LMFDB - Embedded newform 975.2.k.d.343.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(307,975)] 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("975.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,0,-28,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
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	$\chi$	$=$	975.343
Dual form			975.2.k.d.307.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.48675i q^{2} +(0.707107 + 0.707107i) q^{3} -4.18390 q^{4} +(-1.75839 + 1.75839i) q^{6} +0.242414 q^{7} -5.43081i q^{8} +1.00000i q^{9} +(-4.24054 - 4.24054i) q^{11} +(-2.95847 - 2.95847i) q^{12} +(-2.81694 - 2.25052i) q^{13} +0.602823i q^{14} +5.13724 q^{16} +(1.37194 + 1.37194i) q^{17} -2.48675 q^{18} +(-3.91462 - 3.91462i) q^{19} +(0.171413 + 0.171413i) q^{21} +(10.5451 - 10.5451i) q^{22} +(-1.90471 + 1.90471i) q^{23} +(3.84016 - 3.84016i) q^{24} +(5.59648 - 7.00501i) q^{26} +(-0.707107 + 0.707107i) q^{27} -1.01424 q^{28} -5.76992i q^{29} +(-5.69411 + 5.69411i) q^{31} +1.91338i q^{32} -5.99703i q^{33} +(-3.41167 + 3.41167i) q^{34} -4.18390i q^{36} -3.31881 q^{37} +(9.73467 - 9.73467i) q^{38} +(-0.400516 - 3.58324i) q^{39} +(-1.51472 + 1.51472i) q^{41} +(-0.426260 + 0.426260i) q^{42} +(-3.88596 + 3.88596i) q^{43} +(17.7420 + 17.7420i) q^{44} +(-4.73652 - 4.73652i) q^{46} +1.68447 q^{47} +(3.63258 + 3.63258i) q^{48} -6.94124 q^{49} +1.94022i q^{51} +(11.7858 + 9.41597i) q^{52} +(2.22339 + 2.22339i) q^{53} +(-1.75839 - 1.75839i) q^{54} -1.31651i q^{56} -5.53612i q^{57} +14.3483 q^{58} +(5.27843 - 5.27843i) q^{59} +10.2486 q^{61} +(-14.1598 - 14.1598i) q^{62} +0.242414i q^{63} +5.51638 q^{64} +14.9131 q^{66} +15.3086i q^{67} +(-5.74007 - 5.74007i) q^{68} -2.69366 q^{69} +(-0.0780456 + 0.0780456i) q^{71} +5.43081 q^{72} +1.45403i q^{73} -8.25304i q^{74} +(16.3784 + 16.3784i) q^{76} +(-1.02797 - 1.02797i) q^{77} +(8.91060 - 0.995982i) q^{78} +7.60135i q^{79} -1.00000 q^{81} +(-3.76672 - 3.76672i) q^{82} -2.71964 q^{83} +(-0.717175 - 0.717175i) q^{84} +(-9.66338 - 9.66338i) q^{86} +(4.07995 - 4.07995i) q^{87} +(-23.0296 + 23.0296i) q^{88} +(0.887120 - 0.887120i) q^{89} +(-0.682867 - 0.545559i) q^{91} +(7.96910 - 7.96910i) q^{92} -8.05269 q^{93} +4.18886i q^{94} +(-1.35296 + 1.35296i) q^{96} -4.76021i q^{97} -17.2611i q^{98} +(4.24054 - 4.24054i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} - 8 q^{11} - 8 q^{12} + 12 q^{13} + 28 q^{16} + 28 q^{17} + 4 q^{18} + 8 q^{21} + 32 q^{22} - 8 q^{23} - 16 q^{31} + 28 q^{34} - 32 q^{37} + 8 q^{39} + 4 q^{41} + 40 q^{44} - 16 q^{46} + 24 q^{47}+ \cdots + 8 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 - 8 * q^11 - 8 * q^12 + 12 * q^13 + 28 * q^16 + 28 * q^17 + 4 * q^18 + 8 * q^21 + 32 * q^22 - 8 * q^23 - 16 * q^31 + 28 * q^34 - 32 * q^37 + 8 * q^39 + 4 * q^41 + 40 * q^44 - 16 * q^46 + 24 * q^47 + 16 * q^48 - 28 * q^49 - 52 * q^52 - 20 * q^53 + 8 * q^58 + 32 * q^59 + 8 * q^61 - 72 * q^62 - 28 * q^64 + 16 * q^66 - 60 * q^68 + 8 * q^69 + 40 * q^71 - 12 * q^72 - 40 * q^76 + 48 * q^77 - 8 * q^78 - 28 * q^81 - 4 * q^82 + 104 * q^83 - 32 * q^84 + 16 * q^86 + 24 * q^87 - 72 * q^88 - 36 * q^89 - 56 * q^91 + 32 * q^92 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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	$0.658080\pi$
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−4.18390			−2.09195
$5$		0			0
$5$		0			0
$6$	−1.75839	+	1.75839i	−0.717862	+	0.717862i
$7$	0.242414			0.0916240			0.0458120	−	0.998950i	$-0.485412\pi$
$7$	0.242414			0.0916240			0.0458120	+	0.998950i	$0.485412\pi$
$8$		−	5.43081i		−	1.92008i
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−4.24054	−	4.24054i	−1.27857	−	1.27857i	−0.941467	−	0.337104i	$-0.890553\pi$
$11$	−4.24054	−	4.24054i	−1.27857	−	1.27857i	−0.337104	−	0.941467i	$-0.609447\pi$
$12$	−2.95847	−	2.95847i	−0.854036	−	0.854036i
$13$	−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	$0.674397\pi$
$18$	−2.48675			−0.586132
$19$	−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	$0.969015\pi$
$20$		0			0
$21$	0.171413	+	0.171413i	0.0374054	+	0.0374054i
$22$	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	$0.340611\pi$
$24$	3.84016	−	3.84016i	0.783870	−	0.783870i
$25$		0			0
$26$	5.59648	−	7.00501i	1.09756	−	1.37380i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.01424			−0.191673
$29$		−	5.76992i		−	1.07145i	−0.844393	−	0.535724i	$-0.820039\pi$
$29$		−	5.76992i		−	1.07145i	0.844393	−	0.535724i	$-0.179961\pi$
$30$		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
$33$		−	5.99703i		−	1.04395i
$34$	−3.41167	+	3.41167i	−0.585096	+	0.585096i
$35$		0			0
$36$		−	4.18390i		−	0.697317i
$37$	−3.31881			−0.545609			−0.272805	−	0.962069i	$-0.587951\pi$
$37$	−3.31881			−0.545609			−0.272805	+	0.962069i	$0.587951\pi$
$38$	9.73467	−	9.73467i	1.57917	−	1.57917i
$39$	−0.400516	−	3.58324i	−0.0641339	−	0.573777i
$40$		0			0
$41$	−1.51472	+	1.51472i	−0.236559	+	0.236559i	−0.815424	−	0.578865i	$-0.803496\pi$
$41$	−1.51472	+	1.51472i	−0.236559	+	0.236559i	0.578865	+	0.815424i	$0.303496\pi$
$42$	−0.426260	+	0.426260i	−0.0657734	+	0.0657734i
$43$	−3.88596	+	3.88596i	−0.592603	+	0.592603i	−0.938334	−	0.345731i	$-0.887631\pi$
$43$	−3.88596	+	3.88596i	−0.592603	+	0.592603i	0.345731	+	0.938334i	$0.387631\pi$
$44$	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	$0.460796\pi$
$48$	3.63258	+	3.63258i	0.524317	+	0.524317i
$49$	−6.94124			−0.991605
$50$		0			0
$51$			1.94022i			0.271685i
$52$	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	$0.680714\pi$
$54$	−1.75839	−	1.75839i	−0.239287	−	0.239287i
$55$		0			0
$56$		−	1.31651i		−	0.175926i
$57$		−	5.53612i		−	0.733276i
$58$	14.3483			1.88403
$59$	5.27843	−	5.27843i	0.687193	−	0.687193i	−0.274418	−	0.961611i	$-0.588485\pi$
$59$	5.27843	−	5.27843i	0.687193	−	0.687193i	0.961611	+	0.274418i	$0.0884852\pi$
