LMFDB - Embedded newform 62.8.d.a.33.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,8,Mod(33,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.33"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	62.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,-80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$19.3678715800$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			33.2
Character	$\chi$	$=$	62.33
Dual form			62.8.d.a.47.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.47214 - 4.70228i) q^{2} +(-62.8734 + 45.6802i) q^{3} +(19.7771 + 60.8676i) q^{4} +155.004 q^{5} +621.727 q^{6} +(296.473 + 912.449i) q^{7} +(158.217 - 486.941i) q^{8} +(1190.57 - 3664.18i) q^{9} +(-1003.21 - 728.874i) q^{10} +(-385.698 - 1187.06i) q^{11} +(-4023.90 - 2923.53i) q^{12} +(11630.5 - 8450.06i) q^{13} +(2371.78 - 7299.59i) q^{14} +(-9745.65 + 7080.63i) q^{15} +(-3313.73 + 2407.57i) q^{16} +(-25.1576 + 77.4272i) q^{17} +(-24935.5 + 18116.7i) q^{18} +(38723.7 + 28134.4i) q^{19} +(3065.53 + 9434.74i) q^{20} +(-60321.1 - 43825.9i) q^{21} +(-3085.58 + 9496.45i) q^{22} +(-28200.7 + 86792.7i) q^{23} +(12295.9 + 37843.0i) q^{24} -54098.7 q^{25} -115009. q^{26} +(40003.9 + 123119. i) q^{27} +(-49675.3 + 36091.2i) q^{28} +(137620. + 99987.1i) q^{29} +96370.3 q^{30} +(151156. - 68296.7i) q^{31} +32768.0 q^{32} +(78475.2 + 57015.5i) q^{33} +(526.908 - 382.821i) q^{34} +(45954.5 + 141434. i) q^{35} +246576. q^{36} -95969.5 q^{37} +(-118329. - 364179. i) q^{38} +(-345250. + 1.06257e6i) q^{39} +(24524.3 - 75477.9i) q^{40} +(-31159.4 - 22638.6i) q^{41} +(184325. + 567294. i) q^{42} +(-619700. - 450238. i) q^{43} +(64625.3 - 46953.0i) q^{44} +(184543. - 567964. i) q^{45} +(590642. - 429127. i) q^{46} +(-479229. + 348180. i) q^{47} +(98367.5 - 302744. i) q^{48} +(-78407.5 + 56966.3i) q^{49} +(350134. + 254387. i) q^{50} +(-1955.15 - 6017.32i) q^{51} +(744353. + 540804. i) q^{52} +(-473013. + 1.45579e6i) q^{53} +(320031. - 984954. i) q^{54} +(-59784.9 - 183999. i) q^{55} +491216. q^{56} -3.71988e6 q^{57} +(-420531. - 1.29426e6i) q^{58} +(-407939. + 296385. i) q^{59} +(-623722. - 453160. i) q^{60} -741426. q^{61} +(-1.29945e6 - 268753. i) q^{62} +3.69635e6 q^{63} +(-212079. - 154084. i) q^{64} +(1.80278e6 - 1.30980e6i) q^{65} +(-239799. - 738025. i) q^{66} +3.37738e6 q^{67} -5210.36 q^{68} +(-2.19164e6 - 6.74517e6i) q^{69} +(367636. - 1.13147e6i) q^{70} +(-312490. + 961746. i) q^{71} +(-1.59587e6 - 1.15947e6i) q^{72} +(346791. + 1.06731e6i) q^{73} +(621128. + 451276. i) q^{74} +(3.40137e6 - 2.47124e6i) q^{75} +(-946633. + 2.91344e6i) q^{76} +(968780. - 703860. i) q^{77} +(7.23100e6 - 5.25363e6i) q^{78} +(-1.10106e6 + 3.38872e6i) q^{79} +(-513643. + 373183. i) q^{80} +(-1.32254e6 - 960885. i) q^{81} +(95214.5 + 293040. i) q^{82} +(1.09798e6 + 797731. i) q^{83} +(1.47460e6 - 4.53835e6i) q^{84} +(-3899.54 + 12001.6i) q^{85} +(1.89363e6 + 5.82800e6i) q^{86} -1.32201e7 q^{87} -639050. q^{88} +(-1.27251e6 - 3.91639e6i) q^{89} +(-3.86511e6 + 2.80817e6i) q^{90} +(1.11584e7 + 8.10704e6i) q^{91} -5.84059e6 q^{92} +(-6.38390e6 + 1.11989e7i) q^{93} +4.73888e6 q^{94} +(6.00234e6 + 4.36095e6i) q^{95} +(-2.06024e6 + 1.49685e6i) q^{96} +(2.77729e6 + 8.54761e6i) q^{97} +775336. q^{98} -4.80879e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) $ 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−6.47214	−	4.70228i	−0.572061	−	0.415627i
$2$	−6.47214	−	4.70228i	−0.572061	−	0.415627i
$3$	−62.8734	+	45.6802i	−1.34444	+	0.976796i	−0.345176	+	0.938538i	$0.612181\pi$
$3$	−62.8734	+	45.6802i	−1.34444	+	0.976796i	−0.999268	+	0.0382580i	$0.987819\pi$
$4$	19.7771	+	60.8676i	0.154508	+	0.475528i
$5$	155.004			0.554560			0.277280	−	0.960789i	$-0.410567\pi$
$5$	155.004			0.554560			0.277280	+	0.960789i	$0.410567\pi$
$6$	621.727			1.17509
$7$	296.473	+	912.449i	0.326694	+	1.00546i	0.970670	+	0.240416i	$0.0772838\pi$
$7$	296.473	+	912.449i	0.326694	+	1.00546i	−0.643976	+	0.765046i	$0.722716\pi$
$8$	158.217	−	486.941i	0.109254	−	0.336249i
$9$	1190.57	−	3664.18i	0.544383	−	1.67544i
$10$	−1003.21	−	728.874i	−0.317242	−	0.230490i
$11$	−385.698	−	1187.06i	−0.0873722	−	0.268904i	0.897819	−	0.440365i	$-0.145151\pi$
$11$	−385.698	−	1187.06i	−0.0873722	−	0.268904i	−0.985191	+	0.171462i	$0.945151\pi$
$12$	−4023.90	−	2923.53i	−0.672222	−	0.488398i
$13$	11630.5	−	8450.06i	1.46824	−	1.06674i	0.487121	−	0.873334i	$-0.338047\pi$
$13$	11630.5	−	8450.06i	1.46824	−	1.06674i	0.981119	−	0.193405i	$-0.0619531\pi$
$14$	2371.78	−	7299.59i	0.231008	−	0.710969i
$15$	−9745.65	+	7080.63i	−0.745575	+	0.541692i
$16$	−3313.73	+	2407.57i	−0.202254	+	0.146946i
$17$	−25.1576	+	77.4272i	−0.00124193	+	0.00382228i	−0.951676	−	0.307105i	$-0.900640\pi$
$17$	−25.1576	+	77.4272i	−0.00124193	+	0.00382228i	0.950434	+	0.310928i	$0.100640\pi$
$18$	−24935.5	+	18116.7i	−1.00778	+	0.732193i
$19$	38723.7	+	28134.4i	1.29521	+	0.941023i	0.999897	−	0.0143785i	$-0.00457698\pi$
$19$	38723.7	+	28134.4i	1.29521	+	0.941023i	0.295310	+	0.955401i	$0.404577\pi$
$20$	3065.53	+	9434.74i	0.0856843	+	0.263709i
$21$	−60321.1	−	43825.9i	−1.42135	−	1.03267i
$22$	−3085.58	+	9496.45i	−0.0617814	+	0.190144i
$23$	−28200.7	+	86792.7i	−0.483295	+	1.48743i	0.351141	+	0.936323i	$0.385794\pi$
$23$	−28200.7	+	86792.7i	−0.483295	+	1.48743i	−0.834436	+	0.551105i	$0.814206\pi$
$24$	12295.9	+	37843.0i	0.181561	+	0.558787i
$25$	−54098.7			−0.692463
$26$	−115009.			−1.28329
$27$	40003.9	+	123119.i	0.391137	+	1.20380i
$28$	−49675.3	+	36091.2i	−0.427649	+	0.310705i
$29$	137620.	+	99987.1i	1.04783	+	0.761291i	0.971798	−	0.235814i	$-0.0757757\pi$
$29$	137620.	+	99987.1i	1.04783	+	0.761291i	0.0760295	+	0.997106i	$0.475776\pi$
$30$	96370.3			0.651657
$31$	151156.	−	68296.7i	0.911297	−	0.411750i
$31$	151156.	−	68296.7i	0.911297	−	0.411750i
$32$	32768.0			0.176777
$33$	78475.2	+	57015.5i	0.380131	+	0.276181i
$34$	526.908	−	382.821i	0.00229910	−	0.00167040i
$35$	45954.5	+	141434.i	0.181172	+	0.557589i
$36$	246576.			0.880830
$37$	−95969.5			−0.311478			−0.155739	−	0.987798i	$-0.549776\pi$
$37$	−95969.5			−0.311478			−0.155739	+	0.987798i	$0.549776\pi$
$38$	−118329.	−	364179.i	−0.349823	−	1.07665i
$39$	−345250.	+	1.06257e6i	−0.931981	+	2.86834i
$40$	24524.3	−	75477.9i	0.0605879	−	0.186470i
$41$	−31159.4	−	22638.6i	−0.0706066	−	0.0512987i	0.551922	−	0.833896i	$-0.313895\pi$
$41$	−31159.4	−	22638.6i	−0.0706066	−	0.0512987i	−0.622529	+	0.782597i	$0.713895\pi$
$42$	184325.	+	567294.i	0.383894	+	1.18151i
$43$	−619700.	−	450238.i	−1.18862	−	0.863580i	−0.195499	−	0.980704i	$-0.562633\pi$
$43$	−619700.	−	450238.i	−1.18862	−	0.863580i	−0.993117	+	0.117124i	$0.962633\pi$
$44$	64625.3	−	46953.0i	0.114372	−	0.0830959i
$45$	184543.	−	567964.i	0.301893	−	0.929131i
$46$	590642.	−	429127.i	0.894689	−	0.650030i
$47$	−479229.	+	348180.i	−0.673287	+	0.489172i	−0.871124	−	0.491063i	$-0.836608\pi$
$47$	−479229.	+	348180.i	−0.673287	+	0.489172i	0.197837	+	0.980235i	$0.436608\pi$
$48$	98367.5	−	302744.i	0.128383	−	0.395122i
$49$	−78407.5	+	56966.3i	−0.0952075	+	0.0691723i
$50$	350134.	+	254387.i	0.396131	+	0.287806i
$51$	−1955.15	−	6017.32i	−0.00206388	−	0.00635196i
$52$	744353.	+	540804.i	0.734120	+	0.533370i
$53$	−473013.	+	1.45579e6i	−0.436423	+	1.34317i	0.455198	+	0.890390i	$0.349569\pi$
$53$	−473013.	+	1.45579e6i	−0.436423	+	1.34317i	−0.891621	+	0.452782i	$0.850431\pi$
$54$	320031.	−	984954.i	0.276576	−	0.851212i
$55$	−59784.9	−	183999.i	−0.0484531	−	0.149123i
$56$	491216.			0.373778
$57$	−3.71988e6			−2.66052
$58$	−420531.	−	1.29426e6i	−0.283009	−	0.871011i
$59$	−407939.	+	296385.i	−0.258591	+	0.187877i	−0.709525	−	0.704680i	$-0.751091\pi$
$59$	−407939.	+	296385.i	−0.258591	+	0.187877i	0.450935	+	0.892557i	$0.351091\pi$
$60$	−623722.	−	453160.i	−0.372788	−	0.270846i
$61$	−741426.			−0.418228			−0.209114	−	0.977891i	$-0.567058\pi$
$61$	−741426.			−0.418228			−0.209114	+	0.977891i	$0.567058\pi$
$62$	−1.29945e6	−	268753.i	−0.692452	−	0.143213i
$63$	3.69635e6			1.86244
$64$	−212079.	−	154084.i	−0.101127	−	0.0734732i
$65$	1.80278e6	−	1.30980e6i	0.814228	−	0.591571i
$66$	−239799.	−	738025.i	−0.102670	−	0.315986i
$67$	3.37738e6			1.37189			0.685943	−	0.727655i	$-0.259390\pi$
$67$	3.37738e6			1.37189			0.685943	+	0.727655i	$0.259390\pi$
$68$	−5210.36			−0.00200949
$69$	−2.19164e6	−	6.74517e6i	−0.803151	−	2.47184i
$70$	367636.	−	1.13147e6i	0.128108	−	0.394275i
$71$	−312490.	+	961746.i	−0.103617	+	0.318901i	−0.989403	−	0.145192i	$-0.953620\pi$
$71$	−312490.	+	961746.i	−0.103617	+	0.318901i	0.885786	+	0.464094i	$0.153620\pi$
$72$	−1.59587e6	−	1.15947e6i	−0.503889	−	0.366097i
$73$	346791.	+	1.06731e6i	0.104337	+	0.321116i	0.989574	−	0.144024i	$-0.0460041\pi$
$73$	346791.	+	1.06731e6i	0.104337	+	0.321116i	−0.885237	+	0.465140i	$0.846004\pi$
$74$	621128.	+	451276.i	0.178185	+	0.129459i
$75$	3.40137e6	−	2.47124e6i	0.930978	−	0.676395i
$76$	−946633.	+	2.91344e6i	−0.247363	+	0.761304i
$77$	968780.	−	703860.i	0.241829	−	0.175699i
$78$	7.23100e6	−	5.25363e6i	1.72531	−	1.25351i
$79$	−1.10106e6	+	3.38872e6i	−0.251256	+	0.773287i	0.743288	+	0.668971i	$0.233265\pi$
$79$	−1.10106e6	+	3.38872e6i	−0.251256	+	0.773287i	−0.994544	+	0.104315i	$0.966735\pi$
$80$	−513643.	+	373183.i	−0.112162	+	0.0814906i
