LMFDB - Embedded newform 975.2.bc.i.751.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(751,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("975.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.4
Root			$0.500000 - 2.19293i$ of defining polynomial
Character	$\chi$	$=$	975.751
Dual form			975.2.bc.i.901.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14914 - 0.663454i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.119657 + 0.207252i) q^{4} +(1.14914 + 0.663454i) q^{6} +(-0.917086 - 0.529480i) q^{7} +2.97136i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.14914 - 0.663454i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.119657 + 0.207252i) q^{4} +(1.14914 + 0.663454i) q^{6} +(-0.917086 - 0.529480i) q^{7} +2.97136i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.15877 - 1.24637i) q^{11} -0.239314 q^{12} +(-2.68825 + 2.40277i) q^{13} -1.40514 q^{14} +(1.73205 + 3.00000i) q^{16} +(-2.47605 + 4.28864i) q^{17} +1.32691i q^{18} +(5.50552 + 3.17862i) q^{19} -1.05896i q^{21} +(1.65382 - 2.86450i) q^{22} +(1.81259 + 3.13950i) q^{23} +(-2.57328 + 1.48568i) q^{24} +(-1.49504 + 4.54464i) q^{26} -1.00000 q^{27} +(0.219471 - 0.126712i) q^{28} +(0.117075 + 0.202779i) q^{29} -1.31755i q^{31} +(-1.16583 - 0.673091i) q^{32} +(2.15877 + 1.24637i) q^{33} +6.57097i q^{34} +(-0.119657 - 0.207252i) q^{36} +(5.29827 - 3.05896i) q^{37} +8.43547 q^{38} +(-3.42498 - 1.12671i) q^{39} +(-7.66877 + 4.42757i) q^{41} +(-0.702571 - 1.21689i) q^{42} +(-4.83481 + 8.37413i) q^{43} +0.596546i q^{44} +(4.16583 + 2.40514i) q^{46} -5.70173i q^{47} +(-1.73205 + 3.00000i) q^{48} +(-2.93930 - 5.09102i) q^{49} -4.95209 q^{51} +(-0.176310 - 0.844653i) q^{52} +4.98547 q^{53} +(-1.14914 + 0.663454i) q^{54} +(1.57328 - 2.72500i) q^{56} +6.35723i q^{57} +(0.269069 + 0.155347i) q^{58} +(1.82049 + 1.05106i) q^{59} +(-1.52690 + 2.64466i) q^{61} +(-0.874132 - 1.51404i) q^{62} +(0.917086 - 0.529480i) q^{63} -8.71446 q^{64} +3.30763 q^{66} +(6.61171 - 3.81727i) q^{67} +(-0.592551 - 1.02633i) q^{68} +(-1.81259 + 3.13950i) q^{69} +(7.08138 + 4.08844i) q^{71} +(-2.57328 - 1.48568i) q^{72} +3.98716i q^{73} +(4.05896 - 7.03032i) q^{74} +(-1.31755 + 0.760686i) q^{76} -2.63971 q^{77} +(-4.68330 + 0.977575i) q^{78} +15.8359 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-5.87498 + 10.1758i) q^{82} -15.8037i q^{83} +(0.219471 + 0.126712i) q^{84} +12.8307i q^{86} +(-0.117075 + 0.202779i) q^{87} +(3.70342 + 6.41450i) q^{88} +(13.7224 - 7.92261i) q^{89} +(3.73758 - 0.780169i) q^{91} -0.867556 q^{92} +(1.14103 - 0.658774i) q^{93} +(-3.78284 - 6.55206i) q^{94} -1.34618i q^{96} +(-8.70866 - 5.02795i) q^{97} +(-6.75532 - 3.90019i) q^{98} +2.49274i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} + 4 q^{3} + 4 q^{4} - 6 q^{6} - 6 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 6 * q^2 + 4 * q^3 + 4 * q^4 - 6 * q^6 - 6 * q^7 - 4 * q^9	$ 8 q - 6 q^{2} + 4 q^{3} + 4 q^{4} - 6 q^{6} - 6 q^{7} - 4 q^{9} + 12 q^{11} + 8 q^{12} - 6 q^{13} - 4 q^{14} + 2 q^{17} + 12 q^{19} - 4 q^{23} - 12 q^{24} - 4 q^{26} - 8 q^{27} + 12 q^{28} - 6 q^{29} - 12 q^{32} + 12 q^{33} + 4 q^{36} + 12 q^{37} + 16 q^{38} - 30 q^{41} - 2 q^{42} - 6 q^{43} + 36 q^{46} - 8 q^{49} + 4 q^{51} + 20 q^{52} + 32 q^{53} + 6 q^{54} + 4 q^{56} - 12 q^{58} - 30 q^{59} + 30 q^{62} + 6 q^{63} + 32 q^{64} - 30 q^{67} - 16 q^{68} + 4 q^{69} + 18 q^{71} - 12 q^{72} + 12 q^{74} + 8 q^{77} - 14 q^{78} + 56 q^{79} - 4 q^{81} + 24 q^{82} + 12 q^{84} + 6 q^{87} - 8 q^{88} - 18 q^{89} - 16 q^{91} - 40 q^{92} + 24 q^{93} - 16 q^{94} + 6 q^{97} + 12 q^{98}+O(q^{100}) $ 8 * q - 6 * q^2 + 4 * q^3 + 4 * q^4 - 6 * q^6 - 6 * q^7 - 4 * q^9 + 12 * q^11 + 8 * q^12 - 6 * q^13 - 4 * q^14 + 2 * q^17 + 12 * q^19 - 4 * q^23 - 12 * q^24 - 4 * q^26 - 8 * q^27 + 12 * q^28 - 6 * q^29 - 12 * q^32 + 12 * q^33 + 4 * q^36 + 12 * q^37 + 16 * q^38 - 30 * q^41 - 2 * q^42 - 6 * q^43 + 36 * q^46 - 8 * q^49 + 4 * q^51 + 20 * q^52 + 32 * q^53 + 6 * q^54 + 4 * q^56 - 12 * q^58 - 30 * q^59 + 30 * q^62 + 6 * q^63 + 32 * q^64 - 30 * q^67 - 16 * q^68 + 4 * q^69 + 18 * q^71 - 12 * q^72 + 12 * q^74 + 8 * q^77 - 14 * q^78 + 56 * q^79 - 4 * q^81 + 24 * q^82 + 12 * q^84 + 6 * q^87 - 8 * q^88 - 18 * q^89 - 16 * q^91 - 40 * q^92 + 24 * q^93 - 16 * q^94 + 6 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.14914	−	0.663454i	0.812562	−	0.469133i	−0.0352826	−	0.999377i	$-0.511233\pi$
$2$	1.14914	−	0.663454i	0.812562	−	0.469133i	0.847845	+	0.530244i	$0.177900\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.119657	+	0.207252i	−0.0598284	+	0.103626i
$5$		0			0
$5$		0			0
$6$	1.14914	+	0.663454i	0.469133	+	0.270854i
$7$	−0.917086	−	0.529480i	−0.346626	−	0.200125i	0.316572	−	0.948568i	$-0.397468\pi$
$7$	−0.917086	−	0.529480i	−0.346626	−	0.200125i	−0.663198	+	0.748444i	$0.730801\pi$
$8$			2.97136i			1.05054i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.15877	−	1.24637i	0.650895	−	0.375794i	−0.137904	−	0.990446i	$-0.544037\pi$
$11$	2.15877	−	1.24637i	0.650895	−	0.375794i	0.788799	+	0.614651i	$0.210703\pi$
$12$	−0.239314			−0.0690839
$13$	−2.68825	+	2.40277i	−0.745587	+	0.666408i
$13$	−2.68825	+	2.40277i	−0.745587	+	0.666408i
$14$	−1.40514			−0.375540
$15$		0			0
$16$	1.73205	+	3.00000i	0.433013	+	0.750000i
$17$	−2.47605	+	4.28864i	−0.600529	+	1.04015i	0.392212	+	0.919875i	$0.371710\pi$
$17$	−2.47605	+	4.28864i	−0.600529	+	1.04015i	−0.992741	+	0.120272i	$0.961623\pi$
$18$			1.32691i			0.312755i
$19$	5.50552	+	3.17862i	1.26305	+	0.729225i	0.973664	−	0.227987i	$-0.0732143\pi$
$19$	5.50552	+	3.17862i	1.26305	+	0.729225i	0.289390	+	0.957211i	$0.406548\pi$
$20$		0			0
$21$		−	1.05896i		−	0.231084i
$22$	1.65382	−	2.86450i	0.352595	−	0.610712i
$23$	1.81259	+	3.13950i	0.377951	+	0.654631i	0.990764	−	0.135597i	$-0.0432953\pi$
$23$	1.81259	+	3.13950i	0.377951	+	0.654631i	−0.612813	+	0.790228i	$0.709962\pi$
$24$	−2.57328	+	1.48568i	−0.525268	+	0.303264i
$25$		0			0
$26$	−1.49504	+	4.54464i	−0.293202	+	0.891278i
$27$	−1.00000			−0.192450
$28$	0.219471	−	0.126712i	0.0414761	−	0.0239463i
$29$	0.117075	+	0.202779i	0.0217402	+	0.0376551i	0.876691	−	0.481054i	$-0.159746\pi$
$29$	0.117075	+	0.202779i	0.0217402	+	0.0376551i	−0.854951	+	0.518709i	$0.826413\pi$
$30$		0			0
$31$		−	1.31755i		−	0.236638i	−0.992976	−	0.118319i	$-0.962249\pi$
$31$		−	1.31755i		−	0.236638i	0.992976	−	0.118319i	$-0.0377506\pi$
$32$	−1.16583	−	0.673091i	−0.206091	−	0.118987i
$33$	2.15877	+	1.24637i	0.375794	+	0.216965i
$34$			6.57097i			1.12691i
$35$		0			0
$36$	−0.119657	−	0.207252i	−0.0199428	−	0.0345420i
$37$	5.29827	−	3.05896i	0.871031	−	0.502890i	0.00334010	−	0.999994i	$-0.498937\pi$
$37$	5.29827	−	3.05896i	0.871031	−	0.502890i	0.867691	+	0.497105i	$0.165603\pi$
$38$	8.43547			1.36841
$39$	−3.42498	−	1.12671i	−0.548436	−	0.180418i
$40$		0			0
$41$	−7.66877	+	4.42757i	−1.19766	+	0.691470i	−0.960033	−	0.279886i	$-0.909703\pi$
$41$	−7.66877	+	4.42757i	−1.19766	+	0.691470i	−0.237628	+	0.971356i	$0.576370\pi$
$42$	−0.702571	−	1.21689i	−0.108409	−	0.187770i
$43$	−4.83481	+	8.37413i	−0.737301	+	1.27704i	0.216405	+	0.976304i	$0.430567\pi$
$43$	−4.83481	+	8.37413i	−0.737301	+	1.27704i	−0.953706	+	0.300740i	$0.902767\pi$
$44$			0.596546i			0.0899327i
$45$		0			0
$46$	4.16583	+	2.40514i	0.614218	+	0.354619i
$47$		−	5.70173i		−	0.831682i	−0.909437	−	0.415841i	$-0.863487\pi$
$47$		−	5.70173i		−	0.831682i	0.909437	−	0.415841i	$-0.136513\pi$
$48$	−1.73205	+	3.00000i	−0.250000	+	0.433013i
$49$	−2.93930	−	5.09102i	−0.419900	−	0.727289i
$50$		0			0
$51$	−4.95209			−0.693431
$52$	−0.176310	−	0.844653i	−0.0244498	−	0.117132i
$53$	4.98547			0.684808			0.342404	−	0.939553i	$-0.388759\pi$
$53$	4.98547			0.684808			0.342404	+	0.939553i	$0.388759\pi$
$54$	−1.14914	+	0.663454i	−0.156378	+	0.0902847i
$55$		0			0
$56$	1.57328	−	2.72500i	0.210238	−	0.364143i
$57$			6.35723i			0.842036i
$58$	0.269069	+	0.155347i	0.0353305	+	0.0203981i
$59$	1.82049	+	1.05106i	0.237008	+	0.136836i	0.613801	−	0.789461i	$-0.289640\pi$
$59$	1.82049	+	1.05106i	0.237008	+	0.136836i	−0.376793	+	0.926297i	$0.622973\pi$
