LMFDB - Embedded newform 76.5.b.a.39.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("76.39");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.b (of order $2$, degree $1$, 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:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.16
Character	$\chi$	$=$	76.39
Dual form			76.5.b.a.39.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.672122 + 3.94313i) q^{2} +15.5341i q^{3} +(-15.0965 - 5.30053i) q^{4} -5.44730 q^{5} +(-61.2528 - 10.4408i) q^{6} +31.1799i q^{7} +(31.0473 - 55.9648i) q^{8} -160.307 q^{9} +O(q^{10})$	\(q+(-0.672122 + 3.94313i) q^{2} +15.5341i q^{3} +(-15.0965 - 5.30053i) q^{4} -5.44730 q^{5} +(-61.2528 - 10.4408i) q^{6} +31.1799i q^{7} +(31.0473 - 55.9648i) q^{8} -160.307 q^{9} +(3.66125 - 21.4794i) q^{10} +45.9071i q^{11} +(82.3387 - 234.510i) q^{12} +7.06595 q^{13} +(-122.946 - 20.9567i) q^{14} -84.6187i q^{15} +(199.809 + 160.039i) q^{16} +382.648 q^{17} +(107.746 - 632.111i) q^{18} -82.8191i q^{19} +(82.2352 + 28.8736i) q^{20} -484.351 q^{21} +(-181.018 - 30.8552i) q^{22} -212.876i q^{23} +(869.361 + 482.291i) q^{24} -595.327 q^{25} +(-4.74918 + 27.8619i) q^{26} -1231.96i q^{27} +(165.270 - 470.708i) q^{28} -1486.95 q^{29} +(333.662 + 56.8741i) q^{30} +1115.61i q^{31} +(-765.349 + 680.306i) q^{32} -713.124 q^{33} +(-257.186 + 1508.83i) q^{34} -169.847i q^{35} +(2420.07 + 849.712i) q^{36} +720.780 q^{37} +(326.566 + 55.6645i) q^{38} +109.763i q^{39} +(-169.124 + 304.857i) q^{40} -679.649 q^{41} +(325.543 - 1909.86i) q^{42} -1515.76i q^{43} +(243.332 - 693.037i) q^{44} +873.241 q^{45} +(839.398 + 143.079i) q^{46} +3914.10i q^{47} +(-2486.05 + 3103.84i) q^{48} +1428.81 q^{49} +(400.132 - 2347.45i) q^{50} +5944.08i q^{51} +(-106.671 - 37.4532i) q^{52} -3912.52 q^{53} +(4857.77 + 828.027i) q^{54} -250.070i q^{55} +(1744.98 + 968.055i) q^{56} +1286.52 q^{57} +(999.412 - 5863.23i) q^{58} +5161.44i q^{59} +(-448.524 + 1277.45i) q^{60} -1971.58 q^{61} +(-4398.99 - 749.827i) q^{62} -4998.36i q^{63} +(-2168.12 - 3475.12i) q^{64} -38.4904 q^{65} +(479.307 - 2811.94i) q^{66} -2697.51i q^{67} +(-5776.65 - 2028.24i) q^{68} +3306.83 q^{69} +(669.727 + 114.158i) q^{70} -7270.01i q^{71} +(-4977.11 + 8971.55i) q^{72} +8385.78 q^{73} +(-484.452 + 2842.13i) q^{74} -9247.84i q^{75} +(-438.985 + 1250.28i) q^{76} -1431.38 q^{77} +(-432.809 - 73.7740i) q^{78} +3245.82i q^{79} +(-1088.42 - 871.780i) q^{80} +6152.46 q^{81} +(456.807 - 2679.94i) q^{82} +11648.4i q^{83} +(7312.01 + 2567.32i) q^{84} -2084.40 q^{85} +(5976.82 + 1018.77i) q^{86} -23098.4i q^{87} +(2569.19 + 1425.30i) q^{88} +13361.9 q^{89} +(-586.925 + 3443.30i) q^{90} +220.316i q^{91} +(-1128.36 + 3213.69i) q^{92} -17330.0 q^{93} +(-15433.8 - 2630.75i) q^{94} +451.141i q^{95} +(-10567.9 - 11889.0i) q^{96} -3764.95 q^{97} +(-960.336 + 5633.98i) q^{98} -7359.24i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9}+O(q^{10}) $ 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9	$ 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9} + 152 q^{10} + 160 q^{12} + 120 q^{13} - 60 q^{14} - 38 q^{16} - 600 q^{17} + 286 q^{18} - 600 q^{20} + 608 q^{21} + 1080 q^{22} + 958 q^{24} + 4604 q^{25} - 2766 q^{26} - 2250 q^{28} - 168 q^{29} - 1380 q^{30} + 3576 q^{32} + 1440 q^{33} + 908 q^{34} - 5836 q^{36} - 2248 q^{37} - 1716 q^{40} + 1800 q^{41} - 5006 q^{42} - 2520 q^{44} + 88 q^{45} + 6404 q^{46} + 1064 q^{48} - 12188 q^{49} + 3354 q^{50} + 15492 q^{52} - 6600 q^{53} + 1654 q^{54} + 12924 q^{56} + 5450 q^{58} - 11188 q^{60} + 2200 q^{61} - 9972 q^{62} + 12570 q^{64} - 15792 q^{65} + 10500 q^{66} - 22614 q^{68} + 19904 q^{69} + 900 q^{70} - 11376 q^{72} + 11560 q^{73} + 17304 q^{74} + 1680 q^{77} - 24740 q^{78} + 12900 q^{80} + 13604 q^{81} - 18420 q^{82} + 5644 q^{84} - 11552 q^{85} + 24564 q^{86} - 15304 q^{88} + 13800 q^{89} - 60212 q^{90} - 2142 q^{92} + 34592 q^{93} - 23096 q^{94} - 35770 q^{96} + 8200 q^{97} + 25566 q^{98}+O(q^{100}) $ 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9 + 152 * q^10 + 160 * q^12 + 120 * q^13 - 60 * q^14 - 38 * q^16 - 600 * q^17 + 286 * q^18 - 600 * q^20 + 608 * q^21 + 1080 * q^22 + 958 * q^24 + 4604 * q^25 - 2766 * q^26 - 2250 * q^28 - 168 * q^29 - 1380 * q^30 + 3576 * q^32 + 1440 * q^33 + 908 * q^34 - 5836 * q^36 - 2248 * q^37 - 1716 * q^40 + 1800 * q^41 - 5006 * q^42 - 2520 * q^44 + 88 * q^45 + 6404 * q^46 + 1064 * q^48 - 12188 * q^49 + 3354 * q^50 + 15492 * q^52 - 6600 * q^53 + 1654 * q^54 + 12924 * q^56 + 5450 * q^58 - 11188 * q^60 + 2200 * q^61 - 9972 * q^62 + 12570 * q^64 - 15792 * q^65 + 10500 * q^66 - 22614 * q^68 + 19904 * q^69 + 900 * q^70 - 11376 * q^72 + 11560 * q^73 + 17304 * q^74 + 1680 * q^77 - 24740 * q^78 + 12900 * q^80 + 13604 * q^81 - 18420 * q^82 + 5644 * q^84 - 11552 * q^85 + 24564 * q^86 - 15304 * q^88 + 13800 * q^89 - 60212 * q^90 - 2142 * q^92 + 34592 * q^93 - 23096 * q^94 - 35770 * q^96 + 8200 * q^97 + 25566 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.672122	+	3.94313i	−0.168031	+	0.985782i
$2$	−0.672122	+	3.94313i	−0.168031	+	0.985782i
$3$			15.5341i			1.72601i	0.505198	+	0.863003i	$0.331419\pi$
$3$			15.5341i			1.72601i	−0.505198	+	0.863003i	$0.668581\pi$
$4$	−15.0965	−	5.30053i	−0.943531	−	0.331283i
$5$	−5.44730			−0.217892			−0.108946	−	0.994048i	$-0.534748\pi$
$5$	−5.44730			−0.217892			−0.108946	+	0.994048i	$0.534748\pi$
$6$	−61.2528	−	10.4408i	−1.70147	−	0.290022i
$7$			31.1799i			0.636325i	0.948036	+	0.318163i	$0.103066\pi$
$7$			31.1799i			0.636325i	−0.948036	+	0.318163i	$0.896934\pi$
$8$	31.0473	−	55.9648i	0.485115	−	0.874450i
$9$	−160.307			−1.97910
$10$	3.66125	−	21.4794i	0.0366125	−	0.214794i
$11$			45.9071i			0.379398i	0.981842	+	0.189699i	$0.0607512\pi$
$11$			45.9071i			0.379398i	−0.981842	+	0.189699i	$0.939249\pi$
$12$	82.3387	−	234.510i	0.571797	−	1.62854i
$13$	7.06595			0.0418103			0.0209052	−	0.999781i	$-0.493345\pi$
$13$	7.06595			0.0418103			0.0209052	+	0.999781i	$0.493345\pi$
$14$	−122.946	−	20.9567i	−0.627278	−	0.106922i
$15$		−	84.6187i		−	0.376083i
$16$	199.809	+	160.039i	0.780503	+	0.625152i
$17$	382.648			1.32404			0.662021	−	0.749485i	$-0.269699\pi$
$17$	382.648			1.32404			0.662021	+	0.749485i	$0.269699\pi$
$18$	107.746	−	632.111i	0.332549	−	1.95096i
$19$		−	82.8191i		−	0.229416i
$19$		−	82.8191i		−	0.229416i
$20$	82.2352	+	28.8736i	0.205588	+	0.0721840i
$21$	−484.351			−1.09830
$22$	−181.018	−	30.8552i	−0.374004	−	0.0637504i
$23$		−	212.876i		−	0.402412i	−0.979549	−	0.201206i	$-0.935514\pi$
$23$		−	212.876i		−	0.402412i	0.979549	−	0.201206i	$-0.0644861\pi$
$24$	869.361	+	482.291i	1.50931	+	0.837311i
$25$	−595.327			−0.952523
$26$	−4.74918	+	27.8619i	−0.00702541	+	0.0412159i
$27$		−	1231.96i		−	1.68993i
$28$	165.270	−	470.708i	0.210804	−	0.600393i
$29$	−1486.95			−1.76807			−0.884037	−	0.467417i	$-0.845185\pi$
$29$	−1486.95			−1.76807			−0.884037	+	0.467417i	$0.845185\pi$
$30$	333.662	+	56.8741i	0.370736	+	0.0631935i
$31$			1115.61i			1.16089i	0.814301	+	0.580443i	$0.197120\pi$
$31$			1115.61i			1.16089i	−0.814301	+	0.580443i	$0.802880\pi$
$32$	−765.349	+	680.306i	−0.747412	+	0.664361i
$33$	−713.124			−0.654843
$34$	−257.186	+	1508.83i	−0.222479	+	1.30522i
$35$		−	169.847i		−	0.138650i
$36$	2420.07	+	849.712i	1.86734	+	0.655642i
$37$	720.780			0.526501			0.263251	−	0.964727i	$-0.415205\pi$
$37$	720.780			0.526501			0.263251	+	0.964727i	$0.415205\pi$
$38$	326.566	+	55.6645i	0.226154	+	0.0385489i
$39$			109.763i			0.0721649i
$40$	−169.124	+	304.857i	−0.105703	+	0.190536i
$41$	−679.649			−0.404312			−0.202156	−	0.979353i	$-0.564795\pi$
$41$	−679.649			−0.404312			−0.202156	+	0.979353i	$0.564795\pi$
$42$	325.543	−	1909.86i	0.184548	−	1.08269i
$43$		−	1515.76i		−	0.819771i	−0.912137	−	0.409885i	$-0.865569\pi$
$43$		−	1515.76i		−	0.819771i	0.912137	−	0.409885i	$-0.134431\pi$
$44$	243.332	−	693.037i	0.125688	−	0.357974i
$45$	873.241			0.431230
$46$	839.398	+	143.079i	0.396691	+	0.0676176i
$47$			3914.10i			1.77189i	0.463794	+	0.885943i	$0.346488\pi$
$47$			3914.10i			1.77189i	−0.463794	+	0.885943i	$0.653512\pi$
$48$	−2486.05	+	3103.84i	−1.07902	+	1.34715i
$49$	1428.81			0.595090
