LMFDB - Embedded newform 250.4.d.c.51.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,4,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, 4, names="a")

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

chi := DirichletCharacter("250.51");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 4 $
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:	$14.7504775014$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			51.3
Character	$\chi$	$=$	250.51
Dual form			250.4.d.c.201.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61803 + 1.17557i) q^{2} +(-1.35339 + 4.16531i) q^{3} +(1.23607 - 3.80423i) q^{4} +(-2.70679 - 8.33063i) q^{6} -31.2051 q^{7} +(2.47214 + 7.60845i) q^{8} +(6.32528 + 4.59559i) q^{9} +O(q^{10})$	\(q+(-1.61803 + 1.17557i) q^{2} +(-1.35339 + 4.16531i) q^{3} +(1.23607 - 3.80423i) q^{4} +(-2.70679 - 8.33063i) q^{6} -31.2051 q^{7} +(2.47214 + 7.60845i) q^{8} +(6.32528 + 4.59559i) q^{9} +(12.0574 - 8.76021i) q^{11} +(14.1729 + 10.2972i) q^{12} +(-34.5241 - 25.0832i) q^{13} +(50.4909 - 36.6838i) q^{14} +(-12.9443 - 9.40456i) q^{16} +(8.99290 + 27.6773i) q^{17} -15.6370 q^{18} +(-15.9076 - 48.9587i) q^{19} +(42.2328 - 129.979i) q^{21} +(-9.21103 + 28.3486i) q^{22} +(150.283 - 109.187i) q^{23} -35.0374 q^{24} +85.3482 q^{26} +(-123.370 + 89.6334i) q^{27} +(-38.5716 + 118.711i) q^{28} +(-23.7789 + 73.1839i) q^{29} +(-80.3709 - 247.356i) q^{31} +32.0000 q^{32} +(20.1706 + 62.0789i) q^{33} +(-47.0875 - 34.2110i) q^{34} +(25.3011 - 18.3823i) q^{36} +(97.3953 + 70.7618i) q^{37} +(83.2935 + 60.5163i) q^{38} +(151.204 - 109.856i) q^{39} +(248.032 + 180.206i) q^{41} +(84.4656 + 259.958i) q^{42} +504.394 q^{43} +(-18.4221 - 56.6973i) q^{44} +(-114.806 + 353.337i) q^{46} +(60.7022 - 186.822i) q^{47} +(56.6917 - 41.1889i) q^{48} +630.759 q^{49} -127.456 q^{51} +(-138.096 + 100.333i) q^{52} +(139.978 - 430.808i) q^{53} +(94.2462 - 290.060i) q^{54} +(-77.1433 - 237.423i) q^{56} +225.458 q^{57} +(-47.5578 - 146.368i) q^{58} +(-51.9655 - 37.7552i) q^{59} +(110.566 - 80.3305i) q^{61} +(420.827 + 305.749i) q^{62} +(-197.381 - 143.406i) q^{63} +(-51.7771 + 37.6183i) q^{64} +(-105.615 - 76.7337i) q^{66} +(-72.6375 - 223.555i) q^{67} +116.407 q^{68} +(251.407 + 773.750i) q^{69} +(166.664 - 512.939i) q^{71} +(-19.3283 + 59.4865i) q^{72} +(-846.241 + 614.830i) q^{73} -240.774 q^{74} -205.913 q^{76} +(-376.252 + 273.363i) q^{77} +(-115.510 + 355.502i) q^{78} +(109.157 - 335.949i) q^{79} +(-141.150 - 434.416i) q^{81} -613.169 q^{82} +(-301.832 - 928.944i) q^{83} +(-442.267 - 321.326i) q^{84} +(-816.127 + 592.951i) q^{86} +(-272.652 - 198.093i) q^{87} +(96.4592 + 70.0817i) q^{88} +(-891.118 + 647.435i) q^{89} +(1077.33 + 782.724i) q^{91} +(-229.612 - 706.674i) q^{92} +1139.09 q^{93} +(121.404 + 373.644i) q^{94} +(-43.3086 + 133.290i) q^{96} +(448.316 - 1379.77i) q^{97} +(-1020.59 + 741.502i) q^{98} +116.525 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 6 q^{3} - 32 q^{4} - 12 q^{6} + 112 q^{7} - 64 q^{8} - 26 q^{9}+O(q^{10}) $ 32 * q - 16 * q^2 - 6 * q^3 - 32 * q^4 - 12 * q^6 + 112 * q^7 - 64 * q^8 - 26 * q^9	\( 32 q - 16 q^{2} - 6 q^{3} - 32 q^{4} - 12 q^{6} + 112 q^{7} - 64 q^{8} - 26 q^{9} - 106 q^{11} - 24 q^{12} + 14 q^{13} - 56 q^{14} - 128 q^{16} + 92 q^{17} + 848 q^{18} - 110 q^{19} - 36 q^{21} + 68 q^{22} + 124 q^{23} + 192 q^{24} + 808 q^{26} - 630 q^{27} - 112 q^{28} + 10 q^{29} - 486 q^{31} + 1024 q^{32} - 672 q^{33} - 616 q^{34} - 104 q^{36} - 88 q^{37} + 20 q^{38} - 1012 q^{39} - 96 q^{41} - 72 q^{42} + 1804 q^{43} + 136 q^{44} - 832 q^{46} - 328 q^{47} - 96 q^{48} + 2076 q^{49} + 884 q^{51} + 56 q^{52} + 1164 q^{53} + 120 q^{54} - 224 q^{56} + 2800 q^{57} + 20 q^{58} - 2250 q^{59} + 934 q^{61} + 768 q^{62} - 2976 q^{63} - 512 q^{64} + 16 q^{66} - 2248 q^{67} + 1728 q^{68} + 628 q^{69} - 2616 q^{71} - 1488 q^{72} - 3836 q^{73} + 2584 q^{74} + 800 q^{76} + 254 q^{77} + 1816 q^{78} + 2800 q^{79} - 5268 q^{81} + 2128 q^{82} + 304 q^{83} - 624 q^{84} - 692 q^{86} + 2660 q^{87} - 848 q^{88} - 4520 q^{89} + 3764 q^{91} - 1664 q^{92} + 5648 q^{93} - 656 q^{94} - 192 q^{96} - 6228 q^{97} - 2748 q^{98} + 2108 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 6 * q^3 - 32 * q^4 - 12 * q^6 + 112 * q^7 - 64 * q^8 - 26 * q^9 - 106 * q^11 - 24 * q^12 + 14 * q^13 - 56 * q^14 - 128 * q^16 + 92 * q^17 + 848 * q^18 - 110 * q^19 - 36 * q^21 + 68 * q^22 + 124 * q^23 + 192 * q^24 + 808 * q^26 - 630 * q^27 - 112 * q^28 + 10 * q^29 - 486 * q^31 + 1024 * q^32 - 672 * q^33 - 616 * q^34 - 104 * q^36 - 88 * q^37 + 20 * q^38 - 1012 * q^39 - 96 * q^41 - 72 * q^42 + 1804 * q^43 + 136 * q^44 - 832 * q^46 - 328 * q^47 - 96 * q^48 + 2076 * q^49 + 884 * q^51 + 56 * q^52 + 1164 * q^53 + 120 * q^54 - 224 * q^56 + 2800 * q^57 + 20 * q^58 - 2250 * q^59 + 934 * q^61 + 768 * q^62 - 2976 * q^63 - 512 * q^64 + 16 * q^66 - 2248 * q^67 + 1728 * q^68 + 628 * q^69 - 2616 * q^71 - 1488 * q^72 - 3836 * q^73 + 2584 * q^74 + 800 * q^76 + 254 * q^77 + 1816 * q^78 + 2800 * q^79 - 5268 * q^81 + 2128 * q^82 + 304 * q^83 - 624 * q^84 - 692 * q^86 + 2660 * q^87 - 848 * q^88 - 4520 * q^89 + 3764 * q^91 - 1664 * q^92 + 5648 * q^93 - 656 * q^94 - 192 * q^96 - 6228 * q^97 - 2748 * q^98 + 2108 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$3$	−1.35339	+	4.16531i	−0.260461	+	0.801615i	0.732244	+	0.681042i	$0.238473\pi$
$3$	−1.35339	+	4.16531i	−0.260461	+	0.801615i	−0.992704	+	0.120573i	$0.961527\pi$
$4$	1.23607	−	3.80423i	0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	−2.70679	−	8.33063i	−0.184173	−	0.566828i
$7$	−31.2051			−1.68492			−0.842459	−	0.538761i	$-0.818893\pi$
$7$	−31.2051			−1.68492			−0.842459	+	0.538761i	$0.818893\pi$
$8$	2.47214	+	7.60845i	0.109254	+	0.336249i
$9$	6.32528	+	4.59559i	0.234270	+	0.170207i
$10$		0			0
$11$	12.0574	−	8.76021i	0.330495	−	0.240118i	−0.410146	−	0.912020i	$-0.634522\pi$
$11$	12.0574	−	8.76021i	0.330495	−	0.240118i	0.740640	+	0.671902i	$0.234522\pi$
$12$	14.1729	+	10.2972i	0.340947	+	0.247713i
$13$	−34.5241	−	25.0832i	−0.736558	−	0.535141i	0.155073	−	0.987903i	$-0.450439\pi$
$13$	−34.5241	−	25.0832i	−0.736558	−	0.535141i	−0.891631	+	0.452762i	$0.850439\pi$
$14$	50.4909	−	36.6838i	0.963876	−	0.700297i
$15$		0			0
$16$	−12.9443	−	9.40456i	−0.202254	−	0.146946i
$17$	8.99290	+	27.6773i	0.128300	+	0.394867i	0.994488	−	0.104852i	$-0.0334368\pi$
$17$	8.99290	+	27.6773i	0.128300	+	0.394867i	−0.866188	+	0.499718i	$0.833437\pi$
$18$	−15.6370			−0.204759
$19$	−15.9076	−	48.9587i	−0.192077	−	0.591152i	−0.999998	−	0.00186182i	$-0.999407\pi$
$19$	−15.9076	−	48.9587i	−0.192077	−	0.591152i	0.807921	−	0.589290i	$-0.200593\pi$
$20$		0			0
$21$	42.2328	−	129.979i	0.438855	−	1.35066i
$22$	−9.21103	+	28.3486i	−0.0892636	+	0.274725i
$23$	150.283	−	109.187i	1.36244	−	0.989874i	0.364159	−	0.931337i	$-0.381356\pi$
$23$	150.283	−	109.187i	1.36244	−	0.989874i	0.998285	−	0.0585368i	$-0.0186435\pi$
$24$	−35.0374			−0.297999
$25$		0			0
$26$	85.3482			0.643775
$27$	−123.370	+	89.6334i	−0.879353	+	0.638887i
$28$	−38.5716	+	118.711i	−0.260334	+	0.801226i
$29$	−23.7789	+	73.1839i	−0.152263	+	0.468618i	−0.997873	−	0.0651831i	$-0.979237\pi$
$29$	−23.7789	+	73.1839i	−0.152263	+	0.468618i	0.845610	+	0.533801i	$0.179237\pi$
$30$		0			0
$31$	−80.3709	−	247.356i	−0.465646	−	1.43311i	−0.858168	−	0.513369i	$-0.828397\pi$
$31$	−80.3709	−	247.356i	−0.465646	−	1.43311i	0.392522	−	0.919743i	$-0.371603\pi$
$32$	32.0000			0.176777
$33$	20.1706	+	62.0789i	0.106402	+	0.327471i
$34$	−47.0875	−	34.2110i	−0.237513	−	0.172563i
$35$		0			0
$36$	25.3011	−	18.3823i	0.117135	−	0.0851035i
$37$	97.3953	+	70.7618i	0.432748	+	0.314410i	0.782747	−	0.622340i	$-0.213818\pi$
$37$	97.3953	+	70.7618i	0.432748	+	0.314410i	−0.349999	+	0.936750i	$0.613818\pi$
$38$	83.2935	+	60.5163i	0.355579	+	0.258343i
$39$	151.204	−	109.856i	0.620821	−	0.451053i
$40$		0			0
$41$	248.032	+	180.206i	0.944783	+	0.686425i	0.949567	−	0.313563i	$-0.101523\pi$
$41$	248.032	+	180.206i	0.944783	+	0.686425i	−0.00478394	+	0.999989i	$0.501523\pi$
$42$	84.4656	+	259.958i	0.310317	+	0.955058i
$43$	504.394			1.78882			0.894411	−	0.447246i	$-0.147595\pi$
$43$	504.394			1.78882			0.894411	+	0.447246i	$0.147595\pi$
$44$	−18.4221	−	56.6973i	−0.0631189	−	0.194260i
$45$		0			0
$46$	−114.806	+	353.337i	−0.367984	+	1.13254i
$47$	60.7022	−	186.822i	0.188390	−	0.579804i	−0.811600	−	0.584213i	$-0.801403\pi$
$47$	60.7022	−	186.822i	0.188390	−	0.579804i	0.999990	+	0.00440862i	$0.00140331\pi$
