LMFDB - Embedded newform 720.2.z.g.667.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(163,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("720.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.z (of order $4$, degree $2$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			667.4
Root			$1.41303 - 0.0578659i$ of defining polynomial
Character	$\chi$	$=$	720.667
Dual form			720.2.z.g.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.567819 - 1.29521i) q^{2} +(-1.35516 + 1.47090i) q^{4} +(1.42182 + 1.72581i) q^{5} +(-1.60205 - 1.60205i) q^{7} +(2.67461 + 0.920026i) q^{8} +O(q^{10})$	\(q+(-0.567819 - 1.29521i) q^{2} +(-1.35516 + 1.47090i) q^{4} +(1.42182 + 1.72581i) q^{5} +(-1.60205 - 1.60205i) q^{7} +(2.67461 + 0.920026i) q^{8} +(1.42795 - 2.82151i) q^{10} +(-0.754587 + 0.754587i) q^{11} +5.94580i q^{13} +(-1.16532 + 2.98467i) q^{14} +(-0.327065 - 3.98661i) q^{16} +(-1.95574 - 1.95574i) q^{17} +(0.780680 - 0.780680i) q^{19} +(-4.46529 - 0.247399i) q^{20} +(1.40582 + 0.548884i) q^{22} +(-4.93121 + 4.93121i) q^{23} +(-0.956833 + 4.90759i) q^{25} +(7.70109 - 3.37614i) q^{26} +(4.52748 - 0.185408i) q^{28} +(1.44802 + 1.44802i) q^{29} -3.60859i q^{31} +(-4.97780 + 2.68729i) q^{32} +(-1.42260 + 3.64361i) q^{34} +(0.486998 - 5.04266i) q^{35} +10.2364i q^{37} +(-1.45443 - 0.567864i) q^{38} +(2.21504 + 5.92398i) q^{40} +6.93334i q^{41} +9.91344i q^{43} +(-0.0873298 - 2.13251i) q^{44} +(9.18700 + 3.58694i) q^{46} +(-0.104270 + 0.104270i) q^{47} -1.86688i q^{49} +(6.89970 - 1.54732i) q^{50} +(-8.74565 - 8.05753i) q^{52} +4.03213 q^{53} +(-2.37516 - 0.229383i) q^{55} +(-2.81093 - 5.75878i) q^{56} +(1.05328 - 2.69771i) q^{58} +(3.46736 + 3.46736i) q^{59} +(0.680578 - 0.680578i) q^{61} +(-4.67390 + 2.04902i) q^{62} +(6.30711 + 4.92142i) q^{64} +(-10.2613 + 8.45388i) q^{65} -9.04721i q^{67} +(5.52703 - 0.226341i) q^{68} +(-6.80785 + 2.23255i) q^{70} +3.64007 q^{71} +(-2.94030 - 2.94030i) q^{73} +(13.2583 - 5.81242i) q^{74} +(0.0903496 + 2.20625i) q^{76} +2.41777 q^{77} +10.7140 q^{79} +(6.41509 - 6.23270i) q^{80} +(8.98016 - 3.93688i) q^{82} +4.23845 q^{83} +(0.594515 - 6.15595i) q^{85} +(12.8400 - 5.62904i) q^{86} +(-2.71247 + 1.32399i) q^{88} -0.0426256 q^{89} +(9.52546 - 9.52546i) q^{91} +(-0.570698 - 13.9359i) q^{92} +(0.194258 + 0.0758455i) q^{94} +(2.45730 + 0.237315i) q^{95} +(-1.91173 - 1.91173i) q^{97} +(-2.41802 + 1.06005i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) $ 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	$ 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35} - 24 q^{38} + 44 q^{40} + 44 q^{44} + 12 q^{46} - 38 q^{47} + 8 q^{50} + 8 q^{52} - 12 q^{53} - 6 q^{55} - 20 q^{56} + 20 q^{58} - 10 q^{59} + 14 q^{61} + 40 q^{62} + 16 q^{64} + 60 q^{68} - 28 q^{70} - 24 q^{71} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 44 q^{77} - 16 q^{79} + 92 q^{80} + 48 q^{82} - 40 q^{83} + 14 q^{85} + 36 q^{86} - 8 q^{88} - 12 q^{89} + 8 q^{92} - 28 q^{94} - 34 q^{95} + 18 q^{97} + 56 q^{98}+O(q^{100}) $ 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.567819	−	1.29521i	−0.401509	−	0.915855i
$2$	−0.567819	−	1.29521i	−0.401509	−	0.915855i
$3$		0			0
$3$		0			0
$4$	−1.35516	+	1.47090i	−0.677582	+	0.735448i
$5$	1.42182	+	1.72581i	0.635859	+	0.771805i
$5$	1.42182	+	1.72581i	0.635859	+	0.771805i
$6$		0			0
$7$	−1.60205	−	1.60205i	−0.605517	−	0.605517i	0.336254	−	0.941771i	$-0.390840\pi$
$7$	−1.60205	−	1.60205i	−0.605517	−	0.605517i	−0.941771	+	0.336254i	$0.890840\pi$
$8$	2.67461	+	0.920026i	0.945618	+	0.325278i
$9$		0			0
$10$	1.42795	−	2.82151i	0.451559	−	0.892241i
$11$	−0.754587	+	0.754587i	−0.227517	+	0.227517i	−0.811654	−	0.584138i	$-0.801433\pi$
$11$	−0.754587	+	0.754587i	−0.227517	+	0.227517i	0.584138	+	0.811654i	$0.301433\pi$
$12$		0			0
$13$			5.94580i			1.64907i	0.565812	+	0.824534i	$0.308563\pi$
$13$			5.94580i			1.64907i	−0.565812	+	0.824534i	$0.691437\pi$
$14$	−1.16532	+	2.98467i	−0.311446	+	0.797687i
$15$		0			0
$16$	−0.327065	−	3.98661i	−0.0817662	−	0.996652i
$17$	−1.95574	−	1.95574i	−0.474336	−	0.474336i	0.428978	−	0.903315i	$-0.358874\pi$
$17$	−1.95574	−	1.95574i	−0.474336	−	0.474336i	−0.903315	+	0.428978i	$0.858874\pi$
$18$		0			0
$19$	0.780680	−	0.780680i	0.179100	−	0.179100i	−0.611863	−	0.790964i	$-0.709580\pi$
$19$	0.780680	−	0.780680i	0.179100	−	0.179100i	0.790964	+	0.611863i	$0.209580\pi$
$20$	−4.46529	−	0.247399i	−0.998469	−	0.0553201i
$21$		0			0
$22$	1.40582	+	0.548884i	0.299722	+	0.117022i
$23$	−4.93121	+	4.93121i	−1.02823	+	1.02823i	−0.0286378	+	0.999590i	$0.509117\pi$
$23$	−4.93121	+	4.93121i	−1.02823	+	1.02823i	−0.999590	+	0.0286378i	$0.990883\pi$
$24$		0			0
$25$	−0.956833	+	4.90759i	−0.191367	+	0.981519i
$26$	7.70109	−	3.37614i	1.51031	−	0.662115i
$27$		0			0
$28$	4.52748	−	0.185408i	0.855614	−	0.0350388i
$29$	1.44802	+	1.44802i	0.268891	+	0.268891i	0.828653	−	0.559762i	$-0.189108\pi$
$29$	1.44802	+	1.44802i	0.268891	+	0.268891i	−0.559762	+	0.828653i	$0.689108\pi$
$30$		0			0
$31$		−	3.60859i		−	0.648121i	−0.946036	−	0.324061i	$-0.894952\pi$
$31$		−	3.60859i		−	0.648121i	0.946036	−	0.324061i	$-0.105048\pi$
$32$	−4.97780	+	2.68729i	−0.879959	+	0.475050i
$33$		0			0
$34$	−1.42260	+	3.64361i	−0.243973	+	0.624874i
$35$	0.486998	−	5.04266i	0.0823177	−	0.852365i
$36$		0			0
$37$			10.2364i			1.68285i	0.540371	+	0.841427i	$0.318284\pi$
$37$			10.2364i			1.68285i	−0.540371	+	0.841427i	$0.681716\pi$
$38$	−1.45443	−	0.567864i	−0.235940	−	0.0921197i
$39$		0			0
$40$	2.21504	+	5.92398i	0.350229	+	0.936664i
$41$			6.93334i			1.08281i	0.840763	+	0.541403i	$0.182107\pi$
$41$			6.93334i			1.08281i	−0.840763	+	0.541403i	$0.817893\pi$
$42$		0			0
$43$			9.91344i			1.51179i	0.654695	+	0.755893i	$0.272797\pi$
$43$			9.91344i			1.51179i	−0.654695	+	0.755893i	$0.727203\pi$
$44$	−0.0873298	−	2.13251i	−0.0131655	−	0.321488i
$45$		0			0
$46$	9.18700	+	3.58694i	1.35455	+	0.528865i
$47$	−0.104270	+	0.104270i	−0.0152093	+	0.0152093i	−0.714671	−	0.699461i	$-0.753423\pi$
$47$	−0.104270	+	0.104270i	−0.0152093	+	0.0152093i	0.699461	+	0.714671i	$0.253423\pi$
$48$		0			0
$49$		−	1.86688i		−	0.266698i
$50$	6.89970	−	1.54732i	0.975764	−	0.218824i
$51$		0			0
$52$	−8.74565	−	8.05753i	−1.21280	−	1.11738i
$53$	4.03213			0.553856			0.276928	−	0.960891i	$-0.410684\pi$
$53$	4.03213			0.553856			0.276928	+	0.960891i	$0.410684\pi$
$54$		0			0
$55$	−2.37516	−	0.229383i	−0.320267	−	0.0309300i
$56$	−2.81093	−	5.75878i	−0.375627	−	0.769550i
$57$		0			0
$58$	1.05328	−	2.69771i	0.138303	−	0.354227i
$59$	3.46736	+	3.46736i	0.451412	+	0.451412i	0.895823	−	0.444411i	$-0.146587\pi$
$59$	3.46736	+	3.46736i	0.451412	+	0.451412i	−0.444411	+	0.895823i	$0.646587\pi$
$60$		0			0
$61$	0.680578	−	0.680578i	0.0871391	−	0.0871391i	−0.662194	−	0.749333i	$-0.730374\pi$
$61$	0.680578	−	0.680578i	0.0871391	−	0.0871391i	0.749333	+	0.662194i	$0.230374\pi$
$62$	−4.67390	+	2.04902i	−0.593585	+	0.260226i
$63$		0			0
$64$	6.30711	+	4.92142i	0.788388	+	0.615178i
$65$	−10.2613	+	8.45388i	−1.27276	+	1.04857i
$66$		0			0
$67$		−	9.04721i		−	1.10529i	−0.833416	−	0.552646i	$-0.813618\pi$
$67$		−	9.04721i		−	1.10529i	0.833416	−	0.552646i	$-0.186382\pi$
$68$	5.52703	−	0.226341i	0.670251	−	0.0274479i
$69$		0			0
$70$	−6.80785	+	2.23255i	−0.813694	+	0.266841i
$71$	3.64007			0.431997			0.215998	−	0.976394i	$-0.430699\pi$
$71$	3.64007			0.431997			0.215998	+	0.976394i	$0.430699\pi$
$72$		0			0
$73$	−2.94030	−	2.94030i	−0.344136	−	0.344136i	0.513784	−	0.857920i	$-0.328243\pi$
