9i	−1.12274	+	0.364801i
$825$		−	4.46419e8i		−	0.0276792i
$826$	1.72431e10	+	5.60261e9i	1.06459	+	0.345908i
$827$	2.22027e10	−	1.61312e10i	1.36501	−	0.991739i	0.366903	−	0.930259i	$-0.380418\pi$
$827$	2.22027e10	−	1.61312e10i	1.36501	−	0.991739i	0.998108	−	0.0614801i	$-0.0195821\pi$
$828$	−3.90992e9	−	1.27041e9i	−0.239365	−	0.0777745i
$829$	4.29007e9	+	1.32035e10i	0.261531	+	0.804911i	0.992472	+	0.122470i	$0.0390815\pi$
$829$	4.29007e9	+	1.32035e10i	0.261531	+	0.804911i	−0.730941	+	0.682441i	$0.760919\pi$
$830$	1.09424e10	−	3.55541e9i	0.664264	−	0.215832i
$831$	−1.95750e9	+	2.69426e9i	−0.118331	+	0.162868i
$832$	3.16483e9	−	9.74033e9i	0.190510	−	0.586330i
$833$			3.89969e9i			0.233761i
$834$	−1.29088e10	−	3.97291e10i	−0.770555	−	2.37152i
$835$	2.12028e9	−	6.52554e9i	0.126035	−	0.387895i
$836$	2.41564e8	+	3.32484e8i	0.0142991	+	0.0196811i
$837$	−9.62856e9	+	1.32526e10i	−0.567574	+	0.781198i
$838$	−9.58400e9	−	2.94965e10i	−0.562591	−	1.73148i
$839$	−1.62888e10	+	1.18345e10i	−0.952188	+	0.691805i	−0.951323	−	0.308194i	$-0.900275\pi$
$839$	−1.62888e10	+	1.18345e10i	−0.952188	+	0.691805i	−0.000864990		1.00000i	$0.500275\pi$
$840$	1.37893e10			0.802721
$841$	−2.34250e9			−0.135798
$842$	1.38829e10	−	1.00865e10i	0.801473	−	0.582304i
$843$			9.90471e9i			0.569436i
$844$	−4.01974e10	−	5.53270e10i	−2.30144	−	3.16766i
$845$	−1.99795e9	−	1.45160e9i	−0.113917	−	0.0827652i
$846$	2.60986e9	+	3.59217e9i	0.148191	+	0.203967i
$847$	−1.36487e10	+	4.43473e9i	−0.771790	+	0.250770i
$848$	2.62485e9	−	3.61279e9i	0.147815	−	0.203450i
$849$	9.62639e9	+	6.99398e9i	0.539867	+	0.392236i
$850$	1.37157e10	+	9.96503e9i	0.766040	+	0.556560i
$851$	−6.22129e8	+	1.91472e9i	−0.0346041	+	0.106500i
$852$	−3.85320e10	−	1.25198e10i	−2.13443	−	0.693519i
$853$	−3.40914e10			−1.88072			−0.940358	−	0.340187i	$-0.889510\pi$
$853$	−3.40914e10			−1.88072			−0.940358	+	0.340187i	$0.889510\pi$
$854$	−2.33534e10	−	1.12957e10i	−1.28306	−	0.620600i
$855$	−8.54996e8			−0.0467824
$856$	−1.48019e10	−	4.80942e9i	−0.806601	−	0.262081i
$857$	1.63501e8	−	5.03203e8i	0.00887333	−	0.0273093i	−0.946522	−	0.322640i	$-0.895430\pi$
$857$	1.63501e8	−	5.03203e8i	0.00887333	−	0.0273093i	0.955395	+	0.295330i	$0.0954298\pi$
$858$	−7.72336e8	−	5.61135e8i	−0.0417446	−	0.0303292i
$859$	−1.55992e10	−	1.13335e10i	−0.839703	−	0.610080i	0.0825846	−	0.996584i	$-0.473683\pi$
$859$	−1.55992e10	−	1.13335e10i	−0.839703	−	0.610080i	−0.922288	+	0.386504i	$0.873683\pi$
$860$	1.17200e10	−	1.61311e10i	0.628321	−	0.864809i
$861$	−1.05564e10	+	3.42999e9i	−0.563645	+	0.183139i
$862$	−1.93747e9	−	2.66670e9i	−0.103029	−	0.141807i