$48$	56.6917	−	41.1889i	0.170474	−	0.123856i
$49$	630.759			1.83895
$50$		0			0
$51$	−127.456			−0.349948
$52$	−138.096	+	100.333i	−0.368279	+	0.267570i
$53$	139.978	−	430.808i	0.362782	−	1.11653i	−0.588576	−	0.808442i	$-0.700311\pi$
$53$	139.978	−	430.808i	0.362782	−	1.11653i	0.951358	−	0.308087i	$-0.0996887\pi$
$54$	94.2462	−	290.060i	0.237505	−	0.730966i
$55$		0			0
$56$	−77.1433	−	237.423i	−0.184084	−	0.566552i
$57$	225.458			0.523905
$58$	−47.5578	−	146.368i	−0.107666	−	0.331363i
$59$	−51.9655	−	37.7552i	−0.114667	−	0.0833102i	0.528974	−	0.848638i	$-0.322577\pi$
$59$	−51.9655	−	37.7552i	−0.114667	−	0.0833102i	−0.643641	+	0.765328i	$0.722577\pi$
$60$		0			0
$61$	110.566	−	80.3305i	0.232073	−	0.168611i	−0.465671	−	0.884958i	$-0.654187\pi$
$61$	110.566	−	80.3305i	0.232073	−	0.168611i	0.697744	+	0.716347i	$0.254187\pi$
$62$	420.827	+	305.749i	0.862018	+	0.626293i
$63$	−197.381	−	143.406i	−0.394725	−	0.286785i
$64$	−51.7771	+	37.6183i	−0.101127	+	0.0734732i
$65$		0			0
$66$	−105.615	−	76.7337i	−0.196974	−	0.143110i
$67$	−72.6375	−	223.555i	−0.132449	−	0.407636i	0.862735	−	0.505656i	$-0.168749\pi$
$67$	−72.6375	−	223.555i	−0.132449	−	0.407636i	−0.995185	+	0.0980193i	$0.968749\pi$
$68$	116.407			0.207594
$69$	251.407	+	773.750i	0.438635	+	1.34998i
$70$		0			0
$71$	166.664	−	512.939i	0.278583	−	0.857390i	−0.709666	−	0.704538i	$-0.751154\pi$
$71$	166.664	−	512.939i	0.278583	−	0.857390i	0.988249	−	0.152852i	$-0.0488458\pi$
$72$	−19.3283	+	59.4865i	−0.0316370	+	0.0973688i
$73$	−846.241	+	614.830i	−1.35678	+	0.985759i	−0.358139	+	0.933668i	$0.616589\pi$
$73$	−846.241	+	614.830i	−1.35678	+	0.985759i	−0.998642	+	0.0520909i	$0.983411\pi$
$74$	−240.774			−0.378236
$75$		0			0
$76$	−205.913			−0.310787
$77$	−376.252	+	273.363i	−0.556856	+	0.404580i
$78$	−115.510	+	355.502i	−0.167678	+	0.516060i
$79$	109.157	−	335.949i	0.155457	−	0.478446i	−0.842750	−	0.538305i	$-0.819065\pi$
$79$	109.157	−	335.949i	0.155457	−	0.478446i	0.998207	+	0.0598585i	$0.0190649\pi$
$80$		0			0
$81$	−141.150	−	434.416i	−0.193622	−	0.595907i
$82$	−613.169			−0.825771
$83$	−301.832	−	928.944i	−0.399161	−	1.22849i	−0.925673	−	0.378325i	$-0.876500\pi$
$83$	−301.832	−	928.944i	−0.399161	−	1.22849i	0.526512	−	0.850168i	$-0.323500\pi$
$84$	−442.267	−	321.326i	−0.574468	−	0.417376i
$85$		0			0
$86$	−816.127	+	592.951i	−1.02332	+	0.743483i
$87$	−272.652	−	198.093i	−0.335993	−	0.244113i
$88$	96.4592	+	70.0817i	0.116848	+	0.0848947i
$89$	−891.118	+	647.435i	−1.06133	+	0.771101i	−0.974334	−	0.225108i	$-0.927727\pi$
$89$	−891.118	+	647.435i	−1.06133	+	0.771101i	−0.0869953	+	0.996209i	$0.527727\pi$
$90$		0			0
$91$	1077.33	+	782.724i	1.24104	+	0.901668i
$92$	−229.612	−	706.674i	−0.260204	−	0.800825i
$93$	1139.09			1.27009
$94$	121.404	+	373.644i	0.133212	+	0.409984i
$95$		0			0
$96$	−43.3086	+	133.290i	−0.0460434	+	0.141707i
$97$	448.316	−	1379.77i	0.469274	−	1.44428i	−0.384253	−	0.923228i	$-0.625541\pi$
$97$	448.316	−	1379.77i	0.469274	−	1.44428i	0.853527	−	0.521048i	$-0.174459\pi$
$98$	−1020.59	+	741.502i	−1.05199	+	0.764316i
$99$	116.525			0.118295
$100$		0			0
$101$	−305.774			−0.301244			−0.150622	−	0.988591i	$-0.548128\pi$
$101$	−305.774			−0.301244			−0.150622	+	0.988591i	$0.548128\pi$
$102$	206.228	−	149.833i	0.200192	−	0.145448i
$103$	−109.795	+	337.914i	−0.105033	+	0.323259i	−0.989738	−	0.142892i	$-0.954360\pi$
$103$	−109.795	+	337.914i	−0.105033	+	0.323259i	0.884705	+	0.466151i	$0.154360\pi$
$104$	105.496	−	324.684i	0.0994688	−	0.306133i
$105$		0			0
$106$	279.956	+	861.616i	0.256526	+	0.789505i
$107$	−254.177			−0.229647			−0.114823	−	0.993386i	$-0.536630\pi$
$107$	−254.177			−0.229647			−0.114823	+	0.993386i	$0.536630\pi$
$108$	188.492	+	580.120i	0.167942	+	0.516871i
$109$	−723.625	−	525.744i	−0.635878	−	0.461992i	0.222554	−	0.974920i	$-0.428561\pi$
$109$	−723.625	−	525.744i	−0.635878	−	0.461992i	−0.858432	+	0.512928i	$0.828561\pi$
$110$		0			0
$111$	−426.559	+	309.914i	−0.364750	+	0.265006i
$112$	403.927	+	293.470i	0.340782	+	0.247592i
$113$	−1081.45	−	785.716i	−0.900300	−	0.654106i	0.0382434	−	0.999268i	$-0.487824\pi$
$113$	−1081.45	−	785.716i	−0.900300	−	0.654106i	−0.938543	+	0.345163i	$0.887824\pi$
$114$	−364.798	+	265.041i	−0.299706	+	0.217749i
$115$		0			0
$116$	249.016	+	180.921i	0.199315	+	0.144811i
$117$	−103.102	−	317.317i	−0.0814686	−	0.250735i
$118$	128.466			0.100222
$119$	−280.625	−	863.674i	−0.216175	−	0.665318i
$120$		0			0
$121$	−342.662	+	1054.61i	−0.257447	+	0.792341i
$122$	−84.4645	+	259.955i	−0.0626808	+	0.192912i
$123$	−1086.30	+	789.243i	−0.796328	+	0.578566i
$124$	−1040.34			−0.753431
$125$		0			0
$126$	487.953			0.345002
$127$	1226.46	−	891.078i	0.856937	−	0.622601i	−0.0701127	−	0.997539i	$-0.522336\pi$
$127$	1226.46	−	891.078i	0.856937	−	0.622601i	0.927050	+	0.374938i	$0.122336\pi$
$128$	39.5542	−	121.735i	0.0273135	−	0.0840623i
$129$	−682.643	+	2100.96i	−0.465918	+	1.43395i
$130$		0			0
$131$	−385.607	−	1186.78i	−0.257180	−	0.791519i	−0.993392	−	0.114768i	$-0.963387\pi$
$131$	−385.607	−	1186.78i	−0.257180	−	0.791519i	0.736212	−	0.676751i	$-0.236613\pi$
$132$	261.094			0.172162
$133$	496.400	+	1527.76i	0.323634	+	0.996043i
$134$	380.335	+	276.330i	0.245194	+	0.178144i
$135$		0			0
$136$	−188.350	+	136.844i	−0.118756	+	0.0862815i
$137$	−1933.90	−	1405.06i	−1.20602	−	0.876222i	−0.211154	−	0.977453i	$-0.567722\pi$
$137$	−1933.90	−	1405.06i	−1.20602	−	0.876222i	−0.994863	+	0.101231i	$0.967722\pi$
$138$	−1316.38	−	956.408i	−0.812014	−	0.589962i
$139$	−1423.34	+	1034.12i	−0.868534	+	0.631027i	−0.930193	−	0.367071i	$-0.880361\pi$
$139$	−1423.34	+	1034.12i	−0.868534	+	0.631027i	0.0616594	+	0.998097i	$0.480361\pi$
$140$		0			0
$141$	696.019	+	505.687i	0.415712	+	0.302032i
$142$	333.328	+	1025.88i	0.196988	+	0.606266i
$143$	−636.005			−0.371926
$144$	−38.6567	−	118.973i	−0.0223708	−	0.0688501i
$145$		0			0
$146$	646.471	−	1989.63i	0.366454	−	1.12783i
$147$	−853.665	+	2627.31i	−0.478973	+	1.47413i
$148$	389.581	−	283.047i	0.216374	−	0.157205i
$149$	391.623			0.215322			0.107661	−	0.994188i	$-0.465664\pi$
$149$	391.623			0.215322			0.107661	+	0.994188i	$0.465664\pi$
$150$		0			0
$151$	1937.43			1.04414			0.522072	−	0.852901i	$-0.325159\pi$
$151$	1937.43			1.04414			0.522072	+	0.852901i	$0.325159\pi$
$152$	333.174	−	242.065i	0.177789	−	0.129172i
$153$	−70.3108	+	216.394i	−0.0371522	+	0.114343i
$154$	287.431	−	884.622i	0.150402	−	0.462889i
$155$		0			0
$156$	−231.019	−	711.004i	−0.118566	−	0.364910i
$157$	1798.13			0.914052			0.457026	−	0.889453i	$-0.348915\pi$
$157$	1798.13			0.914052			0.457026	+	0.889453i	$0.348915\pi$
$158$	218.313	+	671.899i	0.109924	+	0.338313i
$159$	1605.01	+	1166.10i	0.800536	+	0.581623i
$160$		0			0
$161$	−4689.60	+	3407.20i	−2.29561	+	1.66786i
$162$	739.073	+	536.968i	0.358439	+	0.260421i
$163$	−1079.33	−	784.182i	−0.518650	−	0.376821i	0.297445	−	0.954739i	$-0.403866\pi$
$163$	−1079.33	−	784.182i	−0.518650	−	0.376821i	−0.816095	+	0.577917i	$0.803866\pi$
$164$	992.129	−	720.824i	0.472392	−	0.343213i
$165$		0			0
$166$	1580.41	+	1148.24i	0.738939	+	0.536871i
$167$	−498.847	−	1535.29i	−0.231149	−	0.711404i	−0.997609	−	0.0691116i	$-0.977984\pi$
$167$	−498.847	−	1535.29i	−0.231149	−	0.711404i	0.766460	−	0.642292i	$-0.222016\pi$
$168$	1093.35			0.502104
$169$	−116.166	−	357.522i	−0.0528748	−	0.162732i
$170$		0			0
$171$	124.374	−	382.782i	0.0556204	−	0.171182i
$172$	623.465	−	1918.83i	0.276388	−	0.850636i
$173$	2671.96	−	1941.29i	1.17425	−	0.853142i	0.182738	−	0.983162i	$-0.441504\pi$
$173$	2671.96	−	1941.29i	1.17425	−	0.853142i	0.991511	+	0.130020i	$0.0415040\pi$
$174$	674.033			0.293668
$175$		0			0
$176$	−238.460			−0.102128
$177$	227.592	−	165.355i	0.0966489	−	0.0702195i
$178$	680.753	−	2095.14i	0.286655	−	0.882234i
$179$	854.933	−	2631.21i	0.356987	−	1.09869i	−0.597861	−	0.801600i	$-0.703983\pi$
$179$	854.933	−	2631.21i	0.356987	−	1.09869i	0.954848	−	0.297094i	$-0.0960174\pi$
$180$		0			0
$181$	−1009.96	−	3108.33i	−0.414749	−	1.27647i	−0.912475	−	0.409132i	$-0.865832\pi$
$181$	−1009.96	−	3108.33i	−0.414749	−	1.27647i	0.497726	−	0.867334i	$-0.334168\pi$
$182$	−2663.30			−1.08471
$183$	184.963	+	569.259i	0.0747153	+	0.229950i
$184$	1202.27	+	873.497i	0.481697	+	0.349973i
$185$		0			0
$186$	−1843.09	+	1339.08i	−0.726568	+	0.527882i
$187$	350.890	+	254.937i	0.137217	+	0.0996941i
$188$	−635.681	−	461.850i	−0.246605	−	0.179169i
$189$	3849.77	−	2797.02i	1.48164	−	1.07647i
$190$		0			0
