LMFDB - Embedded newform 675.2.r.a.631.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			631.1
Character	$\chi$	$=$	675.631
Dual form			675.2.r.a.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.77417 + 1.97042i) q^{2} +(-0.525803 - 5.00268i) q^{4} +(1.61775 - 1.54366i) q^{5} +(1.02644 + 1.77785i) q^{7} +(6.50010 + 4.72260i) q^{8} +O(q^{10})$	\(q+(-1.77417 + 1.97042i) q^{2} +(-0.525803 - 5.00268i) q^{4} +(1.61775 - 1.54366i) q^{5} +(1.02644 + 1.77785i) q^{7} +(6.50010 + 4.72260i) q^{8} +(0.171493 + 5.92636i) q^{10} +(3.84053 - 4.26534i) q^{11} +(-1.39743 - 1.55200i) q^{13} +(-5.32421 - 1.13169i) q^{14} +(-10.9972 + 2.33752i) q^{16} +(0.0247468 + 0.0179796i) q^{17} +(-5.30003 - 3.85070i) q^{19} +(-8.57307 - 7.28142i) q^{20} +(1.59074 + 15.1349i) q^{22} +(-3.94065 - 0.837611i) q^{23} +(0.234221 - 4.99451i) q^{25} +5.53738 q^{26} +(8.35433 - 6.06978i) q^{28} +(-2.99836 - 1.33495i) q^{29} +(2.93669 - 1.30750i) q^{31} +(6.87040 - 11.8999i) q^{32} +(-0.0793325 + 0.0168626i) q^{34} +(4.40493 + 1.29164i) q^{35} +(1.37908 - 4.24438i) q^{37} +(16.9906 - 3.61147i) q^{38} +(17.8056 - 2.39397i) q^{40} +(-1.29130 - 1.43413i) q^{41} +(0.309512 + 0.536091i) q^{43} +(-23.3575 - 16.9702i) q^{44} +(8.64184 - 6.27867i) q^{46} +(2.37044 + 1.05539i) q^{47} +(1.39282 - 2.41244i) q^{49} +(9.42573 + 9.32264i) q^{50} +(-7.02940 + 7.80695i) q^{52} +(2.83942 - 2.06296i) q^{53} +(-0.371228 - 12.8287i) q^{55} +(-1.72410 + 16.4037i) q^{56} +(7.95002 - 3.53958i) q^{58} +(5.43616 + 6.03746i) q^{59} +(-5.51851 + 6.12893i) q^{61} +(-2.63388 + 8.10625i) q^{62} +(4.31002 + 13.2649i) q^{64} +(-4.65646 - 0.353593i) q^{65} +(-0.642929 + 0.286250i) q^{67} +(0.0769343 - 0.133254i) q^{68} +(-10.3602 + 6.38797i) q^{70} +(-3.81216 + 2.76970i) q^{71} +(2.55263 + 7.85620i) q^{73} +(5.91647 + 10.2476i) q^{74} +(-16.4770 + 28.5391i) q^{76} +(11.5252 + 2.44977i) q^{77} +(10.9723 + 4.88520i) q^{79} +(-14.1823 + 20.7574i) q^{80} +5.11682 q^{82} +(1.37616 - 13.0933i) q^{83} +(0.0677885 - 0.00911420i) q^{85} +(-1.60545 - 0.341249i) q^{86} +(45.1073 - 9.58785i) q^{88} +(-1.99904 - 6.15242i) q^{89} +(1.32485 - 4.07747i) q^{91} +(-2.11830 + 20.1543i) q^{92} +(-6.28513 + 2.79832i) q^{94} +(-14.5183 + 1.95199i) q^{95} +(-9.33612 - 4.15671i) q^{97} +(2.28241 + 7.02454i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−1.77417	+	1.97042i	−1.25453	+	1.39330i	−0.368527	+	0.929617i	$0.620138\pi$
$2$	−1.77417	+	1.97042i	−1.25453	+	1.39330i	−0.886003	+	0.463679i	$0.846529\pi$
$3$		0			0
$3$		0			0
$4$	−0.525803	−	5.00268i	−0.262902	−	2.50134i
$5$	1.61775	−	1.54366i	0.723479	−	0.690346i
$5$	1.61775	−	1.54366i	0.723479	−	0.690346i
$6$		0			0
$7$	1.02644	+	1.77785i	0.387959	+	0.671966i	0.992175	−	0.124855i	$-0.0398467\pi$
$7$	1.02644	+	1.77785i	0.387959	+	0.671966i	−0.604215	+	0.796821i	$0.706513\pi$
$8$	6.50010	+	4.72260i	2.29813	+	1.66969i
$9$		0			0
$10$	0.171493	+	5.92636i	0.0542308	+	1.87408i
$11$	3.84053	−	4.26534i	1.15796	−	1.28605i	0.206445	−	0.978458i	$-0.433811\pi$
$11$	3.84053	−	4.26534i	1.15796	−	1.28605i	0.951519	−	0.307590i	$-0.0995226\pi$
$12$		0			0
$13$	−1.39743	−	1.55200i	−0.387577	−	0.430448i	0.517508	−	0.855678i	$-0.326860\pi$
$13$	−1.39743	−	1.55200i	−0.387577	−	0.430448i	−0.905085	+	0.425230i	$0.860193\pi$
$14$	−5.32421	−	1.13169i	−1.42295	−	0.302458i
$15$		0			0
$16$	−10.9972	+	2.33752i	−2.74929	+	0.584379i
$17$	0.0247468	+	0.0179796i	0.00600198	+	0.00436070i	0.590782	−	0.806831i	$-0.298819\pi$
$17$	0.0247468	+	0.0179796i	0.00600198	+	0.00436070i	−0.584780	+	0.811192i	$0.698819\pi$
$18$		0			0
$19$	−5.30003	−	3.85070i	−1.21591	−	0.883410i	−0.220156	−	0.975465i	$-0.570657\pi$
$19$	−5.30003	−	3.85070i	−1.21591	−	0.883410i	−0.995754	+	0.0920546i	$0.970657\pi$
$20$	−8.57307	−	7.28142i	−1.91700	−	1.62818i
$21$		0			0
$22$	1.59074	+	15.1349i	0.339147	+	3.22677i
$23$	−3.94065	−	0.837611i	−0.821683	−	0.174654i	−0.222158	−	0.975011i	$-0.571310\pi$
$23$	−3.94065	−	0.837611i	−0.821683	−	0.174654i	−0.599524	+	0.800357i	$0.704644\pi$
$24$		0			0
$25$	0.234221	−	4.99451i	0.0468442	−	0.998902i
$26$	5.53738			1.08597
$27$		0			0
$28$	8.35433	−	6.06978i	1.57882	−	1.14708i
$29$	−2.99836	−	1.33495i	−0.556781	−	0.247895i	0.109000	−	0.994042i	$-0.465235\pi$
$29$	−2.99836	−	1.33495i	−0.556781	−	0.247895i	−0.665781	+	0.746147i	$0.731902\pi$
$30$		0			0
$31$	2.93669	−	1.30750i	0.527446	−	0.234834i	−0.125697	−	0.992069i	$-0.540117\pi$
$31$	2.93669	−	1.30750i	0.527446	−	0.234834i	0.653143	+	0.757235i	$0.273450\pi$
$32$	6.87040	−	11.8999i	1.21453	−	2.10362i
$33$		0			0
$34$	−0.0793325	+	0.0168626i	−0.0136054	+	0.00289192i
$35$	4.40493	+	1.29164i	0.744569	+	0.218327i
$36$		0			0
$37$	1.37908	−	4.24438i	0.226720	−	0.697771i	−0.771393	−	0.636359i	$-0.780440\pi$
$37$	1.37908	−	4.24438i	0.226720	−	0.697771i	0.998112	−	0.0614120i	$-0.0195604\pi$
$38$	16.9906	−	3.61147i	2.75625	−	0.585858i
$39$		0			0
$40$	17.8056	−	2.39397i	2.81531	−	0.378520i
$41$	−1.29130	−	1.43413i	−0.201667	−	0.223974i	0.633825	−	0.773476i	$-0.281484\pi$
$41$	−1.29130	−	1.43413i	−0.201667	−	0.223974i	−0.835492	+	0.549503i	$0.814817\pi$
$42$		0			0
$43$	0.309512	+	0.536091i	0.0472002	+	0.0817531i	0.888660	−	0.458566i	$-0.151637\pi$
$43$	0.309512	+	0.536091i	0.0472002	+	0.0817531i	−0.841460	+	0.540319i	$0.818303\pi$
$44$	−23.3575	−	16.9702i	−3.52128	−	2.55836i
$45$		0			0
$46$	8.64184	−	6.27867i	1.27417	−	0.925739i
$47$	2.37044	+	1.05539i	0.345764	+	0.153944i	0.572269	−	0.820066i	$-0.306063\pi$
$47$	2.37044	+	1.05539i	0.345764	+	0.153944i	−0.226505	+	0.974010i	$0.572730\pi$
$48$		0			0
$49$	1.39282	−	2.41244i	0.198975	−	0.344635i
$50$	9.42573	+	9.32264i	1.33300	+	1.31842i
$51$		0			0
$52$	−7.02940	+	7.80695i	−0.974803	+	1.08263i
$53$	2.83942	−	2.06296i	0.390024	−	0.283369i	−0.375441	−	0.926846i	$-0.622509\pi$
$53$	2.83942	−	2.06296i	0.390024	−	0.283369i	0.765465	+	0.643477i	$0.222509\pi$
$54$		0			0
$55$	−0.371228	−	12.8287i	−0.0500564	−	1.72983i
$56$	−1.72410	+	16.4037i	−0.230392	+	2.19204i
$57$		0			0
$58$	7.95002	−	3.53958i	1.04389	−	0.464769i
$59$	5.43616	+	6.03746i	0.707727	+	0.786011i	0.984586	−	0.174900i	$-0.0559601\pi$
$59$	5.43616	+	6.03746i	0.707727	+	0.786011i	−0.276859	+	0.960911i	$0.589293\pi$
$60$		0			0
$61$	−5.51851	+	6.12893i	−0.706573	+	0.784729i	−0.984408	−	0.175900i	$-0.943716\pi$
$61$	−5.51851	+	6.12893i	−0.706573	+	0.784729i	0.277835	+	0.960629i	$0.410383\pi$
$62$	−2.63388	+	8.10625i	−0.334503	+	1.02949i
$63$		0			0
$64$	4.31002	+	13.2649i	0.538753	+	1.65811i
$65$	−4.65646	−	0.353593i	−0.577562	−	0.0438578i
$66$		0			0
$67$	−0.642929	+	0.286250i	−0.0785463	+	0.0349710i	−0.445634	−	0.895215i	$-0.647022\pi$
$67$	−0.642929	+	0.286250i	−0.0785463	+	0.0349710i	0.367087	+	0.930186i	$0.380355\pi$
$68$	0.0769343	−	0.133254i	0.00932966	−	0.0161594i
$69$		0			0
$70$	−10.3602	+	6.38797i	−1.23828	+	0.763509i
$71$	−3.81216	+	2.76970i	−0.452421	+	0.328703i	−0.790551	−	0.612397i	$-0.790206\pi$
$71$	−3.81216	+	2.76970i	−0.452421	+	0.328703i	0.338130	+	0.941099i	$0.390206\pi$
$72$		0			0
$73$	2.55263	+	7.85620i	0.298763	+	0.919499i	0.981931	+	0.189237i	$0.0606016\pi$
$73$	2.55263	+	7.85620i	0.298763	+	0.919499i	−0.683168	+	0.730261i	$0.739398\pi$
$74$	5.91647	+	10.2476i	0.687776	+	1.19126i
$75$		0			0
$76$	−16.4770	+	28.5391i	−1.89005	+	3.27366i
$77$	11.5252	+	2.44977i	1.31342	+	0.279177i
$78$		0			0
$79$	10.9723	+	4.88520i	1.23448	+	0.549628i	0.917095	−	0.398668i	$-0.130527\pi$
$79$	10.9723	+	4.88520i	1.23448	+	0.549628i	0.317389	+	0.948295i	$0.397194\pi$
$80$	−14.1823	+	20.7574i	−1.58563	+	2.32075i