$50$	400.132	−	2347.45i	0.160053	−	0.938980i
$51$			5944.08i			2.28530i
$52$	−106.671	−	37.4532i	−0.0394494	−	0.0138510i
$53$	−3912.52			−1.39285			−0.696426	−	0.717628i	$-0.745228\pi$
$53$	−3912.52			−1.39285			−0.696426	+	0.717628i	$0.745228\pi$
$54$	4857.77	+	828.027i	1.66590	+	0.283960i
$55$		−	250.070i		−	0.0826678i
$56$	1744.98	+	968.055i	0.556435	+	0.308691i
$57$	1286.52			0.395973
$58$	999.412	−	5863.23i	0.297090	−	1.74294i
$59$			5161.44i			1.48275i	0.671092	+	0.741374i	$0.265825\pi$
$59$			5161.44i			1.48275i	−0.671092	+	0.741374i	$0.734175\pi$
$60$	−448.524	+	1277.45i	−0.124590	+	0.354846i
$61$	−1971.58			−0.529852			−0.264926	−	0.964269i	$-0.585348\pi$
$61$	−1971.58			−0.529852			−0.264926	+	0.964269i	$0.585348\pi$
$62$	−4398.99	−	749.827i	−1.14438	−	0.195064i
$63$		−	4998.36i		−	1.25935i
$64$	−2168.12	−	3475.12i	−0.529327	−	0.848418i
$65$	−38.4904			−0.00911014
$66$	479.307	−	2811.94i	0.110034	−	0.645533i
$67$		−	2697.51i		−	0.600917i	−0.953795	−	0.300458i	$-0.902860\pi$
$67$		−	2697.51i		−	0.600917i	0.953795	−	0.300458i	$-0.0971396\pi$
$68$	−5776.65	−	2028.24i	−1.24927	−	0.438632i
$69$	3306.83			0.694566
$70$	669.727	+	114.158i	0.136679	+	0.0232975i
$71$		−	7270.01i		−	1.44218i	−0.692843	−	0.721089i	$-0.743642\pi$
$71$		−	7270.01i		−	1.44218i	0.692843	−	0.721089i	$-0.256358\pi$
$72$	−4977.11	+	8971.55i	−0.960090	+	1.73062i
$73$	8385.78			1.57361			0.786806	−	0.617200i	$-0.211733\pi$
$73$	8385.78			1.57361			0.786806	+	0.617200i	$0.211733\pi$
$74$	−484.452	+	2842.13i	−0.0884683	+	0.519015i
$75$		−	9247.84i		−	1.64406i
$76$	−438.985	+	1250.28i	−0.0760015	+	0.216461i
$77$	−1431.38			−0.241421
$78$	−432.809	−	73.7740i	−0.0711388	−	0.0121259i
$79$			3245.82i			0.520081i	0.965598	+	0.260040i	$0.0837359\pi$
$79$			3245.82i			0.520081i	−0.965598	+	0.260040i	$0.916264\pi$
$80$	−1088.42	−	871.780i	−0.170066	−	0.136216i
$81$	6152.46			0.937733
$82$	456.807	−	2679.94i	0.0679368	−	0.398564i
$83$			11648.4i			1.69087i	0.534082	+	0.845433i	$0.320657\pi$
$83$			11648.4i			1.69087i	−0.534082	+	0.845433i	$0.679343\pi$
$84$	7312.01	+	2567.32i	1.03628	+	0.363849i
$85$	−2084.40			−0.288498
$86$	5976.82	+	1018.77i	0.808115	+	0.137747i
$87$		−	23098.4i		−	3.05171i
$88$	2569.19	+	1425.30i	0.331765	+	0.184052i
$89$	13361.9			1.68690			0.843449	−	0.537209i	$-0.180522\pi$
$89$	13361.9			1.68690			0.843449	+	0.537209i	$0.180522\pi$
$90$	−586.925	+	3443.30i	−0.0724598	+	0.425099i
$91$			220.316i			0.0266050i
$92$	−1128.36	+	3213.69i	−0.133312	+	0.379689i
$93$	−17330.0			−2.00370
$94$	−15433.8	−	2630.75i	−1.74669	−	0.297731i
$95$			451.141i			0.0499879i
$96$	−10567.9	−	11889.0i	−1.14669	−	1.29004i
$97$	−3764.95			−0.400143			−0.200072	−	0.979781i	$-0.564117\pi$
$97$	−3764.95			−0.400143			−0.200072	+	0.979781i	$0.564117\pi$
$98$	−960.336	+	5633.98i	−0.0999933	+	0.586629i
$99$		−	7359.24i		−	0.750866i
$100$	8987.35	+	3155.55i	0.898735	+	0.315555i
$101$	−2882.53			−0.282573			−0.141287	−	0.989969i	$-0.545124\pi$
$101$	−2882.53			−0.282573			−0.141287	+	0.989969i	$0.545124\pi$
$102$	−23438.3	−	3995.15i	−2.25281	−	0.384001i
$103$		−	2994.43i		−	0.282254i	−0.989992	−	0.141127i	$-0.954927\pi$
$103$		−	2994.43i		−	0.282254i	0.989992	−	0.141127i	$-0.0450725\pi$
$104$	219.379	−	395.444i	0.0202828	−	0.0365611i
$105$	2638.41			0.239311
$106$	2629.69	−	15427.6i	0.234042	−	1.37305i
$107$			15390.7i			1.34428i	0.740423	+	0.672141i	$0.234625\pi$
$107$			15390.7i			1.34428i	−0.740423	+	0.672141i	$0.765375\pi$
$108$	−6530.03	+	18598.3i	−0.559845	+	1.59450i
$109$	11597.8			0.976160			0.488080	−	0.872799i	$-0.337697\pi$
$109$	11597.8			0.976160			0.488080	+	0.872799i	$0.337697\pi$
$110$	986.059	+	168.078i	0.0814924	+	0.0138907i
$111$			11196.6i			0.908745i
$112$	−4990.00	+	6230.03i	−0.397800	+	0.496654i
$113$	1343.71			0.105232			0.0526160	−	0.998615i	$-0.483244\pi$
$113$	1343.71			0.105232			0.0526160	+	0.998615i	$0.483244\pi$
$114$	−864.696	+	5072.90i	−0.0665356	+	0.390343i
$115$			1159.60i			0.0876825i
$116$	22447.8	+	7881.62i	1.66823	+	0.585733i
$117$	−1132.72			−0.0827468
$118$	−20352.2	−	3469.12i	−1.46167	−	0.249147i
$119$			11930.9i			0.842521i
$120$	−4735.67	−	2627.19i	−0.328866	−	0.182444i
$121$	12533.5			0.856057
$122$	1325.14	−	7774.19i	0.0890313	−	0.522318i
$123$		−	10557.7i		−	0.697846i
$124$	5913.32	−	16841.8i	0.384581	−	1.09533i
$125$	6647.49			0.425439
$126$	19709.2	+	3359.51i	1.24145	+	0.211609i
$127$			23136.6i			1.43447i	0.696831	+	0.717235i	$0.254593\pi$
$127$			23136.6i			1.43447i	−0.696831	+	0.717235i	$0.745407\pi$
$128$	15160.1	−	6213.49i	0.925298	−	0.379241i
$129$	23545.8			1.41493
$130$	25.8702	−	151.772i	0.00153078	−	0.00898061i
$131$			17903.0i			1.04324i	0.853179	+	0.521619i	$0.174672\pi$
$131$			17903.0i			1.04324i	−0.853179	+	0.521619i	$0.825328\pi$
$132$	10765.7	+	3779.93i	0.617865	+	0.216938i
$133$	2582.29			0.145983
$134$	10636.6	+	1813.06i	0.592373	+	0.100972i
$135$			6710.86i			0.368223i
$136$	11880.2	−	21414.8i	0.642312	−	1.15781i
$137$	8192.37			0.436484			0.218242	−	0.975895i	$-0.429968\pi$
$137$	8192.37			0.436484			0.218242	+	0.975895i	$0.429968\pi$
$138$	−2222.59	+	13039.3i	−0.116708	+	0.684691i
$139$		−	18723.6i		−	0.969080i	−0.874769	−	0.484540i	$-0.838987\pi$
$139$		−	18723.6i		−	0.969080i	0.874769	−	0.484540i	$-0.161013\pi$
$140$	−900.277	+	2564.09i	−0.0459325	+	0.130821i
$141$	−60801.8			−3.05829
$142$	28666.6	+	4886.34i	1.42167	+	0.242330i
$143$			324.377i			0.0158628i
$144$	−32030.8	−	25655.3i	−1.54469	−	1.23724i
$145$	8099.87			0.385249
$146$	−5636.27	+	33066.2i	−0.264415	+	1.55124i
$147$			22195.2i			1.02713i
$148$	−10881.3	−	3820.51i	−0.496770	−	0.174421i
$149$	1309.10			0.0589658			0.0294829	−	0.999565i	$-0.490614\pi$
$149$	1309.10			0.0589658			0.0294829	+	0.999565i	$0.490614\pi$
$150$	36465.4	+	6215.68i	1.62069	+	0.276252i
$151$			2342.68i			0.102745i	0.998680	+	0.0513723i	$0.0163595\pi$
$151$			2342.68i			0.102745i	−0.998680	+	0.0513723i	$0.983640\pi$
$152$	−4634.96	−	2571.31i	−0.200613	−	0.111293i
$153$	−61341.2			−2.62041
$154$	962.064	−	5644.12i	0.0405660	−	0.237988i
$155$		−	6077.07i		−	0.252948i
$156$	581.801	−	1657.03i	0.0239070	−	0.0680899i
$157$	32923.6			1.33570			0.667848	−	0.744298i	$-0.267216\pi$
$157$	32923.6			1.33570			0.667848	+	0.744298i	$0.267216\pi$
$158$	−12798.7	−	2181.59i	−0.512686	−	0.0873895i
$159$		−	60777.4i		−	2.40407i
$160$	4169.09	−	3705.83i	0.162855	−	0.144759i
$161$	6637.47			0.256065
$162$	−4135.21	+	24259.9i	−0.157568	+	0.924400i
$163$		−	14476.5i		−	0.544866i	−0.962175	−	0.272433i	$-0.912172\pi$
$163$		−	14476.5i		−	0.544866i	0.962175	−	0.272433i	$-0.0878283\pi$
$164$	10260.3	+	3602.50i	0.381481	+	0.133942i
$165$	3884.61			0.142685
$166$	−45931.0	−	7829.13i	−1.66682	−	0.284117i
$167$			8418.63i			0.301862i	0.988544	+	0.150931i	$0.0482272\pi$
$167$			8418.63i			0.301862i	−0.988544	+	0.150931i	$0.951773\pi$
$168$	−15037.8	+	27106.6i	−0.532802	+	0.960411i
$169$	−28511.1			−0.998252
$170$	1400.97	−	8219.05i	0.0484765	−	0.284396i
$171$			13276.5i			0.454036i
$172$	−8034.30	+	22882.6i	−0.271576	+	0.773479i
$173$	−51620.6			−1.72477			−0.862385	−	0.506253i	$-0.831030\pi$
$173$	−51620.6			−1.72477			−0.862385	+	0.506253i	$0.831030\pi$
$174$	91079.8	+	15524.9i	3.00832	+	0.512780i
$175$		−	18562.3i		−	0.606115i
$176$	−7346.93	+	9172.65i	−0.237181	+	0.296121i
$177$	−80178.2			−2.55923
$178$	−8980.84	+	52687.7i	−0.283450	+	1.66291i
$179$			10535.4i			0.328810i	0.986393	+	0.164405i	$0.0525704\pi$
$179$			10535.4i			0.328810i	−0.986393	+	0.164405i	$0.947430\pi$
$180$	−13182.9	−	4628.64i	−0.406879	−	0.142859i
$181$	2807.39			0.0856929			0.0428465	−	0.999082i	$-0.486357\pi$
$181$	2807.39			0.0856929			0.0428465	+	0.999082i	$0.486357\pi$
$182$	−868.733	−	148.079i	−0.0262267	−	0.00447045i
$183$		−	30626.6i		−	0.914528i
$184$	−11913.6	−	6609.24i	−0.351890	−	0.195216i
$185$	−3926.31			−0.114720
$186$	11647.9	−	68334.2i	0.336682	−	1.97521i
$187$			17566.3i			0.502339i
$188$	20746.8	−	59089.2i	0.586996	−	1.67183i
$189$	38412.4			1.07535
$190$	−1778.91	−	303.222i	−0.0492771	−	0.00839949i
$191$		−	10934.7i		−	0.299737i	−0.988706	−	0.149868i	$-0.952115\pi$
