LMFDB - Embedded newform 250.4.e.b.149.1

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			149.1
Character	$\chi$	$=$	250.149
Dual form			250.4.e.b.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90211 - 0.618034i) q^{2} +(-5.49755 + 7.56672i) q^{3} +(3.23607 + 2.35114i) q^{4} +(15.1334 - 10.9951i) q^{6} +11.0064i q^{7} +(-4.70228 - 6.47214i) q^{8} +(-18.6888 - 57.5183i) q^{9} +O(q^{10})$	\(q+(-1.90211 - 0.618034i) q^{2} +(-5.49755 + 7.56672i) q^{3} +(3.23607 + 2.35114i) q^{4} +(15.1334 - 10.9951i) q^{6} +11.0064i q^{7} +(-4.70228 - 6.47214i) q^{8} +(-18.6888 - 57.5183i) q^{9} +(-20.6668 + 63.6057i) q^{11} +(-35.5809 + 11.5609i) q^{12} +(-41.6768 + 13.5416i) q^{13} +(6.80231 - 20.9354i) q^{14} +(4.94427 + 15.2169i) q^{16} +(-5.11002 - 7.03334i) q^{17} +120.957i q^{18} +(-78.8015 + 57.2527i) q^{19} +(-83.2822 - 60.5080i) q^{21} +(78.6210 - 108.213i) q^{22} +(20.4810 + 6.65468i) q^{23} +74.8239 q^{24} +87.6431 q^{26} +(297.797 + 96.7602i) q^{27} +(-25.8775 + 35.6174i) q^{28} +(-16.7286 - 12.1540i) q^{29} +(159.247 - 115.699i) q^{31} -32.0000i q^{32} +(-367.671 - 506.055i) q^{33} +(5.37300 + 16.5364i) q^{34} +(74.7553 - 230.073i) q^{36} +(174.003 - 56.5369i) q^{37} +(185.274 - 60.1990i) q^{38} +(126.654 - 389.802i) q^{39} +(-80.7907 - 248.648i) q^{41} +(121.016 + 166.564i) q^{42} -77.2928i q^{43} +(-216.425 + 157.242i) q^{44} +(-34.8444 - 25.3159i) q^{46} +(-32.5409 + 44.7887i) q^{47} +(-142.323 - 46.2437i) q^{48} +221.860 q^{49} +81.3120 q^{51} +(-166.707 - 54.1664i) q^{52} +(-262.750 + 361.644i) q^{53} +(-506.643 - 368.097i) q^{54} +(71.2347 - 51.7551i) q^{56} -911.019i q^{57} +(24.3080 + 33.4571i) q^{58} +(84.4098 + 259.787i) q^{59} +(203.152 - 625.236i) q^{61} +(-374.411 + 121.654i) q^{62} +(633.068 - 205.696i) q^{63} +(-19.7771 + 60.8676i) q^{64} +(386.592 + 1189.81i) q^{66} +(173.931 + 239.395i) q^{67} -34.7748i q^{68} +(-162.949 + 118.390i) q^{69} +(151.135 + 109.806i) q^{71} +(-284.386 + 391.424i) q^{72} +(153.665 + 49.9287i) q^{73} -365.914 q^{74} -389.616 q^{76} +(-700.068 - 227.466i) q^{77} +(-481.822 + 663.171i) q^{78} +(-790.665 - 574.452i) q^{79} +(-1048.25 + 761.602i) q^{81} +522.889i q^{82} +(-480.309 - 661.089i) q^{83} +(-127.244 - 391.616i) q^{84} +(-47.7696 + 147.020i) q^{86} +(183.932 - 59.7632i) q^{87} +(508.846 - 165.334i) q^{88} +(-286.519 + 881.815i) q^{89} +(-149.044 - 458.710i) q^{91} +(50.6318 + 69.6888i) q^{92} +1841.04i q^{93} +(89.5774 - 65.0818i) q^{94} +(242.135 + 175.922i) q^{96} +(160.683 - 221.162i) q^{97} +(-422.002 - 137.117i) q^{98} +4044.73 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 $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−1.90211	−	0.618034i	−0.672499	−	0.218508i
$2$	−1.90211	−	0.618034i	−0.672499	−	0.218508i
$3$	−5.49755	+	7.56672i	−1.05800	+	1.45622i	−0.176345	+	0.984328i	$0.556427\pi$
$3$	−5.49755	+	7.56672i	−1.05800	+	1.45622i	−0.881658	+	0.471888i	$0.843573\pi$
$4$	3.23607	+	2.35114i	0.404508	+	0.293893i
$5$		0			0
$5$		0			0
$6$	15.1334	−	10.9951i	1.02970	−	0.748121i
$7$			11.0064i			0.594288i	0.954833	+	0.297144i	$0.0960342\pi$
$7$			11.0064i			0.594288i	−0.954833	+	0.297144i	$0.903966\pi$
$8$	−4.70228	−	6.47214i	−0.207813	−	0.286031i
$9$	−18.6888	−	57.5183i	−0.692179	−	2.13031i
$10$		0			0
$11$	−20.6668	+	63.6057i	−0.566478	+	1.74344i	0.0970396	+	0.995281i	$0.469063\pi$
$11$	−20.6668	+	63.6057i	−0.566478	+	1.74344i	−0.663518	+	0.748160i	$0.730937\pi$
$12$	−35.5809	+	11.5609i	−0.855943	+	0.278113i
$13$	−41.6768	+	13.5416i	−0.889159	+	0.288905i	−0.717755	−	0.696296i	$-0.754830\pi$
$13$	−41.6768	+	13.5416i	−0.889159	+	0.288905i	−0.171404	+	0.985201i	$0.554830\pi$
$14$	6.80231	−	20.9354i	0.129857	−	0.399658i
$15$		0			0
$16$	4.94427	+	15.2169i	0.0772542	+	0.237764i
$17$	−5.11002	−	7.03334i	−0.0729037	−	0.100343i	0.771008	−	0.636826i	$-0.219753\pi$
$17$	−5.11002	−	7.03334i	−0.0729037	−	0.100343i	−0.843912	+	0.536482i	$0.819753\pi$
$18$			120.957i			1.58388i
$19$	−78.8015	+	57.2527i	−0.951490	+	0.691298i	−0.951159	−	0.308702i	$-0.900105\pi$
$19$	−78.8015	+	57.2527i	−0.951490	+	0.691298i	−0.000331273		1.00000i	$0.500105\pi$
$20$		0			0
$21$	−83.2822	−	60.5080i	−0.865412	−	0.628759i
$22$	78.6210	−	108.213i	0.761912	−	1.04868i
$23$	20.4810	+	6.65468i	0.185678	+	0.0603303i	0.400380	−	0.916349i	$-0.368878\pi$
$23$	20.4810	+	6.65468i	0.185678	+	0.0603303i	−0.214702	+	0.976680i	$0.568878\pi$
$24$	74.8239			0.636390
$25$		0			0
$26$	87.6431			0.661086
$27$	297.797	+	96.7602i	2.12263	+	0.689685i
$28$	−25.8775	+	35.6174i	−0.174657	+	0.240395i
$29$	−16.7286	−	12.1540i	−0.107118	−	0.0778256i	0.532937	−	0.846155i	$-0.321088\pi$
$29$	−16.7286	−	12.1540i	−0.107118	−	0.0778256i	−0.640055	+	0.768329i	$0.721088\pi$
$30$		0			0
$31$	159.247	−	115.699i	0.922631	−	0.670330i	−0.0215469	−	0.999768i	$-0.506859\pi$
$31$	159.247	−	115.699i	0.922631	−	0.670330i	0.944177	+	0.329438i	$0.106859\pi$
$32$		−	32.0000i		−	0.176777i
$33$	−367.671	−	506.055i	−1.93949	−	2.66948i
$34$	5.37300	+	16.5364i	0.0271018	+	0.0834108i
$35$		0			0
$36$	74.7553	−	230.073i	0.346090	−	1.06515i
$37$	174.003	−	56.5369i	0.773131	−	0.251206i	0.104226	−	0.994554i	$-0.466763\pi$
$37$	174.003	−	56.5369i	0.773131	−	0.251206i	0.668905	+	0.743348i	$0.266763\pi$
$38$	185.274	−	60.1990i	0.790930	−	0.256989i
$39$	126.654	−	389.802i	0.520024	−	1.60047i
$40$		0			0
$41$	−80.7907	−	248.648i	−0.307741	−	0.947130i	−0.978640	−	0.205581i	$-0.934092\pi$
$41$	−80.7907	−	248.648i	−0.307741	−	0.947130i	0.670899	−	0.741549i	$-0.265908\pi$
$42$	121.016	+	166.564i	0.444600	+	0.611939i
$43$		−	77.2928i		−	0.274117i	−0.990563	−	0.137059i	$-0.956235\pi$
$43$		−	77.2928i		−	0.274117i	0.990563	−	0.137059i	$-0.0437649\pi$
$44$	−216.425	+	157.242i	−0.741530	+	0.538753i
$45$		0			0
$46$	−34.8444	−	25.3159i	−0.111685	−	0.0811441i
$47$	−32.5409	+	44.7887i	−0.100991	+	0.139002i	−0.856522	−	0.516111i	$-0.827379\pi$
$47$	−32.5409	+	44.7887i	−0.100991	+	0.139002i	0.755531	+	0.655113i	$0.227379\pi$
$48$	−142.323	−	46.2437i	−0.427971	−	0.139056i
$49$	221.860			0.646822
$50$		0			0
$51$	81.3120			0.223254
$52$	−166.707	−	54.1664i	−0.444579	−	0.144453i
$53$	−262.750	+	361.644i	−0.680971	+	0.937276i	−0.999945	−	0.0104876i	$-0.996662\pi$
$53$	−262.750	+	361.644i	−0.680971	+	0.937276i	0.318974	+	0.947763i	$0.396662\pi$
$54$	−506.643	−	368.097i	−1.27677	−	0.927625i
$55$		0			0
$56$	71.2347	−	51.7551i	0.169985	−	0.123501i
$57$		−	911.019i		−	2.11697i
$58$	24.3080	+	33.4571i	0.0550310	+	0.0757437i
$59$	84.4098	+	259.787i	0.186258	+	0.573243i	0.999968	−	0.00802833i	$-0.00255552\pi$
$59$	84.4098	+	259.787i	0.186258	+	0.573243i	−0.813710	+	0.581271i	$0.802556\pi$
$60$		0			0
$61$	203.152	−	625.236i	0.426408	−	1.31235i	−0.475231	−	0.879861i	$-0.657636\pi$
$61$	203.152	−	625.236i	0.426408	−	1.31235i	0.901640	−	0.432488i	$-0.142364\pi$
$62$	−374.411	+	121.654i	−0.766940	+	0.249194i
$63$	633.068	−	205.696i	1.26602	−	0.411354i
$64$	−19.7771	+	60.8676i	−0.0386271	+	0.118882i
$65$		0			0
$66$	386.592	+	1189.81i	0.721002	+	2.21902i
$67$	173.931	+	239.395i	0.317149	+	0.436519i	0.937594	−	0.347731i	$-0.113048\pi$
$67$	173.931	+	239.395i	0.317149	+	0.436519i	−0.620445	+	0.784250i	$0.713048\pi$
$68$		−	34.7748i		−	0.0620156i
$69$	−162.949	+	118.390i	−0.284302	+	0.206557i
$70$		0			0
$71$	151.135	+	109.806i	0.252626	+	0.183543i	0.706890	−	0.707324i	$-0.250098\pi$
$71$	151.135	+	109.806i	0.252626	+	0.183543i	−0.454264	+	0.890867i	$0.650098\pi$
$72$	−284.386	+	391.424i	−0.465489	+	0.640691i
$73$	153.665	+	49.9287i	0.246371	+	0.0800509i	0.429600	−	0.903019i	$-0.358655\pi$
$73$	153.665	+	49.9287i	0.246371	+	0.0800509i	−0.183228	+	0.983070i	$0.558655\pi$
$74$	−365.914			−0.574820
$75$		0			0
$76$	−389.616			−0.588053
$77$	−700.068	−	227.466i	−1.03611	−	0.336651i
$78$	−481.822	+	663.171i	−0.699431	+	0.962684i
$79$	−790.665	−	574.452i	−1.12603	−	0.818112i	−0.140922	−	0.990021i	$-0.545007\pi$
