LMFDB - Embedded newform 250.2.d.c.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(51,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("250.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$250 = 2 \cdot 5^{3}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	250.d (of order $5$ , 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:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
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:	$5$
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			51.1
Root			$0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	250.51
Dual form			250.2.d.c.201.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.0542543 + 0.166977i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.0542543 + 0.166977i) q^{6} +1.27346 q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.40211 + 1.74524i) q^{9} +(3.52874 - 2.56378i) q^{11} +(0.142040 + 0.103198i) q^{12} +(-3.46589 - 2.51812i) q^{13} +(1.03025 - 0.748520i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(0.0302487 + 0.0930960i) q^{17} +2.96917 q^{18} +(-0.103198 - 0.317610i) q^{19} +(-0.0690905 + 0.212639i) q^{21} +(1.34786 - 4.14828i) q^{22} +(-5.10793 + 3.71113i) q^{23} +0.175571 q^{24} -4.28408 q^{26} +(-0.847859 + 0.616005i) q^{27} +(0.393520 - 1.21113i) q^{28} +(-1.44575 + 4.44955i) q^{29} +(2.48459 + 7.64677i) q^{31} -1.00000 q^{32} +(0.236644 + 0.728316i) q^{33} +(0.0791922 + 0.0575365i) q^{34} +(2.40211 - 1.74524i) q^{36} +(-3.32385 - 2.41492i) q^{37} +(-0.270175 - 0.196294i) q^{38} +(0.608509 - 0.442107i) q^{39} +(-9.24846 - 6.71940i) q^{41} +(0.0690905 + 0.212639i) q^{42} +10.2093 q^{43} +(-1.34786 - 4.14828i) q^{44} +(-1.95106 + 6.00473i) q^{46} +(-3.61710 + 11.1323i) q^{47} +(0.142040 - 0.103198i) q^{48} -5.37831 q^{49} -0.0171861 q^{51} +(-3.46589 + 2.51812i) q^{52} +(0.273457 - 0.841616i) q^{53} +(-0.323853 + 0.996718i) q^{54} +(-0.393520 - 1.21113i) q^{56} +0.0586326 q^{57} +(1.44575 + 4.44955i) q^{58} +(-6.15537 - 4.47214i) q^{59} +(1.35645 - 0.985520i) q^{61} +(6.50473 + 4.72597i) q^{62} +(3.05899 + 2.22249i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.619543 + 0.450124i) q^{66} +(-0.361243 - 1.11179i) q^{67} +0.0978870 q^{68} +(-0.342548 - 1.05425i) q^{69} +(-0.728373 + 2.24170i) q^{71} +(0.917526 - 2.82385i) q^{72} +(1.30127 - 0.945424i) q^{73} -4.10851 q^{74} -0.333955 q^{76} +(4.49370 - 3.26486i) q^{77} +(0.232430 - 0.715345i) q^{78} +(2.51358 - 7.73601i) q^{79} +(2.69572 + 8.29657i) q^{81} -11.4317 q^{82} +(2.29303 + 7.05722i) q^{83} +(0.180881 + 0.131418i) q^{84} +(8.25950 - 6.00088i) q^{86} +(-0.664536 - 0.482814i) q^{87} +(-3.52874 - 2.56378i) q^{88} +(-1.38197 + 1.00406i) q^{89} +(-4.41367 - 3.20672i) q^{91} +(1.95106 + 6.00473i) q^{92} -1.41164 q^{93} +(3.61710 + 11.1323i) q^{94} +(0.0542543 - 0.166977i) q^{96} +(2.04180 - 6.28402i) q^{97} +(-4.35114 + 3.16129i) q^{98} +12.9508 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} + 16 q^{7} + 2 q^{8} + 4 q^{9} - 4 q^{11} - 2 q^{12} - 2 q^{13} + 4 q^{14} - 2 q^{16} - 4 q^{17} - 4 q^{18} - 10 q^{19} + 16 q^{21} - 6 q^{22} - 12 q^{23} - 8 q^{24}+ \cdots + 28 q^{99}+O(q^{100})$ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 + 16 * q^7 + 2 * q^8 + 4 * q^9 - 4 * q^11 - 2 * q^12 - 2 * q^13 + 4 * q^14 - 2 * q^16 - 4 * q^17 - 4 * q^18 - 10 * q^19 + 16 * q^21 - 6 * q^22 - 12 * q^23 - 8 * q^24 - 28 * q^26 + 10 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^31 - 8 * q^32 + 16 * q^33 + 4 * q^34 + 4 * q^36 - 4 * q^37 - 10 * q^38 + 8 * q^39 - 14 * q^41 - 16 * q^42 + 28 * q^43 + 6 * q^44 - 8 * q^46 - 24 * q^47 - 2 * q^48 + 16 * q^49 + 16 * q^51 - 2 * q^52 + 8 * q^53 + 20 * q^54 + 4 * q^56 + 10 * q^58 - 14 * q^61 + 14 * q^62 - 12 * q^63 - 2 * q^64 + 24 * q^66 - 4 * q^67 + 16 * q^68 + 8 * q^69 - 34 * q^71 + 6 * q^72 - 12 * q^73 - 36 * q^74 - 18 * q^77 + 22 * q^78 - 12 * q^81 + 24 * q^82 - 32 * q^83 - 14 * q^84 + 22 * q^86 + 20 * q^87 + 4 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 + 16 * q^93 + 24 * q^94 + 2 * q^96 - 4 * q^97 - 16 * q^98 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$ .

$n$	$127$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	−0.0542543	+	0.166977i	−0.0313237	+	0.0964045i	−0.965496	−	0.260418i	$-0.916140\pi$
$3$	−0.0542543	+	0.166977i	−0.0313237	+	0.0964045i	0.934172	+	0.356822i	$0.116140\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	0.0542543	+	0.166977i	0.0221492	+	0.0681683i
$7$	1.27346			0.481322			0.240661	−	0.970609i	$-0.422636\pi$
$7$	1.27346			0.481322			0.240661	+	0.970609i	$0.422636\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	2.40211	+	1.74524i	0.800704	+	0.581746i
$10$		0			0
$11$	3.52874	−	2.56378i	1.06396	−	0.773009i	0.0891391	−	0.996019i	$-0.471588\pi$
$11$	3.52874	−	2.56378i	1.06396	−	0.773009i	0.974816	+	0.223011i	$0.0715884\pi$
$12$	0.142040	+	0.103198i	0.0410033	+	0.0297906i
$13$	−3.46589	−	2.51812i	−0.961266	−	0.698400i	−0.00782134	−	0.999969i	$-0.502490\pi$
$13$	−3.46589	−	2.51812i	−0.961266	−	0.698400i	−0.953444	+	0.301569i	$0.902490\pi$
$14$	1.03025	−	0.748520i	0.275346	−	0.200050i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.0302487	+	0.0930960i	0.00733640	+	0.0225791i	0.954658	−	0.297706i	$-0.0962214\pi$
$17$	0.0302487	+	0.0930960i	0.00733640	+	0.0225791i	−0.947321	+	0.320285i	$0.896221\pi$
$18$	2.96917			0.699841
$19$	−0.103198	−	0.317610i	−0.0236752	−	0.0728647i	0.938521	−	0.345223i	$-0.112197\pi$
$19$	−0.103198	−	0.317610i	−0.0236752	−	0.0728647i	−0.962196	+	0.272358i	$0.912197\pi$
$20$		0			0
$21$	−0.0690905	+	0.212639i	−0.0150768	+	0.0464016i
$22$	1.34786	−	4.14828i	0.287364	−	0.884417i
$23$	−5.10793	+	3.71113i	−1.06508	+	0.773824i	−0.975021	−	0.222113i	$-0.928705\pi$
$23$	−5.10793	+	3.71113i	−1.06508	+	0.773824i	−0.0900565	+	0.995937i	$0.528705\pi$
$24$	0.175571			0.0358382
$25$		0			0
$26$	−4.28408			−0.840177
$27$	−0.847859	+	0.616005i	−0.163170	+	0.118550i
$28$	0.393520	−	1.21113i	0.0743683	−	0.228882i
$29$	−1.44575	+	4.44955i	−0.268468	+	0.826260i	0.722406	+	0.691469i	$0.243036\pi$
$29$	−1.44575	+	4.44955i	−0.268468	+	0.826260i	−0.990874	+	0.134791i	$0.956964\pi$
$30$		0			0
$31$	2.48459	+	7.64677i	0.446245	+	1.37340i	0.881113	+	0.472907i	$0.156795\pi$
$31$	2.48459	+	7.64677i	0.446245	+	1.37340i	−0.434867	+	0.900494i	$0.643205\pi$
$32$	−1.00000			−0.176777
$33$	0.236644	+	0.728316i	0.0411945	+	0.126784i
$34$	0.0791922	+	0.0575365i	0.0135814	+	0.00986743i
$35$		0			0
$36$	2.40211	−	1.74524i	0.400352	−	0.290873i
$37$	−3.32385	−	2.41492i	−0.546438	−	0.397011i	0.280032	−	0.959991i	$-0.409655\pi$
$37$	−3.32385	−	2.41492i	−0.546438	−	0.397011i	−0.826470	+	0.562980i	$0.809655\pi$
$38$	−0.270175	−	0.196294i	−0.0438282	−	0.0318431i
$39$	0.608509	−	0.442107i	0.0974393	−	0.0707938i
$40$		0			0
$41$	−9.24846	−	6.71940i	−1.44437	−	1.04939i	−0.987107	−	0.160061i	$-0.948831\pi$
$41$	−9.24846	−	6.71940i	−1.44437	−	1.04939i	−0.457260	−	0.889333i	$-0.651169\pi$
$42$	0.0690905	+	0.212639i	0.0106609	+	0.0328109i
$43$	10.2093			1.55690			0.778452	−	0.627704i	$-0.216005\pi$
$43$	10.2093			1.55690			0.778452	+	0.627704i	$0.216005\pi$
$44$	−1.34786	−	4.14828i	−0.203197	−	0.625377i
$45$		0			0
$46$	−1.95106	+	6.00473i	−0.287668	+	0.885350i
$47$	−3.61710	+	11.1323i	−0.527608	+	1.62381i	0.231491	+	0.972837i	$0.425640\pi$
$47$	−3.61710	+	11.1323i	−0.527608	+	1.62381i	−0.759099	+	0.650975i	$0.774360\pi$
$48$	0.142040	−	0.103198i	0.0205016	−	0.0148953i
$49$	−5.37831			−0.768329
$50$		0			0
$51$	−0.0171861			−0.00240653
$52$	−3.46589	+	2.51812i	−0.480633	+	0.349200i
$53$	0.273457	−	0.841616i	0.0375623	−	0.115605i	−0.930517	−	0.366248i	$-0.880642\pi$
$53$	0.273457	−	0.841616i	0.0375623	−	0.115605i	0.968079	+	0.250643i	$0.0806421\pi$
$54$	−0.323853	+	0.996718i	−0.0440708	+	0.135636i
$55$		0			0
$56$	−0.393520	−	1.21113i	−0.0525863	−	0.161844i
$57$	0.0586326			0.00776608
$58$	1.44575	+	4.44955i	0.189836	+	0.584254i