$60$		0			0
$61$	−1.52690	+	2.64466i	−0.195499	+	0.338615i	−0.947064	−	0.321045i	$-0.895966\pi$
$61$	−1.52690	+	2.64466i	−0.195499	+	0.338615i	0.751565	+	0.659659i	$0.229299\pi$
$62$	−0.874132	−	1.51404i	−0.111015	−	0.192284i
$63$	0.917086	−	0.529480i	0.115542	−	0.0667082i
$64$	−8.71446			−1.08931
$65$		0			0
$66$	3.30763			0.407142
$67$	6.61171	−	3.81727i	0.807749	−	0.466354i	−0.0384248	−	0.999261i	$-0.512234\pi$
$67$	6.61171	−	3.81727i	0.807749	−	0.466354i	0.846173	+	0.532908i	$0.178901\pi$
$68$	−0.592551	−	1.02633i	−0.0718574	−	0.124461i
$69$	−1.81259	+	3.13950i	−0.218210	+	0.377951i
$70$		0			0
$71$	7.08138	+	4.08844i	0.840406	+	0.485208i	0.857402	−	0.514647i	$-0.172077\pi$
$71$	7.08138	+	4.08844i	0.840406	+	0.485208i	−0.0169964	+	0.999856i	$0.505410\pi$
$72$	−2.57328	−	1.48568i	−0.303264	−	0.175089i
$73$			3.98716i			0.466662i	0.972397	+	0.233331i	$0.0749626\pi$
$73$			3.98716i			0.466662i	−0.972397	+	0.233331i	$0.925037\pi$
$74$	4.05896	−	7.03032i	0.471844	−	0.817259i
$75$		0			0
$76$	−1.31755	+	0.760686i	−0.151133	+	0.0872567i
$77$	−2.63971			−0.300823
$78$	−4.68330	+	0.977575i	−0.530279	+	0.110689i
$79$	15.8359			1.78167			0.890837	−	0.454324i	$-0.150119\pi$
$79$	15.8359			1.78167			0.890837	+	0.454324i	$0.150119\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.87498	+	10.1758i	−0.648783	+	1.12372i
$83$		−	15.8037i		−	1.73469i	−0.497710	−	0.867343i	$-0.665826\pi$
$83$		−	15.8037i		−	1.73469i	0.497710	−	0.867343i	$-0.334174\pi$
$84$	0.219471	+	0.126712i	0.0239463	+	0.0138254i
$85$		0			0
$86$			12.8307i			1.38357i
$87$	−0.117075	+	0.202779i	−0.0125517	+	0.0217402i
$88$	3.70342	+	6.41450i	0.394785	+	0.683788i
$89$	13.7224	−	7.92261i	1.45457	−	0.839795i	0.455832	−	0.890066i	$-0.349342\pi$
$89$	13.7224	−	7.92261i	1.45457	−	0.839795i	0.998736	+	0.0502708i	$0.0160084\pi$
$90$		0			0
$91$	3.73758	−	0.780169i	0.391804	−	0.0817839i
$92$	−0.867556			−0.0904489
$93$	1.14103	−	0.658774i	0.118319	−	0.0683116i
$94$	−3.78284	−	6.55206i	−0.390170	−	0.675794i
$95$		0			0
$96$		−	1.34618i		−	0.137394i
$97$	−8.70866	−	5.02795i	−0.884231	−	0.510511i	−0.0121798	−	0.999926i	$-0.503877\pi$
$97$	−8.70866	−	5.02795i	−0.884231	−	0.510511i	−0.872051	+	0.489415i	$0.837210\pi$
$98$	−6.75532	−	3.90019i	−0.682390	−	0.393978i
$99$			2.49274i			0.250530i
$100$		0			0
$101$	−5.70572	−	9.88260i	−0.567741	−	0.983355i	−0.996789	−	0.0800739i	$-0.974484\pi$
$101$	−5.70572	−	9.88260i	−0.567741	−	0.983355i	0.429048	−	0.903281i	$-0.358849\pi$
$102$	−5.69063	+	3.28549i	−0.563456	+	0.325312i
$103$	2.89788			0.285537			0.142768	−	0.989756i	$-0.454400\pi$
$103$	2.89788			0.285537			0.142768	+	0.989756i	$0.454400\pi$
$104$	−7.13950	−	7.98778i	−0.700086	−	0.783266i
$105$		0			0
$106$	5.72899	−	3.30763i	0.556449	−	0.321266i
$107$	−7.55659	−	13.0884i	−0.730523	−	1.26530i	−0.956660	−	0.291207i	$-0.905943\pi$
$107$	−7.55659	−	13.0884i	−0.730523	−	1.26530i	0.226137	−	0.974095i	$-0.427390\pi$
$108$	0.119657	−	0.207252i	0.0115140	−	0.0199428i
$109$		−	0.385868i		−	0.0369594i	−0.999829	−	0.0184797i	$-0.994117\pi$
$109$		−	0.385868i		−	0.0369594i	0.999829	−	0.0184797i	$-0.00588261\pi$
$110$		0			0
$111$	5.29827	+	3.05896i	0.502890	+	0.290344i
$112$		−	3.66834i		−	0.346626i
$113$	4.21068	−	7.29311i	0.396107	−	0.686078i	−0.597135	−	0.802141i	$-0.703694\pi$
$113$	4.21068	−	7.29311i	0.396107	−	0.686078i	0.993242	+	0.116063i	$0.0370275\pi$
$114$	4.21773	+	7.30533i	0.395027	+	0.684207i
$115$		0			0
$116$	−0.0560351			−0.00520273
$117$	−0.736731	−	3.52948i	−0.0681108	−	0.326301i
$118$	2.78932			0.256778
$119$	4.54149	−	2.62203i	0.416318	−	0.240361i
$120$		0			0
$121$	−2.39313	+	4.14502i	−0.217557	+	0.376820i
$122$			4.05211i			0.366860i
$123$	−7.66877	−	4.42757i	−0.691470	−	0.399220i
$124$	0.273064	+	0.157654i	0.0245219	+	0.0141577i
$125$		0			0
$126$	0.702571	−	1.21689i	0.0625900	−	0.108409i
$127$	5.69357	+	9.86155i	0.505223	+	0.875071i	0.999982	+	0.00604114i	$0.00192297\pi$
$127$	5.69357	+	9.86155i	0.505223	+	0.875071i	−0.494759	+	0.869030i	$0.664744\pi$
$128$	−7.68245	+	4.43547i	−0.679039	+	0.392044i
$129$	−9.66962			−0.851362
$130$		0			0
$131$	−11.4948			−1.00431			−0.502154	−	0.864778i	$-0.667459\pi$
$131$	−11.4948			−1.00431			−0.502154	+	0.864778i	$0.667459\pi$
$132$	−0.516624	+	0.298273i	−0.0449664	+	0.0259613i
$133$	−3.36603	−	5.83013i	−0.291871	−	0.505536i
$134$	5.06517	−	8.77313i	0.437564	−	0.757883i
$135$		0			0
$136$	−12.7431	−	7.35723i	−1.09271	−	0.630877i
$137$	14.9103	+	8.60849i	1.27388	+	0.735473i	0.975715	−	0.219043i	$-0.0702934\pi$
$137$	14.9103	+	8.60849i	1.27388	+	0.735473i	0.298161	+	0.954516i	$0.403627\pi$
$138$			4.81028i			0.409479i
$139$	−1.20342	+	2.08438i	−0.102072	+	0.176795i	−0.912538	−	0.408991i	$-0.865881\pi$
$139$	−1.20342	+	2.08438i	−0.102072	+	0.176795i	0.810466	+	0.585786i	$0.199214\pi$
$140$		0			0
$141$	4.93784	−	2.85086i	0.415841	−	0.240086i
$142$	10.8500			0.910509
$143$	−2.80860	+	8.53759i	−0.234867	+	0.713949i
$144$	−3.46410			−0.288675
$145$		0			0
$146$	2.64530	+	4.58179i	0.218927	+	0.379192i
$147$	2.93930	−	5.09102i	0.242430	−	0.419900i
$148$			1.46410i			0.120348i
$149$	−2.92924	−	1.69120i	−0.239972	−	0.138548i	0.375192	−	0.926947i	$-0.377577\pi$
$149$	−2.92924	−	1.69120i	−0.239972	−	0.138548i	−0.615164	+	0.788399i	$0.710910\pi$
$150$		0			0
$151$			1.46758i			0.119430i	0.998215	+	0.0597149i	$0.0190192\pi$
$151$			1.46758i			0.119430i	−0.998215	+	0.0597149i	$0.980981\pi$
$152$	−9.44483	+	16.3589i	−0.766077	+	1.32688i
$153$	−2.47605	−	4.28864i	−0.200176	−	0.346716i
$154$	−3.03338	+	1.75133i	−0.244437	+	0.141126i
$155$		0			0
$156$	0.643336	−	0.575015i	0.0515081	−	0.0460381i
$157$	20.7833			1.65869			0.829345	−	0.558736i	$-0.188714\pi$
$157$	20.7833			1.65869			0.829345	+	0.558736i	$0.188714\pi$
$158$	18.1976	−	10.5064i	1.44772	−	0.835842i
$159$	2.49274	+	4.31755i	0.197687	+	0.342404i
$160$		0			0
$161$		−	3.83892i		−	0.302549i
$162$	−1.14914	−	0.663454i	−0.0902847	−	0.0521259i
$163$	−14.4863	−	8.36365i	−1.13465	−	0.655092i	−0.189551	−	0.981871i	$-0.560703\pi$
$163$	−14.4863	−	8.36365i	−1.13465	−	0.655092i	−0.945101	+	0.326779i	$0.894037\pi$
$164$		−	2.11915i		−	0.165478i
$165$		0			0
$166$	−10.4851	−	18.1607i	−0.813799	−	1.40954i
$167$	5.55211	−	3.20551i	0.429635	−	0.248050i	−0.269556	−	0.962985i	$-0.586877\pi$
$167$	5.55211	−	3.20551i	0.429635	−	0.248050i	0.699191	+	0.714935i	$0.253544\pi$
$168$	3.14655			0.242762
$169$	1.45341	−	12.9185i	0.111801	−	0.993731i
$170$		0			0
$171$	−5.50552	+	3.17862i	−0.421018	+	0.243075i
$172$	−1.15704	−	2.00404i	−0.0882231	−	0.152807i
$173$	11.2525	−	19.4900i	0.855514	−	1.48179i	−0.0206534	−	0.999787i	$-0.506575\pi$
$173$	11.2525	−	19.4900i	0.855514	−	1.48179i	0.876167	−	0.482007i	$-0.160092\pi$
$174$			0.310694i			0.0235537i
$175$		0			0
$176$	7.47821	+	4.31755i	0.563691	+	0.325447i
$177$			2.10212i			0.158005i
$178$	10.5126	−	18.2083i	0.787951	−	1.36477i
$179$	2.37797	+	4.11876i	0.177738	+	0.307851i	0.941105	−	0.338114i	$-0.109789\pi$
$179$	2.37797	+	4.11876i	0.177738	+	0.307851i	−0.763368	+	0.645964i	$0.776455\pi$
$180$		0			0
$181$	11.4606			0.851862			0.425931	−	0.904756i	$-0.359947\pi$
$181$	11.4606			0.851862			0.425931	+	0.904756i	$0.359947\pi$
$182$	3.77738	−	3.37623i	0.279998	−	0.250263i
$183$	−3.05379			−0.225743
$184$	−9.32860	+	5.38587i	−0.687713	+	0.397051i
$185$		0			0
$186$	0.874132	−	1.51404i	0.0640945	−	0.111015i
$187$			12.3443i			0.902702i
$188$	1.18169	+	0.682251i	0.0861838	+	0.0497582i
$189$	0.917086	+	0.529480i	0.0667082	+	0.0385140i
$190$		0			0
$191$	2.90103	−	5.02473i	0.209911	−	0.363577i	−0.741775	−	0.670649i	$-0.766016\pi$
$191$	2.90103	−	5.02473i	0.209911	−	0.363577i	0.951686	+	0.307072i	$0.0993492\pi$
$192$	−4.35723	−	7.54695i	−0.314456	−	0.544654i
$193$	−2.10735	+	1.21668i	−0.151691	+	0.0875786i	−0.573924	−	0.818908i	$-0.694580\pi$
$193$	−2.10735	+	1.21668i	−0.151691	+	0.0875786i	0.422234	+	0.906487i	$0.361246\pi$
$194$	−13.3433			−0.957990
$195$		0			0
$196$	1.40683			0.100488
$197$	11.5895	−	6.69120i	0.825717	−	0.476728i	−0.0266669	−	0.999644i	$-0.508489\pi$
