LMFDB - Embedded newform 250.4.d.d.201.6

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			201.6
Character	$\chi$	$=$	250.201
Dual form			250.4.d.d.51.6

$q$-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 $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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	0.992704	+	0.120573i	$0.0384731\pi$
$3$	1.35339	+	4.16531i	0.260461	+	0.801615i	−0.732244	+	0.681042i	$0.761527\pi$
$4$	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	$-0.181107\pi$
$7$	31.2051			1.68492			0.842459	+	0.538761i	$0.181107\pi$
$8$	−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	0.740640	−	0.671902i	$-0.234522\pi$
$11$	12.0574	+	8.76021i	0.330495	+	0.240118i	−0.410146	+	0.912020i	$0.634522\pi$
$12$	−14.1729	+	10.2972i	−0.340947	+	0.247713i
$13$	34.5241	−	25.0832i	0.736558	−	0.535141i	−0.155073	−	0.987903i	$-0.549561\pi$
$13$	34.5241	−	25.0832i	0.736558	−	0.535141i	0.891631	+	0.452762i	$0.149561\pi$
$14$	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	$-0.966563\pi$
$17$	−8.99290	+	27.6773i	−0.128300	+	0.394867i	0.866188	+	0.499718i	$0.166563\pi$
$18$	15.6370			0.204759
$19$	−15.9076	+	48.9587i	−0.192077	+	0.591152i	0.807921	+	0.589290i	$0.200593\pi$
$19$	−15.9076	+	48.9587i	−0.192077	+	0.591152i	−0.999998	+	0.00186182i	$0.999407\pi$
$20$		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	−0.998285	−	0.0585368i	$-0.981356\pi$
$23$	−150.283	−	109.187i	−1.36244	−	0.989874i	−0.364159	−	0.931337i	$-0.618644\pi$
$24$	−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	0.845610	−	0.533801i	$-0.179237\pi$
$29$	−23.7789	−	73.1839i	−0.152263	−	0.468618i	−0.997873	+	0.0651831i	$0.979237\pi$
$30$		0			0
$31$	−80.3709	+	247.356i	−0.465646	+	1.43311i	0.392522	+	0.919743i	$0.371603\pi$
$31$	−80.3709	+	247.356i	−0.465646	+	1.43311i	−0.858168	+	0.513369i	$0.828397\pi$
$32$	−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	$-0.786182\pi$
$37$	−97.3953	+	70.7618i	−0.432748	+	0.314410i	0.349999	+	0.936750i	$0.386182\pi$
$38$	−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	−0.00478394	−	0.999989i	$-0.501523\pi$
$41$	248.032	−	180.206i	0.944783	−	0.686425i	0.949567	+	0.313563i	$0.101523\pi$
$42$	−84.4656	+	259.958i	−0.310317	+	0.955058i
$43$	−504.394			−1.78882			−0.894411	−	0.447246i	$-0.852405\pi$
$43$	−504.394			−1.78882			−0.894411	+	0.447246i	$0.852405\pi$
$44$	−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	$-0.198597\pi$
$47$	−60.7022	−	186.822i	−0.188390	−	0.579804i	−0.999990	+	0.00440862i	$0.998597\pi$
$48$	−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	−0.951358	−	0.308087i	$-0.900311\pi$
$53$	−139.978	−	430.808i	−0.362782	−	1.11653i	0.588576	−	0.808442i	$-0.299689\pi$
$54$	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	−0.643641	−	0.765328i	$-0.722577\pi$
$59$	−51.9655	+	37.7552i	−0.114667	+	0.0833102i	0.528974	+	0.848638i	$0.322577\pi$
$60$		0			0
$61$	110.566	+	80.3305i	0.232073	+	0.168611i	0.697744	−	0.716347i	$-0.254187\pi$
$61$	110.566	+	80.3305i	0.232073	+	0.168611i	−0.465671	+	0.884958i	$0.654187\pi$
$62$	−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	$-0.831251\pi$
$67$	72.6375	−	223.555i	0.132449	−	0.407636i	0.995185	+	0.0980193i	$0.0312507\pi$
$68$	−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	0.988249	+	0.152852i	$0.0488458\pi$
$71$	166.664	+	512.939i	0.278583	+	0.857390i	−0.709666	+	0.704538i	$0.751154\pi$
$72$	19.3283	+	59.4865i	0.0316370	+	0.0973688i