$73$	−2.94030	−	2.94030i	−0.344136	−	0.344136i	−0.857920	+	0.513784i	$0.828243\pi$
$74$	13.2583	−	5.81242i	1.54125	−	0.675681i
$75$		0			0
$76$	0.0903496	+	2.20625i	0.0103638	+	0.253074i
$77$	2.41777			0.275530
$78$		0			0
$79$	10.7140			1.20542			0.602711	−	0.797960i	$-0.294087\pi$
$79$	10.7140			1.20542			0.602711	+	0.797960i	$0.294087\pi$
$80$	6.41509	−	6.23270i	0.717229	−	0.696838i
$81$		0			0
$82$	8.98016	−	3.93688i	0.991693	−	0.434756i
$83$	4.23845			0.465230			0.232615	−	0.972569i	$-0.425272\pi$
$83$	4.23845			0.465230			0.232615	+	0.972569i	$0.425272\pi$
$84$		0			0
$85$	0.594515	−	6.15595i	0.0644842	−	0.667707i
$86$	12.8400	−	5.62904i	1.38458	−	0.606995i
$87$		0			0
$88$	−2.71247	+	1.32399i	−0.289150	+	0.141138i
$89$	−0.0426256			−0.00451831			−0.00225915	−	0.999997i	$-0.500719\pi$
$89$	−0.0426256			−0.00451831			−0.00225915	+	0.999997i	$0.500719\pi$
$90$		0			0
$91$	9.52546	−	9.52546i	0.998539	−	0.998539i
$92$	−0.570698	−	13.9359i	−0.0594993	−	1.45292i
$93$		0			0
$94$	0.194258	+	0.0758455i	0.0200362	+	0.00782287i
$95$	2.45730	+	0.237315i	0.252113	+	0.0243480i
$96$		0			0
$97$	−1.91173	−	1.91173i	−0.194106	−	0.194106i	0.603362	−	0.797468i	$-0.293828\pi$
$97$	−1.91173	−	1.91173i	−0.194106	−	0.194106i	−0.797468	+	0.603362i	$0.793828\pi$
$98$	−2.41802	+	1.06005i	−0.244257	+	0.107081i
$99$		0			0
$100$	−5.92189	−	8.05799i	−0.592189	−	0.805799i
$101$	−4.96537	−	4.96537i	−0.494073	−	0.494073i	0.415514	−	0.909587i	$-0.363602\pi$
$101$	−4.96537	−	4.96537i	−0.494073	−	0.494073i	−0.909587	+	0.415514i	$0.863602\pi$
$102$		0			0
$103$	0.442220	−	0.442220i	0.0435733	−	0.0435733i	−0.684984	−	0.728558i	$-0.740191\pi$
$103$	0.442220	−	0.442220i	0.0435733	−	0.0435733i	0.728558	+	0.684984i	$0.240191\pi$
$104$	−5.47029	+	15.9027i	−0.536406	+	1.55939i
$105$		0			0
$106$	−2.28952	−	5.22248i	−0.222378	−	0.507252i
$107$	−17.5924			−1.70072			−0.850359	−	0.526204i	$-0.823615\pi$
$107$	−17.5924			−1.70072			−0.850359	+	0.526204i	$0.823615\pi$
$108$		0			0
$109$	0.345161	+	0.345161i	0.0330605	+	0.0330605i	0.723444	−	0.690383i	$-0.242558\pi$
$109$	0.345161	+	0.345161i	0.0330605	+	0.0330605i	−0.690383	+	0.723444i	$0.742558\pi$
$110$	1.05156	+	3.20660i	0.100263	+	0.305737i
$111$		0			0
$112$	−5.86276	+	6.91071i	−0.553979	+	0.653001i
$113$	5.43662	−	5.43662i	0.511435	−	0.511435i	−0.403531	−	0.914966i	$-0.632217\pi$
$113$	5.43662	−	5.43662i	0.511435	−	0.511435i	0.914966	+	0.403531i	$0.132217\pi$
$114$		0			0
$115$	−15.5216	−	1.49901i	−1.44740	−	0.139784i
$116$	−4.09219	+	0.167582i	−0.379950	+	0.0155596i
$117$		0			0
$118$	2.52214	−	6.45981i	0.232182	−	0.594673i
$119$			6.26638i			0.574438i
$120$		0			0
$121$			9.86120i			0.896472i
$122$	−1.26794	−	0.495050i	−0.114794	−	0.0448197i
$123$		0			0
$124$	5.30785	+	4.89023i	0.476659	+	0.439155i
$125$	−9.83002	+	5.32642i	−0.879223	+	0.476410i
$126$		0			0
$127$	−6.27150	+	6.27150i	−0.556505	+	0.556505i	−0.928311	−	0.371805i	$-0.878739\pi$
$127$	−6.27150	+	6.27150i	−0.556505	+	0.556505i	0.371805	+	0.928311i	$0.378739\pi$
$128$	2.79301	−	10.9635i	0.246869	−	0.969049i
$129$		0			0
$130$	16.7762	+	8.49033i	1.47137	+	0.744651i
$131$	−1.61521	−	1.61521i	−0.141122	−	0.141122i	0.633017	−	0.774138i	$-0.281816\pi$
$131$	−1.61521	−	1.61521i	−0.141122	−	0.141122i	−0.774138	+	0.633017i	$0.781816\pi$
$132$		0			0
$133$	−2.50138			−0.216897
$134$	−11.7181	+	5.13718i	−1.01229	+	0.443785i
$135$		0			0
$136$	−3.43152	−	7.03018i	−0.294250	−	0.602833i
$137$	−6.83585	+	6.83585i	−0.584026	+	0.584026i	−0.936007	−	0.351981i	$-0.885508\pi$
$137$	−6.83585	+	6.83585i	−0.584026	+	0.584026i	0.351981	+	0.936007i	$0.385508\pi$
$138$		0			0
$139$	−13.7427	−	13.7427i	−1.16564	−	1.16564i	−0.983220	−	0.182423i	$-0.941606\pi$
$139$	−13.7427	−	13.7427i	−1.16564	−	1.16564i	−0.182423	−	0.983220i	$-0.558394\pi$
$140$	6.75726	+	7.54995i	0.571093	+	0.638087i
$141$		0			0
$142$	−2.06690	−	4.71467i	−0.173450	−	0.395647i
$143$	−4.48662	−	4.48662i	−0.375190	−	0.375190i
$144$		0			0
$145$	−0.440176	+	4.55784i	−0.0365547	+	0.378508i
$146$	−2.13876	+	5.47788i	−0.177005	+	0.453353i
$147$		0			0
$148$	−15.0567	−	13.8720i	−1.23765	−	1.14027i
$149$	1.73811	−	1.73811i	0.142391	−	0.142391i	−0.632318	−	0.774709i	$-0.717896\pi$
$149$	1.73811	−	1.73811i	0.142391	−	0.142391i	0.774709	+	0.632318i	$0.217896\pi$
$150$		0			0
$151$	5.83522			0.474864			0.237432	−	0.971404i	$-0.423694\pi$
$151$	5.83522			0.474864			0.237432	+	0.971404i	$0.423694\pi$
$152$	2.80626	−	1.36977i	0.227618	−	0.111103i
$153$		0			0
$154$	−1.37286	−	3.13153i	−0.110628	−	0.252346i
$155$	6.22773	−	5.13078i	0.500223	−	0.412114i
$156$		0			0
$157$	3.14732			0.251183			0.125592	−	0.992082i	$-0.459917\pi$
$157$	3.14732			0.251183			0.125592	+	0.992082i	$0.459917\pi$
$158$	−6.08363	−	13.8770i	−0.483987	−	1.10399i
$159$		0			0
$160$	−11.7153	−	4.76987i	−0.926176	−	0.377092i
$161$	15.8001			1.24522
$162$		0			0
$163$	7.82117			0.612601			0.306301	−	0.951935i	$-0.400909\pi$
$163$	7.82117			0.612601			0.306301	+	0.951935i	$0.400909\pi$
$164$	−10.1982	−	9.39580i	−0.796347	−	0.733689i
$165$		0			0
$166$	−2.40667	−	5.48970i	−0.186794	−	0.426083i
$167$	9.88460	+	9.88460i	0.764893	+	0.764893i	0.977203	−	0.212309i	$-0.0680985\pi$
$167$	9.88460	+	9.88460i	0.764893	+	0.764893i	−0.212309	+	0.977203i	$0.568098\pi$
$168$		0			0
$169$	−22.3525			−1.71942
$170$	−8.31085	+	2.72544i	−0.637413	+	0.209032i
$171$		0			0
$172$	−14.5816	−	13.4343i	−1.11184	−	1.02436i
$173$			3.49245i			0.265526i	0.991148	+	0.132763i	$0.0423849\pi$
$173$			3.49245i			0.265526i	−0.991148	+	0.132763i	$0.957615\pi$
$174$		0			0
$175$	9.39509	−	6.32931i	0.710202	−	0.478451i
$176$	3.25504	+	2.76144i	0.245358	+	0.208152i
$177$		0			0
$178$	0.0242036	+	0.0552094i	0.00181414	+	0.00413812i
$179$	13.0809	−	13.0809i	0.977713	−	0.977713i	−0.0220444	−	0.999757i	$-0.507018\pi$
$179$	13.0809	−	13.0809i	0.977713	−	0.977713i	0.999757	+	0.0220444i	$0.00701753\pi$
$180$		0			0
$181$	13.6393	+	13.6393i	1.01380	+	1.01380i	0.999903	+	0.0138952i	$0.00442312\pi$
$181$	13.6393	+	13.6393i	1.01380	+	1.01380i	0.0138952	+	0.999903i	$0.495577\pi$
$182$	−17.7462	−	6.92878i	−1.31544	−	0.513595i
$183$		0			0
$184$	−17.7259	+	8.65223i	−1.30677	+	0.637851i
$185$	−17.6661	+	14.5544i	−1.29884	+	1.07006i
$186$		0			0
$187$	2.95155			0.215839
$188$	−0.0120674	−	0.294673i	−0.000880102	−	0.0214912i
$189$		0			0
$190$	−1.08792	−	3.31748i	−0.0789264	−	0.240675i
$191$		−	2.92523i		−	0.211662i	−0.994384	−	0.105831i	$-0.966250\pi$
$191$		−	2.92523i		−	0.211662i	0.994384	−	0.105831i	$-0.0337503\pi$
$192$		0			0
$193$	0.0830702	−	0.0830702i	0.00597953	−	0.00597953i	−0.704111	−	0.710090i	$-0.748654\pi$
$193$	0.0830702	−	0.0830702i	0.00597953	−	0.00597953i	0.710090	+	0.704111i	$0.248654\pi$
$194$	−1.39058	+	3.56161i	−0.0998379	+	0.255709i
$195$		0			0
$196$	2.74599	+	2.52993i	0.196142	+	0.180710i
$197$		−	7.80487i		−	0.556074i	−0.960570	−	0.278037i	$-0.910316\pi$
$197$		−	7.80487i		−	0.556074i	0.960570	−	0.278037i	$-0.0896838\pi$
$198$		0			0
$199$			10.9740i			0.777924i	0.921254	+	0.388962i	$0.127166\pi$
$199$			10.9740i			0.777924i	−0.921254	+	0.388962i	$0.872834\pi$
$200$	−7.07427	+	12.2456i	−0.500226	+	0.865895i
$201$		0			0
$202$	−3.61179	+	9.25065i	−0.254125	+	0.650873i
$203$		−	4.63960i		−	0.325636i
$204$		0			0
$205$	−11.9656	+	9.85799i	−0.835715	+	0.688512i
$206$	−0.823871	−	0.321669i	−0.0574018	−	0.0224118i
$207$		0			0
$208$	23.7036	−	1.94466i	1.64355	−	0.134838i
$209$			1.17818i			0.0814966i
$210$		0			0
