LMFDB - Embedded newform 950.2.j.i.349.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(49,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} - 36 x^{13} + 67 x^{12} + 34 x^{11} - 24 x^{10} + 182 x^{9} - 495 x^{8} + \cdots + 16 $ x^16 - 4x^15 + 8x^14 - 36x^13 + 67x^12 + 34x^11 - 24x^10 + 182x^9 - 495x^8 - 166x^7 + 258x^6 - 1292x^5 + 2920x^4 + 1176x^3 + 200x^2 + 80*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.6
Root			$1.61874 + 0.433740i$ of defining polynomial
Character	$\chi$	$=$	950.349
Dual form			950.2.j.i.49.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.410396 + 0.236942i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.236942 + 0.410396i) q^{6} +2.19155i q^{7} -1.00000i q^{8} +(-1.38772 + 2.40360i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.410396 + 0.236942i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.236942 + 0.410396i) q^{6} +2.19155i q^{7} -1.00000i q^{8} +(-1.38772 + 2.40360i) q^{9} -4.96699 q^{11} +0.473885i q^{12} +(-1.97656 - 1.14116i) q^{13} +(1.09578 + 1.89794i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.86770 + 3.38772i) q^{17} +2.77543i q^{18} +(3.12466 + 3.03916i) q^{19} +(-0.519272 - 0.899406i) q^{21} +(-4.30154 + 2.48349i) q^{22} +(-6.65511 - 3.84233i) q^{23} +(0.236942 + 0.410396i) q^{24} -2.28233 q^{26} -2.73689i q^{27} +(1.89794 + 1.09578i) q^{28} +(0.983494 - 1.70346i) q^{29} +7.58388 q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.03843 - 1.17689i) q^{33} +(-3.38772 + 5.86770i) q^{34} +(1.38772 + 2.40360i) q^{36} +7.38864i q^{37} +(4.22562 + 1.06966i) q^{38} +1.08156 q^{39} +(-5.70393 - 9.87950i) q^{41} +(-0.899406 - 0.519272i) q^{42} +(-8.79756 + 5.07927i) q^{43} +(-2.48349 + 4.30154i) q^{44} -7.68466 q^{46} +(3.62999 + 2.09578i) q^{47} +(0.410396 + 0.236942i) q^{48} +2.19709 q^{49} +(1.60539 - 2.78061i) q^{51} +(-1.97656 + 1.14116i) q^{52} +(3.62999 + 2.09578i) q^{53} +(-1.36844 - 2.37022i) q^{54} +2.19155 q^{56} +(-2.00245 - 0.506896i) q^{57} -1.96699i q^{58} +(1.72044 + 2.97988i) q^{59} +(2.36160 - 4.09041i) q^{61} +(6.56783 - 3.79194i) q^{62} +(-5.26761 - 3.04126i) q^{63} -1.00000 q^{64} +(1.17689 - 2.03843i) q^{66} +(0.700134 + 0.404223i) q^{67} +6.77543i q^{68} +3.64164 q^{69} +(5.59854 + 9.69696i) q^{71} +(2.40360 + 1.38772i) q^{72} +(-4.20628 + 2.42850i) q^{73} +(3.69432 + 6.39875i) q^{74} +(4.19432 - 1.18645i) q^{76} -10.8854i q^{77} +(0.936659 - 0.540781i) q^{78} +(7.63427 + 13.2229i) q^{79} +(-3.51467 - 6.08758i) q^{81} +(-9.87950 - 5.70393i) q^{82} +12.7232i q^{83} -1.03854 q^{84} +(-5.07927 + 8.79756i) q^{86} +0.932126i q^{87} +4.96699i q^{88} +(-1.78233 + 3.08709i) q^{89} +(2.50093 - 4.33173i) q^{91} +(-6.65511 + 3.84233i) q^{92} +(-3.11239 + 1.79694i) q^{93} +4.19155 q^{94} +0.473885 q^{96} +(0.149247 - 0.0861680i) q^{97} +(1.90273 - 1.09854i) q^{98} +(6.89277 - 11.9386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{6} + 22 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^6 + 22 * q^9	$ 16 q + 8 q^{4} + 2 q^{6} + 22 q^{9} + 20 q^{11} + 12 q^{14} - 8 q^{16} - 2 q^{21} - 2 q^{24} - 36 q^{26} - 34 q^{29} + 44 q^{31} - 10 q^{34} - 22 q^{36} + 72 q^{39} + 14 q^{41} + 10 q^{44} - 24 q^{46} - 88 q^{49} - 18 q^{51} + 16 q^{54} + 24 q^{56} - 28 q^{59} - 18 q^{61} - 16 q^{64} - 8 q^{66} - 108 q^{69} + 28 q^{71} - 8 q^{74} + 34 q^{79} - 72 q^{81} - 4 q^{84} - 26 q^{86} - 28 q^{89} - 50 q^{91} + 56 q^{94} - 4 q^{96} + 120 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^6 + 22 * q^9 + 20 * q^11 + 12 * q^14 - 8 * q^16 - 2 * q^21 - 2 * q^24 - 36 * q^26 - 34 * q^29 + 44 * q^31 - 10 * q^34 - 22 * q^36 + 72 * q^39 + 14 * q^41 + 10 * q^44 - 24 * q^46 - 88 * q^49 - 18 * q^51 + 16 * q^54 + 24 * q^56 - 28 * q^59 - 18 * q^61 - 16 * q^64 - 8 * q^66 - 108 * q^69 + 28 * q^71 - 8 * q^74 + 34 * q^79 - 72 * q^81 - 4 * q^84 - 26 * q^86 - 28 * q^89 - 50 * q^91 + 56 * q^94 - 4 * q^96 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.410396	+	0.236942i	−0.236942	+	0.136799i	−0.613771	−	0.789484i	$-0.710348\pi$
$3$	−0.410396	+	0.236942i	−0.236942	+	0.136799i	0.376828	+	0.926283i	$0.377015\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.236942	+	0.410396i	−0.0967313	+	0.167544i
$7$			2.19155i			0.828330i	0.910202	+	0.414165i	$0.135926\pi$
$7$			2.19155i			0.828330i	−0.910202	+	0.414165i	$0.864074\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.38772	+	2.40360i	−0.462572	+	0.801199i
$10$		0			0
$11$	−4.96699			−1.49760			−0.748802	−	0.662794i	$-0.769370\pi$
$11$	−4.96699			−1.49760			−0.748802	+	0.662794i	$0.769370\pi$
$12$			0.473885i			0.136799i
$13$	−1.97656	−	1.14116i	−0.548198	−	0.316502i	0.200197	−	0.979756i	$-0.435842\pi$
$13$	−1.97656	−	1.14116i	−0.548198	−	0.316502i	−0.748395	+	0.663253i	$0.769175\pi$
$14$	1.09578	+	1.89794i	0.292859	+	0.507246i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.86770	+	3.38772i	−1.42313	+	0.821642i	−0.996565	−	0.0828169i	$-0.973608\pi$
$17$	−5.86770	+	3.38772i	−1.42313	+	0.821642i	−0.426561	+	0.904459i	$0.640275\pi$
$18$			2.77543i			0.654176i
$19$	3.12466	+	3.03916i	0.716846	+	0.697232i
$19$	3.12466	+	3.03916i	0.716846	+	0.697232i
$20$		0			0
$21$	−0.519272	−	0.899406i	−0.113314	−	0.196266i
$22$	−4.30154	+	2.48349i	−0.917091	+	0.529483i
$23$	−6.65511	−	3.84233i	−1.38769	−	0.801181i	−0.394632	−	0.918839i	$-0.629128\pi$
$23$	−6.65511	−	3.84233i	−1.38769	−	0.801181i	−0.993054	+	0.117658i	$0.962461\pi$
$24$	0.236942	+	0.410396i	0.0483656	+	0.0837718i
$25$		0			0
$26$	−2.28233			−0.447602
$27$		−	2.73689i		−	0.526715i
$28$	1.89794	+	1.09578i	0.358677	+	0.207082i
$29$	0.983494	−	1.70346i	0.182630	−	0.316325i	−0.760145	−	0.649753i	$-0.774872\pi$
$29$	0.983494	−	1.70346i	0.182630	−	0.316325i	0.942775	+	0.333428i	$0.108206\pi$
$30$		0			0
$31$	7.58388			1.36210			0.681052	−	0.732235i	$-0.261523\pi$
$31$	7.58388			1.36210			0.681052	+	0.732235i	$0.261523\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	2.03843	−	1.17689i	0.354846	−	0.204870i
$34$	−3.38772	+	5.86770i	−0.580989	+	1.00630i
$35$		0			0
$36$	1.38772	+	2.40360i	0.231286	+	0.400599i
$37$			7.38864i			1.21469i	0.794440	+	0.607343i	$0.207764\pi$
$37$			7.38864i			1.21469i	−0.794440	+	0.607343i	$0.792236\pi$
$38$	4.22562	+	1.06966i	0.685485	+	0.173522i
$39$	1.08156			0.173188
$40$		0			0
$41$	−5.70393	−	9.87950i	−0.890804	−	1.54292i	−0.838913	−	0.544266i	$-0.816808\pi$
$41$	−5.70393	−	9.87950i	−0.890804	−	1.54292i	−0.0518913	−	0.998653i	$-0.516525\pi$
$42$	−0.899406	−	0.519272i	−0.138781	−	0.0801254i
$43$	−8.79756	+	5.07927i	−1.34161	+	0.774582i	−0.987044	−	0.160448i	$-0.948706\pi$
$43$	−8.79756	+	5.07927i	−1.34161	+	0.774582i	−0.354570	+	0.935029i	$0.615373\pi$
$44$	−2.48349	+	4.30154i	−0.374401	+	0.648481i
$45$		0			0
$46$	−7.68466			−1.13304
$47$	3.62999	+	2.09578i	0.529489	+	0.305701i	0.740808	−	0.671717i	$-0.234443\pi$
$47$	3.62999	+	2.09578i	0.529489	+	0.305701i	−0.211319	+	0.977417i	$0.567776\pi$
$48$	0.410396	+	0.236942i	0.0592356	+	0.0341997i
$49$	2.19709			0.313870
$50$		0			0
$51$	1.60539	−	2.78061i	0.224799	−	0.389364i
$52$	−1.97656	+	1.14116i	−0.274099	+	0.158251i
$53$	3.62999	+	2.09578i	0.498618	+	0.287877i	0.728143	−	0.685426i	$-0.240384\pi$
$53$	3.62999	+	2.09578i	0.498618	+	0.287877i	−0.229525	+	0.973303i	$0.573717\pi$
$54$	−1.36844	−	2.37022i	−0.186222	−	0.322545i
$55$		0			0
$56$	2.19155			0.292859
$57$	−2.00245	−	0.506896i	−0.265232	−	0.0671401i
$58$		−	1.96699i		−	0.258278i
$59$	1.72044	+	2.97988i	0.223982	+	0.387948i	0.956013	−	0.293323i	$-0.0947611\pi$
$59$	1.72044	+	2.97988i	0.223982	+	0.387948i	−0.732032	+	0.681271i	$0.761428\pi$
$60$		0			0
$61$	2.36160	−	4.09041i	0.302372	−	0.523724i	−0.674301	−	0.738457i	$-0.735555\pi$
$61$	2.36160	−	4.09041i	0.302372	−	0.523724i	0.976673	+	0.214733i	$0.0688882\pi$
$62$	6.56783	−	3.79194i	0.834115	−	0.481577i