$81$	−1.32254e6	−	960885.i	−0.276511	−	0.200897i
$82$	95214.5	+	293040.i	0.0190702	+	0.0586920i
$83$	1.09798e6	+	797731.i	0.210777	+	0.153138i	0.688165	−	0.725554i	$-0.258417\pi$
$83$	1.09798e6	+	797731.i	0.210777	+	0.153138i	−0.477388	+	0.878692i	$0.658417\pi$
$84$	1.47460e6	−	4.53835e6i	0.271454	−	0.835451i
$85$	−3899.54	+	12001.6i	−0.000688727	+	0.00211968i
$86$	1.89363e6	+	5.82800e6i	0.321034	+	0.988042i
$87$	−1.32201e7			−2.15237
$88$	−639050.			−0.0999645
$89$	−1.27251e6	−	3.91639e6i	−0.191336	−	0.588872i	−1.00000		0.000601024i	$-0.999809\pi$
$89$	−1.27251e6	−	3.91639e6i	−0.191336	−	0.588872i	0.808664	−	0.588271i	$-0.200191\pi$
$90$	−3.86511e6	+	2.80817e6i	−0.558873	+	0.406045i
$91$	1.11584e7	+	8.10704e6i	1.55223	+	1.12776i
$92$	−5.84059e6			−0.781987
$93$	−6.38390e6	+	1.11989e7i	−0.822992	+	1.44373i
$94$	4.73888e6			0.588475
$95$	6.00234e6	+	4.36095e6i	0.718270	+	0.521854i
$96$	−2.06024e6	+	1.49685e6i	−0.237666	+	0.172675i
$97$	2.77729e6	+	8.54761e6i	0.308972	+	0.950919i	0.978165	+	0.207830i	$0.0666401\pi$
$97$	2.77729e6	+	8.54761e6i	0.308972	+	0.950919i	−0.669193	+	0.743089i	$0.733360\pi$
$98$	775336.			0.0832144
$99$	−4.80879e6			−0.498096
$100$	−1.06991e6	−	3.29286e6i	−0.106991	−	0.329286i
$101$	3.54944e6	−	1.09240e7i	0.342795	−	1.05501i	−0.619958	−	0.784635i	$-0.712851\pi$
$101$	3.54944e6	−	1.09240e7i	0.342795	−	1.05501i	0.962754	−	0.270380i	$-0.0871494\pi$
$102$	−15641.2	+	48138.6i	−0.00145938	+	0.00449151i
$103$	−4.78241e6	−	3.47462e6i	−0.431237	−	0.313312i	0.350906	−	0.936411i	$-0.385874\pi$
$103$	−4.78241e6	−	3.47462e6i	−0.431237	−	0.313312i	−0.782143	+	0.623098i	$0.785874\pi$
$104$	−2.27454e6	−	7.00031e6i	−0.198279	−	0.610240i
$105$	−9.35004e6	−	6.79320e6i	−0.788226	−	0.572680i
$106$	9.90692e6	−	7.19780e6i	0.807920	−	0.586988i
$107$	−7.59668e6	+	2.33802e7i	−0.599488	+	1.84503i	−0.0685062	+	0.997651i	$0.521823\pi$
$107$	−7.59668e6	+	2.33802e7i	−0.599488	+	1.84503i	−0.530982	+	0.847383i	$0.678177\pi$
$108$	−6.70281e6	+	4.86988e6i	−0.512005	+	0.371993i
$109$	−7.01172e6	+	5.09432e6i	−0.518599	+	0.376785i	−0.816076	−	0.577945i	$-0.803855\pi$
$109$	−7.01172e6	+	5.09432e6i	−0.518599	+	0.376785i	0.297477	+	0.954729i	$0.403855\pi$
$110$	−478279.	+	1.47199e6i	−0.0342615	+	0.105446i
$111$	6.03393e6	−	4.38391e6i	0.418765	−	0.304250i
$112$	−3.17922e6	−	2.30984e6i	−0.213824	−	0.155352i
$113$	3.11270e6	+	9.57991e6i	0.202938	+	0.624578i	0.999792	+	0.0204063i	$0.00649598\pi$
$113$	3.11270e6	+	9.57991e6i	0.202938	+	0.624578i	−0.796854	+	0.604172i	$0.793504\pi$
$114$	2.40756e7	+	1.74919e7i	1.52198	+	1.10578i
$115$	−4.37122e6	+	1.34532e7i	−0.268016	+	0.824868i
$116$	−3.36424e6	+	1.03541e7i	−0.200117	+	0.615898i
$117$	−1.71157e7	−	5.26767e7i	−0.987971	−	3.04066i
$118$	4.03392e6			0.226016
$119$	−78107.0			−0.00424889
$120$	1.90592e6	+	5.86583e6i	0.100686	+	0.309881i
$121$	1.45051e7	−	1.05386e7i	0.744342	−	0.540796i
$122$	4.79861e6	+	3.48639e6i	0.239252	+	0.173827i
$123$	2.99323e6			0.145035
$124$	7.14648e6	+	7.84980e6i	0.336602	+	0.369729i
$125$	−2.04952e7			−0.938573
$126$	−2.39233e7	−	1.73813e7i	−1.06543	−	0.774079i
$127$	3.06390e7	−	2.22605e7i	1.32728	−	0.964323i	0.327466	−	0.944863i	$-0.393805\pi$
$127$	3.06390e7	−	2.22605e7i	1.32728	−	0.964323i	0.999811	−	0.0194600i	$-0.00619470\pi$
$128$	648056.	+	1.99451e6i	0.0273135	+	0.0840623i
$129$	5.95296e7			2.44157
$130$	−1.78269e7			−0.711661
$131$	4.51231e6	+	1.38875e7i	0.175368	+	0.539726i	0.999650	−	0.0264529i	$-0.00842121\pi$
$131$	4.51231e6	+	1.38875e7i	0.175368	+	0.539726i	−0.824283	+	0.566179i	$0.808421\pi$
$132$	−1.91839e6	+	5.90420e6i	−0.0725986	+	0.223435i
$133$	−1.41907e7	+	4.36745e7i	−0.523026	+	1.60971i
$134$	−2.18589e7	−	1.58814e7i	−0.784803	−	0.570193i
$135$	6.20077e6	+	1.90840e7i	0.216909	+	0.667577i
$136$	33722.1	+	24500.6i	0.00114955	+	0.000835199i
$137$	−1.40352e7	+	1.01972e7i	−0.466334	+	0.338811i	−0.796011	−	0.605282i	$-0.793060\pi$
$137$	−1.40352e7	+	1.01972e7i	−0.466334	+	0.338811i	0.329677	+	0.944094i	$0.393060\pi$
$138$	−1.75331e7	+	5.39614e7i	−0.567913	+	1.74786i
$139$	1.56728e7	−	1.13870e7i	0.494989	−	0.359631i	−0.312110	−	0.950046i	$-0.601036\pi$
$139$	1.56728e7	−	1.13870e7i	0.494989	−	0.359631i	0.807100	+	0.590415i	$0.201036\pi$
$140$	−7.69988e6	+	5.59429e6i	−0.237157	+	0.172305i
$141$	1.42258e7	−	4.37826e7i	0.427376	−	1.31533i
$142$	6.54488e6	−	4.75513e6i	0.191819	−	0.139365i
$143$	−1.45166e7	−	1.05469e7i	−0.415134	−	0.301612i
$144$	4.87656e6	+	1.50085e7i	0.136096	+	0.418860i
$145$	2.13318e7	+	1.54984e7i	0.581084	+	0.422182i
$146$	2.77433e6	−	8.53851e6i	0.0737774	−	0.227063i
$147$	2.32751e6	−	7.16334e6i	0.0604339	−	0.185997i
$148$	−1.89800e6	−	5.84144e6i	−0.0481260	−	0.148117i
$149$	−2.88218e7			−0.713789			−0.356894	−	0.934145i	$-0.616164\pi$
$149$	−2.88218e7			−0.713789			−0.356894	+	0.934145i	$0.616164\pi$
$150$	−3.36346e7			−0.813704
$151$	3.26508e6	+	1.00489e7i	0.0771747	+	0.237519i	0.982200	−	0.187839i	$-0.0601482\pi$
$151$	3.26508e6	+	1.00489e7i	0.0771747	+	0.237519i	−0.905025	+	0.425358i	$0.860148\pi$
$152$	1.98265e7	−	1.44048e7i	0.457925	−	0.332702i
$153$	253756.	+	184364.i	0.00572791	+	0.00416157i
$154$	−9.57982e6			−0.211366
$155$	2.34298e7	−	1.05863e7i	0.505369	−	0.228340i
$156$	−7.15041e7			−1.50798
$157$	7.72477e7	+	5.61237e7i	1.59308	+	1.15744i	0.899378	+	0.437172i	$0.144020\pi$
$157$	7.72477e7	+	5.61237e7i	1.59308	+	1.15744i	0.693698	+	0.720266i	$0.255980\pi$
$158$	2.30609e7	−	1.67547e7i	0.465133	−	0.337939i
$159$	−3.67606e7	−	1.13138e8i	−0.725259	−	2.23212i
$160$	5.07918e6			0.0980333
$161$	−8.75547e7			−1.65344
$162$	4.04134e6	+	1.24380e7i	0.0746831	+	0.229851i
$163$	−8.89128e6	+	2.73645e7i	−0.160808	+	0.494916i	−0.998703	−	0.0509153i	$-0.983786\pi$
$163$	−8.89128e6	+	2.73645e7i	−0.160808	+	0.494916i	0.837895	+	0.545832i	$0.183786\pi$
$164$	761716.	−	2.34432e6i	0.0134847	−	0.0415015i
$165$	1.21640e7	+	8.83765e6i	0.210806	+	0.153159i
$166$	−3.35514e6	−	1.03261e7i	−0.0569288	−	0.175209i
$167$	−1.52296e7	−	1.10650e7i	−0.253036	−	0.183841i	0.454035	−	0.890984i	$-0.349984\pi$
$167$	−1.52296e7	−	1.10650e7i	−0.253036	−	0.183841i	−0.707071	+	0.707142i	$0.749984\pi$
$168$	−3.08844e7	+	2.24389e7i	−0.502524	+	0.365105i
$169$	4.44749e7	−	1.36880e8i	0.708781	−	2.18140i
$170$	81673.0	−	59338.9i	0.00127499	−	0.000926336i
$171$	1.49193e8	−	1.08395e8i	2.28171	−	1.65776i
$172$	1.51491e7	−	4.66240e7i	0.227005	−	0.698651i
$173$	−5.66532e7	+	4.11610e7i	−0.831885	+	0.604400i	−0.920092	−	0.391702i	$-0.871886\pi$
$173$	−5.66532e7	+	4.11610e7i	−0.831885	+	0.604400i	0.0882069	+	0.996102i	$0.471886\pi$
$174$	8.55623e7	+	6.21646e7i	1.23129	+	0.894584i
$175$	−1.60388e7	−	4.93623e7i	−0.226224	−	0.696245i
$176$	4.13602e6	+	3.00499e6i	0.0571858	+	0.0415479i
$177$	1.21096e7	−	3.72694e7i	0.164143	−	0.505180i
$178$	−1.01801e7	+	3.13311e7i	−0.135295	+	0.416396i
$179$	−2.10089e7	−	6.46588e7i	−0.273790	−	0.842640i	−0.989537	−	0.144280i	$-0.953913\pi$
$179$	−2.10089e7	−	6.46588e7i	−0.273790	−	0.842640i	0.715746	−	0.698360i	$-0.246087\pi$
$180$	3.82203e7			0.488473
$181$	−2.31790e7			−0.290550			−0.145275	−	0.989391i	$-0.546407\pi$
$181$	−2.31790e7			−0.290550			−0.145275	+	0.989391i	$0.546407\pi$
$182$	−3.40970e7	−	1.04940e8i	−0.419243	−	1.29030i
$183$	4.66160e7	−	3.38685e7i	0.562284	−	0.408524i
$184$	3.78011e7	+	2.74641e7i	0.447345	+	0.325015i
$185$	−1.48757e7			−0.172733
$186$	9.39778e7	−	4.24619e7i	1.07085	−	0.483842i
$187$	101614.			0.00113634
$188$	−3.06706e7	−	2.22835e7i	−0.336644	−	0.244586i
$189$	−1.00480e8	+	7.30030e7i	−1.08259	+	0.786546i
$190$	−1.83415e7	−	5.64494e7i	−0.193998	−	0.597065i
$191$	6.14648e7			0.638277			0.319139	−	0.947708i	$-0.396606\pi$
$191$	6.14648e7			0.638277			0.319139	+	0.947708i	$0.396606\pi$
$192$	2.03727e7			0.207728
$193$	6.61859e6	+	2.03699e7i	0.0662697	+	0.203957i	0.978708	−	0.205257i	$-0.0658030\pi$
$193$	6.61859e6	+	2.03699e7i	0.0662697	+	0.203957i	−0.912438	+	0.409214i	$0.865803\pi$
$194$	2.22183e7	−	6.83809e7i	0.218476	−	0.672401i
$195$	−5.35152e7	+	1.64703e8i	−0.516840	+	1.59067i
$196$	−5.01808e6	−	3.64585e6i	−0.0476037	−	0.0345861i
$197$	−5.55872e6	−	1.71080e7i	−0.0518016	−	0.159429i	0.921809	−	0.387644i	$-0.126711\pi$
$197$	−5.55872e6	−	1.71080e7i	−0.0518016	−	0.159429i	−0.973611	+	0.228215i	$0.926711\pi$
$198$	3.11232e7	+	2.26123e7i	0.284941	+	0.207022i
$199$	−1.66563e8	+	1.21015e8i	−1.49828	+	1.08856i	−0.527219	+	0.849730i	$0.676765\pi$
$199$	−1.66563e8	+	1.21015e8i	−1.49828	+	1.08856i	−0.971060	+	0.238834i	$0.923235\pi$
$200$	−8.55931e6	+	2.63429e7i	−0.0756544	+	0.232840i
$201$	−2.12347e8	+	1.54279e8i	−1.84442	+	1.34005i
$202$	−7.43404e7	+	5.40114e7i	−0.634592	+	0.461058i
$203$	−5.04324e7	+	1.55215e8i	−0.423130	+	1.30226i
$204$	327593.	−	238010.i	0.00270165	−	0.00196286i
$205$	−4.82983e6	−	3.50908e6i	−0.0391556	−	0.0284482i
$206$	1.46137e7	+	4.49765e7i	0.116473	+	0.358468i
$207$	2.84450e8	+	2.06665e8i	2.22900	+	1.61946i
$208$	−1.81963e7	+	5.60025e7i	−0.140204	+	0.431505i
$209$	1.84615e7	−	5.68186e7i	0.139880	−	0.430505i
$210$	2.85712e7	+	8.79330e7i	0.212893	+	0.655216i
$211$	−2.24003e8			−1.64159			−0.820794	−	0.571224i	$-0.806469\pi$
$211$	−2.24003e8			−1.64159			−0.820794	+	0.571224i	$0.806469\pi$
