LMFDB - Embedded newform 250.4.e.b.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,4,Mod(49,250)]

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([7]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("250.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	250.e (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.7504775014$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	250.49
Dual form			250.4.e.b.199.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17557 + 1.61803i) q^{2} +(4.16531 - 1.35339i) q^{3} +(-1.23607 - 3.80423i) q^{4} +(-2.70679 + 8.33063i) q^{6} +31.2051i q^{7} +(7.60845 + 2.47214i) q^{8} +(-6.32528 + 4.59559i) q^{9} +O(q^{10})$	\(q+(-1.17557 + 1.61803i) q^{2} +(4.16531 - 1.35339i) q^{3} +(-1.23607 - 3.80423i) q^{4} +(-2.70679 + 8.33063i) q^{6} +31.2051i q^{7} +(7.60845 + 2.47214i) q^{8} +(-6.32528 + 4.59559i) q^{9} +(12.0574 + 8.76021i) q^{11} +(-10.2972 - 14.1729i) q^{12} +(-25.0832 - 34.5241i) q^{13} +(-50.4909 - 36.6838i) q^{14} +(-12.9443 + 9.40456i) q^{16} +(-27.6773 - 8.99290i) q^{17} -15.6370i q^{18} +(15.9076 - 48.9587i) q^{19} +(42.2328 + 129.979i) q^{21} +(-28.3486 + 9.21103i) q^{22} +(-109.187 + 150.283i) q^{23} +35.0374 q^{24} +85.3482 q^{26} +(-89.6334 + 123.370i) q^{27} +(118.711 - 38.5716i) q^{28} +(23.7789 + 73.1839i) q^{29} +(-80.3709 + 247.356i) q^{31} -32.0000i q^{32} +(62.0789 + 20.1706i) q^{33} +(47.0875 - 34.2110i) q^{34} +(25.3011 + 18.3823i) q^{36} +(-70.7618 - 97.3953i) q^{37} +(60.5163 + 83.2935i) q^{38} +(-151.204 - 109.856i) q^{39} +(248.032 - 180.206i) q^{41} +(-259.958 - 84.4656i) q^{42} +504.394i q^{43} +(18.4221 - 56.6973i) q^{44} +(-114.806 - 353.337i) q^{46} +(186.822 - 60.7022i) q^{47} +(-41.1889 + 56.6917i) q^{48} -630.759 q^{49} -127.456 q^{51} +(-100.333 + 138.096i) q^{52} +(-430.808 + 139.978i) q^{53} +(-94.2462 - 290.060i) q^{54} +(-77.1433 + 237.423i) q^{56} -225.458i q^{57} +(-146.368 - 47.5578i) q^{58} +(51.9655 - 37.7552i) q^{59} +(110.566 + 80.3305i) q^{61} +(-305.749 - 420.827i) q^{62} +(-143.406 - 197.381i) q^{63} +(51.7771 + 37.6183i) q^{64} +(-105.615 + 76.7337i) q^{66} +(223.555 + 72.6375i) q^{67} +116.407i q^{68} +(-251.407 + 773.750i) q^{69} +(166.664 + 512.939i) q^{71} +(-59.4865 + 19.3283i) q^{72} +(614.830 - 846.241i) q^{73} +240.774 q^{74} -205.913 q^{76} +(-273.363 + 376.252i) q^{77} +(355.502 - 115.510i) q^{78} +(-109.157 - 335.949i) q^{79} +(-141.150 + 434.416i) q^{81} +613.169i q^{82} +(-928.944 - 301.832i) q^{83} +(442.267 - 321.326i) q^{84} +(-816.127 - 592.951i) q^{86} +(198.093 + 272.652i) q^{87} +(70.0817 + 96.4592i) q^{88} +(891.118 + 647.435i) q^{89} +(1077.33 - 782.724i) q^{91} +(706.674 + 229.612i) q^{92} +1139.09i q^{93} +(-121.404 + 373.644i) q^{94} +(-43.3086 - 133.290i) q^{96} +(1379.77 - 448.316i) q^{97} +(741.502 - 1020.59i) q^{98} -116.525 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 12 q^{6} + 26 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 - 12 * q^6 + 26 * q^9	$ 32 q + 32 q^{4} - 12 q^{6} + 26 q^{9} - 106 q^{11} - 80 q^{12} + 56 q^{14} - 128 q^{16} - 320 q^{17} + 110 q^{19} - 36 q^{21} + 360 q^{22} + 370 q^{23} - 192 q^{24} + 808 q^{26} + 1200 q^{27} + 120 q^{28} - 10 q^{29} - 486 q^{31} - 2560 q^{33} + 616 q^{34} - 104 q^{36} - 680 q^{37} + 1012 q^{39} - 96 q^{41} + 1020 q^{42} - 136 q^{44} - 832 q^{46} - 1040 q^{47} - 320 q^{48} - 2076 q^{49} + 884 q^{51} + 2550 q^{53} - 120 q^{54} - 224 q^{56} + 2250 q^{59} + 934 q^{61} - 4200 q^{62} - 4660 q^{63} + 512 q^{64} + 16 q^{66} + 3780 q^{67} - 628 q^{69} - 2616 q^{71} + 600 q^{73} - 2584 q^{74} + 800 q^{76} + 4320 q^{77} + 6640 q^{78} - 2800 q^{79} - 5268 q^{81} - 4050 q^{83} + 624 q^{84} - 692 q^{86} - 9390 q^{87} + 1680 q^{88} + 4520 q^{89} + 3764 q^{91} - 1280 q^{92} + 656 q^{94} - 192 q^{96} - 1710 q^{97} - 3280 q^{98} - 2108 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 - 12 * q^6 + 26 * q^9 - 106 * q^11 - 80 * q^12 + 56 * q^14 - 128 * q^16 - 320 * q^17 + 110 * q^19 - 36 * q^21 + 360 * q^22 + 370 * q^23 - 192 * q^24 + 808 * q^26 + 1200 * q^27 + 120 * q^28 - 10 * q^29 - 486 * q^31 - 2560 * q^33 + 616 * q^34 - 104 * q^36 - 680 * q^37 + 1012 * q^39 - 96 * q^41 + 1020 * q^42 - 136 * q^44 - 832 * q^46 - 1040 * q^47 - 320 * q^48 - 2076 * q^49 + 884 * q^51 + 2550 * q^53 - 120 * q^54 - 224 * q^56 + 2250 * q^59 + 934 * q^61 - 4200 * q^62 - 4660 * q^63 + 512 * q^64 + 16 * q^66 + 3780 * q^67 - 628 * q^69 - 2616 * q^71 + 600 * q^73 - 2584 * q^74 + 800 * q^76 + 4320 * q^77 + 6640 * q^78 - 2800 * q^79 - 5268 * q^81 - 4050 * q^83 + 624 * q^84 - 692 * q^86 - 9390 * q^87 + 1680 * q^88 + 4520 * q^89 + 3764 * q^91 - 1280 * q^92 + 656 * q^94 - 192 * q^96 - 1710 * q^97 - 3280 * q^98 - 2108 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	−1.17557	+	1.61803i	−0.415627	+	0.572061i
$2$	−1.17557	+	1.61803i	−0.415627	+	0.572061i
$3$	4.16531	−	1.35339i	0.801615	−	0.260461i	0.120573	−	0.992704i	$-0.461527\pi$
$3$	4.16531	−	1.35339i	0.801615	−	0.260461i	0.681042	+	0.732244i	$0.261527\pi$
$4$	−1.23607	−	3.80423i	−0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	−2.70679	+	8.33063i	−0.184173	+	0.566828i
$7$			31.2051i			1.68492i	0.538761	+	0.842459i	$0.318893\pi$
$7$			31.2051i			1.68492i	−0.538761	+	0.842459i	$0.681107\pi$
$8$	7.60845	+	2.47214i	0.336249	+	0.109254i
$9$	−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	$0.634522\pi$
$12$	−10.2972	−	14.1729i	−0.247713	−	0.340947i
$13$	−25.0832	−	34.5241i	−0.535141	−	0.736558i	0.452762	−	0.891631i	$-0.350439\pi$
$13$	−25.0832	−	34.5241i	−0.535141	−	0.736558i	−0.987903	+	0.155073i	$0.950439\pi$
$14$	−50.4909	−	36.6838i	−0.963876	−	0.700297i
$15$		0			0
$16$	−12.9443	+	9.40456i	−0.202254	+	0.146946i
$17$	−27.6773	−	8.99290i	−0.394867	−	0.128300i	0.104852	−	0.994488i	$-0.466563\pi$
$17$	−27.6773	−	8.99290i	−0.394867	−	0.128300i	−0.499718	+	0.866188i	$0.666563\pi$
$18$		−	15.6370i		−	0.204759i
$19$	15.9076	−	48.9587i	0.192077	−	0.591152i	−0.807921	−	0.589290i	$-0.799407\pi$
$19$	15.9076	−	48.9587i	0.192077	−	0.591152i	0.999998	−	0.00186182i	$-0.000592636\pi$
$20$		0			0
$21$	42.2328	+	129.979i	0.438855	+	1.35066i
$22$	−28.3486	+	9.21103i	−0.274725	+	0.0892636i
$23$	−109.187	+	150.283i	−0.989874	+	1.36244i	−0.0585368	+	0.998285i	$0.518644\pi$
$23$	−109.187	+	150.283i	−0.989874	+	1.36244i	−0.931337	+	0.364159i	$0.881356\pi$
$24$	35.0374			0.297999
$25$		0			0
$26$	85.3482			0.643775
$27$	−89.6334	+	123.370i	−0.638887	+	0.879353i
$28$	118.711	−	38.5716i	0.801226	−	0.260334i
$29$	23.7789	+	73.1839i	0.152263	+	0.468618i	0.997873	−	0.0651831i	$-0.0207631\pi$
$29$	23.7789	+	73.1839i	0.152263	+	0.468618i	−0.845610	+	0.533801i	$0.820763\pi$
$30$		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	$0.828397\pi$
$32$		−	32.0000i		−	0.176777i
$33$	62.0789	+	20.1706i	0.327471	+	0.106402i
$34$	47.0875	−	34.2110i	0.237513	−	0.172563i
$35$		0			0
$36$	25.3011	+	18.3823i	0.117135	+	0.0851035i
$37$	−70.7618	−	97.3953i	−0.314410	−	0.432748i	0.622340	−	0.782747i	$-0.286182\pi$
$37$	−70.7618	−	97.3953i	−0.314410	−	0.432748i	−0.936750	+	0.349999i	$0.886182\pi$
$38$	60.5163	+	83.2935i	0.258343	+	0.355579i
$39$	−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	$0.101523\pi$
$42$	−259.958	−	84.4656i	−0.955058	−	0.310317i
$43$			504.394i			1.78882i	0.447246	+	0.894411i	$0.352405\pi$
$43$			504.394i			1.78882i	−0.447246	+	0.894411i	$0.647595\pi$
$44$	18.4221	−	56.6973i	0.0631189	−	0.194260i
$45$		0			0
$46$	−114.806	−	353.337i	−0.367984	−	1.13254i
$47$	186.822	−	60.7022i	0.579804	−	0.188390i	−0.00440862	−	0.999990i	$-0.501403\pi$
$47$	186.822	−	60.7022i	0.579804	−	0.188390i	0.584213	+	0.811600i	$0.301403\pi$
$48$	−41.1889	+	56.6917i	−0.123856	+	0.170474i