$63$	−5.26761	−	3.04126i	−0.663657	−	0.383162i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	1.17689	−	2.03843i	0.144865	−	0.250914i
$67$	0.700134	+	0.404223i	0.0855350	+	0.0493836i	0.542157	−	0.840277i	$-0.317608\pi$
$67$	0.700134	+	0.404223i	0.0855350	+	0.0493836i	−0.456622	+	0.889661i	$0.650941\pi$
$68$			6.77543i			0.821642i
$69$	3.64164			0.438402
$70$		0			0
$71$	5.59854	+	9.69696i	0.664425	+	1.15082i	0.979441	+	0.201731i	$0.0646568\pi$
$71$	5.59854	+	9.69696i	0.664425	+	1.15082i	−0.315016	+	0.949086i	$0.602010\pi$
$72$	2.40360	+	1.38772i	0.283266	+	0.163544i
$73$	−4.20628	+	2.42850i	−0.492308	+	0.284234i	−0.725531	−	0.688189i	$-0.758406\pi$
$73$	−4.20628	+	2.42850i	−0.492308	+	0.284234i	0.233224	+	0.972423i	$0.425073\pi$
$74$	3.69432	+	6.39875i	0.429456	+	0.743840i
$75$		0			0
$76$	4.19432	−	1.18645i	0.481122	−	0.136095i
$77$		−	10.8854i		−	1.24051i
$78$	0.936659	−	0.540781i	0.106056	−	0.0612313i
$79$	7.63427	+	13.2229i	0.858922	+	1.48770i	0.872958	+	0.487796i	$0.162199\pi$
$79$	7.63427	+	13.2229i	0.858922	+	1.48770i	−0.0140356	+	0.999901i	$0.504468\pi$
$80$		0			0
$81$	−3.51467	−	6.08758i	−0.390518	−	0.676398i
$82$	−9.87950	−	5.70393i	−1.09101	−	0.629894i
$83$			12.7232i			1.39655i	0.715828	+	0.698276i	$0.246049\pi$
$83$			12.7232i			1.39655i	−0.715828	+	0.698276i	$0.753951\pi$
$84$	−1.03854			−0.113314
$85$		0			0
$86$	−5.07927	+	8.79756i	−0.547712	+	0.948665i
$87$			0.932126i			0.0999343i
$88$			4.96699i			0.529483i
$89$	−1.78233	+	3.08709i	−0.188927	+	0.327230i	−0.944893	−	0.327380i	$-0.893834\pi$
$89$	−1.78233	+	3.08709i	−0.188927	+	0.327230i	0.755966	+	0.654611i	$0.227167\pi$
$90$		0			0
$91$	2.50093	−	4.33173i	0.262168	−	0.454089i
$92$	−6.65511	+	3.84233i	−0.693843	+	0.400591i
$93$	−3.11239	+	1.79694i	−0.322740	+	0.186334i
$94$	4.19155			0.432326
$95$		0			0
$96$	0.473885			0.0483656
$97$	0.149247	−	0.0861680i	0.0151538	−	0.00874903i	−0.492404	−	0.870367i	$-0.663882\pi$
$97$	0.149247	−	0.0861680i	0.0151538	−	0.00874903i	0.507558	+	0.861618i	$0.330548\pi$
$98$	1.90273	−	1.09854i	0.192205	−	0.110970i
$99$	6.89277	−	11.9386i	0.692750	−	1.19988i
$100$		0			0
$101$	−7.41199	+	12.8379i	−0.737521	+	1.27742i	0.216088	+	0.976374i	$0.430670\pi$
$101$	−7.41199	+	12.8379i	−0.737521	+	1.27742i	−0.953609	+	0.301049i	$0.902663\pi$
$102$		−	3.21077i		−	0.317914i
$103$		−	14.6031i		−	1.43889i	−0.694552	−	0.719443i	$-0.744397\pi$
$103$		−	14.6031i		−	1.43889i	0.694552	−	0.719443i	$-0.255603\pi$
$104$	−1.14116	+	1.97656i	−0.111900	+	0.193817i
$105$		0			0
$106$	4.19155			0.407120
$107$		−	0.363891i		−	0.0351787i	−0.999845	−	0.0175893i	$-0.994401\pi$
$107$		−	0.363891i		−	0.0351787i	0.999845	−	0.0175893i	$-0.00559915\pi$
$108$	−2.37022	−	1.36844i	−0.228074	−	0.131679i
$109$	−6.61776	−	11.4623i	−0.633867	−	1.09789i	−0.986754	−	0.162224i	$-0.948133\pi$
$109$	−6.61776	−	11.4623i	−0.633867	−	1.09789i	0.352887	−	0.935666i	$-0.385200\pi$
$110$		0			0
$111$	−1.75068	−	3.03227i	−0.166167	−	0.287810i
$112$	1.89794	−	1.09578i	0.179339	−	0.103541i
$113$		−	17.4894i		−	1.64527i	−0.568572	−	0.822633i	$-0.692504\pi$
$113$		−	17.4894i		−	1.64527i	0.568572	−	0.822633i	$-0.307496\pi$
$114$	−1.98762	+	0.562242i	−0.186158	+	0.0526588i
$115$		0			0
$116$	−0.983494	−	1.70346i	−0.0913151	−	0.158162i
$117$	5.48580	−	3.16723i	0.507162	−	0.292810i
$118$	2.97988	+	1.72044i	0.274320	+	0.158379i
$119$	−7.42437	−	12.8594i	−0.680591	−	1.17882i
$120$		0			0
$121$	13.6710			1.24282
$122$		−	4.72320i		−	0.427619i
$123$	4.68174	+	2.70301i	0.422138	+	0.243722i
$124$	3.79194	−	6.56783i	0.340526	−	0.589809i
$125$		0			0
$126$	−6.08251			−0.541873
$127$	4.04039	+	2.33272i	0.358527	+	0.206995i	0.668434	−	0.743771i	$-0.266965\pi$
$127$	4.04039	+	2.33272i	0.358527	+	0.206995i	−0.309908	+	0.950767i	$0.600298\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	2.40699	−	4.16903i	0.211924	−	0.367062i
$130$		0			0
$131$	−0.449610	−	0.778747i	−0.0392826	−	0.0680395i	0.845716	−	0.533634i	$-0.179174\pi$
$131$	−0.449610	−	0.778747i	−0.0392826	−	0.0680395i	−0.884998	+	0.465594i	$0.845841\pi$
$132$		−	2.35378i		−	0.204870i
$133$	−6.66049	+	6.84786i	−0.577538	+	0.593785i
$134$	0.808445			0.0698390
$135$		0			0
$136$	3.38772	+	5.86770i	0.290494	+	0.503151i
$137$	−6.47418	−	3.73787i	−0.553126	−	0.319348i	0.197256	−	0.980352i	$-0.436797\pi$
$137$	−6.47418	−	3.73787i	−0.553126	−	0.319348i	−0.750382	+	0.661004i	$0.770130\pi$
$138$	3.15375	−	1.82082i	0.268465	−	0.154999i
$139$	−3.00961	+	5.21280i	−0.255272	+	0.442144i	−0.964969	−	0.262363i	$-0.915498\pi$
$139$	−3.00961	+	5.21280i	−0.255272	+	0.442144i	0.709698	+	0.704506i	$0.248832\pi$
$140$		0			0
$141$	−1.98631			−0.167278
$142$	9.69696	+	5.59854i	0.813751	+	0.469819i
$143$	9.81753	+	5.66815i	0.820983	+	0.473995i
$144$	2.77543			0.231286
$145$		0			0
$146$	−2.42850	+	4.20628i	−0.200984	+	0.348114i
$147$	−0.901676	+	0.520583i	−0.0743690	+	0.0429370i
$148$	6.39875	+	3.69432i	0.525974	+	0.303671i
$149$	2.99034	+	5.17942i	0.244978	+	0.424314i	0.962125	−	0.272607i	$-0.0878859\pi$
$149$	2.99034	+	5.17942i	0.244978	+	0.424314i	−0.717147	+	0.696921i	$0.754553\pi$
$150$		0			0
$151$	6.06777			0.493788			0.246894	−	0.969042i	$-0.420590\pi$
$151$	6.06777			0.493788			0.246894	+	0.969042i	$0.420590\pi$
$152$	3.03916	−	3.12466i	0.246509	−	0.253443i
$153$		−	18.8048i		−	1.52028i
$154$	−5.44271	−	9.42706i	−0.438586	−	0.759654i
$155$		0			0
$156$	0.540781	−	0.936659i	0.0432971	−	0.0749928i
$157$	1.65344	−	0.954613i	0.131959	−	0.0761864i	−0.432567	−	0.901602i	$-0.642392\pi$
$157$	1.65344	−	0.954613i	0.131959	−	0.0761864i	0.564526	+	0.825415i	$0.309059\pi$
$158$	13.2229	+	7.63427i	1.05196	+	0.607350i
$159$	−1.98631			−0.157525
$160$		0			0
$161$	8.42068	−	14.5850i	0.663642	−	1.14946i
$162$	−6.08758	−	3.51467i	−0.478285	−	0.276138i
$163$		−	7.54533i		−	0.590996i	−0.955343	−	0.295498i	$-0.904514\pi$
$163$		−	7.54533i		−	0.590996i	0.955343	−	0.295498i	$-0.0954856\pi$
$164$	−11.4079			−0.890804
$165$		0			0
$166$	6.36160	+	11.0186i	0.493756	+	0.855211i
$167$	−4.63811	−	2.67782i	−0.358908	−	0.207216i	0.309694	−	0.950836i	$-0.399773\pi$
$167$	−4.63811	−	2.67782i	−0.358908	−	0.207216i	−0.668602	+	0.743621i	$0.733107\pi$
$168$	−0.899406	+	0.519272i	−0.0693907	+	0.0400627i
$169$	−3.89549	−	6.74718i	−0.299653	−	0.519014i
$170$		0			0
$171$	−11.6411	+	3.29292i	−0.890214	+	0.251816i
$172$			10.1585i			0.774582i
$173$	1.36849	−	0.790099i	0.104044	−	0.0600701i	−0.447075	−	0.894497i	$-0.647534\pi$
$173$	1.36849	−	0.790099i	0.104044	−	0.0600701i	0.551119	+	0.834426i	$0.314201\pi$
$174$	0.466063	+	0.807244i	0.0353321	+	0.0611970i
$175$		0			0
$176$	2.48349	+	4.30154i	0.187200	+	0.324241i
$177$	−1.41212	−	0.815288i	−0.106142	−	0.0612808i
$178$			3.56466i			0.267183i
$179$	4.18155			0.312544			0.156272	−	0.987714i	$-0.450052\pi$
$179$	4.18155			0.312544			0.156272	+	0.987714i	$0.450052\pi$
$180$		0			0
$181$	1.87350	−	3.24500i	0.139256	−	0.241199i	−0.787959	−	0.615728i	$-0.788862\pi$
$181$	1.87350	−	3.24500i	0.139256	−	0.241199i	0.927215	+	0.374529i	$0.122196\pi$
$182$		−	5.00185i		−	0.370762i
$183$			2.23825i			0.165456i
$184$	−3.84233	+	6.65511i	−0.283260	+	0.490621i
$185$		0			0
$186$	−1.79694	+	3.11239i	−0.131758	+	0.228212i
$187$	29.1448	−	16.8267i	2.13128	−	1.23049i
$188$	3.62999	−	2.09578i	0.264744	−	0.152850i
$189$	5.99804			0.436293
$190$		0			0
$191$	−1.96699			−0.142326			−0.0711631	−	0.997465i	$-0.522671\pi$
$191$	−1.96699			−0.142326			−0.0711631	+	0.997465i	$0.522671\pi$
$192$	0.410396	−	0.236942i	0.0296178	−	0.0170998i
$193$	−11.9965	+	6.92621i	−0.863530	+	0.498559i	−0.865193	−	0.501439i	$-0.832804\pi$
$193$	−11.9965	+	6.92621i	−0.863530	+	0.498559i	0.00166273	+	0.999999i	$0.499471\pi$
$194$	0.0861680	−	0.149247i	0.00618650	−	0.0107153i
$195$		0			0
$196$	1.09854	−	1.90273i	0.0784674	−	0.135910i
$197$			17.2218i			1.22701i	0.789693	+	0.613503i	$0.210240\pi$
$197$			17.2218i			1.22701i	−0.789693	+	0.613503i	$0.789760\pi$
