LMFDB - Embedded newform 1040.2.da.a.641.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(641,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1040.641");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.da (of order $6$, degree $2$, not 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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			641.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1040.641
Dual form			1040.2.da.a.881.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 2.36603i) q^{3} +1.00000i q^{5} +(2.59808 - 1.50000i) q^{7} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})$	\(q+(-1.36603 + 2.36603i) q^{3} +1.00000i q^{5} +(2.59808 - 1.50000i) q^{7} +(-2.23205 - 3.86603i) q^{9} +(2.59808 + 1.50000i) q^{11} +(3.50000 - 0.866025i) q^{13} +(-2.36603 - 1.36603i) q^{15} +(1.09808 + 1.90192i) q^{17} +(5.59808 - 3.23205i) q^{19} +8.19615i q^{21} +(1.26795 - 2.19615i) q^{23} -1.00000 q^{25} +4.00000 q^{27} +(4.73205 - 8.19615i) q^{29} +1.26795i q^{31} +(-7.09808 + 4.09808i) q^{33} +(1.50000 + 2.59808i) q^{35} +(9.69615 + 5.59808i) q^{37} +(-2.73205 + 9.46410i) q^{39} +(-9.00000 - 5.19615i) q^{41} +(1.00000 + 1.73205i) q^{43} +(3.86603 - 2.23205i) q^{45} +3.00000i q^{47} +(1.00000 - 1.73205i) q^{49} -6.00000 q^{51} -6.46410 q^{53} +(-1.50000 + 2.59808i) q^{55} +17.6603i q^{57} +(-9.00000 + 5.19615i) q^{59} +(2.09808 + 3.63397i) q^{61} +(-11.5981 - 6.69615i) q^{63} +(0.866025 + 3.50000i) q^{65} +(3.46410 + 6.00000i) q^{69} +(-5.19615 + 3.00000i) q^{71} +5.66025i q^{73} +(1.36603 - 2.36603i) q^{75} +9.00000 q^{77} -6.19615 q^{79} +(1.23205 - 2.13397i) q^{81} +2.19615i q^{83} +(-1.90192 + 1.09808i) q^{85} +(12.9282 + 22.3923i) q^{87} +(-14.8923 - 8.59808i) q^{89} +(7.79423 - 7.50000i) q^{91} +(-3.00000 - 1.73205i) q^{93} +(3.23205 + 5.59808i) q^{95} +(13.0981 - 7.56218i) q^{97} -13.3923i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^9	$ 4 q - 2 q^{3} - 2 q^{9} + 14 q^{13} - 6 q^{15} - 6 q^{17} + 12 q^{19} + 12 q^{23} - 4 q^{25} + 16 q^{27} + 12 q^{29} - 18 q^{33} + 6 q^{35} + 18 q^{37} - 4 q^{39} - 36 q^{41} + 4 q^{43} + 12 q^{45} + 4 q^{49} - 24 q^{51} - 12 q^{53} - 6 q^{55} - 36 q^{59} - 2 q^{61} - 36 q^{63} + 2 q^{75} + 36 q^{77} - 4 q^{79} - 2 q^{81} - 18 q^{85} + 24 q^{87} - 18 q^{89} - 12 q^{93} + 6 q^{95} + 42 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^9 + 14 * q^13 - 6 * q^15 - 6 * q^17 + 12 * q^19 + 12 * q^23 - 4 * q^25 + 16 * q^27 + 12 * q^29 - 18 * q^33 + 6 * q^35 + 18 * q^37 - 4 * q^39 - 36 * q^41 + 4 * q^43 + 12 * q^45 + 4 * q^49 - 24 * q^51 - 12 * q^53 - 6 * q^55 - 36 * q^59 - 2 * q^61 - 36 * q^63 + 2 * q^75 + 36 * q^77 - 4 * q^79 - 2 * q^81 - 18 * q^85 + 24 * q^87 - 18 * q^89 - 12 * q^93 + 6 * q^95 + 42 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.36603	+	2.36603i	−0.788675	+	1.36603i	0.138104	+	0.990418i	$0.455899\pi$
$3$	−1.36603	+	2.36603i	−0.788675	+	1.36603i	−0.926779	+	0.375608i	$0.877434\pi$
$4$		0			0
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	2.59808	−	1.50000i	0.981981	−	0.566947i	0.0791130	−	0.996866i	$-0.474791\pi$
$7$	2.59808	−	1.50000i	0.981981	−	0.566947i	0.902867	+	0.429919i	$0.141458\pi$
$8$		0			0
$9$	−2.23205	−	3.86603i	−0.744017	−	1.28868i
$10$		0			0
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	0.837616	−	0.546259i	$-0.183949\pi$
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	−0.0542666	+	0.998526i	$0.517282\pi$
$12$		0			0
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$		0			0
$15$	−2.36603	−	1.36603i	−0.610905	−	0.352706i
$16$		0			0
$17$	1.09808	+	1.90192i	0.266323	+	0.461284i	0.967909	−	0.251300i	$-0.0808580\pi$
$17$	1.09808	+	1.90192i	0.266323	+	0.461284i	−0.701587	+	0.712584i	$0.747525\pi$
$18$		0			0
$19$	5.59808	−	3.23205i	1.28429	−	0.741483i	0.306658	−	0.951820i	$-0.400789\pi$
$19$	5.59808	−	3.23205i	1.28429	−	0.741483i	0.977629	+	0.210337i	$0.0674560\pi$
$20$		0			0
$21$			8.19615i			1.78855i
$22$		0			0
$23$	1.26795	−	2.19615i	0.264386	−	0.457929i	−0.703017	−	0.711173i	$-0.748164\pi$
$23$	1.26795	−	2.19615i	0.264386	−	0.457929i	0.967402	+	0.253244i	$0.0814975\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	4.00000			0.769800
$28$		0			0
$29$	4.73205	−	8.19615i	0.878720	−	1.52199i	0.0259731	−	0.999663i	$-0.491732\pi$
$29$	4.73205	−	8.19615i	0.878720	−	1.52199i	0.852747	−	0.522325i	$-0.174935\pi$
$30$		0			0
$31$			1.26795i			0.227730i	0.993496	+	0.113865i	$0.0363232\pi$
$31$			1.26795i			0.227730i	−0.993496	+	0.113865i	$0.963677\pi$
$32$		0			0
$33$	−7.09808	+	4.09808i	−1.23562	+	0.713384i
$34$		0			0
$35$	1.50000	+	2.59808i	0.253546	+	0.439155i
$36$		0			0
$37$	9.69615	+	5.59808i	1.59404	+	0.920318i	0.992604	+	0.121395i	$0.0387368\pi$
$37$	9.69615	+	5.59808i	1.59404	+	0.920318i	0.601433	+	0.798923i	$0.294597\pi$
$38$		0			0
$39$	−2.73205	+	9.46410i	−0.437478	+	1.51547i
$40$		0			0
$41$	−9.00000	−	5.19615i	−1.40556	−	0.811503i	−0.410608	−	0.911812i	$-0.634683\pi$
$41$	−9.00000	−	5.19615i	−1.40556	−	0.811503i	−0.994956	+	0.100309i	$0.968017\pi$
$42$		0			0
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	0.932145	−	0.362084i	$-0.117935\pi$
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	−0.779647	+	0.626219i	$0.784601\pi$
$44$		0			0
$45$	3.86603	−	2.23205i	0.576313	−	0.332734i
$46$		0			0
$47$			3.00000i			0.437595i	0.975770	+	0.218797i	$0.0702134\pi$
$47$			3.00000i			0.437595i	−0.975770	+	0.218797i	$0.929787\pi$
$48$		0			0
$49$	1.00000	−	1.73205i	0.142857	−	0.247436i
$50$		0			0
$51$	−6.00000			−0.840168
$52$		0			0
$53$	−6.46410			−0.887913			−0.443956	−	0.896048i	$-0.646425\pi$
$53$	−6.46410			−0.887913			−0.443956	+	0.896048i	$0.646425\pi$
$54$		0			0
$55$	−1.50000	+	2.59808i	−0.202260	+	0.350325i
$56$		0			0
$57$			17.6603i			2.33916i
$58$		0			0
$59$	−9.00000	+	5.19615i	−1.17170	+	0.676481i	−0.954080	−	0.299552i	$-0.903163\pi$
$59$	−9.00000	+	5.19615i	−1.17170	+	0.676481i	−0.217620	+	0.976034i	$0.569829\pi$
$60$		0			0
$61$	2.09808	+	3.63397i	0.268631	+	0.465283i	0.968509	−	0.248980i	$-0.0800954\pi$
$61$	2.09808	+	3.63397i	0.268631	+	0.465283i	−0.699877	+	0.714263i	$0.746762\pi$
$62$		0			0
$63$	−11.5981	−	6.69615i	−1.46122	−	0.843636i
$64$		0			0
$65$	0.866025	+	3.50000i	0.107417	+	0.434122i
$66$		0			0
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$	3.46410	+	6.00000i	0.417029	+	0.722315i
$70$		0			0
$71$	−5.19615	+	3.00000i	−0.616670	+	0.356034i	−0.775571	−	0.631260i	$-0.782538\pi$
$71$	−5.19615	+	3.00000i	−0.616670	+	0.356034i	0.158901	+	0.987294i	$0.449205\pi$
$72$		0			0
$73$			5.66025i			0.662483i	0.943546	+	0.331241i	$0.107467\pi$