$191$		−	10934.7i		−	0.299737i	0.988706	−	0.149868i	$-0.0478850\pi$
$192$	53982.7	−	33679.8i	1.46437	−	0.913622i
$193$	−18564.3			−0.498384			−0.249192	−	0.968454i	$-0.580165\pi$
$193$	−18564.3			−0.498384			−0.249192	+	0.968454i	$0.580165\pi$
$194$	2530.50	−	14845.7i	0.0672363	−	0.394454i
$195$		−	597.911i		−	0.0157242i
$196$	−21570.1	−	7573.45i	−0.561486	−	0.197143i
$197$	39930.8			1.02891			0.514453	−	0.857519i	$-0.327995\pi$
$197$	39930.8			1.02891			0.514453	+	0.857519i	$0.327995\pi$
$198$	29018.4	+	4946.31i	0.740190	+	0.126168i
$199$		−	45870.3i		−	1.15831i	−0.815217	−	0.579156i	$-0.803382\pi$
$199$		−	45870.3i		−	1.15831i	0.815217	−	0.579156i	$-0.196618\pi$
$200$	−18483.3	+	33317.4i	−0.462083	+	0.832934i
$201$	41903.4			1.03719
$202$	1937.41	−	11366.2i	0.0474810	−	0.278556i
$203$		−	46363.0i		−	1.12507i
$204$	31506.7	−	89734.8i	0.757082	−	2.15626i
$205$	3702.25			0.0880965
$206$	11807.4	+	2012.62i	0.278240	+	0.0474272i
$207$			34125.5i			0.796414i
$208$	1411.84	+	1130.83i	0.0326331	+	0.0261378i
$209$	3801.99			0.0870399
$210$	−1773.33	+	10403.6i	−0.0402116	+	0.235909i
$211$			44200.3i			0.992797i	0.868095	+	0.496398i	$0.165344\pi$
$211$			44200.3i			0.992797i	−0.868095	+	0.496398i	$0.834656\pi$
$212$	59065.4	+	20738.4i	1.31420	+	0.461428i
$213$	112933.			2.48921
$214$	−60687.4	−	10344.4i	−1.32517	−	0.225881i
$215$			8256.78i			0.178622i
$216$	−68946.4	−	38249.1i	−1.47776	−	0.819810i
$217$	−34784.7			−0.738701
$218$	−7795.11	+	45731.4i	−0.164025	+	0.962281i
$219$			130265.i			2.71607i
$220$	−1325.50	+	3775.19i	−0.0273864	+	0.0779997i
$221$	2703.77			0.0553586
$222$	−44149.8	−	7525.51i	−0.895824	−	0.152697i
$223$		−	36075.9i		−	0.725451i	−0.931896	−	0.362725i	$-0.881846\pi$
$223$		−	36075.9i		−	0.725451i	0.931896	−	0.362725i	$-0.118154\pi$
$224$	−21211.9	−	23863.6i	−0.422750	−	0.475597i
$225$	95435.1			1.88514
$226$	−903.136	+	5298.41i	−0.0176822	+	0.103736i
$227$			37041.6i			0.718850i	0.933174	+	0.359425i	$0.117027\pi$
$227$			37041.6i			0.718850i	−0.933174	+	0.359425i	$0.882973\pi$
$228$	−19421.9	−	6819.22i	−0.373613	−	0.131179i
$229$	−43511.1			−0.829715			−0.414857	−	0.909886i	$-0.636169\pi$
$229$	−43511.1			−0.829715			−0.414857	+	0.909886i	$0.636169\pi$
$230$	−4572.45	−	779.394i	−0.0864358	−	0.0147333i
$231$		−	22235.2i		−	0.416693i
$232$	−46165.9	+	83216.9i	−0.857719	+	1.54609i
$233$	−71305.0			−1.31343			−0.656717	−	0.754137i	$-0.728055\pi$
$233$	−71305.0			−1.31343			−0.656717	+	0.754137i	$0.728055\pi$
$234$	761.327	−	4466.46i	0.0139040	−	0.0815702i
$235$		−	21321.3i		−	0.386080i
$236$	27358.4	−	77919.8i	0.491209	−	1.39902i
$237$	−50420.8			−0.897663
$238$	−47045.2	−	8019.05i	−0.830542	−	0.141569i
$239$			42566.9i			0.745206i	0.927991	+	0.372603i	$0.121535\pi$
$239$			42566.9i			0.745206i	−0.927991	+	0.372603i	$0.878465\pi$
$240$	13542.3	−	16907.6i	0.235109	−	0.293534i
$241$	101364.			1.74521			0.872606	−	0.488424i	$-0.162428\pi$
$241$	101364.			1.74521			0.872606	+	0.488424i	$0.162428\pi$
$242$	−8424.07	+	49421.3i	−0.143844	+	0.843886i
$243$		−	4215.97i		−	0.0713979i
$244$	29763.9	+	10450.4i	0.499932	+	0.175531i
$245$	−7783.17			−0.129665
$246$	41630.4	+	7096.07i	0.687923	+	0.117259i
$247$		−	585.195i		−	0.00959195i
$248$	62435.0	+	34636.7i	1.01514	+	0.563163i
$249$	−180947.			−2.91845
$250$	−4467.93	+	26211.9i	−0.0714868	+	0.419390i
$251$			34027.9i			0.540117i	0.962844	+	0.270059i	$0.0870431\pi$
$251$			34027.9i			0.540117i	−0.962844	+	0.270059i	$0.912957\pi$
$252$	−26494.0	+	75457.8i	−0.417201	+	1.18824i
$253$	9772.54			0.152674
$254$	−91230.5	−	15550.6i	−1.41408	−	0.241035i
$255$		−	32379.2i		−	0.497950i
$256$	14311.1	+	63954.3i	0.218371	+	0.975866i
$257$	−6228.83			−0.0943061			−0.0471531	−	0.998888i	$-0.515015\pi$
$257$	−6228.83			−0.0943061			−0.0471531	+	0.998888i	$0.515015\pi$
$258$	−15825.7	+	92844.2i	−0.237751	+	1.39481i
$259$			22473.9i			0.335026i
$260$	581.070	+	204.019i	0.00859571	+	0.00301803i
$261$	238369.			3.49919
$262$	−70593.8	−	12033.0i	−1.02841	−	0.175296i
$263$		−	114845.i		−	1.66036i	−0.557496	−	0.830180i	$-0.688238\pi$
$263$		−	114845.i		−	1.66036i	0.557496	−	0.830180i	$-0.311762\pi$
$264$	−22140.6	+	39909.9i	−0.317674	+	0.572628i
$265$	21312.7			0.303492
$266$	−1735.62	+	10182.3i	−0.0245296	+	0.143907i
$267$			207565.i			2.91160i
$268$	−14298.2	+	40723.0i	−0.199073	+	0.566984i
$269$	31165.1			0.430690			0.215345	−	0.976538i	$-0.430912\pi$
$269$	31165.1			0.430690			0.215345	+	0.976538i	$0.430912\pi$
$270$	−26461.8	−	4510.52i	−0.362987	−	0.0618727i
$271$		−	7569.90i		−	0.103075i	−0.998671	−	0.0515373i	$-0.983588\pi$
$271$		−	7569.90i		−	0.103075i	0.998671	−	0.0515373i	$-0.0164121\pi$
$272$	76456.5	+	61238.6i	1.03342	+	0.827727i
$273$	−3422.40			−0.0459204
$274$	−5506.28	+	32303.6i	−0.0733427	+	0.430278i
$275$		−	27329.8i		−	0.361385i
$276$	−49921.6	−	17527.9i	−0.655345	−	0.230098i
$277$	61436.1			0.800690			0.400345	−	0.916365i	$-0.368890\pi$
$277$	61436.1			0.800690			0.400345	+	0.916365i	$0.368890\pi$
$278$	73829.5	+	12584.5i	0.955301	+	0.162835i
$279$		−	178840.i		−	2.29751i
$280$	−9505.44	−	5273.29i	−0.121243	−	0.0672613i
$281$	21599.9			0.273551			0.136776	−	0.990602i	$-0.456326\pi$
$281$	21599.9			0.273551			0.136776	+	0.990602i	$0.456326\pi$
$282$	40866.2	−	239749.i	0.513886	−	3.01480i
$283$		−	111225.i		−	1.38877i	−0.719605	−	0.694384i	$-0.755677\pi$
$283$		−	111225.i		−	1.38877i	0.719605	−	0.694384i	$-0.244323\pi$
$284$	−38534.9	+	109752.i	−0.477769	+	1.36074i
$285$	−7008.05			−0.0862794
$286$	−1279.06	−	218.021i	−0.0156372	−	0.00266543i
$287$		−	21191.4i		−	0.257274i
$288$	122691.	−	109058.i	1.47920	−	1.31484i
$289$	62898.5			0.753086
$290$	−5444.10	+	31938.8i	−0.0647337	+	0.379772i
$291$		−	58484.9i		−	0.690650i
$292$	−126596.	−	44449.1i	−1.48475	−	0.521311i
$293$	−109684.			−1.27764			−0.638819	−	0.769357i	$-0.720577\pi$
$293$	−109684.			−1.27764			−0.638819	+	0.769357i	$0.720577\pi$
$294$	−87518.6	−	14917.9i	−1.01253	−	0.172589i
$295$		−	28116.0i		−	0.323079i
$296$	22378.3	−	40338.3i	0.255414	−	0.460399i
$297$	56555.7			0.641156
$298$	−879.875	+	5161.95i	−0.00990805	+	0.0581274i
$299$		−	1504.17i		−	0.0168250i
$300$	−49018.4	+	139610.i	−0.544649	+	1.55122i
$301$	47261.2			0.521641
$302$	−9237.48	−	1574.57i	−0.101284	−	0.0172642i
$303$		−	44777.4i		−	0.487723i
$304$	13254.3	−	16548.0i	0.143420	−	0.179060i
$305$	10739.8			0.115451
$306$	41228.8	−	241876.i	0.440309	−	2.58315i
$307$			29663.4i			0.314734i	0.987540	+	0.157367i	$0.0503006\pi$
$307$			29663.4i			0.314734i	−0.987540	+	0.157367i	$0.949699\pi$
$308$	21608.9	+	7587.08i	0.227788	+	0.0799785i
$309$	46515.6			0.487171
$310$	23962.7	+	4084.53i	0.249351	+	0.0425030i
$311$			142527.i			1.47359i	0.676118	+	0.736793i	$0.263661\pi$
$311$			142527.i			1.47359i	−0.676118	+	0.736793i	$0.736339\pi$
$312$	6142.86	+	3407.84i	0.0631046	+	0.0350083i
$313$	110114.			1.12397			0.561985	−	0.827148i	$-0.310038\pi$
$313$	110114.			1.12397			0.561985	+	0.827148i	$0.310038\pi$
$314$	−22128.7	+	129822.i	−0.224438	+	1.31671i
$315$			27227.6i			0.274403i
$316$	17204.6	−	49000.6i	0.172294	−	0.490713i
$317$	−122249.			−1.21654			−0.608270	−	0.793730i	$-0.708136\pi$
$317$	−122249.			−1.21654			−0.608270	+	0.793730i	$0.708136\pi$
$318$	239653.	+	40849.8i	2.36989	+	0.403958i
$319$		−	68261.7i		−	0.670804i
$320$	11810.4	+	18930.0i	0.115336	+	0.184864i
$321$	−239080.			−2.32024
$322$	−4461.19	+	26172.4i	−0.0430268	+	0.252424i
$323$		−	31690.6i		−	0.303756i
$324$	−92880.7	−	32611.3i	−0.884780	−	0.310655i
$325$	−4206.55			−0.0398253
$326$	57082.9	+	9730.01i	0.537119	+	0.0915542i
$327$			180160.i			1.68486i
$328$	−21101.3	+	38036.4i	−0.196138	+	0.353551i
$329$	−122041.			−1.12750
$330$	−2610.93	+	15317.5i	−0.0239755	+	0.140656i
$331$			34223.8i			0.312372i	0.987728	+	0.156186i	$0.0499199\pi$
$331$			34223.8i			0.312372i	−0.987728	+	0.156186i	$0.950080\pi$
$332$	61742.5	−	175850.i	0.560155	−	1.59539i
$333$	−115546.			−1.04200
$334$	−33195.7	−	5658.35i	−0.297570	−	0.0507221i
$335$			14694.2i			0.130935i
$336$	−96777.6	−	77515.0i	−0.857228	−	0.686605i
$337$	−32675.8			−0.287717			−0.143859	−	0.989598i	$-0.545951\pi$
