LMFDB - Embedded newform 261.3.s.a.55.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,3,Mod(10,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([0, 23]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("261.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	261.s (of order $28$, degree $12$, 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:	$7.11173489980$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			55.4
Character	$\chi$	$=$	261.55
Dual form			261.3.s.a.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63282 - 2.59861i) q^{2} +(-2.35117 - 4.88225i) q^{4} +(4.43970 - 1.01333i) q^{5} +(10.7635 + 5.18344i) q^{7} +(-4.32723 - 0.487562i) q^{8} +O(q^{10})$	\(q+(1.63282 - 2.59861i) q^{2} +(-2.35117 - 4.88225i) q^{4} +(4.43970 - 1.01333i) q^{5} +(10.7635 + 5.18344i) q^{7} +(-4.32723 - 0.487562i) q^{8} +(4.61596 - 13.1917i) q^{10} +(-2.90150 + 0.326920i) q^{11} +(2.24911 + 1.79360i) q^{13} +(31.0446 - 19.5066i) q^{14} +(5.18193 - 6.49794i) q^{16} +(-2.44971 - 2.44971i) q^{17} +(-31.9711 - 11.1872i) q^{19} +(-15.3858 - 19.2932i) q^{20} +(-3.88808 + 8.07367i) q^{22} +(-9.24886 + 40.5219i) q^{23} +(-3.84011 + 1.84930i) q^{25} +(8.33326 - 2.91593i) q^{26} -64.7374i q^{28} +(-18.6826 - 22.1802i) q^{29} +(7.40308 - 11.7819i) q^{31} +(-14.1774 - 40.5168i) q^{32} +(-10.3658 + 2.36592i) q^{34} +(53.0394 + 12.1059i) q^{35} +(-19.6990 - 2.21954i) q^{37} +(-81.2741 + 64.8140i) q^{38} +(-19.7057 + 2.22030i) q^{40} +(15.2314 - 15.2314i) q^{41} +(1.58568 - 0.996350i) q^{43} +(8.41802 + 13.3972i) q^{44} +(90.1991 + 90.1991i) q^{46} +(0.858173 + 7.61650i) q^{47} +(58.4343 + 73.2743i) q^{49} +(-1.46458 + 12.9985i) q^{50} +(3.46879 - 15.1978i) q^{52} +(7.13045 + 31.2406i) q^{53} +(-12.5505 + 4.39161i) q^{55} +(-44.0490 - 27.6778i) q^{56} +(-88.1430 + 12.3325i) q^{58} +9.47914 q^{59} +(-19.5711 - 55.9310i) q^{61} +(-18.5288 - 38.4755i) q^{62} +(-96.0255 - 21.9172i) q^{64} +(11.8029 + 5.68397i) q^{65} +(-45.3801 + 36.1895i) q^{67} +(-6.20042 + 17.7198i) q^{68} +(118.062 - 118.062i) q^{70} +(61.2373 + 48.8352i) q^{71} +(40.7753 + 64.8935i) q^{73} +(-37.9326 + 47.5659i) q^{74} +(20.5509 + 182.394i) q^{76} +(-32.9249 - 11.5209i) q^{77} +(10.0312 - 89.0291i) q^{79} +(16.4217 - 34.0999i) q^{80} +(-14.7104 - 64.4505i) q^{82} +(-42.5654 + 20.4984i) q^{83} +(-13.3584 - 8.39361i) q^{85} -5.74743i q^{86} +12.7148 q^{88} +(31.5692 - 50.2421i) q^{89} +(14.9113 + 30.9636i) q^{91} +(219.584 - 50.1186i) q^{92} +(21.1936 + 10.2063i) q^{94} +(-153.279 - 17.2703i) q^{95} +(-41.8847 + 119.700i) q^{97} +(285.824 - 32.2047i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{19}{28}\right)$	$1$

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 $

$2$	1.63282	−	2.59861i	0.816409	−	1.29931i	−0.134835	−	0.990868i	$-0.543050\pi$
$2$	1.63282	−	2.59861i	0.816409	−	1.29931i	0.951244	−	0.308439i	$-0.0998067\pi$
$3$		0			0
$3$		0			0
$4$	−2.35117	−	4.88225i	−0.587792	−	1.22056i
$5$	4.43970	−	1.01333i	0.887940	−	0.202667i	0.245861	−	0.969305i	$-0.420929\pi$
$5$	4.43970	−	1.01333i	0.887940	−	0.202667i	0.642079	+	0.766638i	$0.278072\pi$
$6$		0			0
$7$	10.7635	+	5.18344i	1.53765	+	0.740491i	0.995038	−	0.0994954i	$-0.0317229\pi$
$7$	10.7635	+	5.18344i	1.53765	+	0.740491i	0.542607	+	0.839986i	$0.317437\pi$
$8$	−4.32723	−	0.487562i	−0.540904	−	0.0609452i
$9$		0			0
$10$	4.61596	−	13.1917i	0.461596	−	1.31917i
$11$	−2.90150	+	0.326920i	−0.263772	+	0.0297200i	−0.242860	−	0.970061i	$-0.578086\pi$
$11$	−2.90150	+	0.326920i	−0.263772	+	0.0297200i	−0.0209122	+	0.999781i	$0.506657\pi$
$12$		0			0
$13$	2.24911	+	1.79360i	0.173008	+	0.137969i	0.706166	−	0.708046i	$-0.250423\pi$
$13$	2.24911	+	1.79360i	0.173008	+	0.137969i	−0.533158	+	0.846016i	$0.678995\pi$
$14$	31.0446	−	19.5066i	2.21747	−	1.39333i
$15$		0			0
$16$	5.18193	−	6.49794i	0.323871	−	0.406121i
$17$	−2.44971	−	2.44971i	−0.144101	−	0.144101i	0.631376	−	0.775477i	$-0.282490\pi$
$17$	−2.44971	−	2.44971i	−0.144101	−	0.144101i	−0.775477	+	0.631376i	$0.782490\pi$
$18$		0			0
$19$	−31.9711	−	11.1872i	−1.68269	−	0.588799i	−0.691634	−	0.722248i	$-0.743109\pi$
$19$	−31.9711	−	11.1872i	−1.68269	−	0.588799i	−0.991056	+	0.133450i	$0.957395\pi$
$20$	−15.3858	−	19.2932i	−0.769292	−	0.964662i
$21$		0			0
$22$	−3.88808	+	8.07367i	−0.176731	+	0.366985i
$23$	−9.24886	+	40.5219i	−0.402124	+	1.76182i	0.216647	+	0.976250i	$0.430488\pi$
$23$	−9.24886	+	40.5219i	−0.402124	+	1.76182i	−0.618771	+	0.785571i	$0.712369\pi$
$24$		0			0
$25$	−3.84011	+	1.84930i	−0.153604	+	0.0739720i
$26$	8.33326	−	2.91593i	0.320510	−	0.112151i
$27$		0			0
$28$		−	64.7374i		−	2.31205i
$29$	−18.6826	−	22.1802i	−0.644226	−	0.764835i
$29$	−18.6826	−	22.1802i	−0.644226	−	0.764835i
$30$		0			0
$31$	7.40308	−	11.7819i	0.238809	−	0.380063i	−0.705720	−	0.708491i	$-0.749376\pi$
$31$	7.40308	−	11.7819i	0.238809	−	0.380063i	0.944529	+	0.328429i	$0.106519\pi$
$32$	−14.1774	−	40.5168i	−0.443045	−	1.26615i
$33$		0			0
$34$	−10.3658	+	2.36592i	−0.304876	+	0.0695860i
$35$	53.0394	+	12.1059i	1.51541	+	0.345883i
$36$		0			0
$37$	−19.6990	−	2.21954i	−0.532405	−	0.0599876i	−0.158330	−	0.987386i	$-0.550611\pi$
$37$	−19.6990	−	2.21954i	−0.532405	−	0.0599876i	−0.374075	+	0.927399i	$0.622040\pi$
$38$	−81.2741	+	64.8140i	−2.13879	+	1.70563i
$39$		0			0
$40$	−19.7057	+	2.22030i	−0.492642	+	0.0555074i
$41$	15.2314	−	15.2314i	0.371497	−	0.371497i	−0.496526	−	0.868022i	$-0.665391\pi$
$41$	15.2314	−	15.2314i	0.371497	−	0.371497i	0.868022	+	0.496526i	$0.165391\pi$
$42$		0			0
$43$	1.58568	−	0.996350i	0.0368763	−	0.0231709i	−0.513468	−	0.858109i	$-0.671639\pi$
$43$	1.58568	−	0.996350i	0.0368763	−	0.0231709i	0.550344	+	0.834938i	$0.314497\pi$
$44$	8.41802	+	13.3972i	0.191319	+	0.304482i
$45$		0			0
$46$	90.1991	+	90.1991i	1.96085	+	1.96085i
$47$	0.858173	+	7.61650i	0.0182590	+	0.162053i	0.999533	−	0.0305651i	$-0.00973068\pi$
$47$	0.858173	+	7.61650i	0.0182590	+	0.162053i	−0.981274	+	0.192618i	$0.938302\pi$
$48$		0			0
$49$	58.4343	+	73.2743i	1.19254	+	1.49539i
$50$	−1.46458	+	12.9985i	−0.0292917	+	0.259971i
$51$		0			0
$52$	3.46879	−	15.1978i	0.0667075	−	0.292265i
$53$	7.13045	+	31.2406i	0.134537	+	0.589445i	0.996582	+	0.0826126i	$0.0263264\pi$
$53$	7.13045	+	31.2406i	0.134537	+	0.589445i	−0.862045	+	0.506832i	$0.830816\pi$
$54$		0			0
$55$	−12.5505	+	4.39161i	−0.228191	+	0.0798475i
$56$	−44.0490	−	27.6778i	−0.786589	−	0.494246i
$57$		0			0
$58$	−88.1430	+	12.3325i	−1.51971	+	0.212630i
$59$	9.47914			0.160663			0.0803317	−	0.996768i	$-0.474402\pi$
$59$	9.47914			0.160663			0.0803317	+	0.996768i	$0.474402\pi$
$60$		0			0
$61$	−19.5711	−	55.9310i	−0.320838	−	0.916902i	−0.985488	−	0.169747i	$-0.945705\pi$
$61$	−19.5711	−	55.9310i	−0.320838	−	0.916902i	0.664650	−	0.747155i	$-0.268581\pi$
$62$	−18.5288	−	38.4755i	−0.298852	−	0.620573i
$63$		0			0
$64$	−96.0255	−	21.9172i	−1.50040	−	0.342456i
$65$	11.8029	+	5.68397i	0.181583	+	0.0874457i
$66$		0			0
$67$	−45.3801	+	36.1895i	−0.677315	+	0.540141i	−0.900620	−	0.434608i	$-0.856887\pi$
$67$	−45.3801	+	36.1895i	−0.677315	+	0.540141i	0.223304	+	0.974749i	$0.428316\pi$
$68$	−6.20042	+	17.7198i	−0.0911827	+	0.260585i
$69$		0			0
$70$	118.062	−	118.062i	1.68660	−	1.68660i
$71$	61.2373	+	48.8352i	0.862498	+	0.687819i	0.951312	−	0.308229i	$-0.0997363\pi$
$71$	61.2373	+	48.8352i	0.862498	+	0.687819i	−0.0888143	+	0.996048i	$0.528308\pi$
$72$		0			0
$73$	40.7753	+	64.8935i	0.558566	+	0.888952i	0.999965	−	0.00835868i	$-0.00266068\pi$
$73$	40.7753	+	64.8935i	0.558566	+	0.888952i	−0.441399	+	0.897311i	$0.645518\pi$
