LMFDB - Embedded newform 414.2.j.a.53.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(17,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 7]))

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

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

chi := DirichletCharacter("414.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.j (of order $22$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			53.7
Character	$\chi$	$=$	414.53
Dual form			414.2.j.a.125.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.755750 + 0.654861i) q^{2} +(0.142315 + 0.989821i) q^{4} +(0.922959 + 2.02100i) q^{5} +(0.0130977 + 0.0446065i) q^{7} +(-0.540641 + 0.841254i) q^{8} +O(q^{10})$	\(q+(0.755750 + 0.654861i) q^{2} +(0.142315 + 0.989821i) q^{4} +(0.922959 + 2.02100i) q^{5} +(0.0130977 + 0.0446065i) q^{7} +(-0.540641 + 0.841254i) q^{8} +(-0.625947 + 2.13178i) q^{10} +(1.74253 + 2.01098i) q^{11} +(-1.51348 - 0.444397i) q^{13} +(-0.0193125 + 0.0422885i) q^{14} +(-0.959493 + 0.281733i) q^{16} +(-0.0331173 + 0.230336i) q^{17} +(-2.25463 + 0.324167i) q^{19} +(-1.86908 + 1.20118i) q^{20} +2.66091i q^{22} +(3.05411 + 3.69763i) q^{23} +(0.0417212 - 0.0481489i) q^{25} +(-0.852791 - 1.32697i) q^{26} +(-0.0422885 + 0.0193125i) q^{28} +(6.02540 + 0.866322i) q^{29} +(-6.37932 - 4.09974i) q^{31} +(-0.909632 - 0.415415i) q^{32} +(-0.175866 + 0.152389i) q^{34} +(-0.0780612 + 0.0676404i) q^{35} +(2.80691 + 1.28187i) q^{37} +(-1.91622 - 1.23148i) q^{38} +(-2.19916 - 0.316192i) q^{40} +(-0.764300 + 0.349044i) q^{41} +(-1.64454 - 2.55895i) q^{43} +(-1.74253 + 2.01098i) q^{44} +(-0.113292 + 4.79449i) q^{46} -3.61065i q^{47} +(5.88696 - 3.78332i) q^{49} +(0.0630616 - 0.00906689i) q^{50} +(0.224483 - 1.56132i) q^{52} +(6.15867 - 1.80835i) q^{53} +(-2.45591 + 5.37770i) q^{55} +(-0.0446065 - 0.0130977i) q^{56} +(3.98638 + 4.60052i) q^{58} +(0.296092 - 1.00840i) q^{59} +(5.09375 - 7.92604i) q^{61} +(-2.13641 - 7.27594i) q^{62} +(-0.415415 - 0.909632i) q^{64} +(-0.498752 - 3.46889i) q^{65} +(-4.92015 - 4.26333i) q^{67} -0.232705 q^{68} -0.103290 q^{70} +(-9.95203 - 8.62348i) q^{71} +(0.982079 + 6.83051i) q^{73} +(1.28187 + 2.80691i) q^{74} +(-0.641735 - 2.18555i) q^{76} +(-0.0668799 + 0.104067i) q^{77} +(1.88074 - 6.40520i) q^{79} +(-1.45495 - 1.67911i) q^{80} +(-0.806195 - 0.236720i) q^{82} +(3.50663 - 7.67846i) q^{83} +(-0.496075 + 0.145661i) q^{85} +(0.432898 - 3.01087i) q^{86} +(-2.63383 + 0.378687i) q^{88} +(-14.0917 + 9.05622i) q^{89} -0.0733315i q^{91} +(-3.22535 + 3.54925i) q^{92} +(2.36447 - 2.72875i) q^{94} +(-2.73608 - 4.25742i) q^{95} +(12.6502 - 5.77716i) q^{97} +(6.92661 + 0.995896i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 8 q^{4}+O(q^{10}) $ 80 * q + 8 * q^4	$ 80 q + 8 q^{4} - 16 q^{13} - 8 q^{16} + 24 q^{25} - 16 q^{31} + 88 q^{37} + 88 q^{43} + 8 q^{46} + 8 q^{49} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 176 q^{61} + 8 q^{64} - 88 q^{67} - 176 q^{70} - 56 q^{73} - 176 q^{79} - 88 q^{82} - 88 q^{85} + 16 q^{94}+O(q^{100}) $ 80 * q + 8 * q^4 - 16 * q^13 - 8 * q^16 + 24 * q^25 - 16 * q^31 + 88 * q^37 + 88 * q^43 + 8 * q^46 + 8 * q^49 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 176 * q^61 + 8 * q^64 - 88 * q^67 - 176 * q^70 - 56 * q^73 - 176 * q^79 - 88 * q^82 - 88 * q^85 + 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{19}{22}\right)$

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 $

$2$	0.755750	+	0.654861i	0.534396	+	0.463056i
$2$	0.755750	+	0.654861i	0.534396	+	0.463056i
$3$		0			0
$3$		0			0
$4$	0.142315	+	0.989821i	0.0711574	+	0.494911i
$5$	0.922959	+	2.02100i	0.412760	+	0.903818i	0.995816	+	0.0913859i	$0.0291297\pi$
$5$	0.922959	+	2.02100i	0.412760	+	0.903818i	−0.583056	+	0.812432i	$0.698143\pi$
$6$		0			0
$7$	0.0130977	+	0.0446065i	0.00495045	+	0.0168597i	0.961931	−	0.273292i	$-0.0881125\pi$
$7$	0.0130977	+	0.0446065i	0.00495045	+	0.0168597i	−0.956981	+	0.290152i	$0.906294\pi$
$8$	−0.540641	+	0.841254i	−0.191145	+	0.297428i
$9$		0			0
$10$	−0.625947	+	2.13178i	−0.197942	+	0.674128i
$11$	1.74253	+	2.01098i	0.525391	+	0.606334i	0.954973	−	0.296694i	$-0.0958842\pi$
$11$	1.74253	+	2.01098i	0.525391	+	0.606334i	−0.429581	+	0.903028i	$0.641339\pi$
$12$		0			0
$13$	−1.51348	−	0.444397i	−0.419763	−	0.123253i	0.0650284	−	0.997883i	$-0.479286\pi$
$13$	−1.51348	−	0.444397i	−0.419763	−	0.123253i	−0.484791	+	0.874630i	$0.661104\pi$
$14$	−0.0193125	+	0.0422885i	−0.00516149	+	0.0113021i
$15$		0			0
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	−0.0331173	+	0.230336i	−0.00803213	+	0.0558647i	−0.993443	−	0.114326i	$-0.963529\pi$
$17$	−0.0331173	+	0.230336i	−0.00803213	+	0.0558647i	0.985411	+	0.170191i	$0.0544383\pi$
$18$		0			0
$19$	−2.25463	+	0.324167i	−0.517248	+	0.0743691i	−0.395995	−	0.918253i	$-0.629600\pi$
$19$	−2.25463	+	0.324167i	−0.517248	+	0.0743691i	−0.121253	+	0.992622i	$0.538691\pi$
$20$	−1.86908	+	1.20118i	−0.417938	+	0.268593i
$21$		0			0
$22$			2.66091i			0.567308i
$23$	3.05411	+	3.69763i	0.636825	+	0.771008i
$23$	3.05411	+	3.69763i	0.636825	+	0.771008i
$24$		0			0
$25$	0.0417212	−	0.0481489i	0.00834425	−	0.00962978i
$26$	−0.852791	−	1.32697i	−0.167246	−	0.260240i
$27$		0			0
$28$	−0.0422885	+	0.0193125i	−0.00799178	+	0.00364972i
$29$	6.02540	+	0.866322i	1.11889	+	0.160872i	0.676848	−	0.736123i	$-0.263345\pi$
$29$	6.02540	+	0.866322i	1.11889	+	0.160872i	0.442041	+	0.896995i	$0.354254\pi$
$30$		0			0
$31$	−6.37932	−	4.09974i	−1.14576	−	0.736335i	−0.176969	−	0.984216i	$-0.556629\pi$
$31$	−6.37932	−	4.09974i	−1.14576	−	0.736335i	−0.968790	+	0.247881i	$0.920266\pi$
$32$	−0.909632	−	0.415415i	−0.160802	−	0.0734357i
$33$		0			0
$34$	−0.175866	+	0.152389i	−0.0301608	+	0.0261345i
$35$	−0.0780612	+	0.0676404i	−0.0131947	+	0.0114333i
$36$		0			0
$37$	2.80691	+	1.28187i	0.461452	+	0.210738i	0.632556	−	0.774515i	$-0.282006\pi$
$37$	2.80691	+	1.28187i	0.461452	+	0.210738i	−0.171103	+	0.985253i	$0.554733\pi$
$38$	−1.91622	−	1.23148i	−0.310852	−	0.199773i
$39$		0			0
$40$	−2.19916	−	0.316192i	−0.347718	−	0.0499943i
$41$	−0.764300	+	0.349044i	−0.119364	+	0.0545116i	−0.474202	−	0.880416i	$-0.657263\pi$
$41$	−0.764300	+	0.349044i	−0.119364	+	0.0545116i	0.354838	+	0.934928i	$0.384536\pi$
$42$		0			0
$43$	−1.64454	−	2.55895i	−0.250790	−	0.390237i	0.692918	−	0.721016i	$-0.256325\pi$
$43$	−1.64454	−	2.55895i	−0.250790	−	0.390237i	−0.943708	+	0.330779i	$0.892688\pi$
$44$	−1.74253	+	2.01098i	−0.262696	+	0.303167i
$45$		0			0
$46$	−0.113292	+	4.79449i	−0.0167039	+	0.706909i
$47$		−	3.61065i		−	0.526667i	−0.964705	−	0.263334i	$-0.915178\pi$
$47$		−	3.61065i		−	0.526667i	0.964705	−	0.263334i	$-0.0848220\pi$
$48$		0			0
$49$	5.88696	−	3.78332i	0.840994	−	0.540474i
$50$	0.0630616	−	0.00906689i	0.00891826	−	0.00128225i
$51$		0			0
$52$	0.224483	−	1.56132i	0.0311302	−	0.216515i
$53$	6.15867	−	1.80835i	0.845958	−	0.248396i	0.170099	−	0.985427i	$-0.445591\pi$
$53$	6.15867	−	1.80835i	0.845958	−	0.248396i	0.675859	+	0.737031i	$0.263773\pi$
$54$		0			0
$55$	−2.45591	+	5.37770i	−0.331155	+	0.725129i
$56$	−0.0446065	−	0.0130977i	−0.00596080	−	0.00175025i
$57$		0			0
$58$	3.98638	+	4.60052i	0.523437	+	0.604078i
$59$	0.296092	−	1.00840i	0.0385479	−	0.131282i	−0.937971	−	0.346714i	$-0.887298\pi$
$59$	0.296092	−	1.00840i	0.0385479	−	0.131282i	0.976519	+	0.215431i	$0.0691158\pi$
$60$		0			0
$61$	5.09375	−	7.92604i	0.652188	−	1.01482i	−0.344905	−	0.938638i	$-0.612089\pi$
$61$	5.09375	−	7.92604i	0.652188	−	1.01482i	0.997094	−	0.0761874i	$-0.0242747\pi$
$62$	−2.13641	−	7.27594i	−0.271324	−	0.924046i
$63$		0			0
$64$	−0.415415	−	0.909632i	−0.0519269	−	0.113704i
$65$	−0.498752	−	3.46889i	−0.0618625	−	0.430263i
$66$		0			0
$67$	−4.92015	−	4.26333i	−0.601092	−	0.520849i	0.300305	−	0.953843i	$-0.402912\pi$