$337$	−32675.8			−0.287717			−0.143859	+	0.989598i	$0.545951\pi$
$338$	19162.9	−	112423.i	0.167737	−	0.984059i
$339$			20873.2i			0.181631i
$340$	31467.2	+	11048.4i	0.272207	+	0.0955746i
$341$	−51214.5			−0.440437
$342$	−52350.8	−	8923.42i	−0.447581	−	0.0762920i
$343$			119413.i			1.01500i
$344$	−84829.0	−	47060.2i	−0.716849	−	0.397683i
$345$	−18013.3			−0.151341
$346$	34695.4	−	203547.i	0.289814	−	1.70025i
$347$		−	158863.i		−	1.31936i	−0.751545	−	0.659682i	$-0.770691\pi$
$347$		−	158863.i		−	1.31936i	0.751545	−	0.659682i	$-0.229309\pi$
$348$	−122434.	+	348705.i	−1.01098	+	2.87938i
$349$	68012.4			0.558390			0.279195	−	0.960234i	$-0.409932\pi$
$349$	68012.4			0.558390			0.279195	+	0.960234i	$0.409932\pi$
$350$	73193.3	+	12476.1i	0.597497	+	0.101846i
$351$		−	8704.96i		−	0.0706566i
$352$	−31230.9	−	35135.0i	−0.252057	−	0.283566i
$353$	171339.			1.37501			0.687506	−	0.726179i	$-0.258706\pi$
$353$	171339.			1.37501			0.687506	+	0.726179i	$0.258706\pi$
$354$	53889.5	−	316153.i	0.430029	−	2.52284i
$355$			39602.0i			0.314239i
$356$	−201718.	−	70825.2i	−1.59164	−	0.558840i
$357$	−185336.			−1.45420
$358$	−41542.4	−	7081.07i	−0.324135	−	0.0552501i
$359$		−	96492.1i		−	0.748692i	−0.927289	−	0.374346i	$-0.877867\pi$
$359$		−	96492.1i		−	0.748692i	0.927289	−	0.374346i	$-0.122133\pi$
$360$	27111.8	−	48870.8i	0.209196	−	0.377089i
$361$	−6859.00			−0.0526316
$362$	−1886.91	+	11069.9i	−0.0143990	+	0.0844745i
$363$			194697.i			1.47756i
$364$	1167.79	−	3326.00i	0.00881377	−	0.0251026i
$365$	−45679.9			−0.342878
$366$	120765.	+	20584.8i	0.901525	+	0.153669i
$367$		−	45059.2i		−	0.334542i	−0.985911	−	0.167271i	$-0.946504\pi$
$367$		−	45059.2i		−	0.334542i	0.985911	−	0.167271i	$-0.0534956\pi$
$368$	34068.5	−	42534.5i	0.251569	−	0.314084i
$369$	108952.			0.800174
$370$	2638.96	−	15481.9i	0.0192765	−	0.113089i
$371$		−	121992.i		−	0.886307i
$372$	261622.	+	91857.9i	1.89055	+	0.663790i
$373$	179898.			1.29303			0.646515	−	0.762901i	$-0.276226\pi$
$373$	179898.			1.29303			0.646515	+	0.762901i	$0.276226\pi$
$374$	−69266.1	−	11806.7i	−0.495196	−	0.0844082i
$375$			103263.i			0.734311i
$376$	219052.	+	121522.i	1.54943	+	0.859568i
$377$	−10506.7			−0.0739238
$378$	−25817.8	+	151465.i	−0.180691	+	1.06006i
$379$		−	19852.0i		−	0.138206i	−0.997610	−	0.0691029i	$-0.977986\pi$
$379$		−	19852.0i		−	0.138206i	0.997610	−	0.0691029i	$-0.0220137\pi$
$380$	2391.28	−	6810.65i	0.0165601	−	0.0471651i
$381$	−359405.			−2.47591
$382$	43116.9	+	7349.46i	0.295475	+	0.0503650i
$383$		−	158061.i		−	1.07753i	−0.842457	−	0.538764i	$-0.818891\pi$
$383$		−	158061.i		−	1.07753i	0.842457	−	0.538764i	$-0.181109\pi$
$384$	96520.6	+	235498.i	0.654573	+	1.59707i
$385$	7797.17			0.0526036
$386$	12477.5	−	73201.4i	0.0837438	−	0.491298i
$387$			242986.i			1.62241i
$388$	56837.5	+	19956.2i	0.377548	+	0.132561i
$389$	−10695.6			−0.0706813			−0.0353406	−	0.999375i	$-0.511252\pi$
$389$	−10695.6			−0.0706813			−0.0353406	+	0.999375i	$0.511252\pi$
$390$	2357.64	+	401.870i	0.0155006	+	0.00264214i
$391$		−	81456.6i		−	0.532811i
$392$	44360.8	−	79963.2i	0.288687	−	0.520377i
$393$	−278106.			−1.80064
$394$	−26838.4	+	157452.i	−0.172888	+	1.01428i
$395$		−	17681.0i		−	0.113322i
$396$	−39007.8	+	111099.i	−0.248749	+	0.708466i
$397$	82051.8			0.520604			0.260302	−	0.965527i	$-0.416178\pi$
$397$	82051.8			0.520604			0.260302	+	0.965527i	$0.416178\pi$
$398$	180873.	+	30830.5i	1.14184	+	0.194632i
$399$			40113.5i			0.251968i
$400$	−118952.	−	95275.4i	−0.743447	−	0.595471i
$401$	146978.			0.914036			0.457018	−	0.889458i	$-0.348918\pi$
$401$	146978.			0.914036			0.457018	+	0.889458i	$0.348918\pi$
$402$	−28164.2	+	165230.i	−0.174279	+	1.02244i
$403$			7882.84i			0.0485370i
$404$	43516.1	+	15278.9i	0.266617	+	0.0936117i
$405$	−33514.3			−0.204325
$406$	182815.	+	31161.6i	1.10907	+	0.189046i
$407$			33089.0i			0.199753i
$408$	332659.	+	184548.i	1.99839	+	1.10864i
$409$	−95540.6			−0.571139			−0.285569	−	0.958358i	$-0.592183\pi$
$409$	−95540.6			−0.571139			−0.285569	+	0.958358i	$0.592183\pi$
$410$	−2488.37	+	14598.5i	−0.0148029	+	0.0868439i
$411$			127261.i			0.753375i
$412$	−15872.0	+	45205.4i	−0.0935058	+	0.266315i
$413$	−160934.			−0.943510
$414$	−134561.	−	22936.5i	−0.785090	−	0.133822i
$415$		−	63452.2i		−	0.368426i
$416$	−5407.92	+	4807.00i	−0.0312495	+	0.0277772i
$417$	290853.			1.67264
$418$	−2555.40	+	14991.7i	−0.0146254	+	0.0858023i
$419$			4575.70i			0.0260633i	0.999915	+	0.0130316i	$0.00414822\pi$
$419$			4575.70i			0.0260633i	−0.999915	+	0.0130316i	$0.995852\pi$
$420$	−39830.7	−	13985.0i	−0.225798	−	0.0792798i
$421$	223411.			1.26049			0.630246	−	0.776395i	$-0.282954\pi$
$421$	223411.			1.26049			0.630246	+	0.776395i	$0.282954\pi$
$422$	−174287.	−	29708.0i	−0.978681	−	0.166820i
$423$		−	627457.i		−	3.50674i
$424$	−121473.	+	218964.i	−0.675693	+	1.21798i
$425$	−227801.			−1.26118
$426$	−75904.7	+	445309.i	−0.418263	+	2.45381i
$427$		−	61473.7i		−	0.337158i
$428$	81578.8	−	232346.i	0.445338	−	1.26837i
$429$	−5038.90			−0.0273792
$430$	−32557.5	−	5549.57i	−0.176082	−	0.0300139i
$431$			115385.i			0.621147i	0.950549	+	0.310573i	$0.100521\pi$
$431$			115385.i			0.621147i	−0.950549	+	0.310573i	$0.899479\pi$
$432$	197161.	−	246156.i	1.05646	−	1.31900i
$433$	360178.			1.92106			0.960531	−	0.278172i	$-0.0897284\pi$
$433$	360178.			1.92106			0.960531	+	0.278172i	$0.0897284\pi$
$434$	23379.6	−	137160.i	0.124124	−	0.728198i
$435$			125824.i			0.664943i
$436$	−175086.	−	61474.2i	−0.921038	−	0.323385i
$437$	−17630.2			−0.0923197
$438$	−513652.	−	87554.2i	−2.67745	−	0.456382i
$439$			289556.i			1.50246i	0.660040	+	0.751231i	$0.270539\pi$
$439$			289556.i			1.50246i	−0.660040	+	0.751231i	$0.729461\pi$
$440$	−13995.1	−	7764.02i	−0.0722889	−	0.0401034i
$441$	−229048.			−1.17774
$442$	−1817.26	+	10661.3i	−0.00930194	+	0.0545715i
$443$			127370.i			0.649023i	0.945882	+	0.324512i	$0.105200\pi$
$443$			127370.i			0.649023i	−0.945882	+	0.324512i	$0.894800\pi$
$444$	59348.1	−	169030.i	0.301052	−	0.857429i
$445$	−72786.4			−0.367562
$446$	142252.	+	24247.4i	0.715136	+	0.121898i
$447$			20335.6i			0.101775i
$448$	108354.	−	67602.0i	0.539870	−	0.336824i
$449$	13976.1			0.0693255			0.0346627	−	0.999399i	$-0.488964\pi$
$449$	13976.1			0.0693255			0.0346627	+	0.999399i	$0.488964\pi$
$450$	−64144.0	+	376313.i	−0.316761	+	1.85833i
$451$		−	31200.7i		−	0.153395i
$452$	−20285.3	−	7122.36i	−0.0992897	−	0.0348616i
$453$	−36391.3			−0.177338
$454$	−146060.	−	24896.5i	−0.708630	−	0.120789i
$455$		−	1200.13i		−	0.00579702i
$456$	39942.9	−	71999.7i	0.192092	−	0.346259i
$457$	259414.			1.24211			0.621057	−	0.783766i	$-0.286704\pi$
$457$	259414.			1.24211			0.621057	+	0.783766i	$0.286704\pi$
$458$	29244.8	−	171570.i	0.139417	−	0.817918i
$459$		−	471407.i		−	2.23754i
$460$	6146.50	−	17505.9i	0.0290477	−	0.0827312i
$461$	−203781.			−0.958876			−0.479438	−	0.877576i	$-0.659160\pi$
$461$	−203781.			−0.958876			−0.479438	+	0.877576i	$0.659160\pi$
$462$	87676.1	+	14944.8i	0.410769	+	0.0700172i
$463$			37984.0i			0.177190i	0.996068	+	0.0885949i	$0.0282376\pi$
$463$			37984.0i			0.177190i	−0.996068	+	0.0885949i	$0.971762\pi$
$464$	−297106.	−	237970.i	−1.37999	−	1.10531i
$465$	94401.6			0.436589
$466$	47925.7	−	281165.i	0.220697	−	1.29476i
$467$			188677.i			0.865139i	0.901601	+	0.432569i	$0.142393\pi$
$467$			188677.i			0.865139i	−0.901601	+	0.432569i	$0.857607\pi$
$468$	17100.1	+	6004.02i	0.0780742	+	0.0274126i
$469$	84108.4			0.382379
$470$	84072.5	+	14330.5i	0.380591	+	0.0648732i
$471$			511437.i			2.30542i
$472$	288859.	+	160249.i	1.29659	+	0.719303i
$473$	69584.0			0.311019
$474$	33889.0	−	198816.i	0.150835	−	0.884900i
$475$			49304.4i			0.218524i
$476$	63240.3	−	180116.i	0.279113	−	0.794945i
$477$	627205.			2.75659
$478$	−167847.	−	28610.2i	−0.734610	−	0.125217i
$479$		−	241805.i		−	1.05389i	−0.849900	−	0.526943i	$-0.823338\pi$
$479$		−	241805.i		−	1.05389i	0.849900	−	0.526943i	$-0.176662\pi$
$480$	57566.6	+	64762.9i	0.249855	+	0.281089i
$481$	5092.99			0.0220132
$482$	−68128.8	+	399690.i	−0.293249	+	1.72040i
$483$			103107.i			0.441970i
