LMFDB - Embedded newform 585.2.n.g.343.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [585,2,Mod(307,585)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("585.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(585, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.n (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,0,-28,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.14
Character	$\chi$	$=$	585.343
Dual form			585.2.n.g.307.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.48675i q^{2} -4.18390 q^{4} +(2.00040 - 0.999208i) q^{5} -0.242414 q^{7} -5.43081i q^{8} +(2.48478 + 4.97448i) q^{10} +(4.24054 + 4.24054i) q^{11} +(2.81694 + 2.25052i) q^{13} -0.602823i q^{14} +5.13724 q^{16} +(1.37194 + 1.37194i) q^{17} +(-3.91462 - 3.91462i) q^{19} +(-8.36946 + 4.18059i) q^{20} +(-10.5451 + 10.5451i) q^{22} +(-1.90471 + 1.90471i) q^{23} +(3.00317 - 3.99762i) q^{25} +(-5.59648 + 7.00501i) q^{26} +1.01424 q^{28} +5.76992i q^{29} +(-5.69411 + 5.69411i) q^{31} +1.91338i q^{32} +(-3.41167 + 3.41167i) q^{34} +(-0.484925 + 0.242222i) q^{35} +3.31881 q^{37} +(9.73467 - 9.73467i) q^{38} +(-5.42651 - 10.8638i) q^{40} +(1.51472 - 1.51472i) q^{41} +(3.88596 - 3.88596i) q^{43} +(-17.7420 - 17.7420i) q^{44} +(-4.73652 - 4.73652i) q^{46} +1.68447 q^{47} -6.94124 q^{49} +(9.94107 + 7.46811i) q^{50} +(-11.7858 - 9.41597i) q^{52} +(2.22339 + 2.22339i) q^{53} +(12.7199 + 4.24558i) q^{55} +1.31651i q^{56} -14.3483 q^{58} +(-5.27843 + 5.27843i) q^{59} +10.2486 q^{61} +(-14.1598 - 14.1598i) q^{62} +5.51638 q^{64} +(7.88373 + 1.68723i) q^{65} -15.3086i q^{67} +(-5.74007 - 5.74007i) q^{68} +(-0.602346 - 1.20588i) q^{70} +(0.0780456 - 0.0780456i) q^{71} -1.45403i q^{73} +8.25304i q^{74} +(16.3784 + 16.3784i) q^{76} +(-1.02797 - 1.02797i) q^{77} +7.60135i q^{79} +(10.2765 - 5.13317i) q^{80} +(3.76672 + 3.76672i) q^{82} -2.71964 q^{83} +(4.11528 + 1.37357i) q^{85} +(9.66338 + 9.66338i) q^{86} +(23.0296 - 23.0296i) q^{88} +(-0.887120 + 0.887120i) q^{89} +(-0.682867 - 0.545559i) q^{91} +(7.96910 - 7.96910i) q^{92} +4.18886i q^{94} +(-11.7423 - 3.91927i) q^{95} +4.76021i q^{97} -17.2611i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} - 8 q^{5} + 8 q^{11} - 12 q^{13} + 28 q^{16} + 28 q^{17} - 32 q^{22} - 8 q^{23} - 4 q^{25} - 16 q^{31} + 28 q^{34} + 32 q^{37} - 48 q^{40} - 4 q^{41} - 40 q^{44} - 16 q^{46} + 24 q^{47}+ \cdots - 56 q^{95}+O(q^{100}) $ 28 * q - 28 * q^4 - 8 * q^5 + 8 * q^11 - 12 * q^13 + 28 * q^16 + 28 * q^17 - 32 * q^22 - 8 * q^23 - 4 * q^25 - 16 * q^31 + 28 * q^34 + 32 * q^37 - 48 * q^40 - 4 * q^41 - 40 * q^44 - 16 * q^46 + 24 * q^47 - 28 * q^49 + 32 * q^50 + 52 * q^52 - 20 * q^53 - 8 * q^55 - 8 * q^58 - 32 * q^59 + 8 * q^61 - 72 * q^62 - 28 * q^64 + 8 * q^65 - 60 * q^68 + 64 * q^70 - 40 * q^71 - 40 * q^76 + 48 * q^77 + 32 * q^80 + 4 * q^82 + 104 * q^83 - 4 * q^85 - 16 * q^86 + 72 * q^88 + 36 * q^89 - 56 * q^91 + 32 * q^92 - 56 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$			2.48675i			1.75839i	0.476458	+	0.879197i	$0.341920\pi$
$2$			2.48675i			1.75839i	−0.476458	+	0.879197i	$0.658080\pi$
$3$		0			0
$3$		0			0
$4$	−4.18390			−2.09195
$5$	2.00040	−	0.999208i	0.894604	−	0.446859i
$5$	2.00040	−	0.999208i	0.894604	−	0.446859i
$6$		0			0
$7$	−0.242414			−0.0916240			−0.0458120	−	0.998950i	$-0.514588\pi$
$7$	−0.242414			−0.0916240			−0.0458120	+	0.998950i	$0.514588\pi$
$8$		−	5.43081i		−	1.92008i
$9$		0			0
$10$	2.48478	+	4.97448i	0.785755	+	1.57307i
$11$	4.24054	+	4.24054i	1.27857	+	1.27857i	0.941467	+	0.337104i	$0.109447\pi$
$11$	4.24054	+	4.24054i	1.27857	+	1.27857i	0.337104	+	0.941467i	$0.390553\pi$
$12$		0			0
$13$	2.81694	+	2.25052i	0.781278	+	0.624183i
$13$	2.81694	+	2.25052i	0.781278	+	0.624183i
$14$		−	0.602823i		−	0.161111i
$15$		0			0
$16$	5.13724			1.28431
$17$	1.37194	+	1.37194i	0.332745	+	0.332745i	0.853628	−	0.520883i	$-0.174397\pi$
$17$	1.37194	+	1.37194i	0.332745	+	0.332745i	−0.520883	+	0.853628i	$0.674397\pi$
$18$		0			0
$19$	−3.91462	−	3.91462i	−0.898076	−	0.898076i	0.0971894	−	0.995266i	$-0.469015\pi$
$19$	−3.91462	−	3.91462i	−0.898076	−	0.898076i	−0.995266	+	0.0971894i	$0.969015\pi$
$20$	−8.36946	+	4.18059i	−1.87147	+	0.934808i
$21$		0			0
$22$	−10.5451	+	10.5451i	−2.24823	+	2.24823i
$23$	−1.90471	+	1.90471i	−0.397159	+	0.397159i	−0.877230	−	0.480071i	$-0.840611\pi$
$23$	−1.90471	+	1.90471i	−0.397159	+	0.397159i	0.480071	+	0.877230i	$0.340611\pi$
$24$		0			0
$25$	3.00317	−	3.99762i	0.600633	−	0.799525i
$26$	−5.59648	+	7.00501i	−1.09756	+	1.37380i
$27$		0			0
$28$	1.01424			0.191673
$29$			5.76992i			1.07145i	0.844393	+	0.535724i	$0.179961\pi$
$29$			5.76992i			1.07145i	−0.844393	+	0.535724i	$0.820039\pi$
$30$		0			0
$31$	−5.69411	+	5.69411i	−1.02269	+	1.02269i	−0.0229561	+	0.999736i	$0.507308\pi$
$31$	−5.69411	+	5.69411i	−1.02269	+	1.02269i	−0.999736	+	0.0229561i	$0.992692\pi$
$32$			1.91338i			0.338241i
$33$		0			0
$34$	−3.41167	+	3.41167i	−0.585096	+	0.585096i
$35$	−0.484925	+	0.242222i	−0.0819673	+	0.0409431i
$36$		0			0
$37$	3.31881			0.545609			0.272805	−	0.962069i	$-0.412049\pi$
$37$	3.31881			0.545609			0.272805	+	0.962069i	$0.412049\pi$
$38$	9.73467	−	9.73467i	1.57917	−	1.57917i
$39$		0			0
$40$	−5.42651	−	10.8638i	−0.858007	−	1.71771i
$41$	1.51472	−	1.51472i	0.236559	−	0.236559i	−0.578865	−	0.815424i	$-0.696504\pi$
$41$	1.51472	−	1.51472i	0.236559	−	0.236559i	0.815424	+	0.578865i	$0.196504\pi$
$42$		0			0
$43$	3.88596	−	3.88596i	0.592603	−	0.592603i	−0.345731	−	0.938334i	$-0.612369\pi$
$43$	3.88596	−	3.88596i	0.592603	−	0.592603i	0.938334	+	0.345731i	$0.112369\pi$
$44$	−17.7420	−	17.7420i	−2.67471	−	2.67471i
$45$		0			0
$46$	−4.73652	−	4.73652i	−0.698362	−	0.698362i
$47$	1.68447			0.245706			0.122853	−	0.992425i	$-0.460796\pi$
$47$	1.68447			0.245706			0.122853	+	0.992425i	$0.460796\pi$
$48$		0			0
$49$	−6.94124			−0.991605
$50$	9.94107	+	7.46811i	1.40588	+	1.05615i
$51$		0			0
$52$	−11.7858	−	9.41597i	−1.63440	−	1.30576i
$53$	2.22339	+	2.22339i	0.305406	+	0.305406i	0.843125	−	0.537718i	$-0.180714\pi$
$53$	2.22339	+	2.22339i	0.305406	+	0.305406i	−0.537718	+	0.843125i	$0.680714\pi$
$54$		0			0
$55$	12.7199	+	4.24558i	1.71516	+	0.572474i
$56$			1.31651i			0.175926i
$57$		0			0
$58$	−14.3483			−1.88403
$59$	−5.27843	+	5.27843i	−0.687193	+	0.687193i	−0.961611	−	0.274418i	$-0.911515\pi$
$59$	−5.27843	+	5.27843i	−0.687193	+	0.687193i	0.274418	+	0.961611i	$0.411515\pi$
$60$		0			0
$61$	10.2486			1.31220			0.656101	−	0.754673i	$-0.272204\pi$
$61$	10.2486			1.31220			0.656101	+	0.754673i	$0.272204\pi$
$62$	−14.1598	−	14.1598i	−1.79830	−	1.79830i
$63$		0			0
$64$	5.51638			0.689548
$65$	7.88373	+	1.68723i	0.977857	+	0.209275i
$66$		0			0
$67$		−	15.3086i		−	1.87024i	−0.354328	−	0.935121i	$-0.615290\pi$
$67$		−	15.3086i		−	1.87024i	0.354328	−	0.935121i	$-0.384710\pi$
$68$	−5.74007	−	5.74007i	−0.696086	−	0.696086i
$69$		0			0
$70$	−0.602346	−	1.20588i	−0.0719941	−	0.144131i
$71$	0.0780456	−	0.0780456i	0.00926231	−	0.00926231i	−0.702460	−	0.711723i	$-0.747915\pi$
