LMFDB - Embedded newform 369.2.u.a.244.1

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			244.1
Character	$\chi$	$=$	369.244
Dual form			369.2.u.a.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14785 + 0.372958i) q^{2} +(-0.439578 + 0.319372i) q^{4} +(-1.49595 - 2.05900i) q^{5} +(-1.01547 + 0.517405i) q^{7} +(1.80427 - 2.48337i) q^{8} +O(q^{10})$	\(q+(-1.14785 + 0.372958i) q^{2} +(-0.439578 + 0.319372i) q^{4} +(-1.49595 - 2.05900i) q^{5} +(-1.01547 + 0.517405i) q^{7} +(1.80427 - 2.48337i) q^{8} +(2.48504 + 1.80549i) q^{10} +(0.807883 + 5.10077i) q^{11} +(1.17315 - 2.30243i) q^{13} +(0.972629 - 0.972629i) q^{14} +(-0.809030 + 2.48994i) q^{16} +(3.05576 - 0.483986i) q^{17} +(3.74044 + 7.34102i) q^{19} +(1.31517 + 0.427326i) q^{20} +(-2.82970 - 5.55360i) q^{22} +(1.17869 + 3.62763i) q^{23} +(-0.456519 + 1.40502i) q^{25} +(-0.487884 + 3.08038i) q^{26} +(0.281132 - 0.551752i) q^{28} +(-5.72573 - 0.906866i) q^{29} +(3.65641 + 2.65654i) q^{31} +2.97943i q^{32} +(-3.32705 + 1.69521i) q^{34} +(2.58442 + 1.31683i) q^{35} +(0.584132 - 0.424397i) q^{37} +(-7.03134 - 7.03134i) q^{38} -7.81235 q^{40} +(5.78336 + 2.74822i) q^{41} +(1.75698 - 0.570876i) q^{43} +(-1.98417 - 1.98417i) q^{44} +(-2.70591 - 3.72436i) q^{46} +(3.15704 + 1.60859i) q^{47} +(-3.35104 + 4.61230i) q^{49} -1.78301i q^{50} +(0.219643 + 1.38677i) q^{52} +(5.52741 + 0.875456i) q^{53} +(9.29392 - 9.29392i) q^{55} +(-0.547268 + 3.45532i) q^{56} +(6.91048 - 1.09451i) q^{58} +(-0.242763 - 0.747149i) q^{59} +(6.70623 + 2.17898i) q^{61} +(-5.18778 - 1.68561i) q^{62} +(-2.72926 - 8.39980i) q^{64} +(-6.49567 + 1.02881i) q^{65} +(-0.835907 + 5.27771i) q^{67} +(-1.18868 + 1.18868i) q^{68} +(-3.45764 - 0.547637i) q^{70} +(-0.708805 - 4.47522i) q^{71} +0.149836i q^{73} +(-0.512213 + 0.705000i) q^{74} +(-3.98873 - 2.03236i) q^{76} +(-3.45954 - 4.76165i) q^{77} +(-11.4389 - 11.4389i) q^{79} +(6.33704 - 2.05903i) q^{80} +(-7.66339 - 0.997584i) q^{82} -4.27258 q^{83} +(-5.56779 - 5.56779i) q^{85} +(-1.80383 + 1.31056i) q^{86} +(14.1247 + 7.19691i) q^{88} +(1.51781 - 0.773362i) q^{89} +2.94503i q^{91} +(-1.67669 - 1.21819i) q^{92} +(-4.22374 - 0.668975i) q^{94} +(9.51963 - 18.6833i) q^{95} +(0.687542 - 4.34097i) q^{97} +(2.12628 - 6.54402i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$1$	$e\left(\frac{3}{20}\right)$

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 $

$2$	−1.14785	+	0.372958i	−0.811651	+	0.263721i	−0.685297	−	0.728264i	$-0.740327\pi$
$2$	−1.14785	+	0.372958i	−0.811651	+	0.263721i	−0.126354	+	0.991985i	$0.540327\pi$
$3$		0			0
$3$		0			0
$4$	−0.439578	+	0.319372i	−0.219789	+	0.159686i
$5$	−1.49595	−	2.05900i	−0.669008	−	0.920811i	0.330729	−	0.943726i	$-0.392705\pi$
$5$	−1.49595	−	2.05900i	−0.669008	−	0.920811i	−0.999737	+	0.0229146i	$0.992705\pi$
$6$		0			0
$7$	−1.01547	+	0.517405i	−0.383810	+	0.195561i	−0.635240	−	0.772314i	$-0.719099\pi$
$7$	−1.01547	+	0.517405i	−0.383810	+	0.195561i	0.251431	+	0.967875i	$0.419099\pi$
$8$	1.80427	−	2.48337i	0.637907	−	0.878004i
$9$		0			0
$10$	2.48504	+	1.80549i	0.785839	+	0.570945i
$11$	0.807883	+	5.10077i	0.243586	+	1.53794i	0.741642	+	0.670795i	$0.234047\pi$
$11$	0.807883	+	5.10077i	0.243586	+	1.53794i	−0.498057	+	0.867144i	$0.665953\pi$
$12$		0			0
$13$	1.17315	−	2.30243i	0.325373	−	0.638580i	−0.669147	−	0.743130i	$-0.733340\pi$
$13$	1.17315	−	2.30243i	0.325373	−	0.638580i	0.994520	+	0.104550i	$0.0333403\pi$
$14$	0.972629	−	0.972629i	0.259946	−	0.259946i
$15$		0			0
$16$	−0.809030	+	2.48994i	−0.202257	+	0.622484i
$17$	3.05576	−	0.483986i	0.741132	−	0.117384i	0.225559	−	0.974230i	$-0.427579\pi$
$17$	3.05576	−	0.483986i	0.741132	−	0.117384i	0.515573	+	0.856846i	$0.327579\pi$
$18$		0			0
$19$	3.74044	+	7.34102i	0.858115	+	1.68415i	0.720273	+	0.693691i	$0.244017\pi$
$19$	3.74044	+	7.34102i	0.858115	+	1.68415i	0.137842	+	0.990454i	$0.455983\pi$
$20$	1.31517	+	0.427326i	0.294082	+	0.0955529i
$21$		0			0
$22$	−2.82970	−	5.55360i	−0.603294	−	1.18403i
$23$	1.17869	+	3.62763i	0.245773	+	0.756413i	0.995508	+	0.0946746i	$0.0301811\pi$
$23$	1.17869	+	3.62763i	0.245773	+	0.756413i	−0.749735	+	0.661738i	$0.769819\pi$
$24$		0			0
$25$	−0.456519	+	1.40502i	−0.0913038	+	0.281004i
$26$	−0.487884	+	3.08038i	−0.0956819	+	0.604112i
$27$		0			0
$28$	0.281132	−	0.551752i	0.0531289	−	0.104271i
$29$	−5.72573	−	0.906866i	−1.06324	−	0.168401i	−0.399780	−	0.916611i	$-0.630913\pi$
$29$	−5.72573	−	0.906866i	−1.06324	−	0.168401i	−0.663461	+	0.748211i	$0.730913\pi$
$30$		0			0
$31$	3.65641	+	2.65654i	0.656711	+	0.477129i	0.865551	−	0.500821i	$-0.166969\pi$
$31$	3.65641	+	2.65654i	0.656711	+	0.477129i	−0.208840	+	0.977950i	$0.566969\pi$
$32$			2.97943i			0.526693i
$33$		0			0
$34$	−3.32705	+	1.69521i	−0.570584	+	0.290727i
$35$	2.58442	+	1.31683i	0.436847	+	0.222584i
$36$		0			0
$37$	0.584132	−	0.424397i	0.0960308	−	0.0697704i	−0.538734	−	0.842476i	$-0.681097\pi$
$37$	0.584132	−	0.424397i	0.0960308	−	0.0697704i	0.634765	+	0.772706i	$0.281097\pi$
$38$	−7.03134	−	7.03134i	−1.14063	−	1.14063i
$39$		0			0
$40$	−7.81235			−1.23524
$41$	5.78336	+	2.74822i	0.903210	+	0.429200i
$41$	5.78336	+	2.74822i	0.903210	+	0.429200i
$42$		0			0
$43$	1.75698	−	0.570876i	0.267936	−	0.0870578i	−0.171968	−	0.985103i	$-0.555012\pi$
$43$	1.75698	−	0.570876i	0.267936	−	0.0870578i	0.439904	+	0.898045i	$0.355012\pi$
$44$	−1.98417	−	1.98417i	−0.299125	−	0.299125i
$45$		0			0
$46$	−2.70591	−	3.72436i	−0.398964	−	0.549127i
$47$	3.15704	+	1.60859i	0.460502	+	0.234638i	0.668821	−	0.743423i	$-0.266799\pi$
$47$	3.15704	+	1.60859i	0.460502	+	0.234638i	−0.208319	+	0.978061i	$0.566799\pi$
$48$		0			0
$49$	−3.35104	+	4.61230i	−0.478719	+	0.658901i
$50$		−	1.78301i		−	0.252156i
$51$		0			0
$52$	0.219643	+	1.38677i	0.0304590	+	0.192310i
$53$	5.52741	+	0.875456i	0.759249	+	0.120253i	0.524042	−	0.851692i	$-0.324423\pi$
$53$	5.52741	+	0.875456i	0.759249	+	0.120253i	0.235206	+	0.971945i	$0.424423\pi$
$54$		0			0
$55$	9.29392	−	9.29392i	1.25319	−	1.25319i
$56$	−0.547268	+	3.45532i	−0.0731318	+	0.461736i
$57$		0			0
$58$	6.91048	−	1.09451i	0.907391	−	0.143717i
$59$	−0.242763	−	0.747149i	−0.0316051	−	0.0972705i	0.934010	−	0.357248i	$-0.116285\pi$
$59$	−0.242763	−	0.747149i	−0.0316051	−	0.0972705i	−0.965615	+	0.259977i	$0.916285\pi$
$60$		0			0
$61$	6.70623	+	2.17898i	0.858644	+	0.278990i	0.705062	−	0.709145i	$-0.250919\pi$
$61$	6.70623	+	2.17898i	0.858644	+	0.278990i	0.153582	+	0.988136i	$0.450919\pi$
$62$	−5.18778	−	1.68561i	−0.658849	−	0.214073i
$63$		0			0
$64$	−2.72926	−	8.39980i	−0.341158	−	1.04997i
$65$	−6.49567	+	1.02881i	−0.805689	+	0.127609i
$66$		0			0
$67$	−0.835907	+	5.27771i	−0.102122	+	0.644774i	0.882531	+	0.470254i	$0.155838\pi$
$67$	−0.835907	+	5.27771i	−0.102122	+	0.644774i	−0.984654	+	0.174521i	$0.944162\pi$
$68$	−1.18868	+	1.18868i	−0.144148	+	0.144148i
$69$		0			0
$70$	−3.45764	−	0.547637i	−0.413267	−	0.0654551i
$71$	−0.708805	−	4.47522i	−0.0841197	−	0.531111i	−0.993379	−	0.114881i	$-0.963351\pi$
$71$	−0.708805	−	4.47522i	−0.0841197	−	0.531111i	0.909260	−	0.416230i	$-0.136649\pi$
$72$		0			0
$73$			0.149836i			0.0175369i	0.999962	+	0.00876846i	$0.00279112\pi$
$73$			0.149836i			0.0175369i	−0.999962	+	0.00876846i	$0.997209\pi$
$74$	−0.512213	+	0.705000i	−0.0595435	+	0.0819546i
$75$		0			0
$76$	−3.98873	−	2.03236i	−0.457539	−	0.233128i
$77$	−3.45954	−	4.76165i	−0.394251	−	0.542641i
$78$		0			0
$79$	−11.4389	−	11.4389i	−1.28698	−	1.28698i	−0.936613	−	0.350367i	$-0.886057\pi$
$79$	−11.4389	−	11.4389i	−1.28698	−	1.28698i	−0.350367	−	0.936613i	$-0.613943\pi$
