LMFDB - Embedded newform 171.4.y.a.53.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,4,Mod(53,171)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 11])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("171.53"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	171.y (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$10.0893266110$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.14
Character	$\chi$	$=$	171.53
Dual form			171.4.y.a.71.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.30065 + 0.837369i) q^{2} +(-1.53654 - 1.28931i) q^{4} +(10.9536 + 13.0540i) q^{5} +(-16.1646 + 27.9979i) q^{7} +(-12.2486 - 21.2153i) q^{8} +(14.2695 + 39.2050i) q^{10} +(2.26002 - 1.30482i) q^{11} +(-16.7040 - 2.94537i) q^{13} +(-60.6336 + 50.8776i) q^{14} +(-7.62839 - 43.2628i) q^{16} +(-38.8403 + 106.713i) q^{17} +(80.0856 + 21.1019i) q^{19} -34.1808i q^{20} +(6.29213 - 1.10947i) q^{22} +(-21.2515 + 25.3265i) q^{23} +(-28.7197 + 162.878i) q^{25} +(-35.9638 - 20.7637i) q^{26} +(60.9356 - 22.1788i) q^{28} +(84.8179 - 30.8712i) q^{29} +(139.893 + 80.7674i) q^{31} +(-15.3546 + 87.0804i) q^{32} +(-178.716 + 212.986i) q^{34} +(-542.546 + 95.6655i) q^{35} +197.041i q^{37} +(166.579 + 115.609i) q^{38} +(142.778 - 392.278i) q^{40} +(-75.9623 - 430.804i) q^{41} +(394.699 - 331.192i) q^{43} +(-5.15494 - 0.908955i) q^{44} +(-70.0998 + 40.4721i) q^{46} +(-61.1561 - 168.025i) q^{47} +(-351.087 - 608.100i) q^{49} +(-202.463 + 350.676i) q^{50} +(21.8690 + 26.0625i) q^{52} +(-196.492 - 164.877i) q^{53} +(41.7886 + 15.2098i) q^{55} +791.975 q^{56} +220.987 q^{58} +(300.408 + 109.340i) q^{59} +(-119.382 - 100.173i) q^{61} +(254.213 + 302.960i) q^{62} +(-283.965 + 491.841i) q^{64} +(-144.521 - 250.318i) q^{65} +(367.524 + 1009.76i) q^{67} +(197.266 - 113.892i) q^{68} +(-1328.32 - 234.218i) q^{70} +(664.533 - 557.610i) q^{71} +(36.9153 + 209.357i) q^{73} +(-164.996 + 453.322i) q^{74} +(-95.8482 - 135.680i) q^{76} +84.3675i q^{77} +(599.122 - 105.641i) q^{79} +(481.195 - 573.466i) q^{80} +(185.979 - 1054.74i) q^{82} +(-257.034 - 148.399i) q^{83} +(-1818.48 + 661.872i) q^{85} +(1185.40 - 431.449i) q^{86} +(-55.3642 - 31.9645i) q^{88} +(-40.6753 + 230.681i) q^{89} +(352.478 - 420.067i) q^{91} +(65.3076 - 11.5155i) q^{92} -437.777i q^{94} +(601.765 + 1276.58i) q^{95} +(447.484 - 1229.45i) q^{97} +(-298.524 - 1693.01i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 36 q^{4} - 180 q^{10} - 156 q^{13} + 180 q^{16} + 924 q^{19} + 432 q^{22} - 360 q^{25} - 624 q^{28} + 324 q^{34} + 1440 q^{40} + 1524 q^{43} + 3888 q^{46} - 3228 q^{49} - 6000 q^{52} - 4464 q^{55}+ \cdots + 5904 q^{97}+O(q^{100}) $ 120 * q - 36 * q^4 - 180 * q^10 - 156 * q^13 + 180 * q^16 + 924 * q^19 + 432 * q^22 - 360 * q^25 - 624 * q^28 + 324 * q^34 + 1440 * q^40 + 1524 * q^43 + 3888 * q^46 - 3228 * q^49 - 6000 * q^52 - 4464 * q^55 + 5616 * q^58 - 5736 * q^61 - 4524 * q^64 + 372 * q^67 + 7848 * q^70 - 276 * q^73 + 4320 * q^76 + 10536 * q^79 + 3960 * q^82 - 11592 * q^85 - 11664 * q^88 - 120 * q^91 + 5904 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	2.30065	+	0.837369i	0.813403	+	0.296055i	0.715029	−	0.699095i	$-0.246414\pi$
$2$	2.30065	+	0.837369i	0.813403	+	0.296055i	0.0983743	+	0.995149i	$0.468636\pi$
$3$		0			0
$3$		0			0
$4$	−1.53654	−	1.28931i	−0.192068	−	0.161164i
$5$	10.9536	+	13.0540i	0.979723	+	1.16759i	0.985854	+	0.167608i	$0.0536042\pi$
$5$	10.9536	+	13.0540i	0.979723	+	1.16759i	−0.00613038	+	0.999981i	$0.501951\pi$
$6$		0			0
$7$	−16.1646	+	27.9979i	−0.872805	+	1.51174i	−0.0137216	+	0.999906i	$0.504368\pi$
$7$	−16.1646	+	27.9979i	−0.872805	+	1.51174i	−0.859083	+	0.511836i	$0.828965\pi$
$8$	−12.2486	−	21.2153i	−0.541318	−	0.937591i
$9$		0			0
$10$	14.2695	+	39.2050i	0.451240	+	1.23977i
$11$	2.26002	−	1.30482i	0.0619473	−	0.0357653i	−0.468706	−	0.883354i	$-0.655280\pi$
$11$	2.26002	−	1.30482i	0.0619473	−	0.0357653i	0.530654	+	0.847589i	$0.321946\pi$
$12$		0			0
$13$	−16.7040	−	2.94537i	−0.356375	−	0.0628385i	−0.00740521	−	0.999973i	$-0.502357\pi$
$13$	−16.7040	−	2.94537i	−0.356375	−	0.0628385i	−0.348969	+	0.937134i	$0.613468\pi$
$14$	−60.6336	+	50.8776i	−1.15750	+	0.971258i
$15$		0			0
$16$	−7.62839	−	43.2628i	−0.119194	−	0.675981i
$17$	−38.8403	+	106.713i	−0.554127	+	1.52245i	0.273897	+	0.961759i	$0.411687\pi$
$17$	−38.8403	+	106.713i	−0.554127	+	1.52245i	−0.828024	+	0.560693i	$0.810535\pi$
$18$		0			0
$19$	80.0856	+	21.1019i	0.966995	+	0.254795i
$19$	80.0856	+	21.1019i	0.966995	+	0.254795i
$20$		−	34.1808i		−	0.382153i
$21$		0			0
$22$	6.29213	−	1.10947i	0.0609766	−	0.0107518i
$23$	−21.2515	+	25.3265i	−0.192662	+	0.229606i	−0.853724	−	0.520725i	$-0.825662\pi$
$23$	−21.2515	+	25.3265i	−0.192662	+	0.229606i	0.661062	+	0.750331i	$0.270106\pi$
$24$		0			0
$25$	−28.7197	+	162.878i	−0.229758	+	1.30302i
$26$	−35.9638	−	20.7637i	−0.271273	−	0.156619i
$27$		0			0
$28$	60.9356	−	22.1788i	0.411277	−	0.149693i
$29$	84.8179	−	30.8712i	0.543113	−	0.197677i	−0.0558708	−	0.998438i	$-0.517794\pi$
$29$	84.8179	−	30.8712i	0.543113	−	0.197677i	0.598984	+	0.800761i	$0.295571\pi$
$30$		0			0
$31$	139.893	+	80.7674i	0.810502	+	0.467944i	0.847130	−	0.531385i	$-0.178328\pi$
$31$	139.893	+	80.7674i	0.810502	+	0.467944i	−0.0366282	+	0.999329i	$0.511662\pi$
$32$	−15.3546	+	87.0804i	−0.0848231	+	0.481056i
$33$		0			0
$34$	−178.716	+	212.986i	−0.901458	+	1.07432i
$35$	−542.546	+	95.6655i	−2.62020	+	0.462012i
$36$		0			0
$37$			197.041i			0.875495i	0.899098	+	0.437747i	$0.144224\pi$
$37$			197.041i			0.875495i	−0.899098	+	0.437747i	$0.855776\pi$
$38$	166.579	+	115.609i	0.711124	+	0.493534i
$39$		0			0
$40$	142.778	−	392.278i	0.564378	−	1.55062i
$41$	−75.9623	−	430.804i	−0.289349	−	1.64098i	−0.689323	−	0.724454i	$-0.742092\pi$
$41$	−75.9623	−	430.804i	−0.289349	−	1.64098i	0.399974	−	0.916527i	$-0.369019\pi$
$42$		0			0
$43$	394.699	−	331.192i	1.39979	−	1.17457i	0.438602	−	0.898681i	$-0.355474\pi$
$43$	394.699	−	331.192i	1.39979	−	1.17457i	0.961191	−	0.275884i	$-0.0889707\pi$
$44$	−5.15494	−	0.908955i	−0.0176622	−	0.00311432i
$45$		0			0
$46$	−70.0998	+	40.4721i	−0.224688	+	0.129724i
$47$	−61.1561	−	168.025i	−0.189799	−	0.521467i	0.807896	−	0.589324i	$-0.200606\pi$
$47$	−61.1561	−	168.025i	−0.189799	−	0.521467i	−0.997695	+	0.0678571i	$0.978384\pi$
$48$		0			0
$49$	−351.087	−	608.100i	−1.02358	−	1.77289i
$50$	−202.463	+	350.676i	−0.572651	+	0.991860i
$51$		0			0
$52$	21.8690	+	26.0625i	0.0583209	+	0.0695041i
$53$	−196.492	−	164.877i	−0.509251	−	0.427313i	0.351614	−	0.936145i	$-0.385633\pi$
$53$	−196.492	−	164.877i	−0.509251	−	0.427313i	−0.860866	+	0.508832i	$0.830077\pi$
$54$		0			0
$55$	41.7886	+	15.2098i	0.102450	+	0.0372889i
$56$	791.975			1.88986
$57$		0			0
$58$	220.987			0.500293
$59$	300.408	+	109.340i	0.662878	+	0.241268i	0.651479	−	0.758667i	$-0.274149\pi$
$59$	300.408	+	109.340i	0.662878	+	0.241268i	0.0113998	+	0.999935i	$0.496371\pi$
$60$		0			0
$61$	−119.382	−	100.173i	−0.250578	−	0.210260i	0.508843	−	0.860859i	$-0.330073\pi$
$61$	−119.382	−	100.173i	−0.250578	−	0.210260i	−0.759421	+	0.650599i	$0.774518\pi$
$62$	254.213	+	302.960i	0.520728	+	0.620580i
$63$		0			0
$64$	−283.965	+	491.841i	−0.554619	+	0.960628i
$65$	−144.521	−	250.318i	−0.275779	−	0.477663i
$66$		0			0
$67$	367.524	+	1009.76i	0.670153	+	1.84123i	0.523467	+	0.852046i	$0.324638\pi$
$67$	367.524	+	1009.76i	0.670153	+	1.84123i	0.146686	+	0.989183i	$0.453139\pi$
$68$	197.266	−	113.892i	0.351795	−	0.203109i
$69$		0			0
$70$	−1328.32	−	234.218i	−2.26806	−	0.399920i
$71$	664.533	−	557.610i	1.11078	−	0.932058i	0.112681	−	0.993631i	$-0.464056\pi$