$67$	−4.92015	−	4.26333i	−0.601092	−	0.520849i	−0.901397	+	0.432994i	$0.857457\pi$
$68$	−0.232705			−0.0282196
$69$		0			0
$70$	−0.103290			−0.0123455
$71$	−9.95203	−	8.62348i	−1.18109	−	1.02342i	−0.999196	−	0.0401004i	$-0.987232\pi$
$71$	−9.95203	−	8.62348i	−1.18109	−	1.02342i	−0.181893	−	0.983318i	$-0.558222\pi$
$72$		0			0
$73$	0.982079	+	6.83051i	0.114944	+	0.799451i	0.962992	+	0.269531i	$0.0868687\pi$
$73$	0.982079	+	6.83051i	0.114944	+	0.799451i	−0.848048	+	0.529919i	$0.822222\pi$
$74$	1.28187	+	2.80691i	0.149014	+	0.326296i
$75$		0			0
$76$	−0.641735	−	2.18555i	−0.0736121	−	0.250700i
$77$	−0.0668799	+	0.104067i	−0.00762168	+	0.0118596i
$78$		0			0
$79$	1.88074	−	6.40520i	0.211599	−	0.720641i	−0.783467	−	0.621433i	$-0.786551\pi$
$79$	1.88074	−	6.40520i	0.211599	−	0.720641i	0.995067	−	0.0992080i	$-0.0316309\pi$
$80$	−1.45495	−	1.67911i	−0.162669	−	0.187730i
$81$		0			0
$82$	−0.806195	−	0.236720i	−0.0890293	−	0.0261414i
$83$	3.50663	−	7.67846i	0.384903	−	0.842820i	−0.613677	−	0.789557i	$-0.710310\pi$
$83$	3.50663	−	7.67846i	0.384903	−	0.842820i	0.998581	−	0.0532633i	$-0.0169623\pi$
$84$		0			0
$85$	−0.496075	+	0.145661i	−0.0538069	+	0.0157991i
$86$	0.432898	−	3.01087i	0.0466806	−	0.324671i
$87$		0			0
$88$	−2.63383	+	0.378687i	−0.280767	+	0.0403682i
$89$	−14.0917	+	9.05622i	−1.49372	+	0.959957i	−0.498038	+	0.867155i	$0.665946\pi$
$89$	−14.0917	+	9.05622i	−1.49372	+	0.959957i	−0.995685	+	0.0928018i	$0.970418\pi$
$90$		0			0
$91$		−	0.0733315i		−	0.00768723i
$92$	−3.22535	+	3.54925i	−0.336266	+	0.370034i
$93$		0			0
$94$	2.36447	−	2.72875i	0.243877	−	0.281449i
$95$	−2.73608	−	4.25742i	−0.280715	−	0.436802i
$96$		0			0
$97$	12.6502	−	5.77716i	1.28443	−	0.586581i	0.348023	−	0.937486i	$-0.386853\pi$
$97$	12.6502	−	5.77716i	1.28443	−	0.586581i	0.936411	+	0.350905i	$0.114126\pi$
$98$	6.92661	+	0.995896i	0.699693	+	0.100601i
$99$		0			0
$100$	0.0535964	+	0.0344443i	0.00535964	+	0.00344443i
$101$	−9.27293	−	4.23481i	−0.922691	−	0.421379i	−0.103324	−	0.994648i	$-0.532948\pi$
$101$	−9.27293	−	4.23481i	−0.922691	−	0.421379i	−0.819367	+	0.573269i	$0.805675\pi$
$102$		0			0
$103$	6.72255	−	5.82513i	0.662393	−	0.573967i	−0.257432	−	0.966296i	$-0.582876\pi$
$103$	6.72255	−	5.82513i	0.662393	−	0.573967i	0.919825	+	0.392330i	$0.128331\pi$
$104$	1.19210	−	1.03296i	0.116895	−	0.101290i
$105$		0			0
$106$	5.83863	+	2.66641i	0.567098	+	0.258985i
$107$	−2.28174	−	1.46638i	−0.220584	−	0.141761i	0.425682	−	0.904873i	$-0.360034\pi$
$107$	−2.28174	−	1.46638i	−0.220584	−	0.141761i	−0.646266	+	0.763112i	$0.723670\pi$
$108$		0			0
$109$	8.05101	+	1.15756i	0.771147	+	0.110874i	0.516647	−	0.856198i	$-0.327180\pi$
$109$	8.05101	+	1.15756i	0.771147	+	0.110874i	0.254500	+	0.967073i	$0.418089\pi$
$110$	−5.37770	+	2.45591i	−0.512743	+	0.234162i
$111$		0			0
$112$	−0.0251342	−	0.0391096i	−0.00237496	−	0.00369551i
$113$	−4.42961	+	5.11204i	−0.416703	+	0.480900i	−0.924830	−	0.380382i	$-0.875793\pi$
$113$	−4.42961	+	5.11204i	−0.416703	+	0.480900i	0.508127	+	0.861282i	$0.330338\pi$
$114$		0			0
$115$	−4.65408	+	9.58510i	−0.433996	+	0.893815i
$116$			6.08737i			0.565198i
$117$		0			0
$118$	0.884130	−	0.568196i	0.0813908	−	0.0523067i
$119$	−0.0107083	+	0.00153961i	−0.000981624	+	0.000141136i
$120$		0			0
$121$	0.557811	−	3.87966i	0.0507101	−	0.352696i
$122$	9.04005	−	2.65440i	0.818448	−	0.240318i
$123$		0			0
$124$	3.15014	−	6.89784i	0.282891	−	0.619444i
$125$	10.7947	+	3.16961i	0.965508	+	0.283499i
$126$		0			0
$127$	11.6507	+	13.4457i	1.03384	+	1.19311i	0.980900	+	0.194513i	$0.0623128\pi$
$127$	11.6507	+	13.4457i	1.03384	+	1.19311i	0.0529370	+	0.998598i	$0.483142\pi$
$128$	0.281733	−	0.959493i	0.0249019	−	0.0848080i
$129$		0			0
$130$	1.89471	−	2.94823i	0.166177	−	0.258577i
$131$	0.364203	+	1.24036i	0.0318205	+	0.108371i	0.973872	−	0.227098i	$-0.0729236\pi$
$131$	0.364203	+	1.24036i	0.0318205	+	0.108371i	−0.942051	+	0.335468i	$0.891105\pi$
$132$		0			0
$133$	−0.0439904	−	0.0963255i	−0.00381445	−	0.00835248i
$134$	−0.926511	−	6.44403i	−0.0800384	−	0.556679i
$135$		0			0
$136$	−0.175866	−	0.152389i	−0.0150804	−	0.0130673i
$137$	−9.19016			−0.785169			−0.392584	−	0.919716i	$-0.628419\pi$
$137$	−9.19016			−0.785169			−0.392584	+	0.919716i	$0.628419\pi$
$138$		0			0
$139$	4.56062			0.386827			0.193414	−	0.981117i	$-0.438044\pi$
$139$	4.56062			0.386827			0.193414	+	0.981117i	$0.438044\pi$
$140$	−0.0780612	−	0.0676404i	−0.00659737	−	0.00571665i
$141$		0			0
$142$	−1.87406	−	13.0344i	−0.157268	−	1.09382i
$143$	−1.74360	−	3.81795i	−0.145807	−	0.319273i
$144$		0			0
$145$	3.81037	+	12.9769i	0.316434	+	1.07767i
$146$	−3.73083	+	5.80528i	−0.308765	+	0.480448i
$147$		0			0
$148$	−0.869359	+	2.96076i	−0.0714609	+	0.243373i
$149$	15.2836	+	17.6382i	1.25208	+	1.44497i	0.847780	+	0.530347i	$0.177938\pi$
$149$	15.2836	+	17.6382i	1.25208	+	1.44497i	0.404297	+	0.914628i	$0.367516\pi$
$150$		0			0
$151$	−22.0386	−	6.47112i	−1.79348	−	0.526612i	−0.796523	−	0.604608i	$-0.793330\pi$
$151$	−22.0386	−	6.47112i	−1.79348	−	0.526612i	−0.996954	+	0.0779956i	$0.975148\pi$
$152$	0.946240	−	2.07198i	0.0767502	−	0.168059i
$153$		0			0
$154$	−0.118694	+	0.0348517i	−0.00956464	+	0.00280843i
$155$	2.39772	−	16.6765i	0.192589	−	1.33949i
$156$		0			0
$157$	−8.54975	+	1.22927i	−0.682344	+	0.0981062i	−0.474766	−	0.880112i	$-0.657467\pi$
$157$	−8.54975	+	1.22927i	−0.682344	+	0.0981062i	−0.207578	+	0.978218i	$0.566558\pi$
$158$	5.61588	−	3.60910i	0.446775	−	0.287125i
$159$		0			0
$160$		−	2.22178i		−	0.175647i
$161$	−0.124937	+	0.184663i	−0.00984639	+	0.0145535i
$162$		0			0
$163$	−12.6243	+	14.5692i	−0.988809	+	1.14115i	0.00117993	+	0.999999i	$0.499624\pi$
$163$	−12.6243	+	14.5692i	−0.988809	+	1.14115i	−0.989989	+	0.141147i	$0.954921\pi$
$164$	−0.454263	−	0.706847i	−0.0354720	−	0.0551954i
$165$		0			0
$166$	7.67846	−	3.50663i	0.595964	−	0.272168i
$167$	8.15470	+	1.17247i	0.631029	+	0.0907283i	0.450406	−	0.892824i	$-0.351279\pi$
$167$	8.15470	+	1.17247i	0.631029	+	0.0907283i	0.180624	+	0.983552i	$0.442188\pi$
$168$		0			0
$169$	−8.84317	−	5.68316i	−0.680244	−	0.437166i
$170$	−0.470296	−	0.214777i	−0.0360700	−	0.0164726i
$171$		0			0
$172$	2.29887	−	1.99198i	0.175287	−	0.151887i
$173$	−5.65069	+	4.89635i	−0.429614	+	0.372263i	−0.842659	−	0.538448i	$-0.819011\pi$
$173$	−5.65069	+	4.89635i	−0.429614	+	0.372263i	0.413045	+	0.910711i	$0.364465\pi$
$174$		0			0
$175$	0.00269421	+	0.00123040i	0.000203663	+	9.30097e-5i
$176$	−2.23850	−	1.43860i	−0.168733	−	0.108438i
$177$		0			0
$178$	−16.5804	−	2.38390i	−1.24275	−	0.178681i
$179$	−2.24912	+	1.02714i	−0.168107	+	0.0767720i	−0.497691	−	0.867354i	$-0.665819\pi$
$179$	−2.24912	+	1.02714i	−0.168107	+	0.0767720i	0.329584	+	0.944126i	$0.393091\pi$
$180$		0			0
$181$	3.22755	+	5.02217i	0.239902	+	0.373295i	0.940238	−	0.340519i	$-0.110603\pi$
$181$	3.22755	+	5.02217i	0.239902	+	0.373295i	−0.700336	+	0.713814i	$0.746966\pi$
$182$	0.0480219	−	0.0554202i	0.00355962	−	0.00410802i
$183$		0			0
$184$	−4.76182	+	0.570189i	−0.351046	+	0.0420349i
$185$			6.85587i			0.504053i
$186$		0			0
$187$	−0.520910	+	0.334768i	−0.0380927	+	0.0244807i
$188$	3.57390	−	0.513849i	0.260653	−	0.0374763i
$189$		0			0
$190$	0.720227	−	5.00929i	0.0522508	−	0.363412i
$191$	4.15448	−	1.21987i	0.300608	−	0.0882663i	−0.127951	−	0.991781i	$-0.540840\pi$
$191$	4.15448	−	1.21987i	0.300608	−	0.0882663i	0.428558	+	0.903514i	$0.359022\pi$
$192$		0			0
$193$	−10.6531	+	23.3270i	−0.766826	+	1.67911i	−0.0333064	+	0.999445i	$0.510604\pi$
$193$	−10.6531	+	23.3270i	−0.766826	+	1.67911i	−0.733519	+	0.679669i	$0.762124\pi$
$194$	13.3436	+	3.91804i	0.958016	+	0.281299i
$195$		0			0
$196$	4.58261	+	5.28861i	0.327329	+	0.377758i
$197$	−1.04505	+	3.55911i	−0.0744567	+	0.253576i	−0.988307	−	0.152474i	$-0.951276\pi$
$197$	−1.04505	+	3.55911i	−0.0744567	+	0.253576i	0.913851	+	0.406050i	$0.133094\pi$