$81$		0			0
$82$	5.11682			0.565058
$83$	1.37616	−	13.0933i	0.151053	−	1.43717i	−0.612011	−	0.790849i	$-0.709639\pi$
$83$	1.37616	−	13.0933i	0.151053	−	1.43717i	0.763064	−	0.646323i	$-0.223694\pi$
$84$		0			0
$85$	0.0677885	−	0.00911420i	0.00735270	−	0.000988573i
$86$	−1.60545	−	0.341249i	−0.173120	−	0.0367979i
$87$		0			0
$88$	45.1073	−	9.58785i	4.80845	−	1.02207i
$89$	−1.99904	−	6.15242i	−0.211898	−	0.652155i	−0.999359	−	0.0357910i	$-0.988605\pi$
$89$	−1.99904	−	6.15242i	−0.211898	−	0.652155i	0.787461	−	0.616364i	$-0.211395\pi$
$90$		0			0
$91$	1.32485	−	4.07747i	0.138882	−	0.427435i
$92$	−2.11830	+	20.1543i	−0.220848	+	2.10123i
$93$		0			0
$94$	−6.28513	+	2.79832i	−0.648262	+	0.288625i
$95$	−14.5183	+	1.95199i	−1.48954	+	0.200270i
$96$		0			0
$97$	−9.33612	−	4.15671i	−0.947940	−	0.422050i	−0.126258	−	0.991997i	$-0.540297\pi$
$97$	−9.33612	−	4.15671i	−0.947940	−	0.422050i	−0.821681	+	0.569947i	$0.806964\pi$
$98$	2.28241	+	7.02454i	0.230558	+	0.709585i
$99$		0			0
$100$	−25.1091	+	1.45440i	−2.51091	+	0.145440i
$101$	1.06922	+	1.85194i	0.106391	+	0.184275i	0.914306	−	0.405025i	$-0.132737\pi$
$101$	1.06922	+	1.85194i	0.106391	+	0.184275i	−0.807915	+	0.589300i	$0.799404\pi$
$102$		0			0
$103$	0.126240	+	1.20110i	0.0124388	+	0.118348i	0.998979	−	0.0451695i	$-0.0143828\pi$
$103$	0.126240	+	1.20110i	0.0124388	+	0.118348i	−0.986541	+	0.163517i	$0.947716\pi$
$104$	−1.75394	−	16.6877i	−0.171988	−	1.63636i
$105$		0			0
$106$	−0.972728	+	9.25489i	−0.0944797	+	0.898914i
$107$	11.1600			1.07887			0.539437	−	0.842026i	$-0.318637\pi$
$107$	11.1600			1.07887			0.539437	+	0.842026i	$0.318637\pi$
$108$		0			0
$109$	2.86190	−	8.80802i	0.274120	−	0.843655i	−0.715331	−	0.698786i	$-0.753724\pi$
$109$	2.86190	−	8.80802i	0.274120	−	0.843655i	0.989451	−	0.144869i	$-0.0462761\pi$
$110$	25.9366	+	22.0289i	2.47296	+	2.10037i
$111$		0			0
$112$	−15.4437	−	17.1520i	−1.45929	−	1.62071i
$113$	5.84918	+	6.49617i	0.550244	+	0.611108i	0.952544	−	0.304400i	$-0.0984559\pi$
$113$	5.84918	+	6.49617i	0.550244	+	0.611108i	−0.402300	+	0.915508i	$0.631789\pi$
$114$		0			0
$115$	−7.66797	+	4.72799i	−0.715042	+	0.440887i
$116$	−5.10181	+	15.7018i	−0.473691	+	1.45787i
$117$		0			0
$118$	−21.5410			−1.98301
$119$	−0.00656389	+	0.0624513i	−0.000601711	+	0.00572490i
$120$		0			0
$121$	−2.29365	−	21.8226i	−0.208513	−	1.98387i
$122$	−2.28576	−	21.7476i	−0.206943	−	1.96893i
$123$		0			0
$124$	−8.08513	−	14.0039i	−0.726066	−	1.25758i
$125$	−7.33092	−	8.44142i	−0.655698	−	0.755024i
$126$		0			0
$127$	−0.411180	−	1.26548i	−0.0364863	−	0.112293i	0.931155	−	0.364625i	$-0.118803\pi$
$127$	−0.411180	−	1.26548i	−0.0364863	−	0.112293i	−0.967641	+	0.252331i	$0.918803\pi$
$128$	−8.67841	−	3.86388i	−0.767070	−	0.341522i
$129$		0			0
$130$	8.95808	−	8.54783i	0.785676	−	0.749694i
$131$	15.5424	−	6.91991i	1.35794	−	0.604596i	0.406849	−	0.913495i	$-0.366627\pi$
$131$	15.5424	−	6.91991i	1.35794	−	0.604596i	0.951095	+	0.308900i	$0.0999608\pi$
$132$		0			0
$133$	1.40579	−	13.3752i	0.121897	−	1.15978i
$134$	0.576634	−	1.77470i	0.0498136	−	0.153310i
$135$		0			0
$136$	0.0759462	+	0.233738i	0.00651233	+	0.0200429i
$137$	4.86487	−	1.03406i	0.415634	−	0.0883456i	0.00465171	−	0.999989i	$-0.498519\pi$
$137$	4.86487	−	1.03406i	0.415634	−	0.0883456i	0.410982	+	0.911644i	$0.365186\pi$
$138$		0			0
$139$	12.9544	+	2.75355i	1.09878	+	0.233553i	0.721409	−	0.692510i	$-0.243495\pi$
$139$	12.9544	+	2.75355i	1.09878	+	0.233553i	0.377370	+	0.926062i	$0.376828\pi$
$140$	4.14553	−	22.7156i	0.350361	−	1.91982i
$141$		0			0
$142$	1.30597	−	12.4255i	0.109595	−	1.04272i
$143$	−11.9867			−1.00238
$144$		0			0
$145$	−6.91131	+	2.46883i	−0.573953	+	0.205025i
$146$	−20.0088	−	8.90850i	−1.65594	−	0.737273i
$147$		0			0
$148$	−21.9584	−	4.66740i	−1.80497	−	0.383658i
$149$	−7.12203	+	12.3357i	−0.583459	+	1.01058i	0.411606	+	0.911362i	$0.364968\pi$
$149$	−7.12203	+	12.3357i	−0.583459	+	1.01058i	−0.995066	+	0.0992193i	$0.968365\pi$
$150$		0			0
$151$	9.46978	+	16.4021i	0.770640	+	1.33479i	0.937213	+	0.348758i	$0.113397\pi$
$151$	9.46978	+	16.4021i	0.770640	+	1.33479i	−0.166573	+	0.986029i	$0.553270\pi$
$152$	−16.2654	−	50.0598i	−1.31930	−	4.06038i
$153$		0			0
$154$	−25.2748	+	18.3632i	−2.03670	+	1.47975i
$155$	2.73249	−	6.64847i	0.219479	−	0.534018i
$156$		0			0
$157$	4.74777	−	8.22338i	0.378913	−	0.656297i	−0.611991	−	0.790865i	$-0.709631\pi$
$157$	4.74777	−	8.22338i	0.378913	−	0.656297i	0.990904	+	0.134567i	$0.0429645\pi$
$158$	−29.0927	+	12.9529i	−2.31449	+	1.03048i
$159$		0			0
$160$	−7.25481	−	29.8566i	−0.573543	−	2.36037i
$161$	−2.55571	−	7.86566i	−0.201418	−	0.619901i
$162$		0			0
$163$	−2.92027	+	8.98768i	−0.228733	+	0.703969i	0.769158	+	0.639059i	$0.220676\pi$
$163$	−2.92027	+	8.98768i	−0.228733	+	0.703969i	−0.997891	+	0.0649101i	$0.979324\pi$
$164$	−6.49553	+	7.21402i	−0.507216	+	0.563320i
$165$		0			0
$166$	23.3577	+	25.9413i	1.81291	+	2.01344i
$167$	13.5729	−	6.04304i	1.05030	−	0.467624i	0.192335	−	0.981329i	$-0.438394\pi$
$167$	13.5729	−	6.04304i	1.05030	−	0.467624i	0.857967	+	0.513705i	$0.171727\pi$
$168$		0			0
$169$	0.902967	−	8.59116i	0.0694590	−	0.660858i
$170$	−0.102310	+	0.149742i	−0.00784680	+	0.0114847i
$171$		0			0
$172$	2.51915	−	1.83027i	0.192083	−	0.139557i
$173$	−4.44318	+	4.93465i	−0.337809	+	0.375175i	−0.887984	−	0.459875i	$-0.847894\pi$
$173$	−4.44318	+	4.93465i	−0.337809	+	0.375175i	0.550175	+	0.835049i	$0.314561\pi$
$174$		0			0
$175$	9.11992	−	4.71018i	0.689401	−	0.356056i
$176$	−32.2646	+	55.8839i	−2.43203	+	4.21241i
$177$		0			0
$178$	15.6695	+	6.97651i	1.17448	+	0.522911i
$179$	3.95088	−	2.87048i	0.295303	−	0.214550i	−0.430262	−	0.902704i	$-0.641579\pi$
$179$	3.95088	−	2.87048i	0.295303	−	0.214550i	0.725564	+	0.688154i	$0.241579\pi$
$180$		0			0
$181$	8.58407	+	6.23669i	0.638049	+	0.463570i	0.859179	−	0.511675i	$-0.170975\pi$
$181$	8.58407	+	6.23669i	0.638049	+	0.463570i	−0.221131	+	0.975244i	$0.570975\pi$
$182$	5.68381	+	9.84464i	0.421312	+	0.729734i
$183$		0			0
$184$	−21.6589	−	24.0547i	−1.59672	−	1.77333i
$185$	−4.32087	−	8.99517i	−0.317677	−	0.661338i
$186$		0			0
$187$	0.171730	−	0.0365023i	0.0125581	−	0.00266932i
$188$	4.03339	−	12.4135i	0.294165	−	0.905347i
$189$		0			0
$190$	21.9117	−	32.0703i	1.58964	−	2.32662i
$191$	−23.3711	+	4.96768i	−1.69107	+	0.359448i	−0.950066	−	0.312050i	$-0.898984\pi$
$191$	−23.3711	+	4.96768i	−1.69107	+	0.359448i	−0.741006	+	0.671498i	$0.765651\pi$
$192$		0			0
$193$	−12.8260	+	22.2154i	−0.923239	+	1.59910i	−0.128870	+	0.991662i	$0.541135\pi$
$193$	−12.8260	+	22.2154i	−0.923239	+	1.59910i	−0.794369	+	0.607435i	$0.792198\pi$
$194$	24.7544	−	11.0213i	1.77726	−	0.791287i
$195$		0			0
$196$	−12.8010	−	5.69939i	−0.914360	−	0.407099i
$197$	−12.4362	+	9.03540i	−0.886039	+	0.643745i	−0.934842	−	0.355063i	$-0.884459\pi$
$197$	−12.4362	+	9.03540i	−0.886039	+	0.643745i	0.0488029	+	0.998808i	$0.484459\pi$
$198$		0			0
$199$	−3.19201			−0.226275			−0.113138	−	0.993579i	$-0.536090\pi$
$199$	−3.19201			−0.226275			−0.113138	+	0.993579i	$0.536090\pi$
$200$	25.1095	−	31.3587i	1.77551	−	2.21739i
$201$		0			0
$202$	−5.54607	−	1.17885i	−0.390220	−	0.0829439i
$203$	−0.704293	−	6.70090i	−0.0494317	−	0.470311i
$204$		0			0
$205$	−4.30281	−	0.326738i	−0.300521	−	0.0228204i
$206$	−2.59063	−	1.88221i	−0.180498	−	0.131140i
$207$		0			0
$208$	18.9956	+	13.8011i	1.31711	+	0.956934i
$209$	−36.7794	+	7.81771i	−2.54409	+	0.540762i
$210$		0			0
$211$	26.0148	+	5.52961i	1.79093	+	0.380674i	0.979126	−	0.203254i	$-0.0651517\pi$