$80$	6.33704	−	2.05903i	0.708502	−	0.230206i
$81$		0			0
$82$	−7.66339	−	0.997584i	−0.846280	−	0.110165i
$83$	−4.27258			−0.468977			−0.234488	−	0.972119i	$-0.575341\pi$
$83$	−4.27258			−0.468977			−0.234488	+	0.972119i	$0.575341\pi$
$84$		0			0
$85$	−5.56779	−	5.56779i	−0.603912	−	0.603912i
$86$	−1.80383	+	1.31056i	−0.194512	+	0.141321i
$87$		0			0
$88$	14.1247	+	7.19691i	1.50570	+	0.767193i
$89$	1.51781	−	0.773362i	0.160887	−	0.0819762i	−0.371693	−	0.928356i	$-0.621223\pi$
$89$	1.51781	−	0.773362i	0.160887	−	0.0819762i	0.532580	+	0.846380i	$0.321223\pi$
$90$		0			0
$91$			2.94503i			0.308723i
$92$	−1.67669	−	1.21819i	−0.174807	−	0.127005i
$93$		0			0
$94$	−4.22374	−	0.668975i	−0.435646	−	0.0689995i
$95$	9.51963	−	18.6833i	0.976694	−	1.91687i
$96$		0			0
$97$	0.687542	−	4.34097i	0.0698093	−	0.440758i	−0.927884	−	0.372870i	$-0.878374\pi$
$97$	0.687542	−	4.34097i	0.0698093	−	0.440758i	0.997693	−	0.0678885i	$-0.0216262\pi$
$98$	2.12628	−	6.54402i	0.214787	−	0.661046i
$99$		0			0
$100$	−0.248049	−	0.763417i	−0.0248049	−	0.0763417i
$101$	−1.40554	−	2.75854i	−0.139857	−	0.274485i	0.810445	−	0.585815i	$-0.199225\pi$
$101$	−1.40554	−	2.75854i	−0.139857	−	0.274485i	−0.950302	+	0.311330i	$0.899225\pi$
$102$		0			0
$103$	2.80356	+	0.910931i	0.276243	+	0.0897567i	0.443862	−	0.896095i	$-0.353608\pi$
$103$	2.80356	+	0.910931i	0.276243	+	0.0897567i	−0.167619	+	0.985852i	$0.553608\pi$
$104$	−3.60111	−	7.06758i	−0.353118	−	0.693033i
$105$		0			0
$106$	−6.67114	+	1.05660i	−0.647958	+	0.102626i
$107$	1.04654	−	3.22093i	0.101173	−	0.311379i	−0.887640	−	0.460538i	$-0.847656\pi$
$107$	1.04654	−	3.22093i	0.101173	−	0.311379i	0.988813	+	0.149159i	$0.0476565\pi$
$108$		0			0
$109$	9.65686	−	9.65686i	0.924960	−	0.924960i	−0.0724148	−	0.997375i	$-0.523071\pi$
$109$	9.65686	−	9.65686i	0.924960	−	0.924960i	0.997375	+	0.0724148i	$0.0230705\pi$
$110$	−7.20175	+	14.1342i	−0.686660	+	1.34765i
$111$		0			0
$112$	−0.466765	−	2.94704i	−0.0441052	−	0.278469i
$113$	10.7162	+	7.78581i	1.00810	+	0.732427i	0.963810	−	0.266592i	$-0.0858975\pi$
$113$	10.7162	+	7.78581i	1.00810	+	0.732427i	0.0442897	+	0.999019i	$0.485898\pi$
$114$		0			0
$115$	5.70602	−	7.85366i	0.532089	−	0.732358i
$116$	2.80653	−	1.43000i	0.260580	−	0.132772i
$117$		0			0
$118$	0.557310	+	0.767072i	0.0513046	+	0.0706147i
$119$	−2.85261	+	2.07254i	−0.261498	+	0.189989i
$120$		0			0
$121$	−14.9036	+	4.84246i	−1.35487	+	0.440223i
$122$	−8.51039			−0.770495
$123$		0			0
$124$	−2.45570			−0.220529
$125$	−8.52661	+	2.77046i	−0.762643	+	0.247798i
$126$		0			0
$127$	−10.9310	+	7.94181i	−0.969966	+	0.704721i	−0.955444	−	0.295173i	$-0.904623\pi$
$127$	−10.9310	+	7.94181i	−0.969966	+	0.704721i	−0.0145221	+	0.999895i	$0.504623\pi$
$128$	2.76302	+	3.80298i	0.244219	+	0.336139i
$129$		0			0
$130$	7.07233	−	3.60353i	0.620285	−	0.316051i
$131$	−6.01522	+	8.27923i	−0.525552	+	0.723360i	−0.986444	−	0.164096i	$-0.947529\pi$
$131$	−6.01522	+	8.27923i	−0.525552	+	0.723360i	0.460893	+	0.887456i	$0.347529\pi$
$132$		0			0
$133$	−7.59657	−	5.51923i	−0.658706	−	0.478578i
$134$	−1.00887	−	6.36976i	−0.0871532	−	0.550263i
$135$		0			0
$136$	4.31152	−	8.46184i	0.369710	−	0.725596i
$137$	−4.05839	+	4.05839i	−0.346731	+	0.346731i	−0.858891	−	0.512159i	$-0.828846\pi$
$137$	−4.05839	+	4.05839i	−0.346731	+	0.346731i	0.512159	+	0.858891i	$0.328846\pi$
$138$		0			0
$139$	−4.98324	+	15.3368i	−0.422673	+	1.30085i	0.482532	+	0.875878i	$0.339717\pi$
$139$	−4.98324	+	15.3368i	−0.422673	+	1.30085i	−0.905205	+	0.424975i	$0.860283\pi$
$140$	−1.55661	+	0.246543i	−0.131558	+	0.0208367i
$141$		0			0
$142$	2.48267	+	4.87251i	0.208341	+	0.408892i
$143$	12.6919	+	4.12386i	1.06135	+	0.344855i
$144$		0			0
$145$	6.69816	+	13.1459i	0.556252	+	1.09171i
$146$	−0.0558824	−	0.171988i	−0.00462486	−	0.0142339i
$147$		0			0
$148$	−0.121231	+	0.373111i	−0.00996515	+	0.0306696i
$149$	−0.849406	+	5.36294i	−0.0695860	+	0.439349i	0.928156	+	0.372191i	$0.121393\pi$
$149$	−0.849406	+	5.36294i	−0.0695860	+	0.439349i	−0.997742	+	0.0671583i	$0.978607\pi$
$150$		0			0
$151$	1.53796	−	3.01842i	0.125158	−	0.245636i	−0.819922	−	0.572475i	$-0.805983\pi$
$151$	1.53796	−	3.01842i	0.125158	−	0.245636i	0.945080	+	0.326839i	$0.105983\pi$
$152$	24.9792	+	3.95632i	2.02608	+	0.320900i
$153$		0			0
$154$	5.74692	+	4.17538i	0.463100	+	0.336462i
$155$		−	11.5026i		−	0.923910i
$156$		0			0
$157$	−9.01316	+	4.59244i	−0.719329	+	0.366516i	−0.775024	−	0.631931i	$-0.782262\pi$
$157$	−9.01316	+	4.59244i	−0.719329	+	0.366516i	0.0556954	+	0.998448i	$0.482262\pi$
$158$	17.3964	+	8.86390i	1.38398	+	0.705174i
$159$		0			0
$160$	6.13463	−	4.45707i	0.484985	−	0.352362i
$161$	−3.07387	−	3.07387i	−0.242255	−	0.242255i
$162$		0			0
$163$	18.7430			1.46807			0.734033	−	0.679113i	$-0.237635\pi$
$163$	18.7430			1.46807			0.734033	+	0.679113i	$0.237635\pi$
$164$	−3.41995	+	0.638988i	−0.267053	+	0.0498966i
$165$		0			0
$166$	4.90427	−	1.59349i	0.380645	−	0.123679i
$167$	−2.16228	−	2.16228i	−0.167322	−	0.167322i	0.618479	−	0.785801i	$-0.287749\pi$
$167$	−2.16228	−	2.16228i	−0.167322	−	0.167322i	−0.785801	+	0.618479i	$0.787749\pi$
$168$		0			0
$169$	3.71629	+	5.11503i	0.285868	+	0.393464i
$170$	8.46753	+	4.31442i	0.649430	+	0.330901i
$171$		0			0
$172$	−0.590006	+	0.812074i	−0.0449876	+	0.0619201i
$173$			10.5897i			0.805117i	0.915394	+	0.402558i	$0.131879\pi$
$173$			10.5897i			0.805117i	−0.915394	+	0.402558i	$0.868121\pi$
$174$		0			0
$175$	−0.263386	−	1.66296i	−0.0199101	−	0.125708i
$176$	−13.3542	−	2.11510i	−1.00661	−	0.159431i
$177$		0			0
$178$	−1.45378	+	1.45378i	−0.108965	+	0.108965i
$179$	0.298749	−	1.88623i	0.0223295	−	0.140983i	−0.974005	−	0.226527i	$-0.927263\pi$
$179$	0.298749	−	1.88623i	0.0223295	−	0.140983i	0.996334	+	0.0855440i	$0.0272628\pi$
$180$		0			0
$181$	−5.82173	+	0.922071i	−0.432726	+	0.0685370i	−0.368998	−	0.929430i	$-0.620299\pi$
$181$	−5.82173	+	0.922071i	−0.432726	+	0.0685370i	−0.0637279	+	0.997967i	$0.520299\pi$
$182$	−1.09837	−	3.38045i	−0.0814169	−	0.250576i
$183$		0			0
$184$	11.1354	+	3.61812i	0.820914	+	0.266731i
$185$	−1.74766	−	0.567850i	−0.128491	−	0.0417492i
$186$		0			0
$187$	4.93740	+	15.1957i	0.361058	+	1.11122i
$188$	−1.90151	+	0.301169i	−0.138682	+	0.0219650i
$189$		0			0
$190$	−3.95898	+	24.9960i	−0.287215	+	1.81340i
$191$	2.23597	−	2.23597i	0.161789	−	0.161789i	−0.621570	−	0.783359i	$-0.713505\pi$
$191$	2.23597	−	2.23597i	0.161789	−	0.161789i	0.783359	+	0.621570i	$0.213505\pi$
$192$		0			0
$193$	15.5972	+	2.47036i	1.12271	+	0.177820i	0.690068	−	0.723744i	$-0.257580\pi$
$193$	15.5972	+	2.47036i	1.12271	+	0.177820i	0.432645	+	0.901565i	$0.357580\pi$
$194$	0.829806	+	5.23919i	0.0595766	+	0.376152i
$195$		0			0
$196$		−	3.09770i		−	0.221264i
$197$	−2.67161	+	3.67715i	−0.190344	+	0.261986i	−0.893514	−	0.449036i	$-0.851767\pi$
$197$	−2.67161	+	3.67715i	−0.190344	+	0.261986i	0.703170	+	0.711022i	$0.251767\pi$
$198$		0			0
$199$	8.00456	+	4.07852i	0.567428	+	0.289119i	0.714074	−	0.700070i	$-0.246848\pi$
$199$	8.00456	+	4.07852i	0.567428	+	0.289119i	−0.146646	+	0.989189i	$0.546848\pi$
$200$	2.66550	+	3.66875i	0.188479	+	0.259420i
$201$		0			0
$202$	2.64217	+	2.64217i	0.185902	+	0.185902i
$203$	6.28350	−	2.04163i	0.441015	−	0.143294i
$204$		0			0
$205$	−2.99304	−	16.0191i	−0.209043	−	1.11882i
$206$	−3.55779			−0.247883
$207$		0			0
$208$	4.78380	+	4.78380i	0.331697	+	0.331697i
$209$	−34.4230	+	25.0098i	−2.38109	+	1.72996i
$210$		0			0
$211$	5.75578	+	2.93272i	0.396245	+	0.201897i	0.640747	−	0.767752i	$-0.278625\pi$