$198$		0			0
$199$	−7.22510	+	11.2425i	−0.512174	+	0.796958i	−0.996980	−	0.0776638i	$-0.975254\pi$
$199$	−7.22510	+	11.2425i	−0.512174	+	0.796958i	0.484806	+	0.874622i	$0.338890\pi$
$200$	0.0179492	+	0.0611294i	0.00126920	+	0.00432250i
$201$		0			0
$202$	−4.23481	−	9.27293i	−0.297960	−	0.652441i
$203$	0.0402751	+	0.280119i	0.00282676	+	0.0196605i
$204$		0			0
$205$	−1.41084	−	1.22250i	−0.0985371	−	0.0853828i
$206$	8.89521			0.619759
$207$		0			0
$208$	1.57737			0.109371
$209$	−4.58065	−	3.96916i	−0.316850	−	0.274552i
$210$		0			0
$211$	−0.449420	−	3.12578i	−0.0309393	−	0.215188i	0.968487	−	0.249065i	$-0.0801234\pi$
$211$	−0.449420	−	3.12578i	−0.0309393	−	0.215188i	−0.999426	+	0.0338777i	$0.989214\pi$
$212$	2.66641	+	5.83863i	0.183130	+	0.400999i
$213$		0			0
$214$	−0.764145	−	2.60244i	−0.0522359	−	0.177899i
$215$	3.65380	−	5.68542i	0.249187	−	0.387743i
$216$		0			0
$217$	0.0993210	−	0.338256i	0.00674235	−	0.0229623i
$218$	5.32651	+	6.14712i	0.360757	+	0.416335i
$219$		0			0
$220$	−5.67247	−	1.66559i	−0.382438	−	0.112294i
$221$	0.152483	−	0.333891i	0.0102571	−	0.0224599i
$222$		0			0
$223$	−23.9599	+	7.03527i	−1.60447	+	0.471116i	−0.956787	−	0.290790i	$-0.906082\pi$
$223$	−23.9599	+	7.03527i	−1.60447	+	0.471116i	−0.647688	+	0.761906i	$0.724264\pi$
$224$	0.00661617	−	0.0460165i	0.000442062	−	0.00307461i
$225$		0			0
$226$	−6.69535	+	0.962646i	−0.445368	+	0.0640343i
$227$	−9.18821	+	5.90491i	−0.609843	+	0.391922i	−0.808798	−	0.588086i	$-0.799882\pi$
$227$	−9.18821	+	5.90491i	−0.609843	+	0.391922i	0.198955	+	0.980009i	$0.436245\pi$
$228$		0			0
$229$		−	19.8476i		−	1.31156i	−0.754950	−	0.655782i	$-0.772339\pi$
$229$		−	19.8476i		−	1.31156i	0.754950	−	0.655782i	$-0.227661\pi$
$230$	−9.79423	+	4.19616i	−0.645812	+	0.276687i
$231$		0			0
$232$	−3.98638	+	4.60052i	−0.261718	+	0.302039i
$233$	5.10411	+	7.94216i	0.334382	+	0.520308i	0.967208	−	0.253986i	$-0.0817416\pi$
$233$	5.10411	+	7.94216i	0.334382	+	0.520308i	−0.632826	+	0.774294i	$0.718105\pi$
$234$		0			0
$235$	7.29712	−	3.33248i	0.476012	−	0.217387i
$236$	1.04027	+	0.149568i	0.0677158	+	0.00973607i
$237$		0			0
$238$	−0.00910099	−	0.00584885i	−0.000589930	−	0.000379125i
$239$	−4.78747	−	2.18637i	−0.309676	−	0.141424i	0.254515	−	0.967069i	$-0.418084\pi$
$239$	−4.78747	−	2.18637i	−0.309676	−	0.141424i	−0.564190	+	0.825645i	$0.690812\pi$
$240$		0			0
$241$	14.4634	−	12.5326i	0.931668	−	0.807295i	−0.0498318	−	0.998758i	$-0.515869\pi$
$241$	14.4634	−	12.5326i	0.931668	−	0.807295i	0.981500	+	0.191463i	$0.0613231\pi$
$242$	2.96220	−	2.56676i	0.190417	−	0.164998i
$243$		0			0
$244$	8.57028	+	3.91391i	0.548656	+	0.250563i
$245$	13.0795	+	8.40568i	0.835619	+	0.537019i
$246$		0			0
$247$	3.55639	+	0.511332i	0.226288	+	0.0325353i
$248$	6.89784	−	3.15014i	0.438013	−	0.200034i
$249$		0			0
$250$	6.08244	+	9.46446i	0.384687	+	0.598585i
$251$	−9.71762	+	11.2147i	−0.613371	+	0.707868i	−0.974434	−	0.224674i	$-0.927868\pi$
$251$	−9.71762	+	11.2147i	−0.613371	+	0.707868i	0.361063	+	0.932541i	$0.382414\pi$
$252$		0			0
$253$	−2.11400	+	12.5850i	−0.132906	+	0.791210i
$254$			17.7912i			1.11632i
$255$		0			0
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−24.1042	+	3.46566i	−1.50358	+	0.216182i	−0.844362	−	0.535773i	$-0.820020\pi$
$257$	−24.1042	+	3.46566i	−1.50358	+	0.216182i	−0.659215	+	0.751955i	$0.729111\pi$
$258$		0			0
$259$	−0.0204159	+	0.141996i	−0.00126858	+	0.00882319i
$260$	3.36261	−	0.987350i	0.208540	−	0.0612329i
$261$		0			0
$262$	−0.537017	+	1.17590i	−0.0331770	+	0.0726476i
$263$	24.7861	+	7.27785i	1.52838	+	0.448772i	0.934553	−	0.355824i	$-0.115800\pi$
$263$	24.7861	+	7.27785i	1.52838	+	0.448772i	0.593823	+	0.804596i	$0.297618\pi$
$264$		0			0
$265$	9.33887	+	10.7776i	0.573682	+	0.662064i
$266$	0.0298341	−	0.101606i	0.00182925	−	0.00622984i
$267$		0			0
$268$	3.51973	−	5.47681i	0.215002	−	0.334549i
$269$	3.35103	+	11.4126i	0.204316	+	0.695837i	0.996350	+	0.0853598i	$0.0272040\pi$
$269$	3.35103	+	11.4126i	0.204316	+	0.695837i	−0.792034	+	0.610477i	$0.790978\pi$
$270$		0			0
$271$	−4.35859	−	9.54397i	−0.264765	−	0.579755i	0.729825	−	0.683634i	$-0.239602\pi$
$271$	−4.35859	−	9.54397i	−0.264765	−	0.579755i	−0.994590	+	0.103879i	$0.966874\pi$
$272$	−0.0331173	−	0.230336i	−0.00200803	−	0.0139662i
$273$		0			0
$274$	−6.94546	−	6.01828i	−0.419591	−	0.363577i
$275$	0.169527			0.0102229
$276$		0			0
$277$	6.40498			0.384838			0.192419	−	0.981313i	$-0.438367\pi$
$277$	6.40498			0.384838			0.192419	+	0.981313i	$0.438367\pi$
$278$	3.44669	+	2.98657i	0.206719	+	0.179123i
$279$		0			0
$280$	−0.0146997	−	0.102238i	−0.000878473	−	0.00610991i
$281$	−3.21066	−	7.03036i	−0.191532	−	0.419396i	0.789365	−	0.613924i	$-0.210410\pi$
$281$	−3.21066	−	7.03036i	−0.191532	−	0.419396i	−0.980897	+	0.194528i	$0.937683\pi$
$282$		0			0
$283$	0.995499	+	3.39036i	0.0591763	+	0.201536i	0.983775	−	0.179407i	$-0.0574178\pi$
$283$	0.995499	+	3.39036i	0.0591763	+	0.201536i	−0.924599	+	0.380942i	$0.875600\pi$
$284$	7.11938	−	11.0780i	0.422458	−	0.657357i
$285$		0			0
$286$	1.18250	−	4.02723i	0.0699227	−	0.238135i
$287$	−0.0255802	−	0.0295211i	−0.00150995	−	0.00174258i
$288$		0			0
$289$	16.2594	+	4.77420i	0.956437	+	0.280835i
$290$	−5.61839	+	12.3026i	−0.329923	+	0.722431i
$291$		0			0
$292$	−6.62122	+	1.94417i	−0.387478	+	0.113774i
$293$	3.52663	−	24.5283i	0.206028	−	1.43296i	−0.579925	−	0.814670i	$-0.696918\pi$
$293$	3.52663	−	24.5283i	0.206028	−	1.43296i	0.785953	−	0.618286i	$-0.212173\pi$
$294$		0			0
$295$	2.31125	−	0.332307i	0.134566	−	0.0193477i
$296$	−2.59591	+	1.66829i	−0.150884	+	0.0969672i
$297$		0			0
$298$			23.3386i			1.35197i
$299$	−2.97910	−	6.95350i	−0.172286	−	0.402132i
$300$		0			0
$301$	0.0926065	−	0.106874i	0.00533775	−	0.00616009i
$302$	−12.4180	−	19.3228i	−0.714575	−	1.11190i
$303$		0			0
$304$	2.07198	−	0.946240i	0.118836	−	0.0542706i
$305$	20.7198	+	2.97906i	1.18641	+	0.170581i
$306$		0			0
$307$	−21.9621	−	14.1142i	−1.25344	−	0.805537i	−0.266068	−	0.963954i	$-0.585725\pi$
$307$	−21.9621	−	14.1142i	−1.25344	−	0.805537i	−0.987372	+	0.158417i	$0.949361\pi$
$308$	−0.112526	−	0.0513889i	−0.00641176	−	0.00292815i
$309$		0			0
$310$	12.7329	−	11.0331i	0.723177	−	0.626637i
$311$	−25.6741	+	22.2467i	−1.45585	+	1.26150i	−0.551857	+	0.833939i	$0.686081\pi$
$311$	−25.6741	+	22.2467i	−1.45585	+	1.26150i	−0.903988	+	0.427558i	$0.859374\pi$
$312$		0			0
$313$	14.4536	+	6.60075i	0.816968	+	0.373097i	0.779657	−	0.626207i	$-0.215394\pi$
$313$	14.4536	+	6.60075i	0.816968	+	0.373097i	0.0373109	+	0.999304i	$0.488121\pi$
$314$	−7.26647	−	4.66987i	−0.410070	−	0.263536i
$315$		0			0
$316$	6.60766	+	0.950038i	0.371710	+	0.0534438i
$317$	15.7635	−	7.19897i	0.885369	−	0.404334i	0.0797822	−	0.996812i	$-0.474578\pi$
$317$	15.7635	−	7.19897i	0.885369	−	0.404334i	0.805587	+	0.592478i	$0.201850\pi$
$318$		0			0
$319$	8.75727	+	13.6266i	0.490313	+	0.762942i
$320$	1.45495	−	1.67911i	0.0813344	−	0.0938649i
$321$		0			0
$322$	−0.215350	+	0.0577431i	−0.0120010	+	0.00321790i
$323$		−	0.530059i		−	0.0294933i
$324$		0			0
$325$	−0.0845413	+	0.0543314i	−0.00468951	+	0.00301376i
$326$	−19.0816	+	2.74351i	−1.05683	+	0.151949i
$327$		0			0
$328$	0.119577	−	0.831678i	0.00660255	−	0.0459217i
$329$	0.161059	−	0.0472911i	0.00887945	−	0.00260724i
$330$		0			0
$331$	−2.79260	+	6.11495i	−0.153495	+	0.336108i	−0.970721	−	0.240210i	$-0.922784\pi$
$331$	−2.79260	+	6.11495i	−0.153495	+	0.336108i	0.817226	+	0.576318i	$0.195511\pi$
$332$	8.09935	+	2.37818i	0.444509	+	0.130520i
$333$		0			0
$334$	5.39511	+	6.22628i	0.295207	+	0.340687i
$335$	4.07510	−	13.8785i	0.222646	−	0.758264i
$336$		0			0
$337$	−5.30057	+	8.24784i	−0.288740	+	0.449289i	−0.955075	−	0.296364i	$-0.904226\pi$
$337$	−5.30057	+	8.24784i	−0.288740	+	0.449289i	0.666335	+	0.745653i	$0.267862\pi$
