LMFDB - Embedded newform 125.2.e.a.24.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(24,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("125.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.e (of order $10$, degree $4$, not 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			24.1
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	125.24
Dual form			125.2.e.a.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53884 - 0.500000i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(0.500000 + 0.363271i) q^{4} +(1.30902 - 0.951057i) q^{6} +0.618034i q^{7} +(1.31433 + 1.80902i) q^{8} +(0.618034 + 1.90211i) q^{9} +O(q^{10})$	\(q+(-1.53884 - 0.500000i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(0.500000 + 0.363271i) q^{4} +(1.30902 - 0.951057i) q^{6} +0.618034i q^{7} +(1.31433 + 1.80902i) q^{8} +(0.618034 + 1.90211i) q^{9} +(-1.61803 + 4.97980i) q^{11} +(-0.587785 + 0.190983i) q^{12} +(1.76336 - 0.572949i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-1.50000 - 4.61653i) q^{16} +(3.07768 + 4.23607i) q^{17} -3.23607i q^{18} +(0.690983 - 0.502029i) q^{19} +(-0.500000 - 0.363271i) q^{21} +(4.97980 - 6.85410i) q^{22} +(-3.57971 - 1.16312i) q^{23} -2.23607 q^{24} -3.00000 q^{26} +(-4.75528 - 1.54508i) q^{27} +(-0.224514 + 0.309017i) q^{28} +(-2.92705 - 2.12663i) q^{29} +(2.42705 - 1.76336i) q^{31} +3.38197i q^{32} +(-3.07768 - 4.23607i) q^{33} +(-2.61803 - 8.05748i) q^{34} +(-0.381966 + 1.17557i) q^{36} +(0.224514 - 0.0729490i) q^{37} +(-1.31433 + 0.427051i) q^{38} +(-0.572949 + 1.76336i) q^{39} +(-0.236068 - 0.726543i) q^{41} +(0.587785 + 0.809017i) q^{42} +4.85410i q^{43} +(-2.61803 + 1.90211i) q^{44} +(4.92705 + 3.57971i) q^{46} +(0.363271 - 0.500000i) q^{47} +(4.61653 + 1.50000i) q^{48} +6.61803 q^{49} -5.23607 q^{51} +(1.08981 + 0.354102i) q^{52} +(2.04087 - 2.80902i) q^{53} +(6.54508 + 4.75528i) q^{54} +(-1.11803 + 0.812299i) q^{56} +0.854102i q^{57} +(3.44095 + 4.73607i) q^{58} +(3.35410 + 10.3229i) q^{59} +(2.69098 - 8.28199i) q^{61} +(-4.61653 + 1.50000i) q^{62} +(-1.17557 + 0.381966i) q^{63} +(-1.30902 + 4.02874i) q^{64} +(2.61803 + 8.05748i) q^{66} +(-2.80017 - 3.85410i) q^{67} +3.23607i q^{68} +(3.04508 - 2.21238i) q^{69} +(5.35410 + 3.88998i) q^{71} +(-2.62866 + 3.61803i) q^{72} +(8.55951 + 2.78115i) q^{73} -0.381966 q^{74} +0.527864 q^{76} +(-3.07768 - 1.00000i) q^{77} +(1.76336 - 2.42705i) q^{78} +(-6.54508 - 4.75528i) q^{79} +(-0.809017 + 0.587785i) q^{81} +1.23607i q^{82} +(-3.66547 - 5.04508i) q^{83} +(-0.118034 - 0.363271i) q^{84} +(2.42705 - 7.46969i) q^{86} +(3.44095 - 1.11803i) q^{87} +(-11.1352 + 3.61803i) q^{88} +(2.76393 - 8.50651i) q^{89} +(0.354102 + 1.08981i) q^{91} +(-1.36733 - 1.88197i) q^{92} +3.00000i q^{93} +(-0.809017 + 0.587785i) q^{94} +(-2.73607 - 1.98787i) q^{96} +(-2.26538 + 3.11803i) q^{97} +(-10.1841 - 3.30902i) q^{98} -10.4721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 6 q^{6} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 + 6 * q^6 - 4 * q^9	$ 8 q + 4 q^{4} + 6 q^{6} - 4 q^{9} - 4 q^{11} - 2 q^{14} - 12 q^{16} + 10 q^{19} - 4 q^{21} - 24 q^{26} - 10 q^{29} + 6 q^{31} - 12 q^{34} - 12 q^{36} - 18 q^{39} + 16 q^{41} - 12 q^{44} + 26 q^{46} + 44 q^{49} - 24 q^{51} + 30 q^{54} + 26 q^{61} - 6 q^{64} + 12 q^{66} + 2 q^{69} + 16 q^{71} - 12 q^{74} + 40 q^{76} - 30 q^{79} - 2 q^{81} + 8 q^{84} + 6 q^{86} + 40 q^{89} - 24 q^{91} - 2 q^{94} - 4 q^{96} - 48 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 + 6 * q^6 - 4 * q^9 - 4 * q^11 - 2 * q^14 - 12 * q^16 + 10 * q^19 - 4 * q^21 - 24 * q^26 - 10 * q^29 + 6 * q^31 - 12 * q^34 - 12 * q^36 - 18 * q^39 + 16 * q^41 - 12 * q^44 + 26 * q^46 + 44 * q^49 - 24 * q^51 + 30 * q^54 + 26 * q^61 - 6 * q^64 + 12 * q^66 + 2 * q^69 + 16 * q^71 - 12 * q^74 + 40 * q^76 - 30 * q^79 - 2 * q^81 + 8 * q^84 + 6 * q^86 + 40 * q^89 - 24 * q^91 - 2 * q^94 - 4 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−1.53884	−	0.500000i	−1.08813	−	0.353553i	−0.290604	−	0.956844i	$-0.593856\pi$
$2$	−1.53884	−	0.500000i	−1.08813	−	0.353553i	−0.797522	+	0.603290i	$0.793856\pi$
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i	−0.944254	−	0.329218i	$-0.893215\pi$
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i	0.604896	+	0.796305i	$0.293215\pi$
$4$	0.500000	+	0.363271i	0.250000	+	0.181636i
$5$		0			0
$5$		0			0
$6$	1.30902	−	0.951057i	0.534404	−	0.388267i
$7$			0.618034i			0.233595i	0.993156	+	0.116797i	$0.0372628\pi$
$7$			0.618034i			0.233595i	−0.993156	+	0.116797i	$0.962737\pi$
$8$	1.31433	+	1.80902i	0.464685	+	0.639584i
$9$	0.618034	+	1.90211i	0.206011	+	0.634038i
$10$		0			0
$11$	−1.61803	+	4.97980i	−0.487856	+	1.50147i	0.339946	+	0.940445i	$0.389591\pi$
$11$	−1.61803	+	4.97980i	−0.487856	+	1.50147i	−0.827802	+	0.561020i	$0.810409\pi$
$12$	−0.587785	+	0.190983i	−0.169679	+	0.0551320i
$13$	1.76336	−	0.572949i	0.489067	−	0.158907i	−0.0540944	−	0.998536i	$-0.517227\pi$
$13$	1.76336	−	0.572949i	0.489067	−	0.158907i	0.543161	+	0.839628i	$0.317227\pi$
$14$	0.309017	−	0.951057i	0.0825883	−	0.254181i
$15$		0			0
$16$	−1.50000	−	4.61653i	−0.375000	−	1.15413i
$17$	3.07768	+	4.23607i	0.746448	+	1.02740i	0.998222	+	0.0596113i	$0.0189861\pi$
$17$	3.07768	+	4.23607i	0.746448	+	1.02740i	−0.251774	+	0.967786i	$0.581014\pi$
$18$		−	3.23607i		−	0.762749i
$19$	0.690983	−	0.502029i	0.158522	−	0.115173i	−0.505696	−	0.862712i	$-0.668764\pi$
$19$	0.690983	−	0.502029i	0.158522	−	0.115173i	0.664219	+	0.747538i	$0.268764\pi$
$20$		0			0
$21$	−0.500000	−	0.363271i	−0.109109	−	0.0792723i
$22$	4.97980	−	6.85410i	1.06170	−	1.46130i
$23$	−3.57971	−	1.16312i	−0.746422	−	0.242527i	−0.0889808	−	0.996033i	$-0.528361\pi$
$23$	−3.57971	−	1.16312i	−0.746422	−	0.242527i	−0.657441	+	0.753506i	$0.728361\pi$
$24$	−2.23607			−0.456435
$25$		0			0
$26$	−3.00000			−0.588348
$27$	−4.75528	−	1.54508i	−0.915155	−	0.297352i
$28$	−0.224514	+	0.309017i	−0.0424292	+	0.0583987i
$29$	−2.92705	−	2.12663i	−0.543540	−	0.394905i	0.281858	−	0.959456i	$-0.409049\pi$
$29$	−2.92705	−	2.12663i	−0.543540	−	0.394905i	−0.825398	+	0.564551i	$0.809049\pi$
$30$		0			0
$31$	2.42705	−	1.76336i	0.435911	−	0.316708i	−0.348097	−	0.937459i	$-0.613172\pi$
$31$	2.42705	−	1.76336i	0.435911	−	0.316708i	0.784008	+	0.620750i	$0.213172\pi$
$32$			3.38197i			0.597853i
$33$	−3.07768	−	4.23607i	−0.535756	−	0.737405i
$34$	−2.61803	−	8.05748i	−0.448989	−	1.38185i
$35$		0			0
$36$	−0.381966	+	1.17557i	−0.0636610	+	0.195928i
$37$	0.224514	−	0.0729490i	0.0369099	−	0.0119927i	−0.290504	−	0.956874i	$-0.593823\pi$
$37$	0.224514	−	0.0729490i	0.0369099	−	0.0119927i	0.327414	+	0.944881i	$0.393823\pi$
$38$	−1.31433	+	0.427051i	−0.213212	+	0.0692768i
$39$	−0.572949	+	1.76336i	−0.0917453	+	0.282363i
$40$		0			0
$41$	−0.236068	−	0.726543i	−0.0368676	−	0.113467i	0.930929	−	0.365200i	$-0.118999\pi$
$41$	−0.236068	−	0.726543i	−0.0368676	−	0.113467i	−0.967797	+	0.251733i	$0.918999\pi$
$42$	0.587785	+	0.809017i	0.0906972	+	0.124834i
$43$			4.85410i			0.740244i	0.928983	+	0.370122i	$0.120684\pi$
$43$			4.85410i			0.740244i	−0.928983	+	0.370122i	$0.879316\pi$
$44$	−2.61803	+	1.90211i	−0.394683	+	0.286754i
$45$		0			0
$46$	4.92705	+	3.57971i	0.726454	+	0.527800i
$47$	0.363271	−	0.500000i	0.0529886	−	0.0729325i	−0.781700	−	0.623654i	$-0.785647\pi$
$47$	0.363271	−	0.500000i	0.0529886	−	0.0729325i	0.834689	+	0.550722i	$0.185647\pi$
$48$	4.61653	+	1.50000i	0.666338	+	0.216506i
$49$	6.61803			0.945433
$50$		0			0
$51$	−5.23607			−0.733196
$52$	1.08981	+	0.354102i	0.151130	+	0.0491051i
$53$	2.04087	−	2.80902i	0.280335	−	0.385848i	−0.645510	−	0.763752i	$-0.723355\pi$
$53$	2.04087	−	2.80902i	0.280335	−	0.385848i	0.925845	+	0.377904i	$0.123355\pi$
$54$	6.54508	+	4.75528i	0.890673	+	0.647112i
$55$		0			0
$56$	−1.11803	+	0.812299i	−0.149404	+	0.108548i
$57$			0.854102i			0.113129i
$58$	3.44095	+	4.73607i	0.451820	+	0.621876i
$59$	3.35410	+	10.3229i	0.436667	+	1.34392i	0.891369	+	0.453279i	$0.149746\pi$
$59$	3.35410	+	10.3229i	0.436667	+	1.34392i	−0.454702	+	0.890644i	$0.650254\pi$
$60$		0			0
$61$	2.69098	−	8.28199i	0.344545	−	1.06040i	−0.617282	−	0.786742i	$-0.711766\pi$
$61$	2.69098	−	8.28199i	0.344545	−	1.06040i	0.961827	−	0.273659i	$-0.0882338\pi$
$62$	−4.61653	+	1.50000i	−0.586299	+	0.190500i
$63$	−1.17557	+	0.381966i	−0.148108	+	0.0481232i
$64$	−1.30902	+	4.02874i	−0.163627	+	0.503593i
$65$		0			0