$74$	−37.9326	+	47.5659i	−0.512602	+	0.642783i
$75$		0			0
$76$	20.5509	+	182.394i	0.270406	+	2.39992i
$77$	−32.9249	−	11.5209i	−0.427596	−	0.149622i
$78$		0			0
$79$	10.0312	−	89.0291i	0.126977	−	1.12695i	−0.755022	−	0.655700i	$-0.772374\pi$
$79$	10.0312	−	89.0291i	0.126977	−	1.12695i	0.881999	−	0.471252i	$-0.156198\pi$
$80$	16.4217	−	34.0999i	0.205271	−	0.426249i
$81$		0			0
$82$	−14.7104	−	64.4505i	−0.179395	−	0.785981i
$83$	−42.5654	+	20.4984i	−0.512836	+	0.246969i	−0.672359	−	0.740225i	$-0.734719\pi$
$83$	−42.5654	+	20.4984i	−0.512836	+	0.246969i	0.159523	+	0.987194i	$0.449004\pi$
$84$		0			0
$85$	−13.3584	−	8.39361i	−0.157157	−	0.0987484i
$86$		−	5.74743i		−	0.0668306i
$87$		0			0
$88$	12.7148			0.144487
$89$	31.5692	−	50.2421i	0.354710	−	0.564518i	−0.620938	−	0.783860i	$-0.713248\pi$
$89$	31.5692	−	50.2421i	0.354710	−	0.564518i	0.975648	+	0.219342i	$0.0703909\pi$
$90$		0			0
$91$	14.9113	+	30.9636i	0.163860	+	0.340259i
$92$	219.584	−	50.1186i	2.38678	−	0.544767i
$93$		0			0
$94$	21.1936	+	10.2063i	0.225464	+	0.108578i
$95$	−153.279	−	17.2703i	−1.61346	−	0.181793i
$96$		0			0
$97$	−41.8847	+	119.700i	−0.431802	+	1.23402i	0.498393	+	0.866951i	$0.333924\pi$
$97$	−41.8847	+	119.700i	−0.431802	+	1.23402i	−0.930195	+	0.367067i	$0.880362\pi$
$98$	285.824	−	32.2047i	2.91657	−	0.328619i
$99$		0			0
$100$	18.0575	+	14.4004i	0.180575	+	0.144004i
$101$	59.5271	−	37.4034i	0.589377	−	0.370330i	−0.204082	−	0.978954i	$-0.565421\pi$
$101$	59.5271	−	37.4034i	0.589377	−	0.370330i	0.793459	+	0.608623i	$0.208278\pi$
$102$		0			0
$103$	−54.4757	+	68.3104i	−0.528891	+	0.663208i	−0.972470	−	0.233027i	$-0.925137\pi$
$103$	−54.4757	+	68.3104i	−0.528891	+	0.663208i	0.443580	+	0.896235i	$0.353708\pi$
$104$	−8.85791	−	8.85791i	−0.0851722	−	0.0851722i
$105$		0			0
$106$	92.8249	+	32.4808i	0.875707	+	0.306423i
$107$	−24.4898	−	30.7092i	−0.228877	−	0.287002i	0.654111	−	0.756399i	$-0.273043\pi$
$107$	−24.4898	−	30.7092i	−0.228877	−	0.287002i	−0.882987	+	0.469397i	$0.844471\pi$
$108$		0			0
$109$	48.7351	−	101.200i	0.447111	−	0.928436i	−0.548614	−	0.836076i	$-0.684844\pi$
$109$	48.7351	−	101.200i	0.447111	−	0.928436i	0.995726	−	0.0923607i	$-0.0294413\pi$
$110$	−9.08058	+	39.7846i	−0.0825507	+	0.361678i
$111$		0			0
$112$	89.4575	−	43.0805i	0.798728	−	0.384647i
$113$	32.7521	−	11.4605i	0.289842	−	0.101420i	−0.181442	−	0.983402i	$-0.558076\pi$
$113$	32.7521	−	11.4605i	0.289842	−	0.101420i	0.471284	+	0.881982i	$0.343791\pi$
$114$		0			0
$115$			189.277i			1.64589i
$116$	−64.3635	+	143.362i	−0.554858	+	1.23588i
$117$		0			0
$118$	15.4777	−	24.6326i	0.131167	−	0.208751i
$119$	−13.6696	−	39.0654i	−0.114870	−	0.328281i
$120$		0			0
$121$	−109.654	+	25.0279i	−0.906235	+	0.206842i
$122$	−177.299	−	40.4674i	−1.45327	−	0.331700i
$123$		0			0
$124$	−74.9283	−	8.44239i	−0.604261	−	0.0680838i
$125$	−104.184	+	83.0841i	−0.833473	+	0.664672i
$126$		0			0
$127$	159.395	−	17.9595i	1.25508	−	0.141413i	0.540725	−	0.841199i	$-0.318150\pi$
$127$	159.395	−	17.9595i	1.25508	−	0.141413i	0.714353	+	0.699786i	$0.246721\pi$
$128$	−92.3344	+	92.3344i	−0.721363	+	0.721363i
$129$		0			0
$130$	34.0424	−	21.3903i	0.261865	−	0.164540i
$131$	81.0335	+	128.964i	0.618577	+	0.984459i	0.998238	+	0.0593336i	$0.0188976\pi$
$131$	81.0335	+	128.964i	0.618577	+	0.984459i	−0.379662	+	0.925125i	$0.623960\pi$
$132$		0			0
$133$	−286.134	−	286.134i	−2.15138	−	2.15138i
$134$	19.9449	+	177.016i	0.148843	+	1.32102i
$135$		0			0
$136$	9.40608	+	11.7948i	0.0691623	+	0.0867268i
$137$	−6.05776	+	53.7641i	−0.0442172	+	0.392439i	0.952038	+	0.305979i	$0.0989839\pi$
$137$	−6.05776	+	53.7641i	−0.0442172	+	0.392439i	−0.996255	+	0.0864595i	$0.972445\pi$
$138$		0			0
$139$	−10.2366	+	44.8495i	−0.0736447	+	0.322658i	−0.998309	−	0.0581239i	$-0.981488\pi$
$139$	−10.2366	+	44.8495i	−0.0736447	+	0.322658i	0.924665	+	0.380782i	$0.124345\pi$
$140$	−65.6005	−	287.415i	−0.468575	−	2.05296i
$141$		0			0
$142$	226.893	−	79.3934i	1.59784	−	0.559108i
$143$	−7.11214	−	4.46885i	−0.0497352	−	0.0312507i
$144$		0			0
$145$	−105.421	−	79.5419i	−0.727041	−	0.548565i
$146$	235.212			1.61104
$147$		0			0
$148$	35.4793	+	101.394i	0.239725	+	0.685094i
$149$	−99.1793	−	205.948i	−0.665633	−	1.38220i	−0.910852	−	0.412734i	$-0.864574\pi$
$149$	−99.1793	−	205.948i	−0.665633	−	1.38220i	0.245219	−	0.969468i	$-0.421140\pi$
$150$		0			0
$151$	82.0279	+	18.7223i	0.543231	+	0.123989i	0.485326	−	0.874333i	$-0.338701\pi$
$151$	82.0279	+	18.7223i	0.543231	+	0.123989i	0.0579049	+	0.998322i	$0.481558\pi$
$152$	132.892	+	63.9973i	0.874289	+	0.421035i
$153$		0			0
$154$	−83.6987	+	66.7475i	−0.543498	+	0.433425i
$155$	20.9285	−	59.8101i	0.135022	−	0.385872i
$156$		0			0
$157$	−137.989	+	137.989i	−0.878912	+	0.878912i	−0.993422	−	0.114510i	$-0.963470\pi$
$157$	−137.989	+	137.989i	−0.878912	+	0.878912i	0.114510	+	0.993422i	$0.463470\pi$
$158$	−214.973	−	171.436i	−1.36059	−	1.08503i
$159$		0			0
$160$	−104.001	−	165.516i	−0.650004	−	1.03447i
$161$	−309.593	+	388.217i	−1.92294	+	2.41129i
$162$		0			0
$163$	4.35863	+	38.6839i	0.0267401	+	0.237325i	0.999972	+	0.00749896i	$0.00238702\pi$
$163$	4.35863	+	38.6839i	0.0267401	+	0.237325i	−0.973232	+	0.229826i	$0.926184\pi$
$164$	−110.175	−	38.5519i	−0.671798	−	0.235072i
$165$		0			0
$166$	−16.2341	+	144.081i	−0.0977955	+	0.867959i
$167$	8.15009	−	16.9238i	0.0488029	−	0.101340i	−0.875141	−	0.483867i	$-0.839232\pi$
$167$	8.15009	−	16.9238i	0.0488029	−	0.101340i	0.923944	+	0.382527i	$0.124946\pi$
$168$		0			0
$169$	−35.7646	−	156.695i	−0.211625	−	0.927188i
$170$	−43.6235	+	21.0080i	−0.256609	+	0.123576i
$171$		0			0
$172$	−8.59264	−	5.39911i	−0.0499572	−	0.0313902i
$173$		−	216.808i		−	1.25322i	−0.779332	−	0.626612i	$-0.784441\pi$
$173$		−	216.808i		−	1.25322i	0.779332	−	0.626612i	$-0.215559\pi$
$174$		0			0
$175$	−50.9188			−0.290965
$176$	−12.9111	+	20.5478i	−0.0733583	+	0.116749i
$177$		0			0
$178$	−79.0131	−	164.072i	−0.443894	−	0.921755i
$179$	64.5460	−	14.7322i	0.360592	−	0.0823028i	−0.0383867	−	0.999263i	$-0.512222\pi$
$179$	64.5460	−	14.7322i	0.360592	−	0.0823028i	0.398979	+	0.916960i	$0.369365\pi$
$180$		0			0
$181$	−31.6029	−	15.2191i	−0.174602	−	0.0840837i	0.344541	−	0.938771i	$-0.388034\pi$
$181$	−31.6029	−	15.2191i	−0.174602	−	0.0840837i	−0.519143	+	0.854687i	$0.673749\pi$
$182$	104.810	+	11.8092i	0.575878	+	0.0648859i
$183$		0			0
$184$	59.7788	−	170.838i	0.324885	−	0.928468i
$185$	−89.7067	+	10.1075i	−0.484901	+	0.0546353i
$186$		0			0
$187$	7.90869	+	6.30697i	0.0422924	+	0.0337271i
$188$	35.1680	−	22.0975i	0.187064	−	0.117540i
$189$		0			0
$190$	−295.155	+	370.112i	−1.55345	+	1.94796i
$191$	−100.170	−	100.170i	−0.524450	−	0.524450i	0.394463	−	0.918912i	$-0.370931\pi$
$191$	−100.170	−	100.170i	−0.524450	−	0.524450i	−0.918912	+	0.394463i	$0.870931\pi$
$192$		0			0
$193$	27.8003	+	9.72774i	0.144043	+	0.0504028i	0.401338	−	0.915930i	$-0.368545\pi$
$193$	27.8003	+	9.72774i	0.144043	+	0.0504028i	−0.257295	+	0.966333i	$0.582831\pi$
$194$	242.663	+	304.290i	1.25084	+	1.56851i
$195$		0			0
$196$	220.355	−	457.571i	1.12426	−	2.33455i
$197$	28.3314	−	124.128i	0.143814	−	0.630092i	−0.850714	−	0.525628i	$-0.823830\pi$
$197$	28.3314	−	124.128i	0.143814	−	0.630092i	0.994529	−	0.104464i	$-0.0333126\pi$
$198$		0			0
$199$	272.856	−	131.401i	1.37114	−	0.660304i	0.404046	−	0.914739i	$-0.367604\pi$
$199$	272.856	−	131.401i	1.37114	−	0.660304i	0.967090	+	0.254435i	$0.0818894\pi$
$200$	17.5187	−	6.13005i	0.0875934	−	0.0306503i
$201$		0			0
$202$		−	215.761i		−	1.06812i
$203$	−86.1204	−	335.577i	−0.424238	−	1.65309i
