LMFDB - Embedded newform 975.2.w.j.199.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(49,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,2,0,-4,0,-6,-6,0,4,0,12,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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			199.3
Root			$0.500000 + 1.19293i$ of defining polynomial
Character	$\chi$	$=$	975.199
Dual form			975.2.w.j.49.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

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

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 $

$2$	0.663454	−	1.14914i	0.469133	−	0.812562i	−0.530244	−	0.847845i	$-0.677900\pi$
$2$	0.663454	−	1.14914i	0.469133	−	0.812562i	0.999377	+	0.0352826i	$0.0112331\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.119657	+	0.207252i	0.0598284	+	0.103626i
$5$		0			0
$5$		0			0
$6$	1.14914	−	0.663454i	0.469133	−	0.270854i
$7$	0.529480	+	0.917086i	0.200125	+	0.346626i	0.948568	−	0.316572i	$-0.102532\pi$
$7$	0.529480	+	0.917086i	0.200125	+	0.346626i	−0.748444	+	0.663198i	$0.769199\pi$
$8$	2.97136			1.05054
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	2.15877	+	1.24637i	0.650895	+	0.375794i	0.788799	−	0.614651i	$-0.210703\pi$
$11$	2.15877	+	1.24637i	0.650895	+	0.375794i	−0.137904	+	0.990446i	$0.544037\pi$
$12$			0.239314i			0.0690839i
$13$	2.40277	−	2.68825i	0.666408	−	0.745587i
$13$	2.40277	−	2.68825i	0.666408	−	0.745587i
$14$	1.40514			0.375540
$15$		0			0
$16$	1.73205	−	3.00000i	0.433013	−	0.750000i
$17$	−4.28864	+	2.47605i	−1.04015	+	0.600529i	−0.919875	−	0.392212i	$-0.871710\pi$
$17$	−4.28864	+	2.47605i	−1.04015	+	0.600529i	−0.120272	+	0.992741i	$0.538377\pi$
$18$	1.32691			0.312755
$19$	−5.50552	+	3.17862i	−1.26305	+	0.729225i	−0.973664	−	0.227987i	$-0.926786\pi$
$19$	−5.50552	+	3.17862i	−1.26305	+	0.729225i	−0.289390	+	0.957211i	$0.593452\pi$
$20$		0			0
$21$			1.05896i			0.231084i
$22$	2.86450	−	1.65382i	0.610712	−	0.352595i
$23$	3.13950	+	1.81259i	0.654631	+	0.377951i	0.790228	−	0.612813i	$-0.209962\pi$
$23$	3.13950	+	1.81259i	0.654631	+	0.377951i	−0.135597	+	0.990764i	$0.543295\pi$
$24$	2.57328	+	1.48568i	0.525268	+	0.303264i
$25$		0			0
$26$	−1.49504	−	4.54464i	−0.293202	−	0.891278i
$27$			1.00000i			0.192450i
$28$	−0.126712	+	0.219471i	−0.0239463	+	0.0414761i
$29$	−0.117075	+	0.202779i	−0.0217402	+	0.0376551i	−0.876691	−	0.481054i	$-0.840254\pi$
$29$	−0.117075	+	0.202779i	−0.0217402	+	0.0376551i	0.854951	+	0.518709i	$0.173587\pi$
$30$		0			0
$31$			1.31755i			0.236638i	0.992976	+	0.118319i	$0.0377506\pi$
$31$			1.31755i			0.236638i	−0.992976	+	0.118319i	$0.962249\pi$
$32$	0.673091	+	1.16583i	0.118987	+	0.206091i
$33$	1.24637	+	2.15877i	0.216965	+	0.375794i
$34$			6.57097i			1.12691i
$35$		0			0
$36$	−0.119657	+	0.207252i	−0.0199428	+	0.0345420i
$37$	3.05896	−	5.29827i	0.502890	−	0.871031i	−0.497105	−	0.867691i	$-0.665603\pi$
$37$	3.05896	−	5.29827i	0.502890	−	0.871031i	0.999994	−	0.00334010i	$-0.00106319\pi$
$38$			8.43547i			1.36841i
$39$	3.42498	−	1.12671i	0.548436	−	0.180418i
$40$		0			0
$41$	−7.66877	−	4.42757i	−1.19766	−	0.691470i	−0.237628	−	0.971356i	$-0.576370\pi$
$41$	−7.66877	−	4.42757i	−1.19766	−	0.691470i	−0.960033	+	0.279886i	$0.909703\pi$
$42$	1.21689	+	0.702571i	0.187770	+	0.108409i
$43$	8.37413	−	4.83481i	1.27704	−	0.737301i	0.300740	−	0.953706i	$-0.402767\pi$
$43$	8.37413	−	4.83481i	1.27704	−	0.737301i	0.976304	+	0.216405i	$0.0694332\pi$
$44$			0.596546i			0.0899327i
$45$		0			0
$46$	4.16583	−	2.40514i	0.614218	−	0.354619i
$47$	5.70173			0.831682			0.415841	−	0.909437i	$-0.363487\pi$
$47$	5.70173			0.831682			0.415841	+	0.909437i	$0.363487\pi$
$48$	3.00000	−	1.73205i	0.433013	−	0.250000i
$49$	2.93930	−	5.09102i	0.419900	−	0.727289i
$50$		0			0
$51$	−4.95209			−0.693431
$52$	0.844653	+	0.176310i	0.117132	+	0.0244498i
$53$			4.98547i			0.684808i	0.939553	+	0.342404i	$0.111241\pi$
$53$			4.98547i			0.684808i	−0.939553	+	0.342404i	$0.888759\pi$
$54$	1.14914	+	0.663454i	0.156378	+	0.0902847i
$55$		0			0
$56$	1.57328	+	2.72500i	0.210238	+	0.364143i
$57$	−6.35723			−0.842036
$58$	0.155347	+	0.269069i	0.0203981	+	0.0353305i
$59$	−1.82049	+	1.05106i	−0.237008	+	0.136836i	−0.613801	−	0.789461i	$-0.710360\pi$
$59$	−1.82049	+	1.05106i	−0.237008	+	0.136836i	0.376793	+	0.926297i	$0.377027\pi$
$60$		0			0
$61$	−1.52690	−	2.64466i	−0.195499	−	0.338615i	0.751565	−	0.659659i	$-0.229299\pi$
$61$	−1.52690	−	2.64466i	−0.195499	−	0.338615i	−0.947064	+	0.321045i	$0.895966\pi$
$62$	1.51404	+	0.874132i	0.192284	+	0.111015i
$63$	−0.529480	+	0.917086i	−0.0667082	+	0.115542i
$64$	8.71446			1.08931
$65$		0			0
$66$	3.30763			0.407142
$67$	3.81727	−	6.61171i	0.466354	−	0.807749i	−0.532908	−	0.846173i	$-0.678901\pi$
$67$	3.81727	−	6.61171i	0.466354	−	0.807749i	0.999261	+	0.0384248i	$0.0122340\pi$
$68$	−1.02633	−	0.592551i	−0.124461	−	0.0718574i
$69$	1.81259	+	3.13950i	0.218210	+	0.377951i
$70$		0			0
$71$	7.08138	−	4.08844i	0.840406	−	0.485208i	−0.0169964	−	0.999856i	$-0.505410\pi$
$71$	7.08138	−	4.08844i	0.840406	−	0.485208i	0.857402	+	0.514647i	$0.172077\pi$
$72$	1.48568	+	2.57328i	0.175089	+	0.303264i
$73$	3.98716			0.466662			0.233331	−	0.972397i	$-0.425037\pi$
$73$	3.98716			0.466662			0.233331	+	0.972397i	$0.425037\pi$
$74$	−4.05896	−	7.03032i	−0.471844	−	0.817259i
$75$		0			0
$76$	−1.31755	−	0.760686i	−0.151133	−	0.0872567i
$77$			2.63971i			0.300823i
$78$	0.977575	−	4.68330i	0.110689	−	0.530279i
$79$	−15.8359			−1.78167			−0.890837	−	0.454324i	$-0.849881\pi$
$79$	−15.8359			−1.78167			−0.890837	+	0.454324i	$0.849881\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−10.1758	+	5.87498i	−1.12372	+	0.648783i
$83$	−15.8037			−1.73469			−0.867343	−	0.497710i	$-0.834174\pi$
$83$	−15.8037			−1.73469			−0.867343	+	0.497710i	$0.834174\pi$
$84$	−0.219471	+	0.126712i	−0.0239463	+	0.0138254i
$85$		0			0
$86$		−	12.8307i		−	1.38357i
$87$	−0.202779	+	0.117075i	−0.0217402	+	0.0125517i
$88$	6.41450	+	3.70342i	0.683788	+	0.394785i
$89$	−13.7224	−	7.92261i	−1.45457	−	0.839795i	−0.455832	−	0.890066i	$-0.650658\pi$
$89$	−13.7224	−	7.92261i	−1.45457	−	0.839795i	−0.998736	+	0.0502708i	$0.983992\pi$
$90$		0			0
$91$	3.73758	+	0.780169i	0.391804	+	0.0817839i
$92$			0.867556i			0.0904489i
$93$	−0.658774	+	1.14103i	−0.0683116	+	0.118319i
$94$	3.78284	−	6.55206i	0.390170	−	0.675794i
$95$		0			0
$96$			1.34618i			0.137394i
$97$	5.02795	+	8.70866i	0.510511	+	0.884231i	0.999926	+	0.0121798i	$0.00387705\pi$
$97$	5.02795	+	8.70866i	0.510511	+	0.884231i	−0.489415	+	0.872051i	$0.662790\pi$
$98$	−3.90019	−	6.75532i	−0.393978	−	0.682390i
$99$			2.49274i			0.250530i
$100$		0			0
$101$	−5.70572	+	9.88260i	−0.567741	+	0.983355i	0.429048	+	0.903281i	$0.358849\pi$
$101$	−5.70572	+	9.88260i	−0.567741	+	0.983355i	−0.996789	+	0.0800739i	$0.974484\pi$
$102$	−3.28549	+	5.69063i	−0.325312	+	0.563456i
$103$			2.89788i			0.285537i	0.989756	+	0.142768i	$0.0456004\pi$
$103$			2.89788i			0.285537i	−0.989756	+	0.142768i	$0.954400\pi$