$191$	−286.949	−	208.481i	−0.108706	−	0.0789797i	0.532104	−	0.846679i	$-0.321401\pi$
$191$	−286.949	−	208.481i	−0.108706	−	0.0789797i	−0.640810	+	0.767699i	$0.721401\pi$
$192$	−86.6171	−	266.580i	−0.0325576	−	0.100202i
$193$	2907.82			1.08451			0.542253	−	0.840216i	$-0.317572\pi$
$193$	2907.82			1.08451			0.542253	+	0.840216i	$0.317572\pi$
$194$	896.631	+	2759.55i	0.331827	+	1.02126i
$195$		0			0
$196$	779.661	−	2399.55i	0.284133	−	0.874472i
$197$	−1291.54	+	3974.94i	−0.467098	+	1.43758i	0.389228	+	0.921142i	$0.372742\pi$
$197$	−1291.54	+	3974.94i	−0.467098	+	1.43758i	−0.856325	+	0.516437i	$0.827258\pi$
$198$	−188.541	+	136.983i	−0.0676718	+	0.0491665i
$199$	−1052.08			−0.374772			−0.187386	−	0.982286i	$-0.560002\pi$
$199$	−1052.08			−0.374772			−0.187386	+	0.982286i	$0.560002\pi$
$200$		0			0
$201$	1029.49			0.361265
$202$	494.753	−	359.459i	0.172330	−	0.125205i
$203$	742.023	−	2283.71i	0.256551	−	0.789583i
$204$	−157.544	+	484.870i	−0.0540700	+	0.166410i
$205$		0			0
$206$	−219.590	−	675.828i	−0.0742697	−	0.228579i
$207$	1452.36			0.487663
$208$	210.992	+	649.368i	0.0703350	+	0.216469i
$209$	−620.693	−	450.960i	−0.205427	−	0.149251i
$210$		0			0
$211$	1074.58	−	780.728i	0.350602	−	0.254727i	−0.398519	−	0.917160i	$-0.630476\pi$
$211$	1074.58	−	780.728i	0.350602	−	0.254727i	0.749122	+	0.662432i	$0.230476\pi$
$212$	−1465.87	−	1065.02i	−0.474888	−	0.345026i
$213$	1910.99	+	1388.42i	0.614737	+	0.446633i
$214$	411.267	−	298.803i	0.131372	−	0.0954474i
$215$		0			0
$216$	−986.959	−	717.067i	−0.310898	−	0.225881i
$217$	2507.98	+	7718.77i	0.784576	+	2.41468i
$218$	1788.90			0.555778
$219$	−1415.66	−	4356.97i	−0.436812	−	1.34437i
$220$		0			0
$221$	383.764	−	1181.10i	0.116809	−	0.359501i
$222$	325.862	−	1002.90i	0.0985155	−	0.303200i
$223$	−3613.82	+	2625.59i	−1.08520	+	0.788442i	−0.978582	−	0.205858i	$-0.934001\pi$
$223$	−3613.82	+	2625.59i	−1.08520	+	0.788442i	−0.106616	+	0.994300i	$0.534001\pi$
$224$	−998.564			−0.297854
$225$		0			0
$226$	2673.48			0.786891
$227$	−1494.35	+	1085.71i	−0.436931	+	0.317449i	−0.784414	−	0.620237i	$-0.787036\pi$
$227$	−1494.35	+	1085.71i	−0.436931	+	0.317449i	0.347483	+	0.937686i	$0.387036\pi$
$228$	278.681	−	857.692i	0.0809478	−	0.249132i
$229$	−80.0296	+	246.306i	−0.0230939	+	0.0710757i	−0.961939	−	0.273263i	$-0.911897\pi$
$229$	−80.0296	+	246.306i	−0.0230939	+	0.0710757i	0.938845	+	0.344339i	$0.111897\pi$
$230$		0			0
$231$	−629.427	−	1937.18i	−0.179278	−	0.551762i
$232$	−615.601			−0.174208
$233$	1047.00	+	3222.33i	0.294383	+	0.906018i	0.983428	+	0.181299i	$0.0580303\pi$
$233$	1047.00	+	3222.33i	0.294383	+	0.906018i	−0.689045	+	0.724719i	$0.741970\pi$
$234$	539.852	+	392.225i	0.150817	+	0.109575i
$235$		0			0
$236$	−207.862	+	151.021i	−0.0573333	+	0.0416551i
$237$	1251.60	+	909.343i	0.343040	+	0.249233i
$238$	1469.37	+	1067.56i	0.400189	+	0.290755i
$239$	−2332.67	+	1694.79i	−0.631330	+	0.458688i	−0.856861	−	0.515548i	$-0.827589\pi$
$239$	−2332.67	+	1694.79i	−0.631330	+	0.458688i	0.225530	+	0.974236i	$0.427589\pi$
$240$		0			0
$241$	5114.13	+	3715.63i	1.36693	+	0.993133i	0.997970	+	0.0636877i	$0.0202861\pi$
$241$	5114.13	+	3715.63i	1.36693	+	0.993133i	0.368960	+	0.929445i	$0.379714\pi$
$242$	−685.324	−	2109.21i	−0.182043	−	0.560270i
$243$	−2116.81			−0.558821
$244$	−168.929	−	519.910i	−0.0443220	−	0.136409i
$245$		0			0
$246$	829.859	−	2554.04i	0.215081	−	0.661951i
$247$	−678.844	+	2089.27i	−0.174874	+	0.538206i
$248$	1683.31	−	1223.00i	0.431009	−	0.313146i
$249$	4277.84			1.08874
$250$		0			0
$251$	1232.70			0.309990			0.154995	−	0.987915i	$-0.450464\pi$
$251$	1232.70			0.309990			0.154995	+	0.987915i	$0.450464\pi$
$252$	−789.525	+	573.623i	−0.197363	+	0.143392i
$253$	855.522	−	2633.02i	0.212594	−	0.654296i
$254$	−936.935	+	2883.59i	−0.231451	+	0.712332i
$255$		0			0
$256$	79.1084	+	243.470i	0.0193136	+	0.0594410i
$257$	6483.90			1.57375			0.786877	−	0.617110i	$-0.211697\pi$
$257$	6483.90			1.57375			0.786877	+	0.617110i	$0.211697\pi$
$258$	−1365.29	−	4201.92i	−0.329454	−	1.01395i
$259$	−3039.23	−	2208.13i	−0.729145	−	0.529755i
$260$		0			0
$261$	−486.731	+	353.631i	−0.115433	+	0.0838667i
$262$	2019.06	+	1466.93i	0.476100	+	0.345907i
$263$	646.478	+	469.694i	0.151572	+	0.110124i	0.660987	−	0.750398i	$-0.270138\pi$
$263$	646.478	+	469.694i	0.151572	+	0.110124i	−0.509414	+	0.860521i	$0.670138\pi$
$264$	−422.459	+	306.935i	−0.0984870	+	0.0715550i
$265$		0			0
$266$	−2599.18	−	1888.42i	−0.599121	−	0.435287i
$267$	−1490.74	−	4588.02i	−0.341692	−	1.05162i
$268$	−940.240			−0.214307
$269$	1260.60	+	3879.74i	0.285727	+	0.879376i	0.986180	+	0.165678i	$0.0529811\pi$
$269$	1260.60	+	3879.74i	0.285727	+	0.879376i	−0.700453	+	0.713698i	$0.747019\pi$
$270$		0			0
$271$	135.829	−	418.040i	0.0304467	−	0.0937052i	−0.934678	−	0.355494i	$-0.884313\pi$
$271$	135.829	−	418.040i	0.0304467	−	0.0937052i	0.965125	+	0.261789i	$0.0843125\pi$
$272$	143.886	−	442.837i	0.0320750	−	0.0987167i
$273$	−4718.34	+	3428.08i	−1.04603	+	0.759987i
$274$	4780.86			1.05410
$275$		0			0
$276$	3254.28			0.709726
$277$	−51.9157	+	37.7190i	−0.0112611	+	0.00818164i	−0.593402	−	0.804907i	$-0.702215\pi$
$277$	−51.9157	+	37.7190i	−0.0112611	+	0.00818164i	0.582140	+	0.813088i	$0.302215\pi$
$278$	1087.34	−	3346.47i	0.234583	−	0.721972i
$279$	628.378	−	1933.95i	0.134839	−	0.414991i
$280$		0			0
$281$	−552.262	−	1699.69i	−0.117243	−	0.360836i	0.875166	−	0.483824i	$-0.160752\pi$
$281$	−552.262	−	1699.69i	−0.117243	−	0.360836i	−0.992408	+	0.122988i	$0.960752\pi$
$282$	−1720.65			−0.363345
$283$	1929.30	+	5937.78i	0.405248	+	1.24722i	0.920688	+	0.390299i	$0.127628\pi$
$283$	1929.30	+	5937.78i	0.405248	+	1.24722i	−0.515440	+	0.856926i	$0.672372\pi$
$284$	−1745.33	−	1268.06i	−0.364670	−	0.264948i
$285$		0			0
$286$	1029.08	−	747.668i	0.212764	−	0.154582i
$287$	−7739.87	−	5623.35i	−1.59188	−	1.15657i
$288$	202.409	+	147.059i	0.0414134	+	0.0300886i
$289$	3289.54	−	2389.99i	0.669558	−	0.486462i
$290$		0			0
$291$	5140.44	+	3734.75i	1.03553	+	0.752354i
$292$	1292.94	+	3979.26i	0.259122	+	0.797496i
$293$	2442.29			0.486963			0.243482	−	0.969905i	$-0.421710\pi$
$293$	2442.29			0.486963			0.243482	+	0.969905i	$0.421710\pi$
$294$	−1707.33	−	5254.62i	−0.338685	−	1.04237i
$295$		0			0
$296$	−297.614	+	915.960i	−0.0584407	+	0.179862i
$297$	−702.311	+	2161.49i	−0.137213	+	0.422298i
$298$	−633.660	+	460.381i	−0.123178	+	0.0894937i
$299$	−7927.15			−1.53324
$300$		0			0
$301$	−15739.7			−3.01402
$302$	−3134.83	+	2277.59i	−0.597315	+	0.433975i
$303$	413.832	−	1273.65i	0.0784622	−	0.241482i
$304$	−254.522	+	783.339i	−0.0480193	+	0.147788i
$305$		0			0
$306$	−140.622	−	432.789i	−0.0262706	−	0.0808526i
$307$	−6382.66			−1.18657			−0.593286	−	0.804992i	$-0.702170\pi$
$307$	−6382.66			−1.18657			−0.593286	+	0.804992i	$0.702170\pi$
$308$	574.862	+	1769.24i	0.106350	+	0.327312i
$309$	−1258.92	−	914.661i	−0.231772	−	0.168392i
$310$		0			0
$311$	−2487.41	+	1807.21i	−0.453531	+	0.329510i	−0.790988	−	0.611831i	$-0.790433\pi$
$311$	−2487.41	+	1807.21i	−0.453531	+	0.329510i	0.337457	+	0.941341i	$0.390433\pi$
$312$	1209.63	+	878.850i	0.219494	+	0.159471i
$313$	−4495.09	−	3265.88i	−0.811750	−	0.589771i	0.102587	−	0.994724i	$-0.467288\pi$
$313$	−4495.09	−	3265.88i	−0.811750	−	0.589771i	−0.914337	+	0.404953i	$0.867288\pi$
$314$	−2909.43	+	2113.82i	−0.522894	+	0.379904i
$315$		0			0
$316$	−1143.10	−	830.513i	−0.203495	−	0.147848i
$317$	−1028.23	−	3164.57i	−0.182180	−	0.560693i	0.817708	−	0.575633i	$-0.195244\pi$
$317$	−1028.23	−	3164.57i	−0.182180	−	0.560693i	−0.999888	+	0.0149397i	$0.995244\pi$
$318$	−3967.79			−0.699694
$319$	354.395	+	1090.72i	0.0622016	+	0.191437i
$320$		0			0
$321$	344.001	−	1058.73i	0.0598140	−	0.184088i
$322$	3582.54	−	11025.9i	0.620022	−	1.90823i
$323$	1211.99	−	880.562i	0.208783	−	0.151690i
$324$	−1827.09			−0.313287
$325$		0			0
$326$	2668.26			0.453317
$327$	3169.24	−	2302.59i	0.535961	−	0.389399i
$328$	−757.919	+	2332.63i	−0.127589	+	0.392677i
$329$	−1894.22	+	5829.80i	−0.317421	+	0.976923i
$330$		0			0
$331$	−266.427	−	819.978i	−0.0442422	−	0.136163i	0.926495	−	0.376306i	$-0.122806\pi$
$331$	−266.427	−	819.978i	−0.0442422	−	0.136163i	−0.970738	+	0.240143i	$0.922806\pi$
$332$	−3907.00			−0.645857
$333$	290.861	+	895.177i	0.0478651	+	0.147313i
$334$	2611.99	+	1897.73i	0.427910	+	0.310895i
$335$		0			0
$336$	−1769.07	+	1285.30i	−0.287234	+	0.208688i
$337$	4634.03	+	3366.82i	0.749056	+	0.544221i	0.895534	−	0.444993i	$-0.146794\pi$
