LMFDB - Embedded newform 975.2.t.d.268.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(268,975)] 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("975.268"); 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, 3, 1])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [28,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == 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			268.1
Character	$\chi$	$=$	975.268
Dual form			975.2.t.d.382.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

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

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 $

$2$	−2.48675			−1.75839			−0.879197	−	0.476458i	$-0.841920\pi$
$2$	−2.48675			−1.75839			−0.879197	+	0.476458i	$0.841920\pi$
$3$	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
$7$		−	0.242414i		−	0.0916240i	−0.998950	−	0.0458120i	$-0.985412\pi$
$7$		−	0.242414i		−	0.0916240i	0.998950	−	0.0458120i	$-0.0145875\pi$
$8$	−5.43081			−1.92008
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−4.24054	+	4.24054i	−1.27857	+	1.27857i	−0.337104	+	0.941467i	$0.609447\pi$
$11$	−4.24054	+	4.24054i	−1.27857	+	1.27857i	−0.941467	+	0.337104i	$0.890553\pi$
$12$	2.95847	+	2.95847i	0.854036	+	0.854036i
$13$	−2.25052	−	2.81694i	−0.624183	−	0.781278i
$13$	−2.25052	−	2.81694i	−0.624183	−	0.781278i
$14$			0.602823i			0.161111i
$15$		0			0
$16$	5.13724			1.28431
$17$	−1.37194	−	1.37194i	−0.332745	−	0.332745i	0.520883	−	0.853628i	$-0.325603\pi$
$17$	−1.37194	−	1.37194i	−0.332745	−	0.332745i	−0.853628	+	0.520883i	$0.825603\pi$
$18$		−	2.48675i		−	0.586132i
$19$	3.91462	−	3.91462i	0.898076	−	0.898076i	−0.0971894	−	0.995266i	$-0.530985\pi$
$19$	3.91462	−	3.91462i	0.898076	−	0.898076i	0.995266	+	0.0971894i	$0.0309853\pi$
$20$		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	−0.480071	−	0.877230i	$-0.659389\pi$
$23$	1.90471	−	1.90471i	0.397159	−	0.397159i	0.877230	+	0.480071i	$0.159389\pi$
$24$	−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
$28$		−	1.01424i		−	0.191673i
$29$		−	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	−0.999736	−	0.0229561i	$-0.992692\pi$
$31$	−5.69411	−	5.69411i	−1.02269	−	1.02269i	−0.0229561	−	0.999736i	$-0.507308\pi$
$32$	−1.91338			−0.338241
$33$	−5.99703			−1.04395
$34$	3.41167	+	3.41167i	0.585096	+	0.585096i
$35$		0			0
$36$			4.18390i			0.697317i
$37$			3.31881i			0.545609i	0.962069	+	0.272805i	$0.0879513\pi$
$37$			3.31881i			0.545609i	−0.962069	+	0.272805i	$0.912049\pi$
$38$	−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	0.578865	−	0.815424i	$-0.303496\pi$
$41$	−1.51472	−	1.51472i	−0.236559	−	0.236559i	−0.815424	+	0.578865i	$0.803496\pi$
$42$	−0.426260	+	0.426260i	−0.0657734	+	0.0657734i
$43$	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
$47$		−	1.68447i		−	0.245706i	−0.992425	−	0.122853i	$-0.960796\pi$
$47$		−	1.68447i		−	0.245706i	0.992425	−	0.122853i	$-0.0392043\pi$
$48$	3.63258	+	3.63258i	0.524317	+	0.524317i
$49$	6.94124			0.991605
$50$		0			0
$51$		−	1.94022i		−	0.271685i
$52$	−9.41597	−	11.7858i	−1.30576	−	1.63440i
$53$	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
$57$	5.53612			0.733276
$58$			14.3483i			1.88403i
$59$	−5.27843	−	5.27843i	−0.687193	−	0.687193i	0.274418	−	0.961611i	$-0.411515\pi$
$59$	−5.27843	−	5.27843i	−0.687193	−	0.687193i	−0.961611	+	0.274418i	$0.911515\pi$
$60$		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
$63$	0.242414			0.0305413
$64$	−5.51638			−0.689548
$65$		0			0
$66$	14.9131			1.83567
$67$	−15.3086			−1.87024			−0.935121	−	0.354328i	$-0.884710\pi$
$67$	−15.3086			−1.87024			−0.935121	+	0.354328i	$0.884710\pi$
$68$	−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	0.702460	−	0.711723i	$-0.252085\pi$
$71$	−0.0780456	−	0.0780456i	−0.00926231	−	0.00926231i	−0.711723	+	0.702460i	$0.752085\pi$
$72$		−	5.43081i		−	0.640027i
$73$	1.45403			0.170181			0.0850905	−	0.996373i	$-0.472882\pi$
$73$	1.45403			0.170181			0.0850905	+	0.996373i	$0.472882\pi$
$74$		−	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
$78$	−0.995982	+	8.91060i	−0.112773	+	1.00893i
$79$			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
$83$		−	2.71964i		−	0.298520i	−0.988798	−	0.149260i	$-0.952311\pi$
$83$		−	2.71964i		−	0.298520i	0.988798	−	0.149260i	$-0.0476891\pi$
$84$	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	$-0.271181\pi$
$89$	−0.887120	−	0.887120i	−0.0940345	−	0.0940345i	−0.752559	+	0.658525i	$0.771181\pi$
$90$		0			0
$91$	−0.682867	+	0.545559i	−0.0715839	+	0.0571902i