$211$	−8.92204	−	8.92204i	−0.614218	−	0.614218i	0.329824	−	0.944042i	$-0.393011\pi$
$211$	−8.92204	−	8.92204i	−0.614218	−	0.614218i	−0.944042	+	0.329824i	$0.893011\pi$
$212$	−5.46420	+	5.93085i	−0.375283	+	0.407332i
$213$		0			0
$214$	9.98927	+	22.7859i	0.682853	+	1.55761i
$215$	−17.1087	+	14.0952i	−1.16680	+	0.961283i
$216$		0			0
$217$	−5.78113	+	5.78113i	−0.392449	+	0.392449i
$218$	0.251069	−	0.643047i	0.0170045	−	0.0435527i
$219$		0			0
$220$	3.55613	−	3.18276i	0.239754	−	0.214582i
$221$	11.6284	−	11.6284i	0.782213	−	0.782213i
$222$		0			0
$223$	−13.1678	−	13.1678i	−0.881784	−	0.881784i	0.111931	−	0.993716i	$-0.464296\pi$
$223$	−13.1678	−	13.1678i	−0.881784	−	0.881784i	−0.993716	+	0.111931i	$0.964296\pi$
$224$	12.2798	+	3.66950i	0.820481	+	0.245179i
$225$		0			0
$226$	−10.1286	−	3.95458i	−0.673745	−	0.263055i
$227$		−	19.3432i		−	1.28385i	−0.766766	−	0.641927i	$-0.778135\pi$
$227$		−	19.3432i		−	1.28385i	0.766766	−	0.641927i	$-0.221865\pi$
$228$		0			0
$229$	13.2143	−	13.2143i	0.873223	−	0.873223i	−0.119599	−	0.992822i	$-0.538161\pi$
$229$	13.2143	−	13.2143i	0.873223	−	0.873223i	0.992822	+	0.119599i	$0.0381610\pi$
$230$	6.87193	+	20.9550i	0.453122	+	1.38173i
$231$		0			0
$232$	2.54068	+	5.20511i	0.166804	+	0.341732i
$233$	−20.6884	−	20.6884i	−1.35534	−	1.35534i	−0.879570	−	0.475769i	$-0.842170\pi$
$233$	−20.6884	−	20.6884i	−1.35534	−	1.35534i	−0.475769	−	0.879570i	$-0.657830\pi$
$234$		0			0
$235$	−0.328204	−	0.0316965i	−0.0214096	−	0.00206765i
$236$	−9.79896	+	0.401284i	−0.637858	+	0.0261214i
$237$		0			0
$238$	8.11630	−	3.55817i	0.526102	−	0.230642i
$239$	−14.1053			−0.912395			−0.456198	−	0.889878i	$-0.650789\pi$
$239$	−14.1053			−0.912395			−0.456198	+	0.889878i	$0.650789\pi$
$240$		0			0
$241$	12.8011			0.824592			0.412296	−	0.911050i	$-0.364727\pi$
$241$	12.8011			0.824592			0.412296	+	0.911050i	$0.364727\pi$
$242$	12.7724	−	5.59937i	0.821039	−	0.359941i
$243$		0			0
$244$	0.0787646	+	1.92335i	0.00504238	+	0.123130i
$245$	3.22189	−	2.65438i	0.205839	−	0.169582i
$246$		0			0
$247$	4.64177	+	4.64177i	0.295349	+	0.295349i
$248$	3.31999	−	9.65157i	0.210820	−	0.612876i
$249$		0			0
$250$	12.4805	+	9.70754i	0.789338	+	0.613959i
$251$	6.84118	−	6.84118i	0.431812	−	0.431812i	−0.457433	−	0.889244i	$-0.651231\pi$
$251$	6.84118	−	6.84118i	0.431812	−	0.431812i	0.889244	+	0.457433i	$0.151231\pi$
$252$		0			0
$253$		−	7.44205i		−	0.467878i
$254$	11.6840	+	4.56186i	0.733120	+	0.286237i
$255$		0			0
$256$	−15.7861	+	2.60776i	−0.986629	+	0.162985i
$257$	6.66524	+	6.66524i	0.415766	+	0.415766i	0.883742	−	0.467975i	$-0.155016\pi$
$257$	6.66524	+	6.66524i	0.415766	+	0.415766i	−0.467975	+	0.883742i	$0.655016\pi$
$258$		0			0
$259$	16.3992	−	16.3992i	1.01900	−	1.01900i
$260$	1.47098	−	26.5497i	0.0912265	−	1.64654i
$261$		0			0
$262$	−1.17490	+	3.00919i	−0.0725854	+	0.185908i
$263$	7.32015	−	7.32015i	0.451380	−	0.451380i	−0.444432	−	0.895812i	$-0.646595\pi$
$263$	7.32015	−	7.32015i	0.451380	−	0.451380i	0.895812	+	0.444432i	$0.146595\pi$
$264$		0			0
$265$	5.73298	+	6.95869i	0.352174	+	0.427469i
$266$	1.42033	+	3.23982i	0.0870859	+	0.198646i
$267$		0			0
$268$	13.3075	+	12.2604i	0.812885	+	0.748926i
$269$	15.9801	+	15.9801i	0.974321	+	0.974321i	0.999678	−	0.0253576i	$-0.00807242\pi$
$269$	15.9801	+	15.9801i	0.974321	+	0.974321i	−0.0253576	+	0.999678i	$0.508072\pi$
$270$		0			0
$271$		−	3.59684i		−	0.218492i	−0.994015	−	0.109246i	$-0.965156\pi$
$271$		−	3.59684i		−	0.218492i	0.994015	−	0.109246i	$-0.0348437\pi$
$272$	−7.15711	+	8.43642i	−0.433963	+	0.511533i
$273$		0			0
$274$	12.7354	+	4.97237i	0.769375	+	0.300392i
$275$	−2.98119	−	4.42522i	−0.179773	−	0.266851i
$276$		0			0
$277$		−	20.9416i		−	1.25826i	−0.777300	−	0.629131i	$-0.783411\pi$
$277$		−	20.9416i		−	1.25826i	0.777300	−	0.629131i	$-0.216589\pi$
$278$	−9.99640	+	25.6032i	−0.599545	+	1.53558i
$279$		0			0
$280$	5.94191	−	13.0391i	0.355097	−	0.779236i
$281$			3.26699i			0.194892i	0.995241	+	0.0974462i	$0.0310674\pi$
$281$			3.26699i			0.194892i	−0.995241	+	0.0974462i	$0.968933\pi$
$282$		0			0
$283$		0	0.000151619i		0	9.01279e-6i	−1.00000		4.50640e-6i	$-0.999999\pi$
$283$		0	0.000151619i		0	9.01279e-6i	1.00000		4.50640e-6i	$-1.43443e-6\pi$
$284$	−4.93289	+	5.35416i	−0.292713	+	0.317711i
$285$		0			0
$286$	−3.26355	+	8.35873i	−0.192978	+	0.494262i
$287$	11.1075	−	11.1075i	0.655657	−	0.655657i
$288$		0			0
$289$		−	9.35017i		−	0.550010i
$290$	6.15332	−	2.01790i	0.361335	−	0.118495i
$291$		0			0
$292$	8.30947	−	0.340287i	0.486275	−	0.0199138i
$293$	11.0593			0.646091			0.323045	−	0.946384i	$-0.395293\pi$
$293$	11.0593			0.646091			0.323045	+	0.946384i	$0.395293\pi$
$294$		0			0
$295$	−1.05402	+	10.9140i	−0.0613677	+	0.635436i
$296$	−9.41775	+	27.3784i	−0.547396	+	1.59134i
$297$		0			0
$298$	−3.23815	−	1.26429i	−0.187581	−	0.0732384i
$299$	−29.3200	−	29.3200i	−1.69562	−	1.69562i
$300$		0			0
$301$	15.8818	−	15.8818i	0.915413	−	0.915413i
$302$	−3.31335	−	7.55787i	−0.190662	−	0.434906i
$303$		0			0
$304$	−3.36760	−	2.85693i	−0.193145	−	0.163856i
$305$	2.14221	+	0.206885i	0.122663	+	0.0118462i
$306$		0			0
$307$			15.1317i			0.863613i	0.901966	+	0.431806i	$0.142124\pi$
$307$			15.1317i			0.863613i	−0.901966	+	0.431806i	$0.857876\pi$
$308$	−3.27647	+	3.55629i	−0.186694	+	0.202638i
$309$		0			0
$310$	−10.1817	−	5.15290i	−0.578281	−	0.292665i
$311$	27.1556			1.53985			0.769925	−	0.638134i	$-0.220293\pi$
$311$	27.1556			1.53985			0.769925	+	0.638134i	$0.220293\pi$
$312$		0			0
$313$	−13.6695	−	13.6695i	−0.772646	−	0.772646i	0.205922	−	0.978568i	$-0.433981\pi$
$313$	−13.6695	−	13.6695i	−0.772646	−	0.772646i	−0.978568	+	0.205922i	$0.933981\pi$
$314$	−1.78711	−	4.07645i	−0.100852	−	0.230048i
$315$		0			0
$316$	−14.5193	+	15.7592i	−0.816772	+	0.886525i
$317$	25.8314			1.45084			0.725419	−	0.688307i	$-0.241646\pi$
$317$	25.8314			1.45084			0.725419	+	0.688307i	$0.241646\pi$
$318$		0			0
$319$	−2.18532			−0.122354
$320$	0.474158	+	17.8823i	0.0265062	+	0.999649i
$321$		0			0
$322$	−8.97157	−	20.4645i	−0.499966	−	1.14044i
$323$	−3.05361			−0.169908
$324$		0			0
$325$	−29.1796	−	5.68914i	−1.61859	−	0.315576i
$326$	−4.44101	−	10.1301i	−0.245965	−	0.561054i
$327$		0			0
$328$	−6.37885	+	18.5440i	−0.352213	+	1.02392i
$329$	0.334091			0.0184190
$330$		0			0
$331$	−13.6207	+	13.6207i	−0.748659	+	0.748659i	−0.974227	−	0.225568i	$-0.927576\pi$
$331$	−13.6207	+	13.6207i	−0.748659	+	0.748659i	0.225568	+	0.974227i	$0.427576\pi$
$332$	−5.74379	+	6.23431i	−0.315231	+	0.342152i
$333$		0			0
$334$	7.19002	−	18.4153i	0.393420	−	1.00764i
$335$	15.6138	−	12.8635i	0.853071	−	0.702810i
$336$		0			0
$337$	16.0911	+	16.0911i	0.876536	+	0.876536i	0.993174	−	0.116638i	$-0.0372119\pi$
$337$	16.0911	+	16.0911i	0.876536	+	0.876536i	−0.116638	+	0.993174i	$0.537212\pi$
$338$	12.6922	+	28.9513i	0.690364	+	1.57474i
$339$		0			0
$340$	8.24909	+	9.21679i	0.447370	+	0.499850i
$341$	2.72299	+	2.72299i	0.147458	+	0.147458i
$342$		0			0
$343$	−14.2052	+	14.2052i	−0.767007	+	0.767007i
$344$	−9.12062	+	26.5146i	−0.491751	+	1.42957i
$345$		0			0
$346$	4.52347	−	1.98308i	0.243183	−	0.106611i
$347$	−5.57562			−0.299315			−0.149658	−	0.988738i	$-0.547817\pi$
$347$	−5.57562			−0.299315			−0.149658	+	0.988738i	$0.547817\pi$
$348$		0			0
$349$	15.0811	+	15.0811i	0.807273	+	0.807273i	0.984220	−	0.176947i	$-0.0566222\pi$
$349$	15.0811	+	15.0811i	0.807273	+	0.807273i	−0.176947	+	0.984220i	$0.556622\pi$
$350$	−13.5325	−	8.57476i	−0.723344	−	0.458340i
$351$		0			0
$352$	1.72839	−	5.78398i	0.0921234	−	0.308287i
