LMFDB - Embedded newform 605.2.e.c.362.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("605.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			362.17
Character	$\chi$	$=$	605.362
Dual form			605.2.e.c.483.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38689 - 1.38689i) q^{2} +(-2.07537 + 2.07537i) q^{3} -1.84694i q^{4} +(-2.03181 - 0.933683i) q^{5} +5.75663i q^{6} +(1.48652 - 1.48652i) q^{7} +(0.212274 + 0.212274i) q^{8} -5.61432i q^{9} +O(q^{10})$	\(q+(1.38689 - 1.38689i) q^{2} +(-2.07537 + 2.07537i) q^{3} -1.84694i q^{4} +(-2.03181 - 0.933683i) q^{5} +5.75663i q^{6} +(1.48652 - 1.48652i) q^{7} +(0.212274 + 0.212274i) q^{8} -5.61432i q^{9} +(-4.11281 + 1.52298i) q^{10} +(3.83309 + 3.83309i) q^{12} +(1.72000 + 1.72000i) q^{13} -4.12327i q^{14} +(6.15449 - 2.27901i) q^{15} +4.28269 q^{16} +(3.55353 - 3.55353i) q^{17} +(-7.78646 - 7.78646i) q^{18} -0.415589 q^{19} +(-1.72446 + 3.75263i) q^{20} +6.17014i q^{21} +(4.64435 - 4.64435i) q^{23} -0.881094 q^{24} +(3.25647 + 3.79412i) q^{25} +4.77092 q^{26} +(5.42568 + 5.42568i) q^{27} +(-2.74551 - 2.74551i) q^{28} +8.19047 q^{29} +(5.37487 - 11.6964i) q^{30} -1.41938 q^{31} +(5.51508 - 5.51508i) q^{32} -9.85672i q^{34} +(-4.40824 + 1.63238i) q^{35} -10.3693 q^{36} +(0.431389 + 0.431389i) q^{37} +(-0.576378 + 0.576378i) q^{38} -7.13929 q^{39} +(-0.233103 - 0.629496i) q^{40} +0.329520i q^{41} +(8.55732 + 8.55732i) q^{42} +(-3.73558 - 3.73558i) q^{43} +(-5.24199 + 11.4072i) q^{45} -12.8824i q^{46} +(-6.46918 - 6.46918i) q^{47} +(-8.88816 + 8.88816i) q^{48} +2.58054i q^{49} +(9.77842 + 0.745664i) q^{50} +14.7498i q^{51} +(3.17675 - 3.17675i) q^{52} +(-2.30016 + 2.30016i) q^{53} +15.0497 q^{54} +0.631097 q^{56} +(0.862501 - 0.862501i) q^{57} +(11.3593 - 11.3593i) q^{58} +3.04525i q^{59} +(-4.20921 - 11.3670i) q^{60} +1.43418i q^{61} +(-1.96853 + 1.96853i) q^{62} +(-8.34577 - 8.34577i) q^{63} -6.73227i q^{64} +(-1.88878 - 5.10065i) q^{65} +(-4.17367 - 4.17367i) q^{67} +(-6.56316 - 6.56316i) q^{68} +19.2775i q^{69} +(-3.84983 + 8.37769i) q^{70} +7.59566 q^{71} +(1.19177 - 1.19177i) q^{72} +(-5.52189 - 5.52189i) q^{73} +1.19658 q^{74} +(-14.6326 - 1.11582i) q^{75} +0.767569i q^{76} +(-9.90142 + 9.90142i) q^{78} +3.59595 q^{79} +(-8.70159 - 3.99867i) q^{80} -5.67764 q^{81} +(0.457009 + 0.457009i) q^{82} +(-1.78181 - 1.78181i) q^{83} +11.3959 q^{84} +(-10.5379 + 3.90221i) q^{85} -10.3617 q^{86} +(-16.9983 + 16.9983i) q^{87} +7.76892i q^{89} +(8.55050 + 23.0907i) q^{90} +5.11362 q^{91} +(-8.57784 - 8.57784i) q^{92} +(2.94574 - 2.94574i) q^{93} -17.9441 q^{94} +(0.844397 + 0.388028i) q^{95} +22.8917i q^{96} +(9.70396 + 9.70396i) q^{97} +(3.57894 + 3.57894i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{3} - 4 q^{5}+O(q^{10}) $ 40 * q + 8 * q^3 - 4 * q^5	$ 40 q + 8 q^{3} - 4 q^{5} - 32 q^{12} + 32 q^{15} - 24 q^{16} + 32 q^{20} - 24 q^{23} - 52 q^{25} - 8 q^{26} + 32 q^{27} + 16 q^{31} - 40 q^{36} + 36 q^{37} + 32 q^{38} + 32 q^{42} + 64 q^{45} + 32 q^{47} - 16 q^{48} - 68 q^{53} + 80 q^{56} + 132 q^{58} - 64 q^{60} - 88 q^{67} - 8 q^{70} - 16 q^{75} - 248 q^{78} - 164 q^{80} - 40 q^{81} + 100 q^{82} - 80 q^{86} - 96 q^{91} - 56 q^{92} + 24 q^{93} - 68 q^{97}+O(q^{100}) $ 40 * q + 8 * q^3 - 4 * q^5 - 32 * q^12 + 32 * q^15 - 24 * q^16 + 32 * q^20 - 24 * q^23 - 52 * q^25 - 8 * q^26 + 32 * q^27 + 16 * q^31 - 40 * q^36 + 36 * q^37 + 32 * q^38 + 32 * q^42 + 64 * q^45 + 32 * q^47 - 16 * q^48 - 68 * q^53 + 80 * q^56 + 132 * q^58 - 64 * q^60 - 88 * q^67 - 8 * q^70 - 16 * q^75 - 248 * q^78 - 164 * q^80 - 40 * q^81 + 100 * q^82 - 80 * q^86 - 96 * q^91 - 56 * q^92 + 24 * q^93 - 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.38689	−	1.38689i	0.980681	−	0.980681i	−0.0191357	−	0.999817i	$-0.506091\pi$
$2$	1.38689	−	1.38689i	0.980681	−	0.980681i	0.999817	+	0.0191357i	$0.00609144\pi$
$3$	−2.07537	+	2.07537i	−1.19822	+	1.19822i	−0.223515	+	0.974701i	$0.571753\pi$
$3$	−2.07537	+	2.07537i	−1.19822	+	1.19822i	−0.974701	+	0.223515i	$0.928247\pi$
$4$		−	1.84694i		−	0.923471i
$5$	−2.03181	−	0.933683i	−0.908651	−	0.417556i
$5$	−2.03181	−	0.933683i	−0.908651	−	0.417556i
$6$			5.75663i			2.35013i
$7$	1.48652	−	1.48652i	0.561850	−	0.561850i	−0.367983	−	0.929833i	$-0.619951\pi$
$7$	1.48652	−	1.48652i	0.561850	−	0.561850i	0.929833	+	0.367983i	$0.119951\pi$
$8$	0.212274	+	0.212274i	0.0750502	+	0.0750502i
$9$		−	5.61432i		−	1.87144i
$10$	−4.11281	+	1.52298i	−1.30059	+	0.481608i
$11$		0			0
$11$		0			0
$12$	3.83309	+	3.83309i	1.10652	+	1.10652i
$13$	1.72000	+	1.72000i	0.477043	+	0.477043i	0.904185	−	0.427142i	$-0.140479\pi$
$13$	1.72000	+	1.72000i	0.477043	+	0.477043i	−0.427142	+	0.904185i	$0.640479\pi$
$14$		−	4.12327i		−	1.10199i
$15$	6.15449	−	2.27901i	1.58908	−	0.588439i
$16$	4.28269			1.07067
$17$	3.55353	−	3.55353i	0.861857	−	0.861857i	−0.129697	−	0.991554i	$-0.541400\pi$
$17$	3.55353	−	3.55353i	0.861857	−	0.861857i	0.991554	+	0.129697i	$0.0414003\pi$
$18$	−7.78646	−	7.78646i	−1.83529	−	1.83529i
$19$	−0.415589			−0.0953427			−0.0476713	−	0.998863i	$-0.515180\pi$
$19$	−0.415589			−0.0953427			−0.0476713	+	0.998863i	$0.515180\pi$
$20$	−1.72446	+	3.75263i	−0.385601	+	0.839114i
$21$			6.17014i			1.34643i
$22$		0			0
$23$	4.64435	−	4.64435i	0.968413	−	0.968413i	−0.0311028	−	0.999516i	$-0.509902\pi$
$23$	4.64435	−	4.64435i	0.968413	−	0.968413i	0.999516	+	0.0311028i	$0.00990191\pi$
$24$	−0.881094			−0.179853
$25$	3.25647	+	3.79412i	0.651295	+	0.758825i
$26$	4.77092			0.935654
$27$	5.42568	+	5.42568i	1.04417	+	1.04417i
$28$	−2.74551	−	2.74551i	−0.518852	−	0.518852i
$29$	8.19047			1.52093			0.760466	−	0.649378i	$-0.224971\pi$
$29$	8.19047			1.52093			0.760466	+	0.649378i	$0.224971\pi$
$30$	5.37487	−	11.6964i	0.981312	−	2.13545i
$31$	−1.41938			−0.254928			−0.127464	−	0.991843i	$-0.540684\pi$
$31$	−1.41938			−0.254928			−0.127464	+	0.991843i	$0.540684\pi$
$32$	5.51508	−	5.51508i	0.974938	−	0.974938i
$33$		0			0
$34$		−	9.85672i		−	1.69041i
$35$	−4.40824	+	1.63238i	−0.745129	+	0.275922i
$36$	−10.3693			−1.72822
$37$	0.431389	+	0.431389i	0.0709199	+	0.0709199i	0.741677	−	0.670757i	$-0.234031\pi$
$37$	0.431389	+	0.431389i	0.0709199	+	0.0709199i	−0.670757	+	0.741677i	$0.734031\pi$
$38$	−0.576378	+	0.576378i	−0.0935008	+	0.0935008i
$39$	−7.13929			−1.14320
$40$	−0.233103	−	0.629496i	−0.0368568	−	0.0995321i
$41$			0.329520i			0.0514624i	0.999669	+	0.0257312i	$0.00819140\pi$
$41$			0.329520i			0.0514624i	−0.999669	+	0.0257312i	$0.991809\pi$
$42$	8.55732	+	8.55732i	1.32042	+	1.32042i
$43$	−3.73558	−	3.73558i	−0.569670	−	0.569670i	0.362366	−	0.932036i	$-0.381969\pi$
$43$	−3.73558	−	3.73558i	−0.569670	−	0.569670i	−0.932036	+	0.362366i	$0.881969\pi$
$44$		0			0
$45$	−5.24199	+	11.4072i	−0.781430	+	1.70049i
$46$		−	12.8824i		−	1.89941i
$47$	−6.46918	−	6.46918i	−0.943628	−	0.943628i	0.0548662	−	0.998494i	$-0.482527\pi$
$47$	−6.46918	−	6.46918i	−0.943628	−	0.943628i	−0.998494	+	0.0548662i	$0.982527\pi$
$48$	−8.88816	+	8.88816i	−1.28290	+	1.28290i
$49$			2.58054i			0.368649i
$50$	9.77842	+	0.745664i	1.38288	+	0.105453i
$51$			14.7498i			2.06538i
$52$	3.17675	−	3.17675i	0.440536	−	0.440536i
$53$	−2.30016	+	2.30016i	−0.315951	+	0.315951i	−0.847210	−	0.531258i	$-0.821719\pi$
$53$	−2.30016	+	2.30016i	−0.315951	+	0.315951i	0.531258	+	0.847210i	$0.321719\pi$
$54$	15.0497			2.04800
$55$		0			0
$56$	0.631097			0.0843339
$57$	0.862501	−	0.862501i	0.114241	−	0.114241i
$58$	11.3593	−	11.3593i	1.49155	−	1.49155i
$59$			3.04525i			0.396458i	0.980156	+	0.198229i	$0.0635190\pi$
$59$			3.04525i			0.396458i	−0.980156	+	0.198229i	$0.936481\pi$
$60$	−4.20921	−	11.3670i	−0.543406	−	1.46747i
$61$			1.43418i			0.183629i	0.995776	+	0.0918143i	$0.0292666\pi$
$61$			1.43418i			0.183629i	−0.995776	+	0.0918143i	$0.970733\pi$
$62$	−1.96853	+	1.96853i	−0.250003	+	0.250003i
$63$	−8.34577	−	8.34577i	−1.05147	−	1.05147i
$64$		−	6.73227i		−	0.841534i
$65$	−1.88878	−	5.10065i	−0.234274	−	0.632658i
$66$		0			0
$67$	−4.17367	−	4.17367i	−0.509895	−	0.509895i	0.404599	−	0.914494i	$-0.367411\pi$
$67$	−4.17367	−	4.17367i	−0.509895	−	0.509895i	−0.914494	+	0.404599i	$0.867411\pi$
