LMFDB - Embedded newform 980.2.g.a.391.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(391,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("980.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.11
Character	$\chi$	$=$	980.391
Dual form			980.2.g.a.391.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.976830 + 1.02265i) q^{2} -1.11294 q^{3} +(-0.0916073 - 1.99790i) q^{4} -1.00000i q^{5} +(1.08715 - 1.13814i) q^{6} +(2.13263 + 1.85793i) q^{8} -1.76137 q^{9} +O(q^{10})$	\(q+(-0.976830 + 1.02265i) q^{2} -1.11294 q^{3} +(-0.0916073 - 1.99790i) q^{4} -1.00000i q^{5} +(1.08715 - 1.13814i) q^{6} +(2.13263 + 1.85793i) q^{8} -1.76137 q^{9} +(1.02265 + 0.976830i) q^{10} +1.71377i q^{11} +(0.101953 + 2.22354i) q^{12} +2.45950i q^{13} +1.11294i q^{15} +(-3.98322 + 0.366045i) q^{16} -6.21892i q^{17} +(1.72056 - 1.80126i) q^{18} +0.216513 q^{19} +(-1.99790 + 0.0916073i) q^{20} +(-1.75258 - 1.67406i) q^{22} +6.56656i q^{23} +(-2.37348 - 2.06776i) q^{24} -1.00000 q^{25} +(-2.51519 - 2.40251i) q^{26} +5.29911 q^{27} -2.47123 q^{29} +(-1.13814 - 1.08715i) q^{30} -0.163826 q^{31} +(3.51659 - 4.43098i) q^{32} -1.90732i q^{33} +(6.35975 + 6.07482i) q^{34} +(0.161354 + 3.51904i) q^{36} +7.69679 q^{37} +(-0.211496 + 0.221416i) q^{38} -2.73727i q^{39} +(1.85793 - 2.13263i) q^{40} -8.34130i q^{41} +1.89449i q^{43} +(3.42394 - 0.156994i) q^{44} +1.76137i q^{45} +(-6.71527 - 6.41442i) q^{46} +11.7045 q^{47} +(4.43307 - 0.407385i) q^{48} +(0.976830 - 1.02265i) q^{50} +6.92127i q^{51} +(4.91383 - 0.225308i) q^{52} +13.0276 q^{53} +(-5.17633 + 5.41911i) q^{54} +1.71377 q^{55} -0.240965 q^{57} +(2.41397 - 2.52720i) q^{58} +4.28758 q^{59} +(2.22354 - 0.101953i) q^{60} -7.00039i q^{61} +(0.160030 - 0.167536i) q^{62} +(1.09621 + 7.92454i) q^{64} +2.45950 q^{65} +(1.95051 + 1.86313i) q^{66} +5.17415i q^{67} +(-12.4248 + 0.569698i) q^{68} -7.30818i q^{69} +5.04201i q^{71} +(-3.75635 - 3.27250i) q^{72} +7.61517i q^{73} +(-7.51846 + 7.87109i) q^{74} +1.11294 q^{75} +(-0.0198341 - 0.432571i) q^{76} +(2.79925 + 2.67384i) q^{78} +15.9493i q^{79} +(0.366045 + 3.98322i) q^{80} -0.613471 q^{81} +(8.53020 + 8.14803i) q^{82} +5.47827 q^{83} -6.21892 q^{85} +(-1.93739 - 1.85060i) q^{86} +2.75033 q^{87} +(-3.18406 + 3.65483i) q^{88} +1.78368i q^{89} +(-1.80126 - 1.72056i) q^{90} +(13.1193 - 0.601545i) q^{92} +0.182328 q^{93} +(-11.4333 + 11.9696i) q^{94} -0.216513i q^{95} +(-3.91375 + 4.93141i) q^{96} +10.5305i q^{97} -3.01858i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.976830	+	1.02265i	−0.690723	+	0.723120i
$2$	−0.976830	+	1.02265i	−0.690723	+	0.723120i
$3$	−1.11294			−0.642555			−0.321278	−	0.946985i	$-0.604112\pi$
$3$	−1.11294			−0.642555			−0.321278	+	0.946985i	$0.604112\pi$
$4$	−0.0916073	−	1.99790i	−0.0458036	−	0.998950i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.08715	−	1.13814i	0.443827	−	0.464644i
$7$		0			0
$7$		0			0
$8$	2.13263	+	1.85793i	0.753998	+	0.656876i
$9$	−1.76137			−0.587123
$10$	1.02265	+	0.976830i	0.323389	+	0.308901i
$11$			1.71377i			0.516721i	0.966049	+	0.258360i	$0.0831822\pi$
$11$			1.71377i			0.516721i	−0.966049	+	0.258360i	$0.916818\pi$
$12$	0.101953	+	2.22354i	0.0294314	+	0.641881i
$13$			2.45950i			0.682142i	0.940038	+	0.341071i	$0.110790\pi$
$13$			2.45950i			0.682142i	−0.940038	+	0.341071i	$0.889210\pi$
$14$		0			0
$15$			1.11294i			0.287359i
$16$	−3.98322	+	0.366045i	−0.995804	+	0.0915112i
$17$		−	6.21892i		−	1.50831i	−0.656697	−	0.754155i	$-0.728047\pi$
$17$		−	6.21892i		−	1.50831i	0.656697	−	0.754155i	$-0.271953\pi$
$18$	1.72056	−	1.80126i	0.405539	−	0.424560i
$19$	0.216513			0.0496714			0.0248357	−	0.999692i	$-0.492094\pi$
$19$	0.216513			0.0496714			0.0248357	+	0.999692i	$0.492094\pi$
$20$	−1.99790	+	0.0916073i	−0.446744	+	0.0204840i
$21$		0			0
$22$	−1.75258	−	1.67406i	−0.373651	−	0.356911i
$23$			6.56656i			1.36922i	0.728908	+	0.684612i	$0.240028\pi$
$23$			6.56656i			1.36922i	−0.728908	+	0.684612i	$0.759972\pi$
$24$	−2.37348	−	2.06776i	−0.484485	−	0.422079i
$25$	−1.00000			−0.200000
$26$	−2.51519	−	2.40251i	−0.493270	−	0.471171i
$27$	5.29911			1.01981
$28$		0			0
$29$	−2.47123			−0.458896			−0.229448	−	0.973321i	$-0.573692\pi$
$29$	−2.47123			−0.458896			−0.229448	+	0.973321i	$0.573692\pi$
$30$	−1.13814	−	1.08715i	−0.207795	−	0.198486i
$31$	−0.163826			−0.0294241			−0.0147120	−	0.999892i	$-0.504683\pi$
$31$	−0.163826			−0.0294241			−0.0147120	+	0.999892i	$0.504683\pi$
$32$	3.51659	−	4.43098i	0.621651	−	0.783294i
$33$		−	1.90732i		−	0.332022i
$34$	6.35975	+	6.07482i	1.09069	+	1.04182i
$35$		0			0
$36$	0.161354	+	3.51904i	0.0268924	+	0.586507i
$37$	7.69679			1.26535			0.632673	−	0.774419i	$-0.281958\pi$
$37$	7.69679			1.26535			0.632673	+	0.774419i	$0.281958\pi$
$38$	−0.211496	+	0.221416i	−0.0343092	+	0.0359184i
$39$		−	2.73727i		−	0.438313i
$40$	1.85793	−	2.13263i	0.293764	−	0.337198i
$41$		−	8.34130i		−	1.30269i	−0.758781	−	0.651346i	$-0.774205\pi$
$41$		−	8.34130i		−	1.30269i	0.758781	−	0.651346i	$-0.225795\pi$
$42$		0			0
$43$			1.89449i			0.288907i	0.989512	+	0.144454i	$0.0461425\pi$
$43$			1.89449i			0.288907i	−0.989512	+	0.144454i	$0.953858\pi$
$44$	3.42394	−	0.156994i	0.516179	−	0.0236677i
$45$			1.76137i			0.262569i
$46$	−6.71527	−	6.41442i	−0.990112	−	0.945754i
$47$	11.7045			1.70728			0.853639	−	0.520865i	$-0.174391\pi$
$47$	11.7045			1.70728			0.853639	+	0.520865i	$0.174391\pi$
$48$	4.43307	−	0.407385i	0.639859	−	0.0588010i
$49$		0			0
$50$	0.976830	−	1.02265i	0.138145	−	0.144624i
$51$			6.92127i			0.969172i
$52$	4.91383	−	0.225308i	0.681426	−	0.0312446i
$53$	13.0276			1.78949			0.894743	−	0.446582i	$-0.147359\pi$
$53$	13.0276			1.78949			0.894743	+	0.446582i	$0.147359\pi$
$54$	−5.17633	+	5.41911i	−0.704409	+	0.737447i