$79$	−790.665	−	574.452i	−1.12603	−	0.818112i	−0.985113	+	0.171909i	$0.945007\pi$
$80$		0			0
$81$	−1048.25	+	761.602i	−1.43794	+	1.04472i
$82$			522.889i			0.704188i
$83$	−480.309	−	661.089i	−0.635190	−	0.874264i	0.363158	−	0.931728i	$-0.381699\pi$
$83$	−480.309	−	661.089i	−0.635190	−	0.874264i	−0.998348	+	0.0574637i	$0.981699\pi$
$84$	−127.244	−	391.616i	−0.165279	−	0.508677i
$85$		0			0
$86$	−47.7696	+	147.020i	−0.0598968	+	0.184343i
$87$	183.932	−	59.7632i	0.226662	−	0.0736469i
$88$	508.846	−	165.334i	0.616399	−	0.200280i
$89$	−286.519	+	881.815i	−0.341247	+	1.05025i	0.622316	+	0.782766i	$0.286192\pi$
$89$	−286.519	+	881.815i	−0.341247	+	1.05025i	−0.963563	+	0.267483i	$0.913808\pi$
$90$		0			0
$91$	−149.044	−	458.710i	−0.171693	−	0.528416i
$92$	50.6318	+	69.6888i	0.0573776	+	0.0789734i
$93$			1841.04i			2.05276i
$94$	89.5774	−	65.0818i	0.0982893	−	0.0714114i
$95$		0			0
$96$	242.135	+	175.922i	0.257425	+	0.187030i
$97$	160.683	−	221.162i	0.168195	−	0.231501i	−0.716596	−	0.697488i	$-0.754301\pi$
$97$	160.683	−	221.162i	0.168195	−	0.231501i	0.884791	+	0.465988i	$0.154301\pi$
$98$	−422.002	−	137.117i	−0.434987	−	0.141336i
$99$	4044.73			4.10617
$100$		0			0
$101$	1126.42			1.10974			0.554868	−	0.831939i	$-0.312769\pi$
$101$	1126.42			1.10974			0.554868	+	0.831939i	$0.312769\pi$
$102$	−154.665	−	50.2536i	−0.150138	−	0.0487828i
$103$	779.783	−	1073.28i	0.745965	−	1.02673i	−0.252289	−	0.967652i	$-0.581183\pi$
$103$	779.783	−	1073.28i	0.745965	−	1.02673i	0.998253	−	0.0590801i	$-0.0188167\pi$
$104$	283.619	+	206.061i	0.267415	+	0.194288i
$105$		0			0
$106$	723.288	−	525.499i	0.662754	−	0.481519i
$107$		−	493.813i		−	0.446157i	−0.974801	−	0.223078i	$-0.928389\pi$
$107$		−	493.813i		−	0.446157i	0.974801	−	0.223078i	$-0.0716105\pi$
$108$	736.195	+	1013.29i	0.655930	+	0.902810i
$109$	262.755	+	808.677i	0.230893	+	0.710616i	0.997640	+	0.0686662i	$0.0218743\pi$
$109$	262.755	+	808.677i	0.230893	+	0.710616i	−0.766746	+	0.641950i	$0.778126\pi$
$110$		0			0
$111$	−528.789	+	1627.44i	−0.452166	+	1.39162i
$112$	−167.483	+	54.4185i	−0.141300	+	0.0459113i
$113$	−108.442	+	35.2349i	−0.0902775	+	0.0293329i	−0.353807	−	0.935318i	$-0.615113\pi$
$113$	−108.442	+	35.2349i	−0.0902775	+	0.0293329i	0.263530	+	0.964651i	$0.415113\pi$
$114$	−563.041	+	1732.86i	−0.462575	+	1.42366i
$115$		0			0
$116$	−25.5590	−	78.6624i	−0.0204577	−	0.0629622i
$117$	1557.78	+	2144.10i	1.23091	+	1.69421i
$118$		−	546.312i		−	0.426204i
$119$	77.4116	−	56.2428i	0.0596328	−	0.0433258i
$120$		0			0
$121$	−2541.77	−	1846.71i	−1.90967	−	1.38746i
$122$	−772.834	+	1063.72i	−0.573518	+	0.789379i
$123$	2325.60	+	755.634i	1.70482	+	0.553929i
$124$	787.359			0.570217
$125$		0			0
$126$	−1331.29			−0.941278
$127$	−253.136	−	82.2490i	−0.176868	−	0.0574678i	0.219244	−	0.975670i	$-0.429641\pi$
$127$	−253.136	−	82.2490i	−0.176868	−	0.0574678i	−0.396112	+	0.918202i	$0.629641\pi$
$128$	75.2365	−	103.554i	0.0519534	−	0.0715077i
$129$	584.853	+	424.921i	0.399174	+	0.290017i
$130$		0			0
$131$	−2291.71	+	1665.02i	−1.52845	+	1.11049i	−0.571364	+	0.820697i	$0.693586\pi$
$131$	−2291.71	+	1665.02i	−1.52845	+	1.11049i	−0.957090	+	0.289790i	$0.906414\pi$
$132$		−	2502.07i		−	1.64983i
$133$	−630.144	−	867.319i	−0.410830	−	0.565459i
$134$	−182.882	−	562.852i	−0.117900	−	0.362858i
$135$		0			0
$136$	−21.4920	+	66.1455i	−0.0135509	+	0.0417054i
$137$	−1378.40	+	447.870i	−0.859597	+	0.279300i	−0.705460	−	0.708750i	$-0.749260\pi$
$137$	−1378.40	+	447.870i	−0.859597	+	0.279300i	−0.154137	+	0.988050i	$0.549260\pi$
$138$	383.117	−	124.482i	0.236327	−	0.0767872i
$139$	−582.969	+	1794.20i	−0.355733	+	1.09483i	0.599851	+	0.800112i	$0.295227\pi$
$139$	−582.969	+	1794.20i	−0.355733	+	1.09483i	−0.955584	+	0.294720i	$0.904773\pi$
$140$		0			0
$141$	−160.009	−	492.456i	−0.0955685	−	0.294129i
$142$	−219.612	−	302.270i	−0.129785	−	0.178633i
$143$		−	2930.74i		−	1.71385i
$144$	782.848	−	568.772i	0.453037	−	0.329151i
$145$		0			0
$146$	−261.430	−	189.940i	−0.148193	−	0.107668i
$147$	−1219.68	+	1678.75i	−0.684340	+	0.941913i
$148$	696.010	+	226.147i	0.386566	+	0.125603i
$149$	−2804.20			−1.54181			−0.770903	−	0.636953i	$-0.780194\pi$
$149$	−2804.20			−1.54181			−0.770903	+	0.636953i	$0.780194\pi$
$150$		0			0
$151$	2908.13			1.56729			0.783644	−	0.621210i	$-0.213358\pi$
$151$	2908.13			1.56729			0.783644	+	0.621210i	$0.213358\pi$
$152$	741.094	+	240.796i	0.395465	+	0.128494i
$153$	−309.046	+	425.365i	−0.163300	+	0.224763i
$154$	1191.03	+	865.332i	0.623219	+	0.452795i
$155$		0			0
$156$	1326.34	−	963.645i	0.680721	−	0.494573i
$157$		−	1144.83i		−	0.581956i	−0.956730	−	0.290978i	$-0.906019\pi$
$157$		−	1144.83i		−	0.581956i	0.956730	−	0.290978i	$-0.0939806\pi$
$158$	1148.90	+	1581.33i	0.578493	+	0.796227i
$159$	−1291.98	−	3976.31i	−0.644407	−	1.98328i
$160$		0			0
$161$	−73.2439	+	225.422i	−0.0358536	+	0.110346i
$162$	2464.60	−	800.796i	1.19529	−	0.388373i
$163$	−3828.11	+	1243.83i	−1.83951	+	0.597694i	−0.841129	+	0.540834i	$0.818109\pi$
$163$	−3828.11	+	1243.83i	−1.83951	+	0.597694i	−0.998382	+	0.0568598i	$0.981891\pi$
$164$	323.163	−	994.593i	0.153871	−	0.473565i
$165$		0			0
$166$	505.027	+	1554.31i	0.236131	+	0.726735i
$167$	−505.466	−	695.714i	−0.234216	−	0.322371i	0.675689	−	0.737186i	$-0.263846\pi$
$167$	−505.466	−	695.714i	−0.234216	−	0.322371i	−0.909906	+	0.414816i	$0.863846\pi$
$168$			823.539i			0.378199i
$169$	−223.831	+	162.623i	−0.101880	+	0.0740203i
$170$		0			0
$171$	4765.79	+	3462.55i	2.13128	+	1.54847i
$172$	181.726	−	250.125i	0.0805611	−	0.110883i
$173$	−2076.63	−	674.739i	−0.912622	−	0.296529i	−0.185185	−	0.982704i	$-0.559288\pi$
$173$	−2076.63	−	674.739i	−0.912622	−	0.296529i	−0.727437	+	0.686175i	$0.759288\pi$
$174$	−386.795			−0.168522
$175$		0			0
$176$	−1070.06			−0.458291
$177$	−2429.78	−	789.483i	−1.03183	−	0.335261i
$178$	1089.98	−	1500.23i	0.458976	−	0.631726i
$179$	−2981.05	−	2165.86i	−1.24477	−	0.904381i	−0.246867	−	0.969049i	$-0.579401\pi$
$179$	−2981.05	−	2165.86i	−1.24477	−	0.904381i	−0.997907	+	0.0646683i	$0.979401\pi$
$180$		0			0
$181$	889.674	−	646.386i	0.365353	−	0.265445i	−0.389928	−	0.920845i	$-0.627500\pi$
$181$	889.674	−	646.386i	0.365353	−	0.265445i	0.755281	+	0.655401i	$0.227500\pi$
$182$			964.633i			0.392875i
$183$	3614.15	+	4974.46i	1.45992	+	2.00941i
$184$	−53.2375	−	163.848i	−0.0213300	−	0.0656470i
$185$		0			0
$186$	1137.82	−	3501.86i	0.448545	−	1.38048i
$187$	552.969	−	179.670i	0.216241	−	0.0702610i
$188$	−210.609	+	68.4310i	−0.0817034	+	0.0265470i
$189$	−1064.98	+	3277.67i	−0.409872	+	1.26146i
$190$		0			0
$191$	−335.391	−	1032.23i	−0.127058	−	0.391044i	0.867213	−	0.497938i	$-0.165909\pi$
$191$	−335.391	−	1032.23i	−0.127058	−	0.391044i	−0.994270	+	0.106894i	$0.965909\pi$
$192$	−351.843	−	484.270i	−0.132250	−	0.182027i
$193$		−	1043.82i		−	0.389305i	−0.980872	−	0.194653i	$-0.937642\pi$
$193$		−	1043.82i		−	0.389305i	0.980872	−	0.194653i	$-0.0623579\pi$
$194$	−442.324	+	321.367i	−0.163696	+	0.118932i
$195$		0			0
$196$	717.954	+	521.624i	0.261645	+	0.190096i
$197$	−699.179	+	962.338i	−0.252865	+	0.348039i	−0.916512	−	0.400007i	$-0.869008\pi$
$197$	−699.179	+	962.338i	−0.252865	+	0.348039i	0.663647	+	0.748046i	$0.269008\pi$
$198$	−7693.54	−	2499.78i	−2.76139	−	0.897231i
$199$	1232.23			0.438947			0.219473	−	0.975619i	$-0.429566\pi$
$199$	1232.23			0.438947			0.219473	+	0.975619i	$0.429566\pi$
$200$		0			0
$201$	−2767.63			−0.971211
$202$	−2142.58	−	696.168i	−0.746295	−	0.242486i
$203$	133.772	−	184.121i	0.0462508	−	0.0636588i
$204$	263.131	+	191.176i	0.0903081	+	0.0656127i
$205$		0			0
$206$	−2146.56	+	1559.57i	−0.726009	+	0.527477i
$207$		−	1302.40i		−	0.437310i
$208$	−412.123	−	567.238i	−0.137383	−	0.189091i
$209$	−2013.03	−	6195.46i	−0.666239	−	2.05047i
$210$		0			0
$211$	821.427	−	2528.09i	0.268007	−	0.824839i	−0.722979	−	0.690870i	$-0.757228\pi$