$104$	7.13950	−	7.98778i	0.700086	−	0.783266i
$105$		0			0
$106$	5.72899	+	3.30763i	0.556449	+	0.321266i
$107$	13.0884	+	7.55659i	1.26530	+	0.730523i	0.974095	−	0.226137i	$-0.0726098\pi$
$107$	13.0884	+	7.55659i	1.26530	+	0.730523i	0.291207	+	0.956660i	$0.405943\pi$
$108$	−0.207252	+	0.119657i	−0.0199428	+	0.0115140i
$109$		−	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
$112$	3.66834			0.346626
$113$	−7.29311	+	4.21068i	−0.686078	+	0.396107i	−0.802141	−	0.597135i	$-0.796306\pi$
$113$	−7.29311	+	4.21068i	−0.686078	+	0.396107i	0.116063	+	0.993242i	$0.462973\pi$
$114$	−4.21773	+	7.30533i	−0.395027	+	0.684207i
$115$		0			0
$116$	−0.0560351			−0.00520273
$117$	3.52948	+	0.736731i	0.326301	+	0.0681108i
$118$			2.78932i			0.256778i
$119$	−4.54149	−	2.62203i	−0.416318	−	0.240361i
$120$		0			0
$121$	−2.39313	−	4.14502i	−0.217557	−	0.376820i
$122$	−4.05211			−0.366860
$123$	−4.42757	−	7.66877i	−0.399220	−	0.691470i
$124$	−0.273064	+	0.157654i	−0.0245219	+	0.0141577i
$125$		0			0
$126$	0.702571	+	1.21689i	0.0625900	+	0.108409i
$127$	−9.86155	−	5.69357i	−0.875071	−	0.505223i	−0.00604114	−	0.999982i	$-0.501923\pi$
$127$	−9.86155	−	5.69357i	−0.875071	−	0.505223i	−0.869030	+	0.494759i	$0.835256\pi$
$128$	4.43547	−	7.68245i	0.392044	−	0.679039i
$129$	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	$0.667459\pi$
$132$	−0.298273	+	0.516624i	−0.0259613	+	0.0449664i
$133$	−5.83013	−	3.36603i	−0.505536	−	0.291871i
$134$	−5.06517	−	8.77313i	−0.437564	−	0.757883i
$135$		0			0
$136$	−12.7431	+	7.35723i	−1.09271	+	0.630877i
$137$	−8.60849	−	14.9103i	−0.735473	−	1.27388i	−0.954516	−	0.298161i	$-0.903627\pi$
$137$	−8.60849	−	14.9103i	−0.735473	−	1.27388i	0.219043	−	0.975715i	$-0.429707\pi$
$138$	4.81028			0.409479
$139$	1.20342	+	2.08438i	0.102072	+	0.176795i	0.912538	−	0.408991i	$-0.134119\pi$
$139$	1.20342	+	2.08438i	0.102072	+	0.176795i	−0.810466	+	0.585786i	$0.800786\pi$
$140$		0			0
$141$	4.93784	+	2.85086i	0.415841	+	0.240086i
$142$		−	10.8500i		−	0.910509i
$143$	8.53759	−	2.80860i	0.713949	−	0.234867i
$144$	3.46410			0.288675
$145$		0			0
$146$	2.64530	−	4.58179i	0.218927	−	0.379192i
$147$	5.09102	−	2.93930i	0.419900	−	0.242430i
$148$	1.46410			0.120348
$149$	2.92924	−	1.69120i	0.239972	−	0.138548i	−0.375192	−	0.926947i	$-0.622423\pi$
$149$	2.92924	−	1.69120i	0.239972	−	0.138548i	0.615164	+	0.788399i	$0.289090\pi$
$150$		0			0
$151$		−	1.46758i		−	0.119430i	−0.998215	−	0.0597149i	$-0.980981\pi$
$151$		−	1.46758i		−	0.119430i	0.998215	−	0.0597149i	$-0.0190192\pi$
$152$	−16.3589	+	9.44483i	−1.32688	+	0.766077i
$153$	−4.28864	−	2.47605i	−0.346716	−	0.200176i
$154$	3.03338	+	1.75133i	0.244437	+	0.141126i
$155$		0			0
$156$	0.643336	+	0.575015i	0.0515081	+	0.0460381i
$157$		−	20.7833i		−	1.65869i	−0.558736	−	0.829345i	$-0.688714\pi$
$157$		−	20.7833i		−	1.65869i	0.558736	−	0.829345i	$-0.311286\pi$
$158$	−10.5064	+	18.1976i	−0.835842	+	1.44772i
$159$	−2.49274	+	4.31755i	−0.197687	+	0.342404i
$160$		0			0
$161$			3.83892i			0.302549i
$162$	0.663454	+	1.14914i	0.0521259	+	0.0902847i
$163$	−8.36365	−	14.4863i	−0.655092	−	1.13465i	−0.981871	−	0.189551i	$-0.939297\pi$
$163$	−8.36365	−	14.4863i	−0.655092	−	1.13465i	0.326779	−	0.945101i	$-0.394037\pi$
$164$		−	2.11915i		−	0.165478i
$165$		0			0
$166$	−10.4851	+	18.1607i	−0.813799	+	1.40954i
$167$	3.20551	−	5.55211i	0.248050	−	0.429635i	−0.714935	−	0.699191i	$-0.753544\pi$
$167$	3.20551	−	5.55211i	0.248050	−	0.429635i	0.962985	+	0.269556i	$0.0868769\pi$
$168$			3.14655i			0.242762i
$169$	−1.45341	−	12.9185i	−0.111801	−	0.993731i
$170$		0			0
$171$	−5.50552	−	3.17862i	−0.421018	−	0.243075i
$172$	2.00404	+	1.15704i	0.152807	+	0.0882231i
$173$	−19.4900	+	11.2525i	−1.48179	+	0.855514i	−0.999787	−	0.0206534i	$-0.993425\pi$
$173$	−19.4900	+	11.2525i	−1.48179	+	0.855514i	−0.482007	+	0.876167i	$0.660092\pi$
$174$			0.310694i			0.0235537i
$175$		0			0
$176$	7.47821	−	4.31755i	0.563691	−	0.325447i
$177$	−2.10212			−0.158005
$178$	−18.2083	+	10.5126i	−1.36477	+	0.787951i
$179$	−2.37797	+	4.11876i	−0.177738	+	0.307851i	−0.941105	−	0.338114i	$-0.890211\pi$
$179$	−2.37797	+	4.11876i	−0.177738	+	0.307851i	0.763368	+	0.645964i	$0.223545\pi$
$180$		0			0
$181$	11.4606			0.851862			0.425931	−	0.904756i	$-0.359947\pi$
$181$	11.4606			0.851862			0.425931	+	0.904756i	$0.359947\pi$
$182$	3.37623	−	3.77738i	0.250263	−	0.279998i
$183$		−	3.05379i		−	0.225743i
$184$	9.32860	+	5.38587i	0.687713	+	0.397051i
$185$		0			0
$186$	0.874132	+	1.51404i	0.0640945	+	0.111015i
$187$	−12.3443			−0.902702
$188$	0.682251	+	1.18169i	0.0497582	+	0.0861838i
$189$	−0.917086	+	0.529480i	−0.0667082	+	0.0385140i
$190$		0			0
$191$	2.90103	+	5.02473i	0.209911	+	0.363577i	0.951686	−	0.307072i	$-0.0993492\pi$
$191$	2.90103	+	5.02473i	0.209911	+	0.363577i	−0.741775	+	0.670649i	$0.766016\pi$
$192$	7.54695	+	4.35723i	0.544654	+	0.314456i
$193$	1.21668	−	2.10735i	0.0875786	−	0.151691i	−0.818908	−	0.573924i	$-0.805420\pi$
$193$	1.21668	−	2.10735i	0.0875786	−	0.151691i	0.906487	+	0.422234i	$0.138754\pi$
$194$	13.3433			0.957990
$195$		0			0
$196$	1.40683			0.100488
$197$	6.69120	−	11.5895i	0.476728	−	0.825717i	−0.522916	−	0.852384i	$-0.675156\pi$
$197$	6.69120	−	11.5895i	0.476728	−	0.825717i	0.999644	+	0.0266669i	$0.00848935\pi$
$198$	2.86450	+	1.65382i	0.203571	+	0.117532i
$199$	8.92555	+	15.4595i	0.632716	+	1.09590i	0.986994	+	0.160756i	$0.0513931\pi$
$199$	8.92555	+	15.4595i	0.632716	+	1.09590i	−0.354279	+	0.935140i	$0.615274\pi$
$200$		0			0
$201$	6.61171	−	3.81727i	0.466354	−	0.269250i
$202$	7.57097	+	13.1133i	0.532692	+	0.922649i
$203$	−0.247954			−0.0174030
$204$	−0.592551	−	1.02633i	−0.0414869	−	0.0718574i
$205$		0			0
$206$	3.33006	+	1.92261i	0.232016	+	0.133955i
$207$			3.62518i			0.251968i
$208$	−3.90304	−	11.8645i	−0.270627	−	0.822655i
$209$	−15.8469			−1.09615
$210$		0			0
$211$	−4.99443	+	8.65060i	−0.343830	+	0.595532i	−0.985141	−	0.171750i	$-0.945058\pi$
$211$	−4.99443	+	8.65060i	−0.343830	+	0.595532i	0.641310	+	0.767282i	$0.278391\pi$
$212$	−1.03325	+	0.596546i	−0.0709638	+	0.0409710i
$213$	8.17688			0.560270
$214$	17.3671	−	10.0269i	1.18719	−	0.685425i
$215$		0			0
$216$			2.97136i			0.202176i
$217$	−1.20830	+	0.697615i	−0.0820250	+	0.0473572i
$218$	−0.443415	−	0.256006i	−0.0300318	−	0.0173389i
$219$	3.45298	+	1.99358i	0.233331	+	0.134714i
$220$		0			0
$221$	−3.64836	+	17.4783i	−0.245415	+	1.17572i
$222$		−	8.11792i		−	0.544839i
$223$	10.1179	−	17.5247i	0.677546	−	1.17354i	−0.298172	−	0.954512i	$-0.596377\pi$
$223$	10.1179	−	17.5247i	0.677546	−	1.17354i	0.975718	−	0.219032i	$-0.0702898\pi$
$224$	−0.712776	+	1.23457i	−0.0476244	+	0.0824878i
$225$		0			0
$226$			11.1744i			0.743308i
$227$	−1.59396	−	2.76083i	−0.105795	−	0.183242i	0.808268	−	0.588815i	$-0.200405\pi$
$227$	−1.59396	−	2.76083i	−0.105795	−	0.183242i	−0.914063	+	0.405573i	$0.867072\pi$
$228$	−0.760686	−	1.31755i	−0.0503777	−	0.0872567i
$229$			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
