LMFDB - Embedded newform 845.2.d.d.844.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(844,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("845.844");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 22x^{10} + 147x^{8} + 390x^{6} + 413x^{4} + 128x^{2} + 4 $ x^12 + 22x^10 + 147x^8 + 390x^6 + 413x^4 + 128*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			844.7
Root			$0.669163i$ of defining polynomial
Character	$\chi$	$=$	845.844
Dual form			845.2.d.d.844.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.330837 q^{2} -2.69180i q^{3} -1.89055 q^{4} +(0.702335 - 2.12291i) q^{5} -0.890547i q^{6} -3.35348 q^{7} -1.28714 q^{8} -4.24581 q^{9} +O(q^{10})$	\(q+0.330837 q^{2} -2.69180i q^{3} -1.89055 q^{4} +(0.702335 - 2.12291i) q^{5} -0.890547i q^{6} -3.35348 q^{7} -1.28714 q^{8} -4.24581 q^{9} +(0.232358 - 0.702335i) q^{10} +3.24581i q^{11} +5.08898i q^{12} -1.10945 q^{14} +(-5.71445 - 1.89055i) q^{15} +3.35526 q^{16} -1.94881i q^{17} -1.40467 q^{18} +1.24581i q^{19} +(-1.32780 + 4.01345i) q^{20} +9.02690i q^{21} +1.07383i q^{22} -2.69180i q^{23} +3.46472i q^{24} +(-4.01345 - 2.98198i) q^{25} +3.35348i q^{27} +6.33991 q^{28} -3.00000 q^{29} +(-1.89055 - 0.625462i) q^{30} +3.78109i q^{31} +3.68431 q^{32} +8.73709 q^{33} -0.644737i q^{34} +(-2.35526 + 7.11911i) q^{35} +8.02690 q^{36} -1.94881 q^{37} +0.412160i q^{38} +(-0.904000 + 2.73247i) q^{40} +2.78109i q^{41} +2.98643i q^{42} +8.73709i q^{43} -6.13636i q^{44} +(-2.98198 + 9.01345i) q^{45} -0.890547i q^{46} +6.86960 q^{47} -9.03171i q^{48} +4.24581 q^{49} +(-1.32780 - 0.986548i) q^{50} -5.24581 q^{51} -12.8336i q^{53} +1.10945i q^{54} +(6.89055 + 2.27964i) q^{55} +4.31638 q^{56} +3.35348 q^{57} -0.992510 q^{58} -2.53528i q^{59} +(10.8034 + 3.57417i) q^{60} -7.49162 q^{61} +1.25092i q^{62} +14.2382 q^{63} -5.49162 q^{64} +2.89055 q^{66} -4.01515 q^{67} +3.68431i q^{68} -7.24581 q^{69} +(-0.779207 + 2.35526i) q^{70} +5.24581i q^{71} +5.46493 q^{72} -5.46493 q^{73} -0.644737 q^{74} +(-8.02690 + 10.8034i) q^{75} -2.35526i q^{76} -10.8848i q^{77} -13.7811 q^{79} +(2.35652 - 7.12291i) q^{80} -3.71053 q^{81} +0.920088i q^{82} -8.61955 q^{83} -17.0658i q^{84} +(-4.13713 - 1.36872i) q^{85} +2.89055i q^{86} +8.07541i q^{87} -4.17780i q^{88} +10.3164i q^{89} +(-0.986548 + 2.98198i) q^{90} +5.08898i q^{92} +10.1780 q^{93} +2.27271 q^{94} +(2.64474 + 0.874976i) q^{95} -9.91745i q^{96} -5.26607 q^{97} +1.40467 q^{98} -13.7811i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} - 12 q^{9}+O(q^{10}) $ 12 * q + 8 * q^4 - 12 * q^9	$ 12 q + 8 q^{4} - 12 q^{9} + 14 q^{10} - 44 q^{14} + 32 q^{16} + 2 q^{25} - 36 q^{29} + 8 q^{30} - 20 q^{35} - 4 q^{36} + 70 q^{40} + 12 q^{49} - 24 q^{51} + 52 q^{55} - 32 q^{56} - 12 q^{61} + 12 q^{64} + 4 q^{66} - 48 q^{69} - 16 q^{74} + 4 q^{75} - 104 q^{79} - 28 q^{81} - 62 q^{90} - 112 q^{94} + 40 q^{95}+O(q^{100}) $ 12 * q + 8 * q^4 - 12 * q^9 + 14 * q^10 - 44 * q^14 + 32 * q^16 + 2 * q^25 - 36 * q^29 + 8 * q^30 - 20 * q^35 - 4 * q^36 + 70 * q^40 + 12 * q^49 - 24 * q^51 + 52 * q^55 - 32 * q^56 - 12 * q^61 + 12 * q^64 + 4 * q^66 - 48 * q^69 - 16 * q^74 + 4 * q^75 - 104 * q^79 - 28 * q^81 - 62 * q^90 - 112 * q^94 + 40 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.330837			0.233937			0.116968	−	0.993136i	$-0.462682\pi$
$2$	0.330837			0.233937			0.116968	+	0.993136i	$0.462682\pi$
$3$		−	2.69180i		−	1.55411i	−0.629430	−	0.777057i	$-0.716712\pi$
$3$		−	2.69180i		−	1.55411i	0.629430	−	0.777057i	$-0.283288\pi$
$4$	−1.89055			−0.945274
$5$	0.702335	−	2.12291i	0.314094	−	0.949392i
$5$	0.702335	−	2.12291i	0.314094	−	0.949392i
$6$		−	0.890547i		−	0.363564i
$7$	−3.35348			−1.26750			−0.633748	−	0.773540i	$-0.718484\pi$
$7$	−3.35348			−1.26750			−0.633748	+	0.773540i	$0.718484\pi$
$8$	−1.28714			−0.455071
$9$	−4.24581			−1.41527
$10$	0.232358	−	0.702335i	0.0734780	−	0.222098i
$11$			3.24581i			0.978649i	0.872102	+	0.489324i	$0.162757\pi$
$11$			3.24581i			0.978649i	−0.872102	+	0.489324i	$0.837243\pi$
$12$			5.08898i			1.46906i
$13$		0			0
$13$		0			0
$14$	−1.10945			−0.296514
$15$	−5.71445	−	1.89055i	−1.47546	−	0.488137i
$16$	3.35526			0.838816
$17$		−	1.94881i		−	0.472655i	−0.971673	−	0.236328i	$-0.924056\pi$
$17$		−	1.94881i		−	0.472655i	0.971673	−	0.236328i	$-0.0759439\pi$
$18$	−1.40467			−0.331084
$19$			1.24581i			0.285808i	0.989737	+	0.142904i	$0.0456441\pi$
$19$			1.24581i			0.285808i	−0.989737	+	0.142904i	$0.954356\pi$
$20$	−1.32780	+	4.01345i	−0.296904	+	0.897435i
$21$			9.02690i			1.96983i
$22$			1.07383i			0.228942i
$23$		−	2.69180i		−	0.561280i	−0.959813	−	0.280640i	$-0.909453\pi$
$23$		−	2.69180i		−	0.561280i	0.959813	−	0.280640i	$-0.0905467\pi$
$24$			3.46472i			0.707232i
$25$	−4.01345	−	2.98198i	−0.802690	−	0.596396i
$26$		0			0
$27$			3.35348i			0.645377i
$28$	6.33991			1.19813
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$	−1.89055	−	0.625462i	−0.345165	−	0.114193i
$31$			3.78109i			0.679105i	0.940587	+	0.339552i	$0.110276\pi$
$31$			3.78109i			0.679105i	−0.940587	+	0.339552i	$0.889724\pi$
$32$	3.68431			0.651301
$33$	8.73709			1.52093
$34$		−	0.644737i		−	0.110571i
$35$	−2.35526	+	7.11911i	−0.398112	+	1.20335i
$36$	8.02690			1.33782
$37$	−1.94881			−0.320382			−0.160191	−	0.987086i	$-0.551211\pi$
$37$	−1.94881			−0.320382			−0.160191	+	0.987086i	$0.551211\pi$
$38$			0.412160i			0.0668611i
$39$		0			0
$40$	−0.904000	+	2.73247i	−0.142935	+	0.432041i
$41$			2.78109i			0.434334i	0.976134	+	0.217167i	$0.0696816\pi$
$41$			2.78109i			0.434334i	−0.976134	+	0.217167i	$0.930318\pi$
$42$			2.98643i			0.460816i
$43$			8.73709i			1.33239i	0.745776	+	0.666197i	$0.232079\pi$
$43$			8.73709i			1.33239i	−0.745776	+	0.666197i	$0.767921\pi$
$44$		−	6.13636i		−	0.925091i
$45$	−2.98198	+	9.01345i	−0.444527	+	1.34365i
$46$		−	0.890547i		−	0.131304i
$47$	6.86960			1.00203			0.501017	−	0.865437i	$-0.332959\pi$
$47$	6.86960			1.00203			0.501017	+	0.865437i	$0.332959\pi$
$48$		−	9.03171i		−	1.30362i
$49$	4.24581			0.606544
$50$	−1.32780	−	0.986548i	−0.187779	−	0.139519i
$51$	−5.24581			−0.734560
$52$		0			0
$53$		−	12.8336i		−	1.76282i	−0.472347	−	0.881412i	$-0.656593\pi$
$53$		−	12.8336i		−	1.76282i	0.472347	−	0.881412i	$-0.343407\pi$
$54$			1.10945i			0.150977i
$55$	6.89055	+	2.27964i	0.929121	+	0.307387i
$56$	4.31638			0.576800
$57$	3.35348			0.444179
$58$	−0.992510			−0.130323
$59$		−	2.53528i		−	0.330066i	−0.986288	−	0.165033i	$-0.947227\pi$
$59$		−	2.53528i		−	0.330066i	0.986288	−	0.165033i	$-0.0527730\pi$
$60$	10.8034	+	3.57417i	1.39472	+	0.461423i
$61$	−7.49162			−0.959204			−0.479602	−	0.877486i	$-0.659219\pi$
$61$	−7.49162			−0.959204			−0.479602	+	0.877486i	$0.659219\pi$
$62$			1.25092i			0.158868i
$63$	14.2382			1.79385
$64$	−5.49162			−0.686453
$65$		0			0
$66$	2.89055			0.355802
$67$	−4.01515			−0.490529			−0.245264	−	0.969456i	$-0.578875\pi$
$67$	−4.01515			−0.490529			−0.245264	+	0.969456i	$0.578875\pi$
$68$			3.68431i			0.446789i
$69$	−7.24581			−0.872293
$70$	−0.779207	+	2.35526i	−0.0931331	+	0.281508i
$71$			5.24581i			0.622563i	0.950318	+	0.311282i	$0.100758\pi$