$71$	0.0780456	−	0.0780456i	0.00926231	−	0.00926231i	0.711723	+	0.702460i	$0.247915\pi$
$72$		0			0
$73$		−	1.45403i		−	0.170181i	−0.996373	−	0.0850905i	$-0.972882\pi$
$73$		−	1.45403i		−	0.170181i	0.996373	−	0.0850905i	$-0.0271179\pi$
$74$			8.25304i			0.959397i
$75$		0			0
$76$	16.3784	+	16.3784i	1.87873	+	1.87873i
$77$	−1.02797	−	1.02797i	−0.117148	−	0.117148i
$78$		0			0
$79$			7.60135i			0.855219i	0.903964	+	0.427609i	$0.140644\pi$
$79$			7.60135i			0.855219i	−0.903964	+	0.427609i	$0.859356\pi$
$80$	10.2765	−	5.13317i	1.14895	−	0.573906i
$81$		0			0
$82$	3.76672	+	3.76672i	0.415964	+	0.415964i
$83$	−2.71964			−0.298520			−0.149260	−	0.988798i	$-0.547689\pi$
$83$	−2.71964			−0.298520			−0.149260	+	0.988798i	$0.547689\pi$
$84$		0			0
$85$	4.11528	+	1.37357i	0.446365	+	0.148985i
$86$	9.66338	+	9.66338i	1.04203	+	1.04203i
$87$		0			0
$88$	23.0296	−	23.0296i	2.45496	−	2.45496i
$89$	−0.887120	+	0.887120i	−0.0940345	+	0.0940345i	−0.752559	−	0.658525i	$-0.771181\pi$
$89$	−0.887120	+	0.887120i	−0.0940345	+	0.0940345i	0.658525	+	0.752559i	$0.271181\pi$
$90$		0			0
$91$	−0.682867	−	0.545559i	−0.0715839	−	0.0571902i
$92$	7.96910	−	7.96910i	0.830837	−	0.830837i
$93$		0			0
$94$			4.18886i			0.432048i
$95$	−11.7423	−	3.91927i	−1.20474	−	0.402109i
$96$		0			0
$97$			4.76021i			0.483326i	0.970360	+	0.241663i	$0.0776929\pi$
$97$			4.76021i			0.483326i	−0.970360	+	0.241663i	$0.922307\pi$
$98$		−	17.2611i		−	1.74363i
$99$		0			0
$100$	−12.5650	+	16.7257i	−1.25650	+	1.67257i
$101$		−	11.2837i		−	1.12277i	−0.827553	−	0.561387i	$-0.810268\pi$
$101$		−	11.2837i		−	1.12277i	0.827553	−	0.561387i	$-0.189732\pi$
$102$		0			0
$103$	9.85776	−	9.85776i	0.971314	−	0.971314i	−0.0282861	−	0.999600i	$-0.509005\pi$
$103$	9.85776	−	9.85776i	0.971314	−	0.971314i	0.999600	+	0.0282861i	$0.00900494\pi$
$104$	12.2222	−	15.2983i	1.19848	−	1.50012i
$105$		0			0
$106$	−5.52901	+	5.52901i	−0.537025	+	0.537025i
$107$	4.00248	−	4.00248i	0.386934	−	0.386934i	−0.486658	−	0.873592i	$-0.661784\pi$
$107$	4.00248	−	4.00248i	0.386934	−	0.386934i	0.873592	+	0.486658i	$0.161784\pi$
$108$		0			0
$109$	−4.59552	−	4.59552i	−0.440171	−	0.440171i	0.451899	−	0.892069i	$-0.350747\pi$
$109$	−4.59552	−	4.59552i	−0.440171	−	0.440171i	−0.892069	+	0.451899i	$0.850747\pi$
$110$	−10.5577	+	31.6313i	−1.00663	+	3.01592i
$111$		0			0
$112$	−1.24534			−0.117674
$113$	−12.3277	−	12.3277i	−1.15969	−	1.15969i	−0.984542	−	0.175149i	$-0.943959\pi$
$113$	−12.3277	−	12.3277i	−1.15969	−	1.15969i	−0.175149	−	0.984542i	$-0.556041\pi$
$114$		0			0
$115$	−1.90697	+	5.71336i	−0.177826	+	0.532774i
$116$		−	24.1408i		−	2.24142i
$117$		0			0
$118$	−13.1261	−	13.1261i	−1.20836	−	1.20836i
$119$	−0.332578	−	0.332578i	−0.0304874	−	0.0304874i
$120$		0			0
$121$			24.9644i			2.26949i
$122$			25.4857i			2.30737i
$123$		0			0
$124$	23.8236	−	23.8236i	2.13942	−	2.13942i
$125$	2.01306	−	10.9976i	0.180054	−	0.983657i
$126$		0			0
$127$	−3.83744	−	3.83744i	−0.340518	−	0.340518i	0.516044	−	0.856562i	$-0.327404\pi$
$127$	−3.83744	−	3.83744i	−0.340518	−	0.340518i	−0.856562	+	0.516044i	$0.827404\pi$
$128$			17.5446i			1.55074i
$129$		0			0
$130$	−4.19571	+	19.6048i	−0.367988	+	1.71946i
$131$	5.03941			0.440295			0.220148	−	0.975467i	$-0.429346\pi$
$131$	5.03941			0.440295			0.220148	+	0.975467i	$0.429346\pi$
$132$		0			0
$133$	0.948961	+	0.948961i	0.0822854	+	0.0822854i
$134$	38.0686			3.28862
$135$		0			0
$136$	7.45075	−	7.45075i	0.638897	−	0.638897i
$137$	13.3951			1.14442			0.572209	−	0.820108i	$-0.306087\pi$
$137$	13.3951			1.14442			0.572209	+	0.820108i	$0.306087\pi$
$138$		0			0
$139$		−	6.03788i		−	0.512126i	−0.966660	−	0.256063i	$-0.917575\pi$
$139$		−	6.03788i		−	0.512126i	0.966660	−	0.256063i	$-0.0824255\pi$
$140$	2.02888	−	1.01344i	0.171472	−	0.0856509i
$141$		0			0
$142$	0.194080	+	0.194080i	0.0162868	+	0.0162868i
$143$	2.40191	+	21.4888i	0.200858	+	1.79698i
$144$		0			0
$145$	5.76535	+	11.5421i	0.478786	+	0.958521i
$146$	3.61579			0.299245
$147$		0			0
$148$	−13.8856			−1.14139
$149$	14.7948	+	14.7948i	1.21203	+	1.21203i	0.970356	+	0.241678i	$0.0776979\pi$
$149$	14.7948	+	14.7948i	1.21203	+	1.21203i	0.241678	+	0.970356i	$0.422302\pi$
$150$		0			0
$151$	−14.6792	−	14.6792i	−1.19458	−	1.19458i	−0.975768	−	0.218808i	$-0.929783\pi$
$151$	−14.6792	−	14.6792i	−1.19458	−	1.19458i	−0.218808	−	0.975768i	$-0.570217\pi$
$152$	−21.2596	+	21.2596i	−1.72438	+	1.72438i
$153$		0			0
$154$	2.55630	−	2.55630i	0.205992	−	0.205992i
$155$	−5.70087	+	17.0801i	−0.457905	+	1.37190i
$156$		0			0
$157$	4.26691	−	4.26691i	0.340537	−	0.340537i	−0.516032	−	0.856569i	$-0.672592\pi$
$157$	4.26691	−	4.26691i	0.340537	−	0.340537i	0.856569	+	0.516032i	$0.172592\pi$
$158$	−18.9026			−1.50381
$159$		0			0
$160$	1.91187	+	3.82752i	0.151146	+	0.302592i
$161$	0.461728	−	0.461728i	0.0363893	−	0.0363893i
$162$		0			0
$163$			14.7233i			1.15322i	0.817019	+	0.576611i	$0.195625\pi$
$163$			14.7233i			1.15322i	−0.817019	+	0.576611i	$0.804375\pi$
$164$	−6.33743	+	6.33743i	−0.494870	+	0.494870i
$165$		0			0
$166$		−	6.76306i		−	0.524915i
$167$	−6.08556			−0.470915			−0.235457	−	0.971885i	$-0.575659\pi$
$167$	−6.08556			−0.470915			−0.235457	+	0.971885i	$0.575659\pi$
$168$		0			0
$169$	2.87029	+	12.6792i	0.220791	+	0.975321i
$170$	−3.41572	+	10.2337i	−0.261974	+	0.784886i
$171$		0			0
$172$	−16.2585	+	16.2585i	−1.23970	+	1.23970i
$173$	11.3322	−	11.3322i	0.861570	−	0.861570i	−0.129951	−	0.991520i	$-0.541482\pi$
$173$	11.3322	−	11.3322i	0.861570	−	0.861570i	0.991520	+	0.129951i	$0.0414819\pi$
$174$		0			0
$175$	−0.728011	+	0.969082i	−0.0550324	+	0.0732557i
$176$	21.7847	+	21.7847i	1.64208	+	1.64208i
$177$		0			0
$178$	−2.20604	−	2.20604i	−0.165350	−	0.165350i
$179$	−3.99730			−0.298772			−0.149386	−	0.988779i	$-0.547730\pi$
$179$	−3.99730			−0.298772			−0.149386	+	0.988779i	$0.547730\pi$
$180$		0			0
$181$		−	16.5433i		−	1.22966i	−0.788661	−	0.614828i	$-0.789226\pi$
$181$		−	16.5433i		−	1.22966i	0.788661	−	0.614828i	$-0.210774\pi$
$182$	1.35667	−	1.69812i	0.100563	−	0.125873i
$183$		0			0
$184$	10.3441	+	10.3441i	0.762577	+	0.762577i
$185$	6.63894	−	3.31618i	0.488104	−	0.243811i
$186$		0			0
$187$			11.6355i			0.850876i
$188$	−7.04768			−0.514005
$189$		0			0
$190$	9.74624	−	29.2002i	0.707066	−	2.11840i
$191$	−13.0425			−0.943721			−0.471860	−	0.881673i	$-0.656417\pi$
$191$	−13.0425			−0.943721			−0.471860	+	0.881673i	$0.656417\pi$
$192$		0			0
$193$		−	9.28317i		−	0.668217i	−0.942535	−	0.334109i	$-0.891565\pi$
$193$		−	9.28317i		−	0.668217i	0.942535	−	0.334109i	$-0.108435\pi$
$194$	−11.8374			−0.849879
$195$		0			0
$196$	29.0415			2.07439
$197$		−	12.9124i		−	0.919967i	−0.887927	−	0.459983i	$-0.847855\pi$
$197$		−	12.9124i		−	0.919967i	0.887927	−	0.459983i	$-0.152145\pi$
$198$		0			0
$199$	2.35534			0.166966			0.0834830	−	0.996509i	$-0.473396\pi$
$199$	2.35534			0.166966			0.0834830	+	0.996509i	$0.473396\pi$
$200$	−21.7103	−	16.3096i	−1.53515	−	1.15326i
$201$		0			0
$202$	28.0598			1.97428
$203$		−	1.39871i		−	0.0981703i
$204$		0			0