$71$	664.533	−	557.610i	1.11078	−	0.932058i	0.998103	+	0.0615736i	$0.0196119\pi$
$72$		0			0
$73$	36.9153	+	209.357i	0.0591864	+	0.335663i	0.999995	−	0.00327651i	$-0.00104295\pi$
$73$	36.9153	+	209.357i	0.0591864	+	0.335663i	−0.940808	+	0.338939i	$0.889932\pi$
$74$	−164.996	+	453.322i	−0.259194	+	0.712130i
$75$		0			0
$76$	−95.8482	−	135.680i	−0.144665	−	0.204783i
$77$			84.3675i			0.124864i
$78$		0			0
$79$	599.122	−	105.641i	0.853246	−	0.150450i	0.270115	−	0.962828i	$-0.412938\pi$
$79$	599.122	−	105.641i	0.853246	−	0.150450i	0.583132	+	0.812378i	$0.301827\pi$
$80$	481.195	−	573.466i	0.672491	−	0.801443i
$81$		0			0
$82$	185.979	−	1054.74i	0.250462	−	1.42044i
$83$	−257.034	−	148.399i	−0.339918	−	0.196251i	0.320318	−	0.947310i	$-0.396210\pi$
$83$	−257.034	−	148.399i	−0.339918	−	0.196251i	−0.660236	+	0.751059i	$0.729544\pi$
$84$		0			0
$85$	−1818.48	+	661.872i	−2.32049	+	0.844589i
$86$	1185.40	−	431.449i	1.48633	−	0.540980i
$87$		0			0
$88$	−55.3642	−	31.9645i	−0.0670664	−	0.0387208i
$89$	−40.6753	+	230.681i	−0.0484447	+	0.274743i	−0.999402	−	0.0345787i	$-0.988991\pi$
$89$	−40.6753	+	230.681i	−0.0484447	+	0.274743i	0.950957	+	0.309322i	$0.100102\pi$
$90$		0			0
$91$	352.478	−	420.067i	0.406041	−	0.483901i
$92$	65.3076	−	11.5155i	0.0740086	−	0.0130497i
$93$		0			0
$94$		−	437.777i		−	0.480354i
$95$	601.765	+	1276.58i	0.649892	+	1.37868i
$96$		0			0
$97$	447.484	−	1229.45i	0.468404	−	1.28693i	−0.450617	−	0.892718i	$-0.648796\pi$
$97$	447.484	−	1229.45i	0.468404	−	1.28693i	0.919020	−	0.394211i	$-0.128982\pi$
$98$	−298.524	−	1693.01i	−0.307709	−	1.74511i
$99$		0			0
$100$	254.129	−	213.240i	0.254129	−	0.213240i
$101$	−576.547	−	101.661i	−0.568006	−	0.100155i	−0.117732	−	0.993045i	$-0.537562\pi$
$101$	−576.547	−	101.661i	−0.568006	−	0.100155i	−0.450274	+	0.892891i	$0.648674\pi$
$102$		0			0
$103$	346.380	−	199.983i	0.331358	−	0.191309i	−0.325086	−	0.945684i	$-0.605393\pi$
$103$	346.380	−	199.983i	0.331358	−	0.191309i	0.656444	+	0.754375i	$0.272060\pi$
$104$	142.115	+	390.457i	0.133995	+	0.368149i
$105$		0			0
$106$	−313.998	−	543.861i	−0.287719	−	0.498343i
$107$	−733.666	+	1270.75i	−0.662862	+	1.14811i	0.316999	+	0.948426i	$0.397325\pi$
$107$	−733.666	+	1270.75i	−0.662862	+	1.14811i	−0.979860	+	0.199684i	$0.936008\pi$
$108$		0			0
$109$	619.156	+	737.882i	0.544077	+	0.648406i	0.966097	−	0.258181i	$-0.0831230\pi$
$109$	619.156	+	737.882i	0.544077	+	0.648406i	−0.422019	+	0.906587i	$0.638679\pi$
$110$	83.4048	+	69.9849i	0.0722939	+	0.0606618i
$111$		0			0
$112$	1334.57	+	485.745i	1.12594	+	0.409809i
$113$	432.290			0.359880			0.179940	−	0.983678i	$-0.442410\pi$
$113$	432.290			0.359880			0.179940	+	0.983678i	$0.442410\pi$
$114$		0			0
$115$	−563.394			−0.456841
$116$	−170.129	−	61.9219i	−0.136173	−	0.0495630i
$117$		0			0
$118$	599.577	+	503.105i	0.467759	+	0.392496i
$119$	−2359.90	−	2812.41i	−1.81791	−	2.16650i
$120$		0			0
$121$	−662.095	+	1146.78i	−0.497442	+	0.861594i
$122$	−190.774	−	330.430i	−0.141573	−	0.245211i
$123$		0			0
$124$	−110.818	−	304.469i	−0.0802558	−	0.220501i
$125$	−596.071	+	344.142i	−0.426514	+	0.246248i
$126$		0			0
$127$	−748.419	−	131.966i	−0.522925	−	0.0922057i	−0.0940460	−	0.995568i	$-0.529980\pi$
$127$	−748.419	−	131.966i	−0.522925	−	0.0922057i	−0.428879	+	0.903362i	$0.641091\pi$
$128$	−523.264	+	439.071i	−0.361332	+	0.303193i
$129$		0			0
$130$	−122.884	−	696.912i	−0.0829051	−	0.470178i
$131$	502.382	−	1380.28i	0.335063	−	0.920579i	−0.651709	−	0.758469i	$-0.725948\pi$
$131$	502.382	−	1380.28i	0.335063	−	0.920579i	0.986773	−	0.162110i	$-0.0518300\pi$
$132$		0			0
$133$	−1885.36	+	1901.12i	−1.22918	+	1.23946i
$134$			2630.87i			1.69606i
$135$		0			0
$136$	2739.68	−	483.080i	1.72740	−	0.304586i
$137$	−1678.77	+	2000.68i	−1.04691	+	1.24766i	−0.0788689	+	0.996885i	$0.525131\pi$
$137$	−1678.77	+	2000.68i	−1.04691	+	1.24766i	−0.968045	+	0.250778i	$0.919314\pi$
$138$		0			0
$139$	−73.4203	+	416.387i	−0.0448017	+	0.254083i	−0.998980	−	0.0451558i	$-0.985622\pi$
$139$	−73.4203	+	416.387i	−0.0448017	+	0.254083i	0.954178	+	0.299239i	$0.0967327\pi$
$140$	956.989	+	552.518i	0.577717	+	0.333545i
$141$		0			0
$142$	1995.78	−	726.406i	1.17945	−	0.429286i
$143$	−41.5946	+	15.1392i	−0.0243239	+	0.00885317i
$144$		0			0
$145$	1332.06	+	769.064i	0.762906	+	0.440464i
$146$	−90.3798	+	512.569i	−0.0512321	+	0.290552i
$147$		0			0
$148$	254.047	−	302.762i	0.141098	−	0.168155i
$149$	500.175	−	88.1944i	0.275006	−	0.0484910i	−0.0344441	−	0.999407i	$-0.510966\pi$
$149$	500.175	−	88.1944i	0.275006	−	0.0484910i	0.309450	+	0.950916i	$0.399855\pi$
$150$		0			0
$151$			168.171i			0.0906326i	0.998973	+	0.0453163i	$0.0144296\pi$
$151$			168.171i			0.0906326i	−0.998973	+	0.0453163i	$0.985570\pi$
$152$	−533.258	−	1957.51i	−0.284559	−	1.04457i
$153$		0			0
$154$	−70.6467	+	194.100i	−0.0369667	+	0.101565i
$155$	477.999	+	2710.87i	0.247702	+	1.40479i
$156$		0			0
$157$	481.482	−	404.011i	0.244754	−	0.205373i	−0.512155	−	0.858893i	$-0.671153\pi$
$157$	481.482	−	404.011i	0.244754	−	0.205373i	0.756910	+	0.653520i	$0.226708\pi$
$158$	1466.83	+	258.642i	0.738575	+	0.130231i
$159$		0			0
$160$	−1304.94	+	753.408i	−0.644779	+	0.372263i
$161$	−365.567	−	1004.39i	−0.178949	−	0.491657i
$162$		0			0
$163$	1821.90	+	3155.62i	0.875473	+	1.51636i	0.856258	+	0.516548i	$0.172783\pi$
$163$	1821.90	+	3155.62i	0.875473	+	1.51636i	0.0192146	+	0.999815i	$0.493883\pi$
$164$	−438.722	+	759.888i	−0.208893	+	0.361813i
$165$		0			0
$166$	−467.081	−	556.646i	−0.218389	−	0.260266i
$167$	566.487	+	475.339i	0.262491	+	0.220256i	0.764529	−	0.644589i	$-0.222972\pi$
$167$	566.487	+	475.339i	0.262491	+	0.220256i	−0.502038	+	0.864846i	$0.667416\pi$
$168$		0			0
$169$	−1794.15	−	653.019i	−0.816638	−	0.297232i
$170$	−4737.91			−2.13754
$171$		0			0
$172$	−1033.48			−0.458154
$173$	−1983.64	−	721.987i	−0.871755	−	0.317293i	−0.132877	−	0.991132i	$-0.542422\pi$
$173$	−1983.64	−	721.987i	−0.871755	−	0.317293i	−0.738878	+	0.673840i	$0.764644\pi$
$174$		0			0
$175$	−4095.98	−	3436.94i	−1.76930	−	1.48462i
$176$	−73.6905	−	87.8209i	−0.0315604	−	0.0376122i
$177$		0			0
$178$	−286.745	+	496.657i	−0.120744	+	0.209135i
$179$	−536.327	−	928.945i	−0.223949	−	0.387892i	0.732054	−	0.681246i	$-0.238562\pi$
$179$	−536.327	−	928.945i	−0.223949	−	0.387892i	−0.956004	+	0.293355i	$0.905228\pi$
$180$		0			0
$181$	1139.78	+	3131.51i	0.468061	+	1.28599i	0.919291	+	0.393578i	$0.128763\pi$
$181$	1139.78	+	3131.51i	0.468061	+	1.28599i	−0.451231	+	0.892407i	$0.649015\pi$
$182$	1162.68	−	671.273i	0.473536	−	0.273396i
$183$		0			0
$184$	797.609	+	140.640i	0.319568	+	0.0563485i
$185$	−2572.18	+	2158.31i	−1.02222	+	0.857743i
$186$		0			0
$187$	51.4615	+	291.853i	0.0201243	+	0.114130i
$188$	−122.668	+	337.027i	−0.0475877	+	0.130746i
$189$		0			0
$190$	315.479	+	3440.87i	0.120459	+	1.31383i
$191$		−	192.870i		−	0.0730660i	−0.999332	−	0.0365330i	$-0.988369\pi$
$191$		−	192.870i		−	0.0730660i	0.999332	−	0.0365330i	$-0.0116314\pi$
$192$		0			0
$193$	−400.593	+	70.6354i	−0.149406	+	0.0263443i	−0.247851	−	0.968798i	$-0.579724\pi$
$193$	−400.593	+	70.6354i	−0.149406	+	0.0263443i	0.0984449	+	0.995143i	$0.468613\pi$
$194$	2059.01	−	2453.83i	0.762002	−	0.908118i
$195$		0			0
$196$	−244.571	+	1387.03i	−0.0891295	+	0.505479i
$197$	2815.06	+	1625.28i	1.01810	+	0.587798i	0.913552	−	0.406722i	$-0.133328\pi$
$197$	2815.06	+	1625.28i	1.01810	+	0.587798i	0.104544	+	0.994520i	$0.466662\pi$
$198$		0			0
$199$	1928.78	−	702.019i	0.687074	−	0.250074i	0.0251920	−	0.999683i	$-0.491980\pi$
$199$	1928.78	−	702.019i	0.687074	−	0.250074i	0.661882	+	0.749608i	$0.269758\pi$