$197$	11.5895	−	6.69120i	0.825717	−	0.476728i	0.852384	+	0.522916i	$0.175156\pi$
$198$	1.65382	+	2.86450i	0.117532	+	0.203571i
$199$	−8.92555	+	15.4595i	−0.632716	+	1.09590i	0.354279	+	0.935140i	$0.384726\pi$
$199$	−8.92555	+	15.4595i	−0.632716	+	1.09590i	−0.986994	+	0.160756i	$0.948607\pi$
$200$		0			0
$201$	6.61171	+	3.81727i	0.466354	+	0.269250i
$202$	−13.1133	−	7.57097i	−0.922649	−	0.532692i
$203$		−	0.247954i		−	0.0174030i
$204$	0.592551	−	1.02633i	0.0414869	−	0.0718574i
$205$		0			0
$206$	3.33006	−	1.92261i	0.232016	−	0.133955i
$207$	−3.62518			−0.251968
$208$	−11.8645	−	3.90304i	−0.822655	−	0.270627i
$209$	15.8469			1.09615
$210$		0			0
$211$	−4.99443	−	8.65060i	−0.343830	−	0.595532i	0.641310	−	0.767282i	$-0.278391\pi$
$211$	−4.99443	−	8.65060i	−0.343830	−	0.595532i	−0.985141	+	0.171750i	$0.945058\pi$
$212$	−0.596546	+	1.03325i	−0.0409710	+	0.0709638i
$213$			8.17688i			0.560270i
$214$	−17.3671	−	10.0269i	−1.18719	−	0.685425i
$215$		0			0
$216$		−	2.97136i		−	0.202176i
$217$	−0.697615	+	1.20830i	−0.0473572	+	0.0820250i
$218$	−0.256006	−	0.443415i	−0.0173389	−	0.0300318i
$219$	−3.45298	+	1.99358i	−0.233331	+	0.134714i
$220$		0			0
$221$	−3.64836	−	17.4783i	−0.245415	−	1.17572i
$222$	8.11792			0.544839
$223$	−17.5247	+	10.1179i	−1.17354	+	0.677546i	−0.954512	−	0.298172i	$-0.903623\pi$
$223$	−17.5247	+	10.1179i	−1.17354	+	0.677546i	−0.219032	+	0.975718i	$0.570290\pi$
$224$	0.712776	+	1.23457i	0.0476244	+	0.0824878i
$225$		0			0
$226$		−	11.1744i		−	0.743308i
$227$	2.76083	+	1.59396i	0.183242	+	0.105795i	0.588815	−	0.808268i	$-0.299595\pi$
$227$	2.76083	+	1.59396i	0.183242	+	0.105795i	−0.405573	+	0.914063i	$0.632928\pi$
$228$	−1.31755	−	0.760686i	−0.0872567	−	0.0503777i
$229$			27.3461i			1.80708i	0.428504	+	0.903540i	$0.359041\pi$
$229$			27.3461i			1.80708i	−0.428504	+	0.903540i	$0.640959\pi$
$230$		0			0
$231$	−1.31985	−	2.28605i	−0.0868400	−	0.150411i
$232$	−0.602531	+	0.347871i	−0.0395581	+	0.0228389i
$233$	−12.8534			−0.842057			−0.421029	−	0.907047i	$-0.638331\pi$
$233$	−12.8534			−0.842057			−0.421029	+	0.907047i	$0.638331\pi$
$234$	−3.18825	−	3.56707i	−0.208423	−	0.233186i
$235$		0			0
$236$	−0.435668	+	0.251533i	−0.0283596	+	0.0163734i
$237$	7.91793	+	13.7143i	0.514325	+	0.890837i
$238$	3.47920	−	6.02614i	0.225523	−	0.390617i
$239$			10.3969i			0.672521i	0.941769	+	0.336260i	$0.109162\pi$
$239$			10.3969i			0.672521i	−0.941769	+	0.336260i	$0.890838\pi$
$240$		0			0
$241$	5.30421	+	3.06239i	0.341674	+	0.197266i	0.661012	−	0.750375i	$-0.270127\pi$
$241$	5.30421	+	3.06239i	0.341674	+	0.197266i	−0.319338	+	0.947641i	$0.603461\pi$
$242$			6.35093i			0.408253i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−0.365407	−	0.632904i	−0.0233928	−	0.0405175i
$245$		0			0
$246$	−11.7500			−0.749150
$247$	−22.4377	+	4.68357i	−1.42768	+	0.298009i
$248$	3.91491			0.248597
$249$	13.6864	−	7.90187i	0.867343	−	0.500761i
$250$		0			0
$251$	−3.87671	+	6.71467i	−0.244696	+	0.423826i	−0.962046	−	0.272887i	$-0.912022\pi$
$251$	−3.87671	+	6.71467i	−0.244696	+	0.423826i	0.717350	+	0.696713i	$0.245355\pi$
$252$			0.253423i			0.0159642i
$253$	7.82595	+	4.51831i	0.492013	+	0.284064i
$254$	13.0854	+	7.55485i	0.821050	+	0.474033i
$255$		0			0
$256$	2.82901	−	4.89998i	0.176813	−	0.306249i
$257$	−4.02069	−	6.96403i	−0.250804	−	0.434404i	0.712944	−	0.701221i	$-0.247361\pi$
$257$	−4.02069	−	6.96403i	−0.250804	−	0.434404i	−0.963747	+	0.266817i	$0.914028\pi$
$258$	−11.1117	+	6.41535i	−0.691785	+	0.399402i
$259$	−6.47863			−0.402562
$260$		0			0
$261$	−0.234149			−0.0144935
$262$	−13.2091	+	7.62630i	−0.816064	+	0.471154i
$263$	−8.51573	−	14.7497i	−0.525102	−	0.909504i	−0.999573	−	0.0292325i	$-0.990694\pi$
$263$	−8.51573	−	14.7497i	−0.525102	−	0.909504i	0.474470	−	0.880272i	$-0.342640\pi$
$264$	−3.70342	+	6.41450i	−0.227929	+	0.394785i
$265$		0			0
$266$	−7.73605	−	4.46641i	−0.474327	−	0.273853i
$267$	13.7224	+	7.92261i	0.839795	+	0.484856i
$268$			1.82705i			0.111605i
$269$	4.87587	−	8.44526i	0.297287	−	0.514916i	−0.678227	−	0.734852i	$-0.737251\pi$
$269$	4.87587	−	8.44526i	0.297287	−	0.514916i	0.975514	+	0.219936i	$0.0705848\pi$
$270$		0			0
$271$	−18.4341	+	10.6429i	−1.11979	+	0.646512i	−0.941348	−	0.337438i	$-0.890440\pi$
$271$	−18.4341	+	10.6429i	−1.11979	+	0.646512i	−0.178444	+	0.983950i	$0.557106\pi$
$272$	−17.1545			−1.04015
$273$	2.54443	+	2.84675i	0.153996	+	0.172293i
$274$	22.8454			1.38014
$275$		0			0
$276$	−0.433778	−	0.751325i	−0.0261104	−	0.0452245i
$277$	−12.8324	+	22.2263i	−0.771023	+	1.33545i	0.165979	+	0.986129i	$0.446921\pi$
$277$	−12.8324	+	22.2263i	−0.771023	+	1.33545i	−0.937003	+	0.349322i	$0.886412\pi$
$278$			3.19364i			0.191542i
$279$	1.14103	+	0.658774i	0.0683116	+	0.0394397i
$280$		0			0
$281$		−	16.8364i		−	1.00438i	−0.864758	−	0.502188i	$-0.832529\pi$
$281$		−	16.8364i		−	1.00438i	0.864758	−	0.502188i	$-0.167471\pi$
$282$	3.78284	−	6.55206i	0.225265	−	0.390170i
$283$	9.03975	+	15.6573i	0.537358	+	0.930731i	0.999045	+	0.0436880i	$0.0139108\pi$
$283$	9.03975	+	15.6573i	0.537358	+	0.930731i	−0.461688	+	0.887043i	$0.652756\pi$
$284$	−1.69467	+	0.978419i	−0.100560	+	0.0580585i
$285$		0			0
$286$	2.43684	+	11.6742i	0.144093	+	0.690312i
$287$	9.37723			0.553520
$288$	1.16583	−	0.673091i	0.0686971	−	0.0396623i
$289$	−3.76160	−	6.51528i	−0.221270	−	0.383252i
$290$		0			0
$291$		−	10.0559i		−	0.589487i
$292$	−0.826346	−	0.477091i	−0.0483583	−	0.0279197i
$293$	12.5959	+	7.27222i	0.735858	+	0.424848i	0.820561	−	0.571559i	$-0.193661\pi$
$293$	12.5959	+	7.27222i	0.735858	+	0.424848i	−0.0847036	+	0.996406i	$0.526994\pi$
$294$		−	7.80037i		−	0.454927i
$295$		0			0
$296$	9.08928	+	15.7431i	0.528304	+	0.915049i
$297$	−2.15877	+	1.24637i	−0.125265	+	0.0723216i
$298$	−4.48812			−0.259990
$299$	−12.4162	−	4.08453i	−0.718047	−	0.236215i
$300$		0			0
$301$	8.86787	−	5.11986i	0.511135	−	0.295104i
$302$	0.973671	+	1.68645i	0.0560285	+	0.0970441i
$303$	5.70572	−	9.88260i	0.327785	−	0.567741i
$304$			22.0221i			1.26305i
$305$		0			0
$306$	−5.69063	−	3.28549i	−0.325312	−	0.187819i
$307$		−	34.1062i		−	1.94654i	−0.229654	−	0.973272i	$-0.573759\pi$
$307$		−	34.1062i		−	1.94654i	0.229654	−	0.973272i	$-0.426241\pi$
$308$	0.315859	−	0.547084i	0.0179977	−	0.0311730i
$309$	1.44894	+	2.50964i	0.0824273	+	0.142768i
$310$		0			0
$311$	−4.66962			−0.264790			−0.132395	−	0.991197i	$-0.542267\pi$
$311$	−4.66962			−0.264790			−0.132395	+	0.991197i	$0.542267\pi$
$312$	3.34787	−	10.1769i	0.189536	−	0.576152i
$313$	5.04485			0.285152			0.142576	−	0.989784i	$-0.454462\pi$
$313$	5.04485			0.285152			0.142576	+	0.989784i	$0.454462\pi$
$314$	23.8829	−	13.7888i	1.34779	−	0.778147i
$315$		0			0
$316$	−1.89487	+	3.28201i	−0.106595	+	0.184627i
$317$			14.6107i			0.820616i	0.911947	+	0.410308i	$0.134579\pi$
$317$			14.6107i			0.820616i	−0.911947	+	0.410308i	$0.865421\pi$
$318$	5.72899	+	3.30763i	0.321266	+	0.185483i
$319$	0.505475	+	0.291836i	0.0283012	+	0.0163397i
$320$		0			0
$321$	7.55659	−	13.0884i	0.421767	−	0.730523i
$322$	−2.54695	−	4.41144i	−0.141936	−	0.245840i
$323$	−27.2639	+	15.7408i	−1.51700	+	0.875841i
$324$	0.239314			0.0132952
$325$		0			0
$326$	−22.1956			−1.22930
$327$	0.334171	−	0.192934i	0.0184797	−	0.0106693i
$328$	−13.1559	−	22.7867i	−0.726414	−	1.25819i
$329$	−3.01895	+	5.22897i	−0.166440	+	0.288283i
$330$		0			0
$331$	13.8034	+	7.96942i	0.758706	+	0.438039i	0.828831	−	0.559499i	$-0.189007\pi$
$331$	13.8034	+	7.96942i	0.758706	+	0.438039i	−0.0701252	+	0.997538i	$0.522340\pi$
$332$	3.27535	+	1.89103i	0.179758	+	0.103784i
$333$			6.11792i			0.335260i
$334$	4.25342	−	7.36715i	0.232737	−	0.403112i
$335$		0			0
$336$	3.17688	−	1.83417i	0.173313	−	0.100062i
$337$	−19.8261			−1.08000			−0.539998	−	0.841666i	$-0.681575\pi$
$337$	−19.8261			−1.08000			−0.539998	+	0.841666i	$0.681575\pi$
$338$	−6.90066	−	15.8094i	−0.375347	−	0.859917i
$339$	8.42136			0.457385
$340$		0			0
$341$	−1.64215	−	2.84429i	−0.0889274	−	0.154027i
$342$	−4.21773	+	7.30533i	−0.228069	+	0.395027i
$343$			13.6379i			0.736378i
$344$	−24.8826	−	14.3660i	−1.34158	−	0.774561i
$345$		0			0