$59$	−6.15537	−	4.47214i	−0.801361	−	0.582223i	0.109952	−	0.993937i	$-0.464930\pi$
$59$	−6.15537	−	4.47214i	−0.801361	−	0.582223i	−0.911313	+	0.411714i	$0.864930\pi$
$60$		0			0
$61$	1.35645	−	0.985520i	0.173676	−	0.126183i	−0.497551	−	0.867434i	$-0.665767\pi$
$61$	1.35645	−	0.985520i	0.173676	−	0.126183i	0.671227	+	0.741252i	$0.265767\pi$
$62$	6.50473	+	4.72597i	0.826102	+	0.600198i
$63$	3.05899	+	2.22249i	0.385396	+	0.280007i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$		0			0
$66$	0.619543	+	0.450124i	0.0762604	+	0.0554064i
$67$	−0.361243	−	1.11179i	−0.0441328	−	0.135827i	0.926562	−	0.376142i	$-0.122749\pi$
$67$	−0.361243	−	1.11179i	−0.0441328	−	0.135827i	−0.970695	+	0.240315i	$0.922749\pi$
$68$	0.0978870			0.0118705
$69$	−0.342548	−	1.05425i	−0.0412379	−	0.126917i
$70$		0			0
$71$	−0.728373	+	2.24170i	−0.0864419	+	0.266041i	−0.984929	−	0.172959i	$-0.944667\pi$
$71$	−0.728373	+	2.24170i	−0.0864419	+	0.266041i	0.898487	+	0.439000i	$0.144667\pi$
$72$	0.917526	−	2.82385i	0.108131	−	0.332794i
$73$	1.30127	−	0.945424i	0.152302	−	0.110654i	−0.509025	−	0.860752i	$-0.669994\pi$
$73$	1.30127	−	0.945424i	0.152302	−	0.110654i	0.661326	+	0.750098i	$0.269994\pi$
$74$	−4.10851			−0.477604
$75$		0			0
$76$	−0.333955			−0.0383073
$77$	4.49370	−	3.26486i	0.512105	−	0.372066i
$78$	0.232430	−	0.715345i	0.0263175	−	0.0809968i
$79$	2.51358	−	7.73601i	0.282800	−	0.870369i	−0.704249	−	0.709953i	$-0.748716\pi$
$79$	2.51358	−	7.73601i	0.282800	−	0.870369i	0.987049	−	0.160417i	$-0.0512837\pi$
$80$		0			0
$81$	2.69572	+	8.29657i	0.299524	+	0.921841i
$82$	−11.4317			−1.26242
$83$	2.29303	+	7.05722i	0.251693	+	0.774630i	0.994463	+	0.105084i	$0.0335112\pi$
$83$	2.29303	+	7.05722i	0.251693	+	0.774630i	−0.742771	+	0.669546i	$0.766489\pi$
$84$	0.180881	+	0.131418i	0.0197358	+	0.0143389i
$85$		0			0
$86$	8.25950	−	6.00088i	0.890644	−	0.647091i
$87$	−0.664536	−	0.482814i	−0.0712458	−	0.0517631i
$88$	−3.52874	−	2.56378i	−0.376165	−	0.273300i
$89$	−1.38197	+	1.00406i	−0.146488	+	0.106430i	−0.658615	−	0.752480i	$-0.728858\pi$
$89$	−1.38197	+	1.00406i	−0.146488	+	0.106430i	0.512127	+	0.858910i	$0.328858\pi$
$90$		0			0
$91$	−4.41367	−	3.20672i	−0.462678	−	0.336155i
$92$	1.95106	+	6.00473i	0.203412	+	0.626037i
$93$	−1.41164			−0.146380
$94$	3.61710	+	11.1323i	0.373076	+	1.14821i
$95$		0			0
$96$	0.0542543	−	0.166977i	0.00553730	−	0.0170421i
$97$	2.04180	−	6.28402i	0.207314	−	0.638046i	−0.792297	−	0.610136i	$-0.791115\pi$
$97$	2.04180	−	6.28402i	0.207314	−	0.638046i	0.999610	−	0.0279099i	$-0.00888516\pi$
$98$	−4.35114	+	3.16129i	−0.439532	+	0.319338i
$99$	12.9508			1.30161
$100$		0			0
$101$	−7.02311			−0.698825			−0.349413	−	0.936969i	$-0.613619\pi$
$101$	−7.02311			−0.698825			−0.349413	+	0.936969i	$0.613619\pi$
$102$	−0.0139038	+	0.0101017i	−0.00137668	+	0.00100022i
$103$	3.93893	−	12.1228i	0.388114	−	1.19449i	−0.546082	−	0.837732i	$-0.683881\pi$
$103$	3.93893	−	12.1228i	0.388114	−	1.19449i	0.934196	−	0.356760i	$-0.116119\pi$
$104$	−1.32385	+	4.07440i	−0.129814	+	0.399528i
$105$		0			0
$106$	−0.273457	−	0.841616i	−0.0265605	−	0.0817449i
$107$	12.2022			1.17963			0.589817	−	0.807537i	$-0.299200\pi$
$107$	12.2022			1.17963			0.589817	+	0.807537i	$0.299200\pi$
$108$	0.323853	+	0.996718i	0.0311628	+	0.0959092i
$109$	4.08628	+	2.96885i	0.391394	+	0.284365i	0.766027	−	0.642809i	$-0.222231\pi$
$109$	4.08628	+	2.96885i	0.391394	+	0.284365i	−0.374632	+	0.927173i	$0.622231\pi$
$110$		0			0
$111$	0.583571	−	0.423989i	0.0553901	−	0.0402432i
$112$	−1.03025	−	0.748520i	−0.0973494	−	0.0707284i
$113$	−11.3546	−	8.24962i	−1.06815	−	0.776059i	−0.0925736	−	0.995706i	$-0.529509\pi$
$113$	−11.3546	−	8.24962i	−1.06815	−	0.776059i	−0.975579	+	0.219647i	$0.929509\pi$
$114$	0.0474348	−	0.0344634i	0.00444268	−	0.00322779i
$115$		0			0
$116$	3.78501	+	2.74997i	0.351429	+	0.255328i
$117$	−3.93075	−	12.0976i	−0.363398	−	1.11842i
$118$	−7.60845			−0.700415
$119$	0.0385205	+	0.118554i	0.00353117	+	0.0108678i
$120$		0			0
$121$	2.47985	−	7.63220i	0.225441	−	0.693837i
$122$	0.518118	−	1.59460i	0.0469082	−	0.144369i
$123$	1.62376	−	1.17973i	0.146409	−	0.106373i
$124$	8.04029			0.722040
$125$		0			0
$126$	3.78112			0.336849
$127$	1.06706	−	0.775266i	0.0946864	−	0.0687937i	−0.539435	−	0.842027i	$-0.681362\pi$
$127$	1.06706	−	0.775266i	0.0946864	−	0.0687937i	0.634121	+	0.773234i	$0.281362\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−0.553898	+	1.70472i	−0.0487680	+	0.150093i
$130$		0			0
$131$	−0.550197	−	1.69333i	−0.0480710	−	0.147947i	0.924140	−	0.382054i	$-0.124783\pi$
$131$	−0.550197	−	1.69333i	−0.0480710	−	0.147947i	−0.972211	+	0.234107i	$0.924783\pi$
$132$	0.765797			0.0666541
$133$	−0.131418	−	0.404463i	−0.0113954	−	0.0350714i
$134$	−0.945746	−	0.687124i	−0.0817000	−	0.0593585i
$135$		0			0
$136$	0.0791922	−	0.0575365i	0.00679068	−	0.00493372i
$137$	−7.73508	−	5.61986i	−0.660852	−	0.480137i	0.206098	−	0.978531i	$-0.433923\pi$
$137$	−7.73508	−	5.61986i	−0.660852	−	0.480137i	−0.866951	+	0.498394i	$0.833923\pi$
$138$	−0.896802	−	0.651565i	−0.0763409	−	0.0554649i
$139$	3.72123	−	2.70363i	0.315631	−	0.229319i	−0.418678	−	0.908135i	$-0.637506\pi$
$139$	3.72123	−	2.70363i	0.315631	−	0.229319i	0.734309	+	0.678816i	$0.237506\pi$
$140$		0			0
$141$	−1.66260	−	1.20795i	−0.140016	−	0.101728i
$142$	0.728373	+	2.24170i	0.0611237	+	0.188119i
$143$	−18.6861			−1.56261
$144$	−0.917526	−	2.82385i	−0.0764605	−	0.235321i
$145$		0			0
$146$	0.497039	−	1.52973i	0.0411352	−	0.126601i
$147$	0.291796	−	0.898056i	0.0240669	−	0.0740704i
$148$	−3.32385	+	2.41492i	−0.273219	+	0.198505i
$149$	2.03186			0.166457			0.0832284	−	0.996530i	$-0.473477\pi$
$149$	2.03186			0.166457			0.0832284	+	0.996530i	$0.473477\pi$
$150$		0			0
$151$	18.9655			1.54339			0.771696	−	0.635992i	$-0.219409\pi$
$151$	18.9655			1.54339			0.771696	+	0.635992i	$0.219409\pi$
$152$	−0.270175	+	0.196294i	−0.0219141	+	0.0159215i
$153$	−0.0898138	+	0.276418i	−0.00726101	+	0.0223471i
$154$	1.71644	−	5.28266i	0.138315	−	0.425689i
$155$		0			0
$156$	−0.232430	−	0.715345i	−0.0186093	−	0.0572734i
$157$	14.2430			1.13672			0.568359	−	0.822781i	$-0.307579\pi$
$157$	14.2430			1.13672			0.568359	+	0.822781i	$0.307579\pi$
$158$	−2.51358	−	7.73601i	−0.199970	−	0.615444i
$159$	0.125695	+	0.0913225i	0.00996823	+	0.00724234i
$160$		0			0
$161$	−6.50473	+	4.72597i	−0.512645	+	0.372458i
$162$	7.05748	+	5.12756i	0.554488	+	0.402859i
$163$	15.9495	+	11.5880i	1.24926	+	0.907641i	0.998179	−	0.0603249i	$-0.0192137\pi$
$163$	15.9495	+	11.5880i	1.24926	+	0.907641i	0.251082	+	0.967966i	$0.419214\pi$
$164$	−9.24846	+	6.71940i	−0.722184	+	0.524697i
$165$		0			0
$166$	6.00323	+	4.36160i	0.465941	+	0.338526i
$167$	1.78668	+	5.49885i	0.138258	+	0.425514i	0.996083	−	0.0884287i	$-0.0281845\pi$
$167$	1.78668	+	5.49885i	0.138258	+	0.425514i	−0.857825	+	0.513942i	$0.828185\pi$
$168$	0.223582			0.0172497
$169$	1.65427	+	5.09132i	0.127252	+	0.391640i
$170$		0			0
$171$	0.306412	−	0.943040i	0.0234319	−	0.0721161i
$172$	3.15485	−	9.70962i	0.240555	−	0.740352i
$173$	8.51713	−	6.18806i	0.647545	−	0.470469i	−0.214889	−	0.976639i	$-0.568939\pi$
$173$	8.51713	−	6.18806i	0.647545	−	0.470469i	0.862434	+	0.506169i	$0.168939\pi$
$174$	−0.821412			−0.0622711
$175$		0			0
$176$	−4.36176			−0.328780
$177$	1.08070	−	0.785175i	0.0812305	−	0.0590174i
$178$	−0.527864	+	1.62460i	−0.0395651	+	0.121769i
$179$	3.35558	−	10.3274i	0.250808	−	0.771906i	−0.743819	−	0.668381i	$-0.766988\pi$
$179$	3.35558	−	10.3274i	0.250808	−	0.771906i	0.994627	−	0.103525i	$-0.0330123\pi$
$180$		0			0
$181$	−3.17848	−	9.78234i	−0.236254	−	0.727116i	−0.996953	−	0.0780101i	$-0.975143\pi$
$181$	−3.17848	−	9.78234i	−0.236254	−	0.727116i	0.760698	−	0.649106i	$-0.224857\pi$
$182$	−5.45559			−0.404395
$183$	0.0909663	+	0.279966i	0.00672442	+	0.0206956i
$184$	5.10793	+	3.71113i	0.376562	+	0.273588i
$185$		0			0
$186$	−1.14204	+	0.829740i	−0.0837384	+	0.0608395i
$187$	0.345418	+	0.250961i	0.0252594	+	0.0183521i