$337$	4634.03	+	3366.82i	0.749056	+	0.544221i	−0.146478	+	0.989214i	$0.546794\pi$
$338$	608.253	+	441.921i	0.0978834	+	0.0711164i
$339$	4736.38	−	3441.18i	0.758834	−	0.551325i
$340$		0			0
$341$	−3135.95	−	2278.40i	−0.498010	−	0.361826i
$342$	248.747	+	765.565i	0.0393295	+	0.121044i
$343$	−8979.56			−1.41356
$344$	1246.93	+	3837.66i	0.195436	+	0.601490i
$345$		0			0
$346$	−2041.19	+	6282.15i	−0.317154	+	0.976099i
$347$	715.567	−	2202.29i	0.110702	−	0.340706i	−0.880324	−	0.474373i	$-0.842675\pi$
$347$	715.567	−	2202.29i	0.110702	−	0.340706i	0.991026	+	0.133666i	$0.0426750\pi$
$348$	−1090.61	+	792.373i	−0.167996	+	0.122056i
$349$	−4454.14			−0.683166			−0.341583	−	0.939852i	$-0.610963\pi$
$349$	−4454.14			−0.683166			−0.341583	+	0.939852i	$0.610963\pi$
$350$		0			0
$351$	6507.52			0.989589
$352$	385.837	−	280.327i	0.0584238	−	0.0424473i
$353$	2346.00	−	7220.26i	0.353726	−	1.08866i	−0.603019	−	0.797727i	$-0.706036\pi$
$353$	2346.00	−	7220.26i	0.353726	−	1.08866i	0.956745	−	0.290929i	$-0.0939643\pi$
$354$	−173.865	+	535.101i	−0.0261040	+	0.0803398i
$355$		0			0
$356$	1361.51	+	4190.29i	0.202696	+	0.623834i
$357$	3977.27			0.589634
$358$	1709.87	+	5262.43i	0.252428	+	0.776894i
$359$	7535.11	+	5474.58i	1.10777	+	0.804839i	0.982310	−	0.187261i	$-0.0599609\pi$
$359$	7535.11	+	5474.58i	1.10777	+	0.804839i	0.125455	+	0.992099i	$0.459961\pi$
$360$		0			0
$361$	3405.15	−	2473.98i	0.496450	−	0.360692i
$362$	5288.21	+	3842.11i	0.767796	+	0.557836i
$363$	−3929.01	−	2854.59i	−0.568098	−	0.412747i
$364$	4309.31	−	3130.90i	0.620520	−	0.450834i
$365$		0			0
$366$	−968.481	−	703.643i	−0.138315	−	0.100492i
$367$	−2382.00	−	7331.03i	−0.338799	−	1.04272i	−0.964820	−	0.262910i	$-0.915318\pi$
$367$	−2382.00	−	7331.03i	−0.338799	−	1.04272i	0.626022	−	0.779806i	$-0.284682\pi$
$368$	−2972.16			−0.421018
$369$	740.722	+	2279.71i	0.104500	+	0.321617i
$370$		0			0
$371$	−4368.03	+	13443.4i	−0.611258	+	1.88126i
$372$	1407.99	−	4333.35i	0.196239	−	0.603962i
$373$	7224.67	−	5249.03i	1.00289	−	0.728644i	0.0401863	−	0.999192i	$-0.487205\pi$
$373$	7224.67	−	5249.03i	1.00289	−	0.728644i	0.962707	+	0.270548i	$0.0872049\pi$
$374$	−867.448			−0.119932
$375$		0			0
$376$	1571.49			0.215541
$377$	2656.63	−	1930.16i	0.362927	−	0.263682i
$378$	−2940.96	+	9051.35i	−0.400177	+	1.23162i
$379$	−1311.50	+	4036.39i	−0.177750	+	0.547059i	−0.999748	−	0.0224313i	$-0.992859\pi$
$379$	−1311.50	+	4036.39i	−0.177750	+	0.547059i	0.821998	+	0.569490i	$0.192859\pi$
$380$		0			0
$381$	2051.73	+	6314.59i	0.275888	+	0.849097i
$382$	709.377			0.0950127
$383$	−1686.84	−	5191.55i	−0.225048	−	0.692626i	−0.998287	−	0.0585112i	$-0.981365\pi$
$383$	−1686.84	−	5191.55i	−0.225048	−	0.692626i	0.773239	−	0.634115i	$-0.218635\pi$
$384$	453.533	+	329.511i	0.0602715	+	0.0437898i
$385$		0			0
$386$	−4704.95	+	3418.35i	−0.620403	+	0.450749i
$387$	3190.43	+	2317.99i	0.419067	+	0.304470i
$388$	−4694.82	−	3410.99i	−0.614287	−	0.446306i
$389$	−10460.1	+	7599.69i	−1.36336	+	0.990538i	−0.365136	+	0.930954i	$0.618977\pi$
$389$	−10460.1	+	7599.69i	−1.36336	+	0.990538i	−0.998223	+	0.0595840i	$0.981023\pi$
$390$		0			0
$391$	4373.49	+	3177.53i	0.565670	+	0.410983i
$392$	1559.32	+	4799.10i	0.200912	+	0.618345i
$393$	5465.17			0.701479
$394$	−2583.07	−	7949.89i	−0.330288	−	1.01652i
$395$		0			0
$396$	144.032	−	443.286i	0.0182775	−	0.0562525i
$397$	628.083	−	1933.04i	0.0794020	−	0.244374i	−0.903474	−	0.428643i	$-0.858992\pi$
$397$	628.083	−	1933.04i	0.0794020	−	0.244374i	0.982876	+	0.184269i	$0.0589917\pi$
$398$	1702.29	−	1236.79i	0.214393	−	0.155765i
$399$	−7035.43			−0.882737
$400$		0			0
$401$	−8972.43			−1.11736			−0.558681	−	0.829383i	$-0.688692\pi$
$401$	−8972.43			−1.11736			−0.558681	+	0.829383i	$0.688692\pi$
$402$	−1665.74	+	1210.23i	−0.206666	+	0.150152i
$403$	−3429.75	+	10555.7i	−0.423941	+	1.30476i
$404$	−377.958	+	1163.23i	−0.0465448	+	0.143250i
$405$		0			0
$406$	1484.05	+	4567.43i	0.181409	+	0.558319i
$407$	1794.22			0.218517
$408$	−315.088	−	969.740i	−0.0382332	−	0.117670i
$409$	7002.65	+	5087.72i	0.846599	+	0.615090i	0.924206	−	0.381894i	$-0.124728\pi$
$409$	7002.65	+	5087.72i	0.846599	+	0.615090i	−0.0776075	+	0.996984i	$0.524728\pi$
$410$		0			0
$411$	8469.85	−	6153.71i	1.01651	−	0.738540i
$412$	1149.79	+	835.370i	0.137490	+	0.0998925i
$413$	1621.59	+	1178.15i	0.193204	+	0.140371i
$414$	−2349.97	+	1707.35i	−0.278973	+	0.202686i
$415$		0			0
$416$	−1104.77	−	802.663i	−0.130206	−	0.0946004i
$417$	−2381.09	−	7328.23i	−0.279622	−	0.860587i
$418$	1534.44			0.179550
$419$	−1774.40	−	5461.04i	−0.206886	−	0.636729i	−0.999631	−	0.0271754i	$-0.991349\pi$
$419$	−1774.40	−	5461.04i	−0.206886	−	0.636729i	0.792745	−	0.609554i	$-0.208651\pi$
$420$		0			0
$421$	1139.25	−	3506.25i	0.131885	−	0.405901i	−0.863207	−	0.504850i	$-0.831548\pi$
$421$	1139.25	−	3506.25i	0.131885	−	0.405901i	0.995093	+	0.0989486i	$0.0315479\pi$
$422$	−820.905	+	2526.49i	−0.0946944	+	0.291440i
$423$	1242.52	−	902.740i	0.142821	−	0.103765i
$424$	3623.83			0.415067
$425$		0			0
$426$	−4724.23			−0.537300
$427$	−3450.21	+	2506.72i	−0.391024	+	0.284096i
$428$	−314.180	+	966.947i	−0.0354824	+	0.109204i
$429$	860.764	−	2649.16i	0.0968720	−	0.298141i
$430$		0			0
$431$	−2973.01	−	9149.99i	−0.332262	−	1.02260i	−0.968055	−	0.250738i	$-0.919327\pi$
$431$	−2973.01	−	9149.99i	−0.332262	−	1.02260i	0.635793	−	0.771859i	$-0.280673\pi$
$432$	2439.90			0.271735
$433$	489.167	+	1505.50i	0.0542907	+	0.167090i	0.974525	−	0.224278i	$-0.0720022\pi$
$433$	489.167	+	1505.50i	0.0542907	+	0.167090i	−0.920235	+	0.391367i	$0.872002\pi$
$434$	−13132.0	−	9540.93i	−1.45243	−	1.05525i
$435$		0			0
$436$	−2894.50	+	2102.98i	−0.317939	+	0.230996i
$437$	−7736.31	−	5620.76i	−0.846860	−	0.615280i
$438$	7412.52	+	5385.51i	0.808639	+	0.587510i
$439$	−1345.66	+	977.681i	−0.146298	+	0.106292i	−0.658527	−	0.752557i	$-0.728820\pi$
$439$	−1345.66	+	977.681i	−0.146298	+	0.106292i	0.512229	+	0.858849i	$0.328820\pi$
$440$		0			0
$441$	3989.73	+	2898.71i	0.430810	+	0.313002i
$442$	767.528	+	2362.21i	0.0825964	+	0.254205i
$443$	−6466.22			−0.693497			−0.346748	−	0.937958i	$-0.612714\pi$
$443$	−6466.22			−0.693497			−0.346748	+	0.937958i	$0.612714\pi$
$444$	651.725	+	2005.80i	0.0696610	+	0.214395i
$445$		0			0
$446$	2760.71	−	8496.59i	0.293102	−	0.902075i
$447$	−530.020	+	1631.23i	−0.0560830	+	0.172606i
$448$	1615.71	−	1173.88i	0.170391	−	0.123796i
$449$	5559.14			0.584303			0.292151	−	0.956372i	$-0.405629\pi$
$449$	5559.14			0.584303			0.292151	+	0.956372i	$0.405629\pi$
$450$		0			0
$451$	4569.26			0.477069
$452$	−4325.78	+	3142.87i	−0.450150	+	0.327053i
$453$	−2622.11	+	8070.01i	−0.271959	+	0.837002i
$454$	1141.58	−	3513.42i	0.118011	−	0.363201i
$455$		0			0
$456$	557.362	+	1715.38i	0.0572387	+	0.176163i
$457$	−1317.36			−0.134843			−0.0674216	−	0.997725i	$-0.521477\pi$
$457$	−1317.36			−0.134843			−0.0674216	+	0.997725i	$0.521477\pi$
$458$	−160.059	−	492.611i	−0.0163299	−	0.0502581i
$459$	−3590.27	−	2608.48i	−0.365096	−	0.265258i
$460$		0			0
$461$	6845.97	−	4973.89i	0.691646	−	0.502510i	−0.185555	−	0.982634i	$-0.559408\pi$
$461$	6845.97	−	4973.89i	0.691646	−	0.502510i	0.877201	+	0.480124i	$0.159408\pi$
$462$	3295.72	+	2394.48i	0.331885	+	0.241129i
$463$	10265.9	+	7458.64i	1.03045	+	0.748666i	0.968399	−	0.249407i	$-0.0802356\pi$
$463$	10265.9	+	7458.64i	1.03045	+	0.748666i	0.0620519	+	0.998073i	$0.480236\pi$
$464$	996.064	−	723.683i	0.0996575	−	0.0724054i
$465$		0			0
$466$	−5482.16	−	3983.02i	−0.544971	−	0.395944i
$467$	253.819	+	781.175i	0.0251506	+	0.0774057i	0.962844	−	0.270058i	$-0.0870429\pi$
$467$	253.819	+	781.175i	0.0251506	+	0.0774057i	−0.937693	+	0.347464i	$0.887043\pi$
$468$	−1334.59			−0.131819
$469$	2266.66	+	6976.07i	0.223166	+	0.686834i
$470$		0			0
$471$	−2433.57	+	7489.76i	−0.238074	+	0.732718i
$472$	158.792	−	488.713i	0.0154852	−	0.0476586i
$473$	6081.68	−	4418.60i	0.591196	−	0.429529i
$474$	−3094.13			−0.299828
$475$		0			0
$476$	−3632.48			−0.349778
$477$	2865.21	−	2081.70i	0.275030	−	0.199821i
$478$	1782.00	−	5484.44i	0.170517	−	0.524796i
$479$	3405.28	−	10480.4i	0.324825	−	0.999710i	−0.646694	−	0.762750i	$-0.723849\pi$
$479$	3405.28	−	10480.4i	0.324825	−	0.999710i	0.971519	−	0.236960i	$-0.0761511\pi$
$480$		0			0
$481$	−1587.55	−	4885.97i	−0.150491	−	0.463163i
$482$	−12642.8			−1.19474
$483$	−7845.17	−	24145.0i	−0.739064	−	2.27460i
$484$	3588.40	+	2607.13i	0.337003	+	0.244847i
$485$		0			0
$486$	3425.07	−	2488.46i	0.319680	−	0.232261i