$204$		0			0
$205$	52.1883	−	83.0571i	0.254577	−	0.405157i
$206$	88.5635	+	253.100i	0.429920	+	1.22864i
$207$		0			0
$208$	23.3094	−	5.32023i	0.112065	−	0.0255780i
$209$	96.4213	+	22.0075i	0.461346	+	0.105299i
$210$		0			0
$211$	116.261	+	13.0995i	0.551002	+	0.0620830i	0.383076	−	0.923717i	$-0.374865\pi$
$211$	116.261	+	13.0995i	0.551002	+	0.0620830i	0.167925	+	0.985800i	$0.446293\pi$
$212$	135.759	−	108.265i	0.640375	−	0.510682i
$213$		0			0
$214$	−119.789	+	13.4970i	−0.559761	+	0.0630699i
$215$	6.03032	−	6.03032i	0.0280480	−	0.0280480i
$216$		0			0
$217$	140.754	−	88.4417i	0.648637	−	0.407565i
$218$	−183.403	−	291.884i	−0.841298	−	1.33892i
$219$		0			0
$220$	50.9493	+	50.9493i	0.231588	+	0.231588i
$221$	−1.11585	−	9.90347i	−0.00504911	−	0.0448121i
$222$		0			0
$223$	157.783	+	197.854i	0.707547	+	0.887236i	0.997562	−	0.0697862i	$-0.0222317\pi$
$223$	157.783	+	197.854i	0.707547	+	0.887236i	−0.290015	+	0.957022i	$0.593660\pi$
$224$	57.4171	−	509.591i	0.256326	−	2.27496i
$225$		0			0
$226$	23.6969	−	103.823i	0.104854	−	0.459394i
$227$	21.4599	+	94.0221i	0.0945372	+	0.414194i	0.999946	−	0.0103453i	$-0.00329308\pi$
$227$	21.4599	+	94.0221i	0.0945372	+	0.414194i	−0.905409	+	0.424540i	$0.860436\pi$
$228$		0			0
$229$	56.9198	−	19.9171i	0.248558	−	0.0869742i	−0.203125	−	0.979153i	$-0.565110\pi$
$229$	56.9198	−	19.9171i	0.248558	−	0.0869742i	0.451683	+	0.892179i	$0.350824\pi$
$230$	491.859	+	309.055i	2.13852	+	1.34372i
$231$		0			0
$232$	70.0295	+	105.088i	0.301851	+	0.452965i
$233$	−94.7649			−0.406716			−0.203358	−	0.979104i	$-0.565186\pi$
$233$	−94.7649			−0.406716			−0.203358	+	0.979104i	$0.565186\pi$
$234$		0			0
$235$	11.5281	+	32.9454i	0.0490557	+	0.140193i
$236$	−22.2871	−	46.2796i	−0.0944367	−	0.196100i
$237$		0			0
$238$	−123.836	−	28.2647i	−0.520319	−	0.118759i
$239$	92.0947	+	44.3505i	0.385333	+	0.185567i	0.616514	−	0.787344i	$-0.288544\pi$
$239$	92.0947	+	44.3505i	0.385333	+	0.185567i	−0.231180	+	0.972911i	$0.574259\pi$
$240$		0			0
$241$	−288.328	+	229.934i	−1.19638	+	0.954084i	−0.999652	−	0.0263733i	$-0.991604\pi$
$241$	−288.328	+	229.934i	−1.19638	+	0.954084i	−0.196731	+	0.980457i	$0.563033\pi$
$242$	−114.008	+	325.816i	−0.471107	+	1.34635i
$243$		0			0
$244$	−227.054	+	227.054i	−0.930551	+	0.930551i
$245$	333.682	+	266.103i	1.36197	+	1.08613i
$246$		0			0
$247$	−51.8411	−	82.5046i	−0.209883	−	0.334027i
$248$	−37.7793	+	47.3737i	−0.152336	+	0.191023i
$249$		0			0
$250$	45.7898	+	406.395i	0.183159	+	1.62558i
$251$	346.223	+	121.149i	1.37937	+	0.482663i	0.915171	−	0.403066i	$-0.132055\pi$
$251$	346.223	+	121.149i	1.37937	+	0.482663i	0.464202	+	0.885729i	$0.346341\pi$
$252$		0			0
$253$	13.5881	−	120.598i	0.0537079	−	0.476671i
$254$	213.593	−	443.531i	0.840917	−	1.74618i
$255$		0			0
$256$	1.50755	+	6.60499i	0.00588885	+	0.0258007i
$257$	348.410	−	167.786i	1.35568	−	0.652862i	0.392013	−	0.919960i	$-0.371779\pi$
$257$	348.410	−	167.786i	1.35568	−	0.652862i	0.963670	+	0.267097i	$0.0860645\pi$
$258$		0			0
$259$	−200.525	−	125.999i	−0.774230	−	0.486481i
$260$		−	70.9886i		−	0.273033i
$261$		0			0
$262$	467.441			1.78413
$263$	−181.203	+	288.383i	−0.688986	+	1.09651i	0.300763	+	0.953699i	$0.402759\pi$
$263$	−181.203	+	288.383i	−0.688986	+	1.09651i	−0.989749	+	0.142816i	$0.954384\pi$
$264$		0			0
$265$	63.3142	+	131.473i	0.238921	+	0.496126i
$266$	−1210.75	+	276.347i	−4.55171	+	1.03890i
$267$		0			0
$268$	283.382	+	136.470i	1.05740	+	0.509216i
$269$	−71.8537	−	8.09596i	−0.267114	−	0.0300965i	−0.0226084	−	0.999744i	$-0.507197\pi$
$269$	−71.8537	−	8.09596i	−0.267114	−	0.0300965i	−0.244506	+	0.969648i	$0.578626\pi$
$270$		0			0
$271$	110.702	−	316.368i	0.408495	−	1.16741i	−0.537510	−	0.843257i	$-0.680635\pi$
$271$	110.702	−	316.368i	0.408495	−	1.16741i	0.946005	−	0.324153i	$-0.105079\pi$
$272$	−28.6123	+	3.22383i	−0.105192	+	0.0118523i
$273$		0			0
$274$	129.821	+	103.529i	0.473799	+	0.377842i
$275$	10.5375	−	6.62114i	0.0383181	−	0.0240769i
$276$		0			0
$277$	−187.171	+	234.705i	−0.675707	+	0.847310i	−0.994951	−	0.100362i	$-0.968000\pi$
$277$	−187.171	+	234.705i	−0.675707	+	0.847310i	0.319244	+	0.947673i	$0.396571\pi$
$278$	99.8321	+	99.8321i	0.359108	+	0.359108i
$279$		0			0
$280$	−223.611	−	78.2449i	−0.798611	−	0.279446i
$281$	−212.195	−	266.084i	−0.755142	−	0.946918i	0.244600	−	0.969624i	$-0.421343\pi$
$281$	−212.195	−	266.084i	−0.755142	−	0.946918i	−0.999742	+	0.0227058i	$0.992772\pi$
$282$		0			0
$283$	43.3073	−	89.9286i	0.153029	−	0.317769i	−0.810334	−	0.585968i	$-0.800714\pi$
$283$	43.3073	−	89.9286i	0.153029	−	0.317769i	0.963363	+	0.268199i	$0.0864286\pi$
$284$	94.4462	−	413.796i	0.332557	−	1.45703i
$285$		0			0
$286$	−23.2257	+	11.1849i	−0.0812086	+	0.0391080i
$287$	242.894	−	84.9922i	0.846320	−	0.296140i
$288$		0			0
$289$		−	276.998i		−	0.958470i
$290$	−378.832	+	144.071i	−1.30632	+	0.496797i
$291$		0			0
$292$	220.957	−	351.651i	0.756702	−	1.20428i
$293$	61.7117	+	176.362i	0.210620	+	0.601917i	0.999927	−	0.0120814i	$-0.00384572\pi$
$293$	61.7117	+	176.362i	0.210620	+	0.601917i	−0.789307	+	0.613999i	$0.789560\pi$
$294$		0			0
$295$	42.0846	−	9.60553i	0.142660	−	0.0325611i
$296$	84.1598	+	19.2089i	0.284324	+	0.0648950i
$297$		0			0
$298$	−697.121	−	78.5467i	−2.33933	−	0.263580i
$299$	−93.4818	+	74.5493i	−0.312648	+	0.249329i
$300$		0			0
$301$	22.2320	−	2.50495i	0.0738606	−	0.00832209i
$302$	182.589	−	182.589i	0.604599	−	0.604599i
$303$		0			0
$304$	−238.366	+	149.775i	−0.784098	+	0.492681i
$305$	−143.567	−	228.485i	−0.470710	−	0.749131i
$306$		0			0
$307$	153.936	+	153.936i	0.501419	+	0.501419i	0.911879	−	0.410460i	$-0.134632\pi$
$307$	153.936	+	153.936i	0.501419	+	0.501419i	−0.410460	+	0.911879i	$0.634632\pi$
$308$	21.1639	+	187.835i	0.0687141	+	0.609855i
$309$		0			0
$310$	−121.251	−	152.044i	−0.391132	−	0.490465i
$311$	−1.32892	+	11.7945i	−0.00427306	+	0.0379245i	−0.995668	−	0.0929819i	$-0.970360\pi$
$311$	−1.32892	+	11.7945i	−0.00427306	+	0.0379245i	0.991395	+	0.130906i	$0.0417887\pi$
$312$		0			0
$313$	−66.0161	+	289.235i	−0.210914	+	0.924074i	0.753034	+	0.657982i	$0.228590\pi$
$313$	−66.0161	+	289.235i	−0.210914	+	0.924074i	−0.963948	+	0.266092i	$0.914267\pi$
$314$	133.270	+	583.892i	0.424425	+	1.85953i
$315$		0			0
$316$	−458.248	+	160.348i	−1.45015	+	0.507430i
$317$	−214.084	−	134.518i	−0.675345	−	0.424347i	0.150221	−	0.988652i	$-0.452001\pi$
$317$	−214.084	−	134.518i	−0.675345	−	0.424347i	−0.825566	+	0.564305i	$0.809144\pi$
$318$		0			0
$319$	61.4585	+	58.2481i	0.192660	+	0.182596i
$320$	−448.534			−1.40167
$321$		0			0
$322$	503.318	+	1438.40i	1.56310	+	4.46708i
$323$	50.9146	+	105.725i	0.157630	+	0.327323i
$324$		0			0
$325$	−11.9537	−	2.72836i	−0.0367807	−	0.00839495i
$326$	107.641	+	51.8374i	0.330188	+	0.159010i
$327$		0			0
$328$	−73.3358	+	58.4834i	−0.223585	+	0.178303i
$329$	−30.2427	+	86.4286i	−0.0919230	+	0.262701i
$330$		0			0
$331$	−111.869	+	111.869i	−0.337973	+	0.337973i	−0.855604	−	0.517631i	$-0.826814\pi$
$331$	−111.869	+	111.869i	−0.337973	+	0.337973i	0.517631	+	0.855604i	$0.326814\pi$
$332$	200.157	+	159.620i	0.602882	+	0.480782i
$333$		0			0
$334$	−30.6709	−	48.8125i	−0.0918291	−	0.146145i
$335$	−164.802	+	206.656i	−0.491947	+	0.616882i
$336$		0			0
$337$	−69.1598	−	613.810i	−0.205222	−	1.82140i	−0.500220	−	0.865898i	$-0.666748\pi$
$337$	−69.1598	−	613.810i	−0.205222	−	1.82140i	0.294998	−	0.955498i	$-0.404681\pi$
$338$	−465.586	−	162.916i	−1.37747	−	0.481999i
$339$		0			0
$340$	−9.57198	+	84.9537i	−0.0281529	+	0.249864i
$341$	−17.6283	+	36.6055i	−0.0516958	+	0.107347i