$55$	1.71377			0.231085
$56$		0			0
$57$	−0.240965			−0.0319166
$58$	2.41397	−	2.52720i	0.316970	−	0.331837i
$59$	4.28758			0.558195			0.279098	−	0.960263i	$-0.409965\pi$
$59$	4.28758			0.558195			0.279098	+	0.960263i	$0.409965\pi$
$60$	2.22354	−	0.101953i	0.287058	−	0.0131621i
$61$		−	7.00039i		−	0.896308i	−0.893956	−	0.448154i	$-0.852082\pi$
$61$		−	7.00039i		−	0.896308i	0.893956	−	0.448154i	$-0.147918\pi$
$62$	0.160030	−	0.167536i	0.0203239	−	0.0212771i
$63$		0			0
$64$	1.09621	+	7.92454i	0.137027	+	0.990567i
$65$	2.45950			0.305063
$66$	1.95051	+	1.86313i	0.240091	+	0.229335i
$67$			5.17415i			0.632124i	0.948739	+	0.316062i	$0.102361\pi$
$67$			5.17415i			0.632124i	−0.948739	+	0.316062i	$0.897639\pi$
$68$	−12.4248	+	0.569698i	−1.50673	+	0.0690861i
$69$		−	7.30818i		−	0.879801i
$70$		0			0
$71$			5.04201i			0.598376i	0.954194	+	0.299188i	$0.0967158\pi$
$71$			5.04201i			0.598376i	−0.954194	+	0.299188i	$0.903284\pi$
$72$	−3.75635	−	3.27250i	−0.442690	−	0.385667i
$73$			7.61517i			0.891288i	0.895210	+	0.445644i	$0.147025\pi$
$73$			7.61517i			0.891288i	−0.895210	+	0.445644i	$0.852975\pi$
$74$	−7.51846	+	7.87109i	−0.874003	+	0.914996i
$75$	1.11294			0.128511
$76$	−0.0198341	−	0.432571i	−0.00227513	−	0.0496193i
$77$		0			0
$78$	2.79925	+	2.67384i	0.316953	+	0.302753i
$79$			15.9493i			1.79443i	0.441592	+	0.897216i	$0.354414\pi$
$79$			15.9493i			1.79443i	−0.441592	+	0.897216i	$0.645586\pi$
$80$	0.366045	+	3.98322i	0.0409250	+	0.445337i
$81$	−0.613471			−0.0681635
$82$	8.53020	+	8.14803i	0.942002	+	0.899800i
$83$	5.47827			0.601318			0.300659	−	0.953732i	$-0.402793\pi$
$83$	5.47827			0.601318			0.300659	+	0.953732i	$0.402793\pi$
$84$		0			0
$85$	−6.21892			−0.674536
$86$	−1.93739	−	1.85060i	−0.208915	−	0.199555i
$87$	2.75033			0.294866
$88$	−3.18406	+	3.65483i	−0.339422	+	0.389607i
$89$			1.78368i			0.189069i	0.995522	+	0.0945347i	$0.0301363\pi$
$89$			1.78368i			0.189069i	−0.995522	+	0.0945347i	$0.969864\pi$
$90$	−1.80126	−	1.72056i	−0.189869	−	0.181363i
$91$		0			0
$92$	13.1193	−	0.601545i	1.36779	−	0.0627154i
$93$	0.182328			0.0189066
$94$	−11.4333	+	11.9696i	−1.17926	+	1.23457i
$95$		−	0.216513i		−	0.0222137i
$96$	−3.91375	+	4.93141i	−0.399445	+	0.503310i
$97$			10.5305i			1.06921i	0.845101	+	0.534606i	$0.179540\pi$
$97$			10.5305i			1.06921i	−0.845101	+	0.534606i	$0.820460\pi$
$98$		0			0
$99$		−	3.01858i		−	0.303379i
$100$	0.0916073	+	1.99790i	0.00916073	+	0.199790i
$101$		−	0.449771i		−	0.0447539i	−0.999750	−	0.0223769i	$-0.992877\pi$
$101$		−	0.449771i		−	0.0447539i	0.999750	−	0.0223769i	$-0.00712339\pi$
$102$	−7.07800	−	6.76090i	−0.700827	−	0.669429i
$103$	9.28196			0.914579			0.457289	−	0.889318i	$-0.348820\pi$
$103$	9.28196			0.914579			0.457289	+	0.889318i	$0.348820\pi$
$104$	−4.56957	+	5.24519i	−0.448083	+	0.514334i
$105$		0			0
$106$	−12.7258	+	13.3227i	−1.23604	+	1.29401i
$107$		−	18.5240i		−	1.79078i	−0.445278	−	0.895392i	$-0.646895\pi$
$107$		−	18.5240i		−	1.79078i	0.445278	−	0.895392i	$-0.353105\pi$
$108$	−0.485437	−	10.5871i	−0.0467112	−	1.01874i
$109$	−6.97114			−0.667714			−0.333857	−	0.942624i	$-0.608350\pi$
$109$	−6.97114			−0.667714			−0.333857	+	0.942624i	$0.608350\pi$
$110$	−1.67406	+	1.75258i	−0.159615	+	0.167102i
$111$	−8.56605			−0.813054
$112$		0			0
$113$	0.333646			0.0313868			0.0156934	−	0.999877i	$-0.495004\pi$
$113$	0.333646			0.0313868			0.0156934	+	0.999877i	$0.495004\pi$
$114$	0.235382	−	0.246422i	0.0220455	−	0.0230795i
$115$	6.56656			0.612335
$116$	0.226383	+	4.93728i	0.0210191	+	0.458415i
$117$		−	4.33208i		−	0.400501i
$118$	−4.18824	+	4.38467i	−0.385558	+	0.403642i
$119$		0			0
$120$	−2.06776	+	2.37348i	−0.188760	+	0.216668i
$121$	8.06299			0.732999
$122$	7.15891	+	6.83819i	0.648138	+	0.619100i
$123$			9.28335i			0.837052i
$124$	0.0150077	+	0.327309i	0.00134773	+	0.0293932i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	15.8806i		−	1.40918i	−0.709616	−	0.704589i	$-0.751131\pi$
$127$		−	15.8806i		−	1.40918i	0.709616	−	0.704589i	$-0.248869\pi$
$128$	−9.17481	−	6.61989i	−0.810946	−	0.585121i
$129$		−	2.10845i		−	0.185639i
$130$	−2.40251	+	2.51519i	−0.210714	+	0.220597i
$131$	−3.20657			−0.280159			−0.140080	−	0.990140i	$-0.544736\pi$
$131$	−3.20657			−0.280159			−0.140080	+	0.990140i	$0.544736\pi$
$132$	−3.81063	+	0.174724i	−0.331673	+	0.0152078i
$133$		0			0
$134$	−5.29133	−	5.05427i	−0.457101	−	0.436622i
$135$		−	5.29911i		−	0.456075i
$136$	11.5543	−	13.2626i	0.990773	−	1.13726i
$137$	1.30357			0.111372			0.0556859	−	0.998448i	$-0.482265\pi$
$137$	1.30357			0.111372			0.0556859	+	0.998448i	$0.482265\pi$
$138$	7.47368	+	7.13885i	0.636201	+	0.607699i
$139$	20.8813			1.77113			0.885563	−	0.464519i	$-0.153773\pi$
$139$	20.8813			1.77113			0.885563	+	0.464519i	$0.153773\pi$
$140$		0			0
$141$	−13.0264			−1.09702
$142$	−5.15619	−	4.92518i	−0.432697	−	0.413312i
$143$	−4.21501			−0.352477
$144$	7.01591	−	0.644740i	0.584660	−	0.0537283i
$145$			2.47123i			0.205225i
$146$	−7.78762	−	7.43873i	−0.644508	−	0.615633i
$147$		0			0
$148$	−0.705083	−	15.3774i	−0.0579574	−	1.26402i
$149$	9.73494			0.797517			0.398759	−	0.917056i	$-0.369441\pi$
$149$	9.73494			0.797517			0.398759	+	0.917056i	$0.369441\pi$
$150$	−1.08715	+	1.13814i	−0.0887655	+	0.0929288i
$151$			14.9372i			1.21557i	0.794102	+	0.607784i	$0.207941\pi$
$151$			14.9372i			1.21557i	−0.794102	+	0.607784i	$0.792059\pi$
$152$	0.461741	+	0.402265i	0.0374521	+	0.0326280i
$153$			10.9538i			0.885563i
$154$		0			0
$155$			0.163826i			0.0131588i
$156$	−5.46879	+	0.250754i	−0.437853	+	0.0200764i
$157$			8.22463i			0.656397i	0.944609	+	0.328198i	$0.106441\pi$
$157$			8.22463i			0.656397i	−0.944609	+	0.328198i	$0.893559\pi$
$158$	−16.3104	−	15.5797i	−1.29759	−	1.23946i
$159$	−14.4990			−1.14984
