LMFDB - Embedded newform 1040.2.cd.b.177.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1040,2,Mod(177,1040)] 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, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1040.177"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [2,0,-2,0,-4,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$1$
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			177.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1040.177
Dual form			1040.2.cd.b.993.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.00000i) q^{3} +(-2.00000 - 1.00000i) q^{5} +2.00000 q^{7} +1.00000i q^{9} +(1.00000 - 1.00000i) q^{11} +(-2.00000 - 3.00000i) q^{13} +(3.00000 - 1.00000i) q^{15} +(-1.00000 + 1.00000i) q^{17} +(-5.00000 + 5.00000i) q^{19} +(-2.00000 + 2.00000i) q^{21} +(3.00000 + 3.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} +(-4.00000 - 4.00000i) q^{27} +(-5.00000 - 5.00000i) q^{31} +2.00000i q^{33} +(-4.00000 - 2.00000i) q^{35} +(5.00000 + 1.00000i) q^{39} +(-7.00000 - 7.00000i) q^{41} +(-1.00000 - 1.00000i) q^{43} +(1.00000 - 2.00000i) q^{45} -6.00000 q^{47} -3.00000 q^{49} -2.00000i q^{51} +(5.00000 - 5.00000i) q^{53} +(-3.00000 + 1.00000i) q^{55} -10.0000i q^{57} +(-7.00000 - 7.00000i) q^{59} -14.0000 q^{61} +2.00000i q^{63} +(1.00000 + 8.00000i) q^{65} +4.00000i q^{67} -6.00000 q^{69} +(-1.00000 - 1.00000i) q^{71} +10.0000i q^{73} +(-7.00000 - 1.00000i) q^{75} +(2.00000 - 2.00000i) q^{77} +2.00000i q^{79} +5.00000 q^{81} -6.00000 q^{83} +(3.00000 - 1.00000i) q^{85} +(-5.00000 - 5.00000i) q^{89} +(-4.00000 - 6.00000i) q^{91} +10.0000 q^{93} +(15.0000 - 5.00000i) q^{95} +2.00000i q^{97} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 4 q^{5} + 4 q^{7} + 2 q^{11} - 4 q^{13} + 6 q^{15} - 2 q^{17} - 10 q^{19} - 4 q^{21} + 6 q^{23} + 6 q^{25} - 8 q^{27} - 10 q^{31} - 8 q^{35} + 10 q^{39} - 14 q^{41} - 2 q^{43} + 2 q^{45}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - 4 * q^5 + 4 * q^7 + 2 * q^11 - 4 * q^13 + 6 * q^15 - 2 * q^17 - 10 * q^19 - 4 * q^21 + 6 * q^23 + 6 * q^25 - 8 * q^27 - 10 * q^31 - 8 * q^35 + 10 * q^39 - 14 * q^41 - 2 * q^43 + 2 * q^45 - 12 * q^47 - 6 * q^49 + 10 * q^53 - 6 * q^55 - 14 * q^59 - 28 * q^61 + 2 * q^65 - 12 * q^69 - 2 * q^71 - 14 * q^75 + 4 * q^77 + 10 * q^81 - 12 * q^83 + 6 * q^85 - 10 * q^89 - 8 * q^91 + 20 * q^93 + 30 * q^95 + 2 * q^99

Character values

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

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

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
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		0			0
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	−0.540094	−	0.841605i	$-0.681611\pi$
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	0.841605	+	0.540094i	$0.181611\pi$
$12$		0			0
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$14$		0			0
$15$	3.00000	−	1.00000i	0.774597	−	0.258199i
$16$		0			0
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	−0.817898	−	0.575363i	$-0.804861\pi$
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	0.575363	+	0.817898i	$0.304861\pi$
$18$		0			0
$19$	−5.00000	+	5.00000i	−1.14708	+	1.14708i	−0.159954	+	0.987124i	$0.551135\pi$
$19$	−5.00000	+	5.00000i	−1.14708	+	1.14708i	−0.987124	+	0.159954i	$0.948865\pi$
$20$		0			0
$21$	−2.00000	+	2.00000i	−0.436436	+	0.436436i
$22$		0			0
$23$	3.00000	+	3.00000i	0.625543	+	0.625543i	0.946943	−	0.321400i	$-0.104153\pi$
$23$	3.00000	+	3.00000i	0.625543	+	0.625543i	−0.321400	+	0.946943i	$0.604153\pi$
$24$		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	0.0972349	−	0.995261i	$-0.469000\pi$
$31$	−5.00000	−	5.00000i	−0.898027	−	0.898027i	−0.995261	+	0.0972349i	$0.969000\pi$
$32$		0			0
$33$			2.00000i			0.348155i
$34$		0			0
$35$	−4.00000	−	2.00000i	−0.676123	−	0.338062i
$36$		0			0
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$		0			0
$39$	5.00000	+	1.00000i	0.800641	+	0.160128i
$40$		0			0
$41$	−7.00000	−	7.00000i	−1.09322	−	1.09322i	−0.995183	−	0.0980332i	$-0.968745\pi$
$41$	−7.00000	−	7.00000i	−1.09322	−	1.09322i	−0.0980332	−	0.995183i	$-0.531255\pi$
$42$		0			0
$43$	−1.00000	−	1.00000i	−0.152499	−	0.152499i	0.626734	−	0.779233i	$-0.284391\pi$
$43$	−1.00000	−	1.00000i	−0.152499	−	0.152499i	−0.779233	+	0.626734i	$0.784391\pi$
$44$		0			0
$45$	1.00000	−	2.00000i	0.149071	−	0.298142i
$46$		0			0
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$		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
$57$		−	10.0000i		−	1.32453i
$58$		0			0
$59$	−7.00000	−	7.00000i	−0.911322	−	0.911322i	0.0850540	−	0.996376i	$-0.472894\pi$
$59$	−7.00000	−	7.00000i	−0.911322	−	0.911322i	−0.996376	+	0.0850540i	$0.972894\pi$
$60$		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