$198$		−	13.7855i		−	0.979696i
$199$	4.60723	−	7.97995i	0.326598	−	0.565684i	−0.655237	−	0.755424i	$-0.727431\pi$
$199$	4.60723	−	7.97995i	0.326598	−	0.565684i	0.981834	+	0.189740i	$0.0607644\pi$
$200$		0			0
$201$	−0.383110			−0.0270225
$202$			14.8240i			1.04301i
$203$	3.73323	+	2.15538i	0.262021	+	0.151278i
$204$	−1.60539	−	2.78061i	−0.112400	−	0.194682i
$205$		0			0
$206$	−7.30155	−	12.6467i	−0.508723	−	0.881134i
$207$	18.4708	−	10.6641i	1.28381	−	0.741208i
$208$			2.28233i			0.158251i
$209$	−15.5201	−	15.0955i	−1.07355	−	1.04418i
$210$		0			0
$211$	5.89048	+	10.2026i	0.405518	+	0.702377i	0.994382	−	0.105855i	$-0.0337580\pi$
$211$	5.89048	+	10.2026i	0.405518	+	0.702377i	−0.588864	+	0.808232i	$0.700425\pi$
$212$	3.62999	−	2.09578i	0.249309	−	0.143939i
$213$	−4.59524	−	2.65306i	−0.314861	−	0.181785i
$214$	−0.181945	−	0.315139i	−0.0124375	−	0.0215424i
$215$		0			0
$216$	−2.73689			−0.186222
$217$			16.6205i			1.12827i
$218$	−11.4623	−	6.61776i	−0.776325	−	0.448211i
$219$	1.15083	−	1.99329i	0.0777657	−	0.134694i
$220$		0			0
$221$	15.4638			1.04021
$222$	−3.03227	−	1.75068i	−0.203513	−	0.117498i
$223$	0.517599	−	0.298836i	0.0346610	−	0.0200115i	−0.482569	−	0.875858i	$-0.660296\pi$
$223$	0.517599	−	0.298836i	0.0346610	−	0.0200115i	0.517230	+	0.855846i	$0.326963\pi$
$224$	1.09578	−	1.89794i	0.0732147	−	0.126812i
$225$		0			0
$226$	−8.74471	−	15.1463i	−0.581690	−	1.00752i
$227$			15.3364i			1.01791i	0.860792	+	0.508957i	$0.169969\pi$
$227$			15.3364i			1.01791i	−0.860792	+	0.508957i	$0.830031\pi$
$228$	−1.44021	+	1.48073i	−0.0953804	+	0.0980636i
$229$	−15.5802			−1.02957			−0.514784	−	0.857320i	$-0.672128\pi$
$229$	−15.5802			−1.02957			−0.514784	+	0.857320i	$0.672128\pi$
$230$		0			0
$231$	2.57922	+	4.46734i	0.169700	+	0.293929i
$232$	−1.70346	−	0.983494i	−0.111838	−	0.0645696i
$233$	25.5148	−	14.7310i	1.67153	−	0.965058i	0.704747	−	0.709459i	$-0.251061\pi$
$233$	25.5148	−	14.7310i	1.67153	−	0.965058i	0.966783	−	0.255599i	$-0.0822727\pi$
$234$	3.16723	−	5.48580i	0.207048	−	0.358618i
$235$		0			0
$236$	3.44087			0.223982
$237$	−6.26615	−	3.61776i	−0.407030	−	0.234999i
$238$	−12.8594	−	7.42437i	−0.833550	−	0.481250i
$239$	−1.34825			−0.0872108			−0.0436054	−	0.999049i	$-0.513884\pi$
$239$	−1.34825			−0.0872108			−0.0436054	+	0.999049i	$0.513884\pi$
$240$		0			0
$241$	−13.9331	+	24.1328i	−0.897507	+	1.55453i	−0.0668355	+	0.997764i	$0.521290\pi$
$241$	−13.9331	+	24.1328i	−0.897507	+	1.55453i	−0.830671	+	0.556763i	$0.812043\pi$
$242$	11.8394	−	6.83549i	0.761066	−	0.439402i
$243$	9.99546	+	5.77088i	0.641209	+	0.370202i
$244$	−2.36160	−	4.09041i	−0.151186	−	0.261862i
$245$		0			0
$246$	5.40601			0.344675
$247$	−2.70788	−	9.57282i	−0.172298	−	0.609104i
$248$		−	7.58388i		−	0.481577i
$249$	−3.01467	−	5.22155i	−0.191047	−	0.330902i
$250$		0			0
$251$	−14.4166	+	24.9703i	−0.909968	+	1.57611i	−0.0958610	+	0.995395i	$0.530560\pi$
$251$	−14.4166	+	24.9703i	−0.909968	+	1.57611i	−0.814107	+	0.580715i	$0.802773\pi$
$252$	−5.26761	+	3.04126i	−0.331828	+	0.191581i
$253$	33.0559	+	19.0848i	2.07820	+	1.19985i
$254$	4.66544			0.292736
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.85932	−	1.65083i	−0.178359	−	0.102976i	0.408162	−	0.912909i	$-0.366170\pi$
$257$	−2.85932	−	1.65083i	−0.178359	−	0.102976i	−0.586522	+	0.809934i	$0.699503\pi$
$258$		−	4.81398i		−	0.299705i
$259$	−16.1926			−1.00616
$260$		0			0
$261$	2.72962	+	4.72784i	0.168959	+	0.292646i
$262$	−0.778747	−	0.449610i	−0.0481112	−	0.0277770i
$263$	9.69696	−	5.59854i	0.597940	−	0.345221i	−0.170291	−	0.985394i	$-0.554471\pi$
$263$	9.69696	−	5.59854i	0.597940	−	0.345221i	0.768231	+	0.640173i	$0.221137\pi$
$264$	−1.17689	−	2.03843i	−0.0724326	−	0.125457i
$265$		0			0
$266$	−2.34422	+	9.26067i	−0.143734	+	0.567808i
$267$		−	1.68924i		−	0.103380i
$268$	0.700134	−	0.404223i	0.0427675	−	0.0246918i
$269$	−14.1998	−	24.5948i	−0.865777	−	1.49957i	−0.866273	−	0.499570i	$-0.833491\pi$
$269$	−14.1998	−	24.5948i	−0.865777	−	1.49957i	0.000496384	−	1.00000i	$-0.499842\pi$
$270$		0			0
$271$	−10.2850	−	17.8142i	−0.624772	−	1.08214i	−0.988585	−	0.150665i	$-0.951859\pi$
$271$	−10.2850	−	17.8142i	−0.624772	−	1.08214i	0.363813	−	0.931472i	$-0.381475\pi$
$272$	5.86770	+	3.38772i	0.355781	+	0.205410i
$273$			2.37030i			0.143457i
$274$	−7.47574			−0.451626
$275$		0			0
$276$	1.82082	−	3.15375i	0.109601	−	0.189834i
$277$			8.99447i			0.540425i	0.962801	+	0.270213i	$0.0870940\pi$
$277$			8.99447i			0.540425i	−0.962801	+	0.270213i	$0.912906\pi$
$278$			6.01922i			0.361009i
$279$	−10.5243	+	18.2286i	−0.630072	+	1.09132i
$280$		0			0
$281$	4.78233	−	8.28324i	0.285290	−	0.494137i	−0.687390	−	0.726289i	$-0.741243\pi$
$281$	4.78233	−	8.28324i	0.285290	−	0.494137i	0.972679	+	0.232152i	$0.0745768\pi$
$282$	−1.72020	+	0.993157i	−0.102436	+	0.0591416i
$283$	−2.17902	+	1.25806i	−0.129529	+	0.0747836i	−0.563364	−	0.826209i	$-0.690493\pi$
$283$	−2.17902	+	1.25806i	−0.129529	+	0.0747836i	0.433835	+	0.900992i	$0.357160\pi$
$284$	11.1971			0.664425
$285$		0			0
$286$	11.3363			0.670330
$287$	21.6515	−	12.5005i	1.27805	−	0.737880i
$288$	2.40360	−	1.38772i	0.141633	−	0.0817720i
$289$	14.4532	−	25.0338i	0.850191	−	1.47257i
$290$		0			0
$291$	−0.0408337	+	0.0707260i	−0.00239371	+	0.00414603i
$292$			4.85699i			0.284234i
$293$		−	0.406116i		−	0.0237256i	−0.999930	−	0.0118628i	$-0.996224\pi$
$293$		−	0.406116i		−	0.0237256i	0.999930	−	0.0118628i	$-0.00377613\pi$
$294$	−0.520583	+	0.901676i	−0.0303610	+	0.0525868i
$295$		0			0
$296$	7.38864			0.429456
$297$			13.5941i			0.788809i
$298$	5.17942	+	2.99034i	0.300036	+	0.173226i
$299$	8.76946	+	15.1892i	0.507151	+	0.878411i
$300$		0			0
$301$	−11.1315	−	19.2803i	−0.641609	−	1.11130i
$302$	5.25484	−	3.03388i	0.302382	−	0.174580i
$303$		−	7.02486i		−	0.403568i
$304$	1.06966	−	4.22562i	0.0613493	−	0.242356i
$305$		0			0
$306$	−9.40238	−	16.2854i	−0.537498	−	0.930975i
$307$	−18.1095	+	10.4555i	−1.03357	+	0.596729i	−0.918004	−	0.396571i	$-0.870200\pi$
$307$	−18.1095	+	10.4555i	−1.03357	+	0.596729i	−0.115561	+	0.993300i	$0.536867\pi$
$308$	−9.42706	−	5.44271i	−0.537156	−	0.310127i
$309$	3.46009	+	5.99305i	0.196838	+	0.340933i
$310$		0			0
$311$	−9.92397			−0.562737			−0.281368	−	0.959600i	$-0.590788\pi$
$311$	−9.92397			−0.562737			−0.281368	+	0.959600i	$0.590788\pi$
$312$		−	1.08156i		−	0.0612313i
$313$	12.6919	+	7.32766i	0.717388	+	0.414184i	0.813790	−	0.581158i	$-0.197400\pi$
$313$	12.6919	+	7.32766i	0.717388	+	0.414184i	−0.0964027	+	0.995342i	$0.530734\pi$
$314$	0.954613	−	1.65344i	0.0538719	−	0.0933089i
$315$		0			0
$316$	15.2685			0.858922
$317$	−30.3490	−	17.5220i	−1.70457	−	0.984133i	−0.941001	−	0.338404i	$-0.890113\pi$
$317$	−30.3490	−	17.5220i	−1.70457	−	0.984133i	−0.763567	−	0.645729i	$-0.776554\pi$
$318$	−1.72020	+	0.993157i	−0.0964639	+	0.0556935i
$319$	−4.88500	+	8.46107i	−0.273508	+	0.473729i
$320$		0			0
$321$	0.0862211	+	0.149339i	0.00481239	+	0.00833531i
$322$		−	16.8414i		−	0.938532i
$323$	−28.6304	−	7.24742i	−1.59304	−	0.403257i
$324$	−7.02933			−0.390518
$325$		0			0
$326$	−3.77267	−	6.53445i	−0.208949	−	0.361910i
$327$	5.43181	+	3.13606i	0.300380	+	0.173424i
$328$	−9.87950	+	5.70393i	−0.545504	+	0.314947i
$329$	−4.59301	+	7.95533i	−0.253221	+	0.438591i
$330$		0			0
$331$	21.4464			1.17880			0.589401	−	0.807841i	$-0.299364\pi$
$331$	21.4464			1.17880			0.589401	+	0.807841i	$0.299364\pi$
$332$	11.0186	+	6.36160i	0.604725	+	0.349138i
$333$	−17.7593	−	10.2533i	−0.973204	−	0.561880i
$334$	−5.35563			−0.293047
$335$		0			0
$336$	−0.519272	+	0.899406i	−0.0283286	+	0.0490666i
$337$	−25.7371	+	14.8593i	−1.40199	+	0.809438i	−0.994597	−	0.103815i	$-0.966895\pi$
$337$	−25.7371	+	14.8593i	−1.40199	+	0.809438i	−0.407392	+	0.913254i	$0.633562\pi$
$338$	−6.74718	−	3.89549i	−0.366998	−	0.211886i
$339$	4.14398	+	7.17759i	0.225070	+	0.389833i
$340$		0			0
