LMFDB - Embedded newform 1040.2.bg.a.577.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1040,2,Mod(577,1040)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1040, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1040.577"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [2,0,-2,0,-2,0,0,0,0,0,2,0,6,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(15)] == traces)

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

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			577.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1040.577
Dual form			1040.2.bg.a.593.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.00000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +2.00000i q^{7} +1.00000i q^{9} +(1.00000 + 1.00000i) q^{11} +(3.00000 + 2.00000i) q^{13} +(-1.00000 - 3.00000i) q^{15} +(1.00000 - 1.00000i) q^{17} +(5.00000 + 5.00000i) q^{19} +(-2.00000 - 2.00000i) q^{21} +(-3.00000 - 3.00000i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(-4.00000 - 4.00000i) q^{27} +(-5.00000 + 5.00000i) q^{31} -2.00000 q^{33} +(-4.00000 - 2.00000i) q^{35} +(-5.00000 + 1.00000i) q^{39} +(-7.00000 + 7.00000i) q^{41} +(1.00000 + 1.00000i) q^{43} +(-2.00000 - 1.00000i) q^{45} -6.00000i q^{47} +3.00000 q^{49} +2.00000i q^{51} +(5.00000 - 5.00000i) q^{53} +(-3.00000 + 1.00000i) q^{55} -10.0000 q^{57} +(7.00000 - 7.00000i) q^{59} -14.0000 q^{61} -2.00000 q^{63} +(-7.00000 + 4.00000i) q^{65} +4.00000 q^{67} +6.00000 q^{69} +(-1.00000 + 1.00000i) q^{71} -10.0000 q^{73} +(7.00000 + 1.00000i) q^{75} +(-2.00000 + 2.00000i) q^{77} +2.00000i q^{79} +5.00000 q^{81} +6.00000i q^{83} +(1.00000 + 3.00000i) q^{85} +(5.00000 - 5.00000i) q^{89} +(-4.00000 + 6.00000i) q^{91} -10.0000i q^{93} +(-15.0000 + 5.00000i) q^{95} +2.00000 q^{97} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 2 q^{5} + 2 q^{11} + 6 q^{13} - 2 q^{15} + 2 q^{17} + 10 q^{19} - 4 q^{21} - 6 q^{23} - 6 q^{25} - 8 q^{27} - 10 q^{31} - 4 q^{33} - 8 q^{35} - 10 q^{39} - 14 q^{41} + 2 q^{43} - 4 q^{45}+ \cdots - 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - 2 * q^5 + 2 * q^11 + 6 * q^13 - 2 * q^15 + 2 * q^17 + 10 * q^19 - 4 * q^21 - 6 * q^23 - 6 * q^25 - 8 * q^27 - 10 * q^31 - 4 * q^33 - 8 * q^35 - 10 * q^39 - 14 * q^41 + 2 * q^43 - 4 * q^45 + 6 * q^49 + 10 * q^53 - 6 * q^55 - 20 * q^57 + 14 * q^59 - 28 * q^61 - 4 * q^63 - 14 * q^65 + 8 * q^67 + 12 * q^69 - 2 * q^71 - 20 * q^73 + 14 * q^75 - 4 * q^77 + 10 * q^81 + 2 * q^85 + 10 * q^89 - 8 * q^91 - 30 * q^95 + 4 * q^97 - 2 * q^99

Character values

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

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−1.00000	+	1.00000i	−0.577350	+	0.577350i	−0.934172	−	0.356822i	$-0.883860\pi$
$3$	−1.00000	+	1.00000i	−0.577350	+	0.577350i	0.356822	+	0.934172i	$0.383860\pi$
$4$		0			0
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$		0			0
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	0.841605	−	0.540094i	$-0.181611\pi$
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	−0.540094	+	0.841605i	$0.681611\pi$
$12$		0			0
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$14$		0			0
$15$	−1.00000	−	3.00000i	−0.258199	−	0.774597i
$16$		0			0
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	−0.575363	−	0.817898i	$-0.695139\pi$
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	0.817898	+	0.575363i	$0.195139\pi$
$18$		0			0
$19$	5.00000	+	5.00000i	1.14708	+	1.14708i	0.987124	+	0.159954i	$0.0511347\pi$
$19$	5.00000	+	5.00000i	1.14708	+	1.14708i	0.159954	+	0.987124i	$0.448865\pi$
$20$		0			0
$21$	−2.00000	−	2.00000i	−0.436436	−	0.436436i
$22$		0			0
$23$	−3.00000	−	3.00000i	−0.625543	−	0.625543i	0.321400	−	0.946943i	$-0.395847\pi$
$23$	−3.00000	−	3.00000i	−0.625543	−	0.625543i	−0.946943	+	0.321400i	$0.895847\pi$
$24$		0			0
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$		0			0
$27$	−4.00000	−	4.00000i	−0.769800	−	0.769800i
$28$		0			0
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	−5.00000	+	5.00000i	−0.898027	+	0.898027i	−0.995261	−	0.0972349i	$-0.969000\pi$
$31$	−5.00000	+	5.00000i	−0.898027	+	0.898027i	0.0972349	+	0.995261i	$0.469000\pi$
$32$		0			0
$33$	−2.00000			−0.348155
$34$		0			0
$35$	−4.00000	−	2.00000i	−0.676123	−	0.338062i
$36$		0			0
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$		0			0
$39$	−5.00000	+	1.00000i	−0.800641	+	0.160128i
$40$		0			0
$41$	−7.00000	+	7.00000i	−1.09322	+	1.09322i	−0.0980332	+	0.995183i	$0.531255\pi$
$41$	−7.00000	+	7.00000i	−1.09322	+	1.09322i	−0.995183	+	0.0980332i	$0.968745\pi$
$42$		0			0
$43$	1.00000	+	1.00000i	0.152499	+	0.152499i	0.779233	−	0.626734i	$-0.215609\pi$
$43$	1.00000	+	1.00000i	0.152499	+	0.152499i	−0.626734	+	0.779233i	$0.715609\pi$
$44$		0			0
$45$	−2.00000	−	1.00000i	−0.298142	−	0.149071i
$46$		0			0
$47$		−	6.00000i		−	0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$		−	6.00000i		−	0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$		0			0
$51$			2.00000i			0.280056i
$52$		0			0
$53$	5.00000	−	5.00000i	0.686803	−	0.686803i	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	5.00000	−	5.00000i	0.686803	−	0.686803i	0.961524	+	0.274721i	$0.0885855\pi$
$54$		0			0
$55$	−3.00000	+	1.00000i	−0.404520	+	0.134840i
$56$		0			0
$57$	−10.0000			−1.32453
$58$		0			0
$59$	7.00000	−	7.00000i	0.911322	−	0.911322i	−0.0850540	−	0.996376i	$-0.527106\pi$
$59$	7.00000	−	7.00000i	0.911322	−	0.911322i	0.996376	+	0.0850540i	$0.0271063\pi$
$60$		0			0
$61$	−14.0000			−1.79252			−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000			−1.79252			−0.896258	+	0.443533i	$0.853725\pi$
$62$		0			0
$63$	−2.00000			−0.251976
$64$		0			0
$65$	−7.00000	+	4.00000i	−0.868243	+	0.496139i
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$		0			0
$71$	−1.00000	+	1.00000i	−0.118678	+	0.118678i	−0.763952	−	0.645273i	$-0.776743\pi$
$71$	−1.00000	+	1.00000i	−0.118678	+	0.118678i	0.645273	+	0.763952i	$0.276743\pi$
$72$		0			0
$73$	−10.0000			−1.17041			−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000			−1.17041			−0.585206	+	0.810885i	$0.698986\pi$
$74$		0			0
$75$	7.00000	+	1.00000i	0.808290	+	0.115470i
$76$		0			0
$77$	−2.00000	+	2.00000i	−0.227921	+	0.227921i
