LMFDB - Embedded newform 900.2.bj.f.523.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 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("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			523.17
Character	$\chi$	$=$	900.523
Dual form			900.2.bj.f.487.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.213085 - 1.39807i) q^{2} +(-1.90919 - 0.595816i) q^{4} +(1.90262 + 1.17475i) q^{5} +(2.16308 + 2.16308i) q^{7} +(-1.23981 + 2.54222i) q^{8} +(2.04780 - 2.40967i) q^{10} +(-3.61787 - 4.97957i) q^{11} +(0.749054 + 4.72934i) q^{13} +(3.48505 - 2.56321i) q^{14} +(3.29001 + 2.27505i) q^{16} +(3.51342 + 1.79018i) q^{17} +(0.678754 + 2.08899i) q^{19} +(-2.93253 - 3.37643i) q^{20} +(-7.73269 + 3.99695i) q^{22} +(-0.374565 + 2.36491i) q^{23} +(2.23993 + 4.47020i) q^{25} +(6.77155 - 0.0394750i) q^{26} +(-2.84093 - 5.41853i) q^{28} +(-1.48003 - 0.480891i) q^{29} +(8.29187 - 2.69419i) q^{31} +(3.88173 - 4.11487i) q^{32} +(3.25145 - 4.53054i) q^{34} +(1.57444 + 6.65660i) q^{35} +(4.07167 - 0.644890i) q^{37} +(3.06518 - 0.503811i) q^{38} +(-5.34536 + 3.38041i) q^{40} +(5.32533 + 3.86908i) q^{41} +(-8.72991 + 8.72991i) q^{43} +(3.94029 + 11.6625i) q^{44} +(3.22649 + 1.02759i) q^{46} +(3.47691 - 1.77157i) q^{47} +2.35783i q^{49} +(6.72695 - 2.17904i) q^{50} +(1.38773 - 9.47550i) q^{52} +(5.54447 - 2.82505i) q^{53} +(-1.03369 - 13.7243i) q^{55} +(-8.18083 + 2.81721i) q^{56} +(-0.987690 + 1.96671i) q^{58} +(-7.51879 - 5.46272i) q^{59} +(-0.715358 + 0.519738i) q^{61} +(-1.99979 - 12.1667i) q^{62} +(-4.92573 - 6.30374i) q^{64} +(-4.13062 + 9.87809i) q^{65} +(1.52131 - 2.98575i) q^{67} +(-5.64117 - 5.51114i) q^{68} +(9.64187 - 0.782756i) q^{70} +(-5.96760 - 1.93899i) q^{71} +(0.906675 + 0.143603i) q^{73} +(-0.0339856 - 5.82989i) q^{74} +(-0.0512164 - 4.39269i) q^{76} +(2.94547 - 18.5969i) q^{77} +(2.98135 - 9.17567i) q^{79} +(3.58702 + 8.19349i) q^{80} +(6.54398 - 6.62073i) q^{82} +(6.49903 + 3.31142i) q^{83} +(4.58170 + 7.53341i) q^{85} +(10.3448 + 14.0652i) q^{86} +(17.1446 - 3.02368i) q^{88} +(-0.440547 - 0.606362i) q^{89} +(-8.60967 + 11.8502i) q^{91} +(2.12417 - 4.29189i) q^{92} +(-1.73590 - 5.23845i) q^{94} +(-1.16263 + 4.77192i) q^{95} +(-7.49977 - 14.7191i) q^{97} +(3.29641 + 0.502419i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58}+ \cdots - 256 q^{98}+O(q^{100}) $ 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

Coefficient data

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

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

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

$2$	0.213085	−	1.39807i	0.150674	−	0.988583i
$2$	0.213085	−	1.39807i	0.150674	−	0.988583i
$3$		0			0
$3$		0			0
$4$	−1.90919	−	0.595816i	−0.954595	−	0.297908i
$5$	1.90262	+	1.17475i	0.850878	+	0.525364i
$5$	1.90262	+	1.17475i	0.850878	+	0.525364i
$6$		0			0
$7$	2.16308	+	2.16308i	0.817567	+	0.817567i	0.985755	−	0.168188i	$-0.0537915\pi$
$7$	2.16308	+	2.16308i	0.817567	+	0.817567i	−0.168188	+	0.985755i	$0.553791\pi$
$8$	−1.23981	+	2.54222i	−0.438340	+	0.898809i
$9$		0			0
$10$	2.04780	−	2.40967i	0.647571	−	0.762005i
$11$	−3.61787	−	4.97957i	−1.09083	−	1.50140i	−0.847011	−	0.531575i	$-0.821600\pi$
$11$	−3.61787	−	4.97957i	−1.09083	−	1.50140i	−0.243817	−	0.969821i	$-0.578400\pi$
$12$		0			0
$13$	0.749054	+	4.72934i	0.207750	+	1.31168i	0.842387	+	0.538872i	$0.181150\pi$
$13$	0.749054	+	4.72934i	0.207750	+	1.31168i	−0.634637	+	0.772810i	$0.718850\pi$
$14$	3.48505	−	2.56321i	0.931420	−	0.685047i
$15$		0			0
$16$	3.29001	+	2.27505i	0.822502	+	0.568763i
$17$	3.51342	+	1.79018i	0.852130	+	0.434182i	0.824786	−	0.565444i	$-0.191295\pi$
$17$	3.51342	+	1.79018i	0.852130	+	0.434182i	0.0273432	+	0.999626i	$0.491295\pi$
$18$		0			0
$19$	0.678754	+	2.08899i	0.155717	+	0.479247i	0.998233	−	0.0594243i	$-0.0189265\pi$
$19$	0.678754	+	2.08899i	0.155717	+	0.479247i	−0.842516	+	0.538671i	$0.818926\pi$
$20$	−2.93253	−	3.37643i	−0.655733	−	0.754993i
$21$		0			0
$22$	−7.73269	+	3.99695i	−1.64862	+	0.852153i
$23$	−0.374565	+	2.36491i	−0.0781022	+	0.493118i	0.917368	+	0.398041i	$0.130310\pi$
$23$	−0.374565	+	2.36491i	−0.0781022	+	0.493118i	−0.995470	+	0.0950770i	$0.969690\pi$
$24$		0			0
$25$	2.23993	+	4.47020i	0.447986	+	0.894041i
$26$	6.77155	−	0.0394750i	1.32801	−	0.00774169i
$27$		0			0
$28$	−2.84093	−	5.41853i	−0.536886	−	1.02401i
$29$	−1.48003	−	0.480891i	−0.274834	−	0.0892991i	0.168357	−	0.985726i	$-0.446154\pi$
$29$	−1.48003	−	0.480891i	−0.274834	−	0.0892991i	−0.443192	+	0.896427i	$0.646154\pi$
$30$		0			0
$31$	8.29187	−	2.69419i	1.48926	−	0.483891i	0.552398	−	0.833580i	$-0.313713\pi$
$31$	8.29187	−	2.69419i	1.48926	−	0.483891i	0.936866	+	0.349689i	$0.113713\pi$
$32$	3.88173	−	4.11487i	0.686199	−	0.727414i
$33$		0			0
$34$	3.25145	−	4.53054i	0.557619	−	0.776981i
$35$	1.57444	+	6.65660i	0.266130	+	1.12517i
$36$		0			0
$37$	4.07167	−	0.644890i	0.669379	−	0.106019i	0.187510	−	0.982263i	$-0.439958\pi$
$37$	4.07167	−	0.644890i	0.669379	−	0.106019i	0.481869	+	0.876243i	$0.339958\pi$
$38$	3.06518	−	0.503811i	0.497238	−	0.0817289i
$39$		0			0
$40$	−5.34536	+	3.38041i	−0.845175	+	0.534489i
$41$	5.32533	+	3.86908i	0.831677	+	0.604248i	0.920033	−	0.391840i	$-0.128161\pi$
$41$	5.32533	+	3.86908i	0.831677	+	0.604248i	−0.0883565	+	0.996089i	$0.528161\pi$
$42$		0			0
$43$	−8.72991	+	8.72991i	−1.33130	+	1.33130i	−0.427088	+	0.904210i	$0.640461\pi$
$43$	−8.72991	+	8.72991i	−1.33130	+	1.33130i	−0.904210	+	0.427088i	$0.859539\pi$
$44$	3.94029	+	11.6625i	0.594021	+	1.75819i
$45$		0			0
$46$	3.22649	+	1.02759i	0.475720	+	0.151511i
$47$	3.47691	−	1.77157i	0.507159	−	0.258410i	−0.181637	−	0.983366i	$-0.558140\pi$
$47$	3.47691	−	1.77157i	0.507159	−	0.258410i	0.688796	+	0.724955i	$0.258140\pi$
$48$		0			0
$49$			2.35783i			0.336833i
$50$	6.72695	−	2.17904i	0.951334	−	0.308163i
$51$		0			0
$52$	1.38773	−	9.47550i	0.192444	−	1.31402i
$53$	5.54447	−	2.82505i	0.761592	−	0.388050i	−0.0296448	−	0.999560i	$-0.509438\pi$
$53$	5.54447	−	2.82505i	0.761592	−	0.388050i	0.791237	+	0.611510i	$0.209438\pi$
$54$		0			0
$55$	−1.03369	−	13.7243i	−0.139382	−	1.85059i
$56$	−8.18083	+	2.81721i	−1.09321	+	0.376465i
$57$		0			0
$58$	−0.987690	+	1.96671i	−0.129690	+	0.258242i
$59$	−7.51879	−	5.46272i	−0.978863	−	0.711186i	−0.0214087	−	0.999771i	$-0.506815\pi$
$59$	−7.51879	−	5.46272i	−0.978863	−	0.711186i	−0.957454	+	0.288585i	$0.906815\pi$
$60$		0			0
$61$	−0.715358	+	0.519738i	−0.0915921	+	0.0665456i	−0.632639	−	0.774447i	$-0.718028\pi$
$61$	−0.715358	+	0.519738i	−0.0915921	+	0.0665456i	0.541047	+	0.840993i	$0.318028\pi$
$62$	−1.99979	−	12.1667i	−0.253973	−	1.54517i
$63$		0			0
$64$	−4.92573	−	6.30374i	−0.615717	−	0.787968i
$65$	−4.13062	+	9.87809i	−0.512341	+	1.22523i
$66$		0			0
$67$	1.52131	−	2.98575i	0.185858	−	0.364767i	−0.779211	−	0.626761i	$-0.784380\pi$
$67$	1.52131	−	2.98575i	0.185858	−	0.364767i	0.965069	+	0.261994i	$0.0843801\pi$
$68$	−5.64117	−	5.51114i	−0.684092	−	0.668324i
$69$		0			0
$70$	9.64187	−	0.782756i	1.15242	−	0.0935573i
$71$	−5.96760	−	1.93899i	−0.708224	−	0.230116i	−0.0673136	−	0.997732i	$-0.521443\pi$
$71$	−5.96760	−	1.93899i	−0.708224	−	0.230116i	−0.640910	+	0.767616i	$0.721443\pi$
$72$		0			0
$73$	0.906675	+	0.143603i	0.106118	+	0.0168075i	0.209268	−	0.977858i	$-0.432892\pi$
$73$	0.906675	+	0.143603i	0.106118	+	0.0168075i	−0.103149	+	0.994666i	$0.532892\pi$
$74$	−0.0339856	−	5.82989i	−0.00395074	−	0.677711i
$75$		0			0
$76$	−0.0512164	−	4.39269i	−0.00587493	−	0.503876i
$77$	2.94547	−	18.5969i	0.335667	−	2.11932i
$78$		0			0
$79$	2.98135	−	9.17567i	0.335429	−	1.03234i	−0.631082	−	0.775716i	$-0.717389\pi$
