LMFDB - Embedded newform 975.2.o.m.476.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(476,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("975.476");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.o (of order $4$, 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 $\Q(i)$
Coefficient field:	8.0.619810816.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			476.3
Root			$-1.49094 - 1.49094i$ of defining polynomial
Character	$\chi$	$=$	975.476
Dual form			975.2.o.m.551.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.664640 + 0.664640i) q^{2} +(-1.15558 - 1.29021i) q^{3} +1.11651i q^{4} +(1.62557 + 0.0894818i) q^{6} +(2.20073 - 2.20073i) q^{7} +(-2.07136 - 2.07136i) q^{8} +(-0.329281 + 2.98187i) q^{9} +(-0.820218 - 0.820218i) q^{11} +(1.44053 - 1.29021i) q^{12} +(3.60136 + 0.173703i) q^{13} +2.92539i q^{14} +0.520402 q^{16} -0.688845 q^{17} +(-1.76302 - 2.20073i) q^{18} +(-1.82630 - 1.82630i) q^{19} +(-5.38251 - 0.296288i) q^{21} +1.09030 q^{22} -4.86537 q^{23} +(-0.278871 + 5.06610i) q^{24} +(-2.50906 + 2.27816i) q^{26} +(4.22775 - 3.02095i) q^{27} +(2.45713 + 2.45713i) q^{28} +1.93998i q^{29} +(-0.910518 - 0.910518i) q^{31} +(3.79683 - 3.79683i) q^{32} +(-0.110427 + 2.00608i) q^{33} +(0.457834 - 0.457834i) q^{34} +(-3.32928 - 0.367644i) q^{36} +(1.82630 - 1.82630i) q^{37} +2.42766 q^{38} +(-3.93754 - 4.84724i) q^{39} +(5.96093 - 5.96093i) q^{41} +(3.77436 - 3.38051i) q^{42} +2.50580i q^{43} +(0.915778 - 0.915778i) q^{44} +(3.23372 - 3.23372i) q^{46} +(-8.62839 - 8.62839i) q^{47} +(-0.601365 - 0.671427i) q^{48} -2.68640i q^{49} +(0.796014 + 0.888754i) q^{51} +(-0.193941 + 4.02095i) q^{52} -8.99159i q^{53} +(-0.802092 + 4.81778i) q^{54} -9.11698 q^{56} +(-0.245878 + 4.46673i) q^{57} +(-1.28939 - 1.28939i) q^{58} +(-3.46755 - 3.46755i) q^{59} +13.9094 q^{61} +1.21033 q^{62} +(5.83764 + 7.28695i) q^{63} +6.08786i q^{64} +(-1.25993 - 1.40672i) q^{66} +(-5.39820 - 5.39820i) q^{67} -0.769099i q^{68} +(5.62231 + 6.27734i) q^{69} +(5.58324 - 5.58324i) q^{71} +(6.85858 - 5.49447i) q^{72} +(9.43292 - 9.43292i) q^{73} +2.42766i q^{74} +(2.03907 - 2.03907i) q^{76} -3.61015 q^{77} +(5.83872 + 0.604623i) q^{78} -6.07461 q^{79} +(-8.78315 - 1.96375i) q^{81} +7.92375i q^{82} +(-3.93390 + 3.93390i) q^{83} +(0.330807 - 6.00961i) q^{84} +(-1.66546 - 1.66546i) q^{86} +(2.50298 - 2.24180i) q^{87} +3.39793i q^{88} +(1.07814 + 1.07814i) q^{89} +(8.30790 - 7.54335i) q^{91} -5.43221i q^{92} +(-0.122585 + 2.22693i) q^{93} +11.4696 q^{94} +(-9.28624 - 0.511175i) q^{96} +(-7.02377 - 7.02377i) q^{97} +(1.78549 + 1.78549i) q^{98} +(2.71587 - 2.17570i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} + 2 q^{3} + 4 q^{6} + 14 q^{7} + 12 q^{8} - 4 q^{9} + 4 q^{11} + 14 q^{12} - 2 q^{13} - 8 q^{16} - 28 q^{17} + 30 q^{18} - 2 q^{19} + 8 q^{21} + 24 q^{22} - 36 q^{23} - 18 q^{24} - 32 q^{26}+ \cdots + 28 q^{99}+O(q^{100}) $ 8 * q - 6 * q^2 + 2 * q^3 + 4 * q^6 + 14 * q^7 + 12 * q^8 - 4 * q^9 + 4 * q^11 + 14 * q^12 - 2 * q^13 - 8 * q^16 - 28 * q^17 + 30 * q^18 - 2 * q^19 + 8 * q^21 + 24 * q^22 - 36 * q^23 - 18 * q^24 - 32 * q^26 + 14 * q^27 - 24 * q^28 - 12 * q^31 + 18 * q^32 + 18 * q^33 + 10 * q^34 - 28 * q^36 + 2 * q^37 - 24 * q^38 - 20 * q^39 + 38 * q^41 - 38 * q^42 - 10 * q^44 + 34 * q^46 - 22 * q^47 + 26 * q^48 - 26 * q^51 + 50 * q^52 + 28 * q^54 + 76 * q^56 - 6 * q^57 + 18 * q^58 - 14 * q^59 - 8 * q^61 + 16 * q^62 + 10 * q^63 + 18 * q^66 - 10 * q^71 + 4 * q^72 + 10 * q^73 + 26 * q^76 + 12 * q^77 + 6 * q^78 - 56 * q^79 + 8 * q^81 - 38 * q^83 + 74 * q^84 - 34 * q^86 + 34 * q^87 + 28 * q^89 + 8 * q^91 + 22 * q^93 + 20 * q^94 + 20 * q^96 - 4 * q^97 + 26 * q^98 + 28 * q^99

Character values

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

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

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 $

$2$	−0.664640	+	0.664640i	−0.469972	+	0.469972i	−0.901905	−	0.431934i	$-0.857831\pi$
$2$	−0.664640	+	0.664640i	−0.469972	+	0.469972i	0.431934	+	0.901905i	$0.357831\pi$
$3$	−1.15558	−	1.29021i	−0.667173	−	0.744903i
$3$	−1.15558	−	1.29021i	−0.667173	−	0.744903i
$4$			1.11651i			0.558253i
$5$		0			0
$5$		0			0
$6$	1.62557	+	0.0894818i	0.663636	+	0.0365308i
$7$	2.20073	−	2.20073i	0.831797	−	0.831797i	−0.155966	−	0.987762i	$-0.549849\pi$
$7$	2.20073	−	2.20073i	0.831797	−	0.831797i	0.987762	+	0.155966i	$0.0498489\pi$
$8$	−2.07136	−	2.07136i	−0.732335	−	0.732335i
$9$	−0.329281	+	2.98187i	−0.109760	+	0.993958i
$10$		0			0
$11$	−0.820218	−	0.820218i	−0.247305	−	0.247305i	0.572559	−	0.819864i	$-0.305951\pi$
$11$	−0.820218	−	0.820218i	−0.247305	−	0.247305i	−0.819864	+	0.572559i	$0.805951\pi$
$12$	1.44053	−	1.29021i	0.415844	−	0.372451i
$13$	3.60136	+	0.173703i	0.998839	+	0.0481766i
$13$	3.60136	+	0.173703i	0.998839	+	0.0481766i
$14$			2.92539i			0.781842i
$15$		0			0
$16$	0.520402			0.130100
$17$	−0.688845			−0.167069			−0.0835347	−	0.996505i	$-0.526621\pi$
$17$	−0.688845			−0.167069			−0.0835347	+	0.996505i	$0.526621\pi$
$18$	−1.76302	−	2.20073i	−0.415548	−	0.518716i
$19$	−1.82630	−	1.82630i	−0.418981	−	0.418981i	0.465871	−	0.884852i	$-0.345741\pi$
$19$	−1.82630	−	1.82630i	−0.418981	−	0.418981i	−0.884852	+	0.465871i	$0.845741\pi$
$20$		0			0
$21$	−5.38251	−	0.296288i	−1.17456	−	0.0646554i
$22$	1.09030			0.232453
$23$	−4.86537			−1.01450			−0.507250	−	0.861799i	$-0.669338\pi$
$23$	−4.86537			−1.01450			−0.507250	+	0.861799i	$0.669338\pi$
$24$	−0.278871	+	5.06610i	−0.0569242	+	1.03411i
$25$		0			0
$26$	−2.50906	+	2.27816i	−0.492068	+	0.446784i
$27$	4.22775	−	3.02095i	0.813631	−	0.581381i
$28$	2.45713	+	2.45713i	0.464353	+	0.464353i
$29$			1.93998i			0.360246i	0.983644	+	0.180123i	$0.0576495\pi$
$29$			1.93998i			0.360246i	−0.983644	+	0.180123i	$0.942350\pi$
$30$		0			0
$31$	−0.910518	−	0.910518i	−0.163534	−	0.163534i	0.620596	−	0.784130i	$-0.286891\pi$
$31$	−0.910518	−	0.910518i	−0.163534	−	0.163534i	−0.784130	+	0.620596i	$0.786891\pi$
$32$	3.79683	−	3.79683i	0.671191	−	0.671191i
$33$	−0.110427	+	2.00608i	−0.0192230	+	0.349213i
$34$	0.457834	−	0.457834i	0.0785179	−	0.0785179i
$35$		0			0
$36$	−3.32928	−	0.367644i	−0.554880	−	0.0612740i
$37$	1.82630	−	1.82630i	0.300241	−	0.300241i	−0.540867	−	0.841108i	$-0.681904\pi$
$37$	1.82630	−	1.82630i	0.300241	−	0.300241i	0.841108	+	0.540867i	$0.181904\pi$
$38$	2.42766			0.393819
$39$	−3.93754	−	4.84724i	−0.630511	−	0.776180i
$40$		0			0
$41$	5.96093	−	5.96093i	0.930941	−	0.930941i	−0.0668241	−	0.997765i	$-0.521287\pi$
$41$	5.96093	−	5.96093i	0.930941	−	0.930941i	0.997765	+	0.0668241i	$0.0212866\pi$
$42$	3.77436	−	3.38051i	0.582396	−	0.521624i
$43$			2.50580i			0.382132i	0.981577	+	0.191066i	$0.0611944\pi$
$43$			2.50580i			0.382132i	−0.981577	+	0.191066i	$0.938806\pi$
$44$	0.915778	−	0.915778i	0.138059	−	0.138059i
$45$		0			0
$46$	3.23372	−	3.23372i	0.476786	−	0.476786i
$47$	−8.62839	−	8.62839i	−1.25858	−	1.25858i	−0.951771	−	0.306809i	$-0.900739\pi$
$47$	−8.62839	−	8.62839i	−1.25858	−	1.25858i	−0.306809	−	0.951771i	$-0.599261\pi$
$48$	−0.601365	−	0.671427i	−0.0867995	−	0.0969122i
$49$		−	2.68640i		−	0.383772i
$50$		0			0
$51$	0.796014	+	0.888754i	0.111464	+	0.124450i
$52$	−0.193941	+	4.02095i	−0.0268948	+	0.557605i
$53$		−	8.99159i		−	1.23509i	−0.786536	−	0.617545i	$-0.788127\pi$
$53$		−	8.99159i		−	1.23509i	0.786536	−	0.617545i	$-0.211873\pi$
$54$	−0.802092	+	4.81778i	−0.109151	+	0.655617i
$55$		0			0
$56$	−9.11698			−1.21831
$57$	−0.245878	+	4.46673i	−0.0325673	+	0.591633i
$58$	−1.28939	−	1.28939i	−0.169305	−	0.169305i
$59$	−3.46755	−	3.46755i	−0.451437	−	0.451437i	0.444394	−	0.895831i	$-0.353419\pi$
$59$	−3.46755	−	3.46755i	−0.451437	−	0.451437i	−0.895831	+	0.444394i	$0.853419\pi$
$60$		0			0
$61$	13.9094			1.78091			0.890456	−	0.455069i	$-0.150385\pi$
$61$	13.9094			1.78091			0.890456	+	0.455069i	$0.150385\pi$
$62$	1.21033			0.153713