$212$	−9.79650e7			−0.706148
$213$	−2.42854e7	−	7.47429e7i	−0.172194	−	0.529958i
$214$	1.59107e8	−	1.15598e8i	1.10979	−	0.806309i
$215$	−9.60561e7	−	6.97888e7i	−0.659159	−	0.478907i
$216$	6.62811e7			0.447509
$217$	1.07131e8	+	1.17674e8i	0.711715	+	0.781758i
$218$	6.93357e7			0.453273
$219$	−7.05591e7	−	5.12642e7i	−0.453940	−	0.329807i
$220$	1.00172e7	−	7.27792e6i	0.0634260	−	0.0460817i
$221$	361669.	+	1.11310e6i	0.00225392	+	0.00693685i
$222$	−5.96668e7			−0.366014
$223$	1.57377e8			0.950331			0.475166	−	0.879896i	$-0.342388\pi$
$223$	1.57377e8			0.950331			0.475166	+	0.879896i	$0.342388\pi$
$224$	9.71482e6	+	2.98991e7i	0.0577520	+	0.177742i
$225$	−6.44080e7	+	1.98227e8i	−0.376965	+	1.16018i
$226$	2.49016e7	−	7.66393e7i	0.143499	−	0.441643i
$227$	2.54052e8	+	1.84580e8i	1.44156	+	1.04736i	0.987714	+	0.156275i	$0.0499487\pi$
$227$	2.54052e8	+	1.84580e8i	1.44156	+	1.04736i	0.453847	+	0.891080i	$0.350051\pi$
$228$	−7.35683e7	−	2.26420e8i	−0.411073	−	1.26515i
$229$	1.81308e8	+	1.31728e8i	0.997681	+	0.724858i	0.961590	−	0.274491i	$-0.0885092\pi$
$229$	1.81308e8	+	1.31728e8i	0.997681	+	0.724858i	0.0360916	+	0.999348i	$0.488509\pi$
$230$	9.15521e7	−	6.65165e7i	0.496159	−	0.360481i
$231$	−2.87580e7	+	8.85082e7i	−0.153503	+	0.472434i
$232$	7.04617e7	−	5.11934e7i	0.370463	−	0.269157i
$233$	−1.56698e8	+	1.13848e8i	−0.811553	+	0.589628i	−0.914281	−	0.405082i	$-0.867243\pi$
$233$	−1.56698e8	+	1.13848e8i	−0.811553	+	0.589628i	0.102727	+	0.994710i	$0.467243\pi$
$234$	−1.36926e8	+	4.21414e8i	−0.698601	+	2.15007i
$235$	−7.42825e7	+	5.39694e7i	−0.373378	+	0.271275i
$236$	−2.61081e7	−	1.89686e7i	−0.129295	−	0.0939385i
$237$	−8.55699e7	−	2.63357e8i	−0.417543	−	1.28507i
$238$	505519.	+	367281.i	0.00243063	+	0.00176595i
$239$	1.22259e8	−	3.76275e8i	0.579280	−	1.78284i	−0.0418410	−	0.999124i	$-0.513322\pi$
$239$	1.22259e8	−	3.76275e8i	0.579280	−	1.78284i	0.621121	−	0.783715i	$-0.286678\pi$
$240$	1.52474e7	−	4.69266e7i	0.0711961	−	0.219119i
$241$	−3.13025e7	−	9.63393e7i	−0.144052	−	0.443347i	0.852836	−	0.522179i	$-0.174881\pi$
$241$	−3.13025e7	−	9.63393e7i	−0.144052	−	0.443347i	−0.996888	+	0.0788324i	$0.974881\pi$
$242$	−1.43434e8			−0.650578
$243$	−1.56072e8			−0.697756
$244$	−1.46632e7	−	4.51288e7i	−0.0646198	−	0.198879i
$245$	−1.21535e7	+	8.83003e6i	−0.0527983	+	0.0383602i
$246$	−1.93726e7	−	1.40750e7i	−0.0829689	−	0.0602804i
$247$	6.88114e8			2.90550
$248$	−9.34102e6	−	8.44098e7i	−0.0388878	−	0.351408i
$249$	−1.05474e8			−0.432962
$250$	1.32648e8	+	9.63744e7i	0.536921	+	0.390096i
$251$	−8.93168e7	+	6.48925e7i	−0.356513	+	0.259022i	−0.751596	−	0.659624i	$-0.770716\pi$
$251$	−8.93168e7	+	6.48925e7i	−0.356513	+	0.259022i	0.395083	+	0.918645i	$0.370716\pi$
$252$	7.31031e7	+	2.24988e8i	0.287762	+	0.885641i
$253$	1.13905e8			0.442202
$254$	−3.02975e8			−1.16008
$255$	−303056.	−	932711.i	−0.00114454	−	0.00352254i
$256$	5.18444e6	−	1.59561e7i	0.0193136	−	0.0594410i
$257$	2.68489e7	−	8.26324e7i	0.0986644	−	0.303658i	−0.889527	−	0.456883i	$-0.848966\pi$
$257$	2.68489e7	−	8.26324e7i	0.0986644	−	0.303658i	0.988191	+	0.153225i	$0.0489659\pi$
$258$	−3.85284e8	−	2.79925e8i	−1.39673	−	1.01478i
$259$	−2.84524e7	−	8.75673e7i	−0.101758	−	0.313179i
$260$	1.15378e8	+	8.38269e7i	0.407114	+	0.295786i
$261$	5.30217e8	−	3.85225e8i	1.84592	−	1.34114i
$262$	3.60985e7	−	1.11100e8i	0.124004	−	0.381644i
$263$	−3.66277e8	+	2.66116e8i	−1.24155	+	0.902041i	−0.997701	−	0.0677719i	$-0.978411\pi$
$263$	−3.66277e8	+	2.66116e8i	−1.24155	+	0.902041i	−0.243852	+	0.969813i	$0.578411\pi$
$264$	4.01793e7	−	2.91920e7i	0.134397	−	0.0976449i
$265$	−7.33191e7	+	2.25653e8i	−0.242023	+	0.744870i
$266$	2.97214e8	−	2.15939e8i	0.968241	−	0.703468i
$267$	2.58909e8	+	1.88108e8i	0.832449	+	0.604810i
$268$	6.67947e7	+	2.05573e8i	0.211968	+	0.652371i
$269$	−2.90006e8	−	2.10702e8i	−0.908393	−	0.659986i	0.0322146	−	0.999481i	$-0.489744\pi$
$269$	−2.90006e8	−	2.10702e8i	−0.908393	−	0.659986i	−0.940608	+	0.339494i	$0.889744\pi$
$270$	4.96062e7	−	1.52672e8i	0.153378	−	0.472048i
$271$	8.37727e7	−	2.57826e8i	0.255688	−	0.786926i	−0.738006	−	0.674795i	$-0.764232\pi$
$271$	8.37727e7	−	2.57826e8i	0.255688	−	0.786926i	0.993693	−	0.112131i	$-0.0357677\pi$
$272$	−103046.	−	317142.i	−0.000310483	−	0.000955570i
$273$	−1.07190e9			−3.18848
$274$	1.38788e8			0.407591
$275$	2.08658e7	+	6.42182e7i	0.0605020	+	0.186206i
$276$	3.67218e8	−	2.66800e8i	1.05134	−	0.763842i
$277$	−2.48809e8	−	1.80770e8i	−0.703375	−	0.511032i	0.177654	−	0.984093i	$-0.443149\pi$
$277$	−2.48809e8	−	1.80770e8i	−0.703375	−	0.511032i	−0.881030	+	0.473061i	$0.843149\pi$
$278$	−1.54982e8			−0.432637
$279$	−7.02903e7	−	6.35176e8i	−0.193767	−	1.75097i
$280$	7.61406e7			0.207283
$281$	4.33819e6	+	3.15188e6i	0.0116637	+	0.00847418i	0.593602	−	0.804759i	$-0.297705\pi$
$281$	4.33819e6	+	3.15188e6i	0.0116637	+	0.00847418i	−0.581938	+	0.813233i	$0.697705\pi$
$282$	−2.97949e8	+	2.16473e8i	−0.791171	+	0.574820i
$283$	9.81854e7	+	3.02184e8i	0.257510	+	0.792535i	0.993325	+	0.115352i	$0.0367995\pi$
$283$	9.81854e7	+	3.02184e8i	0.257510	+	0.792535i	−0.735815	+	0.677183i	$0.763201\pi$
$284$	−6.47193e7			−0.167656
$285$	−5.76597e8			−1.47542
$286$	4.43587e7	+	1.36522e8i	0.112124	+	0.345081i
$287$	1.14187e7	−	3.51431e7i	0.0285121	−	0.0877512i
$288$	3.90125e7	−	1.20068e8i	0.0962342	−	0.296178i
$289$	3.31966e8	+	2.41187e8i	0.809004	+	0.587776i
$290$	−6.51840e7	−	2.00616e8i	−0.156945	−	0.483028i
$291$	−5.65074e8	−	4.10550e8i	−1.34425	−	0.976655i
$292$	−5.81063e7	+	4.22167e7i	−0.136579	+	0.0992304i
$293$	2.02893e8	−	6.24440e8i	0.471227	−	1.45029i	−0.379752	−	0.925088i	$-0.623991\pi$
$293$	2.02893e8	−	6.24440e8i	0.471227	−	1.45029i	0.850979	−	0.525200i	$-0.176009\pi$
$294$	−4.87480e7	+	3.54175e7i	−0.111877	+	0.0812835i
$295$	−6.32322e7	+	4.59409e7i	−0.143404	+	0.104189i
$296$	−1.51840e7	+	4.67315e7i	−0.0340302	+	0.104734i
$297$	1.30720e8	−	9.49737e7i	0.289531	−	0.210356i
$298$	1.86539e8	+	1.35528e8i	0.408331	+	0.296670i
$299$	4.05416e8	+	1.24774e9i	0.877105	+	2.69945i
$300$	2.17688e8	+	1.58159e8i	0.465489	+	0.338197i
$301$	2.27095e8	−	6.98928e8i	0.479983	−	1.47724i
$302$	2.61207e7	−	8.03912e7i	0.0545708	−	0.167952i
$303$	2.75847e8	+	8.48971e8i	0.569665	+	1.75325i
$304$	−1.96056e8			−0.400241
$305$	−1.14924e8			−0.231933
$306$	−775409.	−	2.38646e6i	−0.00154705	−	0.00476134i
$307$	1.53895e8	−	1.11811e8i	0.303557	−	0.220547i	−0.425570	−	0.904925i	$-0.639926\pi$
$307$	1.53895e8	−	1.11811e8i	0.303557	−	0.220547i	0.729127	+	0.684379i	$0.239926\pi$
$308$	6.20019e7	+	4.50470e7i	0.120914	+	0.0878494i
$309$	4.59408e8			0.885816
$310$	−2.01421e8	−	4.16579e7i	−0.384006	−	0.0794204i
$311$	9.22430e8			1.73889			0.869445	−	0.494030i	$-0.164477\pi$
$311$	9.22430e8			1.73889			0.869445	+	0.494030i	$0.164477\pi$
$312$	4.62784e8	+	3.36232e8i	0.862655	+	0.626756i
$313$	7.84224e7	−	5.69772e7i	0.144556	−	0.105026i	−0.513157	−	0.858295i	$-0.671524\pi$
$313$	7.84224e7	−	5.69772e7i	0.144556	−	0.105026i	0.657713	+	0.753269i	$0.271524\pi$
$314$	−2.36048e8	−	7.26481e8i	−0.430275	−	1.32425i
$315$	5.72950e8			1.03283
$316$	−2.28039e8			−0.406541
$317$	8.83547e7	+	2.71928e8i	0.155784	+	0.479453i	0.998239	−	0.0593125i	$-0.0188908\pi$
$317$	8.83547e7	+	2.71928e8i	0.155784	+	0.479453i	−0.842456	+	0.538766i	$0.818891\pi$
$318$	−2.94085e8	+	9.05101e8i	−0.512835	+	1.57835i
$319$	6.56104e7	−	2.01928e8i	0.113163	−	0.348281i
$320$	−3.28731e7	−	2.38837e7i	−0.0560811	−	0.0407453i
$321$	−5.90382e8	−	1.81701e9i	−0.996244	−	3.06612i
$322$	5.66666e8	+	4.11707e8i	0.945870	+	0.687215i
$323$	−3.15257e6	+	2.29047e6i	−0.00520541	+	0.00378195i
$324$	3.23307e7	−	9.95036e7i	0.0528089	−	0.162529i
$325$	−6.29195e8	+	4.57137e8i	−1.01670	+	0.738677i
$326$	1.86221e8	−	1.35298e8i	0.297693	−	0.216286i
$327$	2.08142e8	−	6.40594e8i	0.329186	−	1.01313i
$328$	−1.59536e7	+	1.15910e7i	−0.0249632	+	0.0181368i
$329$	−4.59775e8	−	3.34046e8i	−0.711803	−	0.517155i
$330$	−3.71698e7	−	1.14397e8i	−0.0569366	−	0.175233i
$331$	7.02879e8	+	5.10671e8i	1.06533	+	0.774004i	0.975066	−	0.221914i	$-0.0712304\pi$
$331$	7.02879e8	+	5.10671e8i	1.06533	+	0.774004i	0.0902594	+	0.995918i	$0.471230\pi$
$332$	−2.68411e7	+	8.26084e7i	−0.0402547	+	0.123891i
$333$	−1.14258e8	+	3.51650e8i	−0.169563	+	0.521862i
$334$	4.65376e7	+	1.43228e8i	0.0683426	+	0.210337i
$335$	5.23508e8			0.760794
$336$	3.05402e8			0.439222
$337$	−1.61711e8	−	4.97696e8i	−0.230163	−	0.708369i	−0.997726	−	0.0673958i	$-0.978531\pi$
$337$	−1.61711e8	−	4.97696e8i	−0.230163	−	0.708369i	0.767563	−	0.640973i	$-0.221469\pi$
$338$	−9.31495e8	+	6.76771e8i	−1.31212	+	0.953308i
$339$	−6.33319e8	−	4.60133e8i	−0.882924	−	0.641482i
$340$	−807627.			−0.00111438
$341$	−1.39373e8	−	1.53089e8i	−0.190343	−	0.209076i
$342$	−1.47530e9			−1.99429
$343$	5.63990e8	+	4.09762e8i	0.754643	+	0.548280i
$344$	−3.17286e8	+	2.30522e8i	−0.420239	+	0.305322i
$345$	−3.39713e8	−	1.04553e9i	−0.445395	−	1.37079i
$346$	5.60218e8			0.727094
$347$	−9.93818e8			−1.27689			−0.638445	−	0.769667i	$-0.720422\pi$
$347$	−9.93818e8			−1.27689			−0.638445	+	0.769667i	$0.720422\pi$
$348$	−2.61455e8	−	8.04676e8i	−0.332560	−	1.02351i
$349$	−4.08694e8	+	1.25783e9i	−0.514647	+	1.58392i	0.269277	+	0.963063i	$0.413215\pi$