$79$	2.98135	−	9.17567i	0.335429	−	1.03234i	0.966511	−	0.256627i	$-0.0826112\pi$
$80$	3.58702	+	8.19349i	0.401041	+	0.916060i
$81$		0			0
$82$	6.54398	−	6.62073i	0.722662	−	0.731137i
$83$	6.49903	+	3.31142i	0.713361	+	0.363476i	0.772708	−	0.634762i	$-0.218902\pi$
$83$	6.49903	+	3.31142i	0.713361	+	0.363476i	−0.0593466	+	0.998237i	$0.518902\pi$
$84$		0			0
$85$	4.58170	+	7.53341i	0.496955	+	0.817114i
$86$	10.3448	+	14.0652i	1.11551	+	1.51669i
$87$		0			0
$88$	17.1446	−	3.02368i	1.82762	−	0.322325i
$89$	−0.440547	−	0.606362i	−0.0466979	−	0.0642742i	0.785029	−	0.619458i	$-0.212648\pi$
$89$	−0.440547	−	0.606362i	−0.0466979	−	0.0642742i	−0.831727	+	0.555184i	$0.812648\pi$
$90$		0			0
$91$	−8.60967	+	11.8502i	−0.902539	+	1.24224i
$92$	2.12417	−	4.29189i	0.221460	−	0.447460i
$93$		0			0
$94$	−1.73590	−	5.23845i	−0.179045	−	0.540305i
$95$	−1.16263	+	4.77192i	−0.119283	+	0.489589i
$96$		0			0
$97$	−7.49977	−	14.7191i	−0.761486	−	1.49450i	−0.866036	−	0.499981i	$-0.833340\pi$
$97$	−7.49977	−	14.7191i	−0.761486	−	1.49450i	0.104550	−	0.994520i	$-0.466660\pi$
$98$	3.29641	+	0.502419i	0.332987	+	0.0507520i
$99$		0			0
$100$	−1.61303	−	9.86905i	−0.161303	−	0.986905i
$101$	−11.9475			−1.18882			−0.594411	−	0.804162i	$-0.702615\pi$
$101$	−11.9475			−1.18882			−0.594411	+	0.804162i	$0.702615\pi$
$102$		0			0
$103$	−2.47283	−	4.85319i	−0.243655	−	0.478199i	0.736499	−	0.676439i	$-0.236478\pi$
$103$	−2.47283	−	4.85319i	−0.243655	−	0.478199i	−0.980154	+	0.198239i	$0.936478\pi$
$104$	−12.9517	−	3.95923i	−1.27002	−	0.388235i
$105$		0			0
$106$	−2.76817	−	8.35353i	−0.268868	−	0.811366i
$107$	0.462862	+	0.462862i	0.0447466	+	0.0447466i	0.729126	−	0.684379i	$-0.239927\pi$
$107$	0.462862	+	0.462862i	0.0447466	+	0.0447466i	−0.684379	+	0.729126i	$0.739927\pi$
$108$		0			0
$109$	2.19584	−	3.02232i	0.210324	−	0.289486i	−0.690802	−	0.723044i	$-0.742742\pi$
$109$	2.19584	−	3.02232i	0.210324	−	0.289486i	0.901125	+	0.433559i	$0.142742\pi$
$110$	−19.4078	−	1.47929i	−1.85046	−	0.141045i
$111$		0			0
$112$	2.19543	+	12.0377i	0.207449	+	1.13745i
$113$	−0.121019	−	0.764081i	−0.0113845	−	0.0718787i	0.981342	−	0.192270i	$-0.0615850\pi$
$113$	−0.121019	−	0.764081i	−0.0113845	−	0.0718787i	−0.992726	+	0.120392i	$0.961585\pi$
$114$		0			0
$115$	−3.49083	+	4.05951i	−0.325522	+	0.378551i
$116$	2.53913	+	1.79994i	0.235753	+	0.167120i
$117$		0			0
$118$	−9.23940	+	9.34775i	−0.850556	+	0.860530i
$119$	3.72751	+	11.4721i	0.341701	+	1.05165i
$120$		0			0
$121$	−8.30794	+	25.5692i	−0.755268	+	2.32448i
$122$	0.574196	+	1.11087i	0.0519853	+	0.100573i
$123$		0			0
$124$	−17.4360	+	0.203294i	−1.56580	+	0.0182564i
$125$	−0.989632	+	11.1365i	−0.0885154	+	0.996075i
$126$		0			0
$127$	6.14470	+	0.973224i	0.545254	+	0.0863597i	0.422984	−	0.906137i	$-0.360983\pi$
$127$	6.14470	+	0.973224i	0.545254	+	0.0863597i	0.122270	+	0.992497i	$0.460983\pi$
$128$	−9.86266	+	5.54328i	−0.871744	+	0.489961i
$129$		0			0
$130$	12.9301	+	7.87977i	1.13404	+	0.691101i
$131$	1.58146	−	0.513847i	0.138173	−	0.0448950i	−0.239114	−	0.970991i	$-0.576857\pi$
$131$	1.58146	−	0.513847i	0.138173	−	0.0448950i	0.377287	+	0.926096i	$0.376857\pi$
$132$		0			0
$133$	−3.05045	+	5.98685i	−0.264508	+	0.519126i
$134$	−3.85011	−	2.76312i	−0.332599	−	0.238697i
$135$		0			0
$136$	−8.90700	+	6.71239i	−0.763769	+	0.575583i
$137$	−3.67379	+	0.581872i	−0.313873	+	0.0497127i	−0.311384	−	0.950284i	$-0.600792\pi$
$137$	−3.67379	+	0.581872i	−0.313873	+	0.0497127i	−0.00248964	+	0.999997i	$0.500792\pi$
$138$		0			0
$139$	−1.16095	+	0.843477i	−0.0984702	+	0.0715428i	−0.635931	−	0.771746i	$-0.719384\pi$
$139$	−1.16095	+	0.843477i	−0.0984702	+	0.0715428i	0.537461	+	0.843289i	$0.319384\pi$
$140$	0.960194	−	13.6468i	0.0811512	−	1.15336i
$141$		0			0
$142$	−3.98245	+	7.92994i	−0.334200	+	0.665466i
$143$	20.8401	−	20.8401i	1.74274	−	1.74274i
$144$		0			0
$145$	−2.25101	−	2.65361i	−0.186936	−	0.220371i
$146$	0.393966	−	1.23699i	0.0326049	−	0.102374i
$147$		0			0
$148$	−8.15783	−	1.19475i	−0.670569	−	0.0982079i
$149$			20.6530i			1.69196i	0.533217	+	0.845979i	$0.320983\pi$
$149$			20.6530i			1.69196i	−0.533217	+	0.845979i	$0.679017\pi$
$150$		0			0
$151$			16.4775i			1.34092i	0.741946	+	0.670459i	$0.233903\pi$
$151$			16.4775i			1.34092i	−0.741946	+	0.670459i	$0.766097\pi$
$152$	−6.15219	−	0.864414i	−0.499009	−	0.0701132i
$153$		0			0
$154$	−25.3722	−	8.08070i	−2.04455	−	0.651161i
$155$	18.9413	+	4.61484i	1.52140	+	0.370673i
$156$		0			0
$157$	5.04582	−	5.04582i	0.402700	−	0.402700i	−0.476483	−	0.879184i	$-0.658089\pi$
$157$	5.04582	−	5.04582i	0.402700	−	0.402700i	0.879184	+	0.476483i	$0.158089\pi$
$158$	−12.1929	−	6.12334i	−0.970017	−	0.487147i
$159$		0			0
$160$	12.2194	−	3.26899i	0.966028	−	0.258436i
$161$	−5.92570	+	4.30527i	−0.467011	+	0.339303i
$162$		0			0
$163$	−9.51202	+	1.50656i	−0.745039	+	0.118003i	−0.517401	−	0.855743i	$-0.673100\pi$
$163$	−9.51202	+	1.50656i	−0.745039	+	0.118003i	−0.227638	+	0.973746i	$0.573100\pi$
$164$	−7.86180	−	10.5597i	−0.613904	−	0.824575i
$165$		0			0
$166$	6.01444	−	8.38047i	0.466811	−	0.650451i
$167$	−8.48953	+	16.6616i	−0.656939	+	1.28932i	0.286598	+	0.958051i	$0.407475\pi$
$167$	−8.48953	+	16.6616i	−0.656939	+	1.28932i	−0.943538	+	0.331265i	$0.892525\pi$
$168$		0			0
$169$	−9.44183	+	3.06784i	−0.726294	+	0.235987i
$170$	11.5085	−	4.80026i	0.882663	−	0.368163i
$171$		0			0
$172$	21.8685	−	11.4656i	1.66745	−	0.874246i
$173$	−1.08740	−	0.172227i	−0.0826731	−	0.0130941i	0.114961	−	0.993370i	$-0.463326\pi$
$173$	−1.08740	−	0.172227i	−0.0826731	−	0.0130941i	−0.197634	+	0.980276i	$0.563326\pi$
$174$		0			0
$175$	−4.82426	+	14.5146i	−0.364680	+	1.09720i
$176$	−0.574042	−	24.6136i	−0.0432701	−	1.85532i
$177$		0			0
$178$	−0.941609	+	0.486709i	−0.0705766	+	0.0364804i
$179$	3.43461	−	10.5706i	0.256715	−	0.790086i	−0.736772	−	0.676141i	$-0.763651\pi$
$179$	3.43461	−	10.5706i	0.256715	−	0.790086i	0.993487	−	0.113945i	$-0.0363489\pi$
$180$		0			0
$181$	−3.67610	−	11.3139i	−0.273242	−	0.840952i	−0.989679	−	0.143301i	$-0.954228\pi$
$181$	−3.67610	−	11.3139i	−0.273242	−	0.840952i	0.716437	−	0.697652i	$-0.245772\pi$
$182$	14.7328	+	14.5620i	1.09207	+	1.07941i
$183$		0			0
$184$	−5.54772	−	3.88427i	−0.408984	−	0.286352i
$185$	8.50443	+	3.55621i	0.625258	+	0.261458i
$186$		0			0
$187$	−3.79678	−	23.9719i	−0.277648	−	1.75300i
$188$	−7.69360	+	1.31067i	−0.561114	+	0.0955905i
$189$		0			0
$190$	6.42373	+	2.64226i	0.466026	+	0.191690i
$191$	12.4784	−	17.1750i	0.902904	−	1.24274i	−0.0666283	−	0.997778i	$-0.521224\pi$
$191$	12.4784	−	17.1750i	0.902904	−	1.24274i	0.969532	−	0.244963i	$-0.0787758\pi$
$192$		0			0
$193$	7.90062	+	7.90062i	0.568699	+	0.568699i	0.931764	−	0.363065i	$-0.118270\pi$
$193$	7.90062	+	7.90062i	0.568699	+	0.568699i	−0.363065	+	0.931764i	$0.618270\pi$
$194$	−22.1764	+	7.34876i	−1.59217	+	0.527610i
$195$		0			0
$196$	1.40483	−	4.50154i	0.100345	−	0.321539i
$197$	−7.05910	−	13.8543i	−0.502940	−	0.987076i	−0.993301	−	0.115556i	$-0.963135\pi$
$197$	−7.05910	−	13.8543i	−0.502940	−	0.987076i	0.490361	−	0.871520i	$-0.336865\pi$
$198$		0			0
$199$	12.4250			0.880782			0.440391	−	0.897806i	$-0.354840\pi$
$199$	12.4250			0.880782			0.440391	+	0.897806i	$0.354840\pi$
$200$	−14.1413	+	0.152176i	−0.999942	+	0.0107605i
$201$		0			0
$202$	−2.54584	+	16.7034i	−0.179125	+	1.17525i
$203$	−2.16122	−	4.24163i	−0.151688	−	0.297704i
$204$		0			0
$205$	5.58688	+	13.6173i	0.390205	+	0.951074i
$206$	−7.31202	+	2.42303i	−0.509452	+	0.168821i
$207$		0			0
$208$	−8.29509	+	17.2637i	−0.575161	+	1.19702i
$209$	7.94662	−	10.9376i	0.549679	−	0.756569i
$210$		0			0