$346$		−	29.8622i		−	1.60540i
$347$	5.18163	−	8.97484i	0.278164	−	0.481795i	−0.692764	−	0.721164i	$-0.743607\pi$
$347$	5.18163	−	8.97484i	0.278164	−	0.481795i	0.970929	+	0.239369i	$0.0769407\pi$
$348$	−0.0280175	−	0.0485278i	−0.00150190	−	0.00260136i
$349$	−27.5828	+	15.9249i	−1.47647	+	0.852442i	−0.999647	−	0.0265555i	$-0.991546\pi$
$349$	−27.5828	+	15.9249i	−1.47647	+	0.852442i	−0.476826	+	0.878998i	$0.658213\pi$
$350$		0			0
$351$	2.68825	−	2.40277i	0.143488	−	0.128250i
$352$	−3.35568			−0.178858
$353$	1.00117	−	0.578026i	0.0532869	−	0.0307652i	−0.473120	−	0.880998i	$-0.656872\pi$
$353$	1.00117	−	0.578026i	0.0532869	−	0.0307652i	0.526407	+	0.850233i	$0.323539\pi$
$354$	1.39466	+	2.41562i	0.0741254	+	0.128389i
$355$		0			0
$356$			3.79198i			0.200974i
$357$	4.54149	+	2.62203i	0.240361	+	0.138773i
$358$	5.46522	+	3.15535i	0.288846	+	0.166765i
$359$			21.6260i			1.14138i	0.821166	+	0.570689i	$0.193324\pi$
$359$			21.6260i			1.14138i	−0.821166	+	0.570689i	$0.806676\pi$
$360$		0			0
$361$	10.7072	+	18.5454i	0.563537	+	0.976075i
$362$	13.1698	−	7.60360i	0.692191	−	0.399636i
$363$	−4.78626			−0.251214
$364$	−0.285535	+	0.867971i	−0.0149661	+	0.0454941i
$365$		0			0
$366$	−3.50923	+	2.02605i	−0.183430	+	0.105903i
$367$	8.42030	+	14.5844i	0.439536	+	0.761299i	0.997654	−	0.0684628i	$-0.0218094\pi$
$367$	8.42030	+	14.5844i	0.439536	+	0.761299i	−0.558117	+	0.829762i	$0.688476\pi$
$368$	−6.27900	+	10.8755i	−0.327315	+	0.566927i
$369$		−	8.85513i		−	0.460980i
$370$		0			0
$371$	−4.57211	−	2.63971i	−0.237372	−	0.137047i
$372$			0.315307i			0.0163479i
$373$	12.2504	−	21.2184i	0.634303	−	1.09865i	−0.352359	−	0.935865i	$-0.614620\pi$
$373$	12.2504	−	21.2184i	0.634303	−	1.09865i	0.986662	−	0.162781i	$-0.0520463\pi$
$374$	8.18985	+	14.1852i	0.423487	+	0.733501i
$375$		0			0
$376$	16.9419			0.873712
$377$	−0.801957	−	0.263819i	−0.0413029	−	0.0135873i
$378$	1.40514			0.0722727
$379$	28.6376	−	16.5339i	1.47101	−	0.849290i	0.471543	−	0.881843i	$-0.343697\pi$
$379$	28.6376	−	16.5339i	1.47101	−	0.849290i	0.999470	+	0.0325537i	$0.0103640\pi$
$380$		0			0
$381$	−5.69357	+	9.86155i	−0.291690	+	0.505223i
$382$		−	7.69880i		−	0.393905i
$383$	0.866143	+	0.500068i	0.0442578	+	0.0255523i	0.521966	−	0.852966i	$-0.325199\pi$
$383$	0.866143	+	0.500068i	0.0442578	+	0.0255523i	−0.477708	+	0.878519i	$0.658532\pi$
$384$	−7.68245	−	4.43547i	−0.392044	−	0.226346i
$385$		0			0
$386$	−1.61442	+	2.79626i	−0.0821720	+	0.142326i
$387$	−4.83481	−	8.37413i	−0.245767	−	0.425681i
$388$	2.08410	−	1.20326i	0.105804	−	0.0610861i
$389$	−1.26193			−0.0639823			−0.0319912	−	0.999488i	$-0.510185\pi$
$389$	−1.26193			−0.0639823			−0.0319912	+	0.999488i	$0.510185\pi$
$390$		0			0
$391$	−17.9522			−0.907883
$392$	15.1273	−	8.73374i	0.764043	−	0.441120i
$393$	−5.74742	−	9.95482i	−0.289919	−	0.502154i
$394$	8.87861	−	15.3782i	0.447298	−	0.774742i
$395$		0			0
$396$	−0.516624	−	0.298273i	−0.0259613	−	0.0149888i
$397$	9.66131	+	5.57796i	0.484887	+	0.279950i	0.722451	−	0.691422i	$-0.243016\pi$
$397$	9.66131	+	5.57796i	0.484887	+	0.279950i	−0.237564	+	0.971372i	$0.576349\pi$
$398$			23.6868i			1.18731i
$399$	3.36603	−	5.83013i	0.168512	−	0.291871i
$400$		0			0
$401$	28.8148	−	16.6362i	1.43894	−	0.830774i	0.441166	−	0.897426i	$-0.354565\pi$
$401$	28.8148	−	16.6362i	1.43894	−	0.830774i	0.997776	+	0.0666518i	$0.0212317\pi$
$402$	10.1303			0.505255
$403$	3.16576	+	3.54190i	0.157698	+	0.176435i
$404$	2.73091			0.135868
$405$		0			0
$406$	−0.164506	−	0.284933i	−0.00816432	−	0.0141410i
$407$	7.62518	−	13.2072i	0.377966	−	0.654657i
$408$		−	14.7145i		−	0.728475i
$409$	2.09367	+	1.20878i	0.103525	+	0.0597704i	0.550869	−	0.834592i	$-0.314296\pi$
$409$	2.09367	+	1.20878i	0.103525	+	0.0597704i	−0.447343	+	0.894362i	$0.647630\pi$
$410$		0			0
$411$			17.2170i			0.849251i
$412$	−0.346751	+	0.600590i	−0.0170832	+	0.0295890i
$413$	−1.11303	−	1.92782i	−0.0547686	−	0.0948621i
$414$	−4.16583	+	2.40514i	−0.204739	+	0.118206i
$415$		0			0
$416$	4.75133	−	0.991775i	0.232953	−	0.0486258i
$417$	−2.40683			−0.117863
$418$	18.2103	−	10.5137i	0.890693	−	0.514242i
$419$	−13.3459	−	23.1157i	−0.651988	−	1.12928i	−0.982640	−	0.185523i	$-0.940602\pi$
$419$	−13.3459	−	23.1157i	−0.651988	−	1.12928i	0.330652	−	0.943753i	$-0.392731\pi$
$420$		0			0
$421$			40.7370i			1.98540i	0.120614	+	0.992699i	$0.461514\pi$
$421$			40.7370i			1.98540i	−0.120614	+	0.992699i	$0.538486\pi$
$422$	−11.4786	−	6.62715i	−0.558767	−	0.322604i
$423$	4.93784	+	2.85086i	0.240086	+	0.138614i
$424$			14.8137i			0.719415i
$425$		0			0
$426$	5.42498	+	9.39635i	0.262841	+	0.455255i
$427$	2.80059	−	1.61692i	0.135530	−	0.0782484i
$428$	3.61679			0.174824
$429$	−8.79807	+	1.83648i	−0.424775	+	0.0886660i
$430$		0			0
$431$	−6.21354	+	3.58739i	−0.299296	+	0.172798i	−0.642126	−	0.766599i	$-0.721948\pi$
$431$	−6.21354	+	3.58739i	−0.299296	+	0.172798i	0.342831	+	0.939397i	$0.388614\pi$
$432$	−1.73205	−	3.00000i	−0.0833333	−	0.144338i
$433$	14.3671	−	24.8845i	0.690438	−	1.19587i	−0.281257	−	0.959633i	$-0.590751\pi$
$433$	14.3671	−	24.8845i	0.690438	−	1.19587i	0.971695	−	0.236241i	$-0.0759154\pi$
$434$			1.85134i			0.0888672i
$435$		0			0
$436$	0.0799718	+	0.0461717i	0.00382995	+	0.00221123i
$437$			23.0461i			1.10245i
$438$	−2.64530	+	4.58179i	−0.126397	+	0.218927i
$439$	−19.5845	−	33.9213i	−0.934716	−	1.61898i	−0.775139	−	0.631791i	$-0.782320\pi$
$439$	−19.5845	−	33.9213i	−0.934716	−	1.61898i	−0.159578	−	0.987185i	$-0.551013\pi$
$440$		0			0
$441$	5.87861			0.279934
$442$	−15.7885	−	17.6644i	−0.750983	−	0.840211i
$443$	12.5223			0.594954			0.297477	−	0.954729i	$-0.403855\pi$
$443$	12.5223			0.594954			0.297477	+	0.954729i	$0.403855\pi$
$444$	−1.26795	+	0.732051i	−0.0601742	+	0.0347416i
$445$		0			0
$446$	−13.4256	+	23.2537i	−0.635718	+	1.10110i
$447$		−	3.38239i		−	0.159982i
$448$	7.99191	+	4.61413i	0.377582	+	0.217997i
$449$	−9.48926	−	5.47863i	−0.447826	−	0.258552i	0.259086	−	0.965854i	$-0.416579\pi$
$449$	−9.48926	−	5.47863i	−0.447826	−	0.258552i	−0.706912	+	0.707302i	$0.749912\pi$
$450$		0			0
$451$	−11.0368	+	19.1162i	−0.519701	+	0.900148i
$452$	1.00767	+	1.74534i	0.0473969	+	0.0820939i
$453$	−1.27096	+	0.733789i	−0.0597149	+	0.0344764i
$454$	4.23009			0.198528
$455$		0			0
$456$	−18.8897			−0.884589
$457$	14.3629	−	8.29242i	0.671868	−	0.387903i	−0.124916	−	0.992167i	$-0.539866\pi$
$457$	14.3629	−	8.29242i	0.671868	−	0.387903i	0.796784	+	0.604264i	$0.206533\pi$
$458$	18.1429	+	31.4244i	0.847761	+	1.46836i
$459$	2.47605	−	4.28864i	0.115572	−	0.200176i
$460$		0			0
$461$	19.8668	+	11.4701i	0.925290	+	0.534216i	0.885319	−	0.464985i	$-0.153940\pi$
$461$	19.8668	+	11.4701i	0.925290	+	0.534216i	0.0399710	+	0.999201i	$0.487273\pi$
$462$	−3.03338	−	1.75133i	−0.141126	−	0.0814790i
$463$			41.2096i			1.91517i	0.288146	+	0.957587i	$0.406961\pi$
$463$			41.2096i			1.91517i	−0.288146	+	0.957587i	$0.593039\pi$
$464$	−0.405558	+	0.702447i	−0.0188276	+	0.0326103i
$465$		0			0
$466$	−14.7704	+	8.52767i	−0.684224	+	0.395037i
$467$	−31.1867			−1.44315			−0.721574	−	0.692337i	$-0.756581\pi$
$467$	−31.1867			−1.44315			−0.721574	+	0.692337i	$0.756581\pi$
$468$	0.819646	+	0.269638i	0.0378881	+	0.0124640i
$469$	−8.08467			−0.373315
$470$		0			0
$471$	10.3917	+	17.9989i	0.478823	+	0.829345i
$472$	−3.12308	+	5.40934i	−0.143752	+	0.248985i
$473$			24.1038i			1.10829i
$474$	18.1976	+	10.5064i	0.835842	+	0.482574i
$475$		0			0
$476$			1.25498i			0.0575217i
$477$	−2.49274	+	4.31755i	−0.114135	+	0.197687i
$478$	6.89788	+	11.9475i	0.315502	+	0.546465i
$479$	−4.46852	+	2.57990i	−0.204172	+	0.117879i	−0.598600	−	0.801048i	$-0.704276\pi$
$479$	−4.46852	+	2.57990i	−0.204172	+	0.117879i	0.394428	+	0.918927i	$0.370943\pi$
$480$		0			0
$481$	−6.89313	+	20.9538i	−0.314300	+	0.955410i
$482$	8.12701			0.370175
$483$	3.32460	−	1.91946i	0.151275	−	0.0873385i
$484$	−0.572709	−	0.991961i	−0.0260322	−	0.0450891i
$485$		0			0
$486$		−	1.32691i		−	0.0601898i
$487$	22.8250	+	13.1780i	1.03430	+	0.597152i	0.918213	−	0.396087i	$-0.129632\pi$
$487$	22.8250	+	13.1780i	1.03430	+	0.597152i	0.116085	+	0.993239i	$0.462966\pi$