$49$	−630.759			−1.83895
$50$		0			0
$51$	−127.456			−0.349948
$52$	−100.333	+	138.096i	−0.267570	+	0.368279i
$53$	−430.808	+	139.978i	−1.11653	+	0.362782i	−0.808442	−	0.588576i	$-0.799689\pi$
$53$	−430.808	+	139.978i	−1.11653	+	0.362782i	−0.308087	+	0.951358i	$0.599689\pi$
$54$	−94.2462	−	290.060i	−0.237505	−	0.730966i
$55$		0			0
$56$	−77.1433	+	237.423i	−0.184084	+	0.566552i
$57$		−	225.458i		−	0.523905i
$58$	−146.368	−	47.5578i	−0.331363	−	0.107666i
$59$	51.9655	−	37.7552i	0.114667	−	0.0833102i	−0.528974	−	0.848638i	$-0.677423\pi$
$59$	51.9655	−	37.7552i	0.114667	−	0.0833102i	0.643641	+	0.765328i	$0.277423\pi$
$60$		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	$0.654187\pi$
$62$	−305.749	−	420.827i	−0.626293	−	0.862018i
$63$	−143.406	−	197.381i	−0.286785	−	0.394725i
$64$	51.7771	+	37.6183i	0.101127	+	0.0734732i
$65$		0			0
$66$	−105.615	+	76.7337i	−0.196974	+	0.143110i
$67$	223.555	+	72.6375i	0.407636	+	0.132449i	0.505656	−	0.862735i	$-0.331251\pi$
$67$	223.555	+	72.6375i	0.407636	+	0.132449i	−0.0980193	+	0.995185i	$0.531251\pi$
$68$			116.407i			0.207594i
$69$	−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	$0.751154\pi$
$72$	−59.4865	+	19.3283i	−0.0973688	+	0.0316370i
$73$	614.830	−	846.241i	0.985759	−	1.35678i	0.0520909	−	0.998642i	$-0.483411\pi$
$73$	614.830	−	846.241i	0.985759	−	1.35678i	0.933668	−	0.358139i	$-0.116589\pi$
$74$	240.774			0.378236
$75$		0			0
$76$	−205.913			−0.310787
$77$	−273.363	+	376.252i	−0.404580	+	0.556856i
$78$	355.502	−	115.510i	0.516060	−	0.167678i
$79$	−109.157	−	335.949i	−0.155457	−	0.478446i	0.842750	−	0.538305i	$-0.180935\pi$
$79$	−109.157	−	335.949i	−0.155457	−	0.478446i	−0.998207	+	0.0598585i	$0.980935\pi$
$80$		0			0
$81$	−141.150	+	434.416i	−0.193622	+	0.595907i
$82$			613.169i			0.825771i
$83$	−928.944	−	301.832i	−1.22849	−	0.399161i	−0.378325	−	0.925673i	$-0.623500\pi$
$83$	−928.944	−	301.832i	−1.22849	−	0.399161i	−0.850168	+	0.526512i	$0.823500\pi$
$84$	442.267	−	321.326i	0.574468	−	0.417376i
$85$		0			0
$86$	−816.127	−	592.951i	−1.02332	−	0.743483i
$87$	198.093	+	272.652i	0.244113	+	0.335993i
$88$	70.0817	+	96.4592i	0.0848947	+	0.116848i
$89$	891.118	+	647.435i	1.06133	+	0.771101i	0.974334	−	0.225108i	$-0.0722735\pi$
$89$	891.118	+	647.435i	1.06133	+	0.771101i	0.0869953	+	0.996209i	$0.472273\pi$
$90$		0			0
$91$	1077.33	−	782.724i	1.24104	−	0.901668i
$92$	706.674	+	229.612i	0.800825	+	0.260204i
$93$			1139.09i			1.27009i
$94$	−121.404	+	373.644i	−0.133212	+	0.409984i
$95$		0			0
$96$	−43.3086	−	133.290i	−0.0460434	−	0.141707i
$97$	1379.77	−	448.316i	1.44428	−	0.469274i	0.521048	−	0.853527i	$-0.325541\pi$
$97$	1379.77	−	448.316i	1.44428	−	0.469274i	0.923228	+	0.384253i	$0.125541\pi$
$98$	741.502	−	1020.59i	0.764316	−	1.05199i
$99$	−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	$0.548128\pi$
$102$	149.833	−	206.228i	0.145448	−	0.200192i
$103$	337.914	−	109.795i	0.323259	−	0.105033i	−0.142892	−	0.989738i	$-0.545640\pi$
$103$	337.914	−	109.795i	0.323259	−	0.105033i	0.466151	+	0.884705i	$0.345640\pi$
$104$	−105.496	−	324.684i	−0.0994688	−	0.306133i
$105$		0			0
$106$	279.956	−	861.616i	0.256526	−	0.789505i
$107$			254.177i			0.229647i	0.993386	+	0.114823i	$0.0366302\pi$
$107$			254.177i			0.229647i	−0.993386	+	0.114823i	$0.963370\pi$
$108$	580.120	+	188.492i	0.516871	+	0.167942i
$109$	723.625	−	525.744i	0.635878	−	0.461992i	−0.222554	−	0.974920i	$-0.571439\pi$
$109$	723.625	−	525.744i	0.635878	−	0.461992i	0.858432	+	0.512928i	$0.171439\pi$
$110$		0			0
$111$	−426.559	−	309.914i	−0.364750	−	0.265006i
$112$	−293.470	−	403.927i	−0.247592	−	0.340782i
$113$	−785.716	−	1081.45i	−0.654106	−	0.900300i	0.345163	−	0.938543i	$-0.387824\pi$
$113$	−785.716	−	1081.45i	−0.654106	−	0.900300i	−0.999268	+	0.0382434i	$0.987824\pi$
$114$	364.798	+	265.041i	0.299706	+	0.217749i
$115$		0			0
$116$	249.016	−	180.921i	0.199315	−	0.144811i
$117$	317.317	+	103.102i	0.250735	+	0.0814686i
$118$			128.466i			0.100222i
$119$	280.625	−	863.674i	0.216175	−	0.665318i
$120$		0			0
$121$	−342.662	−	1054.61i	−0.257447	−	0.792341i
$122$	−259.955	+	84.4645i	−0.192912	+	0.0626808i
$123$	789.243	−	1086.30i	0.578566	−	0.796328i
$124$	1040.34			0.753431
$125$		0			0
$126$	487.953			0.345002
$127$	891.078	−	1226.46i	0.622601	−	0.856937i	−0.374938	−	0.927050i	$-0.622336\pi$
$127$	891.078	−	1226.46i	0.622601	−	0.856937i	0.997539	+	0.0701127i	$0.0223359\pi$
$128$	−121.735	+	39.5542i	−0.0840623	+	0.0273135i
$129$	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	$0.963387\pi$
$132$		−	261.094i		−	0.172162i
$133$	1527.76	+	496.400i	0.996043	+	0.323634i
$134$	−380.335	+	276.330i	−0.245194	+	0.178144i
$135$		0			0
$136$	−188.350	−	136.844i	−0.118756	−	0.0862815i
$137$	1405.06	+	1933.90i	0.876222	+	1.20602i	0.977453	+	0.211154i	$0.0677220\pi$
$137$	1405.06	+	1933.90i	0.876222	+	1.20602i	−0.101231	+	0.994863i	$0.532278\pi$
$138$	−956.408	−	1316.38i	−0.589962	−	0.812014i
$139$	1423.34	+	1034.12i	0.868534	+	0.631027i	0.930193	−	0.367071i	$-0.119639\pi$
$139$	1423.34	+	1034.12i	0.868534	+	0.631027i	−0.0616594	+	0.998097i	$0.519639\pi$
$140$		0			0
$141$	696.019	−	505.687i	0.415712	−	0.302032i
$142$	−1025.88	−	333.328i	−0.606266	−	0.196988i
$143$		−	636.005i		−	0.371926i
$144$	38.6567	−	118.973i	0.0223708	−	0.0688501i
$145$		0			0
$146$	646.471	+	1989.63i	0.366454	+	1.12783i
$147$	−2627.31	+	853.665i	−1.47413	+	0.478973i
$148$	−283.047	+	389.581i	−0.157205	+	0.216374i
$149$	−391.623			−0.215322			−0.107661	−	0.994188i	$-0.534336\pi$
$149$	−391.623			−0.215322			−0.107661	+	0.994188i	$0.534336\pi$
$150$		0			0
$151$	1937.43			1.04414			0.522072	−	0.852901i	$-0.325159\pi$
$151$	1937.43			1.04414			0.522072	+	0.852901i	$0.325159\pi$
$152$	242.065	−	333.174i	0.129172	−	0.177789i
$153$	216.394	−	70.3108i	0.114343	−	0.0371522i
$154$	−287.431	−	884.622i	−0.150402	−	0.462889i
$155$		0			0
$156$	−231.019	+	711.004i	−0.118566	+	0.364910i
$157$		−	1798.13i		−	0.914052i	−0.889453	−	0.457026i	$-0.848915\pi$
$157$		−	1798.13i		−	0.914052i	0.889453	−	0.457026i	$-0.151085\pi$
$158$	671.899	+	218.313i	0.338313	+	0.109924i
$159$	−1605.01	+	1166.10i	−0.800536	+	0.581623i
$160$		0			0
$161$	−4689.60	−	3407.20i	−2.29561	−	1.66786i
$162$	−536.968	−	739.073i	−0.260421	−	0.358439i
$163$	−784.182	−	1079.33i	−0.376821	−	0.518650i	0.577917	−	0.816095i	$-0.303866\pi$
$163$	−784.182	−	1079.33i	−0.376821	−	0.518650i	−0.954739	+	0.297445i	$0.903866\pi$
$164$	−992.129	−	720.824i	−0.472392	−	0.343213i
$165$		0			0
$166$	1580.41	−	1148.24i	0.738939	−	0.536871i
$167$	1535.29	+	498.847i	0.711404	+	0.231149i	0.642292	−	0.766460i	$-0.277984\pi$
$167$	1535.29	+	498.847i	0.711404	+	0.231149i	0.0691116	+	0.997609i	$0.477984\pi$
$168$			1093.35i			0.502104i
$169$	116.166	−	357.522i	0.0528748	−	0.162732i
$170$		0			0
$171$	124.374	+	382.782i	0.0556204	+	0.171182i
$172$	1918.83	−	623.465i	0.850636	−	0.276388i
$173$	−1941.29	+	2671.96i	−0.853142	+	1.17425i	0.130020	+	0.991511i	$0.458496\pi$
$173$	−1941.29	+	2671.96i	−0.853142	+	1.17425i	−0.983162	+	0.182738i	$0.941504\pi$
$174$	−674.033			−0.293668
$175$		0			0
$176$	−238.460			−0.102128
$177$	165.355	−	227.592i	0.0702195	−	0.0966489i
$178$	−2095.14	+	680.753i	−0.882234	+	0.286655i
$179$	−854.933	−	2631.21i	−0.356987	−	1.09869i	−0.954848	−	0.297094i	$-0.903983\pi$
$179$	−854.933	−	2631.21i	−0.356987	−	1.09869i	0.597861	−	0.801600i	$-0.296017\pi$
$180$		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	$0.865832\pi$
$182$			2663.30i			1.08471i
$183$	569.259	+	184.963i	0.229950	+	0.0747153i
$184$	−1202.27	+	873.497i	−0.481697	+	0.349973i
$185$		0			0
$186$	−1843.09	−	1339.08i	−0.726568	−	0.527882i
$187$	−254.937	−	350.890i	−0.0996941	−	0.137217i