$338$	−2.96154	−	10.0861i	−0.161087	−	0.548611i
$339$		0			0
$340$	−0.214777	−	0.470296i	−0.0116479	−	0.0255054i
$341$	−2.87163	−	19.9726i	−0.155507	−	1.08158i
$342$		0			0
$343$	0.491808	+	0.426154i	0.0265551	+	0.0230102i
$344$	3.04184			0.164005
$345$		0			0
$346$	−7.47694			−0.401963
$347$	−8.35372	−	7.23854i	−0.448451	−	0.388585i	0.401149	−	0.916013i	$-0.368611\pi$
$347$	−8.35372	−	7.23854i	−0.448451	−	0.388585i	−0.849600	+	0.527428i	$0.823157\pi$
$348$		0			0
$349$	−2.95525	−	20.5542i	−0.158191	−	1.10024i	−0.901965	−	0.431810i	$-0.857875\pi$
$349$	−2.95525	−	20.5542i	−0.158191	−	1.10024i	0.743774	−	0.668431i	$-0.233034\pi$
$350$	0.00123040	+	0.00269421i	6.57678e−5	+	0.000144011i
$351$		0			0
$352$	−0.749665	−	2.55313i	−0.0399573	−	0.136082i
$353$	6.65538	−	10.3560i	0.354230	−	0.551193i	−0.617714	−	0.786403i	$-0.711941\pi$
$353$	6.65538	−	10.3560i	0.354230	−	0.551193i	0.971945	+	0.235209i	$0.0755776\pi$
$354$		0			0
$355$	8.24273	−	28.0722i	0.437479	−	1.48992i
$356$	−10.9695	−	12.6595i	−0.581382	−	0.670951i
$357$		0			0
$358$	−2.37241	−	0.696601i	−0.125386	−	0.0368165i
$359$	−8.01543	+	17.5514i	−0.423038	+	0.926325i	0.571367	+	0.820695i	$0.306413\pi$
$359$	−8.01543	+	17.5514i	−0.423038	+	0.926325i	−0.994405	+	0.105630i	$0.966314\pi$
$360$		0			0
$361$	−13.2521	+	3.89116i	−0.697478	+	0.204798i
$362$	−0.849601	+	5.90910i	−0.0446540	+	0.310576i
$363$		0			0
$364$	0.0725851	−	0.0104362i	0.00380449	−	0.000547003i
$365$	−12.8980	+	8.28906i	−0.675114	+	0.433869i
$366$		0			0
$367$		−	7.81117i		−	0.407740i	−0.978998	−	0.203870i	$-0.934648\pi$
$367$		−	7.81117i		−	0.407740i	0.978998	−	0.203870i	$-0.0653519\pi$
$368$	−3.97213	−	2.68741i	−0.207062	−	0.140091i
$369$		0			0
$370$	−4.48964	+	5.18132i	−0.233405	+	0.269364i
$371$	0.161328	+	0.251032i	0.00837575	+	0.0130329i
$372$		0			0
$373$	24.0981	−	11.0052i	1.24775	−	0.569829i	0.321563	−	0.946888i	$-0.395792\pi$
$373$	24.0981	−	11.0052i	1.24775	−	0.569829i	0.926189	+	0.377059i	$0.123065\pi$
$374$	−0.612904	−	0.0881223i	−0.0316925	−	0.00455669i
$375$		0			0
$376$	3.03747	+	1.95206i	0.156646	+	0.100670i
$377$	−8.73432	−	3.98883i	−0.449840	−	0.205435i
$378$		0			0
$379$	21.9220	−	18.9955i	1.12606	−	0.975736i	0.126191	−	0.992006i	$-0.459725\pi$
$379$	21.9220	−	18.9955i	1.12606	−	0.975736i	0.999868	+	0.0162702i	$0.00517918\pi$
$380$	3.82470	−	3.31412i	0.196203	−	0.170011i
$381$		0			0
$382$	3.93859	+	1.79869i	0.201516	+	0.0920291i
$383$	8.72079	+	5.60451i	0.445612	+	0.286377i	0.744140	−	0.668024i	$-0.232859\pi$
$383$	8.72079	+	5.60451i	0.445612	+	0.286377i	−0.298529	+	0.954401i	$0.596496\pi$
$384$		0			0
$385$	−0.272047	−	0.0391145i	−0.0138648	−	0.00199346i
$386$	−23.3270	+	10.6531i	−1.18731	+	0.542228i
$387$		0			0
$388$	7.51867	+	11.6993i	0.381702	+	0.593941i
$389$	10.2330	−	11.8096i	0.518836	−	0.598769i	−0.434503	−	0.900670i	$-0.643076\pi$
$389$	10.2330	−	11.8096i	0.518836	−	0.598769i	0.953339	+	0.301902i	$0.0976214\pi$
$390$		0			0
$391$	−0.952841	+	0.581015i	−0.0481872	+	0.0293832i
$392$			6.99784i			0.353444i
$393$		0			0
$394$	−3.12052	+	2.00544i	−0.157209	+	0.101032i
$395$	14.6807	−	2.11077i	0.738668	−	0.106204i
$396$		0			0
$397$	4.07936	−	28.3726i	0.204737	−	1.42398i	−0.585249	−	0.810853i	$-0.699003\pi$
$397$	4.07936	−	28.3726i	0.204737	−	1.42398i	0.789986	−	0.613124i	$-0.210088\pi$
$398$	−12.8226	+	3.76506i	−0.642740	+	0.188725i
$399$		0			0
$400$	−0.0264661	+	0.0579528i	−0.00132331	+	0.00289764i
$401$	−17.3212	−	5.08596i	−0.864979	−	0.253981i	−0.181000	−	0.983483i	$-0.557934\pi$
$401$	−17.3212	−	5.08596i	−0.864979	−	0.253981i	−0.683978	+	0.729502i	$0.739752\pi$
$402$		0			0
$403$	7.83304	+	9.03981i	0.390191	+	0.450305i
$404$	2.87203	−	9.78122i	0.142889	−	0.486634i
$405$		0			0
$406$	−0.153001	+	0.238075i	−0.00759332	+	0.0118154i
$407$	2.31329	+	7.87833i	0.114665	+	0.390514i
$408$		0			0
$409$	8.38050	+	18.3507i	0.414389	+	0.907385i	0.995606	+	0.0936368i	$0.0298493\pi$
$409$	8.38050	+	18.3507i	0.414389	+	0.907385i	−0.581218	+	0.813748i	$0.697423\pi$
$410$	−0.265674	−	1.84780i	−0.0131207	−	0.0912564i
$411$		0			0
$412$	6.72255	+	5.82513i	0.331196	+	0.286983i
$413$	0.0488592			0.00240420
$414$		0			0
$415$	18.7546			0.920629
$416$	1.19210	+	1.03296i	0.0584474	+	0.0506449i
$417$		0			0
$418$	−0.862580	−	5.99938i	−0.0421902	−	0.293439i
$419$	−3.45220	−	7.55927i	−0.168651	−	0.369295i	0.806368	−	0.591414i	$-0.201430\pi$
$419$	−3.45220	−	7.55927i	−0.168651	−	0.369295i	−0.975020	+	0.222119i	$0.928703\pi$
$420$		0			0
$421$	−10.4846	−	35.7073i	−0.510989	−	1.74027i	−0.659839	−	0.751407i	$-0.729375\pi$
$421$	−10.4846	−	35.7073i	−0.510989	−	1.74027i	0.148850	−	0.988860i	$-0.452443\pi$
$422$	1.70730	−	2.65662i	0.0831102	−	0.129322i
$423$		0			0
$424$	−1.80835	+	6.15867i	−0.0878211	+	0.299091i
$425$	0.00970873	+	0.0112045i	0.000470943	+	0.000543497i
$426$		0			0
$427$	0.420269	+	0.123402i	0.0203383	+	0.00597185i
$428$	1.12673	−	2.46720i	0.0544627	−	0.119257i
$429$		0			0
$430$	6.48452	−	1.90403i	0.312711	−	0.0918203i
$431$	4.59850	−	31.9833i	0.221502	−	1.54058i	−0.510860	−	0.859664i	$-0.670673\pi$
$431$	4.59850	−	31.9833i	0.221502	−	1.54058i	0.732362	−	0.680916i	$-0.238418\pi$
$432$		0			0
$433$	−38.4655	+	5.53050i	−1.84853	+	0.265779i	−0.975197	−	0.221340i	$-0.928957\pi$
$433$	−38.4655	+	5.53050i	−1.84853	+	0.265779i	−0.873336	+	0.487118i	$0.838048\pi$
$434$	0.296573	−	0.190596i	0.0142359	−	0.00914888i
$435$		0			0
$436$			8.13381i			0.389539i
$437$	−8.08453	−	7.34675i	−0.386736	−	0.351443i
$438$		0			0
$439$	14.7903	−	17.0690i	0.705905	−	0.814657i	−0.283633	−	0.958933i	$-0.591540\pi$
$439$	14.7903	−	17.0690i	0.705905	−	0.814657i	0.989538	+	0.144276i	$0.0460852\pi$
$440$	−3.19624	−	4.97345i	−0.152375	−	0.237100i
$441$		0			0
$442$	0.333891	−	0.152483i	0.0158816	−	0.00725287i
$443$	31.8548	+	4.58002i	1.51347	+	0.217604i	0.848470	−	0.529244i	$-0.177524\pi$
$443$	31.8548	+	4.58002i	1.51347	+	0.217604i	0.664996	+	0.746847i	$0.268433\pi$
$444$		0			0
$445$	−31.3087	−	20.1209i	−1.48418	−	0.953822i
$446$	−22.7148	−	10.3735i	−1.07558	−	0.491200i
$447$		0			0
$448$	0.0351346	−	0.0304443i	0.00165995	−	0.00143836i
$449$	−8.21808	+	7.12100i	−0.387835	+	0.336061i	−0.826854	−	0.562417i	$-0.809872\pi$
$449$	−8.21808	+	7.12100i	−0.387835	+	0.336061i	0.439019	+	0.898478i	$0.355326\pi$
$450$		0			0
$451$	−2.03373	−	0.928776i	−0.0957648	−	0.0437343i
$452$	−5.69041	−	3.65700i	−0.267654	−	0.172011i
$453$		0			0
$454$	−10.8109	−	1.55437i	−0.507380	−	0.0729502i
$455$	0.148203	−	0.0676820i	0.00694786	−	0.00317298i
$456$		0			0
$457$	19.0245	+	29.6027i	0.889929	+	1.38476i	0.922792	+	0.385297i	$0.125901\pi$
$457$	19.0245	+	29.6027i	0.889929	+	1.38476i	−0.0328630	+	0.999460i	$0.510463\pi$
$458$	12.9974	−	14.9998i	0.607329	−	0.700895i
$459$		0			0
$460$	−10.1499	−	3.24261i	−0.473241	−	0.151187i
$461$		−	13.6098i		−	0.633870i	−0.948447	−	0.316935i	$-0.897346\pi$
$461$		−	13.6098i		−	0.633870i	0.948447	−	0.316935i	$-0.102654\pi$
$462$		0			0
$463$	−0.904694	+	0.581412i	−0.0420447	+	0.0270205i	−0.561494	−	0.827481i	$-0.689773\pi$
$463$	−0.904694	+	0.581412i	−0.0420447	+	0.0270205i	0.519450	+	0.854501i	$0.326137\pi$
$464$	−6.02540	+	0.866322i	−0.279722	+	0.0402180i
$465$		0			0
$466$	−1.34357	+	9.34477i	−0.0622399	+	0.432888i
$467$	−38.0188	+	11.1633i	−1.75930	+	0.516577i	−0.992168	−	0.124910i	$-0.960136\pi$
$467$	−38.0188	+	11.1633i	−1.75930	+	0.516577i	−0.767133	+	0.641488i	$0.778318\pi$
$468$		0			0
$469$	0.125730	−	0.275311i	0.00580568	−	0.0127127i
$470$	7.69711	+	2.26007i	0.355041	+	0.104249i
$471$		0			0
$472$	0.688238	+	0.794269i	0.0316787	+	0.0365592i
$473$	2.28036	−	7.76619i	0.104851	−	0.357090i
$474$		0			0
$475$	−0.0784578	+	0.122083i	−0.00359989	+	0.00560154i
$476$	−0.00304789	−	0.0103801i	−0.000139700	−	0.000475773i
$477$		0			0