$487$	−6354.39	−	4616.73i	−0.591262	−	0.429577i	0.251504	−	0.967856i	$-0.419075\pi$
$487$	−6354.39	−	4616.73i	−0.591262	−	0.429577i	−0.842767	+	0.538279i	$0.819075\pi$
$488$	884.524	+	642.644i	0.0820503	+	0.0596130i
$489$	4727.13	−	3434.46i	0.437154	−	0.317611i
$490$		0			0
$491$	−16604.1	−	12063.6i	−1.52614	−	1.10881i	−0.958337	−	0.285641i	$-0.907794\pi$
$491$	−16604.1	−	12063.6i	−1.52614	−	1.10881i	−0.567803	−	0.823164i	$-0.692206\pi$
$492$	1659.72	+	5108.09i	0.152085	+	0.468070i
$493$	−2239.38			−0.204577
$494$	−1357.69	−	4178.54i	−0.123654	−	0.380569i
$495$		0			0
$496$	−1285.93	+	3957.70i	−0.116412	+	0.358278i
$497$	−5200.77	+	16006.3i	−0.469389	+	1.44463i
$498$	−6921.70	+	5028.91i	−0.622829	+	0.452511i
$499$	20672.7			1.85458			0.927291	−	0.374341i	$-0.122131\pi$
$499$	20672.7			1.85458			0.927291	+	0.374341i	$0.122131\pi$
$500$		0			0
$501$	7070.11			0.630477
$502$	−1994.55	+	1449.13i	−0.177333	+	0.128840i
$503$	1003.26	−	3087.72i	0.0889329	−	0.273707i	−0.896692	−	0.442655i	$-0.854037\pi$
$503$	1003.26	−	3087.72i	0.0889329	−	0.273707i	0.985625	+	0.168947i	$0.0540368\pi$
$504$	603.143	−	1856.28i	0.0533058	−	0.164058i
$505$		0			0
$506$	1711.04	+	5266.05i	0.150326	+	0.462657i
$507$	1646.41			0.144220
$508$	−1873.87	−	5767.18i	−0.163660	−	0.503695i
$509$	−43.4872	−	31.5953i	−0.00378691	−	0.00275135i	0.585890	−	0.810390i	$-0.300745\pi$
$509$	−43.4872	−	31.5953i	−0.00378691	−	0.00275135i	−0.589677	+	0.807639i	$0.700745\pi$
$510$		0			0
$511$	26407.1	−	19185.8i	2.28606	−	1.66092i
$512$	−414.217	−	300.946i	−0.0357538	−	0.0259767i
$513$	6350.86	+	4614.17i	0.546583	+	0.397116i
$514$	−10491.2	+	7622.28i	−0.900284	+	0.654094i
$515$		0			0
$516$	7148.73	+	5193.86i	0.609894	+	0.443114i
$517$	−904.691	−	2784.35i	−0.0769599	−	0.236858i
$518$	7513.39			0.637296
$519$	4469.88	+	13756.9i	0.378046	+	1.16351i
$520$		0			0
$521$	1555.45	−	4787.17i	0.130797	−	0.402553i	−0.864115	−	0.503294i	$-0.832121\pi$
$521$	1555.45	−	4787.17i	0.130797	−	0.402553i	0.994913	+	0.100741i	$0.0321214\pi$
$522$	371.830	−	1144.37i	0.0311773	−	0.0959538i
$523$	−4809.07	+	3493.99i	−0.402076	+	0.292126i	−0.770386	−	0.637577i	$-0.779937\pi$
$523$	−4809.07	+	3493.99i	−0.402076	+	0.292126i	0.368310	+	0.929703i	$0.379937\pi$
$524$	−4991.40			−0.416126
$525$		0			0
$526$	−1598.18			−0.132479
$527$	6123.38	−	4448.90i	0.506146	−	0.367736i
$528$	322.730	−	993.262i	0.0266004	−	0.0818677i
$529$	6903.40	−	21246.5i	0.567387	−	1.74624i
$530$		0			0
$531$	−155.189	−	477.624i	−0.0126830	−	0.0390341i
$532$	6425.53			0.523651
$533$	−4042.94	−	12442.9i	−0.328554	−	1.01118i
$534$	7805.61	+	5671.10i	0.632550	+	0.459574i
$535$		0			0
$536$	1521.34	−	1105.32i	0.122597	−	0.0890718i
$537$	9802.77	+	7122.13i	0.787748	+	0.572333i
$538$	−6600.61	−	4795.63i	−0.528945	−	0.384301i
$539$	7605.31	−	5525.58i	0.607762	−	0.441565i
$540$		0			0
$541$	−16453.2	−	11953.9i	−1.30754	−	0.949982i	−0.307539	−	0.951535i	$-0.599505\pi$
$541$	−16453.2	−	11953.9i	−1.30754	−	0.949982i	−0.999999	+	0.00155356i	$0.999505\pi$
$542$	271.659	+	836.080i	0.0215290	+	0.0662596i
$543$	14314.0			1.13126
$544$	287.773	+	885.674i	0.0226804	+	0.0698032i
$545$		0			0
$546$	3604.49	−	11093.5i	0.282524	−	0.869519i
$547$	−5636.82	+	17348.4i	−0.440609	+	1.35606i	0.446619	+	0.894724i	$0.352628\pi$
$547$	−5636.82	+	17348.4i	−0.440609	+	1.35606i	−0.887228	+	0.461331i	$0.847372\pi$
$548$	−7735.60	+	5620.24i	−0.603008	+	0.438111i
$549$	1068.52			0.0830665
$550$		0			0
$551$	3961.26			0.306271
$552$	−5265.53	+	3825.63i	−0.406007	+	0.294981i
$553$	−3406.24	+	10483.3i	−0.261932	+	0.806143i
$554$	39.6601	−	122.061i	0.00304151	−	0.00936080i
$555$		0			0
$556$	2174.67	+	6692.95i	0.165875	+	0.510511i
$557$	2617.19			0.199092			0.0995458	−	0.995033i	$-0.468261\pi$
$557$	2617.19			0.199092			0.0995458	+	0.995033i	$0.468261\pi$
$558$	1256.76	+	3867.90i	0.0953454	+	0.293443i
$559$	−17413.7	−	12651.8i	−1.31757	−	0.957272i
$560$		0			0
$561$	−1536.78	+	1116.54i	−0.115656	+	0.0840290i
$562$	2891.68	+	2100.93i	0.217043	+	0.157691i
$563$	12665.1	+	9201.70i	0.948079	+	0.688820i	0.950352	−	0.311178i	$-0.100723\pi$
$563$	12665.1	+	9201.70i	0.948079	+	0.688820i	−0.00227286	+	0.999997i	$0.500723\pi$
$564$	2784.08	−	2022.75i	0.207856	−	0.151016i
$565$		0			0
$566$	−10102.0	−	7339.50i	−0.750207	−	0.545057i
$567$	4404.62	+	13556.0i	0.326237	+	1.00405i
$568$	4314.69			0.318733
$569$	2209.54	+	6800.27i	0.162792	+	0.501023i	0.998867	−	0.0475929i	$-0.0151550\pi$
$569$	2209.54	+	6800.27i	0.162792	+	0.501023i	−0.836075	+	0.548616i	$0.815155\pi$
$570$		0			0
$571$	2342.24	−	7208.67i	0.171663	−	0.528325i	−0.827802	−	0.561020i	$-0.810409\pi$
$571$	2342.24	−	7208.67i	0.171663	−	0.528325i	0.999465	+	0.0326951i	$0.0104090\pi$
$572$	−786.145	+	2419.51i	−0.0574657	+	0.176861i
$573$	1256.74	−	913.076i	0.0916250	−	0.0665695i
$574$	19134.0			1.39136
$575$		0			0
$576$	−500.383			−0.0361967
$577$	−6272.46	+	4557.21i	−0.452558	+	0.328803i	−0.790605	−	0.612327i	$-0.790234\pi$
$577$	−6272.46	+	4557.21i	−0.452558	+	0.328803i	0.338047	+	0.941129i	$0.390234\pi$
$578$	−2512.98	+	7734.17i	−0.180841	+	0.556573i
$579$	−3935.42	+	12112.0i	−0.282471	+	0.869356i
$580$		0			0
$581$	9418.71	+	28987.8i	0.672554	+	2.06991i
$582$	−12707.9			−0.905083
$583$	−2086.20	−	6420.66i	−0.148202	−	0.456117i
$584$	−6769.93	−	4918.64i	−0.479695	−	0.348519i
$585$		0			0
$586$	−3951.71	+	2871.09i	−0.278573	+	0.202395i
$587$	−6946.97	−	5047.27i	−0.488470	−	0.354894i	0.316126	−	0.948717i	$-0.397618\pi$
$587$	−6946.97	−	5047.27i	−0.488470	−	0.354894i	−0.804596	+	0.593823i	$0.797618\pi$
$588$	8939.70	+	6495.07i	0.626984	+	0.455531i
$589$	−10831.7	+	7869.70i	−0.757747	+	0.550536i
$590$		0			0
$591$	−14808.9	−	10759.3i	−1.03072	−	0.748865i
$592$	−595.227	−	1831.92i	−0.0413238	−	0.127182i
$593$	7557.43			0.523350			0.261675	−	0.965156i	$-0.415725\pi$
$593$	7557.43			0.523350			0.261675	+	0.965156i	$0.415725\pi$
$594$	−1404.62	−	4322.98i	−0.0970241	−	0.298610i
$595$		0			0
$596$	484.073	−	1489.82i	0.0332691	−	0.102392i
$597$	1423.87	−	4382.22i	0.0976133	−	0.300423i
$598$	12826.4	−	9318.93i	0.877108	−	0.637256i
$599$	−1555.67			−0.106115			−0.0530577	−	0.998591i	$-0.516897\pi$
$599$	−1555.67			−0.106115			−0.0530577	+	0.998591i	$0.516897\pi$
$600$		0			0
$601$	3958.20			0.268650			0.134325	−	0.990937i	$-0.457113\pi$
$601$	3958.20			0.268650			0.134325	+	0.990937i	$0.457113\pi$
$602$	25467.3	−	18503.1i	1.72420	−	1.25271i
$603$	567.915	−	1747.86i	0.0383537	−	0.118041i
$604$	2394.80	−	7370.42i	0.161329	−	0.496520i
$605$		0			0
$606$	827.665	+	2547.29i	0.0554812	+	0.170753i
$607$	23128.2			1.54653			0.773266	−	0.634081i	$-0.218622\pi$
$607$	23128.2			1.54653			0.773266	+	0.634081i	$0.218622\pi$
$608$	−509.045	−	1566.68i	−0.0339547	−	0.104502i
$609$	8508.14	+	6181.52i	0.566120	+	0.411310i
$610$		0			0
$611$	−6781.78	+	4927.25i	−0.449037	+	0.326244i
$612$	736.305	+	534.957i	0.0486329	+	0.0353339i
$613$	−7510.33	−	5456.58i	−0.494844	−	0.359525i	0.312200	−	0.950016i	$-0.398934\pi$
$613$	−7510.33	−	5456.58i	−0.494844	−	0.359525i	−0.807044	+	0.590491i	$0.798934\pi$
$614$	10327.4	−	7503.26i	0.678792	−	0.493171i
$615$		0			0
$616$	−3010.02	−	2186.91i	−0.196878	−	0.143041i
$617$	1709.05	+	5259.91i	0.111513	+	0.343203i	0.991204	−	0.132344i	$-0.0422503\pi$
$617$	1709.05	+	5259.91i	0.111513	+	0.343203i	−0.879691	+	0.475547i	$0.842250\pi$
$618$	3112.23			0.202576
$619$	−4872.99	−	14997.5i	−0.316417	−	0.973831i	−0.975167	−	0.221469i	$-0.928915\pi$
$619$	−4872.99	−	14997.5i	−0.316417	−	0.973831i	0.658750	−	0.752361i	$-0.271085\pi$
$620$		0			0
$621$	−8753.60	+	26940.8i	−0.565652	+	1.74090i
$622$	1900.21	−	5848.26i	0.122495	−	0.377000i
$623$	27807.4	−	20203.3i	1.78825	−	1.29924i
$624$	−2990.38			−0.191844
$625$		0			0
$626$	11112.5			0.709496
$627$	2718.43	−	1975.06i	0.173148	−	0.125799i
$628$	2222.61	−	6840.48i	0.141229	−	0.434657i
$629$	−1082.63	+	3331.99i	−0.0686285	+	0.211217i
$630$		0			0
$631$	6785.23	+	20882.8i	0.428075	+	1.31748i	0.900019	+	0.435852i	$0.143553\pi$
$631$	6785.23	+	20882.8i	0.428075	+	1.31748i	−0.471943	+	0.881629i	$0.656447\pi$
$632$	2825.90			0.177861
$633$	1797.65	+	5532.59i	0.112875	+	0.347395i
$634$	5383.88	+	3911.62i	0.337258	+	0.245032i
$635$		0			0
$636$	6420.02	−	4664.42i	0.400268	−	0.290812i
$637$	−21776.4	−	15821.5i	−1.35449	−	0.984096i
$638$	−1855.64	−	1348.20i	−0.115149	−	0.0836610i
$639$	3411.45	−	2478.57i	0.211197	−	0.153444i
$640$		0			0