$68$	−6.56316	−	6.56316i	−0.795900	−	0.795900i
$69$			19.2775i			2.32074i
$70$	−3.84983	+	8.37769i	−0.460143	+	1.00133i
$71$	7.59566			0.901439			0.450720	−	0.892666i	$-0.351167\pi$
$71$	7.59566			0.901439			0.450720	+	0.892666i	$0.351167\pi$
$72$	1.19177	−	1.19177i	0.140452	−	0.140452i
$73$	−5.52189	−	5.52189i	−0.646288	−	0.646288i	0.305806	−	0.952094i	$-0.401074\pi$
$73$	−5.52189	−	5.52189i	−0.646288	−	0.646288i	−0.952094	+	0.305806i	$0.901074\pi$
$74$	1.19658			0.139100
$75$	−14.6326	−	1.11582i	−1.68963	−	0.128844i
$76$			0.767569i			0.0880462i
$77$		0			0
$78$	−9.90142	+	9.90142i	−1.12112	+	1.12112i
$79$	3.59595			0.404576			0.202288	−	0.979326i	$-0.435162\pi$
$79$	3.59595			0.404576			0.202288	+	0.979326i	$0.435162\pi$
$80$	−8.70159	−	3.99867i	−0.972868	−	0.447065i
$81$	−5.67764			−0.630849
$82$	0.457009	+	0.457009i	0.0504682	+	0.0504682i
$83$	−1.78181	−	1.78181i	−0.195579	−	0.195579i	0.602523	−	0.798102i	$-0.294162\pi$
$83$	−1.78181	−	1.78181i	−0.195579	−	0.195579i	−0.798102	+	0.602523i	$0.794162\pi$
$84$	11.3959			1.24339
$85$	−10.5379	+	3.90221i	−1.14300	+	0.423254i
$86$	−10.3617			−1.11733
$87$	−16.9983	+	16.9983i	−1.82240	+	1.82240i
$88$		0			0
$89$			7.76892i			0.823504i	0.911296	+	0.411752i	$0.135083\pi$
$89$			7.76892i			0.823504i	−0.911296	+	0.411752i	$0.864917\pi$
$90$	8.55050	+	23.0907i	0.901302	+	2.43397i
$91$	5.11362			0.536053
$92$	−8.57784	−	8.57784i	−0.894302	−	0.894302i
$93$	2.94574	−	2.94574i	0.305459	−	0.305459i
$94$	−17.9441			−1.85080
$95$	0.844397	+	0.388028i	0.0866333	+	0.0398109i
$96$			22.8917i			2.33637i
$97$	9.70396	+	9.70396i	0.985288	+	0.985288i	0.999893	−	0.0146051i	$-0.00464912\pi$
$97$	9.70396	+	9.70396i	0.985288	+	0.985288i	−0.0146051	+	0.999893i	$0.504649\pi$
$98$	3.57894	+	3.57894i	0.361527	+	0.361527i
$99$		0			0
$100$	7.00753	−	6.01452i	0.700753	−	0.601452i
$101$			9.87195i			0.982296i	0.871076	+	0.491148i	$0.163423\pi$
$101$			9.87195i			0.982296i	−0.871076	+	0.491148i	$0.836577\pi$
$102$	20.4563	+	20.4563i	2.02548	+	2.02548i
$103$	5.12035	−	5.12035i	0.504523	−	0.504523i	−0.408317	−	0.912840i	$-0.633884\pi$
$103$	5.12035	−	5.12035i	0.504523	−	0.504523i	0.912840	+	0.408317i	$0.133884\pi$
$104$			0.730224i			0.0716044i
$105$	5.76095	−	12.5365i	0.562211	−	1.22344i
$106$			6.38015i			0.619695i
$107$	−11.3912	+	11.3912i	−1.10123	+	1.10123i	−0.106963	+	0.994263i	$0.534113\pi$
$107$	−11.3912	+	11.3912i	−1.10123	+	1.10123i	−0.994263	+	0.106963i	$0.965887\pi$
$108$	10.0209	−	10.0209i	0.964264	−	0.964264i
$109$	−7.94953			−0.761427			−0.380714	−	0.924693i	$-0.624322\pi$
$109$	−7.94953			−0.761427			−0.380714	+	0.924693i	$0.624322\pi$
$110$		0			0
$111$	−1.79058			−0.169955
$112$	6.36628	−	6.36628i	0.601557	−	0.601557i
$113$	13.6342	−	13.6342i	1.28260	−	1.28260i	0.343415	−	0.939184i	$-0.388416\pi$
$113$	13.6342	−	13.6342i	1.28260	−	1.28260i	0.939184	−	0.343415i	$-0.111584\pi$
$114$		−	2.39239i		−	0.224068i
$115$	−13.7728	+	5.10007i	−1.28432	+	0.475584i
$116$		−	15.1273i		−	1.40454i
$117$	9.65665	−	9.65665i	0.892758	−	0.892758i
$118$	4.22344	+	4.22344i	0.388799	+	0.388799i
$119$		−	10.5647i		−	0.968469i
$120$	1.79021	+	0.822662i	0.163423	+	0.0750985i
$121$		0			0
$122$	1.98906	+	1.98906i	0.180081	+	0.180081i
$123$	−0.683876	−	0.683876i	−0.0616631	−	0.0616631i
$124$			2.62151i			0.235419i
$125$	−3.07402	−	10.7494i	−0.274948	−	0.961459i
$126$	−23.1494			−2.06231
$127$	−14.6481	+	14.6481i	−1.29981	+	1.29981i	−0.371294	+	0.928515i	$0.621086\pi$
$127$	−14.6481	+	14.6481i	−1.29981	+	1.29981i	−0.928515	+	0.371294i	$0.878914\pi$
$128$	1.69322	+	1.69322i	0.149661	+	0.149661i
$129$	15.5054			1.36517
$130$	−9.69358	−	4.45452i	−0.850184	−	0.390688i
$131$		−	6.00178i		−	0.524378i	−0.965017	−	0.262189i	$-0.915556\pi$
$131$		−	6.00178i		−	0.524378i	0.965017	−	0.262189i	$-0.0844444\pi$
$132$		0			0
$133$	−0.617780	+	0.617780i	−0.0535683	+	0.0535683i
$134$	−11.5769			−1.00009
$135$	−5.95807	−	16.0898i	−0.512789	−	1.38479i
$136$	1.50864			0.129365
$137$	−6.39739	−	6.39739i	−0.546566	−	0.546566i	0.378880	−	0.925446i	$-0.376309\pi$
$137$	−6.39739	−	6.39739i	−0.546566	−	0.546566i	−0.925446	+	0.378880i	$0.876309\pi$
$138$	26.7358	+	26.7358i	2.27590	+	2.27590i
$139$	−13.0907			−1.11033			−0.555167	−	0.831739i	$-0.687346\pi$
$139$	−13.0907			−1.11033			−0.555167	+	0.831739i	$0.687346\pi$
$140$	3.01491	+	8.14178i	0.254806	+	0.688106i
$141$	26.8519			2.26134
$142$	10.5344	−	10.5344i	0.884024	−	0.884024i
$143$		0			0
$144$		−	24.0444i		−	2.00370i
$145$	−16.6414	−	7.64730i	−1.38200	−	0.635074i
$146$	−15.3165			−1.26760
$147$	−5.35558	−	5.35558i	−0.441721	−	0.441721i
$148$	0.796750	−	0.796750i	0.0654925	−	0.0654925i
$149$	13.6012			1.11426			0.557128	−	0.830427i	$-0.311903\pi$
$149$	13.6012			1.11426			0.557128	+	0.830427i	$0.311903\pi$
$150$	−21.8414	+	18.7463i	−1.78334	+	1.53063i
$151$		−	8.30403i		−	0.675772i	−0.941187	−	0.337886i	$-0.890288\pi$
$151$		−	8.30403i		−	0.675772i	0.941187	−	0.337886i	$-0.109712\pi$
$152$	−0.0882188	−	0.0882188i	−0.00715549	−	0.00715549i
$153$	−19.9506	−	19.9506i	−1.61291	−	1.61291i
$154$		0			0
$155$	2.88390	+	1.32525i	0.231641	+	0.106447i
$156$			13.1859i			1.05571i
$157$	−2.44484	−	2.44484i	−0.195120	−	0.195120i	0.602784	−	0.797904i	$-0.294058\pi$
$157$	−2.44484	−	2.44484i	−0.195120	−	0.195120i	−0.797904	+	0.602784i	$0.794058\pi$
$158$	4.98719	−	4.98719i	0.396760	−	0.396760i
$159$		−	9.54737i		−	0.757156i
$160$	−16.3549	+	6.05624i	−1.29297	+	0.478788i
$161$		−	13.8078i		−	1.08821i
$162$	−7.87428	+	7.87428i	−0.618662	+	0.618662i
$163$	9.95174	−	9.95174i	0.779480	−	0.779480i	−0.200262	−	0.979742i	$-0.564179\pi$
$163$	9.95174	−	9.95174i	0.779480	−	0.779480i	0.979742	+	0.200262i	$0.0641794\pi$
$164$	0.608605			0.0475241
$165$		0			0
$166$	−4.94236			−0.383601
$167$	5.40983	−	5.40983i	0.418625	−	0.418625i	−0.466104	−	0.884730i	$-0.654343\pi$
$167$	5.40983	−	5.40983i	0.418625	−	0.418625i	0.884730	+	0.466104i	$0.154343\pi$
$168$	−1.30976	+	1.30976i	−0.101050	+	0.101050i
$169$		−	7.08318i		−	0.544860i
$170$	−9.20305	+	20.0270i	−0.705842	+	1.53600i
$171$			2.33325i			0.178428i
$172$	−6.89940	+	6.89940i	−0.526074	+	0.526074i
$173$	14.2692	+	14.2692i	1.08486	+	1.08486i	0.996048	+	0.0888158i	$0.0283083\pi$
$173$	14.2692	+	14.2692i	1.08486	+	1.08486i	0.0888158	+	0.996048i	$0.471692\pi$
$174$			47.1495i			3.57440i
$175$	10.4808	+	0.799226i	0.792276	+	0.0604158i
$176$		0			0
$177$	−6.32002	−	6.32002i	−0.475042	−	0.475042i
$178$	10.7747	+	10.7747i	0.807595	+	0.807595i
$179$			14.1347i			1.05648i	0.849097	+	0.528238i	$0.177147\pi$
$179$			14.1347i			1.05648i	−0.849097	+	0.528238i	$0.822853\pi$
$180$	21.0685	+	9.68166i	1.57035	+	0.721629i
$181$	−2.53648			−0.188535			−0.0942675	−	0.995547i	$-0.530051\pi$
$181$	−2.53648			−0.188535			−0.0942675	+	0.995547i	$0.530051\pi$
$182$	7.09205	−	7.09205i	0.525697	−	0.525697i
$183$	−2.97646	−	2.97646i	−0.220027	−	0.220027i
$184$	1.97175			0.145359
$185$	−0.473718	−	1.27928i	−0.0348285	−	0.0940544i
$186$		−	8.17084i		−	0.599115i
$187$		0			0
$188$	−11.9482	+	11.9482i	−0.871413	+	0.871413i
$189$	16.1307			1.17334
$190$	1.70924	−	0.632934i	0.124001	−	0.0459178i
$191$	9.48245			0.686126			0.343063	−	0.939312i	$-0.388536\pi$
$191$	9.48245			0.686126			0.343063	+	0.939312i	$0.388536\pi$
$192$	13.9720	+	13.9720i	1.00834	+	1.00834i
$193$	−8.12866	−	8.12866i	−0.585114	−	0.585114i	0.351190	−	0.936304i	$-0.385777\pi$
$193$	−8.12866	−	8.12866i	−0.585114	−	0.585114i	−0.936304	+	0.351190i	$0.885777\pi$
$194$	26.9167			1.93251
$195$	14.5056	+	6.66583i	1.03877	+	0.477350i
$196$	4.76612			0.340437
$197$	19.0770	−	19.0770i	1.35918	−	1.35918i	0.484247	−	0.874932i	$-0.339094\pi$
$197$	19.0770	−	19.0770i	1.35918	−	1.35918i	0.874932	−	0.484247i	$-0.160906\pi$
$198$		0			0
$199$			3.29236i			0.233389i	0.993168	+	0.116694i	$0.0372298\pi$
$199$			3.29236i			0.233389i	−0.993168	+	0.116694i	$0.962770\pi$
$200$	−0.114129	+	1.49666i	−0.00807016	+	0.105830i
$201$	17.3238			1.22193
$202$	13.6913	+	13.6913i	0.963319	+	0.963319i
$203$	12.1753	−	12.1753i	0.854536	−	0.854536i
$204$	27.2420			1.90732