$63$			2.00000i			0.251976i
$64$		0			0
$65$	1.00000	+	8.00000i	0.124035	+	0.992278i
$66$		0			0
$67$			4.00000i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$			4.00000i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$		0			0
$69$	−6.00000			−0.722315
$70$		0			0
$71$	−1.00000	−	1.00000i	−0.118678	−	0.118678i	0.645273	−	0.763952i	$-0.276743\pi$
$71$	−1.00000	−	1.00000i	−0.118678	−	0.118678i	−0.763952	+	0.645273i	$0.776743\pi$
$72$		0			0
$73$			10.0000i			1.17041i	0.810885	+	0.585206i	$0.198986\pi$
$73$			10.0000i			1.17041i	−0.810885	+	0.585206i	$0.801014\pi$
$74$		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
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$	3.00000	−	1.00000i	0.325396	−	0.108465i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.00000	−	5.00000i	−0.529999	−	0.529999i	0.390573	−	0.920572i	$-0.372277\pi$
$89$	−5.00000	−	5.00000i	−0.529999	−	0.529999i	−0.920572	+	0.390573i	$0.872277\pi$
$90$		0			0
$91$	−4.00000	−	6.00000i	−0.419314	−	0.628971i
$92$		0			0
$93$	10.0000			1.03695
$94$		0			0
$95$	15.0000	−	5.00000i	1.53897	−	0.512989i
$96$		0			0
$97$			2.00000i			0.203069i	0.994832	+	0.101535i	$0.0323753\pi$
$97$			2.00000i			0.203069i	−0.994832	+	0.101535i	$0.967625\pi$
$98$		0			0
$99$	1.00000	+	1.00000i	0.100504	+	0.100504i
$100$		0			0
$101$		−	12.0000i		−	1.19404i	−0.802225	−	0.597022i	$-0.796350\pi$
$101$		−	12.0000i		−	1.19404i	0.802225	−	0.597022i	$-0.203650\pi$
$102$		0			0
$103$	7.00000	+	7.00000i	0.689730	+	0.689730i	0.962172	−	0.272442i	$-0.0878312\pi$
$103$	7.00000	+	7.00000i	0.689730	+	0.689730i	−0.272442	+	0.962172i	$0.587831\pi$
$104$		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	$-0.958653\pi$
$109$	−9.00000	+	9.00000i	−0.862044	+	0.862044i	0.129532	+	0.991575i	$0.458653\pi$
$110$		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
$115$	−3.00000	−	9.00000i	−0.279751	−	0.839254i
$116$		0			0
$117$	3.00000	−	2.00000i	0.277350	−	0.184900i
$118$		0			0
$119$	−2.00000	+	2.00000i	−0.183340	+	0.183340i
$120$		0			0
$121$			9.00000i			0.818182i
$122$		0			0
$123$	14.0000			1.26234
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	−0.184257	−	0.982878i	$-0.558988\pi$
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	0.982878	+	0.184257i	$0.0589879\pi$
$128$		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
$135$	4.00000	+	12.0000i	0.344265	+	1.03280i
$136$		0			0
$137$	−16.0000			−1.36697			−0.683486	−	0.729964i	$-0.739537\pi$
$137$	−16.0000			−1.36697			−0.683486	+	0.729964i	$0.739537\pi$
$138$		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
$143$	−5.00000	−	1.00000i	−0.418121	−	0.0836242i
$144$		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	$-0.694400\pi$
$149$	3.00000	−	3.00000i	0.245770	−	0.245770i	0.819232	+	0.573462i	$0.194400\pi$
$150$		0			0
$151$	−7.00000	+	7.00000i	−0.569652	+	0.569652i	−0.932031	−	0.362379i	$-0.881965\pi$
$151$	−7.00000	+	7.00000i	−0.569652	+	0.569652i	0.362379	+	0.932031i	$0.381965\pi$
$152$		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
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$		0			0
$165$	2.00000	−	4.00000i	0.155700	−	0.311400i
$166$		0			0
$167$	18.0000			1.39288			0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000			1.39288			0.696441	+	0.717614i	$0.254766\pi$
$168$		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	0.988372	−	0.152057i	$-0.0485898\pi$
$173$	11.0000	+	11.0000i	0.836315	+	0.836315i	−0.152057	+	0.988372i	$0.548590\pi$
$174$		0			0
$175$	6.00000	+	8.00000i	0.453557	+	0.604743i
$176$		0			0
$177$	14.0000			1.05230
$178$		0			0
$179$	−20.0000			−1.49487			−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000			−1.49487			−0.747435	+	0.664335i	$0.768715\pi$
$180$		0			0
$181$			8.00000i			0.594635i	0.954779	+	0.297318i	$0.0960920\pi$
$181$			8.00000i			0.594635i	−0.954779	+	0.297318i	$0.903908\pi$
$182$		0			0
$183$	14.0000	−	14.0000i	1.03491	−	1.03491i
$184$		0			0
$185$		0			0
$186$		0			0
$187$			2.00000i			0.146254i
$188$		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
$193$		−	18.0000i		−	1.29567i	−0.761781	−	0.647834i	$-0.775675\pi$
$193$		−	18.0000i		−	1.29567i	0.761781	−	0.647834i	$-0.224325\pi$
$194$		0			0
$195$	−9.00000	−	7.00000i	−0.644503	−	0.501280i
$196$		0			0
$197$			6.00000i			0.427482i	0.976890	+	0.213741i	$0.0685649\pi$
$197$			6.00000i			0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$		0			0
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$		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
$213$	2.00000			0.137038
$214$		0			0
$215$	1.00000	+	3.00000i	0.0681994	+	0.204598i
$216$		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
