LMFDB - Embedded newform 4020.2.q.l.3781.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4020,2,Mod(841,4020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4020, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4020.q (of order $3$, degree $2$, 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:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3781.9
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.l.841.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} -1.00000 q^{5} +(1.82121 + 3.15443i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} -1.00000 q^{5} +(1.82121 + 3.15443i) q^{7} +1.00000 q^{9} +(1.30569 + 2.26152i) q^{11} +(1.63203 - 2.82676i) q^{13} +1.00000 q^{15} +(2.07433 - 3.59284i) q^{17} +(0.703946 - 1.21927i) q^{19} +(-1.82121 - 3.15443i) q^{21} +(0.502523 - 0.870395i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-1.80555 - 3.12731i) q^{29} +(-3.41308 - 5.91164i) q^{31} +(-1.30569 - 2.26152i) q^{33} +(-1.82121 - 3.15443i) q^{35} +(2.80807 - 4.86373i) q^{37} +(-1.63203 + 2.82676i) q^{39} +(1.37073 + 2.37418i) q^{41} +1.05710 q^{43} -1.00000 q^{45} +(1.31228 + 2.27294i) q^{47} +(-3.13360 + 5.42755i) q^{49} +(-2.07433 + 3.59284i) q^{51} +6.31987 q^{53} +(-1.30569 - 2.26152i) q^{55} +(-0.703946 + 1.21927i) q^{57} -12.1494 q^{59} +(7.36320 - 12.7534i) q^{61} +(1.82121 + 3.15443i) q^{63} +(-1.63203 + 2.82676i) q^{65} +(-5.76325 - 5.81249i) q^{67} +(-0.502523 + 0.870395i) q^{69} +(-1.79974 - 3.11724i) q^{71} +(2.56050 - 4.43491i) q^{73} -1.00000 q^{75} +(-4.75586 + 8.23740i) q^{77} +(6.86632 + 11.8928i) q^{79} +1.00000 q^{81} +(-7.72181 + 13.3746i) q^{83} +(-2.07433 + 3.59284i) q^{85} +(1.80555 + 3.12731i) q^{87} +12.3635 q^{89} +11.8891 q^{91} +(3.41308 + 5.91164i) q^{93} +(-0.703946 + 1.21927i) q^{95} +(-3.74690 + 6.48983i) q^{97} +(1.30569 + 2.26152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	1.82121	+	3.15443i	0.688352	+	1.19226i	0.972371	+	0.233442i	$0.0749989\pi$
$7$	1.82121	+	3.15443i	0.688352	+	1.19226i	−0.284019	+	0.958819i	$0.591668\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	1.30569	+	2.26152i	0.393680	+	0.681874i	0.992932	−	0.118687i	$-0.0378685\pi$
$11$	1.30569	+	2.26152i	0.393680	+	0.681874i	−0.599252	+	0.800561i	$0.704535\pi$
$12$		0			0
$13$	1.63203	−	2.82676i	0.452644	−	0.784003i	−0.545905	−	0.837847i	$-0.683814\pi$
$13$	1.63203	−	2.82676i	0.452644	−	0.784003i	0.998549	+	0.0538443i	$0.0171475\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	2.07433	−	3.59284i	0.503098	−	0.871392i	−0.496895	−	0.867811i	$-0.665527\pi$
$17$	2.07433	−	3.59284i	0.503098	−	0.871392i	0.999994	−	0.00358131i	$-0.00113997\pi$
$18$		0			0
$19$	0.703946	−	1.21927i	0.161496	−	0.279720i	−0.773909	−	0.633297i	$-0.781701\pi$
$19$	0.703946	−	1.21927i	0.161496	−	0.279720i	0.935405	+	0.353577i	$0.115035\pi$
$20$		0			0
$21$	−1.82121	−	3.15443i	−0.397420	−	0.688352i
$22$		0			0
$23$	0.502523	−	0.870395i	0.104783	−	0.181490i	−0.808866	−	0.587992i	$-0.799918\pi$
$23$	0.502523	−	0.870395i	0.104783	−	0.181490i	0.913650	+	0.406503i	$0.133252\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−1.80555	−	3.12731i	−0.335282	−	0.580726i	0.648257	−	0.761422i	$-0.275498\pi$
$29$	−1.80555	−	3.12731i	−0.335282	−	0.580726i	−0.983539	+	0.180696i	$0.942165\pi$
$30$		0			0
$31$	−3.41308	−	5.91164i	−0.613008	−	1.06176i	−0.990730	−	0.135842i	$-0.956626\pi$
$31$	−3.41308	−	5.91164i	−0.613008	−	1.06176i	0.377722	−	0.925919i	$-0.376707\pi$
$32$		0			0
$33$	−1.30569	−	2.26152i	−0.227291	−	0.393680i
$34$		0			0
$35$	−1.82121	−	3.15443i	−0.307840	−	0.533195i
$36$		0			0
$37$	2.80807	−	4.86373i	0.461644	−	0.799591i	−0.537399	−	0.843328i	$-0.680593\pi$
$37$	2.80807	−	4.86373i	0.461644	−	0.799591i	0.999043	+	0.0437368i	$0.0139263\pi$
$38$		0			0
$39$	−1.63203	+	2.82676i	−0.261334	+	0.452644i
$40$		0			0
$41$	1.37073	+	2.37418i	0.214072	+	0.370784i	0.952985	−	0.303017i	$-0.0979938\pi$
$41$	1.37073	+	2.37418i	0.214072	+	0.370784i	−0.738913	+	0.673801i	$0.764660\pi$
$42$		0			0
$43$	1.05710			0.161207			0.0806034	−	0.996746i	$-0.474315\pi$
$43$	1.05710			0.161207			0.0806034	+	0.996746i	$0.474315\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	1.31228	+	2.27294i	0.191416	+	0.331543i	0.945720	−	0.324983i	$-0.105359\pi$
$47$	1.31228	+	2.27294i	0.191416	+	0.331543i	−0.754304	+	0.656526i	$0.772025\pi$
$48$		0			0
$49$	−3.13360	+	5.42755i	−0.447657	+	0.775365i
$50$		0			0
$51$	−2.07433	+	3.59284i	−0.290464	+	0.503098i
$52$		0			0
$53$	6.31987			0.868101			0.434050	−	0.900889i	$-0.357084\pi$
$53$	6.31987			0.868101			0.434050	+	0.900889i	$0.357084\pi$
$54$		0			0
$55$	−1.30569	−	2.26152i	−0.176059	−	0.304943i
$56$		0			0
$57$	−0.703946	+	1.21927i	−0.0932399	+	0.161496i
$58$		0			0
$59$	−12.1494			−1.58172			−0.790858	−	0.612000i	$-0.790365\pi$
$59$	−12.1494			−1.58172			−0.790858	+	0.612000i	$0.790365\pi$
$60$		0			0
$61$	7.36320	−	12.7534i	0.942761	−	1.63291i	0.182587	−	0.983190i	$-0.441553\pi$
$61$	7.36320	−	12.7534i	0.942761	−	1.63291i	0.760173	−	0.649720i	$-0.225114\pi$
$62$		0			0
$63$	1.82121	+	3.15443i	0.229451	+	0.397420i
$64$		0			0
$65$	−1.63203	+	2.82676i	−0.202429	+	0.350617i
$66$		0			0
$67$	−5.76325	−	5.81249i	−0.704093	−	0.710108i
$67$	−5.76325	−	5.81249i	−0.704093	−	0.710108i
$68$		0			0
$69$	−0.502523	+	0.870395i	−0.0604966	+	0.104783i
$70$		0			0
$71$	−1.79974	−	3.11724i	−0.213590	−	0.369948i	0.739246	−	0.673436i	$-0.235182\pi$
$71$	−1.79974	−	3.11724i	−0.213590	−	0.369948i	−0.952835	+	0.303488i	$0.901849\pi$
$72$		0			0
$73$	2.56050	−	4.43491i	0.299684	−	0.519067i	−0.676380	−	0.736553i	$-0.736452\pi$
$73$	2.56050	−	4.43491i	0.299684	−	0.519067i	0.976064	+	0.217486i	$0.0697855\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	−4.75586	+	8.23740i	−0.541981	+	0.938738i
$78$		0			0
$79$	6.86632	+	11.8928i	0.772522	+	1.33805i	0.936177	+	0.351529i	$0.114338\pi$
$79$	6.86632	+	11.8928i	0.772522	+	1.33805i	−0.163655	+	0.986518i	$0.552328\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−7.72181	+	13.3746i	−0.847579	+	1.46805i	0.0357832	+	0.999360i	$0.488607\pi$
$83$	−7.72181	+	13.3746i	−0.847579	+	1.46805i	−0.883362	+	0.468691i	$0.844726\pi$