$71$			5.24581i			0.622563i	−0.950318	+	0.311282i	$0.899242\pi$
$72$	5.46493			0.644048
$73$	−5.46493			−0.639622			−0.319811	−	0.947481i	$-0.603619\pi$
$73$	−5.46493			−0.639622			−0.319811	+	0.947481i	$0.603619\pi$
$74$	−0.644737			−0.0749491
$75$	−8.02690	+	10.8034i	−0.926867	+	1.24747i
$76$		−	2.35526i		−	0.270167i
$77$		−	10.8848i		−	1.24043i
$78$		0			0
$79$	−13.7811			−1.55049			−0.775247	−	0.631658i	$-0.782375\pi$
$79$	−13.7811			−1.55049			−0.775247	+	0.631658i	$0.782375\pi$
$80$	2.35652	−	7.12291i	0.263467	−	0.796365i
$81$	−3.71053			−0.412281
$82$			0.920088i			0.101607i
$83$	−8.61955			−0.946119			−0.473059	−	0.881031i	$-0.656850\pi$
$83$	−8.61955			−0.946119			−0.473059	+	0.881031i	$0.656850\pi$
$84$		−	17.0658i		−	1.86203i
$85$	−4.13713	−	1.36872i	−0.448735	−	0.148458i
$86$			2.89055i			0.311696i
$87$			8.07541i			0.865775i
$88$		−	4.17780i		−	0.445355i
$89$			10.3164i			1.09353i	0.837285	+	0.546767i	$0.184142\pi$
$89$			10.3164i			1.09353i	−0.837285	+	0.546767i	$0.815858\pi$
$90$	−0.986548	+	2.98198i	−0.103991	+	0.314328i
$91$		0			0
$92$			5.08898i			0.530563i
$93$	10.1780			1.05541
$94$	2.27271			0.234413
$95$	2.64474	+	0.874976i	0.271344	+	0.0897706i
$96$		−	9.91745i		−	1.01220i
$97$	−5.26607			−0.534689			−0.267344	−	0.963601i	$-0.586146\pi$
$97$	−5.26607			−0.534689			−0.267344	+	0.963601i	$0.586146\pi$
$98$	1.40467			0.141893
$99$		−	13.7811i		−	1.38505i
$100$	7.58762	+	5.63757i	0.758762	+	0.563757i
$101$	−5.71053			−0.568219			−0.284109	−	0.958792i	$-0.591698\pi$
$101$	−5.71053			−0.568219			−0.284109	+	0.958792i	$0.591698\pi$
$102$	−1.73551			−0.171841
$103$			7.36863i			0.726052i	0.931779	+	0.363026i	$0.118256\pi$
$103$			7.36863i			0.726052i	−0.931779	+	0.363026i	$0.881744\pi$
$104$		0			0
$105$	19.1633	+	6.33991i	1.87014	+	0.618712i
$106$		−	4.24581i		−	0.412390i
$107$		−	8.57444i		−	0.828922i	−0.910067	−	0.414461i	$-0.863970\pi$
$107$		−	8.57444i		−	0.828922i	0.910067	−	0.414461i	$-0.136030\pi$
$108$		−	6.33991i		−	0.610058i
$109$			8.49162i			0.813350i	0.913573	+	0.406675i	$0.133312\pi$
$109$			8.49162i			0.813350i	−0.913573	+	0.406675i	$0.866688\pi$
$110$	2.27964	+	0.754190i	0.217356	+	0.0719092i
$111$			5.24581i			0.497910i
$112$	−11.2518			−1.06320
$113$		−	7.33242i		−	0.689776i	−0.938644	−	0.344888i	$-0.887917\pi$
$113$		−	7.33242i		−	0.689776i	0.938644	−	0.344888i	$-0.112083\pi$
$114$	1.10945			0.103910
$115$	−5.71445	−	1.89055i	−0.532875	−	0.176294i
$116$	5.67164			0.526599
$117$		0			0
$118$		−	0.838765i		−	0.0772145i
$119$			6.53528i			0.599089i
$120$	7.35526	+	2.43339i	0.671441	+	0.222137i
$121$	0.464716			0.0422469
$122$	−2.47850			−0.224393
$123$	7.48616			0.675004
$124$		−	7.14834i		−	0.641940i
$125$	−9.14925	+	6.42583i	−0.818333	+	0.574744i
$126$	4.71053			0.419647
$127$		−	9.16369i		−	0.813146i	−0.913618	−	0.406573i	$-0.866724\pi$
$127$		−	9.16369i		−	0.813146i	0.913618	−	0.406573i	$-0.133276\pi$
$128$	−9.18546			−0.811887
$129$	23.5185			2.07069
$130$		0			0
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$	−16.5179			−1.43770
$133$		−	4.17780i		−	0.362261i
$134$	−1.32836			−0.114753
$135$	7.11911	+	2.35526i	0.612716	+	0.202709i
$136$			2.50838i			0.215092i
$137$	−16.8487			−1.43948			−0.719741	−	0.694242i	$-0.755740\pi$
$137$	−16.8487			−1.43948			−0.719741	+	0.694242i	$0.755740\pi$
$138$	−2.39718			−0.204061
$139$	1.02690			0.0871009			0.0435505	−	0.999051i	$-0.486133\pi$
$139$	1.02690			0.0871009			0.0435505	+	0.999051i	$0.486133\pi$
$140$	4.45274	−	13.4590i	0.376325	−	1.13749i
$141$		−	18.4916i		−	1.55728i
$142$			1.73551i			0.145640i
$143$		0			0
$144$	−14.2458			−1.18715
$145$	−2.10700	+	6.36872i	−0.174977	+	0.528893i
$146$	−1.80800			−0.149631
$147$		−	11.4289i		−	0.942639i
$148$	3.68431			0.302849
$149$		−	15.8517i		−	1.29862i	−0.760524	−	0.649309i	$-0.775058\pi$
$149$		−	15.8517i		−	1.29862i	0.760524	−	0.649309i	$-0.224942\pi$
$150$	−2.65559	+	3.57417i	−0.216828	+	0.291830i
$151$		−	14.5454i		−	1.18369i	−0.806052	−	0.591845i	$-0.798400\pi$
$151$		−	14.5454i		−	1.18369i	0.806052	−	0.591845i	$-0.201600\pi$
$152$		−	1.60353i		−	0.130063i
$153$			8.27427i			0.668935i
$154$		−	3.60107i		−	0.290183i
$155$	8.02690	+	2.65559i	0.644736	+	0.213302i
$156$		0			0
$157$		−	10.9210i		−	0.871588i	−0.900047	−	0.435794i	$-0.856468\pi$
$157$		−	10.9210i		−	0.871588i	0.900047	−	0.435794i	$-0.143532\pi$
$158$	−4.55929			−0.362718
$159$	−34.5454			−2.73963
$160$	2.58762	−	7.82145i	0.204569	−	0.618340i
$161$			9.02690i			0.711420i
$162$	−1.22758			−0.0964476
$163$	−4.17780			−0.327230			−0.163615	−	0.986524i	$-0.552316\pi$
$163$	−4.17780			−0.327230			−0.163615	+	0.986524i	$0.552316\pi$
$164$		−	5.25779i		−	0.410564i
$165$	6.13636	−	18.5480i	0.477715	−	1.44396i
$166$	−2.85166			−0.221332
$167$	3.35348			0.259500			0.129750	−	0.991547i	$-0.458583\pi$
$167$	3.35348			0.259500			0.129750	+	0.991547i	$0.458583\pi$
$168$		−	11.6188i		−	0.896413i
$169$		0			0
$170$	−1.36872	−	0.452821i	−0.104976	−	0.0347298i
$171$		−	5.28947i		−	0.404496i
$172$		−	16.5179i		−	1.25948i
$173$		−	8.73709i		−	0.664268i	−0.943232	−	0.332134i	$-0.892231\pi$
$173$		−	8.73709i		−	0.664268i	0.943232	−	0.332134i	$-0.107769\pi$
$174$			2.67164i			0.202537i
$175$	13.4590	+	10.0000i	1.01741	+	0.755929i
$176$			10.8905i			0.820906i
$177$	−6.82449			−0.512960
$178$			3.41303i			0.255818i
$179$	−18.0101			−1.34614			−0.673071	−	0.739578i	$-0.735025\pi$
$179$	−18.0101			−1.34614			−0.673071	+	0.739578i	$0.735025\pi$
$180$	5.63757	−	17.0404i	0.420200	−	1.27011i
$181$	−1.04366			−0.0775749			−0.0387875	−	0.999247i	$-0.512350\pi$
$181$	−1.04366			−0.0775749			−0.0387875	+	0.999247i	$0.512350\pi$
$182$		0			0
$183$			20.1660i			1.49071i
$184$			3.46472i			0.255422i
$185$	−1.36872	+	4.13713i	−0.100630	+	0.304168i
$186$	3.36724			0.246898
$187$	6.32546			0.462564
$188$	−12.9873			−0.947197
$189$		−	11.2458i		−	0.818012i
$190$	0.874976	+	0.289474i	0.0634774	+	0.0210006i
$191$	25.5185			1.84646			0.923228	−	0.384253i	$-0.125541\pi$
$191$	25.5185			1.84646			0.923228	+	0.384253i	$0.125541\pi$
$192$			14.7824i			1.06683i
$193$	−19.8207			−1.42672			−0.713362	−	0.700795i	$-0.752829\pi$
$193$	−19.8207			−1.42672			−0.713362	+	0.700795i	$0.752829\pi$
$194$	−1.74221			−0.125083
$195$		0			0
$196$	−8.02690			−0.573350
$197$	21.6520			1.54264			0.771319	−	0.636448i	$-0.219597\pi$
$197$	21.6520			1.54264			0.771319	+	0.636448i	$0.219597\pi$
$198$		−	4.55929i		−	0.324015i
$199$	18.2291			1.29222			0.646112	−	0.763243i	$-0.276394\pi$
$199$	18.2291			1.29222			0.646112	+	0.763243i	$0.276394\pi$
$200$	5.16586	+	3.83821i	0.365281	+	0.271402i
$201$			10.8080i			0.762337i
$202$	−1.88925			−0.132927
$203$	10.0604			0.706104
$204$	9.91745			0.694361
$205$	5.90400	+	1.95326i	0.412353	+	0.136422i
$206$			2.43781i			0.169850i
$207$			11.4289i			0.794363i
$208$		0			0
$209$	−4.04366			−0.279706
$210$	6.33991	+	2.09747i	0.437495	+	0.144739i
$211$	19.2996			1.32864			0.664320	−	0.747448i	$-0.268721\pi$
$211$	19.2996			1.32864			0.664320	+	0.747448i	$0.268721\pi$