$223$	−2.00000			−0.133930			−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000			−0.133930			−0.0669650	+	0.997755i	$0.521332\pi$
$224$		0			0
$225$	−4.00000	+	3.00000i	−0.266667	+	0.200000i
$226$		0			0
$227$			12.0000i			0.796468i	0.917284	+	0.398234i	$0.130377\pi$
$227$			12.0000i			0.796468i	−0.917284	+	0.398234i	$0.869623\pi$
$228$		0			0
$229$	3.00000	+	3.00000i	0.198246	+	0.198246i	0.799248	−	0.601002i	$-0.205232\pi$
$229$	3.00000	+	3.00000i	0.198246	+	0.198246i	−0.601002	+	0.799248i	$0.705232\pi$
$230$		0			0
$231$			4.00000i			0.263181i
$232$		0			0
$233$	−1.00000	−	1.00000i	−0.0655122	−	0.0655122i	0.673592	−	0.739104i	$-0.264751\pi$
$233$	−1.00000	−	1.00000i	−0.0655122	−	0.0655122i	−0.739104	+	0.673592i	$0.764751\pi$
$234$		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	$-0.706184\pi$
$239$	3.00000	−	3.00000i	0.194054	−	0.194054i	0.797445	+	0.603391i	$0.206184\pi$
$240$		0			0
$241$	17.0000	−	17.0000i	1.09507	−	1.09507i	0.100088	−	0.994979i	$-0.468088\pi$
$241$	17.0000	−	17.0000i	1.09507	−	1.09507i	0.994979	−	0.100088i	$-0.0319123\pi$
$242$		0			0
$243$	7.00000	−	7.00000i	0.449050	−	0.449050i
$244$		0			0
$245$	6.00000	+	3.00000i	0.383326	+	0.191663i
$246$		0			0
$247$	25.0000	+	5.00000i	1.59071	+	0.318142i
$248$		0			0
$249$	6.00000	−	6.00000i	0.380235	−	0.380235i
$250$		0			0
$251$			2.00000i			0.126239i	0.998006	+	0.0631194i	$0.0201049\pi$
$251$			2.00000i			0.126239i	−0.998006	+	0.0631194i	$0.979895\pi$
$252$		0			0
$253$	6.00000			0.377217
$254$		0			0
$255$	−2.00000	+	4.00000i	−0.125245	+	0.250490i
$256$		0			0
$257$	11.0000	−	11.0000i	0.686161	−	0.686161i	−0.275220	−	0.961381i	$-0.588751\pi$
$257$	11.0000	−	11.0000i	0.686161	−	0.686161i	0.961381	+	0.275220i	$0.0887507\pi$
$258$		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
$265$	−15.0000	+	5.00000i	−0.921443	+	0.307148i
$266$		0			0
$267$	10.0000			0.611990
$268$		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	−0.378777	−	0.925488i	$-0.623655\pi$
$271$	9.00000	−	9.00000i	0.546711	−	0.546711i	0.925488	+	0.378777i	$0.123655\pi$
$272$		0			0
$273$	10.0000	+	2.00000i	0.605228	+	0.121046i
$274$		0			0
$275$	7.00000	+	1.00000i	0.422116	+	0.0603023i
$276$		0			0
$277$	15.0000	−	15.0000i	0.901263	−	0.901263i	−0.0942828	−	0.995545i	$-0.530056\pi$
$277$	15.0000	−	15.0000i	0.901263	−	0.901263i	0.995545	+	0.0942828i	$0.0300558\pi$
$278$		0			0
$279$	5.00000	−	5.00000i	0.299342	−	0.299342i
$280$		0			0
$281$	1.00000	−	1.00000i	0.0596550	−	0.0596550i	−0.676650	−	0.736305i	$-0.736569\pi$
$281$	1.00000	−	1.00000i	0.0596550	−	0.0596550i	0.736305	+	0.676650i	$0.236569\pi$
$282$		0			0
$283$	−9.00000	−	9.00000i	−0.534994	−	0.534994i	0.387060	−	0.922055i	$-0.373491\pi$
$283$	−9.00000	−	9.00000i	−0.534994	−	0.534994i	−0.922055	+	0.387060i	$0.873491\pi$
$284$		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
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$		0			0
$295$	7.00000	+	21.0000i	0.407556	+	1.22267i
$296$		0			0
$297$	−8.00000			−0.464207
$298$		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
$305$	28.0000	+	14.0000i	1.60328	+	0.801638i
$306$		0			0
$307$	−18.0000			−1.02731			−0.513657	−	0.857996i	$-0.671710\pi$
$307$	−18.0000			−1.02731			−0.513657	+	0.857996i	$0.671710\pi$
$308$		0			0
$309$	−14.0000			−0.796432
$310$		0			0
$311$			6.00000i			0.340229i	0.985424	+	0.170114i	$0.0544137\pi$
$311$			6.00000i			0.340229i	−0.985424	+	0.170114i	$0.945586\pi$
$312$		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
$317$		−	14.0000i		−	0.786318i	−0.919470	−	0.393159i	$-0.871382\pi$
$317$		−	14.0000i		−	0.786318i	0.919470	−	0.393159i	$-0.128618\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	14.0000			0.781404
$322$		0			0
$323$		−	10.0000i		−	0.556415i
$324$		0			0
$325$	6.00000	−	17.0000i	0.332820	−	0.942990i
$326$		0			0
$327$		−	18.0000i		−	0.995402i
$328$		0			0
$329$	−12.0000			−0.661581
$330$		0			0
$331$	3.00000	+	3.00000i	0.164895	+	0.164895i	0.784731	−	0.619836i	$-0.212801\pi$
$331$	3.00000	+	3.00000i	0.164895	+	0.164895i	−0.619836	+	0.784731i	$0.712801\pi$
$332$		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	−0.966147	−	0.257992i	$-0.916939\pi$
$337$	−13.0000	+	13.0000i	−0.708155	+	0.708155i	0.257992	+	0.966147i	$0.416939\pi$
$338$		0			0
$339$			10.0000i			0.543125i
$340$		0			0
$341$	−10.0000			−0.541530
$342$		0			0
$343$	−20.0000			−1.07990
$344$		0			0
$345$	12.0000	+	6.00000i	0.646058	+	0.323029i
$346$		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	$-0.360649\pi$
$349$	−9.00000	−	9.00000i	−0.481759	−	0.481759i	−0.905693	+	0.423934i	$0.860649\pi$
$350$		0			0
$351$	−4.00000	+	20.0000i	−0.213504	+	1.06752i
$352$		0			0
$353$	−12.0000			−0.638696			−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000			−0.638696			−0.319348	+	0.947638i	$0.603464\pi$