$863$	2.77053e10	+	2.01291e10i	1.46732	+	1.06607i	0.981379	+	0.192080i	$0.0615233\pi$
$863$	2.77053e10	+	2.01291e10i	1.46732	+	1.06607i	0.485942	+	0.873991i	$0.338477\pi$
$864$	−2.62920e9	−	3.61878e9i	−0.138684	−	0.190882i
$865$		−	2.26787e9i		−	0.119141i
$866$	1.18010e10	−	8.57395e9i	0.617458	−	0.448609i
$867$	1.14122e10			0.594708
$868$	3.81787e10			1.98153
$869$	8.18083e8	−	5.94372e8i	0.0422890	−	0.0307248i
$870$	5.86039e9	+	1.80364e10i	0.301723	+	0.928609i
$871$	8.53914e9	−	1.17531e10i	0.437875	−	0.602684i
$872$	7.64630e9	+	1.05242e10i	0.390521	+	0.537505i
$873$	−1.26046e9	+	3.87930e9i	−0.0641180	+	0.197335i
$874$	1.79681e9	+	5.53001e9i	0.0910357	+	0.280179i
$875$			1.33162e10i			0.671973i
$876$	2.91318e9	−	8.96584e9i	0.146421	−	0.450637i
$877$	2.03975e10	−	2.80748e10i	1.02113	−	1.40546i	0.109714	−	0.993963i	$-0.465007\pi$
$877$	2.03975e10	−	2.80748e10i	1.02113	−	1.40546i	0.911412	−	0.411496i	$-0.134993\pi$
$878$	−1.70239e10	+	5.53140e9i	−0.848845	+	0.275806i
$879$	1.11365e10	+	3.42746e10i	0.553080	+	1.70220i
$880$	−3.46108e8	−	1.12457e8i	−0.0171207	−	0.00556285i
$881$	−1.72957e10	+	1.25661e10i	−0.852162	+	0.619132i	−0.925741	−	0.378157i	$-0.876558\pi$
$881$	−1.72957e10	+	1.25661e10i	−0.852162	+	0.619132i	0.0735790	+	0.997289i	$0.476558\pi$
$882$	−3.12108e9	−	1.01410e9i	−0.153167	−	0.0497670i
$883$		−	2.27401e10i		−	1.11155i	−0.831332	−	0.555776i	$-0.812421\pi$
$883$		−	2.27401e10i		−	1.11155i	0.831332	−	0.555776i	$-0.187579\pi$
$884$	2.32804e10	−	7.56427e9i	1.13347	−	0.368285i
$885$	8.04242e9	−	2.61314e9i	0.390019	−	0.126725i
$886$			7.25693e10i			3.50538i
$887$	1.69917e9	+	5.52095e8i	0.0817533	+	0.0265633i	0.349608	−	0.936896i	$-0.386315\pi$
$887$	1.69917e9	+	5.52095e8i	0.0817533	+	0.0265633i	−0.267855	+	0.963459i	$0.586315\pi$
$888$	8.98428e9	−	6.52746e9i	0.430564	−	0.312823i
$889$	2.06793e10	+	6.71911e9i	0.987141	+	0.320742i
$890$	2.61276e8	+	8.04126e8i	0.0124232	+	0.0382348i
$891$	7.51849e8	−	2.44291e8i	0.0356089	−	0.0115700i
$892$	1.15450e10	−	1.58903e10i	0.544649	−	0.749645i
$893$	1.31026e9	−	4.03258e9i	0.0615714	−	0.189497i
$894$			8.27176e10i			3.87183i
$895$	−5.15613e9	−	1.58689e10i	−0.240405	−	0.739890i
$896$	8.55715e9	−	2.63362e10i	0.397421	−	1.22314i
$897$	−5.36035e9	−	7.37789e9i	−0.247982	−	0.341317i
$898$	1.01645e10	−	1.39902e10i	0.468400	−	0.644697i
$899$	8.41975e9	+	2.59133e10i	0.386492	+	1.18950i
$900$	−7.79302e9	+	5.66196e9i	−0.356334	+	0.258892i
$901$	−3.05479e9			−0.139137
$902$	7.83175e8			0.0355333
$903$	1.81852e10	−	1.32123e10i	0.821885	−	0.597134i
$904$		−	6.78296e10i		−	3.05372i