$205$	0.307667	−	0.669521i	0.0214884	−	0.0467614i
$206$		−	14.2027i		−	0.989552i
$207$	−26.0749	−	26.0749i	−1.81233	−	1.81233i
$208$	7.36624	+	7.36624i	0.510757	+	0.510757i
$209$		0			0
$210$	−9.39700	−	25.3766i	−0.648454	−	1.75115i
$211$			20.9410i			1.44164i	0.693124	+	0.720818i	$0.256234\pi$
$211$			20.9410i			1.44164i	−0.693124	+	0.720818i	$0.743766\pi$
$212$	4.24826	+	4.24826i	0.291772	+	0.291772i
$213$	−15.7638	+	15.7638i	−1.08012	+	1.08012i
$214$			31.5967i			2.15990i
$215$	4.10212	+	11.0778i	0.279763	+	0.755500i
$216$			2.30346i			0.156731i
$217$	−2.10993	+	2.10993i	−0.143231	+	0.143231i
$218$	−11.0251	+	11.0251i	−0.746717	+	0.746717i
$219$	22.9199			1.54878
$220$		0			0
$221$	12.2242			0.822286
$222$	−2.48335	+	2.48335i	−0.166671	+	0.166671i
$223$	−18.9231	+	18.9231i	−1.26719	+	1.26719i	−0.319649	+	0.947536i	$0.603565\pi$
$223$	−18.9231	+	18.9231i	−1.26719	+	1.26719i	−0.947536	+	0.319649i	$0.896435\pi$
$224$		−	16.3965i		−	1.09554i
$225$	21.3014	−	18.2829i	1.42010	−	1.21886i
$226$		−	37.8184i		−	2.51564i
$227$	−4.32939	+	4.32939i	−0.287351	+	0.287351i	−0.836032	−	0.548681i	$-0.815130\pi$
$227$	−4.32939	+	4.32939i	−0.287351	+	0.287351i	0.548681	+	0.836032i	$0.315130\pi$
$228$	−1.59299	−	1.59299i	−0.105498	−	0.105498i
$229$			1.63754i			0.108212i	0.998535	+	0.0541060i	$0.0172309\pi$
$229$			1.63754i			0.108212i	−0.998535	+	0.0541060i	$0.982769\pi$
$230$	−12.0281	+	26.1746i	−0.793109	+	1.72590i
$231$		0			0
$232$	1.73862	+	1.73862i	0.114146	+	0.114146i
$233$	−15.2271	−	15.2271i	−0.997558	−	0.997558i	0.00243879	−	0.999997i	$-0.499224\pi$
$233$	−15.2271	−	15.2271i	−0.997558	−	0.997558i	−0.999997	+	0.00243879i	$0.999224\pi$
$234$		−	26.7855i		−	1.75102i
$235$	7.10396	+	19.1843i	0.463412	+	1.25145i
$236$	5.62441			0.366118
$237$	−7.46292	+	7.46292i	−0.484769	+	0.484769i
$238$	−14.6522	−	14.6522i	−0.949759	−	0.949759i
$239$	−24.5800			−1.58994			−0.794972	−	0.606646i	$-0.792515\pi$
$239$	−24.5800			−1.58994			−0.794972	+	0.606646i	$0.792515\pi$
$240$	26.3577	−	9.76030i	1.70139	−	0.630025i
$241$			19.3936i			1.24925i	0.780923	+	0.624627i	$0.214749\pi$
$241$			19.3936i			1.24925i	−0.780923	+	0.624627i	$0.785251\pi$
$242$		0			0
$243$	−4.49385	+	4.49385i	−0.288280	+	0.288280i
$244$	2.64886			0.169576
$245$	2.40941	−	5.24317i	0.153932	−	0.334974i
$246$	−1.89693			−0.120944
$247$	−0.714815	−	0.714815i	−0.0454826	−	0.0454826i
$248$	−0.301297	−	0.301297i	−0.0191324	−	0.0191324i
$249$	7.39583			0.468692
$250$	−19.1716	−	10.6450i	−1.21252	−	0.673248i
$251$	7.59401			0.479330			0.239665	−	0.970856i	$-0.422962\pi$
$251$	7.59401			0.479330			0.239665	+	0.970856i	$0.422962\pi$
$252$	−15.4142	+	15.4142i	−0.971001	+	0.971001i
$253$		0			0
$254$			40.6307i			2.54940i
$255$	13.7716	−	29.9687i	0.862411	−	1.87671i
$256$	18.1612			1.13507
$257$	−14.3992	−	14.3992i	−0.898199	−	0.898199i	0.0970773	−	0.995277i	$-0.469051\pi$
$257$	−14.3992	−	14.3992i	−0.898199	−	0.898199i	−0.995277	+	0.0970773i	$0.969051\pi$
$258$	21.5043	−	21.5043i	1.33880	−	1.33880i
$259$	1.28253			0.0796927
$260$	−9.42061	+	3.48846i	−0.584241	+	0.216345i
$261$		−	45.9839i		−	2.84633i
$262$	−8.32383	−	8.32383i	−0.514248	−	0.514248i
$263$	−4.23725	−	4.23725i	−0.261280	−	0.261280i	0.564294	−	0.825574i	$-0.309148\pi$
$263$	−4.23725	−	4.23725i	−0.261280	−	0.261280i	−0.825574	+	0.564294i	$0.809148\pi$
$264$		0			0
$265$	6.82110	−	2.52586i	0.419017	−	0.155162i
$266$			1.71359i			0.105067i
$267$	−16.1234	−	16.1234i	−0.986735	−	0.986735i
$268$	−7.70853	+	7.70853i	−0.470873	+	0.470873i
$269$		−	17.2840i		−	1.05382i	−0.849920	−	0.526911i	$-0.823350\pi$
$269$		−	17.2840i		−	1.05382i	0.849920	−	0.526911i	$-0.176650\pi$
$270$	−30.5780	−	14.0516i	−1.86092	−	0.855155i
$271$			18.5440i			1.12647i	0.826297	+	0.563235i	$0.190443\pi$
$271$			18.5440i			1.12647i	−0.826297	+	0.563235i	$0.809557\pi$
$272$	15.2187	−	15.2187i	0.922766	−	0.922766i
$273$	−10.6127	+	10.6127i	−0.642307	+	0.642307i
$274$	−17.7450			−1.07201
$275$		0			0
$276$	35.6044			2.14313
$277$	−7.65186	+	7.65186i	−0.459756	+	0.459756i	−0.898575	−	0.438819i	$-0.855397\pi$
$277$	−7.65186	+	7.65186i	−0.459756	+	0.459756i	0.438819	+	0.898575i	$0.355397\pi$
$278$	−18.1553	+	18.1553i	−1.08888	+	1.08888i
$279$			7.96885i			0.477082i
$280$	−1.28227	−	0.589245i	−0.0766301	−	0.0352141i
$281$			17.4856i			1.04310i	0.853219	+	0.521552i	$0.174647\pi$
$281$			17.4856i			1.04310i	−0.853219	+	0.521552i	$0.825353\pi$
$282$	37.2407	−	37.2407i	2.21765	−	2.21765i
$283$	7.69120	+	7.69120i	0.457194	+	0.457194i	0.897733	−	0.440539i	$-0.145213\pi$
$283$	7.69120	+	7.69120i	0.457194	+	0.457194i	−0.440539	+	0.897733i	$0.645213\pi$
$284$		−	14.0288i		−	0.832453i
$285$	−2.55774	+	0.947133i	−0.151507	+	0.0561033i
$286$		0			0
$287$	0.489837	+	0.489837i	0.0289142	+	0.0289142i
$288$	−30.9634	−	30.9634i	−1.82454	−	1.82454i
$289$		−	8.25512i		−	0.485595i
$290$	−33.6859	+	12.4739i	−1.97810	+	0.732494i
$291$	−40.2786			−2.36118
$292$	−10.1986	+	10.1986i	−0.596828	+	0.596828i
$293$	−0.609501	−	0.609501i	−0.0356074	−	0.0356074i	0.689079	−	0.724686i	$-0.258015\pi$
$293$	−0.609501	−	0.609501i	−0.0356074	−	0.0356074i	−0.724686	+	0.689079i	$0.758015\pi$
$294$	−14.8552			−0.866375
$295$	2.84330	−	6.18736i	0.165543	−	0.360242i
$296$			0.183145i			0.0106451i
$297$		0			0
$298$	18.8634	−	18.8634i	1.09273	−	1.09273i
$299$	15.9766			0.923950
$300$	−2.06086	+	27.0256i	−0.118984	+	1.56032i
$301$	−11.1060			−0.640138
$302$	−11.5168	−	11.5168i	−0.662717	−	0.662717i
$303$	−20.4879	−	20.4879i	−1.17700	−	1.17700i
$304$	−1.77984			−0.102081
$305$	1.33907	−	2.91399i	0.0766751	−	0.166854i
$306$	−55.3388			−3.16351
$307$	4.61342	−	4.61342i	0.263302	−	0.263302i	−0.563092	−	0.826394i	$-0.690388\pi$
$307$	4.61342	−	4.61342i	0.263302	−	0.263302i	0.826394	+	0.563092i	$0.190388\pi$
$308$		0			0
$309$			21.2532i			1.20905i
$310$	5.83764	−	2.16168i	0.331556	−	0.122775i
$311$	5.51408			0.312675			0.156337	−	0.987704i	$-0.450031\pi$
$311$	5.51408			0.312675			0.156337	+	0.987704i	$0.450031\pi$
$312$	−1.51549	−	1.51549i	−0.0857974	−	0.0857974i
$313$	−11.2968	+	11.2968i	−0.638534	+	0.638534i	−0.950194	−	0.311659i	$-0.899115\pi$
$313$	−11.2968	+	11.2968i	−0.638534	+	0.638534i	0.311659	+	0.950194i	$0.399115\pi$
$314$	−6.78147			−0.382701
$315$	9.16469	+	24.7493i	0.516372	+	1.39447i
$316$		−	6.64151i		−	0.373614i
$317$	7.18120	+	7.18120i	0.403337	+	0.403337i	0.879407	−	0.476071i	$-0.157939\pi$
$317$	7.18120	+	7.18120i	0.403337	+	0.403337i	−0.476071	+	0.879407i	$0.657939\pi$
$318$	−13.2412	−	13.2412i	−0.742528	−	0.742528i
$319$		0			0
$320$	−6.28581	+	13.6787i	−0.351387	+	0.764661i
$321$		−	47.2818i		−	2.63901i
$322$	−19.1499	−	19.1499i	−1.06718	−	1.06718i
$323$	−1.47681	+	1.47681i	−0.0821718	+	0.0821718i
$324$			10.4863i			0.582571i
$325$	−0.924761	+	12.1271i	−0.0512965	+	0.672688i
$326$		−	27.6040i		−	1.52884i
$327$	16.4982	−	16.4982i	0.912354	−	0.912354i
$328$	−0.0699486	+	0.0699486i	−0.00386227	+	0.00386227i
$329$	−19.2331			−1.06035
$330$		0			0
$331$	−32.1615			−1.76775			−0.883877	−	0.467719i	$-0.845076\pi$
$331$	−32.1615			−1.76775			−0.883877	+	0.467719i	$0.845076\pi$
$332$	−3.29090	+	3.29090i	−0.180612	+	0.180612i
$333$	2.42196	−	2.42196i	0.132722	−	0.132722i
$334$		−	15.0057i		−	0.821076i
$335$	4.58321	+	12.3770i	0.250407	+	0.676226i
$336$			26.4248i			1.44159i
$337$	−4.18748	+	4.18748i	−0.228107	+	0.228107i	−0.811901	−	0.583795i	$-0.801567\pi$
$337$	−4.18748	+	4.18748i	−0.228107	+	0.228107i	0.583795	+	0.811901i	$0.301567\pi$
$338$	−9.82361	−	9.82361i	−0.534334	−	0.534334i
$339$			56.5921i			3.07366i
$340$	7.20716	+	19.4630i	0.390863	+	1.05553i
$341$		0			0
$342$	3.23597	+	3.23597i	0.174981	+	0.174981i
$343$	14.2416	+	14.2416i	0.768976	+	0.768976i
$344$		−	1.58593i		−	0.0855077i
$345$	17.9990	−	39.1681i	0.969036	−	2.10874i
$346$	39.5796			2.12781
$347$	−0.155138	+	0.155138i	−0.00832822	+	0.00832822i	−0.711259	−	0.702930i	$-0.751875\pi$
$347$	−0.155138	+	0.155138i	−0.00832822	+	0.00832822i	0.702930	+	0.711259i	$0.251875\pi$
$348$	31.3948	+	31.3948i	1.68294	+	1.68294i
$349$	−21.4773			−1.14965			−0.574826	−	0.818275i	$-0.694930\pi$
