LMFDB - Embedded newform 945.2.bv.e.73.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(73,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 9, 2]))

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

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

chi := DirichletCharacter("945.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bv (of order $12$, degree $4$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.25
Character	$\chi$	$=$	945.73
Dual form			945.2.bv.e.712.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.565391 - 0.565391i) q^{2} +1.36066i q^{4} +(1.52247 + 1.63770i) q^{5} +(-2.03359 - 1.69248i) q^{7} +(1.90009 + 1.90009i) q^{8} +O(q^{10})$	\(q+(0.565391 - 0.565391i) q^{2} +1.36066i q^{4} +(1.52247 + 1.63770i) q^{5} +(-2.03359 - 1.69248i) q^{7} +(1.90009 + 1.90009i) q^{8} +(1.78674 + 0.0651510i) q^{10} +(0.948764 + 1.64331i) q^{11} +(-0.343579 - 0.0920618i) q^{13} +(-2.10669 + 0.192862i) q^{14} -0.572739 q^{16} +(1.94672 - 0.521621i) q^{17} +(2.27028 + 3.93224i) q^{19} +(-2.22837 + 2.07158i) q^{20} +(1.46554 + 0.392689i) q^{22} +(1.30061 - 0.348498i) q^{23} +(-0.364152 + 4.98672i) q^{25} +(-0.246308 + 0.142206i) q^{26} +(2.30290 - 2.76704i) q^{28} +(2.25903 + 1.30425i) q^{29} +4.04522i q^{31} +(-4.12400 + 4.12400i) q^{32} +(0.805736 - 1.39558i) q^{34} +(-0.324308 - 5.90718i) q^{35} +(-8.10011 - 2.17042i) q^{37} +(3.50685 + 0.939658i) q^{38} +(-0.218951 + 6.00463i) q^{40} +(-0.370817 + 0.214091i) q^{41} +(-8.10338 + 2.17129i) q^{43} +(-2.23599 + 1.29095i) q^{44} +(0.538318 - 0.932394i) q^{46} +(5.74894 + 5.74894i) q^{47} +(1.27101 + 6.88364i) q^{49} +(2.61356 + 3.02534i) q^{50} +(0.125265 - 0.467496i) q^{52} +(8.46228 - 2.26746i) q^{53} +(-1.24678 + 4.05569i) q^{55} +(-0.648146 - 7.07988i) q^{56} +(2.01465 - 0.539825i) q^{58} -7.41994 q^{59} +4.69334i q^{61} +(2.28713 + 2.28713i) q^{62} +3.51788i q^{64} +(-0.372320 - 0.702843i) q^{65} +(10.4358 - 10.4358i) q^{67} +(0.709751 + 2.64883i) q^{68} +(-3.52323 - 3.15651i) q^{70} +3.22107 q^{71} +(2.41811 + 9.02450i) q^{73} +(-5.80687 + 3.35260i) q^{74} +(-5.35046 + 3.08909i) q^{76} +(0.851867 - 4.94759i) q^{77} -10.1359i q^{79} +(-0.871980 - 0.937977i) q^{80} +(-0.0886114 + 0.330702i) q^{82} +(-4.50725 - 16.8213i) q^{83} +(3.81808 + 2.39399i) q^{85} +(-3.35395 + 5.80922i) q^{86} +(-1.31970 + 4.92517i) q^{88} +(-0.865525 - 1.49913i) q^{89} +(0.542888 + 0.768718i) q^{91} +(0.474189 + 1.76970i) q^{92} +6.50081 q^{94} +(-2.98341 + 9.70478i) q^{95} +(6.33706 - 1.69801i) q^{97} +(4.61057 + 3.17333i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8}+O(q^{10}) $ 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8	$ 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8} - 24 q^{10} + 16 q^{11} - 152 q^{16} + 6 q^{17} - 60 q^{20} + 8 q^{22} - 8 q^{23} + 2 q^{25} + 36 q^{26} + 22 q^{28} - 12 q^{32} + 36 q^{35} - 4 q^{37} + 18 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 44 q^{50} + 54 q^{52} - 8 q^{53} - 148 q^{56} + 28 q^{58} + 124 q^{65} - 24 q^{67} - 42 q^{68} - 34 q^{70} + 40 q^{71} + 36 q^{73} + 96 q^{76} - 58 q^{77} - 36 q^{80} - 66 q^{82} + 138 q^{83} - 20 q^{85} + 16 q^{86} + 46 q^{88} - 48 q^{91} + 26 q^{92} - 188 q^{95} + 48 q^{97} - 102 q^{98}+O(q^{100}) $ 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8 - 24 * q^10 + 16 * q^11 - 152 * q^16 + 6 * q^17 - 60 * q^20 + 8 * q^22 - 8 * q^23 + 2 * q^25 + 36 * q^26 + 22 * q^28 - 12 * q^32 + 36 * q^35 - 4 * q^37 + 18 * q^38 - 6 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 44 * q^50 + 54 * q^52 - 8 * q^53 - 148 * q^56 + 28 * q^58 + 124 * q^65 - 24 * q^67 - 42 * q^68 - 34 * q^70 + 40 * q^71 + 36 * q^73 + 96 * q^76 - 58 * q^77 - 36 * q^80 - 66 * q^82 + 138 * q^83 - 20 * q^85 + 16 * q^86 + 46 * q^88 - 48 * q^91 + 26 * q^92 - 188 * q^95 + 48 * q^97 - 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.565391	−	0.565391i	0.399792	−	0.399792i	−0.478368	−	0.878160i	$-0.658771\pi$
$2$	0.565391	−	0.565391i	0.399792	−	0.399792i	0.878160	+	0.478368i	$0.158771\pi$
$3$		0			0
$3$		0			0
$4$			1.36066i			0.680332i
$5$	1.52247	+	1.63770i	0.680871	+	0.732404i
$5$	1.52247	+	1.63770i	0.680871	+	0.732404i
$6$		0			0
$7$	−2.03359	−	1.69248i	−0.768626	−	0.639698i
$7$	−2.03359	−	1.69248i	−0.768626	−	0.639698i
$8$	1.90009	+	1.90009i	0.671784	+	0.671784i
$9$		0			0
$10$	1.78674	+	0.0651510i	0.565016	+	0.0206025i
$11$	0.948764	+	1.64331i	0.286063	+	0.495476i	0.972866	−	0.231367i	$-0.0743199\pi$
$11$	0.948764	+	1.64331i	0.286063	+	0.495476i	−0.686803	+	0.726843i	$0.740987\pi$
$12$		0			0
$13$	−0.343579	−	0.0920618i	−0.0952918	−	0.0255334i	0.210858	−	0.977517i	$-0.432374\pi$
$13$	−0.343579	−	0.0920618i	−0.0952918	−	0.0255334i	−0.306150	+	0.951983i	$0.599041\pi$
$14$	−2.10669	+	0.192862i	−0.563037	+	0.0515446i
$15$		0			0
$16$	−0.572739			−0.143185
$17$	1.94672	−	0.521621i	0.472148	−	0.126512i	−0.0148962	−	0.999889i	$-0.504742\pi$
$17$	1.94672	−	0.521621i	0.472148	−	0.126512i	0.487044	+	0.873377i	$0.338075\pi$
$18$		0			0
$19$	2.27028	+	3.93224i	0.520838	+	0.902118i	0.999706	+	0.0242311i	$0.00771374\pi$
$19$	2.27028	+	3.93224i	0.520838	+	0.902118i	−0.478868	+	0.877887i	$0.658953\pi$
$20$	−2.22837	+	2.07158i	−0.498278	+	0.463218i
$21$		0			0
$22$	1.46554	+	0.392689i	0.312453	+	0.0837216i
$23$	1.30061	−	0.348498i	0.271197	−	0.0726669i	−0.120658	−	0.992694i	$-0.538500\pi$
$23$	1.30061	−	0.348498i	0.271197	−	0.0726669i	0.391854	+	0.920027i	$0.371834\pi$
$24$		0			0
$25$	−0.364152	+	4.98672i	−0.0728305	+	0.997344i
$26$	−0.246308	+	0.142206i	−0.0483049	+	0.0278889i
$27$		0			0
$28$	2.30290	−	2.76704i	0.435207	−	0.522922i
$29$	2.25903	+	1.30425i	0.419492	+	0.242194i	0.694860	−	0.719145i	$-0.255466\pi$
$29$	2.25903	+	1.30425i	0.419492	+	0.242194i	−0.275368	+	0.961339i	$0.588800\pi$
$30$		0			0
$31$			4.04522i			0.726543i	0.931683	+	0.363271i	$0.118340\pi$
$31$			4.04522i			0.726543i	−0.931683	+	0.363271i	$0.881660\pi$
$32$	−4.12400	+	4.12400i	−0.729028	+	0.729028i
$33$		0			0
$34$	0.805736	−	1.39558i	0.138183	−	0.239339i
$35$	−0.324308	−	5.90718i	−0.0548180	−	0.998496i
$36$		0			0
$37$	−8.10011	−	2.17042i	−1.33165	−	0.356814i	−0.478320	−	0.878186i	$-0.658754\pi$
$37$	−8.10011	−	2.17042i	−1.33165	−	0.356814i	−0.853330	+	0.521371i	$0.825421\pi$
$38$	3.50685	+	0.939658i	0.568886	+	0.152433i
$39$		0			0
$40$	−0.218951	+	6.00463i	−0.0346191	+	0.949415i
$41$	−0.370817	+	0.214091i	−0.0579119	+	0.0334354i	−0.528676	−	0.848823i	$-0.677311\pi$
$41$	−0.370817	+	0.214091i	−0.0579119	+	0.0334354i	0.470764	+	0.882259i	$0.343978\pi$
$42$		0			0
$43$	−8.10338	+	2.17129i	−1.23575	+	0.331119i	−0.816818	−	0.576896i	$-0.804264\pi$
$43$	−8.10338	+	2.17129i	−1.23575	+	0.331119i	−0.418937	+	0.908015i	$0.637597\pi$
$44$	−2.23599	+	1.29095i	−0.337088	+	0.194618i
$45$		0			0
$46$	0.538318	−	0.932394i	0.0793706	−	0.137474i
$47$	5.74894	+	5.74894i	0.838570	+	0.838570i	0.988671	−	0.150101i	$-0.0479598\pi$
$47$	5.74894	+	5.74894i	0.838570	+	0.838570i	−0.150101	+	0.988671i	$0.547960\pi$
$48$		0			0
$49$	1.27101	+	6.88364i	0.181573	+	0.983377i
$50$	2.61356	+	3.02534i	0.369613	+	0.427847i
$51$		0			0
$52$	0.125265	−	0.467496i	0.0173712	−	0.0648301i
$53$	8.46228	−	2.26746i	1.16238	−	0.311460i	0.374466	−	0.927241i	$-0.377826\pi$
$53$	8.46228	−	2.26746i	1.16238	−	0.311460i	0.787917	+	0.615781i	$0.211159\pi$
$54$		0			0
$55$	−1.24678	+	4.05569i	−0.168116	+	0.546869i
$56$	−0.648146	−	7.07988i	−0.0866121	−	0.946089i
$57$		0			0
$58$	2.01465	−	0.539825i	0.264537	−	0.0708824i
$59$	−7.41994			−0.965994			−0.482997	−	0.875622i	$-0.660452\pi$
$59$	−7.41994			−0.965994			−0.482997	+	0.875622i	$0.660452\pi$
$60$		0			0
$61$			4.69334i			0.600920i	0.953794	+	0.300460i	$0.0971402\pi$
$61$			4.69334i			0.600920i	−0.953794	+	0.300460i	$0.902860\pi$
$62$	2.28713	+	2.28713i	0.290466	+	0.290466i
$63$		0			0
$64$			3.51788i			0.439734i
$65$	−0.372320	−	0.702843i	−0.0461807	−	0.0871770i
