LMFDB - Embedded newform 369.2.u.a.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [369,2,Mod(46,369)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(369, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("369.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 369 = 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	369.u (of order $20$, degree $8$, 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:	$2.94647983459$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			226.1
Character	$\chi$	$=$	369.226
Dual form			369.2.u.a.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.698642 - 0.227002i) q^{2} +(-1.18146 - 0.858384i) q^{4} +(0.422124 - 0.581004i) q^{5} +(-1.42228 + 2.79137i) q^{7} +(1.49413 + 2.05650i) q^{8} +O(q^{10})$	\(q+(-0.698642 - 0.227002i) q^{2} +(-1.18146 - 0.858384i) q^{4} +(0.422124 - 0.581004i) q^{5} +(-1.42228 + 2.79137i) q^{7} +(1.49413 + 2.05650i) q^{8} +(-0.426803 + 0.310091i) q^{10} +(-3.06970 - 0.486193i) q^{11} +(-1.79162 + 0.912875i) q^{13} +(1.62731 - 1.62731i) q^{14} +(0.325524 + 1.00186i) q^{16} +(-0.304435 + 1.92213i) q^{17} +(3.91204 + 1.99329i) q^{19} +(-0.997449 + 0.324091i) q^{20} +(2.03426 + 1.03651i) q^{22} +(-0.275748 + 0.848664i) q^{23} +(1.38571 + 4.26477i) q^{25} +(1.45892 - 0.231071i) q^{26} +(4.07644 - 2.07705i) q^{28} +(1.43151 + 9.03822i) q^{29} +(-5.64731 + 4.10301i) q^{31} -5.85778i q^{32} +(0.649020 - 1.27377i) q^{34} +(1.02142 + 2.00465i) q^{35} +(-3.49299 - 2.53781i) q^{37} +(-2.28064 - 2.28064i) q^{38} +1.82554 q^{40} +(2.53101 + 5.88167i) q^{41} +(-10.3243 - 3.35457i) q^{43} +(3.20940 + 3.20940i) q^{44} +(0.385298 - 0.530317i) q^{46} +(-5.24325 - 10.2905i) q^{47} +(-1.65440 - 2.27709i) q^{49} -3.29411i q^{50} +(2.90033 + 0.459367i) q^{52} +(-0.465724 - 2.94046i) q^{53} +(-1.57828 + 1.57828i) q^{55} +(-7.86552 + 1.24578i) q^{56} +(1.05158 - 6.63944i) q^{58} +(-1.37512 + 4.23218i) q^{59} +(11.3577 - 3.69033i) q^{61} +(4.87684 - 1.58458i) q^{62} +(-0.678682 + 2.08877i) q^{64} +(-0.225901 + 1.42628i) q^{65} +(8.00079 - 1.26720i) q^{67} +(2.00960 - 2.00960i) q^{68} +(-0.258547 - 1.63240i) q^{70} +(0.988102 + 0.156500i) q^{71} +6.49752i q^{73} +(1.86426 + 2.56593i) q^{74} +(-2.91093 - 5.71303i) q^{76} +(5.72311 - 7.87719i) q^{77} +(-4.43337 - 4.43337i) q^{79} +(0.719497 + 0.233779i) q^{80} +(-0.433113 - 4.68372i) q^{82} -7.83744 q^{83} +(0.988256 + 0.988256i) q^{85} +(6.45150 + 4.68729i) q^{86} +(-3.58669 - 7.03928i) q^{88} +(6.40964 - 12.5796i) q^{89} -6.29943i q^{91} +(1.05426 - 0.765968i) q^{92} +(1.32719 + 8.37958i) q^{94} +(2.80948 - 1.43150i) q^{95} +(6.34053 - 1.00424i) q^{97} +(0.638929 + 1.96642i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−0.698642	−	0.227002i	−0.494014	−	0.160515i	0.0514057	−	0.998678i	$-0.483630\pi$
$2$	−0.698642	−	0.227002i	−0.494014	−	0.160515i	−0.545420	+	0.838163i	$0.683630\pi$
$3$		0			0
$3$		0			0
$4$	−1.18146	−	0.858384i	−0.590732	−	0.429192i
$5$	0.422124	−	0.581004i	0.188780	−	0.259833i	−0.704128	−	0.710073i	$-0.748662\pi$
$5$	0.422124	−	0.581004i	0.188780	−	0.259833i	0.892907	+	0.450240i	$0.148662\pi$
$6$		0			0
$7$	−1.42228	+	2.79137i	−0.537570	+	1.05504i	0.449279	+	0.893392i	$0.351681\pi$
$7$	−1.42228	+	2.79137i	−0.537570	+	1.05504i	−0.986848	+	0.161648i	$0.948319\pi$
$8$	1.49413	+	2.05650i	0.528256	+	0.727082i
$9$		0			0
$10$	−0.426803	+	0.310091i	−0.134967	+	0.0980592i
$11$	−3.06970	−	0.486193i	−0.925551	−	0.146593i	−0.324575	−	0.945860i	$-0.605221\pi$
$11$	−3.06970	−	0.486193i	−0.925551	−	0.146593i	−0.600976	+	0.799267i	$0.705221\pi$
$12$		0			0
$13$	−1.79162	+	0.912875i	−0.496905	+	0.253186i	−0.684436	−	0.729073i	$-0.739952\pi$
$13$	−1.79162	+	0.912875i	−0.496905	+	0.253186i	0.187531	+	0.982259i	$0.439952\pi$
$14$	1.62731	−	1.62731i	0.434917	−	0.434917i
$15$		0			0
$16$	0.325524	+	1.00186i	0.0813810	+	0.250465i
$17$	−0.304435	+	1.92213i	−0.0738365	+	0.466185i	0.922871	+	0.385108i	$0.125836\pi$
$17$	−0.304435	+	1.92213i	−0.0738365	+	0.466185i	−0.996708	+	0.0810768i	$0.974164\pi$
$18$		0			0
$19$	3.91204	+	1.99329i	0.897485	+	0.457291i	0.840952	−	0.541109i	$-0.181996\pi$
$19$	3.91204	+	1.99329i	0.897485	+	0.457291i	0.0565325	+	0.998401i	$0.481996\pi$
$20$	−0.997449	+	0.324091i	−0.223036	+	0.0724689i
$21$		0			0
$22$	2.03426	+	1.03651i	0.433705	+	0.220984i
$23$	−0.275748	+	0.848664i	−0.0574973	+	0.176959i	−0.975681	−	0.219198i	$-0.929656\pi$
$23$	−0.275748	+	0.848664i	−0.0574973	+	0.176959i	0.918183	+	0.396156i	$0.129656\pi$
$24$		0			0
$25$	1.38571	+	4.26477i	0.277142	+	0.852954i
$26$	1.45892	−	0.231071i	0.286119	−	0.0453167i
$27$		0			0
$28$	4.07644	−	2.07705i	0.770374	−	0.392525i
$29$	1.43151	+	9.03822i	0.265825	+	1.67836i	0.653786	+	0.756680i	$0.273180\pi$
$29$	1.43151	+	9.03822i	0.265825	+	1.67836i	−0.387961	+	0.921676i	$0.626820\pi$
$30$		0			0
$31$	−5.64731	+	4.10301i	−1.01429	+	0.736922i	−0.965104	−	0.261868i	$-0.915662\pi$
$31$	−5.64731	+	4.10301i	−1.01429	+	0.736922i	−0.0491827	+	0.998790i	$0.515662\pi$
$32$		−	5.85778i		−	1.03552i
$33$		0			0
$34$	0.649020	−	1.27377i	0.111306	−	0.218450i
$35$	1.02142	+	2.00465i	0.172652	+	0.338848i
$36$		0			0
$37$	−3.49299	−	2.53781i	−0.574244	−	0.417213i	0.262400	−	0.964959i	$-0.415486\pi$
$37$	−3.49299	−	2.53781i	−0.574244	−	0.417213i	−0.836644	+	0.547746i	$0.815486\pi$
$38$	−2.28064	−	2.28064i	−0.369968	−	0.369968i
$39$		0			0
$40$	1.82554			0.288644
$41$	2.53101	+	5.88167i	0.395277	+	0.918562i
$41$	2.53101	+	5.88167i	0.395277	+	0.918562i
$42$		0			0
$43$	−10.3243	−	3.35457i	−1.57444	−	0.511568i	−0.613826	−	0.789441i	$-0.710370\pi$
$43$	−10.3243	−	3.35457i	−1.57444	−	0.511568i	−0.960618	+	0.277874i	$0.910370\pi$
$44$	3.20940	+	3.20940i	0.483836	+	0.483836i
$45$		0			0
$46$	0.385298	−	0.530317i	0.0568090	−	0.0781909i
$47$	−5.24325	−	10.2905i	−0.764807	−	1.50102i	−0.862642	−	0.505815i	$-0.831192\pi$
$47$	−5.24325	−	10.2905i	−0.764807	−	1.50102i	0.0978352	−	0.995203i	$-0.468808\pi$
$48$		0			0
$49$	−1.65440	−	2.27709i	−0.236343	−	0.325298i
$50$		−	3.29411i		−	0.465857i
$51$		0			0
$52$	2.90033	+	0.459367i	0.402203	+	0.0637027i
$53$	−0.465724	−	2.94046i	−0.0639721	−	0.403904i	−0.998807	−	0.0488225i	$-0.984453\pi$
$53$	−0.465724	−	2.94046i	−0.0639721	−	0.403904i	0.934835	−	0.355081i	$-0.115547\pi$
$54$		0			0
$55$	−1.57828	+	1.57828i	−0.212815	+	0.212815i
$56$	−7.86552	+	1.24578i	−1.05107	+	0.166474i
$57$		0			0
$58$	1.05158	−	6.63944i	0.138080	−	0.871801i
$59$	−1.37512	+	4.23218i	−0.179025	+	0.550982i	−0.999794	−	0.0202774i	$-0.993545\pi$
$59$	−1.37512	+	4.23218i	−0.179025	+	0.550982i	0.820769	+	0.571260i	$0.193545\pi$
$60$		0			0
$61$	11.3577	−	3.69033i	1.45420	−	0.472499i	0.527908	−	0.849301i	$-0.322977\pi$
$61$	11.3577	−	3.69033i	1.45420	−	0.472499i	0.926294	+	0.376803i	$0.122977\pi$
$62$	4.87684	−	1.58458i	0.619359	−	0.201242i
$63$		0			0
$64$	−0.678682	+	2.08877i	−0.0848353	+	0.261096i
$65$	−0.225901	+	1.42628i	−0.0280196	+	0.176909i
$66$		0			0
$67$	8.00079	−	1.26720i	0.977452	−	0.154813i	0.352785	−	0.935704i	$-0.385235\pi$
$67$	8.00079	−	1.26720i	0.977452	−	0.154813i	0.624667	+	0.780891i	$0.285235\pi$
$68$	2.00960	−	2.00960i	0.243700	−	0.243700i
$69$		0			0
$70$	−0.258547	−	1.63240i	−0.0309023	−	0.195109i
$71$	0.988102	+	0.156500i	0.117266	+	0.0185731i	0.214792	−	0.976660i	$-0.431093\pi$
$71$	0.988102	+	0.156500i	0.117266	+	0.0185731i	−0.0975255	+	0.995233i	$0.531093\pi$
$72$		0			0
$73$			6.49752i			0.760477i	0.924889	+	0.380238i	$0.124158\pi$
$73$			6.49752i			0.760477i	−0.924889	+	0.380238i	$0.875842\pi$
$74$	1.86426	+	2.56593i	0.216716	+	0.298284i
$75$		0			0