$341$	−37.6690			−2.03989
$342$	−8.43499	+	8.67228i	−0.456112	+	0.468943i
$343$			20.1559i			1.08832i
$344$	5.07927	+	8.79756i	0.273856	+	0.474332i
$345$		0			0
$346$	0.790099	−	1.36849i	0.0424760	−	0.0735705i
$347$	1.86456	−	1.07651i	0.100095	−	0.0577898i	−0.449117	−	0.893473i	$-0.648261\pi$
$347$	1.86456	−	1.07651i	0.100095	−	0.0577898i	0.549212	+	0.835683i	$0.314928\pi$
$348$	0.807244	+	0.466063i	0.0432728	+	0.0249836i
$349$	−17.5031			−0.936920			−0.468460	−	0.883485i	$-0.655191\pi$
$349$	−17.5031			−0.936920			−0.468460	+	0.883485i	$0.655191\pi$
$350$		0			0
$351$	−3.12324	+	5.40961i	−0.166706	+	0.288744i
$352$	4.30154	+	2.48349i	0.229273	+	0.132371i
$353$			21.3171i			1.13459i	0.823513	+	0.567297i	$0.192011\pi$
$353$			21.3171i			1.13459i	−0.823513	+	0.567297i	$0.807989\pi$
$354$	−1.63058			−0.0866642
$355$		0			0
$356$	1.78233	+	3.08709i	0.0944633	+	0.163615i
$357$	6.09386	+	3.51829i	0.322521	+	0.186208i
$358$	3.62133	−	2.09077i	0.191393	−	0.110501i
$359$	12.8547	+	22.2650i	0.678445	+	1.17510i	0.975449	+	0.220226i	$0.0706793\pi$
$359$	12.8547	+	22.2650i	0.678445	+	1.17510i	−0.297004	+	0.954876i	$0.595987\pi$
$360$		0			0
$361$	0.526988	+	18.9927i	0.0277362	+	0.999615i
$362$		−	3.74700i		−	0.196938i
$363$	−5.61051	+	3.23923i	−0.294476	+	0.170016i
$364$	−2.50093	−	4.33173i	−0.131084	−	0.227044i
$365$		0			0
$366$	1.11913	+	1.93838i	0.0584977	+	0.101321i
$367$	12.4204	+	7.17092i	0.648339	+	0.374319i	0.787820	−	0.615906i	$-0.211210\pi$
$367$	12.4204	+	7.17092i	0.648339	+	0.374319i	−0.139480	+	0.990225i	$0.544543\pi$
$368$			7.68466i			0.400591i
$369$	31.6618			1.64825
$370$		0			0
$371$	−4.59301	+	7.95533i	−0.238457	+	0.413020i
$372$			3.59388i			0.186334i
$373$		−	0.646114i		−	0.0334545i	−0.999860	−	0.0167273i	$-0.994675\pi$
$373$		−	0.646114i		−	0.0334545i	0.999860	−	0.0167273i	$-0.00532470\pi$
$374$	16.8267	−	29.1448i	0.870090	−	1.50704i
$375$		0			0
$376$	2.09578	−	3.62999i	0.108081	−	0.187203i
$377$	−3.88786	+	2.24466i	−0.200235	+	0.115606i
$378$	5.19446	−	2.99902i	0.267174	−	0.154253i
$379$	−13.1255			−0.674213			−0.337107	−	0.941466i	$-0.609448\pi$
$379$	−13.1255			−0.674213			−0.337107	+	0.941466i	$0.609448\pi$
$380$		0			0
$381$	−2.21088			−0.113267
$382$	−1.70346	+	0.983494i	−0.0871567	+	0.0503199i
$383$	9.69696	−	5.59854i	0.495492	−	0.286072i	−0.231358	−	0.972869i	$-0.574317\pi$
$383$	9.69696	−	5.59854i	0.495492	−	0.286072i	0.726850	+	0.686796i	$0.240984\pi$
$384$	0.236942	−	0.410396i	0.0120914	−	0.0209429i
$385$		0			0
$386$	−6.92621	+	11.9965i	−0.352535	+	0.610608i
$387$		−	28.1944i		−	1.43320i
$388$		−	0.172336i		−	0.00874903i
$389$	−11.0037	+	19.0590i	−0.557909	+	0.966327i	0.439761	+	0.898115i	$0.355063\pi$
$389$	−11.0037	+	19.0590i	−0.557909	+	0.966327i	−0.997671	+	0.0682127i	$0.978270\pi$
$390$		0			0
$391$	52.0669			2.63314
$392$		−	2.19709i		−	0.110970i
$393$	0.369036	+	0.213063i	0.0186154	+	0.0107476i
$394$	8.61092	+	14.9145i	0.433812	+	0.751384i
$395$		0			0
$396$	−6.89277	−	11.9386i	−0.346375	−	0.599939i
$397$	−8.27996	+	4.78044i	−0.415559	+	0.239923i	−0.693176	−	0.720769i	$-0.743789\pi$
$397$	−8.27996	+	4.78044i	−0.415559	+	0.239923i	0.277616	+	0.960692i	$0.410456\pi$
$398$		−	9.21446i		−	0.461879i
$399$	1.11089	−	4.38849i	0.0556141	−	0.219699i
$400$		0			0
$401$	−7.71543	−	13.3635i	−0.385290	−	0.667343i	0.606519	−	0.795069i	$-0.292565\pi$
$401$	−7.71543	−	13.3635i	−0.385290	−	0.667343i	−0.991809	+	0.127726i	$0.959232\pi$
$402$	−0.331783	+	0.191555i	−0.0165478	+	0.00955389i
$403$	−14.9900	−	8.65446i	−0.746703	−	0.431109i
$404$	7.41199	+	12.8379i	0.368760	+	0.638712i
$405$		0			0
$406$	4.31076			0.213940
$407$		−	36.6993i		−	1.81912i
$408$	−2.78061	−	1.60539i	−0.137661	−	0.0794785i
$409$	−7.70164	+	13.3396i	−0.380822	+	0.659602i	−0.991180	−	0.132523i	$-0.957692\pi$
$409$	−7.70164	+	13.3396i	−0.380822	+	0.659602i	0.610358	+	0.792125i	$0.291025\pi$
$410$		0			0
$411$	3.54264			0.174745
$412$	−12.6467	−	7.30155i	−0.623056	−	0.359721i
$413$	−6.53058	+	3.77043i	−0.321349	+	0.185531i
$414$	10.6641	−	18.4708i	0.524113	−	0.907791i
$415$		0			0
$416$	1.14116	+	1.97656i	0.0559502	+	0.0969086i
$417$		−	2.85242i		−	0.139683i
$418$	−20.9886	−	5.31300i	−1.02659	−	0.259867i
$419$	37.5581			1.83484			0.917418	−	0.397926i	$-0.130270\pi$
$419$	37.5581			1.83484			0.917418	+	0.397926i	$0.130270\pi$
$420$		0			0
$421$	1.91844	+	3.32283i	0.0934990	+	0.161945i	0.908981	−	0.416837i	$-0.136861\pi$
$421$	1.91844	+	3.32283i	0.0934990	+	0.161945i	−0.815482	+	0.578782i	$0.803528\pi$
$422$	10.2026	+	5.89048i	0.496656	+	0.286744i
$423$	−10.0748	+	5.81669i	−0.489854	+	0.282817i
$424$	2.09578	−	3.62999i	0.101780	−	0.176288i
$425$		0			0
$426$	−5.30613			−0.257083
$427$	8.96437	+	5.17558i	0.433816	+	0.250464i
$428$	−0.315139	−	0.181945i	−0.0152328	−	0.00879466i
$429$	−5.37210			−0.259367
$430$		0			0
$431$	−4.56282	+	7.90303i	−0.219783	+	0.380676i	−0.954742	−	0.297436i	$-0.903868\pi$
$431$	−4.56282	+	7.90303i	−0.219783	+	0.380676i	0.734958	+	0.678112i	$0.237202\pi$
$432$	−2.37022	+	1.36844i	−0.114037	+	0.0658393i
$433$	7.49573	+	4.32766i	0.360222	+	0.207974i	0.669178	−	0.743102i	$-0.266646\pi$
$433$	7.49573	+	4.32766i	0.360222	+	0.207974i	−0.308956	+	0.951076i	$0.599980\pi$
$434$	8.31024	+	14.3938i	0.398904	+	0.690923i
$435$		0			0
$436$	−13.2355			−0.633867
$437$	−9.11749	−	32.2319i	−0.436149	−	1.54186i
$438$		−	2.30166i		−	0.109977i
$439$	−2.03757	−	3.52917i	−0.0972477	−	0.168438i	0.813297	−	0.581849i	$-0.197671\pi$
$439$	−2.03757	−	3.52917i	−0.0972477	−	0.168438i	−0.910544	+	0.413411i	$0.864337\pi$
$440$		0			0
$441$	−3.04893	+	5.28091i	−0.145187	+	0.251472i
$442$	13.3920	−	7.73189i	0.636993	−	0.367768i
$443$	2.37501	+	1.37121i	0.112840	+	0.0651482i	0.555358	−	0.831612i	$-0.312581\pi$
$443$	2.37501	+	1.37121i	0.112840	+	0.0651482i	−0.442518	+	0.896760i	$0.645915\pi$
$444$	−3.50136			−0.166167
$445$		0			0
$446$	0.298836	−	0.517599i	0.0141503	−	0.0245090i
$447$	−2.45445	−	1.41707i	−0.116091	−	0.0670253i
$448$		−	2.19155i		−	0.103541i
$449$	20.7753			0.980448			0.490224	−	0.871596i	$-0.336915\pi$
$449$	20.7753			0.980448			0.490224	+	0.871596i	$0.336915\pi$
$450$		0			0
$451$	28.3314	+	49.0713i	1.33407	+	2.31068i
$452$	−15.1463	−	8.74471i	−0.712421	−	0.411317i
$453$	−2.49019	+	1.43771i	−0.116999	+	0.0675496i
$454$	7.66821	+	13.2817i	0.359887	+	0.623342i
$455$		0			0
$456$	−0.506896	+	2.00245i	−0.0237376	+	0.0937735i
$457$		−	5.15669i		−	0.241220i	−0.992700	−	0.120610i	$-0.961515\pi$
$457$		−	5.15669i		−	0.241220i	0.992700	−	0.120610i	$-0.0384850\pi$
$458$	−13.4928	+	7.79010i	−0.630479	+	0.364007i
$459$	9.27181	+	16.0592i	0.432771	+	0.749581i
$460$		0			0
$461$	−17.7397	−	30.7261i	−0.826221	−	1.43106i	−0.900983	−	0.433855i	$-0.857153\pi$
$461$	−17.7397	−	30.7261i	−0.826221	−	1.43106i	0.0747623	−	0.997201i	$-0.476180\pi$
$462$	4.46734	+	2.57922i	0.207839	+	0.119996i
$463$			39.3280i			1.82773i	0.406019	+	0.913865i	$0.366917\pi$
$463$			39.3280i			1.82773i	−0.406019	+	0.913865i	$0.633083\pi$
$464$	−1.96699			−0.0913151
$465$		0			0
$466$	14.7310	−	25.5148i	0.682399	−	1.18195i
$467$			9.87174i			0.456810i	0.973566	+	0.228405i	$0.0733510\pi$
$467$			9.87174i			0.456810i	−0.973566	+	0.228405i	$0.926649\pi$
$468$		−	6.33445i		−	0.292810i
$469$	−0.885876	+	1.53438i	−0.0409059	+	0.0708512i
$470$		0			0
$471$	−0.452376	+	0.783539i	−0.0208444	+	0.0361036i
$472$	2.97988	−	1.72044i	0.137160	−	0.0791895i
$473$	43.6974	−	25.2287i	2.00921	−	1.16002i
$474$	−7.23553			−0.332339
$475$		0			0
$476$	−14.8487			−0.680591
$477$	−10.0748	+	5.81669i	−0.461294	+	0.266328i
$478$	−1.16762	+	0.674124i	−0.0534055	+	0.0308337i
$479$	−9.36431	+	16.2195i	−0.427866	+	0.741086i	−0.996683	−	0.0813778i	$-0.974068\pi$
$479$	−9.36431	+	16.2195i	−0.427866	+	0.741086i	0.568817	+	0.822464i	$0.307401\pi$
$480$		0			0
$481$	8.43166	−	14.6041i	0.384451	−	0.665888i