$73$			5.66025i			0.662483i	−0.943546	+	0.331241i	$0.892533\pi$
$74$		0			0
$75$	1.36603	−	2.36603i	0.157735	−	0.273205i
$76$		0			0
$77$	9.00000			1.02565
$78$		0			0
$79$	−6.19615			−0.697122			−0.348561	−	0.937286i	$-0.613330\pi$
$79$	−6.19615			−0.697122			−0.348561	+	0.937286i	$0.613330\pi$
$80$		0			0
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$		0			0
$83$			2.19615i			0.241059i	0.992710	+	0.120530i	$0.0384592\pi$
$83$			2.19615i			0.241059i	−0.992710	+	0.120530i	$0.961541\pi$
$84$		0			0
$85$	−1.90192	+	1.09808i	−0.206293	+	0.119103i
$86$		0			0
$87$	12.9282	+	22.3923i	1.38605	+	2.40071i
$88$		0			0
$89$	−14.8923	−	8.59808i	−1.57858	−	0.911394i	−0.995058	−	0.0992979i	$-0.968340\pi$
$89$	−14.8923	−	8.59808i	−1.57858	−	0.911394i	−0.583523	−	0.812096i	$-0.698326\pi$
$90$		0			0
$91$	7.79423	−	7.50000i	0.817057	−	0.786214i
$92$		0			0
$93$	−3.00000	−	1.73205i	−0.311086	−	0.179605i
$94$		0			0
$95$	3.23205	+	5.59808i	0.331601	+	0.574351i
$96$		0			0
$97$	13.0981	−	7.56218i	1.32991	−	0.767823i	0.344623	−	0.938741i	$-0.388007\pi$
$97$	13.0981	−	7.56218i	1.32991	−	0.767823i	0.985285	+	0.170918i	$0.0546734\pi$
$98$		0			0
$99$		−	13.3923i		−	1.34598i
$100$		0			0
$101$	−3.63397	+	6.29423i	−0.361594	+	0.626299i	−0.988223	−	0.153018i	$-0.951101\pi$
$101$	−3.63397	+	6.29423i	−0.361594	+	0.626299i	0.626629	+	0.779317i	$0.284434\pi$
$102$		0			0
$103$	−1.19615			−0.117860			−0.0589302	−	0.998262i	$-0.518769\pi$
$103$	−1.19615			−0.117860			−0.0589302	+	0.998262i	$0.518769\pi$
$104$		0			0
$105$	−8.19615			−0.799863
$106$		0			0
$107$	0.169873	−	0.294229i	0.0164222	−	0.0284442i	−0.857697	−	0.514155i	$-0.828106\pi$
$107$	0.169873	−	0.294229i	0.0164222	−	0.0284442i	0.874120	+	0.485710i	$0.161439\pi$
$108$		0			0
$109$			15.4641i			1.48119i	0.671950	+	0.740596i	$0.265457\pi$
$109$			15.4641i			1.48119i	−0.671950	+	0.740596i	$0.734543\pi$
$110$		0			0
$111$	−26.4904	+	15.2942i	−2.51436	+	1.45166i
$112$		0			0
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	0.981689	−	0.190490i	$-0.0610077\pi$
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	−0.655814	+	0.754923i	$0.727674\pi$
$114$		0			0
$115$	2.19615	+	1.26795i	0.204792	+	0.118237i
$116$		0			0
$117$	−11.1603	−	11.5981i	−1.03177	−	1.07224i
$118$		0			0
$119$	5.70577	+	3.29423i	0.523047	+	0.301981i
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$		0			0
$123$	24.5885	−	14.1962i	2.21707	−	1.28002i
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	10.5981	−	18.3564i	0.940427	−	1.62887i	0.175769	−	0.984431i	$-0.443759\pi$
$127$	10.5981	−	18.3564i	0.940427	−	1.62887i	0.764658	−	0.644436i	$-0.222908\pi$
$128$		0			0
$129$	−5.46410			−0.481087
$130$		0			0
$131$	18.1244			1.58353			0.791766	−	0.610824i	$-0.209162\pi$
$131$	18.1244			1.58353			0.791766	+	0.610824i	$0.209162\pi$
$132$		0			0
$133$	9.69615	−	16.7942i	0.840763	−	1.45624i
$134$		0			0
$135$			4.00000i			0.344265i
$136$		0			0
$137$	7.09808	−	4.09808i	0.606430	−	0.350122i	−0.165137	−	0.986271i	$-0.552807\pi$
$137$	7.09808	−	4.09808i	0.606430	−	0.350122i	0.771567	+	0.636148i	$0.219473\pi$
$138$		0			0
$139$	−4.59808	−	7.96410i	−0.390004	−	0.675506i	0.602446	−	0.798160i	$-0.294193\pi$
$139$	−4.59808	−	7.96410i	−0.390004	−	0.675506i	−0.992450	+	0.122653i	$0.960860\pi$
$140$		0			0
$141$	−7.09808	−	4.09808i	−0.597766	−	0.345120i
$142$		0			0
$143$	10.3923	+	3.00000i	0.869048	+	0.250873i
$144$		0			0
$145$	8.19615	+	4.73205i	0.680653	+	0.392975i
$146$		0			0
$147$	2.73205	+	4.73205i	0.225336	+	0.390293i
$148$		0			0
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	−0.697507	−	0.716578i	$-0.745707\pi$
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	0.271821	+	0.962348i	$0.412374\pi$
$150$		0			0
$151$		−	6.33975i		−	0.515921i	−0.966155	−	0.257961i	$-0.916950\pi$
$151$		−	6.33975i		−	0.515921i	0.966155	−	0.257961i	$-0.0830505\pi$
$152$		0			0
$153$	4.90192	−	8.49038i	0.396297	−	0.686407i
$154$		0			0
$155$	−1.26795			−0.101844
$156$		0			0
$157$	−13.0000			−1.03751			−0.518756	−	0.854922i	$-0.673605\pi$
$157$	−13.0000			−1.03751			−0.518756	+	0.854922i	$0.673605\pi$
$158$		0			0
$159$	8.83013	−	15.2942i	0.700275	−	1.21291i
$160$		0			0
$161$		−	7.60770i		−	0.599570i
$162$		0			0
$163$	−6.29423	+	3.63397i	−0.493002	+	0.284635i	−0.725819	−	0.687886i	$-0.758539\pi$
$163$	−6.29423	+	3.63397i	−0.493002	+	0.284635i	0.232817	+	0.972521i	$0.425206\pi$
$164$		0			0
$165$	−4.09808	−	7.09808i	−0.319035	−	0.552584i
$166$		0			0
$167$	2.59808	+	1.50000i	0.201045	+	0.116073i	0.597143	−	0.802135i	$-0.296303\pi$
$167$	2.59808	+	1.50000i	0.201045	+	0.116073i	−0.396098	+	0.918208i	$0.629636\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		0			0
$171$	−24.9904	−	14.4282i	−1.91106	−	1.10335i
$172$		0			0
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	0.996544	+	0.0830722i	$0.0264732\pi$
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	−0.426329	+	0.904568i	$0.640193\pi$
$174$		0			0
$175$	−2.59808	+	1.50000i	−0.196396	+	0.113389i
$176$		0			0
$177$		−	28.3923i		−	2.13410i
$178$		0			0
$179$	−1.26795	+	2.19615i	−0.0947710	+	0.164148i	−0.909513	−	0.415675i	$-0.863545\pi$
$179$	−1.26795	+	2.19615i	−0.0947710	+	0.164148i	0.814742	+	0.579824i	$0.196879\pi$
$180$		0			0
$181$	−16.5885			−1.23301			−0.616505	−	0.787351i	$-0.711452\pi$
$181$	−16.5885			−1.23301			−0.616505	+	0.787351i	$0.711452\pi$
$182$		0			0
$183$	−11.4641			−0.847451
$184$		0			0
$185$	−5.59808	+	9.69615i	−0.411579	+	0.712875i
$186$		0			0
$187$			6.58846i			0.481796i
$188$		0			0
$189$	10.3923	−	6.00000i	0.755929	−	0.436436i
$190$		0			0
$191$	−9.63397	−	16.6865i	−0.697090	−	1.20740i	−0.969471	−	0.245206i	$-0.921144\pi$
$191$	−9.63397	−	16.6865i	−0.697090	−	1.20740i	0.272381	−	0.962189i	$-0.412189\pi$
$192$		0			0
$193$	−3.80385	−	2.19615i	−0.273807	−	0.158083i	0.356809	−	0.934177i	$-0.383865\pi$
$193$	−3.80385	−	2.19615i	−0.273807	−	0.158083i	−0.630616	+	0.776095i	$0.717198\pi$
$194$		0			0
$195$	−9.46410	−	2.73205i	−0.677738	−	0.195646i
$196$		0			0
$197$	8.30385	+	4.79423i	0.591625	+	0.341575i	0.765740	−	0.643151i	$-0.222373\pi$
$197$	8.30385	+	4.79423i	0.591625	+	0.341575i	−0.174115	+	0.984725i	$0.555706\pi$
$198$		0			0
$199$	7.19615	+	12.4641i	0.510122	+	0.883557i	0.999931	+	0.0117273i	$0.00373299\pi$
$199$	7.19615	+	12.4641i	0.510122	+	0.883557i	−0.489810	+	0.871829i	$0.662934\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	28.3923i		−	1.99275i
$204$		0			0
$205$	5.19615	−	9.00000i	0.362915	−	0.628587i
$206$		0			0
$207$	−11.3205			−0.786830
$208$		0			0
$209$	19.3923			1.34139
$210$		0			0