$478$	−2.18637	−	4.78747i	−0.100002	−	0.218974i
$479$	−1.73581	−	12.0728i	−0.0793113	−	0.551622i	−0.990274	−	0.139133i	$-0.955568\pi$
$479$	−1.73581	−	12.0728i	−0.0793113	−	0.551622i	0.910962	−	0.412489i	$-0.135341\pi$
$480$		0			0
$481$	−3.67853	−	3.18746i	−0.167726	−	0.145336i
$482$	19.1378			0.871703
$483$		0			0
$484$	3.91955			0.178162
$485$	23.3513	+	20.2340i	1.06033	+	0.918778i
$486$		0			0
$487$	−0.876975	−	6.09950i	−0.0397395	−	0.276395i	0.960257	−	0.279118i	$-0.0900421\pi$
$487$	−0.876975	−	6.09950i	−0.0397395	−	0.276395i	−0.999996	+	0.00272360i	$0.999133\pi$
$488$	3.91391	+	8.57028i	0.177175	+	0.387958i
$489$		0			0
$490$	4.38027	+	14.9178i	0.197881	+	0.673919i
$491$	15.0559	−	23.4275i	0.679465	−	1.05727i	−0.314678	−	0.949199i	$-0.601896\pi$
$491$	15.0559	−	23.4275i	0.679465	−	1.05727i	0.994143	−	0.108070i	$-0.0344672\pi$
$492$		0			0
$493$	−0.399091	+	1.35918i	−0.0179741	+	0.0612143i
$494$	2.35289	+	2.71538i	0.105862	+	0.122171i
$495$		0			0
$496$	7.27594	+	2.13641i	0.326699	+	0.0959276i
$497$	0.254315	−	0.556873i	0.0114076	−	0.0249792i
$498$		0			0
$499$	−35.1176	+	10.3115i	−1.57208	+	0.461605i	−0.947606	−	0.319440i	$-0.896505\pi$
$499$	−35.1176	+	10.3115i	−1.57208	+	0.461605i	−0.624475	+	0.781045i	$0.714687\pi$
$500$	−1.60110	+	11.1359i	−0.0716035	+	0.498013i
$501$		0			0
$502$	−14.6882	+	2.11184i	−0.655566	+	0.0942561i
$503$	−15.9099	+	10.2247i	−0.709387	+	0.455896i	−0.844931	−	0.534876i	$-0.820358\pi$
$503$	−15.9099	+	10.2247i	−0.709387	+	0.455896i	0.135543	+	0.990771i	$0.456722\pi$
$504$		0			0
$505$		−	22.6491i		−	1.00787i
$506$	−9.83905	+	8.12670i	−0.437399	+	0.361276i
$507$		0			0
$508$	−11.6507	+	13.4457i	−0.516918	+	0.596556i
$509$	−14.9080	−	23.1972i	−0.660784	−	1.02820i	−0.996281	−	0.0861587i	$-0.972541\pi$
$509$	−14.9080	−	23.1972i	−0.660784	−	1.02820i	0.335498	−	0.942041i	$-0.391096\pi$
$510$		0			0
$511$	−0.291822	+	0.133271i	−0.0129095	+	0.00589555i
$512$	0.989821	+	0.142315i	0.0437443	+	0.00628949i
$513$		0			0
$514$	−20.4862	−	13.1657i	−0.903609	−	0.580714i
$515$	17.9772	+	8.20992i	0.792171	+	0.361772i
$516$		0			0
$517$	7.26095	−	6.29165i	0.319336	−	0.276707i
$518$	−0.108417	+	0.0939437i	−0.00476356	+	0.00412765i
$519$		0			0
$520$	3.18786	+	1.45585i	0.139797	+	0.0638432i
$521$	10.2834	+	6.60872i	0.450523	+	0.289533i	0.746160	−	0.665767i	$-0.231895\pi$
$521$	10.2834	+	6.60872i	0.450523	+	0.289533i	−0.295637	+	0.955300i	$0.595532\pi$
$522$		0			0
$523$	20.5461	+	2.95408i	0.898418	+	0.129173i	0.576024	−	0.817433i	$-0.304603\pi$
$523$	20.5461	+	2.95408i	0.898418	+	0.129173i	0.322394	+	0.946606i	$0.395512\pi$
$524$	−1.17590	+	0.537017i	−0.0513696	+	0.0234597i
$525$		0			0
$526$	13.9661	+	21.7317i	0.608951	+	0.947546i
$527$	1.15558	−	1.33362i	0.0503380	−	0.0580932i
$528$		0			0
$529$	−4.34488	+	22.5859i	−0.188908	+	0.981995i
$530$			14.2608i			0.619452i
$531$		0			0
$532$	0.0890846	−	0.0572512i	0.00386231	−	0.00248215i
$533$	1.31186	−	0.188618i	0.0568232	−	0.00816994i
$534$		0			0
$535$	0.857609	−	5.96480i	0.0370777	−	0.257881i
$536$	6.24658	−	1.83416i	0.269811	−	0.0792237i
$537$		0			0
$538$	−4.94110	+	10.8195i	−0.213026	+	0.466462i
$539$	17.8664	+	5.24604i	0.769559	+	0.225963i
$540$		0			0
$541$	−10.3296	−	11.9209i	−0.444102	−	0.512521i	0.488926	−	0.872325i	$-0.337389\pi$
$541$	−10.3296	−	11.9209i	−0.444102	−	0.512521i	−0.933028	+	0.359804i	$0.882843\pi$
$542$	2.95597	−	10.0671i	0.126970	−	0.432420i
$543$		0			0
$544$	0.125810	−	0.195764i	0.00539404	−	0.00839330i
$545$	5.09133	+	17.3395i	0.218089	+	0.742741i
$546$		0			0
$547$	2.26144	+	4.95187i	0.0966923	+	0.211727i	0.951797	−	0.306729i	$-0.0992345\pi$
$547$	2.26144	+	4.95187i	0.0966923	+	0.211727i	−0.855105	+	0.518455i	$0.826507\pi$
$548$	−1.30790	−	9.09662i	−0.0558706	−	0.388588i
$549$		0			0
$550$	0.128120	+	0.111017i	0.00546305	+	0.00473376i
$551$	−13.8659			−0.590708
$552$		0			0
$553$	0.310347			0.0131973
$554$	4.84056	+	4.19437i	0.205656	+	0.178202i
$555$		0			0
$556$	0.649044	+	4.51420i	0.0275256	+	0.191445i
$557$	2.75063	+	6.02305i	0.116548	+	0.255205i	0.958912	−	0.283705i	$-0.0915636\pi$
$557$	2.75063	+	6.02305i	0.116548	+	0.255205i	−0.842363	+	0.538910i	$0.818836\pi$
$558$		0			0
$559$	1.35178	+	4.60375i	0.0571743	+	0.194718i
$560$	0.0558426	−	0.0868928i	0.00235978	−	0.00367189i
$561$		0			0
$562$	2.17745	−	7.41573i	0.0918504	−	0.312814i
$563$	23.6142	+	27.2522i	0.995219	+	1.14854i	0.988903	+	0.148564i	$0.0474652\pi$
$563$	23.6142	+	27.2522i	0.995219	+	1.14854i	0.00631647	+	0.999980i	$0.497989\pi$
$564$		0			0
$565$	−14.4198	−	4.23403i	−0.606645	−	0.178127i
$566$	−1.46786	+	3.21417i	−0.0616989	+	0.135102i
$567$		0			0
$568$	12.6350	−	3.70997i	0.530153	−	0.155667i
$569$	−1.13089	+	7.86552i	−0.0474094	+	0.329740i	0.952289	+	0.305197i	$0.0987222\pi$
$569$	−1.13089	+	7.86552i	−0.0474094	+	0.329740i	−0.999699	+	0.0245431i	$0.992187\pi$
$570$		0			0
$571$	14.7693	−	2.12350i	0.618076	−	0.0888658i	0.173837	−	0.984774i	$-0.444383\pi$
$571$	14.7693	−	2.12350i	0.618076	−	0.0888658i	0.444238	+	0.895909i	$0.353474\pi$
$572$	3.53095	−	2.26920i	0.147636	−	0.0948801i
$573$		0			0
$574$		−	0.0390620i		−	0.00163042i
$575$	0.305458	+	0.00721782i	0.0127385	+	0.000301004i
$576$		0			0
$577$	−11.2189	+	12.9472i	−0.467047	+	0.539001i	−0.939588	−	0.342308i	$-0.888791\pi$
$577$	−11.2189	+	12.9472i	−0.467047	+	0.539001i	0.472541	+	0.881309i	$0.343337\pi$
$578$	9.16162	+	14.2558i	0.381073	+	0.592961i
$579$		0			0
$580$	−12.3026	+	5.61839i	−0.510836	+	0.233291i
$581$	0.388438	+	0.0558490i	0.0161151	+	0.00231701i
$582$		0			0
$583$	14.3682	+	9.23388i	0.595070	+	0.382428i
$584$	−6.27714	−	2.86667i	−0.259750	−	0.118624i
$585$		0			0
$586$	18.7278	−	16.2278i	0.773640	−	0.670363i
$587$	−19.9192	+	17.2601i	−0.822152	+	0.712399i	−0.960589	−	0.277973i	$-0.910338\pi$
$587$	−19.9192	+	17.2601i	−0.822152	+	0.712399i	0.138437	+	0.990371i	$0.455792\pi$
$588$		0			0
$589$	15.7120	+	7.17544i	0.647403	+	0.295659i
$590$	1.96434	+	1.26240i	0.0808706	+	0.0519724i
$591$		0			0
$592$	−3.05435	−	0.439149i	−0.125533	−	0.0180489i
$593$	20.4544	−	9.34121i	0.839961	−	0.383597i	0.0514932	−	0.998673i	$-0.483602\pi$
$593$	20.4544	−	9.34121i	0.839961	−	0.383597i	0.788468	+	0.615076i	$0.210875\pi$
$594$		0			0
$595$	−0.0129948	−	0.0202204i	−0.000532737	−	0.000828954i
$596$	−15.2836	+	17.6382i	−0.626039	+	0.722487i
$597$		0			0
$598$	2.30212	−	7.20601i	0.0941407	−	0.294675i
$599$			7.97019i			0.325653i	0.986655	+	0.162826i	$0.0520611\pi$
$599$			7.97019i			0.325653i	−0.986655	+	0.162826i	$0.947939\pi$
$600$		0			0
$601$	−20.4910	+	13.1688i	−0.835845	+	0.537165i	−0.887130	−	0.461519i	$-0.847305\pi$
$601$	−20.4910	+	13.1688i	−0.835845	+	0.537165i	0.0512850	+	0.998684i	$0.483668\pi$
$602$	0.139975	−	0.0201253i	0.00570494	−	0.000820246i
$603$		0			0
$604$	3.26883	−	22.7352i	0.133007	−	0.925083i
$605$	8.35562	−	2.45343i	0.339704	−	0.0997462i
$606$		0			0
$607$	−3.23374	+	7.08091i	−0.131254	+	0.287405i	−0.963836	−	0.266496i	$-0.914134\pi$
$607$	−3.23374	+	7.08091i	−0.131254	+	0.287405i	0.832582	+	0.553901i	$0.186861\pi$
$608$	2.18555	+	0.641735i	0.0886358	+	0.0260258i
$609$		0			0
$610$	13.7081	+	15.8200i	0.555026	+	0.640534i
$611$	−1.60456	+	5.46463i	−0.0649136	+	0.221075i
$612$		0			0
$613$	−3.62934	+	5.64736i	−0.146588	+	0.228095i	−0.906781	−	0.421602i	$-0.861468\pi$
$613$	−3.62934	+	5.64736i	−0.146588	+	0.228095i	0.760193	+	0.649697i	$0.225104\pi$
$614$	−7.35501	−	25.0489i	−0.296824	−	1.01089i
$615$		0			0
$616$	−0.0513889	−	0.112526i	−0.00207052	−	0.00453380i
$617$	3.54534	+	24.6584i	0.142730	+	0.992710i	0.927740	+	0.373227i	$0.121749\pi$
$617$	3.54534	+	24.6584i	0.142730	+	0.992710i	−0.785010	+	0.619483i	$0.787342\pi$
$618$		0			0
$619$	18.2505	+	15.8141i	0.733548	+	0.635623i	0.939346	−	0.342972i	$-0.111434\pi$
