LMFDB - Embedded newform 76.5.j.a.41.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.2
Character	$\chi$	$=$	76.41
Dual form			76.5.j.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.13985 - 11.3741i) q^{3} +(-6.25205 + 35.4571i) q^{5} +(-25.8702 - 44.8086i) q^{7} +(-50.1832 + 42.1087i) q^{9} +O(q^{10})$	\(q+(-4.13985 - 11.3741i) q^{3} +(-6.25205 + 35.4571i) q^{5} +(-25.8702 - 44.8086i) q^{7} +(-50.1832 + 42.1087i) q^{9} +(-31.3514 + 54.3022i) q^{11} +(-109.766 + 301.581i) q^{13} +(429.177 - 75.6755i) q^{15} +(342.075 + 287.035i) q^{17} +(-162.907 + 322.153i) q^{19} +(-402.560 + 479.753i) q^{21} +(-90.4845 - 513.163i) q^{23} +(-630.811 - 229.596i) q^{25} +(-162.378 - 93.7490i) q^{27} +(-524.868 - 625.513i) q^{29} +(-1072.59 + 619.262i) q^{31} +(747.431 + 131.792i) q^{33} +(1750.52 - 637.139i) q^{35} -532.840i q^{37} +3884.64 q^{39} +(-355.017 - 975.401i) q^{41} +(-79.7398 + 452.227i) q^{43} +(-1179.31 - 2042.62i) q^{45} +(-2408.38 + 2020.87i) q^{47} +(-138.039 + 239.091i) q^{49} +(1848.64 - 5079.10i) q^{51} +(-1797.47 + 316.942i) q^{53} +(-1729.39 - 1451.13i) q^{55} +(4338.62 + 519.262i) q^{57} +(-365.255 + 435.294i) q^{59} +(93.8036 + 531.987i) q^{61} +(3185.09 + 1159.28i) q^{63} +(-10006.9 - 5777.50i) q^{65} +(4282.23 + 5103.37i) q^{67} +(-5462.20 + 3153.60i) q^{69} +(-1606.46 - 283.262i) q^{71} +(7746.45 - 2819.48i) q^{73} +8125.43i q^{75} +3244.27 q^{77} +(-2379.76 - 6538.35i) q^{79} +(-1315.52 + 7460.68i) q^{81} +(3687.63 + 6387.16i) q^{83} +(-12316.1 + 10334.4i) q^{85} +(-4941.80 + 8559.45i) q^{87} +(2153.49 - 5916.67i) q^{89} +(16353.1 - 2883.49i) q^{91} +(11484.0 + 9636.18i) q^{93} +(-10404.1 - 7790.32i) q^{95} +(-2695.42 + 3212.28i) q^{97} +(-713.283 - 4045.23i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.13985	−	11.3741i	−0.459983	−	1.26379i	−0.925498	−	0.378754i	$-0.876353\pi$
$3$	−4.13985	−	11.3741i	−0.459983	−	1.26379i	0.465514	−	0.885040i	$-0.345869\pi$
$4$		0			0
$5$	−6.25205	+	35.4571i	−0.250082	+	1.41828i	0.558306	+	0.829635i	$0.311451\pi$
$5$	−6.25205	+	35.4571i	−0.250082	+	1.41828i	−0.808388	+	0.588650i	$0.799660\pi$
$6$		0			0
$7$	−25.8702	−	44.8086i	−0.527964	−	0.914461i	−0.999469	−	0.0325971i	$-0.989622\pi$
$7$	−25.8702	−	44.8086i	−0.527964	−	0.914461i	0.471504	−	0.881864i	$-0.343711\pi$
$8$		0			0
$9$	−50.1832	+	42.1087i	−0.619546	+	0.519861i
$10$		0			0
$11$	−31.3514	+	54.3022i	−0.259102	+	0.448778i	−0.966002	−	0.258536i	$-0.916760\pi$
$11$	−31.3514	+	54.3022i	−0.259102	+	0.448778i	0.706899	+	0.707314i	$0.250093\pi$
$12$		0			0
$13$	−109.766	+	301.581i	−0.649506	+	1.78450i	−0.0299481	+	0.999551i	$0.509534\pi$
$13$	−109.766	+	301.581i	−0.649506	+	1.78450i	−0.619558	+	0.784951i	$0.712688\pi$
$14$		0			0
$15$	429.177	−	75.6755i	1.90745	−	0.336335i
$16$		0			0
$17$	342.075	+	287.035i	1.18365	+	0.993202i	0.999948	+	0.0102204i	$0.00325333\pi$
$17$	342.075	+	287.035i	1.18365	+	0.993202i	0.183704	+	0.982982i	$0.441191\pi$
$18$		0			0
$19$	−162.907	+	322.153i	−0.451265	+	0.892390i
$19$	−162.907	+	322.153i	−0.451265	+	0.892390i
$20$		0			0
$21$	−402.560	+	479.753i	−0.912835	+	1.08787i
$22$		0			0
$23$	−90.4845	−	513.163i	−0.171048	−	0.970062i	−0.942607	−	0.333904i	$-0.891634\pi$
$23$	−90.4845	−	513.163i	−0.171048	−	0.970062i	0.771559	−	0.636158i	$-0.219477\pi$
$24$		0			0
$25$	−630.811	−	229.596i	−1.00930	−	0.367354i
$26$		0			0
$27$	−162.378	−	93.7490i	−0.222741	−	0.128599i
$28$		0			0
$29$	−524.868	−	625.513i	−0.624099	−	0.743773i	0.357670	−	0.933848i	$-0.383571\pi$
$29$	−524.868	−	625.513i	−0.624099	−	0.743773i	−0.981770	+	0.190075i	$0.939127\pi$
$30$		0			0
$31$	−1072.59	+	619.262i	−1.11612	+	0.644393i	−0.940408	−	0.340048i	$-0.889557\pi$
$31$	−1072.59	+	619.262i	−1.11612	+	0.644393i	−0.175714	+	0.984441i	$0.556223\pi$
$32$		0			0
$33$	747.431	+	131.792i	0.686346	+	0.121021i
$34$		0			0
$35$	1750.52	−	637.139i	1.42900	−	0.520113i
$36$		0			0
$37$		−	532.840i		−	0.389219i	−0.980881	−	0.194609i	$-0.937656\pi$
$37$		−	532.840i		−	0.389219i	0.980881	−	0.194609i	$-0.0623439\pi$
$38$		0			0
$39$	3884.64			2.55401
$40$		0			0
$41$	−355.017	−	975.401i	−0.211194	−	0.580251i	0.788187	−	0.615436i	$-0.211020\pi$
$41$	−355.017	−	975.401i	−0.211194	−	0.580251i	−0.999381	+	0.0351853i	$0.988798\pi$
$42$		0			0
$43$	−79.7398	+	452.227i	−0.0431259	+	0.244579i	−0.998748	−	0.0500145i	$-0.984073\pi$
$43$	−79.7398	+	452.227i	−0.0431259	+	0.244579i	0.955623	+	0.294594i	$0.0951843\pi$
$44$		0			0
$45$	−1179.31	−	2042.62i	−0.582374	−	1.00870i
$46$		0			0
$47$	−2408.38	+	2020.87i	−1.09026	+	0.914836i	−0.996732	−	0.0807812i	$-0.974259\pi$
$47$	−2408.38	+	2020.87i	−1.09026	+	0.914836i	−0.0935268	+	0.995617i	$0.529814\pi$
$48$		0			0
$49$	−138.039	+	239.091i	−0.0574924	+	0.0995797i
$50$		0			0
$51$	1848.64	−	5079.10i	0.710742	−	1.95275i
$52$		0			0
$53$	−1797.47	+	316.942i	−0.639895	+	0.112831i	−0.484176	−	0.874971i	$-0.660881\pi$
$53$	−1797.47	+	316.942i	−0.639895	+	0.112831i	−0.155719	+	0.987801i	$0.549769\pi$
$54$		0			0
$55$	−1729.39	−	1451.13i	−0.571699	−	0.479712i
$56$		0			0
$57$	4338.62	+	519.262i	1.33537	+	0.159822i
$58$		0			0
$59$	−365.255	+	435.294i	−0.104928	+	0.125049i	−0.815953	−	0.578119i	$-0.803787\pi$
$59$	−365.255	+	435.294i	−0.104928	+	0.125049i	0.711024	+	0.703167i	$0.248231\pi$
$60$		0			0
$61$	93.8036	+	531.987i	0.0252093	+	0.142969i	0.994815	−	0.101706i	$-0.0324300\pi$
$61$	93.8036	+	531.987i	0.0252093	+	0.142969i	−0.969605	+	0.244674i	$0.921319\pi$
$62$		0			0
$63$	3185.09	+	1159.28i	0.802491	+	0.292083i
$64$		0			0
$65$	−10006.9	−	5777.50i	−2.36850	−	1.36746i
$66$		0			0
$67$	4282.23	+	5103.37i	0.953939	+	1.13686i	0.990498	+	0.137529i	$0.0439160\pi$
$67$	4282.23	+	5103.37i	0.953939	+	1.13686i	−0.0365584	+	0.999332i	$0.511640\pi$
$68$		0			0
$69$	−5462.20	+	3153.60i	−1.14728	+	0.662382i
$70$		0			0
$71$	−1606.46	−	283.262i	−0.318678	−	0.0561915i	0.0120212	−	0.999928i	$-0.496173\pi$
$71$	−1606.46	−	283.262i	−0.318678	−	0.0561915i	−0.330699	+	0.943736i	$0.607285\pi$
$72$		0			0
$73$	7746.45	−	2819.48i	1.45364	−	0.529082i	0.510034	−	0.860154i	$-0.329633\pi$
$73$	7746.45	−	2819.48i	1.45364	−	0.529082i	0.943605	+	0.331072i	$0.107410\pi$
$74$		0			0
$75$			8125.43i			1.44452i
$76$		0			0
$77$	3244.27			0.547187
$78$		0			0
$79$	−2379.76	−	6538.35i	−0.381311	−	1.04764i	−0.970805	−	0.239871i	$-0.922895\pi$
$79$	−2379.76	−	6538.35i	−0.381311	−	1.04764i	0.589493	−	0.807773i	$-0.299327\pi$
$80$		0			0
$81$	−1315.52	+	7460.68i	−0.200506	+	1.13713i
$82$		0			0
$83$	3687.63	+	6387.16i	0.535292	+	0.927153i	0.999149	+	0.0412433i	$0.0131319\pi$