$641$	23240.6	+	16885.3i	1.43205	+	1.04045i	0.989630	+	0.143643i	$0.0458817\pi$
$641$	23240.6	+	16885.3i	1.43205	+	1.04045i	0.442425	+	0.896806i	$0.354118\pi$
$642$	688.003	+	2117.45i	0.0422949	+	0.130170i
$643$	−19485.8			−1.19509			−0.597547	−	0.801834i	$-0.703858\pi$
$643$	−19485.8			−1.19509			−0.597547	+	0.801834i	$0.703858\pi$
$644$	7165.08	+	22051.8i	0.438422	+	1.34932i
$645$		0			0
$646$	−925.877	+	2849.56i	−0.0563903	+	0.173552i
$647$	5592.78	−	17212.8i	0.339838	−	1.04591i	−0.624452	−	0.781063i	$-0.714678\pi$
$647$	5592.78	−	17212.8i	0.339838	−	1.04591i	0.964290	−	0.264850i	$-0.0853223\pi$
$648$	2956.29	−	2147.87i	0.179219	−	0.130211i
$649$	−957.312			−0.0579010
$650$		0			0
$651$	−35545.4			−2.13999
$652$	−4317.34	+	3136.73i	−0.259325	+	0.188411i
$653$	−8126.61	+	25011.1i	−0.487012	+	1.49887i	0.342033	+	0.939688i	$0.388885\pi$
$653$	−8126.61	+	25011.1i	−0.487012	+	1.49887i	−0.829045	+	0.559181i	$0.811115\pi$
$654$	−2421.08	+	7451.33i	−0.144758	+	0.445520i
$655$		0			0
$656$	−1515.84	−	4665.27i	−0.0902188	−	0.277665i
$657$	−8178.22			−0.485636
$658$	−3788.44	−	11659.6i	−0.224451	−	0.690789i
$659$	832.956	+	605.178i	0.0492373	+	0.0357730i	0.612132	−	0.790756i	$-0.290312\pi$
$659$	832.956	+	605.178i	0.0492373	+	0.0357730i	−0.562894	+	0.826529i	$0.690312\pi$
$660$		0			0
$661$	3435.86	−	2496.30i	0.202178	−	0.146891i	−0.482090	−	0.876122i	$-0.660122\pi$
$661$	3435.86	−	2496.30i	0.202178	−	0.146891i	0.684267	+	0.729231i	$0.260122\pi$
$662$	1395.03	+	1013.55i	0.0819024	+	0.0595056i
$663$	4400.29	+	3197.00i	0.257757	+	0.187272i
$664$	6321.66	−	4592.95i	0.369470	−	0.268435i
$665$		0			0
$666$	−1522.97	−	1106.50i	−0.0886092	−	0.0643784i
$667$	4417.18	+	13594.7i	0.256422	+	0.789187i
$668$	−6457.21			−0.374007
$669$	−6045.50	−	18606.1i	−0.349376	−	1.07527i
$670$		0			0
$671$	629.420	−	1937.15i	0.0362123	−	0.111450i
$672$	1351.45	−	4159.33i	0.0775793	−	0.238764i
$673$	−11280.4	+	8195.71i	−0.646105	+	0.469422i	−0.861942	−	0.507007i	$-0.830752\pi$
$673$	−11280.4	+	8195.71i	−0.646105	+	0.469422i	0.215837	+	0.976429i	$0.430752\pi$
$674$	−11456.0			−0.654699
$675$		0			0
$676$	−1503.68			−0.0855532
$677$	10884.1	−	7907.76i	0.617887	−	0.448921i	−0.234296	−	0.972165i	$-0.575278\pi$
$677$	10884.1	−	7907.76i	0.617887	−	0.448921i	0.852183	+	0.523244i	$0.175278\pi$
$678$	−3618.27	+	11135.9i	−0.204954	+	0.630784i
$679$	−13989.7	+	43056.0i	−0.790688	+	2.43349i
$680$		0			0
$681$	−2499.87	−	7693.82i	−0.140669	−	0.432934i
$682$	7752.51			0.435277
$683$	5946.43	+	18301.2i	0.333139	+	1.02530i	0.967632	+	0.252367i	$0.0812089\pi$
$683$	5946.43	+	18301.2i	0.333139	+	1.02530i	−0.634493	+	0.772928i	$0.718791\pi$
$684$	−1302.46	−	946.290i	−0.0728080	−	0.0528981i
$685$		0			0
$686$	14529.2	−	10556.1i	0.808642	−	0.587513i
$687$	−917.629	−	666.697i	−0.0509603	−	0.0370248i
$688$	−6529.01	−	4743.61i	−0.361797	−	0.262861i
$689$	−15638.7	+	11362.1i	−0.864710	+	0.628249i
$690$		0			0
$691$	−18585.0	−	13502.8i	−1.02316	−	0.743373i	−0.0562356	−	0.998418i	$-0.517910\pi$
$691$	−18585.0	−	13502.8i	−1.02316	−	0.743373i	−0.966929	+	0.255045i	$0.917910\pi$
$692$	−4082.39	−	12564.3i	−0.224262	−	0.690206i
$693$	−3636.17			−0.199317
$694$	1431.13	+	4404.58i	0.0782783	+	0.240916i
$695$		0			0
$696$	833.150	−	2564.17i	0.0453743	−	0.139648i
$697$	−2757.09	+	8485.44i	−0.149831	+	0.461132i
$698$	7206.96	−	5236.16i	0.390813	−	0.283942i
$699$	−14839.0			−0.802953
$700$		0			0
$701$	−4226.67			−0.227730			−0.113865	−	0.993496i	$-0.536323\pi$
$701$	−4226.67			−0.227730			−0.113865	+	0.993496i	$0.536323\pi$
$702$	−10529.4	+	7650.05i	−0.566106	+	0.411300i
$703$	1915.08	−	5894.00i	0.102743	−	0.316211i
$704$	−294.753	+	907.156i	−0.0157797	+	0.0485650i
$705$		0			0
$706$	4692.01	+	14440.5i	0.250122	+	0.769796i
$707$	9541.71			0.507572
$708$	−347.729	−	1070.20i	−0.0184583	−	0.0568088i
$709$	−18626.9	−	13533.2i	−0.986668	−	0.716856i	−0.0274791	−	0.999622i	$-0.508748\pi$
$709$	−18626.9	−	13533.2i	−0.986668	−	0.716856i	−0.959189	+	0.282766i	$0.908748\pi$
$710$		0			0
$711$	2234.33	−	1623.34i	0.117854	−	0.0856257i
$712$	−7128.94	−	5179.48i	−0.375236	−	0.272625i
$713$	−39086.5	−	28398.0i	−2.05302	−	1.49160i
$714$	−6435.35	+	4675.56i	−0.337307	+	0.245068i
$715$		0			0
$716$	−8952.98	−	6504.72i	−0.467302	−	0.339515i
$717$	−3902.29	−	12010.0i	−0.203255	−	0.625554i
$718$	−18627.8			−0.968222
$719$	−1901.30	−	5851.59i	−0.0986181	−	0.303515i	0.889562	−	0.456815i	$-0.151010\pi$
$719$	−1901.30	−	5851.59i	−0.0986181	−	0.303515i	−0.988180	+	0.153300i	$0.951010\pi$
$720$		0			0
$721$	3426.16	−	10544.7i	0.176972	−	0.544665i
$722$	−2601.30	+	8005.98i	−0.134086	+	0.412676i
$723$	−22398.2	+	16273.3i	−1.15214	+	0.837080i
$724$	−13073.2			−0.671078
$725$		0			0
$726$	9713.04			0.496536
$727$	−23394.3	+	16997.0i	−1.19346	+	0.867101i	−0.993626	−	0.112729i	$-0.964041\pi$
$727$	−23394.3	+	16997.0i	−1.19346	+	0.867101i	−0.199836	+	0.979829i	$0.564041\pi$
$728$	−3292.02	+	10131.8i	−0.167597	+	0.515810i
$729$	6675.94	−	20546.4i	0.339173	−	1.04387i
$730$		0			0
$731$	4535.97	+	13960.3i	0.229506	+	0.706346i
$732$	2394.22			0.120892
$733$	3372.68	+	10380.1i	0.169949	+	0.523051i	0.999367	−	0.0355788i	$-0.0113275\pi$
$733$	3372.68	+	10380.1i	0.169949	+	0.523051i	−0.829417	+	0.558629i	$0.811327\pi$
$734$	12472.3	+	9061.65i	0.627194	+	0.455683i
$735$		0			0
$736$	4809.06	−	3493.99i	0.240848	−	0.174987i
$737$	−2834.21	−	2059.17i	−0.141655	−	0.102918i
$738$	−3878.47	−	2817.87i	−0.193453	−	0.140552i
$739$	11697.6	−	8498.82i	0.582278	−	0.423050i	−0.257266	−	0.966341i	$-0.582822\pi$
$739$	11697.6	−	8498.82i	0.582278	−	0.423050i	0.839545	+	0.543290i	$0.182822\pi$
$740$		0			0
$741$	−7783.72	−	5655.20i	−0.385887	−	0.280363i
$742$	−8736.06	−	26886.8i	−0.432225	−	1.33025i
$743$	−22720.1			−1.12183			−0.560915	−	0.827874i	$-0.689550\pi$
$743$	−22720.1			−1.12183			−0.560915	+	0.827874i	$0.689550\pi$
$744$	2815.98	+	8666.71i	0.138762	+	0.427066i
$745$		0			0
$746$	−5519.15	+	16986.2i	−0.270872	+	0.833659i
$747$	2359.87	−	7262.93i	0.115586	−	0.355739i
$748$	1403.56	−	1019.75i	0.0686086	−	0.0498471i
$749$	7931.62			0.386936
$750$		0			0
$751$	400.556			0.0194627			0.00973135	−	0.999953i	$-0.496902\pi$
$751$	400.556			0.0194627			0.00973135	+	0.999953i	$0.496902\pi$
$752$	−2542.73	+	1847.40i	−0.123303	+	0.0895847i
$753$	−1668.33	+	5134.59i	−0.0807401	+	0.248493i
$754$	−2029.49	+	6246.12i	−0.0980233	+	0.301685i
$755$		0			0
$756$	−5881.92	−	18102.7i	−0.282968	−	0.870885i
$757$	−8445.77			−0.405504			−0.202752	−	0.979230i	$-0.564989\pi$
$757$	−8445.77			−0.405504			−0.202752	+	0.979230i	$0.564989\pi$
$758$	−2623.00	−	8072.77i	−0.125688	−	0.386829i
$759$	9809.52	+	7127.03i	0.469121	+	0.340837i
$760$		0			0
$761$	−7569.25	+	5499.38i	−0.360559	+	0.261961i	−0.753285	−	0.657694i	$-0.771532\pi$
$761$	−7569.25	+	5499.38i	−0.360559	+	0.261961i	0.392726	+	0.919655i	$0.371532\pi$
$762$	−10743.0	−	7805.26i	−0.510733	−	0.371069i
$763$	22580.8	+	16405.9i	1.07140	+	0.778419i
$764$	−1147.80	+	833.922i	−0.0543531	+	0.0394898i
$765$		0			0
$766$	8832.39	+	6417.11i	0.416615	+	0.302689i
$767$	847.041	+	2606.92i	0.0398760	+	0.122726i
$768$	−1121.20			−0.0526793
$769$	−3534.39	−	10877.7i	−0.165739	−	0.510092i	0.833351	−	0.552744i	$-0.186419\pi$
$769$	−3534.39	−	10877.7i	−0.165739	−	0.510092i	−0.999090	+	0.0426520i	$0.986419\pi$
$770$		0			0
$771$	−8775.26	+	27007.5i	−0.409901	+	1.26154i
$772$	3594.26	−	11062.0i	0.167565	−	0.515713i
$773$	−3042.74	+	2210.68i	−0.141578	+	0.102862i	−0.656320	−	0.754483i	$-0.727888\pi$
$773$	−3042.74	+	2210.68i	−0.141578	+	0.102862i	0.514742	+	0.857345i	$0.327888\pi$
$774$	−7887.19			−0.366278
$775$		0			0
$776$	11606.2			0.536907
$777$	13310.8	−	9670.89i	0.614573	−	0.446514i
$778$	7990.78	−	24593.1i	0.368231	−	1.13330i
$779$	4877.04	−	15010.0i	0.224311	−	0.690357i
$780$		0			0
$781$	−2483.92	−	7644.72i	−0.113805	−	0.350256i
$782$	−10811.9			−0.494413
$783$	−3626.13	−	11160.1i	−0.165501	−	0.509360i
$784$	−8164.72	−	5932.01i	−0.371935	−	0.270227i
$785$		0			0
$786$	−8842.83	+	6424.69i	−0.401289	+	0.291554i
$787$	18476.0	+	13423.6i	0.836848	+	0.608005i	0.921488	−	0.388406i	$-0.126974\pi$
$787$	18476.0	+	13423.6i	0.836848	+	0.608005i	−0.0846407	+	0.996412i	$0.526974\pi$
$788$	13525.2	+	9826.60i	0.611439	+	0.444236i
$789$	−2831.36	+	2057.10i	−0.127756	+	0.0928198i
$790$		0			0
$791$	33746.6	+	24518.4i	1.51693	+	1.10211i
$792$	288.065	+	886.573i	0.0129242	+	0.0397765i
$793$	−5832.12			−0.261166
$794$	1256.17	+	3866.08i	0.0561457	+	0.172799i