$211$	−5.73506	−	7.89363i	−0.394818	−	0.543420i	0.564616	−	0.825354i	$-0.309024\pi$
$211$	−5.73506	−	7.89363i	−0.394818	−	0.543420i	−0.959434	+	0.281934i	$0.909024\pi$
$212$	−12.2687	+	2.09007i	−0.842615	+	0.143547i
$213$		0			0
$214$	0.745742	−	0.548484i	0.0509779	−	0.0374936i
$215$	−26.8651	+	6.35425i	−1.83219	+	0.433356i
$216$		0			0
$217$	23.7637	+	12.1082i	1.61319	+	0.821960i
$218$	−3.75751	−	3.71395i	−0.254490	−	0.251541i
$219$		0			0
$220$	−6.20366	+	26.8182i	−0.418251	+	1.80808i
$221$	−5.83461	+	17.9571i	−0.392479	+	1.20792i
$222$		0			0
$223$	2.05317	−	12.9632i	0.137490	−	0.868081i	−0.818462	−	0.574560i	$-0.805173\pi$
$223$	2.05317	−	12.9632i	0.137490	−	0.868081i	0.955953	−	0.293520i	$-0.0948269\pi$
$224$	17.2973	−	0.504313i	1.15572	−	0.0336958i
$225$		0			0
$226$	−1.09402	+	0.00637766i	−0.0727734	+	0.000424235i
$227$	−20.8358	−	3.30006i	−1.38292	−	0.219033i	−0.579754	−	0.814791i	$-0.696852\pi$
$227$	−20.8358	−	3.30006i	−1.38292	−	0.219033i	−0.803164	+	0.595759i	$0.796852\pi$
$228$		0			0
$229$	−10.1735	−	3.30556i	−0.672281	−	0.218437i	−0.0470685	−	0.998892i	$-0.514988\pi$
$229$	−10.1735	−	3.30556i	−0.672281	−	0.218437i	−0.625213	+	0.780454i	$0.714988\pi$
$230$	4.93162	+	5.74544i	0.325181	+	0.378843i
$231$		0			0
$232$	3.05749	−	3.16634i	0.200734	−	0.207880i
$233$	−1.31152	+	2.57401i	−0.0859207	+	0.168629i	−0.929969	−	0.367639i	$-0.880166\pi$
$233$	−1.31152	+	2.57401i	−0.0859207	+	0.168629i	0.844048	+	0.536268i	$0.180166\pi$
$234$		0			0
$235$	8.69639	+	0.713863i	0.567290	+	0.0465673i
$236$	11.1000	+	14.9092i	0.722549	+	0.970505i
$237$		0			0
$238$	16.8331	−	2.76678i	1.09113	−	0.179344i
$239$	−10.0152	+	7.27645i	−0.647828	+	0.470675i	−0.862531	−	0.506005i	$-0.831122\pi$
$239$	−10.0152	+	7.27645i	−0.647828	+	0.470675i	0.214703	+	0.976679i	$0.431122\pi$
$240$		0			0
$241$	−13.7385	−	9.98161i	−0.884975	−	0.642972i	0.0495877	−	0.998770i	$-0.484209\pi$
$241$	−13.7385	−	9.98161i	−0.884975	−	0.642972i	−0.934563	+	0.355798i	$0.884209\pi$
$242$	33.9772	+	17.0635i	2.18414	+	1.09688i
$243$		0			0
$244$	1.67542	−	0.566056i	0.107258	−	0.0362380i
$245$	−2.76986	+	4.48605i	−0.176960	+	0.286603i
$246$		0			0
$247$	−9.37111	+	4.77482i	−0.596270	+	0.303815i
$248$	−3.43114	+	24.4200i	−0.217877	+	1.55067i
$249$		0			0
$250$	15.3586	+	3.75659i	0.971366	+	0.237588i
$251$			15.2933i			0.965305i	0.875812	+	0.482653i	$0.160327\pi$
$251$			15.2933i			0.965305i	−0.875812	+	0.482653i	$0.839673\pi$
$252$		0			0
$253$	13.1314	−	6.69076i	0.825561	−	0.420644i
$254$	2.66998	−	8.38333i	0.167529	−	0.526017i
$255$		0			0
$256$	5.64829	+	14.9699i	0.353018	+	0.935616i
$257$	5.22988	−	5.22988i	0.326231	−	0.326231i	−0.524920	−	0.851151i	$-0.675905\pi$
$257$	5.22988	−	5.22988i	0.326231	−	0.326231i	0.851151	+	0.524920i	$0.175905\pi$
$258$		0			0
$259$	10.2023	+	7.41241i	0.633940	+	0.460584i
$260$	13.7717	−	16.3980i	0.854082	−	1.01696i
$261$		0			0
$262$	−0.381407	−	2.32048i	−0.0235634	−	0.143360i
$263$	−28.6588	+	4.53910i	−1.76718	+	0.279893i	−0.953493	−	0.301415i	$-0.902541\pi$
$263$	−28.6588	+	4.53910i	−1.76718	+	0.279893i	−0.813683	+	0.581309i	$0.802541\pi$
$264$		0			0
$265$	13.8678	+	1.13837i	0.851889	+	0.0699293i
$266$	7.72002	+	5.54045i	0.473345	+	0.339707i
$267$		0			0
$268$	−4.68343	+	4.79393i	−0.286086	+	0.292836i
$269$	−3.35427	+	1.08987i	−0.204514	+	0.0664505i	−0.409482	−	0.912318i	$-0.634291\pi$
$269$	−3.35427	+	1.08987i	−0.204514	+	0.0664505i	0.204969	+	0.978768i	$0.434291\pi$
$270$		0			0
$271$	−5.83745	−	1.89670i	−0.354600	−	0.115216i	0.126300	−	0.991992i	$-0.459690\pi$
$271$	−5.83745	−	1.89670i	−0.354600	−	0.115216i	−0.480900	+	0.876776i	$0.659690\pi$
$272$	7.48643	+	13.8829i	0.453932	+	0.841775i
$273$		0			0
$274$	0.0306646	+	5.26020i	0.00185251	+	0.317781i
$275$	14.1559	−	27.3265i	0.853634	−	1.64785i
$276$		0			0
$277$	3.23161	−	20.4036i	0.194169	−	1.22593i	−0.677384	−	0.735630i	$-0.736886\pi$
$277$	3.23161	−	20.4036i	0.194169	−	1.22593i	0.871552	−	0.490302i	$-0.163114\pi$
$278$	0.931858	+	1.80282i	0.0558891	+	0.108126i
$279$		0			0
$280$	−18.8745	−	4.25035i	−1.12797	−	0.254007i
$281$	−5.87134	−	18.0701i	−0.350255	−	1.07797i	−0.958710	−	0.284385i	$-0.908211\pi$
$281$	−5.87134	−	18.0701i	−0.350255	−	1.07797i	0.608455	−	0.793588i	$-0.291789\pi$
$282$		0			0
$283$	13.1812	+	6.71617i	0.783543	+	0.399235i	0.799522	−	0.600637i	$-0.205086\pi$
$283$	13.1812	+	6.71617i	0.783543	+	0.399235i	−0.0159788	+	0.999872i	$0.505086\pi$
$284$	10.2380	+	7.25749i	0.607513	+	0.430653i
$285$		0			0
$286$	−24.6951	−	33.5766i	−1.46025	−	1.98543i
$287$	3.14999	+	19.8882i	0.185938	+	1.17397i
$288$		0			0
$289$	−0.852962	−	1.17400i	−0.0501742	−	0.0690589i
$290$	−4.18959	+	2.58162i	−0.246021	+	0.151598i
$291$		0			0
$292$	−1.64545	−	0.814377i	−0.0962929	−	0.0476578i
$293$	3.69461	+	3.69461i	0.215842	+	0.215842i	0.806743	−	0.590902i	$-0.201228\pi$
$293$	3.69461	+	3.69461i	0.215842	+	0.215842i	−0.590902	+	0.806743i	$0.701228\pi$
$294$		0			0
$295$	−7.88808	−	19.2262i	−0.459262	−	1.11939i
$296$	−3.40866	+	11.1506i	−0.198124	+	0.648116i
$297$		0			0
$298$	28.8743	+	4.40085i	1.67264	+	0.254934i
$299$	−11.4650			−0.663040
$300$		0			0
$301$	−37.7670			−2.17685
$302$	23.0367	+	3.51111i	1.32561	+	0.202042i
$303$		0			0
$304$	−2.51945	+	8.41699i	−0.144500	+	0.482747i
$305$	−1.97162	+	0.148498i	−0.112894	+	0.00850297i
$306$		0			0
$307$	5.17718	+	5.17718i	0.295477	+	0.295477i	0.839239	−	0.543762i	$-0.183001\pi$
$307$	5.17718	+	5.17718i	0.295477	+	0.295477i	−0.543762	+	0.839239i	$0.683001\pi$
$308$	−16.7038	+	33.7501i	−0.951788	+	1.92309i
$309$		0			0
$310$	10.4880	−	25.4979i	0.595677	−	1.44818i
$311$	2.74588	+	3.77938i	0.155705	+	0.214309i	0.879742	−	0.475452i	$-0.157715\pi$
$311$	2.74588	+	3.77938i	0.155705	+	0.214309i	−0.724037	+	0.689761i	$0.757715\pi$
$312$		0			0
$313$	−3.67466	−	23.2009i	−0.207704	−	1.31139i	−0.842493	−	0.538707i	$-0.818913\pi$
$313$	−3.67466	−	23.2009i	−0.207704	−	1.31139i	0.634789	−	0.772686i	$-0.281087\pi$
$314$	−5.97921	−	8.12959i	−0.337426	−	0.458780i
$315$		0			0
$316$	−11.1590	+	15.7417i	−0.627742	+	0.885542i
$317$	−4.91790	−	2.50580i	−0.276217	−	0.140740i	0.310395	−	0.950608i	$-0.399539\pi$
$317$	−4.91790	−	2.50580i	−0.276217	−	0.140740i	−0.586612	+	0.809868i	$0.699539\pi$
$318$		0			0
$319$	2.95992	+	9.10970i	0.165724	+	0.510046i
$320$	−1.96649	−	17.7801i	−0.109930	−	0.993939i
$321$		0			0
$322$	4.75639	+	9.20193i	0.265063	+	0.512803i
$323$	−1.35491	+	8.55459i	−0.0753894	+	0.475990i
$324$		0			0
$325$	−19.4633	+	13.9418i	−1.07963	+	0.773352i
$326$	0.0793953	+	13.6195i	0.00439730	+	0.754313i
$327$		0			0
$328$	−16.4384	+	8.74121i	−0.907661	+	0.482653i
$329$	11.3529	+	3.68877i	0.625905	+	0.203369i
$330$		0			0
$331$	22.9947	−	7.47144i	1.26390	−	0.410668i	0.401020	−	0.916069i	$-0.368656\pi$
$331$	22.9947	−	7.47144i	1.26390	−	0.410668i	0.862884	+	0.505402i	$0.168656\pi$
$332$	−10.4349	−	10.1944i	−0.572689	−	0.559488i
$333$		0			0
$334$	21.4851	+	15.4193i	1.17561	+	0.843706i
$335$	6.40199	−	3.89358i	0.349778	−	0.212729i
$336$		0			0
$337$	−25.8855	+	4.09986i	−1.41007	+	0.223334i	−0.814591	−	0.580035i	$-0.803039\pi$
$337$	−25.8855	+	4.09986i	−1.41007	+	0.223334i	−0.595482	+	0.803369i	$0.703039\pi$
$338$	2.27713	+	13.8540i	0.123859	+	0.753560i
$339$		0			0
$340$	−4.25880	−	17.1126i	−0.230966	−	0.928059i
$341$	−43.4148	−	31.5427i	−2.35104	−	1.70813i
$342$		0			0
$343$	10.0414	−	10.0414i	0.542184	−	0.542184i
$344$	−11.3699	−	33.0168i	−0.613023	−	1.78014i
$345$		0			0
$346$	−0.472492	+	1.48355i	−0.0254014	+	0.0797564i
$347$	17.8899	−	9.11535i	0.960379	−	0.489337i	0.0977699	−	0.995209i	$-0.468829\pi$