$76$	−2.91093	−	5.71303i	−0.333907	−	0.655330i
$77$	5.72311	−	7.87719i	0.652209	−	0.897689i
$78$		0			0
$79$	−4.43337	−	4.43337i	−0.498793	−	0.498793i	0.412269	−	0.911062i	$-0.364736\pi$
$79$	−4.43337	−	4.43337i	−0.498793	−	0.498793i	−0.911062	+	0.412269i	$0.864736\pi$
$80$	0.719497	+	0.233779i	0.0804422	+	0.0261372i
$81$		0			0
$82$	−0.433113	−	4.68372i	−0.0478294	−	0.517231i
$83$	−7.83744			−0.860271			−0.430136	−	0.902764i	$-0.641534\pi$
$83$	−7.83744			−0.860271			−0.430136	+	0.902764i	$0.641534\pi$
$84$		0			0
$85$	0.988256	+	0.988256i	0.107191	+	0.107191i
$86$	6.45150	+	4.68729i	0.695683	+	0.505444i
$87$		0			0
$88$	−3.58669	−	7.03928i	−0.382343	−	0.750390i
$89$	6.40964	−	12.5796i	0.679420	−	1.33344i	−0.251373	−	0.967890i	$-0.580882\pi$
$89$	6.40964	−	12.5796i	0.679420	−	1.33344i	0.930793	−	0.365547i	$-0.119118\pi$
$90$		0			0
$91$		−	6.29943i		−	0.660360i
$92$	1.05426	−	0.765968i	0.109915	−	0.0798577i
$93$		0			0
$94$	1.32719	+	8.37958i	0.136890	+	0.864287i
$95$	2.80948	−	1.43150i	0.288246	−	0.146869i
$96$		0			0
$97$	6.34053	−	1.00424i	0.643783	−	0.101965i	0.173998	−	0.984746i	$-0.444331\pi$
$97$	6.34053	−	1.00424i	0.643783	−	0.101965i	0.469785	+	0.882781i	$0.344331\pi$
$98$	0.638929	+	1.96642i	0.0645415	+	0.198638i
$99$		0			0
$100$	2.02365	−	6.22814i	0.202365	−	0.622814i
$101$	−10.7210	−	5.46262i	−1.06678	−	0.543551i	−0.169734	−	0.985490i	$-0.554291\pi$
$101$	−10.7210	−	5.46262i	−1.06678	−	0.543551i	−0.897045	+	0.441938i	$0.854291\pi$
$102$		0			0
$103$	−14.6231	+	4.75134i	−1.44086	+	0.468163i	−0.922165	−	0.386797i	$-0.873581\pi$
$103$	−14.6231	+	4.75134i	−1.44086	+	0.468163i	−0.518694	+	0.854960i	$0.673581\pi$
$104$	−4.55424	−	2.32050i	−0.446580	−	0.227544i
$105$		0			0
$106$	−0.342119	+	2.16005i	−0.0332295	+	0.209803i
$107$	0.344730	+	1.06097i	0.0333263	+	0.102568i	0.966336	−	0.257284i	$-0.0828274\pi$
$107$	0.344730	+	1.06097i	0.0333263	+	0.102568i	−0.933010	+	0.359851i	$0.882827\pi$
$108$		0			0
$109$	4.18654	−	4.18654i	0.400998	−	0.400998i	−0.477587	−	0.878585i	$-0.658488\pi$
$109$	4.18654	−	4.18654i	0.400998	−	0.400998i	0.878585	+	0.477587i	$0.158488\pi$
$110$	1.46092	−	0.744378i	0.139294	−	0.0709736i
$111$		0			0
$112$	−3.25955	−	0.516262i	−0.307999	−	0.0487822i
$113$	−12.4975	+	9.07995i	−1.17566	+	0.854170i	−0.991676	−	0.128759i	$-0.958901\pi$
$113$	−12.4975	+	9.07995i	−1.17566	+	0.854170i	−0.183988	+	0.982928i	$0.558901\pi$
$114$		0			0
$115$	0.376677	+	0.518452i	0.0351254	+	0.0483459i
$116$	6.06698	−	11.9071i	0.563305	−	1.10555i
$117$		0			0
$118$	1.92143	−	2.64462i	0.176882	−	0.243457i
$119$	−4.93239	−	3.58359i	−0.452152	−	0.328507i
$120$		0			0
$121$	−1.27492	−	0.414247i	−0.115902	−	0.0376588i
$122$	−8.77266			−0.794240
$123$		0			0
$124$	10.1940			0.915452
$125$	6.47785	+	2.10478i	0.579396	+	0.188257i
$126$		0			0
$127$	3.50780	+	2.54857i	0.311267	+	0.226149i	0.732440	−	0.680832i	$-0.238381\pi$
$127$	3.50780	+	2.54857i	0.311267	+	0.226149i	−0.421173	+	0.906980i	$0.638381\pi$
$128$	−5.93792	+	8.17285i	−0.524843	+	0.722384i
$129$		0			0
$130$	0.481594	−	0.945182i	0.0422386	−	0.0828979i
$131$	9.74217	+	13.4090i	0.851178	+	1.17155i	0.983602	+	0.180352i	$0.0577238\pi$
$131$	9.74217	+	13.4090i	0.851178	+	1.17155i	−0.132424	+	0.991193i	$0.542276\pi$
$132$		0			0
$133$	−11.1280	+	8.08497i	−0.964921	+	0.701056i
$134$	−5.87734	−	0.930880i	−0.507725	−	0.0804157i
$135$		0			0
$136$	−4.40772	+	2.24585i	−0.377959	+	0.192580i
$137$	0.166857	−	0.166857i	0.0142555	−	0.0142555i	−0.699943	−	0.714199i	$-0.746791\pi$
$137$	0.166857	−	0.166857i	0.0142555	−	0.0142555i	0.714199	+	0.699943i	$0.246791\pi$
$138$		0			0
$139$	−0.727856	−	2.24011i	−0.0617360	−	0.190004i	0.915432	−	0.402473i	$-0.131849\pi$
$139$	−0.727856	−	2.24011i	−0.0617360	−	0.190004i	−0.977168	+	0.212470i	$0.931849\pi$
$140$	0.513989	−	3.24520i	0.0434400	−	0.274269i
$141$		0			0
$142$	−0.654803	−	0.333639i	−0.0549499	−	0.0279984i
$143$	5.94357	−	1.93118i	0.497026	−	0.161494i
$144$		0			0
$145$	5.85552	+	2.98354i	0.486275	+	0.247769i
$146$	1.47495	−	4.53944i	0.122068	−	0.375686i
$147$		0			0
$148$	1.94843	+	5.99665i	0.160160	+	0.492922i
$149$	8.28803	−	1.31270i	0.678982	−	0.107540i	0.192588	−	0.981280i	$-0.438312\pi$
$149$	8.28803	−	1.31270i	0.678982	−	0.107540i	0.486394	+	0.873739i	$0.338312\pi$
$150$		0			0
$151$	3.22750	−	1.64449i	0.262650	−	0.133827i	−0.317707	−	0.948189i	$-0.602913\pi$
$151$	3.22750	−	1.64449i	0.262650	−	0.133827i	0.580357	+	0.814362i	$0.302913\pi$
$152$	1.74593	+	11.0233i	0.141613	+	0.894112i
$153$		0			0
$154$	−5.78655	+	4.20417i	−0.466293	+	0.338782i
$155$			5.01309i			0.402661i
$156$		0			0
$157$	6.25608	−	12.2783i	0.499290	−	0.979911i	−0.494557	−	0.869145i	$-0.664670\pi$
$157$	6.25608	−	12.2783i	0.499290	−	0.979911i	0.993847	−	0.110766i	$-0.0353304\pi$
$158$	2.09095	+	4.10373i	0.166347	+	0.326475i
$159$		0			0
$160$	−3.40339	−	2.47271i	−0.269062	−	0.195485i
$161$	−1.97675	−	1.97675i	−0.155790	−	0.155790i
$162$		0			0
$163$	−0.923374			−0.0723243			−0.0361621	−	0.999346i	$-0.511513\pi$
$163$	−0.923374			−0.0723243			−0.0361621	+	0.999346i	$0.511513\pi$
$164$	2.05844	−	9.12155i	0.160737	−	0.712273i
$165$		0			0
$166$	5.47557	+	1.77912i	0.424986	+	0.138086i
$167$	12.0223	+	12.0223i	0.930315	+	0.930315i	0.997725	−	0.0674099i	$-0.0214735\pi$
$167$	12.0223	+	12.0223i	0.930315	+	0.930315i	−0.0674099	+	0.997725i	$0.521474\pi$
$168$		0			0
$169$	−5.26465	+	7.24617i	−0.404973	+	0.557398i
$170$	−0.466100	−	0.914774i	−0.0357483	−	0.0701599i
$171$		0			0
$172$	9.31829	+	12.8255i	0.710513	+	0.977938i
$173$		−	12.1428i		−	0.923198i	−0.887089	−	0.461599i	$-0.847276\pi$
$173$		−	12.1428i		−	0.923198i	0.887089	−	0.461599i	$-0.152724\pi$
$174$		0			0
$175$	−13.8754	−	2.19765i	−1.04888	−	0.166127i
$176$	−0.512165	−	3.23368i	−0.0386059	−	0.243748i
$177$		0			0
$178$	−7.33365	+	7.33365i	−0.549680	+	0.549680i
$179$	2.11231	−	0.334557i	0.157881	−	0.0250060i	−0.0769933	−	0.997032i	$-0.524532\pi$
$179$	2.11231	−	0.334557i	0.157881	−	0.0250060i	0.234875	+	0.972026i	$0.424532\pi$
$180$		0			0
$181$	−0.878821	+	5.54866i	−0.0653222	+	0.412428i	0.933260	+	0.359201i	$0.116951\pi$
$181$	−0.878821	+	5.54866i	−0.0653222	+	0.412428i	−0.998582	+	0.0532273i	$0.983049\pi$
$182$	−1.42999	+	4.40105i	−0.105998	+	0.326227i
$183$		0			0
$184$	−2.15728	+	0.700942i	−0.159037	+	0.0516742i
$185$	−2.94895	+	0.958172i	−0.216811	+	0.0704462i
$186$		0			0
$187$	1.86905	−	5.75236i	0.136679	−	0.420654i
$188$	−2.63845	+	16.6585i	−0.192429	+	1.21495i
$189$		0			0
$190$	−2.28777	+	0.362347i	−0.165972	+	0.0262875i
$191$	−9.27794	+	9.27794i	−0.671328	+	0.671328i	−0.958022	−	0.286694i	$-0.907444\pi$
$191$	−9.27794	+	9.27794i	−0.671328	+	0.671328i	0.286694	+	0.958022i	$0.407444\pi$
$192$		0			0
$193$	2.59319	+	16.3728i	0.186662	+	1.17854i	0.885979	+	0.463726i	$0.153488\pi$
$193$	2.59319	+	16.3728i	0.186662	+	1.17854i	−0.699317	+	0.714812i	$0.746512\pi$
$194$	−4.65772	−	0.737711i	−0.334405	−	0.0529646i
$195$		0			0
$196$			4.11040i			0.293600i
$197$	8.51171	+	11.7154i	0.606434	+	0.834685i	0.996278	−	0.0861961i	$-0.0274711\pi$
$197$	8.51171	+	11.7154i	0.606434	+	0.834685i	−0.389844	+	0.920881i	$0.627471\pi$
$198$		0			0
$199$	8.18953	+	16.0729i	0.580541	+	1.13938i	0.975361	+	0.220617i	$0.0708070\pi$
$199$	8.18953	+	16.0729i	0.580541	+	1.13938i	−0.394820	+	0.918759i	$0.629193\pi$
$200$	−6.70006	+	9.22184i	−0.473766	+	0.652083i
$201$		0			0
$202$	6.25011	+	6.25011i	0.439756	+	0.439756i
$203$	−27.2651	−	8.85895i	−1.91363	−	0.621777i
$204$		0			0
$205$	4.48567	+	1.01227i	0.313293	+	0.0707000i
$206$	11.2949			0.786952