$353$	−2.57880	+	2.57880i	−0.137256	+	0.137256i	−0.772397	−	0.635141i	$-0.780942\pi$
$353$	−2.57880	+	2.57880i	−0.137256	+	0.137256i	0.635141	+	0.772397i	$0.280942\pi$
$354$		0			0
$355$	5.17554	+	6.28206i	0.274689	+	0.333417i
$356$	0.0577647	−	0.0626979i	0.00306152	−	0.00332298i
$357$		0			0
$358$	−24.3702	−	9.51500i	−1.28800	−	0.502883i
$359$			5.77227i			0.304649i	0.988331	+	0.152324i	$0.0486758\pi$
$359$			5.77227i			0.304649i	−0.988331	+	0.152324i	$0.951324\pi$
$360$		0			0
$361$			17.7811i			0.935846i
$362$	9.92115	−	25.4104i	0.521444	−	1.33554i
$363$		0			0
$364$	1.10240	+	26.9195i	0.0577814	+	1.41096i
$365$	0.893807	−	9.25499i	0.0467840	−	0.484428i
$366$		0			0
$367$	8.30496	−	8.30496i	0.433516	−	0.433516i	−0.456307	−	0.889822i	$-0.650828\pi$
$367$	8.30496	−	8.30496i	0.433516	−	0.433516i	0.889822	+	0.456307i	$0.150828\pi$
$368$	21.2716	+	18.0460i	1.10886	+	0.940710i
$369$		0			0
$370$	28.8822	+	14.6171i	1.50151	+	0.759908i
$371$	−6.45967	−	6.45967i	−0.335369	−	0.335369i
$372$		0			0
$373$	16.0484			0.830953			0.415477	−	0.909604i	$-0.363615\pi$
$373$	16.0484			0.830953			0.415477	+	0.909604i	$0.363615\pi$
$374$	−1.67595	−	3.82289i	−0.0866612	−	0.197677i
$375$		0			0
$376$	−0.374813	+	0.182951i	−0.0193295	+	0.00943496i
$377$	−8.60964	+	8.60964i	−0.443419	+	0.443419i
$378$		0			0
$379$	−8.91367	−	8.91367i	−0.457865	−	0.457865i	0.440089	−	0.897954i	$-0.354947\pi$
$379$	−8.91367	−	8.91367i	−0.457865	−	0.457865i	−0.897954	+	0.440089i	$0.854947\pi$
$380$	−3.67910	+	3.29282i	−0.188734	+	0.168918i
$381$		0			0
$382$	−3.78880	+	1.66100i	−0.193852	+	0.0849841i
$383$	24.8928	+	24.8928i	1.27196	+	1.27196i	0.945057	+	0.326904i	$0.106005\pi$
$383$	24.8928	+	24.8928i	1.27196	+	1.27196i	0.326904	+	0.945057i	$0.393995\pi$
$384$		0			0
$385$	3.43764	+	4.17261i	0.175199	+	0.212656i
$386$	−0.154763	−	0.0604250i	−0.00787721	−	0.00307555i
$387$		0			0
$388$	5.40265	−	0.221247i	0.274278	−	0.0112321i
$389$	16.5819	−	16.5819i	0.840738	−	0.840738i	−0.148217	−	0.988955i	$-0.547353\pi$
$389$	16.5819	−	16.5819i	0.840738	−	0.840738i	0.988955	+	0.148217i	$0.0473534\pi$
$390$		0			0
$391$	19.2883			0.975452
$392$	1.71758	−	4.99319i	0.0867510	−	0.252194i
$393$		0			0
$394$	−10.1090	+	4.43176i	−0.509284	+	0.223269i
$395$	15.2335	+	18.4904i	0.766478	+	0.930351i
$396$		0			0
$397$	−8.62531			−0.432892			−0.216446	−	0.976295i	$-0.569447\pi$
$397$	−8.62531			−0.432892			−0.216446	+	0.976295i	$0.569447\pi$
$398$	14.2137	−	6.23123i	0.712466	−	0.312343i
$399$		0			0
$400$	19.8776	+	2.20941i	0.993879	+	0.110471i
$401$	−19.7107			−0.984307			−0.492153	−	0.870508i	$-0.663790\pi$
$401$	−19.7107			−0.984307			−0.492153	+	0.870508i	$0.663790\pi$
$402$		0			0
$403$	21.4559			1.06880
$404$	14.0324	−	0.574651i	0.698139	−	0.0285900i
$405$		0			0
$406$	−6.00928	+	2.63445i	−0.298235	+	0.130746i
$407$	−7.72426	−	7.72426i	−0.382877	−	0.382877i
$408$		0			0
$409$	26.7930			1.32483			0.662414	−	0.749138i	$-0.269532\pi$
$409$	26.7930			1.32483			0.662414	+	0.749138i	$0.269532\pi$
$410$	19.5625	+	9.90049i	0.966124	+	0.488950i
$411$		0			0
$412$	0.0511790	+	1.24974i	0.00252141	+	0.0615703i
$413$		−	11.1098i		−	0.546675i
$414$		0			0
$415$	6.02633	+	7.31475i	0.295821	+	0.359067i
$416$	−15.9781	−	29.5970i	−0.783390	−	1.45111i
$417$		0			0
$418$	1.52600	−	0.668995i	0.0746391	−	0.0327216i
$419$	−11.0752	+	11.0752i	−0.541061	+	0.541061i	−0.923840	−	0.382779i	$-0.874967\pi$
$419$	−11.0752	+	11.0752i	−0.541061	+	0.541061i	0.382779	+	0.923840i	$0.374967\pi$
$420$		0			0
$421$	−0.243092	−	0.243092i	−0.0118476	−	0.0118476i	0.701158	−	0.713006i	$-0.252667\pi$
$421$	−0.243092	−	0.243092i	−0.0118476	−	0.0118476i	−0.713006	+	0.701158i	$0.752667\pi$
$422$	−6.48985	+	16.6221i	−0.315921	+	0.809149i
$423$		0			0
$424$	10.7844	+	3.70967i	0.523737	+	0.180157i
$425$	11.4693	−	7.72666i	0.556342	−	0.374798i
$426$		0			0
$427$	−2.18064			−0.105528
$428$	23.8405	−	25.8765i	1.15237	−	1.25079i
$429$		0			0
$430$	27.9709	+	14.1560i	1.34888	+	0.682661i
$431$			20.7024i			0.997200i	0.866832	+	0.498600i	$0.166152\pi$
$431$			20.7024i			0.997200i	−0.866832	+	0.498600i	$0.833848\pi$
$432$		0			0
$433$	−5.68221	+	5.68221i	−0.273069	+	0.273069i	−0.830335	−	0.557265i	$-0.811851\pi$
$433$	−5.68221	+	5.68221i	−0.273069	+	0.273069i	0.557265	+	0.830335i	$0.311851\pi$
$434$	10.7704	+	4.20517i	0.516998	+	0.201855i
$435$		0			0
$436$	−0.975446	+	0.0399462i	−0.0467154	+	0.00191307i
$437$			7.69939i			0.368312i
$438$		0			0
$439$		−	18.7902i		−	0.896808i	−0.893831	−	0.448404i	$-0.851993\pi$
$439$		−	18.7902i		−	0.896808i	0.893831	−	0.448404i	$-0.148007\pi$
$440$	−6.14160	−	2.79872i	−0.292789	−	0.133424i
$441$		0			0
$442$	−21.6642	−	8.45848i	−1.03046	−	0.402329i
$443$			12.1641i			0.577934i	0.957339	+	0.288967i	$0.0933119\pi$
$443$			12.1641i			0.577934i	−0.957339	+	0.288967i	$0.906688\pi$
$444$		0			0
$445$	−0.0606062	−	0.0735637i	−0.00287301	−	0.00348725i
$446$	−9.57824	+	24.5321i	−0.453543	+	1.16163i
$447$		0			0
$448$	−2.21993	−	17.9886i	−0.104882	−	0.849884i
$449$		−	27.2708i		−	1.28699i	−0.765452	−	0.643493i	$-0.777484\pi$
$449$		−	27.2708i		−	1.28699i	0.765452	−	0.643493i	$-0.222516\pi$
$450$		0			0
$451$	−5.23181	−	5.23181i	−0.246356	−	0.246356i
$452$	0.629191	+	15.3642i	0.0295946	+	0.722672i
$453$		0			0
$454$	−25.0536	+	10.9834i	−1.17582	+	0.515479i
$455$	29.9826	+	2.89559i	1.40561	+	0.135748i
$456$		0			0
$457$	19.7514	−	19.7514i	0.923933	−	0.923933i	−0.0733714	−	0.997305i	$-0.523376\pi$
$457$	19.7514	−	19.7514i	0.923933	−	0.923933i	0.997305	+	0.0733714i	$0.0233758\pi$
$458$	−24.6186	−	9.61200i	−1.15035	−	0.449139i
$459$		0			0
$460$	23.2392	−	20.7993i	1.08353	−	0.969771i
$461$	−12.9262	+	12.9262i	−0.602035	+	0.602035i	−0.940852	−	0.338818i	$-0.889973\pi$
$461$	−12.9262	+	12.9262i	−0.602035	+	0.602035i	0.338818	+	0.940852i	$0.389973\pi$
$462$		0			0
$463$	14.5647	+	14.5647i	0.676879	+	0.676879i	0.959293	−	0.282414i	$-0.0911351\pi$
$463$	14.5647	+	14.5647i	0.676879	+	0.676879i	−0.282414	+	0.959293i	$0.591135\pi$
$464$	5.29909	−	6.24629i	0.246004	−	0.289977i
$465$		0			0
$466$	−15.0486	+	38.5431i	−0.697114	+	1.78547i
$467$			42.3556i			1.95998i	0.199040	+	0.979991i	$0.436218\pi$
$467$			42.3556i			1.95998i	−0.199040	+	0.979991i	$0.563782\pi$
$468$		0			0
$469$	−14.4941	+	14.4941i	−0.669274	+	0.669274i
$470$	0.145306	+	0.443092i	0.00670248	+	0.0204383i
$471$		0			0
$472$	6.08378	+	12.4639i	0.280029	+	0.573698i
$473$	−7.48056	−	7.48056i	−0.343956	−	0.343956i
$474$		0			0
$475$	3.08428	+	4.57824i	0.141517	+	0.210064i
$476$	−9.21718	−	8.49196i	−0.422469	−	0.389229i
$477$		0			0
$478$	8.00925	+	18.2694i	0.366335	+	0.835622i
$479$	−27.0905			−1.23780			−0.618899	−	0.785470i	$-0.712421\pi$
$479$	−27.0905			−1.23780			−0.618899	+	0.785470i	$0.712421\pi$
$480$		0			0
$481$	−60.8636			−2.77514
$482$	−7.26871	−	16.5802i	−0.331081	−	0.755207i
$483$		0			0
$484$	−14.5048	−	13.3635i	−0.659308	−	0.607433i
$485$	0.581136	−	6.01741i	0.0263880	−	0.273236i
$486$		0			0
$487$	21.9674	+	21.9674i	0.995436	+	0.995436i	0.999990	−	0.00455390i	$-0.00144956\pi$
$487$	21.9674	+	21.9674i	0.995436	+	0.995436i	−0.00455390	+	0.999990i	$0.501450\pi$
$488$	2.44643	−	1.19413i	0.110745	−	0.0540559i
$489$		0			0
$490$	−5.26744	−	2.66583i	−0.237959	−	0.120430i
$491$	6.11955	−	6.11955i	0.276171	−	0.276171i	−0.555407	−	0.831579i	$-0.687438\pi$
$491$	6.11955	−	6.11955i	0.276171	−	0.276171i	0.831579	+	0.555407i	$0.187438\pi$
$492$		0			0
$493$		−	5.66390i		−	0.255089i