$188$	9.46969	+	6.88014i	0.690648	+	0.501785i
$189$	−1.07971	+	0.784457i	−0.0785375	+	0.0570608i
$190$		0			0
$191$	7.79944	+	5.66662i	0.564347	+	0.410022i	0.833047	−	0.553202i	$-0.186594\pi$
$191$	7.79944	+	5.66662i	0.564347	+	0.410022i	−0.268700	+	0.963224i	$0.586594\pi$
$192$	−0.0542543	−	0.166977i	−0.00391546	−	0.0120506i
$193$	6.00000			0.431889			0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000			0.431889			0.215945	+	0.976406i	$0.430717\pi$
$194$	−2.04180	−	6.28402i	−0.146593	−	0.451167i
$195$		0			0
$196$	−1.66199	+	5.11507i	−0.118713	+	0.365362i
$197$	−6.41164	+	19.7330i	−0.456810	+	1.40592i	0.412186	+	0.911100i	$0.364765\pi$
$197$	−6.41164	+	19.7330i	−0.456810	+	1.40592i	−0.868997	+	0.494818i	$0.835235\pi$
$198$	10.4774	−	7.61231i	0.744600	−	0.540983i
$199$	−19.0629			−1.35133			−0.675666	−	0.737208i	$-0.736144\pi$
$199$	−19.0629			−1.35133			−0.675666	+	0.737208i	$0.736144\pi$
$200$		0			0
$201$	0.205243			0.0144767
$202$	−5.68181	+	4.12808i	−0.399771	+	0.290451i
$203$	−1.84110	+	5.66631i	−0.129220	+	0.397697i
$204$	−0.00531079	+	0.0163449i	−0.000371829	+	0.00114437i
$205$		0			0
$206$	−3.93893	−	12.1228i	−0.274438	−	0.844633i
$207$	−18.7466			−1.30298
$208$	1.32385	+	4.07440i	0.0917927	+	0.282509i
$209$	−1.17844	−	0.856187i	−0.0815144	−	0.0592237i
$210$		0			0
$211$	−13.7691	+	10.0039i	−0.947906	+	0.688694i	−0.950311	−	0.311303i	$-0.899235\pi$
$211$	−13.7691	+	10.0039i	−0.947906	+	0.688694i	0.00240468	+	0.999997i	$0.499235\pi$
$212$	−0.715921	−	0.520147i	−0.0491697	−	0.0357238i
$213$	−0.334796	−	0.243244i	−0.0229399	−	0.0166668i
$214$	9.87181	−	7.17229i	0.674823	−	0.490288i
$215$		0			0
$216$	0.847859	+	0.616005i	0.0576895	+	0.0419139i
$217$	3.16402	+	9.73784i	0.214787	+	0.661048i
$218$	5.05092			0.342091
$219$	0.0872654	+	0.268575i	0.00589685	+	0.0181486i
$220$		0			0
$221$	0.129588	−	0.398831i	0.00871703	−	0.0268283i
$222$	0.222904	−	0.686028i	0.0149603	−	0.0460432i
$223$	−4.02723	+	2.92595i	−0.269683	+	0.195936i	−0.714405	−	0.699732i	$-0.753303\pi$
$223$	−4.02723	+	2.92595i	−0.269683	+	0.195936i	0.444722	+	0.895669i	$0.353303\pi$
$224$	−1.27346			−0.0850865
$225$		0			0
$226$	−14.0351			−0.933600
$227$	0.830673	−	0.603519i	0.0551337	−	0.0400570i	−0.559877	−	0.828576i	$-0.689152\pi$
$227$	0.830673	−	0.603519i	0.0551337	−	0.0400570i	0.615011	+	0.788519i	$0.289152\pi$
$228$	0.0181185	−	0.0557630i	0.00119993	−	0.00369299i
$229$	−1.26236	+	3.88514i	−0.0834189	+	0.256737i	−0.984063	−	0.177821i	$-0.943095\pi$
$229$	−1.26236	+	3.88514i	−0.0834189	+	0.256737i	0.900644	+	0.434558i	$0.143095\pi$
$230$		0			0
$231$	0.301356	+	0.927480i	0.0198278	+	0.0610237i
$232$	4.67853			0.307161
$233$	−1.36363	−	4.19681i	−0.0893342	−	0.274942i	0.896402	−	0.443243i	$-0.146172\pi$
$233$	−1.36363	−	4.19681i	−0.0893342	−	0.274942i	−0.985736	+	0.168301i	$0.946172\pi$
$234$	−10.2908	−	7.47673i	−0.672733	−	0.488769i
$235$		0			0
$236$	−6.15537	+	4.47214i	−0.400680	+	0.291111i
$237$	1.15537	+	0.839423i	0.0750492	+	0.0545264i
$238$	0.100848	+	0.0732703i	0.00653700	+	0.00474941i
$239$	−17.5979	+	12.7856i	−1.13831	+	0.827032i	−0.986883	−	0.161437i	$-0.948387\pi$
$239$	−17.5979	+	12.7856i	−1.13831	+	0.827032i	−0.151428	+	0.988468i	$0.548387\pi$
$240$		0			0
$241$	12.8328	+	9.32358i	0.826633	+	0.600584i	0.918605	−	0.395177i	$-0.129317\pi$
$241$	12.8328	+	9.32358i	0.826633	+	0.600584i	−0.0919714	+	0.995762i	$0.529317\pi$
$242$	−2.47985	−	7.63220i	−0.159411	−	0.490617i
$243$	−4.67563			−0.299942
$244$	−0.518118	−	1.59460i	−0.0331691	−	0.102084i
$245$		0			0
$246$	0.620220	−	1.90884i	0.0395438	−	0.121703i
$247$	−0.442107	+	1.36067i	−0.0281306	+	0.0865771i
$248$	6.50473	−	4.72597i	0.413051	−	0.300099i
$249$	−1.30280			−0.0825618
$250$		0			0
$251$	−8.49087			−0.535939			−0.267970	−	0.963427i	$-0.586353\pi$
$251$	−8.49087			−0.535939			−0.267970	+	0.963427i	$0.586353\pi$
$252$	3.05899	−	2.22249i	0.192698	−	0.140003i
$253$	−8.51005	+	26.1912i	−0.535022	+	1.64663i
$254$	0.407581	−	1.25441i	0.0255739	−	0.0787085i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−9.98572			−0.622892			−0.311446	−	0.950264i	$-0.600813\pi$
$257$	−9.98572			−0.622892			−0.311446	+	0.950264i	$0.600813\pi$
$258$	0.553898	+	1.70472i	0.0344842	+	0.106131i
$259$	−4.23279	−	3.07530i	−0.263013	−	0.191090i
$260$		0			0
$261$	−11.2384	+	8.16515i	−0.695637	+	0.505410i
$262$	−1.44043	−	1.04654i	−0.0889904	−	0.0646553i
$263$	6.25720	+	4.54612i	0.385836	+	0.280326i	0.763747	−	0.645516i	$-0.223358\pi$
$263$	6.25720	+	4.54612i	0.385836	+	0.280326i	−0.377911	+	0.925842i	$0.623358\pi$
$264$	0.619543	−	0.450124i	0.0381302	−	0.0277032i
$265$		0			0
$266$	−0.344057	−	0.249972i	−0.0210955	−	0.0153268i
$267$	−0.0926774	−	0.285232i	−0.00567176	−	0.0174559i
$268$	−1.16901			−0.0714084
$269$	−2.26777	−	6.97948i	−0.138268	−	0.425546i	0.857816	−	0.513957i	$-0.171821\pi$
$269$	−2.26777	−	6.97948i	−0.138268	−	0.425546i	−0.996084	+	0.0884112i	$0.971821\pi$
$270$		0			0
$271$	4.10960	−	12.6481i	0.249641	−	0.768315i	−0.745198	−	0.666844i	$-0.767645\pi$
$271$	4.10960	−	12.6481i	0.249641	−	0.768315i	0.994838	−	0.101472i	$-0.0323551\pi$
$272$	0.0302487	−	0.0930960i	0.00183410	−	0.00564478i
$273$	0.774910	−	0.563005i	0.0468997	−	0.0340746i
$274$	−9.56108			−0.577606
$275$		0			0
$276$	−1.10851			−0.0667244
$277$	−15.8511	+	11.5165i	−0.952399	+	0.691959i	−0.951373	−	0.308041i	$-0.900327\pi$
$277$	−15.8511	+	11.5165i	−0.952399	+	0.691959i	−0.00102623	+	0.999999i	$0.500327\pi$
$278$	1.42138	−	4.37457i	0.0852489	−	0.262369i
$279$	−7.37718	+	22.7046i	−0.441660	+	1.35929i
$280$		0			0
$281$	−3.55571	−	10.9433i	−0.212116	−	0.652825i	−0.999346	−	0.0361656i	$-0.988486\pi$
$281$	−3.55571	−	10.9433i	−0.212116	−	0.652825i	0.787230	−	0.616659i	$-0.211514\pi$
$282$	−2.05509			−0.122379
$283$	−6.07363	−	18.6927i	−0.361040	−	1.11117i	−0.952424	−	0.304776i	$-0.901418\pi$
$283$	−6.07363	−	18.6927i	−0.361040	−	1.11117i	0.591384	−	0.806390i	$-0.298582\pi$
$284$	1.90690	+	1.38545i	0.113154	+	0.0822111i
$285$		0			0
$286$	−15.1174	+	10.9834i	−0.893911	+	0.649464i
$287$	−11.7775	−	8.55687i	−0.695205	−	0.505096i
$288$	−2.40211	−	1.74524i	−0.141546	−	0.102839i
$289$	13.7455	−	9.98672i	0.808561	−	0.587454i
$290$		0			0
$291$	0.938514	+	0.681870i	0.0550166	+	0.0399719i
$292$	−0.497039	−	1.52973i	−0.0290870	−	0.0895206i
$293$	6.12203			0.357653			0.178827	−	0.983881i	$-0.442770\pi$
$293$	6.12203			0.357653			0.178827	+	0.983881i	$0.442770\pi$
$294$	−0.291796	−	0.898056i	−0.0170179	−	0.0523757i
$295$		0			0
$296$	−1.26960	+	3.90742i	−0.0737939	+	0.227114i
$297$	−1.41257	+	4.34745i	−0.0819657	+	0.252264i
$298$	1.64381	−	1.19430i	0.0952235	−	0.0691839i
$299$	27.0486			1.56426
$300$		0			0
$301$	13.0011			0.749371
$302$	15.3434	−	11.1477i	0.882915	−	0.641475i
$303$	0.381034	−	1.17270i	0.0218898	−	0.0673699i
$304$	−0.103198	+	0.317610i	−0.00591880	+	0.0182162i
$305$		0			0
$306$	0.0898138	+	0.276418i	0.00513431	+	0.0158018i
$307$	14.1935			0.810064			0.405032	−	0.914302i	$-0.367260\pi$
$307$	14.1935			0.810064			0.405032	+	0.914302i	$0.367260\pi$
$308$	−1.71644	−	5.28266i	−0.0978033	−	0.301008i
$309$	1.81053	+	1.31542i	0.102997	+	0.0748319i
$310$		0			0
$311$	−5.81375	+	4.22394i	−0.329668	+	0.239518i	−0.740290	−	0.672288i	$-0.765312\pi$
$311$	−5.81375	+	4.22394i	−0.329668	+	0.239518i	0.410622	+	0.911806i	$0.365312\pi$
$312$	−0.608509	−	0.442107i	−0.0344500	−	0.0250294i
$313$	−0.506152	−	0.367741i	−0.0286094	−	0.0207859i	0.573389	−	0.819283i	$-0.305629\pi$
$313$	−0.506152	−	0.367741i	−0.0286094	−	0.0207859i	−0.601998	+	0.798498i	$0.705629\pi$
$314$	11.5229	−	8.37184i	0.650272	−	0.472450i
$315$		0			0
$316$	−6.58064	−	4.78112i	−0.370190	−	0.268959i
$317$	−2.22803	−	6.85717i	−0.125139	−	0.385137i	0.868788	−	0.495185i	$-0.164900\pi$
$317$	−2.22803	−	6.85717i	−0.125139	−	0.385137i	−0.993926	+	0.110048i	$0.964900\pi$
$318$	0.155367			0.00871255
$319$	6.30600	+	19.4079i	0.353068	+	1.08663i