$200$	3807.27	−	1385.73i	1.34607	−	0.489930i
$201$		0			0
$202$	−1241.31	−	716.668i	−0.432366	−	0.249627i
$203$	−506.717	+	2873.74i	−0.175195	+	0.993581i
$204$		0			0
$205$	4791.66	−	5710.48i	1.63251	−	1.94555i
$206$	964.359	−	170.043i	0.326165	−	0.0575118i
$207$		0			0
$208$			745.132i			0.248392i
$209$	208.529	−	56.8068i	0.0690156	−	0.0188010i
$210$		0			0
$211$	−300.913	+	826.752i	−0.0981787	+	0.269744i	−0.979053	−	0.203607i	$-0.934734\pi$
$211$	−300.913	+	826.752i	−0.0981787	+	0.269744i	0.880874	+	0.473351i	$0.156956\pi$
$212$	89.3415	+	506.681i	0.0289434	+	0.164146i
$213$		0			0
$214$	−2751.99	+	2309.20i	−0.879077	+	0.737633i
$215$	8646.79	+	1524.66i	2.74282	+	0.483633i
$216$		0			0
$217$	−4522.63	+	2611.14i	−1.41482	+	0.816847i
$218$	806.584	+	2216.07i	0.250591	+	0.688492i
$219$		0			0
$220$	−44.5998	−	77.2492i	−0.0136678	−	0.0236734i
$221$	963.100	−	1668.14i	0.293145	−	0.507743i
$222$		0			0
$223$	−2886.49	−	3439.99i	−0.866788	−	1.03300i	−0.999126	−	0.0417931i	$-0.986693\pi$
$223$	−2886.49	−	3439.99i	−0.866788	−	1.03300i	0.132338	−	0.991205i	$-0.457751\pi$
$224$	−2189.86	−	1837.51i	−0.653199	−	0.548099i
$225$		0			0
$226$	994.548	+	361.986i	0.292727	+	0.106544i
$227$	−2040.31			−0.596564			−0.298282	−	0.954478i	$-0.596414\pi$
$227$	−2040.31			−0.596564			−0.298282	+	0.954478i	$0.596414\pi$
$228$		0			0
$229$	6298.92			1.81766			0.908831	−	0.417165i	$-0.136976\pi$
$229$	6298.92			1.81766			0.908831	+	0.417165i	$0.136976\pi$
$230$	−1296.17	−	471.768i	−0.371596	−	0.135250i
$231$		0			0
$232$	−1693.84	−	1421.30i	−0.479337	−	0.402212i
$233$	−2507.59	−	2988.43i	−0.705055	−	0.840252i	0.288033	−	0.957620i	$-0.406999\pi$
$233$	−2507.59	−	2988.43i	−0.705055	−	0.840252i	−0.993088	+	0.117369i	$0.962554\pi$
$234$		0			0
$235$	1523.52	−	2638.82i	0.422909	−	0.732501i
$236$	−320.618	−	555.326i	−0.0884340	−	0.153172i
$237$		0			0
$238$	−3074.27	−	8446.49i	−0.837291	−	2.30044i
$239$	3786.59	−	2186.19i	1.02483	−	0.591686i	0.109330	−	0.994005i	$-0.465129\pi$
$239$	3786.59	−	2186.19i	1.02483	−	0.591686i	0.915499	+	0.402320i	$0.131796\pi$
$240$		0			0
$241$	4029.56	+	710.520i	1.07704	+	0.189911i	0.683906	−	0.729570i	$-0.260280\pi$
$241$	4029.56	+	710.520i	1.07704	+	0.189911i	0.393134	+	0.919481i	$0.371391\pi$
$242$	−2483.53	+	2083.93i	−0.659699	+	0.553554i
$243$		0			0
$244$	54.2807	+	307.841i	0.0142417	+	0.0807685i
$245$	4092.48	−	11244.0i	1.06718	−	2.93205i
$246$		0			0
$247$	−1275.60	−	588.369i	−0.328602	−	0.151567i
$248$		−	3957.16i		−	1.01323i
$249$		0			0
$250$	−1659.52	+	292.619i	−0.419830	+	0.0740274i
$251$	−2037.95	+	2428.73i	−0.512487	+	0.610758i	−0.958787	−	0.284125i	$-0.908297\pi$
$251$	−2037.95	+	2428.73i	−0.512487	+	0.610758i	0.446300	+	0.894883i	$0.352741\pi$
$252$		0			0
$253$	−14.9821	+	84.9676i	−0.00372299	+	0.0211141i
$254$	−1611.35	−	930.311i	−0.398051	−	0.229815i
$255$		0			0
$256$	2697.92	−	981.963i	0.658672	−	0.239737i
$257$	−6424.96	+	2338.49i	−1.55945	+	0.567593i	−0.970610	−	0.240659i	$-0.922637\pi$
$257$	−6424.96	+	2338.49i	−1.55945	+	0.567593i	−0.588838	+	0.808251i	$0.700414\pi$
$258$		0			0
$259$	−5516.72	−	3185.08i	−1.32352	−	0.764136i
$260$	−100.675	+	570.958i	−0.0240139	+	0.136190i
$261$		0			0
$262$	2311.61	−	2754.87i	0.545083	−	0.649605i
$263$	2411.70	−	425.248i	0.565445	−	0.0997032i	0.116384	−	0.993204i	$-0.462870\pi$
$263$	2411.70	−	425.248i	0.565445	−	0.0997032i	0.449061	+	0.893501i	$0.351759\pi$
$264$		0			0
$265$		−	4371.02i		−	1.01324i
$266$	−5929.49	+	2795.08i	−1.36677	+	0.644277i
$267$		0			0
$268$	737.186	−	2025.40i	0.168025	−	0.461646i
$269$	−914.845	−	5188.35i	−0.207357	−	1.17598i	−0.893687	−	0.448691i	$-0.851890\pi$
$269$	−914.845	−	5188.35i	−0.207357	−	1.17598i	0.686330	−	0.727290i	$-0.259221\pi$
$270$		0			0
$271$	1602.35	−	1344.53i	0.359172	−	0.301381i	−0.445289	−	0.895387i	$-0.646899\pi$
$271$	1602.35	−	1344.53i	0.359172	−	0.301381i	0.804461	+	0.594006i	$0.202454\pi$
$272$	4912.99	+	866.292i	1.09520	+	0.193113i
$273$		0			0
$274$	−5537.58	+	3197.12i	−1.22094	+	0.704909i
$275$	147.619	+	405.580i	0.0323700	+	0.0889360i
$276$		0			0
$277$	−2549.88	−	4416.52i	−0.553095	−	0.957989i	−0.998049	−	0.0624355i	$-0.980113\pi$
$277$	−2549.88	−	4416.52i	−0.553095	−	0.957989i	0.444954	−	0.895554i	$-0.353220\pi$
$278$	−517.584	+	896.482i	−0.111664	+	0.193408i
$279$		0			0
$280$	8675.01	+	10338.5i	1.85154	+	2.20658i
$281$	4828.42	+	4051.53i	1.02505	+	0.860121i	0.990254	−	0.139274i	$-0.0444768\pi$
$281$	4828.42	+	4051.53i	1.02505	+	0.860121i	0.0347978	+	0.999394i	$0.488921\pi$
$282$		0			0
$283$	−817.471	−	297.535i	−0.171709	−	0.0624970i	0.254735	−	0.967011i	$-0.418012\pi$
$283$	−817.471	−	297.535i	−0.171709	−	0.0624970i	−0.426444	+	0.904514i	$0.640234\pi$
$284$	−1740.02			−0.363560
$285$		0			0
$286$	−108.372			−0.0224061
$287$	13289.5	+	4836.97i	2.73329	+	0.994835i
$288$		0			0
$289$	−6115.50	−	5131.51i	−1.24476	−	1.04448i
$290$	2420.61	+	2884.77i	0.490149	+	0.584137i
$291$		0			0
$292$	213.205	−	369.282i	0.0427290	−	0.0740089i
$293$	−1570.46	−	2720.11i	−0.313130	−	0.542357i	0.665908	−	0.746034i	$-0.268044\pi$
$293$	−1570.46	−	2720.11i	−0.313130	−	0.542357i	−0.979038	+	0.203677i	$0.934711\pi$
$294$		0			0
$295$	1863.24	+	5119.21i	0.367736	+	1.01035i
$296$	4180.27	−	2413.48i	0.820855	−	0.473921i
$297$		0			0
$298$	1224.58	+	215.926i	0.238047	+	0.0419741i
$299$	429.581	−	360.462i	0.0830881	−	0.0697192i
$300$		0			0
$301$	2892.52	+	16404.3i	0.553895	+	3.14129i
$302$	−140.821	+	386.902i	−0.0268322	+	0.0737209i
$303$		0			0
$304$	302.001	−	3625.70i	0.0569768	−	0.684040i
$305$		−	2655.67i		−	0.498569i
$306$		0			0
$307$	6872.64	−	1211.83i	1.27766	−	0.225286i	0.506675	−	0.862137i	$-0.330875\pi$
$307$	6872.64	−	1211.83i	1.27766	−	0.225286i	0.770987	+	0.636851i	$0.219763\pi$
$308$	108.776	−	129.634i	0.0201237	−	0.0239825i
$309$		0			0
$310$	−1170.29	+	6637.02i	−0.214412	+	1.21599i
$311$	−2030.32	−	1172.20i	−0.370189	−	0.213728i	0.303352	−	0.952878i	$-0.401894\pi$
$311$	−2030.32	−	1172.20i	−0.370189	−	0.213728i	−0.673541	+	0.739150i	$0.735227\pi$
$312$		0			0
$313$	−7889.33	+	2871.48i	−1.42470	+	0.518548i	−0.935408	−	0.353571i	$-0.884967\pi$
$313$	−7889.33	+	2871.48i	−1.42470	+	0.518548i	−0.489292	+	0.872120i	$0.662745\pi$
$314$	1446.03	−	526.311i	0.259886	−	0.0945906i
$315$		0			0
$316$	−1056.78	−	610.134i	−0.188129	−	0.108616i
$317$	1032.78	−	5857.18i	0.182986	−	1.03777i	−0.745529	−	0.666473i	$-0.767803\pi$
$317$	1032.78	−	5857.18i	0.182986	−	1.03777i	0.928515	−	0.371294i	$-0.121086\pi$
$318$		0			0
$319$	151.408	−	180.441i	0.0265744	−	0.0316702i
$320$	−9530.96	+	1680.57i	−1.66499	+	0.293583i
$321$		0			0
$322$		−	2616.86i		−	0.452894i
$323$	−5362.40	+	7726.57i	−0.923751	+	1.33101i
$324$		0			0
$325$	959.471	−	2636.12i	0.163760	−	0.449926i
$326$	1549.14	+	8785.58i	0.263186	+	1.49260i
$327$		0			0
$328$	−8209.17	+	6888.31i	−1.38194	+	1.15958i
$329$	5692.90	+	1003.81i	0.953981	+	0.168213i
$330$		0			0
$331$	−2300.18	+	1328.01i	−0.381961	+	0.220525i	−0.678671	−	0.734442i	$-0.737444\pi$
$331$	−2300.18	+	1328.01i	−0.381961	+	0.220525i	0.296710	+	0.954968i	$0.404110\pi$
$332$	203.612	+	559.419i	0.0336586	+	0.0924762i
$333$		0			0
$334$	905.255	+	1567.95i	0.148303	+	0.256869i
$335$	−9155.78	+	15858.3i	−1.49323	+	2.58636i
$336$		0			0
$337$	−6279.14	−	7483.19i	−1.01498	−	1.20960i	−0.977637	−	0.210298i	$-0.932557\pi$
$337$	−6279.14	−	7483.19i	−1.01498	−	1.20960i	−0.0373380	−	0.999303i	$-0.511888\pi$
$338$	−3580.91	−	3004.74i	−0.576259	−	0.483539i
$339$		0			0
$340$	3647.53	+	1327.59i	0.581810	+	0.211761i
