LMFDB - Embedded newform 288.2.v.b.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(37,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("288.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.v (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.2
Root			$0.500000 - 2.10607i$ of defining polynomial
Character	$\chi$	$=$	288.109
Dual form			288.2.v.b.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26330 - 0.635665i) q^{2} +(1.19186 - 1.60607i) q^{4} +(-0.707107 + 0.292893i) q^{5} +(1.68554 - 1.68554i) q^{7} +(0.484753 - 2.78658i) q^{8} +O(q^{10})$	\(q+(1.26330 - 0.635665i) q^{2} +(1.19186 - 1.60607i) q^{4} +(-0.707107 + 0.292893i) q^{5} +(1.68554 - 1.68554i) q^{7} +(0.484753 - 2.78658i) q^{8} +(-0.707107 + 0.819496i) q^{10} +(0.334743 + 0.808140i) q^{11} +(1.09083 + 0.451835i) q^{13} +(1.05791 - 3.20079i) q^{14} +(-1.15894 - 3.82843i) q^{16} -0.224777i q^{17} +(-2.87740 - 1.19186i) q^{19} +(-0.372364 + 1.48475i) q^{20} +(0.936588 + 0.808140i) q^{22} +(3.68554 + 3.68554i) q^{23} +(-3.12132 + 3.12132i) q^{25} +(1.66526 - 0.122597i) q^{26} +(-0.698175 - 4.71604i) q^{28} +(-2.34610 + 5.66398i) q^{29} +6.82843 q^{31} +(-3.89769 - 4.09976i) q^{32} +(-0.142883 - 0.283962i) q^{34} +(-0.698175 + 1.68554i) q^{35} +(-9.87613 + 4.09083i) q^{37} +(-4.39265 + 0.323388i) q^{38} +(0.473398 + 2.11239i) q^{40} +(-6.37109 - 6.37109i) q^{41} +(1.90790 + 4.60607i) q^{43} +(1.69690 + 0.425569i) q^{44} +(6.99872 + 2.31318i) q^{46} -0.542661i q^{47} +1.31788i q^{49} +(-1.95905 + 5.92728i) q^{50} +(2.02579 - 1.21342i) q^{52} +(3.91925 + 9.46191i) q^{53} +(-0.473398 - 0.473398i) q^{55} +(-3.87983 - 5.51397i) q^{56} +(0.636568 + 8.64665i) q^{58} +(3.36524 - 1.39393i) q^{59} +(0.398630 - 0.962379i) q^{61} +(8.62636 - 4.34059i) q^{62} +(-7.53003 - 2.70160i) q^{64} -0.903670 q^{65} +(1.48105 - 3.57558i) q^{67} +(-0.361009 - 0.267903i) q^{68} +(0.189436 + 2.57316i) q^{70} +(5.39978 - 5.39978i) q^{71} +(-5.15894 - 5.15894i) q^{73} +(-9.87613 + 11.4459i) q^{74} +(-5.34367 + 3.20079i) q^{76} +(1.92638 + 0.797933i) q^{77} +8.39218i q^{79} +(1.94082 + 2.36766i) q^{80} +(-12.0985 - 3.99872i) q^{82} +(-11.2180 - 4.64665i) q^{83} +(0.0658358 + 0.158942i) q^{85} +(5.33817 + 4.60607i) q^{86} +(2.41421 - 0.541038i) q^{88} +(5.92638 - 5.92638i) q^{89} +(2.60022 - 1.07705i) q^{91} +(10.3119 - 1.52660i) q^{92} +(-0.344951 - 0.685544i) q^{94} +2.38372 q^{95} -4.19951 q^{97} +(0.837733 + 1.66488i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8	$ 8 q + 4 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8} - 4 q^{11} - 8 q^{13} - 12 q^{14} + 4 q^{19} - 4 q^{20} + 4 q^{22} + 8 q^{23} - 8 q^{25} + 20 q^{26} - 16 q^{28} + 32 q^{31} + 24 q^{32} - 16 q^{35} - 8 q^{37} - 8 q^{38} + 16 q^{40} - 8 q^{41} - 12 q^{43} - 20 q^{44} + 12 q^{46} - 16 q^{50} + 12 q^{52} - 8 q^{53} - 16 q^{55} - 8 q^{56} - 12 q^{58} + 20 q^{59} + 24 q^{61} + 24 q^{62} - 8 q^{64} - 36 q^{67} - 16 q^{68} - 8 q^{70} + 24 q^{71} - 32 q^{73} - 8 q^{74} - 20 q^{76} - 16 q^{77} - 8 q^{80} - 20 q^{82} - 20 q^{83} + 8 q^{85} - 4 q^{86} + 8 q^{88} + 16 q^{89} + 40 q^{91} + 16 q^{92} - 24 q^{94} + 8 q^{95} + 32 q^{97} + 24 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8 - 4 * q^11 - 8 * q^13 - 12 * q^14 + 4 * q^19 - 4 * q^20 + 4 * q^22 + 8 * q^23 - 8 * q^25 + 20 * q^26 - 16 * q^28 + 32 * q^31 + 24 * q^32 - 16 * q^35 - 8 * q^37 - 8 * q^38 + 16 * q^40 - 8 * q^41 - 12 * q^43 - 20 * q^44 + 12 * q^46 - 16 * q^50 + 12 * q^52 - 8 * q^53 - 16 * q^55 - 8 * q^56 - 12 * q^58 + 20 * q^59 + 24 * q^61 + 24 * q^62 - 8 * q^64 - 36 * q^67 - 16 * q^68 - 8 * q^70 + 24 * q^71 - 32 * q^73 - 8 * q^74 - 20 * q^76 - 16 * q^77 - 8 * q^80 - 20 * q^82 - 20 * q^83 + 8 * q^85 - 4 * q^86 + 8 * q^88 + 16 * q^89 + 40 * q^91 + 16 * q^92 - 24 * q^94 + 8 * q^95 + 32 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	1.26330	−	0.635665i	0.893289	−	0.449483i
$2$	1.26330	−	0.635665i	0.893289	−	0.449483i
$3$		0			0
$3$		0			0
$4$	1.19186	−	1.60607i	0.595930	−	0.803037i
$5$	−0.707107	+	0.292893i	−0.316228	+	0.130986i	−0.535151	−	0.844756i	$-0.679745\pi$
$5$	−0.707107	+	0.292893i	−0.316228	+	0.130986i	0.218924	+	0.975742i	$0.429745\pi$
$6$		0			0
$7$	1.68554	−	1.68554i	0.637076	−	0.637076i	−0.312757	−	0.949833i	$-0.601253\pi$
$7$	1.68554	−	1.68554i	0.637076	−	0.637076i	0.949833	+	0.312757i	$0.101253\pi$
$8$	0.484753	−	2.78658i	0.171386	−	0.985204i
$9$		0			0
$10$	−0.707107	+	0.819496i	−0.223607	+	0.259147i
$11$	0.334743	+	0.808140i	0.100929	+	0.243664i	0.966276	−	0.257510i	$-0.0829019\pi$
$11$	0.334743	+	0.808140i	0.100929	+	0.243664i	−0.865347	+	0.501173i	$0.832902\pi$
$12$		0			0
$13$	1.09083	+	0.451835i	0.302541	+	0.125316i	0.528789	−	0.848753i	$-0.322646\pi$
$13$	1.09083	+	0.451835i	0.302541	+	0.125316i	−0.226249	+	0.974070i	$0.572646\pi$
$14$	1.05791	−	3.20079i	0.282738	−	0.855447i
$15$		0			0
$16$	−1.15894	−	3.82843i	−0.289735	−	0.957107i
$17$		−	0.224777i		−	0.0545165i	−0.999628	−	0.0272583i	$-0.991322\pi$
$17$		−	0.224777i		−	0.0545165i	0.999628	−	0.0272583i	$-0.00867765\pi$
$18$		0			0
$19$	−2.87740	−	1.19186i	−0.660122	−	0.273431i	0.0273681	−	0.999625i	$-0.491287\pi$
$19$	−2.87740	−	1.19186i	−0.660122	−	0.273431i	−0.687490	+	0.726194i	$0.741287\pi$
$20$	−0.372364	+	1.48475i	−0.0832631	+	0.332001i
$21$		0			0
$22$	0.936588	+	0.808140i	0.199681	+	0.172296i
$23$	3.68554	+	3.68554i	0.768489	+	0.768489i	0.977840	−	0.209351i	$-0.0671353\pi$
$23$	3.68554	+	3.68554i	0.768489	+	0.768489i	−0.209351	+	0.977840i	$0.567135\pi$
$24$		0			0
$25$	−3.12132	+	3.12132i	−0.624264	+	0.624264i
$26$	1.66526	−	0.122597i	0.326584	−	0.0240432i
$27$		0			0
$28$	−0.698175	−	4.71604i	−0.131943	−	0.891247i
$29$	−2.34610	+	5.66398i	−0.435659	+	1.05177i	0.541773	+	0.840525i	$0.317753\pi$
$29$	−2.34610	+	5.66398i	−0.435659	+	1.05177i	−0.977432	+	0.211250i	$0.932247\pi$
$30$		0			0
$31$	6.82843			1.22642			0.613211	−	0.789919i	$-0.289878\pi$
$31$	6.82843			1.22642			0.613211	+	0.789919i	$0.289878\pi$
$32$	−3.89769	−	4.09976i	−0.689021	−	0.724742i
$33$		0			0
$34$	−0.142883	−	0.283962i	−0.0245043	−	0.0486990i
$35$	−0.698175	+	1.68554i	−0.118013	+	0.284909i
$36$		0			0
$37$	−9.87613	+	4.09083i	−1.62363	+	0.672528i	−0.994496	−	0.104773i	$-0.966588\pi$
$37$	−9.87613	+	4.09083i	−1.62363	+	0.672528i	−0.629129	+	0.777301i	$0.716588\pi$
$38$	−4.39265	+	0.323388i	−0.712582	+	0.0524604i
$39$		0			0
$40$	0.473398	+	2.11239i	0.0748508	+	0.333998i
$41$	−6.37109	−	6.37109i	−0.994997	−	0.994997i	0.00499079	−	0.999988i	$-0.498411\pi$
$41$	−6.37109	−	6.37109i	−0.994997	−	0.994997i	−0.999988	+	0.00499079i	$0.998411\pi$
$42$		0			0
$43$	1.90790	+	4.60607i	0.290952	+	0.702420i	0.999996	−	0.00274415i	$-0.000873491\pi$
$43$	1.90790	+	4.60607i	0.290952	+	0.702420i	−0.709045	+	0.705164i	$0.750873\pi$
$44$	1.69690	+	0.425569i	0.255817	+	0.0641569i
$45$		0			0
$46$	6.99872	+	2.31318i	1.03191	+	0.341060i
$47$		−	0.542661i		−	0.0791552i	−0.999216	−	0.0395776i	$-0.987399\pi$
$47$		−	0.542661i		−	0.0791552i	0.999216	−	0.0395776i	$-0.0126012\pi$
$48$		0			0
$49$			1.31788i			0.188269i
$50$	−1.95905	+	5.92728i	−0.277052	+	0.838244i
$51$		0			0
$52$	2.02579	−	1.21342i	0.280927	−	0.168271i
$53$	3.91925	+	9.46191i	0.538351	+	1.29969i	0.925873	+	0.377834i	$0.123331\pi$
$53$	3.91925	+	9.46191i	0.538351	+	1.29969i	−0.387523	+	0.921860i	$0.626669\pi$
$54$		0			0
$55$	−0.473398	−	0.473398i	−0.0638329	−	0.0638329i
$56$	−3.87983	−	5.51397i	−0.518464	−	0.736835i
$57$		0			0
$58$	0.636568	+	8.64665i	0.0835854	+	1.13536i
$59$	3.36524	−	1.39393i	0.438117	−	0.181474i	−0.152712	−	0.988271i	$-0.548801\pi$
$59$	3.36524	−	1.39393i	0.438117	−	0.181474i	0.590829	+	0.806797i	$0.298801\pi$
$60$		0			0
$61$	0.398630	−	0.962379i	0.0510394	−	0.123220i	−0.896303	−	0.443442i	$-0.853757\pi$
$61$	0.398630	−	0.962379i	0.0510394	−	0.123220i	0.947343	+	0.320222i	$0.103757\pi$
$62$	8.62636	−	4.34059i	1.09555	−	0.551256i
$63$		0			0
$64$	−7.53003	−	2.70160i	−0.941254	−	0.337700i