$211$	6.79423	−	11.7679i	0.467734	−	0.810139i	−0.531586	−	0.847004i	$-0.678404\pi$
$211$	6.79423	−	11.7679i	0.467734	−	0.810139i	0.999320	+	0.0368651i	$0.0117372\pi$
$212$		0			0
$213$		−	16.3923i		−	1.12318i
$214$		0			0
$215$	−1.73205	+	1.00000i	−0.118125	+	0.0681994i
$216$		0			0
$217$	1.90192	+	3.29423i	0.129111	+	0.223627i
$218$		0			0
$219$	−13.3923	−	7.73205i	−0.904968	−	0.522484i
$220$		0			0
$221$	5.49038	+	5.70577i	0.369323	+	0.383812i
$222$		0			0
$223$	0.401924	+	0.232051i	0.0269148	+	0.0155393i	0.513397	−	0.858151i	$-0.328387\pi$
$223$	0.401924	+	0.232051i	0.0269148	+	0.0155393i	−0.486482	+	0.873690i	$0.661720\pi$
$224$		0			0
$225$	2.23205	+	3.86603i	0.148803	+	0.257735i
$226$		0			0
$227$	−3.80385	+	2.19615i	−0.252470	+	0.145764i	−0.620895	−	0.783894i	$-0.713231\pi$
$227$	−3.80385	+	2.19615i	−0.252470	+	0.145764i	0.368425	+	0.929658i	$0.379897\pi$
$228$		0			0
$229$			4.73205i			0.312703i	0.987701	+	0.156351i	$0.0499732\pi$
$229$			4.73205i			0.312703i	−0.987701	+	0.156351i	$0.950027\pi$
$230$		0			0
$231$	−12.2942	+	21.2942i	−0.808901	+	1.40106i
$232$		0			0
$233$	1.26795			0.0830661			0.0415331	−	0.999137i	$-0.486776\pi$
$233$	1.26795			0.0830661			0.0415331	+	0.999137i	$0.486776\pi$
$234$		0			0
$235$	−3.00000			−0.195698
$236$		0			0
$237$	8.46410	−	14.6603i	0.549802	−	0.952286i
$238$		0			0
$239$		−	8.19615i		−	0.530165i	−0.964226	−	0.265083i	$-0.914601\pi$
$239$		−	8.19615i		−	0.530165i	0.964226	−	0.265083i	$-0.0853992\pi$
$240$		0			0
$241$	−7.50000	+	4.33013i	−0.483117	+	0.278928i	−0.721715	−	0.692191i	$-0.756646\pi$
$241$	−7.50000	+	4.33013i	−0.483117	+	0.278928i	0.238597	+	0.971119i	$0.423312\pi$
$242$		0			0
$243$	9.36603	+	16.2224i	0.600831	+	1.04067i
$244$		0			0
$245$	1.73205	+	1.00000i	0.110657	+	0.0638877i
$246$		0			0
$247$	16.7942	−	16.1603i	1.06859	−	1.02825i
$248$		0			0
$249$	−5.19615	−	3.00000i	−0.329293	−	0.190117i
$250$		0			0
$251$	3.40192	+	5.89230i	0.214728	+	0.371919i	0.953188	−	0.302378i	$-0.0977803\pi$
$251$	3.40192	+	5.89230i	0.214728	+	0.371919i	−0.738461	+	0.674296i	$0.764447\pi$
$252$		0			0
$253$	6.58846	−	3.80385i	0.414213	−	0.239146i
$254$		0			0
$255$		−	6.00000i		−	0.375735i
$256$		0			0
$257$	−6.92820	+	12.0000i	−0.432169	+	0.748539i	−0.997060	−	0.0766265i	$-0.975585\pi$
$257$	−6.92820	+	12.0000i	−0.432169	+	0.748539i	0.564890	+	0.825166i	$0.308918\pi$
$258$		0			0
$259$	33.5885			2.08709
$260$		0			0
$261$	−42.2487			−2.61513
$262$		0			0
$263$	−13.7942	+	23.8923i	−0.850589	+	1.47326i	0.0300894	+	0.999547i	$0.490421\pi$
$263$	−13.7942	+	23.8923i	−0.850589	+	1.47326i	−0.880678	+	0.473715i	$0.842913\pi$
$264$		0			0
$265$		−	6.46410i		−	0.397087i
$266$		0			0
$267$	40.6865	−	23.4904i	2.48998	−	1.43759i
$268$		0			0
$269$	1.43782	+	2.49038i	0.0876656	+	0.151841i	0.906524	−	0.422154i	$-0.138726\pi$
$269$	1.43782	+	2.49038i	0.0876656	+	0.151841i	−0.818858	+	0.573996i	$0.805393\pi$
$270$		0			0
$271$	2.19615	+	1.26795i	0.133407	+	0.0770224i	0.565218	−	0.824942i	$-0.308792\pi$
$271$	2.19615	+	1.26795i	0.133407	+	0.0770224i	−0.431811	+	0.901964i	$0.642125\pi$
$272$		0			0
$273$	7.09808	+	28.6865i	0.429595	+	1.73619i
$274$		0			0
$275$	−2.59808	−	1.50000i	−0.156670	−	0.0904534i
$276$		0			0
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$		0			0
$279$	4.90192	−	2.83013i	0.293471	−	0.169435i
$280$		0			0
$281$		−	10.3923i		−	0.619953i	−0.950744	−	0.309976i	$-0.899679\pi$
$281$		−	10.3923i		−	0.619953i	0.950744	−	0.309976i	$-0.100321\pi$
$282$		0			0
$283$	−15.1962	+	26.3205i	−0.903317	+	1.56459i	−0.0801576	+	0.996782i	$0.525542\pi$
$283$	−15.1962	+	26.3205i	−0.903317	+	1.56459i	−0.823160	+	0.567810i	$0.807791\pi$
$284$		0			0
$285$	−17.6603			−1.04610
$286$		0			0
$287$	−31.1769			−1.84032
$288$		0			0
$289$	6.08846	−	10.5455i	0.358145	−	0.620325i
$290$		0			0
$291$			41.3205i			2.42225i
$292$		0			0
$293$	−0.696152	+	0.401924i	−0.0406697	+	0.0234806i	−0.520197	−	0.854046i	$-0.674141\pi$
$293$	−0.696152	+	0.401924i	−0.0406697	+	0.0234806i	0.479527	+	0.877527i	$0.340808\pi$
$294$		0			0
$295$	−5.19615	−	9.00000i	−0.302532	−	0.524000i
$296$		0			0
$297$	10.3923	+	6.00000i	0.603023	+	0.348155i
$298$		0			0
$299$	2.53590	−	8.78461i	0.146655	−	0.508027i
$300$		0			0
$301$	5.19615	+	3.00000i	0.299501	+	0.172917i
$302$		0			0
$303$	−9.92820	−	17.1962i	−0.570360	−	0.987893i
$304$		0			0
$305$	−3.63397	+	2.09808i	−0.208081	+	0.120135i
$306$		0			0
$307$		−	20.5359i		−	1.17205i	−0.810295	−	0.586023i	$-0.800693\pi$
$307$		−	20.5359i		−	1.17205i	0.810295	−	0.586023i	$-0.199307\pi$
$308$		0			0
$309$	1.63397	−	2.83013i	0.0929536	−	0.161000i
$310$		0			0
$311$	−15.1244			−0.857624			−0.428812	−	0.903394i	$-0.641068\pi$
$311$	−15.1244			−0.857624			−0.428812	+	0.903394i	$0.641068\pi$
$312$		0			0
$313$	5.60770			0.316966			0.158483	−	0.987362i	$-0.449340\pi$
$313$	5.60770			0.316966			0.158483	+	0.987362i	$0.449340\pi$
$314$		0			0
$315$	6.69615	−	11.5981i	0.377285	−	0.653478i
$316$		0			0
$317$			12.8038i			0.719136i	0.933119	+	0.359568i	$0.117076\pi$
$317$			12.8038i			0.719136i	−0.933119	+	0.359568i	$0.882924\pi$
$318$		0			0
$319$	24.5885	−	14.1962i	1.37669	−	0.794832i
$320$		0			0
$321$	0.464102	+	0.803848i	0.0259036	+	0.0448664i
$322$		0			0
$323$	12.2942	+	7.09808i	0.684069	+	0.394948i
$324$		0			0
$325$	−3.50000	+	0.866025i	−0.194145	+	0.0480384i
$326$		0			0
$327$	−36.5885	−	21.1244i	−2.02335	−	1.16818i
$328$		0			0
$329$	4.50000	+	7.79423i	0.248093	+	0.429710i
$330$		0			0
$331$	−0.803848	+	0.464102i	−0.0441835	+	0.0255093i	−0.521929	−	0.852989i	$-0.674787\pi$
$331$	−0.803848	+	0.464102i	−0.0441835	+	0.0255093i	0.477746	+	0.878498i	$0.341454\pi$
$332$		0			0
$333$		−	49.9808i		−	2.73893i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−4.19615			−0.228579			−0.114289	−	0.993447i	$-0.536459\pi$
$337$	−4.19615			−0.228579			−0.114289	+	0.993447i	$0.536459\pi$
$338$		0			0
$339$	−18.9282			−1.02804
$340$		0			0
$341$	−1.90192	+	3.29423i	−0.102995	+	0.178392i
$342$		0			0
$343$			15.0000i			0.809924i
$344$		0			0
$345$	−6.00000	+	3.46410i	−0.323029	+	0.186501i
$346$		0			0
$347$	−12.6340	−	21.8827i	−0.678227	−	1.17472i	−0.975514	−	0.219936i	$-0.929415\pi$
$347$	−12.6340	−	21.8827i	−0.678227	−	1.17472i	0.297287	−	0.954788i	$-0.403918\pi$
$348$		0			0
$349$	−29.4904	−	17.0263i	−1.57858	−	0.911396i	−0.995057	−	0.0993018i	$-0.968339\pi$
$349$	−29.4904	−	17.0263i	−1.57858	−	0.911396i	−0.583527	−	0.812094i	$-0.698328\pi$
$350$		0			0
$351$	14.0000	−	3.46410i	0.747265	−	0.184900i
$352$		0			0
$353$	−17.4904	−	10.0981i	−0.930919	−	0.537466i	−0.0438169	−	0.999040i	$-0.513952\pi$