$212$			24.2624i			1.66635i
$213$	14.1207			0.967534
$214$		−	2.83674i		−	0.193915i
$215$	18.5480	+	6.13636i	1.26496	+	0.418496i
$216$		−	4.31638i		−	0.293692i
$217$		−	12.6798i		−	0.860762i
$218$			2.80934i			0.190272i
$219$			14.7105i			0.994045i
$220$	−13.0269	−	4.30978i	−0.878274	−	0.290565i
$221$		0			0
$222$			1.73551i			0.116480i
$223$	−12.3707			−0.828406			−0.414203	−	0.910184i	$-0.635940\pi$
$223$	−12.3707			−0.828406			−0.414203	+	0.910184i	$0.635940\pi$
$224$	−12.3553			−0.825521
$225$	17.0404	+	12.6609i	1.13602	+	0.844061i
$226$		−	2.42583i		−	0.161364i
$227$	−6.16282			−0.409040			−0.204520	−	0.978862i	$-0.565563\pi$
$227$	−6.16282			−0.409040			−0.204520	+	0.978862i	$0.565563\pi$
$228$	−6.33991			−0.419871
$229$		−	26.9832i		−	1.78310i	−0.452920	−	0.891551i	$-0.649618\pi$
$229$		−	26.9832i		−	1.78310i	0.452920	−	0.891551i	$-0.350382\pi$
$230$	−1.89055	−	0.625462i	−0.124659	−	0.0412417i
$231$	−29.2996			−1.92777
$232$	3.86141			0.253514
$233$		−	0.824319i		−	0.0540029i	−0.999635	−	0.0270015i	$-0.991404\pi$
$233$		−	0.824319i		−	0.0540029i	0.999635	−	0.0270015i	$-0.00859588\pi$
$234$		0			0
$235$	4.82476	−	14.5835i	0.314733	−	0.951323i
$236$			4.79307i			0.312003i
$237$			37.0960i			2.40964i
$238$			2.16211i			0.140149i
$239$		−	4.00000i		−	0.258738i	−0.991596	−	0.129369i	$-0.958705\pi$
$239$		−	4.00000i		−	0.258738i	0.991596	−	0.129369i	$-0.0412952\pi$
$240$	−19.1735	−	6.34328i	−1.23764	−	0.409457i
$241$		−	22.6938i		−	1.46183i	−0.682466	−	0.730917i	$-0.739093\pi$
$241$		−	22.6938i		−	1.46183i	0.682466	−	0.730917i	$-0.260907\pi$
$242$	0.153745			0.00988310
$243$			20.0484i			1.28611i
$244$	14.1633			0.906710
$245$	2.98198	−	9.01345i	0.190512	−	0.575848i
$246$	2.47670			0.157908
$247$		0			0
$248$		−	4.86678i		−	0.309041i
$249$			23.2021i			1.47038i
$250$	−3.02690	+	2.12590i	−0.191438	+	0.134454i
$251$	−19.0269			−1.20097			−0.600484	−	0.799637i	$-0.705025\pi$
$251$	−19.0269			−1.20097			−0.600484	+	0.799637i	$0.705025\pi$
$252$	−26.9180			−1.69568
$253$	8.73709			0.549296
$254$		−	3.03168i		−	0.190225i
$255$	−3.68431	+	11.1364i	−0.230721	+	0.697386i
$256$	7.94436			0.496522
$257$		−	2.11145i		−	0.131709i	−0.997829	−	0.0658544i	$-0.979023\pi$
$257$		−	2.11145i		−	0.131709i	0.997829	−	0.0658544i	$-0.0209773\pi$
$258$	7.78079			0.484411
$259$	6.53528			0.406083
$260$		0			0
$261$	12.7374			0.788427
$262$	3.30837			0.204391
$263$			29.9173i			1.84478i	0.386257	+	0.922391i	$0.373768\pi$
$263$			29.9173i			1.84478i	−0.386257	+	0.922391i	$0.626232\pi$
$264$	−11.2458			−0.692132
$265$	−27.2444	−	9.01345i	−1.67361	−	0.553692i
$266$		−	1.38217i		−	0.0847461i
$267$	27.7697			1.69948
$268$	7.59083			0.463684
$269$	−18.5891			−1.13340			−0.566699	−	0.823925i	$-0.691780\pi$
$269$	−18.5891			−1.13340			−0.566699	+	0.823925i	$0.691780\pi$
$270$	2.35526	+	0.779207i	0.143337	+	0.0474210i
$271$		−	5.82476i		−	0.353829i	−0.984226	−	0.176914i	$-0.943388\pi$
$271$		−	5.82476i		−	0.353829i	0.984226	−	0.176914i	$-0.0566116\pi$
$272$		−	6.53876i		−	0.396471i
$273$		0			0
$274$	−5.57417			−0.336748
$275$	9.67894	−	13.0269i	0.583662	−	0.785552i
$276$	13.6985			0.824556
$277$		−	13.5403i		−	0.813560i	−0.913526	−	0.406780i	$-0.866651\pi$
$277$		−	13.5403i		−	0.813560i	0.913526	−	0.406780i	$-0.133349\pi$
$278$	0.339738			0.0203761
$279$		−	16.0538i		−	0.961116i
$280$	3.03154	−	9.16326i	0.181169	−	0.547610i
$281$			0.464716i			0.0277226i	0.999904	+	0.0138613i	$0.00441233\pi$
$281$			0.464716i			0.0277226i	−0.999904	+	0.0138613i	$0.995588\pi$
$282$		−	6.11770i		−	0.364304i
$283$			10.0604i			0.598031i	0.954248	+	0.299015i	$0.0966582\pi$
$283$			10.0604i			0.598031i	−0.954248	+	0.299015i	$0.903342\pi$
$284$		−	9.91745i		−	0.588492i
$285$	2.35526	−	7.11911i	0.139514	−	0.421700i
$286$		0			0
$287$		−	9.32634i		−	0.550516i
$288$	−15.6429			−0.921767
$289$	13.2021			0.776597
$290$	−0.697074	+	2.10700i	−0.0409336	+	0.123728i
$291$			14.1752i			0.830967i
$292$	10.3317			0.604618
$293$	−13.4501			−0.785764			−0.392882	−	0.919589i	$-0.628522\pi$
$293$	−13.4501			−0.785764			−0.392882	+	0.919589i	$0.628522\pi$
$294$		−	3.78109i		−	0.220518i
$295$	−5.38217	−	1.78062i	−0.313362	−	0.103672i
$296$	2.50838			0.145797
$297$	−10.8848			−0.631597
$298$		−	5.24431i		−	0.303795i
$299$		0			0
$300$	15.1752	−	20.4244i	0.876143	−	1.17920i
$301$		−	29.2996i		−	1.68880i
$302$		−	4.81216i		−	0.276909i
$303$			15.3716i			0.883076i
$304$			4.18002i			0.239741i
$305$	−5.26162	+	15.9040i	−0.301280	+	0.910660i
$306$			2.73743i			0.156488i
$307$	24.6077			1.40444			0.702219	−	0.711961i	$-0.252193\pi$
$307$	24.6077			1.40444			0.702219	+	0.711961i	$0.252193\pi$
$308$			20.5781i			1.17255i
$309$	19.8349			1.12837
$310$	2.65559	+	0.878567i	0.150828	+	0.0498993i
$311$	−2.43781			−0.138236			−0.0691178	−	0.997609i	$-0.522018\pi$
$311$	−2.43781			−0.138236			−0.0691178	+	0.997609i	$0.522018\pi$
$312$		0			0
$313$			19.2965i			1.09071i	0.838207	+	0.545353i	$0.183604\pi$
$313$			19.2965i			1.09071i	−0.838207	+	0.545353i	$0.816396\pi$
$314$		−	3.61305i		−	0.203896i
$315$	10.0000	−	30.2264i	0.563436	−	1.70307i
$316$	26.0538			1.46564
$317$	28.8217			1.61879			0.809395	−	0.587265i	$-0.199795\pi$
$317$	28.8217			1.61879			0.809395	+	0.587265i	$0.199795\pi$
$318$	−11.4289			−0.640900
$319$		−	9.73743i		−	0.545191i
$320$	−3.85695	+	11.6582i	−0.215610	+	0.651713i
$321$	−23.0807			−1.28824
$322$			2.98643i			0.166427i
$323$	2.42785			0.135089
$324$	7.01492			0.389718
$325$		0			0
$326$	−1.38217			−0.0765512
$327$	22.8578			1.26404
$328$		−	3.57964i		−	0.197653i
$329$	−23.0371			−1.27007
$330$	2.03013	−	6.13636i	0.111755	−	0.337795i
$331$		−	2.97310i		−	0.163416i	−0.996656	−	0.0817081i	$-0.973962\pi$
$331$		−	2.97310i		−	0.163416i	0.996656	−	0.0817081i	$-0.0260375\pi$
$332$	16.2957			0.894341
$333$	8.27427			0.453427
$334$	1.10945			0.0607066
$335$	−2.81998	+	8.52378i	−0.154072	+	0.465704i
$336$			30.2876i			1.65233i
$337$		−	1.90370i		−	0.103701i	−0.998655	−	0.0518505i	$-0.983488\pi$
$337$		−	1.90370i		−	0.103701i	0.998655	−	0.0518505i	$-0.0165119\pi$
$338$		0			0
$339$	−19.7374			−1.07199
$340$	7.82145	+	2.58762i	0.424178	+	0.140333i
$341$	−12.2727			−0.664605
$342$		−	1.74995i		−	0.0946265i
$343$	9.23611			0.498703
$344$		−	11.2458i		−	0.606333i
$345$	−5.08898	+	15.3822i	−0.273982	+	0.828148i
$346$		−	2.89055i		−	0.155397i
$347$		−	12.6347i		−	0.678266i	−0.940738	−	0.339133i	$-0.889866\pi$
$347$		−	12.6347i		−	0.678266i	0.940738	−	0.339133i	$-0.110134\pi$
$348$		−	15.2669i		−	0.818394i
$349$			8.97310i			0.480319i	0.970733	+	0.240159i	$0.0771997\pi$
$349$			8.97310i			0.480319i	−0.970733	+	0.240159i	$0.922800\pi$
$350$	4.45274	+	3.30837i	0.238009	+	0.176840i
$351$		0			0
$352$			11.9586i			0.637395i
$353$	−34.2505			−1.82297			−0.911484	−	0.411336i	$-0.865062\pi$
$353$	−34.2505			−1.82297			−0.911484	+	0.411336i	$0.865062\pi$
$354$	−2.25779			−0.120000
$355$	11.1364	+	3.68431i	0.591056	+	0.195543i
$356$		−	19.5036i		−	1.03369i
$357$	17.5917			0.931052
$358$	−5.95841			−0.314912
$359$			22.4043i			1.18245i	0.806505	+	0.591227i	$0.201356\pi$