$78$		0			0
$79$			2.00000i			0.225018i	0.993651	+	0.112509i	$0.0358886\pi$
$79$			2.00000i			0.225018i	−0.993651	+	0.112509i	$0.964111\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$		0			0
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$		0			0
$85$	1.00000	+	3.00000i	0.108465	+	0.325396i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.00000	−	5.00000i	0.529999	−	0.529999i	−0.390573	−	0.920572i	$-0.627723\pi$
$89$	5.00000	−	5.00000i	0.529999	−	0.529999i	0.920572	+	0.390573i	$0.127723\pi$
$90$		0			0
$91$	−4.00000	+	6.00000i	−0.419314	+	0.628971i
$92$		0			0
$93$		−	10.0000i		−	1.03695i
$94$		0			0
$95$	−15.0000	+	5.00000i	−1.53897	+	0.512989i
$96$		0			0
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$	−1.00000	+	1.00000i	−0.100504	+	0.100504i
$100$		0			0
$101$			12.0000i			1.19404i	0.802225	+	0.597022i	$0.203650\pi$
$101$			12.0000i			1.19404i	−0.802225	+	0.597022i	$0.796350\pi$
$102$		0			0
$103$	−7.00000	−	7.00000i	−0.689730	−	0.689730i	0.272442	−	0.962172i	$-0.412169\pi$
$103$	−7.00000	−	7.00000i	−0.689730	−	0.689730i	−0.962172	+	0.272442i	$0.912169\pi$
$104$		0			0
$105$	6.00000	−	2.00000i	0.585540	−	0.195180i
$106$		0			0
$107$	−7.00000	−	7.00000i	−0.676716	−	0.676716i	0.282540	−	0.959256i	$-0.408823\pi$
$107$	−7.00000	−	7.00000i	−0.676716	−	0.676716i	−0.959256	+	0.282540i	$0.908823\pi$
$108$		0			0
$109$	9.00000	+	9.00000i	0.862044	+	0.862044i	0.991575	−	0.129532i	$-0.0413474\pi$
$109$	9.00000	+	9.00000i	0.862044	+	0.862044i	−0.129532	+	0.991575i	$0.541347\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.00000	−	5.00000i	0.470360	−	0.470360i	−0.431671	−	0.902031i	$-0.642076\pi$
$113$	5.00000	−	5.00000i	0.470360	−	0.470360i	0.902031	+	0.431671i	$0.142076\pi$
$114$		0			0
$115$	9.00000	−	3.00000i	0.839254	−	0.279751i
$116$		0			0
$117$	−2.00000	+	3.00000i	−0.184900	+	0.277350i
$118$		0			0
$119$	2.00000	+	2.00000i	0.183340	+	0.183340i
$120$		0			0
$121$		−	9.00000i		−	0.818182i
$122$		0			0
$123$		−	14.0000i		−	1.26234i
$124$		0			0
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$	−9.00000	+	9.00000i	−0.798621	+	0.798621i	−0.982878	−	0.184257i	$-0.941012\pi$
$127$	−9.00000	+	9.00000i	−0.798621	+	0.798621i	0.184257	+	0.982878i	$0.441012\pi$
$128$		0			0
$129$	−2.00000			−0.176090
$130$		0			0
$131$	20.0000			1.74741			0.873704	−	0.486458i	$-0.161711\pi$
$131$	20.0000			1.74741			0.873704	+	0.486458i	$0.161711\pi$
$132$		0			0
$133$	−10.0000	+	10.0000i	−0.867110	+	0.867110i
$134$		0			0
$135$	12.0000	−	4.00000i	1.03280	−	0.344265i
$136$		0			0
$137$		−	16.0000i		−	1.36697i	−0.729964	−	0.683486i	$-0.760463\pi$
$137$		−	16.0000i		−	1.36697i	0.729964	−	0.683486i	$-0.239537\pi$
$138$		0			0
$139$			14.0000i			1.18746i	0.804663	+	0.593732i	$0.202346\pi$
$139$			14.0000i			1.18746i	−0.804663	+	0.593732i	$0.797654\pi$
$140$		0			0
$141$	6.00000	+	6.00000i	0.505291	+	0.505291i
$142$		0			0
$143$	1.00000	+	5.00000i	0.0836242	+	0.418121i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−3.00000	+	3.00000i	−0.247436	+	0.247436i
$148$		0			0
$149$	−3.00000	−	3.00000i	−0.245770	−	0.245770i	0.573462	−	0.819232i	$-0.305600\pi$
$149$	−3.00000	−	3.00000i	−0.245770	−	0.245770i	−0.819232	+	0.573462i	$0.805600\pi$
$150$		0			0
$151$	−7.00000	−	7.00000i	−0.569652	−	0.569652i	0.362379	−	0.932031i	$-0.381965\pi$
$151$	−7.00000	−	7.00000i	−0.569652	−	0.569652i	−0.932031	+	0.362379i	$0.881965\pi$
$152$		0			0
$153$	1.00000	+	1.00000i	0.0808452	+	0.0808452i
$154$		0			0
$155$	−5.00000	−	15.0000i	−0.401610	−	1.20483i
$156$		0			0
$157$	13.0000	+	13.0000i	1.03751	+	1.03751i	0.999268	+	0.0382445i	$0.0121766\pi$
$157$	13.0000	+	13.0000i	1.03751	+	1.03751i	0.0382445	+	0.999268i	$0.487823\pi$
$158$		0			0
$159$			10.0000i			0.793052i
$160$		0			0
$161$	6.00000	−	6.00000i	0.472866	−	0.472866i
$162$		0			0
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$		0			0
$165$	2.00000	−	4.00000i	0.155700	−	0.311400i
$166$		0			0
$167$			18.0000i			1.39288i	0.717614	+	0.696441i	$0.245234\pi$
$167$			18.0000i			1.39288i	−0.717614	+	0.696441i	$0.754766\pi$
$168$		0			0
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$		0			0
$171$	−5.00000	+	5.00000i	−0.382360	+	0.382360i
$172$		0			0
$173$	−11.0000	−	11.0000i	−0.836315	−	0.836315i	0.152057	−	0.988372i	$-0.451410\pi$
$173$	−11.0000	−	11.0000i	−0.836315	−	0.836315i	−0.988372	+	0.152057i	$0.951410\pi$
$174$		0			0
$175$	8.00000	−	6.00000i	0.604743	−	0.453557i
$176$		0			0
$177$			14.0000i			1.05230i
$178$		0			0
$179$	20.0000			1.49487			0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000			1.49487			0.747435	+	0.664335i	$0.231285\pi$
$180$		0			0
$181$		−	8.00000i		−	0.594635i	−0.954779	−	0.297318i	$-0.903908\pi$
$181$		−	8.00000i		−	0.594635i	0.954779	−	0.297318i	$-0.0960920\pi$
$182$		0			0
$183$	14.0000	−	14.0000i	1.03491	−	1.03491i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.00000			0.146254
$188$		0			0
$189$	8.00000	−	8.00000i	0.581914	−	0.581914i
$190$		0			0
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$		0			0
$193$	18.0000			1.29567			0.647834	−	0.761781i	$-0.275675\pi$
$193$	18.0000			1.29567			0.647834	+	0.761781i	$0.275675\pi$
$194$		0			0
$195$	3.00000	−	11.0000i	0.214834	−	0.787726i
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$		0			0
$201$	−4.00000	+	4.00000i	−0.282138	+	0.282138i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−7.00000	−	21.0000i	−0.488901	−	1.46670i
$206$		0			0
$207$	3.00000	−	3.00000i	0.208514	−	0.208514i
$208$		0			0
$209$			10.0000i			0.691714i
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$		−	2.00000i		−	0.137038i
$214$		0			0
$215$	−3.00000	+	1.00000i	−0.204598	+	0.0681994i
$216$		0			0
$217$	−10.0000	−	10.0000i	−0.678844	−	0.678844i
$218$		0			0
$219$	10.0000	−	10.0000i	0.675737	−	0.675737i
$220$		0			0
$221$	5.00000	−	1.00000i	0.336336	−	0.0672673i
$222$		0			0
$223$			2.00000i			0.133930i	0.997755	+	0.0669650i	$0.0213316\pi$
$223$			2.00000i			0.133930i	−0.997755	+	0.0669650i	$0.978668\pi$
$224$		0			0
$225$	4.00000	−	3.00000i	0.266667	−	0.200000i
$226$		0			0
$227$	12.0000			0.796468			0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000			0.796468			0.398234	+	0.917284i	$0.369623\pi$