$354$		0			0
$355$	1.00000	+	3.00000i	0.0530745	+	0.159223i
$356$		0			0
$357$		−	4.00000i		−	0.211702i
$358$		0			0
$359$	1.00000	+	1.00000i	0.0527780	+	0.0527780i	0.733003	−	0.680225i	$-0.238118\pi$
$359$	1.00000	+	1.00000i	0.0527780	+	0.0527780i	−0.680225	+	0.733003i	$0.738118\pi$
$360$		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
$375$	13.0000	+	9.00000i	0.671317	+	0.464758i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.00000	+	1.00000i	−0.0513665	+	0.0513665i	−0.732323	−	0.680957i	$-0.761564\pi$
$379$	−1.00000	+	1.00000i	−0.0513665	+	0.0513665i	0.680957	+	0.732323i	$0.261564\pi$
$380$		0			0
$381$			18.0000i			0.922168i
$382$		0			0
$383$	30.0000			1.53293			0.766464	−	0.642287i	$-0.222014\pi$
$383$	30.0000			1.53293			0.766464	+	0.642287i	$0.222014\pi$
$384$		0			0
$385$	−6.00000	+	2.00000i	−0.305788	+	0.101929i
$386$		0			0
$387$	1.00000	−	1.00000i	0.0508329	−	0.0508329i
$388$		0			0
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$		0			0
$391$	−6.00000			−0.303433
$392$		0			0
$393$	−20.0000	+	20.0000i	−1.00887	+	1.00887i
$394$		0			0
$395$	2.00000	−	4.00000i	0.100631	−	0.201262i
$396$		0			0
$397$	16.0000			0.803017			0.401508	−	0.915855i	$-0.368486\pi$
$397$	16.0000			0.803017			0.401508	+	0.915855i	$0.368486\pi$
$398$		0			0
$399$		−	20.0000i		−	1.00125i
$400$		0			0
$401$	−11.0000	+	11.0000i	−0.549314	+	0.549314i	−0.926242	−	0.376929i	$-0.876980\pi$
$401$	−11.0000	+	11.0000i	−0.549314	+	0.549314i	0.376929	+	0.926242i	$0.376980\pi$
$402$		0			0
$403$	−5.00000	+	25.0000i	−0.249068	+	1.24534i
$404$		0			0
$405$	−10.0000	−	5.00000i	−0.496904	−	0.248452i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	7.00000	−	7.00000i	0.346128	−	0.346128i	−0.512537	−	0.858665i	$-0.671294\pi$
$409$	7.00000	−	7.00000i	0.346128	−	0.346128i	0.858665	+	0.512537i	$0.171294\pi$
$410$		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	0.386276	−	0.922383i	$-0.373761\pi$
$421$	−11.0000	−	11.0000i	−0.536107	−	0.536107i	−0.922383	+	0.386276i	$0.873761\pi$
$422$		0			0
$423$		−	6.00000i		−	0.291730i
$424$		0			0
$425$	−7.00000	−	1.00000i	−0.339550	−	0.0485071i
$426$		0			0
$427$	−28.0000			−1.35501
$428$		0			0
$429$	6.00000	−	4.00000i	0.289683	−	0.193122i
$430$		0			0
$431$	−13.0000	−	13.0000i	−0.626188	−	0.626188i	0.320919	−	0.947107i	$-0.396008\pi$
$431$	−13.0000	−	13.0000i	−0.626188	−	0.626188i	−0.947107	+	0.320919i	$0.896008\pi$
$432$		0			0
$433$	−17.0000	−	17.0000i	−0.816968	−	0.816968i	0.168700	−	0.985668i	$-0.446043\pi$
$433$	−17.0000	−	17.0000i	−0.816968	−	0.816968i	−0.985668	+	0.168700i	$0.946043\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−30.0000			−1.43509
$438$		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
$447$			6.00000i			0.283790i
$448$		0			0
$449$	3.00000	+	3.00000i	0.141579	+	0.141579i	0.774344	−	0.632765i	$-0.218080\pi$
$449$	3.00000	+	3.00000i	0.141579	+	0.141579i	−0.632765	+	0.774344i	$0.718080\pi$
$450$		0			0
$451$	−14.0000			−0.659234
$452$		0			0
$453$		−	14.0000i		−	0.657777i
$454$		0			0
$455$	2.00000	+	16.0000i	0.0937614	+	0.750092i
$456$		0			0
$457$			2.00000i			0.0935561i	0.998905	+	0.0467780i	$0.0148953\pi$
$457$			2.00000i			0.0935561i	−0.998905	+	0.0467780i	$0.985105\pi$
$458$		0			0
$459$	8.00000			0.373408
$460$		0			0
$461$	17.0000	+	17.0000i	0.791769	+	0.791769i	0.981782	−	0.190013i	$-0.0608529\pi$
$461$	17.0000	+	17.0000i	0.791769	+	0.791769i	−0.190013	+	0.981782i	$0.560853\pi$
$462$		0			0
$463$		−	24.0000i		−	1.11537i	−0.830051	−	0.557687i	$-0.811689\pi$
$463$		−	24.0000i		−	1.11537i	0.830051	−	0.557687i	$-0.188311\pi$
$464$		0			0
$465$	−20.0000	−	10.0000i	−0.927478	−	0.463739i
$466$		0			0
$467$	9.00000	−	9.00000i	0.416470	−	0.416470i	−0.467515	−	0.883985i	$-0.654851\pi$
$467$	9.00000	−	9.00000i	0.416470	−	0.416470i	0.883985	+	0.467515i	$0.154851\pi$
$468$		0			0
$469$			8.00000i			0.369406i
$470$		0			0
$471$	−26.0000			−1.19802
$472$		0			0
$473$	−2.00000			−0.0919601
$474$		0			0
$475$	−35.0000	−	5.00000i	−1.60591	−	0.229416i
$476$		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	$-0.322617\pi$
$479$	−7.00000	−	7.00000i	−0.319838	−	0.319838i	−0.848705	+	0.528867i	$0.822617\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−12.0000			−0.546019
$484$		0			0
$485$	2.00000	−	4.00000i	0.0908153	−	0.181631i
$486$		0			0
$487$		−	16.0000i		−	0.725029i	−0.931978	−	0.362515i	$-0.881918\pi$
$487$		−	16.0000i		−	0.725029i	0.931978	−	0.362515i	$-0.118082\pi$
$488$		0			0
$489$	−4.00000	−	4.00000i	−0.180886	−	0.180886i
$490$		0			0
$491$		−	22.0000i		−	0.992846i	−0.868081	−	0.496423i	$-0.834646\pi$
$491$		−	22.0000i		−	0.992846i	0.868081	−	0.496423i	$-0.165354\pi$
$492$		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	$-0.719727\pi$
