LMFDB - Embedded newform 750.2.o.a.469.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, degree $20$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			469.7
Character	$\chi$	$=$	750.469
Dual form			750.2.o.a.379.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.998027 - 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-2.21909 - 0.275059i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(-0.591103 - 0.813584i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})$	\(q+(0.998027 - 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-2.21909 - 0.275059i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(-0.591103 - 0.813584i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(-2.23198 - 0.135178i) q^{10} +(0.286195 + 4.54893i) q^{11} +(-0.844328 + 0.535827i) q^{12} +(0.824799 + 0.682333i) q^{13} +(-0.641022 - 0.774863i) q^{14} +(2.12500 - 0.695960i) q^{15} +(0.968583 - 0.248690i) q^{16} +(-0.674033 + 5.33552i) q^{17} +(0.587785 - 0.809017i) q^{18} +(-0.821848 + 1.74652i) q^{19} +(-2.23606 + 0.00523549i) q^{20} +(0.881254 + 0.484473i) q^{21} +(0.571260 + 4.52199i) q^{22} +(2.62370 + 6.62671i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(4.84869 + 1.22076i) q^{25} +(0.866016 + 0.629197i) q^{26} +(-0.248690 + 0.968583i) q^{27} +(-0.688412 - 0.733084i) q^{28} +(2.35477 - 2.21128i) q^{29} +(2.07711 - 0.828017i) q^{30} +(-9.46875 - 1.19618i) q^{31} +(0.951057 - 0.309017i) q^{32} +(-2.19580 - 3.99414i) q^{33} +(-0.337683 + 5.36731i) q^{34} +(1.08793 + 1.96800i) q^{35} +(0.535827 - 0.844328i) q^{36} +(1.94244 + 7.56530i) q^{37} +(-0.710562 + 1.79467i) q^{38} +(-1.03682 - 0.266211i) q^{39} +(-2.23132 + 0.145629i) q^{40} +(-2.47704 - 0.980730i) q^{41} +(0.909935 + 0.428183i) q^{42} +(-6.89180 - 2.23928i) q^{43} +(0.854071 + 4.47720i) q^{44} +(-1.62643 + 1.53451i) q^{45} +(3.03462 + 6.44889i) q^{46} +(9.48860 + 1.81005i) q^{47} +(-0.770513 + 0.637424i) q^{48} +(1.85060 - 5.69557i) q^{49} +(4.91577 + 0.913897i) q^{50} +(-1.66187 - 5.11471i) q^{51} +(0.903814 + 0.573578i) q^{52} +(-4.40820 + 8.01849i) q^{53} +(-0.187381 + 0.982287i) q^{54} +(0.616133 - 10.1732i) q^{55} +(-0.733084 - 0.688412i) q^{56} -1.93022i q^{57} +(2.21128 - 2.35477i) q^{58} +(2.04413 + 3.22104i) q^{59} +(2.02102 - 0.956806i) q^{60} +(-1.90364 + 0.753705i) q^{61} +(-9.52517 - 0.599273i) q^{62} +(-1.00366 - 0.0631450i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-1.64262 - 1.74102i) q^{65} +(-2.44226 - 3.84839i) q^{66} +(2.00998 - 2.14042i) q^{67} +5.37792i q^{68} +(-5.19551 - 4.87891i) q^{69} +(1.20935 + 1.89581i) q^{70} +(1.73575 - 9.09915i) q^{71} +(0.481754 - 0.876307i) q^{72} +(-9.38715 - 5.95727i) q^{73} +(2.41363 + 7.42840i) q^{74} +(-4.90700 + 0.959895i) q^{75} +(-0.596471 + 1.83575i) q^{76} +(3.53177 - 2.92173i) q^{77} +(-1.05149 - 0.200583i) q^{78} +(4.97488 + 10.5722i) q^{79} +(-2.21777 + 0.285447i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(-2.53373 - 0.823260i) q^{82} +(-0.234923 - 0.110547i) q^{83} +(0.935025 + 0.370203i) q^{84} +(2.96332 - 11.6546i) q^{85} +(-7.01880 - 1.80212i) q^{86} +(-1.18914 + 3.00343i) q^{87} +(1.13351 + 4.41473i) q^{88} +(6.82604 - 10.7561i) q^{89} +(-1.52687 + 1.63360i) q^{90} +(0.0675938 - 1.07437i) q^{91} +(3.43356 + 6.24562i) q^{92} +(9.07689 - 2.94926i) q^{93} +(9.58353 + 1.21068i) q^{94} +(2.30415 - 3.64961i) q^{95} +(-0.728969 + 0.684547i) q^{96} +(-7.67633 - 8.17446i) q^{97} +(1.48932 - 5.80053i) q^{98} +(3.68744 + 2.67908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42} - 10 q^{46} + 140 q^{47} + 50 q^{49} + 20 q^{50} + 10 q^{51} - 80 q^{52} + 30 q^{53} - 10 q^{55} - 30 q^{58} + 20 q^{59} + 40 q^{60} - 100 q^{61} - 10 q^{62} - 10 q^{63} - 20 q^{65} - 40 q^{66} - 10 q^{67} - 10 q^{69} + 10 q^{70} + 80 q^{71} + 20 q^{73} - 80 q^{75} + 10 q^{76} + 20 q^{77} + 140 q^{79} + 100 q^{82} - 70 q^{83} - 20 q^{85} + 20 q^{86} + 30 q^{87} - 10 q^{88} + 40 q^{89} + 10 q^{90} + 170 q^{91} + 120 q^{92} + 50 q^{93} - 30 q^{94} + 220 q^{95} - 60 q^{97} - 120 q^{98} - 20 q^{99}+O(q^{100}) $ 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{49}{50}\right)$	$1$

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 $

$2$	0.998027	−	0.0627905i	0.705711	−	0.0443996i
$2$	0.998027	−	0.0627905i	0.705711	−	0.0443996i
$3$	−0.904827	+	0.425779i	−0.522402	+	0.245824i
$3$	−0.904827	+	0.425779i	−0.522402	+	0.245824i
$4$	0.992115	−	0.125333i	0.496057	−	0.0626666i
$5$	−2.21909	−	0.275059i	−0.992405	−	0.123010i
$5$	−2.21909	−	0.275059i	−0.992405	−	0.123010i
$6$	−0.876307	+	0.481754i	−0.357751	+	0.196675i
$7$	−0.591103	−	0.813584i	−0.223416	−	0.307506i	0.682564	−	0.730826i	$-0.260865\pi$
$7$	−0.591103	−	0.813584i	−0.223416	−	0.307506i	−0.905980	+	0.423320i	$0.860865\pi$
$8$	0.982287	−	0.187381i	0.347291	−	0.0662493i
$9$	0.637424	−	0.770513i	0.212475	−	0.256838i
$10$	−2.23198	−	0.135178i	−0.705813	−	0.0427471i
$11$	0.286195	+	4.54893i	0.0862909	+	1.37156i	0.768243	+	0.640158i	$0.221131\pi$
$11$	0.286195	+	4.54893i	0.0862909	+	1.37156i	−0.681952	+	0.731397i	$0.738869\pi$
$12$	−0.844328	+	0.535827i	−0.243736	+	0.154680i
$13$	0.824799	+	0.682333i	0.228758	+	0.189245i	0.744741	−	0.667354i	$-0.232573\pi$
$13$	0.824799	+	0.682333i	0.228758	+	0.189245i	−0.515983	+	0.856599i	$0.672573\pi$
$14$	−0.641022	−	0.774863i	−0.171320	−	0.207091i
$15$	2.12500	−	0.695960i	0.548674	−	0.179696i
$16$	0.968583	−	0.248690i	0.242146	−	0.0621725i
$17$	−0.674033	+	5.33552i	−0.163477	+	1.29405i	0.670357	+	0.742038i	$0.266141\pi$
$17$	−0.674033	+	5.33552i	−0.163477	+	1.29405i	−0.833834	+	0.552015i	$0.813859\pi$
$18$	0.587785	−	0.809017i	0.138542	−	0.190687i
$19$	−0.821848	+	1.74652i	−0.188545	+	0.400678i	−0.976642	−	0.214872i	$-0.931066\pi$
$19$	−0.821848	+	1.74652i	−0.188545	+	0.400678i	0.788097	+	0.615551i	$0.211066\pi$
$20$	−2.23606	+	0.00523549i	−0.499999	+	0.00117069i
$21$	0.881254	+	0.484473i	0.192305	+	0.105721i
$22$	0.571260	+	4.52199i	0.121793	+	0.964091i
$23$	2.62370	+	6.62671i	0.547079	+	1.38176i	0.895766	+	0.444525i	$0.146628\pi$
$23$	2.62370	+	6.62671i	0.547079	+	1.38176i	−0.348687	+	0.937239i	$0.613372\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	4.84869	+	1.22076i	0.969737	+	0.244152i
$26$	0.866016	+	0.629197i	0.169840	+	0.123396i
$27$	−0.248690	+	0.968583i	−0.0478604	+	0.186404i
$28$	−0.688412	−	0.733084i	−0.130098	−	0.138540i
$29$	2.35477	−	2.21128i	0.437270	−	0.410624i	−0.434398	−	0.900721i	$-0.643039\pi$
$29$	2.35477	−	2.21128i	0.437270	−	0.410624i	0.871668	+	0.490097i	$0.163039\pi$
$30$	2.07711	−	0.828017i	0.379227	−	0.151175i
$31$	−9.46875	−	1.19618i	−1.70064	−	0.214840i	−0.785748	−	0.618546i	$-0.787722\pi$
$31$	−9.46875	−	1.19618i	−1.70064	−	0.214840i	−0.914889	+	0.403706i	$0.867722\pi$
$32$	0.951057	−	0.309017i	0.168125	−	0.0546270i
$33$	−2.19580	−	3.99414i	−0.382240	−	0.695291i
$34$	−0.337683	+	5.36731i	−0.0579121	+	0.920486i
$35$	1.08793	+	1.96800i	0.183893	+	0.332653i
$36$	0.535827	−	0.844328i	0.0893045	−	0.140721i
$37$	1.94244	+	7.56530i	0.319335	+	1.24373i	0.902257	+	0.431199i	$0.141909\pi$
$37$	1.94244	+	7.56530i	0.319335	+	1.24373i	−0.582922	+	0.812528i	$0.698091\pi$
$38$	−0.710562	+	1.79467i	−0.115268	+	0.291135i
$39$	−1.03682	−	0.266211i	−0.166025	−	0.0426279i
$40$	−2.23132	+	0.145629i	−0.352803	+	0.0230259i
$41$	−2.47704	−	0.980730i	−0.386849	−	0.153164i	0.166646	−	0.986017i	$-0.446706\pi$
$41$	−2.47704	−	0.980730i	−0.386849	−	0.153164i	−0.553495	+	0.832852i	$0.686706\pi$
$42$	0.909935	+	0.428183i	0.140406	+	0.0660701i
$43$	−6.89180	−	2.23928i	−1.05099	−	0.341487i	−0.267933	−	0.963438i	$-0.586340\pi$
$43$	−6.89180	−	2.23928i	−1.05099	−	0.341487i	−0.783057	+	0.621951i	$0.786340\pi$
$44$	0.854071	+	4.47720i	0.128756	+	0.674963i
$45$	−1.62643	+	1.53451i	−0.242455	+	0.228751i
$46$	3.03462	+	6.44889i	0.447430	+	0.950837i
$47$	9.48860	+	1.81005i	1.38405	+	0.264023i	0.825011	−	0.565116i	$-0.191169\pi$
$47$	9.48860	+	1.81005i	1.38405	+	0.264023i	0.559043	+	0.829139i	$0.311169\pi$
$48$	−0.770513	+	0.637424i	−0.111214	+	0.0920042i
$49$	1.85060	−	5.69557i	0.264372	−	0.813653i
$50$	4.91577	+	0.913897i	0.695195	+	0.129245i
$51$	−1.66187	−	5.11471i	−0.232708	−	0.716203i
$52$	0.903814	+	0.573578i	0.125337	+	0.0795410i
$53$	−4.40820	+	8.01849i	−0.605513	+	1.10142i	0.378881	+	0.925445i	$0.376309\pi$
$53$	−4.40820	+	8.01849i	−0.605513	+	1.10142i	−0.984394	+	0.175979i	$0.943691\pi$
$54$	−0.187381	+	0.982287i	−0.0254994	+	0.133672i
$55$	0.616133	−	10.1732i	0.0830794	−	1.37175i
$56$	−0.733084	−	0.688412i	−0.0979625	−	0.0919929i
$57$		−	1.93022i		−	0.255664i
$58$	2.21128	−	2.35477i	0.290355	−	0.309196i
$59$	2.04413	+	3.22104i	0.266124	+	0.419344i	0.950942	−	0.309371i	$-0.100118\pi$
$59$	2.04413	+	3.22104i	0.266124	+	0.419344i	−0.684818	+	0.728714i	$0.740118\pi$
$60$	2.02102	−	0.956806i	0.260913	−	0.123523i
$61$	−1.90364	+	0.753705i	−0.243736	+	0.0965021i	−0.486817	−	0.873504i	$-0.661842\pi$
$61$	−1.90364	+	0.753705i	−0.243736	+	0.0965021i	0.243080	+	0.970006i	$0.421842\pi$
$62$	−9.52517	−	0.599273i	−1.20970	−	0.0761077i
$63$	−1.00366	−	0.0631450i	−0.126449	−	0.00795552i
$64$	0.929776	−	0.368125i	0.116222	−	0.0460156i
$65$	−1.64262	−	1.74102i	−0.203742	−	0.215947i
$66$	−2.44226	−	3.84839i	−0.300621	−	0.473704i
$67$	2.00998	−	2.14042i	0.245559	−	0.261493i	−0.594368	−	0.804193i	$-0.702598\pi$
$67$	2.00998	−	2.14042i	0.245559	−	0.261493i	0.839927	+	0.542700i	$0.182598\pi$
$68$			5.37792i			0.652169i
$69$	−5.19551	−	4.87891i	−0.625466	−	0.587351i
$70$	1.20935	+	1.89581i	0.144545	+	0.226592i
