LMFDB - Embedded newform 924.2.r.d.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [924,2,Mod(169,924)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(924, base_ring=CyclotomicField(10))

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("924.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 924 = 2^{2} \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	924.r (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.37817714677$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			169.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	924.169
Dual form			924.2.r.d.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 + 0.951057i) q^{3} +(2.61803 - 1.90211i) q^{5} +(0.309017 + 0.951057i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(2.19098 - 2.48990i) q^{11} +(-1.61803 - 1.17557i) q^{13} +(1.00000 + 3.07768i) q^{15} +(4.23607 - 3.07768i) q^{17} -1.00000 q^{21} -1.85410 q^{23} +(1.69098 - 5.20431i) q^{25} +(0.809017 - 0.587785i) q^{27} +(0.500000 + 1.53884i) q^{29} +(-1.00000 - 0.726543i) q^{31} +(1.69098 + 2.85317i) q^{33} +(2.61803 + 1.90211i) q^{35} +(-0.663119 - 2.04087i) q^{37} +(1.61803 - 1.17557i) q^{39} +(2.76393 - 8.50651i) q^{41} +2.85410 q^{43} -3.23607 q^{45} +(-2.61803 + 8.05748i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(1.61803 + 4.97980i) q^{51} +(-1.92705 - 1.40008i) q^{53} +(1.00000 - 10.6861i) q^{55} +(4.61803 + 14.2128i) q^{59} +(5.23607 - 3.80423i) q^{61} +(0.309017 - 0.951057i) q^{63} -6.47214 q^{65} +5.32624 q^{67} +(0.572949 - 1.76336i) q^{69} +(2.92705 - 2.12663i) q^{71} +(-0.381966 - 1.17557i) q^{73} +(4.42705 + 3.21644i) q^{75} +(3.04508 + 1.31433i) q^{77} +(6.16312 + 4.47777i) q^{79} +(0.309017 + 0.951057i) q^{81} +(3.85410 - 2.80017i) q^{83} +(5.23607 - 16.1150i) q^{85} -1.61803 q^{87} -2.76393 q^{89} +(0.618034 - 1.90211i) q^{91} +(1.00000 - 0.726543i) q^{93} +(-9.85410 - 7.15942i) q^{97} +(-3.23607 + 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} + 6 q^{5} - q^{7} - q^{9} + 11 q^{11} - 2 q^{13} + 4 q^{15} + 8 q^{17} - 4 q^{21} + 6 q^{23} + 9 q^{25} + q^{27} + 2 q^{29} - 4 q^{31} + 9 q^{33} + 6 q^{35} + 13 q^{37} + 2 q^{39} + 20 q^{41}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q + q^3 + 6 * q^5 - q^7 - q^9 + 11 * q^11 - 2 * q^13 + 4 * q^15 + 8 * q^17 - 4 * q^21 + 6 * q^23 + 9 * q^25 + q^27 + 2 * q^29 - 4 * q^31 + 9 * q^33 + 6 * q^35 + 13 * q^37 + 2 * q^39 + 20 * q^41 - 2 * q^43 - 4 * q^45 - 6 * q^47 - q^49 + 2 * q^51 - q^53 + 4 * q^55 + 14 * q^59 + 12 * q^61 - q^63 - 8 * q^65 - 10 * q^67 + 9 * q^69 + 5 * q^71 - 6 * q^73 + 11 * q^75 + q^77 + 9 * q^79 - q^81 + 2 * q^83 + 12 * q^85 - 2 * q^87 - 20 * q^89 - 2 * q^91 + 4 * q^93 - 26 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/924\mathbb{Z}\right)^\times$.

$n$	$463$	$617$	$661$	$673$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$		0			0
$5$	2.61803	−	1.90211i	1.17082	−	0.850651i	0.179714	−	0.983719i	$-0.442483\pi$
$5$	2.61803	−	1.90211i	1.17082	−	0.850651i	0.991107	+	0.133068i	$0.0424829\pi$
$6$		0			0
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	2.19098	−	2.48990i	0.660606	−	0.750733i
$11$	2.19098	−	2.48990i	0.660606	−	0.750733i
$12$		0			0
$13$	−1.61803	−	1.17557i	−0.448762	−	0.326045i	0.340345	−	0.940301i	$-0.389456\pi$
$13$	−1.61803	−	1.17557i	−0.448762	−	0.326045i	−0.789107	+	0.614256i	$0.789456\pi$
$14$		0			0
$15$	1.00000	+	3.07768i	0.258199	+	0.794654i
$16$		0			0
$17$	4.23607	−	3.07768i	1.02740	−	0.746448i	0.0596113	−	0.998222i	$-0.481014\pi$
$17$	4.23607	−	3.07768i	1.02740	−	0.746448i	0.967786	+	0.251774i	$0.0810139\pi$
$18$		0			0
$19$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$19$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	−1.85410			−0.386607			−0.193303	−	0.981139i	$-0.561920\pi$
$23$	−1.85410			−0.386607			−0.193303	+	0.981139i	$0.561920\pi$
$24$		0			0
$25$	1.69098	−	5.20431i	0.338197	−	1.04086i
$26$		0			0
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$		0			0
$29$	0.500000	+	1.53884i	0.0928477	+	0.285756i	0.986687	−	0.162632i	$-0.0519984\pi$
$29$	0.500000	+	1.53884i	0.0928477	+	0.285756i	−0.893839	+	0.448388i	$0.851998\pi$
$30$		0			0
$31$	−1.00000	−	0.726543i	−0.179605	−	0.130491i	0.494350	−	0.869263i	$-0.335406\pi$
$31$	−1.00000	−	0.726543i	−0.179605	−	0.130491i	−0.673955	+	0.738772i	$0.735406\pi$
$32$		0			0
$33$	1.69098	+	2.85317i	0.294362	+	0.496673i
$34$		0			0
$35$	2.61803	+	1.90211i	0.442529	+	0.321516i
$36$		0			0
$37$	−0.663119	−	2.04087i	−0.109016	−	0.335517i	0.881636	−	0.471930i	$-0.156443\pi$
$37$	−0.663119	−	2.04087i	−0.109016	−	0.335517i	−0.990652	+	0.136413i	$0.956443\pi$
$38$		0			0
$39$	1.61803	−	1.17557i	0.259093	−	0.188242i
$40$		0			0
$41$	2.76393	−	8.50651i	0.431654	−	1.32849i	−0.464823	−	0.885403i	$-0.653882\pi$
$41$	2.76393	−	8.50651i	0.431654	−	1.32849i	0.896477	−	0.443090i	$-0.146118\pi$
$42$		0			0
$43$	2.85410			0.435246			0.217623	−	0.976033i	$-0.430170\pi$
$43$	2.85410			0.435246			0.217623	+	0.976033i	$0.430170\pi$
$44$		0			0
$45$	−3.23607			−0.482405
$46$		0			0
$47$	−2.61803	+	8.05748i	−0.381880	+	1.17530i	0.556839	+	0.830620i	$0.312014\pi$
$47$	−2.61803	+	8.05748i	−0.381880	+	1.17530i	−0.938719	+	0.344684i	$0.887986\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$		0			0
$51$	1.61803	+	4.97980i	0.226570	+	0.697311i
$52$		0			0
$53$	−1.92705	−	1.40008i	−0.264701	−	0.192316i	0.447516	−	0.894276i	$-0.352309\pi$
$53$	−1.92705	−	1.40008i	−0.264701	−	0.192316i	−0.712217	+	0.701960i	$0.752309\pi$
$54$		0			0
$55$	1.00000	−	10.6861i	0.134840	−	1.44092i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.61803	+	14.2128i	0.601217	+	1.85036i	0.520960	+	0.853581i	$0.325574\pi$
$59$	4.61803	+	14.2128i	0.601217	+	1.85036i	0.0802564	+	0.996774i	$0.474426\pi$
$60$		0			0
$61$	5.23607	−	3.80423i	0.670410	−	0.487081i	−0.199753	−	0.979846i	$-0.564014\pi$
$61$	5.23607	−	3.80423i	0.670410	−	0.487081i	0.870162	+	0.492765i	$0.164014\pi$
$62$		0			0
$63$	0.309017	−	0.951057i	0.0389325	−	0.119822i
$64$		0			0
$65$	−6.47214			−0.802770
$66$		0			0
$67$	5.32624			0.650704			0.325352	−	0.945593i	$-0.394517\pi$
$67$	5.32624			0.650704			0.325352	+	0.945593i	$0.394517\pi$
$68$		0			0
$69$	0.572949	−	1.76336i	0.0689750	−	0.212283i
$70$		0			0
$71$	2.92705	−	2.12663i	0.347377	−	0.252384i	−0.400391	−	0.916344i	$-0.631126\pi$
$71$	2.92705	−	2.12663i	0.347377	−	0.252384i	0.747768	+	0.663960i	$0.231126\pi$
$72$		0			0
$73$	−0.381966	−	1.17557i	−0.0447057	−	0.137590i	0.926212	−	0.377003i	$-0.123045\pi$