$494$	3.37640	−	8.64777i	0.151912	−	0.389082i
$495$		0			0
$496$	−14.3860	+	1.18024i	−0.645951	+	0.0529945i
$497$	−5.83157	−	5.83157i	−0.261581	−	0.261581i
$498$		0			0
$499$	15.4115	−	15.4115i	0.689914	−	0.689914i	−0.272298	−	0.962213i	$-0.587784\pi$
$499$	15.4115	−	15.4115i	0.689914	−	0.689914i	0.962213	+	0.272298i	$0.0877838\pi$
$500$	5.48667	−	21.6771i	0.245371	−	0.969429i
$501$		0			0
$502$	−12.7454	−	4.97625i	−0.568853	−	0.222101i
$503$	−26.4312	+	26.4312i	−1.17851	+	1.17851i	−0.198387	+	0.980124i	$0.563570\pi$
$503$	−26.4312	+	26.4312i	−1.17851	+	1.17851i	−0.980124	+	0.198387i	$0.936430\pi$
$504$		0			0
$505$	1.50940	−	15.6292i	0.0671673	−	0.695488i
$506$	−9.63905	+	4.22574i	−0.428508	+	0.187857i
$507$		0			0
$508$	−0.725812	−	17.7236i	−0.0322027	−	0.786358i
$509$	0.233714	+	0.233714i	0.0103592	+	0.0103592i	0.712267	−	0.701908i	$-0.247668\pi$
$509$	0.233714	+	0.233714i	0.0103592	+	0.0103592i	−0.701908	+	0.712267i	$0.747668\pi$
$510$		0			0
$511$			9.42101i			0.416761i
$512$	12.3412	+	18.9656i	0.545410	+	0.838169i
$513$		0			0
$514$	4.84827	−	12.4176i	0.213848	−	0.547716i
$515$	1.39195	+	0.134428i	0.0613365	+	0.00592362i
$516$		0			0
$517$		−	0.157362i		−	0.00692075i
$518$	−30.5523	−	11.9287i	−1.34239	−	0.524118i
$519$		0			0
$520$	−35.2228	+	13.1702i	−1.54462	+	0.577551i
$521$			4.50147i			0.197213i	0.995127	+	0.0986064i	$0.0314385\pi$
$521$			4.50147i			0.197213i	−0.995127	+	0.0986064i	$0.968562\pi$
$522$		0			0
$523$			12.6042i			0.551141i	0.961281	+	0.275571i	$0.0888668\pi$
$523$			12.6042i			0.551141i	−0.961281	+	0.275571i	$0.911133\pi$
$524$	4.56468	−	0.186931i	0.199409	−	0.00816613i
$525$		0			0
$526$	−13.6377	−	5.32465i	−0.594632	−	0.232166i
$527$	−7.05746	+	7.05746i	−0.307428	+	0.307428i
$528$		0			0
$529$		−	25.6336i		−	1.11450i
$530$	5.75770	−	11.3767i	0.250099	−	0.494173i
$531$		0			0
$532$	3.38977	−	3.67926i	0.146965	−	0.159516i
$533$	−41.2242			−1.78562
$534$		0			0
$535$	−25.0132	−	30.3610i	−1.08142	−	1.31262i
$536$	8.32367	−	24.1978i	0.359528	−	1.04519i
$537$		0			0
$538$	11.6238	−	29.7714i	0.501139	−	1.28354i
$539$	1.40873	+	1.40873i	0.0606782	+	0.0606782i
$540$		0			0
$541$	14.5013	−	14.5013i	0.623459	−	0.623459i	−0.322955	−	0.946414i	$-0.604676\pi$
$541$	14.5013	−	14.5013i	0.623459	−	0.623459i	0.946414	+	0.322955i	$0.104676\pi$
$542$	−4.65868	+	2.04235i	−0.200107	+	0.0877266i
$543$		0			0
$544$	14.9909	+	4.47964i	0.642730	+	0.192063i
$545$	−0.104924	+	1.08644i	−0.00449444	+	0.0465380i
$546$		0			0
$547$			30.2936i			1.29526i	0.761955	+	0.647630i	$0.224240\pi$
$547$			30.2936i			1.29526i	−0.761955	+	0.647630i	$0.775760\pi$
$548$	−0.791125	−	19.3185i	−0.0337952	−	0.825246i
$549$		0			0
$550$	−4.03883	+	6.37401i	−0.172216	+	0.271789i
$551$	2.26088			0.0963169
$552$		0			0
$553$	−17.1644	−	17.1644i	−0.729904	−	0.729904i
$554$	−27.1239	+	11.8911i	−1.15239	+	0.505203i
$555$		0			0
$556$	38.8378	−	1.59047i	1.64709	−	0.0674510i
$557$	9.72758			0.412171			0.206085	−	0.978534i	$-0.433928\pi$
$557$	9.72758			0.412171			0.206085	+	0.978534i	$0.433928\pi$
$558$		0			0
$559$	−58.9433			−2.49304
$560$	−20.2624	−	0.292193i	−0.856242	−	0.0123474i
$561$		0			0
$562$	4.23146	−	1.85506i	0.178493	−	0.0782510i
$563$	17.7853			0.749562			0.374781	−	0.927113i	$-0.377718\pi$
$563$	17.7853			0.749562			0.374781	+	0.927113i	$0.377718\pi$
$564$		0			0
$565$	17.1125	+	1.65265i	0.719928	+	0.0695276i
$566$	−0.000196379	0	8.60919e-5i	−8.25441e−6	0	3.61871e-6i
$567$		0			0
$568$	9.73578	+	3.34896i	0.408504	+	0.140519i
$569$	−15.7897			−0.661938			−0.330969	−	0.943642i	$-0.607376\pi$
$569$	−15.7897			−0.661938			−0.330969	+	0.943642i	$0.607376\pi$
$570$		0			0
$571$	23.3108	−	23.3108i	0.975528	−	0.975528i	−0.0241793	−	0.999708i	$-0.507697\pi$
$571$	23.3108	−	23.3108i	0.975528	−	0.975528i	0.999708	+	0.0241793i	$0.00769727\pi$
$572$	12.6795	−	0.519245i	0.530155	−	0.0217107i
$573$		0			0
$574$	−20.6937	−	8.07958i	−0.863739	−	0.337235i
$575$	−19.4820	−	28.9187i	−0.812456	−	1.20599i
$576$		0			0
$577$	25.7383	+	25.7383i	1.07150	+	1.07150i	0.997239	+	0.0742597i	$0.0236594\pi$
$577$	25.7383	+	25.7383i	1.07150	+	1.07150i	0.0742597	+	0.997239i	$0.476341\pi$
$578$	−12.1105	+	5.30920i	−0.503729	+	0.220834i
$579$		0			0
$580$	−6.10759	−	6.82407i	−0.253604	−	0.283354i
$581$	−6.79020	−	6.79020i	−0.281705	−	0.281705i
$582$		0			0
$583$	−3.04260	+	3.04260i	−0.126011	+	0.126011i
$584$	−5.15902	−	10.5693i	−0.213482	−	0.437362i
$585$		0			0
$586$	−6.27967	−	14.3242i	−0.259411	−	0.591725i
$587$	−23.1327			−0.954790			−0.477395	−	0.878689i	$-0.658419\pi$
$587$	−23.1327			−0.954790			−0.477395	+	0.878689i	$0.658419\pi$
$588$		0			0
$589$	−2.81715	−	2.81715i	−0.116079	−	0.116079i
$590$	14.7344	−	4.83197i	0.606607	−	0.198929i
$591$		0			0
$592$	40.8085	−	3.34797i	1.67722	−	0.137601i
$593$	25.5047	−	25.5047i	1.04735	−	1.04735i	0.0485322	−	0.998822i	$-0.484546\pi$
$593$	25.5047	−	25.5047i	1.04735	−	1.04735i	0.998822	−	0.0485322i	$-0.0154543\pi$
$594$		0			0
$595$	−10.8146	+	8.90969i	−0.443354	+	0.365261i
$596$	0.201154	+	4.91199i	0.00823960	+	0.201203i
$597$		0			0
$598$	−21.3272	+	54.6241i	−0.872135	+	2.23374i
$599$		−	11.0699i		−	0.452304i	−0.974092	−	0.226152i	$-0.927385\pi$
$599$		−	11.0699i		−	0.452304i	0.974092	−	0.226152i	$-0.0726146\pi$
$600$		0			0
$601$			13.7579i			0.561197i	0.959825	+	0.280599i	$0.0905330\pi$
$601$			13.7579i			0.561197i	−0.959825	+	0.280599i	$0.909467\pi$
$602$	−29.5884	−	11.5524i	−1.20593	−	0.470839i
$603$		0			0
$604$	−7.90768	+	8.58300i	−0.321759	+	0.349237i
$605$	−17.0185	+	14.0209i	−0.691902	+	0.570030i
$606$		0			0
$607$	−18.4675	+	18.4675i	−0.749573	+	0.749573i	−0.974399	−	0.224826i	$-0.927819\pi$
$607$	−18.4675	+	18.4675i	−0.749573	+	0.749573i	0.224826	+	0.974399i	$0.427819\pi$
$608$	−1.78815	+	5.98398i	−0.0725193	+	0.242683i
$609$		0			0
$610$	−0.948426	−	2.89210i	−0.0384007	−	0.117098i
$611$	−0.619968	−	0.619968i	−0.0250812	−	0.0250812i
$612$		0			0
$613$	−11.6810			−0.471790			−0.235895	−	0.971779i	$-0.575802\pi$
$613$	−11.6810			−0.471790			−0.235895	+	0.971779i	$0.575802\pi$
$614$	19.5988	−	8.59208i	0.790944	−	0.346748i
$615$		0			0
$616$	6.46660	+	2.22441i	0.260547	+	0.0896240i
$617$	29.1000	−	29.1000i	1.17152	−	1.17152i	0.189677	−	0.981847i	$-0.439256\pi$
$617$	29.1000	−	29.1000i	1.17152	−	1.17152i	0.981847	−	0.189677i	$-0.0607441\pi$
$618$		0			0
$619$	4.23279	+	4.23279i	0.170130	+	0.170130i	0.787036	−	0.616906i	$-0.211614\pi$
$619$	4.23279	+	4.23279i	0.170130	+	0.170130i	−0.616906	+	0.787036i	$0.711614\pi$
$620$	−0.892760	+	16.1134i	−0.0358541	+	0.647129i
$621$		0			0
$622$	−15.4194	−	35.1723i	−0.618263	−	1.41028i
$623$	0.0682883	+	0.0682883i	0.00273591	+	0.00273591i
$624$		0			0
$625$	−23.1689	−	9.39149i	−0.926758	−	0.375660i
$626$	−9.94314	+	25.4668i	−0.397408	+	1.01786i
$627$		0			0
$628$	−4.26513	+	4.62938i	−0.170197	+	0.184732i
$629$	20.0197	−	20.0197i	0.798239	−	0.798239i
$630$		0			0
$631$	−1.33886			−0.0532991			−0.0266496	−	0.999645i	$-0.508484\pi$
$631$	−1.33886			−0.0532991			−0.0266496	+	0.999645i	$0.508484\pi$
$632$	28.6559	+	9.85718i	1.13987	+	0.392097i
$633$		0			0
$634$	−14.6676	−	33.4573i	−0.582524	−	1.32876i
$635$	−19.7404	−	1.90644i	−0.783373	−	0.0756548i
$636$		0			0
$637$	11.1001			0.439803
$638$	1.24086	+	2.83045i	0.0491263	+	0.112059i
$639$		0			0
$640$	22.8921	−	10.7680i	0.904891	−	0.425643i
$641$	−24.5069			−0.967965			−0.483982	−	0.875078i	$-0.660810\pi$
$641$	−24.5069			−0.967965			−0.483982	+	0.875078i	$0.660810\pi$
$642$		0			0