$484$	−189213.	−	66434.3i	−0.807717	−	0.283597i
$485$	20508.8			0.0871880
$486$	16624.1	+	2833.65i	0.0703827	+	0.0119970i
$487$		−	4265.26i		−	0.0179840i	−0.999960	−	0.00899202i	$-0.997138\pi$
$487$		−	4265.26i		−	0.0179840i	0.999960	−	0.00899202i	$-0.00286229\pi$
$488$	−61212.3	+	110339.i	−0.257039	+	0.463329i
$489$	224880.			0.940443
$490$	5231.24	−	30690.0i	0.0217878	−	0.127822i
$491$			265426.i			1.10098i	0.834841	+	0.550492i	$0.185560\pi$
$491$			265426.i			1.10098i	−0.834841	+	0.550492i	$0.814440\pi$
$492$	−55961.4	+	159384.i	−0.231184	+	0.658439i
$493$	−568979.			−2.34100
$494$	2307.50	+	393.323i	0.00945557	+	0.00161174i
$495$			40088.0i			0.163608i
$496$	−178541.	+	222909.i	−0.725729	+	0.906075i
$497$	226679.			0.917694
$498$	121618.	−	713495.i	0.490388	−	2.87695i
$499$			331646.i			1.33191i	0.745993	+	0.665954i	$0.231975\pi$
$499$			331646.i			1.33191i	−0.745993	+	0.665954i	$0.768025\pi$
$500$	−100354.	−	35235.2i	−0.401415	−	0.140941i
$501$	−130776.			−0.521016
$502$	−134176.	−	22870.9i	−0.532438	−	0.0907562i
$503$		−	412793.i		−	1.63153i	−0.578381	−	0.815767i	$-0.696315\pi$
$503$		−	412793.i		−	1.63153i	0.578381	−	0.815767i	$-0.303685\pi$
$504$	−279733.	−	155186.i	−1.10124	−	0.610930i
$505$	15702.0			0.0615705
$506$	−6568.34	+	38534.4i	−0.0256540	+	0.150504i
$507$		−	442893.i		−	1.72299i
$508$	122636.	−	349281.i	0.475216	−	1.35347i
$509$	−231234.			−0.892515			−0.446257	−	0.894905i	$-0.647243\pi$
$509$	−231234.			−0.892515			−0.446257	+	0.894905i	$0.647243\pi$
$510$	127675.	+	21762.8i	0.490870	+	0.0836708i
$511$			261468.i			1.00133i
$512$	−261799.	+	13445.5i	−0.998684	+	0.0512904i
$513$	−102030.			−0.387697
$514$	4186.53	−	24561.1i	0.0158463	−	0.0929653i
$515$			16311.6i			0.0615008i
$516$	−355460.	−	124805.i	−1.33503	−	0.468742i
$517$	−179685.			−0.672250
$518$	−88617.4	−	15105.2i	−0.330263	−	0.0562946i
$519$		−	801878.i		−	2.97696i
$520$	−1195.02	+	2154.11i	−0.00441946	+	0.00796637i
$521$	485238.			1.78764			0.893819	−	0.448428i	$-0.148016\pi$
$521$	485238.			1.78764			0.893819	+	0.448428i	$0.148016\pi$
$522$	−160213.	+	939917.i	−0.587971	+	3.44944i
$523$		−	91506.2i		−	0.334539i	−0.985911	−	0.167270i	$-0.946505\pi$
$523$		−	91506.2i		−	0.334539i	0.985911	−	0.167270i	$-0.0534951\pi$
$524$	94895.4	−	270273.i	0.345607	−	0.984328i
$525$	288347.			1.04616
$526$	452850.	+	77190.2i	1.63675	+	0.278991i
$527$			426886.i			1.53706i
$528$	−142489.	−	114128.i	−0.511107	−	0.409376i
$529$	234525.			0.838064
$530$	−14324.7	+	84038.7i	−0.0509959	+	0.299176i
$531$		−	827416.i		−	2.93450i
$532$	−38983.6	−	13687.5i	−0.137740	−	0.0483617i
$533$	−4802.36			−0.0169044
$534$	−818454.	−	139509.i	−2.87020	−	0.489237i
$535$		−	83837.8i		−	0.292909i
$536$	−150966.	−	83750.7i	−0.525472	−	0.291514i
$537$	−163657.			−0.567528
$538$	−20946.8	+	122888.i	−0.0723690	+	0.424566i
$539$			65592.6i			0.225776i
$540$	35571.1	−	101310.i	0.121986	−	0.347430i
$541$	−393983.			−1.34612			−0.673059	−	0.739589i	$-0.735020\pi$
$541$	−393983.			−1.34612			−0.673059	+	0.739589i	$0.735020\pi$
$542$	29849.1	+	5087.90i	0.101609	+	0.0173197i
$543$			43610.1i			0.147907i
$544$	−292859.	+	260318.i	−0.989604	+	0.879642i
$545$	−63176.5			−0.212698
$546$	2300.27	−	13495.0i	0.00771602	−	0.0452675i
$547$			480109.i			1.60459i	0.596926	+	0.802296i	$0.296389\pi$
$547$			480109.i			1.60459i	−0.596926	+	0.802296i	$0.703611\pi$
$548$	−123676.	−	43423.9i	−0.411837	−	0.144600i
$549$	316058.			1.04863
$550$	107765.	+	18368.9i	0.356247	+	0.0607238i
$551$			123148.i			0.405624i
$552$	102668.	−	185066.i	0.336944	−	0.607364i
$553$	−101205.			−0.330941
$554$	−41292.6	+	242250.i	−0.134540	+	0.789305i
$555$		−	60991.5i		−	0.198008i
$556$	−99244.9	+	282661.i	−0.321040	+	0.914357i
$557$	595819.			1.92045			0.960227	−	0.279221i	$-0.0900761\pi$
$557$	595819.			1.92045			0.960227	+	0.279221i	$0.0900761\pi$
$558$	705190.	+	120202.i	2.26484	+	0.386051i
$559$		−	10710.2i		−	0.0342749i
$560$	27182.1	−	33936.9i	0.0866775	−	0.108217i
$561$	−272876.			−0.867040
$562$	−14517.8	+	85171.1i	−0.0459650	+	0.269662i
$563$		−	68501.8i		−	0.216115i	−0.994145	−	0.108058i	$-0.965537\pi$
$563$		−	68501.8i		−	0.216115i	0.994145	−	0.108058i	$-0.0344631\pi$
$564$	917894.	+	322282.i	2.88559	+	1.01316i
$565$	−7319.58			−0.0229292
$566$	438574.	+	74756.8i	1.36902	+	0.233355i
$567$			191833.i			0.596703i
$568$	−406865.	−	225715.i	−1.26111	−	0.699621i
$569$	104936.			0.324116			0.162058	−	0.986781i	$-0.448187\pi$
$569$	104936.			0.324116			0.162058	+	0.986781i	$0.448187\pi$
$570$	4710.26	−	27633.6i	0.0144976	−	0.0850527i
$571$		−	586890.i		−	1.80005i	−0.435839	−	0.900024i	$-0.643548\pi$
$571$		−	586890.i		−	1.80005i	0.435839	−	0.900024i	$-0.356452\pi$
$572$	1719.37	−	4896.96i	0.00525506	−	0.0149670i
$573$	169860.			0.517348
$574$	83560.4	+	14243.2i	0.253616	+	0.0432299i
$575$			126731.i			0.383307i
$576$	347565.	+	557086.i	1.04759	+	1.67910i
$577$	−477851.			−1.43529			−0.717647	−	0.696407i	$-0.754781\pi$
$577$	−477851.			−1.43529			−0.717647	+	0.696407i	$0.754781\pi$
$578$	−42275.5	+	248017.i	−0.126542	+	0.742379i
$579$		−	288379.i		−	0.860214i
$580$	−122280.	−	42933.6i	−0.363495	−	0.127627i
$581$	−363196.			−1.07594
$582$	230613.	+	39309.0i	0.680830	+	0.116050i
$583$		−	179613.i		−	0.528445i
$584$	260356.	−	469309.i	0.763383	−	1.37605i
$585$	6170.27			0.0180299
$586$	73721.0	−	432498.i	0.214682	−	1.25947i
$587$		−	534495.i		−	1.55120i	−0.631225	−	0.775600i	$-0.717448\pi$
$587$		−	534495.i		−	1.55120i	0.631225	−	0.775600i	$-0.282552\pi$
$588$	117646.	−	335070.i	0.340270	−	0.969129i
$589$	92393.8			0.266325
$590$	110865.	+	18897.4i	0.318485	+	0.0542872i
$591$			620287.i			1.77590i
$592$	144018.	+	115353.i	0.410936	+	0.329143i
$593$	−432491.			−1.22989			−0.614947	−	0.788569i	$-0.710823\pi$
$593$	−432491.			−1.22989			−0.614947	+	0.788569i	$0.710823\pi$
$594$	−38012.4	+	223006.i	−0.107734	+	0.632040i
$595$		−	64991.5i		−	0.183579i
$596$	−19762.8	−	6938.92i	−0.0556361	−	0.0195344i
$597$	712552.			1.99925
$598$	5931.14	+	1010.99i	0.0165858	+	0.00282711i
$599$			215147.i			0.599628i	0.953998	+	0.299814i	$0.0969247\pi$
$599$			215147.i			0.599628i	−0.953998	+	0.299814i	$0.903075\pi$
$600$	−517554.	−	287121.i	−1.43765	−	0.797558i
$601$	−99217.8			−0.274689			−0.137344	−	0.990523i	$-0.543857\pi$
$601$	−99217.8			−0.274689			−0.137344	+	0.990523i	$0.543857\pi$
$602$	−31765.3	+	186357.i	−0.0876516	+	0.514224i
$603$			432430.i			1.18927i
$604$	12417.4	−	35366.3i	0.0340375	−	0.0969428i
$605$	−68274.0			−0.186528
$606$	176563.	+	30095.9i	0.480789	+	0.0819525i
$607$			283531.i			0.769525i	0.923016	+	0.384763i	$0.125717\pi$
$607$			283531.i			0.769525i	−0.923016	+	0.384763i	$0.874283\pi$
$608$	56342.3	+	63385.5i	0.152415	+	0.171468i
$609$	720206.			1.94188
$610$	−7218.45	+	42348.3i	−0.0193992	+	0.113809i
$611$			27656.8i			0.0740831i
$612$	926037.	+	325140.i	2.47244	+	0.868097i
$613$	−490186.			−1.30449			−0.652244	−	0.758009i	$-0.726172\pi$
$613$	−490186.			−1.30449			−0.652244	+	0.758009i	$0.726172\pi$
$614$	−116967.	−	19937.4i	−0.310260	−	0.0528850i
$615$			57511.0i			0.152055i
$616$	−44440.6	+	80107.1i	−0.117117	+	0.211110i
$617$	86974.3			0.228465			0.114233	−	0.993454i	$-0.463559\pi$
$617$	86974.3			0.228465			0.114233	+	0.993454i	$0.463559\pi$
$618$	−31264.2	+	183417.i	−0.0818597	+	0.480245i
$619$		−	145024.i		−	0.378494i	−0.981929	−	0.189247i	$-0.939395\pi$
$619$		−	145024.i		−	0.378494i	0.981929	−	0.189247i	$-0.0606047\pi$
$620$	−32211.7	+	91742.5i	−0.0837973	+	0.238664i
$621$	−262255.			−0.680049
$622$	−562001.	−	95795.4i	−1.45263	−	0.247608i
$623$			416624.i			1.07342i
$624$	−17566.3	+	21931.6i	−0.0451140	+	0.0563249i
$625$	335868.			0.859823
$626$	−74010.2	+	434194.i	−0.188861	+	1.10799i
$627$			59060.3i			0.150231i
$628$	−497031.	−	174512.i	−1.26027	−	0.442493i
$629$	275805.			0.697110
$630$	−107362.	−	18300.3i	−0.270501	−	0.0461080i
$631$			147441.i			0.370304i	0.982710	+	0.185152i	$0.0592778\pi$
$631$			147441.i			0.370304i	−0.982710	+	0.185152i	$0.940722\pi$
$632$	181652.	+	100774.i	0.454785	+	0.252299i
$633$	−686610.			−1.71357
$634$	82166.2	−	482043.i	0.204416	−	1.19924i
$635$		−	126032.i		−	0.312560i