$188$	−461.850	−	635.681i	−0.179169	−	0.246605i
$189$	−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	$0.321401\pi$
$192$	266.580	+	86.6171i	0.100202	+	0.0325576i
$193$			2907.82i			1.08451i	0.840216	+	0.542253i	$0.182428\pi$
$193$			2907.82i			1.08451i	−0.840216	+	0.542253i	$0.817572\pi$
$194$	−896.631	+	2759.55i	−0.331827	+	1.02126i
$195$		0			0
$196$	779.661	+	2399.55i	0.284133	+	0.874472i
$197$	−3974.94	+	1291.54i	−1.43758	+	0.467098i	−0.921142	−	0.389228i	$-0.872742\pi$
$197$	−3974.94	+	1291.54i	−1.43758	+	0.467098i	−0.516437	+	0.856325i	$0.672742\pi$
$198$	136.983	−	188.541i	0.0491665	−	0.0676718i
$199$	1052.08			0.374772			0.187386	−	0.982286i	$-0.439998\pi$
$199$	1052.08			0.374772			0.187386	+	0.982286i	$0.439998\pi$
$200$		0			0
$201$	1029.49			0.361265
$202$	359.459	−	494.753i	0.125205	−	0.172330i
$203$	−2283.71	+	742.023i	−0.789583	+	0.256551i
$204$	157.544	+	484.870i	0.0540700	+	0.166410i
$205$		0			0
$206$	−219.590	+	675.828i	−0.0742697	+	0.228579i
$207$		−	1452.36i		−	0.487663i
$208$	649.368	+	210.992i	0.216469	+	0.0703350i
$209$	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	$0.630476\pi$
$212$	1065.02	+	1465.87i	0.345026	+	0.474888i
$213$	1388.42	+	1910.99i	0.446633	+	0.614737i
$214$	−411.267	−	298.803i	−0.131372	−	0.0954474i
$215$		0			0
$216$	−986.959	+	717.067i	−0.310898	+	0.225881i
$217$	−7718.77	−	2507.98i	−2.41468	−	0.784576i
$218$			1788.90i			0.555778i
$219$	1415.66	−	4356.97i	0.436812	−	1.34437i
$220$		0			0
$221$	383.764	+	1181.10i	0.116809	+	0.359501i
$222$	1002.90	−	325.862i	0.303200	−	0.0985155i
$223$	2625.59	−	3613.82i	0.788442	−	1.08520i	−0.205858	−	0.978582i	$-0.565999\pi$
$223$	2625.59	−	3613.82i	0.788442	−	1.08520i	0.994300	−	0.106616i	$-0.0340014\pi$
$224$	998.564			0.297854
$225$		0			0
$226$	2673.48			0.786891
$227$	−1085.71	+	1494.35i	−0.317449	+	0.436931i	−0.937686	−	0.347483i	$-0.887036\pi$
$227$	−1085.71	+	1494.35i	−0.317449	+	0.436931i	0.620237	+	0.784414i	$0.287036\pi$
$228$	−857.692	+	278.681i	−0.249132	+	0.0809478i
$229$	80.0296	+	246.306i	0.0230939	+	0.0710757i	0.961939	−	0.273263i	$-0.0881030\pi$
$229$	80.0296	+	246.306i	0.0230939	+	0.0710757i	−0.938845	+	0.344339i	$0.888103\pi$
$230$		0			0
$231$	−629.427	+	1937.18i	−0.179278	+	0.551762i
$232$			615.601i			0.174208i
$233$	3222.33	+	1047.00i	0.906018	+	0.294383i	0.724719	−	0.689045i	$-0.241970\pi$
$233$	3222.33	+	1047.00i	0.906018	+	0.294383i	0.181299	+	0.983428i	$0.441970\pi$
$234$	−539.852	+	392.225i	−0.150817	+	0.109575i
$235$		0			0
$236$	−207.862	−	151.021i	−0.0573333	−	0.0416551i
$237$	−909.343	−	1251.60i	−0.249233	−	0.343040i
$238$	1067.56	+	1469.37i	0.290755	+	0.400189i
$239$	2332.67	+	1694.79i	0.631330	+	0.458688i	0.856861	−	0.515548i	$-0.172411\pi$
$239$	2332.67	+	1694.79i	0.631330	+	0.458688i	−0.225530	+	0.974236i	$0.572411\pi$
$240$		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	$-0.0202861\pi$
$242$	2109.21	+	685.324i	0.560270	+	0.182043i
$243$		−	2116.81i		−	0.558821i
$244$	168.929	−	519.910i	0.0443220	−	0.136409i
$245$		0			0
$246$	829.859	+	2554.04i	0.215081	+	0.661951i
$247$	−2089.27	+	678.844i	−0.538206	+	0.174874i
$248$	−1223.00	+	1683.31i	−0.313146	+	0.431009i
$249$	−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	$0.450464\pi$
$252$	−573.623	+	789.525i	−0.143392	+	0.197363i
$253$	−2633.02	+	855.522i	−0.654296	+	0.212594i
$254$	936.935	+	2883.59i	0.231451	+	0.712332i
$255$		0			0
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$		−	6483.90i		−	1.57375i	−0.617110	−	0.786877i	$-0.711697\pi$
$257$		−	6483.90i		−	1.57375i	0.617110	−	0.786877i	$-0.288303\pi$
$258$	−4201.92	−	1365.29i	−1.01395	−	0.329454i
$259$	3039.23	−	2208.13i	0.729145	−	0.529755i
$260$		0			0
$261$	−486.731	−	353.631i	−0.115433	−	0.0838667i
$262$	−1466.93	−	2019.06i	−0.345907	−	0.476100i
$263$	469.694	+	646.478i	0.110124	+	0.151572i	0.860521	−	0.509414i	$-0.170138\pi$
$263$	469.694	+	646.478i	0.110124	+	0.151572i	−0.750398	+	0.660987i	$0.770138\pi$
$264$	422.459	+	306.935i	0.0984870	+	0.0715550i
$265$		0			0
$266$	−2599.18	+	1888.42i	−0.599121	+	0.435287i
$267$	4588.02	+	1490.74i	1.05162	+	0.341692i
$268$		−	940.240i		−	0.214307i
$269$	−1260.60	+	3879.74i	−0.285727	+	0.879376i	0.700453	+	0.713698i	$0.252981\pi$
$269$	−1260.60	+	3879.74i	−0.285727	+	0.879376i	−0.986180	+	0.165678i	$0.947019\pi$
$270$		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	$0.884313\pi$
$272$	442.837	−	143.886i	0.0987167	−	0.0320750i
$273$	3428.08	−	4718.34i	0.759987	−	1.04603i
$274$	−4780.86			−1.05410
$275$		0			0
$276$	3254.28			0.709726
$277$	−37.7190	+	51.9157i	−0.00818164	+	0.0112611i	−0.813088	−	0.582140i	$-0.802215\pi$
$277$	−37.7190	+	51.9157i	−0.00818164	+	0.0112611i	0.804907	+	0.593402i	$0.202215\pi$
$278$	−3346.47	+	1087.34i	−0.721972	+	0.234583i
$279$	−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	$0.160752\pi$
$282$			1720.65i			0.363345i
$283$	5937.78	+	1929.30i	1.24722	+	0.405248i	0.856926	−	0.515440i	$-0.172372\pi$
$283$	5937.78	+	1929.30i	1.24722	+	0.405248i	0.390299	+	0.920688i	$0.372372\pi$
$284$	1745.33	−	1268.06i	0.364670	−	0.264948i
$285$		0			0
$286$	1029.08	+	747.668i	0.212764	+	0.154582i
$287$	5623.35	+	7739.87i	1.15657	+	1.59188i
$288$	147.059	+	202.409i	0.0300886	+	0.0414134i
$289$	−3289.54	−	2389.99i	−0.669558	−	0.486462i
$290$		0			0
$291$	5140.44	−	3734.75i	1.03553	−	0.752354i
$292$	−3979.26	−	1292.94i	−0.797496	−	0.259122i
$293$			2442.29i			0.486963i	0.969905	+	0.243482i	$0.0782896\pi$
$293$			2442.29i			0.486963i	−0.969905	+	0.243482i	$0.921710\pi$
$294$	1707.33	−	5254.62i	0.338685	−	1.04237i
$295$		0			0
$296$	−297.614	−	915.960i	−0.0584407	−	0.179862i
$297$	−2161.49	+	702.311i	−0.422298	+	0.137213i
$298$	460.381	−	633.660i	0.0894937	−	0.123178i
$299$	7927.15			1.53324
$300$		0			0
$301$	−15739.7			−3.01402
$302$	−2277.59	+	3134.83i	−0.433975	+	0.597315i
$303$	−1273.65	+	413.832i	−0.241482	+	0.0784622i
$304$	254.522	+	783.339i	0.0480193	+	0.147788i
$305$		0			0
$306$	−140.622	+	432.789i	−0.0262706	+	0.0808526i
$307$			6382.66i			1.18657i	0.804992	+	0.593286i	$0.202170\pi$
$307$			6382.66i			1.18657i	−0.804992	+	0.593286i	$0.797830\pi$
$308$	1769.24	+	574.862i	0.327312	+	0.106350i
$309$	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	$0.790433\pi$
$312$	−878.850	−	1209.63i	−0.159471	−	0.219494i
$313$	−3265.88	−	4495.09i	−0.589771	−	0.811750i	0.404953	−	0.914337i	$-0.367288\pi$
$313$	−3265.88	−	4495.09i	−0.589771	−	0.811750i	−0.994724	+	0.102587i	$0.967288\pi$
$314$	2909.43	+	2113.82i	0.522894	+	0.379904i
$315$		0			0
$316$	−1143.10	+	830.513i	−0.203495	+	0.147848i
$317$	3164.57	+	1028.23i	0.560693	+	0.182180i	0.575633	−	0.817708i	$-0.304756\pi$
$317$	3164.57	+	1028.23i	0.560693	+	0.182180i	−0.0149397	+	0.999888i	$0.504756\pi$
$318$		−	3967.79i		−	0.699694i
$319$	−354.395	+	1090.72i	−0.0622016	+	0.191437i
$320$		0			0
$321$	344.001	+	1058.73i	0.0598140	+	0.184088i
$322$	11025.9	−	3582.54i	1.90823	−	0.620022i
$323$	−880.562	+	1211.99i	−0.151690	+	0.208783i
$324$	1827.09			0.313287
$325$		0			0
$326$	2668.26			0.453317
$327$	2302.59	−	3169.24i	0.389399	−	0.535961i
$328$	2332.63	−	757.919i	0.392677	−	0.127589i
$329$	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	$0.122806\pi$
$332$			3907.00i			0.645857i
$333$	895.177	+	290.861i	0.147313	+	0.0478651i
$334$	−2611.99	+	1897.73i	−0.427910	+	0.310895i
$335$		0			0
$336$	−1769.07	−	1285.30i	−0.287234	−	0.208688i
$337$	−3366.82	−	4634.03i	−0.544221	−	0.749056i	0.444993	−	0.895534i	$-0.353206\pi$
$337$	−3366.82	−	4634.03i	−0.544221	−	0.749056i	−0.989214	+	0.146478i	$0.953206\pi$
$338$	441.921	+	608.253i	0.0711164	+	0.0978834i
$339$	−4736.38	−	3441.18i	−0.758834	−	0.551325i