$65$	−0.903670			−0.112086
$66$		0			0
$67$	1.48105	−	3.57558i	0.180939	−	0.436826i	−0.807221	−	0.590249i	$-0.799030\pi$
$67$	1.48105	−	3.57558i	0.180939	−	0.436826i	0.988161	+	0.153423i	$0.0490296\pi$
$68$	−0.361009	−	0.267903i	−0.0437788	−	0.0324880i
$69$		0			0
$70$	0.189436	+	2.57316i	0.0226419	+	0.307551i
$71$	5.39978	−	5.39978i	0.640836	−	0.640836i	−0.309925	−	0.950761i	$-0.600304\pi$
$71$	5.39978	−	5.39978i	0.640836	−	0.640836i	0.950761	+	0.309925i	$0.100304\pi$
$72$		0			0
$73$	−5.15894	−	5.15894i	−0.603808	−	0.603808i	0.337513	−	0.941321i	$-0.390414\pi$
$73$	−5.15894	−	5.15894i	−0.603808	−	0.603808i	−0.941321	+	0.337513i	$0.890414\pi$
$74$	−9.87613	+	11.4459i	−1.14808	+	1.33055i
$75$		0			0
$76$	−5.34367	+	3.20079i	−0.612961	+	0.367156i
$77$	1.92638	+	0.797933i	0.219531	+	0.0909329i
$78$		0			0
$79$			8.39218i			0.944194i	0.881547	+	0.472097i	$0.156503\pi$
$79$			8.39218i			0.944194i	−0.881547	+	0.472097i	$0.843497\pi$
$80$	1.94082	+	2.36766i	0.216990	+	0.264713i
$81$		0			0
$82$	−12.0985	−	3.99872i	−1.33605	−	0.441585i
$83$	−11.2180	−	4.64665i	−1.23134	−	0.510036i	−0.330339	−	0.943862i	$-0.607163\pi$
$83$	−11.2180	−	4.64665i	−1.23134	−	0.510036i	−0.900996	+	0.433827i	$0.857163\pi$
$84$		0			0
$85$	0.0658358	+	0.158942i	0.00714089	+	0.0172396i
$86$	5.33817	+	4.60607i	0.575630	+	0.496686i
$87$		0			0
$88$	2.41421	−	0.541038i	0.257356	−	0.0576749i
$89$	5.92638	−	5.92638i	0.628195	−	0.628195i	−0.319419	−	0.947614i	$-0.603488\pi$
$89$	5.92638	−	5.92638i	0.628195	−	0.628195i	0.947614	+	0.319419i	$0.103488\pi$
$90$		0			0
$91$	2.60022	−	1.07705i	0.272577	−	0.112905i
$92$	10.3119	−	1.52660i	1.07509	−	0.159159i
$93$		0			0
$94$	−0.344951	−	0.685544i	−0.0355789	−	0.0707085i
$95$	2.38372			0.244564
$96$		0			0
$97$	−4.19951			−0.426396			−0.213198	−	0.977009i	$-0.568388\pi$
$97$	−4.19951			−0.426396			−0.213198	+	0.977009i	$0.568388\pi$
$98$	0.837733	+	1.66488i	0.0846238	+	0.168179i
$99$		0			0
$100$	1.29289	+	8.73324i	0.129289	+	0.873324i
$101$	−4.46191	+	1.84819i	−0.443977	+	0.183901i	−0.593461	−	0.804863i	$-0.702239\pi$
$101$	−4.46191	+	1.84819i	−0.443977	+	0.183901i	0.149484	+	0.988764i	$0.452239\pi$
$102$		0			0
$103$	10.9635	−	10.9635i	1.08027	−	1.08027i	0.0837844	−	0.996484i	$-0.473299\pi$
$103$	10.9635	−	10.9635i	1.08027	−	1.08027i	0.996484	−	0.0837844i	$-0.0267007\pi$
$104$	1.78785	−	2.82064i	0.175313	−	0.276587i
$105$		0			0
$106$	10.9658	+	9.46191i	1.06509	+	0.919022i
$107$	−3.34737	−	8.08128i	−0.323603	−	0.781246i	−0.999039	−	0.0438280i	$-0.986045\pi$
$107$	−3.34737	−	8.08128i	−0.323603	−	0.781246i	0.675436	−	0.737418i	$-0.263955\pi$
$108$		0			0
$109$	8.62086	+	3.57088i	0.825728	+	0.342028i	0.755210	−	0.655483i	$-0.227535\pi$
$109$	8.62086	+	3.57088i	0.825728	+	0.342028i	0.0705180	+	0.997511i	$0.477535\pi$
$110$	−0.898966	−	0.297121i	−0.0857131	−	0.0283294i
$111$		0			0
$112$	−8.40643	−	4.49954i	−0.794333	−	0.425166i
$113$			2.42429i			0.228058i	0.993477	+	0.114029i	$0.0363757\pi$
$113$			2.42429i			0.228058i	−0.993477	+	0.114029i	$0.963624\pi$
$114$		0			0
$115$	−3.68554	−	1.52660i	−0.343679	−	0.142356i
$116$	6.30055	+	10.5187i	0.584991	+	0.976634i
$117$		0			0
$118$	3.36524	−	3.90011i	0.309795	−	0.359035i
$119$	−0.378872	−	0.378872i	−0.0347312	−	0.0347312i
$120$		0			0
$121$	7.23714	−	7.23714i	0.657921	−	0.657921i
$122$	−0.108161	−	1.46917i	−0.00979239	−	0.133012i
$123$		0			0
$124$	8.13853	−	10.9670i	0.730861	−	0.984861i
$125$	2.75736	−	6.65685i	0.246626	−	0.595407i
$126$		0			0
$127$	−2.19266			−0.194567			−0.0972836	−	0.995257i	$-0.531015\pi$
$127$	−2.19266			−0.194567			−0.0972836	+	0.995257i	$0.531015\pi$
$128$	−11.2300	+	1.37364i	−0.992602	+	0.121414i
$129$		0			0
$130$	−1.14161	+	0.574431i	−0.100126	+	0.0503810i
$131$	−3.16317	+	7.63657i	−0.276367	+	0.667210i	−0.999729	−	0.0232589i	$-0.992596\pi$
$131$	−3.16317	+	7.63657i	−0.276367	+	0.667210i	0.723362	+	0.690469i	$0.242596\pi$
$132$		0			0
$133$	−6.85892	+	2.84106i	−0.594744	+	0.246351i
$134$	−0.401855	−	5.45849i	−0.0347150	−	0.471541i
$135$		0			0
$136$	−0.626360	−	0.108961i	−0.0537099	−	0.00934337i
$137$	−7.76744	−	7.76744i	−0.663617	−	0.663617i	0.292614	−	0.956231i	$-0.405475\pi$
$137$	−7.76744	−	7.76744i	−0.663617	−	0.663617i	−0.956231	+	0.292614i	$0.905475\pi$
$138$		0			0
$139$	0.357453	+	0.862967i	0.0303188	+	0.0731959i	0.938314	−	0.345785i	$-0.112387\pi$
$139$	0.357453	+	0.862967i	0.0303188	+	0.0731959i	−0.907995	+	0.418981i	$0.862387\pi$
$140$	1.87498	+	3.13025i	0.158465	+	0.264555i
$141$		0			0
$142$	3.38909	−	10.2540i	0.284406	−	0.860496i
$143$			1.03279i			0.0863662i
$144$		0			0
$145$		−	4.69220i		−	0.389666i
$146$	−9.79666	−	3.23794i	−0.810777	−	0.267974i
$147$		0			0
$148$	−5.20079	+	20.7375i	−0.427502	+	1.70461i
$149$	−2.34610	−	5.66398i	−0.192200	−	0.464011i	0.798175	−	0.602426i	$-0.205799\pi$
$149$	−2.34610	−	5.66398i	−0.192200	−	0.464011i	−0.990374	+	0.138415i	$0.955799\pi$
$150$		0			0
$151$	−8.17083	−	8.17083i	−0.664932	−	0.664932i	0.291606	−	0.956538i	$-0.405810\pi$
$151$	−8.17083	−	8.17083i	−0.664932	−	0.664932i	−0.956538	+	0.291606i	$0.905810\pi$
$152$	−4.71604	+	7.44035i	−0.382521	+	0.603492i
$153$		0			0
$154$	2.94082	−	0.216503i	0.236978	−	0.0174463i
$155$	−4.82843	+	2.00000i	−0.387829	+	0.160644i
$156$		0			0
$157$	4.88391	−	11.7908i	0.389779	−	0.941009i	−0.600208	−	0.799844i	$-0.704915\pi$
$157$	4.88391	−	11.7908i	0.389779	−	0.941009i	0.989986	−	0.141164i	$-0.0450846\pi$
$158$	5.33461	+	10.6018i	0.424399	+	0.843437i
$159$		0			0
$160$	3.95687	+	1.75736i	0.312818	+	0.138931i
$161$	12.4243			0.979171
$162$		0			0
$163$	0.753131	−	1.81822i	0.0589898	−	0.142414i	−0.891636	−	0.452752i	$-0.850442\pi$
$163$	0.753131	−	1.81822i	0.0589898	−	0.142414i	0.950626	+	0.310338i	$0.100442\pi$
$164$	−17.8259	+	2.63899i	−1.39197	+	0.206071i
$165$		0			0
$166$	−17.1254	+	1.26078i	−1.32919	+	0.0978552i
$167$	15.1630	−	15.1630i	1.17335	−	1.17335i	0.191946	−	0.981406i	$-0.438520\pi$
$167$	15.1630	−	15.1630i	1.17335	−	1.17335i	0.981406	−	0.191946i	$-0.0614798\pi$
$168$		0			0
$169$	−8.20664	−	8.20664i	−0.631280	−	0.631280i
$170$	0.184204	+	0.158942i	0.0141278	+	0.0121903i
$171$		0			0
$172$	9.67164	+	2.42557i	0.737455	+	0.184948i
$173$	−4.54817	−	1.88391i	−0.345791	−	0.143231i	0.203027	−	0.979173i	$-0.434922\pi$
$173$	−4.54817	−	1.88391i	−0.345791	−	0.143231i	−0.548818	+	0.835942i	$0.684922\pi$
$174$		0			0
$175$			10.5222i			0.795407i
$176$	2.70596	−	2.21813i	0.203969	−	0.167198i
$177$		0			0
$178$	3.71961	−	11.2540i	0.278796	−	0.843523i
$179$	−7.27899	−	3.01505i	−0.544057	−	0.225356i	0.0936904	−	0.995601i	$-0.470134\pi$
$179$	−7.27899	−	3.01505i	−0.544057	−	0.225356i	−0.637747	+	0.770246i	$0.720134\pi$
$180$		0			0
$181$	6.12132	+	14.7782i	0.454994	+	1.09845i	0.970399	+	0.241506i	$0.0776415\pi$
$181$	6.12132	+	14.7782i	0.454994	+	1.09845i	−0.515405	+	0.856947i	$0.672359\pi$
$182$	2.60022	−	3.01351i	0.192741	−	0.223376i
$183$		0			0
$184$	12.0566	−	8.48348i	0.888827	−	0.625410i
$185$	5.78530	−	5.78530i	0.425344	−	0.425344i
$186$		0			0
$187$	0.181652	−	0.0752426i	0.0132837	−	0.00550228i
$188$	−0.871553	−	0.646775i	−0.0635645	−	0.0471709i
$189$		0			0
$190$	3.01136	−	1.51525i	0.218467	−	0.109928i
$191$	15.4642			1.11895			0.559475	−	0.828847i	$-0.311003\pi$
$191$	15.4642			1.11895			0.559475	+	0.828847i	$0.311003\pi$
$192$		0			0
$193$	13.2206			0.951640			0.475820	−	0.879543i	$-0.342151\pi$
$193$	13.2206			0.951640			0.475820	+	0.879543i	$0.342151\pi$
$194$	−5.30525	+	2.66949i	−0.380895	+	0.191658i
$195$		0			0
$196$	2.11662	+	1.57073i	0.151187	+	0.112195i
$197$	0.602992	−	0.249768i	0.0429614	−	0.0177952i	−0.361099	−	0.932527i	$-0.617598\pi$
$197$	0.602992	−	0.249768i	0.0429614	−	0.0177952i	0.404061	+	0.914732i	$0.367598\pi$
$198$		0			0
$199$	−1.86490	+	1.86490i	−0.132199	+	0.132199i	−0.770110	−	0.637911i	$-0.779799\pi$
$199$	−1.86490	+	1.86490i	−0.132199	+	0.132199i	0.637911	+	0.770110i	$0.279799\pi$