$205$	1.51652	−	4.54355i	0.105918	−	0.317336i
$206$	24.5137	+	24.5137i	1.70795	+	1.70795i
$207$		0			0
$208$	14.4713	+	11.5615i	1.00340	+	0.801644i
$209$		−	33.2003i		−	2.29651i
$210$		0			0
$211$	−21.9810			−1.51323			−0.756617	−	0.653858i	$-0.773149\pi$
$211$	−21.9810			−1.51323			−0.756617	+	0.653858i	$0.773149\pi$
$212$	−9.30245	−	9.30245i	−0.638895	−	0.638895i
$213$		0			0
$214$	9.95315	+	9.95315i	0.680383	+	0.680383i
$215$	3.89057	−	11.6563i	0.265335	−	0.794955i
$216$		0			0
$217$	1.38033	−	1.38033i	0.0937032	−	0.0937032i
$218$	11.4279	−	11.4279i	0.773993	−	0.773993i
$219$		0			0
$220$	−53.2190	−	17.7631i	−3.58802	−	1.19759i
$221$	0.777089	+	6.95226i	0.0522727	+	0.467660i
$222$		0			0
$223$	−8.72020			−0.583948			−0.291974	−	0.956426i	$-0.594312\pi$
$223$	−8.72020			−0.583948			−0.291974	+	0.956426i	$0.594312\pi$
$224$		−	0.463831i		−	0.0309910i
$225$		0			0
$226$	30.6558	−	30.6558i	2.03919	−	2.03919i
$227$		−	18.3913i		−	1.22068i	−0.792141	−	0.610338i	$-0.791034\pi$
$227$		−	18.3913i		−	1.22068i	0.792141	−	0.610338i	$-0.208966\pi$
$228$		0			0
$229$	16.7151	−	16.7151i	1.10456	−	1.10456i	0.110712	−	0.993852i	$-0.464687\pi$
$229$	16.7151	−	16.7151i	1.10456	−	1.10456i	0.993852	−	0.110712i	$-0.0353133\pi$
$230$	−14.2077	−	4.74214i	−0.936827	−	0.312688i
$231$		0			0
$232$	31.3353			2.05727
$233$	−0.600932	+	0.600932i	−0.0393684	+	0.0393684i	−0.726517	−	0.687149i	$-0.758862\pi$
$233$	−0.600932	+	0.600932i	−0.0393684	+	0.0393684i	0.687149	+	0.726517i	$0.258862\pi$
$234$		0			0
$235$	3.36962	−	1.68314i	0.219809	−	0.109796i
$236$	22.0844	−	22.0844i	1.43757	−	1.43757i
$237$		0			0
$238$	0.827038	−	0.827038i	0.0536089	−	0.0536089i
$239$	8.71291	+	8.71291i	0.563591	+	0.563591i	0.930326	−	0.366735i	$-0.119524\pi$
$239$	8.71291	+	8.71291i	0.563591	+	0.563591i	−0.366735	+	0.930326i	$0.619524\pi$
$240$		0			0
$241$	−6.37606	−	6.37606i	−0.410718	−	0.410718i	0.471271	−	0.881989i	$-0.343796\pi$
$241$	−6.37606	−	6.37606i	−0.410718	−	0.410718i	−0.881989	+	0.471271i	$0.843796\pi$
$242$	−62.0801			−3.99066
$243$		0			0
$244$	−42.8793			−2.74506
$245$	−13.8852	+	6.93574i	−0.887094	+	0.443108i
$246$		0			0
$247$	−2.21730	−	19.8372i	−0.141084	−	1.26221i
$248$	30.9236	+	30.9236i	1.96365	+	1.96365i
$249$		0			0
$250$	27.3483	+	5.00598i	1.72966	+	0.316606i
$251$			8.17534i			0.516023i	0.966142	+	0.258011i	$0.0830672\pi$
$251$			8.17534i			0.516023i	−0.966142	+	0.258011i	$0.916933\pi$
$252$		0			0
$253$	−16.1540			−1.01559
$254$	9.54274	−	9.54274i	0.598765	−	0.598765i
$255$		0			0
$256$	−32.5962			−2.03726
$257$	9.97233	+	9.97233i	0.622057	+	0.622057i	0.946057	−	0.324000i	$-0.105028\pi$
$257$	9.97233	+	9.97233i	0.622057	+	0.622057i	−0.324000	+	0.946057i	$0.605028\pi$
$258$		0			0
$259$	−0.804528			−0.0499909
$260$	−32.9848	−	7.05920i	−2.04563	−	0.437793i
$261$		0			0
$262$			12.5317i			0.774212i
$263$	−16.5535	−	16.5535i	−1.02073	−	1.02073i	−0.999780	−	0.0209533i	$-0.993330\pi$
$263$	−16.5535	−	16.5535i	−1.02073	−	1.02073i	−0.0209533	−	0.999780i	$-0.506670\pi$
$264$		0			0
$265$	6.66929	+	2.22603i	0.409691	+	0.136744i
$266$	−2.35983	+	2.35983i	−0.144690	+	0.144690i
$267$		0			0
$268$			64.0497i			3.91246i
$269$		−	16.7169i		−	1.01925i	−0.860397	−	0.509625i	$-0.829784\pi$
$269$		−	16.7169i		−	1.01925i	0.860397	−	0.509625i	$-0.170216\pi$
$270$		0			0
$271$	12.5904	+	12.5904i	0.764814	+	0.764814i	0.977188	−	0.212374i	$-0.0681195\pi$
$271$	12.5904	+	12.5904i	0.764814	+	0.764814i	−0.212374	+	0.977188i	$0.568120\pi$
$272$	7.04799	+	7.04799i	0.427347	+	0.427347i
$273$		0			0
$274$			33.3101i			2.01234i
$275$	29.6871	−	4.21704i	1.79020	−	0.254297i
$276$		0			0
$277$	−17.8939	−	17.8939i	−1.07514	−	1.07514i	−0.996937	−	0.0782056i	$-0.975081\pi$
$277$	−17.8939	−	17.8939i	−1.07514	−	1.07514i	−0.0782056	−	0.996937i	$-0.524919\pi$
$278$	15.0147			0.900520
$279$		0			0
$280$	1.31546	+	2.63353i	0.0786140	+	0.157384i
$281$	2.64673	+	2.64673i	0.157891	+	0.157891i	0.781631	−	0.623741i	$-0.214388\pi$
$281$	2.64673	+	2.64673i	0.157891	+	0.157891i	−0.623741	+	0.781631i	$0.714388\pi$
$282$		0			0
$283$	2.64156	−	2.64156i	0.157025	−	0.157025i	−0.624222	−	0.781247i	$-0.714584\pi$
$283$	2.64156	−	2.64156i	0.157025	−	0.157025i	0.781247	+	0.624222i	$0.214584\pi$
$284$	−0.326535	+	0.326535i	−0.0193763	+	0.0193763i
$285$		0			0
$286$	−53.4371	+	5.97293i	−3.15980	+	0.353187i
$287$	−0.367189	+	0.367189i	−0.0216745	+	0.0216745i
$288$		0			0
$289$		−	13.2356i		−	0.778562i
$290$	−28.7023	+	14.3370i	−1.68546	+	0.841895i
$291$		0			0
$292$			6.08351i			0.356010i
$293$			8.87232i			0.518327i	0.965834	+	0.259163i	$0.0834468\pi$
$293$			8.87232i			0.518327i	−0.965834	+	0.259163i	$0.916553\pi$
$294$		0			0
$295$	−5.28469	+	15.8332i	−0.307687	+	0.921844i
$296$		−	18.0238i		−	1.04761i
$297$		0			0
$298$	−36.7908	+	36.7908i	−2.13124	+	2.13124i
$299$	−9.65203	+	1.07885i	−0.558191	+	0.0623918i
$300$		0			0
$301$	−0.942012	+	0.942012i	−0.0542966	+	0.0542966i
$302$	36.5034	−	36.5034i	2.10054	−	2.10054i
$303$		0			0
$304$	−20.1104	−	20.1104i	−1.15341	−	1.15341i
$305$	20.5013	−	10.2405i	1.17390	−	0.586370i
$306$		0			0
$307$	25.1833			1.43729			0.718644	−	0.695378i	$-0.244763\pi$
$307$	25.1833			1.43729			0.718644	+	0.695378i	$0.244763\pi$
$308$	4.30092	+	4.30092i	0.245068	+	0.245068i
$309$		0			0
$310$	−42.4738	−	14.1766i	−2.41235	−	0.805178i
$311$			7.05837i			0.400243i	0.979771	+	0.200122i	$0.0641337\pi$
$311$			7.05837i			0.400243i	−0.979771	+	0.200122i	$0.935866\pi$
$312$		0			0
$313$	−3.85568	−	3.85568i	−0.217936	−	0.217936i	0.589692	−	0.807628i	$-0.299249\pi$
$313$	−3.85568	−	3.85568i	−0.217936	−	0.217936i	−0.807628	+	0.589692i	$0.799249\pi$
$314$	10.6107	+	10.6107i	0.598798	+	0.598798i
$315$		0			0
$316$		−	31.8033i		−	1.78908i
$317$			13.9177i			0.781695i	0.920456	+	0.390847i	$0.127818\pi$
$317$			13.9177i			0.781695i	−0.920456	+	0.390847i	$0.872182\pi$
$318$		0			0
$319$	−24.4676	+	24.4676i	−1.36992	+	1.36992i
$320$	11.0350	−	5.51202i	0.616873	−	0.308131i
$321$		0			0
$322$	1.14820	+	1.14820i	0.0639867	+	0.0639867i
$323$		−	10.7413i		−	0.597660i
$324$		0			0
$325$	17.4565	−	4.50236i	0.968311	−	0.249746i
$326$	−36.6132			−2.02782
$327$		0			0
$328$	−8.22614	−	8.22614i	−0.454213	−	0.454213i
$329$	−0.408341			−0.0225126
$330$		0			0
$331$	−6.88277	+	6.88277i	−0.378311	+	0.378311i	−0.870493	−	0.492181i	$-0.836200\pi$
$331$	−6.88277	+	6.88277i	−0.378311	+	0.378311i	0.492181	+	0.870493i	$0.336200\pi$
$332$	11.3787			0.624489
$333$		0			0
$334$		−	15.1332i		−	0.828054i
$335$	−15.2965	−	30.6232i	−0.835736	−	1.67313i
$336$		0			0
$337$	0.812119	+	0.812119i	0.0442389	+	0.0442389i	0.728880	−	0.684641i	$-0.240041\pi$
$337$	0.812119	+	0.812119i	0.0442389	+	0.0442389i	−0.684641	+	0.728880i	$0.740041\pi$
$338$	−31.5299	+	7.13768i	−1.71500	+	0.388238i
$339$		0			0
$340$	−17.2179	−	5.74689i	−0.933774	−	0.311669i
$341$	−48.2922			−2.61517
$342$		0			0
$343$	3.37956			0.182479
$344$	−21.1039	−	21.1039i	−1.13785	−	1.13785i
$345$		0			0
$346$	28.1803	+	28.1803i	1.51498	+	1.51498i