$71$	1.73575	−	9.09915i	0.205996	−	1.07987i	−0.717586	−	0.696470i	$-0.754753\pi$
$71$	1.73575	−	9.09915i	0.205996	−	1.07987i	0.923582	−	0.383400i	$-0.125247\pi$
$72$	0.481754	−	0.876307i	0.0567752	−	0.103274i
$73$	−9.38715	−	5.95727i	−1.09868	−	0.697246i	−0.142436	−	0.989804i	$-0.545493\pi$
$73$	−9.38715	−	5.95727i	−1.09868	−	0.697246i	−0.956248	+	0.292559i	$0.905493\pi$
$74$	2.41363	+	7.42840i	0.280579	+	0.863534i
$75$	−4.90700	+	0.959895i	−0.566611	+	0.110839i
$76$	−0.596471	+	1.83575i	−0.0684199	+	0.210575i
$77$	3.53177	−	2.92173i	0.402483	−	0.332963i
$78$	−1.05149	−	0.200583i	−0.119058	−	0.0227116i
$79$	4.97488	+	10.5722i	0.559717	+	1.18946i	0.961774	+	0.273845i	$0.0882956\pi$
$79$	4.97488	+	10.5722i	0.559717	+	1.18946i	−0.402056	+	0.915615i	$0.631704\pi$
$80$	−2.21777	+	0.285447i	−0.247955	+	0.0319140i
$81$	−0.187381	−	0.982287i	−0.0208201	−	0.109143i
$82$	−2.53373	−	0.823260i	−0.279804	−	0.0909138i
$83$	−0.234923	−	0.110547i	−0.0257862	−	0.0121341i	0.412843	−	0.910802i	$-0.364536\pi$
$83$	−0.234923	−	0.110547i	−0.0257862	−	0.0121341i	−0.438629	+	0.898668i	$0.644536\pi$
$84$	0.935025	+	0.370203i	0.102020	+	0.0403924i
$85$	2.96332	−	11.6546i	0.321417	−	1.26412i
$86$	−7.01880	−	1.80212i	−0.756857	−	0.194328i
$87$	−1.18914	+	3.00343i	−0.127490	+	0.322002i
$88$	1.13351	+	4.41473i	0.120833	+	0.470612i
$89$	6.82604	−	10.7561i	0.723558	−	1.14015i	−0.261042	−	0.965327i	$-0.584066\pi$
$89$	6.82604	−	10.7561i	0.723558	−	1.14015i	0.984601	−	0.174818i	$-0.0559338\pi$
$90$	−1.52687	+	1.63360i	−0.160947	+	0.172197i
$91$	0.0675938	−	1.07437i	0.00708576	−	0.112625i
$92$	3.43356	+	6.24562i	0.357973	+	0.651151i
$93$	9.07689	−	2.94926i	0.941229	−	0.305824i
$94$	9.58353	+	1.21068i	0.988466	+	0.124872i
$95$	2.30415	−	3.64961i	0.236400	−	0.374442i
$96$	−0.728969	+	0.684547i	−0.0744000	+	0.0698663i
$97$	−7.67633	−	8.17446i	−0.779413	−	0.829991i	0.209605	−	0.977786i	$-0.432782\pi$
$97$	−7.67633	−	8.17446i	−0.779413	−	0.829991i	−0.989018	+	0.147795i	$0.952782\pi$
$98$	1.48932	−	5.80053i	0.150444	−	0.585942i
$99$	3.68744	+	2.67908i	0.370602	+	0.269258i
$100$	4.96345	+	0.603430i	0.496345	+	0.0603430i
$101$	12.9955	−	9.44180i	1.29310	−	0.939494i	0.293239	−	0.956039i	$-0.405267\pi$
$101$	12.9955	−	9.44180i	1.29310	−	0.939494i	0.999863	+	0.0165453i	$0.00526677\pi$
$102$	−1.97975	−	5.00027i	−0.196024	−	0.495100i
$103$	1.01375	+	8.02468i	0.0998880	+	0.790695i	0.959885	+	0.280395i	$0.0904656\pi$
$103$	1.01375	+	8.02468i	0.0998880	+	0.790695i	−0.859997	+	0.510300i	$0.829534\pi$
$104$	0.938046	+	0.515695i	0.0919830	+	0.0505681i
$105$	−1.82232	−	1.31748i	−0.177840	−	0.128573i
$106$	−3.89602	+	8.27946i	−0.378415	+	0.804172i
$107$	−9.07166	+	12.4861i	−0.876990	+	1.20707i	0.100255	+	0.994962i	$0.468034\pi$
$107$	−9.07166	+	12.4861i	−0.876990	+	1.20707i	−0.977245	+	0.212112i	$0.931966\pi$
$108$	−0.125333	+	0.992115i	−0.0120602	+	0.0954663i
$109$	19.3580	−	4.97030i	1.85416	−	0.476068i	0.855065	−	0.518520i	$-0.173517\pi$
$109$	19.3580	−	4.97030i	1.85416	−	0.476068i	0.999099	+	0.0424516i	$0.0135168\pi$
$110$	−0.0238630	−	10.1918i	−0.00227525	−	0.971751i
$111$	−4.97872	−	6.01823i	−0.472559	−	0.571226i
$112$	−0.774863	−	0.641022i	−0.0732177	−	0.0605709i
$113$	−8.25395	+	5.23812i	−0.776466	+	0.492760i	−0.864056	−	0.503396i	$-0.832084\pi$
$113$	−8.25395	+	5.23812i	−0.776466	+	0.492760i	0.0875895	+	0.996157i	$0.472084\pi$
$114$	−0.121200	−	1.92641i	−0.0113514	−	0.180425i
$115$	−3.99948	−	15.4269i	−0.372954	−	1.43857i
$116$	2.05906	−	2.48897i	0.191179	−	0.231095i
$117$	1.05149	−	0.200583i	0.0972106	−	0.0185439i
$118$	2.24235	+	3.08633i	0.206425	+	0.284120i
$119$	4.73932	−	2.60546i	0.434452	−	0.238842i
$120$	1.95695	−	1.08182i	0.178645	−	0.0987561i
$121$	−9.69764	+	1.22510i	−0.881603	+	0.111372i
$122$	−1.85256	+	0.871749i	−0.167723	+	0.0789244i
$123$	2.65887	−	0.167282i	0.239742	−	0.0150833i
$124$	−9.54400			−0.857077
$125$	−10.4239	−	4.04264i	−0.932339	−	0.361585i
$126$	−1.00565			−0.0895900
$127$	10.9904	−	0.691460i	0.975244	−	0.0613571i	0.432836	−	0.901473i	$-0.357513\pi$
$127$	10.9904	−	0.691460i	0.975244	−	0.0613571i	0.542408	+	0.840116i	$0.317513\pi$
$128$	0.904827	−	0.425779i	0.0799762	−	0.0376339i
$129$	7.18932	−	0.908223i	0.632985	−	0.0799646i
$130$	−1.74870	−	1.63445i	−0.153371	−	0.143351i
$131$	−11.6689	+	6.41502i	−1.01951	+	0.560483i	−0.901613	−	0.432543i	$-0.857617\pi$
$131$	−11.6689	+	6.41502i	−1.01951	+	0.560483i	−0.117901	+	0.993025i	$0.537617\pi$
$132$	−2.67908	−	3.68744i	−0.233184	−	0.320951i
$133$	1.90674	−	0.363729i	0.165335	−	0.0315393i
$134$	1.87162	−	2.26240i	0.161683	−	0.195442i
$135$	0.818281	−	2.08097i	0.0704265	−	0.179101i
$136$	0.337683	+	5.36731i	0.0289560	+	0.460243i
$137$	4.02758	−	2.55598i	0.344099	−	0.218372i	−0.352535	−	0.935799i	$-0.614680\pi$
$137$	4.02758	−	2.55598i	0.344099	−	0.218372i	0.696634	+	0.717427i	$0.254680\pi$
$138$	−5.49161	−	4.54305i	−0.467477	−	0.386730i
$139$	5.91813	+	7.15379i	0.501969	+	0.606777i	0.959254	−	0.282544i	$-0.0911782\pi$
$139$	5.91813	+	7.15379i	0.501969	+	0.606777i	−0.457285	+	0.889320i	$0.651178\pi$
$140$	1.32600	+	1.81613i	0.112068	+	0.153491i
$141$	−9.35622	+	2.40227i	−0.787936	+	0.202308i
$142$	1.16099	−	9.19018i	0.0974281	−	0.771223i
$143$	−2.86784	+	3.94724i	−0.239820	+	0.330085i
$144$	0.425779	−	0.904827i	0.0354816	−	0.0754023i
$145$	−5.83367	+	4.25931i	−0.484460	+	0.353717i
$146$	−9.74269	−	5.35609i	−0.806311	−	0.443273i
$147$	0.750580	+	5.94146i	0.0619068	+	0.490043i
$148$	2.87530	+	7.26219i	0.236349	+	0.596948i
$149$	−5.14511	+	3.73814i	−0.421504	+	0.306240i	−0.778243	−	0.627964i	$-0.783889\pi$
$149$	−5.14511	+	3.73814i	−0.421504	+	0.306240i	0.356739	+	0.934204i	$0.383889\pi$
$150$	−4.83704	+	1.26611i	−0.394943	+	0.103378i
$151$	−2.60034	−	1.88926i	−0.211613	−	0.153746i	0.476930	−	0.878941i	$-0.341749\pi$
$151$	−2.60034	−	1.88926i	−0.211613	−	0.153746i	−0.688543	+	0.725195i	$0.741749\pi$
$152$	−0.480026	+	1.86958i	−0.0389353	+	0.151643i
$153$	3.68144	+	3.92034i	0.297627	+	0.316941i
$154$	3.34134	−	3.13773i	0.269253	−	0.252846i
$155$	20.6829	+	5.25889i	1.66129	+	0.422404i
$156$	−1.06201	−	0.134163i	−0.0850291	−	0.0107417i
$157$	−3.69493	+	1.20056i	−0.294888	+	0.0958149i	−0.452725	−	0.891650i	$-0.649548\pi$
$157$	−3.69493	+	1.20056i	−0.294888	+	0.0958149i	0.157837	+	0.987465i	$0.449548\pi$
$158$	5.62889	+	10.2389i	0.447811	+	0.814564i
$159$	0.574553	−	9.13227i	0.0455651	−	0.724236i
$160$	−2.19547	+	0.424139i	−0.173567	+	0.0335311i
$161$	3.84051	−	6.05167i	0.302674	−	0.476938i
$162$	−0.248690	−	0.968583i	−0.0195389	−	0.0760991i
$163$	1.68342	−	4.25184i	0.131856	−	0.333029i	−0.848816	−	0.528688i	$-0.822684\pi$
$163$	1.68342	−	4.25184i	0.131856	−	0.333029i	0.980672	+	0.195658i	$0.0626843\pi$
$164$	−2.58043	−	0.662541i	−0.201497	−	0.0517358i
$165$	3.77404	+	9.46732i	0.293809	+	0.737030i
$166$	−0.241401	−	0.0955774i	−0.0187364	−	0.00741825i
$167$	8.56450	+	4.03015i	0.662741	+	0.311862i	0.727569	−	0.686034i	$-0.240650\pi$
$167$	8.56450	+	4.03015i	0.662741	+	0.311862i	−0.0648285	+	0.997896i	$0.520650\pi$
$168$	0.956425	+	0.310761i	0.0737898	+	0.0239758i
$169$	−2.22124	−	11.6442i	−0.170865	−	0.895705i
$170$	2.22567	−	11.8176i	0.170701	−	0.906372i
$171$	0.821848	+	1.74652i	0.0628483	+	0.133559i
$172$	−7.11811	−	1.35785i	−0.542751	−	0.103535i
$173$	0.938798	−	0.776641i	0.0713755	−	0.0590469i	−0.601052	−	0.799210i	$-0.705252\pi$
$173$	0.938798	−	0.776641i	0.0713755	−	0.0590469i	0.672428	+	0.740163i	$0.265252\pi$
$174$	−0.998210	+	3.07218i	−0.0756741	+	0.232901i
$175$	−1.87289	−	4.66641i	−0.141577	−	0.352747i
$176$	1.40848	+	4.33485i	0.106168	+	0.326751i
$177$	−3.22104	−	2.04413i	−0.242108	−	0.153646i
$178$	6.13718	−	11.1635i	0.460001	−	0.836740i
$179$	−0.162002	+	0.849247i	−0.0121086	+	0.0634757i	−0.987829	−	0.155546i	$-0.950286\pi$
$179$	−0.162002	+	0.849247i	−0.0121086	+	0.0634757i	0.975720	+	0.219021i	$0.0702864\pi$
$180$	−1.42129	+	1.72625i	−0.105936	+	0.128667i
$181$	−9.33476	−	8.76592i	−0.693847	−	0.651566i	0.255132	−	0.966906i	$-0.417881\pi$
$181$	−9.33476	−	8.76592i	−0.693847	−	0.651566i	−0.948979	+	0.315341i	$0.897881\pi$
$182$		−	1.07650i		−	0.0797953i
$183$	1.40156	−	1.49250i	0.103606	−	0.110329i
$184$	3.81895	+	6.01770i	0.281537	+	0.443631i
$185$	−2.22954	−	17.3223i	−0.163919	−	1.27356i
$186$	8.87379	−	3.51338i	0.650658	−	0.257614i
$187$	−24.4638	−	1.53913i	−1.78897	−	0.112553i
$188$	9.64064	+	0.606538i	0.703116	+	0.0442363i
$189$	0.935025	−	0.370203i	0.0680131	−	0.0269283i
$190$	2.07044	−	3.78709i	0.150205	−	0.274744i
$191$	0.926692	+	1.46023i	0.0670530	+	0.105659i	0.876200	−	0.481948i	$-0.160070\pi$
$191$	0.926692	+	1.46023i	0.0670530	+	0.105659i	−0.809147	+	0.587606i	$0.800070\pi$
$192$	−0.684547	+	0.728969i	−0.0494029	+	0.0526088i
$193$		−	21.3669i		−	1.53802i	−0.639235	−	0.769012i	$-0.720749\pi$
$193$		−	21.3669i		−	1.53802i	0.639235	−	0.769012i	$-0.279251\pi$
$194$	−8.17446	−	7.67633i	−0.586892	−	0.551128i
$195$	2.22758	+	0.875933i	0.159520	+	0.0627269i
$196$	1.12217	−	5.88260i	0.0801547	−	0.420186i
$197$	−6.27691	+	11.4176i	−0.447211	+	0.813474i	−0.999800	−	0.0199798i	$-0.993640\pi$
$197$	−6.27691	+	11.4176i	−0.447211	+	0.813474i	0.552589	+	0.833454i	$0.313640\pi$
$198$	3.84839	+	2.44226i	0.273493	+	0.173564i
$199$	−4.01858	−	12.3679i	−0.284870	−	0.876739i	−0.986438	−	0.164136i	$-0.947516\pi$
$199$	−4.01858	−	12.3679i	−0.284870	−	0.876739i	0.701568	−	0.712603i	$-0.252484\pi$
$200$	4.99155	+	0.290582i	0.352956	+	0.0205472i
$201$	−0.907343	+	2.79252i	−0.0639991	+	0.196969i