$347$	17.8899	−	9.11535i	0.960379	−	0.489337i	0.862609	+	0.505872i	$0.168829\pi$
$348$		0			0
$349$		−	1.31111i		−	0.0701821i	−0.999384	−	0.0350910i	$-0.988828\pi$
$349$		−	1.31111i		−	0.0701821i	0.999384	−	0.0350910i	$-0.0111721\pi$
$350$	19.2644	+	9.83749i	1.02972	+	0.525836i
$351$		0			0
$352$	−34.5339	−	4.44226i	−1.84066	−	0.236773i
$353$	26.1678	−	13.3332i	1.39277	−	0.709654i	0.413182	−	0.910649i	$-0.364417\pi$
$353$	26.1678	−	13.3332i	1.39277	−	0.709654i	0.979592	+	0.200995i	$0.0644175\pi$
$354$		0			0
$355$	−9.07625	−	10.6996i	−0.481717	−	0.567875i
$356$	0.479809	+	1.42014i	0.0254298	+	0.0752675i
$357$		0			0
$358$	−14.0466	−	7.05426i	−0.742386	−	0.372829i
$359$	−2.37394	−	1.72477i	−0.125292	−	0.0910299i	0.523374	−	0.852103i	$-0.324673\pi$
$359$	−2.37394	−	1.72477i	−0.125292	−	0.0910299i	−0.648666	+	0.761073i	$0.724673\pi$
$360$		0			0
$361$	11.4682	−	8.33210i	0.603587	−	0.438532i
$362$	−16.6009	+	2.72861i	−0.872522	+	0.143413i
$363$		0			0
$364$	23.4980	−	17.4945i	1.23163	−	0.916961i
$365$	1.55636	+	1.33834i	0.0814637	+	0.0700518i
$366$		0			0
$367$	1.44407	−	2.83414i	0.0753796	−	0.147941i	−0.850241	−	0.526394i	$-0.823544\pi$
$367$	1.44407	−	2.83414i	0.0753796	−	0.147941i	0.925621	+	0.378453i	$0.123544\pi$
$368$	−6.61261	+	6.92841i	−0.344706	+	0.361169i
$369$		0			0
$370$	6.78400	−	11.1320i	0.352683	−	0.578725i
$371$	18.1039	+	5.88233i	0.939910	+	0.305395i
$372$		0			0
$373$	8.95416	+	1.41820i	0.463629	+	0.0734316i	0.383879	−	0.923383i	$-0.374588\pi$
$373$	8.95416	+	1.41820i	0.463629	+	0.0734316i	0.0797497	+	0.996815i	$0.474588\pi$
$374$	−34.3234	+	0.200090i	−1.77482	+	0.0103464i
$375$		0			0
$376$	0.193013	+	11.0355i	0.00995386	+	0.569111i
$377$	1.16567	−	7.35977i	0.0600352	−	0.379047i
$378$		0			0
$379$	−9.24861	+	28.4643i	−0.475069	+	1.46211i	0.370795	+	0.928715i	$0.379085\pi$
$379$	−9.24861	+	28.4643i	−0.475069	+	1.46211i	−0.845864	+	0.533398i	$0.820915\pi$
$380$	5.06286	−	8.41778i	0.259719	−	0.431823i
$381$		0			0
$382$	−21.3529	−	21.1054i	−1.09251	−	1.07984i
$383$	15.4391	+	7.86660i	0.788900	+	0.401965i	0.801529	−	0.597956i	$-0.204020\pi$
$383$	15.4391	+	7.86660i	0.788900	+	0.401965i	−0.0126293	+	0.999920i	$0.504020\pi$
$384$		0			0
$385$	27.4508	−	31.9227i	1.39902	−	1.62693i
$386$	12.7291	−	9.36210i	0.647895	−	0.476518i
$387$		0			0
$388$	5.54859	+	32.5701i	0.281687	+	1.65349i
$389$	2.48759	+	3.42387i	0.126126	+	0.173597i	0.867410	−	0.497594i	$-0.165783\pi$
$389$	2.48759	+	3.42387i	0.126126	+	0.173597i	−0.741284	+	0.671191i	$0.765783\pi$
$390$		0			0
$391$	−5.54961	+	7.63838i	−0.280656	+	0.386290i
$392$	−5.99411	−	2.92326i	−0.302748	−	0.147647i
$393$		0			0
$394$	−20.8734	+	6.91697i	−1.05159	+	0.348472i
$395$	16.4515	−	13.9555i	0.827764	−	0.702176i
$396$		0			0
$397$	−10.9532	−	21.4968i	−0.549723	−	1.07889i	−0.984009	−	0.178118i	$-0.942999\pi$
$397$	−10.9532	−	21.4968i	−0.549723	−	1.07889i	0.434286	−	0.900775i	$-0.357001\pi$
$398$	2.64758	−	17.3709i	0.132711	−	0.870726i
$399$		0			0
$400$	−2.80056	+	19.8030i	−0.140028	+	0.990148i
$401$	−11.0326			−0.550942			−0.275471	−	0.961309i	$-0.588834\pi$
$401$	−11.0326			−0.550942			−0.275471	+	0.961309i	$0.588834\pi$
$402$		0			0
$403$	18.9528	+	37.1970i	0.944107	+	1.85291i
$404$	22.8100	+	7.11851i	1.13484	+	0.354159i
$405$		0			0
$406$	−6.39061	+	2.11770i	−0.317160	+	0.105100i
$407$	−17.9420	−	17.9420i	−0.889354	−	0.889354i
$408$		0			0
$409$	17.6926	−	24.3518i	0.874843	−	1.20412i	−0.102980	−	0.994683i	$-0.532838\pi$
$409$	17.6926	−	24.3518i	0.874843	−	1.20412i	0.977823	−	0.209435i	$-0.0671624\pi$
$410$	20.2284	−	4.90919i	0.999010	−	0.242448i
$411$		0			0
$412$	1.82948	+	10.7390i	0.0901321	+	0.529073i
$413$	−4.44744	−	28.0800i	−0.218844	−	1.38173i
$414$		0			0
$415$	8.47510	+	13.9351i	0.416026	+	0.684048i
$416$	22.3683	+	15.2757i	1.09669	+	0.748955i
$417$		0			0
$418$	−13.5982	−	13.4406i	−0.665109	−	0.657399i
$419$	−4.26390	−	13.1229i	−0.208305	−	0.641097i	−0.999561	−	0.0296124i	$-0.990573\pi$
$419$	−4.26390	−	13.1229i	−0.208305	−	0.641097i	0.791256	−	0.611484i	$-0.209427\pi$
$420$		0			0
$421$	4.03666	−	12.4236i	0.196735	−	0.605487i	−0.803217	−	0.595686i	$-0.796880\pi$
$421$	4.03666	−	12.4236i	0.196735	−	0.605487i	0.999952	−	0.00980083i	$-0.00311975\pi$
$422$	−12.2579	+	6.33598i	−0.596705	+	0.308431i
$423$		0			0
$424$	0.307789	+	17.5978i	0.0149475	+	0.854624i
$425$	−0.132643	+	19.7156i	−0.00643413	+	0.956346i
$426$		0			0
$427$	−2.67161	−	0.423141i	−0.129288	−	0.0204772i
$428$	−0.607911	−	1.15947i	−0.0293845	−	0.0560452i
$429$		0			0
$430$	3.15910	+	38.9133i	0.152345	+	1.87657i
$431$	−23.7995	+	7.73293i	−1.14638	+	0.372482i	−0.819779	−	0.572680i	$-0.805904\pi$
$431$	−23.7995	+	7.73293i	−1.14638	+	0.372482i	−0.326603	+	0.945162i	$0.605904\pi$
$432$		0			0
$433$	−8.85686	+	17.3826i	−0.425634	+	0.835353i	0.574228	+	0.818696i	$0.305302\pi$
$433$	−8.85686	+	17.3826i	−0.425634	+	0.835353i	−0.999861	+	0.0166575i	$0.994698\pi$
$434$	21.9918	−	30.6432i	1.05564	−	1.47092i
$435$		0			0
$436$	−5.99303	+	4.46186i	−0.287014	+	0.213684i
$437$	−5.19451	+	0.822729i	−0.248487	+	0.0393565i
$438$		0			0
$439$	5.96431	−	4.33333i	0.284661	−	0.206818i	−0.436287	−	0.899808i	$-0.643707\pi$
$439$	5.96431	−	4.33333i	0.284661	−	0.206818i	0.720948	+	0.692989i	$0.243707\pi$
$440$	36.1718	+	14.3877i	1.72442	+	0.685907i
$441$		0			0
$442$	23.8620	+	11.9836i	1.13500	+	0.570001i
$443$	−11.9556	+	11.9556i	−0.568027	+	0.568027i	−0.931575	−	0.363548i	$-0.881565\pi$
$443$	−11.9556	+	11.9556i	−0.568027	+	0.568027i	0.363548	+	0.931575i	$0.381565\pi$
$444$		0			0
$445$	−0.125872	−	1.67121i	−0.00596690	−	0.0792229i
$446$	−17.6859	−	5.63274i	−0.837454	−	0.266718i
$447$		0			0
$448$	2.98074	−	24.2903i	0.140827	−	1.14761i
$449$			17.9404i			0.846658i	0.905976	+	0.423329i	$0.139139\pi$
$449$			17.9404i			0.846658i	−0.905976	+	0.423329i	$0.860861\pi$
$450$		0			0
$451$		−	40.5157i		−	1.90781i
$452$	−0.224204	+	1.53088i	−0.0105457	+	0.0720065i
$453$		0			0
$454$	−9.05351	+	28.4266i	−0.424902	+	1.33413i
$455$	−30.3020	+	12.4322i	−1.42058	+	0.582832i
$456$		0			0
$457$	15.2228	−	15.2228i	0.712092	−	0.712092i	−0.254880	−	0.966973i	$-0.582036\pi$
$457$	15.2228	−	15.2228i	0.712092	−	0.712092i	0.966973	+	0.254880i	$0.0820360\pi$
$458$	−6.78921	+	13.5188i	−0.317239	+	0.631693i
$459$		0			0
$460$	9.08337	−	5.67047i	0.423514	−	0.264387i
$461$	10.4823	−	7.61580i	0.488207	−	0.354703i	−0.316287	−	0.948663i	$-0.602436\pi$
$461$	10.4823	−	7.61580i	0.488207	−	0.354703i	0.804494	+	0.593960i	$0.202436\pi$
$462$		0			0
$463$	−1.76416	+	0.279416i	−0.0819876	+	0.0129856i	−0.197293	−	0.980344i	$-0.563215\pi$
$463$	−1.76416	+	0.279416i	−0.0819876	+	0.0129856i	0.115306	+	0.993330i	$0.463215\pi$
$464$	−3.77526	−	4.94927i	−0.175262	−	0.229764i
$465$		0			0
$466$	3.31917	+	2.38208i	0.153758	+	0.110348i
$467$	9.95367	−	19.5352i	0.460601	−	0.903980i	−0.537552	−	0.843230i	$-0.680651\pi$
$467$	9.95367	−	19.5352i	0.460601	−	0.903980i	0.998153	−	0.0607495i	$-0.0193491\pi$
$468$		0			0
$469$	9.74913	−	3.16768i	0.450173	−	0.146270i
$470$	2.85110	−	12.0060i	0.131512	−	0.553797i
$471$		0			0
$472$	23.2093	−	12.3416i	1.06829	−	0.568070i
$473$	75.0548	+	11.8875i	3.45102	+	0.546588i
$474$		0			0
$475$	−7.81785	+	7.71335i	−0.358707	+	0.353913i
$476$	−0.281265	−	24.1233i	−0.0128918	−	1.10569i
$477$		0			0
$478$	8.03889	+	15.5524i	0.367690	+	0.711351i
$479$	−1.58785	+	4.88691i	−0.0725509	+	0.223289i	−0.980756	−	0.195236i	$-0.937453\pi$
$479$	−1.58785	+	4.88691i	−0.0725509	+	0.223289i	0.908205	+	0.418525i	$0.137453\pi$
$480$		0			0
$481$	6.09980	+	18.7733i	0.278127	+	0.855987i
$482$	−16.8825	+	17.0804i	−0.768975	+	0.777993i