$353$	−17.4904	−	10.0981i	−0.930919	−	0.537466i	−0.887102	+	0.461573i	$0.847285\pi$
$354$		0			0
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$		0			0
$357$	−15.5885	+	9.00000i	−0.825029	+	0.476331i
$358$		0			0
$359$			22.3923i			1.18182i	0.806737	+	0.590910i	$0.201231\pi$
$359$			22.3923i			1.18182i	−0.806737	+	0.590910i	$0.798769\pi$
$360$		0			0
$361$	11.3923	−	19.7321i	0.599595	−	1.03853i
$362$		0			0
$363$	5.46410			0.286791
$364$		0			0
$365$	−5.66025			−0.296271
$366$		0			0
$367$	−13.1962	+	22.8564i	−0.688834	+	1.19309i	0.283382	+	0.959007i	$0.408544\pi$
$367$	−13.1962	+	22.8564i	−0.688834	+	1.19309i	−0.972216	+	0.234088i	$0.924790\pi$
$368$		0			0
$369$			46.3923i			2.41509i
$370$		0			0
$371$	−16.7942	+	9.69615i	−0.871913	+	0.503399i
$372$		0			0
$373$	−10.1962	−	17.6603i	−0.527937	−	0.914413i	−0.999470	−	0.0325648i	$-0.989632\pi$
$373$	−10.1962	−	17.6603i	−0.527937	−	0.914413i	0.471533	−	0.881848i	$-0.343701\pi$
$374$		0			0
$375$	2.36603	+	1.36603i	0.122181	+	0.0705412i
$376$		0			0
$377$	9.46410	−	32.7846i	0.487426	−	1.68849i
$378$		0			0
$379$	−10.2058	−	5.89230i	−0.524235	−	0.302667i	0.214430	−	0.976739i	$-0.431210\pi$
$379$	−10.2058	−	5.89230i	−0.524235	−	0.302667i	−0.738666	+	0.674072i	$0.764544\pi$
$380$		0			0
$381$	28.9545	+	50.1506i	1.48338	+	2.56929i
$382$		0			0
$383$	1.39230	−	0.803848i	0.0711435	−	0.0410747i	−0.464006	−	0.885832i	$-0.653589\pi$
$383$	1.39230	−	0.803848i	0.0711435	−	0.0410747i	0.535150	+	0.844757i	$0.320255\pi$
$384$		0			0
$385$			9.00000i			0.458682i
$386$		0			0
$387$	4.46410	−	7.73205i	0.226923	−	0.393042i
$388$		0			0
$389$	19.2679			0.976924			0.488462	−	0.872585i	$-0.337558\pi$
$389$	19.2679			0.976924			0.488462	+	0.872585i	$0.337558\pi$
$390$		0			0
$391$	5.56922			0.281648
$392$		0			0
$393$	−24.7583	+	42.8827i	−1.24889	+	2.16315i
$394$		0			0
$395$		−	6.19615i		−	0.311762i
$396$		0			0
$397$	0.696152	−	0.401924i	0.0349389	−	0.0201720i	−0.482429	−	0.875935i	$-0.660245\pi$
$397$	0.696152	−	0.401924i	0.0349389	−	0.0201720i	0.517368	+	0.855763i	$0.326912\pi$
$398$		0			0
$399$	26.4904	+	45.8827i	1.32618	+	2.29701i
$400$		0			0
$401$	−4.50000	−	2.59808i	−0.224719	−	0.129742i	0.383414	−	0.923576i	$-0.374748\pi$
$401$	−4.50000	−	2.59808i	−0.224719	−	0.129742i	−0.608134	+	0.793835i	$0.708081\pi$
$402$		0			0
$403$	1.09808	+	4.43782i	0.0546991	+	0.221064i
$404$		0			0
$405$	2.13397	+	1.23205i	0.106038	+	0.0612211i
$406$		0			0
$407$	16.7942	+	29.0885i	0.832459	+	1.44186i
$408$		0			0
$409$	17.0885	−	9.86603i	0.844970	−	0.487844i	−0.0139806	−	0.999902i	$-0.504450\pi$
$409$	17.0885	−	9.86603i	0.844970	−	0.487844i	0.858950	+	0.512059i	$0.171117\pi$
$410$		0			0
$411$			22.3923i			1.10453i
$412$		0			0
$413$	−15.5885	+	27.0000i	−0.767058	+	1.32858i
$414$		0			0
$415$	−2.19615			−0.107805
$416$		0			0
$417$	25.1244			1.23034
$418$		0			0
$419$	8.66025	−	15.0000i	0.423081	−	0.732798i	−0.573158	−	0.819445i	$-0.694282\pi$
$419$	8.66025	−	15.0000i	0.423081	−	0.732798i	0.996239	+	0.0866469i	$0.0276152\pi$
$420$		0			0
$421$		−	27.1244i		−	1.32196i	−0.750403	−	0.660980i	$-0.770141\pi$
$421$		−	27.1244i		−	1.32196i	0.750403	−	0.660980i	$-0.229859\pi$
$422$		0			0
$423$	11.5981	−	6.69615i	0.563918	−	0.325578i
$424$		0			0
$425$	−1.09808	−	1.90192i	−0.0532645	−	0.0922569i
$426$		0			0
$427$	10.9019	+	6.29423i	0.527581	+	0.304599i
$428$		0			0
$429$	−21.2942	+	20.4904i	−1.02810	+	0.989285i
$430$		0			0
$431$	1.90192	+	1.09808i	0.0916124	+	0.0528925i	0.545106	−	0.838367i	$-0.316489\pi$
$431$	1.90192	+	1.09808i	0.0916124	+	0.0528925i	−0.453494	+	0.891259i	$0.649823\pi$
$432$		0			0
$433$	6.19615	+	10.7321i	0.297768	+	0.515749i	0.975625	−	0.219444i	$-0.0704245\pi$
$433$	6.19615	+	10.7321i	0.297768	+	0.515749i	−0.677857	+	0.735194i	$0.737091\pi$
$434$		0			0
$435$	−22.3923	+	12.9282i	−1.07363	+	0.619860i
$436$		0			0
$437$		−	16.3923i		−	0.784150i
$438$		0			0
$439$	−17.2942	+	29.9545i	−0.825408	+	1.42965i	0.0761982	+	0.997093i	$0.475722\pi$
$439$	−17.2942	+	29.9545i	−0.825408	+	1.42965i	−0.901607	+	0.432557i	$0.857612\pi$
$440$		0			0
$441$	−8.92820			−0.425153
$442$		0			0
$443$	1.60770			0.0763839			0.0381920	−	0.999270i	$-0.487840\pi$
$443$	1.60770			0.0763839			0.0381920	+	0.999270i	$0.487840\pi$
$444$		0			0
$445$	8.59808	−	14.8923i	0.407588	−	0.705963i
$446$		0			0
$447$		−	16.3923i		−	0.775329i
$448$		0			0
$449$	13.5000	−	7.79423i	0.637104	−	0.367832i	−0.146394	−	0.989226i	$-0.546767\pi$
$449$	13.5000	−	7.79423i	0.637104	−	0.367832i	0.783498	+	0.621394i	$0.213433\pi$
$450$		0			0
$451$	−15.5885	−	27.0000i	−0.734032	−	1.27138i
$452$		0			0
$453$	15.0000	+	8.66025i	0.704761	+	0.406894i
$454$		0			0
$455$	7.50000	+	7.79423i	0.351605	+	0.365399i
$456$		0			0
$457$	−30.8827	−	17.8301i	−1.44463	−	0.834058i	−0.446477	−	0.894795i	$-0.647322\pi$
$457$	−30.8827	−	17.8301i	−1.44463	−	0.834058i	−0.998154	+	0.0607368i	$0.980655\pi$
$458$		0			0
$459$	4.39230	+	7.60770i	0.205015	+	0.355097i
$460$		0			0
$461$	−0.509619	+	0.294229i	−0.0237353	+	0.0137036i	−0.511821	−	0.859092i	$-0.671029\pi$
$461$	−0.509619	+	0.294229i	−0.0237353	+	0.0137036i	0.488085	+	0.872796i	$0.337695\pi$
$462$		0			0
$463$		−	0.928203i		−	0.0431373i	−0.999767	−	0.0215686i	$-0.993134\pi$
$463$		−	0.928203i		−	0.0431373i	0.999767	−	0.0215686i	$-0.00686604\pi$
$464$		0			0
$465$	1.73205	−	3.00000i	0.0803219	−	0.139122i
$466$		0			0
$467$	10.1436			0.469390			0.234695	−	0.972069i	$-0.424591\pi$
$467$	10.1436			0.469390			0.234695	+	0.972069i	$0.424591\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	17.7583	−	30.7583i	0.818261	−	1.41727i
$472$		0			0
$473$			6.00000i			0.275880i
$474$		0			0
$475$	−5.59808	+	3.23205i	−0.256857	+	0.148297i
$476$		0			0
$477$	14.4282	+	24.9904i	0.660622	+	1.14423i
$478$		0			0
$479$	9.50962	+	5.49038i	0.434506	+	0.250862i	0.701264	−	0.712901i	$-0.252619\pi$
$479$	9.50962	+	5.49038i	0.434506	+	0.250862i	−0.266759	+	0.963763i	$0.585953\pi$
$480$		0			0
$481$	38.7846	+	11.1962i	1.76843	+	0.510501i
$482$		0			0
$483$	18.0000	+	10.3923i	0.819028	+	0.472866i
$484$		0			0
$485$	7.56218	+	13.0981i	0.343381	+	0.594753i
$486$		0			0
$487$	28.7942	−	16.6244i	1.30479	−	0.753321i	0.323569	−	0.946204i	$-0.395117\pi$
$487$	28.7942	−	16.6244i	1.30479	−	0.753321i	0.981222	+	0.192883i	$0.0617838\pi$
$488$		0			0
$489$		−	19.8564i		−	0.897938i
$490$		0			0
$491$	1.66987	−	2.89230i	0.0753603	−	0.130528i	−0.825883	−	0.563842i	$-0.809323\pi$
$491$	1.66987	−	2.89230i	0.0753603	−	0.130528i	0.901243	+	0.433314i	$0.142656\pi$
$492$		0			0
$493$	20.7846			0.936092
$494$		0			0
$495$	13.3923			0.601939