$619$	18.2505	+	15.8141i	0.733548	+	0.635623i	−0.205798	+	0.978594i	$0.565979\pi$
$620$	16.8480			0.676631
$621$		0			0
$622$	−33.9717			−1.36214
$623$	−0.588535	−	0.509969i	−0.0235792	−	0.0204315i
$624$		0			0
$625$	3.51196	+	24.4262i	0.140478	+	0.977048i
$626$	6.60075	+	14.4536i	0.263819	+	0.577683i
$627$		0			0
$628$	−2.43351	−	8.28778i	−0.0971077	−	0.330718i
$629$	−0.388218	+	0.604079i	−0.0154793	+	0.0240862i
$630$		0			0
$631$	11.0207	−	37.5330i	0.438726	−	1.49417i	−0.382712	−	0.923868i	$-0.625010\pi$
$631$	11.0207	−	37.5330i	0.438726	−	1.49417i	0.821438	−	0.570297i	$-0.193172\pi$
$632$	4.37159	+	5.04509i	0.173893	+	0.200683i
$633$		0			0
$634$	16.6276	+	4.88231i	0.660367	+	0.193901i
$635$	−16.4205	+	35.9560i	−0.651629	+	1.42687i
$636$		0			0
$637$	−10.5911	+	3.10982i	−0.419633	+	0.123215i
$638$	−2.30521	+	16.0331i	−0.0912640	+	0.634755i
$639$		0			0
$640$	2.19916	−	0.316192i	0.0869295	−	0.0124986i
$641$	−27.7530	+	17.8358i	−1.09618	+	0.704471i	−0.958239	−	0.285970i	$-0.907684\pi$
$641$	−27.7530	+	17.8358i	−1.09618	+	0.704471i	−0.137939	+	0.990441i	$0.544048\pi$
$642$		0			0
$643$			26.1154i			1.02989i	0.857223	+	0.514946i	$0.172188\pi$
$643$			26.1154i			1.02989i	−0.857223	+	0.514946i	$0.827812\pi$
$644$	−0.200564	−	0.0973847i	−0.00790333	−	0.00383749i
$645$		0			0
$646$	0.347115	−	0.400592i	0.0136570	−	0.0157611i
$647$	17.6026	+	27.3901i	0.692028	+	1.07682i	0.992407	+	0.122997i	$0.0392505\pi$
$647$	17.6026	+	27.3901i	0.692028	+	1.07682i	−0.300379	+	0.953820i	$0.597113\pi$
$648$		0			0
$649$	2.54381	−	1.16172i	0.0998535	−	0.0456016i
$650$	−0.0994716	−	0.0143019i	−0.00390160	−	0.000560965i
$651$		0			0
$652$	−16.2175	−	10.4224i	−0.635127	−	0.408171i
$653$	17.4974	+	7.99081i	0.684728	+	0.312705i	0.727232	−	0.686392i	$-0.240806\pi$
$653$	17.4974	+	7.99081i	0.684728	+	0.312705i	−0.0425043	+	0.999096i	$0.513534\pi$
$654$		0			0
$655$	−2.17062	+	1.88086i	−0.0848132	+	0.0734911i
$656$	0.635004	−	0.550234i	0.0247927	−	0.0214830i
$657$		0			0
$658$	0.152689	+	0.0697308i	0.00595244	+	0.00271839i
$659$	8.88254	+	5.70846i	0.346014	+	0.222370i	0.702092	−	0.712087i	$-0.252250\pi$
$659$	8.88254	+	5.70846i	0.346014	+	0.222370i	−0.356077	+	0.934457i	$0.615886\pi$
$660$		0			0
$661$	−44.7385	−	6.43243i	−1.74013	−	0.250192i	−0.802207	−	0.597046i	$-0.796341\pi$
$661$	−44.7385	−	6.43243i	−1.74013	−	0.250192i	−0.937919	+	0.346853i	$0.887250\pi$
$662$	−6.11495	+	2.79260i	−0.237664	+	0.108538i
$663$		0			0
$664$	4.56370	+	7.10126i	0.177106	+	0.275582i
$665$	0.154072	−	0.177809i	0.00597467	−	0.00689514i
$666$		0			0
$667$	15.1989	+	24.9255i	0.588503	+	0.965121i
$668$			8.23855i			0.318759i
$669$		0			0
$670$	12.1682	−	7.82005i	0.470100	−	0.302115i
$671$	24.8151	−	3.56788i	0.957977	−	0.137736i
$672$		0			0
$673$	−3.15628	+	21.9524i	−0.121666	+	0.846204i	0.834003	+	0.551760i	$0.186043\pi$
$673$	−3.15628	+	21.9524i	−0.121666	+	0.846204i	−0.955669	+	0.294444i	$0.904866\pi$
$674$	−9.40709	+	2.76217i	−0.362348	+	0.106395i
$675$		0			0
$676$	4.36680	−	9.56196i	0.167954	−	0.367768i
$677$	−21.1861	−	6.22079i	−0.814246	−	0.239084i	−0.152010	−	0.988379i	$-0.548574\pi$
$677$	−21.1861	−	6.22079i	−0.814246	−	0.239084i	−0.662237	+	0.749295i	$0.730393\pi$
$678$		0			0
$679$	0.423387	+	0.488615i	0.0162481	+	0.0187513i
$680$	0.145661	−	0.496075i	0.00558583	−	0.0190236i
$681$		0			0
$682$	10.9090	−	16.9748i	0.417729	−	0.649999i
$683$	−1.23411	−	4.20298i	−0.0472218	−	0.160823i	0.932507	−	0.361153i	$-0.117617\pi$
$683$	−1.23411	−	4.20298i	−0.0472218	−	0.160823i	−0.979728	+	0.200330i	$0.935799\pi$
$684$		0			0
$685$	−8.48215	−	18.5733i	−0.324086	−	0.709650i
$686$	0.0926121	+	0.644132i	0.00353595	+	0.0245931i
$687$		0			0
$688$	2.29887	+	1.99198i	0.0876434	+	0.0759435i
$689$	−10.1246			−0.385717
$690$		0			0
$691$	14.0177			0.533259			0.266629	−	0.963799i	$-0.414090\pi$
$691$	14.0177			0.533259			0.266629	+	0.963799i	$0.414090\pi$
$692$	−5.65069	−	4.89635i	−0.214807	−	0.186131i
$693$		0			0
$694$	−1.57309	−	10.9411i	−0.0597135	−	0.415317i
$695$	4.20927	+	9.21702i	0.159667	+	0.349621i
$696$		0			0
$697$	−0.0550859	−	0.187605i	−0.00208653	−	0.00710606i
$698$	11.2267	−	17.4691i	0.424937	−	0.661215i
$699$		0			0
$700$	−0.000834453		0.00284189i	−3.15394e−5		0.000107413i
$701$	11.8434	+	13.6680i	0.447319	+	0.516234i	0.933964	−	0.357366i	$-0.116325\pi$
$701$	11.8434	+	13.6680i	0.447319	+	0.516234i	−0.486645	+	0.873600i	$0.661780\pi$
$702$		0			0
$703$	−6.74408	−	1.98024i	−0.254358	−	0.0746862i
$704$	1.10538	−	2.42045i	0.0416607	−	0.0912241i
$705$		0			0
$706$	11.8115	−	3.46818i	0.444533	−	0.130527i
$707$	0.0674463	−	0.469099i	0.00253658	−	0.0176423i
$708$		0			0
$709$	−26.8646	+	3.86254i	−1.00892	+	0.145061i	−0.626905	−	0.779096i	$-0.715679\pi$
$709$	−26.8646	+	3.86254i	−1.00892	+	0.145061i	−0.382014	+	0.924156i	$0.624770\pi$
$710$	24.6128	−	15.8177i	0.923702	−	0.593627i
$711$		0			0
$712$		−	16.7509i		−	0.627766i
$713$	−4.32381	−	36.1094i	−0.161928	−	1.35231i
$714$		0			0
$715$	6.10680	−	7.04762i	0.228381	−	0.263566i
$716$	−1.33677	−	2.08005i	−0.0499573	−	0.0777351i
$717$		0			0
$718$	−17.5514	+	8.01543i	−0.655011	+	0.299133i
$719$	−30.2496	−	4.34924i	−1.12812	−	0.162199i	−0.447114	−	0.894477i	$-0.647548\pi$
$719$	−30.2496	−	4.34924i	−1.12812	−	0.162199i	−0.681006	+	0.732278i	$0.738457\pi$
$720$		0			0
$721$	0.347888	+	0.223574i	0.0129560	+	0.00832634i
$722$	−12.5634	−	5.73752i	−0.467562	−	0.213529i
$723$		0			0
$724$	−4.51172	+	3.90943i	−0.167677	+	0.145293i
$725$	0.293100	−	0.253972i	0.0108855	−	0.00943230i
$726$		0			0
$727$	34.3027	+	15.6655i	1.27222	+	0.581002i	0.933058	−	0.359727i	$-0.117130\pi$
$727$	34.3027	+	15.6655i	1.27222	+	0.581002i	0.339159	+	0.940729i	$0.389857\pi$
$728$	0.0616904	+	0.0396460i	0.00228640	+	0.00146938i
$729$		0			0
$730$	−15.1759	−	2.18196i	−0.561684	−	0.0807579i
$731$	0.643882	−	0.294051i	0.0238148	−	0.0108759i
$732$		0			0
$733$	0.757727	+	1.17905i	0.0279873	+	0.0435491i	0.854965	−	0.518685i	$-0.173578\pi$
$733$	0.757727	+	1.17905i	0.0279873	+	0.0435491i	−0.826978	+	0.562234i	$0.809942\pi$
$734$	5.11523	−	5.90329i	0.188806	−	0.217894i
$735$		0			0
$736$	−1.24206	−	4.63220i	−0.0457830	−	0.170745i
$737$		−	17.3233i		−	0.638112i
$738$		0			0
$739$	−32.5071	+	20.8911i	−1.19579	+	0.768491i	−0.978224	−	0.207554i	$-0.933450\pi$
$739$	−32.5071	+	20.8911i	−1.19579	+	0.768491i	−0.217571	+	0.976044i	$0.569813\pi$
$740$	−6.78608	+	0.975692i	−0.249461	+	0.0358671i
$741$		0			0
$742$	−0.0424670	+	0.295365i	−0.00155901	+	0.0108432i
$743$	32.0517	−	9.41123i	1.17586	−	0.345264i	0.365285	−	0.930896i	$-0.380971\pi$
$743$	32.0517	−	9.41123i	1.17586	−	0.345264i	0.810578	+	0.585631i	$0.199153\pi$
$744$		0			0
$745$	−21.5406	+	47.1674i	−0.789187	+	1.72808i
$746$	25.4190	+	7.46370i	0.930656	+	0.273265i
$747$		0			0
$748$	−0.405494	−	0.467965i	−0.0148263	−	0.0171105i
$749$	0.0355249	−	0.120987i	0.00129805	−	0.00442076i
$750$		0			0
$751$	−3.33228	+	5.18512i	−0.121596	+	0.189208i	−0.896715	−	0.442607i	$-0.854054\pi$
$751$	−3.33228	+	5.18512i	−0.121596	+	0.189208i	0.775119	+	0.631815i	$0.217690\pi$
$752$	1.01724	+	3.46439i	0.0370948	+	0.126333i
$753$		0			0
$754$	−3.98883	−	8.73432i	−0.145265	−	0.318085i
$755$	−7.26261	−	50.5126i	−0.264314	−	1.83834i
$756$		0			0
$757$	−17.0984	−	14.8159i	−0.621454	−	0.538493i	0.286223	−	0.958163i	$-0.407600\pi$
$757$	−17.0984	−	14.8159i	−0.621454	−	0.538493i	−0.907677	+	0.419670i	$0.862146\pi$
$758$	29.0070			1.05358
$759$		0			0
$760$	5.06080			0.183575
$761$	−25.3619	−	21.9762i	−0.919369	−	0.796637i	0.0601087	−	0.998192i	$-0.480855\pi$
$761$	−25.3619	−	21.9762i	−0.919369	−	0.796637i	−0.979477	+	0.201554i	$0.935401\pi$
$762$		0			0
$763$	0.0538147	+	0.374289i	0.00194822	+	0.0135502i
$764$	1.79869	+	3.93859i	0.0650744	+	0.142493i
$765$		0			0