$211$	821.427	−	2528.09i	0.268007	−	0.824839i	0.990985	−	0.133969i	$-0.0427723\pi$
$212$	−1700.55	+	552.543i	−0.550917	+	0.179004i
$213$	−1661.74	+	539.933i	−0.534557	+	0.173688i
$214$	−305.193	+	939.289i	−0.0974888	+	0.300040i
$215$		0			0
$216$	−774.081	−	2382.38i	−0.243841	−	0.750464i
$217$	1273.43	+	1752.73i	0.398369	+	0.548308i
$218$		−	1700.59i		−	0.528340i
$219$	−1222.58	+	888.254i	−0.377233	+	0.274076i
$220$		0			0
$221$	308.212	+	223.929i	0.0938127	+	0.0681589i
$222$	2011.63	−	2768.77i	0.608161	−	0.837062i
$223$	3881.22	+	1261.09i	1.16550	+	0.378693i	0.826960	−	0.562260i	$-0.190068\pi$
$223$	3881.22	+	1261.09i	1.16550	+	0.378693i	0.338537	+	0.940953i	$0.390068\pi$
$224$	352.204			0.105056
$225$		0			0
$226$	228.045			0.0671209
$227$	3149.49	+	1023.33i	0.920876	+	0.299211i	0.730826	−	0.682564i	$-0.239135\pi$
$227$	3149.49	+	1023.33i	0.920876	+	0.299211i	0.190050	+	0.981774i	$0.439135\pi$
$228$	2141.93	−	2948.12i	0.622162	−	0.856333i
$229$	2955.33	+	2147.17i	0.852811	+	0.619603i	0.925920	−	0.377721i	$-0.123292\pi$
$229$	2955.33	+	2147.17i	0.852811	+	0.619603i	−0.0731088	+	0.997324i	$0.523292\pi$
$230$		0			0
$231$	5569.83	−	4046.72i	1.58644	−	1.15262i
$232$			165.421i			0.0468122i
$233$	−1007.16	−	1386.23i	−0.283180	−	0.389764i	0.643604	−	0.765359i	$-0.277438\pi$
$233$	−1007.16	−	1386.23i	−0.283180	−	0.389764i	−0.926784	+	0.375595i	$0.877438\pi$
$234$	−1637.95	−	5041.09i	−0.457590	−	1.40832i
$235$		0			0
$236$	−337.639	+	1039.15i	−0.0931290	+	0.286621i
$237$	8693.43	−	2824.67i	2.38270	−	0.774185i
$238$	−182.006	+	59.1372i	−0.0495700	+	0.0161063i
$239$	−816.343	+	2512.45i	−0.220941	+	0.679986i	0.777738	+	0.628589i	$0.216367\pi$
$239$	−816.343	+	2512.45i	−0.220941	+	0.679986i	−0.998678	+	0.0513966i	$0.983633\pi$
$240$		0			0
$241$	−619.128	−	1905.48i	−0.165484	−	0.509306i	0.833588	−	0.552387i	$-0.186283\pi$
$241$	−619.128	−	1905.48i	−0.165484	−	0.509306i	−0.999072	+	0.0430806i	$0.986283\pi$
$242$	3693.41	+	5083.55i	0.981081	+	1.35034i
$243$		−	3664.49i		−	0.967396i
$244$	2127.43	−	1545.67i	0.558175	−	0.405538i
$245$		0			0
$246$	−3956.55	−	2874.60i	−1.02545	−	0.745033i
$247$	2508.90	−	3453.21i	0.646306	−	0.889564i
$248$	−1497.65	−	486.615i	−0.383470	−	0.124597i
$249$	7642.80			1.94515
$250$		0			0
$251$	561.737			0.141261			0.0706305	−	0.997503i	$-0.477499\pi$
$251$	561.737			0.141261			0.0706305	+	0.997503i	$0.477499\pi$
$252$	2532.27	+	822.785i	0.633008	+	0.205677i
$253$	−846.552	+	1165.18i	−0.210365	+	0.289542i
$254$	430.661	+	312.894i	0.106386	+	0.0772941i
$255$		0			0
$256$	−207.108	+	150.473i	−0.0505636	+	0.0367366i
$257$			6131.77i			1.48829i	0.668020	+	0.744143i	$0.267142\pi$
$257$			6131.77i			1.48829i	−0.668020	+	0.744143i	$0.732858\pi$
$258$	−849.842	−	1169.71i	−0.205073	−	0.282259i
$259$	622.266	+	1915.14i	0.149288	+	0.459463i
$260$		0			0
$261$	−386.441	+	1189.34i	−0.0916479	+	0.282063i
$262$	5388.13	−	1750.71i	1.27053	−	0.412821i
$263$	−3835.00	+	1246.07i	−0.899150	+	0.292152i	−0.721886	−	0.692012i	$-0.756725\pi$
$263$	−3835.00	+	1246.07i	−0.899150	+	0.292152i	−0.177264	+	0.984163i	$0.556725\pi$
$264$	−1546.37	+	4759.23i	−0.360501	+	1.10951i
$265$		0			0
$266$	662.573	+	2039.19i	0.152725	+	0.470040i
$267$	−5097.30	−	7015.83i	−1.16835	−	1.60810i
$268$			1183.63i			0.269783i
$269$	−1042.37	+	757.328i	−0.236262	+	0.171655i	−0.699617	−	0.714519i	$-0.746646\pi$
$269$	−1042.37	+	757.328i	−0.236262	+	0.171655i	0.463354	+	0.886173i	$0.346646\pi$
$270$		0			0
$271$	−2429.42	−	1765.08i	−0.544564	−	0.395649i	0.281213	−	0.959645i	$-0.409263\pi$
$271$	−2429.42	−	1765.08i	−0.544564	−	0.395649i	−0.825777	+	0.563997i	$0.809263\pi$
$272$	81.7604	−	112.534i	0.0182259	−	0.0250858i
$273$	4290.31	+	1394.01i	0.951140	+	0.309044i
$274$	2898.67			0.639107
$275$		0			0
$276$	−805.667			−0.175708
$277$	−5069.69	−	1647.24i	−1.09967	−	0.357304i	−0.297694	−	0.954661i	$-0.596217\pi$
$277$	−5069.69	−	1647.24i	−1.09967	−	0.357304i	−0.801975	+	0.597357i	$0.796217\pi$
$278$	2217.75	−	3052.47i	0.478459	−	0.658543i
$279$	−9630.97	−	6997.31i	−2.06664	−	1.50150i
$280$		0			0
$281$	1055.18	−	766.631i	0.224009	−	0.162752i	−0.470120	−	0.882602i	$-0.655789\pi$
$281$	1055.18	−	766.631i	0.224009	−	0.162752i	0.694130	+	0.719850i	$0.255789\pi$
$282$			1035.60i			0.218684i
$283$	−787.606	−	1084.05i	−0.165436	−	0.227703i	0.718248	−	0.695787i	$-0.244944\pi$
$283$	−787.606	−	1084.05i	−0.165436	−	0.227703i	−0.883684	+	0.468084i	$0.844944\pi$
$284$	230.914	+	710.679i	0.0482472	+	0.148490i
$285$		0			0
$286$	−1811.30	+	5574.61i	−0.374491	+	1.15256i
$287$	2736.71	−	889.212i	0.562868	−	0.182887i
$288$	−1840.59	+	598.043i	−0.376589	+	0.122361i
$289$	1494.84	−	4600.66i	0.304263	−	0.936426i
$290$		0			0
$291$	790.106	+	2431.69i	0.159164	+	0.489857i
$292$	379.880	+	522.861i	0.0761329	+	0.104788i
$293$			6330.65i			1.26225i	0.775680	+	0.631127i	$0.217407\pi$
$293$			6330.65i			1.26225i	−0.775680	+	0.631127i	$0.782593\pi$
$294$	3357.50	−	2439.37i	0.666033	−	0.483901i
$295$		0			0
$296$	−1184.12	−	860.316i	−0.232520	−	0.168935i
$297$	−12309.0	+	16941.9i	−2.40485	+	3.30999i
$298$	5333.90	+	1733.09i	1.03686	+	0.336897i
$299$	−943.698			−0.182527
$300$		0			0
$301$	850.713			0.162905
$302$	−5531.60	−	1797.33i	−1.05400	−	0.342465i
$303$	−6192.56	+	8523.33i	−1.17410	+	1.61602i
$304$	−1260.82	−	916.043i	−0.237873	−	0.172825i
$305$		0			0
$306$	850.730	−	618.092i	0.158931	−	0.115470i
$307$		−	6554.21i		−	1.21846i	−0.792992	−	0.609232i	$-0.791478\pi$
$307$		−	6554.21i		−	1.21846i	0.792992	−	0.609232i	$-0.208522\pi$
$308$	−1730.66	−	2382.05i	−0.320174	−	0.440682i
$309$	3834.32	+	11800.8i	0.705911	+	2.17257i
$310$		0			0
$311$	−2547.69	+	7840.97i	−0.464521	+	1.42965i	0.395063	+	0.918654i	$0.370723\pi$
$311$	−2547.69	+	7840.97i	−0.464521	+	1.42965i	−0.859584	+	0.510995i	$0.829277\pi$
$312$	−3118.42	+	1013.24i	−0.565852	+	0.183856i
$313$	4632.79	−	1505.29i	0.836616	−	0.271833i	0.140787	−	0.990040i	$-0.455037\pi$
$313$	4632.79	−	1505.29i	0.836616	−	0.271833i	0.695830	+	0.718207i	$0.255037\pi$
$314$	−707.542	+	2177.59i	−0.127162	+	0.391364i
$315$		0			0
$316$	−1208.03	−	3717.93i	−0.215053	−	0.661867i
$317$	4056.25	+	5582.95i	0.718681	+	0.989180i	0.999567	+	0.0294384i	$0.00937189\pi$
$317$	4056.25	+	5582.95i	0.718681	+	0.989180i	−0.280885	+	0.959741i	$0.590628\pi$
$318$			8361.88i			1.47456i
$319$	1118.79	−	812.848i	0.196364	−	0.142667i
$320$		0			0
$321$	3736.55	+	2714.76i	0.649701	+	0.472035i
$322$	278.636	−	383.510i	0.0482230	−	0.0663732i
$323$	805.355	+	261.676i	0.138734	+	0.0450775i
$324$	−5182.86			−0.888693
$325$		0			0
$326$	8050.22			1.36767
$327$	−7563.54	−	2457.54i	−1.27910	−	0.415604i
$328$	−1229.38	+	1692.10i	−0.206956	+	0.284850i
$329$	−492.961	−	358.157i	−0.0826073	−	0.0600177i
$330$		0			0
$331$	−1547.88	+	1124.60i	−0.257037	+	0.186748i	−0.708840	−	0.705370i	$-0.750781\pi$
$331$	−1547.88	+	1124.60i	−0.257037	+	0.186748i	0.451803	+	0.892118i	$0.350781\pi$
$332$		−	3268.60i		−	0.540325i
$333$	−6503.81	−	8951.73i	−1.07029	−	1.47313i
$334$	531.478	+	1635.72i	0.0870694	+	0.267972i
$335$		0			0
$336$	508.975	−	1566.46i	0.0826395	−	0.254338i
$337$	−4954.49	+	1609.81i	−0.800856	+	0.260214i	−0.680720	−	0.732544i	$-0.738333\pi$
$337$	−4954.49	+	1609.81i	−0.800856	+	0.260214i	−0.120136	+	0.992757i	$0.538333\pi$
$338$	526.258	−	170.991i	0.0846883	−	0.0275169i
$339$	329.551	−	1014.26i	0.0527988	−	0.162498i
$340$		0			0
$341$	4068.04	+	12520.1i	0.646031	+	1.98828i
$342$	−6925.09	−	9531.57i	−1.09493	−	1.50704i
$343$			6217.06i			0.978686i
$344$	−500.250	+	363.453i	−0.0784060	+	0.0569653i
$345$		0			0
$346$	3532.98	+	2566.86i	0.548943	+	0.398830i
$347$	6308.75	−	8683.25i	0.975998	−	1.34335i	0.0370402	−	0.999314i	$-0.488207\pi$
$347$	6308.75	−	8683.25i	0.975998	−	1.34335i	0.938958	−	0.344032i	$-0.111793\pi$
$348$	735.728	+	239.053i	0.113331	+	0.0368235i
$349$	2715.52			0.416500			0.208250	−	0.978076i	$-0.433223\pi$