$84$		0			0
$85$	−2.07433	+	3.59284i	−0.224992	+	0.389698i
$86$		0			0
$87$	1.80555	+	3.12731i	0.193575	+	0.335282i
$88$		0			0
$89$	12.3635			1.31053			0.655263	−	0.755401i	$-0.272558\pi$
$89$	12.3635			1.31053			0.655263	+	0.755401i	$0.272558\pi$
$90$		0			0
$91$	11.8891			1.24631
$92$		0			0
$93$	3.41308	+	5.91164i	0.353920	+	0.613008i
$94$		0			0
$95$	−0.703946	+	1.21927i	−0.0722233	+	0.125094i
$96$		0			0
$97$	−3.74690	+	6.48983i	−0.380441	+	0.658942i	−0.991125	−	0.132932i	$-0.957561\pi$
$97$	−3.74690	+	6.48983i	−0.380441	+	0.658942i	0.610685	+	0.791874i	$0.290894\pi$
$98$		0			0
$99$	1.30569	+	2.26152i	0.131227	+	0.227291i
$100$		0			0
$101$	−2.74729	−	4.75844i	−0.273365	−	0.473482i	0.696356	−	0.717696i	$-0.254803\pi$
$101$	−2.74729	−	4.75844i	−0.273365	−	0.473482i	−0.969721	+	0.244214i	$0.921470\pi$
$102$		0			0
$103$	1.28008	+	2.21717i	0.126130	+	0.218464i	0.922174	−	0.386775i	$-0.126411\pi$
$103$	1.28008	+	2.21717i	0.126130	+	0.218464i	−0.796044	+	0.605239i	$0.793078\pi$
$104$		0			0
$105$	1.82121	+	3.15443i	0.177732	+	0.307840i
$106$		0			0
$107$	−10.2714			−0.992978			−0.496489	−	0.868043i	$-0.665378\pi$
$107$	−10.2714			−0.992978			−0.496489	+	0.868043i	$0.665378\pi$
$108$		0			0
$109$	13.6659			1.30896			0.654478	−	0.756081i	$-0.272889\pi$
$109$	13.6659			1.30896			0.654478	+	0.756081i	$0.272889\pi$
$110$		0			0
$111$	−2.80807	+	4.86373i	−0.266530	+	0.461644i
$112$		0			0
$113$	−10.2461	−	17.7468i	−0.963875	−	1.66948i	−0.712608	−	0.701563i	$-0.752486\pi$
$113$	−10.2461	−	17.7468i	−0.963875	−	1.66948i	−0.251267	−	0.967918i	$-0.580847\pi$
$114$		0			0
$115$	−0.502523	+	0.870395i	−0.0468605	+	0.0811647i
$116$		0			0
$117$	1.63203	−	2.82676i	0.150881	−	0.261334i
$118$		0			0
$119$	15.1111			1.38523
$120$		0			0
$121$	2.09035	−	3.62060i	0.190032	−	0.329145i
$122$		0			0
$123$	−1.37073	−	2.37418i	−0.123595	−	0.214072i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−0.698579	−	1.20997i	−0.0619888	−	0.107368i	0.833365	−	0.552722i	$-0.186411\pi$
$127$	−0.698579	−	1.20997i	−0.0619888	−	0.107368i	−0.895354	+	0.445355i	$0.853078\pi$
$128$		0			0
$129$	−1.05710			−0.0930728
$130$		0			0
$131$	20.6388			1.80322			0.901611	−	0.432548i	$-0.142385\pi$
$131$	20.6388			1.80322			0.901611	+	0.432548i	$0.142385\pi$
$132$		0			0
$133$	5.12813			0.444665
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	6.85069			0.585294			0.292647	−	0.956221i	$-0.405464\pi$
$137$	6.85069			0.585294			0.292647	+	0.956221i	$0.405464\pi$
$138$		0			0
$139$	4.13729			0.350920			0.175460	−	0.984487i	$-0.443859\pi$
$139$	4.13729			0.350920			0.175460	+	0.984487i	$0.443859\pi$
$140$		0			0
$141$	−1.31228	−	2.27294i	−0.110514	−	0.191416i
$142$		0			0
$143$	8.52370			0.712788
$144$		0			0
$145$	1.80555	+	3.12731i	0.149943	+	0.259709i
$146$		0			0
$147$	3.13360	−	5.42755i	0.258455	−	0.447657i
$148$		0			0
$149$	−15.8039			−1.29471			−0.647353	−	0.762190i	$-0.724124\pi$
$149$	−15.8039			−1.29471			−0.647353	+	0.762190i	$0.724124\pi$
$150$		0			0
$151$	8.58459	−	14.8689i	0.698604	−	1.21002i	−0.270347	−	0.962763i	$-0.587138\pi$
$151$	8.58459	−	14.8689i	0.698604	−	1.21002i	0.968951	−	0.247254i	$-0.0795282\pi$
$152$		0			0
$153$	2.07433	−	3.59284i	0.167699	−	0.290464i
$154$		0			0
$155$	3.41308	+	5.91164i	0.274146	+	0.474834i
$156$		0			0
$157$	11.0035	−	19.0587i	0.878179	−	1.52105i	0.0248414	−	0.999691i	$-0.492092\pi$
$157$	11.0035	−	19.0587i	0.878179	−	1.52105i	0.853337	−	0.521359i	$-0.174575\pi$
$158$		0			0
$159$	−6.31987			−0.501198
$160$		0			0
$161$	3.66079			0.288511
$162$		0			0
$163$	−8.03401	−	13.9153i	−0.629272	−	1.08993i	−0.987698	−	0.156373i	$-0.950020\pi$
$163$	−8.03401	−	13.9153i	−0.629272	−	1.08993i	0.358426	−	0.933558i	$-0.383314\pi$
$164$		0			0
$165$	1.30569	+	2.26152i	0.101648	+	0.176059i
$166$		0			0
$167$	12.0741	+	20.9130i	0.934324	+	1.61830i	0.775835	+	0.630936i	$0.217329\pi$
$167$	12.0741	+	20.9130i	0.934324	+	1.61830i	0.158489	+	0.987361i	$0.449338\pi$
$168$		0			0
$169$	1.17295	+	2.03160i	0.0902266	+	0.156277i
$170$		0			0
$171$	0.703946	−	1.21927i	0.0538321	−	0.0932399i
$172$		0			0
$173$	−10.5394	+	18.2548i	−0.801296	+	1.38789i	0.117468	+	0.993077i	$0.462522\pi$
$173$	−10.5394	+	18.2548i	−0.801296	+	1.38789i	−0.918763	+	0.394808i	$0.870811\pi$
$174$		0			0
$175$	1.82121	+	3.15443i	0.137670	+	0.238452i
$176$		0			0
$177$	12.1494			0.913204
$178$		0			0
$179$	5.38462			0.402466			0.201233	−	0.979543i	$-0.435505\pi$
$179$	5.38462			0.402466			0.201233	+	0.979543i	$0.435505\pi$
$180$		0			0
$181$	9.51402	+	16.4788i	0.707172	+	1.22486i	0.965902	+	0.258908i	$0.0833626\pi$
$181$	9.51402	+	16.4788i	0.707172	+	1.22486i	−0.258730	+	0.965950i	$0.583304\pi$
$182$		0			0
$183$	−7.36320	+	12.7534i	−0.544303	+	0.942761i
$184$		0			0
$185$	−2.80807	+	4.86373i	−0.206454	+	0.357588i
$186$		0			0
$187$	10.8337			0.792239
$188$		0			0
$189$	−1.82121	−	3.15443i	−0.132473	−	0.229451i
$190$		0			0
$191$	2.19404	−	3.80019i	0.158755	−	0.274972i	−0.775665	−	0.631145i	$-0.782585\pi$
$191$	2.19404	−	3.80019i	0.158755	−	0.274972i	0.934420	+	0.356173i	$0.115919\pi$
$192$		0			0
$193$	−1.53758			−0.110677			−0.0553387	−	0.998468i	$-0.517624\pi$
$193$	−1.53758			−0.110677			−0.0553387	+	0.998468i	$0.517624\pi$
$194$		0			0
$195$	1.63203	−	2.82676i	0.116872	−	0.202429i
$196$		0			0
$197$	−3.67344	−	6.36259i	−0.261722	−	0.453316i	0.704978	−	0.709230i	$-0.250957\pi$
$197$	−3.67344	−	6.36259i	−0.261722	−	0.453316i	−0.966700	+	0.255914i	$0.917624\pi$
$198$		0			0
$199$	−8.66810	+	15.0136i	−0.614465	+	1.06428i	0.376013	+	0.926614i	$0.377295\pi$
$199$	−8.66810	+	15.0136i	−0.614465	+	1.06428i	−0.990478	+	0.137670i	$0.956039\pi$
$200$		0			0
$201$	5.76325	+	5.81249i	0.406508	+	0.409981i
$202$		0			0
$203$	6.57657	−	11.3909i	0.461584	−	0.799488i
$204$		0			0
$205$	−1.37073	−	2.37418i	−0.0957361	−	0.165820i
$206$		0			0
$207$	0.502523	−	0.870395i	0.0349277	−	0.0604966i
$208$		0			0
$209$	3.67654			0.254311
$210$		0			0
$211$	13.4978	−	23.3790i	0.929230	−	1.60947i	0.144617	−	0.989488i	$-0.453805\pi$
$211$	13.4978	−	23.3790i	0.929230	−	1.60947i	0.784613	−	0.619986i	$-0.212862\pi$
$212$		0			0