$643$	−10.8979			−0.429771			−0.214885	−	0.976639i	$-0.568938\pi$
$643$	−10.8979			−0.429771			−0.214885	+	0.976639i	$0.568938\pi$
$644$	−21.4117	+	23.2402i	−0.843738	+	0.915793i
$645$		0			0
$646$	1.73390	+	3.95509i	0.0682194	+	0.155611i
$647$	11.6612	+	11.6612i	0.458448	+	0.458448i	0.898146	−	0.439698i	$-0.144915\pi$
$647$	11.6612	+	11.6612i	0.458448	+	0.458448i	−0.439698	+	0.898146i	$0.644915\pi$
$648$		0			0
$649$	−5.23285			−0.205407
$650$	9.20006	+	41.0242i	0.360856	+	1.60910i
$651$		0			0
$652$	−10.5990	+	11.5041i	−0.415087	+	0.450536i
$653$			5.28393i			0.206776i	0.994641	+	0.103388i	$0.0329684\pi$
$653$			5.28393i			0.206776i	−0.994641	+	0.103388i	$0.967032\pi$
$654$		0			0
$655$	0.491000	−	5.08409i	0.0191849	−	0.198652i
$656$	27.6405	−	2.26765i	1.07918	−	0.0885369i
$657$		0			0
$658$	−0.189703	−	0.432720i	−0.00739540	−	0.0168692i
$659$	16.2902	−	16.2902i	0.634578	−	0.634578i	−0.314635	−	0.949213i	$-0.601882\pi$
$659$	16.2902	−	16.2902i	0.634578	−	0.634578i	0.949213	+	0.314635i	$0.101882\pi$
$660$		0			0
$661$	−12.7924	−	12.7924i	−0.497566	−	0.497566i	0.413114	−	0.910679i	$-0.364441\pi$
$661$	−12.7924	−	12.7924i	−0.497566	−	0.497566i	−0.910679	+	0.413114i	$0.864441\pi$
$662$	25.3757	+	9.90761i	0.986256	+	0.385070i
$663$		0			0
$664$	11.3362	+	3.89948i	0.439930	+	0.151329i
$665$	−3.55652	−	4.31690i	−0.137916	−	0.167402i
$666$		0			0
$667$	−14.2810			−0.552962
$668$	−27.9344	+	1.14396i	−1.08082	+	0.0442613i
$669$		0			0
$670$	−25.5268	−	12.9190i	−0.986188	−	0.499105i
$671$			1.02711i			0.0396512i
$672$		0			0
$673$	11.9553	−	11.9553i	0.460841	−	0.460841i	−0.438090	−	0.898931i	$-0.644345\pi$
$673$	11.9553	−	11.9553i	0.460841	−	0.460841i	0.898931	+	0.438090i	$0.144345\pi$
$674$	11.7046	−	29.9782i	0.450843	−	1.15472i
$675$		0			0
$676$	30.2913	−	32.8782i	1.16505	−	1.26455i
$677$			3.18699i			0.122486i	0.998123	+	0.0612430i	$0.0195065\pi$
$677$			3.18699i			0.122486i	−0.998123	+	0.0612430i	$0.980494\pi$
$678$		0			0
$679$			6.12535i			0.235069i
$680$	7.25373	−	15.9178i	0.278168	−	0.610420i
$681$		0			0
$682$	1.98069	−	5.07303i	0.0758447	−	0.194256i
$683$			35.1661i			1.34559i	0.739827	+	0.672797i	$0.234907\pi$
$683$			35.1661i			1.34559i	−0.739827	+	0.672797i	$0.765093\pi$
$684$		0			0
$685$	−21.5167	−	2.07799i	−0.822112	−	0.0793961i
$686$	26.4647	+	10.3328i	1.01043	+	0.394508i
$687$		0			0
$688$	39.5210	−	3.24234i	1.50672	−	0.123613i
$689$			23.9743i			0.913346i
$690$		0			0
$691$	2.90121	+	2.90121i	0.110367	+	0.110367i	0.760134	−	0.649767i	$-0.225133\pi$
$691$	2.90121	+	2.90121i	0.110367	+	0.110367i	−0.649767	+	0.760134i	$0.725133\pi$
$692$	−5.13703	−	4.73284i	−0.195280	−	0.179916i
$693$		0			0
$694$	3.16594	+	7.22163i	0.120178	+	0.274129i
$695$	4.17758	−	43.2571i	0.158465	−	1.64083i
$696$		0			0
$697$	13.5598	−	13.5598i	0.513614	−	0.513614i
$698$	10.9699	−	28.0966i	0.415218	−	1.06347i
$699$		0			0
$700$	−3.42214	+	22.3964i	−0.129345	+	0.846506i
$701$	−15.7397	+	15.7397i	−0.594481	+	0.594481i	−0.938839	−	0.344358i	$-0.888097\pi$
$701$	−15.7397	+	15.7397i	−0.594481	+	0.594481i	0.344358	+	0.938839i	$0.388097\pi$
$702$		0			0
$703$	7.99136	+	7.99136i	0.301400	+	0.301400i
$704$	−8.47290	+	1.04562i	−0.319335	+	0.0394082i
$705$		0			0
$706$	4.80440	+	1.87581i	0.180816	+	0.0705971i
$707$			15.9095i			0.598339i
$708$		0			0
$709$	1.95755	−	1.95755i	0.0735172	−	0.0735172i	−0.669392	−	0.742909i	$-0.733445\pi$
$709$	1.95755	−	1.95755i	0.0735172	−	0.0735172i	0.742909	+	0.669392i	$0.233445\pi$
$710$	5.19785	−	10.2705i	0.195072	−	0.385445i
$711$		0			0
$712$	−0.114007	−	0.0392167i	−0.00427260	−	0.00146971i
$713$	17.7947	+	17.7947i	0.666416	+	0.666416i
$714$		0			0
$715$	1.36387	−	14.1222i	0.0510057	−	0.528142i
$716$	1.51388	+	36.9674i	0.0565762	+	1.38154i
$717$		0			0
$718$	7.47633	−	3.27760i	0.279014	−	0.122319i
$719$	−0.0658604			−0.00245618			−0.00122809	−	0.999999i	$-0.500391\pi$
$719$	−0.0658604			−0.00245618			−0.00122809	+	0.999999i	$0.500391\pi$
$720$		0			0
$721$	−1.41692			−0.0527687
$722$	23.0303	−	10.0964i	0.857100	−	0.375750i
$723$		0			0
$724$	−38.5454	+	1.57850i	−1.43253	+	0.0586644i
$725$	−8.49181	+	5.72078i	−0.315378	+	0.212465i
$726$		0			0
$727$	−16.2286	−	16.2286i	−0.601885	−	0.601885i	0.338927	−	0.940813i	$-0.389936\pi$
$727$	−16.2286	−	16.2286i	−0.601885	−	0.601885i	−0.940813	+	0.338927i	$0.889936\pi$
$728$	34.2406	−	16.7132i	1.26904	−	0.619434i
$729$		0			0
$730$	−12.4947	+	4.09749i	−0.462451	+	0.151655i
$731$	19.3881	−	19.3881i	0.717095	−	0.717095i
$732$		0			0
$733$			0.669106i			0.0247140i	0.999924	+	0.0123570i	$0.00393345\pi$
$733$			0.669106i			0.0247140i	−0.999924	+	0.0123570i	$0.996067\pi$
$734$	−15.4724	−	6.04100i	−0.571098	−	0.222977i
$735$		0			0
$736$	11.2950	−	37.7981i	0.416338	−	1.39326i
$737$	6.82691	+	6.82691i	0.251472	+	0.251472i
$738$		0			0
$739$	−23.4183	+	23.4183i	−0.861454	+	0.861454i	−0.991507	−	0.130053i	$-0.958485\pi$
$739$	−23.4183	+	23.4183i	−0.861454	+	0.861454i	0.130053	+	0.991507i	$0.458485\pi$
$740$	2.53247	−	45.7085i	0.0930956	−	1.68028i
$741$		0			0
$742$	−4.69874	+	12.0346i	−0.172496	+	0.441804i
$743$	−30.0968	+	30.0968i	−1.10414	+	1.10414i	−0.110238	+	0.993905i	$0.535161\pi$
$743$	−30.0968	+	30.0968i	−1.10414	+	1.10414i	−0.993905	+	0.110238i	$0.964839\pi$
$744$		0			0
$745$	5.47092	+	0.528358i	0.200439	+	0.0193575i
$746$	−9.11257	−	20.7861i	−0.333635	−	0.761033i
$747$		0			0
$748$	−3.99983	+	4.34142i	−0.146248	+	0.158738i
$749$	28.1838	+	28.1838i	1.02981	+	1.02981i
$750$		0			0
$751$			53.2724i			1.94394i	0.235107	+	0.971970i	$0.424456\pi$
$751$			53.2724i			1.94394i	−0.235107	+	0.971970i	$0.575544\pi$
$752$	0.449786	+	0.381580i	0.0164020	+	0.0139148i
$753$		0			0
$754$	16.0401	+	6.26262i	0.584144	+	0.228071i
$755$	8.29666	+	10.0705i	0.301946	+	0.366502i
$756$		0			0
$757$		−	27.1717i		−	0.987574i	−0.869583	−	0.493787i	$-0.835612\pi$
$757$		−	27.1717i		−	0.987574i	0.869583	−	0.493787i	$-0.164388\pi$
$758$	−6.48377	+	16.6065i	−0.235501	+	0.603174i
$759$		0			0
$760$	6.35398	+	2.89550i	0.230483	+	0.105031i
$761$			12.9068i			0.467870i	0.972252	+	0.233935i	$0.0751604\pi$
$761$			12.9068i			0.467870i	−0.972252	+	0.233935i	$0.924840\pi$
$762$		0			0
$763$		−	1.10593i		−	0.0400374i
$764$	4.30270	+	3.96416i	0.155666	+	0.143418i
$765$		0			0
$766$	18.1069	−	46.3761i	0.654229	−	1.67564i
$767$	−20.6162	+	20.6162i	−0.744409	+	0.744409i
$768$		0			0
$769$		−	34.4858i		−	1.24359i	−0.783180	−	0.621795i	$-0.786404\pi$
$769$		−	34.4858i		−	1.24359i	0.783180	−	0.621795i	$-0.213596\pi$
$770$	3.45247	−	6.82177i	0.124418	−	0.245840i
$771$		0			0
$772$	0.00961387	+	0.234761i	0.000346011	+	0.00844925i
$773$	−26.6789			−0.959574			−0.479787	−	0.877385i	$-0.659286\pi$
$773$	−26.6789			−0.959574			−0.479787	+	0.877385i	$0.659286\pi$
$774$		0			0
$775$	17.7095	+	3.45281i	0.636143	+	0.124029i
$776$	−3.35429	−	6.87196i	−0.120412	−	0.246689i
$777$		0			0
$778$	−30.8927	−	12.0616i	−1.10756	−	0.432431i
$779$	5.41272	+	5.41272i	0.193931	+	0.193931i
$780$		0			0
$781$	−2.74675	+	2.74675i	−0.0982864	+	0.0982864i
$782$	−10.9523	−	24.9825i	−0.391652	−	0.893373i
$783$		0			0
$784$	−7.44253	+	0.610593i	−0.265805	+	0.0218069i
$785$	4.47493	+	5.43167i	0.159717	+	0.193865i
$786$		0			0
$787$		−	33.2611i		−	1.18563i	−0.805338	−	0.592815i	$-0.798016\pi$
$787$		−	33.2611i		−	1.18563i	0.805338	−	0.592815i	$-0.201984\pi$
$788$	11.4802	+	10.5769i	0.408963	+	0.376786i
$789$		0			0
$790$	15.2991	−	30.2298i	0.544319	−	1.07553i
$791$	−17.4195			−0.619365
$792$		0			0