$341$	421.548			0.0669446
$342$		0			0
$343$	11611.8			1.82792
$344$	−11860.9	−	4317.00i	−1.85899	−	0.676619i
$345$		0			0
$346$	−3959.10	−	3322.08i	−0.615152	−	0.516174i
$347$	−936.152	−	1115.66i	−0.144828	−	0.172599i	0.688754	−	0.724995i	$-0.258158\pi$
$347$	−936.152	−	1115.66i	−0.144828	−	0.172599i	−0.833582	+	0.552396i	$0.813714\pi$
$348$		0			0
$349$	−3585.66	+	6210.54i	−0.549959	+	0.952557i	0.448317	+	0.893874i	$0.352023\pi$
$349$	−3585.66	+	6210.54i	−0.549959	+	0.952557i	−0.998277	+	0.0586830i	$0.981310\pi$
$350$	−6545.44	−	11337.0i	−0.999624	−	1.73140i
$351$		0			0
$352$	78.9227	+	216.838i	0.0119505	+	0.0328339i
$353$	3806.11	−	2197.46i	0.573878	−	0.331329i	−0.184819	−	0.982773i	$-0.559170\pi$
$353$	3806.11	−	2197.46i	0.573878	−	0.331329i	0.758697	+	0.651444i	$0.225836\pi$
$354$		0			0
$355$	14558.1	+	2566.99i	2.17652	+	0.383779i
$356$	359.920	−	302.009i	0.0535835	−	0.0449619i
$357$		0			0
$358$	−456.031	−	2586.28i	−0.0673240	−	0.381814i
$359$	−1689.39	+	4641.56i	−0.248363	+	0.682373i	0.751383	+	0.659866i	$0.229387\pi$
$359$	−1689.39	+	4641.56i	−0.248363	+	0.682373i	−0.999747	+	0.0225069i	$0.992835\pi$
$360$		0			0
$361$	5968.42	+	3379.92i	0.870159	+	0.492771i
$362$			8158.93i			1.18460i
$363$		0			0
$364$	−1083.20	+	190.997i	−0.155975	+	0.0275026i
$365$	−2328.60	+	2775.12i	−0.333930	+	0.397962i
$366$		0			0
$367$	1214.96	−	6890.38i	0.172808	−	0.980041i	−0.767836	−	0.640646i	$-0.778667\pi$
$367$	1214.96	−	6890.38i	0.172808	−	0.980041i	0.940644	−	0.339395i	$-0.110222\pi$
$368$	1257.81	+	726.196i	0.178173	+	0.102868i
$369$		0			0
$370$	−7724.99	+	2811.67i	−1.08541	+	0.395058i
$371$	7792.41	−	2836.21i	1.09046	−	0.396896i
$372$		0			0
$373$	4373.56	+	2525.08i	0.607116	+	0.350519i	0.771836	−	0.635822i	$-0.219339\pi$
$373$	4373.56	+	2525.08i	0.607116	+	0.350519i	−0.164720	+	0.986340i	$0.552672\pi$
$374$	−125.993	+	714.543i	−0.0174197	+	0.0987919i
$375$		0			0
$376$	−2815.61	+	3355.52i	−0.386181	+	0.460233i
$377$	−1507.73	+	265.853i	−0.205973	+	0.0363187i
$378$		0			0
$379$		−	3835.52i		−	0.519835i	−0.965631	−	0.259917i	$-0.916305\pi$
$379$		−	3835.52i		−	0.519835i	0.965631	−	0.259917i	$-0.0836954\pi$
$380$	721.279	−	2737.39i	0.0973706	−	0.369540i
$381$		0			0
$382$	161.504	−	443.728i	0.0216315	−	0.0594322i
$383$	−1414.56	−	8022.38i	−0.188723	−	1.07030i	−0.921078	−	0.389377i	$-0.872690\pi$
$383$	−1414.56	−	8022.38i	−0.188723	−	1.07030i	0.732356	−	0.680922i	$-0.238421\pi$
$384$		0			0
$385$	−1101.34	+	924.131i	−0.145790	+	0.122333i
$386$	−980.774	−	172.937i	−0.129327	−	0.0228038i
$387$		0			0
$388$	−2272.73	+	1312.16i	−0.297372	+	0.171688i
$389$	−2353.66	−	6466.62i	−0.306774	−	0.842855i	−0.993281	−	0.115731i	$-0.963079\pi$
$389$	−2353.66	−	6466.62i	−0.306774	−	0.842855i	0.686506	−	0.727124i	$-0.259143\pi$
$390$		0			0
$391$	−1877.25	−	3251.49i	−0.242805	−	0.420550i
$392$	−8600.66	+	14896.8i	−1.10816	+	1.91939i
$393$		0			0
$394$	5115.52	+	6096.44i	0.654102	+	0.779529i
$395$	7941.61	+	6663.80i	1.01161	+	0.848841i
$396$		0			0
$397$	−121.007	−	44.0431i	−0.0152977	−	0.00556791i	0.334360	−	0.942445i	$-0.391480\pi$
$397$	−121.007	−	44.0431i	−0.0152977	−	0.00556791i	−0.349658	+	0.936878i	$0.613702\pi$
$398$	5025.30			0.632904
$399$		0			0
$400$	7265.62			0.908202
$401$	−2279.37	−	829.624i	−0.283857	−	0.103315i	0.196168	−	0.980570i	$-0.437150\pi$
$401$	−2279.37	−	829.624i	−0.283857	−	0.103315i	−0.480025	+	0.877255i	$0.659372\pi$
$402$		0			0
$403$	−2098.89	−	1761.18i	−0.259437	−	0.217694i
$404$	754.818	+	899.557i	0.0929544	+	0.110779i
$405$		0			0
$406$	−3572.16	+	6187.16i	−0.436658	+	0.756314i
$407$	257.103	+	445.315i	0.0313123	+	0.0542345i
$408$		0			0
$409$	−3272.99	−	8992.46i	−0.395694	−	1.08716i	−0.964360	−	0.264592i	$-0.914763\pi$
$409$	−3272.99	−	8992.46i	−0.395694	−	1.08716i	0.568666	−	0.822568i	$-0.307460\pi$
$410$	15805.7	−	9125.44i	1.90388	−	1.09920i
$411$		0			0
$412$	−790.069	−	139.310i	−0.0944755	−	0.0166586i
$413$	−7917.25	+	6643.36i	−0.943298	+	0.791521i
$414$		0			0
$415$	−878.256	−	4980.84i	−0.103884	−	0.589156i
$416$	512.969	−	1409.37i	0.0604576	−	0.166106i
$417$		0			0
$418$	527.321	+	43.9229i	0.0617036	+	0.00513957i
$419$			2423.96i			0.282621i	0.989965	+	0.141310i	$0.0451315\pi$
$419$			2423.96i			0.282621i	−0.989965	+	0.141310i	$0.954868\pi$
$420$		0			0
$421$	7855.37	−	1385.11i	0.909376	−	0.160348i	0.300656	−	0.953733i	$-0.402794\pi$
$421$	7855.37	−	1385.11i	0.909376	−	0.160348i	0.608720	+	0.793385i	$0.291683\pi$
$422$	−1384.59	+	1650.09i	−0.159718	+	0.190344i
$423$		0			0
$424$	−1091.14	+	6188.15i	−0.124977	+	0.708781i
$425$	−16265.7	−	9390.98i	−1.85647	−	1.07183i
$426$		0			0
$427$	4734.39	−	1723.18i	0.536564	−	0.195293i
$428$	2765.70	−	1006.63i	0.312349	−	0.113686i
$429$		0			0
$430$	18616.5	+	10748.3i	2.08784	+	1.20541i
$431$	849.727	−	4819.04i	0.0949650	−	0.538573i	−0.899793	−	0.436317i	$-0.856283\pi$
$431$	849.727	−	4819.04i	0.0949650	−	0.538573i	0.994758	−	0.102257i	$-0.0326063\pi$
$432$		0			0
$433$	−6248.92	+	7447.17i	−0.693542	+	0.826531i	−0.991779	−	0.127960i	$-0.959157\pi$
$433$	−6248.92	+	7447.17i	−0.693542	+	0.826531i	0.298237	+	0.954492i	$0.403601\pi$
$434$	−12591.5	+	2220.22i	−1.39265	+	0.245562i
$435$		0			0
$436$		−	1932.08i		−	0.212224i
$437$	−2236.37	+	1579.84i	−0.244806	+	0.172939i
$438$		0			0
$439$	2819.73	−	7747.15i	0.306557	−	0.842258i	−0.686765	−	0.726880i	$-0.740970\pi$
$439$	2819.73	−	7747.15i	0.306557	−	0.842258i	0.993322	−	0.115379i	$-0.0368081\pi$
$440$	−189.173	−	1072.85i	−0.0204965	−	0.116242i
$441$		0			0
$442$	3612.60	−	3031.34i	0.388765	−	0.326213i
$443$	6967.14	+	1228.49i	0.747220	+	0.131755i	0.534277	−	0.845309i	$-0.320584\pi$
$443$	6967.14	+	1228.49i	0.747220	+	0.131755i	0.212943	+	0.977065i	$0.431695\pi$
$444$		0			0
$445$	−3456.87	+	1995.82i	−0.368250	+	0.212609i
$446$	−3760.27	−	10331.3i	−0.399224	−	1.09686i
$447$		0			0
$448$	−9180.33	−	15900.8i	−0.968147	−	1.67688i
$449$	−1736.16	+	3007.12i	−0.182482	+	0.316069i	−0.942725	−	0.333570i	$-0.891747\pi$
$449$	−1736.16	+	3007.12i	−0.182482	+	0.316069i	0.760243	+	0.649639i	$0.225080\pi$
$450$		0			0
$451$	−733.798	−	874.506i	−0.0766146	−	0.0913057i
$452$	−664.233	−	557.357i	−0.0691214	−	0.0579997i
$453$		0			0
$454$	−4694.04	−	1708.49i	−0.485247	−	0.176616i
$455$	9344.49			0.962805
$456$		0			0
$457$	−1998.52			−0.204566			−0.102283	−	0.994755i	$-0.532615\pi$
$457$	−1998.52			−0.204566			−0.102283	+	0.994755i	$0.532615\pi$
$458$	14491.6	+	5274.52i	1.47849	+	0.538127i
$459$		0			0
$460$	865.680	+	726.392i	0.0877447	+	0.0736265i
$461$	−10807.1	−	12879.4i	−1.09184	−	1.30120i	−0.950323	−	0.311265i	$-0.899247\pi$
$461$	−10807.1	−	12879.4i	−1.09184	−	1.30120i	−0.141514	−	0.989936i	$-0.545197\pi$
$462$		0			0
$463$	1588.00	−	2750.49i	0.159396	−	0.276083i	−0.775255	−	0.631649i	$-0.782379\pi$
$463$	1588.00	−	2750.49i	0.159396	−	0.276083i	0.934651	+	0.355566i	$0.115712\pi$
$464$	−1982.60	−	3433.96i	−0.198362	−	0.343572i
$465$		0			0
$466$	−3266.68	−	8975.12i	−0.324734	−	0.892198i
$467$	−4214.42	+	2433.20i	−0.417602	+	0.241102i	−0.694051	−	0.719926i	$-0.744176\pi$
$467$	−4214.42	+	2433.20i	−0.417602	+	0.241102i	0.276449	+	0.961029i	$0.410842\pi$
$468$		0			0
$469$	−34212.1	−	6032.52i	−3.36838	−	0.593936i
$470$	5714.76	−	4795.25i	0.560856	−	0.470614i
$471$		0			0
$472$	−1359.92	−	7712.50i	−0.132618	−	0.752111i
$473$	459.881	−	1263.51i	0.0447047	−	0.122825i
$474$		0			0
$475$	−5737.06	+	12438.1i	−0.554178	+	1.20147i
$476$			7364.05i			0.709098i
$477$		0			0
$478$	10542.3	−	1858.89i	1.00877	−	0.177874i
$479$	6383.28	−	7607.30i	0.608893	−	0.725650i	−0.370225	−	0.928942i	$-0.620720\pi$