$342$		0			0
$343$	118.886	+	520.873i	0.346606	+	1.51858i
$344$	−7.34739	+	3.53832i	−0.0213587	+	0.0102858i
$345$		0			0
$346$	−563.399	−	354.007i	−1.62832	−	1.02314i
$347$			195.864i			0.564450i	0.959348	+	0.282225i	$0.0910724\pi$
$347$			195.864i			0.564450i	−0.959348	+	0.282225i	$0.908928\pi$
$348$		0			0
$349$	350.810			1.00519			0.502593	−	0.864523i	$-0.332380\pi$
$349$	350.810			1.00519			0.502593	+	0.864523i	$0.332380\pi$
$350$	−83.1411	+	132.318i	−0.237546	+	0.378052i
$351$		0			0
$352$	54.3815	+	112.924i	0.154493	+	0.320808i
$353$	326.927	−	74.6189i	0.926139	−	0.211385i	0.267251	−	0.963627i	$-0.413885\pi$
$353$	326.927	−	74.6189i	0.926139	−	0.211385i	0.658887	+	0.752242i	$0.271027\pi$
$354$		0			0
$355$	321.362	+	154.760i	0.905245	+	0.435943i
$356$	−319.519	−	36.0012i	−0.897526	−	0.101127i
$357$		0			0
$358$	67.1085	−	191.785i	0.187454	−	0.535713i
$359$	329.831	−	37.1631i	0.918751	−	0.103518i	0.360093	−	0.932917i	$-0.382745\pi$
$359$	329.831	−	37.1631i	0.918751	−	0.103518i	0.558658	+	0.829398i	$0.311317\pi$
$360$		0			0
$361$	614.757	+	490.253i	1.70293	+	1.35804i
$362$	−91.1504	+	57.2736i	−0.251797	+	0.158214i
$363$		0			0
$364$	116.113	−	145.601i	0.318992	−	0.400003i
$365$	246.789	+	246.789i	0.676134	+	0.676134i
$366$		0			0
$367$	−308.985	−	108.119i	−0.841921	−	0.294601i	−0.125348	−	0.992113i	$-0.540005\pi$
$367$	−308.985	−	108.119i	−0.841921	−	0.294601i	−0.716573	+	0.697512i	$0.754290\pi$
$368$	215.382	+	270.080i	0.585277	+	0.733914i
$369$		0			0
$370$	−120.209	+	249.617i	−0.324890	+	0.674641i
$371$	−85.1847	+	373.219i	−0.229608	+	1.00598i
$372$		0			0
$373$	369.998	−	178.182i	0.991951	−	0.477698i	0.133752	−	0.991015i	$-0.457298\pi$
$373$	369.998	−	178.182i	0.991951	−	0.477698i	0.858199	+	0.513316i	$0.171583\pi$
$374$	29.3028	−	10.2535i	0.0783498	−	0.0274158i
$375$		0			0
$376$		−	33.3767i		−	0.0887679i
$377$	−2.23659	−	83.3948i	−0.00593259	−	0.221206i
$378$		0			0
$379$	197.597	−	314.473i	0.521363	−	0.829745i	−0.477440	−	0.878665i	$-0.658435\pi$
$379$	197.597	−	314.473i	0.521363	−	0.829745i	0.998803	+	0.0489200i	$0.0155779\pi$
$380$	276.066	+	788.950i	0.726488	+	2.07618i
$381$		0			0
$382$	−423.862	+	96.7437i	−1.10959	+	0.253256i
$383$	418.965	+	95.6261i	1.09390	+	0.249676i	0.731156	−	0.682211i	$-0.238981\pi$
$383$	418.965	+	95.6261i	1.09390	+	0.249676i	0.362748	+	0.931887i	$0.381838\pi$
$384$		0			0
$385$	−157.851	−	17.7856i	−0.410003	−	0.0461962i
$386$	70.6714	−	56.3586i	0.183087	−	0.146007i
$387$		0			0
$388$	682.883	−	76.9424i	1.76001	−	0.198305i
$389$	−261.614	+	261.614i	−0.672531	+	0.672531i	−0.958299	−	0.285768i	$-0.907751\pi$
$389$	−261.614	+	261.614i	−0.672531	+	0.672531i	0.285768	+	0.958299i	$0.407751\pi$
$390$		0			0
$391$	121.924	−	76.6099i	0.311826	−	0.195933i
$392$	−217.133	−	345.565i	−0.553910	−	0.881543i
$393$		0			0
$394$	−276.301	−	276.301i	−0.701272	−	0.701272i
$395$	−45.6807	−	405.428i	−0.115647	−	1.02640i
$396$		0			0
$397$	−93.5455	−	117.302i	−0.235631	−	0.295472i	0.649931	−	0.759993i	$-0.274798\pi$
$397$	−93.5455	−	117.302i	−0.235631	−	0.295472i	−0.885562	+	0.464521i	$0.846226\pi$
$398$	104.065	−	923.601i	0.261469	−	2.32060i
$399$		0			0
$400$	−7.88256	+	34.5357i	−0.0197064	+	0.0863394i
$401$	−52.5601	−	230.281i	−0.131073	−	0.574266i	−0.997222	−	0.0744818i	$-0.976270\pi$
$401$	−52.5601	−	230.281i	−0.131073	−	0.574266i	0.866150	−	0.499784i	$-0.166587\pi$
$402$		0			0
$403$	37.7824	−	13.2206i	0.0937530	−	0.0328056i
$404$	−322.571	−	202.685i	−0.798443	−	0.501695i
$405$		0			0
$406$	−1012.65	−	324.142i	−2.49422	−	0.798381i
$407$	57.8821			0.142217
$408$		0			0
$409$	13.0580	+	37.3176i	0.0319266	+	0.0912410i	0.958744	−	0.284273i	$-0.0917521\pi$
$409$	13.0580	+	37.3176i	0.0319266	+	0.0912410i	−0.926817	+	0.375514i	$0.877466\pi$
$410$	−130.620	−	271.234i	−0.318584	−	0.661547i
$411$		0			0
$412$	461.590	+	105.355i	1.12037	+	0.255716i
$413$	102.029	+	49.1345i	0.247043	+	0.118970i
$414$		0			0
$415$	−168.206	+	134.140i	−0.405315	+	0.323228i
$416$	40.7844	−	116.555i	0.0980395	−	0.280181i
$417$		0			0
$418$	214.628	−	214.628i	0.513463	−	0.513463i
$419$	−490.816	−	391.413i	−1.17140	−	0.934160i	−0.172691	−	0.984976i	$-0.555246\pi$
$419$	−490.816	−	391.413i	−1.17140	−	0.934160i	−0.998708	+	0.0508160i	$0.983818\pi$
$420$		0			0
$421$	−188.794	−	300.464i	−0.448442	−	0.713692i	0.543635	−	0.839322i	$-0.317048\pi$
$421$	−188.794	−	300.464i	−0.448442	−	0.713692i	−0.992077	+	0.125630i	$0.959905\pi$
$422$	223.874	−	280.729i	0.530508	−	0.665235i
$423$		0			0
$424$	−15.6234	−	138.662i	−0.0368477	−	0.327032i
$425$	13.9374	+	4.87691i	0.0327939	+	0.0114751i
$426$		0			0
$427$	79.2609	−	703.460i	0.185623	−	1.64745i
$428$	−92.3506	+	191.768i	−0.215772	+	0.448056i
$429$		0			0
$430$	−5.82406	−	25.5169i	−0.0135443	−	0.0593416i
$431$	433.295	−	208.664i	1.00532	−	0.484139i	0.142583	−	0.989783i	$-0.454459\pi$
$431$	433.295	−	208.664i	1.00532	−	0.484139i	0.862742	+	0.505644i	$0.168745\pi$
$432$		0			0
$433$	255.849	+	160.760i	0.590875	+	0.371271i	0.794033	−	0.607875i	$-0.207978\pi$
$433$	255.849	+	160.760i	0.590875	+	0.371271i	−0.203158	+	0.979146i	$0.565121\pi$
$434$		−	510.175i		−	1.17552i
$435$		0			0
$436$	−608.666			−1.39602
$437$	749.022	−	1192.06i	1.71401	−	2.72783i
$438$		0			0
$439$	60.9039	+	126.468i	0.138733	+	0.288083i	0.958747	−	0.284262i	$-0.0917484\pi$
$439$	60.9039	+	126.468i	0.138733	+	0.288083i	−0.820013	+	0.572344i	$0.806034\pi$
$440$	56.4501	−	12.8844i	0.128296	−	0.0292826i
$441$		0			0
$442$	−27.5573	−	13.2709i	−0.0623468	−	0.0300246i
$443$	454.976	+	51.2635i	1.02703	+	0.115719i	0.609372	−	0.792884i	$-0.291421\pi$
$443$	454.976	+	51.2635i	1.02703	+	0.115719i	0.417661	+	0.908603i	$0.362850\pi$
$444$		0			0
$445$	89.2459	−	255.050i	0.200553	−	0.573146i
$446$	771.776	−	86.9583i	1.73044	−	0.194974i
$447$		0			0
$448$	−919.965	−	733.648i	−2.05349	−	1.63761i
$449$	−422.069	+	265.204i	−0.940021	+	0.590654i	−0.912549	−	0.408968i	$-0.865889\pi$
$449$	−422.069	+	265.204i	−0.940021	+	0.590654i	−0.0274722	+	0.999623i	$0.508746\pi$
$450$		0			0
$451$	−39.2143	+	49.1732i	−0.0869497	+	0.109031i
$452$	−132.959	−	132.959i	−0.294157	−	0.294157i
$453$		0			0
$454$	279.367	+	97.7549i	0.615347	+	0.215319i
$455$	97.5780	+	122.359i	0.214457	+	0.268921i
$456$		0			0
$457$	−4.22710	+	8.77767i	−0.00924968	+	0.0192071i	−0.905543	−	0.424256i	$-0.860536\pi$
$457$	−4.22710	+	8.77767i	−0.00924968	+	0.0192071i	0.896293	+	0.443463i	$0.146250\pi$
$458$	41.1828	−	180.434i	0.0899188	−	0.393960i
$459$		0			0
$460$	924.100	−	445.023i	2.00891	−	0.967441i
$461$	−736.203	+	257.609i	−1.59697	+	0.558804i	−0.974607	−	0.223924i	$-0.928113\pi$
$461$	−736.203	+	257.609i	−1.59697	+	0.558804i	−0.622364	+	0.782728i	$0.713828\pi$
$462$		0			0
$463$		−	21.7764i		−	0.0470332i	−0.999723	−	0.0235166i	$-0.992514\pi$
$463$		−	21.7764i		−	0.0470332i	0.999723	−	0.0235166i	$-0.00748626\pi$
$464$	−240.938	+	6.46177i	−0.519262	+	0.0139262i
$465$		0			0
$466$	−154.734	+	246.258i	−0.332047	+	0.528450i
$467$	94.2773	+	269.429i	0.201878	+	0.576936i	0.999662	−	0.0260088i	$-0.00827980\pi$
$467$	94.2773	+	269.429i	0.201878	+	0.576936i	−0.797783	+	0.602944i	$0.793994\pi$
$468$		0			0
$469$	−676.036	+	154.301i	−1.44144	+	0.328999i
$470$	104.436	+	23.8367i	0.222203	+	0.0507165i
$471$		0			0
$472$	−41.0184	−	4.62167i	−0.0869034	−	0.00979166i
$473$	−4.27512	+	3.40930i	−0.00903831	+	0.00720781i
$474$		0			0
$475$	143.461	−	16.1642i	0.302023	−	0.0340298i
$476$	−158.588	+	158.588i	−0.333168	+	0.333168i
$477$		0			0
$478$	265.624	−	166.902i	0.555698	−	0.349168i