$211$	26.0148	+	5.52961i	1.79093	+	0.380674i	0.811805	+	0.583928i	$0.198485\pi$
$212$	−11.8133	−	13.1200i	−0.811341	−	0.901085i
$213$		0			0
$214$	−19.7997	+	21.9898i	−1.35348	+	1.50319i
$215$	1.32826	+	0.389478i	0.0905863	+	0.0265622i
$216$		0			0
$217$	5.33890	+	3.87893i	0.362428	+	0.263319i
$218$	12.2780	+	21.2661i	0.831570	+	1.44032i
$219$		0			0
$220$	−63.9829	+	8.60252i	−4.31372	+	0.579982i
$221$	−0.00667752	−	0.0635323i	−0.000449178	−	0.00427365i
$222$		0			0
$223$	−11.4373	+	12.7024i	−0.765898	+	0.850616i	−0.992356	−	0.123405i	$-0.960619\pi$
$223$	−11.4373	+	12.7024i	−0.765898	+	0.850616i	0.226458	+	0.974021i	$0.427285\pi$
$224$	28.2083			1.88475
$225$		0			0
$226$	−23.1776			−1.54175
$227$	8.24685	−	9.15906i	0.547363	−	0.607908i	−0.404460	−	0.914556i	$-0.632541\pi$
$227$	8.24685	−	9.15906i	0.547363	−	0.607908i	0.951823	+	0.306648i	$0.0992073\pi$
$228$		0			0
$229$	−2.14725	−	20.4298i	−0.141895	−	1.35004i	−0.801306	−	0.598254i	$-0.795861\pi$
$229$	−2.14725	−	20.4298i	−0.141895	−	1.35004i	0.659412	−	0.751782i	$-0.270805\pi$
$230$	4.28820	−	23.4974i	0.282755	−	1.54937i
$231$		0			0
$232$	−13.1852	−	22.8374i	−0.865648	−	1.49935i
$233$	6.68678	+	4.85823i	0.438065	+	0.318273i	0.784866	−	0.619666i	$-0.212732\pi$
$233$	6.68678	+	4.85823i	0.438065	+	0.318273i	−0.346800	+	0.937939i	$0.612732\pi$
$234$		0			0
$235$	5.46394	−	1.95181i	0.356428	−	0.127322i
$236$	27.3452	−	30.3699i	1.78002	−	1.97691i
$237$		0			0
$238$	−0.111410	−	0.123733i	−0.00722162	−	0.00802042i
$239$	−17.6630	−	3.75440i	−1.14253	−	0.242852i	−0.402495	−	0.915422i	$-0.631857\pi$
$239$	−17.6630	−	3.75440i	−1.14253	−	0.242852i	−0.740033	+	0.672571i	$0.765190\pi$
$240$		0			0
$241$	−12.6786	+	2.69491i	−0.816698	+	0.173595i	−0.597276	−	0.802035i	$-0.703750\pi$
$241$	−12.6786	+	2.69491i	−0.816698	+	0.173595i	−0.219422	+	0.975630i	$0.570417\pi$
$242$	47.0690	+	34.1976i	3.02571	+	2.19831i
$243$		0			0
$244$	33.5627	+	24.3848i	2.14863	+	1.56107i
$245$	−1.47075	−	6.05277i	−0.0939630	−	0.386698i
$246$		0			0
$247$	1.43013	+	13.6067i	0.0909967	+	0.865776i
$248$	25.2636	+	5.36994i	1.60424	+	0.340992i
$249$		0			0
$250$	29.6395	+	0.531557i	1.87456	+	0.0336186i
$251$	8.02701			0.506661			0.253330	−	0.967380i	$-0.418474\pi$
$251$	8.02701			0.506661			0.253330	+	0.967380i	$0.418474\pi$
$252$		0			0
$253$	−18.7069	+	13.5914i	−1.17609	+	0.854481i
$254$	3.22303	+	1.43499i	0.202231	+	0.0900391i
$255$		0			0
$256$	−2.47295	+	1.10103i	−0.154559	+	0.0688143i
$257$	−6.92454	+	11.9937i	−0.431941	+	0.748144i	−0.997040	−	0.0768792i	$-0.975504\pi$
$257$	−6.92454	+	11.9937i	−0.431941	+	0.748144i	0.565100	+	0.825023i	$0.308838\pi$
$258$		0			0
$259$	8.96143	−	1.90481i	0.556836	−	0.118359i
$260$	0.679467	+	23.4807i	0.0421388	+	1.45621i
$261$		0			0
$262$	−13.9397	+	42.9021i	−0.861200	+	2.65050i
$263$	−15.3140	+	3.25510i	−0.944304	+	0.200718i	−0.654238	−	0.756289i	$-0.727011\pi$
$263$	−15.3140	+	3.25510i	−0.944304	+	0.200718i	−0.290066	+	0.957007i	$0.593677\pi$
$264$		0			0
$265$	1.40896	−	7.72045i	0.0865515	−	0.474263i
$266$	23.8606	+	26.4999i	1.46299	+	1.62481i
$267$		0			0
$268$	1.77007	+	3.06586i	0.108124	+	0.187277i
$269$	5.63335	+	4.09287i	0.343472	+	0.249547i	0.746125	−	0.665806i	$-0.231912\pi$
$269$	5.63335	+	4.09287i	0.343472	+	0.249547i	−0.402654	+	0.915352i	$0.631912\pi$
$270$		0			0
$271$	14.6785	−	10.6646i	0.891658	−	0.647828i	−0.0446517	−	0.999003i	$-0.514218\pi$
$271$	14.6785	−	10.6646i	0.891658	−	0.647828i	0.936310	+	0.351175i	$0.114218\pi$
$272$	−0.314172	−	0.139878i	−0.0190495	−	0.00848137i
$273$		0			0
$274$	−6.59358	+	11.4204i	−0.398333	+	0.689933i
$275$	−20.4038	−	20.1806i	−1.23039	−	1.21694i
$276$		0			0
$277$	−10.5077	+	11.6700i	−0.631348	+	0.701183i	−0.970922	−	0.239396i	$-0.923050\pi$
$277$	−10.5077	+	11.6700i	−0.631348	+	0.701183i	0.339574	+	0.940579i	$0.389717\pi$
$278$	−28.4090	+	20.6404i	−1.70386	+	1.23793i
$279$		0			0
$280$	22.5326	+	29.1985i	1.34658	+	1.74494i
$281$	−2.01464	+	19.1680i	−0.120183	+	1.14347i	0.753662	+	0.657262i	$0.228286\pi$
$281$	−2.01464	+	19.1680i	−0.120183	+	1.14347i	−0.873845	+	0.486204i	$0.838381\pi$
$282$		0			0
$283$	5.77953	−	2.57321i	0.343558	−	0.152962i	−0.227703	−	0.973731i	$-0.573121\pi$
$283$	5.77953	−	2.57321i	0.343558	−	0.152962i	0.571260	+	0.820769i	$0.306455\pi$
$284$	15.8604	+	17.6147i	0.941140	+	1.04524i
$285$		0			0
$286$	21.2665	−	23.6188i	1.25751	−	1.39661i
$287$	1.22423	−	3.76779i	0.0722640	−	0.222406i
$288$		0			0
$289$	−5.25300	−	16.1671i	−0.309000	−	0.951004i
$290$	7.39723	−	17.9983i	0.434380	−	1.05690i
$291$		0			0
$292$	37.9599	−	16.9008i	2.22143	−	0.989047i
$293$	−11.3054	+	19.5815i	−0.660467	+	1.14396i	0.320026	+	0.947409i	$0.396309\pi$
$293$	−11.3054	+	19.5815i	−0.660467	+	1.14396i	−0.980493	+	0.196554i	$0.937025\pi$
$294$		0			0
$295$	18.1141	+	1.37552i	1.05465	+	0.0800856i
$296$	29.0086	−	21.0760i	1.68609	−	1.22502i
$297$		0			0
$298$	−11.6708	−	35.9191i	−0.676072	−	2.08074i
$299$	4.20681	+	7.28640i	0.243286	+	0.421384i
$300$		0			0
$301$	−0.635394	+	1.10053i	−0.0366235	+	0.0634338i
$302$	−49.1201	−	10.4408i	−2.82655	−	0.600801i
$303$		0			0
$304$	67.2863	+	29.9578i	3.85913	+	1.71820i
$305$	0.533423	+	18.4338i	0.0305437	+	1.05551i
$306$		0			0
$307$	1.98814			0.113469			0.0567346	−	0.998389i	$-0.481931\pi$
$307$	1.98814			0.113469			0.0567346	+	0.998389i	$0.481931\pi$
$308$	6.19539	−	58.9452i	0.353015	−	3.35872i
$309$		0			0
$310$	8.25234	+	17.1797i	0.468702	+	0.975741i
$311$	8.61147	+	1.83042i	0.488312	+	0.103794i	0.445486	−	0.895289i	$-0.353031\pi$
$311$	8.61147	+	1.83042i	0.488312	+	0.103794i	0.0428252	+	0.999083i	$0.486364\pi$
$312$		0			0
$313$	−32.1133	+	6.82590i	−1.81515	+	0.385822i	−0.985116	−	0.171888i	$-0.945013\pi$
$313$	−32.1133	+	6.82590i	−1.81515	+	0.385822i	−0.830035	+	0.557711i	$0.811680\pi$
$314$	7.78014	+	23.9448i	0.439059	+	1.35128i
$315$		0			0
$316$	18.6698	−	57.4598i	1.05026	−	3.23237i
$317$	1.63358	−	15.5425i	0.0917512	−	0.872954i	−0.847747	−	0.530401i	$-0.822042\pi$
$317$	1.63358	−	15.5425i	0.0917512	−	0.872954i	0.939498	−	0.342554i	$-0.111292\pi$
$318$		0			0
$319$	−17.2093	+	7.66208i	−0.963537	+	0.428994i
$320$	27.4490	+	14.8060i	1.53445	+	0.827683i
$321$		0			0
$322$	20.0329	+	8.91923i	1.11639	+	0.497049i
$323$	−0.0619248	−	0.190585i	−0.00344559	−	0.0106044i
$324$		0			0
$325$	−8.07880	+	6.61596i	−0.448131	+	0.366988i
$326$	−12.5284	−	21.6999i	−0.693885	−	1.20184i
$327$		0			0
$328$	−1.62073	−	15.4203i	−0.0894901	−	0.851441i
$329$	0.556800	+	5.29760i	0.0306974	+	0.292066i
$330$		0			0
$331$	2.25995	−	21.5019i	0.124218	−	1.18185i	−0.737815	−	0.675002i	$-0.764143\pi$
$331$	2.25995	−	21.5019i	0.124218	−	1.18185i	0.862033	−	0.506852i	$-0.169191\pi$
$332$	−66.2251			−3.63457
$333$		0			0
$334$	−12.1733	+	37.4657i	−0.666095	+	2.05003i
$335$	−0.598224	+	1.45555i	−0.0326845	+	0.0795249i
$336$		0			0
$337$	9.52716	+	10.5810i	0.518977	+	0.576383i	0.944478	−	0.328576i	$-0.106569\pi$
$337$	9.52716	+	10.5810i	0.518977	+	0.576383i	−0.425500	+	0.904958i	$0.639902\pi$
$338$	15.3262	+	17.0214i	0.833633	+	0.925843i
$339$		0			0
$340$	−0.0812389	−	0.334332i	−0.00440580	−	0.0181317i
$341$	5.70153	−	17.5475i	0.308755	−	0.950250i
$342$		0			0
$343$	20.0888			1.08470
$344$	−0.519881	+	4.94634i	−0.0280301	+	0.266689i
$345$		0			0
$346$	−1.84036	−	17.5099i	−0.0989384	−	0.941336i
$347$	1.98457	+	18.8819i	0.106537	+	1.01363i	0.908962	+	0.416879i	$0.136876\pi$
$347$	1.98457	+	18.8819i	0.106537	+	1.01363i	−0.802425	+	0.596753i	$0.796457\pi$
$348$		0			0
$349$	−1.26140	−	2.18481i	−0.0675211	−	0.116950i	0.830288	−	0.557334i	$-0.188176\pi$