$793$	4.04658	+	4.04658i	0.143698	+	0.143698i
$794$	4.89762	+	11.1716i	0.173810	+	0.396466i
$795$		0			0
$796$	−16.1416	−	14.8715i	−0.572122	−	0.527107i
$797$	−15.9072			−0.563461			−0.281730	−	0.959494i	$-0.590908\pi$
$797$	−15.9072			−0.563461			−0.281730	+	0.959494i	$0.590908\pi$
$798$		0			0
$799$	0.407850			0.0144287
$800$	−8.42521	−	27.0003i	−0.297876	−	0.954605i
$801$		0			0
$802$	11.1921	+	25.5296i	0.395208	+	0.901483i
$803$	4.43743			0.156593
$804$		0			0
$805$	22.4649	+	27.2679i	0.791784	+	0.961067i
$806$	−12.1831	−	27.7900i	−0.429131	−	0.978863i
$807$		0			0
$808$	−8.71217	−	17.8487i	−0.306493	−	0.627915i
$809$	12.4922			0.439204			0.219602	−	0.975590i	$-0.429524\pi$
$809$	12.4922			0.439204			0.219602	+	0.975590i	$0.429524\pi$
$810$		0			0
$811$	−35.4886	+	35.4886i	−1.24617	+	1.24617i	−0.288777	+	0.957396i	$0.593249\pi$
$811$	−35.4886	+	35.4886i	−1.24617	+	1.24617i	−0.957396	+	0.288777i	$0.906751\pi$
$812$	6.82436	+	6.28741i	0.239488	+	0.220645i
$813$		0			0
$814$	−5.61859	+	14.3906i	−0.196932	+	0.504389i
$815$	11.1203	+	13.4978i	0.389528	+	0.472809i
$816$		0			0
$817$	7.73923	+	7.73923i	0.270761	+	0.270761i
$818$	−15.2136	−	34.7027i	−0.531930	−	1.21335i
$819$		0			0
$820$	1.71530	−	30.9593i	0.0599009	−	1.08115i
$821$	15.9683	+	15.9683i	0.557299	+	0.557299i	0.928537	−	0.371239i	$-0.121067\pi$
$821$	15.9683	+	15.9683i	0.557299	+	0.557299i	−0.371239	+	0.928537i	$0.621067\pi$
$822$		0			0
$823$	−21.7278	+	21.7278i	−0.757384	+	0.757384i	−0.975846	−	0.218462i	$-0.929896\pi$
$823$	−21.7278	+	21.7278i	−0.757384	+	0.757384i	0.218462	+	0.975846i	$0.429896\pi$
$824$	1.58962	−	0.775914i	0.0553771	−	0.0270302i
$825$		0			0
$826$	−14.3895	+	6.30833i	−0.500675	+	0.219495i
$827$	39.2381			1.36444			0.682221	−	0.731146i	$-0.261014\pi$
$827$	39.2381			1.36444			0.682221	+	0.731146i	$0.261014\pi$
$828$		0			0
$829$	18.6072	+	18.6072i	0.646254	+	0.646254i	0.952086	−	0.305831i	$-0.0989344\pi$
$829$	18.6072	+	18.6072i	0.646254	+	0.646254i	−0.305831	+	0.952086i	$0.598934\pi$
$830$	6.05231	−	11.9588i	0.210079	−	0.415098i
$831$		0			0
$832$	−29.2618	+	37.5008i	−1.01447	+	1.30011i
$833$	−3.65114	+	3.65114i	−0.126504	+	0.126504i
$834$		0			0
$835$	−3.00477	+	31.1131i	−0.103984	+	1.07671i
$836$	−1.73298	−	1.59663i	−0.0599365	−	0.0552206i
$837$		0			0
$838$	20.6335	+	8.05608i	0.712774	+	0.278293i
$839$		−	12.5955i		−	0.434845i	−0.976078	−	0.217422i	$-0.930235\pi$
$839$		−	12.5955i		−	0.434845i	0.976078	−	0.217422i	$-0.0697649\pi$
$840$		0			0
$841$		−	24.8065i		−	0.855396i
$842$	−0.176824	+	0.452889i	−0.00609377	+	0.0156076i
$843$		0			0
$844$	25.2142	−	1.03256i	0.867909	−	0.0355423i
$845$	−31.7814	−	38.5762i	−1.09331	−	1.32706i
$846$		0			0
$847$	15.7981	−	15.7981i	0.542829	−	0.542829i
$848$	−1.31877	−	16.0745i	−0.0452867	−	0.552002i
$849$		0			0
$850$	−16.5202	−	10.4679i	−0.566637	−	0.359044i
$851$	−50.4778	−	50.4778i	−1.73036	−	1.73036i
$852$		0			0
$853$	−43.6914			−1.49597			−0.747983	−	0.663718i	$-0.768978\pi$
$853$	−43.6914			−1.49597			−0.747983	+	0.663718i	$0.768978\pi$
$854$	1.23821	+	2.82439i	0.0423706	+	0.0966488i
$855$		0			0
$856$	−47.0527	−	16.1854i	−1.60823	−	0.553206i
$857$	28.9373	−	28.9373i	0.988478	−	0.988478i	−0.0114561	−	0.999934i	$-0.503647\pi$
$857$	28.9373	−	28.9373i	0.988478	−	0.988478i	0.999934	+	0.0114561i	$0.00364668\pi$
$858$		0			0
$859$	28.1247	+	28.1247i	0.959602	+	0.959602i	0.999215	−	0.0396134i	$-0.0126126\pi$
$859$	28.1247	+	28.1247i	0.959602	+	0.959602i	−0.0396134	+	0.999215i	$0.512613\pi$
$860$	2.45257	−	44.2664i	0.0836321	−	1.50947i
$861$		0			0
$862$	26.8141	−	11.7552i	0.913291	−	0.400384i
$863$	22.2144	+	22.2144i	0.756186	+	0.756186i	0.975626	−	0.219440i	$-0.0704229\pi$
$863$	22.2144	+	22.2144i	0.756186	+	0.756186i	−0.219440	+	0.975626i	$0.570423\pi$
$864$		0			0
$865$	−6.02730	+	4.96565i	−0.204934	+	0.168837i
$866$	10.5861	+	4.13322i	0.359732	+	0.140452i
$867$		0			0
$868$	−0.669061	−	16.3378i	−0.0227094	−	0.554541i
$869$	−8.08466	+	8.08466i	−0.274253	+	0.274253i
$870$		0			0
$871$	53.7929			1.82270
$872$	0.605616	+	1.24073i	0.0205087	+	0.0420164i
$873$		0			0
$874$	9.97237	−	4.37186i	0.337320	−	0.147880i
$875$	24.2813	+	7.21497i	0.820859	+	0.243911i
$876$		0			0
$877$	−5.13889			−0.173528			−0.0867640	−	0.996229i	$-0.527653\pi$
$877$	−5.13889			−0.173528			−0.0867640	+	0.996229i	$0.527653\pi$
$878$	−24.3374	+	10.6694i	−0.821346	+	0.360076i
$879$		0			0
$880$	−0.137627	+	9.54386i	−0.00463941	+	0.321724i
$881$	4.34528			0.146396			0.0731982	−	0.997317i	$-0.476679\pi$
$881$	4.34528			0.146396			0.0731982	+	0.997317i	$0.476679\pi$
$882$		0			0
$883$	35.4317			1.19237			0.596186	−	0.802846i	$-0.296682\pi$
$883$	35.4317			1.19237			0.596186	+	0.802846i	$0.296682\pi$
$884$	1.34578	+	32.8626i	0.0452635	+	1.10529i
$885$		0			0
$886$	15.7551	−	6.90701i	0.529304	−	0.232046i
$887$	−37.4644	−	37.4644i	−1.25793	−	1.25793i	−0.952078	−	0.305855i	$-0.901058\pi$
$887$	−37.4644	−	37.4644i	−1.25793	−	1.25793i	−0.305855	−	0.952078i	$-0.598942\pi$
$888$		0			0
$889$	20.0945			0.673947
$890$	−0.0608675	+	0.120269i	−0.00204028	+	0.00403142i
$891$		0			0
$892$	37.2131	−	1.52394i	1.24599	−	0.0510253i
$893$			0.162803i			0.00544799i
$894$		0			0
$895$	41.1739	+	3.97640i	1.37629	+	0.132916i
$896$	−22.0386	+	13.0896i	−0.736259	+	0.437292i
$897$		0			0
$898$	−35.3215	+	15.4849i	−1.17869	+	0.516736i
$899$	5.22531	−	5.22531i	0.174274	−	0.174274i
$900$		0			0
$901$	−7.88580	−	7.88580i	−0.262714	−	0.262714i
$902$	−3.80560	+	9.74703i	−0.126712	+	0.324541i
$903$		0			0
$904$	19.5427	−	9.53903i	0.649980	−	0.317263i
$905$	−4.14613	+	42.9314i	−0.137822	+	1.42709i
$906$		0			0
$907$	0.181405			0.00602345			0.00301173	−	0.999995i	$-0.499041\pi$
$907$	0.181405			0.00602345			0.00301173	+	0.999995i	$0.499041\pi$
$908$	28.4518	+	26.2132i	0.944208	+	0.869916i
$909$		0			0
$910$	−13.2743	−	40.4781i	−0.440039	−	1.34184i
$911$			23.4249i			0.776101i	0.921638	+	0.388050i	$0.126851\pi$
$911$			23.4249i			0.776101i	−0.921638	+	0.388050i	$0.873149\pi$
$912$		0			0
$913$	−3.19828	+	3.19828i	−0.105848	+	0.105848i
$914$	−36.7976	−	14.3671i	−1.21716	−	0.475222i
$915$		0			0
$916$	1.52931	+	37.3443i	0.0505299	+	1.23389i
$917$			5.17529i			0.170903i
$918$		0			0
$919$		−	3.05885i		−	0.100902i	−0.998727	−	0.0504511i	$-0.983934\pi$
$919$		−	3.05885i		−	0.100902i	0.998727	−	0.0504511i	$-0.0160659\pi$
$920$	−40.1352	−	18.2896i	−1.32322	−	0.602989i
$921$		0			0
$922$	24.0820	+	9.40249i	0.793099	+	0.309654i
$923$			21.6431i			0.712392i
$924$		0			0
$925$	−50.2361	−	9.79453i	−1.65175	−	0.322042i
$926$	10.5943	−	27.1345i	0.348150	−	0.891696i
$927$		0			0
$928$	−11.0992	−	3.31670i	−0.364349	−	0.108876i
$929$			59.9772i			1.96779i	0.178752	+	0.983894i	$0.442794\pi$
$929$			59.9772i			1.96779i	−0.178752	+	0.983894i	$0.557206\pi$
$930$		0			0
$931$	−1.45744	−	1.45744i	−0.0477657	−	0.0477657i
$932$	58.4665	−	2.39430i	1.91513	−	0.0784280i
$933$		0			0
$934$	54.8596	−	24.0503i	1.79506	−	0.786950i
$935$	4.19659	+	5.09381i	0.137243	+	0.166586i
$936$		0			0
$937$	−23.7463	+	23.7463i	−0.775759	+	0.775759i	−0.979107	−	0.203347i	$-0.934818\pi$
$937$	−23.7463	+	23.7463i	−0.775759	+	0.775759i	0.203347	+	0.979107i	$0.434818\pi$
$938$	27.0029	+	10.5429i	0.881677	+	0.344239i
$939$		0			0
$940$	0.491392	−	0.439799i	0.0160274	−	0.0143447i
$941$	35.2727	−	35.2727i	1.14986	−	1.14986i	0.163278	−	0.986580i	$-0.447793\pi$
$941$	35.2727	−	35.2727i	1.14986	−	1.14986i	0.986580	−	0.163278i	$-0.0522068\pi$
$942$		0			0
$943$	−34.1897	−	34.1897i	−1.11337	−	1.11337i