$207$		0			0
$208$	−1.49779	−	1.49779i	−0.103853	−	0.103853i
$209$	−11.0397	−	8.02081i	−0.763632	−	0.554811i
$210$		0			0
$211$	6.12962	+	12.0301i	0.421980	+	0.828183i	0.999927	+	0.0121083i	$0.00385430\pi$
$211$	6.12962	+	12.0301i	0.421980	+	0.828183i	−0.577946	+	0.816075i	$0.696146\pi$
$212$	−1.97381	+	3.87382i	−0.135562	+	0.266055i
$213$		0			0
$214$		−	0.819492i		−	0.0560193i
$215$	−6.30717	+	4.58242i	−0.430145	+	0.312519i
$216$		0			0
$217$	−3.42100	−	21.5994i	−0.232233	−	1.46626i
$218$	−3.87525	+	1.97454i	−0.262465	+	0.133733i
$219$		0			0
$220$	3.21944	−	0.509910i	0.217055	−	0.0343781i
$221$	−1.20923	−	3.72163i	−0.0813418	−	0.250344i
$222$		0			0
$223$	−2.34538	+	7.21835i	−0.157059	+	0.483377i	−0.998364	−	0.0571840i	$-0.981788\pi$
$223$	−2.34538	+	7.21835i	−0.157059	+	0.483377i	0.841305	+	0.540561i	$0.181788\pi$
$224$	16.3512	+	8.33138i	1.09251	+	0.556664i
$225$		0			0
$226$	10.7924	−	3.50667i	0.717902	−	0.233260i
$227$	19.3474	+	9.85797i	1.28413	+	0.654297i	0.956837	−	0.290626i	$-0.0938636\pi$
$227$	19.3474	+	9.85797i	1.28413	+	0.654297i	0.327293	+	0.944923i	$0.393864\pi$
$228$		0			0
$229$	−0.463354	+	2.92550i	−0.0306193	+	0.193323i	−0.998257	−	0.0590222i	$-0.981202\pi$
$229$	−0.463354	+	2.92550i	−0.0306193	+	0.193323i	0.967637	+	0.252345i	$0.0812017\pi$
$230$	−0.145473	−	0.447719i	−0.00959219	−	0.0295217i
$231$		0			0
$232$	−16.4482	+	16.4482i	−1.07988	+	1.07988i
$233$	15.5044	−	7.89988i	1.01573	−	0.517538i	0.134840	−	0.990867i	$-0.456948\pi$
$233$	15.5044	−	7.89988i	1.01573	−	0.517538i	0.880886	+	0.473329i	$0.156948\pi$
$234$		0			0
$235$	−8.19210	−	1.29750i	−0.534394	−	0.0846397i
$236$	5.25748	−	3.81978i	0.342233	−	0.248647i
$237$		0			0
$238$	2.63249	+	3.62331i	0.170639	+	0.234864i
$239$	2.69685	−	5.29286i	0.174444	−	0.342366i	−0.787186	−	0.616716i	$-0.788463\pi$
$239$	2.69685	−	5.29286i	0.174444	−	0.342366i	0.961630	+	0.274350i	$0.0884626\pi$
$240$		0			0
$241$	5.16221	−	7.10518i	0.332527	−	0.457685i	−0.609713	−	0.792622i	$-0.708715\pi$
$241$	5.16221	−	7.10518i	0.332527	−	0.457685i	0.942240	+	0.334938i	$0.108715\pi$
$242$	0.796678	+	0.578820i	0.0512124	+	0.0372080i
$243$		0			0
$244$	−16.5864	−	5.38925i	−1.06184	−	0.345011i
$245$	−2.02136			−0.129140
$246$		0			0
$247$	−8.82851			−0.561745
$248$	−16.8757	−	5.48324i	−1.07161	−	0.348186i
$249$		0			0
$250$	−4.04790	−	2.94098i	−0.256012	−	0.186004i
$251$	3.01355	−	4.14780i	0.190214	−	0.261807i	−0.703250	−	0.710943i	$-0.748268\pi$
$251$	3.01355	−	4.14780i	0.190214	−	0.261807i	0.893463	+	0.449137i	$0.148268\pi$
$252$		0			0
$253$	1.25908	−	2.47108i	0.0791576	−	0.155355i
$254$	−1.87216	−	2.57681i	−0.117470	−	0.161684i
$255$		0			0
$256$	9.55736	−	6.94383i	0.597335	−	0.433989i
$257$	1.08576	+	0.171967i	0.0677277	+	0.0107270i	0.190206	−	0.981744i	$-0.439084\pi$
$257$	1.08576	+	0.171967i	0.0677277	+	0.0107270i	−0.122479	+	0.992471i	$0.539084\pi$
$258$		0			0
$259$	12.0520	−	6.14078i	0.748872	−	0.381569i
$260$	1.49119	−	1.49119i	0.0924799	−	0.0924799i
$261$		0			0
$262$	−3.76242	−	11.5796i	−0.232443	−	0.715387i
$263$	1.99659	−	12.6060i	0.123115	−	0.777317i	−0.846447	−	0.532472i	$-0.821263\pi$
$263$	1.99659	−	12.6060i	0.123115	−	0.777317i	0.969562	−	0.244845i	$-0.0787369\pi$
$264$		0			0
$265$	−1.90502	−	0.970654i	−0.117024	−	0.0596268i
$266$	9.60980	−	3.12241i	0.589215	−	0.191448i
$267$		0			0
$268$	−10.5404	−	5.37059i	−0.643856	−	0.328061i
$269$	−0.170602	+	0.525059i	−0.0104018	+	0.0320134i	−0.956123	−	0.292967i	$-0.905358\pi$
$269$	−0.170602	+	0.525059i	−0.0104018	+	0.0320134i	0.945721	+	0.324980i	$0.105358\pi$
$270$		0			0
$271$	−0.852971	−	2.62518i	−0.0518143	−	0.159468i	0.921801	−	0.387663i	$-0.126718\pi$
$271$	−0.852971	−	2.62518i	−0.0518143	−	0.159468i	−0.973615	+	0.228195i	$0.926718\pi$
$272$	−2.02481	+	0.320698i	−0.122772	+	0.0194452i
$273$		0			0
$274$	−0.154450	+	0.0786962i	−0.00933067	+	0.00475421i
$275$	−2.18021	−	13.7653i	−0.131472	−	0.830079i
$276$		0			0
$277$	17.2011	−	12.4974i	1.03352	−	0.750894i	0.0645072	−	0.997917i	$-0.479452\pi$
$277$	17.2011	−	12.4974i	1.03352	−	0.750894i	0.969010	+	0.247023i	$0.0794525\pi$
$278$			1.73026i			0.103774i
$279$		0			0
$280$	−2.59643	+	5.09578i	−0.155166	+	0.304531i
$281$	0.813754	+	1.59708i	0.0485445	+	0.0952739i	0.914004	−	0.405704i	$-0.132974\pi$
$281$	0.813754	+	1.59708i	0.0485445	+	0.0952739i	−0.865460	+	0.500978i	$0.832974\pi$
$282$		0			0
$283$	−3.00831	−	2.18566i	−0.178825	−	0.129924i	0.494772	−	0.869023i	$-0.335252\pi$
$283$	−3.00831	−	2.18566i	−0.178825	−	0.129924i	−0.673597	+	0.739099i	$0.735252\pi$
$284$	−1.03307	−	1.03307i	−0.0613014	−	0.0613014i
$285$		0			0
$286$	−4.59081			−0.271460
$287$	−20.0177	−	1.30037i	−1.18161	−	0.0767585i
$288$		0			0
$289$	12.5661	+	4.08296i	0.739180	+	0.240174i
$290$	−3.41364	−	3.41364i	−0.200456	−	0.200456i
$291$		0			0
$292$	5.57736	−	7.67658i	0.326390	−	0.449238i
$293$	6.31176	+	12.3875i	0.368737	+	0.723687i	0.998593	−	0.0530245i	$-0.0168861\pi$
$293$	6.31176	+	12.3875i	0.368737	+	0.723687i	−0.629856	+	0.776712i	$0.716886\pi$
$294$		0			0
$295$	1.87844	+	2.58545i	0.109367	+	0.150531i
$296$		−	10.9751i		−	0.637917i
$297$		0			0
$298$	−6.08835	−	0.964300i	−0.352689	−	0.0558604i
$299$	−0.280690	−	1.77220i	−0.0162327	−	0.102489i
$300$		0			0
$301$	24.0479	−	24.0479i	1.38610	−	1.38610i
$302$	−2.62817	+	0.416261i	−0.151234	+	0.0239532i
$303$		0			0
$304$	−0.723529	+	4.56818i	−0.0414973	+	0.262003i
$305$	2.65025	−	8.15664i	0.151753	−	0.467048i
$306$		0			0
$307$	−20.7993	+	6.75809i	−1.18708	+	0.385705i	−0.834991	−	0.550263i	$-0.814527\pi$
$307$	−20.7993	+	6.75809i	−1.18708	+	0.385705i	−0.352086	+	0.935968i	$0.614527\pi$
$308$	−13.5233	+	4.39399i	−0.770562	+	0.250371i
$309$		0			0
$310$	1.13798	−	3.50235i	0.0646331	−	0.198920i
$311$	2.49509	−	15.7534i	0.141483	−	0.893291i	−0.810188	−	0.586171i	$-0.800635\pi$
$311$	2.49509	−	15.7534i	0.141483	−	0.893291i	0.951671	−	0.307120i	$-0.0993653\pi$
$312$		0			0
$313$	−0.811177	+	0.128478i	−0.0458504	+	0.00726199i	−0.179318	−	0.983791i	$-0.557389\pi$
$313$	−0.811177	+	0.128478i	−0.0458504	+	0.00726199i	0.133467	+	0.991053i	$0.457389\pi$
$314$	−7.15796	+	7.15796i	−0.403947	+	0.403947i
$315$		0			0
$316$	1.43233	+	9.04340i	0.0805751	+	0.508731i
$317$	−27.9438	−	4.42587i	−1.56948	−	0.248582i	−0.689749	−	0.724048i	$-0.742279\pi$
$317$	−27.9438	−	4.42587i	−1.56948	−	0.248582i	−0.879734	+	0.475467i	$0.842279\pi$
$318$		0			0
$319$		−	28.4407i		−	1.59237i
$320$	0.927096	+	1.27604i	0.0518262	+	0.0713327i
$321$		0			0
$322$	0.932312	+	1.82977i	0.0519557	+	0.101969i
$323$	−5.02232	+	6.91263i	−0.279449	+	0.384629i
$324$		0			0
$325$	−6.37586	−	6.37586i	−0.353669	−	0.353669i
$326$	0.645108	+	0.209608i	0.0357292	+	0.0116091i
$327$		0			0
$328$	−8.31398	+	13.9930i	−0.459063	+	0.772634i
$329$	36.1819			1.99477
$330$		0			0
$331$	21.7469	+	21.7469i	1.19532	+	1.19532i	0.975554	+	0.219762i	$0.0705281\pi$
$331$	21.7469	+	21.7469i	1.19532	+	1.19532i	0.219762	+	0.975554i	$0.429472\pi$
$332$	9.25966	+	6.72753i	0.508190	+	0.369221i
$333$		0			0
$334$	−5.67020	−	11.1284i	−0.310260	−	0.608919i
$335$	2.64108	−	5.18341i	0.144297	−	0.283200i
$336$		0			0
$337$		−	26.0552i		−	1.41932i	−0.704546	−	0.709658i	$-0.748849\pi$
$337$		−	26.0552i		−	1.41932i	0.704546	−	0.709658i	$-0.251151\pi$
$338$	5.32301	−	3.86739i	0.289533	−	0.210358i
$339$		0			0
$340$	−0.319286	−	2.01589i	−0.0173157	−	0.109327i
$341$	19.3304	−	9.84934i	1.04680	−	0.533372i
$342$		0			0
$343$	−12.9506	+	2.05118i	−0.699268	+	0.110753i
$344$	−8.52723	−	26.2441i	−0.459758	−	1.41499i
$345$		0			0