$795$		0			0
$796$	−1300.44	+	4002.33i	−0.0579055	+	0.178215i
$797$	49.8475	−	153.415i	0.00221542	−	0.00681836i	−0.949943	−	0.312424i	$-0.898859\pi$
$797$	49.8475	−	153.415i	0.00221542	−	0.00681836i	0.952158	+	0.305606i	$0.0988590\pi$
$798$	11383.6	−	8270.65i	0.504980	−	0.366889i
$799$	5716.62			0.253116
$800$		0			0
$801$	−8611.91			−0.379884
$802$	14517.7	−	10547.7i	0.639199	−	0.464405i
$803$	−4817.42	+	14826.5i	−0.211710	+	0.651576i
$804$	1272.51	−	3916.40i	0.0558185	−	0.171792i
$805$		0			0
$806$	−6859.51	−	21111.4i	−0.299772	−	0.922602i
$807$	−17866.4			−0.779342
$808$	−755.915	−	2326.47i	−0.0329121	−	0.101293i
$809$	−8390.60	−	6096.13i	−0.364645	−	0.264930i	0.390342	−	0.920670i	$-0.372357\pi$
$809$	−8390.60	−	6096.13i	−0.364645	−	0.264930i	−0.754987	+	0.655740i	$0.772357\pi$
$810$		0			0
$811$	−34337.8	+	24947.9i	−1.48676	+	1.08020i	−0.511463	+	0.859305i	$0.670896\pi$
$811$	−34337.8	+	24947.9i	−1.48676	+	1.08020i	−0.975299	+	0.220890i	$0.929104\pi$
$812$	−7770.57	−	5645.65i	−0.335830	−	0.243994i
$813$	1557.44	+	1131.54i	0.0671854	+	0.0488130i
$814$	−2903.11	+	2109.23i	−0.125005	+	0.0908214i
$815$		0			0
$816$	1649.82	+	1198.66i	0.0707785	+	0.0514236i
$817$	−8023.72	−	24694.5i	−0.343592	−	1.05747i
$818$	−17311.5			−0.739954
$819$	3217.32	+	9901.91i	0.137268	+	0.422467i
$820$		0			0
$821$	8552.50	−	26321.9i	0.363562	−	1.11893i	−0.587315	−	0.809359i	$-0.699815\pi$
$821$	8552.50	−	26321.9i	0.363562	−	1.11893i	0.950877	−	0.309570i	$-0.100185\pi$
$822$	−6470.39	+	19913.8i	−0.274551	+	0.844980i
$823$	−9200.39	+	6684.48i	−0.389679	+	0.283118i	−0.765324	−	0.643645i	$-0.777421\pi$
$823$	−9200.39	+	6684.48i	−0.389679	+	0.283118i	0.375645	+	0.926764i	$0.377421\pi$
$824$	−2842.43			−0.120171
$825$		0			0
$826$	−4008.79			−0.168866
$827$	−2678.57	+	1946.09i	−0.112628	+	0.0818287i	−0.642673	−	0.766140i	$-0.722175\pi$
$827$	−2678.57	+	1946.09i	−0.112628	+	0.0818287i	0.530046	+	0.847969i	$0.322175\pi$
$828$	1795.22	−	5525.12i	0.0753480	−	0.231897i
$829$	−7520.64	+	23146.2i	−0.315082	+	0.969722i	0.660639	+	0.750704i	$0.270285\pi$
$829$	−7520.64	+	23146.2i	−0.315082	+	0.969722i	−0.975721	+	0.219018i	$0.929715\pi$
$830$		0			0
$831$	−86.8491	−	267.294i	−0.00362547	−	0.0111580i
$832$	2731.14			0.113804
$833$	5672.36	+	17457.7i	0.235937	+	0.726139i
$834$	12467.5	+	9058.19i	0.517644	+	0.376090i
$835$		0			0
$836$	−2482.77	+	1803.84i	−0.102713	+	0.0746257i
$837$	32086.7	+	23312.4i	1.32506	+	0.962716i
$838$	9290.88	+	6750.22i	0.382993	+	0.278261i
$839$	11147.2	−	8098.89i	0.458692	−	0.333260i	−0.334326	−	0.942458i	$-0.608509\pi$
$839$	11147.2	−	8098.89i	0.458692	−	0.333260i	0.793018	+	0.609198i	$0.208509\pi$
$840$		0			0
$841$	14940.7	+	10855.0i	0.612598	+	0.445079i
$842$	2278.50	+	7012.51i	0.0932570	+	0.287015i
$843$	7827.16			0.319789
$844$	−1641.81	−	5052.97i	−0.0669591	−	0.206079i
$845$		0			0
$846$	−949.197	+	2921.33i	−0.0385746	+	0.118720i
$847$	10692.8	−	32909.1i	0.433777	−	1.33503i
$848$	−5863.47	+	4260.06i	−0.237444	+	0.172513i
$849$	−27343.8			−1.10535
$850$		0			0
$851$	22363.2			0.900822
$852$	7643.97	−	5553.67i	0.307369	−	0.223316i
$853$	4042.80	−	12442.5i	0.162278	−	0.499439i	−0.836548	−	0.547894i	$-0.815430\pi$
$853$	4042.80	−	12442.5i	0.162278	−	0.499439i	0.998825	+	0.0484548i	$0.0154297\pi$
$854$	2635.73	−	8111.93i	0.105612	−	0.325040i
$855$		0			0
$856$	−628.360	−	1933.89i	−0.0250898	−	0.0772186i
$857$	−17624.7			−0.702508			−0.351254	−	0.936280i	$-0.614245\pi$
$857$	−17624.7			−0.702508			−0.351254	+	0.936280i	$0.614245\pi$
$858$	1721.53	+	5298.32i	0.0684988	+	0.210818i
$859$	834.395	+	606.224i	0.0331423	+	0.0240793i	0.604233	−	0.796808i	$-0.293480\pi$
$859$	834.395	+	606.224i	0.0331423	+	0.0240793i	−0.571091	+	0.820887i	$0.693480\pi$
$860$		0			0
$861$	33898.1	−	24628.4i	1.34175	−	0.974836i
$862$	15566.9	+	11310.0i	0.615093	+	0.446891i
$863$	29957.6	+	21765.5i	1.18166	+	0.858523i	0.992357	−	0.123396i	$-0.0393786\pi$
$863$	29957.6	+	21765.5i	1.18166	+	0.858523i	0.189299	+	0.981920i	$0.439379\pi$
$864$	−3947.83	+	2868.27i	−0.155449	+	0.112940i
$865$		0			0
$866$	−2561.31	−	1860.90i	−0.100505	−	0.0730209i
$867$	5503.02	+	16936.6i	0.215562	+	0.663432i
$868$	32464.0			1.26947
$869$	−1626.84	−	5006.91i	−0.0635062	−	0.195452i
$870$		0			0
$871$	−3099.74	+	9540.02i	−0.120586	+	0.371127i
$872$	2211.20	−	6805.38i	0.0858724	−	0.264288i
$873$	9176.59	−	6667.18i	0.355762	−	0.258477i
$874$	19125.2			0.740183
$875$		0			0
$876$	−18324.7			−0.706776
$877$	−34138.6	+	24803.1i	−1.31446	+	0.955008i	−0.314472	+	0.949267i	$0.601827\pi$
$877$	−34138.6	+	24803.1i	−1.31446	+	0.955008i	−0.999984	+	0.00574075i	$0.998173\pi$
$878$	1027.99	−	3163.84i	0.0395138	−	0.121611i
$879$	−3305.38	+	10172.9i	−0.126835	+	0.390357i
$880$		0			0
$881$	−2050.56	−	6310.96i	−0.0784165	−	0.241341i	0.904162	−	0.427190i	$-0.140497\pi$
$881$	−2050.56	−	6310.96i	−0.0784165	−	0.241341i	−0.982578	+	0.185849i	$0.940497\pi$
$882$	−9863.15			−0.376542
$883$	1739.74	+	5354.36i	0.0663044	+	0.204064i	0.978720	−	0.205202i	$-0.0657850\pi$
$883$	1739.74	+	5354.36i	0.0663044	+	0.204064i	−0.912415	+	0.409266i	$0.865785\pi$
$884$	−4018.83	−	2919.85i	−0.152905	−	0.111092i
$885$		0			0
$886$	10462.6	−	7601.49i	0.396723	−	0.288236i
$887$	26624.6	+	19343.9i	1.00786	+	0.732250i	0.963758	−	0.266777i	$-0.0859589\pi$
$887$	26624.6	+	19343.9i	1.00786	+	0.732250i	0.0440972	+	0.999027i	$0.485959\pi$
$888$	−3412.47	−	2479.31i	−0.128959	−	0.0936938i
$889$	−38271.9	+	27806.2i	−1.44387	+	1.04903i
$890$		0			0
$891$	−5507.49	−	4001.42i	−0.207079	−	0.150452i
$892$	5521.42	+	16993.2i	0.207254	+	0.637863i
$893$	−10112.2			−0.378938
$894$	−1060.04	−	3262.47i	−0.0396567	−	0.122051i
$895$		0			0
$896$	−1234.29	+	3798.76i	−0.0460210	+	0.141638i
$897$	10728.6	−	33019.1i	0.399349	−	1.22907i
$898$	−8994.87	+	6535.16i	−0.334257	+	0.242852i
$899$	20013.6			0.742483
$900$		0			0
$901$	13182.4			0.487425
$902$	−7393.22	+	5371.49i	−0.272913	+	0.198283i
$903$	21302.0	−	65560.7i	0.785033	−	2.41608i
$904$	3304.60	−	10170.5i	0.121581	−	0.374189i
$905$		0			0
$906$	−5244.21	−	16140.0i	−0.192304	−	0.591850i
$907$	23738.5			0.869046			0.434523	−	0.900661i	$-0.356917\pi$
$907$	23738.5			0.869046			0.434523	+	0.900661i	$0.356917\pi$
$908$	2283.16	+	7026.85i	0.0834464	+	0.256822i
$909$	−1934.11	−	1405.21i	−0.0705724	−	0.0512738i
$910$		0			0
$911$	−10584.2	+	7689.85i	−0.384928	+	0.279666i	−0.763374	−	0.645957i	$-0.776459\pi$
$911$	−10584.2	+	7689.85i	−0.384928	+	0.279666i	0.378446	+	0.925623i	$0.376459\pi$
$912$	−2918.39	−	2120.33i	−0.105962	−	0.0769859i
$913$	−11777.1	−	8556.53i	−0.426904	−	0.310164i
$914$	2131.53	−	1548.65i	0.0771386	−	0.0560445i
$915$		0			0
$916$	838.081	+	608.901i	0.0302303	+	0.0219636i
$917$	12032.9	+	37033.5i	0.433328	+	1.33364i
$918$	8875.62			0.319106
$919$	−983.027	−	3025.45i	−0.0352852	−	0.108597i	0.931863	−	0.362811i	$-0.118183\pi$
$919$	−983.027	−	3025.45i	−0.0352852	−	0.108597i	−0.967148	+	0.254215i	$0.918183\pi$
$920$		0			0
$921$	8638.24	−	26585.8i	0.309055	−	0.951174i
$922$	−5229.86	+	16095.8i	−0.186807	+	0.574933i
$923$	−18620.1	+	13528.3i	−0.664017	+	0.482436i
$924$	−8147.48			−0.290078
$925$		0			0
$926$	−25378.8			−0.900647
$927$	−2247.40	+	1632.83i	−0.0796270	+	0.0578524i
$928$	−760.925	+	2341.89i	−0.0269166	+	0.0828407i
$929$	12964.0	−	39899.2i	0.457843	−	1.40910i	−0.409921	−	0.912121i	$-0.634444\pi$
$929$	12964.0	−	39899.2i	0.457843	−	1.40910i	0.867764	−	0.496976i	$-0.165556\pi$
$930$		0			0
$931$	−10033.9	−	30881.1i	−0.353220	−	1.08710i
$932$	13552.7			0.476322
$933$	−4161.16	−	12806.7i	−0.146013	−	0.449382i
$934$	−1329.01	−	965.585i	−0.0465596	−	0.0338275i
$935$		0			0
$936$	2159.41	−	1568.90i	0.0754085	−	0.0547875i
$937$	−3361.80	−	2442.49i	−0.117210	−	0.0851577i	0.527636	−	0.849470i	$-0.323078\pi$
$937$	−3361.80	−	2442.49i	−0.117210	−	0.0851577i	−0.644846	+	0.764313i	$0.723078\pi$
$938$	−11868.4	−	8622.90i	−0.413131	−	0.300157i
$939$	19687.0	−	14303.5i	0.684198	−	0.497099i
$940$		0			0
$941$	−14793.5	−	10748.1i	−0.512490	−	0.372346i	0.301277	−	0.953537i	$-0.402587\pi$
$941$	−14793.5	−	10748.1i	−0.512490	−	0.372346i	−0.813767	+	0.581191i	$0.802587\pi$
$942$	−4867.14	−	14979.5i	−0.168344	−	0.518110i
$943$	56951.2			1.96669
$944$	317.585	+	977.426i	0.0109497	+	0.0336997i
$945$		0			0
$946$	−4645.99	+	14298.9i	−0.159677	+	0.491434i
$947$	−14999.2	+	46162.9i	−0.514688	+	1.58405i	0.269160	+	0.963096i	$0.413254\pi$