$488$	−7.85826	−	4.53697i	−0.355727	−	0.205379i
$489$		−	16.7273i		−	0.756435i
$490$		0			0
$491$	−9.36114	−	16.2140i	−0.422462	−	0.731726i	0.573717	−	0.819053i	$-0.305501\pi$
$491$	−9.36114	−	16.2140i	−0.422462	−	0.731726i	−0.996180	+	0.0873273i	$0.972167\pi$
$492$	1.83524	−	1.05958i	0.0827391	−	0.0477694i
$493$	−1.15953			−0.0522225
$494$	−22.6767	+	20.2685i	−1.02027	+	0.911921i
$495$		0			0
$496$	3.95264	−	2.28206i	0.177479	−	0.102467i
$497$	−4.32949	−	7.49890i	−0.194204	−	0.336372i
$498$	10.4851	−	18.1607i	0.469847	−	0.813799i
$499$			9.31449i			0.416974i	0.978025	+	0.208487i	$0.0668538\pi$
$499$			9.31449i			0.416974i	−0.978025	+	0.208487i	$0.933146\pi$
$500$		0			0
$501$	5.55211	+	3.20551i	0.248050	+	0.143212i
$502$			10.2881i			0.459180i
$503$	7.02558	−	12.1687i	0.313255	−	0.542573i	−0.665810	−	0.746121i	$-0.731914\pi$
$503$	7.02558	−	12.1687i	0.313255	−	0.542573i	0.979065	+	0.203548i	$0.0652472\pi$
$504$	1.57328	+	2.72500i	0.0700793	+	0.121381i
$505$		0			0
$506$	11.9908			0.533055
$507$	11.9145	−	5.20056i	0.529139	−	0.230965i
$508$	−2.72510			−0.120907
$509$	19.0832	−	11.0177i	0.845848	−	0.488350i	−0.0133999	−	0.999910i	$-0.504265\pi$
$509$	19.0832	−	11.0177i	0.845848	−	0.488350i	0.859248	+	0.511560i	$0.170932\pi$
$510$		0			0
$511$	2.11112	−	3.65657i	0.0933905	−	0.161757i
$512$		−	25.2495i		−	1.11588i
$513$	−5.50552	−	3.17862i	−0.243075	−	0.140339i
$514$	−9.24064	−	5.33508i	−0.407587	−	0.235320i
$515$		0			0
$516$	1.15704	−	2.00404i	0.0509357	−	0.0882231i
$517$	−7.10645	−	12.3087i	−0.312541	−	0.541338i
$518$	−7.44483	+	4.29827i	−0.327107	+	0.188855i
$519$	22.5051			0.987862
$520$		0			0
$521$	29.6165			1.29752			0.648762	−	0.760991i	$-0.275287\pi$
$521$	29.6165			1.29752			0.648762	+	0.760991i	$0.275287\pi$
$522$	−0.269069	+	0.155347i	−0.0117768	+	0.00679936i
$523$	5.83376	+	10.1044i	0.255092	+	0.441833i	0.964921	−	0.262542i	$-0.0845608\pi$
$523$	5.83376	+	10.1044i	0.255092	+	0.441833i	−0.709828	+	0.704375i	$0.751227\pi$
$524$	1.37544	−	2.38233i	0.0600862	−	0.104072i
$525$		0			0
$526$	−19.5715	−	11.2996i	−0.853357	−	0.492686i
$527$	5.65048	+	3.26231i	0.246139	+	0.142108i
$528$			8.63509i			0.375794i
$529$	4.92903	−	8.53733i	0.214306	−	0.371188i
$530$		0			0
$531$	−1.82049	+	1.05106i	−0.0790025	+	0.0456121i
$532$	1.61107			0.0698488
$533$	9.97718	−	30.3287i	0.432160	−	1.31368i
$534$	21.0252			0.909848
$535$		0			0
$536$	11.3425	+	19.6458i	0.489922	+	0.848569i
$537$	−2.37797	+	4.11876i	−0.102617	+	0.177738i
$538$		−	12.9397i		−	0.557869i
$539$	−12.6906	−	7.32691i	−0.546622	−	0.315592i
$540$		0			0
$541$		−	32.7583i		−	1.40839i	−0.710006	−	0.704196i	$-0.751308\pi$
$541$		−	32.7583i		−	1.40839i	0.710006	−	0.704196i	$-0.248692\pi$
$542$	−14.1222	+	24.4603i	−0.606600	+	1.05066i
$543$	5.73031	+	9.92519i	0.245911	+	0.425931i
$544$	5.77329	−	3.33321i	0.247528	−	0.142910i
$545$		0			0
$546$	4.81259	+	1.58319i	0.205960	+	0.0677543i
$547$	10.8406			0.463511			0.231755	−	0.972774i	$-0.425553\pi$
$547$	10.8406			0.463511			0.231755	+	0.972774i	$0.425553\pi$
$548$	−3.56825	+	2.06013i	−0.152428	+	0.0880044i
$549$	−1.52690	−	2.64466i	−0.0651664	−	0.112872i
$550$		0			0
$551$			1.48854i			0.0634140i
$552$	−9.32860	−	5.38587i	−0.397051	−	0.229238i
$553$	−14.5228	−	8.38477i	−0.617574	−	0.356557i
$554$			34.0548i			1.44685i
$555$		0			0
$556$	−0.287994	−	0.498820i	−0.0122137	−	0.0211547i
$557$	17.9382	−	10.3566i	0.760065	−	0.438824i	−0.0692540	−	0.997599i	$-0.522062\pi$
$557$	17.9382	−	10.3566i	0.760065	−	0.438824i	0.829319	+	0.558775i	$0.188729\pi$
$558$	1.74826			0.0740100
$559$	−7.12391	−	34.1287i	−0.301309	−	1.44349i
$560$		0			0
$561$	−10.6904	+	6.17213i	−0.451351	+	0.260588i
$562$	−11.1702	−	19.3473i	−0.471186	−	0.816118i
$563$	−18.5889	+	32.1969i	−0.783428	+	1.35694i	0.146506	+	0.989210i	$0.453197\pi$
$563$	−18.5889	+	32.1969i	−0.783428	+	1.35694i	−0.929934	+	0.367727i	$0.880136\pi$
$564$			1.36450i			0.0574559i
$565$		0			0
$566$	20.7758	+	11.9949i	0.873273	+	0.504184i
$567$			1.05896i			0.0444721i
$568$	−12.1482	+	21.0414i	−0.509729	+	0.882876i
$569$	23.0048	+	39.8455i	0.964413	+	1.67041i	0.711184	+	0.703006i	$0.248159\pi$
$569$	23.0048	+	39.8455i	0.964413	+	1.67041i	0.253229	+	0.967406i	$0.418507\pi$
$570$		0			0
$571$	41.4861			1.73614			0.868070	−	0.496442i	$-0.165361\pi$
$571$	41.4861			1.73614			0.868070	+	0.496442i	$0.165361\pi$
$572$	−1.43336	−	1.60367i	−0.0599319	−	0.0670527i
$573$	5.80206			0.242385
$574$	10.7757	−	6.22136i	0.449770	−	0.259675i
$575$		0			0
$576$	4.35723	−	7.54695i	0.181551	−	0.314456i
$577$			13.0556i			0.543513i	0.962366	+	0.271756i	$0.0876045\pi$
$577$			13.0556i			0.543513i	−0.962366	+	0.271756i	$0.912396\pi$
$578$	−8.64518	−	4.99130i	−0.359592	−	0.207611i
$579$	−2.10735	−	1.21668i	−0.0875786	−	0.0505635i
$580$		0			0
$581$	−8.36776	+	14.4934i	−0.347153	+	0.601287i
$582$	−6.67163	−	11.5556i	−0.276548	−	0.478995i
$583$	10.7625	−	6.21374i	0.445738	−	0.257347i
$584$	−11.8473			−0.490245
$585$		0			0
$586$	19.2991			0.797240
$587$	−14.6720	+	8.47088i	−0.605578	+	0.349631i	−0.771233	−	0.636553i	$-0.780360\pi$
$587$	−14.6720	+	8.47088i	−0.605578	+	0.349631i	0.165655	+	0.986184i	$0.447026\pi$
$588$	0.703415	+	1.21835i	0.0290084	+	0.0502439i
$589$	4.18798	−	7.25379i	0.172563	−	0.298887i
$590$		0			0
$591$	11.5895	+	6.69120i	0.476728	+	0.275239i
$592$	18.3538	+	10.5965i	0.754335	+	0.435515i
$593$			45.0621i			1.85048i	0.379384	+	0.925239i	$0.376136\pi$
$593$			45.0621i			1.85048i	−0.379384	+	0.925239i	$0.623864\pi$
$594$	−1.65382	+	2.86450i	−0.0678569	+	0.117532i
$595$		0			0
$596$	0.701007	−	0.404726i	0.0287143	−	0.0165782i
$597$	−17.8511			−0.730597
$598$	−16.9778	+	3.54389i	−0.694274	+	0.144920i
$599$	24.1055			0.984924			0.492462	−	0.870334i	$-0.336097\pi$
$599$	24.1055			0.984924			0.492462	+	0.870334i	$0.336097\pi$
$600$		0			0
$601$	−14.0845	−	24.3950i	−0.574518	−	0.995095i	−0.996094	−	0.0883014i	$-0.971856\pi$
$601$	−14.0845	−	24.3950i	−0.574518	−	0.995095i	0.421576	−	0.906793i	$-0.361477\pi$
$602$	6.79359	−	11.7668i	0.276886	−	0.479581i
$603$			7.63454i			0.310903i
$604$	−0.304158	−	0.175606i	−0.0123760	−	0.00714530i
$605$		0			0
$606$		−	15.1419i		−	0.615099i
$607$	2.87287	−	4.97596i	0.116606	−	0.201968i	−0.801814	−	0.597573i	$-0.796132\pi$
$607$	2.87287	−	4.97596i	0.116606	−	0.201968i	0.918421	+	0.395605i	$0.129465\pi$
$608$	−4.27900	−	7.41144i	−0.173536	−	0.300574i
$609$	0.214735	−	0.123977i	0.00870149	−	0.00502381i
$610$		0			0
$611$	13.6999	+	15.3277i	0.554240	+	0.620092i
$612$	1.18510			0.0479049
$613$	11.3549	−	6.55576i	0.458620	−	0.264785i	−0.252844	−	0.967507i	$-0.581366\pi$
$613$	11.3549	−	6.55576i	0.458620	−	0.264785i	0.711464	+	0.702723i	$0.248032\pi$
$614$	−22.6279	−	39.1927i	−0.913188	−	1.58169i
$615$		0			0
$616$		−	7.84353i		−	0.316025i
$617$	−39.5257	−	22.8202i	−1.59124	−	0.918705i	−0.993094	−	0.117321i	$-0.962569\pi$
$617$	−39.5257	−	22.8202i	−1.59124	−	0.918705i	−0.598150	−	0.801384i	$-0.704097\pi$
$618$	3.33006	+	1.92261i	0.133955	+	0.0773387i
$619$			2.88239i			0.115853i	0.998321	+	0.0579264i	$0.0184489\pi$
$619$			2.88239i			0.115853i	−0.998321	+	0.0579264i	$0.981551\pi$
$620$		0			0
$621$	−1.81259	−	3.13950i	−0.0727368	−	0.125984i
$622$	−5.36603	+	3.09808i	−0.215158	+	0.124222i
$623$	−16.7794			−0.672254
$624$	−2.55211	−	12.2265i	−0.102166	−	0.489451i
$625$		0			0
$626$	5.79722	−	3.34703i	0.231704	−	0.133774i
$627$	7.92345	+	13.7238i	0.316432	+	0.548077i
$628$	−2.48687	+	4.30738i	−0.0992369	+	0.171883i
$629$			30.2965i			1.20800i
$630$		0			0
$631$	−10.3097	−	5.95230i	−0.410422	−	0.236957i	0.280549	−	0.959840i	$-0.409483\pi$
$631$	−10.3097	−	5.95230i	−0.410422	−	0.236957i	−0.690971	+	0.722882i	$0.742817\pi$
$632$			47.0541i			1.87171i
$633$	4.99443	−	8.65060i	0.198511	−	0.343830i
$634$	9.69350	+	16.7896i	0.384978	+	0.666802i
$635$		0			0
$636$	−1.19309			−0.0473092
$637$	20.1341	+	6.62349i	0.797743	+	0.262432i
$638$	0.774480			0.0306619
$639$	−7.08138	+	4.08844i	−0.280135	+	0.161736i
$640$		0			0
$641$	11.1489	−	19.3104i	0.440354	−	0.762715i	−0.557362	−	0.830270i	$-0.688186\pi$