$479$	6383.28	−	7607.30i	0.608893	−	0.725650i	0.979118	+	0.203292i	$0.0651640\pi$
$480$		0			0
$481$	580.359	−	3291.38i	0.0550147	−	0.312004i
$482$	8675.64	+	5008.88i	0.819843	+	0.473337i
$483$		0			0
$484$	2495.90	−	908.434i	0.234401	−	0.0853150i
$485$	20950.9	−	7625.51i	1.96151	−	0.713931i
$486$		0			0
$487$	16637.4	+	9605.60i	1.54807	+	0.893781i	0.998289	+	0.0584752i	$0.0186239\pi$
$487$	16637.4	+	9605.60i	1.54807	+	0.893781i	0.549785	+	0.835306i	$0.314709\pi$
$488$	−662.936	+	3759.70i	−0.0614953	+	0.348757i
$489$		0			0
$490$	18830.8	−	22441.6i	1.73610	−	2.06900i
$491$	10979.8	−	1936.04i	1.00919	−	0.177947i	0.355472	−	0.934687i	$-0.384320\pi$
$491$	10979.8	−	1936.04i	1.00919	−	0.177947i	0.653716	+	0.756740i	$0.273209\pi$
$492$		0			0
$493$			10250.2i			0.936402i
$494$	−2442.03	−	2421.78i	−0.222413	−	0.220569i
$495$		0			0
$496$	2427.06	−	6668.29i	0.219714	−	0.603660i
$497$	4869.98	+	27619.0i	0.439534	+	2.49272i
$498$		0			0
$499$	−5839.90	+	4900.26i	−0.523908	+	0.439611i	−0.865992	−	0.500059i	$-0.833312\pi$
$499$	−5839.90	+	4900.26i	−0.523908	+	0.439611i	0.342084	+	0.939669i	$0.388867\pi$
$500$	1359.60	+	239.733i	0.121606	+	0.0214424i
$501$		0			0
$502$	−6722.35	+	3881.15i	−0.597676	+	0.345068i
$503$	−5034.21	−	13831.4i	−0.446251	−	1.22607i	−0.935315	−	0.353817i	$-0.884883\pi$
$503$	−5034.21	−	13831.4i	−0.446251	−	1.22607i	0.489063	−	0.872248i	$-0.337339\pi$
$504$		0			0
$505$	−4988.20	−	8639.82i	−0.439549	−	0.761321i
$506$	−105.618	+	182.935i	−0.00927922	+	0.0160721i
$507$		0			0
$508$	979.833	+	1167.72i	0.0855769	+	0.101987i
$509$	11873.6	+	9963.11i	1.03396	+	0.867597i	0.991317	−	0.131493i	$-0.0419771\pi$
$509$	11873.6	+	9963.11i	1.03396	+	0.867597i	0.0426450	+	0.999090i	$0.486422\pi$
$510$		0			0
$511$	−6458.27	−	2350.62i	−0.559094	−	0.203494i
$512$	12493.8			1.07843
$513$		0			0
$514$	−16739.8			−1.43650
$515$	6404.70	+	2331.12i	0.548010	+	0.199459i
$516$		0			0
$517$	−357.456	−	299.941i	−0.0304080	−	0.0255153i
$518$	−10025.0	−	11947.3i	−0.850331	−	1.01339i
$519$		0			0
$520$	−3540.37	+	6132.10i	−0.298568	+	0.517136i
$521$	−7461.16	−	12923.1i	−0.627408	−	1.08670i	−0.988070	−	0.154005i	$-0.950783\pi$
$521$	−7461.16	−	12923.1i	−0.627408	−	1.08670i	0.360663	−	0.932696i	$-0.382551\pi$
$522$		0			0
$523$	4857.34	+	13345.4i	0.406112	+	1.11578i	0.959216	+	0.282673i	$0.0912210\pi$
$523$	4857.34	+	13345.4i	0.406112	+	1.11578i	−0.553104	+	0.833112i	$0.686557\pi$
$524$	−2551.55	+	1473.14i	−0.212719	+	0.122814i
$525$		0			0
$526$	5904.58	+	1041.14i	0.489452	+	0.0863036i
$527$	−14052.4	+	11791.4i	−1.16154	+	0.974650i
$528$		0			0
$529$	1922.97	+	10905.7i	0.158048	+	0.896335i
$530$	3660.16	−	10056.2i	0.299976	−	0.824176i
$531$		0			0
$532$	5348.08	−	490.344i	0.435844	−	0.0399607i
$533$			7419.90i			0.602986i
$534$		0			0
$535$	−24624.7	+	4342.00i	−1.98994	+	0.350880i
$536$	16920.7	−	20165.3i	1.36355	−	1.62502i
$537$		0			0
$538$	2239.82	−	12702.6i	0.179490	−	1.01794i
$539$	−1586.92	−	916.210i	−0.126816	−	0.0732170i
$540$		0			0
$541$	−10891.7	+	3964.26i	−0.865567	+	0.315041i	−0.736371	−	0.676579i	$-0.763462\pi$
$541$	−10891.7	+	3964.26i	−0.865567	+	0.315041i	−0.129196	+	0.991619i	$0.541240\pi$
$542$	4812.31	−	1751.54i	0.381377	−	0.138810i
$543$		0			0
$544$	−8696.23	−	5020.77i	−0.685382	−	0.395705i
$545$	−2850.32	+	16165.0i	−0.224026	+	1.27052i
$546$		0			0
$547$	6787.60	−	8089.15i	0.530561	−	0.632298i	−0.432483	−	0.901642i	$-0.642362\pi$
$547$	6787.60	−	8089.15i	0.530561	−	0.632298i	0.963044	+	0.269344i	$0.0868068\pi$
$548$	5159.02	−	909.674i	0.402157	−	0.0709112i
$549$		0			0
$550$			1056.71i			0.0819241i
$551$	7444.13	−	682.522i	0.575555	−	0.0527703i
$552$		0			0
$553$	−6726.81	+	18481.8i	−0.517275	+	1.42120i
$554$	−2168.13	−	12296.1i	−0.166272	−	0.942978i
$555$		0			0
$556$	649.668	−	545.136i	0.0495540	−	0.0415808i
$557$	−7815.31	−	1378.05i	−0.594516	−	0.104829i	−0.131709	−	0.991288i	$-0.542046\pi$
$557$	−7815.31	−	1378.05i	−0.594516	−	0.104829i	−0.462807	+	0.886459i	$0.653158\pi$
$558$		0			0
$559$	−7568.56	+	4369.71i	−0.572659	+	0.330625i
$560$	8277.51	+	22742.3i	0.624622	+	1.71614i
$561$		0			0
$562$	7715.89	+	13364.3i	0.579138	+	1.00310i
$563$	−1775.92	+	3075.98i	−0.132941	+	0.230261i	−0.924809	−	0.380431i	$-0.875776\pi$
$563$	−1775.92	+	3075.98i	−0.132941	+	0.230261i	0.791868	+	0.610693i	$0.209109\pi$
$564$		0			0
$565$	4735.15	+	5643.13i	0.352582	+	0.420191i
$566$	−1631.57	−	1369.05i	−0.121166	−	0.101670i
$567$		0			0
$568$	−19969.5	−	7268.29i	−1.47518	−	0.536920i
$569$	−13506.7			−0.995134			−0.497567	−	0.867425i	$-0.665773\pi$
$569$	−13506.7			−0.995134			−0.497567	+	0.867425i	$0.665773\pi$
$570$		0			0
$571$	4998.36			0.366331			0.183166	−	0.983082i	$-0.441366\pi$
$571$	4998.36			0.366331			0.183166	+	0.983082i	$0.441366\pi$
$572$	83.4312	+	30.3665i	0.00609866	+	0.00221973i
$573$		0			0
$574$	26524.1	+	22256.4i	1.92874	+	1.61840i
$575$	−3514.78	−	4188.76i	−0.254916	−	0.303797i
$576$		0			0
$577$	2403.19	−	4162.45i	0.173390	−	0.300321i	−0.766213	−	0.642587i	$-0.777861\pi$
$577$	2403.19	−	4162.45i	0.173390	−	0.300321i	0.939603	+	0.342266i	$0.111194\pi$
$578$	−9772.67	−	16926.8i	−0.703269	−	1.21810i
$579$		0			0
$580$	−1055.20	−	2899.14i	−0.0755429	−	0.207552i
$581$	8309.69	−	4797.60i	0.593363	−	0.342578i
$582$		0			0
$583$	−659.211	−	116.237i	−0.0468297	−	0.00825734i
$584$	3989.40	−	3347.50i	0.282676	−	0.237193i
$585$		0			0
$586$	−1335.34	−	7573.08i	−0.0941336	−	0.533858i
$587$	2865.68	−	7873.39i	0.201498	−	0.553611i	−0.797249	−	0.603650i	$-0.793712\pi$
$587$	2865.68	−	7873.39i	0.201498	−	0.553611i	0.998747	+	0.0500391i	$0.0159346\pi$
$588$		0			0
$589$	9499.09	+	9420.32i	0.664522	+	0.659011i
$590$			13337.7i			0.930688i
$591$		0			0
$592$	8524.53	−	1503.10i	0.591817	−	0.104353i
$593$	6750.49	−	8044.92i	0.467470	−	0.557109i	−0.479870	−	0.877340i	$-0.659316\pi$
$593$	6750.49	−	8044.92i	0.467470	−	0.557109i	0.947339	+	0.320231i	$0.103761\pi$
$594$		0			0
$595$	10863.9	−	61612.4i	0.748533	−	4.24514i
$596$	−882.252	−	509.368i	−0.0606350	−	0.0350076i
$597$		0			0
$598$	1290.16	−	469.579i	0.0882248	−	0.0321112i
$599$	−11532.6	+	4197.52i	−0.786659	+	0.286320i	−0.703947	−	0.710253i	$-0.748581\pi$
$599$	−11532.6	+	4197.52i	−0.786659	+	0.286320i	−0.0827125	+	0.996573i	$0.526358\pi$
$600$		0			0
$601$	4123.91	+	2380.94i	0.279897	+	0.161598i	0.633377	−	0.773844i	$-0.281668\pi$
$601$	4123.91	+	2380.94i	0.279897	+	0.161598i	−0.353480	+	0.935442i	$0.615002\pi$
$602$	−7081.77	+	40162.7i	−0.479454	+	2.71912i
$603$		0			0
$604$	216.825	−	258.402i	0.0146067	−	0.0174076i
$605$	−22222.5	+	3918.42i	−1.49334	+	0.263317i
$606$		0			0
$607$			18072.8i			1.20849i	0.796799	+	0.604244i	$0.206525\pi$
$607$			18072.8i			1.20849i	−0.796799	+	0.604244i	$0.793475\pi$
$608$	−3067.25	+	6649.88i	−0.204594	+	0.443566i
$609$		0			0
$610$	2223.78	−	6109.78i	0.147604	−	0.405537i
$611$	526.658	+	2986.83i	0.0348712	+	0.197764i
$612$		0			0
$613$	20316.8	−	17047.8i	1.33864	−	1.12325i	0.356668	−	0.934231i	$-0.383913\pi$
$613$	20316.8	−	17047.8i	1.33864	−	1.12325i	0.981973	−	0.189021i	$-0.0605316\pi$
$614$	16826.3	+	2966.93i	1.10595	+	0.195009i
$615$		0			0
$616$	1789.88	−	1033.39i	0.117072	−	0.0675914i
$617$	4200.28	+	11540.2i	0.274063	+	0.752982i	0.998006	+	0.0631219i	$0.0201057\pi$
$617$	4200.28	+	11540.2i	0.274063	+	0.752982i	−0.723943	+	0.689860i	$0.757672\pi$
$618$		0			0
$619$	−6540.26	−	11328.1i	−0.424677	−	0.735563i	0.571713	−	0.820454i	$-0.306279\pi$
$619$	−6540.26	−	11328.1i	−0.424677	−	0.735563i	−0.996390	+	0.0848909i	$0.972946\pi$