$63$	5.83764	+	7.28695i	0.735473	+	0.918070i
$64$			6.08786i			0.760982i
$65$		0			0
$66$	−1.25993	−	1.40672i	−0.155086	−	0.173155i
$67$	−5.39820	−	5.39820i	−0.659495	−	0.659495i	0.295766	−	0.955260i	$-0.404425\pi$
$67$	−5.39820	−	5.39820i	−0.659495	−	0.659495i	−0.955260	+	0.295766i	$0.904425\pi$
$68$		−	0.769099i		−	0.0932670i
$69$	5.62231	+	6.27734i	0.676847	+	0.755703i
$70$		0			0
$71$	5.58324	−	5.58324i	0.662609	−	0.662609i	−0.293386	−	0.955994i	$-0.594782\pi$
$71$	5.58324	−	5.58324i	0.662609	−	0.662609i	0.955994	+	0.293386i	$0.0947820\pi$
$72$	6.85858	−	5.49447i	0.808292	−	0.647529i
$73$	9.43292	−	9.43292i	1.10404	−	1.10404i	0.110122	−	0.993918i	$-0.464876\pi$
$73$	9.43292	−	9.43292i	1.10404	−	1.10404i	0.993918	−	0.110122i	$-0.0351241\pi$
$74$			2.42766i			0.282210i
$75$		0			0
$76$	2.03907	−	2.03907i	0.233898	−	0.233898i
$77$	−3.61015			−0.411415
$78$	5.83872	+	0.604623i	0.661105	+	0.0684601i
$79$	−6.07461			−0.683448			−0.341724	−	0.939800i	$-0.611011\pi$
$79$	−6.07461			−0.683448			−0.341724	+	0.939800i	$0.611011\pi$
$80$		0			0
$81$	−8.78315	−	1.96375i	−0.975905	−	0.218194i
$82$			7.92375i			0.875032i
$83$	−3.93390	+	3.93390i	−0.431802	+	0.431802i	−0.889241	−	0.457439i	$-0.848767\pi$
$83$	−3.93390	+	3.93390i	−0.431802	+	0.431802i	0.457439	+	0.889241i	$0.348767\pi$
$84$	0.330807	−	6.00961i	0.0360941	−	0.655702i
$85$		0			0
$86$	−1.66546	−	1.66546i	−0.179591	−	0.179591i
$87$	2.50298	−	2.24180i	0.268348	−	0.240346i
$88$			3.39793i			0.362220i
$89$	1.07814	+	1.07814i	0.114283	+	0.114283i	0.761936	−	0.647653i	$-0.224249\pi$
$89$	1.07814	+	1.07814i	0.114283	+	0.114283i	−0.647653	+	0.761936i	$0.724249\pi$
$90$		0			0
$91$	8.30790	−	7.54335i	0.870904	−	0.790758i
$92$		−	5.43221i		−	0.566347i
$93$	−0.122585	+	2.22693i	−0.0127114	+	0.230922i
$94$	11.4696			1.18299
$95$		0			0
$96$	−9.28624	−	0.511175i	−0.947773	−	0.0521715i
$97$	−7.02377	−	7.02377i	−0.713155	−	0.713155i	0.254039	−	0.967194i	$-0.418241\pi$
$97$	−7.02377	−	7.02377i	−0.713155	−	0.713155i	−0.967194	+	0.254039i	$0.918241\pi$
$98$	1.78549	+	1.78549i	0.180362	+	0.180362i
$99$	2.71587	−	2.17570i	0.272955	−	0.218667i
$100$		0			0
$101$	19.0737			1.89791			0.948954	−	0.315415i	$-0.102144\pi$
$101$	19.0737			1.89791			0.948954	+	0.315415i	$0.102144\pi$
$102$	−1.11976	−	0.0616391i	−0.110873	−	0.00610318i
$103$		−	14.1165i		−	1.39094i	−0.718555	−	0.695470i	$-0.755196\pi$
$103$		−	14.1165i		−	1.39094i	0.718555	−	0.695470i	$-0.244804\pi$
$104$	−7.09991	−	7.81951i	−0.696203	−	0.766766i
$105$		0			0
$106$	5.97618	+	5.97618i	0.580457	+	0.580457i
$107$		−	18.1484i		−	1.75447i	−0.480064	−	0.877234i	$-0.659386\pi$
$107$		−	18.1484i		−	1.75447i	0.480064	−	0.877234i	$-0.340614\pi$
$108$	3.37290	+	4.72031i	0.324558	+	0.454212i
$109$	−9.49294	−	9.49294i	−0.909259	−	0.909259i	0.0869537	−	0.996212i	$-0.472287\pi$
$109$	−9.49294	−	9.49294i	−0.909259	−	0.909259i	−0.996212	+	0.0869537i	$0.972287\pi$
$110$		0			0
$111$	−4.46673	−	0.245878i	−0.423964	−	0.0233377i
$112$	1.14526	−	1.14526i	0.108217	−	0.108217i
$113$			7.29303i			0.686070i	0.939323	+	0.343035i	$0.111455\pi$
$113$			7.29303i			0.686070i	−0.939323	+	0.343035i	$0.888545\pi$
$114$	−2.80535	−	3.13219i	−0.262745	−	0.293357i
$115$		0			0
$116$	−2.16600			−0.201108
$117$	−1.70382	+	10.6816i	−0.157518	+	0.987516i
$118$	4.60935			0.424325
$119$	−1.51596	+	1.51596i	−0.138968	+	0.138968i
$120$		0			0
$121$		−	9.65448i		−	0.877680i
$122$	−9.24473	+	9.24473i	−0.836979	+	0.836979i
$123$	−14.5792	−	0.802531i	−1.31456	−	0.0723618i
$124$	1.01660	−	1.01660i	0.0912933	−	0.0912933i
$125$		0			0
$126$	−8.72313	−	0.963274i	−0.777118	−	0.0858152i
$127$			12.1706i			1.07996i	0.841677	+	0.539981i	$0.181569\pi$
$127$			12.1706i			1.07996i	−0.841677	+	0.539981i	$0.818431\pi$
$128$	3.54743	+	3.54743i	0.313551	+	0.313551i
$129$	3.23301	−	2.89565i	0.284651	−	0.254948i
$130$		0			0
$131$			9.06213i			0.791762i	0.918302	+	0.395881i	$0.129561\pi$
$131$			9.06213i			0.791762i	−0.918302	+	0.395881i	$0.870439\pi$
$132$	−2.23980	−	0.123293i	−0.194949	−	0.0107313i
$133$	−8.03836			−0.697014
$134$	7.17572			0.619888
$135$		0			0
$136$	1.42684	+	1.42684i	0.122351	+	0.122351i
$137$	13.0162	+	13.0162i	1.11205	+	1.11205i	0.992874	+	0.119172i	$0.0380240\pi$
$137$	13.0162	+	13.0162i	1.11205	+	1.11205i	0.119172	+	0.992874i	$0.461976\pi$
$138$	−7.90899	−	0.435362i	−0.673258	−	0.0370605i
$139$	5.96375			0.505839			0.252919	−	0.967487i	$-0.418609\pi$
$139$	5.96375			0.505839			0.252919	+	0.967487i	$0.418609\pi$
$140$		0			0
$141$	−1.16166	+	21.1032i	−0.0978291	+	1.77721i
$142$			7.42169i			0.622815i
$143$	−2.81143	−	3.09638i	−0.235104	−	0.258932i
$144$	−0.171358	+	1.55177i	−0.0142799	+	0.129314i
$145$		0			0
$146$			12.5390i			1.03774i
$147$	−3.46602	+	3.10435i	−0.285873	+	0.256042i
$148$	2.03907	+	2.03907i	0.167611	+	0.167611i
$149$	−3.10679	+	3.10679i	−0.254518	+	0.254518i	−0.822820	−	0.568302i	$-0.807601\pi$
$149$	−3.10679	+	3.10679i	−0.254518	+	0.254518i	0.568302	+	0.822820i	$0.307601\pi$
$150$		0			0
$151$	0.0298443	−	0.0298443i	0.00242869	−	0.00242869i	−0.705891	−	0.708320i	$-0.749453\pi$
$151$	0.0298443	−	0.0298443i	0.00242869	−	0.00242869i	0.708320	+	0.705891i	$0.249453\pi$
$152$			7.56582i			0.613669i
$153$	0.226823	−	2.05405i	0.0183376	−	0.166060i
$154$	2.39945	−	2.39945i	0.193353	−	0.193353i
$155$		0			0
$156$	5.41198	−	4.39629i	0.433305	−	0.351985i
$157$	−18.6772			−1.49060			−0.745300	−	0.666729i	$-0.767694\pi$
$157$	−18.6772			−1.49060			−0.745300	+	0.666729i	$0.767694\pi$
$158$	4.03743	−	4.03743i	0.321201	−	0.321201i
$159$	−11.6010	+	10.3905i	−0.920022	+	0.824019i
$160$		0			0
$161$	−10.7074	+	10.7074i	−0.843857	+	0.843857i
$162$	7.14282	−	4.53245i	0.561193	−	0.356103i
$163$	2.74196	−	2.74196i	0.214767	−	0.214767i	−0.591522	−	0.806289i	$-0.701473\pi$
$163$	2.74196	−	2.74196i	0.214767	−	0.214767i	0.806289	+	0.591522i	$0.201473\pi$
$164$	6.65541	+	6.65541i	0.519700	+	0.519700i
$165$		0			0
$166$		−	5.22926i		−	0.405870i
$167$	12.0831	+	12.0831i	0.935016	+	0.935016i	0.998014	−	0.0629973i	$-0.0200660\pi$
$167$	12.0831	+	12.0831i	0.935016	+	0.935016i	−0.0629973	+	0.998014i	$0.520066\pi$
$168$	10.5354	+	11.7628i	0.812822	+	0.907521i
$169$	12.9397	+	1.25114i	0.995358	+	0.0962414i
$170$		0			0
$171$	6.04715	−	4.84442i	0.462437	−	0.370462i
$172$	−2.79775			−0.213326
$173$	−24.0678			−1.82984			−0.914919	−	0.403637i	$-0.867746\pi$
$173$	−24.0678			−1.82984			−0.914919	+	0.403637i	$0.867746\pi$
$174$	−0.173593	+	3.15358i	−0.0131601	+	0.239072i
$175$		0			0
$176$	−0.426843	−	0.426843i	−0.0321745	−	0.0321745i
$177$	−0.466843	+	8.48089i	−0.0350901	+	0.637463i
$178$	−1.43315			−0.107419
$179$	−9.42733			−0.704632			−0.352316	−	0.935881i	$-0.614606\pi$
$179$	−9.42733			−0.704632			−0.352316	+	0.935881i	$0.614606\pi$
$180$		0			0
$181$			17.8034i			1.32332i	0.749806	+	0.661658i	$0.230147\pi$
$181$			17.8034i			1.32332i	−0.749806	+	0.661658i	$0.769853\pi$
$182$	−0.508149	+	10.5354i	−0.0376665	+	0.780934i
$183$	−16.0734	−	17.9460i	−1.18818	−	1.32661i
$184$	10.0779	+	10.0779i	0.742953	+	0.742953i
$185$		0			0
$186$	−1.39864	−	1.56158i	−0.102553	−	0.114501i
$187$	0.565003	+	0.565003i	0.0413171	+	0.0413171i
$188$	9.63365	−	9.63365i	0.702606	−	0.702606i
$189$	2.65585	−	15.9524i	0.193185	−	1.16037i
$190$		0			0
$191$		−	7.08269i		−	0.512486i	−0.966612	−	0.256243i	$-0.917515\pi$
$191$		−	7.08269i		−	0.512486i	0.966612	−	0.256243i	$-0.0824847\pi$
$192$	7.85461	−	7.03499i	0.566858	−	0.507707i
$193$	−4.47645	+	4.47645i	−0.322222	+	0.322222i	−0.849619	−	0.527397i	$-0.823168\pi$
$193$	−4.47645	+	4.47645i	−0.322222	+	0.322222i	0.527397	+	0.849619i	$0.323168\pi$
$194$	9.33656			0.670326
$195$		0			0
$196$	2.99939			0.214242
$197$	−17.0750	+	17.0750i	−1.21654	+	1.21654i	−0.247708	+	0.968835i	$0.579677\pi$
$197$	−17.0750	+	17.0750i	−1.21654	+	1.21654i	−0.968835	+	0.247708i	$0.920323\pi$
$198$	−0.359015	+	3.25114i	−0.0255141	+	0.231048i