$200$	7.18473	+	10.2109i	0.508037	+	0.722018i
$201$		0			0
$202$	−4.46191	+	5.17110i	−0.313939	+	0.363837i
$203$	5.59244	+	13.5013i	0.392512	+	0.947608i
$204$		0			0
$205$	6.37109	+	2.63899i	0.444976	+	0.184315i
$206$	6.88110	−	20.8194i	0.479429	−	1.45055i
$207$		0			0
$208$	0.465613	−	4.69980i	0.0322845	−	0.325872i
$209$		−	2.72431i		−	0.188445i
$210$		0			0
$211$	−19.0338	−	7.88406i	−1.31034	−	0.542761i	−0.385357	−	0.922768i	$-0.625922\pi$
$211$	−19.0338	−	7.88406i	−1.31034	−	0.542761i	−0.924984	+	0.380007i	$0.875922\pi$
$212$	19.8677	+	4.98267i	1.36452	+	0.342211i
$213$		0			0
$214$	−9.36573	−	8.08128i	−0.640228	−	0.552425i
$215$	−2.69818	−	2.69818i	−0.184014	−	0.184014i
$216$		0			0
$217$	11.5096	−	11.5096i	0.781324	−	0.781324i
$218$	13.1606	−	0.968887i	0.891349	−	0.0656213i
$219$		0			0
$220$	−1.32453	+	0.196088i	−0.0893001	+	0.0132202i
$221$	0.101562	−	0.245193i	0.00683182	−	0.0164935i
$222$		0			0
$223$	−17.2119			−1.15259			−0.576297	−	0.817241i	$-0.695503\pi$
$223$	−17.2119			−1.15259			−0.576297	+	0.817241i	$0.695503\pi$
$224$	−13.4800	−	0.340593i	−0.900674	−	0.0227569i
$225$		0			0
$226$	1.54104	+	3.06261i	0.102508	+	0.203722i
$227$	0.629916	−	1.52075i	0.0418090	−	0.100936i	−0.901596	−	0.432580i	$-0.857603\pi$
$227$	0.629916	−	1.52075i	0.0418090	−	0.100936i	0.943405	+	0.331644i	$0.107603\pi$
$228$		0			0
$229$	2.45021	−	1.01491i	0.161915	−	0.0670672i	−0.300254	−	0.953859i	$-0.597071\pi$
$229$	2.45021	−	1.01491i	0.161915	−	0.0670672i	0.462169	+	0.886792i	$0.347071\pi$
$230$	−5.62636	+	0.414214i	−0.370991	+	0.0273124i
$231$		0			0
$232$	14.6458	+	9.28321i	0.961547	+	0.609473i
$233$	10.9475	+	10.9475i	0.717192	+	0.717192i	0.968029	−	0.250837i	$-0.0807058\pi$
$233$	10.9475	+	10.9475i	0.717192	+	0.717192i	−0.250837	+	0.968029i	$0.580706\pi$
$234$		0			0
$235$	0.158942	+	0.383719i	0.0103682	+	0.0250311i
$236$	1.77214	−	7.06618i	0.115357	−	0.459969i
$237$		0			0
$238$	−0.719466	−	0.237794i	−0.0466360	−	0.0154139i
$239$			18.2858i			1.18281i	0.806375	+	0.591404i	$0.201426\pi$
$239$			18.2858i			1.18281i	−0.806375	+	0.591404i	$0.798574\pi$
$240$		0			0
$241$			27.8155i			1.79176i	0.444300	+	0.895878i	$0.353452\pi$
$241$			27.8155i			1.79176i	−0.444300	+	0.895878i	$0.646548\pi$
$242$	4.54229	−	13.7431i	0.291989	−	0.883439i
$243$		0			0
$244$	−1.07054	−	1.78725i	−0.0685342	−	0.114417i
$245$	−0.385999	−	0.931884i	−0.0246606	−	0.0595359i
$246$		0			0
$247$	−2.60022	−	2.60022i	−0.165448	−	0.165448i
$248$	3.31010	−	19.0279i	0.210191	−	1.20828i
$249$		0			0
$250$	−0.748155	−	10.1624i	−0.0473175	−	0.642725i
$251$	−9.37694	+	3.88406i	−0.591867	+	0.245159i	−0.658454	−	0.752621i	$-0.728789\pi$
$251$	−9.37694	+	3.88406i	−0.591867	+	0.245159i	0.0665866	+	0.997781i	$0.478789\pi$
$252$		0			0
$253$	−1.74473	+	4.21215i	−0.109690	+	0.264815i
$254$	−2.76999	+	1.39380i	−0.173805	+	0.0874547i
$255$		0			0
$256$	−13.3137	+	8.87385i	−0.832107	+	0.554615i
$257$	−20.0656			−1.25166			−0.625828	−	0.779961i	$-0.715239\pi$
$257$	−20.0656			−1.25166			−0.625828	+	0.779961i	$0.715239\pi$
$258$		0			0
$259$	−9.75138	+	23.5419i	−0.605921	+	1.46282i
$260$	−1.07705	+	1.45136i	−0.0667956	+	0.0900095i
$261$		0			0
$262$	0.858264	+	11.6580i	0.0530237	+	0.720234i
$263$	−17.9782	+	17.9782i	−1.10858	+	1.10858i	−0.115244	+	0.993337i	$0.536765\pi$
$263$	−17.9782	+	17.9782i	−1.10858	+	1.10858i	−0.993337	+	0.115244i	$0.963235\pi$
$264$		0			0
$265$	−5.54266	−	5.54266i	−0.340483	−	0.340483i
$266$	−6.85892	+	7.94909i	−0.420547	+	0.487390i
$267$		0			0
$268$	−3.97743	−	6.64027i	−0.242960	−	0.405619i
$269$	25.6598	+	10.6286i	1.56451	+	0.648040i	0.985865	−	0.167543i	$-0.0535832\pi$
$269$	25.6598	+	10.6286i	1.56451	+	0.648040i	0.578641	+	0.815582i	$0.303583\pi$
$270$		0			0
$271$			16.4921i			1.00183i	0.865498	+	0.500913i	$0.167002\pi$
$271$			16.4921i			1.00183i	−0.865498	+	0.500913i	$0.832998\pi$
$272$	−0.860544	+	0.260504i	−0.0521781	+	0.0157954i
$273$		0			0
$274$	−14.7501	−	4.87512i	−0.891086	−	0.294517i
$275$	−3.56730	−	1.47763i	−0.215117	−	0.0891042i
$276$		0			0
$277$	−2.31978	−	5.60044i	−0.139382	−	0.336498i	0.838739	−	0.544533i	$-0.183293\pi$
$277$	−2.31978	−	5.60044i	−0.139382	−	0.336498i	−0.978121	+	0.208035i	$0.933293\pi$
$278$	1.00013	+	0.862967i	0.0599837	+	0.0517573i
$279$		0			0
$280$	4.35846	+	2.76259i	0.260468	+	0.165096i
$281$	−9.80801	+	9.80801i	−0.585097	+	0.585097i	−0.936299	−	0.351203i	$-0.885773\pi$
$281$	−9.80801	+	9.80801i	−0.585097	+	0.585097i	0.351203	+	0.936299i	$0.385773\pi$
$282$		0			0
$283$	21.3627	−	8.84871i	1.26988	−	0.526001i	0.356952	−	0.934123i	$-0.383816\pi$
$283$	21.3627	−	8.84871i	1.26988	−	0.526001i	0.912928	+	0.408121i	$0.133816\pi$
$284$	−2.23666	−	15.1082i	−0.132721	−	0.896508i
$285$		0			0
$286$	0.656508	+	1.30472i	0.0388201	+	0.0771499i
$287$	−21.4775			−1.26778
$288$		0			0
$289$	16.9495			0.997028
$290$	−2.98267	−	5.92766i	−0.175148	−	0.348084i
$291$		0			0
$292$	−14.4344	+	2.13690i	−0.844708	+	0.125053i
$293$	−20.4415	+	8.46715i	−1.19421	+	0.494656i	−0.889122	−	0.457670i	$-0.848684\pi$
$293$	−20.4415	+	8.46715i	−1.19421	+	0.494656i	−0.305083	+	0.952326i	$0.598684\pi$
$294$		0			0
$295$	−1.97131	+	1.97131i	−0.114774	+	0.114774i
$296$	6.61192	+	29.5036i	0.384310	+	1.71486i
$297$		0			0
$298$	−6.56422	−	5.66398i	−0.380255	−	0.328106i
$299$	2.35503	+	5.68554i	0.136195	+	0.328803i
$300$		0			0
$301$	10.9796	+	4.54789i	0.632853	+	0.262136i
$302$	−15.5161	−	5.12830i	−0.892852	−	0.295101i
$303$		0			0
$304$	−1.22820	+	12.3972i	−0.0704424	+	0.711030i
$305$			0.797261i			0.0456510i
$306$		0			0
$307$	−15.6196	−	6.46984i	−0.891456	−	0.369253i	−0.110527	−	0.993873i	$-0.535254\pi$
$307$	−15.6196	−	6.46984i	−0.891456	−	0.369253i	−0.780929	+	0.624620i	$0.785254\pi$
$308$	3.57751	−	2.14288i	0.203848	−	0.122102i
$309$		0			0
$310$	−4.82843	+	5.59587i	−0.274236	+	0.317824i
$311$	−7.24929	−	7.24929i	−0.411070	−	0.411070i	0.471041	−	0.882111i	$-0.343878\pi$
$311$	−7.24929	−	7.24929i	−0.411070	−	0.411070i	−0.882111	+	0.471041i	$0.843878\pi$
$312$		0			0
$313$	−10.1596	+	10.1596i	−0.574255	+	0.574255i	−0.933315	−	0.359059i	$-0.883098\pi$
$313$	−10.1596	+	10.1596i	−0.574255	+	0.574255i	0.359059	+	0.933315i	$0.383098\pi$
$314$	−1.32515	−	17.9999i	−0.0747827	−	1.01579i
$315$		0			0
$316$	13.4784	+	10.0023i	0.758222	+	0.562673i
$317$	1.34287	−	3.24198i	0.0754233	−	0.182088i	−0.881671	−	0.471865i	$-0.843581\pi$
$317$	1.34287	−	3.24198i	0.0754233	−	0.182088i	0.957094	+	0.289777i	$0.0935811\pi$
$318$		0			0
$319$	−5.36263			−0.300250
$320$	6.11582	−	0.295173i	0.341885	−	0.0165007i
$321$		0			0
$322$	15.6956	−	7.89769i	0.874683	−	0.440121i
$323$	−0.267903	+	0.646775i	−0.0149065	+	0.0359875i
$324$		0			0
$325$	−4.81514	+	1.99450i	−0.267096	+	0.110635i
$326$	−0.204347	−	2.77570i	−0.0113178	−	0.153732i
$327$		0			0
$328$	−20.8419	+	14.6651i	−1.15080	+	0.809746i
$329$	−0.914679	−	0.914679i	−0.0504279	−	0.0504279i
$330$		0			0
$331$	6.43270	+	15.5299i	0.353573	+	0.853601i	0.996173	+	0.0873991i	$0.0278555\pi$
$331$	6.43270	+	15.5299i	0.353573	+	0.853601i	−0.642600	+	0.766201i	$0.722144\pi$
$332$	−20.8331	+	12.4788i	−1.14337	+	0.684862i
$333$		0			0
$334$	9.51687	−	28.7941i	0.520740	−	1.57554i
$335$			2.96211i			0.161837i
$336$		0			0
$337$		−	2.10641i		−	0.114743i	−0.998353	−	0.0573717i	$-0.981728\pi$
$337$		−	2.10641i		−	0.114743i	0.998353	−	0.0573717i	$-0.0182720\pi$
$338$	−15.5841	−	5.15078i	−0.847665	−	0.280166i
$339$		0			0
$340$	0.333739	+	0.0836990i	0.0180995	+	0.00453922i
$341$	2.28577	+	5.51833i	0.123781	+	0.298834i
$342$		0			0
$343$	14.0202	+	14.0202i	0.757017	+	0.757017i
$344$	13.7600	−	3.08370i	0.741892	−	0.166262i
$345$		0			0
$346$	−6.94324	+	0.511162i	−0.373271	+	0.0274803i
$347$	12.3896	−	5.13193i	0.665107	−	0.275496i	−0.0244788	−	0.999700i	$-0.507793\pi$
$347$	12.3896	−	5.13193i	0.665107	−	0.275496i	0.689586	+	0.724204i	$0.257793\pi$
$348$		0			0
$349$	7.52453	−	18.1658i	0.402779	−	0.972394i	−0.584210	−	0.811603i	$-0.698596\pi$