$83$	3687.63	+	6387.16i	0.535292	+	0.927153i	−0.463857	+	0.885910i	$0.653535\pi$
$84$		0			0
$85$	−12316.1	+	10334.4i	−1.70465	+	1.43037i
$86$		0			0
$87$	−4941.80	+	8559.45i	−0.652900	+	1.13086i
$88$		0			0
$89$	2153.49	−	5916.67i	0.271871	−	0.746960i	−0.726349	−	0.687326i	$-0.758784\pi$
$89$	2153.49	−	5916.67i	0.271871	−	0.746960i	0.998220	−	0.0596339i	$-0.0189933\pi$
$90$		0			0
$91$	16353.1	−	2883.49i	1.97477	−	0.348206i
$92$		0			0
$93$	11484.0	+	9636.18i	1.32778	+	1.11414i
$94$		0			0
$95$	−10404.1	−	7790.32i	−1.15281	−	0.863193i
$96$		0			0
$97$	−2695.42	+	3212.28i	−0.286473	+	0.341405i	−0.890019	−	0.455923i	$-0.849309\pi$
$97$	−2695.42	+	3212.28i	−0.286473	+	0.341405i	0.603546	+	0.797328i	$0.293754\pi$
$98$		0			0
$99$	−713.283	−	4045.23i	−0.0727765	−	0.412736i
$100$		0			0
$101$	3566.13	+	1297.97i	0.349587	+	0.127239i	0.510844	−	0.859673i	$-0.329333\pi$
$101$	3566.13	+	1297.97i	0.349587	+	0.127239i	−0.161258	+	0.986912i	$0.551555\pi$
$102$		0			0
$103$	2896.28	+	1672.17i	0.273003	+	0.157618i	0.630251	−	0.776391i	$-0.282952\pi$
$103$	2896.28	+	1672.17i	0.273003	+	0.157618i	−0.357249	+	0.934009i	$0.616285\pi$
$104$		0			0
$105$	−14493.8	−	17273.1i	−1.31463	−	1.56672i
$106$		0			0
$107$	8891.77	−	5133.67i	0.776642	−	0.448394i	−0.0585971	−	0.998282i	$-0.518663\pi$
$107$	8891.77	−	5133.67i	0.776642	−	0.448394i	0.835239	+	0.549887i	$0.185329\pi$
$108$		0			0
$109$	−20233.7	−	3567.75i	−1.70303	−	0.300290i	−0.764279	−	0.644886i	$-0.776905\pi$
$109$	−20233.7	−	3567.75i	−1.70303	−	0.300290i	−0.938751	+	0.344596i	$0.888016\pi$
$110$		0			0
$111$	−6060.61	+	2205.88i	−0.491892	+	0.179034i
$112$		0			0
$113$			9155.56i			0.717015i	0.933527	+	0.358507i	$0.116714\pi$
$113$			9155.56i			0.717015i	−0.933527	+	0.358507i	$0.883286\pi$
$114$		0			0
$115$	18761.0			1.41860
$116$		0			0
$117$	−7190.75	−	19756.4i	−0.525294	−	1.44323i
$118$		0			0
$119$	4012.07	−	22753.6i	0.283318	−	1.60678i
$120$		0			0
$121$	5354.68	+	9274.58i	0.365732	+	0.633466i
$122$		0			0
$123$	−9624.64	+	8076.03i	−0.636172	+	0.533811i
$124$		0			0
$125$	833.406	−	1443.50i	0.0533380	−	0.0923841i
$126$		0			0
$127$	−1123.59	+	3087.05i	−0.0696630	+	0.191397i	−0.969638	−	0.244543i	$-0.921362\pi$
$127$	−1123.59	+	3087.05i	−0.0696630	+	0.191397i	0.899975	+	0.435941i	$0.143584\pi$
$128$		0			0
$129$	5473.81	−	965.180i	0.328935	−	0.0580001i
$130$		0			0
$131$	−10134.1	−	8503.54i	−0.590532	−	0.495515i	0.297855	−	0.954611i	$-0.403729\pi$
$131$	−10134.1	−	8503.54i	−0.590532	−	0.495515i	−0.888387	+	0.459096i	$0.848173\pi$
$132$		0			0
$133$	18649.6	−	1034.55i	1.05431	−	0.0584853i
$134$		0			0
$135$	4339.26	−	5171.33i	0.238094	−	0.283749i
$136$		0			0
$137$	−742.666	−	4211.87i	−0.0395688	−	0.224406i	0.958611	−	0.284720i	$-0.0919007\pi$
$137$	−742.666	−	4211.87i	−0.0395688	−	0.224406i	−0.998179	+	0.0603146i	$0.980790\pi$
$138$		0			0
$139$	−6529.51	−	2376.55i	−0.337949	−	0.123003i	0.167471	−	0.985877i	$-0.446440\pi$
$139$	−6529.51	−	2376.55i	−0.337949	−	0.123003i	−0.505419	+	0.862874i	$0.668662\pi$
$140$		0			0
$141$	32956.0	+	19027.2i	1.65766	+	0.957053i
$142$		0			0
$143$	−12935.2	−	15415.5i	−0.632558	−	0.753853i
$144$		0			0
$145$	25460.4	−	14699.6i	1.21096	−	0.699147i
$146$		0			0
$147$	3290.92	+	580.277i	0.152294	+	0.0268535i
$148$		0			0
$149$	41071.4	−	14948.8i	1.84998	−	0.673337i	0.864724	−	0.502247i	$-0.167493\pi$
$149$	41071.4	−	14948.8i	1.84998	−	0.673337i	0.985255	−	0.171090i	$-0.0547290\pi$
$150$		0			0
$151$			22893.0i			1.00403i	0.864858	+	0.502017i	$0.167409\pi$
$151$			22893.0i			1.00403i	−0.864858	+	0.502017i	$0.832591\pi$
$152$		0			0
$153$	−29253.1			−1.24965
$154$		0			0
$155$	−15251.3	−	41902.7i	−0.634811	−	1.74413i
$156$		0			0
$157$	−4649.04	+	26366.0i	−0.188610	+	1.06966i	0.732619	+	0.680639i	$0.238298\pi$
$157$	−4649.04	+	26366.0i	−0.188610	+	1.06966i	−0.921229	+	0.389021i	$0.872813\pi$
$158$		0			0
$159$	11046.2	+	19132.5i	0.436936	+	0.756796i
$160$		0			0
$161$	−20653.2	+	17330.1i	−0.796777	+	0.668575i
$162$		0			0
$163$	−17362.1	+	30072.0i	−0.653472	+	1.13185i	0.328803	+	0.944399i	$0.393355\pi$
$163$	−17362.1	+	30072.0i	−0.653472	+	1.13185i	−0.982275	+	0.187448i	$0.939978\pi$
$164$		0			0
$165$	−9345.95	+	25677.8i	−0.343285	+	0.943169i
$166$		0			0
$167$	−45243.1	+	7977.57i	−1.62226	+	0.286047i	−0.909606	−	0.415473i	$-0.863616\pi$
$167$	−45243.1	+	7977.57i	−1.62226	+	0.286047i	−0.712650	+	0.701520i	$0.752505\pi$
$168$		0			0
$169$	−57023.4	−	47848.3i	−1.99655	−	1.67530i
$170$		0			0
$171$	−5390.25	−	23026.5i	−0.184339	−	0.787472i
$172$		0			0
$173$	33628.3	−	40076.7i	1.12360	−	1.33906i	0.189571	−	0.981867i	$-0.439290\pi$
$173$	33628.3	−	40076.7i	1.12360	−	1.33906i	0.934032	−	0.357191i	$-0.116265\pi$
$174$		0			0
$175$	6031.35	+	34205.5i	0.196942	+	1.11691i
$176$		0			0
$177$	6463.20	+	2352.41i	0.206301	+	0.0750874i
$178$		0			0
$179$	−3772.59	−	2178.10i	−0.117743	−	0.0679787i	0.439972	−	0.898011i	$-0.354988\pi$
$179$	−3772.59	−	2178.10i	−0.117743	−	0.0679787i	−0.557715	+	0.830033i	$0.688322\pi$
$180$		0			0
$181$	22208.2	+	26466.7i	0.677886	+	0.807873i	0.989834	−	0.142226i	$-0.0454261\pi$
$181$	22208.2	+	26466.7i	0.677886	+	0.807873i	−0.311948	+	0.950099i	$0.600982\pi$
$182$		0			0
$183$	5662.56	−	3269.28i	0.169087	−	0.0976226i
$184$		0			0
$185$	18893.0	+	3331.34i	0.552023	+	0.0973365i
$186$		0			0
$187$	−26311.2	+	9576.49i	−0.752415	+	0.273857i
$188$		0			0
$189$			9701.24i			0.271584i
$190$		0			0
$191$	2319.58			0.0635833			0.0317917	−	0.999495i	$-0.489879\pi$
$191$	2319.58			0.0635833			0.0317917	+	0.999495i	$0.489879\pi$
$192$		0			0
$193$	11685.7	+	32106.2i	0.313719	+	0.861935i	0.991898	+	0.127038i	$0.0405471\pi$
$193$	11685.7	+	32106.2i	0.313719	+	0.861935i	−0.678179	+	0.734896i	$0.737231\pi$
$194$		0			0
$195$	−24287.0	+	137738.i	−0.638710	+	3.62231i
$196$		0			0
$197$	6488.54	+	11238.5i	0.167192	+	0.289585i	0.937431	−	0.348170i	$-0.113197\pi$
$197$	6488.54	+	11238.5i	0.167192	+	0.289585i	−0.770240	+	0.637755i	$0.779863\pi$
$198$		0			0
$199$	39079.4	−	32791.5i	0.986828	−	0.828047i	0.00172223	−	0.999999i	$-0.499452\pi$
$199$	39079.4	−	32791.5i	0.986828	−	0.828047i	0.985105	+	0.171952i	$0.0550074\pi$
$200$		0			0
$201$	40318.6	−	69833.9i	0.997961	−	1.72852i
$202$		0			0
$203$	−14449.9	+	39700.7i	−0.350649	+	0.963400i
$204$		0			0
$205$	36804.5	−	6489.63i	0.875776	−	0.154423i
$206$		0			0
$207$	26149.4	+	21942.0i	0.610270	+	0.512077i
$208$		0			0
$209$	−12386.2	−	18946.1i	−0.283561	−	0.433738i
$210$		0			0
$211$	17233.3	−	20537.9i	0.387083	−	0.461308i	−0.536953	−	0.843612i	$-0.680425\pi$
$211$	17233.3	−	20537.9i	0.387083	−	0.461308i	0.924037	+	0.382304i	$0.124869\pi$