$73$	846.241	+	614.830i	1.35678	+	0.985759i	0.998642	+	0.0520909i	$0.0165886\pi$
$73$	846.241	+	614.830i	1.35678	+	0.985759i	0.358139	+	0.933668i	$0.383411\pi$
$74$	−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	0.998207	−	0.0598585i	$-0.0190649\pi$
$79$	109.157	+	335.949i	0.155457	+	0.478446i	−0.842750	+	0.538305i	$0.819065\pi$
$80$		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	−0.526512	−	0.850168i	$-0.676500\pi$
$83$	301.832	−	928.944i	0.399161	−	1.22849i	0.925673	−	0.378325i	$-0.123500\pi$
$84$	−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	−0.0869953	−	0.996209i	$-0.527727\pi$
$89$	−891.118	−	647.435i	−1.06133	−	0.771101i	−0.974334	+	0.225108i	$0.927727\pi$
$90$		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	−0.853527	−	0.521048i	$-0.825541\pi$
$97$	−448.316	−	1379.77i	−0.469274	−	1.44428i	0.384253	−	0.923228i	$-0.374459\pi$
$98$	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	$-0.0456402\pi$
$103$	109.795	+	337.914i	0.105033	+	0.323259i	−0.884705	+	0.466151i	$0.845640\pi$
$104$	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	$-0.463370\pi$
$107$	254.177			0.229647			0.114823	+	0.993386i	$0.463370\pi$
$108$	−188.492	+	580.120i	−0.167942	+	0.516871i
$109$	−723.625	+	525.744i	−0.635878	+	0.461992i	−0.858432	−	0.512928i	$-0.828561\pi$
$109$	−723.625	+	525.744i	−0.635878	+	0.461992i	0.222554	+	0.974920i	$0.428561\pi$
$110$		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	$-0.512176\pi$
$113$	1081.45	−	785.716i	0.900300	−	0.654106i	0.938543	+	0.345163i	$0.112176\pi$
$114$	−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	$-0.477664\pi$
$127$	−1226.46	−	891.078i	−0.856937	−	0.622601i	−0.927050	+	0.374938i	$0.877664\pi$
$128$	−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	0.736212	+	0.676751i	$0.236613\pi$
$131$	−385.607	+	1186.78i	−0.257180	+	0.791519i	−0.993392	+	0.114768i	$0.963387\pi$
$132$	−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	$-0.432278\pi$
$137$	1933.90	−	1405.06i	1.20602	−	0.876222i	0.994863	+	0.101231i	$0.0322780\pi$
$138$	1316.38	−	956.408i	0.812014	−	0.589962i
$139$	−1423.34	−	1034.12i	−0.868534	−	0.631027i	0.0616594	−	0.998097i	$-0.480361\pi$
$139$	−1423.34	−	1034.12i	−0.868534	−	0.631027i	−0.930193	+	0.367071i	$0.880361\pi$
$140$		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	$-0.651085\pi$
$157$	−1798.13			−0.914052			−0.457026	+	0.889453i	$0.651085\pi$
$158$	−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	$-0.596134\pi$
$163$	1079.33	−	784.182i	0.518650	−	0.376821i	0.816095	+	0.577917i	$0.196134\pi$
$164$	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	−0.766460	−	0.642292i	$-0.777984\pi$
$167$	498.847	−	1535.29i	0.231149	−	0.711404i	0.997609	−	0.0691116i	$-0.0220165\pi$
$168$	−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	$-0.558496\pi$
$173$	−2671.96	−	1941.29i	−1.17425	−	0.853142i	−0.991511	+	0.130020i	$0.958496\pi$
$174$	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	0.954848	+	0.297094i	$0.0960174\pi$
$179$	854.933	+	2631.21i	0.356987	+	1.09869i	−0.597861	+	0.801600i	$0.703983\pi$
$180$		0			0
$181$	−1009.96	+	3108.33i	−0.414749	+	1.27647i	0.497726	+	0.867334i	$0.334168\pi$
$181$	−1009.96	+	3108.33i	−0.414749	+	1.27647i	−0.912475	+	0.409132i	$0.865832\pi$
$182$	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	−0.640810	−	0.767699i	$-0.721401\pi$
$191$	−286.949	+	208.481i	−0.108706	+	0.0789797i	0.532104	+	0.846679i	$0.321401\pi$
$192$	86.6171	−	266.580i	0.0325576	−	0.100202i