$228$		0			0
$229$	−3.00000	+	3.00000i	−0.198246	+	0.198246i	−0.799248	−	0.601002i	$-0.794768\pi$
$229$	−3.00000	+	3.00000i	−0.198246	+	0.198246i	0.601002	+	0.799248i	$0.294768\pi$
$230$		0			0
$231$		−	4.00000i		−	0.263181i
$232$		0			0
$233$	1.00000	+	1.00000i	0.0655122	+	0.0655122i	0.739104	−	0.673592i	$-0.235249\pi$
$233$	1.00000	+	1.00000i	0.0655122	+	0.0655122i	−0.673592	+	0.739104i	$0.735249\pi$
$234$		0			0
$235$	12.0000	+	6.00000i	0.782794	+	0.391397i
$236$		0			0
$237$	−2.00000	−	2.00000i	−0.129914	−	0.129914i
$238$		0			0
$239$	−3.00000	−	3.00000i	−0.194054	−	0.194054i	0.603391	−	0.797445i	$-0.293816\pi$
$239$	−3.00000	−	3.00000i	−0.194054	−	0.194054i	−0.797445	+	0.603391i	$0.793816\pi$
$240$		0			0
$241$	17.0000	+	17.0000i	1.09507	+	1.09507i	0.994979	+	0.100088i	$0.0319123\pi$
$241$	17.0000	+	17.0000i	1.09507	+	1.09507i	0.100088	+	0.994979i	$0.468088\pi$
$242$		0			0
$243$	7.00000	−	7.00000i	0.449050	−	0.449050i
$244$		0			0
$245$	−3.00000	+	6.00000i	−0.191663	+	0.383326i
$246$		0			0
$247$	5.00000	+	25.0000i	0.318142	+	1.59071i
$248$		0			0
$249$	−6.00000	−	6.00000i	−0.380235	−	0.380235i
$250$		0			0
$251$		−	2.00000i		−	0.126239i	−0.998006	−	0.0631194i	$-0.979895\pi$
$251$		−	2.00000i		−	0.126239i	0.998006	−	0.0631194i	$-0.0201049\pi$
$252$		0			0
$253$		−	6.00000i		−	0.377217i
$254$		0			0
$255$	−4.00000	−	2.00000i	−0.250490	−	0.125245i
$256$		0			0
$257$	−11.0000	+	11.0000i	−0.686161	+	0.686161i	−0.961381	−	0.275220i	$-0.911249\pi$
$257$	−11.0000	+	11.0000i	−0.686161	+	0.686161i	0.275220	+	0.961381i	$0.411249\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.00000	+	1.00000i	−0.0616626	+	0.0616626i	−0.737266	−	0.675603i	$-0.763883\pi$
$263$	−1.00000	+	1.00000i	−0.0616626	+	0.0616626i	0.675603	+	0.737266i	$0.263883\pi$
$264$		0			0
$265$	5.00000	+	15.0000i	0.307148	+	0.921443i
$266$		0			0
$267$			10.0000i			0.611990i
$268$		0			0
$269$			12.0000i			0.731653i	0.930683	+	0.365826i	$0.119214\pi$
$269$			12.0000i			0.731653i	−0.930683	+	0.365826i	$0.880786\pi$
$270$		0			0
$271$	9.00000	+	9.00000i	0.546711	+	0.546711i	0.925488	−	0.378777i	$-0.123655\pi$
$271$	9.00000	+	9.00000i	0.546711	+	0.546711i	−0.378777	+	0.925488i	$0.623655\pi$
$272$		0			0
$273$	−2.00000	−	10.0000i	−0.121046	−	0.605228i
$274$		0			0
$275$	1.00000	−	7.00000i	0.0603023	−	0.422116i
$276$		0			0
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	−0.995545	−	0.0942828i	$-0.969944\pi$
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	0.0942828	+	0.995545i	$0.469944\pi$
$278$		0			0
$279$	−5.00000	−	5.00000i	−0.299342	−	0.299342i
$280$		0			0
$281$	1.00000	+	1.00000i	0.0596550	+	0.0596550i	0.736305	−	0.676650i	$-0.236569\pi$
$281$	1.00000	+	1.00000i	0.0596550	+	0.0596550i	−0.676650	+	0.736305i	$0.736569\pi$
$282$		0			0
$283$	9.00000	+	9.00000i	0.534994	+	0.534994i	0.922055	−	0.387060i	$-0.126509\pi$
$283$	9.00000	+	9.00000i	0.534994	+	0.534994i	−0.387060	+	0.922055i	$0.626509\pi$
$284$		0			0
$285$	10.0000	−	20.0000i	0.592349	−	1.18470i
$286$		0			0
$287$	−14.0000	−	14.0000i	−0.826394	−	0.826394i
$288$		0			0
$289$			15.0000i			0.882353i
$290$		0			0
$291$	−2.00000	+	2.00000i	−0.117242	+	0.117242i
$292$		0			0
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$	7.00000	+	21.0000i	0.407556	+	1.22267i
$296$		0			0
$297$		−	8.00000i		−	0.464207i
$298$		0			0
$299$	−3.00000	−	15.0000i	−0.173494	−	0.867472i
$300$		0			0
$301$	−2.00000	+	2.00000i	−0.115278	+	0.115278i
$302$		0			0
$303$	−12.0000	−	12.0000i	−0.689382	−	0.689382i
$304$		0			0
$305$	14.0000	−	28.0000i	0.801638	−	1.60328i
$306$		0			0
$307$		−	18.0000i		−	1.02731i	−0.857996	−	0.513657i	$-0.828290\pi$
$307$		−	18.0000i		−	1.02731i	0.857996	−	0.513657i	$-0.171710\pi$
$308$		0			0
$309$	14.0000			0.796432
$310$		0			0
$311$		−	6.00000i		−	0.340229i	−0.985424	−	0.170114i	$-0.945586\pi$
$311$		−	6.00000i		−	0.340229i	0.985424	−	0.170114i	$-0.0544137\pi$
$312$		0			0
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	−0.405420	−	0.914130i	$-0.632875\pi$
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	0.914130	+	0.405420i	$0.132875\pi$
$314$		0			0
$315$	2.00000	−	4.00000i	0.112687	−	0.225374i
$316$		0			0
$317$	−14.0000			−0.786318			−0.393159	−	0.919470i	$-0.628618\pi$
$317$	−14.0000			−0.786318			−0.393159	+	0.919470i	$0.628618\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	14.0000			0.781404
$322$		0			0
$323$	10.0000			0.556415
$324$		0			0
$325$	−1.00000	−	18.0000i	−0.0554700	−	0.998460i
$326$		0			0
$327$	−18.0000			−0.995402
$328$		0			0
$329$	12.0000			0.661581
$330$		0			0
$331$	3.00000	−	3.00000i	0.164895	−	0.164895i	−0.619836	−	0.784731i	$-0.712801\pi$
$331$	3.00000	−	3.00000i	0.164895	−	0.164895i	0.784731	+	0.619836i	$0.212801\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.00000	+	8.00000i	−0.218543	+	0.437087i
$336$		0			0
$337$	13.0000	−	13.0000i	0.708155	−	0.708155i	−0.257992	−	0.966147i	$-0.583061\pi$
$337$	13.0000	−	13.0000i	0.708155	−	0.708155i	0.966147	+	0.257992i	$0.0830608\pi$
$338$		0			0
$339$			10.0000i			0.543125i
$340$		0			0
$341$	−10.0000			−0.541530
$342$		0			0
$343$			20.0000i			1.07990i
$344$		0			0
$345$	−6.00000	+	12.0000i	−0.323029	+	0.646058i
$346$		0			0
$347$	−3.00000	−	3.00000i	−0.161048	−	0.161048i	0.621983	−	0.783031i	$-0.286327\pi$
$347$	−3.00000	−	3.00000i	−0.161048	−	0.161048i	−0.783031	+	0.621983i	$0.786327\pi$
$348$		0			0
$349$	9.00000	−	9.00000i	0.481759	−	0.481759i	−0.423934	−	0.905693i	$-0.639351\pi$
$349$	9.00000	−	9.00000i	0.481759	−	0.481759i	0.905693	+	0.423934i	$0.139351\pi$
$350$		0			0
$351$	−4.00000	−	20.0000i	−0.213504	−	1.06752i
$352$		0			0
$353$			12.0000i			0.638696i	0.947638	+	0.319348i	$0.103464\pi$
$353$			12.0000i			0.638696i	−0.947638	+	0.319348i	$0.896536\pi$
$354$		0			0
$355$	−1.00000	−	3.00000i	−0.0530745	−	0.159223i
$356$		0			0
$357$	−4.00000			−0.211702
$358$		0			0
$359$	−1.00000	+	1.00000i	−0.0527780	+	0.0527780i	−0.733003	−	0.680225i	$-0.761882\pi$
$359$	−1.00000	+	1.00000i	−0.0527780	+	0.0527780i	0.680225	+	0.733003i	$0.261882\pi$
$360$		0			0
$361$			31.0000i			1.63158i
$362$		0			0