$212$		0			0
$213$	3428.63	+	19444.7i	0.0755721	+	0.428591i
$214$		0			0
$215$	−15536.1	−	5654.69i	−0.336098	−	0.122330i
$216$		0			0
$217$	55496.5	+	32040.9i	1.17854	+	0.680433i
$218$		0			0
$219$	−64138.3	−	76437.0i	−1.33730	−	1.59373i
$220$		0			0
$221$	−124113.	+	71656.6i	−2.54116	+	1.46714i
$222$		0			0
$223$	36556.3	+	6445.86i	0.735110	+	0.129620i	0.528655	−	0.848837i	$-0.322696\pi$
$223$	36556.3	+	6445.86i	0.735110	+	0.129620i	0.206454	+	0.978456i	$0.433808\pi$
$224$		0			0
$225$	41324.2	−	15040.8i	0.816280	−	0.297101i
$226$		0			0
$227$		−	58042.3i		−	1.12640i	−0.826320	−	0.563200i	$-0.809570\pi$
$227$		−	58042.3i		−	1.12640i	0.826320	−	0.563200i	$-0.190430\pi$
$228$		0			0
$229$	−47979.8			−0.914930			−0.457465	−	0.889228i	$-0.651242\pi$
$229$	−47979.8			−0.914930			−0.457465	+	0.889228i	$0.651242\pi$
$230$		0			0
$231$	−13430.8	−	36900.8i	−0.251697	−	0.691532i
$232$		0			0
$233$	15332.4	−	86954.6i	0.282422	−	1.60170i	−0.431927	−	0.901909i	$-0.642166\pi$
$233$	15332.4	−	86954.6i	0.282422	−	1.60170i	0.714350	−	0.699789i	$-0.246723\pi$
$234$		0			0
$235$	−56597.0	−	98028.8i	−1.02484	−	1.77508i
$236$		0			0
$237$	−64516.3	+	54135.6i	−1.14861	+	0.963798i
$238$		0			0
$239$	−21266.4	+	36834.6i	−0.372305	+	0.644851i	−0.989920	−	0.141629i	$-0.954766\pi$
$239$	−21266.4	+	36834.6i	−0.372305	+	0.644851i	0.617615	+	0.786481i	$0.288099\pi$
$240$		0			0
$241$	−378.914	+	1041.06i	−0.00652390	+	0.0179243i	−0.942912	−	0.333042i	$-0.891925\pi$
$241$	−378.914	+	1041.06i	−0.00652390	+	0.0179243i	0.936388	+	0.350967i	$0.114147\pi$
$242$		0			0
$243$	75348.3	−	13285.9i	1.27603	−	0.224999i
$244$		0			0
$245$	−7614.45	−	6389.28i	−0.126855	−	0.106444i
$246$		0			0
$247$	−79273.4	−	84491.2i	−1.29937	−	1.38490i
$248$		0			0
$249$	57382.3	−	68385.5i	0.925505	−	1.10297i
$250$		0			0
$251$	−5413.15	−	30699.5i	−0.0859217	−	0.487286i	−0.997154	−	0.0753931i	$-0.975979\pi$
$251$	−5413.15	−	30699.5i	−0.0859217	−	0.487286i	0.911232	−	0.411893i	$-0.135132\pi$
$252$		0			0
$253$	30702.7	+	11174.9i	0.479662	+	0.174583i
$254$		0			0
$255$	168532.	+	97302.2i	2.59181	+	1.49638i
$256$		0			0
$257$	50379.6	+	60040.0i	0.762760	+	0.909023i	0.998019	−	0.0629103i	$-0.0200382\pi$
$257$	50379.6	+	60040.0i	0.762760	+	0.909023i	−0.235259	+	0.971933i	$0.575594\pi$
$258$		0			0
$259$	−23875.8	+	13784.7i	−0.355925	+	0.205494i
$260$		0			0
$261$	52679.1	+	9288.75i	0.773317	+	0.136357i
$262$		0			0
$263$	82030.2	−	29856.6i	1.18594	−	0.431647i	0.327643	−	0.944802i	$-0.393746\pi$
$263$	82030.2	−	29856.6i	1.18594	−	0.431647i	0.858296	+	0.513155i	$0.171523\pi$
$264$		0			0
$265$		−	65714.5i		−	0.935771i
$266$		0			0
$267$	−76212.2			−1.06906
$268$		0			0
$269$	2186.85	+	6008.31i	0.0302213	+	0.0830325i	0.953886	−	0.300170i	$-0.0970434\pi$
$269$	2186.85	+	6008.31i	0.0302213	+	0.0830325i	−0.923664	+	0.383202i	$0.874821\pi$
$270$		0			0
$271$	718.640	−	4075.61i	0.00978527	−	0.0554950i	−0.979524	−	0.201327i	$-0.935475\pi$
$271$	718.640	−	4075.61i	0.00978527	−	0.0554950i	0.989309	+	0.145832i	$0.0465858\pi$
$272$		0			0
$273$	−100497.	−	174065.i	−1.34842	−	2.33554i
$274$		0			0
$275$	32244.4	−	27056.3i	0.426372	−	0.357769i
$276$		0			0
$277$	−57251.9	+	99163.2i	−0.746157	+	1.29238i	0.203495	+	0.979076i	$0.434770\pi$
$277$	−57251.9	+	99163.2i	−0.746157	+	1.29238i	−0.949652	+	0.313306i	$0.898563\pi$
$278$		0			0
$279$	27749.9	−	76242.1i	0.356494	−	0.979460i
$280$		0			0
$281$	−75809.1	+	13367.2i	−0.960082	+	0.169288i	−0.631663	−	0.775243i	$-0.717627\pi$
$281$	−75809.1	+	13367.2i	−0.960082	+	0.169288i	−0.328420	+	0.944532i	$0.606516\pi$
$282$		0			0
$283$	16680.1	+	13996.3i	0.208270	+	0.174759i	0.740956	−	0.671554i	$-0.234373\pi$
$283$	16680.1	+	13996.3i	0.208270	+	0.174759i	−0.532686	+	0.846313i	$0.678817\pi$
$284$		0			0
$285$	−45536.8	+	150589.i	−0.560625	+	1.85397i
$286$		0			0
$287$	−34522.0	+	41141.7i	−0.419114	+	0.499480i
$288$		0			0
$289$	20123.0	+	114123.i	0.240934	+	1.36640i
$290$		0			0
$291$	47695.6	+	17359.8i	0.563239	+	0.205002i
$292$		0			0
$293$	−6337.52	−	3658.97i	−0.0738217	−	0.0426210i	0.462635	−	0.886549i	$-0.346904\pi$
$293$	−6337.52	−	3658.97i	−0.0738217	−	0.0426210i	−0.536456	+	0.843928i	$0.680237\pi$
$294$		0			0
$295$	−13150.7	−	15672.4i	−0.151114	−	0.180090i
$296$		0			0
$297$	10181.6	−	5878.32i	0.115425	−	0.0666408i
$298$		0			0
$299$	164692.	+	29039.7i	1.84218	+	0.324825i
$300$		0			0
$301$	22326.5	−	8126.20i	0.246427	−	0.0896921i
$302$		0			0
$303$		−	45935.1i		−	0.500333i
$304$		0			0
$305$	−19449.2			−0.209075
$306$		0			0
$307$	15214.4	+	41801.2i	0.161428	+	0.443519i	0.993865	−	0.110600i	$-0.0352773\pi$
$307$	15214.4	+	41801.2i	0.161428	+	0.443519i	−0.832437	+	0.554119i	$0.813055\pi$
$308$		0			0
$309$	7029.33	−	39865.3i	0.0736202	−	0.417521i
$310$		0			0
$311$	−27129.2	−	46989.2i	−0.280489	−	0.485822i	0.691016	−	0.722840i	$-0.257163\pi$
$311$	−27129.2	−	46989.2i	−0.280489	−	0.485822i	−0.971505	+	0.237018i	$0.923830\pi$
$312$		0			0
$313$	−133986.	+	112427.i	−1.36763	+	1.14758i	−0.394093	+	0.919071i	$0.628941\pi$
$313$	−133986.	+	112427.i	−1.36763	+	1.14758i	−0.973541	+	0.228510i	$0.926614\pi$
$314$		0			0
$315$	−61017.9	+	105686.i	−0.614945	+	1.06512i
$316$		0			0
$317$	17422.9	−	47869.1i	0.173381	−	0.476361i	−0.822316	−	0.569032i	$-0.807318\pi$
$317$	17422.9	−	47869.1i	0.173381	−	0.476361i	0.995697	+	0.0926706i	$0.0295404\pi$
$318$		0			0
$319$	50422.0	−	8890.77i	0.495495	−	0.0873691i
$320$		0			0
$321$	−95201.7	−	79883.7i	−0.923920	−	0.775261i
$322$		0			0
$323$	−148196.	+	63440.5i	−1.42046	+	0.608081i
$324$		0			0
$325$	138484.	−	165039.i	1.31109	−	1.56250i
$326$		0			0
$327$	43184.4	+	244911.i	0.403861	+	2.29041i
$328$		0			0
$329$	152858.	+	55635.7i	1.41220	+	0.513998i
$330$		0			0
$331$	42178.2	+	24351.6i	0.384975	+	0.222265i	0.679980	−	0.733230i	$-0.261988\pi$
$331$	42178.2	+	24351.6i	0.384975	+	0.222265i	−0.295006	+	0.955495i	$0.595322\pi$
$332$		0			0
$333$	22437.2	+	26739.7i	0.202340	+	0.241139i
$334$		0			0
$335$	−207723.	+	119929.i	−1.85095	+	1.06865i
$336$		0			0
$337$	−172939.	−	30493.9i	−1.52277	−	0.268505i	−0.651248	−	0.758865i	$-0.725754\pi$
$337$	−172939.	−	30493.9i	−1.52277	−	0.268505i	−0.871520	+	0.490360i	$0.836865\pi$
$338$		0			0
$339$	104137.	−	37902.7i	0.906159	−	0.329815i
$340$		0			0
$341$		−	77658.9i		−	0.667855i
$342$		0			0
$343$	−109944.			−0.934513
$344$		0			0
$345$	−77667.7	−	213390.i	−0.652533	−	1.79282i
$346$		0			0
$347$	−35555.2	+	201644.i	−0.295287	+	1.67466i	0.370747	+	0.928734i	$0.379102\pi$
$347$	−35555.2	+	201644.i	−0.295287	+	1.67466i	−0.666034	+	0.745921i	$0.732009\pi$