$199$		−	2.76666i		−	0.196123i	−0.995180	−	0.0980616i	$-0.968736\pi$
$199$		−	2.76666i		−	0.196123i	0.995180	−	0.0980616i	$-0.0312642\pi$
$200$		0			0
$201$	−0.726769	+	13.2028i	−0.0512624	+	0.931256i
$202$	−12.6772	+	12.6772i	−0.891963	+	0.891963i
$203$	4.26937	+	4.26937i	0.299651	+	0.299651i
$204$	−0.992299	+	0.888754i	−0.0694749	+	0.0622252i
$205$		0			0
$206$	9.38240	+	9.38240i	0.653703	+	0.653703i
$207$	1.60207	−	14.5079i	0.111352	−	1.00837i
$208$	1.87416	+	0.0903955i	0.129949	+	0.00626780i
$209$			2.99592i			0.207232i
$210$		0			0
$211$	−8.53412			−0.587513			−0.293757	−	0.955880i	$-0.594906\pi$
$211$	−8.53412			−0.587513			−0.293757	+	0.955880i	$0.594906\pi$
$212$	10.0392			0.689493
$213$	−13.6554	−	0.751682i	−0.935654	−	0.0515044i
$214$	12.0621	+	12.0621i	0.824550	+	0.824550i
$215$		0			0
$216$	−15.0146	−	2.49973i	−1.02162	−	0.170085i
$217$	−4.00761			−0.272054
$218$	12.6188			0.854652
$219$	−23.0709	−	1.26997i	−1.55899	−	0.0858168i
$220$		0			0
$221$	−2.48078	−	0.119655i	−0.166875	−	0.00804884i
$222$	3.13219	−	2.80535i	0.210219	−	0.188283i
$223$	17.3123	+	17.3123i	1.15932	+	1.15932i	0.984622	+	0.174698i	$0.0558949\pi$
$223$	17.3123	+	17.3123i	1.15932	+	1.15932i	0.174698	+	0.984622i	$0.444105\pi$
$224$		−	16.7116i		−	1.11659i
$225$		0			0
$226$	−4.84724	−	4.84724i	−0.322434	−	0.322434i
$227$	−7.27653	+	7.27653i	−0.482960	+	0.482960i	−0.906076	−	0.423116i	$-0.860936\pi$
$227$	−7.27653	+	7.27653i	−0.482960	+	0.482960i	0.423116	+	0.906076i	$0.360936\pi$
$228$	−4.98713	−	0.274524i	−0.330281	−	0.0181808i
$229$	15.2314	−	15.2314i	1.00652	−	1.00652i	0.00653900	−	0.999979i	$-0.497919\pi$
$229$	15.2314	−	15.2314i	1.00652	−	1.00652i	0.999979	−	0.00653900i	$-0.00208144\pi$
$230$		0			0
$231$	4.17181	+	4.65785i	0.274485	+	0.306464i
$232$	4.01840	−	4.01840i	0.263821	−	0.263821i
$233$	10.5507			0.691198			0.345599	−	0.938382i	$-0.387676\pi$
$233$	10.5507			0.691198			0.345599	+	0.938382i	$0.387676\pi$
$234$	−5.96701	−	8.23187i	−0.390075	−	0.538134i
$235$		0			0
$236$	3.87154	−	3.87154i	0.252016	−	0.252016i
$237$	7.01969	+	7.83753i	0.455978	+	0.509102i
$238$		−	2.01514i		−	0.130622i
$239$	10.7892	−	10.7892i	0.697897	−	0.697897i	−0.266060	−	0.963957i	$-0.585722\pi$
$239$	10.7892	−	10.7892i	0.697897	−	0.697897i	0.963957	+	0.266060i	$0.0857218\pi$
$240$		0			0
$241$	4.73192	−	4.73192i	0.304810	−	0.304810i	−0.538082	−	0.842892i	$-0.680851\pi$
$241$	4.73192	−	4.73192i	0.304810	−	0.304810i	0.842892	+	0.538082i	$0.180851\pi$
$242$	6.41676	+	6.41676i	0.412485	+	0.412485i
$243$	7.61596	+	13.6014i	0.488564	+	0.872528i
$244$			15.5299i			0.994200i
$245$		0			0
$246$	10.2233	−	9.15651i	0.651814	−	0.583798i
$247$	−6.25993	−	6.89439i	−0.398310	−	0.438680i
$248$			3.77201i			0.239523i
$249$	9.62149	+	0.529629i	0.609737	+	0.0335639i
$250$		0			0
$251$	−23.8077			−1.50273			−0.751365	−	0.659887i	$-0.770604\pi$
$251$	−23.8077			−1.50273			−0.751365	+	0.659887i	$0.770604\pi$
$252$	−8.13593	+	6.51776i	−0.512515	+	0.410580i
$253$	3.99066	+	3.99066i	0.250891	+	0.250891i
$254$	−8.08904	−	8.08904i	−0.507552	−	0.507552i
$255$		0			0
$256$	−16.8912			−1.05570
$257$	27.4019			1.70929			0.854643	−	0.519217i	$-0.173776\pi$
$257$	27.4019			1.70929			0.854643	+	0.519217i	$0.173776\pi$
$258$	−0.224224	+	4.07336i	−0.0139596	+	0.253596i
$259$		−	8.03836i		−	0.499480i
$260$		0			0
$261$	−5.78478	−	0.638799i	−0.358069	−	0.0395407i
$262$	−6.02306	−	6.02306i	−0.372106	−	0.372106i
$263$			21.4135i			1.32042i	0.751083	+	0.660208i	$0.229532\pi$
$263$			21.4135i			1.32042i	−0.751083	+	0.660208i	$0.770468\pi$
$264$	4.38404	−	3.92657i	0.269819	−	0.241664i
$265$		0			0
$266$	5.34262	−	5.34262i	0.327577	−	0.327577i
$267$	0.145152	−	2.63691i	0.00888318	−	0.161376i
$268$	6.02712	−	6.02712i	0.368165	−	0.368165i
$269$		−	2.04786i		−	0.124860i	−0.998049	−	0.0624301i	$-0.980115\pi$
$269$		−	2.04786i		−	0.124860i	0.998049	−	0.0624301i	$-0.0198851\pi$
$270$		0			0
$271$	−12.9996	+	12.9996i	−0.789667	+	0.789667i	−0.981439	−	0.191772i	$-0.938576\pi$
$271$	−12.9996	+	12.9996i	−0.789667	+	0.789667i	0.191772	+	0.981439i	$0.438576\pi$
$272$	−0.358476			−0.0217358
$273$	−19.3329	−	2.00200i	−1.17008	−	0.121167i
$274$	−17.3021			−1.04526
$275$		0			0
$276$	−7.00869	+	6.27734i	−0.421874	+	0.377852i
$277$			3.90482i			0.234618i	0.993095	+	0.117309i	$0.0374268\pi$
$277$			3.90482i			0.234618i	−0.993095	+	0.117309i	$0.962573\pi$
$278$	−3.96375	+	3.96375i	−0.237730	+	0.237730i
$279$	3.01487	−	2.41523i	0.180495	−	0.144596i
$280$		0			0
$281$	−11.0540	−	11.0540i	−0.659429	−	0.659429i	0.295816	−	0.955245i	$-0.404409\pi$
$281$	−11.0540	−	11.0540i	−0.659429	−	0.659429i	−0.955245	+	0.295816i	$0.904409\pi$
$282$	−13.2540	−	14.7981i	−0.789262	−	0.881216i
$283$			4.52473i			0.268967i	0.990916	+	0.134484i	$0.0429376\pi$
$283$			4.52473i			0.268967i	−0.990916	+	0.134484i	$0.957062\pi$
$284$	6.23372	+	6.23372i	0.369903	+	0.369903i
$285$		0			0
$286$	3.92657	+	0.189389i	0.232183	+	0.0111988i
$287$		−	26.2368i		−	1.54871i
$288$	10.0715	+	12.5719i	0.593466	+	0.740806i
$289$	−16.5255			−0.972088
$290$		0			0
$291$	−0.945623	+	17.1786i	−0.0554334	+	1.00703i
$292$	10.5319	+	10.5319i	0.616334	+	0.616334i
$293$	7.37736	+	7.37736i	0.430990	+	0.430990i	0.888965	−	0.457975i	$-0.151425\pi$
$293$	7.37736	+	7.37736i	0.430990	+	0.430990i	−0.457975	+	0.888965i	$0.651425\pi$
$294$	0.240384	−	4.36694i	0.0140195	−	0.254685i
$295$		0			0
$296$	−7.56582			−0.439754
$297$	−5.94551	−	0.989844i	−0.344994	−	0.0574366i
$298$		−	4.12980i		−	0.239233i
$299$	−17.5220	−	0.845131i	−1.01332	−	0.0488752i
$300$		0			0
$301$	5.51459	+	5.51459i	0.317856	+	0.317856i
$302$			0.0396715i			0.00228284i
$303$	−22.0412	−	24.6091i	−1.26623	−	1.41376i
$304$	−0.950408	−	0.950408i	−0.0545096	−	0.0545096i
$305$		0			0
$306$	1.21445	+	1.51596i	0.0694254	+	0.0866617i
$307$	1.80981	−	1.80981i	0.103291	−	0.103291i	−0.653573	−	0.756864i	$-0.726731\pi$
$307$	1.80981	−	1.80981i	0.103291	−	0.103291i	0.756864	+	0.653573i	$0.226731\pi$
$308$		−	4.03076i		−	0.229674i
$309$	−18.2132	+	16.3127i	−1.03612	+	0.927998i
$310$		0			0
$311$	12.9697			0.735445			0.367723	−	0.929936i	$-0.380138\pi$
$311$	12.9697			0.735445			0.367723	+	0.929936i	$0.380138\pi$
$312$	−1.88431	+	18.1964i	−0.106678	+	1.03017i
$313$	−25.7774			−1.45703			−0.728513	−	0.685032i	$-0.759788\pi$
$313$	−25.7774			−1.45703			−0.728513	+	0.685032i	$0.759788\pi$
$314$	12.4136	−	12.4136i	0.700540	−	0.700540i
$315$		0			0
$316$		−	6.78234i		−	0.381537i
$317$	1.18422	−	1.18422i	0.0665126	−	0.0665126i	−0.673068	−	0.739581i	$-0.735024\pi$
$317$	1.18422	−	1.18422i	0.0665126	−	0.0665126i	0.739581	+	0.673068i	$0.235024\pi$
$318$	0.804584	−	14.6165i	0.0451188	−	0.819650i
$319$	1.59121	−	1.59121i	0.0890906	−	0.0890906i
$320$		0			0
$321$	−23.4152	+	20.9718i	−1.30691	+	1.17053i
$322$		−	14.2331i		−	0.793178i
$323$	1.25804	+	1.25804i	0.0699989	+	0.0699989i
$324$	2.19254	−	9.80644i	0.121808	−	0.544802i
$325$		0			0
$326$			3.64484i			0.201869i
$327$	−1.27805	+	23.2177i	−0.0706764	+	1.28394i
$328$	−24.6944			−1.36352
$329$	−37.9775			−2.09377
$330$		0			0
$331$	1.79656	+	1.79656i	0.0987480	+	0.0987480i	0.754755	−	0.656007i	$-0.227756\pi$
$331$	1.79656	+	1.79656i	0.0987480	+	0.0987480i	−0.656007	+	0.754755i	$0.727756\pi$
$332$	−4.39223	−	4.39223i	−0.241055	−	0.241055i
$333$	4.84442	+	6.04715i	0.265473	+	0.331382i
$334$	−16.0618			−0.878863
$335$		0			0
$336$	−2.80107	−	0.154189i	−0.152811	−	0.00841169i
$337$		−	10.2757i		−	0.559753i	−0.960036	−	0.279877i	$-0.909706\pi$
$337$		−	10.2757i		−	0.559753i	0.960036	−	0.279877i	$-0.0902936\pi$
$338$	−9.43177	+	7.76866i	−0.513021	+	0.422559i
$339$	9.40954	−	8.42766i	0.511056	−	0.457728i
$340$		0			0
$341$			1.49365i			0.0808855i
$342$	−0.799383	+	7.23898i	−0.0432257	+	0.391439i
$343$	9.49305	+	9.49305i	0.512576	+	0.512576i
$344$	5.19041	−	5.19041i	0.279848	−	0.279848i