$340$		0			0
$341$	−3135.95	+	2278.40i	−0.498010	+	0.361826i
$342$	−765.565	−	248.747i	−0.121044	−	0.0393295i
$343$		−	8979.56i		−	1.41356i
$344$	−1246.93	+	3837.66i	−0.195436	+	0.601490i
$345$		0			0
$346$	−2041.19	−	6282.15i	−0.317154	−	0.976099i
$347$	2202.29	−	715.567i	0.340706	−	0.110702i	−0.133666	−	0.991026i	$-0.542675\pi$
$347$	2202.29	−	715.567i	0.340706	−	0.110702i	0.474373	+	0.880324i	$0.342675\pi$
$348$	792.373	−	1090.61i	0.122056	−	0.167996i
$349$	4454.14			0.683166			0.341583	−	0.939852i	$-0.389037\pi$
$349$	4454.14			0.683166			0.341583	+	0.939852i	$0.389037\pi$
$350$		0			0
$351$	6507.52			0.989589
$352$	280.327	−	385.837i	0.0424473	−	0.0584238i
$353$	−7220.26	+	2346.00i	−1.08866	+	0.353726i	−0.797727	−	0.603019i	$-0.793964\pi$
$353$	−7220.26	+	2346.00i	−1.08866	+	0.353726i	−0.290929	+	0.956745i	$0.593964\pi$
$354$	173.865	+	535.101i	0.0261040	+	0.0803398i
$355$		0			0
$356$	1361.51	−	4190.29i	0.202696	−	0.623834i
$357$		−	3977.27i		−	0.589634i
$358$	5262.43	+	1709.87i	0.776894	+	0.252428i
$359$	−7535.11	+	5474.58i	−1.10777	+	0.804839i	−0.982310	−	0.187261i	$-0.940039\pi$
$359$	−7535.11	+	5474.58i	−1.10777	+	0.804839i	−0.125455	+	0.992099i	$0.540039\pi$
$360$		0			0
$361$	3405.15	+	2473.98i	0.496450	+	0.360692i
$362$	−3842.11	−	5288.21i	−0.557836	−	0.767796i
$363$	−2854.59	−	3929.01i	−0.412747	−	0.568098i
$364$	−4309.31	−	3130.90i	−0.620520	−	0.450834i
$365$		0			0
$366$	−968.481	+	703.643i	−0.138315	+	0.100492i
$367$	7331.03	+	2382.00i	1.04272	+	0.338799i	0.779806	−	0.626022i	$-0.215318\pi$
$367$	7331.03	+	2382.00i	1.04272	+	0.338799i	0.262910	+	0.964820i	$0.415318\pi$
$368$		−	2972.16i		−	0.421018i
$369$	−740.722	+	2279.71i	−0.104500	+	0.321617i
$370$		0			0
$371$	−4368.03	−	13443.4i	−0.611258	−	1.88126i
$372$	4333.35	−	1407.99i	0.603962	−	0.196239i
$373$	−5249.03	+	7224.67i	−0.728644	+	1.00289i	0.270548	+	0.962707i	$0.412795\pi$
$373$	−5249.03	+	7224.67i	−0.728644	+	1.00289i	−0.999192	+	0.0401863i	$0.987205\pi$
$374$	867.448			0.119932
$375$		0			0
$376$	1571.49			0.215541
$377$	1930.16	−	2656.63i	0.263682	−	0.362927i
$378$	9051.35	−	2940.96i	1.23162	−	0.400177i
$379$	1311.50	+	4036.39i	0.177750	+	0.547059i	0.999748	−	0.0224313i	$-0.00714069\pi$
$379$	1311.50	+	4036.39i	0.177750	+	0.547059i	−0.821998	+	0.569490i	$0.807141\pi$
$380$		0			0
$381$	2051.73	−	6314.59i	0.275888	−	0.849097i
$382$		−	709.377i		−	0.0950127i
$383$	−5191.55	−	1686.84i	−0.692626	−	0.225048i	−0.0585112	−	0.998287i	$-0.518635\pi$
$383$	−5191.55	−	1686.84i	−0.692626	−	0.225048i	−0.634115	+	0.773239i	$0.718635\pi$
$384$	−453.533	+	329.511i	−0.0602715	+	0.0437898i
$385$		0			0
$386$	−4704.95	−	3418.35i	−0.620403	−	0.450749i
$387$	−2317.99	−	3190.43i	−0.304470	−	0.419067i
$388$	−3410.99	−	4694.82i	−0.446306	−	0.614287i
$389$	10460.1	+	7599.69i	1.36336	+	0.990538i	0.998223	+	0.0595840i	$0.0189774\pi$
$389$	10460.1	+	7599.69i	1.36336	+	0.990538i	0.365136	+	0.930954i	$0.381023\pi$
$390$		0			0
$391$	4373.49	−	3177.53i	0.565670	−	0.410983i
$392$	−4799.10	−	1559.32i	−0.618345	−	0.200912i
$393$			5465.17i			0.701479i
$394$	2583.07	−	7949.89i	0.330288	−	1.01652i
$395$		0			0
$396$	144.032	+	443.286i	0.0182775	+	0.0562525i
$397$	1933.04	−	628.083i	0.244374	−	0.0794020i	−0.184269	−	0.982876i	$-0.558992\pi$
$397$	1933.04	−	628.083i	0.244374	−	0.0794020i	0.428643	+	0.903474i	$0.358992\pi$
$398$	−1236.79	+	1702.29i	−0.155765	+	0.214393i
$399$	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	$0.688692\pi$
$402$	−1210.23	+	1665.74i	−0.150152	+	0.206666i
$403$	10555.7	−	3429.75i	1.30476	−	0.423941i
$404$	377.958	+	1163.23i	0.0465448	+	0.143250i
$405$		0			0
$406$	1484.05	−	4567.43i	0.181409	−	0.558319i
$407$		−	1794.22i		−	0.218517i
$408$	−969.740	−	315.088i	−0.117670	−	0.0382332i
$409$	−7002.65	+	5087.72i	−0.846599	+	0.615090i	−0.924206	−	0.381894i	$-0.875272\pi$
$409$	−7002.65	+	5087.72i	−0.846599	+	0.615090i	0.0776075	+	0.996984i	$0.475272\pi$
$410$		0			0
$411$	8469.85	+	6153.71i	1.01651	+	0.738540i
$412$	−835.370	−	1149.79i	−0.0998925	−	0.137490i
$413$	1178.15	+	1621.59i	0.140371	+	0.193204i
$414$	2349.97	+	1707.35i	0.278973	+	0.202686i
$415$		0			0
$416$	−1104.77	+	802.663i	−0.130206	+	0.0946004i
$417$	7328.23	+	2381.09i	0.860587	+	0.279622i
$418$			1534.44i			0.179550i
$419$	1774.40	−	5461.04i	0.206886	−	0.636729i	−0.792745	−	0.609554i	$-0.791349\pi$
$419$	1774.40	−	5461.04i	0.206886	−	0.636729i	0.999631	−	0.0271754i	$-0.00865126\pi$
$420$		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	$0.831548\pi$
$422$	−2526.49	+	820.905i	−0.291440	+	0.0946944i
$423$	−902.740	+	1242.52i	−0.103765	+	0.142821i
$424$	−3623.83			−0.415067
$425$		0			0
$426$	−4724.23			−0.537300
$427$	−2506.72	+	3450.21i	−0.284096	+	0.391024i
$428$	966.947	−	314.180i	0.109204	−	0.0354824i
$429$	−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	$0.919327\pi$
$432$		−	2439.90i		−	0.271735i
$433$	1505.50	+	489.167i	0.167090	+	0.0542907i	0.391367	−	0.920235i	$-0.372002\pi$
$433$	1505.50	+	489.167i	0.167090	+	0.0542907i	−0.224278	+	0.974525i	$0.572002\pi$
$434$	13132.0	−	9540.93i	1.45243	−	1.05525i
$435$		0			0
$436$	−2894.50	−	2102.98i	−0.317939	−	0.230996i
$437$	5620.76	+	7736.31i	0.615280	+	0.846860i
$438$	5385.51	+	7412.52i	0.587510	+	0.808639i
$439$	1345.66	+	977.681i	0.146298	+	0.106292i	0.658527	−	0.752557i	$-0.271180\pi$
$439$	1345.66	+	977.681i	0.146298	+	0.106292i	−0.512229	+	0.858849i	$0.671180\pi$
$440$		0			0
$441$	3989.73	−	2898.71i	0.430810	−	0.313002i
$442$	−2362.21	−	767.528i	−0.254205	−	0.0825964i
$443$		−	6466.22i		−	0.693497i	−0.937958	−	0.346748i	$-0.887286\pi$
$443$		−	6466.22i		−	0.693497i	0.937958	−	0.346748i	$-0.112714\pi$
$444$	−651.725	+	2005.80i	−0.0696610	+	0.214395i
$445$		0			0
$446$	2760.71	+	8496.59i	0.293102	+	0.902075i
$447$	−1631.23	+	530.020i	−0.172606	+	0.0560830i
$448$	−1173.88	+	1615.71i	−0.123796	+	0.170391i
$449$	−5559.14			−0.584303			−0.292151	−	0.956372i	$-0.594371\pi$
$449$	−5559.14			−0.584303			−0.292151	+	0.956372i	$0.594371\pi$
$450$		0			0
$451$	4569.26			0.477069
$452$	−3142.87	+	4325.78i	−0.327053	+	0.450150i
$453$	8070.01	−	2622.11i	0.837002	−	0.271959i
$454$	−1141.58	−	3513.42i	−0.118011	−	0.363201i
$455$		0			0
$456$	557.362	−	1715.38i	0.0572387	−	0.176163i
$457$			1317.36i			0.134843i	0.997725	+	0.0674216i	$0.0214773\pi$
$457$			1317.36i			0.134843i	−0.997725	+	0.0674216i	$0.978523\pi$
$458$	−492.611	−	160.059i	−0.0502581	−	0.0163299i
$459$	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	$0.559408\pi$
$462$	−2394.48	−	3295.72i	−0.241129	−	0.331885i
$463$	7458.64	+	10265.9i	0.748666	+	1.03045i	0.998073	+	0.0620519i	$0.0197644\pi$
$463$	7458.64	+	10265.9i	0.748666	+	1.03045i	−0.249407	+	0.968399i	$0.580236\pi$
$464$	−996.064	−	723.683i	−0.0996575	−	0.0724054i
$465$		0			0
$466$	−5482.16	+	3983.02i	−0.544971	+	0.395944i
$467$	−781.175	−	253.819i	−0.0774057	−	0.0251506i	0.270058	−	0.962844i	$-0.412957\pi$
$467$	−781.175	−	253.819i	−0.0774057	−	0.0251506i	−0.347464	+	0.937693i	$0.612957\pi$
$468$		−	1334.59i		−	0.131819i
$469$	−2266.66	+	6976.07i	−0.223166	+	0.686834i
$470$		0			0
$471$	−2433.57	−	7489.76i	−0.238074	−	0.732718i
$472$	488.713	−	158.792i	0.0476586	−	0.0154852i
$473$	−4418.60	+	6081.68i	−0.429529	+	0.591196i
$474$	3094.13			0.299828
$475$		0			0
$476$	−3632.48			−0.349778
$477$	2081.70	−	2865.21i	0.199821	−	0.275030i
$478$	−5484.44	+	1782.00i	−0.524796	+	0.170517i
$479$	−3405.28	−	10480.4i	−0.324825	−	0.999710i	−0.971519	−	0.236960i	$-0.923849\pi$
$479$	−3405.28	−	10480.4i	−0.324825	−	0.999710i	0.646694	−	0.762750i	$-0.276151\pi$
$480$		0			0
$481$	−1587.55	+	4885.97i	−0.150491	+	0.463163i
$482$			12642.8i			1.19474i
$483$	−24145.0	−	7845.17i	−2.27460	−	0.739064i