$348$		0			0
$349$	14177.9	+	24556.8i	0.116402	+	0.201614i	0.918339	−	0.395794i	$-0.129531\pi$
$349$	14177.9	+	24556.8i	0.116402	+	0.201614i	−0.801937	+	0.597408i	$0.796197\pi$
$350$		0			0
$351$	46096.6	−	38679.6i	0.374158	−	0.313955i
$352$		0			0
$353$	31647.8	−	54815.5i	0.253976	−	0.439900i	−0.710641	−	0.703555i	$-0.751595\pi$
$353$	31647.8	−	54815.5i	0.253976	−	0.439900i	0.964617	+	0.263655i	$0.0849281\pi$
$354$		0			0
$355$	20087.3	−	55189.3i	0.159391	−	0.437924i
$356$		0			0
$357$	−275412.	+	48562.6i	−2.16096	+	0.381035i
$358$		0			0
$359$	138189.	+	115954.i	1.07222	+	0.899699i	0.995252	−	0.0973344i	$-0.0310316\pi$
$359$	138189.	+	115954.i	1.07222	+	0.899699i	0.0769680	+	0.997034i	$0.475476\pi$
$360$		0			0
$361$	−77243.7	−	104962.i	−0.592719	−	0.805409i
$362$		0			0
$363$	83322.9	−	99300.3i	0.632340	−	0.753594i
$364$		0			0
$365$	51539.3	+	292294.i	0.386859	+	2.19399i
$366$		0			0
$367$	155098.	+	56451.0i	1.15153	+	0.419121i	0.846063	−	0.533083i	$-0.178966\pi$
$367$	155098.	+	56451.0i	1.15153	+	0.419121i	0.305463	+	0.952204i	$0.401189\pi$
$368$		0			0
$369$	58888.8	+	33999.5i	0.432494	+	0.249701i
$370$		0			0
$371$	60702.6	+	72342.5i	0.441021	+	0.525589i
$372$		0			0
$373$	17104.7	−	9875.42i	0.122942	−	0.0709803i	−0.437268	−	0.899331i	$-0.644054\pi$
$373$	17104.7	−	9875.42i	0.122942	−	0.0709803i	0.560210	+	0.828351i	$0.310721\pi$
$374$		0			0
$375$	−19868.8	−	3503.40i	−0.141289	−	0.0249131i
$376$		0			0
$377$	246256.	−	89629.7i	1.73262	−	0.630622i
$378$		0			0
$379$			62884.2i			0.437787i	0.975749	+	0.218894i	$0.0702448\pi$
$379$			62884.2i			0.437787i	−0.975749	+	0.218894i	$0.929755\pi$
$380$		0			0
$381$	39764.1			0.273931
$382$		0			0
$383$	−87776.5	−	241164.i	−0.598385	−	1.64405i	−0.754492	−	0.656309i	$-0.772117\pi$
$383$	−87776.5	−	241164.i	−0.598385	−	1.64405i	0.156107	−	0.987740i	$-0.450105\pi$
$384$		0			0
$385$	−20283.3	+	115033.i	−0.136842	+	0.776067i
$386$		0			0
$387$	−15041.1	−	26052.0i	−0.100429	−	0.173948i
$388$		0			0
$389$	57339.1	−	48113.2i	0.378924	−	0.317955i	−0.433356	−	0.901223i	$-0.642671\pi$
$389$	57339.1	−	48113.2i	0.378924	−	0.317955i	0.812280	+	0.583268i	$0.198226\pi$
$390$		0			0
$391$	116343.	−	201513.i	0.761006	−	1.31810i
$392$		0			0
$393$	−54766.7	+	150470.i	−0.354594	+	0.974240i
$394$		0			0
$395$	246709.	−	43501.5i	1.58122	−	0.278811i
$396$		0			0
$397$	76222.8	+	63958.5i	0.483619	+	0.405805i	0.851733	−	0.523976i	$-0.175552\pi$
$397$	76222.8	+	63958.5i	0.483619	+	0.405805i	−0.368114	+	0.929781i	$0.619996\pi$
$398$		0			0
$399$	−88973.8	−	207841.i	−0.558877	−	1.30553i
$400$		0			0
$401$	−17594.1	+	20967.9i	−0.109416	+	0.130396i	−0.817973	−	0.575257i	$-0.804902\pi$
$401$	−17594.1	+	20967.9i	−0.109416	+	0.130396i	0.708557	+	0.705653i	$0.249346\pi$
$402$		0			0
$403$	−69022.8	−	391448.i	−0.424994	−	2.41026i
$404$		0			0
$405$	−256309.	−	93289.0i	−1.56262	−	0.568749i
$406$		0			0
$407$	28934.4	+	16705.3i	0.174673	+	0.100847i
$408$		0			0
$409$	−31610.0	−	37671.3i	−0.188963	−	0.225198i	0.663242	−	0.748405i	$-0.269180\pi$
$409$	−31610.0	−	37671.3i	−0.188963	−	0.225198i	−0.852206	+	0.523207i	$0.824735\pi$
$410$		0			0
$411$	−44831.9	+	25883.7i	−0.265402	+	0.153230i
$412$		0			0
$413$	28954.1	+	5105.40i	0.169750	+	0.0299316i
$414$		0			0
$415$	−249525.	+	90819.8i	−1.44883	+	0.527333i
$416$		0			0
$417$			84106.1i			0.483677i
$418$		0			0
$419$	172898.			0.984829			0.492415	−	0.870361i	$-0.336114\pi$
$419$	172898.			0.984829			0.492415	+	0.870361i	$0.336114\pi$
$420$		0			0
$421$	−31024.7	−	85239.6i	−0.175042	−	0.480925i	0.820884	−	0.571095i	$-0.193481\pi$
$421$	−31024.7	−	85239.6i	−0.175042	−	0.480925i	−0.995926	+	0.0901699i	$0.971259\pi$
$422$		0			0
$423$	35764.0	−	202828.i	0.199878	−	1.13357i
$424$		0			0
$425$	−149883.	−	259604.i	−0.829800	−	1.43726i
$426$		0			0
$427$	21410.9	−	17965.8i	0.117430	−	0.0985353i
$428$		0			0
$429$	−121789.	+	210945.i	−0.661749	+	1.14618i
$430$		0			0
$431$	−57800.6	+	158806.i	−0.311156	+	0.854894i	0.681268	+	0.732034i	$0.261429\pi$
$431$	−57800.6	+	158806.i	−0.311156	+	0.854894i	−0.992424	+	0.122860i	$0.960793\pi$
$432$		0			0
$433$	62509.0	−	11022.0i	0.333401	−	0.0587876i	−0.00444187	−	0.999990i	$-0.501414\pi$
$433$	62509.0	−	11022.0i	0.333401	−	0.0587876i	0.337843	+	0.941203i	$0.390303\pi$
$434$		0			0
$435$	−272597.	−	228736.i	−1.44060	−	1.20880i
$436$		0			0
$437$	180057.	+	54447.9i	0.942862	+	0.285114i
$438$		0			0
$439$	78416.9	−	93453.6i	0.406893	−	0.484916i	−0.523216	−	0.852200i	$-0.675268\pi$
$439$	78416.9	−	93453.6i	0.406893	−	0.484916i	0.930109	+	0.367284i	$0.119712\pi$
$440$		0			0
$441$	−3140.56	−	17811.0i	−0.0161484	−	0.0915823i
$442$		0			0
$443$	−39956.5	−	14543.0i	−0.203601	−	0.0741047i	0.238207	−	0.971214i	$-0.423440\pi$
$443$	−39956.5	−	14543.0i	−0.203601	−	0.0741047i	−0.441808	+	0.897110i	$0.645663\pi$
$444$		0			0
$445$	196324.	+	113348.i	0.991411	+	0.572392i
$446$		0			0
$447$	−340059.	−	405266.i	−1.70192	−	2.02827i
$448$		0			0
$449$	244799.	−	141335.i	1.21427	−	0.701061i	0.250585	−	0.968094i	$-0.419377\pi$
$449$	244799.	−	141335.i	1.21427	−	0.701061i	0.963687	+	0.267034i	$0.0860436\pi$
$450$		0			0
$451$	64096.7	+	11302.0i	0.315125	+	0.0555650i
$452$		0			0
$453$	260388.	−	94773.6i	1.26889	−	0.461839i
$454$		0			0
$455$			597861.i			2.88787i
$456$		0			0
$457$	−245414.			−1.17508			−0.587539	−	0.809196i	$-0.699903\pi$
$457$	−245414.			−1.17508			−0.587539	+	0.809196i	$0.699903\pi$
$458$		0			0
$459$	−28636.3	−	78677.5i	−0.135922	−	0.373444i
$460$		0			0
$461$	−54578.8	+	309532.i	−0.256816	+	1.45648i	0.534552	+	0.845136i	$0.320480\pi$
$461$	−54578.8	+	309532.i	−0.256816	+	1.45648i	−0.791368	+	0.611340i	$0.790631\pi$
$462$		0			0
$463$	207033.	+	358592.i	0.965779	+	1.67278i	0.707507	+	0.706706i	$0.249820\pi$
$463$	207033.	+	358592.i	0.965779	+	1.67278i	0.258272	+	0.966072i	$0.416847\pi$
$464$		0			0
$465$	−413469.	+	346942.i	−1.91222	+	1.60454i
$466$		0			0
$467$	−126489.	+	219086.i	−0.579990	+	1.00457i	0.415489	+	0.909598i	$0.363610\pi$
$467$	−126489.	+	219086.i	−0.579990	+	1.00457i	−0.995480	+	0.0949745i	$0.969723\pi$
$468$		0			0
$469$	117892.	−	323906.i	0.535969	−	1.47256i
$470$		0			0
$471$	319138.	−	56272.6i	1.43859	−	0.253662i
$472$		0			0
$473$	−22057.0	−	18508.0i	−0.0985879	−	0.0827250i
$474$		0			0
$475$	176729.	−	165815.i	0.783284	−	0.734913i
$476$		0			0
$477$	76856.6	−	91594.2i	0.337788	−	0.402560i
$478$		0			0
$479$	−3378.29	−	19159.3i	−0.0147240	−	0.0835040i	0.976560	−	0.215244i	$-0.0690547\pi$
$479$	−3378.29	−	19159.3i	−0.0147240	−	0.0835040i	−0.991284	+	0.131740i	$0.957944\pi$