$92$	7.96910	−	7.96910i	0.830837	−	0.830837i
$93$		−	8.05269i		−	0.835025i
$94$			4.18886i			0.432048i
$95$		0			0
$96$	−1.35296	−	1.35296i	−0.138086	−	0.138086i
$97$	4.76021			0.483326			0.241663	−	0.970360i	$-0.422307\pi$
$97$	4.76021			0.483326			0.241663	+	0.970360i	$0.422307\pi$
$98$	−17.2611			−1.74363
$99$	−4.24054	−	4.24054i	−0.426190	−	0.426190i
$100$		0			0
$101$		−	11.2837i		−	1.12277i	−0.827553	−	0.561387i	$-0.810268\pi$
$101$		−	11.2837i		−	1.12277i	0.827553	−	0.561387i	$-0.189732\pi$
$102$			4.82483i			0.477729i
$103$	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	$0.161784\pi$
$108$	−2.95847	+	2.95847i	−0.284679	+	0.284679i
$109$	4.59552	−	4.59552i	0.440171	−	0.440171i	−0.451899	−	0.892069i	$-0.649253\pi$
$109$	4.59552	−	4.59552i	0.440171	−	0.440171i	0.892069	+	0.451899i	$0.149253\pi$
$110$		0			0
$111$	−2.34675	+	2.34675i	−0.222744	+	0.222744i
$112$		−	1.24534i		−	0.117674i
$113$	−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
$117$	2.81694	−	2.25052i	0.260426	−	0.208061i
$118$	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
$122$	−25.4857			−2.30737
$123$		−	2.14213i		−	0.193150i
$124$	−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	0.516044	−	0.856562i	$-0.327404\pi$
$127$	−3.83744	−	3.83744i	−0.340518	−	0.340518i	−0.856562	+	0.516044i	$0.827404\pi$
$128$	17.5446			1.55074
$129$	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	$0.570654\pi$
$132$	−25.0910			−2.18389
$133$	−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
$137$		−	13.3951i		−	1.14442i	−0.820108	−	0.572209i	$-0.806087\pi$
$137$		−	13.3951i		−	1.14442i	0.820108	−	0.572209i	$-0.193913\pi$
$138$	−6.69845			−0.570210
$139$		−	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
$143$	21.4888	+	2.40191i	1.79698	+	0.200858i
$144$			5.13724i			0.428103i
$145$		0			0
$146$	−3.61579			−0.299245
$147$	4.90819	+	4.90819i	0.404821	+	0.404821i
$148$			13.8856i			1.14139i
$149$	14.7948	−	14.7948i	1.21203	−	1.21203i	0.241678	−	0.970356i	$-0.422302\pi$
$149$	14.7948	−	14.7948i	1.21203	−	1.21203i	0.970356	−	0.241678i	$-0.0776979\pi$
$150$		0			0
$151$	−14.6792	+	14.6792i	−1.19458	+	1.19458i	−0.218808	+	0.975768i	$0.570217\pi$
$151$	−14.6792	+	14.6792i	−1.19458	+	1.19458i	−0.975768	+	0.218808i	$0.929783\pi$
$152$	−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	$0.327408\pi$
$158$		−	18.9026i		−	1.50381i
$159$			3.14435i			0.249363i
$160$		0			0
$161$	−0.461728	−	0.461728i	−0.0363893	−	0.0363893i
$162$	2.48675			0.195377
$163$	−14.7233			−1.15322			−0.576611	−	0.817019i	$-0.695625\pi$
$163$	−14.7233			−1.15322			−0.576611	+	0.817019i	$0.695625\pi$
$164$	−6.33743	−	6.33743i	−0.494870	−	0.494870i
$165$		0			0
$166$			6.76306i			0.524915i
$167$			6.08556i			0.470915i	0.971885	+	0.235457i	$0.0756588\pi$
$167$			6.08556i			0.470915i	−0.971885	+	0.235457i	$0.924341\pi$
$168$	−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	−0.991520	−	0.129951i	$-0.958518\pi$
$173$	−11.3322	+	11.3322i	−0.861570	+	0.861570i	0.129951	+	0.991520i	$0.458518\pi$
$174$	−10.1458	+	10.1458i	−0.769151	+	0.769151i
$175$		0			0
$176$	−21.7847	+	21.7847i	−1.64208	+	1.64208i
$177$		−	7.46482i		−	0.561090i
$178$	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	$0.210774\pi$
$181$			16.5433i			1.22966i	−0.788661	+	0.614828i	$0.789226\pi$
$182$	1.69812	−	1.35667i	0.125873	−	0.100563i
$183$	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
$187$	11.6355			0.850876
$188$		−	7.04768i		−	0.514005i
$189$	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
$193$	9.28317			0.668217			0.334109	−	0.942535i	$-0.391565\pi$
$193$	9.28317			0.668217			0.334109	+	0.942535i	$0.391565\pi$
$194$	−11.8374			−0.849879
$195$		0			0
$196$	29.0415			2.07439
$197$	12.9124			0.919967			0.459983	−	0.887927i	$-0.347855\pi$
$197$	12.9124			0.919967			0.459983	+	0.887927i	$0.347855\pi$
$198$	10.5451	+	10.5451i	0.749411	+	0.749411i
$199$	−2.35534			−0.166966			−0.0834830	−	0.996509i	$-0.526604\pi$
$199$	−2.35534			−0.166966			−0.0834830	+	0.996509i	$0.526604\pi$
$200$		0			0
$201$	−10.8248	−	10.8248i	−0.763523	−	0.763523i
$202$			28.0598i			1.97428i
$203$	−1.39871			−0.0981703
$204$		−	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
$208$	−11.5615	−	14.4713i	−0.801644	−	1.00340i
$209$			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
$213$		−	0.110373i		−	0.00756264i
$214$	−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
$223$			8.72020i			0.583948i	0.956426	+	0.291974i	$0.0943120\pi$
$223$			8.72020i			0.583948i	−0.956426	+	0.291974i	$0.905688\pi$