$363$	9.00000	+	9.00000i	0.472377	+	0.472377i
$364$		0			0
$365$	10.0000	−	20.0000i	0.523424	−	1.04685i
$366$		0			0
$367$	1.00000	+	1.00000i	0.0521996	+	0.0521996i	0.732725	−	0.680525i	$-0.238248\pi$
$367$	1.00000	+	1.00000i	0.0521996	+	0.0521996i	−0.680525	+	0.732725i	$0.738248\pi$
$368$		0			0
$369$	−7.00000	−	7.00000i	−0.364405	−	0.364405i
$370$		0			0
$371$	10.0000	+	10.0000i	0.519174	+	0.519174i
$372$		0			0
$373$	−15.0000	+	15.0000i	−0.776671	+	0.776671i	−0.979263	−	0.202593i	$-0.935063\pi$
$373$	−15.0000	+	15.0000i	−0.776671	+	0.776671i	0.202593	+	0.979263i	$0.435063\pi$
$374$		0			0
$375$	−9.00000	+	13.0000i	−0.464758	+	0.671317i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.00000	+	1.00000i	0.0513665	+	0.0513665i	0.732323	−	0.680957i	$-0.238436\pi$
$379$	1.00000	+	1.00000i	0.0513665	+	0.0513665i	−0.680957	+	0.732323i	$0.738436\pi$
$380$		0			0
$381$		−	18.0000i		−	0.922168i
$382$		0			0
$383$		−	30.0000i		−	1.53293i	−0.642287	−	0.766464i	$-0.722014\pi$
$383$		−	30.0000i		−	1.53293i	0.642287	−	0.766464i	$-0.277986\pi$
$384$		0			0
$385$	−2.00000	−	6.00000i	−0.101929	−	0.305788i
$386$		0			0
$387$	−1.00000	+	1.00000i	−0.0508329	+	0.0508329i
$388$		0			0
$389$	−18.0000			−0.912636			−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000			−0.912636			−0.456318	+	0.889817i	$0.650832\pi$
$390$		0			0
$391$	−6.00000			−0.303433
$392$		0			0
$393$	−20.0000	+	20.0000i	−1.00887	+	1.00887i
$394$		0			0
$395$	−4.00000	−	2.00000i	−0.201262	−	0.100631i
$396$		0			0
$397$			16.0000i			0.803017i	0.915855	+	0.401508i	$0.131514\pi$
$397$			16.0000i			0.803017i	−0.915855	+	0.401508i	$0.868486\pi$
$398$		0			0
$399$		−	20.0000i		−	1.00125i
$400$		0			0
$401$	−11.0000	−	11.0000i	−0.549314	−	0.549314i	0.376929	−	0.926242i	$-0.376980\pi$
$401$	−11.0000	−	11.0000i	−0.549314	−	0.549314i	−0.926242	+	0.376929i	$0.876980\pi$
$402$		0			0
$403$	−25.0000	+	5.00000i	−1.24534	+	0.249068i
$404$		0			0
$405$	−5.00000	+	10.0000i	−0.248452	+	0.496904i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−7.00000	−	7.00000i	−0.346128	−	0.346128i	0.512537	−	0.858665i	$-0.328706\pi$
$409$	−7.00000	−	7.00000i	−0.346128	−	0.346128i	−0.858665	+	0.512537i	$0.828706\pi$
$410$		0			0
$411$	16.0000	+	16.0000i	0.789222	+	0.789222i
$412$		0			0
$413$	14.0000	+	14.0000i	0.688895	+	0.688895i
$414$		0			0
$415$	−12.0000	−	6.00000i	−0.589057	−	0.294528i
$416$		0			0
$417$	−14.0000	−	14.0000i	−0.685583	−	0.685583i
$418$		0			0
$419$			38.0000i			1.85642i	0.372055	+	0.928211i	$0.378653\pi$
$419$			38.0000i			1.85642i	−0.372055	+	0.928211i	$0.621347\pi$
$420$		0			0
$421$	−11.0000	+	11.0000i	−0.536107	+	0.536107i	−0.922383	−	0.386276i	$-0.873761\pi$
$421$	−11.0000	+	11.0000i	−0.536107	+	0.536107i	0.386276	+	0.922383i	$0.373761\pi$
$422$		0			0
$423$	6.00000			0.291730
$424$		0			0
$425$	−7.00000	−	1.00000i	−0.339550	−	0.0485071i
$426$		0			0
$427$		−	28.0000i		−	1.35501i
$428$		0			0
$429$	−6.00000	−	4.00000i	−0.289683	−	0.193122i
$430$		0			0
$431$	−13.0000	+	13.0000i	−0.626188	+	0.626188i	−0.947107	−	0.320919i	$-0.896008\pi$
$431$	−13.0000	+	13.0000i	−0.626188	+	0.626188i	0.320919	+	0.947107i	$0.396008\pi$
$432$		0			0
$433$	17.0000	+	17.0000i	0.816968	+	0.816968i	0.985668	−	0.168700i	$-0.0539568\pi$
$433$	17.0000	+	17.0000i	0.816968	+	0.816968i	−0.168700	+	0.985668i	$0.553957\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	30.0000i		−	1.43509i
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$			3.00000i			0.142857i
$442$		0			0
$443$	−25.0000	+	25.0000i	−1.18779	+	1.18779i	−0.210108	+	0.977678i	$0.567381\pi$
$443$	−25.0000	+	25.0000i	−1.18779	+	1.18779i	−0.977678	+	0.210108i	$0.932619\pi$
$444$		0			0
$445$	5.00000	+	15.0000i	0.237023	+	0.711068i
$446$		0			0
$447$	6.00000			0.283790
$448$		0			0
$449$	−3.00000	+	3.00000i	−0.141579	+	0.141579i	−0.774344	−	0.632765i	$-0.781920\pi$
$449$	−3.00000	+	3.00000i	−0.141579	+	0.141579i	0.632765	+	0.774344i	$0.281920\pi$
$450$		0			0
$451$	−14.0000			−0.659234
$452$		0			0
$453$	14.0000			0.657777
$454$		0			0
$455$	−8.00000	−	14.0000i	−0.375046	−	0.656330i
$456$		0			0
$457$	2.00000			0.0935561			0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000			0.0935561			0.0467780	+	0.998905i	$0.485105\pi$
$458$		0			0
$459$	−8.00000			−0.373408
$460$		0			0
$461$	17.0000	−	17.0000i	0.791769	−	0.791769i	−0.190013	−	0.981782i	$-0.560853\pi$
$461$	17.0000	−	17.0000i	0.791769	−	0.791769i	0.981782	+	0.190013i	$0.0608529\pi$
$462$		0			0
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$		0			0
$465$	20.0000	+	10.0000i	0.927478	+	0.463739i
$466$		0			0
$467$	−9.00000	+	9.00000i	−0.416470	+	0.416470i	−0.883985	−	0.467515i	$-0.845149\pi$
$467$	−9.00000	+	9.00000i	−0.416470	+	0.416470i	0.467515	+	0.883985i	$0.345149\pi$
$468$		0			0
$469$			8.00000i			0.369406i
$470$		0			0
$471$	−26.0000			−1.19802
$472$		0			0
$473$			2.00000i			0.0919601i
$474$		0			0
$475$	5.00000	−	35.0000i	0.229416	−	1.60591i
$476$		0			0
$477$	5.00000	+	5.00000i	0.228934	+	0.228934i
$478$		0			0
$479$	7.00000	−	7.00000i	0.319838	−	0.319838i	−0.528867	−	0.848705i	$-0.677383\pi$
$479$	7.00000	−	7.00000i	0.319838	−	0.319838i	0.848705	+	0.528867i	$0.177383\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$			12.0000i			0.546019i
$484$		0			0
$485$	−2.00000	+	4.00000i	−0.0908153	+	0.181631i
$486$		0			0
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$		0			0
$489$	4.00000	−	4.00000i	0.180886	−	0.180886i
$490$		0			0
$491$			22.0000i			0.992846i	0.868081	+	0.496423i	$0.165354\pi$
$491$			22.0000i			0.992846i	−0.868081	+	0.496423i	$0.834646\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−1.00000	−	3.00000i	−0.0449467	−	0.134840i
$496$		0			0
$497$	−2.00000	−	2.00000i	−0.0897123	−	0.0897123i
$498$		0			0
$499$	−3.00000	−	3.00000i	−0.134298	−	0.134298i	0.636762	−	0.771060i	$-0.280273\pi$
$499$	−3.00000	−	3.00000i	−0.134298	−	0.134298i	−0.771060	+	0.636762i	$0.780273\pi$
$500$		0			0
$501$	−18.0000	−	18.0000i	−0.804181	−	0.804181i
$502$		0			0
$503$	3.00000	−	3.00000i	0.133763	−	0.133763i	−0.637055	−	0.770818i	$-0.719848\pi$
$503$	3.00000	−	3.00000i	0.133763	−	0.133763i	0.770818	+	0.637055i	$0.219848\pi$
$504$		0			0