$480$		0			0
$481$	160695.	+	58488.0i	0.694562	+	0.252800i
$482$		0			0
$483$	282617.	+	163169.i	1.21145	+	0.699428i
$484$		0			0
$485$	−97046.3	−	115655.i	−0.412568	−	0.491679i
$486$		0			0
$487$	−138308.	+	79852.2i	−0.583162	+	0.336689i	−0.762389	−	0.647119i	$-0.775974\pi$
$487$	−138308.	+	79852.2i	−0.583162	+	0.336689i	0.179227	+	0.983808i	$0.442640\pi$
$488$		0			0
$489$	413920.	+	72985.3i	1.73101	+	0.305223i
$490$		0			0
$491$	−61049.3	+	22220.1i	−0.253232	+	0.0921687i	−0.465517	−	0.885039i	$-0.654132\pi$
$491$	−61049.3	+	22220.1i	−0.253232	+	0.0921687i	0.212285	+	0.977208i	$0.431909\pi$
$492$		0			0
$493$		−	364628.i		−	1.50022i
$494$		0			0
$495$	147892.			0.603577
$496$		0			0
$497$	28866.9	+	79311.1i	0.116866	+	0.321086i
$498$		0			0
$499$	−10083.2	+	57184.4i	−0.0404944	+	0.229655i	−0.998338	−	0.0576361i	$-0.981644\pi$
$499$	−10083.2	+	57184.4i	−0.0404944	+	0.229655i	0.957843	+	0.287291i	$0.0927548\pi$
$500$		0			0
$501$	278038.	+	481575.i	1.10772	+	1.91862i
$502$		0			0
$503$	−280926.	+	235725.i	−1.11034	+	0.931686i	−0.998077	−	0.0619926i	$-0.980254\pi$
$503$	−280926.	+	235725.i	−1.11034	+	0.931686i	−0.112263	+	0.993678i	$0.535810\pi$
$504$		0			0
$505$	−68317.8	+	118330.i	−0.267887	+	0.463993i
$506$		0			0
$507$	−308165.	+	846677.i	−1.19886	+	3.29384i
$508$		0			0
$509$	−327355.	+	57721.5i	−1.26352	+	0.222793i	−0.764970	−	0.644066i	$-0.777246\pi$
$509$	−327355.	+	57721.5i	−1.26352	+	0.222793i	−0.498553	+	0.866859i	$0.666135\pi$
$510$		0			0
$511$	−326739.	−	274167.i	−1.25129	−	1.04996i
$512$		0			0
$513$	56654.0	−	37038.2i	0.215276	−	0.140739i
$514$		0			0
$515$	−77398.0	+	92239.4i	−0.291820	+	0.347778i
$516$		0			0
$517$	−34231.7	−	194137.i	−0.128070	−	0.726321i
$518$		0			0
$519$	−595054.	−	216582.i	−2.20913	−	0.804058i
$520$		0			0
$521$	−154075.	−	88955.0i	−0.567617	−	0.327714i	0.188580	−	0.982058i	$-0.439612\pi$
$521$	−154075.	−	88955.0i	−0.567617	−	0.327714i	−0.756197	+	0.654344i	$0.772945\pi$
$522$		0			0
$523$	−7225.72	−	8611.28i	−0.0264167	−	0.0314821i	0.752674	−	0.658393i	$-0.228763\pi$
$523$	−7225.72	−	8611.28i	−0.0264167	−	0.0314821i	−0.779091	+	0.626911i	$0.784319\pi$
$524$		0			0
$525$	364089.	−	210207.i	1.32096	−	0.762655i
$526$		0			0
$527$	−544658.	−	96037.9i	−1.96111	−	0.345797i
$528$		0			0
$529$	7815.74	−	2844.70i	0.0279292	−	0.0101654i
$530$		0			0
$531$		−	37224.9i		−	0.132021i
$532$		0			0
$533$	333131.			1.17263
$534$		0			0
$535$	126433.	+	347372.i	0.441727	+	1.21363i
$536$		0			0
$537$	−9156.13	+	51927.0i	−0.0317514	+	0.180071i
$538$		0			0
$539$	−8655.44	−	14991.7i	−0.0297928	−	0.0516027i
$540$		0			0
$541$	−381628.	+	320224.i	−1.30391	+	1.09411i	−0.314450	+	0.949274i	$0.601820\pi$
$541$	−381628.	+	320224.i	−1.30391	+	1.09411i	−0.989456	+	0.144833i	$0.953736\pi$
$542$		0			0
$543$	209098.	−	362168.i	0.709169	−	1.22832i
$544$		0			0
$545$	253004.	−	695123.i	0.851794	−	2.34028i
$546$		0			0
$547$	276.343	−	48.7267i	0.000923578	−	0.000162852i	−0.173186	−	0.984889i	$-0.555406\pi$
$547$	276.343	−	48.7267i	0.000923578	−	0.000162852i	0.174110	+	0.984726i	$0.444295\pi$
$548$		0			0
$549$	−27108.7	−	22746.9i	−0.0899422	−	0.0754704i
$550$		0			0
$551$	287015.	−	67187.2i	0.945370	−	0.221301i
$552$		0			0
$553$	−231409.	+	275783.i	−0.756711	+	0.901813i
$554$		0			0
$555$	−40323.0	−	228683.i	−0.130908	−	0.742416i
$556$		0			0
$557$	107948.	+	39289.8i	0.347940	+	0.126640i	0.510078	−	0.860128i	$-0.329617\pi$
$557$	107948.	+	39289.8i	0.347940	+	0.126640i	−0.162138	+	0.986768i	$0.551839\pi$
$558$		0			0
$559$	−127630.	−	73687.4i	−0.408442	−	0.235814i
$560$		0			0
$561$	217849.	+	259622.i	0.692196	+	0.824928i
$562$		0			0
$563$	43650.6	−	25201.7i	0.137713	−	0.0795084i	−0.429561	−	0.903038i	$-0.641332\pi$
$563$	43650.6	−	25201.7i	0.137713	−	0.0795084i	0.567273	+	0.823530i	$0.307998\pi$
$564$		0			0
$565$	−324630.	−	57241.0i	−1.01693	−	0.179312i
$566$		0			0
$567$	368335.	−	134063.i	1.14572	−	0.417007i
$568$		0			0
$569$			51452.5i			0.158921i	0.996838	+	0.0794606i	$0.0253198\pi$
$569$			51452.5i			0.158921i	−0.996838	+	0.0794606i	$0.974680\pi$
$570$		0			0
$571$	−313784.			−0.962406			−0.481203	−	0.876609i	$-0.659800\pi$
$571$	−313784.			−0.962406			−0.481203	+	0.876609i	$0.659800\pi$
$572$		0			0
$573$	−9602.73	−	26383.3i	−0.0292473	−	0.0803562i
$574$		0			0
$575$	−60741.8	+	344484.i	−0.183718	+	1.04192i
$576$		0			0
$577$	292982.	+	507460.i	0.880014	+	1.52423i	0.851324	+	0.524640i	$0.175800\pi$
$577$	292982.	+	507460.i	0.880014	+	1.52423i	0.0286892	+	0.999588i	$0.490867\pi$
$578$		0			0
$579$	316804.	−	265830.i	0.945002	−	0.792951i
$580$		0			0
$581$	190800.	−	330475.i	0.565230	−	0.979008i
$582$		0			0
$583$	39142.4	−	107543.i	0.115162	−	0.316406i
$584$		0			0
$585$	745463.	−	131445.i	2.17828	−	0.384090i
$586$		0			0
$587$	86046.8	+	72201.8i	0.249723	+	0.209542i	0.759053	−	0.651029i	$-0.225662\pi$
$587$	86046.8	+	72201.8i	0.249723	+	0.209542i	−0.509330	+	0.860571i	$0.670107\pi$
$588$		0			0
$589$	−24764.2	−	446421.i	−0.0713828	−	1.28681i
$590$		0			0
$591$	100967.	−	120327.i	0.289070	−	0.344500i
$592$		0			0
$593$	66008.9	+	374355.i	0.187712	+	1.06457i	0.922421	+	0.386187i	$0.126208\pi$
$593$	66008.9	+	374355.i	0.187712	+	1.06457i	−0.734708	+	0.678383i	$0.762681\pi$
$594$		0			0
$595$	781693.	+	284513.i	2.20802	+	0.803652i
$596$		0			0
$597$	−534758.	−	308743.i	−1.50040	−	0.866259i
$598$		0			0
$599$	−37860.1	−	45119.9i	−0.105518	−	0.125752i	0.710700	−	0.703495i	$-0.248378\pi$
$599$	−37860.1	−	45119.9i	−0.105518	−	0.125752i	−0.816219	+	0.577743i	$0.803934\pi$
$600$		0			0
$601$	−276837.	+	159832.i	−0.766435	+	0.442502i	−0.831602	−	0.555373i	$-0.812576\pi$
$601$	−276837.	+	159832.i	−0.766435	+	0.442502i	0.0651661	+	0.997874i	$0.479242\pi$
$602$		0			0
$603$	−429793.	−	75784.0i	−1.18202	−	0.208422i
$604$		0			0
$605$	−362328.	+	131876.i	−0.989899	+	0.360294i
$606$		0			0
$607$			350213.i			0.950507i	0.879849	+	0.475253i	$0.157644\pi$
$607$			350213.i			0.950507i	−0.879849	+	0.475253i	$0.842356\pi$
$608$		0			0
$609$	511382.			1.37883
$610$		0			0
$611$	−345097.	−	948146.i	−0.924397	−	2.53976i
$612$		0			0
$613$	−12206.6	+	69227.1i	−0.0324844	+	0.184228i	−0.996733	−	0.0807729i	$-0.974261\pi$
$613$	−12206.6	+	69227.1i	−0.0324844	+	0.184228i	0.964248	+	0.265001i	$0.0853722\pi$
$614$		0			0
$615$	−226179.	−	391754.i	−0.598002	−	1.03577i
$616$		0			0
$617$	542281.	−	455027.i	1.42447	−	1.19527i	0.475579	−	0.879673i	$-0.342239\pi$
$617$	542281.	−	455027.i	1.42447	−	1.19527i	0.948892	−	0.315600i	$-0.102206\pi$
$618$		0			0