$224$			0.463831i			0.0309910i
$225$		0			0
$226$	30.6558	+	30.6558i	2.03919	+	2.03919i
$227$	18.3913			1.22068			0.610338	−	0.792141i	$-0.291034\pi$
$227$	18.3913			1.22068			0.610338	+	0.792141i	$0.291034\pi$
$228$	23.1626			1.53398
$229$	−16.7151	−	16.7151i	−1.10456	−	1.10456i	−0.993852	−	0.110712i	$-0.964687\pi$
$229$	−16.7151	−	16.7151i	−1.10456	−	1.10456i	−0.110712	−	0.993852i	$-0.535313\pi$
$230$		0			0
$231$			1.45377i			0.0956508i
$232$			31.3353i			2.05727i
$233$	0.600932	−	0.600932i	0.0393684	−	0.0393684i	−0.687149	−	0.726517i	$-0.741138\pi$
$233$	0.600932	−	0.600932i	0.0393684	−	0.0393684i	0.726517	+	0.687149i	$0.241138\pi$
$234$	−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	$-0.619524\pi$
$239$	8.71291	−	8.71291i	0.563591	−	0.563591i	0.930326	+	0.366735i	$0.119524\pi$
$240$		0			0
$241$	−6.37606	+	6.37606i	−0.410718	+	0.410718i	−0.881989	−	0.471271i	$-0.843796\pi$
$241$	−6.37606	+	6.37606i	−0.410718	+	0.410718i	0.471271	+	0.881989i	$0.343796\pi$
$242$			62.0801i			3.99066i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	42.8793			2.74506
$245$		0			0
$246$			5.32694i			0.339633i
$247$	−19.8372	−	2.21730i	−1.26221	−	0.141084i
$248$	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	$0.0830672\pi$
$251$			8.17534i			0.516023i	−0.966142	+	0.258011i	$0.916933\pi$
$252$	1.01424			0.0638910
$253$			16.1540i			1.01559i
$254$	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	0.324000	−	0.946057i	$-0.394972\pi$
$257$	−9.97233	−	9.97233i	−0.622057	−	0.622057i	−0.946057	+	0.324000i	$0.894972\pi$
$258$	−13.6661			−0.850813
$259$	0.804528			0.0499909
$260$		0			0
$261$	5.76992			0.357149
$262$	12.5317			0.774212
$263$	−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
$267$		−	1.25458i		−	0.0767789i
$268$	−64.0497			−3.91246
$269$			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	−0.212374	−	0.977188i	$-0.568120\pi$
$271$	12.5904	−	12.5904i	0.764814	−	0.764814i	0.977188	+	0.212374i	$0.0681195\pi$
$272$	−7.04799	−	7.04799i	−0.427347	−	0.427347i
$273$	−0.868628	−	0.0970909i	−0.0525718	−	0.00587621i
$274$			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	$-0.975081\pi$
$277$	−17.8939	−	17.8939i	−1.07514	−	1.07514i	−0.0782056	−	0.996937i	$-0.524919\pi$
$278$			15.0147i			0.900520i
$279$	5.69411	−	5.69411i	0.340898	−	0.340898i
$280$		0			0
$281$	−2.64673	+	2.64673i	−0.157891	+	0.157891i	−0.781631	−	0.623741i	$-0.785612\pi$
$281$	−2.64673	+	2.64673i	−0.157891	+	0.157891i	0.623741	+	0.781631i	$0.285612\pi$
$282$	−2.96197	+	2.96197i	−0.176383	+	0.176383i
$283$	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
$288$		−	1.91338i		−	0.112747i
$289$		−	13.2356i		−	0.778562i
$290$		0			0
$291$	3.36598	+	3.36598i	0.197317	+	0.197317i
$292$	6.08351			0.356010
$293$	8.87232			0.518327			0.259163	−	0.965834i	$-0.416553\pi$
$293$	8.87232			0.518327			0.259163	+	0.965834i	$0.416553\pi$
$294$	−12.2054	−	12.2054i	−0.711835	−	0.711835i
$295$		0			0
$296$		−	18.0238i		−	1.04761i
$297$		−	5.99703i		−	0.347983i
$298$	−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
$307$			25.1833i			1.43729i	0.695378	+	0.718644i	$0.255237\pi$
$307$			25.1833i			1.43729i	−0.695378	+	0.718644i	$0.744763\pi$
$308$	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	$0.0641337\pi$
$311$			7.05837i			0.400243i	−0.979771	+	0.200122i	$0.935866\pi$
$312$	−2.17513	+	19.4599i	−0.123142	+	1.10170i
$313$	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
$317$	−13.9177			−0.781695			−0.390847	−	0.920456i	$-0.627818\pi$
$317$	−13.9177			−0.781695			−0.390847	+	0.920456i	$0.627818\pi$
$318$		−	7.81920i		−	0.438479i
$319$	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
$323$	−10.7413			−0.597660
$324$	−4.18390			−0.232439
$325$		0			0
$326$	36.6132			2.02782
$327$	6.49904			0.359398
$328$	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	0.492181	−	0.870493i	$-0.336200\pi$
$331$	−6.88277	−	6.88277i	−0.378311	−	0.378311i	−0.870493	+	0.492181i	$0.836200\pi$
$332$		−	11.3787i		−	0.624489i
$333$	−3.31881			−0.181870
$334$		−	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	0.728880	−	0.684641i	$-0.240041\pi$
$337$	0.812119	+	0.812119i	0.0442389	+	0.0442389i	−0.684641	+	0.728880i	$0.740041\pi$
$338$	7.13768	−	31.5299i	0.388238	−	1.71500i
$339$		−	17.4340i		−	0.946884i
$340$		0			0
$341$	48.2922			2.61517
$342$	−9.73467	−	9.73467i	−0.526391	−	0.526391i
$343$		−	3.37956i		−	0.182479i
$344$	−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	$-0.308833\pi$