$766$	2.92056	+	9.94651i	0.105524	+	0.359382i
$767$	−0.896256	+	1.39460i	−0.0323619	+	0.0503561i
$768$		0			0
$769$	1.72019	−	5.85842i	0.0620316	−	0.211260i	−0.922645	−	0.385650i	$-0.873977\pi$
$769$	1.72019	−	5.85842i	0.0620316	−	0.211260i	0.984677	+	0.174390i	$0.0557954\pi$
$770$	−0.179985	−	0.207714i	−0.00648621	−	0.00748548i
$771$		0			0
$772$	−24.6057	−	7.22487i	−0.885577	−	0.260029i
$773$	−1.49152	+	3.26598i	−0.0536463	+	0.117469i	−0.934557	−	0.355814i	$-0.884204\pi$
$773$	−1.49152	+	3.26598i	−0.0536463	+	0.117469i	0.880911	+	0.473283i	$0.156931\pi$
$774$		0			0
$775$	−0.463551	+	0.136111i	−0.0166512	+	0.00488925i
$776$	−1.97917	+	13.7654i	−0.0710479	+	0.494149i
$777$		0			0
$778$	15.4672	−	2.22385i	0.554527	−	0.0797290i
$779$	1.61007	−	1.03473i	0.0576867	−	0.0370730i
$780$		0			0
$781$		−	35.0400i		−	1.25383i
$782$	−1.10059	−	0.184876i	−0.0393571	−	0.00661115i
$783$		0			0
$784$	−4.58261	+	5.28861i	−0.163665	+	0.188879i
$785$	−10.3754	−	16.1445i	−0.370314	−	0.576221i
$786$		0			0
$787$	12.3070	−	5.62042i	0.438697	−	0.200346i	−0.183808	−	0.982962i	$-0.558842\pi$
$787$	12.3070	−	5.62042i	0.438697	−	0.200346i	0.622505	+	0.782616i	$0.286115\pi$
$788$	−3.67161	−	0.527898i	−0.130796	−	0.0188056i
$789$		0			0
$790$	12.4772	+	8.01862i	0.443920	+	0.285290i
$791$	−0.286048	−	0.130634i	−0.0101707	−	0.00464480i
$792$		0			0
$793$	−11.2316	+	9.73222i	−0.398845	+	0.345601i
$794$	21.6630	−	18.7711i	0.768793	−	0.666163i
$795$		0			0
$796$	−12.1563	−	5.55159i	−0.430868	−	0.196771i
$797$	−13.6739	−	8.78766i	−0.484353	−	0.311275i	0.275578	−	0.961279i	$-0.411131\pi$
$797$	−13.6739	−	8.78766i	−0.484353	−	0.311275i	−0.759931	+	0.650004i	$0.774767\pi$
$798$		0			0
$799$	0.831663	+	0.119575i	0.0294221	+	0.00423026i
$800$	−0.0579528	+	0.0264661i	−0.00204894	+	0.000935719i
$801$		0			0
$802$	−9.75988	−	15.1867i	−0.344633	−	0.536260i
$803$	−12.0247	+	13.8773i	−0.424344	+	0.489719i
$804$		0			0
$805$	−0.488516	−	0.0820602i	−0.0172179	−	0.00289224i
$806$			11.9614i			0.421322i
$807$		0			0
$808$	8.57587	−	5.51138i	0.301698	−	0.193890i
$809$	21.0765	−	3.03034i	0.741009	−	0.106541i	0.238536	−	0.971134i	$-0.423333\pi$
$809$	21.0765	−	3.03034i	0.741009	−	0.106541i	0.502473	+	0.864593i	$0.332424\pi$
$810$		0			0
$811$	6.58878	−	45.8259i	0.231363	−	1.60917i	−0.460853	−	0.887476i	$-0.652456\pi$
$811$	6.58878	−	45.8259i	0.231363	−	1.60917i	0.692216	−	0.721690i	$-0.256634\pi$
$812$	−0.271536	+	0.0797303i	−0.00952906	+	0.00279798i
$813$		0			0
$814$	−3.41094	+	7.46892i	−0.119554	+	0.261786i
$815$	−41.0960	−	12.0669i	−1.43953	−	0.422684i
$816$		0			0
$817$	4.53736	+	5.23640i	0.158742	+	0.183198i
$818$	−5.68361	+	19.3566i	−0.198723	+	0.676788i
$819$		0			0
$820$	1.00927	−	1.57046i	0.0352452	−	0.0548427i
$821$	−8.19118	−	27.8966i	−0.285874	−	0.973598i	−0.969770	−	0.244019i	$-0.921534\pi$
$821$	−8.19118	−	27.8966i	−0.285874	−	0.973598i	0.683896	−	0.729579i	$-0.260284\pi$
$822$		0			0
$823$	4.58165	+	10.0324i	0.159706	+	0.349708i	0.972521	−	0.232814i	$-0.0747933\pi$
$823$	4.58165	+	10.0324i	0.159706	+	0.349708i	−0.812815	+	0.582522i	$0.802066\pi$
$824$	1.26592	+	8.80467i	0.0441004	+	0.306725i
$825$		0			0
$826$	0.0369253	+	0.0319960i	0.00128480	+	0.00111328i
$827$	−29.3931			−1.02210			−0.511050	−	0.859551i	$-0.670743\pi$
$827$	−29.3931			−1.02210			−0.511050	+	0.859551i	$0.670743\pi$
$828$		0			0
$829$	48.0938			1.67037			0.835184	−	0.549971i	$-0.185361\pi$
$829$	48.0938			1.67037			0.835184	+	0.549971i	$0.185361\pi$
$830$	14.1738	+	12.2817i	0.491980	+	0.426303i
$831$		0			0
$832$	0.224483	+	1.56132i	0.00778256	+	0.0541289i
$833$	0.676474	+	1.48127i	0.0234384	+	0.0513230i
$834$		0			0
$835$	5.15690	+	17.5628i	0.178462	+	0.607785i
$836$	3.27686	−	5.09890i	0.113333	−	0.176349i
$837$		0			0
$838$	2.34127	−	7.97363i	0.0808778	−	0.275444i
$839$	1.97573	+	2.28011i	0.0682097	+	0.0787181i	0.788829	−	0.614613i	$-0.210688\pi$
$839$	1.97573	+	2.28011i	0.0682097	+	0.0787181i	−0.720619	+	0.693331i	$0.756142\pi$
$840$		0			0
$841$	7.72969	+	2.26964i	0.266541	+	0.0782636i
$842$	15.4596	−	33.8517i	0.532772	−	1.16661i
$843$		0			0
$844$	3.03001	−	0.889690i	0.104297	−	0.0306244i
$845$	3.32378	−	23.1174i	0.114341	−	0.795262i
$846$		0			0
$847$	0.180364	−	0.0259324i	0.00619739	−	0.000891049i
$848$	−5.39973	+	3.47019i	−0.185427	+	0.119167i
$849$		0			0
$850$			0.0148256i			0.000508515i
$851$	3.83271	+	14.2939i	0.131383	+	0.489987i
$852$		0			0
$853$	−2.74102	+	3.16330i	−0.0938507	+	0.108309i	−0.800732	−	0.599023i	$-0.795556\pi$
$853$	−2.74102	+	3.16330i	−0.0938507	+	0.108309i	0.706881	+	0.707332i	$0.250101\pi$
$854$	0.236807	+	0.368479i	0.00810337	+	0.0126091i
$855$		0			0
$856$	2.46720	−	1.12673i	0.0843272	−	0.0385109i
$857$	−25.1870	−	3.62134i	−0.860372	−	0.123703i	−0.302014	−	0.953303i	$-0.597659\pi$
$857$	−25.1870	−	3.62134i	−0.860372	−	0.123703i	−0.558357	+	0.829601i	$0.688568\pi$
$858$		0			0
$859$	13.4173	+	8.62274i	0.457791	+	0.294204i	0.749139	−	0.662413i	$-0.230467\pi$
$859$	13.4173	+	8.62274i	0.457791	+	0.294204i	−0.291348	+	0.956617i	$0.594104\pi$
$860$	6.14755	+	2.80749i	0.209630	+	0.0957346i
$861$		0			0
$862$	24.4199	−	21.1600i	0.831745	−	0.720711i
$863$	−22.9264	+	19.8658i	−0.780422	+	0.676240i	−0.951030	−	0.309099i	$-0.899972\pi$
$863$	−22.9264	+	19.8658i	−0.780422	+	0.676240i	0.170608	+	0.985339i	$0.445427\pi$
$864$		0			0
$865$	−15.1109	−	6.90091i	−0.513785	−	0.234638i
$866$	−32.6920	−	21.0099i	−1.11092	−	0.713944i
$867$		0			0
$868$	0.348948	+	0.0501712i	0.0118441	+	0.00170292i
$869$	16.1580	−	7.37910i	0.548121	−	0.250319i
$870$		0			0
$871$	5.55192	+	8.63895i	0.188120	+	0.292720i
$872$	−5.32651	+	6.14712i	−0.180378	+	0.208168i
$873$		0			0
$874$	−1.29879	−	10.8465i	−0.0439321	−	0.366890i
$875$			0.523029i			0.0176816i
$876$		0			0
$877$	−7.40709	+	4.76025i	−0.250120	+	0.160742i	−0.659693	−	0.751535i	$-0.729314\pi$
$877$	−7.40709	+	4.76025i	−0.250120	+	0.160742i	0.409574	+	0.912277i	$0.365677\pi$
$878$	22.3556	−	3.21425i	0.754465	−	0.108476i
$879$		0			0
$880$	0.841358	−	5.85177i	0.0283622	−	0.197263i
$881$	−2.67146	+	0.784410i	−0.0900037	+	0.0264275i	−0.326424	−	0.945223i	$-0.605844\pi$
$881$	−2.67146	+	0.784410i	−0.0900037	+	0.0264275i	0.236421	+	0.971651i	$0.424026\pi$
$882$		0			0
$883$	22.1435	−	48.4874i	0.745187	−	1.63173i	−0.0296411	−	0.999561i	$-0.509436\pi$
$883$	22.1435	−	48.4874i	0.745187	−	1.63173i	0.774828	−	0.632172i	$-0.217836\pi$
$884$	0.352193	+	0.103413i	0.0118455	+	0.00347816i
$885$		0			0
$886$	21.0750	+	24.3218i	0.708027	+	0.817107i
$887$	−0.102799	+	0.350102i	−0.00345166	+	0.0117553i	−0.961201	−	0.275850i	$-0.911041\pi$
$887$	−0.102799	+	0.350102i	−0.00345166	+	0.0117553i	0.957749	+	0.287605i	$0.0928590\pi$
$888$		0			0
$889$	−0.447168	+	0.695807i	−0.0149975	+	0.0233366i
$890$	−10.4852	−	35.7092i	−0.351464	−	1.19698i
$891$		0			0
$892$	−10.3735	−	22.7148i	−0.347331	−	0.760548i
$893$	1.17045	+	8.14069i	0.0391678	+	0.272418i
$894$		0			0
$895$	−4.15169	−	3.59746i	−0.138776	−	0.120250i
$896$	0.0464897			0.00155311
$897$		0			0
$898$	−10.8741			−0.362873
$899$	−34.8863	−	30.2291i	−1.16352	−	1.00820i
$900$		0			0
$901$	0.212569	+	1.47845i	0.00708171	+	0.0492543i
$902$	−0.928776	−	2.03373i	−0.0309248	−	0.0677160i
$903$		0			0
$904$	−1.90570	−	6.49020i	−0.0633825	−	0.215861i
$905$	−7.17090	+	11.1581i	−0.238369	+	0.370909i
$906$		0			0
$907$	4.21833	−	14.3663i	0.140067	−	0.477025i	−0.859342	−	0.511402i	$-0.829126\pi$
$907$	4.21833	−	14.3663i	0.140067	−	0.477025i	0.999409	+	0.0343766i	$0.0109446\pi$
$908$	−7.15242	−	8.25433i	−0.237361	−	0.273930i
$909$		0			0
$910$	0.156327	+	0.0459016i	0.00518217	+	0.00152162i
$911$	4.67853	−	10.2446i	0.155007	−	0.339417i	−0.816157	−	0.577830i	$-0.803900\pi$
$911$	4.67853	−	10.2446i	0.155007	−	0.339417i	0.971164	+	0.238412i	$0.0766270\pi$
$912$		0			0