$73$	−0.381966	−	1.17557i	−0.0447057	−	0.137590i	−0.970918	+	0.239412i	$0.923045\pi$
$74$		0			0
$75$	4.42705	+	3.21644i	0.511192	+	0.371403i
$76$		0			0
$77$	3.04508	+	1.31433i	0.347020	+	0.149782i
$78$		0			0
$79$	6.16312	+	4.47777i	0.693405	+	0.503788i	0.877778	−	0.479068i	$-0.159025\pi$
$79$	6.16312	+	4.47777i	0.693405	+	0.503788i	−0.184373	+	0.982856i	$0.559025\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	3.85410	−	2.80017i	0.423043	−	0.307358i	−0.355818	−	0.934555i	$-0.615798\pi$
$83$	3.85410	−	2.80017i	0.423043	−	0.307358i	0.778861	+	0.627197i	$0.215798\pi$
$84$		0			0
$85$	5.23607	−	16.1150i	0.567931	−	1.74791i
$86$		0			0
$87$	−1.61803			−0.173471
$88$		0			0
$89$	−2.76393			−0.292976			−0.146488	−	0.989212i	$-0.546797\pi$
$89$	−2.76393			−0.292976			−0.146488	+	0.989212i	$0.546797\pi$
$90$		0			0
$91$	0.618034	−	1.90211i	0.0647876	−	0.199396i
$92$		0			0
$93$	1.00000	−	0.726543i	0.103695	−	0.0753390i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−9.85410	−	7.15942i	−1.00053	−	0.726929i	−0.0383302	−	0.999265i	$-0.512204\pi$
$97$	−9.85410	−	7.15942i	−1.00053	−	0.726929i	−0.962202	+	0.272336i	$0.912204\pi$
$98$		0			0
$99$	−3.23607	+	0.726543i	−0.325237	+	0.0730203i
$100$		0			0
$101$	13.0902	+	9.51057i	1.30252	+	0.946337i	0.999977	−	0.00679891i	$-0.00216418\pi$
$101$	13.0902	+	9.51057i	1.30252	+	0.946337i	0.302544	+	0.953136i	$0.402164\pi$
$102$		0			0
$103$	4.85410	+	14.9394i	0.478289	+	1.47202i	0.841470	+	0.540303i	$0.181691\pi$
$103$	4.85410	+	14.9394i	0.478289	+	1.47202i	−0.363181	+	0.931718i	$0.618309\pi$
$104$		0			0
$105$	−2.61803	+	1.90211i	−0.255494	+	0.185627i
$106$		0			0
$107$	0.572949	−	1.76336i	0.0553891	−	0.170470i	−0.919535	−	0.393008i	$-0.871434\pi$
$107$	0.572949	−	1.76336i	0.0553891	−	0.170470i	0.974924	+	0.222538i	$0.0714343\pi$
$108$		0			0
$109$	1.85410			0.177591			0.0887954	−	0.996050i	$-0.471698\pi$
$109$	1.85410			0.177591			0.0887954	+	0.996050i	$0.471698\pi$
$110$		0			0
$111$	2.14590			0.203680
$112$		0			0
$113$	−2.97214	+	9.14729i	−0.279595	+	0.860505i	0.708372	+	0.705839i	$0.249430\pi$
$113$	−2.97214	+	9.14729i	−0.279595	+	0.860505i	−0.987967	+	0.154666i	$0.950570\pi$
$114$		0			0
$115$	−4.85410	+	3.52671i	−0.452647	+	0.328868i
$116$		0			0
$117$	0.618034	+	1.90211i	0.0571373	+	0.175850i
$118$		0			0
$119$	4.23607	+	3.07768i	0.388320	+	0.282131i
$120$		0			0
$121$	−1.39919	−	10.9106i	−0.127199	−	0.991877i
$122$		0			0
$123$	7.23607	+	5.25731i	0.652454	+	0.474036i
$124$		0			0
$125$	−0.472136	−	1.45309i	−0.0422291	−	0.129968i
$126$		0			0
$127$	−3.73607	+	2.71441i	−0.331522	+	0.240865i	−0.741076	−	0.671421i	$-0.765684\pi$
$127$	−3.73607	+	2.71441i	−0.331522	+	0.240865i	0.409554	+	0.912286i	$0.365684\pi$
$128$		0			0
$129$	−0.881966	+	2.71441i	−0.0776528	+	0.238991i
$130$		0			0
$131$	−18.0000			−1.57267			−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000			−1.57267			−0.786334	+	0.617802i	$0.788023\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.00000	−	3.07768i	0.0860663	−	0.264885i
$136$		0			0
$137$	−9.97214	+	7.24518i	−0.851977	+	0.618998i	−0.925690	−	0.378282i	$-0.876515\pi$
$137$	−9.97214	+	7.24518i	−0.851977	+	0.618998i	0.0737134	+	0.997279i	$0.476515\pi$
$138$		0			0
$139$	−3.38197	−	10.4086i	−0.286855	−	0.882848i	−0.985837	−	0.167708i	$-0.946363\pi$
$139$	−3.38197	−	10.4086i	−0.286855	−	0.882848i	0.698982	−	0.715139i	$-0.253637\pi$
$140$		0			0
$141$	−6.85410	−	4.97980i	−0.577220	−	0.419375i
$142$		0			0
$143$	−6.47214	+	1.45309i	−0.541227	+	0.121513i
$144$		0			0
$145$	4.23607	+	3.07768i	0.351786	+	0.255588i
$146$		0			0
$147$	−0.309017	−	0.951057i	−0.0254873	−	0.0784418i
$148$		0			0
$149$	−14.5623	+	10.5801i	−1.19299	+	0.866758i	−0.993577	−	0.113157i	$-0.963904\pi$
$149$	−14.5623	+	10.5801i	−1.19299	+	0.866758i	−0.199413	+	0.979915i	$0.563904\pi$
$150$		0			0
$151$	3.98936	−	12.2780i	0.324649	−	0.999168i	−0.646949	−	0.762533i	$-0.723956\pi$
$151$	3.98936	−	12.2780i	0.324649	−	0.999168i	0.971599	−	0.236635i	$-0.0760445\pi$
$152$		0			0
$153$	−5.23607			−0.423311
$154$		0			0
$155$	−4.00000			−0.321288
$156$		0			0
$157$	0.708204	−	2.17963i	0.0565208	−	0.173953i	−0.918811	−	0.394699i	$-0.870849\pi$
$157$	0.708204	−	2.17963i	0.0565208	−	0.173953i	0.975331	+	0.220745i	$0.0708490\pi$
$158$		0			0
$159$	1.92705	−	1.40008i	0.152825	−	0.111034i
$160$		0			0
$161$	−0.572949	−	1.76336i	−0.0451547	−	0.138972i
$162$		0			0
$163$	−17.4443	−	12.6740i	−1.36634	−	0.992705i	−0.998013	−	0.0630087i	$-0.979930\pi$
$163$	−17.4443	−	12.6740i	−1.36634	−	0.992705i	−0.368328	−	0.929696i	$-0.620070\pi$
$164$		0			0
$165$	9.85410	+	4.25325i	0.767141	+	0.331115i
$166$		0			0
$167$	3.61803	+	2.62866i	0.279972	+	0.203411i	0.718905	−	0.695108i	$-0.244644\pi$
$167$	3.61803	+	2.62866i	0.279972	+	0.203411i	−0.438933	+	0.898520i	$0.644644\pi$
$168$		0			0
$169$	−2.78115	−	8.55951i	−0.213935	−	0.658424i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.61803	+	8.05748i	−0.199045	+	0.612599i	0.800860	+	0.598852i	$0.204376\pi$
$173$	−2.61803	+	8.05748i	−0.199045	+	0.612599i	−0.999906	+	0.0137473i	$0.995624\pi$
$174$		0			0
$175$	5.47214			0.413655
$176$		0			0
$177$	−14.9443			−1.12328
$178$		0			0
$179$	−3.33688	+	10.2699i	−0.249410	+	0.767606i	0.745470	+	0.666540i	$0.232225\pi$
$179$	−3.33688	+	10.2699i	−0.249410	+	0.767606i	−0.994880	+	0.101066i	$0.967775\pi$
$180$		0			0
$181$	−19.1803	+	13.9353i	−1.42566	+	1.03581i	−0.434860	+	0.900498i	$0.643202\pi$
$181$	−19.1803	+	13.9353i	−1.42566	+	1.03581i	−0.990804	+	0.135307i	$0.956798\pi$
$182$		0			0
$183$	2.00000	+	6.15537i	0.147844	+	0.455018i
$184$		0			0
$185$	−5.61803	−	4.08174i	−0.413046	−	0.300096i
$186$		0			0
$187$	1.61803	−	17.2905i	0.118322	−	1.26441i
$188$		0			0
$189$	0.809017	+	0.587785i	0.0588473	+	0.0427551i
$190$		0			0
$191$	−3.82624	−	11.7759i	−0.276857	−	0.852078i	−0.988722	−	0.149762i	$-0.952149\pi$
$191$	−3.82624	−	11.7759i	−0.276857	−	0.852078i	0.711865	−	0.702316i	$-0.247851\pi$
$192$		0			0
$193$	−16.3992	+	11.9147i	−1.18044	+	0.857639i	−0.992221	−	0.124488i	$-0.960271\pi$
$193$	−16.3992	+	11.9147i	−1.18044	+	0.857639i	−0.188218	+	0.982127i	$0.560271\pi$
$194$		0			0
$195$	2.00000	−	6.15537i	0.143223	−	0.440795i
$196$		0			0
$197$	−4.90983			−0.349811			−0.174905	−	0.984585i	$-0.555962\pi$
$197$	−4.90983			−0.349811			−0.174905	+	0.984585i	$0.555962\pi$
$198$		0			0
$199$	−19.2361			−1.36361			−0.681804	−	0.731535i	$-0.738804\pi$
$199$	−19.2361			−1.36361			−0.681804	+	0.731535i	$0.738804\pi$
$200$		0			0