$349$	−4.85536	−	4.85536i	−0.259902	−	0.259902i	−0.825014	+	0.565112i	$0.808833\pi$
$350$		0			0
$351$	3.58324	+	0.400516i	0.191259	+	0.0213780i
$352$	8.11377	−	8.11377i	0.432465	−	0.432465i
$353$		−	25.9459i		−	1.38096i	−0.723351	−	0.690480i	$-0.757399\pi$
$353$		−	25.9459i		−	1.38096i	0.723351	−	0.690480i	$-0.242601\pi$
$354$			18.5631i			0.986618i
$355$		0			0
$356$	−3.71162	−	3.71162i	−0.196716	−	0.196716i
$357$	−0.470337			−0.0248929
$358$	9.94027			0.525359
$359$	2.31461	+	2.31461i	0.122160	+	0.122160i	0.765544	−	0.643384i	$-0.222470\pi$
$359$	2.31461	+	2.31461i	0.122160	+	0.122160i	−0.643384	+	0.765544i	$0.722470\pi$
$360$		0			0
$361$		−	11.6486i		−	0.613083i
$362$		−	41.1390i		−	2.16222i
$363$	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
$372$		−	33.6917i		−	1.74683i
$373$	−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
$377$	−16.2535	+	12.9853i	−0.837098	+	0.668779i
$378$	−0.426260	−	0.426260i	−0.0219245	−	0.0219245i
$379$	−4.89160	+	4.89160i	−0.251265	+	0.251265i	−0.821489	−	0.570224i	$-0.806856\pi$
$379$	−4.89160	+	4.89160i	−0.251265	+	0.251265i	0.570224	+	0.821489i	$0.306856\pi$
$380$		0			0
$381$		−	5.42696i		−	0.278032i
$382$	−32.4333			−1.65943
$383$		−	0.331496i		−	0.0169386i	−0.999964	−	0.00846932i	$-0.997304\pi$
$383$		−	0.331496i		−	0.0169386i	0.999964	−	0.00846932i	$-0.00269590\pi$
$384$	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
$388$	19.9163			1.01110
$389$	−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
$392$	−37.6965			−1.90396
$393$	−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
$397$			25.7273i			1.29121i	0.763670	+	0.645607i	$0.223396\pi$
$397$			25.7273i			1.29121i	−0.763670	+	0.645607i	$0.776604\pi$
$398$	5.85714			0.293592
$399$		−	1.34203i		−	0.0671857i
$400$		0			0
$401$	7.72622	−	7.72622i	0.385829	−	0.385829i	−0.487368	−	0.873197i	$-0.662043\pi$
$401$	7.72622	−	7.72622i	0.385829	−	0.385829i	0.873197	+	0.487368i	$0.162043\pi$
$402$	26.9185	+	26.9185i	1.34258	+	1.34258i
$403$	−3.22523	+	28.8547i	−0.160660	+	1.43735i
$404$		−	47.2101i		−	2.34879i
$405$		0			0
$406$	3.47824			0.172622
$407$	−14.0736	−	14.0736i	−0.697601	−	0.697601i
$408$			10.5370i			0.521657i
$409$	−7.15874	+	7.15874i	−0.353977	+	0.353977i	−0.861587	−	0.507610i	$-0.830529\pi$
$409$	−7.15874	+	7.15874i	−0.353977	+	0.353977i	0.507610	+	0.861587i	$0.330529\pi$
$410$		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
$418$		−	82.5606i		−	4.03817i
$419$			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	0.699182	−	0.714943i	$-0.253548\pi$
$421$	−0.323390	−	0.323390i	−0.0157611	−	0.0157611i	−0.714943	+	0.699182i	$0.753548\pi$
$422$	54.6612			2.66086
$423$	1.68447			0.0819019
$424$	−12.0748	−	12.0748i	−0.586405	−	0.586405i
$425$		0			0
$426$			0.274470i			0.0132981i
$427$		−	2.48442i		−	0.120229i
$428$	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	0.746225	−	0.665694i	$-0.231864\pi$
$431$	1.67187	+	1.67187i	0.0805312	+	0.0805312i	−0.665694	+	0.746225i	$0.731864\pi$
$432$	−3.63258	+	3.63258i	−0.174772	+	0.174772i
$433$	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
$437$		−	14.9124i		−	0.713358i
$438$	−2.55675	−	2.55675i	−0.122166	−	0.122166i
$439$	20.2491			0.966437			0.483219	−	0.875500i	$-0.339468\pi$
$439$	20.2491			0.966437			0.483219	+	0.875500i	$0.339468\pi$
$440$		0			0
$441$			6.94124i			0.330535i
$442$	1.93242	−	17.2885i	0.0919159	−	0.822330i
$443$	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
$447$	20.9230			0.989622
$448$			1.33725i			0.0631792i
$449$	−23.3059	−	23.3059i	−1.09988	−	1.09988i	−0.994425	−	0.105451i	$-0.966372\pi$
$449$	−23.3059	−	23.3059i	−1.09988	−	1.09988i	−0.105451	−	0.994425i	$-0.533628\pi$
$450$		0			0
$451$	12.8464			0.604916
$452$	−51.5778	−	51.5778i	−2.42602	−	2.42602i
$453$	−20.7595			−0.975367
$454$	−45.7346			−2.14643
$455$		0			0
$456$	−30.0656			−1.40795
$457$	15.5860			0.729085			0.364542	−	0.931187i	$-0.381225\pi$
$457$	15.5860			0.729085			0.364542	+	0.931187i	$0.381225\pi$
$458$	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	0.999655	−	0.0262742i	$-0.00836429\pi$
$461$	20.8994	+	20.8994i	0.973381	+	0.973381i	−0.0262742	+	0.999655i	$0.508364\pi$
$462$		−	3.61515i		−	0.168192i
$463$	8.32123			0.386720			0.193360	−	0.981128i	$-0.438061\pi$
$463$	8.32123			0.386720			0.193360	+	0.981128i	$0.438061\pi$
$464$		−	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	$-0.994805\pi$
$467$	−21.9600	−	21.9600i	−1.01619	−	1.01619i	−0.0163185	−	0.999867i	$-0.505195\pi$
$468$	11.7858	−	9.41597i	0.544799	−	0.435253i