$913$	21.5516	−	6.32813i	0.713255	−	0.209431i
$914$	−5.00789	+	34.8307i	−0.165646	+	1.15210i
$915$		0			0
$916$	19.6456	−	2.82460i	0.649107	−	0.0933276i
$917$	−0.0505580	+	0.0324916i	−0.00166957	+	0.00107297i
$918$		0			0
$919$			11.6487i			0.384255i	0.981370	+	0.192128i	$0.0615388\pi$
$919$			11.6487i			0.384255i	−0.981370	+	0.192128i	$0.938461\pi$
$920$	−5.54731	−	9.09736i	−0.182889	−	0.299931i
$921$		0			0
$922$	8.91250	−	10.2856i	0.293518	−	0.338737i
$923$	11.2299	+	17.4741i	0.369637	+	0.575166i
$924$		0			0
$925$	0.178828	−	0.0816681i	0.00587984	−	0.00268523i
$926$	−1.06447	−	0.153047i	−0.0349805	−	0.00502944i
$927$		0			0
$928$	−5.12102	−	3.29108i	−0.168106	−	0.108035i
$929$	−27.6642	−	12.6338i	−0.907633	−	0.414502i	−0.0937931	−	0.995592i	$-0.529899\pi$
$929$	−27.6642	−	12.6338i	−0.907633	−	0.414502i	−0.813839	+	0.581090i	$0.802627\pi$
$930$		0			0
$931$	−12.0465	+	10.4383i	−0.394808	+	0.342103i
$932$	−7.13493	+	6.18245i	−0.233712	+	0.202513i
$933$		0			0
$934$	−36.0431	−	16.4603i	−1.17937	−	0.538599i
$935$	−1.15734	−	0.743780i	−0.0378492	−	0.0243242i
$936$		0			0
$937$	−4.54428	−	0.653369i	−0.148455	−	0.0213446i	0.0676865	−	0.997707i	$-0.478438\pi$
$937$	−4.54428	−	0.653369i	−0.148455	−	0.0213446i	−0.216142	+	0.976362i	$0.569347\pi$
$938$	0.275311	−	0.125730i	0.00898921	−	0.00410523i
$939$		0			0
$940$	4.33705	+	6.74858i	0.141459	+	0.220115i
$941$	32.8534	−	37.9149i	1.07099	−	1.23599i	0.100479	−	0.994939i	$-0.467962\pi$
$941$	32.8534	−	37.9149i	1.07099	−	1.23599i	0.970512	−	0.241051i	$-0.0774922\pi$
$942$		0			0
$943$	−3.62489	−	1.76008i	−0.118043	−	0.0573161i
$944$			1.05097i			0.0342061i
$945$		0			0
$946$	6.80915	−	4.37598i	0.221385	−	0.142275i
$947$	56.0261	−	8.05534i	1.82060	−	0.261763i	0.854413	−	0.519594i	$-0.173917\pi$
$947$	56.0261	−	8.05534i	1.82060	−	0.261763i	0.966190	+	0.257831i	$0.0830077\pi$
$948$		0			0
$949$	1.54910	−	10.7742i	0.0502860	−	0.349747i
$950$	−0.139242	+	0.0408850i	−0.00451759	+	0.00132649i
$951$		0			0
$952$	0.00449411	−	0.00984074i	0.000145655	−	0.000318940i
$953$	−11.8900	−	3.49123i	−0.385156	−	0.113092i	0.0834216	−	0.996514i	$-0.473415\pi$
$953$	−11.8900	−	3.49123i	−0.385156	−	0.113092i	−0.468578	+	0.883422i	$0.655233\pi$
$954$		0			0
$955$	6.29976	+	7.27031i	0.203855	+	0.235262i
$956$	1.48278	−	5.04990i	0.0479566	−	0.163325i
$957$		0			0
$958$	6.59419	−	10.2608i	0.213049	−	0.331510i
$959$	−0.120370	−	0.409941i	−0.00388694	−	0.0132377i
$960$		0			0
$961$	11.0100	+	24.1085i	0.355161	+	0.777694i
$962$	−0.692701	−	4.81784i	−0.0223336	−	0.155334i
$963$		0			0
$964$	14.4634	+	12.5326i	0.465834	+	0.403648i
$965$	−56.9762			−1.83413
$966$		0			0
$967$	31.5553			1.01475			0.507374	−	0.861726i	$-0.330616\pi$
$967$	31.5553			1.01475			0.507374	+	0.861726i	$0.330616\pi$
$968$	2.96220	+	2.56676i	0.0952087	+	0.0824988i
$969$		0			0
$970$	4.39726	+	30.5836i	0.141188	+	0.981981i
$971$	1.00035	+	2.19046i	0.0321028	+	0.0702953i	0.925004	−	0.379957i	$-0.124061\pi$
$971$	1.00035	+	2.19046i	0.0321028	+	0.0702953i	−0.892901	+	0.450252i	$0.851334\pi$
$972$		0			0
$973$	0.0597335	+	0.203434i	0.00191497	+	0.00652178i
$974$	3.33155	−	5.18399i	0.106750	−	0.166106i
$975$		0			0
$976$	−2.65440	+	9.04005i	−0.0849652	+	0.289365i
$977$	25.8096	+	29.7859i	0.825723	+	0.952935i	0.999493	−	0.0318515i	$-0.0101404\pi$
$977$	25.8096	+	29.7859i	0.825723	+	0.952935i	−0.173770	+	0.984786i	$0.555595\pi$
$978$		0			0
$979$	−42.7671	−	12.5576i	−1.36684	−	0.401341i
$980$	−6.45872	+	14.1426i	−0.206316	+	0.451770i
$981$		0			0
$982$	26.7203	−	7.84578i	0.852679	−	0.250369i
$983$	−1.75178	+	12.1839i	−0.0558732	+	0.388606i	0.942627	+	0.333849i	$0.108348\pi$
$983$	−1.75178	+	12.1839i	−0.0558732	+	0.388606i	−0.998500	+	0.0547573i	$0.982561\pi$
$984$		0			0
$985$	−8.15750	+	1.17287i	−0.259920	+	0.0373708i
$986$	−1.19168	+	0.765849i	−0.0379510	+	0.0243896i
$987$		0			0
$988$			3.59296i			0.114307i
$989$	4.43946	−	13.8962i	0.141167	−	0.441874i
$990$		0			0
$991$	5.85703	−	6.75938i	0.186055	−	0.214719i	−0.655058	−	0.755579i	$-0.727356\pi$
$991$	5.85703	−	6.75938i	0.186055	−	0.214719i	0.841113	+	0.540860i	$0.181901\pi$
$992$	4.09974	+	6.37932i	0.130167	+	0.202544i
$993$		0			0
$994$	0.556873	−	0.254315i	0.0176629	−	0.00806639i
$995$	−29.3895	−	4.22557i	−0.931710	−	0.133960i
$996$		0			0
$997$	32.3793	+	20.8089i	1.02546	+	0.659024i	0.941350	−	0.337432i	$-0.109558\pi$
$997$	32.3793	+	20.8089i	1.02546	+	0.659024i	0.0841114	+	0.996456i	$0.473195\pi$
$998$	−33.2927	−	15.2043i	−1.05386	−	0.481283i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.j.a.53.7	yes	80
3.2	odd	2	inner	414.2.j.a.53.2	✓	80
23.10	odd	22	inner	414.2.j.a.125.2	yes	80
69.56	even	22	inner	414.2.j.a.125.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.j.a.53.2	✓	80	3.2	odd	2	inner
414.2.j.a.53.7	yes	80	1.1	even	1	trivial
414.2.j.a.125.2	yes	80	23.10	odd	22	inner
414.2.j.a.125.7	yes	80	69.56	even	22	inner

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.755750 + 0.654861i) q^{2} +(0.142315 + 0.989821i) q^{4} +(0.922959 + 2.02100i) q^{5} +(0.0130977 + 0.0446065i) q^{7} +(-0.540641 + 0.841254i) q^{8} +O(q^{10})\)	\(q+(0.755750 + 0.654861i) q^{2} +(0.142315 + 0.989821i) q^{4} +(0.922959 + 2.02100i) q^{5} +(0.0130977 + 0.0446065i) q^{7} +(-0.540641 + 0.841254i) q^{8} +(-0.625947 + 2.13178i) q^{10} +(1.74253 + 2.01098i) q^{11} +(-1.51348 - 0.444397i) q^{13} +(-0.0193125 + 0.0422885i) q^{14} +(-0.959493 + 0.281733i) q^{16} +(-0.0331173 + 0.230336i) q^{17} +(-2.25463 + 0.324167i) q^{19} +(-1.86908 + 1.20118i) q^{20} +2.66091i q^{22} +(3.05411 + 3.69763i) q^{23} +(0.0417212 - 0.0481489i) q^{25} +(-0.852791 - 1.32697i) q^{26} +(-0.0422885 + 0.0193125i) q^{28} +(6.02540 + 0.866322i) q^{29} +(-6.37932 - 4.09974i) q^{31} +(-0.909632 - 0.415415i) q^{32} +(-0.175866 + 0.152389i) q^{34} +(-0.0780612 + 0.0676404i) q^{35} +(2.80691 + 1.28187i) q^{37} +(-1.91622 - 1.23148i) q^{38} +(-2.19916 - 0.316192i) q^{40} +(-0.764300 + 0.349044i) q^{41} +(-1.64454 - 2.55895i) q^{43} +(-1.74253 + 2.01098i) q^{44} +(-0.113292 + 4.79449i) q^{46} -3.61065i q^{47} +(5.88696 - 3.78332i) q^{49} +(0.0630616 - 0.00906689i) q^{50} +(0.224483 - 1.56132i) q^{52} +(6.15867 - 1.80835i) q^{53} +(-2.45591 + 5.37770i) q^{55} +(-0.0446065 - 0.0130977i) q^{56} +(3.98638 + 4.60052i) q^{58} +(0.296092 - 1.00840i) q^{59} +(5.09375 - 7.92604i) q^{61} +(-2.13641 - 7.27594i) q^{62} +(-0.415415 - 0.909632i) q^{64} +(-0.498752 - 3.46889i) q^{65} +(-4.92015 - 4.26333i) q^{67} -0.232705 q^{68} -0.103290 q^{70} +(-9.95203 - 8.62348i) q^{71} +(0.982079 + 6.83051i) q^{73} +(1.28187 + 2.80691i) q^{74} +(-0.641735 - 2.18555i) q^{76} +(-0.0668799 + 0.104067i) q^{77} +(1.88074 - 6.40520i) q^{79} +(-1.45495 - 1.67911i) q^{80} +(-0.806195 - 0.236720i) q^{82} +(3.50663 - 7.67846i) q^{83} +(-0.496075 + 0.145661i) q^{85} +(0.432898 - 3.01087i) q^{86} +(-2.63383 + 0.378687i) q^{88} +(-14.0917 + 9.05622i) q^{89} -0.0733315i q^{91} +(-3.22535 + 3.54925i) q^{92} +(2.36447 - 2.72875i) q^{94} +(-2.73608 - 4.25742i) q^{95} +(12.6502 - 5.77716i) q^{97} +(6.92661 + 0.995896i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{4}+O(q^{10}) \) 80 * q + 8 * q^4	\( 80 q + 8 q^{4} - 16 q^{13} - 8 q^{16} + 24 q^{25} - 16 q^{31} + 88 q^{37} + 88 q^{43} + 8 q^{46} + 8 q^{49} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 176 q^{61} + 8 q^{64} - 88 q^{67} - 176 q^{70} - 56 q^{73} - 176 q^{79} - 88 q^{82} - 88 q^{85} + 16 q^{94}+O(q^{100}) \) 80 * q + 8 * q^4 - 16 * q^13 - 8 * q^16 + 24 * q^25 - 16 * q^31 + 88 * q^37 + 88 * q^43 + 8 * q^46 + 8 * q^49 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 176 * q^61 + 8 * q^64 - 88 * q^67 - 176 * q^70 - 56 * q^73 - 176 * q^79 - 88 * q^82 - 88 * q^85 + 16 * q^94

Introduction

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