$345$		0			0
$346$	15.9964	−	15.9964i	0.859972	−	0.859972i
$347$		−	16.8673i		−	0.905482i	−0.891642	−	0.452741i	$-0.850446\pi$
$347$		−	16.8673i		−	0.905482i	0.891642	−	0.452741i	$-0.149554\pi$
$348$	2.50298	+	2.79460i	0.134174	+	0.149806i
$349$	14.9509	−	14.9509i	0.800302	−	0.800302i	−0.182840	−	0.983143i	$-0.558529\pi$
$349$	14.9509	−	14.9509i	0.800302	−	0.800302i	0.983143	+	0.182840i	$0.0585291\pi$
$350$		0			0
$351$	15.7504	−	10.1452i	0.840695	−	0.541508i
$352$	−6.22846			−0.331978
$353$	6.54324	−	6.54324i	0.348261	−	0.348261i	−0.511200	−	0.859462i	$-0.670799\pi$
$353$	6.54324	−	6.54324i	0.348261	−	0.348261i	0.859462	+	0.511200i	$0.170799\pi$
$354$	−5.32646	−	5.94703i	−0.283098	−	0.316081i
$355$		0			0
$356$	−1.20375	+	1.20375i	−0.0637988	+	0.0637988i
$357$	3.70772	+	0.204097i	0.196233	+	0.0108019i
$358$	6.26579	−	6.26579i	0.331157	−	0.331157i
$359$	13.2705	+	13.2705i	0.700388	+	0.700388i	0.964494	−	0.264106i	$-0.0850767\pi$
$359$	13.2705	+	13.2705i	0.700388	+	0.700388i	−0.264106	+	0.964494i	$0.585077\pi$
$360$		0			0
$361$		−	12.3293i		−	0.648910i
$362$	−11.8329	−	11.8329i	−0.621921	−	0.621921i
$363$	−12.4563	+	11.1565i	−0.653787	+	0.585565i
$364$	8.42220	+	9.27582i	0.441443	+	0.486185i
$365$		0			0
$366$	22.6106	+	1.24464i	1.18188	+	0.0650581i
$367$	15.3590			0.801734			0.400867	−	0.916136i	$-0.368709\pi$
$367$	15.3590			0.801734			0.400867	+	0.916136i	$0.368709\pi$
$368$	−2.53195			−0.131987
$369$	15.8119	+	19.7376i	0.823136	+	1.02750i
$370$		0			0
$371$	−19.7880	−	19.7880i	−1.02734	−	1.02734i
$372$	−2.48639	−	0.136867i	−0.128913	−	0.00709621i
$373$	−8.55388			−0.442903			−0.221452	−	0.975171i	$-0.571080\pi$
$373$	−8.55388			−0.442903			−0.221452	+	0.975171i	$0.571080\pi$
$374$	−0.751048			−0.0388357
$375$		0			0
$376$			35.7449i			1.84340i
$377$	−0.336981	+	6.98659i	−0.0173554	+	0.359827i
$378$	8.83743	+	12.3678i	0.454548	+	0.636131i
$379$	−12.1073	−	12.1073i	−0.621909	−	0.621909i	0.324110	−	0.946019i	$-0.394935\pi$
$379$	−12.1073	−	12.1073i	−0.621909	−	0.621909i	−0.946019	+	0.324110i	$0.894935\pi$
$380$		0			0
$381$	15.7026	−	14.0640i	0.804467	−	0.720522i
$382$	4.70745	+	4.70745i	0.240854	+	0.240854i
$383$	17.3280	−	17.3280i	0.885421	−	0.885421i	−0.108658	−	0.994079i	$-0.534655\pi$
$383$	17.3280	−	17.3280i	0.885421	−	0.885421i	0.994079	+	0.108658i	$0.0346555\pi$
$384$	0.477597	−	8.67625i	0.0243723	−	0.442758i
$385$		0			0
$386$		−	5.95046i		−	0.302870i
$387$	−7.47199	−	0.825113i	−0.379823	−	0.0419429i
$388$	7.84208	−	7.84208i	0.398121	−	0.398121i
$389$	18.7474			0.950533			0.475267	−	0.879842i	$-0.342352\pi$
$389$	18.7474			0.950533			0.475267	+	0.879842i	$0.342352\pi$
$390$		0			0
$391$	3.35148			0.169492
$392$	−5.56450	+	5.56450i	−0.281050	+	0.281050i
$393$	11.6920	−	10.4720i	0.589786	−	0.528242i
$394$		−	22.6975i		−	1.14348i
$395$		0			0
$396$	2.42919	+	3.03228i	0.122071	+	0.152378i
$397$	−18.5498	+	18.5498i	−0.930988	+	0.930988i	−0.997768	−	0.0667796i	$-0.978728\pi$
$397$	−18.5498	+	18.5498i	−0.930988	+	0.930988i	0.0667796	+	0.997768i	$0.478728\pi$
$398$	1.83883	+	1.83883i	0.0921724	+	0.0921724i
$399$	9.28895	+	10.3712i	0.465029	+	0.519208i
$400$		0			0
$401$	20.2282	+	20.2282i	1.01015	+	1.01015i	0.999948	+	0.0102015i	$0.00324729\pi$
$401$	20.2282	+	20.2282i	1.01015	+	1.01015i	0.0102015	+	0.999948i	$0.496753\pi$
$402$	−8.29210	−	9.25818i	−0.413572	−	0.461756i
$403$	−3.12095	−	3.43727i	−0.155465	−	0.171223i
$404$			21.2959i			1.05951i
$405$		0			0
$406$	−5.67520			−0.281655
$407$	−2.99592			−0.148502
$408$	0.192099	−	3.48975i	0.00951030	−	0.172769i
$409$	−1.85494	−	1.85494i	−0.0917210	−	0.0917210i	0.659758	−	0.751479i	$-0.270659\pi$
$409$	−1.85494	−	1.85494i	−0.0917210	−	0.0917210i	−0.751479	+	0.659758i	$0.770659\pi$
$410$		0			0
$411$	1.75239	−	31.8348i	0.0864390	−	1.57029i
$412$	15.7612			0.776497
$413$	−15.2623			−0.751007
$414$	8.57775	+	10.7074i	0.421573	+	0.526238i
$415$		0			0
$416$	14.3333	−	13.0143i	0.702748	−	0.638076i
$417$	−6.89157	−	7.69448i	−0.337482	−	0.376801i
$418$	−1.99121	−	1.99121i	−0.0973933	−	0.0973933i
$419$			22.6906i			1.10851i	0.832347	+	0.554255i	$0.186997\pi$
$419$			22.6906i			1.10851i	−0.832347	+	0.554255i	$0.813003\pi$
$420$		0			0
$421$	0.559853	+	0.559853i	0.0272856	+	0.0272856i	0.720618	−	0.693332i	$-0.243858\pi$
$421$	0.559853	+	0.559853i	0.0272856	+	0.0272856i	−0.693332	+	0.720618i	$0.743858\pi$
$422$	5.67212	−	5.67212i	0.276115	−	0.276115i
$423$	28.5699	−	22.8876i	1.38912	−	1.11283i
$424$	−18.6248	+	18.6248i	−0.904500	+	0.904500i
$425$		0			0
$426$	9.57554	−	8.57634i	0.463936	−	0.415525i
$427$	30.6107	−	30.6107i	1.48136	−	1.48136i
$428$	20.2627			0.979437
$429$	−0.746152	+	7.20544i	−0.0360246	+	0.347882i
$430$		0			0
$431$	25.5824	−	25.5824i	1.23226	−	1.23226i	0.269165	−	0.963094i	$-0.413252\pi$
$431$	25.5824	−	25.5824i	1.23226	−	1.23226i	0.963094	−	0.269165i	$-0.0867477\pi$
$432$	2.20013	−	1.57211i	0.105854	−	0.0756380i
$433$		−	18.8544i		−	0.906087i	−0.891488	−	0.453043i	$-0.850338\pi$
$433$		−	18.8544i		−	0.906087i	0.891488	−	0.453043i	$-0.149662\pi$
$434$	2.66362	−	2.66362i	0.127858	−	0.127858i
$435$		0			0
$436$	10.5989	−	10.5989i	0.507596	−	0.507596i
$437$	8.88561	+	8.88561i	0.425056	+	0.425056i
$438$	16.1779	−	14.4898i	0.773012	−	0.692349i
$439$			18.3463i			0.875620i	0.899068	+	0.437810i	$0.144246\pi$
$439$			18.3463i			0.875620i	−0.899068	+	0.437810i	$0.855754\pi$
$440$		0			0
$441$	8.01052	+	0.884582i	0.381453	+	0.0421229i
$442$	1.72836	−	1.56930i	0.0822095	−	0.0746440i
$443$		−	7.32597i		−	0.348067i	−0.984740	−	0.174034i	$-0.944320\pi$
$443$		−	7.32597i		−	0.348067i	0.984740	−	0.174034i	$-0.0556802\pi$
$444$	0.274524	−	4.98713i	0.0130283	−	0.236679i
$445$		0			0
$446$	−23.0130			−1.08970
$447$	7.59854	+	0.418273i	0.359399	+	0.0197836i
$448$	13.3977	+	13.3977i	0.632983	+	0.632983i
$449$	20.5433	+	20.5433i	0.969498	+	0.969498i	0.999548	−	0.0300506i	$-0.00956684\pi$
$449$	20.5433	+	20.5433i	0.969498	+	0.969498i	−0.0300506	+	0.999548i	$0.509567\pi$
$450$		0			0
$451$	−9.77852			−0.460453
$452$	−8.14271			−0.383001
$453$	−0.0729928	−	0.00401799i	−0.00342950	−	0.000188782i
$454$		−	9.67255i		−	0.453955i
$455$		0			0
$456$	9.76149	−	8.74289i	0.457124	−	0.409424i
$457$	−12.2258	−	12.2258i	−0.571898	−	0.571898i	0.360760	−	0.932659i	$-0.382517\pi$
$457$	−12.2258	−	12.2258i	−0.571898	−	0.571898i	−0.932659	+	0.360760i	$0.882517\pi$
$458$			20.2468i			0.946070i
$459$	−2.91227	+	2.08096i	−0.135933	+	0.0971310i
$460$		0			0
$461$	−20.3228	+	20.3228i	−0.946525	+	0.946525i	−0.998641	−	0.0521156i	$-0.983404\pi$
$461$	−20.3228	+	20.3228i	−0.946525	+	0.946525i	0.0521156	+	0.998641i	$0.483404\pi$
$462$	−5.86855	−	0.323043i	−0.273030	−	0.0150293i
$463$	6.93836	−	6.93836i	0.322453	−	0.322453i	−0.527254	−	0.849707i	$-0.676779\pi$
$463$	6.93836	−	6.93836i	0.322453	−	0.322453i	0.849707	+	0.527254i	$0.176779\pi$
$464$			1.00957i			0.0468681i
$465$		0			0
$466$	−7.01241	+	7.01241i	−0.324844	+	0.324844i
$467$	−14.5021			−0.671075			−0.335538	−	0.942027i	$-0.608918\pi$
$467$	−14.5021			−0.671075			−0.335538	+	0.942027i	$0.608918\pi$
$468$	−11.9261	−	1.90233i	−0.551284	−	0.0879351i
$469$	−23.7599			−1.09713
$470$		0			0
$471$	21.5829	+	24.0975i	0.994488	+	1.11035i
$472$			14.3651i			0.661206i
$473$	2.05531	−	2.05531i	0.0945031	−	0.0945031i
$474$	−9.87471	−	0.543567i	−0.453560	−	0.0249669i
$475$		0			0
$476$	−1.69258	−	1.69258i	−0.0775792	−	0.0775792i
$477$	26.8118	+	2.96076i	1.22763	+	0.135564i
$478$			14.3419i			0.655984i
$479$	12.9148	+	12.9148i	0.590095	+	0.590095i	0.937657	−	0.347562i	$-0.112990\pi$
$479$	12.9148	+	12.9148i	0.590095	+	0.590095i	−0.347562	+	0.937657i	$0.612990\pi$
$480$		0			0
$481$	6.89439	−	6.25993i	0.314357	−	0.285428i
$482$			6.29005i			0.286504i
$483$	26.1879	+	1.44155i	1.19159	+	0.0655928i
$484$	10.7793			0.489968
$485$		0			0
$486$	−14.1019	−	3.97814i	−0.639675	−	0.180452i