$201$	−1.64590	+	5.06555i	−0.116093	+	0.357297i
$202$		0			0
$203$	−1.30902	+	0.951057i	−0.0918750	+	0.0667511i
$204$		0			0
$205$	−8.94427	−	27.5276i	−0.624695	−	1.92261i
$206$		0			0
$207$	1.50000	+	1.08981i	0.104257	+	0.0757473i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−16.4443	−	11.9475i	−1.13207	−	0.822497i	−0.146076	−	0.989273i	$-0.546664\pi$
$211$	−16.4443	−	11.9475i	−1.13207	−	0.822497i	−0.985995	+	0.166776i	$0.946664\pi$
$212$		0			0
$213$	1.11803	+	3.44095i	0.0766064	+	0.235770i
$214$		0			0
$215$	7.47214	−	5.42882i	0.509595	−	0.370243i
$216$		0			0
$217$	0.381966	−	1.17557i	0.0259295	−	0.0798029i
$218$		0			0
$219$	1.23607			0.0835257
$220$		0			0
$221$	−10.4721			−0.704432
$222$		0			0
$223$	−5.90983	+	18.1886i	−0.395751	+	1.21800i	0.532623	+	0.846352i	$0.321206\pi$
$223$	−5.90983	+	18.1886i	−0.395751	+	1.21800i	−0.928375	+	0.371645i	$0.878794\pi$
$224$		0			0
$225$	−4.42705	+	3.21644i	−0.295137	+	0.214429i
$226$		0			0
$227$	4.70820	+	14.4904i	0.312494	+	0.961759i	0.976774	+	0.214274i	$0.0687387\pi$
$227$	4.70820	+	14.4904i	0.312494	+	0.961759i	−0.664279	+	0.747485i	$0.731261\pi$
$228$		0			0
$229$	17.7984	+	12.9313i	1.17615	+	0.854523i	0.991732	−	0.128325i	$-0.0409601\pi$
$229$	17.7984	+	12.9313i	1.17615	+	0.854523i	0.184418	+	0.982848i	$0.440960\pi$
$230$		0			0
$231$	−2.19098	+	2.48990i	−0.144156	+	0.163823i
$232$		0			0
$233$	−6.09017	−	4.42477i	−0.398980	−	0.289876i	0.370145	−	0.928974i	$-0.379308\pi$
$233$	−6.09017	−	4.42477i	−0.398980	−	0.289876i	−0.769126	+	0.639098i	$0.779308\pi$
$234$		0			0
$235$	8.47214	+	26.0746i	0.552661	+	1.70092i
$236$		0			0
$237$	−6.16312	+	4.47777i	−0.400338	+	0.290862i
$238$		0			0
$239$	6.11803	−	18.8294i	0.395743	−	1.21797i	−0.532639	−	0.846343i	$-0.678800\pi$
$239$	6.11803	−	18.8294i	0.395743	−	1.21797i	0.928382	−	0.371628i	$-0.121200\pi$
$240$		0			0
$241$	29.1246			1.87608			0.938041	−	0.346525i	$-0.112639\pi$
$241$	29.1246			1.87608			0.938041	+	0.346525i	$0.112639\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−1.00000	+	3.07768i	−0.0638877	+	0.196626i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	1.47214	+	4.53077i	0.0932928	+	0.287126i
$250$		0			0
$251$	19.5623	+	14.2128i	1.23476	+	0.897107i	0.997238	−	0.0742747i	$-0.0236642\pi$
$251$	19.5623	+	14.2128i	1.23476	+	0.897107i	0.237524	+	0.971382i	$0.423664\pi$
$252$		0			0
$253$	−4.06231	+	4.61653i	−0.255395	+	0.290238i
$254$		0			0
$255$	13.7082	+	9.95959i	0.858441	+	0.623694i
$256$		0			0
$257$	2.52786	+	7.77997i	0.157684	+	0.485301i	0.998423	−	0.0561395i	$-0.0178792\pi$
$257$	2.52786	+	7.77997i	0.157684	+	0.485301i	−0.840739	+	0.541440i	$0.817879\pi$
$258$		0			0
$259$	1.73607	−	1.26133i	0.107874	−	0.0783751i
$260$		0			0
$261$	0.500000	−	1.53884i	0.0309492	−	0.0952519i
$262$		0			0
$263$	2.09017			0.128885			0.0644427	−	0.997921i	$-0.479473\pi$
$263$	2.09017			0.128885			0.0644427	+	0.997921i	$0.479473\pi$
$264$		0			0
$265$	−7.70820			−0.473511
$266$		0			0
$267$	0.854102	−	2.62866i	0.0522702	−	0.160871i
$268$		0			0
$269$	18.4164	−	13.3803i	1.12287	−	0.815812i	0.138227	−	0.990401i	$-0.455860\pi$
$269$	18.4164	−	13.3803i	1.12287	−	0.815812i	0.984641	+	0.174589i	$0.0558597\pi$
$270$		0			0
$271$	−0.437694	−	1.34708i	−0.0265880	−	0.0818295i	0.936882	−	0.349646i	$-0.113698\pi$
$271$	−0.437694	−	1.34708i	−0.0265880	−	0.0818295i	−0.963470	+	0.267816i	$0.913698\pi$
$272$		0			0
$273$	1.61803	+	1.17557i	0.0979279	+	0.0711488i
$274$		0			0
$275$	−9.25329	−	15.6129i	−0.557994	−	0.941495i
$276$		0			0
$277$	−1.73607	−	1.26133i	−0.104310	−	0.0757858i	0.534407	−	0.845227i	$-0.320535\pi$
$277$	−1.73607	−	1.26133i	−0.104310	−	0.0757858i	−0.638718	+	0.769441i	$0.720535\pi$
$278$		0			0
$279$	0.381966	+	1.17557i	0.0228677	+	0.0703796i
$280$		0			0
$281$	3.92705	−	2.85317i	0.234268	−	0.170206i	−0.464458	−	0.885595i	$-0.653751\pi$
$281$	3.92705	−	2.85317i	0.234268	−	0.170206i	0.698726	+	0.715389i	$0.253751\pi$
$282$		0			0
$283$	−6.38197	+	19.6417i	−0.379369	+	1.16758i	0.561115	+	0.827738i	$0.310372\pi$
$283$	−6.38197	+	19.6417i	−0.379369	+	1.16758i	−0.940484	+	0.339839i	$0.889628\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.94427			0.527964
$288$		0			0
$289$	3.21885	−	9.90659i	0.189344	−	0.582741i
$290$		0			0
$291$	9.85410	−	7.15942i	0.577658	−	0.419693i
$292$		0			0
$293$	4.81966	+	14.8334i	0.281568	+	0.866576i	0.987407	+	0.158203i	$0.0505702\pi$
$293$	4.81966	+	14.8334i	0.281568	+	0.866576i	−0.705839	+	0.708372i	$0.749430\pi$
$294$		0			0
$295$	39.1246	+	28.4257i	2.27792	+	1.65501i
$296$		0			0
$297$	0.309017	−	3.30220i	0.0179310	−	0.191613i
$298$		0			0
$299$	3.00000	+	2.17963i	0.173494	+	0.126051i
$300$		0			0
$301$	0.881966	+	2.71441i	0.0508357	+	0.156456i
$302$		0			0
$303$	−13.0902	+	9.51057i	−0.752011	+	0.546368i
$304$		0			0
$305$	6.47214	−	19.9192i	0.370593	−	1.14057i
$306$		0			0
$307$	−33.7082			−1.92383			−0.961914	−	0.273351i	$-0.911868\pi$
$307$	−33.7082			−1.92383			−0.961914	+	0.273351i	$0.911868\pi$
$308$		0			0
$309$	−15.7082			−0.893609
$310$		0			0
$311$	−6.14590	+	18.9151i	−0.348502	+	1.07258i	0.611180	+	0.791491i	$0.290695\pi$
$311$	−6.14590	+	18.9151i	−0.348502	+	1.07258i	−0.959682	+	0.281087i	$0.909305\pi$
$312$		0			0
$313$	9.94427	−	7.22494i	0.562083	−	0.408378i	−0.270137	−	0.962822i	$-0.587069\pi$
$313$	9.94427	−	7.22494i	0.562083	−	0.408378i	0.832221	+	0.554444i	$0.187069\pi$
$314$		0			0
$315$	−1.00000	−	3.07768i	−0.0563436	−	0.173408i
$316$		0			0
$317$	−9.92705	−	7.21242i	−0.557559	−	0.405090i	0.273006	−	0.962012i	$-0.411982\pi$
$317$	−9.92705	−	7.21242i	−0.557559	−	0.405090i	−0.830565	+	0.556922i	$0.811982\pi$
$318$		0			0
$319$	4.92705	+	2.12663i	0.275862	+	0.119068i
$320$		0			0
$321$	1.50000	+	1.08981i	0.0837218	+	0.0608275i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−8.85410	+	6.43288i	−0.491137	+	0.356832i
$326$		0			0
$327$	−0.572949	+	1.76336i	−0.0316842	+	0.0975138i
$328$		0			0
$329$	−8.47214			−0.467084
$330$		0			0
$331$	7.67376			0.421788			0.210894	−	0.977509i	$-0.432362\pi$
$331$	7.67376			0.421788			0.210894	+	0.977509i	$0.432362\pi$
$332$		0			0
$333$	−0.663119	+	2.04087i	−0.0363387	+	0.111839i
$334$		0			0
$335$	13.9443	−	10.1311i	0.761857	−	0.553521i
$336$		0			0
$337$	−10.6631	−	32.8177i	−0.580857	−	1.78769i	−0.615307	−	0.788288i	$-0.710968\pi$
$337$	−10.6631	−	32.8177i	−0.580857	−	1.78769i	0.0344495	−	0.999406i	$-0.489032\pi$
$338$		0			0
$339$	−7.78115	−	5.65334i	−0.422614	−	0.307047i
$340$		0			0
$341$	−4.00000	+	0.898056i	−0.216612	+	0.0486325i