$211$	5.75578	+	2.93272i	0.396245	+	0.201897i	−0.244503	+	0.969649i	$0.578625\pi$
$212$	−2.70933	+	1.38047i	−0.186077	+	0.0948112i
$213$		0			0
$214$			4.08746i			0.279413i
$215$	−3.80378	−	2.76361i	−0.259415	−	0.188476i
$216$		0			0
$217$	−5.08747	−	0.805776i	−0.345360	−	0.0546996i
$218$	−7.48300	+	14.6862i	−0.506813	+	0.994676i
$219$		0			0
$220$	−1.11718	+	7.05362i	−0.0753205	+	0.475555i
$221$	2.47052	−	7.60348i	0.166185	−	0.511465i
$222$		0			0
$223$	−1.26478	−	3.89258i	−0.0846956	−	0.260666i	0.899736	−	0.436435i	$-0.143759\pi$
$223$	−1.26478	−	3.89258i	−0.0846956	−	0.260666i	−0.984432	+	0.175768i	$0.943759\pi$
$224$	−1.54157	−	3.02550i	−0.103001	−	0.202150i
$225$		0			0
$226$	−15.2044	−	4.94021i	−1.01138	−	0.328618i
$227$	0.260675	+	0.511604i	0.0173016	+	0.0339564i	0.899496	−	0.436930i	$-0.143934\pi$
$227$	0.260675	+	0.511604i	0.0173016	+	0.0339564i	−0.882194	+	0.470886i	$0.843934\pi$
$228$		0			0
$229$	−23.7418	+	3.76033i	−1.56890	+	0.248490i	−0.879504	−	0.475892i	$-0.842125\pi$
$229$	−23.7418	+	3.76033i	−1.56890	+	0.248490i	−0.689399	+	0.724382i	$0.742125\pi$
$230$	−3.62055	+	11.1429i	−0.238732	+	0.734742i
$231$		0			0
$232$	−12.5829	+	12.5829i	−0.826105	+	0.826105i
$233$	5.63580	−	11.0609i	0.369213	−	0.724622i	−0.629410	−	0.777073i	$-0.716703\pi$
$233$	5.63580	−	11.0609i	0.369213	−	0.724622i	0.998623	+	0.0524514i	$0.0167035\pi$
$234$		0			0
$235$	−1.41069	−	8.90672i	−0.0920230	−	0.581010i
$236$	0.345332	+	0.250898i	0.0224792	+	0.0163321i
$237$		0			0
$238$	2.50139	−	3.44286i	0.162141	−	0.223168i
$239$	6.04489	−	3.08002i	0.391011	−	0.199230i	−0.247421	−	0.968908i	$-0.579583\pi$
$239$	6.04489	−	3.08002i	0.391011	−	0.199230i	0.638433	+	0.769678i	$0.279583\pi$
$240$		0			0
$241$	−11.2730	−	15.5159i	−0.726155	−	0.999467i	−0.999297	−	0.0374932i	$-0.988063\pi$
$241$	−11.2730	−	15.5159i	−0.726155	−	0.999467i	0.273142	−	0.961974i	$-0.411937\pi$
$242$	15.3010	−	11.1168i	0.983584	−	0.714615i
$243$		0			0
$244$	−3.64382	+	1.18395i	−0.233272	+	0.0757945i
$245$	14.5097			0.926990
$246$		0			0
$247$	21.2903			1.35467
$248$	13.1943	−	4.28710i	0.837841	−	0.272231i
$249$		0			0
$250$	8.75398	−	6.36014i	0.553650	−	0.402251i
$251$	−1.10805	−	1.52510i	−0.0699397	−	0.0962637i	0.772614	−	0.634876i	$-0.218949\pi$
$251$	−1.10805	−	1.52510i	−0.0699397	−	0.0962637i	−0.842554	+	0.538612i	$0.818949\pi$
$252$		0			0
$253$	−17.5515	+	8.94292i	−1.10345	+	0.562236i
$254$	9.58511	−	13.1928i	0.601423	−	0.827788i
$255$		0			0
$256$	9.70071	+	7.04798i	0.606294	+	0.440499i
$257$	−4.37877	−	27.6464i	−0.273140	−	1.72454i	−0.618256	−	0.785977i	$-0.712160\pi$
$257$	−4.37877	−	27.6464i	−0.273140	−	1.72454i	0.345116	−	0.938560i	$-0.387840\pi$
$258$		0			0
$259$	−0.373581	+	0.733194i	−0.0232132	+	0.0455584i
$260$	2.52678	−	2.52678i	0.156704	−	0.156704i
$261$		0			0
$262$	3.81674	−	11.7467i	0.235799	−	0.725715i
$263$	−4.08854	+	0.647561i	−0.252110	+	0.0399303i	−0.281210	−	0.959646i	$-0.590736\pi$
$263$	−4.08854	+	0.647561i	−0.252110	+	0.0399303i	0.0291002	+	0.999576i	$0.490736\pi$
$264$		0			0
$265$	−6.46616	−	12.6906i	−0.397213	−	0.779575i
$266$	10.7781	+	3.50203i	0.660850	+	0.214723i
$267$		0			0
$268$	−1.31811	−	2.58693i	−0.0805162	−	0.158022i
$269$	9.19596	+	28.3022i	0.560687	+	1.72562i	0.680430	+	0.732813i	$0.261793\pi$
$269$	9.19596	+	28.3022i	0.560687	+	1.72562i	−0.119742	+	0.992805i	$0.538207\pi$
$270$		0			0
$271$	7.16633	−	22.0557i	0.435324	−	1.33979i	−0.457431	−	0.889245i	$-0.651230\pi$
$271$	7.16633	−	22.0557i	0.435324	−	1.33979i	0.892754	−	0.450544i	$-0.148770\pi$
$272$	−1.26711	+	8.00022i	−0.0768299	+	0.485085i
$273$		0			0
$274$	3.14480	−	6.17202i	0.189984	−	0.372865i
$275$	−7.53551	−	1.19351i	−0.454408	−	0.0719712i
$276$		0			0
$277$	20.0368	+	14.5576i	1.20389	+	0.874680i	0.994662	−	0.103187i	$-0.0329039\pi$
$277$	20.0368	+	14.5576i	1.20389	+	0.874680i	0.209231	+	0.977866i	$0.432904\pi$
$278$		−	19.4629i		−	1.16731i
$279$		0			0
$280$	7.93317	−	4.04215i	0.474098	−	0.241565i
$281$	0.189482	+	0.0965459i	0.0113035	+	0.00575945i	0.459633	−	0.888109i	$-0.347981\pi$
$281$	0.189482	+	0.0965459i	0.0113035	+	0.00575945i	−0.448330	+	0.893868i	$0.647981\pi$
$282$		0			0
$283$	8.92649	−	6.48547i	0.530625	−	0.385521i	−0.289967	−	0.957037i	$-0.593644\pi$
$283$	8.92649	−	6.48547i	0.530625	−	0.385521i	0.820591	+	0.571515i	$0.193644\pi$
$284$	1.74084	+	1.74084i	0.103300	+	0.103300i
$285$		0			0
$286$	−16.1064			−0.952394
$287$	−7.29475	+	0.201622i	−0.430595	+	0.0119014i
$288$		0			0
$289$	−7.06450	+	2.29540i	−0.415559	+	0.135023i
$290$	−12.5913	−	12.5913i	−0.739388	−	0.739388i
$291$		0			0
$292$	−0.0478533	−	0.0658645i	−0.00280040	−	0.00385443i
$293$	−6.77986	−	3.45451i	−0.396083	−	0.201815i	0.244593	−	0.969626i	$-0.421346\pi$
$293$	−6.77986	−	3.45451i	−0.396083	−	0.201815i	−0.640676	+	0.767811i	$0.721346\pi$
$294$		0			0
$295$	−1.17521	+	1.61754i	−0.0684237	+	0.0941771i
$296$		−	2.21635i		−	0.128822i
$297$		0			0
$298$	−1.02516	−	6.47263i	−0.0593861	−	0.374949i
$299$	9.73515	+	1.54190i	0.562998	+	0.0891702i
$300$		0			0
$301$	−1.48877	+	1.48877i	−0.0858115	+	0.0858115i
$302$	−0.639602	+	4.03829i	−0.0368049	+	0.232377i
$303$		0			0
$304$	−21.3048	+	3.37435i	−1.22191	+	0.193532i
$305$	−5.54565	−	17.0677i	−0.317543	−	0.977296i
$306$		0			0
$307$	−29.8761	−	9.70732i	−1.70512	−	0.554026i	−0.715608	−	0.698502i	$-0.753850\pi$
$307$	−29.8761	−	9.70732i	−1.70512	−	0.554026i	−0.989508	+	0.144476i	$0.953850\pi$
$308$	3.04148	+	0.988237i	0.173304	+	0.0563100i
$309$		0			0
$310$	4.28998	+	13.2032i	0.243655	+	0.749892i
$311$	−14.5714	+	2.30789i	−0.826270	+	0.130868i	−0.555227	−	0.831699i	$-0.687369\pi$
$311$	−14.5714	+	2.30789i	−0.826270	+	0.130868i	−0.271043	+	0.962567i	$0.587369\pi$
$312$		0			0
$313$	−2.59799	+	16.4031i	−0.146847	+	0.927155i	0.798714	+	0.601711i	$0.205514\pi$
$313$	−2.59799	+	16.4031i	−0.146847	+	0.927155i	−0.945561	+	0.325445i	$0.894486\pi$
$314$	8.63295	−	8.63295i	0.487186	−	0.487186i
$315$		0			0
$316$	8.68158	+	1.37503i	0.488377	+	0.0773513i
$317$	−5.09527	−	32.1703i	−0.286179	−	1.80686i	−0.542264	−	0.840208i	$-0.682433\pi$
$317$	−5.09527	−	32.1703i	−0.286179	−	1.80686i	0.256085	−	0.966654i	$-0.417567\pi$
$318$		0			0
$319$		−	29.9383i		−	1.67622i
$320$	−13.2123	+	18.1852i	−0.738591	+	1.01658i
$321$		0			0
$322$	4.67476	+	2.38191i	0.260514	+	0.132739i
$323$	14.9828	+	20.6221i	0.833667	+	1.14744i
$324$		0			0
$325$	2.69940	+	2.69940i	0.149736	+	0.149736i
$326$	−21.5141	+	6.99036i	−1.19156	+	0.387160i
$327$		0			0
$328$	17.2596	−	9.40369i	0.953003	−	0.519232i
$329$	−4.03816			−0.222631
$330$		0			0
$331$	−1.33145	−	1.33145i	−0.0731829	−	0.0731829i	0.669568	−	0.742751i	$-0.266479\pi$
$331$	−1.33145	−	1.33145i	−0.0731829	−	0.0731829i	−0.742751	+	0.669568i	$0.766479\pi$
$332$	1.87813	−	1.36454i	0.103076	−	0.0748891i
$333$		0			0
$334$	3.28840	+	1.67553i	0.179934	+	0.0916807i
$335$	12.1173	−	6.17405i	0.662036	−	0.337324i
$336$		0			0
$337$		−	29.3757i		−	1.60020i	−0.599870	−	0.800098i	$-0.704781\pi$
$337$		−	29.3757i		−	1.60020i	0.599870	−	0.800098i	$-0.295219\pi$
$338$	−6.17342	−	4.48526i	−0.335790	−	0.243966i
$339$		0			0
$340$	4.22568	+	0.669282i	0.229170	+	0.0362969i
$341$	−10.5964	+	20.7967i	−0.573830	+	1.12620i
$342$		0			0
$343$	2.26443	−	14.2970i	0.122268	−	0.771968i
$344$	1.75237	−	5.39324i	0.0944814	−	0.290784i
$345$		0			0
$346$	−3.94950	−	12.1553i	−0.212326	−	0.653473i
$347$	12.7217	+	24.9677i	0.682936	+	1.34034i	0.928636	+	0.370992i	$0.120982\pi$
$347$	12.7217	+	24.9677i	0.682936	+	1.34034i	−0.245700	+	0.969346i	$0.579018\pi$