$479$	−390.644	−	621.706i	−0.815540	−	1.29792i	−0.951636	−	0.307229i	$-0.900598\pi$
$479$	−390.644	−	621.706i	−0.815540	−	1.29792i	0.136095	−	0.990696i	$-0.456545\pi$
$480$		0			0
$481$	−40.3241	−	40.3241i	−0.0838339	−	0.0838339i
$482$	126.723	+	1124.70i	0.262910	+	2.33339i
$483$		0			0
$484$	380.009	+	476.516i	0.785142	+	0.984537i
$485$	−64.6601	+	573.874i	−0.133320	+	1.18325i
$486$		0			0
$487$	−142.396	+	623.876i	−0.292394	+	1.28106i	0.588790	+	0.808286i	$0.299604\pi$
$487$	−142.396	+	623.876i	−0.292394	+	1.28106i	−0.881184	+	0.472774i	$0.843253\pi$
$488$	57.4189	+	251.568i	0.117662	+	0.515509i
$489$		0			0
$490$	1236.34	−	432.614i	2.52314	−	0.882886i
$491$	−110.365	−	69.3472i	−0.224777	−	0.141237i	0.414936	−	0.909851i	$-0.363804\pi$
$491$	−110.365	−	69.3472i	−0.224777	−	0.141237i	−0.639713	+	0.768614i	$0.720947\pi$
$492$		0			0
$493$	−8.56823	+	100.102i	−0.0173798	+	0.203047i
$494$	−299.045			−0.605354
$495$		0			0
$496$	−38.1960	−	109.158i	−0.0770082	−	0.220077i
$497$	405.995	+	843.058i	0.816892	+	1.69629i
$498$		0			0
$499$	66.2987	+	15.1322i	0.132863	+	0.0303251i	0.288435	−	0.957499i	$-0.406865\pi$
$499$	66.2987	+	15.1322i	0.132863	+	0.0303251i	−0.155572	+	0.987825i	$0.549722\pi$
$500$	650.592	+	313.309i	1.30118	+	0.626617i
$501$		0			0
$502$	880.137	−	701.886i	1.75326	−	1.39818i
$503$	287.544	−	821.754i	0.571658	−	1.63371i	−0.187106	−	0.982340i	$-0.559911\pi$
$503$	287.544	−	821.754i	0.571658	−	1.63371i	0.758764	−	0.651365i	$-0.225803\pi$
$504$		0			0
$505$	226.381	−	226.381i	0.448278	−	0.448278i
$506$	−291.200	−	232.224i	−0.575494	−	0.458941i
$507$		0			0
$508$	−462.447	−	735.980i	−0.910329	−	1.44878i
$509$	154.547	−	193.796i	0.303629	−	0.380739i	−0.606486	−	0.795094i	$-0.707421\pi$
$509$	154.547	−	193.796i	0.303629	−	0.380739i	0.910115	+	0.414355i	$0.135993\pi$
$510$		0			0
$511$	102.514	+	909.838i	0.200615	+	1.78051i
$512$	−473.386	−	165.645i	−0.924582	−	0.323525i
$513$		0			0
$514$	132.881	−	1179.35i	0.258523	−	2.29445i
$515$	−172.635	+	358.480i	−0.335213	+	0.696078i
$516$		0			0
$517$	−4.97997	−	21.8187i	−0.00963244	−	0.0422025i
$518$	−654.843	+	315.356i	−1.26418	+	0.608795i
$519$		0			0
$520$	−48.3025	−	30.3505i	−0.0928894	−	0.0583663i
$521$		−	250.623i		−	0.481041i	−0.970644	−	0.240521i	$-0.922682\pi$
$521$		−	250.623i		−	0.481041i	0.970644	−	0.240521i	$-0.0773182\pi$
$522$		0			0
$523$	190.538			0.364318			0.182159	−	0.983269i	$-0.441691\pi$
$523$	190.538			0.364318			0.182159	+	0.983269i	$0.441691\pi$
$524$	439.112	−	698.843i	0.838000	−	1.33367i
$525$		0			0
$526$	453.525	+	941.755i	0.862215	+	1.79041i
$527$	−46.9978	+	10.7269i	−0.0891798	+	0.0203547i
$528$		0			0
$529$	−1079.87	−	520.038i	−2.04134	−	0.983058i
$530$	445.029	+	50.1427i	0.839677	+	0.0946089i
$531$		0			0
$532$	−724.228	+	2069.72i	−1.36133	+	3.89046i
$533$	61.5760	−	6.93794i	0.115527	−	0.0130168i
$534$		0			0
$535$	−139.846	−	111.523i	−0.261394	−	0.208455i
$536$	214.015	−	134.474i	0.399281	−	0.250885i
$537$		0			0
$538$	−138.362	+	173.501i	−0.257179	+	0.322492i
$539$	−193.502	−	193.502i	−0.359001	−	0.359001i
$540$		0			0
$541$	−692.929	−	242.466i	−1.28083	−	0.448182i	−0.397789	−	0.917477i	$-0.630222\pi$
$541$	−692.929	−	242.466i	−1.28083	−	0.448182i	−0.883041	+	0.469295i	$0.844508\pi$
$542$	−641.363	−	804.243i	−1.18333	−	1.48384i
$543$		0			0
$544$	−64.5238	+	133.985i	−0.118610	+	0.246296i
$545$	113.821	−	498.681i	0.208845	−	0.915011i
$546$		0			0
$547$	−646.089	+	311.140i	−1.18115	+	0.568812i	−0.918246	−	0.396010i	$-0.870394\pi$
$547$	−646.089	+	311.140i	−1.18115	+	0.568812i	−0.262904	+	0.964822i	$0.584680\pi$
$548$	276.733	−	96.8330i	0.504987	−	0.176703i
$549$		0			0
$550$		−	38.1940i		−	0.0694436i
$551$	349.168	+	918.131i	0.633699	+	1.66630i
$552$		0			0
$553$	569.448	−	906.271i	1.02974	−	1.63883i
$554$	304.292	+	869.616i	0.549263	+	1.56970i
$555$		0			0
$556$	243.035	−	55.4711i	0.437113	−	0.0997681i
$557$	−292.506	−	66.7627i	−0.525146	−	0.119861i	−0.0482744	−	0.998834i	$-0.515372\pi$
$557$	−292.506	−	66.7627i	−0.525146	−	0.119861i	−0.476872	+	0.878973i	$0.658229\pi$
$558$		0			0
$559$	5.35342	+	0.603186i	0.00957678	+	0.00107904i
$560$	353.510	−	281.915i	0.631268	−	0.503419i
$561$		0			0
$562$	−1037.93	+	116.946i	−1.84684	+	0.208089i
$563$	−748.523	+	748.523i	−1.32953	+	1.32953i	−0.423743	+	0.905782i	$0.639284\pi$
$563$	−748.523	+	748.523i	−1.32953	+	1.32953i	−0.905782	+	0.423743i	$0.860716\pi$
$564$		0			0
$565$	133.796	−	84.0699i	0.236808	−	0.148796i
$566$	−162.977	−	259.376i	−0.287945	−	0.458262i
$567$		0			0
$568$	−241.178	−	241.178i	−0.424609	−	0.424609i
$569$	37.2315	+	330.438i	0.0654331	+	0.580735i	0.983059	+	0.183290i	$0.0586746\pi$
$569$	37.2315	+	330.438i	0.0654331	+	0.580735i	−0.917626	+	0.397445i	$0.869897\pi$
$570$		0			0
$571$	632.274	+	792.847i	1.10731	+	1.38852i	0.913184	+	0.407546i	$0.133616\pi$
$571$	632.274	+	792.847i	1.10731	+	1.38852i	0.194126	+	0.980977i	$0.437813\pi$
$572$	−5.09623	+	45.2303i	−0.00890949	+	0.0790739i
$573$		0			0
$574$	175.739	−	769.964i	0.306166	−	1.34140i
$575$	−39.4205	−	172.712i	−0.0685573	−	0.300369i
$576$		0			0
$577$	598.835	−	209.541i	1.03784	−	0.363156i	0.243034	−	0.970018i	$-0.421857\pi$
$577$	598.835	−	209.541i	1.03784	−	0.363156i	0.794808	+	0.606861i	$0.207572\pi$
$578$	−719.811	−	452.287i	−1.24535	−	0.782503i
$579$		0			0
$580$	−140.481	+	701.708i	−0.242209	+	1.20984i
$581$	−564.405			−0.971438
$582$		0			0
$583$	−30.9022	−	88.3133i	−0.0530054	−	0.151481i
$584$	−144.804	−	300.689i	−0.247953	−	0.514879i
$585$		0			0
$586$	559.060	+	127.602i	0.954028	+	0.217751i
$587$	114.477	+	55.1294i	0.195021	+	0.0939171i	0.528846	−	0.848718i	$-0.322625\pi$
$587$	114.477	+	55.1294i	0.195021	+	0.0939171i	−0.333825	+	0.942635i	$0.608339\pi$
$588$		0			0
$589$	−368.491	+	293.862i	−0.625622	+	0.498917i
$590$	43.7554	−	125.046i	0.0741616	−	0.211942i
$591$		0			0
$592$	−116.501	+	116.501i	−0.196793	+	0.196793i
$593$	80.0236	+	63.8167i	0.134947	+	0.107617i	0.688637	−	0.725106i	$-0.258209\pi$
$593$	80.0236	+	63.8167i	0.134947	+	0.107617i	−0.553690	+	0.832723i	$0.686781\pi$
$594$		0			0
$595$	−100.275	−	159.587i	−0.168530	−	0.268214i
$596$	−772.303	+	968.437i	−1.29581	+	1.62489i
$597$		0			0
$598$	41.0860	+	364.649i	0.0687057	+	0.609780i
$599$	−552.540	−	193.342i	−0.922438	−	0.322775i	−0.173055	−	0.984912i	$-0.555364\pi$
$599$	−552.540	−	193.342i	−0.922438	−	0.322775i	−0.749383	+	0.662137i	$0.769650\pi$
$600$		0			0
$601$	−97.2205	+	862.856i	−0.161765	+	1.43570i	0.606253	+	0.795272i	$0.292672\pi$
$601$	−97.2205	+	862.856i	−0.161765	+	1.43570i	−0.768018	+	0.640429i	$0.778757\pi$
$602$	29.7915	−	61.8626i	0.0494875	−	0.102762i
$603$		0			0
$604$	−101.454	−	444.500i	−0.167971	−	0.735928i
$605$	−461.472	+	222.233i	−0.762763	+	0.367327i
$606$		0			0
$607$	12.0856	+	7.59388i	0.0199104	+	0.0125105i	0.541950	−	0.840410i	$-0.317686\pi$
$607$	12.0856	+	7.59388i	0.0199104	+	0.0125105i	−0.522040	+	0.852921i	$0.674829\pi$
$608$			1453.97i			2.39140i
$609$		0			0
$610$	−828.163			−1.35764
$611$	−11.7308	+	18.6695i	−0.0191994	+	0.0305557i
$612$		0			0
$613$	−210.870	−	437.876i	−0.343997	−	0.714317i	0.655155	−	0.755495i	$-0.272603\pi$
$613$	−210.870	−	437.876i	−0.343997	−	0.714317i	−0.999152	+	0.0411775i	$0.986889\pi$
$614$	651.368	−	148.671i	1.06086	−	0.242134i
$615$		0			0
$616$	136.856	+	65.9065i	0.222169	+	0.106991i
$617$	−90.2086	−	10.1641i	−0.146205	−	0.0164734i	0.0385585	−	0.999256i	$-0.487723\pi$
$617$	−90.2086	−	10.1641i	−0.146205	−	0.0164734i	−0.184764	+	0.982783i	$0.559152\pi$
$618$		0			0