$160$	−4.43098	−	3.51659i	−0.350300	−	0.278011i
$161$		0			0
$162$	0.599257	−	0.627364i	0.0470821	−	0.0492903i
$163$			11.9866i			0.938863i	0.882969	+	0.469431i	$0.155541\pi$
$163$			11.9866i			0.938863i	−0.882969	+	0.469431i	$0.844459\pi$
$164$	−16.6651	+	0.764124i	−1.30133	+	0.0596681i
$165$	−1.90732			−0.148485
$166$	−5.35133	+	5.60232i	−0.415344	+	0.434825i
$167$	−14.8103			−1.14606			−0.573029	−	0.819535i	$-0.694232\pi$
$167$	−14.8103			−1.14606			−0.573029	+	0.819535i	$0.694232\pi$
$168$		0			0
$169$	6.95088			0.534683
$170$	6.07482	−	6.35975i	0.465918	−	0.487770i
$171$	−0.381359			−0.0291632
$172$	3.78501	−	0.173549i	0.288604	−	0.0132330i
$173$		−	15.6209i		−	1.18763i	−0.804600	−	0.593817i	$-0.797620\pi$
$173$		−	15.6209i		−	1.18763i	0.804600	−	0.593817i	$-0.202380\pi$
$174$	−2.68660	+	2.81261i	−0.203671	+	0.213224i
$175$		0			0
$176$	−0.627316	−	6.82631i	−0.0472857	−	0.514553i
$177$	−4.77181			−0.358671
$178$	−1.82407	−	1.74235i	−0.136720	−	0.130595i
$179$		−	6.38903i		−	0.477538i	−0.971076	−	0.238769i	$-0.923256\pi$
$179$		−	6.38903i		−	0.477538i	0.971076	−	0.238769i	$-0.0767439\pi$
$180$	3.51904	−	0.161354i	0.262294	−	0.0120266i
$181$		−	1.18770i		−	0.0882808i	−0.999025	−	0.0441404i	$-0.985945\pi$
$181$		−	1.18770i		−	0.0882808i	0.999025	−	0.0441404i	$-0.0140549\pi$
$182$		0			0
$183$			7.79100i			0.575927i
$184$	−12.2002	+	14.0040i	−0.899411	+	1.03239i
$185$		−	7.69679i		−	0.565880i
$186$	−0.178104	+	0.186457i	−0.0130592	+	0.0136717i
$187$	10.6578			0.779375
$188$	−1.07222	−	23.3844i	−0.0781996	−	1.70549i
$189$		0			0
$190$	0.221416	+	0.211496i	0.0160632	+	0.0153435i
$191$		−	10.5610i		−	0.764166i	−0.924128	−	0.382083i	$-0.875207\pi$
$191$		−	10.5610i		−	0.764166i	0.924128	−	0.382083i	$-0.124793\pi$
$192$	−1.22002	−	8.81952i	−0.0880471	−	0.636494i
$193$	5.40807			0.389281			0.194641	−	0.980875i	$-0.437646\pi$
$193$	5.40807			0.389281			0.194641	+	0.980875i	$0.437646\pi$
$194$	−10.7690	−	10.2865i	−0.773168	−	0.738529i
$195$	−2.73727			−0.196020
$196$		0			0
$197$	17.9504			1.27892			0.639458	−	0.768826i	$-0.279159\pi$
$197$	17.9504			1.27892			0.639458	+	0.768826i	$0.279159\pi$
$198$	3.08694	+	2.94864i	0.219379	+	0.209551i
$199$	−7.65076			−0.542348			−0.271174	−	0.962530i	$-0.587412\pi$
$199$	−7.65076			−0.542348			−0.271174	+	0.962530i	$0.587412\pi$
$200$	−2.13263	−	1.85793i	−0.150800	−	0.131375i
$201$		−	5.75851i		−	0.406174i
$202$	0.459956	+	0.439349i	0.0323624	+	0.0309125i
$203$		0			0
$204$	13.8280	−	0.634039i	0.968154	−	0.0443916i
$205$	−8.34130			−0.582582
$206$	−9.06689	+	9.49215i	−0.631720	+	0.661350i
$207$		−	11.5661i		−	0.803903i
$208$	−0.900285	−	9.79671i	−0.0624236	−	0.679279i
$209$			0.371053i			0.0256662i
$210$		0			0
$211$		−	15.5710i		−	1.07195i	−0.844234	−	0.535975i	$-0.819944\pi$
$211$		−	15.5710i		−	1.07195i	0.844234	−	0.535975i	$-0.180056\pi$
$212$	−1.19343	−	26.0279i	−0.0819649	−	1.78761i
$213$		−	5.61144i		−	0.384490i
$214$	18.9435	+	18.0948i	1.29495	+	1.23694i
$215$	1.89449			0.129203
$216$	11.3010	+	9.84536i	0.768938	+	0.669892i
$217$		0			0
$218$	6.80962	−	7.12900i	0.461205	−	0.482837i
$219$		−	8.47521i		−	0.572702i
$220$	−0.156994	−	3.42394i	−0.0105845	−	0.230842i
$221$	15.2954			1.02888
$222$	8.36758	−	8.76004i	0.561595	−	0.587935i
$223$	−11.4678			−0.767938			−0.383969	−	0.923346i	$-0.625443\pi$
$223$	−11.4678			−0.767938			−0.383969	+	0.923346i	$0.625443\pi$
$224$		0			0
$225$	1.76137			0.117425
$226$	−0.325915	+	0.341202i	−0.0216796	+	0.0226964i
$227$	8.95435			0.594321			0.297161	−	0.954828i	$-0.403960\pi$
$227$	8.95435			0.594321			0.297161	+	0.954828i	$0.403960\pi$
$228$	0.0220742	+	0.481424i	0.00146190	+	0.0318831i
$229$			2.40675i			0.159042i	0.996833	+	0.0795212i	$0.0253391\pi$
$229$			2.40675i			0.159042i	−0.996833	+	0.0795212i	$0.974661\pi$
$230$	−6.41442	+	6.71527i	−0.422954	+	0.442792i
$231$		0			0
$232$	−5.27022	−	4.59137i	−0.346007	−	0.301438i
$233$	−2.56075			−0.167761			−0.0838803	−	0.996476i	$-0.526731\pi$
$233$	−2.56075			−0.167761			−0.0838803	+	0.996476i	$0.526731\pi$
$234$	4.43018	+	4.23171i	0.289610	+	0.276635i
$235$		−	11.7045i		−	0.763518i
$236$	−0.392774	−	8.56616i	−0.0255674	−	0.557610i
$237$		−	17.7505i		−	1.15302i
$238$		0			0
$239$		−	6.31200i		−	0.408289i	−0.978941	−	0.204145i	$-0.934559\pi$
$239$		−	6.31200i		−	0.408289i	0.978941	−	0.204145i	$-0.0654413\pi$
$240$	−0.407385	−	4.43307i	−0.0262966	−	0.286154i
$241$			9.62616i			0.620076i	0.950724	+	0.310038i	$0.100342\pi$
$241$			9.62616i			0.620076i	−0.950724	+	0.310038i	$0.899658\pi$
$242$	−7.87617	+	8.24558i	−0.506300	+	0.530046i
$243$	−15.2146			−0.976015
$244$	−13.9861	+	0.641286i	−0.895367	+	0.0410542i
$245$		0			0
$246$	−9.49358	−	9.06825i	−0.605288	−	0.578171i
$247$			0.532512i			0.0338829i
$248$	−0.349380	−	0.304377i	−0.0221857	−	0.0193280i
$249$	−6.09697			−0.386380
$250$	−1.02265	−	0.976830i	−0.0646778	−	0.0617801i
$251$	−24.9508			−1.57488			−0.787440	−	0.616391i	$-0.788594\pi$
$251$	−24.9508			−1.57488			−0.787440	+	0.616391i	$0.788594\pi$
$252$		0			0
$253$	−11.2536			−0.707506
$254$	16.2402	+	15.5127i	1.01900	+	0.973351i
$255$	6.92127			0.433427
$256$	15.7320	−	2.91607i	0.983251	−	0.182254i
$257$			16.9763i			1.05895i	0.848325	+	0.529475i	$0.177611\pi$
$257$			16.9763i			1.05895i	−0.848325	+	0.529475i	$0.822389\pi$
$258$	2.15620	+	2.05960i	0.134239	+	0.128225i
$259$		0			0
$260$	−0.225308	−	4.91383i	−0.0139730	−	0.304743i
$261$	4.35275			0.269429
$262$	3.13227	−	3.27918i	0.193512	−	0.202589i
$263$			15.0335i			0.927005i	0.886096	+	0.463503i	$0.153408\pi$
$263$			15.0335i			0.927005i	−0.886096	+	0.463503i	$0.846592\pi$
$264$	3.54366	−	4.06760i	0.218097	−	0.250344i
$265$		−	13.0276i		−	0.800282i
$266$		0			0
$267$		−	1.98512i		−	0.121487i