$505$	−24.0000	−	12.0000i	−1.06799	−	0.533993i
$506$		0			0
$507$	−17.0000	−	7.00000i	−0.754997	−	0.310881i
$508$		0			0
$509$	13.0000	+	13.0000i	0.576215	+	0.576215i	0.933858	−	0.357643i	$-0.116420\pi$
$509$	13.0000	+	13.0000i	0.576215	+	0.576215i	−0.357643	+	0.933858i	$0.616420\pi$
$510$		0			0
$511$		−	20.0000i		−	0.884748i
$512$		0			0
$513$		−	40.0000i		−	1.76604i
$514$		0			0
$515$	21.0000	−	7.00000i	0.925371	−	0.308457i
$516$		0			0
$517$	6.00000	−	6.00000i	0.263880	−	0.263880i
$518$		0			0
$519$	22.0000			0.965693
$520$		0			0
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$	−9.00000	+	9.00000i	−0.393543	+	0.393543i	−0.875948	−	0.482405i	$-0.839763\pi$
$523$	−9.00000	+	9.00000i	−0.393543	+	0.393543i	0.482405	+	0.875948i	$0.339763\pi$
$524$		0			0
$525$	−2.00000	+	14.0000i	−0.0872872	+	0.611010i
$526$		0			0
$527$			10.0000i			0.435607i
$528$		0			0
$529$		−	5.00000i		−	0.217391i
$530$		0			0
$531$	7.00000	+	7.00000i	0.303774	+	0.303774i
$532$		0			0
$533$	−35.0000	+	7.00000i	−1.51602	+	0.303204i
$534$		0			0
$535$	21.0000	−	7.00000i	0.907909	−	0.302636i
$536$		0			0
$537$	−20.0000	+	20.0000i	−0.863064	+	0.863064i
$538$		0			0
$539$	3.00000	+	3.00000i	0.129219	+	0.129219i
$540$		0			0
$541$	9.00000	+	9.00000i	0.386940	+	0.386940i	0.873595	−	0.486654i	$-0.161783\pi$
$541$	9.00000	+	9.00000i	0.386940	+	0.386940i	−0.486654	+	0.873595i	$0.661783\pi$
$542$		0			0
$543$	8.00000	+	8.00000i	0.343313	+	0.343313i
$544$		0			0
$545$	−27.0000	+	9.00000i	−1.15655	+	0.385518i
$546$		0			0
$547$	9.00000	+	9.00000i	0.384812	+	0.384812i	0.872832	−	0.488020i	$-0.162281\pi$
$547$	9.00000	+	9.00000i	0.384812	+	0.384812i	−0.488020	+	0.872832i	$0.662281\pi$
$548$		0			0
$549$		−	14.0000i		−	0.597505i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−4.00000			−0.170097
$554$		0			0
$555$		0			0
$556$		0			0
$557$			24.0000i			1.01691i	0.861088	+	0.508456i	$0.169784\pi$
$557$			24.0000i			1.01691i	−0.861088	+	0.508456i	$0.830216\pi$
$558$		0			0
$559$	1.00000	+	5.00000i	0.0422955	+	0.211477i
$560$		0			0
$561$	−2.00000	+	2.00000i	−0.0844401	+	0.0844401i
$562$		0			0
$563$	−15.0000	−	15.0000i	−0.632175	−	0.632175i	0.316438	−	0.948613i	$-0.397513\pi$
$563$	−15.0000	−	15.0000i	−0.632175	−	0.632175i	−0.948613	+	0.316438i	$0.897513\pi$
$564$		0			0
$565$	5.00000	+	15.0000i	0.210352	+	0.631055i
$566$		0			0
$567$			10.0000i			0.419961i
$568$		0			0
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$		0			0
$571$			6.00000i			0.251092i	0.992088	+	0.125546i	$0.0400683\pi$
$571$			6.00000i			0.251092i	−0.992088	+	0.125546i	$0.959932\pi$
$572$		0			0
$573$	8.00000	−	8.00000i	0.334205	−	0.334205i
$574$		0			0
$575$	−3.00000	+	21.0000i	−0.125109	+	0.875761i
$576$		0			0
$577$	46.0000			1.91501			0.957503	−	0.288425i	$-0.0931316\pi$
$577$	46.0000			1.91501			0.957503	+	0.288425i	$0.0931316\pi$
$578$		0			0
$579$	−18.0000	+	18.0000i	−0.748054	+	0.748054i
$580$		0			0
$581$	−12.0000			−0.497844
$582$		0			0
$583$	10.0000			0.414158
$584$		0			0
$585$	−4.00000	−	7.00000i	−0.165380	−	0.289414i
$586$		0			0
$587$	4.00000			0.165098			0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000			0.165098			0.0825488	+	0.996587i	$0.473694\pi$
$588$		0			0
$589$	−50.0000			−2.06021
$590$		0			0
$591$	−6.00000	+	6.00000i	−0.246807	+	0.246807i
$592$		0			0
$593$	10.0000			0.410651			0.205325	−	0.978694i	$-0.434175\pi$
$593$	10.0000			0.410651			0.205325	+	0.978694i	$0.434175\pi$
$594$		0			0
$595$	−6.00000	+	2.00000i	−0.245976	+	0.0819920i
$596$		0			0
$597$	−8.00000	+	8.00000i	−0.327418	+	0.327418i
$598$		0			0
$599$		−	30.0000i		−	1.22577i	−0.790173	−	0.612883i	$-0.790010\pi$
$599$		−	30.0000i		−	1.22577i	0.790173	−	0.612883i	$-0.209990\pi$
$600$		0			0
$601$	−38.0000			−1.55005			−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000			−1.55005			−0.775026	+	0.631929i	$0.782263\pi$
$602$		0			0
$603$			4.00000i			0.162893i
$604$		0			0
$605$	18.0000	+	9.00000i	0.731804	+	0.365902i
$606$		0			0
$607$	13.0000	+	13.0000i	0.527654	+	0.527654i	0.919872	−	0.392218i	$-0.128292\pi$
$607$	13.0000	+	13.0000i	0.527654	+	0.527654i	−0.392218	+	0.919872i	$0.628292\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	12.0000	−	18.0000i	0.485468	−	0.728202i
$612$		0			0
$613$			20.0000i			0.807792i	0.914805	+	0.403896i	$0.132344\pi$
$613$			20.0000i			0.807792i	−0.914805	+	0.403896i	$0.867656\pi$
$614$		0			0
$615$	28.0000	+	14.0000i	1.12907	+	0.564534i
$616$		0			0
$617$	−22.0000			−0.885687			−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000			−0.885687			−0.442843	+	0.896599i	$0.646030\pi$
$618$		0			0
$619$	−25.0000	+	25.0000i	−1.00483	+	1.00483i	−0.00484658	+	0.999988i	$0.501543\pi$
$619$	−25.0000	+	25.0000i	−1.00483	+	1.00483i	−0.999988	+	0.00484658i	$0.998457\pi$
$620$		0			0
$621$			24.0000i			0.963087i
$622$		0			0
$623$	10.0000	+	10.0000i	0.400642	+	0.400642i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		0			0
$627$	−10.0000	−	10.0000i	−0.399362	−	0.399362i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−11.0000	−	11.0000i	−0.437903	−	0.437903i	0.453403	−	0.891306i	$-0.350210\pi$
$631$	−11.0000	−	11.0000i	−0.437903	−	0.437903i	−0.891306	+	0.453403i	$0.850210\pi$
$632$		0			0
$633$	4.00000	−	4.00000i	0.158986	−	0.158986i
$634$		0			0
$635$	−9.00000	−	27.0000i	−0.357154	−	1.07146i
$636$		0			0
$637$	9.00000	+	6.00000i	0.356593	+	0.237729i
$638$		0			0
$639$	−1.00000	−	1.00000i	−0.0395594	−	0.0395594i
$640$		0			0
$641$		−	24.0000i		−	0.947943i	−0.880540	−	0.473972i	$-0.842820\pi$
$641$		−	24.0000i		−	0.947943i	0.880540	−	0.473972i	$-0.157180\pi$
$642$		0			0
$643$		−	34.0000i		−	1.34083i	−0.741987	−	0.670415i	$-0.766116\pi$
$643$		−	34.0000i		−	1.34083i	0.741987	−	0.670415i	$-0.233884\pi$
$644$		0			0
$645$	2.00000	−	4.00000i	0.0787499	−	0.157500i
$646$		0			0
$647$	−1.00000	+	1.00000i	−0.0393141	+	0.0393141i	−0.726491	−	0.687176i	$-0.758850\pi$
$647$	−1.00000	+	1.00000i	−0.0393141	+	0.0393141i	0.687176	+	0.726491i	$0.258850\pi$
$648$		0			0
$649$	14.0000			0.549548
$650$		0			0
$651$	20.0000			0.783862
$652$		0			0
$653$	13.0000	−	13.0000i	0.508729	−	0.508729i	−0.405407	−	0.914136i	$-0.632870\pi$