$349$	−1.26140	−	2.18481i	−0.0675211	−	0.116950i	−0.897810	+	0.440384i	$0.854842\pi$
$350$	−6.89930	+	26.3267i	−0.368783	+	1.40722i
$351$		0			0
$352$	−24.3711	−	75.0065i	−1.29898	−	3.99786i
$353$	−4.05214	−	1.80413i	−0.215674	−	0.0960241i	0.296056	−	0.955171i	$-0.404328\pi$
$353$	−4.05214	−	1.80413i	−0.215674	−	0.0960241i	−0.511730	+	0.859146i	$0.670995\pi$
$354$		0			0
$355$	−1.89165	+	10.3654i	−0.100398	+	0.550136i
$356$	−29.7275	+	13.2355i	−1.57555	+	0.701482i
$357$		0			0
$358$	−1.35349	+	12.8776i	−0.0715343	+	0.680603i
$359$	10.5484	−	32.4646i	0.556722	−	1.71341i	−0.134630	−	0.990896i	$-0.542985\pi$
$359$	10.5484	−	32.4646i	0.556722	−	1.71341i	0.691352	−	0.722518i	$-0.257015\pi$
$360$		0			0
$361$	7.39111	+	22.7475i	0.389006	+	1.19724i
$362$	−27.5185	+	5.84924i	−1.44634	+	0.307429i
$363$		0			0
$364$	−21.0949	−	4.48386i	−1.10567	−	0.235018i
$365$	16.2568	+	8.76895i	0.850921	+	0.458988i
$366$		0			0
$367$	−1.13659	+	10.8139i	−0.0593296	+	0.564483i	0.923967	+	0.382472i	$0.124927\pi$
$367$	−1.13659	+	10.8139i	−0.0593296	+	0.564483i	−0.983297	+	0.182011i	$0.941739\pi$
$368$	45.2939			2.36111
$369$		0			0
$370$	25.3902	+	7.44506i	1.31997	+	0.387050i
$371$	6.58214	+	2.93056i	0.341728	+	0.152147i
$372$		0			0
$373$	23.8047	+	5.05984i	1.23256	+	0.261989i	0.777735	−	0.628593i	$-0.216369\pi$
$373$	23.8047	+	5.05984i	1.23256	+	0.261989i	0.454824	+	0.890581i	$0.349702\pi$
$374$	−0.232754	+	0.403141i	−0.0120354	+	0.0208459i
$375$		0			0
$376$	10.4239	+	18.0548i	0.537573	+	0.931104i
$377$	2.11814	+	6.51896i	0.109090	+	0.335744i
$378$		0			0
$379$	−4.12810	+	2.99924i	−0.212046	+	0.154061i	−0.688739	−	0.725009i	$-0.741835\pi$
$379$	−4.12810	+	2.99924i	−0.212046	+	0.154061i	0.476693	+	0.879070i	$0.341835\pi$
$380$	17.3989	+	71.6040i	0.892547	+	3.67321i
$381$		0			0
$382$	31.6759	−	54.8643i	1.62068	−	2.80710i
$383$	18.7507	−	8.34835i	0.958116	−	0.426581i	0.132732	−	0.991152i	$-0.457625\pi$
$383$	18.7507	−	8.34835i	0.958116	−	0.426581i	0.825384	+	0.564571i	$0.190958\pi$
$384$		0			0
$385$	22.4266	−	13.8280i	1.14296	−	0.704738i
$386$	−21.0179	−	64.6866i	−1.06979	−	3.29246i
$387$		0			0
$388$	−15.8857	+	48.8913i	−0.806476	+	2.48208i
$389$	7.98747	−	8.87098i	0.404981	−	0.449777i	−0.505810	−	0.862645i	$-0.668806\pi$
$389$	7.98747	−	8.87098i	0.404981	−	0.449777i	0.910791	+	0.412868i	$0.135473\pi$
$390$		0			0
$391$	−0.0824586	−	0.0915796i	−0.00417011	−	0.00463138i
$392$	20.4465	−	9.10336i	1.03270	−	0.459789i
$393$		0			0
$394$	4.26038	−	40.5348i	0.214635	−	2.04211i
$395$	25.2916	−	9.03455i	1.27256	−	0.454577i
$396$		0			0
$397$	−11.3426	+	8.24087i	−0.569268	+	0.413597i	−0.834839	−	0.550494i	$-0.814439\pi$
$397$	−11.3426	+	8.24087i	−0.569268	+	0.413597i	0.265571	+	0.964091i	$0.414439\pi$
$398$	5.66317	−	6.28959i	0.283869	−	0.315269i
$399$		0			0
$400$	9.09899	+	55.4729i	0.454949	+	2.77364i
$401$	0.970609	−	1.68114i	0.0484699	−	0.0839523i	−0.840773	−	0.541388i	$-0.817899\pi$
$401$	0.970609	−	1.68114i	0.0484699	−	0.0839523i	0.889242	+	0.457436i	$0.151232\pi$
$402$		0			0
$403$	−6.13306	−	2.73062i	−0.305510	−	0.136022i
$404$	8.70247	−	6.32271i	0.432964	−	0.314567i
$405$		0			0
$406$	14.4531	+	10.5008i	0.717296	+	0.521146i
$407$	−12.8073	−	22.1829i	−0.634835	−	1.09957i
$408$		0			0
$409$	7.32900	+	8.13967i	0.362396	+	0.402481i	0.896576	−	0.442889i	$-0.146047\pi$
$409$	7.32900	+	8.13967i	0.362396	+	0.402481i	−0.534181	+	0.845370i	$0.679380\pi$
$410$	8.27773	−	7.89864i	0.408808	−	0.390086i
$411$		0			0
$412$	5.94233	−	1.26308i	0.292757	−	0.0622275i
$413$	−5.15382	+	15.8618i	−0.253603	+	0.780509i
$414$		0			0
$415$	−17.9853	−	23.3059i	−0.882863	−	1.14404i
$416$	−28.0696	+	5.96637i	−1.37622	+	0.292525i
$417$		0			0
$418$	49.8489	−	86.3409i	2.43819	−	4.22307i
$419$	−15.2038	+	6.76918i	−0.742755	+	0.330696i	−0.742989	−	0.669304i	$-0.766592\pi$
$419$	−15.2038	+	6.76918i	−0.742755	+	0.330696i	0.000233416		1.00000i	$0.499926\pi$
$420$		0			0
$421$	7.03341	+	3.13148i	0.342787	+	0.152619i	0.570908	−	0.821014i	$-0.306591\pi$
$421$	7.03341	+	3.13148i	0.342787	+	0.152619i	−0.228120	+	0.973633i	$0.573258\pi$
$422$	−57.0504	+	41.4495i	−2.77717	+	2.01773i
$423$		0			0
$424$	28.1990			1.36946
$425$	0.0955956	−	0.119387i	0.00463707	−	0.00579112i
$426$		0			0
$427$	−16.5608	−	3.52010i	−0.801432	−	0.170350i
$428$	−5.86794	−	55.8297i	−0.283638	−	2.69863i
$429$		0			0
$430$	−3.12399	+	1.92622i	−0.150652	+	0.0928904i
$431$	26.1475	+	18.9973i	1.25948	+	0.915066i	0.998732	−	0.0503406i	$-0.0160307\pi$
$431$	26.1475	+	18.9973i	1.25948	+	0.915066i	0.260748	+	0.965407i	$0.416031\pi$
$432$		0			0
$433$	−25.4573	−	18.4958i	−1.22340	−	0.888852i	−0.227022	−	0.973890i	$-0.572899\pi$
$433$	−25.4573	−	18.4958i	−1.22340	−	0.888852i	−0.996378	+	0.0850377i	$0.972899\pi$
$434$	−17.1153	+	3.63796i	−0.821558	+	0.174628i
$435$		0			0
$436$	−45.5685	−	9.68589i	−2.18234	−	0.463870i
$437$	17.6602	+	19.6136i	0.844801	+	0.938246i
$438$		0			0
$439$	−12.1190	+	13.4595i	−0.578409	+	0.642389i	−0.959353	−	0.282210i	$-0.908933\pi$
$439$	−12.1190	+	13.4595i	−0.578409	+	0.642389i	0.380943	+	0.924598i	$0.375599\pi$
$440$	58.1719	−	85.1411i	2.77324	−	4.05894i
$441$		0			0
$442$	0.137032	+	0.0995598i	0.00651797	+	0.00473558i
$443$	19.3559	+	33.5254i	0.919626	+	1.59284i	0.799984	+	0.600022i	$0.204841\pi$
$443$	19.3559	+	33.5254i	0.919626	+	1.59284i	0.119642	+	0.992817i	$0.461825\pi$
$444$		0			0
$445$	−12.7312	−	6.86722i	−0.603517	−	0.325538i
$446$	−4.73731	−	45.0725i	−0.224318	−	2.13425i
$447$		0			0
$448$	−19.1590	+	21.2783i	−0.905179	+	1.00530i
$449$	4.76841			0.225035			0.112518	−	0.993650i	$-0.464109\pi$
$449$	4.76841			0.225035			0.112518	+	0.993650i	$0.464109\pi$
$450$		0			0
$451$	−11.0763			−0.521564
$452$	29.4228	−	32.6773i	1.38393	−	1.53701i
$453$		0			0
$454$	3.41584	+	32.4995i	0.160313	+	1.52528i
$455$	−4.15096	−	8.64144i	−0.194600	−	0.405117i
$456$		0			0
$457$	2.37786	+	4.11857i	0.111232	+	0.192659i	0.916267	−	0.400568i	$-0.131187\pi$
$457$	2.37786	+	4.11857i	0.111232	+	0.192659i	−0.805035	+	0.593227i	$0.797854\pi$
$458$	44.0648	+	32.0149i	2.05901	+	1.49596i
$459$		0			0
$460$	27.6845	+	35.8744i	1.29079	+	1.67265i
$461$	−5.92471	+	6.58006i	−0.275941	+	0.306464i	−0.865146	−	0.501520i	$-0.832774\pi$
$461$	−5.92471	+	6.58006i	−0.275941	+	0.306464i	0.589205	+	0.807984i	$0.299441\pi$
$462$		0			0
$463$	1.03602	+	1.15062i	0.0481481	+	0.0534739i	0.766738	−	0.641960i	$-0.221879\pi$
$463$	1.03602	+	1.15062i	0.0481481	+	0.0534739i	−0.718590	+	0.695434i	$0.755212\pi$
$464$	36.0939	+	7.67199i	1.67562	+	0.356163i
$465$		0			0
$466$	−21.4362	+	4.55641i	−0.993015	+	0.211072i
$467$	−27.9575	−	20.3123i	−1.29372	−	0.939942i	−0.293846	−	0.955853i	$-0.594935\pi$
$467$	−27.9575	−	20.3123i	−1.29372	−	0.939942i	−0.999873	+	0.0159111i	$0.994935\pi$
$468$		0			0
$469$	−1.16884	−	0.849213i	−0.0539721	−	0.0392130i
$470$	−5.84810	+	14.2291i	−0.269753	+	0.656339i
$471$		0			0
$472$	6.82304	+	64.9169i	0.314056	+	2.98804i
$473$	3.47530	+	0.738698i	0.159794	+	0.0339654i
$474$		0			0
$475$	−20.4737	+	25.5691i	−0.939399	+	1.17319i
$476$	0.315875			0.0144781
$477$		0			0
$478$	38.7350	−	28.1427i	1.77170	−	1.28722i
$479$	22.3481	+	9.95002i	1.02111	+	0.454628i	0.847843	−	0.530247i	$-0.177901\pi$
$479$	22.3481	+	9.95002i	1.02111	+	0.454628i	0.173268	+	0.984875i	$0.444567\pi$
$480$		0			0
$481$	−8.51445	+	3.79088i	−0.388226	+	0.172849i
$482$	17.1839	−	29.7633i	0.782704	−	1.35568i
$483$		0			0
$484$	−107.966	+	22.9488i	−4.90753	+	1.04313i
$485$	−21.5200	+	7.68730i	−0.977175	+	0.349062i
$486$		0			0