$496$		0			0
$497$	−9.00000	+	15.5885i	−0.403705	+	0.699238i
$498$		0			0
$499$		−	1.85641i		−	0.0831042i	−0.999136	−	0.0415521i	$-0.986770\pi$
$499$		−	1.85641i		−	0.0831042i	0.999136	−	0.0415521i	$-0.0132302\pi$
$500$		0			0
$501$	−7.09808	+	4.09808i	−0.317119	+	0.183089i
$502$		0			0
$503$	−4.66987	−	8.08846i	−0.208219	−	0.360646i	0.742934	−	0.669364i	$-0.233433\pi$
$503$	−4.66987	−	8.08846i	−0.208219	−	0.360646i	−0.951154	+	0.308718i	$0.900100\pi$
$504$		0			0
$505$	−6.29423	−	3.63397i	−0.280089	−	0.161710i
$506$		0			0
$507$	−1.36603	+	35.4904i	−0.0606673	+	1.57618i
$508$		0			0
$509$	1.39230	+	0.803848i	0.0617128	+	0.0356299i	0.530539	−	0.847661i	$-0.321990\pi$
$509$	1.39230	+	0.803848i	0.0617128	+	0.0356299i	−0.468826	+	0.883290i	$0.655323\pi$
$510$		0			0
$511$	8.49038	+	14.7058i	0.375592	+	0.650545i
$512$		0			0
$513$	22.3923	−	12.9282i	0.988644	−	0.570794i
$514$		0			0
$515$		−	1.19615i		−	0.0527088i
$516$		0			0
$517$	−4.50000	+	7.79423i	−0.197910	+	0.342790i
$518$		0			0
$519$	−40.9808			−1.79886
$520$		0			0
$521$	−0.464102			−0.0203327			−0.0101663	−	0.999948i	$-0.503236\pi$
$521$	−0.464102			−0.0203327			−0.0101663	+	0.999948i	$0.503236\pi$
$522$		0			0
$523$	9.19615	−	15.9282i	0.402120	−	0.696492i	−0.591862	−	0.806039i	$-0.701607\pi$
$523$	9.19615	−	15.9282i	0.402120	−	0.696492i	0.993982	+	0.109548i	$0.0349402\pi$
$524$		0			0
$525$		−	8.19615i		−	0.357709i
$526$		0			0
$527$	−2.41154	+	1.39230i	−0.105048	+	0.0606498i
$528$		0			0
$529$	8.28461	+	14.3494i	0.360200	+	0.623885i
$530$		0			0
$531$	40.1769	+	23.1962i	1.74353	+	1.00663i
$532$		0			0
$533$	−36.0000	−	10.3923i	−1.55933	−	0.450141i
$534$		0			0
$535$	0.294229	+	0.169873i	0.0127206	+	0.00734425i
$536$		0			0
$537$	−3.46410	−	6.00000i	−0.149487	−	0.258919i
$538$		0			0
$539$	5.19615	−	3.00000i	0.223814	−	0.129219i
$540$		0			0
$541$			16.0526i			0.690153i	0.938574	+	0.345077i	$0.112147\pi$
$541$			16.0526i			0.690153i	−0.938574	+	0.345077i	$0.887853\pi$
$542$		0			0
$543$	22.6603	−	39.2487i	0.972445	−	1.68432i
$544$		0			0
$545$	−15.4641			−0.662409
$546$		0			0
$547$	−34.7846			−1.48728			−0.743641	−	0.668579i	$-0.766903\pi$
$547$	−34.7846			−1.48728			−0.743641	+	0.668579i	$0.766903\pi$
$548$		0			0
$549$	9.36603	−	16.2224i	0.399732	−	0.692357i
$550$		0			0
$551$		−	61.1769i		−	2.60622i
$552$		0			0
$553$	−16.0981	+	9.29423i	−0.684560	+	0.395231i
$554$		0			0
$555$	−15.2942	−	26.4904i	−0.649204	−	1.12445i
$556$		0			0
$557$	14.8923	+	8.59808i	0.631007	+	0.364312i	0.781142	−	0.624353i	$-0.214637\pi$
$557$	14.8923	+	8.59808i	0.631007	+	0.364312i	−0.150135	+	0.988666i	$0.547971\pi$
$558$		0			0
$559$	5.00000	+	5.19615i	0.211477	+	0.219774i
$560$		0			0
$561$	−15.5885	−	9.00000i	−0.658145	−	0.379980i
$562$		0			0
$563$	10.7321	+	18.5885i	0.452302	+	0.783410i	0.998529	−	0.0542274i	$-0.0172696\pi$
$563$	10.7321	+	18.5885i	0.452302	+	0.783410i	−0.546227	+	0.837637i	$0.683936\pi$
$564$		0			0
$565$	−6.00000	+	3.46410i	−0.252422	+	0.145736i
$566$		0			0
$567$		−	7.39230i		−	0.310448i
$568$		0			0
$569$	−10.6244	+	18.4019i	−0.445396	+	0.771449i	−0.998080	−	0.0619424i	$-0.980270\pi$
$569$	−10.6244	+	18.4019i	−0.445396	+	0.771449i	0.552684	+	0.833391i	$0.313604\pi$
$570$		0			0
$571$	−34.3731			−1.43847			−0.719234	−	0.694768i	$-0.755507\pi$
$571$	−34.3731			−1.43847			−0.719234	+	0.694768i	$0.755507\pi$
$572$		0			0
$573$	52.6410			2.19911
$574$		0			0
$575$	−1.26795	+	2.19615i	−0.0528771	+	0.0915859i
$576$		0			0
$577$		−	32.4449i		−	1.35070i	−0.737499	−	0.675349i	$-0.763993\pi$
$577$		−	32.4449i		−	1.35070i	0.737499	−	0.675349i	$-0.236007\pi$
$578$		0			0
$579$	10.3923	−	6.00000i	0.431889	−	0.249351i
$580$		0			0
$581$	3.29423	+	5.70577i	0.136668	+	0.236715i
$582$		0			0
$583$	−16.7942	−	9.69615i	−0.695546	−	0.401574i
$584$		0			0
$585$	11.5981	−	11.1603i	0.479521	−	0.461420i
$586$		0			0
$587$	25.9808	+	15.0000i	1.07234	+	0.619116i	0.928820	−	0.370531i	$-0.120824\pi$
$587$	25.9808	+	15.0000i	1.07234	+	0.619116i	0.143521	+	0.989647i	$0.454158\pi$
$588$		0			0
$589$	4.09808	+	7.09808i	0.168858	+	0.292471i
$590$		0			0
$591$	−22.6865	+	13.0981i	−0.933199	+	0.538783i
$592$		0			0
$593$		−	20.7846i		−	0.853522i	−0.904365	−	0.426761i	$-0.859655\pi$
$593$		−	20.7846i		−	0.853522i	0.904365	−	0.426761i	$-0.140345\pi$
$594$		0			0
$595$	−3.29423	+	5.70577i	−0.135050	+	0.233914i
$596$		0			0
$597$	−39.3205			−1.60928
$598$		0			0
$599$	−7.85641			−0.321004			−0.160502	−	0.987036i	$-0.551311\pi$
$599$	−7.85641			−0.321004			−0.160502	+	0.987036i	$0.551311\pi$
$600$		0			0
$601$	−1.89230	+	3.27757i	−0.0771887	+	0.133695i	−0.902036	−	0.431661i	$-0.857928\pi$
$601$	−1.89230	+	3.27757i	−0.0771887	+	0.133695i	0.824847	+	0.565356i	$0.191261\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.73205	−	1.00000i	0.0704179	−	0.0406558i
$606$		0			0
$607$	−3.20577	−	5.55256i	−0.130118	−	0.225371i	0.793604	−	0.608435i	$-0.208202\pi$
$607$	−3.20577	−	5.55256i	−0.130118	−	0.225371i	−0.923722	+	0.383064i	$0.874869\pi$
$608$		0			0
$609$	67.1769	+	38.7846i	2.72215	+	1.57163i
$610$		0			0
$611$	2.59808	+	10.5000i	0.105107	+	0.424785i
$612$		0			0
$613$	23.3038	+	13.4545i	0.941234	+	0.543421i	0.890347	−	0.455283i	$-0.150462\pi$
$613$	23.3038	+	13.4545i	0.941234	+	0.543421i	0.0508868	+	0.998704i	$0.483795\pi$
$614$		0			0
$615$	14.1962	+	24.5885i	0.572444	+	0.991502i
$616$		0			0
$617$	−15.5885	+	9.00000i	−0.627568	+	0.362326i	−0.779809	−	0.626017i	$-0.784684\pi$
$617$	−15.5885	+	9.00000i	−0.627568	+	0.362326i	0.152242	+	0.988343i	$0.451351\pi$
$618$		0			0
$619$		−	10.6077i		−	0.426359i	−0.977013	−	0.213180i	$-0.931618\pi$
$619$		−	10.6077i		−	0.426359i	0.977013	−	0.213180i	$-0.0683820\pi$
$620$		0			0
$621$	5.07180	−	8.78461i	0.203524	−	0.352514i
$622$		0			0
$623$	−51.5885			−2.06685
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−26.4904	+	45.8827i	−1.05792	+	1.83238i
$628$		0			0
$629$			24.5885i			0.980406i
$630$		0			0
$631$	18.0000	−	10.3923i	0.716569	−	0.413711i	−0.0969198	−	0.995292i	$-0.530899\pi$
$631$	18.0000	−	10.3923i	0.716569	−	0.413711i	0.813488	+	0.581581i	$0.197566\pi$
$632$		0			0
$633$	18.5622	+	32.1506i	0.737780	+	1.27787i
$634$		0			0
$635$	18.3564	+	10.5981i	0.728452	+	0.420572i
$636$		0			0
$637$	2.00000	−	6.92820i	0.0792429	−	0.274505i
$638$		0			0
$639$	23.1962	+	13.3923i	0.917626	+	0.529791i
$640$		0			0
$641$	−22.9641	−	39.7750i	−0.907027	−	1.57102i	−0.818172	−	0.574973i	$-0.805012\pi$
$641$	−22.9641	−	39.7750i	−0.907027	−	1.57102i	−0.0888552	−	0.996045i	$-0.528321\pi$
$642$		0			0
$643$	−6.29423	+	3.63397i	−0.248220	+	0.143310i	−0.618949	−	0.785431i	$-0.712441\pi$