$66$	2.61803	+	8.05748i	0.322258	+	0.991807i
$67$	−2.80017	−	3.85410i	−0.342095	−	0.470853i	0.602957	−	0.797774i	$-0.293989\pi$
$67$	−2.80017	−	3.85410i	−0.342095	−	0.470853i	−0.945052	+	0.326920i	$0.893989\pi$
$68$			3.23607i			0.392431i
$69$	3.04508	−	2.21238i	0.366585	−	0.266340i
$70$		0			0
$71$	5.35410	+	3.88998i	0.635415	+	0.461656i	0.858272	−	0.513195i	$-0.171538\pi$
$71$	5.35410	+	3.88998i	0.635415	+	0.461656i	−0.222857	+	0.974851i	$0.571538\pi$
$72$	−2.62866	+	3.61803i	−0.309790	+	0.426389i
$73$	8.55951	+	2.78115i	1.00181	+	0.325509i	0.763590	−	0.645701i	$-0.223435\pi$
$73$	8.55951	+	2.78115i	1.00181	+	0.325509i	0.238224	+	0.971210i	$0.423435\pi$
$74$	−0.381966			−0.0444026
$75$		0			0
$76$	0.527864			0.0605502
$77$	−3.07768	−	1.00000i	−0.350735	−	0.113961i
$78$	1.76336	−	2.42705i	0.199661	−	0.274809i
$79$	−6.54508	−	4.75528i	−0.736380	−	0.535011i	0.155196	−	0.987884i	$-0.450399\pi$
$79$	−6.54508	−	4.75528i	−0.736380	−	0.535011i	−0.891575	+	0.452873i	$0.850399\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$			1.23607i			0.136501i
$83$	−3.66547	−	5.04508i	−0.402337	−	0.553770i	0.558991	−	0.829174i	$-0.311189\pi$
$83$	−3.66547	−	5.04508i	−0.402337	−	0.553770i	−0.961329	+	0.275404i	$0.911189\pi$
$84$	−0.118034	−	0.363271i	−0.0128786	−	0.0396361i
$85$		0			0
$86$	2.42705	−	7.46969i	0.261716	−	0.805478i
$87$	3.44095	−	1.11803i	0.368909	−	0.119866i
$88$	−11.1352	+	3.61803i	−1.18701	+	0.385684i
$89$	2.76393	−	8.50651i	0.292976	−	0.901688i	−0.690918	−	0.722934i	$-0.742793\pi$
$89$	2.76393	−	8.50651i	0.292976	−	0.901688i	0.983894	−	0.178754i	$-0.0572068\pi$
$90$		0			0
$91$	0.354102	+	1.08981i	0.0371200	+	0.114244i
$92$	−1.36733	−	1.88197i	−0.142554	−	0.196209i
$93$			3.00000i			0.311086i
$94$	−0.809017	+	0.587785i	−0.0834437	+	0.0606254i
$95$		0			0
$96$	−2.73607	−	1.98787i	−0.279249	−	0.202886i
$97$	−2.26538	+	3.11803i	−0.230015	+	0.316588i	−0.908387	−	0.418130i	$-0.862686\pi$
$97$	−2.26538	+	3.11803i	−0.230015	+	0.316588i	0.678372	+	0.734718i	$0.262686\pi$
$98$	−10.1841	−	3.30902i	−1.02875	−	0.334261i
$99$	−10.4721			−1.05249
$100$		0			0
$101$	1.47214			0.146483			0.0732415	−	0.997314i	$-0.476666\pi$
$101$	1.47214			0.146483			0.0732415	+	0.997314i	$0.476666\pi$
$102$	8.05748	+	2.61803i	0.797809	+	0.259224i
$103$	−5.03280	+	6.92705i	−0.495896	+	0.682543i	−0.981462	−	0.191658i	$-0.938614\pi$
$103$	−5.03280	+	6.92705i	−0.495896	+	0.682543i	0.485566	+	0.874200i	$0.338614\pi$
$104$	3.35410	+	2.43690i	0.328897	+	0.238957i
$105$		0			0
$106$	−4.54508	+	3.30220i	−0.441458	+	0.320738i
$107$		−	16.4164i		−	1.58703i	−0.608548	−	0.793517i	$-0.708248\pi$
$107$		−	16.4164i		−	1.58703i	0.608548	−	0.793517i	$-0.291752\pi$
$108$	−1.81636	−	2.50000i	−0.174779	−	0.240563i
$109$	−3.09017	−	9.51057i	−0.295985	−	0.910947i	−0.982889	−	0.184199i	$-0.941031\pi$
$109$	−3.09017	−	9.51057i	−0.295985	−	0.910947i	0.686904	−	0.726748i	$-0.258969\pi$
$110$		0			0
$111$	−0.0729490	+	0.224514i	−0.00692401	+	0.0213099i
$112$	2.85317	−	0.927051i	0.269599	−	0.0875981i
$113$	16.0292	−	5.20820i	1.50790	−	0.489947i	0.565590	−	0.824687i	$-0.308648\pi$
$113$	16.0292	−	5.20820i	1.50790	−	0.489947i	0.942311	+	0.334740i	$0.108648\pi$
$114$	0.427051	−	1.31433i	0.0399970	−	0.123098i
$115$		0			0
$116$	−0.690983	−	2.12663i	−0.0641562	−	0.197452i
$117$	2.17963	+	3.00000i	0.201507	+	0.277350i
$118$		−	17.5623i		−	1.61674i
$119$	−2.61803	+	1.90211i	−0.239995	+	0.174366i
$120$		0			0
$121$	−13.2812	−	9.64932i	−1.20738	−	0.877211i
$122$	−8.28199	+	11.3992i	−0.749817	+	1.03203i
$123$	0.726543	+	0.236068i	0.0655101	+	0.0212855i
$124$	1.85410			0.166503
$125$		0			0
$126$	2.00000			0.178174
$127$	18.9151	+	6.14590i	1.67845	+	0.545360i	0.984609	−	0.174772i	$-0.0559187\pi$
$127$	18.9151	+	6.14590i	1.67845	+	0.545360i	0.693837	+	0.720132i	$0.255919\pi$
$128$	8.00448	−	11.0172i	0.707503	−	0.973794i
$129$	−3.92705	−	2.85317i	−0.345758	−	0.251208i
$130$		0			0
$131$	−5.50000	+	3.99598i	−0.480537	+	0.349131i	−0.801534	−	0.597950i	$-0.795982\pi$
$131$	−5.50000	+	3.99598i	−0.480537	+	0.349131i	0.320996	+	0.947080i	$0.395982\pi$
$132$		−	3.23607i		−	0.281664i
$133$	0.310271	+	0.427051i	0.0269039	+	0.0370300i
$134$	2.38197	+	7.33094i	0.205771	+	0.633297i
$135$		0			0
$136$	−3.61803	+	11.1352i	−0.310244	+	0.954832i
$137$	11.3597	−	3.69098i	0.970523	−	0.315342i	0.219496	−	0.975613i	$-0.429559\pi$
$137$	11.3597	−	3.69098i	0.970523	−	0.315342i	0.751027	+	0.660271i	$0.229559\pi$
$138$	−5.79210	+	1.88197i	−0.493056	+	0.160204i
$139$	−1.54508	+	4.75528i	−0.131052	+	0.403338i	−0.994955	−	0.100321i	$-0.968013\pi$
$139$	−1.54508	+	4.75528i	−0.131052	+	0.403338i	0.863903	+	0.503659i	$0.168013\pi$
$140$		0			0
$141$	0.190983	+	0.587785i	0.0160837	+	0.0495004i
$142$	−6.29412	−	8.66312i	−0.528191	−	0.726993i
$143$			9.70820i			0.811841i
$144$	7.85410	−	5.70634i	0.654508	−	0.475528i
$145$		0			0
$146$	−11.7812	−	8.55951i	−0.975015	−	0.708390i
$147$	−3.88998	+	5.35410i	−0.320840	+	0.441599i
$148$	0.138757	+	0.0450850i	0.0114058	+	0.00370596i
$149$	3.94427			0.323127			0.161564	−	0.986862i	$-0.448346\pi$
$149$	3.94427			0.323127			0.161564	+	0.986862i	$0.448346\pi$
$150$		0			0
$151$	14.5623			1.18506			0.592532	−	0.805547i	$-0.298128\pi$
$151$	14.5623			1.18506			0.592532	+	0.805547i	$0.298128\pi$
$152$	1.81636	+	0.590170i	0.147326	+	0.0478691i
$153$	−6.15537	+	8.47214i	−0.497632	+	0.684932i
$154$	4.23607	+	3.07768i	0.341352	+	0.248007i
$155$		0			0
$156$	−0.927051	+	0.673542i	−0.0742235	+	0.0539265i
$157$			13.1803i			1.05191i	0.850514	+	0.525953i	$0.176291\pi$
$157$			13.1803i			1.05191i	−0.850514	+	0.525953i	$0.823709\pi$
$158$	7.69421	+	10.5902i	0.612118	+	0.842509i
$159$	1.07295	+	3.30220i	0.0850904	+	0.261881i
$160$		0			0
$161$	0.718847	−	2.21238i	0.0566531	−	0.174360i
$162$	1.53884	−	0.500000i	0.120903	−	0.0392837i
$163$	10.4616	−	3.39919i	0.819417	−	0.266245i	0.130836	−	0.991404i	$-0.458234\pi$
$163$	10.4616	−	3.39919i	0.819417	−	0.266245i	0.688581	+	0.725159i	$0.258234\pi$
$164$	0.145898	−	0.449028i	0.0113927	−	0.0350632i
$165$		0			0
$166$	3.11803	+	9.59632i	0.242006	+	0.744819i
$167$	−8.55951	−	11.7812i	−0.662355	−	0.911653i	0.337202	−	0.941432i	$-0.390520\pi$
$167$	−8.55951	−	11.7812i	−0.662355	−	0.911653i	−0.999556	+	0.0297794i	$0.990520\pi$
$168$		−	1.38197i		−	0.106621i
$169$	−7.73607	+	5.62058i	−0.595082	+	0.432352i
$170$		0			0
$171$	1.38197	+	1.00406i	0.105682	+	0.0767822i
$172$	−1.76336	+	2.42705i	−0.134455	+	0.185061i
$173$	−17.9641	−	5.83688i	−1.36578	−	0.443770i	−0.467813	−	0.883827i	$-0.654958\pi$
$173$	−17.9641	−	5.83688i	−1.36578	−	0.443770i	−0.897970	+	0.440057i	$0.854958\pi$
$174$	−5.85410			−0.443798
$175$		0			0
$176$	25.4164			1.91583
$177$	−10.3229	−	3.35410i	−0.775914	−	0.252110i
$178$	−8.50651	+	11.7082i	−0.637590	+	0.877567i
$179$	−0.427051	−	0.310271i	−0.0319193	−	0.0231907i	0.571711	−	0.820455i	$-0.306280\pi$
$179$	−0.427051	−	0.310271i	−0.0319193	−	0.0231907i	−0.603631	+	0.797264i	$0.706280\pi$
$180$		0			0
$181$	−0.236068	+	0.171513i	−0.0175468	+	0.0127485i	−0.596524	−	0.802595i	$-0.703452\pi$
$181$	−0.236068	+	0.171513i	−0.0175468	+	0.0127485i	0.578977	+	0.815344i	$0.303452\pi$
$182$		−	1.85410i		−	0.137435i
$183$	5.11855	+	7.04508i	0.378374	+	0.520788i
$184$	−2.60081	−	8.00448i	−0.191734	−	0.590098i
$185$		0			0
$186$	1.50000	−	4.61653i	0.109985	−	0.338500i
$187$	−26.0746	+	8.47214i	−1.90676	+	0.619544i
$188$	0.363271	−	0.118034i	0.0264943	−	0.00860851i
$189$	0.954915	−	2.93893i	0.0694598	−	0.213775i
$190$		0			0
$191$	−0.562306	−	1.73060i	−0.0406870	−	0.125222i	0.928650	−	0.370958i	$-0.120970\pi$
$191$	−0.562306	−	1.73060i	−0.0406870	−	0.125222i	−0.969337	+	0.245736i	$0.920970\pi$
$192$	−2.48990	−	3.42705i	−0.179693	−	0.247326i
$193$		−	7.70820i		−	0.554849i	−0.960747	−	0.277424i	$-0.910519\pi$
$193$		−	7.70820i		−	0.554849i	0.960747	−	0.277424i	$-0.0894808\pi$
$194$	5.04508	−	3.66547i	0.362216	−	0.263165i
$195$		0			0
$196$	3.30902	+	2.40414i	0.236358	+	0.171724i
$197$	2.17963	−	3.00000i	0.155292	−	0.213741i	−0.724281	−	0.689505i	$-0.757828\pi$
$197$	2.17963	−	3.00000i	0.155292	−	0.213741i	0.879573	+	0.475764i	$0.157828\pi$
$198$	16.1150	+	5.23607i	1.14524	+	0.372111i
$199$	17.5623			1.24496			0.622479	−	0.782636i	$-0.286125\pi$
$199$	17.5623			1.24496			0.622479	+	0.782636i	$0.286125\pi$
$200$		0			0
$201$	4.76393			0.336022
$202$	−2.26538	−	0.736068i	−0.159392	−	0.0517896i