$487$	−2.48442	−	2.48442i	−0.112580	−	0.112580i	0.648573	−	0.761153i	$-0.275366\pi$
$487$	−2.48442	−	2.48442i	−0.112580	−	0.112580i	−0.761153	+	0.648573i	$0.775366\pi$
$488$	−28.8113	−	28.8113i	−1.30422	−	1.30422i
$489$	−6.70626	−	0.369156i	−0.303268	−	0.0166938i
$490$		0			0
$491$	16.8134			0.758780			0.379390	−	0.925237i	$-0.376134\pi$
$491$	16.8134			0.758780			0.379390	+	0.925237i	$0.376134\pi$
$492$	0.896031	−	16.2777i	0.0403962	−	0.733856i
$493$		−	1.33635i		−	0.0601860i
$494$	8.74289	+	0.421693i	0.393361	+	0.0189729i
$495$		0			0
$496$	−0.473835	−	0.473835i	−0.0212758	−	0.0212758i
$497$		−	24.5744i		−	1.10231i
$498$	−6.74685	+	6.04282i	−0.302333	+	0.270785i
$499$	−11.5502	−	11.5502i	−0.517060	−	0.517060i	0.399621	−	0.916681i	$-0.369142\pi$
$499$	−11.5502	−	11.5502i	−0.517060	−	0.517060i	−0.916681	+	0.399621i	$0.869142\pi$
$500$		0			0
$501$	1.62677	−	29.5526i	0.0726786	−	1.32031i
$502$	15.8236	−	15.8236i	0.706241	−	0.706241i
$503$		−	11.9608i		−	0.533304i	−0.963793	−	0.266652i	$-0.914083\pi$
$503$		−	11.9608i		−	0.533304i	0.963793	−	0.266652i	$-0.0859174\pi$
$504$	3.00205	−	27.1857i	0.133722	−	1.21095i
$505$		0			0
$506$	−5.30471			−0.235823
$507$	−13.3385	−	18.1407i	−0.592386	−	0.805655i
$508$	−13.5885			−0.602892
$509$	−1.50135	+	1.50135i	−0.0665461	+	0.0665461i	−0.739597	−	0.673050i	$-0.764984\pi$
$509$	−1.50135	+	1.50135i	−0.0665461	+	0.0665461i	0.673050	+	0.739597i	$0.264984\pi$
$510$		0			0
$511$		−	41.5186i		−	1.83667i
$512$	4.13175	−	4.13175i	0.182599	−	0.182599i
$513$	−13.2383	−	2.20399i	−0.584484	−	0.0973084i
$514$	−18.2124	+	18.2124i	−0.803316	+	0.803316i
$515$		0			0
$516$	3.23301	+	3.60968i	0.142325	+	0.158907i
$517$			14.1543i			0.622506i
$518$	5.34262	+	5.34262i	0.234741	+	0.234741i
$519$	27.8122	+	31.0525i	1.22082	+	1.36305i
$520$		0			0
$521$			8.71097i			0.381635i	0.981626	+	0.190817i	$0.0611138\pi$
$521$			8.71097i			0.381635i	−0.981626	+	0.190817i	$0.938886\pi$
$522$	4.26937	−	3.42023i	0.186865	−	0.149699i
$523$	−5.25678			−0.229863			−0.114931	−	0.993373i	$-0.536665\pi$
$523$	−5.25678			−0.229863			−0.114931	+	0.993373i	$0.536665\pi$
$524$	−10.1179			−0.442003
$525$		0			0
$526$	−14.2323	−	14.2323i	−0.620558	−	0.620558i
$527$	0.627206	+	0.627206i	0.0273215	+	0.0273215i
$528$	−0.0574667	+	1.04397i	−0.00250092	+	0.0454328i
$529$	0.671807			0.0292090
$530$		0			0
$531$	11.4816	−	9.19800i	0.498259	−	0.399159i
$532$		−	8.97488i		−	0.389110i
$533$	22.5029	−	20.4320i	0.974709	−	0.885010i
$534$	1.65612	+	1.84907i	0.0716674	+	0.0800171i
$535$		0			0
$536$			22.3632i			0.965942i
$537$	10.8940	+	12.1632i	0.470111	+	0.524882i
$538$	1.36109	+	1.36109i	0.0586808	+	0.0586808i
$539$	−2.20344	+	2.20344i	−0.0949088	+	0.0949088i
$540$		0			0
$541$	−7.12828	+	7.12828i	−0.306469	+	0.306469i	−0.843538	−	0.537069i	$-0.819531\pi$
$541$	−7.12828	+	7.12828i	−0.306469	+	0.306469i	0.537069	+	0.843538i	$0.319531\pi$
$542$		−	17.2801i		−	0.742243i
$543$	22.9701	−	20.5732i	0.985741	−	0.882880i
$544$	−2.61543	+	2.61543i	−0.112136	+	0.112136i
$545$		0			0
$546$	14.1801	−	11.5188i	0.606850	−	0.492960i
$547$	34.7849			1.48730			0.743648	−	0.668571i	$-0.233094\pi$
$547$	34.7849			1.48730			0.743648	+	0.668571i	$0.233094\pi$
$548$	−14.5326	+	14.5326i	−0.620803	+	0.620803i
$549$	−4.58009	+	41.4760i	−0.195473	+	1.77015i
$550$		0			0
$551$	3.54298	−	3.54298i	0.150936	−	0.150936i
$552$	1.35681	−	24.6484i	0.0577496	−	1.04911i
$553$	−13.3686	+	13.3686i	−0.568490	+	0.568490i
$554$	−2.59530	−	2.59530i	−0.110264	−	0.110264i
$555$		0			0
$556$			6.65856i			0.282386i
$557$	−7.60755	−	7.60755i	−0.322342	−	0.322342i	0.527323	−	0.849665i	$-0.323196\pi$
$557$	−7.60755	−	7.60755i	−0.322342	−	0.322342i	−0.849665	+	0.527323i	$0.823196\pi$
$558$	−0.398540	+	3.60907i	−0.0168715	+	0.152784i
$559$	−0.435267	+	9.02431i	−0.0184098	+	0.381688i
$560$		0			0
$561$	0.0760674	−	1.38188i	0.00321157	−	0.0583429i
$562$	14.6939			0.619826
$563$	−21.5401			−0.907807			−0.453903	−	0.891051i	$-0.649969\pi$
$563$	−21.5401			−0.907807			−0.453903	+	0.891051i	$0.649969\pi$
$564$	−23.5619	−	1.29700i	−0.992133	−	0.0546134i
$565$		0			0
$566$	−3.00732	−	3.00732i	−0.126407	−	0.126407i
$567$	−23.6510	+	15.0076i	−0.993248	+	0.630262i
$568$	−23.1298			−0.970503
$569$	30.7745			1.29013			0.645067	−	0.764126i	$-0.276829\pi$
$569$	30.7745			1.29013			0.645067	+	0.764126i	$0.276829\pi$
$570$		0			0
$571$			25.0540i			1.04848i	0.851572	+	0.524238i	$0.175650\pi$
$571$			25.0540i			1.04848i	−0.851572	+	0.524238i	$0.824350\pi$
$572$	3.45713	−	3.13898i	0.144550	−	0.131247i
$573$	−9.13816	+	8.18460i	−0.381752	+	0.341917i
$574$	17.4380	+	17.4380i	0.727849	+	0.727849i
$575$		0			0
$576$	−18.1532	−	2.00462i	−0.756385	−	0.0835257i
$577$	13.6669	+	13.6669i	0.568959	+	0.568959i	0.931837	−	0.362878i	$-0.118206\pi$
$577$	13.6669	+	13.6669i	0.568959	+	0.568959i	−0.362878	+	0.931837i	$0.618206\pi$
$578$	10.9835	−	10.9835i	0.456854	−	0.456854i
$579$	10.9484	+	0.602673i	0.455002	+	0.0250462i
$580$		0			0
$581$			17.3149i			0.718343i
$582$	−10.7891	−	12.0461i	−0.447223	−	0.499328i
$583$	−7.37507	+	7.37507i	−0.305444	+	0.305444i
$584$	−39.0779			−1.61705
$585$		0			0
$586$	−9.80659			−0.405106
$587$	5.19514	−	5.19514i	0.214426	−	0.214426i	−0.591718	−	0.806145i	$-0.701550\pi$
$587$	5.19514	−	5.19514i	0.214426	−	0.214426i	0.806145	+	0.591718i	$0.201550\pi$
$588$	−3.46602	−	3.86984i	−0.142936	−	0.159589i
$589$			3.32575i			0.137035i
$590$		0			0
$591$	41.7618	+	2.29884i	1.71785	+	0.0945616i
$592$	0.950408	−	0.950408i	0.0390615	−	0.0390615i
$593$	4.27083	+	4.27083i	0.175382	+	0.175382i	0.789339	−	0.613957i	$-0.210423\pi$
$593$	4.27083	+	4.27083i	0.175382	+	0.175382i	−0.613957	+	0.789339i	$0.710423\pi$
$594$	4.60952	−	3.29374i	0.189131	−	0.135144i
$595$		0			0
$596$	−3.46875	−	3.46875i	−0.142086	−	0.142086i
$597$	−3.56957	+	3.19709i	−0.146093	+	0.130848i
$598$	12.2075	−	11.0841i	0.499202	−	0.453262i
$599$		−	17.0139i		−	0.695171i	−0.937648	−	0.347585i	$-0.887002\pi$
$599$		−	17.0139i		−	0.695171i	0.937648	−	0.347585i	$-0.112998\pi$
$600$		0			0
$601$	−36.2957			−1.48053			−0.740266	−	0.672314i	$-0.765300\pi$
$601$	−36.2957			−1.48053			−0.740266	+	0.672314i	$0.765300\pi$
$602$	−7.33044			−0.298767
$603$	17.8743	−	14.3192i	0.727896	−	0.583124i
$604$	0.0333213	+	0.0333213i	0.00135583	+	0.00135583i
$605$		0			0
$606$	31.0057	+	1.70675i	1.25952	+	0.0693321i
$607$	37.6421			1.52785			0.763924	−	0.645306i	$-0.223270\pi$
$607$	37.6421			1.52785			0.763924	+	0.645306i	$0.223270\pi$
$608$	−13.8683			−0.562433
$609$	0.574794	−	10.4420i	0.0232918	−	0.423130i
$610$		0			0
$611$	−29.5752	−	32.5728i	−1.19648	−	1.31775i
$612$	2.29336	+	0.253250i	0.0927035	+	0.0102370i
$613$	10.7888	+	10.7888i	0.435755	+	0.435755i	0.890581	−	0.454826i	$-0.150298\pi$
$613$	10.7888	+	10.7888i	0.435755	+	0.435755i	−0.454826	+	0.890581i	$0.650298\pi$
$614$			2.40574i			0.0970879i
$615$		0			0
$616$	7.47791	+	7.47791i	0.301294	+	0.301294i
$617$	−27.1551	+	27.1551i	−1.09322	+	1.09322i	−0.0980399	+	0.995182i	$0.531257\pi$
$617$	−27.1551	+	27.1551i	−1.09322	+	1.09322i	−0.995182	+	0.0980399i	$0.968743\pi$
$618$	1.26317	−	22.9474i	0.0508122	−	0.923078i
$619$	12.5227	−	12.5227i	0.503329	−	0.503329i	−0.409142	−	0.912471i	$-0.634172\pi$
$619$	12.5227	−	12.5227i	0.503329	−	0.503329i	0.912471	+	0.409142i	$0.134172\pi$
$620$		0			0
$621$	−20.5696	+	14.6980i	−0.825428	+	0.589811i
$622$	−8.62020	+	8.62020i	−0.345638	+	0.345638i
$623$	4.74540			0.190120
$624$	−2.04910	−	2.52251i	−0.0820298	−	0.100981i
$625$		0			0
$626$	17.1327	−	17.1327i	0.684761	−	0.684761i
$627$	3.86537	−	3.46202i	0.154368	−	0.138260i
$628$		−	20.8532i		−	0.832132i
$629$	−1.25804	+	1.25804i	−0.0501611	+	0.0501611i
$630$		0			0
$631$	−0.0650570	+	0.0650570i	−0.00258988	+	0.00258988i	−0.708401	−	0.705811i	$-0.750583\pi$
$631$	−0.0650570	+	0.0650570i	−0.00258988	+	0.00258988i	0.705811	+	0.708401i	$0.250583\pi$