$349$	−4.08694e8	+	1.25783e9i	−0.514647	+	1.58392i	−0.783924	+	0.620857i	$0.786785\pi$
$350$	−1.28310e8	+	3.94898e8i	−0.159964	+	0.492320i
$351$	1.50563e9	+	1.09390e9i	1.85842	+	1.35022i
$352$	−1.26386e7	−	3.88975e7i	−0.0154454	−	0.0475359i
$353$	4.97220e8	+	3.61251e8i	0.601641	+	0.437117i	0.846461	−	0.532451i	$-0.178729\pi$
$353$	4.97220e8	+	3.61251e8i	0.601641	+	0.437117i	−0.244820	+	0.969568i	$0.578729\pi$
$354$	−2.53626e8	+	1.84270e8i	−0.303867	+	0.220772i
$355$	−4.84373e7	+	1.49075e8i	−0.0574620	+	0.176850i
$356$	2.13215e8	−	1.54910e8i	0.250462	−	0.181972i
$357$	4.91085e6	−	3.56794e6i	0.00571239	−	0.00415030i
$358$	−1.68071e8	+	5.17271e8i	−0.193599	+	0.595837i
$359$	7.30908e8	−	5.31036e8i	0.833743	−	0.605750i	−0.0868726	−	0.996219i	$-0.527687\pi$
$359$	7.30908e8	−	5.31036e8i	0.833743	−	0.605750i	0.920616	+	0.390470i	$0.127687\pi$
$360$	−2.47367e8	−	1.79723e8i	−0.279437	−	0.203023i
$361$	4.31758e8	+	1.32881e9i	0.483020	+	1.48658i
$362$	1.50018e8	+	1.08994e8i	0.166212	+	0.120760i
$363$	−4.30581e8	+	1.32519e9i	−0.472479	+	1.45414i
$364$	−2.72776e8	+	8.39518e8i	−0.296450	+	0.912379i
$365$	5.37541e7	+	1.65438e8i	0.0578611	+	0.178078i
$366$	−4.60964e8			−0.491455
$367$	−2.00797e8			−0.212044			−0.106022	−	0.994364i	$-0.533811\pi$
$367$	−2.00797e8			−0.212044			−0.106022	+	0.994364i	$0.533811\pi$
$368$	−1.15510e8	−	3.55503e8i	−0.120824	−	0.371857i
$369$	−1.20049e8	+	8.72209e7i	−0.124385	+	0.0903708i
$370$	9.62775e7	+	6.99497e7i	0.0988140	+	0.0717926i
$371$	−1.46857e9			−1.49309
$372$	−8.07905e8	−	1.67091e8i	−0.813692	−	0.168288i
$373$	−5.65711e8			−0.564435			−0.282217	−	0.959350i	$-0.591070\pi$
$373$	−5.65711e8			−0.564435			−0.282217	+	0.959350i	$0.591070\pi$
$374$	−657658.	−	477816.i	−0.000650054	−	0.000472292i
$375$	1.28861e9	−	9.36227e8i	1.26186	−	0.916794i
$376$	9.37212e7	+	2.88444e8i	0.0909243	+	0.279836i
$377$	2.44549e9			2.35056
$378$	9.93601e8			0.946217
$379$	2.09679e7	+	6.45325e7i	0.0197842	+	0.0608894i	0.960461	−	0.278414i	$-0.0898087\pi$
$379$	2.09679e7	+	6.45325e7i	0.0197842	+	0.0608894i	−0.940677	+	0.339303i	$0.889809\pi$
$380$	−1.46732e8	+	4.51595e8i	−0.137177	+	0.422189i
$381$	−9.09513e8	+	2.79919e9i	−0.842503	+	2.59296i
$382$	−3.97808e8	−	2.89025e8i	−0.365134	−	0.265285i
$383$	−5.73120e8	−	1.76388e9i	−0.521255	−	1.60426i	−0.771605	−	0.636102i	$-0.780546\pi$
$383$	−5.73120e8	−	1.76388e9i	−0.521255	−	1.60426i	0.250351	−	0.968155i	$-0.419454\pi$
$384$	−1.31855e8	−	9.57984e7i	−0.118833	−	0.0863374i
$385$	1.50165e8	−	1.09101e8i	0.134109	−	0.0974355i
$386$	5.29487e7	−	1.62959e8i	0.0468597	−	0.144219i
$387$	−2.38755e9	+	1.73466e9i	−2.09394	+	1.52133i
$388$	−4.65346e8	+	3.38094e8i	−0.404450	+	0.293850i
$389$	3.27007e8	−	1.00643e9i	0.281666	−	0.866878i	−0.705713	−	0.708498i	$-0.749373\pi$
$389$	3.27007e8	−	1.00643e9i	0.281666	−	0.866878i	0.987378	−	0.158380i	$-0.0506270\pi$
$390$	1.12084e9	−	8.14335e8i	0.956789	−	0.695148i
$391$	−6.01066e6	−	4.36700e6i	−0.00508515	−	0.00369457i
$392$	1.53339e7	+	4.71928e7i	0.0128573	+	0.0395708i
$393$	−9.18086e8	−	6.67029e8i	−0.762974	−	0.554333i
$394$	−4.44698e7	+	1.36864e8i	−0.0366293	+	0.112733i
$395$	−1.70669e8	+	5.25266e8i	−0.139337	+	0.428834i
$396$	−9.51039e7	−	2.92700e8i	−0.0769600	−	0.236859i
$397$	−6.27971e8			−0.503701			−0.251850	−	0.967766i	$-0.581039\pi$
$397$	−6.27971e8			−0.503701			−0.251850	+	0.967766i	$0.581039\pi$
$398$	1.64707e9			1.30954
$399$	−1.10284e9	−	3.39420e9i	−0.869177	−	2.67505i
$400$	1.79269e8	−	1.30246e8i	0.140054	−	0.101755i
$401$	8.75868e8	+	6.36355e8i	0.678318	+	0.492827i	0.872799	−	0.488079i	$-0.162302\pi$
$401$	8.75868e8	+	6.36355e8i	0.678318	+	0.492827i	−0.194481	+	0.980906i	$0.562302\pi$
$402$	2.09981e9			1.61209
$403$	1.18091e9	−	2.07160e9i	0.898773	−	1.57666i
$404$	7.35118e8			0.554654
$405$	−2.05000e8	−	1.48941e8i	−0.153342	−	0.111410i
$406$	1.05627e9	−	7.67426e8i	0.783311	−	0.569109i
$407$	3.70153e7	+	1.13921e8i	0.0272145	+	0.0837576i
$408$	−3.23942e6			−0.00236133
$409$	1.01618e9			0.734411			0.367205	−	0.930140i	$-0.380315\pi$
$409$	1.01618e9			0.734411			0.367205	+	0.930140i	$0.380315\pi$
$410$	1.47587e7	+	4.54225e7i	0.0105756	+	0.0325482i
$411$	4.16632e8	−	1.28226e9i	0.296010	−	0.911026i
$412$	1.16910e8	−	3.59812e8i	0.0823590	−	0.253475i
$413$	−3.91379e8	−	2.84353e8i	−0.273383	−	0.198625i
$414$	−8.69201e8	−	2.67513e9i	−0.602031	−	1.85286i
$415$	1.70192e8	+	1.23652e8i	0.116888	+	0.0849243i
$416$	3.81109e8	−	2.76892e8i	0.259551	−	0.188575i
$417$	−4.65245e8	+	1.43188e9i	−0.314200	+	0.967007i
$418$	−3.86662e8	+	2.80927e8i	−0.258949	+	0.188138i
$419$	−2.37064e8	+	1.72237e8i	−0.157441	+	0.114387i	−0.663716	−	0.747984i	$-0.731022\pi$
$419$	−2.37064e8	+	1.72237e8i	−0.157441	+	0.114387i	0.506276	+	0.862372i	$0.331022\pi$
$420$	2.28569e8	−	7.03464e8i	0.150538	−	0.463308i
$421$	3.99316e7	−	2.90120e7i	0.0260813	−	0.0189492i	−0.574668	−	0.818386i	$-0.694869\pi$
$421$	3.99316e7	−	2.90120e7i	0.0260813	−	0.0189492i	0.600750	+	0.799437i	$0.294869\pi$
$422$	1.44978e9	+	1.05332e9i	0.939090	+	0.682289i
$423$	7.05243e8	+	2.17051e9i	0.453051	+	1.39435i
$424$	6.34043e8	+	4.60659e8i	0.403960	+	0.293494i
$425$	1.36099e6	−	4.18871e6i	0.000859993	−	0.00264679i
$426$	−1.94283e8	+	5.97943e8i	−0.121759	+	0.374737i
$427$	−2.19813e8	−	6.76514e8i	−0.136633	−	0.420513i
$428$	−1.57334e9			−0.969992
$429$	1.39449e9			0.852737
$430$	2.93521e8	+	9.03366e8i	0.178033	+	0.547929i
$431$	−2.19385e9	+	1.59392e9i	−1.31989	+	0.958953i	−0.319952	+	0.947434i	$0.603667\pi$
$431$	−2.19385e9	+	1.59392e9i	−1.31989	+	0.958953i	−0.999934	+	0.0115188i	$0.996333\pi$
$432$	−4.28980e8	−	3.11672e8i	−0.256002	−	0.185997i
$433$	2.21967e9			1.31396			0.656979	−	0.753909i	$-0.271834\pi$
$433$	2.21967e9			1.31396			0.656979	+	0.753909i	$0.271834\pi$
$434$	−1.40029e8	−	1.26536e9i	−0.0822248	−	0.743021i
$435$	−2.04917e9			−1.19362
$436$	−4.48750e8	−	3.26036e8i	−0.259300	−	0.188392i
$437$	−3.53390e9	+	2.56753e9i	−2.02567	+	1.47174i
$438$	2.15609e8	+	6.63578e8i	0.122605	+	0.377340i
$439$	−1.04183e9			−0.587721			−0.293861	−	0.955848i	$-0.594940\pi$
$439$	−1.04183e9			−0.587721			−0.293861	+	0.955848i	$0.594940\pi$
$440$	−9.90555e7			−0.0554363
$441$	1.15386e8	+	3.55121e8i	0.0640646	+	0.197170i
$442$	2.89335e6	−	8.90482e6i	0.00159376	−	0.00490509i
$443$	−6.95453e8	+	2.14038e9i	−0.380062	+	1.16971i	0.559937	+	0.828535i	$0.310825\pi$
$443$	−6.95453e8	+	2.14038e9i	−0.380062	+	1.16971i	−0.939999	+	0.341176i	$0.889175\pi$
$444$	3.86172e8	+	2.80570e8i	0.209382	+	0.152125i
$445$	−1.97245e8	−	6.07058e8i	−0.106107	−	0.326565i
$446$	−1.01857e9	−	7.40032e8i	−0.543648	−	0.394983i
$447$	1.81213e9	−	1.31659e9i	0.959649	−	0.697226i
$448$	7.77186e7	−	2.39193e8i	0.0408368	−	0.125683i
$449$	2.97945e9	−	2.16470e9i	1.55337	−	1.12859i	0.612171	−	0.790725i	$-0.290296\pi$
$449$	2.97945e9	−	2.16470e9i	1.55337	−	1.12859i	0.941196	−	0.337862i	$-0.109704\pi$
$450$	1.34898e9	−	9.80091e8i	0.697849	−	0.507017i
$451$	−1.48552e7	+	4.57196e7i	−0.00762536	+	0.0234684i
$452$	−5.21546e8	+	3.78925e8i	−0.265649	+	0.193005i
$453$	−6.64323e8	−	4.82659e8i	−0.335765	−	0.243948i
$454$	−7.76315e8	−	2.38925e9i	−0.389352	−	1.19830i
$455$	1.72960e9	+	1.25663e9i	0.860806	+	0.625412i
$456$	−5.88547e8	+	1.81136e9i	−0.290673	+	0.894598i
$457$	1.21433e9	−	3.73733e9i	0.595156	−	1.83170i	0.0412070	−	0.999151i	$-0.486880\pi$
$457$	1.21433e9	−	3.73733e9i	0.595156	−	1.83170i	0.553949	−	0.832551i	$-0.313120\pi$
$458$	−5.54027e8	−	1.70512e9i	−0.269465	−	0.829326i
$459$	−1.05392e7			−0.00508701
$460$	−9.05317e8			−0.433659
$461$	−7.62967e8	−	2.34817e9i	−0.362704	−	1.11629i	−0.951406	−	0.307938i	$-0.900361\pi$
$461$	−7.62967e8	−	2.34817e9i	−0.362704	−	1.11629i	0.588702	−	0.808350i	$-0.299639\pi$
$462$	6.02316e8	−	4.37608e8i	0.284170	−	0.206461i
$463$	−1.65692e9	−	1.20382e9i	−0.775832	−	0.563675i	0.127893	−	0.991788i	$-0.459178\pi$
$463$	−1.65692e9	−	1.20382e9i	−0.775832	−	0.563675i	−0.903725	+	0.428113i	$0.859178\pi$
$464$	−6.96763e8			−0.323797
$465$	−9.89532e8	+	1.73588e9i	−0.456399	+	0.800633i
$466$	1.54951e9			0.709324
$467$	1.94605e8	+	1.41389e8i	0.0884187	+	0.0642399i	0.631116	−	0.775688i	$-0.282597\pi$
$467$	1.94605e8	+	1.41389e8i	0.0884187	+	0.0642399i	−0.542698	+	0.839928i	$0.682597\pi$
$468$	2.86781e9	−	2.08358e9i	1.29327	−	0.939616i
$469$	1.00130e9	+	3.08169e9i	0.448188	+	1.37938i
$470$	7.34546e8			0.326345
$471$	−7.42057e9			−3.27238
$472$	7.97792e7	+	2.45535e8i	0.0349215	+	0.107477i
$473$	−2.95441e8	+	9.09275e8i	−0.128368	+	0.395076i
$474$	−6.84559e8	+	2.10686e9i	−0.295248	+	0.908679i
$475$	−2.09490e9	−	1.52203e9i	−0.896883	−	0.651624i
$476$	−1.54473e6	−	4.75419e6i	−0.000656490	−	0.00202047i
$477$	4.77111e9	+	3.46642e9i	2.01282	+	1.46240i
$478$	−2.56063e9	+	1.86040e9i	−1.07238	+	0.779129i
$479$	6.04262e8	−	1.85973e9i	0.251218	−	0.773170i	−0.743333	−	0.668921i	$-0.766756\pi$
$479$	6.04262e8	−	1.85973e9i	0.251218	−	0.773170i	0.994551	−	0.104248i	$-0.0332437\pi$
$480$	−3.19345e8	+	2.32018e8i	−0.131800	+	0.0957585i
$481$	−1.11618e9	+	8.10949e8i	−0.457325	+	0.332266i
$482$	−2.50420e8	+	7.70714e8i	−0.101860	+	0.313494i
$483$	5.50486e9	−	3.99952e9i	2.22296	−	1.61507i
$484$	9.28327e8	+	6.74469e8i	0.372171	+	0.270398i
$485$	4.30491e8	+	1.32492e9i	0.171344	+	0.527342i