$60$		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
$63$			0.242414i			0.0305413i
$64$	5.51638			0.689548
$65$		0			0
$66$	14.9131			1.83567
$67$			15.3086i			1.87024i	0.354328	+	0.935121i	$0.384710\pi$
$67$			15.3086i			1.87024i	−0.354328	+	0.935121i	$0.615290\pi$
$68$	−5.74007	−	5.74007i	−0.696086	−	0.696086i
$69$	−2.69366			−0.324279
$70$		0			0
$71$	−0.0780456	+	0.0780456i	−0.00926231	+	0.00926231i	−0.711723	−	0.702460i	$-0.752085\pi$
$71$	−0.0780456	+	0.0780456i	−0.00926231	+	0.00926231i	0.702460	+	0.711723i	$0.252085\pi$
$72$	5.43081			0.640027
$73$			1.45403i			0.170181i	0.996373	+	0.0850905i	$0.0271179\pi$
$73$			1.45403i			0.170181i	−0.996373	+	0.0850905i	$0.972882\pi$
$74$		−	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
$78$	8.91060	−	0.995982i	1.00893	−	0.112773i
$79$			7.60135i			0.855219i	0.903964	+	0.427609i	$0.140644\pi$
$79$			7.60135i			0.855219i	−0.903964	+	0.427609i	$0.859356\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	−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	$0.547689\pi$
$84$	−0.717175	−	0.717175i	−0.0782502	−	0.0782502i
$85$		0			0
$86$	−9.66338	−	9.66338i	−1.04203	−	1.04203i
$87$	4.07995	−	4.07995i	0.437416	−	0.437416i
$88$	−23.0296	+	23.0296i	−2.45496	+	2.45496i
$89$	0.887120	−	0.887120i	0.0940345	−	0.0940345i	−0.658525	−	0.752559i	$-0.728819\pi$
$89$	0.887120	−	0.887120i	0.0940345	−	0.0940345i	0.752559	+	0.658525i	$0.228819\pi$
$90$		0			0
$91$	−0.682867	−	0.545559i	−0.0715839	−	0.0571902i
$92$	7.96910	−	7.96910i	0.830837	−	0.830837i
$93$	−8.05269			−0.835025
$94$			4.18886i			0.432048i
$95$		0			0
$96$	−1.35296	+	1.35296i	−0.138086	+	0.138086i
$97$		−	4.76021i		−	0.483326i	−0.970360	−	0.241663i	$-0.922307\pi$
$97$		−	4.76021i		−	0.483326i	0.970360	−	0.241663i	$-0.0776929\pi$
$98$		−	17.2611i		−	1.74363i
$99$	4.24054	−	4.24054i	0.426190	−	0.426190i
$100$		0			0
$101$			11.2837i			1.12277i	0.827553	+	0.561387i	$0.189732\pi$
$101$			11.2837i			1.12277i	−0.827553	+	0.561387i	$0.810268\pi$
$102$	−4.82483			−0.477729
$103$	−9.85776	+	9.85776i	−0.971314	+	0.971314i	−0.999600	−	0.0282861i	$-0.990995\pi$
$103$	−9.85776	+	9.85776i	−0.971314	+	0.971314i	0.0282861	+	0.999600i	$0.490995\pi$
$104$	−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	$0.161784\pi$
$108$	2.95847	−	2.95847i	0.284679	−	0.284679i
$109$	−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	$0.850747\pi$
$110$		0			0
$111$	−2.34675	−	2.34675i	−0.222744	−	0.222744i
$112$	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	$-0.556041\pi$
$114$	13.7669			1.28939
$115$		0			0
$116$			24.1408i			2.24142i
$117$	2.25052	−	2.81694i	0.208061	−	0.260426i
$118$	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
$123$	−2.14213			−0.193150
$124$	23.8236	−	23.8236i	2.13942	−	2.13942i
$125$		0			0
$126$	−0.602823			−0.0537037
$127$	3.83744	+	3.83744i	0.340518	+	0.340518i	0.856562	−	0.516044i	$-0.172596\pi$
$127$	3.83744	+	3.83744i	0.340518	+	0.340518i	−0.516044	+	0.856562i	$0.672596\pi$
$128$			17.5446i			1.55074i
$129$	−5.49557			−0.483858
$130$		0			0
$131$	−5.03941			−0.440295			−0.220148	−	0.975467i	$-0.570654\pi$
$131$	−5.03941			−0.440295			−0.220148	+	0.975467i	$0.570654\pi$
$132$			25.0910i			2.18389i
$133$	−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	$0.306087\pi$
$138$		−	6.69845i		−	0.570210i
$139$		−	6.03788i		−	0.512126i	−0.966660	−	0.256063i	$-0.917575\pi$
$139$		−	6.03788i		−	0.512126i	0.966660	−	0.256063i	$-0.0824255\pi$
$140$		0			0
$141$	1.19110	+	1.19110i	0.100309	+	0.100309i
$142$	−0.194080	−	0.194080i	−0.0162868	−	0.0162868i
$143$	2.40191	+	21.4888i	0.200858	+	1.79698i
$144$			5.13724i			0.428103i
$145$		0			0
$146$	−3.61579			−0.299245
$147$	−4.90819	−	4.90819i	−0.404821	−	0.404821i
$148$	13.8856			1.14139
$149$	−14.7948	−	14.7948i	−1.21203	−	1.21203i	−0.970356	−	0.241678i	$-0.922302\pi$
$149$	−14.7948	−	14.7948i	−1.21203	−	1.21203i	−0.241678	−	0.970356i	$-0.577698\pi$
$150$		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
$153$	−1.37194	+	1.37194i	−0.110915	+	0.110915i
$154$	2.55630	−	2.55630i	0.205992	−	0.205992i
$155$		0			0
$156$	1.67572	+	14.9919i	0.134165	+	1.20031i
$157$	−4.26691	+	4.26691i	−0.340537	+	0.340537i	−0.856569	−	0.516032i	$-0.827408\pi$
$157$	−4.26691	+	4.26691i	−0.340537	+	0.340537i	0.516032	+	0.856569i	$0.327408\pi$
$158$	−18.9026			−1.50381
$159$			3.14435i			0.249363i
$160$		0			0
$161$	−0.461728	+	0.461728i	−0.0363893	+	0.0363893i
$162$		−	2.48675i		−	0.195377i
$163$		−	14.7233i		−	1.15322i	−0.817019	−	0.576611i	$-0.804375\pi$
$163$		−	14.7233i		−	1.15322i	0.817019	−	0.576611i	$-0.195625\pi$
$164$	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	$0.575659\pi$
$168$	0.930911	−	0.930911i	0.0718213	−	0.0718213i
$169$	2.87029	+	12.6792i	0.220791	+	0.975321i
$170$		0			0
$171$	3.91462	−	3.91462i	0.299359	−	0.299359i
$172$	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	$0.0414819\pi$
$174$	10.1458	+	10.1458i	0.769151	+	0.769151i
$175$		0			0
$176$	−21.7847	−	21.7847i	−1.64208	−	1.64208i
$177$	7.46482			0.561090
$178$	2.20604	+	2.20604i	0.165350	+	0.165350i
$179$	3.99730			0.298772			0.149386	−	0.988779i	$-0.452270\pi$
$179$	3.99730			0.298772			0.149386	+	0.988779i	$0.452270\pi$
$180$		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
$183$	7.24688	+	7.24688i	0.535705	+	0.535705i
$184$	10.3441	+	10.3441i	0.762577	+	0.762577i
$185$		0			0
$186$		−	20.0250i		−	1.46830i
$187$		−	11.6355i		−	0.850876i
$188$	−7.04768			−0.514005
$189$	−0.171413	+	0.171413i	−0.0124685	+	0.0124685i
$190$		0			0
$191$	13.0425			0.943721			0.471860	−	0.881673i	$-0.343583\pi$
$191$	13.0425			0.943721			0.471860	+	0.881673i	$0.343583\pi$
$192$	3.90067	+	3.90067i	0.281507	+	0.281507i
$193$			9.28317i			0.668217i	0.942535	+	0.334109i	$0.108435\pi$