$66$		0			0
$67$	10.4358	−	10.4358i	1.27493	−	1.27493i	0.331463	−	0.943468i	$-0.392458\pi$
$67$	10.4358	−	10.4358i	1.27493	−	1.27493i	0.943468	−	0.331463i	$-0.107542\pi$
$68$	0.709751	+	2.64883i	0.0860700	+	0.321217i
$69$		0			0
$70$	−3.52323	−	3.15651i	−0.421107	−	0.377275i
$71$	3.22107			0.382270			0.191135	−	0.981564i	$-0.438783\pi$
$71$	3.22107			0.382270			0.191135	+	0.981564i	$0.438783\pi$
$72$		0			0
$73$	2.41811	+	9.02450i	0.283018	+	1.05624i	0.950275	+	0.311411i	$0.100801\pi$
$73$	2.41811	+	9.02450i	0.283018	+	1.05624i	−0.667257	+	0.744827i	$0.732532\pi$
$74$	−5.80687	+	3.35260i	−0.675035	+	0.389731i
$75$		0			0
$76$	−5.35046	+	3.08909i	−0.613740	+	0.354343i
$77$	0.851867	−	4.94759i	0.0970792	−	0.563830i
$78$		0			0
$79$		−	10.1359i		−	1.14037i	−0.821515	−	0.570187i	$-0.806871\pi$
$79$		−	10.1359i		−	1.14037i	0.821515	−	0.570187i	$-0.193129\pi$
$80$	−0.871980	−	0.937977i	−0.0974903	−	0.104869i
$81$		0			0
$82$	−0.0886114	+	0.330702i	−0.00978549	+	0.0365199i
$83$	−4.50725	−	16.8213i	−0.494735	−	1.84637i	−0.531512	−	0.847051i	$-0.678376\pi$
$83$	−4.50725	−	16.8213i	−0.494735	−	1.84637i	0.0367774	−	0.999323i	$-0.488291\pi$
$84$		0			0
$85$	3.81808	+	2.39399i	0.414129	+	0.259665i
$86$	−3.35395	+	5.80922i	−0.361666	+	0.626424i
$87$		0			0
$88$	−1.31970	+	4.92517i	−0.140680	+	0.525025i
$89$	−0.865525	−	1.49913i	−0.0917455	−	0.158908i	0.816500	−	0.577345i	$-0.195911\pi$
$89$	−0.865525	−	1.49913i	−0.0917455	−	0.158908i	−0.908246	+	0.418437i	$0.862578\pi$
$90$		0			0
$91$	0.542888	+	0.768718i	0.0569102	+	0.0805836i
$92$	0.474189	+	1.76970i	0.0494377	+	0.184504i
$93$		0			0
$94$	6.50081			0.670507
$95$	−2.98341	+	9.70478i	−0.306091	+	0.995689i
$96$		0			0
$97$	6.33706	−	1.69801i	0.643431	−	0.172407i	0.0776741	−	0.996979i	$-0.475251\pi$
$97$	6.33706	−	1.69801i	0.643431	−	0.172407i	0.565757	+	0.824572i	$0.308584\pi$
$98$	4.61057	+	3.17333i	0.465738	+	0.320555i
$99$		0			0
$100$	−6.78526	−	0.495489i	−0.678526	−	0.0495489i
$101$	14.8374	−	8.56641i	1.47638	−	0.852389i	0.476737	−	0.879046i	$-0.341820\pi$
$101$	14.8374	−	8.56641i	1.47638	−	0.852389i	0.999645	+	0.0266569i	$0.00848618\pi$
$102$		0			0
$103$	−4.10756	−	15.3296i	−0.404729	−	1.51047i	−0.804554	−	0.593879i	$-0.797596\pi$
$103$	−4.10756	−	15.3296i	−0.404729	−	1.51047i	0.399825	−	0.916592i	$-0.369071\pi$
$104$	−0.477906	−	0.827758i	−0.0468626	−	0.0811684i
$105$		0			0
$106$	3.50250	−	6.06650i	0.340193	−	0.589231i
$107$	−4.26877	−	1.14381i	−0.412677	−	0.110577i	0.0465063	−	0.998918i	$-0.485191\pi$
$107$	−4.26877	−	1.14381i	−0.412677	−	0.110577i	−0.459183	+	0.888341i	$0.651858\pi$
$108$		0			0
$109$	5.17609	+	2.98842i	0.495779	+	0.286238i	0.726969	−	0.686670i	$-0.240928\pi$
$109$	5.17609	+	2.98842i	0.495779	+	0.286238i	−0.231190	+	0.972909i	$0.574262\pi$
$110$	1.58813	+	2.99797i	0.151422	+	0.285845i
$111$		0			0
$112$	1.16472	+	0.969350i	0.110056	+	0.0915950i
$113$	4.91835	−	18.3555i	0.462679	−	1.72674i	−0.201791	−	0.979429i	$-0.564676\pi$
$113$	4.91835	−	18.3555i	0.462679	−	1.72674i	0.664470	−	0.747315i	$-0.268657\pi$
$114$		0			0
$115$	2.55089	+	1.59944i	0.237871	+	0.149149i
$116$	−1.77465	+	3.07379i	−0.164772	+	0.285394i
$117$		0			0
$118$	−4.19517	+	4.19517i	−0.386197	+	0.386197i
$119$	−4.84166	−	2.23401i	−0.443835	−	0.204792i
$120$		0			0
$121$	3.69969	−	6.40806i	0.336336	−	0.582551i
$122$	2.65357	+	2.65357i	0.240243	+	0.240243i
$123$		0			0
$124$	−5.50419			−0.494291
$125$	−8.72119	+	6.99577i	−0.780047	+	0.625721i
$126$		0			0
$127$	−5.71266	+	5.71266i	−0.506917	+	0.506917i	−0.913579	−	0.406662i	$-0.866693\pi$
$127$	−5.71266	+	5.71266i	−0.506917	+	0.506917i	0.406662	+	0.913579i	$0.366693\pi$
$128$	−6.25903	−	6.25903i	−0.553225	−	0.553225i
$129$		0			0
$130$	−0.607888	−	0.186875i	−0.0533153	−	0.0163900i
$131$	8.45569	+	4.88189i	0.738777	+	0.426533i	0.821624	−	0.570029i	$-0.193068\pi$
$131$	8.45569	+	4.88189i	0.738777	+	0.426533i	−0.0828477	+	0.996562i	$0.526401\pi$
$132$		0			0
$133$	2.03842	−	11.8390i	0.176753	−	1.02657i
$134$		−	11.8006i		−	1.01941i
$135$		0			0
$136$	4.69006	+	2.70781i	0.402170	+	0.232193i
$137$	18.1023	+	4.85048i	1.54658	+	0.414405i	0.928385	−	0.371620i	$-0.121198\pi$
$137$	18.1023	+	4.85048i	1.54658	+	0.414405i	0.618195	+	0.786025i	$0.287864\pi$
$138$		0			0
$139$	1.20016	+	2.07873i	0.101796	+	0.176316i	0.912425	−	0.409245i	$-0.134208\pi$
$139$	1.20016	+	2.07873i	0.101796	+	0.176316i	−0.810629	+	0.585561i	$0.800874\pi$
$140$	8.03770	−	0.441274i	0.679310	−	0.0372945i
$141$		0			0
$142$	1.82116	−	1.82116i	0.152829	−	0.152829i
$143$	−0.174690	−	0.651952i	−0.0146083	−	0.0545189i
$144$		0			0
$145$	1.30334	+	5.68532i	0.108236	+	0.472140i
$146$	6.46955	+	3.73520i	0.535424	+	0.309127i
$147$		0			0
$148$	2.95321	−	11.0215i	0.242752	−	0.905964i
$149$	3.59293	+	2.07438i	0.294344	+	0.169940i	0.639899	−	0.768459i	$-0.278976\pi$
$149$	3.59293	+	2.07438i	0.294344	+	0.169940i	−0.345555	+	0.938398i	$0.612309\pi$
$150$		0			0
$151$	−7.78315	−	13.4808i	−0.633384	−	1.09705i	−0.986855	−	0.161608i	$-0.948332\pi$
$151$	−7.78315	−	13.4808i	−0.633384	−	1.09705i	0.353471	−	0.935445i	$-0.385001\pi$
$152$	−3.15788	+	11.7854i	−0.256138	+	0.955918i
$153$		0			0
$154$	−2.31569	−	3.27896i	−0.186603	−	0.264226i
$155$	−6.62487	+	6.15874i	−0.532123	+	0.494682i
$156$		0			0
$157$	14.7560	+	14.7560i	1.17766	+	1.17766i	0.980340	+	0.197317i	$0.0632229\pi$
$157$	14.7560	+	14.7560i	1.17766	+	1.17766i	0.197317	+	0.980340i	$0.436777\pi$
$158$	−5.73073	−	5.73073i	−0.455913	−	0.455913i
$159$		0			0
$160$	−13.0326	−	0.475216i	−1.03032	−	0.0375691i
$161$	−3.23475	−	1.49256i	−0.254934	−	0.117630i
$162$		0			0
$163$	3.33601	−	12.4502i	0.261296	−	0.975172i	−0.703182	−	0.711010i	$-0.748238\pi$
$163$	3.33601	−	12.4502i	0.261296	−	0.975172i	0.964478	−	0.264162i	$-0.0850953\pi$
$164$	−0.291307	−	0.504558i	−0.0227472	−	0.0393993i
$165$		0			0
$166$	−12.0590	−	6.96224i	−0.935957	−	0.540375i
$167$	2.28189	−	8.51613i	0.176578	−	0.658998i	−0.819700	−	0.572794i	$-0.805860\pi$
$167$	2.28189	−	8.51613i	0.176578	−	0.658998i	0.996277	−	0.0862041i	$-0.0274737\pi$
$168$		0			0
$169$	−11.1488	−	6.43674i	−0.857597	−	0.495134i
$170$	3.51225	−	0.805169i	0.269378	−	0.0617536i
$171$		0			0
$172$	−2.95440	−	11.0260i	−0.225271	−	0.840724i
$173$	−16.2398	+	16.2398i	−1.23469	+	1.23469i	−0.272548	+	0.962142i	$0.587866\pi$
$173$	−16.2398	+	16.2398i	−1.23469	+	1.23469i	−0.962142	+	0.272548i	$0.912134\pi$
$174$		0			0
$175$	9.18047	−	9.52465i	0.693978	−	0.719996i
$176$	−0.543394	−	0.941186i	−0.0409599	−	0.0709446i
$177$		0			0
$178$	−1.33696	−	0.358237i	−0.100209	−	0.0268510i
$179$	−5.47867	−	3.16311i	−0.409495	−	0.236422i	0.281078	−	0.959685i	$-0.409308\pi$
$179$	−5.47867	−	3.16311i	−0.409495	−	0.236422i	−0.690573	+	0.723263i	$0.742641\pi$
$180$		0			0
$181$			19.4981i			1.44928i	0.689128	+	0.724640i	$0.257994\pi$
$181$			19.4981i			1.44928i	−0.689128	+	0.724640i	$0.742006\pi$
$182$	0.741571	+	0.127682i	0.0549689	+	0.00946445i
$183$		0			0
$184$	3.13346	+	1.80911i	0.231002	+	0.133369i
$185$	−8.77769	−	16.5700i	−0.645349	−	1.21825i
$186$		0			0
$187$	2.70416	+	2.70416i	0.197748	+	0.197748i
$188$	−7.82239	+	7.82239i	−0.570506	+	0.570506i
$189$		0			0
$190$	3.80020	+	7.17379i	0.275696	+	0.520442i
$191$	−22.2730			−1.61162			−0.805809	−	0.592176i	$-0.798269\pi$
$191$	−22.2730			−1.61162			−0.805809	+	0.592176i	$0.798269\pi$
$192$		0			0
$193$	−6.69608	−	6.69608i	−0.481994	−	0.481994i	0.423774	−	0.905768i	$-0.360705\pi$
$193$	−6.69608	−	6.69608i	−0.481994	−	0.481994i	−0.905768	+	0.423774i	$0.860705\pi$
$194$	2.62288	−	4.54296i	0.188312	−	0.326166i
$195$		0			0
$196$	−9.36633	+	1.72942i	−0.669024	+	0.123530i
$197$	−3.48413	+	3.48413i	−0.248234	+	0.248234i	−0.820245	−	0.572012i	$-0.806163\pi$
$197$	−3.48413	+	3.48413i	−0.248234	+	0.248234i	0.572012	+	0.820245i	$0.306163\pi$
$198$		0			0
$199$	−0.232271	+	0.402305i	−0.0164653	+	0.0285187i	−0.874141	−	0.485673i	$-0.838575\pi$