$486$	1.01012e9	+	7.33896e8i	0.399159	+	0.290006i
$487$	1.21543e9	−	3.74070e9i	0.476845	−	1.46758i	−0.366607	−	0.930376i	$-0.619481\pi$
$487$	1.21543e9	−	3.74070e9i	0.476845	−	1.46758i	0.843453	−	0.537204i	$-0.180519\pi$
$488$	−1.17306e8	+	3.61031e8i	−0.0456931	+	0.140629i
$489$	−6.90993e8	−	2.12666e9i	−0.267235	−	0.822464i
$490$	1.20180e8			0.0461474
$491$	−3.34426e9			−1.27501			−0.637506	−	0.770445i	$-0.720034\pi$
$491$	−3.34426e9			−1.27501			−0.637506	+	0.770445i	$0.720034\pi$
$492$	5.91974e7	+	1.82191e8i	0.0224091	+	0.0689682i
$493$	−1.12039e7	+	8.14013e6i	−0.00421120	+	0.00305962i
$494$	−4.45357e9	−	3.23571e9i	−1.66213	−	1.20760i
$495$	−7.45383e8			−0.276224
$496$	−3.36462e8	+	5.90236e8i	−0.123809	+	0.217190i
$497$	−9.70189e8			−0.354494
$498$	6.82645e8	+	4.95971e8i	0.247681	+	0.179951i
$499$	1.29483e9	−	9.40750e8i	0.466510	−	0.338939i	−0.329569	−	0.944131i	$-0.606904\pi$
$499$	1.29483e9	−	9.40750e8i	0.466510	−	0.338939i	0.796080	+	0.605192i	$0.206904\pi$
$500$	−4.05336e8	−	1.24750e9i	−0.145017	−	0.446318i
$501$	1.46299e9			0.519768
$502$	8.83213e8			0.311604
$503$	6.63526e6	+	2.04212e7i	0.00232472	+	0.00715475i	0.952212	−	0.305437i	$-0.0988027\pi$
$503$	6.63526e6	+	2.04212e7i	0.00232472	+	0.00715475i	−0.949887	+	0.312592i	$0.898803\pi$
$504$	5.84825e8	−	1.79991e9i	0.203479	−	0.626243i
$505$	5.50178e8	−	1.69327e9i	0.190101	−	0.585069i
$506$	−7.37207e8	−	5.35613e8i	−0.252966	−	0.183791i
$507$	3.45641e9	+	1.06377e10i	1.17787	+	3.62511i
$508$	1.96090e9	+	1.42467e9i	0.663638	+	0.482161i
$509$	2.58026e9	−	1.87467e9i	0.867264	−	0.630104i	−0.0625871	−	0.998040i	$-0.519935\pi$
$509$	2.58026e9	−	1.87467e9i	0.867264	−	0.630104i	0.929851	+	0.367935i	$0.119935\pi$
$510$	−2.42445e6	+	7.46168e6i	−0.000809314	+	0.00249081i
$511$	−8.71056e8	+	6.32859e8i	−0.288784	+	0.209814i
$512$	−1.08584e8	+	7.88912e7i	−0.0357538	+	0.0259767i
$513$	−1.91479e9	+	5.89312e9i	−0.626196	+	1.92723i
$514$	−5.62331e8	+	4.08557e8i	−0.182650	+	0.132703i
$515$	−7.41294e8	−	5.38581e8i	−0.239147	−	0.173750i
$516$	1.17732e9	+	3.62343e9i	0.377243	+	1.16104i
$517$	5.98147e8	+	4.34579e8i	0.190367	+	0.138310i
$518$	−2.27619e8	+	7.00539e8i	−0.0719538	+	0.221451i
$519$	1.68174e9	−	5.17586e9i	0.528048	−	1.62516i
$520$	−3.52563e8	−	1.08508e9i	−0.109958	−	0.338415i
$521$	−3.76608e8			−0.116670			−0.0583348	−	0.998297i	$-0.518579\pi$
$521$	−3.76608e8			−0.116670			−0.0583348	+	0.998297i	$0.518579\pi$
$522$	−5.24308e9			−1.61339
$523$	1.16184e8	+	3.57578e8i	0.0355133	+	0.109299i	0.967242	−	0.253857i	$-0.0816993\pi$
$523$	1.16184e8	+	3.57578e8i	0.0355133	+	0.109299i	−0.931728	+	0.363156i	$0.881699\pi$
$524$	−7.56056e8	+	5.49307e8i	−0.229559	+	0.166784i
$525$	3.26329e9	+	2.37092e9i	0.984235	+	0.715088i
$526$	3.62195e9			1.08516
$527$	1.48529e6	+	1.34218e7i	0.000442053	+	0.00399460i
$528$	−3.97315e8			−0.117467
$529$	−3.98314e9	−	2.89392e9i	−1.16985	−	0.849946i
$530$	1.53562e9	−	1.11569e9i	0.448040	−	0.325520i
$531$	6.00331e8	+	1.84763e9i	0.174004	+	0.535530i
$532$	−2.93901e9			−0.846274
$533$	−5.53697e8			−0.158390
$534$	−7.91155e8	−	2.43493e9i	−0.224837	−	0.691976i
$535$	−1.17752e9	+	3.62403e9i	−0.332452	+	1.02318i
$536$	5.34358e8	−	1.64458e9i	0.149884	−	0.461296i
$537$	4.27453e9	+	3.10563e9i	1.19118	+	0.865446i
$538$	8.86179e8	+	2.72738e9i	0.245349	+	0.755106i
$539$	9.78639e7	+	7.11023e7i	0.0269192	+	0.0195579i
$540$	−1.03896e9	+	7.54852e8i	−0.283937	+	0.206293i
$541$	7.73050e8	−	2.37920e9i	0.209902	−	0.646013i	−0.789574	−	0.613655i	$-0.789699\pi$
$541$	7.73050e8	−	2.37920e9i	0.209902	−	0.646013i	0.999476	−	0.0323574i	$-0.0103015\pi$
$542$	−1.75456e9	+	1.27476e9i	−0.473337	+	0.343899i
$543$	1.45735e9	−	1.05882e9i	0.390628	−	0.283808i
$544$	−824365.	+	2.53714e6i	−0.000219545	+	0.000675690i
$545$	−1.08685e9	+	7.89641e8i	−0.287595	+	0.208950i
$546$	6.93747e9	+	5.04036e9i	1.82401	+	1.32522i
$547$	−1.16414e9	−	3.58287e9i	−0.304124	−	0.935998i	−0.980003	−	0.198985i	$-0.936236\pi$
$547$	−1.16414e9	−	3.58287e9i	−0.304124	−	0.935998i	0.675878	−	0.737013i	$-0.263764\pi$
$548$	−8.98253e8	−	6.52619e8i	−0.233167	−	0.169406i
$549$	−8.82716e8	+	2.71672e9i	−0.227676	+	0.700716i
$550$	1.66926e8	−	5.13745e8i	0.0427814	−	0.131668i
$551$	2.51609e9	+	7.74374e9i	0.640761	+	1.97206i
$552$	−3.63125e9			−0.918903
$553$	−3.41847e9			−0.859594
$554$	7.60293e8	+	2.33994e9i	0.189975	+	0.584683i
$555$	9.35286e8	−	6.79525e8i	0.232230	−	0.168725i
$556$	1.00306e9	+	7.28767e8i	0.247495	+	0.179815i
$557$	3.09033e9			0.757725			0.378862	−	0.925453i	$-0.376315\pi$
$557$	3.09033e9			0.757725			0.378862	+	0.925453i	$0.376315\pi$
$558$	−2.53185e9	+	4.44147e9i	−0.616904	+	1.08220i
$559$	−1.10120e10			−2.66639
$560$	−4.92792e8	−	3.58034e8i	−0.118578	−	0.0861523i
$561$	−6.38880e6	+	4.64174e6i	−0.00152774	+	0.00110997i
$562$	−1.32563e7	−	4.07988e7i	−0.00315026	−	0.00969550i
$563$	−2.75696e9			−0.651105			−0.325552	−	0.945524i	$-0.605550\pi$
$563$	−2.75696e9			−0.651105			−0.325552	+	0.945524i	$0.605550\pi$
$564$	2.94629e9			0.691509
$565$	4.82482e8	+	1.48493e9i	0.112541	+	0.346366i
$566$	7.85483e8	−	2.41747e9i	0.182087	−	0.560407i
$567$	4.84660e8	−	1.49163e9i	0.111660	−	0.343653i
$568$	4.18872e8	+	3.04329e8i	0.0959097	+	0.0696825i
$569$	4.62647e8	+	1.42388e9i	0.105283	+	0.324027i	0.989797	−	0.142487i	$-0.0455099\pi$
$569$	4.62647e8	+	1.42388e9i	0.105283	+	0.324027i	−0.884514	+	0.466514i	$0.845510\pi$
$570$	3.73181e9	+	2.71132e9i	0.844030	+	0.613224i
$571$	6.80424e8	−	4.94357e8i	0.152951	−	0.111126i	−0.508677	−	0.860957i	$-0.669865\pi$
$571$	6.80424e8	−	4.94357e8i	0.152951	−	0.111126i	0.661629	+	0.749831i	$0.269865\pi$
$572$	3.54870e8	−	1.09218e9i	0.0792835	−	0.244009i
$573$	−3.86450e9	+	2.80772e9i	−0.858128	+	0.623467i
$574$	−2.39156e8	+	1.73757e8i	−0.0527824	+	0.0383487i
$575$	1.52562e9	−	4.69537e9i	0.334664	−	1.02999i
$576$	−8.17087e8	+	5.93649e8i	−0.178152	+	0.129435i
$577$	−2.81368e9	−	2.04425e9i	−0.609760	−	0.443016i	0.239570	−	0.970879i	$-0.422994\pi$
$577$	−2.81368e9	−	2.04425e9i	−0.609760	−	0.443016i	−0.849330	+	0.527863i	$0.822994\pi$
$578$	−1.01440e9	−	3.12199e9i	−0.218504	−	0.672488i
$579$	−1.34664e9	−	9.78388e8i	−0.288320	−	0.209477i
$580$	−5.21472e8	+	1.60493e9i	−0.110977	+	0.341552i
$581$	−4.02367e8	+	1.23836e9i	−0.0851150	+	0.261957i
$582$	1.72671e9	+	5.31428e9i	0.363069	+	1.11741i
$583$	1.91054e9			0.399316
$584$	5.74587e8			0.119374
$585$	−2.65301e9	−	8.16511e9i	−0.547889	−	1.68623i
$586$	−4.24945e9	+	3.08740e9i	−0.872350	+	0.633799i
$587$	1.79976e9	+	1.30760e9i	0.367266	+	0.266834i	0.756076	−	0.654484i	$-0.227114\pi$
$587$	1.79976e9	+	1.30760e9i	0.367266	+	0.266834i	−0.388811	+	0.921318i	$0.627114\pi$
$588$	4.82047e8			0.0977842
$589$	7.77481e9	+	1.60799e9i	1.56778	+	0.324250i
$590$	6.25275e8			0.125340
$591$	1.13099e9	+	8.21714e8i	0.225374	+	0.163744i
$592$	3.18017e8	−	2.31053e8i	0.0629977	−	0.0457705i
$593$	2.35825e9	+	7.25795e9i	0.464407	+	1.42930i	0.859727	+	0.510753i	$0.170633\pi$
$593$	2.35825e9	+	7.25795e9i	0.464407	+	1.42930i	−0.395321	+	0.918543i	$0.629367\pi$
$594$	−1.29263e9			−0.253059
$595$	−1.21069e7			−0.00235626
$596$	−5.70012e8	−	1.75432e9i	−0.110286	−	0.339427i
$597$	4.94439e9	−	1.52173e10i	0.951048	−	2.92703i
$598$	3.24333e9	−	9.98193e9i	0.620207	−	1.90880i
$599$	1.62796e9	+	1.18279e9i	0.309493	+	0.224860i	0.731679	−	0.681649i	$-0.238737\pi$
$599$	1.62796e9	+	1.18279e9i	0.309493	+	0.224860i	−0.422186	+	0.906509i	$0.638737\pi$
$600$	−6.65194e8	−	2.04726e9i	−0.125724	−	0.386939i
$601$	−3.66486e9	−	2.66268e9i	−0.688647	−	0.500331i	0.187568	−	0.982252i	$-0.439939\pi$
$601$	−3.66486e9	−	2.66268e9i	−0.688647	−	0.500331i	−0.876215	+	0.481920i	$0.839939\pi$
$602$	−4.75635e9	+	3.45569e9i	−0.888558	+	0.645575i
$603$	4.02099e9	−	1.23753e10i	0.746832	−	2.29851i
$604$	−5.47078e8	+	3.97476e8i	−0.101023	+	0.0733975i
$605$	2.24835e9	−	1.63353e9i	0.412782	−	0.299904i
$606$	2.20678e9	−	6.79177e9i	0.402814	−	1.23973i
$607$	−5.50659e9	+	4.00077e9i	−0.999361	+	0.726078i	−0.961951	−	0.273222i	$-0.911911\pi$
$607$	−5.50659e9	+	4.00077e9i	−0.999361	+	0.726078i	−0.0374095	+	0.999300i	$0.511911\pi$
$608$	1.26890e9	+	9.21908e8i	0.228962	+	0.166351i
$609$	−3.91940e9	−	1.20627e10i	−0.703168	−	2.16413i
$610$	7.43805e8	+	5.40406e8i	0.132680	+	0.0963975i
$611$	−2.63153e9	+	8.09903e9i	−0.466729	+	1.43644i
$612$	−6.20327e6	+	1.90917e7i	−0.00109393	+	0.00336678i
$613$	−1.86246e9	−	5.73207e9i	−0.326570	−	1.00508i	−0.970727	−	0.240185i	$-0.922792\pi$
$613$	−1.86246e9	−	5.73207e9i	−0.326570	−	1.00508i	0.644157	−	0.764893i	$-0.277208\pi$
$614$	−1.52180e9			−0.265318
$615$	4.63964e8			0.0804306
$616$	−1.89461e8	−	5.83101e8i	−0.0326578	−	0.100510i
$617$	6.55503e9	−	4.76251e9i	1.12351	−	0.816277i	0.138772	−	0.990324i	$-0.455685\pi$
$617$	6.55503e9	−	4.76251e9i	1.12351	−	0.816277i	0.984737	+	0.174047i	$0.0556846\pi$
$618$	−2.97335e9	−	2.16027e9i	−0.506741	−	0.368169i
$619$	8.88564e7			0.0150581			0.00752907	−	0.999972i	$-0.497603\pi$
$619$	8.88564e7			0.0150581			0.00752907	+	0.999972i	$0.497603\pi$
$620$	1.10774e9	+	1.21675e9i	0.186666	+	0.205037i
$621$	−1.18140e10			−1.97959
$622$	−5.97009e9	−	4.33752e9i	−0.994751	−	0.722729i
$623$	3.19624e9	−	2.32221e9i	0.529580	−	0.384763i
$624$	−1.41414e9	−	4.35228e9i	−0.232995	−	0.717086i