$213$	1.79974	+	3.11724i	0.123316	+	0.213590i
$214$		0			0
$215$	−1.05710			−0.0720939
$216$		0			0
$217$	12.4319	−	21.5326i	0.843931	−	1.46173i
$218$		0			0
$219$	−2.56050	+	4.43491i	−0.173022	+	0.299684i
$220$		0			0
$221$	−6.77074	−	11.7273i	−0.455449	−	0.788861i
$222$		0			0
$223$	19.0470			1.27548			0.637742	−	0.770250i	$-0.279869\pi$
$223$	19.0470			1.27548			0.637742	+	0.770250i	$0.279869\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	1.36485	+	2.36399i	0.0905884	+	0.156904i	0.907759	−	0.419492i	$-0.137792\pi$
$227$	1.36485	+	2.36399i	0.0905884	+	0.156904i	−0.817170	+	0.576396i	$0.804459\pi$
$228$		0			0
$229$	−0.116389	+	0.201591i	−0.00769120	+	0.0133215i	−0.869845	−	0.493324i	$-0.835782\pi$
$229$	−0.116389	+	0.201591i	−0.00769120	+	0.0133215i	0.862154	+	0.506646i	$0.169115\pi$
$230$		0			0
$231$	4.75586	−	8.23740i	0.312913	−	0.541981i
$232$		0			0
$233$	−14.6726	−	25.4138i	−0.961237	−	1.66491i	−0.719402	−	0.694594i	$-0.755584\pi$
$233$	−14.6726	−	25.4138i	−0.961237	−	1.66491i	−0.241835	−	0.970317i	$-0.577749\pi$
$234$		0			0
$235$	−1.31228	−	2.27294i	−0.0856039	−	0.148270i
$236$		0			0
$237$	−6.86632	−	11.8928i	−0.446016	−	0.772522i
$238$		0			0
$239$	−7.81920	−	13.5433i	−0.505782	−	0.876041i	−0.999978	−	0.00668966i	$-0.997871\pi$
$239$	−7.81920	−	13.5433i	−0.505782	−	0.876041i	0.494195	−	0.869351i	$-0.335463\pi$
$240$		0			0
$241$	−8.60145			−0.554068			−0.277034	−	0.960860i	$-0.589351\pi$
$241$	−8.60145			−0.554068			−0.277034	+	0.960860i	$0.589351\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	3.13360	−	5.42755i	0.200198	−	0.346754i
$246$		0			0
$247$	−2.29772	−	3.97977i	−0.146201	−	0.253227i
$248$		0			0
$249$	7.72181	−	13.3746i	0.489350	−	0.847579i
$250$		0			0
$251$	10.5464	−	18.2669i	0.665683	−	1.15300i	−0.313417	−	0.949616i	$-0.601474\pi$
$251$	10.5464	−	18.2669i	0.665683	−	1.15300i	0.979100	−	0.203381i	$-0.0651930\pi$
$252$		0			0
$253$	2.62455			0.165004
$254$		0			0
$255$	2.07433	−	3.59284i	0.129899	−	0.224992i
$256$		0			0
$257$	12.9895	+	22.4984i	0.810262	+	1.40341i	0.912681	+	0.408673i	$0.134008\pi$
$257$	12.9895	+	22.4984i	0.810262	+	1.40341i	−0.102419	+	0.994741i	$0.532658\pi$
$258$		0			0
$259$	20.4563			1.27110
$260$		0			0
$261$	−1.80555	−	3.12731i	−0.111761	−	0.193575i
$262$		0			0
$263$	−12.9416			−0.798014			−0.399007	−	0.916948i	$-0.630645\pi$
$263$	−12.9416			−0.798014			−0.399007	+	0.916948i	$0.630645\pi$
$264$		0			0
$265$	−6.31987			−0.388227
$266$		0			0
$267$	−12.3635			−0.756632
$268$		0			0
$269$	8.74352			0.533102			0.266551	−	0.963821i	$-0.414116\pi$
$269$	8.74352			0.533102			0.266551	+	0.963821i	$0.414116\pi$
$270$		0			0
$271$	12.3673			0.751259			0.375630	−	0.926770i	$-0.377427\pi$
$271$	12.3673			0.751259			0.375630	+	0.926770i	$0.377427\pi$
$272$		0			0
$273$	−11.8891			−0.719560
$274$		0			0
$275$	1.30569	+	2.26152i	0.0787360	+	0.136375i
$276$		0			0
$277$	−16.7425			−1.00596			−0.502981	−	0.864297i	$-0.667763\pi$
$277$	−16.7425			−1.00596			−0.502981	+	0.864297i	$0.667763\pi$
$278$		0			0
$279$	−3.41308	−	5.91164i	−0.204336	−	0.353920i
$280$		0			0
$281$	−3.32890	+	5.76583i	−0.198586	+	0.343961i	−0.948070	−	0.318061i	$-0.896968\pi$
$281$	−3.32890	+	5.76583i	−0.198586	+	0.343961i	0.749484	+	0.662022i	$0.230301\pi$
$282$		0			0
$283$	13.0417			0.775251			0.387626	−	0.921817i	$-0.373295\pi$
$283$	13.0417			0.775251			0.387626	+	0.921817i	$0.373295\pi$
$284$		0			0
$285$	0.703946	−	1.21927i	0.0416981	−	0.0722233i
$286$		0			0
$287$	−4.99278	+	8.64775i	−0.294714	+	0.510460i
$288$		0			0
$289$	−0.105668	−	0.183023i	−0.00621579	−	0.0107661i
$290$		0			0
$291$	3.74690	−	6.48983i	0.219647	−	0.380441i
$292$		0			0
$293$	14.6140			0.853759			0.426879	−	0.904309i	$-0.359613\pi$
$293$	14.6140			0.853759			0.426879	+	0.904309i	$0.359613\pi$
$294$		0			0
$295$	12.1494			0.707365
$296$		0			0
$297$	−1.30569	−	2.26152i	−0.0757637	−	0.131227i
$298$		0			0
$299$	−1.64027	−	2.84102i	−0.0948590	−	0.164301i
$300$		0			0
$301$	1.92521	+	3.33455i	0.110967	+	0.192200i
$302$		0			0
$303$	2.74729	+	4.75844i	0.157827	+	0.273365i
$304$		0			0
$305$	−7.36320	+	12.7534i	−0.421615	+	0.730259i
$306$		0			0
$307$	10.6273	−	18.4069i	0.606530	−	1.05054i	−0.385278	−	0.922800i	$-0.625895\pi$
$307$	10.6273	−	18.4069i	0.606530	−	1.05054i	0.991808	−	0.127739i	$-0.0407721\pi$
$308$		0			0
$309$	−1.28008	−	2.21717i	−0.0728213	−	0.126130i
$310$		0			0
$311$	27.3867			1.55296			0.776478	−	0.630145i	$-0.217004\pi$
$311$	27.3867			1.55296			0.776478	+	0.630145i	$0.217004\pi$
$312$		0			0
$313$	−15.2522			−0.862108			−0.431054	−	0.902326i	$-0.641858\pi$
$313$	−15.2522			−0.862108			−0.431054	+	0.902326i	$0.641858\pi$
$314$		0			0
$315$	−1.82121	−	3.15443i	−0.102613	−	0.177732i
$316$		0			0
$317$	3.81626	−	6.60996i	0.214343	−	0.371252i	−0.738726	−	0.674005i	$-0.764572\pi$
$317$	3.81626	−	6.60996i	0.214343	−	0.371252i	0.953069	+	0.302753i	$0.0979058\pi$
$318$		0			0
$319$	4.71497	−	8.16657i	0.263988	−	0.457240i
$320$		0			0
$321$	10.2714			0.573296
$322$		0			0
$323$	−2.92043	−	5.05833i	−0.162497	−	0.281453i
$324$		0			0
$325$	1.63203	−	2.82676i	0.0905288	−	0.156801i
$326$		0			0
$327$	−13.6659			−0.755726
$328$		0			0
$329$	−4.77988	+	8.27900i	−0.263523	+	0.456436i
$330$		0			0
$331$	10.4339	+	18.0721i	0.573499	+	0.993330i	0.996203	+	0.0870622i	$0.0277479\pi$
$331$	10.4339	+	18.0721i	0.573499	+	0.993330i	−0.422703	+	0.906268i	$0.638919\pi$
$332$		0			0
$333$	2.80807	−	4.86373i	0.153881	−	0.266530i
$334$		0			0
$335$	5.76325	+	5.81249i	0.314880	+	0.317570i
$336$		0			0
$337$	−3.95312	+	6.84701i	−0.215340	+	0.372981i	−0.953378	−	0.301779i	$-0.902419\pi$
$337$	−3.95312	+	6.84701i	−0.215340	+	0.372981i	0.738037	+	0.674760i	$0.235753\pi$
$338$		0			0
$339$	10.2461	+	17.7468i	0.556493	+	0.963875i
$340$		0			0
$341$	8.91285	−	15.4375i	0.482658	−	0.835988i
$342$		0			0
$343$	2.66917			0.144122
$344$		0			0
$345$	0.502523	−	0.870395i	0.0270549	−	0.0468605i
$346$		0			0
$347$	2.71240	+	4.69801i	0.145609	+	0.252202i	0.929600	−	0.368570i	$-0.120152\pi$
$347$	2.71240	+	4.69801i	0.145609	+	0.252202i	−0.783991	+	0.620772i	$0.786819\pi$
$348$		0			0