$342$		0			0
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$		0			0
$345$	−1.85410	−	5.70634i	−0.0998215	−	0.307219i
$346$		0			0
$347$	−10.6353	+	7.72696i	−0.570930	+	0.414805i	−0.835443	−	0.549577i	$-0.814789\pi$
$347$	−10.6353	+	7.72696i	−0.570930	+	0.414805i	0.264513	+	0.964382i	$0.414789\pi$
$348$		0			0
$349$	−1.52786	+	4.70228i	−0.0817847	+	0.251707i	−0.983585	−	0.180446i	$-0.942246\pi$
$349$	−1.52786	+	4.70228i	−0.0817847	+	0.251707i	0.901800	+	0.432153i	$0.142246\pi$
$350$		0			0
$351$	−2.00000			−0.106752
$352$		0			0
$353$	−1.52786			−0.0813200			−0.0406600	−	0.999173i	$-0.512946\pi$
$353$	−1.52786			−0.0813200			−0.0406600	+	0.999173i	$0.512946\pi$
$354$		0			0
$355$	3.61803	−	11.1352i	0.192025	−	0.590993i
$356$		0			0
$357$	−4.23607	+	3.07768i	−0.224196	+	0.162888i
$358$		0			0
$359$	−10.2812	−	31.6421i	−0.542618	−	1.67001i	−0.726586	−	0.687076i	$-0.758894\pi$
$359$	−10.2812	−	31.6421i	−0.542618	−	1.67001i	0.183967	−	0.982932i	$-0.441106\pi$
$360$		0			0
$361$	15.3713	+	11.1679i	0.809017	+	0.587785i
$362$		0			0
$363$	10.8090	+	2.04087i	0.567326	+	0.107118i
$364$		0			0
$365$	−3.23607	−	2.35114i	−0.169384	−	0.123064i
$366$		0			0
$367$	7.94427	+	24.4500i	0.414688	+	1.27628i	0.912530	+	0.409010i	$0.134126\pi$
$367$	7.94427	+	24.4500i	0.414688	+	1.27628i	−0.497842	+	0.867268i	$0.665874\pi$
$368$		0			0
$369$	−7.23607	+	5.25731i	−0.376695	+	0.273685i
$370$		0			0
$371$	0.736068	−	2.26538i	0.0382147	−	0.117613i
$372$		0			0
$373$	10.5836			0.547998			0.273999	−	0.961730i	$-0.411654\pi$
$373$	10.5836			0.547998			0.273999	+	0.961730i	$0.411654\pi$
$374$		0			0
$375$	1.52786			0.0788986
$376$		0			0
$377$	1.00000	−	3.07768i	0.0515026	−	0.158509i
$378$		0			0
$379$	−17.6803	+	12.8455i	−0.908178	+	0.659830i	−0.940553	−	0.339646i	$-0.889693\pi$
$379$	−17.6803	+	12.8455i	−0.908178	+	0.659830i	0.0323754	+	0.999476i	$0.489693\pi$
$380$		0			0
$381$	−1.42705	−	4.39201i	−0.0731100	−	0.225010i
$382$		0			0
$383$	24.1803	+	17.5680i	1.23556	+	0.897685i	0.997294	−	0.0735154i	$-0.0234218\pi$
$383$	24.1803	+	17.5680i	1.23556	+	0.897685i	0.238264	+	0.971201i	$0.423422\pi$
$384$		0			0
$385$	10.4721	−	2.35114i	0.533709	−	0.119825i
$386$		0			0
$387$	−2.30902	−	1.67760i	−0.117374	−	0.0852772i
$388$		0			0
$389$	−3.13525	−	9.64932i	−0.158964	−	0.489240i	0.839577	−	0.543240i	$-0.182803\pi$
$389$	−3.13525	−	9.64932i	−0.158964	−	0.489240i	−0.998541	+	0.0540004i	$0.982803\pi$
$390$		0			0
$391$	−7.85410	+	5.70634i	−0.397199	+	0.288582i
$392$		0			0
$393$	5.56231	−	17.1190i	0.280581	−	0.863540i
$394$		0			0
$395$	24.6525			1.24040
$396$		0			0
$397$	−11.1246			−0.558328			−0.279164	−	0.960243i	$-0.590057\pi$
$397$	−11.1246			−0.558328			−0.279164	+	0.960243i	$0.590057\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	22.6803	−	16.4782i	1.13260	−	0.822884i	0.146531	−	0.989206i	$-0.453189\pi$
$401$	22.6803	−	16.4782i	1.13260	−	0.822884i	0.986071	+	0.166323i	$0.0531893\pi$
$402$		0			0
$403$	0.763932	+	2.35114i	0.0380542	+	0.117119i
$404$		0			0
$405$	2.61803	+	1.90211i	0.130091	+	0.0945168i
$406$		0			0
$407$	−6.53444	−	2.82041i	−0.323900	−	0.139803i
$408$		0			0
$409$	20.9443	+	15.2169i	1.03563	+	0.752427i	0.969427	−	0.245379i	$-0.0789124\pi$
$409$	20.9443	+	15.2169i	1.03563	+	0.752427i	0.0662003	+	0.997806i	$0.478912\pi$
$410$		0			0
$411$	−3.80902	−	11.7229i	−0.187885	−	0.578250i
$412$		0			0
$413$	−12.0902	+	8.78402i	−0.594918	+	0.432233i
$414$		0			0
$415$	4.76393	−	14.6619i	0.233852	−	0.719723i
$416$		0			0
$417$	10.9443			0.535943
$418$		0			0
$419$	−14.6525			−0.715820			−0.357910	−	0.933756i	$-0.616511\pi$
$419$	−14.6525			−0.715820			−0.357910	+	0.933756i	$0.616511\pi$
$420$		0			0
$421$	4.01064	−	12.3435i	0.195467	−	0.601585i	−0.804504	−	0.593947i	$-0.797569\pi$
$421$	4.01064	−	12.3435i	0.195467	−	0.601585i	0.999971	−	0.00763774i	$-0.00243119\pi$
$422$		0			0
$423$	6.85410	−	4.97980i	0.333258	−	0.242126i
$424$		0			0
$425$	−8.85410	−	27.2501i	−0.429487	−	1.32183i
$426$		0			0
$427$	5.23607	+	3.80423i	0.253391	+	0.184099i
$428$		0			0
$429$	0.618034	−	6.60440i	0.0298390	−	0.318863i
$430$		0			0
$431$	−4.20820	−	3.05744i	−0.202702	−	0.147272i	0.481804	−	0.876279i	$-0.339982\pi$
$431$	−4.20820	−	3.05744i	−0.202702	−	0.147272i	−0.684506	+	0.729008i	$0.739982\pi$
$432$		0			0
$433$	−2.85410	−	8.78402i	−0.137159	−	0.422133i	0.858760	−	0.512378i	$-0.171235\pi$
$433$	−2.85410	−	8.78402i	−0.137159	−	0.422133i	−0.995920	+	0.0902444i	$0.971235\pi$
$434$		0			0
$435$	−4.23607	+	3.07768i	−0.203104	+	0.147564i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−2.76393			−0.131915			−0.0659576	−	0.997822i	$-0.521010\pi$
$439$	−2.76393			−0.131915			−0.0659576	+	0.997822i	$0.521010\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$		0			0
$443$	−2.64590	+	8.14324i	−0.125710	+	0.386897i	−0.994030	−	0.109109i	$-0.965200\pi$
$443$	−2.64590	+	8.14324i	−0.125710	+	0.386897i	0.868319	+	0.496005i	$0.165200\pi$
$444$		0			0
$445$	−7.23607	+	5.25731i	−0.343023	+	0.249220i
$446$		0			0
$447$	−5.56231	−	17.1190i	−0.263088	−	0.809702i
$448$		0			0
$449$	15.2082	+	11.0494i	0.717720	+	0.521454i	0.885655	−	0.464344i	$-0.153710\pi$
$449$	15.2082	+	11.0494i	0.717720	+	0.521454i	−0.167935	+	0.985798i	$0.553710\pi$
$450$		0			0
$451$	−15.1246	−	25.5195i	−0.712190	−	1.20167i
$452$		0			0
$453$	10.4443	+	7.58821i	0.490715	+	0.356525i
$454$		0			0
$455$	−2.00000	−	6.15537i	−0.0937614	−	0.288568i
$456$		0			0
$457$	15.6803	−	11.3924i	0.733495	−	0.532916i	−0.157172	−	0.987571i	$-0.550238\pi$
$457$	15.6803	−	11.3924i	0.733495	−	0.532916i	0.890667	+	0.454656i	$0.150238\pi$
$458$		0			0
$459$	1.61803	−	4.97980i	0.0755234	−	0.232437i
$460$		0			0
$461$	−14.1803			−0.660444			−0.330222	−	0.943903i	$-0.607124\pi$
$461$	−14.1803			−0.660444			−0.330222	+	0.943903i	$0.607124\pi$
$462$		0			0
$463$	−14.2705			−0.663207			−0.331603	−	0.943419i	$-0.607590\pi$
$463$	−14.2705			−0.663207			−0.331603	+	0.943419i	$0.607590\pi$
$464$		0			0
$465$	1.23607	−	3.80423i	0.0573213	−	0.176417i
$466$		0			0
$467$	16.7984	−	12.2047i	0.777336	−	0.564768i	−0.126842	−	0.991923i	$-0.540484\pi$
$467$	16.7984	−	12.2047i	0.777336	−	0.564768i	0.904178	+	0.427155i	$0.140484\pi$
$468$		0			0
$469$	1.64590	+	5.06555i	0.0760005	+	0.233906i
$470$		0			0
$471$	1.85410	+	1.34708i	0.0854325	+	0.0620704i
$472$		0			0
$473$	6.25329	−	7.10642i	0.287527	−	0.326754i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.736068	+	2.26538i	0.0337022	+	0.103725i
$478$		0			0