$484$	−3588.40	+	2607.13i	−0.337003	+	0.244847i
$485$		0			0
$486$	3425.07	+	2488.46i	0.319680	+	0.232261i
$487$	4616.73	+	6354.39i	0.429577	+	0.591262i	0.967856	−	0.251504i	$-0.0809253\pi$
$487$	4616.73	+	6354.39i	0.429577	+	0.591262i	−0.538279	+	0.842767i	$0.680925\pi$
$488$	642.644	+	884.524i	0.0596130	+	0.0820503i
$489$	−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	$0.907794\pi$
$492$	−5108.09	−	1659.72i	−0.468070	−	0.152085i
$493$		−	2239.38i		−	0.204577i
$494$	1357.69	−	4178.54i	0.123654	−	0.380569i
$495$		0			0
$496$	−1285.93	−	3957.70i	−0.116412	−	0.358278i
$497$	−16006.3	+	5200.77i	−1.44463	+	0.469389i
$498$	5028.91	−	6921.70i	0.452511	−	0.622829i
$499$	−20672.7			−1.85458			−0.927291	−	0.374341i	$-0.877869\pi$
$499$	−20672.7			−1.85458			−0.927291	+	0.374341i	$0.877869\pi$
$500$		0			0
$501$	7070.11			0.630477
$502$	−1449.13	+	1994.55i	−0.128840	+	0.177333i
$503$	−3087.72	+	1003.26i	−0.273707	+	0.0889329i	−0.442655	−	0.896692i	$-0.645963\pi$
$503$	−3087.72	+	1003.26i	−0.273707	+	0.0889329i	0.168947	+	0.985625i	$0.445963\pi$
$504$	−603.143	−	1856.28i	−0.0533058	−	0.164058i
$505$		0			0
$506$	1711.04	−	5266.05i	0.150326	−	0.462657i
$507$		−	1646.41i		−	0.144220i
$508$	−5767.18	−	1873.87i	−0.503695	−	0.163660i
$509$	43.4872	−	31.5953i	0.00378691	−	0.00275135i	−0.585890	−	0.810390i	$-0.699255\pi$
$509$	43.4872	−	31.5953i	0.00378691	−	0.00275135i	0.589677	+	0.807639i	$0.299255\pi$
$510$		0			0
$511$	26407.1	+	19185.8i	2.28606	+	1.66092i
$512$	300.946	+	414.217i	0.0259767	+	0.0357538i
$513$	4614.17	+	6350.86i	0.397116	+	0.546583i
$514$	10491.2	+	7622.28i	0.900284	+	0.654094i
$515$		0			0
$516$	7148.73	−	5193.86i	0.609894	−	0.443114i
$517$	2784.35	+	904.691i	0.236858	+	0.0769599i
$518$			7513.39i			0.637296i
$519$	−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	$0.832121\pi$
$522$	1144.37	−	371.830i	0.0959538	−	0.0311773i
$523$	3493.99	−	4809.07i	0.292126	−	0.402076i	−0.637577	−	0.770386i	$-0.720063\pi$
$523$	3493.99	−	4809.07i	0.292126	−	0.402076i	0.929703	+	0.368310i	$0.120063\pi$
$524$	4991.40			0.416126
$525$		0			0
$526$	−1598.18			−0.132479
$527$	4448.90	−	6123.38i	0.367736	−	0.506146i
$528$	−993.262	+	322.730i	−0.0818677	+	0.0266004i
$529$	−6903.40	−	21246.5i	−0.567387	−	1.74624i
$530$		0			0
$531$	−155.189	+	477.624i	−0.0126830	+	0.0390341i
$532$		−	6425.53i		−	0.523651i
$533$	−12442.9	−	4042.94i	−1.01118	−	0.328554i
$534$	−7805.61	+	5671.10i	−0.632550	+	0.459574i
$535$		0			0
$536$	1521.34	+	1105.32i	0.122597	+	0.0890718i
$537$	−7122.13	−	9802.77i	−0.572333	−	0.787748i
$538$	−4795.63	−	6600.61i	−0.384301	−	0.528945i
$539$	−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	$0.599505\pi$
$542$	−836.080	−	271.659i	−0.0662596	−	0.0215290i
$543$			14314.0i			1.13126i
$544$	−287.773	+	885.674i	−0.0226804	+	0.0698032i
$545$		0			0
$546$	3604.49	+	11093.5i	0.282524	+	0.869519i
$547$	−17348.4	+	5636.82i	−1.35606	+	0.440609i	−0.894724	−	0.446619i	$-0.852628\pi$
$547$	−17348.4	+	5636.82i	−1.35606	+	0.440609i	−0.461331	+	0.887228i	$0.652628\pi$
$548$	5620.24	−	7735.60i	0.438111	−	0.603008i
$549$	−1068.52			−0.0830665
$550$		0			0
$551$	3961.26			0.306271
$552$	−3825.63	+	5265.53i	−0.294981	+	0.406007i
$553$	10483.3	−	3406.24i	0.806143	−	0.261932i
$554$	−39.6601	−	122.061i	−0.00304151	−	0.00936080i
$555$		0			0
$556$	2174.67	−	6692.95i	0.165875	−	0.510511i
$557$		−	2617.19i		−	0.199092i	−0.995033	−	0.0995458i	$-0.968261\pi$
$557$		−	2617.19i		−	0.199092i	0.995033	−	0.0995458i	$-0.0317390\pi$
$558$	3867.90	+	1256.76i	0.293443	+	0.0953454i
$559$	17413.7	−	12651.8i	1.31757	−	0.957272i
$560$		0			0
$561$	−1536.78	−	1116.54i	−0.115656	−	0.0840290i
$562$	−2100.93	−	2891.68i	−0.157691	−	0.217043i
$563$	9201.70	+	12665.1i	0.688820	+	0.948079i	0.999997	−	0.00227286i	$-0.000723474\pi$
$563$	9201.70	+	12665.1i	0.688820	+	0.948079i	−0.311178	+	0.950352i	$0.600723\pi$
$564$	−2784.08	−	2022.75i	−0.207856	−	0.151016i
$565$		0			0
$566$	−10102.0	+	7339.50i	−0.750207	+	0.545057i
$567$	−13556.0	−	4404.62i	−1.00405	−	0.326237i
$568$			4314.69i			0.318733i
$569$	−2209.54	+	6800.27i	−0.162792	+	0.501023i	−0.998867	−	0.0475929i	$-0.984845\pi$
$569$	−2209.54	+	6800.27i	−0.162792	+	0.501023i	0.836075	+	0.548616i	$0.184845\pi$
$570$		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	$0.810409\pi$
$572$	−2419.51	+	786.145i	−0.176861	+	0.0574657i
$573$	−913.076	+	1256.74i	−0.0665695	+	0.0916250i
$574$	−19134.0			−1.39136
$575$		0			0
$576$	−500.383			−0.0361967
$577$	−4557.21	+	6272.46i	−0.328803	+	0.452558i	−0.941129	−	0.338047i	$-0.890234\pi$
$577$	−4557.21	+	6272.46i	−0.328803	+	0.452558i	0.612327	+	0.790605i	$0.290234\pi$
$578$	7734.17	−	2512.98i	0.556573	−	0.180841i
$579$	3935.42	+	12112.0i	0.282471	+	0.869356i
$580$		0			0
$581$	9418.71	−	28987.8i	0.672554	−	2.06991i
$582$			12707.9i			0.905083i
$583$	−6420.66	−	2086.20i	−0.456117	−	0.148202i
$584$	6769.93	−	4918.64i	0.479695	−	0.348519i
$585$		0			0
$586$	−3951.71	−	2871.09i	−0.278573	−	0.202395i
$587$	5047.27	+	6946.97i	0.354894	+	0.488470i	0.948717	−	0.316126i	$-0.102382\pi$
$587$	5047.27	+	6946.97i	0.354894	+	0.488470i	−0.593823	+	0.804596i	$0.702382\pi$
$588$	6495.07	+	8939.70i	0.455531	+	0.626984i
$589$	10831.7	+	7869.70i	0.757747	+	0.550536i
$590$		0			0
$591$	−14808.9	+	10759.3i	−1.03072	+	0.748865i
$592$	1831.92	+	595.227i	0.127182	+	0.0413238i
$593$			7557.43i			0.523350i	0.965156	+	0.261675i	$0.0842748\pi$
$593$			7557.43i			0.523350i	−0.965156	+	0.261675i	$0.915725\pi$
$594$	1404.62	−	4322.98i	0.0970241	−	0.298610i
$595$		0			0
$596$	484.073	+	1489.82i	0.0332691	+	0.102392i
$597$	4382.22	−	1423.87i	0.300423	−	0.0976133i
$598$	−9318.93	+	12826.4i	−0.637256	+	0.877108i
$599$	1555.67			0.106115			0.0530577	−	0.998591i	$-0.483103\pi$
$599$	1555.67			0.106115			0.0530577	+	0.998591i	$0.483103\pi$
$600$		0			0
$601$	3958.20			0.268650			0.134325	−	0.990937i	$-0.457113\pi$
$601$	3958.20			0.268650			0.134325	+	0.990937i	$0.457113\pi$
$602$	18503.1	−	25467.3i	1.25271	−	1.72420i
$603$	−1747.86	+	567.915i	−0.118041	+	0.0383537i
$604$	−2394.80	−	7370.42i	−0.161329	−	0.496520i
$605$		0			0
$606$	827.665	−	2547.29i	0.0554812	−	0.170753i
$607$		−	23128.2i		−	1.54653i	−0.634081	−	0.773266i	$-0.718622\pi$
$607$		−	23128.2i		−	1.54653i	0.634081	−	0.773266i	$-0.281378\pi$
$608$	−1566.68	−	509.045i	−0.104502	−	0.0339547i
$609$	−8508.14	+	6181.52i	−0.566120	+	0.411310i
$610$		0			0
$611$	−6781.78	−	4927.25i	−0.449037	−	0.326244i
$612$	−534.957	−	736.305i	−0.0353339	−	0.0486329i
$613$	−5456.58	−	7510.33i	−0.359525	−	0.494844i	0.590491	−	0.807044i	$-0.298934\pi$
$613$	−5456.58	−	7510.33i	−0.359525	−	0.494844i	−0.950016	+	0.312200i	$0.898934\pi$
$614$	−10327.4	−	7503.26i	−0.678792	−	0.493171i
$615$		0			0
$616$	−3010.02	+	2186.91i	−0.196878	+	0.143041i
$617$	−5259.91	−	1709.05i	−0.343203	−	0.111513i	0.132344	−	0.991204i	$-0.457750\pi$
$617$	−5259.91	−	1709.05i	−0.343203	−	0.111513i	−0.475547	+	0.879691i	$0.657750\pi$
$618$			3112.23i			0.202576i
$619$	4872.99	−	14997.5i	0.316417	−	0.973831i	−0.658750	−	0.752361i	$-0.728915\pi$
$619$	4872.99	−	14997.5i	0.316417	−	0.973831i	0.975167	−	0.221469i	$-0.0710853\pi$
$620$		0			0
$621$	−8753.60	−	26940.8i	−0.565652	−	1.74090i
$622$	5848.26	−	1900.21i	0.377000	−	0.122495i
$623$	−20203.3	+	27807.4i	−1.29924	+	1.78825i
$624$	2990.38			0.191844
$625$		0			0
$626$	11112.5			0.709496
$627$	1975.06	−	2718.43i	0.125799	−	0.173148i
$628$	−6840.48	+	2222.61i	−0.434657	+	0.141229i
$629$	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	$-0.143553\pi$
$632$		−	2825.90i		−	0.177861i
$633$	5532.59	+	1797.65i	0.347395	+	0.112875i
$634$	−5383.88	+	3911.62i	−0.337258	+	0.245032i