$346$	−2.75644	+	8.48345i	−0.148187	+	0.456073i
$347$	5.78097	+	2.94555i	0.310339	+	0.158126i	0.602223	−	0.798328i	$-0.294282\pi$
$347$	5.78097	+	2.94555i	0.310339	+	0.158126i	−0.291884	+	0.956454i	$0.594282\pi$
$348$		0			0
$349$	7.18918	−	2.33591i	0.384828	−	0.125038i	−0.110213	−	0.993908i	$-0.535153\pi$
$349$	7.18918	−	2.33591i	0.384828	−	0.125038i	0.495041	+	0.868870i	$0.335153\pi$
$350$	9.19508	+	4.68513i	0.491498	+	0.250431i
$351$		0			0
$352$	−2.84801	+	17.9817i	−0.151800	+	0.958425i
$353$	11.4959	+	35.3808i	0.611866	+	1.88313i	0.439967	+	0.898014i	$0.354990\pi$
$353$	11.4959	+	35.3808i	0.611866	+	1.88313i	0.171899	+	0.985115i	$0.445010\pi$
$354$		0			0
$355$	0.508029	−	0.508029i	0.0269634	−	0.0269634i
$356$	−18.3709	+	9.36044i	−0.973655	+	0.496102i
$357$		0			0
$358$	−1.55169	−	0.245764i	−0.0820095	−	0.0129890i
$359$	−17.5992	+	12.7866i	−0.928849	+	0.674848i	−0.945711	−	0.325009i	$-0.894633\pi$
$359$	−17.5992	+	12.7866i	−0.928849	+	0.674848i	0.0168617	+	0.999858i	$0.494633\pi$
$360$		0			0
$361$	0.162984	+	0.224329i	0.00857813	+	0.0118068i
$362$	1.87354	−	3.67703i	0.0984711	−	0.193260i
$363$		0			0
$364$	−5.40733	+	7.44255i	−0.283421	+	0.390096i
$365$	3.77508	+	2.74276i	0.197597	+	0.143563i
$366$		0			0
$367$	−16.6389	−	5.40631i	−0.868544	−	0.282207i	−0.159352	−	0.987222i	$-0.550940\pi$
$367$	−16.6389	−	5.40631i	−0.868544	−	0.282207i	−0.709193	+	0.705015i	$0.750940\pi$
$368$	−0.940005			−0.0490011
$369$		0			0
$370$	2.27777			0.118416
$371$	8.87032	+	2.88214i	0.460524	+	0.149633i
$372$		0			0
$373$	5.79680	+	4.21162i	0.300147	+	0.218070i	0.727657	−	0.685941i	$-0.240609\pi$
$373$	5.79680	+	4.21162i	0.300147	+	0.218070i	−0.427510	+	0.904011i	$0.640609\pi$
$374$	−2.61160	+	3.59456i	−0.135043	+	0.185870i
$375$		0			0
$376$	13.3282	−	26.1581i	0.687349	−	1.34900i
$377$	−10.8155	−	14.8862i	−0.557026	−	0.766681i
$378$		0			0
$379$	6.38423	−	4.63842i	0.327936	−	0.238260i	−0.411618	−	0.911356i	$-0.635036\pi$
$379$	6.38423	−	4.63842i	0.327936	−	0.238260i	0.739554	+	0.673097i	$0.235036\pi$
$380$	−4.54807	−	0.720344i	−0.233311	−	0.0369529i
$381$		0			0
$382$	8.58807	−	4.37584i	0.439404	−	0.223887i
$383$	4.35320	−	4.35320i	0.222438	−	0.222438i	−0.587086	−	0.809524i	$-0.699725\pi$
$383$	4.35320	−	4.35320i	0.222438	−	0.222438i	0.809524	+	0.587086i	$0.199725\pi$
$384$		0			0
$385$	−2.16082	−	6.65031i	−0.110125	−	0.338931i
$386$	1.90495	−	12.0274i	0.0969592	−	0.612177i
$387$		0			0
$388$	−8.35313	−	4.25613i	−0.424066	−	0.216072i
$389$	21.1299	−	6.86553i	1.07133	−	0.348096i	0.280324	−	0.959905i	$-0.409558\pi$
$389$	21.1299	−	6.86553i	1.07133	−	0.348096i	0.791005	+	0.611809i	$0.209558\pi$
$390$		0			0
$391$	−1.54729	−	0.788386i	−0.0782501	−	0.0398704i
$392$	2.21093	−	6.80454i	0.111669	−	0.343681i
$393$		0			0
$394$	−3.28722	−	10.1170i	−0.165608	−	0.509688i
$395$	−4.44724	+	0.704374i	−0.223765	+	0.0354409i
$396$		0			0
$397$	5.81775	−	2.96429i	0.291984	−	0.148773i	−0.301863	−	0.953351i	$-0.597608\pi$
$397$	5.81775	−	2.96429i	0.291984	−	0.148773i	0.593847	+	0.804578i	$0.297608\pi$
$398$	−2.07297	−	13.0882i	−0.103909	−	0.656053i
$399$		0			0
$400$	−3.82162	+	2.77657i	−0.191081	+	0.138829i
$401$			21.3099i			1.06416i	0.846693	+	0.532082i	$0.178590\pi$
$401$			21.3099i			1.06416i	−0.846693	+	0.532082i	$0.821410\pi$
$402$		0			0
$403$	6.37228	−	12.5063i	0.317426	−	0.622984i
$404$	7.97745	+	15.6566i	0.396893	+	0.778946i
$405$		0			0
$406$	17.0375	+	12.3785i	0.845557	+	0.614333i
$407$	9.48858	+	9.48858i	0.470331	+	0.470331i
$408$		0			0
$409$	3.89625			0.192657			0.0963287	−	0.995350i	$-0.469290\pi$
$409$	3.89625			0.192657			0.0963287	+	0.995350i	$0.469290\pi$
$410$	−2.90409	−	1.72547i	−0.143423	−	0.0852150i
$411$		0			0
$412$	21.3552	+	6.93871i	1.05209	+	0.341846i
$413$	−9.85779	−	9.85779i	−0.485070	−	0.485070i
$414$		0			0
$415$	−3.30838	+	4.55359i	−0.162402	+	0.223527i
$416$	5.34742	+	10.4949i	0.262179	+	0.514555i
$417$		0			0
$418$	5.89205	+	8.10971i	0.288190	+	0.396659i
$419$		−	14.8236i		−	0.724179i	−0.932143	−	0.362089i	$-0.882063\pi$
$419$		−	14.8236i		−	0.724179i	0.932143	−	0.362089i	$-0.117937\pi$
$420$		0			0
$421$	−10.9908	−	1.74076i	−0.535657	−	0.0848397i	−0.117255	−	0.993102i	$-0.537410\pi$
$421$	−10.9908	−	1.74076i	−0.535657	−	0.0848397i	−0.418402	+	0.908262i	$0.637410\pi$
$422$	−1.55156	−	9.79614i	−0.0755286	−	0.476869i
$423$		0			0
$424$	5.35121	−	5.35121i	0.259878	−	0.259878i
$425$	−8.61930	+	1.36516i	−0.418098	+	0.0662202i
$426$		0			0
$427$	−5.85265	+	36.9522i	−0.283230	+	1.78824i
$428$	0.503433	−	1.54941i	0.0243343	−	0.0748934i
$429$		0			0
$430$	5.44667	−	1.76973i	0.262662	−	0.0853440i
$431$	−25.1750	+	8.17986i	−1.21264	+	0.394010i	−0.844396	−	0.535720i	$-0.820040\pi$
$431$	−25.1750	+	8.17986i	−1.21264	+	0.394010i	−0.368242	+	0.929730i	$0.620040\pi$
$432$		0			0
$433$	0.144494	−	0.444707i	0.00694395	−	0.0213713i	−0.947525	−	0.319683i	$-0.896424\pi$
$433$	0.144494	−	0.444707i	0.00694395	−	0.0213713i	0.954468	+	0.298312i	$0.0964235\pi$
$434$	−2.51305	+	15.8668i	−0.120630	+	0.761630i
$435$		0			0
$436$	−8.53990	+	1.35259i	−0.408987	+	0.0647772i
$437$	−2.77037	+	2.77037i	−0.132525	+	0.132525i
$438$		0			0
$439$	−3.05677	−	19.2997i	−0.145892	−	0.921123i	−0.946680	−	0.322176i	$-0.895586\pi$
$439$	−3.05677	−	19.2997i	−0.145892	−	0.921123i	0.800788	−	0.598947i	$-0.204414\pi$
$440$	−5.60388	−	0.887568i	−0.267155	−	0.0423131i
$441$		0			0
$442$			2.87459i			0.136730i
$443$	−4.37823	−	6.02611i	−0.208016	−	0.286309i	0.692243	−	0.721665i	$-0.256623\pi$
$443$	−4.37823	−	6.02611i	−0.208016	−	0.286309i	−0.900259	+	0.435355i	$0.856623\pi$
$444$		0			0
$445$	−4.60315	−	9.03419i	−0.218210	−	0.428262i
$446$	3.27717	−	4.51063i	0.155178	−	0.213585i
$447$		0			0
$448$	−4.86526	−	4.86526i	−0.229862	−	0.229862i
$449$	−24.2920	−	7.89296i	−1.14641	−	0.372492i	−0.326621	−	0.945155i	$-0.605910\pi$
$449$	−24.2920	−	7.89296i	−1.14641	−	0.372492i	−0.819790	+	0.572664i	$0.805910\pi$
$450$		0			0
$451$	−4.90981	−	19.2855i	−0.231194	−	0.908121i
$452$	22.5594			1.06110
$453$		0			0
$454$	−11.2791	−	11.2791i	−0.529354	−	0.529354i
$455$	−3.66000	−	2.65914i	−0.171583	−	0.124663i
$456$		0			0
$457$	16.0293	+	31.4593i	0.749820	+	1.47161i	0.877391	+	0.479776i	$0.159282\pi$
$457$	16.0293	+	31.4593i	0.749820	+	1.47161i	−0.127571	+	0.991829i	$0.540718\pi$
$458$	0.987815	−	1.93870i	0.0461576	−	0.0905893i
$459$		0			0
$460$		−	0.935866i		−	0.0436350i
$461$	−23.0488	+	16.7459i	−1.07349	+	0.779936i	−0.976536	−	0.215353i	$-0.930910\pi$
$461$	−23.0488	+	16.7459i	−1.07349	+	0.779936i	−0.0969530	+	0.995289i	$0.530910\pi$
$462$		0			0
$463$	−2.00832	−	12.6801i	−0.0933348	−	0.589293i	−0.989383	−	0.145335i	$-0.953574\pi$
$463$	−2.00832	−	12.6801i	−0.0933348	−	0.589293i	0.896048	−	0.443958i	$-0.146426\pi$
$464$	−8.58904	+	4.37633i	−0.398736	+	0.203166i
$465$		0			0
$466$	−12.6253	+	1.99965i	−0.584856	+	0.0926321i
$467$	−9.10432	−	28.0202i	−0.421297	−	1.29662i	−0.906495	−	0.422216i	$-0.861252\pi$
$467$	−9.10432	−	28.0202i	−0.421297	−	1.29662i	0.485198	−	0.874404i	$-0.338748\pi$
$468$		0			0
$469$	−7.84210	+	24.1355i	−0.362114	+	1.11447i
$470$	5.42881	+	2.76612i	0.250412	+	0.127591i
$471$		0			0
$472$	−10.7581	+	3.49551i	−0.495180	+	0.160894i
$473$	30.0616	+	15.3172i	1.38224	+	0.704284i
$474$		0			0
$475$	−3.07996	+	19.4461i	−0.141318	+	0.892248i
$476$	2.75134	+	8.46777i	0.126108	+	0.388120i
$477$		0			0
$478$	−3.08562	+	3.08562i	−0.141133	+	0.141133i
$479$	23.8053	−	12.1294i	1.08769	−	0.554207i	0.184234	−	0.982882i	$-0.441020\pi$
$479$	23.8053	−	12.1294i	1.08769	−	0.554207i	0.903459	+	0.428675i	$0.141020\pi$