$479$	19.7082	−	14.3188i	0.900491	−	0.654245i	−0.0381012	−	0.999274i	$-0.512131\pi$
$479$	19.7082	−	14.3188i	0.900491	−	0.654245i	0.938592	+	0.345029i	$0.112131\pi$
$480$		0			0
$481$	−1.32624	+	4.08174i	−0.0604712	+	0.186111i
$482$		0			0
$483$	1.85410			0.0843646
$484$		0			0
$485$	−39.4164			−1.78981
$486$		0			0
$487$	−7.11803	+	21.9071i	−0.322549	+	0.992703i	0.649986	+	0.759946i	$0.274775\pi$
$487$	−7.11803	+	21.9071i	−0.322549	+	0.992703i	−0.972535	+	0.232757i	$0.925225\pi$
$488$		0			0
$489$	17.4443	−	12.6740i	0.788857	−	0.573138i
$490$		0			0
$491$	4.58359	+	14.1068i	0.206855	+	0.636633i	0.999632	+	0.0271219i	$0.00863424\pi$
$491$	4.58359	+	14.1068i	0.206855	+	0.636633i	−0.792778	+	0.609511i	$0.791366\pi$
$492$		0			0
$493$	6.85410	+	4.97980i	0.308693	+	0.224279i
$494$		0			0
$495$	−7.09017	+	8.05748i	−0.318679	+	0.362157i
$496$		0			0
$497$	2.92705	+	2.12663i	0.131296	+	0.0953923i
$498$		0			0
$499$	−2.77051	−	8.52675i	−0.124025	−	0.381710i	0.869697	−	0.493586i	$-0.164314\pi$
$499$	−2.77051	−	8.52675i	−0.124025	−	0.381710i	−0.993722	+	0.111876i	$0.964314\pi$
$500$		0			0
$501$	−3.61803	+	2.62866i	−0.161642	+	0.117440i
$502$		0			0
$503$	12.9098	−	39.7324i	0.575621	−	1.77158i	−0.0584345	−	0.998291i	$-0.518611\pi$
$503$	12.9098	−	39.7324i	0.575621	−	1.77158i	0.634055	−	0.773288i	$-0.281389\pi$
$504$		0			0
$505$	52.3607			2.33002
$506$		0			0
$507$	9.00000			0.399704
$508$		0			0
$509$	−12.2361	+	37.6587i	−0.542354	+	1.66919i	0.184845	+	0.982768i	$0.440822\pi$
$509$	−12.2361	+	37.6587i	−0.542354	+	1.66919i	−0.727199	+	0.686427i	$0.759178\pi$
$510$		0			0
$511$	1.00000	−	0.726543i	0.0442374	−	0.0321403i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	41.1246	+	29.8788i	1.81217	+	1.31662i
$516$		0			0
$517$	14.3262	+	24.1724i	0.630067	+	1.06310i
$518$		0			0
$519$	−6.85410	−	4.97980i	−0.300862	−	0.218589i
$520$		0			0
$521$	−12.0000	−	36.9322i	−0.525730	−	1.61803i	−0.762869	−	0.646553i	$-0.776210\pi$
$521$	−12.0000	−	36.9322i	−0.525730	−	1.61803i	0.237139	−	0.971476i	$-0.423790\pi$
$522$		0			0
$523$	5.70820	−	4.14725i	0.249602	−	0.181347i	−0.455948	−	0.890006i	$-0.650700\pi$
$523$	5.70820	−	4.14725i	0.249602	−	0.181347i	0.705551	+	0.708660i	$0.250700\pi$
$524$		0			0
$525$	−1.69098	+	5.20431i	−0.0738005	+	0.227135i
$526$		0			0
$527$	−6.47214			−0.281931
$528$		0			0
$529$	−19.5623			−0.850535
$530$		0			0
$531$	4.61803	−	14.2128i	0.200406	−	0.616785i
$532$		0			0
$533$	−14.4721	+	10.5146i	−0.626858	+	0.455439i
$534$		0			0
$535$	−1.85410	−	5.70634i	−0.0801598	−	0.246707i
$536$		0			0
$537$	−8.73607	−	6.34712i	−0.376989	−	0.273899i
$538$		0			0
$539$	−0.309017	+	3.30220i	−0.0133103	+	0.142236i
$540$		0			0
$541$	34.9164	+	25.3683i	1.50117	+	1.09067i	0.969911	+	0.243459i	$0.0782822\pi$
$541$	34.9164	+	25.3683i	1.50117	+	1.09067i	0.531262	+	0.847207i	$0.321718\pi$
$542$		0			0
$543$	−7.32624	−	22.5478i	−0.314399	−	0.967621i
$544$		0			0
$545$	4.85410	−	3.52671i	0.207927	−	0.151068i
$546$		0			0
$547$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$547$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$548$		0			0
$549$	−6.47214			−0.276224
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−2.35410	+	7.24518i	−0.100107	+	0.308096i
$554$		0			0
$555$	5.61803	−	4.08174i	0.238472	−	0.173260i
$556$		0			0
$557$	7.97214	+	24.5357i	0.337790	+	1.03961i	0.965331	+	0.261028i	$0.0840615\pi$
$557$	7.97214	+	24.5357i	0.337790	+	1.03961i	−0.627541	+	0.778584i	$0.715939\pi$
$558$		0			0
$559$	−4.61803	−	3.35520i	−0.195322	−	0.141910i
$560$		0			0
$561$	15.9443	+	6.88191i	0.673168	+	0.290554i
$562$		0			0
$563$	22.7082	+	16.4985i	0.957037	+	0.695328i	0.952461	−	0.304662i	$-0.0985434\pi$
$563$	22.7082	+	16.4985i	0.957037	+	0.695328i	0.00457605	+	0.999990i	$0.498543\pi$
$564$		0			0
$565$	9.61803	+	29.6013i	0.404634	+	1.24533i
$566$		0			0
$567$	−0.809017	+	0.587785i	−0.0339755	+	0.0246847i
$568$		0			0
$569$	−11.8541	+	36.4832i	−0.496950	+	1.52945i	0.316946	+	0.948444i	$0.397343\pi$
$569$	−11.8541	+	36.4832i	−0.496950	+	1.52945i	−0.813896	+	0.581011i	$0.802657\pi$
$570$		0			0
$571$	9.56231			0.400170			0.200085	−	0.979779i	$-0.435878\pi$
$571$	9.56231			0.400170			0.200085	+	0.979779i	$0.435878\pi$
$572$		0			0
$573$	12.3820			0.517264
$574$		0			0
$575$	−3.13525	+	9.64932i	−0.130749	+	0.402405i
$576$		0			0
$577$	30.1246	−	21.8868i	1.25410	−	0.911160i	0.255651	−	0.966769i	$-0.417710\pi$
$577$	30.1246	−	21.8868i	1.25410	−	0.911160i	0.998453	+	0.0556091i	$0.0177101\pi$
$578$		0			0
$579$	−6.26393	−	19.2784i	−0.260320	−	0.801183i
$580$		0			0
$581$	3.85410	+	2.80017i	0.159895	+	0.116171i
$582$		0			0
$583$	−7.70820	+	1.73060i	−0.319241	+	0.0716741i
$584$		0			0
$585$	5.23607	+	3.80423i	0.216485	+	0.157285i
$586$		0			0
$587$	−4.88854	−	15.0454i	−0.201772	−	0.620990i	−0.999831	−	0.0184101i	$-0.994140\pi$
$587$	−4.88854	−	15.0454i	−0.201772	−	0.620990i	0.798059	−	0.602580i	$-0.205860\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	1.51722	−	4.66953i	0.0624101	−	0.192079i
$592$		0			0
$593$	38.0689			1.56330			0.781651	−	0.623716i	$-0.214378\pi$
$593$	38.0689			1.56330			0.781651	+	0.623716i	$0.214378\pi$
$594$		0			0
$595$	16.9443			0.694647
$596$		0			0
$597$	5.94427	−	18.2946i	0.243283	−	0.748748i
$598$		0			0
$599$	2.73607	−	1.98787i	0.111793	−	0.0812222i	−0.530484	−	0.847695i	$-0.677990\pi$
$599$	2.73607	−	1.98787i	0.111793	−	0.0812222i	0.642277	+	0.766473i	$0.277990\pi$
$600$		0			0
$601$	−12.7082	−	39.1118i	−0.518378	−	1.59540i	−0.777050	−	0.629439i	$-0.783285\pi$
$601$	−12.7082	−	39.1118i	−0.518378	−	1.59540i	0.258671	−	0.965965i	$-0.416715\pi$
$602$		0			0
$603$	−4.30902	−	3.13068i	−0.175477	−	0.127491i
$604$		0			0
$605$	−24.4164	−	25.9030i	−0.992668	−	1.05311i
$606$		0			0
$607$	14.0902	+	10.2371i	0.571902	+	0.415511i	0.835796	−	0.549040i	$-0.185007\pi$
$607$	14.0902	+	10.2371i	0.571902	+	0.415511i	−0.263893	+	0.964552i	$0.585007\pi$
$608$		0			0
$609$	−0.500000	−	1.53884i	−0.0202610	−	0.0623570i
$610$		0			0
$611$	13.7082	−	9.95959i	0.554575	−	0.402922i
$612$		0			0
$613$	−1.50000	+	4.61653i	−0.0605844	+	0.186460i	−0.976768	−	0.214299i	$-0.931253\pi$
$613$	−1.50000	+	4.61653i	−0.0605844	+	0.186460i	0.916184	+	0.400759i	$0.131253\pi$
$614$		0			0
$615$	28.9443			1.16715
$616$		0			0
$617$	−31.9098			−1.28464			−0.642321	−	0.766436i	$-0.722028\pi$
$617$	−31.9098			−1.28464			−0.642321	+	0.766436i	$0.722028\pi$
$618$		0			0
$619$	5.38197	−	16.5640i	0.216319	−	0.665763i	−0.782738	−	0.622352i	$-0.786177\pi$