$203$	1.31433	−	1.80902i	0.0922477	−	0.126968i
$204$	−2.61803	−	1.90211i	−0.183299	−	0.133175i
$205$		0			0
$206$	11.2082	−	8.14324i	0.780913	−	0.567366i
$207$		−	7.52786i		−	0.523223i
$208$	−5.29007	−	7.28115i	−0.366800	−	0.504857i
$209$	1.38197	+	4.25325i	0.0955926	+	0.294204i
$210$		0			0
$211$	−2.83688	+	8.73102i	−0.195299	+	0.601068i	0.804674	+	0.593717i	$0.202340\pi$
$211$	−2.83688	+	8.73102i	−0.195299	+	0.601068i	−0.999973	+	0.00735149i	$0.997660\pi$
$212$	2.04087	−	0.663119i	0.140168	−	0.0455432i
$213$	−6.29412	+	2.04508i	−0.431266	+	0.140127i
$214$	−8.20820	+	25.2623i	−0.561101	+	1.72689i
$215$		0			0
$216$	−3.45492	−	10.6331i	−0.235077	−	0.723493i
$217$	1.08981	+	1.50000i	0.0739814	+	0.101827i
$218$			16.1803i			1.09587i
$219$	−7.28115	+	5.29007i	−0.492015	+	0.357470i
$220$		0			0
$221$	7.85410	+	5.70634i	0.528324	+	0.383850i
$222$	0.224514	−	0.309017i	0.0150684	−	0.0207399i
$223$	0.171513	+	0.0557281i	0.0114854	+	0.00373183i	0.314754	−	0.949173i	$-0.398078\pi$
$223$	0.171513	+	0.0557281i	0.0114854	+	0.00373183i	−0.303269	+	0.952905i	$0.598078\pi$
$224$	−2.09017			−0.139655
$225$		0			0
$226$	−27.2705			−1.81401
$227$	14.0413	+	4.56231i	0.931956	+	0.302811i	0.735362	−	0.677674i	$-0.237012\pi$
$227$	14.0413	+	4.56231i	0.931956	+	0.302811i	0.196594	+	0.980485i	$0.437012\pi$
$228$	−0.310271	+	0.427051i	−0.0205482	+	0.0282821i
$229$	17.5623	+	12.7598i	1.16055	+	0.843189i	0.989847	−	0.142134i	$-0.0453963\pi$
$229$	17.5623	+	12.7598i	1.16055	+	0.843189i	0.170702	+	0.985323i	$0.445396\pi$
$230$		0			0
$231$	2.61803	−	1.90211i	0.172254	−	0.125150i
$232$		−	8.09017i		−	0.531146i
$233$	−1.73060	−	2.38197i	−0.113375	−	0.156048i	0.748558	−	0.663069i	$-0.230746\pi$
$233$	−1.73060	−	2.38197i	−0.113375	−	0.156048i	−0.861933	+	0.507021i	$0.830746\pi$
$234$	−1.85410	−	5.70634i	−0.121206	−	0.373035i
$235$		0			0
$236$	−2.07295	+	6.37988i	−0.134937	+	0.415295i
$237$	7.69421	−	2.50000i	0.499793	−	0.162392i
$238$	4.97980	−	1.61803i	0.322792	−	0.104882i
$239$	6.34346	−	19.5232i	0.410324	−	1.26285i	−0.506043	−	0.862508i	$-0.668892\pi$
$239$	6.34346	−	19.5232i	0.410324	−	1.26285i	0.916367	−	0.400340i	$-0.131108\pi$
$240$		0			0
$241$	0.781153	+	2.40414i	0.0503185	+	0.154864i	0.973058	−	0.230559i	$-0.0740554\pi$
$241$	0.781153	+	2.40414i	0.0503185	+	0.154864i	−0.922740	+	0.385423i	$0.874055\pi$
$242$	15.6129	+	21.4894i	1.00364	+	1.38139i
$243$		−	16.0000i		−	1.02640i
$244$	4.35410	−	3.16344i	0.278743	−	0.202519i
$245$		0			0
$246$	−1.00000	−	0.726543i	−0.0637577	−	0.0463227i
$247$	0.930812	−	1.28115i	0.0592262	−	0.0815178i
$248$	6.37988	+	2.07295i	0.405123	+	0.131632i
$249$	6.23607			0.395195
$250$		0			0
$251$	−29.1803			−1.84185			−0.920923	−	0.389744i	$-0.872564\pi$
$251$	−29.1803			−1.84185			−0.920923	+	0.389744i	$0.872564\pi$
$252$	−0.726543	−	0.236068i	−0.0457679	−	0.0148709i
$253$	11.5842	−	15.9443i	0.728292	−	1.00241i
$254$	−26.0344	−	18.9151i	−1.63355	−	1.18684i
$255$		0			0
$256$	−10.9721	+	7.97172i	−0.685758	+	0.498233i
$257$			22.8541i			1.42560i	0.701367	+	0.712800i	$0.252573\pi$
$257$			22.8541i			1.42560i	−0.701367	+	0.712800i	$0.747427\pi$
$258$	4.61653	+	6.35410i	0.287412	+	0.395589i
$259$	0.0450850	+	0.138757i	0.00280144	+	0.00862196i
$260$		0			0
$261$	2.23607	−	6.88191i	0.138409	−	0.425980i
$262$	10.4616	−	3.39919i	0.646321	−	0.210002i
$263$	−10.3759	+	3.37132i	−0.639803	+	0.207885i	−0.610913	−	0.791698i	$-0.709197\pi$
$263$	−10.3759	+	3.37132i	−0.639803	+	0.207885i	−0.0288905	+	0.999583i	$0.509197\pi$
$264$	3.61803	−	11.1352i	0.222675	−	0.685322i
$265$		0			0
$266$	−0.263932	−	0.812299i	−0.0161827	−	0.0498053i
$267$	5.25731	+	7.23607i	0.321742	+	0.442840i
$268$		−	2.94427i		−	0.179850i
$269$	−10.3262	+	7.50245i	−0.629602	+	0.457433i	−0.856262	−	0.516541i	$-0.827219\pi$
$269$	−10.3262	+	7.50245i	−0.629602	+	0.457433i	0.226660	+	0.973974i	$0.427219\pi$
$270$		0			0
$271$	6.47214	+	4.70228i	0.393154	+	0.285643i	0.766747	−	0.641950i	$-0.221874\pi$
$271$	6.47214	+	4.70228i	0.393154	+	0.285643i	−0.373593	+	0.927593i	$0.621874\pi$
$272$	14.9394	−	20.5623i	0.905834	−	1.24677i
$273$	−1.08981	−	0.354102i	−0.0659585	−	0.0214312i
$274$	−19.3262			−1.16754
$275$		0			0
$276$	2.32624			0.140023
$277$	−23.4989	−	7.63525i	−1.41191	−	0.458758i	−0.498889	−	0.866666i	$-0.666258\pi$
$277$	−23.4989	−	7.63525i	−1.41191	−	0.458758i	−0.913023	+	0.407908i	$0.866258\pi$
$278$	4.75528	−	6.54508i	0.285203	−	0.392548i
$279$	4.85410	+	3.52671i	0.290607	+	0.211139i
$280$		0			0
$281$	−8.16312	+	5.93085i	−0.486971	+	0.353805i	−0.804018	−	0.594605i	$-0.797309\pi$
$281$	−8.16312	+	5.93085i	−0.486971	+	0.353805i	0.317047	+	0.948410i	$0.397309\pi$
$282$		−	1.00000i		−	0.0595491i
$283$	−17.5478	−	24.1525i	−1.04311	−	1.43572i	−0.894634	−	0.446799i	$-0.852564\pi$
$283$	−17.5478	−	24.1525i	−1.04311	−	1.43572i	−0.148474	−	0.988916i	$-0.547436\pi$
$284$	1.26393	+	3.88998i	0.0750006	+	0.230828i
$285$		0			0
$286$	4.85410	−	14.9394i	0.287029	−	0.883385i
$287$	0.449028	−	0.145898i	0.0265053	−	0.00861209i
$288$	−6.43288	+	2.09017i	−0.379061	+	0.123164i
$289$	−3.21885	+	9.90659i	−0.189344	+	0.582741i
$290$		0			0
$291$	−1.19098	−	3.66547i	−0.0698167	−	0.214874i
$292$	3.26944	+	4.50000i	0.191330	+	0.263343i
$293$			19.5279i			1.14083i	0.821357	+	0.570415i	$0.193218\pi$
$293$			19.5279i			1.14083i	−0.821357	+	0.570415i	$0.806782\pi$
$294$	8.66312	−	6.29412i	0.505243	−	0.367081i
$295$		0			0
$296$	0.427051	+	0.310271i	0.0248218	+	0.0180341i
$297$	15.3884	−	21.1803i	0.892927	−	1.22901i
$298$	−6.06961	−	1.97214i	−0.351603	−	0.114243i
$299$	−6.97871			−0.403589
$300$		0			0
$301$	−3.00000			−0.172917
$302$	−22.4091	−	7.28115i	−1.28950	−	0.418983i
$303$	−0.865300	+	1.19098i	−0.0497102	+	0.0684202i
$304$	−3.35410	−	2.43690i	−0.192371	−	0.139766i
$305$		0			0
$306$	13.7082	−	9.95959i	0.783646	−	0.569352i
$307$			9.23607i			0.527130i	0.964642	+	0.263565i	$0.0848984\pi$
$307$			9.23607i			0.527130i	−0.964642	+	0.263565i	$0.915102\pi$
$308$	−1.17557	−	1.61803i	−0.0669843	−	0.0921960i
$309$	−2.64590	−	8.14324i	−0.150520	−	0.463253i
$310$		0			0
$311$	2.62868	−	8.09024i	0.149059	−	0.458755i	−0.848452	−	0.529272i	$-0.822465\pi$
$311$	2.62868	−	8.09024i	0.149059	−	0.458755i	0.997511	+	0.0705172i	$0.0224650\pi$
$312$	−3.94298	+	1.28115i	−0.223227	+	0.0725310i
$313$	−15.9434	+	5.18034i	−0.901177	+	0.292810i	−0.722723	−	0.691138i	$-0.757110\pi$
$313$	−15.9434	+	5.18034i	−0.901177	+	0.292810i	−0.178454	+	0.983948i	$0.557110\pi$
$314$	6.59017	−	20.2825i	0.371905	−	1.14461i
$315$		0			0
$316$	−1.54508	−	4.75528i	−0.0869178	−	0.267506i
$317$	−4.49801	−	6.19098i	−0.252634	−	0.347720i	0.663798	−	0.747912i	$-0.268944\pi$
$317$	−4.49801	−	6.19098i	−0.252634	−	0.347720i	−0.916431	+	0.400192i	$0.868944\pi$
$318$		−	5.61803i		−	0.315044i
$319$	15.3262	−	11.1352i	0.858105	−	0.623449i
$320$		0			0
$321$	13.2812	+	9.64932i	0.741282	+	0.538573i
$322$	−2.21238	+	3.04508i	−0.123291	+	0.169696i
$323$	4.25325	+	1.38197i	0.236657	+	0.0768946i
$324$	−0.618034			−0.0343352
$325$		0			0
$326$	−17.7984			−0.985761
$327$	9.51057	+	3.09017i	0.525935	+	0.170887i
$328$	1.00406	−	1.38197i	0.0554398	−	0.0763063i
$329$	0.309017	+	0.224514i	0.0170367	+	0.0123779i
$330$		0			0
$331$	18.7082	−	13.5923i	1.02830	−	0.747101i	0.0603290	−	0.998179i	$-0.480785\pi$
$331$	18.7082	−	13.5923i	1.02830	−	0.747101i	0.967967	+	0.251078i	$0.0807850\pi$
$332$		−	3.85410i		−	0.211521i
$333$	0.277515	+	0.381966i	0.0152077	+	0.0209316i
$334$	7.28115	+	22.4091i	0.398407	+	1.22617i
$335$		0			0
$336$	−0.927051	+	2.85317i	−0.0505748	+	0.155653i
$337$	−7.46969	+	2.42705i	−0.406900	+	0.132210i	−0.505314	−	0.862936i	$-0.668623\pi$
$337$	−7.46969	+	2.42705i	−0.406900	+	0.132210i	0.0984135	+	0.995146i	$0.468623\pi$
$338$	14.7149	−	4.78115i	0.800384	−	0.260060i
$339$	−5.20820	+	16.0292i	−0.282871	+	0.870587i
$340$		0			0
$341$	4.85410	+	14.9394i	0.262864	+	0.809013i
$342$	−1.62460	−	2.23607i	−0.0878482	−	0.120913i
$343$			8.41641i			0.454443i
$344$	−8.78115	+	6.37988i	−0.473448	+	0.343980i
$345$		0			0
$346$	24.7254	+	17.9641i	1.32925	+	0.965755i
$347$	−11.7027	+	16.1074i	−0.628234	+	0.864690i	−0.997920	−	0.0644668i	$-0.979465\pi$
$347$	−11.7027	+	16.1074i	−0.628234	+	0.864690i	0.369686	+	0.929157i	$0.379465\pi$
$348$	2.12663	+	0.690983i	0.113999	+	0.0370406i
$349$	−21.7082			−1.16201			−0.581007	−	0.813899i	$-0.697341\pi$