$359$			22.4043i			1.18245i	−0.806505	+	0.591227i	$0.798644\pi$
$360$	3.83821	−	11.6015i	0.202291	−	0.611454i
$361$	17.4480			0.918314
$362$	−0.345282			−0.0181476
$363$		−	1.25092i		−	0.0656565i
$364$		0			0
$365$	−3.83821	+	11.6015i	−0.200901	+	0.607252i
$366$			6.67164i			0.348732i
$367$		−	13.1951i		−	0.688777i	−0.938827	−	0.344388i	$-0.888086\pi$
$367$		−	13.1951i		−	0.688777i	0.938827	−	0.344388i	$-0.111914\pi$
$368$		−	9.03171i		−	0.470811i
$369$		−	11.8080i		−	0.614700i
$370$	−0.452821	+	1.36872i	−0.0235410	+	0.0711561i
$371$			43.0371i			2.23437i
$372$	−19.2419			−0.997647
$373$			15.2614i			0.790206i	0.918637	+	0.395103i	$0.129291\pi$
$373$			15.2614i			0.790206i	−0.918637	+	0.395103i	$0.870709\pi$
$374$	2.09269			0.108211
$375$	17.2971	+	24.6280i	0.893217	+	1.27178i
$376$	−8.84210			−0.455997
$377$		0			0
$378$		−	3.72052i		−	0.191363i
$379$		−	18.2291i		−	0.936363i	−0.883632	−	0.468182i	$-0.844909\pi$
$379$		−	18.2291i		−	0.936363i	0.883632	−	0.468182i	$-0.155091\pi$
$380$	−5.00000	−	1.65418i	−0.256495	−	0.0848578i
$381$	−24.6669			−1.26372
$382$	8.44246			0.431954
$383$	1.44088			0.0736255			0.0368128	−	0.999322i	$-0.488279\pi$
$383$	1.44088			0.0736255			0.0368128	+	0.999322i	$0.488279\pi$
$384$			24.7255i			1.26177i
$385$	−23.1073	−	7.64474i	−1.17766	−	0.389612i
$386$	−6.55741			−0.333763
$387$		−	37.0960i		−	1.88570i
$388$	9.95576			0.505427
$389$	−18.7912			−0.952754			−0.476377	−	0.879241i	$-0.658050\pi$
$389$	−18.7912			−0.952754			−0.476377	+	0.879241i	$0.658050\pi$
$390$		0			0
$391$	−5.24581			−0.265292
$392$	−5.46493			−0.276021
$393$		−	26.9180i		−	1.35784i
$394$	7.16326			0.360880
$395$	−9.67894	+	29.2560i	−0.487000	+	1.47203i
$396$			26.0538i			1.30925i
$397$	−17.0927			−0.857857			−0.428928	−	0.903338i	$-0.641109\pi$
$397$	−17.0927			−0.857857			−0.428928	+	0.903338i	$0.641109\pi$
$398$	6.03084			0.302298
$399$	−11.2458			−0.562995
$400$	−13.4662	−	10.0053i	−0.673309	−	0.500266i
$401$		−	22.2021i		−	1.10872i	−0.832276	−	0.554361i	$-0.812963\pi$
$401$		−	22.2021i		−	1.10872i	0.832276	−	0.554361i	$-0.187037\pi$
$402$			3.57568i			0.178339i
$403$		0			0
$404$	10.7960			0.537122
$405$	−2.60603	+	7.87709i	−0.129495	+	0.391416i
$406$	3.32836			0.165184
$407$		−	6.32546i		−	0.313541i
$408$	6.75207			0.334277
$409$			9.63276i			0.476309i	0.971227	+	0.238155i	$0.0765425\pi$
$409$			9.63276i			0.476309i	−0.971227	+	0.238155i	$0.923458\pi$
$410$	1.95326	+	0.646209i	0.0964646	+	0.0319140i
$411$			45.3534i			2.23712i
$412$		−	13.9307i		−	0.686318i
$413$			8.50202i			0.418357i
$414$			3.78109i			0.185831i
$415$	−6.05381	+	18.2985i	−0.297170	+	0.898238i
$416$		0			0
$417$		−	2.76423i		−	0.135365i
$418$	−1.33779			−0.0654335
$419$	1.95634			0.0955733			0.0477866	−	0.998858i	$-0.484783\pi$
$419$	1.95634			0.0955733			0.0477866	+	0.998858i	$0.484783\pi$
$420$	−36.2291	−	11.9859i	−1.76780	−	0.584852i
$421$		−	12.0807i		−	0.588778i	−0.955686	−	0.294389i	$-0.904884\pi$
$421$		−	12.0807i		−	0.588778i	0.955686	−	0.294389i	$-0.0951161\pi$
$422$	6.38502			0.310818
$423$	−29.1670			−1.41815
$424$			16.5185i			0.802210i
$425$	−5.81131	+	7.82145i	−0.281890	+	0.379396i
$426$	4.67164			0.226342
$427$	25.1230			1.21579
$428$			16.2104i			0.783558i
$429$		0			0
$430$	6.13636	+	2.03013i	0.295921	+	0.0979016i
$431$			24.5891i			1.18441i	0.805786	+	0.592207i	$0.201743\pi$
$431$			24.5891i			1.18441i	−0.805786	+	0.592207i	$0.798257\pi$
$432$			11.2518i			0.541352i
$433$		−	36.0728i		−	1.73355i	−0.498700	−	0.866775i	$-0.666189\pi$
$433$		−	36.0728i		−	1.73355i	0.498700	−	0.866775i	$-0.333811\pi$
$434$		−	4.19495i		−	0.201364i
$435$	17.1433	+	5.67164i	0.821960	+	0.271934i
$436$		−	16.0538i		−	0.768838i
$437$	3.35348			0.160419
$438$			4.86678i			0.232544i
$439$	2.53528			0.121003			0.0605013	−	0.998168i	$-0.480730\pi$
$439$	2.53528			0.121003			0.0605013	+	0.998168i	$0.480730\pi$
$440$	−8.86907	−	2.93421i	−0.422816	−	0.139883i
$441$	−18.0269			−0.858424
$442$		0			0
$443$			19.3579i			0.919721i	0.887991	+	0.459860i	$0.152101\pi$
$443$			19.3579i			0.919721i	−0.887991	+	0.459860i	$0.847899\pi$
$444$		−	9.91745i		−	0.470661i
$445$	21.9007	+	7.24555i	1.03819	+	0.343472i
$446$	−4.09269			−0.193795
$447$	−42.6696			−2.01820
$448$	18.4160			0.870075
$449$		−	24.8080i		−	1.17076i	−0.810758	−	0.585381i	$-0.800945\pi$
$449$		−	24.8080i		−	1.17076i	0.810758	−	0.585381i	$-0.199055\pi$
$450$	5.63757	+	4.18869i	0.265758	+	0.197457i
$451$	−9.02690			−0.425060
$452$			13.8623i			0.652027i
$453$	−39.1534			−1.83959
$454$	−2.03888			−0.0956896
$455$		0			0
$456$	−4.31638			−0.202133
$457$	−7.56748			−0.353992			−0.176996	−	0.984212i	$-0.556638\pi$
$457$	−7.56748			−0.353992			−0.176996	+	0.984212i	$0.556638\pi$
$458$		−	8.92704i		−	0.417133i
$459$	6.53528			0.305041
$460$	10.8034	+	3.57417i	0.503712	+	0.166646i
$461$		−	12.3433i		−	0.574884i	−0.957798	−	0.287442i	$-0.907195\pi$
$461$		−	12.3433i		−	0.574884i	0.957798	−	0.287442i	$-0.0928049\pi$
$462$	−9.69338			−0.450977
$463$	−22.8578			−1.06229			−0.531146	−	0.847281i	$-0.678238\pi$
$463$	−22.8578			−1.06229			−0.531146	+	0.847281i	$0.678238\pi$
$464$	−10.0658			−0.467293
$465$	7.14834	−	21.6069i	0.331496	−	1.00199i
$466$		−	0.272715i		−	0.0126333i
$467$			15.2976i			0.707889i	0.935266	+	0.353945i	$0.115160\pi$
$467$			15.2976i			0.707889i	−0.935266	+	0.353945i	$0.884840\pi$
$468$		0			0
$469$	13.4647			0.621743
$470$	1.59621	−	4.82476i	0.0736275	−	0.222549i
$471$	−29.3971			−1.35455
$472$			3.26325i			0.150203i
$473$	−28.3589			−1.30394
$474$			12.2727i			0.563704i
$475$	3.71498	−	5.00000i	0.170455	−	0.229416i
$476$		−	12.3553i		−	0.566303i
$477$			54.4889i			2.49487i
$478$		−	1.32335i		−	0.0605284i
$479$			24.2829i			1.10951i	0.832013	+	0.554756i	$0.187188\pi$
$479$			24.2829i			1.10951i	−0.832013	+	0.554756i	$0.812812\pi$
$480$	−21.0538	−	6.96537i	−0.960971	−	0.317924i
$481$		0			0
$482$		−	7.50793i		−	0.341977i
$483$	24.2987			1.10563
$484$	−0.878567			−0.0399349
$485$	−3.69855	+	11.1794i	−0.167942	+	0.507629i
$486$			6.63276i			0.300868i
$487$	−36.8883			−1.67157			−0.835783	−	0.549060i	$-0.814986\pi$
$487$	−36.8883			−1.67157			−0.835783	+	0.549060i	$0.814986\pi$
$488$	9.64273			0.436506
$489$			11.2458i			0.508553i
$490$	0.986548	−	2.98198i	0.0445677	−	0.134712i
$491$	35.3534			1.59548			0.797739	−	0.603003i	$-0.206029\pi$
$491$	35.3534			1.59548			0.797739	+	0.603003i	$0.206029\pi$
$492$	−14.1529			−0.638064
$493$			5.84642i			0.263310i
$494$		0			0
$495$	−29.2560	−	9.67894i	−1.31496	−	0.435036i
$496$			12.6866i			0.569644i
$497$		−	17.5917i		−	0.789096i
$498$			7.67612i			0.343975i
$499$		−	16.2189i		−	0.726058i	−0.931778	−	0.363029i	$-0.881743\pi$
$499$		−	16.2189i		−	0.726058i	0.931778	−	0.363029i	$-0.118257\pi$
$500$	17.2971	−	12.1483i	0.773549	−	0.543290i
$501$		−	9.02690i		−	0.403292i
$502$	−6.29480			−0.280950
$503$		−	20.2384i		−	0.902386i	−0.892427	−	0.451193i	$-0.850999\pi$
$503$		−	20.2384i		−	0.902386i	0.892427	−	0.451193i	$-0.149001\pi$
$504$	−18.3265			−0.816328