$199$	−0.232271	+	0.402305i	−0.0164653	+	0.0285187i	0.857675	+	0.514192i	$0.171908\pi$
$200$	−10.1671	+	8.78330i	−0.718926	+	0.621073i
$201$		0			0
$202$	3.54559	−	13.2323i	0.249467	−	0.931024i
$203$	−2.38653	−	6.47570i	−0.167502	−	0.454505i
$204$		0			0
$205$	−0.915177	−	0.281340i	−0.0639187	−	0.0196497i
$206$	−10.9896	−	6.34485i	−0.765682	−	0.442067i
$207$		0			0
$208$	0.196781	+	0.0527274i	0.0136443	+	0.00365599i
$209$	−4.30792	+	7.46154i	−0.297985	+	0.516125i
$210$		0			0
$211$	−11.0638	−	19.1630i	−0.761663	−	1.31924i	−0.941993	−	0.335632i	$-0.891050\pi$
$211$	−11.0638	−	19.1630i	−0.761663	−	1.31924i	0.180331	−	0.983606i	$-0.442283\pi$
$212$	3.08525	+	11.5143i	0.211896	+	0.790807i
$213$		0			0
$214$	−3.06023	+	1.76682i	−0.209193	+	0.120777i
$215$	−15.8931	−	9.96521i	−1.08390	−	0.679622i
$216$		0			0
$217$	6.84646	−	8.22634i	0.464768	−	0.558440i
$218$	4.61614	−	1.23689i	0.312644	−	0.0837728i
$219$		0			0
$220$	−5.51843	−	1.69646i	−0.372053	−	0.114375i
$221$	−0.716873			−0.0482221
$222$		0			0
$223$	−0.546729	−	2.04042i	−0.0366116	−	0.136637i	0.945201	−	0.326489i	$-0.105866\pi$
$223$	−0.546729	−	2.04042i	−0.0366116	−	0.136637i	−0.981813	+	0.189853i	$0.939199\pi$
$224$	15.3664	−	1.40675i	1.02671	−	0.0939925i
$225$		0			0
$226$	−7.59727	−	13.1589i	−0.505363	−	0.875314i
$227$	0.592460	−	2.21109i	0.0393229	−	0.146755i	−0.943473	−	0.331449i	$-0.892463\pi$
$227$	0.592460	−	2.21109i	0.0393229	−	0.146755i	0.982796	+	0.184694i	$0.0591293\pi$
$228$		0			0
$229$	−0.0658670	+	0.114085i	−0.00435262	+	0.00753895i	−0.868194	−	0.496226i	$-0.834719\pi$
$229$	−0.0658670	+	0.114085i	−0.00435262	+	0.00753895i	0.863841	+	0.503765i	$0.168052\pi$
$230$	2.34656	−	0.537939i	0.154728	−	0.0354706i
$231$		0			0
$232$	1.81417	+	6.77057i	0.119106	+	0.444510i
$233$	1.96018	−	7.31550i	0.128416	−	0.479254i	−0.871523	−	0.490355i	$-0.836867\pi$
$233$	1.96018	−	7.31550i	0.128416	−	0.479254i	0.999938	+	0.0111012i	$0.00353370\pi$
$234$		0			0
$235$	−0.662460	+	18.1677i	−0.0432141	+	1.18513i
$236$		−	10.0960i		−	0.657197i
$237$		0			0
$238$	−4.00053	+	1.47434i	−0.259316	+	0.0955674i
$239$	7.82313	−	4.51669i	0.506036	−	0.292160i	−0.225167	−	0.974320i	$-0.572293\pi$
$239$	7.82313	−	4.51669i	0.506036	−	0.292160i	0.731203	+	0.682160i	$0.238959\pi$
$240$		0			0
$241$	13.9256	−	8.03997i	0.897029	−	0.517900i	0.0207939	−	0.999784i	$-0.493381\pi$
$241$	13.9256	−	8.03997i	0.897029	−	0.517900i	0.876235	+	0.481884i	$0.160047\pi$
$242$	−1.53129	−	5.71484i	−0.0984348	−	0.367364i
$243$		0			0
$244$	−6.38606			−0.408826
$245$	−9.33829	+	12.5617i	−0.596601	+	0.802538i
$246$		0			0
$247$	−0.418012	−	1.56004i	−0.0265975	−	0.0992632i
$248$	−7.68629	+	7.68629i	−0.488080	+	0.488080i
$249$		0			0
$250$	−0.975534	+	8.88624i	−0.0616982	+	0.562015i
$251$			11.2568i			0.710521i	0.934767	+	0.355260i	$0.115608\pi$
$251$			11.2568i			0.710521i	−0.934767	+	0.355260i	$0.884392\pi$
$252$		0			0
$253$	1.80667	+	1.80667i	0.113584	+	0.113584i
$254$			6.45978i			0.405323i
$255$		0			0
$256$	−14.1134			−0.882085
$257$	5.46560	−	1.46450i	0.340935	−	0.0913531i	−0.0842894	−	0.996441i	$-0.526862\pi$
$257$	5.46560	−	1.46450i	0.340935	−	0.0913531i	0.425224	+	0.905088i	$0.360195\pi$
$258$		0			0
$259$	12.7989	+	18.1230i	0.795288	+	1.12611i
$260$	0.956334	−	0.506603i	0.0593093	−	0.0314182i
$261$		0			0
$262$	7.54095	−	2.02059i	0.465882	−	0.124833i
$263$	0.631038	−	2.35507i	0.0389115	−	0.145220i	−0.943737	−	0.330697i	$-0.892716\pi$
$263$	0.631038	−	2.35507i	0.0389115	−	0.145220i	0.982649	+	0.185477i	$0.0593830\pi$
$264$		0			0
$265$	16.5970	+	10.4066i	1.01955	+	0.639270i
$266$	−5.54116	−	7.84617i	−0.339750	−	0.481079i
$267$		0			0
$268$	14.1996	+	14.1996i	0.867377	+	0.867377i
$269$	−2.87950	+	4.98744i	−0.175566	+	0.304090i	−0.940357	−	0.340189i	$-0.889509\pi$
$269$	−2.87950	+	4.98744i	−0.175566	+	0.304090i	0.764791	+	0.644279i	$0.222842\pi$
$270$		0			0
$271$	−22.3773	+	12.9196i	−1.35933	+	0.784808i	−0.989533	−	0.144306i	$-0.953905\pi$
$271$	−22.3773	+	12.9196i	−1.35933	+	0.784808i	−0.369793	+	0.929114i	$0.620572\pi$
$272$	−1.11496	+	0.298753i	−0.0676044	+	0.0181145i
$273$		0			0
$274$	12.9773	−	7.49244i	0.783986	−	0.452635i
$275$	−8.54021	+	4.13281i	−0.514994	+	0.249218i
$276$		0			0
$277$	16.4361	+	4.40404i	0.987550	+	0.264613i	0.716221	−	0.697873i	$-0.245870\pi$
$277$	16.4361	+	4.40404i	0.987550	+	0.264613i	0.271329	+	0.962487i	$0.412537\pi$
$278$	1.85386	+	0.496739i	0.111187	+	0.0297924i
$279$		0			0
$280$	10.6080	−	11.8404i	0.633948	−	0.707599i
$281$	16.1409	−	27.9568i	0.962884	−	1.66776i	0.247688	−	0.968840i	$-0.420329\pi$
$281$	16.1409	−	27.9568i	0.962884	−	1.66776i	0.715196	−	0.698924i	$-0.246337\pi$
$282$		0			0
$283$	0.866870	−	0.866870i	0.0515300	−	0.0515300i	−0.680872	−	0.732402i	$-0.738399\pi$
$283$	0.866870	−	0.866870i	0.0515300	−	0.0515300i	0.732402	+	0.680872i	$0.238399\pi$
$284$			4.38279i			0.260071i
$285$		0			0
$286$	−0.467376	−	0.269840i	−0.0276365	−	0.0159560i
$287$	1.11644	+	0.192226i	0.0659012	+	0.0113467i
$288$		0			0
$289$	−11.2048	+	6.46911i	−0.659107	+	0.380536i
$290$	3.95133	+	2.47754i	0.232030	+	0.145486i
$291$		0			0
$292$	−12.2793	+	3.29023i	−0.718593	+	0.192546i
$293$	5.65776	+	1.51599i	0.330530	+	0.0885653i	0.420268	−	0.907400i	$-0.361936\pi$
$293$	5.65776	+	1.51599i	0.330530	+	0.0885653i	−0.0897376	+	0.995965i	$0.528603\pi$
$294$		0			0
$295$	−11.2967	−	12.1517i	−0.657717	−	0.707497i
$296$	−11.2670	−	19.5149i	−0.654878	−	1.13428i
$297$		0			0
$298$	3.20424	−	0.858575i	0.185617	−	0.0497359i
$299$	−0.478947			−0.0276982
$300$		0			0
$301$	20.1539	+	9.29929i	1.16165	+	0.536002i
$302$	−12.0225	−	3.22141i	−0.691815	−	0.185371i
$303$		0			0
$304$	−1.30028	−	2.25215i	−0.0745760	−	0.129169i
$305$	−7.68630	+	7.14548i	−0.440116	+	0.409149i
$306$		0			0
$307$	3.77724	+	3.77724i	0.215578	+	0.215578i	0.806632	−	0.591054i	$-0.201288\pi$
$307$	3.77724	+	3.77724i	0.215578	+	0.215578i	−0.591054	+	0.806632i	$0.701288\pi$
$308$	6.73201	+	1.15910i	0.383592	+	0.0660461i
$309$		0			0
$310$	−0.263550	+	7.22775i	−0.0149686	+	0.410508i
$311$			20.9633i			1.18872i	0.804200	+	0.594359i	$0.202594\pi$
$311$			20.9633i			1.18872i	−0.804200	+	0.594359i	$0.797406\pi$
$312$		0			0
$313$	8.80999	−	8.80999i	0.497970	−	0.497970i	−0.412835	−	0.910806i	$-0.635462\pi$
$313$	8.80999	−	8.80999i	0.497970	−	0.497970i	0.910806	+	0.412835i	$0.135462\pi$
$314$	16.6858			0.941636
$315$		0			0
$316$	13.7915			0.775834
$317$	−10.4508	+	10.4508i	−0.586975	+	0.586975i	−0.936811	−	0.349836i	$-0.886237\pi$
$317$	−10.4508	+	10.4508i	−0.586975	+	0.586975i	0.349836	+	0.936811i	$0.386237\pi$
$318$		0			0
$319$			4.94972i			0.277131i
$320$	−5.76124	+	5.35587i	−0.322063	+	0.299402i
$321$		0			0
$322$	−2.67278	+	0.985018i	−0.148948	+	0.0548929i
$323$	6.47073	+	6.47073i	0.360041	+	0.360041i
$324$		0			0
$325$	0.584202	−	1.67981i	0.0324057	−	0.0931791i
$326$	−5.15306	−	8.92537i	−0.285402	−	0.494330i
$327$		0			0
$328$	−1.11138	−	0.297793i	−0.0613656	−	0.0164429i
$329$	−1.96104	−	21.4210i	−0.108116	−	1.18098i
$330$		0			0
$331$	−6.56728			−0.360970			−0.180485	−	0.983578i	$-0.557767\pi$
$331$	−6.56728			−0.360970			−0.180485	+	0.983578i	$0.557767\pi$
$332$	22.8881	−	6.13285i	1.25615	−	0.336584i
$333$		0			0
$334$	−3.52479	−	6.10511i	−0.192868	−	0.334057i
$335$	32.9789	+	1.20253i	1.80183	+	0.0657012i
$336$		0			0
$337$	13.6413	+	3.65517i	0.743087	+	0.199110i	0.610450	−	0.792055i	$-0.290989\pi$
$337$	13.6413	+	3.65517i	0.743087	+	0.199110i	0.132638	+	0.991165i	$0.457655\pi$
$338$	−9.94269	+	2.66414i	−0.540811	+	0.144910i
$339$		0			0
$340$	−3.25742	+	5.19513i	−0.176658	+	0.281746i
$341$	−6.64754	+	3.83796i	−0.359985	+	0.207837i
$342$		0			0
$343$	9.06571	−	16.1497i	0.489503	−	0.872002i
$344$	−19.5228	−	11.2715i	−1.05260	−	0.607719i
$345$		0			0
$346$			18.3637i			0.987239i
$347$	19.3772	−	19.3772i	1.04022	−	1.04022i	0.0410644	−	0.999157i	$-0.486925\pi$