$620$	2760.69	−	4781.66i	0.178826	−	0.309736i
$621$		0			0
$622$	−3689.48	−	4396.95i	−0.237837	−	0.283443i
$623$	−5801.08	−	4867.69i	−0.373059	−	0.313033i
$624$		0			0
$625$	8405.41	+	3059.32i	0.537946	+	0.195796i
$626$	−20555.1			−1.31237
$627$		0			0
$628$	−1260.72			−0.0801083
$629$	−21026.8	−	7653.13i	−1.33290	−	0.485135i
$630$		0			0
$631$	3647.90	+	3060.95i	0.230144	+	0.193113i	0.750566	−	0.660796i	$-0.229781\pi$
$631$	3647.90	+	3060.95i	0.230144	+	0.193113i	−0.520422	+	0.853909i	$0.674225\pi$
$632$	−9579.63	−	11416.6i	−0.602939	−	0.718554i
$633$		0			0
$634$	7280.68	−	12610.5i	0.456077	−	0.789949i
$635$	−6475.21	−	11215.4i	−0.404663	−	0.700897i
$636$		0			0
$637$	4073.49	+	11191.8i	0.253371	+	0.696131i
$638$	499.434	−	288.348i	0.0309918	−	0.0178931i
$639$		0			0
$640$	−11463.3	−	2021.29i	−0.708010	−	0.124841i
$641$	−40.8048	+	34.2393i	−0.00251434	+	0.00210978i	−0.644044	−	0.764989i	$-0.722745\pi$
$641$	−40.8048	+	34.2393i	−0.00251434	+	0.00210978i	0.641530	+	0.767098i	$0.278300\pi$
$642$		0			0
$643$	1647.83	+	9345.28i	0.101064	+	0.573160i	0.992720	+	0.120447i	$0.0384328\pi$
$643$	1647.83	+	9345.28i	0.101064	+	0.573160i	−0.891656	+	0.452713i	$0.850456\pi$
$644$	−733.261	+	2014.62i	−0.0448673	+	0.123272i
$645$		0			0
$646$	−18807.0	+	13285.8i	−1.14544	+	0.809171i
$647$			28173.2i			1.71190i	0.517056	+	0.855951i	$0.327028\pi$
$647$			28173.2i			1.71190i	−0.517056	+	0.855951i	$0.672972\pi$
$648$		0			0
$649$	821.596	−	144.870i	0.0496926	−	0.00876214i
$650$	4414.82	−	5261.37i	0.266405	−	0.317489i
$651$		0			0
$652$	1269.16	−	7197.75i	0.0762332	−	0.432340i
$653$	−1929.79	−	1114.16i	−0.115649	−	0.0667697i	0.441060	−	0.897478i	$-0.354603\pi$
$653$	−1929.79	−	1114.16i	−0.115649	−	0.0667697i	−0.556709	+	0.830708i	$0.687936\pi$
$654$		0			0
$655$	23521.2	−	8561.01i	1.40313	−	0.510697i
$656$	−18058.3	+	6572.68i	−1.07478	+	0.391189i
$657$		0			0
$658$	12256.8	+	7076.48i	0.726171	+	0.419255i
$659$	4062.38	−	23038.9i	0.240134	−	1.36187i	−0.591394	−	0.806382i	$-0.701422\pi$
$659$	4062.38	−	23038.9i	0.240134	−	1.36187i	0.831528	−	0.555483i	$-0.187467\pi$
$660$		0			0
$661$	−16275.1	+	19395.9i	−0.957680	+	1.14132i	0.0322105	+	0.999481i	$0.489745\pi$
$661$	−16275.1	+	19395.9i	−0.957680	+	1.14132i	−0.989890	+	0.141837i	$0.954699\pi$
$662$	−6403.93	+	1129.19i	−0.375976	+	0.0662947i
$663$		0			0
$664$			7270.72i			0.424938i
$665$	−45468.9	−	3787.31i	−2.65144	−	0.220850i
$666$		0			0
$667$	−1020.64	+	2804.20i	−0.0592496	+	0.162787i
$668$	−257.571	−	1460.76i	−0.0149188	−	0.0846085i
$669$		0			0
$670$	−34343.5	+	28817.6i	−1.98030	+	1.66167i
$671$	−400.513	−	70.6212i	−0.0230426	−	0.00406304i
$672$		0			0
$673$	16420.8	−	9480.55i	0.940527	−	0.543014i	0.0504017	−	0.998729i	$-0.483950\pi$
$673$	16420.8	−	9480.55i	0.940527	−	0.543014i	0.890126	+	0.455715i	$0.150617\pi$
$674$	−8179.93	−	22474.2i	−0.467476	−	1.28438i
$675$		0			0
$676$	1914.85	+	3316.62i	0.108947	+	0.188702i
$677$	13691.0	−	23713.6i	0.777237	−	1.34621i	−0.156292	−	0.987711i	$-0.549954\pi$
$677$	13691.0	−	23713.6i	0.777237	−	1.34621i	0.933529	−	0.358502i	$-0.116712\pi$
$678$		0			0
$679$	27188.7	+	32402.2i	1.53668	+	1.83134i
$680$	36315.6	+	30472.4i	2.04800	+	1.71848i
$681$		0			0
$682$	969.835	+	352.991i	0.0544529	+	0.0198192i
$683$	−20863.2			−1.16882			−0.584412	−	0.811457i	$-0.698675\pi$
$683$	−20863.2			−1.16882			−0.584412	+	0.811457i	$0.698675\pi$
$684$		0			0
$685$	−44505.7			−2.48244
$686$	26714.6	+	9723.32i	1.48683	+	0.541164i
$687$		0			0
$688$	−17339.2	−	14549.3i	−0.960830	−	0.806232i
$689$	2796.60	+	3332.85i	0.154633	+	0.184284i
$690$		0			0
$691$	−1711.52	+	2964.45i	−0.0942249	+	0.163202i	−0.909285	−	0.416174i	$-0.863371\pi$
$691$	−1711.52	+	2964.45i	−0.0942249	+	0.163202i	0.815060	+	0.579377i	$0.196704\pi$
$692$	2117.09	+	3666.90i	0.116300	+	0.201438i
$693$		0			0
$694$	−1219.54	−	3350.66i	−0.0667047	−	0.183270i
$695$	−6239.76	+	3602.52i	−0.340557	+	0.196621i
$696$		0			0
$697$	48922.7	+	8626.39i	2.65865	+	0.468792i
$698$	−13449.9	+	11285.8i	−0.729347	+	0.611995i
$699$		0			0
$700$	1862.37	+	10562.0i	0.100558	+	0.570295i
$701$	2400.09	−	6594.20i	0.129316	−	0.355292i	−0.858090	−	0.513499i	$-0.828349\pi$
$701$	2400.09	−	6594.20i	0.129316	−	0.355292i	0.987406	+	0.158207i	$0.0505713\pi$
$702$		0			0
$703$	−4157.93	+	15780.1i	−0.223072	+	0.846599i
$704$			1482.09i			0.0793444i
$705$		0			0
$706$	10596.6	−	1868.47i	0.564885	−	0.0996045i
$707$	12165.9	−	14498.8i	0.647166	−	0.771263i
$708$		0			0
$709$	439.853	−	2494.53i	0.0232991	−	0.132136i	−0.970940	−	0.239325i	$-0.923074\pi$
$709$	439.853	−	2494.53i	0.0232991	−	0.132136i	0.994239	+	0.107189i	$0.0341850\pi$
$710$	31343.6	+	18096.3i	1.65677	+	0.956536i
$711$		0			0
$712$	5392.18	−	1962.59i	0.283821	−	0.103302i
$713$	−5018.49	+	1826.58i	−0.263596	+	0.0959411i
$714$		0			0
$715$	−653.240	−	377.148i	−0.0341675	−	0.0197266i
$716$	−373.612	+	2118.86i	−0.0195008	+	0.110594i
$717$		0			0
$718$	−7773.39	+	9263.96i	−0.404039	+	0.481515i
$719$	−8839.76	+	1558.69i	−0.458508	+	0.0808474i	−0.398132	−	0.917328i	$-0.630341\pi$
$719$	−8839.76	+	1558.69i	−0.458508	+	0.0808474i	−0.0603767	+	0.998176i	$0.519230\pi$
$720$		0			0
$721$			12930.5i			0.667903i
$722$	10901.0	+	12773.8i	0.561903	+	0.658436i
$723$		0			0
$724$	2286.18	−	6281.24i	0.117355	−	0.322431i
$725$	2592.28	+	14701.5i	0.132793	+	0.753105i
$726$		0			0
$727$	10032.2	−	8418.06i	0.511796	−	0.429448i	−0.349965	−	0.936763i	$-0.613806\pi$
$727$	10032.2	−	8418.06i	0.511796	−	0.429448i	0.861761	+	0.507315i	$0.169362\pi$
$728$	−13229.2	−	2332.66i	−0.673498	−	0.118756i
$729$		0			0
$730$	−7681.09	+	4434.68i	−0.389438	+	0.224842i
$731$	20012.2	+	54983.1i	1.01256	+	2.78198i
$732$		0			0
$733$	−8807.48	−	15255.0i	−0.443808	−	0.768699i	0.554160	−	0.832410i	$-0.313040\pi$
$733$	−8807.48	−	15255.0i	−0.443808	−	0.768699i	−0.997968	+	0.0637114i	$0.979706\pi$
$734$	8564.99	−	14835.0i	0.430708	−	0.746008i
$735$		0			0
$736$	−1879.13	−	2239.47i	−0.0941112	−	0.112157i
$737$	2148.17	+	1802.53i	0.107366	+	0.0900910i
$738$		0			0
$739$	−26825.4	−	9763.64i	−1.33530	−	0.486010i	−0.426971	−	0.904265i	$-0.640420\pi$
$739$	−26825.4	−	9763.64i	−1.33530	−	0.486010i	−0.908330	+	0.418255i	$0.862642\pi$
$740$	6735.01			0.334573
$741$		0			0
$742$	20302.6			1.00449
$743$	8990.70	+	3272.35i	0.443926	+	0.161576i	0.554305	−	0.832314i	$-0.312984\pi$
$743$	8990.70	+	3272.35i	0.443926	+	0.161576i	−0.110379	+	0.993890i	$0.535206\pi$
$744$		0			0
$745$	6630.03	+	5563.26i	0.326048	+	0.273586i
$746$	7947.62	+	9471.60i	0.390058	+	0.464853i
$747$		0			0
$748$	297.217	−	514.795i	0.0145285	−	0.0251641i
$749$	−23718.8	−	41082.2i	−1.15710	−	2.00415i
$750$		0			0
$751$	−8575.14	−	23560.0i	−0.416660	−	1.14476i	−0.953583	−	0.301132i	$-0.902636\pi$
$751$	−8575.14	−	23560.0i	−0.416660	−	1.14476i	0.536923	−	0.843631i	$-0.319587\pi$
$752$	−6802.70	+	3927.54i	−0.329879	+	0.190456i
$753$		0			0
$754$	−3691.38	−	650.889i	−0.178292	−	0.0314376i
$755$	−2195.31	+	1842.08i	−0.105822	+	0.0887949i
$756$		0			0
$757$	−4134.93	−	23450.3i	−0.198529	−	1.12591i	−0.907303	−	0.420478i	$-0.861862\pi$
$757$	−4134.93	−	23450.3i	−0.198529	−	1.12591i	0.708774	−	0.705436i	$-0.249249\pi$
$758$	3211.74	−	8824.20i	0.153899	−	0.422835i
$759$		0			0
$760$	19712.3	−	28403.0i	0.940840	−	1.35564i
$761$		−	16594.8i		−	0.790488i	−0.918576	−	0.395244i	$-0.870660\pi$
$761$		−	16594.8i		−	0.790488i	0.918576	−	0.395244i	$-0.129340\pi$
$762$		0			0
$763$	−30667.5	+	5407.51i	−1.45510	+	0.256573i
$764$	−248.671	+	296.354i	−0.0117756	+	0.0140337i
$765$		0			0
$766$	3463.28	−	19641.2i	0.163359	−	0.926457i