$632$	12.5827	+	12.5827i	0.500513	+	0.500513i
$633$	9.86184	+	11.0108i	0.391973	+	0.437640i
$634$			1.57417i			0.0625181i
$635$		0			0
$636$	−11.6010	−	12.9526i	−0.460011	−	0.513605i
$637$	0.466637	−	9.67472i	0.0184888	−	0.383326i
$638$			2.11516i			0.0837401i
$639$	14.8101	+	18.4870i	0.585877	+	0.731333i
$640$		0			0
$641$	5.72335			0.226059			0.113029	−	0.993592i	$-0.463945\pi$
$641$	5.72335			0.226059			0.113029	+	0.993592i	$0.463945\pi$
$642$	1.62395	−	29.5014i	0.0640921	−	1.16433i
$643$	24.0577	+	24.0577i	0.948742	+	0.948742i	0.998749	−	0.0500069i	$-0.0159243\pi$
$643$	24.0577	+	24.0577i	0.948742	+	0.948742i	−0.0500069	+	0.998749i	$0.515924\pi$
$644$	−11.9548	−	11.9548i	−0.471086	−	0.471086i
$645$		0			0
$646$	−1.67228			−0.0657951
$647$	−33.6947			−1.32468			−0.662338	−	0.749205i	$-0.730436\pi$
$647$	−33.6947			−1.32468			−0.662338	+	0.749205i	$0.730436\pi$
$648$	14.1254	+	22.2606i	0.554898	+	0.874481i
$649$			5.68830i			0.223285i
$650$		0			0
$651$	4.63110	+	5.17065i	0.181507	+	0.202654i
$652$	3.06142	+	3.06142i	0.119894	+	0.119894i
$653$			6.47341i			0.253324i	0.991946	+	0.126662i	$0.0404264\pi$
$653$			6.47341i			0.253324i	−0.991946	+	0.126662i	$0.959574\pi$
$654$	−14.5820	−	16.2809i	−0.570201	−	0.636632i
$655$		0			0
$656$	3.10208	−	3.10208i	0.121116	−	0.121116i
$657$	25.0217	+	31.2339i	0.976190	+	1.21855i
$658$	25.2414	−	25.2414i	0.984011	−	0.984011i
$659$		−	0.908137i		−	0.0353760i	−0.999844	−	0.0176880i	$-0.994369\pi$
$659$		−	0.908137i		−	0.0353760i	0.999844	−	0.0176880i	$-0.00563056\pi$
$660$		0			0
$661$	−22.4502	+	22.4502i	−0.873210	+	0.873210i	−0.992821	−	0.119610i	$-0.961835\pi$
$661$	−22.4502	+	22.4502i	−0.873210	+	0.873210i	0.119610	+	0.992821i	$0.461835\pi$
$662$	−2.38814			−0.0928176
$663$	2.71236	+	3.33900i	0.105339	+	0.129676i
$664$	16.2970			0.632448
$665$		0			0
$666$	−7.23898	−	0.799383i	−0.280505	−	0.0309754i
$667$		−	9.43873i		−	0.365469i
$668$	−13.4908	+	13.4908i	−0.521976	+	0.521976i
$669$	2.33079	−	42.3423i	0.0901137	−	1.63705i
$670$		0			0
$671$	−11.4087	−	11.4087i	−0.440429	−	0.440429i
$672$	−21.5614	+	19.3115i	−0.831751	+	0.744959i
$673$			40.5282i			1.56225i	0.624377	+	0.781123i	$0.285353\pi$
$673$			40.5282i			1.56225i	−0.624377	+	0.781123i	$0.714647\pi$
$674$	6.82965	+	6.82965i	0.263068	+	0.263068i
$675$		0			0
$676$	−1.39690	+	14.4472i	−0.0537270	+	0.555662i
$677$			16.4579i			0.632527i	0.948671	+	0.316264i	$0.102428\pi$
$677$			16.4579i			0.632527i	−0.948671	+	0.316264i	$0.897572\pi$
$678$	−0.652593	+	11.8553i	−0.0250627	+	0.455301i
$679$	−30.9148			−1.18640
$680$		0			0
$681$	17.7968	+	0.979652i	0.681976	+	0.0375404i
$682$	−0.992738	−	0.992738i	−0.0380139	−	0.0380139i
$683$	−8.30681	−	8.30681i	−0.317851	−	0.317851i	0.530090	−	0.847941i	$-0.322158\pi$
$683$	−8.30681	−	8.30681i	−0.317851	−	0.317851i	−0.847941	+	0.530090i	$0.822158\pi$
$684$	5.40883	+	6.75168i	0.206812	+	0.258157i
$685$		0			0
$686$	−12.6189			−0.481793
$687$	−37.2527	−	2.05063i	−1.42128	−	0.0782364i
$688$			1.30402i			0.0497155i
$689$	1.56187	−	32.3820i	0.0595025	−	1.23366i
$690$		0			0
$691$	24.4080	+	24.4080i	0.928524	+	0.928524i	0.997611	−	0.0690863i	$-0.0220084\pi$
$691$	24.4080	+	24.4080i	0.928524	+	0.928524i	−0.0690863	+	0.997611i	$0.522008\pi$
$692$		−	26.8718i		−	1.02151i
$693$	1.18875	−	10.7650i	0.0451570	−	0.408929i
$694$	11.2107	+	11.2107i	0.425551	+	0.425551i
$695$		0			0
$696$	−9.82814	−	0.541004i	−0.372535	−	0.0205067i
$697$	−4.10615	+	4.10615i	−0.155532	+	0.155532i
$698$			19.8739i			0.752239i
$699$	−12.1921	−	13.6126i	−0.461149	−	0.514876i
$700$		0			0
$701$	25.2071			0.952058			0.476029	−	0.879430i	$-0.342076\pi$
$701$	25.2071			0.952058			0.476029	+	0.879430i	$0.342076\pi$
$702$	−3.72549	+	17.2112i	−0.140610	+	0.649597i
$703$	−6.67072			−0.251591
$704$	4.99337	−	4.99337i	0.188195	−	0.188195i
$705$		0			0
$706$			8.69780i			0.327346i
$707$	41.9761	−	41.9761i	1.57867	−	1.57867i
$708$	−9.46897	−	0.521233i	−0.355866	−	0.0195891i
$709$	3.27176	−	3.27176i	0.122873	−	0.122873i	−0.642996	−	0.765869i	$-0.722309\pi$
$709$	3.27176	−	3.27176i	0.122873	−	0.122873i	0.765869	+	0.642996i	$0.222309\pi$
$710$		0			0
$711$	2.00025	−	18.1137i	0.0750154	−	0.679318i
$712$		−	4.46644i		−	0.167387i
$713$	4.43001	+	4.43001i	0.165905	+	0.165905i
$714$	−2.59995	+	2.32865i	−0.0973006	+	0.0871474i
$715$		0			0
$716$		−	10.5257i		−	0.393363i
$717$	−26.3882	−	1.45257i	−0.985484	−	0.0542474i
$718$	−17.6402			−0.658325
$719$	−12.3985			−0.462385			−0.231192	−	0.972908i	$-0.574263\pi$
$719$	−12.3985			−0.462385			−0.231192	+	0.972908i	$0.574263\pi$
$720$		0			0
$721$	−31.0666	−	31.0666i	−1.15698	−	1.15698i
$722$	8.19454	+	8.19454i	0.304969	+	0.304969i
$723$	−11.5733	−	0.637067i	−0.430414	−	0.0236928i
$724$	−19.8776			−0.738745
$725$		0			0
$726$	0.863901	−	15.6940i	0.0320624	−	0.582460i
$727$		−	14.6064i		−	0.541722i	−0.962619	−	0.270861i	$-0.912692\pi$
$727$		−	14.6064i		−	0.541722i	0.962619	−	0.270861i	$-0.0873083\pi$
$728$	−32.8336	−	1.58365i	−1.21689	−	0.0586940i
$729$	8.74777	−	25.5436i	0.323992	−	0.946060i
$730$		0			0
$731$		−	1.72611i		−	0.0638425i
$732$	20.0368	−	17.9460i	0.740582	−	0.663303i
$733$	−24.5952	−	24.5952i	−0.908445	−	0.908445i	0.0877014	−	0.996147i	$-0.472048\pi$
$733$	−24.5952	−	24.5952i	−0.908445	−	0.908445i	−0.996147	+	0.0877014i	$0.972048\pi$
$734$	−10.2082	+	10.2082i	−0.376792	+	0.376792i
$735$		0			0
$736$	−18.4730	+	18.4730i	−0.680923	+	0.680923i
$737$			8.85540i			0.326193i
$738$	−23.6276	−	2.60914i	−0.869745	−	0.0960437i
$739$	−32.1016	+	32.1016i	−1.18088	+	1.18088i	−0.201357	+	0.979518i	$0.564535\pi$
$739$	−32.1016	+	32.1016i	−1.18088	+	1.18088i	−0.979518	+	0.201357i	$0.935465\pi$
$740$		0			0
$741$	−1.66138	+	16.0436i	−0.0610324	+	0.589377i
$742$	26.3039			0.965645
$743$	31.6922	−	31.6922i	1.16268	−	1.16268i	0.178788	−	0.983888i	$-0.442782\pi$
$743$	31.6922	−	31.6922i	1.16268	−	1.16268i	0.983888	−	0.178788i	$-0.0572177\pi$
$744$	4.86669	−	4.35886i	0.178421	−	0.159803i
$745$		0			0
$746$	5.68526	−	5.68526i	0.208152	−	0.208152i
$747$	−10.4350	−	13.0258i	−0.381798	−	0.476588i
$748$	−0.630829	+	0.630829i	−0.0230654	+	0.0230654i
$749$	−39.9396	−	39.9396i	−1.45936	−	1.45936i
$750$		0			0
$751$			8.44360i			0.308111i	0.988062	+	0.154056i	$0.0492335\pi$
$751$			8.44360i			0.308111i	−0.988062	+	0.154056i	$0.950766\pi$
$752$	−4.49023	−	4.49023i	−0.163742	−	0.163742i
$753$	27.5117	+	30.7169i	1.00258	+	1.11939i
$754$	−4.41960	−	4.86754i	−0.160952	−	0.177265i
$755$		0			0
$756$	17.8110	+	2.96528i	0.647778	+	0.107846i
$757$	−33.4040			−1.21409			−0.607045	−	0.794667i	$-0.707645\pi$
$757$	−33.4040			−1.21409			−0.607045	+	0.794667i	$0.707645\pi$
$758$	16.0940			0.584559
$759$	0.537270	−	9.76031i	0.0195017	−	0.354277i
$760$		0			0
$761$	2.45709	+	2.45709i	0.0890694	+	0.0890694i	0.750238	−	0.661168i	$-0.229939\pi$
$761$	2.45709	+	2.45709i	0.0890694	+	0.0890694i	−0.661168	+	0.750238i	$0.729939\pi$
$762$	−1.08904	+	19.7841i	−0.0394519	+	0.716701i
$763$	−41.7827			−1.51264
$764$	7.90787			0.286097
$765$		0			0
$766$			23.0338i			0.832245i
$767$	−11.8856	−	13.0902i	−0.429164	−	0.472661i
$768$	19.5191	+	21.7932i	0.704336	+	0.786396i
$769$	10.9256	+	10.9256i	0.393987	+	0.393987i	0.876106	−	0.482119i	$-0.160133\pi$
$769$	10.9256	+	10.9256i	0.393987	+	0.393987i	−0.482119	+	0.876106i	$0.660133\pi$
$770$		0			0
$771$	−31.6651	−	35.3542i	−1.14039	−	1.27325i
$772$	−4.99798	−	4.99798i	−0.179881	−	0.179881i
$773$	−28.7466	+	28.7466i	−1.03394	+	1.03394i	−0.0345388	+	0.999403i	$0.510996\pi$
$773$	−28.7466	+	28.7466i	−1.03394	+	1.03394i	−0.999403	+	0.0345388i	$0.989004\pi$
$774$	5.51459	−	4.41779i	0.198218	−	0.158794i
$775$		0			0
$776$			29.0974i			1.04454i
$777$	−10.3712	+	9.28895i	−0.372064	+	0.333239i
$778$	−12.4603	+	12.4603i	−0.446724	+	0.446724i
$779$	−21.7728			−0.780093
$780$		0			0
$781$	−9.15895			−0.327733