$320$		0			0
$321$	−0.662023	+	2.03750i	−0.0369505	+	0.113722i
$322$	−2.48459	+	7.64677i	−0.138461	+	0.426138i
$323$	0.0264466	−	0.0192146i	0.00147153	−	0.00106913i
$324$	8.72353			0.484640
$325$		0			0
$326$	19.7147			1.09189
$327$	−0.717430	+	0.521243i	−0.0396739	+	0.0288248i
$328$	−3.53260	+	10.8722i	−0.195055	+	0.600318i
$329$	−4.60623	+	14.1765i	−0.253949	+	0.781576i
$330$		0			0
$331$	−7.48266	−	23.0292i	−0.411284	−	1.26580i	−0.915533	−	0.402244i	$-0.868231\pi$
$331$	−7.48266	−	23.0292i	−0.411284	−	1.26580i	0.504249	−	0.863558i	$-0.331769\pi$
$332$	7.42040			0.407247
$333$	−3.76966	−	11.6018i	−0.206576	−	0.635776i
$334$	4.67760	+	3.39847i	0.255947	+	0.185956i
$335$		0			0
$336$	0.180881	−	0.131418i	0.00986788	−	0.00716944i
$337$	17.9615	+	13.0498i	0.978423	+	0.710866i	0.957356	−	0.288912i	$-0.0932936\pi$
$337$	17.9615	+	13.0498i	0.978423	+	0.710866i	0.0210674	+	0.999778i	$0.493294\pi$
$338$	4.33094	+	3.14661i	0.235572	+	0.171153i
$339$	1.99354	−	1.44839i	0.108274	−	0.0786657i
$340$		0			0
$341$	28.3721	+	20.6135i	1.53644	+	1.11629i
$342$	−0.306412	−	0.943040i	−0.0165689	−	0.0509937i
$343$	−15.7632			−0.851135
$344$	−3.15485	−	9.70962i	−0.170098	−	0.523508i
$345$		0			0
$346$	3.25325	−	10.0125i	0.174896	−	0.538275i
$347$	7.77436	−	23.9270i	0.417349	−	1.28447i	−0.492783	−	0.870152i	$-0.664021\pi$
$347$	7.77436	−	23.9270i	0.417349	−	1.28447i	0.910133	−	0.414317i	$-0.135979\pi$
$348$	−0.664536	+	0.482814i	−0.0356229	+	0.0258815i
$349$	−25.4708			−1.36342			−0.681710	−	0.731622i	$-0.738764\pi$
$349$	−25.4708			−1.36342			−0.681710	+	0.731622i	$0.738764\pi$
$350$		0			0
$351$	4.48976			0.239646
$352$	−3.52874	+	2.56378i	−0.188082	+	0.136650i
$353$	−8.93720	+	27.5059i	−0.475679	+	1.46399i	0.369361	+	0.929286i	$0.379577\pi$
$353$	−8.93720	+	27.5059i	−0.475679	+	1.46399i	−0.845040	+	0.534703i	$0.820423\pi$
$354$	0.412791	−	1.27044i	0.0219396	−	0.0675231i
$355$		0			0
$356$	0.527864	+	1.62460i	0.0279767	+	0.0861035i
$357$	−0.0218857			−0.00115832
$358$	−3.35558	−	10.3274i	−0.177348	−	0.545820i
$359$	6.82792	+	4.96077i	0.360364	+	0.261820i	0.753204	−	0.657787i	$-0.228507\pi$
$359$	6.82792	+	4.96077i	0.360364	+	0.261820i	−0.392840	+	0.919607i	$0.628507\pi$
$360$		0			0
$361$	15.2811	−	11.1024i	0.804268	−	0.584335i
$362$	−8.32136	−	6.04582i	−0.437361	−	0.317761i
$363$	1.13986	+	0.828159i	0.0598273	+	0.0434671i
$364$	−4.41367	+	3.20672i	−0.231339	+	0.168078i
$365$		0			0
$366$	0.238153	+	0.173028i	0.0124485	+	0.00904433i
$367$	0.926153	+	2.85041i	0.0483448	+	0.148790i	0.972315	−	0.233675i	$-0.0750752\pi$
$367$	0.926153	+	2.85041i	0.0483448	+	0.148790i	−0.923970	+	0.382465i	$0.875075\pi$
$368$	6.31375			0.329127
$369$	−10.4889	−	32.2815i	−0.546030	−	1.68051i
$370$		0			0
$371$	0.348236	−	1.07176i	0.0180795	−	0.0556431i
$372$	−0.436220	+	1.34255i	−0.0226170	+	0.0696079i
$373$	14.1877	−	10.3080i	0.734613	−	0.533728i	−0.156406	−	0.987693i	$-0.549991\pi$
$373$	14.1877	−	10.3080i	0.734613	−	0.533728i	0.891019	+	0.453965i	$0.149991\pi$
$374$	0.426960			0.0220776
$375$		0			0
$376$	11.7052			0.603649
$377$	16.2153	−	11.7811i	0.835130	−	0.606757i
$378$	−0.412413	+	1.26928i	−0.0212123	+	0.0652846i
$379$	9.82469	−	30.2373i	0.504661	−	1.55319i	−0.296680	−	0.954977i	$-0.595879\pi$
$379$	9.82469	−	30.2373i	0.504661	−	1.55319i	0.801340	−	0.598209i	$-0.204121\pi$
$380$		0			0
$381$	0.0715593	+	0.220237i	0.00366609	+	0.0112831i
$382$	9.64063			0.493258
$383$	−6.06804	−	18.6755i	−0.310062	−	0.954273i	−0.977740	−	0.209822i	$-0.932711\pi$
$383$	−6.06804	−	18.6755i	−0.310062	−	0.954273i	0.667677	−	0.744451i	$-0.267289\pi$
$384$	−0.142040	−	0.103198i	−0.00724842	−	0.00526629i
$385$		0			0
$386$	4.85410	−	3.52671i	0.247067	−	0.179505i
$387$	24.5239	+	17.8177i	1.24662	+	0.905722i
$388$	−5.34551	−	3.88374i	−0.271377	−	0.197167i
$389$	23.8930	−	17.3593i	1.21142	−	0.880150i	0.216063	−	0.976379i	$-0.430678\pi$
$389$	23.8930	−	17.3593i	1.21142	−	0.880150i	0.995359	+	0.0962298i	$0.0306784\pi$
$390$		0			0
$391$	−0.500000	−	0.363271i	−0.0252861	−	0.0183714i
$392$	1.66199	+	5.11507i	0.0839431	+	0.258350i
$393$	0.312599			0.0157685
$394$	6.41164	+	19.7330i	0.323014	+	0.994134i
$395$		0			0
$396$	4.00203	−	12.3170i	0.201110	−	0.618951i
$397$	6.88254	−	21.1823i	0.345425	−	1.06311i	−0.615931	−	0.787800i	$-0.711220\pi$
$397$	6.88254	−	21.1823i	0.345425	−	1.06311i	0.961356	−	0.275308i	$-0.0887800\pi$
$398$	−15.4222	+	11.2049i	−0.773045	+	0.561650i
$399$	0.0746662			0.00373798
$400$		0			0
$401$	7.37458			0.368269			0.184134	−	0.982901i	$-0.441052\pi$
$401$	7.37458			0.368269			0.184134	+	0.982901i	$0.441052\pi$
$402$	0.166045	−	0.120639i	0.00828157	−	0.00601692i
$403$	10.6442	−	32.7594i	0.530224	−	1.63186i
$404$	−2.17026	+	6.67937i	−0.107974	+	0.332311i
$405$		0			0
$406$	1.84110	+	5.66631i	0.0913720	+	0.281214i
$407$	−17.9203			−0.888278
$408$	0.00531079	+	0.0163449i	0.000262923	+	0.000809194i
$409$	14.9117	+	10.8340i	0.737335	+	0.535705i	0.891875	−	0.452281i	$-0.149390\pi$
$409$	14.9117	+	10.8340i	0.737335	+	0.535705i	−0.154541	+	0.987986i	$0.549390\pi$
$410$		0			0
$411$	1.35805	−	0.986682i	0.0669878	−	0.0486695i
$412$	−10.3122	−	7.49228i	−0.508048	−	0.369118i
$413$	−7.83860	−	5.69507i	−0.385712	−	0.280236i
$414$	−15.1663	+	11.0190i	−0.745385	+	0.541554i
$415$		0			0
$416$	3.46589	+	2.51812i	0.169929	+	0.123461i
$417$	0.249553	+	0.768046i	0.0122207	+	0.0376114i
$418$	−1.45663			−0.0712462
$419$	3.58315	+	11.0278i	0.175048	+	0.538744i	0.999636	−	0.0269911i	$-0.00859259\pi$
$419$	3.58315	+	11.0278i	0.175048	+	0.538744i	−0.824587	+	0.565735i	$0.808593\pi$
$420$		0			0
$421$	−0.902012	+	2.77611i	−0.0439614	+	0.135299i	−0.970628	−	0.240585i	$-0.922661\pi$
$421$	−0.902012	+	2.77611i	−0.0439614	+	0.135299i	0.926667	+	0.375884i	$0.122661\pi$
$422$	−5.25934	+	16.1866i	−0.256021	+	0.787951i
$423$	−28.1172	+	20.4283i	−1.36710	+	0.993259i
$424$	−0.884927			−0.0429759
$425$		0			0
$426$	−0.413831			−0.0200502
$427$	1.72738	−	1.25502i	0.0835940	−	0.0607346i
$428$	3.77070	−	11.6050i	0.182263	−	0.560949i
$429$	1.01380	−	3.12016i	0.0489469	−	0.150643i
$430$		0			0
$431$	2.34092	+	7.20460i	0.112758	+	0.347033i	0.991473	−	0.130314i	$-0.0415984\pi$
$431$	2.34092	+	7.20460i	0.112758	+	0.347033i	−0.878715	+	0.477347i	$0.841598\pi$
$432$	1.04801			0.0504225
$433$	8.89418	+	27.3735i	0.427427	+	1.31548i	0.900651	+	0.434543i	$0.143090\pi$
$433$	8.89418	+	27.3735i	0.427427	+	1.31548i	−0.473224	+	0.880942i	$0.656910\pi$
$434$	8.28350	+	6.01832i	0.397621	+	0.288888i
$435$		0			0
$436$	4.08628	−	2.96885i	0.195697	−	0.142182i
$437$	1.70582	+	1.23935i	0.0816004	+	0.0592862i
$438$	0.228464	+	0.165989i	0.0109164	+	0.00793124i
$439$	−14.3588	+	10.4323i	−0.685310	+	0.497907i	−0.875115	−	0.483915i	$-0.839214\pi$
$439$	−14.3588	+	10.4323i	−0.685310	+	0.497907i	0.189805	+	0.981822i	$0.439214\pi$
$440$		0			0
$441$	−12.9193	−	9.38642i	−0.615205	−	0.446972i
$442$	−0.129588	−	0.398831i	−0.00616387	−	0.0189704i
$443$	19.3439			0.919058			0.459529	−	0.888163i	$-0.348018\pi$
$443$	19.3439			0.919058			0.459529	+	0.888163i	$0.348018\pi$
$444$	−0.222904	−	0.686028i	−0.0105786	−	0.0325575i
$445$		0			0
$446$	−1.53827	+	4.73429i	−0.0728390	+	0.224175i
$447$	−0.110237	+	0.339276i	−0.00521405	+	0.0160472i
$448$	−1.03025	+	0.748520i	−0.0486747	+	0.0353642i
$449$	11.2932			0.532960			0.266480	−	0.963840i	$-0.414139\pi$
$449$	11.2932			0.532960			0.266480	+	0.963840i	$0.414139\pi$
$450$		0			0
$451$	−49.8625			−2.34793
$452$	−11.3546	+	8.24962i	−0.534076	+	0.388029i
$453$	−1.02896	+	3.16681i	−0.0483448	+	0.148790i
$454$	0.317289	−	0.976514i	0.0148911	−	0.0458301i
$455$		0			0
$456$	−0.0181185	−	0.0557630i	−0.000848476	−	0.00261134i
$457$	−2.60741			−0.121970			−0.0609848	−	0.998139i	$-0.519424\pi$
$457$	−2.60741			−0.121970			−0.0609848	+	0.998139i	$0.519424\pi$
$458$	1.26236	+	3.88514i	0.0589861	+	0.181540i
$459$	−0.0829943	−	0.0602989i	−0.00387384	−	0.00281451i
$460$		0			0