$232$	−0.347871	+	0.602531i	−0.0228389	+	0.0395581i
$233$		−	12.8534i		−	0.842057i	−0.907047	−	0.421029i	$-0.861669\pi$
$233$		−	12.8534i		−	0.842057i	0.907047	−	0.421029i	$-0.138331\pi$
$234$	3.18825	−	3.56707i	0.208423	−	0.233186i
$235$		0			0
$236$	−0.435668	−	0.251533i	−0.0283596	−	0.0163734i
$237$	−13.7143	−	7.91793i	−0.890837	−	0.514325i
$238$	−6.02614	+	3.47920i	−0.390617	+	0.225523i
$239$			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	−0.319338	−	0.947641i	$-0.603461\pi$
$241$	5.30421	−	3.06239i	0.341674	−	0.197266i	0.661012	+	0.750375i	$0.270127\pi$
$242$	−6.35093			−0.408253
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	0.365407	−	0.632904i	0.0233928	−	0.0405175i
$245$		0			0
$246$	−11.7500			−0.749150
$247$	−4.68357	+	22.4377i	−0.298009	+	1.42768i
$248$			3.91491i			0.248597i
$249$	−13.6864	−	7.90187i	−0.867343	−	0.500761i
$250$		0			0
$251$	−3.87671	−	6.71467i	−0.244696	−	0.423826i	0.717350	−	0.696713i	$-0.245355\pi$
$251$	−3.87671	−	6.71467i	−0.244696	−	0.423826i	−0.962046	+	0.272887i	$0.912022\pi$
$252$	−0.253423			−0.0159642
$253$	4.51831	+	7.82595i	0.284064	+	0.492013i
$254$	−13.0854	+	7.55485i	−0.821050	+	0.474033i
$255$		0			0
$256$	2.82901	+	4.89998i	0.176813	+	0.306249i
$257$	6.96403	+	4.02069i	0.434404	+	0.250804i	0.701221	−	0.712944i	$-0.252639\pi$
$257$	6.96403	+	4.02069i	0.434404	+	0.250804i	−0.266817	+	0.963747i	$0.585972\pi$
$258$	6.41535	−	11.1117i	0.399402	−	0.691785i
$259$	6.47863			0.402562
$260$		0			0
$261$	−0.234149			−0.0144935
$262$	−7.62630	+	13.2091i	−0.471154	+	0.816064i
$263$	−14.7497	−	8.51573i	−0.909504	−	0.525102i	−0.0292325	−	0.999573i	$-0.509306\pi$
$263$	−14.7497	−	8.51573i	−0.909504	−	0.525102i	−0.880272	+	0.474470i	$0.842640\pi$
$264$	3.70342	+	6.41450i	0.227929	+	0.394785i
$265$		0			0
$266$	−7.73605	+	4.46641i	−0.474327	+	0.273853i
$267$	−7.92261	−	13.7224i	−0.484856	−	0.839795i
$268$	1.82705			0.111605
$269$	−4.87587	−	8.44526i	−0.297287	−	0.514916i	0.678227	−	0.734852i	$-0.262749\pi$
$269$	−4.87587	−	8.44526i	−0.297287	−	0.514916i	−0.975514	+	0.219936i	$0.929415\pi$
$270$		0			0
$271$	−18.4341	−	10.6429i	−1.11979	−	0.646512i	−0.178444	−	0.983950i	$-0.557106\pi$
$271$	−18.4341	−	10.6429i	−1.11979	−	0.646512i	−0.941348	+	0.337438i	$0.890440\pi$
$272$			17.1545i			1.04015i
$273$	2.84675	+	2.54443i	0.172293	+	0.153996i
$274$	−22.8454			−1.38014
$275$		0			0
$276$	−0.433778	+	0.751325i	−0.0261104	+	0.0452245i
$277$	−22.2263	+	12.8324i	−1.33545	+	0.771023i	−0.986129	−	0.165979i	$-0.946921\pi$
$277$	−22.2263	+	12.8324i	−1.33545	+	0.771023i	−0.349322	+	0.937003i	$0.613588\pi$
$278$	3.19364			0.191542
$279$	−1.14103	+	0.658774i	−0.0683116	+	0.0394397i
$280$		0			0
$281$			16.8364i			1.00438i	0.864758	+	0.502188i	$0.167471\pi$
$281$			16.8364i			1.00438i	−0.864758	+	0.502188i	$0.832529\pi$
$282$	6.55206	−	3.78284i	0.390170	−	0.225265i
$283$	15.6573	+	9.03975i	0.930731	+	0.537358i	0.887043	−	0.461688i	$-0.152756\pi$
$283$	15.6573	+	9.03975i	0.930731	+	0.537358i	0.0436880	+	0.999045i	$0.486089\pi$
$284$	1.69467	+	0.978419i	0.100560	+	0.0580585i
$285$		0			0
$286$	2.43684	−	11.6742i	0.144093	−	0.690312i
$287$		−	9.37723i		−	0.553520i
$288$	−0.673091	+	1.16583i	−0.0396623	+	0.0686971i
$289$	3.76160	−	6.51528i	0.221270	−	0.383252i
$290$		0			0
$291$			10.0559i			0.589487i
$292$	0.477091	+	0.826346i	0.0279197	+	0.0483583i
$293$	7.27222	+	12.5959i	0.424848	+	0.735858i	0.996406	−	0.0847036i	$-0.0269943\pi$
$293$	7.27222	+	12.5959i	0.424848	+	0.735858i	−0.571559	+	0.820561i	$0.693661\pi$
$294$		−	7.80037i		−	0.454927i
$295$		0			0
$296$	9.08928	−	15.7431i	0.528304	−	0.915049i
$297$	−1.24637	+	2.15877i	−0.0723216	+	0.125265i
$298$		−	4.48812i		−	0.259990i
$299$	12.4162	−	4.08453i	0.718047	−	0.236215i
$300$		0			0
$301$	8.86787	+	5.11986i	0.511135	+	0.295104i
$302$	−1.68645	−	0.973671i	−0.0970441	−	0.0560285i
$303$	−9.88260	+	5.70572i	−0.567741	+	0.327785i
$304$			22.0221i			1.26305i
$305$		0			0
$306$	−5.69063	+	3.28549i	−0.325312	+	0.187819i
$307$	34.1062			1.94654			0.973272	−	0.229654i	$-0.0737595\pi$
$307$	34.1062			1.94654			0.973272	+	0.229654i	$0.0737595\pi$
$308$	−0.547084	+	0.315859i	−0.0311730	+	0.0179977i
$309$	−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	$0.542267\pi$
$312$	10.1769	−	3.34787i	0.576152	−	0.189536i
$313$			5.04485i			0.285152i	0.989784	+	0.142576i	$0.0455385\pi$
$313$			5.04485i			0.285152i	−0.989784	+	0.142576i	$0.954462\pi$
$314$	−23.8829	−	13.7888i	−1.34779	−	0.778147i
$315$		0			0
$316$	−1.89487	−	3.28201i	−0.106595	−	0.184627i
$317$	−14.6107			−0.820616			−0.410308	−	0.911947i	$-0.634579\pi$
$317$	−14.6107			−0.820616			−0.410308	+	0.911947i	$0.634579\pi$
$318$	3.30763	+	5.72899i	0.185483	+	0.321266i
$319$	−0.505475	+	0.291836i	−0.0283012	+	0.0163397i
$320$		0			0
$321$	7.55659	+	13.0884i	0.421767	+	0.730523i
$322$	4.41144	+	2.54695i	0.245840	+	0.141936i
$323$	15.7408	−	27.2639i	0.875841	−	1.51700i
$324$	−0.239314			−0.0132952
$325$		0			0
$326$	−22.1956			−1.22930
$327$	0.192934	−	0.334171i	0.0106693	−	0.0184797i
$328$	−22.7867	−	13.1559i	−1.25819	−	0.726414i
$329$	3.01895	+	5.22897i	0.166440	+	0.288283i
$330$		0			0
$331$	13.8034	−	7.96942i	0.758706	−	0.438039i	−0.0701252	−	0.997538i	$-0.522340\pi$
$331$	13.8034	−	7.96942i	0.758706	−	0.438039i	0.828831	+	0.559499i	$0.189007\pi$
$332$	−1.89103	−	3.27535i	−0.103784	−	0.179758i
$333$	6.11792			0.335260
$334$	−4.25342	−	7.36715i	−0.232737	−	0.403112i
$335$		0			0
$336$	3.17688	+	1.83417i	0.173313	+	0.100062i
$337$			19.8261i			1.08000i	0.841666	+	0.539998i	$0.181575\pi$
$337$			19.8261i			1.08000i	−0.841666	+	0.539998i	$0.818425\pi$
$338$	−15.8094	−	6.90066i	−0.859917	−	0.375347i
$339$	−8.42136			−0.457385
$340$		0			0
$341$	−1.64215	+	2.84429i	−0.0889274	+	0.154027i
$342$	−7.30533	+	4.21773i	−0.395027	+	0.228069i
$343$	13.6379			0.736378
$344$	24.8826	−	14.3660i	1.34158	−	0.774561i
$345$		0			0
$346$			29.8622i			1.60540i
$347$	8.97484	−	5.18163i	0.481795	−	0.278164i	−0.239369	−	0.970929i	$-0.576941\pi$
$347$	8.97484	−	5.18163i	0.481795	−	0.278164i	0.721164	+	0.692764i	$0.243607\pi$
$348$	−0.0485278	−	0.0280175i	−0.00260136	−	0.00150190i
$349$	27.5828	+	15.9249i	1.47647	+	0.852442i	0.999647	−	0.0265555i	$-0.00845388\pi$
$349$	27.5828	+	15.9249i	1.47647	+	0.852442i	0.476826	+	0.878998i	$0.341787\pi$
$350$		0			0
$351$	2.68825	+	2.40277i	0.143488	+	0.128250i
$352$			3.35568i			0.178858i
$353$	−0.578026	+	1.00117i	−0.0307652	+	0.0532869i	−0.880998	−	0.473120i	$-0.843128\pi$
$353$	−0.578026	+	1.00117i	−0.0307652	+	0.0532869i	0.850233	+	0.526407i	$0.176461\pi$
$354$	−1.39466	+	2.41562i	−0.0741254	+	0.128389i
$355$		0			0
$356$		−	3.79198i		−	0.200974i
$357$	−2.62203	−	4.54149i	−0.138773	−	0.240361i
$358$	3.15535	+	5.46522i	0.166765	+	0.288846i
$359$			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
$362$	7.60360	−	13.1698i	0.399636	−	0.692191i
$363$		−	4.78626i		−	0.251214i
$364$	0.285535	+	0.867971i	0.0149661	+	0.0454941i