$349$	7.89468			0.422593			0.211296	−	0.977422i	$-0.432231\pi$
$349$	7.89468			0.422593			0.211296	+	0.977422i	$0.432231\pi$
$350$		0			0
$351$	−1.63203	+	2.82676i	−0.0871114	+	0.150881i
$352$		0			0
$353$	5.27632	−	9.13886i	0.280830	−	0.486412i	−0.690759	−	0.723085i	$-0.742724\pi$
$353$	5.27632	−	9.13886i	0.280830	−	0.486412i	0.971589	+	0.236673i	$0.0760569\pi$
$354$		0			0
$355$	1.79974	+	3.11724i	0.0955202	+	0.165446i
$356$		0			0
$357$	−15.1111			−0.799766
$358$		0			0
$359$	−20.6033			−1.08740			−0.543700	−	0.839279i	$-0.682977\pi$
$359$	−20.6033			−1.08740			−0.543700	+	0.839279i	$0.682977\pi$
$360$		0			0
$361$	8.50892	+	14.7379i	0.447838	+	0.775678i
$362$		0			0
$363$	−2.09035	+	3.62060i	−0.109715	+	0.190032i
$364$		0			0
$365$	−2.56050	+	4.43491i	−0.134023	+	0.232134i
$366$		0			0
$367$	0.144567	+	0.250397i	0.00754634	+	0.0130706i	0.869774	−	0.493450i	$-0.164265\pi$
$367$	0.144567	+	0.250397i	0.00754634	+	0.0130706i	−0.862228	+	0.506521i	$0.830931\pi$
$368$		0			0
$369$	1.37073	+	2.37418i	0.0713575	+	0.123595i
$370$		0			0
$371$	11.5098	+	19.9356i	0.597559	+	1.03500i
$372$		0			0
$373$	2.12442	+	3.67960i	0.109998	+	0.190523i	0.915769	−	0.401705i	$-0.131582\pi$
$373$	2.12442	+	3.67960i	0.109998	+	0.190523i	−0.805771	+	0.592227i	$0.798249\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	−11.7869			−0.607054
$378$		0			0
$379$	2.51951	−	4.36393i	0.129419	−	0.224160i	−0.794033	−	0.607875i	$-0.792022\pi$
$379$	2.51951	−	4.36393i	0.129419	−	0.224160i	0.923452	+	0.383715i	$0.125356\pi$
$380$		0			0
$381$	0.698579	+	1.20997i	0.0357893	+	0.0619888i
$382$		0			0
$383$	−7.32894	+	12.6941i	−0.374491	+	0.648638i	−0.990251	−	0.139296i	$-0.955516\pi$
$383$	−7.32894	+	12.6941i	−0.374491	+	0.648638i	0.615759	+	0.787934i	$0.288849\pi$
$384$		0			0
$385$	4.75586	−	8.23740i	0.242381	−	0.419817i
$386$		0			0
$387$	1.05710			0.0537356
$388$		0			0
$389$	−3.61816	+	6.26683i	−0.183448	+	0.317741i	−0.943052	−	0.332644i	$-0.892059\pi$
$389$	−3.61816	+	6.26683i	−0.183448	+	0.317741i	0.759605	+	0.650385i	$0.225393\pi$
$390$		0			0
$391$	−2.08479	−	3.61097i	−0.105433	−	0.182614i
$392$		0			0
$393$	−20.6388			−1.04109
$394$		0			0
$395$	−6.86632	−	11.8928i	−0.345482	−	0.598393i
$396$		0			0
$397$	−28.3217			−1.42142			−0.710712	−	0.703484i	$-0.751627\pi$
$397$	−28.3217			−1.42142			−0.710712	+	0.703484i	$0.751627\pi$
$398$		0			0
$399$	−5.12813			−0.256727
$400$		0			0
$401$	10.0669			0.502716			0.251358	−	0.967894i	$-0.419123\pi$
$401$	10.0669			0.502716			0.251358	+	0.967894i	$0.419123\pi$
$402$		0			0
$403$	−22.2811			−1.10990
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	14.6659			0.726961
$408$		0			0
$409$	7.80875	+	13.5251i	0.386118	+	0.668775i	0.991924	−	0.126837i	$-0.0404825\pi$
$409$	7.80875	+	13.5251i	0.386118	+	0.668775i	−0.605806	+	0.795612i	$0.707149\pi$
$410$		0			0
$411$	−6.85069			−0.337920
$412$		0			0
$413$	−22.1266	−	38.3244i	−1.08878	−	1.88582i
$414$		0			0
$415$	7.72181	−	13.3746i	0.379049	−	0.656532i
$416$		0			0
$417$	−4.13729			−0.202604
$418$		0			0
$419$	16.3871	−	28.3834i	0.800564	−	1.38662i	−0.118681	−	0.992932i	$-0.537866\pi$
$419$	16.3871	−	28.3834i	0.800564	−	1.38662i	0.919245	−	0.393686i	$-0.128800\pi$
$420$		0			0
$421$	−3.95297	+	6.84674i	−0.192656	+	0.333690i	−0.946130	−	0.323788i	$-0.895043\pi$
$421$	−3.95297	+	6.84674i	−0.192656	+	0.333690i	0.753474	+	0.657478i	$0.228377\pi$
$422$		0			0
$423$	1.31228	+	2.27294i	0.0638054	+	0.110514i
$424$		0			0
$425$	2.07433	−	3.59284i	0.100620	−	0.174278i
$426$		0			0
$427$	53.6397			2.59581
$428$		0			0
$429$	−8.52370			−0.411528
$430$		0			0
$431$	16.6914	+	28.9103i	0.803996	+	1.39256i	0.916967	+	0.398964i	$0.130630\pi$
$431$	16.6914	+	28.9103i	0.803996	+	1.39256i	−0.112971	+	0.993598i	$0.536037\pi$
$432$		0			0
$433$	6.16195	+	10.6728i	0.296125	+	0.512903i	0.975246	−	0.221123i	$-0.0709723\pi$
$433$	6.16195	+	10.6728i	0.296125	+	0.512903i	−0.679121	+	0.734026i	$0.737639\pi$
$434$		0			0
$435$	−1.80555	−	3.12731i	−0.0865695	−	0.149943i
$436$		0			0
$437$	−0.707497	−	1.22542i	−0.0338442	−	0.0586199i
$438$		0			0
$439$	−9.59893	+	16.6258i	−0.458132	+	0.793508i	−0.998862	−	0.0476883i	$-0.984815\pi$
$439$	−9.59893	+	16.6258i	−0.458132	+	0.793508i	0.540730	+	0.841196i	$0.318148\pi$
$440$		0			0
$441$	−3.13360	+	5.42755i	−0.149219	+	0.258455i
$442$		0			0
$443$	0.980447	+	1.69818i	0.0465824	+	0.0806831i	0.888376	−	0.459116i	$-0.151834\pi$
$443$	0.980447	+	1.69818i	0.0465824	+	0.0806831i	−0.841794	+	0.539799i	$0.818500\pi$
$444$		0			0
$445$	−12.3635			−0.586085
$446$		0			0
$447$	15.8039			0.747499
$448$		0			0
$449$	−11.0489	−	19.1373i	−0.521432	−	0.903146i	−0.999689	−	0.0249267i	$-0.992065\pi$
$449$	−11.0489	−	19.1373i	−0.521432	−	0.903146i	0.478257	−	0.878220i	$-0.341269\pi$
$450$		0			0
$451$	−3.57950	+	6.19988i	−0.168552	+	0.291941i
$452$		0			0
$453$	−8.58459	+	14.8689i	−0.403339	+	0.698604i
$454$		0			0
$455$	−11.8891			−0.557369
$456$		0			0
$457$	7.35633	+	12.7415i	0.344114	+	0.596024i	0.985192	−	0.171452i	$-0.0548458\pi$
$457$	7.35633	+	12.7415i	0.344114	+	0.596024i	−0.641078	+	0.767476i	$0.721513\pi$
$458$		0			0
$459$	−2.07433	+	3.59284i	−0.0968213	+	0.167699i
$460$		0			0
$461$	−2.95152			−0.137466			−0.0687331	−	0.997635i	$-0.521896\pi$
$461$	−2.95152			−0.137466			−0.0687331	+	0.997635i	$0.521896\pi$
$462$		0			0
$463$	−10.5910	+	18.3442i	−0.492206	+	0.852526i	−0.999960	−	0.00897612i	$-0.997143\pi$
$463$	−10.5910	+	18.3442i	−0.492206	+	0.852526i	0.507753	+	0.861502i	$0.330476\pi$
$464$		0			0
$465$	−3.41308	−	5.91164i	−0.158278	−	0.274146i
$466$		0			0
$467$	−4.95909	+	8.58940i	−0.229479	+	0.397470i	−0.957654	−	0.287922i	$-0.907036\pi$
$467$	−4.95909	+	8.58940i	−0.229479	+	0.397470i	0.728175	+	0.685392i	$0.240369\pi$
$468$		0			0
$469$	7.83898	−	28.7655i	0.361971	−	1.32827i
$470$		0			0
$471$	−11.0035	+	19.0587i	−0.507017	+	0.878179i
$472$		0			0
$473$	1.38025	+	2.39066i	0.0634639	+	0.109923i
$474$		0			0
$475$	0.703946	−	1.21927i	0.0322992	−	0.0559439i
$476$		0			0
$477$	6.31987			0.289367
$478$		0			0
$479$	−9.55602	+	16.5515i	−0.436626	+	0.756258i	−0.997427	−	0.0716929i	$-0.977160\pi$