$487$	1.67643	−	5.15952i	0.0759663	−	0.233800i	−0.905862	−	0.423574i	$-0.860775\pi$
$487$	1.67643	−	5.15952i	0.0759663	−	0.233800i	0.981828	+	0.189774i	$0.0607754\pi$
$488$	−64.8153	+	13.7769i	−2.93405	+	0.623652i
$489$		0			0
$490$	14.5359	+	7.84067i	0.656664	+	0.354205i
$491$	−14.7320	−	16.3615i	−0.664845	−	0.738385i	0.312528	−	0.949909i	$-0.398824\pi$
$491$	−14.7320	−	16.3615i	−0.664845	−	0.738385i	−0.977373	+	0.211523i	$0.932158\pi$
$492$		0			0
$493$	−0.0501978	−	0.0869451i	−0.00226080	−	0.00391581i
$494$	−29.3482	−	21.3227i	−1.32044	−	0.959356i
$495$		0			0
$496$	−29.2390	+	21.2433i	−1.31287	+	0.953854i
$497$	−8.83709	−	3.93453i	−0.396398	−	0.176488i
$498$		0			0
$499$	−20.3177	+	35.1912i	−0.909544	+	1.57538i	−0.0948451	+	0.995492i	$0.530236\pi$
$499$	−20.3177	+	35.1912i	−0.909544	+	1.57538i	−0.814699	+	0.579884i	$0.803098\pi$
$500$	−38.3751	+	41.1128i	−1.71619	+	1.83862i
$501$		0			0
$502$	−14.2413	+	15.8166i	−0.635621	+	0.705928i
$503$	−32.8363	+	23.8569i	−1.46410	+	1.06373i	−0.481825	+	0.876268i	$0.660026\pi$
$503$	−32.8363	+	23.8569i	−1.46410	+	1.06373i	−0.982272	+	0.187461i	$0.939974\pi$
$504$		0			0
$505$	4.58849	+	1.34546i	0.204185	+	0.0598723i
$506$	6.40861	−	60.9738i	0.284897	−	2.71062i
$507$		0			0
$508$	−6.11460	+	2.72240i	−0.271292	+	0.120787i
$509$	29.6993	+	32.9844i	1.31640	+	1.46201i	0.791983	+	0.610543i	$0.209049\pi$
$509$	29.6993	+	32.9844i	1.31640	+	1.46201i	0.524414	+	0.851463i	$0.324284\pi$
$510$		0			0
$511$	−11.3470	+	12.6022i	−0.501963	+	0.557487i
$512$	8.08909	−	24.8957i	0.357491	−	1.10024i
$513$		0			0
$514$	−11.3472	−	34.9231i	−0.500503	−	1.54039i
$515$	2.05831	+	1.74820i	0.0907000	+	0.0770349i
$516$		0			0
$517$	13.6053	−	6.05749i	0.598362	−	0.266408i
$518$	−12.1459	+	21.0372i	−0.533658	+	0.924323i
$519$		0			0
$520$	−28.5975	−	24.2889i	−1.25408	−	1.06514i
$521$	7.98161	−	5.79898i	0.349681	−	0.254058i	−0.399054	−	0.916927i	$-0.630662\pi$
$521$	7.98161	−	5.79898i	0.349681	−	0.254058i	0.748735	+	0.662869i	$0.230662\pi$
$522$		0			0
$523$	−2.46257	−	7.57903i	−0.107681	−	0.331408i	0.882669	−	0.469994i	$-0.155744\pi$
$523$	−2.46257	−	7.57903i	−0.107681	−	0.331408i	−0.990350	+	0.138587i	$0.955744\pi$
$524$	−42.7904	−	74.1151i	−1.86931	−	3.23773i
$525$		0			0
$526$	20.7558	−	35.9502i	0.904998	−	1.56750i
$527$	0.0961821	+	0.0204441i	0.00418976	+	0.000890561i
$528$		0			0
$529$	−6.18440	−	2.75347i	−0.268887	−	0.119716i
$530$	12.7128	+	16.4736i	0.552208	+	0.715569i
$531$		0			0
$532$	−67.6511			−2.93305
$533$	−0.421278	+	4.00819i	−0.0182476	+	0.173614i
$534$		0			0
$535$	18.0540	−	17.2272i	0.780543	−	0.744797i
$536$	−5.53094	−	1.17564i	−0.238900	−	0.0507798i
$537$		0			0
$538$	−18.0592	+	3.83860i	−0.778588	+	0.165494i
$539$	−4.94071	−	15.2059i	−0.212811	−	0.654966i
$540$		0			0
$541$	−3.72498	+	11.4643i	−0.160149	+	0.492889i	−0.998646	−	0.0520177i	$-0.983435\pi$
$541$	−3.72498	+	11.4643i	−0.160149	+	0.492889i	0.838497	+	0.544906i	$0.183435\pi$
$542$	−5.02858	+	47.8437i	−0.215996	+	2.05506i
$543$		0			0
$544$	0.383976	−	0.170957i	0.0164628	−	0.00732972i
$545$	−8.96676	−	18.6670i	−0.384094	−	0.799605i
$546$		0			0
$547$	1.14311	+	0.508944i	0.0488757	+	0.0217609i	0.431029	−	0.902338i	$-0.358151\pi$
$547$	1.14311	+	0.508944i	0.0488757	+	0.0217609i	−0.382153	+	0.924099i	$0.624817\pi$
$548$	−7.73103	−	23.7937i	−0.330253	−	1.01642i
$549$		0			0
$550$	75.9640	−	4.40007i	3.23912	−	0.187620i
$551$	10.7509	+	18.6211i	0.458003	+	0.793284i
$552$		0			0
$553$	2.57732	+	24.5216i	0.109599	+	1.04276i
$554$	−4.35229	−	41.4092i	−0.184911	−	1.75931i
$555$		0			0
$556$	6.96364	−	66.2547i	0.295324	−	2.80982i
$557$	44.8687			1.90115			0.950574	−	0.310498i	$-0.100496\pi$
$557$	44.8687			1.90115			0.950574	+	0.310498i	$0.100496\pi$
$558$		0			0
$559$	0.399493	−	1.22951i	0.0168967	−	0.0520028i
$560$	−51.4609	−	3.90774i	−2.17462	−	0.165132i
$561$		0			0
$562$	−34.1946	−	37.9770i	−1.44241	−	1.60196i
$563$	−26.2271	−	29.1282i	−1.10534	−	1.22761i	−0.971610	−	0.236589i	$-0.923971\pi$
$563$	−26.2271	−	29.1282i	−1.10534	−	1.22761i	−0.133732	−	0.991018i	$-0.542696\pi$
$564$		0			0
$565$	19.4904	+	1.48002i	0.819966	+	0.0622650i
$566$	−5.18358	+	15.9534i	−0.217882	+	0.670573i
$567$		0			0
$568$	−37.8596			−1.58855
$569$	−2.71156	+	25.7988i	−0.113675	+	1.08154i	0.777813	+	0.628496i	$0.216329\pi$
$569$	−2.71156	+	25.7988i	−0.113675	+	1.08154i	−0.891487	+	0.453046i	$0.850337\pi$
$570$		0			0
$571$	−1.13569	−	10.8054i	−0.0475272	−	0.452191i	−0.992244	−	0.124304i	$-0.960330\pi$
$571$	−1.13569	−	10.8054i	−0.0475272	−	0.452191i	0.944717	−	0.327887i	$-0.106337\pi$
$572$	6.30264	+	59.9656i	0.263527	+	2.50729i
$573$		0			0
$574$	5.25213	+	9.09696i	0.219220	+	0.379700i
$575$	−5.10644	+	19.4854i	−0.212953	+	0.812599i
$576$		0			0
$577$	−1.77776	−	5.47137i	−0.0740090	−	0.227776i	0.907208	−	0.420681i	$-0.138209\pi$
$577$	−1.77776	−	5.47137i	−0.0740090	−	0.227776i	−0.981217	+	0.192905i	$0.938209\pi$
$578$	41.1756	+	18.3326i	1.71268	+	0.762534i
$579$		0			0
$580$	15.9847	+	33.2770i	0.663730	+	1.38175i
$581$	24.6905	−	10.9929i	1.02433	−	0.456062i
$582$		0			0
$583$	2.10565	−	20.0339i	0.0872072	−	0.829721i
$584$	−20.5093	+	63.1211i	−0.848680	+	2.61197i
$585$		0			0
$586$	−18.5260	−	57.0173i	−0.765304	−	2.35536i
$587$	6.76644	−	1.43825i	0.279281	−	0.0593630i	−0.0661417	−	0.997810i	$-0.521069\pi$
$587$	6.76644	−	1.43825i	0.279281	−	0.0593630i	0.345423	+	0.938447i	$0.387736\pi$
$588$		0			0
$589$	−20.5993	−	4.37852i	−0.848781	−	0.180414i
$590$	−34.8480	+	33.2520i	−1.43467	+	1.36896i
$591$		0			0
$592$	−5.24467	+	49.8997i	−0.215555	+	2.05086i
$593$	−18.6586			−0.766219			−0.383109	−	0.923703i	$-0.625147\pi$
$593$	−18.6586			−0.766219			−0.383109	+	0.923703i	$0.625147\pi$
$594$		0			0
$595$	0.0857849	+	0.111163i	0.00351684	+	0.00455723i
$596$	65.4565	+	29.1431i	2.68120	+	1.19375i
$597$		0			0
$598$	−21.8209	−	4.63817i	−0.892322	−	0.189669i
$599$	3.61776	−	6.26614i	0.147818	−	0.256027i	−0.782603	−	0.622521i	$-0.786108\pi$
$599$	3.61776	−	6.26614i	0.147818	−	0.256027i	0.930421	+	0.366494i	$0.119442\pi$
$600$		0			0
$601$	3.28224	+	5.68501i	0.133886	+	0.231897i	0.925171	−	0.379550i	$-0.123921\pi$
$601$	3.28224	+	5.68501i	0.133886	+	0.231897i	−0.791286	+	0.611447i	$0.790588\pi$
$602$	−1.04122	−	3.20453i	−0.0424368	−	0.130607i
$603$		0			0
$604$	77.0755	−	55.9986i	3.13616	−	2.27855i
$605$	−37.3972	−	31.7629i	−1.52041	−	1.29134i
$606$		0			0
$607$	−8.23189	+	14.2580i	−0.334122	+	0.578716i	−0.983316	−	0.181907i	$-0.941773\pi$
$607$	−8.23189	+	14.2580i	−0.334122	+	0.578716i	0.649194	+	0.760623i	$0.275106\pi$
$608$	−82.2362	+	36.6139i	−3.33512	+	1.48489i
$609$		0			0
$610$	−37.2686	−	31.6536i	−1.50896	−	1.28162i
$611$	−1.67456	−	5.15376i	−0.0677454	−	0.208499i
$612$		0			0
$613$	5.27406	−	16.2319i	0.213017	−	0.655599i	−0.786271	−	0.617881i	$-0.787991\pi$
$613$	5.27406	−	16.2319i	0.213017	−	0.655599i	0.999288	−	0.0377179i	$-0.0120088\pi$
$614$	−3.52730	+	3.91747i	−0.142350	+	0.158096i
$615$		0			0
$616$	63.3459	+	70.3528i	2.55228	+	2.83459i
$617$	2.05173	−	0.913488i	0.0825994	−	0.0367756i	−0.365021	−	0.930999i	$-0.618938\pi$
$617$	2.05173	−	0.913488i	0.0825994	−	0.0367756i	0.447621	+	0.894224i	$0.352272\pi$
$618$		0			0
$619$	1.09152	−	10.3851i	0.0438717	−	0.417412i	−0.950440	−	0.310907i	$-0.899367\pi$
$619$	1.09152	−	10.3851i	0.0438717	−	0.417412i	0.994312	−	0.106505i	$-0.0339660\pi$
$620$	−34.6969	−	10.1740i	−1.39346	−	0.408599i
$621$		0			0
$622$	−18.8849	+	13.7207i	−0.757217	+	0.550150i
$623$	8.88620	−	9.86912i	0.356018	−	0.395398i
$624$		0			0