$365$		0			0
$366$	−3.50923	−	2.02605i	−0.183430	−	0.105903i
$367$	−14.5844	−	8.42030i	−0.761299	−	0.439536i	0.0684628	−	0.997654i	$-0.478191\pi$
$367$	−14.5844	−	8.42030i	−0.761299	−	0.439536i	−0.829762	+	0.558117i	$0.811524\pi$
$368$	10.8755	−	6.27900i	0.566927	−	0.327315i
$369$		−	8.85513i		−	0.460980i
$370$		0			0
$371$	−4.57211	+	2.63971i	−0.237372	+	0.137047i
$372$	−0.315307			−0.0163479
$373$	−21.2184	+	12.2504i	−1.09865	+	0.634303i	−0.935865	−	0.352359i	$-0.885380\pi$
$373$	−21.2184	+	12.2504i	−1.09865	+	0.634303i	−0.162781	+	0.986662i	$0.552046\pi$
$374$	−8.18985	+	14.1852i	−0.423487	+	0.733501i
$375$		0			0
$376$	16.9419			0.873712
$377$	0.263819	+	0.801957i	0.0135873	+	0.0413029i
$378$			1.40514i			0.0722727i
$379$	−28.6376	−	16.5339i	−1.47101	−	0.849290i	−0.471543	−	0.881843i	$-0.656303\pi$
$379$	−28.6376	−	16.5339i	−1.47101	−	0.849290i	−0.999470	+	0.0325537i	$0.989636\pi$
$380$		0			0
$381$	−5.69357	−	9.86155i	−0.291690	−	0.505223i
$382$	7.69880			0.393905
$383$	0.500068	+	0.866143i	0.0255523	+	0.0442578i	0.878519	−	0.477708i	$-0.158532\pi$
$383$	0.500068	+	0.866143i	0.0255523	+	0.0442578i	−0.852966	+	0.521966i	$0.825199\pi$
$384$	7.68245	−	4.43547i	0.392044	−	0.226346i
$385$		0			0
$386$	−1.61442	−	2.79626i	−0.0821720	−	0.142326i
$387$	8.37413	+	4.83481i	0.425681	+	0.245767i
$388$	−1.20326	+	2.08410i	−0.0610861	+	0.105804i
$389$	1.26193			0.0639823			0.0319912	−	0.999488i	$-0.489815\pi$
$389$	1.26193			0.0639823			0.0319912	+	0.999488i	$0.489815\pi$
$390$		0			0
$391$	−17.9522			−0.907883
$392$	8.73374	−	15.1273i	0.441120	−	0.764043i
$393$	−9.95482	−	5.74742i	−0.502154	−	0.289919i
$394$	−8.87861	−	15.3782i	−0.447298	−	0.774742i
$395$		0			0
$396$	−0.516624	+	0.298273i	−0.0259613	+	0.0149888i
$397$	−5.57796	−	9.66131i	−0.279950	−	0.484887i	0.691422	−	0.722451i	$-0.256984\pi$
$397$	−5.57796	−	9.66131i	−0.279950	−	0.484887i	−0.971372	+	0.237564i	$0.923651\pi$
$398$	23.6868			1.18731
$399$	−3.36603	−	5.83013i	−0.168512	−	0.291871i
$400$		0			0
$401$	28.8148	+	16.6362i	1.43894	+	0.830774i	0.997776	−	0.0666518i	$-0.0212317\pi$
$401$	28.8148	+	16.6362i	1.43894	+	0.830774i	0.441166	+	0.897426i	$0.354565\pi$
$402$		−	10.1303i		−	0.505255i
$403$	3.54190	+	3.16576i	0.176435	+	0.157698i
$404$	−2.73091			−0.135868
$405$		0			0
$406$	−0.164506	+	0.284933i	−0.00816432	+	0.0141410i
$407$	13.2072	−	7.62518i	0.654657	−	0.377966i
$408$	−14.7145			−0.728475
$409$	−2.09367	+	1.20878i	−0.103525	+	0.0597704i	−0.550869	−	0.834592i	$-0.685704\pi$
$409$	−2.09367	+	1.20878i	−0.103525	+	0.0597704i	0.447343	+	0.894362i	$0.352370\pi$
$410$		0			0
$411$		−	17.2170i		−	0.849251i
$412$	−0.600590	+	0.346751i	−0.0295890	+	0.0170832i
$413$	−1.92782	−	1.11303i	−0.0948621	−	0.0547686i
$414$	4.16583	+	2.40514i	0.204739	+	0.118206i
$415$		0			0
$416$	4.75133	+	0.991775i	0.232953	+	0.0486258i
$417$			2.40683i			0.117863i
$418$	−10.5137	+	18.2103i	−0.514242	+	0.890693i
$419$	13.3459	−	23.1157i	0.651988	−	1.12928i	−0.330652	−	0.943753i	$-0.607269\pi$
$419$	13.3459	−	23.1157i	0.651988	−	1.12928i	0.982640	−	0.185523i	$-0.0593980\pi$
$420$		0			0
$421$		−	40.7370i		−	1.98540i	−0.120614	−	0.992699i	$-0.538486\pi$
$421$		−	40.7370i		−	1.98540i	0.120614	−	0.992699i	$-0.461514\pi$
$422$	6.62715	+	11.4786i	0.322604	+	0.558767i
$423$	2.85086	+	4.93784i	0.138614	+	0.240086i
$424$			14.8137i			0.719415i
$425$		0			0
$426$	5.42498	−	9.39635i	0.262841	−	0.455255i
$427$	1.61692	−	2.80059i	0.0782484	−	0.135530i
$428$			3.61679i			0.174824i
$429$	8.79807	+	1.83648i	0.424775	+	0.0886660i
$430$		0			0
$431$	−6.21354	−	3.58739i	−0.299296	−	0.172798i	0.342831	−	0.939397i	$-0.388614\pi$
$431$	−6.21354	−	3.58739i	−0.299296	−	0.172798i	−0.642126	+	0.766599i	$0.721948\pi$
$432$	3.00000	+	1.73205i	0.144338	+	0.0833333i
$433$	−24.8845	+	14.3671i	−1.19587	+	0.690438i	−0.959633	−	0.281257i	$-0.909249\pi$
$433$	−24.8845	+	14.3671i	−1.19587	+	0.690438i	−0.236241	+	0.971695i	$0.575915\pi$
$434$			1.85134i			0.0888672i
$435$		0			0
$436$	0.0799718	−	0.0461717i	0.00382995	−	0.00221123i
$437$	−23.0461			−1.10245
$438$	4.58179	−	2.64530i	0.218927	−	0.126397i
$439$	19.5845	−	33.9213i	0.934716	−	1.61898i	0.159578	−	0.987185i	$-0.448987\pi$
$439$	19.5845	−	33.9213i	0.934716	−	1.61898i	0.775139	−	0.631791i	$-0.217680\pi$
$440$		0			0
$441$	5.87861			0.279934
$442$	17.6644	+	15.7885i	0.840211	+	0.750983i
$443$			12.5223i			0.594954i	0.954729	+	0.297477i	$0.0961452\pi$
$443$			12.5223i			0.594954i	−0.954729	+	0.297477i	$0.903855\pi$
$444$	1.26795	+	0.732051i	0.0601742	+	0.0347416i
$445$		0			0
$446$	−13.4256	−	23.2537i	−0.635718	−	1.10110i
$447$	3.38239			0.159982
$448$	4.61413	+	7.99191i	0.217997	+	0.377582i
$449$	9.48926	−	5.47863i	0.447826	−	0.258552i	−0.259086	−	0.965854i	$-0.583421\pi$
$449$	9.48926	−	5.47863i	0.447826	−	0.258552i	0.706912	+	0.707302i	$0.250088\pi$
$450$		0			0
$451$	−11.0368	−	19.1162i	−0.519701	−	0.900148i
$452$	−1.74534	−	1.00767i	−0.0820939	−	0.0473969i
$453$	0.733789	−	1.27096i	0.0344764	−	0.0597149i
$454$	−4.23009			−0.198528
$455$		0			0
$456$	−18.8897			−0.884589
$457$	8.29242	−	14.3629i	0.387903	−	0.671868i	−0.604264	−	0.796784i	$-0.706533\pi$
$457$	8.29242	−	14.3629i	0.387903	−	0.671868i	0.992167	+	0.124916i	$0.0398662\pi$
$458$	31.4244	+	18.1429i	1.46836	+	0.847761i
$459$	−2.47605	−	4.28864i	−0.115572	−	0.200176i
$460$		0			0
$461$	19.8668	−	11.4701i	0.925290	−	0.534216i	0.0399710	−	0.999201i	$-0.487273\pi$
$461$	19.8668	−	11.4701i	0.925290	−	0.534216i	0.885319	+	0.464985i	$0.153940\pi$
$462$	1.75133	+	3.03338i	0.0814790	+	0.141126i
$463$	41.2096			1.91517			0.957587	−	0.288146i	$-0.0930388\pi$
$463$	41.2096			1.91517			0.957587	+	0.288146i	$0.0930388\pi$
$464$	0.405558	+	0.702447i	0.0188276	+	0.0326103i
$465$		0			0
$466$	−14.7704	−	8.52767i	−0.684224	−	0.395037i
$467$			31.1867i			1.44315i	0.692337	+	0.721574i	$0.256581\pi$
$467$			31.1867i			1.44315i	−0.692337	+	0.721574i	$0.743419\pi$
$468$	0.269638	+	0.819646i	0.0124640	+	0.0378881i
$469$	8.08467			0.373315
$470$		0			0
$471$	10.3917	−	17.9989i	0.478823	−	0.829345i
$472$	−5.40934	+	3.12308i	−0.248985	+	0.143752i
$473$	24.1038			1.10829
$474$	−18.1976	+	10.5064i	−0.835842	+	0.482574i
$475$		0			0
$476$		−	1.25498i		−	0.0575217i
$477$	−4.31755	+	2.49274i	−0.197687	+	0.114135i
$478$	11.9475	+	6.89788i	0.546465	+	0.315502i
$479$	4.46852	+	2.57990i	0.204172	+	0.117879i	0.598600	−	0.801048i	$-0.295724\pi$
$479$	4.46852	+	2.57990i	0.204172	+	0.117879i	−0.394428	+	0.918927i	$0.629057\pi$
$480$		0			0
$481$	−6.89313	−	20.9538i	−0.314300	−	0.955410i
$482$		−	8.12701i		−	0.370175i
$483$	−1.91946	+	3.32460i	−0.0873385	+	0.151275i
$484$	0.572709	−	0.991961i	0.0260322	−	0.0450891i
$485$		0			0
$486$			1.32691i			0.0601898i
$487$	−13.1780	−	22.8250i	−0.597152	−	1.03430i	−0.993239	−	0.116085i	$-0.962966\pi$
$487$	−13.1780	−	22.8250i	−0.597152	−	1.03430i	0.396087	−	0.918213i	$-0.370368\pi$
$488$	−4.53697	−	7.85826i	−0.205379	−	0.355727i