$782$	−2.22753	+	2.22753i	−0.0796564	+	0.0796564i
$783$	5.86058	+	8.20177i	0.209440	+	0.293107i
$784$		−	1.39801i		−	0.0499289i
$785$		0			0
$786$	−0.810896	+	14.7311i	−0.0289237	+	0.525442i
$787$	17.0605	−	17.0605i	0.608141	−	0.608141i	−0.334319	−	0.942460i	$-0.608506\pi$
$787$	17.0605	−	17.0605i	0.608141	−	0.608141i	0.942460	+	0.334319i	$0.108506\pi$
$788$	−19.0643	−	19.0643i	−0.679139	−	0.679139i
$789$	27.6280	−	24.7450i	0.983581	−	0.880946i
$790$		0			0
$791$	16.0500	+	16.0500i	0.570671	+	0.570671i
$792$	−10.1322	−	1.11887i	−0.360032	−	0.0397574i
$793$	50.0927	+	2.41610i	1.77884	+	0.0857984i
$794$		−	24.6579i		−	0.875076i
$795$		0			0
$796$	3.08899			0.109486
$797$	43.7007			1.54796			0.773979	−	0.633212i	$-0.218264\pi$
$797$	43.7007			1.54796			0.773979	+	0.633212i	$0.218264\pi$
$798$	−13.0669	−	0.719287i	−0.462564	−	0.0254625i
$799$	5.94362	+	5.94362i	0.210270	+	0.210270i
$800$		0			0
$801$	−3.56990	+	2.85987i	−0.126136	+	0.101049i
$802$	−26.8890			−0.949483
$803$	−15.4741			−0.546069
$804$	−14.7411	−	0.811442i	−0.519877	−	0.0286174i
$805$		0			0
$806$	4.35886	+	0.210239i	0.153534	+	0.00740536i
$807$	−2.64217	+	2.36646i	−0.0930087	+	0.0833034i
$808$	−39.5085	−	39.5085i	−1.38990	−	1.38990i
$809$		−	37.8152i		−	1.32951i	−0.747060	−	0.664757i	$-0.768535\pi$
$809$		−	37.8152i		−	1.32951i	0.747060	−	0.664757i	$-0.231465\pi$
$810$		0			0
$811$	−33.4507	−	33.4507i	−1.17461	−	1.17461i	−0.981098	−	0.193514i	$-0.938012\pi$
$811$	−33.4507	−	33.4507i	−1.17461	−	1.17461i	−0.193514	−	0.981098i	$-0.561988\pi$
$812$	−4.76678	+	4.76678i	−0.167281	+	0.167281i
$813$	31.7942	+	1.75016i	1.11507	+	0.0613806i
$814$	1.99121	−	1.99121i	0.0697919	−	0.0697919i
$815$		0			0
$816$	0.414247	+	0.462509i	0.0145015	+	0.0161911i
$817$	4.57634	−	4.57634i	0.160106	−	0.160106i
$818$	2.46574			0.0862126
$819$	19.7577	+	27.2570i	0.690389	+	0.952436i
$820$		0			0
$821$	9.07369	−	9.07369i	0.316674	−	0.316674i	−0.530814	−	0.847488i	$-0.678114\pi$
$821$	9.07369	−	9.07369i	0.316674	−	0.316674i	0.847488	+	0.530814i	$0.178114\pi$
$822$	19.9940	+	22.3234i	0.697369	+	0.778617i
$823$			45.6468i			1.59115i	0.605856	+	0.795574i	$0.292831\pi$
$823$			45.6468i			1.59115i	−0.605856	+	0.795574i	$0.707169\pi$
$824$	−29.2403	+	29.2403i	−1.01863	+	1.01863i
$825$		0			0
$826$	10.1439	−	10.1439i	0.352952	−	0.352952i
$827$	4.08085	+	4.08085i	0.141905	+	0.141905i	0.774491	−	0.632585i	$-0.218006\pi$
$827$	4.08085	+	4.08085i	0.141905	+	0.141905i	−0.632585	+	0.774491i	$0.718006\pi$
$828$	16.1982	+	1.78872i	0.562926	+	0.0621625i
$829$		−	33.3484i		−	1.15824i	−0.815243	−	0.579119i	$-0.803397\pi$
$829$		−	33.3484i		−	1.15824i	0.815243	−	0.579119i	$-0.196603\pi$
$830$		0			0
$831$	5.03803	−	4.51232i	0.174767	−	0.156531i
$832$	−1.05748	+	21.9246i	−0.0366616	+	0.760099i
$833$			1.85052i			0.0641166i
$834$	9.69448	+	0.533647i	0.335693	+	0.0184787i
$835$		0			0
$836$	−3.34497			−0.115688
$837$	−6.60007	−	1.09882i	−0.228132	−	0.0379807i
$838$	−15.0811	−	15.0811i	−0.520968	−	0.520968i
$839$	24.9303	+	24.9303i	0.860690	+	0.860690i	0.991418	−	0.130728i	$-0.0417315\pi$
$839$	24.9303	+	24.9303i	0.860690	+	0.860690i	−0.130728	+	0.991418i	$0.541732\pi$
$840$		0			0
$841$	25.2365			0.870223
$842$	−0.744202			−0.0256469
$843$	−1.48823	+	27.0358i	−0.0512573	+	0.931164i
$844$		−	9.52840i		−	0.327981i
$845$		0			0
$846$	−3.77670	+	34.2008i	−0.129846	+	1.17585i
$847$	−21.2469	−	21.2469i	−0.730052	−	0.730052i
$848$		−	4.67924i		−	0.160686i
$849$	5.83785	−	5.22868i	0.200355	−	0.179448i
$850$		0			0
$851$	−8.88561	+	8.88561i	−0.304595	+	0.304595i
$852$	0.839258	−	15.2464i	0.0287525	−	0.522331i
$853$	−15.5260	+	15.5260i	−0.531602	+	0.531602i	−0.921049	−	0.389447i	$-0.872666\pi$
$853$	−15.5260	+	15.5260i	−0.531602	+	0.531602i	0.389447	+	0.921049i	$0.372666\pi$
$854$			40.6903i			1.39239i
$855$		0			0
$856$	−37.5917	+	37.5917i	−1.28486	+	1.28486i
$857$	−7.92513			−0.270717			−0.135359	−	0.990797i	$-0.543219\pi$
$857$	−7.92513			−0.270717			−0.135359	+	0.990797i	$0.543219\pi$
$858$	−4.29310	−	5.28495i	−0.146564	−	0.180425i
$859$	28.7269			0.980148			0.490074	−	0.871681i	$-0.336970\pi$
$859$	28.7269			0.980148			0.490074	+	0.871681i	$0.336970\pi$
$860$		0			0
$861$	−33.8509	+	30.3186i	−1.15364	+	1.03326i
$862$			34.0061i			1.15825i
$863$	−3.03332	+	3.03332i	−0.103255	+	0.103255i	−0.756847	−	0.653592i	$-0.773261\pi$
$863$	−3.03332	+	3.03332i	−0.103255	+	0.103255i	0.653592	+	0.756847i	$0.273261\pi$
$864$	4.58204	−	27.5221i	0.155884	−	0.936320i
$865$		0			0
$866$	12.5314	+	12.5314i	0.425835	+	0.425835i
$867$	19.0965	+	21.3213i	0.648551	+	0.724111i
$868$		−	4.47452i		−	0.151875i
$869$	4.98251	+	4.98251i	0.169020	+	0.169020i
$870$		0			0
$871$	−18.5032	−	20.3786i	−0.626957	−	0.690501i
$872$			39.3265i			1.33176i
$873$	23.2568	−	18.6312i	0.787123	−	0.630570i
$874$	−11.8115			−0.399529
$875$		0			0
$876$	1.41793	−	25.7588i	0.0479075	−	0.870310i
$877$	0.402259	+	0.402259i	0.0135833	+	0.0135833i	0.713866	−	0.700283i	$-0.246943\pi$
$877$	0.402259	+	0.402259i	0.0135833	+	0.0135833i	−0.700283	+	0.713866i	$0.746943\pi$
$878$	−12.1937	−	12.1937i	−0.411517	−	0.411517i
$879$	0.993228	−	18.0435i	0.0335007	−	0.608591i
$880$		0			0
$881$	−38.6903			−1.30351			−0.651755	−	0.758430i	$-0.725967\pi$
$881$	−38.6903			−1.30351			−0.651755	+	0.758430i	$0.725967\pi$
$882$	−5.91204	+	4.73619i	−0.199069	+	0.159476i
$883$		−	23.4454i		−	0.789000i	−0.918896	−	0.394500i	$-0.870918\pi$
$883$		−	23.4454i		−	0.789000i	0.918896	−	0.394500i	$-0.129082\pi$
$884$	0.133595	−	2.76981i	0.00449329	−	0.0931587i
$885$		0			0
$886$	4.86914	+	4.86914i	0.163582	+	0.163582i
$887$			37.0936i			1.24548i	0.782429	+	0.622740i	$0.213981\pi$
$887$			37.0936i			1.24548i	−0.782429	+	0.622740i	$0.786019\pi$
$888$	8.74289	+	9.76149i	0.293392	+	0.327574i
$889$	26.7841	+	26.7841i	0.898309	+	0.898309i
$890$		0			0
$891$	5.59339	+	8.81480i	0.187386	+	0.295307i
$892$	−19.3293	+	19.3293i	−0.647194	+	0.647194i
$893$			31.5160i			1.05464i
$894$	−5.32830	+	4.77230i	−0.178205	+	0.159610i
$895$		0			0
$896$	15.6138			0.521622
$897$	19.1576	+	23.5836i	0.639653	+	0.787434i
$898$	−27.3078			−0.911273
$899$	1.76639	−	1.76639i	0.0589124	−	0.0589124i
$900$		0			0
$901$			6.19381i			0.206346i
$902$	6.49920	−	6.49920i	0.216400	−	0.216400i
$903$	0.742440	−	13.4875i	0.0247069	−	0.448837i
$904$	15.1065	−	15.1065i	0.502433	−	0.502433i
$905$		0			0
$906$	0.0511845	−	0.0458435i	0.00170049	−	0.00152305i
$907$			23.1351i			0.768189i	0.923294	+	0.384094i	$0.125486\pi$
$907$			23.1351i			0.768189i	−0.923294	+	0.384094i	$0.874514\pi$
$908$	−8.12429	−	8.12429i	−0.269614	−	0.269614i
$909$	−6.28062	+	56.8755i	−0.208315	+	1.88644i
$910$		0			0
$911$			51.2489i			1.69795i	0.528432	+	0.848976i	$0.322780\pi$
$911$			51.2489i			1.69795i	−0.528432	+	0.848976i	$0.677220\pi$
$912$	−0.127955	+	2.32450i	−0.00423702	+	0.0769717i
$913$	6.45332			0.213574
$914$	16.2515			0.537552
$915$		0			0
$916$	17.0059	+	17.0059i	0.561892	+	0.561892i
$917$	19.9433	+	19.9433i	0.658585	+	0.658585i
$918$	0.552517	−	3.31870i	0.0182358	−	0.109533i
$919$	−52.3805			−1.72787			−0.863936	−	0.503602i	$-0.832008\pi$
$919$	−52.3805			−1.72787			−0.863936	+	0.503602i	$0.832008\pi$
$920$		0			0
$921$	−4.42640	−	0.243658i	−0.145855	−	0.00802880i
$922$		−	27.0147i		−	0.889680i
$923$	21.0771	−	19.1375i	0.693761	−	0.629917i
$924$	−5.20052	+	4.65785i	−0.171085	+	0.153232i
$925$		0			0
$926$			9.22303i			0.303088i
$927$	42.0936	+	4.64830i	1.38254	+	0.152670i
$928$	7.36579	+	7.36579i	0.241794	+	0.241794i
$929$	−35.5168	+	35.5168i	−1.16527	+	1.16527i	−0.181963	+	0.983305i	$0.558245\pi$
$929$	−35.5168	+	35.5168i	−1.16527	+	1.16527i	−0.983305	+	0.181963i	$0.941755\pi$
$930$		0			0
$931$	−4.90617	+	4.90617i	−0.160793	+	0.160793i
$932$			11.7799i			0.385864i
$933$	−14.9875	−	16.7337i	−0.490669	−	0.547835i
$934$	9.63865	−	9.63865i	0.315386	−	0.315386i
$935$		0			0