$193$			9.28317i			0.668217i	−0.942535	+	0.334109i	$0.891565\pi$
$194$	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	$-0.152145\pi$
$198$	10.5451	+	10.5451i	0.749411	+	0.749411i
$199$	2.35534			0.166966			0.0834830	−	0.996509i	$-0.473396\pi$
$199$	2.35534			0.166966			0.0834830	+	0.996509i	$0.473396\pi$
$200$		0			0
$201$	−10.8248	+	10.8248i	−0.763523	+	0.763523i
$202$	−28.0598			−1.97428
$203$		−	1.39871i		−	0.0981703i
$204$		−	8.11768i		−	0.568352i
$205$		0			0
$206$	−24.5137	−	24.5137i	−1.70795	−	1.70795i
$207$	−1.90471	−	1.90471i	−0.132386	−	0.132386i
$208$	−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
$213$	−0.110373			−0.00756264
$214$	9.95315	+	9.95315i	0.680383	+	0.680383i
$215$		0			0
$216$	3.84016	+	3.84016i	0.261290	+	0.261290i
$217$	−1.38033	+	1.38033i	−0.0937032	+	0.0937032i
$218$	11.4279	−	11.4279i	0.773993	−	0.773993i
$219$	−1.02815	+	1.02815i	−0.0694761	+	0.0694761i
$220$		0			0
$221$	−0.777089	−	6.95226i	−0.0522727	−	0.467660i
$222$	5.83578	−	5.83578i	0.391672	−	0.391672i
$223$	8.72020			0.583948			0.291974	−	0.956426i	$-0.405688\pi$
$223$	8.72020			0.583948			0.291974	+	0.956426i	$0.405688\pi$
$224$			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	$-0.208966\pi$
$228$			23.1626i			1.53398i
$229$	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	$-0.0353133\pi$
$230$		0			0
$231$		−	1.45377i		−	0.0956508i
$232$	−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	$0.258862\pi$
$234$	7.00501	+	5.59648i	0.457932	+	0.365853i
$235$		0			0
$236$	−22.0844	+	22.0844i	−1.43757	+	1.43757i
$237$	−5.37497	+	5.37497i	−0.349141	+	0.349141i
$238$	−0.827038	+	0.827038i	−0.0536089	+	0.0536089i
$239$	−8.71291	−	8.71291i	−0.563591	−	0.563591i	0.366735	−	0.930326i	$-0.380476\pi$
$239$	−8.71291	−	8.71291i	−0.563591	−	0.563591i	−0.930326	+	0.366735i	$0.880476\pi$
$240$		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
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−42.8793			−2.74506
$245$		0			0
$246$		−	5.32694i		−	0.339633i
$247$	2.21730	+	19.8372i	0.141084	+	1.26221i
$248$	30.9236	+	30.9236i	1.96365	+	1.96365i
$249$	−1.92308	−	1.92308i	−0.121870	−	0.121870i
$250$		0			0
$251$		−	8.17534i		−	0.516023i	−0.966142	−	0.258011i	$-0.916933\pi$
$251$		−	8.17534i		−	0.516023i	0.966142	−	0.258011i	$-0.0830672\pi$
$252$		−	1.01424i		−	0.0638910i
$253$	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	$0.605028\pi$
$258$		−	13.6661i		−	0.850813i
$259$	−0.804528			−0.0499909
$260$		0			0
$261$	5.76992			0.357149
$262$		−	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	$-0.506670\pi$
$264$	−32.5687			−2.00447
$265$		0			0
$266$	2.35983	−	2.35983i	0.144690	−	0.144690i
$267$	1.25458			0.0767789
$268$		−	64.0497i		−	3.91246i
$269$			16.7169i			1.01925i	0.860397	+	0.509625i	$0.170216\pi$
$269$			16.7169i			1.01925i	−0.860397	+	0.509625i	$0.829784\pi$
$270$		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
$273$	−0.0970909	−	0.868628i	−0.00587621	−	0.0525718i
$274$			33.3101i			2.01234i
$275$		0			0
$276$	11.2700			0.678375
$277$	17.8939	+	17.8939i	1.07514	+	1.07514i	0.996937	+	0.0782056i	$0.0249191\pi$
$277$	17.8939	+	17.8939i	1.07514	+	1.07514i	0.0782056	+	0.996937i	$0.475081\pi$
$278$	15.0147			0.900520
$279$	−5.69411	−	5.69411i	−0.340898	−	0.340898i
$280$		0			0
$281$	−2.64673	−	2.64673i	−0.157891	−	0.157891i	0.623741	−	0.781631i	$-0.285612\pi$
$281$	−2.64673	−	2.64673i	−0.157891	−	0.157891i	−0.781631	+	0.623741i	$0.785612\pi$
$282$	−2.96197	+	2.96197i	−0.176383	+	0.176383i
$283$	−2.64156	+	2.64156i	−0.157025	+	0.157025i	−0.781247	−	0.624222i	$-0.785416\pi$
$283$	−2.64156	+	2.64156i	−0.157025	+	0.157025i	0.624222	+	0.781247i	$0.285416\pi$
$284$	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
$288$	−1.91338			−0.112747
$289$		−	13.2356i		−	0.778562i
$290$		0			0
$291$	3.36598	−	3.36598i	0.197317	−	0.197317i
$292$		−	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	$0.916553\pi$
$294$	12.2054	−	12.2054i	0.711835	−	0.711835i
$295$		0			0
$296$			18.0238i			1.04761i
$297$	5.99703			0.347983
$298$	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
$303$	−7.97881	+	7.97881i	−0.458370	+	0.458370i
$304$	−20.1104	−	20.1104i	−1.15341	−	1.15341i
$305$		0			0
$306$	−3.41167	−	3.41167i	−0.195032	−	0.195032i
$307$	−25.1833			−1.43729			−0.718644	−	0.695378i	$-0.755237\pi$
$307$	−25.1833			−1.43729			−0.718644	+	0.695378i	$0.755237\pi$
$308$	4.30092	+	4.30092i	0.245068	+	0.245068i
$309$	−13.9410			−0.793074
$310$		0			0
$311$		−	7.05837i		−	0.400243i	−0.979771	−	0.200122i	$-0.935866\pi$
$311$		−	7.05837i		−	0.400243i	0.979771	−	0.200122i	$-0.0641337\pi$
$312$	−19.4599	+	2.17513i	−1.10170	+	0.123142i
$313$	3.85568	+	3.85568i	0.217936	+	0.217936i	0.807628	−	0.589692i	$-0.200751\pi$
$313$	3.85568	+	3.85568i	0.217936	+	0.217936i	−0.589692	+	0.807628i	$0.700751\pi$
$314$	−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	$0.872182\pi$
$318$	−7.81920			−0.438479
$319$	−24.4676	+	24.4676i	−1.36992	+	1.36992i
$320$		0			0
$321$	5.66036			0.315931
$322$	−1.14820	−	1.14820i	−0.0639867	−	0.0639867i
$323$		−	10.7413i		−	0.597660i
$324$	4.18390			0.232439
$325$		0			0
$326$	36.6132			2.02782
$327$		−	6.49904i		−	0.359398i
$328$	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
$333$		−	3.31881i		−	0.181870i
$334$		−	15.1332i		−	0.828054i
$335$		0			0
$336$	0.880589	+	0.880589i	0.0480400	+	0.0480400i
$337$	−0.812119	−	0.812119i	−0.0442389	−	0.0442389i	0.684641	−	0.728880i	$-0.259959\pi$
$337$	−0.812119	−	0.812119i	−0.0442389	−	0.0442389i	−0.728880	+	0.684641i	$0.759959\pi$
$338$	−31.5299	+	7.13768i	−1.71500	+	0.388238i
$339$		−	17.4340i		−	0.946884i
$340$		0			0
$341$	48.2922			2.61517
$342$	9.73467	+	9.73467i	0.526391	+	0.526391i
$343$	−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	$0.843538\pi$
$348$	−17.0701	+	17.0701i	−0.915054	+	0.915054i