$482$			27.8661i			1.26927i
$483$			7.98086i			0.363142i
$484$	6.83549	−	11.8394i	0.310704	−	0.538155i
$485$		0			0
$486$	11.5418			0.523545
$487$			17.9129i			0.811711i	0.913937	+	0.405856i	$0.133026\pi$
$487$			17.9129i			0.811711i	−0.913937	+	0.405856i	$0.866974\pi$
$488$	−4.09041	−	2.36160i	−0.185164	−	0.106905i
$489$	1.78781	+	3.09658i	0.0808475	+	0.140032i
$490$		0			0
$491$	−15.0101	−	25.9982i	−0.677396	−	1.17328i	−0.975762	−	0.218832i	$-0.929775\pi$
$491$	−15.0101	−	25.9982i	−0.677396	−	1.17328i	0.298367	−	0.954451i	$-0.403558\pi$
$492$	4.68174	−	2.70301i	0.211069	−	0.121861i
$493$			13.3272i			0.600227i
$494$	−7.13150	−	6.93637i	−0.320861	−	0.312082i
$495$		0			0
$496$	−3.79194	−	6.56783i	−0.170263	−	0.294904i
$497$	−21.2514	+	12.2695i	−0.953257	+	0.550363i
$498$	−5.22155	−	3.01467i	−0.233983	−	0.135090i
$499$	4.73966	+	8.20932i	0.212176	+	0.367500i	0.952395	−	0.304866i	$-0.0986116\pi$
$499$	4.73966	+	8.20932i	0.212176	+	0.367500i	−0.740219	+	0.672366i	$0.765278\pi$
$500$		0			0
$501$	2.53795			0.113387
$502$			28.8332i			1.28689i
$503$	4.20947	+	2.43034i	0.187691	+	0.108363i	0.590901	−	0.806744i	$-0.298772\pi$
$503$	4.20947	+	2.43034i	0.187691	+	0.108363i	−0.403210	+	0.915107i	$0.632106\pi$
$504$	−3.04126	+	5.26761i	−0.135468	+	0.234638i
$505$		0			0
$506$	38.1696			1.69685
$507$	3.19738	+	1.84601i	0.142001	+	0.0819842i
$508$	4.04039	−	2.33272i	0.179263	−	0.103498i
$509$	−14.5467	+	25.1957i	−0.644773	+	1.11678i	0.339581	+	0.940577i	$0.389715\pi$
$509$	−14.5467	+	25.1957i	−0.644773	+	1.11678i	−0.984354	+	0.176202i	$0.943619\pi$
$510$		0			0
$511$	−5.32218	−	9.21829i	−0.235440	−	0.407793i
$512$			1.00000i			0.0441942i
$513$	8.31785	−	8.55185i	0.367242	−	0.377573i
$514$	−3.30166			−0.145630
$515$		0			0
$516$	−2.40699	−	4.16903i	−0.105962	−	0.183531i
$517$	−18.0301	−	10.4097i	−0.792964	−	0.457818i
$518$	−14.0232	+	8.09631i	−0.616145	+	0.355731i
$519$	−0.374416	+	0.648507i	−0.0164350	+	0.0284663i
$520$		0			0
$521$	−8.76175			−0.383859			−0.191930	−	0.981409i	$-0.561475\pi$
$521$	−8.76175			−0.383859			−0.191930	+	0.981409i	$0.561475\pi$
$522$	4.72784	+	2.72962i	0.206932	+	0.119472i
$523$	2.33365	+	1.34733i	0.102043	+	0.0589147i	0.550153	−	0.835064i	$-0.314569\pi$
$523$	2.33365	+	1.34733i	0.102043	+	0.0589147i	−0.448110	+	0.893978i	$0.647903\pi$
$524$	−0.899220			−0.0392826
$525$		0			0
$526$	5.59854	−	9.69696i	0.244108	−	0.422808i
$527$	−44.4999	+	25.6920i	−1.93845	+	1.11916i
$528$	−2.03843	−	1.17689i	−0.0887114	−	0.0512176i
$529$	18.0270	+	31.2237i	0.783782	+	1.35755i
$530$		0			0
$531$	−9.54991			−0.414431
$532$	2.60018	+	9.19208i	0.112732	+	0.398527i
$533$			26.0365i			1.12777i
$534$	−0.844619	−	1.46292i	−0.0365502	−	0.0633068i
$535$		0			0
$536$	0.404223	−	0.700134i	0.0174598	−	0.0302412i
$537$	−1.71609	+	0.990786i	−0.0740548	+	0.0427556i
$538$	−24.5948	−	14.1998i	−1.06036	−	0.612197i
$539$	−10.9129			−0.470052
$540$		0			0
$541$	21.9890	−	38.0861i	0.945382	−	1.63745i	0.190398	−	0.981707i	$-0.439022\pi$
$541$	21.9890	−	38.0861i	0.945382	−	1.63745i	0.754984	−	0.655743i	$-0.227644\pi$
$542$	−17.8142	−	10.2850i	−0.765186	−	0.441780i
$543$			1.77565i			0.0762003i
$544$	6.77543			0.290494
$545$		0			0
$546$	1.18515	+	2.05274i	0.0507197	+	0.0878492i
$547$	16.4393	+	9.49121i	0.702892	+	0.405815i	0.808424	−	0.588601i	$-0.200321\pi$
$547$	16.4393	+	9.49121i	0.702892	+	0.405815i	−0.105532	+	0.994416i	$0.533654\pi$
$548$	−6.47418	+	3.73787i	−0.276563	+	0.159674i
$549$	6.55447	+	11.3527i	0.279738	+	0.484520i
$550$		0			0
$551$	8.25018	−	2.33374i	0.351469	−	0.0994206i
$552$		−	3.64164i		−	0.154999i
$553$	−28.9788	+	16.7309i	−1.23230	+	0.711471i
$554$	4.49723	+	7.78944i	0.191069	+	0.330941i
$555$		0			0
$556$	3.00961	+	5.21280i	0.127636	+	0.221072i
$557$	4.36351	+	2.51927i	0.184888	+	0.106745i	0.589587	−	0.807705i	$-0.299290\pi$
$557$	4.36351	+	2.51927i	0.184888	+	0.106745i	−0.404699	+	0.914450i	$0.632624\pi$
$558$			21.0485i			0.891056i
$559$	23.1851			0.980627
$560$		0			0
$561$	−7.97394	+	13.8113i	−0.336660	+	0.583112i
$562$		−	9.56466i		−	0.403461i
$563$			0.334560i			0.0141000i	0.999975	+	0.00705002i	$0.00224411\pi$
$563$			0.334560i			0.0141000i	−0.999975	+	0.00705002i	$0.997756\pi$
$564$	−0.993157	+	1.72020i	−0.0418194	+	0.0724334i
$565$		0			0
$566$	−1.25806	+	2.17902i	−0.0528800	+	0.0915909i
$567$	13.3413	−	7.70258i	0.560280	−	0.323478i
$568$	9.69696	−	5.59854i	0.406875	−	0.234910i
$569$	−2.30155			−0.0964859			−0.0482430	−	0.998836i	$-0.515362\pi$
$569$	−2.30155			−0.0964859			−0.0482430	+	0.998836i	$0.515362\pi$
$570$		0			0
$571$	−23.6131			−0.988178			−0.494089	−	0.869411i	$-0.664498\pi$
$571$	−23.6131			−0.988178			−0.494089	+	0.869411i	$0.664498\pi$
$572$	9.81753	−	5.66815i	0.410491	−	0.236997i
$573$	0.807244	−	0.466063i	0.0337231	−	0.0194701i
$574$	12.5005	−	21.6515i	0.521760	−	0.903715i
$575$		0			0
$576$	1.38772	−	2.40360i	0.0578215	−	0.100150i
$577$			1.59399i			0.0663587i	0.999449	+	0.0331793i	$0.0105632\pi$
$577$			1.59399i			0.0663587i	−0.999449	+	0.0331793i	$0.989437\pi$
$578$		−	28.9065i		−	1.20235i
$579$	3.28222	−	5.68498i	0.136405	−	0.236260i
$580$		0			0
$581$	−27.8836			−1.15681
$582$			0.0816674i			0.00338522i
$583$	−18.0301	−	10.4097i	−0.746732	−	0.431126i
$584$	2.42850	+	4.20628i	0.100492	+	0.174057i
$585$		0			0
$586$	−0.203058	−	0.351707i	−0.00838826	−	0.0145289i
$587$	8.42524	−	4.86431i	0.347747	−	0.200772i	−0.315946	−	0.948777i	$-0.602322\pi$
$587$	8.42524	−	4.86431i	0.347747	−	0.200772i	0.663692	+	0.748006i	$0.268988\pi$
$588$			1.04117i			0.0429370i
$589$	23.6970	+	23.0486i	0.976419	+	0.949702i
$590$		0			0
$591$	−4.08058	−	7.06778i	−0.167853	−	0.290729i
$592$	6.39875	−	3.69432i	0.262987	−	0.151836i
$593$	−14.0254	−	8.09757i	−0.575954	−	0.332527i	0.183570	−	0.983007i	$-0.441235\pi$
$593$	−14.0254	−	8.09757i	−0.575954	−	0.332527i	−0.759524	+	0.650480i	$0.774568\pi$
$594$	6.79705	+	11.7728i	0.278886	+	0.483045i
$595$		0			0
$596$	5.98067			0.244978
$597$			4.36659i			0.178713i
$598$	15.1892	+	8.76946i	0.621131	+	0.358610i
$599$	11.6159	−	20.1194i	0.474614	−	0.822055i	−0.524964	−	0.851125i	$-0.675921\pi$
$599$	11.6159	−	20.1194i	0.474614	−	0.822055i	0.999577	+	0.0290696i	$0.00925444\pi$
$600$		0			0
$601$	44.9899			1.83518			0.917588	−	0.397532i	$-0.130133\pi$
$601$	44.9899			1.83518			0.917588	+	0.397532i	$0.130133\pi$
$602$	−19.2803	−	11.1315i	−0.785807	−	0.453686i
$603$	−1.94318	+	1.12189i	−0.0791322	+	0.0456870i
$604$	3.03388	−	5.25484i	0.123447	−	0.213816i
$605$		0			0
$606$	−3.51243	−	6.08371i	−0.142683	−	0.247134i
$607$		−	36.6965i		−	1.48947i	−0.667363	−	0.744733i	$-0.732577\pi$
$607$		−	36.6965i		−	1.48947i	0.667363	−	0.744733i	$-0.267423\pi$
$608$	−1.18645	−	4.19432i	−0.0481170	−	0.170102i
$609$	−2.04280			−0.0827786
$610$		0			0
$611$	−4.78326	−	8.28484i	−0.193510	−	0.335169i
$612$	−16.2854	−	9.40238i	−0.658298	−	0.380069i
$613$	20.2806	−	11.7090i	0.819124	−	0.472921i	−0.0309903	−	0.999520i	$-0.509866\pi$
$613$	20.2806	−	11.7090i	0.819124	−	0.472921i	0.850114	+	0.526598i	$0.176533\pi$
$614$	−10.4555	+	18.1095i	−0.421951	+	0.730841i
$615$		0			0
$616$	−10.8854			−0.438586
$617$	14.8398	+	8.56777i	0.597428	+	0.344925i	0.768029	−	0.640415i	$-0.221238\pi$
$617$	14.8398	+	8.56777i	0.597428	+	0.344925i	−0.170601	+	0.985340i	$0.554571\pi$
$618$	5.99305	+	3.46009i	0.241076	+	0.139185i
$619$	−25.3556			−1.01913			−0.509564	−	0.860433i	$-0.670193\pi$
$619$	−25.3556			−1.01913			−0.509564	+	0.860433i	$0.670193\pi$
$620$		0			0
$621$	−10.5160	+	18.2143i	−0.421994	+	0.730915i
$622$	−8.59441	+	4.96199i	−0.344604	+	0.198957i
$623$	−6.76552	−	3.90607i	−0.271055	−	0.156494i
$624$	−0.540781	−	0.936659i	−0.0216485	−	0.0374964i
$625$		0			0
$626$	14.6553			0.585745
$627$	9.94617	+	2.51775i	0.397212	+	0.100549i
$628$		−	1.90923i		−	0.0761864i
$629$	−25.0306	−	43.3543i	−0.998036	−	1.72865i
$630$		0			0