$619$	−167678.	+	290427.i	−0.437617	+	0.757976i	−0.997505	−	0.0705929i	$-0.977511\pi$
$619$	−167678.	+	290427.i	−0.437617	+	0.757976i	0.559888	+	0.828568i	$0.310844\pi$
$620$		0			0
$621$	−33415.8	+	91809.2i	−0.0866501	+	0.238069i
$622$		0			0
$623$	−320829.	+	56570.8i	−0.826604	+	0.145753i
$624$		0			0
$625$	−275429.	−	231113.i	−0.705099	−	0.591648i
$626$		0			0
$627$	−164219.	+	219317.i	−0.417723	+	0.557876i
$628$		0			0
$629$	152944.	−	182272.i	0.386573	−	0.460700i
$630$		0			0
$631$	−40019.6	−	226962.i	−0.100511	−	0.570026i	−0.992919	−	0.118796i	$-0.962096\pi$
$631$	−40019.6	−	226962.i	−0.100511	−	0.570026i	0.892408	−	0.451230i	$-0.149015\pi$
$632$		0			0
$633$	−304944.	−	110991.i	−0.761050	−	0.277000i
$634$		0			0
$635$	−102433.	−	59139.8i	−0.254035	−	0.146667i
$636$		0			0
$637$	−56953.2	−	67874.2i	−0.140359	−	0.167273i
$638$		0			0
$639$	92545.0	−	53430.9i	0.226648	−	0.130855i
$640$		0			0
$641$	391871.	+	69097.5i	0.953734	+	0.168169i	0.628800	−	0.777567i	$-0.283547\pi$
$641$	391871.	+	69097.5i	0.953734	+	0.168169i	0.324935	+	0.945736i	$0.394658\pi$
$642$		0			0
$643$	131116.	−	47722.2i	0.317126	−	0.115425i	−0.178553	−	0.983930i	$-0.557141\pi$
$643$	131116.	−	47722.2i	0.317126	−	0.115425i	0.495679	+	0.868506i	$0.334919\pi$
$644$		0			0
$645$			200120.i			0.481028i
$646$		0			0
$647$	27790.7			0.0663883			0.0331941	−	0.999449i	$-0.489432\pi$
$647$	27790.7			0.0663883			0.0331941	+	0.999449i	$0.489432\pi$
$648$		0			0
$649$	−12186.2	−	33481.2i	−0.0289320	−	0.0794899i
$650$		0			0
$651$	134691.	−	763870.i	0.317816	−	1.80243i
$652$		0			0
$653$	−319447.	−	553298.i	−0.749155	−	1.29758i	−0.948228	−	0.317590i	$-0.897126\pi$
$653$	−319447.	−	553298.i	−0.749155	−	1.29758i	0.199073	−	0.979985i	$-0.436207\pi$
$654$		0			0
$655$	364870.	−	306162.i	0.850463	−	0.713623i
$656$		0			0
$657$	−270017.	+	467683.i	−0.625548	+	1.08348i
$658$		0			0
$659$	26699.8	−	73357.1i	0.0614805	−	0.168916i	−0.905149	−	0.425094i	$-0.860241\pi$
$659$	26699.8	−	73357.1i	0.0614805	−	0.168916i	0.966630	+	0.256178i	$0.0824632\pi$
$660$		0			0
$661$	−49357.5	+	8703.06i	−0.112967	+	0.0199191i	−0.229846	−	0.973227i	$-0.573822\pi$
$661$	−49357.5	+	8703.06i	−0.112967	+	0.0199191i	0.116879	+	0.993146i	$0.462711\pi$
$662$		0			0
$663$	1.32884e6	+	1.11503e6i	3.02305	+	2.53664i
$664$		0			0
$665$	−79916.4	+	667731.i	−0.180714	+	1.50993i
$666$		0			0
$667$	−273498.	+	325942.i	−0.614755	+	0.732636i
$668$		0			0
$669$	−78021.4	−	442481.i	−0.174326	−	0.988650i
$670$		0			0
$671$	−31828.9	−	11584.8i	−0.0706931	−	0.0257302i
$672$		0			0
$673$	−615226.	−	355201.i	−1.35833	−	0.784231i	−0.368929	−	0.929457i	$-0.620276\pi$
$673$	−615226.	−	355201.i	−1.35833	−	0.784231i	−0.989398	+	0.145227i	$0.953609\pi$
$674$		0			0
$675$	80905.4	+	96419.3i	0.177570	+	0.211620i
$676$		0			0
$677$	−318414.	+	183836.i	−0.694727	+	0.401101i	−0.805380	−	0.592758i	$-0.798039\pi$
$677$	−318414.	+	183836.i	−0.694727	+	0.401101i	0.110653	+	0.993859i	$0.464706\pi$
$678$		0			0
$679$	213669.	+	37675.6i	0.463449	+	0.0817186i
$680$		0			0
$681$	−660182.	+	240286.i	−1.42354	+	0.518126i
$682$		0			0
$683$		−	47025.2i		−	0.100807i	−0.998729	−	0.0504033i	$-0.983949\pi$
$683$		−	47025.2i		−	0.100807i	0.998729	−	0.0504033i	$-0.0160507\pi$
$684$		0			0
$685$	153984.			0.328167
$686$		0			0
$687$	198629.	+	545730.i	0.420853	+	1.15628i
$688$		0			0
$689$	101718.	−	576871.i	0.214269	−	1.21518i
$690$		0			0
$691$	153603.	+	266049.i	0.321695	+	0.557192i	0.980838	−	0.194826i	$-0.0624141\pi$
$691$	153603.	+	266049.i	0.321695	+	0.557192i	−0.659143	+	0.752018i	$0.729081\pi$
$692$		0			0
$693$	−162808.	+	136612.i	−0.339008	+	0.284461i
$694$		0			0
$695$	125088.	−	216659.i	0.258968	−	0.448546i
$696$		0			0
$697$	158532.	−	435563.i	0.326326	−	0.896573i
$698$		0			0
$699$	−1.05251e6	+	185586.i	−2.15413	+	0.379830i
$700$		0			0
$701$	46126.4	+	38704.6i	0.0938671	+	0.0787639i	0.688514	−	0.725223i	$-0.258264\pi$
$701$	46126.4	+	38704.6i	0.0938671	+	0.0787639i	−0.594646	+	0.803987i	$0.702708\pi$
$702$		0			0
$703$	171656.	+	86803.3i	0.347335	+	0.175641i
$704$		0			0
$705$	−880691.	+	1.04957e6i	−1.77193	+	2.11170i
$706$		0			0
$707$	−34096.7	−	193372.i	−0.0682140	−	0.386861i
$708$		0			0
$709$	233239.	+	84891.9i	0.463989	+	0.168878i	0.563428	−	0.826165i	$-0.309482\pi$
$709$	233239.	+	84891.9i	0.463989	+	0.168878i	−0.0994384	+	0.995044i	$0.531705\pi$
$710$		0			0
$711$	394746.	+	227907.i	0.780869	+	0.450835i
$712$		0			0
$713$	414835.	+	494382.i	0.816012	+	0.972486i
$714$		0			0
$715$	627462.	−	362265.i	1.22737	−	0.708622i
$716$		0			0
$717$	507002.	+	89398.1i	0.986214	+	0.173896i
$718$		0			0
$719$	−520380.	+	189403.i	−1.00661	+	0.366377i	−0.792131	−	0.610351i	$-0.791029\pi$
$719$	−520380.	+	189403.i	−1.00661	+	0.366377i	−0.214482	+	0.976728i	$0.568806\pi$
$720$		0			0
$721$		−	173038.i		−	0.332867i
$722$		0			0
$723$	13409.8			0.0256535
$724$		0			0
$725$	187477.	+	515088.i	0.356674	+	0.979954i
$726$		0			0
$727$	67242.9	−	381353.i	0.127226	−	0.721537i	−0.852734	−	0.522345i	$-0.825057\pi$
$727$	67242.9	−	381353.i	0.127226	−	0.721537i	0.979961	−	0.199192i	$-0.0638317\pi$
$728$		0			0
$729$	−156228.	−	270595.i	−0.293971	−	0.509172i
$730$		0			0
$731$	−157082.	+	131808.i	−0.293963	+	0.246664i
$732$		0			0
$733$	2211.44	−	3830.33i	0.00411593	−	0.00712900i	−0.863960	−	0.503560i	$-0.832023\pi$
$733$	2211.44	−	3830.33i	0.00411593	−	0.00712900i	0.868076	+	0.496431i	$0.165357\pi$
$734$		0			0
$735$	−41149.9	+	113059.i	−0.0761718	+	0.209280i
$736$		0			0
$737$	−411378.	+	72537.0i	−0.757366	+	0.133544i
$738$		0			0
$739$	305398.	+	256259.i	0.559213	+	0.469236i	0.878047	−	0.478575i	$-0.158847\pi$
$739$	305398.	+	256259.i	0.559213	+	0.469236i	−0.318833	+	0.947811i	$0.603291\pi$
$740$		0			0
$741$	−632835.	+	1.25145e6i	−1.15253	+	2.27917i
$742$		0			0
$743$	474303.	−	565252.i	0.859168	−	1.02392i	−0.140261	−	0.990115i	$-0.544794\pi$
$743$	474303.	−	565252.i	0.859168	−	1.02392i	0.999429	−	0.0338014i	$-0.0107614\pi$
$744$		0			0
$745$	273260.	+	1.54973e6i	0.492338	+	2.79219i
$746$		0			0
$747$	−454012.	−	165247.i	−0.813629	−	0.296137i
$748$		0			0
$749$	−460065.	−	265618.i	−0.820078	−	0.473472i
$750$		0			0
$751$	542438.	+	646452.i	0.961768	+	1.14619i	0.989201	+	0.146567i	$0.0468222\pi$
$751$	542438.	+	646452.i	0.961768	+	1.14619i	−0.0274331	+	0.999624i	$0.508733\pi$
$752$		0			0
$753$	−326771.	+	188661.i	−0.576307	+	0.332731i
$754$		0			0
$755$	−811720.	−	143128.i	−1.42401	−	0.251091i
$756$		0			0
$757$	787851.	−	286754.i	1.37484	−	0.500401i	0.454231	−	0.890884i	$-0.349914\pi$
$757$	787851.	−	286754.i	1.37484	−	0.500401i	0.920610	+	0.390483i	$0.127692\pi$