$349$	−21.7082			−1.16201			−0.581007	+	0.813899i	$0.697341\pi$
$350$		0			0
$351$	−9.27051			−0.494823
$352$	−16.8415	−	5.47214i	−0.897655	−	0.291666i
$353$	−7.58821	+	10.4443i	−0.403880	+	0.555893i	−0.961712	−	0.274061i	$-0.911633\pi$
$353$	−7.58821	+	10.4443i	−0.403880	+	0.555893i	0.557833	+	0.829953i	$0.311633\pi$
$354$	14.2082	+	10.3229i	0.755158	+	0.548654i
$355$		0			0
$356$	4.47214	−	3.24920i	0.237023	−	0.172207i
$357$		−	3.23607i		−	0.171271i
$358$	0.502029	+	0.690983i	0.0265330	+	0.0365196i
$359$	−4.24671	−	13.0700i	−0.224133	−	0.689810i	−0.998378	−	0.0569247i	$-0.981870\pi$
$359$	−4.24671	−	13.0700i	−0.224133	−	0.689810i	0.774246	−	0.632885i	$-0.218130\pi$
$360$		0			0
$361$	−5.64590	+	17.3763i	−0.297153	+	0.914541i
$362$	0.449028	−	0.145898i	0.0236004	−	0.00766823i
$363$	15.6129	−	5.07295i	0.819466	−	0.266261i
$364$	−0.218847	+	0.673542i	−0.0114707	+	0.0353032i
$365$		0			0
$366$	−4.35410	−	13.4005i	−0.227593	−	0.700458i
$367$	15.0251	+	20.6803i	0.784306	+	1.07950i	0.994794	+	0.101908i	$0.0324949\pi$
$367$	15.0251	+	20.6803i	0.784306	+	1.07950i	−0.210488	+	0.977597i	$0.567505\pi$
$368$			18.2705i			0.952416i
$369$	1.23607	−	0.898056i	0.0643471	−	0.0467509i
$370$		0			0
$371$	1.73607	+	1.26133i	0.0901322	+	0.0654848i
$372$	−1.08981	+	1.50000i	−0.0565042	+	0.0777714i
$373$	26.8869	+	8.73607i	1.39215	+	0.452336i	0.906644	−	0.421897i	$-0.138636\pi$
$373$	26.8869	+	8.73607i	1.39215	+	0.452336i	0.485505	+	0.874234i	$0.338636\pi$
$374$	44.3607			2.29384
$375$		0			0
$376$	1.38197			0.0712695
$377$	−6.37988	−	2.07295i	−0.328581	−	0.106762i
$378$	−2.93893	+	4.04508i	−0.151162	+	0.208057i
$379$	11.8090	+	8.57975i	0.606588	+	0.440712i	0.848211	−	0.529658i	$-0.177680\pi$
$379$	11.8090	+	8.57975i	0.606588	+	0.440712i	−0.241623	+	0.970370i	$0.577680\pi$
$380$		0			0
$381$	−16.0902	+	11.6902i	−0.824324	+	0.598907i
$382$			2.94427i			0.150642i
$383$	19.6089	+	26.9894i	1.00197	+	1.37909i	0.924110	+	0.382127i	$0.124808\pi$
$383$	19.6089	+	26.9894i	1.00197	+	1.37909i	0.0778591	+	0.996964i	$0.475192\pi$
$384$	4.20820	+	12.9515i	0.214749	+	0.660929i
$385$		0			0
$386$	−3.85410	+	11.8617i	−0.196169	+	0.603745i
$387$	−9.23305	+	3.00000i	−0.469342	+	0.152499i
$388$	−2.26538	+	0.736068i	−0.115007	+	0.0373682i
$389$	−4.63525	+	14.2658i	−0.235017	+	0.723307i	0.762102	+	0.647456i	$0.224167\pi$
$389$	−4.63525	+	14.2658i	−0.235017	+	0.723307i	−0.997119	+	0.0758507i	$0.975833\pi$
$390$		0			0
$391$	−6.09017	−	18.7436i	−0.307993	−	0.947905i
$392$	8.69827	+	11.9721i	0.439329	+	0.604684i
$393$		−	6.79837i		−	0.342933i
$394$	−4.85410	+	3.52671i	−0.244546	+	0.177673i
$395$		0			0
$396$	−5.23607	−	3.80423i	−0.263122	−	0.191170i
$397$	17.0660	−	23.4894i	0.856519	−	1.17890i	−0.125870	−	0.992047i	$-0.540172\pi$
$397$	17.0660	−	23.4894i	0.856519	−	1.17890i	0.982388	−	0.186850i	$-0.0598279\pi$
$398$	−27.0256	−	8.78115i	−1.35467	−	0.440159i
$399$	−0.527864			−0.0264263
$400$		0			0
$401$	26.5967			1.32818			0.664089	−	0.747653i	$-0.268820\pi$
$401$	26.5967			1.32818			0.664089	+	0.747653i	$0.268820\pi$
$402$	−7.33094	−	2.38197i	−0.365634	−	0.118802i
$403$	3.26944	−	4.50000i	0.162862	−	0.224161i
$404$	0.736068	+	0.534785i	0.0366208	+	0.0266065i
$405$		0			0
$406$	−2.92705	+	2.12663i	−0.145267	+	0.105543i
$407$			1.23607i			0.0612696i
$408$	−6.88191	−	9.47214i	−0.340705	−	0.468941i
$409$	−0.489357	−	1.50609i	−0.0241971	−	0.0744711i	0.938229	−	0.346016i	$-0.112466\pi$
$409$	−0.489357	−	1.50609i	−0.0241971	−	0.0744711i	−0.962426	+	0.271544i	$0.912466\pi$
$410$		0			0
$411$	−3.69098	+	11.3597i	−0.182063	+	0.560332i
$412$	−5.03280	+	1.63525i	−0.247948	+	0.0805632i
$413$	−6.37988	+	2.07295i	−0.313933	+	0.102003i
$414$	−3.76393	+	11.5842i	−0.184987	+	0.569332i
$415$		0			0
$416$	1.93769	+	5.96361i	0.0950033	+	0.292390i
$417$	−2.93893	−	4.04508i	−0.143920	−	0.198089i
$418$		−	7.23607i		−	0.353928i
$419$	−7.66312	+	5.56758i	−0.374368	+	0.271994i	−0.759020	−	0.651068i	$-0.774321\pi$
$419$	−7.66312	+	5.56758i	−0.374368	+	0.271994i	0.384652	+	0.923062i	$0.374321\pi$
$420$		0			0
$421$	−25.8885	−	18.8091i	−1.26173	−	0.916701i	−0.262889	−	0.964826i	$-0.584675\pi$
$421$	−25.8885	−	18.8091i	−1.26173	−	0.916701i	−0.998841	+	0.0481252i	$0.984675\pi$
$422$	8.73102	−	12.0172i	0.425020	−	0.584989i
$423$	1.17557	+	0.381966i	0.0571582	+	0.0185718i
$424$	7.76393			0.377050
$425$		0			0
$426$	10.7082			0.518814
$427$	5.11855	+	1.66312i	0.247704	+	0.0804840i
$428$	5.96361	−	8.20820i	0.288262	−	0.396759i
$429$	−7.85410	−	5.70634i	−0.379200	−	0.275505i
$430$		0			0
$431$	24.1353	−	17.5353i	1.16255	−	0.844645i	0.172456	−	0.985017i	$-0.444830\pi$
$431$	24.1353	−	17.5353i	1.16255	−	0.844645i	0.990099	+	0.140372i	$0.0448299\pi$
$432$			24.2705i			1.16772i
$433$	15.7844	+	21.7254i	0.758552	+	1.04406i	0.997333	+	0.0729839i	$0.0232522\pi$
$433$	15.7844	+	21.7254i	0.758552	+	1.04406i	−0.238781	+	0.971073i	$0.576748\pi$
$434$	−0.927051	−	2.85317i	−0.0444999	−	0.136957i
$435$		0			0
$436$	1.90983	−	5.87785i	0.0914643	−	0.281498i
$437$	−3.05744	+	0.993422i	−0.146257	+	0.0475218i
$438$	13.8496	−	4.50000i	0.661758	−	0.215018i
$439$	12.6631	−	38.9731i	0.604378	−	1.86008i	0.103365	−	0.994644i	$-0.467039\pi$
$439$	12.6631	−	38.9731i	0.604378	−	1.86008i	0.501013	−	0.865440i	$-0.332961\pi$
$440$		0			0
$441$	4.09017	+	12.5882i	0.194770	+	0.599440i
$442$	−9.23305	−	12.7082i	−0.439171	−	0.604468i
$443$		−	29.9443i		−	1.42270i	−0.702840	−	0.711348i	$-0.748085\pi$
$443$		−	29.9443i		−	1.42270i	0.702840	−	0.711348i	$-0.251915\pi$
$444$	−0.118034	+	0.0857567i	−0.00560165	+	0.00406983i
$445$		0			0
$446$	−0.236068	−	0.171513i	−0.0111781	−	0.00812140i
$447$	−2.31838	+	3.19098i	−0.109656	+	0.150928i
$448$	−2.48990	−	0.809017i	−0.117637	−	0.0382225i
$449$	−4.67376			−0.220568			−0.110284	−	0.993900i	$-0.535176\pi$
$449$	−4.67376			−0.220568			−0.110284	+	0.993900i	$0.535176\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$	9.90659	+	3.21885i	0.465967	+	0.151402i
$453$	−8.55951	+	11.7812i	−0.402161	+	0.553527i
$454$	−19.3262	−	14.0413i	−0.907025	−	0.658992i
$455$		0			0
$456$	−1.54508	+	1.12257i	−0.0723552	+	0.0525692i
$457$		−	21.4164i		−	1.00182i	−0.865500	−	0.500909i	$-0.832999\pi$
$457$		−	21.4164i		−	1.00182i	0.865500	−	0.500909i	$-0.167001\pi$
$458$	−20.6457	−	28.4164i	−0.964712	−	1.32781i
$459$	−8.09017	−	24.8990i	−0.377617	−	1.16218i
$460$		0			0
$461$	0.253289	−	0.779543i	0.0117968	−	0.0363069i	−0.944985	−	0.327114i	$-0.893924\pi$
$461$	0.253289	−	0.779543i	0.0117968	−	0.0363069i	0.956782	+	0.290807i	$0.0939238\pi$
$462$	−4.97980	+	1.61803i	−0.231681	+	0.0752778i
$463$	−22.9439	+	7.45492i	−1.06629	+	0.346459i	−0.789042	−	0.614339i	$-0.789423\pi$
$463$	−22.9439	+	7.45492i	−1.06629	+	0.346459i	−0.277250	+	0.960798i	$0.589423\pi$
$464$	−5.42705	+	16.7027i	−0.251945	+	0.775405i
$465$		0			0
$466$	1.47214	+	4.53077i	0.0681954	+	0.209884i
$467$	−16.1352	−	22.2082i	−0.746648	−	1.02767i	−0.998208	−	0.0598315i	$-0.980944\pi$
$467$	−16.1352	−	22.2082i	−0.746648	−	1.02767i	0.251560	−	0.967842i	$-0.419056\pi$
$468$			2.29180i			0.105938i
$469$	2.38197	−	1.73060i	0.109989	−	0.0799117i
$470$		0			0
$471$	−10.6631	−	7.74721i	−0.491331	−	0.356973i
$472$	−14.2658	+	19.6353i	−0.656639	+	0.903786i
$473$	−24.1724	−	7.85410i	−1.11145	−	0.361132i
$474$	−13.0902			−0.601251
$475$		0			0
$476$	−2.00000			−0.0916698
$477$	6.60440	+	2.14590i	0.302394	+	0.0982539i
$478$	−19.5232	+	26.8713i	−0.892969	+	1.22907i
$479$	−8.78115	−	6.37988i	−0.401221	−	0.291504i	0.368817	−	0.929502i	$-0.379763\pi$
$479$	−8.78115	−	6.37988i	−0.401221	−	0.291504i	−0.770038	+	0.637998i	$0.779763\pi$
$480$		0			0
$481$	0.354102	−	0.257270i	0.0161457	−	0.0117305i
$482$		−	4.09017i		−	0.186302i
$483$	1.36733	+	1.88197i	0.0622156	+	0.0856324i
$484$	−3.13525	−	9.64932i	−0.142512	−	0.438606i
$485$		0			0
$486$	−8.00000	+	24.6215i	−0.362887	+	1.11685i
$487$	34.6341	−	11.2533i	1.56942	−	0.509935i	0.610116	−	0.792312i	$-0.291123\pi$
$487$	34.6341	−	11.2533i	1.56942	−	0.509935i	0.959303	+	0.282377i	$0.0911230\pi$
$488$	18.5191	−	6.01722i	0.838320	−	0.272387i
$489$	−3.39919	+	10.4616i	−0.153717	+	0.473091i
$490$		0			0
$491$	−13.3647	−	41.1325i	−0.603143	−	1.85628i	−0.509088	−	0.860715i	$-0.670017\pi$
$491$	−13.3647	−	41.1325i	−0.603143	−	1.85628i	−0.0940550	−	0.995567i	$-0.529983\pi$
$492$	0.277515	+	0.381966i	0.0125113	+	0.0172204i