$619$	357.144	−	1020.66i	0.576969	−	1.64888i	−0.171094	−	0.985255i	$-0.554730\pi$
$619$	357.144	−	1020.66i	0.576969	−	1.64888i	0.748063	−	0.663628i	$-0.230984\pi$
$620$	−341.214	+	38.4456i	−0.550346	+	0.0620091i
$621$		0			0
$622$	28.4795	+	22.7116i	0.0457870	+	0.0365139i
$623$	600.223	−	377.145i	0.963439	−	0.605369i
$624$		0			0
$625$	−311.919	+	391.134i	−0.499070	+	0.625814i
$626$	643.819	+	643.819i	1.02846	+	1.02846i
$627$		0			0
$628$	998.134	+	349.262i	1.58939	+	0.556150i
$629$	42.8196	+	53.6940i	0.0680756	+	0.0853641i
$630$		0			0
$631$	−36.5938	+	75.9878i	−0.0579933	+	0.120424i	−0.927951	−	0.372702i	$-0.878432\pi$
$631$	−36.5938	+	75.9878i	−0.0579933	+	0.120424i	0.869958	+	0.493126i	$0.164146\pi$
$632$	−86.8144	+	380.359i	−0.137365	+	0.601833i
$633$		0			0
$634$	−699.121	+	336.679i	−1.10272	+	0.531040i
$635$	689.467	−	241.255i	1.08577	−	0.379929i
$636$		0			0
$637$			269.610i			0.423249i
$638$	251.715	−	64.5985i	0.394538	−	0.101252i
$639$		0			0
$640$	−316.372	+	503.503i	−0.494331	+	0.786723i
$641$	−254.096	−	726.165i	−0.396406	−	1.13286i	−0.953233	−	0.302235i	$-0.902267\pi$
$641$	−254.096	−	726.165i	−0.396406	−	1.13286i	0.556827	−	0.830628i	$-0.312018\pi$
$642$		0			0
$643$	−511.993	+	116.859i	−0.796256	+	0.181740i	−0.601249	−	0.799062i	$-0.705330\pi$
$643$	−511.993	+	116.859i	−0.796256	+	0.181740i	−0.195007	+	0.980802i	$0.562473\pi$
$644$	2623.28	+	598.747i	4.07342	+	0.929731i
$645$		0			0
$646$	357.874	+	40.3227i	0.553984	+	0.0624190i
$647$	−810.314	+	646.204i	−1.25242	+	0.998769i	−0.252907	+	0.967491i	$0.581387\pi$
$647$	−810.314	+	646.204i	−1.25242	+	0.998769i	−0.999511	+	0.0312788i	$0.990042\pi$
$648$		0			0
$649$	−27.5037	+	3.09892i	−0.0423786	+	0.00477492i
$650$	−26.6082	+	26.6082i	−0.0409357	+	0.0409357i
$651$		0			0
$652$	178.617	−	112.232i	0.273952	−	0.172135i
$653$	−172.974	−	275.286i	−0.264891	−	0.421571i	0.687623	−	0.726068i	$-0.258654\pi$
$653$	−172.974	−	275.286i	−0.264891	−	0.421571i	−0.952513	+	0.304497i	$0.901512\pi$
$654$		0			0
$655$	490.448	+	490.448i	0.748776	+	0.748776i
$656$	−20.0446	−	177.900i	−0.0305557	−	0.271190i
$657$		0			0
$658$	175.214	+	219.711i	0.266282	+	0.333908i
$659$	74.6830	−	662.830i	0.113328	−	1.00581i	−0.800395	−	0.599473i	$-0.795377\pi$
$659$	74.6830	−	662.830i	0.113328	−	1.00581i	0.913723	−	0.406339i	$-0.133195\pi$
$660$		0			0
$661$	156.741	−	686.726i	0.237127	−	1.03892i	−0.706450	−	0.707763i	$-0.749704\pi$
$661$	156.741	−	686.726i	0.237127	−	1.03892i	0.943576	−	0.331156i	$-0.107439\pi$
$662$	108.043	+	473.367i	0.163207	+	0.715056i
$663$		0			0
$664$	194.184	−	67.9481i	0.292446	−	0.102331i
$665$	−1560.30	−	980.399i	−2.34631	−	1.47428i
$666$		0			0
$667$	1071.58	−	551.911i	1.60656	−	0.827453i
$668$	−101.789			−0.152378
$669$		0			0
$670$	267.926	+	765.689i	0.399890	+	1.14282i
$671$	75.0705	+	155.885i	0.111878	+	0.232318i
$672$		0			0
$673$	−764.739	−	174.547i	−1.13631	−	0.259356i	−0.387328	−	0.921942i	$-0.626602\pi$
$673$	−764.739	−	174.547i	−1.13631	−	0.259356i	−0.748986	+	0.662586i	$0.769459\pi$
$674$	−1707.98	−	822.521i	−2.53410	−	1.22036i
$675$		0			0
$676$	−680.935	+	543.028i	−1.00730	+	0.803295i
$677$	−145.674	+	416.312i	−0.215176	+	0.614937i	−0.999988	−	0.00479615i	$-0.998473\pi$
$677$	−145.674	+	416.312i	−0.215176	+	0.614937i	0.784813	+	0.619733i	$0.212759\pi$
$678$		0			0
$679$	−1071.28	+	1071.28i	−1.57774	+	1.57774i
$680$	53.7123	+	42.8341i	0.0789887	+	0.0629913i
$681$		0			0
$682$	66.3398	+	105.579i	0.0972724	+	0.154808i
$683$	−158.493	+	198.744i	−0.232054	+	0.290986i	−0.884202	−	0.467106i	$-0.845297\pi$
$683$	−158.493	+	198.744i	−0.232054	+	0.290986i	0.652148	+	0.758092i	$0.273868\pi$
$684$		0			0
$685$	27.5863	+	244.835i	0.0402720	+	0.357424i
$686$	1547.67	+	541.552i	2.25607	+	0.789434i
$687$		0			0
$688$	1.74268	−	15.4667i	0.00253296	−	0.0224806i
$689$	−39.9960	+	83.0525i	−0.0580493	+	0.120541i
$690$		0			0
$691$	−100.393	−	439.849i	−0.145286	−	0.636539i	−0.994157	−	0.107940i	$-0.965575\pi$
$691$	−100.393	−	439.849i	−0.145286	−	0.636539i	0.848871	−	0.528599i	$-0.177283\pi$
$692$	−1058.51	+	509.751i	−1.52964	+	0.736635i
$693$		0			0
$694$	508.975	+	319.810i	0.733394	+	0.460822i
$695$			209.492i			0.301427i
$696$		0			0
$697$	−74.6249			−0.107066
$698$	572.808	−	911.619i	0.820642	−	1.30604i
$699$		0			0
$700$	119.719	+	248.599i	0.171027	+	0.355141i
$701$	−391.700	+	89.4029i	−0.558773	+	0.127536i	−0.492574	−	0.870270i	$-0.663944\pi$
$701$	−391.700	+	89.4029i	−0.558773	+	0.127536i	−0.0661981	+	0.997806i	$0.521087\pi$
$702$		0			0
$703$	604.968	+	291.337i	0.860552	+	0.414420i
$704$	285.783	+	32.2000i	0.405941	+	0.0457386i
$705$		0			0
$706$	339.906	−	971.396i	0.481454	−	1.37592i
$707$	834.599	−	94.0367i	1.18048	−	0.133008i
$708$		0			0
$709$	−587.061	−	468.165i	−0.828012	−	0.660318i	0.114893	−	0.993378i	$-0.463347\pi$
$709$	−587.061	−	468.165i	−0.828012	−	0.660318i	−0.942906	+	0.333060i	$0.891919\pi$
$710$	926.886	−	582.401i	1.30547	−	0.820283i
$711$		0			0
$712$	−161.103	+	202.017i	−0.226269	+	0.283732i
$713$	408.956	+	408.956i	0.573571	+	0.573571i
$714$		0			0
$715$	−36.1042	−	12.6334i	−0.0504954	−	0.0176691i
$716$	−223.685	−	280.492i	−0.312409	−	0.391748i
$717$		0			0
$718$	441.982	−	917.785i	0.615574	−	1.27825i
$719$	−147.275	+	645.255i	−0.204834	+	0.897434i	0.763110	+	0.646268i	$0.223671\pi$
$719$	−147.275	+	645.255i	−0.204834	+	0.897434i	−0.967944	+	0.251166i	$0.919186\pi$
$720$		0			0
$721$	−940.433	+	452.889i	−1.30435	+	0.628140i
$722$	2277.76	−	797.024i	3.15480	−	1.10391i
$723$		0			0
$724$			190.076i			0.262536i
$725$	112.761	+	50.6248i	0.155532	+	0.0698273i
$726$		0			0
$727$	−43.7196	+	69.5794i	−0.0601370	+	0.0957075i	−0.875439	−	0.483328i	$-0.839428\pi$
$727$	−43.7196	+	69.5794i	−0.0601370	+	0.0957075i	0.815302	+	0.579035i	$0.196571\pi$
$728$	−49.4278	−	141.257i	−0.0678954	−	0.194034i
$729$		0			0
$730$	1044.27	−	238.348i	1.43051	−	0.326504i
$731$	−6.32523	−	1.44369i	−0.00865285	−	0.00197496i
$732$		0			0
$733$	531.014	+	59.8309i	0.724440	+	0.0816248i	0.466481	−	0.884531i	$-0.345522\pi$
$733$	531.014	+	59.8309i	0.724440	+	0.0816248i	0.257959	+	0.966156i	$0.416950\pi$
$734$	−785.475	+	626.395i	−1.07013	+	0.853400i
$735$		0			0
$736$	1772.94	−	199.763i	2.40889	−	0.271416i
$737$	119.839	−	119.839i	0.162604	−	0.162604i
$738$		0			0
$739$	−592.189	+	372.097i	−0.801338	+	0.503514i	−0.869366	−	0.494169i	$-0.835472\pi$
$739$	−592.189	+	372.097i	−0.801338	+	0.503514i	0.0680274	+	0.997683i	$0.478329\pi$
$740$	260.263	+	414.207i	0.351707	+	0.559739i
$741$		0			0
$742$	830.760	+	830.760i	1.11962	+	1.11962i
$743$	−90.3001	−	801.435i	−0.121534	−	1.07865i	−0.895389	−	0.445284i	$-0.853103\pi$
$743$	−90.3001	−	801.435i	−0.121534	−	1.07865i	0.773855	−	0.633363i	$-0.218326\pi$
$744$		0			0
$745$	−649.021	−	813.846i	−0.871169	−	1.09241i
$746$	141.114	−	1252.42i	0.189161	−	1.67885i
$747$		0			0
$748$	12.1976	−	53.4410i	0.0163069	−	0.0714451i
$749$	−104.417	−	457.481i	−0.139408	−	0.610788i
$750$		0			0
$751$	45.2480	−	15.8329i	0.0602503	−	0.0210825i	−0.299986	−	0.953944i	$-0.596982\pi$
$751$	45.2480	−	15.8329i	0.0602503	−	0.0210825i	0.360236	+	0.932861i	$0.382696\pi$
$752$	53.9385	+	33.8918i	0.0717268	+	0.0450689i
$753$		0			0
$754$	−220.363	−	130.356i	−0.292258	−	0.172886i
$755$	383.151			0.507485
$756$		0			0
$757$	241.576	+	690.385i	0.319123	+	0.912002i	0.985987	+	0.166822i	$0.0533506\pi$
$757$	241.576	+	690.385i	0.319123	+	0.912002i	−0.666864	+	0.745180i	$0.732364\pi$
$758$	−494.555	−	1026.95i	−0.652448	−	1.35482i
$759$		0			0
$760$	654.851	+	149.465i	0.861646	+	0.196665i