$505$	−4.01070	+	12.1229i	−0.178474	+	0.539462i
$506$	2.89055			0.128500
$507$		0			0
$508$			17.3244i			0.768646i
$509$			20.0371i			0.888127i	0.895995	+	0.444063i	$0.146463\pi$
$509$			20.0371i			0.888127i	−0.895995	+	0.444063i	$0.853537\pi$
$510$	−1.21891	+	3.68431i	−0.0539740	+	0.163144i
$511$	18.3265			0.810718
$512$	20.9992			0.928042
$513$	−4.17780			−0.184454
$514$		−	0.698546i		−	0.0308116i
$515$	15.6429	+	5.17524i	0.689308	+	0.228048i
$516$	−44.4629			−1.95737
$517$			22.2974i			0.980639i
$518$	2.16211			0.0949977
$519$	−23.5185			−1.03235
$520$		0			0
$521$	16.0269			0.702151			0.351076	−	0.936347i	$-0.385816\pi$
$521$	16.0269			0.702151			0.351076	+	0.936347i	$0.385816\pi$
$522$	4.21401			0.184442
$523$			11.7380i			0.513265i	0.966509	+	0.256633i	$0.0826130\pi$
$523$			11.7380i			0.513265i	−0.966509	+	0.256633i	$0.917387\pi$
$524$	−18.9055			−0.825889
$525$	26.9180	−	36.2291i	1.17480	−	1.58117i
$526$			9.89775i			0.431562i
$527$	7.36863			0.320982
$528$	29.3152			1.27578
$529$	15.7542			0.684965
$530$	−9.01345	−	2.98198i	−0.391519	−	0.129529i
$531$			10.7643i			0.467132i
$532$			7.89832i			0.342436i
$533$		0			0
$534$	9.18722			0.397570
$535$	−18.2027	−	6.02213i	−0.786972	−	0.260359i
$536$	5.16804			0.223225
$537$			48.4798i			2.09206i
$538$	−6.14995			−0.265143
$539$			13.7811i			0.593594i
$540$	−13.4590	−	4.45274i	−0.579184	−	0.191615i
$541$			21.8080i			0.937599i	0.883305	+	0.468800i	$0.155313\pi$
$541$			21.8080i			0.937599i	−0.883305	+	0.468800i	$0.844687\pi$
$542$		−	1.92704i		−	0.0827736i
$543$			2.80934i			0.120560i
$544$		−	7.18002i		−	0.307841i
$545$	18.0269	+	5.96396i	0.772188	+	0.255468i
$546$		0			0
$547$		−	6.30924i		−	0.269764i	−0.990862	−	0.134882i	$-0.956935\pi$
$547$		−	6.30924i		−	0.269764i	0.990862	−	0.134882i	$-0.0430655\pi$
$548$	31.8533			1.36070
$549$	31.8080			1.35753
$550$	3.20215	−	4.30978i	0.136540	−	0.183769i
$551$		−	3.73743i		−	0.159220i
$552$	9.32634			0.396955
$553$	46.2146			1.96524
$554$		−	4.47964i		−	0.190322i
$555$	11.1364	+	3.68431i	0.472712	+	0.156390i
$556$	−1.94141			−0.0823342
$557$	35.8378			1.51849			0.759247	−	0.650802i	$-0.225567\pi$
$557$	35.8378			1.51849			0.759247	+	0.650802i	$0.225567\pi$
$558$		−	5.31119i		−	0.224840i
$559$		0			0
$560$	−7.90253	+	23.8865i	−0.333943	+	1.00939i
$561$		−	17.0269i		−	0.718876i
$562$			0.153745i			0.00648534i
$563$			5.00212i			0.210814i	0.994429	+	0.105407i	$0.0336145\pi$
$563$			5.00212i			0.210814i	−0.994429	+	0.105407i	$0.966385\pi$
$564$			34.9593i			1.47205i
$565$	−15.5660	−	5.14981i	−0.654868	−	0.216654i
$566$			3.32836i			0.139901i
$567$	12.4432			0.522564
$568$		−	6.75207i		−	0.283310i
$569$	−13.1680			−0.552033			−0.276017	−	0.961153i	$-0.589014\pi$
$569$	−13.1680			−0.552033			−0.276017	+	0.961153i	$0.589014\pi$
$570$	0.779207	−	2.35526i	0.0326374	−	0.0986511i
$571$	−19.8349			−0.830065			−0.415032	−	0.909807i	$-0.636230\pi$
$571$	−19.8349			−0.830065			−0.415032	+	0.909807i	$0.636230\pi$
$572$		0			0
$573$		−	68.6909i		−	2.86960i
$574$		−	3.08549i		−	0.128786i
$575$	−8.02690	+	10.8034i	−0.334745	+	0.450534i
$576$	23.3164			0.971516
$577$	−10.9210			−0.454646			−0.227323	−	0.973819i	$-0.572997\pi$
$577$	−10.9210			−0.454646			−0.227323	+	0.973819i	$0.572997\pi$
$578$	4.36775			0.181675
$579$			53.3534i			2.21729i
$580$	3.98339	−	12.0404i	0.165401	−	0.499949i
$581$	28.9055			1.19920
$582$			4.68969i			0.194394i
$583$	41.6553			1.72519
$584$	7.03411			0.291073
$585$		0			0
$586$	−4.44979			−0.183819
$587$	−40.4495			−1.66953			−0.834764	−	0.550607i	$-0.814396\pi$
$587$	−40.4495			−1.66953			−0.834764	+	0.550607i	$0.814396\pi$
$588$			21.6069i			0.891052i
$589$	−4.71053			−0.194094
$590$	−1.78062	−	0.589093i	−0.0733069	−	0.0242526i
$591$		−	58.2829i		−	2.39744i
$592$	−6.53876			−0.268742
$593$	−1.47709			−0.0606569			−0.0303284	−	0.999540i	$-0.509655\pi$
$593$	−1.47709			−0.0606569			−0.0303284	+	0.999540i	$0.509655\pi$
$594$	−3.60107			−0.147754
$595$	13.8738	+	4.58996i	0.568770	+	0.188170i
$596$			29.9683i			1.22755i
$597$		−	49.0690i		−	2.00826i
$598$		0			0
$599$	−2.27271			−0.0928606			−0.0464303	−	0.998922i	$-0.514785\pi$
$599$	−2.27271			−0.0928606			−0.0464303	+	0.998922i	$0.514785\pi$
$600$	10.3317	−	13.9055i	0.421790	−	0.567689i
$601$	7.40429			0.302027			0.151014	−	0.988532i	$-0.451746\pi$
$601$	7.40429			0.302027			0.151014	+	0.988532i	$0.451746\pi$
$602$		−	9.69338i		−	0.395073i
$603$	17.0476			0.694231
$604$			27.4988i			1.11891i
$605$	0.326386	−	0.986548i	0.0132695	−	0.0401089i
$606$			5.08549i			0.206584i
$607$		−	10.6932i		−	0.434024i	−0.976169	−	0.217012i	$-0.930369\pi$
$607$		−	10.6932i		−	0.434024i	0.976169	−	0.217012i	$-0.0696311\pi$
$608$			4.58996i			0.186147i
$609$		−	27.0807i		−	1.09737i
$610$	−1.74074	+	5.26162i	−0.0704804	+	0.213037i
$611$		0			0
$612$		−	15.6429i		−	0.632327i
$613$	6.08149			0.245629			0.122815	−	0.992430i	$-0.460808\pi$
$613$	6.08149			0.245629			0.122815	+	0.992430i	$0.460808\pi$
$614$	8.14114			0.328550
$615$	5.25779	−	15.8924i	0.212015	−	0.640844i
$616$			14.0101i			0.564485i
$617$	−31.8388			−1.28178			−0.640892	−	0.767631i	$-0.721435\pi$
$617$	−31.8388			−1.28178			−0.640892	+	0.767631i	$0.721435\pi$
$618$	6.56211			0.263967
$619$		−	26.4043i		−	1.06128i	−0.847598	−	0.530639i	$-0.821952\pi$
$619$		−	26.4043i		−	1.06128i	0.847598	−	0.530639i	$-0.178048\pi$
$620$	−15.1752	−	5.02052i	−0.609452	−	0.201629i
$621$	9.02690			0.362237
$622$	−0.806517			−0.0323384
$623$		−	34.5957i		−	1.38605i
$624$		0			0
$625$	7.21560	+	23.9361i	0.288624	+	0.957443i
$626$			6.38400i			0.255156i
$627$			10.8848i			0.434695i
$628$			20.6466i			0.823889i
$629$			3.79785i			0.151430i
$630$	3.30837	−	10.0000i	0.131808	−	0.398410i
$631$		−	35.1680i		−	1.40002i	−0.714134	−	0.700009i	$-0.753179\pi$
$631$		−	35.1680i		−	1.40002i	0.714134	−	0.700009i	$-0.246821\pi$
$632$	17.7381			0.705585
$633$		−	51.9508i		−	2.06486i
$634$	9.53528			0.378695
$635$	−19.4536	−	6.43598i	−0.771994	−	0.255404i
$636$	65.3098			2.58970
$637$		0			0
$638$		−	3.22150i		−	0.127540i
$639$		−	22.2727i		−	0.881095i
$640$	−6.45126	+	19.4999i	−0.255009	+	0.770799i
$641$	−5.52514			−0.218230			−0.109115	−	0.994029i	$-0.534802\pi$
$641$	−5.52514			−0.218230			−0.109115	+	0.994029i	$0.534802\pi$
$642$	−7.63594			−0.301367
$643$	−32.1552			−1.26808			−0.634039	−	0.773301i	$-0.718604\pi$
$643$	−32.1552			−1.26808			−0.634039	+	0.773301i	$0.718604\pi$
$644$		−	17.0658i		−	0.672486i
$645$	16.5179	−	49.9276i	0.650391	−	1.96590i
$646$	0.803220			0.0316023
$647$			13.7843i			0.541917i	0.962591	+	0.270959i	$0.0873407\pi$
$647$			13.7843i			0.541917i	−0.962591	+	0.270959i	$0.912659\pi$
$648$	4.77595			0.187617
$649$	8.22905			0.323019
$650$		0			0
$651$	−34.1316			−1.33772
$652$	7.89832			0.309322
$653$		−	8.50202i		−	0.332710i	−0.986066	−	0.166355i	$-0.946800\pi$
$653$		−	8.50202i		−	0.332710i	0.986066	−	0.166355i	$-0.0531997\pi$
$654$	7.56219			0.295705
$655$	7.02335	−	21.2291i	0.274425	−	0.829488i
$656$			9.33130i			0.364326i
$657$	23.2031			0.905238
$658$	−7.62150			−0.297117