$202$	12.3770	−	10.2392i	0.870844	−	0.720425i
$203$	−3.19097	−	0.608710i	−0.223962	−	0.0427231i
$204$	−2.28981	−	4.86609i	−0.160319	−	0.340695i
$205$	5.22701	+	2.85766i	0.365070	+	0.199587i
$206$	1.51563	+	7.94519i	0.105599	+	0.553568i
$207$	6.77838	+	2.20243i	0.471130	+	0.153079i
$208$	0.968576	+	0.455777i	0.0671587	+	0.0316025i
$209$	−8.18000	−	3.23869i	−0.565822	−	0.224025i
$210$	−1.90145	−	1.20046i	−0.131212	−	0.0828396i
$211$	−1.46128	−	0.375192i	−0.100599	−	0.0258293i	0.198055	−	0.980191i	$-0.436538\pi$
$211$	−1.46128	−	0.375192i	−0.100599	−	0.0258293i	−0.298654	+	0.954362i	$0.596538\pi$
$212$	−3.36846	+	8.50775i	−0.231347	+	0.584315i
$213$	2.30367	+	8.97220i	0.157845	+	0.614765i
$214$	−8.26975	+	13.0310i	−0.565309	+	0.890784i
$215$	14.6776	+	6.86481i	1.00100	+	0.468176i
$216$	−0.0627905	+	0.998027i	−0.00427235	+	0.0679071i
$217$	4.62382	+	8.41069i	0.313885	+	0.570955i
$218$	19.0078	−	6.17599i	1.28737	−	0.418291i
$219$	11.0302	+	1.39344i	0.745354	+	0.0941601i
$220$	−0.663765	−	10.1702i	−0.0447510	−	0.685675i
$221$	−4.19654	+	3.94082i	−0.282290	+	0.265088i
$222$	−5.34678	−	5.69374i	−0.358852	−	0.382139i
$223$	−1.60378	+	6.24633i	−0.107397	+	0.418285i	−0.999433	−	0.0336807i	$-0.989277\pi$
$223$	−1.60378	+	6.24633i	−0.107397	+	0.418285i	0.892035	+	0.451966i	$0.149277\pi$
$224$	−0.813584	−	0.591103i	−0.0543599	−	0.0394948i
$225$	4.03128	−	2.95784i	0.268752	−	0.197189i
$226$	−7.90876	+	5.74605i	−0.526083	+	0.382221i
$227$	9.07563	+	22.9224i	0.602371	+	1.52141i	0.835796	+	0.549040i	$0.185007\pi$
$227$	9.07563	+	22.9224i	0.602371	+	1.52141i	−0.233425	+	0.972375i	$0.574993\pi$
$228$	−0.241921	−	1.91500i	−0.0160216	−	0.126824i
$229$	21.6831	+	11.9204i	1.43286	+	0.787722i	0.993847	−	0.110759i	$-0.0353280\pi$
$229$	21.6831	+	11.9204i	1.43286	+	0.787722i	0.439014	+	0.898480i	$0.355328\pi$
$230$	−4.96025	−	15.1453i	−0.327069	−	0.998654i
$231$	−1.95163	+	4.14742i	−0.128408	+	0.272880i
$232$	1.89871	−	2.61335i	0.124656	−	0.171575i
$233$	1.03182	−	8.16768i	0.0675966	−	0.535082i	−0.921562	−	0.388231i	$-0.873086\pi$
$233$	1.03182	−	8.16768i	0.0675966	−	0.535082i	0.989159	−	0.146851i	$-0.0469138\pi$
$234$	1.03682	−	0.266211i	0.0677793	−	0.0174028i
$235$	−20.5582	−	6.62657i	−1.34107	−	0.432270i
$236$	2.43172	+	2.93944i	0.158291	+	0.191341i
$237$	−9.00281	−	7.44777i	−0.584795	−	0.483785i
$238$	4.56637	−	2.89790i	0.295993	−	0.187843i
$239$	0.198241	+	3.15096i	0.0128232	+	0.203818i	0.999222	+	0.0394469i	$0.0125596\pi$
$239$	0.198241	+	3.15096i	0.0128232	+	0.203818i	−0.986399	+	0.164372i	$0.947440\pi$
$240$	1.88516	−	1.20256i	0.121687	−	0.0776251i
$241$	7.02976	−	8.49752i	0.452827	−	0.547373i	−0.493855	−	0.869544i	$-0.664413\pi$
$241$	7.02976	−	8.49752i	0.452827	−	0.547373i	0.946681	+	0.322171i	$0.104413\pi$
$242$	−9.60158	+	1.83160i	−0.617213	+	0.117740i
$243$	0.587785	+	0.809017i	0.0377064	+	0.0518985i
$244$	−1.79417	+	0.986352i	−0.114860	+	0.0631447i
$245$	−5.67326	+	12.1299i	−0.362452	+	0.774953i
$246$	2.64312	−	0.333903i	0.168519	−	0.0212889i
$247$	−1.86957	+	0.879751i	−0.118958	+	0.0559772i
$248$	−9.52517	+	0.599273i	−0.604849	+	0.0380539i
$249$	0.259633			0.0164536
$250$	−10.6571	−	3.38014i	−0.674017	−	0.213779i
$251$	−18.5536			−1.17109			−0.585546	−	0.810639i	$-0.699120\pi$
$251$	−18.5536			−1.17109			−0.585546	+	0.810639i	$0.699120\pi$
$252$	−1.00366	+	0.0631450i	−0.0632247	+	0.00397776i
$253$	−29.3936	+	13.8316i	−1.84796	+	0.869583i
$254$	10.9253	−	1.38019i	0.685516	−	0.0866009i
$255$	2.28099	+	11.8071i	0.142841	+	0.739389i
$256$	0.876307	−	0.481754i	0.0547692	−	0.0301096i
$257$	−10.2317	−	14.0827i	−0.638234	−	0.878453i	0.360286	−	0.932842i	$-0.382679\pi$
$257$	−10.2317	−	14.0827i	−0.638234	−	0.878453i	−0.998520	+	0.0543886i	$0.982679\pi$
$258$	7.11811	−	1.35785i	0.443154	−	0.0845362i
$259$	5.00682	−	6.05221i	0.311109	−	0.376066i
$260$	−1.84787	−	1.52142i	−0.114600	−	0.0943545i
$261$	−0.202831	−	3.22390i	−0.0125549	−	0.199555i
$262$	−11.2430	+	7.13505i	−0.694598	+	0.440805i
$263$	15.6243	+	12.9255i	0.963434	+	0.797022i	0.979209	−	0.202854i	$-0.0650215\pi$
$263$	15.6243	+	12.9255i	0.963434	+	0.797022i	−0.0157749	+	0.999876i	$0.505022\pi$
$264$	−2.90533	−	3.51194i	−0.178811	−	0.216145i
$265$	11.9877	−	16.5812i	0.736401	−	1.01858i
$266$	1.88013	−	0.482736i	0.115278	−	0.0295985i
$267$	−1.59665	+	12.6388i	−0.0977135	+	0.773482i
$268$	1.72587	−	2.37546i	0.105424	−	0.145104i
$269$	−10.6104	+	22.5482i	−0.646926	+	1.37479i	0.264925	+	0.964269i	$0.414653\pi$
$269$	−10.6104	+	22.5482i	−0.646926	+	1.37479i	−0.911852	+	0.410520i	$0.865347\pi$
$270$	0.686002	−	2.12824i	0.0417487	−	0.129521i
$271$	−19.4521	−	10.6939i	−1.18163	−	0.649606i	−0.235020	−	0.971991i	$-0.575515\pi$
$271$	−19.4521	−	10.6939i	−1.18163	−	0.649606i	−0.946609	+	0.322385i	$0.895515\pi$
$272$	0.674033	+	5.33552i	0.0408692	+	0.323513i
$273$	0.396285	+	1.00090i	0.0239843	+	0.0605773i
$274$	3.85914	−	2.80383i	0.233139	−	0.169385i
$275$	−4.16548	+	22.4057i	−0.251188	+	1.35112i
$276$	−5.76603	−	4.18927i	−0.347074	−	0.252164i
$277$	2.25281	−	8.77412i	0.135358	−	0.527186i	−0.864347	−	0.502897i	$-0.832268\pi$
$277$	2.25281	−	8.77412i	0.135358	−	0.527186i	0.999705	−	0.0242895i	$-0.00773235\pi$
$278$	6.35564	+	6.76807i	0.381186	+	0.405922i
$279$	−6.95728	+	6.53332i	−0.416521	+	0.391140i
$280$	1.43742	+	1.72929i	0.0859024	+	0.103345i
$281$	7.33422	+	0.926528i	0.437523	+	0.0552720i	0.341010	−	0.940060i	$-0.389231\pi$
$281$	7.33422	+	0.926528i	0.437523	+	0.0552720i	0.0965131	+	0.995332i	$0.469231\pi$
$282$	−9.18692	+	2.98501i	−0.547073	+	0.177755i
$283$	13.6798	+	24.8834i	0.813179	+	1.47917i	0.876621	+	0.481182i	$0.159792\pi$
$283$	13.6798	+	24.8834i	0.813179	+	1.47917i	−0.0634416	+	0.997986i	$0.520208\pi$
$284$	0.581643	−	9.24494i	0.0345141	−	0.548587i
$285$	−0.530924	+	4.28333i	−0.0314492	+	0.253722i
$286$	−2.61433	+	4.11952i	−0.154588	+	0.243592i
$287$	0.666281	+	2.59499i	0.0393293	+	0.153178i
$288$	0.368125	−	0.929776i	0.0216919	−	0.0547876i
$289$	−11.5475	−	2.96490i	−0.679265	−	0.174406i
$290$	−5.55471	+	4.61721i	−0.326184	+	0.271132i
$291$	10.4263	+	4.12805i	0.611199	+	0.241991i
$292$	−10.0598	−	4.73377i	−0.588704	−	0.277023i
$293$	10.4173	+	3.38478i	0.608584	+	0.197741i	0.597065	−	0.802193i	$-0.296333\pi$
$293$	10.4173	+	3.38478i	0.608584	+	0.197741i	0.0115189	+	0.999934i	$0.496333\pi$
$294$	1.12217	+	5.88260i	0.0654461	+	0.343080i
$295$	−3.65013	−	7.71002i	−0.212519	−	0.448895i
$296$	3.32563	+	7.06732i	0.193298	+	0.410779i
$297$	−4.47720	−	0.854071i	−0.259793	−	0.0495582i
$298$	−4.90024	+	4.05383i	−0.283863	+	0.234832i
$299$	−2.35760	+	7.25594i	−0.136343	+	0.419622i
$300$	−4.74800	+	1.56734i	−0.274126	+	0.0904902i
$301$	2.25192	+	6.93070i	0.129799	+	0.399479i
$302$	−2.71384	−	1.72225i	−0.156164	−	0.0991046i
$303$	−7.73857	+	14.0764i	−0.444569	+	0.808669i
$304$	−0.361687	+	1.89603i	−0.0207442	+	0.108745i
$305$	4.43166	−	1.14892i	0.253756	−	0.0657872i
$306$	3.92034	+	3.68144i	0.224111	+	0.210454i
$307$		−	26.8932i		−	1.53488i	−0.641122	−	0.767439i	$-0.721531\pi$
$307$		−	26.8932i		−	1.53488i	0.641122	−	0.767439i	$-0.278469\pi$
$308$	3.13773	−	3.34134i	0.178789	−	0.190391i
$309$	−4.33401	−	6.82931i	−0.246553	−	0.388506i
$310$	20.9723	+	3.94982i	1.19115	+	0.224335i
$311$	9.81761	−	3.88707i	0.556706	−	0.220415i	−0.0728878	−	0.997340i	$-0.523221\pi$
$311$	9.81761	−	3.88707i	0.556706	−	0.220415i	0.629593	+	0.776925i	$0.283221\pi$
$312$	−1.06834	−	0.0672144i	−0.0604830	−	0.00380526i
$313$	19.0757	+	1.20014i	1.07822	+	0.0678359i	0.591952	−	0.805973i	$-0.298357\pi$
$313$	19.0757	+	1.20014i	1.07822	+	0.0678359i	0.486269	+	0.873809i	$0.338357\pi$
$314$	−3.61226	+	1.43019i	−0.203852	+	0.0807106i
$315$	2.20984	+	0.416190i	0.124510	+	0.0234496i
$316$	6.26069	+	9.86527i	0.352191	+	0.554965i
$317$	16.1751	−	17.2247i	0.908484	−	0.967437i	−0.0911129	−	0.995841i	$-0.529042\pi$
$317$	16.1751	−	17.2247i	0.908484	−	0.967437i	0.999597	+	0.0284037i	$0.00904241\pi$
$318$		−	9.15032i		−	0.513125i
$319$	10.7329	+	10.0788i	0.600926	+	0.564307i
$320$	−2.16451	+	0.561157i	−0.121000	+	0.0313696i
$321$	2.89197	−	15.1603i	0.161414	−	0.846163i
$322$	3.45294	−	6.28088i	0.192425	−	0.350020i
$323$	−8.76462	−	5.56219i	−0.487676	−	0.309489i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	3.16623	+	4.31530i	0.175631	+	0.239370i
$326$	1.41312	−	4.34915i	0.0782657	−	0.240877i
$327$	−15.3994	+	12.7395i	−0.851590	+	0.704497i
$328$	−2.61694	−	0.499207i	−0.144496	−	0.0275641i
$329$	−4.13612	−	8.78970i	−0.228032	−	0.484592i
$330$	4.36105	+	9.21167i	0.240068	+	0.507085i
$331$	6.05821	+	31.7582i	0.332989	+	1.74559i	0.617179	+	0.786823i	$0.288275\pi$
$331$	6.05821	+	31.7582i	0.332989	+	1.74559i	−0.284190	+	0.958768i	$0.591725\pi$
$332$	−0.246926	−	0.0802311i	−0.0135518	−	0.00440326i
$333$	7.06732	+	3.32563i	0.387287	+	0.182243i
$334$	8.80065	+	3.48442i	0.481550	+	0.190659i
$335$	−5.04907	+	4.19690i	−0.275860	+	0.229301i
$336$	0.974051	+	0.250094i	0.0531388	+	0.0136437i
$337$	0.985753	−	2.48973i	0.0536974	−	0.135624i	−0.900452	−	0.434956i	$-0.856764\pi$
$337$	0.985753	−	2.48973i	0.0536974	−	0.135624i	0.954149	+	0.299332i	$0.0967638\pi$
$338$	−2.94800	−	11.4817i	−0.160350	−	0.624523i
$339$	5.23812	−	8.25395i	0.284495	−	0.448293i
$340$	1.47924	−	11.9341i	0.0802233	−	0.647216i
$341$	2.73144	−	43.4151i	0.147916	−	2.35106i
$342$	0.929891	+	1.69147i	0.0502828	+	0.0914640i
$343$	−12.4227	+	4.03638i	−0.670763	+	0.217944i
$344$	−7.18932	−	0.908223i	−0.387622	−	0.0489681i
$345$	10.1873	+	12.2558i	0.548466	+	0.659829i