$653$	13.0000	−	13.0000i	0.508729	−	0.508729i	0.914136	+	0.405407i	$0.132870\pi$
$654$		0			0
$655$	−20.0000	+	40.0000i	−0.781465	+	1.56293i
$656$		0			0
$657$		−	10.0000i		−	0.390137i
$658$		0			0
$659$		−	26.0000i		−	1.01282i	−0.862294	−	0.506408i	$-0.830973\pi$
$659$		−	26.0000i		−	1.01282i	0.862294	−	0.506408i	$-0.169027\pi$
$660$		0			0
$661$	17.0000	+	17.0000i	0.661223	+	0.661223i	0.955668	−	0.294445i	$-0.0951348\pi$
$661$	17.0000	+	17.0000i	0.661223	+	0.661223i	−0.294445	+	0.955668i	$0.595135\pi$
$662$		0			0
$663$	−4.00000	+	6.00000i	−0.155347	+	0.233021i
$664$		0			0
$665$	−10.0000	−	30.0000i	−0.387783	−	1.16335i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−2.00000	−	2.00000i	−0.0773245	−	0.0773245i
$670$		0			0
$671$	−14.0000	−	14.0000i	−0.540464	−	0.540464i
$672$		0			0
$673$	−15.0000	−	15.0000i	−0.578208	−	0.578208i	0.356202	−	0.934409i	$-0.384072\pi$
$673$	−15.0000	−	15.0000i	−0.578208	−	0.578208i	−0.934409	+	0.356202i	$0.884072\pi$
$674$		0			0
$675$	−4.00000	+	28.0000i	−0.153960	+	1.07772i
$676$		0			0
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	0.109973	−	0.993935i	$-0.464924\pi$
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	−0.993935	+	0.109973i	$0.964924\pi$
$678$		0			0
$679$			4.00000i			0.153506i
$680$		0			0
$681$	−12.0000	+	12.0000i	−0.459841	+	0.459841i
$682$		0			0
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$		0			0
$685$	32.0000	+	16.0000i	1.22266	+	0.611329i
$686$		0			0
$687$		−	6.00000i		−	0.228914i
$688$		0			0
$689$	25.0000	−	5.00000i	0.952424	−	0.190485i
$690$		0			0
$691$	3.00000	−	3.00000i	0.114125	−	0.114125i	−0.647738	−	0.761863i	$-0.724285\pi$
$691$	3.00000	−	3.00000i	0.114125	−	0.114125i	0.761863	+	0.647738i	$0.224285\pi$
$692$		0			0
$693$	−2.00000	−	2.00000i	−0.0759737	−	0.0759737i
$694$		0			0
$695$	−28.0000	−	14.0000i	−1.06210	−	0.531050i
$696$		0			0
$697$			14.0000i			0.530288i
$698$		0			0
$699$	−2.00000			−0.0756469
$700$		0			0
$701$			12.0000i			0.453234i	0.973984	+	0.226617i	$0.0727665\pi$
$701$			12.0000i			0.453234i	−0.973984	+	0.226617i	$0.927233\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−18.0000	+	6.00000i	−0.677919	+	0.225973i
$706$		0			0
$707$	−24.0000			−0.902613
$708$		0			0
$709$	29.0000	−	29.0000i	1.08912	−	1.08912i	0.0934984	−	0.995619i	$-0.470195\pi$
$709$	29.0000	−	29.0000i	1.08912	−	1.08912i	0.995619	−	0.0934984i	$-0.0298050\pi$
$710$		0			0
$711$	−2.00000			−0.0750059
$712$		0			0
$713$	30.0000			1.12351
$714$		0			0
$715$	−11.0000	−	3.00000i	−0.411377	−	0.112194i
$716$		0			0
$717$	6.00000			0.224074
$718$		0			0
$719$	8.00000			0.298350			0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000			0.298350			0.149175	+	0.988811i	$0.452338\pi$
$720$		0			0
$721$	14.0000	−	14.0000i	0.521387	−	0.521387i
$722$		0			0
$723$	−34.0000			−1.26447
$724$		0			0
$725$		0			0
$726$		0			0
$727$	35.0000	−	35.0000i	1.29808	−	1.29808i	0.368418	−	0.929660i	$-0.379900\pi$
$727$	35.0000	−	35.0000i	1.29808	−	1.29808i	0.929660	−	0.368418i	$-0.120100\pi$
$728$		0			0
$729$			29.0000i			1.07407i
$730$		0			0
$731$	2.00000			0.0739727
$732$		0			0
$733$			4.00000i			0.147743i	0.997268	+	0.0738717i	$0.0235355\pi$
$733$			4.00000i			0.147743i	−0.997268	+	0.0738717i	$0.976464\pi$
$734$		0			0
$735$	−3.00000	−	9.00000i	−0.110657	−	0.331970i
$736$		0			0
$737$	4.00000	+	4.00000i	0.147342	+	0.147342i
$738$		0			0
$739$	3.00000	−	3.00000i	0.110357	−	0.110357i	−0.649772	−	0.760129i	$-0.725136\pi$
$739$	3.00000	−	3.00000i	0.110357	−	0.110357i	0.760129	+	0.649772i	$0.225136\pi$
$740$		0			0
$741$	−30.0000	−	20.0000i	−1.10208	−	0.734718i
$742$		0			0
$743$			34.0000i			1.24734i	0.781688	+	0.623670i	$0.214359\pi$
$743$			34.0000i			1.24734i	−0.781688	+	0.623670i	$0.785641\pi$
$744$		0			0
$745$	9.00000	−	3.00000i	0.329734	−	0.109911i
$746$		0			0
$747$	−6.00000			−0.219529
$748$		0			0
$749$	14.0000	−	14.0000i	0.511549	−	0.511549i
$750$		0			0
$751$			50.0000i			1.82453i	0.409605	+	0.912263i	$0.365667\pi$
$751$			50.0000i			1.82453i	−0.409605	+	0.912263i	$0.634333\pi$
$752$		0			0
$753$	2.00000	+	2.00000i	0.0728841	+	0.0728841i
$754$		0			0
$755$	21.0000	−	7.00000i	0.764268	−	0.254756i
$756$		0			0
$757$	−35.0000	−	35.0000i	−1.27210	−	1.27210i	−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−35.0000	−	35.0000i	−1.27210	−	1.27210i	−0.327111	−	0.944986i	$-0.606075\pi$
$758$		0			0
$759$	6.00000	+	6.00000i	0.217786	+	0.217786i
$760$		0			0
$761$	−7.00000	−	7.00000i	−0.253750	−	0.253750i	0.568756	−	0.822506i	$-0.307425\pi$
$761$	−7.00000	−	7.00000i	−0.253750	−	0.253750i	−0.822506	+	0.568756i	$0.807425\pi$
$762$		0			0
$763$	−18.0000	+	18.0000i	−0.651644	+	0.651644i
$764$		0			0
$765$	−3.00000	+	1.00000i	−0.108465	+	0.0361551i
$766$		0			0
$767$	35.0000	−	7.00000i	1.26378	−	0.252755i
$768$		0			0
$769$	−15.0000	−	15.0000i	−0.540914	−	0.540914i	0.382883	−	0.923797i	$-0.374931\pi$
$769$	−15.0000	−	15.0000i	−0.540914	−	0.540914i	−0.923797	+	0.382883i	$0.874931\pi$
$770$		0			0
$771$		−	22.0000i		−	0.792311i
$772$		0			0
$773$			32.0000i			1.15096i	0.817816	+	0.575480i	$0.195185\pi$
$773$			32.0000i			1.15096i	−0.817816	+	0.575480i	$0.804815\pi$
$774$		0			0
$775$	35.0000	+	5.00000i	1.25724	+	0.179605i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−70.0000			−2.50801
$780$		0			0
$781$	−2.00000			−0.0715656
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−39.0000	+	13.0000i	−1.39197	+	0.463990i
$786$		0			0
$787$			22.0000i			0.784215i	0.919919	+	0.392108i	$0.128254\pi$
$787$			22.0000i			0.784215i	−0.919919	+	0.392108i	$0.871746\pi$
$788$		0			0
$789$		−	2.00000i		−	0.0712019i
$790$		0			0
$791$	10.0000	+	10.0000i	0.355559	+	0.355559i
$792$		0			0
$793$	−42.0000	−	28.0000i	−1.49146	−	0.994309i
$794$		0			0
$795$	−20.0000	−	10.0000i	−0.709327	−	0.354663i
$796$		0			0
$797$	17.0000	−	17.0000i	0.602171	−	0.602171i	−0.338717	−	0.940888i	$-0.609993\pi$
$797$	17.0000	−	17.0000i	0.602171	−	0.602171i	0.940888	+	0.338717i	$0.109993\pi$
$798$		0			0
$799$	−6.00000	−	6.00000i	−0.212265	−	0.212265i
$800$		0			0
$801$	5.00000	+	5.00000i	0.176666	+	0.176666i
$802$		0			0
$803$	−10.0000	−	10.0000i	−0.352892	−	0.352892i
$804$		0			0