$349$	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	$0.191167\pi$
$350$		0			0
$351$	3.58324	−	0.400516i	0.191259	−	0.0213780i
$352$	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	$0.742601\pi$
$354$			18.5631i			0.986618i
$355$		0			0
$356$	−3.71162	+	3.71162i	−0.196716	+	0.196716i
$357$			0.470337i			0.0248929i
$358$			9.94027i			0.525359i
$359$	−2.31461	+	2.31461i	−0.122160	+	0.122160i	−0.765544	−	0.643384i	$-0.777530\pi$
$359$	−2.31461	+	2.31461i	−0.122160	+	0.122160i	0.643384	+	0.765544i	$0.277530\pi$
$360$		0			0
$361$			11.6486i			0.613083i
$362$	41.1390			2.16222
$363$	−17.6525	+	17.6525i	−0.926515	+	0.926515i
$364$	2.85705	+	2.28257i	0.149750	+	0.119639i
$365$		0			0
$366$	−18.0211	+	18.0211i	−0.941980	+	0.941980i
$367$	−10.2557	+	10.2557i	−0.535346	+	0.535346i	−0.922158	−	0.386813i	$-0.873576\pi$
$367$	−10.2557	+	10.2557i	−0.535346	+	0.535346i	0.386813	+	0.922158i	$0.373576\pi$
$368$	−9.78493	+	9.78493i	−0.510075	+	0.510075i
$369$	−1.51472	−	1.51472i	−0.0788531	−	0.0788531i
$370$		0			0
$371$	0.538982	+	0.538982i	0.0279826	+	0.0279826i
$372$	33.6917			1.74683
$373$	−5.33438	−	5.33438i	−0.276204	−	0.276204i	0.555388	−	0.831592i	$-0.312570\pi$
$373$	−5.33438	−	5.33438i	−0.276204	−	0.276204i	−0.831592	+	0.555388i	$0.812570\pi$
$374$	28.9346			1.49618
$375$		0			0
$376$		−	9.14806i		−	0.471775i
$377$	−12.9853	+	16.2535i	−0.668779	+	0.837098i
$378$	−0.426260	−	0.426260i	−0.0219245	−	0.0219245i
$379$	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	$0.693144\pi$
$380$		0			0
$381$			5.42696i			0.278032i
$382$			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	$0.502696\pi$
$384$	−12.4059	+	12.4059i	−0.633086	+	0.633086i
$385$		0			0
$386$	−23.0849			−1.17499
$387$	−3.88596	−	3.88596i	−0.197534	−	0.197534i
$388$			19.9163i			1.01110i
$389$	6.77907			0.343713			0.171856	−	0.985122i	$-0.445024\pi$
$389$	6.77907			0.343713			0.171856	+	0.985122i	$0.445024\pi$
$390$		0			0
$391$	−5.22629			−0.264305
$392$			37.6965i			1.90396i
$393$	−3.56340	−	3.56340i	−0.179750	−	0.179750i
$394$	32.1097			1.61766
$395$		0			0
$396$	−17.7420	+	17.7420i	−0.891570	+	0.891570i
$397$	−25.7273			−1.29121			−0.645607	−	0.763670i	$-0.723396\pi$
$397$	−25.7273			−1.29121			−0.645607	+	0.763670i	$0.723396\pi$
$398$			5.85714i			0.293592i
$399$		−	1.34203i		−	0.0671857i
$400$		0			0
$401$	7.72622	+	7.72622i	0.385829	+	0.385829i	0.873197	−	0.487368i	$-0.162043\pi$
$401$	7.72622	+	7.72622i	0.385829	+	0.385829i	−0.487368	+	0.873197i	$0.662043\pi$
$402$	−26.9185	−	26.9185i	−1.34258	−	1.34258i
$403$	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
$408$	10.5370			0.521657
$409$	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	$0.669471\pi$
$410$		0			0
$411$	9.47174	+	9.47174i	0.467207	+	0.467207i
$412$	41.2439	−	41.2439i	2.03194	−	2.03194i
$413$	1.27957	−	1.27957i	0.0629634	−	0.0629634i
$414$	4.73652	−	4.73652i	0.232787	−	0.232787i
$415$		0			0
$416$	4.30611	−	5.38988i	0.211124	−	0.264260i
$417$	4.26942	−	4.26942i	0.209075	−	0.209075i
$418$	−82.5606			−4.03817
$419$			23.1087i			1.12894i	0.825455	+	0.564468i	$0.190919\pi$
$419$			23.1087i			1.12894i	−0.825455	+	0.564468i	$0.809081\pi$
$420$		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
$423$			1.68447i			0.0819019i
$424$	12.0748	−	12.0748i	0.586405	−	0.586405i
$425$		0			0
$426$		−	0.274470i		−	0.0132981i
$427$	2.48442			0.120229
$428$	−16.7460	+	16.7460i	−0.809448	+	0.809448i
$429$	−13.4965	+	16.8933i	−0.651615	+	0.815615i
$430$		0			0
$431$	1.67187	−	1.67187i	0.0805312	−	0.0805312i	−0.665694	−	0.746225i	$-0.731864\pi$
$431$	1.67187	−	1.67187i	0.0805312	−	0.0805312i	0.746225	+	0.665694i	$0.231864\pi$
$432$	−3.63258	+	3.63258i	−0.174772	+	0.174772i
$433$	−10.8483	+	10.8483i	−0.521337	+	0.521337i	−0.917975	−	0.396638i	$-0.870177\pi$
$433$	−10.8483	+	10.8483i	−0.521337	+	0.521337i	0.396638	+	0.917975i	$0.370177\pi$
$434$	−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
$438$	−2.55675	−	2.55675i	−0.122166	−	0.122166i
$439$	−20.2491			−0.966437			−0.483219	−	0.875500i	$-0.660532\pi$
$439$	−20.2491			−0.966437			−0.483219	+	0.875500i	$0.660532\pi$
$440$		0			0
$441$		−	6.94124i		−	0.330535i
$442$	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	$0.602676\pi$
$444$	9.81859	+	9.81859i	0.465970	+	0.465970i
$445$		0			0
$446$			21.6849i			1.02681i
$447$		−	20.9230i		−	0.989622i
$448$	1.33725			0.0631792
$449$	23.3059	−	23.3059i	1.09988	−	1.09988i	0.105451	−	0.994425i	$-0.466372\pi$
$449$	23.3059	−	23.3059i	1.09988	−	1.09988i	0.994425	−	0.105451i	$-0.0336285\pi$
$450$		0			0
$451$	12.8464			0.604916
$452$	51.5778	+	51.5778i	2.42602	+	2.42602i
$453$		−	20.7595i		−	0.975367i
$454$	45.7346			2.14643
$455$		0			0
$456$	−30.0656			−1.40795
$457$		−	15.5860i		−	0.729085i	−0.931187	−	0.364542i	$-0.881225\pi$
$457$		−	15.5860i		−	0.729085i	0.931187	−	0.364542i	$-0.118775\pi$
$458$	41.5662	+	41.5662i	1.94226	+	1.94226i
$459$	−1.94022			−0.0905616
$460$		0			0
$461$	20.8994	−	20.8994i	0.973381	−	0.973381i	−0.0262742	−	0.999655i	$-0.508364\pi$
$461$	20.8994	−	20.8994i	0.973381	−	0.973381i	0.999655	+	0.0262742i	$0.00836429\pi$
$462$	3.61515			0.168192
$463$			8.32123i			0.386720i	0.981128	+	0.193360i	$0.0619386\pi$
$463$			8.32123i			0.386720i	−0.981128	+	0.193360i	$0.938061\pi$
$464$		−	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	$0.494805\pi$
$468$	−9.41597	+	11.7858i	−0.435253	+	0.544799i
$469$			3.71102i			0.171359i
$470$		0			0
$471$	−6.03433			−0.278047
$472$	−28.6661	−	28.6661i	−1.31947	−	1.31947i
$473$	32.9571			1.51537
$474$	−13.3662	−	13.3662i	−0.613929	−	0.613929i
$475$		0			0
$476$	−1.39148	−	1.39148i	−0.0637782	−	0.0637782i
$477$	−2.22339	+	2.22339i	−0.101802	+	0.101802i
$478$	21.6668	−	21.6668i	0.991015	−	0.991015i
$479$	12.9813	−	12.9813i	0.593132	−	0.593132i	−0.345344	−	0.938476i	$-0.612238\pi$