$346$	0.888180	−	0.834056i	0.0477488	−	0.0448391i
$347$	2.63495	+	2.80594i	0.141452	+	0.150631i	0.795793	−	0.605568i	$-0.207054\pi$
$347$	2.63495	+	2.80594i	0.141452	+	0.150631i	−0.654342	+	0.756199i	$0.727054\pi$
$348$	−0.803337	+	3.12879i	−0.0430634	+	0.167721i
$349$	2.12053	+	1.54065i	0.113509	+	0.0824693i	0.643092	−	0.765789i	$-0.277651\pi$
$349$	2.12053	+	1.54065i	0.113509	+	0.0824693i	−0.529582	+	0.848258i	$0.677651\pi$
$350$	−2.16220	−	4.53960i	−0.115574	−	0.242652i
$351$	−0.866016	+	0.629197i	−0.0462245	+	0.0335841i
$352$	1.67789	+	4.23785i	0.0894316	+	0.225878i
$353$	4.00068	+	31.6687i	0.212935	+	1.68555i	0.629937	+	0.776647i	$0.283081\pi$
$353$	4.00068	+	31.6687i	0.212935	+	1.68555i	−0.417002	+	0.908906i	$0.636919\pi$
$354$	−3.34304	−	1.83785i	−0.177680	−	0.0976806i
$355$	−6.35459	+	19.7144i	−0.337267	+	1.04633i
$356$	5.42411	−	11.5268i	0.287477	−	0.610921i
$357$	−3.17891	+	4.37539i	−0.168246	+	0.231570i
$358$	−0.108358	+	0.857743i	−0.00572691	+	0.0453331i
$359$	−11.9928	+	3.07922i	−0.632954	+	0.162515i	−0.551517	−	0.834163i	$-0.685951\pi$
$359$	−11.9928	+	3.07922i	−0.632954	+	0.162515i	−0.0814369	+	0.996678i	$0.525951\pi$
$360$	−1.31009	+	1.81209i	−0.0690477	+	0.0955055i
$361$	9.73617	+	11.7690i	0.512430	+	0.619422i
$362$	−9.86675	−	8.16249i	−0.518585	−	0.429011i
$363$	8.25306	−	5.23755i	0.433173	−	0.274900i
$364$	−0.0675938	−	1.07437i	−0.00354288	−	0.0563124i
$365$	19.1923	+	15.8017i	1.00457	+	0.827099i
$366$	1.30507	−	1.57756i	0.0682173	−	0.0824606i
$367$	32.4705	−	6.19408i	1.69495	−	0.323328i	0.752730	−	0.658330i	$-0.228737\pi$
$367$	32.4705	−	6.19408i	1.69495	−	0.323328i	0.942218	+	0.335001i	$0.108737\pi$
$368$	4.18927	+	5.76603i	0.218381	+	0.300575i
$369$	−2.33459	+	1.28345i	−0.121534	+	0.0668138i
$370$	−3.31282	−	17.1482i	−0.172225	−	0.891490i
$371$	9.12942	−	1.15331i	0.473976	−	0.0598771i
$372$	8.63567	−	4.06364i	0.447739	−	0.210690i
$373$	−13.0471	+	0.820856i	−0.675555	+	0.0425023i	−0.396862	−	0.917878i	$-0.629901\pi$
$373$	−13.0471	+	0.820856i	−0.675555	+	0.0425023i	−0.278692	+	0.960380i	$0.589901\pi$
$374$	−24.5122			−1.26750
$375$	11.1531	−	0.780379i	0.575942	−	0.0402986i
$376$	9.65970			0.498161
$377$	3.45104	−	0.217121i	0.177738	−	0.0111823i
$378$	0.909935	−	0.428183i	0.0468020	−	0.0220234i
$379$	23.3772	−	2.95323i	1.20081	−	0.151697i	0.500627	−	0.865663i	$-0.333103\pi$
$379$	23.3772	−	2.95323i	1.20081	−	0.151697i	0.700181	+	0.713966i	$0.253103\pi$
$380$	1.82856	−	3.90962i	0.0938031	−	0.200559i
$381$	−9.65004	+	5.30515i	−0.494386	+	0.271791i
$382$	1.01655	+	1.39916i	0.0520113	+	0.0715874i
$383$	−0.579194	+	0.110487i	−0.0295954	+	0.00564563i	−0.202158	−	0.979353i	$-0.564795\pi$
$383$	−0.579194	+	0.110487i	−0.0295954	+	0.00564563i	0.172562	+	0.984999i	$0.444795\pi$
$384$	−0.637424	+	0.770513i	−0.0325284	+	0.0393201i
$385$	−8.64095	+	5.51214i	−0.440384	+	0.280924i
$386$	−1.34164	−	21.3247i	−0.0682876	−	1.08540i
$387$	−6.11839	+	3.88285i	−0.311015	+	0.197376i
$388$	−8.64033	−	7.14790i	−0.438646	−	0.362880i
$389$	−18.7483	−	22.6628i	−0.950578	−	1.14905i	−0.988720	−	0.149778i	$-0.952144\pi$
$389$	−18.7483	−	22.6628i	−0.950578	−	1.14905i	0.0381421	−	0.999272i	$-0.487856\pi$
$390$	2.27818	+	0.734334i	0.115360	+	0.0371844i
$391$	−37.1254	+	9.53218i	−1.87751	+	0.482063i
$392$	0.750580	−	5.94146i	0.0379100	−	0.300089i
$393$	7.82693	−	10.7728i	0.394816	−	0.543418i
$394$	−5.54760	+	11.7892i	−0.279484	+	0.593934i
$395$	−8.13172	−	24.8289i	−0.409151	−	1.24928i
$396$	3.99414	+	2.19580i	0.200713	+	0.110343i
$397$	1.73849	+	13.7616i	0.0872523	+	0.690673i	0.973698	+	0.227841i	$0.0731667\pi$
$397$	1.73849	+	13.7616i	0.0872523	+	0.690673i	−0.886446	+	0.462832i	$0.846833\pi$
$398$	−4.78724	−	12.0912i	−0.239963	−	0.606077i
$399$	−1.57040	+	1.14096i	−0.0786182	+	0.0571195i
$400$	4.99995	−	0.0234138i	0.249997	−	0.00117069i
$401$	−19.7298	−	14.3346i	−0.985261	−	0.715834i	−0.0263827	−	0.999652i	$-0.508399\pi$
$401$	−19.7298	−	14.3346i	−0.985261	−	0.715834i	−0.958878	+	0.283818i	$0.908399\pi$
$402$	−0.730209	+	2.84398i	−0.0364195	+	0.141845i
$403$	−6.99362	−	7.44745i	−0.348377	−	0.370984i
$404$	11.7097	−	10.9961i	0.582578	−	0.547077i
$405$	0.145629	+	2.23132i	0.00723635	+	0.110875i
$406$	−3.22290	−	0.407147i	−0.159950	−	0.0202063i
$407$	−33.8581	+	11.0012i	−1.67828	+	0.545308i
$408$	−2.59083	−	4.71271i	−0.128265	−	0.233314i
$409$	0.858655	−	13.6479i	0.0424578	−	0.674847i	−0.918028	−	0.396516i	$-0.870219\pi$
$409$	0.858655	−	13.6479i	0.0424578	−	0.674847i	0.960485	−	0.278330i	$-0.0897810\pi$
$410$	5.39613	+	2.52381i	0.266496	+	0.124642i
$411$	−2.55598	+	4.02758i	−0.126077	+	0.198666i
$412$	2.01152	+	7.83435i	0.0991004	+	0.385970i
$413$	1.41229	−	3.56704i	0.0694943	−	0.175523i
$414$	6.90329	+	1.77246i	0.339278	+	0.0871119i
$415$	0.490908	+	0.309930i	0.0240977	+	0.0152139i
$416$	0.995283	+	0.394060i	0.0487978	+	0.0193204i
$417$	−8.40082	−	3.95313i	−0.411390	−	0.193585i
$418$	−8.36721	−	2.71867i	−0.409254	−	0.132975i
$419$	−2.00442	−	10.5075i	−0.0979223	−	0.513327i	−0.997124	−	0.0757917i	$-0.975852\pi$
$419$	−2.00442	−	10.5075i	−0.0979223	−	0.513327i	0.899201	−	0.437535i	$-0.144148\pi$
$420$	−1.97307	−	1.07870i	−0.0962762	−	0.0526351i
$421$	9.30727	+	19.7789i	0.453608	+	0.963967i	0.992574	+	0.121639i	$0.0388151\pi$
$421$	9.30727	+	19.7789i	0.453608	+	0.963967i	−0.538966	+	0.842328i	$0.681185\pi$
$422$	−1.48195	−	0.282698i	−0.0721403	−	0.0137615i
$423$	7.44293	−	6.15732i	0.361887	−	0.299379i
$424$	−2.82761	+	8.70247i	−0.137321	+	0.422629i
$425$	−9.78155	+	25.0474i	−0.474475	+	1.21498i
$426$	2.86249	+	8.80985i	0.138688	+	0.426839i
$427$	1.73845	+	1.10326i	0.0841296	+	0.0533903i
$428$	−7.43521	+	13.5246i	−0.359394	+	0.653736i
$429$	0.914244	−	4.79263i	0.0441401	−	0.231390i
$430$	15.0796	+	5.92965i	0.727205	+	0.285953i
$431$	18.2529	+	17.1406i	0.879212	+	0.825635i	0.985671	−	0.168682i	$-0.0539511\pi$
$431$	18.2529	+	17.1406i	0.879212	+	0.825635i	−0.106458	+	0.994317i	$0.533951\pi$
$432$			1.00000i			0.0481125i
$433$	1.79950	−	1.91627i	0.0864782	−	0.0920900i	−0.684274	−	0.729225i	$-0.739881\pi$
$433$	1.79950	−	1.91627i	0.0864782	−	0.0920900i	0.770752	+	0.637135i	$0.219881\pi$
$434$	5.14280	+	8.10376i	0.246862	+	0.388993i
$435$	3.46493	−	6.33780i	0.166131	−	0.303874i
$436$	18.5825	−	7.35731i	0.889938	−	0.352351i
$437$	−13.7299	−	0.863814i	−0.656792	−	0.0413218i
$438$	11.0960	+	0.698099i	0.530186	+	0.0333564i
$439$	1.25676	−	0.497588i	0.0599821	−	0.0237486i	−0.337942	−	0.941167i	$-0.609731\pi$
$439$	1.25676	−	0.497588i	0.0599821	−	0.0237486i	0.397924	+	0.917418i	$0.369731\pi$
$440$	−1.30105	−	10.1085i	−0.0620250	−	0.481902i
$441$	−3.20889	−	5.05641i	−0.152804	−	0.240781i
$442$	−3.94082	+	4.19654i	−0.187445	+	0.199609i
$443$		−	1.52947i		−	0.0726674i	−0.999340	−	0.0363337i	$-0.988432\pi$
$443$		−	1.52947i		−	0.0726674i	0.999340	−	0.0363337i	$-0.0115679\pi$
$444$	−5.69374	−	5.34678i	−0.270213	−	0.253747i
$445$	−18.1061	+	21.9912i	−0.858313	+	1.04248i
$446$	−1.20841	+	6.33471i	−0.0572199	+	0.299957i
$447$	3.06381	−	5.57305i	0.144913	−	0.263596i
$448$	−0.849094	−	0.538852i	−0.0401159	−	0.0254583i
$449$	−6.71265	−	20.6594i	−0.316789	−	0.974977i	−0.975012	−	0.222154i	$-0.928691\pi$
$449$	−6.71265	−	20.6594i	−0.316789	−	0.974977i	0.658222	−	0.752824i	$-0.271309\pi$
$450$	3.83760	−	3.20513i	0.180906	−	0.151091i
$451$	3.75236	−	11.5486i	0.176692	−	0.543801i
$452$	−7.53235	+	6.23131i	−0.354292	+	0.293096i
$453$	3.15727	+	0.602281i	0.148341	+	0.0282976i
$454$	10.4970	+	22.3073i	0.492650	+	1.04693i
$455$	−0.445512	+	2.36553i	−0.0208859	+	0.110898i
$456$	−0.361687	−	1.89603i	−0.0169376	−	0.0887898i
$457$	24.6242	+	8.00088i	1.15187	+	0.374265i	0.821847	−	0.569708i	$-0.192944\pi$
$457$	24.6242	+	8.00088i	1.15187	+	0.374265i	0.330023	+	0.943973i	$0.392944\pi$
$458$	22.3888	+	10.5354i	1.04616	+	0.492286i
$459$	−5.00027	−	1.97975i	−0.233392	−	0.0924066i
$460$	−5.90145	−	14.8040i	−0.275156	−	0.690240i
$461$	38.7671	+	9.95371i	1.80557	+	0.463590i	0.992881	−	0.119113i	$-0.0380052\pi$
$461$	38.7671	+	9.95371i	1.80557	+	0.463590i	0.812685	+	0.582704i	$0.198005\pi$
$462$	−1.68736	+	4.26178i	−0.0785030	+	0.198276i
$463$	3.35963	+	13.0849i	0.156135	+	0.608107i	0.997690	+	0.0679348i	$0.0216410\pi$
$463$	3.35963	+	13.0849i	0.156135	+	0.608107i	−0.841554	+	0.540172i	$0.818359\pi$
$464$	1.73087	−	2.72741i	0.0803536	−	0.126617i
$465$	−20.9536	+	4.04798i	−0.971701	+	0.187721i
$466$	0.516929	−	8.21635i	0.0239463	−	0.380615i
$467$	7.46883	+	13.5857i	0.345616	+	0.628673i	0.990797	−	0.135357i	$-0.0432180\pi$
$467$	7.46883	+	13.5857i	0.345616	+	0.628673i	−0.645181	+	0.764030i	$0.723218\pi$
$468$	1.01806	−	0.330789i	0.0470600	−	0.0152907i
$469$	−2.92952	−	0.370084i	−0.135273	−	0.0170889i
$470$	−20.9337	−	5.32264i	−0.965598	−	0.245515i
$471$	2.83210	−	2.65952i	0.130496	−	0.122544i
$472$	2.61149	+	2.78095i	0.120204	+	0.128004i
$473$	8.21395	−	31.9912i	0.377678	−	1.47096i
$474$	−9.45269	−	6.86778i	−0.434177	−	0.315448i
$475$	−6.11696	+	7.46503i	−0.280665	+	0.342519i
$476$	4.37539	−	3.17891i	0.200546	−	0.145705i
$477$	3.36846	+	8.50775i	0.154231	+	0.389543i
$478$	0.395700	+	3.13229i	0.0180989	+	0.143268i
$479$	17.0408	+	9.36827i	0.778615	+	0.428047i	0.820910	−	0.571058i	$-0.193467\pi$
$479$	17.0408	+	9.36827i	0.778615	+	0.428047i	−0.0422946	+	0.999105i	$0.513467\pi$
$480$	1.80593	−	1.31856i	0.0824293	−	0.0601837i
$481$	−3.55993	+	7.56524i	−0.162319	+	0.344945i
$482$	6.48232	−	8.92215i	0.295262	−	0.406393i
$483$	−0.898319	+	7.11092i	−0.0408749	+	0.323558i