$480$		0			0
$481$	8.57480	+	1.35812i	0.390977	+	0.0619247i
$482$	−5.21943	+	3.79214i	−0.237739	+	0.172727i
$483$		0			0
$484$	1.15069	+	1.58379i	0.0523041	+	0.0719904i
$485$	2.09302	−	4.10779i	0.0950393	−	0.186525i
$486$		0			0
$487$	6.82210	−	9.38981i	0.309139	−	0.425493i	−0.625974	−	0.779844i	$-0.715298\pi$
$487$	6.82210	−	9.38981i	0.309139	−	0.425493i	0.935112	+	0.354351i	$0.115298\pi$
$488$	24.5591	+	17.8432i	1.11174	+	0.807724i
$489$		0			0
$490$	1.41221	+	0.458853i	0.0637969	+	0.0207289i
$491$	26.8852			1.21331			0.606656	−	0.794964i	$-0.292511\pi$
$491$	26.8852			1.21331			0.606656	+	0.794964i	$0.292511\pi$
$492$		0			0
$493$	−17.8084			−0.802052
$494$	6.16797	+	2.00409i	0.277510	+	0.0901685i
$495$		0			0
$496$	−5.94898	−	4.32218i	−0.267117	−	0.194072i
$497$	−1.84220	+	2.53557i	−0.0826341	+	0.113736i
$498$		0			0
$499$	5.83710	−	11.4559i	0.261304	−	0.512839i	−0.722660	−	0.691204i	$-0.757081\pi$
$499$	5.83710	−	11.4559i	0.261304	−	0.512839i	0.983964	+	0.178365i	$0.0570808\pi$
$500$	−5.84663	−	8.04720i	−0.261469	−	0.359882i
$501$		0			0
$502$	−3.04695	+	2.21374i	−0.135992	+	0.0988041i
$503$	−11.9300	−	1.88953i	−0.531934	−	0.0842501i	−0.115311	−	0.993329i	$-0.536786\pi$
$503$	−11.9300	−	1.88953i	−0.531934	−	0.0842501i	−0.416623	+	0.909079i	$0.636786\pi$
$504$		0			0
$505$	−7.69940	+	3.92304i	−0.342619	+	0.174573i
$506$	−1.44059	+	1.44059i	−0.0640419	+	0.0640419i
$507$		0			0
$508$	−1.95669	−	6.02208i	−0.0868141	−	0.267186i
$509$	−4.55017	+	28.7287i	−0.201683	+	1.27338i	0.654246	+	0.756282i	$0.272986\pi$
$509$	−4.55017	+	28.7287i	−0.201683	+	1.27338i	−0.855929	+	0.517094i	$0.827014\pi$
$510$		0			0
$511$	−18.1370	−	9.24126i	−0.802333	−	0.408809i
$512$	10.9621	−	3.56179i	0.484460	−	0.157411i
$513$		0			0
$514$	−0.719519	−	0.366613i	−0.0317366	−	0.0161706i
$515$	−3.41223	+	10.5017i	−0.150361	+	0.462762i
$516$		0			0
$517$	11.0921	+	34.1379i	0.487829	+	1.50138i
$518$	−9.81397	+	1.55438i	−0.431201	+	0.0682956i
$519$		0			0
$520$	−3.27068	+	1.66649i	−0.143429	+	0.0730806i
$521$	−3.39562	−	21.4391i	−0.148765	−	0.939264i	−0.943275	−	0.332013i	$-0.892272\pi$
$521$	−3.39562	−	21.4391i	−0.148765	−	0.939264i	0.794510	−	0.607251i	$-0.207728\pi$
$522$		0			0
$523$	−12.7639	+	9.27355i	−0.558128	+	0.405504i	−0.830773	−	0.556611i	$-0.812102\pi$
$523$	−12.7639	+	9.27355i	−0.558128	+	0.405504i	0.272645	+	0.962115i	$0.412102\pi$
$524$		−	24.2047i		−	1.05739i
$525$		0			0
$526$	−4.25648	+	8.35382i	−0.185592	+	0.364244i
$527$	−6.16728	−	12.1040i	−0.268651	−	0.527257i
$528$		0			0
$529$	17.9632	+	13.0510i	0.781009	+	0.567436i
$530$	1.11058	+	1.11058i	0.0482406	+	0.0482406i
$531$		0			0
$532$	20.0874			0.870897
$533$	−9.90382	−	8.22721i	−0.428982	−	0.356360i
$534$		0			0
$535$	0.761946	+	0.247571i	0.0329418	+	0.0107034i
$536$	14.5602	+	14.5602i	0.628907	+	0.628907i
$537$		0			0
$538$	0.238379	−	0.328101i	0.0102773	−	0.0141454i
$539$	3.97141	+	7.79434i	0.171061	+	0.335726i
$540$		0			0
$541$	2.48515	+	3.42051i	0.106845	+	0.147059i	0.859091	−	0.511823i	$-0.171030\pi$
$541$	2.48515	+	3.42051i	0.106845	+	0.147059i	−0.752246	+	0.658882i	$0.771030\pi$
$542$			2.02768i			0.0870965i
$543$		0			0
$544$	11.2594	+	1.78332i	0.482743	+	0.0764590i
$545$	−0.665157	−	4.19964i	−0.0284922	−	0.179893i
$546$		0			0
$547$	−1.68661	+	1.68661i	−0.0721143	+	0.0721143i	−0.742244	−	0.670130i	$-0.766238\pi$
$547$	−1.68661	+	1.68661i	−0.0721143	+	0.0721143i	0.670130	+	0.742244i	$0.266238\pi$
$548$	−0.340362	+	0.0539081i	−0.0145396	+	0.00230284i
$549$		0			0
$550$	−1.60157	+	10.1119i	−0.0682913	+	0.431174i
$551$	−12.4156	+	38.2113i	−0.528923	+	1.62786i
$552$		0			0
$553$	18.6807	−	6.06972i	0.794383	−	0.258111i
$554$	−14.8544	+	4.82648i	−0.631102	+	0.205057i
$555$		0			0
$556$	−1.06294	+	3.27139i	−0.0450787	+	0.138738i
$557$	−1.20951	+	7.63657i	−0.0512487	+	0.323572i	0.948723	+	0.316107i	$0.102376\pi$
$557$	−1.20951	+	7.63657i	−0.0512487	+	0.323572i	−0.999972	+	0.00746438i	$0.997624\pi$
$558$		0			0
$559$	21.5595	−	3.41470i	0.911871	−	0.144426i
$560$	−1.67589	+	1.67589i	−0.0708191	+	0.0708191i
$561$		0			0
$562$	−0.205981	−	1.30051i	−0.00868878	−	0.0548588i
$563$	−29.4356	−	4.66214i	−1.24056	−	0.196486i	−0.498543	−	0.866865i	$-0.666131\pi$
$563$	−29.4356	−	4.66214i	−1.24056	−	0.196486i	−0.742019	+	0.670379i	$0.766131\pi$
$564$		0			0
$565$			11.0940i			0.466726i
$566$	1.60558	+	2.20989i	0.0674875	+	0.0928885i
$567$		0			0
$568$	1.15451	+	2.26586i	0.0484423	+	0.0950734i
$569$	5.19710	−	7.15320i	0.217874	−	0.299878i	−0.686064	−	0.727541i	$-0.740663\pi$
$569$	5.19710	−	7.15320i	0.217874	−	0.299878i	0.903938	+	0.427663i	$0.140663\pi$
$570$		0			0
$571$	15.7965	+	15.7965i	0.661063	+	0.661063i	0.955631	−	0.294567i	$-0.0951756\pi$
$571$	15.7965	+	15.7965i	0.661063	+	0.661063i	−0.294567	+	0.955631i	$0.595176\pi$
$572$	−8.67981	−	2.82024i	−0.362921	−	0.117920i
$573$		0			0
$574$	13.6900	+	5.45256i	0.571411	+	0.227586i
$575$	−4.00146			−0.166872
$576$		0			0
$577$	8.51989	+	8.51989i	0.354688	+	0.354688i	0.861850	−	0.507163i	$-0.169306\pi$
$577$	8.51989	+	8.51989i	0.354688	+	0.354688i	−0.507163	+	0.861850i	$0.669306\pi$
$578$	−7.85233	−	5.70505i	−0.326614	−	0.237299i
$579$		0			0
$580$	−4.35707	−	8.55122i	−0.180917	−	0.355070i
$581$	11.1470	−	21.8772i	0.462456	−	0.907621i
$582$		0			0
$583$			9.25279i			0.383211i
$584$	−13.3621	+	9.70816i	−0.552929	+	0.401726i
$585$		0			0
$586$	−1.59766	−	10.0872i	−0.0659988	−	0.416700i
$587$	22.9909	−	11.7145i	0.948936	−	0.483507i	0.0901991	−	0.995924i	$-0.471250\pi$
$587$	22.9909	−	11.7145i	0.948936	−	0.483507i	0.858737	+	0.512417i	$0.171250\pi$
$588$		0			0
$589$	−30.2710	+	4.79445i	−1.24729	+	0.197552i
$590$	−0.725454	−	2.23272i	−0.0298664	−	0.0919195i
$591$		0			0
$592$	1.40547	−	4.32560i	0.0577646	−	0.177781i
$593$	−18.5585	−	9.45605i	−0.762108	−	0.388313i	0.0293248	−	0.999570i	$-0.490664\pi$
$593$	−18.5585	−	9.45605i	−0.762108	−	0.388313i	−0.791432	+	0.611257i	$0.790664\pi$
$594$		0			0
$595$	−4.16416	+	1.35302i	−0.170714	+	0.0554684i
$596$	−10.9188	−	5.56341i	−0.447252	−	0.227886i
$597$		0			0
$598$	−0.206193	+	1.30185i	−0.00843187	+	0.0532367i
$599$	5.67622	+	17.4696i	0.231924	+	0.713789i	0.997515	+	0.0704605i	$0.0224469\pi$
$599$	5.67622	+	17.4696i	0.231924	+	0.713789i	−0.765591	+	0.643328i	$0.777553\pi$
$600$		0			0
$601$	−7.61945	+	7.61945i	−0.310804	+	0.310804i	−0.845221	−	0.534417i	$-0.820531\pi$
$601$	−7.61945	+	7.61945i	−0.310804	+	0.310804i	0.534417	+	0.845221i	$0.320531\pi$
$602$	−22.2598	+	11.3419i	−0.907241	+	0.462263i
$603$		0			0
$604$	−5.22478	−	0.827524i	−0.212593	−	0.0336715i
$605$	−0.778854	+	0.565870i	−0.0316649	+	0.0230059i
$606$		0			0
$607$	−8.17357	−	11.2500i	−0.331755	−	0.456622i	0.610256	−	0.792205i	$-0.291067\pi$
$607$	−8.17357	−	11.2500i	−0.331755	−	0.456622i	−0.942011	+	0.335583i	$0.891067\pi$
$608$	11.6762	−	22.9159i	0.473534	−	0.929362i
$609$		0			0
$610$	−3.70315	+	5.09695i	−0.149936	+	0.206370i
$611$	18.7878	+	13.6501i	0.760073	+	0.552226i
$612$		0			0
$613$	−14.1988	−	4.61346i	−0.573482	−	0.186336i	0.00789628	−	0.999969i	$-0.497487\pi$
$613$	−14.1988	−	4.61346i	−0.573482	−	0.186336i	−0.581379	+	0.813633i	$0.697487\pi$
$614$	16.0653			0.648344
$615$		0			0
$616$	24.7505			0.997227
$617$	−7.99439	−	2.59753i	−0.321842	−	0.104573i	0.143640	−	0.989630i	$-0.454119\pi$
$617$	−7.99439	−	2.59753i	−0.321842	−	0.104573i	−0.465482	+	0.885057i	$0.654119\pi$
$618$		0			0
$619$	−22.0401	−	16.0131i	−0.885866	−	0.643619i	0.0489312	−	0.998802i	$-0.484418\pi$
$619$	−22.0401	−	16.0131i	−0.885866	−	0.643619i	−0.934797	+	0.355183i	$0.884418\pi$