$499$	3.00000	−	3.00000i	0.134298	−	0.134298i	0.771060	+	0.636762i	$0.219727\pi$
$500$		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
$505$	−12.0000	+	24.0000i	−0.533993	+	1.06799i
$506$		0			0
$507$	−7.00000	−	17.0000i	−0.310881	−	0.754997i
$508$		0			0
$509$	−13.0000	+	13.0000i	−0.576215	+	0.576215i	−0.933858	−	0.357643i	$-0.883580\pi$
$509$	−13.0000	+	13.0000i	−0.576215	+	0.576215i	0.357643	+	0.933858i	$0.383580\pi$
$510$		0			0
$511$			20.0000i			0.884748i
$512$		0			0
$513$	40.0000			1.76604
$514$		0			0
$515$	−7.00000	−	21.0000i	−0.308457	−	0.925371i
$516$		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
$525$	−14.0000	−	2.00000i	−0.611010	−	0.0872872i
$526$		0			0
$527$	10.0000			0.435607
$528$		0			0
$529$		−	5.00000i		−	0.217391i
$530$		0			0
$531$	7.00000	−	7.00000i	0.303774	−	0.303774i
$532$		0			0
$533$	−7.00000	+	35.0000i	−0.303204	+	1.51602i
$534$		0			0
$535$	7.00000	+	21.0000i	0.302636	+	0.907909i
$536$		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	−0.486654	−	0.873595i	$-0.661783\pi$
$541$	9.00000	−	9.00000i	0.386940	−	0.386940i	0.873595	+	0.486654i	$0.161783\pi$
$542$		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
$553$			4.00000i			0.170097i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	24.0000			1.01691			0.508456	−	0.861088i	$-0.330216\pi$
$557$	24.0000			1.01691			0.508456	+	0.861088i	$0.330216\pi$
$558$		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	0.948613	−	0.316438i	$-0.102487\pi$
$563$	15.0000	+	15.0000i	0.632175	+	0.632175i	−0.316438	+	0.948613i	$0.602487\pi$
$564$		0			0
$565$	−15.0000	+	5.00000i	−0.631055	+	0.210352i
$566$		0			0
$567$	10.0000			0.419961
$568$		0			0
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$		0			0
$571$		−	6.00000i		−	0.251092i	−0.992088	−	0.125546i	$-0.959932\pi$
$571$		−	6.00000i		−	0.251092i	0.992088	−	0.125546i	$-0.0400683\pi$
$572$		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
$577$			46.0000i			1.91501i	0.288425	+	0.957503i	$0.406868\pi$
$577$			46.0000i			1.91501i	−0.288425	+	0.957503i	$0.593132\pi$
$578$		0			0
$579$	18.0000	+	18.0000i	0.748054	+	0.748054i
$580$		0			0
$581$	−12.0000			−0.497844
$582$		0			0
$583$		−	10.0000i		−	0.414158i
$584$		0			0
$585$	−8.00000	+	1.00000i	−0.330759	+	0.0413449i
$586$		0			0
$587$			4.00000i			0.165098i	0.996587	+	0.0825488i	$0.0263060\pi$
$587$			4.00000i			0.165098i	−0.996587	+	0.0825488i	$0.973694\pi$
$588$		0			0
$589$	50.0000			2.06021
$590$		0			0
$591$	−6.00000	−	6.00000i	−0.246807	−	0.246807i
$592$		0			0
$593$		−	10.0000i		−	0.410651i	−0.978694	−	0.205325i	$-0.934175\pi$
$593$		−	10.0000i		−	0.410651i	0.978694	−	0.205325i	$-0.0658253\pi$
$594$		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
$603$	−4.00000			−0.162893
$604$		0			0
$605$	9.00000	−	18.0000i	0.365902	−	0.731804i
$606$		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
$613$	−20.0000			−0.807792			−0.403896	−	0.914805i	$-0.632344\pi$
$613$	−20.0000			−0.807792			−0.403896	+	0.914805i	$0.632344\pi$
$614$		0			0
$615$	−28.0000	−	14.0000i	−1.12907	−	0.564534i
$616$		0			0
$617$		−	22.0000i		−	0.885687i	−0.896599	−	0.442843i	$-0.853970\pi$
$617$		−	22.0000i		−	0.885687i	0.896599	−	0.442843i	$-0.146030\pi$
$618$		0			0
$619$	25.0000	+	25.0000i	1.00483	+	1.00483i	0.999988	+	0.00484658i	$0.00154272\pi$
$619$	25.0000	+	25.0000i	1.00483	+	1.00483i	0.00484658	+	0.999988i	$0.498457\pi$
$620$		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	−0.891306	−	0.453403i	$-0.850210\pi$
$631$	−11.0000	+	11.0000i	−0.437903	+	0.437903i	0.453403	+	0.891306i	$0.350210\pi$
$632$		0			0
$633$	4.00000	−	4.00000i	0.158986	−	0.158986i
$634$		0			0
$635$	−27.0000	+	9.00000i	−1.07146	+	0.357154i
$636$		0			0
$637$	6.00000	+	9.00000i	0.237729	+	0.356593i
$638$		0			0
$639$	1.00000	−	1.00000i	0.0395594	−	0.0395594i
$640$		0			0
$641$			24.0000i			0.947943i	0.880540	+	0.473972i	$0.157180\pi$
$641$			24.0000i			0.947943i	−0.880540	+	0.473972i	$0.842820\pi$
$642$		0			0
$643$	34.0000			1.34083			0.670415	−	0.741987i	$-0.266116\pi$
$643$	34.0000			1.34083			0.670415	+	0.741987i	$0.266116\pi$
$644$		0			0
$645$	−4.00000	−	2.00000i	−0.157500	−	0.0787499i
$646$		0			0
$647$	1.00000	−	1.00000i	0.0393141	−	0.0393141i	−0.687176	−	0.726491i	$-0.741150\pi$
$647$	1.00000	−	1.00000i	0.0393141	−	0.0393141i	0.726491	+	0.687176i	$0.241150\pi$
$648$		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
$655$	−40.0000	−	20.0000i	−1.56293	−	0.781465i
$656$		0			0
$657$	−10.0000			−0.390137
$658$		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	−0.294445	−	0.955668i	$-0.595135\pi$
$661$	17.0000	−	17.0000i	0.661223	−	0.661223i	0.955668	+	0.294445i	$0.0951348\pi$
$662$		0			0
$663$	−6.00000	+	4.00000i	−0.233021	+	0.155347i