$484$	−9.46762	+	2.43087i	−0.430346	+	0.110494i
$485$	14.7860	+	20.2513i	0.671397	+	0.919563i
$486$	0.637424	+	0.770513i	0.0289141	+	0.0349512i
$487$	12.9596	+	10.7211i	0.587255	+	0.485820i	0.882953	−	0.469462i	$-0.155552\pi$
$487$	12.9596	+	10.7211i	0.587255	+	0.485820i	−0.295698	+	0.955282i	$0.595552\pi$
$488$	−1.72869	+	1.09706i	−0.0782543	+	0.0496617i
$489$	0.287139	+	4.56394i	0.0129849	+	0.206389i
$490$	−4.90042	+	12.4622i	−0.221379	+	0.562986i
$491$	20.1836	−	24.3978i	0.910875	−	1.10106i	−0.0836436	−	0.996496i	$-0.526656\pi$
$491$	20.1836	−	24.3978i	0.910875	−	1.10106i	0.994518	−	0.104563i	$-0.0333443\pi$
$492$	2.61694	−	0.499207i	0.117981	−	0.0225060i
$493$	10.2111	+	14.0544i	0.459885	+	0.632978i
$494$	−1.81064	+	0.995406i	−0.0814644	+	0.0447854i
$495$	−7.44585	−	6.95938i	−0.334666	−	0.312801i
$496$	−9.46875	+	1.19618i	−0.425159	+	0.0537101i
$497$	−8.42893	+	3.96635i	−0.378089	+	0.177915i
$498$	0.259121	−	0.0163025i	0.0116115	−	0.000730533i
$499$	20.5628			0.920519			0.460259	−	0.887785i	$-0.347756\pi$
$499$	20.5628			0.920519			0.460259	+	0.887785i	$0.347756\pi$
$500$	−10.8484	−	2.70430i	−0.485153	−	0.120940i
$501$	−9.46534			−0.422880
$502$	−18.5170	+	1.16499i	−0.826452	+	0.0519960i
$503$	−33.2703	+	15.6558i	−1.48345	+	0.698059i	−0.985583	−	0.169194i	$-0.945884\pi$
$503$	−33.2703	+	15.6558i	−1.48345	+	0.698059i	−0.497868	+	0.867253i	$0.665884\pi$
$504$	−0.997715	+	0.126041i	−0.0444418	+	0.00561430i
$505$	−31.4352	+	17.3776i	−1.39885	+	0.773294i
$506$	−28.4671	+	15.6499i	−1.26552	+	0.695723i
$507$	6.96768	+	9.59019i	0.309446	+	0.425915i
$508$	10.8171	−	2.06347i	0.479932	−	0.0915519i
$509$	5.91826	−	7.15395i	0.262322	−	0.317093i	−0.622864	−	0.782330i	$-0.714031\pi$
$509$	5.91826	−	7.15395i	0.262322	−	0.317093i	0.885186	+	0.465237i	$0.154031\pi$
$510$	3.01786	+	11.6406i	0.133633	+	0.515453i
$511$	0.702040	+	11.1586i	0.0310564	+	0.493627i
$512$	0.844328	−	0.535827i	0.0373144	−	0.0236804i
$513$	−1.48726	−	1.23037i	−0.0656642	−	0.0543221i
$514$	−11.0957	−	13.4124i	−0.489412	−	0.591597i
$515$	−0.0423470	−	18.0863i	−0.00186603	−	0.796977i
$516$	7.01880	−	1.80212i	0.308986	−	0.0793340i
$517$	−5.51820	+	43.6810i	−0.242690	+	1.92109i
$518$	4.61692	−	6.35465i	0.202856	−	0.279207i
$519$	−0.518772	+	1.10245i	−0.0227716	+	0.0483920i
$520$	−1.93976	−	1.40239i	−0.0850640	−	0.0614989i
$521$	−25.0522	−	13.7726i	−1.09756	−	0.603387i	−0.173189	−	0.984889i	$-0.555407\pi$
$521$	−25.0522	−	13.7726i	−1.09756	−	0.603387i	−0.924368	+	0.381502i	$0.875407\pi$
$522$	−0.404861	−	3.20480i	−0.0177203	−	0.140270i
$523$	−2.45048	−	6.18921i	−0.107152	−	0.270635i	0.866301	−	0.499523i	$-0.166491\pi$
$523$	−2.45048	−	6.18921i	−0.107152	−	0.270635i	−0.973453	+	0.228887i	$0.926491\pi$
$524$	−10.7728	+	7.82693i	−0.470614	+	0.341921i
$525$	3.68150	+	3.42486i	0.160674	+	0.149473i
$526$	16.4050	+	11.9190i	0.715294	+	0.519692i
$527$	12.7645	−	49.7144i	0.556030	−	2.16559i
$528$	−3.12012	−	3.32259i	−0.135786	−	0.144597i
$529$	−20.2632	+	19.0284i	−0.881008	+	0.827322i
$530$	10.9229	−	17.3012i	0.474462	−	0.751516i
$531$	3.78483	+	0.478136i	0.164248	+	0.0207493i
$532$	1.84611	−	0.599838i	0.0800391	−	0.0260063i
$533$	−1.37388	−	2.49907i	−0.0595092	−	0.108247i
$534$	−0.799905	+	12.7141i	−0.0346153	+	0.550194i
$535$	23.5652	−	25.2124i	1.01881	−	1.09003i
$536$	1.57331	−	2.47914i	0.0679565	−	0.107082i
$537$	−0.215007	−	0.837399i	−0.00927825	−	0.0361364i
$538$	−9.17363	+	23.1699i	−0.395503	+	0.998927i
$539$	26.4384	+	6.78823i	1.13878	+	0.292390i
$540$	0.551015	−	2.16711i	0.0237119	−	0.0932577i
$541$	−11.8331	−	4.68506i	−0.508745	−	0.201426i	0.0997072	−	0.995017i	$-0.468209\pi$
$541$	−11.8331	−	4.68506i	−0.508745	−	0.201426i	−0.608452	+	0.793590i	$0.708209\pi$
$542$	−20.0851	−	9.45135i	−0.862731	−	0.405970i
$543$	12.1787	+	3.95710i	0.522638	+	0.169815i
$544$	1.00772	+	5.28267i	0.0432057	+	0.226492i
$545$	−44.3243	+	5.70493i	−1.89864	+	0.244372i
$546$	0.458350	+	0.974044i	0.0196156	+	0.0416852i
$547$	19.3275	+	3.68692i	0.826385	+	0.157641i	0.583190	−	0.812336i	$-0.301805\pi$
$547$	19.3275	+	3.68692i	0.826385	+	0.157641i	0.243195	+	0.969977i	$0.421805\pi$
$548$	3.67547	−	3.04061i	0.157008	−	0.129889i
$549$	−0.632687	+	1.94721i	−0.0270024	+	0.0831050i
$550$	−2.75039	+	22.6231i	−0.117277	+	0.964651i
$551$	1.92677	+	5.92998i	0.0820830	+	0.252626i
$552$	−6.01770	−	3.81895i	−0.256130	−	0.162545i
$553$	5.66067	−	10.2967i	0.240716	−	0.437861i
$554$	1.69744	−	8.89827i	0.0721171	−	0.378051i
$555$	9.39283	+	14.7244i	0.398704	+	0.625017i
$556$	6.76807	+	6.35564i	0.287030	+	0.269539i
$557$			0.633828i			0.0268562i	0.999910	+	0.0134281i	$0.00427442\pi$
$557$			0.633828i			0.0268562i	−0.999910	+	0.0134281i	$0.995726\pi$
$558$	−6.53332	+	6.95728i	−0.276578	+	0.294525i
$559$	−4.15641	−	6.54946i	−0.175798	−	0.277013i
$560$	1.54317	+	1.63562i	0.0652108	+	0.0691174i
$561$	22.7909	−	9.02354i	0.962231	−	0.380974i
$562$	7.37793	+	0.464180i	0.311219	+	0.0195802i
$563$	−34.0582	−	2.14276i	−1.43538	−	0.0903065i	−0.674057	−	0.738679i	$-0.735450\pi$
$563$	−34.0582	−	2.14276i	−1.43538	−	0.0903065i	−0.761323	+	0.648372i	$0.775450\pi$
$564$	−8.98136	+	3.55597i	−0.378184	+	0.149733i
$565$	19.7570	−	9.35351i	0.831184	−	0.393505i
$566$	15.2152	+	23.9754i	0.639544	+	1.00776i
$567$	−0.688412	+	0.733084i	−0.0289106	+	0.0307866i
$568$		−	9.26322i		−	0.388676i
$569$	−12.0792	−	11.3431i	−0.506385	−	0.475527i	0.388737	−	0.921349i	$-0.372911\pi$
$569$	−12.0792	−	11.3431i	−0.506385	−	0.475527i	−0.895122	+	0.445822i	$0.852911\pi$
$570$	−0.260924	+	4.30821i	−0.0109289	+	0.180451i
$571$	0.0796128	−	0.417345i	0.00333169	−	0.0174653i	−0.980583	−	0.196107i	$-0.937170\pi$
$571$	0.0796128	−	0.417345i	0.00333169	−	0.0174653i	0.983914	+	0.178641i	$0.0571701\pi$
$572$	−2.35050	+	4.27555i	−0.0982794	+	0.178770i
$573$	−1.46023	−	0.926692i	−0.0610021	−	0.0387131i
$574$	0.827907	+	2.54804i	0.0345562	+	0.106353i
$575$	4.63189	+	35.3337i	0.193163	+	1.47352i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	7.66508	−	6.34110i	0.319101	−	0.263984i	−0.464058	−	0.885805i	$-0.653607\pi$
$577$	7.66508	−	6.34110i	0.319101	−	0.263984i	0.783159	+	0.621821i	$0.213607\pi$
$578$	−11.7109	−	2.23397i	−0.487109	−	0.0929210i
$579$	9.09758	+	19.3333i	0.378083	+	0.803467i
$580$	−5.25383	+	4.95688i	−0.218154	+	0.205823i
$581$	0.0489251	+	0.256474i	0.00202976	+	0.0106403i
$582$	10.6649	+	3.46523i	0.442074	+	0.143639i
$583$	−37.7372	−	17.7578i	−1.56291	−	0.735452i
$584$	−10.3372	−	4.09277i	−0.427755	−	0.169360i
$585$	−2.38853	+	0.155889i	−0.0987534	+	0.00644521i
$586$	10.6093	+	2.72399i	0.438264	+	0.112527i
$587$	2.68483	−	6.78110i	0.110815	−	0.279886i	−0.863777	−	0.503874i	$-0.831908\pi$
$587$	2.68483	−	6.78110i	0.110815	−	0.279886i	0.974592	+	0.223988i	$0.0719076\pi$
$588$	1.48932	+	5.80053i	0.0614187	+	0.239210i
$589$	9.87102	−	15.5542i	0.406728	−	0.640901i
$590$	−4.12705	−	7.46561i	−0.169908	−	0.307354i
$591$	0.818116	−	13.0036i	0.0336528	−	0.534896i
$592$	3.76283	+	6.84455i	0.154651	+	0.281309i
$593$	13.7697	−	4.47404i	0.565453	−	0.183727i	−0.0123201	−	0.999924i	$-0.503922\pi$
$593$	13.7697	−	4.47404i	0.565453	−	0.183727i	0.577773	+	0.816197i	$0.303922\pi$
$594$	−4.52199	−	0.571260i	−0.185539	−	0.0234391i
$595$	−11.2336	+	4.47815i	−0.460533	+	0.183586i
$596$	−4.63603	+	4.35352i	−0.189899	+	0.178327i
$597$	8.90213	+	9.47980i	0.364340	+	0.387983i
$598$	−1.89734	+	7.38966i	−0.0775881	+	0.302186i
$599$	−13.6017	−	9.88222i	−0.555751	−	0.403776i	0.274151	−	0.961687i	$-0.411603\pi$
$599$	−13.6017	−	9.88222i	−0.555751	−	0.403776i	−0.829901	+	0.557910i	$0.811603\pi$
$600$	−4.64021	+	1.86237i	−0.189436	+	0.0760310i
$601$	−29.3723	+	21.3402i	−1.19812	+	0.870487i	−0.994099	−	0.108479i	$-0.965402\pi$
$601$	−29.3723	+	21.3402i	−1.19812	+	0.870487i	−0.204024	+	0.978966i	$0.565402\pi$
$602$	2.68266	+	6.77563i	0.109337	+	0.276154i
$603$	−0.368007	−	2.91307i	−0.0149864	−	0.118629i
$604$	−2.81662	−	1.54845i	−0.114607	−	0.0630056i
$605$	21.8569	−	0.0511754i	0.888608	−	0.00208058i
$606$	−6.83944	+	14.5345i	−0.277833	+	0.590426i
$607$	12.8696	−	17.7135i	0.522363	−	0.718971i	−0.463580	−	0.886055i	$-0.653435\pi$
$607$	12.8696	−	17.7135i	0.522363	−	0.718971i	0.985943	+	0.167085i	$0.0534353\pi$
$608$	−0.241921	+	1.91500i	−0.00981119	+	0.0776635i
$609$	3.14645	−	0.807872i	0.127501	−	0.0327366i
$610$	4.35077	−	1.42492i	0.176158	−	0.0576934i
$611$	6.59113	+	7.96731i	0.266649	+	0.322323i
$612$	4.14376	+	3.42802i	0.167502	+	0.138569i
$613$	−4.19502	+	2.66224i	−0.169435	+	0.107527i	−0.617840	−	0.786304i	$-0.711992\pi$
$613$	−4.19502	+	2.66224i	−0.169435	+	0.107527i	0.448405	+	0.893830i	$0.351992\pi$
$614$	−1.68864	−	26.8402i	−0.0681480	−	1.08318i
$615$	−5.94627	−	0.360132i	−0.239777	−	0.0145219i
$616$	2.92173	−	3.53177i	0.117720	−	0.142299i
$617$	−7.30515	+	1.39353i	−0.294094	+	0.0561015i	−0.332317	−	0.943168i	$-0.607830\pi$
$617$	−7.30515	+	1.39353i	−0.294094	+	0.0561015i	0.0382227	+	0.999269i	$0.487830\pi$
$618$	−4.75428	−	6.54370i	−0.191245	−	0.263226i
$619$	3.13986	−	1.72615i	0.126201	−	0.0693798i	−0.417402	−	0.908722i	$-0.637059\pi$
$619$	3.13986	−	1.72615i	0.126201	−	0.0693798i	0.543604	+	0.839342i	$0.317059\pi$
$620$	21.1790	+	2.62516i	0.850568	+	0.105429i
$621$	−7.07101	+	0.893276i	−0.283750	+	0.0358459i
$622$	9.55417	−	4.49585i	0.383087	−	0.180267i
$623$	−12.7859	+	0.804420i	−0.512256	+	0.0322284i
$624$	−1.07045			−0.0428525
$625$	22.0195	+	11.8381i	0.880780	+	0.473526i
$626$	19.1134			0.763925
$627$	8.78045	−	0.552419i	0.350657	−	0.0220615i