$479$	12.9813	−	12.9813i	0.593132	−	0.593132i	0.938476	+	0.345344i	$0.112238\pi$
$480$		0			0
$481$	9.34889	+	7.46907i	0.426273	+	0.340560i
$482$	15.8556	−	15.8556i	0.722204	−	0.722204i
$483$	−0.652982			−0.0297117
$484$		−	104.449i		−	4.74766i
$485$		0			0
$486$	1.75839	−	1.75839i	0.0797624	−	0.0797624i
$487$			12.6406i			0.572801i	0.958110	+	0.286400i	$0.0924587\pi$
$487$			12.6406i			0.572801i	−0.958110	+	0.286400i	$0.907541\pi$
$488$		−	55.6584i		−	2.51954i
$489$	10.4110	−	10.4110i	0.470801	−	0.470801i
$490$		0			0
$491$		−	27.8197i		−	1.25549i	−0.778421	−	0.627743i	$-0.783979\pi$
$491$		−	27.8197i		−	1.25549i	0.778421	−	0.627743i	$-0.216021\pi$
$492$	8.96248			0.404060
$493$	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
$498$	4.78221	−	4.78221i	0.214296	−	0.214296i
$499$	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	$0.748468\pi$
$500$		0			0
$501$	−4.30314	−	4.30314i	−0.192250	−	0.192250i
$502$	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	$0.703754\pi$
$504$	1.31651			0.0586419
$505$		0			0
$506$			40.1708i			1.78581i
$507$	−6.93593	+	10.9951i	−0.308035	+	0.488311i
$508$	−16.0555	−	16.0555i	−0.712347	−	0.712347i
$509$	−11.1303	−	11.1303i	−0.493341	−	0.493341i	0.416016	−	0.909357i	$-0.363426\pi$
$509$	−11.1303	−	11.1303i	−0.493341	−	0.493341i	−0.909357	+	0.416016i	$0.863426\pi$
$510$		0			0
$511$			0.352477i			0.0155927i
$512$		−	45.9692i		−	2.03157i
$513$	5.53612			0.244425
$514$	−24.7986	+	24.7986i	−1.09382	+	1.09382i
$515$		0			0
$516$	22.9929			1.01221
$517$	−7.14308	−	7.14308i	−0.314152	−	0.314152i
$518$		−	2.00066i		−	0.0879038i
$519$	16.0261			0.703469
$520$		0			0
$521$	−13.6076			−0.596161			−0.298080	−	0.954541i	$-0.596346\pi$
$521$	−13.6076			−0.596161			−0.298080	+	0.954541i	$0.596346\pi$
$522$			14.3483i			0.628009i
$523$	12.9591	+	12.9591i	0.566664	+	0.566664i	0.931192	−	0.364528i	$-0.118770\pi$
$523$	12.9591	+	12.9591i	0.566664	+	0.566664i	−0.364528	+	0.931192i	$0.618770\pi$
$524$	21.0844			0.921076
$525$		0			0
$526$	41.1644	−	41.1644i	1.79485	−	1.79485i
$527$	−15.6240			−0.680591
$528$		−	30.8082i		−	1.34075i
$529$			15.7442i			0.684530i
$530$		0			0
$531$	5.27843	+	5.27843i	0.229064	+	0.229064i
$532$	3.97036	+	3.97036i	0.172137	+	0.172137i
$533$	7.67577	−	0.857959i	0.332475	−	0.0371623i
$534$			3.11981i			0.135008i
$535$		0			0
$536$	83.1381			3.59102
$537$	2.82652	+	2.82652i	0.121973	+	0.121973i
$538$	−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
$543$	11.6979	−	11.6979i	0.502005	−	0.502005i
$544$	−2.62505	+	2.62505i	−0.112548	+	0.112548i
$545$		0			0
$546$	2.16006	−	0.241440i	0.0924419	−	0.0103327i
$547$	18.6456	−	18.6456i	0.797229	−	0.797229i	−0.185428	−	0.982658i	$-0.559367\pi$
$547$	18.6456	−	18.6456i	0.797229	−	0.797229i	0.982658	+	0.185428i	$0.0593673\pi$
$548$	−56.0437			−2.39407
$549$			10.2486i			0.437401i
$550$		0			0
$551$	−22.5871	+	22.5871i	−0.962241	+	0.962241i
$552$			14.6288i			0.622641i
$553$			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	$0.491038\pi$
$558$	14.1598	−	14.1598i	0.599432	−	0.599432i
$559$	19.6919	−	2.20106i	0.832880	−	0.0930951i
$560$		0			0
$561$	8.22758	−	8.22758i	0.347369	−	0.347369i
$562$	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	$0.0998629\pi$
$564$	−4.98346	−	4.98346i	−0.209842	−	0.209842i
$565$		0			0
$566$	−6.56889	−	6.56889i	−0.276111	−	0.276111i
$567$	−0.242414			−0.0101804
$568$	0.423851	+	0.423851i	0.0177844	+	0.0177844i
$569$	31.7042			1.32911			0.664555	−	0.747239i	$-0.268621\pi$
$569$	31.7042			1.32911			0.664555	+	0.747239i	$0.268621\pi$
$570$		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
$573$	9.22243	+	9.22243i	0.385272	+	0.385272i
$574$	−0.913107	−	0.913107i	−0.0381123	−	0.0381123i
$575$		0			0
$576$			5.51638i			0.229849i
$577$		−	38.7401i		−	1.61277i	−0.591391	−	0.806385i	$-0.701421\pi$
$577$		−	38.7401i		−	1.61277i	0.591391	−	0.806385i	$-0.298579\pi$
$578$	32.9135			1.36902
$579$	−6.56419	+	6.56419i	−0.272799	+	0.272799i
$580$		0			0
$581$	−0.659281			−0.0273516
$582$	8.37033	+	8.37033i	0.346962	+	0.346962i
$583$		−	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	$0.923764\pi$
$588$	20.5354	+	20.5354i	0.846866	+	0.846866i
$589$	44.5806			1.83691
$590$		0			0
$591$	9.13041	−	9.13041i	0.375575	−	0.375575i
$592$	−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	$0.839579\pi$
$594$			14.9131i			0.611891i
$595$		0			0
$596$	61.8999	+	61.8999i	2.53552	+	2.53552i
$597$	1.66548	+	1.66548i	0.0681636	+	0.0681636i
$598$	2.68284	+	24.0021i	0.109709	+	0.981520i
$599$			15.0098i			0.613282i	0.951825	+	0.306641i	$0.0992051\pi$
$599$			15.0098i			0.613282i	−0.951825	+	0.306641i	$0.900795\pi$
$600$		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
$603$	−15.3086			−0.623414
$604$	61.4163	+	61.4163i	2.49900	+	2.49900i
$605$		0			0
$606$	−19.8413	−	19.8413i	−0.805996	−	0.805996i
$607$	1.90926	−	1.90926i	0.0774945	−	0.0774945i	−0.667297	−	0.744792i	$-0.732549\pi$
$607$	1.90926	−	1.90926i	0.0774945	−	0.0774945i	0.744792	+	0.667297i	$0.232549\pi$
$608$	7.49017	−	7.49017i	0.303766	−	0.303766i
$609$	0.989038	−	0.989038i	0.0400779	−	0.0400779i
$610$		0			0
$611$	−4.74506	−	3.79095i	−0.191965	−	0.153365i
$612$	5.74007	−	5.74007i	0.232029	−	0.232029i
$613$	8.40716			0.339562			0.169781	−	0.985482i	$-0.445694\pi$
$613$	8.40716			0.339562			0.169781	+	0.985482i	$0.445694\pi$
$614$		−	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	$-0.0322267\pi$
$618$		−	34.6677i		−	1.39454i
$619$	−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	$0.945595\pi$
$620$		0			0
$621$		−	2.69366i		−	0.108093i
$622$	17.5524			0.703786
$623$	0.215051	−	0.215051i	0.00861582	−	0.00861582i
$624$	−2.05755	−	18.4079i	−0.0823678	−	0.736907i
$625$		0			0
$626$	−9.58810	+	9.58810i	−0.383218	+	0.383218i