$636$	−322152.	+	917525.i	−0.796428	+	2.26832i
$637$	10095.9			0.0248809
$638$	269164.	+	45880.2i	0.661266	+	0.112716i
$639$			1.16543e6i			2.85421i
$640$	−82581.6	+	33846.7i	−0.201615	+	0.0826336i
$641$	−112093.			−0.272810			−0.136405	−	0.990653i	$-0.543555\pi$
$641$	−112093.			−0.272810			−0.136405	+	0.990653i	$0.543555\pi$
$642$	160691.	−	942722.i	0.389871	−	2.28725i
$643$			380540.i			0.920403i	0.887814	+	0.460202i	$0.152223\pi$
$643$			380540.i			0.920403i	−0.887814	+	0.460202i	$0.847777\pi$
$644$	−100203.	−	35182.1i	−0.241606	−	0.0848300i
$645$	−128261.			−0.308302
$646$	124960.	+	21299.9i	0.299437	+	0.0510403i
$647$			49590.9i			0.118466i	0.998244	+	0.0592330i	$0.0188655\pi$
$647$			49590.9i			0.118466i	−0.998244	+	0.0592330i	$0.981135\pi$
$648$	191018.	−	344322.i	0.454908	−	0.820001i
$649$	−236947.			−0.562551
$650$	2827.31	−	16587.0i	0.00669187	−	0.0392591i
$651$		−	540347.i		−	1.27500i
$652$	−76733.3	+	218545.i	−0.180505	+	0.514098i
$653$	−230295.			−0.540080			−0.270040	−	0.962849i	$-0.587037\pi$
$653$	−230295.			−0.540080			−0.270040	+	0.962849i	$0.587037\pi$
$654$	−710395.	−	121090.i	−1.66090	−	0.283108i
$655$		−	97523.1i		−	0.227313i
$656$	−135800.	−	108770.i	−0.315567	−	0.252757i
$657$	−1.34430e6			−3.11433
$658$	82026.7	−	481224.i	0.189454	−	1.11146i
$659$		−	33208.1i		−	0.0764669i	−0.999269	−	0.0382334i	$-0.987827\pi$
$659$		−	33208.1i		−	0.0764669i	0.999269	−	0.0382334i	$-0.0121730\pi$
$660$	−58644.0	−	20590.5i	−0.134628	−	0.0472692i
$661$	−230853.			−0.528363			−0.264182	−	0.964473i	$-0.585102\pi$
$661$	−230853.			−0.528363			−0.264182	+	0.964473i	$0.585102\pi$
$662$	−134949.	−	23002.6i	−0.307931	−	0.0524880i
$663$			42000.5i			0.0955493i
$664$	651899.	+	361651.i	1.47858	+	0.820264i
$665$	−14066.5			−0.0318086
$666$	77661.1	−	455613.i	0.175087	−	1.02718i
$667$			316536.i			0.711495i
$668$	44623.2	−	127092.i	0.100002	−	0.284816i
$669$	560406.			1.25213
$670$	−57941.0	−	9876.29i	−0.129073	−	0.0220011i
$671$		−	90509.6i		−	0.201025i
$672$	370698.	−	329507.i	0.820884	−	0.729669i
$673$	−246736.			−0.544757			−0.272379	−	0.962190i	$-0.587810\pi$
$673$	−246736.			−0.544757			−0.272379	+	0.962190i	$0.587810\pi$
$674$	21962.1	−	128845.i	0.0483453	−	0.283626i
$675$			733419.i			1.60970i
$676$	430418.	+	151124.i	0.941882	+	0.330704i
$677$	−235346.			−0.513486			−0.256743	−	0.966480i	$-0.582649\pi$
$677$	−235346.			−0.513486			−0.256743	+	0.966480i	$0.582649\pi$
$678$	−82305.8	−	14029.4i	−0.179049	−	0.0305196i
$679$		−	117391.i		−	0.254621i
$680$	−64715.1	+	116653.i	−0.139955	+	0.252277i
$681$	−575407.			−1.24074
$682$	34422.4	−	201945.i	0.0740069	−	0.434175i
$683$			422740.i			0.906217i	0.891455	+	0.453109i	$0.149685\pi$
$683$			422740.i			0.906217i	−0.891455	+	0.453109i	$0.850315\pi$
$684$	70372.3	−	200428.i	0.150414	−	0.428398i
$685$	−44626.3			−0.0951065
$686$	−470862.	−	80260.3i	−1.00056	−	0.170550i
$687$		−	675904.i		−	1.43209i
$688$	242580.	−	302861.i	0.512481	−	0.639834i
$689$	−27645.7			−0.0582356
$690$	12107.1	−	71028.8i	0.0254298	−	0.149189i
$691$		−	28634.6i		−	0.0599701i	−0.999550	−	0.0299851i	$-0.990454\pi$
$691$		−	28634.6i		−	0.0599701i	0.999550	−	0.0299851i	$-0.00954598\pi$
$692$	779291.	+	273617.i	1.62737	+	0.571387i
$693$	229461.			0.477795
$694$	626418.	+	106776.i	1.30061	+	0.221693i
$695$			101993.i			0.211155i
$696$	−1.29270e6	−	717143.i	−2.66857	−	1.48043i
$697$	−260066.			−0.535326
$698$	−45712.7	+	268182.i	−0.0938265	+	0.550450i
$699$		−	1.10766e6i		−	2.26699i
$700$	−98389.8	+	280225.i	−0.200795	+	0.571888i
$701$	920465.			1.87314			0.936572	−	0.350476i	$-0.113980\pi$
$701$	920465.			1.87314			0.936572	+	0.350476i	$0.113980\pi$
$702$	34324.8	+	5850.80i	0.0696519	+	0.0118725i
$703$		−	59694.3i		−	0.120788i
$704$	159533.	−	99532.4i	0.321888	−	0.200826i
$705$	331206.			0.666377
$706$	−115161.	+	675611.i	−0.231044	+	1.35546i
$707$		−	89877.2i		−	0.179809i
$708$	1.21041e6	+	424987.i	2.41472	+	0.847830i
$709$	128382.			0.255395			0.127697	−	0.991813i	$-0.459241\pi$
$709$	128382.			0.255395			0.127697	+	0.991813i	$0.459241\pi$
$710$	−156156.	−	26617.4i	−0.309771	−	0.0528018i
$711$		−	520328.i		−	1.02929i
$712$	414852.	−	747797.i	0.818339	−	1.47511i
$713$	237487.			0.467155
$714$	124568.	−	730803.i	0.244350	−	1.43352i
$715$		−	1766.98i		−	0.00345637i
$716$	55843.1	−	159048.i	0.108929	−	0.310242i
$717$	−661237.			−1.28623
$718$	380481.	+	64854.5i	0.738047	+	0.125803i
$719$		−	568906.i		−	1.10048i	−0.835006	−	0.550240i	$-0.814536\pi$
$719$		−	568906.i		−	1.10048i	0.835006	−	0.550240i	$-0.185464\pi$
$720$	174481.	+	139752.i	0.336576	+	0.269584i
$721$	93366.1			0.179605
$722$	4610.09	−	27045.9i	0.00884371	−	0.0518833i
$723$			1.57459e6i			3.01225i
$724$	−42381.7	−	14880.6i	−0.0808540	−	0.0283886i
$725$	885221.			1.68413
$726$	−767714.	−	130860.i	−1.45655	−	0.248275i
$727$		−	694969.i		−	1.31491i	−0.753493	−	0.657456i	$-0.771633\pi$
$727$		−	694969.i		−	1.31491i	0.753493	−	0.657456i	$-0.228367\pi$
$728$	12329.9	+	6840.22i	0.0232647	+	0.0129065i
$729$	563841.			1.06097
$730$	30702.5	−	180122.i	0.0576140	−	0.338003i
$731$		−	580001.i		−	1.08541i
$732$	−162337.	+	462355.i	−0.302967	+	0.862886i
$733$	520347.			0.968468			0.484234	−	0.874938i	$-0.339098\pi$
$733$	520347.			0.968468			0.484234	+	0.874938i	$0.339098\pi$
$734$	177674.	+	30285.3i	0.329786	+	0.0562134i
$735$		−	120904.i		−	0.223803i
$736$	144821.	+	162925.i	0.267347	+	0.300768i
$737$	123835.			0.227987
$738$	−73229.4	+	429613.i	−0.134454	+	0.788797i
$739$		−	694723.i		−	1.27210i	−0.771646	−	0.636052i	$-0.780566\pi$
$739$		−	694723.i		−	1.27210i	0.771646	−	0.636052i	$-0.219434\pi$
$740$	59273.5	+	20811.5i	0.108242	+	0.0380049i
$741$	9090.46			0.0165558
$742$	481031.	+	81993.7i	0.873706	+	0.148927i
$743$			121174.i			0.219498i	0.993959	+	0.109749i	$0.0350048\pi$
$743$			121174.i			0.219498i	−0.993959	+	0.109749i	$0.964995\pi$
$744$	−538049.	+	969868.i	−0.972022	+	1.75213i
$745$	−7131.06			−0.0128482
$746$	−120913.	+	709361.i	−0.217269	+	1.27465i
$747$		−	1.86732e6i		−	3.34639i
$748$	93110.5	−	265189.i	0.166416	−	0.473972i
$749$	−479881.			−0.855401
$750$	−407177.	−	69405.0i	−0.723871	−	0.123387i
$751$		−	597992.i		−	1.06027i	−0.847914	−	0.530134i	$-0.822142\pi$
$751$		−	597992.i		−	1.06027i	0.847914	−	0.530134i	$-0.177858\pi$
$752$	−626407.	+	782071.i	−1.10770	+	1.38296i
$753$	−528592.			−0.932246
$754$	7061.79	−	41429.3i	0.0124215	−	0.0728727i
$755$		−	12761.3i		−	0.0223872i
$756$	−579893.	−	203606.i	−1.01462	−	0.356244i
$757$	−852384.			−1.48745			−0.743727	−	0.668483i	$-0.766944\pi$
$757$	−852384.			−1.48745			−0.743727	+	0.668483i	$0.766944\pi$
$758$	78279.0	+	13343.0i	0.136241	+	0.0232228i
$759$			151807.i			0.263517i
$760$	25248.0	+	14006.7i	0.0437119	+	0.0242499i
$761$	413703.			0.714364			0.357182	−	0.934035i	$-0.383738\pi$
$761$	413703.			0.714364			0.357182	+	0.934035i	$0.383738\pi$
$762$	241564.	−	1.41718e6i	0.416028	−	2.44070i
$763$			361617.i			0.621155i
$764$	−57959.7	+	165076.i	−0.0992977	+	0.282811i
$765$	334144.			0.570967
$766$	623257.	+	106237.i	1.06221	+	0.181058i
$767$			36470.5i			0.0619942i
$768$	−993471.	+	222310.i	−1.68435	+	0.376909i
$769$	−150022.			−0.253690			−0.126845	−	0.991923i	$-0.540485\pi$
$769$	−150022.			−0.253690			−0.126845	+	0.991923i	$0.540485\pi$
$770$	−5240.65	+	30745.3i	−0.00883902	+	0.0518557i
$771$		−	96759.0i		−	0.162773i
$772$	280256.	+	98400.6i	0.470241	+	0.165106i
$773$	−407186.			−0.681449			−0.340725	−	0.940163i	$-0.610672\pi$
$773$	−407186.			−0.681449			−0.340725	+	0.940163i	$0.610672\pi$
$774$	−958126.	−	163316.i	−1.59934	−	0.272614i
$775$		−	664153.i		−	1.10577i
$776$	−116892.	+	210705.i	−0.194115	+	0.349905i
$777$	−349111.			−0.578257
$778$	7188.73	−	42174.0i	0.0118766	−	0.0696763i
$779$			56287.9i			0.0927556i
$780$	−3169.25	+	9026.37i	−0.00520915	+	0.0148362i
$781$	333746.			0.547159
$782$	321194.	+	54748.8i	0.525235	+	0.0895285i
$783$			1.83186e6i			2.98792i
$784$	285489.	+	228665.i	0.464470	+	0.372022i
$785$	−179345.			−0.291038
$786$	186921.	−	1.09661e6i	0.302562	−	1.77503i
$787$		−	577185.i		−	0.931892i	−0.884813	−	0.465946i	$-0.845714\pi$