$349$	7.52453	−	18.1658i	0.402779	−	0.972394i	0.986988	−	0.160791i	$-0.0514045\pi$
$350$	6.68862	+	13.2928i	0.357522	+	0.710528i
$351$		0			0
$352$	2.00846	−	4.52225i	0.107051	−	0.241036i
$353$	28.7013			1.52762			0.763809	−	0.645442i	$-0.223327\pi$
$353$	28.7013			1.52762			0.763809	+	0.645442i	$0.223327\pi$
$354$		0			0
$355$	−2.23666	+	5.39978i	−0.118710	+	0.286590i
$356$	−2.45479	−	16.5816i	−0.130103	−	0.878824i
$357$		0			0
$358$	−11.1121	+	0.818076i	−0.587294	+	0.0432367i
$359$	−6.39199	+	6.39199i	−0.337356	+	0.337356i	−0.855372	−	0.518015i	$-0.826671\pi$
$359$	−6.39199	+	6.39199i	−0.337356	+	0.337356i	0.518015	+	0.855372i	$0.326671\pi$
$360$		0			0
$361$	−6.57611	−	6.57611i	−0.346111	−	0.346111i
$362$	17.1270	+	14.7782i	0.900177	+	0.776724i
$363$		0			0
$364$	1.36928	−	5.45984i	0.0717699	−	0.286173i
$365$	5.15894	+	2.13690i	0.270031	+	0.111851i
$366$		0			0
$367$		−	14.5985i		−	0.762038i	−0.924567	−	0.381019i	$-0.875573\pi$
$367$		−	14.5985i		−	0.762038i	0.924567	−	0.381019i	$-0.124427\pi$
$368$	9.83851	−	18.3812i	0.512868	−	0.958185i
$369$		0			0
$370$	3.63106	−	10.9861i	0.188770	−	0.571140i
$371$	22.5545	+	9.34240i	1.17097	+	0.485033i
$372$		0			0
$373$	−6.03762	−	14.5761i	−0.312616	−	0.754722i	−0.999606	−	0.0280555i	$-0.991068\pi$
$373$	−6.03762	−	14.5761i	−0.312616	−	0.754722i	0.686990	−	0.726667i	$-0.258932\pi$
$374$	0.181652	−	0.210524i	0.00939299	−	0.0108859i
$375$		0			0
$376$	−1.51217	−	0.263056i	−0.0779840	−	0.0135661i
$377$	−5.11837	+	5.11837i	−0.263609	+	0.263609i
$378$		0			0
$379$	−5.68312	+	2.35403i	−0.291922	+	0.120918i	−0.523839	−	0.851818i	$-0.675500\pi$
$379$	−5.68312	+	2.35403i	−0.291922	+	0.120918i	0.231916	+	0.972736i	$0.425500\pi$
$380$	2.84106	−	3.82843i	0.145743	−	0.196394i
$381$		0			0
$382$	19.5359	−	9.83005i	0.999545	−	0.502949i
$383$	−12.4633			−0.636843			−0.318422	−	0.947949i	$-0.603153\pi$
$383$	−12.4633			−0.636843			−0.318422	+	0.947949i	$0.603153\pi$
$384$		0			0
$385$	−1.59587			−0.0813328
$386$	16.7016	−	8.40388i	0.850089	−	0.427746i
$387$		0			0
$388$	−5.00523	+	6.74473i	−0.254102	+	0.342412i
$389$	14.1298	−	5.85275i	0.716408	−	0.296746i	0.00545476	−	0.999985i	$-0.498264\pi$
$389$	14.1298	−	5.85275i	0.716408	−	0.296746i	0.710953	+	0.703239i	$0.248264\pi$
$390$		0			0
$391$	0.828427	−	0.828427i	0.0418954	−	0.0418954i
$392$	3.67238	+	0.638848i	0.185483	+	0.0322667i
$393$		0			0
$394$	0.602992	−	0.698833i	0.0303783	−	0.0352067i
$395$	−2.45801	−	5.93416i	−0.123676	−	0.298580i
$396$		0			0
$397$	−25.5736	−	10.5929i	−1.28350	−	0.531643i	−0.366458	−	0.930434i	$-0.619430\pi$
$397$	−25.5736	−	10.5929i	−1.28350	−	0.531643i	−0.917042	+	0.398791i	$0.869430\pi$
$398$	−1.17048	+	3.54138i	−0.0586708	+	0.177514i
$399$		0			0
$400$	15.5672	+	8.33232i	0.778359	+	0.416616i
$401$			16.5018i			0.824062i	0.911170	+	0.412031i	$0.135180\pi$
$401$			16.5018i			0.824062i	−0.911170	+	0.412031i	$0.864820\pi$
$402$		0			0
$403$	7.44862	+	3.08532i	0.371042	+	0.153691i
$404$	−2.34965	+	9.36894i	−0.116900	+	0.466122i
$405$		0			0
$406$	15.6473	+	13.5013i	0.776561	+	0.670060i
$407$	−6.61192	−	6.61192i	−0.327741	−	0.327741i
$408$		0			0
$409$	1.28577	−	1.28577i	0.0635771	−	0.0635771i	−0.674603	−	0.738180i	$-0.735685\pi$
$409$	1.28577	−	1.28577i	0.0635771	−	0.0635771i	0.738180	+	0.674603i	$0.235685\pi$
$410$	9.72612	−	0.716038i	0.480339	−	0.0353626i
$411$		0			0
$412$	−4.54124	−	30.6752i	−0.223731	−	1.51126i
$413$	3.32273	−	8.02178i	0.163501	−	0.394726i
$414$		0			0
$415$	9.29329			0.456190
$416$	−2.39929	−	6.23323i	−0.117635	−	0.305609i
$417$		0			0
$418$	−1.73175	−	3.44163i	−0.0847027	−	0.168335i
$419$	14.9887	−	36.1858i	0.732244	−	1.76779i	0.0972723	−	0.995258i	$-0.468988\pi$
$419$	14.9887	−	36.1858i	0.732244	−	1.76779i	0.634972	−	0.772535i	$-0.281012\pi$
$420$		0			0
$421$	13.6131	−	5.63872i	0.663460	−	0.274814i	−0.0254334	−	0.999677i	$-0.508097\pi$
$421$	13.6131	−	5.63872i	0.663460	−	0.274814i	0.688894	+	0.724862i	$0.258097\pi$
$422$	−29.0570	+	2.13918i	−1.41447	+	0.104134i
$423$		0			0
$424$	28.2662	−	6.33461i	1.37273	−	0.307636i
$425$	0.701602	+	0.701602i	0.0340327	+	0.0340327i
$426$		0			0
$427$	−0.950223	−	2.29404i	−0.0459845	−	0.111016i
$428$	−16.9687	−	4.25562i	−0.820214	−	0.205703i
$429$		0			0
$430$	−5.12374	−	1.69347i	−0.247089	−	0.0816665i
$431$		−	2.85730i		−	0.137631i	−0.997629	−	0.0688156i	$-0.978078\pi$
$431$		−	2.85730i		−	0.137631i	0.997629	−	0.0688156i	$-0.0219220\pi$
$432$		0			0
$433$			22.5174i			1.08212i	0.840985	+	0.541059i	$0.181976\pi$
$433$			22.5174i			1.08212i	−0.840985	+	0.541059i	$0.818024\pi$
$434$	7.22385	−	21.8564i	0.346756	−	1.04914i
$435$		0			0
$436$	16.0099	−	9.58974i	0.766737	−	0.459265i
$437$	−6.21215	−	14.9974i	−0.297167	−	0.717425i
$438$		0			0
$439$	−8.87727	−	8.87727i	−0.423689	−	0.423689i	0.462783	−	0.886472i	$-0.346851\pi$
$439$	−8.87727	−	8.87727i	−0.423689	−	0.423689i	−0.886472	+	0.462783i	$0.846851\pi$
$440$	−1.54864	+	1.08968i	−0.0738285	+	0.0519484i
$441$		0			0
$442$	−0.0275569	−	0.374312i	−0.00131075	−	0.0178042i
$443$	23.7377	−	9.83247i	1.12781	−	0.467155i	0.260775	−	0.965400i	$-0.416022\pi$
$443$	23.7377	−	9.83247i	1.12781	−	0.467155i	0.867036	+	0.498245i	$0.166022\pi$
$444$		0			0
$445$	−2.45479	+	5.92638i	−0.116368	+	0.280937i
$446$	−21.7438	+	10.9410i	−1.02960	+	0.518071i
$447$		0			0
$448$	−17.2459	+	8.13853i	−0.814791	+	0.384509i
$449$	−8.83528			−0.416963			−0.208481	−	0.978026i	$-0.566852\pi$
$449$	−8.83528			−0.416963			−0.208481	+	0.978026i	$0.566852\pi$
$450$		0			0
$451$	3.01606	−	7.28141i	0.142021	−	0.342868i
$452$	3.89359	+	2.88942i	0.183139	+	0.135907i
$453$		0			0
$454$	−0.170915	−	2.32158i	−0.00802145	−	0.108957i
$455$	−1.52318	+	1.52318i	−0.0714075	+	0.0714075i
$456$		0			0
$457$	7.58808	+	7.58808i	0.354955	+	0.354955i	0.861950	−	0.506994i	$-0.169243\pi$
$457$	7.58808	+	7.58808i	0.354955	+	0.354955i	−0.506994	+	0.861950i	$0.669243\pi$
$458$	2.45021	−	2.83965i	0.114491	−	0.132688i
$459$		0			0
$460$	−6.84449	+	4.09976i	−0.319126	+	0.191152i
$461$	−15.2534	−	6.31816i	−0.710421	−	0.294266i	−0.00194197	−	0.999998i	$-0.500618\pi$
$461$	−15.2534	−	6.31816i	−0.710421	−	0.294266i	−0.708479	+	0.705732i	$0.750618\pi$
$462$		0			0
$463$		−	18.7996i		−	0.873689i	−0.899537	−	0.436845i	$-0.856096\pi$
$463$		−	18.7996i		−	0.873689i	0.899537	−	0.436845i	$-0.143904\pi$
$464$	24.4031	+	2.41764i	1.13289	+	0.112236i
$465$		0			0
$466$	20.7889	+	6.87102i	0.963026	+	0.318294i
$467$	−9.28999	−	3.84804i	−0.429890	−	0.178066i	0.157238	−	0.987561i	$-0.449741\pi$
$467$	−9.28999	−	3.84804i	−0.429890	−	0.178066i	−0.587127	+	0.809495i	$0.699741\pi$
$468$		0			0
$469$	−3.53041	−	8.52318i	−0.163019	−	0.393564i
$470$	0.444708	+	0.383719i	0.0205129	+	0.0176996i
$471$		0			0
$472$	−2.25298	−	10.0532i	−0.103702	−	0.462736i
$473$	−3.08370	+	3.08370i	−0.141789	+	0.141789i
$474$		0			0
$475$	12.7015	−	5.26112i	0.582784	−	0.241397i
$476$	−1.06006	+	0.156934i	−0.0485877	+	0.00719306i
$477$		0			0
$478$	11.6236	+	23.1004i	0.531652	+	1.05659i
$479$	14.7779			0.675220			0.337610	−	0.941286i	$-0.390382\pi$
$479$	14.7779			0.675220			0.337610	+	0.941286i	$0.390382\pi$
$480$		0			0
$481$	−12.6215			−0.575491
$482$	17.6814	+	35.1394i	0.805364	+	1.60056i
$483$		0			0
$484$	−2.99772	−	20.2490i	−0.136260	−	0.920410i
$485$	2.96951	−	1.23001i	0.134838	−	0.0558519i
$486$		0			0
$487$	13.0855	−	13.0855i	0.592961	−	0.592961i	−0.345469	−	0.938430i	$-0.612280\pi$
$487$	13.0855	−	13.0855i	0.592961	−	0.592961i	0.938430	+	0.345469i	$0.112280\pi$
$488$	−2.48851	−	1.57733i	−0.112649	−	0.0714024i
$489$		0			0
$490$	−1.08000	−	0.931884i	−0.0487894	−	0.0420982i
$491$	11.7944	+	28.4741i	0.532273	+	1.28502i	0.930015	+	0.367523i	$0.119794\pi$
$491$	11.7944	+	28.4741i	0.532273	+	1.28502i	−0.397742	+	0.917497i	$0.630206\pi$
$492$		0			0
$493$	1.27314	+	0.527350i	0.0573391	+	0.0237506i
$494$	−4.93773	−	1.63199i	−0.222159	−	0.0734268i
$495$		0			0
$496$	−7.91375	−	26.1421i	−0.355338	−	1.17382i