$641$	11.1489	−	19.3104i	0.440354	−	0.762715i	0.997716	+	0.0675549i	$0.0215198\pi$
$642$		−	20.0538i		−	0.791460i
$643$	−2.20220	−	1.27144i	−0.0868465	−	0.0501408i	0.455948	−	0.890007i	$-0.349300\pi$
$643$	−2.20220	−	1.27144i	−0.0868465	−	0.0501408i	−0.542794	+	0.839866i	$0.682634\pi$
$644$	0.795623	+	0.459353i	0.0313519	+	0.0181010i
$645$		0			0
$646$	−20.8866	+	36.1766i	−0.821772	+	1.42335i
$647$	−9.21257	−	15.9566i	−0.362183	−	0.627320i	0.626136	−	0.779713i	$-0.284635\pi$
$647$	−9.21257	−	15.9566i	−0.362183	−	0.627320i	−0.988320	+	0.152393i	$0.951302\pi$
$648$	2.57328	−	1.48568i	0.101088	−	0.0583631i
$649$	5.24003			0.205689
$650$		0			0
$651$	−1.39523			−0.0546833
$652$	3.46676	−	2.00154i	0.135769	−	0.0783862i
$653$	−4.21801	−	7.30581i	−0.165063	−	0.285898i	0.771614	−	0.636091i	$-0.219450\pi$
$653$	−4.21801	−	7.30581i	−0.165063	−	0.285898i	−0.936678	+	0.350192i	$0.886116\pi$
$654$	0.256006	−	0.443415i	0.0100106	−	0.0173389i
$655$		0			0
$656$	−26.5654	−	15.3375i	−1.03720	−	0.598830i
$657$	−3.45298	−	1.99358i	−0.134714	−	0.0777770i
$658$			8.01174i			0.312330i
$659$	−24.7303	+	42.8341i	−0.963354	+	1.66858i	−0.249381	+	0.968405i	$0.580227\pi$
$659$	−24.7303	+	42.8341i	−0.963354	+	1.66858i	−0.713973	+	0.700173i	$0.753106\pi$
$660$		0			0
$661$	−2.83376	+	1.63607i	−0.110221	+	0.0636359i	−0.554097	−	0.832452i	$-0.686936\pi$
$661$	−2.83376	+	1.63607i	−0.110221	+	0.0636359i	0.443876	+	0.896088i	$0.353603\pi$
$662$	21.1494			0.821994
$663$	13.3125	−	11.8987i	0.517014	−	0.462108i
$664$	46.9587			1.82235
$665$		0			0
$666$	4.05896	+	7.03032i	0.157281	+	0.272420i
$667$	−0.424417	+	0.735111i	−0.0164335	+	0.0284636i
$668$			1.53425i			0.0593618i
$669$	−17.5247	−	10.1179i	−0.677546	−	0.391181i
$670$		0			0
$671$			7.61231i			0.293870i
$672$	−0.712776	+	1.23457i	−0.0274959	+	0.0476244i
$673$	4.43371	+	7.67941i	0.170907	+	0.296020i	0.938737	−	0.344634i	$-0.111997\pi$
$673$	4.43371	+	7.67941i	0.170907	+	0.296020i	−0.767830	+	0.640653i	$0.778664\pi$
$674$	−22.7829	+	13.1537i	−0.877564	+	0.506662i
$675$		0			0
$676$	2.50347	+	1.84701i	0.0962873	+	0.0710388i
$677$	−45.0533			−1.73154			−0.865769	−	0.500444i	$-0.833170\pi$
$677$	−45.0533			−1.73154			−0.865769	+	0.500444i	$0.833170\pi$
$678$	9.67729	−	5.58718i	0.371654	−	0.214575i
$679$	5.32439	+	9.22212i	0.204331	+	0.353913i
$680$		0			0
$681$			3.18793i			0.122162i
$682$	−3.77411	−	2.17898i	−0.144518	−	0.0834375i
$683$	−18.4888	−	10.6745i	−0.707454	−	0.408449i	0.102664	−	0.994716i	$-0.467263\pi$
$683$	−18.4888	−	10.6745i	−0.707454	−	0.408449i	−0.810117	+	0.586268i	$0.800597\pi$
$684$		−	1.52137i		−	0.0581711i
$685$		0			0
$686$	9.04814	+	15.6718i	0.345459	+	0.598353i
$687$	−23.6824	+	13.6730i	−0.903540	+	0.521659i
$688$	−33.4965			−1.27704
$689$	−13.4022	+	11.9789i	−0.510584	+	0.456361i
$690$		0			0
$691$	−20.2844	+	11.7112i	−0.771654	+	0.445515i	−0.833464	−	0.552573i	$-0.813646\pi$
$691$	−20.2844	+	11.7112i	−0.771654	+	0.445515i	0.0618100	+	0.998088i	$0.480313\pi$
$692$	2.69288	+	4.66421i	0.102368	+	0.177307i
$693$	1.31985	−	2.28605i	0.0501371	−	0.0868400i
$694$		−	13.7511i		−	0.521984i
$695$		0			0
$696$	−0.602531	−	0.347871i	−0.0228389	−	0.0131860i
$697$		−	43.8514i		−	1.66099i
$698$	−21.1309	+	36.5998i	−0.799818	+	1.38532i
$699$	−6.42672	−	11.1314i	−0.243081	−	0.421029i
$700$		0			0
$701$	−43.7290			−1.65162			−0.825811	−	0.563948i	$-0.809282\pi$
$701$	−43.7290			−1.65162			−0.825811	+	0.563948i	$0.809282\pi$
$702$	1.49504	−	4.54464i	0.0564268	−	0.171526i
$703$	38.8930			1.46688
$704$	−18.8126	+	10.8614i	−0.709025	+	0.409356i
$705$		0			0
$706$	0.766987	−	1.32846i	0.0288659	−	0.0499973i
$707$			12.0843i			0.454475i
$708$	−0.435668	−	0.251533i	−0.0163734	−	0.00945319i
$709$	−7.86925	−	4.54331i	−0.295536	−	0.170628i	0.344900	−	0.938639i	$-0.387913\pi$
$709$	−7.86925	−	4.54331i	−0.295536	−	0.170628i	−0.640436	+	0.768012i	$0.721246\pi$
$710$		0			0
$711$	−7.91793	+	13.7143i	−0.296946	+	0.514325i
$712$	23.5410	+	40.7741i	0.882235	+	1.52808i
$713$	4.13644	−	2.38817i	0.154911	−	0.0894378i
$714$	6.95839			0.260411
$715$		0			0
$716$	−1.13816			−0.0425351
$717$	−9.00399	+	5.19846i	−0.336260	+	0.194140i
$718$	14.3479	+	24.8513i	0.535458	+	0.927441i
$719$	−5.42357	+	9.39390i	−0.202265	+	0.350333i	−0.949258	−	0.314499i	$-0.898164\pi$
$719$	−5.42357	+	9.39390i	−0.202265	+	0.350333i	0.746993	+	0.664832i	$0.231497\pi$
$720$		0			0
$721$	−2.65760	−	1.53437i	−0.0989743	−	0.0571429i
$722$	24.6081	+	14.2075i	0.915818	+	0.528748i
$723$			6.12477i			0.227783i
$724$	−1.37134	+	2.37523i	−0.0509655	+	0.0882749i
$725$		0			0
$726$	−5.50007	+	3.17547i	−0.204127	+	0.117853i
$727$	41.2173			1.52866			0.764332	−	0.644822i	$-0.223069\pi$
$727$	41.2173			1.52866			0.764332	+	0.644822i	$0.223069\pi$
$728$	2.31817	+	11.1057i	0.0859169	+	0.411605i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−23.9424	−	41.4695i	−0.885542	−	1.53380i
$732$	0.365407	−	0.632904i	0.0135058	−	0.0233928i
$733$		−	23.4406i		−	0.865799i	−0.901442	−	0.432900i	$-0.857490\pi$
$733$		−	23.4406i		−	0.865799i	0.901442	−	0.432900i	$-0.142510\pi$
$734$	19.3522	+	11.1730i	0.714301	+	0.412402i
$735$		0			0
$736$		−	4.88016i		−	0.179885i
$737$	9.51545	−	16.4813i	0.350506	−	0.607095i
$738$	−5.87498	−	10.1758i	−0.216261	−	0.374575i
$739$	−14.5603	+	8.40641i	−0.535611	+	0.309235i	−0.743298	−	0.668960i	$-0.766740\pi$
$739$	−14.5603	+	8.40641i	−0.535611	+	0.309235i	0.207688	+	0.978195i	$0.433406\pi$
$740$		0			0
$741$	−15.2750	−	17.0899i	−0.561139	−	0.627811i
$742$	−7.00530			−0.257173
$743$	−18.3867	+	10.6155i	−0.674541	+	0.389447i	−0.797795	−	0.602929i	$-0.794000\pi$
$743$	−18.3867	+	10.6155i	−0.674541	+	0.389447i	0.123254	+	0.992375i	$0.460667\pi$
$744$	1.95746	+	3.39041i	0.0717638	+	0.124299i
$745$		0			0
$746$		−	32.5104i		−	1.19029i
$747$	13.6864	+	7.90187i	0.500761	+	0.289114i
$748$	−2.55837	−	1.47707i	−0.0935432	−	0.0540072i
$749$			16.0042i			0.584782i
$750$		0			0
$751$	−11.1589	−	19.3278i	−0.407195	−	0.705282i	0.587379	−	0.809312i	$-0.300160\pi$
$751$	−11.1589	−	19.3278i	−0.407195	−	0.705282i	−0.994574	+	0.104029i	$0.966826\pi$
$752$	17.1052	−	9.87568i	0.623762	−	0.360129i
$753$	−7.75343			−0.282551
$754$	−1.09659	+	0.228898i	−0.0399354	+	0.00833599i
$755$		0			0
$756$	−0.219471	+	0.126712i	−0.00798209	+	0.00460846i
$757$	−3.96088	−	6.86045i	−0.143961	−	0.249347i	0.785024	−	0.619465i	$-0.212651\pi$
$757$	−3.96088	−	6.86045i	−0.143961	−	0.249347i	−0.928985	+	0.370118i	$0.879317\pi$
$758$	21.9390	−	37.9994i	0.796860	−	1.38020i
$759$			9.03662i			0.328009i
$760$		0			0
$761$	−10.5400	−	6.08529i	−0.382076	−	0.220592i	0.296645	−	0.954988i	$-0.404132\pi$
$761$	−10.5400	−	6.08529i	−0.382076	−	0.220592i	−0.678721	+	0.734396i	$0.737465\pi$
$762$			15.1097i			0.547366i
$763$	−0.204309	+	0.353874i	−0.00739649	+	0.0128111i
$764$	0.694256	+	1.20249i	0.0251173	+	0.0435044i
$765$		0			0
$766$	1.32709			0.0479497
$767$	−7.41939	+	1.54870i	−0.267899	+	0.0559203i
$768$	5.65801			0.204166
$769$	18.3243	−	10.5796i	0.660793	−	0.381509i	−0.131786	−	0.991278i	$-0.542071\pi$
$769$	18.3243	−	10.5796i	0.660793	−	0.381509i	0.792579	+	0.609769i	$0.208738\pi$
$770$		0			0
$771$	4.02069	−	6.96403i	0.144801	−	0.250804i
$772$		−	0.582337i		−	0.0209588i
$773$	3.80856	+	2.19887i	0.136984	+	0.0790880i	0.566926	−	0.823769i	$-0.308133\pi$
$773$	3.80856	+	2.19887i	0.136984	+	0.0790880i	−0.429942	+	0.902857i	$0.641466\pi$
$774$	−11.1117	−	6.41535i	−0.399402	−	0.230595i
$775$		0			0
$776$	14.9399	−	25.8766i	0.536310	−	0.928916i
$777$	−3.23931	−	5.61066i	−0.116210	−	0.201281i
$778$	−1.45013	+	0.837232i	−0.0519896	+	0.0300162i
$779$	−56.2941			−2.01695
$780$		0			0
$781$	20.3828			0.729354
$782$	−20.6296	+	11.9105i	−0.737712	+	0.425918i
$783$	−0.117075	−	0.202779i	−0.00418390	−	0.00724673i
$784$	10.1820	−	17.6358i	0.363644	−	0.629851i
$785$		0			0
$786$	−13.2091	−	7.62630i	−0.471154	−	0.272021i
$787$	−37.3374	−	21.5567i	−1.33093	−	0.768415i	−0.345491	−	0.938422i	$-0.612288\pi$
$787$	−37.3374	−	21.5567i	−1.33093	−	0.768415i	−0.985443	+	0.170007i	$0.945621\pi$
$788$			3.20259i			0.114088i