$349$	−21.4773			−1.14965			−0.574826	+	0.818275i	$0.694930\pi$
$350$	15.6442	−	13.4273i	0.836219	−	0.717721i
$351$			18.6644i			0.996231i
$352$		0			0
$353$	17.5847	−	17.5847i	0.935941	−	0.935941i	−0.0621273	−	0.998068i	$-0.519788\pi$
$353$	17.5847	−	17.5847i	0.935941	−	0.935941i	0.998068	+	0.0621273i	$0.0197885\pi$
$354$	−17.5304			−0.931730
$355$	−15.4329	−	7.09194i	−0.819094	−	0.376401i
$356$	14.3488			0.760483
$357$	21.9258	+	21.9258i	1.16043	+	1.16043i
$358$	19.6033	+	19.6033i	1.03607	+	1.03607i
$359$	−11.8900			−0.627531			−0.313766	−	0.949500i	$-0.601591\pi$
$359$	−11.8900			−0.627531			−0.313766	+	0.949500i	$0.601591\pi$
$360$	−3.53419	+	1.30872i	−0.186268	+	0.0689754i
$361$	−18.8273			−0.990910
$362$	−3.51782	+	3.51782i	−0.184893	+	0.184893i
$363$		0			0
$364$		−	9.44457i		−	0.495030i
$365$	6.06371	+	16.3751i	0.317389	+	0.857111i
$366$	−8.25607			−0.431552
$367$	3.21911	+	3.21911i	0.168036	+	0.168036i	0.786116	−	0.618079i	$-0.212089\pi$
$367$	3.21911	+	3.21911i	0.168036	+	0.168036i	−0.618079	+	0.786116i	$0.712089\pi$
$368$	19.8903	−	19.8903i	1.03685	−	1.03685i
$369$	1.85003			0.0963089
$370$	−2.43122	−	1.11723i	−0.126393	−	0.0580818i
$371$			6.83845i			0.355034i
$372$	−5.44061	−	5.44061i	−0.282082	−	0.282082i
$373$	25.4846	+	25.4846i	1.31954	+	1.31954i	0.914138	+	0.405402i	$0.132869\pi$
$373$	25.4846	+	25.4846i	1.31954	+	1.31954i	0.405402	+	0.914138i	$0.367131\pi$
$374$		0			0
$375$	28.6888	+	15.9293i	1.48148	+	0.822588i
$376$		−	2.74648i		−	0.141639i
$377$	14.0876	+	14.0876i	0.725550	+	0.725550i
$378$	22.3716	−	22.3716i	1.15067	−	1.15067i
$379$		−	7.11670i		−	0.365560i	−0.983154	−	0.182780i	$-0.941490\pi$
$379$		−	7.11670i		−	0.365560i	0.983154	−	0.182780i	$-0.0585097\pi$
$380$	0.716666	−	1.55955i	0.0367642	−	0.0800033i
$381$		−	60.8005i		−	3.11490i
$382$	13.1511	−	13.1511i	0.672871	−	0.672871i
$383$	−6.35141	+	6.35141i	−0.324542	+	0.324542i	−0.850507	−	0.525964i	$-0.823704\pi$
$383$	−6.35141	+	6.35141i	−0.324542	+	0.324542i	0.525964	+	0.850507i	$0.323704\pi$
$384$	−7.02811			−0.358652
$385$		0			0
$386$	−22.5472			−1.14762
$387$	−20.9727	+	20.9727i	−1.06610	+	1.06610i
$388$	17.9227	−	17.9227i	0.909885	−	0.909885i
$389$			32.6292i			1.65437i	0.561931	+	0.827184i	$0.310059\pi$
$389$			32.6292i			1.65437i	−0.561931	+	0.827184i	$0.689941\pi$
$390$	29.3626	−	10.8730i	1.48683	−	0.550575i
$391$		−	33.0076i		−	1.66927i
$392$	−0.547783	+	0.547783i	−0.0276672	+	0.0276672i
$393$	12.4559	+	12.4559i	0.628318	+	0.628318i
$394$		−	52.9154i		−	2.66584i
$395$	−7.30627	−	3.35747i	−0.367618	−	0.168933i
$396$		0			0
$397$	−14.3673	−	14.3673i	−0.721076	−	0.721076i	0.247748	−	0.968824i	$-0.420309\pi$
$397$	−14.3673	−	14.3673i	−0.721076	−	0.721076i	−0.968824	+	0.247748i	$0.920309\pi$
$398$	4.56614	+	4.56614i	0.228880	+	0.228880i
$399$		−	2.56424i		−	0.128373i
$400$	13.9465	+	16.2491i	0.697323	+	0.812453i
$401$	2.63501			0.131586			0.0657931	−	0.997833i	$-0.479042\pi$
$401$	2.63501			0.131586			0.0657931	+	0.997833i	$0.479042\pi$
$402$	24.0263	−	24.0263i	1.19832	−	1.19832i
$403$	−2.44134	−	2.44134i	−0.121612	−	0.121612i
$404$	18.2329			0.907122
$405$	11.5359	+	5.30111i	0.573222	+	0.263415i
$406$		−	33.7716i		−	1.67605i
$407$		0			0
$408$	−3.13099	+	3.13099i	−0.155007	+	0.155007i
$409$	17.2531			0.853113			0.426557	−	0.904461i	$-0.359726\pi$
$409$	17.2531			0.853113			0.426557	+	0.904461i	$0.359726\pi$
$410$	−0.501853	−	1.35526i	−0.0247847	−	0.0669313i
$411$	26.5539			1.30981
$412$	−9.45699	−	9.45699i	−0.465912	−	0.465912i
$413$	4.52681	+	4.52681i	0.222750	+	0.222750i
$414$	−72.3261			−3.55463
$415$	1.95665	+	5.28394i	0.0960480	+	0.259378i
$416$	18.9719			0.930175
$417$	27.1679	−	27.1679i	1.33042	−	1.33042i
$418$		0			0
$419$		−	24.0620i		−	1.17551i	−0.809041	−	0.587753i	$-0.800013\pi$
$419$		−	24.0620i		−	1.17551i	0.809041	−	0.587753i	$-0.199987\pi$
$420$	−23.1542	−	10.6401i	−1.12981	−	0.519186i
$421$	−20.6674			−1.00727			−0.503634	−	0.863917i	$-0.668004\pi$
$421$	−20.6674			−1.00727			−0.503634	+	0.863917i	$0.668004\pi$
$422$	29.0429	+	29.0429i	1.41379	+	1.41379i
$423$	−36.3201	+	36.3201i	−1.76594	+	1.76594i
$424$	−0.976529			−0.0474244
$425$	25.0545	+	1.91056i	1.21532	+	0.0926756i
$426$			43.7254i			2.11850i
$427$	2.13194	+	2.13194i	0.103172	+	0.103172i
$428$	21.0388	+	21.0388i	1.01695	+	1.01695i
$429$		0			0
$430$	21.0529	+	9.67453i	1.01526	+	0.466547i
$431$			34.2884i			1.65161i	0.563953	+	0.825807i	$0.309280\pi$
$431$			34.2884i			1.65161i	−0.563953	+	0.825807i	$0.690720\pi$
$432$	23.2365	+	23.2365i	1.11797	+	1.11797i
$433$	2.26541	−	2.26541i	0.108869	−	0.108869i	−0.650574	−	0.759443i	$-0.725472\pi$
$433$	2.26541	−	2.26541i	0.108869	−	0.108869i	0.759443	+	0.650574i	$0.225472\pi$
$434$			5.85249i			0.280928i
$435$	50.4081	−	18.6662i	2.41689	−	0.894975i
$436$			14.6823i			0.703156i
$437$	−1.93014	+	1.93014i	−0.0923311	+	0.0923311i
$438$	31.7875	−	31.7875i	1.51886	−	1.51886i
$439$	−12.3536			−0.589607			−0.294803	−	0.955558i	$-0.595254\pi$
$439$	−12.3536			−0.589607			−0.294803	+	0.955558i	$0.595254\pi$
$440$		0			0
$441$	14.4880			0.689905
$442$	16.9536	−	16.9536i	0.806400	−	0.806400i
$443$	1.79612	−	1.79612i	0.0853361	−	0.0853361i	−0.663150	−	0.748486i	$-0.730781\pi$
$443$	1.79612	−	1.79612i	0.0853361	−	0.0853361i	0.748486	+	0.663150i	$0.230781\pi$
$444$			3.30710i			0.156948i
$445$	7.25371	−	15.7849i	0.343859	−	0.748278i
$446$			52.4886i			2.48541i
$447$	−28.2276	+	28.2276i	−1.33512	+	1.33512i
$448$	−10.0076	−	10.0076i	−0.472816	−	0.472816i
$449$			25.7460i			1.21503i	0.794309	+	0.607514i	$0.207833\pi$
$449$			25.7460i			1.21503i	−0.794309	+	0.607514i	$0.792167\pi$
$450$	4.18640	−	54.8992i	0.197349	−	2.58797i
$451$		0			0
$452$	−25.1816	−	25.1816i	−1.18444	−	1.18444i
$453$	17.2339	+	17.2339i	0.809721	+	0.809721i
$454$			12.0088i			0.563600i
$455$	−10.3899	−	4.77450i	−0.487086	−	0.223832i
$456$	0.366173			0.0171476
$457$	−7.76151	+	7.76151i	−0.363068	+	0.363068i	−0.864941	−	0.501873i	$-0.832644\pi$
$457$	−7.76151	+	7.76151i	−0.363068	+	0.363068i	0.501873	+	0.864941i	$0.332644\pi$
$458$	2.27110	+	2.27110i	0.106121	+	0.106121i
$459$	38.5606			1.79986
$460$	9.41953	+	25.4375i	0.439188	+	1.18603i
$461$		−	4.12125i		−	0.191946i	−0.995384	−	0.0959728i	$-0.969404\pi$
$461$		−	4.12125i		−	0.191946i	0.995384	−	0.0959728i	$-0.0305962\pi$
$462$		0			0
$463$	7.07687	−	7.07687i	0.328890	−	0.328890i	−0.523274	−	0.852164i	$-0.675290\pi$
$463$	7.07687	−	7.07687i	0.328890	−	0.328890i	0.852164	+	0.523274i	$0.175290\pi$
$464$	35.0772			1.62842
$465$	−8.73555	+	3.23478i	−0.405101	+	0.150009i
$466$	−42.2366			−1.95657
$467$	−5.18571	−	5.18571i	−0.239966	−	0.239966i	0.576870	−	0.816836i	$-0.304274\pi$
$467$	−5.18571	−	5.18571i	−0.239966	−	0.239966i	−0.816836	+	0.576870i	$0.804274\pi$
$468$	−17.8353	−	17.8353i	−0.824436	−	0.824436i
$469$	−12.4084			−0.572969
$470$	36.4590	+	16.7541i	1.68173	+	0.772810i
$471$	10.1479			0.467591
$472$	−0.646428	+	0.646428i	−0.0297543	+	0.0297543i
$473$		0			0
$474$			20.7005i			0.950808i
$475$	−1.35336	−	1.57680i	−0.0620962	−	0.0723484i
$476$	−19.5125			−0.894353
$477$	12.9138	+	12.9138i	0.591284	+	0.591284i
$478$	−34.0898	+	34.0898i	−1.55923	+	1.55923i
$479$	−5.38529			−0.246060			−0.123030	−	0.992403i	$-0.539261\pi$
$479$	−5.38529			−0.246060			−0.123030	+	0.992403i	$0.539261\pi$
$480$	21.3736	−	46.5114i	0.975565	−	2.12295i
$481$			1.48398i			0.0676637i
$482$	26.8969	+	26.8969i	1.22512	+	1.22512i
$483$	28.6563	+	28.6563i	1.30391	+	1.30391i
$484$		0			0
$485$	−10.6562	−	28.7770i	−0.483871	−	1.30670i
$486$			12.4650i			0.565422i
$487$	−9.86485	−	9.86485i	−0.447019	−	0.447019i	0.447343	−	0.894362i	$-0.352370\pi$
$487$	−9.86485	−	9.86485i	−0.447019	−	0.447019i	−0.894362	+	0.447343i	$0.852370\pi$
$488$	−0.304440	+	0.304440i	−0.0137814	+	0.0137814i
$489$			41.3071i			1.86797i
$490$	−3.93012	−	10.6133i	−0.177545	−	0.479460i
$491$			32.6224i			1.47223i	0.676857	+	0.736114i	$0.263341\pi$
$491$			32.6224i			1.47223i	−0.676857	+	0.736114i	$0.736659\pi$
$492$	−1.26308	+	1.26308i	−0.0569441	+	0.0569441i