$479$	−9.55602	+	16.5515i	−0.436626	+	0.756258i	0.560801	+	0.827950i	$0.310493\pi$
$480$		0			0
$481$	−9.16573	−	15.8755i	−0.417921	−	0.723861i
$482$		0			0
$483$	−3.66079			−0.166572
$484$		0			0
$485$	3.74690	−	6.48983i	0.170138	−	0.294688i
$486$		0			0
$487$	−4.02263	+	6.96740i	−0.182283	+	0.315723i	−0.942657	−	0.333762i	$-0.891682\pi$
$487$	−4.02263	+	6.96740i	−0.182283	+	0.315723i	0.760375	+	0.649485i	$0.225015\pi$
$488$		0			0
$489$	8.03401	+	13.9153i	0.363311	+	0.629272i
$490$		0			0
$491$	24.3996			1.10114			0.550569	−	0.834789i	$-0.314411\pi$
$491$	24.3996			1.10114			0.550569	+	0.834789i	$0.314411\pi$
$492$		0			0
$493$	−14.9812			−0.674720
$494$		0			0
$495$	−1.30569	−	2.26152i	−0.0586863	−	0.101648i
$496$		0			0
$497$	6.55540	−	11.3543i	0.294050	−	0.509309i
$498$		0			0
$499$	13.4560	−	23.3064i	0.602372	−	1.04334i	−0.390088	−	0.920777i	$-0.627556\pi$
$499$	13.4560	−	23.3064i	0.602372	−	1.04334i	0.992461	−	0.122562i	$-0.0391111\pi$
$500$		0			0
$501$	−12.0741	−	20.9130i	−0.539432	−	0.934324i
$502$		0			0
$503$	2.99528	+	5.18798i	0.133553	+	0.231320i	0.925044	−	0.379861i	$-0.124028\pi$
$503$	2.99528	+	5.18798i	0.133553	+	0.231320i	−0.791491	+	0.611181i	$0.790695\pi$
$504$		0			0
$505$	2.74729	+	4.75844i	0.122253	+	0.211748i
$506$		0			0
$507$	−1.17295	−	2.03160i	−0.0520923	−	0.0902266i
$508$		0			0
$509$	−35.5567			−1.57602			−0.788012	−	0.615660i	$-0.788889\pi$
$509$	−35.5567			−1.57602			−0.788012	+	0.615660i	$0.788889\pi$
$510$		0			0
$511$	18.6528			0.825151
$512$		0			0
$513$	−0.703946	+	1.21927i	−0.0310800	+	0.0538321i
$514$		0			0
$515$	−1.28008	−	2.21717i	−0.0564072	−	0.0977001i
$516$		0			0
$517$	−3.42687	+	5.93551i	−0.150713	+	0.261043i
$518$		0			0
$519$	10.5394	−	18.2548i	0.462628	−	0.801296i
$520$		0			0
$521$	−14.6607			−0.642299			−0.321149	−	0.947029i	$-0.604069\pi$
$521$	−14.6607			−0.642299			−0.321149	+	0.947029i	$0.604069\pi$
$522$		0			0
$523$	−15.1324	+	26.2101i	−0.661694	+	1.14609i	0.318476	+	0.947931i	$0.396829\pi$
$523$	−15.1324	+	26.2101i	−0.661694	+	1.14609i	−0.980170	+	0.198157i	$0.936504\pi$
$524$		0			0
$525$	−1.82121	−	3.15443i	−0.0794840	−	0.137670i
$526$		0			0
$527$	−28.3194			−1.23361
$528$		0			0
$529$	10.9949	+	19.0438i	0.478041	+	0.827991i
$530$		0			0
$531$	−12.1494			−0.527239
$532$		0			0
$533$	8.94832			0.387595
$534$		0			0
$535$	10.2714			0.444073
$536$		0			0
$537$	−5.38462			−0.232364
$538$		0			0
$539$	−16.3660			−0.704934
$540$		0			0
$541$	32.5443			1.39919			0.699594	−	0.714541i	$-0.253364\pi$
$541$	32.5443			1.39919			0.699594	+	0.714541i	$0.253364\pi$
$542$		0			0
$543$	−9.51402	−	16.4788i	−0.408286	−	0.707172i
$544$		0			0
$545$	−13.6659			−0.585383
$546$		0			0
$547$	−12.6984	−	21.9944i	−0.542946	−	0.940411i	−0.998733	−	0.0503215i	$-0.983975\pi$
$547$	−12.6984	−	21.9944i	−0.542946	−	0.940411i	0.455787	−	0.890089i	$-0.349358\pi$
$548$		0			0
$549$	7.36320	−	12.7534i	0.314254	−	0.544303i
$550$		0			0
$551$	−5.08404			−0.216587
$552$		0			0
$553$	−25.0100	+	43.3186i	−1.06353	+	1.84209i
$554$		0			0
$555$	2.80807	−	4.86373i	0.119196	−	0.206454i
$556$		0			0
$557$	−1.93976	−	3.35976i	−0.0821903	−	0.142358i	0.822000	−	0.569487i	$-0.192858\pi$
$557$	−1.93976	−	3.35976i	−0.0821903	−	0.142358i	−0.904190	+	0.427129i	$0.859525\pi$
$558$		0			0
$559$	1.72523	−	2.98818i	0.0729693	−	0.126387i
$560$		0			0
$561$	−10.8337			−0.457399
$562$		0			0
$563$	−24.4443			−1.03020			−0.515101	−	0.857129i	$-0.672246\pi$
$563$	−24.4443			−1.03020			−0.515101	+	0.857129i	$0.672246\pi$
$564$		0			0
$565$	10.2461	+	17.7468i	0.431058	+	0.746614i
$566$		0			0
$567$	1.82121	+	3.15443i	0.0764836	+	0.132473i
$568$		0			0
$569$	8.70282	+	15.0737i	0.364841	+	0.631924i	0.988751	−	0.149573i	$-0.0477899\pi$
$569$	8.70282	+	15.0737i	0.364841	+	0.631924i	−0.623909	+	0.781497i	$0.714457\pi$
$570$		0			0
$571$	20.8192	+	36.0599i	0.871257	+	1.50906i	0.860697	+	0.509117i	$0.170028\pi$
$571$	20.8192	+	36.0599i	0.871257	+	1.50906i	0.0105596	+	0.999944i	$0.496639\pi$
$572$		0			0
$573$	−2.19404	+	3.80019i	−0.0916573	+	0.158755i
$574$		0			0
$575$	0.502523	−	0.870395i	0.0209566	−	0.0362980i
$576$		0			0
$577$	14.3924	+	24.9283i	0.599161	+	1.03778i	0.992945	+	0.118575i	$0.0378326\pi$
$577$	14.3924	+	24.9283i	0.599161	+	1.03778i	−0.393784	+	0.919203i	$0.628834\pi$
$578$		0			0
$579$	1.53758			0.0638997
$580$		0			0
$581$	−56.2521			−2.33373
$582$		0			0
$583$	8.25178	+	14.2925i	0.341754	+	0.591935i
$584$		0			0
$585$	−1.63203	+	2.82676i	−0.0674762	+	0.116872i
$586$		0			0
$587$	−8.57478	+	14.8520i	−0.353919	+	0.613006i	−0.986932	−	0.161135i	$-0.948485\pi$
$587$	−8.57478	+	14.8520i	−0.353919	+	0.613006i	0.633013	+	0.774141i	$0.281818\pi$
$588$		0			0
$589$	−9.61051			−0.395994
$590$		0			0
$591$	3.67344	+	6.36259i	0.151105	+	0.261722i
$592$		0			0
$593$	4.37872	−	7.58417i	0.179813	−	0.311444i	−0.762004	−	0.647573i	$-0.775784\pi$
$593$	4.37872	−	7.58417i	0.179813	−	0.311444i	0.941816	+	0.336128i	$0.109118\pi$
$594$		0			0
$595$	−15.1111			−0.619496
$596$		0			0
$597$	8.66810	−	15.0136i	0.354762	−	0.614465i
$598$		0			0
$599$	7.52619	+	13.0357i	0.307512	+	0.532626i	0.977817	−	0.209459i	$-0.0671703\pi$
$599$	7.52619	+	13.0357i	0.307512	+	0.532626i	−0.670306	+	0.742085i	$0.733837\pi$
$600$		0			0
$601$	19.9520	−	34.5579i	0.813860	−	1.40965i	−0.0962834	−	0.995354i	$-0.530696\pi$
$601$	19.9520	−	34.5579i	0.813860	−	1.40965i	0.910144	−	0.414293i	$-0.135971\pi$
$602$		0			0
$603$	−5.76325	−	5.81249i	−0.234698	−	0.236703i
$604$		0			0
$605$	−2.09035	+	3.62060i	−0.0849850	+	0.147198i
$606$		0			0
$607$	−2.82578	−	4.89439i	−0.114695	−	0.198657i	0.802963	−	0.596029i	$-0.203256\pi$
$607$	−2.82578	−	4.89439i	−0.114695	−	0.198657i	−0.917658	+	0.397372i	$0.869922\pi$
$608$		0			0
$609$	−6.57657	+	11.3909i	−0.266496	+	0.461584i
$610$		0			0
$611$	8.56675			0.346574
$612$		0			0
$613$	14.8424	−	25.7078i	0.599479	−	1.03833i	−0.393419	−	0.919359i	$-0.628708\pi$
$613$	14.8424	−	25.7078i	0.599479	−	1.03833i	0.992898	−	0.118969i	$-0.0379588\pi$
$614$		0			0
$615$	1.37073	+	2.37418i	0.0552733	+	0.0957361i
$616$		0			0
$617$	−5.05547			−0.203526			−0.101763	−	0.994809i	$-0.532448\pi$