$489$		−	16.7273i		−	0.756435i
$490$		0			0
$491$	−9.36114	+	16.2140i	−0.422462	+	0.731726i	−0.996180	−	0.0873273i	$-0.972167\pi$
$491$	−9.36114	+	16.2140i	−0.422462	+	0.731726i	0.573717	+	0.819053i	$0.305501\pi$
$492$	1.05958	−	1.83524i	0.0477694	−	0.0827391i
$493$		−	1.15953i		−	0.0522225i
$494$	22.6767	+	20.2685i	1.02027	+	0.911921i
$495$		0			0
$496$	3.95264	+	2.28206i	0.177479	+	0.102467i
$497$	7.49890	+	4.32949i	0.336372	+	0.194204i
$498$	−18.1607	+	10.4851i	−0.813799	+	0.469847i
$499$			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
$502$	−10.2881			−0.459180
$503$	−12.1687	+	7.02558i	−0.542573	+	0.313255i	−0.746121	−	0.665810i	$-0.768086\pi$
$503$	−12.1687	+	7.02558i	−0.542573	+	0.313255i	0.203548	+	0.979065i	$0.434753\pi$
$504$	−1.57328	+	2.72500i	−0.0700793	+	0.121381i
$505$		0			0
$506$	11.9908			0.533055
$507$	5.20056	−	11.9145i	0.230965	−	0.529139i
$508$		−	2.72510i		−	0.120907i
$509$	−19.0832	−	11.0177i	−0.845848	−	0.488350i	0.0133999	−	0.999910i	$-0.495735\pi$
$509$	−19.0832	−	11.0177i	−0.845848	−	0.488350i	−0.859248	+	0.511560i	$0.829068\pi$
$510$		0			0
$511$	2.11112	+	3.65657i	0.0933905	+	0.161757i
$512$	25.2495			1.11588
$513$	−3.17862	−	5.50552i	−0.140339	−	0.243075i
$514$	9.24064	−	5.33508i	0.407587	−	0.235320i
$515$		0			0
$516$	1.15704	+	2.00404i	0.0509357	+	0.0882231i
$517$	12.3087	+	7.10645i	0.541338	+	0.312541i
$518$	4.29827	−	7.44483i	0.188855	−	0.327107i
$519$	−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	$0.275287\pi$
$522$	−0.155347	+	0.269069i	−0.00679936	+	0.0117768i
$523$	10.1044	+	5.83376i	0.441833	+	0.255092i	0.704375	−	0.709828i	$-0.251227\pi$
$523$	10.1044	+	5.83376i	0.441833	+	0.255092i	−0.262542	+	0.964921i	$0.584561\pi$
$524$	−1.37544	−	2.38233i	−0.0600862	−	0.104072i
$525$		0			0
$526$	−19.5715	+	11.2996i	−0.853357	+	0.492686i
$527$	−3.26231	−	5.65048i	−0.142108	−	0.246139i
$528$	8.63509			0.375794
$529$	−4.92903	−	8.53733i	−0.214306	−	0.371188i
$530$		0			0
$531$	−1.82049	−	1.05106i	−0.0790025	−	0.0456121i
$532$		−	1.61107i		−	0.0698488i
$533$	−30.3287	+	9.97718i	−1.31368	+	0.432160i
$534$	−21.0252			−0.909848
$535$		0			0
$536$	11.3425	−	19.6458i	0.489922	−	0.848569i
$537$	−4.11876	+	2.37797i	−0.177738	+	0.102617i
$538$	−12.9397			−0.557869
$539$	12.6906	−	7.32691i	0.546622	−	0.315592i
$540$		0			0
$541$			32.7583i			1.40839i	0.710006	+	0.704196i	$0.248692\pi$
$541$			32.7583i			1.40839i	−0.710006	+	0.704196i	$0.751308\pi$
$542$	−24.4603	+	14.1222i	−1.05066	+	0.606600i
$543$	9.92519	+	5.73031i	0.425931	+	0.245911i
$544$	−5.77329	−	3.33321i	−0.247528	−	0.142910i
$545$		0			0
$546$	4.81259	−	1.58319i	0.205960	−	0.0677543i
$547$		−	10.8406i		−	0.463511i	−0.972774	−	0.231755i	$-0.925553\pi$
$547$		−	10.8406i		−	0.463511i	0.972774	−	0.231755i	$-0.0744469\pi$
$548$	2.06013	−	3.56825i	0.0880044	−	0.152428i
$549$	1.52690	−	2.64466i	0.0651664	−	0.112872i
$550$		0			0
$551$		−	1.48854i		−	0.0634140i
$552$	5.38587	+	9.32860i	0.229238	+	0.397051i
$553$	−8.38477	−	14.5228i	−0.356557	−	0.617574i
$554$			34.0548i			1.44685i
$555$		0			0
$556$	−0.287994	+	0.498820i	−0.0122137	+	0.0211547i
$557$	10.3566	−	17.9382i	0.438824	−	0.760065i	−0.558775	−	0.829319i	$-0.688729\pi$
$557$	10.3566	−	17.9382i	0.438824	−	0.760065i	0.997599	+	0.0692540i	$0.0220619\pi$
$558$			1.74826i			0.0740100i
$559$	7.12391	−	34.1287i	0.301309	−	1.44349i
$560$		0			0
$561$	−10.6904	−	6.17213i	−0.451351	−	0.260588i
$562$	19.3473	+	11.1702i	0.816118	+	0.471186i
$563$	32.1969	−	18.5889i	1.35694	−	0.783428i	0.367727	−	0.929934i	$-0.380136\pi$
$563$	32.1969	−	18.5889i	1.35694	−	0.783428i	0.989210	+	0.146506i	$0.0468029\pi$
$564$			1.36450i			0.0574559i
$565$		0			0
$566$	20.7758	−	11.9949i	0.873273	−	0.504184i
$567$	−1.05896			−0.0444721
$568$	21.0414	−	12.1482i	0.882876	−	0.509729i
$569$	−23.0048	+	39.8455i	−0.964413	+	1.67041i	−0.253229	+	0.967406i	$0.581493\pi$
$569$	−23.0048	+	39.8455i	−0.964413	+	1.67041i	−0.711184	+	0.703006i	$0.751841\pi$
$570$		0			0
$571$	41.4861			1.73614			0.868070	−	0.496442i	$-0.165361\pi$
$571$	41.4861			1.73614			0.868070	+	0.496442i	$0.165361\pi$
$572$	1.60367	+	1.43336i	0.0670527	+	0.0599319i
$573$			5.80206i			0.242385i
$574$	−10.7757	−	6.22136i	−0.449770	−	0.259675i
$575$		0			0
$576$	4.35723	+	7.54695i	0.181551	+	0.314456i
$577$	−13.0556			−0.543513			−0.271756	−	0.962366i	$-0.587604\pi$
$577$	−13.0556			−0.543513			−0.271756	+	0.962366i	$0.587604\pi$
$578$	−4.99130	−	8.64518i	−0.207611	−	0.359592i
$579$	2.10735	−	1.21668i	0.0875786	−	0.0505635i
$580$		0			0
$581$	−8.36776	−	14.4934i	−0.347153	−	0.601287i
$582$	11.5556	+	6.67163i	0.478995	+	0.276548i
$583$	−6.21374	+	10.7625i	−0.257347	+	0.445738i
$584$	11.8473			0.490245
$585$		0			0
$586$	19.2991			0.797240
$587$	−8.47088	+	14.6720i	−0.349631	+	0.605578i	−0.986184	−	0.165655i	$-0.947026\pi$
$587$	−8.47088	+	14.6720i	−0.349631	+	0.605578i	0.636553	+	0.771233i	$0.280360\pi$
$588$	1.21835	+	0.703415i	0.0502439	+	0.0290084i
$589$	−4.18798	−	7.25379i	−0.172563	−	0.298887i
$590$		0			0
$591$	11.5895	−	6.69120i	0.476728	−	0.275239i
$592$	−10.5965	−	18.3538i	−0.435515	−	0.754335i
$593$	45.0621			1.85048			0.925239	−	0.379384i	$-0.123864\pi$
$593$	45.0621			1.85048			0.925239	+	0.379384i	$0.123864\pi$
$594$	1.65382	+	2.86450i	0.0678569	+	0.117532i
$595$		0			0
$596$	0.701007	+	0.404726i	0.0287143	+	0.0165782i
$597$			17.8511i			0.730597i
$598$	3.54389	−	16.9778i	0.144920	−	0.694274i
$599$	−24.1055			−0.984924			−0.492462	−	0.870334i	$-0.663903\pi$
$599$	−24.1055			−0.984924			−0.492462	+	0.870334i	$0.663903\pi$
$600$		0			0
$601$	−14.0845	+	24.3950i	−0.574518	+	0.995095i	0.421576	+	0.906793i	$0.361477\pi$
$601$	−14.0845	+	24.3950i	−0.574518	+	0.995095i	−0.996094	+	0.0883014i	$0.971856\pi$
$602$	11.7668	−	6.79359i	0.479581	−	0.276886i
$603$	7.63454			0.310903
$604$	0.304158	−	0.175606i	0.0123760	−	0.00714530i
$605$		0			0
$606$			15.1419i			0.615099i
$607$	4.97596	−	2.87287i	0.201968	−	0.116606i	−0.395605	−	0.918421i	$-0.629465\pi$
$607$	4.97596	−	2.87287i	0.201968	−	0.116606i	0.597573	+	0.801814i	$0.296132\pi$
$608$	−7.41144	−	4.27900i	−0.300574	−	0.173536i
$609$	−0.214735	−	0.123977i	−0.00870149	−	0.00502381i
$610$		0			0
$611$	13.6999	−	15.3277i	0.554240	−	0.620092i
$612$		−	1.18510i		−	0.0479049i
$613$	−6.55576	+	11.3549i	−0.264785	+	0.458620i	−0.967507	−	0.252844i	$-0.918634\pi$
$613$	−6.55576	+	11.3549i	−0.264785	+	0.458620i	0.702723	+	0.711464i	$0.251968\pi$
$614$	22.6279	−	39.1927i	0.913188	−	1.58169i
$615$		0			0
$616$			7.84353i			0.316025i
$617$	22.8202	+	39.5257i	0.918705	+	1.59124i	0.801384	+	0.598150i	$0.204097\pi$
$617$	22.8202	+	39.5257i	0.918705	+	1.59124i	0.117321	+	0.993094i	$0.462569\pi$
$618$	1.92261	+	3.33006i	0.0773387	+	0.133955i
$619$			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
$622$	−3.09808	+	5.36603i	−0.124222	+	0.215158i
$623$		−	16.7794i		−	0.672254i
$624$	2.55211	−	12.2265i	0.102166	−	0.489451i
$625$		0			0