$193$	−2907.82			−1.08451			−0.542253	−	0.840216i	$-0.682428\pi$
$193$	−2907.82			−1.08451			−0.542253	+	0.840216i	$0.682428\pi$
$194$	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	0.856325	+	0.516437i	$0.172742\pi$
$197$	1291.54	+	3974.94i	0.467098	+	1.43758i	−0.389228	+	0.921142i	$0.627258\pi$
$198$	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	0.749122	−	0.662432i	$-0.230476\pi$
$211$	1074.58	+	780.728i	0.350602	+	0.254727i	−0.398519	+	0.917160i	$0.630476\pi$
$212$	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	$-0.0659986\pi$
$223$	3613.82	+	2625.59i	1.08520	+	0.788442i	0.106616	+	0.994300i	$0.465999\pi$
$224$	−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	$-0.212964\pi$
$227$	1494.35	+	1085.71i	0.436931	+	0.317449i	−0.347483	+	0.937686i	$0.612964\pi$
$228$	−278.681	−	857.692i	−0.0809478	−	0.249132i
$229$	−80.0296	−	246.306i	−0.0230939	−	0.0710757i	0.938845	−	0.344339i	$-0.111897\pi$
$229$	−80.0296	−	246.306i	−0.0230939	−	0.0710757i	−0.961939	+	0.273263i	$0.911897\pi$
$230$		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	0.689045	+	0.724719i	$0.258030\pi$
$233$	−1047.00	+	3222.33i	−0.294383	+	0.906018i	−0.983428	+	0.181299i	$0.941970\pi$
$234$	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	0.225530	−	0.974236i	$-0.427589\pi$
$239$	−2332.67	−	1694.79i	−0.631330	−	0.458688i	−0.856861	+	0.515548i	$0.827589\pi$
$240$		0			0
$241$	5114.13	−	3715.63i	1.36693	−	0.993133i	0.368960	−	0.929445i	$-0.379714\pi$
$241$	5114.13	−	3715.63i	1.36693	−	0.993133i	0.997970	−	0.0636877i	$-0.0202861\pi$
$242$	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	$-0.788303\pi$
$257$	−6483.90			−1.57375			−0.786877	+	0.617110i	$0.788303\pi$
$258$	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	$-0.729862\pi$
$263$	−646.478	+	469.694i	−0.151572	+	0.110124i	0.509414	+	0.860521i	$0.329862\pi$
$264$	−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	−0.700453	−	0.713698i	$-0.747019\pi$
$269$	1260.60	−	3879.74i	0.285727	−	0.879376i	0.986180	−	0.165678i	$-0.0529811\pi$
$270$		0			0
$271$	135.829	+	418.040i	0.0304467	+	0.0937052i	0.965125	−	0.261789i	$-0.0843125\pi$
$271$	135.829	+	418.040i	0.0304467	+	0.0937052i	−0.934678	+	0.355494i	$0.884313\pi$
$272$	−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	$-0.297785\pi$
$277$	51.9157	+	37.7190i	0.0112611	+	0.00818164i	−0.582140	+	0.813088i	$0.697785\pi$
$278$	−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	−0.992408	−	0.122988i	$-0.960752\pi$
$281$	−552.262	+	1699.69i	−0.117243	+	0.360836i	0.875166	+	0.483824i	$0.160752\pi$
$282$	1720.65			0.363345
$283$	−1929.30	+	5937.78i	−0.405248	+	1.24722i	0.515440	+	0.856926i	$0.327628\pi$
$283$	−1929.30	+	5937.78i	−0.405248	+	1.24722i	−0.920688	+	0.390299i	$0.872372\pi$
$284$	−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	$-0.578290\pi$
$293$	−2442.29			−0.486963			−0.243482	+	0.969905i	$0.578290\pi$
$294$	−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	$-0.297830\pi$
$307$	6382.66			1.18657			0.593286	+	0.804992i	$0.297830\pi$
$308$	−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	0.337457	−	0.941341i	$-0.390433\pi$
$311$	−2487.41	−	1807.21i	−0.453531	−	0.329510i	−0.790988	+	0.611831i	$0.790433\pi$
$312$	−1209.63	+	878.850i	−0.219494	+	0.159471i
$313$	4495.09	−	3265.88i	0.811750	−	0.589771i	−0.102587	−	0.994724i	$-0.532712\pi$
$313$	4495.09	−	3265.88i	0.811750	−	0.589771i	0.914337	+	0.404953i	$0.132712\pi$