$664$		0			0
$665$	30.0000	−	10.0000i	1.16335	−	0.387783i
$666$		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	0.934409	−	0.356202i	$-0.115928\pi$
$673$	15.0000	+	15.0000i	0.578208	+	0.578208i	−0.356202	+	0.934409i	$0.615928\pi$
$674$		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
$683$		−	12.0000i		−	0.459167i	−0.973289	−	0.229584i	$-0.926264\pi$
$683$		−	12.0000i		−	0.459167i	0.973289	−	0.229584i	$-0.0737364\pi$
$684$		0			0
$685$	32.0000	+	16.0000i	1.22266	+	0.611329i
$686$		0			0
$687$	−6.00000			−0.228914
$688$		0			0
$689$	−25.0000	−	5.00000i	−0.952424	−	0.190485i
$690$		0			0
$691$	3.00000	+	3.00000i	0.114125	+	0.114125i	0.761863	−	0.647738i	$-0.224285\pi$
$691$	3.00000	+	3.00000i	0.114125	+	0.114125i	−0.647738	+	0.761863i	$0.724285\pi$
$692$		0			0
$693$	2.00000	+	2.00000i	0.0759737	+	0.0759737i
$694$		0			0
$695$	14.0000	−	28.0000i	0.531050	−	1.06210i
$696$		0			0
$697$	14.0000			0.530288
$698$		0			0
$699$	2.00000			0.0756469
$700$		0			0
$701$		−	12.0000i		−	0.453234i	−0.973984	−	0.226617i	$-0.927233\pi$
$701$		−	12.0000i		−	0.453234i	0.973984	−	0.226617i	$-0.0727665\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−18.0000	+	6.00000i	−0.677919	+	0.225973i
$706$		0			0
$707$		−	24.0000i		−	0.902613i
$708$		0			0
$709$	−29.0000	−	29.0000i	−1.08912	−	1.08912i	−0.995619	−	0.0934984i	$-0.970195\pi$
$709$	−29.0000	−	29.0000i	−1.08912	−	1.08912i	−0.0934984	−	0.995619i	$-0.529805\pi$
$710$		0			0
$711$	−2.00000			−0.0750059
$712$		0			0
$713$		−	30.0000i		−	1.12351i
$714$		0			0
$715$	9.00000	+	7.00000i	0.336581	+	0.261785i
$716$		0			0
$717$			6.00000i			0.224074i
$718$		0			0
$719$	−8.00000			−0.298350			−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000			−0.298350			−0.149175	+	0.988811i	$0.547662\pi$
$720$		0			0
$721$	14.0000	+	14.0000i	0.521387	+	0.521387i
$722$		0			0
$723$			34.0000i			1.26447i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−35.0000	+	35.0000i	−1.29808	+	1.29808i	−0.368418	+	0.929660i	$0.620100\pi$
$727$	−35.0000	+	35.0000i	−1.29808	+	1.29808i	−0.929660	+	0.368418i	$0.879900\pi$
$728$		0			0
$729$			29.0000i			1.07407i
$730$		0			0
$731$	2.00000			0.0739727
$732$		0			0
$733$	−4.00000			−0.147743			−0.0738717	−	0.997268i	$-0.523536\pi$
$733$	−4.00000			−0.147743			−0.0738717	+	0.997268i	$0.523536\pi$
$734$		0			0
$735$	−9.00000	+	3.00000i	−0.331970	+	0.110657i
$736$		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	$-0.274864\pi$
$739$	−3.00000	−	3.00000i	−0.110357	−	0.110357i	−0.760129	+	0.649772i	$0.774864\pi$
$740$		0			0
$741$	−30.0000	+	20.0000i	−1.10208	+	0.734718i
$742$		0			0
$743$	−34.0000			−1.24734			−0.623670	−	0.781688i	$-0.714359\pi$
$743$	−34.0000			−1.24734			−0.623670	+	0.781688i	$0.714359\pi$
$744$		0			0
$745$	−9.00000	+	3.00000i	−0.329734	+	0.109911i
$746$		0			0
$747$		−	6.00000i		−	0.219529i
$748$		0			0
$749$	−14.0000	−	14.0000i	−0.511549	−	0.511549i
$750$		0			0
$751$		−	50.0000i		−	1.82453i	−0.409605	−	0.912263i	$-0.634333\pi$
$751$		−	50.0000i		−	1.82453i	0.409605	−	0.912263i	$-0.365667\pi$
$752$		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	−0.822506	−	0.568756i	$-0.807425\pi$
$761$	−7.00000	+	7.00000i	−0.253750	+	0.253750i	0.568756	+	0.822506i	$0.307425\pi$
$762$		0			0
$763$	−18.0000	+	18.0000i	−0.651644	+	0.651644i
$764$		0			0
$765$	1.00000	+	3.00000i	0.0361551	+	0.108465i
$766$		0			0
$767$	−7.00000	+	35.0000i	−0.252755	+	1.26378i
$768$		0			0
$769$	15.0000	−	15.0000i	0.540914	−	0.540914i	−0.382883	−	0.923797i	$-0.625069\pi$
$769$	15.0000	−	15.0000i	0.540914	−	0.540914i	0.923797	+	0.382883i	$0.125069\pi$
$770$		0			0
$771$			22.0000i			0.792311i
$772$		0			0
$773$	−32.0000			−1.15096			−0.575480	−	0.817816i	$-0.695185\pi$
$773$	−32.0000			−1.15096			−0.575480	+	0.817816i	$0.695185\pi$
$774$		0			0
$775$	5.00000	−	35.0000i	0.179605	−	1.25724i
$776$		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
$785$	−13.0000	−	39.0000i	−0.463990	−	1.39197i
$786$		0			0
$787$	22.0000			0.784215			0.392108	−	0.919919i	$-0.371746\pi$
$787$	22.0000			0.784215			0.392108	+	0.919919i	$0.371746\pi$
$788$		0			0
$789$		−	2.00000i		−	0.0712019i
$790$		0			0
$791$	10.0000	−	10.0000i	0.355559	−	0.355559i
$792$		0			0
$793$	28.0000	+	42.0000i	0.994309	+	1.49146i
$794$		0			0
$795$	10.0000	−	20.0000i	0.354663	−	0.709327i
$796$		0			0
$797$	−17.0000	+	17.0000i	−0.602171	+	0.602171i	−0.940888	−	0.338717i	$-0.890007\pi$
$797$	−17.0000	+	17.0000i	−0.602171	+	0.602171i	0.338717	+	0.940888i	$0.390007\pi$
$798$		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	0.998718	−	0.0506198i	$-0.0161197\pi$
$811$	27.0000	+	27.0000i	0.948098	+	0.948098i	−0.0506198	+	0.998718i	$0.516120\pi$
$812$		0			0
$813$			18.0000i			0.631288i