$268$	10.3374	−	0.473990i	0.631460	−	0.0289536i
$269$		−	31.4313i		−	1.91640i	−0.286097	−	0.958201i	$-0.592358\pi$
$269$		−	31.4313i		−	1.91640i	0.286097	−	0.958201i	$-0.407642\pi$
$270$	5.41911	+	5.17633i	0.329796	+	0.315021i
$271$	3.31771			0.201536			0.100768	−	0.994910i	$-0.467870\pi$
$271$	3.31771			0.201536			0.100768	+	0.994910i	$0.467870\pi$
$272$	2.27640	+	24.7713i	0.138027	+	1.50198i
$273$		0			0
$274$	−1.27337	+	1.33309i	−0.0769270	+	0.0805351i
$275$		−	1.71377i		−	0.103344i
$276$	−14.6010	+	0.669483i	−0.878878	+	0.0402981i
$277$	14.7459			0.885994			0.442997	−	0.896523i	$-0.353915\pi$
$277$	14.7459			0.885994			0.442997	+	0.896523i	$0.353915\pi$
$278$	−20.3974	+	21.3541i	−1.22336	+	1.28074i
$279$	0.288558			0.0172755
$280$		0			0
$281$	20.5438			1.22554			0.612769	−	0.790262i	$-0.290056\pi$
$281$	20.5438			1.22554			0.612769	+	0.790262i	$0.290056\pi$
$282$	12.7246	−	13.3214i	0.757737	−	0.793277i
$283$	−27.8362			−1.65469			−0.827346	−	0.561692i	$-0.810151\pi$
$283$	−27.8362			−1.65469			−0.827346	+	0.561692i	$0.810151\pi$
$284$	10.0734	−	0.461885i	0.597748	−	0.0274078i
$285$			0.240965i			0.0142735i
$286$	4.11735	−	4.31046i	0.243464	−	0.254883i
$287$		0			0
$288$	−6.19401	+	7.80459i	−0.364986	+	0.459890i
$289$	−21.6749			−1.27500
$290$	−2.52720	−	2.41397i	−0.148402	−	0.141753i
$291$		−	11.7198i		−	0.687027i
$292$	15.2144	−	0.697605i	0.890353	−	0.0408243i
$293$			4.28428i			0.250290i	0.992138	+	0.125145i	$0.0399396\pi$
$293$			4.28428i			0.250290i	−0.992138	+	0.125145i	$0.960060\pi$
$294$		0			0
$295$		−	4.28758i		−	0.249633i
$296$	16.4144	+	14.3001i	0.954068	+	0.831176i
$297$			9.08145i			0.526959i
$298$	−9.50938	+	9.95539i	−0.550864	+	0.576700i
$299$	−16.1504			−0.934004
$300$	−0.101953	−	2.22354i	−0.00588627	−	0.128376i
$301$		0			0
$302$	−15.2754	−	14.5911i	−0.879001	−	0.839621i
$303$			0.500567i			0.0287568i
$304$	−0.862416	+	0.0792533i	−0.0494630	+	0.00454549i
$305$	−7.00039			−0.400841
$306$	−11.2019	−	10.7000i	−0.640368	−	0.611679i
$307$	−14.3171			−0.817117			−0.408559	−	0.912732i	$-0.633968\pi$
$307$	−14.3171			−0.817117			−0.408559	+	0.912732i	$0.633968\pi$
$308$		0			0
$309$	−10.3302			−0.587667
$310$	−0.167536	−	0.160030i	−0.00951541	−	0.00908911i
$311$	−25.6631			−1.45522			−0.727609	−	0.685992i	$-0.759369\pi$
$311$	−25.6631			−1.45522			−0.727609	+	0.685992i	$0.759369\pi$
$312$	5.08564	−	5.83757i	0.287918	−	0.330488i
$313$			32.5054i			1.83731i	0.395059	+	0.918656i	$0.370724\pi$
$313$			32.5054i			1.83731i	−0.395059	+	0.918656i	$0.629276\pi$
$314$	−8.41088	−	8.03406i	−0.474653	−	0.453388i
$315$		0			0
$316$	31.8650	−	1.46107i	1.79255	−	0.0821915i
$317$	2.92067			0.164041			0.0820205	−	0.996631i	$-0.473863\pi$
$317$	2.92067			0.164041			0.0820205	+	0.996631i	$0.473863\pi$
$318$	14.1630	−	14.8273i	0.794223	−	0.831474i
$319$		−	4.23512i		−	0.237121i
$320$	7.92454	−	1.09621i	0.442995	−	0.0612801i
$321$			20.6161i			1.15068i
$322$		0			0
$323$		−	1.34647i		−	0.0749198i
$324$	0.0561984	+	1.22565i	0.00312214	+	0.0680919i
$325$		−	2.45950i		−	0.136428i
$326$	−12.2580	−	11.7089i	−0.678910	−	0.648494i
$327$	7.75845			0.429043
$328$	15.4975	−	17.7889i	0.855708	−	0.982228i
$329$		0			0
$330$	1.86313	−	1.95051i	0.102562	−	0.107372i
$331$			3.94866i			0.217038i	0.994094	+	0.108519i	$0.0346108\pi$
$331$			3.94866i			0.217038i	−0.994094	+	0.108519i	$0.965389\pi$
$332$	−0.501849	−	10.9450i	−0.0275425	−	0.600687i
$333$	−13.5569			−0.742913
$334$	14.4672	−	15.1457i	0.791609	−	0.828737i
$335$	5.17415			0.282694
$336$		0			0
$337$	−10.0467			−0.547280			−0.273640	−	0.961832i	$-0.588228\pi$
$337$	−10.0467			−0.547280			−0.273640	+	0.961832i	$0.588228\pi$
$338$	−6.78982	+	7.10828i	−0.369318	+	0.386640i
$339$	−0.371327			−0.0201677
$340$	0.569698	+	12.4248i	0.0308962	+	0.673828i
$341$		−	0.280760i		−	0.0152040i
$342$	0.372522	−	0.389995i	0.0201437	−	0.0210885i
$343$		0			0
$344$	−3.51983	+	4.04025i	−0.189776	+	0.217836i
$345$	−7.30818			−0.393459
$346$	15.9746	+	15.2589i	0.858801	+	0.820326i
$347$			0.0201100i			0.00107956i	1.00000		0.000539780i	$0.000171817\pi$
$347$			0.0201100i			0.00107956i	−1.00000		0.000539780i	$0.999828\pi$
$348$	−0.251950	−	5.49489i	−0.0135060	−	0.294557i
$349$		−	5.60366i		−	0.299957i	−0.988689	−	0.149978i	$-0.952080\pi$
$349$		−	5.60366i		−	0.299957i	0.988689	−	0.149978i	$-0.0479204\pi$
$350$		0			0
$351$			13.0331i			0.695657i
$352$	7.59368	+	6.02662i	0.404744	+	0.321220i
$353$			25.4844i			1.35640i	0.734880	+	0.678198i	$0.237239\pi$
$353$			25.4844i			1.35640i	−0.734880	+	0.678198i	$0.762761\pi$
$354$	4.66125	−	4.87987i	0.247742	−	0.259362i
$355$	5.04201			0.267602
$356$	3.56361	−	0.163398i	0.188871	−	0.00866007i
$357$		0			0
$358$	6.53371	+	6.24099i	0.345317	+	0.329847i
$359$		−	19.3484i		−	1.02117i	−0.859827	−	0.510586i	$-0.829428\pi$
$359$		−	19.3484i		−	1.02117i	0.859827	−	0.510586i	$-0.170572\pi$
$360$	−3.27250	+	3.75635i	−0.172476	+	0.197977i
$361$	−18.9531			−0.997533
$362$	1.21459	+	1.16018i	0.0638375	+	0.0609776i
$363$	−8.97361			−0.470993
$364$		0			0
$365$	7.61517			0.398596
$366$	−7.96743	−	7.61048i	−0.416464	−	0.397806i
$367$	17.2951			0.902799			0.451399	−	0.892322i	$-0.350925\pi$
$367$	17.2951			0.902799			0.451399	+	0.892322i	$0.350925\pi$
$368$	−2.40366	−	26.1560i	−0.125299	−	1.36348i
$369$			14.6921i			0.764841i
$370$	7.87109	+	7.51846i	0.409199	+	0.390866i
$371$		0			0
$372$	−0.0167026	−	0.364274i	−0.000865990	−	0.0188867i
$373$	11.1097			0.575237			0.287618	−	0.957745i	$-0.407137\pi$
$373$	11.1097			0.575237			0.287618	+	0.957745i	$0.407137\pi$
$374$	−10.4108	+	10.8991i	−0.538332	+	0.563581i
$375$		−	1.11294i		−	0.0574719i
$376$	24.9614	+	21.7461i	1.28728	+	1.12147i
$377$		−	6.07799i		−	0.313032i
$378$		0			0