$767$	−4695.99	−	2711.23i	−0.221072	−	0.127636i
$768$		0			0
$769$	−55.5825	+	20.2304i	−0.00260644	+	0.000948668i	−0.343323	−	0.939217i	$-0.611553\pi$
$769$	−55.5825	+	20.2304i	−0.00260644	+	0.000948668i	0.340717	+	0.940166i	$0.389330\pi$
$770$	−3307.63	+	1203.88i	−0.154803	+	0.0563439i
$771$		0			0
$772$	706.601	+	407.956i	0.0329419	+	0.0190190i
$773$	543.482	−	3082.24i	0.0252881	−	0.143416i	−0.969550	−	0.244895i	$-0.921246\pi$
$773$	543.482	−	3082.24i	0.0252881	−	0.143416i	0.994838	+	0.101479i	$0.0323576\pi$
$774$		0			0
$775$	−17172.9	+	20465.8i	−0.795959	+	0.948587i
$776$	−31564.2	+	5565.62i	−1.46017	+	0.257467i
$777$		0			0
$778$		−	16848.3i		−	0.776403i
$779$	3007.28	−	36104.1i	0.138314	−	1.66055i
$780$		0			0
$781$	774.275	−	2127.30i	0.0354747	−	0.0974660i
$782$	−1596.20	−	9052.51i	−0.0729924	−	0.413960i
$783$		0			0
$784$	−23629.9	+	19827.8i	−1.07643	+	0.903234i
$785$	10548.0	+	1859.89i	0.479583	+	0.0845634i
$786$		0			0
$787$	−27158.9	+	15680.2i	−1.23013	+	0.710215i	−0.967057	−	0.254561i	$-0.918069\pi$
$787$	−27158.9	+	15680.2i	−1.23013	+	0.710215i	−0.263072	+	0.964776i	$0.584736\pi$
$788$	−2229.98	−	6126.81i	−0.100812	−	0.276978i
$789$		0			0
$790$	12690.8	+	21981.1i	0.571543	+	0.989942i
$791$	−6987.78	+	12103.2i	−0.314105	+	0.544045i
$792$		0			0
$793$	1699.11	+	2024.92i	0.0760872	+	0.0906772i
$794$	−241.515	−	202.656i	−0.0107948	−	0.00905790i
$795$		0			0
$796$	−3868.78	−	1408.12i	−0.172268	−	0.0627004i
$797$	35869.3			1.59417			0.797087	−	0.603864i	$-0.206373\pi$
$797$	35869.3			1.59417			0.797087	+	0.603864i	$0.206373\pi$
$798$		0			0
$799$	20305.8			0.899082
$800$	−13742.5	−	5001.85i	−0.607337	−	0.221053i
$801$		0			0
$802$	−4549.34	−	3817.35i	−0.200303	−	0.168074i
$803$	356.603	+	424.982i	0.0156715	+	0.0186766i
$804$		0			0
$805$	9107.02	−	15773.8i	0.398733	−	0.690626i
$806$	−3354.06	−	5809.41i	−0.146578	−	0.253881i
$807$		0			0
$808$	4905.15	+	13476.8i	0.213568	+	0.586772i
$809$	37114.6	−	21428.1i	1.61295	−	0.931239i	0.624272	−	0.781207i	$-0.285396\pi$
$809$	37114.6	−	21428.1i	1.61295	−	0.931239i	0.988681	−	0.150032i	$-0.0479378\pi$
$810$		0			0
$811$	5904.43	+	1041.11i	0.255650	+	0.0450781i	0.300004	−	0.953938i	$-0.403012\pi$
$811$	5904.43	+	1041.11i	0.255650	+	0.0450781i	−0.0443540	+	0.999016i	$0.514123\pi$
$812$	4483.75	−	3762.31i	0.193779	−	0.162600i
$813$		0			0
$814$	218.611	+	1239.81i	0.00941316	+	0.0533847i
$815$	−21237.2	+	58348.7i	−0.912768	+	2.50781i
$816$		0			0
$817$	38598.5	−	18194.8i	1.65287	−	0.779139i
$818$		−	23429.2i		−	1.00145i
$819$		0			0
$820$	−14725.2	+	2596.45i	−0.627106	+	0.110576i
$821$	−8788.15	+	10473.3i	−0.373579	+	0.445214i	−0.919777	−	0.392442i	$-0.871630\pi$
$821$	−8788.15	+	10473.3i	−0.373579	+	0.445214i	0.546198	+	0.837656i	$0.316075\pi$
$822$		0			0
$823$	−5002.89	+	28372.8i	−0.211895	+	1.20172i	0.674318	+	0.738441i	$0.264438\pi$
$823$	−5002.89	+	28372.8i	−0.211895	+	1.20172i	−0.886214	+	0.463277i	$0.846674\pi$
$824$	−8485.36	−	4899.03i	−0.358740	−	0.207119i
$825$		0			0
$826$	−23777.8	+	8654.40i	−1.00162	+	0.364558i
$827$	32340.0	−	11770.8i	1.35982	−	0.494935i	0.443823	−	0.896114i	$-0.353622\pi$
$827$	32340.0	−	11770.8i	1.35982	−	0.494935i	0.916000	+	0.401179i	$0.131400\pi$
$828$		0			0
$829$	−6194.42	−	3576.35i	−0.259519	−	0.149833i	0.364596	−	0.931166i	$-0.381207\pi$
$829$	−6194.42	−	3576.35i	−0.259519	−	0.149833i	−0.624115	+	0.781332i	$0.714540\pi$
$830$	2150.24	−	12194.6i	0.0899227	−	0.509977i
$831$		0			0
$832$	6192.02	−	7379.36i	0.258016	−	0.307492i
$833$	78528.4	−	13846.7i	3.26633	−	0.575941i
$834$		0			0
$835$			12601.6i			0.522272i
$836$	−393.656	−	181.573i	−0.0162857	−	0.00751177i
$837$		0			0
$838$	−2029.74	+	5576.68i	−0.0836711	+	0.229884i
$839$	5460.15	+	30966.1i	0.224679	+	1.27422i	0.863299	+	0.504694i	$0.168394\pi$
$839$	5460.15	+	30966.1i	0.224679	+	1.27422i	−0.638620	+	0.769522i	$0.720494\pi$
$840$		0			0
$841$	−12442.0	+	10440.1i	−0.510149	+	0.428066i
$842$	19232.3	+	3391.18i	0.787161	+	0.138798i
$843$		0			0
$844$	1528.31	−	882.370i	0.0623301	−	0.0359863i
$845$	−11128.0	−	30573.9i	−0.453035	−	1.24470i
$846$		0			0
$847$	−21405.0	−	37074.5i	−0.868339	−	1.50401i
$848$	−5634.10	+	9758.55i	−0.228156	+	0.395177i
$849$		0			0
$850$	−29557.9	−	35225.7i	−1.19274	−	1.42145i
$851$	−4990.35	−	4187.40i	−0.201019	−	0.168675i
$852$		0			0
$853$	−18106.4	−	6590.20i	−0.726790	−	0.264530i	−0.0479848	−	0.998848i	$-0.515280\pi$
$853$	−18106.4	−	6590.20i	−0.726790	−	0.264530i	−0.678806	+	0.734318i	$0.737502\pi$
$854$	12335.1			0.494261
$855$		0			0
$856$	35945.6			1.43528
$857$	22331.1	+	8127.85i	0.890099	+	0.323970i	0.746278	−	0.665634i	$-0.231839\pi$
$857$	22331.1	+	8127.85i	0.890099	+	0.323970i	0.143821	+	0.989604i	$0.454061\pi$
$858$		0			0
$859$	23588.3	+	19792.9i	0.936928	+	0.786176i	0.977048	−	0.213019i	$-0.0683296\pi$
$859$	23588.3	+	19792.9i	0.936928	+	0.786176i	−0.0401201	+	0.999195i	$0.512774\pi$
$860$	−11320.4	−	13491.1i	−0.448864	−	0.534935i
$861$		0			0
$862$	5990.24	−	10375.4i	0.236692	−	0.409963i
$863$	18889.7	+	32718.0i	0.745091	+	1.29054i	0.950152	+	0.311787i	$0.100927\pi$
$863$	18889.7	+	32718.0i	0.745091	+	1.29054i	−0.205061	+	0.978749i	$0.565739\pi$
$864$		0			0
$865$	−12303.3	−	33802.9i	−0.483611	−	1.32871i
$866$	−20612.6	+	11900.7i	−0.808828	+	0.466977i
$867$		0			0
$868$	10315.8	+	1818.95i	0.403388	+	0.0711282i
$869$	1216.18	−	1020.50i	0.0474754	−	0.0398366i
$870$		0			0
$871$	−3165.01	−	17949.6i	−0.123125	−	0.698279i
$872$	8070.53	−	22173.6i	0.313420	−	0.861116i
$873$		0			0
$874$	−6468.03	+	1762.00i	−0.250325	+	0.0681928i
$875$		−	22251.6i		−	0.859705i
$876$		0			0
$877$	5895.28	−	1039.50i	0.226989	−	0.0400243i	−0.0589965	−	0.998258i	$-0.518790\pi$
$877$	5895.28	−	1039.50i	0.226989	−	0.0400243i	0.285986	+	0.958234i	$0.407679\pi$
$878$	12974.4	−	15462.3i	0.498709	−	0.594338i
$879$		0			0
$880$	339.238	−	1923.92i	0.0129951	−	0.0736991i
$881$	−31843.6	−	18384.9i	−1.21775	−	0.703068i	−0.253313	−	0.967384i	$-0.581520\pi$
$881$	−31843.6	−	18384.9i	−1.21775	−	0.703068i	−0.964436	+	0.264316i	$0.914854\pi$
$882$		0			0
$883$	10135.0	−	3688.85i	0.386263	−	0.140588i	−0.141587	−	0.989926i	$-0.545220\pi$
$883$	10135.0	−	3688.85i	0.386263	−	0.140588i	0.527850	+	0.849337i	$0.322998\pi$
$884$	−3630.60	+	1321.43i	−0.138134	+	0.0502766i
$885$		0			0
$886$	15000.3	+	8660.40i	0.568785	+	0.328388i
$887$	7275.65	−	41262.2i	0.275414	−	1.56195i	−0.462229	−	0.886761i	$-0.652950\pi$
$887$	7275.65	−	41262.2i	0.275414	−	1.56195i	0.737643	−	0.675191i	$-0.235939\pi$
$888$		0			0
$889$	15792.6	−	18820.9i	0.595802	−	0.710049i
$890$	−9624.28	+	1697.02i	−0.362479	+	0.0639149i
$891$		0			0
$892$			9007.29i			0.338101i
$893$	−1352.08	−	14746.9i	−0.0506671	−	0.552616i
$894$		0			0
$895$	6251.76	−	17176.6i	0.233490	−	0.641507i
$896$	−3834.70	−	21747.7i	−0.142978	−	0.810868i
$897$		0			0
$898$	−6512.37	+	5464.53i	−0.242005	+	0.203066i
$899$	14358.8	+	2531.85i	0.532696	+	0.0939287i
$900$		0			0
$901$	25226.3	−	14564.4i	0.932753	−	0.538525i
$902$	−955.929	−	2626.39i	−0.0352871	−	0.0969504i
$903$		0			0
$904$	−5294.96	−	9171.14i	−0.194809	−	0.337420i
$905$	−28394.2	+	49180.1i	−1.04293	+	1.80641i
$906$		0			0
$907$	6133.23	+	7309.29i	0.224532	+	0.267587i	0.866536	−	0.499114i	$-0.166341\pi$
$907$	6133.23	+	7309.29i	0.224532	+	0.267587i	−0.642004	+	0.766701i	$0.721897\pi$
$908$	3135.03	+	2630.60i	0.114581	+	0.0961449i
$909$		0			0
$910$	21498.4	+	7824.78i	0.783149	+	0.285043i
$911$	−28305.2			−1.02941			−0.514705	−	0.857367i	$-0.672098\pi$
$911$	−28305.2			−1.02941			−0.514705	+	0.857367i	$0.672098\pi$