$348$		0			0
$349$	19.4391	+	6.31615i	1.04055	+	0.338096i	0.778954	−	0.627081i	$-0.215751\pi$
$349$	19.4391	+	6.31615i	1.04055	+	0.338096i	0.261598	+	0.965177i	$0.415751\pi$
$350$	0.922541	+	1.81059i	0.0493119	+	0.0967800i
$351$		0			0
$352$	−15.1974	+	2.40703i	−0.810022	+	0.128295i
$353$	8.94631	−	27.5339i	0.476164	−	1.46548i	−0.368217	−	0.929740i	$-0.620032\pi$
$353$	8.94631	−	27.5339i	0.476164	−	1.46548i	0.844381	−	0.535743i	$-0.179968\pi$
$354$		0			0
$355$	−8.15412	+	8.15412i	−0.432776	+	0.432776i
$356$	−0.420205	+	0.824699i	−0.0222708	+	0.0437090i
$357$		0			0
$358$	0.360565	+	2.27652i	0.0190565	+	0.120318i
$359$	−17.5745	−	12.7687i	−0.927549	−	0.673904i	0.0178425	−	0.999841i	$-0.494320\pi$
$359$	−17.5745	−	12.7687i	−0.927549	−	0.673904i	−0.945391	+	0.325937i	$0.894320\pi$
$360$		0			0
$361$	−28.7318	+	39.5459i	−1.51220	+	2.08136i
$362$	6.33856	−	3.22966i	0.333147	−	0.169747i
$363$		0			0
$364$	−0.940562	−	1.29457i	−0.0492989	−	0.0678541i
$365$	0.308511	−	0.224146i	0.0161482	−	0.0117324i
$366$		0			0
$367$	16.4047	−	5.33020i	0.856316	−	0.278234i	0.152227	−	0.988346i	$-0.451355\pi$
$367$	16.4047	−	5.33020i	0.856316	−	0.278234i	0.704089	+	0.710112i	$0.251355\pi$
$368$	−9.98616			−0.520565
$369$		0			0
$370$	2.21784			0.115300
$371$	−6.06586	+	1.97092i	−0.314924	+	0.102325i
$372$		0			0
$373$	−13.7898	+	10.0189i	−0.714007	+	0.518756i	−0.884464	−	0.466609i	$-0.845476\pi$
$373$	−13.7898	+	10.0189i	−0.714007	+	0.518756i	0.170457	+	0.985365i	$0.445476\pi$
$374$	−11.3348	−	15.6010i	−0.586106	−	0.806706i
$375$		0			0
$376$	9.69091	−	4.93776i	0.499770	−	0.254646i
$377$	−8.80513	+	12.1192i	−0.453487	+	0.624171i
$378$		0			0
$379$	−29.9726	−	21.7764i	−1.53959	−	1.11858i	−0.950593	−	0.310439i	$-0.899524\pi$
$379$	−29.9726	−	21.7764i	−1.53959	−	1.11858i	−0.588995	−	0.808137i	$-0.700476\pi$
$380$	1.78231	+	11.2531i	0.0914308	+	0.577271i
$381$		0			0
$382$	−1.73263	+	3.40048i	−0.0886491	+	0.173984i
$383$	23.8870	−	23.8870i	1.22057	−	1.22057i	0.253137	−	0.967430i	$-0.418538\pi$
$383$	23.8870	−	23.8870i	1.22057	−	1.22057i	0.967430	−	0.253137i	$-0.0814624\pi$
$384$		0			0
$385$	−4.62893	+	14.2464i	−0.235912	+	0.726062i
$386$	−18.8246	+	2.98152i	−0.958146	+	0.151755i
$387$		0			0
$388$	1.08416	+	2.12778i	0.0550397	+	0.108021i
$389$	8.46056	+	2.74900i	0.428967	+	0.139380i	0.515540	−	0.856866i	$-0.327591\pi$
$389$	8.46056	+	2.74900i	0.428967	+	0.139380i	−0.0865726	+	0.996246i	$0.527591\pi$
$390$		0			0
$391$	5.35751	+	10.5147i	0.270941	+	0.531752i
$392$	5.40787	+	16.6437i	0.273139	+	0.840635i
$393$		0			0
$394$	1.69517	−	5.21721i	0.0854016	−	0.262839i
$395$	−6.44066	+	40.6647i	−0.324065	+	2.04606i
$396$		0			0
$397$	3.80671	−	7.47109i	0.191053	−	0.374963i	−0.775532	−	0.631308i	$-0.782518\pi$
$397$	3.80671	−	7.47109i	0.191053	−	0.374963i	0.966585	+	0.256345i	$0.0825183\pi$
$398$	−10.7091	−	1.69616i	−0.536800	−	0.0850208i
$399$		0			0
$400$	−3.12908	−	2.27341i	−0.156454	−	0.113670i
$401$		−	24.8940i		−	1.24315i	−0.783356	−	0.621573i	$-0.786494\pi$
$401$		−	24.8940i		−	1.24315i	0.783356	−	0.621573i	$-0.213506\pi$
$402$		0			0
$403$	10.4060	−	5.30213i	0.518361	−	0.264118i
$404$	1.49885	+	0.763701i	0.0745705	+	0.0379955i
$405$		0			0
$406$	−6.45105	+	4.68696i	−0.320160	+	0.232610i
$407$	2.63666	+	2.63666i	0.130694	+	0.130694i
$408$		0			0
$409$	−8.75194			−0.432756			−0.216378	−	0.976310i	$-0.569424\pi$
$409$	−8.75194			−0.432756			−0.216378	+	0.976310i	$0.569424\pi$
$410$	9.41001	+	17.2712i	0.464727	+	0.852965i
$411$		0			0
$412$	−1.52331	+	0.494953i	−0.0750480	+	0.0243846i
$413$	0.633096	+	0.633096i	0.0311526	+	0.0311526i
$414$		0			0
$415$	6.39156	+	8.79722i	0.313749	+	0.431839i
$416$	6.85993	+	3.49531i	0.336336	+	0.171372i
$417$		0			0
$418$	30.1848	−	41.5458i	1.47638	−	2.03207i
$419$		−	24.9286i		−	1.21784i	−0.793232	−	0.608920i	$-0.791603\pi$
$419$		−	24.9286i		−	1.21784i	0.793232	−	0.608920i	$-0.208397\pi$
$420$		0			0
$421$	−1.70359	−	10.7560i	−0.0830279	−	0.524217i	−0.993789	−	0.111283i	$-0.964504\pi$
$421$	−1.70359	−	10.7560i	−0.0830279	−	0.524217i	0.910761	−	0.412934i	$-0.135496\pi$
$422$	−7.70054	−	1.21965i	−0.374857	−	0.0593714i
$423$		0			0
$424$	12.1470	−	12.1470i	0.589913	−	0.589913i
$425$	−0.715005	+	4.51436i	−0.0346828	+	0.218979i
$426$		0			0
$427$	−7.93736	+	1.25715i	−0.384116	+	0.0608380i
$428$	0.568639	+	1.75009i	0.0274862	+	0.0845938i
$429$		0			0
$430$	5.39686	+	1.75355i	0.260260	+	0.0845636i
$431$	18.5078	+	6.01355i	0.891490	+	0.289663i	0.718720	−	0.695300i	$-0.244728\pi$
$431$	18.5078	+	6.01355i	0.891490	+	0.289663i	0.172770	+	0.984962i	$0.444728\pi$
$432$		0			0
$433$	−1.43880	−	4.42816i	−0.0691441	−	0.212804i	0.910514	−	0.413479i	$-0.135686\pi$
$433$	−1.43880	−	4.42816i	−0.0691441	−	0.212804i	−0.979658	+	0.200675i	$0.935686\pi$
$434$	6.14016	−	0.972505i	0.294737	−	0.0466818i
$435$		0			0
$436$	−1.16081	+	7.32908i	−0.0555928	+	0.350999i
$437$	−22.2217	+	22.2217i	−1.06301	+	1.06301i
$438$		0			0
$439$	12.3177	+	1.95093i	0.587891	+	0.0931127i	0.443291	−	0.896378i	$-0.353811\pi$
$439$	12.3177	+	1.95093i	0.587891	+	0.0931127i	0.144599	+	0.989490i	$0.453811\pi$
$440$	−6.31146	−	39.8490i	−0.300887	−	1.89973i
$441$		0			0
$442$			9.64904i			0.458958i
$443$	−8.10317	+	11.1531i	−0.384993	+	0.529897i	−0.956899	−	0.290422i	$-0.906204\pi$
$443$	−8.10317	+	11.1531i	−0.384993	+	0.529897i	0.571906	+	0.820319i	$0.306204\pi$
$444$		0			0
$445$	−3.86291	−	1.96825i	−0.183120	−	0.0933041i
$446$	2.90354	+	3.99638i	0.137487	+	0.189234i
$447$		0			0
$448$	7.11757	+	7.11757i	0.336274	+	0.336274i
$449$	5.07254	−	1.64817i	0.239388	−	0.0777819i	−0.186866	−	0.982385i	$-0.559833\pi$
$449$	5.07254	−	1.64817i	0.239388	−	0.0777819i	0.426254	+	0.904604i	$0.359833\pi$
$450$		0			0
$451$	−9.34576	+	31.7198i	−0.440075	+	1.49363i
$452$	−7.19720			−0.338528
$453$		0			0
$454$	−0.490022	−	0.490022i	−0.0229979	−	0.0229979i
$455$	6.06381	−	4.40562i	0.284276	−	0.206539i
$456$		0			0
$457$	−9.05273	−	4.61259i	−0.423469	−	0.215768i	0.229251	−	0.973367i	$-0.426372\pi$
$457$	−9.05273	−	4.61259i	−0.423469	−	0.215768i	−0.652720	+	0.757599i	$0.726372\pi$
$458$	25.8495	−	13.1710i	1.20787	−	0.615440i
$459$		0			0
$460$			5.27464i			0.245932i
$461$	24.0238	+	17.4543i	1.11890	+	0.812927i	0.984042	−	0.177938i	$-0.0569428\pi$
$461$	24.0238	+	17.4543i	1.11890	+	0.812927i	0.134856	+	0.990865i	$0.456943\pi$
$462$		0			0
$463$	37.9429	+	6.00956i	1.76336	+	0.279288i	0.952185	−	0.305521i	$-0.0988307\pi$
$463$	37.9429	+	6.00956i	1.76336	+	0.279288i	0.811171	+	0.584809i	$0.198831\pi$
$464$	6.89032	−	13.5230i	0.319875	−	0.627790i
$465$		0			0
$466$	−2.34379	+	14.7981i	−0.108574	+	0.685509i
$467$	−0.851187	+	2.61968i	−0.0393882	+	0.121224i	−0.968817	−	0.247777i	$-0.920300\pi$
$467$	−0.851187	+	2.61968i	−0.0393882	+	0.121224i	0.929429	+	0.369001i	$0.120300\pi$
$468$		0			0
$469$	−1.88188	−	5.79183i	−0.0868971	−	0.267442i
$470$	4.94108	+	9.69742i	0.227915	+	0.447309i
$471$		0			0
$472$	−2.29346	−	0.745190i	−0.105565	−	0.0343001i
$473$	4.33134	+	8.50073i	0.199155	+	0.390864i
$474$		0			0
$475$	−12.0219	+	1.90408i	−0.551601	+	0.0873651i
$476$	0.592032	−	1.82209i	0.0271357	−	0.0835152i
$477$		0			0
$478$	−5.78989	+	5.78989i	−0.264823	+	0.264823i
$479$	−16.3580	+	32.1043i	−0.747415	+	1.46688i	0.132213	+	0.991221i	$0.457792\pi$
$479$	−16.3580	+	32.1043i	−0.747415	+	1.46688i	−0.879628	+	0.475663i	$0.842208\pi$
$480$		0			0
$481$	−0.291872	−	1.84281i	−0.0133082	−	0.0840247i
$482$	18.7264	+	13.6055i	0.852965	+	0.619715i