$483$		0			0
$484$	31.0960	−	43.8665i	1.41345	−	1.99393i
$485$	3.02206	−	36.8152i	0.137225	−	1.67169i
$486$		0			0
$487$	2.07383	+	13.0936i	0.0939741	+	0.593329i	0.989069	+	0.147453i	$0.0471076\pi$
$487$	2.07383	+	13.0936i	0.0939741	+	0.593329i	−0.895095	+	0.445876i	$0.852892\pi$
$488$	−0.434377	−	2.46297i	−0.0196633	−	0.111493i
$489$		0			0
$490$	5.68159	+	4.82836i	0.256668	+	0.218123i
$491$	4.99246	−	6.87153i	0.225307	−	0.310108i	−0.681366	−	0.731943i	$-0.738614\pi$
$491$	4.99246	−	6.87153i	0.225307	−	0.310108i	0.906673	+	0.421835i	$0.138614\pi$
$492$		0			0
$493$	−4.33908	−	4.33908i	−0.195423	−	0.195423i
$494$	4.67868	+	14.1189i	0.210504	+	0.635239i
$495$		0			0
$496$	33.4097	+	10.0005i	1.50014	+	0.449036i
$497$	−8.71420	−	17.1026i	−0.390885	−	0.767156i
$498$		0			0
$499$	−25.0509			−1.12143			−0.560716	−	0.828008i	$-0.689474\pi$
$499$	−25.0509			−1.12143			−0.560716	+	0.828008i	$0.689474\pi$
$500$	8.52467	−	20.6720i	0.381235	−	0.924478i
$501$		0			0
$502$	21.3811	+	3.25878i	0.954285	+	0.145446i
$503$	1.99779	+	3.92088i	0.0890770	+	0.174823i	0.931247	−	0.364389i	$-0.118722\pi$
$503$	1.99779	+	3.92088i	0.0890770	+	0.174823i	−0.842170	+	0.539212i	$0.818722\pi$
$504$		0			0
$505$	−22.7316	−	14.0353i	−1.01154	−	0.624564i
$506$	−6.55604	−	19.7842i	−0.291451	−	0.879516i
$507$		0			0
$508$	−11.1515	−	5.51918i	−0.494769	−	0.244874i
$509$	21.3937	−	29.4458i	0.948257	−	1.30516i	−0.00404015	−	0.999992i	$-0.501286\pi$
$509$	21.3937	−	29.4458i	0.948257	−	1.30516i	0.952297	−	0.305172i	$-0.0987140\pi$
$510$		0			0
$511$	1.65059	+	2.27184i	0.0730176	+	0.100500i
$512$	22.1325	−	4.70684i	0.978126	−	0.208015i
$513$		0			0
$514$	−6.19732	−	8.42614i	−0.273352	−	0.371661i
$515$	0.996436	−	12.1387i	0.0439082	−	0.534897i
$516$		0			0
$517$	−21.4007	−	10.9042i	−0.941200	−	0.479565i
$518$	12.5370	−	12.6840i	0.550845	−	0.557305i
$519$		0			0
$520$	−19.9910	−	22.7479i	−0.876665	−	0.997562i
$521$	−6.05775	+	18.6438i	−0.265395	+	0.816801i	0.726208	+	0.687476i	$0.241281\pi$
$521$	−6.05775	+	18.6438i	−0.265395	+	0.816801i	−0.991602	+	0.129325i	$0.958719\pi$
$522$		0			0
$523$	4.80315	−	30.3259i	0.210027	−	1.32606i	−0.627052	−	0.778978i	$-0.715738\pi$
$523$	4.80315	−	30.3259i	0.210027	−	1.32606i	0.837079	−	0.547082i	$-0.184262\pi$
$524$	−3.32546	+	0.0387731i	−0.145273	+	0.00169381i
$525$		0			0
$526$	0.239210	+	41.0341i	0.0104301	+	1.78917i
$527$	33.9559	+	5.37809i	1.47914	+	0.234273i
$528$		0			0
$529$	16.4218	+	5.33577i	0.713991	+	0.231990i
$530$	4.54653	−	19.1455i	0.197489	−	0.831627i
$531$		0			0
$532$	9.39095	−	9.61252i	0.407149	−	0.416756i
$533$	−14.3092	+	28.0834i	−0.619801	+	1.21643i
$534$		0			0
$535$	0.336904	+	1.42440i	0.0145656	+	0.0615821i
$536$	5.70427	+	7.56927i	0.246387	+	0.326943i
$537$		0			0
$538$	0.808965	+	4.92174i	0.0348769	+	0.212191i
$539$	11.7410	−	8.53032i	0.505719	−	0.367427i
$540$		0			0
$541$	−22.0987	−	16.0556i	−0.950098	−	0.690286i	0.000732404	−	1.00000i	$-0.499767\pi$
$541$	−22.0987	−	16.0556i	−0.950098	−	0.690286i	−0.950830	+	0.309713i	$0.899767\pi$
$542$	−3.89559	+	7.75699i	−0.167330	+	0.333191i
$543$		0			0
$544$	21.0045	−	7.50830i	0.900560	−	0.321916i
$545$	7.72833	−	3.17076i	0.331045	−	0.135821i
$546$		0			0
$547$	−20.0141	+	10.1977i	−0.855739	+	0.436021i	−0.826089	−	0.563539i	$-0.809439\pi$
$547$	−20.0141	+	10.1977i	−0.855739	+	0.436021i	−0.0296502	+	0.999560i	$0.509439\pi$
$548$	7.36066	+	1.07800i	0.314432	+	0.0460499i
$549$		0			0
$550$	−35.1879	−	25.6138i	−1.50042	−	1.09218i
$551$		−	3.41817i		−	0.145619i
$552$		0			0
$553$	26.2966	−	13.3988i	1.11825	−	0.569775i
$554$	−27.8370	−	8.86571i	−1.18268	−	0.376668i
$555$		0			0
$556$	2.71902	−	0.918647i	0.115312	−	0.0389593i
$557$	1.72925	−	1.72925i	0.0732707	−	0.0732707i	−0.669522	−	0.742792i	$-0.733501\pi$
$557$	1.72925	−	1.72925i	0.0732707	−	0.0732707i	0.742792	+	0.669522i	$0.233501\pi$
$558$		0			0
$559$	−47.8258	−	34.7475i	−2.02282	−	1.46966i
$560$	−9.96416	+	25.4822i	−0.421063	+	1.07682i
$561$		0			0
$562$	−26.5144	+	4.35805i	−1.11844	+	0.183833i
$563$	−10.7903	+	1.70902i	−0.454758	+	0.0720266i	−0.379612	−	0.925146i	$-0.623942\pi$
$563$	−10.7903	+	1.70902i	−0.454758	+	0.0720266i	−0.0751463	+	0.997173i	$0.523942\pi$
$564$		0			0
$565$	0.667351	−	1.59592i	0.0280757	−	0.0671410i
$566$	12.1984	−	16.9971i	0.512737	−	0.714443i
$567$		0			0
$568$	12.3280	−	12.7669i	0.517273	−	0.535689i
$569$	40.3160	−	13.0995i	1.69014	−	0.549158i	0.703301	−	0.710892i	$-0.251709\pi$
$569$	40.3160	−	13.0995i	1.69014	−	0.549158i	0.986834	+	0.161734i	$0.0517086\pi$
$570$		0			0
$571$	−22.9908	−	7.47016i	−0.962135	−	0.312617i	−0.214498	−	0.976724i	$-0.568812\pi$
$571$	−22.9908	−	7.47016i	−0.962135	−	0.312617i	−0.747637	+	0.664108i	$0.768812\pi$
$572$	−52.2045	+	27.3708i	−2.18278	+	1.14443i
$573$		0			0
$574$	28.4763	−	0.166004i	1.18858	−	0.00692887i
$575$	−11.4106	+	3.62285i	−0.475856	+	0.151083i
$576$		0			0
$577$	−2.35827	+	14.8895i	−0.0981760	+	0.619859i	0.888714	+	0.458463i	$0.151600\pi$
$577$	−2.35827	+	14.8895i	−0.0981760	+	0.619859i	−0.986890	+	0.161396i	$0.948400\pi$
$578$	−1.82309	+	0.942336i	−0.0758304	+	0.0391960i
$579$		0			0
$580$	2.71653	+	6.40744i	0.112798	+	0.266054i
$581$	6.89505	+	21.2208i	0.286055	+	0.880387i
$582$		0			0
$583$	−34.1267	−	17.3884i	−1.41338	−	0.720155i
$584$	−1.48918	+	2.12692i	−0.0616226	+	0.0880127i
$585$		0			0
$586$	5.95259	−	4.37805i	0.245899	−	0.180856i
$587$	5.76093	+	36.3731i	0.237779	+	1.50128i	0.760815	+	0.648968i	$0.224799\pi$
$587$	5.76093	+	36.3731i	0.237779	+	1.50128i	−0.523036	+	0.852310i	$0.675201\pi$
$588$		0			0
$589$	11.2563	+	15.4929i	0.463807	+	0.638375i
$590$	−28.5603	+	6.93125i	−1.17581	+	0.285355i
$591$		0			0
$592$	14.8630	+	7.14157i	0.610865	+	0.293517i
$593$	−31.3538	−	31.3538i	−1.28755	−	1.28755i	−0.936273	−	0.351274i	$-0.885749\pi$
$593$	−31.3538	−	31.3538i	−1.28755	−	1.28755i	−0.351274	−	0.936273i	$-0.614251\pi$
$594$		0			0
$595$	−6.38480	+	26.2060i	−0.261751	+	1.07434i
$596$	12.3054	−	39.4304i	0.504048	−	1.61513i
$597$		0			0
$598$	−2.44303	+	16.0289i	−0.0999029	+	0.655470i
$599$	44.9068			1.83484			0.917421	−	0.397917i	$-0.130267\pi$
$599$	44.9068			1.83484			0.917421	+	0.397917i	$0.130267\pi$
$600$		0			0
$601$	33.0206			1.34694			0.673468	−	0.739216i	$-0.264804\pi$
$601$	33.0206			1.34694			0.673468	+	0.739216i	$0.264804\pi$
$602$	−8.04759	+	52.8008i	−0.327995	+	2.15200i
$603$		0			0
$604$	9.81755	−	31.4586i	0.399470	−	1.28003i
$605$	−45.8443	+	38.8888i	−1.86384	+	1.58105i
$606$		0			0
$607$	25.5333	+	25.5333i	1.03636	+	1.03636i	0.999313	+	0.0370508i	$0.0117963\pi$
$607$	25.5333	+	25.5333i	1.03636	+	1.03636i	0.0370508	+	0.999313i	$0.488204\pi$
$608$	11.2307	+	5.31590i	0.455464	+	0.215588i
$609$		0			0
$610$	−0.212512	+	2.78810i	−0.00860437	+	0.112887i
$611$	10.9828	+	15.1165i	0.444315	+	0.611547i
$612$		0			0
$613$	1.23030	+	7.76779i	0.0496912	+	0.313738i	0.999997	+	0.00242026i	$0.000770394\pi$
$613$	1.23030	+	7.76779i	0.0496912	+	0.313738i	−0.950306	+	0.311318i	$0.899230\pi$
$614$	8.34123	−	6.13487i	0.336625	−	0.247583i
$615$		0			0
$616$	43.6256	+	30.5447i	1.75773	+	1.23068i
$617$	−7.71828	−	3.93266i	−0.310726	−	0.158323i	0.291672	−	0.956518i	$-0.405788\pi$
$617$	−7.71828	−	3.93266i	−0.310726	−	0.158323i	−0.602399	+	0.798195i	$0.705788\pi$
$618$		0			0
$619$	−1.99490	−	6.13966i	−0.0801817	−	0.246774i	0.902928	−	0.429792i	$-0.141413\pi$
$619$	−1.99490	−	6.13966i	−0.0801817	−	0.246774i	−0.983109	+	0.183018i	$0.941413\pi$
$620$	−33.4129	−	20.0961i	−1.34189	−	0.807080i
$621$		0			0
$622$	5.86894	−	3.03360i	0.235323	−	0.121636i