$626$	5.79722	+	3.34703i	0.231704	+	0.133774i
$627$	−13.7238	−	7.92345i	−0.548077	−	0.316432i
$628$	4.30738	−	2.48687i	0.171883	−	0.0992369i
$629$			30.2965i			1.20800i
$630$		0			0
$631$	−10.3097	+	5.95230i	−0.410422	+	0.236957i	−0.690971	−	0.722882i	$-0.742817\pi$
$631$	−10.3097	+	5.95230i	−0.410422	+	0.236957i	0.280549	+	0.959840i	$0.409483\pi$
$632$	−47.0541			−1.87171
$633$	−8.65060	+	4.99443i	−0.343830	+	0.198511i
$634$	−9.69350	+	16.7896i	−0.384978	+	0.666802i
$635$		0			0
$636$	−1.19309			−0.0473092
$637$	−6.62349	−	20.1341i	−0.262432	−	0.797743i
$638$			0.774480i			0.0306619i
$639$	7.08138	+	4.08844i	0.280135	+	0.161736i
$640$		0			0
$641$	11.1489	+	19.3104i	0.440354	+	0.762715i	0.997716	−	0.0675549i	$-0.0215198\pi$
$641$	11.1489	+	19.3104i	0.440354	+	0.762715i	−0.557362	+	0.830270i	$0.688186\pi$
$642$	20.0538			0.791460
$643$	−1.27144	−	2.20220i	−0.0501408	−	0.0868465i	0.839866	−	0.542794i	$-0.182634\pi$
$643$	−1.27144	−	2.20220i	−0.0501408	−	0.0868465i	−0.890007	+	0.455948i	$0.849300\pi$
$644$	−0.795623	+	0.459353i	−0.0313519	+	0.0181010i
$645$		0			0
$646$	−20.8866	−	36.1766i	−0.821772	−	1.42335i
$647$	15.9566	+	9.21257i	0.627320	+	0.362183i	0.779713	−	0.626136i	$-0.215365\pi$
$647$	15.9566	+	9.21257i	0.627320	+	0.362183i	−0.152393	+	0.988320i	$0.548698\pi$
$648$	−1.48568	+	2.57328i	−0.0583631	+	0.101088i
$649$	−5.24003			−0.205689
$650$		0			0
$651$	−1.39523			−0.0546833
$652$	2.00154	−	3.46676i	0.0783862	−	0.135769i
$653$	−7.30581	−	4.21801i	−0.285898	−	0.165063i	0.350192	−	0.936678i	$-0.386116\pi$
$653$	−7.30581	−	4.21801i	−0.285898	−	0.165063i	−0.636091	+	0.771614i	$0.719450\pi$
$654$	−0.256006	−	0.443415i	−0.0100106	−	0.0173389i
$655$		0			0
$656$	−26.5654	+	15.3375i	−1.03720	+	0.598830i
$657$	1.99358	+	3.45298i	0.0777770	+	0.134714i
$658$	8.01174			0.312330
$659$	24.7303	+	42.8341i	0.963354	+	1.66858i	0.713973	+	0.700173i	$0.246894\pi$
$659$	24.7303	+	42.8341i	0.963354	+	1.66858i	0.249381	+	0.968405i	$0.419773\pi$
$660$		0			0
$661$	−2.83376	−	1.63607i	−0.110221	−	0.0636359i	0.443876	−	0.896088i	$-0.353603\pi$
$661$	−2.83376	−	1.63607i	−0.110221	−	0.0636359i	−0.554097	+	0.832452i	$0.686936\pi$
$662$		−	21.1494i		−	0.821994i
$663$	−11.8987	+	13.3125i	−0.462108	+	0.517014i
$664$	−46.9587			−1.82235
$665$		0			0
$666$	4.05896	−	7.03032i	0.157281	−	0.272420i
$667$	−0.735111	+	0.424417i	−0.0284636	+	0.0164335i
$668$	1.53425			0.0593618
$669$	17.5247	−	10.1179i	0.677546	−	0.391181i
$670$		0			0
$671$		−	7.61231i		−	0.293870i
$672$	−1.23457	+	0.712776i	−0.0476244	+	0.0274959i
$673$	7.67941	+	4.43371i	0.296020	+	0.170907i	0.640653	−	0.767830i	$-0.278664\pi$
$673$	7.67941	+	4.43371i	0.296020	+	0.170907i	−0.344634	+	0.938737i	$0.611997\pi$
$674$	22.7829	+	13.1537i	0.877564	+	0.506662i
$675$		0			0
$676$	2.50347	−	1.84701i	0.0962873	−	0.0710388i
$677$			45.0533i			1.73154i	0.500444	+	0.865769i	$0.333170\pi$
$677$			45.0533i			1.73154i	−0.500444	+	0.865769i	$0.666830\pi$
$678$	−5.58718	+	9.67729i	−0.214575	+	0.371654i
$679$	−5.32439	+	9.22212i	−0.204331	+	0.353913i
$680$		0			0
$681$		−	3.18793i		−	0.122162i
$682$	2.17898	+	3.77411i	0.0834375	+	0.144518i
$683$	−10.6745	−	18.4888i	−0.408449	−	0.707454i	0.586268	−	0.810117i	$-0.300597\pi$
$683$	−10.6745	−	18.4888i	−0.408449	−	0.707454i	−0.994716	+	0.102664i	$0.967263\pi$
$684$		−	1.52137i		−	0.0581711i
$685$		0			0
$686$	9.04814	−	15.6718i	0.345459	−	0.598353i
$687$	−13.6730	+	23.6824i	−0.521659	+	0.903540i
$688$		−	33.4965i		−	1.27704i
$689$	13.4022	+	11.9789i	0.510584	+	0.456361i
$690$		0			0
$691$	−20.2844	−	11.7112i	−0.771654	−	0.445515i	0.0618100	−	0.998088i	$-0.480313\pi$
$691$	−20.2844	−	11.7112i	−0.771654	−	0.445515i	−0.833464	+	0.552573i	$0.813646\pi$
$692$	−4.66421	−	2.69288i	−0.177307	−	0.102368i
$693$	−2.28605	+	1.31985i	−0.0868400	+	0.0501371i
$694$		−	13.7511i		−	0.521984i
$695$		0			0
$696$	−0.602531	+	0.347871i	−0.0228389	+	0.0131860i
$697$	43.8514			1.66099
$698$	36.5998	−	21.1309i	1.38532	−	0.799818i
$699$	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	$0.809282\pi$
$702$	4.54464	−	1.49504i	0.171526	−	0.0564268i
$703$			38.8930i			1.46688i
$704$	18.8126	+	10.8614i	0.709025	+	0.409356i
$705$		0			0
$706$	0.766987	+	1.32846i	0.0288659	+	0.0499973i
$707$	−12.0843			−0.454475
$708$	−0.251533	−	0.435668i	−0.00945319	−	0.0163734i
$709$	7.86925	−	4.54331i	0.295536	−	0.170628i	−0.344900	−	0.938639i	$-0.612087\pi$
$709$	7.86925	−	4.54331i	0.295536	−	0.170628i	0.640436	+	0.768012i	$0.278754\pi$
$710$		0			0
$711$	−7.91793	−	13.7143i	−0.296946	−	0.514325i
$712$	−40.7741	−	23.5410i	−1.52808	−	0.882235i
$713$	−2.38817	+	4.13644i	−0.0894378	+	0.154911i
$714$	−6.95839			−0.260411
$715$		0			0
$716$	−1.13816			−0.0425351
$717$	−5.19846	+	9.00399i	−0.194140	+	0.336260i
$718$	24.8513	+	14.3479i	0.927441	+	0.535458i
$719$	5.42357	+	9.39390i	0.202265	+	0.350333i	0.949258	−	0.314499i	$-0.101836\pi$
$719$	5.42357	+	9.39390i	0.202265	+	0.350333i	−0.746993	+	0.664832i	$0.768503\pi$
$720$		0			0
$721$	−2.65760	+	1.53437i	−0.0989743	+	0.0571429i
$722$	−14.2075	−	24.6081i	−0.528748	−	0.915818i
$723$	6.12477			0.227783
$724$	1.37134	+	2.37523i	0.0509655	+	0.0882749i
$725$		0			0
$726$	−5.50007	−	3.17547i	−0.204127	−	0.117853i
$727$		−	41.2173i		−	1.52866i	−0.644822	−	0.764332i	$-0.723069\pi$
$727$		−	41.2173i		−	1.52866i	0.644822	−	0.764332i	$-0.276931\pi$
$728$	11.1057	+	2.31817i	0.411605	+	0.0859169i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−23.9424	+	41.4695i	−0.885542	+	1.53380i
$732$	0.632904	−	0.365407i	0.0233928	−	0.0135058i
$733$	−23.4406			−0.865799			−0.432900	−	0.901442i	$-0.642510\pi$
$733$	−23.4406			−0.865799			−0.432900	+	0.901442i	$0.642510\pi$
$734$	−19.3522	+	11.1730i	−0.714301	+	0.412402i
$735$		0			0
$736$			4.88016i			0.179885i
$737$	16.4813	−	9.51545i	0.607095	−	0.350506i
$738$	−10.1758	−	5.87498i	−0.374575	−	0.216261i
$739$	14.5603	+	8.40641i	0.535611	+	0.309235i	0.743298	−	0.668960i	$-0.233260\pi$
$739$	14.5603	+	8.40641i	0.535611	+	0.309235i	−0.207688	+	0.978195i	$0.566594\pi$
$740$		0			0
$741$	−15.2750	+	17.0899i	−0.561139	+	0.627811i
$742$			7.00530i			0.257173i
$743$	10.6155	−	18.3867i	0.389447	−	0.674541i	−0.602929	−	0.797795i	$-0.706000\pi$
$743$	10.6155	−	18.3867i	0.389447	−	0.674541i	0.992375	+	0.123254i	$0.0393330\pi$
$744$	−1.95746	+	3.39041i	−0.0717638	+	0.124299i
$745$		0			0
$746$			32.5104i			1.19029i
$747$	−7.90187	−	13.6864i	−0.289114	−	0.500761i
$748$	−1.47707	−	2.55837i	−0.0540072	−	0.0935432i
$749$			16.0042i			0.584782i
$750$		0			0
$751$	−11.1589	+	19.3278i	−0.407195	+	0.705282i	−0.994574	−	0.104029i	$-0.966826\pi$
$751$	−11.1589	+	19.3278i	−0.407195	+	0.705282i	0.587379	+	0.809312i	$0.300160\pi$
$752$	9.87568	−	17.1052i	0.360129	−	0.623762i
$753$		−	7.75343i		−	0.282551i
$754$	1.09659	+	0.228898i	0.0399354	+	0.00833599i
$755$		0			0
$756$	−0.219471	−	0.126712i	−0.00798209	−	0.00460846i
$757$	6.86045	+	3.96088i	0.249347	+	0.143961i	0.619465	−	0.785024i	$-0.287349\pi$