$314$	−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	$-0.804756\pi$
$317$	1028.23	−	3164.57i	0.182180	−	0.560693i	0.999888	+	0.0149397i	$0.00475564\pi$
$318$	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	−0.970738	−	0.240143i	$-0.922806\pi$
$331$	−266.427	+	819.978i	−0.0442422	+	0.136163i	0.926495	+	0.376306i	$0.122806\pi$
$332$	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	$-0.853206\pi$
$337$	−4634.03	+	3366.82i	−0.749056	+	0.544221i	0.146478	+	0.989214i	$0.453206\pi$
$338$	−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	$-0.157325\pi$
$347$	−715.567	−	2202.29i	−0.110702	−	0.340706i	−0.991026	+	0.133666i	$0.957325\pi$
$348$	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	−0.956745	−	0.290929i	$-0.906036\pi$
$353$	−2346.00	−	7220.26i	−0.353726	−	1.08866i	0.603019	−	0.797727i	$-0.293964\pi$
$354$	−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	0.125455	−	0.992099i	$-0.459961\pi$
$359$	7535.11	−	5474.58i	1.10777	−	0.804839i	0.982310	+	0.187261i	$0.0599609\pi$
$360$		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	−0.626022	−	0.779806i	$-0.715318\pi$
$367$	2382.00	−	7331.03i	0.338799	−	1.04272i	0.964820	−	0.262910i	$-0.0846821\pi$
$368$	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	$-0.512795\pi$
$373$	−7224.67	−	5249.03i	−1.00289	−	0.728644i	−0.962707	+	0.270548i	$0.912795\pi$
$374$	−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	0.821998	−	0.569490i	$-0.192859\pi$
$379$	−1311.50	−	4036.39i	−0.177750	−	0.547059i	−0.999748	+	0.0224313i	$0.992859\pi$
$380$		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	−0.773239	−	0.634115i	$-0.781365\pi$
$383$	1686.84	−	5191.55i	0.225048	−	0.692626i	0.998287	−	0.0585112i	$-0.0186353\pi$
$384$	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	−0.998223	−	0.0595840i	$-0.981023\pi$
$389$	−10460.1	−	7599.69i	−1.36336	−	0.990538i	−0.365136	−	0.930954i	$-0.618977\pi$
$390$		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	$-0.141008\pi$
$397$	−628.083	−	1933.04i	−0.0794020	−	0.244374i	−0.982876	+	0.184269i	$0.941008\pi$
$398$	−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	−0.0776075	−	0.996984i	$-0.524728\pi$
$409$	7002.65	−	5087.72i	0.846599	−	0.615090i	0.924206	+	0.381894i	$0.124728\pi$
$410$		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	0.792745	+	0.609554i	$0.208651\pi$
$419$	−1774.40	+	5461.04i	−0.206886	+	0.636729i	−0.999631	+	0.0271754i	$0.991349\pi$
$420$		0			0
$421$	1139.25	+	3506.25i	0.131885	+	0.405901i	0.995093	−	0.0989486i	$-0.0315479\pi$
$421$	1139.25	+	3506.25i	0.131885	+	0.405901i	−0.863207	+	0.504850i	$0.831548\pi$
$422$	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	0.635793	+	0.771859i	$0.280673\pi$
$431$	−2973.01	+	9149.99i	−0.332262	+	1.02260i	−0.968055	+	0.250738i	$0.919327\pi$
$432$	−2439.90			−0.271735
$433$	−489.167	+	1505.50i	−0.0542907	+	0.167090i	−0.974525	−	0.224278i	$-0.927998\pi$
$433$	−489.167	+	1505.50i	−0.0542907	+	0.167090i	0.920235	+	0.391367i	$0.127998\pi$
$434$	−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	0.512229	−	0.858849i	$-0.328820\pi$
$439$	−1345.66	−	977.681i	−0.146298	−	0.106292i	−0.658527	+	0.752557i	$0.728820\pi$
$440$		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	$-0.387286\pi$
$443$	6466.22			0.693497			0.346748	+	0.937958i	$0.387286\pi$
$444$	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	$-0.478523\pi$
$457$	1317.36			0.134843			0.0674216	+	0.997725i	$0.478523\pi$