$461$	1.58366	−	1.15060i	0.0737585	−	0.0535887i	−0.550295	−	0.834970i	$-0.685485\pi$
$461$	1.58366	−	1.15060i	0.0737585	−	0.0535887i	0.624053	+	0.781382i	$0.285485\pi$
$462$	0.788961	+	0.573214i	0.0367058	+	0.0266683i
$463$	−1.17952	−	0.856972i	−0.0548170	−	0.0398269i	0.560039	−	0.828466i	$-0.310786\pi$
$463$	−1.17952	−	0.856972i	−0.0548170	−	0.0398269i	−0.614856	+	0.788639i	$0.710786\pi$
$464$	3.78501	−	2.74997i	0.175715	−	0.127664i
$465$		0			0
$466$	−3.57002	−	2.59377i	−0.165378	−	0.120154i
$467$	−7.90629	−	24.3331i	−0.365860	−	1.12600i	−0.949441	−	0.313945i	$-0.898349\pi$
$467$	−7.90629	−	24.3331i	−0.365860	−	1.12600i	0.583581	−	0.812055i	$-0.301651\pi$
$468$	−12.7202			−0.587991
$469$	−0.460027	−	1.41582i	−0.0212421	−	0.0653764i
$470$		0			0
$471$	−0.772745	+	2.37827i	−0.0356062	+	0.109585i
$472$	−2.35114	+	7.23607i	−0.108220	+	0.333067i
$473$	36.0260	−	26.1744i	1.65648	−	1.20350i
$474$	1.42811			0.0655954
$475$		0			0
$476$	0.124655			0.00571355
$477$	2.12569	−	1.54441i	0.0973289	−	0.0707136i
$478$	−6.72179	+	20.6875i	−0.307447	+	0.946226i
$479$	−2.12209	+	6.53112i	−0.0969608	+	0.298415i	−0.987760	−	0.155983i	$-0.950145\pi$
$479$	−2.12209	+	6.53112i	−0.0969608	+	0.298415i	0.890799	+	0.454398i	$0.150145\pi$
$480$		0			0
$481$	5.43906	+	16.7397i	0.248000	+	0.763265i
$482$	15.8622			0.722504
$483$	−0.436220	−	1.34255i	−0.0198487	−	0.0610880i
$484$	−6.49234	−	4.71696i	−0.295106	−	0.214407i
$485$		0			0
$486$	−3.78266	+	2.74826i	−0.171585	+	0.124664i
$487$	−34.2403	−	24.8770i	−1.55157	−	1.12728i	−0.942517	−	0.334159i	$-0.891548\pi$
$487$	−34.2403	−	24.8770i	−1.55157	−	1.12728i	−0.609058	−	0.793126i	$-0.708452\pi$
$488$	−1.35645	−	0.985520i	−0.0614037	−	0.0446124i
$489$	−2.80026	+	2.03451i	−0.126632	+	0.0920036i
$490$		0			0
$491$	−10.4767	−	7.61178i	−0.472808	−	0.343515i	0.325727	−	0.945464i	$-0.394391\pi$
$491$	−10.4767	−	7.61178i	−0.472808	−	0.343515i	−0.798535	+	0.601949i	$0.794391\pi$
$492$	−0.620220	−	1.90884i	−0.0279617	−	0.0860572i
$493$	−0.457967			−0.0206258
$494$	0.442107	+	1.36067i	0.0198913	+	0.0612193i
$495$		0			0
$496$	2.48459	−	7.64677i	0.111561	−	0.343350i
$497$	−0.927551	+	2.85471i	−0.0416064	+	0.128051i
$498$	−1.05399	+	0.765768i	−0.0472304	+	0.0343149i
$499$	−12.9767			−0.580915			−0.290458	−	0.956888i	$-0.593808\pi$
$499$	−12.9767			−0.580915			−0.290458	+	0.956888i	$0.593808\pi$
$500$		0			0
$501$	−1.01512			−0.0453522
$502$	−6.86926	+	4.99081i	−0.306590	+	0.222751i
$503$	6.56414	−	20.2024i	0.292681	−	0.900778i	−0.691310	−	0.722558i	$-0.742966\pi$
$503$	6.56414	−	20.2024i	0.292681	−	0.900778i	0.983991	−	0.178220i	$-0.0570339\pi$
$504$	1.16843	−	3.59606i	0.0520460	−	0.160181i
$505$		0			0
$506$	8.51005	+	26.1912i	0.378318	+	1.16434i
$507$	−0.939887			−0.0417419
$508$	−0.407581	−	1.25441i	−0.0180835	−	0.0556553i
$509$	−11.5303	−	8.37728i	−0.511073	−	0.371317i	0.302157	−	0.953258i	$-0.402293\pi$
$509$	−11.5303	−	8.37728i	−0.511073	−	0.371317i	−0.813231	+	0.581942i	$0.802293\pi$
$510$		0			0
$511$	1.65711	−	1.20396i	0.0733060	−	0.0532600i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	0.283147	+	0.205718i	0.0125012	+	0.00908267i
$514$	−8.07862	+	5.86946i	−0.356332	+	0.258891i
$515$		0			0
$516$	1.45012	+	1.05358i	0.0638382	+	0.0463811i
$517$	15.7769	+	48.5564i	0.693869	+	2.13551i
$518$	−5.23201			−0.229881
$519$	0.571175	+	1.75790i	0.0250718	+	0.0771631i
$520$		0			0
$521$	−9.07543	+	27.9313i	−0.397602	+	1.22369i	0.529315	+	0.848426i	$0.322449\pi$
$521$	−9.07543	+	27.9313i	−0.397602	+	1.22369i	−0.926917	+	0.375268i	$0.877551\pi$
$522$	−4.29267	+	13.2115i	−0.187885	+	0.578251i
$523$	−12.3293	+	8.95773i	−0.539121	+	0.391694i	−0.823758	−	0.566941i	$-0.808127\pi$
$523$	−12.3293	+	8.95773i	−0.539121	+	0.391694i	0.284638	+	0.958635i	$0.408127\pi$
$524$	−1.78048			−0.0777804
$525$		0			0
$526$	7.73433			0.337233
$527$	−0.636729	+	0.462611i	−0.0277363	+	0.0201516i
$528$	0.236644	−	0.728316i	0.0102986	−	0.0316959i
$529$	5.21110	−	16.0381i	0.226569	−	0.697309i
$530$		0			0
$531$	−6.98095	−	21.4852i	−0.302947	−	0.932376i
$532$	−0.425277			−0.0184381
$533$	15.1339	+	46.5775i	0.655523	+	2.01749i
$534$	−0.242632	−	0.176283i	−0.0104997	−	0.00762850i
$535$		0			0
$536$	−0.945746	+	0.687124i	−0.0408500	+	0.0296793i
$537$	1.54239	+	1.12061i	0.0665590	+	0.0483579i
$538$	−5.93710	−	4.31355i	−0.255966	−	0.185970i
$539$	−18.9786	+	13.7888i	−0.817468	+	0.593925i
$540$		0			0
$541$	−24.5392	−	17.8288i	−1.05502	−	0.766520i	−0.0818632	−	0.996644i	$-0.526087\pi$
$541$	−24.5392	−	17.8288i	−1.05502	−	0.766520i	−0.973161	+	0.230123i	$0.926087\pi$
$542$	−4.10960	−	12.6481i	−0.176523	−	0.543281i
$543$	1.80588			0.0774976
$544$	−0.0302487	−	0.0930960i	−0.00129690	−	0.00399146i
$545$		0			0
$546$	0.295989	−	0.910961i	0.0126672	−	0.0389855i
$547$	9.59449	−	29.5288i	0.410231	−	1.26256i	−0.506217	−	0.862406i	$-0.668956\pi$
$547$	9.59449	−	29.5288i	0.410231	−	1.26256i	0.916448	−	0.400155i	$-0.131044\pi$
$548$	−7.73508	+	5.61986i	−0.330426	+	0.240069i
$549$	4.97832			0.212469
$550$		0			0
$551$	1.56242			0.0665613
$552$	−0.896802	+	0.651565i	−0.0381704	+	0.0277324i
$553$	3.20094	−	9.85148i	0.136118	−	0.418928i
$554$	−6.05458	+	18.6341i	−0.257234	+	0.791686i
$555$		0			0
$556$	−1.42138	−	4.37457i	−0.0602801	−	0.185523i
$557$	−28.0537			−1.18867			−0.594337	−	0.804216i	$-0.702585\pi$
$557$	−28.0537			−1.18867			−0.594337	+	0.804216i	$0.702585\pi$
$558$	7.37718	+	22.7046i	0.312301	+	0.961163i
$559$	−35.3843	−	25.7082i	−1.49660	−	1.08734i
$560$		0			0
$561$	−0.0606452	+	0.0440613i	−0.00256044	+	0.00186027i
$562$	−9.30896	−	6.76336i	−0.392675	−	0.285295i
$563$	18.7384	+	13.6142i	0.789729	+	0.573772i	0.907883	−	0.419223i	$-0.137698\pi$
$563$	18.7384	+	13.6142i	0.789729	+	0.573772i	−0.118154	+	0.992995i	$0.537698\pi$
$564$	−1.66260	+	1.20795i	−0.0700081	+	0.0508638i
$565$		0			0
$566$	−15.9010	−	11.5527i	−0.668367	−	0.485597i
$567$	3.43288	+	10.5653i	0.144167	+	0.443702i
$568$	2.35706			0.0989002
$569$	−4.16602	−	12.8217i	−0.174649	−	0.537514i	0.824968	−	0.565179i	$-0.191193\pi$
$569$	−4.16602	−	12.8217i	−0.174649	−	0.537514i	−0.999617	+	0.0276651i	$0.991193\pi$
$570$		0			0
$571$	−12.0389	+	37.0519i	−0.503813	+	1.55058i	0.298945	+	0.954270i	$0.403365\pi$
$571$	−12.0389	+	37.0519i	−0.503813	+	1.55058i	−0.802758	+	0.596305i	$0.796635\pi$
$572$	−5.77433	+	17.7716i	−0.241437	+	0.743067i
$573$	−1.36935	+	0.994892i	−0.0572054	+	0.0415622i
$574$	−14.5578			−0.607632
$575$		0			0
$576$	−2.96917			−0.123716
$577$	−35.9417	+	26.1132i	−1.49627	+	1.08711i	−0.524437	+	0.851449i	$0.675724\pi$
$577$	−35.9417	+	26.1132i	−1.49627	+	1.08711i	−0.971836	+	0.235657i	$0.924276\pi$
$578$	5.25033	−	16.1588i	0.218385	−	0.672119i
$579$	−0.325526	+	1.00186i	−0.0135284	+	0.0416361i
$580$		0			0
$581$	2.92007	+	8.98706i	0.121145	+	0.372846i
$582$	1.16007			0.0480863
$583$	−1.19276	−	3.67093i	−0.0493989	−	0.152034i
$584$	−1.30127	−	0.945424i	−0.0538467	−	0.0391219i
$585$		0			0
$586$	4.95283	−	3.59844i	0.204600	−	0.148650i
$587$	31.7512	+	23.0686i	1.31051	+	0.952144i	0.999999	+	0.00157480i	$0.000501276\pi$
$587$	31.7512	+	23.0686i	1.31051	+	0.952144i	0.310514	+	0.950569i	$0.399499\pi$
$588$	−0.763932	−	0.555029i	−0.0315040	−	0.0228890i
$589$	2.17229	−	1.57826i	0.0895076	−	0.0650311i
$590$		0			0
$591$	−2.94711	−	2.14120i	−0.121228	−	0.0880771i
$592$	1.26960	+	3.90742i	0.0521802	+	0.160594i
$593$	23.5637			0.967644			0.483822	−	0.875167i	$-0.339248\pi$
$593$	23.5637			0.967644			0.483822	+	0.875167i	$0.339248\pi$
$594$	1.41257	+	4.34745i	0.0579585	+	0.178378i
$595$		0			0
$596$	0.627881	−	1.93242i	0.0257190	−	0.0791549i
$597$	1.03424	−	3.18307i	0.0423288	−	0.130275i
$598$	21.8828	−	15.8988i	0.894854	−	0.650149i
$599$	39.2513			1.60376			0.801882	−	0.597483i	$-0.203832\pi$
$599$	39.2513			1.60376			0.801882	+	0.597483i	$0.203832\pi$
$600$		0			0
$601$	−13.1067			−0.534635			−0.267317	−	0.963609i	$-0.586137\pi$
$601$	−13.1067			−0.534635			−0.267317	+	0.963609i	$0.586137\pi$