$493$		−	18.9443i		−	0.853207i
$494$	−2.07295	+	1.50609i	−0.0932664	+	0.0677620i
$495$		0			0
$496$	−11.7812	−	8.55951i	−0.528989	−	0.384333i
$497$	−2.40414	+	3.30902i	−0.107840	+	0.148430i
$498$	−9.59632	−	3.11803i	−0.430021	−	0.139722i
$499$	−7.56231			−0.338535			−0.169268	−	0.985570i	$-0.554140\pi$
$499$	−7.56231			−0.338535			−0.169268	+	0.985570i	$0.554140\pi$
$500$		0			0
$501$	14.5623			0.650596
$502$	44.9039	+	14.5902i	2.00416	+	0.651191i
$503$	21.9928	−	30.2705i	0.980611	−	1.34970i	0.0441115	−	0.999027i	$-0.485954\pi$
$503$	21.9928	−	30.2705i	0.980611	−	1.34970i	0.936500	−	0.350669i	$-0.114046\pi$
$504$	−2.23607	−	1.62460i	−0.0996024	−	0.0723654i
$505$		0			0
$506$	−25.7984	+	18.7436i	−1.14688	+	0.833255i
$507$		−	9.56231i		−	0.424677i
$508$	7.22494	+	9.94427i	0.320555	+	0.441206i
$509$	6.28115	+	19.3314i	0.278407	+	0.856849i	0.988298	+	0.152537i	$0.0487444\pi$
$509$	6.28115	+	19.3314i	0.278407	+	0.856849i	−0.709891	+	0.704312i	$0.751256\pi$
$510$		0			0
$511$	−1.71885	+	5.29007i	−0.0760373	+	0.234019i
$512$	−5.03280	+	1.63525i	−0.222420	+	0.0722687i
$513$	−4.06150	+	1.31966i	−0.179319	+	0.0582644i
$514$	11.4271	−	35.1688i	0.504026	−	1.55123i
$515$		0			0
$516$	−0.927051	−	2.85317i	−0.0408111	−	0.125604i
$517$	1.90211	+	2.61803i	0.0836548	+	0.115141i
$518$		−	0.236068i		−	0.0103722i
$519$	15.2812	−	11.1024i	0.670768	−	0.487342i
$520$		0			0
$521$	−23.7533	−	17.2578i	−1.04065	−	0.756077i	−0.0702381	−	0.997530i	$-0.522376\pi$
$521$	−23.7533	−	17.2578i	−1.04065	−	0.756077i	−0.970412	+	0.241453i	$0.922376\pi$
$522$	−6.88191	+	9.47214i	−0.301213	+	0.414584i
$523$	12.5025	+	4.06231i	0.546696	+	0.177632i	0.569326	−	0.822112i	$-0.307204\pi$
$523$	12.5025	+	4.06231i	0.546696	+	0.177632i	−0.0226305	+	0.999744i	$0.507204\pi$
$524$	−4.20163			−0.183549
$525$		0			0
$526$	17.6525			0.769685
$527$	14.9394	+	4.85410i	0.650770	+	0.211448i
$528$	−14.9394	+	20.5623i	−0.650153	+	0.894860i
$529$	−7.14590	−	5.19180i	−0.310691	−	0.225730i
$530$		0			0
$531$	−17.5623	+	12.7598i	−0.762139	+	0.553727i
$532$			0.326238i			0.0141442i
$533$	−0.832544	−	1.14590i	−0.0360615	−	0.0496344i
$534$	−4.47214	−	13.7638i	−0.193528	−	0.595619i
$535$		0			0
$536$	3.29180	−	10.1311i	0.142184	−	0.437597i
$537$	0.502029	−	0.163119i	0.0216641	−	0.00703910i
$538$	19.6417	−	6.38197i	0.846813	−	0.275146i
$539$	−10.7082	+	32.9565i	−0.461235	+	1.41954i
$540$		0			0
$541$	8.38197	+	25.7970i	0.360369	+	1.10910i	0.952831	+	0.303503i	$0.0981561\pi$
$541$	8.38197	+	25.7970i	0.360369	+	1.10910i	−0.592462	+	0.805599i	$0.701844\pi$
$542$	−7.60845	−	10.4721i	−0.326811	−	0.449817i
$543$		−	0.291796i		−	0.0125222i
$544$	−14.3262	+	10.4086i	−0.614232	+	0.446266i
$545$		0			0
$546$	1.50000	+	1.08981i	0.0641941	+	0.0466397i
$547$	−12.5150	+	17.2254i	−0.535103	+	0.736506i	−0.987897	−	0.155109i	$-0.950427\pi$
$547$	−12.5150	+	17.2254i	−0.535103	+	0.736506i	0.452794	+	0.891615i	$0.350427\pi$
$548$	7.02067	+	2.28115i	0.299908	+	0.0974460i
$549$	17.4164			0.743314
$550$		0			0
$551$	−3.09017			−0.131646
$552$	8.00448	+	2.60081i	0.340693	+	0.110698i
$553$	2.93893	−	4.04508i	0.124976	−	0.172015i
$554$	32.3435	+	23.4989i	1.37414	+	0.998373i
$555$		0			0
$556$	−2.50000	+	1.81636i	−0.106024	+	0.0770307i
$557$			4.76393i			0.201854i	0.994894	+	0.100927i	$0.0321809\pi$
$557$			4.76393i			0.201854i	−0.994894	+	0.100927i	$0.967819\pi$
$558$	−5.70634	−	7.85410i	−0.241569	−	0.332491i
$559$	2.78115	+	8.55951i	0.117630	+	0.362029i
$560$		0			0
$561$	8.47214	−	26.0746i	0.357694	−	1.10087i
$562$	15.5272	−	5.04508i	0.654974	−	0.212814i
$563$	7.02067	−	2.28115i	0.295886	−	0.0961391i	−0.157312	−	0.987549i	$-0.550283\pi$
$563$	7.02067	−	2.28115i	0.295886	−	0.0961391i	0.453198	+	0.891410i	$0.350283\pi$
$564$	−0.118034	+	0.363271i	−0.00497013	+	0.0152965i
$565$		0			0
$566$	14.9271	+	45.9407i	0.627431	+	1.93103i
$567$	−0.363271	−	0.500000i	−0.0152560	−	0.0209980i
$568$			14.7984i			0.620926i
$569$	16.6074	−	12.0660i	0.696218	−	0.505832i	−0.182480	−	0.983210i	$-0.558413\pi$
$569$	16.6074	−	12.0660i	0.696218	−	0.505832i	0.878698	+	0.477377i	$0.158413\pi$
$570$		0			0
$571$	6.57295	+	4.77553i	0.275069	+	0.199850i	0.716764	−	0.697316i	$-0.245623\pi$
$571$	6.57295	+	4.77553i	0.275069	+	0.199850i	−0.441695	+	0.897165i	$0.645623\pi$
$572$	−3.52671	+	4.85410i	−0.147459	+	0.202960i
$573$	1.73060	+	0.562306i	0.0722968	+	0.0234907i
$574$	−0.763932			−0.0318859
$575$		0			0
$576$	−8.47214			−0.353006
$577$	−32.1239	−	10.4377i	−1.33734	−	0.434527i	−0.448923	−	0.893571i	$-0.648192\pi$
$577$	−32.1239	−	10.4377i	−1.33734	−	0.434527i	−0.888414	+	0.459044i	$0.848192\pi$
$578$	9.90659	−	13.6353i	0.412060	−	0.567152i
$579$	6.23607	+	4.53077i	0.259162	+	0.188292i
$580$		0			0
$581$	3.11803	−	2.26538i	0.129358	−	0.0939840i
$582$			6.23607i			0.258493i
$583$	10.6861	+	14.7082i	0.442575	+	0.609152i
$584$	6.21885	+	19.1396i	0.257338	+	0.792004i
$585$		0			0
$586$	9.76393	−	30.0503i	0.403344	−	1.24137i
$587$	−5.03280	+	1.63525i	−0.207726	+	0.0674942i	−0.411032	−	0.911621i	$-0.634831\pi$
$587$	−5.03280	+	1.63525i	−0.207726	+	0.0674942i	0.203306	+	0.979115i	$0.434831\pi$
$588$	−3.88998	+	1.26393i	−0.160420	+	0.0521237i
$589$	0.791796	−	2.43690i	0.0326254	−	0.100411i
$590$		0			0
$591$	1.14590	+	3.52671i	0.0471359	+	0.145070i
$592$	−0.673542	−	0.927051i	−0.0276824	−	0.0381016i
$593$			10.9098i			0.448013i	0.974588	+	0.224007i	$0.0719137\pi$
$593$			10.9098i			0.448013i	−0.974588	+	0.224007i	$0.928086\pi$
$594$	−34.2705	+	24.8990i	−1.40614	+	1.02162i
$595$		0			0
$596$	1.97214	+	1.43284i	0.0807818	+	0.0586914i
$597$	−10.3229	+	14.2082i	−0.422487	+	0.581503i
$598$	10.7391	+	3.48936i	0.439156	+	0.142690i
$599$	9.47214			0.387021			0.193510	−	0.981098i	$-0.438013\pi$
$599$	9.47214			0.387021			0.193510	+	0.981098i	$0.438013\pi$
$600$		0			0
$601$	2.72949			0.111338			0.0556691	−	0.998449i	$-0.482271\pi$
$601$	2.72949			0.111338			0.0556691	+	0.998449i	$0.482271\pi$
$602$	4.61653	+	1.50000i	0.188156	+	0.0611354i
$603$	5.60034	−	7.70820i	0.228063	−	0.313902i
$604$	7.28115	+	5.29007i	0.296266	+	0.215250i
$605$		0			0
$606$	1.92705	−	1.40008i	0.0782811	−	0.0568745i
$607$		−	35.5623i		−	1.44343i	−0.692191	−	0.721715i	$-0.743354\pi$
$607$		−	35.5623i		−	1.44343i	0.692191	−	0.721715i	$-0.256646\pi$
$608$	1.69784	+	2.33688i	0.0688566	+	0.0947730i
$609$	0.690983	+	2.12663i	0.0280000	+	0.0861753i
$610$		0			0
$611$	0.354102	−	1.08981i	0.0143254	−	0.0440891i
$612$	−6.15537	+	2.00000i	−0.248816	+	0.0808452i
$613$	−14.2456	+	4.62868i	−0.575374	+	0.186951i	−0.582227	−	0.813026i	$-0.697819\pi$
$613$	−14.2456	+	4.62868i	−0.575374	+	0.186951i	0.00685287	+	0.999977i	$0.497819\pi$
$614$	4.61803	−	14.2128i	0.186369	−	0.573584i
$615$		0			0
$616$	−2.23607	−	6.88191i	−0.0900937	−	0.277280i
$617$	−8.36775	−	11.5172i	−0.336873	−	0.463666i	0.606652	−	0.794968i	$-0.292512\pi$
$617$	−8.36775	−	11.5172i	−0.336873	−	0.463666i	−0.943525	+	0.331302i	$0.892512\pi$
$618$			13.8541i			0.557294i
$619$	24.6976	−	17.9438i	0.992679	−	0.721223i	0.0321727	−	0.999482i	$-0.489757\pi$
$619$	24.6976	−	17.9438i	0.992679	−	0.721223i	0.960506	+	0.278259i	$0.0897573\pi$
$620$		0			0
$621$	15.2254	+	11.0619i	0.610975	+	0.443900i
$622$	−8.09024	+	11.1353i	−0.324389	+	0.446483i
$623$	5.25731	+	1.70820i	0.210630	+	0.0684377i
$624$	9.00000			0.360288
$625$		0			0
$626$	27.1246			1.08412
$627$	−4.25325	−	1.38197i	−0.169859	−	0.0551904i
$628$	−4.78804	+	6.59017i	−0.191064	+	0.262976i
$629$	1.00000	+	0.726543i	0.0398726	+	0.0289691i
$630$		0			0
$631$	8.28115	−	6.01661i	0.329667	−	0.239517i	−0.410622	−	0.911806i	$-0.634688\pi$
$631$	8.28115	−	6.01661i	0.329667	−	0.239517i	0.740290	+	0.672288i	$0.234688\pi$
$632$		−	18.0902i		−	0.719588i
$633$	−5.39607	−	7.42705i	−0.214474	−	0.295199i
$634$	3.82624	+	11.7759i	0.151959	+	0.467683i
$635$		0			0
$636$	−0.663119	+	2.04087i	−0.0262944	+	0.0809258i
$637$	11.6699	−	3.79180i	0.462380	−	0.150236i
$638$	−29.1522	+	9.47214i	−1.15415	+	0.375005i
$639$	−4.09017	+	12.5882i	−0.161805	+	0.497983i
$640$		0			0
$641$	−0.336881	−	1.03681i	−0.0133060	−	0.0409517i	0.944183	−	0.329421i	$-0.106854\pi$
$641$	−0.336881	−	1.03681i	−0.0133060	−	0.0409517i	−0.957489	+	0.288470i	$0.906854\pi$
$642$	−15.6129	−	21.4894i	−0.616193	−	0.848117i
$643$			30.8328i			1.21593i	0.793965	+	0.607964i	$0.208013\pi$
$643$			30.8328i			1.21593i	−0.793965	+	0.607964i	$0.791987\pi$