$635$		0			0
$636$	6420.02	+	4664.42i	0.400268	+	0.290812i
$637$	15821.5	+	21776.4i	0.984096	+	1.35449i
$638$	−1348.20	−	1855.64i	−0.0836610	−	0.115149i
$639$	−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	$-0.0458817\pi$
$642$	−2117.45	−	688.003i	−0.130170	−	0.0422949i
$643$		−	19485.8i		−	1.19509i	−0.801834	−	0.597547i	$-0.796142\pi$
$643$		−	19485.8i		−	1.19509i	0.801834	−	0.597547i	$-0.203858\pi$
$644$	−7165.08	+	22051.8i	−0.438422	+	1.34932i
$645$		0			0
$646$	−925.877	−	2849.56i	−0.0563903	−	0.173552i
$647$	17212.8	−	5592.78i	1.04591	−	0.339838i	0.264850	−	0.964290i	$-0.414678\pi$
$647$	17212.8	−	5592.78i	1.04591	−	0.339838i	0.781063	+	0.624452i	$0.214678\pi$
$648$	−2147.87	+	2956.29i	−0.130211	+	0.179219i
$649$	957.312			0.0579010
$650$		0			0
$651$	−35545.4			−2.13999
$652$	−3136.73	+	4317.34i	−0.188411	+	0.259325i
$653$	25011.1	−	8126.61i	1.49887	−	0.487012i	0.559181	−	0.829045i	$-0.311115\pi$
$653$	25011.1	−	8126.61i	1.49887	−	0.487012i	0.939688	+	0.342033i	$0.111115\pi$
$654$	2421.08	+	7451.33i	0.144758	+	0.445520i
$655$		0			0
$656$	−1515.84	+	4665.27i	−0.0902188	+	0.277665i
$657$			8178.22i			0.485636i
$658$	−11659.6	−	3788.44i	−0.690789	−	0.224451i
$659$	−832.956	+	605.178i	−0.0492373	+	0.0357730i	−0.612132	−	0.790756i	$-0.709688\pi$
$659$	−832.956	+	605.178i	−0.0492373	+	0.0357730i	0.562894	+	0.826529i	$0.309688\pi$
$660$		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	$0.660122\pi$
$662$	−1013.55	−	1395.03i	−0.0595056	−	0.0819024i
$663$	3197.00	+	4400.29i	0.187272	+	0.257757i
$664$	−6321.66	−	4592.95i	−0.369470	−	0.268435i
$665$		0			0
$666$	−1522.97	+	1106.50i	−0.0886092	+	0.0643784i
$667$	−13594.7	−	4417.18i	−0.789187	−	0.256422i
$668$		−	6457.21i		−	0.374007i
$669$	6045.50	−	18606.1i	0.349376	−	1.07527i
$670$		0			0
$671$	629.420	+	1937.15i	0.0362123	+	0.111450i
$672$	4159.33	−	1351.45i	0.238764	−	0.0775793i
$673$	8195.71	−	11280.4i	0.469422	−	0.646105i	−0.507007	−	0.861942i	$-0.669248\pi$
$673$	8195.71	−	11280.4i	0.469422	−	0.646105i	0.976429	+	0.215837i	$0.0692481\pi$
$674$	11456.0			0.654699
$675$		0			0
$676$	−1503.68			−0.0855532
$677$	7907.76	−	10884.1i	0.448921	−	0.617887i	−0.523244	−	0.852183i	$-0.675278\pi$
$677$	7907.76	−	10884.1i	0.448921	−	0.617887i	0.972165	+	0.234296i	$0.0752784\pi$
$678$	11135.9	−	3618.27i	0.630784	−	0.204954i
$679$	13989.7	+	43056.0i	0.790688	+	2.43349i
$680$		0			0
$681$	−2499.87	+	7693.82i	−0.140669	+	0.432934i
$682$		−	7752.51i		−	0.435277i
$683$	18301.2	+	5946.43i	1.02530	+	0.333139i	0.772928	−	0.634493i	$-0.218791\pi$
$683$	18301.2	+	5946.43i	1.02530	+	0.333139i	0.252367	+	0.967632i	$0.418791\pi$
$684$	1302.46	−	946.290i	0.0728080	−	0.0528981i
$685$		0			0
$686$	14529.2	+	10556.1i	0.808642	+	0.587513i
$687$	666.697	+	917.629i	0.0370248	+	0.0509603i
$688$	−4743.61	−	6529.01i	−0.262861	−	0.361797i
$689$	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	$0.517910\pi$
$692$	12564.3	+	4082.39i	0.690206	+	0.224262i
$693$		−	3636.17i		−	0.199317i
$694$	−1431.13	+	4404.58i	−0.0782783	+	0.240916i
$695$		0			0
$696$	833.150	+	2564.17i	0.0453743	+	0.139648i
$697$	−8485.44	+	2757.09i	−0.461132	+	0.149831i
$698$	−5236.16	+	7206.96i	−0.283942	+	0.390813i
$699$	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	$0.536323\pi$
$702$	−7650.05	+	10529.4i	−0.411300	+	0.566106i
$703$	−5894.00	+	1915.08i	−0.316211	+	0.102743i
$704$	294.753	+	907.156i	0.0157797	+	0.0485650i
$705$		0			0
$706$	4692.01	−	14440.5i	0.250122	−	0.769796i
$707$		−	9541.71i		−	0.507572i
$708$	−1070.20	−	347.729i	−0.0568088	−	0.0184583i
$709$	18626.9	−	13533.2i	0.986668	−	0.716856i	0.0274791	−	0.999622i	$-0.491252\pi$
$709$	18626.9	−	13533.2i	0.986668	−	0.716856i	0.959189	+	0.282766i	$0.0912520\pi$
$710$		0			0
$711$	2234.33	+	1623.34i	0.117854	+	0.0856257i
$712$	5179.48	+	7128.94i	0.272625	+	0.375236i
$713$	−28398.0	−	39086.5i	−1.49160	−	2.05302i
$714$	6435.35	+	4675.56i	0.337307	+	0.245068i
$715$		0			0
$716$	−8952.98	+	6504.72i	−0.467302	+	0.339515i
$717$	12010.0	+	3902.29i	0.625554	+	0.203255i
$718$		−	18627.8i		−	0.968222i
$719$	1901.30	−	5851.59i	0.0986181	−	0.303515i	−0.889562	−	0.456815i	$-0.848990\pi$
$719$	1901.30	−	5851.59i	0.0986181	−	0.303515i	0.988180	+	0.153300i	$0.0489901\pi$
$720$		0			0
$721$	3426.16	+	10544.7i	0.176972	+	0.544665i
$722$	−8005.98	+	2601.30i	−0.412676	+	0.134086i
$723$	16273.3	−	22398.2i	0.837080	−	1.15214i
$724$	13073.2			0.671078
$725$		0			0
$726$	9713.04			0.496536
$727$	−16997.0	+	23394.3i	−0.867101	+	1.19346i	0.112729	+	0.993626i	$0.464041\pi$
$727$	−16997.0	+	23394.3i	−0.867101	+	1.19346i	−0.979829	+	0.199836i	$0.935959\pi$
$728$	10131.8	−	3292.02i	0.515810	−	0.167597i
$729$	−6675.94	−	20546.4i	−0.339173	−	1.04387i
$730$		0			0
$731$	4535.97	−	13960.3i	0.229506	−	0.706346i
$732$		−	2394.22i		−	0.120892i
$733$	10380.1	+	3372.68i	0.523051	+	0.169949i	0.558629	−	0.829417i	$-0.311327\pi$
$733$	10380.1	+	3372.68i	0.523051	+	0.169949i	−0.0355788	+	0.999367i	$0.511327\pi$
$734$	−12472.3	+	9061.65i	−0.627194	+	0.455683i
$735$		0			0
$736$	4809.06	+	3493.99i	0.240848	+	0.174987i
$737$	2059.17	+	2834.21i	0.102918	+	0.141655i
$738$	−2817.87	−	3878.47i	−0.140552	−	0.193453i
$739$	−11697.6	−	8498.82i	−0.582278	−	0.423050i	0.257266	−	0.966341i	$-0.417178\pi$
$739$	−11697.6	−	8498.82i	−0.582278	−	0.423050i	−0.839545	+	0.543290i	$0.817178\pi$
$740$		0			0
$741$	−7783.72	+	5655.20i	−0.385887	+	0.280363i
$742$	26886.8	+	8736.06i	1.33025	+	0.432225i
$743$		−	22720.1i		−	1.12183i	−0.827874	−	0.560915i	$-0.810450\pi$
$743$		−	22720.1i		−	1.12183i	0.827874	−	0.560915i	$-0.189550\pi$
$744$	−2815.98	+	8666.71i	−0.138762	+	0.427066i
$745$		0			0
$746$	−5519.15	−	16986.2i	−0.270872	−	0.833659i
$747$	7262.93	−	2359.87i	0.355739	−	0.115586i
$748$	−1019.75	+	1403.56i	−0.0498471	+	0.0686086i
$749$	−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	$0.496902\pi$
$752$	−1847.40	+	2542.73i	−0.0895847	+	0.123303i
$753$	5134.59	−	1668.33i	0.248493	−	0.0807401i
$754$	2029.49	+	6246.12i	0.0980233	+	0.301685i
$755$		0			0
$756$	−5881.92	+	18102.7i	−0.282968	+	0.870885i
$757$			8445.77i			0.405504i	0.979230	+	0.202752i	$0.0649886\pi$
$757$			8445.77i			0.405504i	−0.979230	+	0.202752i	$0.935011\pi$
$758$	−8072.77	−	2623.00i	−0.386829	−	0.125688i
$759$	−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	$0.771532\pi$
$762$	7805.26	+	10743.0i	0.371069	+	0.510733i
$763$	16405.9	+	22580.8i	0.778419	+	1.07140i
$764$	1147.80	+	833.922i	0.0543531	+	0.0394898i
$765$		0			0
$766$	8832.39	−	6417.11i	0.416615	−	0.302689i
$767$	−2606.92	−	847.041i	−0.122726	−	0.0398760i
$768$		−	1121.20i		−	0.0526793i
$769$	3534.39	−	10877.7i	0.165739	−	0.510092i	−0.833351	−	0.552744i	$-0.813581\pi$
$769$	3534.39	−	10877.7i	0.165739	−	0.510092i	0.999090	+	0.0426520i	$0.0135807\pi$
$770$		0			0
$771$	−8775.26	−	27007.5i	−0.409901	−	1.26154i
$772$	11062.0	−	3594.26i	0.515713	−	0.167565i
$773$	2210.68	−	3042.74i	0.102862	−	0.141578i	−0.754483	−	0.656320i	$-0.772112\pi$
$773$	2210.68	−	3042.74i	0.102862	−	0.141578i	0.857345	+	0.514742i	$0.172112\pi$
$774$	7887.19			0.366278
$775$		0			0
$776$	11606.2			0.536907
$777$	9670.89	−	13310.8i	0.446514	−	0.614573i
$778$	−24593.1	+	7990.78i	−1.13330	+	0.368231i
$779$	−4877.04	−	15010.0i	−0.224311	−	0.690357i
$780$		0			0
$781$	−2483.92	+	7644.72i	−0.113805	+	0.350256i
$782$			10811.9i			0.494413i
$783$	−11160.1	−	3626.13i	−0.509360	−	0.165501i
$784$	8164.72	−	5932.01i	0.371935	−	0.270227i
$785$		0			0
$786$	−8842.83	−	6424.69i	−0.401289	−	0.291554i
$787$	−13423.6	−	18476.0i	−0.608005	−	0.836848i	0.388406	−	0.921488i	$-0.373026\pi$
$787$	−13423.6	−	18476.0i	−0.608005	−	0.836848i	−0.996412	+	0.0846407i	$0.973026\pi$