$349$	2715.52			0.416500			0.208250	+	0.978076i	$0.433223\pi$
$350$		0			0
$351$	−13721.5			−2.08661
$352$	2035.38	+	661.336i	0.308200	+	0.100140i
$353$	384.780	−	529.605i	0.0580164	−	0.0798527i	−0.779023	−	0.626995i	$-0.784284\pi$
$353$	384.780	−	529.605i	0.0580164	−	0.0798527i	0.837039	+	0.547143i	$0.184284\pi$
$354$	4133.79	+	3003.37i	0.620645	+	0.450925i
$355$		0			0
$356$	−3000.47	+	2179.97i	−0.446698	+	0.324545i
$357$			894.950i			0.132677i
$358$	4331.73	+	5962.11i	0.639494	+	0.880188i
$359$	−102.092	−	314.207i	−0.0150089	−	0.0461928i	0.943272	−	0.332022i	$-0.107731\pi$
$359$	−102.092	−	314.207i	−0.0150089	−	0.0461928i	−0.958281	+	0.285829i	$0.907731\pi$
$360$		0			0
$361$	812.267	−	2499.90i	0.118423	−	0.364470i
$362$	−2091.75	+	679.650i	−0.303701	+	0.0986785i
$363$	27947.0	−	9080.54i	4.04088	−	1.31296i
$364$	596.176	−	1834.84i	0.0858464	−	0.264208i
$365$		0			0
$366$	−3800.15	−	11695.7i	−0.542724	−	1.67033i
$367$	5681.67	+	7820.14i	0.808121	+	1.11228i	0.991610	+	0.129262i	$0.0412608\pi$
$367$	5681.67	+	7820.14i	0.808121	+	1.11228i	−0.183489	+	0.983022i	$0.558739\pi$
$368$			344.560i			0.0488083i
$369$	−12791.9	+	9293.89i	−1.80467	+	1.31117i
$370$		0			0
$371$	−3980.39	−	2891.92i	−0.557012	−	0.404693i
$372$	−4328.54	+	5957.73i	−0.603292	+	0.830360i
$373$	−3659.22	−	1188.95i	−0.507954	−	0.165044i	0.0438173	−	0.999040i	$-0.486048\pi$
$373$	−3659.22	−	1188.95i	−0.507954	−	0.165044i	−0.551772	+	0.833995i	$0.686048\pi$
$374$	−1162.85			−0.160774
$375$		0			0
$376$	442.895			0.0607462
$377$	861.777	+	280.008i	0.117729	+	0.0382524i
$378$	4051.42	−	5576.30i	0.551276	−	0.758767i
$379$	−7104.78	−	5161.93i	−0.962924	−	0.699605i	−0.00909611	−	0.999959i	$-0.502895\pi$
$379$	−7104.78	−	5161.93i	−0.962924	−	0.699605i	−0.953828	+	0.300353i	$0.902895\pi$
$380$		0			0
$381$	2013.98	−	1463.25i	0.270812	−	0.196757i
$382$			2170.70i			0.290740i
$383$	−2840.64	−	3909.80i	−0.378981	−	0.521622i	0.576333	−	0.817215i	$-0.304483\pi$
$383$	−2840.64	−	3909.80i	−0.378981	−	0.521622i	−0.955314	+	0.295592i	$0.904483\pi$
$384$	369.950	+	1138.59i	0.0491638	+	0.151311i
$385$		0			0
$386$	−645.117	+	1985.47i	−0.0850663	+	0.261807i
$387$	−4445.75	+	1444.51i	−0.583954	+	0.189738i
$388$	1039.97	−	337.905i	0.136073	−	0.0442127i
$389$	3804.86	−	11710.2i	0.495923	−	1.52629i	−0.319591	−	0.947556i	$-0.603545\pi$
$389$	3804.86	−	11710.2i	0.495923	−	1.52629i	0.815513	−	0.578738i	$-0.196455\pi$
$390$		0			0
$391$	−57.8538	−	178.056i	−0.00748284	−	0.0230298i
$392$	−1043.25	−	1435.91i	−0.134418	−	0.185011i
$393$		−	26494.3i		−	3.40066i
$394$	1924.68	−	1398.36i	0.246101	−	0.178803i
$395$		0			0
$396$	13089.0	+	9509.74i	1.66098	+	1.20677i
$397$	3408.69	−	4691.66i	0.430926	−	0.593118i	−0.537240	−	0.843430i	$-0.680533\pi$
$397$	3408.69	−	4691.66i	0.430926	−	0.593118i	0.968165	+	0.250311i	$0.0805330\pi$
$398$	−2343.84	−	761.559i	−0.295191	−	0.0959133i
$399$	10027.0			1.25809
$400$		0			0
$401$	−15149.2			−1.88657			−0.943284	−	0.331987i	$-0.892281\pi$
$401$	−15149.2			−1.88657			−0.943284	+	0.331987i	$0.892281\pi$
$402$	5264.34	+	1710.49i	0.653138	+	0.212217i
$403$	−5070.13	+	6978.44i	−0.626703	+	0.862583i
$404$	3645.18	+	2648.38i	0.448897	+	0.326143i
$405$		0			0
$406$	−368.241	+	267.543i	−0.0450136	+	0.0327043i
$407$			12236.0i			1.49021i
$408$	−382.352	−	526.262i	−0.0463952	−	0.0638575i
$409$	4376.11	+	13468.3i	0.529058	+	1.62827i	0.756149	+	0.654399i	$0.227078\pi$
$409$	4376.11	+	13468.3i	0.529058	+	1.62827i	−0.227091	+	0.973873i	$0.572922\pi$
$410$		0			0
$411$	4188.92	−	12892.2i	0.502735	−	1.54726i
$412$	5046.86	−	1639.83i	0.603498	−	0.196088i
$413$	−2859.31	+	929.045i	−0.340671	+	0.110691i
$414$	−804.929	+	2477.32i	−0.0955558	+	0.294090i
$415$		0			0
$416$	433.332	+	1333.66i	0.0510717	+	0.157183i
$417$	−10371.3	−	14274.8i	−1.21795	−	1.67636i
$418$			13028.6i			1.52452i
$419$	1662.86	−	1208.14i	0.193881	−	0.140863i	−0.486610	−	0.873620i	$-0.661767\pi$
$419$	1662.86	−	1208.14i	0.193881	−	0.140863i	0.680491	+	0.732757i	$0.261767\pi$
$420$		0			0
$421$	−4504.60	−	3272.78i	−0.521474	−	0.378873i	0.295685	−	0.955286i	$-0.404452\pi$
$421$	−4504.60	−	3272.78i	−0.521474	−	0.378873i	−0.817159	+	0.576412i	$0.804452\pi$
$422$	−3124.89	+	4301.05i	−0.360468	+	0.496142i
$423$	3184.32	+	1034.65i	0.366021	+	0.118927i
$424$	3576.13			0.409605
$425$		0			0
$426$	3494.52			0.397441
$427$	6881.58	+	2235.96i	0.779913	+	0.253409i
$428$	1161.03	−	1598.01i	0.131122	−	0.180474i
$429$	22176.1	+	16111.9i	2.49574	+	1.81326i
$430$		0			0
$431$	−3508.68	+	2549.20i	−0.392128	+	0.284898i	−0.766327	−	0.642451i	$-0.777918\pi$
$431$	−3508.68	+	2549.20i	−0.392128	+	0.284898i	0.374199	+	0.927348i	$0.377918\pi$
$432$			5009.96i			0.557967i
$433$	4447.60	+	6121.60i	0.493621	+	0.679411i	0.981051	−	0.193751i	$-0.0620654\pi$
$433$	4447.60	+	6121.60i	0.493621	+	0.679411i	−0.487429	+	0.873162i	$0.662065\pi$
$434$	−1338.96	−	4120.91i	−0.148093	−	0.455783i
$435$		0			0
$436$	−1051.02	+	3234.71i	−0.115447	+	0.355308i
$437$	−1994.93	+	648.193i	−0.218377	+	0.0709549i
$438$	2874.45	−	933.966i	0.313577	−	0.101887i
$439$	−880.956	+	2711.30i	−0.0957762	+	0.294769i	−0.987455	−	0.157899i	$-0.949528\pi$
$439$	−880.956	+	2711.30i	−0.0957762	+	0.294769i	0.891679	+	0.452668i	$0.149528\pi$
$440$		0			0
$441$	−4146.30	−	12761.0i	−0.447716	−	1.37793i
$442$	−447.859	−	616.424i	−0.0481956	−	0.0663356i
$443$		−	4745.22i		−	0.508922i	−0.967083	−	0.254461i	$-0.918102\pi$
$443$		−	4745.22i		−	0.508922i	0.967083	−	0.254461i	$-0.0818980\pi$
$444$	−5537.55	+	4023.26i	−0.591892	+	0.430035i
$445$		0			0
$446$	−6603.13	−	4797.45i	−0.701048	−	0.509341i
$447$	15416.2	−	21218.6i	1.63124	−	2.24520i
$448$	−669.931	−	217.674i	−0.0706502	−	0.0229556i
$449$	−3614.47			−0.379905			−0.189953	−	0.981793i	$-0.560833\pi$
$449$	−3614.47			−0.379905			−0.189953	+	0.981793i	$0.560833\pi$
$450$		0			0
$451$	17485.1			1.82559
$452$	−433.767	−	140.940i	−0.0451387	−	0.0146665i
$453$	−15987.6	+	22005.0i	−1.65820	+	2.28231i
$454$	−5358.23	−	3892.98i	−0.553908	−	0.402438i
$455$		0			0
$456$	−5896.24	+	4283.87i	−0.605519	+	0.439935i
$457$		−	5105.92i		−	0.522637i	−0.965253	−	0.261318i	$-0.915843\pi$
$457$		−	5105.92i		−	0.522637i	0.965253	−	0.261318i	$-0.0841572\pi$
$458$	−4294.35	−	5910.66i	−0.438126	−	0.603028i
$459$	−841.203	−	2588.96i	−0.0855425	−	0.263273i
$460$		0			0
$461$	2324.86	−	7155.19i	0.234880	−	0.722886i	−0.762257	−	0.647274i	$-0.775909\pi$
$461$	2324.86	−	7155.19i	0.234880	−	0.722886i	0.997137	−	0.0756121i	$-0.0240911\pi$
$462$	−13095.5	+	4254.97i	−1.31874	+	0.428483i
$463$	−4470.39	+	1452.52i	−0.448718	+	0.145797i	−0.524654	−	0.851315i	$-0.675805\pi$
$463$	−4470.39	+	1452.52i	−0.448718	+	0.145797i	0.0759363	+	0.997113i	$0.475805\pi$
$464$	102.236	−	314.650i	0.0102288	−	0.0314811i
$465$		0			0
$466$	1058.99	+	3259.22i	0.105272	+	0.323993i
$467$	2460.90	+	3387.14i	0.243848	+	0.335627i	0.913345	−	0.407187i	$-0.133490\pi$
$467$	2460.90	+	3387.14i	0.243848	+	0.335627i	−0.669497	+	0.742815i	$0.733490\pi$
$468$			10601.0i			1.04708i
$469$	−2634.87	+	1914.35i	−0.259418	+	0.188478i
$470$		0			0
$471$	8662.58	+	6293.74i	0.847454	+	0.615711i
$472$	1284.46	−	1767.90i	0.125258	−	0.172403i
$473$	4916.27	+	1597.39i	0.477907	+	0.155282i
$474$	−18281.6			−1.77153
$475$		0			0
$476$	382.744			0.0368551
$477$	25711.6	+	8354.22i	2.46804	+	0.801915i
$478$	3105.55	−	4274.43i	0.297165	−	0.409012i
$479$	−1554.74	−	1129.58i	−0.148304	−	0.107749i	0.511159	−	0.859486i	$-0.329216\pi$
$479$	−1554.74	−	1129.58i	−0.148304	−	0.107749i	−0.659463	+	0.751737i	$0.729216\pi$
$480$		0			0
$481$	−6486.27	+	4712.55i	−0.614862	+	0.446723i
$482$			4007.08i			0.378667i
$483$	−1303.04	−	1793.48i	−0.122755	−	0.168957i
$484$	−3883.48	−	11952.1i	−0.364715	−	1.12248i
$485$		0			0
$486$	−2264.78	+	6970.28i	−0.211384	+	0.650573i
$487$	−19207.4	+	6240.86i	−1.78721	+	0.580699i	−0.999380	−	0.0351985i	$-0.988794\pi$