$789$	8.51573	−	14.7497i	0.303168	−	0.525102i
$790$		0			0
$791$	−7.72311	+	4.45894i	−0.274602	+	0.158542i
$792$	−7.40683			−0.263190
$793$	−2.24983	−	10.7783i	−0.0798937	−	0.382749i
$794$	14.8029			0.525335
$795$		0			0
$796$	−2.13601	−	3.69967i	−0.0757088	−	0.131131i
$797$	17.0323	−	29.5008i	0.603315	−	1.04497i	−0.389001	−	0.921237i	$-0.627180\pi$
$797$	17.0323	−	29.5008i	0.603315	−	1.04497i	0.992315	−	0.123734i	$-0.0394870\pi$
$798$		−	8.93282i		−	0.316218i
$799$	24.4526	+	14.1177i	0.865072	+	0.499449i
$800$		0			0
$801$			15.8452i			0.559863i
$802$	22.0748	−	38.2346i	0.779487	−	1.35011i
$803$	4.96947	+	8.60738i	0.175369	+	0.303748i
$804$	−1.58227	+	0.913525i	−0.0558024	+	0.0322176i
$805$		0			0
$806$	5.98778	+	1.96979i	0.210911	+	0.0693829i
$807$	9.75174			0.343278
$808$	29.3648	−	16.9538i	1.03305	−	0.596432i
$809$	−7.86797	−	13.6277i	−0.276623	−	0.479125i	0.693920	−	0.720052i	$-0.255882\pi$
$809$	−7.86797	−	13.6277i	−0.276623	−	0.479125i	−0.970543	+	0.240927i	$0.922549\pi$
$810$		0			0
$811$			47.5686i			1.67036i	0.549976	+	0.835180i	$0.314637\pi$
$811$			47.5686i			1.67036i	−0.549976	+	0.835180i	$0.685363\pi$
$812$	0.0513890	+	0.0296694i	0.00180340	+	0.00104119i
$813$	−18.4341	−	10.6429i	−0.646512	−	0.373264i
$814$		−	20.2358i		−	0.709266i
$815$		0			0
$816$	−8.57727	−	14.8563i	−0.300265	−	0.520073i
$817$	−53.2363	+	30.7360i	−1.86250	+	1.07532i
$818$	3.20789			0.112161
$819$	−1.19314	+	3.62692i	−0.0416918	+	0.126735i
$820$		0			0
$821$	10.5205	−	6.07404i	0.367169	−	0.211985i	−0.305052	−	0.952336i	$-0.598674\pi$
$821$	10.5205	−	6.07404i	0.367169	−	0.211985i	0.672221	+	0.740350i	$0.265340\pi$
$822$	11.4227	+	19.7847i	0.398412	+	0.690069i
$823$	1.82787	−	3.16596i	0.0637156	−	0.110359i	−0.832408	−	0.554163i	$-0.813038\pi$
$823$	1.82787	−	3.16596i	0.0637156	−	0.110359i	0.896124	+	0.443805i	$0.146372\pi$
$824$			8.61066i			0.299966i
$825$		0			0
$826$	−2.55805	−	1.47689i	−0.0890058	−	0.0513875i
$827$			30.5084i			1.06088i	0.847722	+	0.530441i	$0.177974\pi$
$827$			30.5084i			1.06088i	−0.847722	+	0.530441i	$0.822026\pi$
$828$	0.433778	−	0.751325i	0.0150748	−	0.0261104i
$829$	26.0329	+	45.0903i	0.904161	+	1.56605i	0.822040	+	0.569430i	$0.192836\pi$
$829$	26.0329	+	45.0903i	0.904161	+	1.56605i	0.0821211	+	0.996622i	$0.473831\pi$
$830$		0			0
$831$	−25.6648			−0.890301
$832$	23.4267	−	20.9388i	0.812174	−	0.725924i
$833$	29.1114			1.00865
$834$	−2.76578	+	1.59682i	−0.0957710	+	0.0552934i
$835$		0			0
$836$	−1.89619	+	3.28430i	−0.0655811	+	0.113590i
$837$			1.31755i			0.0455411i
$838$	−30.6724	−	17.7087i	−1.05956	−	0.611738i
$839$	−37.4902	−	21.6450i	−1.29431	−	0.747268i	−0.314891	−	0.949128i	$-0.601968\pi$
$839$	−37.4902	−	21.6450i	−1.29431	−	0.747268i	−0.979414	+	0.201860i	$0.935301\pi$
$840$		0			0
$841$	14.4726	−	25.0673i	0.499055	−	0.864388i
$842$	27.0271	+	46.8124i	0.931416	+	1.61326i
$843$	14.5808	−	8.41821i	0.502188	−	0.289938i
$844$	2.39047			0.0822833
$845$		0			0
$846$	7.56567			0.260113
$847$	4.38941	−	2.53423i	0.150822	−	0.0870771i
$848$	8.63509	+	14.9564i	0.296530	+	0.513606i
$849$	−9.03975	+	15.6573i	−0.310244	+	0.537358i
$850$		0			0
$851$	19.2072	+	11.0893i	0.658414	+	0.380136i
$852$	−1.69467	−	0.978419i	−0.0580585	−	0.0335201i
$853$		−	7.62729i		−	0.261153i	−0.991438	−	0.130577i	$-0.958317\pi$
$853$		−	7.62729i		−	0.261153i	0.991438	−	0.130577i	$-0.0416829\pi$
$854$	2.14551	−	3.71613i	0.0734178	−	0.127163i
$855$		0			0
$856$	38.8904	−	22.4534i	1.32925	−	0.767440i
$857$	−34.6287			−1.18289			−0.591447	−	0.806344i	$-0.701443\pi$
$857$	−34.6287			−1.18289			−0.591447	+	0.806344i	$0.701443\pi$
$858$	−8.89176	+	7.94748i	−0.303560	+	0.271322i
$859$	−15.1648			−0.517415			−0.258707	−	0.965956i	$-0.583297\pi$
$859$	−15.1648			−0.517415			−0.258707	+	0.965956i	$0.583297\pi$
$860$		0			0
$861$	4.68861	+	8.12092i	0.159788	+	0.276760i
$862$	−4.76013	+	8.24479i	−0.162131	+	0.280819i
$863$			17.7187i			0.603150i	0.953442	+	0.301575i	$0.0975124\pi$
$863$			17.7187i			0.603150i	−0.953442	+	0.301575i	$0.902488\pi$
$864$	1.16583	+	0.673091i	0.0396623	+	0.0228990i
$865$		0			0
$866$		−	38.1276i		−	1.29563i
$867$	3.76160	−	6.51528i	0.127751	−	0.221270i
$868$	−0.166949	−	0.289164i	−0.00566661	−	0.00981485i
$869$	34.1860	−	19.7373i	1.15968	−	0.669543i
$870$		0			0
$871$	−8.60193	+	26.1482i	−0.291465	+	0.885998i
$872$	1.14655			0.0388272
$873$	8.70866	−	5.02795i	0.294744	−	0.170170i
$874$	15.2900	+	26.4831i	0.517194	+	0.895806i
$875$		0			0
$876$		−	0.954183i		−	0.0322388i
$877$	2.08295	+	1.20259i	0.0703361	+	0.0406086i	0.534756	−	0.845007i	$-0.320404\pi$
$877$	2.08295	+	1.20259i	0.0703361	+	0.0406086i	−0.464420	+	0.885615i	$0.653737\pi$
$878$	−45.0105	−	25.9868i	−1.51903	−	0.877013i
$879$			14.5444i			0.490572i
$880$		0			0
$881$	−13.2458	−	22.9423i	−0.446261	−	0.772946i	0.551878	−	0.833925i	$-0.313911\pi$
$881$	−13.2458	−	22.9423i	−0.446261	−	0.772946i	−0.998139	+	0.0609784i	$0.980578\pi$
$882$	6.75532	−	3.90019i	0.227463	−	0.131326i
$883$	−14.5464			−0.489525			−0.244763	−	0.969583i	$-0.578710\pi$
$883$	−14.5464			−0.489525			−0.244763	+	0.969583i	$0.578710\pi$
$884$	4.05896	+	1.33527i	0.136518	+	0.0449100i
$885$		0			0
$886$	14.3899	−	8.30800i	0.483437	−	0.279113i
$887$	−17.6184	−	30.5160i	−0.591568	−	1.02463i	−0.994021	−	0.109185i	$-0.965176\pi$
$887$	−17.6184	−	30.5160i	−0.591568	−	1.02463i	0.402453	−	0.915441i	$-0.368158\pi$
$888$	−9.08928	+	15.7431i	−0.305016	+	0.528304i
$889$		−	12.0585i		−	0.404430i
$890$		0			0
$891$	−2.15877	−	1.24637i	−0.0723216	−	0.0417549i
$892$		−	4.84271i		−	0.162146i
$893$	18.1236	−	31.3910i	0.606483	−	1.05046i
$894$	−2.24406	−	3.88683i	−0.0750527	−	0.129995i
$895$		0			0
$896$	9.39396			0.313830
$897$	−2.67079	−	12.7950i	−0.0891749	−	0.427213i
$898$	−14.5393			−0.485182
$899$	0.267171	−	0.154251i	0.00891065	−	0.00514457i
$900$		0			0
$901$	−12.3443	+	21.3809i	−0.411247	+	0.712301i
$902$			29.2895i			0.975235i
$903$	8.86787	+	5.11986i	0.295104	+	0.170378i
$904$	21.6705	+	12.5115i	0.720750	+	0.416125i
$905$		0			0
$906$	−0.973671	+	1.68645i	−0.0323480	+	0.0560285i
$907$	8.31939	+	14.4096i	0.276241	+	0.478463i	0.970447	−	0.241313i	$-0.0775780\pi$
$907$	8.31939	+	14.4096i	0.276241	+	0.478463i	−0.694207	+	0.719776i	$0.744245\pi$
$908$	−0.660703	+	0.381457i	−0.0219262	+	0.0126591i
$909$	11.4114			0.378494
$910$		0			0
$911$	−11.3931			−0.377471			−0.188736	−	0.982028i	$-0.560439\pi$
$911$	−11.3931			−0.377471			−0.188736	+	0.982028i	$0.560439\pi$
$912$	−19.0717	+	11.0110i	−0.631527	+	0.364612i
$913$	−19.6973	−	34.1167i	−0.651885	−	1.12910i
$914$	11.0033	−	19.0583i	0.363956	−	0.630391i
$915$		0			0
$916$	−5.66752	−	3.27215i	−0.187260	−	0.108115i
$917$	10.5418	+	6.08628i	0.348119	+	0.200987i
$918$		−	6.57097i		−	0.216874i
$919$	13.3893	−	23.1909i	0.441672	−	0.764998i	−0.556142	−	0.831088i	$-0.687719\pi$
$919$	13.3893	−	23.1909i	0.441672	−	0.764998i	0.997814	+	0.0660891i	$0.0210521\pi$
$920$		0			0
$921$	29.5369	−	17.0531i	0.973272	−	0.561919i
$922$	30.4396			1.00247
$923$	−28.8601	+	6.02416i	−0.949943	+	0.198288i
$924$	0.631718			0.0207820
$925$		0			0
$926$	27.3407	+	47.3555i	0.898471	+	1.55620i
$927$	−1.44894	+	2.50964i	−0.0475894	+	0.0824273i
$928$		−	0.315208i		−	0.0103472i
$929$	−16.8755	−	9.74310i	−0.553669	−	0.319661i	0.196932	−	0.980417i	$-0.436902\pi$
$929$	−16.8755	−	9.74310i	−0.553669	−	0.319661i	−0.750600	+	0.660756i	$0.770236\pi$
$930$		0			0
$931$		−	37.3717i		−	1.22481i
$932$	1.53800	−	2.66390i	0.0503790	−	0.0872589i
$933$	−2.33481	−	4.04401i	−0.0764382	−	0.132395i
$934$	−35.8378	+	20.6909i	−1.17265	+	0.677028i
$935$		0			0
$936$	10.4874	−	2.18910i	0.342790	−	0.0715529i
$937$	9.81448			0.320625			0.160313	−	0.987066i	$-0.448750\pi$
$937$	9.81448			0.320625			0.160313	+	0.987066i	$0.448750\pi$
$938$	−9.29039	+	5.36381i	−0.303342	+	0.175135i
$939$	2.52242	+	4.36897i	0.0823162	+	0.142576i
$940$		0			0
$941$		−	47.0242i		−	1.53295i	−0.642277	−	0.766473i	$-0.722010\pi$
$941$		−	47.0242i		−	1.53295i	0.642277	−	0.766473i	$-0.277990\pi$
$942$	23.8829	+	13.7888i	0.778147	+	0.449263i