$602$	10.5181	−	7.64186i	0.428687	−	0.311459i
$603$	1.07259	−	3.30110i	0.0436794	−	0.134431i
$604$	5.86067	−	18.0373i	0.238467	−	0.733926i
$605$		0			0
$606$	−0.381034	−	1.17270i	−0.0154784	−	0.0476377i
$607$	6.14712			0.249504			0.124752	−	0.992188i	$-0.460186\pi$
$607$	6.14712			0.249504			0.124752	+	0.992188i	$0.460186\pi$
$608$	0.103198	+	0.317610i	0.00418522	+	0.0128808i
$609$	−0.846259	−	0.614843i	−0.0342921	−	0.0249147i
$610$		0			0
$611$	40.5689	−	29.4750i	1.64124	−	1.19243i
$612$	0.235136	+	0.170836i	0.00950479	+	0.00690564i
$613$	−17.9202	−	13.0198i	−0.723790	−	0.525865i	0.163803	−	0.986493i	$-0.447624\pi$
$613$	−17.9202	−	13.0198i	−0.723790	−	0.525865i	−0.887593	+	0.460629i	$0.847624\pi$
$614$	11.4828	−	8.34271i	0.463406	−	0.336684i
$615$		0			0
$616$	−4.49370	−	3.26486i	−0.181056	−	0.131545i
$617$	−3.74675	−	11.5313i	−0.150838	−	0.464233i	0.846877	−	0.531789i	$-0.178480\pi$
$617$	−3.74675	−	11.5313i	−0.150838	−	0.464233i	−0.997715	+	0.0675559i	$0.978480\pi$
$618$	2.23793			0.0900229
$619$	4.06963	+	12.5250i	0.163572	+	0.503424i	0.998928	−	0.0462856i	$-0.0147384\pi$
$619$	4.06963	+	12.5250i	0.163572	+	0.503424i	−0.835356	+	0.549709i	$0.814738\pi$
$620$		0			0
$621$	2.04473	−	6.29303i	0.0820521	−	0.252531i
$622$	−2.22066	+	6.83447i	−0.0890402	+	0.274037i
$623$	−1.75987	+	1.27862i	−0.0705079	+	0.0512270i
$624$	−0.752158			−0.0301104
$625$		0			0
$626$	−0.625638			−0.0250055
$627$	0.206899	−	0.150321i	0.00826276	−	0.00600325i
$628$	4.40134	−	13.5459i	0.175633	−	0.540541i
$629$	0.124277	−	0.382486i	0.00495526	−	0.0152507i
$630$		0			0
$631$	10.0018	+	30.7824i	0.398165	+	1.22543i	0.926469	+	0.376371i	$0.122828\pi$
$631$	10.0018	+	30.7824i	0.398165	+	1.22543i	−0.528304	+	0.849055i	$0.677172\pi$
$632$	−8.13412			−0.323558
$633$	−0.923385	−	2.84189i	−0.0367013	−	0.112955i
$634$	−5.83306	−	4.23796i	−0.231660	−	0.168311i
$635$		0			0
$636$	0.125695	−	0.0913225i	0.00498412	−	0.00362117i
$637$	18.6406	+	13.5432i	0.738569	+	0.536602i
$638$	16.5093	+	11.9947i	0.653610	+	0.474876i
$639$	−5.66193	+	4.11363i	−0.223983	+	0.162733i
$640$		0			0
$641$	11.5106	+	8.36292i	0.454640	+	0.330315i	0.791425	−	0.611266i	$-0.209340\pi$
$641$	11.5106	+	8.36292i	0.454640	+	0.330315i	−0.336785	+	0.941582i	$0.609340\pi$
$642$	0.662023	+	2.03750i	0.0261280	+	0.0804136i
$643$	−18.7825			−0.740708			−0.370354	−	0.928891i	$-0.620764\pi$
$643$	−18.7825			−0.740708			−0.370354	+	0.928891i	$0.620764\pi$
$644$	2.48459	+	7.64677i	0.0979065	+	0.301325i
$645$		0			0
$646$	0.0101017	−	0.0310899i	0.000397447	−	0.00122322i
$647$	−4.64749	+	14.3035i	−0.182712	+	0.562328i	−0.999901	−	0.0140402i	$-0.995531\pi$
$647$	−4.64749	+	14.3035i	−0.182712	+	0.562328i	0.817190	+	0.576369i	$0.195531\pi$
$648$	7.05748	−	5.12756i	0.277244	−	0.201430i
$649$	−33.1863			−1.30267
$650$		0			0
$651$	−1.79766			−0.0704559
$652$	15.9495	−	11.5880i	0.624630	−	0.453820i
$653$	7.33698	−	22.5809i	0.287118	−	0.883659i	−0.698637	−	0.715476i	$-0.746210\pi$
$653$	7.33698	−	22.5809i	0.287118	−	0.883659i	0.985756	−	0.168183i	$-0.0537901\pi$
$654$	−0.274034	+	0.843389i	−0.0107156	+	0.0329791i
$655$		0			0
$656$	3.53260	+	10.8722i	0.137925	+	0.424489i
$657$	4.77578			0.186321
$658$	4.60623	+	14.1765i	0.179569	+	0.552658i
$659$	5.30922	+	3.85737i	0.206818	+	0.150262i	0.686373	−	0.727250i	$-0.259202\pi$
$659$	5.30922	+	3.85737i	0.206818	+	0.150262i	−0.479555	+	0.877512i	$0.659202\pi$
$660$		0			0
$661$	25.9148	−	18.8282i	1.00797	−	0.732331i	0.0441853	−	0.999023i	$-0.485931\pi$
$661$	25.9148	−	18.8282i	1.00797	−	0.732331i	0.963782	+	0.266692i	$0.0859308\pi$
$662$	−19.5898	−	14.2329i	−0.761381	−	0.553176i
$663$	0.0595651	+	0.0432765i	0.00231332	+	0.00168072i
$664$	6.00323	−	4.36160i	0.232970	−	0.169263i
$665$		0			0
$666$	−9.86910	−	7.17032i	−0.382420	−	0.277844i
$667$	−9.12808	−	28.0933i	−0.353441	−	1.08778i
$668$	5.78183			0.223706
$669$	−0.270074	−	0.831202i	−0.0104417	−	0.0321361i
$670$		0			0
$671$	2.25991	−	6.95529i	0.0872429	−	0.268506i
$672$	0.0690905	−	0.212639i	0.00266522	−	0.00820272i
$673$	−40.2530	+	29.2455i	−1.55164	+	1.12733i	−0.609171	+	0.793039i	$0.708498\pi$
$673$	−40.2530	+	29.2455i	−1.55164	+	1.12733i	−0.942469	+	0.334294i	$0.891502\pi$
$674$	22.2016			0.855173
$675$		0			0
$676$	5.35333			0.205897
$677$	23.2044	−	16.8590i	0.891818	−	0.647943i	−0.0445337	−	0.999008i	$-0.514180\pi$
$677$	23.2044	−	16.8590i	0.891818	−	0.647943i	0.936351	+	0.351064i	$0.114180\pi$
$678$	0.761463	−	2.34354i	0.0292438	−	0.0900032i
$679$	2.60015	−	8.00244i	0.0997846	−	0.307105i
$680$		0			0
$681$	0.0557065	+	0.171447i	0.00213468	+	0.00656987i
$682$	35.0699			1.34289
$683$	10.8399	+	33.3619i	0.414779	+	1.27656i	0.912449	+	0.409192i	$0.134189\pi$
$683$	10.8399	+	33.3619i	0.414779	+	1.27656i	−0.497670	+	0.867367i	$0.665811\pi$
$684$	−0.802198	−	0.582831i	−0.0306728	−	0.0222851i
$685$		0			0
$686$	−12.7527	+	9.26540i	−0.486902	+	0.353755i
$687$	−0.580242	−	0.421570i	−0.0221376	−	0.0160839i
$688$	−8.25950	−	6.00088i	−0.314890	−	0.228781i
$689$	−3.06706	+	2.22835i	−0.116846	+	0.0848934i
$690$		0			0
$691$	1.37666	+	1.00020i	0.0523704	+	0.0380493i	0.613663	−	0.789568i	$-0.289696\pi$
$691$	1.37666	+	1.00020i	0.0523704	+	0.0380493i	−0.561292	+	0.827618i	$0.689696\pi$
$692$	−3.25325	−	10.0125i	−0.123670	−	0.380618i
$693$	16.4923			0.626492
$694$	−7.77436	−	23.9270i	−0.295110	−	0.908257i
$695$		0			0
$696$	−0.253830	+	0.781209i	−0.00962141	+	0.0296117i
$697$	0.345795	−	1.06425i	0.0130979	−	0.0403113i
$698$	−20.6063	+	14.9714i	−0.779960	+	0.566674i
$699$	0.774756			0.0293040
$700$		0			0
$701$	−5.26104			−0.198707			−0.0993534	−	0.995052i	$-0.531677\pi$
$701$	−5.26104			−0.198707			−0.0993534	+	0.995052i	$0.531677\pi$
$702$	3.63229	−	2.63902i	0.137092	−	0.0996032i
$703$	−0.423989	+	1.30490i	−0.0159910	+	0.0492154i
$704$	−1.34786	+	4.14828i	−0.0507993	+	0.156344i
$705$		0			0
$706$	8.93720	+	27.5059i	0.336356	+	1.03520i
$707$	−8.94363			−0.336360
$708$	−0.412791	−	1.27044i	−0.0155136	−	0.0477461i
$709$	35.0458	+	25.4622i	1.31617	+	0.956254i	0.999971	+	0.00756154i	$0.00240694\pi$
$709$	35.0458	+	25.4622i	1.31617	+	0.956254i	0.316200	+	0.948693i	$0.397593\pi$
$710$		0			0
$711$	19.5391	−	14.1960i	0.732773	−	0.532391i
$712$	1.38197	+	1.00406i	0.0517914	+	0.0376286i
$713$	−41.0693	−	29.8386i	−1.53806	−	1.11746i
$714$	−0.0177059	+	0.0128641i	−0.000662627	+	0.000481427i
$715$		0			0
$716$	−8.78501	−	6.38268i	−0.328311	−	0.238532i
$717$	−1.18015	−	3.63212i	−0.0440734	−	0.135644i
$718$	8.43977			0.314970
$719$	7.61145	+	23.4256i	0.283859	+	0.873629i	0.986738	+	0.162319i	$0.0518974\pi$
$719$	7.61145	+	23.4256i	0.283859	+	0.873629i	−0.702879	+	0.711309i	$0.748103\pi$
$720$		0			0
$721$	5.01606	−	15.4378i	0.186808	−	0.574935i
$722$	5.83686	−	17.9640i	0.217225	−	0.668551i
$723$	−2.25306	+	1.63695i	−0.0837923	+	0.0608786i
$724$	−10.2858			−0.382267
$725$		0			0
$726$	1.40895			0.0522910
$727$	11.3741	−	8.26374i	0.421841	−	0.306485i	−0.356537	−	0.934281i	$-0.616043\pi$
$727$	11.3741	−	8.26374i	0.421841	−	0.306485i	0.778378	+	0.627796i	$0.216043\pi$
$728$	−1.68587	+	5.18858i	−0.0624825	+	0.192301i
$729$	−7.83348	+	24.1090i	−0.290129	+	0.892925i
$730$		0			0
$731$	0.308818	+	0.950445i	0.0114221	+	0.0351535i
$732$	0.294373			0.0108803
$733$	−8.72468	−	26.8518i	−0.322253	−	0.991794i	−0.972665	−	0.232212i	$-0.925404\pi$
$733$	−8.72468	−	26.8518i	−0.322253	−	0.991794i	0.650412	−	0.759582i	$-0.274596\pi$
$734$	2.42470	+	1.76165i	0.0894974	+	0.0650236i
$735$		0			0
$736$	5.10793	−	3.71113i	0.188281	−	0.136794i
$737$	−4.12512	−	2.99707i	−0.151951	−	0.110399i
$738$	−27.4603	−	19.9511i	−1.01083	−	0.734409i
$739$	28.0840	−	20.4042i	1.03309	−	0.750582i	0.0641632	−	0.997939i	$-0.479562\pi$
$739$	28.0840	−	20.4042i	1.03309	−	0.750582i	0.968924	+	0.247357i	$0.0795622\pi$
$740$		0			0
$741$	−0.203214	−	0.147644i	−0.00746527	−	0.00542384i
$742$	−0.348236	−	1.07176i	−0.0127842	−	0.0393456i