$631$	−14.2956	+	24.7607i	−0.569098	+	0.985707i	0.427557	+	0.903988i	$0.359374\pi$
$631$	−14.2956	+	24.7607i	−0.569098	+	0.985707i	−0.996655	+	0.0817184i	$0.973959\pi$
$632$	13.2229	−	7.63427i	0.525980	−	0.303675i
$633$	−4.83486	−	2.79141i	−0.192169	−	0.110949i
$634$	−35.0440			−1.39177
$635$		0			0
$636$	−0.993157	+	1.72020i	−0.0393812	+	0.0682103i
$637$	−4.34267	−	2.50724i	−0.172063	−	0.0993404i
$638$			9.77001i			0.386798i
$639$	−31.0768			−1.22938
$640$		0			0
$641$	−1.82404	−	3.15932i	−0.0720451	−	0.124786i	0.827752	−	0.561094i	$-0.189619\pi$
$641$	−1.82404	−	3.15932i	−0.0720451	−	0.124786i	−0.899797	+	0.436308i	$0.856286\pi$
$642$	0.149339	+	0.0862211i	0.00589396	+	0.00340288i
$643$	25.8870	−	14.9459i	1.02088	−	0.589408i	0.106524	−	0.994310i	$-0.466028\pi$
$643$	25.8870	−	14.9459i	1.02088	−	0.589408i	0.914360	+	0.404902i	$0.132694\pi$
$644$	−8.42068	−	14.5850i	−0.331821	−	0.574731i
$645$		0			0
$646$	−28.4183	+	8.03873i	−1.11810	+	0.316280i
$647$			30.0091i			1.17978i	0.807483	+	0.589890i	$0.200829\pi$
$647$			30.0091i			1.17978i	−0.807483	+	0.589890i	$0.799171\pi$
$648$	−6.08758	+	3.51467i	−0.239143	+	0.138069i
$649$	−8.54539	−	14.8010i	−0.335436	−	0.580992i
$650$		0			0
$651$	−3.93810	−	6.82098i	−0.154346	−	0.267335i
$652$	−6.53445	−	3.77267i	−0.255909	−	0.147749i
$653$			26.4776i			1.03615i	0.855336	+	0.518074i	$0.173351\pi$
$653$			26.4776i			1.03615i	−0.855336	+	0.518074i	$0.826649\pi$
$654$	6.27211			0.245259
$655$		0			0
$656$	−5.70393	+	9.87950i	−0.222701	+	0.385730i
$657$		−	13.4803i		−	0.525915i
$658$			9.18602i			0.358108i
$659$	0.581112	−	1.00652i	0.0226369	−	0.0392083i	−0.854485	−	0.519476i	$-0.826127\pi$
$659$	0.581112	−	1.00652i	0.0226369	−	0.0392083i	0.877122	+	0.480268i	$0.159460\pi$
$660$		0			0
$661$	−15.9899	+	27.6953i	−0.621935	+	1.07722i	0.367190	+	0.930146i	$0.380320\pi$
$661$	−15.9899	+	27.6953i	−0.621935	+	1.07722i	−0.989125	+	0.147077i	$0.953013\pi$
$662$	18.5731	−	10.7232i	0.721865	−	0.416769i
$663$	−6.34627	+	3.66402i	−0.246469	+	0.142299i
$664$	12.7232			0.493756
$665$		0			0
$666$	−20.5067			−0.794618
$667$	−13.0905	+	7.55782i	−0.506867	+	0.292640i
$668$	−4.63811	+	2.67782i	−0.179454	+	0.103608i
$669$	−0.141614	+	0.245282i	−0.00547510	+	0.00948315i
$670$		0			0
$671$	−11.7300	+	20.3170i	−0.452833	+	0.784330i
$672$			1.03854i			0.0400627i
$673$		−	48.3529i		−	1.86387i	−0.362629	−	0.931934i	$-0.618121\pi$
$673$		−	48.3529i		−	1.86387i	0.362629	−	0.931934i	$-0.381879\pi$
$674$	−14.8593	+	25.7371i	−0.572359	+	0.991355i
$675$		0			0
$676$	−7.79097			−0.299653
$677$			33.6964i			1.29506i	0.762041	+	0.647529i	$0.224198\pi$
$677$			33.6964i			1.29506i	−0.762041	+	0.647529i	$0.775802\pi$
$678$	7.17759	+	4.14398i	0.275654	+	0.159149i
$679$	0.188842	+	0.327084i	0.00724708	+	0.0125523i
$680$		0			0
$681$	−3.63384	−	6.29400i	−0.139249	−	0.241187i
$682$	−32.6223	+	18.8345i	−1.24917	+	0.721211i
$683$		−	18.3886i		−	0.703622i	−0.936071	−	0.351811i	$-0.885566\pi$
$683$		−	18.3886i		−	0.703622i	0.936071	−	0.351811i	$-0.114434\pi$
$684$	−2.96878	+	11.7279i	−0.113514	+	0.448428i
$685$		0			0
$686$	10.0780	+	17.4555i	0.384778	+	0.666456i
$687$	6.39405	−	3.69161i	0.243948	−	0.140844i
$688$	8.79756	+	5.07927i	0.335404	+	0.193645i
$689$	−4.78326	−	8.28484i	−0.182228	−	0.315627i
$690$		0			0
$691$	18.2779			0.695322			0.347661	−	0.937620i	$-0.386976\pi$
$691$	18.2779			0.695322			0.347661	+	0.937620i	$0.386976\pi$
$692$		−	1.58020i		−	0.0600701i
$693$	26.1642	+	15.1059i	0.993895	+	0.573825i
$694$	1.07651	−	1.86456i	0.0408636	−	0.0707778i
$695$		0			0
$696$	0.932126			0.0353321
$697$	66.9379	+	38.6466i	2.53545	+	1.46384i
$698$	−15.1581	+	8.75155i	−0.573744	+	0.331251i
$699$	−6.98078	+	12.0911i	−0.264037	+	0.457326i
$700$		0			0
$701$	4.80292	+	8.31891i	0.181404	+	0.314201i	0.942359	−	0.334604i	$-0.108603\pi$
$701$	4.80292	+	8.31891i	0.181404	+	0.314201i	−0.760955	+	0.648805i	$0.775269\pi$
$702$			6.24648i			0.235758i
$703$	−22.4553	+	23.0870i	−0.846917	+	0.870742i
$704$	4.96699			0.187200
$705$		0			0
$706$	10.6585	+	18.4611i	0.401140	+	0.694794i
$707$	−28.1351	−	16.2438i	−1.05813	−	0.610910i
$708$	−1.41212	+	0.815288i	−0.0530708	+	0.0306404i
$709$	10.2630	−	17.7760i	0.385435	−	0.667593i	−0.606394	−	0.795164i	$-0.707385\pi$
$709$	10.2630	−	17.7760i	0.385435	−	0.667593i	0.991829	+	0.127571i	$0.0407180\pi$
$710$		0			0
$711$	−42.3768			−1.58925
$712$	3.08709	+	1.78233i	0.115693	+	0.0667956i
$713$	−50.4715	−	29.1398i	−1.89017	−	1.09129i
$714$	7.03659			0.263338
$715$		0			0
$716$	2.09077	−	3.62133i	0.0781359	−	0.135335i
$717$	0.553315	−	0.319457i	0.0206639	−	0.0119303i
$718$	22.2650	+	12.8547i	0.830922	+	0.479733i
$719$	−4.32220	−	7.48626i	−0.161191	−	0.279190i	0.774105	−	0.633057i	$-0.218200\pi$
$719$	−4.32220	−	7.48626i	−0.161191	−	0.279190i	−0.935296	+	0.353866i	$0.884867\pi$
$720$		0			0
$721$	32.0035			1.19187
$722$	9.95273	+	16.1847i	0.370402	+	0.602331i
$723$		−	13.2053i		−	0.491111i
$724$	−1.87350	−	3.24500i	−0.0696281	−	0.120599i
$725$		0			0
$726$	−3.23923	+	5.61051i	−0.120219	+	0.208226i
$727$	−17.9348	+	10.3547i	−0.665164	+	0.384033i	−0.794242	−	0.607602i	$-0.792132\pi$
$727$	−17.9348	+	10.3547i	−0.665164	+	0.384033i	0.129078	+	0.991634i	$0.458798\pi$
$728$	−4.33173	−	2.50093i	−0.160545	−	0.0926905i
$729$	15.6185			0.578464
$730$		0			0
$731$	34.4143	−	59.6073i	1.27286	−	2.20465i
$732$	1.93838	+	1.11913i	0.0716447	+	0.0413641i
$733$			24.8157i			0.916590i	0.888800	+	0.458295i	$0.151540\pi$
$733$			24.8157i			0.916590i	−0.888800	+	0.458295i	$0.848460\pi$
$734$	14.3418			0.529367
$735$		0			0
$736$	3.84233	+	6.65511i	0.141630	+	0.245311i
$737$	−3.47756	−	2.00777i	−0.128097	−	0.0739571i
$738$	27.4199	−	15.8309i	1.00934	−	0.582743i
$739$	2.07422	+	3.59265i	0.0763013	+	0.132158i	0.901651	−	0.432464i	$-0.142356\pi$
$739$	2.07422	+	3.59265i	0.0763013	+	0.132158i	−0.825350	+	0.564621i	$0.809022\pi$
$740$		0			0
$741$	3.37951	+	3.28704i	0.124149	+	0.120752i
$742$			9.18602i			0.337229i
$743$	0.695343	−	0.401456i	0.0255097	−	0.0147280i	−0.487191	−	0.873295i	$-0.661978\pi$
$743$	0.695343	−	0.401456i	0.0255097	−	0.0147280i	0.512701	+	0.858567i	$0.328645\pi$
$744$	1.79694	+	3.11239i	0.0658791	+	0.114106i
$745$		0			0
$746$	−0.323057	−	0.559551i	−0.0118280	−	0.0204866i
$747$	−30.5814	−	17.6562i	−1.11892	−	0.646007i
$748$		−	33.6535i		−	1.23049i
$749$	0.797487			0.0291395
$750$		0			0
$751$	−16.1292	+	27.9366i	−0.588563	+	1.01942i	0.405858	+	0.913936i	$0.366973\pi$
$751$	−16.1292	+	27.9366i	−0.588563	+	1.01942i	−0.994421	+	0.105485i	$0.966360\pi$
$752$		−	4.19155i		−	0.152850i
$753$		−	13.6636i		−	0.497930i
$754$	−2.24466	+	3.88786i	−0.0817456	+	0.141588i
$755$		0			0
$756$	2.99902	−	5.19446i	0.109073	−	0.188921i
$757$	31.2689	−	18.0531i	1.13649	−	0.656151i	0.190929	−	0.981604i	$-0.438850\pi$
$757$	31.2689	−	18.0531i	1.13649	−	0.656151i	0.945558	+	0.325453i	$0.105517\pi$
$758$	−11.3670	+	6.56277i	−0.412870	+	0.238370i
$759$	−18.0880			−0.656552
$760$		0			0
$761$	3.07513			0.111473			0.0557367	−	0.998446i	$-0.482249\pi$
$761$	3.07513			0.111473			0.0557367	+	0.998446i	$0.482249\pi$
$762$	−1.91468	+	1.10544i	−0.0693615	+	0.0400459i
$763$	25.1203	−	14.5032i	0.909415	−	0.525051i
$764$	−0.983494	+	1.70346i	−0.0355816	+	0.0616291i
$765$		0			0
$766$	5.59854	−	9.69696i	0.202284	−	0.350365i
$767$		−	7.85321i		−	0.283563i
$768$		−	0.473885i		−	0.0170998i
$769$	0.423890	−	0.734199i	0.0152859	−	0.0264759i	−0.858281	−	0.513180i	$-0.828467\pi$
$769$	0.423890	−	0.734199i	0.0152859	−	0.0264759i	0.873567	+	0.486704i	$0.161801\pi$
$770$		0			0
$771$	1.56460			0.0563478
$772$			13.8524i			0.498559i
$773$	6.09237	+	3.51743i	0.219127	+	0.126513i	0.605546	−	0.795810i	$-0.292955\pi$
$773$	6.09237	+	3.51743i	0.219127	+	0.126513i	−0.386419	+	0.922323i	$0.626288\pi$
$774$	−14.0972	−	24.4170i	−0.506713	−	0.877652i
$775$		0			0