$758$		0			0
$759$		−	395479.i		−	0.686499i
$760$		0			0
$761$	258202.			0.445851			0.222925	−	0.974836i	$-0.428439\pi$
$761$	258202.			0.445851			0.222925	+	0.974836i	$0.428439\pi$
$762$		0			0
$763$	363585.	+	998942.i	0.624535	+	1.71590i
$764$		0			0
$765$	182892.	−	1.03723e6i	0.312516	−	1.77236i
$766$		0			0
$767$	−91183.6	−	157935.i	−0.154998	−	0.268464i
$768$		0			0
$769$	202961.	−	170305.i	0.343211	−	0.287988i	−0.454846	−	0.890570i	$-0.650306\pi$
$769$	202961.	−	170305.i	0.343211	−	0.287988i	0.798057	+	0.602582i	$0.205861\pi$
$770$		0			0
$771$	474340.	−	821581.i	0.797960	−	1.38211i
$772$		0			0
$773$	66157.2	−	181765.i	0.110718	−	0.304195i	−0.871943	−	0.489608i	$-0.837140\pi$
$773$	66157.2	−	181765.i	0.110718	−	0.304195i	0.982661	+	0.185413i	$0.0593622\pi$
$774$		0			0
$775$	818784.	−	144374.i	1.36322	−	0.240372i
$776$		0			0
$777$	255632.	+	214500.i	0.423421	+	0.355293i
$778$		0			0
$779$	372063.	+	44529.8i	0.613114	+	0.0733797i
$780$		0			0
$781$	65746.3	−	78353.4i	0.107788	−	0.128456i
$782$		0			0
$783$	26585.8	+	150775.i	0.0433636	+	0.245927i
$784$		0			0
$785$	−905798.	−	329683.i	−1.46991	−	0.535005i
$786$		0			0
$787$	90304.7	+	52137.4i	0.145801	+	0.0841783i	0.571126	−	0.820862i	$-0.306507\pi$
$787$	90304.7	+	52137.4i	0.145801	+	0.0841783i	−0.425325	+	0.905041i	$0.639840\pi$
$788$		0			0
$789$	−679186.	−	809422.i	−1.09102	−	1.30023i
$790$		0			0
$791$	410248.	−	236857.i	0.655682	−	0.378558i
$792$		0			0
$793$	−170734.	−	30104.9i	−0.271502	−	0.0478731i
$794$		0			0
$795$	−747446.	+	272048.i	−1.18262	+	0.430439i
$796$		0			0
$797$		−	1.02433e6i		−	1.61259i	−0.591515	−	0.806294i	$-0.701470\pi$
$797$		−	1.02433e6i		−	1.61259i	0.591515	−	0.806294i	$-0.298530\pi$
$798$		0			0
$799$	−1.40391e6			−2.19910
$800$		0			0
$801$	141074.	+	387598.i	0.219878	+	0.604111i
$802$		0			0
$803$	−89758.1	+	509043.i	−0.139201	+	0.789448i
$804$		0			0
$805$	−485351.	−	840653.i	−0.748970	−	1.29725i
$806$		0			0
$807$	59286.2	−	49747.0i	0.0910346	−	0.0763871i
$808$		0			0
$809$	69501.1	−	120379.i	0.106193	−	0.183931i	−0.808032	−	0.589138i	$-0.799467\pi$
$809$	69501.1	−	120379.i	0.106193	−	0.183931i	0.914225	+	0.405207i	$0.132801\pi$
$810$		0			0
$811$	−33162.9	+	91114.3i	−0.0504209	+	0.138530i	−0.962347	−	0.271825i	$-0.912373\pi$
$811$	−33162.9	+	91114.3i	−0.0504209	+	0.138530i	0.911926	+	0.410355i	$0.134595\pi$
$812$		0			0
$813$	−49331.6	+	8698.50i	−0.0746353	+	0.0131602i
$814$		0			0
$815$	−957719.	−	803621.i	−1.44186	−	1.20986i
$816$		0			0
$817$	−132696.	−	99359.3i	−0.198799	−	0.148855i
$818$		0			0
$819$	−699231.	+	833311.i	−1.04244	+	1.24234i
$820$		0			0
$821$	−97133.2	−	550870.i	−0.144106	−	0.817265i	−0.968081	−	0.250639i	$-0.919359\pi$
$821$	−97133.2	−	550870.i	−0.144106	−	0.817265i	0.823975	−	0.566626i	$-0.191752\pi$
$822$		0			0
$823$	42360.5	+	15418.0i	0.0625405	+	0.0227629i	0.373101	−	0.927791i	$-0.378294\pi$
$823$	42360.5	+	15418.0i	0.0625405	+	0.0227629i	−0.310560	+	0.950554i	$0.600517\pi$
$824$		0			0
$825$	−441229.	−	254744.i	−0.648270	−	0.374279i
$826$		0			0
$827$	388588.	+	463101.i	0.568170	+	0.677118i	0.971254	−	0.238044i	$-0.0765064\pi$
$827$	388588.	+	463101.i	0.568170	+	0.677118i	−0.403085	+	0.915163i	$0.632062\pi$
$828$		0			0
$829$	−637152.	+	367860.i	−0.927116	+	0.535271i	−0.885898	−	0.463880i	$-0.846457\pi$
$829$	−637152.	+	367860.i	−0.927116	+	0.535271i	−0.0412175	+	0.999150i	$0.513124\pi$
$830$		0			0
$831$	1.36491e6	+	240671.i	1.97653	+	0.348515i
$832$		0			0
$833$	−115847.	+	42165.0i	−0.166954	+	0.0607662i
$834$		0			0
$835$		−	1.65407e6i		−	2.37235i
$836$		0			0
$837$	232221.			0.331475
$838$		0			0
$839$	327167.	+	898883.i	0.464777	+	1.27697i	0.921854	+	0.387538i	$0.126674\pi$
$839$	327167.	+	898883.i	0.464777	+	1.27697i	−0.457076	+	0.889427i	$0.651103\pi$
$840$		0			0
$841$	7037.72	−	39912.9i	0.00995039	−	0.0564315i
$842$		0			0
$843$	465879.	+	806925.i	0.655568	+	1.13548i
$844$		0			0
$845$	2.05308e6	−	1.72273e6i	2.87536	−	2.41271i
$846$		0			0
$847$	277054.	−	479871.i	0.386187	−	0.668895i
$848$		0			0
$849$	90142.4	−	247664.i	0.125059	−	0.343596i
$850$		0			0
$851$	−273434.	+	48213.8i	−0.377566	+	0.0665751i
$852$		0			0
$853$	358823.	+	301088.i	0.493153	+	0.413805i	0.855155	−	0.518373i	$-0.173462\pi$
$853$	358823.	+	301088.i	0.493153	+	0.413805i	−0.362002	+	0.932177i	$0.617907\pi$
$854$		0			0
$855$	850152.	−	47160.3i	1.16296	−	0.0645125i
$856$		0			0
$857$	21649.4	−	25800.7i	0.0294770	−	0.0351293i	−0.751105	−	0.660183i	$-0.770479\pi$
$857$	21649.4	−	25800.7i	0.0294770	−	0.0351293i	0.780582	+	0.625054i	$0.214923\pi$
$858$		0			0
$859$	−129727.	−	735720.i	−0.175811	−	0.997072i	−0.937204	−	0.348782i	$-0.886596\pi$
$859$	−129727.	−	735720.i	−0.175811	−	0.997072i	0.761393	−	0.648290i	$-0.224516\pi$
$860$		0			0
$861$	610867.	+	222338.i	0.824025	+	0.299921i
$862$		0			0
$863$	−837032.	−	483261.i	−1.12388	−	0.648873i	−0.181493	−	0.983392i	$-0.558093\pi$
$863$	−837032.	−	483261.i	−1.12388	−	0.648873i	−0.942389	+	0.334519i	$0.891426\pi$
$864$		0			0
$865$	1.21076e6	+	1.44292e6i	1.61817	+	1.92846i
$866$		0			0
$867$	1.21475e6	−	701336.i	1.61603	−	0.933014i
$868$		0			0
$869$	429655.	+	75759.8i	0.568959	+	0.100323i
$870$		0			0
$871$	−2.00912e6	+	731261.i	−2.64832	+	0.963910i
$872$		0			0
$873$		−	274704.i		−	0.360442i
$874$		0			0
$875$	−86241.7			−0.112642
$876$		0			0
$877$	476224.	+	1.30842e6i	0.619174	+	1.70117i	0.709000	+	0.705208i	$0.249147\pi$
$877$	476224.	+	1.30842e6i	0.619174	+	1.70117i	−0.0898265	+	0.995957i	$0.528631\pi$
$878$		0			0
$879$	−15381.3	+	87231.4i	−0.0199074	+	0.112900i
$880$		0			0
$881$	306465.	+	530813.i	0.394847	+	0.683895i	0.993082	−	0.117426i	$-0.0374643\pi$
$881$	306465.	+	530813.i	0.394847	+	0.683895i	−0.598235	+	0.801321i	$0.704131\pi$
$882$		0			0
$883$	1.05100e6	−	881896.i	1.34798	−	1.13109i	0.368478	−	0.929637i	$-0.379879\pi$
$883$	1.05100e6	−	881896.i	1.34798	−	1.13109i	0.979499	−	0.201450i	$-0.0645654\pi$
$884$		0			0
$885$	−123818.	+	214459.i	−0.158087	+	0.273815i
$886$		0			0
$887$	−311606.	+	856129.i	−0.396057	+	1.08816i	0.568131	+	0.822938i	$0.307667\pi$
$887$	−311606.	+	856129.i	−0.396057	+	1.08816i	−0.964188	+	0.265220i	$0.914555\pi$
$888$		0			0
$889$	167394.	−	29516.1i	0.211805	−	0.0373469i
$890$		0			0
$891$	−363888.	−	305338.i	−0.458366	−	0.384614i
$892$		0			0
$893$	−258688.	−	1.10508e6i	−0.324394	−	1.38577i
$894$		0			0
$895$	100816.	−	120147.i	0.125858	−	0.149992i
$896$		0			0
$897$	−351500.	−	1.99345e6i	−0.436858	−	2.47754i
$898$		0			0
$899$	950326.	+	345890.i	1.17585	+	0.427976i
$900$		0			0