$347$	19.3772	−	19.3772i	1.04022	−	1.04022i	0.999157	−	0.0410644i	$-0.0130749\pi$
$348$		0			0
$349$	5.35414	−	9.27365i	0.286601	−	0.496407i	−0.686395	−	0.727229i	$-0.740808\pi$
$349$	5.35414	−	9.27365i	0.286601	−	0.496407i	0.972996	+	0.230822i	$0.0741414\pi$
$350$	−0.194594	−	10.5757i	−0.0104015	−	0.565296i
$351$		0			0
$352$	−10.6897	−	2.86430i	−0.569764	−	0.152668i
$353$	17.6374	+	4.72592i	0.938742	+	0.251535i	0.695579	−	0.718450i	$-0.255148\pi$
$353$	17.6374	+	4.72592i	0.938742	+	0.251535i	0.243164	+	0.969985i	$0.421815\pi$
$354$		0			0
$355$	4.90399	+	5.27516i	0.260277	+	0.279976i
$356$	2.03982	−	1.17769i	0.108110	−	0.0624174i
$357$		0			0
$358$	−4.88599	+	1.30920i	−0.258233	+	0.0691932i
$359$	−6.12023	+	3.53352i	−0.323013	+	0.186492i	−0.652735	−	0.757586i	$-0.726378\pi$
$359$	−6.12023	+	3.53352i	−0.323013	+	0.186492i	0.329722	+	0.944078i	$0.393045\pi$
$360$		0			0
$361$	−0.808341	+	1.40009i	−0.0425442	+	0.0736888i
$362$	11.0240	+	11.0240i	0.579411	+	0.579411i
$363$		0			0
$364$	−1.04597	+	0.738689i	−0.0548236	+	0.0387178i
$365$	−11.0980	+	17.6997i	−0.580894	+	0.926445i
$366$		0			0
$367$	5.65810	−	21.1163i	0.295350	−	1.10226i	−0.645588	−	0.763686i	$-0.723388\pi$
$367$	5.65810	−	21.1163i	0.295350	−	1.10226i	0.940939	−	0.338577i	$-0.109946\pi$
$368$	−0.744912	+	0.199599i	−0.0388312	+	0.0104048i
$369$		0			0
$370$	−14.3314	−	4.40570i	−0.745052	−	0.229041i
$371$	−21.0465	−	9.71115i	−1.09268	−	0.504178i
$372$		0			0
$373$	−18.0746	+	4.84308i	−0.935868	+	0.250765i	−0.694355	−	0.719632i	$-0.744310\pi$
$373$	−18.0746	+	4.84308i	−0.935868	+	0.250765i	−0.241513	+	0.970398i	$0.577644\pi$
$374$	3.05781			0.158116
$375$		0			0
$376$			21.8470i			1.12668i
$377$	−0.656086	−	0.656086i	−0.0337901	−	0.0337901i
$378$		0			0
$379$		−	14.4563i		−	0.742571i	−0.928519	−	0.371285i	$-0.878917\pi$
$379$		−	14.4563i		−	0.742571i	0.928519	−	0.371285i	$-0.121083\pi$
$380$	−13.2049	−	4.05942i	−0.677400	−	0.208244i
$381$		0			0
$382$	−12.5930	+	12.5930i	−0.644312	+	0.644312i
$383$	2.48787	+	9.28486i	0.127124	+	0.474434i	0.999906	−	0.0136757i	$-0.00435326\pi$
$383$	2.48787	+	9.28486i	0.127124	+	0.474434i	−0.872782	+	0.488110i	$0.837687\pi$
$384$		0			0
$385$	9.39963	−	6.13746i	0.479049	−	0.312794i
$386$	−7.57181			−0.385395
$387$		0			0
$388$	2.31042	+	8.62262i	0.117294	+	0.437747i
$389$	3.85305	−	2.22456i	0.195357	−	0.112790i	−0.399131	−	0.916894i	$-0.630688\pi$
$389$	3.85305	−	2.22456i	0.195357	−	0.112790i	0.594488	+	0.804104i	$0.297355\pi$
$390$		0			0
$391$	2.35014	−	1.35685i	0.118852	−	0.0686191i
$392$	−10.6645	+	15.4946i	−0.538639	+	0.782595i
$393$		0			0
$394$			3.93979i			0.198484i
$395$	16.5996	−	15.4316i	0.835214	−	0.776447i
$396$		0			0
$397$	1.78834	−	6.67418i	0.0897542	−	0.334967i	−0.906418	−	0.422382i	$-0.861194\pi$
$397$	1.78834	−	6.67418i	0.0897542	−	0.334967i	0.996172	+	0.0874150i	$0.0278606\pi$
$398$	0.0961359	+	0.358784i	0.00481886	+	0.0179842i
$399$		0			0
$400$	0.208564	−	2.85609i	0.0104282	−	0.142804i
$401$	13.7579	−	23.8294i	0.687037	−	1.18998i	−0.285755	−	0.958303i	$-0.592244\pi$
$401$	13.7579	−	23.8294i	0.687037	−	1.18998i	0.972792	−	0.231680i	$-0.0744224\pi$
$402$		0			0
$403$	0.372410	−	1.38985i	0.0185511	−	0.0692336i
$404$	11.6560	+	20.1888i	0.579908	+	1.00443i
$405$		0			0
$406$	−5.01063	−	2.31198i	−0.248673	−	0.114742i
$407$	−4.11843	−	15.3702i	−0.204143	−	0.761872i
$408$		0			0
$409$	−33.8152			−1.67205			−0.836026	−	0.548689i	$-0.815127\pi$
$409$	−33.8152			−1.67205			−0.836026	+	0.548689i	$0.815127\pi$
$410$	−0.676501	+	0.358366i	−0.0334100	+	0.0176984i
$411$		0			0
$412$	20.8585	−	5.58901i	1.02762	−	0.275351i
$413$	15.0891	+	12.5581i	0.742488	+	0.617944i
$414$		0			0
$415$	20.6861	−	32.9915i	1.01544	−	1.61949i
$416$	1.79659	−	1.03726i	0.0880849	−	0.0508558i
$417$		0			0
$418$	1.78303	+	6.65435i	0.0872107	+	0.325475i
$419$	12.1462	+	21.0378i	0.593380	+	1.02776i	0.993773	+	0.111421i	$0.0355402\pi$
$419$	12.1462	+	21.0378i	0.593380	+	1.02776i	−0.400393	+	0.916343i	$0.631127\pi$
$420$		0			0
$421$	−2.49624	+	4.32361i	−0.121659	+	0.210720i	−0.920422	−	0.390926i	$-0.872155\pi$
$421$	−2.49624	+	4.32361i	−0.121659	+	0.210720i	0.798763	+	0.601646i	$0.205488\pi$
$422$	−17.0900	−	4.57925i	−0.831928	−	0.222914i
$423$		0			0
$424$	20.3875	+	11.7707i	0.990104	+	0.571637i
$425$	1.89228	+	9.89768i	0.0917889	+	0.480108i
$426$		0			0
$427$	7.94339	−	9.54435i	0.384407	−	0.461883i
$428$	1.55635	−	5.80836i	0.0752288	−	0.280758i
$429$		0			0
$430$	−14.6201	+	3.35159i	−0.705043	+	0.161628i
$431$	2.71752	−	4.70688i	0.130898	−	0.226723i	−0.793125	−	0.609059i	$-0.791547\pi$
$431$	2.71752	−	4.70688i	0.130898	−	0.226723i	0.924023	+	0.382337i	$0.124881\pi$
$432$		0			0
$433$	−12.6985	+	12.6985i	−0.610249	+	0.610249i	−0.943011	−	0.332762i	$-0.892019\pi$
$433$	−12.6985	+	12.6985i	−0.610249	+	0.610249i	0.332762	+	0.943011i	$0.392019\pi$
$434$	−0.780170	−	8.52203i	−0.0374494	−	0.409071i
$435$		0			0
$436$	−4.06623	+	7.04292i	−0.194737	+	0.337295i
$437$	4.32314	+	4.32314i	0.206804	+	0.206804i
$438$		0			0
$439$	−10.1789			−0.485812			−0.242906	−	0.970050i	$-0.578101\pi$
$439$	−10.1789			−0.485812			−0.242906	+	0.970050i	$0.578101\pi$
$440$	−10.0752	+	5.33717i	−0.480315	+	0.254440i
$441$		0			0
$442$	−0.405314	+	0.405314i	−0.0192788	+	0.0192788i
$443$	−3.28434	−	3.28434i	−0.156043	−	0.156043i	0.624767	−	0.780811i	$-0.285194\pi$
$443$	−3.28434	−	3.28434i	−0.156043	−	0.156043i	−0.780811	+	0.624767i	$0.785194\pi$
$444$		0			0
$445$	1.13740	−	3.69986i	0.0539179	−	0.175390i
$446$	−1.46275	−	0.844520i	−0.0692633	−	0.0399892i
$447$		0			0
$448$	5.95394	−	7.15393i	0.281297	−	0.337992i
$449$			36.0848i			1.70295i	0.524398	+	0.851474i	$0.324291\pi$
$449$			36.0848i			1.70295i	−0.524398	+	0.851474i	$0.675709\pi$
$450$		0			0
$451$	−0.703636	−	0.406244i	−0.0331329	−	0.0191293i
$452$	24.9757	+	6.69223i	1.17476	+	0.314776i
$453$		0			0
$454$	−0.915160	−	1.58510i	−0.0429506	−	0.0743926i
$455$	−0.432401	+	2.05944i	−0.0202713	+	0.0965482i
$456$		0			0
$457$	−19.3194	+	19.3194i	−0.903725	+	0.903725i	−0.995756	−	0.0920315i	$-0.970664\pi$
$457$	−19.3194	+	19.3194i	−0.903725	+	0.903725i	0.0920315	+	0.995756i	$0.470664\pi$
$458$	0.0272621	+	0.101743i	0.00127387	+	0.00475415i
$459$		0			0
$460$	−2.17630	+	3.47090i	−0.101471	+	0.161832i
$461$	−2.22321	−	1.28357i	−0.103545	−	0.0597819i	0.447333	−	0.894367i	$-0.352374\pi$
$461$	−2.22321	−	1.28357i	−0.103545	−	0.0597819i	−0.550878	+	0.834586i	$0.685707\pi$
$462$		0			0
$463$	−6.43065	+	23.9995i	−0.298858	+	1.11535i	0.639247	+	0.769001i	$0.279246\pi$
$463$	−6.43065	+	23.9995i	−0.298858	+	1.11535i	−0.938105	+	0.346351i	$0.887421\pi$
$464$	−1.29384	−	0.746997i	−0.0600649	−	0.0346785i
$465$		0			0
$466$	−3.02785	−	5.24439i	−0.140262	−	0.242942i
$467$	−5.15827	+	19.2509i	−0.238696	+	0.890827i	0.737751	+	0.675073i	$0.235888\pi$
$467$	−5.15827	+	19.2509i	−0.238696	+	0.890827i	−0.976448	+	0.215755i	$0.930779\pi$
$468$		0			0
$469$	−38.8844	+	3.55977i	−1.79552	+	0.164375i
$470$	9.89731	+	10.6464i	0.456529	+	0.491082i
$471$		0			0
$472$	−14.0986	−	14.0986i	−0.648939	−	0.648939i
$473$	−11.2563	−	11.2563i	−0.517565	−	0.517565i
$474$		0			0
$475$	−20.4357	+	9.88932i	−0.937655	+	0.453753i
$476$	3.03975	−	6.58788i	0.139327	−	0.301955i
$477$		0			0
$478$	1.86944	−	6.97683i	0.0855060	−	0.319113i
$479$	−6.81934	−	11.8114i	−0.311584	−	0.539679i	0.667122	−	0.744949i	$-0.267526\pi$
$479$	−6.81934	−	11.8114i	−0.311584	−	0.539679i	−0.978705	+	0.205270i	$0.934193\pi$
$480$		0			0
$481$	2.58322	+	1.49142i	0.117785	+	0.0680030i
$482$	3.32771	−	12.4192i	0.151573	−	0.565678i
$483$		0			0
$484$	8.71922	+	5.03404i	0.396328	+	0.228820i
$485$	12.4288	+	7.79306i	0.564365	+	0.353865i
$486$		0			0
$487$	−0.218040	−	0.813737i	−0.00988034	−	0.0368739i	0.960810	−	0.277209i	$-0.0894094\pi$
$487$	−0.218040	−	0.813737i	−0.00988034	−	0.0368739i	−0.970690	+	0.240335i	$0.922743\pi$