$776$	−0.0861680	−	0.149247i	−0.00309325	−	0.00535767i
$777$	6.64539	−	3.83672i	0.238402	−	0.137641i
$778$			22.0074i			0.789003i
$779$	12.2026	−	48.2052i	0.437202	−	1.72713i
$780$		0			0
$781$	−27.8079	−	48.1647i	−0.995045	−	1.72347i
$782$	45.0913	−	26.0334i	1.61246	−	0.930954i
$783$	−4.66219	−	2.69171i	−0.166613	−	0.0961940i
$784$	−1.09854	−	1.90273i	−0.0392337	−	0.0679548i
$785$		0			0
$786$	0.426127			0.0151994
$787$		−	33.5875i		−	1.19726i	−0.801024	−	0.598632i	$-0.795711\pi$
$787$		−	33.5875i		−	1.19726i	0.801024	−	0.598632i	$-0.204289\pi$
$788$	14.9145	+	8.61092i	0.531309	+	0.306751i
$789$	−2.65306	+	4.59524i	−0.0944516	+	0.163595i
$790$		0			0
$791$	38.3290			1.36282
$792$	−11.9386	−	6.89277i	−0.424221	−	0.244924i
$793$	−9.33567	+	5.38995i	−0.331519	+	0.191403i
$794$	−4.78044	+	8.27996i	−0.169651	+	0.293845i
$795$		0			0
$796$	−4.60723	−	7.97995i	−0.163299	−	0.282842i
$797$			33.8799i			1.20009i	0.799967	+	0.600044i	$0.204850\pi$
$797$			33.8799i			1.20009i	−0.799967	+	0.600044i	$0.795150\pi$
$798$	−1.23218	−	4.35599i	−0.0436188	−	0.154200i
$799$	−28.3996			−1.00471
$800$		0			0
$801$	−4.94674	−	8.56800i	−0.174784	−	0.302735i
$802$	−13.3635	−	7.71543i	−0.471882	−	0.272441i
$803$	20.8925	−	12.0623i	0.737282	−	0.425670i
$804$	−0.191555	+	0.331783i	−0.00675562	+	0.0117011i
$805$		0			0
$806$	−17.3089			−0.609680
$807$	11.6551	+	6.72907i	0.410278	+	0.236874i
$808$	12.8379	+	7.41199i	0.451637	+	0.260753i
$809$	27.2832			0.959225			0.479613	−	0.877480i	$-0.340777\pi$
$809$	27.2832			0.959225			0.479613	+	0.877480i	$0.340777\pi$
$810$		0			0
$811$	−20.2039	+	34.9942i	−0.709456	+	1.22881i	0.255603	+	0.966782i	$0.417726\pi$
$811$	−20.2039	+	34.9942i	−0.709456	+	1.22881i	−0.965059	+	0.262032i	$0.915607\pi$
$812$	3.73323	−	2.15538i	0.131011	−	0.0756391i
$813$	8.44188	+	4.87392i	0.296070	+	0.170936i
$814$	−18.3496	−	31.7825i	−0.643155	−	1.11398i
$815$		0			0
$816$	−3.21077			−0.112400
$817$	−42.9261	−	10.8662i	−1.50179	−	0.380161i
$818$			15.4033i			0.538563i
$819$	6.94115	+	12.0224i	0.242543	+	0.420098i
$820$		0			0
$821$	−4.12932	+	7.15219i	−0.144114	+	0.249613i	−0.929042	−	0.369974i	$-0.879367\pi$
$821$	−4.12932	+	7.15219i	−0.144114	+	0.249613i	0.784928	+	0.619587i	$0.212700\pi$
$822$	3.06801	−	1.77132i	0.107009	−	0.0617818i
$823$	21.0823	+	12.1719i	0.734884	+	0.424285i	0.820206	−	0.572068i	$-0.193859\pi$
$823$	21.0823	+	12.1719i	0.734884	+	0.424285i	−0.0853224	+	0.996353i	$0.527192\pi$
$824$	−14.6031			−0.508723
$825$		0			0
$826$	−3.77043	+	6.53058i	−0.131190	+	0.227228i
$827$	33.4393	+	19.3062i	1.16280	+	0.671341i	0.951973	−	0.306183i	$-0.0990519\pi$
$827$	33.4393	+	19.3062i	1.16280	+	0.671341i	0.210824	+	0.977524i	$0.432385\pi$
$828$		−	21.3283i		−	0.741208i
$829$	−22.7836			−0.791307			−0.395654	−	0.918400i	$-0.629482\pi$
$829$	−22.7836			−0.791307			−0.395654	+	0.918400i	$0.629482\pi$
$830$		0			0
$831$	−2.13117	−	3.69129i	−0.0739295	−	0.128050i
$832$	1.97656	+	1.14116i	0.0685247	+	0.0395628i
$833$	−12.8918	+	7.44311i	−0.446676	+	0.257888i
$834$	−1.42621	−	2.47026i	−0.0493855	−	0.0855383i
$835$		0			0
$836$	−20.8331	+	5.89310i	−0.720529	+	0.203817i
$837$		−	20.7562i		−	0.717440i
$838$	32.5263	−	18.7791i	1.12360	−	0.648712i
$839$	7.41470	+	12.8426i	0.255984	+	0.443377i	0.965162	−	0.261652i	$-0.0842672\pi$
$839$	7.41470	+	12.8426i	0.255984	+	0.443377i	−0.709178	+	0.705029i	$0.750934\pi$
$840$		0			0
$841$	12.5655	+	21.7640i	0.433292	+	0.750484i
$842$	3.32283	+	1.91844i	0.114512	+	0.0661138i
$843$			4.53255i			0.156109i
$844$	11.7810			0.405518
$845$		0			0
$846$	−5.81669	+	10.0748i	−0.199982	+	0.346379i
$847$			29.9607i			1.02946i
$848$		−	4.19155i		−	0.143939i
$849$	0.596173	−	1.03260i	0.0204606	−	0.0354388i
$850$		0			0
$851$	28.3896	−	49.1722i	0.973183	−	1.68560i
$852$	−4.59524	+	2.65306i	−0.157430	+	0.0908925i
$853$	−6.59245	+	3.80616i	−0.225721	+	0.130320i	−0.608597	−	0.793480i	$-0.708267\pi$
$853$	−6.59245	+	3.80616i	−0.225721	+	0.130320i	0.382875	+	0.923800i	$0.374934\pi$
$854$	10.3512			0.354209
$855$		0			0
$856$	−0.363891			−0.0124375
$857$	18.1865	−	10.5000i	0.621240	−	0.358673i	−0.156112	−	0.987739i	$-0.549896\pi$
$857$	18.1865	−	10.5000i	0.621240	−	0.358673i	0.777352	+	0.629066i	$0.216563\pi$
$858$	−4.65238	+	2.68605i	−0.158829	+	0.0917002i
$859$	0.264422	−	0.457992i	0.00902195	−	0.0156265i	−0.861479	−	0.507793i	$-0.830462\pi$
$859$	0.264422	−	0.457992i	0.00902195	−	0.0156265i	0.870501	+	0.492166i	$0.163795\pi$
$860$		0			0
$861$	−5.92378	+	10.2603i	−0.201882	+	0.349670i
$862$			9.12564i			0.310820i
$863$		−	45.5463i		−	1.55041i	−0.631707	−	0.775207i	$-0.717645\pi$
$863$		−	45.5463i		−	1.55041i	0.631707	−	0.775207i	$-0.282355\pi$
$864$	−1.36844	+	2.37022i	−0.0465554	+	0.0806364i
$865$		0			0
$866$	8.65533			0.294120
$867$			13.6983i			0.465220i
$868$	14.3938	+	8.31024i	0.488556	+	0.282068i
$869$	−37.9193	−	65.6782i	−1.28632	−	2.22798i
$870$		0			0
$871$	−0.922569	−	1.59794i	−0.0312601	−	0.0541440i
$872$	−11.4623	+	6.61776i	−0.388162	+	0.224106i
$873$			0.478307i			0.0161882i
$874$	−24.0119	−	23.3549i	−0.812216	−	0.789992i
$875$		0			0
$876$	−1.15083	−	1.99329i	−0.0388829	−	0.0673471i
$877$	27.3850	−	15.8107i	0.924725	−	0.533890i	0.0395854	−	0.999216i	$-0.487396\pi$
$877$	27.3850	−	15.8107i	0.924725	−	0.533890i	0.885139	+	0.465326i	$0.154063\pi$
$878$	−3.52917	−	2.03757i	−0.119104	−	0.0687645i
$879$	0.0962262	+	0.166669i	0.00324563	+	0.00562159i
$880$		0			0
$881$	44.7865			1.50890			0.754448	−	0.656360i	$-0.227905\pi$
$881$	44.7865			1.50890			0.754448	+	0.656360i	$0.227905\pi$
$882$			6.09787i			0.205326i
$883$	−19.2859	−	11.1347i	−0.649024	−	0.374714i	0.139058	−	0.990284i	$-0.455592\pi$
$883$	−19.2859	−	11.1347i	−0.649024	−	0.374714i	−0.788082	+	0.615570i	$0.788926\pi$
$884$	7.73189	−	13.3920i	0.260051	−	0.450422i
$885$		0			0
$886$	2.74242			0.0921335
$887$	−13.9873	−	8.07559i	−0.469649	−	0.271152i	0.246444	−	0.969157i	$-0.420738\pi$
$887$	−13.9873	−	8.07559i	−0.469649	−	0.271152i	−0.716093	+	0.698005i	$0.754071\pi$
$888$	−3.03227	+	1.75068i	−0.101756	+	0.0587490i
$889$	−5.11228	+	8.85473i	−0.171460	+	0.296978i
$890$		0			0
$891$	17.4573	+	30.2369i	0.584842	+	1.01298i
$892$		−	0.597671i		−	0.0200115i
$893$	4.97308	+	17.5807i	0.166418	+	0.588317i
$894$	−2.83415			−0.0947882
$895$		0			0
$896$	−1.09578	−	1.89794i	−0.0366074	−	0.0634058i
$897$	−7.19791	−	4.15571i	−0.240331	−	0.138755i
$898$	17.9920	−	10.3877i	0.600400	−	0.346641i
$899$	7.45870	−	12.9188i	0.248762	−	0.430868i
$900$		0			0
$901$	−28.3996			−0.946128
$902$	49.0713	+	28.3314i	1.63390	+	0.943331i
$903$	9.13665	+	5.27505i	0.304049	+	0.175543i
$904$	−17.4894			−0.581690
$905$		0			0
$906$	−1.43771	+	2.49019i	−0.0477648	+	0.0827310i
$907$	14.8622	−	8.58067i	0.493490	−	0.284917i	−0.232531	−	0.972589i	$-0.574701\pi$
$907$	14.8622	−	8.58067i	0.493490	−	0.284917i	0.726021	+	0.687672i	$0.241367\pi$
$908$	13.2817	+	7.66821i	0.440769	+	0.254478i
$909$	−20.5715	−	35.6309i	−0.682313	−	1.18180i
$910$		0			0
$911$	−12.2089			−0.404500			−0.202250	−	0.979334i	$-0.564825\pi$
$911$	−12.2089			−0.404500			−0.202250	+	0.979334i	$0.564825\pi$
$912$	0.562242	+	1.98762i	0.0186177	+	0.0658168i
$913$		−	63.1960i		−	2.09148i
$914$	−2.57835	−	4.46583i	−0.0852841	−	0.147716i
$915$		0			0
$916$	−7.79010	+	13.4928i	−0.257392	+	0.445816i
$917$	1.70667	−	0.985345i	0.0563591	−	0.0325390i
$918$	16.0592	+	9.27181i	0.530034	+	0.306015i
$919$	0.442810			0.0146069			0.00730347	−	0.999973i	$-0.497675\pi$
$919$	0.442810			0.0146069			0.00730347	+	0.999973i	$0.497675\pi$
$920$		0			0
$921$	4.95472	−	8.58182i	0.163264	−	0.282781i
$922$	−30.7261	−	17.7397i	−1.01191	−	0.584226i
$923$		−	25.5554i		−	0.841168i
$924$	5.15844			0.169700
$925$		0			0
$926$	19.6640	+	34.0591i	0.646200	+	1.11925i
$927$	35.0999	+	20.2650i	1.15283	+	0.665589i
$928$	−1.70346	+	0.983494i	−0.0559189	+	0.0322848i