$644$	1.16312	−	0.845055i	0.0458333	−	0.0332998i
$645$		0			0
$646$	−5.85410	−	4.25325i	−0.230327	−	0.167342i
$647$	−21.4783	+	29.5623i	−0.844398	+	1.16221i	0.140671	+	0.990056i	$0.455074\pi$
$647$	−21.4783	+	29.5623i	−0.844398	+	1.16221i	−0.985069	+	0.172158i	$0.944926\pi$
$648$	−2.12663	−	0.690983i	−0.0835418	−	0.0271444i
$649$	−56.8328			−2.23088
$650$		0			0
$651$	−1.85410			−0.0726680
$652$	6.46564	+	2.10081i	0.253214	+	0.0822742i
$653$	−11.2209	+	15.4443i	−0.439109	+	0.604381i	−0.970014	−	0.243050i	$-0.921852\pi$
$653$	−11.2209	+	15.4443i	−0.439109	+	0.604381i	0.530905	+	0.847431i	$0.321852\pi$
$654$	−13.0902	−	9.51057i	−0.511866	−	0.371893i
$655$		0			0
$656$	−3.00000	+	2.17963i	−0.117130	+	0.0851002i
$657$			18.0000i			0.702247i
$658$	−0.363271	−	0.500000i	−0.0141618	−	0.0194920i
$659$	−4.79837	−	14.7679i	−0.186918	−	0.575275i	0.813058	−	0.582183i	$-0.197801\pi$
$659$	−4.79837	−	14.7679i	−0.186918	−	0.575275i	−0.999976	+	0.00690786i	$0.997801\pi$
$660$		0			0
$661$	6.08359	−	18.7234i	0.236624	−	0.728255i	−0.760277	−	0.649598i	$-0.774937\pi$
$661$	6.08359	−	18.7234i	0.236624	−	0.728255i	0.996902	−	0.0786563i	$-0.0250630\pi$
$662$	−35.5851	+	11.5623i	−1.38305	+	0.449382i
$663$	−9.23305	+	3.00000i	−0.358582	+	0.116510i
$664$	4.30902	−	13.2618i	0.167222	−	0.514657i
$665$		0			0
$666$	−0.236068	−	0.726543i	−0.00914745	−	0.0281530i
$667$	8.00448	+	11.0172i	0.309935	+	0.426588i
$668$		−	9.00000i		−	0.348220i
$669$	−0.145898	+	0.106001i	−0.00564074	+	0.00409824i
$670$		0			0
$671$	36.8885	+	26.8011i	1.42407	+	1.03464i
$672$	1.22857	−	1.69098i	0.0473932	−	0.0652311i
$673$	−11.5842	−	3.76393i	−0.446538	−	0.145089i	0.0771122	−	0.997022i	$-0.475430\pi$
$673$	−11.5842	−	3.76393i	−0.446538	−	0.145089i	−0.523650	+	0.851934i	$0.675430\pi$
$674$	12.7082			0.489502
$675$		0			0
$676$	−5.90983			−0.227301
$677$	10.0984	+	3.28115i	0.388111	+	0.126105i	0.496571	−	0.867996i	$-0.334592\pi$
$677$	10.0984	+	3.28115i	0.388111	+	0.126105i	−0.108460	+	0.994101i	$0.534592\pi$
$678$	16.0292	−	22.0623i	0.615598	−	0.847298i
$679$	−1.92705	−	1.40008i	−0.0739534	−	0.0537303i
$680$		0			0
$681$	−11.9443	+	8.67802i	−0.457705	+	0.332543i
$682$		−	25.4164i		−	0.973245i
$683$	−7.91872	−	10.8992i	−0.303002	−	0.417046i	0.630181	−	0.776448i	$-0.282981\pi$
$683$	−7.91872	−	10.8992i	−0.303002	−	0.417046i	−0.933183	+	0.359402i	$0.882981\pi$
$684$	0.326238	+	1.00406i	0.0124740	+	0.0383911i
$685$		0			0
$686$	4.20820	−	12.9515i	0.160670	−	0.494491i
$687$	−20.6457	+	6.70820i	−0.787684	+	0.255934i
$688$	22.4091	−	7.28115i	0.854338	−	0.277591i
$689$	1.98936	−	6.12261i	0.0757885	−	0.233253i
$690$		0			0
$691$	11.2082	+	34.4953i	0.426380	+	1.31226i	0.901667	+	0.432432i	$0.142344\pi$
$691$	11.2082	+	34.4953i	0.426380	+	1.31226i	−0.475286	+	0.879831i	$0.657656\pi$
$692$	−6.86167	−	9.44427i	−0.260841	−	0.359017i
$693$		−	6.47214i		−	0.245856i
$694$	26.0623	−	18.9354i	0.989312	−	0.718777i
$695$		0			0
$696$	6.54508	+	4.75528i	0.248091	+	0.180249i
$697$	2.35114	−	3.23607i	0.0890558	−	0.122575i
$698$	33.4055	+	10.8541i	1.26442	+	0.410834i
$699$	2.94427			0.111363
$700$		0			0
$701$	−41.0132			−1.54905			−0.774523	−	0.632546i	$-0.782010\pi$
$701$	−41.0132			−1.54905			−0.774523	+	0.632546i	$0.782010\pi$
$702$	14.2658	+	4.63525i	0.538430	+	0.174946i
$703$	0.118513	−	0.163119i	0.00446980	−	0.00615215i
$704$	−17.9443	−	13.0373i	−0.676300	−	0.491361i
$705$		0			0
$706$	16.8992	−	12.2780i	0.636009	−	0.462088i
$707$			0.909830i			0.0342177i
$708$	−3.94298	−	5.42705i	−0.148186	−	0.203961i
$709$	10.3647	+	31.8994i	0.389256	+	1.19801i	0.933345	+	0.358980i	$0.116875\pi$
$709$	10.3647	+	31.8994i	0.389256	+	1.19801i	−0.544089	+	0.839027i	$0.683125\pi$
$710$		0			0
$711$	5.00000	−	15.3884i	0.187515	−	0.577111i
$712$	19.0211	−	6.18034i	0.712847	−	0.231618i
$713$	−10.7391	+	3.48936i	−0.402184	+	0.130677i
$714$	−1.61803	+	4.97980i	−0.0605534	+	0.186364i
$715$		0			0
$716$	−0.100813	−	0.310271i	−0.00376756	−	0.0115954i
$717$	12.0660	+	16.6074i	0.450612	+	0.620214i
$718$			22.2361i			0.829843i
$719$	−18.8435	+	13.6906i	−0.702742	+	0.510572i	−0.880824	−	0.473443i	$-0.843011\pi$
$719$	−18.8435	+	13.6906i	−0.702742	+	0.510572i	0.178082	+	0.984016i	$0.443011\pi$
$720$		0			0
$721$	−4.28115	−	3.11044i	−0.159438	−	0.115839i
$722$	17.3763	−	23.9164i	0.646678	−	0.890077i
$723$	−2.40414	−	0.781153i	−0.0894110	−	0.0290514i
$724$	−0.180340			−0.00670228
$725$		0			0
$726$	−26.5623			−0.985820
$727$	23.3601	+	7.59017i	0.866380	+	0.281504i	0.708291	−	0.705921i	$-0.249467\pi$
$727$	23.3601	+	7.59017i	0.866380	+	0.281504i	0.158089	+	0.987425i	$0.449467\pi$
$728$	−1.50609	+	2.07295i	−0.0558192	+	0.0768286i
$729$	10.5172	+	7.64121i	0.389527	+	0.283008i
$730$		0			0
$731$	−20.5623	+	14.9394i	−0.760524	+	0.552553i
$732$			5.38197i			0.198923i
$733$	−11.7432	−	16.1631i	−0.433745	−	0.596998i	0.535063	−	0.844812i	$-0.320288\pi$
$733$	−11.7432	−	16.1631i	−0.433745	−	0.596998i	−0.968808	+	0.247814i	$0.920288\pi$
$734$	−12.7812	−	39.3363i	−0.471761	−	1.45193i
$735$		0			0
$736$	3.93363	−	12.1065i	0.144995	−	0.446250i
$737$	23.7234	−	7.70820i	0.873863	−	0.283935i
$738$	−2.35114	+	0.763932i	−0.0865467	+	0.0281207i
$739$	−4.93769	+	15.1967i	−0.181636	+	0.559018i	−0.999874	−	0.0158612i	$-0.994951\pi$
$739$	−4.93769	+	15.1967i	−0.181636	+	0.559018i	0.818238	+	0.574879i	$0.194951\pi$
$740$		0			0
$741$	0.489357	+	1.50609i	0.0179770	+	0.0553274i
$742$	−2.04087	−	2.80902i	−0.0749227	−	0.103122i
$743$		−	28.3607i		−	1.04045i	−0.854029	−	0.520226i	$-0.825848\pi$
$743$		−	28.3607i		−	1.04045i	0.854029	−	0.520226i	$-0.174152\pi$
$744$	−5.42705	+	3.94298i	−0.198965	+	0.144557i
$745$		0			0
$746$	−37.0066	−	26.8869i	−1.35491	−	0.984398i
$747$	7.33094	−	10.0902i	0.268225	−	0.369180i
$748$	−16.1150	−	5.23607i	−0.589221	−	0.191450i
$749$	10.1459			0.370723
$750$		0			0
$751$	−5.11146			−0.186520			−0.0932598	−	0.995642i	$-0.529729\pi$
$751$	−5.11146			−0.186520			−0.0932598	+	0.995642i	$0.529729\pi$
$752$	−2.85317	−	0.927051i	−0.104044	−	0.0338061i
$753$	17.1518	−	23.6074i	0.625045	−	0.860301i
$754$	8.78115	+	6.37988i	0.319791	+	0.232342i
$755$		0			0
$756$	1.54508	−	1.12257i	0.0561942	−	0.0408275i
$757$			30.4164i			1.10550i	0.833346	+	0.552752i	$0.186422\pi$
$757$			30.4164i			1.10550i	−0.833346	+	0.552752i	$0.813578\pi$
$758$	−13.8823	−	19.1074i	−0.504229	−	0.694012i
$759$	6.09017	+	18.7436i	0.221059	+	0.680350i
$760$		0			0
$761$	−5.70163	+	17.5478i	−0.206684	+	0.636107i	0.792956	+	0.609279i	$0.208541\pi$
$761$	−5.70163	+	17.5478i	−0.206684	+	0.636107i	−0.999640	+	0.0268287i	$0.991459\pi$
$762$	30.6053	−	9.94427i	1.10871	−	0.360243i
$763$	5.87785	−	1.90983i	0.212793	−	0.0691405i
$764$	0.347524	−	1.06957i	0.0125730	−	0.0386957i
$765$		0			0
$766$	−16.6803	−	51.3368i	−0.602685	−	1.85487i
$767$	11.8290	+	16.2812i	0.427119	+	0.587878i
$768$		−	13.5623i		−	0.489388i
$769$	10.8541	−	7.88597i	0.391409	−	0.284375i	−0.374624	−	0.927177i	$-0.622228\pi$
$769$	10.8541	−	7.88597i	0.391409	−	0.284375i	0.766033	+	0.642802i	$0.222228\pi$
$770$		0			0
$771$	−18.4894	−	13.4333i	−0.665878	−	0.483789i
$772$	2.80017	−	3.85410i	0.100780	−	0.138712i
$773$	34.3893	+	11.1738i	1.23690	+	0.401892i	0.853208	−	0.521570i	$-0.174654\pi$
$773$	34.3893	+	11.1738i	1.23690	+	0.401892i	0.383689	+	0.923462i	$0.374654\pi$
$774$	15.7082			0.564620
$775$		0			0
$776$	−8.61803			−0.309369
$777$	−0.138757	−	0.0450850i	−0.00497789	−	0.00161741i
$778$	14.2658	−	19.6353i	0.511455	−	0.703958i
$779$	−0.527864	−	0.383516i	−0.0189127	−	0.0137409i
$780$		0			0
$781$	−28.0344	+	20.3682i	−1.00315	+	0.728832i
$782$			31.8885i			1.14033i
$783$	10.6331	+	14.6353i	0.379997	+	0.523021i
$784$	−9.92705	−	30.5523i	−0.354538	−	1.09115i
$785$		0			0
$786$	−3.39919	+	10.4616i	−0.121245	+	0.373154i
$787$	11.2412	−	3.65248i	0.400704	−	0.130197i	−0.101730	−	0.994812i	$-0.532438\pi$
$787$	11.2412	−	3.65248i	0.400704	−	0.130197i	0.502434	+	0.864615i	$0.332438\pi$
$788$	2.17963	−	0.708204i	0.0776460	−	0.0252287i
$789$	3.37132	−	10.3759i	0.120022	−	0.369391i
$790$		0			0
$791$	3.21885	+	9.90659i	0.114449	+	0.352238i
$792$	−13.7638	−	18.9443i	−0.489076	−	0.673155i
$793$		−	16.1459i		−	0.573358i
$794$	−38.0066	+	27.6134i	−1.34880	+	0.979963i
$795$		0			0
$796$	8.78115	+	6.37988i	0.311240	+	0.226129i
$797$	5.73910	−	7.89919i	0.203289	−	0.279804i	−0.695184	−	0.718832i	$-0.744677\pi$