$379$			14.3198i			0.735558i	0.929913	+	0.367779i	$0.119882\pi$
$379$			14.3198i			0.735558i	−0.929913	+	0.367779i	$0.880118\pi$
$380$	−0.432571	+	0.0198341i	−0.0221904	+	0.00101747i
$381$			17.6741i			0.905474i
$382$	10.8001	+	10.3163i	0.552583	+	0.527827i
$383$	−10.4539			−0.534167			−0.267084	−	0.963673i	$-0.586060\pi$
$383$	−10.4539			−0.534167			−0.267084	+	0.963673i	$0.586060\pi$
$384$	10.2110	+	7.36753i	0.521077	+	0.375972i
$385$		0			0
$386$	−5.28276	+	5.53054i	−0.268886	+	0.281497i
$387$		−	3.33690i		−	0.169624i
$388$	21.0389	−	0.964672i	1.06809	−	0.0489738i
$389$	−30.1257			−1.52744			−0.763718	−	0.645550i	$-0.776628\pi$
$389$	−30.1257			−1.52744			−0.763718	+	0.645550i	$0.776628\pi$
$390$	2.67384	−	2.79925i	0.135395	−	0.141746i
$391$	40.8369			2.06521
$392$		0			0
$393$	3.56871			0.180018
$394$	−17.5345	+	18.3569i	−0.883377	+	0.924809i
$395$	15.9493			0.802494
$396$	−6.03082	+	0.276524i	−0.303060	+	0.0138959i
$397$		−	13.4379i		−	0.674429i	−0.941428	−	0.337215i	$-0.890515\pi$
$397$		−	13.4379i		−	0.674429i	0.941428	−	0.337215i	$-0.109485\pi$
$398$	7.47349	−	7.82401i	0.374612	−	0.392182i
$399$		0			0
$400$	3.98322	−	0.366045i	0.199161	−	0.0183022i
$401$	−28.8847			−1.44243			−0.721216	−	0.692710i	$-0.756416\pi$
$401$	−28.8847			−1.44243			−0.721216	+	0.692710i	$0.756416\pi$
$402$	5.88892	+	5.62509i	0.293712	+	0.280554i
$403$		−	0.402930i		−	0.0200714i
$404$	−0.898597	+	0.0412023i	−0.0447069	+	0.00204989i
$405$			0.613471i			0.0304836i
$406$		0			0
$407$			13.1905i			0.653830i
$408$	−12.8592	+	14.7605i	−0.636626	+	0.730754i
$409$		−	25.9031i		−	1.28083i	−0.768030	−	0.640413i	$-0.778763\pi$
$409$		−	25.9031i		−	1.28083i	0.768030	−	0.640413i	$-0.221237\pi$
$410$	8.14803	−	8.53020i	0.402403	−	0.421276i
$411$	−1.45080			−0.0715625
$412$	−0.850295	−	18.5444i	−0.0418910	−	0.913619i
$413$		0			0
$414$	11.8281	+	11.2982i	0.581318	+	0.555274i
$415$		−	5.47827i		−	0.268917i
$416$	10.8980	+	8.64904i	0.534318	+	0.424054i
$417$	−23.2396			−1.13805
$418$	−0.379455	−	0.362455i	−0.0185598	−	0.0177283i
$419$	28.1022			1.37288			0.686441	−	0.727185i	$-0.259172\pi$
$419$	28.1022			1.37288			0.686441	+	0.727185i	$0.259172\pi$
$420$		0			0
$421$	15.6269			0.761608			0.380804	−	0.924656i	$-0.375647\pi$
$421$	15.6269			0.761608			0.380804	+	0.924656i	$0.375647\pi$
$422$	15.9236	+	15.2102i	0.775148	+	0.740420i
$423$	−20.6160			−1.00238
$424$	27.7831	+	24.2044i	1.34927	+	1.17547i
$425$			6.21892i			0.301662i
$426$	5.73851	+	5.48142i	0.278032	+	0.265576i
$427$		0			0
$428$	−37.0092	+	1.69694i	−1.78890	+	0.0820245i
$429$	4.69104			0.226486
$430$	−1.85060	+	1.93739i	−0.0892437	+	0.0934294i
$431$			19.9499i			0.960953i	0.877008	+	0.480477i	$0.159536\pi$
$431$			19.9499i			0.960953i	−0.877008	+	0.480477i	$0.840464\pi$
$432$	−21.1075	+	1.93971i	−1.01553	+	0.0933243i
$433$			11.8294i			0.568487i	0.958752	+	0.284243i	$0.0917424\pi$
$433$			11.8294i			0.568487i	−0.958752	+	0.284243i	$0.908258\pi$
$434$		0			0
$435$		−	2.75033i		−	0.131868i
$436$	0.638607	+	13.9276i	0.0305837	+	0.667013i
$437$			1.42174i			0.0680112i
$438$	8.66714	+	8.27884i	0.414132	+	0.395578i
$439$	−27.8949			−1.33135			−0.665675	−	0.746242i	$-0.731856\pi$
$439$	−27.8949			−1.33135			−0.665675	+	0.746242i	$0.731856\pi$
$440$	3.65483	+	3.18406i	0.174237	+	0.151794i
$441$		0			0
$442$	−14.9410	+	15.6418i	−0.710671	+	0.744003i
$443$		−	19.1991i		−	0.912177i	−0.889934	−	0.456088i	$-0.849250\pi$
$443$		−	19.1991i		−	0.912177i	0.889934	−	0.456088i	$-0.150750\pi$
$444$	0.784713	+	17.1141i	0.0372408	+	0.812201i
$445$	1.78368			0.0845544
$446$	11.2021	−	11.7275i	0.530433	−	0.555311i
$447$	−10.8344			−0.512449
$448$		0			0
$449$	−4.94035			−0.233150			−0.116575	−	0.993182i	$-0.537191\pi$
$449$	−4.94035			−0.233150			−0.116575	+	0.993182i	$0.537191\pi$
$450$	−1.72056	+	1.80126i	−0.0811079	+	0.0849120i
$451$	14.2951			0.673129
$452$	−0.0305644	−	0.666592i	−0.00143763	−	0.0313538i
$453$		−	16.6241i		−	0.781070i
$454$	−8.74688	+	9.15713i	−0.410511	+	0.429765i
$455$		0			0
$456$	−0.513889	−	0.447696i	−0.0240651	−	0.0209653i
$457$	−26.1243			−1.22204			−0.611022	−	0.791614i	$-0.709241\pi$
$457$	−26.1243			−1.22204			−0.611022	+	0.791614i	$0.709241\pi$
$458$	−2.46125	−	2.35098i	−0.115007	−	0.109854i
$459$		−	32.9547i		−	1.53819i
$460$	−0.601545	−	13.1193i	−0.0280472	−	0.611693i
$461$			13.3894i			0.623609i	0.950146	+	0.311804i	$0.100933\pi$
$461$			13.3894i			0.623609i	−0.950146	+	0.311804i	$0.899067\pi$
$462$		0			0
$463$			16.4019i			0.762259i	0.924522	+	0.381130i	$0.124465\pi$
$463$			16.4019i			0.762259i	−0.924522	+	0.381130i	$0.875535\pi$
$464$	9.84346	−	0.904582i	0.456971	−	0.0419941i
$465$		−	0.182328i		−	0.00845528i
$466$	2.50142	−	2.61874i	0.115876	−	0.121311i
$467$	−11.9333			−0.552206			−0.276103	−	0.961128i	$-0.589043\pi$
$467$	−11.9333			−0.552206			−0.276103	+	0.961128i	$0.589043\pi$
$468$	−8.65507	+	0.396850i	−0.400081	+	0.0183444i
$469$		0			0
$470$	11.9696	+	11.4333i	0.552115	+	0.527379i
$471$		−	9.15350i		−	0.421771i
$472$	9.14382	+	7.96601i	0.420878	+	0.366665i
$473$	−3.24672			−0.149285
$474$	18.1525	+	17.3393i	0.833772	+	0.796418i
$475$	−0.216513			−0.00993428
$476$		0			0
$477$	−22.9465			−1.05065
$478$	6.45494	+	6.16575i	0.295242	+	0.282015i
$479$	37.1777			1.69869			0.849347	−	0.527834i	$-0.176996\pi$
$479$	37.1777			1.69869			0.849347	+	0.527834i	$0.176996\pi$
$480$	4.93141	+	3.91375i	0.225087	+	0.178637i
$481$			18.9302i			0.863145i
$482$	−9.84415	−	9.40312i	−0.448389	−	0.428300i
$483$		0			0
$484$	−0.738629	−	16.1091i	−0.0335741	−	0.732230i
$485$	10.5305			0.478166
$486$	14.8620	−	15.5591i	0.674156	−	0.705776i
$487$			0.978376i			0.0443344i	0.999754	+	0.0221672i	$0.00705662\pi$