$488$	−8.91777	+	8.91777i	−0.403688	+	0.403688i
$489$		0			0
$490$	1.82249	+	12.3821i	0.0823317	+	0.559365i
$491$	12.3106	+	21.3225i	0.555568	+	0.962271i	0.997859	+	0.0653999i	$0.0208323\pi$
$491$	12.3106	+	21.3225i	0.555568	+	0.962271i	−0.442292	+	0.896871i	$0.645834\pi$
$492$		0			0
$493$	5.07802	+	1.36065i	0.228703	+	0.0612807i
$494$	−1.11838	−	0.645694i	−0.0503181	−	0.0290512i
$495$		0			0
$496$		−	2.31686i		−	0.104030i
$497$	−6.55034	−	5.45160i	−0.293823	−	0.244537i
$498$		0			0
$499$	6.39584	+	3.69264i	0.286317	+	0.165305i	0.636280	−	0.771458i	$-0.280472\pi$
$499$	6.39584	+	3.69264i	0.286317	+	0.165305i	−0.349963	+	0.936764i	$0.613806\pi$
$500$	−9.51891	−	11.8666i	−0.425698	−	0.530691i
$501$		0			0
$502$	6.36448	+	6.36448i	0.284061	+	0.284061i
$503$	28.2531	−	28.2531i	1.25974	−	1.25974i	0.308530	−	0.951215i	$-0.400163\pi$
$503$	28.2531	−	28.2531i	1.25974	−	1.25974i	0.951215	−	0.308530i	$-0.0998370\pi$
$504$		0			0
$505$	36.6189	+	11.2572i	1.62952	+	0.500940i
$506$	2.04295			0.0908200
$507$		0			0
$508$	−7.77302	−	7.77302i	−0.344872	−	0.344872i
$509$	6.15311	−	10.6575i	0.272732	−	0.472385i	−0.696829	−	0.717238i	$-0.745406\pi$
$509$	6.15311	−	10.6575i	0.272732	−	0.472385i	0.969560	+	0.244853i	$0.0787395\pi$
$510$		0			0
$511$	10.3564	−	22.4448i	0.458138	−	0.992899i
$512$	4.53849	−	4.53849i	0.200575	−	0.200575i
$513$		0			0
$514$	2.26218	−	3.91822i	0.0997807	−	0.172825i
$515$	18.8517	−	30.0659i	0.830706	−	1.32486i
$516$		0			0
$517$	−3.99289	+	14.9017i	−0.175607	+	0.655375i
$518$	17.4830	+	3.01019i	0.768160	+	0.132260i
$519$		0			0
$520$	0.628024	−	2.04291i	0.0275407	−	0.0895875i
$521$	30.8984	+	17.8392i	1.35368	+	0.781550i	0.988763	−	0.149489i	$-0.0477629\pi$
$521$	30.8984	+	17.8392i	1.35368	+	0.781550i	0.364920	+	0.931039i	$0.381096\pi$
$522$		0			0
$523$	−12.7230	−	3.40911i	−0.556336	−	0.149070i	−0.0303136	−	0.999540i	$-0.509651\pi$
$523$	−12.7230	−	3.40911i	−0.556336	−	0.149070i	−0.526023	+	0.850471i	$0.676317\pi$
$524$	−6.64262	+	11.5054i	−0.290184	+	0.502614i
$525$		0			0
$526$	−0.974751	−	1.68832i	−0.0425012	−	0.0736142i
$527$	2.11007	+	7.87489i	0.0919161	+	0.343036i
$528$		0			0
$529$	−18.3484	+	10.5935i	−0.797758	+	0.460586i
$530$	15.2676	−	3.50003i	0.663182	−	0.152032i
$531$		0			0
$532$	16.1089	+	2.77360i	0.698409	+	0.120251i
$533$	0.147115	−	0.0394193i	0.00637225	−	0.00170744i
$534$		0			0
$535$	−4.62585	−	8.73240i	−0.199993	−	0.377535i
$536$	39.6578			1.71296
$537$		0			0
$538$	1.19181	+	4.44790i	0.0513826	+	0.191763i
$539$	−10.1061	+	8.61962i	−0.435298	+	0.371273i
$540$		0			0
$541$	−10.4309	−	18.0669i	−0.448460	−	0.776756i	0.549826	−	0.835279i	$-0.314694\pi$
$541$	−10.4309	−	18.0669i	−0.448460	−	0.776756i	−0.998286	+	0.0585236i	$0.981361\pi$
$542$	−5.34735	+	19.9566i	−0.229688	+	0.857208i
$543$		0			0
$544$	−5.87710	+	10.1794i	−0.251978	+	0.436439i
$545$	2.98631	+	13.0267i	0.127920	+	0.558002i
$546$		0			0
$547$	7.30369	+	27.2577i	0.312283	+	1.16546i	0.926492	+	0.376314i	$0.122808\pi$
$547$	7.30369	+	27.2577i	0.312283	+	1.16546i	−0.614209	+	0.789143i	$0.710525\pi$
$548$	−6.59988	+	24.6311i	−0.281933	+	1.05219i
$549$		0			0
$550$	−2.49191	+	7.16522i	−0.106255	+	0.305526i
$551$			11.8441i			0.504575i
$552$		0			0
$553$	−17.1548	+	20.6122i	−0.729495	+	0.876522i
$554$	11.7828	−	6.80283i	0.500605	−	0.289024i
$555$		0			0
$556$	−2.82846	+	1.63301i	−0.119953	+	0.0692551i
$557$	−4.27411	−	15.9512i	−0.181100	−	0.675875i	−0.995432	−	0.0954749i	$-0.969563\pi$
$557$	−4.27411	−	15.9512i	−0.181100	−	0.675875i	0.814332	−	0.580400i	$-0.197104\pi$
$558$		0			0
$559$	2.98405			0.126212
$560$	0.185744	+	3.38327i	0.00784910	+	0.142969i
$561$		0			0
$562$	−6.68063	−	24.9325i	−0.281805	−	1.05171i
$563$	11.3493	−	11.3493i	0.478318	−	0.478318i	−0.426276	−	0.904593i	$-0.640175\pi$
$563$	11.3493	−	11.3493i	0.478318	−	0.478318i	0.904593	+	0.426276i	$0.140175\pi$
$564$		0			0
$565$	37.5490	−	19.8910i	1.57970	−	0.836821i
$566$		−	0.980241i		−	0.0412026i
$567$		0			0
$568$	6.12032	+	6.12032i	0.256803	+	0.256803i
$569$		−	0.550495i		−	0.0230780i	−0.999933	−	0.0115390i	$-0.996327\pi$
$569$		−	0.550495i		−	0.0230780i	0.999933	−	0.0115390i	$-0.00367305\pi$
$570$		0			0
$571$	32.7420			1.37021			0.685105	−	0.728445i	$-0.259756\pi$
$571$	32.7420			1.37021			0.685105	+	0.728445i	$0.259756\pi$
$572$	0.887088	−	0.237694i	0.0370910	−	0.00993851i
$573$		0			0
$574$	0.739907	−	0.522541i	0.0308831	−	0.0218104i
$575$	1.26424	+	6.61270i	0.0527226	+	0.275769i
$576$		0			0
$577$	12.8283	−	3.43734i	0.534050	−	0.143098i	0.0182920	−	0.999833i	$-0.494177\pi$
$577$	12.8283	−	3.43734i	0.534050	−	0.143098i	0.515758	+	0.856735i	$0.327510\pi$
$578$	−2.67753	+	9.99269i	−0.111371	+	0.415641i
$579$		0			0
$580$	−7.73582	+	1.77340i	−0.321212	+	0.0736366i
$581$	−19.3038	+	41.8361i	−0.800856	+	1.73565i
$582$		0			0
$583$	11.7548	+	11.7548i	0.486836	+	0.486836i
$584$	−12.5528	+	21.7420i	−0.519437	+	0.899690i
$585$		0			0
$586$	4.05598	−	2.34172i	0.167551	−	0.0967356i
$587$	−5.88487	+	1.57685i	−0.242895	+	0.0650834i	−0.378212	−	0.925719i	$-0.623461\pi$
$587$	−5.88487	+	1.57685i	−0.242895	+	0.0650834i	0.135318	+	0.990802i	$0.456794\pi$
$588$		0			0
$589$	−15.9068	+	9.18378i	−0.655427	+	0.378411i
$590$	−13.2575	−	0.483416i	−0.545802	−	0.0199019i
$591$		0			0
$592$	4.63925	+	1.24308i	0.190672	+	0.0510904i
$593$	0.733049	+	0.196420i	0.0301027	+	0.00806599i	0.273839	−	0.961776i	$-0.411706\pi$
$593$	0.733049	+	0.196420i	0.0301027	+	0.00806599i	−0.243736	+	0.969842i	$0.578373\pi$
$594$		0			0
$595$	−3.71264	−	11.3304i	−0.152204	−	0.464503i
$596$	−2.82253	+	4.88877i	−0.115615	+	0.200252i
$597$		0			0
$598$	−0.270793	+	0.270793i	−0.0110735	+	0.0110735i
$599$			32.8038i			1.34033i	0.742214	+	0.670163i	$0.233776\pi$
$599$			32.8038i			1.34033i	−0.742214	+	0.670163i	$0.766224\pi$
$600$		0			0
$601$	−15.5085	−	8.95386i	−0.632607	−	0.365236i	0.149154	−	0.988814i	$-0.452345\pi$
$601$	−15.5085	−	8.95386i	−0.632607	−	0.365236i	−0.781761	+	0.623578i	$0.785678\pi$
$602$	16.6526	−	6.13709i	0.678708	−	0.250129i
$603$		0			0
$604$	18.3429	−	10.5903i	0.746361	−	0.430912i
$605$	16.1272	−	3.69709i	0.655663	−	0.150308i
$606$		0			0
$607$	−30.9634	+	8.29661i	−1.25676	+	0.336749i	−0.824946	−	0.565212i	$-0.808794\pi$
$607$	−30.9634	+	8.29661i	−1.25676	+	0.336749i	−0.431818	+	0.901961i	$0.642128\pi$
$608$	−25.5792	−	6.85393i	−1.03737	−	0.277964i
$609$		0			0
$610$	−0.305775	+	8.38576i	−0.0123805	+	0.339530i
$611$	−1.44596	−	2.50448i	−0.0584973	−	0.101320i
$612$		0			0
$613$	−1.79129	+	0.479975i	−0.0723495	+	0.0193860i	−0.294812	−	0.955555i	$-0.595257\pi$
$613$	−1.79129	+	0.479975i	−0.0723495	+	0.0193860i	0.222463	+	0.974941i	$0.428590\pi$
$614$	4.27123			0.172373
$615$		0			0
$616$	11.0195	−	7.78224i	0.443988	−	0.313556i
$617$	−22.6208	−	6.06122i	−0.910679	−	0.244016i	−0.227082	−	0.973876i	$-0.572919\pi$
$617$	−22.6208	−	6.06122i	−0.910679	−	0.244016i	−0.683597	+	0.729860i	$0.739585\pi$
$618$		0			0
$619$	13.6210	+	23.5923i	0.547476	+	0.948256i	0.998447	+	0.0557175i	$0.0177446\pi$
$619$	13.6210	+	23.5923i	0.547476	+	0.948256i	−0.450971	+	0.892539i	$0.648922\pi$
$620$	−8.37998	−	9.01423i	−0.336548	−	0.362020i
$621$		0			0
$622$	11.8524	+	11.8524i	0.475240	+	0.475240i
$623$	−0.777129	+	4.51351i	−0.0311350	+	0.180830i
$624$		0			0
$625$	−24.7348	−	3.63185i	−0.989391	−	0.145274i
$626$		−	9.96219i		−	0.398169i
$627$		0			0
$628$	−20.0780	+	20.0780i	−0.801198	+	0.801198i
$629$	−16.9007			−0.673877
$630$		0			0
$631$	22.8338			0.908998			0.454499	−	0.890747i	$-0.349818\pi$
$631$	22.8338			0.908998			0.454499	+	0.890747i	$0.349818\pi$
$632$	19.2591	−	19.2591i	0.766085	−	0.766085i
$633$		0			0
$634$			11.8176i			0.469336i
$635$	−18.0530	−	0.658279i	−0.716413	−	0.0261230i
$636$		0			0
$637$	0.197027	−	2.48209i	0.00780649	−	0.0983440i
$638$	2.79853	+	2.79853i	0.110795	+	0.110795i
$639$		0			0