$497$		−	18.2031i		−	0.816522i
$498$		0			0
$499$	22.4253	+	9.28886i	1.00389	+	0.415827i	0.823224	−	0.567717i	$-0.192173\pi$
$499$	22.4253	+	9.28886i	1.00389	+	0.415827i	0.180670	+	0.983544i	$0.442173\pi$
$500$	−7.40501	−	12.3626i	−0.331162	−	0.552870i
$501$		0			0
$502$	−9.37694	+	10.8673i	−0.418513	+	0.485032i
$503$	−23.5062	−	23.5062i	−1.04809	−	1.04809i	−0.998784	−	0.0493053i	$-0.984299\pi$
$503$	−23.5062	−	23.5062i	−1.04809	−	1.04809i	−0.0493053	−	0.998784i	$-0.515701\pi$
$504$		0			0
$505$	2.61373	−	2.61373i	0.116309	−	0.116309i
$506$	0.473398	+	6.43027i	0.0210451	+	0.285860i
$507$		0			0
$508$	−2.61334	+	3.52157i	−0.115948	+	0.156245i
$509$	13.1651	−	31.7834i	0.583534	−	1.40877i	−0.306056	−	0.952014i	$-0.599009\pi$
$509$	13.1651	−	31.7834i	0.583534	−	1.40877i	0.889589	−	0.456761i	$-0.150991\pi$
$510$		0			0
$511$	−17.3912			−0.769343
$512$	−11.1784	+	19.6734i	−0.494021	+	0.869450i
$513$		0			0
$514$	−25.3489	+	12.7550i	−1.11809	+	0.562598i
$515$	−4.54124	+	10.9635i	−0.200111	+	0.483111i
$516$		0			0
$517$	0.438546	−	0.181652i	0.0192872	−	0.00798903i
$518$	2.64585	+	35.9391i	0.116252	+	1.57908i
$519$		0			0
$520$	−0.438056	+	2.51815i	−0.0192100	+	0.110428i
$521$	10.8936	+	10.8936i	0.477257	+	0.477257i	0.904253	−	0.426996i	$-0.140428\pi$
$521$	10.8936	+	10.8936i	0.477257	+	0.477257i	−0.426996	+	0.904253i	$0.640428\pi$
$522$		0			0
$523$	−6.48657	−	15.6600i	−0.283638	−	0.684763i	0.716277	−	0.697816i	$-0.245845\pi$
$523$	−6.48657	−	15.6600i	−0.283638	−	0.684763i	−0.999915	+	0.0130536i	$0.995845\pi$
$524$	8.49483	+	14.1820i	0.371098	+	0.619543i
$525$		0			0
$526$	−11.2837	+	34.1399i	−0.491995	+	1.48857i
$527$		−	1.53488i		−	0.0668603i
$528$		0			0
$529$			4.16647i			0.181151i
$530$	−10.5253	−	3.47877i	−0.457191	−	0.151108i
$531$		0			0
$532$	−3.61192	+	14.4021i	−0.156597	+	0.624409i
$533$	−4.07107	−	9.82843i	−0.176338	−	0.425716i
$534$		0			0
$535$	4.73390	+	4.73390i	0.204664	+	0.204664i
$536$	−9.24568	−	5.86034i	−0.399353	−	0.253128i
$537$		0			0
$538$	39.1723	−	2.88387i	1.68884	−	0.124333i
$539$	−1.06503	+	0.441152i	−0.0458743	+	0.0190018i
$540$		0			0
$541$	1.10183	−	2.66006i	0.0473716	−	0.114365i	−0.898422	−	0.439132i	$-0.855286\pi$
$541$	1.10183	−	2.66006i	0.0473716	−	0.114365i	0.945794	+	0.324767i	$0.105286\pi$
$542$	10.4835	+	20.8345i	0.450304	+	0.894920i
$543$		0			0
$544$	−0.921533	+	0.876113i	−0.0395104	+	0.0375630i
$545$	−7.14175			−0.305919
$546$		0			0
$547$	10.4159	−	25.1462i	0.445351	−	1.07517i	−0.528693	−	0.848813i	$-0.677318\pi$
$547$	10.4159	−	25.1462i	0.445351	−	1.07517i	0.974044	−	0.226360i	$-0.0726825\pi$
$548$	−21.7328	+	3.21738i	−0.928378	+	0.137440i
$549$		0			0
$550$	−5.44586	+	0.400925i	−0.232212	+	0.0170955i
$551$	13.5013	−	13.5013i	0.575176	−	0.575176i
$552$		0			0
$553$	14.1454	+	14.1454i	0.601523	+	0.601523i
$554$	−6.49058	−	5.60044i	−0.275758	−	0.237940i
$555$		0			0
$556$	1.81202	+	0.454441i	0.0768469	+	0.0192726i
$557$	−26.4367	−	10.9504i	−1.12016	−	0.463984i	−0.255733	−	0.966748i	$-0.582317\pi$
$557$	−26.4367	−	10.9504i	−1.12016	−	0.463984i	−0.864424	+	0.502763i	$0.832317\pi$
$558$		0			0
$559$			5.88648i			0.248972i
$560$	7.26213	+	0.719466i	0.306881	+	0.0304030i
$561$		0			0
$562$	−6.15586	+	18.6251i	−0.259669	+	0.785652i
$563$	22.9131	+	9.49093i	0.965673	+	0.399995i	0.809100	−	0.587671i	$-0.199955\pi$
$563$	22.9131	+	9.49093i	0.965673	+	0.399995i	0.156574	+	0.987666i	$0.449955\pi$
$564$		0			0
$565$	−0.710059	−	1.71423i	−0.0298724	−	0.0721184i
$566$	21.3627	−	24.7581i	0.897941	−	1.04066i
$567$		0			0
$568$	−12.4293	−	17.6645i	−0.521524	−	0.741184i
$569$	−12.2981	+	12.2981i	−0.515565	+	0.515565i	−0.916226	−	0.400661i	$-0.868780\pi$
$569$	−12.2981	+	12.2981i	−0.515565	+	0.515565i	0.400661	+	0.916226i	$0.368780\pi$
$570$		0			0
$571$	4.93839	−	2.04555i	0.206665	−	0.0856036i	−0.276950	−	0.960884i	$-0.589324\pi$
$571$	4.93839	−	2.04555i	0.206665	−	0.0856036i	0.483615	+	0.875281i	$0.339324\pi$
$572$	1.65873	+	1.23094i	0.0693552	+	0.0514682i
$573$		0			0
$574$	−27.1325	+	13.6525i	−1.13249	+	0.569844i
$575$	−23.0075			−0.959480
$576$		0			0
$577$	2.06423			0.0859352			0.0429676	−	0.999076i	$-0.486319\pi$
$577$	2.06423			0.0859352			0.0429676	+	0.999076i	$0.486319\pi$
$578$	21.4123	−	10.7742i	0.890634	−	0.448147i
$579$		0			0
$580$	−7.53601	−	5.59244i	−0.312916	−	0.232213i
$581$	−26.7406	+	11.0763i	−1.10939	+	0.459522i
$582$		0			0
$583$	−6.33461	+	6.33461i	−0.262353	+	0.262353i
$584$	−16.8766	+	11.8750i	−0.698359	+	0.491390i
$585$		0			0
$586$	−20.4415	+	23.6905i	−0.844431	+	0.978646i
$587$	−8.74223	−	21.1056i	−0.360830	−	0.871122i	−0.995179	−	0.0980746i	$-0.968732\pi$
$587$	−8.74223	−	21.1056i	−0.360830	−	0.871122i	0.634349	−	0.773047i	$-0.281268\pi$
$588$		0			0
$589$	−19.6481	−	8.13853i	−0.809588	−	0.335342i
$590$	−1.23727	+	3.74345i	−0.0509374	+	0.154115i
$591$		0			0
$592$	27.1073	+	33.0690i	1.11410	+	1.35913i
$593$			24.2771i			0.996939i	0.866907	+	0.498470i	$0.166104\pi$
$593$			24.2771i			0.996939i	−0.866907	+	0.498470i	$0.833896\pi$
$594$		0			0
$595$	0.378872	+	0.156934i	0.0155322	+	0.00643367i
$596$	−11.8930	−	2.98267i	−0.487156	−	0.122175i
$597$		0			0
$598$	6.58921	+	5.68554i	0.269453	+	0.232499i
$599$	33.3626	+	33.3626i	1.36316	+	1.36316i	0.869862	+	0.493295i	$0.164208\pi$
$599$	33.3626	+	33.3626i	1.36316	+	1.36316i	0.493295	+	0.869862i	$0.335792\pi$
$600$		0			0
$601$	−21.0676	+	21.0676i	−0.859365	+	0.859365i	−0.991263	−	0.131898i	$-0.957893\pi$
$601$	−21.0676	+	21.0676i	−0.859365	+	0.859365i	0.131898	+	0.991263i	$0.457893\pi$
$602$	16.7615	−	1.23398i	0.683146	−	0.0502933i
$603$		0			0
$604$	−22.8614	+	3.38447i	−0.930218	+	0.137712i
$605$	−2.99772	+	7.23714i	−0.121875	+	0.294231i
$606$		0			0
$607$	3.82750			0.155353			0.0776767	−	0.996979i	$-0.475250\pi$
$607$	3.82750			0.155353			0.0776767	+	0.996979i	$0.475250\pi$
$608$	6.32889	+	16.4422i	0.256670	+	0.666817i
$609$		0			0
$610$	0.506791	+	1.00718i	0.0205194	+	0.0407795i
$611$	0.245193	−	0.591948i	0.00991945	−	0.0239477i
$612$		0			0
$613$	−29.0883	+	12.0488i	−1.17486	+	0.486645i	−0.882798	−	0.469753i	$-0.844343\pi$
$613$	−29.0883	+	12.0488i	−1.17486	+	0.486645i	−0.292067	+	0.956398i	$0.594343\pi$
$614$	−23.8449	+	1.75546i	−0.962301	+	0.0708448i
$615$		0			0
$616$	3.15732	−	4.98121i	0.127212	−	0.200699i
$617$	−22.2479	−	22.2479i	−0.895666	−	0.895666i	0.0993836	−	0.995049i	$-0.468313\pi$
$617$	−22.2479	−	22.2479i	−0.895666	−	0.895666i	−0.995049	+	0.0993836i	$0.968313\pi$
$618$		0			0
$619$	2.70650	+	6.53408i	0.108784	+	0.262627i	0.968892	−	0.247485i	$-0.0796041\pi$
$619$	2.70650	+	6.53408i	0.108784	+	0.262627i	−0.860108	+	0.510112i	$0.829604\pi$
$620$	−2.54266	+	10.1385i	−0.102116	+	0.407173i
$621$		0			0
$622$	−13.7662	−	4.54992i	−0.551973	−	0.182435i
$623$		−	19.9783i		−	0.800416i
$624$		0			0
$625$		−	16.5563i		−	0.662254i
$626$	−6.37654	+	19.2928i	−0.254858	+	0.771094i
$627$		0			0
$628$	−13.1160	−	21.8969i	−0.523384	−	0.873782i
$629$	0.919525	+	2.21993i	0.0366639	+	0.0885144i
$630$		0			0
$631$	1.24929	+	1.24929i	0.0497335	+	0.0497335i	0.731536	−	0.681803i	$-0.238804\pi$
$631$	1.24929	+	1.24929i	0.0497335	+	0.0497335i	−0.681803	+	0.731536i	$0.738804\pi$
$632$	23.3854	+	4.06813i	0.930223	+	0.161822i
$633$		0			0
$634$	−0.364362	−	4.94922i	−0.0144707	−	0.196559i
$635$	1.55045	−	0.642215i	0.0615275	−	0.0254855i
$636$		0			0
$637$	−0.595466	+	1.43758i	−0.0235932	+	0.0569590i
$638$	−6.77462	+	3.40884i	−0.268210	+	0.134957i
$639$		0			0
$640$	7.53849	−	4.26050i	0.297985	−	0.168411i
$641$	−11.2362			−0.443802			−0.221901	−	0.975069i	$-0.571226\pi$
$641$	−11.2362			−0.443802			−0.221901	+	0.975069i	$0.571226\pi$
$642$		0			0
$643$	5.74440	−	13.8682i	0.226537	−	0.546908i	−0.769215	−	0.638991i	$-0.779352\pi$
$643$	5.74440	−	13.8682i	0.226537	−	0.546908i	0.995751	+	0.0920822i	$0.0293523\pi$
$644$	14.8080	−	19.9543i	0.583517	−	0.786310i
$645$		0			0
$646$	0.0726903	+	0.987369i	0.00285996	+	0.0388475i