$617$	−5.05547			−0.203526			−0.101763	+	0.994809i	$0.532448\pi$
$618$		0			0
$619$	−14.1760	+	24.5536i	−0.569782	+	0.986892i	0.426805	+	0.904344i	$0.359639\pi$
$619$	−14.1760	+	24.5536i	−0.569782	+	0.986892i	−0.996587	+	0.0825480i	$0.973694\pi$
$620$		0			0
$621$	−0.502523	+	0.870395i	−0.0201655	+	0.0349277i
$622$		0			0
$623$	22.5165	+	38.9997i	0.902103	+	1.56249i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−3.67654			−0.146827
$628$		0			0
$629$	−11.6497	−	20.1779i	−0.464505	−	0.804546i
$630$		0			0
$631$	12.4910	−	21.6351i	0.497261	−	0.861281i	−0.502734	−	0.864441i	$-0.667673\pi$
$631$	12.4910	−	21.6351i	0.497261	−	0.861281i	0.999995	+	0.00316020i	$0.00100592\pi$
$632$		0			0
$633$	−13.4978	+	23.3790i	−0.536491	+	0.929230i
$634$		0			0
$635$	0.698579	+	1.20997i	0.0277223	+	0.0480164i
$636$		0			0
$637$	10.2283	+	17.7159i	0.405259	+	0.701929i
$638$		0			0
$639$	−1.79974	−	3.11724i	−0.0711966	−	0.123316i
$640$		0			0
$641$	2.87972	+	4.98782i	0.113742	+	0.197007i	0.917276	−	0.398252i	$-0.130383\pi$
$641$	2.87972	+	4.98782i	0.113742	+	0.197007i	−0.803534	+	0.595259i	$0.797050\pi$
$642$		0			0
$643$	−2.63228			−0.103807			−0.0519036	−	0.998652i	$-0.516529\pi$
$643$	−2.63228			−0.103807			−0.0519036	+	0.998652i	$0.516529\pi$
$644$		0			0
$645$	1.05710			0.0416234
$646$		0			0
$647$	4.44075	−	7.69160i	0.174584	−	0.302388i	−0.765433	−	0.643515i	$-0.777475\pi$
$647$	4.44075	−	7.69160i	0.174584	−	0.302388i	0.940017	+	0.341127i	$0.110809\pi$
$648$		0			0
$649$	−15.8633	−	27.4761i	−0.622690	−	1.07853i
$650$		0			0
$651$	−12.4319	+	21.5326i	−0.487244	+	0.843931i
$652$		0			0
$653$	−13.6690	+	23.6754i	−0.534910	+	0.926492i	0.464258	+	0.885700i	$0.346321\pi$
$653$	−13.6690	+	23.6754i	−0.534910	+	0.926492i	−0.999168	+	0.0407913i	$0.987012\pi$
$654$		0			0
$655$	−20.6388			−0.806425
$656$		0			0
$657$	2.56050	−	4.43491i	0.0998945	−	0.173022i
$658$		0			0
$659$	−15.9846	−	27.6861i	−0.622671	−	1.07850i	−0.988986	−	0.148007i	$-0.952714\pi$
$659$	−15.9846	−	27.6861i	−0.622671	−	1.07850i	0.366315	−	0.930491i	$-0.380619\pi$
$660$		0			0
$661$	−33.0701			−1.28628			−0.643139	−	0.765749i	$-0.722368\pi$
$661$	−33.0701			−1.28628			−0.643139	+	0.765749i	$0.722368\pi$
$662$		0			0
$663$	6.77074	+	11.7273i	0.262954	+	0.455449i
$664$		0			0
$665$	−5.12813			−0.198860
$666$		0			0
$667$	−3.62932			−0.140528
$668$		0			0
$669$	−19.0470			−0.736401
$670$		0			0
$671$	38.4562			1.48458
$672$		0			0
$673$	−33.6815			−1.29833			−0.649163	−	0.760649i	$-0.724881\pi$
$673$	−33.6815			−1.29833			−0.649163	+	0.760649i	$0.724881\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	10.3155	+	17.8670i	0.396458	+	0.686686i	0.993286	−	0.115683i	$-0.0369057\pi$
$677$	10.3155	+	17.8670i	0.396458	+	0.686686i	−0.596828	+	0.802369i	$0.703572\pi$
$678$		0			0
$679$	−27.2956			−1.04751
$680$		0			0
$681$	−1.36485	−	2.36399i	−0.0523012	−	0.0905884i
$682$		0			0
$683$	−12.8986	+	22.3410i	−0.493551	+	0.854856i	−0.999972	−	0.00743052i	$-0.997635\pi$
$683$	−12.8986	+	22.3410i	−0.493551	+	0.854856i	0.506421	+	0.862286i	$0.330968\pi$
$684$		0			0
$685$	−6.85069			−0.261751
$686$		0			0
$687$	0.116389	−	0.201591i	0.00444051	−	0.00769120i
$688$		0			0
$689$	10.3142	−	17.8648i	0.392941	−	0.680593i
$690$		0			0
$691$	−0.346025	−	0.599332i	−0.0131634	−	0.0227997i	0.859369	−	0.511357i	$-0.170857\pi$
$691$	−0.346025	−	0.599332i	−0.0131634	−	0.0227997i	−0.872532	+	0.488557i	$0.837523\pi$
$692$		0			0
$693$	−4.75586	+	8.23740i	−0.180660	+	0.312913i
$694$		0			0
$695$	−4.13729			−0.156936
$696$		0			0
$697$	11.3734			0.430798
$698$		0			0
$699$	14.6726	+	25.4138i	0.554970	+	0.961237i
$700$		0			0
$701$	−10.7270	−	18.5797i	−0.405153	−	0.701745i	0.589187	−	0.807997i	$-0.299448\pi$
$701$	−10.7270	−	18.5797i	−0.405153	−	0.701745i	−0.994339	+	0.106252i	$0.966115\pi$
$702$		0			0
$703$	−3.95346	−	6.84760i	−0.149108	−	0.258262i
$704$		0			0
$705$	1.31228	+	2.27294i	0.0494234	+	0.0856039i
$706$		0			0
$707$	10.0068	−	17.3322i	0.376343	−	0.651845i
$708$		0			0
$709$	22.2726	−	38.5773i	0.836466	−	1.44880i	−0.0563649	−	0.998410i	$-0.517951\pi$
$709$	22.2726	−	38.5773i	0.836466	−	1.44880i	0.892831	−	0.450392i	$-0.148716\pi$
$710$		0			0
$711$	6.86632	+	11.8928i	0.257507	+	0.446016i
$712$		0			0
$713$	−6.86061			−0.256932
$714$		0			0
$715$	−8.52370			−0.318768
$716$		0			0
$717$	7.81920	+	13.5433i	0.292014	+	0.505782i
$718$		0			0
$719$	−0.126352	+	0.218847i	−0.00471212	+	0.00816163i	−0.868372	−	0.495914i	$-0.834833\pi$
$719$	−0.126352	+	0.218847i	−0.00471212	+	0.00816163i	0.863660	+	0.504075i	$0.168167\pi$
$720$		0			0
$721$	−4.66259	+	8.07585i	−0.173644	+	0.300760i
$722$		0			0
$723$	8.60145			0.319891
$724$		0			0
$725$	−1.80555	−	3.12731i	−0.0670565	−	0.116145i
$726$		0			0
$727$	6.40582	−	11.0952i	0.237579	−	0.411498i	−0.722440	−	0.691433i	$-0.756980\pi$
$727$	6.40582	−	11.0952i	0.237579	−	0.411498i	0.960019	+	0.279935i	$0.0903129\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	2.19278	−	3.79800i	0.0811028	−	0.140474i
$732$		0			0
$733$	−26.5049	−	45.9079i	−0.978982	−	1.69565i	−0.666114	−	0.745850i	$-0.732043\pi$
$733$	−26.5049	−	45.9079i	−0.978982	−	1.69565i	−0.312868	−	0.949796i	$-0.601290\pi$
$734$		0			0
$735$	−3.13360	+	5.42755i	−0.115585	+	0.200198i
$736$		0			0
$737$	5.62005	−	20.6230i	0.207017	−	0.759658i
$738$		0			0
$739$	9.91081	−	17.1660i	0.364575	−	0.631463i	−0.624133	−	0.781318i	$-0.714548\pi$
$739$	9.91081	−	17.1660i	0.364575	−	0.631463i	0.988708	+	0.149856i	$0.0478809\pi$
$740$		0			0
$741$	2.29772	+	3.97977i	0.0844090	+	0.146201i
$742$		0			0
$743$	−17.0050	+	29.4536i	−0.623855	+	1.08055i	0.364907	+	0.931044i	$0.381101\pi$
$743$	−17.0050	+	29.4536i	−0.623855	+	1.08055i	−0.988761	+	0.149504i	$0.952232\pi$
$744$		0			0
$745$	15.8039			0.579010
$746$		0			0
$747$	−7.72181	+	13.3746i	−0.282526	+	0.489350i
$748$		0			0
$749$	−18.7064	−	32.4005i	−0.683518	−	1.18389i
$750$		0			0
$751$	8.75761			0.319570			0.159785	−	0.987152i	$-0.448920\pi$
$751$	8.75761			0.319570			0.159785	+	0.987152i	$0.448920\pi$
$752$		0			0
$753$	−10.5464	+	18.2669i	−0.384332	+	0.665683i
$754$		0			0
$755$	−8.58459	+	14.8689i	−0.312425	+	0.541136i