$787$		−	577185.i		−	0.931892i	0.884813	−	0.465946i	$-0.154286\pi$
$788$	−602815.	−	211654.i	−0.970804	−	0.340859i
$789$	1.78402e6			2.86579
$790$	69718.4	+	11883.8i	0.111710	+	0.0190415i
$791$			41896.7i			0.0669618i
$792$	−411858.	−	228485.i	−0.656595	−	0.364256i
$793$	−13931.1			−0.0221533
$794$	−55148.9	+	323541.i	−0.0874773	+	0.513202i
$795$			331073.i			0.523828i
$796$	−243137.	+	692482.i	−0.383729	+	1.09290i
$797$	−534990.			−0.842226			−0.421113	−	0.907008i	$-0.638360\pi$
$797$	−534990.			−0.842226			−0.421113	+	0.907008i	$0.638360\pi$
$798$	−158173.	−	26961.2i	−0.248385	−	0.0423383i
$799$			1.49772e6i			2.34605i
$800$	455633.	−	405004.i	0.711927	−	0.632819i
$801$	−2.14201e6			−3.33854
$802$	−98787.1	+	579552.i	−0.153586	+	0.901040i
$803$			384967.i			0.597025i
$804$	−632594.	−	222110.i	−0.978618	−	0.343602i
$805$	−36156.3			−0.0557946
$806$	−31083.1	−	5298.23i	−0.0478469	−	0.00815570i
$807$			484121.i			0.743373i
$808$	−89494.9	+	161320.i	−0.137081	+	0.247096i
$809$	433797.			0.662811			0.331406	−	0.943488i	$-0.392477\pi$
$809$	433797.			0.662811			0.331406	+	0.943488i	$0.392477\pi$
$810$	22525.7	−	132151.i	0.0343328	−	0.201419i
$811$		−	983634.i		−	1.49552i	−0.663969	−	0.747760i	$-0.731130\pi$
$811$		−	983634.i		−	1.49552i	0.663969	−	0.747760i	$-0.268870\pi$
$812$	−245748.	+	699920.i	−0.372717	+	1.06154i
$813$	117591.			0.177907
$814$	−130474.	−	22239.8i	−0.196913	−	0.0335647i
$815$			78858.2i			0.118722i
$816$	−951283.	+	1.18768e6i	−1.42866	+	1.78369i
$817$	−125534.			−0.188068
$818$	64215.0	−	376729.i	0.0959687	−	0.563018i
$819$		−	35318.2i		−	0.0526539i
$820$	−55891.1	−	19623.9i	−0.0831218	−	0.0291849i
$821$	84781.3			0.125781			0.0628903	−	0.998020i	$-0.479968\pi$
$821$	84781.3			0.125781			0.0628903	+	0.998020i	$0.479968\pi$
$822$	−501806.	−	85534.8i	−0.742663	−	0.126590i
$823$			634835.i			0.937263i	0.883394	+	0.468632i	$0.155253\pi$
$823$			634835.i			0.937263i	−0.883394	+	0.468632i	$0.844747\pi$
$824$	−167583.	−	92969.0i	−0.246817	−	0.136925i
$825$	424542.			0.623753
$826$	108167.	−	634581.i	0.158539	−	0.930095i
$827$			93822.5i			0.137182i	0.997645	+	0.0685908i	$0.0218503\pi$
$827$			93822.5i			0.137182i	−0.997645	+	0.0685908i	$0.978150\pi$
$828$	180883.	−	515176.i	0.263838	−	0.751442i
$829$	312289.			0.454410			0.227205	−	0.973847i	$-0.427041\pi$
$829$	312289.			0.454410			0.227205	+	0.973847i	$0.427041\pi$
$830$	250200.	+	42647.7i	0.363188	+	0.0619069i
$831$			954352.i			1.38200i
$832$	−15319.8	−	24555.0i	−0.0221313	−	0.0354726i
$833$	546732.			0.787924
$834$	−195489.	+	1.14687e6i	−0.281054	+	1.64886i
$835$		−	45858.9i		−	0.0657734i
$836$	−57396.7	−	20152.5i	−0.0821248	−	0.0288348i
$837$	1.37439e6			1.96182
$838$	−18042.6	−	3075.43i	−0.0256927	−	0.00437943i
$839$			1.08938e6i			1.54759i	0.633439	+	0.773793i	$0.281643\pi$
$839$			1.08938e6i			1.54759i	−0.633439	+	0.773793i	$0.718357\pi$
$840$	81915.6	−	147658.i	0.116093	−	0.209266i
$841$	1.50374e6			2.12609
$842$	−150160.	+	880938.i	−0.211801	+	1.24257i
$843$			335534.i			0.472151i
$844$	234285.	−	667270.i	0.328897	−	0.936735i
$845$	155308.			0.217511
$846$	2.47414e6	+	421728.i	3.45688	+	0.589239i
$847$			390795.i			0.544731i
$848$	−781756.	−	626156.i	−1.08713	−	0.870744i
$849$	1.72778e6			2.39702
$850$	153110.	−	898247.i	0.211917	−	1.24325i
$851$		−	153437.i		−	0.211871i
$852$	−1.70489e6	−	598604.i	−2.34865	−	0.824632i
$853$	−1.15762e6			−1.59100			−0.795499	−	0.605955i	$-0.792791\pi$
$853$	−1.15762e6			−1.59100			−0.795499	+	0.605955i	$0.792791\pi$
$854$	242399.	+	41317.8i	0.332364	+	0.0566529i
$855$		−	72321.0i		−	0.0989310i
$856$	861337.	+	477840.i	1.17551	+	0.652131i
$857$	718124.			0.977772			0.488886	−	0.872348i	$-0.337403\pi$
$857$	718124.			0.977772			0.488886	+	0.872348i	$0.337403\pi$
$858$	3386.76	−	19869.0i	0.00460054	−	0.0269899i
$859$			263161.i			0.356644i	0.983972	+	0.178322i	$0.0570668\pi$
$859$			263161.i			0.356644i	−0.983972	+	0.178322i	$0.942933\pi$
$860$	43765.3	−	124649.i	0.0591743	−	0.168535i
$861$	329189.			0.444057
$862$	−454977.	−	77552.7i	−0.612315	−	0.104372i
$863$		−	1.01885e6i		−	1.36801i	−0.729475	−	0.684007i	$-0.760236\pi$
$863$		−	1.01885e6i		−	1.36801i	0.729475	−	0.684007i	$-0.239764\pi$
$864$	838109.	+	942879.i	1.12272	+	1.26307i
$865$	281193.			0.375814
$866$	−242084.	+	1.42023e6i	−0.322797	+	1.89375i
$867$			977069.i			1.29983i
$868$	525127.	+	184377.i	0.696987	+	0.244719i
$869$	−149007.			−0.197318
$870$	−496139.	−	84569.0i	−0.655489	−	0.111731i
$871$		−	19060.5i		−	0.0251245i
$872$	360080.	−	649066.i	0.473550	−	0.853604i
$873$	603547.			0.791923
$874$	11849.7	−	69518.2i	0.0155125	−	0.0910071i
$875$			207268.i			0.270718i
$876$	690474.	−	1.96655e6i	0.899786	−	2.56269i
$877$	−786573.			−1.02268			−0.511340	−	0.859378i	$-0.670851\pi$
$877$	−786573.			−1.02268			−0.511340	+	0.859378i	$0.670851\pi$
$878$	−1.14176e6	−	194617.i	−1.48110	−	0.252459i
$879$		−	1.70384e6i		−	2.20521i
$880$	40020.9	−	49966.2i	0.0516799	−	0.0645225i
$881$	391035.			0.503807			0.251904	−	0.967752i	$-0.418943\pi$
$881$	391035.			0.503807			0.251904	+	0.967752i	$0.418943\pi$
$882$	153949.	−	903167.i	0.197897	−	1.16100i
$883$		−	1.21339e6i		−	1.55625i	−0.628106	−	0.778127i	$-0.716170\pi$
$883$		−	1.21339e6i		−	1.55625i	0.628106	−	0.778127i	$-0.283830\pi$
$884$	−40817.5	−	14331.4i	−0.0522326	−	0.0183394i
$885$	436755.			0.557637
$886$	−502237.	−	85608.3i	−0.639795	−	0.109056i
$887$			681615.i			0.866346i	0.901311	+	0.433173i	$0.142606\pi$
$887$			681615.i			0.866346i	−0.901311	+	0.433173i	$0.857394\pi$
$888$	626618.	+	347626.i	0.794652	+	0.440845i
$889$	−721397.			−0.912790
$890$	48921.4	−	287006.i	0.0617616	−	0.362336i
$891$			282442.i			0.355774i
$892$	−191222.	+	544621.i	−0.240329	+	0.684486i
$893$	324162.			0.406498
$894$	−80186.0	−	13668.0i	−0.100328	−	0.0171014i
$895$		−	57389.5i		−	0.0716451i
$896$	193736.	+	472690.i	0.241321	+	0.588791i
$897$	23365.9			0.0290401
$898$	−9393.64	+	55109.5i	−0.0116488	+	0.0683398i
$899$		−	1.65886e6i		−	2.05253i
$900$	−1.44074e6	−	505856.i	−1.77869	−	0.624514i
$901$	−1.49712e6			−1.84419
$902$	123028.	+	20970.7i	0.151214	+	0.0257751i
$903$			734158.i			0.900356i
$904$	41718.6	−	75200.4i	0.0510496	−	0.0920202i
$905$	−15292.7			−0.0186718
$906$	24459.4	−	143496.i	0.0297982	−	0.174816i
$907$		−	760868.i		−	0.924900i	−0.886645	−	0.462450i	$-0.846970\pi$
$907$		−	760868.i		−	0.924900i	0.886645	−	0.462450i	$-0.153030\pi$
$908$	196340.	−	559199.i	0.238143	−	0.678258i
$909$	462090.			0.559241
$910$	4732.25	+	806.632i	0.00571459	+	0.000974076i
$911$			811511.i			0.977817i	0.872335	+	0.488909i	$0.162605\pi$
$911$			811511.i			0.977817i	−0.872335	+	0.488909i	$0.837395\pi$
$912$	257057.	+	205893.i	0.309058	+	0.247543i
$913$	−534744.			−0.641511
$914$	−174358.	+	1.02290e6i	−0.208713	+	1.22445i
$915$			166832.i			0.199268i
$916$	656865.	+	230632.i	0.782862	+	0.274870i
$917$	−558215.			−0.663839
$918$	1.85882e6	+	316843.i	2.20572	+	0.375975i
$919$		−	756808.i		−	0.896096i	−0.894009	−	0.448048i	$-0.852119\pi$
$919$		−	756808.i		−	0.896096i	0.894009	−	0.448048i	$-0.147881\pi$
$920$	64896.9	+	36002.5i	0.0766740	+	0.0425361i
$921$	−460793.			−0.543234
$922$	136966.	−	803536.i	0.161121	−	0.945243i
$923$		−	51369.5i		−	0.0602979i
$924$	−117858.	+	335673.i	−0.138043	+	0.393163i
$925$	−429100.			−0.501505
$926$	−149776.	−	25529.9i	−0.174670	−	0.0297733i
$927$			480028.i			0.558608i
$928$	1.13804e6	−	1.01158e6i	1.32148	−	1.17464i
$929$	−869931.			−1.00798			−0.503992	−	0.863708i	$-0.668136\pi$
$929$	−869931.			−1.00798			−0.503992	+	0.863708i	$0.668136\pi$
$930$	−63449.4	+	372237.i	−0.0733604	+	0.430382i
$931$		−	118333.i		−	0.136523i
$932$	1.07646e6	+	377954.i	1.23927	+	0.435118i
$933$	−2.21402e6			−2.54342
$934$	−743978.	−	126814.i	−0.852838	−	0.145370i
$935$		−	95688.9i		−	0.109456i
$936$	−35168.0	+	63392.5i	−0.0401417	+	0.0723579i
$937$	1.09740e6			1.24993			0.624964	−	0.780654i	$-0.285114\pi$
$937$	1.09740e6			1.24993			0.624964	+	0.780654i	$0.285114\pi$
$938$	−56531.1	+	331650.i	−0.0642513	+	0.376942i
$939$			1.71052e6i			1.93998i
$940$	−113014.	+	321877.i	−0.127902	+	0.364279i