$619$	5.38197	−	16.5640i	0.216319	−	0.665763i	0.999057	−	0.0434113i	$-0.0138226\pi$
$620$		0			0
$621$	−1.50000	+	1.08981i	−0.0601929	+	0.0437327i
$622$		0			0
$623$	−0.854102	−	2.62866i	−0.0342189	−	0.105315i
$624$		0			0
$625$	18.1353	+	13.1760i	0.725410	+	0.527041i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−9.09017	−	6.60440i	−0.362449	−	0.263334i
$630$		0			0
$631$	0.572949	+	1.76336i	0.0228087	+	0.0701981i	0.961813	−	0.273707i	$-0.0882500\pi$
$631$	0.572949	+	1.76336i	0.0228087	+	0.0701981i	−0.939004	+	0.343906i	$0.888250\pi$
$632$		0			0
$633$	16.4443	−	11.9475i	0.653601	−	0.474869i
$634$		0			0
$635$	−4.61803	+	14.2128i	−0.183261	+	0.564020i
$636$		0			0
$637$	2.00000			0.0792429
$638$		0			0
$639$	−3.61803			−0.143127
$640$		0			0
$641$	4.50000	−	13.8496i	0.177739	−	0.547025i	−0.822009	−	0.569475i	$-0.807147\pi$
$641$	4.50000	−	13.8496i	0.177739	−	0.547025i	0.999748	+	0.0224496i	$0.00714654\pi$
$642$		0			0
$643$	−37.6525	+	27.3561i	−1.48487	+	1.07882i	−0.508922	+	0.860813i	$0.669956\pi$
$643$	−37.6525	+	27.3561i	−1.48487	+	1.07882i	−0.975947	+	0.218007i	$0.930044\pi$
$644$		0			0
$645$	2.85410	+	8.78402i	0.112380	+	0.345871i
$646$		0			0
$647$	−5.38197	−	3.91023i	−0.211587	−	0.153727i	0.476944	−	0.878933i	$-0.341744\pi$
$647$	−5.38197	−	3.91023i	−0.211587	−	0.153727i	−0.688531	+	0.725207i	$0.741744\pi$
$648$		0			0
$649$	45.5066	+	19.6417i	1.78629	+	0.771003i
$650$		0			0
$651$	1.00000	+	0.726543i	0.0391931	+	0.0284754i
$652$		0			0
$653$	7.33688	+	22.5806i	0.287114	+	0.883647i	0.985757	+	0.168176i	$0.0537878\pi$
$653$	7.33688	+	22.5806i	0.287114	+	0.883647i	−0.698643	+	0.715471i	$0.746212\pi$
$654$		0			0
$655$	−47.1246	+	34.2380i	−1.84131	+	1.33779i
$656$		0			0
$657$	−0.381966	+	1.17557i	−0.0149019	+	0.0458634i
$658$		0			0
$659$	−38.4721			−1.49866			−0.749331	−	0.662196i	$-0.769625\pi$
$659$	−38.4721			−1.49866			−0.749331	+	0.662196i	$0.769625\pi$
$660$		0			0
$661$	−27.2361			−1.05936			−0.529680	−	0.848197i	$-0.677688\pi$
$661$	−27.2361			−1.05936			−0.529680	+	0.848197i	$0.677688\pi$
$662$		0			0
$663$	3.23607	−	9.95959i	0.125678	−	0.386799i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.927051	−	2.85317i	−0.0358956	−	0.110475i
$668$		0			0
$669$	−15.4721	−	11.2412i	−0.598187	−	0.434609i
$670$		0			0
$671$	2.00000	−	21.3723i	0.0772091	−	0.825067i
$672$		0			0
$673$	38.1074	+	27.6866i	1.46893	+	1.06724i	0.980922	+	0.194404i	$0.0622772\pi$
$673$	38.1074	+	27.6866i	1.46893	+	1.06724i	0.488010	+	0.872838i	$0.337723\pi$
$674$		0			0
$675$	−1.69098	−	5.20431i	−0.0650860	−	0.200314i
$676$		0			0
$677$	5.23607	−	3.80423i	0.201238	−	0.146208i	−0.482602	−	0.875840i	$-0.660308\pi$
$677$	5.23607	−	3.80423i	0.201238	−	0.146208i	0.683841	+	0.729631i	$0.260308\pi$
$678$		0			0
$679$	3.76393	−	11.5842i	0.144446	−	0.444560i
$680$		0			0
$681$	−15.2361			−0.583847
$682$		0			0
$683$	34.5066			1.32036			0.660179	−	0.751109i	$-0.270481\pi$
$683$	34.5066			1.32036			0.660179	+	0.751109i	$0.270481\pi$
$684$		0			0
$685$	−12.3262	+	37.9363i	−0.470961	+	1.44947i
$686$		0			0
$687$	−17.7984	+	12.9313i	−0.679050	+	0.493359i
$688$		0			0
$689$	1.47214	+	4.53077i	0.0560839	+	0.172609i
$690$		0			0
$691$	−37.2705	−	27.0786i	−1.41784	−	1.03012i	−0.992124	−	0.125261i	$-0.960023\pi$
$691$	−37.2705	−	27.0786i	−1.41784	−	1.03012i	−0.425713	−	0.904858i	$-0.639977\pi$
$692$		0			0
$693$	−1.69098	−	2.85317i	−0.0642351	−	0.108383i
$694$		0			0
$695$	−28.6525	−	20.8172i	−1.08685	−	0.789643i
$696$		0			0
$697$	−14.4721	−	44.5407i	−0.548171	−	1.68710i
$698$		0			0
$699$	6.09017	−	4.42477i	0.230351	−	0.167360i
$700$		0			0
$701$	13.4058	−	41.2587i	0.506329	−	1.55832i	−0.292196	−	0.956358i	$-0.594386\pi$
$701$	13.4058	−	41.2587i	0.506329	−	1.55832i	0.798525	−	0.601961i	$-0.205614\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−27.4164			−1.03256
$706$		0			0
$707$	−5.00000	+	15.3884i	−0.188044	+	0.578741i
$708$		0			0
$709$	−11.7812	+	8.55951i	−0.442450	+	0.321459i	−0.786608	−	0.617453i	$-0.788165\pi$
$709$	−11.7812	+	8.55951i	−0.442450	+	0.321459i	0.344157	+	0.938912i	$0.388165\pi$
$710$		0			0
$711$	−2.35410	−	7.24518i	−0.0882857	−	0.271716i
$712$		0			0
$713$	1.85410	+	1.34708i	0.0694367	+	0.0504487i
$714$		0			0
$715$	−14.1803	+	16.1150i	−0.530315	+	0.602665i
$716$		0			0
$717$	16.0172	+	11.6372i	0.598174	+	0.434599i
$718$		0			0
$719$	4.14590	+	12.7598i	0.154616	+	0.475859i	0.998122	−	0.0612611i	$-0.0195122\pi$
$719$	4.14590	+	12.7598i	0.154616	+	0.475859i	−0.843506	+	0.537120i	$0.819512\pi$
$720$		0			0
$721$	−12.7082	+	9.23305i	−0.473278	+	0.343857i
$722$		0			0
$723$	−9.00000	+	27.6992i	−0.334714	+	1.03014i
$724$		0			0
$725$	8.85410			0.328833
$726$		0			0
$727$	−12.0000			−0.445055			−0.222528	−	0.974926i	$-0.571431\pi$
$727$	−12.0000			−0.445055			−0.222528	+	0.974926i	$0.571431\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	12.0902	−	8.78402i	0.447171	−	0.324889i
$732$		0			0
$733$	3.43769	+	10.5801i	0.126974	+	0.390786i	0.994256	−	0.107032i	$-0.0341347\pi$
$733$	3.43769	+	10.5801i	0.126974	+	0.390786i	−0.867281	+	0.497818i	$0.834135\pi$
$734$		0			0
$735$	−2.61803	−	1.90211i	−0.0965676	−	0.0701605i
$736$		0			0
$737$	11.6697	−	13.2618i	0.429859	−	0.488504i
$738$		0			0
$739$	−21.2533	−	15.4414i	−0.781815	−	0.568022i	0.123708	−	0.992319i	$-0.460521\pi$
$739$	−21.2533	−	15.4414i	−0.781815	−	0.568022i	−0.905523	+	0.424297i	$0.860521\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−22.1976	+	16.1275i	−0.814350	+	0.591660i	−0.915088	−	0.403253i	$-0.867879\pi$
$743$	−22.1976	+	16.1275i	−0.814350	+	0.591660i	0.100739	+	0.994913i	$0.467879\pi$
$744$		0			0
$745$	−18.0000	+	55.3983i	−0.659469	+	2.02964i
$746$		0			0
$747$	−4.76393			−0.174303
$748$		0			0
$749$	1.85410			0.0677474
$750$		0			0
$751$	−10.1008	+	31.0871i	−0.368584	+	1.13438i	0.579122	+	0.815241i	$0.303395\pi$
$751$	−10.1008	+	31.0871i	−0.368584	+	1.13438i	−0.947706	+	0.319144i	$0.896605\pi$
$752$		0			0
$753$	−19.5623	+	14.2128i	−0.712890	+	0.517945i
$754$		0			0
$755$	−12.9098	−	39.7324i	−0.469837	−	1.44601i
$756$		0			0
$757$	14.3992	+	10.4616i	0.523347	+	0.380234i	0.817863	−	0.575412i	$-0.195158\pi$
$757$	14.3992	+	10.4616i	0.523347	+	0.380234i	−0.294516	+	0.955647i	$0.595158\pi$
$758$		0			0
$759$	−3.13525	−	5.29007i	−0.113803	−	0.192017i
$760$		0			0
$761$	−6.52786	−	4.74277i	−0.236635	−	0.171925i	0.463148	−	0.886281i	$-0.346720\pi$
$761$	−6.52786	−	4.74277i	−0.236635	−	0.171925i	−0.699783	+	0.714356i	$0.746720\pi$
$762$		0			0