$929$	−24.7489	−	42.8663i	−0.811984	−	1.40640i	−0.911473	−	0.411360i	$-0.865054\pi$
$929$	−24.7489	−	42.8663i	−0.811984	−	1.40640i	0.0994888	−	0.995039i	$-0.468279\pi$
$930$		0			0
$931$	6.86515	+	6.67730i	0.224996	+	0.218840i
$932$		−	29.4619i		−	0.965058i
$933$	4.07276	−	2.35141i	0.133336	−	0.0769817i
$934$	4.93587	+	8.54918i	0.161507	+	0.279738i
$935$		0			0
$936$	−3.16723	−	5.48580i	−0.103524	−	0.179309i
$937$	−12.5696	−	7.25703i	−0.410629	−	0.237077i	0.280431	−	0.959874i	$-0.409523\pi$
$937$	−12.5696	−	7.25703i	−0.410629	−	0.237077i	−0.691060	+	0.722797i	$0.742856\pi$
$938$			1.77175i			0.0578497i
$939$	−6.94493			−0.226639
$940$		0			0
$941$	−6.72821	+	11.6536i	−0.219333	+	0.379896i	−0.954604	−	0.297877i	$-0.903722\pi$
$941$	−6.72821	+	11.6536i	−0.219333	+	0.379896i	0.735271	+	0.677773i	$0.237055\pi$
$942$			0.904752i			0.0294784i
$943$			87.6655i			2.85478i
$944$	1.72044	−	2.97988i	0.0559954	−	0.0969869i
$945$		0			0
$946$	25.2287	−	43.6974i	0.820255	−	1.42072i
$947$	18.2064	−	10.5115i	0.591627	−	0.341576i	−0.174113	−	0.984726i	$-0.555706\pi$
$947$	18.2064	−	10.5115i	0.591627	−	0.341576i	0.765741	+	0.643149i	$0.222373\pi$
$948$	−6.26615	+	3.61776i	−0.203515	+	0.117499i
$949$	11.0853			0.359843
$950$		0			0
$951$	16.6068			0.538512
$952$	−12.8594	+	7.42437i	−0.416775	+	0.240625i
$953$	31.2101	−	18.0192i	1.01099	−	0.583698i	0.0995119	−	0.995036i	$-0.468272\pi$
$953$	31.2101	−	18.0192i	1.01099	−	0.583698i	0.911483	+	0.411338i	$0.134939\pi$
$954$	−5.81669	+	10.0748i	−0.188322	+	0.326184i
$955$		0			0
$956$	−0.674124	+	1.16762i	−0.0218027	+	0.0377634i
$957$		−	4.62986i		−	0.149662i
$958$			18.7286i			0.605095i
$959$	8.19174	−	14.1885i	0.264525	−	0.458171i
$960$		0			0
$961$	26.5152			0.855329
$962$		−	16.8633i		−	0.543695i
$963$	0.874646	+	0.504977i	0.0281851	+	0.0162727i
$964$	13.9331	+	24.1328i	0.448753	+	0.777264i
$965$		0			0
$966$	3.99043	+	6.91163i	0.128390	+	0.222378i
$967$	41.9527	−	24.2214i	1.34911	−	0.778907i	0.360984	−	0.932572i	$-0.382441\pi$
$967$	41.9527	−	24.2214i	1.34911	−	0.778907i	0.988123	+	0.153665i	$0.0491075\pi$
$968$		−	13.6710i		−	0.439402i
$969$	13.4670	−	3.80943i	0.432623	−	0.122377i
$970$		0			0
$971$	19.0779	+	33.0438i	0.612237	+	1.06043i	0.990862	+	0.134876i	$0.0430637\pi$
$971$	19.0779	+	33.0438i	0.612237	+	1.06043i	−0.378625	+	0.925550i	$0.623603\pi$
$972$	9.99546	−	5.77088i	0.320604	−	0.185101i
$973$	−11.4241	−	6.59572i	−0.366241	−	0.211449i
$974$	8.95645	+	15.5130i	0.286983	+	0.497070i
$975$		0			0
$976$	−4.72320			−0.151186
$977$		−	46.7789i		−	1.49659i	−0.663366	−	0.748295i	$-0.730873\pi$
$977$		−	46.7789i		−	1.49659i	0.663366	−	0.748295i	$-0.269127\pi$
$978$	3.09658	+	1.78781i	0.0990176	+	0.0571678i
$979$	8.85281	−	15.3335i	0.282937	−	0.490061i
$980$		0			0
$981$	36.7343			1.17284
$982$	−25.9982	−	15.0101i	−0.829637	−	0.478991i
$983$	15.6487	−	9.03476i	0.499115	−	0.288164i	−0.229233	−	0.973372i	$-0.573622\pi$
$983$	15.6487	−	9.03476i	0.499115	−	0.288164i	0.728348	+	0.685208i	$0.240289\pi$
$984$	2.70301	−	4.68174i	0.0861687	−	0.149248i
$985$		0			0
$986$	6.66360	+	11.5417i	0.212212	+	0.367562i
$987$		−	4.35311i		−	0.138561i
$988$	−9.64425	−	2.44132i	−0.306824	−	0.0776688i
$989$	78.0649			2.48232
$990$		0			0
$991$	−22.5449	−	39.0489i	−0.716162	−	1.24043i	−0.962510	−	0.271248i	$-0.912564\pi$
$991$	−22.5449	−	39.0489i	−0.716162	−	1.24043i	0.246347	−	0.969182i	$-0.420770\pi$
$992$	−6.56783	−	3.79194i	−0.208529	−	0.120394i
$993$	−8.80152	+	5.08156i	−0.279308	+	0.161258i
$994$	−12.2695	+	21.2514i	−0.389165	+	0.674054i
$995$		0			0
$996$	−6.02933			−0.191047
$997$	−38.7465	−	22.3703i	−1.22711	−	0.708474i	−0.260689	−	0.965423i	$-0.583950\pi$
$997$	−38.7465	−	22.3703i	−1.22711	−	0.708474i	−0.966425	+	0.256949i	$0.917283\pi$
$998$	8.20932	+	4.73966i	0.259862	+	0.150031i
$999$	20.2219			0.639792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.j.i.349.6		16
5.2	odd	4		950.2.e.m.501.3	yes	8
5.3	odd	4		950.2.e.l.501.2	yes	8
5.4	even	2	inner	950.2.j.i.349.3		16
19.11	even	3	inner	950.2.j.i.49.3		16
95.49	even	6	inner	950.2.j.i.49.6		16
95.68	odd	12		950.2.e.l.201.2	✓	8
95.87	odd	12		950.2.e.m.201.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.e.l.201.2	✓	8	95.68	odd	12
950.2.e.l.501.2	yes	8	5.3	odd	4
950.2.e.m.201.3	yes	8	95.87	odd	12
950.2.e.m.501.3	yes	8	5.2	odd	4
950.2.j.i.49.3		16	19.11	even	3	inner
950.2.j.i.49.6		16	95.49	even	6	inner
950.2.j.i.349.3		16	5.4	even	2	inner
950.2.j.i.349.6		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.410396 + 0.236942i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.236942 + 0.410396i) q^{6} +2.19155i q^{7} -1.00000i q^{8} +(-1.38772 + 2.40360i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.410396 + 0.236942i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.236942 + 0.410396i) q^{6} +2.19155i q^{7} -1.00000i q^{8} +(-1.38772 + 2.40360i) q^{9} -4.96699 q^{11} +0.473885i q^{12} +(-1.97656 - 1.14116i) q^{13} +(1.09578 + 1.89794i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.86770 + 3.38772i) q^{17} +2.77543i q^{18} +(3.12466 + 3.03916i) q^{19} +(-0.519272 - 0.899406i) q^{21} +(-4.30154 + 2.48349i) q^{22} +(-6.65511 - 3.84233i) q^{23} +(0.236942 + 0.410396i) q^{24} -2.28233 q^{26} -2.73689i q^{27} +(1.89794 + 1.09578i) q^{28} +(0.983494 - 1.70346i) q^{29} +7.58388 q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.03843 - 1.17689i) q^{33} +(-3.38772 + 5.86770i) q^{34} +(1.38772 + 2.40360i) q^{36} +7.38864i q^{37} +(4.22562 + 1.06966i) q^{38} +1.08156 q^{39} +(-5.70393 - 9.87950i) q^{41} +(-0.899406 - 0.519272i) q^{42} +(-8.79756 + 5.07927i) q^{43} +(-2.48349 + 4.30154i) q^{44} -7.68466 q^{46} +(3.62999 + 2.09578i) q^{47} +(0.410396 + 0.236942i) q^{48} +2.19709 q^{49} +(1.60539 - 2.78061i) q^{51} +(-1.97656 + 1.14116i) q^{52} +(3.62999 + 2.09578i) q^{53} +(-1.36844 - 2.37022i) q^{54} +2.19155 q^{56} +(-2.00245 - 0.506896i) q^{57} -1.96699i q^{58} +(1.72044 + 2.97988i) q^{59} +(2.36160 - 4.09041i) q^{61} +(6.56783 - 3.79194i) q^{62} +(-5.26761 - 3.04126i) q^{63} -1.00000 q^{64} +(1.17689 - 2.03843i) q^{66} +(0.700134 + 0.404223i) q^{67} +6.77543i q^{68} +3.64164 q^{69} +(5.59854 + 9.69696i) q^{71} +(2.40360 + 1.38772i) q^{72} +(-4.20628 + 2.42850i) q^{73} +(3.69432 + 6.39875i) q^{74} +(4.19432 - 1.18645i) q^{76} -10.8854i q^{77} +(0.936659 - 0.540781i) q^{78} +(7.63427 + 13.2229i) q^{79} +(-3.51467 - 6.08758i) q^{81} +(-9.87950 - 5.70393i) q^{82} +12.7232i q^{83} -1.03854 q^{84} +(-5.07927 + 8.79756i) q^{86} +0.932126i q^{87} +4.96699i q^{88} +(-1.78233 + 3.08709i) q^{89} +(2.50093 - 4.33173i) q^{91} +(-6.65511 + 3.84233i) q^{92} +(-3.11239 + 1.79694i) q^{93} +4.19155 q^{94} +0.473885 q^{96} +(0.149247 - 0.0861680i) q^{97} +(1.90273 - 1.09854i) q^{98} +(6.89277 - 11.9386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{6} + 22 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^6 + 22 * q^9	\( 16 q + 8 q^{4} + 2 q^{6} + 22 q^{9} + 20 q^{11} + 12 q^{14} - 8 q^{16} - 2 q^{21} - 2 q^{24} - 36 q^{26} - 34 q^{29} + 44 q^{31} - 10 q^{34} - 22 q^{36} + 72 q^{39} + 14 q^{41} + 10 q^{44} - 24 q^{46} - 88 q^{49} - 18 q^{51} + 16 q^{54} + 24 q^{56} - 28 q^{59} - 18 q^{61} - 16 q^{64} - 8 q^{66} - 108 q^{69} + 28 q^{71} - 8 q^{74} + 34 q^{79} - 72 q^{81} - 4 q^{84} - 26 q^{86} - 28 q^{89} - 50 q^{91} + 56 q^{94} - 4 q^{96} + 120 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^6 + 22 * q^9 + 20 * q^11 + 12 * q^14 - 8 * q^16 - 2 * q^21 - 2 * q^24 - 36 * q^26 - 34 * q^29 + 44 * q^31 - 10 * q^34 - 22 * q^36 + 72 * q^39 + 14 * q^41 + 10 * q^44 - 24 * q^46 - 88 * q^49 - 18 * q^51 + 16 * q^54 + 24 * q^56 - 28 * q^59 - 18 * q^61 - 16 * q^64 - 8 * q^66 - 108 * q^69 + 28 * q^71 - 8 * q^74 + 34 * q^79 - 72 * q^81 - 4 * q^84 - 26 * q^86 - 28 * q^89 - 50 * q^91 + 56 * q^94 - 4 * q^96 + 120 * q^99

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