$458$	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	0.877201	−	0.480124i	$-0.159408\pi$
$461$	6845.97	+	4973.89i	0.691646	+	0.502510i	−0.185555	+	0.982634i	$0.559408\pi$
$462$	−3295.72	+	2394.48i	−0.331885	+	0.241129i
$463$	−10265.9	+	7458.64i	−1.03045	+	0.748666i	−0.968399	−	0.249407i	$-0.919764\pi$
$463$	−10265.9	+	7458.64i	−1.03045	+	0.748666i	−0.0620519	+	0.998073i	$0.519764\pi$
$464$	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	$-0.912957\pi$
$467$	−253.819	+	781.175i	−0.0251506	+	0.0774057i	0.937693	+	0.347464i	$0.112957\pi$
$468$	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	0.971519	+	0.236960i	$0.0761511\pi$
$479$	3405.28	+	10480.4i	0.324825	+	0.999710i	−0.646694	+	0.762750i	$0.723849\pi$
$480$		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	$-0.580925\pi$
$487$	6354.39	−	4616.73i	0.591262	−	0.429577i	0.842767	+	0.538279i	$0.180925\pi$
$488$	−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	−0.567803	+	0.823164i	$0.692206\pi$
$491$	−16604.1	+	12063.6i	−1.52614	+	1.10881i	−0.958337	+	0.285641i	$0.907794\pi$
$492$	−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	$-0.145963\pi$
$503$	−1003.26	−	3087.72i	−0.0889329	−	0.273707i	−0.985625	+	0.168947i	$0.945963\pi$
$504$	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	−0.589677	−	0.807639i	$-0.700745\pi$
$509$	−43.4872	+	31.5953i	−0.00378691	+	0.00275135i	0.585890	+	0.810390i	$0.300745\pi$
$510$		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	0.994913	−	0.100741i	$-0.0321214\pi$
$521$	1555.45	+	4787.17i	0.130797	+	0.402553i	−0.864115	+	0.503294i	$0.832121\pi$
$522$	−371.830	−	1144.37i	−0.0311773	−	0.0959538i
$523$	4809.07	+	3493.99i	0.402076	+	0.292126i	0.770386	−	0.637577i	$-0.220063\pi$
$523$	4809.07	+	3493.99i	0.402076	+	0.292126i	−0.368310	+	0.929703i	$0.620063\pi$
$524$	−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	−0.999999	−	0.00155356i	$-0.999505\pi$
$541$	−16453.2	+	11953.9i	−1.30754	+	0.949982i	−0.307539	+	0.951535i	$0.599505\pi$
$542$	−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	0.887228	+	0.461331i	$0.152628\pi$
$547$	5636.82	+	17348.4i	0.440609	+	1.35606i	−0.446619	+	0.894724i	$0.647372\pi$
$548$	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	$-0.531739\pi$
$557$	−2617.19			−0.199092			−0.0995458	+	0.995033i	$0.531739\pi$
$558$	−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	$-0.899277\pi$
$563$	−12665.1	+	9201.70i	−0.948079	+	0.688820i	0.00227286	+	0.999997i	$0.499277\pi$
$564$	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	−0.836075	−	0.548616i	$-0.815155\pi$
$569$	2209.54	−	6800.27i	0.162792	−	0.501023i	0.998867	+	0.0475929i	$0.0151550\pi$
$570$		0			0
$571$	2342.24	+	7208.67i	0.171663	+	0.528325i	0.999465	−	0.0326951i	$-0.0104090\pi$
$571$	2342.24	+	7208.67i	0.171663	+	0.528325i	−0.827802	+	0.561020i	$0.810409\pi$
$572$	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	$-0.209766\pi$
$577$	6272.46	+	4557.21i	0.452558	+	0.328803i	−0.338047	+	0.941129i	$0.609766\pi$
$578$	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	$-0.602382\pi$
$587$	6946.97	−	5047.27i	0.488470	−	0.354894i	0.804596	+	0.593823i	$0.202382\pi$
$588$	−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	$-0.584275\pi$
$593$	−7557.43			−0.523350			−0.261675	+	0.965156i	$0.584275\pi$
$594$	−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	$-0.781378\pi$
$607$	−23128.2			−1.54653			−0.773266	+	0.634081i	$0.781378\pi$