$627$	−23.4761	+	23.4761i	−0.937546	+	0.937546i
$628$	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
$633$	−15.5429	−	15.5429i	−0.617775	−	0.617775i
$634$	−34.6097			−1.37453
$635$		0			0
$636$		−	13.1557i		−	0.521656i
$637$	19.5530	+	15.6214i	0.774719	+	0.618943i
$638$	−60.8446	−	60.8446i	−2.40886	−	2.40886i
$639$	−0.0780456	−	0.0780456i	−0.00308744	−	0.00308744i
$640$		0			0
$641$			8.55187i			0.337779i	0.985635	+	0.168889i	$0.0540181\pi$
$641$			8.55187i			0.337779i	−0.985635	+	0.168889i	$0.945982\pi$
$642$			14.0759i			0.555531i
$643$	3.11521			0.122852			0.0614259	−	0.998112i	$-0.480435\pi$
$643$	3.11521			0.122852			0.0614259	+	0.998112i	$0.480435\pi$
$644$	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	$-0.513032\pi$
$648$			5.43081i			0.213342i
$649$	−44.7668			−1.75725
$650$		0			0
$651$	−1.95209			−0.0765084
$652$			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	$0.664299\pi$
$654$	16.1615			0.631963
$655$		0			0
$656$	−7.78146	+	7.78146i	−0.303815	+	0.303815i
$657$	−1.45403			−0.0567270
$658$			1.01544i			0.0395860i
$659$		−	15.1490i		−	0.590122i	−0.955478	−	0.295061i	$-0.904660\pi$
$659$		−	15.1490i		−	0.590122i	0.955478	−	0.295061i	$-0.0953400\pi$
$660$		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
$663$	4.36651	−	5.46548i	0.169581	−	0.212262i
$664$			14.7699i			0.573182i
$665$		0			0
$666$	8.25304			0.319799
$667$	10.9900	+	10.9900i	0.425534	+	0.425534i
$668$	25.4614			0.985131
$669$	6.16611	+	6.16611i	0.238396	+	0.238396i
$670$		0			0
$671$	−43.4597	−	43.4597i	−1.67774	−	1.67774i
$672$	−0.327978	+	0.327978i	−0.0126520	+	0.0126520i
$673$	−26.4650	+	26.4650i	−1.02015	+	1.02015i	−0.0203584	+	0.999793i	$0.506481\pi$
$673$	−26.4650	+	26.4650i	−1.02015	+	1.02015i	−0.999793	+	0.0203584i	$0.993519\pi$
$674$	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	$0.128537\pi$
$678$	43.3539			1.66500
$679$		−	1.15394i		−	0.0442843i
$680$		0			0
$681$	13.0046	−	13.0046i	0.498339	−	0.498339i
$682$			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	$0.909568\pi$
$684$	−16.3784	+	16.3784i	−0.626244	+	0.626244i
$685$		0			0
$686$		−	8.40410i		−	0.320870i
$687$	23.6387			0.901873
$688$	−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
$693$	1.02797	−	1.02797i	0.0390493	−	0.0390493i
$694$	−62.7023	−	62.7023i	−2.38015	−	2.38015i
$695$		0			0
$696$	−22.1574	−	22.1574i	−0.839875	−	0.839875i
$697$	−4.15621			−0.157428
$698$	12.0740	+	12.0740i	0.457009	+	0.457009i
$699$	−0.849846			−0.0321441
$700$		0			0
$701$			13.7058i			0.517659i	0.965923	+	0.258830i	$0.0833369\pi$
$701$			13.7058i			0.517659i	−0.965923	+	0.258830i	$0.916663\pi$
$702$	0.995982	+	8.91060i	0.0375909	+	0.336309i
$703$	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
$708$	−31.2321			−1.17377
$709$	−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			0
$711$	−7.60135			−0.285073
$712$	−4.81778	−	4.81778i	−0.180554	−	0.180554i
$713$		−	21.6912i		−	0.812342i
$714$	−1.16961			−0.0437715
$715$		0			0
$716$	−16.7243			−0.625017
$717$		−	12.3219i		−	0.460170i
$718$	−5.75584	−	5.75584i	−0.214806	−	0.214806i
$719$	−27.4328			−1.02307			−0.511536	−	0.859262i	$-0.670923\pi$
$719$	−27.4328			−1.02307			−0.511536	+	0.859262i	$0.670923\pi$
$720$		0			0
$721$	−2.38966	+	2.38966i	−0.0889957	+	0.0889957i
$722$	−28.9670			−1.07804
$723$		−	9.01711i		−	0.335350i
$724$			69.2157i			2.57238i
$725$		0			0
$726$	−43.8972	−	43.8972i	−1.62918	−	1.62918i
$727$	−27.8372	−	27.8372i	−1.03243	−	1.03243i	−0.999456	−	0.0329694i	$-0.989504\pi$
$727$	−27.8372	−	27.8372i	−1.03243	−	1.03243i	−0.0329694	−	0.999456i	$-0.510496\pi$
$728$	−2.96283	+	3.70852i	−0.109810	+	0.137447i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−10.6626			−0.394371
$732$	−30.3202	−	30.3202i	−1.12067	−	1.12067i
$733$	−16.0974			−0.594571			−0.297285	−	0.954789i	$-0.596081\pi$
$733$	−16.0974			−0.594571			−0.297285	+	0.954789i	$0.596081\pi$
$734$	−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
$738$	3.76672	−	3.76672i	0.138655	−	0.138655i
$739$	−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	$0.330961\pi$
$740$		0			0
$741$	−12.4592	+	15.5949i	−0.457699	+	0.572893i
$742$	−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	$0.496146\pi$
$744$			43.7326i			1.60332i
$745$		0			0
$746$	13.2653	−	13.2653i	0.485675	−	0.485675i
$747$		−	2.71964i		−	0.0995066i
$748$			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
$753$	5.78084	−	5.78084i	0.210665	−	0.210665i
$754$	−40.4183	−	32.2912i	−1.47195	−	1.17598i
$755$		0			0
$756$	0.717175	−	0.717175i	0.0260834	−	0.0260834i
$757$	−10.5506	+	10.5506i	−0.383469	+	0.383469i	−0.872350	−	0.488881i	$-0.837405\pi$
$757$	−10.5506	+	10.5506i	−0.383469	+	0.383469i	0.488881	+	0.872350i	$0.337405\pi$
$758$	−12.1642	+	12.1642i	−0.441823	+	0.441823i
$759$	11.4226	+	11.4226i	0.414613	+	0.414613i
$760$		0			0
$761$	22.4488	+	22.4488i	0.813767	+	0.813767i	0.985196	−	0.171429i	$-0.0548386\pi$
$761$	22.4488	+	22.4488i	0.813767	+	0.813767i	−0.171429	+	0.985196i	$0.554839\pi$
$762$	−13.4955			−0.488890
$763$	−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
$768$	−23.0490	−	23.0490i	−0.831709	−	0.831709i
$769$	−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	$0.778020\pi$
$770$		0			0
$771$			14.1030i			0.507907i
$772$		−	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	$0.651847\pi$
$774$	9.66338	−	9.66338i	0.347343	−	0.347343i
$775$		0			0
$776$	−25.8518			−0.928026
$777$	−0.568887	−	0.568887i	−0.0204087	−	0.0204087i
$778$			16.8578i			0.604383i
$779$	11.8591			0.424896
$780$		0			0
$781$	0.661911			0.0236850
$782$		−	12.9965i		−	0.464752i
$783$	4.07995	+	4.07995i	0.145805	+	0.145805i
$784$	−35.6588			−1.27353
$785$		0			0
$786$	8.86127	−	8.86127i	0.316071	−	0.316071i
$787$	15.5693			0.554986			0.277493	−	0.960728i	$-0.410496\pi$