$487$			0.978376i			0.0443344i	−0.999754	+	0.0221672i	$0.992943\pi$
$488$	13.0062	−	14.9292i	0.588763	−	0.675814i
$489$		−	13.3403i		−	0.603271i
$490$		0			0
$491$			18.4167i			0.831132i	0.909563	+	0.415566i	$0.136417\pi$
$491$			18.4167i			0.831132i	−0.909563	+	0.415566i	$0.863583\pi$
$492$	18.5472	−	0.850423i	0.836173	−	0.0383400i
$493$			15.3684i			0.692158i
$494$	−0.544571	−	0.520174i	−0.0245014	−	0.0234037i
$495$	−3.01858			−0.135675
$496$	0.652555	−	0.0599677i	0.0293006	−	0.00269263i
$497$		0			0
$498$	5.95570	−	6.23504i	0.266881	−	0.279399i
$499$			19.5338i			0.874451i	0.899352	+	0.437226i	$0.144039\pi$
$499$			19.5338i			0.874451i	−0.899352	+	0.437226i	$0.855961\pi$
$500$	1.99790	−	0.0916073i	0.0893488	−	0.00409680i
$501$	16.4830			0.736406
$502$	24.3727	−	25.5158i	1.08781	−	1.13883i
$503$	11.7007			0.521707			0.260853	−	0.965378i	$-0.415996\pi$
$503$	11.7007			0.521707			0.260853	+	0.965378i	$0.415996\pi$
$504$		0			0
$505$	−0.449771			−0.0200145
$506$	10.9928	−	11.5084i	0.488691	−	0.511612i
$507$	−7.73590			−0.343563
$508$	−31.7279	+	1.45478i	−1.40770	+	0.0645455i
$509$			2.14293i			0.0949838i	0.998872	+	0.0474919i	$0.0151228\pi$
$509$			2.14293i			0.0949838i	−0.998872	+	0.0474919i	$0.984877\pi$
$510$	−6.76090	+	7.07800i	−0.299378	+	0.313419i
$511$		0			0
$512$	−12.3854	+	18.9368i	−0.547363	+	0.836896i
$513$	1.14732			0.0506556
$514$	−17.3607	−	16.5829i	−0.765748	−	0.731441i
$515$		−	9.28196i		−	0.409012i
$516$	−4.21248	+	0.193150i	−0.185444	+	0.00850294i
$517$			20.0588i			0.882186i
$518$		0			0
$519$			17.3851i			0.763120i
$520$	5.24519	+	4.56957i	0.230017	+	0.200389i
$521$		−	13.6715i		−	0.598960i	−0.954103	−	0.299480i	$-0.903187\pi$
$521$		−	13.6715i		−	0.598960i	0.954103	−	0.299480i	$-0.0968131\pi$
$522$	−4.25190	+	4.45132i	−0.186101	+	0.194829i
$523$	37.5656			1.64263			0.821316	−	0.570474i	$-0.193241\pi$
$523$	37.5656			1.64263			0.821316	+	0.570474i	$0.193241\pi$
$524$	0.293745	+	6.40640i	0.0128323	+	0.279865i
$525$		0			0
$526$	−15.3739	−	14.6852i	−0.670336	−	0.640304i
$527$			1.01882i			0.0443806i
$528$	0.698164	+	7.59726i	0.0303837	+	0.330628i
$529$	−20.1198			−0.874773
$530$	13.3227	+	12.7258i	0.578700	+	0.552773i
$531$	−7.55201			−0.327729
$532$		0			0
$533$	20.5154			0.888621
$534$	2.03008	+	1.93913i	0.0878499	+	0.0839142i
$535$	−18.5240			−0.800863
$536$	−9.61320	+	11.0346i	−0.415227	+	0.476620i
$537$			7.11059i			0.306845i
$538$	32.1431	+	30.7030i	1.38579	+	1.32370i
$539$		0			0
$540$	−10.5871	+	0.485437i	−0.455596	+	0.0208899i
$541$	26.6104			1.14407			0.572034	−	0.820230i	$-0.306154\pi$
$541$	26.6104			1.14407			0.572034	+	0.820230i	$0.306154\pi$
$542$	−3.24083	+	3.39284i	−0.139206	+	0.145735i
$543$			1.32183i			0.0567253i
$544$	−27.5559	−	21.8694i	−1.18145	−	0.937642i
$545$			6.97114i			0.298611i
$546$		0			0
$547$			24.0582i			1.02865i	0.857594	+	0.514327i	$0.171958\pi$
$547$			24.0582i			1.02865i	−0.857594	+	0.514327i	$0.828042\pi$
$548$	−0.119417	−	2.60441i	−0.00510123	−	0.111255i
$549$			12.3303i			0.526243i
$550$	1.75258	+	1.67406i	0.0747302	+	0.0713822i
$551$	−0.535053			−0.0227940
$552$	13.5781	−	15.5856i	0.577921	−	0.663369i
$553$		0			0
$554$	−14.4042	+	15.0798i	−0.611976	+	0.640679i
$555$			8.56605i			0.363609i
$556$	−1.91288	−	41.7187i	−0.0811240	−	1.76927i
$557$	26.7419			1.13309			0.566546	−	0.824030i	$-0.308279\pi$
$557$	26.7419			1.13309			0.566546	+	0.824030i	$0.308279\pi$
$558$	−0.281872	+	0.295093i	−0.0119326	+	0.0124923i
$559$	−4.65950			−0.197076
$560$		0			0
$561$	−11.8615			−0.500791
$562$	−20.0678	+	21.0090i	−0.846507	+	0.886210i
$563$	17.4713			0.736329			0.368165	−	0.929761i	$-0.379986\pi$
$563$	17.4713			0.736329			0.368165	+	0.929761i	$0.379986\pi$
$564$	1.19331	+	26.0254i	0.0502475	+	1.09587i
$565$		−	0.333646i		−	0.0140366i
$566$	27.1913	−	28.4666i	1.14293	−	1.19654i
$567$		0			0
$568$	−9.36768	+	10.7527i	−0.393059	+	0.451175i
$569$	−20.3584			−0.853468			−0.426734	−	0.904377i	$-0.640336\pi$
$569$	−20.3584			−0.853468			−0.426734	+	0.904377i	$0.640336\pi$
$570$	−0.246422	−	0.235382i	−0.0103215	−	0.00985906i
$571$		−	22.2550i		−	0.931342i	−0.884958	−	0.465671i	$-0.845813\pi$
$571$		−	22.2550i		−	0.931342i	0.884958	−	0.465671i	$-0.154187\pi$
$572$	0.386126	+	8.42117i	0.0161447	+	0.352107i
$573$			11.7537i			0.491019i
$574$		0			0
$575$		−	6.56656i		−	0.273845i
$576$	−1.93083	−	13.9580i	−0.0804515	−	0.581585i
$577$		−	0.971128i		−	0.0404286i	−0.999796	−	0.0202143i	$-0.993565\pi$
$577$		−	0.971128i		−	0.0404286i	0.999796	−	0.0202143i	$-0.00643485\pi$
$578$	21.1727	−	22.1658i	0.880669	−	0.921975i
$579$	−6.01885			−0.250135
$580$	4.93728	−	0.226383i	0.205009	−	0.00940004i
$581$		0			0
$582$	11.9852	+	11.4483i	0.496803	+	0.474546i
$583$			22.3264i			0.924664i
$584$	−14.1484	+	16.2403i	−0.585466	+	0.672030i
$585$	−4.33208			−0.179110
$586$	−4.38130	−	4.18501i	−0.180990	−	0.172881i
$587$	17.6042			0.726602			0.363301	−	0.931672i	$-0.381650\pi$
$587$	17.6042			0.726602			0.363301	+	0.931672i	$0.381650\pi$
$588$		0			0
$589$	−0.0354704			−0.00146153
$590$	4.38467	+	4.18824i	0.180514	+	0.172427i
$591$	−19.9777			−0.821774
$592$	−30.6580	+	2.81737i	−1.26004	+	0.115793i
$593$		−	22.3772i		−	0.918922i	−0.888198	−	0.459461i	$-0.848043\pi$
$593$		−	22.3772i		−	0.918922i	0.888198	−	0.459461i	$-0.151957\pi$
$594$	−9.28710	−	8.87103i	−0.381054	−	0.363983i
$595$		0			0
$596$	−0.891792	−	19.4494i	−0.0365292	−	0.796680i
$597$	8.51482			0.348488
$598$	15.7762	−	16.5162i	0.645138	−	0.675397i
$599$		−	18.3668i		−	0.750446i	−0.926935	−	0.375223i	$-0.877566\pi$
$599$		−	18.3668i		−	0.750446i	0.926935	−	0.375223i	$-0.122434\pi$
$600$	2.37348	+	2.06776i	0.0968971	+	0.0844159i
$601$			11.9668i			0.488136i	0.969758	+	0.244068i	$0.0784820\pi$