$608$	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	$-0.601066\pi$
$613$	7510.33	−	5456.58i	0.494844	−	0.359525i	0.807044	+	0.590491i	$0.201066\pi$
$614$	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	$-0.957750\pi$
$617$	−1709.05	+	5259.91i	−0.111513	+	0.343203i	0.879691	+	0.475547i	$0.157750\pi$
$618$	−3112.23			−0.202576
$619$	−4872.99	+	14997.5i	−0.316417	+	0.973831i	0.658750	+	0.752361i	$0.271085\pi$
$619$	−4872.99	+	14997.5i	−0.316417	+	0.973831i	−0.975167	+	0.221469i	$0.928915\pi$
$620$		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	−0.471943	−	0.881629i	$-0.656447\pi$
$631$	6785.23	−	20882.8i	0.428075	−	1.31748i	0.900019	−	0.435852i	$-0.143553\pi$
$632$	−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	0.442425	−	0.896806i	$-0.354118\pi$
$641$	23240.6	−	16885.3i	1.43205	−	1.04045i	0.989630	−	0.143643i	$-0.0458817\pi$
$642$	−688.003	+	2117.45i	−0.0422949	+	0.130170i
$643$	19485.8			1.19509			0.597547	−	0.801834i	$-0.296142\pi$
$643$	19485.8			1.19509			0.597547	+	0.801834i	$0.296142\pi$
$644$	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	−0.964290	−	0.264850i	$-0.914678\pi$
$647$	−5592.78	−	17212.8i	−0.339838	−	1.04591i	0.624452	−	0.781063i	$-0.285322\pi$
$648$	−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	0.829045	+	0.559181i	$0.188885\pi$
$653$	8126.61	+	25011.1i	0.487012	+	1.49887i	−0.342033	+	0.939688i	$0.611115\pi$
$654$	−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	−0.562894	−	0.826529i	$-0.690312\pi$
$659$	832.956	−	605.178i	0.0492373	−	0.0357730i	0.612132	+	0.790756i	$0.290312\pi$
$660$		0			0
$661$	3435.86	+	2496.30i	0.202178	+	0.146891i	0.684267	−	0.729231i	$-0.260122\pi$
$661$	3435.86	+	2496.30i	0.202178	+	0.146891i	−0.482090	+	0.876122i	$0.660122\pi$
$662$	−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	$-0.169248\pi$
$673$	11280.4	+	8195.71i	0.646105	+	0.469422i	−0.215837	+	0.976429i	$0.569248\pi$
$674$	−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	$-0.424722\pi$
$677$	−10884.1	−	7907.76i	−0.617887	−	0.448921i	−0.852183	+	0.523244i	$0.824722\pi$
$678$	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	0.634493	+	0.772928i	$0.281209\pi$
$683$	−5946.43	+	18301.2i	−0.333139	+	1.02530i	−0.967632	+	0.252367i	$0.918791\pi$
$684$	−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	−0.966929	−	0.255045i	$-0.917910\pi$
$691$	−18585.0	+	13502.8i	−1.02316	+	0.743373i	−0.0562356	+	0.998418i	$0.517910\pi$
$692$	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	−0.959189	−	0.282766i	$-0.908748\pi$
$709$	−18626.9	+	13533.2i	−0.986668	+	0.716856i	−0.0274791	+	0.999622i	$0.508748\pi$
$710$		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	−0.988180	−	0.153300i	$-0.951010\pi$
$719$	−1901.30	+	5851.59i	−0.0986181	+	0.303515i	0.889562	+	0.456815i	$0.151010\pi$
$720$		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	$-0.0359590\pi$
$727$	23394.3	+	16997.0i	1.19346	+	0.867101i	0.199836	+	0.979829i	$0.435959\pi$
$728$	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	$-0.988673\pi$
$733$	−3372.68	+	10380.1i	−0.169949	+	0.523051i	0.829417	+	0.558629i	$0.188673\pi$
$734$	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	0.839545	−	0.543290i	$-0.182822\pi$
$739$	11697.6	+	8498.82i	0.582278	+	0.423050i	−0.257266	+	0.966341i	$0.582822\pi$
$740$		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	$-0.310450\pi$
$743$	22720.1			1.12183			0.560915	+	0.827874i	$0.310450\pi$
$744$	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	$-0.435011\pi$