$905$	−5.35046e9	−	7.36428e9i	−0.239950	−	0.330263i
$906$	6.16190e10	+	4.47689e10i	2.75275	+	1.99999i
$907$	1.09163e10	+	1.50250e10i	0.485792	+	0.668636i	0.979605	−	0.200933i	$-0.0643972\pi$
$907$	1.09163e10	+	1.50250e10i	0.485792	+	0.668636i	−0.493813	+	0.869568i	$0.664397\pi$
$908$	−2.35691e10	+	7.65806e9i	−1.04482	+	0.339483i
$909$	1.17175e9	−	1.61278e9i	0.0517442	−	0.0712197i
$910$	1.01336e10	+	7.36252e9i	0.445780	+	0.323878i
$911$	−1.04351e10	−	7.58154e9i	−0.457280	−	0.332233i	0.335183	−	0.942153i	$-0.391202\pi$
$911$	−1.04351e10	−	7.58154e9i	−0.457280	−	0.332233i	−0.792463	+	0.609920i	$0.791202\pi$
$912$	3.70717e9	−	1.14095e10i	0.161831	−	0.498064i
$913$	−5.87672e8	−	1.90946e8i	−0.0255557	−	0.00830354i
$914$	−2.56247e10			−1.11006
$915$	−1.19089e10	+	2.14007e9i	−0.513921	+	0.0923536i
$916$	2.68642e10			1.15489
$917$	1.03468e10	+	3.36187e9i	0.443110	+	0.143975i
$918$	−7.18606e9	+	2.21164e10i	−0.306578	+	0.943551i
$919$	−8.40440e9	−	6.10615e9i	−0.357192	−	0.259515i	0.394688	−	0.918815i	$-0.370853\pi$
$919$	−8.40440e9	−	6.10615e9i	−0.357192	−	0.259515i	−0.751880	+	0.659300i	$0.770853\pi$
$920$	−7.51925e9	−	5.46305e9i	−0.318359	−	0.231301i
$921$	2.02588e10	−	2.78839e10i	0.854487	−	1.17610i
$922$	−3.73133e10	+	1.21238e10i	−1.56785	+	0.509427i
$923$	−1.12252e10	−	1.54501e10i	−0.469880	−	0.646735i
$924$	−1.15459e9	−	8.38857e8i	−0.0481476	−	0.0349813i
$925$	2.77271e9	+	3.81631e9i	0.115188	+	0.158543i
$926$			1.63624e10i			0.677188i
$927$	−3.30259e9	+	2.39947e9i	−0.136168	+	0.0989321i
$928$	−7.44010e9			−0.305605
$929$	−1.47036e10			−0.601682			−0.300841	−	0.953674i	$-0.597267\pi$
$929$	−1.47036e10			−0.601682			−0.300841	+	0.953674i	$0.597267\pi$
$930$	2.13369e10	−	1.55022e10i	0.869844	−	0.631979i
$931$	9.68409e8	+	2.98046e9i	0.0393310	+	0.121048i
$932$	3.88246e10	−	5.34374e10i	1.57091	−	2.16217i
$933$	4.50259e9	+	6.19728e9i	0.181500	+	0.249813i
$934$	−9.52398e9	+	2.93118e10i	−0.382476	+	1.17714i
$935$	7.69276e7	+	2.36759e8i	0.00307781	+	0.00947252i
$936$			1.06893e10i			0.426072i
$937$	6.78686e9	−	2.08878e10i	0.269513	−	0.829477i	−0.721106	−	0.692825i	$-0.756366\pi$
$937$	6.78686e9	−	2.08878e10i	0.269513	−	0.829477i	0.990619	−	0.136652i	$-0.0436341\pi$
$938$	1.89067e10	−	2.60228e10i	0.748007	−	1.02954i
$939$	4.98818e10	−	1.62076e10i	1.96613	−	0.638835i
$940$	4.03611e9	+	1.24219e10i	0.158495	+	0.487797i
$941$	−3.45091e10	−	1.12127e10i	−1.35011	−	0.438678i	−0.457383	−	0.889270i	$-0.651213\pi$
$941$	−3.45091e10	−	1.12127e10i	−1.35011	−	0.438678i	−0.892730	+	0.450592i	$0.851213\pi$
$942$	−7.32354e10	+	5.32087e10i	−2.85459	+	2.07398i