$347$	−25.2146	+	25.2146i	−1.35359	+	1.35359i	−0.471983	+	0.881608i	$0.656462\pi$
$347$	−25.2146	+	25.2146i	−1.35359	+	1.35359i	−0.881608	+	0.471983i	$0.843538\pi$
$348$		0			0
$349$	4.85536	−	4.85536i	0.259902	−	0.259902i	−0.565112	−	0.825014i	$-0.691167\pi$
$349$	4.85536	−	4.85536i	0.259902	−	0.259902i	0.825014	+	0.565112i	$0.191167\pi$
$350$	−2.40986	−	1.81038i	−0.128812	−	0.0967688i
$351$		0			0
$352$	−8.11377	+	8.11377i	−0.432465	+	0.432465i
$353$	−25.9459			−1.38096			−0.690480	−	0.723351i	$-0.742601\pi$
$353$	−25.9459			−1.38096			−0.690480	+	0.723351i	$0.742601\pi$
$354$		0			0
$355$	0.0781383	−	0.234106i	0.00414715	−	0.0124250i
$356$	3.71162	−	3.71162i	0.196716	−	0.196716i
$357$		0			0
$358$		−	9.94027i		−	0.525359i
$359$	2.31461	−	2.31461i	0.122160	−	0.122160i	−0.643384	−	0.765544i	$-0.722470\pi$
$359$	2.31461	−	2.31461i	0.122160	−	0.122160i	0.765544	+	0.643384i	$0.222470\pi$
$360$		0			0
$361$			11.6486i			0.613083i
$362$	41.1390			2.16222
$363$		0			0
$364$	2.85705	+	2.28257i	0.149750	+	0.119639i
$365$	−1.45287	−	2.90863i	−0.0760470	−	0.152245i
$366$		0			0
$367$	10.2557	−	10.2557i	0.535346	−	0.535346i	−0.386813	−	0.922158i	$-0.626424\pi$
$367$	10.2557	−	10.2557i	0.535346	−	0.535346i	0.922158	+	0.386813i	$0.126424\pi$
$368$	−9.78493	+	9.78493i	−0.510075	+	0.510075i
$369$		0			0
$370$	8.24651	+	16.5094i	0.428715	+	0.858280i
$371$	−0.538982	−	0.538982i	−0.0279826	−	0.0279826i
$372$		0			0
$373$	5.33438	+	5.33438i	0.276204	+	0.276204i	0.831592	−	0.555388i	$-0.187430\pi$
$373$	5.33438	+	5.33438i	0.276204	+	0.276204i	−0.555388	+	0.831592i	$0.687430\pi$
$374$	−28.9346			−1.49618
$375$		0			0
$376$		−	9.14806i		−	0.471775i
$377$	−12.9853	+	16.2535i	−0.668779	+	0.837098i
$378$		0			0
$379$	4.89160	+	4.89160i	0.251265	+	0.251265i	0.821489	−	0.570224i	$-0.193144\pi$
$379$	4.89160	+	4.89160i	0.251265	+	0.251265i	−0.570224	+	0.821489i	$0.693144\pi$
$380$	49.1287	+	16.3979i	2.52025	+	0.841193i
$381$		0			0
$382$		−	32.4333i		−	1.65943i
$383$	−0.331496			−0.0169386			−0.00846932	−	0.999964i	$-0.502696\pi$
$383$	−0.331496			−0.0169386			−0.00846932	+	0.999964i	$0.502696\pi$
$384$		0			0
$385$	−3.08350	−	1.02919i	−0.157150	−	0.0524523i
$386$	23.0849			1.17499
$387$		0			0
$388$		−	19.9163i		−	1.01110i
$389$	−6.77907			−0.343713			−0.171856	−	0.985122i	$-0.554976\pi$
$389$	−6.77907			−0.343713			−0.171856	+	0.985122i	$0.554976\pi$
$390$		0			0
$391$	−5.22629			−0.264305
$392$			37.6965i			1.90396i
$393$		0			0
$394$	32.1097			1.61766
$395$	7.59533	+	15.2057i	0.382162	+	0.765082i
$396$		0			0
$397$	25.7273			1.29121			0.645607	−	0.763670i	$-0.276604\pi$
$397$	25.7273			1.29121			0.645607	+	0.763670i	$0.276604\pi$
$398$			5.85714i			0.293592i
$399$		0			0
$400$	15.4280	−	20.5367i	0.771399	−	1.02684i
$401$	−7.72622	−	7.72622i	−0.385829	−	0.385829i	0.487368	−	0.873197i	$-0.337957\pi$
$401$	−7.72622	−	7.72622i	−0.385829	−	0.385829i	−0.873197	+	0.487368i	$0.837957\pi$
$402$		0			0
$403$	−28.8547	+	3.22523i	−1.43735	+	0.160660i
$404$			47.2101i			2.34879i
$405$		0			0
$406$	3.47824			0.172622
$407$	14.0736	+	14.0736i	0.697601	+	0.697601i
$408$		0			0
$409$	7.15874	+	7.15874i	0.353977	+	0.353977i	0.861587	−	0.507610i	$-0.169471\pi$
$409$	7.15874	+	7.15874i	0.353977	+	0.353977i	−0.507610	+	0.861587i	$0.669471\pi$
$410$	11.2987	+	3.77119i	0.558001	+	0.186246i
$411$		0			0
$412$	−41.2439	+	41.2439i	−2.03194	+	2.03194i
$413$	1.27957	−	1.27957i	0.0629634	−	0.0629634i
$414$		0			0
$415$	−5.44036	+	2.71749i	−0.267057	+	0.133396i
$416$	−4.30611	+	5.38988i	−0.211124	+	0.264260i
$417$		0			0
$418$	82.5606			4.03817
$419$		−	23.1087i		−	1.12894i	−0.825455	−	0.564468i	$-0.809081\pi$
$419$		−	23.1087i		−	1.12894i	0.825455	−	0.564468i	$-0.190919\pi$
$420$		0			0
$421$	−0.323390	+	0.323390i	−0.0157611	+	0.0157611i	−0.714943	−	0.699182i	$-0.753548\pi$
$421$	−0.323390	+	0.323390i	−0.0157611	+	0.0157611i	0.699182	+	0.714943i	$0.253548\pi$
$422$		−	54.6612i		−	2.66086i
$423$		0			0
$424$	12.0748	−	12.0748i	0.586405	−	0.586405i
$425$	9.60467	−	1.36434i	0.465895	−	0.0661800i
$426$		0			0
$427$	−2.48442			−0.120229
$428$	−16.7460	+	16.7460i	−0.809448	+	0.809448i
$429$		0			0
$430$	28.9863	+	9.67486i	1.39784	+	0.466563i
$431$	−1.67187	+	1.67187i	−0.0805312	+	0.0805312i	−0.746225	−	0.665694i	$-0.768136\pi$
$431$	−1.67187	+	1.67187i	−0.0805312	+	0.0805312i	0.665694	+	0.746225i	$0.268136\pi$
$432$		0			0
$433$	10.8483	−	10.8483i	0.521337	−	0.521337i	−0.396638	−	0.917975i	$-0.629823\pi$
$433$	10.8483	−	10.8483i	0.521337	−	0.521337i	0.917975	+	0.396638i	$0.129823\pi$
$434$	3.43254	+	3.43254i	0.164767	+	0.164767i
$435$		0			0
$436$	19.2272	+	19.2272i	0.920815	+	0.920815i
$437$	14.9124			0.713358
$438$		0			0
$439$	−20.2491			−0.966437			−0.483219	−	0.875500i	$-0.660532\pi$
$439$	−20.2491			−0.966437			−0.483219	+	0.875500i	$0.660532\pi$
$440$	23.0569	−	69.0796i	1.09920	−	3.29324i
$441$		0			0
$442$	−17.2885	+	1.93242i	−0.822330	+	0.0919159i
$443$	13.2900	+	13.2900i	0.631425	+	0.631425i	0.948426	−	0.317000i	$-0.102676\pi$
$443$	13.2900	+	13.2900i	0.631425	+	0.631425i	−0.317000	+	0.948426i	$0.602676\pi$
$444$		0			0
$445$	−0.888174	+	2.66101i	−0.0421035	+	0.126144i
$446$		−	21.6849i		−	1.02681i
$447$		0			0
$448$	−1.33725			−0.0631792
$449$	−23.3059	+	23.3059i	−1.09988	+	1.09988i	−0.105451	+	0.994425i	$0.533628\pi$
$449$	−23.3059	+	23.3059i	−1.09988	+	1.09988i	−0.994425	+	0.105451i	$0.966372\pi$
$450$		0			0
$451$	12.8464			0.604916
$452$	51.5778	+	51.5778i	2.42602	+	2.42602i
$453$		0			0
$454$	45.7346			2.14643
$455$	−1.91113	−	0.409009i	−0.0895952	−	0.0191746i
$456$		0			0
$457$			15.5860i			0.729085i	0.931187	+	0.364542i	$0.118775\pi$
$457$			15.5860i			0.729085i	−0.931187	+	0.364542i	$0.881225\pi$
$458$	41.5662	+	41.5662i	1.94226	+	1.94226i
$459$		0			0
$460$	7.97857	−	23.9042i	0.372003	−	1.11454i
$461$	−20.8994	+	20.8994i	−0.973381	+	0.973381i	−0.999655	−	0.0262742i	$-0.991636\pi$
$461$	−20.8994	+	20.8994i	−0.973381	+	0.973381i	0.0262742	+	0.999655i	$0.491636\pi$
$462$		0			0
$463$		−	8.32123i		−	0.386720i	−0.981128	−	0.193360i	$-0.938061\pi$
$463$		−	8.32123i		−	0.386720i	0.981128	−	0.193360i	$-0.0619386\pi$
$464$			29.6414i			1.37607i
$465$		0			0
$466$	−1.49436	−	1.49436i	−0.0692251	−	0.0692251i
$467$	21.9600	+	21.9600i	1.01619	+	1.01619i	0.999867	+	0.0163185i	$0.00519457\pi$
$467$	21.9600	+	21.9600i	1.01619	+	1.01619i	0.0163185	+	0.999867i	$0.494805\pi$
$468$		0			0
$469$			3.71102i			0.171359i
$470$	4.18554	+	8.37937i	0.193065	+	0.386512i
$471$		0			0
$472$	28.6661	+	28.6661i	1.31947	+	1.31947i
$473$	32.9571			1.51537
$474$		0			0
$475$	−27.4055	+	3.89293i	−1.25745	+	0.178620i
$476$	1.39148	+	1.39148i	0.0637782	+	0.0637782i
$477$		0			0
$478$	−21.6668	+	21.6668i	−0.991015	+	0.991015i
$479$	−12.9813	+	12.9813i	−0.593132	+	0.593132i	−0.938476	−	0.345344i	$-0.887762\pi$
$479$	−12.9813	+	12.9813i	−0.593132	+	0.593132i	0.345344	+	0.938476i	$0.387762\pi$
$480$		0			0
$481$	9.34889	+	7.46907i	0.426273	+	0.340560i
$482$	15.8556	−	15.8556i	0.722204	−	0.722204i
$483$		0			0