$487$	−19207.4	+	6240.86i	−1.78721	+	0.580699i	−0.787827	+	0.615897i	$0.788794\pi$
$488$	−5001.89	+	1625.21i	−0.463985	+	0.150758i
$489$	11633.5	−	35804.2i	1.07584	−	3.31109i
$490$		0			0
$491$	5469.48	+	16833.3i	0.502718	+	1.54721i	0.804574	+	0.593852i	$0.202394\pi$
$491$	5469.48	+	16833.3i	0.502718	+	1.54721i	−0.301856	+	0.953353i	$0.597606\pi$
$492$	5749.21	+	7913.11i	0.526818	+	0.725102i
$493$			179.765i			0.0164223i
$494$	−6906.41	+	5017.80i	−0.629017	+	0.457007i
$495$		0			0
$496$	2547.95	+	1851.19i	0.230658	+	0.167583i
$497$	−1208.56	+	1663.45i	−0.109078	+	0.150132i
$498$	−14537.5	−	4723.51i	−1.30811	−	0.425031i
$499$	1132.59			0.101606			0.0508032	−	0.998709i	$-0.483822\pi$
$499$	1132.59			0.101606			0.0508032	+	0.998709i	$0.483822\pi$
$500$		0			0
$501$	8043.09			0.717243
$502$	−1068.49	−	347.173i	−0.0949979	−	0.0308667i
$503$	10214.7	−	14059.3i	0.905466	−	1.24627i	−0.0632248	−	0.997999i	$-0.520139\pi$
$503$	10214.7	−	14059.3i	0.905466	−	1.24627i	0.968691	−	0.248268i	$-0.0798615\pi$
$504$	−4308.16	−	3130.06i	−0.380755	−	0.276635i
$505$		0			0
$506$	2330.36	−	1693.10i	0.204737	−	0.148750i
$507$		−	2587.69i		−	0.226673i
$508$	−625.787	−	861.322i	−0.0546552	−	0.0752264i
$509$	−387.359	−	1192.17i	−0.0337316	−	0.103815i	0.932773	−	0.360464i	$-0.117382\pi$
$509$	−387.359	−	1192.17i	−0.0337316	−	0.103815i	−0.966505	+	0.256649i	$0.917382\pi$
$510$		0			0
$511$	−549.534	+	1691.29i	−0.0475733	+	0.146416i
$512$	486.941	−	158.217i	0.0420312	−	0.0136568i
$513$	−29006.6	+	9424.83i	−2.49644	+	0.811143i
$514$	3789.64	−	11663.3i	0.325202	−	1.00087i
$515$		0			0
$516$	893.577	+	2750.15i	0.0762355	+	0.234629i
$517$	−2176.30	−	2995.42i	−0.185133	−	0.254813i
$518$		−	4027.39i		−	0.341609i
$519$	16522.0	−	12003.9i	1.39737	−	1.01525i
$520$		0			0
$521$	−17812.3	−	12941.4i	−1.49783	−	1.08824i	−0.971234	−	0.238126i	$-0.923467\pi$
$521$	−17812.3	−	12941.4i	−1.49783	−	1.08824i	−0.526599	−	0.850114i	$-0.676533\pi$
$522$	1470.11	−	2023.43i	0.123266	−	0.169661i
$523$	−2342.85	−	761.237i	−0.195881	−	0.0636454i	0.209434	−	0.977823i	$-0.432838\pi$
$523$	−2342.85	−	761.237i	−0.195881	−	0.0636454i	−0.405314	+	0.914177i	$0.632838\pi$
$524$	−11330.8			−0.944637
$525$		0			0
$526$	8064.72			0.668515
$527$	−1627.51	−	528.810i	−0.134526	−	0.0437103i
$528$	5882.73	−	8096.88i	0.484873	−	0.667370i
$529$	−9468.12	−	6878.99i	−0.778181	−	0.565381i
$530$		0			0
$531$	13365.0	−	9710.22i	1.09226	−	0.793573i
$532$		−	4288.26i		−	0.349473i
$533$	6734.20	+	9268.83i	0.547262	+	0.753241i
$534$	5359.62	+	16495.2i	0.434332	+	1.33674i
$535$		0			0
$536$	731.526	−	2251.41i	0.0589498	−	0.181429i
$537$	32777.0	−	10649.9i	2.63395	−	0.855822i
$538$	2450.77	−	796.302i	0.196394	−	0.0638123i
$539$	−4585.12	+	14111.6i	−0.366410	+	1.12770i
$540$		0			0
$541$	−2089.04	−	6429.40i	−0.166016	−	0.510945i	0.833093	−	0.553132i	$-0.186568\pi$
$541$	−2089.04	−	6429.40i	−0.166016	−	0.510945i	−0.999110	+	0.0421867i	$0.986568\pi$
$542$	3530.15	+	4858.84i	0.279766	+	0.385065i
$543$			10285.4i			0.812875i
$544$	−225.067	+	163.521i	−0.0177384	+	0.0128877i
$545$		0			0
$546$	−7299.11	−	5303.11i	−0.572112	−	0.415664i
$547$	−3902.37	+	5371.14i	−0.305033	+	0.419842i	−0.933824	−	0.357732i	$-0.883550\pi$
$547$	−3902.37	+	5371.14i	−0.305033	+	0.419842i	0.628791	+	0.777574i	$0.283550\pi$
$548$	−5513.60	−	1791.48i	−0.429798	−	0.139650i
$549$	−39759.2			−3.09086
$550$		0			0
$551$	2014.09			0.155722
$552$	1532.47	+	497.929i	0.118163	+	0.0383936i
$553$	6322.63	−	8702.35i	0.486194	−	0.669189i
$554$	8625.08	+	6266.49i	0.661452	+	0.480573i
$555$		0			0
$556$	−6104.93	+	4435.49i	−0.465660	+	0.338322i
$557$		−	13052.1i		−	0.992880i	−0.868071	−	0.496440i	$-0.834640\pi$
$557$		−	13052.1i		−	0.992880i	0.868071	−	0.496440i	$-0.165360\pi$
$558$	13994.6	+	19261.9i	1.06172	+	1.46133i
$559$	1046.67	+	3221.32i	0.0791939	+	0.243734i
$560$		0			0
$561$	−1680.45	+	5171.91i	−0.126469	+	0.389230i
$562$	−2480.87	+	806.084i	−0.186209	+	0.0605028i
$563$	−8513.33	+	2766.15i	−0.637290	+	0.207068i	−0.609801	−	0.792554i	$-0.708751\pi$
$563$	−8513.33	+	2766.15i	−0.637290	+	0.207068i	−0.0274881	+	0.999622i	$0.508751\pi$
$564$	640.034	−	1969.82i	0.0477842	−	0.147065i
$565$		0			0
$566$	828.138	+	2548.75i	0.0615004	+	0.189279i
$567$	−8382.47	−	11537.5i	−0.620865	−	0.854548i
$568$		−	1494.50i		−	0.110401i
$569$	6918.89	−	5026.87i	0.509763	−	0.370364i	−0.302971	−	0.953000i	$-0.597979\pi$
$569$	6918.89	−	5026.87i	0.509763	−	0.370364i	0.812734	+	0.582636i	$0.197979\pi$
$570$		0			0
$571$	−4165.15	−	3026.16i	−0.305264	−	0.221788i	0.424597	−	0.905382i	$-0.360416\pi$
$571$	−4165.15	−	3026.16i	−0.305264	−	0.221788i	−0.729862	+	0.683595i	$0.760416\pi$
$572$	6890.59	−	9484.09i	0.503689	−	0.693269i
$573$	9654.41	+	3136.91i	0.703872	+	0.228702i
$574$	−5755.10			−0.418490
$575$		0			0
$576$	3870.61			0.279992
$577$	−21483.6	−	6980.44i	−1.55004	−	0.503639i	−0.595916	−	0.803047i	$-0.703211\pi$
$577$	−21483.6	−	6980.44i	−1.55004	−	0.503639i	−0.954125	+	0.299408i	$0.903211\pi$
$578$	−5686.73	+	7827.11i	−0.409233	+	0.563261i
$579$	7898.31	+	5738.46i	0.566913	+	0.411886i
$580$		0			0
$581$	7276.19	−	5286.46i	0.519565	−	0.377486i
$582$		−	5113.67i		−	0.364207i
$583$	−17572.4	−	24186.4i	−1.24833	−	1.71818i
$584$	−399.430	−	1229.32i	−0.0283023	−	0.0871054i
$585$		0			0
$586$	3912.56	−	12041.6i	0.275813	−	0.848864i
$587$	−18362.5	+	5966.33i	−1.29114	+	0.419517i	−0.872491	−	0.488630i	$-0.837497\pi$
$587$	−18362.5	+	5966.33i	−1.29114	+	0.419517i	−0.418651	+	0.908147i	$0.637497\pi$
$588$	−7893.97	+	2564.91i	−0.553642	+	0.179889i
$589$	−5924.78	+	18234.6i	−0.414476	+	1.27563i
$590$		0			0
$591$	−3437.97	−	10581.0i	−0.239288	−	0.736453i
$592$	1720.63	+	2368.25i	0.119455	+	0.164416i
$593$		−	23184.3i		−	1.60551i	−0.596311	−	0.802753i	$-0.703368\pi$
$593$		−	23184.3i		−	1.60551i	0.596311	−	0.802753i	$-0.296632\pi$
$594$	33883.8	−	24618.0i	2.34052	−	1.70049i
$595$		0			0
$596$	−9074.58	−	6593.07i	−0.623673	−	0.453125i
$597$	−6774.23	+	9323.93i	−0.464407	+	0.639201i
$598$	1795.02	+	583.237i	0.122749	+	0.0398835i
$599$	−13668.4			−0.932345			−0.466173	−	0.884694i	$-0.654367\pi$
$599$	−13668.4			−0.932345			−0.466173	+	0.884694i	$0.654367\pi$
$600$		0			0
$601$	10686.9			0.725337			0.362668	−	0.931918i	$-0.381866\pi$
$601$	10686.9			0.725337			0.362668	+	0.931918i	$0.381866\pi$
$602$	−1618.15	−	525.770i	−0.109553	−	0.0355960i
$603$	10519.0	−	14478.2i	0.710395	−	0.977775i
$604$	9410.92	+	6837.43i	0.633982	+	0.460615i
$605$		0			0
$606$	17046.7	−	12385.1i	1.14270	−	0.830217i
$607$			18467.8i			1.23490i	0.786611	+	0.617449i	$0.211834\pi$
$607$			18467.8i			1.23490i	−0.786611	+	0.617449i	$0.788166\pi$
$608$	1832.09	+	2521.65i	0.122205	+	0.168201i
$609$	657.775	+	2024.42i	0.0437675	+	0.134702i
$610$		0			0
$611$	749.689	−	2307.30i	0.0496385	−	0.152772i
$612$	−2000.19	+	649.900i	−0.132112	+	0.0429259i
$613$	1594.34	−	518.034i	0.105049	−	0.0341324i	−0.256021	−	0.966671i	$-0.582412\pi$
$613$	1594.34	−	518.034i	0.105049	−	0.0341324i	0.361070	+	0.932539i	$0.382412\pi$
$614$	−4050.73	+	12466.9i	−0.266244	+	0.819416i
$615$		0			0
$616$	1819.73	+	5600.55i	0.119024	+	0.366319i
$617$	12382.7	+	17043.4i	0.807958	+	1.11206i	0.991635	+	0.129072i	$0.0411998\pi$
$617$	12382.7	+	17043.4i	0.807958	+	1.11206i	−0.183678	+	0.982987i	$0.558800\pi$
$618$		−	24816.2i		−	1.61530i
$619$	14622.2	−	10623.6i	0.949457	−	0.689821i	−0.00122114	−	0.999999i	$-0.500389\pi$
$619$	14622.2	−	10623.6i	0.949457	−	0.689821i	0.950678	+	0.310178i	$0.100389\pi$
$620$		0			0
$621$	5455.28	+	3963.49i	0.352517	+	0.256118i
$622$	9691.97	−	13339.9i	0.624779	−	0.859935i
$623$	−9705.58	−	3153.53i	−0.624151	−	0.202799i
$624$	6557.80			0.420709
$625$		0			0
$626$	−9742.41			−0.622021
$627$	57946.0	+	18827.8i	3.69081	+	1.19922i
$628$	2691.65	−	3704.74i	0.171033	−	0.235406i
$629$	−1286.80	−	934.915i	−0.0815709	−	0.0592647i