$943$	−27.8007	−	16.0507i	−0.905315	−	0.522684i
$944$			7.28196i			0.237008i
$945$		0			0
$946$	15.9918	+	27.6986i	0.519937	+	0.900558i
$947$	20.7176	−	11.9613i	0.673232	−	0.388690i	−0.124068	−	0.992274i	$-0.539594\pi$
$947$	20.7176	−	11.9613i	0.673232	−	0.388690i	0.797300	+	0.603583i	$0.206261\pi$
$948$	−3.78974			−0.123085
$949$	−9.58023	−	10.7185i	−0.310987	−	0.347937i
$950$		0			0
$951$	−12.6532	+	7.30533i	−0.410308	+	0.236891i
$952$	7.79101	+	13.4944i	0.252508	+	0.437357i
$953$	12.8242	−	22.2122i	0.415416	−	0.719522i	−0.580056	−	0.814577i	$-0.696969\pi$
$953$	12.8242	−	22.2122i	0.415416	−	0.719522i	0.995472	+	0.0950546i	$0.0303026\pi$
$954$			6.61527i			0.214177i
$955$		0			0
$956$	−2.15478	−	1.24406i	−0.0696905	−	0.0402358i
$957$			0.583672i			0.0188674i
$958$	−3.42330	+	5.92932i	−0.110602	+	0.191568i
$959$	−9.11604	−	15.7894i	−0.294372	−	0.509868i
$960$		0			0
$961$	29.2641			0.944002
$962$	5.98073	+	28.6520i	0.192826	+	0.923778i
$963$	15.1132			0.487015
$964$	−1.26937	+	0.732871i	−0.0408836	+	0.0236042i
$965$		0			0
$966$	2.54695	−	4.41144i	0.0819467	−	0.141936i
$967$		−	25.1221i		−	0.807873i	−0.914787	−	0.403936i	$-0.867642\pi$
$967$		−	25.1221i		−	0.807873i	0.914787	−	0.403936i	$-0.132358\pi$
$968$	−12.3164	−	7.11086i	−0.395863	−	0.228552i
$969$	−27.2639	−	15.7408i	−0.875841	−	0.505667i
$970$		0			0
$971$	−19.8822	+	34.4370i	−0.638050	+	1.10513i	0.347811	+	0.937565i	$0.386925\pi$
$971$	−19.8822	+	34.4370i	−0.638050	+	1.10513i	−0.985860	+	0.167570i	$0.946408\pi$
$972$	0.119657	+	0.207252i	0.00383799	+	0.00664760i
$973$	2.20727	−	1.27437i	0.0707618	−	0.0408544i
$974$	34.9720			1.12058
$975$		0			0
$976$	−10.5787			−0.338615
$977$	−8.80888	+	5.08581i	−0.281821	+	0.162709i	−0.634247	−	0.773130i	$-0.718690\pi$
$977$	−8.80888	+	5.08581i	−0.281821	+	0.162709i	0.352427	+	0.935839i	$0.385357\pi$
$978$	−11.0978	−	19.2220i	−0.354869	−	0.614650i
$979$	19.7490	−	34.2062i	0.631180	−	1.09324i
$980$		0			0
$981$	0.334171	+	0.192934i	0.0106693	+	0.00615991i
$982$	−21.5144	−	12.4214i	−0.686554	−	0.396382i
$983$		−	37.0857i		−	1.18285i	−0.806360	−	0.591425i	$-0.798566\pi$
$983$		−	37.0857i		−	1.18285i	0.806360	−	0.591425i	$-0.201434\pi$
$984$	13.1559	−	22.7867i	0.419395	−	0.726414i
$985$		0			0
$986$	−1.33246	+	0.769294i	−0.0424340	+	0.0244993i
$987$	−6.03790			−0.192188
$988$	1.71415	−	5.21068i	0.0545343	−	0.165774i
$989$	−35.0541			−1.11466
$990$		0			0
$991$	−8.57901	−	14.8593i	−0.272521	−	0.472021i	0.696986	−	0.717085i	$-0.254524\pi$
$991$	−8.57901	−	14.8593i	−0.272521	−	0.472021i	−0.969507	+	0.245065i	$0.921191\pi$
$992$	−0.886830	+	1.53603i	−0.0281569	+	0.0487691i
$993$			15.9388i			0.505804i
$994$	−9.95035	−	5.74484i	−0.315606	−	0.182215i
$995$		0			0
$996$			3.78205i			0.119839i
$997$	−17.3983	+	30.1347i	−0.551008	+	0.954374i	0.447194	+	0.894437i	$0.352423\pi$
$997$	−17.3983	+	30.1347i	−0.551008	+	0.954374i	−0.998202	+	0.0599374i	$0.980910\pi$
$998$	6.17974	+	10.7036i	0.195616	+	0.338817i
$999$	−5.29827	+	3.05896i	−0.167630	+	0.0967812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bc.i.751.4		8
5.2	odd	4		975.2.w.j.49.3		8
5.3	odd	4		975.2.w.g.49.2		8
5.4	even	2		195.2.bb.c.166.1	yes	8
13.4	even	6	inner	975.2.bc.i.901.4		8
15.14	odd	2		585.2.bu.b.361.4		8
65.4	even	6		195.2.bb.c.121.1	✓	8
65.17	odd	12		975.2.w.g.199.2		8
65.24	odd	12		2535.2.a.bl.1.3		4
65.43	odd	12		975.2.w.j.199.3		8
65.54	odd	12		2535.2.a.bi.1.2		4
195.89	even	12		7605.2.a.cg.1.2		4
195.119	even	12		7605.2.a.ck.1.3		4
195.134	odd	6		585.2.bu.b.316.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.c.121.1	✓	8	65.4	even	6
195.2.bb.c.166.1	yes	8	5.4	even	2
585.2.bu.b.316.4		8	195.134	odd	6
585.2.bu.b.361.4		8	15.14	odd	2
975.2.w.g.49.2		8	5.3	odd	4
975.2.w.g.199.2		8	65.17	odd	12
975.2.w.j.49.3		8	5.2	odd	4
975.2.w.j.199.3		8	65.43	odd	12
975.2.bc.i.751.4		8	1.1	even	1	trivial
975.2.bc.i.901.4		8	13.4	even	6	inner
2535.2.a.bi.1.2		4	65.54	odd	12
2535.2.a.bl.1.3		4	65.24	odd	12
7605.2.a.cg.1.2		4	195.89	even	12
7605.2.a.ck.1.3		4	195.119	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14914 - 0.663454i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.119657 + 0.207252i) q^{4} +(1.14914 + 0.663454i) q^{6} +(-0.917086 - 0.529480i) q^{7} +2.97136i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.14914 - 0.663454i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.119657 + 0.207252i) q^{4} +(1.14914 + 0.663454i) q^{6} +(-0.917086 - 0.529480i) q^{7} +2.97136i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.15877 - 1.24637i) q^{11} -0.239314 q^{12} +(-2.68825 + 2.40277i) q^{13} -1.40514 q^{14} +(1.73205 + 3.00000i) q^{16} +(-2.47605 + 4.28864i) q^{17} +1.32691i q^{18} +(5.50552 + 3.17862i) q^{19} -1.05896i q^{21} +(1.65382 - 2.86450i) q^{22} +(1.81259 + 3.13950i) q^{23} +(-2.57328 + 1.48568i) q^{24} +(-1.49504 + 4.54464i) q^{26} -1.00000 q^{27} +(0.219471 - 0.126712i) q^{28} +(0.117075 + 0.202779i) q^{29} -1.31755i q^{31} +(-1.16583 - 0.673091i) q^{32} +(2.15877 + 1.24637i) q^{33} +6.57097i q^{34} +(-0.119657 - 0.207252i) q^{36} +(5.29827 - 3.05896i) q^{37} +8.43547 q^{38} +(-3.42498 - 1.12671i) q^{39} +(-7.66877 + 4.42757i) q^{41} +(-0.702571 - 1.21689i) q^{42} +(-4.83481 + 8.37413i) q^{43} +0.596546i q^{44} +(4.16583 + 2.40514i) q^{46} -5.70173i q^{47} +(-1.73205 + 3.00000i) q^{48} +(-2.93930 - 5.09102i) q^{49} -4.95209 q^{51} +(-0.176310 - 0.844653i) q^{52} +4.98547 q^{53} +(-1.14914 + 0.663454i) q^{54} +(1.57328 - 2.72500i) q^{56} +6.35723i q^{57} +(0.269069 + 0.155347i) q^{58} +(1.82049 + 1.05106i) q^{59} +(-1.52690 + 2.64466i) q^{61} +(-0.874132 - 1.51404i) q^{62} +(0.917086 - 0.529480i) q^{63} -8.71446 q^{64} +3.30763 q^{66} +(6.61171 - 3.81727i) q^{67} +(-0.592551 - 1.02633i) q^{68} +(-1.81259 + 3.13950i) q^{69} +(7.08138 + 4.08844i) q^{71} +(-2.57328 - 1.48568i) q^{72} +3.98716i q^{73} +(4.05896 - 7.03032i) q^{74} +(-1.31755 + 0.760686i) q^{76} -2.63971 q^{77} +(-4.68330 + 0.977575i) q^{78} +15.8359 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-5.87498 + 10.1758i) q^{82} -15.8037i q^{83} +(0.219471 + 0.126712i) q^{84} +12.8307i q^{86} +(-0.117075 + 0.202779i) q^{87} +(3.70342 + 6.41450i) q^{88} +(13.7224 - 7.92261i) q^{89} +(3.73758 - 0.780169i) q^{91} -0.867556 q^{92} +(1.14103 - 0.658774i) q^{93} +(-3.78284 - 6.55206i) q^{94} -1.34618i q^{96} +(-8.70866 - 5.02795i) q^{97} +(-6.75532 - 3.90019i) q^{98} +2.49274i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} + 4 q^{3} + 4 q^{4} - 6 q^{6} - 6 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 6 * q^2 + 4 * q^3 + 4 * q^4 - 6 * q^6 - 6 * q^7 - 4 * q^9	\( 8 q - 6 q^{2} + 4 q^{3} + 4 q^{4} - 6 q^{6} - 6 q^{7} - 4 q^{9} + 12 q^{11} + 8 q^{12} - 6 q^{13} - 4 q^{14} + 2 q^{17} + 12 q^{19} - 4 q^{23} - 12 q^{24} - 4 q^{26} - 8 q^{27} + 12 q^{28} - 6 q^{29} - 12 q^{32} + 12 q^{33} + 4 q^{36} + 12 q^{37} + 16 q^{38} - 30 q^{41} - 2 q^{42} - 6 q^{43} + 36 q^{46} - 8 q^{49} + 4 q^{51} + 20 q^{52} + 32 q^{53} + 6 q^{54} + 4 q^{56} - 12 q^{58} - 30 q^{59} + 30 q^{62} + 6 q^{63} + 32 q^{64} - 30 q^{67} - 16 q^{68} + 4 q^{69} + 18 q^{71} - 12 q^{72} + 12 q^{74} + 8 q^{77} - 14 q^{78} + 56 q^{79} - 4 q^{81} + 24 q^{82} + 12 q^{84} + 6 q^{87} - 8 q^{88} - 18 q^{89} - 16 q^{91} - 40 q^{92} + 24 q^{93} - 16 q^{94} + 6 q^{97} + 12 q^{98}+O(q^{100}) \) 8 * q - 6 * q^2 + 4 * q^3 + 4 * q^4 - 6 * q^6 - 6 * q^7 - 4 * q^9 + 12 * q^11 + 8 * q^12 - 6 * q^13 - 4 * q^14 + 2 * q^17 + 12 * q^19 - 4 * q^23 - 12 * q^24 - 4 * q^26 - 8 * q^27 + 12 * q^28 - 6 * q^29 - 12 * q^32 + 12 * q^33 + 4 * q^36 + 12 * q^37 + 16 * q^38 - 30 * q^41 - 2 * q^42 - 6 * q^43 + 36 * q^46 - 8 * q^49 + 4 * q^51 + 20 * q^52 + 32 * q^53 + 6 * q^54 + 4 * q^56 - 12 * q^58 - 30 * q^59 + 30 * q^62 + 6 * q^63 + 32 * q^64 - 30 * q^67 - 16 * q^68 + 4 * q^69 + 18 * q^71 - 12 * q^72 + 12 * q^74 + 8 * q^77 - 14 * q^78 + 56 * q^79 - 4 * q^81 + 24 * q^82 + 12 * q^84 + 6 * q^87 - 8 * q^88 - 18 * q^89 - 16 * q^91 - 40 * q^92 + 24 * q^93 - 16 * q^94 + 6 * q^97 + 12 * q^98

Introduction

L-functions

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