$757$	8445.77			0.405504			0.202752	+	0.979230i	$0.435011\pi$
$758$	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	0.392726	−	0.919655i	$-0.371532\pi$
$761$	−7569.25	−	5499.38i	−0.360559	−	0.261961i	−0.753285	+	0.657694i	$0.771532\pi$
$762$	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	−0.999090	−	0.0426520i	$-0.986419\pi$
$769$	−3534.39	+	10877.7i	−0.165739	+	0.510092i	0.833351	+	0.552744i	$0.186419\pi$
$770$		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	$-0.272112\pi$
$773$	3042.74	+	2210.68i	0.141578	+	0.102862i	−0.514742	+	0.857345i	$0.672112\pi$
$774$	−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	$-0.873026\pi$
$787$	−18476.0	+	13423.6i	−0.836848	+	0.608005i	0.0846407	+	0.996412i	$0.473026\pi$
$788$	−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	$-0.101141\pi$
$797$	−49.8475	−	153.415i	−0.00221542	−	0.00681836i	−0.952158	+	0.305606i	$0.901141\pi$
$798$	−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	−0.754987	−	0.655740i	$-0.772357\pi$
$809$	−8390.60	+	6096.13i	−0.364645	+	0.264930i	0.390342	+	0.920670i	$0.372357\pi$
$810$		0			0
$811$	−34337.8	−	24947.9i	−1.48676	−	1.08020i	−0.975299	−	0.220890i	$-0.929104\pi$
$811$	−34337.8	−	24947.9i	−1.48676	−	1.08020i	−0.511463	−	0.859305i	$-0.670896\pi$
$812$	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	0.950877	+	0.309570i	$0.100185\pi$
$821$	8552.50	+	26321.9i	0.363562	+	1.11893i	−0.587315	+	0.809359i	$0.699815\pi$
$822$	6470.39	+	19913.8i	0.274551	+	0.844980i
$823$	9200.39	+	6684.48i	0.389679	+	0.283118i	0.765324	−	0.643645i	$-0.222579\pi$
$823$	9200.39	+	6684.48i	0.389679	+	0.283118i	−0.375645	+	0.926764i	$0.622579\pi$
$824$	−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	$-0.277825\pi$
$827$	2678.57	+	1946.09i	0.112628	+	0.0818287i	−0.530046	+	0.847969i	$0.677825\pi$
$828$	−1795.22	−	5525.12i	−0.0753480	−	0.231897i
$829$	−7520.64	−	23146.2i	−0.315082	−	0.969722i	−0.975721	−	0.219018i	$-0.929715\pi$
$829$	−7520.64	−	23146.2i	−0.315082	−	0.969722i	0.660639	−	0.750704i	$-0.270285\pi$
$830$		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	0.793018	−	0.609198i	$-0.208509\pi$
$839$	11147.2	+	8098.89i	0.458692	+	0.333260i	−0.334326	+	0.942458i	$0.608509\pi$
$840$		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	$-0.184570\pi$
$853$	−4042.80	−	12442.5i	−0.162278	−	0.499439i	−0.998825	+	0.0484548i	$0.984570\pi$
$854$	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	$-0.385755\pi$
$857$	17624.7			0.702508			0.351254	+	0.936280i	$0.385755\pi$
$858$	−1721.53	+	5298.32i	−0.0684988	+	0.210818i
$859$	834.395	−	606.224i	0.0331423	−	0.0240793i	−0.571091	−	0.820887i	$-0.693480\pi$
$859$	834.395	−	606.224i	0.0331423	−	0.0240793i	0.604233	+	0.796808i	$0.293480\pi$
$860$		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	$-0.960621\pi$
$863$	−29957.6	+	21765.5i	−1.18166	+	0.858523i	−0.189299	+	0.981920i	$0.560621\pi$
$864$	−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	0.999984	+	0.00574075i	$0.00182735\pi$
$877$	34138.6	+	24803.1i	1.31446	+	0.955008i	0.314472	+	0.949267i	$0.398173\pi$
$878$	−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	−0.982578	−	0.185849i	$-0.940497\pi$
$881$	−2050.56	+	6310.96i	−0.0784165	+	0.241341i	0.904162	+	0.427190i	$0.140497\pi$
$882$	9863.15			0.376542
$883$	−1739.74	+	5354.36i	−0.0663044	+	0.204064i	−0.978720	−	0.205202i	$-0.934215\pi$
$883$	−1739.74	+	5354.36i	−0.0663044	+	0.204064i	0.912415	+	0.409266i	$0.134215\pi$