$901$	−705842.	−	407518.i	−0.869477	−	0.501993i
$902$		0			0
$903$	−184857.	−	220304.i	−0.226705	−	0.270176i
$904$		0			0
$905$	−1.07728e6	+	621968.i	−1.31532	+	0.759401i
$906$		0			0
$907$	−1.39765e6	−	246443.i	−1.69896	−	0.299572i	−0.761628	−	0.648014i	$-0.775600\pi$
$907$	−1.39765e6	−	246443.i	−1.69896	−	0.299572i	−0.937330	+	0.348442i	$0.886711\pi$
$908$		0			0
$909$	−233616.	+	85029.2i	−0.282732	+	0.102906i
$910$		0			0
$911$			994499.i			1.19831i	0.800635	+	0.599153i	$0.204496\pi$
$911$			994499.i			1.19831i	−0.800635	+	0.599153i	$0.795504\pi$
$912$		0			0
$913$	−462449.			−0.554782
$914$		0			0
$915$	80516.7	+	221218.i	0.0961709	+	0.264227i
$916$		0			0
$917$	−118859.	+	674084.i	−0.141349	+	0.801633i
$918$		0			0
$919$	−105274.	−	182340.i	−0.124649	−	0.215899i	0.796947	−	0.604050i	$-0.206447\pi$
$919$	−105274.	−	182340.i	−0.124649	−	0.215899i	−0.921596	+	0.388151i	$0.873114\pi$
$920$		0			0
$921$	412468.	−	346102.i	0.486263	−	0.408023i
$922$		0			0
$923$	261761.	−	453384.i	0.307257	−	0.532185i
$924$		0			0
$925$	−122338.	+	336122.i	−0.142981	+	0.392838i
$926$		0			0
$927$	−215758.	+	38043.9i	−0.251077	+	0.0442717i
$928$		0			0
$929$	−8081.27	−	6780.99i	−0.00936372	−	0.00785709i	0.638094	−	0.769959i	$-0.279723\pi$
$929$	−8081.27	−	6780.99i	−0.00936372	−	0.00785709i	−0.647457	+	0.762102i	$0.724168\pi$
$930$		0			0
$931$	−54536.3	−	83419.3i	−0.0629196	−	0.0962425i
$932$		0			0
$933$	−422151.	+	503100.i	−0.484958	+	0.577951i
$934$		0			0
$935$	−175056.	−	992791.i	−0.200241	−	1.13562i
$936$		0			0
$937$	31055.5	+	11303.3i	0.0353720	+	0.0128744i	0.359646	−	0.933089i	$-0.382898\pi$
$937$	31055.5	+	11303.3i	0.0353720	+	0.0128744i	−0.324274	+	0.945963i	$0.605120\pi$
$938$		0			0
$939$	1.83345e6	+	1.05854e6i	2.07940	+	1.20054i
$940$		0			0
$941$	−894179.	−	1.06564e6i	−1.00982	−	1.20346i	−0.978984	−	0.203936i	$-0.934627\pi$
$941$	−894179.	−	1.06564e6i	−1.00982	−	1.20346i	−0.0308387	−	0.999524i	$-0.509818\pi$
$942$		0			0
$943$	−468416.	+	270440.i	−0.526755	+	0.304122i
$944$		0			0
$945$	−343978.	−	60652.6i	−0.385183	−	0.0679181i
$946$		0			0
$947$	−385244.	+	140217.i	−0.429572	+	0.156351i	−0.547752	−	0.836641i	$-0.684516\pi$
$947$	−385244.	+	140217.i	−0.429572	+	0.156351i	0.118180	+	0.992992i	$0.462294\pi$
$948$		0			0
$949$			2.64566e6i			2.93767i
$950$		0			0
$951$	−616598.			−0.681775
$952$		0			0
$953$	60967.8	+	167508.i	0.0671297	+	0.184437i	0.968721	−	0.248151i	$-0.0798228\pi$
$953$	60967.8	+	167508.i	0.0671297	+	0.184437i	−0.901592	+	0.432588i	$0.857601\pi$
$954$		0			0
$955$	−14502.1	+	82245.7i	−0.0159010	+	0.0901793i
$956$		0			0
$957$	−309865.	−	536701.i	−0.338336	−	0.586015i
$958$		0			0
$959$	−169515.	+	142240.i	−0.184319	+	0.154662i
$960$		0			0
$961$	305210.	−	528640.i	0.330486	−	0.572418i
$962$		0			0
$963$	−230046.	+	632045.i	−0.248063	+	0.681547i
$964$		0			0
$965$	−1.21145e6	+	213612.i	−1.30092	+	0.229388i
$966$		0			0
$967$	−1.11852e6	−	938550.i	−1.19616	−	1.00370i	−0.999731	−	0.0231844i	$-0.992620\pi$
$967$	−1.11852e6	−	938550.i	−1.19616	−	1.00370i	−0.196434	−	0.980517i	$-0.562936\pi$
$968$		0			0
$969$	1.33509e6	+	1.42296e6i	1.42188	+	1.51547i
$970$		0			0
$971$	−274314.	+	326915.i	−0.290944	+	0.346734i	−0.891641	−	0.452743i	$-0.850445\pi$
$971$	−274314.	+	326915.i	−0.290944	+	0.346734i	0.600697	+	0.799477i	$0.294890\pi$
$972$		0			0
$973$	62430.3	+	354060.i	0.0659431	+	0.373982i
$974$		0			0
$975$	−2.45048e6	−	891900.i	−2.57775	−	0.938225i
$976$		0			0
$977$	1.57184e6	+	907502.i	1.64672	+	0.950733i	0.978365	+	0.206889i	$0.0663338\pi$
$977$	1.57184e6	+	907502.i	1.64672	+	0.950733i	0.668353	+	0.743844i	$0.267000\pi$
$978$		0			0
$979$	253773.	+	302435.i	0.264777	+	0.315549i
$980$		0			0
$981$	1.16563e6	−	672974.i	1.21121	−	0.699295i
$982$		0			0
$983$	1.50159e6	+	264772.i	1.55398	+	0.274009i	0.883684	−	0.468084i	$-0.155056\pi$
$983$	1.50159e6	+	264772.i	1.55398	+	0.274009i	0.670297	+	0.742093i	$0.266167\pi$
$984$		0			0
$985$	−439051.	+	159802.i	−0.452525	+	0.164706i
$986$		0			0
$987$		−	1.96895e6i		−	2.02116i
$988$		0			0
$989$	239281.			0.244634
$990$		0			0
$991$	119897.	+	329413.i	0.122084	+	0.335424i	0.985647	−	0.168817i	$-0.0539946\pi$
$991$	119897.	+	329413.i	0.122084	+	0.335424i	−0.863563	+	0.504241i	$0.831772\pi$
$992$		0			0
$993$	102367.	−	580553.i	0.103815	−	0.588767i
$994$		0			0
$995$	918365.	+	1.59066e6i	0.927618	+	1.60668i
$996$		0			0
$997$	−17591.6	+	14761.1i	−0.0176976	+	0.0148501i	−0.651594	−	0.758568i	$-0.725899\pi$
$997$	−17591.6	+	14761.1i	−0.0176976	+	0.0148501i	0.633896	+	0.773418i	$0.281455\pi$
$998$		0			0
$999$	−49953.3	+	86521.6i	−0.0500533	+	0.0866949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.j.a.41.2	yes	42
19.13	odd	18	inner	76.5.j.a.13.2	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.13.2	✓	42	19.13	odd	18	inner
76.5.j.a.41.2	yes	42	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.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.13985 - 11.3741i) q^{3} +(-6.25205 + 35.4571i) q^{5} +(-25.8702 - 44.8086i) q^{7} +(-50.1832 + 42.1087i) q^{9} +O(q^{10})\)	\(q+(-4.13985 - 11.3741i) q^{3} +(-6.25205 + 35.4571i) q^{5} +(-25.8702 - 44.8086i) q^{7} +(-50.1832 + 42.1087i) q^{9} +(-31.3514 + 54.3022i) q^{11} +(-109.766 + 301.581i) q^{13} +(429.177 - 75.6755i) q^{15} +(342.075 + 287.035i) q^{17} +(-162.907 + 322.153i) q^{19} +(-402.560 + 479.753i) q^{21} +(-90.4845 - 513.163i) q^{23} +(-630.811 - 229.596i) q^{25} +(-162.378 - 93.7490i) q^{27} +(-524.868 - 625.513i) q^{29} +(-1072.59 + 619.262i) q^{31} +(747.431 + 131.792i) q^{33} +(1750.52 - 637.139i) q^{35} -532.840i q^{37} +3884.64 q^{39} +(-355.017 - 975.401i) q^{41} +(-79.7398 + 452.227i) q^{43} +(-1179.31 - 2042.62i) q^{45} +(-2408.38 + 2020.87i) q^{47} +(-138.039 + 239.091i) q^{49} +(1848.64 - 5079.10i) q^{51} +(-1797.47 + 316.942i) q^{53} +(-1729.39 - 1451.13i) q^{55} +(4338.62 + 519.262i) q^{57} +(-365.255 + 435.294i) q^{59} +(93.8036 + 531.987i) q^{61} +(3185.09 + 1159.28i) q^{63} +(-10006.9 - 5777.50i) q^{65} +(4282.23 + 5103.37i) q^{67} +(-5462.20 + 3153.60i) q^{69} +(-1606.46 - 283.262i) q^{71} +(7746.45 - 2819.48i) q^{73} +8125.43i q^{75} +3244.27 q^{77} +(-2379.76 - 6538.35i) q^{79} +(-1315.52 + 7460.68i) q^{81} +(3687.63 + 6387.16i) q^{83} +(-12316.1 + 10334.4i) q^{85} +(-4941.80 + 8559.45i) q^{87} +(2153.49 - 5916.67i) q^{89} +(16353.1 - 2883.49i) q^{91} +(11484.0 + 9636.18i) q^{93} +(-10404.1 - 7790.32i) q^{95} +(-2695.42 + 3212.28i) q^{97} +(-713.283 - 4045.23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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