$912$		0			0
$913$	−774.535			−0.0280760
$914$	−4597.89	−	1673.50i	−0.166395	−	0.0605627i
$915$		0			0
$916$	−9678.58	−	8121.29i	−0.349115	−	0.292942i
$917$	30524.2	+	36377.3i	1.09923	+	1.31002i
$918$		0			0
$919$	5187.97	−	8985.82i	0.186219	−	0.322541i	−0.757768	−	0.652524i	$-0.773710\pi$
$919$	5187.97	−	8985.82i	0.186219	−	0.322541i	0.943987	+	0.329984i	$0.107043\pi$
$920$	6900.81	+	11952.5i	0.247297	+	0.428330i
$921$		0			0
$922$	−14078.6	−	38680.6i	−0.502877	−	1.38164i
$923$	−12742.8	+	7357.04i	−0.454424	+	0.262362i
$924$		0			0
$925$	−32093.5	−	5658.95i	−1.14079	−	0.201152i
$926$	5956.61	−	4998.19i	0.211389	−	0.177377i
$927$		0			0
$928$	1385.93	+	7859.99i	0.0490251	+	0.278035i
$929$	5190.41	−	14260.5i	0.183307	−	0.503631i	−0.813670	−	0.581326i	$-0.802534\pi$
$929$	5190.41	−	14260.5i	0.183307	−	0.503631i	0.996977	+	0.0776953i	$0.0247561\pi$
$930$		0			0
$931$	−15284.9	−	56108.7i	−0.538071	−	1.97517i
$932$			7824.93i			0.275015i
$933$		0			0
$934$	−11733.4	+	2068.91i	−0.411058	+	0.0724806i
$935$	−3246.17	+	3868.63i	−0.113541	+	0.135313i
$936$		0			0
$937$	−8010.55	+	45430.1i	−0.279288	+	1.58392i	0.445714	+	0.895176i	$0.352950\pi$
$937$	−8010.55	+	45430.1i	−0.279288	+	1.58392i	−0.725002	+	0.688747i	$0.758161\pi$
$938$	−73658.7	−	42526.9i	−2.56401	−	1.48033i
$939$		0			0
$940$	−5743.23	+	2090.36i	−0.199280	+	0.0725321i
$941$	−24346.8	+	8861.51i	−0.843446	+	0.306989i	−0.727365	−	0.686251i	$-0.759255\pi$
$941$	−24346.8	+	8861.51i	−0.843446	+	0.306989i	−0.116081	+	0.993240i	$0.537033\pi$
$942$		0			0
$943$	12525.1	+	7231.35i	0.432526	+	0.249719i
$944$	2438.70	−	13830.6i	0.0840816	−	0.476851i
$945$		0			0
$946$	2116.05	−	2521.81i	0.0727259	−	0.0866714i
$947$	−39550.3	+	6973.79i	−1.35714	+	0.239301i	−0.804417	−	0.594064i	$-0.797522\pi$
$947$	−39550.3	+	6973.79i	−1.35714	+	0.239301i	−0.552723	+	0.833365i	$0.686411\pi$
$948$		0			0
$949$		−	3605.84i		−	0.123341i
$950$	−23614.3	+	23811.7i	−0.806471	+	0.813215i
$951$		0			0
$952$	−30760.6	+	84514.0i	−1.04722	+	2.87722i
$953$	7987.31	+	45298.3i	0.271495	+	1.53972i	0.749881	+	0.661573i	$0.230111\pi$
$953$	7987.31	+	45298.3i	0.271495	+	1.53972i	−0.478386	+	0.878150i	$0.658778\pi$
$954$		0			0
$955$	2517.74	−	2112.63i	0.0853111	−	0.0715845i
$956$	−8636.95	−	1522.93i	−0.292196	−	0.0515220i
$957$		0			0
$958$	21055.8	−	12156.6i	0.710107	−	0.409981i
$959$	−28878.2	−	79342.2i	−0.972394	−	2.67163i
$960$		0			0
$961$	−1848.76	−	3202.15i	−0.0620577	−	0.107487i
$962$	4091.30	−	7086.34i	0.137119	−	0.237498i
$963$		0			0
$964$	−5275.51	−	6287.11i	−0.176258	−	0.210056i
$965$	−5310.03	−	4455.65i	−0.177136	−	0.148635i
$966$		0			0
$967$	30278.8	+	11020.6i	1.00693	+	0.366493i	0.792253	−	0.610193i	$-0.208908\pi$
$967$	30278.8	+	11020.6i	1.00693	+	0.366493i	0.214677	+	0.976685i	$0.431130\pi$
$968$	32439.0			1.07710
$969$		0			0
$970$	54586.1			1.80686
$971$	33015.3	+	12016.6i	1.09115	+	0.397148i	0.824049	−	0.566519i	$-0.191710\pi$
$971$	33015.3	+	12016.6i	1.09115	+	0.397148i	0.267106	+	0.963667i	$0.413933\pi$
$972$		0			0
$973$	−10471.1	−	8786.33i	−0.345005	−	0.289493i
$974$	30233.4	+	36030.8i	0.994601	+	1.18532i
$975$		0			0
$976$	−3423.08	+	5928.94i	−0.112264	+	0.194448i
$977$	25463.9	+	44104.7i	0.833840	+	1.44425i	0.894971	+	0.446123i	$0.147196\pi$
$977$	25463.9	+	44104.7i	0.833840	+	1.44425i	−0.0611314	+	0.998130i	$0.519471\pi$
$978$		0			0
$979$	209.071	+	574.418i	0.00682526	+	0.0187523i
$980$	−20785.3	+	12000.4i	−0.677514	+	0.391163i
$981$		0			0
$982$	26881.9	+	4740.00i	0.873559	+	0.154032i
$983$	34776.7	−	29181.1i	1.12839	−	0.946830i	0.129390	−	0.991594i	$-0.458698\pi$
$983$	34776.7	−	29181.1i	1.12839	−	0.946830i	0.998998	+	0.0447638i	$0.0142535\pi$
$984$		0			0
$985$	9618.75	+	54550.7i	0.311146	+	1.76460i
$986$	−8583.20	+	23582.2i	−0.277226	+	0.761672i
$987$		0			0
$988$	1201.43	+	2548.71i	0.0386867	+	0.0820700i
$989$			17034.7i			0.547696i
$990$		0			0
$991$	−15231.5	+	2685.73i	−0.488239	+	0.0860897i	−0.412348	−	0.911026i	$-0.635291\pi$
$991$	−15231.5	+	2685.73i	−0.488239	+	0.0860897i	−0.0758911	+	0.997116i	$0.524180\pi$
$992$	−9181.27	+	10941.8i	−0.293856	+	0.350204i
$993$		0			0
$994$	−11923.2	+	67619.7i	−0.380463	+	2.15771i
$995$	30291.4	+	17488.7i	0.965126	+	0.557216i
$996$		0			0
$997$	−5433.95	+	1977.79i	−0.172613	+	0.0628259i	−0.426881	−	0.904308i	$-0.640388\pi$
$997$	−5433.95	+	1977.79i	−0.172613	+	0.0628259i	0.254268	+	0.967134i	$0.418165\pi$
$998$	−17538.9	+	6383.64i	−0.556297	+	0.202476i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.y.a.53.14	yes	120
3.2	odd	2	inner	171.4.y.a.53.7	✓	120
19.14	odd	18	inner	171.4.y.a.71.7	yes	120
57.14	even	18	inner	171.4.y.a.71.14	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.4.y.a.53.7	✓	120	3.2	odd	2	inner
171.4.y.a.53.14	yes	120	1.1	even	1	trivial
171.4.y.a.71.7	yes	120	19.14	odd	18	inner
171.4.y.a.71.14	yes	120	57.14	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	171.y (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.30065 + 0.837369i) q^{2} +(-1.53654 - 1.28931i) q^{4} +(10.9536 + 13.0540i) q^{5} +(-16.1646 + 27.9979i) q^{7} +(-12.2486 - 21.2153i) q^{8} +(14.2695 + 39.2050i) q^{10} +(2.26002 - 1.30482i) q^{11} +(-16.7040 - 2.94537i) q^{13} +(-60.6336 + 50.8776i) q^{14} +(-7.62839 - 43.2628i) q^{16} +(-38.8403 + 106.713i) q^{17} +(80.0856 + 21.1019i) q^{19} -34.1808i q^{20} +(6.29213 - 1.10947i) q^{22} +(-21.2515 + 25.3265i) q^{23} +(-28.7197 + 162.878i) q^{25} +(-35.9638 - 20.7637i) q^{26} +(60.9356 - 22.1788i) q^{28} +(84.8179 - 30.8712i) q^{29} +(139.893 + 80.7674i) q^{31} +(-15.3546 + 87.0804i) q^{32} +(-178.716 + 212.986i) q^{34} +(-542.546 + 95.6655i) q^{35} +197.041i q^{37} +(166.579 + 115.609i) q^{38} +(142.778 - 392.278i) q^{40} +(-75.9623 - 430.804i) q^{41} +(394.699 - 331.192i) q^{43} +(-5.15494 - 0.908955i) q^{44} +(-70.0998 + 40.4721i) q^{46} +(-61.1561 - 168.025i) q^{47} +(-351.087 - 608.100i) q^{49} +(-202.463 + 350.676i) q^{50} +(21.8690 + 26.0625i) q^{52} +(-196.492 - 164.877i) q^{53} +(41.7886 + 15.2098i) q^{55} +791.975 q^{56} +220.987 q^{58} +(300.408 + 109.340i) q^{59} +(-119.382 - 100.173i) q^{61} +(254.213 + 302.960i) q^{62} +(-283.965 + 491.841i) q^{64} +(-144.521 - 250.318i) q^{65} +(367.524 + 1009.76i) q^{67} +(197.266 - 113.892i) q^{68} +(-1328.32 - 234.218i) q^{70} +(664.533 - 557.610i) q^{71} +(36.9153 + 209.357i) q^{73} +(-164.996 + 453.322i) q^{74} +(-95.8482 - 135.680i) q^{76} +84.3675i q^{77} +(599.122 - 105.641i) q^{79} +(481.195 - 573.466i) q^{80} +(185.979 - 1054.74i) q^{82} +(-257.034 - 148.399i) q^{83} +(-1818.48 + 661.872i) q^{85} +(1185.40 - 431.449i) q^{86} +(-55.3642 - 31.9645i) q^{88} +(-40.6753 + 230.681i) q^{89} +(352.478 - 420.067i) q^{91} +(65.3076 - 11.5155i) q^{92} -437.777i q^{94} +(601.765 + 1276.58i) q^{95} +(447.484 - 1229.45i) q^{97} +(-298.524 - 1693.01i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 36 q^{4} - 180 q^{10} - 156 q^{13} + 180 q^{16} + 924 q^{19} + 432 q^{22} - 360 q^{25} - 624 q^{28} + 324 q^{34} + 1440 q^{40} + 1524 q^{43} + 3888 q^{46} - 3228 q^{49} - 6000 q^{52} - 4464 q^{55}+ \cdots + 5904 q^{97}+O(q^{100}) \) 120 * q - 36 * q^4 - 180 * q^10 - 156 * q^13 + 180 * q^16 + 924 * q^19 + 432 * q^22 - 360 * q^25 - 624 * q^28 + 324 * q^34 + 1440 * q^40 + 1524 * q^43 + 3888 * q^46 - 3228 * q^49 - 6000 * q^52 - 4464 * q^55 + 5616 * q^58 - 5736 * q^61 - 4524 * q^64 + 372 * q^67 + 7848 * q^70 - 276 * q^73 + 4320 * q^76 + 10536 * q^79 + 3960 * q^82 - 11592 * q^85 - 11664 * q^88 - 120 * q^91 + 5904 * q^97

Introduction

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