$620$	4.30315	−	5.92278i	0.172819	−	0.237865i
$621$		0			0
$622$	−5.31922	+	10.4396i	−0.213281	+	0.418588i
$623$	25.9981	+	35.7834i	1.04159	+	1.43363i
$624$		0			0
$625$	−14.1818	+	10.3037i	−0.567272	+	0.412148i
$626$	0.595887	+	0.0943792i	0.0238164	+	0.00377215i
$627$		0			0
$628$	−17.9308	+	9.13619i	−0.715516	+	0.364574i
$629$	5.94138	−	5.94138i	0.236898	−	0.236898i
$630$		0			0
$631$	0.989181	+	3.04439i	0.0393787	+	0.121195i	0.968813	−	0.247792i	$-0.0797048\pi$
$631$	0.989181	+	3.04439i	0.0393787	+	0.121195i	−0.929435	+	0.368987i	$0.879705\pi$
$632$	2.49317	−	15.7413i	0.0991731	−	0.626154i
$633$		0			0
$634$	18.5181	+	9.43542i	0.735446	+	0.374728i
$635$	2.96145	−	0.962235i	0.117522	−	0.0381851i
$636$		0			0
$637$	5.04275	+	2.56941i	0.199801	+	0.101804i
$638$	−6.45610	+	19.8698i	−0.255599	+	0.786654i
$639$		0			0
$640$	2.24192	+	6.89991i	0.0886196	+	0.272743i
$641$	42.6511	−	6.75528i	1.68462	−	0.266817i	0.760615	−	0.649203i	$-0.224897\pi$
$641$	42.6511	−	6.75528i	1.68462	−	0.266817i	0.924003	+	0.382385i	$0.124897\pi$
$642$		0			0
$643$	−3.56855	+	1.81827i	−0.140730	+	0.0717054i	−0.522937	−	0.852371i	$-0.675164\pi$
$643$	−3.56855	+	1.81827i	−0.140730	+	0.0717054i	0.382208	+	0.924076i	$0.375164\pi$
$644$	0.638648	+	4.03226i	0.0251663	+	0.158893i
$645$		0			0
$646$	5.07799	−	3.68937i	0.199791	−	0.145156i
$647$			16.9523i			0.666465i	0.942845	+	0.333232i	$0.108139\pi$
$647$			16.9523i			0.666465i	−0.942845	+	0.333232i	$0.891861\pi$
$648$		0			0
$649$	6.27886	−	12.3230i	0.246467	−	0.483718i
$650$	3.00711	+	5.90178i	0.117948	+	0.231487i
$651$		0			0
$652$	1.09093	+	0.792609i	0.0427242	+	0.0310410i
$653$	−12.3449	−	12.3449i	−0.483092	−	0.483092i	0.423026	−	0.906118i	$-0.360968\pi$
$653$	−12.3449	−	12.3449i	−0.483092	−	0.483092i	−0.906118	+	0.423026i	$0.860968\pi$
$654$		0			0
$655$	11.9031			0.465091
$656$	−5.06870	+	4.45034i	−0.197900	+	0.173757i
$657$		0			0
$658$	−25.2782	−	8.21337i	−0.985445	−	0.320191i
$659$	19.4232	+	19.4232i	0.756620	+	0.756620i	0.975706	−	0.219086i	$-0.0703075\pi$
$659$	19.4232	+	19.4232i	0.756620	+	0.756620i	−0.219086	+	0.975706i	$0.570308\pi$
$660$		0			0
$661$	−4.42412	+	6.08928i	−0.172078	+	0.236846i	−0.886342	−	0.463031i	$-0.846762\pi$
$661$	−4.42412	+	6.08928i	−0.172078	+	0.236846i	0.714264	+	0.699877i	$0.246762\pi$
$662$	−10.2567	−	20.1299i	−0.398637	−	0.782369i
$663$		0			0
$664$	−11.7102	−	16.1177i	−0.454443	−	0.625488i
$665$			9.87829i			0.383063i
$666$		0			0
$667$	−8.06515	−	1.27739i	−0.312284	−	0.0494609i
$668$	−3.88417	−	24.5237i	−0.150283	−	0.948851i
$669$		0			0
$670$	−3.02181	+	3.02181i	−0.116743	+	0.116743i
$671$	−36.6589	+	5.80620i	−1.41520	+	0.224146i
$672$		0			0
$673$	6.65260	−	42.0029i	0.256439	−	1.61909i	−0.437610	−	0.899165i	$-0.644175\pi$
$673$	6.65260	−	42.0029i	0.256439	−	1.61909i	0.694049	−	0.719927i	$-0.255825\pi$
$674$	−5.91459	+	18.2032i	−0.227822	+	0.701163i
$675$		0			0
$676$	12.4400	−	4.04200i	0.478461	−	0.155462i
$677$	44.0320	−	14.3069i	1.69229	−	0.549857i	0.705056	−	0.709152i	$-0.250922\pi$
$677$	44.0320	−	14.3069i	1.69229	−	0.549857i	0.987231	+	0.159294i	$0.0509219\pi$
$678$		0			0
$679$	−6.21477	+	19.1271i	−0.238501	+	0.734030i
$680$	−0.555760	+	3.50893i	−0.0213124	+	0.134561i
$681$		0			0
$682$	−15.7409	+	2.49311i	−0.602749	+	0.0954661i
$683$	−10.8884	+	10.8884i	−0.416633	+	0.416633i	−0.884041	−	0.467409i	$-0.845188\pi$
$683$	−10.8884	+	10.8884i	−0.416633	+	0.416633i	0.467409	+	0.884041i	$0.345188\pi$
$684$		0			0
$685$	−0.0265102	−	0.167379i	−0.00101290	−	0.00639522i
$686$	9.51347	+	1.50679i	0.363226	+	0.0575293i
$687$		0			0
$688$		−	11.4355i		−	0.435975i
$689$	3.51868	+	4.84304i	0.134051	+	0.184505i
$690$		0			0
$691$	19.4697	+	38.2115i	0.740664	+	1.45363i	0.885724	+	0.464212i	$0.153662\pi$
$691$	19.4697	+	38.2115i	0.740664	+	1.45363i	−0.145060	+	0.989423i	$0.546338\pi$
$692$	−10.4232	+	14.3462i	−0.396229	+	0.545363i
$693$		0			0
$694$	−3.37018	−	3.37018i	−0.127930	−	0.127930i
$695$	−1.60876	−	0.522718i	−0.0610237	−	0.0198278i
$696$		0			0
$697$	−12.0759	+	3.07433i	−0.457406	+	0.116449i
$698$	−5.55292			−0.210181
$699$		0			0
$700$	14.5069	+	14.5069i	0.548309	+	0.548309i
$701$	−23.6599	−	17.1899i	−0.893623	−	0.649255i	0.0431974	−	0.999067i	$-0.486246\pi$
$701$	−23.6599	−	17.1899i	−0.893623	−	0.649255i	−0.936820	+	0.349812i	$0.886246\pi$
$702$		0			0
$703$	−8.60616	−	16.8905i	−0.324587	−	0.637039i
$704$	3.09890	−	6.08193i	0.116794	−	0.229222i
$705$		0			0
$706$		−	27.3281i		−	1.02851i
$707$	30.4964	−	22.1570i	1.14694	−	0.833298i
$708$		0			0
$709$	1.32698	+	8.37821i	0.0498357	+	0.314650i	0.999996	+	0.00288796i	$0.000919268\pi$
$709$	1.32698	+	8.37821i	0.0498357	+	0.314650i	−0.950160	+	0.311762i	$0.899081\pi$
$710$	−0.470254	+	0.239606i	−0.0176483	+	0.00899227i
$711$		0			0
$712$	35.4468	−	5.61423i	1.32843	−	0.210402i
$713$	−1.92484	−	5.92406i	−0.0720860	−	0.221858i
$714$		0			0
$715$	1.38690	−	4.26844i	0.0518671	−	0.159631i
$716$	−2.78279	−	1.41790i	−0.103998	−	0.0529896i
$717$		0			0
$718$	15.1981	−	4.93816i	0.567188	−	0.184291i
$719$	−34.3184	−	17.4861i	−1.27986	−	0.652121i	−0.324031	−	0.946046i	$-0.605038\pi$
$719$	−34.3184	−	17.4861i	−1.27986	−	0.652121i	−0.955828	+	0.293926i	$0.905038\pi$
$720$		0			0
$721$	7.53535	−	47.5763i	0.280631	−	1.77183i
$722$	−0.0629445	−	0.193723i	−0.00234255	−	0.00720964i
$723$		0			0
$724$	5.80117	−	5.80117i	0.215599	−	0.215599i
$725$	−36.5623	+	18.6294i	−1.35789	+	0.691879i
$726$		0			0
$727$	−51.1019	−	8.09374i	−1.89526	−	0.300180i	−0.903533	−	0.428518i	$-0.859036\pi$
$727$	−51.1019	−	8.09374i	−1.89526	−	0.300180i	−0.991730	+	0.128338i	$0.959036\pi$
$728$	12.9548	−	9.41220i	0.480136	−	0.348839i
$729$		0			0
$730$	−2.01482	−	2.77316i	−0.0745718	−	0.102639i
$731$	9.59102	−	18.8234i	0.354737	−	0.696210i
$732$		0			0
$733$	0.369332	−	0.508342i	0.0136416	−	0.0187760i	−0.802142	−	0.597134i	$-0.796306\pi$
$733$	0.369332	−	0.508342i	0.0136416	−	0.0187760i	0.815783	+	0.578358i	$0.196306\pi$
$734$	10.3974	+	7.55415i	0.383775	+	0.278829i
$735$		0			0
$736$	4.97128	+	1.61527i	0.183244	+	0.0595396i
$737$	−25.1762			−0.927376
$738$		0			0
$739$	40.6971			1.49707			0.748533	−	0.663097i	$-0.230758\pi$
$739$	40.6971			1.49707			0.748533	+	0.663097i	$0.230758\pi$
$740$	4.30656	+	1.39929i	0.158312	+	0.0514388i
$741$		0			0
$742$	−5.54292	−	4.02717i	−0.203487	−	0.147842i
$743$	−9.43650	+	12.9882i	−0.346192	+	0.476492i	−0.946237	−	0.323474i	$-0.895149\pi$
$743$	−9.43650	+	12.9882i	−0.346192	+	0.476492i	0.600045	+	0.799966i	$0.295149\pi$
$744$		0			0
$745$	2.73590	−	5.36950i	0.100236	−	0.196723i
$746$	−3.09384	−	4.25830i	−0.113273	−	0.155908i
$747$		0			0
$748$	−7.14595	+	5.19184i	−0.261282	+	0.189832i
$749$	−3.45186	−	0.546721i	−0.126128	−	0.0199768i
$750$		0			0
$751$	26.2079	−	13.3536i	0.956339	−	0.487279i	0.0950935	−	0.995468i	$-0.469685\pi$
$751$	26.2079	−	13.3536i	0.956339	−	0.487279i	0.861245	+	0.508189i	$0.169685\pi$
$752$	8.60280	−	8.60280i	0.313712	−	0.313712i
$753$		0			0
$754$	4.17694	+	12.8553i	0.152115	+	0.468162i
$755$	0.406949	−	2.56937i	0.0148104	−	0.0935090i
$756$		0			0
$757$	32.6350	+	16.6284i	1.18614	+	0.604369i	0.931880	−	0.362767i	$-0.118168\pi$
$757$	32.6350	+	16.6284i	1.18614	+	0.604369i	0.254260	+	0.967136i	$0.418168\pi$
$758$	−5.51323	+	1.79136i	−0.200249	+	0.0650650i
$759$		0			0
$760$	7.14161	+	3.63883i	0.259053	+	0.131994i
$761$	8.21482	−	25.2826i	0.297787	−	0.916494i	−0.684484	−	0.729028i	$-0.739972\pi$
$761$	8.21482	−	25.2826i	0.297787	−	0.916494i	0.982271	−	0.187466i	$-0.0600276\pi$
$762$		0			0