$936$	25.6547	−	18.5962i	0.838549	−	0.607836i
$937$	−28.4360			−0.928962			−0.464481	−	0.885583i	$-0.653759\pi$
$937$	−28.4360			−0.928962			−0.464481	+	0.885583i	$0.653759\pi$
$938$	15.7918	−	15.7918i	0.515621	−	0.515621i
$939$	29.7878	+	33.2583i	0.972089	+	1.08534i
$940$		0			0
$941$	7.42076	−	7.42076i	0.241910	−	0.241910i	−0.575730	−	0.817640i	$-0.695282\pi$
$941$	7.42076	−	7.42076i	0.241910	−	0.241910i	0.817640	+	0.575730i	$0.195282\pi$
$942$	−30.3610	−	1.67127i	−0.989215	−	0.0544528i
$943$	−29.0021	+	29.0021i	−0.944439	+	0.944439i
$944$	−1.80452	−	1.80452i	−0.0587321	−	0.0587321i
$945$		0			0
$946$			2.73208i			0.0888275i
$947$	−0.253519	−	0.253519i	−0.00823827	−	0.00823827i	0.702976	−	0.711214i	$-0.251854\pi$
$947$	−0.253519	−	0.253519i	−0.00823827	−	0.00823827i	−0.711214	+	0.702976i	$0.751854\pi$
$948$	−8.75065	+	7.83753i	−0.284208	+	0.254551i
$949$	35.6099	−	32.3329i	1.15595	−	1.04957i
$950$		0			0
$951$	−2.89636	−	0.159434i	−0.0939209	−	0.00517001i
$952$	6.28019			0.203542
$953$	52.1909			1.69063			0.845315	−	0.534268i	$-0.179413\pi$
$953$	52.1909			1.69063			0.845315	+	0.534268i	$0.179413\pi$
$954$	−19.7880	+	15.8524i	−0.640662	+	0.513239i
$955$		0			0
$956$	12.0462	+	12.0462i	0.389603	+	0.389603i
$957$	−3.89176	−	0.214227i	−0.125803	−	0.00692499i
$958$	−17.1675			−0.554656
$959$	57.2900			1.84999
$960$		0			0
$961$		−	29.3419i		−	0.946513i
$962$	−0.421693	+	8.74289i	−0.0135959	+	0.281882i
$963$	54.1161	+	5.97591i	1.74387	+	0.192571i
$964$	5.28322	+	5.28322i	0.170161	+	0.170161i
$965$		0			0
$966$	−18.3636	+	16.4474i	−0.590841	+	0.529187i
$967$	18.9172	+	18.9172i	0.608336	+	0.608336i	0.942511	−	0.334175i	$-0.108458\pi$
$967$	18.9172	+	18.9172i	0.608336	+	0.608336i	−0.334175	+	0.942511i	$0.608458\pi$
$968$	−19.9979	+	19.9979i	−0.642756	+	0.642756i
$969$	0.169372	−	3.07689i	0.00544100	−	0.0988438i
$970$		0			0
$971$			30.9230i			0.992367i	0.868218	+	0.496183i	$0.165266\pi$
$971$			30.9230i			0.992367i	−0.868218	+	0.496183i	$0.834734\pi$
$972$	−15.1860	+	8.50327i	−0.487091	+	0.272742i
$973$	13.1246	−	13.1246i	0.420755	−	0.420755i
$974$	3.30249			0.105819
$975$		0			0
$976$	7.23846			0.231698
$977$	−14.2630	+	14.2630i	−0.456313	+	0.456313i	−0.897443	−	0.441130i	$-0.854578\pi$
$977$	−14.2630	+	14.2630i	−0.456313	+	0.456313i	0.441130	+	0.897443i	$0.354578\pi$
$978$	4.70261	−	4.21190i	0.150373	−	0.134682i
$979$		−	1.76862i		−	0.0565255i
$980$		0			0
$981$	31.4326	−	25.1809i	1.00357	−	0.803964i
$982$	−11.1749	+	11.1749i	−0.356605	+	0.356605i
$983$	−23.7893	−	23.7893i	−0.758760	−	0.758760i	0.217337	−	0.976097i	$-0.430263\pi$
$983$	−23.7893	−	23.7893i	−0.758760	−	0.758760i	−0.976097	+	0.217337i	$0.930263\pi$
$984$	28.5363	+	31.8610i	0.909704	+	1.01569i
$985$		0			0
$986$	0.888190	+	0.888190i	0.0282857	+	0.0282857i
$987$	43.8859	+	48.9989i	1.39690	+	1.55965i
$988$	7.69763	−	6.98925i	0.244894	−	0.222358i
$989$		−	12.1917i		−	0.387672i
$990$		0			0
$991$	−47.6939			−1.51505			−0.757523	−	0.652809i	$-0.773591\pi$
$991$	−47.6939			−1.51505			−0.757523	+	0.652809i	$0.773591\pi$
$992$	−6.91417			−0.219525
$993$	0.241875	−	4.39401i	0.00767566	−	0.139440i
$994$	16.3331	+	16.3331i	0.518055	+	0.518055i
$995$		0			0
$996$	−0.591334	+	10.7425i	−0.0187371	+	0.340388i
$997$	−51.2235			−1.62226			−0.811132	−	0.584863i	$-0.801148\pi$
$997$	−51.2235			−1.62226			−0.811132	+	0.584863i	$0.801148\pi$
$998$	15.3535			0.486007
$999$	2.20399	−	13.2383i	0.0697310	−	0.418840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.o.m.476.3	yes	8
3.2	odd	2		975.2.o.o.476.2	yes	8
5.2	odd	4		975.2.n.n.749.3		8
5.3	odd	4		975.2.n.p.749.2		8
5.4	even	2		975.2.o.n.476.2	yes	8
13.5	odd	4		975.2.o.o.551.2	yes	8
15.2	even	4		975.2.n.o.749.2		8
15.8	even	4		975.2.n.m.749.3		8
15.14	odd	2		975.2.o.l.476.3	✓	8
39.5	even	4	inner	975.2.o.m.551.3	yes	8
65.18	even	4		975.2.n.o.824.2		8
65.44	odd	4		975.2.o.l.551.3	yes	8
65.57	even	4		975.2.n.m.824.3		8
195.44	even	4		975.2.o.n.551.2	yes	8
195.83	odd	4		975.2.n.n.824.3		8
195.122	odd	4		975.2.n.p.824.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.n.m.749.3		8	15.8	even	4
975.2.n.m.824.3		8	65.57	even	4
975.2.n.n.749.3		8	5.2	odd	4
975.2.n.n.824.3		8	195.83	odd	4
975.2.n.o.749.2		8	15.2	even	4
975.2.n.o.824.2		8	65.18	even	4
975.2.n.p.749.2		8	5.3	odd	4
975.2.n.p.824.2		8	195.122	odd	4
975.2.o.l.476.3	✓	8	15.14	odd	2
975.2.o.l.551.3	yes	8	65.44	odd	4
975.2.o.m.476.3	yes	8	1.1	even	1	trivial
975.2.o.m.551.3	yes	8	39.5	even	4	inner
975.2.o.n.476.2	yes	8	5.4	even	2
975.2.o.n.551.2	yes	8	195.44	even	4
975.2.o.o.476.2	yes	8	3.2	odd	2
975.2.o.o.551.2	yes	8	13.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.664640 + 0.664640i) q^{2} +(-1.15558 - 1.29021i) q^{3} +1.11651i q^{4} +(1.62557 + 0.0894818i) q^{6} +(2.20073 - 2.20073i) q^{7} +(-2.07136 - 2.07136i) q^{8} +(-0.329281 + 2.98187i) q^{9} +(-0.820218 - 0.820218i) q^{11} +(1.44053 - 1.29021i) q^{12} +(3.60136 + 0.173703i) q^{13} +2.92539i q^{14} +0.520402 q^{16} -0.688845 q^{17} +(-1.76302 - 2.20073i) q^{18} +(-1.82630 - 1.82630i) q^{19} +(-5.38251 - 0.296288i) q^{21} +1.09030 q^{22} -4.86537 q^{23} +(-0.278871 + 5.06610i) q^{24} +(-2.50906 + 2.27816i) q^{26} +(4.22775 - 3.02095i) q^{27} +(2.45713 + 2.45713i) q^{28} +1.93998i q^{29} +(-0.910518 - 0.910518i) q^{31} +(3.79683 - 3.79683i) q^{32} +(-0.110427 + 2.00608i) q^{33} +(0.457834 - 0.457834i) q^{34} +(-3.32928 - 0.367644i) q^{36} +(1.82630 - 1.82630i) q^{37} +2.42766 q^{38} +(-3.93754 - 4.84724i) q^{39} +(5.96093 - 5.96093i) q^{41} +(3.77436 - 3.38051i) q^{42} +2.50580i q^{43} +(0.915778 - 0.915778i) q^{44} +(3.23372 - 3.23372i) q^{46} +(-8.62839 - 8.62839i) q^{47} +(-0.601365 - 0.671427i) q^{48} -2.68640i q^{49} +(0.796014 + 0.888754i) q^{51} +(-0.193941 + 4.02095i) q^{52} -8.99159i q^{53} +(-0.802092 + 4.81778i) q^{54} -9.11698 q^{56} +(-0.245878 + 4.46673i) q^{57} +(-1.28939 - 1.28939i) q^{58} +(-3.46755 - 3.46755i) q^{59} +13.9094 q^{61} +1.21033 q^{62} +(5.83764 + 7.28695i) q^{63} +6.08786i q^{64} +(-1.25993 - 1.40672i) q^{66} +(-5.39820 - 5.39820i) q^{67} -0.769099i q^{68} +(5.62231 + 6.27734i) q^{69} +(5.58324 - 5.58324i) q^{71} +(6.85858 - 5.49447i) q^{72} +(9.43292 - 9.43292i) q^{73} +2.42766i q^{74} +(2.03907 - 2.03907i) q^{76} -3.61015 q^{77} +(5.83872 + 0.604623i) q^{78} -6.07461 q^{79} +(-8.78315 - 1.96375i) q^{81} +7.92375i q^{82} +(-3.93390 + 3.93390i) q^{83} +(0.330807 - 6.00961i) q^{84} +(-1.66546 - 1.66546i) q^{86} +(2.50298 - 2.24180i) q^{87} +3.39793i q^{88} +(1.07814 + 1.07814i) q^{89} +(8.30790 - 7.54335i) q^{91} -5.43221i q^{92} +(-0.122585 + 2.22693i) q^{93} +11.4696 q^{94} +(-9.28624 - 0.511175i) q^{96} +(-7.02377 - 7.02377i) q^{97} +(1.78549 + 1.78549i) q^{98} +(2.71587 - 2.17570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} + 2 q^{3} + 4 q^{6} + 14 q^{7} + 12 q^{8} - 4 q^{9} + 4 q^{11} + 14 q^{12} - 2 q^{13} - 8 q^{16} - 28 q^{17} + 30 q^{18} - 2 q^{19} + 8 q^{21} + 24 q^{22} - 36 q^{23} - 18 q^{24} - 32 q^{26}+ \cdots + 28 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 + 2 * q^3 + 4 * q^6 + 14 * q^7 + 12 * q^8 - 4 * q^9 + 4 * q^11 + 14 * q^12 - 2 * q^13 - 8 * q^16 - 28 * q^17 + 30 * q^18 - 2 * q^19 + 8 * q^21 + 24 * q^22 - 36 * q^23 - 18 * q^24 - 32 * q^26 + 14 * q^27 - 24 * q^28 - 12 * q^31 + 18 * q^32 + 18 * q^33 + 10 * q^34 - 28 * q^36 + 2 * q^37 - 24 * q^38 - 20 * q^39 + 38 * q^41 - 38 * q^42 - 10 * q^44 + 34 * q^46 - 22 * q^47 + 26 * q^48 - 26 * q^51 + 50 * q^52 + 28 * q^54 + 76 * q^56 - 6 * q^57 + 18 * q^58 - 14 * q^59 - 8 * q^61 + 16 * q^62 + 10 * q^63 + 18 * q^66 - 10 * q^71 + 4 * q^72 + 10 * q^73 + 26 * q^76 + 12 * q^77 + 6 * q^78 - 56 * q^79 + 8 * q^81 - 38 * q^83 + 74 * q^84 - 34 * q^86 + 34 * q^87 + 28 * q^89 + 8 * q^91 + 22 * q^93 + 20 * q^94 + 20 * q^96 - 4 * q^97 + 26 * q^98 + 28 * q^99

Introduction

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