$884$	−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	$-0.914041\pi$
$887$	−26624.6	+	19343.9i	−1.00786	+	0.732250i	−0.0440972	+	0.999027i	$0.514041\pi$
$888$	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	$-0.643083\pi$
$907$	−23738.5			−0.869046			−0.434523	+	0.900661i	$0.643083\pi$
$908$	−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	0.378446	−	0.925623i	$-0.376459\pi$
$911$	−10584.2	−	7689.85i	−0.384928	−	0.279666i	−0.763374	+	0.645957i	$0.776459\pi$
$912$	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	−0.967148	−	0.254215i	$-0.918183\pi$
$919$	−983.027	+	3025.45i	−0.0352852	+	0.108597i	0.931863	+	0.362811i	$0.118183\pi$
$920$		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	0.867764	+	0.496976i	$0.165556\pi$
$929$	12964.0	+	39899.2i	0.457843	+	1.40910i	−0.409921	+	0.912121i	$0.634444\pi$
$930$		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	$-0.676922\pi$
$937$	3361.80	−	2442.49i	0.117210	−	0.0851577i	0.644846	+	0.764313i	$0.276922\pi$
$938$	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	−0.813767	−	0.581191i	$-0.802587\pi$
$941$	−14793.5	+	10748.1i	−0.512490	+	0.372346i	0.301277	+	0.953537i	$0.402587\pi$
$942$	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	0.783848	+	0.620953i	$0.213254\pi$
$947$	14999.2	+	46162.9i	0.514688	+	1.58405i	−0.269160	+	0.963096i	$0.586746\pi$
$948$	−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	−0.952676	−	0.303988i	$-0.901682\pi$
$953$	−10609.5	−	32652.7i	−0.360625	−	1.10989i	0.592051	−	0.805900i	$-0.298318\pi$
$954$	−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	$-0.865505\pi$
$967$	2010.06	−	6186.33i	0.0668451	−	0.205728i	0.978900	+	0.204340i	$0.0655049\pi$
$968$	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	0.987321	+	0.158735i	$0.0507416\pi$
$971$	8528.41	+	26247.7i	0.281864	+	0.867487i	−0.705457	+	0.708752i	$0.749258\pi$
$972$	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	$-0.408285\pi$
$977$	−16486.8	−	11978.4i	−0.539877	−	0.392244i	−0.824039	+	0.566533i	$0.808285\pi$
$978$	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	$-0.926332\pi$
$983$	−1573.89	+	4843.95i	−0.0510675	+	0.157170i	0.922270	+	0.386545i	$0.126332\pi$
$984$	−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	−0.605110	−	0.796142i	$-0.706871\pi$
$991$	−1089.49	+	791.563i	−0.0349232	+	0.0253732i	0.570187	+	0.821515i	$0.306871\pi$
$992$	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	−0.998767	−	0.0496443i	$-0.984191\pi$
$997$	−6923.45	−	21308.2i	−0.219928	−	0.676868i	0.778839	−	0.627224i	$-0.215809\pi$
$998$	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.d.201.6		32
5.2	odd	4		250.4.e.b.49.3		32
5.3	odd	4		50.4.e.a.9.6	✓	32
5.4	even	2		250.4.d.c.201.3		32
25.2	odd	20		50.4.e.a.39.6	yes	32
25.6	even	5		1250.4.a.m.1.12		16
25.11	even	5	inner	250.4.d.d.51.6		32
25.14	even	10		250.4.d.c.51.3		32
25.19	even	10		1250.4.a.n.1.5		16
25.23	odd	20		250.4.e.b.199.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.e.a.9.6	✓	32	5.3	odd	4
50.4.e.a.39.6	yes	32	25.2	odd	20
250.4.d.c.51.3		32	25.14	even	10
250.4.d.c.201.3		32	5.4	even	2
250.4.d.d.51.6		32	25.11	even	5	inner
250.4.d.d.201.6		32	1.1	even	1	trivial
250.4.e.b.49.3		32	5.2	odd	4
250.4.e.b.199.3		32	25.23	odd	20
1250.4.a.m.1.12		16	25.6	even	5
1250.4.a.n.1.5		16	25.19	even	10

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

Modular forms

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