$814$		0			0
$815$	4.00000	−	8.00000i	0.140114	−	0.280228i
$816$		0			0
$817$	10.0000			0.349856
$818$		0			0
$819$	6.00000	−	4.00000i	0.209657	−	0.139771i
$820$		0			0
$821$	9.00000	+	9.00000i	0.314102	+	0.314102i	0.846496	−	0.532394i	$-0.178708\pi$
$821$	9.00000	+	9.00000i	0.314102	+	0.314102i	−0.532394	+	0.846496i	$0.678708\pi$
$822$		0			0
$823$	−9.00000	−	9.00000i	−0.313720	−	0.313720i	0.532629	−	0.846349i	$-0.321204\pi$
$823$	−9.00000	−	9.00000i	−0.313720	−	0.313720i	−0.846349	+	0.532629i	$0.821204\pi$
$824$		0			0
$825$	−8.00000	+	6.00000i	−0.278524	+	0.208893i
$826$		0			0
$827$	46.0000			1.59958			0.799788	−	0.600282i	$-0.204945\pi$
$827$	46.0000			1.59958			0.799788	+	0.600282i	$0.204945\pi$
$828$		0			0
$829$	−34.0000			−1.18087			−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000			−1.18087			−0.590434	+	0.807086i	$0.701044\pi$
$830$		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
$837$			40.0000i			1.38260i
$838$		0			0
$839$	−35.0000	−	35.0000i	−1.20833	−	1.20833i	−0.971566	−	0.236768i	$-0.923912\pi$
$839$	−35.0000	−	35.0000i	−1.20833	−	1.20833i	−0.236768	−	0.971566i	$-0.576088\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$			2.00000i			0.0688837i
$844$		0			0
$845$	22.0000	−	19.0000i	0.756823	−	0.653620i
$846$		0			0
$847$			18.0000i			0.618487i
$848$		0			0
$849$	18.0000			0.617758
$850$		0			0
$851$		0			0
$852$		0			0
$853$		−	26.0000i		−	0.890223i	−0.895475	−	0.445112i	$-0.853164\pi$
$853$		−	26.0000i		−	0.890223i	0.895475	−	0.445112i	$-0.146836\pi$
$854$		0			0
$855$	5.00000	+	15.0000i	0.170996	+	0.512989i
$856$		0			0
$857$	3.00000	−	3.00000i	0.102478	−	0.102478i	−0.654009	−	0.756487i	$-0.726914\pi$
$857$	3.00000	−	3.00000i	0.102478	−	0.102478i	0.756487	+	0.654009i	$0.226914\pi$
$858$		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
$863$	30.0000			1.02121			0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000			1.02121			0.510606	+	0.859815i	$0.329421\pi$
$864$		0			0
$865$	−11.0000	−	33.0000i	−0.374011	−	1.12203i
$866$		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
$873$	−2.00000			−0.0676897
$874$		0			0
$875$	−4.00000	−	22.0000i	−0.135225	−	0.743736i
$876$		0			0
$877$			38.0000i			1.28317i	0.767052	+	0.641584i	$0.221723\pi$
$877$			38.0000i			1.28317i	−0.767052	+	0.641584i	$0.778277\pi$
$878$		0			0
$879$	−6.00000	−	6.00000i	−0.202375	−	0.202375i
$880$		0			0
$881$			52.0000i			1.75192i	0.482380	+	0.875962i	$0.339773\pi$
$881$			52.0000i			1.75192i	−0.482380	+	0.875962i	$0.660227\pi$
$882$		0			0
$883$	39.0000	+	39.0000i	1.31245	+	1.31245i	0.919601	+	0.392853i	$0.128512\pi$
$883$	39.0000	+	39.0000i	1.31245	+	1.31245i	0.392853	+	0.919601i	$0.371488\pi$
$884$		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
$895$	40.0000	+	20.0000i	1.33705	+	0.668526i
$896$		0			0
$897$	12.0000	+	18.0000i	0.400668	+	0.601003i
$898$		0			0
$899$		0			0
$900$		0			0
$901$			10.0000i			0.333148i
$902$		0			0
$903$	4.00000			0.133112
$904$		0			0
$905$	8.00000	−	16.0000i	0.265929	−	0.531858i
$906$		0			0
$907$	−39.0000	+	39.0000i	−1.29497	+	1.29497i	−0.363303	+	0.931671i	$0.618351\pi$
$907$	−39.0000	+	39.0000i	−1.29497	+	1.29497i	−0.931671	+	0.363303i	$0.881649\pi$
$908$		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
$915$	−42.0000	+	14.0000i	−1.38848	+	0.462826i
$916$		0			0
$917$	40.0000			1.32092
$918$		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
$923$	−1.00000	+	5.00000i	−0.0329154	+	0.164577i
$924$		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	$-0.604699\pi$
$929$	19.0000	−	19.0000i	0.623370	−	0.623370i	0.946392	+	0.323022i	$0.104699\pi$
$930$		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	0.961029	−	0.276448i	$-0.0891575\pi$
$941$	21.0000	+	21.0000i	0.684580	+	0.684580i	−0.276448	+	0.961029i	$0.589157\pi$
$942$		0			0
$943$		−	42.0000i		−	1.36771i
$944$		0			0
$945$	8.00000	+	24.0000i	0.260240	+	0.780720i
$946$		0			0
$947$	−18.0000			−0.584921			−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000			−0.584921			−0.292461	+	0.956278i	$0.594474\pi$
$948$		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	0.464475	−	0.885586i	$-0.346243\pi$
$953$	−13.0000	−	13.0000i	−0.421111	−	0.421111i	−0.885586	+	0.464475i	$0.846243\pi$
$954$		0			0
$955$	16.0000	+	8.00000i	0.517748	+	0.258874i
$956$		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		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$		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
$973$			28.0000i			0.897639i
$974$		0			0
$975$	11.0000	+	23.0000i	0.352282	+	0.736590i
$976$		0			0
$977$			62.0000i			1.98356i	0.127971	+	0.991778i	$0.459153\pi$
$977$			62.0000i			1.98356i	−0.127971	+	0.991778i	$0.540847\pi$
$978$		0			0
$979$	−10.0000			−0.319601