$643$	−6.29423	+	3.63397i	−0.248220	+	0.143310i	0.370729	+	0.928741i	$0.379108\pi$
$644$		0			0
$645$		−	5.46410i		−	0.215149i
$646$		0			0
$647$	−5.59808	+	9.69615i	−0.220083	+	0.381195i	−0.954833	−	0.297143i	$-0.903966\pi$
$647$	−5.59808	+	9.69615i	−0.220083	+	0.381195i	0.734750	+	0.678338i	$0.237300\pi$
$648$		0			0
$649$	−31.1769			−1.22380
$650$		0			0
$651$	−10.3923			−0.407307
$652$		0			0
$653$	9.69615	−	16.7942i	0.379440	−	0.657209i	−0.611541	−	0.791213i	$-0.709450\pi$
$653$	9.69615	−	16.7942i	0.379440	−	0.657209i	0.990981	+	0.134004i	$0.0427834\pi$
$654$		0			0
$655$			18.1244i			0.708177i
$656$		0			0
$657$	21.8827	−	12.6340i	0.853725	−	0.492898i
$658$		0			0
$659$	14.6603	+	25.3923i	0.571082	+	0.989144i	0.996455	+	0.0841255i	$0.0268097\pi$
$659$	14.6603	+	25.3923i	0.571082	+	0.989144i	−0.425373	+	0.905018i	$0.639857\pi$
$660$		0			0
$661$	25.9019	+	14.9545i	1.00747	+	0.581662i	0.910449	−	0.413621i	$-0.135736\pi$
$661$	25.9019	+	14.9545i	1.00747	+	0.581662i	0.0970187	+	0.995283i	$0.469069\pi$
$662$		0			0
$663$	−21.0000	+	5.19615i	−0.815572	+	0.201802i
$664$		0			0
$665$	16.7942	+	9.69615i	0.651252	+	0.376001i
$666$		0			0
$667$	−12.0000	−	20.7846i	−0.464642	−	0.804783i
$668$		0			0
$669$	−1.09808	+	0.633975i	−0.0424541	+	0.0245109i
$670$		0			0
$671$			12.5885i			0.485972i
$672$		0			0
$673$	−1.80385	+	3.12436i	−0.0695332	+	0.120435i	−0.898696	−	0.438572i	$-0.855484\pi$
$673$	−1.80385	+	3.12436i	−0.0695332	+	0.120435i	0.829163	+	0.559007i	$0.188818\pi$
$674$		0			0
$675$	−4.00000			−0.153960
$676$		0			0
$677$	1.85641			0.0713475			0.0356737	−	0.999363i	$-0.488642\pi$
$677$	1.85641			0.0713475			0.0356737	+	0.999363i	$0.488642\pi$
$678$		0			0
$679$	22.6865	−	39.2942i	0.870629	−	1.50797i
$680$		0			0
$681$		−	12.0000i		−	0.459841i
$682$		0			0
$683$	−27.0000	+	15.5885i	−1.03313	+	0.596476i	−0.917879	−	0.396861i	$-0.870099\pi$
$683$	−27.0000	+	15.5885i	−1.03313	+	0.596476i	−0.115248	+	0.993337i	$0.536766\pi$
$684$		0			0
$685$	4.09808	+	7.09808i	0.156579	+	0.271204i
$686$		0			0
$687$	−11.1962	−	6.46410i	−0.427160	−	0.246621i
$688$		0			0
$689$	−22.6244	+	5.59808i	−0.861919	+	0.213270i
$690$		0			0
$691$	16.2058	+	9.35641i	0.616497	+	0.355934i	0.775504	−	0.631343i	$-0.217496\pi$
$691$	16.2058	+	9.35641i	0.616497	+	0.355934i	−0.159007	+	0.987277i	$0.550829\pi$
$692$		0			0
$693$	−20.0885	−	34.7942i	−0.763097	−	1.32172i
$694$		0			0
$695$	7.96410	−	4.59808i	0.302096	−	0.174415i
$696$		0			0
$697$		−	22.8231i		−	0.864486i
$698$		0			0
$699$	−1.73205	+	3.00000i	−0.0655122	+	0.113470i
$700$		0			0
$701$	−29.9090			−1.12965			−0.564823	−	0.825212i	$-0.691056\pi$
$701$	−29.9090			−1.12965			−0.564823	+	0.825212i	$0.691056\pi$
$702$		0			0
$703$	72.3731			2.72960
$704$		0			0
$705$	4.09808	−	7.09808i	0.154342	−	0.267329i
$706$		0			0
$707$			21.8038i			0.820018i
$708$		0			0
$709$	35.4904	−	20.4904i	1.33287	−	0.769532i	0.347131	−	0.937817i	$-0.387156\pi$
$709$	35.4904	−	20.4904i	1.33287	−	0.769532i	0.985738	+	0.168284i	$0.0538227\pi$
$710$		0			0
$711$	13.8301	+	23.9545i	0.518670	+	0.898363i
$712$		0			0
$713$	2.78461	+	1.60770i	0.104284	+	0.0602087i
$714$		0			0
$715$	−3.00000	+	10.3923i	−0.112194	+	0.388650i
$716$		0			0
$717$	19.3923	+	11.1962i	0.724219	+	0.418128i
$718$		0			0
$719$	−0.928203	−	1.60770i	−0.0346161	−	0.0599569i	0.848198	−	0.529679i	$-0.177688\pi$
$719$	−0.928203	−	1.60770i	−0.0346161	−	0.0599569i	−0.882814	+	0.469722i	$0.844354\pi$
$720$		0			0
$721$	−3.10770	+	1.79423i	−0.115737	+	0.0668206i
$722$		0			0
$723$		−	23.6603i		−	0.879934i
$724$		0			0
$725$	−4.73205	+	8.19615i	−0.175744	+	0.304397i
$726$		0			0
$727$	38.3731			1.42318			0.711589	−	0.702596i	$-0.247976\pi$
$727$	38.3731			1.42318			0.711589	+	0.702596i	$0.247976\pi$
$728$		0			0
$729$	−43.7846			−1.62165
$730$		0			0
$731$	−2.19615	+	3.80385i	−0.0812276	+	0.140690i
$732$		0			0
$733$			50.9090i			1.88037i	0.340670	+	0.940183i	$0.389346\pi$
$733$			50.9090i			1.88037i	−0.340670	+	0.940183i	$0.610654\pi$
$734$		0			0
$735$	−4.73205	+	2.73205i	−0.174544	+	0.100773i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−43.7942	−	25.2846i	−1.61100	−	0.930109i	−0.989140	−	0.146979i	$-0.953045\pi$
$739$	−43.7942	−	25.2846i	−1.61100	−	0.930109i	−0.621857	−	0.783131i	$-0.713622\pi$
$740$		0			0
$741$	15.2942	+	61.8109i	0.561848	+	2.27068i
$742$		0			0
$743$	−29.7846	−	17.1962i	−1.09269	−	0.630866i	−0.158400	−	0.987375i	$-0.550633\pi$
$743$	−29.7846	−	17.1962i	−1.09269	−	0.630866i	−0.934292	+	0.356509i	$0.883967\pi$
$744$		0			0
$745$	−3.00000	−	5.19615i	−0.109911	−	0.190372i
$746$		0			0
$747$	8.49038	−	4.90192i	0.310647	−	0.179352i
$748$		0			0
$749$		−	1.01924i		−	0.0372421i
$750$		0			0
$751$	0.196152	−	0.339746i	0.00715770	−	0.0123975i	−0.862424	−	0.506186i	$-0.831055\pi$
$751$	0.196152	−	0.339746i	0.00715770	−	0.0123975i	0.869582	+	0.493788i	$0.164388\pi$
$752$		0			0
$753$	−18.5885			−0.677401
$754$		0			0
$755$	6.33975			0.230727
$756$		0			0
$757$	−1.89230	+	3.27757i	−0.0687770	+	0.119125i	−0.898363	−	0.439253i	$-0.855243\pi$
$757$	−1.89230	+	3.27757i	−0.0687770	+	0.119125i	0.829586	+	0.558379i	$0.188576\pi$
$758$		0			0
$759$			20.7846i			0.754434i
$760$		0			0
$761$	−25.2846	+	14.5981i	−0.916566	+	0.529180i	−0.882538	−	0.470241i	$-0.844167\pi$
$761$	−25.2846	+	14.5981i	−0.916566	+	0.529180i	−0.0340283	+	0.999421i	$0.510834\pi$
$762$		0			0
$763$	23.1962	+	40.1769i	0.839757	+	1.45450i
$764$		0			0
$765$	8.49038	+	4.90192i	0.306970	+	0.177229i
$766$		0			0
$767$	−27.0000	+	25.9808i	−0.974913	+	0.938111i
$768$		0			0
$769$	−33.0000	−	19.0526i	−1.19001	−	0.687053i	−0.231701	−	0.972787i	$-0.574429\pi$
$769$	−33.0000	−	19.0526i	−1.19001	−	0.687053i	−0.958309	+	0.285734i	$0.907763\pi$
$770$		0			0
$771$	−18.9282	−	32.7846i	−0.681683	−	1.18071i
$772$		0			0
$773$	−29.0885	+	16.7942i	−1.04624	+	0.604046i	−0.921594	−	0.388155i	$-0.873113\pi$
$773$	−29.0885	+	16.7942i	−1.04624	+	0.604046i	−0.124645	+	0.992201i	$0.539779\pi$
$774$		0			0
$775$		−	1.26795i		−	0.0455461i
$776$		0			0
$777$	−45.8827	+	79.4711i	−1.64603	+	2.85101i
$778$		0			0
$779$	−67.1769			−2.40686
$780$		0			0
$781$	−18.0000			−0.644091
$782$		0			0
$783$	18.9282	−	32.7846i	0.676439	−	1.17163i
$784$		0			0
$785$		−	13.0000i		−	0.463990i
$786$		0			0
$787$	31.9019	−	18.4186i	1.13718	−	0.656552i	0.191450	−	0.981502i	$-0.438681\pi$
$787$	31.9019	−	18.4186i	1.13718	−	0.656552i	0.945731	+	0.324951i	$0.105348\pi$
$788$		0			0
$789$	−37.6865	−	65.2750i	−1.34168	−	2.32385i
$790$		0			0
$791$	18.0000	+	10.3923i	0.640006	+	0.369508i
$792$		0			0