$943$	7.11527e9	+	2.31189e9i	0.276312	+	0.0897793i
$944$			2.52130e10i			0.975488i
$945$	−7.64111e9	+	2.48275e9i	−0.294541	+	0.0957021i
$946$	−1.50840e9	+	4.90108e8i	−0.0579291	+	0.0188223i
$947$			2.17699e10i			0.832973i	0.909142	+	0.416486i	$0.136739\pi$
$947$			2.17699e10i			0.832973i	−0.909142	+	0.416486i	$0.863261\pi$
$948$	−9.76573e10	−	3.17308e10i	−3.72285	−	1.20963i
$949$	3.59503e9	−	2.61194e9i	0.136543	−	0.0992046i
$950$	1.29573e10	+	4.21007e9i	0.490321	+	0.159315i
$951$	−3.77957e9	−	1.16323e10i	−0.142499	−	0.438565i
$952$	2.67477e10	−	8.69086e9i	1.00475	−	0.326463i
$953$	−1.28849e9	+	1.77346e9i	−0.0482232	+	0.0663736i	−0.832448	−	0.554104i	$-0.813061\pi$
$953$	−1.28849e9	+	1.77346e9i	−0.0482232	+	0.0663736i	0.784224	+	0.620477i	$0.213061\pi$
$954$	7.94388e8	−	2.44487e9i	0.0296219	−	0.0911669i
$955$			7.52867e9i			0.279709i
$956$	4.94966e9	+	1.52335e10i	0.183220	+	0.563893i
$957$	3.14737e8	−	9.68661e8i	0.0116080	−	0.0357256i
$958$	−2.13240e10	−	2.93500e10i	−0.783593	−	1.07852i
$959$	−1.03696e10	+	1.42726e10i	−0.379662	+	0.522560i
$960$	−3.26831e9	−	1.00588e10i	−0.119227	−	0.366943i
$961$	8.39705e9	−	6.10081e9i	0.305207	−	0.221746i
$962$	1.00877e10			0.365324
$963$	−3.35111e9			−0.120920
$964$	−3.20401e10	+	2.32785e10i	−1.15192	+	0.836922i
$965$			1.25078e10i			0.448059i
$966$	−1.18685e10	−	1.63355e10i	−0.423618	−	0.583060i
$967$	1.81553e10	+	1.31906e10i	0.645672	+	0.469108i	0.861794	−	0.507258i	$-0.169341\pi$
$967$	1.81553e10	+	1.31906e10i	0.645672	+	0.469108i	−0.216122	+	0.976366i	$0.569341\pi$
$968$	−3.13621e10	−	4.31663e10i	−1.11133	−	1.52961i
$969$	−7.80480e9	+	2.53593e9i	−0.275568	+	0.0895374i
$970$	−1.04455e10	+	1.43769e10i	−0.367474	+	0.505784i
$971$	−3.36135e10	−	2.44216e10i	−1.17827	−	0.856066i	−0.186298	−	0.982493i	$-0.559649\pi$
$971$	−3.36135e10	−	2.44216e10i	−1.17827	−	0.856066i	−0.991976	+	0.126427i	$0.959649\pi$
$972$	−2.53291e10	−	1.84027e10i	−0.884684	−	0.642760i
$973$	9.09631e9	−	2.79956e10i	0.316571	−	0.974304i
$974$	−6.55784e10	−	2.13077e10i	−2.27407	−	0.738892i
$975$	−2.13679e10			−0.738321
$976$	4.90380e9	−	3.57409e10i	0.168834	−	1.23053i
$977$	−3.31003e10			−1.13554			−0.567769	−	0.823188i	$-0.692193\pi$
$977$	−3.31003e10			−1.13554			−0.567769	+	0.823188i	$0.692193\pi$
$978$	−4.97741e10	−	1.61726e10i	−1.70144	−	0.552832i
$979$	1.40321e7	−	4.31862e7i	0.000477949	−	0.00147098i
$980$	−7.80975e9	−	5.67412e9i	−0.265061	−	0.192578i
$981$	2.26605e9	+	1.64638e9i	0.0766350	+	0.0556786i
$982$	−2.42099e10	+	3.33221e10i	−0.815836	+	1.12290i
$983$	7.37185e8	−	2.39526e8i	0.0247537	−	0.00804295i	−0.296614	−	0.954997i	$-0.595857\pi$