$469$			3.71102i			0.171359i
$470$		0			0
$471$	−6.03433			−0.278047
$472$	28.6661	+	28.6661i	1.31947	+	1.31947i
$473$			32.9571i			1.51537i
$474$	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	$-0.387762\pi$
$479$	−12.9813	−	12.9813i	−0.593132	−	0.593132i	−0.938476	+	0.345344i	$0.887762\pi$
$480$		0			0
$481$	9.34889	−	7.46907i	0.426273	−	0.340560i
$482$	15.8556	−	15.8556i	0.722204	−	0.722204i
$483$		−	0.652982i		−	0.0297117i
$484$		−	104.449i		−	4.74766i
$485$		0			0
$486$	1.75839	+	1.75839i	0.0797624	+	0.0797624i
$487$	−12.6406			−0.572801			−0.286400	−	0.958110i	$-0.592459\pi$
$487$	−12.6406			−0.572801			−0.286400	+	0.958110i	$0.592459\pi$
$488$	−55.6584			−2.51954
$489$	−10.4110	−	10.4110i	−0.470801	−	0.470801i
$490$		0			0
$491$			27.8197i			1.25549i	0.778421	+	0.627743i	$0.216021\pi$
$491$			27.8197i			1.25549i	−0.778421	+	0.627743i	$0.783979\pi$
$492$		−	8.96248i		−	0.404060i
$493$	−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	$-0.751532\pi$
$499$	−0.152074	+	0.152074i	−0.00680776	+	0.00680776i	0.703695	+	0.710502i	$0.251532\pi$
$500$		0			0
$501$	−4.30314	+	4.30314i	−0.192250	+	0.192250i
$502$		−	20.3300i		−	0.907372i
$503$	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
$507$	−10.9951	+	6.93593i	−0.488311	+	0.308035i
$508$	−16.0555	−	16.0555i	−0.712347	−	0.712347i
$509$	11.1303	−	11.1303i	0.493341	−	0.493341i	−0.416016	−	0.909357i	$-0.636574\pi$
$509$	11.1303	−	11.1303i	0.493341	−	0.493341i	0.909357	+	0.416016i	$0.136574\pi$
$510$		0			0
$511$		−	0.352477i		−	0.0155927i
$512$	45.9692			2.03157
$513$			5.53612i			0.244425i
$514$	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
$518$	−2.00066			−0.0879038
$519$	−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	$0.596346\pi$
$522$	−14.3483			−0.628009
$523$	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
$527$			15.6240i			0.680591i
$528$	−30.8082			−1.34075
$529$			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
$533$	−0.857959	+	7.67577i	−0.0371623	+	0.332475i
$534$			3.11981i			0.135008i
$535$		0			0
$536$	83.1381			3.59102
$537$	−2.82652	−	2.82652i	−0.121973	−	0.121973i
$538$		−	41.5708i		−	1.79224i
$539$	−29.4346	+	29.4346i	−1.26784	+	1.26784i
$540$		0			0
$541$	−24.0220	+	24.0220i	−1.03279	+	1.03279i	−0.0333420	+	0.999444i	$0.510615\pi$
$541$	−24.0220	+	24.0220i	−1.03279	+	1.03279i	−0.999444	+	0.0333420i	$0.989385\pi$
$542$	−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	$0.0593673\pi$
$548$		−	56.0437i		−	2.39407i
$549$			10.2486i			0.437401i
$550$		0			0
$551$	−22.5871	−	22.5871i	−0.962241	−	0.962241i
$552$	−14.6288			−0.622641
$553$	1.84268			0.0783586
$554$	44.4977	+	44.4977i	1.89053	+	1.89053i
$555$		0			0
$556$		−	25.2619i		−	1.07134i
$557$		−	1.32872i		−	0.0562996i	−0.999604	−	0.0281498i	$-0.991038\pi$
$557$		−	1.32872i		−	0.0562996i	0.999604	−	0.0281498i	$-0.00896155\pi$
$558$	−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	−0.951190	−	0.308607i	$-0.900137\pi$
$563$	−15.2469	+	15.2469i	−0.642582	+	0.642582i	0.308607	+	0.951190i	$0.400137\pi$
$564$	4.98346	−	4.98346i	0.209842	−	0.209842i
$565$		0			0
$566$	−6.56889	+	6.56889i	−0.276111	+	0.276111i
$567$			0.242414i			0.0101804i
$568$	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	$0.0251482\pi$
$571$			3.77184i			0.157847i	−0.996881	+	0.0789233i	$0.974852\pi$
$572$	89.9070	+	10.0493i	3.75920	+	0.420184i
$573$	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
$577$	38.7401			1.61277			0.806385	−	0.591391i	$-0.201421\pi$
$577$	38.7401			1.61277			0.806385	+	0.591391i	$0.201421\pi$
$578$			32.9135i			1.36902i
$579$	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
$583$	−18.8568			−0.780967
$584$	−7.89654			−0.326761
$585$		0			0
$586$	−22.0632			−0.911423
$587$	−11.4947			−0.474438			−0.237219	−	0.971456i	$-0.576236\pi$
$587$	−11.4947			−0.474438			−0.237219	+	0.971456i	$0.576236\pi$
$588$	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
$592$			17.0495i			0.700731i
$593$	23.5194			0.965824			0.482912	−	0.875669i	$-0.339579\pi$
$593$	23.5194			0.965824			0.482912	+	0.875669i	$0.339579\pi$
$594$			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
$598$	24.0021	+	2.68284i	0.981520	+	0.109709i
$599$			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
$603$		−	15.3086i		−	0.623414i
$604$	−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
$613$			8.40716i			0.339562i	0.985482	+	0.169781i	$0.0543060\pi$
$613$			8.40716i			0.339562i	−0.985482	+	0.169781i	$0.945694\pi$