$763$	5.73178	+	17.6406i	0.207504	+	0.638633i
$764$	18.9256	−	2.99752i	0.684703	−	0.108446i
$765$		0			0
$766$	−4.02951	+	2.05314i	−0.145592	+	0.0741830i
$767$	−1.39976	−	8.83775i	−0.0505425	−	0.319113i
$768$		0			0
$769$	−17.8728	+	12.9853i	−0.644509	+	0.468263i	−0.861396	−	0.507933i	$-0.830410\pi$
$769$	−17.8728	+	12.9853i	−0.644509	+	0.468263i	0.216887	+	0.976197i	$0.430410\pi$
$770$			5.13669i			0.185114i
$771$		0			0
$772$	10.9904	−	21.5698i	0.395552	−	0.776314i
$773$	15.6700	+	30.7541i	0.563610	+	1.10615i	0.980377	+	0.197133i	$0.0631632\pi$
$773$	15.6700	+	30.7541i	0.563610	+	1.10615i	−0.416767	+	0.909014i	$0.636837\pi$
$774$		0			0
$775$	−25.3239	−	18.3989i	−0.909662	−	0.660908i
$776$	11.5388	+	11.5388i	0.414219	+	0.414219i
$777$		0			0
$778$	−16.3207			−0.585127
$779$	−1.82244	+	28.0544i	−0.0652957	+	1.00515i
$780$		0			0
$781$	−2.95709	−	0.960817i	−0.105813	−	0.0343807i
$782$	0.902039	+	0.902039i	0.0322569	+	0.0322569i
$783$		0			0
$784$	1.74277	−	2.39872i	0.0622419	−	0.0856687i
$785$	−4.49287	−	8.81776i	−0.160358	−	0.314719i
$786$		0			0
$787$	4.79695	+	6.60244i	0.170993	+	0.235351i	0.885909	−	0.463858i	$-0.153535\pi$
$787$	4.79695	+	6.60244i	0.170993	+	0.235351i	−0.714917	+	0.699210i	$0.753535\pi$
$788$		−	21.1476i		−	0.753351i
$789$		0			0
$790$	3.26692	+	0.517430i	0.116232	+	0.0184093i
$791$	−7.57067	−	47.7993i	−0.269182	−	1.69955i
$792$		0			0
$793$	−16.9798	+	16.9798i	−0.602971	+	0.602971i
$794$	−4.73742	+	0.750334i	−0.168125	+	0.0266284i
$795$		0			0
$796$	4.12105	−	26.0193i	0.146067	−	0.922229i
$797$	−14.2797	+	43.9483i	−0.505812	+	1.55673i	0.293590	+	0.955931i	$0.405150\pi$
$797$	−14.2797	+	43.9483i	−0.505812	+	1.55673i	−0.799402	+	0.600797i	$0.794850\pi$
$798$		0			0
$799$	21.3758	−	6.94543i	0.756223	−	0.245712i
$800$	24.9821	−	8.11717i	0.883250	−	0.286985i
$801$		0			0
$802$	4.83739	−	14.8880i	0.170814	−	0.525712i
$803$	3.15905	−	19.9455i	0.111480	−	0.703860i
$804$		0			0
$805$	−1.98293	+	0.314066i	−0.0698892	+	0.0110694i
$806$	−7.29091	+	7.29091i	−0.256811	+	0.256811i
$807$		0			0
$808$	−4.78473	−	30.2096i	−0.168326	−	1.06277i
$809$	−0.358629	−	0.0568012i	−0.0126087	−	0.00199703i	0.150127	−	0.988667i	$-0.452032\pi$
$809$	−0.358629	−	0.0568012i	−0.0126087	−	0.00199703i	−0.162736	+	0.986670i	$0.552032\pi$
$810$		0			0
$811$			22.6805i			0.796419i	0.917295	+	0.398209i	$0.130368\pi$
$811$			22.6805i			0.796419i	−0.917295	+	0.398209i	$0.869632\pi$
$812$	24.6083	+	33.8704i	0.863582	+	1.18862i
$813$		0			0
$814$	−4.47519	−	8.78305i	−0.156855	−	0.307846i
$815$	−0.389779	+	0.536484i	−0.0136534	+	0.0187922i
$816$		0			0
$817$	−33.7026	−	33.7026i	−1.17910	−	1.17910i
$818$	−2.72209	−	0.884459i	−0.0951755	−	0.0309244i
$819$		0			0
$820$	−4.43074	−	5.04639i	−0.154728	−	0.176227i
$821$	12.5246			0.437111			0.218556	−	0.975824i	$-0.429865\pi$
$821$	12.5246			0.437111			0.218556	+	0.975824i	$0.429865\pi$
$822$		0			0
$823$	−21.7847	−	21.7847i	−0.759365	−	0.759365i	0.216842	−	0.976207i	$-0.430425\pi$
$823$	−21.7847	−	21.7847i	−0.759365	−	0.759365i	−0.976207	+	0.216842i	$0.930425\pi$
$824$	−31.6200	−	22.9733i	−1.10154	−	0.800312i
$825$		0			0
$826$	4.64932	+	9.12480i	0.161771	+	0.317493i
$827$	5.75807	−	11.3008i	0.200228	−	0.392969i	−0.768958	−	0.639299i	$-0.779225\pi$
$827$	5.75807	−	11.3008i	0.200228	−	0.392969i	0.969186	+	0.246330i	$0.0792247\pi$
$828$		0			0
$829$			47.8117i			1.66057i	0.557341	+	0.830284i	$0.311822\pi$
$829$			47.8117i			1.66057i	−0.557341	+	0.830284i	$0.688178\pi$
$830$	3.34505	−	2.43032i	0.116108	−	0.0843576i
$831$		0			0
$832$	−0.690846	−	4.36183i	−0.0239508	−	0.151219i
$833$	4.88051	−	2.48675i	0.169100	−	0.0861606i
$834$		0			0
$835$	12.0599	−	1.91011i	0.417351	−	0.0661020i
$836$	6.15807	+	18.9526i	0.212981	+	0.655489i
$837$		0			0
$838$	−3.36499	+	10.3564i	−0.116242	+	0.357755i
$839$	5.31936	+	2.71035i	0.183645	+	0.0935717i	0.543396	−	0.839477i	$-0.317138\pi$
$839$	5.31936	+	2.71035i	0.183645	+	0.0935717i	−0.359751	+	0.933048i	$0.617138\pi$
$840$		0			0
$841$	−52.0596	+	16.9152i	−1.79516	+	0.583282i
$842$	7.28344	+	3.71110i	0.251004	+	0.127893i
$843$		0			0
$844$	3.08448	−	19.4746i	0.106172	−	0.670345i
$845$	1.98772	+	6.11757i	0.0683796	+	0.210451i
$846$		0			0
$847$	2.96961	−	2.96961i	0.102037	−	0.102037i
$848$	2.79433	−	1.42378i	0.0959577	−	0.0488929i
$849$		0			0
$850$	6.33170	+	1.00284i	0.217176	+	0.0343972i
$851$	3.11693	−	2.26458i	0.106847	−	0.0776288i
$852$		0			0
$853$	−3.50643	−	4.82618i	−0.120058	−	0.165245i	0.744758	−	0.667335i	$-0.232565\pi$
$853$	−3.50643	−	4.82618i	−0.120058	−	0.165245i	−0.864816	+	0.502089i	$0.832565\pi$
$854$	12.4771	−	24.4878i	0.426959	−	0.837955i
$855$		0			0
$856$	−1.66681	+	2.29417i	−0.0569704	+	0.0784130i
$857$	−6.99504	−	5.08219i	−0.238946	−	0.173604i	0.461868	−	0.886949i	$-0.347180\pi$
$857$	−6.99504	−	5.08219i	−0.238946	−	0.173604i	−0.700814	+	0.713344i	$0.747180\pi$
$858$		0			0
$859$	34.4964	+	11.2086i	1.17700	+	0.382432i	0.831253	−	0.555895i	$-0.187624\pi$
$859$	34.4964	+	11.2086i	1.17700	+	0.382432i	0.345751	+	0.938326i	$0.387624\pi$
$860$	11.3852			0.388231
$861$		0			0
$862$	19.4452			0.662305
$863$	32.6565	+	10.6107i	1.11164	+	0.361193i	0.806571	−	0.591137i	$-0.201321\pi$
$863$	32.6565	+	10.6107i	1.11164	+	0.361193i	0.305068	+	0.952331i	$0.401321\pi$
$864$		0			0
$865$	−7.05500	−	5.12576i	−0.239877	−	0.174281i
$866$	−0.201899	+	0.277891i	−0.00686082	+	0.00944311i
$867$		0			0
$868$	−14.4987	+	28.4554i	−0.492119	+	0.965839i
$869$	11.4537	+	15.7646i	0.388539	+	0.534778i
$870$		0			0
$871$	−13.1776	+	9.57406i	−0.446505	+	0.324405i
$872$	14.8649	+	2.35436i	0.503388	+	0.0797288i
$873$		0			0
$874$	2.56437	−	1.30661i	0.0867412	−	0.0441969i
$875$	−15.0885	+	15.0885i	−0.510085	+	0.510085i
$876$		0			0
$877$	−13.8957	−	42.7666i	−0.469225	−	1.44413i	−0.853591	−	0.520944i	$-0.825580\pi$
$877$	−13.8957	−	42.7666i	−0.469225	−	1.44413i	0.384366	−	0.923181i	$-0.374420\pi$
$878$	−2.24549	+	14.1775i	−0.0757815	+	0.478466i
$879$		0			0
$880$	−2.09498	−	1.06745i	−0.0706218	−	0.0359836i
$881$	−26.6642	+	8.66372i	−0.898339	+	0.291888i	−0.721551	−	0.692361i	$-0.756571\pi$
$881$	−26.6642	+	8.66372i	−0.898339	+	0.291888i	−0.176788	+	0.984249i	$0.556571\pi$
$882$		0			0
$883$	34.0612	+	17.3551i	1.14625	+	0.584044i	0.920733	−	0.390194i	$-0.127592\pi$
$883$	34.0612	+	17.3551i	1.14625	+	0.584044i	0.225519	+	0.974239i	$0.427592\pi$
$884$	−1.76593	+	5.43496i	−0.0593945	+	0.182798i
$885$		0			0
$886$	1.69087	+	5.20396i	0.0568059	+	0.174830i
$887$	−15.7052	+	2.48746i	−0.527329	+	0.0835207i	−0.414422	−	0.910085i	$-0.636016\pi$
$887$	−15.7052	+	2.48746i	−0.527329	+	0.0835207i	−0.112907	+	0.993606i	$0.536016\pi$
$888$		0			0
$889$	−12.1031	+	6.16682i	−0.405923	+	0.206828i
$890$	1.16517	+	7.35659i	0.0390566	+	0.246593i
$891$		0			0
$892$	8.96710	−	6.51498i	0.300241	−	0.218138i
$893$		−	50.7080i		−	1.69688i
$894$		0			0
$895$	0.697278	−	1.36849i	0.0233074	−	0.0457434i
$896$	−14.3681	−	28.1990i	−0.480005	−	0.942062i
$897$		0			0
$898$	15.1797	+	11.0287i	0.506553	+	0.368032i
$899$	−45.1681	−	45.1681i	−1.50644	−	1.50644i
$900$		0			0
$901$	5.79374			0.193017
$902$	−0.947666	+	14.5882i	−0.0315538	+	0.485735i
$903$		0			0
$904$	−37.3458	−	12.1344i	−1.24210	−	0.403584i
$905$	2.85282	+	2.85282i	0.0948310	+	0.0948310i
$906$		0			0
$907$	25.3442	−	34.8834i	0.841542	−	1.15828i	−0.144122	−	0.989560i	$-0.546036\pi$
$907$	25.3442	−	34.8834i	0.841542	−	1.15828i	0.985664	−	0.168723i	$-0.0539643\pi$
$908$	−14.3963	−	28.2543i	−0.477757	−	0.937652i
$909$		0			0
$910$	1.95340	+	2.68862i	0.0647544	+	0.0891268i