$761$	152.528	+	73.4534i	0.200431	+	0.0965222i	0.531407	−	0.847117i	$-0.321664\pi$
$761$	152.528	+	73.4534i	0.200431	+	0.0965222i	−0.330976	+	0.943639i	$0.607378\pi$
$762$		0			0
$763$	1049.12	−	836.648i	1.37500	−	1.09652i
$764$	−253.538	+	724.571i	−0.331856	+	0.948391i
$765$		0			0
$766$	932.589	−	932.589i	1.21748	−	1.21748i
$767$	21.3196	+	17.0018i	0.0277961	+	0.0221666i
$768$		0			0
$769$	−247.966	−	394.636i	−0.322453	−	0.513180i	0.645683	−	0.763605i	$-0.276573\pi$
$769$	−247.966	−	394.636i	−0.322453	−	0.513180i	−0.968136	+	0.250425i	$0.919430\pi$
$770$	−303.960	+	381.154i	−0.394753	+	0.495005i
$771$		0			0
$772$	−17.8699	−	158.600i	−0.0231475	−	0.205440i
$773$	1232.54	+	431.285i	1.59449	+	0.557937i	0.974053	−	0.226318i	$-0.0726689\pi$
$773$	1232.54	+	431.285i	1.59449	+	0.557937i	0.620439	+	0.784255i	$0.286955\pi$
$774$		0			0
$775$	−6.64032	+	58.9345i	−0.00856815	+	0.0760445i
$776$	239.606	−	497.547i	0.308770	−	0.641169i
$777$		0			0
$778$	252.666	+	1107.00i	0.324764	+	1.42288i
$779$	−657.359	+	316.568i	−0.843850	+	0.406377i
$780$		0			0
$781$	−193.645	−	121.675i	−0.247945	−	0.155794i
$782$		−	441.923i		−	0.565119i
$783$		0			0
$784$	778.935			0.993539
$785$	−472.802	+	752.460i	−0.602295	+	0.958548i
$786$		0			0
$787$	148.519	+	308.402i	0.188715	+	0.391871i	0.973763	−	0.227564i	$-0.0730761\pi$
$787$	148.519	+	308.402i	0.188715	+	0.391871i	−0.785048	+	0.619435i	$0.787362\pi$
$788$	−672.637	+	153.525i	−0.853600	+	0.194829i
$789$		0			0
$790$	−1128.14	−	543.283i	−1.42802	−	0.687700i
$791$	411.933	+	46.4137i	0.520775	+	0.0586772i
$792$		0			0
$793$	56.3005	−	160.898i	0.0709969	−	0.202897i
$794$	−457.566	+	51.5554i	−0.576280	+	0.0649312i
$795$		0			0
$796$	−1283.06	−	1023.21i	−1.61189	−	1.28544i
$797$	−110.748	+	69.5877i	−0.138956	+	0.0873120i	−0.599716	−	0.800213i	$-0.704720\pi$
$797$	−110.748	+	69.5877i	−0.138956	+	0.0873120i	0.460760	+	0.887525i	$0.347577\pi$
$798$		0			0
$799$	16.5559	−	20.7605i	0.0207208	−	0.0259831i
$800$	129.371	+	129.371i	0.161713	+	0.161713i
$801$		0			0
$802$	−684.232	−	239.423i	−0.853157	−	0.298533i
$803$	−139.524	−	174.958i	−0.173754	−	0.217880i
$804$		0			0
$805$	−981.107	+	2037.29i	−1.21877	+	2.53079i
$806$	27.3365	−	119.769i	0.0339162	−	0.148597i
$807$		0			0
$808$	−275.824	+	132.830i	−0.341366	+	0.164393i
$809$	−533.286	+	186.605i	−0.659192	+	0.230661i	−0.639084	−	0.769137i	$-0.720687\pi$
$809$	−533.286	+	186.605i	−0.659192	+	0.230661i	−0.0201076	+	0.999798i	$0.506401\pi$
$810$		0			0
$811$		−	993.150i		−	1.22460i	−0.790626	−	0.612299i	$-0.790245\pi$
$811$		−	993.150i		−	1.22460i	0.790626	−	0.612299i	$-0.209755\pi$
$812$	−1435.89	+	1209.46i	−1.76834	+	1.48948i
$813$		0			0
$814$	94.5110	−	150.413i	0.116107	−	0.184783i
$815$	58.5507	+	167.328i	0.0718414	+	0.205311i
$816$		0			0
$817$	−61.8423	+	14.1151i	−0.0756944	+	0.0172768i
$818$	118.295	+	27.0001i	0.144615	+	0.0330075i
$819$		0			0
$820$	−528.209	−	59.5149i	−0.644158	−	0.0725792i
$821$	1213.23	−	967.523i	1.47775	−	1.17847i	0.535056	−	0.844816i	$-0.320290\pi$
$821$	1213.23	−	967.523i	1.47775	−	1.17847i	0.942696	−	0.333652i	$-0.108281\pi$
$822$		0			0
$823$	−862.029	+	97.1274i	−1.04742	+	0.118016i	−0.618865	−	0.785498i	$-0.712407\pi$
$823$	−862.029	+	97.1274i	−1.04742	+	0.118016i	−0.428559	+	0.903514i	$0.640979\pi$
$824$	269.035	−	269.035i	0.326498	−	0.326498i
$825$		0			0
$826$	294.276	−	184.906i	0.356267	−	0.223857i
$827$	409.943	+	652.420i	0.495698	+	0.788899i	0.997083	−	0.0763251i	$-0.0243187\pi$
$827$	409.943	+	652.420i	0.495698	+	0.788899i	−0.501385	+	0.865224i	$0.667176\pi$
$828$		0			0
$829$	862.319	+	862.319i	1.04019	+	1.04019i	0.999158	+	0.0410337i	$0.0130651\pi$
$829$	862.319	+	862.319i	1.04019	+	1.04019i	0.0410337	+	0.999158i	$0.486935\pi$
$830$	73.9279	+	656.128i	0.0890697	+	0.790516i
$831$		0			0
$832$	−176.661	−	221.526i	−0.212333	−	0.266257i
$833$	36.3537	−	322.648i	0.0436419	−	0.387333i
$834$		0			0
$835$	19.0345	−	83.3956i	0.0227958	−	0.0998749i
$836$	−119.257	−	522.497i	−0.142651	−	0.624996i
$837$		0			0
$838$	−1818.55	+	636.337i	−2.17010	+	0.759351i
$839$	1047.00	+	657.873i	1.24791	+	0.784116i	0.983607	−	0.180323i	$-0.0577142\pi$
$839$	1047.00	+	657.873i	1.24791	+	0.784116i	0.264306	+	0.964439i	$0.414857\pi$
$840$		0			0
$841$	−142.924	+	828.766i	−0.169945	+	0.985454i
$842$	−1089.06			−1.29342
$843$		0			0
$844$	−209.395	−	598.417i	−0.248098	−	0.709024i
$845$	−317.568	−	659.437i	−0.375820	−	0.780399i
$846$		0			0
$847$	−1310.00	−	298.999i	−1.54663	−	0.353009i
$848$	239.949	+	115.553i	0.282959	+	0.136266i
$849$		0			0
$850$	35.4305	−	28.2548i	0.0416829	−	0.0332410i
$851$	272.133	−	777.712i	0.319780	−	0.913880i
$852$		0			0
$853$	−554.406	+	554.406i	−0.649948	+	0.649948i	−0.952980	−	0.303032i	$-0.902001\pi$
$853$	−554.406	+	554.406i	−0.649948	+	0.649948i	0.303032	+	0.952980i	$0.402001\pi$
$854$	−1698.60	−	1354.59i	−1.98900	−	1.58617i
$855$		0			0
$856$	91.0003	+	144.826i	0.106309	+	0.169189i
$857$	362.365	−	454.392i	0.422830	−	0.530212i	−0.524098	−	0.851658i	$-0.675597\pi$
$857$	362.365	−	454.392i	0.422830	−	0.530212i	0.946928	+	0.321446i	$0.104169\pi$
$858$		0			0
$859$	7.77894	+	69.0400i	0.00905581	+	0.0803725i	0.997427	−	0.0716866i	$-0.0228381\pi$
$859$	7.77894	+	69.0400i	0.00905581	+	0.0803725i	−0.988371	+	0.152059i	$0.951410\pi$
$860$	−43.6198	−	15.2632i	−0.0507208	−	0.0177480i
$861$		0			0
$862$	165.255	−	1466.68i	0.191711	−	1.70148i
$863$	−387.142	+	803.910i	−0.448601	+	0.931529i	0.546938	+	0.837173i	$0.315793\pi$
$863$	−387.142	+	803.910i	−0.448601	+	0.931529i	−0.995539	+	0.0943559i	$0.969921\pi$
$864$		0			0
$865$	−219.698	−	962.561i	−0.253986	−	1.11279i
$866$	835.509	−	402.360i	0.964791	−	0.464619i
$867$		0			0
$868$	−762.732	−	479.256i	−0.878723	−	0.552138i
$869$			261.597i			0.301032i
$870$		0			0
$871$	−166.974			−0.191704
$872$	−260.229	+	414.152i	−0.298428	+	0.474945i
$873$		0			0
$874$	−1874.69	−	3892.84i	−2.14496	−	4.45405i
$875$	−1552.05	+	354.245i	−1.77377	+	0.404851i
$876$		0			0
$877$	1395.06	+	671.826i	1.59072	+	0.766051i	0.999190	−	0.0402322i	$-0.0128098\pi$
$877$	1395.06	+	671.826i	1.59072	+	0.766051i	0.591530	+	0.806283i	$0.298524\pi$
$878$	428.087	+	48.2339i	0.487571	+	0.0549361i
$879$		0			0
$880$	−36.4994	+	104.309i	−0.0414766	+	0.118533i
$881$	−566.141	+	63.7888i	−0.642612	+	0.0724050i	−0.427256	−	0.904131i	$-0.640520\pi$
$881$	−566.141	+	63.7888i	−0.642612	+	0.0724050i	−0.215356	+	0.976536i	$0.569091\pi$
$882$		0			0
$883$	957.430	+	763.525i	1.08429	+	0.864694i	0.991385	−	0.130981i	$-0.0418126\pi$
$883$	957.430	+	763.525i	1.08429	+	0.864694i	0.0929071	+	0.995675i	$0.470384\pi$
$884$	−45.7277	+	28.7326i	−0.0517281	+	0.0325029i
$885$		0			0
$886$	876.107	−	1098.60i	0.988834	−	1.23996i
$887$	−105.074	−	105.074i	−0.118460	−	0.118460i	0.645392	−	0.763852i	$-0.276694\pi$
$887$	−105.074	−	105.074i	−0.118460	−	0.118460i	−0.763852	+	0.645392i	$0.776694\pi$
$888$		0			0
$889$	1808.74	+	632.906i	2.03458	+	0.711930i
$890$	−517.055	−	648.366i	−0.580960	−	0.728501i
$891$		0			0
$892$	594.997	−	1235.52i	0.667037	−	1.38512i
$893$	57.7703	−	253.108i	0.0646924	−	0.283436i
$894$		0			0
$895$	271.636	−	130.813i	0.303504	−	0.146160i
$896$	−1472.45	+	515.234i	−1.64336	+	0.575037i
$897$		0			0
$898$			1529.82i			1.70359i
$899$	−399.635	+	55.9149i	−0.444532	+	0.0621967i
$900$		0			0
$901$	59.0628	−	93.9979i	0.0655525	−	0.104326i
$902$	63.7523	+	182.194i	0.0706789	+	0.201989i
$903$		0			0
$904$	−147.314	+	33.6234i	−0.162958	+	0.0371940i
$905$	−155.729	−	35.5442i	−0.172077	−	0.0392754i