$757$	6.86045	+	3.96088i	0.249347	+	0.143961i	−0.370118	+	0.928985i	$0.620683\pi$
$758$	−37.9994	+	21.9390i	−1.38020	+	0.796860i
$759$			9.03662i			0.328009i
$760$		0			0
$761$	−10.5400	+	6.08529i	−0.382076	+	0.220592i	−0.678721	−	0.734396i	$-0.737465\pi$
$761$	−10.5400	+	6.08529i	−0.382076	+	0.220592i	0.296645	+	0.954988i	$0.404132\pi$
$762$	−15.1097			−0.547366
$763$	0.353874	−	0.204309i	0.0128111	−	0.00739649i
$764$	−0.694256	+	1.20249i	−0.0251173	+	0.0435044i
$765$		0			0
$766$	1.32709			0.0479497
$767$	−1.54870	+	7.41939i	−0.0559203	+	0.267899i
$768$			5.65801i			0.204166i
$769$	−18.3243	−	10.5796i	−0.660793	−	0.381509i	0.131786	−	0.991278i	$-0.457929\pi$
$769$	−18.3243	−	10.5796i	−0.660793	−	0.381509i	−0.792579	+	0.609769i	$0.791262\pi$
$770$		0			0
$771$	4.02069	+	6.96403i	0.144801	+	0.250804i
$772$	0.582337			0.0209588
$773$	2.19887	+	3.80856i	0.0790880	+	0.136984i	0.902857	−	0.429942i	$-0.141466\pi$
$773$	2.19887	+	3.80856i	0.0790880	+	0.136984i	−0.823769	+	0.566926i	$0.808133\pi$
$774$	11.1117	−	6.41535i	0.399402	−	0.230595i
$775$		0			0
$776$	14.9399	+	25.8766i	0.536310	+	0.928916i
$777$	5.61066	+	3.23931i	0.201281	+	0.116210i
$778$	0.837232	−	1.45013i	0.0300162	−	0.0519896i
$779$	56.2941			2.01695
$780$		0			0
$781$	20.3828			0.729354
$782$	−11.9105	+	20.6296i	−0.425918	+	0.737712i
$783$	−0.202779	−	0.117075i	−0.00724673	−	0.00418390i
$784$	−10.1820	−	17.6358i	−0.363644	−	0.629851i
$785$		0			0
$786$	−13.2091	+	7.62630i	−0.471154	+	0.272021i
$787$	21.5567	+	37.3374i	0.768415	+	1.33093i	0.938422	+	0.345491i	$0.112288\pi$
$787$	21.5567	+	37.3374i	0.768415	+	1.33093i	−0.170007	+	0.985443i	$0.554379\pi$
$788$	3.20259			0.114088
$789$	−8.51573	−	14.7497i	−0.303168	−	0.525102i
$790$		0			0
$791$	−7.72311	−	4.45894i	−0.274602	−	0.158542i
$792$			7.40683i			0.263190i
$793$	−10.7783	−	2.24983i	−0.382749	−	0.0798937i
$794$	−14.8029			−0.525335
$795$		0			0
$796$	−2.13601	+	3.69967i	−0.0757088	+	0.131131i
$797$	29.5008	−	17.0323i	1.04497	−	0.603315i	0.123734	−	0.992315i	$-0.460513\pi$
$797$	29.5008	−	17.0323i	1.04497	−	0.603315i	0.921237	+	0.389001i	$0.127180\pi$
$798$	−8.93282			−0.316218
$799$	−24.4526	+	14.1177i	−0.865072	+	0.499449i
$800$		0			0
$801$		−	15.8452i		−	0.559863i
$802$	38.2346	−	22.0748i	1.35011	−	0.779487i
$803$	8.60738	+	4.96947i	0.303748	+	0.175369i
$804$	1.58227	+	0.913525i	0.0558024	+	0.0322176i
$805$		0			0
$806$	5.98778	−	1.96979i	0.210911	−	0.0693829i
$807$		−	9.75174i		−	0.343278i
$808$	−16.9538	+	29.3648i	−0.596432	+	1.03305i
$809$	7.86797	−	13.6277i	0.276623	−	0.479125i	−0.693920	−	0.720052i	$-0.744118\pi$
$809$	7.86797	−	13.6277i	0.276623	−	0.479125i	0.970543	+	0.240927i	$0.0774513\pi$
$810$		0			0
$811$		−	47.5686i		−	1.67036i	−0.549976	−	0.835180i	$-0.685363\pi$
$811$		−	47.5686i		−	1.67036i	0.549976	−	0.835180i	$-0.314637\pi$
$812$	−0.0296694	−	0.0513890i	−0.00104119	−	0.00180340i
$813$	−10.6429	−	18.4341i	−0.373264	−	0.646512i
$814$		−	20.2358i		−	0.709266i
$815$		0			0
$816$	−8.57727	+	14.8563i	−0.300265	+	0.520073i
$817$	−30.7360	+	53.2363i	−1.07532	+	1.86250i
$818$			3.20789i			0.112161i
$819$	1.19314	+	3.62692i	0.0416918	+	0.126735i
$820$		0			0
$821$	10.5205	+	6.07404i	0.367169	+	0.211985i	0.672221	−	0.740350i	$-0.265340\pi$
$821$	10.5205	+	6.07404i	0.367169	+	0.211985i	−0.305052	+	0.952336i	$0.598674\pi$
$822$	−19.7847	−	11.4227i	−0.690069	−	0.398412i
$823$	−3.16596	+	1.82787i	−0.110359	+	0.0637156i	−0.554163	−	0.832408i	$-0.686962\pi$
$823$	−3.16596	+	1.82787i	−0.110359	+	0.0637156i	0.443805	+	0.896124i	$0.353628\pi$
$824$			8.61066i			0.299966i
$825$		0			0
$826$	−2.55805	+	1.47689i	−0.0890058	+	0.0513875i
$827$	−30.5084			−1.06088			−0.530441	−	0.847722i	$-0.677974\pi$
$827$	−30.5084			−1.06088			−0.530441	+	0.847722i	$0.677974\pi$
$828$	−0.751325	+	0.433778i	−0.0261104	+	0.0150748i
$829$	−26.0329	+	45.0903i	−0.904161	+	1.56605i	−0.0821211	+	0.996622i	$0.526169\pi$
$829$	−26.0329	+	45.0903i	−0.904161	+	1.56605i	−0.822040	+	0.569430i	$0.807164\pi$
$830$		0			0
$831$	−25.6648			−0.890301
$832$	20.9388	−	23.4267i	0.725924	−	0.812174i
$833$			29.1114i			1.00865i
$834$	2.76578	+	1.59682i	0.0957710	+	0.0552934i
$835$		0			0
$836$	−1.89619	−	3.28430i	−0.0655811	−	0.113590i
$837$	−1.31755			−0.0455411
$838$	−17.7087	−	30.6724i	−0.611738	−	1.05956i
$839$	37.4902	−	21.6450i	1.29431	−	0.747268i	0.314891	−	0.949128i	$-0.398032\pi$
$839$	37.4902	−	21.6450i	1.29431	−	0.747268i	0.979414	+	0.201860i	$0.0646987\pi$
$840$		0			0
$841$	14.4726	+	25.0673i	0.499055	+	0.864388i
$842$	−46.8124	−	27.0271i	−1.61326	−	0.931416i
$843$	−8.41821	+	14.5808i	−0.289938	+	0.502188i
$844$	−2.39047			−0.0822833
$845$		0			0
$846$	7.56567			0.260113
$847$	2.53423	−	4.38941i	0.0870771	−	0.150822i
$848$	14.9564	+	8.63509i	0.513606	+	0.296530i
$849$	9.03975	+	15.6573i	0.310244	+	0.537358i
$850$		0			0
$851$	19.2072	−	11.0893i	0.658414	−	0.380136i
$852$	0.978419	+	1.69467i	0.0335201	+	0.0580585i
$853$	−7.62729			−0.261153			−0.130577	−	0.991438i	$-0.541683\pi$
$853$	−7.62729			−0.261153			−0.130577	+	0.991438i	$0.541683\pi$
$854$	−2.14551	−	3.71613i	−0.0734178	−	0.127163i
$855$		0			0
$856$	38.8904	+	22.4534i	1.32925	+	0.767440i
$857$			34.6287i			1.18289i	0.806344	+	0.591447i	$0.201443\pi$
$857$			34.6287i			1.18289i	−0.806344	+	0.591447i	$0.798557\pi$
$858$	7.94748	−	8.89176i	0.271322	−	0.303560i
$859$	15.1648			0.517415			0.258707	−	0.965956i	$-0.416703\pi$
$859$	15.1648			0.517415			0.258707	+	0.965956i	$0.416703\pi$
$860$		0			0
$861$	4.68861	−	8.12092i	0.159788	−	0.276760i
$862$	−8.24479	+	4.76013i	−0.280819	+	0.162131i
$863$	17.7187			0.603150			0.301575	−	0.953442i	$-0.402488\pi$
$863$	17.7187			0.603150			0.301575	+	0.953442i	$0.402488\pi$
$864$	−1.16583	+	0.673091i	−0.0396623	+	0.0228990i
$865$		0			0
$866$			38.1276i			1.29563i
$867$	6.51528	−	3.76160i	0.221270	−	0.127751i
$868$	−0.289164	−	0.166949i	−0.00981485	−	0.00566661i
$869$	−34.1860	−	19.7373i	−1.15968	−	0.669543i
$870$		0			0
$871$	−8.60193	−	26.1482i	−0.291465	−	0.885998i
$872$		−	1.14655i		−	0.0388272i
$873$	−5.02795	+	8.70866i	−0.170170	+	0.294744i
$874$	−15.2900	+	26.4831i	−0.517194	+	0.895806i
$875$		0			0
$876$			0.954183i			0.0322388i
$877$	−1.20259	−	2.08295i	−0.0406086	−	0.0703361i	0.845007	−	0.534756i	$-0.179596\pi$
$877$	−1.20259	−	2.08295i	−0.0406086	−	0.0703361i	−0.885615	+	0.464420i	$0.846263\pi$
$878$	−25.9868	−	45.0105i	−0.877013	−	1.51903i
$879$			14.5444i			0.490572i
$880$		0			0
$881$	−13.2458	+	22.9423i	−0.446261	+	0.772946i	−0.998139	−	0.0609784i	$-0.980578\pi$
$881$	−13.2458	+	22.9423i	−0.446261	+	0.772946i	0.551878	+	0.833925i	$0.313911\pi$
$882$	3.90019	−	6.75532i	0.131326	−	0.227463i
$883$		−	14.5464i		−	0.489525i	−0.969583	−	0.244763i	$-0.921290\pi$
$883$		−	14.5464i		−	0.489525i	0.969583	−	0.244763i	$-0.0787100\pi$
$884$	−4.05896	+	1.33527i	−0.136518	+	0.0449100i
$885$		0			0
$886$	14.3899	+	8.30800i	0.483437	+	0.279113i