$484$		−	104.449i		−	4.74766i
$485$	4.75644	+	9.52231i	0.215979	+	0.432386i
$486$		0			0
$487$		−	12.6406i		−	0.572801i	−0.958110	−	0.286400i	$-0.907541\pi$
$487$		−	12.6406i		−	0.572801i	0.958110	−	0.286400i	$-0.0924587\pi$
$488$		−	55.6584i		−	2.51954i
$489$		0			0
$490$	−17.2474	−	34.5290i	−0.779159	−	1.55986i
$491$			27.8197i			1.25549i	0.778421	+	0.627743i	$0.216021\pi$
$491$			27.8197i			1.25549i	−0.778421	+	0.627743i	$0.783979\pi$
$492$		0			0
$493$	−7.91599	+	7.91599i	−0.356518	+	0.356518i
$494$	49.3301	−	5.51387i	2.21947	−	0.248081i
$495$		0			0
$496$	−29.2520	+	29.2520i	−1.31345	+	1.31345i
$497$	−0.0189194	+	0.0189194i	−0.000848650	+	0.000848650i
$498$		0			0
$499$	0.152074	+	0.152074i	0.00680776	+	0.00680776i	0.710502	−	0.703695i	$-0.248468\pi$
$499$	0.152074	+	0.152074i	0.00680776	+	0.00680776i	−0.703695	+	0.710502i	$0.748468\pi$
$500$	−8.42246	+	46.0130i	−0.376664	+	2.05776i
$501$		0			0
$502$	−20.3300			−0.907372
$503$	4.59193	+	4.59193i	0.204744	+	0.204744i	0.802029	−	0.597285i	$-0.203754\pi$
$503$	4.59193	+	4.59193i	0.204744	+	0.204744i	−0.597285	+	0.802029i	$0.703754\pi$
$504$		0			0
$505$	−11.2748	−	22.5719i	−0.501722	−	1.00444i
$506$		−	40.1708i		−	1.78581i
$507$		0			0
$508$	16.0555	+	16.0555i	0.712347	+	0.712347i
$509$	11.1303	+	11.1303i	0.493341	+	0.493341i	0.909357	−	0.416016i	$-0.136574\pi$
$509$	11.1303	+	11.1303i	0.493341	+	0.493341i	−0.416016	+	0.909357i	$0.636574\pi$
$510$		0			0
$511$			0.352477i			0.0155927i
$512$		−	45.9692i		−	2.03157i
$513$		0			0
$514$	−24.7986	+	24.7986i	−1.09382	+	1.09382i
$515$	9.86947	−	29.5694i	0.434901	−	1.30298i
$516$		0			0
$517$	7.14308	+	7.14308i	0.314152	+	0.314152i
$518$		−	2.00066i		−	0.0879038i
$519$		0			0
$520$	9.16302	−	42.8151i	0.401825	−	1.87756i
$521$	13.6076			0.596161			0.298080	−	0.954541i	$-0.403654\pi$
$521$	13.6076			0.596161			0.298080	+	0.954541i	$0.403654\pi$
$522$		0			0
$523$	−12.9591	−	12.9591i	−0.566664	−	0.566664i	0.364528	−	0.931192i	$-0.381230\pi$
$523$	−12.9591	−	12.9591i	−0.566664	−	0.566664i	−0.931192	+	0.364528i	$0.881230\pi$
$524$	−21.0844			−0.921076
$525$		0			0
$526$	41.1644	−	41.1644i	1.79485	−	1.79485i
$527$	−15.6240			−0.680591
$528$		0			0
$529$			15.7442i			0.684530i
$530$	−5.53558	+	16.5848i	−0.240450	+	0.720399i
$531$		0			0
$532$	−3.97036	−	3.97036i	−0.172137	−	0.172137i
$533$	7.67577	−	0.857959i	0.332475	−	0.0371623i
$534$		0			0
$535$	4.00723	−	12.0059i	0.173248	−	0.519058i
$536$	−83.1381			−3.59102
$537$		0			0
$538$	41.5708			1.79224
$539$	−29.4346	−	29.4346i	−1.26784	−	1.26784i
$540$		0			0
$541$	−24.0220	−	24.0220i	−1.03279	−	1.03279i	−0.999444	−	0.0333420i	$-0.989385\pi$
$541$	−24.0220	−	24.0220i	−1.03279	−	1.03279i	−0.0333420	−	0.999444i	$-0.510615\pi$
$542$	−31.3092	+	31.3092i	−1.34485	+	1.34485i
$543$		0			0
$544$	−2.62505	+	2.62505i	−0.112548	+	0.112548i
$545$	−13.7847	−	4.60097i	−0.590473	−	0.197084i
$546$		0			0
$547$	−18.6456	+	18.6456i	−0.797229	+	0.797229i	−0.982658	−	0.185428i	$-0.940633\pi$
$547$	−18.6456	+	18.6456i	−0.797229	+	0.797229i	0.185428	+	0.982658i	$0.440633\pi$
$548$	−56.0437			−2.39407
$549$		0			0
$550$	10.4867	+	73.8244i	0.447154	+	3.14788i
$551$	22.5871	−	22.5871i	0.962241	−	0.962241i
$552$		0			0
$553$		−	1.84268i		−	0.0783586i
$554$	44.4977	−	44.4977i	1.89053	−	1.89053i
$555$		0			0
$556$			25.2619i			1.07134i
$557$	1.32872			0.0562996			0.0281498	−	0.999604i	$-0.491038\pi$
$557$	1.32872			0.0562996			0.0281498	+	0.999604i	$0.491038\pi$
$558$		0			0
$559$	19.6919	−	2.20106i	0.832880	−	0.0930951i
$560$	−2.49117	+	1.24435i	−0.105271	+	0.0525836i
$561$		0			0
$562$	−6.58175	+	6.58175i	−0.277634	+	0.277634i
$563$	15.2469	−	15.2469i	0.642582	−	0.642582i	−0.308607	−	0.951190i	$-0.599863\pi$
$563$	15.2469	−	15.2469i	0.642582	−	0.642582i	0.951190	+	0.308607i	$0.0998629\pi$
$564$		0			0
$565$	−36.9782	−	12.3423i	−1.55568	−	0.519246i
$566$	6.56889	+	6.56889i	0.276111	+	0.276111i
$567$		0			0
$568$	−0.423851	−	0.423851i	−0.0177844	−	0.0177844i
$569$	−31.7042			−1.32911			−0.664555	−	0.747239i	$-0.731379\pi$
$569$	−31.7042			−1.32911			−0.664555	+	0.747239i	$0.731379\pi$
$570$		0			0
$571$		−	3.77184i		−	0.157847i	−0.996881	−	0.0789233i	$-0.974852\pi$
$571$		−	3.77184i		−	0.157847i	0.996881	−	0.0789233i	$-0.0251482\pi$
$572$	−10.0493	−	89.9070i	−0.420184	−	3.75920i
$573$		0			0
$574$	−0.913107	−	0.913107i	−0.0381123	−	0.0381123i
$575$	1.89415	+	13.3344i	0.0789914	+	0.556085i
$576$		0			0
$577$			38.7401i			1.61277i	0.591391	+	0.806385i	$0.298579\pi$
$577$			38.7401i			1.61277i	−0.591391	+	0.806385i	$0.701421\pi$
$578$	32.9135			1.36902
$579$		0			0
$580$	−24.1217	−	48.2911i	−1.00160	−	2.00518i
$581$	0.659281			0.0273516
$582$		0			0
$583$			18.8568i			0.780967i
$584$	−7.89654			−0.326761
$585$		0			0
$586$	−22.0632			−0.911423
$587$			11.4947i			0.474438i	0.971456	+	0.237219i	$0.0762358\pi$
$587$			11.4947i			0.474438i	−0.971456	+	0.237219i	$0.923764\pi$
$588$		0			0
$589$	44.5806			1.83691
$590$	−39.3731	−	13.1417i	−1.62097	−	0.541035i
$591$		0			0
$592$	17.0495			0.700731
$593$			23.5194i			0.965824i	0.875669	+	0.482912i	$0.160421\pi$
$593$			23.5194i			0.965824i	−0.875669	+	0.482912i	$0.839579\pi$
$594$		0			0
$595$	−0.997603	−	0.332973i	−0.0408978	−	0.0136506i
$596$	−61.8999	−	61.8999i	−2.53552	−	2.53552i
$597$		0			0
$598$	−2.68284	−	24.0021i	−0.109709	−	0.981520i
$599$		−	15.0098i		−	0.613282i	−0.951825	−	0.306641i	$-0.900795\pi$
$599$		−	15.0098i		−	0.613282i	0.951825	−	0.306641i	$-0.0992051\pi$
$600$		0			0
$601$	−9.20174			−0.375347			−0.187673	−	0.982231i	$-0.560095\pi$
$601$	−9.20174			−0.375347			−0.187673	+	0.982231i	$0.560095\pi$
$602$	−2.34254	−	2.34254i	−0.0954749	−	0.0954749i
$603$		0			0
$604$	61.4163	+	61.4163i	2.49900	+	2.49900i
$605$	24.9446	+	49.9386i	1.01414	+	2.03029i
$606$		0			0
$607$	−1.90926	+	1.90926i	−0.0774945	+	0.0774945i	−0.744792	−	0.667297i	$-0.767451\pi$
$607$	−1.90926	+	1.90926i	−0.0774945	+	0.0774945i	0.667297	+	0.744792i	$0.267451\pi$
$608$	7.49017	−	7.49017i	0.303766	−	0.303766i
$609$		0			0
$610$	25.4656	+	50.9816i	1.03107	+	2.06418i
$611$	4.74506	+	3.79095i	0.191965	+	0.153365i
$612$		0			0
$613$	−8.40716			−0.339562			−0.169781	−	0.985482i	$-0.554306\pi$
$613$	−8.40716			−0.339562			−0.169781	+	0.985482i	$0.554306\pi$
$614$			62.6245i			2.52732i
$615$		0			0
$616$	−5.58270	+	5.58270i	−0.224933	+	0.224933i
$617$		−	5.02106i		−	0.202140i	−0.994879	−	0.101070i	$-0.967773\pi$
$617$		−	5.02106i		−	0.202140i	0.994879	−	0.101070i	$-0.0322267\pi$
$618$		0			0
$619$	−28.7489	+	28.7489i	−1.15552	+	1.15552i	−0.170089	+	0.985429i	$0.554405\pi$
$619$	−28.7489	+	28.7489i	−1.15552	+	1.15552i	−0.985429	+	0.170089i	$0.945595\pi$
$620$	23.8519	−	71.4614i	0.957915	−	2.86996i
$621$		0			0
$622$	−17.5524			−0.703786
$623$	0.215051	−	0.215051i	0.00861582	−	0.00861582i
$624$		0			0
$625$	−6.96198	−	24.0111i	−0.278479	−	0.960442i
$626$	9.58810	−	9.58810i	0.383218	−	0.383218i
$627$		0			0
$628$	−17.8524	+	17.8524i	−0.712386	+	0.712386i
$629$	4.55322	+	4.55322i	0.181549	+	0.181549i