$601$			11.9668i			0.488136i	−0.969758	+	0.244068i	$0.921518\pi$
$602$		0			0
$603$		−	9.11360i		−	0.371134i
$604$	29.8430	−	1.36835i	1.21429	−	0.0556775i
$605$		−	8.06299i		−	0.327807i
$606$	−0.511902	−	0.488969i	−0.0207946	−	0.0198630i
$607$	−16.3726			−0.664542			−0.332271	−	0.943184i	$-0.607815\pi$
$607$	−16.3726			−0.664542			−0.332271	+	0.943184i	$0.607815\pi$
$608$	0.761386	−	0.959363i	0.0308783	−	0.0389073i
$609$		0			0
$610$	6.83819	−	7.15891i	0.276870	−	0.289856i
$611$			28.7872i			1.16461i
$612$	21.8846	−	1.00345i	0.884634	−	0.0405620i
$613$	45.7436			1.84757			0.923783	−	0.382916i	$-0.125080\pi$
$613$	45.7436			1.84757			0.923783	+	0.382916i	$0.125080\pi$
$614$	13.9853	−	14.6413i	0.564402	−	0.590873i
$615$	9.28335			0.374341
$616$		0			0
$617$	3.88479			0.156396			0.0781979	−	0.996938i	$-0.475083\pi$
$617$	3.88479			0.156396			0.0781979	+	0.996938i	$0.475083\pi$
$618$	10.0909	−	10.5642i	0.405915	−	0.424954i
$619$	20.4330			0.821272			0.410636	−	0.911799i	$-0.365307\pi$
$619$	20.4330			0.821272			0.410636	+	0.911799i	$0.365307\pi$
$620$	0.327309	−	0.0150077i	0.0131450	−	0.000602723i
$621$			34.7969i			1.39635i
$622$	25.0684	−	26.2442i	1.00515	−	1.05230i
$623$		0			0
$624$	1.00196	+	10.9031i	0.0401106	+	0.436474i
$625$	1.00000			0.0400000
$626$	−33.2414	−	31.7522i	−1.32860	−	1.26907i
$627$		−	0.412959i		−	0.0164920i
$628$	16.4320	−	0.753436i	0.655708	−	0.0300654i
$629$		−	47.8657i		−	1.90853i
$630$		0			0
$631$		−	23.7070i		−	0.943762i	−0.881662	−	0.471881i	$-0.843575\pi$
$631$		−	23.7070i		−	0.943762i	0.881662	−	0.471881i	$-0.156425\pi$
$632$	−29.6326	+	34.0139i	−1.17872	+	1.35300i
$633$			17.3295i			0.688786i
$634$	−2.85299	+	2.98681i	−0.113307	+	0.118621i
$635$	−15.8806			−0.630203
$636$	1.32821	+	28.9675i	0.0526670	+	1.14864i
$637$		0			0
$638$	4.33103	+	4.13700i	0.171467	+	0.163785i
$639$		−	8.88084i		−	0.351320i
$640$	−6.61989	+	9.17481i	−0.261674	+	0.362666i
$641$	14.3937			0.568515			0.284258	−	0.958748i	$-0.408253\pi$
$641$	14.3937			0.568515			0.284258	+	0.958748i	$0.408253\pi$
$642$	−21.0829	−	20.1384i	−0.832077	−	0.794799i
$643$	−47.6127			−1.87766			−0.938830	−	0.344380i	$-0.888089\pi$
$643$	−47.6127			−1.87766			−0.938830	+	0.344380i	$0.888089\pi$
$644$		0			0
$645$	−2.10845			−0.0830202
$646$	1.37697	+	1.31528i	0.0541760	+	0.0517488i
$647$	0.0108286			0.000425715			0.000212858	−	1.00000i	$-0.499932\pi$
$647$	0.0108286			0.000425715			0.000212858		1.00000i	$0.499932\pi$
$648$	−1.30831	−	1.13978i	−0.0513951	−	0.0447750i
$649$			7.34792i			0.288431i
$650$	2.51519	+	2.40251i	0.0986540	+	0.0942342i
$651$		0			0
$652$	23.9480	−	1.09806i	0.937877	−	0.0430033i
$653$	−10.6223			−0.415681			−0.207841	−	0.978163i	$-0.566644\pi$
$653$	−10.6223			−0.415681			−0.207841	+	0.978163i	$0.566644\pi$
$654$	−7.57868	+	7.93414i	−0.296350	+	0.310249i
$655$			3.20657i			0.125291i
$656$	3.05329	+	33.2252i	0.119211	+	1.29723i
$657$		−	13.4131i		−	0.523296i
$658$		0			0
$659$			13.3688i			0.520773i	0.965505	+	0.260386i	$0.0838499\pi$
$659$			13.3688i			0.520773i	−0.965505	+	0.260386i	$0.916150\pi$
$660$	0.174724	+	3.81063i	0.00680114	+	0.148329i
$661$		−	7.50536i		−	0.291925i	−0.989290	−	0.145962i	$-0.953372\pi$
$661$		−	7.50536i		−	0.291925i	0.989290	−	0.145962i	$-0.0466278\pi$
$662$	−4.03808	−	3.85717i	−0.156944	−	0.149913i
$663$	−17.0228			−0.661112
$664$	11.6831	+	10.1782i	0.453393	+	0.394992i
$665$		0			0
$666$	13.2428	−	13.8639i	0.513147	−	0.537215i
$667$		−	16.2275i		−	0.628332i
$668$	1.35674	+	29.5896i	0.0524937	+	1.14486i
$669$	12.7629			0.493443
$670$	−5.05427	+	5.29133i	−0.195263	+	0.204422i
$671$	11.9970			0.463141
$672$		0			0
$673$	19.9107			0.767501			0.383751	−	0.923437i	$-0.374632\pi$
$673$	19.9107			0.767501			0.383751	+	0.923437i	$0.374632\pi$
$674$	9.81395	−	10.2742i	0.378019	−	0.395749i
$675$	−5.29911			−0.203963
$676$	−0.636751	−	13.8872i	−0.0244904	−	0.534122i
$677$		−	26.0053i		−	0.999466i	−0.866180	−	0.499733i	$-0.833431\pi$
$677$		−	26.0053i		−	0.999466i	0.866180	−	0.499733i	$-0.166569\pi$
$678$	0.362724	−	0.379736i	0.0139303	−	0.0145837i
$679$		0			0
$680$	−13.2626	−	11.5543i	−0.508599	−	0.443087i
$681$	−9.96564			−0.381884
$682$	0.287118	+	0.274255i	0.0109943	+	0.0105018i
$683$			14.8200i			0.567071i	0.958962	+	0.283536i	$0.0915074\pi$
$683$			14.8200i			0.567071i	−0.958962	+	0.283536i	$0.908493\pi$
$684$	0.0349352	+	0.761917i	0.00133578	+	0.0291326i
$685$		−	1.30357i		−	0.0498070i
$686$		0			0
$687$		−	2.67856i		−	0.102194i
$688$	−0.693469	−	7.54617i	−0.0264383	−	0.287695i
$689$			32.0415i			1.22068i
$690$	7.13885	−	7.47368i	0.271771	−	0.284518i
$691$	26.4910			1.00776			0.503882	−	0.863773i	$-0.331905\pi$
$691$	26.4910			1.00776			0.503882	+	0.863773i	$0.331905\pi$
$692$	−31.2090	+	1.43099i	−1.18639	+	0.0543980i
$693$		0			0
$694$	−0.0205654	−	0.0196440i	−0.000780651	−	0.000745677i
$695$		−	20.8813i		−	0.792072i
$696$	5.86543	+	5.10991i	0.222329	+	0.193691i
$697$	−51.8739			−1.96486
$698$	5.73055	+	5.47382i	0.216905	+	0.207187i
$699$	2.84996			0.107795
$700$		0			0
$701$	−0.713553			−0.0269505			−0.0134753	−	0.999909i	$-0.504289\pi$
$701$	−0.713553			−0.0269505			−0.0134753	+	0.999909i	$0.504289\pi$
$702$	−13.3283	−	12.7312i	−0.503043	−	0.480507i
$703$	1.66645			0.0628515
$704$	−13.5808	+	1.87866i	−0.511847	+	0.0708045i
$705$			13.0264i			0.490602i
$706$	−26.0615	−	24.8939i	−0.980836	−	0.936893i
$707$		0			0
$708$	0.437133	+	9.53361i	0.0164285	+	0.358295i
$709$	−19.1317			−0.718505			−0.359253	−	0.933240i	$-0.616968\pi$
$709$	−19.1317			−0.718505			−0.359253	+	0.933240i	$0.616968\pi$
$710$	−4.92518	+	5.15619i	−0.184839	+	0.193508i
$711$		−	28.0925i		−	1.05355i
$712$	−3.31394	+	3.80392i	−0.124195	+	0.142558i
$713$		−	1.07578i		−	0.0402881i
$714$		0			0
$715$			4.21501i			0.157632i