$887$	30.5160	+	17.6184i	1.02463	+	0.591568i	0.915441	−	0.402453i	$-0.131842\pi$
$887$	30.5160	+	17.6184i	1.02463	+	0.591568i	0.109185	+	0.994021i	$0.465176\pi$
$888$	15.7431	−	9.08928i	0.528304	−	0.305016i
$889$		−	12.0585i		−	0.404430i
$890$		0			0
$891$	−2.15877	+	1.24637i	−0.0723216	+	0.0417549i
$892$	4.84271			0.162146
$893$	−31.3910	+	18.1236i	−1.05046	+	0.606483i
$894$	2.24406	−	3.88683i	0.0750527	−	0.129995i
$895$		0			0
$896$	9.39396			0.313830
$897$	12.7950	+	2.67079i	0.427213	+	0.0891749i
$898$		−	14.5393i		−	0.485182i
$899$	−0.267171	−	0.154251i	−0.00891065	−	0.00514457i
$900$		0			0
$901$	−12.3443	−	21.3809i	−0.411247	−	0.712301i
$902$	−29.2895			−0.975235
$903$	5.11986	+	8.86787i	0.170378	+	0.295104i
$904$	−21.6705	+	12.5115i	−0.720750	+	0.416125i
$905$		0			0
$906$	−0.973671	−	1.68645i	−0.0323480	−	0.0560285i
$907$	−14.4096	−	8.31939i	−0.478463	−	0.276241i	0.241313	−	0.970447i	$-0.422422\pi$
$907$	−14.4096	−	8.31939i	−0.478463	−	0.276241i	−0.719776	+	0.694207i	$0.755755\pi$
$908$	0.381457	−	0.660703i	0.0126591	−	0.0219262i
$909$	−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	$0.560439\pi$
$912$	−11.0110	+	19.0717i	−0.364612	+	0.631527i
$913$	−34.1167	−	19.6973i	−1.12910	−	0.651885i
$914$	−11.0033	−	19.0583i	−0.363956	−	0.630391i
$915$		0			0
$916$	−5.66752	+	3.27215i	−0.187260	+	0.108115i
$917$	−6.08628	−	10.5418i	−0.200987	−	0.348119i
$918$	−6.57097			−0.216874
$919$	−13.3893	−	23.1909i	−0.441672	−	0.764998i	0.556142	−	0.831088i	$-0.312281\pi$
$919$	−13.3893	−	23.1909i	−0.441672	−	0.764998i	−0.997814	+	0.0660891i	$0.978948\pi$
$920$		0			0
$921$	29.5369	+	17.0531i	0.973272	+	0.561919i
$922$		−	30.4396i		−	1.00247i
$923$	6.02416	−	28.8601i	0.198288	−	0.949943i
$924$	−0.631718			−0.0207820
$925$		0			0
$926$	27.3407	−	47.3555i	0.898471	−	1.55620i
$927$	−2.50964	+	1.44894i	−0.0824273	+	0.0475894i
$928$	−0.315208			−0.0103472
$929$	16.8755	−	9.74310i	0.553669	−	0.319661i	−0.196932	−	0.980417i	$-0.563098\pi$
$929$	16.8755	−	9.74310i	0.553669	−	0.319661i	0.750600	+	0.660756i	$0.229764\pi$
$930$		0			0
$931$			37.3717i			1.22481i
$932$	2.66390	−	1.53800i	0.0872589	−	0.0503790i
$933$	−4.04401	−	2.33481i	−0.132395	−	0.0764382i
$934$	35.8378	+	20.6909i	1.17265	+	0.677028i
$935$		0			0
$936$	10.4874	+	2.18910i	0.342790	+	0.0715529i
$937$		−	9.81448i		−	0.320625i	−0.987066	−	0.160313i	$-0.948750\pi$
$937$		−	9.81448i		−	0.320625i	0.987066	−	0.160313i	$-0.0512502\pi$
$938$	5.36381	−	9.29039i	0.175135	−	0.303342i
$939$	−2.52242	+	4.36897i	−0.0823162	+	0.142576i
$940$		0			0
$941$			47.0242i			1.53295i	0.642277	+	0.766473i	$0.277990\pi$
$941$			47.0242i			1.53295i	−0.642277	+	0.766473i	$0.722010\pi$
$942$	−13.7888	−	23.8829i	−0.449263	−	0.778147i
$943$	−16.0507	−	27.8007i	−0.522684	−	0.905315i
$944$			7.28196i			0.237008i
$945$		0			0
$946$	15.9918	−	27.6986i	0.519937	−	0.900558i
$947$	11.9613	−	20.7176i	0.388690	−	0.673232i	−0.603583	−	0.797300i	$-0.706261\pi$
$947$	11.9613	−	20.7176i	0.388690	−	0.673232i	0.992274	+	0.124068i	$0.0395942\pi$
$948$		−	3.78974i		−	0.123085i
$949$	9.58023	−	10.7185i	0.310987	−	0.347937i
$950$		0			0
$951$	−12.6532	−	7.30533i	−0.410308	−	0.236891i
$952$	−13.4944	−	7.79101i	−0.437357	−	0.252508i
$953$	−22.2122	+	12.8242i	−0.719522	+	0.415416i	−0.814577	−	0.580056i	$-0.803031\pi$
$953$	−22.2122	+	12.8242i	−0.719522	+	0.415416i	0.0950546	+	0.995472i	$0.469697\pi$
$954$			6.61527i			0.214177i
$955$		0			0
$956$	−2.15478	+	1.24406i	−0.0696905	+	0.0402358i
$957$	−0.583672			−0.0188674
$958$	5.92932	−	3.42330i	0.191568	−	0.110602i
$959$	9.11604	−	15.7894i	0.294372	−	0.509868i
$960$		0			0
$961$	29.2641			0.944002
$962$	−28.6520	−	5.98073i	−0.923778	−	0.192826i
$963$			15.1132i			0.487015i
$964$	1.26937	+	0.732871i	0.0408836	+	0.0236042i
$965$		0			0
$966$	2.54695	+	4.41144i	0.0819467	+	0.141936i
$967$	25.1221			0.807873			0.403936	−	0.914787i	$-0.367642\pi$
$967$	25.1221			0.807873			0.403936	+	0.914787i	$0.367642\pi$
$968$	−7.11086	−	12.3164i	−0.228552	−	0.395863i
$969$	27.2639	−	15.7408i	0.875841	−	0.505667i
$970$		0			0
$971$	−19.8822	−	34.4370i	−0.638050	−	1.10513i	−0.985860	−	0.167570i	$-0.946408\pi$
$971$	−19.8822	−	34.4370i	−0.638050	−	1.10513i	0.347811	−	0.937565i	$-0.386925\pi$
$972$	−0.207252	−	0.119657i	−0.00664760	−	0.00383799i
$973$	−1.27437	+	2.20727i	−0.0408544	+	0.0707618i
$974$	−34.9720			−1.12058
$975$		0			0
$976$	−10.5787			−0.338615
$977$	−5.08581	+	8.80888i	−0.162709	+	0.281821i	−0.935839	−	0.352427i	$-0.885357\pi$
$977$	−5.08581	+	8.80888i	−0.162709	+	0.281821i	0.773130	+	0.634247i	$0.218690\pi$
$978$	−19.2220	−	11.0978i	−0.614650	−	0.354869i
$979$	−19.7490	−	34.2062i	−0.631180	−	1.09324i
$980$		0			0
$981$	0.334171	−	0.192934i	0.0106693	−	0.00615991i
$982$	12.4214	+	21.5144i	0.396382	+	0.686554i
$983$	−37.0857			−1.18285			−0.591425	−	0.806360i	$-0.701434\pi$
$983$	−37.0857			−1.18285			−0.591425	+	0.806360i	$0.701434\pi$
$984$	−13.1559	−	22.7867i	−0.419395	−	0.726414i
$985$		0			0
$986$	−1.33246	−	0.769294i	−0.0424340	−	0.0244993i
$987$			6.03790i			0.192188i
$988$	−5.21068	+	1.71415i	−0.165774	+	0.0545343i
$989$	35.0541			1.11466
$990$		0			0
$991$	−8.57901	+	14.8593i	−0.272521	+	0.472021i	−0.969507	−	0.245065i	$-0.921191\pi$
$991$	−8.57901	+	14.8593i	−0.272521	+	0.472021i	0.696986	+	0.717085i	$0.254524\pi$
$992$	−1.53603	+	0.886830i	−0.0487691	+	0.0281569i
$993$	15.9388			0.505804
$994$	9.95035	−	5.74484i	0.315606	−	0.182215i
$995$		0			0
$996$		−	3.78205i		−	0.119839i
$997$	−30.1347	+	17.3983i	−0.954374	+	0.551008i	−0.894437	−	0.447194i	$-0.852423\pi$
$997$	−30.1347	+	17.3983i	−0.954374	+	0.551008i	−0.0599374	+	0.998202i	$0.519090\pi$
$998$	10.7036	+	6.17974i	0.338817	+	0.195616i
$999$	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.w.j.199.3		8
5.2	odd	4		975.2.bc.i.901.4		8
5.3	odd	4		195.2.bb.c.121.1	✓	8
5.4	even	2		975.2.w.g.199.2		8
13.10	even	6		975.2.w.g.49.2		8
15.8	even	4		585.2.bu.b.316.4		8
65.23	odd	12		195.2.bb.c.166.1	yes	8
65.33	even	12		2535.2.a.bi.1.2		4
65.49	even	6	inner	975.2.w.j.49.3		8
65.58	even	12		2535.2.a.bl.1.3		4
65.62	odd	12		975.2.bc.i.751.4		8
195.23	even	12		585.2.bu.b.361.4		8
195.98	odd	12		7605.2.a.ck.1.3		4
195.188	odd	12		7605.2.a.cg.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.c.121.1	✓	8	5.3	odd	4
195.2.bb.c.166.1	yes	8	65.23	odd	12
585.2.bu.b.316.4		8	15.8	even	4
585.2.bu.b.361.4		8	195.23	even	12
975.2.w.g.49.2		8	13.10	even	6
975.2.w.g.199.2		8	5.4	even	2
975.2.w.j.49.3		8	65.49	even	6	inner
975.2.w.j.199.3		8	1.1	even	1	trivial
975.2.bc.i.751.4		8	65.62	odd	12
975.2.bc.i.901.4		8	5.2	odd	4
2535.2.a.bi.1.2		4	65.33	even	12
2535.2.a.bl.1.3		4	65.58	even	12
7605.2.a.cg.1.2		4	195.188	odd	12
7605.2.a.ck.1.3		4	195.98	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.w (of order \(6\), degree \(2\), not minimal)

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

Introduction

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