$614$		−	62.6245i		−	2.52732i
$615$		0			0
$616$	−5.58270	−	5.58270i	−0.224933	−	0.224933i
$617$	5.02106			0.202140			0.101070	−	0.994879i	$-0.467773\pi$
$617$	5.02106			0.202140			0.101070	+	0.994879i	$0.467773\pi$
$618$	−34.6677			−1.39454
$619$	28.7489	+	28.7489i	1.15552	+	1.15552i	0.985429	+	0.170089i	$0.0544054\pi$
$619$	28.7489	+	28.7489i	1.15552	+	1.15552i	0.170089	+	0.985429i	$0.445595\pi$
$620$		0			0
$621$			2.69366i			0.108093i
$622$		−	17.5524i		−	0.703786i
$623$	−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	−0.126553	−	0.991960i	$-0.540391\pi$
$631$	21.7388	−	21.7388i	0.865407	−	0.865407i	0.991960	+	0.126553i	$0.0403913\pi$
$632$		−	41.2815i		−	1.64209i
$633$	−15.5429	−	15.5429i	−0.617775	−	0.617775i
$634$	34.6097			1.37453
$635$		0			0
$636$			13.1557i			0.521656i
$637$	−15.6214	−	19.5530i	−0.618943	−	0.774719i
$638$	−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	$-0.945982\pi$
$641$		−	8.55187i		−	0.337779i	0.985635	−	0.168889i	$-0.0540181\pi$
$642$	−14.0759			−0.555531
$643$			3.11521i			0.122852i	0.998112	+	0.0614259i	$0.0195648\pi$
$643$			3.11521i			0.122852i	−0.998112	+	0.0614259i	$0.980435\pi$
$644$	−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	$0.0130324\pi$
$647$	26.4560	+	26.4560i	1.04009	+	1.04009i	0.0409311	+	0.999162i	$0.486968\pi$
$648$	5.43081			0.213342
$649$	44.7668			1.75725
$650$		0			0
$651$	−1.95209			−0.0765084
$652$	−61.6010			−2.41248
$653$	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
$657$			1.45403i			0.0567270i
$658$	1.01544			0.0395860
$659$		−	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	−0.233449	−	0.972369i	$-0.575001\pi$
$661$	18.9976	−	18.9976i	0.738920	−	0.738920i	0.972369	+	0.233449i	$0.0750013\pi$
$662$	17.1157	+	17.1157i	0.665220	+	0.665220i
$663$	−5.46548	+	4.36651i	−0.212262	+	0.169581i
$664$			14.7699i			0.573182i
$665$		0			0
$666$	8.25304			0.319799
$667$	−10.9900	−	10.9900i	−0.425534	−	0.425534i
$668$			25.4614i			0.985131i
$669$	−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	$-0.493519\pi$
$673$	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	$0.128537\pi$
$678$			43.3539i			1.66500i
$679$		−	1.15394i		−	0.0442843i
$680$		0			0
$681$	13.0046	+	13.0046i	0.498339	+	0.498339i
$682$	−120.090			−4.59850
$683$	14.6506			0.560588			0.280294	−	0.959914i	$-0.409568\pi$
$683$	14.6506			0.560588			0.280294	+	0.959914i	$0.409568\pi$
$684$	16.3784	+	16.3784i	0.626244	+	0.626244i
$685$		0			0
$686$			8.40410i			0.320870i
$687$		−	23.6387i		−	0.901873i
$688$	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	−0.911789	−	0.410660i	$-0.865298\pi$
$691$	−34.7630	−	34.7630i	−1.32245	−	1.32245i	−0.410660	−	0.911789i	$-0.634702\pi$
$692$	−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
$697$			4.15621i			0.157428i
$698$	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	$-0.916663\pi$
$701$		−	13.7058i		−	0.517659i	0.965923	−	0.258830i	$-0.0833369\pi$
$702$	−8.91060	−	0.995982i	−0.336309	−	0.0375909i
$703$	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
$707$	−2.73534			−0.102873
$708$		−	31.2321i		−	1.17377i
$709$	4.33781	+	4.33781i	0.162910	+	0.162910i	0.783854	−	0.620945i	$-0.213251\pi$
$709$	4.33781	+	4.33781i	0.162910	+	0.162910i	−0.620945	+	0.783854i	$0.713251\pi$
$710$		0			0
$711$	−7.60135			−0.285073
$712$	4.81778	+	4.81778i	0.180554	+	0.180554i
$713$	−21.6912			−0.812342
$714$	1.16961			0.0437715
$715$		0			0
$716$	−16.7243			−0.625017
$717$	12.3219			0.460170
$718$	−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
$722$			28.9670i			1.07804i
$723$	−9.01711			−0.335350
$724$			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	$0.0104964\pi$
$727$	27.8372	+	27.8372i	1.03243	+	1.03243i	0.0329694	+	0.999456i	$0.489504\pi$
$728$	3.70852	−	2.96283i	0.137447	−	0.109810i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−10.6626			−0.394371
$732$	30.3202	+	30.3202i	1.12067	+	1.12067i
$733$		−	16.0974i		−	0.594571i	−0.954789	−	0.297285i	$-0.903919\pi$
$733$		−	16.0974i		−	0.594571i	0.954789	−	0.297285i	$-0.0960813\pi$
$734$	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	$-0.169039\pi$
$739$	9.67318	+	9.67318i	0.355834	+	0.355834i	−0.506441	+	0.862275i	$0.669039\pi$
$740$		0			0
$741$	−12.4592	−	15.5949i	−0.457699	−	0.572893i
$742$	−1.34031	+	1.34031i	−0.0492044	+	0.0492044i
$743$			0.660092i			0.0242164i	0.999927	+	0.0121082i	$0.00385426\pi$
$743$			0.660092i			0.0242164i	−0.999927	+	0.0121082i	$0.996146\pi$
$744$			43.7326i			1.60332i
$745$		0			0