$647$	−13.9424	+	13.9424i	−0.548134	+	0.548134i	−0.925901	−	0.377767i	$-0.876692\pi$
$647$	−13.9424	+	13.9424i	−0.548134	+	0.548134i	0.377767	+	0.925901i	$0.376692\pi$
$648$		0			0
$649$	2.25298	+	2.25298i	0.0884371	+	0.0884371i
$650$	−4.81514	+	5.58046i	−0.188865	+	0.218884i
$651$		0			0
$652$	−2.02257	−	3.37665i	−0.0792098	−	0.132240i
$653$	0.361667	+	0.149807i	0.0141531	+	0.00586241i	0.389749	−	0.920921i	$-0.372562\pi$
$653$	0.361667	+	0.149807i	0.0141531	+	0.00586241i	−0.375596	+	0.926784i	$0.622562\pi$
$654$		0			0
$655$		−	6.32634i		−	0.247191i
$656$	−17.0075	+	31.7750i	−0.664032	+	1.24060i
$657$		0			0
$658$	−1.73694	−	0.574085i	−0.0677131	−	0.0223802i
$659$	18.5077	+	7.66613i	0.720957	+	0.298630i	0.712830	−	0.701337i	$-0.247413\pi$
$659$	18.5077	+	7.66613i	0.720957	+	0.298630i	0.00812687	+	0.999967i	$0.497413\pi$
$660$		0			0
$661$	12.4139	+	29.9699i	0.482846	+	1.16569i	0.958251	+	0.285927i	$0.0923015\pi$
$661$	12.4139	+	29.9699i	0.482846	+	1.16569i	−0.475405	+	0.879767i	$0.657698\pi$
$662$	17.9982	+	15.5299i	0.699522	+	0.603587i
$663$		0			0
$664$	−18.3862	+	29.0073i	−0.713523	+	1.12570i
$665$	4.01786	−	4.01786i	0.155806	−	0.155806i
$666$		0			0
$667$	−29.5215	+	12.2282i	−1.14308	+	0.473478i
$668$	−6.28074	−	42.4252i	−0.243009	−	1.64148i
$669$		0			0
$670$	1.88291	+	3.74203i	0.0727431	+	0.144567i
$671$	0.911176			0.0351755
$672$		0			0
$673$	−47.5269			−1.83203			−0.916014	−	0.401146i	$-0.868612\pi$
$673$	−47.5269			−1.83203			−0.916014	+	0.401146i	$0.868612\pi$
$674$	−1.33897	−	2.66103i	−0.0515752	−	0.102499i
$675$		0			0
$676$	−22.9616	+	3.39930i	−0.883140	+	0.130742i
$677$	41.7848	−	17.3078i	1.60592	−	0.665194i	0.613682	−	0.789553i	$-0.289688\pi$
$677$	41.7848	−	17.3078i	1.60592	−	0.665194i	0.992237	+	0.124360i	$0.0396877\pi$
$678$		0			0
$679$	−7.07847	+	7.07847i	−0.271647	+	0.271647i
$680$	0.474817	−	0.106409i	0.0182084	−	0.00408060i
$681$		0			0
$682$	6.39542	+	5.51833i	0.244893	+	0.211308i
$683$	−13.2754	−	32.0496i	−0.507968	−	1.22634i	−0.945051	−	0.326922i	$-0.893988\pi$
$683$	−13.2754	−	32.0496i	−0.507968	−	1.22634i	0.437083	−	0.899421i	$-0.356012\pi$
$684$		0			0
$685$	7.76744	+	3.21738i	0.296779	+	0.122930i
$686$	26.6238	+	8.79956i	1.01650	+	0.335969i
$687$		0			0
$688$	15.4229	−	12.6424i	0.587992	−	0.481988i
$689$			12.0922i			0.460674i
$690$		0			0
$691$	46.1276	+	19.1067i	1.75478	+	0.726852i	0.997255	+	0.0740401i	$0.0235893\pi$
$691$	46.1276	+	19.1067i	1.75478	+	0.726852i	0.757520	+	0.652812i	$0.226411\pi$
$692$	−8.44647	+	5.05933i	−0.321087	+	0.192327i
$693$		0			0
$694$	12.3896	−	14.3588i	0.470302	−	0.545052i
$695$	−0.505515	−	0.505515i	−0.0191753	−	0.0191753i
$696$		0			0
$697$	−1.43208	+	1.43208i	−0.0542438	+	0.0542438i
$698$	−2.04163	−	27.7320i	−0.0772769	−	1.04967i
$699$		0			0
$700$	16.8995	+	12.5410i	0.638741	+	0.474007i
$701$	−5.34543	+	12.9050i	−0.201894	+	0.487415i	−0.992104	−	0.125422i	$-0.959972\pi$
$701$	−5.34543	+	12.9050i	−0.201894	+	0.487415i	0.790210	+	0.612837i	$0.209972\pi$
$702$		0			0
$703$	33.2933			1.25568
$704$	−0.337349	−	6.98966i	−0.0127143	−	0.263433i
$705$		0			0
$706$	36.2584	−	18.2444i	1.36460	−	0.686639i
$707$	−4.40555	+	10.6359i	−0.165688	+	0.400006i
$708$		0			0
$709$	31.1013	−	12.8826i	1.16803	−	0.483815i	0.287491	−	0.957783i	$-0.407179\pi$
$709$	31.1013	−	12.8826i	1.16803	−	0.483815i	0.880542	+	0.473968i	$0.157179\pi$
$710$	0.606874	+	8.24331i	0.0227756	+	0.309366i
$711$		0			0
$712$	−13.6415	−	19.3871i	−0.511236	−	0.726564i
$713$	25.1665	+	25.1665i	0.942492	+	0.942492i
$714$		0			0
$715$	−0.302497	−	0.730292i	−0.0113127	−	0.0273114i
$716$	−13.5179	+	8.09706i	−0.505189	+	0.302601i
$717$		0			0
$718$	−4.01184	+	12.1382i	−0.149721	+	0.452993i
$719$		−	0.571168i		−	0.0213010i	−0.999943	−	0.0106505i	$-0.996610\pi$
$719$		−	0.571168i		−	0.0213010i	0.999943	−	0.0106505i	$-0.00339022\pi$
$720$		0			0
$721$		−	36.9590i		−	1.37643i
$722$	−12.4878	−	4.12740i	−0.464748	−	0.153606i
$723$		0			0
$724$	31.0306	+	7.78222i	1.15324	+	0.289224i
$725$	−10.3562	−	25.0020i	−0.384619	−	0.928552i
$726$		0			0
$727$	−23.0479	−	23.0479i	−0.854800	−	0.854800i	0.135920	−	0.990720i	$-0.456601\pi$
$727$	−23.0479	−	23.0479i	−0.854800	−	0.854800i	−0.990720	+	0.135920i	$0.956601\pi$
$728$	−1.74081	−	7.76782i	−0.0645188	−	0.287895i
$729$		0			0
$730$	7.87565	−	0.579807i	0.291491	−	0.0214596i
$731$	1.03534	−	0.428852i	0.0382935	−	0.0158617i
$732$		0			0
$733$	−11.8891	+	28.7029i	−0.439136	+	1.06017i	0.537112	+	0.843511i	$0.319515\pi$
$733$	−11.8891	+	28.7029i	−0.439136	+	1.06017i	−0.976248	+	0.216656i	$0.930485\pi$
$734$	−9.27979	−	18.4424i	−0.342523	−	0.680720i
$735$		0			0
$736$	0.744728	−	29.4749i	0.0274510	−	1.08646i
$737$	3.38534			0.124701
$738$		0			0
$739$	2.87645	−	6.94437i	0.105812	−	0.255453i	−0.862102	−	0.506735i	$-0.830852\pi$
$739$	2.87645	−	6.94437i	0.105812	−	0.255453i	0.967914	+	0.251282i	$0.0808522\pi$
$740$	−2.39635	−	16.1869i	−0.0880916	−	0.595042i
$741$		0			0
$742$	34.4318	−	2.53488i	1.26403	−	0.0930582i
$743$	16.6576	−	16.6576i	0.611108	−	0.611108i	−0.332127	−	0.943235i	$-0.607766\pi$
$743$	16.6576	−	16.6576i	0.611108	−	0.611108i	0.943235	+	0.332127i	$0.107766\pi$
$744$		0			0
$745$	3.31788	+	3.31788i	0.121558	+	0.121558i
$746$	−16.8929	−	14.5761i	−0.618491	−	0.533669i
$747$		0			0
$748$	0.0956582	−	0.381425i	0.00349761	−	0.0139463i
$749$	−19.2635	−	7.97920i	−0.703873	−	0.291554i
$750$		0			0
$751$			31.1077i			1.13514i	0.823326	+	0.567569i	$0.192116\pi$
$751$			31.1077i			1.13514i	−0.823326	+	0.567569i	$0.807884\pi$
$752$	−2.07754	+	0.628912i	−0.0757600	+	0.0229341i
$753$		0			0
$754$	−3.21247	+	9.71961i	−0.116991	+	0.353967i
$755$	8.17083	+	3.38447i	0.297367	+	0.123173i
$756$		0			0
$757$	−2.35711	−	5.69056i	−0.0856705	−	0.206827i	0.875238	−	0.483692i	$-0.160704\pi$
$757$	−2.35711	−	5.69056i	−0.0856705	−	0.206827i	−0.960909	+	0.276865i	$0.910704\pi$
$758$	−5.68312	+	6.58641i	−0.206420	+	0.239229i
$759$		0			0
$760$	1.15551	−	6.64242i	0.0419149	−	0.240946i
$761$	14.2913	−	14.2913i	0.518059	−	0.518059i	−0.398925	−	0.916984i	$-0.630617\pi$
$761$	14.2913	−	14.2913i	0.518059	−	0.518059i	0.916984	+	0.398925i	$0.130617\pi$
$762$		0			0
$763$	20.5497	−	8.51196i	0.743949	−	0.308154i
$764$	18.4311	−	24.8366i	0.666815	−	0.898558i
$765$		0			0
$766$	−15.7449	+	7.92246i	−0.568885	+	0.286250i
$767$	4.30071			0.155290
$768$		0			0
$769$	8.95004			0.322747			0.161373	−	0.986893i	$-0.448408\pi$
$769$	8.95004			0.322747			0.161373	+	0.986893i	$0.448408\pi$
$770$	−2.01606	+	1.01444i	−0.0726537	+	0.0365577i
$771$		0			0
$772$	15.7571	−	21.2333i	0.567110	−	0.764202i
$773$	26.6270	−	11.0293i	0.957707	−	0.396695i	0.151585	−	0.988444i	$-0.451562\pi$
$773$	26.6270	−	11.0293i	0.957707	−	0.396695i	0.806122	+	0.591749i	$0.201562\pi$
$774$		0			0
$775$	−21.3137	+	21.3137i	−0.765611	+	0.765611i
$776$	−2.03573	+	11.7023i	−0.0730783	+	0.420087i
$777$		0			0
$778$	14.1298	−	16.3756i	0.506577	−	0.587093i
$779$	10.7387	+	25.9256i	0.384756	+	0.928882i
$780$		0			0
$781$	6.17132	+	2.55624i	0.220827	+	0.0914695i
$782$	0.519951	−	1.57316i	0.0185934	−	0.0562559i
$783$		0			0
$784$	5.04542	−	1.52735i	0.180194	−	0.0545482i
$785$			9.76782i			0.348629i
$786$		0			0
$787$	4.45056	+	1.84348i	0.158645	+	0.0657130i	0.460593	−	0.887611i	$-0.347637\pi$
$787$	4.45056	+	1.84348i	0.158645	+	0.0657130i	−0.301948	+	0.953324i	$0.597637\pi$
$788$	0.317537	−	1.26614i	0.0113118	−	0.0451043i
$789$		0			0
$790$	−6.87735	−	5.93416i	−0.244685	−	0.211128i
$791$	4.08625	+	4.08625i	0.145290	+	0.145290i
$792$		0			0
$793$	0.869673	−	0.869673i	0.0308830	−	0.0308830i
$794$	−39.0406	+	2.87418i	−1.38550	+	0.102001i
$795$		0			0
$796$	0.772467	+	5.21787i	0.0273794	+	0.184942i
$797$	−14.9972	+	36.2064i	−0.531227	+	1.28250i	0.399484	+	0.916740i	$0.369189\pi$
$797$	−14.9972	+	36.2064i	−0.531227	+	1.28250i	−0.930711	+	0.365756i	$0.880811\pi$
$798$		0			0
$799$	−0.121978			−0.00431527