$493$	29.1051	−	29.1051i	1.31083	−	1.31083i
$494$	−1.98274			−0.0892078
$495$		0			0
$496$	−6.07876			−0.272944
$497$	11.2911	−	11.2911i	0.506474	−	0.506474i
$498$	10.2572	−	10.2572i	0.459637	−	0.459637i
$499$		−	38.9369i		−	1.74306i	−0.490346	−	0.871528i	$-0.663130\pi$
$499$		−	38.9369i		−	1.74306i	0.490346	−	0.871528i	$-0.336870\pi$
$500$	−19.8536	+	5.67753i	−0.887880	+	0.253907i
$501$			22.4548i			1.00321i
$502$	10.5321	−	10.5321i	0.470070	−	0.470070i
$503$	−29.6308	−	29.6308i	−1.32117	−	1.32117i	−0.912829	−	0.408343i	$-0.866107\pi$
$503$	−29.6308	−	29.6308i	−1.32117	−	1.32117i	−0.408343	−	0.912829i	$-0.633893\pi$
$504$		−	3.54318i		−	0.157826i
$505$	9.21727	−	20.0579i	0.410163	−	0.892564i
$506$		0			0
$507$	14.7002	+	14.7002i	0.652859	+	0.652859i
$508$	27.0542	+	27.0542i	1.20034	+	1.20034i
$509$			18.2206i			0.807612i	0.914845	+	0.403806i	$0.132313\pi$
$509$			18.2206i			0.807612i	−0.914845	+	0.403806i	$0.867687\pi$
$510$	−22.4636	−	60.6631i	−0.994705	−	2.68621i
$511$	−16.4167			−0.726234
$512$	21.8012	−	21.8012i	0.963484	−	0.963484i
$513$	−2.25486	−	2.25486i	−0.0995543	−	0.0995543i
$514$	−39.9404			−1.76169
$515$	−15.1843	+	5.62277i	−0.669102	+	0.247769i
$516$		−	28.6376i		−	1.26070i
$517$		0			0
$518$	1.77873	−	1.77873i	0.0781531	−	0.0781531i
$519$	−59.2276			−2.59980
$520$	0.681797	−	1.48367i	0.0298988	−	0.0650634i
$521$	17.3674			0.760881			0.380441	−	0.924805i	$-0.375772\pi$
$521$	17.3674			0.760881			0.380441	+	0.924805i	$0.375772\pi$
$522$	−63.7748	−	63.7748i	−2.79135	−	2.79135i
$523$	12.3950	+	12.3950i	0.541995	+	0.541995i	0.924113	−	0.382118i	$-0.124805\pi$
$523$	12.3950	+	12.3950i	0.541995	+	0.541995i	−0.382118	+	0.924113i	$0.624805\pi$
$524$	−11.0849			−0.484248
$525$	−23.4103	+	20.0929i	−1.02171	+	0.876926i
$526$	−11.7532			−0.512465
$527$	−5.04380	+	5.04380i	−0.219711	+	0.219711i
$528$		0			0
$529$		−	20.1399i		−	0.875649i
$530$	5.95704	−	12.9632i	0.258757	−	0.563087i
$531$	17.0970			0.741948
$532$	1.14100	+	1.14100i	0.0494688	+	0.0494688i
$533$	−0.566776	+	0.566776i	−0.0245498	+	0.0245498i
$534$	−44.7228			−1.93535
$535$	33.7804	−	12.5089i	1.46045	−	0.540807i
$536$		−	1.77192i		−	0.0765354i
$537$	−29.3347	−	29.3347i	−1.26589	−	1.26589i
$538$	−23.9710	−	23.9710i	−1.03346	−	1.03346i
$539$		0			0
$540$	−29.7170	+	11.0042i	−1.27881	+	0.473546i
$541$		−	0.124643i		−	0.00535882i	−0.999996	−	0.00267941i	$-0.999147\pi$
$541$		−	0.124643i		−	0.00535882i	0.999996	−	0.00267941i	$-0.000852884\pi$
$542$	25.7186	+	25.7186i	1.10471	+	1.10471i
$543$	5.26413	−	5.26413i	0.225905	−	0.225905i
$544$		−	39.1960i		−	1.68051i
$545$	16.1519	+	7.42234i	0.691872	+	0.317938i
$546$			29.4372i			1.25980i
$547$	1.48945	−	1.48945i	0.0636842	−	0.0636842i	−0.674547	−	0.738232i	$-0.735661\pi$
$547$	1.48945	−	1.48945i	0.0636842	−	0.0636842i	0.738232	+	0.674547i	$0.235661\pi$
$548$	−11.8156	+	11.8156i	−0.504738	+	0.504738i
$549$	8.05197			0.343650
$550$		0			0
$551$	−3.40387			−0.145010
$552$	−4.09211	+	4.09211i	−0.174172	+	0.174172i
$553$	5.34543	−	5.34543i	0.227311	−	0.227311i
$554$			21.2246i			0.901748i
$555$	3.63812	+	1.67184i	0.154429	+	0.0709655i
$556$			24.1777i			1.02536i
$557$	−21.6170	+	21.6170i	−0.915941	+	0.915941i	−0.996731	−	0.0807905i	$-0.974256\pi$
$557$	−21.6170	+	21.6170i	−0.915941	+	0.915941i	0.0807905	+	0.996731i	$0.474256\pi$
$558$	11.0519	+	11.0519i	0.467866	+	0.467866i
$559$		−	12.8504i		−	0.543514i
$560$	−18.8791	+	6.99096i	−0.797789	+	0.295422i
$561$		0			0
$562$	24.2507	+	24.2507i	1.02295	+	1.02295i
$563$	−17.8239	−	17.8239i	−0.751186	−	0.751186i	0.223515	−	0.974701i	$-0.428247\pi$
$563$	−17.8239	−	17.8239i	−0.751186	−	0.751186i	−0.974701	+	0.223515i	$0.928247\pi$
$564$		−	49.5939i		−	2.08828i
$565$	−40.4321	+	14.9720i	−1.70099	+	0.629879i
$566$	21.3337			0.896724
$567$	−8.43990	+	8.43990i	−0.354442	+	0.354442i
$568$	1.61236	+	1.61236i	0.0676532	+	0.0676532i
$569$	15.6153			0.654629			0.327315	−	0.944915i	$-0.393856\pi$
$569$	15.6153			0.654629			0.327315	+	0.944915i	$0.393856\pi$
$570$	−2.23374	+	4.86088i	−0.0935609	+	0.203600i
$571$			13.3555i			0.558911i	0.960159	+	0.279455i	$0.0901539\pi$
$571$			13.3555i			0.558911i	−0.960159	+	0.279455i	$0.909846\pi$
$572$		0			0
$573$	−19.6796	+	19.6796i	−0.822126	+	0.822126i
$574$	1.35870			0.0567111
$575$	32.7454	+	2.49704i	1.36558	+	0.104134i
$576$	−37.7972			−1.57488
$577$	24.6719	+	24.6719i	1.02710	+	1.02710i	0.999622	+	0.0274825i	$0.00874906\pi$
$577$	24.6719	+	24.6719i	1.02710	+	1.02710i	0.0274825	+	0.999622i	$0.491251\pi$
$578$	−11.4490	−	11.4490i	−0.476214	−	0.476214i
$579$	33.7400			1.40219
$580$	−14.1241	+	30.7358i	−0.586472	+	1.27623i
$581$	−5.29737			−0.219772
$582$	−55.8621	+	55.8621i	−2.31556	+	2.31556i
$583$		0			0
$584$		−	2.34431i		−	0.0970081i
$585$	−28.6367	+	10.6042i	−1.18398	+	0.438430i
$586$	−1.69062			−0.0698390
$587$	10.5433	+	10.5433i	0.435170	+	0.435170i	0.890383	−	0.455213i	$-0.150437\pi$
$587$	10.5433	+	10.5433i	0.435170	+	0.435170i	−0.455213	+	0.890383i	$0.650437\pi$
$588$	−9.89146	+	9.89146i	−0.407917	+	0.407917i
$589$	0.589878			0.0243055
$590$	−4.63786	−	12.5246i	−0.190938	−	0.515628i
$591$			79.1836i			3.25718i
$592$	1.84750	+	1.84750i	0.0759319	+	0.0759319i
$593$	0.611093	+	0.611093i	0.0250946	+	0.0250946i	0.719543	−	0.694448i	$-0.244351\pi$
$593$	0.611093	+	0.611093i	0.0250946	+	0.0250946i	−0.694448	+	0.719543i	$0.744351\pi$
$594$		0			0
$595$	−9.86412	+	21.4655i	−0.404390	+	0.880000i
$596$		−	25.1207i		−	1.02898i
$597$	−6.83286	−	6.83286i	−0.279650	−	0.279650i
$598$	22.1578	−	22.1578i	0.906100	−	0.906100i
$599$		−	5.67671i		−	0.231944i	−0.993252	−	0.115972i	$-0.963002\pi$
$599$		−	5.67671i		−	0.231944i	0.993252	−	0.115972i	$-0.0369983\pi$
$600$	−2.86926	−	3.34298i	−0.117137	−	0.136477i
$601$			6.66774i			0.271983i	0.990710	+	0.135991i	$0.0434219\pi$
$601$			6.66774i			0.271983i	−0.990710	+	0.135991i	$0.956578\pi$
$602$	−15.4028	+	15.4028i	−0.627772	+	0.627772i
$603$	−23.4323	+	23.4323i	−0.954238	+	0.954238i
$604$	−15.3371			−0.624056
$605$		0			0
$606$	−56.8292			−2.30853
$607$	−23.2899	+	23.2899i	−0.945308	+	0.945308i	−0.998580	−	0.0532721i	$-0.983035\pi$
$607$	−23.2899	+	23.2899i	−0.945308	+	0.945308i	0.0532721	+	0.998580i	$0.483035\pi$
$608$	−2.29201	+	2.29201i	−0.0929532	+	0.0929532i
$609$			50.5363i			2.04784i
$610$	−2.18423	−	5.89854i	−0.0884371	−	0.238825i
$611$		−	22.2540i		−	0.900302i
$612$	−36.8477	+	36.8477i	−1.48948	+	1.48948i
$613$	11.8613	+	11.8613i	0.479075	+	0.479075i	0.904836	−	0.425761i	$-0.139993\pi$
$613$	11.8613	+	11.8613i	0.479075	+	0.479075i	−0.425761	+	0.904836i	$0.639993\pi$
$614$		−	12.7966i		−	0.516430i
$615$	0.750981	+	2.02803i	0.0302825	+	0.0817780i
$616$		0			0
$617$	0.420747	+	0.420747i	0.0169386	+	0.0169386i	0.715525	−	0.698587i	$-0.246187\pi$
$617$	0.420747	+	0.420747i	0.0169386	+	0.0169386i	−0.698587	+	0.715525i	$0.746187\pi$
$618$	29.4759	+	29.4759i	1.18570	+	1.18570i
$619$		−	6.11184i		−	0.245656i	−0.992428	−	0.122828i	$-0.960804\pi$
$619$		−	6.11184i		−	0.245656i	0.992428	−	0.122828i	$-0.0391963\pi$
$620$	2.44766	−	5.32640i	0.0983004	−	0.213913i
$621$	50.3975			2.02238
$622$	7.64743	−	7.64743i	0.306634	−	0.306634i
$623$	11.5486	+	11.5486i	0.462686	+	0.462686i
$624$	−30.5753			−1.22399
$625$	−3.79076	+	24.7109i	−0.151630	+	0.988437i
$626$			31.3350i			1.25240i
$627$		0			0
$628$	−4.51549	+	4.51549i	−0.180188	+	0.180188i
$629$	3.06590			0.122246
$630$	47.0351	+	21.6142i	1.87392	+	0.861130i
$631$	−30.9763			−1.23315			−0.616573	−	0.787298i	$-0.711480\pi$
$631$	−30.9763			−1.23315			−0.616573	+	0.787298i	$0.711480\pi$
$632$	0.763327	+	0.763327i	0.0303635	+	0.0303635i
$633$	−43.4603	−	43.4603i	−1.72739	−	1.72739i
$634$	19.9191			0.791089
$635$	43.4388	−	16.0854i	1.72382	−	0.638331i
$636$	−17.6334			−0.699211
$637$	−4.43854	+	4.43854i	−0.175862	+	0.175862i
$638$		0			0
$639$		−	42.6445i		−	1.68699i
$640$	−1.85936	−	5.02122i	−0.0734978	−	0.198481i
$641$	17.1528			0.677496			0.338748	−	0.940877i	$-0.389997\pi$
$641$	17.1528			0.677496			0.338748	+	0.940877i	$0.389997\pi$
$642$	−65.5748	−	65.5748i	−2.58803	−	2.58803i