$628$	−3.51533	+	1.65419i	−0.140277	+	0.0660093i
$629$	−41.6740	+	5.26465i	−1.66165	+	0.209916i
$630$	2.23161	+	0.276611i	0.0889096	+	0.0110205i
$631$	3.97556	−	2.18558i	0.158264	−	0.0870066i	−0.400653	−	0.916230i	$-0.631217\pi$
$631$	3.97556	−	2.18558i	0.158264	−	0.0870066i	0.558918	+	0.829223i	$0.311217\pi$
$632$	6.86778	+	9.45269i	0.273186	+	0.376008i
$633$	1.48195	−	0.282698i	0.0589023	−	0.0112362i
$634$	15.0616	−	18.2064i	0.598174	−	0.723068i
$635$	−24.5789	−	1.48861i	−0.975385	−	0.0590735i
$636$	−0.574553	−	9.13227i	−0.0227825	−	0.362118i
$637$	5.41265	−	3.43497i	0.214457	−	0.136099i
$638$	11.3445	+	9.38503i	0.449135	+	0.371557i
$639$	−5.90460	−	7.13744i	−0.233582	−	0.282353i
$640$	−2.12500	+	0.695960i	−0.0839981	+	0.0275102i
$641$	39.0608	−	10.0291i	1.54281	−	0.396126i	0.621013	−	0.783800i	$-0.286721\pi$
$641$	39.0608	−	10.0291i	1.54281	−	0.396126i	0.921797	+	0.387674i	$0.126721\pi$
$642$	1.93435	−	15.3119i	0.0763426	−	0.604314i
$643$	4.96374	−	6.83200i	0.195751	−	0.269428i	−0.699847	−	0.714293i	$-0.746748\pi$
$643$	4.96374	−	6.83200i	0.195751	−	0.269428i	0.895598	+	0.444865i	$0.146748\pi$
$644$	3.05175	−	6.48529i	0.120256	−	0.255556i
$645$	−16.2035	+	0.0379388i	−0.638014	+	0.00149384i
$646$	−9.09657	−	5.00088i	−0.357900	−	0.196757i
$647$	−5.51500	−	43.6557i	−0.216817	−	1.71628i	−0.606289	−	0.795245i	$-0.707342\pi$
$647$	−5.51500	−	43.6557i	−0.216817	−	1.71628i	0.389472	−	0.921038i	$-0.372658\pi$
$648$	−0.368125	−	0.929776i	−0.0144613	−	0.0365251i
$649$	−14.0673	+	10.2205i	−0.552189	+	0.401189i
$650$	3.43094	+	4.10797i	0.134573	+	0.161128i
$651$	−7.76485	−	5.64149i	−0.304328	−	0.221108i
$652$	1.13725	−	4.42930i	0.0445382	−	0.173465i
$653$	16.9418	+	18.0412i	0.662983	+	0.706005i	0.969288	−	0.245928i	$-0.0790927\pi$
$653$	16.9418	+	18.0412i	0.662983	+	0.706005i	−0.306305	+	0.951933i	$0.599093\pi$
$654$	−14.5691	+	13.6813i	−0.569698	+	0.534982i
$655$	27.6587	−	11.0259i	1.08072	−	0.430816i
$656$	−2.64312	−	0.333903i	−0.103196	−	0.0130367i
$657$	−10.5738	+	3.43562i	−0.412521	+	0.134036i
$658$	−4.67987	−	8.51265i	−0.182440	−	0.331858i
$659$	0.934144	−	14.8478i	0.0363891	−	0.578388i	−0.937014	−	0.349291i	$-0.886423\pi$
$659$	0.934144	−	14.8478i	0.0363891	−	0.578388i	0.973403	−	0.229097i	$-0.0735774\pi$
$660$	4.93085	+	8.91966i	0.191933	+	0.347197i
$661$	9.65096	−	15.2075i	0.375379	−	0.591502i	−0.603146	−	0.797631i	$-0.706086\pi$
$661$	9.65096	−	15.2075i	0.375379	−	0.591502i	0.978525	+	0.206128i	$0.0660865\pi$
$662$	8.04037	+	31.3152i	0.312498	+	1.21710i
$663$	2.11923	−	5.35256i	0.0823040	−	0.207876i
$664$	−0.251477	−	0.0645682i	−0.00975918	−	0.00250573i
$665$	−4.33126	+	0.282682i	−0.167959	+	0.0109620i
$666$	7.26219	+	2.87530i	0.281404	+	0.111416i
$667$	20.8317	+	9.80265i	0.806606	+	0.379560i
$668$	9.00208	+	2.92495i	0.348301	+	0.113170i
$669$	−1.20841	−	6.33471i	−0.0467198	−	0.244914i
$670$	−4.77558	+	4.50565i	−0.184497	+	0.174069i
$671$	−3.97337	−	8.44384i	−0.153390	−	0.325971i
$672$	0.987833	+	0.188439i	0.0381065	+	0.00726920i
$673$	−0.701573	+	0.580392i	−0.0270437	+	0.0223725i	−0.650848	−	0.759208i	$-0.725586\pi$
$673$	−0.701573	+	0.580392i	−0.0270437	+	0.0223725i	0.623804	+	0.781581i	$0.285586\pi$
$674$	0.827477	−	2.54671i	0.0318732	−	0.0980957i
$675$	−2.38822	+	4.39277i	−0.0919228	+	0.169078i
$676$	−3.66313	−	11.2739i	−0.140889	−	0.433613i
$677$	1.74816	+	1.10942i	0.0671873	+	0.0426384i	0.568996	−	0.822340i	$-0.307332\pi$
$677$	1.74816	+	1.10942i	0.0671873	+	0.0426384i	−0.501809	+	0.864979i	$0.667332\pi$
$678$	4.70951	−	8.56657i	0.180868	−	0.328997i
$679$	−2.11311	+	11.0773i	−0.0810936	+	0.425107i
$680$	0.726979	−	12.0034i	0.0278784	−	0.460310i
$681$	−17.9718	−	16.8766i	−0.688680	−	0.646713i
$682$		−	43.5009i		−	1.66574i
$683$	−5.08344	+	5.41332i	−0.194513	+	0.207135i	−0.818830	−	0.574036i	$-0.805377\pi$
$683$	−5.08344	+	5.41332i	−0.194513	+	0.207135i	0.624318	+	0.781171i	$0.285377\pi$
$684$	1.03426	+	1.62974i	0.0395461	+	0.0623147i
$685$	−9.64059	+	4.56412i	−0.368348	+	0.174386i
$686$	−12.1447	+	4.80844i	−0.463688	+	0.183587i
$687$	−24.6949	−	1.55367i	−0.942170	−	0.0592763i
$688$	−7.23217	−	0.455009i	−0.275724	−	0.0173471i
$689$	−9.10716	+	3.60578i	−0.346955	+	0.137369i
$690$	10.9367	+	11.5919i	0.416355	+	0.441297i
$691$	−15.7162	−	24.7647i	−0.597872	−	0.942095i	−0.999653	−	0.0263591i	$-0.991609\pi$
$691$	−15.7162	−	24.7647i	−0.597872	−	0.942095i	0.401781	−	0.915736i	$-0.368391\pi$
$692$	0.834056	−	0.888180i	0.0317061	−	0.0337635i
$693$		−	4.58366i		−	0.174119i
$694$	2.80594	+	2.63495i	0.106512	+	0.100021i
$695$	−11.1651	−	17.5027i	−0.423517	−	0.663916i
$696$	−0.605293	+	3.17306i	−0.0229436	+	0.120274i
$697$	6.90231	−	12.5552i	0.261444	−	0.475564i
$698$	2.21308	+	1.40447i	0.0837664	+	0.0531598i
$699$	2.54401	+	7.82966i	0.0962234	+	0.296145i
$700$	−2.44297	−	4.39488i	−0.0923357	−	0.166111i
$701$	5.13808	−	15.8134i	0.194063	−	0.597264i	−0.805923	−	0.592020i	$-0.798331\pi$
$701$	5.13808	−	15.8134i	0.194063	−	0.597264i	0.999986	−	0.00524405i	$-0.00166924\pi$
$702$	−0.824799	+	0.682333i	−0.0311300	+	0.0257530i
$703$	−14.8093	−	2.82503i	−0.558543	−	0.106548i
$704$	1.94067	+	4.12414i	0.0731418	+	0.155434i
$705$	21.4230	−	2.75733i	0.806838	−	0.103847i
$706$	5.98128	+	31.3550i	0.225108	+	1.18006i
$707$	−15.3634	−	4.99187i	−0.577800	−	0.187739i
$708$	−3.45184	−	1.62431i	−0.129728	−	0.0610454i
$709$	33.7647	+	13.3684i	1.26806	+	0.502061i	0.903288	−	0.429035i	$-0.141146\pi$
$709$	33.7647	+	13.3684i	1.26806	+	0.502061i	0.364773	+	0.931096i	$0.381146\pi$
$710$	−5.10417	+	20.0745i	−0.191556	+	0.753381i
$711$	11.3171	+	2.90574i	0.424424	+	0.108974i
$712$	4.68963	−	11.8447i	0.175751	−	0.443898i
$713$	−16.9164	−	65.8850i	−0.633524	−	2.46741i
$714$	−2.89790	+	4.56637i	−0.108451	+	0.170892i
$715$	7.44970	−	7.97044i	0.278603	−	0.298077i
$716$	−0.0542862	+	0.862854i	−0.00202877	+	0.0322464i
$717$	−1.52099	−	2.76666i	−0.0568023	−	0.103323i
$718$	−11.7758	+	3.82618i	−0.439467	+	0.142792i
$719$	−7.63217	−	0.964167i	−0.284632	−	0.0359574i	−0.0182789	−	0.999833i	$-0.505819\pi$
$719$	−7.63217	−	0.964167i	−0.284632	−	0.0359574i	−0.266353	+	0.963876i	$0.585819\pi$
$720$	−1.19372	+	1.89077i	−0.0444874	+	0.0704650i
$721$	5.92952	−	5.56819i	0.220827	−	0.207370i
$722$	10.4559	+	11.1344i	0.389130	+	0.414381i
$723$	−2.74265	+	10.6819i	−0.102000	+	0.397265i
$724$	−10.3598	−	7.52684i	−0.385019	−	0.279733i
$725$	14.1170	−	7.84718i	0.524291	−	0.291437i
$726$	7.90791	−	5.74543i	0.293490	−	0.213233i
$727$	−15.8099	−	39.9312i	−0.586355	−	1.48096i	−0.855468	−	0.517856i	$-0.826730\pi$
$727$	−15.8099	−	39.9312i	−0.586355	−	1.48096i	0.269113	−	0.963109i	$-0.413270\pi$
$728$	−0.134921	−	1.06801i	−0.00500050	−	0.0395830i
$729$	−0.876307	−	0.481754i	−0.0324558	−	0.0178427i
$730$	20.1466	+	14.5654i	0.745660	+	0.539091i
$731$	16.5930	−	35.2620i	0.613715	−	1.30421i
$732$	1.20344	−	1.65640i	0.0444805	−	0.0612222i
$733$	0.791442	−	6.26491i	0.0292326	−	0.231400i	−0.970729	−	0.240178i	$-0.922794\pi$
$733$	0.791442	−	6.26491i	0.0292326	−	0.231400i	0.999961	+	0.00877821i	$0.00279423\pi$
$734$	32.0175	−	8.22070i	1.18179	−	0.303432i
$735$	−0.0313537	−	13.3911i	−0.00115650	−	0.493936i
$736$	4.54305	+	5.49161i	0.167459	+	0.202423i
$737$	10.3119	+	8.53071i	0.379842	+	0.314233i
$738$	−2.24940	+	1.42751i	−0.0828014	+	0.0525474i
$739$	0.984501	+	15.6482i	0.0362154	+	0.575628i	0.973733	+	0.227691i	$0.0731176\pi$
$739$	0.984501	+	15.6482i	0.0362154	+	0.575628i	−0.937518	+	0.347937i	$0.886882\pi$
$740$	−4.38302	−	16.9063i	−0.161123	−	0.621488i
$741$	1.31705	−	1.59204i	0.0483832	−	0.0584852i
$742$	9.03899	−	1.72428i	0.331832	−	0.0633003i
$743$	−22.4831	−	30.9454i	−0.824826	−	1.13528i	−0.988864	−	0.148822i	$-0.952452\pi$
$743$	−22.4831	−	30.9454i	−0.824826	−	1.13528i	0.164038	−	0.986454i	$-0.447548\pi$
$744$	8.36347	−	4.59786i	0.306620	−	0.168566i
$745$	12.4456	−	6.88005i	0.455973	−	0.252065i
$746$	−12.9698	+	1.63847i	−0.474860	+	0.0599887i
$747$	−0.234923	+	0.110547i	−0.00859540	+	0.00404469i
$748$	−24.4638	+	1.53913i	−0.894486	+	0.0562763i
$749$	15.5208			0.567116
$750$	11.0821	−	1.47915i	0.404660	−	0.0540108i
$751$	36.7179			1.33986			0.669928	−	0.742426i	$-0.266325\pi$
$751$	36.7179			1.33986			0.669928	+	0.742426i	$0.266325\pi$
$752$	9.64064	−	0.606538i	0.351558	−	0.0221182i
$753$	16.7878	−	7.89973i	0.611781	−	0.287882i
$754$	3.43060	−	0.433385i	0.124935	−	0.0157830i
$755$	5.25073	+	4.90768i	0.191093	+	0.178609i
$756$	0.881254	−	0.484473i	0.0320509	−	0.0176201i
$757$	−20.5354	−	28.2645i	−0.746371	−	1.02729i	−0.998227	−	0.0595269i	$-0.981041\pi$
$757$	−20.5354	−	28.2645i	−0.746371	−	1.02729i	0.251856	−	0.967765i	$-0.418959\pi$
$758$	23.1457	−	4.41527i	0.840688	−	0.160370i
$759$	20.7069	−	25.0303i	0.751613	−	0.908544i
$760$	1.57946	−	4.01672i	0.0572932	−	0.145702i
$761$	0.826619	+	13.1387i	0.0299649	+	0.476279i	0.984182	+	0.177163i	$0.0566918\pi$
$761$	0.826619	+	13.1387i	0.0299649	+	0.476279i	−0.954217	+	0.299116i	$0.903308\pi$
$762$	−9.29788	+	5.90061i	−0.336827	+	0.213757i
$763$	−15.4864	−	12.8114i	−0.560644	−	0.463805i
$764$	1.10240	+	1.33257i	0.0398834	+	0.0482108i
$765$	−7.09111	−	9.71218i	−0.256380	−	0.351145i
$766$	−0.571113	+	0.146637i	−0.0206352	+	0.00529821i
$767$	−0.511822	+	4.05149i	−0.0184808	+	0.146291i
$768$	−0.587785	+	0.809017i	−0.0212099	+	0.0291929i
$769$	12.6686	−	26.9221i	0.456840	−	0.970834i	−0.535178	−	0.844739i	$-0.679756\pi$
$769$	12.6686	−	26.9221i	0.456840	−	0.970834i	0.992018	−	0.126095i	$-0.0402444\pi$