$623$	0.358669	−	2.26455i	0.0143698	−	0.0907272i
$624$		0			0
$625$	−14.9654	+	20.0259i	−0.598617	+	0.801035i
$626$	−33.2195	+	0.193654i	−1.32772	+	0.00773997i
$627$		0			0
$628$	−12.6398	+	6.62705i	−0.504383	+	0.264448i
$629$	15.4600	+	5.02325i	0.616429	+	0.200290i
$630$		0			0
$631$	13.7963	−	4.48269i	0.549222	−	0.178453i	−0.0212442	−	0.999774i	$-0.506763\pi$
$631$	13.7963	−	4.48269i	0.549222	−	0.178453i	0.570466	+	0.821321i	$0.306763\pi$
$632$	19.6302	+	18.9553i	0.780848	+	0.754003i
$633$		0			0
$634$	−4.55121	+	6.34162i	−0.180752	+	0.251858i
$635$	10.5477	+	9.07015i	0.418574	+	0.359938i
$636$		0			0
$637$	−11.1510	+	1.76614i	−0.441818	+	0.0699770i
$638$	13.3667	−	2.19703i	0.529193	−	0.0869812i
$639$		0			0
$640$	−25.2769	−	1.03940i	−0.999156	−	0.0410858i
$641$	15.6806	+	11.3926i	0.619348	+	0.449982i	0.852694	−	0.522411i	$-0.174967\pi$
$641$	15.6806	+	11.3926i	0.619348	+	0.449982i	−0.233346	+	0.972394i	$0.574967\pi$
$642$		0			0
$643$	7.59067	−	7.59067i	0.299347	−	0.299347i	−0.541411	−	0.840758i	$-0.682110\pi$
$643$	7.59067	−	7.59067i	0.299347	−	0.299347i	0.840758	+	0.541411i	$0.182110\pi$
$644$	13.8784	−	4.68896i	0.546887	−	0.184771i
$645$		0			0
$646$	11.6712	+	3.71712i	0.459197	+	0.146248i
$647$	21.3418	−	10.8742i	0.839034	−	0.427509i	0.0189968	−	0.999820i	$-0.493953\pi$
$647$	21.3418	−	10.8742i	0.839034	−	0.427509i	0.820037	+	0.572310i	$0.193953\pi$
$648$		0			0
$649$			57.2037i			2.24544i
$650$	15.3443	+	30.1818i	0.601851	+	1.18383i
$651$		0			0
$652$	19.0579	+	2.79111i	0.746364	+	0.109308i
$653$	9.13921	−	4.65666i	0.357645	−	0.182229i	−0.265931	−	0.963992i	$-0.585679\pi$
$653$	9.13921	−	4.65666i	0.357645	−	0.182229i	0.623576	+	0.781763i	$0.285679\pi$
$654$		0			0
$655$	3.61256	+	0.880161i	0.141154	+	0.0343907i
$656$	8.71802	+	24.8447i	0.340382	+	0.970022i
$657$		0			0
$658$	7.57629	−	15.0861i	0.295355	−	0.588117i
$659$	34.9138	+	25.3664i	1.36005	+	0.988134i	0.998442	+	0.0558045i	$0.0177724\pi$
$659$	34.9138	+	25.3664i	1.36005	+	0.988134i	0.361609	+	0.932330i	$0.382228\pi$
$660$		0			0
$661$	−8.24772	+	5.99232i	−0.320799	+	0.233074i	−0.736516	−	0.676420i	$-0.763531\pi$
$661$	−8.24772	+	5.99232i	−0.320799	+	0.233074i	0.415717	+	0.909494i	$0.363531\pi$
$662$	−5.54574	−	33.7403i	−0.215541	−	1.31135i
$663$		0			0
$664$	−16.4759	+	12.4164i	−0.639390	+	0.481850i
$665$	−12.8369	+	7.80719i	−0.497794	+	0.302750i
$666$		0			0
$667$	1.69163	−	3.32001i	0.0655002	−	0.128551i
$668$	26.1354	−	26.7520i	1.01121	−	1.03507i
$669$		0			0
$670$	−4.07932	−	9.78008i	−0.157598	−	0.377837i
$671$	5.17614	+	1.68183i	0.199823	+	0.0649263i
$672$		0			0
$673$	−0.702378	−	0.111246i	−0.0270747	−	0.00428821i	0.142882	−	0.989740i	$-0.454363\pi$
$673$	−0.702378	−	0.111246i	−0.0270747	−	0.00428821i	−0.169957	+	0.985451i	$0.554363\pi$
$674$	0.216062	+	37.0633i	0.00832240	+	1.42763i
$675$		0			0
$676$	19.8541	−	0.231488i	0.763619	−	0.00890340i
$677$	0.150123	−	0.947838i	0.00576969	−	0.0364284i	−0.984636	−	0.174622i	$-0.944130\pi$
$677$	0.150123	−	0.947838i	0.00576969	−	0.0364284i	0.990405	+	0.138194i	$0.0441296\pi$
$678$		0			0
$679$	15.6160	−	48.0612i	0.599289	−	1.84442i
$680$	−24.8320	+	2.30765i	−0.952264	+	0.0884944i
$681$		0			0
$682$	−53.3499	+	53.9756i	−2.04287	+	2.06683i
$683$	−31.1864	−	15.8902i	−1.19331	−	0.608023i	−0.259485	−	0.965747i	$-0.583553\pi$
$683$	−31.1864	−	15.8902i	−1.19331	−	0.608023i	−0.933827	+	0.357724i	$0.883553\pi$
$684$		0			0
$685$	−7.67339	−	3.20871i	−0.293185	−	0.122598i
$686$	−11.8989	−	16.1782i	−0.454301	−	0.617687i
$687$		0			0
$688$	−48.5824	+	8.86047i	−1.85219	+	0.337802i
$689$	17.5137	+	24.1056i	0.667220	+	0.918349i
$690$		0			0
$691$	−13.7471	+	18.9213i	−0.522964	+	0.719799i	−0.986038	−	0.166521i	$-0.946747\pi$
$691$	−13.7471	+	18.9213i	−0.522964	+	0.719799i	0.463074	+	0.886320i	$0.346747\pi$
$692$	1.97343	+	0.976700i	0.0750185	+	0.0371286i
$693$		0			0
$694$	−8.93180	−	26.9536i	−0.339047	−	1.02314i
$695$	−3.19971	+	0.240996i	−0.121372	+	0.00914149i
$696$		0			0
$697$	11.7838	+	23.1270i	0.446343	+	0.875997i
$698$	−1.83302	−	0.279378i	−0.0693808	−	0.0105746i
$699$		0			0
$700$	17.8584	−	24.8367i	0.674985	−	0.938737i
$701$	−41.4474			−1.56545			−0.782723	−	0.622370i	$-0.786170\pi$
$701$	−41.4474			−1.56545			−0.782723	+	0.622370i	$0.786170\pi$
$702$		0			0
$703$	4.11083	+	8.06796i	0.155043	+	0.304289i
$704$	−13.5692	+	47.3341i	−0.511410	+	1.78397i
$705$		0			0
$706$	−13.0647	−	39.4255i	−0.491697	−	1.48380i
$707$	−25.8434	−	25.8434i	−0.971941	−	0.971941i
$708$		0			0
$709$	13.9526	−	19.2041i	0.524001	−	0.721226i	−0.462200	−	0.886776i	$-0.652940\pi$
$709$	13.9526	−	19.2041i	0.524001	−	0.721226i	0.986201	+	0.165550i	$0.0529399\pi$
$710$	−16.8928	+	10.4093i	−0.633975	+	0.390653i
$711$		0			0
$712$	2.08770	−	0.368193i	0.0782398	−	0.0137986i
$713$	3.26568	+	20.6187i	0.122301	+	0.772175i
$714$		0			0
$715$	64.1327	−	15.1689i	2.39843	−	0.567285i
$716$	−12.8555	+	18.1349i	−0.480431	+	0.677735i
$717$		0			0
$718$	−2.91720	+	2.95141i	−0.108869	+	0.110146i
$719$	−0.654007	−	2.01283i	−0.0243904	−	0.0750658i	0.938120	−	0.346309i	$-0.112565\pi$
$719$	−0.654007	−	2.01283i	−0.0243904	−	0.0750658i	−0.962511	+	0.271243i	$0.912565\pi$
$720$		0			0
$721$	5.14893	−	15.8468i	0.191756	−	0.590164i
$722$	−9.20515	−	17.8087i	−0.342580	−	0.662772i
$723$		0			0
$724$	0.277385	+	23.7906i	0.0103090	+	0.884170i
$725$	−1.16548	−	7.69319i	−0.0432849	−	0.285718i
$726$		0			0
$727$	12.6019	+	1.99595i	0.467379	+	0.0740255i	0.385682	−	0.922632i	$-0.373966\pi$
$727$	12.6019	+	1.99595i	0.467379	+	0.0740255i	0.0816966	+	0.996657i	$0.473966\pi$
$728$	−19.4514	−	36.5797i	−0.720917	−	1.35573i
$729$		0			0
$730$	2.20273	−	1.89072i	0.0815265	−	0.0699786i
$731$	−46.2999	+	15.0437i	−1.71246	+	0.556413i
$732$		0			0
$733$	−8.55620	+	16.7925i	−0.316030	+	0.620245i	−0.993310	−	0.115481i	$-0.963159\pi$
$733$	−8.55620	+	16.7925i	−0.316030	+	0.620245i	0.677279	+	0.735726i	$0.263159\pi$
$734$	−3.65461	−	2.62282i	−0.134894	−	0.0968099i
$735$		0			0
$736$	8.27734	+	10.7212i	0.305107	+	0.395189i
$737$	−20.3716	+	3.22655i	−0.750399	+	0.118852i
$738$		0			0
$739$	−14.1263	+	10.2634i	−0.519645	+	0.377544i	−0.816470	−	0.577387i	$-0.804072\pi$
$739$	−14.1263	+	10.2634i	−0.519645	+	0.377544i	0.296825	+	0.954932i	$0.404072\pi$
$740$	−14.1177	−	11.8566i	−0.518978	−	0.435856i
$741$		0			0
$742$	12.0816	−	24.0571i	0.443529	−	0.883164i
$743$	−15.1611	+	15.1611i	−0.556207	+	0.556207i	−0.928225	−	0.372019i	$-0.878666\pi$
$743$	−15.1611	+	15.1611i	−0.556207	+	0.556207i	0.372019	+	0.928225i	$0.378666\pi$
$744$		0			0
$745$	−24.2621	+	39.2948i	−0.888893	+	1.43965i
$746$	3.89074	−	12.2163i	0.142450	−	0.447272i
$747$		0			0
$748$	−7.03409	+	48.0292i	−0.257192	+	1.75612i
$749$			2.00242i			0.0731667i
$750$		0			0
$751$			5.28907i			0.193001i	0.995333	+	0.0965004i	$0.0307649\pi$
$751$			5.28907i			0.193001i	−0.995333	+	0.0965004i	$0.969235\pi$
$752$	15.4695	+	2.08165i	0.564113	+	0.0759101i
$753$		0			0
$754$	−10.0411	−	3.19795i	−0.365674	−	0.116462i
$755$	−19.3569	+	31.3504i	−0.704470	+	1.14096i
$756$		0			0
$757$	11.0805	−	11.0805i	0.402727	−	0.402727i	−0.476466	−	0.879193i	$-0.658082\pi$
$757$	11.0805	−	11.0805i	0.402727	−	0.402727i	0.879193	+	0.476466i	$0.158082\pi$
$758$	37.8243	+	18.9955i	1.37384	+	0.689948i
$759$		0			0
$760$	−10.6898	−	8.87193i	−0.387760	−	0.321819i
$761$	4.11949	−	2.99298i	0.149331	−	0.108496i	−0.510611	−	0.859812i	$-0.670581\pi$
$761$	4.11949	−	2.99298i	0.149331	−	0.108496i	0.659942	+	0.751316i	$0.270581\pi$
$762$		0			0
$763$	11.2873	−	1.78773i	0.408628	−	0.0647203i
$764$	−34.0567	+	25.3555i	−1.23213	+	0.917331i
$765$		0			0