$983$	7.37185e8	−	2.39526e8i	0.0247537	−	0.00804295i	0.321368	+	0.946955i	$0.395857\pi$
$984$	−2.42567e10	−	3.33864e10i	−0.811611	−	1.11709i
$985$	1.59438e9	+	1.15838e9i	0.0531575	+	0.0386212i
$986$	2.27353e10	+	3.12925e10i	0.755322	+	1.03961i
$987$			1.47242e10i			0.487442i
$988$	1.59144e10	−	1.15625e10i	0.524977	−	0.381418i
$989$	−1.51508e10			−0.498021
$990$	−2.09493e8			−0.00686193
$991$	−2.02718e10	+	1.47283e10i	−0.661660	+	0.480724i	−0.867223	−	0.497920i	$-0.834097\pi$
$991$	−2.02718e10	+	1.47283e10i	−0.661660	+	0.480724i	0.205563	+	0.978644i	$0.434097\pi$
$992$	3.19736e9	+	9.84045e9i	0.103992	+	0.320055i
$993$	3.48443e10	−	4.79591e10i	1.12930	−	1.55435i
$994$	−2.48539e10	−	3.42085e10i	−0.802680	−	1.10479i
$995$	−3.88608e9	+	1.19601e10i	−0.125064	+	0.384906i
$996$	1.93897e10	+	5.96752e10i	0.621817	+	1.91375i
$997$		−	6.15614e10i		−	1.96732i	−0.180035	−	0.983660i	$-0.557621\pi$
$997$		−	6.15614e10i		−	1.96732i	0.180035	−	0.983660i	$-0.442379\pi$
$998$	3.67769e9	−	1.13188e10i	0.117117	−	0.360448i
$999$	−3.80323e9	+	5.23470e9i	−0.120691	+	0.166116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.8.g.a.3.3	✓	136
61.41	even	10	inner	61.8.g.a.41.3	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.8.g.a.3.3	✓	136	1.1	even	1	trivial
61.8.g.a.41.3	yes	136	61.41	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	61.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-18.8795 - 6.13431i) q^{2} +(16.2847 - 50.1192i) q^{3} +(215.250 + 156.388i) q^{4} +(104.780 + 76.1270i) q^{5} +(-614.893 + 846.327i) q^{6} +(-701.080 + 227.795i) q^{7} +(-1610.95 - 2217.28i) q^{8} +(-477.419 - 346.865i) q^{9} +O(q^{10})\)	\(q+(-18.8795 - 6.13431i) q^{2} +(16.2847 - 50.1192i) q^{3} +(215.250 + 156.388i) q^{4} +(104.780 + 76.1270i) q^{5} +(-614.893 + 846.327i) q^{6} +(-701.080 + 227.795i) q^{7} +(-1610.95 - 2217.28i) q^{8} +(-477.419 - 346.865i) q^{9} +(-1511.20 - 2079.99i) q^{10} +138.078i q^{11} +(11343.3 - 8241.42i) q^{12} +6609.11 q^{13} +14633.4 q^{14} +(5521.73 - 4011.77i) q^{15} +(6288.44 + 19353.8i) q^{16} +(8182.28 - 11261.9i) q^{17} +(6885.63 + 9477.26i) q^{18} +(3456.88 - 10639.2i) q^{19} +(10648.5 + 32772.7i) q^{20} +38847.1i q^{21} +(847.013 - 2606.84i) q^{22} +(15390.5 - 21183.2i) q^{23} +(-137362. + 44631.7i) q^{24} +(-18958.5 - 58348.2i) q^{25} +(-124777. - 40542.4i) q^{26} +(68081.2 - 49463.9i) q^{27} +(-186532. - 60608.0i) q^{28} -139973. i q^{29} +(-128857. + 41868.1i) q^{30} +(-185131. + 60152.8i) q^{31} -53153.9i q^{32} +(6920.35 + 2248.56i) q^{33} +(-223561. + 162427. i) q^{34} +(-90800.3 - 29502.8i) q^{35} +(-48518.8 - 149325. i) q^{36} +(-73125.9 + 23760.0i) q^{37} +(-130528. + 179657. i) q^{38} +(107627. - 331243. i) q^{39} -354963. i q^{40} +(88294.5 + 271743. i) q^{41} +(238300. - 733413. i) q^{42} +(-340111. - 468122. i) q^{43} +(-21593.8 + 29721.3i) q^{44} +(-23618.0 - 72688.9i) q^{45} +(-420508. + 305517. i) q^{46} +379031. q^{47} +1.07240e6 q^{48} +(-226637. + 164662. i) q^{49} +1.21788e6i q^{50} +(-431193. - 593486. i) q^{51} +(1.42261e6 + 1.03359e6i) q^{52} +(-128986. - 177535. i) q^{53} +(-1.58876e6 + 516220. i) q^{54} +(-10511.5 + 14467.8i) q^{55} +(1.63449e6 + 1.18753e6i) q^{56} +(-476933. - 346512. i) q^{57} +(-858636. + 2.64261e6i) q^{58} +(1.17834e6 + 382865. i) q^{59} +1.81595e6 q^{60} +(-1.59590e6 - 771915. i) q^{61} +3.86417e6 q^{62} +(413723. + 134427. i) q^{63} +(478858. - 1.47377e6i) q^{64} +(692502. + 503132. i) q^{65} +(-116859. - 84903.2i) q^{66} +(1.29202e6 - 1.77832e6i) q^{67} +(3.52248e6 - 1.14452e6i) q^{68} +(-811054. - 1.11632e6i) q^{69} +(1.53328e6 + 1.11399e6i) q^{70} +(-1.69844e6 - 2.33770e6i) q^{71} +1.61735e6i q^{72} +(543950. - 395203. i) q^{73} +1.52633e6 q^{74} -3.23309e6 q^{75} +(2.40794e6 - 1.74947e6i) q^{76} +(-31453.4 - 96803.7i) q^{77} +(-4.06390e6 + 5.59347e6i) q^{78} +(-4.30461e6 - 5.92479e6i) q^{79} +(-814447. + 2.50661e6i) q^{80} +(-1.76922e6 - 5.44510e6i) q^{81} -5.67198e6i q^{82} +(-1.38289e6 + 4.25609e6i) q^{83} +(-6.07524e6 + 8.36185e6i) q^{84} +(1.71468e6 - 557132. i) q^{85} +(3.54950e6 + 1.09242e7i) q^{86} +(-7.01532e6 - 2.27941e6i) q^{87} +(306158. - 222437. i) q^{88} +(-312767. - 101624. i) q^{89} +1.51721e6i q^{90} +(-4.63352e6 + 1.50552e6i) q^{91} +(6.62561e6 - 2.15279e6i) q^{92} +1.02582e7i q^{93} +(-7.15590e6 - 2.32509e6i) q^{94} +(1.17214e6 - 851610. i) q^{95} +(-2.66403e6 - 865596. i) q^{96} +(-2.13593e6 - 6.57373e6i) q^{97} +(5.28888e6 - 1.71846e6i) q^{98} +(47894.4 - 65921.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 5 q^{2} - 57 q^{3} + 1969 q^{4} + 414 q^{5} - 275 q^{6} - 2650 q^{7} - 5 q^{8} - 22677 q^{9}+O(q^{10}) \) 136 * q - 5 * q^2 - 57 * q^3 + 1969 * q^4 + 414 * q^5 - 275 * q^6 - 2650 * q^7 - 5 * q^8 - 22677 * q^9	\( 136 q - 5 q^{2} - 57 q^{3} + 1969 q^{4} + 414 q^{5} - 275 q^{6} - 2650 q^{7} - 5 q^{8} - 22677 q^{9} + 18405 q^{10} - 14698 q^{12} - 41840 q^{13} + 51126 q^{14} + 7203 q^{15} - 94007 q^{16} - 31920 q^{17} + 72980 q^{18} + 102795 q^{19} + 147581 q^{20} - 168127 q^{22} - 277935 q^{23} + 921540 q^{24} - 609554 q^{25} - 341870 q^{26} - 139608 q^{27} - 355845 q^{28} + 218815 q^{30} - 235615 q^{31} + 96625 q^{33} + 1996448 