$800$	24.9626	+	0.630717i	0.882561	+	0.0222992i
$801$		0			0
$802$	10.4896	+	20.8468i	0.370402	+	0.736125i
$803$	2.44223	−	5.89607i	0.0861845	−	0.208068i
$804$		0			0
$805$	−8.78530	+	3.63899i	−0.309641	+	0.128258i
$806$	11.3711	−	0.837141i	0.400529	−	0.0294870i
$807$		0			0
$808$	2.98719	+	13.3294i	0.105089	+	0.468926i
$809$	18.3458	+	18.3458i	0.645005	+	0.645005i	0.951782	−	0.306777i	$-0.0992505\pi$
$809$	18.3458	+	18.3458i	0.645005	+	0.645005i	−0.306777	+	0.951782i	$0.599250\pi$
$810$		0			0
$811$	−14.5476	−	35.1209i	−0.510834	−	1.23326i	−0.943399	−	0.331660i	$-0.892391\pi$
$811$	−14.5476	−	35.1209i	−0.510834	−	1.23326i	0.432565	−	0.901603i	$-0.357609\pi$
$812$	28.3495	+	7.10984i	0.994874	+	0.249506i
$813$		0			0
$814$	−12.5558	−	4.14988i	−0.440081	−	0.145453i
$815$			1.50626i			0.0527621i
$816$		0			0
$817$		−	15.5275i		−	0.543238i
$818$	0.806993	−	2.44163i	0.0282159	−	0.0853695i
$819$		0			0
$820$	11.8319	−	7.08713i	0.413186	−	0.247493i
$821$	10.1999	+	24.6248i	0.355979	+	0.859410i	0.995857	+	0.0909335i	$0.0289851\pi$
$821$	10.1999	+	24.6248i	0.355979	+	0.859410i	−0.639877	+	0.768477i	$0.721015\pi$
$822$		0			0
$823$	−1.53506	−	1.53506i	−0.0535088	−	0.0535088i	0.679846	−	0.733355i	$-0.262047\pi$
$823$	−1.53506	−	1.53506i	−0.0535088	−	0.0535088i	−0.733355	+	0.679846i	$0.762047\pi$
$824$	−25.2361	−	35.8653i	−0.879142	−	1.24943i
$825$		0			0
$826$	−0.901558	−	12.2461i	−0.0313692	−	0.426095i
$827$	−18.6205	+	7.71287i	−0.647499	+	0.268203i	−0.682167	−	0.731196i	$-0.738962\pi$
$827$	−18.6205	+	7.71287i	−0.647499	+	0.268203i	0.0346687	+	0.999399i	$0.488962\pi$
$828$		0			0
$829$	−9.98710	+	24.1110i	−0.346866	+	0.837409i	0.650120	+	0.759831i	$0.274719\pi$
$829$	−9.98710	+	24.1110i	−0.346866	+	0.837409i	−0.996986	+	0.0775776i	$0.975281\pi$
$830$	11.7402	−	5.90742i	0.407509	−	0.205050i
$831$		0			0
$832$	−6.99327	−	6.34931i	−0.242448	−	0.220123i
$833$	0.296230			0.0102638
$834$		0			0
$835$	−6.28074	+	15.1630i	−0.217354	+	0.524739i
$836$	−4.37545	−	3.24700i	−0.151328	−	0.112300i
$837$		0			0
$838$	−4.06688	−	55.2414i	−0.140488	−	1.90828i
$839$	−31.2561	+	31.2561i	−1.07908	+	1.07908i	−0.0824901	+	0.996592i	$0.526287\pi$
$839$	−31.2561	+	31.2561i	−1.07908	+	1.07908i	−0.996592	+	0.0824901i	$0.973713\pi$
$840$		0			0
$841$	−6.07041	−	6.07041i	−0.209324	−	0.209324i
$842$	13.6131	−	15.7768i	0.469137	−	0.543703i
$843$		0			0
$844$	−35.3480	+	21.1730i	−1.21673	+	0.728804i
$845$	8.20664	+	3.39930i	0.282317	+	0.116940i
$846$		0			0
$847$		−	24.3970i		−	0.838292i
$848$	31.6821	−	25.9704i	1.08797	−	0.891827i
$849$		0			0
$850$	1.33232	+	0.440351i	0.0456982	+	0.0151039i
$851$	−51.4758	−	21.3220i	−1.76457	−	0.730908i
$852$		0			0
$853$	−7.73304	−	18.6692i	−0.264774	−	0.639222i	0.734447	−	0.678666i	$-0.237441\pi$
$853$	−7.73304	−	18.6692i	−0.264774	−	0.639222i	−0.999222	+	0.0394438i	$0.987441\pi$
$854$	−2.65866	−	2.29404i	−0.0909774	−	0.0785004i
$855$		0			0
$856$	−24.1418	+	5.41030i	−0.825148	+	0.184920i
$857$	−4.21699	+	4.21699i	−0.144050	+	0.144050i	−0.775454	−	0.631404i	$-0.782479\pi$
$857$	−4.21699	+	4.21699i	−0.144050	+	0.144050i	0.631404	+	0.775454i	$0.282479\pi$
$858$		0			0
$859$	−32.3968	+	13.4192i	−1.10536	+	0.457857i	−0.859339	−	0.511407i	$-0.829125\pi$
$859$	−32.3968	+	13.4192i	−1.10536	+	0.457857i	−0.246025	+	0.969263i	$0.579125\pi$
$860$	−7.54931	+	1.11762i	−0.257429	+	0.0381106i
$861$		0			0
$862$	−1.81629	−	3.60963i	−0.0618629	−	0.122944i
$863$	18.7779			0.639207			0.319604	−	0.947551i	$-0.396450\pi$
$863$	18.7779			0.639207			0.319604	+	0.947551i	$0.396450\pi$
$864$		0			0
$865$	3.76782			0.128110
$866$	14.3135	+	28.4463i	0.486393	+	0.966643i
$867$		0			0
$868$	−4.76744	−	32.2031i	−0.161817	−	1.09305i
$869$	−6.78206	+	2.80922i	−0.230066	+	0.0952963i
$870$		0			0
$871$	3.23114	−	3.23114i	0.109483	−	0.109483i
$872$	14.1295	−	22.2917i	0.478485	−	0.754892i
$873$		0			0
$874$	−17.3812	−	14.9974i	−0.587927	−	0.507296i
$875$	−6.57277	−	15.8681i	−0.222200	−	0.536439i
$876$		0			0
$877$	5.59652	+	2.31816i	0.188981	+	0.0782786i	0.475167	−	0.879895i	$-0.342388\pi$
$877$	5.59652	+	2.31816i	0.188981	+	0.0782786i	−0.286186	+	0.958174i	$0.592388\pi$
$878$	−16.8576	−	5.57170i	−0.568918	−	0.188036i
$879$		0			0
$880$	−1.26373	+	2.36101i	−0.0426003	+	0.0795896i
$881$		−	16.3413i		−	0.550552i	−0.961365	−	0.275276i	$-0.911231\pi$
$881$		−	16.3413i		−	0.550552i	0.961365	−	0.275276i	$-0.0887692\pi$
$882$		0			0
$883$	−0.366860	−	0.151958i	−0.0123458	−	0.00511380i	0.376502	−	0.926416i	$-0.377127\pi$
$883$	−0.366860	−	0.151958i	−0.0123458	−	0.00511380i	−0.388848	+	0.921302i	$0.627127\pi$
$884$	−0.272750	−	0.455352i	−0.00917357	−	0.0153151i
$885$		0			0
$886$	23.7377	−	27.5106i	0.797483	−	0.924237i
$887$	6.38554	+	6.38554i	0.214406	+	0.214406i	0.806136	−	0.591730i	$-0.201555\pi$
$887$	6.38554	+	6.38554i	0.214406	+	0.214406i	−0.591730	+	0.806136i	$0.701555\pi$
$888$		0			0
$889$	−3.69583	+	3.69583i	−0.123954	+	0.123954i
$890$	0.666058	+	9.04722i	0.0223263	+	0.303264i
$891$		0			0
$892$	−20.5142	+	27.6436i	−0.686865	+	0.925575i
$893$	−0.646775	+	1.56145i	−0.0216435	+	0.0522521i
$894$		0			0
$895$	6.03011			0.201564
$896$	−16.6133	+	21.2440i	−0.555013	+	0.709712i
$897$		0			0
$898$	−11.1616	+	5.61628i	−0.372468	+	0.187418i
$899$	−16.0202	+	38.6761i	−0.534302	+	1.28992i
$900$		0			0
$901$	2.12682	−	0.880960i	0.0708548	−	0.0293490i
$902$	−0.818348	−	11.1158i	−0.0272480	−	0.370116i
$903$		0			0
$904$	6.75548	+	1.17518i	0.224684	+	0.0390860i
$905$	−8.65685	−	8.65685i	−0.287764	−	0.287764i
$906$		0			0
$907$	14.6313	+	35.3230i	0.485823	+	1.17288i	0.956803	+	0.290737i	$0.0939004\pi$
$907$	14.6313	+	35.3230i	0.485823	+	1.17288i	−0.470980	+	0.882144i	$0.656100\pi$
$908$	−1.69167	−	2.82421i	−0.0561399	−	0.0937248i
$909$		0			0
$910$	−0.955999	+	2.89246i	−0.0316911	+	0.0958841i
$911$		−	30.2904i		−	1.00356i	−0.864994	−	0.501782i	$-0.832678\pi$
$911$		−	30.2904i		−	1.00356i	0.864994	−	0.501782i	$-0.167322\pi$
$912$		0			0
$913$		−	10.6211i		−	0.351509i
$914$	14.4095	+	4.76255i	0.476624	+	0.157531i
$915$		0			0
$916$	1.29029	−	5.14485i	0.0426323	−	0.169991i
$917$	7.54011	+	18.2034i	0.248996	+	0.601130i
$918$		0			0
$919$	42.1116	+	42.1116i	1.38913	+	1.38913i	0.827146	+	0.561987i	$0.189963\pi$
$919$	42.1116	+	42.1116i	1.38913	+	1.38913i	0.561987	+	0.827146i	$0.310037\pi$
$920$	−6.04057	+	9.53003i	−0.199152	+	0.314196i
$921$		0			0
$922$	−23.2858	+	1.71431i	−0.766878	+	0.0564577i
$923$	8.33002	−	3.45041i	0.274186	−	0.113572i
$924$		0			0
$925$	18.0578	−	43.5953i	0.593736	−	1.43341i
$926$	−11.9502	−	23.7495i	−0.392709	−	0.780457i
$927$		0			0
$928$	32.3653	−	12.4580i	1.06244	−	0.408954i
$929$	−25.2271			−0.827674			−0.413837	−	0.910351i	$-0.635812\pi$
$929$	−25.2271			−0.827674			−0.413837	+	0.910351i	$0.635812\pi$
$930$		0			0
$931$	1.57073	−	3.79208i	0.0514787	−	0.124280i
$932$	30.6303	−	4.53459i	1.00333	−	0.148535i
$933$		0			0
$934$	−14.1821	+	1.04409i	−0.464053	+	0.0341637i
$935$	−0.106409	+	0.106409i	−0.00347995	+	0.00347995i
$936$		0			0
$937$	30.3001	+	30.3001i	0.989863	+	0.989863i	0.999949	−	0.0100865i	$-0.00321068\pi$
$937$	30.3001	+	30.3001i	0.989863	+	0.989863i	−0.0100865	+	0.999949i	$0.503211\pi$
$938$	−9.87786	−	8.52318i	−0.322524	−	0.278292i
$939$		0			0
$940$	0.805717	+	0.202067i	0.0262796	+	0.00659071i
$941$	1.05940	+	0.438818i	0.0345355	+	0.0143051i	0.399884	−	0.916566i	$-0.369050\pi$
$941$	1.05940	+	0.438818i	0.0345355	+	0.0143051i	−0.365349	+	0.930871i	$0.619050\pi$
$942$		0			0
$943$		−	46.9618i		−	1.52929i
$944$	−9.23666	−	11.2681i	−0.300628	−	0.366745i
$945$		0			0
$946$	−1.93544	+	5.85584i	−0.0629266	+	0.190390i
$947$	25.2985	+	10.4790i	0.822089	+	0.340520i	0.753766	−	0.657143i	$-0.228235\pi$
$947$	25.2985	+	10.4790i	0.822089	+	0.340520i	0.0683231	+	0.997663i	$0.478235\pi$
$948$		0			0
$949$	−3.29652	−	7.95850i	−0.107009	−	0.258344i
$950$	12.7015	−	14.7203i	0.412090	−	0.477589i
$951$		0			0
$952$	−1.23942	+	0.872098i	−0.0401697	+	0.0282648i