$787$	15.5693			0.554986			0.277493	+	0.960728i	$0.410496\pi$
$788$			54.0240i			1.92453i
$789$		−	23.4102i		−	0.833426i
$790$		0			0
$791$	−2.98841	−	2.98841i	−0.106256	−	0.106256i
$792$	−23.0296	−	23.0296i	−0.818320	−	0.818320i
$793$	−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	$0.691033\pi$
$798$	3.33730			0.118139
$799$	2.31100	+	2.31100i	0.0817573	+	0.0817573i
$800$		0			0
$801$	0.887120	+	0.887120i	0.0313448	+	0.0313448i
$802$	−19.2132	+	19.2132i	−0.678440	+	0.678440i
$803$	6.16586	−	6.16586i	0.217588	−	0.217588i
$804$	45.2900	−	45.2900i	1.59725	−	1.59725i
$805$		0			0
$806$	8.02033	+	71.7543i	0.282504	+	2.52744i
$807$	−11.8207	+	11.8207i	−0.416107	+	0.416107i
$808$	61.2798			2.15582
$809$			32.8074i			1.15345i	0.816939	+	0.576724i	$0.195669\pi$
$809$			32.8074i			1.15345i	−0.816939	+	0.576724i	$0.804331\pi$
$810$		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
$813$			17.8056i			0.624468i
$814$	−34.9974	+	34.9974i	−1.22666	+	1.22666i
$815$		0			0
$816$			9.96736i			0.348927i
$817$	30.4241			1.06440
$818$	−17.8020	+	17.8020i	−0.622431	+	0.622431i
$819$	0.545559	−	0.682867i	0.0190634	−	0.0238613i
$820$		0			0
$821$	28.3481	−	28.3481i	0.989357	−	0.989357i	−0.0105868	−	0.999944i	$-0.503370\pi$
$821$	28.3481	−	28.3481i	0.989357	−	0.989357i	0.999944	+	0.0105868i	$0.00336993\pi$
$822$	−23.5538	+	23.5538i	−0.821534	+	0.821534i
$823$	33.0457	−	33.0457i	1.15190	−	1.15190i	0.165729	−	0.986171i	$-0.447002\pi$
$823$	33.0457	−	33.0457i	1.15190	−	1.15190i	0.986171	−	0.165729i	$-0.0529977\pi$
$824$	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	$0.836915\pi$
$828$	7.96910	+	7.96910i	0.276946	+	0.276946i
$829$	28.1449			0.977512			0.488756	−	0.872420i	$-0.337451\pi$
$829$	28.1449			0.977512			0.488756	+	0.872420i	$0.337451\pi$
$830$		0			0
$831$			25.3059i			0.877850i
$832$	−15.5393	−	12.4148i	−0.538729	−	0.430404i
$833$	−9.52297	−	9.52297i	−0.329951	−	0.329951i
$834$	10.6170	+	10.6170i	0.367636	+	0.367636i
$835$		0			0
$836$		−	138.907i		−	4.80419i
$837$		−	8.05269i		−	0.278342i
$838$	−57.4655			−1.98511
$839$	−25.8159	+	25.8159i	−0.891264	+	0.891264i	−0.994642	−	0.103378i	$-0.967035\pi$
$839$	−25.8159	+	25.8159i	−0.891264	+	0.891264i	0.103378	+	0.994642i	$0.467035\pi$
$840$		0			0
$841$	−4.29196			−0.147999
$842$	−0.804189	−	0.804189i	−0.0277142	−	0.0277142i
$843$		−	3.74304i		−	0.128917i
$844$	91.9664			3.16561
$845$		0			0
$846$	−4.18886			−0.144016
$847$			6.05173i			0.207940i
$848$	11.4221	+	11.4221i	0.392236	+	0.392236i
$849$	−3.73573			−0.128210
$850$		0			0
$851$	6.32136	−	6.32136i	0.216694	−	0.216694i
$852$	0.461790			0.0158207
$853$		−	6.25026i		−	0.214005i	−0.994259	−	0.107002i	$-0.965875\pi$
$853$		−	6.25026i		−	0.214005i	0.994259	−	0.107002i	$-0.0341253\pi$
$854$			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	$0.654583\pi$
$858$	−42.0093	−	33.5623i	−1.43417	−	1.14580i
$859$		−	25.0493i		−	0.854670i	−0.904093	−	0.427335i	$-0.859452\pi$
$859$		−	25.0493i		−	0.854670i	0.904093	−	0.427335i	$-0.140548\pi$
$860$		0			0
$861$	−0.519284			−0.0176972
$862$	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	$0.357409\pi$
$864$	−1.35296	−	1.35296i	−0.0460288	−	0.0460288i
$865$		0			0
$866$	−26.9770	−	26.9770i	−0.916716	−	0.916716i
$867$	9.35895	−	9.35895i	0.317847	−	0.317847i
$868$	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
$873$	4.76021			0.161109
$874$			37.0834i			1.25436i
$875$		0			0
$876$	4.30169	−	4.30169i	0.145341	−	0.145341i
$877$		−	21.2930i		−	0.719015i	−0.933142	−	0.359507i	$-0.882945\pi$
$877$		−	21.2930i		−	0.719015i	0.933142	−	0.359507i	$-0.117055\pi$
$878$		−	50.3544i		−	1.69938i
$879$	−6.27368	+	6.27368i	−0.211606	+	0.211606i
$880$		0			0
$881$		−	10.5084i		−	0.354037i	−0.984208	−	0.177018i	$-0.943355\pi$
$881$		−	10.5084i		−	0.354037i	0.984208	−	0.177018i	$-0.0566452\pi$
$882$	17.2611			0.581211
$883$	−9.86276	+	9.86276i	−0.331908	+	0.331908i	−0.853311	−	0.521403i	$-0.825409\pi$
$883$	−9.86276	+	9.86276i	−0.331908	+	0.331908i	0.521403	+	0.853311i	$0.325409\pi$
$884$	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	$0.421270\pi$
$888$	−12.7448	+	12.7448i	−0.427687	+	0.427687i
$889$	0.930252	+	0.930252i	0.0311996	+	0.0311996i
$890$		0			0
$891$	4.24054	+	4.24054i	0.142063	+	0.142063i
$892$	−36.4845			−1.22159
$893$	−6.59408	−	6.59408i	−0.220663	−	0.220663i
$894$	52.0301			1.74015
$895$		0			0
$896$			4.25307i			0.142085i
$897$	7.58788	+	6.06215i	0.253352	+	0.202409i
$898$	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
$903$	−1.33221			−0.0443330
$904$	−66.9493	+	66.9493i	−2.22670	+	2.22670i
$905$		0			0
$906$	51.6236			1.71508
$907$	−14.1974	−	14.1974i	−0.471417	−	0.471417i	0.430956	−	0.902373i	$-0.358177\pi$
$907$	−14.1974	−	14.1974i	−0.471417	−	0.471417i	−0.902373	+	0.430956i	$0.858177\pi$
$908$			76.9475i			2.55359i
$909$	−11.2837			−0.374258
$910$		0			0
$911$	−6.62609			−0.219532			−0.109766	−	0.993957i	$-0.535010\pi$
$911$	−6.62609			−0.219532			−0.109766	+	0.993957i	$0.535010\pi$
$912$		−	28.4403i		−	0.941754i
$913$	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
$918$		−	4.82483i		−	0.159243i
$919$		−	56.0617i		−	1.84930i	−0.380813	−	0.924652i	$-0.624356\pi$
$919$		−	56.0617i		−	1.84930i	0.380813	−	0.924652i	$-0.375644\pi$
$920$		0			0
$921$	−17.8073	−	17.8073i	−0.586770	−	0.586770i
$922$	51.9714	+	51.9714i	1.71159	+	1.71159i
$923$	0.395493	−	0.0442062i	0.0130178	−	0.00145507i
$924$			6.08242i			0.200097i
$925$		0			0
$926$	−20.6928			−0.680007
$927$	−9.85776	−	9.85776i	−0.323771	−	0.323771i
$928$	11.0400			0.362407
$929$	−16.7396	−	16.7396i	−0.549210	−	0.549210i	0.377003	−	0.926212i	$-0.376955\pi$
$929$	−16.7396	−	16.7396i	−0.549210	−	0.549210i	−0.926212	+	0.377003i	$0.876955\pi$
$930$		0			0
$931$	27.1723	+	27.1723i	0.890537	+	0.890537i
$932$	2.51424	−	2.51424i	0.0823567	−	0.0823567i