$643$	25.4201	−	25.4201i	1.00247	−	1.00247i	0.00247377	−	0.999997i	$-0.499213\pi$
$643$	25.4201	−	25.4201i	1.00247	−	1.00247i	0.999997	−	0.00247377i	$-0.000787426\pi$
$644$	−25.5022			−1.00493
$645$	−31.5040	−	14.4771i	−1.24047	−	0.570036i
$646$			4.09635i			0.161169i
$647$	−1.24998	−	1.24998i	−0.0491416	−	0.0491416i	0.682109	−	0.731251i	$-0.261063\pi$
$647$	−1.24998	−	1.24998i	−0.0491416	−	0.0491416i	−0.731251	+	0.682109i	$0.761063\pi$
$648$	−1.20522	−	1.20522i	−0.0473453	−	0.0473453i
$649$		0			0
$650$	15.5364	+	18.1015i	0.609387	+	0.709998i
$651$		−	8.75776i		−	0.343244i
$652$	−18.3803	−	18.3803i	−0.719828	−	0.719828i
$653$	−19.9585	+	19.9585i	−0.781037	+	0.781037i	−0.980006	−	0.198969i	$-0.936241\pi$
$653$	−19.9585	+	19.9585i	−0.781037	+	0.781037i	0.198969	+	0.980006i	$0.436241\pi$
$654$		−	45.7625i		−	1.78946i
$655$	−5.60376	+	12.1945i	−0.218957	+	0.476477i
$656$			1.41123i			0.0550994i
$657$	−31.0016	+	31.0016i	−1.20949	+	1.20949i
$658$	−26.6742	+	26.6742i	−1.03987	+	1.03987i
$659$	−26.3172			−1.02517			−0.512586	−	0.858636i	$-0.671312\pi$
$659$	−26.3172			−1.02517			−0.512586	+	0.858636i	$0.671312\pi$
$660$		0			0
$661$	−31.2578			−1.21579			−0.607893	−	0.794019i	$-0.707985\pi$
$661$	−31.2578			−1.21579			−0.607893	+	0.794019i	$0.707985\pi$
$662$	−44.6045	+	44.6045i	−1.73360	+	1.73360i
$663$	−25.3697	+	25.3697i	−0.985276	+	0.985276i
$664$		−	0.756464i		−	0.0293565i
$665$	1.83202	−	0.678398i	0.0710426	−	0.0263072i
$666$		−	6.71798i		−	0.260317i
$667$	38.0394	−	38.0394i	1.47289	−	1.47289i
$668$	−9.99165	−	9.99165i	−0.386588	−	0.386588i
$669$		−	78.5449i		−	3.03672i
$670$	23.5219	+	10.8091i	0.908732	+	0.417593i
$671$		0			0
$672$	34.0288	+	34.0288i	1.31269	+	1.31269i
$673$	−15.8925	−	15.8925i	−0.612610	−	0.612610i	0.331016	−	0.943625i	$-0.392609\pi$
$673$	−15.8925	−	15.8925i	−0.612610	−	0.612610i	−0.943625	+	0.331016i	$0.892609\pi$
$674$			11.6152i			0.447400i
$675$	−2.91712	+	38.2543i	−0.112280	+	1.47241i
$676$	−13.0822			−0.503162
$677$	2.06101	−	2.06101i	0.0792109	−	0.0792109i	−0.666391	−	0.745602i	$-0.732162\pi$
$677$	2.06101	−	2.06101i	0.0792109	−	0.0792109i	0.745602	+	0.666391i	$0.232162\pi$
$678$	78.4871	+	78.4871i	3.01428	+	3.01428i
$679$	28.8502			1.10717
$680$	−3.06527	−	1.40859i	−0.117548	−	0.0540171i
$681$		−	17.9702i		−	0.688618i
$682$		0			0
$683$	13.6345	−	13.6345i	0.521710	−	0.521710i	−0.396378	−	0.918087i	$-0.629733\pi$
$683$	13.6345	−	13.6345i	0.521710	−	0.521710i	0.918087	+	0.396378i	$0.129733\pi$
$684$	4.30938			0.164773
$685$	7.02512	+	18.9714i	0.268416	+	0.724859i
$686$	39.5032			1.50824
$687$	−3.39851	−	3.39851i	−0.129661	−	0.129661i
$688$	−15.9983	−	15.9983i	−0.609930	−	0.609930i
$689$	−7.91257			−0.301445
$690$	−29.3592	−	79.2847i	−1.11769	−	3.01832i
$691$	17.3677			0.660700			0.330350	−	0.943859i	$-0.392833\pi$
$691$	17.3677			0.660700			0.330350	+	0.943859i	$0.392833\pi$
$692$	26.3543	−	26.3543i	1.00184	−	1.00184i
$693$		0			0
$694$			0.430318i			0.0163347i
$695$	26.5977	+	12.2225i	1.00891	+	0.463626i
$696$	−7.21658			−0.273544
$697$	1.17096	+	1.17096i	0.0443533	+	0.0443533i
$698$	−29.7867	+	29.7867i	−1.12744	+	1.12744i
$699$	63.2036			2.39058
$700$	1.47612	−	19.3575i	0.0557923	−	0.731644i
$701$		−	32.2681i		−	1.21875i	−0.792883	−	0.609375i	$-0.791421\pi$
$701$		−	32.2681i		−	1.21875i	0.792883	−	0.609375i	$-0.208579\pi$
$702$	25.8855	+	25.8855i	0.976985	+	0.976985i
$703$	−0.179281	−	0.179281i	−0.00676169	−	0.00676169i
$704$		0			0
$705$	−54.5579	−	25.0712i	−2.05477	−	0.944234i
$706$		−	48.7763i		−	1.83572i
$707$	14.6748	+	14.6748i	0.551903	+	0.551903i
$708$	−11.6727	+	11.6727i	−0.438688	+	0.438688i
$709$		−	1.96656i		−	0.0738558i	−0.999318	−	0.0369279i	$-0.988243\pi$
$709$		−	1.96656i		−	0.0738558i	0.999318	−	0.0369279i	$-0.0117572\pi$
$710$	−31.2396	+	11.5680i	−1.17240	+	0.434141i
$711$		−	20.1888i		−	0.757140i
$712$	−1.64914	+	1.64914i	−0.0618042	+	0.0618042i
$713$	−6.59209	+	6.59209i	−0.246876	+	0.246876i
$714$	60.8174			2.27603
$715$		0			0
$716$	26.1059			0.975625
$717$	51.0125	−	51.0125i	1.90510	−	1.90510i
$718$	−16.4902	+	16.4902i	−0.615408	+	0.615408i
$719$			1.35375i			0.0504863i	0.999681	+	0.0252432i	$0.00803600\pi$
$719$			1.35375i			0.0504863i	−0.999681	+	0.0252432i	$0.991964\pi$
$720$	−22.4498	+	48.8535i	−0.836656	+	1.82066i
$721$		−	15.2229i		−	0.566932i
$722$	−26.1114	+	26.1114i	−0.971767	+	0.971767i
$723$	−40.2490	−	40.2490i	−1.49688	−	1.49688i
$724$			4.68473i			0.174107i
$725$	26.6720	+	31.0757i	0.990575	+	1.15412i
$726$		0			0
$727$	17.8003	+	17.8003i	0.660177	+	0.660177i	0.955422	−	0.295245i	$-0.0954012\pi$
$727$	17.8003	+	17.8003i	0.660177	+	0.660177i	−0.295245	+	0.955422i	$0.595401\pi$
$728$	1.08549	+	1.08549i	0.0402309	+	0.0402309i
$729$		−	35.6857i		−	1.32169i
$730$	31.1202	+	14.3008i	1.15181	+	0.529295i
$731$	−26.5489			−0.981948
$732$	−5.49736	+	5.49736i	−0.203188	+	0.203188i
$733$	−23.9574	−	23.9574i	−0.884885	−	0.884885i	0.109141	−	0.994026i	$-0.465190\pi$
$733$	−23.9574	−	23.9574i	−0.884885	−	0.884885i	−0.994026	+	0.109141i	$0.965190\pi$
$734$	8.92912			0.329580
$735$	5.88109	+	15.8819i	0.216927	+	0.585814i
$736$		−	51.2279i		−	1.88829i
$737$		0			0
$738$	2.56580	−	2.56580i	0.0944483	−	0.0944483i
$739$	−34.7794			−1.27938			−0.639691	−	0.768632i	$-0.720938\pi$
$739$	−34.7794			−1.27938			−0.639691	+	0.768632i	$0.720938\pi$
$740$	−2.36275	+	0.874930i	−0.0868566	+	0.0321631i
$741$	2.96701			0.108996
$742$	9.48419	+	9.48419i	0.348176	+	0.348176i
$743$	−6.11201	−	6.11201i	−0.224228	−	0.224228i	0.586048	−	0.810276i	$-0.300683\pi$
$743$	−6.11201	−	6.11201i	−0.224228	−	0.224228i	−0.810276	+	0.586048i	$0.800683\pi$
$744$	1.25061			0.0458495
$745$	−27.6351	−	12.6992i	−1.01247	−	0.465264i
$746$	70.6887			2.58810
$747$	−10.0037	+	10.0037i	−0.366014	+	0.366014i
$748$		0			0
$749$			33.8663i			1.23745i
$750$	61.8806	−	17.6960i	2.25956	−	0.646166i
$751$	49.1760			1.79446			0.897228	−	0.441568i	$-0.145577\pi$
$751$	49.1760			1.79446			0.897228	+	0.441568i	$0.145577\pi$
$752$	−27.7055	−	27.7055i	−1.01032	−	1.01032i
$753$	−15.7604	+	15.7604i	−0.574341	+	0.574341i
$754$	39.0761			1.42307
$755$	−7.75333	+	16.8722i	−0.282172	+	0.614041i
$756$		−	29.7925i		−	1.08354i
$757$	7.03096	+	7.03096i	0.255545	+	0.255545i	0.823239	−	0.567695i	$-0.192165\pi$
$757$	7.03096	+	7.03096i	0.255545	+	0.255545i	−0.567695	+	0.823239i	$0.692165\pi$
$758$	−9.87010	−	9.87010i	−0.358498	−	0.358498i
$759$		0			0
$760$	0.0968751	+	0.261612i	0.00351403	+	0.00948966i
$761$		−	32.9440i		−	1.19422i	−0.802160	−	0.597109i	$-0.796316\pi$
$761$		−	32.9440i		−	1.19422i	0.802160	−	0.597109i	$-0.203684\pi$
$762$	−84.3237	−	84.3237i	−3.05473	−	3.05473i
$763$	−11.8171	+	11.8171i	−0.427808	+	0.427808i
$764$		−	17.5135i		−	0.633617i
$765$	21.9083	+	59.1634i	0.792095	+	2.13906i
$766$			17.6175i			0.636545i
$767$	−5.23784	+	5.23784i	−0.189128	+	0.189128i
$768$	−37.6912	+	37.6912i	−1.36006	+	1.36006i
$769$	48.3159			1.74232			0.871159	−	0.491002i	$-0.163369\pi$
$769$	48.3159			1.74232			0.871159	+	0.491002i	$0.163369\pi$
$770$		0			0
$771$	59.7675			2.15247
$772$	−15.0132	+	15.0132i	−0.540336	+	0.540336i
$773$	−0.774548	+	0.774548i	−0.0278586	+	0.0278586i	−0.720899	−	0.693040i	$-0.756271\pi$
$773$	−0.774548	+	0.774548i	−0.0278586	+	0.0278586i	0.693040	+	0.720899i	$0.256271\pi$
$774$			58.1738i			2.09102i
$775$	−4.62217	−	5.38530i	−0.166033	−	0.193446i
$776$			4.11980i			0.147892i
$777$	−2.66173	+	2.66173i	−0.0954890	+	0.0954890i
$778$	45.2533	+	45.2533i	1.62241	+	1.62241i
$779$		−	0.136945i		−	0.00490657i
$780$	12.3114	−	26.7911i	0.440819	−	0.959275i
$781$		0			0
$782$	−45.7781	−	45.7781i	−1.63702	−	1.63702i
$783$	44.4389	+	44.4389i	1.58812	+	1.58812i
$784$			11.0517i			0.394702i
$785$	2.68474	+	7.25016i	0.0958225	+	0.258769i
$786$	34.5500			1.23236
$787$	36.4591	−	36.4591i	1.29963	−	1.29963i	0.370992	−	0.928636i	$-0.379018\pi$
$787$	36.4591	−	36.4591i	1.29963	−	1.29963i	0.928636	−	0.370992i	$-0.120982\pi$
$788$	−35.2341	−	35.2341i	−1.25516	−	1.25516i
$789$	17.5877			0.626140
$790$	−14.7895	+	5.47656i	−0.526186	+	0.194847i
$791$		−	40.5349i		−	1.44126i