$659$	−4.04366			−0.157519			−0.0787594	−	0.996894i	$-0.525096\pi$
$659$	−4.04366			−0.157519			−0.0787594	+	0.996894i	$0.525096\pi$
$660$	−11.6011	+	35.0659i	−0.451571	+	1.36494i
$661$		−	31.2727i		−	1.21637i	−0.793796	−	0.608184i	$-0.791898\pi$
$661$		−	31.2727i		−	1.21637i	0.793796	−	0.608184i	$-0.208102\pi$
$662$		−	0.983609i		−	0.0382290i
$663$		0			0
$664$	11.0945			0.430551
$665$	−8.86907	−	2.93421i	−0.343928	−	0.113784i
$666$	2.73743			0.106073
$667$			8.07541i			0.312681i
$668$	−6.33991			−0.245298
$669$			33.2996i			1.28744i
$670$	−0.932952	+	2.81998i	−0.0360431	+	0.108945i
$671$		−	24.3164i		−	0.938723i
$672$			33.2579i			1.28295i
$673$		−	32.0739i		−	1.23636i	−0.786037	−	0.618179i	$-0.787871\pi$
$673$		−	32.0739i		−	1.23636i	0.786037	−	0.618179i	$-0.212129\pi$
$674$		−	0.629812i		−	0.0242595i
$675$	10.0000	−	13.4590i	0.384900	−	0.518038i
$676$		0			0
$677$			14.2382i			0.547220i	0.961841	+	0.273610i	$0.0882177\pi$
$677$			14.2382i			0.547220i	−0.961841	+	0.273610i	$0.911782\pi$
$678$	−6.52986			−0.250778
$679$	17.6597			0.677716
$680$	5.32505	+	1.76172i	0.204206	+	0.0675589i
$681$			16.5891i			0.635695i
$682$	−4.06026			−0.155475
$683$	25.7847			0.986622			0.493311	−	0.869853i	$-0.335786\pi$
$683$	25.7847			0.986622			0.493311	+	0.869853i	$0.335786\pi$
$684$			10.0000i			0.382360i
$685$	−11.8334	+	35.7682i	−0.452132	+	1.36663i
$686$	3.05564			0.116665
$687$	−72.6336			−2.77114
$688$			29.3152i			1.11763i
$689$		0			0
$690$	−1.68362	+	5.08898i	−0.0640944	+	0.193734i
$691$		−	0.0436636i		−	0.00166104i	−1.00000		0.000830522i	$-0.999736\pi$
$691$		−	0.0436636i		−	0.00166104i	1.00000		0.000830522i	$-0.000264363\pi$
$692$			16.5179i			0.627915i
$693$			46.2146i			1.75555i
$694$		−	4.18002i		−	0.158671i
$695$	0.721231	−	2.18002i	0.0273578	−	0.0826929i
$696$		−	10.3941i		−	0.393989i
$697$	5.41982			0.205290
$698$			2.96863i			0.112364i
$699$	−2.21891			−0.0839267
$700$	−25.4449	−	18.9055i	−0.961727	−	0.714560i
$701$	14.5454			0.549373			0.274687	−	0.961534i	$-0.411426\pi$
$701$	14.5454			0.549373			0.274687	+	0.961534i	$0.411426\pi$
$702$		0			0
$703$		−	2.42785i		−	0.0915679i
$704$		−	17.8248i		−	0.671796i
$705$	−39.2560	−	12.9873i	−1.47846	−	0.489130i
$706$	−11.3313			−0.426459
$707$	19.1501			0.720214
$708$	12.9020			0.484888
$709$			19.6328i			0.737324i	0.929564	+	0.368662i	$0.120184\pi$
$709$			19.6328i			0.737324i	−0.929564	+	0.368662i	$0.879816\pi$
$710$	3.68431	+	1.21891i	0.138270	+	0.0457447i
$711$	58.5119			2.19437
$712$		−	13.2786i		−	0.497636i
$713$	10.1780			0.381168
$714$	5.81998			0.217807
$715$		0			0
$716$	34.0490			1.27247
$717$	−10.7672			−0.402109
$718$			7.41216i			0.276619i
$719$	47.4312			1.76889			0.884443	−	0.466649i	$-0.154539\pi$
$719$	47.4312			1.76889			0.884443	+	0.466649i	$0.154539\pi$
$720$	−10.0053	+	30.2425i	−0.372876	+	1.12707i
$721$		−	24.7105i		−	0.920268i
$722$	5.77242			0.214827
$723$	−61.0872			−2.27186
$724$	1.97310			0.0733295
$725$	12.0404	+	8.94594i	0.447168	+	0.332244i
$726$		−	0.413851i		−	0.0153595i
$727$		−	34.0951i		−	1.26452i	−0.774757	−	0.632259i	$-0.782128\pi$
$727$		−	34.0951i		−	1.26452i	0.774757	−	0.632259i	$-0.217872\pi$
$728$		0			0
$729$	42.8349			1.58648
$730$	−1.26982	+	3.83821i	−0.0469982	+	0.142059i
$731$	17.0269			0.629763
$732$		−	38.1247i		−	1.40913i
$733$	−14.3920			−0.531580			−0.265790	−	0.964031i	$-0.585633\pi$
$733$	−14.3920			−0.531580			−0.265790	+	0.964031i	$0.585633\pi$
$734$		−	4.36541i		−	0.161130i
$735$	−24.2624	−	8.02690i	−0.894934	−	0.296077i
$736$		−	9.91745i		−	0.365562i
$737$		−	13.0324i		−	0.480055i
$738$		−	3.90652i		−	0.143801i
$739$		−	34.4480i		−	1.26719i	−0.773665	−	0.633594i	$-0.781579\pi$
$739$		−	34.4480i		−	1.26719i	0.773665	−	0.633594i	$-0.218421\pi$
$740$	2.58762	−	7.82145i	0.0951228	−	0.287522i
$741$		0			0
$742$			14.2382i			0.522702i
$743$	40.7134			1.49363			0.746816	−	0.665031i	$-0.231582\pi$
$743$	40.7134			1.49363			0.746816	+	0.665031i	$0.231582\pi$
$744$	−13.1004			−0.480285
$745$	−33.6516	−	11.1332i	−1.23290	−	0.407888i
$746$			5.04903i			0.184858i
$747$	36.5970			1.33901
$748$	−11.9586			−0.437249
$749$			28.7542i			1.05066i
$750$	5.72251	+	8.14783i	0.208956	+	0.297517i
$751$	−32.5018			−1.18601			−0.593003	−	0.805200i	$-0.702058\pi$
$751$	−32.5018			−1.18601			−0.593003	+	0.805200i	$0.702058\pi$
$752$	23.0493			0.840522
$753$			51.2167i			1.86644i
$754$		0			0
$755$	−30.8786	−	10.2158i	−1.12379	−	0.371790i
$756$			21.2607i			0.773245i
$757$		−	13.0324i		−	0.473671i	−0.971550	−	0.236836i	$-0.923890\pi$
$757$		−	13.0324i		−	0.473671i	0.971550	−	0.236836i	$-0.0761103\pi$
$758$		−	6.03084i		−	0.219050i
$759$		−	23.5185i		−	0.853668i
$760$	−3.40413	−	1.12621i	−0.123481	−	0.0408520i
$761$			3.98985i			0.144632i	0.997382	+	0.0723161i	$0.0230390\pi$
$761$			3.98985i			0.144632i	−0.997382	+	0.0723161i	$0.976961\pi$
$762$	−8.16070			−0.295631
$763$		−	28.4765i		−	1.03092i
$764$	−48.2440			−1.74541
$765$	17.5655	+	5.81131i	0.635082	+	0.210108i
$766$	0.476696			0.0172237
$767$		0			0
$768$		−	21.3847i		−	0.771652i
$769$		−	6.66686i		−	0.240413i	−0.992749	−	0.120207i	$-0.961644\pi$
$769$		−	6.66686i		−	0.240413i	0.992749	−	0.120207i	$-0.0383557\pi$
$770$	−7.64474	−	2.52916i	−0.275497	−	0.0911445i
$771$	−5.68362			−0.204691
$772$	37.4720			1.34865
$773$	48.3349			1.73849			0.869244	−	0.494384i	$-0.164606\pi$
$773$	48.3349			1.73849			0.869244	+	0.494384i	$0.164606\pi$
$774$		−	12.2727i		−	0.441134i
$775$	11.2751	−	15.1752i	0.405015	−	0.545111i
$776$	6.77815			0.243321
$777$		−	17.5917i		−	0.631099i
$778$	−6.21683			−0.222884
$779$	−3.46472			−0.124136
$780$		0			0
$781$	−17.0269			−0.609271
$782$	−1.73551			−0.0620616
$783$		−	10.0604i		−	0.359531i
$784$	14.2458			0.508779
$785$	−23.1842	−	7.67017i	−0.827478	−	0.273760i
$786$		−	8.90547i		−	0.317648i
$787$	−27.9612			−0.996709			−0.498355	−	0.866973i	$-0.666062\pi$
$787$	−27.9612			−0.996709			−0.498355	+	0.866973i	$0.666062\pi$
$788$	−40.9341			−1.45822
$789$	80.5316			2.86700
$790$	−3.20215	+	9.67894i	−0.113927	+	0.344361i
$791$			24.5891i			0.874288i
$792$			17.7381i			0.630297i
$793$		0			0
$794$	−5.65488			−0.200684
$795$	−24.2624	+	73.3367i	−0.860500	+	2.60098i
$796$	−34.4629			−1.22150
$797$		−	37.2424i		−	1.31919i	−0.751619	−	0.659597i	$-0.770727\pi$
$797$		−	37.2424i		−	1.31919i	0.751619	−	0.659597i	$-0.229273\pi$
$798$	−3.72052			−0.131705
$799$		−	13.3875i		−	0.473617i
$800$	−14.7868	−	10.9865i	−0.522793	−	0.388433i
$801$		−	43.8014i		−	1.54765i
$802$		−	7.34528i		−	0.259371i
$803$		−	17.7381i		−	0.625965i
$804$		−	20.4330i		−	0.720617i
$805$	19.1633	+	6.33991i	0.675416	+	0.223452i
$806$		0			0
$807$			50.0382i			1.76143i
$808$	7.35022			0.258580
$809$	−14.5287			−0.510801			−0.255400	−	0.966835i	$-0.582207\pi$
$809$	−14.5287			−0.510801			−0.255400	+	0.966835i	$0.582207\pi$
$810$	−0.862170	+	2.60603i	−0.0302936	+	0.0915666i
$811$			44.0538i			1.54694i	0.633834	+	0.773469i	$0.281480\pi$
$811$			44.0538i			1.54694i	−0.633834	+	0.773469i	$0.718520\pi$
$812$	−19.0197			−0.667461
$813$	−15.6791			−0.549890