$941$	−1931.45			−0.00218124			−0.00109062	−	0.999999i	$-0.500347\pi$
$941$	−1931.45			−0.00218124			−0.00109062	+	0.999999i	$0.500347\pi$
$942$	−2.01666e6	−	343748.i	−2.27264	−	0.387381i
$943$			144681.i			0.162700i
$944$	−826032.	+	1.03130e6i	−0.926942	+	1.15729i
$945$	−209244.			−0.234309
$946$	−46769.0	+	274379.i	−0.0522607	+	0.306597i
$947$			754601.i			0.841428i	0.907193	+	0.420714i	$0.138220\pi$
$947$			754601.i			0.841428i	−0.907193	+	0.420714i	$0.861780\pi$
$948$	761178.	+	267257.i	0.846973	+	0.297380i
$949$	59253.5			0.0657933
$950$	−194414.	−	33138.6i	−0.215417	−	0.0367187i
$951$		−	1.89902e6i		−	2.09976i
$952$	667713.	+	370424.i	0.736743	+	0.408720i
$953$	197202.			0.217133			0.108567	−	0.994089i	$-0.465374\pi$
$953$	197202.			0.217133			0.108567	+	0.994089i	$0.465374\pi$
$954$	−421558.	+	2.47315e6i	−0.463192	+	2.71740i
$955$			59564.6i			0.0653103i
$956$	225627.	−	642611.i	0.246874	−	0.703125i
$957$	1.06038e6			1.15781
$958$	953467.	+	162522.i	1.03890	+	0.177085i
$959$			255438.i			0.277746i
$960$	−294060.	+	183464.i	−0.319076	+	0.199071i
$961$	−321066.			−0.347654
$962$	−3423.11	+	20082.3i	−0.00369889	+	0.0217002i
$963$		−	2.46723e6i		−	2.66047i
$964$	−1.53024e6	−	537281.i	−1.64666	−	0.578159i
$965$	101125.			0.108594
$966$	−406563.	−	69300.4i	−0.435686	−	0.0742645i
$967$		−	961010.i		−	1.02772i	−0.857874	−	0.513860i	$-0.828215\pi$
$967$		−	961010.i		−	1.02772i	0.857874	−	0.513860i	$-0.171785\pi$
$968$	389133.	−	701437.i	0.415286	−	0.748580i
$969$	492283.			0.524285
$970$	−13784.4	+	80868.8i	−0.0146503	+	0.0859484i
$971$		−	263208.i		−	0.279165i	−0.990210	−	0.139582i	$-0.955424\pi$
$971$		−	263208.i		−	0.279165i	0.990210	−	0.139582i	$-0.0445760\pi$
$972$	−22346.9	+	63646.5i	−0.0236529	+	0.0673662i
$973$	583800.			0.616650
$974$	16818.5	+	2866.77i	0.0177283	+	0.00302187i
$975$		−	65344.8i		−	0.0687387i
$976$	−393939.	−	315529.i	−0.413551	−	0.331238i
$977$	30338.0			0.0317832			0.0158916	−	0.999874i	$-0.494941\pi$
$977$	30338.0			0.0317832			0.0158916	+	0.999874i	$0.494941\pi$
$978$	−151147.	+	886729.i	−0.158023	+	0.927071i
$979$			613408.i			0.640005i
$980$	117499.	+	41254.9i	0.122343	+	0.0429559i
$981$	−1.85920e6			−1.93192
$982$	−1.04661e6	−	178399.i	−1.08533	−	0.184999i
$983$		−	250080.i		−	0.258805i	−0.991592	−	0.129402i	$-0.958694\pi$
$983$		−	250080.i		−	0.258805i	0.991592	−	0.129402i	$-0.0413059\pi$
$984$	−590860.	−	327789.i	−0.610231	−	0.338535i
$985$	−217515.			−0.224190
$986$	382423.	−	2.24356e6i	0.393360	−	2.30772i
$987$		−	1.89580e6i		−	1.94607i
$988$	−3101.84	+	8834.40i	−0.00317765	+	0.00905030i
$989$	−322668.			−0.329886
$990$	−158072.	−	26944.0i	−0.161282	−	0.0274911i
$991$			458278.i			0.466639i	0.972400	+	0.233320i	$0.0749588\pi$
$991$			458278.i			0.466639i	−0.972400	+	0.233320i	$0.925041\pi$
$992$	−758956.	−	853832.i	−0.771247	−	0.867659i
$993$	−531634.			−0.539156
$994$	−152356.	+	893823.i	−0.154201	+	0.904646i
$995$			249870.i			0.252387i
$996$	2.73166e6	+	959112.i	2.75364	+	0.966831i
$997$	−1.56972e6			−1.57919			−0.789593	−	0.613631i	$-0.789708\pi$
$997$	−1.56972e6			−1.57919			−0.789593	+	0.613631i	$0.789708\pi$
$998$	−1.30772e6	−	222907.i	−1.31297	−	0.223801i
$999$		−	887972.i		−	0.889750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.b.a.39.16	yes	36
4.3	odd	2	inner	76.5.b.a.39.15	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.b.a.39.15	✓	36	4.3	odd	2	inner
76.5.b.a.39.16	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.672122 + 3.94313i) q^{2} +15.5341i q^{3} +(-15.0965 - 5.30053i) q^{4} -5.44730 q^{5} +(-61.2528 - 10.4408i) q^{6} +31.1799i q^{7} +(31.0473 - 55.9648i) q^{8} -160.307 q^{9} +O(q^{10})\)	\(q+(-0.672122 + 3.94313i) q^{2} +15.5341i q^{3} +(-15.0965 - 5.30053i) q^{4} -5.44730 q^{5} +(-61.2528 - 10.4408i) q^{6} +31.1799i q^{7} +(31.0473 - 55.9648i) q^{8} -160.307 q^{9} +(3.66125 - 21.4794i) q^{10} +45.9071i q^{11} +(82.3387 - 234.510i) q^{12} +7.06595 q^{13} +(-122.946 - 20.9567i) q^{14} -84.6187i q^{15} +(199.809 + 160.039i) q^{16} +382.648 q^{17} +(107.746 - 632.111i) q^{18} -82.8191i q^{19} +(82.2352 + 28.8736i) q^{20} -484.351 q^{21} +(-181.018 - 30.8552i) q^{22} -212.876i q^{23} +(869.361 + 482.291i) q^{24} -595.327 q^{25} +(-4.74918 + 27.8619i) q^{26} -1231.96i q^{27} +(165.270 - 470.708i) q^{28} -1486.95 q^{29} +(333.662 + 56.8741i) q^{30} +1115.61i q^{31} +(-765.349 + 680.306i) q^{32} -713.124 q^{33} +(-257.186 + 1508.83i) q^{34} -169.847i q^{35} +(2420.07 + 849.712i) q^{36} +720.780 q^{37} +(326.566 + 55.6645i) q^{38} +109.763i q^{39} +(-169.124 + 304.857i) q^{40} -679.649 q^{41} +(325.543 - 1909.86i) q^{42} -1515.76i q^{43} +(243.332 - 693.037i) q^{44} +873.241 q^{45} +(839.398 + 143.079i) q^{46} +3914.10i q^{47} +(-2486.05 + 3103.84i) q^{48} +1428.81 q^{49} +(400.132 - 2347.45i) q^{50} +5944.08i q^{51} +(-106.671 - 37.4532i) q^{52} -3912.52 q^{53} +(4857.77 + 828.027i) q^{54} -250.070i q^{55} +(1744.98 + 968.055i) q^{56} +1286.52 q^{57} +(999.412 - 5863.23i) q^{58} +5161.44i q^{59} +(-448.524 + 1277.45i) q^{60} -1971.58 q^{61} +(-4398.99 - 749.827i) q^{62} -4998.36i q^{63} +(-2168.12 - 3475.12i) q^{64} -38.4904 q^{65} +(479.307 - 2811.94i) q^{66} -2697.51i q^{67} +(-5776.65 - 2028.24i) q^{68} +3306.83 q^{69} +(669.727 + 114.158i) q^{70} -7270.01i q^{71} +(-4977.11 + 8971.55i) q^{72} +8385.78 q^{73} +(-484.452 + 2842.13i) q^{74} -9247.84i q^{75} +(-438.985 + 1250.28i) q^{76} -1431.38 q^{77} +(-432.809 - 73.7740i) q^{78} +3245.82i q^{79} +(-1088.42 - 871.780i) q^{80} +6152.46 q^{81} +(456.807 - 2679.94i) q^{82} +11648.4i q^{83} +(7312.01 + 2567.32i) q^{84} -2084.40 q^{85} +(5976.82 + 1018.77i) q^{86} -23098.4i q^{87} +(2569.19 + 1425.30i) q^{88} +13361.9 q^{89} +(-586.925 + 3443.30i) q^{90} +220.316i q^{91} +(-1128.36 + 3213.69i) q^{92} -17330.0 q^{93} +(-15433.8 - 2630.75i) q^{94} +451.141i q^{95} +(-10567.9 - 11889.0i) q^{96} -3764.95 q^{97} +(-960.336 + 5633.98i) q^{98} -7359.24i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9}+O(q^{10}) \) 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9	\( 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9} + 152 q^{10} + 160 q^{12} + 120 q^{13} - 60 q^{14} - 38 q^{16} - 600 q^{17} + 286 q^{18} - 600 q^{20} + 608 q^{21} + 1080 q^{22} + 958 q^{24} + 4604 q^{25} - 2766 q^{26} - 2250 q^{28} - 168 q^{29} - 1380 q^{30} + 3576 q^{32} + 1440 q^{33} + 908 q^{34} - 5836 q^{36} - 2248 q^{37} - 1716 q^{40} + 1800 q^{41} - 5006 q^{42} - 2520 q^{44} + 88 q^{45} + 6404 q^{46} + 1064 q^{48} - 12188 q^{49} + 3354 q^{50} + 15492 q^{52} - 6600 q^{53} + 1654 q^{54} + 12924 q^{56} + 5450 q^{58} - 11188 q^{60} + 2200 q^{61} - 9972 q^{62} + 12570 q^{64} - 15792 q^{65} + 10500 q^{66} - 22614 q^{68} + 19904 q^{69} + 900 q^{70} - 11376 q^{72} + 11560 q^{73} + 17304 q^{74} + 1680 q^{77} - 24740 q^{78} + 12900 q^{80} + 13604 q^{81} - 18420 q^{82} + 5644 q^{84} - 11552 q^{85} + 24564 q^{86} - 15304 q^{88} + 13800 q^{89} - 60212 q^{90} - 2142 q^{92} + 34592 q^{93} - 23096 q^{94} - 35770 q^{96} + 8200 q^{97} + 25566 q^{98}+O(q^{100}) \) 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9 + 152 * q^10 + 160 * q^12 + 120 * q^13 - 60 * q^14 - 38 * q^16 - 600 * q^17 + 286 * q^18 - 600 * q^20 + 608 * q^21 + 1080 * q^22 + 958 * q^24 + 4604 * q^25 - 2766 * q^26 - 2250 * q^28 - 168 * q^29 - 1380 * q^30 + 3576 * q^32 + 1440 * q^33 + 908 * q^34 - 5836 * q^36 - 2248 * q^37 - 1716 * q^40 + 1800 * q^41 - 5006 * q^42 - 2520 * q^44 + 88 * q^45 + 6404 * q^46 + 1064 * q^48 - 12188 * q^49 + 3354 * q^50 + 15492 * q^52 - 6600 * q^53 + 1654 * q^54 + 12924 * q^56 + 5450 * q^58 - 11188 * q^60 + 2200 * q^61 - 9972 * q^62 + 12570 * q^64 - 15792 * q^65 + 10500 * q^66 - 22614 * q^68 + 19904 * q^69 + 900 * q^70 - 11376 * q^72 + 11560 * q^73 + 17304 * q^74 + 1680 * q^77 - 24740 * q^78 + 12900 * q^80 + 13604 * q^81 - 18420 * q^82 + 5644 * q^84 - 11552 * q^85 + 24564 * q^86 - 15304 * q^88 + 13800 * q^89 - 60212 * q^90 - 2142 * q^92 + 34592 * q^93 - 23096 * q^94 - 35770 * q^96 + 8200 * q^97 + 25566 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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