$766$	14.2879	−	19.9086i	0.516242	−	0.719328i
$767$	20.2031	−	39.6508i	0.729491	−	1.43171i
$768$		0			0
$769$	34.6499	−	11.2584i	1.24951	−	0.405990i	0.391763	−	0.920066i	$-0.371865\pi$
$769$	34.6499	−	11.2584i	1.24951	−	0.405990i	0.857744	+	0.514076i	$0.171865\pi$
$770$	−38.7808	−	45.1804i	−1.39756	−	1.62819i
$771$		0			0
$772$	−10.3765	−	19.7911i	−0.373457	−	0.712297i
$773$	−32.6907	−	5.17769i	−1.17580	−	0.186229i	−0.462197	−	0.886777i	$-0.652939\pi$
$773$	−32.6907	−	5.17769i	−1.17580	−	0.186229i	−0.713604	+	0.700549i	$0.752939\pi$
$774$		0			0
$775$	30.6168	+	31.0316i	1.09979	+	1.11469i
$776$	46.7175	−	0.817098i	1.67706	−	0.0293321i
$777$		0			0
$778$	5.31688	−	2.74824i	0.190619	−	0.0985293i
$779$	−4.46787	+	13.7507i	−0.160078	+	0.492670i
$780$		0			0
$781$	11.9346	+	36.7311i	0.427055	+	1.31434i
$782$	9.49644	+	9.38636i	0.339592	+	0.335656i
$783$		0			0
$784$	−5.36418	+	7.75727i	−0.191578	+	0.277046i
$785$	15.5279	−	3.67271i	0.554213	−	0.131085i
$786$		0			0
$787$	−5.67435	−	35.8265i	−0.202269	−	1.27708i	−0.854658	−	0.519191i	$-0.826233\pi$
$787$	−5.67435	−	35.8265i	−0.202269	−	1.27708i	0.652389	−	0.757884i	$-0.273767\pi$
$788$	5.22257	+	30.6564i	0.186046	+	1.09209i
$789$		0			0
$790$	−16.0051	−	25.9740i	−0.569437	−	0.924114i
$791$	1.39100	−	1.91454i	0.0494581	−	0.0680732i
$792$		0			0
$793$	−2.99386	−	2.99386i	−0.106315	−	0.106315i
$794$	−32.3879	+	10.7326i	−1.14940	+	0.380886i
$795$		0			0
$796$	−23.7216	−	7.40299i	−0.840789	−	0.262392i
$797$	5.84580	+	11.4730i	0.207069	+	0.406395i	0.971062	−	0.238830i	$-0.0767637\pi$
$797$	5.84580	+	11.4730i	0.207069	+	0.406395i	−0.763993	+	0.645225i	$0.776764\pi$
$798$		0			0
$799$	15.3873			0.544362
$800$	27.0891	+	8.13509i	0.957745	+	0.287619i
$801$		0			0
$802$	−2.35089	+	15.4243i	−0.0830127	+	0.544652i
$803$	−2.56515	−	5.03439i	−0.0905221	−	0.177660i
$804$		0			0
$805$	−16.3320	+	1.23009i	−0.575627	+	0.0433550i
$806$	56.0425	−	18.5712i	1.97401	−	0.654142i
$807$		0			0
$808$	14.8127	−	30.3732i	0.521107	−	1.06852i
$809$	−22.9504	+	31.5886i	−0.806894	+	1.11059i	0.184901	+	0.982757i	$0.440804\pi$
$809$	−22.9504	+	31.5886i	−0.806894	+	1.11059i	−0.991795	+	0.127837i	$0.959196\pi$
$810$		0			0
$811$	−3.23075	−	4.44674i	−0.113447	−	0.156146i	0.748518	−	0.663115i	$-0.230766\pi$
$811$	−3.23075	−	4.44674i	−0.113447	−	0.156146i	−0.861964	+	0.506969i	$0.830766\pi$
$812$	1.59894	+	9.38575i	0.0561119	+	0.329375i
$813$		0			0
$814$	−28.9074	+	21.2610i	−1.01320	+	0.745198i
$815$	−19.8676	−	8.30784i	−0.695932	−	0.291011i
$816$		0			0
$817$	−24.1621	−	12.3112i	−0.845326	−	0.430715i
$818$	−30.2754	−	29.9245i	−1.05856	−	1.04628i
$819$		0			0
$820$	−2.55301	−	29.3268i	−0.0891549	−	1.02414i
$821$	6.85514	−	21.0979i	0.239246	−	0.736323i	−0.757284	−	0.653086i	$-0.773474\pi$
$821$	6.85514	−	21.0979i	0.239246	−	0.736323i	0.996530	−	0.0832374i	$-0.0265260\pi$
$822$		0			0
$823$	−3.98090	+	25.1344i	−0.138765	+	0.876130i	0.815845	+	0.578271i	$0.196272\pi$
$823$	−3.98090	+	25.1344i	−0.138765	+	0.876130i	−0.954610	+	0.297859i	$0.903728\pi$
$824$	15.4037	−	0.269414i	0.536614	−	0.00938548i
$825$		0			0
$826$	−40.2055	+	0.234379i	−1.39893	+	0.00815510i
$827$	−37.7357	−	5.97675i	−1.31220	−	0.207832i	−0.539167	−	0.842199i	$-0.681261\pi$
$827$	−37.7357	−	5.97675i	−1.31220	−	0.207832i	−0.773032	+	0.634367i	$0.781261\pi$
$828$		0			0
$829$	−41.3764	−	13.4440i	−1.43706	−	0.466929i	−0.516081	−	0.856540i	$-0.672610\pi$
$829$	−41.3764	−	13.4440i	−1.43706	−	0.466929i	−0.920980	+	0.389610i	$0.872610\pi$
$830$	21.2882	−	8.87940i	0.738923	−	0.308208i
$831$		0			0
$832$	26.1229	−	28.0173i	0.905648	−	0.971325i
$833$	−4.22093	+	8.28404i	−0.146247	+	0.287025i
$834$		0			0
$835$	−35.7256	+	21.7277i	−1.23633	+	0.751918i
$836$	−21.6884	+	16.1472i	−0.750109	+	0.558463i
$837$		0			0
$838$	−19.2553	+	3.16491i	−0.665164	+	0.109330i
$839$	4.45082	−	3.23371i	0.153659	−	0.111640i	−0.508299	−	0.861181i	$-0.669726\pi$
$839$	4.45082	−	3.23371i	0.153659	−	0.111640i	0.661958	+	0.749541i	$0.269726\pi$
$840$		0			0
$841$	−21.5023	−	15.6223i	−0.741457	−	0.538700i
$842$	−16.5088	−	8.29080i	−0.568932	−	0.285720i
$843$		0			0
$844$	6.24616	+	18.4875i	0.215002	+	0.636365i
$845$	−21.5682	−	5.25485i	−0.741967	−	0.180772i
$846$		0			0
$847$	−73.2790	+	37.3375i	−2.51790	+	1.28293i
$848$	24.6685	+	3.31952i	0.847119	+	0.113993i
$849$		0			0
$850$	27.5354	+	4.38654i	0.944458	+	0.150457i
$851$			9.87069i			0.338363i
$852$		0			0
$853$	−4.42032	+	2.25226i	−0.151349	+	0.0771161i	−0.528025	−	0.849229i	$-0.677067\pi$
$853$	−4.42032	+	2.25226i	−0.151349	+	0.0771161i	0.376676	+	0.926345i	$0.377067\pi$
$854$	−1.16086	+	3.64493i	−0.0397239	+	0.124727i
$855$		0			0
$856$	−1.75056	+	0.602834i	−0.0598329	+	0.0206045i
$857$	10.3827	−	10.3827i	0.354667	−	0.354667i	−0.507176	−	0.861843i	$-0.669311\pi$
$857$	10.3827	−	10.3827i	0.354667	−	0.354667i	0.861843	+	0.507176i	$0.169311\pi$
$858$		0			0
$859$	34.9173	+	25.3689i	1.19136	+	0.865575i	0.993408	−	0.114636i	$-0.0365702\pi$
$859$	34.9173	+	25.3689i	1.19136	+	0.865575i	0.197954	+	0.980211i	$0.436570\pi$
$860$	55.0766	+	3.87522i	1.87810	+	0.132144i
$861$		0			0
$862$	5.73983	+	34.9211i	0.195500	+	1.18942i
$863$	52.7195	−	8.34994i	1.79459	−	0.284235i	0.831917	−	0.554899i	$-0.187243\pi$
$863$	52.7195	−	8.34994i	1.79459	−	0.284235i	0.962674	+	0.270664i	$0.0872433\pi$
$864$		0			0
$865$	−1.86658	−	1.60510i	−0.0634655	−	0.0545750i
$866$	22.4148	+	16.0865i	0.761684	+	0.546641i
$867$		0			0
$868$	−38.1552	−	37.2757i	−1.29507	−	1.26522i
$869$	−56.4770	+	18.3505i	−1.91585	+	0.622498i
$870$		0			0
$871$	15.2602	+	4.95832i	0.517071	+	0.168006i
$872$	4.96096	+	9.32942i	0.167999	+	0.315934i
$873$		0			0
$874$	0.0433577	+	7.43759i	0.00146660	+	0.251580i
$875$	−26.2297	+	21.9484i	−0.886726	+	0.741991i
$876$		0			0
$877$	−8.50704	+	53.7113i	−0.287262	+	1.81370i	0.247711	+	0.968834i	$0.420322\pi$
$877$	−8.50704	+	53.7113i	−0.287262	+	1.81370i	−0.534973	+	0.844869i	$0.679678\pi$
$878$	−4.78738	−	9.26189i	−0.161566	−	0.312574i
$879$		0			0
$880$	27.8227	−	47.5048i	0.937902	−	1.60139i
$881$	−3.94503	−	12.1416i	−0.132912	−	0.409060i	0.862348	−	0.506316i	$-0.168993\pi$
$881$	−3.94503	−	12.1416i	−0.132912	−	0.409060i	−0.995259	+	0.0972568i	$0.968993\pi$
$882$		0			0
$883$	13.0041	+	6.62594i	0.437624	+	0.222980i	0.658900	−	0.752231i	$-0.271022\pi$
$883$	13.0041	+	6.62594i	0.437624	+	0.222980i	−0.221276	+	0.975211i	$0.571022\pi$
$884$	21.8385	−	30.8071i	0.734508	−	1.03616i
$885$		0			0
$886$	14.1672	+	19.2623i	0.475955	+	0.647129i
$887$	−6.89961	−	43.5624i	−0.231666	−	1.46268i	−0.779661	−	0.626202i	$-0.784609\pi$
$887$	−6.89961	−	43.5624i	−0.231666	−	1.46268i	0.547995	−	0.836482i	$-0.315391\pi$
$888$		0			0
$889$	11.1863	+	15.3966i	0.375177	+	0.516386i
$890$	−2.36329	−	0.180133i	−0.0792175	−	0.00603806i
$891$		0			0
$892$	−11.6436	+	23.5259i	−0.389856	+	0.787706i
$893$	6.06076	+	6.06076i	0.202816	+	0.202816i
$894$		0			0
$895$	18.9526	−	16.0771i	0.633515	−	0.537398i
$896$	−33.3243	−	9.34317i	−1.11329	−	0.312133i
$897$		0			0
$898$	25.0818	+	3.82283i	0.836992	+	0.127569i
$899$	−13.5678			−0.452512
$900$		0			0
$901$	24.5374			0.817459
$902$	−56.6436	−	8.63330i	−1.88603	−	0.287457i
$903$		0			0
$904$	2.09250	+	0.639661i	0.0695955	+	0.0212748i
$905$	6.29673	−	25.8445i	0.209310	−	0.859099i
$906$		0			0
$907$	4.84284	+	4.84284i	0.160804	+	0.160804i	0.782923	−	0.622119i	$-0.213728\pi$
$907$	4.84284	+	4.84284i	0.160804	+	0.160804i	−0.622119	+	0.782923i	$0.713728\pi$
$908$	37.8132	+	18.7147i	1.25487	+	0.621070i
$909$		0			0
$910$	10.9242	+	45.0133i	0.362134	+	1.49218i