$814$		−	2.09269i		−	0.0733489i
$815$	−2.93421	+	8.86907i	−0.102781	+	0.310670i
$816$	−17.6011			−0.616161
$817$	−10.8848			−0.380809
$818$			3.18687i			0.111426i
$819$		0			0
$820$	−11.1618	−	3.69273i	−0.389787	−	0.128956i
$821$			27.0269i			0.943245i	0.881800	+	0.471623i	$0.156332\pi$
$821$			27.0269i			0.943245i	−0.881800	+	0.471623i	$0.843668\pi$
$822$			15.0046i			0.523345i
$823$		−	39.5963i		−	1.38024i	−0.723695	−	0.690120i	$-0.757558\pi$
$823$		−	39.5963i		−	1.38024i	0.723695	−	0.690120i	$-0.242442\pi$
$824$		−	9.48442i		−	0.330405i
$825$	−35.0659	−	26.0538i	−1.22084	−	0.907077i
$826$			2.81278i			0.0978691i
$827$	−26.5639			−0.923716			−0.461858	−	0.886954i	$-0.652817\pi$
$827$	−26.5639			−0.923716			−0.461858	+	0.886954i	$0.652817\pi$
$828$		−	21.6069i		−	0.750890i
$829$	13.9832			0.485658			0.242829	−	0.970069i	$-0.421925\pi$
$829$	13.9832			0.485658			0.242829	+	0.970069i	$0.421925\pi$
$830$	−2.00282	+	6.05381i	−0.0695189	+	0.210131i
$831$	−36.4480			−1.26437
$832$		0			0
$833$		−	8.27427i		−	0.286686i
$834$		−	0.914507i		−	0.0316668i
$835$	2.35526	−	7.11911i	0.0815072	−	0.246367i
$836$	7.64474			0.264399
$837$	−12.6798			−0.438278
$838$	0.647228			0.0223581
$839$			14.3941i			0.496941i	0.968639	+	0.248471i	$0.0799279\pi$
$839$			14.3941i			0.496941i	−0.968639	+	0.248471i	$0.920072\pi$
$840$	−24.6657	−	8.16032i	−0.851048	−	0.281558i
$841$	−20.0000			−0.689655
$842$		−	3.99674i		−	0.137737i
$843$	1.25092			0.0430841
$844$	−36.4868			−1.25593
$845$		0			0
$846$	−9.64952			−0.331757
$847$	−1.55841			−0.0535477
$848$		−	43.0600i		−	1.47869i
$849$	27.0807			0.929408
$850$	−1.92259	+	2.58762i	−0.0659444	+	0.0887547i
$851$			5.24581i			0.179824i
$852$	−26.6958			−0.914584
$853$	27.2633			0.933478			0.466739	−	0.884395i	$-0.345429\pi$
$853$	27.2633			0.933478			0.466739	+	0.884395i	$0.345429\pi$
$854$	8.31160			0.284417
$855$	−11.2291	−	3.71498i	−0.384025	−	0.127050i
$856$			11.0365i			0.377219i
$857$			50.6201i			1.72915i	0.502503	+	0.864575i	$0.332413\pi$
$857$			50.6201i			1.72915i	−0.502503	+	0.864575i	$0.667587\pi$
$858$		0			0
$859$	−1.27992			−0.0436702			−0.0218351	−	0.999762i	$-0.506951\pi$
$859$	−1.27992			−0.0436702			−0.0218351	+	0.999762i	$0.506951\pi$
$860$	−35.0659	−	11.6011i	−1.19574	−	0.395593i
$861$	−25.1047			−0.855565
$862$			8.13497i			0.277078i
$863$	8.38448			0.285411			0.142706	−	0.989765i	$-0.454420\pi$
$863$	8.38448			0.285411			0.142706	+	0.989765i	$0.454420\pi$
$864$			12.3553i			0.420335i
$865$	−18.5480	−	6.13636i	−0.630651	−	0.208642i
$866$		−	11.9342i		−	0.405541i
$867$		−	35.5376i		−	1.20692i
$868$			23.9718i			0.813655i
$869$		−	44.7308i		−	1.51739i
$870$	5.67164	+	1.87639i	0.192287	+	0.0636155i
$871$		0			0
$872$		−	10.9299i		−	0.370132i
$873$	22.3588			0.756729
$874$	1.10945			0.0375278
$875$	30.6818	−	21.5489i	1.03723	−	0.728485i
$876$		−	27.8109i		−	0.939645i
$877$	55.8862			1.88714			0.943572	−	0.331169i	$-0.107443\pi$
$877$	55.8862			1.88714			0.943572	+	0.331169i	$0.107443\pi$
$878$	0.838765			0.0283069
$879$			36.2051i			1.22117i
$880$	23.1196	+	7.64881i	0.779362	+	0.257841i
$881$	−25.1949			−0.848839			−0.424420	−	0.905466i	$-0.639522\pi$
$881$	−25.1949			−0.848839			−0.424420	+	0.905466i	$0.639522\pi$
$882$	−5.96396			−0.200817
$883$		−	30.7868i		−	1.03606i	−0.855363	−	0.518029i	$-0.826666\pi$
$883$		−	30.7868i		−	1.03606i	0.855363	−	0.518029i	$-0.173334\pi$
$884$		0			0
$885$	−4.79307	+	14.4877i	−0.161117	+	0.487000i
$886$			6.40429i			0.215156i
$887$		−	12.4721i		−	0.418771i	−0.977833	−	0.209385i	$-0.932854\pi$
$887$		−	12.4721i		−	0.418771i	0.977833	−	0.209385i	$-0.0671463\pi$
$888$		−	6.75207i		−	0.226585i
$889$			30.7302i			1.03066i
$890$	7.24555	+	2.39709i	0.242871	+	0.0803507i
$891$		−	12.0437i		−	0.403478i
$892$	23.3875			0.783071
$893$			8.55822i			0.286390i
$894$	−14.1167			−0.472132
$895$	−12.6491	+	38.2338i	−0.422814	+	1.27802i
$896$	30.8032			1.02906
$897$		0			0
$898$		−	8.20739i		−	0.273884i
$899$		−	11.3433i		−	0.378320i
$900$	−32.2156	−	23.9361i	−1.07385	−	0.797869i
$901$	−25.0101			−0.833209
$902$	−2.98643			−0.0994372
$903$	−78.8688			−2.62459
$904$			9.43781i			0.313897i
$905$	−0.733001	+	2.21560i	−0.0243658	+	0.0736490i
$906$	−12.9534			−0.430348
$907$			38.8911i			1.29136i	0.763609	+	0.645678i	$0.223425\pi$
$907$			38.8911i			1.29136i	−0.763609	+	0.645678i	$0.776575\pi$
$908$	11.6511			0.386655
$909$	24.2458			0.804183
$910$		0			0
$911$	0.165096			0.00546989			0.00273494	−	0.999996i	$-0.499129\pi$
$911$	0.165096			0.00546989			0.00273494	+	0.999996i	$0.499129\pi$
$912$	11.2518			0.372584
$913$		−	27.9774i		−	0.925918i
$914$	−2.50360			−0.0828117
$915$	42.8105	+	14.1633i	1.41527	+	0.468223i
$916$			51.0131i			1.68552i
$917$	−33.5348			−1.10742
$918$	2.16211			0.0713603
$919$	−0.895326			−0.0295341			−0.0147670	−	0.999891i	$-0.504701\pi$
$919$	−0.895326			−0.0295341			−0.0147670	+	0.999891i	$0.504701\pi$
$920$	7.35526	+	2.43339i	0.242496	+	0.0802265i
$921$		−	66.2392i		−	2.18266i
$922$		−	4.08361i		−	0.134486i
$923$		0			0
$924$	55.3923			1.82227
$925$	7.82145	+	5.81131i	0.257168	+	0.191075i
$926$	−7.56219			−0.248509
$927$		−	31.2858i		−	1.02756i
$928$	−11.0529			−0.362831
$929$			12.2895i			0.403205i	0.979467	+	0.201602i	$0.0646148\pi$
$929$			12.2895i			0.403205i	−0.979467	+	0.201602i	$0.935385\pi$
$930$	2.36493	−	7.14834i	0.0775491	−	0.234403i
$931$			5.28947i			0.173356i
$932$			1.55841i			0.0510476i
$933$			6.56211i			0.214834i
$934$			5.06101i			0.165601i
$935$	4.44259	−	13.4284i	0.145288	−	0.439154i
$936$		0			0
$937$		−	5.77242i		−	0.188577i	−0.995545	−	0.0942884i	$-0.969942\pi$
$937$		−	5.77242i		−	0.188577i	0.995545	−	0.0942884i	$-0.0300576\pi$
$938$	4.45462			0.145448
$939$	51.9425			1.69508
$940$	−9.12143	+	27.5708i	−0.297508	+	0.899261i
$941$		−	55.8887i		−	1.82192i	−0.412495	−	0.910960i	$-0.635342\pi$
$941$		−	55.8887i		−	1.82192i	0.412495	−	0.910960i	$-0.364658\pi$
$942$	−9.72563			−0.316878
$943$	7.48616			0.243783
$944$		−	8.50655i		−	0.276864i
$945$	−23.8738	−	7.89832i	−0.776614	−	0.256932i
$946$	−9.38217			−0.305041
$947$	−1.89638			−0.0616239			−0.0308120	−	0.999525i	$-0.509809\pi$
$947$	−1.89638			−0.0616239			−0.0308120	+	0.999525i	$0.509809\pi$
$948$		−	70.1318i		−	2.27777i
$949$		0			0
$950$	1.22905	−	1.65418i	0.0398757	−	0.0536688i
$951$		−	77.5825i		−	2.51578i
$952$		−	8.41179i		−	0.272628i
$953$			33.6523i			1.09011i	0.838402	+	0.545053i	$0.183490\pi$
$953$			33.6523i			1.09011i	−0.838402	+	0.545053i	$0.816510\pi$
$954$			18.0269i			0.583643i
$955$	17.9225	−	54.1734i	0.579960	−	1.75301i
$956$			7.56219i			0.244579i
$957$	−26.2113			−0.847290
$958$			8.03366i			0.259556i
$959$	56.5018			1.82454
$960$	31.3816	+	10.3822i	1.01284	+	0.335083i
$961$	16.7033			0.538817
$962$		0			0
$963$			36.4054i			1.17315i
$964$			42.9036i			1.38183i
$965$	−13.9208	+	42.0775i	−0.448125	+	1.35452i
$966$	8.03888			0.258647
$967$	23.0493			0.741216			0.370608	−	0.928789i	$-0.379149\pi$
$967$	23.0493			0.741216			0.370608	+	0.928789i	$0.379149\pi$
$968$	−0.598152			−0.0192253