$746$	13.2653	+	13.2653i	0.485675	+	0.485675i
$747$	2.71964			0.0995066
$748$	48.6820			1.77999
$749$	−0.970259	−	0.970259i	−0.0354525	−	0.0354525i
$750$		0			0
$751$			35.4818i			1.29475i	0.762171	+	0.647375i	$0.224133\pi$
$751$			35.4818i			1.29475i	−0.762171	+	0.647375i	$0.775867\pi$
$752$		−	8.65354i		−	0.315562i
$753$	−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	−0.171429	−	0.985196i	$-0.554839\pi$
$761$	22.4488	−	22.4488i	0.813767	−	0.813767i	0.985196	+	0.171429i	$0.0548386\pi$
$762$			13.4955i			0.488890i
$763$	−1.11402	−	1.11402i	−0.0403302	−	0.0403302i
$764$	54.5685			1.97422
$765$		0			0
$766$			0.824345i			0.0297848i
$767$	−2.98978	+	26.7482i	−0.107955	+	0.965822i
$768$	−23.0490	−	23.0490i	−0.831709	−	0.831709i
$769$	3.44776	−	3.44776i	0.124329	−	0.124329i	−0.642204	−	0.766534i	$-0.721980\pi$
$769$	3.44776	−	3.44776i	0.124329	−	0.124329i	0.766534	+	0.642204i	$0.221980\pi$
$770$		0			0
$771$		−	14.1030i		−	0.507907i
$772$	38.8399			1.39788
$773$		−	25.5316i		−	0.918307i	−0.888357	−	0.459154i	$-0.848153\pi$
$773$		−	25.5316i		−	0.918307i	0.888357	−	0.459154i	$-0.151847\pi$
$774$	−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
$778$	16.8578			0.604383
$779$	−11.8591			−0.424896
$780$		0			0
$781$	0.661911			0.0236850
$782$	12.9965			0.464752
$783$	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
$787$		−	15.5693i		−	0.554986i	−0.960728	−	0.277493i	$-0.910496\pi$
$787$		−	15.5693i		−	0.554986i	0.960728	−	0.277493i	$-0.0895035\pi$
$788$	54.0240			1.92453
$789$		−	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
$793$	−23.0648	−	28.8698i	−0.819055	−	1.02520i
$794$		−	63.9772i		−	2.27046i
$795$		0			0
$796$	−9.85453			−0.349285
$797$	−7.35388	−	7.35388i	−0.260488	−	0.260488i	0.564764	−	0.825252i	$-0.308967\pi$
$797$	−7.35388	−	7.35388i	−0.260488	−	0.260488i	−0.825252	+	0.564764i	$0.808967\pi$
$798$			3.33730i			0.118139i
$799$	−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
$808$			61.2798i			2.15582i
$809$			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	0.162149	−	0.986766i	$-0.448158\pi$
$811$	−23.4835	−	23.4835i	−0.824618	−	0.824618i	−0.986766	+	0.162149i	$0.948158\pi$
$812$	−5.85207			−0.205368
$813$	17.8056			0.624468
$814$	34.9974	+	34.9974i	1.22666	+	1.22666i
$815$		0			0
$816$		−	9.96736i		−	0.348927i
$817$		−	30.4241i		−	1.06440i
$818$	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	0.999944	−	0.0105868i	$-0.00336993\pi$
$821$	28.3481	+	28.3481i	0.989357	+	0.989357i	−0.0105868	+	0.999944i	$0.503370\pi$
$822$	−23.5538	+	23.5538i	−0.821534	+	0.821534i
$823$	−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
$827$			50.1300i			1.74319i	0.490225	+	0.871596i	$0.336915\pi$
$827$			50.1300i			1.74319i	−0.490225	+	0.871596i	$0.663085\pi$
$828$	7.96910	+	7.96910i	0.276946	+	0.276946i
$829$	−28.1449			−0.977512			−0.488756	−	0.872420i	$-0.662549\pi$
$829$	−28.1449			−0.977512			−0.488756	+	0.872420i	$0.662549\pi$
$830$		0			0
$831$		−	25.3059i		−	0.877850i
$832$	12.4148	+	15.5393i	0.430404	+	0.538729i
$833$	−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
$837$	8.05269			0.278342
$838$		−	57.4655i		−	1.98511i
$839$	25.8159	+	25.8159i	0.891264	+	0.891264i	0.994642	−	0.103378i	$-0.0329651\pi$
$839$	25.8159	+	25.8159i	0.891264	+	0.891264i	−0.103378	+	0.994642i	$0.532965\pi$
$840$		0			0
$841$	−4.29196			−0.147999
$842$	0.804189	+	0.804189i	0.0277142	+	0.0277142i
$843$	−3.74304			−0.128917
$844$	−91.9664			−3.16561
$845$		0			0
$846$	−4.18886			−0.144016
$847$	−6.05173			−0.207940
$848$	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
$852$		−	0.461790i		−	0.0158207i
$853$	−6.25026			−0.214005			−0.107002	−	0.994259i	$-0.534125\pi$
$853$	−6.25026			−0.214005			−0.107002	+	0.994259i	$0.534125\pi$
$854$			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	0.466771	−	0.884378i	$-0.345417\pi$
$857$	−12.2252	−	12.2252i	−0.417607	−	0.417607i	−0.884378	+	0.466771i	$0.845417\pi$
$858$	−33.5623	−	42.0093i	−1.14580	−	1.43417i
$859$		−	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
$863$			25.4480i			0.866261i	0.901331	+	0.433130i	$0.142591\pi$
$863$			25.4480i			0.866261i	−0.901331	+	0.433130i	$0.857409\pi$
$864$	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
$873$			4.76021i			0.161109i
$874$			37.0834i			1.25436i
$875$		0			0
$876$	4.30169	+	4.30169i	0.145341	+	0.145341i
$877$	21.2930			0.719015			0.359507	−	0.933142i	$-0.382945\pi$
$877$	21.2930			0.719015			0.359507	+	0.933142i	$0.382945\pi$
$878$	−50.3544			−1.69938