q^{34} - 821930 q^{35} + 1923233 q^{36} - 5 q^{37} + 164715 q^{38} - 55295 q^{39} - 2738004 q^{41} - 3935531 q^{42} - 124265 q^{43} + 496870 q^{44} - 1705580 q^{45} + 3949707 q^{46} - 6522690 q^{47} + 4081416 q^{48} + 4581948 q^{49} + 3506350 q^{51} - 4794960 q^{52} + 2288650 q^{53} + 13111480 q^{54} - 7615700 q^{55} - 8104924 q^{56} - 1851487 q^{57} + 2821869 q^{58} + 512285 q^{59} - 11303002 q^{60} + 4003165 q^{61} + 11267092 q^{62} - 3732265 q^{63} + 4089213 q^{64} + 14201480 q^{65} - 4750133 q^{66} - 2990255 q^{67} - 28116100 q^{68} + 6452165 q^{69} + 2929505 q^{70} - 20770790 q^{71} + 4931233 q^{73} - 2981520 q^{74} + 43273192 q^{75} + 6320137 q^{76} - 4357269 q^{77} + 32574470 q^{78} - 1203220 q^{79} - 64168363 q^{80} + 16681123 q^{81} + 20705839 q^{83} - 25806085 q^{84} - 36617415 q^{85} + 463139 q^{86} - 4611115 q^{87} + 52109661 q^{88} + 39392730 q^{89} - 31163475 q^{91} - 31104005 q^{92} + 15981295 q^{94} + 8937948 q^{95} + 91723305 q^{96} + 5094353 q^{97} - 84253670 q^{98} - 55470065 q^{99}+O(q^{100}) \) 136 * q - 5 * q^2 - 57 * q^3 + 1969 * q^4 + 414 * q^5 - 275 * q^6 - 2650 * q^7 - 5 * q^8 - 22677 * q^9 + 18405 * q^10 - 14698 * q^12 - 41840 * q^13 + 51126 * q^14 + 7203 * q^15 - 94007 * q^16 - 31920 * q^17 + 72980 * q^18 + 102795 * q^19 + 147581 * q^20 - 168127 * q^22 - 277935 * q^23 + 921540 * q^24 - 609554 * q^25 - 341870 * q^26 - 139608 * q^27 - 355845 * q^28 + 218815 * q^30 - 235615 * q^31 + 96625 * q^33 + 1996448 * q^34 - 821930 * q^35 + 1923233 * q^36 - 5 * q^37 + 164715 * q^38 - 55295 * q^39 - 2738004 * q^41 - 3935531 * q^42 - 124265 * q^43 + 496870 * q^44 - 1705580 * q^45 + 3949707 * q^46 - 6522690 * q^47 + 4081416 * q^48 + 4581948 * q^49 + 3506350 * q^51 - 4794960 * q^52 + 2288650 * q^53 + 13111480 * q^54 - 7615700 * q^55 - 8104924 * q^56 - 1851487 * q^57 + 2821869 * q^58 + 512285 * q^59 - 11303002 * q^60 + 4003165 * q^61 + 11267092 * q^62 - 3732265 * q^63 + 4089213 * q^64 + 14201480 * q^65 - 4750133 * q^66 - 2990255 * q^67 - 28116100 * q^68 + 6452165 * q^69 + 2929505 * q^70 - 20770790 * q^71 + 4931233 * q^73 - 2981520 * q^74 + 43273192 * q^75 + 6320137 * q^76 - 4357269 * q^77 + 32574470 * q^78 - 1203220 * q^79 - 64168363 * q^80 + 16681123 * q^81 + 20705839 * q^83 - 25806085 * q^84 - 36617415 * q^85 + 463139 * q^86 - 4611115 * q^87 + 52109661 * q^88 + 39392730 * q^89 - 31163475 * q^91 - 31104005 * q^92 + 15981295 * q^94 + 8937948 * q^95 + 91723305 * q^96 + 5094353 * q^97 - 84253670 * q^98 - 55470065 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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