$969$		−	6.53528i		−	0.209944i
$970$	−1.22361	+	3.69855i	−0.0392879	+	0.118753i
$971$	14.9193			0.478783			0.239391	−	0.970923i	$-0.423052\pi$
$971$	14.9193			0.478783			0.239391	+	0.970923i	$0.423052\pi$
$972$		−	37.9025i		−	1.21572i
$973$	−3.44370			−0.110400
$974$	−12.2040			−0.391041
$975$		0			0
$976$	−25.1364			−0.804595
$977$	23.3641			0.747485			0.373742	−	0.927533i	$-0.378074\pi$
$977$	23.3641			0.747485			0.373742	+	0.927533i	$0.378074\pi$
$978$			3.72052i			0.118969i
$979$	−33.4850			−1.07019
$980$	−5.63757	+	17.0404i	−0.180086	+	0.544334i
$981$		−	36.0538i		−	1.15111i
$982$	11.6962			0.373241
$983$	−5.31119			−0.169401			−0.0847003	−	0.996406i	$-0.526993\pi$
$983$	−5.31119			−0.169401			−0.0847003	+	0.996406i	$0.526993\pi$
$984$	−9.63570			−0.307175
$985$	15.2069	−	45.9651i	0.484533	−	1.46457i
$986$			1.93421i			0.0615978i
$987$			62.0112i			1.97384i
$988$		0			0
$989$	23.5185			0.747846
$990$	−9.67894	−	3.20215i	−0.307617	−	0.101771i
$991$	−24.0879			−0.765178			−0.382589	−	0.923919i	$-0.624967\pi$
$991$	−24.0879			−0.765178			−0.382589	+	0.923919i	$0.624967\pi$
$992$			13.9307i			0.442301i
$993$	−8.00299			−0.253967
$994$		−	5.81998i		−	0.184599i
$995$	12.8029	−	38.6985i	0.405879	−	1.22683i
$996$		−	43.8648i		−	1.38991i
$997$			20.4099i			0.646389i	0.946332	+	0.323195i	$0.104757\pi$
$997$			20.4099i			0.646389i	−0.946332	+	0.323195i	$0.895243\pi$
$998$		−	5.36581i		−	0.169852i
$999$		−	6.53528i		−	0.206767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.d.d.844.7		12
5.4	even	2	inner	845.2.d.d.844.6		12
13.2	odd	12		65.2.n.a.9.4	yes	12
13.3	even	3		845.2.l.f.654.6		24
13.4	even	6		845.2.l.f.699.7		24
13.5	odd	4		845.2.b.d.339.3		6
13.6	odd	12		65.2.n.a.29.3	yes	12
13.7	odd	12		845.2.n.e.484.4		12
13.8	odd	4		845.2.b.e.339.4		6
13.9	even	3		845.2.l.f.699.5		24
13.10	even	6		845.2.l.f.654.8		24
13.11	odd	12		845.2.n.e.529.3		12
13.12	even	2	inner	845.2.d.d.844.5		12
39.2	even	12		585.2.bs.a.334.3		12
39.32	even	12		585.2.bs.a.289.4		12
52.15	even	12		1040.2.dh.a.529.1		12
52.19	even	12		1040.2.dh.a.289.6		12
65.2	even	12		325.2.e.e.126.3		12
65.4	even	6		845.2.l.f.699.6		24
65.8	even	4		4225.2.a.bq.1.4		6
65.9	even	6		845.2.l.f.699.8		24
65.18	even	4		4225.2.a.br.1.3		6
65.19	odd	12		65.2.n.a.29.4	yes	12
65.24	odd	12		845.2.n.e.529.4		12
65.28	even	12		325.2.e.e.126.4		12
65.29	even	6		845.2.l.f.654.7		24
65.32	even	12		325.2.e.e.276.3		12
65.34	odd	4		845.2.b.e.339.3		6
65.44	odd	4		845.2.b.d.339.4		6
65.47	even	4		4225.2.a.bq.1.3		6
65.49	even	6		845.2.l.f.654.5		24
65.54	odd	12		65.2.n.a.9.3	✓	12
65.57	even	4		4225.2.a.br.1.4		6
65.58	even	12		325.2.e.e.276.4		12
65.59	odd	12		845.2.n.e.484.3		12
65.64	even	2	inner	845.2.d.d.844.8		12
195.119	even	12		585.2.bs.a.334.4		12
195.149	even	12		585.2.bs.a.289.3		12
260.19	even	12		1040.2.dh.a.289.1		12
260.119	even	12		1040.2.dh.a.529.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.3	✓	12	65.54	odd	12
65.2.n.a.9.4	yes	12	13.2	odd	12
65.2.n.a.29.3	yes	12	13.6	odd	12
65.2.n.a.29.4	yes	12	65.19	odd	12
325.2.e.e.126.3		12	65.2	even	12
325.2.e.e.126.4		12	65.28	even	12
325.2.e.e.276.3		12	65.32	even	12
325.2.e.e.276.4		12	65.58	even	12
585.2.bs.a.289.3		12	195.149	even	12
585.2.bs.a.289.4		12	39.32	even	12
585.2.bs.a.334.3		12	39.2	even	12
585.2.bs.a.334.4		12	195.119	even	12
845.2.b.d.339.3		6	13.5	odd	4
845.2.b.d.339.4		6	65.44	odd	4
845.2.b.e.339.3		6	65.34	odd	4
845.2.b.e.339.4		6	13.8	odd	4
845.2.d.d.844.5		12	13.12	even	2	inner
845.2.d.d.844.6		12	5.4	even	2	inner
845.2.d.d.844.7		12	1.1	even	1	trivial
845.2.d.d.844.8		12	65.64	even	2	inner
845.2.l.f.654.5		24	65.49	even	6
845.2.l.f.654.6		24	13.3	even	3
845.2.l.f.654.7		24	65.29	even	6
845.2.l.f.654.8		24	13.10	even	6
845.2.l.f.699.5		24	13.9	even	3
845.2.l.f.699.6		24	65.4	even	6
845.2.l.f.699.7		24	13.4	even	6
845.2.l.f.699.8		24	65.9	even	6
845.2.n.e.484.3		12	65.59	odd	12
845.2.n.e.484.4		12	13.7	odd	12
845.2.n.e.529.3		12	13.11	odd	12
845.2.n.e.529.4		12	65.24	odd	12
1040.2.dh.a.289.1		12	260.19	even	12
1040.2.dh.a.289.6		12	52.19	even	12
1040.2.dh.a.529.1		12	52.15	even	12
1040.2.dh.a.529.6		12	260.119	even	12
4225.2.a.bq.1.3		6	65.47	even	4
4225.2.a.bq.1.4		6	65.8	even	4
4225.2.a.br.1.3		6	65.18	even	4
4225.2.a.br.1.4		6	65.57	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.330837 q^{2} -2.69180i q^{3} -1.89055 q^{4} +(0.702335 - 2.12291i) q^{5} -0.890547i q^{6} -3.35348 q^{7} -1.28714 q^{8} -4.24581 q^{9} +O(q^{10})\)	\(q+0.330837 q^{2} -2.69180i q^{3} -1.89055 q^{4} +(0.702335 - 2.12291i) q^{5} -0.890547i q^{6} -3.35348 q^{7} -1.28714 q^{8} -4.24581 q^{9} +(0.232358 - 0.702335i) q^{10} +3.24581i q^{11} +5.08898i q^{12} -1.10945 q^{14} +(-5.71445 - 1.89055i) q^{15} +3.35526 q^{16} -1.94881i q^{17} -1.40467 q^{18} +1.24581i q^{19} +(-1.32780 + 4.01345i) q^{20} +9.02690i q^{21} +1.07383i q^{22} -2.69180i q^{23} +3.46472i q^{24} +(-4.01345 - 2.98198i) q^{25} +3.35348i q^{27} +6.33991 q^{28} -3.00000 q^{29} +(-1.89055 - 0.625462i) q^{30} +3.78109i q^{31} +3.68431 q^{32} +8.73709 q^{33} -0.644737i q^{34} +(-2.35526 + 7.11911i) q^{35} +8.02690 q^{36} -1.94881 q^{37} +0.412160i q^{38} +(-0.904000 + 2.73247i) q^{40} +2.78109i q^{41} +2.98643i q^{42} +8.73709i q^{43} -6.13636i q^{44} +(-2.98198 + 9.01345i) q^{45} -0.890547i q^{46} +6.86960 q^{47} -9.03171i q^{48} +4.24581 q^{49} +(-1.32780 - 0.986548i) q^{50} -5.24581 q^{51} -12.8336i q^{53} +1.10945i q^{54} +(6.89055 + 2.27964i) q^{55} +4.31638 q^{56} +3.35348 q^{57} -0.992510 q^{58} -2.53528i q^{59} +(10.8034 + 3.57417i) q^{60} -7.49162 q^{61} +1.25092i q^{62} +14.2382 q^{63} -5.49162 q^{64} +2.89055 q^{66} -4.01515 q^{67} +3.68431i q^{68} -7.24581 q^{69} +(-0.779207 + 2.35526i) q^{70} +5.24581i q^{71} +5.46493 q^{72} -5.46493 q^{73} -0.644737 q^{74} +(-8.02690 + 10.8034i) q^{75} -2.35526i q^{76} -10.8848i q^{77} -13.7811 q^{79} +(2.35652 - 7.12291i) q^{80} -3.71053 q^{81} +0.920088i q^{82} -8.61955 q^{83} -17.0658i q^{84} +(-4.13713 - 1.36872i) q^{85} +2.89055i q^{86} +8.07541i q^{87} -4.17780i q^{88} +10.3164i q^{89} +(-0.986548 + 2.98198i) q^{90} +5.08898i q^{92} +10.1780 q^{93} +2.27271 q^{94} +(2.64474 + 0.874976i) q^{95} -9.91745i q^{96} -5.26607 q^{97} +1.40467 q^{98} -13.7811i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} - 12 q^{9}+O(q^{10}) \) 12 * q + 8 * q^4 - 12 * q^9	\( 12 q + 8 q^{4} - 12 q^{9} + 14 q^{10} - 44 q^{14} + 32 q^{16} + 2 q^{25} - 36 q^{29} + 8 q^{30} - 20 q^{35} - 4 q^{36} + 70 q^{40} + 12 q^{49} - 24 q^{51} + 52 q^{55} - 32 q^{56} - 12 q^{61} + 12 q^{64} + 4 q^{66} - 48 q^{69} - 16 q^{74} + 4 q^{75} - 104 q^{79} - 28 q^{81} - 62 q^{90} - 112 q^{94} + 40 q^{95}+O(q^{100}) \) 12 * q + 8 * q^4 - 12 * q^9 + 14 * q^10 - 44 * q^14 + 32 * q^16 + 2 * q^25 - 36 * q^29 + 8 * q^30 - 20 * q^35 - 4 * q^36 + 70 * q^40 + 12 * q^49 - 24 * q^51 + 52 * q^55 - 32 * q^56 - 12 * q^61 + 12 * q^64 + 4 * q^66 - 48 * q^69 - 16 * q^74 + 4 * q^75 - 104 * q^79 - 28 * q^81 - 62 * q^90 - 112 * q^94 + 40 * q^95

Introduction

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