$797$	5.73910	−	7.89919i	0.203289	−	0.279804i	0.898473	+	0.439028i	$0.144677\pi$
$798$	0.812299	+	0.263932i	0.0287551	+	0.00934309i
$799$	3.23607			0.114484
$800$		0			0
$801$	17.8885			0.632061
$802$	−40.9282	−	13.2984i	−1.44522	−	0.469582i
$803$	−27.6992	+	38.1246i	−0.977482	+	1.34539i
$804$	2.38197	+	1.73060i	0.0840055	+	0.0610335i
$805$		0			0
$806$	−7.28115	+	5.29007i	−0.256468	+	0.186335i
$807$		−	12.7639i		−	0.449312i
$808$	1.93487	+	2.66312i	0.0680685	+	0.0936882i
$809$	−9.57295	−	29.4625i	−0.336567	−	1.03585i	−0.965945	−	0.258747i	$-0.916690\pi$
$809$	−9.57295	−	29.4625i	−0.336567	−	1.03585i	0.629378	−	0.777099i	$-0.283310\pi$
$810$		0			0
$811$	−4.54508	+	13.9883i	−0.159600	+	0.491197i	−0.998598	−	0.0529372i	$-0.983142\pi$
$811$	−4.54508	+	13.9883i	−0.159600	+	0.491197i	0.838998	+	0.544134i	$0.183142\pi$
$812$	1.31433	−	0.427051i	0.0461239	−	0.0149866i
$813$	−7.60845	+	2.47214i	−0.266840	+	0.0867016i
$814$	0.618034	−	1.90211i	0.0216621	−	0.0666690i
$815$		0			0
$816$	7.85410	+	24.1724i	0.274949	+	0.846205i
$817$	2.43690	+	3.35410i	0.0852563	+	0.117345i
$818$			2.56231i			0.0895889i
$819$	−1.85410	+	1.34708i	−0.0647876	+	0.0470709i
$820$		0			0
$821$	32.9164	+	23.9152i	1.14879	+	0.834645i	0.988320	−	0.152395i	$-0.0486987\pi$
$821$	32.9164	+	23.9152i	1.14879	+	0.834645i	0.160471	+	0.987041i	$0.448699\pi$
$822$	11.3597	−	15.6353i	0.396214	−	0.545342i
$823$	−45.3732	−	14.7426i	−1.58161	−	0.513896i	−0.619139	−	0.785281i	$-0.712518\pi$
$823$	−45.3732	−	14.7426i	−1.58161	−	0.513896i	−0.962471	+	0.271385i	$0.912518\pi$
$824$	−19.1459			−0.666979
$825$		0			0
$826$	10.8541			0.377663
$827$	−0.918300	−	0.298374i	−0.0319324	−	0.0103755i	0.293007	−	0.956110i	$-0.405344\pi$
$827$	−0.918300	−	0.298374i	−0.0319324	−	0.0103755i	−0.324940	+	0.945735i	$0.605344\pi$
$828$	2.73466	−	3.76393i	0.0950359	−	0.130806i
$829$	−29.0066	−	21.0745i	−1.00744	−	0.731948i	−0.0437695	−	0.999042i	$-0.513937\pi$
$829$	−29.0066	−	21.0745i	−1.00744	−	0.731948i	−0.963671	+	0.267094i	$0.913937\pi$
$830$		0			0
$831$	19.9894	−	14.5231i	0.693423	−	0.503801i
$832$			7.85410i			0.272292i
$833$	20.3682	+	28.0344i	0.705717	+	0.971336i
$834$	2.50000	+	7.69421i	0.0865679	+	0.266429i
$835$		0			0
$836$	−0.854102	+	2.62866i	−0.0295397	+	0.0909140i
$837$	−14.2658	+	4.63525i	−0.493100	+	0.160218i
$838$	14.5761	−	4.73607i	0.503524	−	0.163605i
$839$	−3.35410	+	10.3229i	−0.115796	+	0.356385i	−0.992112	−	0.125352i	$-0.959994\pi$
$839$	−3.35410	+	10.3229i	−0.115796	+	0.356385i	0.876316	+	0.481737i	$0.159994\pi$
$840$		0			0
$841$	−4.91641	−	15.1311i	−0.169531	−	0.521764i
$842$	30.4338	+	41.8885i	1.04882	+	1.44357i
$843$		−	10.0902i		−	0.347524i
$844$	−4.59017	+	3.33495i	−0.158000	+	0.114794i
$845$		0			0
$846$	−1.61803	−	1.17557i	−0.0556292	−	0.0404169i
$847$	5.96361	−	8.20820i	0.204912	−	0.282037i
$848$	−16.0292	−	5.20820i	−0.550445	−	0.178850i
$849$	29.8541			1.02459
$850$		0			0
$851$	−0.888544			−0.0304589
$852$	−3.88998	−	1.26393i	−0.133269	−	0.0433016i
$853$	8.99602	−	12.3820i	0.308018	−	0.423950i	−0.626744	−	0.779225i	$-0.715613\pi$
$853$	8.99602	−	12.3820i	0.308018	−	0.423950i	0.934762	+	0.355275i	$0.115613\pi$
$854$	−7.04508	−	5.11855i	−0.241078	−	0.175153i
$855$		0			0
$856$	29.6976	−	21.5765i	1.01504	−	0.737471i
$857$			19.6869i			0.672492i	0.941774	+	0.336246i	$0.109157\pi$
$857$			19.6869i			0.672492i	−0.941774	+	0.336246i	$0.890843\pi$
$858$	9.23305	+	12.7082i	0.315211	+	0.433851i
$859$	0.489357	+	1.50609i	0.0166966	+	0.0513870i	0.959058	−	0.283211i	$-0.0913996\pi$
$859$	0.489357	+	1.50609i	0.0166966	+	0.0513870i	−0.942361	+	0.334598i	$0.891400\pi$
$860$		0			0
$861$	−0.145898	+	0.449028i	−0.00497219	+	0.0153028i
$862$	−45.9080	+	14.9164i	−1.56363	+	0.508055i
$863$	−20.3885	+	6.62461i	−0.694031	+	0.225504i	−0.634728	−	0.772736i	$-0.718888\pi$
$863$	−20.3885	+	6.62461i	−0.694031	+	0.225504i	−0.0593032	+	0.998240i	$0.518888\pi$
$864$	5.22542	−	16.0822i	0.177773	−	0.547128i
$865$		0			0
$866$	−13.4271	−	41.3242i	−0.456270	−	1.40425i
$867$	−6.12261	−	8.42705i	−0.207935	−	0.286198i
$868$			1.14590i			0.0388943i
$869$	34.2705	−	24.8990i	1.16255	−	0.844640i
$870$		0			0
$871$	−7.14590	−	5.19180i	−0.242130	−	0.175917i
$872$	13.1433	−	18.0902i	0.445088	−	0.612610i
$873$	−7.33094	−	2.38197i	−0.248115	−	0.0806173i
$874$	5.20163			0.175948
$875$		0			0
$876$	−5.56231			−0.187933
$877$	−34.7526	−	11.2918i	−1.17351	−	0.381297i	−0.343559	−	0.939131i	$-0.611632\pi$
$877$	−34.7526	−	11.2918i	−1.17351	−	0.381297i	−0.829952	+	0.557834i	$0.811632\pi$
$878$	−38.9731	+	53.6418i	−1.31528	+	1.81032i
$879$	−15.7984	−	11.4782i	−0.532866	−	0.387150i
$880$		0			0
$881$	32.6525	−	23.7234i	1.10009	−	0.799262i	0.119015	−	0.992892i	$-0.462026\pi$
$881$	32.6525	−	23.7234i	1.10009	−	0.799262i	0.981075	+	0.193630i	$0.0620262\pi$
$882$		−	21.4164i		−	0.721128i
$883$	−12.0987	−	16.6525i	−0.407155	−	0.560400i	0.555367	−	0.831605i	$-0.312578\pi$
$883$	−12.0987	−	16.6525i	−0.407155	−	0.560400i	−0.962522	+	0.271205i	$0.912578\pi$
$884$	1.85410	+	5.70634i	0.0623602	+	0.191925i
$885$		0			0
$886$	−14.9721	+	46.0795i	−0.502999	+	1.54807i
$887$	−28.4257	+	9.23607i	−0.954441	+	0.310117i	−0.744519	−	0.667601i	$-0.767321\pi$
$887$	−28.4257	+	9.23607i	−0.954441	+	0.310117i	−0.209922	+	0.977718i	$0.567321\pi$
$888$	−0.502029	+	0.163119i	−0.0168470	+	0.00547391i
$889$	−3.79837	+	11.6902i	−0.127393	+	0.392076i
$890$		0			0
$891$	−1.61803	−	4.97980i	−0.0542062	−	0.166829i
$892$	0.0655123	+	0.0901699i	0.00219351	+	0.00301911i
$893$		−	0.527864i		−	0.0176643i
$894$	5.16312	−	3.75123i	0.172681	−	0.125460i
$895$		0			0
$896$	6.80902	+	4.94704i	0.227473	+	0.165269i
$897$	4.10199	−	5.64590i	0.136961	−	0.188511i
$898$	7.19218	+	2.33688i	0.240006	+	0.0779827i
$899$	−10.8541			−0.362005
$900$		0			0
$901$	18.1803			0.605675
$902$	−6.15537	−	2.00000i	−0.204951	−	0.0665927i
$903$	1.76336	−	2.42705i	0.0586808	−	0.0807672i
$904$	30.4894	+	22.1518i	1.01406	+	0.736758i
$905$		0			0
$906$	19.0623	−	13.8496i	0.633303	−	0.460121i
$907$		−	33.2492i		−	1.10402i	−0.833837	−	0.552011i	$-0.813861\pi$
$907$		−	33.2492i		−	1.10402i	0.833837	−	0.552011i	$-0.186139\pi$
$908$	5.36331	+	7.38197i	0.177988	+	0.244979i
$909$	0.909830	+	2.80017i	0.0301772	+	0.0928757i
$910$		0			0
$911$	−12.4336	+	38.2668i	−0.411944	+	1.26783i	0.503011	+	0.864280i	$0.332226\pi$
$911$	−12.4336	+	38.2668i	−0.411944	+	1.26783i	−0.914955	+	0.403555i	$0.867774\pi$
$912$	3.94298	−	1.28115i	0.130565	−	0.0424232i
$913$	31.0543	−	10.0902i	1.02775	−	0.333936i
$914$	−10.7082	+	32.9565i	−0.354196	+	1.09010i
$915$		0			0
$916$	4.14590	+	12.7598i	0.136984	+	0.421594i
$917$	−2.46965	−	3.39919i	−0.0815552	−	0.112251i
$918$			42.3607i			1.39811i
$919$	−43.0517	+	31.2789i	−1.42014	+	1.03179i	−0.428395	+	0.903591i	$0.640921\pi$
$919$	−43.0517	+	31.2789i	−1.42014	+	1.03179i	−0.991748	+	0.128203i	$0.959079\pi$
$920$		0			0
$921$	−7.47214	−	5.42882i	−0.246215	−	0.178886i
$922$	−0.779543	+	1.07295i	−0.0256729	+	0.0353357i
$923$	11.6699	+	3.79180i	0.384121	+	0.124808i
$924$	2.00000			0.0657952
$925$		0			0
$926$	39.0344			1.28275
$927$	−16.2865	−	5.29180i	−0.534918	−	0.173805i
$928$	7.19218	−	9.89919i	0.236095	−	0.324957i
$929$	33.6803	+	24.4702i	1.10502	+	0.802841i	0.981872	−	0.189548i	$-0.0607021\pi$
$929$	33.6803	+	24.4702i	1.10502	+	0.802841i	0.123145	+	0.992389i	$0.460702\pi$
$930$		0			0
$931$	4.57295	−	3.32244i	0.149872	−	0.108889i
$932$		−	1.81966i		−	0.0596049i
$933$	5.00004	+	6.88197i	0.163694	+	0.225305i
$934$	13.7254	+	42.2425i	0.449110	+	1.38222i
$935$		0			0
$936$	−2.56231	+	7.88597i	−0.0837516	+	0.257761i
$937$	−16.8617	+	5.47871i	−0.550849	+	0.178982i	−0.571200	−	0.820811i	$-0.693522\pi$
$937$	−16.8617	+	5.47871i	−0.550849	+	0.178982i	0.0203504	+	0.999793i	$0.493522\pi$
$938$	−4.53077	+	1.47214i	−0.147935	+	0.0480669i
$939$	5.18034	−	15.9434i	0.169054	−	0.520295i
$940$		0			0
$941$	−14.3435	−	44.1446i	−0.467583	−	1.43907i	−0.855704	−	0.517465i	$-0.826876\pi$
$941$	−14.3435	−	44.1446i	−0.467583	−	1.43907i	0.388121	−	0.921608i	$-0.373124\pi$
$942$	12.5352	+	17.2533i	0.408420	+	0.562143i
$943$			2.87539i			0.0936355i
$944$	42.6246	−	30.9686i	1.38731	−	1.00794i
$945$		0			0
$946$	33.2705	+	24.1724i	1.08172	+	0.785914i
$947$	1.55909	−	2.14590i	0.0506635	−	0.0697323i	−0.782934	−	0.622105i	$-0.786278\pi$
$947$	1.55909	−	2.14590i	0.0506635	−	0.0697323i	0.833597	+	0.552373i	$0.186278\pi$