$483$		0			0
$484$	5.00473	−	6.88842i	0.227488	−	0.313110i
$485$	−9.96656	+	5.07822i	−0.452558	+	0.230590i
$486$		0			0
$487$	−8.99982	−	12.3872i	−0.407821	−	0.561317i	0.554865	−	0.831941i	$-0.312770\pi$
$487$	−8.99982	−	12.3872i	−0.407821	−	0.561317i	−0.962685	+	0.270624i	$0.912770\pi$
$488$	17.5111	−	12.7226i	0.792690	−	0.575923i
$489$		0			0
$490$	−16.6549	+	5.41151i	−0.752392	+	0.244467i
$491$	−8.39830			−0.379010			−0.189505	−	0.981880i	$-0.560688\pi$
$491$	−8.39830			−0.379010			−0.189505	+	0.981880i	$0.560688\pi$
$492$		0			0
$493$	−17.9354			−0.807769
$494$	−24.4380	+	7.94039i	−1.09952	+	0.357255i
$495$		0			0
$496$	−9.57276	+	6.95502i	−0.429830	+	0.312290i
$497$	3.03527	+	4.17769i	0.136150	+	0.187395i
$498$		0			0
$499$	6.86475	−	3.49776i	0.307308	−	0.156581i	−0.293535	−	0.955948i	$-0.594832\pi$
$499$	6.86475	−	3.49776i	0.307308	−	0.156581i	0.600843	+	0.799367i	$0.294832\pi$
$500$	2.86330	−	3.94100i	0.128051	−	0.176247i
$501$		0			0
$502$	1.84068	+	1.33733i	0.0821534	+	0.0596879i
$503$	−2.90709	−	18.3546i	−0.129621	−	0.818392i	−0.963747	−	0.266818i	$-0.914028\pi$
$503$	−2.90709	−	18.3546i	−0.129621	−	0.818392i	0.834126	−	0.551574i	$-0.185972\pi$
$504$		0			0
$505$	−3.57720	+	7.02064i	−0.159183	+	0.312414i
$506$	16.8111	−	16.8111i	0.747343	−	0.747343i
$507$		0			0
$508$	2.26862	−	6.98209i	0.100654	−	0.309780i
$509$	17.4808	−	2.76869i	0.774823	−	0.122720i	0.243513	−	0.969898i	$-0.421700\pi$
$509$	17.4808	−	2.76869i	0.774823	−	0.122720i	0.531310	+	0.847178i	$0.321700\pi$
$510$		0			0
$511$	−0.0775257	−	0.152153i	−0.00342954	−	0.00673085i
$512$	−22.7049	−	7.37726i	−1.00342	−	0.326032i
$513$		0			0
$514$	15.3371	+	30.1008i	0.676491	+	1.32769i
$515$	−2.31837	−	7.13522i	−0.102160	−	0.314415i
$516$		0			0
$517$	−5.65455	+	17.4029i	−0.248687	+	0.765379i
$518$	0.155363	−	0.980925i	0.00682627	−	0.0430994i
$519$		0			0
$520$	−9.16504	+	17.9874i	−0.401914	+	0.788800i
$521$	25.2617	+	4.00106i	1.10673	+	0.175289i	0.682944	−	0.730471i	$-0.260699\pi$
$521$	25.2617	+	4.00106i	1.10673	+	0.175289i	0.423790	+	0.905760i	$0.360699\pi$
$522$		0			0
$523$	21.3827	+	15.5354i	0.934998	+	0.679316i	0.947211	−	0.320609i	$-0.103888\pi$
$523$	21.3827	+	15.5354i	0.934998	+	0.679316i	−0.0122132	+	0.999925i	$0.503888\pi$
$524$		−	5.56046i		−	0.242910i
$525$		0			0
$526$	4.45150	−	2.26815i	0.194095	−	0.0988962i
$527$	12.4589	+	6.34811i	0.542717	+	0.276528i
$528$		0			0
$529$	6.83700	−	4.96737i	0.297261	−	0.215973i
$530$	12.1552	+	12.1552i	0.527989	+	0.527989i
$531$		0			0
$532$	5.10197			0.221199
$533$	13.1123	−	10.0917i	0.567958	−	0.437122i
$534$		0			0
$535$	−8.19747	+	2.66352i	−0.354407	+	0.115154i
$536$	11.5983	+	11.5983i	0.500970	+	0.500970i
$537$		0			0
$538$	−21.1111	−	29.0569i	−0.910165	−	1.25273i
$539$	−26.2335	−	13.3667i	−1.12996	−	0.575743i
$540$		0			0
$541$	11.1474	−	15.3431i	0.479266	−	0.659653i	−0.499098	−	0.866546i	$-0.666335\pi$
$541$	11.1474	−	15.3431i	0.479266	−	0.659653i	0.978364	+	0.206893i	$0.0663351\pi$
$542$			27.9893i			1.20224i
$543$		0			0
$544$	1.44200	+	9.10442i	0.0618252	+	0.390349i
$545$	−34.3296	−	5.43728i	−1.47052	−	0.232907i
$546$		0			0
$547$	11.0744	−	11.0744i	0.473506	−	0.473506i	−0.429541	−	0.903047i	$-0.641325\pi$
$547$	11.0744	−	11.0744i	0.473506	−	0.473506i	0.903047	+	0.429541i	$0.141325\pi$
$548$	0.487842	−	3.08011i	0.0208396	−	0.131576i
$549$		0			0
$550$	9.09474	−	1.44047i	0.387801	−	0.0614216i
$551$	−14.7594	−	45.4247i	−0.628771	−	1.93516i
$552$		0			0
$553$	17.5344	+	5.69727i	0.745638	+	0.242273i
$554$	−28.4285	−	9.23699i	−1.20781	−	0.392442i
$555$		0			0
$556$	−2.70764	−	8.33325i	−0.114829	−	0.353408i
$557$	−30.3636	+	4.80913i	−1.28655	+	0.203769i	−0.761981	−	0.647600i	$-0.775773\pi$
$557$	−30.3636	+	4.80913i	−1.28655	+	0.203769i	−0.524567	+	0.851369i	$0.675773\pi$
$558$		0			0
$559$	0.746789	−	4.71504i	0.0315858	−	0.199425i
$560$	−5.36969	+	5.36969i	−0.226911	+	0.226911i
$561$		0			0
$562$	−0.253504	−	0.0401511i	−0.0106934	−	0.00169367i
$563$	3.47564	+	21.9443i	0.146481	+	0.924844i	0.945991	+	0.324192i	$0.105092\pi$
$563$	3.47564	+	21.9443i	0.146481	+	0.924844i	−0.799510	+	0.600652i	$0.794908\pi$
$564$		0			0
$565$		−	33.7119i		−	1.41827i
$566$	−7.82744	+	10.7735i	−0.329012	+	0.452846i
$567$		0			0
$568$	−12.3925	−	6.31429i	−0.519978	−	0.264942i
$569$	−2.76582	−	3.80682i	−0.115949	−	0.159590i	0.747098	−	0.664714i	$-0.231447\pi$
$569$	−2.76582	−	3.80682i	−0.115949	−	0.159590i	−0.863047	+	0.505124i	$0.831447\pi$
$570$		0			0
$571$	9.49358	+	9.49358i	0.397294	+	0.397294i	0.877278	−	0.479983i	$-0.159357\pi$
$571$	9.49358	+	9.49358i	0.397294	+	0.397294i	−0.479983	+	0.877278i	$0.659357\pi$
$572$	−6.89615	+	2.24070i	−0.288343	+	0.0936882i
$573$		0			0
$574$	8.29806	−	2.95207i	0.346354	−	0.123217i
$575$	−5.63499			−0.234995
$576$		0			0
$577$	−11.7501	−	11.7501i	−0.489162	−	0.489162i	0.418880	−	0.908042i	$-0.362423\pi$
$577$	−11.7501	−	11.7501i	−0.489162	−	0.489162i	−0.908042	+	0.418880i	$0.862423\pi$
$578$	7.25289	−	5.26953i	0.301680	−	0.219184i
$579$		0			0
$580$	−7.14279	−	3.63944i	−0.296588	−	0.151119i
$581$	4.33866	−	2.21066i	0.179998	−	0.0917135i
$582$		0			0
$583$			28.9013i			1.19697i
$584$	0.372097	+	0.270344i	0.0153975	+	0.0111869i
$585$		0			0
$586$	9.07063	+	1.43665i	0.374704	+	0.0593473i
$587$	11.9109	−	23.3764i	0.491615	−	0.964849i	−0.503298	−	0.864113i	$-0.667880\pi$
$587$	11.9109	−	23.3764i	0.491615	−	0.964849i	0.994913	−	0.100736i	$-0.0321197\pi$
$588$		0			0
$589$	−5.82513	+	36.7784i	−0.240020	+	1.51543i
$590$	0.745691	−	2.29500i	0.0306996	−	0.0944837i
$591$		0			0
$592$	0.584142	+	1.79780i	0.0240081	+	0.0738892i
$593$	−1.10491	−	2.16850i	−0.0453730	−	0.0890496i	0.867207	−	0.497948i	$-0.165913\pi$
$593$	−1.10491	−	2.16850i	−0.0453730	−	0.0890496i	−0.912580	+	0.408898i	$0.865913\pi$
$594$		0			0
$595$	8.53470	+	2.77309i	0.349889	+	0.113686i
$596$	−1.33939	−	2.62871i	−0.0548637	−	0.107676i
$597$		0			0
$598$	−11.7495	+	1.86094i	−0.480474	+	0.0760996i
$599$	−5.18017	+	15.9429i	−0.211656	+	0.651410i	0.787718	+	0.616036i	$0.211262\pi$
$599$	−5.18017	+	15.9429i	−0.211656	+	0.651410i	−0.999374	+	0.0353745i	$0.988738\pi$
$600$		0			0
$601$	−8.61367	+	8.61367i	−0.351359	+	0.351359i	−0.860615	−	0.509256i	$-0.829921\pi$
$601$	−8.61367	+	8.61367i	−0.351359	+	0.351359i	0.509256	+	0.860615i	$0.329921\pi$
$602$	1.15363	−	2.26413i	0.0470186	−	0.0922793i
$603$		0			0
$604$	0.287946	+	1.81802i	0.0117163	+	0.0739740i
$605$	32.2656	+	23.4423i	1.31178	+	0.953065i
$606$		0			0
$607$	2.60922	−	3.59129i	0.105905	−	0.145766i	−0.752775	−	0.658278i	$-0.771285\pi$
$607$	2.60922	−	3.59129i	0.105905	−	0.145766i	0.858680	+	0.512512i	$0.171285\pi$
$608$	−21.8720	+	11.1443i	−0.887027	+	0.451963i
$609$		0			0
$610$	12.7311	+	17.5229i	0.515468	+	0.709480i
$611$	7.40736	−	5.38176i	0.299670	−	0.217723i
$612$		0			0
$613$	45.1753	−	14.6783i	1.82461	−	0.592852i	0.824996	−	0.565139i	$-0.191177\pi$
$613$	45.1753	−	14.6783i	1.82461	−	0.592852i	0.999616	−	0.0277136i	$-0.00882263\pi$
$614$	37.9136			1.53007
$615$		0			0
$616$	−18.0669			−0.727936
$617$	35.6237	−	11.5748i	1.43416	−	0.465985i	0.514086	−	0.857739i	$-0.328131\pi$
$617$	35.6237	−	11.5748i	1.43416	−	0.465985i	0.920070	+	0.391753i	$0.128131\pi$
$618$		0			0
$619$	−12.2778	+	8.92032i	−0.493485	+	0.358538i	−0.806523	−	0.591203i	$-0.798653\pi$
$619$	−12.2778	+	8.92032i	−0.493485	+	0.358538i	0.313038	+	0.949741i	$0.398653\pi$
$620$	3.67361	+	5.05629i	0.147536	+	0.203065i
$621$		0			0
$622$	15.8650	−	8.08364i	0.636130	−	0.324125i