$788$	9826.60	+	13525.2i	0.444236	+	0.611439i
$789$	2831.36	+	2057.10i	0.127756	+	0.0928198i
$790$		0			0
$791$	33746.6	−	24518.4i	1.51693	−	1.10211i
$792$	−886.573	−	288.065i	−0.0397765	−	0.0129242i
$793$		−	5832.12i		−	0.261166i
$794$	−1256.17	+	3866.08i	−0.0561457	+	0.172799i
$795$		0			0
$796$	−1300.44	−	4002.33i	−0.0579055	−	0.178215i
$797$	153.415	−	49.8475i	0.00681836	−	0.00221542i	−0.305606	−	0.952158i	$-0.598859\pi$
$797$	153.415	−	49.8475i	0.00681836	−	0.00221542i	0.312424	+	0.949943i	$0.398859\pi$
$798$	−8270.65	+	11383.6i	−0.366889	+	0.504980i
$799$	−5716.62			−0.253116
$800$		0			0
$801$	−8611.91			−0.379884
$802$	10547.7	−	14517.7i	0.464405	−	0.639199i
$803$	14826.5	−	4817.42i	0.651576	−	0.211710i
$804$	−1272.51	−	3916.40i	−0.0558185	−	0.171792i
$805$		0			0
$806$	−6859.51	+	21111.4i	−0.299772	+	0.922602i
$807$			17866.4i			0.779342i
$808$	−2326.47	−	755.915i	−0.101293	−	0.0329121i
$809$	8390.60	−	6096.13i	0.364645	−	0.264930i	−0.390342	−	0.920670i	$-0.627643\pi$
$809$	8390.60	−	6096.13i	0.364645	−	0.264930i	0.754987	+	0.655740i	$0.227643\pi$
$810$		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	$-0.670896\pi$
$812$	5645.65	+	7770.57i	0.243994	+	0.335830i
$813$	1131.54	+	1557.44i	0.0488130	+	0.0671854i
$814$	2903.11	+	2109.23i	0.125005	+	0.0908214i
$815$		0			0
$816$	1649.82	−	1198.66i	0.0707785	−	0.0514236i
$817$	24694.5	+	8023.72i	1.05747	+	0.343592i
$818$		−	17311.5i		−	0.739954i
$819$	−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	$0.699815\pi$
$822$	−19913.8	+	6470.39i	−0.844980	+	0.274551i
$823$	6684.48	−	9200.39i	0.283118	−	0.389679i	−0.643645	−	0.765324i	$-0.722579\pi$
$823$	6684.48	−	9200.39i	0.283118	−	0.389679i	0.926764	+	0.375645i	$0.122579\pi$
$824$	2842.43			0.120171
$825$		0			0
$826$	−4008.79			−0.168866
$827$	−1946.09	+	2678.57i	−0.0818287	+	0.112628i	−0.847969	−	0.530046i	$-0.822175\pi$
$827$	−1946.09	+	2678.57i	−0.0818287	+	0.112628i	0.766140	+	0.642673i	$0.222175\pi$
$828$	−5525.12	+	1795.22i	−0.231897	+	0.0753480i
$829$	7520.64	+	23146.2i	0.315082	+	0.969722i	0.975721	+	0.219018i	$0.0702854\pi$
$829$	7520.64	+	23146.2i	0.315082	+	0.969722i	−0.660639	+	0.750704i	$0.729715\pi$
$830$		0			0
$831$	−86.8491	+	267.294i	−0.00362547	+	0.0111580i
$832$		−	2731.14i		−	0.113804i
$833$	17457.7	+	5672.36i	0.726139	+	0.235937i
$834$	−12467.5	+	9058.19i	−0.517644	+	0.376090i
$835$		0			0
$836$	−2482.77	−	1803.84i	−0.102713	−	0.0746257i
$837$	−23312.4	−	32086.7i	−0.962716	−	1.32506i
$838$	6750.22	+	9290.88i	0.278261	+	0.382993i
$839$	−11147.2	−	8098.89i	−0.458692	−	0.333260i	0.334326	−	0.942458i	$-0.391491\pi$
$839$	−11147.2	−	8098.89i	−0.458692	−	0.333260i	−0.793018	+	0.609198i	$0.791491\pi$
$840$		0			0
$841$	14940.7	−	10855.0i	0.612598	−	0.445079i
$842$	−7012.51	−	2278.50i	−0.287015	−	0.0932570i
$843$			7827.16i			0.319789i
$844$	1641.81	−	5052.97i	0.0669591	−	0.206079i
$845$		0			0
$846$	−949.197	−	2921.33i	−0.0385746	−	0.118720i
$847$	32909.1	−	10692.8i	1.33503	−	0.433777i
$848$	4260.06	−	5863.47i	0.172513	−	0.237444i
$849$	27343.8			1.10535
$850$		0			0
$851$	22363.2			0.900822
$852$	5553.67	−	7643.97i	0.223316	−	0.307369i
$853$	−12442.5	+	4042.80i	−0.499439	+	0.162278i	−0.547894	−	0.836548i	$-0.684570\pi$
$853$	−12442.5	+	4042.80i	−0.499439	+	0.162278i	0.0484548	+	0.998825i	$0.484570\pi$
$854$	−2635.73	−	8111.93i	−0.105612	−	0.325040i
$855$		0			0
$856$	−628.360	+	1933.89i	−0.0250898	+	0.0772186i
$857$			17624.7i			0.702508i	0.936280	+	0.351254i	$0.114245\pi$
$857$			17624.7i			0.702508i	−0.936280	+	0.351254i	$0.885755\pi$
$858$	5298.32	+	1721.53i	0.210818	+	0.0684988i
$859$	−834.395	+	606.224i	−0.0331423	+	0.0240793i	−0.604233	−	0.796808i	$-0.706520\pi$
$859$	−834.395	+	606.224i	−0.0331423	+	0.0240793i	0.571091	+	0.820887i	$0.306520\pi$
$860$		0			0
$861$	33898.1	+	24628.4i	1.34175	+	0.974836i
$862$	−11310.0	−	15566.9i	−0.446891	−	0.615093i
$863$	21765.5	+	29957.6i	0.858523	+	1.18166i	0.981920	+	0.189299i	$0.0606214\pi$
$863$	21765.5	+	29957.6i	0.858523	+	1.18166i	−0.123396	+	0.992357i	$0.539379\pi$
$864$	3947.83	+	2868.27i	0.155449	+	0.112940i
$865$		0			0
$866$	−2561.31	+	1860.90i	−0.100505	+	0.0730209i
$867$	−16936.6	−	5503.02i	−0.663432	−	0.215562i
$868$			32464.0i			1.26947i
$869$	1626.84	−	5006.91i	0.0635062	−	0.195452i
$870$		0			0
$871$	−3099.74	−	9540.02i	−0.120586	−	0.371127i
$872$	6805.38	−	2211.20i	0.264288	−	0.0858724i
$873$	−6667.18	+	9176.59i	−0.258477	+	0.355762i
$874$	−19125.2			−0.740183
$875$		0			0
$876$	−18324.7			−0.706776
$877$	−24803.1	+	34138.6i	−0.955008	+	1.31446i	−0.00574075	+	0.999984i	$0.501827\pi$
$877$	−24803.1	+	34138.6i	−0.955008	+	1.31446i	−0.949267	+	0.314472i	$0.898173\pi$
$878$	−3163.84	+	1027.99i	−0.121611	+	0.0395138i
$879$	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	$0.140497\pi$
$882$			9863.15i			0.376542i
$883$	5354.36	+	1739.74i	0.204064	+	0.0663044i	0.409266	−	0.912415i	$-0.365785\pi$
$883$	5354.36	+	1739.74i	0.204064	+	0.0663044i	−0.205202	+	0.978720i	$0.565785\pi$
$884$	4018.83	−	2919.85i	0.152905	−	0.111092i
$885$		0			0
$886$	10462.6	+	7601.49i	0.396723	+	0.288236i
$887$	−19343.9	−	26624.6i	−0.732250	−	1.00786i	−0.999027	−	0.0440972i	$-0.985959\pi$
$887$	−19343.9	−	26624.6i	−0.732250	−	1.00786i	0.266777	−	0.963758i	$-0.414041\pi$
$888$	−2479.31	−	3412.47i	−0.0936938	−	0.128959i
$889$	38271.9	+	27806.2i	1.44387	+	1.04903i
$890$		0			0
$891$	−5507.49	+	4001.42i	−0.207079	+	0.150452i
$892$	−16993.2	−	5521.42i	−0.637863	−	0.207254i
$893$		−	10112.2i		−	0.378938i
$894$	1060.04	−	3262.47i	0.0396567	−	0.122051i
$895$		0			0
$896$	−1234.29	−	3798.76i	−0.0460210	−	0.141638i
$897$	33019.1	−	10728.6i	1.22907	−	0.399349i
$898$	6535.16	−	8994.87i	0.242852	−	0.334257i
$899$	−20013.6			−0.742483
$900$		0			0
$901$	13182.4			0.487425
$902$	−5371.49	+	7393.22i	−0.198283	+	0.272913i
$903$	−65560.7	+	21302.0i	−2.41608	+	0.785033i
$904$	−3304.60	−	10170.5i	−0.121581	−	0.374189i
$905$		0			0
$906$	−5244.21	+	16140.0i	−0.192304	+	0.591850i
$907$		−	23738.5i		−	0.869046i	−0.900661	−	0.434523i	$-0.856917\pi$
$907$		−	23738.5i		−	0.869046i	0.900661	−	0.434523i	$-0.143083\pi$
$908$	7026.85	+	2283.16i	0.256822	+	0.0834464i
$909$	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	$0.776459\pi$
$912$	2120.33	+	2918.39i	0.0769859	+	0.105962i
$913$	−8556.53	−	11777.1i	−0.310164	−	0.426904i
$914$	−2131.53	−	1548.65i	−0.0771386	−	0.0560445i
$915$		0			0
$916$	838.081	−	608.901i	0.0302303	−	0.0219636i
$917$	−37033.5	−	12032.9i	−1.33364	−	0.433328i
$918$			8875.62i			0.319106i
$919$	983.027	−	3025.45i	0.0352852	−	0.108597i	−0.931863	−	0.362811i	$-0.881817\pi$
$919$	983.027	−	3025.45i	0.0352852	−	0.108597i	0.967148	+	0.254215i	$0.0818170\pi$
$920$		0			0
$921$	8638.24	+	26585.8i	0.309055	+	0.951174i
$922$	−16095.8	+	5229.86i	−0.574933	+	0.186807i
$923$	13528.3	−	18620.1i	0.482436	−	0.664017i
$924$	8147.48			0.290078
$925$		0			0
$926$	−25378.8			−0.900647
$927$	−1632.83	+	2247.40i	−0.0578524	+	0.0796270i
$928$	2341.89	−	760.925i	0.0828407	−	0.0269166i
$929$	−12964.0	−	39899.2i	−0.457843	−	1.40910i	−0.867764	−	0.496976i	$-0.834444\pi$
$929$	−12964.0	−	39899.2i	−0.457843	−	1.40910i	0.409921	−	0.912121i	$-0.365556\pi$
$930$		0			0
$931$	−10033.9	+	30881.1i	−0.353220	+	1.08710i
$932$		−	13552.7i		−	0.476322i
$933$	−12806.7	−	4161.16i	−0.449382	−	0.146013i
$934$	1329.01	−	965.585i	0.0465596	−	0.0338275i
$935$		0			0
$936$	2159.41	+	1568.90i	0.0754085	+	0.0547875i
$937$	2442.49	+	3361.80i	0.0851577	+	0.117210i	0.849470	−	0.527636i	$-0.176922\pi$
$937$	2442.49	+	3361.80i	0.0851577	+	0.117210i	−0.764313	+	0.644846i	$0.776922\pi$
$938$	−8622.90	−	11868.4i	−0.300157	−	0.413131i