$640$	0.721238	−	19.7797i	0.0285094	−	0.781859i
$641$	−9.20899	−	15.9504i	−0.363733	−	0.630004i	0.624839	−	0.780754i	$-0.285165\pi$
$641$	−9.20899	−	15.9504i	−0.363733	−	0.630004i	−0.988572	+	0.150749i	$0.951831\pi$
$642$		0			0
$643$	45.7457	+	12.2575i	1.80403	+	0.483389i	0.994596	−	0.103819i	$-0.0331061\pi$
$643$	45.7457	+	12.2575i	1.80403	+	0.483389i	0.809436	+	0.587208i	$0.199773\pi$
$644$	2.03087	−	4.40141i	0.0800276	−	0.173440i
$645$		0			0
$646$	7.31699			0.287883
$647$	2.36279	−	0.633107i	0.0928907	−	0.0248900i	−0.212074	−	0.977254i	$-0.568022\pi$
$647$	2.36279	−	0.633107i	0.0928907	−	0.0248900i	0.304965	+	0.952364i	$0.401355\pi$
$648$		0			0
$649$	−7.03977	−	12.1932i	−0.276335	−	0.478627i
$650$	−0.619448	−	1.28005i	−0.0242967	−	0.0502078i
$651$		0			0
$652$	16.9405	+	4.53919i	0.663441	+	0.177768i
$653$	22.6660	−	6.07335i	0.886991	−	0.237669i	0.213570	−	0.976928i	$-0.431491\pi$
$653$	22.6660	−	6.07335i	0.886991	−	0.237669i	0.673421	+	0.739259i	$0.264824\pi$
$654$		0			0
$655$	4.87846	+	21.2805i	0.190617	+	0.831497i
$656$	0.212381	−	0.122618i	0.00829210	−	0.00478745i
$657$		0			0
$658$	−13.2200	−	11.0025i	−0.515370	−	0.428922i
$659$	−17.3437	−	10.0134i	−0.675615	−	0.390067i	0.122586	−	0.992458i	$-0.460881\pi$
$659$	−17.3437	−	10.0134i	−0.675615	−	0.390067i	−0.798201	+	0.602391i	$0.794215\pi$
$660$		0			0
$661$		−	0.722232i		−	0.0280916i	−0.999901	−	0.0140458i	$-0.995529\pi$
$661$		−	0.722232i		−	0.0280916i	0.999901	−	0.0140458i	$-0.00447106\pi$
$662$	−3.71309	+	3.71309i	−0.144313	+	0.144313i
$663$		0			0
$664$	23.3978	−	40.5261i	0.908010	−	1.57272i
$665$	22.4922	−	14.6862i	0.872210	−	0.569507i
$666$		0			0
$667$	3.39266	+	0.909061i	0.131364	+	0.0351990i
$668$	11.5876	+	3.10489i	0.448338	+	0.120132i
$669$		0			0
$670$	19.3259	−	17.9661i	0.746623	−	0.694090i
$671$	−7.71260	+	4.45287i	−0.297742	+	0.171901i
$672$		0			0
$673$	−26.4663	+	7.09161i	−1.02020	+	0.273362i	−0.729885	−	0.683570i	$-0.760426\pi$
$673$	−26.4663	+	7.09161i	−1.02020	+	0.273362i	−0.290314	+	0.956931i	$0.593760\pi$
$674$	9.77926	−	5.64606i	0.376683	−	0.217478i
$675$		0			0
$676$	8.75824	−	15.1697i	0.336856	−	0.583451i
$677$	−22.4237	−	22.4237i	−0.861814	−	0.861814i	0.129735	−	0.991549i	$-0.458587\pi$
$677$	−22.4237	−	22.4237i	−0.861814	−	0.861814i	−0.991549	+	0.129735i	$0.958587\pi$
$678$		0			0
$679$	−15.7609	−	7.27230i	−0.604847	−	0.279085i
$680$	2.70590	+	11.8035i	0.103767	+	0.452644i
$681$		0			0
$682$	−1.58851	+	5.92841i	−0.0608273	+	0.227011i
$683$	−21.8149	+	5.84528i	−0.834724	+	0.223663i	−0.650773	−	0.759272i	$-0.725555\pi$
$683$	−21.8149	+	5.84528i	−0.834724	+	0.223663i	−0.183950	+	0.982936i	$0.558889\pi$
$684$		0			0
$685$	19.6165	+	37.0309i	0.749509	+	1.41488i
$686$	−4.00523	−	14.2566i	−0.152920	−	0.544319i
$687$		0			0
$688$	4.64112	−	1.24359i	0.176941	−	0.0474112i
$689$	−3.11621			−0.118718
$690$		0			0
$691$			8.95201i			0.340550i	0.985397	+	0.170275i	$0.0544657\pi$
$691$			8.95201i			0.340550i	−0.985397	+	0.170275i	$0.945534\pi$
$692$	−22.0969	−	22.0969i	−0.840000	−	0.840000i
$693$		0			0
$694$		−	21.9114i		−	0.831744i
$695$	−1.57714	+	5.13032i	−0.0598245	+	0.194604i
$696$		0			0
$697$	−0.610201	+	0.610201i	−0.0231130	+	0.0231130i
$698$	−2.21605	−	8.27043i	−0.0838789	−	0.313040i
$699$		0			0
$700$	12.9599	+	12.4915i	0.489836	+	0.472136i
$701$	−28.2460			−1.06684			−0.533419	−	0.845851i	$-0.679093\pi$
$701$	−28.2460			−1.06684			−0.533419	+	0.845851i	$0.679093\pi$
$702$		0			0
$703$	−9.85491	−	36.7790i	−0.371685	−	1.38715i
$704$	−5.78095	+	3.33763i	−0.217878	+	0.125792i
$705$		0			0
$706$	12.6440	−	7.30002i	0.475864	−	0.274740i
$707$	−44.6718	−	7.69152i	−1.68006	−	0.289269i
$708$		0			0
$709$			19.1786i			0.720268i	0.932901	+	0.360134i	$0.117269\pi$
$709$			19.1786i			0.720268i	−0.932901	+	0.360134i	$0.882731\pi$
$710$	5.75520	+	0.209856i	0.215989	+	0.00787574i
$711$		0			0
$712$	1.20391	−	4.49307i	0.0451186	−	0.168385i
$713$	1.40975	+	5.26127i	0.0527956	+	0.197036i
$714$		0			0
$715$	0.801744	−	1.27867i	0.0299835	−	0.0478195i
$716$	4.30394	−	7.45463i	0.160846	−	0.278593i
$717$		0			0
$718$	−1.46251	+	5.45814i	−0.0545802	+	0.203696i
$719$	−13.9884	−	24.2287i	−0.521681	−	0.903578i	−0.999682	−	0.0252186i	$-0.991972\pi$
$719$	−13.9884	−	24.2287i	−0.521681	−	0.903578i	0.478001	−	0.878359i	$-0.341362\pi$
$720$		0			0
$721$	−17.5920	+	38.1262i	−0.655159	+	1.41989i
$722$	0.334568	+	1.24863i	0.0124513	+	0.0464691i
$723$		0			0
$724$	−26.5303			−0.985992
$725$	−7.32658	+	10.7902i	−0.272102	+	0.400739i
$726$		0			0
$727$	−48.8362	+	13.0856i	−1.81123	+	0.485319i	−0.995638	−	0.0933035i	$-0.970257\pi$
$727$	−48.8362	+	13.0856i	−1.81123	+	0.485319i	−0.815596	+	0.578622i	$0.803591\pi$
$728$	−0.429098	+	2.49217i	−0.0159034	+	0.0923660i
$729$		0			0
$730$	3.73257	+	16.2820i	0.138149	+	0.602622i
$731$	−14.6424	+	8.45379i	−0.541568	+	0.312675i
$732$		0			0
$733$	−3.21092	−	11.9833i	−0.118598	−	0.442614i	0.880933	−	0.473241i	$-0.156916\pi$
$733$	−3.21092	−	11.9833i	−0.118598	−	0.442614i	−0.999531	+	0.0306273i	$0.990249\pi$
$734$	−8.73994	−	15.1380i	−0.322597	−	0.558755i
$735$		0			0
$736$	−3.92653	+	6.80094i	−0.144734	+	0.250686i
$737$	27.0502	+	7.24809i	0.996409	+	0.266987i
$738$		0			0
$739$	6.03461	+	3.48408i	0.221987	+	0.128164i	0.606870	−	0.794801i	$-0.292425\pi$
$739$	6.03461	+	3.48408i	0.221987	+	0.128164i	−0.384883	+	0.922965i	$0.625758\pi$
$740$	22.5462	−	11.9435i	0.828815	−	0.439052i
$741$		0			0
$742$	−17.3901	+	6.40889i	−0.638411	+	0.235278i
$743$	−0.714284	+	2.66574i	−0.0262045	+	0.0977966i	−0.977790	−	0.209589i	$-0.932787\pi$
$743$	−0.714284	+	2.66574i	−0.0262045	+	0.0977966i	0.951585	+	0.307385i	$0.0994541\pi$
$744$		0			0
$745$	2.07292	+	9.04233i	0.0759458	+	0.331285i
$746$	−7.48100	+	12.9575i	−0.273899	+	0.474407i
$747$		0			0
$748$	−3.67945	+	3.67945i	−0.134534	+	0.134534i
$749$	6.74506	+	9.55086i	0.246459	+	0.348981i
$750$		0			0
$751$	−0.806068	+	1.39615i	−0.0294138	+	0.0509463i	−0.880358	−	0.474311i	$-0.842697\pi$
$751$	−0.806068	+	1.39615i	−0.0294138	+	0.0509463i	0.850944	+	0.525257i	$0.176031\pi$
$752$	−3.29264	−	3.29264i	−0.120070	−	0.120070i
$753$		0			0
$754$	−0.741890			−0.0270181
$755$	10.2280	−	33.2707i	0.372233	−	1.21084i
$756$		0			0
$757$	−20.4552	+	20.4552i	−0.743458	+	0.743458i	−0.973242	−	0.229784i	$-0.926198\pi$
$757$	−20.4552	+	20.4552i	−0.743458	+	0.743458i	0.229784	+	0.973242i	$0.426198\pi$
$758$	−8.17347	−	8.17347i	−0.296874	−	0.296874i
$759$		0			0
$760$	−24.1087	+	12.7712i	−0.874515	+	0.463261i
$761$	8.22171	+	4.74681i	0.298037	+	0.172072i	0.641561	−	0.767072i	$-0.278287\pi$
$761$	8.22171	+	4.74681i	0.298037	+	0.172072i	−0.343524	+	0.939144i	$0.611621\pi$
$762$		0			0
$763$	−5.46822	−	14.8377i	−0.197963	−	0.537159i
$764$		−	30.3061i		−	1.09644i
$765$		0			0
$766$	6.65620	+	3.84296i	0.240498	+	0.138852i
$767$	2.54934	+	0.683093i	0.0920513	+	0.0246651i
$768$		0			0
$769$	17.6473	+	30.5659i	0.636376	+	1.10224i	0.986222	+	0.165429i	$0.0529007\pi$
$769$	17.6473	+	30.5659i	0.636376	+	1.10224i	−0.349846	+	0.936807i	$0.613766\pi$
$770$	1.84440	−	8.78454i	0.0664676	−	0.316573i
$771$		0			0
$772$	9.11112	−	9.11112i	0.327916	−	0.327916i
$773$	−10.7202	−	40.0084i	−0.385579	−	1.43900i	−0.837252	−	0.546817i	$-0.815839\pi$
$773$	−10.7202	−	40.0084i	−0.385579	−	1.43900i	0.451673	−	0.892184i	$-0.350827\pi$
$774$		0			0
$775$	−20.1724	−	1.47308i	−0.724613	−	0.0529145i
$776$	15.2674	+	8.81462i	0.548067	+	0.316427i
$777$		0			0
$778$	0.920735	−	3.43623i	0.0330099	−	0.123195i
$779$	−1.68372	−	0.972094i	−0.0603254	−	0.0348289i
$780$		0			0
$781$	3.05603	+	5.29320i	0.109353	+	0.189406i
$782$	0.561595	−	2.09590i	0.0200826	−	0.0749493i
$783$		0			0
$784$	−0.727958	−	3.94253i	−0.0259985	−	0.140805i
$785$	−1.70036	+	46.6316i	−0.0606884	+	1.66435i
$786$		0			0
$787$	17.4022	+	17.4022i	0.620323	+	0.620323i	0.945614	−	0.325291i	$-0.105462\pi$