$630$		0			0
$631$	21.7388	+	21.7388i	0.865407	+	0.865407i	0.991960	−	0.126553i	$-0.0403913\pi$
$631$	21.7388	+	21.7388i	0.865407	+	0.865407i	−0.126553	+	0.991960i	$0.540391\pi$
$632$	41.2815			1.64209
$633$		0			0
$634$	−34.6097			−1.37453
$635$	−11.5108	−	3.84200i	−0.456793	−	0.152465i
$636$		0			0
$637$	−19.5530	−	15.6214i	−0.774719	−	0.618943i
$638$	−60.8446	−	60.8446i	−2.40886	−	2.40886i
$639$		0			0
$640$	17.5307	+	35.0962i	0.692962	+	1.38730i
$641$		−	8.55187i		−	0.337779i	−0.985635	−	0.168889i	$-0.945982\pi$
$641$		−	8.55187i		−	0.337779i	0.985635	−	0.168889i	$-0.0540181\pi$
$642$		0			0
$643$	−3.11521			−0.122852			−0.0614259	−	0.998112i	$-0.519565\pi$
$643$	−3.11521			−0.122852			−0.0614259	+	0.998112i	$0.519565\pi$
$644$	−1.93183	+	1.93183i	−0.0761246	+	0.0761246i
$645$		0			0
$646$	26.7108			1.05092
$647$	−26.4560	−	26.4560i	−1.04009	−	1.04009i	−0.999162	−	0.0409311i	$-0.986968\pi$
$647$	−26.4560	−	26.4560i	−1.04009	−	1.04009i	−0.0409311	−	0.999162i	$-0.513032\pi$
$648$		0			0
$649$	−44.7668			−1.75725
$650$	11.1962	+	43.4098i	0.439152	+	1.70267i
$651$		0			0
$652$		−	61.6010i		−	2.41248i
$653$	9.61272	+	9.61272i	0.376175	+	0.376175i	0.869720	−	0.493545i	$-0.164299\pi$
$653$	9.61272	+	9.61272i	0.376175	+	0.376175i	−0.493545	+	0.869720i	$0.664299\pi$
$654$		0			0
$655$	10.0808	−	5.03542i	0.393890	−	0.196750i
$656$	7.78146	−	7.78146i	0.303815	−	0.303815i
$657$		0			0
$658$		−	1.01544i		−	0.0395860i
$659$			15.1490i			0.590122i	0.955478	+	0.295061i	$0.0953400\pi$
$659$			15.1490i			0.590122i	−0.955478	+	0.295061i	$0.904660\pi$
$660$		0			0
$661$	18.9976	+	18.9976i	0.738920	+	0.738920i	0.972369	−	0.233449i	$-0.0750013\pi$
$661$	18.9976	+	18.9976i	0.738920	+	0.738920i	−0.233449	+	0.972369i	$0.575001\pi$
$662$	−17.1157	−	17.1157i	−0.665220	−	0.665220i
$663$		0			0
$664$			14.7699i			0.573182i
$665$	2.84651	+	0.950089i	0.110383	+	0.0368429i
$666$		0			0
$667$	−10.9900	−	10.9900i	−0.425534	−	0.425534i
$668$	25.4614			0.985131
$669$		0			0
$670$	76.1522	−	38.0384i	2.94202	−	1.46955i
$671$	43.4597	+	43.4597i	1.67774	+	1.67774i
$672$		0			0
$673$	26.4650	−	26.4650i	1.02015	−	1.02015i	0.0203584	−	0.999793i	$-0.493519\pi$
$673$	26.4650	−	26.4650i	1.02015	−	1.02015i	0.999793	−	0.0203584i	$-0.00648074\pi$
$674$	−2.01953	+	2.01953i	−0.0777895	+	0.0777895i
$675$		0			0
$676$	−12.0090	−	53.0484i	−0.461885	−	2.04032i
$677$	13.7029	−	13.7029i	0.526645	−	0.526645i	−0.392925	−	0.919570i	$-0.628537\pi$
$677$	13.7029	−	13.7029i	0.526645	−	0.526645i	0.919570	+	0.392925i	$0.128537\pi$
$678$		0			0
$679$		−	1.15394i		−	0.0442843i
$680$	7.45960	−	22.3493i	0.286063	−	0.857057i
$681$		0			0
$682$		−	120.090i		−	4.59850i
$683$			14.6506i			0.560588i	0.959914	+	0.280294i	$0.0904320\pi$
$683$			14.6506i			0.560588i	−0.959914	+	0.280294i	$0.909568\pi$
$684$		0			0
$685$	26.7954	−	13.3845i	1.02380	−	0.511394i
$686$			8.40410i			0.320870i
$687$		0			0
$688$	19.9631	−	19.9631i	0.761085	−	0.761085i
$689$	1.25936	+	11.2670i	0.0479779	+	0.429237i
$690$		0			0
$691$	−34.7630	+	34.7630i	−1.32245	+	1.32245i	−0.410660	+	0.911789i	$0.634702\pi$
$691$	−34.7630	+	34.7630i	−1.32245	+	1.32245i	−0.911789	+	0.410660i	$0.865298\pi$
$692$	−47.4128	+	47.4128i	−1.80236	+	1.80236i
$693$		0			0
$694$	−62.7023	−	62.7023i	−2.38015	−	2.38015i
$695$	−6.03310	−	12.0781i	−0.228848	−	0.458150i
$696$		0			0
$697$	4.15621			0.157428
$698$	12.0740	+	12.0740i	0.457009	+	0.457009i
$699$		0			0
$700$	3.04593	−	4.05454i	0.115125	−	0.153247i
$701$		−	13.7058i		−	0.517659i	−0.965923	−	0.258830i	$-0.916663\pi$
$701$		−	13.7058i		−	0.517659i	0.965923	−	0.258830i	$-0.0833369\pi$
$702$		0			0
$703$	−12.9919	−	12.9919i	−0.489999	−	0.489999i
$704$	23.3925	+	23.3925i	0.881636	+	0.881636i
$705$		0			0
$706$		−	64.5208i		−	2.42827i
$707$			2.73534i			0.102873i
$708$		0			0
$709$	−4.33781	+	4.33781i	−0.162910	+	0.162910i	−0.783854	−	0.620945i	$-0.786749\pi$
$709$	−4.33781	+	4.33781i	−0.162910	+	0.162910i	0.620945	+	0.783854i	$0.286749\pi$
$710$	0.582162	+	0.194310i	0.0218481	+	0.00729232i
$711$		0			0
$712$	4.81778	+	4.81778i	0.180554	+	0.180554i
$713$		−	21.6912i		−	0.812342i
$714$		0			0
$715$	26.2765	+	40.5861i	0.982687	+	1.51783i
$716$	16.7243			0.625017
$717$		0			0
$718$	5.75584	+	5.75584i	0.214806	+	0.214806i
$719$	27.4328			1.02307			0.511536	−	0.859262i	$-0.329077\pi$
$719$	27.4328			1.02307			0.511536	+	0.859262i	$0.329077\pi$
$720$		0			0
$721$	−2.38966	+	2.38966i	−0.0889957	+	0.0889957i
$722$	−28.9670			−1.07804
$723$		0			0
$724$			69.2157i			2.57238i
$725$	23.0660	+	17.3280i	0.856648	+	0.643547i
$726$		0			0
$727$	27.8372	+	27.8372i	1.03243	+	1.03243i	0.999456	+	0.0329694i	$0.0104964\pi$
$727$	27.8372	+	27.8372i	1.03243	+	1.03243i	0.0329694	+	0.999456i	$0.489504\pi$
$728$	−2.96283	+	3.70852i	−0.109810	+	0.137447i
$729$		0			0
$730$	7.23302	−	3.61293i	0.267706	−	0.133721i
$731$	10.6626			0.394371
$732$		0			0
$733$	16.0974			0.594571			0.297285	−	0.954789i	$-0.403919\pi$
$733$	16.0974			0.594571			0.297285	+	0.954789i	$0.403919\pi$
$734$	25.5034	+	25.5034i	0.941349	+	0.941349i
$735$		0			0
$736$	−3.64443	−	3.64443i	−0.134335	−	0.134335i
$737$	64.9167	−	64.9167i	2.39124	−	2.39124i
$738$		0			0
$739$	−9.67318	+	9.67318i	−0.355834	+	0.355834i	−0.862275	−	0.506441i	$-0.830961\pi$
$739$	−9.67318	+	9.67318i	−0.355834	+	0.355834i	0.506441	+	0.862275i	$0.330961\pi$
$740$	−27.7767	+	13.8746i	−1.02109	+	0.510040i
$741$		0			0
$742$	1.34031	−	1.34031i	0.0492044	−	0.0492044i
$743$	0.660092			0.0242164			0.0121082	−	0.999927i	$-0.496146\pi$
$743$	0.660092			0.0242164			0.0121082	+	0.999927i	$0.496146\pi$
$744$		0			0
$745$	44.3784	+	14.8123i	1.62590	+	0.542682i
$746$	−13.2653	+	13.2653i	−0.485675	+	0.485675i
$747$		0			0
$748$		−	48.6820i		−	1.77999i
$749$	−0.970259	+	0.970259i	−0.0354525	+	0.0354525i
$750$		0			0
$751$		−	35.4818i		−	1.29475i	−0.762171	−	0.647375i	$-0.775867\pi$
$751$		−	35.4818i		−	1.29475i	0.762171	−	0.647375i	$-0.224133\pi$
$752$	8.65354			0.315562
$753$		0			0
$754$	−40.4183	−	32.2912i	−1.47195	−	1.17598i
$755$	−44.0318	−	14.6966i	−1.60248	−	0.534865i
$756$		0			0
$757$	10.5506	−	10.5506i	0.383469	−	0.383469i	−0.488881	−	0.872350i	$-0.662595\pi$
$757$	10.5506	−	10.5506i	0.383469	−	0.383469i	0.872350	+	0.488881i	$0.162595\pi$
$758$	−12.1642	+	12.1642i	−0.441823	+	0.441823i
$759$		0			0
$760$	−21.2848	+	63.7703i	−0.772082	+	2.31319i
$761$	−22.4488	−	22.4488i	−0.813767	−	0.813767i	0.171429	−	0.985196i	$-0.445161\pi$
$761$	−22.4488	−	22.4488i	−0.813767	−	0.813767i	−0.985196	+	0.171429i	$0.945161\pi$
$762$		0			0
$763$	1.11402	+	1.11402i	0.0403302	+	0.0403302i
$764$	54.5685			1.97422
$765$		0			0
$766$		−	0.824345i		−	0.0297848i
$767$	−26.7482	+	2.98978i	−0.965822	+	0.107955i
$768$		0			0
$769$	−3.44776	−	3.44776i	−0.124329	−	0.124329i	0.642204	−	0.766534i	$-0.278020\pi$
$769$	−3.44776	−	3.44776i	−0.124329	−	0.124329i	−0.766534	+	0.642204i	$0.778020\pi$
$770$	2.55933	−	7.66787i	0.0922319	−	0.276331i
$771$		0			0
$772$			38.8399i			1.39788i