$911$		−	26.3499i		−	0.873010i	−0.899702	−	0.436505i	$-0.856216\pi$
$911$		−	26.3499i		−	0.873010i	0.899702	−	0.436505i	$-0.143784\pi$
$912$		0			0
$913$	24.0586	+	3.81051i	0.796225	+	0.126110i
$914$	−4.05741	−	25.6175i	−0.134207	−	0.847352i
$915$		0			0
$916$	3.05864	−	3.05864i	0.101060	−	0.101060i
$917$	−51.2854	+	8.12282i	−1.69359	+	0.268239i
$918$		0			0
$919$	4.74106	−	29.9339i	0.156393	−	0.987427i	−0.777242	−	0.629202i	$-0.783382\pi$
$919$	4.74106	−	29.9339i	0.156393	−	0.987427i	0.933635	−	0.358226i	$-0.116618\pi$
$920$	−0.503389	+	1.54927i	−0.0165963	+	0.0510780i
$921$		0			0
$922$	19.9042	−	6.46727i	0.655510	−	0.212988i
$923$	−1.91317	+	0.621625i	−0.0629726	+	0.0204610i
$924$		0			0
$925$	5.98289	−	18.4135i	0.196716	−	0.605431i
$926$	−1.47531	+	9.31472i	−0.0484816	+	0.306101i
$927$		0			0
$928$	52.9439	−	8.38549i	1.73797	−	0.275267i
$929$	14.3945	−	14.3945i	0.472267	−	0.472267i	−0.430381	−	0.902647i	$-0.641621\pi$
$929$	14.3945	−	14.3945i	0.472267	−	0.472267i	0.902647	+	0.430381i	$0.141621\pi$
$930$		0			0
$931$	−1.93320	−	12.2058i	−0.0633581	−	0.400027i
$932$	−25.0990	−	3.97529i	−0.822145	−	0.130215i
$933$		0			0
$934$			21.6428i			0.708174i
$935$	−2.55317	−	3.51414i	−0.0834976	−	0.114925i
$936$		0			0
$937$	−16.9622	−	33.2901i	−0.554130	−	1.08754i	−0.982902	−	0.184129i	$-0.941054\pi$
$937$	−16.9622	−	33.2901i	−0.554130	−	1.08754i	0.428772	−	0.903413i	$-0.358946\pi$
$938$	10.9576	−	15.0819i	0.357779	−	0.492441i
$939$		0			0
$940$	8.56492	+	8.56492i	0.279357	+	0.279357i
$941$	23.3267	+	7.57929i	0.760427	+	0.247078i	0.663462	−	0.748210i	$-0.269086\pi$
$941$	23.3267	+	7.57929i	0.760427	+	0.247078i	0.0969652	+	0.995288i	$0.469086\pi$
$942$		0			0
$943$	−5.68948	+	0.526117i	−0.185275	+	0.0171327i
$944$	−4.68768			−0.152571
$945$		0			0
$946$	−17.5253	−	17.5253i	−0.569796	−	0.569796i
$947$	46.3059	+	33.6432i	1.50474	+	1.09326i	0.968446	+	0.249224i	$0.0801755\pi$
$947$	46.3059	+	33.6432i	1.50474	+	1.09326i	0.536292	+	0.844032i	$0.319825\pi$
$948$		0			0
$949$	−5.93142	−	11.6411i	−0.192542	−	0.377885i
$950$	6.56610	−	12.8867i	0.213032	−	0.418099i
$951$		0			0
$952$		−	15.4978i		−	0.502287i
$953$	−20.8828	+	15.1723i	−0.676461	+	0.491478i	−0.872182	−	0.489182i	$-0.837295\pi$
$953$	−20.8828	+	15.1723i	−0.676461	+	0.491478i	0.195721	+	0.980660i	$0.437295\pi$
$954$		0			0
$955$	1.47408	+	9.30696i	0.0477000	+	0.301166i
$956$	−7.72953	+	3.93839i	−0.249991	+	0.127377i
$957$		0			0
$958$	−19.3848	+	3.07025i	−0.626294	+	0.0991953i
$959$	0.228443	+	0.703076i	0.00737682	+	0.0227035i
$960$		0			0
$961$	5.47787	−	16.8592i	0.176706	−	0.543844i
$962$	−5.68242	−	2.89534i	−0.183209	−	0.0933494i
$963$		0			0
$964$	−12.1979	+	3.96335i	−0.392869	+	0.127651i
$965$	10.6073	+	5.40469i	0.341461	+	0.173983i
$966$		0			0
$967$	−7.85597	+	49.6006i	−0.252631	+	1.59505i	0.456336	+	0.889807i	$0.349161\pi$
$967$	−7.85597	+	49.6006i	−0.252631	+	1.59505i	−0.708967	+	0.705241i	$0.750839\pi$
$968$	−1.05300	−	3.24081i	−0.0338448	−	0.104164i
$969$		0			0
$970$	−2.39475	+	2.39475i	−0.0768908	+	0.0768908i
$971$	21.9048	−	11.1611i	0.702960	−	0.358176i	−0.0656949	−	0.997840i	$-0.520926\pi$
$971$	21.9048	−	11.1611i	0.702960	−	0.358176i	0.768655	+	0.639664i	$0.220926\pi$
$972$		0			0
$973$	7.28820	+	1.15434i	0.233649	+	0.0370064i
$974$	−6.89771	+	5.01148i	−0.221017	+	0.160578i
$975$		0			0
$976$	7.39440	+	10.1775i	0.236689	+	0.325774i
$977$	16.7259	−	32.8265i	0.535110	−	1.05021i	−0.452275	−	0.891878i	$-0.649388\pi$
$977$	16.7259	−	32.8265i	0.535110	−	1.05021i	0.987386	−	0.158334i	$-0.0506124\pi$
$978$		0			0
$979$	−25.7918	+	35.4994i	−0.824310	+	1.13457i
$980$	2.38816	+	1.73510i	0.0762870	+	0.0554258i
$981$		0			0
$982$	−18.7831	−	6.10301i	−0.599394	−	0.194755i
$983$	−24.1327			−0.769713			−0.384857	−	0.922976i	$-0.625749\pi$
$983$	−24.1327			−0.769713			−0.384857	+	0.922976i	$0.625749\pi$
$984$		0			0
$985$	10.3997			0.331361
$986$	12.4417	+	4.04256i	0.396225	+	0.128741i
$987$		0			0
$988$	10.4306	+	7.57825i	0.331841	+	0.241096i
$989$	5.69381	−	7.83686i	0.181053	−	0.249198i
$990$		0			0
$991$	−3.15702	+	6.19601i	−0.100286	+	0.196823i	−0.935698	−	0.352802i	$-0.885229\pi$
$991$	−3.15702	+	6.19601i	−0.100286	+	0.196823i	0.835412	+	0.549624i	$0.185229\pi$
$992$	24.0345	+	33.0807i	0.763097	+	1.05031i
$993$		0			0
$994$	1.86262	−	1.35327i	0.0590788	−	0.0429232i
$995$	12.7954	+	2.02659i	0.405642	+	0.0642473i
$996$		0			0
$997$	−29.1900	+	14.8731i	−0.924458	+	0.471035i	−0.850351	−	0.526216i	$-0.823610\pi$
$997$	−29.1900	+	14.8731i	−0.924458	+	0.471035i	−0.0741065	+	0.997250i	$0.523610\pi$
$998$	−6.67857	+	6.67857i	−0.211406	+	0.211406i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.2.u.a.226.1		24
3.2	odd	2		41.2.g.a.21.3	yes	24
12.11	even	2		656.2.bs.d.513.2		24
41.2	even	20	inner	369.2.u.a.289.1		24
123.2	odd	20		41.2.g.a.2.3	✓	24
123.17	even	40		1681.2.a.m.1.9		24
123.65	even	40		1681.2.a.m.1.10		24
492.371	even	20		656.2.bs.d.289.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.2.3	✓	24	123.2	odd	20
41.2.g.a.21.3	yes	24	3.2	odd	2
369.2.u.a.226.1		24	1.1	even	1	trivial
369.2.u.a.289.1		24	41.2	even	20	inner
656.2.bs.d.289.2		24	492.371	even	20
656.2.bs.d.513.2		24	12.11	even	2
1681.2.a.m.1.9		24	123.17	even	40
1681.2.a.m.1.10		24	123.65	even	40

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:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	369.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.698642 - 0.227002i) q^{2} +(-1.18146 - 0.858384i) q^{4} +(0.422124 - 0.581004i) q^{5} +(-1.42228 + 2.79137i) q^{7} +(1.49413 + 2.05650i) q^{8} +O(q^{10})\)	\(q+(-0.698642 - 0.227002i) q^{2} +(-1.18146 - 0.858384i) q^{4} +(0.422124 - 0.581004i) q^{5} +(-1.42228 + 2.79137i) q^{7} +(1.49413 + 2.05650i) q^{8} +(-0.426803 + 0.310091i) q^{10} +(-3.06970 - 0.486193i) q^{11} +(-1.79162 + 0.912875i) q^{13} +(1.62731 - 1.62731i) q^{14} +(0.325524 + 1.00186i) q^{16} +(-0.304435 + 1.92213i) q^{17} +(3.91204 + 1.99329i) q^{19} +(-0.997449 + 0.324091i) q^{20} +(2.03426 + 1.03651i) q^{22} +(-0.275748 + 0.848664i) q^{23} +(1.38571 + 4.26477i) q^{25} +(1.45892 - 0.231071i) q^{26} +(4.07644 - 2.07705i) q^{28} +(1.43151 + 9.03822i) q^{29} +(-5.64731 + 4.10301i) q^{31} -5.85778i q^{32} +(0.649020 - 1.27377i) q^{34} +(1.02142 + 2.00465i) q^{35} +(-3.49299 - 2.53781i) q^{37} +(-2.28064 - 2.28064i) q^{38} +1.82554 q^{40} +(2.53101 + 5.88167i) q^{41} +(-10.3243 - 3.35457i) q^{43} +(3.20940 + 3.20940i) q^{44} +(0.385298 - 0.530317i) q^{46} +(-5.24325 - 10.2905i) q^{47} +(-1.65440 - 2.27709i) q^{49} -3.29411i q^{50} +(2.90033 + 0.459367i) q^{52} +(-0.465724 - 2.94046i) q^{53} +(-1.57828 + 1.57828i) q^{55} +(-7.86552 + 1.24578i) q^{56} +(1.05158 - 6.63944i) q^{58} +(-1.37512 + 4.23218i) q^{59} +(11.3577 - 3.69033i) q^{61} +(4.87684 - 1.58458i) q^{62} +(-0.678682 + 2.08877i) q^{64} +(-0.225901 + 1.42628i) q^{65} +(8.00079 - 1.26720i) q^{67} +(2.00960 - 2.00960i) q^{68} +(-0.258547 - 1.63240i) q^{70} +(0.988102 + 0.156500i) q^{71} +6.49752i q^{73} +(1.86426 + 2.56593i) q^{74} +(-2.91093 - 5.71303i) q^{76} +(5.72311 - 7.87719i) q^{77} +(-4.43337 - 4.43337i) q^{79} +(0.719497 + 0.233779i) q^{80} +(-0.433113 - 4.68372i) q^{82} -7.83744 q^{83} +(0.988256 + 0.988256i) q^{85} +(6.45150 + 4.68729i) q^{86} +(-3.58669 - 7.03928i) q^{88} +(6.40964 - 12.5796i) q^{89} -6.29943i q^{91} +(1.05426 - 0.765968i) q^{92} +(1.32719 + 8.37958i) q^{94} +(2.80948 - 1.43150i) q^{95} +(6.34053 - 1.00424i) q^{97} +(0.638929 + 1.96642i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

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