$787$	17.4022	+	17.4022i	0.620323	+	0.620323i	−0.325291	+	0.945614i	$0.605462\pi$
$788$	−4.74073	−	4.74073i	−0.168881	−	0.168881i
$789$		0			0
$790$	0.660361	−	18.1101i	0.0234946	−	0.644330i
$791$	−41.0683	+	29.0035i	−1.46022	+	1.03125i
$792$		0			0
$793$	0.432077	−	1.61253i	0.0153435	−	0.0572628i
$794$	−2.76241	−	4.78463i	−0.0980343	−	0.169800i
$795$		0			0
$796$	−0.547403	−	0.316043i	−0.0194022	−	0.0112018i
$797$	−6.22974	+	23.2497i	−0.220669	+	0.823547i	0.763425	+	0.645897i	$0.223516\pi$
$797$	−6.22974	+	23.2497i	−0.220669	+	0.823547i	−0.984094	+	0.177651i	$0.943150\pi$
$798$		0			0
$799$	14.1903	+	8.19279i	0.502018	+	0.289840i
$800$	−19.0635	−	22.0670i	−0.673996	−	0.780187i
$801$		0			0
$802$	−5.69433	−	21.2515i	−0.201074	−	0.750418i
$803$	−12.5358	+	12.5358i	−0.442379	+	0.442379i
$804$		0			0
$805$	−2.48044	−	7.56994i	−0.0874241	−	0.266805i
$806$	−0.575254	−	0.996369i	−0.0202625	−	0.0350956i
$807$		0			0
$808$	44.4695	+	11.9156i	1.56443	+	0.419188i
$809$	4.30673	+	2.48649i	0.151417	+	0.0874204i	0.573794	−	0.819000i	$-0.305471\pi$
$809$	4.30673	+	2.48649i	0.151417	+	0.0874204i	−0.422377	+	0.906420i	$0.638804\pi$
$810$		0			0
$811$		−	36.7094i		−	1.28904i	−0.764586	−	0.644521i	$-0.777057\pi$
$811$		−	36.7094i		−	1.28904i	0.764586	−	0.644521i	$-0.222943\pi$
$812$	8.81125	−	3.24727i	0.309214	−	0.113957i
$813$		0			0
$814$	−11.0187	−	6.36165i	−0.386205	−	0.222976i
$815$	25.4687	−	13.4916i	0.892128	−	0.472591i
$816$		0			0
$817$	−26.9350	−	26.9350i	−0.942336	−	0.942336i
$818$	−19.1188	+	19.1188i	−0.668474	+	0.668474i
$819$		0			0
$820$	0.382810	−	1.24525i	0.0133683	−	0.0434860i
$821$	49.9596			1.74360			0.871801	−	0.489861i	$-0.162952\pi$
$821$	49.9596			1.74360			0.871801	+	0.489861i	$0.162952\pi$
$822$		0			0
$823$	−20.6485	−	20.6485i	−0.719763	−	0.719763i	0.248793	−	0.968557i	$-0.419966\pi$
$823$	−20.6485	−	20.6485i	−0.719763	−	0.719763i	−0.968557	+	0.248793i	$0.919966\pi$
$824$	21.3229	−	36.9324i	0.742819	−	1.28660i
$825$		0			0
$826$	15.6315	−	1.43103i	0.543890	−	0.0497918i
$827$	9.28844	−	9.28844i	0.322991	−	0.322991i	−0.526923	−	0.849913i	$-0.676654\pi$
$827$	9.28844	−	9.28844i	0.322991	−	0.322991i	0.849913	+	0.526923i	$0.176654\pi$
$828$		0			0
$829$	−19.5190	+	33.8079i	−0.677923	+	1.17420i	0.297683	+	0.954665i	$0.403786\pi$
$829$	−19.5190	+	33.8079i	−0.677923	+	1.17420i	−0.975605	+	0.219532i	$0.929547\pi$
$830$	−6.95734	−	30.3488i	−0.241493	−	1.05342i
$831$		0			0
$832$	0.323862	−	1.20867i	0.0112279	−	0.0419031i
$833$	6.06495	+	12.7375i	0.210138	+	0.441328i
$834$		0			0
$835$	17.4210	−	9.22851i	0.602879	−	0.319366i
$836$	−10.1527	−	5.86164i	−0.351137	−	0.202729i
$837$		0			0
$838$	18.7619	+	5.02725i	0.648121	+	0.173663i
$839$	−3.93769	+	6.82027i	−0.135944	+	0.235462i	−0.925958	−	0.377627i	$-0.876740\pi$
$839$	−3.93769	+	6.82027i	−0.135944	+	0.235462i	0.790014	+	0.613089i	$0.210073\pi$
$840$		0			0
$841$	−11.0978	−	19.2220i	−0.382684	−	0.662829i
$842$	1.03318	+	3.85589i	0.0356058	+	0.132883i
$843$		0			0
$844$	26.0745	−	15.0541i	0.897521	−	0.518184i
$845$	−6.43221	−	28.0581i	−0.221275	−	0.965229i
$846$		0			0
$847$	−18.3692	+	6.76973i	−0.631173	+	0.232611i
$848$	−4.84668	+	1.29866i	−0.166436	+	0.0445963i
$849$		0			0
$850$	6.66594	+	4.52618i	0.228640	+	0.155247i
$851$	−11.2915			−0.387067
$852$		0			0
$853$	−9.44853	−	35.2624i	−0.323512	−	1.20736i	−0.915800	−	0.401635i	$-0.868442\pi$
$853$	−9.44853	−	35.2624i	−0.323512	−	1.20736i	0.592288	−	0.805726i	$-0.298225\pi$
$854$	−0.905168	−	9.88742i	−0.0309742	−	0.338340i
$855$		0			0
$856$	−5.93770	−	10.2844i	−0.202946	−	0.351513i
$857$	−8.19624	+	30.5888i	−0.279978	+	1.04489i	0.672453	+	0.740140i	$0.265241\pi$
$857$	−8.19624	+	30.5888i	−0.279978	+	1.04489i	−0.952431	+	0.304753i	$0.901426\pi$
$858$		0			0
$859$	29.1009	−	50.4042i	0.992910	−	1.71977i	0.393510	−	0.919320i	$-0.371261\pi$
$859$	29.1009	−	50.4042i	0.992910	−	1.71977i	0.599400	−	0.800450i	$-0.295406\pi$
$860$	13.5593	−	21.6252i	0.462369	−	0.737414i
$861$		0			0
$862$	−1.12477	−	4.19769i	−0.0383098	−	0.142974i
$863$	0.909305	−	3.39357i	0.0309531	−	0.115519i	−0.948721	−	0.316115i	$-0.897621\pi$
$863$	0.909305	−	3.39357i	0.0309531	−	0.115519i	0.979674	+	0.200597i	$0.0642881\pi$
$864$		0			0
$865$	−51.3207	−	1.87134i	−1.74496	−	0.0636275i
$866$			14.3592i			0.487945i
$867$		0			0
$868$	11.1933	+	9.31574i	0.379925	+	0.316197i
$869$	16.6563	−	9.61655i	0.565028	−	0.326219i
$870$		0			0
$871$	−4.54625	+	2.62478i	−0.154044	+	0.0889372i
$872$	4.15678	+	15.5133i	0.140766	+	0.525347i
$873$		0			0
$874$	4.88853			0.165357
$875$	29.5756	+	0.533882i	0.999837	+	0.0180485i
$876$		0			0
$877$	0.504963	+	1.88455i	0.0170514	+	0.0636366i	0.973927	−	0.226860i	$-0.0728461\pi$
$877$	0.504963	+	1.88455i	0.0170514	+	0.0636366i	−0.956876	+	0.290497i	$0.906179\pi$
$878$	−5.75505	+	5.75505i	−0.194224	+	0.194224i
$879$		0			0
$880$	0.714082	−	2.32285i	0.0240717	−	0.0783033i
$881$		−	1.32904i		−	0.0447765i	−0.999749	−	0.0223883i	$-0.992873\pi$
$881$		−	1.32904i		−	0.0447765i	0.999749	−	0.0223883i	$-0.00712700\pi$
$882$		0			0
$883$	24.9117	+	24.9117i	0.838347	+	0.838347i	0.988641	−	0.150295i	$-0.0480222\pi$
$883$	24.9117	+	24.9117i	0.838347	+	0.838347i	−0.150295	+	0.988641i	$0.548022\pi$
$884$		−	0.975424i		−	0.0328070i
$885$		0			0
$886$	−3.71387			−0.124770
$887$	−27.8298	+	7.45696i	−0.934432	+	0.250380i	−0.693744	−	0.720222i	$-0.744040\pi$
$887$	−27.8298	+	7.45696i	−0.934432	+	0.250380i	−0.240688	+	0.970602i	$0.577373\pi$
$888$		0			0
$889$	21.2858	−	1.94866i	0.713903	−	0.0653560i
$890$	−1.44880	−	2.73495i	−0.0485638	−	0.0916756i
$891$		0			0
$892$	2.77633	−	0.743914i	0.0929583	−	0.0249081i
$893$	−9.55452	+	35.6579i	−0.319730	+	1.19325i
$894$		0			0
$895$	−3.16088	−	13.7882i	−0.105657	−	0.460889i
$896$	2.13504	+	23.3216i	0.0713266	+	0.779121i
$897$		0			0
$898$	20.4020	+	20.4020i	0.680825	+	0.680825i
$899$	−5.27599	+	9.13829i	−0.175964	+	0.304779i
$900$		0			0
$901$	15.2909	−	8.82820i	0.509413	−	0.294110i
$902$	−0.627517	+	0.168143i	−0.0208940	+	0.00559854i
$903$		0			0
$904$	44.2225	−	25.5319i	1.47082	−	0.849177i
$905$	−31.9321	+	29.6853i	−1.06146	+	0.986772i
$906$		0			0
$907$	−32.7377	−	8.77204i	−1.08704	−	0.291271i	−0.329562	−	0.944134i	$-0.606901\pi$
$907$	−32.7377	−	8.77204i	−1.08704	−	0.291271i	−0.757476	+	0.652863i	$0.773568\pi$
$908$	3.00855	+	0.806139i	0.0998423	+	0.0267527i
$909$		0			0
$910$	0.919916	+	1.40887i	0.0304949	+	0.0467035i
$911$	−3.92417	+	6.79686i	−0.130013	+	0.225190i	−0.923681	−	0.383161i	$-0.874835\pi$
$911$	−3.92417	+	6.79686i	−0.130013	+	0.225190i	0.793668	+	0.608351i	$0.208169\pi$
$912$		0			0
$913$	23.3662	−	23.3662i	0.773309	−	0.773309i
$914$			21.8461i			0.722604i
$915$		0			0
$916$	−0.155232	−	0.0896229i	−0.00512899	−	0.00296123i
$917$	−8.93292	−	24.2389i	−0.294991	−	0.800438i
$918$		0			0
$919$	45.5357	−	26.2901i	1.50208	−	0.867229i	0.502088	−	0.864817i	$-0.332565\pi$
$919$	45.5357	−	26.2901i	1.50208	−	0.867229i	0.999997	−	0.00241227i	$-0.000767849\pi$
$920$	1.80783	+	7.88600i	0.0596025	+	0.259994i
$921$		0			0
$922$	−1.98271	+	0.531264i	−0.0652969	+	0.0174963i
$923$	−1.10669	−	0.296537i	−0.0364272	−	0.00976064i
$924$		0			0
$925$	13.7729	−	39.6026i	0.452851	−	1.30213i
$926$	9.93329	+	17.2050i	0.326428	+	0.565390i
$927$		0			0
$928$	−14.6950	+	3.93752i	−0.482387	+	0.129255i
$929$	38.9194			1.27690			0.638452	−	0.769661i	$-0.279575\pi$
$929$	38.9194			1.27690			0.638452	+	0.769661i	$0.279575\pi$
$930$		0			0
$931$	−24.1826	+	20.6257i	−0.792552	+	0.675981i
$932$	9.95394	+	2.66715i	0.326052	+	0.0873654i
$933$		0			0
$934$	7.96787	+	13.8008i	0.260717	+	0.451575i
$935$	−0.311604	+	8.54562i	−0.0101906	+	0.279472i
$936$		0			0
$937$	−20.1650	−	20.1650i	−0.658760	−	0.658760i	0.296326	−	0.955087i	$-0.404238\pi$
$937$	−20.1650	−	20.1650i	−0.658760	−	0.658760i	−0.955087	+	0.296326i	$0.904238\pi$
$938$	−19.9723	+	23.9976i	−0.652118	+	0.783549i
$939$		0			0