$716$	−12.7646	+	0.585282i	−0.477037	+	0.0218730i
$717$			7.02486i			0.262348i
$718$	19.7866	+	18.9001i	0.738429	+	0.705347i
$719$	40.0572			1.49388			0.746941	−	0.664890i	$-0.231522\pi$
$719$	40.0572			1.49388			0.746941	+	0.664890i	$0.231522\pi$
$720$	−0.644740	−	7.01591i	−0.0240280	−	0.261468i
$721$		0			0
$722$	18.5140	−	19.3823i	0.689019	−	0.721335i
$723$		−	10.7133i		−	0.398433i
$724$	−2.37290	+	0.108802i	−0.0881881	+	0.00404358i
$725$	2.47123			0.0917793
$726$	8.76569	−	9.17682i	0.325325	−	0.340584i
$727$	14.4074			0.534341			0.267171	−	0.963649i	$-0.413911\pi$
$727$	14.4074			0.534341			0.267171	+	0.963649i	$0.413911\pi$
$728$		0			0
$729$	18.7733			0.695307
$730$	−7.43873	+	7.78762i	−0.275320	+	0.288233i
$731$	11.7817			0.435762
$732$	15.5656	−	0.713712i	0.575322	−	0.0263796i
$733$		−	0.774526i		−	0.0286078i	−0.999898	−	0.0143039i	$-0.995447\pi$
$733$		−	0.774526i		−	0.0286078i	0.999898	−	0.0143039i	$-0.00455322\pi$
$734$	−16.8944	+	17.6868i	−0.623584	+	0.652831i
$735$		0			0
$736$	29.0963	+	23.0919i	1.07250	+	0.851179i
$737$	−8.86731			−0.326631
$738$	−15.0248	−	14.3517i	−0.553071	−	0.528293i
$739$		−	8.19740i		−	0.301546i	−0.988568	−	0.150773i	$-0.951824\pi$
$739$		−	8.19740i		−	0.301546i	0.988568	−	0.150773i	$-0.0481763\pi$
$740$	−15.3774	+	0.705083i	−0.565286	+	0.0259194i
$741$		−	0.592653i		−	0.0217716i
$742$		0			0
$743$		−	8.66498i		−	0.317887i	−0.987288	−	0.158944i	$-0.949191\pi$
$743$		−	8.66498i		−	0.317887i	0.987288	−	0.158944i	$-0.0508088\pi$
$744$	0.388839	+	0.338753i	0.0142555	+	0.0124193i
$745$		−	9.73494i		−	0.356661i
$746$	−10.8523	+	11.3613i	−0.397329	+	0.415965i
$747$	−9.64925			−0.353048
$748$	−0.976331	−	21.2932i	−0.0356982	−	0.778557i
$749$		0			0
$750$	1.13814	+	1.08715i	0.0415590	+	0.0396971i
$751$		−	7.77354i		−	0.283661i	−0.989891	−	0.141830i	$-0.954701\pi$
$751$		−	7.77354i		−	0.283661i	0.989891	−	0.141830i	$-0.0452987\pi$
$752$	−46.6216	+	4.28437i	−1.70011	+	0.156235i
$753$	27.7687			1.01195
$754$	6.21563	+	5.93716i	0.226360	+	0.216219i
$755$	14.9372			0.543619
$756$		0			0
$757$	−5.10767			−0.185641			−0.0928206	−	0.995683i	$-0.529588\pi$
$757$	−5.10767			−0.185641			−0.0928206	+	0.995683i	$0.529588\pi$
$758$	−14.6441	−	13.9880i	−0.531896	−	0.508066i
$759$	12.5245			0.454612
$760$	0.402265	−	0.461741i	0.0145917	−	0.0167491i
$761$			4.80634i			0.174230i	0.996198	+	0.0871149i	$0.0277647\pi$
$761$			4.80634i			0.174230i	−0.996198	+	0.0871149i	$0.972235\pi$
$762$	−18.0744	−	17.2646i	−0.654766	−	0.625432i
$763$		0			0
$764$	−21.0998	+	0.967463i	−0.763364	+	0.0350016i
$765$	10.9538			0.396036
$766$	10.2116	−	10.6906i	0.368961	−	0.386267i
$767$			10.5453i			0.380768i
$768$	−17.5088	+	3.24540i	−0.631793	+	0.117108i
$769$			24.7841i			0.893738i	0.894600	+	0.446869i	$0.147461\pi$
$769$			24.7841i			0.893738i	−0.894600	+	0.446869i	$0.852539\pi$
$770$		0			0
$771$		−	18.8935i		−	0.680434i
$772$	−0.495419	−	10.8048i	−0.0178305	−	0.388873i
$773$		−	25.3120i		−	0.910410i	−0.890387	−	0.455205i	$-0.849566\pi$
$773$		−	25.3120i		−	0.910410i	0.890387	−	0.455205i	$-0.150434\pi$
$774$	3.41247	+	3.25958i	0.122659	+	0.117163i
$775$	0.163826			0.00588481
$776$	−19.5649	+	22.4577i	−0.702340	+	0.806184i
$777$		0			0
$778$	29.4277	−	30.8080i	1.05504	−	1.10452i
$779$		−	1.80600i		−	0.0647066i
$780$	0.250754	+	5.46879i	0.00897842	+	0.195814i
$781$	−8.64084			−0.309193
$782$	−39.8907	+	41.7617i	−1.42649	+

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.976830 + 1.02265i) q^{2} -1.11294 q^{3} +(-0.0916073 - 1.99790i) q^{4} -1.00000i q^{5} +(1.08715 - 1.13814i) q^{6} +(2.13263 + 1.85793i) q^{8} -1.76137 q^{9} +O(q^{10})\)	\(q+(-0.976830 + 1.02265i) q^{2} -1.11294 q^{3} +(-0.0916073 - 1.99790i) q^{4} -1.00000i q^{5} +(1.08715 - 1.13814i) q^{6} +(2.13263 + 1.85793i) q^{8} -1.76137 q^{9} +(1.02265 + 0.976830i) q^{10} +1.71377i q^{11} +(0.101953 + 2.22354i) q^{12} +2.45950i q^{13} +1.11294i q^{15} +(-3.98322 + 0.366045i) q^{16} -6.21892i q^{17} +(1.72056 - 1.80126i) q^{18} +0.216513 q^{19} +(-1.99790 + 0.0916073i) q^{20} +(-1.75258 - 1.67406i) q^{22} +6.56656i q^{23} +(-2.37348 - 2.06776i) q^{24} -1.00000 q^{25} +(-2.51519 - 2.40251i) q^{26} +5.29911 q^{27} -2.47123 q^{29} +(-1.13814 - 1.08715i) q^{30} -0.163826 q^{31} +(3.51659 - 4.43098i) q^{32} -1.90732i q^{33} +(6.35975 + 6.07482i) q^{34} +(0.161354 + 3.51904i) q^{36} +7.69679 q^{37} +(-0.211496 + 0.221416i) q^{38} -2.73727i q^{39} +(1.85793 - 2.13263i) q^{40} -8.34130i q^{41} +1.89449i q^{43} +(3.42394 - 0.156994i) q^{44} +1.76137i q^{45} +(-6.71527 - 6.41442i) q^{46} +11.7045 q^{47} +(4.43307 - 0.407385i) q^{48} +(0.976830 - 1.02265i) q^{50} +6.92127i q^{51} +(4.91383 - 0.225308i) q^{52} +13.0276 q^{53} +(-5.17633 + 5.41911i) q^{54} +1.71377 q^{55} -0.240965 q^{57} +(2.41397 - 2.52720i) q^{58} +4.28758 q^{59} +(2.22354 - 0.101953i) q^{60} -7.00039i q^{61} +(0.160030 - 0.167536i) q^{62} +(1.09621 + 7.92454i) q^{64} +2.45950 q^{65} +(1.95051 + 1.86313i) q^{66} +5.17415i q^{67} +(-12.4248 + 0.569698i) q^{68} -7.30818i q^{69} +5.04201i q^{71} +(-3.75635 - 3.27250i) q^{72} +7.61517i q^{73} +(-7.51846 + 7.87109i) q^{74} +1.11294 q^{75} +(-0.0198341 - 0.432571i) q^{76} +(2.79925 + 2.67384i) q^{78} +15.9493i q^{79} +(0.366045 + 3.98322i) q^{80} -0.613471 q^{81} +(8.53020 + 8.14803i) q^{82} +5.47827 q^{83} -6.21892 q^{85} +(-1.93739 - 1.85060i) q^{86} +2.75033 q^{87} +(-3.18406 + 3.65483i) q^{88} +1.78368i q^{89} +(-1.80126 - 1.72056i) q^{90} +(13.1193 - 0.601545i) q^{92} +0.182328 q^{93} +(-11.4333 + 11.9696i) q^{94} -0.216513i q^{95} +(-3.91375 + 4.93141i) q^{96} +10.5305i q^{97} -3.01858i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

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