$906$		0			0
$907$	64.5156	+	7.26917i	0.0711308	+	0.00801452i	0.147458	−	0.989068i	$-0.452891\pi$
$907$	64.5156	+	7.26917i	0.0711308	+	0.00801452i	−0.0763273	+	0.997083i	$0.524319\pi$
$908$	408.584	−	325.835i	0.449982	−	0.358849i
$909$		0			0
$910$	477.291	−	53.7778i	0.524496	−	0.0590965i
$911$	−50.2732	+	50.2732i	−0.0551846	+	0.0551846i	−0.734161	−	0.678976i	$-0.762424\pi$
$911$	−50.2732	+	50.2732i	−0.0551846	+	0.0551846i	0.678976	+	0.734161i	$0.262424\pi$
$912$		0			0
$913$	116.802	−	73.3915i	0.127932	−	0.0803850i
$914$	15.9077	+	25.3169i	0.0174045	+	0.0276991i
$915$		0			0
$916$	−231.068	−	231.068i	−0.252258	−	0.252258i
$917$	203.728	+	1808.14i	0.222168	+	1.97180i
$918$		0			0
$919$	−357.509	−	448.302i	−0.389020	−	0.487815i	0.548302	−	0.836280i	$-0.315274\pi$
$919$	−357.509	−	448.302i	−0.389020	−	0.487815i	−0.937322	+	0.348465i	$0.886703\pi$
$920$	92.2843	−	819.046i	0.100309	−	0.890268i
$921$		0			0
$922$	−532.660	+	2333.74i	−0.577723	+	2.53117i
$923$	50.1385	+	219.671i	0.0543212	+	0.237997i
$924$		0			0
$925$	79.7508	−	27.9060i	0.0862171	−	0.0301687i
$926$	−56.5884	−	35.5568i	−0.0611106	−	0.0383983i
$927$		0			0
$928$	−633.800	+	1071.42i	−0.682974	+	1.15454i
$929$	627.487			0.675444			0.337722	−	0.941246i	$-0.390344\pi$
$929$	627.487			0.675444			0.337722	+	0.941246i	$0.390344\pi$
$930$		0			0
$931$	−1048.48	−	2996.37i	−1.12618	−	3.21845i
$932$	222.808	+	462.666i	0.239065	+	0.496423i
$933$		0			0
$934$	854.079	+	194.938i	0.914432	+	0.208713i
$935$	41.5033	+	19.9869i	0.0443885	+	0.0213764i
$936$		0			0
$937$	566.153	−	451.492i	0.604219	−	0.481848i	−0.272952	−	0.962028i	$-0.588000\pi$
$937$	566.153	−	451.492i	0.604219	−	0.481848i	0.877170	+	0.480180i	$0.159428\pi$
$938$	−702.875	+	2008.70i	−0.749334	+	2.14147i
$939$		0			0
$940$	133.743	−	133.743i	0.142280	−	0.142280i
$941$	882.450	+	703.730i	0.937779	+	0.747854i	0.967807	−	0.251695i	$-0.0809881\pi$
$941$	882.450	+	703.730i	0.937779	+	0.747854i	−0.0300275	+	0.999549i	$0.509559\pi$
$942$		0			0
$943$	476.331	+	758.076i	0.505123	+	0.803898i
$944$	49.1203	−	61.5949i	0.0520342	−	0.0652488i
$945$		0			0
$946$	1.87895	+	16.6762i	0.00198621	+	0.0176281i
$947$	−1457.95	−	510.160i	−1.53955	−	0.538711i	−0.578642	−	0.815582i	$-0.696417\pi$
$947$	−1457.95	−	510.160i	−1.53955	−	0.538711i	−0.960907	+	0.276871i	$0.910703\pi$
$948$		0			0
$949$	−24.6852	+	219.087i	−0.0260118	+	0.230861i
$950$	192.241	−	399.193i	0.202359	−	0.420203i
$951$		0			0
$952$	40.1046	+	175.710i	0.0421267	+	0.184569i
$953$	1087.83	−	523.870i	1.14148	−	0.549707i	0.235015	−	0.971992i	$-0.424486\pi$
$953$	1087.83	−	523.870i	1.14148	−	0.549707i	0.906463	+	0.422285i	$0.138772\pi$
$954$		0			0
$955$	−546.230	−	343.219i	−0.571968	−	0.359392i
$956$		−	553.905i		−	0.579398i
$957$		0			0
$958$	−2253.42			−2.35222
$959$	−343.886	+	547.291i	−0.358588	+	0.570689i
$960$		0			0
$961$	332.954	+	691.386i	0.346466	+	0.719444i
$962$	−170.629	+	38.9449i	−0.177369	+	0.0404833i
$963$		0			0
$964$	1800.51	+	867.078i	1.86775	+	0.899459i
$965$	133.282	+	15.0173i	0.138116	+	0.0155620i
$966$		0			0
$967$	−529.706	+	1513.81i	−0.547783	+	1.56547i	0.253592	+	0.967311i	$0.418388\pi$
$967$	−529.706	+	1513.81i	−0.547783	+	1.56547i	−0.801375	+	0.598163i	$0.795898\pi$
$968$	486.703	−	54.8382i	0.502792	−	0.0566511i
$969$		0			0
$970$	1385.70	+	1105.06i	1.42856	+	1.13924i
$971$	827.123	−	519.716i	0.851826	−	0.535238i	−0.0339110	−	0.999425i	$-0.510796\pi$
$971$	827.123	−	519.716i	0.851826	−	0.535238i	0.885737	+	0.464187i	$0.153653\pi$
$972$		0			0
$973$	−342.657	+	429.678i	−0.352165	+	0.441601i
$974$	1388.71	+	1388.71i	1.42578	+	1.42578i
$975$		0			0
$976$	−464.853	−	162.659i	−0.476283	−	0.166659i
$977$	−543.900	−	682.030i	−0.556705	−	0.698086i	0.421240	−	0.906949i	$-0.361595\pi$
$977$	−543.900	−	682.030i	−0.556705	−	0.698086i	−0.977945	+	0.208864i	$0.933024\pi$
$978$		0			0
$979$	−75.1728	+	156.098i	−0.0767853	+	0.159446i
$980$	514.637	−	2254.77i	0.525140	−	2.30079i
$981$		0			0
$982$	−360.413	+	173.566i	−0.367020	+	0.176747i
$983$	−1119.36	+	391.682i	−1.13872	+	0.398456i	−0.832785	−	0.553596i	$-0.813255\pi$
$983$	−1119.36	+	391.682i	−1.13872	+	0.398456i	−0.305937	+	0.952052i	$0.598970\pi$
$984$		0			0
$985$		−	579.801i		−	0.588630i
$986$	246.136	+	185.714i	0.249631	+	0.188351i
$987$		0			0
$988$	−280.921	+	447.084i	−0.284333	+	0.452514i
$989$	25.7082	+	73.4699i	0.0259942	+	0.0742871i
$990$		0			0
$991$	1151.11	−	262.734i	1.16157	−	0.265120i	0.402055	−	0.915615i	$-0.368296\pi$
$991$	1151.11	−	262.734i	1.16157	−	0.265120i	0.759510	+	0.650496i	$0.225439\pi$
$992$	−582.323	−	132.911i	−0.587019	−	0.133983i
$993$		0			0
$994$	2853.70	+	321.535i	2.87092	+	0.323476i
$995$	1078.25	−	859.873i	1.08367	−	0.864194i
$996$		0			0
$997$	1215.35	−	136.937i	1.21901	−	0.137349i	0.521075	−	0.853511i	$-0.325531\pi$
$997$	1215.35	−	136.937i	1.21901	−	0.137349i	0.697935	+	0.716161i	$0.254102\pi$
$998$	147.577	−	147.577i	0.147872	−	0.147872i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.55.4		48
3.2	odd	2		29.3.f.a.26.1	yes	48
29.19	odd	28	inner	261.3.s.a.19.4		48
87.77	even	28		29.3.f.a.19.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.19.1	✓	48	87.77	even	28
29.3.f.a.26.1	yes	48	3.2	odd	2
261.3.s.a.19.4		48	29.19	odd	28	inner
261.3.s.a.55.4		48	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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	261.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63282 - 2.59861i) q^{2} +(-2.35117 - 4.88225i) q^{4} +(4.43970 - 1.01333i) q^{5} +(10.7635 + 5.18344i) q^{7} +(-4.32723 - 0.487562i) q^{8} +O(q^{10})\)	\(q+(1.63282 - 2.59861i) q^{2} +(-2.35117 - 4.88225i) q^{4} +(4.43970 - 1.01333i) q^{5} +(10.7635 + 5.18344i) q^{7} +(-4.32723 - 0.487562i) q^{8} +(4.61596 - 13.1917i) q^{10} +(-2.90150 + 0.326920i) q^{11} +(2.24911 + 1.79360i) q^{13} +(31.0446 - 19.5066i) q^{14} +(5.18193 - 6.49794i) q^{16} +(-2.44971 - 2.44971i) q^{17} +(-31.9711 - 11.1872i) q^{19} +(-15.3858 - 19.2932i) q^{20} +(-3.88808 + 8.07367i) q^{22} +(-9.24886 + 40.5219i) q^{23} +(-3.84011 + 1.84930i) q^{25} +(8.33326 - 2.91593i) q^{26} -64.7374i q^{28} +(-18.6826 - 22.1802i) q^{29} +(7.40308 - 11.7819i) q^{31} +(-14.1774 - 40.5168i) q^{32} +(-10.3658 + 2.36592i) q^{34} +(53.0394 + 12.1059i) q^{35} +(-19.6990 - 2.21954i) q^{37} +(-81.2741 + 64.8140i) q^{38} +(-19.7057 + 2.22030i) q^{40} +(15.2314 - 15.2314i) q^{41} +(1.58568 - 0.996350i) q^{43} +(8.41802 + 13.3972i) q^{44} +(90.1991 + 90.1991i) q^{46} +(0.858173 + 7.61650i) q^{47} +(58.4343 + 73.2743i) q^{49} +(-1.46458 + 12.9985i) q^{50} +(3.46879 - 15.1978i) q^{52} +(7.13045 + 31.2406i) q^{53} +(-12.5505 + 4.39161i) q^{55} +(-44.0490 - 27.6778i) q^{56} +(-88.1430 + 12.3325i) q^{58} +9.47914 q^{59} +(-19.5711 - 55.9310i) q^{61} +(-18.5288 - 38.4755i) q^{62} +(-96.0255 - 21.9172i) q^{64} +(11.8029 + 5.68397i) q^{65} +(-45.3801 + 36.1895i) q^{67} +(-6.20042 + 17.7198i) q^{68} +(118.062 - 118.062i) q^{70} +(61.2373 + 48.8352i) q^{71} +(40.7753 + 64.8935i) q^{73} +(-37.9326 + 47.5659i) q^{74} +(20.5509 + 182.394i) q^{76} +(-32.9249 - 11.5209i) q^{77} +(10.0312 - 89.0291i) q^{79} +(16.4217 - 34.0999i) q^{80} +(-14.7104 - 64.4505i) q^{82} +(-42.5654 + 20.4984i) q^{83} +(-13.3584 - 8.39361i) q^{85} -5.74743i q^{86} +12.7148 q^{88} +(31.5692 - 50.2421i) q^{89} +(14.9113 + 30.9636i) q^{91} +(219.584 - 50.1186i) q^{92} +(21.1936 + 10.2063i) q^{94} +(-153.279 - 17.2703i) q^{95} +(-41.8847 + 119.700i) q^{97} +(285.824 - 32.2047i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more