$763$	0.572949	+	1.76336i	0.0207421	+	0.0638378i
$764$		0			0
$765$	−13.7082	+	9.95959i	−0.495621	+	0.360090i
$766$		0			0
$767$	9.23607	−	28.4257i	0.333495	−	1.02639i
$768$		0			0
$769$	0.180340			0.00650322			0.00325161	−	0.999995i	$-0.498965\pi$
$769$	0.180340			0.00650322			0.00325161	+	0.999995i	$0.498965\pi$
$770$		0			0
$771$	−8.18034			−0.294608
$772$		0			0
$773$	−9.12461	+	28.0827i	−0.328189	+	1.01006i	0.641791	+	0.766880i	$0.278192\pi$
$773$	−9.12461	+	28.0827i	−0.328189	+	1.01006i	−0.969980	+	0.243184i	$0.921808\pi$
$774$		0			0
$775$	−5.47214	+	3.97574i	−0.196565	+	0.142813i
$776$		0			0
$777$	0.663119	+	2.04087i	0.0237893	+	0.0732158i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	1.11803	−	11.9475i	0.0400064	−	0.427514i
$782$		0			0
$783$	1.30902	+	0.951057i	0.0467805	+	0.0339880i
$784$		0			0
$785$	−2.29180	−	7.05342i	−0.0817977	−	0.251747i
$786$		0			0
$787$	−17.7984	+	12.9313i	−0.634444	+	0.460950i	−0.857937	−	0.513755i	$-0.828254\pi$
$787$	−17.7984	+	12.9313i	−0.634444	+	0.460950i	0.223493	+	0.974705i	$0.428254\pi$
$788$		0			0
$789$	−0.645898	+	1.98787i	−0.0229946	+	0.0707700i
$790$		0			0
$791$	−9.61803			−0.341978
$792$		0			0
$793$	−12.9443			−0.459665
$794$		0			0
$795$	2.38197	−	7.33094i	0.0844796	−	0.260002i
$796$		0			0
$797$	11.4721	−	8.33499i	0.406364	−	0.295241i	−0.365764	−	0.930708i	$-0.619192\pi$
$797$	11.4721	−	8.33499i	0.406364	−	0.295241i	0.772128	+	0.635467i	$0.219192\pi$
$798$		0			0
$799$	13.7082	+	42.1895i	0.484961	+	1.49256i
$800$		0			0
$801$	2.23607	+	1.62460i	0.0790076	+	0.0574024i
$802$		0			0
$803$	−3.76393	−	1.62460i	−0.132826	−	0.0573308i
$804$		0			0
$805$	−4.85410	−	3.52671i	−0.171085	−	0.124300i
$806$		0			0
$807$	7.03444	+	21.6498i	0.247624	+	0.762109i
$808$		0			0
$809$	35.8607	−	26.0543i	1.26079	−	0.916021i	0.261998	−	0.965068i	$-0.415619\pi$
$809$	35.8607	−	26.0543i	1.26079	−	0.916021i	0.998796	+	0.0490477i	$0.0156186\pi$
$810$		0			0
$811$	5.50658	−	16.9475i	0.193362	−	0.595107i	−0.806630	−	0.591057i	$-0.798711\pi$
$811$	5.50658	−	16.9475i	0.193362	−	0.595107i	0.999992	−	0.00405022i	$-0.00128923\pi$
$812$		0			0
$813$	1.41641			0.0496756
$814$		0			0
$815$	−69.7771			−2.44418
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−1.61803	+	1.17557i	−0.0565387	+	0.0410778i
$820$		0			0
$821$	14.6180	+	44.9897i	0.510173	+	1.57015i	0.791897	+	0.610655i	$0.209094\pi$
$821$	14.6180	+	44.9897i	0.510173	+	1.57015i	−0.281724	+	0.959496i	$0.590906\pi$
$822$		0			0
$823$	−28.3435	−	20.5927i	−0.987991	−	0.717817i	−0.0285107	−	0.999593i	$-0.509076\pi$
$823$	−28.3435	−	20.5927i	−0.987991	−	0.717817i	−0.959480	+	0.281776i	$0.909076\pi$
$824$		0			0
$825$	17.7082	−	3.97574i	0.616521	−	0.138417i
$826$		0			0
$827$	−27.4164	−	19.9192i	−0.953362	−	0.692658i	−0.00176229	−	0.999998i	$-0.500561\pi$
$827$	−27.4164	−	19.9192i	−0.953362	−	0.692658i	−0.951600	+	0.307340i	$0.900561\pi$
$828$		0			0
$829$	3.56231	+	10.9637i	0.123724	+	0.380783i	0.993666	−	0.112370i	$-0.0358442\pi$
$829$	3.56231	+	10.9637i	0.123724	+	0.380783i	−0.869942	+	0.493153i	$0.835844\pi$
$830$		0			0
$831$	1.73607	−	1.26133i	0.0602235	−	0.0437550i
$832$		0			0
$833$	−1.61803	+	4.97980i	−0.0560616	+	0.172540i
$834$		0			0
$835$	14.4721			0.500829
$836$		0			0
$837$	−1.23607			−0.0427248
$838$		0			0
$839$	−0.854102	+	2.62866i	−0.0294869	+	0.0907513i	−0.964717	−	0.263289i	$-0.915193\pi$
$839$	−0.854102	+	2.62866i	−0.0294869	+	0.0907513i	0.935230	+	0.354041i	$0.115193\pi$
$840$		0			0
$841$	21.3435	−	15.5069i	0.735981	−	0.534722i
$842$		0			0
$843$	1.50000	+	4.61653i	0.0516627	+	0.159002i
$844$		0			0
$845$	−23.5623	−	17.1190i	−0.810568	−	0.588912i
$846$		0			0
$847$	9.94427	−	4.70228i	0.341689	−	0.161572i
$848$		0			0
$849$	−16.7082	−	12.1392i	−0.573424	−	0.416617i
$850$		0			0
$851$	1.22949	+	3.78398i	0.0421464	+	0.129713i
$852$		0			0
$853$	−29.5623	+	21.4783i	−1.01219	+	0.735402i	−0.964668	−	0.263468i	$-0.915134\pi$
$853$	−29.5623	+	21.4783i	−1.01219	+	0.735402i	−0.0475259	+	0.998870i	$0.515134\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.41641			−0.0483836			−0.0241918	−	0.999707i	$-0.507701\pi$
$857$	−1.41641			−0.0483836			−0.0241918	+	0.999707i	$0.507701\pi$
$858$		0			0
$859$	10.5836			0.361108			0.180554	−	0.983565i	$-0.442211\pi$
$859$	10.5836			0.361108			0.180554	+	0.983565i	$0.442211\pi$
$860$		0			0
$861$	−2.76393	+	8.50651i	−0.0941946	+	0.289901i
$862$		0			0
$863$	33.1246	−	24.0664i	1.12757	−	0.819231i	0.142235	−	0.989833i	$-0.454571\pi$
$863$	33.1246	−	24.0664i	1.12757	−	0.819231i	0.985340	+	0.170602i	$0.0545712\pi$
$864$		0			0
$865$	8.47214	+	26.0746i	0.288061	+	0.886561i
$866$		0			0
$867$	8.42705	+	6.12261i	0.286198	+	0.207935i
$868$		0			0
$869$	24.6525	−	5.53483i	0.836278	−	0.187756i
$870$		0			0
$871$	−8.61803	−	6.26137i	−0.292011	−	0.212158i
$872$		0			0
$873$	3.76393	+	11.5842i	0.127390	+	0.392065i
$874$		0			0
$875$	1.23607	−	0.898056i	0.0417867	−	0.0303598i
$876$		0			0
$877$	0.680340	−	2.09387i	0.0229734	−	0.0707050i	−0.938913	−	0.344156i	$-0.888165\pi$
$877$	0.680340	−	2.09387i	0.0229734	−	0.0707050i	0.961886	+	0.273451i	$0.0881651\pi$
$878$		0			0
$879$	−15.5967			−0.526065
$880$		0			0
$881$	24.5410			0.826808			0.413404	−	0.910548i	$-0.364340\pi$
$881$	24.5410			0.826808			0.413404	+	0.910548i	$0.364340\pi$
$882$		0			0
$883$	11.8197	−	36.3772i	0.397763	−	1.22419i	−0.529025	−	0.848606i	$-0.677442\pi$
$883$	11.8197	−	36.3772i	0.397763	−	1.22419i	0.926789	−	0.375583i	$-0.122558\pi$
$884$		0			0
$885$	−39.1246	+	28.4257i	−1.31516	+	0.955519i
$886$		0			0
$887$	−14.7082	−	45.2672i	−0.493853	−	1.51992i	−0.818736	−	0.574170i	$-0.805325\pi$
$887$	−14.7082	−	45.2672i	−0.493853	−	1.51992i	0.324883	−	0.945754i	$-0.394675\pi$
$888$		0			0
$889$	−3.73607	−	2.71441i	−0.125304	−	0.0910385i
$890$		0			0
$891$	3.04508	+	1.31433i	0.102014	+	0.0440316i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	10.7984	+	33.2340i	0.360950	+	1.11089i
$896$		0			0
$897$	−3.00000	+	2.17963i	−0.100167	+	0.0727756i
$898$		0			0
$899$	0.618034	−	1.90211i	0.0206126	−	0.0634390i
$900$		0			0
$901$	−12.4721			−0.415507
$902$		0			0
$903$	−2.85410			−0.0949786
$904$		0			0
$905$	−23.7082	+	72.9663i	−0.788087	+	2.42548i
$906$		0			0
$907$	−11.1074	+	8.06999i	−0.368815	+	0.267960i	−0.756719	−	0.653740i	$-0.773199\pi$
$907$	−11.1074	+	8.06999i	−0.368815	+	0.267960i	0.387904	+	0.921700i	$0.373199\pi$
$908$		0			0
$909$	−5.00000	−	15.3884i	−0.165840	−	0.510402i
$910$		0			0
$911$	16.9443	+	12.3107i	0.561389	+	0.407873i	0.831967	−	0.554825i	$-0.187215\pi$