$793$	10.4904	+	10.9019i	0.372524	+	0.387139i
$794$		0			0
$795$	15.2942	+	8.83013i	0.542430	+	0.313172i
$796$		0			0
$797$	−0.464102	−	0.803848i	−0.0164393	−	0.0284737i	0.857689	−	0.514169i	$-0.171900\pi$
$797$	−0.464102	−	0.803848i	−0.0164393	−	0.0284737i	−0.874128	+	0.485696i	$0.838566\pi$
$798$		0			0
$799$	−5.70577	+	3.29423i	−0.201856	+	0.116541i
$800$		0			0
$801$			76.7654i			2.71237i
$802$		0			0
$803$	−8.49038	+	14.7058i	−0.299619	+	0.518955i
$804$		0			0
$805$	7.60770			0.268136
$806$		0			0
$807$	−7.85641			−0.276559
$808$		0			0
$809$	−12.0000	+	20.7846i	−0.421898	+	0.730748i	−0.996125	−	0.0879478i	$-0.971969\pi$
$809$	−12.0000	+	20.7846i	−0.421898	+	0.730748i	0.574228	+	0.818696i	$0.305302\pi$
$810$		0			0
$811$			22.6077i			0.793864i	0.917848	+	0.396932i	$0.129925\pi$
$811$			22.6077i			0.793864i	−0.917848	+	0.396932i	$0.870075\pi$
$812$		0			0
$813$	−6.00000	+	3.46410i	−0.210429	+	0.121491i
$814$		0			0
$815$	−3.63397	−	6.29423i	−0.127293	−	0.220477i
$816$		0			0
$817$	11.1962	+	6.46410i	0.391704	+	0.226150i
$818$		0			0
$819$	−46.3923	−	13.3923i	−1.62108	−	0.467965i
$820$		0			0
$821$	−8.49038	−	4.90192i	−0.296316	−	0.171078i	0.344471	−	0.938797i	$-0.388058\pi$
$821$	−8.49038	−	4.90192i	−0.296316	−	0.171078i	−0.640787	+	0.767719i	$0.721392\pi$
$822$		0			0
$823$	−8.40192	−	14.5526i	−0.292873	−	0.507270i	0.681615	−	0.731711i	$-0.261278\pi$
$823$	−8.40192	−	14.5526i	−0.292873	−	0.507270i	−0.974488	+	0.224441i	$0.927945\pi$
$824$		0			0
$825$	7.09808	−	4.09808i	0.247123	−	0.142677i
$826$		0			0
$827$		−	11.4115i		−	0.396818i	−0.980119	−	0.198409i	$-0.936423\pi$
$827$		−	11.4115i		−	0.396818i	0.980119	−	0.198409i	$-0.0635775\pi$
$828$		0			0
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	−0.638457	−	0.769657i	$-0.720427\pi$
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	0.985771	+	0.168091i	$0.0537604\pi$
$830$		0			0
$831$	−2.73205			−0.0947738
$832$		0			0
$833$	4.39230			0.152184
$834$		0			0
$835$	−1.50000	+	2.59808i	−0.0519096	+	0.0899101i
$836$		0			0
$837$			5.07180i			0.175307i
$838$		0			0
$839$	27.8827	−	16.0981i	0.962617	−	0.555767i	0.0656397	−	0.997843i	$-0.479091\pi$
$839$	27.8827	−	16.0981i	0.962617	−	0.555767i	0.896978	+	0.442076i	$0.145758\pi$
$840$		0			0
$841$	−30.2846	−	52.4545i	−1.04430	−	1.80878i
$842$		0			0
$843$	24.5885	+	14.1962i	0.846871	+	0.488941i
$844$		0			0
$845$	6.06218	+	11.5000i	0.208545	+	0.395612i
$846$		0			0
$847$	−5.19615	−	3.00000i	−0.178542	−	0.103081i
$848$		0			0
$849$	−41.5167	−	71.9090i	−1.42485	−	2.46791i
$850$		0			0
$851$	24.5885	−	14.1962i	0.842881	−	0.486638i
$852$		0			0
$853$			13.8564i			0.474434i	0.971457	+	0.237217i	$0.0762353\pi$
$853$			13.8564i			0.474434i	−0.971457	+	0.237217i	$0.923765\pi$
$854$		0			0
$855$	14.4282	−	24.9904i	0.493434	−	0.854653i
$856$		0			0
$857$	−13.2679			−0.453225			−0.226612	−	0.973985i	$-0.572765\pi$
$857$	−13.2679			−0.453225			−0.226612	+	0.973985i	$0.572765\pi$
$858$		0			0
$859$	−52.3731			−1.78695			−0.893473	−	0.449117i	$-0.851739\pi$
$859$	−52.3731			−1.78695			−0.893473	+	0.449117i	$0.851739\pi$
$860$		0			0
$861$	42.5885	−	73.7654i	1.45141	−	2.51392i
$862$		0			0
$863$		−	19.1769i		−	0.652790i	−0.945234	−	0.326395i	$-0.894166\pi$
$863$		−	19.1769i		−	0.652790i	0.945234	−	0.326395i	$-0.105834\pi$
$864$		0			0
$865$	−12.9904	+	7.50000i	−0.441686	+	0.255008i
$866$		0			0
$867$	16.6340	+	28.8109i	0.564919	+	0.978469i
$868$		0			0
$869$	−16.0981	−	9.29423i	−0.546090	−	0.315285i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−58.4711	−	33.7583i	−1.97895	−	1.14255i
$874$		0			0
$875$	−1.50000	−	2.59808i	−0.0507093	−	0.0878310i
$876$		0			0
$877$	17.7846	−	10.2679i	0.600544	−	0.346724i	−0.168712	−	0.985665i	$-0.553961\pi$
$877$	17.7846	−	10.2679i	0.600544	−	0.346724i	0.769255	+	0.638941i	$0.220627\pi$
$878$		0			0
$879$		−	2.19615i		−	0.0740744i
$880$		0			0
$881$	4.16025	−	7.20577i	0.140163	−	0.242769i	−0.787395	−	0.616449i	$-0.788571\pi$
$881$	4.16025	−	7.20577i	0.140163	−	0.242769i	0.927558	+	0.373680i	$0.121904\pi$
$882$		0			0
$883$	26.5885			0.894773			0.447386	−	0.894341i	$-0.352355\pi$
$883$	26.5885			0.894773			0.447386	+	0.894341i	$0.352355\pi$
$884$		0			0
$885$	28.3923			0.954397
$886$		0			0
$887$	26.3827	−	45.6962i	0.885844	−	1.53433i	0.0411005	−	0.999155i	$-0.486914\pi$
$887$	26.3827	−	45.6962i	0.885844	−	1.53433i	0.844743	−	0.535172i	$-0.179753\pi$
$888$		0			0
$889$		−	63.5885i		−	2.13269i
$890$		0			0
$891$	6.40192	−	3.69615i	0.214473	−	0.123826i
$892$		0			0
$893$	9.69615	+	16.7942i	0.324469	+	0.561997i
$894$		0			0
$895$	−2.19615	−	1.26795i	−0.0734093	−	0.0423829i
$896$		0			0
$897$	17.3205	+	18.0000i	0.578315	+	0.601003i
$898$		0			0
$899$	10.3923	+	6.00000i	0.346603	+	0.200111i
$900$		0			0
$901$	−7.09808	−	12.2942i	−0.236471	−	0.409580i
$902$		0			0
$903$	−14.1962	+	8.19615i	−0.472418	+	0.272751i
$904$		0			0
$905$		−	16.5885i		−	0.551419i
$906$		0			0
$907$	−13.2942	+	23.0263i	−0.441428	+	0.764575i	−0.997796	−	0.0663609i	$-0.978861\pi$
$907$	−13.2942	+	23.0263i	−0.441428	+	0.764575i	0.556368	+	0.830936i	$0.312194\pi$
$908$		0			0
$909$	32.4449			1.07613
$910$		0			0
$911$	14.5359			0.481596			0.240798	−	0.970575i	$-0.422591\pi$
$911$	14.5359			0.481596			0.240798	+	0.970575i	$0.422591\pi$
$912$		0			0
$913$	−3.29423	+	5.70577i	−0.109023	+	0.188833i
$914$		0			0
$915$		−	11.4641i		−	0.378992i
$916$		0			0
$917$	47.0885	−	27.1865i	1.55500	−	0.897778i
$918$		0			0
$919$	−5.39230	−	9.33975i	−0.177876	−	0.308090i	0.763277	−	0.646071i	$-0.223589\pi$
$919$	−5.39230	−	9.33975i	−0.177876	−	0.308090i	−0.941153	+	0.337982i	$0.890256\pi$
$920$		0			0
$921$	48.5885	+	28.0526i	1.60104	+	0.924363i
$922$		0			0
$923$	−15.5885	+	15.0000i	−0.513100	+	0.493731i
$924$		0			0
$925$	−9.69615	−	5.59808i	−0.318808	−	0.184064i
$926$		0			0
$927$	2.66987	+	4.62436i	0.0876901	+	0.151884i
$928$		0			0
$929$	38.7846	−	22.3923i	1.27248	−	0.734668i	0.297027	−	0.954869i	$-0.404005\pi$
$929$	38.7846	−	22.3923i	1.27248	−	0.734668i	0.975454	+	0.220201i	$0.0706714\pi$
$930$		0			0
$931$		−	12.9282i		−	0.423705i
$932$		0			0
$933$	20.6603	−	35.7846i	0.676386	−	1.17154i
$934$		0			0
$935$	−6.58846			−0.215466
$936$		0			0
$937$	−30.3923			−0.992873			−0.496437	−	0.868073i	$-0.665359\pi$
$937$	−30.3923			−0.992873			−0.496437	+	0.868073i	$0.665359\pi$
$938$		0			0
$939$	−7.66025	+	13.2679i	−0.249983	+	0.432983i
$940$		0			0
$941$		−	44.7846i		−	1.45994i	−0.683481	−	0.729968i	$-0.739535\pi$
$941$		−	44.7846i		−	1.45994i	0.683481	−	0.729968i	$-0.260465\pi$
$942$		0			0
$943$	−22.8231	+	13.1769i	−0.743222	+	0.429099i