$773$	−25.5316			−0.918307			−0.459154	−	0.888357i	$-0.651847\pi$
$773$	−25.5316			−0.918307			−0.459154	+	0.888357i	$0.651847\pi$
$774$		0			0
$775$	5.66255	+	39.8633i	0.203405	+	1.43193i
$776$	25.8518			0.928026
$777$		0			0
$778$		−	16.8578i		−	0.604383i
$779$	−11.8591			−0.424896
$780$		0			0
$781$	0.661911			0.0236850
$782$		−	12.9965i		−	0.464752i
$783$		0			0
$784$	−35.6588			−1.27353
$785$	4.27198	−	12.7991i	0.152474	−	0.456818i
$786$		0			0
$787$	−15.5693			−0.554986			−0.277493	−	0.960728i	$-0.589504\pi$
$787$	−15.5693			−0.554986			−0.277493	+	0.960728i	$0.589504\pi$
$788$			54.0240i			1.92453i
$789$		0			0
$790$	−37.8127	+	18.8876i	−1.34532	+	0.671992i
$791$	2.98841	+	2.98841i	0.106256	+	0.106256i
$792$		0			0
$793$	28.8698	+	23.0648i	1.02520	+	0.819055i
$794$			63.9772i			2.27046i
$795$		0			0
$796$	−9.85453			−0.349285
$797$	7.35388	+	7.35388i	0.260488	+	0.260488i	0.825252	−	0.564764i	$-0.191033\pi$
$797$	7.35388	+	7.35388i	0.260488	+	0.260488i	−0.564764	+	0.825252i	$0.691033\pi$
$798$		0			0
$799$	2.31100	+	2.31100i	0.0817573	+	0.0817573i
$800$	7.64897	+	5.74620i	0.270432	+	0.203159i
$801$		0			0
$802$	19.2132	−	19.2132i	0.678440	−	0.678440i
$803$	6.16586	−	6.16586i	0.217588	−	0.217588i
$804$		0			0
$805$	0.462277	−	1.38500i	0.0162931	−	0.0488149i
$806$	−8.02033	−	71.7543i	−0.282504	−	2.52744i
$807$		0			0
$808$	−61.2798			−2.15582
$809$		−	32.8074i		−	1.15345i	−0.816939	−	0.576724i	$-0.804331\pi$
$809$		−	32.8074i		−	1.15345i	0.816939	−	0.576724i	$-0.195669\pi$
$810$		0			0
$811$	−23.4835	+	23.4835i	−0.824618	+	0.824618i	−0.986766	−	0.162149i	$-0.948158\pi$
$811$	−23.4835	+	23.4835i	−0.824618	+	0.824618i	0.162149	+	0.986766i	$0.448158\pi$
$812$			5.85207i			0.205368i
$813$		0			0
$814$	−34.9974	+	34.9974i	−1.22666	+	1.22666i
$815$	14.7117	+	29.4525i	0.515328	+	1.03168i
$816$		0			0
$817$	−30.4241			−1.06440
$818$	−17.8020	+	17.8020i	−0.622431	+	0.622431i
$819$		0			0
$820$	−6.34496	+	19.0098i	−0.221576	+	0.663850i
$821$	−28.3481	+	28.3481i	−0.989357	+	0.989357i	−0.999944	−	0.0105868i	$-0.996630\pi$
$821$	−28.3481	+	28.3481i	−0.989357	+	0.989357i	0.0105868	+	0.999944i	$0.496630\pi$
$822$		0			0
$823$	−33.0457	+	33.0457i	−1.15190	+	1.15190i	−0.165729	+	0.986171i	$0.552998\pi$
$823$	−33.0457	+	33.0457i	−1.15190	+	1.15190i	−0.986171	+	0.165729i	$0.947002\pi$
$824$	−53.5356	−	53.5356i	−1.86500	−	1.86500i
$825$		0			0
$826$	3.18196	+	3.18196i	0.110714	+	0.110714i
$827$	−50.1300			−1.74319			−0.871596	−	0.490225i	$-0.836915\pi$
$827$	−50.1300			−1.74319			−0.871596	+	0.490225i	$0.836915\pi$
$828$		0			0
$829$	28.1449			0.977512			0.488756	−	0.872420i	$-0.337451\pi$
$829$	28.1449			0.977512			0.488756	+	0.872420i	$0.337451\pi$
$830$	−6.75771	−	13.5288i	−0.234563	−	0.469592i
$831$		0			0
$832$	15.5393	+	12.4148i	0.538729	+	0.430404i
$833$	−9.52297	−	9.52297i	−0.329951	−	0.329951i
$834$		0			0
$835$	−12.1735	+	6.08074i	−0.421282	+	0.210433i
$836$			138.907i			4.80419i
$837$		0			0
$838$	57.4655			1.98511
$839$	25.8159	−	25.8159i	0.891264	−	0.891264i	−0.103378	−	0.994642i	$-0.532965\pi$
$839$	25.8159	−	25.8159i	0.891264	−	0.891264i	0.994642	+	0.103378i	$0.0329651\pi$
$840$		0			0
$841$	−4.29196			−0.147999
$842$	−0.804189	−	0.804189i	−0.0277142	−	0.0277142i
$843$		0			0
$844$	91.9664			3.16561
$845$	18.4108	+	22.4953i	0.633352	+	0.773864i
$846$		0			0
$847$		−	6.05173i		−	0.207940i
$848$	11.4221	+	11.4221i	0.392236	+	0.392236i
$849$		0			0
$850$	3.39276	+	23.8844i	0.116371	+	0.819227i
$851$	−6.32136	+	6.32136i	−0.216694	+	0.216694i
$852$		0			0
$853$			6.25026i			0.214005i	0.994259	+	0.107002i	$0.0341253\pi$
$853$			6.25026i			0.214005i	−0.994259	+	0.107002i	$0.965875\pi$
$854$		−	6.17811i		−	0.211411i
$855$		0			0
$856$	−21.7367	−	21.7367i	−0.742945	−	0.742945i
$857$	12.2252	+	12.2252i	0.417607	+	0.417607i	0.884378	−	0.466771i	$-0.154583\pi$
$857$	12.2252	+	12.2252i	0.417607	+	0.417607i	−0.466771	+	0.884378i	$0.654583\pi$
$858$		0			0
$859$		−	25.0493i		−	0.854670i	−0.904093	−	0.427335i	$-0.859452\pi$
$859$		−	25.0493i		−	0.854670i	0.904093	−	0.427335i	$-0.140548\pi$
$860$	−16.2778	+	48.7689i	−0.555067	+	1.66301i
$861$		0			0
$862$	−4.15752	−	4.15752i	−0.141606	−	0.141606i
$863$	25.4480			0.866261			0.433130	−	0.901331i	$-0.357409\pi$
$863$	25.4480			0.866261			0.433130	+	0.901331i	$0.357409\pi$
$864$		0			0
$865$	11.3456	−	33.9921i	0.385763	−	1.15576i
$866$	26.9770	+	26.9770i	0.916716	+	0.916716i
$867$		0			0
$868$	−5.77519	+	5.77519i	−0.196023	+	0.196023i
$869$	−32.2338	+	32.2338i	−1.09346	+	1.09346i
$870$		0			0
$871$	34.4524	−	43.1234i	1.16737	−	1.46118i
$872$	−24.9574	+	24.9574i	−0.845163	+	0.845163i
$873$		0			0
$874$			37.0834i			1.25436i
$875$	−0.487996	+	2.66598i	−0.0164973	+	0.0901266i
$876$		0			0
$877$			21.2930i			0.719015i	0.933142	+	0.359507i	$0.117055\pi$
$877$			21.2930i			0.719015i	−0.933142	+	0.359507i	$0.882945\pi$
$878$		−	50.3544i		−	1.69938i
$879$		0			0
$880$	65.3454	+	21.8105i	2.20279	+	0.735233i
$881$			10.5084i			0.354037i	0.984208	+	0.177018i	$0.0566452\pi$
$881$			10.5084i			0.354037i	−0.984208	+	0.177018i	$0.943355\pi$
$882$		0			0
$883$	9.86276	−	9.86276i	0.331908	−	0.331908i	−0.521403	−	0.853311i	$-0.674591\pi$
$883$	9.86276	−	9.86276i	0.331908	−	0.331908i	0.853311	+	0.521403i	$0.174591\pi$
$884$	−3.25126	−	29.0876i	−0.109352	−	0.978321i
$885$		0			0
$886$	−33.0488	+	33.0488i	−1.11030	+	1.11030i
$887$	−21.5847	+	21.5847i	−0.724745	+	0.724745i	−0.969568	−	0.244823i	$-0.921270\pi$
$887$	−21.5847	+	21.5847i	−0.724745	+	0.724745i	0.244823	+	0.969568i	$0.421270\pi$
$888$		0			0
$889$	0.930252	+	0.930252i	0.0311996	+	0.0311996i
$890$	−6.61725	−	2.20866i	−0.221811	−	0.0740345i
$891$		0			0
$892$	36.4845			1.22159
$893$	−6.59408	−	6.59408i	−0.220663	−	0.220663i
$894$		0			0
$895$	−7.99618	+	3.99413i	−0.267283	+	0.133509i
$896$		−	4.25307i		−	0.142085i
$897$		0			0
$898$	−57.9559	−	57.9559i	−1.93401	−	1.93401i
$899$	−32.8546	−	32.8546i	−1.09576	−	1.09576i
$900$		0			0
$901$			6.10073i			0.203245i
$902$			31.9458i			1.06368i
$903$		0			0
$904$	−66.9493	+	66.9493i	−2.22670	+	2.22670i
$905$	−16.5302	−	33.0932i	−0.549483	−	1.10005i
$906$		0			0
$907$	14.1974	+	14.1974i	0.471417	+	0.471417i	0.902373	−	0.430956i	$-0.141823\pi$
$907$	14.1974	+	14.1974i	0.471417	+	0.471417i	−0.430956	+	0.902373i	$0.641823\pi$
$908$			76.9475i			2.55359i
$909$		0			0
$910$	1.01710	−	4.75250i	0.0337166	−	0.157544i
$911$	6.62609			0.219532			0.109766	−	0.993957i	$-0.464990\pi$
$911$	6.62609			0.219532			0.109766	+	0.993957i	$0.464990\pi$
$912$		0			0
$913$	−11.5328	−	11.5328i	−0.381679	−	0.381679i
$914$	−38.7585			−1.28202
$915$		0			0
$916$	−69.9344	+	69.9344i	−2.31070	+	2.31070i
$917$	−1.22162			−0.0403416
$918$		0			0
$919$		−	56.0617i		−	1.84930i	−0.380813	−	0.924652i	$-0.624356\pi$
$919$		−	56.0617i		−	1.84930i	0.380813	−	0.924652i	$-0.375644\pi$
$920$	31.0282	+	10.3564i	1.02297	+	0.341440i
$921$		0			0
$922$	−51.9714	−	51.9714i	−1.71159	−	1.71159i
$923$	0.395493	−	0.0442062i	0.0130178	−	0.00145507i