$623$	−1.14114	+	1.57064i	−0.0457188	+	0.0629265i
$624$		0			0
$625$	24.4357	+	17.7535i	0.977427	+	0.710142i
$626$	−3.13556	−	19.7971i	−0.125322	−	0.791253i
$627$		0			0
$628$	2.49529	−	4.89729i	0.0995731	−	0.195423i
$629$	1.57957	−	1.57957i	0.0629816	−	0.0629816i
$630$		0			0
$631$	−1.82817	+	5.62652i	−0.0727782	+	0.223988i	−0.980829	−	0.194873i	$-0.937571\pi$
$631$	−1.82817	+	5.62652i	−0.0727782	+	0.223988i	0.908050	+	0.418861i	$0.137571\pi$
$632$	−49.0460	+	7.76813i	−1.95095	+	0.308999i
$633$		0			0
$634$	17.8468	+	35.0262i	0.708785	+	1.39107i
$635$	32.7043	+	10.6263i	1.29783	+	0.421691i
$636$		0			0
$637$	6.68826	+	13.1264i	0.264999	+	0.520089i
$638$	11.1657	+	34.3646i	0.442055	+	1.36051i
$639$		0			0
$640$	3.69697	−	11.3781i	0.146136	−	0.449759i
$641$	5.46005	−	34.4734i	0.215659	−	1.36162i	−0.607732	−	0.794143i	$-0.707920\pi$
$641$	5.46005	−	34.4734i	0.215659	−	1.36162i	0.823391	−	0.567475i	$-0.192080\pi$
$642$		0			0
$643$	−14.6680	+	28.7876i	−0.578451	+	1.13527i	0.397565	+	0.917574i	$0.369855\pi$
$643$	−14.6680	+	28.7876i	−0.578451	+	1.13527i	−0.976016	+	0.217700i	$0.930145\pi$
$644$	2.33292	+	0.369498i	0.0919298	+	0.0145603i
$645$		0			0
$646$	−24.8892	−	18.0831i	−0.979252	−	0.711468i
$647$		−	0.686839i		−	0.0270024i	−0.999909	−	0.0135012i	$-0.995702\pi$
$647$		−	0.686839i		−	0.0270024i	0.999909	−	0.0135012i	$-0.00429770\pi$
$648$		0			0
$649$	3.61491	−	1.84189i	0.141898	−	0.0723004i
$650$	−4.10527	−	2.09174i	−0.161022	−	0.0820447i
$651$		0			0
$652$	−8.23903	+	5.98600i	−0.322665	+	0.234430i
$653$	−33.7065	−	33.7065i	−1.31904	−	1.31904i	−0.914538	−	0.404500i	$-0.867446\pi$
$653$	−33.7065	−	33.7065i	−1.31904	−	1.31904i	−0.404500	−	0.914538i	$-0.632554\pi$
$654$		0			0
$655$	26.0454			1.01768
$656$	−11.5218	+	12.1768i	−0.449851	+	0.475425i
$657$		0			0
$658$	4.63520	−	1.50607i	0.180699	−	0.0587126i
$659$	−31.4326	−	31.4326i	−1.22444	−	1.22444i	−0.966037	−	0.258404i	$-0.916803\pi$
$659$	−31.4326	−	31.4326i	−1.22444	−	1.22444i	−0.258404	−	0.966037i	$-0.583197\pi$
$660$		0			0
$661$	−14.1153	−	19.4280i	−0.549020	−	0.755662i	0.440859	−	0.897577i	$-0.354674\pi$
$661$	−14.1153	−	19.4280i	−0.549020	−	0.755662i	−0.989879	+	0.141915i	$0.954674\pi$
$662$	2.02487	+	1.03172i	0.0786989	+	0.0400991i
$663$		0			0
$664$	−7.70890	+	10.6104i	−0.299163	+	0.411763i
$665$			23.8978i			0.926716i
$666$		0			0
$667$	−3.45907	−	21.8397i	−0.133936	−	0.845638i
$668$	1.64106	+	0.259919i	0.0634946	+	0.0100566i
$669$		0			0
$670$	−11.6061	+	11.6061i	−0.448382	+	0.448382i
$671$	−5.69666	+	35.9673i	−0.219917	+	1.38850i
$672$		0			0
$673$	15.1756	−	2.40357i	0.584975	−	0.0926510i	0.143070	−	0.989713i	$-0.454303\pi$
$673$	15.1756	−	2.40357i	0.584975	−	0.0926510i	0.441906	+	0.897062i	$0.354303\pi$
$674$	10.9559	+	33.7188i	0.422006	+	1.29880i
$675$		0			0
$676$	−3.26720	−	1.06158i	−0.125662	−	0.0408299i
$677$	30.7055	+	9.97682i	1.18011	+	0.383440i	0.832407	−	0.554165i	$-0.186962\pi$
$677$	30.7055	+	9.97682i	1.18011	+	0.383440i	0.347701	+	0.937605i	$0.386962\pi$
$678$		0			0
$679$	1.54787	+	4.76384i	0.0594016	+	0.182819i
$680$	−23.8727	+	3.78106i	−0.915476	+	0.144997i
$681$		0			0
$682$	4.40680	−	27.8235i	0.168745	−	1.06542i
$683$	−11.8785	+	11.8785i	−0.454518	+	0.454518i	−0.896851	−	0.442333i	$-0.854151\pi$
$683$	−11.8785	+	11.8785i	−0.454518	+	0.454518i	0.442333	+	0.896851i	$0.354151\pi$
$684$		0			0
$685$	14.4273	+	2.28507i	0.551240	+	0.0873079i
$686$	2.73298	+	17.2554i	0.104346	+	0.658813i
$687$		0			0
$688$			4.83661i			0.184394i
$689$	8.50015	−	11.6995i	0.323830	−	0.445714i
$690$		0			0
$691$	−23.1214	−	11.7810i	−0.879581	−	0.448169i	−0.0449572	−	0.998989i	$-0.514315\pi$
$691$	−23.1214	−	11.7810i	−0.879581	−	0.448169i	−0.834624	+	0.550820i	$0.814315\pi$
$692$	−3.38204	−	4.65498i	−0.128566	−	0.176956i
$693$		0			0
$694$	−23.9145	−	23.9145i	−0.907781	−	0.907781i
$695$	39.0332	−	12.6826i	1.48061	−	0.481080i
$696$		0			0
$697$	19.0027	+	5.59885i	0.719778	+	0.212072i
$698$	−24.6688			−0.933727
$699$		0			0
$700$	0.646881	+	0.646881i	0.0244498	+	0.0244498i
$701$	−22.0790	+	16.0413i	−0.833911	+	0.605872i	−0.920663	−	0.390358i	$-0.872351\pi$
$701$	−22.0790	+	16.0413i	−0.833911	+	0.605872i	0.0867523	+	0.996230i	$0.472351\pi$
$702$		0			0
$703$	5.30042	+	2.70070i	0.199909	+	0.101859i
$704$	40.6405	−	20.7074i	1.53170	−	0.780439i
$705$		0			0
$706$			34.9413i			1.31503i
$707$	2.85456	+	2.07396i	0.107357	+	0.0779994i
$708$		0			0
$709$	−44.8571	−	7.10466i	−1.68464	−	0.266821i	−0.760631	−	0.649185i	$-0.775110\pi$
$709$	−44.8571	−	7.10466i	−1.68464	−	0.266821i	−0.924012	+	0.382364i	$0.875110\pi$
$710$	6.31854	−	12.4008i	0.237131	−	0.465395i
$711$		0			0
$712$	0.817998	−	5.16463i	0.0306558	−	0.193553i
$713$	−5.32717	+	16.3953i	−0.199504	+	0.614010i
$714$		0			0
$715$	−10.4955	−	32.3018i	−0.392509	−	1.20802i
$716$	0.471085	+	0.924556i	0.0176053	+	0.0345523i
$717$		0			0
$718$	24.9351	+	8.10189i	0.930569	+	0.302360i
$719$	12.6131	+	24.7546i	0.470390	+	0.923192i	0.997312	+	0.0732784i	$0.0233462\pi$
$719$	12.6131	+	24.7546i	0.470390	+	0.923192i	−0.526922	+	0.849914i	$0.676654\pi$
$720$		0			0
$721$	−3.31824	+	0.525557i	−0.123578	+	0.0195728i
$722$	18.2307	−	56.1084i	0.678477	−	2.08814i
$723$		0			0
$724$	2.26462	−	2.26462i	0.0841640	−	0.0841640i
$725$	3.88807	−	7.63077i	0.144399	−	0.283400i
$726$		0			0
$727$	−2.75993	−	17.4255i	−0.102360	−	0.646276i	−0.984513	−	0.175313i	$-0.943906\pi$
$727$	−2.75993	−	17.4255i	−0.102360	−	0.646276i	0.882153	−	0.470963i	$-0.156094\pi$
$728$	7.31361	+	5.31365i	0.271060	+	0.196937i
$729$		0			0
$730$	−0.270526	+	0.372347i	−0.0100126	+	0.0137812i
$731$	5.09261	−	2.59481i	0.188357	−	0.0959726i
$732$		0			0
$733$	−5.53747	−	7.62168i	−0.204531	−	0.281513i	0.694413	−	0.719577i	$-0.255664\pi$
$733$	−5.53747	−	7.62168i	−0.204531	−	0.281513i	−0.898944	+	0.438064i	$0.855664\pi$
$734$	−16.8421	+	12.2365i	−0.621653	+	0.451658i
$735$		0			0
$736$	−10.8083	+	3.51181i	−0.398397	+	0.129447i
$737$	−27.5957			−1.01650
$738$		0			0
$739$	0.347492			0.0127827			0.00639135	−	0.999980i	$-0.497966\pi$
$739$	0.347492			0.0127827			0.00639135	+	0.999980i	$0.497966\pi$
$740$	0.949591	−	0.308541i	0.0349077	−	0.0113422i
$741$		0			0
$742$	6.22761	−	4.52463i	0.228623	−	0.166104i
$743$	−4.23794	−	5.83302i	−0.155475	−	0.213993i	0.724173	−	0.689618i	$-0.242222\pi$
$743$	−4.23794	−	5.83302i	−0.155475	−	0.213993i	−0.879648	+	0.475626i	$0.842222\pi$
$744$		0			0
$745$	12.3129	−	6.27375i	0.451111	−	0.229853i
$746$	12.0919	−	16.6431i	0.442717	−	0.609348i
$747$		0			0
$748$	−7.02347	−	5.10285i	−0.256804	−	0.186579i
$749$	0.603799	+	3.81223i	0.0220623	+	0.139296i
$750$		0			0
$751$	8.85526	−	17.3794i	0.323133	−	0.634184i	−0.671107	−	0.741361i	$-0.734181\pi$
$751$	8.85526	−	17.3794i	0.323133	−	0.634184i	0.994240	+	0.107176i	$0.0341809\pi$
$752$	−6.55944	+	6.55944i	−0.239198	+	0.239198i
$753$		0			0
$754$	5.58698	−	17.1950i	0.203466	−	0.626203i
$755$	−8.51564	+	1.34874i	−0.309916	+	0.0490858i
$756$		0			0
$757$	−7.98828	−	15.6779i	−0.290339	−	0.569823i	0.699057	−	0.715066i	$-0.253603\pi$
$757$	−7.98828	−	15.6779i	−0.290339	−	0.569823i	−0.989396	+	0.145244i	$0.953603\pi$
$758$	42.5256	+	13.8174i	1.54460	+	0.501871i
$759$		0			0
$760$	−29.2216	−	57.3506i	−1.05998	−	2.08032i
$761$	−7.86010	−	24.1909i	−0.284928	−	0.876919i	−0.986420	−	0.164242i	$-0.947482\pi$
$761$	−7.86010	−	24.1909i	−0.284928	−	0.876919i	0.701492	−	0.712678i	$-0.252518\pi$
$762$		0			0
$763$	−4.80970	+	14.8027i	−0.174123	+	0.535895i
$764$	−0.268777	+	1.69699i	−0.00972402	+	0.0613950i