$980$		0			0
$981$	−9.00000	−	9.00000i	−0.287348	−	0.287348i
$982$		0			0
$983$		−	24.0000i		−	0.765481i	−0.923856	−	0.382741i	$-0.874980\pi$
$983$		−	24.0000i		−	0.765481i	0.923856	−	0.382741i	$-0.125020\pi$
$984$		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
$993$	−6.00000			−0.190404
$994$		0			0
$995$	16.0000	+	8.00000i	0.507234	+	0.253617i
$996$		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.cd.b.177.1		2
4.3	odd	2		65.2.f.a.47.1	yes	2
5.3	odd	4		1040.2.bg.a.593.1		2
12.11	even	2		585.2.n.c.307.1		2
13.5	odd	4		1040.2.bg.a.577.1		2
20.3	even	4		65.2.k.a.8.1	yes	2
20.7	even	4		325.2.k.a.268.1		2
20.19	odd	2		325.2.f.a.307.1		2
52.3	odd	6		845.2.t.a.657.1		4
52.7	even	12		845.2.o.b.587.1		4
52.11	even	12		845.2.o.b.357.1		4
52.15	even	12		845.2.o.a.357.1		4
52.19	even	12		845.2.o.a.587.1		4
52.23	odd	6		845.2.t.b.657.1		4
52.31	even	4		65.2.k.a.57.1	yes	2
52.35	odd	6		845.2.t.a.427.1		4
52.43	odd	6		845.2.t.b.427.1		4
52.47	even	4		845.2.k.a.577.1		2
52.51	odd	2		845.2.f.a.437.1		2
60.23	odd	4		585.2.w.b.73.1		2
65.18	even	4	inner	1040.2.cd.b.993.1		2
156.83	odd	4		585.2.w.b.577.1		2
260.3	even	12		845.2.o.a.488.1		4
260.23	even	12		845.2.o.b.488.1		4
260.43	even	12		845.2.o.b.258.1		4
260.63	odd	12		845.2.t.b.188.1		4
260.83	odd	4		65.2.f.a.18.1	✓	2
260.103	even	4		845.2.k.a.268.1		2
260.123	odd	12		845.2.t.a.418.1		4
260.163	odd	12		845.2.t.b.418.1		4
260.187	odd	4		325.2.f.a.18.1		2
260.203	odd	4		845.2.f.a.408.1		2
260.223	odd	12		845.2.t.a.188.1		4
260.239	even	4		325.2.k.a.57.1		2
260.243	even	12		845.2.o.a.258.1		4
780.83	even	4		585.2.n.c.343.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.a.18.1	✓	2	260.83	odd	4
65.2.f.a.47.1	yes	2	4.3	odd	2
65.2.k.a.8.1	yes	2	20.3	even	4
65.2.k.a.57.1	yes	2	52.31	even	4
325.2.f.a.18.1		2	260.187	odd	4
325.2.f.a.307.1		2	20.19	odd	2
325.2.k.a.57.1		2	260.239	even	4
325.2.k.a.268.1		2	20.7	even	4
585.2.n.c.307.1		2	12.11	even	2
585.2.n.c.343.1		2	780.83	even	4
585.2.w.b.73.1		2	60.23	odd	4
585.2.w.b.577.1		2	156.83	odd	4
845.2.f.a.408.1		2	260.203	odd	4
845.2.f.a.437.1		2	52.51	odd	2
845.2.k.a.268.1		2	260.103	even	4
845.2.k.a.577.1		2	52.47	even	4
845.2.o.a.258.1		4	260.243	even	12
845.2.o.a.357.1		4	52.15	even	12
845.2.o.a.488.1		4	260.3	even	12
845.2.o.a.587.1		4	52.19	even	12
845.2.o.b.258.1		4	260.43	even	12
845.2.o.b.357.1		4	52.11	even	12
845.2.o.b.488.1		4	260.23	even	12
845.2.o.b.587.1		4	52.7	even	12
845.2.t.a.188.1		4	260.223	odd	12
845.2.t.a.418.1		4	260.123	odd	12
845.2.t.a.427.1		4	52.35	odd	6
845.2.t.a.657.1		4	52.3	odd	6
845.2.t.b.188.1		4	260.63	odd	12
845.2.t.b.418.1		4	260.163	odd	12
845.2.t.b.427.1		4	52.43	odd	6
845.2.t.b.657.1		4	52.23	odd	6
1040.2.bg.a.577.1		2	13.5	odd	4
1040.2.bg.a.593.1		2	5.3	odd	4
1040.2.cd.b.177.1		2	1.1	even	1	trivial
1040.2.cd.b.993.1		2	65.18	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{3} +(-2.00000 - 1.00000i) q^{5} +2.00000 q^{7} +1.00000i q^{9} +(1.00000 - 1.00000i) q^{11} +(-2.00000 - 3.00000i) q^{13} +(3.00000 - 1.00000i) q^{15} +(-1.00000 + 1.00000i) q^{17} +(-5.00000 + 5.00000i) q^{19} +(-2.00000 + 2.00000i) q^{21} +(3.00000 + 3.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} +(-4.00000 - 4.00000i) q^{27} +(-5.00000 - 5.00000i) q^{31} +2.00000i q^{33} +(-4.00000 - 2.00000i) q^{35} +(5.00000 + 1.00000i) q^{39} +(-7.00000 - 7.00000i) q^{41} +(-1.00000 - 1.00000i) q^{43} +(1.00000 - 2.00000i) q^{45} -6.00000 q^{47} -3.00000 q^{49} -2.00000i q^{51} +(5.00000 - 5.00000i) q^{53} +(-3.00000 + 1.00000i) q^{55} -10.0000i q^{57} +(-7.00000 - 7.00000i) q^{59} -14.0000 q^{61} +2.00000i q^{63} +(1.00000 + 8.00000i) q^{65} +4.00000i q^{67} -6.00000 q^{69} +(-1.00000 - 1.00000i) q^{71} +10.0000i q^{73} +(-7.00000 - 1.00000i) q^{75} +(2.00000 - 2.00000i) q^{77} +2.00000i q^{79} +5.00000 q^{81} -6.00000 q^{83} +(3.00000 - 1.00000i) q^{85} +(-5.00000 - 5.00000i) q^{89} +(-4.00000 - 6.00000i) q^{91} +10.0000 q^{93} +(15.0000 - 5.00000i) q^{95} +2.00000i q^{97} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 4 q^{5} + 4 q^{7} + 2 q^{11} - 4 q^{13} + 6 q^{15} - 2 q^{17} - 10 q^{19} - 4 q^{21} + 6 q^{23} + 6 q^{25} - 8 q^{27} - 10 q^{31} - 8 q^{35} + 10 q^{39} - 14 q^{41} - 2 q^{43} + 2 q^{45}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - 4 * q^5 + 4 * q^7 + 2 * q^11 - 4 * q^13 + 6 * q^15 - 2 * q^17 - 10 * q^19 - 4 * q^21 + 6 * q^23 + 6 * q^25 - 8 * q^27 - 10 * q^31 - 8 * q^35 + 10 * q^39 - 14 * q^41 - 2 * q^43 + 2 * q^45 - 12 * q^47 - 6 * q^49 + 10 * q^53 - 6 * q^55 - 14 * q^59 - 28 * q^61 + 2 * q^65 - 12 * q^69 - 2 * q^71 - 14 * q^75 + 4 * q^77 + 10 * q^81 - 12 * q^83 + 6 * q^85 - 10 * q^89 - 8 * q^91 + 20 * q^93 + 30 * q^95 + 2 * q^99

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