$770$	−8.27779	+	6.04383i	−0.298311	+	0.217804i
$771$	15.2540	+	8.38596i	0.549359	+	0.302013i
$772$	−2.67798	−	21.1984i	−0.0963827	−	0.762948i
$773$	−16.0790	−	40.6109i	−0.578322	−	1.46067i	−0.864567	−	0.502517i	$-0.832407\pi$
$773$	−16.0790	−	40.6109i	−0.578322	−	1.46067i	0.286246	−	0.958156i	$-0.407593\pi$
$774$	−5.86251	+	4.25937i	−0.210724	+	0.153100i
$775$	−44.4507	−	17.3590i	−1.59672	−	0.623552i
$776$	−9.07210	−	6.59127i	−0.325669	−	0.236613i
$777$	−1.95340	+	7.60800i	−0.0700780	+	0.272936i
$778$	−20.1343	−	21.4409i	−0.721851	−	0.768693i
$779$	3.74861	−	3.52018i	0.134308	−	0.126124i
$780$	2.31980	+	0.589836i	0.0830620	+	0.0211195i
$781$	41.8882	+	5.29171i	1.49888	+	0.189352i
$782$	−36.4536	+	11.8445i	−1.30358	+	0.423558i
$783$	1.55620	+	2.83071i	0.0556140	+	0.101161i
$784$	0.376032	−	5.97686i	0.0134297	−	0.213459i
$785$	8.52960	−	1.64782i	0.304435	−	0.0588131i
$786$	7.13505	−	11.2430i	0.254499	−	0.401026i
$787$	−1.98569	−	7.73376i	−0.0707823	−	0.275679i	0.923334	−	0.383998i	$-0.125453\pi$
$787$	−1.98569	−	7.73376i	−0.0707823	−	0.275679i	−0.994116	+	0.108319i	$0.965453\pi$
$788$	−4.79640	+	12.1143i	−0.170865	+	0.431555i
$789$	−19.6407	−	5.04287i	−0.699227	−	0.179531i
$790$	−9.67469	−	24.2693i	−0.344210	−	0.863463i
$791$	9.14059	+	3.61901i	0.325002	+	0.128677i
$792$	4.12414	+	1.94067i	0.146545	+	0.0689588i
$793$	−2.08440	−	0.677263i	−0.0740192	−	0.0240503i
$794$	2.59916	+	13.6252i	0.0922406	+	0.483542i
$795$	−3.78689	+	20.1072i	−0.134307	+	0.713131i
$796$	−5.53701	−	11.7667i	−0.196254	−	0.417061i
$797$	8.97993	+	1.71301i	0.318085	+	0.0606780i	0.343952	−	0.938987i	$-0.388234\pi$
$797$	8.97993	+	1.71301i	0.318085	+	0.0606780i	−0.0258663	+	0.999665i	$0.508234\pi$
$798$	−1.49566	+	1.23732i	−0.0529457	+	0.0438005i
$799$	−16.0532	+	49.4066i	−0.567920	+	1.74788i
$800$	4.98861	−	0.337317i	0.176374	−	0.0119259i
$801$	−3.93665	−	12.1158i	−0.139095	−	0.428089i
$802$	−20.5910	−	13.0674i	−0.727093	−	0.461427i
$803$	24.4127	−	44.4065i	0.861504	−	1.56707i
$804$	−0.550194	+	2.88422i	−0.0194038	+	0.101718i
$805$	−10.1870	+	12.3728i	−0.359044	+	0.436084i
$806$	−7.44745	−	6.99362i	−0.262325	−	0.246340i
$807$		−	24.9199i		−	0.877222i
$808$	10.9961	−	11.7097i	0.386842	−	0.411945i
$809$	10.1923	+	16.0605i	0.358342	+	0.564657i	0.974897	−	0.222655i	$-0.0714722\pi$
$809$	10.1923	+	16.0605i	0.358342	+	0.564657i	−0.616555	+	0.787312i	$0.711472\pi$
$810$	0.285447	+	2.21777i	0.0100296	+	0.0779246i
$811$	−45.9646	+	18.1987i	−1.61403	+	0.639041i	−0.989835	−	0.142223i	$-0.954575\pi$
$811$	−45.9646	+	18.1987i	−1.61403	+	0.639041i	−0.624200	+	0.781265i	$0.714575\pi$
$812$	−3.24210	−	0.203976i	−0.113775	−	0.00715815i
$813$	22.1540	+	1.39381i	0.776974	+	0.0488830i
$814$	−33.1005	+	13.1054i	−1.16017	+	0.459345i
$815$	−4.90516	+	8.97215i	−0.171820	+	0.314281i
$816$	−2.88164	−	4.54073i	−0.100877	−	0.158957i
$817$	9.57495	−	10.1963i	0.334985	−	0.356723i
$818$		−	13.6749i		−	0.478132i
$819$	−0.784733	−	0.736913i	−0.0274208	−	0.0257498i
$820$	5.54395	+	2.18000i	0.193603	+	0.0761290i
$821$	4.54447	−	23.8230i	0.158603	−	0.831427i	−0.810682	−	0.585487i	$-0.800903\pi$
$821$	4.54447	−	23.8230i	0.158603	−	0.831427i	0.969285	−	0.245940i	$-0.0790966\pi$
$822$	−2.29804	+	4.18012i	−0.0801534	+	0.145798i
$823$	−40.0859	−	25.4393i	−1.39731	−	0.886757i	−0.397778	−	0.917482i	$-0.630218\pi$
$823$	−40.0859	−	25.4393i	−1.39731	−	0.886757i	−0.999528	+	0.0307248i	$0.990218\pi$
$824$	2.49947	+	7.69258i	0.0870732	+	0.267984i
$825$	−5.77086	−	22.0469i	−0.200915	−	0.767574i
$826$	1.18553	−	3.64868i	0.0412498	−	0.126954i
$827$	42.2937	−	34.9884i	1.47070	−	1.21667i	0.544977	−	0.838451i	$-0.316538\pi$
$827$	42.2937	−	34.9884i	1.47070	−	1.21667i	0.925718	−	0.378214i	$-0.123462\pi$
$828$	7.00096	+	1.33551i	0.243300	+	0.0464120i
$829$	6.65594	+	14.1446i	0.231170	+	0.491262i	0.986434	−	0.164159i	$-0.0524911\pi$
$829$	6.65594	+	14.1446i	0.231170	+	0.491262i	−0.755264	+	0.655421i	$0.772491\pi$
$830$	0.509400	+	0.278494i	0.0176815	+	0.00966667i
$831$	1.69744	+	8.89827i	0.0588834	+	0.308677i
$832$	1.01806	+	0.330789i	0.0352950	+	0.0114680i
$833$	29.1414	+	13.7129i	1.00969	+	0.475125i
$834$	−8.63246	−	3.41783i	−0.298918	−	0.118350i
$835$	−17.8968	−	11.2990i	−0.619345	−	0.391017i
$836$	−8.52141	−	2.18793i	−0.294719	−	0.0756710i
$837$	3.51338	−	8.87379i	0.121440	−	0.306723i
$838$	−2.66024	−	10.3609i	−0.0918964	−	0.357913i
$839$	4.07245	−	6.41716i	0.140597	−	0.221545i	−0.766732	−	0.641968i	$-0.778118\pi$
$839$	4.07245	−	6.41716i	0.140597	−	0.221545i	0.907328	+	0.420423i	$0.138118\pi$
$840$	−2.03691	−	0.952680i	−0.0702802	−	0.0328706i
$841$	−1.16573	+	18.5287i	−0.0401974	+	0.638920i
$842$	10.5308	+	19.1555i	0.362916	+	0.660142i
$843$	−7.03070	+	2.28441i	−0.242150	+	0.0786794i
$844$	−1.49678	−	0.189087i	−0.0515213	−	0.00650865i
$845$	1.72630	+	26.4504i	0.0593865	+	0.909920i
$846$	7.04162	−	6.61252i	0.242096	−	0.227343i
$847$	6.72903	+	7.16568i	0.231212	+	0.246216i
$848$	−2.27559	+	8.86285i	−0.0781442	+	0.304351i
$849$	−22.9727	−	16.6906i	−0.788421	−	0.572821i
$850$	−8.18950	+	25.6122i	−0.280898	+	0.878490i
$851$	−45.0366	+	32.7210i	−1.54384	+	1.12166i
$852$	3.41002	+	8.61273i	0.116825	+	0.295067i
$853$	3.05858	+	24.2112i	0.104724	+	0.828975i	0.953745	+	0.300616i	$0.0971923\pi$
$853$	3.05858	+	24.2112i	0.104724	+	0.828975i	−0.849021	+	0.528359i	$0.822808\pi$
$854$	1.80430	+	0.991920i	0.0617417	+	0.0339428i
$855$	−1.34336	−	4.10173i	−0.0459419	−	0.140276i
$856$	−6.57132	+	13.9648i	−0.224603	+	0.477306i
$857$	−5.75777	+	7.92489i	−0.196682	+	0.270709i	−0.895955	−	0.444146i	$-0.853507\pi$
$857$	−5.75777	+	7.92489i	−0.196682	+	0.270709i	0.699273	+	0.714855i	$0.253507\pi$
$858$	0.611508	−	4.84058i	0.0208765	−	0.165255i
$859$	−0.367608	+	0.0943856i	−0.0125426	+	0.00322039i	−0.254956	−	0.966953i	$-0.582061\pi$
$859$	−0.367608	+	0.0943856i	−0.0125426	+	0.00322039i	0.242413	+	0.970173i	$0.422061\pi$
$860$	15.4222	+	4.97109i	0.525893	+	0.169513i
$861$	−1.70776	−	2.06433i	−0.0582004	−	0.0703522i
$862$	19.2932	+	15.9607i	0.657128	+	0.543623i
$863$	37.4121	−	23.7424i	1.27352	−	0.808202i	0.284890	−	0.958560i	$-0.408043\pi$
$863$	37.4121	−	23.7424i	1.27352	−	0.808202i	0.988632	+	0.150358i	$0.0480428\pi$
$864$	0.0627905	+	0.998027i	0.00213618	+	0.0339536i
$865$	−2.29690	+	1.46521i	−0.0780968	+	0.0498186i
$866$	1.67562	−	2.02548i	0.0569399	−	0.0688285i
$867$	11.7109	−	2.23397i	0.397723	−	0.0758697i
$868$	5.64149	+	7.76485i	0.191485	+	0.263556i
$869$	−46.6682	+	25.6561i	−1.58311	+	0.870323i
$870$	3.06014	−	6.54285i	0.103749	−	0.221824i
$871$	3.11831	−	0.393934i	0.105660	−	0.0133479i
$872$	18.0838	−	8.50960i	0.612395	−	0.288171i
$873$	−11.1916	+	0.704116i	−0.378778	+	0.0238307i
$874$	−13.7571			−0.465340
$875$	2.87256	+	10.8703i	0.0971102	+	0.367484i
$876$	11.1179			0.375639
$877$	56.3632	−	3.54607i	1.90325	−	0.119742i	0.932702	−	0.360648i	$-0.117444\pi$
$877$	56.3632	−	3.54607i	1.90325	−	0.119742i	0.970549	+	0.240906i	$0.0774444\pi$
$878$	1.22304	−	0.575519i	0.0412756	−	0.0194228i
$879$	−10.8670	+	1.37282i	−0.366535	+	0.0463042i
$880$	−1.93320	−	10.0068i	−0.0651680	−	0.337330i
$881$	6.00021	−	3.29864i	0.202152	−	0.111134i	−0.377462	−	0.926025i	$-0.623203\pi$
$881$	6.00021	−	3.29864i	0.202152	−	0.111134i	0.579614	+	0.814891i	$0.303203\pi$
$882$	−3.52006	−	4.84494i	−0.118526	−	0.163138i
$883$	−1.56970	+	0.299436i	−0.0528245	+	0.0100768i	−0.213726	−	0.976894i	$-0.568560\pi$
$883$	−1.56970	+	0.299436i	−0.0528245	+	0.0100768i	0.160901	+	0.986970i	$0.448560\pi$
$884$	−3.66954	+	4.43571i	−0.123420	+	0.149189i
$885$	6.58551	+	5.42208i	0.221369	+	0.182261i
$886$	−0.0960363	−	1.52645i	−0.00322640	−	0.0512822i
$887$	−5.77168	+	3.66282i	−0.193794	+	0.122985i	−0.629184	−	0.777257i	$-0.716611\pi$
$887$	−5.77168	+	3.66282i	−0.193794	+	0.122985i	0.435390	+	0.900242i	$0.356611\pi$
$888$	−6.01823	−	4.97872i	−0.201959	−	0.167075i
$889$	−7.05905	−	8.53292i	−0.236753	−	0.286185i
$890$	−16.6896	+	23.0847i	−0.559435	+	0.773800i
$891$	4.41473	−	1.13351i	0.147899	−	0.0379740i
$892$	−0.808266	+	6.39808i	−0.0270627	+	0.214224i
$893$	−10.9595	+	15.0844i	−0.366745	+	0.504781i
$894$	2.70783	−	5.75443i	0.0905634	−	0.192457i
$895$	0.593090	−	1.83999i	0.0198248	−	0.0615041i
$896$	−0.881254	−	0.484473i	−0.0294406	−	0.0161851i
$897$	−0.956211	−	7.56919i	−0.0319269	−	0.252728i
$898$	−7.99661	−	20.1971i	−0.266850	−	0.673987i
$899$	−24.9418	+	18.1213i	−0.831856	+	0.604379i
$900$	3.62878	−	3.43977i	0.120959	−	0.114659i
$901$	−39.8115	−	28.9248i	−1.32631	−	0.963623i
$902$	3.01981	−	11.7614i	0.100549	−	0.391612i
$903$	−4.98855	−	5.31227i	−0.166009	−	0.176781i
$904$	−7.12622	+	6.69197i	−0.237015	+	0.222572i
$905$	18.3035	+	22.0199i	0.608428	+	0.731967i
$906$	3.18885	+	0.402846i	0.105943	+	0.0133837i
$907$	−9.94024	+	3.22978i	−0.330060	+	0.107243i	−0.469359	−	0.883007i	$-0.655515\pi$
$907$	−9.94024	+	3.22978i	−0.330060	+	0.107243i	0.139299	+	0.990250i	$0.455515\pi$
$908$	11.8770	+	21.6042i	0.394152	+	0.716961i
$909$	1.00863	−	16.0316i	0.0334540	−	0.531736i
$910$	−0.296100	+	2.38884i	−0.00981562	+	0.0791893i
$911$	−18.2666	+	28.7836i	−0.605201	+	0.953644i	0.394200	+	0.919025i	$0.371022\pi$
$911$	−18.2666	+	28.7836i	−0.605201	+	0.953644i	−0.999401	+	0.0346190i	$0.988978\pi$
$912$	−0.480026	−	1.86958i	−0.0158953	−	0.0619080i
$913$	0.435635	−	1.10029i	0.0144174	−	0.0364142i
$914$	25.0780	+	6.43893i	0.829505	+	0.212981i
$915$	−3.52070	+	2.92649i	−0.116391	+	0.0967466i
$916$	23.0062	+	9.10878i	0.760145	+	0.300963i
$917$	12.1167	+	5.70167i	0.400128	+	0.188286i