$940$	−24.7201	−	0.901386i	−0.806282	−	0.0294000i
$941$		−	7.21932i		−	0.235343i	−0.993053	−	0.117672i	$-0.962457\pi$
$941$		−	7.21932i		−	0.235343i	0.993053	−	0.117672i	$-0.0375430\pi$
$942$		0			0
$943$	−0.407679	+	0.407679i	−0.0132759	+	0.0132759i
$944$	4.24969			0.138316
$945$		0			0
$946$	−12.7284			−0.413837
$947$	−25.8448	+	25.8448i	−0.839842	+	0.839842i	−0.988838	−	0.148996i	$-0.952396\pi$
$947$	−25.8448	+	25.8448i	−0.839842	+	0.839842i	0.148996	+	0.988838i	$0.452396\pi$
$948$		0			0
$949$		−	3.32325i		−	0.107877i
$950$	−5.96284	+	17.1455i	−0.193460	+	0.556274i
$951$		0			0
$952$	−4.95477	−	13.4444i	−0.160585	−	0.435737i
$953$	22.4458	+	22.4458i	0.727090	+	0.727090i	0.970039	−	0.242949i	$-0.0781147\pi$
$953$	22.4458	+	22.4458i	0.727090	+	0.727090i	−0.242949	+	0.970039i	$0.578115\pi$
$954$		0			0
$955$	−33.9100	−	36.4766i	−1.09730	−	1.18035i
$956$	6.14570	+	10.6447i	0.198766	+	0.344273i
$957$		0			0
$958$	−10.5337	−	2.82249i	−0.340328	−	0.0911906i
$959$	−28.6033	−	40.5016i	−0.923648	−	1.30787i
$960$		0			0
$961$	14.6362			0.472135
$962$	2.30377	−	0.617292i	0.0742764	−	0.0199023i
$963$		0			0
$964$	10.9397	+	18.9481i	0.352344	+	0.610278i
$965$	0.771600	−	21.1608i	0.0248387	−	0.681190i
$966$		0			0
$967$	−54.9695	−	14.7290i	−1.76770	−	0.473654i	−0.779446	−	0.626470i	$-0.784499\pi$
$967$	−54.9695	−	14.7290i	−1.76770	−	0.473654i	−0.988255	+	0.152816i	$0.951166\pi$
$968$	19.2056	−	5.14614i	0.617293	−	0.165403i
$969$		0			0
$970$	11.4333	−	2.62103i	0.367101	−	0.0841563i
$971$	−16.7190	+	9.65271i	−0.536538	+	0.309770i	−0.743675	−	0.668542i	$-0.766919\pi$
$971$	−16.7190	+	9.65271i	−0.536538	+	0.309770i	0.207137	+	0.978312i	$0.433585\pi$
$972$		0			0
$973$	1.07758	−	6.25854i	0.0345458	−	0.200640i
$974$	−0.583358	−	0.336802i	−0.0186920	−	0.0107918i
$975$		0			0
$976$		−	2.68806i		−	0.0860426i
$977$	13.3217	−	13.3217i	0.426198	−	0.426198i	−0.461133	−	0.887331i	$-0.652557\pi$
$977$	13.3217	−	13.3217i	0.426198	−	0.426198i	0.887331	+	0.461133i	$0.152557\pi$
$978$		0			0
$979$	1.64236	−	2.84465i	0.0524900	−	0.0909153i
$980$	−17.0923	−	12.7063i	−0.545992	−	0.405887i
$981$		0			0
$982$	19.0158	+	5.09528i	0.606820	+	0.162597i
$983$	−38.3668	−	10.2803i	−1.22371	−	0.327892i	−0.411583	−	0.911372i	$-0.635024\pi$
$983$	−38.3668	−	10.2803i	−1.22371	−	0.327892i	−0.812127	+	0.583480i	$0.801691\pi$
$984$		0			0
$985$	−11.0105	−	0.401481i	−0.350822	−	0.0127923i
$986$	3.64037	−	2.10177i	0.115933	−	0.0669340i
$987$		0			0
$988$	2.12270	−	0.568775i	0.0675319	−	0.0180951i
$989$	−9.78268	+	5.64803i	−0.311071	+	0.179597i
$990$		0			0
$991$	23.0121	−	39.8581i	0.731003	−	1.26613i	−0.225452	−	0.974254i	$-0.572386\pi$
$991$	23.0121	−	39.8581i	0.731003	−	1.26613i	0.956455	−	0.291880i	$-0.0942809\pi$
$992$	−16.6825	−	16.6825i	−0.529670	−	0.529670i
$993$		0			0
$994$	−6.78579	+	0.621222i	−0.215232	+	0.0197040i
$995$	−1.01248	+	0.232107i	−0.0320979	+	0.00735830i
$996$		0			0
$997$	5.03879	−	18.8050i	0.159580	−	0.595561i	−0.839089	−	0.543993i	$-0.816912\pi$
$997$	5.03879	−	18.8050i	0.159580	−	0.595561i	0.998670	−	0.0515674i	$-0.0164217\pi$
$998$	5.70394	−	1.52837i	0.180555	−	0.0483796i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bv.e.73.25		160
3.2	odd	2		315.2.bs.e.178.16	yes	160
5.2	odd	4	inner	945.2.bv.e.262.25		160
7.5	odd	6		945.2.cj.e.208.16		160
9.4	even	3		945.2.cj.e.388.25		160
9.5	odd	6		315.2.cg.e.283.16	yes	160
15.2	even	4		315.2.bs.e.52.16	✓	160
21.5	even	6		315.2.cg.e.313.25	yes	160
35.12	even	12		945.2.cj.e.397.25		160
45.22	odd	12		945.2.cj.e.577.16		160
45.32	even	12		315.2.cg.e.157.25	yes	160
63.5	even	6		315.2.bs.e.103.16	yes	160
63.40	odd	6	inner	945.2.bv.e.523.25		160
105.47	odd	12		315.2.cg.e.187.16	yes	160
315.257	odd	12		315.2.bs.e.292.16	yes	160
315.292	even	12	inner	945.2.bv.e.712.25		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.16	✓	160	15.2	even	4
315.2.bs.e.103.16	yes	160	63.5	even	6
315.2.bs.e.178.16	yes	160	3.2	odd	2
315.2.bs.e.292.16	yes	160	315.257	odd	12
315.2.cg.e.157.25	yes	160	45.32	even	12
315.2.cg.e.187.16	yes	160	105.47	odd	12
315.2.cg.e.283.16	yes	160	9.5	odd	6
315.2.cg.e.313.25	yes	160	21.5	even	6
945.2.bv.e.73.25		160	1.1	even	1	trivial
945.2.bv.e.262.25		160	5.2	odd	4	inner
945.2.bv.e.523.25		160	63.40	odd	6	inner
945.2.bv.e.712.25		160	315.292	even	12	inner
945.2.cj.e.208.16		160	7.5	odd	6
945.2.cj.e.388.25		160	9.4	even	3
945.2.cj.e.397.25		160	35.12	even	12
945.2.cj.e.577.16		160	45.22	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bv (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.565391 - 0.565391i) q^{2} +1.36066i q^{4} +(1.52247 + 1.63770i) q^{5} +(-2.03359 - 1.69248i) q^{7} +(1.90009 + 1.90009i) q^{8} +O(q^{10})\)	\(q+(0.565391 - 0.565391i) q^{2} +1.36066i q^{4} +(1.52247 + 1.63770i) q^{5} +(-2.03359 - 1.69248i) q^{7} +(1.90009 + 1.90009i) q^{8} +(1.78674 + 0.0651510i) q^{10} +(0.948764 + 1.64331i) q^{11} +(-0.343579 - 0.0920618i) q^{13} +(-2.10669 + 0.192862i) q^{14} -0.572739 q^{16} +(1.94672 - 0.521621i) q^{17} +(2.27028 + 3.93224i) q^{19} +(-2.22837 + 2.07158i) q^{20} +(1.46554 + 0.392689i) q^{22} +(1.30061 - 0.348498i) q^{23} +(-0.364152 + 4.98672i) q^{25} +(-0.246308 + 0.142206i) q^{26} +(2.30290 - 2.76704i) q^{28} +(2.25903 + 1.30425i) q^{29} +4.04522i q^{31} +(-4.12400 + 4.12400i) q^{32} +(0.805736 - 1.39558i) q^{34} +(-0.324308 - 5.90718i) q^{35} +(-8.10011 - 2.17042i) q^{37} +(3.50685 + 0.939658i) q^{38} +(-0.218951 + 6.00463i) q^{40} +(-0.370817 + 0.214091i) q^{41} +(-8.10338 + 2.17129i) q^{43} +(-2.23599 + 1.29095i) q^{44} +(0.538318 - 0.932394i) q^{46} +(5.74894 + 5.74894i) q^{47} +(1.27101 + 6.88364i) q^{49} +(2.61356 + 3.02534i) q^{50} +(0.125265 - 0.467496i) q^{52} +(8.46228 - 2.26746i) q^{53} +(-1.24678 + 4.05569i) q^{55} +(-0.648146 - 7.07988i) q^{56} +(2.01465 - 0.539825i) q^{58} -7.41994 q^{59} +4.69334i q^{61} +(2.28713 + 2.28713i) q^{62} +3.51788i q^{64} +(-0.372320 - 0.702843i) q^{65} +(10.4358 - 10.4358i) q^{67} +(0.709751 + 2.64883i) q^{68} +(-3.52323 - 3.15651i) q^{70} +3.22107 q^{71} +(2.41811 + 9.02450i) q^{73} +(-5.80687 + 3.35260i) q^{74} +(-5.35046 + 3.08909i) q^{76} +(0.851867 - 4.94759i) q^{77} -10.1359i q^{79} +(-0.871980 - 0.937977i) q^{80} +(-0.0886114 + 0.330702i) q^{82} +(-4.50725 - 16.8213i) q^{83} +(3.81808 + 2.39399i) q^{85} +(-3.35395 + 5.80922i) q^{86} +(-1.31970 + 4.92517i) q^{88} +(-0.865525 - 1.49913i) q^{89} +(0.542888 + 0.768718i) q^{91} +(0.474189 + 1.76970i) q^{92} +6.50081 q^{94} +(-2.98341 + 9.70478i) q^{95} +(6.33706 - 1.69801i) q^{97} +(4.61057 + 3.17333i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8}+O(q^{10}) \) 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8	\( 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8} - 24 q^{10} + 16 q^{11} - 152 q^{16} + 6 q^{17} - 60 q^{20} + 8 q^{22} - 8 q^{23} + 2 q^{25} + 36 q^{26} + 22 q^{28} - 12 q^{32} + 36 q^{35} - 4 q^{37} + 18 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 44 q^{50} + 54 q^{52} - 8 q^{53} - 148 q^{56} + 28 q^{58} + 124 q^{65} - 24 q^{67} - 42 q^{68} - 34 q^{70} + 40 q^{71} + 36 q^{73} + 96 q^{76} - 58 q^{77} - 36 q^{80} - 66 q^{82} + 138 q^{83} - 20 q^{85} + 16 q^{86} + 46 q^{88} - 48 q^{91} + 26 q^{92} - 188 q^{95} + 48 q^{97} - 102 q^{98}+O(q^{100}) \) 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8 - 24 * q^10 + 16 * q^11 - 152 * q^16 + 6 * q^17 - 60 * q^20 + 8 * q^22 - 8 * q^23 + 2 * q^25 + 36 * q^26 + 22 * q^28 - 12 * q^32 + 36 * q^35 - 4 * q^37 + 18 * q^38 - 6 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 44 * q^50 + 54 * q^52 - 8 * q^53 - 148 * q^56 + 28 * q^58 + 124 * q^65 - 24 * q^67 - 42 * q^68 - 34 * q^70 + 40 * q^71 + 36 * q^73 + 96 * q^76 - 58 * q^77 - 36 * q^80 - 66 * q^82 + 138 * q^83 - 20 * q^85 + 16 * q^86 + 46 * q^88 - 48 * q^91 + 26 * q^92 - 188 * q^95 + 48 * q^97 - 102 * q^98

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