$948$	4.75528	+	1.54508i	0.154444	+	0.0501820i
$949$	16.6869			0.541680
$950$		0			0
$951$	7.65248			0.248149
$952$	−6.88191	−	2.23607i	−0.223044	−	0.0724714i
$953$	4.55101	−	6.26393i	0.147422	−	0.202909i	−0.728919	−	0.684599i	$-0.759977\pi$
$953$	4.55101	−	6.26393i	0.147422	−	0.202909i	0.876341	+	0.481691i	$0.159977\pi$
$954$	−9.09017	−	6.60440i	−0.294305	−	0.213825i
$955$		0			0
$956$	10.2639	−	7.45718i	0.331959	−	0.241183i
$957$			18.9443i			0.612381i
$958$	10.3229	+	14.2082i	0.333517	+	0.459046i
$959$	2.28115	+	7.02067i	0.0736623	+	0.226709i
$960$		0			0
$961$	−6.79837	+	20.9232i	−0.219302	+	0.674943i
$962$	−0.673542	+	0.218847i	−0.0217159	+	0.00705591i
$963$	31.2259	−	10.1459i	1.00624	−	0.326947i
$964$	−0.482779	+	1.48584i	−0.0155493	+	0.0478557i
$965$		0			0
$966$	−1.16312	−	3.57971i	−0.0374227	−	0.115175i
$967$	−2.41665	−	3.32624i	−0.0777143	−	0.106965i	0.768390	−	0.639982i	$-0.221058\pi$
$967$	−2.41665	−	3.32624i	−0.0777143	−	0.106965i	−0.846104	+	0.533017i	$0.821058\pi$
$968$		−	36.7082i		−	1.17985i
$969$	−3.61803	+	2.62866i	−0.116228	+	0.0844446i
$970$		0			0
$971$	−4.54508	−	3.30220i	−0.145859	−	0.105973i	0.512463	−	0.858709i	$-0.328733\pi$
$971$	−4.54508	−	3.30220i	−0.145859	−	0.105973i	−0.658321	+	0.752737i	$0.728733\pi$
$972$	5.81234	−	8.00000i	0.186431	−	0.256600i
$973$	−2.93893	−	0.954915i	−0.0942177	−	0.0306132i
$974$	−58.9230			−1.88801
$975$		0			0
$976$	−42.2705			−1.35305
$977$	−2.23263	−	0.725425i	−0.0714281	−	0.0232084i	0.273085	−	0.961990i	$-0.411956\pi$
$977$	−2.23263	−	0.725425i	−0.0714281	−	0.0232084i	−0.344513	+	0.938782i	$0.611956\pi$
$978$	10.4616	−	14.3992i	0.334526	−	0.460435i
$979$	37.8885	+	27.5276i	1.21092	+	0.879787i
$980$		0			0
$981$	16.1803	−	11.7557i	0.516598	−	0.375331i
$982$			69.9787i			2.23311i
$983$	5.65334	+	7.78115i	0.180313	+	0.248180i	0.889600	−	0.456740i	$-0.150983\pi$
$983$	5.65334	+	7.78115i	0.180313	+	0.248180i	−0.709287	+	0.704920i	$0.750983\pi$
$984$	0.527864	+	1.62460i	0.0168277	+	0.0517903i
$985$		0			0
$986$	−9.47214	+	29.1522i	−0.301654	+	0.928396i
$987$	−0.363271	+	0.118034i	−0.0115631	+	0.00375706i
$988$	0.930812	−	0.302439i	0.0296131	−	0.00962187i
$989$	5.64590	−	17.3763i	0.179529	−	0.552534i
$990$		0			0
$991$	−4.74671	−	14.6089i	−0.150784	−	0.464066i	0.846925	−	0.531712i	$-0.178451\pi$
$991$	−4.74671	−	14.6089i	−0.150784	−	0.464066i	−0.997709	+	0.0676459i	$0.978451\pi$
$992$	5.96361	+	8.20820i	0.189345	+	0.260611i
$993$			23.1246i			0.733837i
$994$	5.35410	−	3.88998i	0.169822	−	0.123383i
$995$		0			0
$996$	3.11803	+	2.26538i	0.0987987	+	0.0717814i
$997$	14.6291	−	20.1353i	0.463309	−	0.637690i	−0.511882	−	0.859056i	$-0.671051\pi$
$997$	14.6291	−	20.1353i	0.463309	−	0.637690i	0.975191	+	0.221366i	$0.0710515\pi$
$998$	11.6372	+	3.78115i	0.368369	+	0.119690i
$999$	−1.18034			−0.0373443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.e.a.24.1		8
5.2	odd	4		125.2.d.a.101.1		4
5.3	odd	4		25.2.d.a.21.1	yes	4
5.4	even	2	inner	125.2.e.a.24.2		8
15.8	even	4		225.2.h.b.46.1		4
20.3	even	4		400.2.u.b.321.1		4
25.2	odd	20		625.2.d.b.376.1		4
25.3	odd	20		625.2.d.h.251.1		4
25.4	even	10		625.2.e.c.374.1		8
25.6	even	5	inner	125.2.e.a.99.2		8
25.8	odd	20		25.2.d.a.6.1	✓	4
25.9	even	10		625.2.b.a.624.4		4
25.11	even	5		625.2.e.c.249.1		8
25.12	odd	20		625.2.a.c.1.2		2
25.13	odd	20		625.2.a.b.1.1		2
25.14	even	10		625.2.e.c.249.2		8
25.16	even	5		625.2.b.a.624.1		4
25.17	odd	20		125.2.d.a.26.1		4
25.19	even	10	inner	125.2.e.a.99.1		8
25.21	even	5		625.2.e.c.374.2		8
25.22	odd	20		625.2.d.b.251.1		4
25.23	odd	20		625.2.d.h.376.1		4
75.8	even	20		225.2.h.b.181.1		4
75.38	even	20		5625.2.a.f.1.2		2
75.62	even	20		5625.2.a.d.1.1		2
100.63	even	20		10000.2.a.c.1.1		2
100.83	even	20		400.2.u.b.81.1		4
100.87	even	20		10000.2.a.l.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.d.a.6.1	✓	4	25.8	odd	20
25.2.d.a.21.1	yes	4	5.3	odd	4
125.2.d.a.26.1		4	25.17	odd	20
125.2.d.a.101.1		4	5.2	odd	4
125.2.e.a.24.1		8	1.1	even	1	trivial
125.2.e.a.24.2		8	5.4	even	2	inner
125.2.e.a.99.1		8	25.19	even	10	inner
125.2.e.a.99.2		8	25.6	even	5	inner
225.2.h.b.46.1		4	15.8	even	4
225.2.h.b.181.1		4	75.8	even	20
400.2.u.b.81.1		4	100.83	even	20
400.2.u.b.321.1		4	20.3	even	4
625.2.a.b.1.1		2	25.13	odd	20
625.2.a.c.1.2		2	25.12	odd	20
625.2.b.a.624.1		4	25.16	even	5
625.2.b.a.624.4		4	25.9	even	10
625.2.d.b.251.1		4	25.22	odd	20
625.2.d.b.376.1		4	25.2	odd	20
625.2.d.h.251.1		4	25.3	odd	20
625.2.d.h.376.1		4	25.23	odd	20
625.2.e.c.249.1		8	25.11	even	5
625.2.e.c.249.2		8	25.14	even	10
625.2.e.c.374.1		8	25.4	even	10
625.2.e.c.374.2		8	25.21	even	5
5625.2.a.d.1.1		2	75.62	even	20
5625.2.a.f.1.2		2	75.38	even	20
10000.2.a.c.1.1		2	100.63	even	20
10000.2.a.l.1.2		2	100.87	even	20

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.53884 - 0.500000i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(0.500000 + 0.363271i) q^{4} +(1.30902 - 0.951057i) q^{6} +0.618034i q^{7} +(1.31433 + 1.80902i) q^{8} +(0.618034 + 1.90211i) q^{9} +O(q^{10})\)	\(q+(-1.53884 - 0.500000i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(0.500000 + 0.363271i) q^{4} +(1.30902 - 0.951057i) q^{6} +0.618034i q^{7} +(1.31433 + 1.80902i) q^{8} +(0.618034 + 1.90211i) q^{9} +(-1.61803 + 4.97980i) q^{11} +(-0.587785 + 0.190983i) q^{12} +(1.76336 - 0.572949i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-1.50000 - 4.61653i) q^{16} +(3.07768 + 4.23607i) q^{17} -3.23607i q^{18} +(0.690983 - 0.502029i) q^{19} +(-0.500000 - 0.363271i) q^{21} +(4.97980 - 6.85410i) q^{22} +(-3.57971 - 1.16312i) q^{23} -2.23607 q^{24} -3.00000 q^{26} +(-4.75528 - 1.54508i) q^{27} +(-0.224514 + 0.309017i) q^{28} +(-2.92705 - 2.12663i) q^{29} +(2.42705 - 1.76336i) q^{31} +3.38197i q^{32} +(-3.07768 - 4.23607i) q^{33} +(-2.61803 - 8.05748i) q^{34} +(-0.381966 + 1.17557i) q^{36} +(0.224514 - 0.0729490i) q^{37} +(-1.31433 + 0.427051i) q^{38} +(-0.572949 + 1.76336i) q^{39} +(-0.236068 - 0.726543i) q^{41} +(0.587785 + 0.809017i) q^{42} +4.85410i q^{43} +(-2.61803 + 1.90211i) q^{44} +(4.92705 + 3.57971i) q^{46} +(0.363271 - 0.500000i) q^{47} +(4.61653 + 1.50000i) q^{48} +6.61803 q^{49} -5.23607 q^{51} +(1.08981 + 0.354102i) q^{52} +(2.04087 - 2.80902i) q^{53} +(6.54508 + 4.75528i) q^{54} +(-1.11803 + 0.812299i) q^{56} +0.854102i q^{57} +(3.44095 + 4.73607i) q^{58} +(3.35410 + 10.3229i) q^{59} +(2.69098 - 8.28199i) q^{61} +(-4.61653 + 1.50000i) q^{62} +(-1.17557 + 0.381966i) q^{63} +(-1.30902 + 4.02874i) q^{64} +(2.61803 + 8.05748i) q^{66} +(-2.80017 - 3.85410i) q^{67} +3.23607i q^{68} +(3.04508 - 2.21238i) q^{69} +(5.35410 + 3.88998i) q^{71} +(-2.62866 + 3.61803i) q^{72} +(8.55951 + 2.78115i) q^{73} -0.381966 q^{74} +0.527864 q^{76} +(-3.07768 - 1.00000i) q^{77} +(1.76336 - 2.42705i) q^{78} +(-6.54508 - 4.75528i) q^{79} +(-0.809017 + 0.587785i) q^{81} +1.23607i q^{82} +(-3.66547 - 5.04508i) q^{83} +(-0.118034 - 0.363271i) q^{84} +(2.42705 - 7.46969i) q^{86} +(3.44095 - 1.11803i) q^{87} +(-11.1352 + 3.61803i) q^{88} +(2.76393 - 8.50651i) q^{89} +(0.354102 + 1.08981i) q^{91} +(-1.36733 - 1.88197i) q^{92} +3.00000i q^{93} +(-0.809017 + 0.587785i) q^{94} +(-2.73607 - 1.98787i) q^{96} +(-2.26538 + 3.11803i) q^{97} +(-10.1841 - 3.30902i) q^{98} -10.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 6 q^{6} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 + 6 * q^6 - 4 * q^9	\( 8 q + 4 q^{4} + 6 q^{6} - 4 q^{9} - 4 q^{11} - 2 q^{14} - 12 q^{16} + 10 q^{19} - 4 q^{21} - 24 q^{26} - 10 q^{29} + 6 q^{31} - 12 q^{34} - 12 q^{36} - 18 q^{39} + 16 q^{41} - 12 q^{44} + 26 q^{46} + 44 q^{49} - 24 q^{51} + 30 q^{54} + 26 q^{61} - 6 q^{64} + 12 q^{66} + 2 q^{69} + 16 q^{71} - 12 q^{74} + 40 q^{76} - 30 q^{79} - 2 q^{81} + 8 q^{84} + 6 q^{86} + 40 q^{89} - 24 q^{91} - 2 q^{94} - 4 q^{96} - 48 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 + 6 * q^6 - 4 * q^9 - 4 * q^11 - 2 * q^14 - 12 * q^16 + 10 * q^19 - 4 * q^21 - 24 * q^26 - 10 * q^29 + 6 * q^31 - 12 * q^34 - 12 * q^36 - 18 * q^39 + 16 * q^41 - 12 * q^44 + 26 * q^46 + 44 * q^49 - 24 * q^51 + 30 * q^54 + 26 * q^61 - 6 * q^64 + 12 * q^66 + 2 * q^69 + 16 * q^71 - 12 * q^74 + 40 * q^76 - 30 * q^79 - 2 * q^81 + 8 * q^84 + 6 * q^86 + 40 * q^89 - 24 * q^91 - 2 * q^94 - 4 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

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