$879$	6.27368	+	6.27368i	0.211606	+	0.211606i
$880$		0			0
$881$			10.5084i			0.354037i	0.984208	+	0.177018i	$0.0566452\pi$
$881$			10.5084i			0.354037i	−0.984208	+	0.177018i	$0.943355\pi$
$882$		−	17.2611i		−	0.581211i
$883$	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	$0.421270\pi$
$888$	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
$892$			36.4845i			1.22159i
$893$	−6.59408	−	6.59408i	−0.220663	−	0.220663i
$894$	−52.0301			−1.74015
$895$		0			0
$896$		−	4.25307i		−	0.142085i
$897$	−6.06215	−	7.58788i	−0.202409	−	0.253352i
$898$	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
$902$	−31.9458			−1.06368
$903$		−	1.33221i		−	0.0443330i
$904$	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	0.902373	−	0.430956i	$-0.141823\pi$
$907$	14.1974	+	14.1974i	0.471417	+	0.471417i	−0.430956	+	0.902373i	$0.641823\pi$
$908$	76.9475			2.55359
$909$	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	$0.535010\pi$
$912$	28.4403			0.941754
$913$	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
$917$			1.22162i			0.0403416i
$918$	−4.82483			−0.159243
$919$		−	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
$923$	−0.0442062	+	0.395493i	−0.00145507	+	0.0130178i
$924$			6.08242i			0.200097i
$925$		0			0
$926$	−20.6928			−0.680007
$927$	9.85776	+	9.85776i	0.323771	+	0.323771i
$928$			11.0400i			0.362407i
$929$	16.7396	−	16.7396i	0.549210	−	0.549210i	−0.377003	−	0.926212i	$-0.623045\pi$
$929$	16.7396	−	16.7396i	0.549210	−	0.549210i	0.926212	+	0.377003i	$0.123045\pi$
$930$		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	$0.342152\pi$
$938$		−	9.22837i		−	0.301317i
$939$			5.45276i			0.177944i
$940$		0			0
$941$	18.8531	+	18.8531i	0.614594	+	0.614594i	0.944140	−	0.329545i	$-0.106895\pi$
$941$	18.8531	+	18.8531i	0.614594	+	0.614594i	−0.329545	+	0.944140i	$0.606895\pi$
$942$	15.0058			0.488917
$943$	−5.77018			−0.187903
$944$	−27.1165	−	27.1165i	−0.882568	−	0.882568i
$945$		0			0
$946$		−	81.9559i		−	2.66462i
$947$			13.5380i			0.439926i	0.975508	+	0.219963i	$0.0705937\pi$
$947$			13.5380i			0.439926i	−0.975508	+	0.219963i	$0.929406\pi$
$948$	−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	−0.860247	−	0.509878i	$-0.829691\pi$
$953$	−10.8161	+	10.8161i	−0.350369	+	0.350369i	0.509878	+	0.860247i	$0.329691\pi$
$954$	5.52901	−	5.52901i	0.179008	−	0.179008i
$955$		0			0
$956$	36.4540	−	36.4540i	1.17901	−	1.17901i
$957$			34.6024i			1.11854i
$958$	32.2812	+	32.2812i	1.04296	+	1.04296i
$959$	−3.24716			−0.104856
$960$		0			0
$961$			33.8458i			1.09180i
$962$	−23.2483	+	18.5737i	−0.749556	+	0.598839i
$963$	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
$967$	16.5180			0.531183			0.265591	−	0.964086i	$-0.414433\pi$
$967$	16.5180			0.531183			0.265591	+	0.964086i	$0.414433\pi$
$968$			135.577i			4.35760i
$969$	−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
$973$	−1.46367			−0.0469231
$974$	31.4340			1.00721
$975$		0			0
$976$	52.6497			1.68527
$977$	1.92441			0.0615674			0.0307837	−	0.999526i	$-0.490200\pi$
$977$	1.92441			0.0615674			0.0307837	+	0.999526i	$0.490200\pi$
$978$	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
$982$		−	69.1805i		−	2.20764i
$983$	−59.7525			−1.90581			−0.952904	−	0.303273i	$-0.901921\pi$
$983$	−59.7525			−1.90581			−0.952904	+	0.303273i	$0.901921\pi$
$984$			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
$988$	−82.9970	−	9.27698i	−2.64049	−	0.295140i
$989$		−	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
$993$		−	9.73371i		−	0.308890i
$994$	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.t.d.268.1		28
5.2	odd	4		975.2.k.d.307.1		28
5.3	odd	4		195.2.k.a.112.14	✓	28
5.4	even	2		195.2.t.a.73.14	yes	28
13.5	odd	4		975.2.k.d.343.14		28
15.8	even	4		585.2.n.g.307.1		28
15.14	odd	2		585.2.w.g.73.1		28
65.18	even	4		195.2.t.a.187.14	yes	28
65.44	odd	4		195.2.k.a.148.1	yes	28
65.57	even	4	inner	975.2.t.d.382.1		28
195.44	even	4		585.2.n.g.343.14		28
195.83	odd	4		585.2.w.g.577.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.k.a.112.14	✓	28	5.3	odd	4
195.2.k.a.148.1	yes	28	65.44	odd	4
195.2.t.a.73.14	yes	28	5.4	even	2
195.2.t.a.187.14	yes	28	65.18	even	4
585.2.n.g.307.1		28	15.8	even	4
585.2.n.g.343.14		28	195.44	even	4
585.2.w.g.73.1		28	15.14	odd	2
585.2.w.g.577.1		28	195.83	odd	4
975.2.k.d.307.1		28	5.2	odd	4
975.2.k.d.343.14		28	13.5	odd	4
975.2.t.d.268.1		28	1.1	even	1	trivial
975.2.t.d.382.1		28	65.57	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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