$939$	−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	$0.402587\pi$
$942$	14979.5	+	4867.14i	0.518110	+	0.168344i
$943$			56951.2i			1.96669i
$944$	−317.585	+	977.426i	−0.0109497	+	0.0336997i
$945$		0			0
$946$	−4645.99	−	14298.9i	−0.159677	−	0.491434i
$947$	−46162.9	+	14999.2i	−1.58405	+	0.514688i	−0.963096	−	0.269160i	$-0.913254\pi$
$947$	−46162.9	+	14999.2i	−1.58405	+	0.514688i	−0.620953	+	0.783848i	$0.713254\pi$
$948$	−3637.37	+	5006.41i	−0.124616	+	0.171520i
$949$	−44637.6			−1.52687
$950$		0			0
$951$	14573.0			0.496911
$952$	4270.24	−	5877.48i	0.145377	−	0.200095i
$953$	−32652.7	+	10609.5i	−1.10989	+	0.360625i	−0.805900	−	0.592051i	$-0.798318\pi$
$953$	−32652.7	+	10609.5i	−1.10989	+	0.360625i	−0.303988	+	0.952676i	$0.598318\pi$
$954$	2188.83	+	6736.52i	0.0742830	+	0.228620i
$955$		0			0
$956$	3564.01	−	10968.9i	0.120573	−	0.371087i
$957$			5022.81i			0.169660i
$958$	20960.8	+	6810.57i	0.706902	+	0.229686i
$959$	−60347.6	+	43845.1i	−2.03204	+	1.47636i
$960$		0			0
$961$	−30624.1	−	22249.7i	−1.02797	−	0.746861i
$962$	−6039.39	−	8312.51i	−0.202409	−	0.278593i
$963$	−1168.09	−	1607.74i	−0.0390875	−	0.0537993i
$964$	−20456.5	−	14862.5i	−0.683465	−	0.496566i
$965$		0			0
$966$	41077.9	−	29844.8i	1.36818	−	0.994038i
$967$	6186.33	+	2010.06i	0.205728	+	0.0668451i	0.410068	−	0.912055i	$-0.365505\pi$
$967$	6186.33	+	2010.06i	0.205728	+	0.0668451i	−0.204340	+	0.978900i	$0.565505\pi$
$968$		−	8871.02i		−	0.294551i
$969$	−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	$0.749258\pi$
$972$	−8052.83	+	2616.52i	−0.265735	+	0.0863426i
$973$	−32269.8	+	44415.5i	−1.06323	+	1.46341i
$974$	−15708.9			−0.516782
$975$		0			0
$976$	−2186.66			−0.0717146
$977$	11978.4	−	16486.8i	0.392244	−	0.539877i	−0.566533	−	0.824039i	$-0.691715\pi$
$977$	11978.4	−	16486.8i	0.392244	−	0.539877i	0.958776	+	0.284162i	$0.0917155\pi$
$978$	11114.1	−	3611.21i	0.363386	−	0.118071i
$979$	5072.89	+	15612.8i	0.165608	+	0.509689i
$980$		0			0
$981$	−2161.03	+	6650.96i	−0.0703327	+	0.216462i
$982$		−	41047.7i		−	1.33390i
$983$	4843.95	+	1573.89i	0.157170	+	0.0510675i	0.386545	−	0.922270i	$-0.373668\pi$
$983$	4843.95	+	1573.89i	0.157170	+	0.0510675i	−0.229375	+	0.973338i	$0.573668\pi$
$984$	8690.40	−	6313.94i	0.281544	−	0.204554i
$985$		0			0
$986$	3623.39	+	2632.54i	0.117031	+	0.0850277i
$987$	15780.0	+	21719.3i	0.508900	+	0.700440i
$988$	5164.96	+	7108.95i	0.166315	+	0.228913i
$989$	−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	$0.306871\pi$
$992$	7915.39	+	2571.87i	0.253341	+	0.0823154i
$993$			3776.05i			0.120674i
$994$	10401.5	−	32012.7i	0.331908	−	1.02151i
$995$		0			0
$996$	5287.71	+	16273.9i	0.168220	+	0.517729i
$997$	21308.2	−	6923.45i	0.676868	−	0.219928i	0.0496443	−	0.998767i	$-0.484191\pi$
$997$	21308.2	−	6923.45i	0.676868	−	0.219928i	0.627224	+	0.778839i	$0.284191\pi$
$998$	24302.2	−	33449.1i	0.770814	−	1.06093i
$999$	18358.3			0.581411

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.e.a.9.6	✓	32	5.4	even	2
50.4.e.a.39.6	yes	32	25.11	even	5
250.4.d.c.51.3		32	25.2	odd	20
250.4.d.c.201.3		32	5.2	odd	4
250.4.d.d.51.6		32	25.23	odd	20
250.4.d.d.201.6		32	5.3	odd	4
250.4.e.b.49.3		32	1.1	even	1	trivial
250.4.e.b.199.3		32	25.14	even	10	inner
1250.4.a.m.1.12		16	25.8	odd	20
1250.4.a.n.1.5		16	25.17	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	250.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.17557 + 1.61803i) q^{2} +(4.16531 - 1.35339i) q^{3} +(-1.23607 - 3.80423i) q^{4} +(-2.70679 + 8.33063i) q^{6} +31.2051i q^{7} +(7.60845 + 2.47214i) q^{8} +(-6.32528 + 4.59559i) q^{9} +O(q^{10})\)	\(q+(-1.17557 + 1.61803i) q^{2} +(4.16531 - 1.35339i) q^{3} +(-1.23607 - 3.80423i) q^{4} +(-2.70679 + 8.33063i) q^{6} +31.2051i q^{7} +(7.60845 + 2.47214i) q^{8} +(-6.32528 + 4.59559i) q^{9} +(12.0574 + 8.76021i) q^{11} +(-10.2972 - 14.1729i) q^{12} +(-25.0832 - 34.5241i) q^{13} +(-50.4909 - 36.6838i) q^{14} +(-12.9443 + 9.40456i) q^{16} +(-27.6773 - 8.99290i) q^{17} -15.6370i q^{18} +(15.9076 - 48.9587i) q^{19} +(42.2328 + 129.979i) q^{21} +(-28.3486 + 9.21103i) q^{22} +(-109.187 + 150.283i) q^{23} +35.0374 q^{24} +85.3482 q^{26} +(-89.6334 + 123.370i) q^{27} +(118.711 - 38.5716i) q^{28} +(23.7789 + 73.1839i) q^{29} +(-80.3709 + 247.356i) q^{31} -32.0000i q^{32} +(62.0789 + 20.1706i) q^{33} +(47.0875 - 34.2110i) q^{34} +(25.3011 + 18.3823i) q^{36} +(-70.7618 - 97.3953i) q^{37} +(60.5163 + 83.2935i) q^{38} +(-151.204 - 109.856i) q^{39} +(248.032 - 180.206i) q^{41} +(-259.958 - 84.4656i) q^{42} +504.394i q^{43} +(18.4221 - 56.6973i) q^{44} +(-114.806 - 353.337i) q^{46} +(186.822 - 60.7022i) q^{47} +(-41.1889 + 56.6917i) q^{48} -630.759 q^{49} -127.456 q^{51} +(-100.333 + 138.096i) q^{52} +(-430.808 + 139.978i) q^{53} +(-94.2462 - 290.060i) q^{54} +(-77.1433 + 237.423i) q^{56} -225.458i q^{57} +(-146.368 - 47.5578i) q^{58} +(51.9655 - 37.7552i) q^{59} +(110.566 + 80.3305i) q^{61} +(-305.749 - 420.827i) q^{62} +(-143.406 - 197.381i) q^{63} +(51.7771 + 37.6183i) q^{64} +(-105.615 + 76.7337i) q^{66} +(223.555 + 72.6375i) q^{67} +116.407i q^{68} +(-251.407 + 773.750i) q^{69} +(166.664 + 512.939i) q^{71} +(-59.4865 + 19.3283i) q^{72} +(614.830 - 846.241i) q^{73} +240.774 q^{74} -205.913 q^{76} +(-273.363 + 376.252i) q^{77} +(355.502 - 115.510i) q^{78} +(-109.157 - 335.949i) q^{79} +(-141.150 + 434.416i) q^{81} +613.169i q^{82} +(-928.944 - 301.832i) q^{83} +(442.267 - 321.326i) q^{84} +(-816.127 - 592.951i) q^{86} +(198.093 + 272.652i) q^{87} +(70.0817 + 96.4592i) q^{88} +(891.118 + 647.435i) q^{89} +(1077.33 - 782.724i) q^{91} +(706.674 + 229.612i) q^{92} +1139.09i q^{93} +(-121.404 + 373.644i) q^{94} +(-43.3086 - 133.290i) q^{96} +(1379.77 - 448.316i) q^{97} +(741.502 - 1020.59i) q^{98} -116.525 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 12 q^{6} + 26 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 - 12 * q^6 + 26 * q^9	\( 32 q + 32 q^{4} - 12 q^{6} + 26 q^{9} - 106 q^{11} - 80 q^{12} + 56 q^{14} - 128 q^{16} - 320 q^{17} + 110 q^{19} - 36 q^{21} + 360 q^{22} + 370 q^{23} - 192 q^{24} + 808 q^{26} + 1200 q^{27} + 120 q^{28} - 10 q^{29} - 486 q^{31} - 2560 q^{33} + 616 q^{34} - 104 q^{36} - 680 q^{37} + 1012 q^{39} - 96 q^{41} + 1020 q^{42} - 136 q^{44} - 832 q^{46} - 1040 q^{47} - 320 q^{48} - 2076 q^{49} + 884 q^{51} + 2550 q^{53} - 120 q^{54} - 224 q^{56} + 2250 q^{59} + 934 q^{61} - 4200 q^{62} - 4660 q^{63} + 512 q^{64} + 16 q^{66} + 3780 q^{67} - 628 q^{69} - 2616 q^{71} + 600 q^{73} - 2584 q^{74} + 800 q^{76} + 4320 q^{77} + 6640 q^{78} - 2800 q^{79} - 5268 q^{81} - 4050 q^{83} + 624 q^{84} - 692 q^{86} - 9390 q^{87} + 1680 q^{88} + 4520 q^{89} + 3764 q^{91} - 1280 q^{92} + 656 q^{94} - 192 q^{96} - 1710 q^{97} - 3280 q^{98} - 2108 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 12 * q^6 + 26 * q^9 - 106 * q^11 - 80 * q^12 + 56 * q^14 - 128 * q^16 - 320 * q^17 + 110 * q^19 - 36 * q^21 + 360 * q^22 + 370 * q^23 - 192 * q^24 + 808 * q^26 + 1200 * q^27 + 120 * q^28 - 10 * q^29 - 486 * q^31 - 2560 * q^33 + 616 * q^34 - 104 * q^36 - 680 * q^37 + 1012 * q^39 - 96 * q^41 + 1020 * q^42 - 136 * q^44 - 832 * q^46 - 1040 * q^47 - 320 * q^48 - 2076 * q^49 + 884 * q^51 + 2550 * q^53 - 120 * q^54 - 224 * q^56 + 2250 * q^59 + 934 * q^61 - 4200 * q^62 - 4660 * q^63 + 512 * q^64 + 16 * q^66 + 3780 * q^67 - 628 * q^69 - 2616 * q^71 + 600 * q^73 - 2584 * q^74 + 800 * q^76 + 4320 * q^77 + 6640 * q^78 - 2800 * q^79 - 5268 * q^81 - 4050 * q^83 + 624 * q^84 - 692 * q^86 - 9390 * q^87 + 1680 * q^88 + 4520 * q^89 + 3764 * q^91 - 1280 * q^92 + 656 * q^94 - 192 * q^96 - 1710 * q^97 - 3280 * q^98 - 2108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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