$933$	4.99102	−	4.99102i	0.163399	−	0.163399i
$934$	−54.6088	+	54.6088i	−1.78685	+	1.78685i
$935$		0			0
$936$	−15.2983	−	12.2222i	−0.500039	−	0.399494i
$937$	−12.3582	+	12.3582i	−0.403724	+	0.403724i	−0.879543	−	0.475819i	$-0.842152\pi$
$937$	−12.3582	+	12.3582i	−0.403724	+	0.403724i	0.475819	+	0.879543i	$0.342152\pi$
$938$	−9.22837			−0.301317
$939$			5.45276i			0.177944i
$940$		0			0
$941$	18.8531	−	18.8531i	0.614594	−	0.614594i	−0.329545	−	0.944140i	$-0.606895\pi$
$941$	18.8531	−	18.8531i	0.614594	−	0.614594i	0.944140	+	0.329545i	$0.106895\pi$
$942$		−	15.0058i		−	0.488917i
$943$		−	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	$0.570594\pi$
$948$	22.4883	−	22.4883i	0.730387	−	0.730387i
$949$	3.27232	−	4.09590i	0.106224	−	0.132959i
$950$		0			0
$951$	−9.84128	+	9.84128i	−0.319125	+	0.319125i
$952$	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	$0.170309\pi$
$954$	−5.52901	−	5.52901i	−0.179008	−	0.179008i
$955$		0			0
$956$	36.4540	+	36.4540i	1.17901	+	1.17901i
$957$	−34.6024			−1.11854
$958$	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
$963$	4.00248	+	4.00248i	0.128978	+	0.128978i
$964$	26.6768	+	26.6768i	0.859202	+	0.859202i
$965$		0			0
$966$		−	1.62380i		−	0.0522449i
$967$		−	16.5180i		−	0.531183i	−0.964086	−	0.265591i	$-0.914433\pi$
$967$		−	16.5180i		−	0.531183i	0.964086	−	0.265591i	$-0.0855672\pi$
$968$	135.577			4.35760
$969$	7.59523	−	7.59523i	0.243994	−	0.243994i
$970$		0			0
$971$	−40.8913			−1.31226			−0.656132	−	0.754646i	$-0.727809\pi$
$971$	−40.8913			−1.31226			−0.656132	+	0.754646i	$0.727809\pi$
$972$	2.95847	+	2.95847i	0.0948928	+	0.0948928i
$973$		−	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	$-0.00980030\pi$
$978$	25.8894	+	25.8894i	0.827853	+	0.827853i
$979$	−7.52374			−0.240460
$980$		0			0
$981$	4.59552	−	4.59552i	0.146724	−	0.146724i
$982$	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	$-0.401921\pi$
$984$			11.6335i			0.370863i
$985$		0			0
$986$	19.6851	+	19.6851i	0.626900	+	0.626900i
$987$	0.288741	+	0.288741i	0.00919071	+	0.00919071i
$988$	−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
$993$	−9.73371			−0.308890
$994$	−0.0470477	−	0.0470477i	−0.00149226	−	0.00149226i
$995$		0			0
$996$	8.04597	+	8.04597i	0.254946	+	0.254946i
$997$	34.3919	−	34.3919i	1.08920	−	1.08920i	0.0935912	−	0.995611i	$-0.470165\pi$
$997$	34.3919	−	34.3919i	1.08920	−	1.08920i	0.995611	−	0.0935912i	$-0.0298347\pi$
$998$	−0.378169	+	0.378169i	−0.0119707	+	0.0119707i
$999$	2.34675	−	2.34675i	0.0742480	−	0.0742480i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.k.a.112.14	✓	28	65.8	even	4
195.2.k.a.148.1	yes	28	5.4	even	2
195.2.t.a.73.14	yes	28	65.34	odd	4
195.2.t.a.187.14	yes	28	5.3	odd	4
585.2.n.g.307.1		28	195.8	odd	4
585.2.n.g.343.14		28	15.14	odd	2
585.2.w.g.73.1		28	195.164	even	4
585.2.w.g.577.1		28	15.8	even	4
975.2.k.d.307.1		28	65.47	even	4	inner
975.2.k.d.343.14		28	1.1	even	1	trivial
975.2.t.d.268.1		28	13.8	odd	4
975.2.t.d.382.1		28	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.48675i q^{2} +(0.707107 + 0.707107i) q^{3} -4.18390 q^{4} +(-1.75839 + 1.75839i) q^{6} +0.242414 q^{7} -5.43081i q^{8} +1.00000i q^{9} +(-4.24054 - 4.24054i) q^{11} +(-2.95847 - 2.95847i) q^{12} +(-2.81694 - 2.25052i) q^{13} +0.602823i q^{14} +5.13724 q^{16} +(1.37194 + 1.37194i) q^{17} -2.48675 q^{18} +(-3.91462 - 3.91462i) q^{19} +(0.171413 + 0.171413i) q^{21} +(10.5451 - 10.5451i) q^{22} +(-1.90471 + 1.90471i) q^{23} +(3.84016 - 3.84016i) q^{24} +(5.59648 - 7.00501i) q^{26} +(-0.707107 + 0.707107i) q^{27} -1.01424 q^{28} -5.76992i q^{29} +(-5.69411 + 5.69411i) q^{31} +1.91338i q^{32} -5.99703i q^{33} +(-3.41167 + 3.41167i) q^{34} -4.18390i q^{36} -3.31881 q^{37} +(9.73467 - 9.73467i) q^{38} +(-0.400516 - 3.58324i) q^{39} +(-1.51472 + 1.51472i) q^{41} +(-0.426260 + 0.426260i) q^{42} +(-3.88596 + 3.88596i) q^{43} +(17.7420 + 17.7420i) q^{44} +(-4.73652 - 4.73652i) q^{46} +1.68447 q^{47} +(3.63258 + 3.63258i) q^{48} -6.94124 q^{49} +1.94022i q^{51} +(11.7858 + 9.41597i) q^{52} +(2.22339 + 2.22339i) q^{53} +(-1.75839 - 1.75839i) q^{54} -1.31651i q^{56} -5.53612i q^{57} +14.3483 q^{58} +(5.27843 - 5.27843i) q^{59} +10.2486 q^{61} +(-14.1598 - 14.1598i) q^{62} +0.242414i q^{63} +5.51638 q^{64} +14.9131 q^{66} +15.3086i q^{67} +(-5.74007 - 5.74007i) q^{68} -2.69366 q^{69} +(-0.0780456 + 0.0780456i) q^{71} +5.43081 q^{72} +1.45403i q^{73} -8.25304i q^{74} +(16.3784 + 16.3784i) q^{76} +(-1.02797 - 1.02797i) q^{77} +(8.91060 - 0.995982i) q^{78} +7.60135i q^{79} -1.00000 q^{81} +(-3.76672 - 3.76672i) q^{82} -2.71964 q^{83} +(-0.717175 - 0.717175i) q^{84} +(-9.66338 - 9.66338i) q^{86} +(4.07995 - 4.07995i) q^{87} +(-23.0296 + 23.0296i) q^{88} +(0.887120 - 0.887120i) q^{89} +(-0.682867 - 0.545559i) q^{91} +(7.96910 - 7.96910i) q^{92} -8.05269 q^{93} +4.18886i q^{94} +(-1.35296 + 1.35296i) q^{96} -4.76021i q^{97} -17.2611i q^{98} +(4.24054 - 4.24054i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} - 8 q^{11} - 8 q^{12} + 12 q^{13} + 28 q^{16} + 28 q^{17} + 4 q^{18} + 8 q^{21} + 32 q^{22} - 8 q^{23} - 16 q^{31} + 28 q^{34} - 32 q^{37} + 8 q^{39} + 4 q^{41} + 40 q^{44} - 16 q^{46} + 24 q^{47}+ \cdots + 8 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 - 8 * q^11 - 8 * q^12 + 12 * q^13 + 28 * q^16 + 28 * q^17 + 4 * q^18 + 8 * q^21 + 32 * q^22 - 8 * q^23 - 16 * q^31 + 28 * q^34 - 32 * q^37 + 8 * q^39 + 4 * q^41 + 40 * q^44 - 16 * q^46 + 24 * q^47 + 16 * q^48 - 28 * q^49 - 52 * q^52 - 20 * q^53 + 8 * q^58 + 32 * q^59 + 8 * q^61 - 72 * q^62 - 28 * q^64 + 16 * q^66 - 60 * q^68 + 8 * q^69 + 40 * q^71 - 12 * q^72 - 40 * q^76 + 48 * q^77 - 8 * q^78 - 28 * q^81 - 4 * q^82 + 104 * q^83 - 32 * q^84 + 16 * q^86 + 24 * q^87 - 72 * q^88 - 36 * q^89 - 56 * q^91 + 32 * q^92 + 8 * q^99

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