$743$	−35.3024			−1.29512			−0.647559	−	0.762015i	$-0.724210\pi$
$743$	−35.3024			−1.29512			−0.647559	+	0.762015i	$0.724210\pi$
$744$	0.436220	+	1.34255i	0.0159926	+	0.0492202i
$745$		0			0
$746$	5.41923	−	16.6787i	0.198412	−	0.610650i
$747$	−6.80840	+	20.9541i	−0.249106	+	0.766671i
$748$	0.345418	−	0.250961i	0.0126297	−	0.00917603i
$749$	15.5390			0.567783
$750$		0			0
$751$	14.5513			0.530983			0.265491	−	0.964113i	$-0.414466\pi$
$751$	14.5513			0.530983			0.265491	+	0.964113i	$0.414466\pi$
$752$	9.46969	−	6.88014i	0.345324	−	0.250893i
$753$	0.460666	−	1.41778i	0.0167876	−	0.0516669i
$754$	6.19369	−	19.0622i	0.225561	−	0.694205i
$755$		0			0
$756$	0.412413	+	1.26928i	0.0149993	+	0.0461632i
$757$	−23.9496			−0.870462			−0.435231	−	0.900319i	$-0.643333\pi$
$757$	−23.9496			−0.870462			−0.435231	+	0.900319i	$0.643333\pi$
$758$	−9.82469	−	30.2373i	−0.356849	−	1.09827i
$759$	−3.91164	−	2.84197i	−0.141983	−	0.103157i
$760$		0			0
$761$	17.4988	−	12.7137i	0.634333	−	0.460870i	−0.223566	−	0.974689i	$-0.571770\pi$
$761$	17.4988	−	12.7137i	0.634333	−	0.460870i	0.857899	+	0.513819i	$0.171770\pi$
$762$	0.187345	+	0.136114i	0.00678678	+	0.00493088i
$763$	5.20370	+	3.78071i	0.188387	+	0.136871i
$764$	7.79944	−	5.66662i	0.282174	−	0.205011i
$765$		0			0
$766$	−15.8863	−	11.5421i	−0.573996	−	0.417033i
$767$	10.0725	+	30.9999i	0.363696	+	1.11934i
$768$	−0.175571			−0.00633535
$769$	13.7177	+	42.2187i	0.494672	+	1.52244i	0.817467	+	0.575975i	$0.195377\pi$
$769$	13.7177	+	42.2187i	0.494672	+	1.52244i	−0.322795	+	0.946469i	$0.604623\pi$
$770$		0			0
$771$	0.541768	−	1.66739i	0.0195113	−	0.0600496i
$772$	1.85410	−	5.70634i	0.0667306	−	0.205376i
$773$	−9.37675	+	6.81261i	−0.337258	+	0.245032i	−0.743504	−	0.668731i	$-0.766838\pi$
$773$	−9.37675	+	6.81261i	−0.337258	+	0.245032i	0.406246	+	0.913764i	$0.366838\pi$
$774$	30.3132			1.08959
$775$		0			0
$776$	−6.60741			−0.237192
$777$	0.743152	−	0.539932i	0.0266604	−	0.0193699i
$778$	9.12631	−	28.0879i	0.327194	−	1.00700i
$779$	−1.17973	+	3.63083i	−0.0422682	+	0.130088i
$780$		0			0
$781$	3.17699	+	9.77776i	0.113682	+	0.349876i
$782$	−0.618034			−0.0221009
$783$	−1.51516	−	4.66318i	−0.0541473	−	0.166648i
$784$	4.35114	+	3.16129i	0.155398	+	0.112903i
$785$		0			0
$786$	0.252898	−	0.183741i	0.00902057	−	0.00655383i
$787$	−6.27159	−	4.55658i	−0.223558	−	0.162424i	0.470369	−	0.882470i	$-0.344121\pi$
$787$	−6.27159	−	4.55658i	−0.223558	−	0.162424i	−0.693927	+	0.720045i	$0.744121\pi$
$788$	16.7859	+	12.1957i	0.597972	+	0.434452i
$789$	−1.09858	+	0.798165i	−0.0391105	+	0.0284154i
$790$		0			0
$791$	−14.4596	−	10.5055i	−0.514125	−	0.373534i
$792$	−4.00203	−	12.3170i	−0.142206	−	0.437665i
$793$	−7.18297			−0.255075
$794$	−6.88254	−	21.1823i	−0.244252	−	0.751731i
$795$		0			0
$796$	−5.89076	+	18.1299i	−0.208792	+	0.642597i
$797$	12.4846	−	38.4237i	0.442228	−	1.36104i	−0.443267	−	0.896390i	$-0.646181\pi$
$797$	12.4846	−	38.4237i	0.442228	−	1.36104i	0.885495	−	0.464649i	$-0.153819\pi$
$798$	0.0604062	−	0.0438877i	0.00213836	−	0.00155361i
$799$	−1.14579			−0.0405350
$800$		0			0
$801$	−5.07196			−0.179209
$802$	5.96616	−	4.33467i	0.210672	−	0.153062i
$803$	2.16797	−	6.67231i	0.0765059	−	0.235461i
$804$	0.0634236	−	0.195198i	0.00223678	−	0.00688409i
$805$		0			0
$806$	−10.6442	−	32.7594i	−0.374925	−	1.15390i
$807$	1.28845			0.0453556
$808$	2.17026	+	6.67937i	0.0763495	+	0.234980i
$809$	−7.99707	−	5.81021i	−0.281162	−	0.204276i	0.438262	−	0.898847i	$-0.355594\pi$
$809$	−7.99707	−	5.81021i	−0.281162	−	0.204276i	−0.719424	+	0.694571i	$0.755594\pi$
$810$		0			0
$811$	−4.56597	+	3.31737i	−0.160333	+	0.116489i	−0.665059	−	0.746791i	$-0.731594\pi$
$811$	−4.56597	+	3.31737i	−0.160333	+	0.116489i	0.504726	+	0.863280i	$0.331594\pi$
$812$	4.82005	+	3.50197i	0.169151	+	0.122895i
$813$	1.88898	+	1.37242i	0.0662493	+	0.0481330i
$814$	−14.4979	+	10.5333i	−0.508150	+	0.369192i
$815$		0			0
$816$	0.0139038	+	0.0101017i	0.000486731	+	0.000353631i
$817$	−1.05358	−	3.24258i	−0.0368600	−	0.113443i
$818$	18.4318			0.644454
$819$	−5.00565	−	15.4058i	−0.174911	−	0.538322i
$820$		0			0
$821$	−2.57398	+	7.92189i	−0.0898325	+	0.276476i	−0.985873	−	0.167497i	$-0.946431\pi$
$821$	−2.57398	+	7.92189i	−0.0898325	+	0.276476i	0.896040	+	0.443973i	$0.146431\pi$
$822$	0.518730	−	1.59649i	0.0180928	−	0.0556838i
$823$	7.28710	−	5.29439i	0.254012	−	0.184551i	−0.453491	−	0.891261i	$-0.649822\pi$
$823$	7.28710	−	5.29439i	0.254012	−	0.184551i	0.707503	+	0.706710i	$0.249822\pi$
$824$	−12.7466			−0.444050
$825$		0			0
$826$	−9.68904			−0.337125
$827$	−38.1615	+	27.7260i	−1.32701	+	0.964126i	−0.327189	+	0.944959i	$0.606101\pi$
$827$	−38.1615	+	27.7260i	−1.32701	+	0.964126i	−0.999816	+	0.0191672i	$0.993899\pi$
$828$	−5.79303	+	17.8291i	−0.201322	+	0.619604i
$829$	−8.20305	+	25.2464i	−0.284904	+	0.876844i	0.701524	+	0.712646i	$0.252503\pi$
$829$	−8.20305	+	25.2464i	−0.284904	+	0.876844i	−0.986427	+	0.164197i	$0.947497\pi$
$830$		0			0
$831$	−1.06300	−	3.27159i	−0.0368752	−	0.113490i
$832$	4.28408			0.148524
$833$	−0.162687	−	0.500699i	−0.00563677	−	0.0173482i
$834$	0.653339	+	0.474678i	0.0226233	+	0.0164368i
$835$		0			0
$836$	−1.17844	+	0.856187i	−0.0407572	+	0.0296118i
$837$	−6.81703	−	4.95286i	−0.235631	−	0.171196i
$838$	9.38081	+	6.81556i	0.324055	+	0.235440i
$839$	−0.237312	+	0.172417i	−0.00819291	+	0.00595250i	−0.591874	−	0.806030i	$-0.701612\pi$
$839$	−0.237312	+	0.172417i	−0.00819291	+	0.00595250i	0.583681	+	0.811983i	$0.301612\pi$
$840$		0			0
$841$	5.75320	+	4.17994i	0.198386	+	0.144136i
$842$	0.902012	+	2.77611i	0.0310854	+	0.0956710i
$843$	2.02020			0.0695795
$844$	5.25934	+	16.1866i	0.181034	+	0.557165i
$845$		0			0
$846$	−10.7398	+	33.0537i	−0.369242	+	1.13641i
$847$	3.15799	−	9.71929i	0.108510	−	0.333959i
$848$	−0.715921	+	0.520147i	−0.0245848	+	0.0178619i
$849$	3.45078			0.118430
$850$		0			0
$851$	25.9401			0.889215
$852$	−0.334796	+	0.243244i	−0.0114699	+	0.00833339i
$853$	−15.5859	+	47.9683i	−0.533650	+	1.64240i	0.212899	+	0.977074i	$0.431709\pi$
$853$	−15.5859	+	47.9683i	−0.533650	+	1.64240i	−0.746549	+	0.665330i	$0.768291\pi$
$854$	0.659802	−	2.03066i	0.0225780	−	0.0694878i
$855$		0			0
$856$	−3.77070	−	11.6050i	−0.128880	−	0.396651i
$857$	42.6554			1.45708			0.728540	−	0.685003i	$-0.240199\pi$
$857$	42.6554			1.45708			0.728540	+	0.685003i	$0.240199\pi$
$858$	−1.01380	−	3.12016i	−0.0346107	−	0.106521i
$859$	24.0952	+	17.5062i	0.822118	+	0.597304i	0.917318	−	0.398155i	$-0.130349\pi$
$859$	24.0952	+	17.5062i	0.822118	+	0.597304i	−0.0952006	+	0.995458i	$0.530349\pi$
$860$		0			0
$861$	2.06779	−	1.50233i	0.0704700	−	0.0511994i
$862$	6.12860	+	4.45269i	0.208741	+	0.151659i
$863$	−22.1793	−	16.1142i	−0.754992	−	0.548534i	0.142378	−	0.989812i	$-0.454525\pi$
$863$	−22.1793	−	16.1142i	−0.754992	−	0.548534i	−0.897370	+	0.441278i	$0.854525\pi$
$864$	0.847859	−	0.616005i	0.0288447	−	0.0209569i
$865$		0			0
$866$	23.2853	+	16.9177i	0.791265	+	0.574888i
$867$	0.921803	+	2.83702i	0.0313061	+	0.0963502i
$868$	10.2390			0.347533
$869$	−10.9637	−	33.7426i	−0.371916	−	1.14464i
$870$		0			0
$871$	−1.54759	+	4.76300i	−0.0524382	+	0.161388i
$872$	1.56082	−	4.80371i	0.0528560	−	0.162674i
$873$	15.8718	−	11.5315i	0.537177	−	0.390282i
$874$	2.10851			0.0713214
$875$		0			0
$876$	0.282397			0.00954130
$877$	2.69624	−	1.95893i	0.0910455	−	0.0661484i	−0.541331	−	0.840809i	$-0.682079\pi$
$877$	2.69624	−	1.95893i	0.0910455	−	0.0661484i	0.632377	+	0.774661i	$0.282079\pi$
$878$	−5.48459	+	16.8798i	−0.185096	+	0.569666i
$879$	−0.332147	+	1.02224i	−0.0112030	+	0.0344794i
$880$		0			0
$881$	−2.40321	−	7.39632i	−0.0809662	−	0.249188i	0.902377	−	0.430948i	$-0.141821\pi$
$881$	−2.40321	−	7.39632i	−0.0809662	−	0.249188i	−0.983343	+	0.181760i	$0.941821\pi$
$882$	−15.9691			−0.537709
$883$	−1.74090	−	5.35794i	−0.0585859	−	0.180309i	0.917481	−	0.397780i	$-0.130219\pi$
$883$	−1.74090	−	5.35794i	−0.0585859	−	0.180309i	−0.976067	+	0.217471i	$0.930219\pi$