$918$	−5.11471	−	1.66187i	−0.168811	−	0.0548499i
$919$	−8.10303	−	42.4776i	−0.267294	−	1.40121i	−0.822155	−	0.569263i	$-0.807229\pi$
$919$	−8.10303	−	42.4776i	−0.267294	−	1.40121i	0.554861	−	0.831943i	$-0.312771\pi$
$920$	−6.81935	−	14.4042i	−0.224827	−	0.474893i
$921$	11.4506	+	24.3337i	0.377309	+	0.801823i
$922$	39.3156	+	7.49986i	1.29479	+	0.246995i
$923$	7.64030	−	6.32061i	0.251484	−	0.208045i
$924$	−1.41643	+	4.35932i	−0.0465971	+	0.143411i
$925$	0.182877	+	39.0530i	0.00601297	+	1.28405i
$926$	4.17461	+	12.8481i	0.137186	+	0.422216i
$927$	6.82931	+	4.33401i	0.224304	+	0.142348i
$928$	1.55620	−	2.83071i	0.0510847	−	0.0929227i
$929$	−9.14999	+	47.9659i	−0.300201	+	1.57371i	0.437902	+	0.899023i	$0.355722\pi$
$929$	−9.14999	+	47.9659i	−0.300201	+	1.57371i	−0.738103	+	0.674688i	$0.764278\pi$
$930$	−20.6581	+	5.35568i	−0.677406	+	0.175620i
$931$	8.42649	+	7.91300i	0.276167	+	0.259338i
$932$		−	8.23259i		−	0.269668i
$933$	−7.22821	+	7.69726i	−0.236641	+	0.251997i
$934$	8.30715	+	13.0900i	0.271818	+	0.428317i
$935$	53.8640	+	10.1445i	1.76154	+	0.331759i
$936$	0.995283	−	0.394060i	0.0325318	−	0.0128803i
$937$	6.91317	+	0.434940i	0.225843	+	0.0142089i	0.175309	−	0.984513i	$-0.443908\pi$
$937$	6.91317	+	0.434940i	0.225843	+	0.0142089i	0.0505343	+	0.998722i	$0.483908\pi$
$938$	−2.94697	−	0.185408i	−0.0962221	−	0.00605378i
$939$	−17.7712	+	7.03611i	−0.579941	+	0.229615i
$940$	−21.2266	−	3.99770i	−0.692334	−	0.130391i
$941$	17.7264	+	27.9323i	0.577863	+	0.910566i	0.999992	+	0.00403020i	$0.00128286\pi$
$941$	17.7264	+	27.9323i	0.577863	+	0.910566i	−0.422129	+	0.906536i	$0.638717\pi$
$942$	2.65952	−	2.83210i	0.0866519	−	0.0922749i
$943$		−	18.9878i		−	0.618327i
$944$	2.78095	+	2.61149i	0.0905123	+	0.0849967i
$945$	−2.17673	+	0.564325i	−0.0708090	+	0.0183575i
$946$	6.18899	−	32.4438i	0.201222	−	1.05484i
$947$	−6.05549	+	11.0149i	−0.196777	+	0.357936i	−0.956225	−	0.292632i	$-0.905469\pi$
$947$	−6.05549	+	11.0149i	−0.196777	+	0.357936i	0.759448	+	0.650568i	$0.225469\pi$
$948$	−9.86527	−	6.26069i	−0.320409	−	0.203338i
$949$	−3.67767	−	11.3187i	−0.119382	−	0.367421i
$950$	−5.63615	+	7.83439i	−0.182861	+	0.254181i
$951$	−7.30173	+	22.4724i	−0.236775	+	0.728718i
$952$	4.16715	−	3.44737i	0.135058	−	0.111730i
$953$	−21.0208	−	4.00993i	−0.680930	−	0.129894i	−0.164699	−	0.986344i	$-0.552665\pi$
$953$	−21.0208	−	4.00993i	−0.680930	−	0.129894i	−0.516231	+	0.856450i	$0.672665\pi$
$954$	3.89602	+	8.27946i	0.126138	+	0.268057i
$955$	−1.65476	−	3.49528i	−0.0535467	−	0.113104i
$956$	0.591598	+	3.10126i	0.0191336	+	0.100302i
$957$	−14.0028	−	4.54977i	−0.452645	−	0.147073i
$958$	17.5954	+	8.27978i	0.568483	+	0.267508i
$959$	−4.46022	−	1.76593i	−0.144028	−	0.0570247i
$960$	1.71958	−	1.42935i	0.0554991	−	0.0461322i
$961$	58.2002	+	14.9433i	1.87743	+	0.482041i
$962$	−3.07788	+	7.77384i	−0.0992349	+	0.250639i
$963$	3.83819	+	14.9488i	0.123684	+	0.481717i
$964$	5.90931	−	9.31158i	0.190326	−	0.299906i
$965$	−5.87715	+	47.4150i	−0.189192	+	1.52634i
$966$	−0.450047	+	7.15330i	−0.0144800	+	0.230154i
$967$	28.9514	+	52.6624i	0.931015	+	1.69351i	0.691161	+	0.722701i	$0.257100\pi$
$967$	28.9514	+	52.6624i	0.931015	+	1.69351i	0.239855	+	0.970809i	$0.422900\pi$
$968$	−9.29630	+	3.02055i	−0.298795	+	0.0970842i
$969$	10.2987	+	1.30103i	0.330843	+	0.0417952i
$970$	16.0284	+	19.2829i	0.514641	+	0.619136i
$971$	−32.4187	+	30.4432i	−1.04037	+	0.976969i	−0.999753	−	0.0222057i	$-0.992931\pi$
$971$	−32.4187	+	30.4432i	−1.04037	+	0.976969i	−0.0406131	+	0.999175i	$0.512931\pi$
$972$	0.684547	+	0.728969i	0.0219569	+	0.0233817i
$973$	2.32198	−	9.04353i	0.0744394	−	0.289922i
$974$	13.6072	+	9.88621i	0.436003	+	0.316775i
$975$	−4.70225	−	2.55648i	−0.150593	−	0.0818730i
$976$	−1.65640	+	1.20344i	−0.0530200	+	0.0385213i
$977$	−16.2866	−	41.1353i	−0.521055	−	1.31604i	−0.917412	−	0.397939i	$-0.869726\pi$
$977$	−16.2866	−	41.1353i	−0.521055	−	1.31604i	0.396356	−	0.918097i	$-0.370274\pi$
$978$	0.573145	+	4.53691i	0.0183271	+	0.145074i
$979$	50.8824	+	27.9728i	1.62621	+	0.894016i
$980$	−4.10824	+	12.7453i	−0.131233	+	0.407135i
$981$	8.50960	−	18.0838i	0.271691	−	0.577372i
$982$	18.6119	−	25.6170i	0.593928	−	0.817472i
$983$	2.55607	−	20.2334i	0.0815260	−	0.645345i	−0.897413	−	0.441192i	$-0.854556\pi$
$983$	2.55607	−	20.2334i	0.0815260	−	0.645345i	0.978939	−	0.204153i	$-0.0654441\pi$
$984$	2.58043	−	0.662541i	0.0822610	−	0.0211210i
$985$	17.0695	−	23.6102i	0.543880	−	0.752284i
$986$	11.0734	+	13.3855i	0.352650	+	0.426281i
$987$	7.48494	+	6.19208i	0.238248	+	0.197096i
$988$	−1.74456	+	1.10713i	−0.0555019	+	0.0352226i
$989$	−3.24294	−	51.5451i	−0.103120	−	1.63904i
$990$	−7.86814	−	6.47812i	−0.250066	−	0.205888i
$991$	−30.3549	+	36.6927i	−0.964254	+	1.16558i	0.0219016	+	0.999760i	$0.493028\pi$
$991$	−30.3549	+	36.6927i	−0.964254	+	1.16558i	−0.986156	+	0.165823i	$0.946972\pi$
$992$	−9.37495	+	1.78837i	−0.297655	+	0.0567807i
$993$	−19.0036	−	26.1563i	−0.603062	−	0.830044i
$994$	−8.16325	+	4.48778i	−0.258923	+	0.142344i
$995$	5.51567	+	28.5508i	0.174859	+	0.905122i
$996$	0.257586	−	0.0325407i	0.00816193	−	0.00103109i
$997$	1.75324	−	0.825013i	0.0555258	−	0.0261284i	−0.397816	−	0.917465i	$-0.630232\pi$
$997$	1.75324	−	0.825013i	0.0555258	−	0.0261284i	0.453342	+	0.891337i	$0.350232\pi$
$998$	20.5223	−	1.29115i	0.649621	−	0.0408707i
$999$	−7.81068			−0.247119

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.a.469.7	yes	240
125.4	even	50	inner	750.2.o.a.379.7	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.a.379.7	✓	240	125.4	even	50	inner
750.2.o.a.469.7	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.998027 - 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-2.21909 - 0.275059i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(-0.591103 - 0.813584i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})\)	\(q+(0.998027 - 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-2.21909 - 0.275059i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(-0.591103 - 0.813584i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(-2.23198 - 0.135178i) q^{10} +(0.286195 + 4.54893i) q^{11} +(-0.844328 + 0.535827i) q^{12} +(0.824799 + 0.682333i) q^{13} +(-0.641022 - 0.774863i) q^{14} +(2.12500 - 0.695960i) q^{15} +(0.968583 - 0.248690i) q^{16} +(-0.674033 + 5.33552i) q^{17} +(0.587785 - 0.809017i) q^{18} +(-0.821848 + 1.74652i) q^{19} +(-2.23606 + 0.00523549i) q^{20} +(0.881254 + 0.484473i) q^{21} +(0.571260 + 4.52199i) q^{22} +(2.62370 + 6.62671i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(4.84869 + 1.22076i) q^{25} +(0.866016 + 0.629197i) q^{26} +(-0.248690 + 0.968583i) q^{27} +(-0.688412 - 0.733084i) q^{28} +(2.35477 - 2.21128i) q^{29} +(2.07711 - 0.828017i) q^{30} +(-9.46875 - 1.19618i) q^{31} +(0.951057 - 0.309017i) q^{32} +(-2.19580 - 3.99414i) q^{33} +(-0.337683 + 5.36731i) q^{34} +(1.08793 + 1.96800i) q^{35} +(0.535827 - 0.844328i) q^{36} +(1.94244 + 7.56530i) q^{37} +(-0.710562 + 1.79467i) q^{38} +(-1.03682 - 0.266211i) q^{39} +(-2.23132 + 0.145629i) q^{40} +(-2.47704 - 0.980730i) q^{41} +(0.909935 + 0.428183i) q^{42} +(-6.89180 - 2.23928i) q^{43} +(0.854071 + 4.47720i) q^{44} +(-1.62643 + 1.53451i) q^{45} +(3.03462 + 6.44889i) q^{46} +(9.48860 + 1.81005i) q^{47} +(-0.770513 + 0.637424i) q^{48} +(1.85060 - 5.69557i) q^{49} +(4.91577 + 0.913897i) q^{50} +(-1.66187 - 5.11471i) q^{51} +(0.903814 + 0.573578i) q^{52} +(-4.40820 + 8.01849i) q^{53} +(-0.187381 + 0.982287i) q^{54} +(0.616133 - 10.1732i) q^{55} +(-0.733084 - 0.688412i) q^{56} -1.93022i q^{57} +(2.21128 - 2.35477i) q^{58} +(2.04413 + 3.22104i) q^{59} +(2.02102 - 0.956806i) q^{60} +(-1.90364 + 0.753705i) q^{61} +(-9.52517 - 0.599273i) q^{62} +(-1.00366 - 0.0631450i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-1.64262 - 1.74102i) q^{65} +(-2.44226 - 3.84839i) q^{66} +(2.00998 - 2.14042i) q^{67} +5.37792i q^{68} +(-5.19551 - 4.87891i) q^{69} +(1.20935 + 1.89581i) q^{70} +(1.73575 - 9.09915i) q^{71} +(0.481754 - 0.876307i) q^{72} +(-9.38715 - 5.95727i) q^{73} +(2.41363 + 7.42840i) q^{74} +(-4.90700 + 0.959895i) q^{75} +(-0.596471 + 1.83575i) q^{76} +(3.53177 - 2.92173i) q^{77} +(-1.05149 - 0.200583i) q^{78} +(4.97488 + 10.5722i) q^{79} +(-2.21777 + 0.285447i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(-2.53373 - 0.823260i) q^{82} +(-0.234923 - 0.110547i) q^{83} +(0.935025 + 0.370203i) q^{84} +(2.96332 - 11.6546i) q^{85} +(-7.01880 - 1.80212i) q^{86} +(-1.18914 + 3.00343i) q^{87} +(1.13351 + 4.41473i) q^{88} +(6.82604 - 10.7561i) q^{89} +(-1.52687 + 1.63360i) q^{90} +(0.0675938 - 1.07437i) q^{91} +(3.43356 + 6.24562i) q^{92} +(9.07689 - 2.94926i) q^{93} +(9.58353 + 1.21068i) q^{94} +(2.30415 - 3.64961i) q^{95} +(-0.728969 + 0.684547i) q^{96} +(-7.67633 - 8.17446i) q^{97} +(1.48932 - 5.80053i) q^{98} +(3.68744 + 2.67908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42} - 10 q^{46} + 140 q^{47} + 50 q^{49} + 20 q^{50} + 10 q^{51} - 80 q^{52} + 30 q^{53} - 10 q^{55} - 30 q^{58} + 20 q^{59} + 40 q^{60} - 100 q^{61} - 10 q^{62} - 10 q^{63} - 20 q^{65} - 40 q^{66} - 10 q^{67} - 10 q^{69} + 10 q^{70} + 80 q^{71} + 20 q^{73} - 80 q^{75} + 10 q^{76} + 20 q^{77} + 140 q^{79} + 100 q^{82} - 70 q^{83} - 20 q^{85} + 20 q^{86} + 30 q^{87} - 10 q^{88} + 40 q^{89} + 10 q^{90} + 170 q^{91} + 120 q^{92} + 50 q^{93} - 30 q^{94} + 220 q^{95} - 60 q^{97} - 120 q^{98} - 20 q^{99}+O(q^{100}) \) 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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