$911$	16.9443	+	12.3107i	0.561389	+	0.407873i	−0.270578	+	0.962698i	$0.587215\pi$
$912$		0			0
$913$	1.47214	−	15.7314i	0.0487206	−	0.520635i
$914$		0			0
$915$	16.9443	+	12.3107i	0.560160	+	0.406980i
$916$		0			0
$917$	−5.56231	−	17.1190i	−0.183684	−	0.565320i
$918$		0			0
$919$	28.9615	−	21.0418i	0.955351	−	0.694103i	0.00328499	−	0.999995i	$-0.498954\pi$
$919$	28.9615	−	21.0418i	0.955351	−	0.694103i	0.952067	+	0.305891i	$0.0989544\pi$
$920$		0			0
$921$	10.4164	−	32.0584i	0.343232	−	1.05636i
$922$		0			0
$923$	−7.23607			−0.238178
$924$		0			0
$925$	−11.7426			−0.386096
$926$		0			0
$927$	4.85410	−	14.9394i	0.159430	−	0.490674i
$928$		0			0
$929$	−10.1459	+	7.37143i	−0.332876	+	0.241849i	−0.741650	−	0.670787i	$-0.765956\pi$
$929$	−10.1459	+	7.37143i	−0.332876	+	0.241849i	0.408774	+	0.912636i	$0.365956\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−16.0902	−	11.6902i	−0.526769	−	0.382720i
$934$		0			0
$935$	−28.6525	−	48.3449i	−0.937036	−	1.58105i
$936$		0			0
$937$	1.70820	+	1.24108i	0.0558046	+	0.0405444i	0.615338	−	0.788263i	$-0.289020\pi$
$937$	1.70820	+	1.24108i	0.0558046	+	0.0405444i	−0.559533	+	0.828808i	$0.689020\pi$
$938$		0			0
$939$	3.79837	+	11.6902i	0.123955	+	0.381495i
$940$		0			0
$941$	27.0902	−	19.6822i	0.883114	−	0.641620i	−0.0509593	−	0.998701i	$-0.516228\pi$
$941$	27.0902	−	19.6822i	0.883114	−	0.641620i	0.934074	+	0.357081i	$0.116228\pi$
$942$		0			0
$943$	−5.12461	+	15.7719i	−0.166880	+	0.513605i
$944$		0			0
$945$	3.23607			0.105269
$946$		0			0
$947$	44.7214			1.45325			0.726624	−	0.687035i	$-0.241088\pi$
$947$	44.7214			1.45325			0.726624	+	0.687035i	$0.241088\pi$
$948$		0			0
$949$	−0.763932	+	2.35114i	−0.0247983	+	0.0763213i
$950$		0			0
$951$	9.92705	−	7.21242i	0.321907	−	0.233879i
$952$		0			0
$953$	12.8435	+	39.5281i	0.416040	+	1.28044i	0.911317	+	0.411705i	$0.135067\pi$
$953$	12.8435	+	39.5281i	0.416040	+	1.28044i	−0.495277	+	0.868735i	$0.664933\pi$
$954$		0			0
$955$	−32.4164	−	23.5519i	−1.04897	−	0.762122i
$956$		0			0
$957$	−3.54508	+	4.02874i	−0.114596	+	0.130231i
$958$		0			0
$959$	−9.97214	−	7.24518i	−0.322017	−	0.233959i
$960$		0			0
$961$	−9.10739	−	28.0297i	−0.293787	−	0.904183i
$962$		0			0
$963$	−1.50000	+	1.08981i	−0.0483368	+	0.0351188i
$964$		0			0
$965$	−20.2705	+	62.3862i	−0.652531	+	2.00828i
$966$		0			0
$967$	−22.1459			−0.712164			−0.356082	−	0.934455i	$-0.615888\pi$
$967$	−22.1459			−0.712164			−0.356082	+	0.934455i	$0.615888\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	3.74265	−	11.5187i	0.120107	−	0.369652i	−0.872871	−	0.487952i	$-0.837744\pi$
$971$	3.74265	−	11.5187i	0.120107	−	0.369652i	0.992978	+	0.118299i	$0.0377443\pi$
$972$		0			0
$973$	8.85410	−	6.43288i	0.283849	−	0.206229i
$974$		0			0
$975$	−3.38197	−	10.4086i	−0.108310	−	0.333343i
$976$		0			0
$977$	35.9164	+	26.0948i	1.14907	+	0.834847i	0.988357	−	0.152155i	$-0.0486213\pi$
$977$	35.9164	+	26.0948i	1.14907	+	0.834847i	0.160711	+	0.987002i	$0.448621\pi$
$978$		0			0
$979$	−6.05573	+	6.88191i	−0.193542	+	0.219947i
$980$		0			0
$981$	−1.50000	−	1.08981i	−0.0478913	−	0.0347951i
$982$		0			0
$983$	15.0557	+	46.3368i	0.480203	+	1.47791i	0.838810	+	0.544425i	$0.183252\pi$
$983$	15.0557	+	46.3368i	0.480203	+	1.47791i	−0.358607	+	0.933489i	$0.616748\pi$
$984$		0			0
$985$	−12.8541	+	9.33905i	−0.409566	+	0.297567i
$986$		0			0
$987$	2.61803	−	8.05748i	0.0833329	−	0.256472i
$988$		0			0
$989$	−5.29180			−0.168269
$990$		0			0
$991$	−41.5279			−1.31918			−0.659588	−	0.751627i	$-0.729269\pi$
$991$	−41.5279			−1.31918			−0.659588	+	0.751627i	$0.729269\pi$
$992$		0			0
$993$	−2.37132	+	7.29818i	−0.0752517	+	0.231601i
$994$		0			0
$995$	−50.3607	+	36.5892i	−1.59654	+	1.15995i
$996$		0			0
$997$	11.8541	+	36.4832i	0.375423	+	1.15543i	0.943193	+	0.332246i	$0.107806\pi$
$997$	11.8541	+	36.4832i	0.375423	+	1.15543i	−0.567770	+	0.823188i	$0.692194\pi$
$998$		0			0
$999$	−1.73607	−	1.26133i	−0.0549268	−	0.0399066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	924.2.r.d.169.1	✓	4
11.3	even	5	inner	924.2.r.d.421.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
924.2.r.d.169.1	✓	4	1.1	even	1	trivial
924.2.r.d.421.1	yes	4	11.3	even	5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 924 = 2^{2} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	924.r (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{3} +(2.61803 - 1.90211i) q^{5} +(0.309017 + 0.951057i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(2.19098 - 2.48990i) q^{11} +(-1.61803 - 1.17557i) q^{13} +(1.00000 + 3.07768i) q^{15} +(4.23607 - 3.07768i) q^{17} -1.00000 q^{21} -1.85410 q^{23} +(1.69098 - 5.20431i) q^{25} +(0.809017 - 0.587785i) q^{27} +(0.500000 + 1.53884i) q^{29} +(-1.00000 - 0.726543i) q^{31} +(1.69098 + 2.85317i) q^{33} +(2.61803 + 1.90211i) q^{35} +(-0.663119 - 2.04087i) q^{37} +(1.61803 - 1.17557i) q^{39} +(2.76393 - 8.50651i) q^{41} +2.85410 q^{43} -3.23607 q^{45} +(-2.61803 + 8.05748i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(1.61803 + 4.97980i) q^{51} +(-1.92705 - 1.40008i) q^{53} +(1.00000 - 10.6861i) q^{55} +(4.61803 + 14.2128i) q^{59} +(5.23607 - 3.80423i) q^{61} +(0.309017 - 0.951057i) q^{63} -6.47214 q^{65} +5.32624 q^{67} +(0.572949 - 1.76336i) q^{69} +(2.92705 - 2.12663i) q^{71} +(-0.381966 - 1.17557i) q^{73} +(4.42705 + 3.21644i) q^{75} +(3.04508 + 1.31433i) q^{77} +(6.16312 + 4.47777i) q^{79} +(0.309017 + 0.951057i) q^{81} +(3.85410 - 2.80017i) q^{83} +(5.23607 - 16.1150i) q^{85} -1.61803 q^{87} -2.76393 q^{89} +(0.618034 - 1.90211i) q^{91} +(1.00000 - 0.726543i) q^{93} +(-9.85410 - 7.15942i) q^{97} +(-3.23607 + 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} + 6 q^{5} - q^{7} - q^{9} + 11 q^{11} - 2 q^{13} + 4 q^{15} + 8 q^{17} - 4 q^{21} + 6 q^{23} + 9 q^{25} + q^{27} + 2 q^{29} - 4 q^{31} + 9 q^{33} + 6 q^{35} + 13 q^{37} + 2 q^{39} + 20 q^{41}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q + q^3 + 6 * q^5 - q^7 - q^9 + 11 * q^11 - 2 * q^13 + 4 * q^15 + 8 * q^17 - 4 * q^21 + 6 * q^23 + 9 * q^25 + q^27 + 2 * q^29 - 4 * q^31 + 9 * q^33 + 6 * q^35 + 13 * q^37 + 2 * q^39 + 20 * q^41 - 2 * q^43 - 4 * q^45 - 6 * q^47 - q^49 + 2 * q^51 - q^53 + 4 * q^55 + 14 * q^59 + 12 * q^61 - q^63 - 8 * q^65 - 10 * q^67 + 9 * q^69 + 5 * q^71 - 6 * q^73 + 11 * q^75 + q^77 + 9 * q^79 - q^81 + 2 * q^83 + 12 * q^85 - 2 * q^87 - 20 * q^89 - 2 * q^91 + 4 * q^93 - 26 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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