$630$		0			0
$631$	−10654.4	+	7740.89i	−0.672180	+	0.488367i	−0.870754	−	0.491718i	$-0.836369\pi$
$631$	−10654.4	+	7740.89i	−0.672180	+	0.488367i	0.198574	+	0.980086i	$0.436369\pi$
$632$			7818.52i			0.492095i
$633$	14613.5	+	20113.8i	0.917593	+	1.26296i
$634$	−4265.00	−	13126.3i	−0.267168	−	0.822259i
$635$		0			0
$636$	5167.92	−	15905.2i	0.322204	−	0.991641i
$637$	−9246.41	+	3004.34i	−0.575127	+	0.186870i
$638$	−2630.43	+	854.679i	−0.163229	+	0.0530362i
$639$	3491.32	−	10745.2i	0.216141	−	0.665215i
$640$		0			0
$641$	−1749.20	−	5383.47i	−0.107783	−	0.331723i	0.882590	−	0.470143i	$-0.155798\pi$
$641$	−1749.20	−	5383.47i	−0.107783	−	0.331723i	−0.990374	+	0.138420i	$0.955798\pi$
$642$	−5429.53	−	7473.10i	−0.333779	−	0.459408i
$643$		−	9823.57i		−	0.602494i	−0.953546	−	0.301247i	$-0.902597\pi$
$643$		−	9823.57i		−	0.602494i	0.953546	−	0.301247i	$-0.0974029\pi$
$644$	−767.020	+	557.273i	−0.0469330	+	0.0340988i
$645$		0			0
$646$	−1370.15	−	995.474i	−0.0834488	−	0.0606291i
$647$	10130.3	−	13943.1i	0.615552	−	0.847234i	−0.381468	−	0.924382i	$-0.624581\pi$
$647$	10130.3	−	13943.1i	0.615552	−	0.847234i	0.997020	+	0.0771477i	$0.0245813\pi$
$648$	9858.38	+	3203.18i	0.597645	+	0.194187i
$649$	−18268.4			−1.10493
$650$		0			0
$651$	−20263.2			−1.21993
$652$	−15312.4	−	4975.31i	−0.919756	−	0.298847i
$653$	9498.34	−	13073.3i	0.569217	−	0.783460i	−0.423245	−	0.906015i	$-0.639109\pi$
$653$	9498.34	−	13073.3i	0.569217	−	0.783460i	0.992462	+	0.122555i	$0.0391089\pi$
$654$	12867.9	+	9349.05i	0.769378	+	0.558986i
$655$		0			0
$656$	3384.21	−	2458.77i	0.201419	−	0.146340i
$657$		−	9771.65i		−	0.580257i
$658$	716.314	+	985.921i	0.0424389	+	0.0584122i
$659$	2500.21	+	7694.84i	0.147791	+	0.454854i	0.997359	−	0.0726248i	$-0.0231376\pi$
$659$	2500.21	+	7694.84i	0.147791	+	0.454854i	−0.849568	+	0.527478i	$0.823138\pi$
$660$		0			0
$661$	1877.83	−	5779.37i	0.110498	−	0.340078i	−0.880483	−	0.474077i	$-0.842782\pi$
$661$	1877.83	−	5779.37i	0.110498	−	0.340078i	0.990981	+	0.133999i	$0.0427819\pi$
$662$	3639.28	−	1182.47i	0.213663	−	0.0694232i
$663$	−3388.82	+	1101.10i	−0.198508	+	0.0644992i
$664$	−2020.11	+	6217.25i	−0.118065	+	0.363368i
$665$		0			0
$666$	6838.51	+	21046.8i	0.397878	+	1.22454i
$667$	−261.737	−	360.250i	−0.0151941	−	0.0209129i
$668$		−	3439.80i		−	0.199236i
$669$	−30879.5	+	22435.3i	−1.78456	+	1.29656i
$670$		0			0
$671$	35570.1	+	25843.2i	2.04645	+	1.48683i
$672$	−1936.26	+	2665.03i	−0.111150	+	0.152985i
$673$	−1672.54	−	543.441i	−0.0957974	−	0.0311265i	0.260726	−	0.965413i	$-0.416038\pi$
$673$	−1672.54	−	543.441i	−0.0957974	−	0.0311265i	−0.356524	+	0.934286i	$0.616038\pi$
$674$	10418.9			0.595433
$675$		0			0
$676$	−1106.68			−0.0629654
$677$	−20969.5	−	6813.39i	−1.19043	−	0.386794i	−0.354199	−	0.935170i	$-0.615246\pi$
$677$	−20969.5	−	6813.39i	−1.19043	−	0.386794i	−0.836232	+	0.548376i	$0.815246\pi$
$678$	−1253.69	+	1725.55i	−0.0710142	+	0.0977426i
$679$	2434.19	+	1768.54i	0.137578	+	0.0999564i
$680$		0			0
$681$	−25057.7	+	18205.5i	−1.41001	+	1.02443i
$682$		−	26328.9i		−	1.47828i
$683$	20901.2	+	28768.0i	1.17096	+	1.61168i	0.657094	+	0.753809i	$0.271786\pi$
$683$	20901.2	+	28768.0i	1.17096	+	1.61168i	0.513862	+	0.857873i	$0.328214\pi$
$684$	7281.47	+	22410.1i	0.407038	+	1.25273i
$685$		0			0
$686$	3842.35	−	11825.5i	0.213851	−	0.658165i
$687$	−32494.1	+	10558.0i	−1.80455	+	0.586335i
$688$	1176.16	−	382.157i	0.0651753	−	0.0211767i
$689$	6053.32	−	18630.2i	0.334707	−	1.03012i
$690$		0			0
$691$	−2426.04	−	7466.60i	−0.133562	−	0.411060i	0.861802	−	0.507245i	$-0.169336\pi$
$691$	−2426.04	−	7466.60i	−0.133562	−	0.411060i	−0.995364	+	0.0961846i	$0.969336\pi$
$692$	−5133.72	−	7065.96i	−0.282016	−	0.388161i
$693$			44517.8i			2.44025i
$694$	−17366.5	+	12617.5i	−0.949889	+	0.690135i
$695$		0			0
$696$	−1251.70	−	909.410i	−0.0681687	−	0.0495274i
$697$	−1335.99	+	1838.83i	−0.0726027	+	0.0999291i
$698$	−5165.22	−	1678.28i	−0.280095	−	0.0910085i
$699$	16026.1			0.867186
$700$		0			0
$701$	6401.45			0.344906			0.172453	−	0.985018i	$-0.444831\pi$
$701$	6401.45			0.344906			0.172453	+	0.985018i	$0.444831\pi$
$702$	26099.9	+	8480.36i	1.40324	+	0.455941i
$703$	−10474.8	+	14417.3i	−0.561969	+	0.773484i
$704$	−3462.80	−	2515.87i	−0.185382	−	0.134688i
$705$		0			0
$706$	−1059.21	+	769.561i	−0.0564644	+	0.0410238i
$707$			12397.8i			0.659503i
$708$	−6006.75	−	8267.58i	−0.318852	−	0.438862i
$709$	2259.46	+	6953.91i	0.119684	+	0.368349i	0.992895	−	0.118993i	$-0.0379665\pi$
$709$	2259.46	+	6953.91i	0.119684	+	0.368349i	−0.873211	+	0.487342i	$0.837967\pi$
$710$		0			0
$711$	−18264.9	+	56213.5i	−0.963413	+	2.96508i
$712$	7054.52	−	2292.15i	0.371319	−	0.120649i
$713$	4031.48	−	1309.91i	0.211753	−	0.0688028i
$714$	553.109	−	1702.30i	0.0289910	−	0.0892252i
$715$		0			0
$716$	−4554.65	−	14017.8i	−0.237731	−	0.731660i
$717$	−14523.1	−	19989.3i	−0.756451	−	1.04116i
$718$			660.754i			0.0343442i
$719$	−3501.99	+	2544.35i	−0.181644	+	0.131972i	−0.674892	−	0.737917i	$-0.735810\pi$
$719$	−3501.99	+	2544.35i	−0.181644	+	0.131972i	0.493247	+	0.869889i	$0.335810\pi$
$720$		0			0
$721$	11812.9	+	8582.58i	0.610175	+	0.443318i
$722$	−3090.05	+	4253.08i	−0.159279	+	0.219229i
$723$	17821.9	+	5790.69i	0.916742	+	0.297868i
$724$	4398.79			0.225801
$725$		0			0
$726$	−58770.5			−3.00438
$727$	−28842.1	−	9371.37i	−1.47138	−	0.478081i	−0.539857	−	0.841757i	$-0.681522\pi$
$727$	−28842.1	−	9371.37i	−1.47138	−	0.478081i	−0.931526	+	0.363676i	$0.881522\pi$
$728$	−2267.99	+	3121.62i	−0.115463	+	0.158921i
$729$	−574.680	−	417.529i	−0.0291967	−	0.0212127i
$730$		0			0
$731$	−543.627	+	394.968i	−0.0275058	+	0.0199842i
$732$			24595.1i			1.24189i
$733$	−10512.7	−	14469.5i	−0.529736	−	0.729119i	0.457354	−	0.889285i	$-0.348797\pi$
$733$	−10512.7	−	14469.5i	−0.529736	−	0.729119i	−0.987090	+	0.160166i	$0.948797\pi$
$734$	−5974.06	−	18386.3i	−0.300418	−	0.924590i
$735$		0			0
$736$	212.950	−	655.392i	0.0106650	−	0.0328235i
$737$	−18821.5	+	6115.47i	−0.940703	+	0.305653i
$738$	30075.7	−	9772.18i	1.50014	−	0.487424i
$739$	−4274.15	+	13154.5i	−0.212757	+	0.654797i	0.786549	+	0.617528i	$0.211866\pi$
$739$	−4274.15	+	13154.5i	−0.212757	+	0.654797i	−0.999305	+	0.0372691i	$0.988134\pi$
$740$		0			0
$741$	12336.7	+	37968.3i	0.611604	+	1.88232i
$742$	5783.84	+	7960.77i	0.286161	+	0.393867i
$743$			8682.92i			0.428729i	0.976754	+	0.214364i	$0.0687680\pi$
$743$			8682.92i			0.428729i	−0.976754	+	0.214364i	$0.931232\pi$
$744$	11915.5	−	8657.08i	0.587153	−	0.426592i
$745$		0			0
$746$	6225.43	+	4523.04i	0.305535	+	0.221984i
$747$	−29048.3	+	39981.5i	−1.42279	+	1.95830i
$748$	2211.87	+	718.682i	0.108121	+	0.0351305i
$749$	5435.09			0.265146
$750$		0			0
$751$	4892.32			0.237714			0.118857	−	0.992911i	$-0.462077\pi$
$751$	4892.32			0.237714			0.118857	+	0.992911i	$0.462077\pi$
$752$	−842.436	−	273.724i	−0.0408517	−	0.0132735i
$753$	−3088.18	+	4250.51i	−0.149455	+	0.205707i
$754$	−1466.14	−	1065.22i	−0.0708141	−	0.0514494i
$755$		0			0
$756$	−11152.6	+	8102.83i	−0.536529	+	0.389811i
$757$			35983.3i			1.72765i	0.503789	+	0.863827i	$0.331939\pi$
$757$			35983.3i			1.72765i	−0.503789	+	0.863827i	$0.668061\pi$
$758$	10323.9	+	14209.6i	0.494696	+	0.680890i
$759$	−4162.63	−	12811.3i	−0.199070	−	0.612673i
$760$		0			0
$761$	6748.63	−	20770.1i	0.321468	−	0.989378i	−0.651541	−	0.758613i	$-0.725877\pi$
$761$	6748.63	−	20770.1i	0.321468	−	0.989378i	0.973010	−	0.230765i	$-0.0741228\pi$
$762$	−4735.16	+	1538.55i	−0.225114	+	0.0731439i
$763$	−8900.59	+	2891.98i	−0.422311	+	0.137217i
$764$	1341.56	−	4128.91i	0.0635289	−	0.195522i
$765$		0			0
$766$	2986.82	+	9192.49i	0.140885	+	0.433601i
$767$	−7035.86	−	9684.03i	−0.331226	−	0.455893i
$768$		−	2394.36i		−	0.112499i
$769$	410.314	−	298.110i	0.0192410	−	0.0139794i	−0.578123	−	0.815949i	$-0.696215\pi$
$769$	410.314	−	298.110i	0.0192410	−	0.0139794i	0.597364	+	0.801970i	$0.296215\pi$