$944$	12.6889	−	14.9570i	0.412990	−	0.486810i
$945$		0			0
$946$	−5.44133	+	13.9365i	−0.176913	+	0.453116i
$947$			19.9140i			0.647118i	0.946208	+	0.323559i	$0.104879\pi$
$947$			19.9140i			0.647118i	−0.946208	+	0.323559i	$0.895121\pi$
$948$		0			0
$949$	17.4824	−	17.4824i	0.567504	−	0.567504i
$950$	4.17849	−	6.59442i	0.135568	−	0.213951i
$951$		0			0
$952$	−5.76523	+	16.7601i	−0.186852	+	0.543199i
$953$	−23.1060	−	23.1060i	−0.748477	−	0.748477i	0.225716	−	0.974193i	$-0.427528\pi$
$953$	−23.1060	−	23.1060i	−0.748477	−	0.748477i	−0.974193	+	0.225716i	$0.927528\pi$
$954$		0			0
$955$	5.04838	−	4.15916i	0.163362	−	0.134587i
$956$	19.1150	−	20.7474i	0.618222	−	0.671019i
$957$		0			0
$958$	15.3825	+	35.0881i	0.496987	+	1.13364i
$959$	21.9027			0.707276
$960$		0			0
$961$	17.9781			0.579939
$962$	34.5595	+	78.8314i	1.11424	+	2.54163i
$963$		0			0
$964$	−17.3476	+	18.8291i	−0.558728	+	0.606444i
$965$	0.261475	+	0.0252521i	0.00841717	+	0.000812894i
$966$		0			0
$967$	−41.7332	−	41.7332i	−1.34205	−	1.34205i	−0.894018	−	0.448030i	$-0.852126\pi$
$967$	−41.7332	−	41.7332i	−1.34205	−	1.34205i	−0.448030	−	0.894018i	$-0.647874\pi$
$968$	−9.07255	+	26.3749i	−0.291603	+	0.847721i
$969$		0			0
$970$	−8.12382	+	2.66410i	−0.260840	+	0.0855392i
$971$	−33.5030	+	33.5030i	−1.07516	+	1.07516i	−0.0782268	+	0.996936i	$0.524926\pi$
$971$	−33.5030	+	33.5030i	−1.07516	+	1.07516i	−0.996936	+	0.0782268i	$0.975074\pi$
$972$		0			0
$973$			44.0330i			1.41163i
$974$	15.9790	−	40.9259i	0.511999	−	1.31135i
$975$		0			0
$976$	−2.93579	−	2.49060i	−0.0939723	−	0.0797223i
$977$	−9.16848	−	9.16848i	−0.293326	−	0.293326i	0.545067	−	0.838393i	$-0.316504\pi$
$977$	−9.16848	−	9.16848i	−0.293326	−	0.293326i	−0.838393	+	0.545067i	$0.816504\pi$
$978$		0			0
$979$	0.0321648	−	0.0321648i	0.00102799	−	0.00102799i
$980$	−0.461865	+	8.33618i	−0.0147537	+	0.266289i
$981$		0			0
$982$	−11.4009	−	4.45134i	−0.363818	−	0.142048i
$983$	39.1183	−	39.1183i	1.24768	−	1.24768i	0.290936	−	0.956742i	$-0.406033\pi$
$983$	39.1183	−	39.1183i	1.24768	−	1.24768i	0.956742	−	0.290936i	$-0.0939668\pi$
$984$		0			0
$985$	13.4697	−	11.0972i	0.429181	−	0.353585i
$986$	−7.33597	+	3.21607i	−0.233625	+	0.102421i
$987$		0			0
$988$	−13.1179	+	0.537201i	−0.417336	+	0.0170906i
$989$	−48.8852	−	48.8852i	−1.55446	−	1.55446i
$990$		0			0
$991$		−	12.9925i		−	0.412722i	−0.978476	−	0.206361i	$-0.933838\pi$
$991$		−	12.9925i		−	0.412722i	0.978476	−	0.206361i	$-0.0661621\pi$
$992$	9.69732	+	17.9628i	0.307890	+	0.570320i
$993$		0			0
$994$	−4.24186	+	10.8644i	−0.134544	+	0.344598i
$995$	−18.9390	+	15.6031i	−0.600406	+	0.494650i
$996$		0			0
$997$		−	8.89509i		−	0.281710i	−0.990030	−	0.140855i	$-0.955015\pi$
$997$		−	8.89509i		−	0.281710i	0.990030	−	0.140855i	$-0.0449852\pi$
$998$	−28.7122	−	11.2103i	−0.908868	−	0.354855i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.z.g.667.4		18
3.2	odd	2		80.2.s.b.27.6	yes	18
5.3	odd	4		720.2.bd.g.523.1		18
12.11	even	2		320.2.s.b.207.2		18
15.2	even	4		400.2.j.d.43.1		18
15.8	even	4		80.2.j.b.43.9	✓	18
15.14	odd	2		400.2.s.d.107.4		18
16.3	odd	4		720.2.bd.g.307.1		18
24.5	odd	2		640.2.s.d.287.2		18
24.11	even	2		640.2.s.c.287.8		18
48.5	odd	4		640.2.j.c.607.2		18
48.11	even	4		640.2.j.d.607.8		18
48.29	odd	4		320.2.j.b.47.8		18
48.35	even	4		80.2.j.b.67.9	yes	18
60.23	odd	4		320.2.j.b.143.2		18
60.47	odd	4		1600.2.j.d.143.8		18
60.59	even	2		1600.2.s.d.207.8		18
80.3	even	4	inner	720.2.z.g.163.4		18
120.53	even	4		640.2.j.d.543.2		18
120.83	odd	4		640.2.j.c.543.8		18
240.29	odd	4		1600.2.j.d.1007.2		18
240.53	even	4		640.2.s.c.223.8		18
240.77	even	4		1600.2.s.d.943.8		18
240.83	odd	4		80.2.s.b.3.6	yes	18
240.173	even	4		320.2.s.b.303.2		18
240.179	even	4		400.2.j.d.307.1		18
240.203	odd	4		640.2.s.d.223.2		18
240.227	odd	4		400.2.s.d.243.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.9	✓	18	15.8	even	4
80.2.j.b.67.9	yes	18	48.35	even	4
80.2.s.b.3.6	yes	18	240.83	odd	4
80.2.s.b.27.6	yes	18	3.2	odd	2
320.2.j.b.47.8		18	48.29	odd	4
320.2.j.b.143.2		18	60.23	odd	4
320.2.s.b.207.2		18	12.11	even	2
320.2.s.b.303.2		18	240.173	even	4
400.2.j.d.43.1		18	15.2	even	4
400.2.j.d.307.1		18	240.179	even	4
400.2.s.d.107.4		18	15.14	odd	2
400.2.s.d.243.4		18	240.227	odd	4
640.2.j.c.543.8		18	120.83	odd	4
640.2.j.c.607.2		18	48.5	odd	4
640.2.j.d.543.2		18	120.53	even	4
640.2.j.d.607.8		18	48.11	even	4
640.2.s.c.223.8		18	240.53	even	4
640.2.s.c.287.8		18	24.11	even	2
640.2.s.d.223.2		18	240.203	odd	4
640.2.s.d.287.2		18	24.5	odd	2
720.2.z.g.163.4		18	80.3	even	4	inner
720.2.z.g.667.4		18	1.1	even	1	trivial
720.2.bd.g.307.1		18	16.3	odd	4
720.2.bd.g.523.1		18	5.3	odd	4
1600.2.j.d.143.8		18	60.47	odd	4
1600.2.j.d.1007.2		18	240.29	odd	4
1600.2.s.d.207.8		18	60.59	even	2
1600.2.s.d.943.8		18	240.77	even	4

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.z (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.567819 - 1.29521i) q^{2} +(-1.35516 + 1.47090i) q^{4} +(1.42182 + 1.72581i) q^{5} +(-1.60205 - 1.60205i) q^{7} +(2.67461 + 0.920026i) q^{8} +O(q^{10})\)	\(q+(-0.567819 - 1.29521i) q^{2} +(-1.35516 + 1.47090i) q^{4} +(1.42182 + 1.72581i) q^{5} +(-1.60205 - 1.60205i) q^{7} +(2.67461 + 0.920026i) q^{8} +(1.42795 - 2.82151i) q^{10} +(-0.754587 + 0.754587i) q^{11} +5.94580i q^{13} +(-1.16532 + 2.98467i) q^{14} +(-0.327065 - 3.98661i) q^{16} +(-1.95574 - 1.95574i) q^{17} +(0.780680 - 0.780680i) q^{19} +(-4.46529 - 0.247399i) q^{20} +(1.40582 + 0.548884i) q^{22} +(-4.93121 + 4.93121i) q^{23} +(-0.956833 + 4.90759i) q^{25} +(7.70109 - 3.37614i) q^{26} +(4.52748 - 0.185408i) q^{28} +(1.44802 + 1.44802i) q^{29} -3.60859i q^{31} +(-4.97780 + 2.68729i) q^{32} +(-1.42260 + 3.64361i) q^{34} +(0.486998 - 5.04266i) q^{35} +10.2364i q^{37} +(-1.45443 - 0.567864i) q^{38} +(2.21504 + 5.92398i) q^{40} +6.93334i q^{41} +9.91344i q^{43} +(-0.0873298 - 2.13251i) q^{44} +(9.18700 + 3.58694i) q^{46} +(-0.104270 + 0.104270i) q^{47} -1.86688i q^{49} +(6.89970 - 1.54732i) q^{50} +(-8.74565 - 8.05753i) q^{52} +4.03213 q^{53} +(-2.37516 - 0.229383i) q^{55} +(-2.81093 - 5.75878i) q^{56} +(1.05328 - 2.69771i) q^{58} +(3.46736 + 3.46736i) q^{59} +(0.680578 - 0.680578i) q^{61} +(-4.67390 + 2.04902i) q^{62} +(6.30711 + 4.92142i) q^{64} +(-10.2613 + 8.45388i) q^{65} -9.04721i q^{67} +(5.52703 - 0.226341i) q^{68} +(-6.80785 + 2.23255i) q^{70} +3.64007 q^{71} +(-2.94030 - 2.94030i) q^{73} +(13.2583 - 5.81242i) q^{74} +(0.0903496 + 2.20625i) q^{76} +2.41777 q^{77} +10.7140 q^{79} +(6.41509 - 6.23270i) q^{80} +(8.98016 - 3.93688i) q^{82} +4.23845 q^{83} +(0.594515 - 6.15595i) q^{85} +(12.8400 - 5.62904i) q^{86} +(-2.71247 + 1.32399i) q^{88} -0.0426256 q^{89} +(9.52546 - 9.52546i) q^{91} +(-0.570698 - 13.9359i) q^{92} +(0.194258 + 0.0758455i) q^{94} +(2.45730 + 0.237315i) q^{95} +(-1.91173 - 1.91173i) q^{97} +(-2.41802 + 1.06005i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	\( 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35} - 24 q^{38} + 44 q^{40} + 44 q^{44} + 12 q^{46} - 38 q^{47} + 8 q^{50} + 8 q^{52} - 12 q^{53} - 6 q^{55} - 20 q^{56} + 20 q^{58} - 10 q^{59} + 14 q^{61} + 40 q^{62} + 16 q^{64} + 60 q^{68} - 28 q^{70} - 24 q^{71} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 44 q^{77} - 16 q^{79} + 92 q^{80} + 48 q^{82} - 40 q^{83} + 14 q^{85} + 36 q^{86} - 8 q^{88} - 12 q^{89} + 8 q^{92} - 28 q^{94} - 34 q^{95} + 18 q^{97} + 56 q^{98}+O(q^{100}) \) 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more