$911$	−8.76056	−	12.0579i	−0.290250	−	0.399495i	0.638845	−	0.769335i	$-0.279412\pi$
$911$	−8.76056	−	12.0579i	−0.290250	−	0.399495i	−0.929095	+	0.369840i	$0.879412\pi$
$912$		0			0
$913$	−7.02319	−	44.3427i	−0.232434	−	1.46753i
$914$	−18.0388	−	24.5263i	−0.596669	−	0.811257i
$915$		0			0
$916$	17.4536	+	12.3724i	0.576682	+	0.408797i
$917$	4.53231	+	2.30933i	0.149670	+	0.0762607i
$918$		0			0
$919$	−7.90817	−	24.3388i	−0.260866	−	0.802864i	−0.992617	−	0.121292i	$-0.961296\pi$
$919$	−7.90817	−	24.3388i	−0.260866	−	0.802864i	0.731751	−	0.681572i	$-0.238704\pi$
$920$	−5.99217	−	13.9075i	−0.197556	−	0.458516i
$921$		0			0
$922$	−8.41380	−	16.2777i	−0.277094	−	0.536078i
$923$	4.70009	−	29.6752i	0.154705	−	0.976771i
$924$		0			0
$925$	12.0030	+	16.7567i	0.394658	+	0.550957i
$926$	0.0147252	+	2.52596i	0.000483899	+	0.0830081i
$927$		0			0
$928$	−7.72387	+	4.22345i	−0.253549	+	0.138641i
$929$	14.8414	+	4.82227i	0.486931	+	0.158214i	0.542186	−	0.840259i	$-0.317597\pi$
$929$	14.8414	+	4.82227i	0.486931	+	0.158214i	−0.0552544	+	0.998472i	$0.517597\pi$
$930$		0			0
$931$	−4.92548	+	1.60039i	−0.161426	+	0.0524505i
$932$	4.03758	−	4.13284i	0.132255	−	0.135376i
$933$		0			0
$934$	−25.1905	−	18.0786i	−0.824259	−	0.591549i
$935$	20.9372	−	50.0698i	0.684719	−	1.63746i
$936$		0			0
$937$	13.6370	−	2.15989i	0.445502	−	0.0705605i	0.0703466	−	0.997523i	$-0.477589\pi$
$937$	13.6370	−	2.15989i	0.445502	−	0.0705605i	0.375155	+	0.926962i	$0.377589\pi$
$938$	−2.35124	−	14.3049i	−0.0767708	−	0.467073i
$939$		0			0
$940$	−16.1777	−	6.54435i	−0.527659	−	0.213453i
$941$	−19.0308	−	13.8267i	−0.620386	−	0.450737i	0.232671	−	0.972556i	$-0.425254\pi$
$941$	−19.0308	−	13.8267i	−0.620386	−	0.450737i	−0.853056	+	0.521819i	$0.825254\pi$
$942$		0			0
$943$	−11.1447	+	11.1447i	−0.362921	+	0.362921i
$944$	−12.3089	−	35.0780i	−0.400621	−	1.14169i
$945$		0			0
$946$	32.6126	−	102.399i	1.06033	−	3.32927i
$947$	22.7069	−	11.5698i	0.737877	−	0.375967i	−0.0443045	−	0.999018i	$-0.514107\pi$
$947$	22.7069	−	11.5698i	0.737877	−	0.375967i	0.782181	+	0.623051i	$0.214107\pi$
$948$		0			0
$949$			4.39554i			0.142685i
$950$	9.11793	+	12.5735i	0.295825	+	0.407938i
$951$		0			0
$952$	−33.7860	−	4.74710i	−1.09501	−	0.153854i
$953$	18.7735	−	9.56559i	0.608134	−	0.309860i	−0.122670	−	0.992448i	$-0.539146\pi$
$953$	18.7735	−	9.56559i	0.608134	−	0.309860i	0.730804	+	0.682588i	$0.239146\pi$
$954$		0			0
$955$	43.9180	−	18.0186i	1.42115	−	0.583067i
$956$	23.4563	−	7.92492i	0.758631	−	0.256310i
$957$		0			0
$958$	6.49388	+	3.26126i	0.209808	+	0.105366i
$959$	−9.20535	−	6.68808i	−0.297256	−	0.215969i
$960$		0			0
$961$	36.4169	−	26.4585i	1.17474	−	0.853499i
$962$	27.5461	−	4.52763i	0.888121	−	0.145977i
$963$		0			0
$964$	20.2822	+	27.2424i	0.653246	+	0.877419i
$965$	5.75064	+	24.3131i	0.185120	+	0.782668i
$966$		0			0
$967$	−12.9924	+	25.4990i	−0.417808	+	0.819994i	0.582168	+	0.813068i	$0.302204\pi$
$967$	−12.9924	+	25.4990i	−0.417808	+	0.819994i	−0.999976	+	0.00692551i	$0.997796\pi$
$968$	−54.7022	−	52.8216i	−1.75820	−	1.69775i
$969$		0			0
$970$	−50.8263	−	12.0698i	−1.63193	−	0.387539i
$971$	12.1175	+	3.93722i	0.388869	+	0.126351i	0.496925	−	0.867794i	$-0.334462\pi$
$971$	12.1175	+	3.93722i	0.388869	+	0.126351i	−0.108056	+	0.994145i	$0.534462\pi$
$972$		0			0
$973$	−4.33573	−	0.686712i	−0.138997	−	0.0220150i
$974$	18.7477	−	0.109290i	0.600715	−	0.00350189i
$975$		0			0
$976$	−3.53596	+	0.0824661i	−0.113183	+	0.00263967i
$977$	−7.04607	+	44.4872i	−0.225424	+	1.42327i	0.572200	+	0.820114i	$0.306090\pi$
$977$	−7.04607	+	44.4872i	−0.225424	+	1.42327i	−0.797623	+	0.603156i	$0.793910\pi$
$978$		0			0
$979$	−1.42558	+	4.38747i	−0.0455616	+	0.140224i
$980$	7.96104	−	6.91440i	0.254306	−	0.220872i
$981$		0			0
$982$	−8.54305	−	8.44402i	−0.272620	−	0.269460i
$983$	18.7209	+	9.53878i	0.597104	+	0.304240i	0.726298	−	0.687379i	$-0.241239\pi$
$983$	18.7209	+	9.53878i	0.597104	+	0.304240i	−0.129194	+	0.991619i	$0.541239\pi$
$984$		0			0
$985$	2.84450	−	34.6521i	0.0906332	−	1.10411i
$986$	−6.99093	+	5.14174i	−0.222637	+	0.163746i
$987$		0			0
$988$	20.7361	−	3.53258i	0.659705	−	0.112386i
$989$	−17.3755	−	23.9153i	−0.552509	−	0.760464i
$990$		0			0
$991$	6.89129	−	9.48504i	0.218909	−	0.301302i	−0.685412	−	0.728155i	$-0.740378\pi$
$991$	6.89129	−	9.48504i	0.218909	−	0.301302i	0.904321	+	0.426853i	$0.140378\pi$
$992$	21.1005	−	44.5781i	0.669943	−	1.41536i
$993$		0			0
$994$	−25.7674	+	8.53874i	−0.817294	+	0.270832i
$995$	23.6400	+	14.5962i	0.749438	+	0.462731i
$996$		0			0
$997$	24.9244	+	48.9168i	0.789362	+	1.54921i	0.834998	+	0.550253i	$0.185469\pi$
$997$	24.9244	+	48.9168i	0.789362	+	1.54921i	−0.0456360	+	0.998958i	$0.514531\pi$
$998$	−5.33798	+	35.0228i	−0.168971	+	1.10863i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.523.17		240
3.2	odd	2		300.2.w.a.223.14	yes	240
4.3	odd	2	inner	900.2.bj.f.523.18		240
12.11	even	2		300.2.w.a.223.13	yes	240
25.12	odd	20	inner	900.2.bj.f.487.18		240
75.62	even	20		300.2.w.a.187.13	✓	240
100.87	even	20	inner	900.2.bj.f.487.17		240
300.287	odd	20		300.2.w.a.187.14	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.13	✓	240	75.62	even	20
300.2.w.a.187.14	yes	240	300.287	odd	20
300.2.w.a.223.13	yes	240	12.11	even	2
300.2.w.a.223.14	yes	240	3.2	odd	2
900.2.bj.f.487.17		240	100.87	even	20	inner
900.2.bj.f.487.18		240	25.12	odd	20	inner
900.2.bj.f.523.17		240	1.1	even	1	trivial
900.2.bj.f.523.18		240	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.213085 - 1.39807i) q^{2} +(-1.90919 - 0.595816i) q^{4} +(1.90262 + 1.17475i) q^{5} +(2.16308 + 2.16308i) q^{7} +(-1.23981 + 2.54222i) q^{8} +(2.04780 - 2.40967i) q^{10} +(-3.61787 - 4.97957i) q^{11} +(0.749054 + 4.72934i) q^{13} +(3.48505 - 2.56321i) q^{14} +(3.29001 + 2.27505i) q^{16} +(3.51342 + 1.79018i) q^{17} +(0.678754 + 2.08899i) q^{19} +(-2.93253 - 3.37643i) q^{20} +(-7.73269 + 3.99695i) q^{22} +(-0.374565 + 2.36491i) q^{23} +(2.23993 + 4.47020i) q^{25} +(6.77155 - 0.0394750i) q^{26} +(-2.84093 - 5.41853i) q^{28} +(-1.48003 - 0.480891i) q^{29} +(8.29187 - 2.69419i) q^{31} +(3.88173 - 4.11487i) q^{32} +(3.25145 - 4.53054i) q^{34} +(1.57444 + 6.65660i) q^{35} +(4.07167 - 0.644890i) q^{37} +(3.06518 - 0.503811i) q^{38} +(-5.34536 + 3.38041i) q^{40} +(5.32533 + 3.86908i) q^{41} +(-8.72991 + 8.72991i) q^{43} +(3.94029 + 11.6625i) q^{44} +(3.22649 + 1.02759i) q^{46} +(3.47691 - 1.77157i) q^{47} +2.35783i q^{49} +(6.72695 - 2.17904i) q^{50} +(1.38773 - 9.47550i) q^{52} +(5.54447 - 2.82505i) q^{53} +(-1.03369 - 13.7243i) q^{55} +(-8.18083 + 2.81721i) q^{56} +(-0.987690 + 1.96671i) q^{58} +(-7.51879 - 5.46272i) q^{59} +(-0.715358 + 0.519738i) q^{61} +(-1.99979 - 12.1667i) q^{62} +(-4.92573 - 6.30374i) q^{64} +(-4.13062 + 9.87809i) q^{65} +(1.52131 - 2.98575i) q^{67} +(-5.64117 - 5.51114i) q^{68} +(9.64187 - 0.782756i) q^{70} +(-5.96760 - 1.93899i) q^{71} +(0.906675 + 0.143603i) q^{73} +(-0.0339856 - 5.82989i) q^{74} +(-0.0512164 - 4.39269i) q^{76} +(2.94547 - 18.5969i) q^{77} +(2.98135 - 9.17567i) q^{79} +(3.58702 + 8.19349i) q^{80} +(6.54398 - 6.62073i) q^{82} +(6.49903 + 3.31142i) q^{83} +(4.58170 + 7.53341i) q^{85} +(10.3448 + 14.0652i) q^{86} +(17.1446 - 3.02368i) q^{88} +(-0.440547 - 0.606362i) q^{89} +(-8.60967 + 11.8502i) q^{91} +(2.12417 - 4.29189i) q^{92} +(-1.73590 - 5.23845i) q^{94} +(-1.16263 + 4.77192i) q^{95} +(-7.49977 - 14.7191i) q^{97} +(3.29641 + 0.502419i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58}+ \cdots - 256 q^{98}+O(q^{100}) \) 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Introduction

L-functions

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