$947$	−14999.2	+	46162.9i	−0.514688	+	1.58405i	−0.783848	+	0.620953i	$0.786746\pi$
$948$	5006.41	−	3637.37i	0.171520	−	0.124616i
$949$	44637.6			1.52687
$950$		0			0
$951$	14573.0			0.496911
$952$	5877.48	−	4270.24i	0.200095	−	0.145377i
$953$	10609.5	−	32652.7i	0.360625	−	1.10989i	−0.592051	−	0.805900i	$-0.701682\pi$
$953$	10609.5	−	32652.7i	0.360625	−	1.10989i	0.952676	−	0.303988i	$-0.0983184\pi$
$954$	−2188.83	+	6736.52i	−0.0742830	+	0.228620i
$955$		0			0
$956$	3564.01	+	10968.9i	0.120573	+	0.371087i
$957$	−5022.81			−0.169660
$958$	6810.57	+	20960.8i	0.229686	+	0.706902i
$959$	60347.6	+	43845.1i	2.03204	+	1.47636i
$960$		0			0
$961$	−30624.1	+	22249.7i	−1.02797	+	0.746861i
$962$	8312.51	+	6039.39i	0.278593	+	0.202409i
$963$	−1607.74	−	1168.09i	−0.0537993	−	0.0390875i
$964$	20456.5	−	14862.5i	0.683465	−	0.496566i
$965$		0			0
$966$	41077.9	+	29844.8i	1.36818	+	0.994038i
$967$	−2010.06	−	6186.33i	−0.0668451	−	0.205728i	0.912055	−	0.410068i	$-0.134495\pi$
$967$	−2010.06	−	6186.33i	−0.0668451	−	0.205728i	−0.978900	+	0.204340i	$0.934495\pi$
$968$	−8871.02			−0.294551
$969$	2027.52	+	6240.06i	0.0672170	+	0.206873i
$970$		0			0
$971$	8528.41	−	26247.7i	0.281864	−	0.867487i	−0.705457	−	0.708752i	$-0.749258\pi$
$971$	8528.41	−	26247.7i	0.281864	−	0.867487i	0.987321	−	0.158735i	$-0.0507416\pi$
$972$	−2616.52	+	8052.83i	−0.0863426	+	0.265735i
$973$	44415.5	−	32269.8i	1.46341	−	1.06323i
$974$	15708.9			0.516782
$975$		0			0
$976$	−2186.66			−0.0717146
$977$	16486.8	−	11978.4i	0.539877	−	0.392244i	−0.284162	−	0.958776i	$-0.591715\pi$
$977$	16486.8	−	11978.4i	0.539877	−	0.392244i	0.824039	+	0.566533i	$0.191715\pi$
$978$	−3611.21	+	11114.1i	−0.118071	+	0.363386i
$979$	−5072.89	+	15612.8i	−0.165608	+	0.509689i
$980$		0			0
$981$	−2161.03	−	6650.96i	−0.0703327	−	0.216462i
$982$	41047.7			1.33390
$983$	1573.89	+	4843.95i	0.0510675	+	0.157170i	0.973338	−	0.229375i	$-0.0736683\pi$
$983$	1573.89	+	4843.95i	0.0510675	+	0.157170i	−0.922270	+	0.386545i	$0.873668\pi$
$984$	−8690.40	−	6313.94i	−0.281544	−	0.204554i
$985$		0			0
$986$	3623.39	−	2632.54i	0.117031	−	0.0850277i
$987$	−21719.3	−	15780.0i	−0.700440	−	0.508900i
$988$	7108.95	+	5164.96i	0.228913	+	0.166315i
$989$	75801.9	−	55073.3i	2.43717	−	1.77071i
$990$		0			0
$991$	−1089.49	−	791.563i	−0.0349232	−	0.0253732i	0.570187	−	0.821515i	$-0.306871\pi$
$991$	−1089.49	−	791.563i	−0.0349232	−	0.0253732i	−0.605110	+	0.796142i	$0.706871\pi$
$992$	−2571.87	−	7915.39i	−0.0823154	−	0.253341i
$993$	3776.05			0.120674
$994$	−10401.5	−	32012.7i	−0.331908	−	1.02151i
$995$		0			0
$996$	5287.71	−	16273.9i	0.168220	−	0.517729i
$997$	6923.45	−	21308.2i	0.219928	−	0.676868i	−0.778839	−	0.627224i	$-0.784191\pi$
$997$	6923.45	−	21308.2i	0.219928	−	0.676868i	0.998767	−	0.0496443i	$-0.0158088\pi$
$998$	−33449.1	+	24302.2i	−1.06093	+	0.770814i
$999$	−18358.3			−0.581411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.4.d.c.51.3		32
5.2	odd	4		250.4.e.b.199.3		32
5.3	odd	4		50.4.e.a.39.6	yes	32
5.4	even	2		250.4.d.d.51.6		32
25.4	even	10		1250.4.a.m.1.12		16
25.9	even	10		250.4.d.d.201.6		32
25.12	odd	20		50.4.e.a.9.6	✓	32
25.13	odd	20		250.4.e.b.49.3		32
25.16	even	5	inner	250.4.d.c.201.3		32
25.21	even	5		1250.4.a.n.1.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.e.a.9.6	✓	32	25.12	odd	20
50.4.e.a.39.6	yes	32	5.3	odd	4
250.4.d.c.51.3		32	1.1	even	1	trivial
250.4.d.c.201.3		32	25.16	even	5	inner
250.4.d.d.51.6		32	5.4	even	2
250.4.d.d.201.6		32	25.9	even	10
250.4.e.b.49.3		32	25.13	odd	20
250.4.e.b.199.3		32	5.2	odd	4
1250.4.a.m.1.12		16	25.4	even	10
1250.4.a.n.1.5		16	25.21	even	5

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	250.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.61803 + 1.17557i) q^{2} +(-1.35339 + 4.16531i) q^{3} +(1.23607 - 3.80423i) q^{4} +(-2.70679 - 8.33063i) q^{6} -31.2051 q^{7} +(2.47214 + 7.60845i) q^{8} +(6.32528 + 4.59559i) q^{9} +O(q^{10})\)	\(q+(-1.61803 + 1.17557i) q^{2} +(-1.35339 + 4.16531i) q^{3} +(1.23607 - 3.80423i) q^{4} +(-2.70679 - 8.33063i) q^{6} -31.2051 q^{7} +(2.47214 + 7.60845i) q^{8} +(6.32528 + 4.59559i) q^{9} +(12.0574 - 8.76021i) q^{11} +(14.1729 + 10.2972i) q^{12} +(-34.5241 - 25.0832i) q^{13} +(50.4909 - 36.6838i) q^{14} +(-12.9443 - 9.40456i) q^{16} +(8.99290 + 27.6773i) q^{17} -15.6370 q^{18} +(-15.9076 - 48.9587i) q^{19} +(42.2328 - 129.979i) q^{21} +(-9.21103 + 28.3486i) q^{22} +(150.283 - 109.187i) q^{23} -35.0374 q^{24} +85.3482 q^{26} +(-123.370 + 89.6334i) q^{27} +(-38.5716 + 118.711i) q^{28} +(-23.7789 + 73.1839i) q^{29} +(-80.3709 - 247.356i) q^{31} +32.0000 q^{32} +(20.1706 + 62.0789i) q^{33} +(-47.0875 - 34.2110i) q^{34} +(25.3011 - 18.3823i) q^{36} +(97.3953 + 70.7618i) q^{37} +(83.2935 + 60.5163i) q^{38} +(151.204 - 109.856i) q^{39} +(248.032 + 180.206i) q^{41} +(84.4656 + 259.958i) q^{42} +504.394 q^{43} +(-18.4221 - 56.6973i) q^{44} +(-114.806 + 353.337i) q^{46} +(60.7022 - 186.822i) q^{47} +(56.6917 - 41.1889i) q^{48} +630.759 q^{49} -127.456 q^{51} +(-138.096 + 100.333i) q^{52} +(139.978 - 430.808i) q^{53} +(94.2462 - 290.060i) q^{54} +(-77.1433 - 237.423i) q^{56} +225.458 q^{57} +(-47.5578 - 146.368i) q^{58} +(-51.9655 - 37.7552i) q^{59} +(110.566 - 80.3305i) q^{61} +(420.827 + 305.749i) q^{62} +(-197.381 - 143.406i) q^{63} +(-51.7771 + 37.6183i) q^{64} +(-105.615 - 76.7337i) q^{66} +(-72.6375 - 223.555i) q^{67} +116.407 q^{68} +(251.407 + 773.750i) q^{69} +(166.664 - 512.939i) q^{71} +(-19.3283 + 59.4865i) q^{72} +(-846.241 + 614.830i) q^{73} -240.774 q^{74} -205.913 q^{76} +(-376.252 + 273.363i) q^{77} +(-115.510 + 355.502i) q^{78} +(109.157 - 335.949i) q^{79} +(-141.150 - 434.416i) q^{81} -613.169 q^{82} +(-301.832 - 928.944i) q^{83} +(-442.267 - 321.326i) q^{84} +(-816.127 + 592.951i) q^{86} +(-272.652 - 198.093i) q^{87} +(96.4592 + 70.0817i) q^{88} +(-891.118 + 647.435i) q^{89} +(1077.33 + 782.724i) q^{91} +(-229.612 - 706.674i) q^{92} +1139.09 q^{93} +(121.404 + 373.644i) q^{94} +(-43.3086 + 133.290i) q^{96} +(448.316 - 1379.77i) q^{97} +(-1020.59 + 741.502i) q^{98} +116.525 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 6 q^{3} - 32 q^{4} - 12 q^{6} + 112 q^{7} - 64 q^{8} - 26 q^{9}+O(q^{10}) \) 32 * q - 16 * q^2 - 6 * q^3 - 32 * q^4 - 12 * q^6 + 112 * q^7 - 64 * q^8 - 26 * q^9	\( 32 q - 16 q^{2} - 6 q^{3} - 32 q^{4} - 12 q^{6} + 112 q^{7} - 64 q^{8} - 26 q^{9} - 106 q^{11} - 24 q^{12} + 14 q^{13} - 56 q^{14} - 128 q^{16} + 92 q^{17} + 848 q^{18} - 110 q^{19} - 36 q^{21} + 68 q^{22} + 124 q^{23} + 192 q^{24} + 808 q^{26} - 630 q^{27} - 112 q^{28} + 10 q^{29} - 486 q^{31} + 1024 q^{32} - 672 q^{33} - 616 q^{34} - 104 q^{36} - 88 q^{37} + 20 q^{38} - 1012 q^{39} - 96 q^{41} - 72 q^{42} + 1804 q^{43} + 136 q^{44} - 832 q^{46} - 328 q^{47} - 96 q^{48} + 2076 q^{49} + 884 q^{51} + 56 q^{52} + 1164 q^{53} + 120 q^{54} - 224 q^{56} + 2800 q^{57} + 20 q^{58} - 2250 q^{59} + 934 q^{61} + 768 q^{62} - 2976 q^{63} - 512 q^{64} + 16 q^{66} - 2248 q^{67} + 1728 q^{68} + 628 q^{69} - 2616 q^{71} - 1488 q^{72} - 3836 q^{73} + 2584 q^{74} + 800 q^{76} + 254 q^{77} + 1816 q^{78} + 2800 q^{79} - 5268 q^{81} + 2128 q^{82} + 304 q^{83} - 624 q^{84} - 692 q^{86} + 2660 q^{87} - 848 q^{88} - 4520 q^{89} + 3764 q^{91} - 1664 q^{92} + 5648 q^{93} - 656 q^{94} - 192 q^{96} - 6228 q^{97} - 2748 q^{98} + 2108 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 6 * q^3 - 32 * q^4 - 12 * q^6 + 112 * q^7 - 64 * q^8 - 26 * q^9 - 106 * q^11 - 24 * q^12 + 14 * q^13 - 56 * q^14 - 128 * q^16 + 92 * q^17 + 848 * q^18 - 110 * q^19 - 36 * q^21 + 68 * q^22 + 124 * q^23 + 192 * q^24 + 808 * q^26 - 630 * q^27 - 112 * q^28 + 10 * q^29 - 486 * q^31 + 1024 * q^32 - 672 * q^33 - 616 * q^34 - 104 * q^36 - 88 * q^37 + 20 * q^38 - 1012 * q^39 - 96 * q^41 - 72 * q^42 + 1804 * q^43 + 136 * q^44 - 832 * q^46 - 328 * q^47 - 96 * q^48 + 2076 * q^49 + 884 * q^51 + 56 * q^52 + 1164 * q^53 + 120 * q^54 - 224 * q^56 + 2800 * q^57 + 20 * q^58 - 2250 * q^59 + 934 * q^61 + 768 * q^62 - 2976 * q^63 - 512 * q^64 + 16 * q^66 - 2248 * q^67 + 1728 * q^68 + 628 * q^69 - 2616 * q^71 - 1488 * q^72 - 3836 * q^73 + 2584 * q^74 + 800 * q^76 + 254 * q^77 + 1816 * q^78 + 2800 * q^79 - 5268 * q^81 + 2128 * q^82 + 304 * q^83 - 624 * q^84 - 692 * q^86 + 2660 * q^87 - 848 * q^88 - 4520 * q^89 + 3764 * q^91 - 1664 * q^92 + 5648 * q^93 - 656 * q^94 - 192 * q^96 - 6228 * q^97 - 2748 * q^98 + 2108 * q^99

Introduction

L-functions

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