$625$	−24.8903	−	2.33964i	−0.995611	−	0.0935856i
$626$	43.5247	−	75.3870i	1.73960	−	3.01307i
$627$		0			0
$628$	−43.6354	−	19.4277i	−1.74124	−	0.775251i
$629$	0.110440	−	0.0802394i	0.00440353	−	0.00319936i
$630$		0			0
$631$	3.19101	+	2.31840i	0.127032	+	0.0922941i	0.649487	−	0.760373i	$-0.274984\pi$
$631$	3.19101	+	2.31840i	0.127032	+	0.0922941i	−0.522455	+	0.852667i	$0.674984\pi$
$632$	48.2504	+	83.5722i	1.91930	+	3.32432i
$633$		0			0
$634$	27.7270	+	30.7939i	1.10118	+	1.22298i
$635$	−2.61866	−	1.41251i	−0.103918	−	0.0560537i
$636$		0			0
$637$	−5.69049	+	1.20955i	−0.225465	+	0.0479242i
$638$	15.4348	−	47.5034i	0.611070	−	1.88068i
$639$		0			0
$640$	−20.0040	+	7.14574i	−0.790727	+	0.282460i
$641$	12.9263	−	2.74756i	0.510557	−	0.108522i	0.0545722	−	0.998510i	$-0.482620\pi$
$641$	12.9263	−	2.74756i	0.510557	−	0.108522i	0.455985	+	0.889988i	$0.349287\pi$
$642$		0			0
$643$	−7.49326	+	12.9787i	−0.295505	+	0.511831i	−0.975102	−	0.221755i	$-0.928821\pi$
$643$	−7.49326	+	12.9787i	−0.295505	+	0.511831i	0.679597	+	0.733586i	$0.262155\pi$
$644$	−38.0056	+	16.9212i	−1.49763	+	0.666789i
$645$		0			0
$646$	0.485397	+	0.216113i	0.0190977	+	0.00850284i
$647$	40.6013	−	29.4986i	1.59620	−	1.15971i	0.701867	−	0.712308i	$-0.252350\pi$
$647$	40.6013	−	29.4986i	1.59620	−	1.15971i	0.894334	−	0.447400i	$-0.147650\pi$
$648$		0			0
$649$	46.6296			1.83037
$650$	1.29697	−	27.6565i	0.0508714	−	1.08478i
$651$		0			0
$652$	46.4980	+	9.88345i	1.82100	+	0.387066i
$653$	0.734841	+	6.99155i	0.0287566	+	0.273600i	0.999447	+	0.0332654i	$0.0105906\pi$
$653$	0.734841	+	6.99155i	0.0287566	+	0.273600i	−0.970690	+	0.240335i	$0.922743\pi$
$654$		0			0
$655$	14.4617	−	35.1868i	0.565064	−	1.37486i
$656$	17.5529	+	12.7529i	0.685325	+	0.497918i
$657$		0			0
$658$	−11.4263	−	8.30172i	−0.445445	−	0.323635i
$659$	34.6451	−	7.36404i	1.34958	−	0.286862i	0.524276	−	0.851549i	$-0.324336\pi$
$659$	34.6451	−	7.36404i	1.34958	−	0.286862i	0.825306	+	0.564686i	$0.191003\pi$
$660$		0			0
$661$	5.03987	+	1.07126i	0.196028	+	0.0416671i	0.304879	−	0.952391i	$-0.401384\pi$
$661$	5.03987	+	1.07126i	0.196028	+	0.0416671i	−0.108851	+	0.994058i	$0.534717\pi$
$662$	38.3583	+	42.6012i	1.49084	+	1.65574i
$663$		0			0
$664$	70.7794	−	78.6085i	2.74677	−	3.05060i
$665$	−18.3726	−	23.8078i	−0.712457	−	0.923226i
$666$		0			0
$667$	10.6973	+	7.77205i	0.414201	+	0.300935i
$668$	−37.3681	−	64.7234i	−1.44581	−	2.50422i
$669$		0			0
$670$	−1.80668	−	3.76114i	−0.0697982	−	0.145306i
$671$	4.94796	+	47.0767i	0.191014	+	1.81737i
$672$		0			0
$673$	13.1777	−	14.6353i	0.507962	−	0.564149i	−0.433550	−	0.901130i	$-0.642739\pi$
$673$	13.1777	−	14.6353i	0.507962	−	0.564149i	0.941511	+	0.336981i	$0.109406\pi$
$674$	−37.7518			−1.45414
$675$		0			0
$676$	−43.4536			−1.67129
$677$	5.89101	−	6.54263i	0.226410	−	0.251454i	−0.619227	−	0.785212i	$-0.712554\pi$
$677$	5.89101	−	6.54263i	0.226410	−	0.251454i	0.845637	+	0.533758i	$0.179221\pi$
$678$		0			0
$679$	−2.19299	−	20.8649i	−0.0841592	−	0.800721i
$680$	0.483675	+	0.260895i	0.0185481	+	0.0100049i
$681$		0			0
$682$	24.4604	+	42.3667i	0.936638	+	1.62230i
$683$	22.8601	+	16.6088i	0.874716	+	0.635519i	0.931848	−	0.362848i	$-0.118196\pi$
$683$	22.8601	+	16.6088i	0.874716	+	0.635519i	−0.0571320	+	0.998367i	$0.518196\pi$
$684$		0			0
$685$	6.27389	−	9.18255i	0.239713	−	0.350847i
$686$	−35.6411	+	39.5834i	−1.36078	+	1.51130i
$687$		0			0
$688$	−4.65687	−	5.17198i	−0.177542	−	0.197180i
$689$	−7.16960	−	1.52395i	−0.273140	−	0.0580577i
$690$		0			0
$691$	49.4141	−	10.5033i	1.87980	−	0.399564i	0.882330	−	0.470631i	$-0.155974\pi$
$691$	49.4141	−	10.5033i	1.87980	−	0.399564i	0.997472	+	0.0710668i	$0.0226403\pi$
$692$	27.0227	+	19.6332i	1.02725	+	0.746341i
$693$		0			0
$694$	−40.7262	−	29.5893i	−1.54594	−	1.12319i
$695$	25.2075	−	15.5427i	0.956176	−	0.589567i
$696$		0			0
$697$	−0.00617037	−	0.0587072i	−0.000233719	−	0.00222369i
$698$	6.54293	+	1.39074i	0.247653	+	0.0526404i
$699$		0			0
$700$	−28.3588	−	43.1475i	−1.07186	−	1.63082i
$701$	−30.7464			−1.16128			−0.580638	−	0.814162i	$-0.697197\pi$
$701$	−30.7464			−1.16128			−0.580638	+	0.814162i	$0.697197\pi$
$702$		0			0
$703$	−23.6530	+	17.1849i	−0.892089	+	0.648140i
$704$	73.1320	+	32.5605i	2.75627	+	1.22717i
$705$		0			0
$706$	10.7441	−	4.78358i	0.404359	−	0.180032i
$707$	−2.19498	+	3.80182i	−0.0825509	+	0.142982i
$708$		0			0
$709$	25.9024	−	5.50573i	0.972787	−	0.206772i	0.306009	−	0.952029i	$-0.401006\pi$
$709$	25.9024	−	5.50573i	0.972787	−	0.206772i	0.666778	+	0.745257i	$0.267673\pi$
$710$	−17.0680	−	22.1173i	−0.640551	−	0.830047i
$711$		0			0
$712$	16.0614	−	49.4320i	0.601927	−	1.85254i
$713$	−12.6677	+	2.69259i	−0.474408	+	0.100838i
$714$		0			0
$715$	−19.3914	+	18.5034i	−0.725199	+	0.691987i
$716$	−16.4375	−	18.2557i	−0.614298	−	0.682247i
$717$		0			0
$718$	45.2541	+	78.3825i	1.68887	+	2.92521i
$719$	−2.59090	−	1.88240i	−0.0966244	−	0.0702017i	0.538424	−	0.842674i	$-0.319020\pi$
$719$	−2.59090	−	1.88240i	−0.0966244	−	0.0702017i	−0.635048	+	0.772472i	$0.719020\pi$
$720$		0			0
$721$	−2.00579	+	1.45730i	−0.0746997	+	0.0542725i
$722$	−57.9352	−	25.7944i	−2.15613	−	0.959969i
$723$		0			0
$724$	26.6867	−	46.2227i	0.991802	−	1.71785i
$725$	−7.36972	+	14.6627i	−0.273705	+	0.544557i
$726$		0			0
$727$	27.4745	−	30.5136i	1.01897	−	1.13169i	0.0277340	−	0.999615i	$-0.491171\pi$
$727$	27.4745	−	30.5136i	1.01897	−	1.13169i	0.991240	−	0.132070i	$-0.0421625\pi$
$728$	27.8679	−	20.2472i	1.03285	−	0.750411i
$729$		0			0
$730$	−46.1209	+	16.4751i	−1.70701	+	0.609772i
$731$	−0.00197926	+	0.0188314i	−7.32057e−5	+	0.000696506i
$732$		0			0
$733$	−38.0712	+	16.9504i	−1.40619	+	0.626077i	−0.962791	−	0.270246i	$-0.912895\pi$
$733$	−38.0712	+	16.9504i	−1.40619	+	0.626077i	−0.443401	+	0.896323i	$0.646228\pi$
$734$	−19.2915	−	21.4254i	−0.712062	−	0.790825i
$735$		0			0
$736$	−37.0413	+	41.1386i	−1.36536	+	1.51639i
$737$	−1.24823	+	3.84166i	−0.0459792	+	0.141509i
$738$		0			0
$739$	7.60793	+	23.4148i	0.279862	+	0.861327i	0.987892	+	0.155144i	$0.0495842\pi$
$739$	7.60793	+	23.4148i	0.279862	+	0.861327i	−0.708030	+	0.706183i	$0.750416\pi$
$740$	−42.7281	+	26.3456i	−1.57071	+	0.968485i
$741$		0			0
$742$	−17.4523	+	7.77026i	−0.640694	+	0.285255i
$743$	1.29297	−	2.23949i	0.0474346	−	0.0821591i	−0.841333	−	0.540517i	$-0.818229\pi$
$743$	1.29297	−	2.23949i	0.0474346	−	0.0821591i	0.888768	+	0.458358i	$0.151562\pi$
$744$		0			0
$745$	7.52051	+	30.9501i	0.275530	+	1.13392i
$746$	−52.2036	+	37.9281i	−1.91131	+	1.38865i
$747$		0			0
$748$	−0.272906	−	0.839918i	−0.00997843	−	0.0307104i
$749$	11.4551	+	19.8408i	0.418559	+	0.724966i
$750$		0			0
$751$	−1.67267	+	2.89715i	−0.0610367	+	0.105719i	−0.894929	−	0.446208i	$-0.852774\pi$
$751$	−1.67267	+	2.89715i	−0.0610367	+	0.105719i	0.833892	+	0.551927i	$0.186107\pi$
$752$	−28.5351	−	6.06532i	−1.04057	−	0.221180i
$753$		0			0
$754$	−16.6030	−	7.39215i	−0.604647	−	0.269206i
$755$	40.6391	+	11.9164i	1.47901	+	0.433683i
$756$		0			0
$757$	−12.7280			−0.462606			−0.231303	−	0.972882i	$-0.574299\pi$
$757$	−12.7280			−0.462606			−0.231303	+	0.972882i	$0.574299\pi$
$758$	1.41421	−	13.4553i	0.0513662	−	0.488717i
$759$		0			0
$760$	−103.589	−	55.8759i	−3.75756	−	2.02683i
$761$	−21.8602	−	4.64654i	−0.792433	−	0.168437i	−0.206126	−	0.978526i	$-0.566086\pi$
$761$	−21.8602	−	4.64654i	−0.792433	−	0.168437i	−0.586307	+	0.810089i	$0.699419\pi$
$762$		0			0
$763$	18.5969	−	3.95290i	0.673255	−	0.143105i
$764$	37.1403	+	114.306i	1.34369	+	4.13545i
$765$		0			0
$766$	−16.8172	+	51.7582i	−0.607632	+	1.87010i