$625$	1.04961e9			0.171968
$626$	−7.75484e8			−0.126346
$627$	1.43475e9	+	4.41570e9i	0.232455	+	0.715424i
$628$	−1.88838e9	+	5.81184e9i	−0.304250	+	0.936387i
$629$	2.41437e6	−	7.43065e6i	0.000386835	−	0.00119056i
$630$	−3.70821e9	−	2.69417e9i	−0.590844	−	0.429273i
$631$	1.14577e9	+	3.52632e9i	0.181550	+	0.558752i	0.999872	−	0.0160075i	$-0.00509556\pi$
$631$	1.14577e9	+	3.52632e9i	0.181550	+	0.558752i	−0.818322	+	0.574760i	$0.805096\pi$
$632$	1.47590e9	+	1.07230e9i	0.232566	+	0.168969i
$633$	1.40838e10	−	1.02325e10i	2.20702	−	1.60350i
$634$	7.06838e8	−	2.17542e9i	0.110156	−	0.339025i
$635$	4.74918e9	−	3.45048e9i	0.736055	−	0.534775i
$636$	6.15940e9	−	4.47506e9i	0.949376	−	0.689762i
$637$	−4.30550e8	+	1.32510e9i	−0.0659987	+	0.203123i
$638$	−1.37416e9	+	9.98387e8i	−0.209491	+	0.152204i
$639$	3.15197e9	+	2.29004e9i	0.477892	+	0.347209i
$640$	1.00451e8	+	3.09158e8i	0.0151470	+	0.0466176i
$641$	3.73596e9	+	2.71433e9i	0.560272	+	0.407061i	0.831559	−	0.555437i	$-0.187449\pi$
$641$	3.73596e9	+	2.71433e9i	0.560272	+	0.407061i	−0.271286	+	0.962499i	$0.587449\pi$
$642$	−4.72306e9	+	1.45361e10i	−0.704451	+	2.16808i
$643$	1.55420e9	−	4.78333e9i	0.230552	−	0.709565i	−0.767129	−	0.641493i	$-0.778315\pi$
$643$	1.55420e9	−	4.78333e9i	0.230552	−	0.709565i	0.997680	−	0.0680720i	$-0.0216847\pi$
$644$	−1.73158e9	−	5.32925e9i	−0.255471	−	0.786258i
$645$	9.22735e9			1.35400
$646$	3.11743e7			0.00454970
$647$	2.68653e9	+	8.26830e9i	0.389966	+	1.20019i	0.932813	+	0.360361i	$0.117347\pi$
$647$	2.68653e9	+	8.26830e9i	0.389966	+	1.20019i	−0.542846	+	0.839832i	$0.682653\pi$
$648$	−6.77143e8	+	4.91973e8i	−0.0977614	+	0.0710278i
$649$	5.09167e8	+	3.69931e8i	0.0731145	+	0.0531208i
$650$	6.22183e9			0.888630
$651$	−1.21111e10	−	2.50482e9i	−1.72048	−	0.355830i
$652$	−1.84146e9			−0.260193
$653$	5.37167e9	+	3.90275e9i	0.754941	+	0.548497i	0.897355	−	0.441310i	$-0.145486\pi$
$653$	5.37167e9	+	3.90275e9i	0.754941	+	0.548497i	−0.142413	+	0.989807i	$0.545486\pi$
$654$	−4.35938e9	+	3.16727e9i	−0.609400	+	0.442755i
$655$	6.99427e8	+	2.15262e9i	0.0972519	+	0.299310i
$656$	1.57758e8			0.0218186
$657$	4.32371e9			0.594810
$658$	1.40495e9	+	4.32398e9i	0.192251	+	0.591689i
$659$	3.51081e9	−	1.08052e10i	0.477869	−	1.47073i	−0.364180	−	0.931329i	$-0.618651\pi$
$659$	3.51081e9	−	1.08052e10i	0.477869	−	1.47073i	0.842049	−	0.539401i	$-0.181349\pi$
$660$	−2.97359e8	+	9.15176e8i	−0.0402603	+	0.123908i
$661$	1.66329e8	+	1.20845e8i	0.0224007	+	0.0162751i	0.598929	−	0.800802i	$-0.295593\pi$
$661$	1.66329e8	+	1.20845e8i	0.0224007	+	0.0162751i	−0.576529	+	0.817077i	$0.695593\pi$
$662$	−2.14781e9	−	6.61027e9i	−0.287735	−	0.885556i
$663$	−7.35861e7	−	5.34634e7i	−0.00980615	−	0.00712458i
$664$	5.62167e8	−	4.08438e8i	0.0745208	−	0.0541425i
$665$	−2.19962e9	+	6.76973e9i	−0.290049	+	0.892680i
$666$	2.39305e9	−	1.73865e9i	0.313901	−	0.228062i
$667$	−1.25591e10	+	9.12475e9i	−1.63878	+	1.19064i
$668$	3.72301e8	−	1.14583e9i	0.0483256	−	0.148731i
$669$	−9.89485e9	+	7.18903e9i	−1.27767	+	0.928280i
$670$	−3.38822e9	−	2.46168e9i	−0.435221	−	0.316206i
$671$	2.85967e8	+	8.80114e8i	0.0365415	+	0.112463i
$672$	−1.97660e9	−	1.43609e9i	−0.251262	−	0.182553i
$673$	−6.03489e8	+	1.85735e9i	−0.0763162	+	0.234877i	−0.981936	−	0.189214i	$-0.939406\pi$
$673$	−6.03489e8	+	1.85735e9i	−0.0763162	+	0.234877i	0.905620	+	0.424091i	$0.139406\pi$
$674$	−1.29369e9	+	3.98157e9i	−0.162750	+	0.500893i
$675$	−2.16416e9	−	6.66059e9i	−0.270848	−	0.833584i
$676$	9.21113e9			1.14683
$677$	−1.10079e9			−0.136347			−0.0681735	−	0.997673i	$-0.521717\pi$
$677$	−1.10079e9			−0.136347			−0.0681735	+	0.997673i	$0.521717\pi$
$678$	1.93525e9	+	5.95608e9i	0.238470	+	0.733934i
$679$	−6.97587e9	+	5.06827e9i	−0.855173	+	0.621320i
$680$	5.22707e6	+	3.79769e6i	0.000637496	+	0.000463168i
$681$	−2.44048e10			−2.96115
$682$	1.82171e8	+	1.64618e9i	0.0219904	+	0.198716i
$683$	−5.24745e7			−0.00630197			−0.00315098	−	0.999995i	$-0.501003\pi$
$683$	−5.24745e7			−0.00630197			−0.00315098	+	0.999995i	$0.501003\pi$
$684$	9.54834e9	+	6.93727e9i	1.14086	+	0.828881i
$685$	−2.17552e9	+	1.58061e9i	−0.258610	+	0.187891i
$686$	−1.72340e9	−	5.30408e9i	−0.203822	−	0.627300i
$687$	−1.74168e10			−2.04937
$688$	3.13750e9			0.367303
$689$	6.80009e9	+	2.09285e10i	0.792041	+	2.43765i
$690$	−2.71771e9	+	8.36424e9i	−0.314942	+	0.969292i
$691$	−2.25441e9	+	6.93836e9i	−0.259932	+	0.799989i	0.732886	+	0.680352i	$0.238173\pi$
$691$	−2.25441e9	+	6.93836e9i	−0.259932	+	0.799989i	−0.992818	+	0.119637i	$0.961827\pi$
$692$	−3.62581e9	−	2.63430e9i	−0.415943	−	0.302200i
$693$	−1.42568e9	−	4.38778e9i	−0.162725	−	0.500816i
$694$	6.43213e9	+	4.67321e9i	0.730460	+	0.530710i
$695$	2.42936e9	−	1.76503e9i	0.274501	−	0.199437i
$696$	−2.09164e9	+	6.43741e9i	−0.235155	+	0.723734i
$697$	2.53674e6	−	1.84305e6i	0.000283767	−	0.000206168i
$698$	8.55980e9	−	6.21906e9i	0.952729	−	0.692198i
$699$	4.65154e9	−	1.43160e10i	0.515142	−	1.58544i
$700$	2.68737e9	−	1.95249e9i	0.296131	−	0.215152i
$701$	1.41240e10	+	1.02617e10i	1.54862	+	1.12514i	0.944628	+	0.328144i	$0.106423\pi$
$701$	1.41240e10	+	1.02617e10i	1.54862	+	1.12514i	0.603989	+	0.796993i	$0.293577\pi$
$702$	−4.60080e9	−	1.41598e10i	−0.501942	−	1.54482i
$703$	−3.71629e9	−	2.70005e9i	−0.403428	−	0.293108i
$704$	−1.01108e8	+	3.11180e8i	−0.0109215	+	0.0336130i
$705$	2.20506e9	−	6.78648e9i	0.237006	−	0.729429i
$706$	−1.51937e9	−	4.67614e9i	−0.162498	−	0.500116i
$707$	1.10199e10			1.17277
$708$	2.50799e9			0.265589
$709$	−2.97571e9	−	9.15829e9i	−0.313566	−	0.965056i	−0.976341	−	0.216237i	$-0.930622\pi$
$709$	−2.97571e9	−	9.15829e9i	−0.313566	−	0.965056i	0.662775	−	0.748818i	$-0.269378\pi$
$710$	1.01448e9	−	7.37066e8i	0.106375	−	0.0772862i
$711$	1.11060e10	+	8.06898e9i	1.15881	+	0.841928i
$712$	−2.10838e9			−0.218912
$713$	1.66495e9	+	1.50453e10i	0.172024	+	1.55448i
$714$	−4.85612e7			−0.00499282
$715$	−2.25013e9	−	1.63482e9i	−0.230217	−	0.167262i
$716$	3.52013e9	−	2.55753e9i	0.358396	−	0.260390i
$717$	9.50146e9	+	2.92425e10i	0.962661	+	2.96277i
$718$	−7.22762e9			−0.728718
$719$	−1.19111e10			−1.19509			−0.597547	−	0.801834i	$-0.703858\pi$
$719$	−1.19111e10			−1.19509			−0.597547	+	0.801834i	$0.703858\pi$
$720$	7.55887e8	+	2.32638e9i	0.0754733	+	0.232283i
$721$	1.75256e9	−	5.39384e9i	0.174141	−	0.535950i
$722$	3.45406e9	−	1.06305e10i	0.341547	−	1.05117i
$723$	6.36890e9	+	4.62727e9i	0.626730	+	0.455346i
$724$	−4.58414e8	−	1.41085e9i	−0.0448924	−	0.138165i
$725$	−7.44508e9	−	5.40917e9i	−0.725582	−	0.527166i
$726$	9.01822e9	−	6.55212e9i	0.874666	−	0.635482i
$727$	3.43245e9	−	1.05640e10i	0.331309	−	1.01966i	−0.637203	−	0.770696i	$-0.719909\pi$
$727$	3.43245e9	−	1.05640e10i	0.331309	−	1.01966i	0.968512	−	0.248968i	$-0.0800915\pi$
$728$	5.71309e9	−	4.15081e9i	0.548797	−	0.398724i
$729$	1.27052e10	−	9.23087e9i	1.21461	−	0.882463i
$730$	4.30033e8	−	1.32351e9i	0.0409140	−	0.125920i
$731$	5.04509e7	−	3.66547e7i	0.00477703	−	0.00347071i
$732$	2.98342e9	+	2.16758e9i	0.281142	+	0.204262i
$733$	5.40639e9	+	1.66392e10i	0.507042	+	1.56051i	0.797311	+	0.603568i	$0.206255\pi$
$733$	5.40639e9	+	1.66392e10i	0.507042	+	1.56051i	−0.290270	+	0.956945i	$0.593745\pi$
$734$	1.29958e9	+	9.44203e8i	0.121302	+	0.0881311i
$735$	3.60774e8	−	1.11035e9i	0.0335143	−	0.103146i
$736$	−9.24079e8	+	2.84402e9i	−0.0854352	+	0.262943i
$737$	−1.30265e9	−	4.00914e9i	−0.119865	−	0.368906i
$738$	1.18711e9			0.108716
$739$	1.62448e10			1.48067			0.740335	−	0.672238i	$-0.234667\pi$
$739$	1.62448e10			1.48067			0.740335	+	0.672238i	$0.234667\pi$
$740$	−2.94198e8	−	9.05448e8i	−0.0266888	−	0.0821396i
$741$	−4.32641e10	+	3.14332e10i	−3.90628	+	2.83808i
$742$	9.50476e9	+	6.90561e9i	0.854137	+	0.620567i
$743$	−1.32809e10			−1.18786			−0.593931	−	0.804516i	$-0.702425\pi$
$743$	−1.32809e10			−1.18786			−0.593931	+	0.804516i	$0.702425\pi$
$744$	4.44316e9	+	4.88043e9i	0.395537	+	0.434463i
$745$	−4.46751e9			−0.395839
$746$	3.66136e9	+	2.66013e9i	0.322891	+	0.234594i
$747$	4.23025e9	−	3.07346e9i	0.371317	−	0.269777i
$748$	2.00962e6	+	6.18499e6i	0.000175574	+	0.000540360i
$749$	−2.35854e10			−2.05096
$750$	−1.27424e10			−1.10290
$751$	−5.90371e9	−	1.81698e10i	−0.508611	−	1.56534i	−0.794614	−	0.607114i	$-0.792327\pi$
$751$	−5.90371e9	−	1.81698e10i	−0.508611	−	1.56534i	0.286004	−	0.958228i	$-0.407673\pi$
$752$	7.49769e8	−	2.30755e9i	0.0642932	−	0.197874i
$753$	2.65135e9	−	8.16002e9i	0.226300	−	0.696481i
$754$	−1.58276e10	−	1.14994e10i	−1.34467	−	0.976957i
$755$	5.06102e8	+	1.55762e9i	0.0427980	+	0.131719i
$756$	−6.43072e9	−	4.67219e9i	−0.541294	−	0.393273i
$757$	−2.74087e9	+	1.99136e9i	−0.229643	+	0.166845i	−0.696657	−	0.717405i	$-0.745330\pi$
$757$	−2.74087e9	+	1.99136e9i	−0.229643	+	0.166845i	0.467014	+	0.884250i	$0.345330\pi$
$758$	1.67743e8	−	5.16260e8i	0.0139895	−	0.0430553i
$759$	−7.16159e9	+	5.20320e9i	−0.594515	+	0.431941i
$760$	3.07320e9	−	2.23281e9i	0.253947	−	0.184503i
$761$	6.06833e9	−	1.86764e10i	0.499141	−	1.53620i	−0.311262	−	0.950324i	$-0.600752\pi$
$761$	6.06833e9	−	1.86764e10i	0.499141	−	1.53620i	0.810403	−	0.585873i	$-0.199248\pi$
$762$	1.90491e10	−	1.38400e10i	1.55967	−	1.13316i
$763$	−6.72709e9	−	4.88752e9i	−0.548266	−	0.398339i
$764$	1.21559e9	+	3.74121e9i	0.0986193	+	0.303519i