$756$		0			0
$757$	6.84039	+	11.8479i	0.248618	+	0.430619i	0.963143	−	0.268991i	$-0.0866903\pi$
$757$	6.84039	+	11.8479i	0.248618	+	0.430619i	−0.714525	+	0.699610i	$0.753357\pi$
$758$		0			0
$759$	−2.62455			−0.0952652
$760$		0			0
$761$	−21.1716			−0.767470			−0.383735	−	0.923443i	$-0.625362\pi$
$761$	−21.1716			−0.767470			−0.383735	+	0.923443i	$0.625362\pi$
$762$		0			0
$763$	24.8884	+	43.1081i	0.901022	+	1.56062i
$764$		0			0
$765$	−2.07433	+	3.59284i	−0.0749975	+	0.129899i
$766$		0			0
$767$	−19.8282	+	34.3434i	−0.715955	+	1.24007i
$768$		0			0
$769$	−2.25858	−	3.91198i	−0.0814466	−	0.141070i	0.822425	−	0.568874i	$-0.192621\pi$
$769$	−2.25858	−	3.91198i	−0.0814466	−	0.141070i	−0.903872	+	0.427804i	$0.859287\pi$
$770$		0			0
$771$	−12.9895	−	22.4984i	−0.467805	−	0.810262i
$772$		0			0
$773$	14.5815	+	25.2559i	0.524460	+	0.908392i	0.999594	+	0.0284786i	$0.00906625\pi$
$773$	14.5815	+	25.2559i	0.524460	+	0.908392i	−0.475134	+	0.879913i	$0.657600\pi$
$774$		0			0
$775$	−3.41308	−	5.91164i	−0.122602	−	0.212352i
$776$		0			0
$777$	−20.4563			−0.733867
$778$		0			0
$779$	3.85969			0.138288
$780$		0			0
$781$	4.69980	−	8.14029i	0.168172	−	0.291282i
$782$		0			0
$783$	1.80555	+	3.12731i	0.0645251	+	0.111761i
$784$		0			0
$785$	−11.0035	+	19.0587i	−0.392734	+	0.680234i
$786$		0			0
$787$	13.1830	−	22.8336i	0.469923	−	0.813931i	−0.529485	−	0.848319i	$-0.677615\pi$
$787$	13.1830	−	22.8336i	0.469923	−	0.813931i	0.999409	+	0.0343882i	$0.0109483\pi$
$788$		0			0
$789$	12.9416			0.460734
$790$		0			0
$791$	37.3207	−	64.6413i	1.32697	−	2.29838i
$792$		0			0
$793$	−24.0339	−	41.6280i	−0.853470	−	1.47825i
$794$		0			0
$795$	6.31987			0.224143
$796$		0			0
$797$	−18.8583	−	32.6635i	−0.667995	−	1.15700i	−0.978464	−	0.206417i	$-0.933820\pi$
$797$	−18.8583	−	32.6635i	−0.667995	−	1.15700i	0.310469	−	0.950583i	$-0.399514\pi$
$798$		0			0
$799$	10.8884			0.385205
$800$		0			0
$801$	12.3635			0.436842
$802$		0			0
$803$	13.3729			0.471918
$804$		0			0
$805$	−3.66079			−0.129026
$806$		0			0
$807$	−8.74352			−0.307787
$808$		0			0
$809$	1.92595			0.0677128			0.0338564	−	0.999427i	$-0.489221\pi$
$809$	1.92595			0.0677128			0.0338564	+	0.999427i	$0.489221\pi$
$810$		0			0
$811$	−2.34501	−	4.06167i	−0.0823443	−	0.142625i	0.821912	−	0.569614i	$-0.192907\pi$
$811$	−2.34501	−	4.06167i	−0.0823443	−	0.142625i	−0.904256	+	0.426990i	$0.859574\pi$
$812$		0			0
$813$	−12.3673			−0.433740
$814$		0			0
$815$	8.03401	+	13.9153i	0.281419	+	0.487432i
$816$		0			0
$817$	0.744143	−	1.28889i	0.0260343	−	0.0450927i
$818$		0			0
$819$	11.8891			0.415438
$820$		0			0
$821$	−0.708922	+	1.22789i	−0.0247416	+	0.0428536i	−0.878131	−	0.478420i	$-0.841210\pi$
$821$	−0.708922	+	1.22789i	−0.0247416	+	0.0428536i	0.853390	+	0.521274i	$0.174543\pi$
$822$		0			0
$823$	−1.36075	+	2.35689i	−0.0474327	+	0.0821559i	−0.888767	−	0.458359i	$-0.848437\pi$
$823$	−1.36075	+	2.35689i	−0.0474327	+	0.0821559i	0.841334	+	0.540515i	$0.181771\pi$
$824$		0			0
$825$	−1.30569	−	2.26152i	−0.0454582	−	0.0787360i
$826$		0			0
$827$	−18.5997	+	32.2156i	−0.646775	+	1.12025i	0.337113	+	0.941464i	$0.390550\pi$
$827$	−18.5997	+	32.2156i	−0.646775	+	1.12025i	−0.983888	+	0.178784i	$0.942784\pi$
$828$		0			0
$829$	15.4520			0.536671			0.268335	−	0.963326i	$-0.413526\pi$
$829$	15.4520			0.536671			0.268335	+	0.963326i	$0.413526\pi$
$830$		0			0
$831$	16.7425			0.580792
$832$		0			0
$833$	13.0002	+	22.5170i	0.450431	+	0.780169i
$834$		0			0
$835$	−12.0741	−	20.9130i	−0.417842	−	0.723724i
$836$		0			0
$837$	3.41308	+	5.91164i	0.117973	+	0.204336i
$838$		0			0
$839$	9.51582	+	16.4819i	0.328522	+	0.569018i	0.982219	−	0.187739i	$-0.0601160\pi$
$839$	9.51582	+	16.4819i	0.328522	+	0.569018i	−0.653696	+	0.756757i	$0.726783\pi$
$840$		0			0
$841$	7.97998	−	13.8217i	0.275172	−	0.476611i
$842$		0			0
$843$	3.32890	−	5.76583i	0.114654	−	0.198586i
$844$		0			0
$845$	−1.17295	−	2.03160i	−0.0403505	−	0.0698892i
$846$		0			0
$847$	15.2279			0.523236
$848$		0			0
$849$	−13.0417			−0.447592
$850$		0			0
$851$	−2.82224	−	4.88826i	−0.0967452	−	0.167568i
$852$		0			0
$853$	−13.4037	+	23.2159i	−0.458935	+	0.794898i	−0.998905	−	0.0467858i	$-0.985102\pi$
$853$	−13.4037	+	23.2159i	−0.458935	+	0.794898i	0.539970	+	0.841684i	$0.318436\pi$
$854$		0			0
$855$	−0.703946	+	1.21927i	−0.0240744	+	0.0416981i
$856$		0			0
$857$	−39.7549			−1.35800			−0.679001	−	0.734137i	$-0.737587\pi$
$857$	−39.7549			−1.35800			−0.679001	+	0.734137i	$0.737587\pi$
$858$		0			0
$859$	−14.6491	−	25.3729i	−0.499819	−	0.865713i	0.500181	−	0.865921i	$-0.333267\pi$
$859$	−14.6491	−	25.3729i	−0.499819	−	0.865713i	−1.00000		0.000208569i	$0.999934\pi$
$860$		0			0
$861$	4.99278	−	8.64775i	0.170153	−	0.294714i
$862$		0			0
$863$	−34.6172			−1.17838			−0.589191	−	0.807994i	$-0.700554\pi$
$863$	−34.6172			−1.17838			−0.589191	+	0.807994i	$0.700554\pi$
$864$		0			0
$865$	10.5394	−	18.2548i	0.358350	−	0.620681i
$866$		0			0
$867$	0.105668	+	0.183023i	0.00358869	+	0.00621579i
$868$		0			0
$869$	−17.9306	+	31.0566i	−0.608253	+	1.05352i
$870$		0			0
$871$	−25.8363	+	6.80516i	−0.875430	+	0.230584i
$872$		0			0
$873$	−3.74690	+	6.48983i	−0.126814	+	0.219647i
$874$		0			0
$875$	−1.82121	−	3.15443i	−0.0615681	−	0.106639i
$876$		0			0
$877$	−3.90813	+	6.76908i	−0.131968	+	0.228575i	−0.924435	−	0.381339i	$-0.875463\pi$
$877$	−3.90813	+	6.76908i	−0.131968	+	0.228575i	0.792467	+	0.609915i	$0.208796\pi$
$878$		0			0
$879$	−14.6140			−0.492918
$880$		0			0
$881$	4.35452	−	7.54225i	0.146707	−	0.254105i	−0.783301	−	0.621642i	$-0.786466\pi$
$881$	4.35452	−	7.54225i	0.146707	−	0.254105i	0.930009	+	0.367538i	$0.119799\pi$
$882$		0			0
$883$	3.19358	+	5.53143i	0.107472	+	0.186148i	0.914746	−	0.404030i	$-0.132391\pi$
$883$	3.19358	+	5.53143i	0.107472	+	0.186148i	−0.807273	+	0.590178i	$0.799058\pi$
$884$		0			0
$885$	−12.1494			−0.408397
$886$		0			0
$887$	2.53032	−	4.38265i	0.0849599	−	0.147155i	−0.820414	−	0.571770i	$-0.806257\pi$
$887$	2.53032	−	4.38265i	0.0849599	−	0.147155i	0.905374	+	0.424615i	$0.139590\pi$
$888$		0			0
$889$	2.54451	−	4.40723i	0.0853403	−	0.147814i
$890$		0			0
$891$	1.30569	+	2.26152i	0.0437422	+	0.0757637i
$892$		0			0