$767$	1.77351	−	16.8739i	0.0640379	−	0.609280i
$768$		0			0
$769$	32.4894	−	14.4652i	1.17160	−	0.521628i	0.273691	−	0.961818i	$-0.411755\pi$
$769$	32.4894	−	14.4652i	1.17160	−	0.521628i	0.897905	+	0.440189i	$0.145089\pi$
$770$	−12.5417	+	68.7229i	−0.451972	+	2.47660i
$771$		0			0
$772$	117.880	+	52.4837i	4.24261	+	1.88893i
$773$	−5.00935	−	15.4172i	−0.180174	−	0.554518i	0.819658	−	0.572853i	$-0.194163\pi$
$773$	−5.00935	−	15.4172i	−0.180174	−	0.554518i	−0.999832	+	0.0183350i	$0.994163\pi$
$774$		0			0
$775$	−5.84249	−	14.9736i	−0.209868	−	0.537867i
$776$	−41.0552	−	71.1097i	−1.47380	−	2.55269i
$777$		0			0
$778$	3.30840	+	31.4773i	0.118612	+	1.12852i
$779$	1.32151	+	12.5733i	0.0473480	+	0.450486i
$780$		0			0
$781$	−2.82702	+	26.8973i	−0.101159	+	0.962461i
$782$	0.326746			0.0116844
$783$		0			0
$784$	−9.67798	+	29.7857i	−0.345642	+	1.06378i
$785$	−5.01341	−	20.6323i	−0.178936	−	0.736399i
$786$		0			0
$787$	−15.0507	−	16.7155i	−0.536499	−	0.595843i	0.412564	−	0.910929i	$-0.364633\pi$
$787$	−15.0507	−	16.7155i	−0.536499	−	0.595843i	−0.949063	+	0.315086i	$0.897967\pi$
$788$	51.7402	+	57.4633i	1.84317	+	2.04705i
$789$		0			0
$790$	−27.0698	+	65.8638i	−0.963100	+	2.34333i
$791$	−5.54538	+	17.0669i	−0.197171	+	0.606830i
$792$		0			0
$793$	17.2238			0.611636
$794$	3.88574	−	36.9704i	0.137900	−	1.31203i
$795$		0			0
$796$	1.67837	+	15.9686i	0.0594881	+	0.565992i
$797$	1.31161	+	12.4791i	0.0464595	+	0.442032i	0.992882	+	0.119102i	$0.0380014\pi$
$797$	1.31161	+	12.4791i	0.0464595	+	0.442032i	−0.946423	+	0.322931i	$0.895332\pi$
$798$		0			0
$799$	0.0396854	+	0.0687371i	0.00140397	+	0.00243174i
$800$	−57.8249	−	37.1015i	−2.04442	−	1.31174i
$801$		0			0
$802$	1.59053	+	4.89515i	0.0561635	+	0.172854i
$803$	43.3128	+	19.2841i	1.52848	+	0.680522i
$804$		0			0
$805$	−16.2764	−	8.77952i	−0.573668	−	0.309437i
$806$	16.2616	−	7.24012i	0.572790	−	0.255022i
$807$		0			0
$808$	−1.79594	+	17.0873i	−0.0631811	+	0.601128i
$809$	11.1962	−	34.4583i	0.393636	−	1.21149i	−0.536382	−	0.843975i	$-0.680209\pi$
$809$	11.1962	−	34.4583i	0.393636	−	1.21149i	0.930018	−	0.367513i	$-0.119791\pi$
$810$		0			0
$811$	4.95557	+	15.2517i	0.174014	+	0.535559i	0.999587	−	0.0287359i	$-0.00914817\pi$
$811$	4.95557	+	15.2517i	0.174014	+	0.535559i	−0.825573	+	0.564295i	$0.809148\pi$
$812$	−33.1522	+	7.04671i	−1.16341	+	0.247291i
$813$		0			0
$814$	66.4320	+	14.1206i	2.32844	+	0.494925i
$815$	9.14966	+	19.0477i	0.320499	+	0.667212i
$816$		0			0
$817$	0.423899	−	4.03313i	0.0148304	−	0.141101i
$818$	−29.0415			−1.01541
$819$		0			0
$820$	0.627863	+	21.6974i	0.0219259	+	0.757705i
$821$	−3.95527	−	1.76100i	−0.138040	−	0.0614594i	0.336554	−	0.941664i	$-0.390738\pi$
$821$	−3.95527	−	1.76100i	−0.138040	−	0.0614594i	−0.474594	+	0.880205i	$0.657405\pi$
$822$		0			0
$823$	39.0257	+	8.29516i	1.36035	+	0.289151i	0.829591	−	0.558372i	$-0.188574\pi$
$823$	39.0257	+	8.29516i	1.36035	+	0.289151i	0.530758	+	0.847523i	$0.321907\pi$
$824$	−4.85172	+	8.40342i	−0.169018	+	0.292747i
$825$		0			0
$826$	−22.1107	−	38.2968i	−0.769328	−	1.33252i
$827$	2.65398	+	8.16812i	0.0922881	+	0.284033i	0.986537	−	0.163536i	$-0.0522899\pi$
$827$	2.65398	+	8.16812i	0.0922881	+	0.284033i	−0.894249	+	0.447569i	$0.852290\pi$
$828$		0			0
$829$	−34.9992	+	25.4284i	−1.21557	+	0.883164i	−0.995725	−	0.0923701i	$-0.970556\pi$
$829$	−34.9992	+	25.4284i	−1.21557	+	0.883164i	−0.219847	+	0.975534i	$0.570556\pi$
$830$	77.8315	+	5.91021i	2.70157	+	0.205146i
$831$		0			0
$832$	14.5642	−	25.2259i	0.504922	−	0.874551i
$833$	0.0778427	−	0.0346578i	0.00269709	−	0.00120082i
$834$		0			0
$835$	12.6291	−	30.7281i	0.437049	−	1.06339i
$836$	58.4483	+	179.885i	2.02148	+	6.22147i
$837$		0			0
$838$	13.6361	−	41.9676i	0.471051	−	1.44975i
$839$	−15.4326	+	17.1397i	−0.532794	+	0.591727i	−0.948107	−	0.317951i	$-0.897005\pi$
$839$	−15.4326	+	17.1397i	−0.532794	+	0.591727i	0.415313	+	0.909678i	$0.363672\pi$
$840$		0			0
$841$	−12.1967	−	13.5459i	−0.420577	−	0.467099i
$842$	−18.6488	+	8.30298i	−0.642680	+	0.286140i
$843$		0			0
$844$	13.9842	−	133.051i	0.481358	−	4.57981i
$845$	−11.8011	−	15.2922i	−0.405969	−	0.526068i
$846$		0			0
$847$	36.4431	−	26.4775i	1.25220	−	0.909776i
$848$	−26.4033	+	29.3238i	−0.906693	+	1.00699i
$849$		0			0
$850$	0.0656393	+	0.400176i	0.00225141	+	0.0137259i
$851$	−8.98962	+	15.5705i	−0.308160	+	0.533749i
$852$		0			0
$853$	2.39604	+	1.06678i	0.0820387	+	0.0365260i	0.447346	−	0.894361i	$-0.352369\pi$
$853$	2.39604	+	1.06678i	0.0820387	+	0.0365260i	−0.365307	+	0.930887i	$0.619036\pi$
$854$	36.3178	−	26.3864i	1.24277	−	0.902924i
$855$		0			0
$856$	72.5408	+	52.7040i	2.47939	+	1.80138i
$857$	3.83097	+	6.63543i	0.130863	+	0.226662i	0.924010	−	0.382369i	$-0.124892\pi$
$857$	3.83097	+	6.63543i	0.130863	+	0.226662i	−0.793146	+	0.609031i	$0.791558\pi$
$858$		0			0
$859$	−24.6556	−	27.3828i	−0.841237	−	0.934288i	0.157344	−	0.987544i	$-0.449707\pi$
$859$	−24.6556	−	27.3828i	−0.841237	−	0.934288i	−0.998581	+	0.0532555i	$0.983040\pi$
$860$	1.25004	−	6.84963i	0.0426259	−	0.233570i
$861$		0			0
$862$	−83.8228	+	17.8171i	−2.85501	+	0.606852i
$863$	11.1912	−	34.4429i	0.380952	−	1.17245i	−0.558423	−	0.829557i	$-0.688593\pi$
$863$	11.1912	−	34.4429i	0.380952	−	1.17245i	0.939375	−	0.342893i	$-0.111407\pi$
$864$		0			0
$865$	0.429481	+	14.8418i	0.0146028	+	0.504636i
$866$	81.6101	−	17.3468i	2.77323	−	0.589467i
$867$		0			0
$868$	16.5979	−	28.7484i	0.563369	−	0.975783i
$869$	62.9766	−	28.0390i	2.13634	−	0.951158i
$870$		0			0
$871$	1.34271	+	0.597812i	0.0454960	+	0.0202561i
$872$	60.1993	−	43.7374i	2.03861	−	1.48113i
$873$		0			0
$874$	−69.9792			−2.36708
$875$	7.48283	−	21.6980i	0.252966	−	0.733525i
$876$		0			0
$877$	3.33451	+	0.708771i	0.112598	+	0.0239335i	0.263866	−	0.964559i	$-0.415002\pi$
$877$	3.33451	+	0.708771i	0.112598	+	0.0239335i	−0.151268	+	0.988493i	$0.548336\pi$
$878$	−5.01968	−	47.7591i	−0.169406	−	1.61179i
$879$		0			0
$880$	34.0698	+	140.212i	1.14849	+	4.72654i
$881$	−6.16387	−	4.47831i	−0.207666	−	0.150878i	0.479091	−	0.877765i	$-0.340966\pi$
$881$	−6.16387	−	4.47831i	−0.207666	−	0.150878i	−0.686757	+	0.726887i	$0.740966\pi$
$882$		0			0
$883$	37.7740	+	27.4444i	1.27120	+	0.923578i	0.999250	−	0.0387346i	$-0.0123327\pi$
$883$	37.7740	+	27.4444i	1.27120	+	0.923578i	0.271946	+	0.962312i	$0.412333\pi$
$884$	−0.314321	+	0.0668110i	−0.0105718	+	0.00224710i
$885$		0			0
$886$	−100.400	−	21.3406i	−3.37299	−	0.716952i
$887$	−15.7233	−	17.4625i	−0.527936	−	0.586333i	0.418906	−	0.908029i	$-0.362414\pi$
$887$	−15.7233	−	17.4625i	−0.527936	−	0.586333i	−0.946843	+	0.321697i	$0.895747\pi$
$888$		0			0
$889$	1.82779	−	2.02996i	0.0613020	−	0.0680828i
$890$	36.1187	−	12.9021i	1.21070	−	0.432481i
$891$		0			0
$892$	69.5599	+	50.5382i	2.32904	+	1.69214i
$893$	−8.49943	−	14.7214i	−0.284422	−	0.492634i
$894$		0			0
$895$	1.96048	−	10.7425i	0.0655316	−	0.359083i
$896$	−2.03850	−	19.3950i	−0.0681014	−	0.647941i
$897$		0			0
$898$	−8.45998	+	9.39576i	−0.282313	+	0.313541i
$899$	−10.5507			−0.351886
$900$		0			0
$901$	0.107358			0.00357660
$902$	19.6513	−	21.8250i	0.654317	−	0.726693i
$903$		0			0
$904$	7.34143	+	69.8490i	0.244172	+	2.32314i
$905$	23.5142	−	3.16149i	0.781638	−	0.105092i
$906$		0			0
$907$	−7.40266	−	12.8218i	−0.245801	−	0.425740i	0.716555	−	0.697530i	$-0.245718\pi$
$907$	−7.40266	−	12.8218i	−0.245801	−	0.425740i	−0.962357	+	0.271790i	$0.912384\pi$
$908$	−50.1561	−	36.4405i	−1.66449	−	1.20932i
$909$		0			0
$910$	24.3918	+	7.15229i	0.808579	+	0.237096i
$911$	−32.9858	+	36.6345i	−1.09287	+	1.21375i	−0.117524	+	0.993070i	$0.537496\pi$