$884$	−0.339266	−	0.246491i	−0.0114107	−	0.00829039i
$885$		0			0
$886$	15.6496	−	11.3701i	0.525758	−	0.381985i
$887$	17.8316	+	12.9554i	0.598728	+	0.435001i	0.845427	−	0.534091i	$-0.179346\pi$
$887$	17.8316	+	12.9554i	0.598728	+	0.435001i	−0.246699	+	0.969092i	$0.579346\pi$
$888$	−0.583571	−	0.423989i	−0.0195833	−	0.0142281i
$889$	1.35886	−	0.987268i	0.0455746	−	0.0331119i
$890$		0			0
$891$	30.7831	+	22.3652i	1.03127	+	0.749262i
$892$	1.53827	+	4.73429i	0.0515049	+	0.158516i
$893$	3.90900			0.130810
$894$	0.110237	+	0.339276i	0.00368689	+	0.0113471i
$895$		0			0
$896$	−0.393520	+	1.21113i	−0.0131466	+	0.0404610i
$897$	−1.46750	+	4.51651i	−0.0489985	+	0.150802i
$898$	9.13641	−	6.63799i	0.304886	−	0.221513i
$899$	−37.6168			−1.25459
$900$		0			0
$901$	0.0866228			0.00288582
$902$	−40.3396	+	29.3084i	−1.34316	+	0.975864i
$903$	−0.705366	+	2.17089i	−0.0234731	+	0.0722428i
$904$	−4.33708	+	13.3482i	−0.144249	+	0.443953i
$905$		0			0
$906$	1.02896	+	3.16681i	0.0341849	+	0.105210i
$907$	−10.7033			−0.355398			−0.177699	−	0.984085i	$-0.556865\pi$
$907$	−10.7033			−0.355398			−0.177699	+	0.984085i	$0.556865\pi$
$908$	−0.317289	−	0.976514i	−0.0105296	−	0.0324068i
$909$	−16.8703	−	12.2570i	−0.559553	−	0.406539i
$910$		0			0
$911$	−44.2253	+	32.1316i	−1.46525	+	1.06457i	−0.483294	+	0.875458i	$0.660560\pi$
$911$	−44.2253	+	32.1316i	−1.46525	+	1.06457i	−0.981956	+	0.189108i	$0.939440\pi$
$912$	−0.0474348	−	0.0344634i	−0.00157072	−	0.00114120i
$913$	26.1846	+	19.0243i	0.866585	+	0.629611i
$914$	−2.10944	+	1.53260i	−0.0697741	+	0.0506939i
$915$		0			0
$916$	3.30489	+	2.40115i	0.109197	+	0.0793361i
$917$	−0.700653	−	2.15639i	−0.0231376	−	0.0712102i
$918$	−0.102587			−0.00338586
$919$	−13.9687	−	42.9912i	−0.460785	−	1.41815i	−0.864207	−	0.503136i	$-0.832179\pi$
$919$	−13.9687	−	42.9912i	−0.460785	−	1.41815i	0.403422	−	0.915014i	$-0.367821\pi$
$920$		0			0
$921$	−0.770056	+	2.36999i	−0.0253742	+	0.0780938i
$922$	0.604905	−	1.86171i	0.0199215	−	0.0613120i
$923$	8.16933	−	5.93536i	0.268897	−	0.195365i
$924$	0.975210			0.0320820
$925$		0			0
$926$	−1.45797			−0.0479118
$927$	30.6189	−	22.2459i	1.00566	−	0.730651i
$928$	1.44575	−	4.44955i	0.0474589	−	0.146064i
$929$	11.4615	−	35.2748i	0.376039	−	1.15733i	−0.566736	−	0.823899i	$-0.691794\pi$
$929$	11.4615	−	35.2748i	0.376039	−	1.15733i	0.942775	−	0.333429i	$-0.108206\pi$
$930$		0			0
$931$	0.555029	+	1.70820i	0.0181903	+	0.0559841i
$932$	−4.41279			−0.144546
$933$	−0.389882	−	1.19993i	−0.0127642	−	0.0392840i
$934$	−20.6989	−	15.0387i	−0.677290	−	0.492080i
$935$		0			0
$936$	−10.2908	+	7.47673i	−0.336367	+	0.244385i
$937$	−36.3028	−	26.3755i	−1.18596	−	0.861651i	−0.193129	−	0.981173i	$-0.561864\pi$
$937$	−36.3028	−	26.3755i	−1.18596	−	0.861651i	−0.992831	+	0.119522i	$0.961864\pi$
$938$	−1.20437	−	0.875024i	−0.0393240	−	0.0285705i
$939$	0.0888654	−	0.0645645i	0.00290001	−	0.00210698i
$940$		0			0
$941$	−37.8128	−	27.4726i	−1.23266	−	0.895582i	−0.235575	−	0.971856i	$-0.575697\pi$
$941$	−37.8128	−	27.4726i	−1.23266	−	0.895582i	−0.997087	+	0.0762745i	$0.975697\pi$
$942$	0.772745	+	2.37827i	0.0251774	+	0.0774881i
$943$	72.1771			2.35041
$944$	2.35114	+	7.23607i	0.0765231	+	0.235514i
$945$		0			0
$946$	13.7607	−	42.3511i	0.447399	−	1.37695i
$947$	−10.6200	+	32.6851i	−0.345105	+	1.06212i	0.616423	+	0.787415i	$0.288581\pi$
$947$	−10.6200	+	32.6851i	−0.345105	+	1.06212i	−0.961528	+	0.274708i	$0.911419\pi$
$948$	1.15537	−	0.839423i	0.0375246	−	0.0272632i
$949$	−6.89074			−0.223683
$950$		0			0
$951$	1.26587			0.0410487
$952$	0.100848	−	0.0732703i	0.00326850	−	0.00237470i
$953$	−4.68815	+	14.4287i	−0.151864	+	0.467390i	−0.997830	−	0.0658477i	$-0.979025\pi$
$953$	−4.68815	+	14.4287i	−0.151864	+	0.467390i	0.845965	+	0.533238i	$0.179025\pi$
$954$	0.811943	−	2.49890i	0.0262876	−	0.0809050i
$955$		0			0
$956$	6.72179	+	20.6875i	0.217398	+	0.669083i
$957$	−3.58280			−0.115816
$958$	2.12209	+	6.53112i	0.0685617	+	0.211011i
$959$	−9.85029	−	7.15666i	−0.318083	−	0.231101i
$960$		0			0
$961$	−27.2205	+	19.7768i	−0.878079	+	0.637962i
$962$	14.2396	+	10.3457i	0.459105	+	0.333559i
$963$	29.3111	+	21.2958i	0.944538	+	0.686247i
$964$	12.8328	−	9.32358i	0.413317	−	0.300292i
$965$		0			0
$966$	−1.14204	−	0.829740i	−0.0367445	−	0.0266965i
$967$	16.5106	+	50.8143i	0.530944	+	1.63408i	0.752253	+	0.658874i	$0.228967\pi$
$967$	16.5106	+	50.8143i	0.530944	+	1.63408i	−0.221309	+	0.975204i	$0.571033\pi$
$968$	−8.02497			−0.257932
$969$	0.00177356	+	0.00545847i	5.69751e−5	+	0.000175351i
$970$		0			0
$971$	8.39505	−	25.8373i	0.269410	−	0.829159i	−0.721234	−	0.692691i	$-0.756425\pi$
$971$	8.39505	−	25.8373i	0.269410	−	0.829159i	0.990645	−	0.136468i	$-0.0435750\pi$
$972$	−1.44485	+	4.44679i	−0.0463435	+	0.142631i
$973$	4.73883	−	3.44296i	0.151920	−	0.110376i
$974$	−42.3233			−1.35613
$975$		0			0
$976$	−1.67667			−0.0536688
$977$	−9.21727	+	6.69674i	−0.294886	+	0.214248i	−0.725384	−	0.688344i	$-0.758338\pi$
$977$	−9.21727	+	6.69674i	−0.294886	+	0.214248i	0.430498	+	0.902592i	$0.358338\pi$
$978$	−1.06960	+	3.29190i	−0.0342022	+	0.105263i
$979$	−2.30242	+	7.08611i	−0.0735856	+	0.226473i
$980$		0			0
$981$	4.63434	+	14.2630i	0.147963	+	0.455384i
$982$	−12.9499			−0.413249
$983$	2.81212	+	8.65482i	0.0896927	+	0.276046i	0.985834	−	0.167723i	$-0.0536413\pi$
$983$	2.81212	+	8.65482i	0.0896927	+	0.276046i	−0.896142	+	0.443768i	$0.853641\pi$
$984$	−1.62376	−	1.17973i	−0.0517635	−	0.0376084i
$985$		0			0
$986$	−0.370503	+	0.269186i	−0.0117992	+	0.00857264i
$987$	−2.11725	−	1.53827i	−0.0673928	−	0.0489637i
$988$	1.15745	+	0.840938i	0.0368235	+	0.0267538i
$989$	−52.1484	+	37.8880i	−1.65822	+	1.20477i
$990$		0			0
$991$	−4.04514	−	2.93897i	−0.128498	−	0.0933594i	0.521680	−	0.853141i	$-0.325306\pi$
$991$	−4.04514	−	2.93897i	−0.128498	−	0.0933594i	−0.650178	+	0.759782i	$0.725306\pi$
$992$	−2.48459	−	7.64677i	−0.0788857	−	0.242785i
$993$	4.25133			0.134912
$994$	0.927551	+	2.85471i	0.0294201	+	0.0905459i
$995$		0			0
$996$	−0.402588	+	1.23904i	−0.0127565	+	0.0392604i
$997$	−15.2511	+	46.9380i	−0.483006	+	1.48654i	0.351841	+	0.936060i	$0.385556\pi$
$997$	−15.2511	+	46.9380i	−0.483006	+	1.48654i	−0.834848	+	0.550481i	$0.814444\pi$
$998$	−10.4983	+	7.62749i	−0.332319	+	0.241444i
$999$	4.30576			0.136228

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.d.c.51.1		8
5.2	odd	4		50.2.e.a.39.2	yes	8
5.3	odd	4		250.2.e.a.199.1		8
5.4	even	2		250.2.d.b.51.2		8
15.2	even	4		450.2.l.b.289.1		8
20.7	even	4		400.2.y.a.289.2		8
25.3	odd	20		1250.2.b.c.1249.6		8
25.4	even	10		1250.2.a.i.1.3		4
25.9	even	10		250.2.d.b.201.2		8
25.12	odd	20		250.2.e.a.49.1		8
25.13	odd	20		50.2.e.a.9.2	✓	8
25.16	even	5	inner	250.2.d.c.201.1		8
25.21	even	5		1250.2.a.h.1.2		4
25.22	odd	20		1250.2.b.c.1249.3		8
75.38	even	20		450.2.l.b.109.1		8
100.63	even	20		400.2.y.a.209.2		8
100.71	odd	10		10000.2.a.o.1.3		4
100.79	odd	10		10000.2.a.bb.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.e.a.9.2	✓	8	25.13	odd	20
50.2.e.a.39.2	yes	8	5.2	odd	4
250.2.d.b.51.2		8	5.4	even	2
250.2.d.b.201.2		8	25.9	even	10
250.2.d.c.51.1		8	1.1	even	1	trivial
250.2.d.c.201.1		8	25.16	even	5	inner
250.2.e.a.49.1		8	25.12	odd	20
250.2.e.a.199.1		8	5.3	odd	4
400.2.y.a.209.2		8	100.63	even	20
400.2.y.a.289.2		8	20.7	even	4
450.2.l.b.109.1		8	75.38	even	20
450.2.l.b.289.1		8	15.2	even	4
1250.2.a.h.1.2		4	25.21	even	5
1250.2.a.i.1.3		4	25.4	even	10
1250.2.b.c.1249.3		8	25.22	odd	20
1250.2.b.c.1249.6		8	25.3	odd	20
10000.2.a.o.1.3		4	100.71	odd	10
10000.2.a.bb.1.2		4	100.79	odd	10

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

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Modular forms

Varieties

Fields

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Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	250.2.d.c.51.1

Level	$250$
Weight	$2$
Character	250.51
Analytic conductor	$1.996$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$