$893$	3.69510			0.123652
$894$		0			0
$895$	−5.38462			−0.179988
$896$		0			0
$897$	1.64027	+	2.84102i	0.0547669	+	0.0948590i
$898$		0			0
$899$	−12.3250	+	21.3475i	−0.411062	+	0.711980i
$900$		0			0
$901$	13.1095	−	22.7063i	0.436740	−	0.756456i
$902$		0			0
$903$	−1.92521	−	3.33455i	−0.0640668	−	0.110967i
$904$		0			0
$905$	−9.51402	−	16.4788i	−0.316257	−	0.547773i
$906$		0			0
$907$	−20.6590	−	35.7824i	−0.685970	−	1.18814i	−0.973131	−	0.230253i	$-0.926045\pi$
$907$	−20.6590	−	35.7824i	−0.685970	−	1.18814i	0.287161	−	0.957882i	$-0.407289\pi$
$908$		0			0
$909$	−2.74729	−	4.75844i	−0.0911217	−	0.157827i
$910$		0			0
$911$	−16.5807			−0.549344			−0.274672	−	0.961538i	$-0.588569\pi$
$911$	−16.5807			−0.549344			−0.274672	+	0.961538i	$0.588569\pi$
$912$		0			0
$913$	−40.3291			−1.33470
$914$		0			0
$915$	7.36320	−	12.7534i	0.243420	−	0.421615i
$916$		0			0
$917$	37.5876	+	65.1036i	1.24125	+	2.14991i
$918$		0			0
$919$	9.01121	−	15.6079i	0.297252	−	0.514856i	−0.678254	−	0.734828i	$-0.737263\pi$
$919$	9.01121	−	15.6079i	0.297252	−	0.514856i	0.975506	+	0.219971i	$0.0705964\pi$
$920$		0			0
$921$	−10.6273	+	18.4069i	−0.350180	+	0.606530i
$922$		0			0
$923$	−11.7489			−0.386720
$924$		0			0
$925$	2.80807	−	4.86373i	0.0923289	−	0.159918i
$926$		0			0
$927$	1.28008	+	2.21717i	0.0420434	+	0.0728213i
$928$		0			0
$929$	−12.9612			−0.425244			−0.212622	−	0.977135i	$-0.568200\pi$
$929$	−12.9612			−0.425244			−0.212622	+	0.977135i	$0.568200\pi$
$930$		0			0
$931$	4.41177	+	7.64141i	0.144590	+	0.250437i
$932$		0			0
$933$	−27.3867			−0.896599
$934$		0			0
$935$	−10.8337			−0.354300
$936$		0			0
$937$	38.5314			1.25877			0.629383	−	0.777096i	$-0.283308\pi$
$937$	38.5314			1.25877			0.629383	+	0.777096i	$0.283308\pi$
$938$		0			0
$939$	15.2522			0.497738
$940$		0			0
$941$	−31.0884			−1.01345			−0.506727	−	0.862107i	$-0.669145\pi$
$941$	−31.0884			−1.01345			−0.506727	+	0.862107i	$0.669145\pi$
$942$		0			0
$943$	2.75530			0.0897248
$944$		0			0
$945$	1.82121	+	3.15443i	0.0592439	+	0.102613i
$946$		0			0
$947$	−0.860818			−0.0279728			−0.0139864	−	0.999902i	$-0.504452\pi$
$947$	−0.860818			−0.0279728			−0.0139864	+	0.999902i	$0.504452\pi$
$948$		0			0
$949$	−8.35763	−	14.4758i	−0.271300	−	0.469906i
$950$		0			0
$951$	−3.81626	+	6.60996i	−0.123751	+	0.214343i
$952$		0			0
$953$	26.6456			0.863137			0.431568	−	0.902080i	$-0.357960\pi$
$953$	26.6456			0.863137			0.431568	+	0.902080i	$0.357960\pi$
$954$		0			0
$955$	−2.19404	+	3.80019i	−0.0709974	+	0.122971i
$956$		0			0
$957$	−4.71497	+	8.16657i	−0.152413	+	0.263988i
$958$		0			0
$959$	12.4765	+	21.6100i	0.402888	+	0.697823i
$960$		0			0
$961$	−7.79830	+	13.5070i	−0.251558	+	0.435711i
$962$		0			0
$963$	−10.2714			−0.330993
$964$		0			0
$965$	1.53758			0.0494965
$966$		0			0
$967$	1.58324	+	2.74225i	0.0509135	+	0.0881848i	0.890359	−	0.455259i	$-0.150453\pi$
$967$	1.58324	+	2.74225i	0.0509135	+	0.0881848i	−0.839445	+	0.543444i	$0.817120\pi$
$968$		0			0
$969$	2.92043	+	5.05833i	0.0938177	+	0.162497i
$970$		0			0
$971$	7.72153	+	13.3741i	0.247796	+	0.429195i	0.962914	−	0.269809i	$-0.0869605\pi$
$971$	7.72153	+	13.3741i	0.247796	+	0.429195i	−0.715118	+	0.699004i	$0.753627\pi$
$972$		0			0
$973$	7.53487	+	13.0508i	0.241557	+	0.418389i
$974$		0			0
$975$	−1.63203	+	2.82676i	−0.0522668	+	0.0905288i
$976$		0			0
$977$	14.9418	−	25.8799i	0.478029	−	0.827971i	−0.521653	−	0.853157i	$-0.674685\pi$
$977$	14.9418	−	25.8799i	0.478029	−	0.827971i	0.999683	+	0.0251864i	$0.00801793\pi$
$978$		0			0
$979$	16.1429	+	27.9602i	0.515928	+	0.893613i
$980$		0			0
$981$	13.6659			0.436319
$982$		0			0
$983$	−20.8448			−0.664846			−0.332423	−	0.943130i	$-0.607866\pi$
$983$	−20.8448			−0.664846			−0.332423	+	0.943130i	$0.607866\pi$
$984$		0			0
$985$	3.67344	+	6.36259i	0.117046	+	0.202729i
$986$		0			0
$987$	4.77988	−	8.27900i	0.152145	−	0.263523i
$988$		0			0
$989$	0.531218	−	0.920097i	0.0168918	−	0.0292574i
$990$		0			0
$991$	−43.1703			−1.37135			−0.685675	−	0.727908i	$-0.740493\pi$
$991$	−43.1703			−1.37135			−0.685675	+	0.727908i	$0.740493\pi$
$992$		0			0
$993$	−10.4339	−	18.0721i	−0.331110	−	0.573499i
$994$		0			0
$995$	8.66810	−	15.0136i	0.274797	−	0.475963i
$996$		0			0
$997$	53.8171			1.70440			0.852202	−	0.523213i	$-0.175267\pi$
$997$	53.8171			1.70440			0.852202	+	0.523213i	$0.175267\pi$
$998$		0			0
$999$	−2.80807	+	4.86373i	−0.0888435	+	0.153881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.l.3781.9	yes	22
67.37	even	3	inner	4020.2.q.l.841.9	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.l.841.9	✓	22	67.37	even	3	inner
4020.2.q.l.3781.9	yes	22	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:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(1.82121 + 3.15443i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(1.82121 + 3.15443i) q^{7} +1.00000 q^{9} +(1.30569 + 2.26152i) q^{11} +(1.63203 - 2.82676i) q^{13} +1.00000 q^{15} +(2.07433 - 3.59284i) q^{17} +(0.703946 - 1.21927i) q^{19} +(-1.82121 - 3.15443i) q^{21} +(0.502523 - 0.870395i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-1.80555 - 3.12731i) q^{29} +(-3.41308 - 5.91164i) q^{31} +(-1.30569 - 2.26152i) q^{33} +(-1.82121 - 3.15443i) q^{35} +(2.80807 - 4.86373i) q^{37} +(-1.63203 + 2.82676i) q^{39} +(1.37073 + 2.37418i) q^{41} +1.05710 q^{43} -1.00000 q^{45} +(1.31228 + 2.27294i) q^{47} +(-3.13360 + 5.42755i) q^{49} +(-2.07433 + 3.59284i) q^{51} +6.31987 q^{53} +(-1.30569 - 2.26152i) q^{55} +(-0.703946 + 1.21927i) q^{57} -12.1494 q^{59} +(7.36320 - 12.7534i) q^{61} +(1.82121 + 3.15443i) q^{63} +(-1.63203 + 2.82676i) q^{65} +(-5.76325 - 5.81249i) q^{67} +(-0.502523 + 0.870395i) q^{69} +(-1.79974 - 3.11724i) q^{71} +(2.56050 - 4.43491i) q^{73} -1.00000 q^{75} +(-4.75586 + 8.23740i) q^{77} +(6.86632 + 11.8928i) q^{79} +1.00000 q^{81} +(-7.72181 + 13.3746i) q^{83} +(-2.07433 + 3.59284i) q^{85} +(1.80555 + 3.12731i) q^{87} +12.3635 q^{89} +11.8891 q^{91} +(3.41308 + 5.91164i) q^{93} +(-0.703946 + 1.21927i) q^{95} +(-3.74690 + 6.48983i) q^{97} +(1.30569 + 2.26152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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