$911$	−32.9858	+	36.6345i	−1.09287	+	1.21375i	−0.975345	+	0.220684i	$0.929171\pi$
$912$		0			0
$913$	−50.5621	−	56.1549i	−1.67336	−	1.85845i
$914$	−12.3341	−	2.62168i	−0.407974	−	0.0867176i
$915$		0			0
$916$	−101.075	+	21.4841i	−3.33960	+	0.709853i
$917$	28.2560	+	20.5292i	0.933094	+	0.677933i
$918$		0			0
$919$	14.7084	+	10.6863i	0.485185	+	0.352508i	0.803330	−	0.595535i	$-0.203060\pi$
$919$	14.7084	+	10.6863i	0.485185	+	0.352508i	−0.318145	+	0.948042i	$0.603060\pi$
$920$	−72.1709	−	5.48037i	−2.37940	−	0.180683i
$921$		0			0
$922$	−2.45401	−	23.3483i	−0.0808184	−	0.768936i
$923$	9.62581	+	2.04603i	0.316837	+	0.0673459i
$924$		0			0
$925$	−20.8756	−	7.88196i	−0.686385	−	0.259157i
$926$	−4.10529			−0.134908
$927$		0			0
$928$	−36.4857	+	26.5084i	−1.19770	+	0.870182i
$929$	−21.1377	−	9.41112i	−0.693506	−	0.308769i	0.0295449	−	0.999563i	$-0.490594\pi$
$929$	−21.1377	−	9.41112i	−0.693506	−	0.308769i	−0.723051	+	0.690795i	$0.757261\pi$
$930$		0			0
$931$	−16.6716	+	7.42267i	−0.546389	+	0.243268i
$932$	20.7882	−	36.0063i	0.680942	−	1.17943i
$933$		0			0
$934$	89.6252	−	19.0504i	2.93263	−	0.623349i
$935$	0.221469	−	0.324145i	0.00724280	−	0.0106007i
$936$		0			0
$937$	11.0255	−	33.9329i	0.360186	−	1.10854i	−0.592755	−	0.805383i	$-0.701960\pi$
$937$	11.0255	−	33.9329i	0.360186	−	1.10854i	0.952941	−	0.303156i	$-0.0980402\pi$
$938$	3.74703	−	0.796457i	0.122345	−	0.0260052i
$939$		0			0
$940$	−12.6372	−	26.3081i	−0.412181	−	0.858076i
$941$	18.0052	+	19.9968i	0.586953	+	0.651877i	0.961330	−	0.275399i	$-0.0888101\pi$
$941$	18.0052	+	19.9968i	0.586953	+	0.651877i	−0.374377	+	0.927277i	$0.622143\pi$
$942$		0			0
$943$	3.88731	+	6.73301i	0.126588	+	0.219257i
$944$	−73.8949	−	53.6878i	−2.40507	−	1.74739i
$945$		0			0
$946$	−7.62133	+	5.53722i	−0.247791	+	0.180031i
$947$	2.53281	+	1.12768i	0.0823052	+	0.0366446i	0.447476	−	0.894296i	$-0.352323\pi$
$947$	2.53281	+	1.12768i	0.0823052	+	0.0366446i	−0.365171	+	0.930940i	$0.618990\pi$
$948$		0			0
$949$	8.62572	−	14.9402i	0.280003	−	0.484979i
$950$	−14.0580	−	85.7059i	−0.456101	−	2.78067i
$951$		0			0
$952$	−0.337598	+	0.374941i	−0.0109416	+	0.0121519i
$953$	−18.2158	+	13.2345i	−0.590067	+	0.428709i	−0.842339	−	0.538948i	$-0.818822\pi$
$953$	−18.2158	+	13.2345i	−0.590067	+	0.428709i	0.252273	+	0.967656i	$0.418822\pi$
$954$		0			0
$955$	−30.1401	+	44.1135i	−0.975311	+	1.42748i
$956$	−9.49477	+	90.3367i	−0.307083	+	2.92170i
$957$		0			0
$958$	−59.2551	+	26.3821i	−1.91445	+	0.852366i
$959$	6.83192	+	7.58761i	0.220614	+	0.245017i
$960$		0			0
$961$	−13.8284	+	15.3580i	−0.446079	+	0.495421i
$962$	7.63649	−	23.5027i	0.246210	−	0.757758i
$963$		0			0
$964$	20.1482	+	62.0099i	0.648931	+	1.99720i
$965$	13.5437	+	55.7379i	0.435986	+	1.79427i
$966$		0			0
$967$	15.7915	−	7.03081i	0.507819	−	0.226096i	−0.136801	−	0.990599i	$-0.543682\pi$
$967$	15.7915	−	7.03081i	0.507819	−	0.226096i	0.644620	+	0.764503i	$0.277016\pi$
$968$	88.1504	−	152.681i	2.83326	−	4.90735i
$969$		0			0
$970$	23.0331	−	56.0421i	0.739548	−	1.79940i
$971$	12.0003	−	8.71872i	0.385108	−	0.279797i	−0.378340	−	0.925667i	$-0.623505\pi$
$971$	12.0003	−	8.71872i	0.385108	−	0.279797i	0.763448	+	0.645869i	$0.223505\pi$
$972$		0			0
$973$	8.40158	+	25.8574i	0.269342	+	0.828951i
$974$	7.19214	+	12.4572i	0.230451	+	0.399153i
$975$		0			0
$976$	46.3614	−	80.3003i	1.48399	−	2.57035i
$977$	−35.7718	−	7.60352i	−1.14444	−	0.243258i	−0.403597	−	0.914937i	$-0.632240\pi$
$977$	−35.7718	−	7.60352i	−1.14444	−	0.243258i	−0.740843	+	0.671679i	$0.765574\pi$
$978$		0			0
$979$	−33.9195	−	15.1020i	−1.08407	−	0.482661i
$980$	−29.5068	+	10.5403i	−0.942560	+	0.336697i
$981$		0			0
$982$	58.3761			1.86286
$983$	−2.13617	+	20.3243i	−0.0681334	+	0.648246i	0.906156	+	0.422944i	$0.139003\pi$
$983$	−2.13617	+	20.3243i	−0.0681334	+	0.648246i	−0.974289	+	0.225302i	$0.927663\pi$
$984$		0			0
$985$	−6.17098	+	33.8142i	−0.196624	+	1.07741i
$986$	0.260378	+	0.0553450i	0.00829212	+	0.00176255i
$987$		0			0
$988$	67.3182	−	14.3089i	2.14168	−	0.455228i
$989$	−0.770644	−	2.37180i	−0.0245050	−	0.0754188i
$990$		0			0
$991$	7.58313	−	23.3385i	0.240886	−	0.741371i	−0.755400	−	0.655264i	$-0.772557\pi$
$991$	7.58313	−	23.3385i	0.240886	−	0.741371i	0.996286	−	0.0861070i	$-0.0274427\pi$
$992$	4.61716	−	43.9294i	0.146595	−	1.39476i
$993$		0			0
$994$	23.4312	−	10.4322i	0.743192	−	0.330891i
$995$	−5.16386	+	4.92737i	−0.163705	+	0.156208i
$996$		0			0
$997$	−35.7216	−	15.9043i	−1.13131	−	0.503693i	−0.246269	−	0.969201i	$-0.579205\pi$
$997$	−35.7216	−	15.9043i	−1.13131	−	0.503693i	−0.885043	+	0.465508i	$0.845871\pi$
$998$	−33.2944	−	102.470i	−1.05392	−	3.24362i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.631.1		224
3.2	odd	2		225.2.q.a.31.28	✓	224
9.2	odd	6		225.2.q.a.106.1	yes	224
9.7	even	3	inner	675.2.r.a.181.28		224
25.21	even	5	inner	675.2.r.a.496.28		224
75.71	odd	10		225.2.q.a.121.1	yes	224
225.146	odd	30		225.2.q.a.196.28	yes	224
225.196	even	15	inner	675.2.r.a.46.1		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.28	✓	224	3.2	odd	2
225.2.q.a.106.1	yes	224	9.2	odd	6
225.2.q.a.121.1	yes	224	75.71	odd	10
225.2.q.a.196.28	yes	224	225.146	odd	30
675.2.r.a.46.1		224	225.196	even	15	inner
675.2.r.a.181.28		224	9.7	even	3	inner
675.2.r.a.496.28		224	25.21	even	5	inner
675.2.r.a.631.1		224	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.77417 + 1.97042i) q^{2} +(-0.525803 - 5.00268i) q^{4} +(1.61775 - 1.54366i) q^{5} +(1.02644 + 1.77785i) q^{7} +(6.50010 + 4.72260i) q^{8} +O(q^{10})\)	\(q+(-1.77417 + 1.97042i) q^{2} +(-0.525803 - 5.00268i) q^{4} +(1.61775 - 1.54366i) q^{5} +(1.02644 + 1.77785i) q^{7} +(6.50010 + 4.72260i) q^{8} +(0.171493 + 5.92636i) q^{10} +(3.84053 - 4.26534i) q^{11} +(-1.39743 - 1.55200i) q^{13} +(-5.32421 - 1.13169i) q^{14} +(-10.9972 + 2.33752i) q^{16} +(0.0247468 + 0.0179796i) q^{17} +(-5.30003 - 3.85070i) q^{19} +(-8.57307 - 7.28142i) q^{20} +(1.59074 + 15.1349i) q^{22} +(-3.94065 - 0.837611i) q^{23} +(0.234221 - 4.99451i) q^{25} +5.53738 q^{26} +(8.35433 - 6.06978i) q^{28} +(-2.99836 - 1.33495i) q^{29} +(2.93669 - 1.30750i) q^{31} +(6.87040 - 11.8999i) q^{32} +(-0.0793325 + 0.0168626i) q^{34} +(4.40493 + 1.29164i) q^{35} +(1.37908 - 4.24438i) q^{37} +(16.9906 - 3.61147i) q^{38} +(17.8056 - 2.39397i) q^{40} +(-1.29130 - 1.43413i) q^{41} +(0.309512 + 0.536091i) q^{43} +(-23.3575 - 16.9702i) q^{44} +(8.64184 - 6.27867i) q^{46} +(2.37044 + 1.05539i) q^{47} +(1.39282 - 2.41244i) q^{49} +(9.42573 + 9.32264i) q^{50} +(-7.02940 + 7.80695i) q^{52} +(2.83942 - 2.06296i) q^{53} +(-0.371228 - 12.8287i) q^{55} +(-1.72410 + 16.4037i) q^{56} +(7.95002 - 3.53958i) q^{58} +(5.43616 + 6.03746i) q^{59} +(-5.51851 + 6.12893i) q^{61} +(-2.63388 + 8.10625i) q^{62} +(4.31002 + 13.2649i) q^{64} +(-4.65646 - 0.353593i) q^{65} +(-0.642929 + 0.286250i) q^{67} +(0.0769343 - 0.133254i) q^{68} +(-10.3602 + 6.38797i) q^{70} +(-3.81216 + 2.76970i) q^{71} +(2.55263 + 7.85620i) q^{73} +(5.91647 + 10.2476i) q^{74} +(-16.4770 + 28.5391i) q^{76} +(11.5252 + 2.44977i) q^{77} +(10.9723 + 4.88520i) q^{79} +(-14.1823 + 20.7574i) q^{80} +5.11682 q^{82} +(1.37616 - 13.0933i) q^{83} +(0.0677885 - 0.00911420i) q^{85} +(-1.60545 - 0.341249i) q^{86} +(45.1073 - 9.58785i) q^{88} +(-1.99904 - 6.15242i) q^{89} +(1.32485 - 4.07747i) q^{91} +(-2.11830 + 20.1543i) q^{92} +(-6.28513 + 2.79832i) q^{94} +(-14.5183 + 1.95199i) q^{95} +(-9.33612 - 4.15671i) q^{97} +(2.28241 + 7.02454i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

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