$770$		0			0
$771$	−46397.4	−	33709.7i	−2.16727	−	1.57461i
$772$	2454.17	−	3377.88i	0.114414	−	0.157477i
$773$	14362.9	+	4666.78i	0.668301	+	0.217144i	0.623466	−	0.781850i	$-0.285724\pi$
$773$	14362.9	+	4666.78i	0.668301	+	0.217144i	0.0448347	+	0.998994i	$0.485724\pi$
$774$	9349.08			0.434168
$775$		0			0
$776$	−2186.97			−0.101170
$777$	−17912.2	−	5820.04i	−0.827025	−	0.268717i
$778$	−14474.5	+	19922.5i	−0.667015	+	0.918067i
$779$	20602.2	+	14968.4i	0.947562	+	0.688444i
$780$		0			0
$781$	−10107.8	+	7343.71i	−0.463104	+	0.336464i
$782$			374.438i			0.0171226i
$783$	−3805.69	−	5238.09i	−0.173697	−	0.239073i
$784$	1096.94	+	3376.02i	0.0499697	+	0.153791i
$785$		0			0
$786$	−16374.4	+	50395.1i	−0.743071	+	2.28694i
$787$	298.302	−	96.9241i	0.0135112	−	0.00439005i	−0.302254	−	0.953228i	$-0.597739\pi$
$787$	298.302	−	96.9241i	0.0135112	−	0.00439005i	0.315765	+	0.948837i	$0.397739\pi$
$788$	−4525.18	+	1470.32i	−0.204572	+	0.0664696i
$789$	11654.5	−	35868.7i	0.525868	−	1.61845i
$790$		0			0
$791$	−387.808	−	1193.55i	−0.0174322	−	0.0536508i
$792$	−19019.5	−	26178.1i	−0.853318	−	1.17449i
$793$			28808.8i			1.29008i
$794$	−9383.33	+	6817.39i	−0.419398	+	0.304710i
$795$		0			0
$796$	3987.58	+	2897.14i	0.177558	+	0.129003i
$797$	18430.7	−	25367.7i	0.819133	−	1.12744i	−0.170716	−	0.985320i	$-0.554608\pi$
$797$	18430.7	−	25367.7i	0.819133	−	1.12744i	0.989849	−	0.142120i	$-0.0453919\pi$
$798$	−19072.5	−	6197.03i	−0.846064	−	0.274903i
$799$	481.299			0.0213106
$800$		0			0
$801$	56075.2			2.47356
$802$	28815.4	+	9362.70i	1.26871	+	0.412230i
$803$	−6351.51	+	8742.10i	−0.279128	+	0.384187i
$804$	−8956.23	−	6507.08i	−0.392863	−	0.285432i
$805$		0			0
$806$	13956.9	−	10140.3i	0.609938	−	0.443146i
$807$		−	12050.8i		−	0.525661i
$808$	−5296.76	−	7290.36i	−0.230618	−	0.317418i
$809$	7092.37	+	21828.1i	0.308225	+	0.948620i	0.978454	+	0.206465i	$0.0661961\pi$
$809$	7092.37	+	21828.1i	0.308225	+	0.948620i	−0.670228	+	0.742155i	$0.733804\pi$
$810$		0			0
$811$	3303.67	−	10167.6i	0.143043	−	0.440240i	−0.853712	−	0.520746i	$-0.825654\pi$
$811$	3303.67	−	10167.6i	0.143043	−	0.440240i	0.996754	+	0.0805065i	$0.0256538\pi$
$812$	865.787	−	281.311i	0.0374177	−	0.0121578i
$813$	26711.7	−	8679.16i	1.15230	−	0.374405i
$814$	7562.26	−	23274.2i	0.325623	−	1.00216i
$815$		0			0
$816$	402.029	+	1237.32i	0.0172473	+	0.0530818i
$817$	4425.22	+	6090.79i	0.189497	+	0.260820i
$818$		−	28322.8i		−	1.21061i
$819$	−23598.8	+	17145.5i	−1.00685	+	0.731517i
$820$		0			0
$821$	−5693.66	−	4136.68i	−0.242034	−	0.175848i	0.460155	−	0.887839i	$-0.347794\pi$
$821$	−5693.66	−	4136.68i	−0.242034	−	0.175848i	−0.702189	+	0.711991i	$0.747794\pi$
$822$	−15935.6	+	21933.5i	−0.676177	+	0.930678i
$823$	19273.5	+	6262.34i	0.816321	+	0.265239i	0.687273	−	0.726400i	$-0.258808\pi$
$823$	19273.5	+	6262.34i	0.816321	+	0.265239i	0.129048	+	0.991638i	$0.458808\pi$
$824$	−10613.2			−0.448698
$825$		0			0
$826$	6012.91			0.253288
$827$	17118.2	+	5562.03i	0.719779	+	0.233870i	0.645927	−	0.763399i	$-0.276471\pi$
$827$	17118.2	+	5562.03i	0.719779	+	0.233870i	0.0738518	+	0.997269i	$0.476471\pi$
$828$	3062.13	−	4214.66i	0.128522	−	0.176896i
$829$	27631.7	+	20075.6i	1.15765	+	0.841080i	0.989479	−	0.144678i	$-0.0462148\pi$
$829$	27631.7	+	20075.6i	1.15765	+	0.841080i	0.168168	+	0.985758i	$0.446215\pi$
$830$		0			0
$831$	40335.1	−	29305.2i	1.68377	−	1.22333i
$832$		−	2804.58i		−	0.116865i
$833$	−1133.71	−	1560.42i	−0.0471557	−	0.0649042i
$834$	10905.0	+	33562.2i	0.452769	+	1.39348i
$835$		0			0
$836$	8052.10	−	24781.8i	0.333119	−	1.02524i
$837$	58618.3	−	19046.2i	2.42072	−	0.786540i
$838$	−3909.63	+	1270.32i	−0.161165	+	0.0523655i
$839$	−7893.72	+	24294.4i	−0.324817	+	0.999684i	0.646706	+	0.762739i	$0.276146\pi$
$839$	−7893.72	+	24294.4i	−0.324817	+	0.999684i	−0.971523	+	0.236945i	$0.923854\pi$
$840$		0			0
$841$	−7404.49	−	22788.7i	−0.303600	−	0.934384i
$842$	6545.56	+	9009.19i	0.267904	+	0.368738i
$843$			12198.8i			0.498399i
$844$	8602.10	−	6249.79i	0.350825	−	0.254889i
$845$		0			0
$846$	−5417.49	−	3936.04i	−0.220162	−	0.159957i
$847$	20325.5	−	27975.7i	0.824550	−	1.13490i
$848$	−6802.21	−	2210.17i	−0.275458	−	0.0895019i
$849$	12532.6			0.506616
$850$		0			0
$851$	3939.98			0.158708
$852$	−6646.97	−	2159.73i	−0.267279	−	0.0868441i
$853$	20523.3	−	28248.0i	0.823805	−	1.13387i	−0.165239	−	0.986254i	$-0.552840\pi$
$853$	20523.3	−	28248.0i	0.823805	−	1.13387i	0.989045	−	0.147617i	$-0.0471604\pi$
$854$	−11707.6	−	8506.10i	−0.469119	−	0.340835i
$855$		0			0
$856$	−3196.03	+	2322.05i	−0.127614	+	0.0927173i
$857$		−	24807.3i		−	0.988801i	−0.869234	−	0.494400i	$-0.835388\pi$
$857$		−	24807.3i		−	0.988801i	0.869234	−	0.494400i	$-0.164612\pi$
$858$	−32223.8	−	44352.3i	−1.28217	−	1.76476i
$859$	8878.09	+	27324.0i	0.352639	+	1.08531i	0.957366	+	0.288877i	$0.0932820\pi$
$859$	8878.09	+	27324.0i	0.352639	+	1.08531i	−0.604728	+	0.796432i	$0.706718\pi$
$860$		0			0
$861$	−8316.79	+	25596.5i	−0.329193	+	1.01315i
$862$	8249.40	−	2680.39i	0.325958	−	0.105910i
$863$	−7574.40	+	2461.07i	−0.298767	+	0.0970751i	−0.454565	−	0.890714i	$-0.650205\pi$
$863$	−7574.40	+	2461.07i	−0.298767	+	0.0970751i	0.155798	+	0.987789i	$0.450205\pi$
$864$	3096.32	−	9529.51i	0.121920	−	0.375232i
$865$		0			0
$866$	−4676.48	−	14392.7i	−0.183503	−	0.564763i
$867$	26593.9	+	36603.4i	1.04173	+	1.43381i
$868$			8665.96i			0.338873i
$869$	52878.9	−	38418.8i	2.06420	−	1.49973i
$870$		0			0
$871$	−10490.7	−	7621.92i	−0.408109	−	0.296508i
$872$	3998.32	−	5503.21i	0.155275	−	0.213718i
$873$	−15723.8	−	5108.99i	−0.609589	−	0.198068i
$874$	4195.19			0.162362
$875$		0			0
$876$	−6044.75			−0.233143
$877$	7357.12	+	2390.47i	0.283275	+	0.0920416i	0.447208	−	0.894430i	$-0.352418\pi$
$877$	7357.12	+	2390.47i	0.283275	+	0.0920416i	−0.163933	+	0.986471i	$0.552418\pi$
$878$	3351.36	−	4612.75i	0.128819	−	0.177304i
$879$	−47902.3	−	34803.0i	−1.83812	−	1.33547i
$880$		0			0
$881$	−27445.1	+	19940.0i	−1.04954	+	0.762539i	−0.972126	−	0.234460i	$-0.924668\pi$
$881$	−27445.1	+	19940.0i	−1.04954	+	0.762539i	−0.0774188	+	0.996999i	$0.524668\pi$
$882$			26835.4i			1.02449i
$883$	−25619.9	−	35262.7i	−0.976418	−	1.34392i	−0.938737	−	0.344635i	$-0.888003\pi$
$883$	−25619.9	−	35262.7i	−0.976418	−	1.34392i	−0.0376815	−	0.999290i	$-0.511997\pi$
$884$	470.906	+	1449.30i	0.0179166	+	0.0551417i
$885$		0			0
$886$	−2932.71	+	9025.95i	−0.111203	+	0.342249i
$887$	23699.5	−	7700.42i	0.897125	−	0.291494i	0.176075	−	0.984377i	$-0.443660\pi$
$887$	23699.5	−	7700.42i	0.897125	−	0.291494i	0.721050	+	0.692883i	$0.243660\pi$
$888$	13019.5	−	4230.31i	0.492013	−	0.159865i
$889$	905.263	−	2786.11i	0.0341525	−	0.105110i
$890$		0			0
$891$	−26778.2	−	82414.9i	−1.00685	−	3.09877i
$892$	9594.91	+	13206.3i	0.360158	+	0.495716i
$893$		−	5392.47i		−	0.202074i
$894$	−42437.2	+	30832.4i	−1.58760	+	1.15346i
$895$		0			0
$896$	1139.76	+	828.081i	0.0424962	+	0.0308753i
$897$	5188.02	−	7140.70i	0.193114	−	0.265798i
$898$	6875.13	+	2233.87i	0.255486	+	0.0830123i
$899$	−4070.18			−0.150999
$900$		0			0
$901$	3886.22			0.143695
$902$	−33258.7	−	10806.4i	−1.22771	−	0.398907i
$903$	−4676.84	+	6437.11i	−0.172354	+	0.237225i
$904$	737.969	+	536.166i	0.0271510	+	0.0197263i
$905$		0			0
$906$	44010.1	−	31975.2i	1.61384	−	1.17252i
$907$			22241.5i			0.814241i	0.913375	+	0.407120i	$0.133467\pi$
$907$			22241.5i			0.814241i	−0.913375	+	0.407120i	$0.866533\pi$
$908$	7785.97	+	10716.5i	0.284566	+	0.391672i
$909$	−21051.5	−	64790.0i	−0.768136	−	2.36408i
$910$		0			0
$911$	3136.73	−	9653.87i	0.114077	−	0.351094i	−0.877676	−	0.479254i	$-0.840907\pi$
$911$	3136.73	−	9653.87i	0.114077	−	0.351094i	0.991753	+	0.128160i	$0.0409071\pi$
$912$	13862.9	−	4504.32i	0.503340	−	0.163545i
$913$	51975.5	−	16887.9i	1.88405	−	0.612165i
$914$	−3155.63	+	9712.04i	−0.114200	+	0.351472i
$915$		0			0
$916$	4515.34	+	13896.8i	0.162872	+	0.501270i