$792$		0			0
$793$	−2.46680	+	2.46680i	−0.0875987	+	0.0875987i
$794$	−39.8519			−1.41429
$795$	−8.91421	+	19.3984i	−0.316154	+	0.687990i
$796$	6.08079			0.215528
$797$	−1.50601	−	1.50601i	−0.0533456	−	0.0533456i	0.679931	−	0.733276i	$-0.262010\pi$
$797$	−1.50601	−	1.50601i	−0.0533456	−	0.0533456i	−0.733276	+	0.679931i	$0.762010\pi$
$798$	−3.55633	−	3.55633i	−0.125893	−	0.125893i
$799$	−45.9769			−1.62654
$800$	38.8846	+	2.96519i	1.37478	+	0.104835i
$801$	43.6172			1.54114
$802$	3.65448	−	3.65448i	0.129044	−	0.129044i
$803$		0			0
$804$		−	31.9961i		−	1.12842i
$805$	−12.8921	+	28.0548i	−0.454387	+	0.988800i
$806$	−6.77174			−0.238524
$807$	35.8706	+	35.8706i	1.26271	+	1.26271i
$808$	−2.09556	+	2.09556i	−0.0737215	+	0.0737215i
$809$	−14.7669			−0.519177			−0.259589	−	0.965719i	$-0.583587\pi$
$809$	−14.7669			−0.519177			−0.259589	+	0.965719i	$0.583587\pi$
$810$	23.3511	−	8.64693i	0.820474	−	0.303822i
$811$		−	40.6913i		−	1.42886i	−0.699705	−	0.714432i	$-0.746685\pi$
$811$		−	40.6913i		−	1.42886i	0.699705	−	0.714432i	$-0.253315\pi$
$812$	−22.4870	−	22.4870i	−0.789139	−	0.789139i
$813$	−38.4857	−	38.4857i	−1.34975	−	1.34975i
$814$		0			0
$815$	−29.5118	+	10.9282i	−1.03375	+	0.382799i
$816$			63.1687i			2.21135i
$817$	1.55247	+	1.55247i	0.0543139	+	0.0543139i
$818$	23.9283	−	23.9283i	0.836632	−	0.836632i
$819$		−	28.7095i		−	1.00319i
$820$	−1.23657	−	0.568244i	−0.0431828	−	0.0198439i
$821$			4.22766i			0.147546i	0.997275	+	0.0737731i	$0.0235041\pi$
$821$			4.22766i			0.147546i	−0.997275	+	0.0737731i	$0.976496\pi$
$822$	36.8274	−	36.8274i	1.28450	−	1.28450i
$823$	12.5673	−	12.5673i	0.438069	−	0.438069i	−0.453293	−	0.891362i	$-0.649751\pi$
$823$	12.5673	−	12.5673i	0.438069	−	0.438069i	0.891362	+	0.453293i	$0.149751\pi$
$824$	2.17383			0.0757291
$825$		0			0
$826$	12.5564			0.436893
$827$	14.0948	−	14.0948i	0.490125	−	0.490125i	−0.418221	−	0.908346i	$-0.637346\pi$
$827$	14.0948	−	14.0948i	0.490125	−	0.490125i	0.908346	+	0.418221i	$0.137346\pi$
$828$	−48.1588	+	48.1588i	−1.67363	+	1.67363i
$829$		−	29.0707i		−	1.00967i	−0.863217	−	0.504833i	$-0.831554\pi$
$829$		−	29.0707i		−	1.00967i	0.863217	−	0.504833i	$-0.168446\pi$
$830$	10.0419	+	4.61459i	0.348560	+	0.160175i
$831$		−	31.7609i		−	1.10177i
$832$	11.5795	−	11.5795i	0.401448	−	0.401448i
$833$	9.17004	+	9.17004i	0.317723	+	0.317723i
$834$		−	75.3580i		−	2.60944i
$835$	−16.0428	+	5.94066i	−0.555184	+	0.205585i
$836$		0			0
$837$	−7.70110	−	7.70110i	−0.266189	−	0.266189i
$838$	−33.3714	−	33.3714i	−1.15280	−	1.15280i
$839$		−	35.1355i		−	1.21301i	−0.795078	−	0.606507i	$-0.792570\pi$
$839$		−	35.1355i		−	1.21301i	0.795078	−	0.606507i	$-0.207430\pi$
$840$	3.88408	−	1.43828i	0.134013	−	0.0496253i
$841$	38.0838			1.31323
$842$	−28.6635	+	28.6635i	−0.987809	+	0.987809i
$843$	−36.2891	−	36.2891i	−1.24986	−	1.24986i
$844$	38.6768			1.33131
$845$	−6.61344	+	14.3916i	−0.227509	+	0.495088i
$846$			100.744i			3.46365i
$847$		0			0
$848$	−9.85087	+	9.85087i	−0.338280	+	0.338280i
$849$	−31.9242			−1.09564
$850$	37.3976	−	32.0982i	1.28273	−	1.10096i
$851$	4.00704			0.137360
$852$	29.1149	+	29.1149i	0.997458	+	0.997458i
$853$	28.5384	+	28.5384i	0.977138	+	0.977138i	0.999744	−	0.0226067i	$-0.00719656\pi$
$853$	28.5384	+	28.5384i	0.977138	+	0.977138i	−0.0226067	+	0.999744i	$0.507197\pi$
$854$	5.91354			0.202357
$855$	2.17852	−	4.74071i	0.0745037	−	0.162129i
$856$	−4.83610			−0.165294
$857$	−27.5489	+	27.5489i	−0.941052	+	0.941052i	−0.998357	−	0.0573050i	$-0.981749\pi$
$857$	−27.5489	+	27.5489i	−0.941052	+	0.941052i	0.0573050	+	0.998357i	$0.481749\pi$
$858$		0			0
$859$			39.9841i			1.36424i	0.731240	+	0.682120i	$0.238942\pi$
$859$			39.9841i			1.36424i	−0.731240	+	0.682120i	$0.761058\pi$
$860$	20.4601	−	7.57639i	0.697683	−	0.258353i
$861$	−2.03319			−0.0692908
$862$	47.5543	+	47.5543i	1.61971	+	1.61971i
$863$	4.76109	−	4.76109i	0.162069	−	0.162069i	−0.621414	−	0.783483i	$-0.713441\pi$
$863$	4.76109	−	4.76109i	0.162069	−	0.162069i	0.783483	+	0.621414i	$0.213441\pi$
$864$	59.8462			2.03601
$865$	−15.6693	−	42.3150i	−0.532772	−	1.43875i
$866$		−	6.28376i		−	0.213531i
$867$	17.1324	+	17.1324i	0.581848	+	0.581848i
$868$	3.89692	+	3.89692i	0.132270	+	0.132270i
$869$		0			0
$870$	44.0227	−	95.7987i	1.49251	−	3.24788i
$871$		−	14.3574i		−	0.486484i
$872$	−1.68748	−	1.68748i	−0.0571453	−	0.0571453i
$873$	54.4812	−	54.4812i	1.84391	−	1.84391i
$874$			5.35380i			0.181095i
$875$	−20.5488	−	11.4096i	−0.694675	−	0.385716i
$876$		−	42.3318i		−	1.43026i
$877$	−30.9177	+	30.9177i	−1.04402	+	1.04402i	−0.0450311	+	0.998986i	$0.514339\pi$
$877$	−30.9177	+	30.9177i	−1.04402	+	1.04402i	−0.998986	+	0.0450311i	$0.985661\pi$
$878$	−17.1332	+	17.1332i	−0.578216	+	0.578216i
$879$	2.52988			0.0853307
$880$		0			0
$881$	57.5099			1.93756			0.968779	−	0.247928i	$-0.0797496\pi$
$881$	57.5099			1.93756			0.968779	+	0.247928i	$0.0797496\pi$
$882$	20.0933	−	20.0933i	0.676577	−	0.676577i
$883$	−14.1589	+	14.1589i	−0.476485	+	0.476485i	−0.904006	−	0.427521i	$-0.859387\pi$
$883$	−14.1589	+	14.1589i	−0.476485	+	0.476485i	0.427521	+	0.904006i	$0.359387\pi$
$884$		−	22.5773i		−	0.759357i
$885$	6.94017	+	18.7420i	0.233291	+	0.630004i
$886$		−	4.98205i		−	0.167375i
$887$	−19.8276	+	19.8276i	−0.665745	+	0.665745i	−0.956728	−	0.290983i	$-0.906018\pi$
$887$	−19.8276	+	19.8276i	−0.665745	+	0.665745i	0.290983	+	0.956728i	$0.406018\pi$
$888$	−0.380094	−	0.380094i	−0.0127551	−	0.0127551i
$889$			43.5493i			1.46060i
$890$	−11.8319	−	31.9521i	−0.396607	−	1.07104i
$891$		0			0
$892$	34.9499	+	34.9499i	1.17021	+	1.17021i
$893$	2.68852	+	2.68852i	0.0899680	+	0.0899680i
$894$			78.2973i			2.61865i
$895$	13.1973	−	28.7189i	0.441137	−	0.959968i
$896$	5.03399			0.168174
$897$	−33.1573	+	33.1573i	−1.10709	+	1.10709i
$898$	35.7069	+	35.7069i	1.19156	+	1.19156i
$899$	−11.6254			−0.387728
$900$	−33.7674	−	39.3425i	−1.12558	−	1.31142i
$901$			16.3474i			0.544610i
$902$		0			0
$903$	23.0490	−	23.0490i	0.767023	−	0.767023i
$904$	5.78838			0.192519
$905$	5.15363	+	2.36827i	0.171313	+	0.0787238i
$906$	47.8032			1.58816
$907$	39.1963	+	39.1963i	1.30149	+	1.30149i	0.927385	+	0.374108i	$0.122051\pi$
$907$	39.1963	+	39.1963i	1.30149	+	1.30149i	0.374108	+	0.927385i	$0.377949\pi$
$908$	7.99613	+	7.99613i	0.265361	+	0.265361i
$909$	55.4243			1.83831
$910$	−21.0314	+	7.78794i	−0.697184	+	0.258168i
$911$	−4.11600			−0.136369			−0.0681847	−	0.997673i	$-0.521721\pi$
$911$	−4.11600			−0.136369			−0.0681847	+	0.997673i	$0.521721\pi$
$912$	3.69382	−	3.69382i	0.122315	−	0.122315i
$913$		0			0
$914$			21.5288i			0.712108i
$915$	3.26853	+	8.82667i	0.108054	+	0.291801i
$916$	3.02445			0.0999306
$917$	−8.92174	−	8.92174i	−0.294622	−	0.294622i
$918$	53.4795	−	53.4795i	1.76509	−	1.76509i
$919$	−13.6377			−0.449866			−0.224933	−	0.974374i	$-0.572216\pi$
$919$	−13.6377			−0.449866			−0.224933	+	0.974374i	$0.572216\pi$
$920$	−4.00621	−	1.84099i	−0.132081	−	0.0606956i
$921$			19.1491i			0.630984i
$922$	−5.71573	−	5.71573i	−0.188237	−	0.188237i
$923$	13.0646	+	13.0646i	0.430025	+	0.430025i
$924$		0			0
$925$	−0.231937	+	3.04155i	−0.00762603	+	0.100006i
$926$		−	19.6297i		−	0.645073i
$927$	−28.7473	−	28.7473i	−0.944184	−	0.944184i
$928$	45.1711	−	45.1711i	1.48281	−	1.48281i
$929$			37.4259i			1.22791i	0.789343	+	0.613953i	$0.210421\pi$
$929$			37.4259i			1.22791i	−0.789343	+	0.613953i	$0.789579\pi$
$930$	−7.62897	+	16.6016i	−0.250164	+	0.544387i
$931$		−	1.07245i		−	0.0351480i
$932$	−28.1235	+	28.1235i	−0.921216	+	0.921216i
$933$	−11.4437	+	11.4437i	−0.374652	+	0.374652i
$934$	−14.3841			−0.470661
$935$		0			0
$936$	4.09971			0.134003
$937$	15.2477	−	15.2477i	0.498119	−	0.498119i	−0.412733	−	0.910852i	$-0.635426\pi$
$937$	15.2477	−	15.2477i	0.498119	−	0.498119i	0.910852	+	0.412733i	$0.135426\pi$
$938$	−17.2092	+	17.2092i	−0.561900	+	0.561900i
$939$		−	46.8902i		−	1.53020i
$940$	35.4323	−	13.1206i	1.15567	−	0.427947i
$941$		−	12.8201i		−	0.417922i	−0.977924	−	0.208961i	$-0.932992\pi$
$941$		−	12.8201i		−	0.417922i	0.977924	−	0.208961i	$-0.0670082\pi$
$942$	14.0741	−	14.0741i	0.458558	−	0.458558i