$765$		0			0
$766$	−18.5098	+	36.3274i	−0.668785	+	1.31256i
$767$	−2.00506	−	0.317570i	−0.0723984	−	0.0114668i
$768$		0			0
$769$	−10.8491	−	7.88236i	−0.391230	−	0.284245i	0.374729	−	0.927134i	$-0.377736\pi$
$769$	−10.8491	−	7.88236i	−0.391230	−	0.284245i	−0.765959	+	0.642889i	$0.777736\pi$
$770$		−	18.0791i		−	0.651524i
$771$		0			0
$772$	−7.64517	+	3.89541i	−0.275156	+	0.140199i
$773$	−33.8688	−	17.2570i	−1.21817	−	0.620691i	−0.277737	−	0.960657i	$-0.589584\pi$
$773$	−33.8688	−	17.2570i	−1.21817	−	0.620691i	−0.940438	+	0.339966i	$0.889584\pi$
$774$		0			0
$775$	−5.40172	+	3.92458i	−0.194035	+	0.140975i
$776$	−9.53971	−	9.53971i	−0.342456	−	0.342456i
$777$		0			0
$778$	−10.7367			−0.384929
$779$	1.45757	+	52.7353i	0.0522228	+	1.88944i
$780$		0			0
$781$	22.2544	−	7.23090i	0.796326	−	0.258742i
$782$	−10.0712	−	10.0712i	−0.360144	−	0.360144i
$783$		0			0
$784$	−8.77326	−	12.0754i	−0.313331	−	0.431263i
$785$	22.9390	+	11.6880i	0.818729	+	0.417163i
$786$		0			0
$787$	−28.9010	+	39.7788i	−1.03021	+	1.41796i	−0.125417	+	0.992104i	$0.540027\pi$
$787$	−28.9010	+	39.7788i	−1.03021	+	1.41796i	−0.904791	+	0.425856i	$0.859973\pi$
$788$		−	2.46963i		−	0.0879771i
$789$		0			0
$790$	−7.77335	−	49.0790i	−0.276563	−	1.74615i
$791$	−14.9104	−	2.36157i	−0.530152	−	0.0839679i
$792$		0			0
$793$	12.8844	−	12.8844i	0.457537	−	0.457537i
$794$	−1.58312	+	9.99541i	−0.0561827	+	0.354724i
$795$		0			0
$796$	−4.82120	+	0.763603i	−0.170883	+	0.0270652i
$797$	−1.66232	−	5.11611i	−0.0588825	−	0.181222i	0.917289	−	0.398222i	$-0.130373\pi$
$797$	−1.66232	−	5.11611i	−0.0588825	−	0.181222i	−0.976172	+	0.217000i	$0.930373\pi$
$798$		0			0
$799$	10.4257	+	3.38752i	0.368836	+	0.119842i
$800$	−4.18616	−	1.36016i	−0.148003	−	0.0480891i
$801$		0			0
$802$	9.28442	+	28.5745i	0.327844	+	1.00900i
$803$	−0.764277	+	0.121050i	−0.0269707	+	0.00427175i
$804$		0			0
$805$	−1.73074	+	10.9274i	−0.0610005	+	0.385142i
$806$	−9.96704	+	9.96704i	−0.351074	+	0.351074i
$807$		0			0
$808$	−9.38645	−	1.48667i	−0.330214	−	0.0523008i
$809$	4.90251	+	30.9532i	0.172363	+	1.08826i	0.910470	+	0.413574i	$0.135720\pi$
$809$	4.90251	+	30.9532i	0.172363	+	1.08826i	−0.738107	+	0.674683i	$0.764280\pi$
$810$		0			0
$811$			18.8699i			0.662610i	0.943524	+	0.331305i	$0.107489\pi$
$811$			18.8699i			0.662610i	−0.943524	+	0.331305i	$0.892511\pi$
$812$	−2.11005	+	2.90423i	−0.0740482	+	0.101919i
$813$		0			0
$814$	−4.00985	−	2.04312i	−0.140545	−	0.0716113i
$815$	−28.0386	−	38.5918i	−0.982149	−	1.35181i
$816$		0			0
$817$	10.7627	+	10.7627i	0.376538	+	0.376538i
$818$	10.0459	−	3.26411i	0.351246	−	0.114127i
$819$		0			0
$820$	6.43174	+	6.08576i	0.224606	+	0.212524i
$821$	−1.59911			−0.0558094			−0.0279047	−	0.999611i	$-0.508883\pi$
$821$	−1.59911			−0.0558094			−0.0279047	+	0.999611i	$0.508883\pi$
$822$		0			0
$823$	−18.3789	−	18.3789i	−0.640647	−	0.640647i	0.310068	−	0.950715i	$-0.399648\pi$
$823$	−18.3789	−	18.3789i	−0.640647	−	0.640647i	−0.950715	+	0.310068i	$0.899648\pi$
$824$	7.32056	−	5.31870i	0.255024	−	0.185286i
$825$		0			0
$826$	−0.962817	−	0.490580i	−0.0335007	−	0.0170694i
$827$	−7.57401	+	3.85915i	−0.263374	+	0.134196i	−0.580692	−	0.814124i	$-0.697218\pi$
$827$	−7.57401	+	3.85915i	−0.263374	+	0.134196i	0.317318	+	0.948319i	$0.397218\pi$
$828$		0			0
$829$			0.285264i			0.00990764i	0.999988	+	0.00495382i	$0.00157686\pi$
$829$			0.285264i			0.00990764i	−0.999988	+	0.00495382i	$0.998423\pi$
$830$	−10.6175	−	7.71409i	−0.368540	−	0.267760i
$831$		0			0
$832$	−22.5418	−	3.57027i	−0.781496	−	0.123777i
$833$	−8.00769	+	15.7160i	−0.277450	+	0.544526i
$834$		0			0
$835$	−1.21747	+	7.68678i	−0.0421322	+	0.266012i
$836$	7.14418	−	21.9875i	0.247087	−	0.760454i
$837$		0			0
$838$	9.29731	+	28.6142i	0.321170	+	0.988460i
$839$	5.30778	+	10.4171i	0.183245	+	0.359638i	0.964295	−	0.264830i	$-0.0853157\pi$
$839$	5.30778	+	10.4171i	0.183245	+	0.359638i	−0.781050	+	0.624468i	$0.785316\pi$
$840$		0			0
$841$	4.38091	+	1.42344i	0.151066	+	0.0490843i
$842$	5.96702	+	11.7109i	0.205637	+	0.403585i
$843$		0			0
$844$	−3.46675	+	0.549079i	−0.119330	+	0.0189001i
$845$	4.97246	−	15.3036i	0.171058	−	0.526461i
$846$		0			0
$847$	12.6285	−	12.6285i	0.433921	−	0.433921i
$848$	−6.65167	+	13.0546i	−0.228419	+	0.448298i
$849$		0			0
$850$	−0.862953	−	5.44847i	−0.0295990	−	0.186881i
$851$	2.22807	+	1.61878i	0.0763771	+	0.0554912i
$852$		0			0
$853$	−14.3175	+	19.7064i	−0.490223	+	0.674734i	−0.980429	−	0.196873i	$-0.936921\pi$
$853$	−14.3175	+	19.7064i	−0.490223	+	0.674734i	0.490206	+	0.871607i	$0.336921\pi$
$854$	8.64201	−	4.40332i	0.295723	−	0.150679i
$855$		0			0
$856$	−6.11052	−	8.41040i	−0.208853	−	0.287462i
$857$	4.13061	−	3.00106i	0.141099	−	0.102514i	−0.514997	−	0.857192i	$-0.672207\pi$
$857$	4.13061	−	3.00106i	0.141099	−	0.102514i	0.656096	+	0.754678i	$0.272207\pi$
$858$		0			0
$859$	0.384709	−	0.125000i	0.0131261	−	0.00426493i	−0.302447	−	0.953166i	$-0.597803\pi$
$859$	0.384709	−	0.125000i	0.0131261	−	0.00426493i	0.315573	+	0.948901i	$0.397803\pi$
$860$	2.55468			0.0871137
$861$		0			0
$862$	−23.4869			−0.799969
$863$	−36.1033	+	11.7307i	−1.22897	+	0.399316i	−0.850341	−	0.526232i	$-0.823604\pi$
$863$	−36.1033	+	11.7307i	−1.22897	+	0.399316i	−0.378629	+	0.925549i	$0.623604\pi$
$864$		0			0
$865$	21.8041	−	15.8416i	0.741360	−	0.538630i
$866$	3.30304	+	4.54624i	0.112242	+	0.154488i
$867$		0			0
$868$	2.49368	−	1.27060i	0.0846411	−	0.0431268i
$869$	49.1060	−	67.5886i	1.66581	−	2.29279i
$870$		0			0
$871$	11.1709	+	8.11615i	0.378512	+	0.275005i
$872$	−6.55794	−	41.4052i	−0.222080	−	1.40216i
$873$		0			0
$874$	17.2193	−	33.7949i	0.582453	−	1.14313i
$875$	7.22503	−	7.22503i	0.244250	−	0.244250i
$876$		0			0
$877$	11.4052	−	35.1015i	0.385125	−	1.18529i	−0.551264	−	0.834331i	$-0.685854\pi$
$877$	11.4052	−	35.1015i	0.385125	−	1.18529i	0.936389	−	0.350963i	$-0.114146\pi$
$878$	−14.8664	+	2.35461i	−0.501718	+	0.0794643i
$879$		0			0
$880$	15.6222	+	30.6603i	0.526625	+	1.03356i
$881$	10.6200	+	3.45065i	0.357798	+	0.116255i	0.482399	−	0.875951i	$-0.339765\pi$
$881$	10.6200	+	3.45065i	0.357798	+	0.116255i	−0.124602	+	0.992207i	$0.539765\pi$
$882$		0			0
$883$	−10.6504	−	20.9026i	−0.358415	−	0.703429i	0.639444	−	0.768838i	$-0.279165\pi$
$883$	−10.6504	−	20.9026i	−0.358415	−	0.703429i	−0.997859	+	0.0654092i	$0.979165\pi$
$884$	1.34235	+	4.13134i	0.0451483	+	0.138952i
$885$		0			0
$886$	5.14158	−	15.8241i	0.172735	−	0.531622i
$887$	−4.35893	+	27.5212i	−0.146358	+	0.924071i	0.799776	+	0.600298i	$0.204951\pi$
$887$	−4.35893	+	27.5212i	−0.146358	+	0.924071i	−0.946135	+	0.323773i	$0.895049\pi$
$888$		0			0
$889$	6.99088	−	13.7204i	0.234467	−	0.460166i
$890$	5.16811	+	0.818548i	0.173235	+	0.0274378i
$891$		0			0
$892$	1.79915	+	1.30716i	0.0602400	+	0.0437669i
$893$			29.1928i			0.976899i
$894$		0			0
$895$	−4.33064	+	2.20657i	−0.144757	+	0.0737576i
$896$	−4.77344	−	2.43219i	−0.159469	−	0.0812537i
$897$		0			0
$898$	−5.20780	+	3.78369i	−0.173787	+	0.126263i
$899$	−18.5265	−	18.5265i	−0.617893	−	0.617893i
$900$		0			0
$901$	17.3142			0.576819
$902$	−1.10267	−	39.8951i	−0.0367150	−	1.32836i
$903$		0			0
$904$	38.6701	−	12.5647i	1.28615	−	0.417895i
$905$	10.6075	+	10.6075i	0.352607	+	0.352607i
$906$		0			0
$907$	22.2821	+	30.6687i	0.739865	+	1.01834i	0.998626	+	0.0523958i	$0.0166857\pi$
$907$	22.2821	+	30.6687i	0.739865	+	1.01834i	−0.258761	+	0.965941i	$0.583314\pi$
$908$	−0.277979	−	0.141638i	−0.00922507	−	0.00470041i
$909$		0			0
$910$	−5.31722	+	7.31853i	−0.176264	+	0.242607i