$953$	−8.84307	+	8.84307i	−0.286455	+	0.286455i	−0.835677	−	0.549222i	$-0.814924\pi$
$953$	−8.84307	+	8.84307i	−0.286455	+	0.286455i	0.549222	+	0.835677i	$0.314924\pi$
$954$		0			0
$955$	−10.9348	+	4.52936i	−0.353843	+	0.146567i
$956$	29.3683	+	21.7941i	0.949838	+	0.704870i
$957$		0			0
$958$	18.6689	−	9.39380i	0.603166	−	0.303500i
$959$	−26.1847			−0.845549
$960$		0			0
$961$	15.6274			0.504110
$962$	−15.9448	+	8.02306i	−0.514080	+	0.258674i
$963$		0			0
$964$	44.6738	+	33.1522i	1.43885	+	1.06776i
$965$	−9.34838	+	3.87222i	−0.300935	+	0.124651i
$966$		0			0
$967$	−33.2189	+	33.2189i	−1.06825	+	1.06825i	−0.0707549	+	0.997494i	$0.522541\pi$
$967$	−33.2189	+	33.2189i	−1.06825	+	1.06825i	−0.997494	+	0.0707549i	$0.977459\pi$
$968$	−16.6586	−	23.6751i	−0.535428	−	0.760945i
$969$		0			0
$970$	2.96951	−	3.44148i	0.0953451	−	0.110499i
$971$	1.16696	+	2.81729i	0.0374495	+	0.0904111i	0.941498	−	0.337019i	$-0.109419\pi$
$971$	1.16696	+	2.81729i	0.0374495	+	0.0904111i	−0.904048	+	0.427431i	$0.859419\pi$
$972$		0			0
$973$	2.05707	+	0.852067i	0.0659467	+	0.0273160i
$974$	8.21293	−	24.8489i	0.263159	−	0.796211i
$975$		0			0
$976$	−4.14639	−	0.410786i	−0.132723	−	0.0131489i
$977$			13.5807i			0.434484i	0.976118	+	0.217242i	$0.0697061\pi$
$977$			13.5807i			0.434484i	−0.976118	+	0.217242i	$0.930294\pi$
$978$		0			0
$979$	6.77316	+	2.80553i	0.216471	+	0.0896653i
$980$	−1.95673	−	0.490732i	−0.0625055	−	0.0156759i
$981$		0			0
$982$	32.9999	+	28.4741i	1.05307	+	0.908646i
$983$	29.0855	+	29.0855i	0.927684	+	0.927684i	0.997556	−	0.0698724i	$-0.0222592\pi$
$983$	29.0855	+	29.0855i	0.927684	+	0.927684i	−0.0698724	+	0.997556i	$0.522259\pi$
$984$		0			0
$985$	−0.353225	+	0.353225i	−0.0112547	+	0.0112547i
$986$	1.94357	−	0.143086i	0.0618959	−	0.00455679i
$987$		0			0
$988$	−7.27525	+	1.07705i	−0.231456	+	0.0342654i
$989$	−9.94424	+	24.0075i	−0.316209	+	0.763395i
$990$		0			0
$991$	6.64680			0.211143			0.105571	−	0.994412i	$-0.466333\pi$
$991$	6.64680			0.211143			0.105571	+	0.994412i	$0.466333\pi$
$992$	−26.6151	−	27.9949i	−0.845030	−	0.888839i
$993$		0			0
$994$	−11.5711	−	22.9960i	−0.367013	−	0.729390i
$995$	0.772467	−	1.86490i	0.0244889	−	0.0591213i
$996$		0			0
$997$	44.0238	−	18.2353i	1.39425	−	0.577516i	0.445996	−	0.895035i	$-0.352850\pi$
$997$	44.0238	−	18.2353i	1.39425	−	0.577516i	0.948252	+	0.317519i	$0.102850\pi$
$998$	34.2345	−	2.52035i	1.08367	−	0.0797803i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.b.109.2		8
3.2	odd	2		32.2.g.b.13.1	yes	8
4.3	odd	2		1152.2.v.b.145.1		8
12.11	even	2		128.2.g.b.17.2		8
15.2	even	4		800.2.ba.d.749.1		8
15.8	even	4		800.2.ba.c.749.2		8
15.14	odd	2		800.2.y.b.301.2		8
24.5	odd	2		256.2.g.d.33.2		8
24.11	even	2		256.2.g.c.33.1		8
32.5	even	8	inner	288.2.v.b.37.2		8
32.27	odd	8		1152.2.v.b.1009.1		8
48.5	odd	4		512.2.g.h.321.2		8
48.11	even	4		512.2.g.f.321.1		8
48.29	odd	4		512.2.g.e.321.1		8
48.35	even	4		512.2.g.g.321.2		8
96.5	odd	8		32.2.g.b.5.1	✓	8
96.11	even	8		256.2.g.c.225.1		8
96.29	odd	8		512.2.g.e.193.1		8
96.35	even	8		512.2.g.g.193.2		8
96.53	odd	8		256.2.g.d.225.2		8
96.59	even	8		128.2.g.b.113.2		8
96.77	odd	8		512.2.g.h.193.2		8
96.83	even	8		512.2.g.f.193.1		8
192.5	odd	16		4096.2.a.k.1.1		8
192.59	even	16		4096.2.a.q.1.8		8
192.101	odd	16		4096.2.a.k.1.8		8
192.155	even	16		4096.2.a.q.1.1		8
480.197	even	8		800.2.ba.c.549.2		8
480.293	even	8		800.2.ba.d.549.1		8
480.389	odd	8		800.2.y.b.101.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.5.1	✓	8	96.5	odd	8
32.2.g.b.13.1	yes	8	3.2	odd	2
128.2.g.b.17.2		8	12.11	even	2
128.2.g.b.113.2		8	96.59	even	8
256.2.g.c.33.1		8	24.11	even	2
256.2.g.c.225.1		8	96.11	even	8
256.2.g.d.33.2		8	24.5	odd	2
256.2.g.d.225.2		8	96.53	odd	8
288.2.v.b.37.2		8	32.5	even	8	inner
288.2.v.b.109.2		8	1.1	even	1	trivial
512.2.g.e.193.1		8	96.29	odd	8
512.2.g.e.321.1		8	48.29	odd	4
512.2.g.f.193.1		8	96.83	even	8
512.2.g.f.321.1		8	48.11	even	4
512.2.g.g.193.2		8	96.35	even	8
512.2.g.g.321.2		8	48.35	even	4
512.2.g.h.193.2		8	96.77	odd	8
512.2.g.h.321.2		8	48.5	odd	4
800.2.y.b.101.2		8	480.389	odd	8
800.2.y.b.301.2		8	15.14	odd	2
800.2.ba.c.549.2		8	480.197	even	8
800.2.ba.c.749.2		8	15.8	even	4
800.2.ba.d.549.1		8	480.293	even	8
800.2.ba.d.749.1		8	15.2	even	4
1152.2.v.b.145.1		8	4.3	odd	2
1152.2.v.b.1009.1		8	32.27	odd	8
4096.2.a.k.1.1		8	192.5	odd	16
4096.2.a.k.1.8		8	192.101	odd	16
4096.2.a.q.1.1		8	192.155	even	16
4096.2.a.q.1.8		8	192.59	even	16

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26330 - 0.635665i) q^{2} +(1.19186 - 1.60607i) q^{4} +(-0.707107 + 0.292893i) q^{5} +(1.68554 - 1.68554i) q^{7} +(0.484753 - 2.78658i) q^{8} +O(q^{10})\)	\(q+(1.26330 - 0.635665i) q^{2} +(1.19186 - 1.60607i) q^{4} +(-0.707107 + 0.292893i) q^{5} +(1.68554 - 1.68554i) q^{7} +(0.484753 - 2.78658i) q^{8} +(-0.707107 + 0.819496i) q^{10} +(0.334743 + 0.808140i) q^{11} +(1.09083 + 0.451835i) q^{13} +(1.05791 - 3.20079i) q^{14} +(-1.15894 - 3.82843i) q^{16} -0.224777i q^{17} +(-2.87740 - 1.19186i) q^{19} +(-0.372364 + 1.48475i) q^{20} +(0.936588 + 0.808140i) q^{22} +(3.68554 + 3.68554i) q^{23} +(-3.12132 + 3.12132i) q^{25} +(1.66526 - 0.122597i) q^{26} +(-0.698175 - 4.71604i) q^{28} +(-2.34610 + 5.66398i) q^{29} +6.82843 q^{31} +(-3.89769 - 4.09976i) q^{32} +(-0.142883 - 0.283962i) q^{34} +(-0.698175 + 1.68554i) q^{35} +(-9.87613 + 4.09083i) q^{37} +(-4.39265 + 0.323388i) q^{38} +(0.473398 + 2.11239i) q^{40} +(-6.37109 - 6.37109i) q^{41} +(1.90790 + 4.60607i) q^{43} +(1.69690 + 0.425569i) q^{44} +(6.99872 + 2.31318i) q^{46} -0.542661i q^{47} +1.31788i q^{49} +(-1.95905 + 5.92728i) q^{50} +(2.02579 - 1.21342i) q^{52} +(3.91925 + 9.46191i) q^{53} +(-0.473398 - 0.473398i) q^{55} +(-3.87983 - 5.51397i) q^{56} +(0.636568 + 8.64665i) q^{58} +(3.36524 - 1.39393i) q^{59} +(0.398630 - 0.962379i) q^{61} +(8.62636 - 4.34059i) q^{62} +(-7.53003 - 2.70160i) q^{64} -0.903670 q^{65} +(1.48105 - 3.57558i) q^{67} +(-0.361009 - 0.267903i) q^{68} +(0.189436 + 2.57316i) q^{70} +(5.39978 - 5.39978i) q^{71} +(-5.15894 - 5.15894i) q^{73} +(-9.87613 + 11.4459i) q^{74} +(-5.34367 + 3.20079i) q^{76} +(1.92638 + 0.797933i) q^{77} +8.39218i q^{79} +(1.94082 + 2.36766i) q^{80} +(-12.0985 - 3.99872i) q^{82} +(-11.2180 - 4.64665i) q^{83} +(0.0658358 + 0.158942i) q^{85} +(5.33817 + 4.60607i) q^{86} +(2.41421 - 0.541038i) q^{88} +(5.92638 - 5.92638i) q^{89} +(2.60022 - 1.07705i) q^{91} +(10.3119 - 1.52660i) q^{92} +(-0.344951 - 0.685544i) q^{94} +2.38372 q^{95} -4.19951 q^{97} +(0.837733 + 1.66488i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8	\( 8 q + 4 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8} - 4 q^{11} - 8 q^{13} - 12 q^{14} + 4 q^{19} - 4 q^{20} + 4 q^{22} + 8 q^{23} - 8 q^{25} + 20 q^{26} - 16 q^{28} + 32 q^{31} + 24 q^{32} - 16 q^{35} - 8 q^{37} - 8 q^{38} + 16 q^{40} - 8 q^{41} - 12 q^{43} - 20 q^{44} + 12 q^{46} - 16 q^{50} + 12 q^{52} - 8 q^{53} - 16 q^{55} - 8 q^{56} - 12 q^{58} + 20 q^{59} + 24 q^{61} + 24 q^{62} - 8 q^{64} - 36 q^{67} - 16 q^{68} - 8 q^{70} + 24 q^{71} - 32 q^{73} - 8 q^{74} - 20 q^{76} - 16 q^{77} - 8 q^{80} - 20 q^{82} - 20 q^{83} + 8 q^{85} - 4 q^{86} + 8 q^{88} + 16 q^{89} + 40 q^{91} + 16 q^{92} - 24 q^{94} + 8 q^{95} + 32 q^{97} + 24 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8 - 4 * q^11 - 8 * q^13 - 12 * q^14 + 4 * q^19 - 4 * q^20 + 4 * q^22 + 8 * q^23 - 8 * q^25 + 20 * q^26 - 16 * q^28 + 32 * q^31 + 24 * q^32 - 16 * q^35 - 8 * q^37 - 8 * q^38 + 16 * q^40 - 8 * q^41 - 12 * q^43 - 20 * q^44 + 12 * q^46 - 16 * q^50 + 12 * q^52 - 8 * q^53 - 16 * q^55 - 8 * q^56 - 12 * q^58 + 20 * q^59 + 24 * q^61 + 24 * q^62 - 8 * q^64 - 36 * q^67 - 16 * q^68 - 8 * q^70 + 24 * q^71 - 32 * q^73 - 8 * q^74 - 20 * q^76 - 16 * q^77 - 8 * q^80 - 20 * q^82 - 20 * q^83 + 8 * q^85 - 4 * q^86 + 8 * q^88 + 16 * q^89 + 40 * q^91 + 16 * q^92 - 24 * q^94 + 8 * q^95 + 32 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more