$943$	1.53041	+	1.53041i	0.0498369	+	0.0498369i
$944$			13.0419i			0.424477i
$945$	−32.7745	−	15.0610i	−1.06615	−	0.489934i
$946$		0			0
$947$	−2.58080	−	2.58080i	−0.0838646	−	0.0838646i	0.663930	−	0.747795i	$-0.268887\pi$
$947$	−2.58080	−	2.58080i	−0.0838646	−	0.0838646i	−0.747795	+	0.663930i	$0.768887\pi$
$948$	13.7836	+	13.7836i	0.447670	+	0.447670i
$949$		−	18.9953i		−	0.616614i
$950$	−4.06381	−	0.309890i	−0.131847	−	0.0100542i
$951$	−29.8073			−0.966568
$952$	2.24262	−	2.24262i	0.0726838	−	0.0726838i
$953$	21.0759	+	21.0759i	0.682714	+	0.682714i	0.960611	−	0.277897i	$-0.0896373\pi$
$953$	21.0759	+	21.0759i	0.682714	+	0.682714i	−0.277897	+	0.960611i	$0.589637\pi$
$954$	35.8202			1.15972
$955$	−19.2665	−	8.85360i	−0.623449	−	0.286496i
$956$			45.3978i			1.46827i
$957$		0			0
$958$	−7.46881	+	7.46881i	−0.241306	+	0.241306i
$959$	−19.0196			−0.614176
$960$	−15.3429	−	41.4337i	−0.495191	−	1.33727i
$961$	−28.9854			−0.935012
$962$	2.05812	+	2.05812i	0.0663565	+	0.0663565i
$963$	63.9537	+	63.9537i	2.06088	+	2.06088i
$964$	35.8190			1.15365
$965$	8.92628	+	24.1055i	0.287347	+	0.775982i
$966$	79.4863			2.55743
$967$	−12.1066	+	12.1066i	−0.389321	+	0.389321i	−0.874445	−	0.485124i	$-0.838774\pi$
$967$	−12.1066	+	12.1066i	−0.389321	+	0.389321i	0.485124	+	0.874445i	$0.338774\pi$
$968$		0			0
$969$		−	6.12984i		−	0.196919i
$970$	−54.6895	−	25.1317i	−1.75598	−	0.806929i
$971$	−47.0304			−1.50928			−0.754639	−	0.656140i	$-0.772188\pi$
$971$	−47.0304			−1.50928			−0.754639	+	0.656140i	$0.772188\pi$
$972$	8.29988	+	8.29988i	0.266219	+	0.266219i
$973$	−19.4595	+	19.4595i	−0.623841	+	0.623841i
$974$	−27.3630			−0.876766
$975$	−23.2489	−	27.0873i	−0.744561	−	0.867489i
$976$			6.14217i			0.196606i
$977$	−41.6754	−	41.6754i	−1.33331	−	1.33331i	−0.902388	−	0.430925i	$-0.858187\pi$
$977$	−41.6754	−	41.6754i	−1.33331	−	1.33331i	−0.430925	−	0.902388i	$-0.641813\pi$
$978$	57.2885	+	57.2885i	1.83188	+	1.83188i
$979$		0			0
$980$	−9.68383	−	4.45004i	−0.309339	−	0.142151i
$981$			44.6312i			1.42497i
$982$	45.2438	+	45.2438i	1.44379	+	1.44379i
$983$	−4.44301	+	4.44301i	−0.141710	+	0.141710i	−0.774403	−	0.632693i	$-0.781950\pi$
$983$	−4.44301	+	4.44301i	−0.141710	+	0.141710i	0.632693	+	0.774403i	$0.281950\pi$
$984$		−	0.290338i		−	0.00925565i
$985$	−56.5726	+	20.9489i	−1.80255	+	0.667487i
$986$		−	80.7312i		−	2.57101i
$987$	39.9158	−	39.9158i	1.27053	−	1.27053i
$988$	−1.32022	+	1.32022i	−0.0420018	+	0.0420018i
$989$	−34.6986			−1.10335
$990$		0			0
$991$	−18.0262			−0.572622			−0.286311	−	0.958137i	$-0.592429\pi$
$991$	−18.0262			−0.572622			−0.286311	+	0.958137i	$0.592429\pi$
$992$	−7.82799	+	7.82799i	−0.248539	+	0.248539i
$993$	66.7470	−	66.7470i	2.11815	−	2.11815i
$994$		−	31.3190i		−	0.993378i
$995$	3.07402	−	6.68943i	0.0974528	−	0.212069i
$996$		−	13.6597i		−	0.432823i
$997$	−26.5471	+	26.5471i	−0.840756	+	0.840756i	−0.988957	−	0.148202i	$-0.952652\pi$
$997$	−26.5471	+	26.5471i	−0.840756	+	0.840756i	0.148202	+	0.988957i	$0.452652\pi$
$998$	−54.0013	−	54.0013i	−1.70938	−	1.70938i
$999$			4.68116i			0.148105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.c.362.17	yes	40
5.3	odd	4	inner	605.2.e.c.483.4	yes	40
11.2	odd	10		605.2.m.g.282.17		160
11.3	even	5		605.2.m.g.112.4		160
11.4	even	5		605.2.m.g.457.17		160
11.5	even	5		605.2.m.g.602.4		160
11.6	odd	10		605.2.m.g.602.17		160
11.7	odd	10		605.2.m.g.457.4		160
11.8	odd	10		605.2.m.g.112.17		160
11.9	even	5		605.2.m.g.282.4		160
11.10	odd	2	inner	605.2.e.c.362.4	✓	40
55.3	odd	20		605.2.m.g.233.4		160
55.8	even	20		605.2.m.g.233.17		160
55.13	even	20		605.2.m.g.403.4		160
55.18	even	20		605.2.m.g.578.4		160
55.28	even	20		605.2.m.g.118.4		160
55.38	odd	20		605.2.m.g.118.17		160
55.43	even	4	inner	605.2.e.c.483.17	yes	40
55.48	odd	20		605.2.m.g.578.17		160
55.53	odd	20		605.2.m.g.403.17		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.c.362.4	✓	40	11.10	odd	2	inner
605.2.e.c.362.17	yes	40	1.1	even	1	trivial
605.2.e.c.483.4	yes	40	5.3	odd	4	inner
605.2.e.c.483.17	yes	40	55.43	even	4	inner
605.2.m.g.112.4		160	11.3	even	5
605.2.m.g.112.17		160	11.8	odd	10
605.2.m.g.118.4		160	55.28	even	20
605.2.m.g.118.17		160	55.38	odd	20
605.2.m.g.233.4		160	55.3	odd	20
605.2.m.g.233.17		160	55.8	even	20
605.2.m.g.282.4		160	11.9	even	5
605.2.m.g.282.17		160	11.2	odd	10
605.2.m.g.403.4		160	55.13	even	20
605.2.m.g.403.17		160	55.53	odd	20
605.2.m.g.457.4		160	11.7	odd	10
605.2.m.g.457.17		160	11.4	even	5
605.2.m.g.578.4		160	55.18	even	20
605.2.m.g.578.17		160	55.48	odd	20
605.2.m.g.602.4		160	11.5	even	5
605.2.m.g.602.17		160	11.6	odd	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38689 - 1.38689i) q^{2} +(-2.07537 + 2.07537i) q^{3} -1.84694i q^{4} +(-2.03181 - 0.933683i) q^{5} +5.75663i q^{6} +(1.48652 - 1.48652i) q^{7} +(0.212274 + 0.212274i) q^{8} -5.61432i q^{9} +O(q^{10})\)	\(q+(1.38689 - 1.38689i) q^{2} +(-2.07537 + 2.07537i) q^{3} -1.84694i q^{4} +(-2.03181 - 0.933683i) q^{5} +5.75663i q^{6} +(1.48652 - 1.48652i) q^{7} +(0.212274 + 0.212274i) q^{8} -5.61432i q^{9} +(-4.11281 + 1.52298i) q^{10} +(3.83309 + 3.83309i) q^{12} +(1.72000 + 1.72000i) q^{13} -4.12327i q^{14} +(6.15449 - 2.27901i) q^{15} +4.28269 q^{16} +(3.55353 - 3.55353i) q^{17} +(-7.78646 - 7.78646i) q^{18} -0.415589 q^{19} +(-1.72446 + 3.75263i) q^{20} +6.17014i q^{21} +(4.64435 - 4.64435i) q^{23} -0.881094 q^{24} +(3.25647 + 3.79412i) q^{25} +4.77092 q^{26} +(5.42568 + 5.42568i) q^{27} +(-2.74551 - 2.74551i) q^{28} +8.19047 q^{29} +(5.37487 - 11.6964i) q^{30} -1.41938 q^{31} +(5.51508 - 5.51508i) q^{32} -9.85672i q^{34} +(-4.40824 + 1.63238i) q^{35} -10.3693 q^{36} +(0.431389 + 0.431389i) q^{37} +(-0.576378 + 0.576378i) q^{38} -7.13929 q^{39} +(-0.233103 - 0.629496i) q^{40} +0.329520i q^{41} +(8.55732 + 8.55732i) q^{42} +(-3.73558 - 3.73558i) q^{43} +(-5.24199 + 11.4072i) q^{45} -12.8824i q^{46} +(-6.46918 - 6.46918i) q^{47} +(-8.88816 + 8.88816i) q^{48} +2.58054i q^{49} +(9.77842 + 0.745664i) q^{50} +14.7498i q^{51} +(3.17675 - 3.17675i) q^{52} +(-2.30016 + 2.30016i) q^{53} +15.0497 q^{54} +0.631097 q^{56} +(0.862501 - 0.862501i) q^{57} +(11.3593 - 11.3593i) q^{58} +3.04525i q^{59} +(-4.20921 - 11.3670i) q^{60} +1.43418i q^{61} +(-1.96853 + 1.96853i) q^{62} +(-8.34577 - 8.34577i) q^{63} -6.73227i q^{64} +(-1.88878 - 5.10065i) q^{65} +(-4.17367 - 4.17367i) q^{67} +(-6.56316 - 6.56316i) q^{68} +19.2775i q^{69} +(-3.84983 + 8.37769i) q^{70} +7.59566 q^{71} +(1.19177 - 1.19177i) q^{72} +(-5.52189 - 5.52189i) q^{73} +1.19658 q^{74} +(-14.6326 - 1.11582i) q^{75} +0.767569i q^{76} +(-9.90142 + 9.90142i) q^{78} +3.59595 q^{79} +(-8.70159 - 3.99867i) q^{80} -5.67764 q^{81} +(0.457009 + 0.457009i) q^{82} +(-1.78181 - 1.78181i) q^{83} +11.3959 q^{84} +(-10.5379 + 3.90221i) q^{85} -10.3617 q^{86} +(-16.9983 + 16.9983i) q^{87} +7.76892i q^{89} +(8.55050 + 23.0907i) q^{90} +5.11362 q^{91} +(-8.57784 - 8.57784i) q^{92} +(2.94574 - 2.94574i) q^{93} -17.9441 q^{94} +(0.844397 + 0.388028i) q^{95} +22.8917i q^{96} +(9.70396 + 9.70396i) q^{97} +(3.57894 + 3.57894i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 4 q^{5}+O(q^{10}) \) 40 * q + 8 * q^3 - 4 * q^5	\( 40 q + 8 q^{3} - 4 q^{5} - 32 q^{12} + 32 q^{15} - 24 q^{16} + 32 q^{20} - 24 q^{23} - 52 q^{25} - 8 q^{26} + 32 q^{27} + 16 q^{31} - 40 q^{36} + 36 q^{37} + 32 q^{38} + 32 q^{42} + 64 q^{45} + 32 q^{47} - 16 q^{48} - 68 q^{53} + 80 q^{56} + 132 q^{58} - 64 q^{60} - 88 q^{67} - 8 q^{70} - 16 q^{75} - 248 q^{78} - 164 q^{80} - 40 q^{81} + 100 q^{82} - 80 q^{86} - 96 q^{91} - 56 q^{92} + 24 q^{93} - 68 q^{97}+O(q^{100}) \) 40 * q + 8 * q^3 - 4 * q^5 - 32 * q^12 + 32 * q^15 - 24 * q^16 + 32 * q^20 - 24 * q^23 - 52 * q^25 - 8 * q^26 + 32 * q^27 + 16 * q^31 - 40 * q^36 + 36 * q^37 + 32 * q^38 + 32 * q^42 + 64 * q^45 + 32 * q^47 - 16 * q^48 - 68 * q^53 + 80 * q^56 + 132 * q^58 - 64 * q^60 - 88 * q^67 - 8 * q^70 - 16 * q^75 - 248 * q^78 - 164 * q^80 - 40 * q^81 + 100 * q^82 - 80 * q^86 - 96 * q^91 - 56 * q^92 + 24 * q^93 - 68 * q^97

Introduction

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