$911$		−	23.3777i		−	0.774537i	−0.921967	−	0.387269i	$-0.873419\pi$
$911$		−	23.3777i		−	0.774537i	0.921967	−	0.387269i	$-0.126581\pi$
$912$		0			0
$913$	−3.45174	−	21.7934i	−0.114236	−	0.721258i
$914$	12.1115	+	1.91827i	0.400611	+	0.0634506i
$915$		0			0
$916$	9.23544	−	9.23544i	0.305147	−	0.305147i
$917$	1.82452	−	11.5196i	0.0602510	−	0.380410i
$918$		0			0
$919$	19.4344	−	3.07810i	0.641080	−	0.101537i	0.172573	−	0.984997i	$-0.444792\pi$
$919$	19.4344	−	3.07810i	0.641080	−	0.101537i	0.468507	+	0.883460i	$0.344792\pi$
$920$	−9.20832	−	28.3403i	−0.303589	−	0.934352i
$921$		0			0
$922$	−34.0853	−	11.0750i	−1.12254	−	0.364735i
$923$	−11.1354	−	3.61812i	−0.366527	−	0.119092i
$924$		0			0
$925$	0.329619	+	1.01446i	0.0108378	+	0.0333554i
$926$	−45.7940	+	7.25305i	−1.50488	+	0.238350i
$927$		0			0
$928$	2.70194	−	17.0594i	0.0886955	−	0.560001i
$929$	−5.06327	+	5.06327i	−0.166120	+	0.166120i	−0.785272	−	0.619151i	$-0.787477\pi$
$929$	−5.06327	+	5.06327i	−0.166120	+	0.166120i	0.619151	+	0.785272i	$0.287477\pi$
$930$		0			0
$931$	−46.3933	−	7.34798i	−1.52048	−	0.240820i
$932$	1.05516	+	6.66204i	0.0345630	+	0.218222i
$933$		0			0
$934$		−	3.32445i		−	0.108779i
$935$	23.9019	−	32.8981i	0.781676	−	1.07588i
$936$		0			0
$937$	38.9861	+	19.8644i	1.27362	+	0.648942i	0.954341	−	0.298718i	$-0.0965590\pi$
$937$	38.9861	+	19.8644i	1.27362	+	0.648942i	0.319280	+	0.947660i	$0.396559\pi$
$938$	4.32022	+	5.94627i	0.141060	+	0.194153i
$939$		0			0
$940$	3.46467	+	3.46467i	0.113005	+	0.113005i
$941$	24.9275	−	8.09943i	0.812613	−	0.264034i	0.126909	−	0.991914i	$-0.459494\pi$
$941$	24.9275	−	8.09943i	0.812613	−	0.264034i	0.685704	+	0.727881i	$0.259494\pi$
$942$		0			0
$943$	−3.15274	+	24.2192i	−0.102667	+	0.788685i
$944$	2.05676			0.0669417
$945$		0			0
$946$	−8.14213	−	8.14213i	−0.264723	−	0.264723i
$947$	−26.7046	+	19.4020i	−0.867781	+	0.630480i	−0.929991	−	0.367583i	$-0.880185\pi$
$947$	−26.7046	+	19.4020i	−0.867781	+	0.630480i	0.0622093	+	0.998063i	$0.480185\pi$
$948$		0			0
$949$	0.344986	+	0.175779i	0.0111987	+	0.00570604i
$950$	13.0891	−	6.66925i	0.424667	−	0.216379i
$951$		0			0
$952$			10.8235i			0.350792i
$953$	2.15205	+	1.56356i	0.0697119	+	0.0506486i	0.622095	−	0.782941i	$-0.286282\pi$
$953$	2.15205	+	1.56356i	0.0697119	+	0.0506486i	−0.552384	+	0.833590i	$0.686282\pi$
$954$		0			0
$955$	−7.94876	−	1.25896i	−0.257216	−	0.0407390i
$956$	−1.67353	+	3.28448i	−0.0541257	+	0.106228i
$957$		0			0
$958$	6.80288	−	42.9517i	0.219791	−	1.38771i
$959$	2.02132	−	6.22098i	0.0652718	−	0.200886i
$960$		0			0
$961$	−3.26738	−	10.0559i	−0.105399	−	0.324385i
$962$	1.02231	+	2.00640i	0.0329607	+	0.0646891i
$963$		0			0
$964$	9.91070	+	3.22018i	0.319202	+	0.103715i
$965$	−18.2462	−	35.8102i	−0.587366	−	1.15277i
$966$		0			0
$967$	12.8463	−	2.03466i	0.413110	−	0.0654303i	0.0535799	−	0.998564i	$-0.482937\pi$
$967$	12.8463	−	2.03466i	0.413110	−	0.0654303i	0.359531	+	0.933133i	$0.382937\pi$
$968$	−14.8645	+	45.7482i	−0.477762	+	1.47040i
$969$		0			0
$970$	9.54613	−	9.54613i	0.306508	−	0.306508i
$971$	3.29747	−	6.47166i	0.105821	−	0.207685i	−0.832024	−	0.554739i	$-0.812818\pi$
$971$	3.29747	−	6.47166i	0.105821	−	0.207685i	0.937845	+	0.347054i	$0.112818\pi$
$972$		0			0
$973$	−2.87505	−	18.1524i	−0.0921700	−	0.581939i
$974$	14.9503	+	10.8620i	0.479039	+	0.348042i
$975$		0			0
$976$	−10.8511	+	14.9352i	−0.347334	+	0.478065i
$977$	−26.7289	+	13.6190i	−0.855132	+	0.435711i	−0.825870	−	0.563860i	$-0.809316\pi$
$977$	−26.7289	+	13.6190i	−0.855132	+	0.435711i	−0.0292617	+	0.999572i	$0.509316\pi$
$978$		0			0
$979$	5.17095	+	7.11720i	0.165264	+	0.227467i
$980$	−6.37815	+	4.63399i	−0.203742	+	0.148028i
$981$		0			0
$982$	9.63997	−	3.13222i	0.307624	−	0.0999530i
$983$	47.8093			1.52488			0.762439	−	0.647060i	$-0.224002\pi$
$983$	47.8093			1.52488			0.762439	+	0.647060i	$0.224002\pi$
$984$		0			0
$985$	11.5678			0.368582
$986$	20.5871	−	6.68915i	0.655626	−	0.213026i
$987$		0			0
$988$	−9.35875	+	6.79953i	−0.297741	+	0.216322i
$989$	4.14185	+	5.70077i	0.131703	+	0.181274i
$990$		0			0
$991$	−37.8416	+	19.2812i	−1.20208	+	0.612489i	−0.936183	−	0.351513i	$-0.885667\pi$
$991$	−37.8416	+	19.2812i	−1.20208	+	0.612489i	−0.265894	+	0.964002i	$0.585667\pi$
$992$	−7.91496	+	10.8940i	−0.251300	+	0.345885i
$993$		0			0
$994$	−5.04213	−	3.66332i	−0.159927	−	0.116193i
$995$	−3.57673	−	22.5826i	−0.113390	−	0.715917i
$996$		0			0
$997$	−19.2309	+	37.7427i	−0.609048	+	1.19532i	0.356303	+	0.934370i	$0.384037\pi$
$997$	−19.2309	+	37.7427i	−0.609048	+	1.19532i	−0.965351	+	0.260954i	$0.915963\pi$
$998$	−6.57516	+	6.57516i	−0.208133	+	0.208133i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.2.u.a.244.1		24
3.2	odd	2		41.2.g.a.39.3	yes	24
12.11	even	2		656.2.bs.d.449.2		24
41.20	even	20	inner	369.2.u.a.307.1		24
123.20	odd	20		41.2.g.a.20.3	✓	24
123.26	even	40		1681.2.a.m.1.16		24
123.56	even	40		1681.2.a.m.1.15		24
492.143	even	20		656.2.bs.d.225.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.20.3	✓	24	123.20	odd	20
41.2.g.a.39.3	yes	24	3.2	odd	2
369.2.u.a.244.1		24	1.1	even	1	trivial
369.2.u.a.307.1		24	41.20	even	20	inner
656.2.bs.d.225.2		24	492.143	even	20
656.2.bs.d.449.2		24	12.11	even	2
1681.2.a.m.1.15		24	123.56	even	40
1681.2.a.m.1.16		24	123.26	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)

\(f(q)\)	\(=\)	\(q+(-1.14785 + 0.372958i) q^{2} +(-0.439578 + 0.319372i) q^{4} +(-1.49595 - 2.05900i) q^{5} +(-1.01547 + 0.517405i) q^{7} +(1.80427 - 2.48337i) q^{8} +O(q^{10})\)	\(q+(-1.14785 + 0.372958i) q^{2} +(-0.439578 + 0.319372i) q^{4} +(-1.49595 - 2.05900i) q^{5} +(-1.01547 + 0.517405i) q^{7} +(1.80427 - 2.48337i) q^{8} +(2.48504 + 1.80549i) q^{10} +(0.807883 + 5.10077i) q^{11} +(1.17315 - 2.30243i) q^{13} +(0.972629 - 0.972629i) q^{14} +(-0.809030 + 2.48994i) q^{16} +(3.05576 - 0.483986i) q^{17} +(3.74044 + 7.34102i) q^{19} +(1.31517 + 0.427326i) q^{20} +(-2.82970 - 5.55360i) q^{22} +(1.17869 + 3.62763i) q^{23} +(-0.456519 + 1.40502i) q^{25} +(-0.487884 + 3.08038i) q^{26} +(0.281132 - 0.551752i) q^{28} +(-5.72573 - 0.906866i) q^{29} +(3.65641 + 2.65654i) q^{31} +2.97943i q^{32} +(-3.32705 + 1.69521i) q^{34} +(2.58442 + 1.31683i) q^{35} +(0.584132 - 0.424397i) q^{37} +(-7.03134 - 7.03134i) q^{38} -7.81235 q^{40} +(5.78336 + 2.74822i) q^{41} +(1.75698 - 0.570876i) q^{43} +(-1.98417 - 1.98417i) q^{44} +(-2.70591 - 3.72436i) q^{46} +(3.15704 + 1.60859i) q^{47} +(-3.35104 + 4.61230i) q^{49} -1.78301i q^{50} +(0.219643 + 1.38677i) q^{52} +(5.52741 + 0.875456i) q^{53} +(9.29392 - 9.29392i) q^{55} +(-0.547268 + 3.45532i) q^{56} +(6.91048 - 1.09451i) q^{58} +(-0.242763 - 0.747149i) q^{59} +(6.70623 + 2.17898i) q^{61} +(-5.18778 - 1.68561i) q^{62} +(-2.72926 - 8.39980i) q^{64} +(-6.49567 + 1.02881i) q^{65} +(-0.835907 + 5.27771i) q^{67} +(-1.18868 + 1.18868i) q^{68} +(-3.45764 - 0.547637i) q^{70} +(-0.708805 - 4.47522i) q^{71} +0.149836i q^{73} +(-0.512213 + 0.705000i) q^{74} +(-3.98873 - 2.03236i) q^{76} +(-3.45954 - 4.76165i) q^{77} +(-11.4389 - 11.4389i) q^{79} +(6.33704 - 2.05903i) q^{80} +(-7.66339 - 0.997584i) q^{82} -4.27258 q^{83} +(-5.56779 - 5.56779i) q^{85} +(-1.80383 + 1.31056i) q^{86} +(14.1247 + 7.19691i) q^{88} +(1.51781 - 0.773362i) q^{89} +2.94503i q^{91} +(-1.67669 - 1.21819i) q^{92} +(-4.22374 - 0.668975i) q^{94} +(9.51963 - 18.6833i) q^{95} +(0.687542 - 4.34097i) q^{97} +(2.12628 - 6.54402i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) \) 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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