$805$	6.00000	+	18.0000i	0.211472	+	0.634417i
$806$		0			0
$807$	−12.0000	−	12.0000i	−0.422420	−	0.422420i
$808$		0			0
$809$			28.0000i			0.984428i	0.870474	+	0.492214i	$0.163812\pi$
$809$			28.0000i			0.984428i	−0.870474	+	0.492214i	$0.836188\pi$
$810$		0			0
$811$	27.0000	−	27.0000i	0.948098	−	0.948098i	−0.0506198	−	0.998718i	$-0.516120\pi$
$811$	27.0000	−	27.0000i	0.948098	−	0.948098i	0.998718	+	0.0506198i	$0.0161197\pi$
$812$		0			0
$813$	−18.0000			−0.631288
$814$		0			0
$815$	4.00000	−	8.00000i	0.140114	−	0.280228i
$816$		0			0
$817$			10.0000i			0.349856i
$818$		0			0
$819$	−6.00000	−	4.00000i	−0.209657	−	0.139771i
$820$		0			0
$821$	9.00000	−	9.00000i	0.314102	−	0.314102i	−0.532394	−	0.846496i	$-0.678708\pi$
$821$	9.00000	−	9.00000i	0.314102	−	0.314102i	0.846496	+	0.532394i	$0.178708\pi$
$822$		0			0
$823$	9.00000	+	9.00000i	0.313720	+	0.313720i	0.846349	−	0.532629i	$-0.178796\pi$
$823$	9.00000	+	9.00000i	0.313720	+	0.313720i	−0.532629	+	0.846349i	$0.678796\pi$
$824$		0			0
$825$	6.00000	+	8.00000i	0.208893	+	0.278524i
$826$		0			0
$827$			46.0000i			1.59958i	0.600282	+	0.799788i	$0.295055\pi$
$827$			46.0000i			1.59958i	−0.600282	+	0.799788i	$0.704945\pi$
$828$		0			0
$829$	34.0000			1.18087			0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000			1.18087			0.590434	+	0.807086i	$0.298956\pi$
$830$		0			0
$831$		−	30.0000i		−	1.04069i
$832$		0			0
$833$	3.00000	−	3.00000i	0.103944	−	0.103944i
$834$		0			0
$835$	−36.0000	−	18.0000i	−1.24583	−	0.622916i
$836$		0			0
$837$	40.0000			1.38260
$838$		0			0
$839$	35.0000	−	35.0000i	1.20833	−	1.20833i	0.236768	−	0.971566i	$-0.423912\pi$
$839$	35.0000	−	35.0000i	1.20833	−	1.20833i	0.971566	−	0.236768i	$-0.0760881\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$	−2.00000			−0.0688837
$844$		0			0
$845$	−29.0000	−	2.00000i	−0.997630	−	0.0688021i
$846$		0			0
$847$	18.0000			0.618487
$848$		0			0
$849$	−18.0000			−0.617758
$850$		0			0
$851$		0			0
$852$		0			0
$853$	26.0000			0.890223			0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000			0.890223			0.445112	+	0.895475i	$0.353164\pi$
$854$		0			0
$855$	−5.00000	−	15.0000i	−0.170996	−	0.512989i
$856$		0			0
$857$	−3.00000	+	3.00000i	−0.102478	+	0.102478i	−0.756487	−	0.654009i	$-0.773086\pi$
$857$	−3.00000	+	3.00000i	−0.102478	+	0.102478i	0.654009	+	0.756487i	$0.273086\pi$
$858$		0			0
$859$			30.0000i			1.02359i	0.859109	+	0.511793i	$0.171019\pi$
$859$			30.0000i			1.02359i	−0.859109	+	0.511793i	$0.828981\pi$
$860$		0			0
$861$	28.0000			0.954237
$862$		0			0
$863$		−	30.0000i		−	1.02121i	−0.859815	−	0.510606i	$-0.829421\pi$
$863$		−	30.0000i		−	1.02121i	0.859815	−	0.510606i	$-0.170579\pi$
$864$		0			0
$865$	33.0000	−	11.0000i	1.12203	−	0.374011i
$866$		0			0
$867$	−15.0000	−	15.0000i	−0.509427	−	0.509427i
$868$		0			0
$869$	−2.00000	+	2.00000i	−0.0678454	+	0.0678454i
$870$		0			0
$871$	12.0000	+	8.00000i	0.406604	+	0.271070i
$872$		0			0
$873$			2.00000i			0.0676897i
$874$		0			0
$875$	4.00000	+	22.0000i	0.135225	+	0.743736i
$876$		0			0
$877$	38.0000			1.28317			0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000			1.28317			0.641584	+	0.767052i	$0.278277\pi$
$878$		0			0
$879$	6.00000	−	6.00000i	0.202375	−	0.202375i
$880$		0			0
$881$		−	52.0000i		−	1.75192i	−0.482380	−	0.875962i	$-0.660227\pi$
$881$		−	52.0000i		−	1.75192i	0.482380	−	0.875962i	$-0.339773\pi$
$882$		0			0
$883$	−39.0000	−	39.0000i	−1.31245	−	1.31245i	−0.919601	−	0.392853i	$-0.871488\pi$
$883$	−39.0000	−	39.0000i	−1.31245	−	1.31245i	−0.392853	−	0.919601i	$-0.628512\pi$
$884$		0			0
$885$	−28.0000	−	14.0000i	−0.941210	−	0.470605i
$886$		0			0
$887$	1.00000	+	1.00000i	0.0335767	+	0.0335767i	0.723696	−	0.690119i	$-0.242442\pi$
$887$	1.00000	+	1.00000i	0.0335767	+	0.0335767i	−0.690119	+	0.723696i	$0.742442\pi$
$888$		0			0
$889$	−18.0000	−	18.0000i	−0.603701	−	0.603701i
$890$		0			0
$891$	5.00000	+	5.00000i	0.167506	+	0.167506i
$892$		0			0
$893$	30.0000	−	30.0000i	1.00391	−	1.00391i
$894$		0			0
$895$	−20.0000	+	40.0000i	−0.668526	+	1.33705i
$896$		0			0
$897$	18.0000	+	12.0000i	0.601003	+	0.400668i
$898$		0			0
$899$		0			0
$900$		0			0
$901$		−	10.0000i		−	0.333148i
$902$		0			0
$903$		−	4.00000i		−	0.133112i
$904$		0			0
$905$	16.0000	+	8.00000i	0.531858	+	0.265929i
$906$		0			0
$907$	39.0000	−	39.0000i	1.29497	−	1.29497i	0.363303	−	0.931671i	$-0.381649\pi$
$907$	39.0000	−	39.0000i	1.29497	−	1.29497i	0.931671	−	0.363303i	$-0.118351\pi$
$908$		0			0
$909$	−12.0000			−0.398015
$910$		0			0
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$		0			0
$913$	−6.00000	+	6.00000i	−0.198571	+	0.198571i
$914$		0			0
$915$	14.0000	+	42.0000i	0.462826	+	1.38848i
$916$		0			0
$917$			40.0000i			1.32092i
$918$		0			0
$919$			10.0000i			0.329870i	0.986304	+	0.164935i	$0.0527414\pi$
$919$			10.0000i			0.329870i	−0.986304	+	0.164935i	$0.947259\pi$
$920$		0			0
$921$	18.0000	+	18.0000i	0.593120	+	0.593120i
$922$		0			0
$923$	−5.00000	+	1.00000i	−0.164577	+	0.0329154i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	7.00000	−	7.00000i	0.229910	−	0.229910i
$928$		0			0
$929$	−19.0000	−	19.0000i	−0.623370	−	0.623370i	0.323022	−	0.946392i	$-0.395301\pi$
$929$	−19.0000	−	19.0000i	−0.623370	−	0.623370i	−0.946392	+	0.323022i	$0.895301\pi$
$930$		0			0
$931$	15.0000	+	15.0000i	0.491605	+	0.491605i
$932$		0			0
$933$	6.00000	+	6.00000i	0.196431	+	0.196431i
$934$		0			0
$935$	−2.00000	+	4.00000i	−0.0654070	+	0.130814i
$936$		0			0
$937$	−7.00000	−	7.00000i	−0.228680	−	0.228680i	0.583461	−	0.812141i	$-0.301698\pi$
$937$	−7.00000	−	7.00000i	−0.228680	−	0.228680i	−0.812141	+	0.583461i	$0.801698\pi$
$938$		0			0
$939$			18.0000i			0.587408i
$940$		0			0
$941$	21.0000	−	21.0000i	0.684580	−	0.684580i	−0.276448	−	0.961029i	$-0.589157\pi$
$941$	21.0000	−	21.0000i	0.684580	−	0.684580i	0.961029	+	0.276448i	$0.0891575\pi$
$942$		0			0
$943$	42.0000			1.36771
$944$		0			0
$945$	8.00000	+	24.0000i	0.260240	+	0.780720i
$946$		0			0
$947$		−	18.0000i		−	0.584921i	−0.956278	−	0.292461i	$-0.905526\pi$
$947$		−	18.0000i		−	0.584921i	0.956278	−	0.292461i	$-0.0944741\pi$
$948$		0			0
$949$	−30.0000	−	20.0000i	−0.973841	−	0.649227i
$950$		0			0