$917$	−18325.9	−	25223.4i	−0.659949	−	0.908342i
$918$			5444.38i			0.195742i
$919$	−42411.8	+	30814.0i	−1.52235	+	1.10605i	−0.562039	+	0.827111i	$0.689983\pi$
$919$	−42411.8	+	30814.0i	−1.52235	+	1.10605i	−0.960309	+	0.278940i	$0.910017\pi$
$920$		0			0
$921$	49593.9	+	36032.1i	1.77435	+	1.28914i
$922$	−8844.30	+	12173.1i	−0.315913	+	0.434817i
$923$	−7785.77	−	2529.75i	−0.277651	−	0.0902142i
$924$	27538.8			0.980475
$925$		0			0
$926$	9400.89			0.333620
$927$	−76306.5	−	24793.5i	−2.70360	−	0.878452i
$928$	−388.928	+	535.314i	−0.0137578	+	0.0189359i
$929$	7076.50	+	5141.38i	0.249917	+	0.181575i	0.705690	−	0.708521i	$-0.250637\pi$
$929$	7076.50	+	5141.38i	0.249917	+	0.181575i	−0.455773	+	0.890096i	$0.650637\pi$
$930$		0			0
$931$	−17482.9	+	12702.1i	−0.615444	+	0.447147i
$932$		−	6853.90i		−	0.240887i
$933$	−45324.4	−	62383.7i	−1.59041	−	2.18902i
$934$	−2587.54	−	7963.64i	−0.0906499	−	0.278992i
$935$		0			0
$936$	6551.79	−	20164.3i	0.228795	−	0.704158i
$937$	20205.6	−	6565.19i	0.704469	−	0.228896i	0.0651926	−	0.997873i	$-0.479234\pi$
$937$	20205.6	−	6565.19i	0.704469	−	0.228896i	0.639277	+	0.768977i	$0.279234\pi$
$938$	6194.95	−	2012.86i	0.215642	−	0.0700664i
$939$	−14078.9	+	43330.4i	−0.489295	+	1.50590i
$940$		0			0
$941$	6544.57	+	20142.1i	0.226724	+	0.697784i	0.998112	+	0.0614191i	$0.0195626\pi$
$941$	6544.57	+	20142.1i	0.226724	+	0.697784i	−0.771388	+	0.636365i	$0.780437\pi$
$942$	−12587.5	−	17325.2i	−0.435374	−	0.599240i
$943$		−	5630.21i		−	0.194427i
$944$	−3535.80	+	2568.91i	−0.121907	+	0.0885709i
$945$		0			0
$946$	−8364.05	−	6076.84i	−0.287462	−	0.208853i
$947$	789.022	−	1085.99i	0.0270747	−	0.0372651i	−0.795265	−	0.606262i	$-0.792668\pi$
$947$	789.022	−	1085.99i	0.0270747	−	0.0372651i	0.822340	+	0.568997i	$0.192668\pi$
$948$	34773.7	+	11298.7i	1.19135	+	0.387093i
$949$	−7080.37			−0.242190
$950$		0			0
$951$	−64544.1			−2.20083
$952$	−728.022	−	236.549i	−0.0247850	−	0.00805314i
$953$	−27497.5	+	37847.0i	−0.934659	+	1.28645i	0.0233546	+	0.999727i	$0.492565\pi$
$953$	−27497.5	+	37847.0i	−0.934659	+	1.28645i	−0.958014	+	0.286721i	$0.907435\pi$
$954$	−43743.2	−	31781.3i	−1.48453	−	1.07857i
$955$		0			0
$956$	−8548.85	+	6211.11i	−0.289215	+	0.210127i
$957$			12934.2i			0.436891i
$958$	2259.17	+	3109.48i	0.0761904	+	0.104867i
$959$	−4929.42	−	15171.2i	−0.165985	−	0.510848i
$960$		0			0
$961$	2767.21	−	8516.59i	0.0928873	−	0.285878i
$962$	15250.1	−	4955.07i	0.511106	−	0.166068i
$963$	−28403.3	+	9228.80i	−0.950451	+	0.308820i
$964$	2476.51	−	7621.92i	0.0827418	−	0.254653i
$965$		0			0
$966$	1370.10	+	4216.73i	0.0456337	+	0.140446i
$967$	582.336	+	801.517i	0.0193657	+	0.0266546i	0.818590	−	0.574378i	$-0.194756\pi$
$967$	582.336	+	801.517i	0.0193657	+	0.0266546i	−0.799224	+	0.601033i	$0.794756\pi$
$968$			25134.4i			0.834557i
$969$	−6407.51	+	4655.33i	−0.212424	+	0.154335i
$970$		0			0
$971$	37672.2	+	27370.4i	1.24506	+	0.904592i	0.997925	−	0.0643878i	$-0.0205095\pi$
$971$	37672.2	+	27370.4i	1.24506	+	0.904592i	0.247139	+	0.968980i	$0.420509\pi$
$972$	8615.74	−	11858.5i	0.284311	−	0.391320i
$973$	−19747.6	−	6416.38i	−0.650646	−	0.211408i
$974$	40391.7			1.32878
$975$		0			0
$976$	10518.6			0.344971
$977$	31115.3	+	10110.0i	1.01890	+	0.331061i	0.770393	−	0.637569i	$-0.220060\pi$
$977$	31115.3	+	10110.0i	1.01890	+	0.331061i	0.248508	+	0.968630i	$0.420060\pi$
$978$	−44256.4	+	60913.8i	−1.44700	+	1.99162i
$979$	−50167.1	−	36448.5i	−1.63774	−	1.18989i
$980$		0			0
$981$	41603.1	−	30226.4i	1.35401	−	0.983747i
$982$		−	35399.2i		−	1.15034i
$983$	29689.4	+	40864.0i	0.963322	+	1.32590i	0.945349	+	0.326060i	$0.105721\pi$
$983$	29689.4	+	40864.0i	0.963322	+	1.32590i	0.0179729	+	0.999838i	$0.494279\pi$
$984$	−6045.08	−	18604.8i	−0.195843	−	0.602744i
$985$		0			0
$986$	111.101	−	341.933i	0.00358841	−	0.0110440i
$987$	5420.15	−	1761.11i	0.174798	−	0.0567952i
$988$	16238.0	−	5276.03i	0.522873	−	0.169892i
$989$	514.359	−	1583.04i	0.0165376	−	0.0508975i
$990$		0			0
$991$	−8001.15	−	24625.0i	−0.256473	−	0.789343i	−0.993536	−	0.113519i	$-0.963788\pi$
$991$	−8001.15	−	24625.0i	−0.256473	−	0.789343i	0.737063	−	0.675824i	$-0.236212\pi$
$992$	−3702.38	−	5095.89i	−0.118499	−	0.163100i
$993$		−	17894.9i		−	0.571881i
$994$	3326.89	−	2417.13i	0.106160	−	0.0771295i
$995$		0			0
$996$	24732.6	+	17969.3i	0.786830	+	0.571666i
$997$	−34311.9	+	47226.3i	−1.08994	+	1.50017i	−0.241856	+	0.970312i	$0.577756\pi$
$997$	−34311.9	+	47226.3i	−1.08994	+	1.50017i	−0.848084	+	0.529862i	$0.822244\pi$
$998$	−2154.31	−	699.978i	−0.0683302	−	0.0222018i
$999$	57288.0			1.81433

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.4.e.b.149.1		32
5.2	odd	4		250.4.d.c.101.8		32
5.3	odd	4		250.4.d.d.101.1		32
5.4	even	2		50.4.e.a.29.8	yes	32
25.6	even	5		50.4.e.a.19.8	✓	32
25.8	odd	20		250.4.d.d.151.1		32
25.12	odd	20		1250.4.a.n.1.1		16
25.13	odd	20		1250.4.a.m.1.16		16
25.17	odd	20		250.4.d.c.151.8		32
25.19	even	10	inner	250.4.e.b.99.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.e.a.19.8	✓	32	25.6	even	5
50.4.e.a.29.8	yes	32	5.4	even	2
250.4.d.c.101.8		32	5.2	odd	4
250.4.d.c.151.8		32	25.17	odd	20
250.4.d.d.101.1		32	5.3	odd	4
250.4.d.d.151.1		32	25.8	odd	20
250.4.e.b.99.1		32	25.19	even	10	inner
250.4.e.b.149.1		32	1.1	even	1	trivial
1250.4.a.m.1.16		16	25.13	odd	20
1250.4.a.n.1.1		16	25.12	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)

\(f(q)\)	\(=\)	\(q+(-1.90211 - 0.618034i) q^{2} +(-5.49755 + 7.56672i) q^{3} +(3.23607 + 2.35114i) q^{4} +(15.1334 - 10.9951i) q^{6} +11.0064i q^{7} +(-4.70228 - 6.47214i) q^{8} +(-18.6888 - 57.5183i) q^{9} +O(q^{10})\)	\(q+(-1.90211 - 0.618034i) q^{2} +(-5.49755 + 7.56672i) q^{3} +(3.23607 + 2.35114i) q^{4} +(15.1334 - 10.9951i) q^{6} +11.0064i q^{7} +(-4.70228 - 6.47214i) q^{8} +(-18.6888 - 57.5183i) q^{9} +(-20.6668 + 63.6057i) q^{11} +(-35.5809 + 11.5609i) q^{12} +(-41.6768 + 13.5416i) q^{13} +(6.80231 - 20.9354i) q^{14} +(4.94427 + 15.2169i) q^{16} +(-5.11002 - 7.03334i) q^{17} +120.957i q^{18} +(-78.8015 + 57.2527i) q^{19} +(-83.2822 - 60.5080i) q^{21} +(78.6210 - 108.213i) q^{22} +(20.4810 + 6.65468i) q^{23} +74.8239 q^{24} +87.6431 q^{26} +(297.797 + 96.7602i) q^{27} +(-25.8775 + 35.6174i) q^{28} +(-16.7286 - 12.1540i) q^{29} +(159.247 - 115.699i) q^{31} -32.0000i q^{32} +(-367.671 - 506.055i) q^{33} +(5.37300 + 16.5364i) q^{34} +(74.7553 - 230.073i) q^{36} +(174.003 - 56.5369i) q^{37} +(185.274 - 60.1990i) q^{38} +(126.654 - 389.802i) q^{39} +(-80.7907 - 248.648i) q^{41} +(121.016 + 166.564i) q^{42} -77.2928i q^{43} +(-216.425 + 157.242i) q^{44} +(-34.8444 - 25.3159i) q^{46} +(-32.5409 + 44.7887i) q^{47} +(-142.323 - 46.2437i) q^{48} +221.860 q^{49} +81.3120 q^{51} +(-166.707 - 54.1664i) q^{52} +(-262.750 + 361.644i) q^{53} +(-506.643 - 368.097i) q^{54} +(71.2347 - 51.7551i) q^{56} -911.019i q^{57} +(24.3080 + 33.4571i) q^{58} +(84.4098 + 259.787i) q^{59} +(203.152 - 625.236i) q^{61} +(-374.411 + 121.654i) q^{62} +(633.068 - 205.696i) q^{63} +(-19.7771 + 60.8676i) q^{64} +(386.592 + 1189.81i) q^{66} +(173.931 + 239.395i) q^{67} -34.7748i q^{68} +(-162.949 + 118.390i) q^{69} +(151.135 + 109.806i) q^{71} +(-284.386 + 391.424i) q^{72} +(153.665 + 49.9287i) q^{73} -365.914 q^{74} -389.616 q^{76} +(-700.068 - 227.466i) q^{77} +(-481.822 + 663.171i) q^{78} +(-790.665 - 574.452i) q^{79} +(-1048.25 + 761.602i) q^{81} +522.889i q^{82} +(-480.309 - 661.089i) q^{83} +(-127.244 - 391.616i) q^{84} +(-47.7696 + 147.020i) q^{86} +(183.932 - 59.7632i) q^{87} +(508.846 - 165.334i) q^{88} +(-286.519 + 881.815i) q^{89} +(-149.044 - 458.710i) q^{91} +(50.6318 + 69.6888i) q^{92} +1841.04i q^{93} +(89.5774 - 65.0818i) q^{94} +(242.135 + 175.922i) q^{96} +(160.683 - 221.162i) q^{97} +(-422.002 - 137.117i) q^{98} +4044.73 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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