$765$	3.93332e7	+	2.85773e7i	0.00317647	+	0.00230784i
$766$	−4.58496e9	+	1.41111e10i	−0.368583	+	1.13438i
$767$	−2.24007e9	+	6.89421e9i	−0.179257	+	0.551697i
$768$	4.02913e8	+	1.24004e9i	0.0320957	+	0.0987806i
$769$	2.04295e10			1.62000			0.810000	−	0.586429i	$-0.199467\pi$
$769$	2.04295e10			1.62000			0.810000	+	0.586429i	$0.199467\pi$
$770$	−1.48491e9			−0.117215
$771$	2.08658e9	+	6.42185e9i	0.163963	+	0.504626i
$772$	−1.10897e9	+	8.05715e8i	−0.0867481	+	0.0630262i
$773$	9.88578e9	+	7.18244e9i	0.769809	+	0.559299i	0.901903	−	0.431938i	$-0.142170\pi$
$773$	9.88578e9	+	7.18244e9i	0.769809	+	0.559299i	−0.132095	+	0.991237i	$0.542170\pi$
$774$	2.36094e10			1.83017
$775$	−8.17735e9	+	3.69476e9i	−0.631039	+	0.285122i
$776$	4.60159e9			0.353502
$777$	5.78899e9	+	4.20595e9i	0.442720	+	0.321655i
$778$	−6.84893e9	+	4.97604e9i	−0.521428	+	0.378840i
$779$	−5.69682e8	−	1.75330e9i	−0.0431769	−	0.132885i
$780$	−1.10834e10			−0.836264
$781$	1.26217e9			0.0948070
$782$	1.83669e7	+	5.65276e7i	0.00137345	+	0.00422705i
$783$	−6.80498e9	+	2.09436e10i	−0.506595	+	1.55914i
$784$	1.22671e8	−	3.77543e8i	0.00909151	−	0.0279808i
$785$	1.19737e10	+	8.69942e9i	0.883457	+	0.641869i
$786$	2.80542e9	+	8.63420e9i	0.206072	+	0.634225i
$787$	−5.70974e9	−	4.14837e9i	−0.417547	−	0.303365i	0.359103	−	0.933298i	$-0.383083\pi$
$787$	−5.70974e9	−	4.14837e9i	−0.417547	−	0.303365i	−0.776650	+	0.629932i	$0.783083\pi$
$788$	9.31387e8	−	6.76692e8i	0.0678092	−	0.0492662i
$789$	1.08729e10	−	3.34633e10i	0.788088	−	2.42549i
$790$	3.57454e9	−	2.59706e9i	0.257944	−	0.187407i
$791$	−7.81835e9	+	5.68036e9i	−0.561691	+	0.408092i
$792$	−7.60831e8	+	2.34160e9i	−0.0544190	+	0.167484i
$793$	−8.62316e9	+	6.26509e9i	−0.614060	+	0.446140i
$794$	4.06431e9	+	2.95290e9i	0.288148	+	0.209352i
$795$	−5.69806e9	−	1.75368e10i	−0.402200	−	1.23784i
$796$	−1.06600e10	−	7.74497e9i	−0.749140	−	0.544282i
$797$	1.41303e9	−	4.34887e9i	0.0988662	−	0.304279i	−0.889376	−	0.457177i	$-0.848861\pi$
$797$	1.41303e9	−	4.34887e9i	0.0988662	−	0.304279i	0.988242	+	0.152898i	$0.0488606\pi$
$798$	−8.82274e9	+	2.71536e10i	−0.614601	+	1.89155i
$799$	−1.49024e7	−	4.58647e7i	−0.00103357	−	0.00318101i
$800$	−1.77271e9			−0.122411
$801$	−1.58654e10			−1.09078
$802$	−2.67641e9	−	8.23716e9i	−0.183207	−	0.563854i
$803$	1.13321e9	−	8.23322e8i	0.0772332	−	0.0561132i
$804$	−1.35902e10	−	9.87389e9i	−0.922212	−	0.670026i
$805$	−1.35714e10			−0.916933
$806$	−1.73843e10	+	7.85472e9i	−1.16946	+	0.528394i
$807$	2.78586e10			1.86596
$808$	−4.75778e9	−	3.45673e9i	−0.317296	−	0.230529i
$809$	8.27299e9	−	6.01068e9i	0.549342	−	0.399120i	−0.278201	−	0.960523i	$-0.589738\pi$
$809$	8.27299e9	−	6.01068e9i	0.549342	−	0.399120i	0.827543	+	0.561403i	$0.189738\pi$
$810$	6.26424e8	+	1.92794e9i	0.0414163	+	0.127466i
$811$	1.23165e10			0.810798			0.405399	−	0.914140i	$-0.367133\pi$
$811$	1.23165e10			0.810798			0.405399	+	0.914140i	$0.367133\pi$
$812$	−1.04450e10			−0.684639
$813$	6.51046e9	+	2.00371e10i	0.424908	+	1.30773i
$814$	2.96122e8	−	9.11370e8i	0.0192436	−	0.0592256i
$815$	−1.37819e9	+	4.24162e9i	−0.0891777	+	0.274461i
$816$	2.09659e7	+	1.52327e7i	0.00135082	+	0.000981431i
$817$	−1.13299e10	−	3.48698e10i	−0.726855	−	2.23703i
$818$	−6.57686e9	−	4.77837e9i	−0.420128	−	0.305241i
$819$	4.29905e10	−	3.12344e10i	2.73450	−	1.98673i
$820$	1.18069e8	−	3.63380e8i	0.00747805	−	0.0230151i
$821$	4.93762e9	−	3.58739e9i	0.311399	−	0.226244i	−0.421098	−	0.907015i	$-0.638355\pi$
$821$	4.93762e9	−	3.58739e9i	0.311399	−	0.226244i	0.732496	+	0.680771i	$0.238355\pi$
$822$	−8.72606e9	+	6.33986e9i	−0.547983	+	0.398133i
$823$	−7.84609e9	+	2.41478e10i	−0.490630	+	1.51000i	0.333028	+	0.942917i	$0.391930\pi$
$823$	−7.84609e9	+	2.41478e10i	−0.490630	+	1.51000i	−0.823658	+	0.567087i	$0.808070\pi$
$824$	−2.44859e9	+	1.77901e9i	−0.152465	+	0.110773i
$825$	−4.24540e9	−	3.08447e9i	−0.263227	−	0.191245i
$826$	1.19595e9	+	3.68075e9i	0.0738383	+	0.227251i
$827$	−3.38532e9	−	2.45958e9i	−0.208128	−	0.151214i	0.478838	−	0.877903i	$-0.341058\pi$
$827$	−3.38532e9	−	2.45958e9i	−0.208128	−	0.151214i	−0.686966	+	0.726689i	$0.741058\pi$
$828$	−6.95361e9	+	2.14010e10i	−0.425700	+	1.31017i
$829$	−2.17151e9	+	6.68323e9i	−0.132380	+	0.407423i	−0.995173	−	0.0981335i	$-0.968713\pi$
$829$	−2.17151e9	+	6.68323e9i	−0.132380	+	0.407423i	0.862794	+	0.505556i	$0.168713\pi$
$830$	−5.20061e8	−	1.60058e9i	−0.0315704	−	0.0971638i
$831$	2.39011e10			1.44482
$832$	−3.76861e9			−0.226856
$833$	−2.43820e6	−	7.50401e6i	−0.000146154	−	0.000449817i
$834$	9.74422e9	−	7.07959e9i	0.581656	−	0.422598i
$835$	−2.36066e9	−	1.71512e9i	−0.140324	−	0.101951i
$836$	3.82353e9			0.226330
$837$	1.44555e10	+	1.58781e10i	0.852105	+	0.935964i
$838$	2.34422e9			0.137608
$839$	−1.50499e10	−	1.09344e10i	−0.879768	−	0.639189i	0.0534222	−	0.998572i	$-0.482987\pi$
$839$	−1.50499e10	−	1.09344e10i	−0.879768	−	0.639189i	−0.933190	+	0.359383i	$0.882987\pi$
$840$	−4.78722e9	+	3.47812e9i	−0.278680	+	0.202473i
$841$	3.61146e9	+	1.11149e10i	0.209361	+	0.644348i
$842$	−3.94866e8			−0.0227959
$843$	−4.16735e8			−0.0239587
$844$	−4.43012e9	−	1.36345e10i	−0.253639	−	0.780622i
$845$	6.89381e9	−	2.12170e10i	0.393062	−	1.20972i
$846$	5.64194e9	−	1.73641e10i	0.320356	−	0.985953i
$847$	1.39163e10	+	1.01108e10i	0.786922	+	0.571732i
$848$	−1.93746e9	−	5.96290e9i	−0.109106	−	0.335793i
$849$	−1.99771e10	−	1.45142e10i	−1.12035	−	0.813984i
$850$	−2.85050e7	+	2.07101e7i	−0.00159205	+	0.00115669i
$851$	2.70640e9	−	8.32946e9i	0.150536	−	0.463301i
$852$	4.06913e9	−	2.95639e9i	0.225404	−	0.163766i
$853$	5.35158e9	−	3.88815e9i	0.295230	−	0.214497i	−0.430303	−	0.902684i	$-0.641593\pi$
$853$	5.35158e9	−	3.88815e9i	0.295230	−	0.214497i	0.725533	+	0.688187i	$0.241593\pi$
$854$	−1.75850e9	+	5.41211e9i	−0.0966140	+	0.297347i
$855$	2.31255e10	−	1.68017e10i	1.26535	−	0.919329i
$856$	1.01828e10	+	7.39827e9i	0.554895	+	0.403155i
$857$	−8.16715e9	−	2.51359e10i	−0.443238	−	1.36415i	−0.884404	−	0.466722i	$-0.845435\pi$
$857$	−8.16715e9	−	2.51359e10i	−0.443238	−	1.36415i	0.441166	−	0.897426i	$-0.354565\pi$
$858$	−9.02534e9	−	6.55729e9i	−0.487818	−	0.354421i
$859$	−3.24439e9	+	9.98521e9i	−0.174645	+	0.537503i	−0.999617	−	0.0276707i	$-0.991191\pi$
$859$	−3.24439e9	+	9.98521e9i	−0.174645	+	0.537503i	0.824972	+	0.565174i	$0.191191\pi$
$860$	2.34817e9	−	7.22693e9i	0.125888	−	0.387444i
$861$	8.87412e8	+	2.73117e9i	0.0473821	+	0.145827i
$862$	2.16940e10			1.15362
$863$	−9.22944e9			−0.488807			−0.244404	−	0.969674i	$-0.578592\pi$
$863$	−9.22944e9			−0.488807			−0.244404	+	0.969674i	$0.578592\pi$
$864$	1.31085e9	+	4.03437e9i	0.0691439	+	0.212803i
$865$	−8.78149e9	+	6.38013e9i	−0.461330	+	0.335176i
$866$	−1.43660e10	−	1.04375e10i	−0.751665	−	0.546116i
$867$	−3.18893e10			−1.66180
$868$	−5.04381e9	+	8.84806e9i	−0.261782	+	0.459229i
$869$	4.44728e9			0.229893
$870$	1.32625e10	+	9.63579e9i	0.682824	+	0.496101i
$871$	3.92807e10	−	2.85391e10i	2.01426	−	1.46344i
$872$	1.37126e9	+	4.22030e9i	0.0700345	+	0.215544i
$873$	3.46266e10			1.76141
$874$	3.49451e10			1.77050
$875$	−6.07628e9	−	1.87009e10i	−0.306626	−	0.943699i
$876$	1.72488e9	−	5.30862e9i	0.0866949	−	0.266819i
$877$	9.68409e9	−	2.98046e10i	0.484797	−	1.49205i	−0.347477	−	0.937689i	$-0.612961\pi$
$877$	9.68409e9	−	2.98046e10i	0.484797	−	1.49205i	0.832274	−	0.554364i	$-0.187039\pi$
$878$	6.74287e9	+	4.89898e9i	0.336213	+	0.244273i
$879$	1.57680e10	+	4.85289e10i	0.783097	+	2.41012i
$880$	6.41101e8	+	4.65787e8i	0.0317130	+	0.0230408i
$881$	1.10253e10	−	8.01038e9i	0.543221	−	0.394673i	−0.282059	−	0.959397i	$-0.591017\pi$
$881$	1.10253e10	−	8.01038e9i	0.543221	−	0.394673i	0.825280	+	0.564724i	$0.191017\pi$
$882$	9.23088e8	−	2.84097e9i	0.0453005	−	0.139421i
$883$	−2.38280e10	+	1.73120e10i	−1.16473	+	0.846224i	−0.990368	−	0.138458i	$-0.955785\pi$
$883$	−2.38280e10	+	1.73120e10i	−1.16473	+	0.846224i	−0.174359	+	0.984682i	$0.555785\pi$
$884$	−6.05991e7	+	4.40278e7i	−0.00295042	+	0.00214360i
$885$	1.87704e9	−	5.77692e9i	0.0910272	−	0.280153i
$886$	1.45658e10	−	1.05826e10i	0.703582	−	0.511182i
$887$	−1.74590e10	−	1.26847e10i	−0.840013	−	0.610305i	0.0823612	−	0.996603i	$-0.473754\pi$
$887$	−1.74590e10	−	1.26847e10i	−0.840013	−	0.610305i	−0.922374	+	0.386297i	$0.873754\pi$
$888$	−1.18004e9	−	3.63178e9i	−0.0565522	−	0.174050i
$889$	2.93952e10	+	2.13569e10i	1.40320	+	1.01949i
$890$	−1.57796e9	+	4.85646e9i	−0.0750293	+	0.230916i
$891$	−6.30522e8	+	1.94055e9i	−0.0298626	+	0.0919077i
$892$	3.11246e9	+	9.57918e9i	0.146834	+	0.451909i
$893$	−2.83534e10			−1.33237
$894$	−1.79193e10			−0.838764
$895$	−3.25647e9	−	1.00224e10i	−0.151833	−	0.467295i
$896$	−1.62776e9	+	1.18264e9i	−0.0755983	+	0.0549254i
$897$	−8.24870e10	−	5.99303e10i	−3.81603	−	2.77251i
$898$	−2.94624e10			−1.35769
$899$	2.76310e10	+	5.71465e9i	1.26834	+	0.262319i
$900$	−1.33394e10			−0.609942
$901$	−1.00818e8	−	7.32482e7i	−0.00459197	−	0.00333626i
$902$	3.11131e8	−	2.26050e8i	0.0141163	−	0.0102561i
$903$	1.76489e10	+	5.43178e10i	0.797647	+	2.45491i
$904$	5.15733e9			0.232186
$905$	−3.59285e9			−0.161127
$906$	2.02999e9	+	6.24767e9i	0.0906870	+	0.279106i
$907$	−6.05993e9	+	1.86505e10i	−0.269676	+	0.829977i	0.720903	+	0.693036i	$0.243727\pi$
$907$	−6.05993e9	+	1.86505e10i	−0.269676	+	0.829977i	−0.990579	+	0.136941i	$0.956273\pi$