$951$	14.0000	−	14.0000i	0.453981	−	0.453981i
$952$		0			0
$953$	13.0000	+	13.0000i	0.421111	+	0.421111i	0.885586	−	0.464475i	$-0.153757\pi$
$953$	13.0000	+	13.0000i	0.421111	+	0.421111i	−0.464475	+	0.885586i	$0.653757\pi$
$954$		0			0
$955$	8.00000	−	16.0000i	0.258874	−	0.517748i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	32.0000			1.03333
$960$		0			0
$961$		−	19.0000i		−	0.612903i
$962$		0			0
$963$	7.00000	−	7.00000i	0.225572	−	0.225572i
$964$		0			0
$965$	−18.0000	+	36.0000i	−0.579441	+	1.15888i
$966$		0			0
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$		0			0
$969$	−10.0000	+	10.0000i	−0.321246	+	0.321246i
$970$		0			0
$971$	60.0000			1.92549			0.962746	−	0.270408i	$-0.0871586\pi$
$971$	60.0000			1.92549			0.962746	+	0.270408i	$0.0871586\pi$
$972$		0			0
$973$	−28.0000			−0.897639
$974$		0			0
$975$	19.0000	+	17.0000i	0.608487	+	0.544436i
$976$		0			0
$977$	62.0000			1.98356			0.991778	−	0.127971i	$-0.0408466\pi$
$977$	62.0000			1.98356			0.991778	+	0.127971i	$0.0408466\pi$
$978$		0			0
$979$	10.0000			0.319601
$980$		0			0
$981$	−9.00000	+	9.00000i	−0.287348	+	0.287348i
$982$		0			0
$983$	24.0000			0.765481			0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000			0.765481			0.382741	+	0.923856i	$0.374980\pi$
$984$		0			0
$985$	−6.00000	+	12.0000i	−0.191176	+	0.382352i
$986$		0			0
$987$	−12.0000	+	12.0000i	−0.381964	+	0.381964i
$988$		0			0
$989$		−	6.00000i		−	0.190789i
$990$		0			0
$991$		0			0			−	1.00000i	$-0.5\pi$
$991$		0			0				1.00000i	$0.5\pi$
$992$		0			0
$993$			6.00000i			0.190404i
$994$		0			0
$995$	−8.00000	+	16.0000i	−0.253617	+	0.507234i
$996$		0			0
$997$	9.00000	+	9.00000i	0.285033	+	0.285033i	0.835112	−	0.550079i	$-0.185403\pi$
$997$	9.00000	+	9.00000i	0.285033	+	0.285033i	−0.550079	+	0.835112i	$0.685403\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.bg.a.577.1		2
4.3	odd	2		65.2.k.a.57.1	yes	2
5.3	odd	4		1040.2.cd.b.993.1		2
12.11	even	2		585.2.w.b.577.1		2
13.8	odd	4		1040.2.cd.b.177.1		2
20.3	even	4		65.2.f.a.18.1	✓	2
20.7	even	4		325.2.f.a.18.1		2
20.19	odd	2		325.2.k.a.57.1		2
52.3	odd	6		845.2.o.a.357.1		4
52.7	even	12		845.2.t.a.427.1		4
52.11	even	12		845.2.t.a.657.1		4
52.15	even	12		845.2.t.b.657.1		4
52.19	even	12		845.2.t.b.427.1		4
52.23	odd	6		845.2.o.b.357.1		4
52.31	even	4		845.2.f.a.437.1		2
52.35	odd	6		845.2.o.a.587.1		4
52.43	odd	6		845.2.o.b.587.1		4
52.47	even	4		65.2.f.a.47.1	yes	2
52.51	odd	2		845.2.k.a.577.1		2
60.23	odd	4		585.2.n.c.343.1		2
65.8	even	4	inner	1040.2.bg.a.593.1		2
156.47	odd	4		585.2.n.c.307.1		2
260.3	even	12		845.2.t.a.188.1		4
260.23	even	12		845.2.t.b.188.1		4
260.43	even	12		845.2.t.b.418.1		4
260.47	odd	4		325.2.k.a.268.1		2
260.63	odd	12		845.2.o.a.488.1		4
260.83	odd	4		845.2.k.a.268.1		2
260.99	even	4		325.2.f.a.307.1		2
260.103	even	4		845.2.f.a.408.1		2
260.123	odd	12		845.2.o.b.258.1		4
260.163	odd	12		845.2.o.a.258.1		4
260.203	odd	4		65.2.k.a.8.1	yes	2
260.223	odd	12		845.2.o.b.488.1		4
260.243	even	12		845.2.t.a.418.1		4
780.203	even	4		585.2.w.b.73.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.a.18.1	✓	2	20.3	even	4
65.2.f.a.47.1	yes	2	52.47	even	4
65.2.k.a.8.1	yes	2	260.203	odd	4
65.2.k.a.57.1	yes	2	4.3	odd	2
325.2.f.a.18.1		2	20.7	even	4
325.2.f.a.307.1		2	260.99	even	4
325.2.k.a.57.1		2	20.19	odd	2
325.2.k.a.268.1		2	260.47	odd	4
585.2.n.c.307.1		2	156.47	odd	4
585.2.n.c.343.1		2	60.23	odd	4
585.2.w.b.73.1		2	780.203	even	4
585.2.w.b.577.1		2	12.11	even	2
845.2.f.a.408.1		2	260.103	even	4
845.2.f.a.437.1		2	52.31	even	4
845.2.k.a.268.1		2	260.83	odd	4
845.2.k.a.577.1		2	52.51	odd	2
845.2.o.a.258.1		4	260.163	odd	12
845.2.o.a.357.1		4	52.3	odd	6
845.2.o.a.488.1		4	260.63	odd	12
845.2.o.a.587.1		4	52.35	odd	6
845.2.o.b.258.1		4	260.123	odd	12
845.2.o.b.357.1		4	52.23	odd	6
845.2.o.b.488.1		4	260.223	odd	12
845.2.o.b.587.1		4	52.43	odd	6
845.2.t.a.188.1		4	260.3	even	12
845.2.t.a.418.1		4	260.243	even	12
845.2.t.a.427.1		4	52.7	even	12
845.2.t.a.657.1		4	52.11	even	12
845.2.t.b.188.1		4	260.23	even	12
845.2.t.b.418.1		4	260.43	even	12
845.2.t.b.427.1		4	52.19	even	12
845.2.t.b.657.1		4	52.15	even	12
1040.2.bg.a.577.1		2	1.1	even	1	trivial
1040.2.bg.a.593.1		2	65.8	even	4	inner
1040.2.cd.b.177.1		2	13.8	odd	4
1040.2.cd.b.993.1		2	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +2.00000i q^{7} +1.00000i q^{9} +(1.00000 + 1.00000i) q^{11} +(3.00000 + 2.00000i) q^{13} +(-1.00000 - 3.00000i) q^{15} +(1.00000 - 1.00000i) q^{17} +(5.00000 + 5.00000i) q^{19} +(-2.00000 - 2.00000i) q^{21} +(-3.00000 - 3.00000i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(-4.00000 - 4.00000i) q^{27} +(-5.00000 + 5.00000i) q^{31} -2.00000 q^{33} +(-4.00000 - 2.00000i) q^{35} +(-5.00000 + 1.00000i) q^{39} +(-7.00000 + 7.00000i) q^{41} +(1.00000 + 1.00000i) q^{43} +(-2.00000 - 1.00000i) q^{45} -6.00000i q^{47} +3.00000 q^{49} +2.00000i q^{51} +(5.00000 - 5.00000i) q^{53} +(-3.00000 + 1.00000i) q^{55} -10.0000 q^{57} +(7.00000 - 7.00000i) q^{59} -14.0000 q^{61} -2.00000 q^{63} +(-7.00000 + 4.00000i) q^{65} +4.00000 q^{67} +6.00000 q^{69} +(-1.00000 + 1.00000i) q^{71} -10.0000 q^{73} +(7.00000 + 1.00000i) q^{75} +(-2.00000 + 2.00000i) q^{77} +2.00000i q^{79} +5.00000 q^{81} +6.00000i q^{83} +(1.00000 + 3.00000i) q^{85} +(5.00000 - 5.00000i) q^{89} +(-4.00000 + 6.00000i) q^{91} -10.0000i q^{93} +(-15.0000 + 5.00000i) q^{95} +2.00000 q^{97} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 2 q^{5} + 2 q^{11} + 6 q^{13} - 2 q^{15} + 2 q^{17} + 10 q^{19} - 4 q^{21} - 6 q^{23} - 6 q^{25} - 8 q^{27} - 10 q^{31} - 4 q^{33} - 8 q^{35} - 10 q^{39} - 14 q^{41} + 2 q^{43} - 4 q^{45}+ \cdots - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - 2 * q^5 + 2 * q^11 + 6 * q^13 - 2 * q^15 + 2 * q^17 + 10 * q^19 - 4 * q^21 - 6 * q^23 - 6 * q^25 - 8 * q^27 - 10 * q^31 - 4 * q^33 - 8 * q^35 - 10 * q^39 - 14 * q^41 + 2 * q^43 - 4 * q^45 + 6 * q^49 + 10 * q^53 - 6 * q^55 - 20 * q^57 + 14 * q^59 - 28 * q^61 - 4 * q^63 - 14 * q^65 + 8 * q^67 + 12 * q^69 - 2 * q^71 - 20 * q^73 + 14 * q^75 - 4 * q^77 + 10 * q^81 + 2 * q^85 + 10 * q^89 - 8 * q^91 - 30 * q^95 + 4 * q^97 - 2 * q^99

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