$924$		0			0
$925$	9.96695	−	13.2674i	0.327711	−	0.436228i
$926$	20.6928			0.680007
$927$		0			0
$928$	−11.0400			−0.362407
$929$	16.7396	+	16.7396i	0.549210	+	0.549210i	0.926212	−	0.377003i	$-0.123045\pi$
$929$	16.7396	+	16.7396i	0.549210	+	0.549210i	−0.377003	+	0.926212i	$0.623045\pi$
$930$		0			0
$931$	27.1723	+	27.1723i	0.890537	+	0.890537i
$932$	2.51424	−	2.51424i	0.0823567	−	0.0823567i
$933$		0			0
$934$	−54.6088	+	54.6088i	−1.78685	+	1.78685i
$935$	11.6263	+	23.2757i	0.380222	+	0.761197i
$936$		0			0
$937$	12.3582	−	12.3582i	0.403724	−	0.403724i	−0.475819	−	0.879543i	$-0.657848\pi$
$937$	12.3582	−	12.3582i	0.403724	−	0.403724i	0.879543	+	0.475819i	$0.157848\pi$
$938$	−9.22837			−0.301317
$939$		0			0
$940$	−14.0981	+	7.04210i	−0.459831	+	0.229688i
$941$	−18.8531	+	18.8531i	−0.614594	+	0.614594i	−0.944140	−	0.329545i	$-0.893105\pi$
$941$	−18.8531	+	18.8531i	−0.614594	+	0.614594i	0.329545	+	0.944140i	$0.393105\pi$
$942$		0			0
$943$			5.77018i			0.187903i
$944$	−27.1165	+	27.1165i	−0.882568	+	0.882568i
$945$		0			0
$946$			81.9559i			2.66462i
$947$	−13.5380			−0.439926			−0.219963	−	0.975508i	$-0.570594\pi$
$947$	−13.5380			−0.439926			−0.219963	+	0.975508i	$0.570594\pi$
$948$		0			0
$949$	3.27232	−	4.09590i	0.106224	−	0.132959i
$950$	−9.68071	−	68.1504i	−0.314084	−	2.21109i
$951$		0			0
$952$	−1.80617	+	1.80617i	−0.0585383	+	0.0585383i
$953$	10.8161	−	10.8161i	0.350369	−	0.350369i	−0.509878	−	0.860247i	$-0.670309\pi$
$953$	10.8161	−	10.8161i	0.350369	−	0.350369i	0.860247	+	0.509878i	$0.170309\pi$
$954$		0			0
$955$	−26.0901	+	13.0322i	−0.844257	+	0.421711i
$956$	−36.4540	−	36.4540i	−1.17901	−	1.17901i
$957$		0			0
$958$	−32.2812	−	32.2812i	−1.04296	−	1.04296i
$959$	−3.24716			−0.104856
$960$		0			0
$961$		−	33.8458i		−	1.09180i
$962$	−18.5737	+	23.2483i	−0.598839	+	0.749556i
$963$		0			0
$964$	26.6768	+	26.6768i	0.859202	+	0.859202i
$965$	−9.27582	−	18.5700i	−0.298599	−	0.597790i
$966$		0			0
$967$			16.5180i			0.531183i	0.964086	+	0.265591i	$0.0855672\pi$
$967$			16.5180i			0.531183i	−0.964086	+	0.265591i	$0.914433\pi$
$968$	135.577			4.35760
$969$		0			0
$970$	−23.6796	+	11.8281i	−0.760305	+	0.379776i
$971$	40.8913			1.31226			0.656132	−	0.754646i	$-0.272191\pi$
$971$	40.8913			1.31226			0.656132	+	0.754646i	$0.272191\pi$
$972$		0			0
$973$			1.46367i			0.0469231i
$974$	31.4340			1.00721
$975$		0			0
$976$	52.6497			1.68527
$977$		−	1.92441i		−	0.0615674i	−0.999526	−	0.0307837i	$-0.990200\pi$
$977$		−	1.92441i		−	0.0615674i	0.999526	−	0.0307837i	$-0.00980030\pi$
$978$		0			0
$979$	−7.52374			−0.240460
$980$	58.0944	−	29.0185i	1.85576	−	0.926961i
$981$		0			0
$982$	−69.1805			−2.20764
$983$		−	59.7525i		−	1.90581i	−0.303273	−	0.952904i	$-0.598079\pi$
$983$		−	59.7525i		−	1.90581i	0.303273	−	0.952904i	$-0.401921\pi$
$984$		0			0
$985$	−12.9021	−	25.8298i	−0.411096	−	0.823006i
$986$	−19.6851	−	19.6851i	−0.626900	−	0.626900i
$987$		0			0
$988$	9.27698	+	82.9970i	0.295140	+	2.64049i
$989$			14.8032i			0.470714i
$990$		0			0
$991$	29.3438			0.932136			0.466068	−	0.884749i	$-0.345670\pi$
$991$	29.3438			0.932136			0.466068	+	0.884749i	$0.345670\pi$
$992$	−10.8950	−	10.8950i	−0.345917	−	0.345917i
$993$		0			0
$994$	−0.0470477	−	0.0470477i	−0.00149226	−	0.00149226i
$995$	4.71162	−	2.35348i	0.149368	−	0.0746103i
$996$		0			0
$997$	−34.3919	+	34.3919i	−1.08920	+	1.08920i	−0.0935912	+	0.995611i	$0.529835\pi$
$997$	−34.3919	+	34.3919i	−1.08920	+	1.08920i	−0.995611	+	0.0935912i	$0.970165\pi$
$998$	−0.378169	+	0.378169i	−0.0119707	+	0.0119707i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.n.g.343.14		28
3.2	odd	2		195.2.k.a.148.1	yes	28
5.2	odd	4		585.2.w.g.577.1		28
13.8	odd	4		585.2.w.g.73.1		28
15.2	even	4		195.2.t.a.187.14	yes	28
15.8	even	4		975.2.t.d.382.1		28
15.14	odd	2		975.2.k.d.343.14		28
39.8	even	4		195.2.t.a.73.14	yes	28
65.47	even	4	inner	585.2.n.g.307.1		28
195.8	odd	4		975.2.k.d.307.1		28
195.47	odd	4		195.2.k.a.112.14	✓	28
195.164	even	4		975.2.t.d.268.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.k.a.112.14	✓	28	195.47	odd	4
195.2.k.a.148.1	yes	28	3.2	odd	2
195.2.t.a.73.14	yes	28	39.8	even	4
195.2.t.a.187.14	yes	28	15.2	even	4
585.2.n.g.307.1		28	65.47	even	4	inner
585.2.n.g.343.14		28	1.1	even	1	trivial
585.2.w.g.73.1		28	13.8	odd	4
585.2.w.g.577.1		28	5.2	odd	4
975.2.k.d.307.1		28	195.8	odd	4
975.2.k.d.343.14		28	15.14	odd	2
975.2.t.d.268.1		28	195.164	even	4
975.2.t.d.382.1		28	15.8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.48675i q^{2} -4.18390 q^{4} +(2.00040 - 0.999208i) q^{5} -0.242414 q^{7} -5.43081i q^{8} +(2.48478 + 4.97448i) q^{10} +(4.24054 + 4.24054i) q^{11} +(2.81694 + 2.25052i) q^{13} -0.602823i q^{14} +5.13724 q^{16} +(1.37194 + 1.37194i) q^{17} +(-3.91462 - 3.91462i) q^{19} +(-8.36946 + 4.18059i) q^{20} +(-10.5451 + 10.5451i) q^{22} +(-1.90471 + 1.90471i) q^{23} +(3.00317 - 3.99762i) q^{25} +(-5.59648 + 7.00501i) q^{26} +1.01424 q^{28} +5.76992i q^{29} +(-5.69411 + 5.69411i) q^{31} +1.91338i q^{32} +(-3.41167 + 3.41167i) q^{34} +(-0.484925 + 0.242222i) q^{35} +3.31881 q^{37} +(9.73467 - 9.73467i) q^{38} +(-5.42651 - 10.8638i) q^{40} +(1.51472 - 1.51472i) q^{41} +(3.88596 - 3.88596i) q^{43} +(-17.7420 - 17.7420i) q^{44} +(-4.73652 - 4.73652i) q^{46} +1.68447 q^{47} -6.94124 q^{49} +(9.94107 + 7.46811i) q^{50} +(-11.7858 - 9.41597i) q^{52} +(2.22339 + 2.22339i) q^{53} +(12.7199 + 4.24558i) q^{55} +1.31651i q^{56} -14.3483 q^{58} +(-5.27843 + 5.27843i) q^{59} +10.2486 q^{61} +(-14.1598 - 14.1598i) q^{62} +5.51638 q^{64} +(7.88373 + 1.68723i) q^{65} -15.3086i q^{67} +(-5.74007 - 5.74007i) q^{68} +(-0.602346 - 1.20588i) q^{70} +(0.0780456 - 0.0780456i) q^{71} -1.45403i q^{73} +8.25304i q^{74} +(16.3784 + 16.3784i) q^{76} +(-1.02797 - 1.02797i) q^{77} +7.60135i q^{79} +(10.2765 - 5.13317i) q^{80} +(3.76672 + 3.76672i) q^{82} -2.71964 q^{83} +(4.11528 + 1.37357i) q^{85} +(9.66338 + 9.66338i) q^{86} +(23.0296 - 23.0296i) q^{88} +(-0.887120 + 0.887120i) q^{89} +(-0.682867 - 0.545559i) q^{91} +(7.96910 - 7.96910i) q^{92} +4.18886i q^{94} +(-11.7423 - 3.91927i) q^{95} +4.76021i q^{97} -17.2611i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} - 8 q^{5} + 8 q^{11} - 12 q^{13} + 28 q^{16} + 28 q^{17} - 32 q^{22} - 8 q^{23} - 4 q^{25} - 16 q^{31} + 28 q^{34} + 32 q^{37} - 48 q^{40} - 4 q^{41} - 40 q^{44} - 16 q^{46} + 24 q^{47}+ \cdots - 56 q^{95}+O(q^{100}) \) 28 * q - 28 * q^4 - 8 * q^5 + 8 * q^11 - 12 * q^13 + 28 * q^16 + 28 * q^17 - 32 * q^22 - 8 * q^23 - 4 * q^25 - 16 * q^31 + 28 * q^34 + 32 * q^37 - 48 * q^40 - 4 * q^41 - 40 * q^44 - 16 * q^46 + 24 * q^47 - 28 * q^49 + 32 * q^50 + 52 * q^52 - 20 * q^53 - 8 * q^55 - 8 * q^58 - 32 * q^59 + 8 * q^61 - 72 * q^62 - 28 * q^64 + 8 * q^65 - 60 * q^68 + 64 * q^70 - 40 * q^71 - 40 * q^76 + 48 * q^77 + 32 * q^80 + 4 * q^82 + 104 * q^83 - 4 * q^85 - 16 * q^86 + 72 * q^88 + 36 * q^89 - 56 * q^91 + 32 * q^92 - 56 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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