$908$	−6.21052e9	+	1.91140e10i	−0.275314	+	0.847328i
$909$	−3.58019e10	−	2.60116e10i	−1.58100	−	1.14866i
$910$	−5.28518e9	−	1.62661e10i	−0.232496	−	0.715548i
$911$	3.39990e10	+	2.47017e10i	1.48988	+	1.08246i	0.974202	+	0.225680i	$0.0724603\pi$
$911$	3.39990e10	+	2.47017e10i	1.48988	+	1.08246i	0.515679	+	0.856782i	$0.327540\pi$
$912$	1.23267e10	−	8.95586e9i	0.538102	−	0.390954i
$913$	5.23462e8	−	1.61105e9i	0.0227634	−	0.0700586i
$914$	−2.54333e10	+	1.84784e10i	−1.10177	+	0.800483i
$915$	7.22568e9	−	5.24976e9i	0.311821	−	0.226551i
$916$	−4.43221e9	+	1.36410e10i	−0.190540	+	0.586422i
$917$	−1.13338e10	+	8.23451e9i	−0.485382	+	0.352651i
$918$	6.82110e7	+	4.95582e7i	0.00291008	+	0.00211430i
$919$	−1.13945e10	−	3.50686e10i	−0.484272	−	1.49044i	−0.833032	−	0.553225i	$-0.813397\pi$
$919$	−1.13945e10	−	3.50686e10i	−0.484272	−	1.49044i	0.348760	−	0.937212i	$-0.386603\pi$
$920$	5.85933e9	+	4.25706e9i	0.248080	+	0.180240i
$921$	−4.56834e9	+	1.40599e10i	−0.192686	+	0.593026i
$922$	−6.10373e9	+	1.87854e10i	−0.256471	+	0.789335i
$923$	4.49239e9	+	1.38262e10i	0.188049	+	0.578756i
$924$	−5.95603e9			−0.248373
$925$	5.19182e9			0.215687
$926$	5.06309e9	+	1.55826e10i	0.209545	+	0.644913i
$927$	−1.84254e10	+	1.33869e10i	−0.759694	+	0.551950i
$928$	4.50955e9	+	3.27638e9i	0.185232	+	0.134579i
$929$	−1.17047e10			−0.478966			−0.239483	−	0.970901i	$-0.576978\pi$
$929$	−1.17047e10			−0.478966			−0.239483	+	0.970901i	$0.576978\pi$
$930$	1.45670e10	−	6.58177e9i	0.593853	−	0.268320i
$931$	−4.63894e9			−0.188406
$932$	−1.00287e10	−	7.28625e9i	−0.405777	−	0.294814i
$933$	−5.79963e10	+	4.21368e10i	−2.33784	+	1.69854i
$934$	−5.94659e8	−	1.83017e9i	−0.0238811	−	0.0734984i
$935$	1.57506e7			0.000630167
$936$	−2.83584e10			−1.13036
$937$	−5.25778e9	−	1.61818e10i	−0.208792	−	0.642596i	−0.999536	−	0.0304491i	$-0.990306\pi$
$937$	−5.25778e9	−	1.61818e10i	−0.208792	−	0.642596i	0.790744	−	0.612147i	$-0.209694\pi$
$938$	8.01041e9	−	2.46535e10i	0.316916	−	0.975369i
$939$	−2.32795e9	+	7.16471e9i	−0.0917582	+	0.282403i
$940$	−4.75408e9	−	3.45404e9i	−0.186689	−	0.135638i
$941$	5.12547e9	+	1.57746e10i	0.200526	+	0.617154i	0.999868	+	0.0162778i	$0.00518161\pi$
$941$	5.12547e9	+	1.57746e10i	0.200526	+	0.617154i	−0.799342	+	0.600876i	$0.794818\pi$
$942$	4.80269e10	+	3.48936e10i	1.87200	+	1.36009i
$943$	2.84358e9	−	2.06598e9i	0.110427	−	0.0802298i
$944$	6.38233e8	−	1.96428e9i	0.0246932	−	0.0759979i
$945$	−1.55748e10	+	1.13158e10i	−0.600360	+	0.436187i
$946$	6.18780e9	−	4.49570e9i	0.237639	−	0.172655i
$947$	2.14155e9	−	6.59101e9i	0.0819413	−	0.252189i	−0.901690	−	0.432384i	$-0.857673\pi$
$947$	2.14155e9	−	6.59101e9i	0.0819413	−	0.252189i	0.983631	+	0.180194i	$0.0576726\pi$
$948$	1.43376e10	−	1.04169e10i	0.546571	−	0.397107i
$949$	1.30522e10	+	9.48300e9i	0.495739	+	0.360175i
$950$	6.40145e9	+	1.97016e10i	0.242240	+	0.745537i
$951$	−1.79769e10	−	1.30610e10i	−0.677770	−	0.492429i
$952$	−1.23578e7	+	3.80335e7i	−0.000464208	+	0.00142869i
$953$	1.93198e8	−	5.94602e8i	0.00723065	−	0.0222536i	−0.947376	−	0.320123i	$-0.896276\pi$
$953$	1.93198e8	−	5.94602e8i	0.00723065	−	0.0222536i	0.954607	+	0.297869i	$0.0962759\pi$
$954$	−1.45792e10	−	4.48702e10i	−0.543645	−	1.67317i
$955$	9.52730e9			0.353963
$956$	2.53209e10			0.937294
$957$	5.09897e9	+	1.56930e10i	0.188057	+	0.578781i
$958$	−1.26558e10	+	9.19499e9i	−0.465062	+	0.337888i
$959$	−1.34655e10	−	9.78323e9i	−0.493011	−	0.358193i
$960$	3.15786e9			0.115198
$961$	1.81837e10	−	2.06469e10i	0.660924	−	0.750453i
$962$	1.10373e10			0.399716
$963$	7.66249e10	+	5.56712e10i	2.76489	+	2.00881i
$964$	5.24487e9	−	3.81062e9i	0.188567	−	0.137002i
$965$	1.02591e9	+	3.15742e9i	0.0367505	+	0.113106i
$966$	−5.44351e10			−1.94294
$967$	7.08490e9			0.251965			0.125983	−	0.992032i	$-0.459792\pi$
$967$	7.08490e9			0.251965			0.125983	+	0.992032i	$0.459792\pi$
$968$	−2.83672e9	−	8.73051e9i	−0.100520	−	0.309368i
$969$	9.35833e7	−	2.88020e8i	0.00330419	−	0.0101693i
$970$	3.44393e9	−	1.05993e10i	0.121158	−	0.372887i
$971$	8.35863e9	+	6.07290e9i	0.293000	+	0.212877i	0.724568	−	0.689204i	$-0.242039\pi$
$971$	8.35863e9	+	6.07290e9i	0.293000	+	0.212877i	−0.431568	+	0.902081i	$0.642039\pi$
$972$	−3.08665e9	−	9.49975e9i	−0.107809	−	0.331803i
$973$	1.50366e10	+	1.09247e10i	0.523305	+	0.380204i
$974$	−2.54562e10	+	1.84950e10i	−0.882750	+	0.641356i
$975$	1.86775e10	−	5.74836e10i	0.645362	−	1.98622i
$976$	2.45689e9	−	1.78503e9i	0.0845884	−	0.0614571i
$977$	−2.38034e10	+	1.72942e10i	−0.816596	+	0.593292i	−0.915735	−	0.401782i	$-0.868391\pi$
$977$	−2.38034e10	+	1.72942e10i	−0.816596	+	0.593292i	0.0991395	+	0.995074i	$0.468391\pi$
$978$	−5.52795e9	+	1.70133e10i	−0.188963	+	0.581570i
$979$	−4.15817e9	+	3.02109e9i	−0.141633	+	0.102902i
$980$	−7.77823e8	−	5.65122e8i	−0.0263991	−	0.0191801i
$981$	1.03186e10	+	3.17574e10i	0.348963	+	1.07400i
$982$	2.16445e10	+	1.57256e10i	0.729385	+	0.529929i
$983$	1.90879e8	−	5.87465e8i	0.00640944	−	0.0197262i	−0.947801	−	0.318863i	$-0.896699\pi$
$983$	1.90879e8	−	5.87465e8i	0.00640944	−	0.0197262i	0.954210	+	0.299137i	$0.0966988\pi$
$984$	4.73579e8	−	1.45753e9i	0.0158456	−	0.0487679i
$985$	−8.61626e8	−	2.65181e9i	−0.0287271	−	0.0884129i
$986$	1.10791e8			0.00368073
$987$	4.41669e10			1.46213
$988$	1.36089e10	+	4.18839e10i	0.448925	+	1.38165i
$989$	5.65533e10	−	4.10884e10i	1.85897	−	1.35062i
$990$	4.82422e9	+	3.50500e9i	0.158017	+	0.114806i
$991$	1.87511e10			0.612023			0.306012	−	0.952028i	$-0.401005\pi$
$991$	1.87511e10			0.612023			0.306012	+	0.952028i	$0.401005\pi$
$992$	4.95308e9	−	2.23795e9i	0.161096	−	0.0727878i
$993$	−6.75200e10			−2.18832
$994$	6.27920e9	+	4.56210e9i	0.202792	+	0.147337i
$995$	−2.58180e10	+	1.87579e10i	−0.830886	+	0.603674i
$996$	−2.08598e9	−	6.41998e9i	−0.0668963	−	0.205886i
$997$	3.06805e10			0.980458			0.490229	−	0.871594i	$-0.336913\pi$
$997$	3.06805e10			0.980458			0.490229	+	0.871594i	$0.336913\pi$
$998$	−1.28040e10			−0.407745
$999$	−3.83915e9	−	1.18157e10i	−0.121831	−	0.374956i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.8.d.a.33.2	✓	40
31.16	even	5	inner	62.8.d.a.47.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.8.d.a.33.2	✓	40	1.1	even	1	trivial
62.8.d.a.47.2	yes	40	31.16	even	5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.47214 - 4.70228i) q^{2} +(-62.8734 + 45.6802i) q^{3} +(19.7771 + 60.8676i) q^{4} +155.004 q^{5} +621.727 q^{6} +(296.473 + 912.449i) q^{7} +(158.217 - 486.941i) q^{8} +(1190.57 - 3664.18i) q^{9} +(-1003.21 - 728.874i) q^{10} +(-385.698 - 1187.06i) q^{11} +(-4023.90 - 2923.53i) q^{12} +(11630.5 - 8450.06i) q^{13} +(2371.78 - 7299.59i) q^{14} +(-9745.65 + 7080.63i) q^{15} +(-3313.73 + 2407.57i) q^{16} +(-25.1576 + 77.4272i) q^{17} +(-24935.5 + 18116.7i) q^{18} +(38723.7 + 28134.4i) q^{19} +(3065.53 + 9434.74i) q^{20} +(-60321.1 - 43825.9i) q^{21} +(-3085.58 + 9496.45i) q^{22} +(-28200.7 + 86792.7i) q^{23} +(12295.9 + 37843.0i) q^{24} -54098.7 q^{25} -115009. q^{26} +(40003.9 + 123119. i) q^{27} +(-49675.3 + 36091.2i) q^{28} +(137620. + 99987.1i) q^{29} +96370.3 q^{30} +(151156. - 68296.7i) q^{31} +32768.0 q^{32} +(78475.2 + 57015.5i) q^{33} +(526.908 - 382.821i) q^{34} +(45954.5 + 141434. i) q^{35} +246576. q^{36} -95969.5 q^{37} +(-118329. - 364179. i) q^{38} +(-345250. + 1.06257e6i) q^{39} +(24524.3 - 75477.9i) q^{40} +(-31159.4 - 22638.6i) q^{41} +(184325. + 567294. i) q^{42} +(-619700. - 450238. i) q^{43} +(64625.3 - 46953.0i) q^{44} +(184543. - 567964. i) q^{45} +(590642. - 429127. i) q^{46} +(-479229. + 348180. i) q^{47} +(98367.5 - 302744. i) q^{48} +(-78407.5 + 56966.3i) q^{49} +(350134. + 254387. i) q^{50} +(-1955.15 - 6017.32i) q^{51} +(744353. + 540804. i) q^{52} +(-473013. + 1.45579e6i) q^{53} +(320031. - 984954. i) q^{54} +(-59784.9 - 183999. i) q^{55} +491216. q^{56} -3.71988e6 q^{57} +(-420531. - 1.29426e6i) q^{58} +(-407939. + 296385. i) q^{59} +(-623722. - 453160. i) q^{60} -741426. q^{61} +(-1.29945e6 - 268753. i) q^{62} +3.69635e6 q^{63} +(-212079. - 154084. i) q^{64} +(1.80278e6 - 1.30980e6i) q^{65} +(-239799. - 738025. i) q^{66} +3.37738e6 q^{67} -5210.36 q^{68} +(-2.19164e6 - 6.74517e6i) q^{69} +(367636. - 1.13147e6i) q^{70} +(-312490. + 961746. i) q^{71} +(-1.59587e6 - 1.15947e6i) q^{72} +(346791. + 1.06731e6i) q^{73} +(621128. + 451276. i) q^{74} +(3.40137e6 - 2.47124e6i) q^{75} +(-946633. + 2.91344e6i) q^{76} +(968780. - 703860. i) q^{77} +(7.23100e6 - 5.25363e6i) q^{78} +(-1.10106e6 + 3.38872e6i) q^{79} +(-513643. + 373183. i) q^{80} +(-1.32254e6 - 960885. i) q^{81} +(95214.5 + 293040. i) q^{82} +(1.09798e6 + 797731. i) q^{83} +(1.47460e6 - 4.53835e6i) q^{84} +(-3899.54 + 12001.6i) q^{85} +(1.89363e6 + 5.82800e6i) q^{86} -1.32201e7 q^{87} -639050. q^{88} +(-1.27251e6 - 3.91639e6i) q^{89} +(-3.86511e6 + 2.80817e6i) q^{90} +(1.11584e7 + 8.10704e6i) q^{91} -5.84059e6 q^{92} +(-6.38390e6 + 1.11989e7i) q^{93} +4.73888e6 q^{94} +(6.00234e6 + 4.36095e6i) q^{95} +(-2.06024e6 + 1.49685e6i) q^{96} +(2.77729e6 + 8.54761e6i) q^{97} +775336. q^{98} -4.80879e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) \) 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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