$944$		0			0
$945$	6.00000	+	10.3923i	0.195180	+	0.338062i
$946$		0			0
$947$	−49.6865	−	28.6865i	−1.61460	−	0.932187i	−0.988286	−	0.152612i	$-0.951231\pi$
$947$	−49.6865	−	28.6865i	−1.61460	−	0.932187i	−0.626309	−	0.779575i	$-0.715435\pi$
$948$		0			0
$949$	4.90192	+	19.8109i	0.159123	+	0.643089i
$950$		0			0
$951$	−30.2942	−	17.4904i	−0.982358	−	0.567164i
$952$		0			0
$953$	−12.2942	−	21.2942i	−0.398249	−	0.689788i	0.595261	−	0.803533i	$-0.297049\pi$
$953$	−12.2942	−	21.2942i	−0.398249	−	0.689788i	−0.993510	+	0.113745i	$0.963715\pi$
$954$		0			0
$955$	16.6865	−	9.63397i	0.539964	−	0.311748i
$956$		0			0
$957$			77.5692i			2.50746i
$958$		0			0
$959$	12.2942	−	21.2942i	0.397001	−	0.687627i
$960$		0			0
$961$	29.3923			0.948139
$962$		0			0
$963$	−1.51666			−0.0488737
$964$		0			0
$965$	2.19615	−	3.80385i	0.0706966	−	0.122450i
$966$		0			0
$967$			38.5692i			1.24030i	0.784482	+	0.620151i	$0.212929\pi$
$967$			38.5692i			1.24030i	−0.784482	+	0.620151i	$0.787071\pi$
$968$		0			0
$969$	−33.5885	+	19.3923i	−1.07902	+	0.622971i
$970$		0			0
$971$	−23.3827	−	40.5000i	−0.750386	−	1.29971i	−0.947636	−	0.319354i	$-0.896534\pi$
$971$	−23.3827	−	40.5000i	−0.750386	−	1.29971i	0.197250	−	0.980353i	$-0.436799\pi$
$972$		0			0
$973$	−23.8923	−	13.7942i	−0.765952	−	0.442223i
$974$		0			0
$975$	2.73205	−	9.46410i	0.0874957	−	0.303094i
$976$		0			0
$977$	3.80385	+	2.19615i	0.121696	+	0.0702611i	0.559612	−	0.828755i	$-0.310950\pi$
$977$	3.80385	+	2.19615i	0.121696	+	0.0702611i	−0.437916	+	0.899016i	$0.644283\pi$
$978$		0			0
$979$	−25.7942	−	44.6769i	−0.824387	−	1.42788i
$980$		0			0
$981$	59.7846	−	34.5167i	1.90878	−	1.10203i
$982$		0			0
$983$		−	38.5692i		−	1.23017i	−0.788462	−	0.615084i	$-0.789122\pi$
$983$		−	38.5692i		−	1.23017i	0.788462	−	0.615084i	$-0.210878\pi$
$984$		0			0
$985$	−4.79423	+	8.30385i	−0.152757	+	0.264583i
$986$		0			0
$987$	−24.5885			−0.782659
$988$		0			0
$989$	5.07180			0.161274
$990$		0			0
$991$	25.5885	−	44.3205i	0.812844	−	1.40789i	−0.0980215	−	0.995184i	$-0.531251\pi$
$991$	25.5885	−	44.3205i	0.812844	−	1.40789i	0.910866	−	0.412703i	$-0.135415\pi$
$992$		0			0
$993$		−	2.53590i		−	0.0804743i
$994$		0			0
$995$	−12.4641	+	7.19615i	−0.395139	+	0.228133i
$996$		0			0
$997$	21.2846	+	36.8660i	0.674090	+	1.16756i	0.976734	+	0.214455i	$0.0687975\pi$
$997$	21.2846	+	36.8660i	0.674090	+	1.16756i	−0.302644	+	0.953104i	$0.597869\pi$
$998$		0			0
$999$	38.7846	+	22.3923i	1.22709	+	0.708461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.da.a.641.1		4
4.3	odd	2		130.2.l.a.121.2	yes	4
12.11	even	2		1170.2.bs.c.901.1		4
13.10	even	6	inner	1040.2.da.a.881.1		4
20.3	even	4		650.2.n.b.199.2		4
20.7	even	4		650.2.n.a.199.1		4
20.19	odd	2		650.2.m.a.251.1		4
52.3	odd	6		1690.2.l.g.361.1		4
52.7	even	12		1690.2.a.m.1.1		2
52.11	even	12		1690.2.e.l.991.2		4
52.15	even	12		1690.2.e.n.991.2		4
52.19	even	12		1690.2.a.j.1.1		2
52.23	odd	6		130.2.l.a.101.2	✓	4
52.31	even	4		1690.2.e.n.191.2		4
52.35	odd	6		1690.2.d.f.1351.1		4
52.43	odd	6		1690.2.d.f.1351.3		4
52.47	even	4		1690.2.e.l.191.2		4
52.51	odd	2		1690.2.l.g.1161.1		4
156.23	even	6		1170.2.bs.c.361.1		4
260.19	even	12		8450.2.a.bm.1.2		2
260.23	even	12		650.2.n.a.49.1		4
260.59	even	12		8450.2.a.bf.1.2		2
260.127	even	12		650.2.n.b.49.2		4
260.179	odd	6		650.2.m.a.101.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.a.101.2	✓	4	52.23	odd	6
130.2.l.a.121.2	yes	4	4.3	odd	2
650.2.m.a.101.1		4	260.179	odd	6
650.2.m.a.251.1		4	20.19	odd	2
650.2.n.a.49.1		4	260.23	even	12
650.2.n.a.199.1		4	20.7	even	4
650.2.n.b.49.2		4	260.127	even	12
650.2.n.b.199.2		4	20.3	even	4
1040.2.da.a.641.1		4	1.1	even	1	trivial
1040.2.da.a.881.1		4	13.10	even	6	inner
1170.2.bs.c.361.1		4	156.23	even	6
1170.2.bs.c.901.1		4	12.11	even	2
1690.2.a.j.1.1		2	52.19	even	12
1690.2.a.m.1.1		2	52.7	even	12
1690.2.d.f.1351.1		4	52.35	odd	6
1690.2.d.f.1351.3		4	52.43	odd	6
1690.2.e.l.191.2		4	52.47	even	4
1690.2.e.l.991.2		4	52.11	even	12
1690.2.e.n.191.2		4	52.31	even	4
1690.2.e.n.991.2		4	52.15	even	12
1690.2.l.g.361.1		4	52.3	odd	6
1690.2.l.g.1161.1		4	52.51	odd	2
8450.2.a.bf.1.2		2	260.59	even	12
8450.2.a.bm.1.2		2	260.19	even	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.da (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 2.36603i) q^{3} +1.00000i q^{5} +(2.59808 - 1.50000i) q^{7} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})\)	\(q+(-1.36603 + 2.36603i) q^{3} +1.00000i q^{5} +(2.59808 - 1.50000i) q^{7} +(-2.23205 - 3.86603i) q^{9} +(2.59808 + 1.50000i) q^{11} +(3.50000 - 0.866025i) q^{13} +(-2.36603 - 1.36603i) q^{15} +(1.09808 + 1.90192i) q^{17} +(5.59808 - 3.23205i) q^{19} +8.19615i q^{21} +(1.26795 - 2.19615i) q^{23} -1.00000 q^{25} +4.00000 q^{27} +(4.73205 - 8.19615i) q^{29} +1.26795i q^{31} +(-7.09808 + 4.09808i) q^{33} +(1.50000 + 2.59808i) q^{35} +(9.69615 + 5.59808i) q^{37} +(-2.73205 + 9.46410i) q^{39} +(-9.00000 - 5.19615i) q^{41} +(1.00000 + 1.73205i) q^{43} +(3.86603 - 2.23205i) q^{45} +3.00000i q^{47} +(1.00000 - 1.73205i) q^{49} -6.00000 q^{51} -6.46410 q^{53} +(-1.50000 + 2.59808i) q^{55} +17.6603i q^{57} +(-9.00000 + 5.19615i) q^{59} +(2.09808 + 3.63397i) q^{61} +(-11.5981 - 6.69615i) q^{63} +(0.866025 + 3.50000i) q^{65} +(3.46410 + 6.00000i) q^{69} +(-5.19615 + 3.00000i) q^{71} +5.66025i q^{73} +(1.36603 - 2.36603i) q^{75} +9.00000 q^{77} -6.19615 q^{79} +(1.23205 - 2.13397i) q^{81} +2.19615i q^{83} +(-1.90192 + 1.09808i) q^{85} +(12.9282 + 22.3923i) q^{87} +(-14.8923 - 8.59808i) q^{89} +(7.79423 - 7.50000i) q^{91} +(-3.00000 - 1.73205i) q^{93} +(3.23205 + 5.59808i) q^{95} +(13.0981 - 7.56218i) q^{97} -13.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^9	\( 4 q - 2 q^{3} - 2 q^{9} + 14 q^{13} - 6 q^{15} - 6 q^{17} + 12 q^{19} + 12 q^{23} - 4 q^{25} + 16 q^{27} + 12 q^{29} - 18 q^{33} + 6 q^{35} + 18 q^{37} - 4 q^{39} - 36 q^{41} + 4 q^{43} + 12 q^{45} + 4 q^{49} - 24 q^{51} - 12 q^{53} - 6 q^{55} - 36 q^{59} - 2 q^{61} - 36 q^{63} + 2 q^{75} + 36 q^{77} - 4 q^{79} - 2 q^{81} - 18 q^{85} + 24 q^{87} - 18 q^{89} - 12 q^{93} + 6 q^{95} + 42 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^9 + 14 * q^13 - 6 * q^15 - 6 * q^17 + 12 * q^19 + 12 * q^23 - 4 * q^25 + 16 * q^27 + 12 * q^29 - 18 * q^33 + 6 * q^35 + 18 * q^37 - 4 * q^39 - 36 * q^41 + 4 * q^43 + 12 * q^45 + 4 * q^49 - 24 * q^51 - 12 * q^53 - 6 * q^55 - 36 * q^59 - 2 * q^61 - 36 * q^63 + 2 * q^75 + 36 * q^77 - 4 * q^79 - 2 * q^81 - 18 * q^85 + 24 * q^87 - 18 * q^89 - 12 * q^93 + 6 * q^95 + 42 * q^97

Introduction

L-functions

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