LMFDB - Embedded newform 250.4.e.b.99.6

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			99.6
Character	$\chi$	$=$	250.99
Dual form			250.4.e.b.149.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.90211 - 0.618034i) q^{2} +(-2.86980 - 3.94994i) q^{3} +(3.23607 - 2.35114i) q^{4} +(-7.89989 - 5.73960i) q^{6} -32.3828i q^{7} +(4.70228 - 6.47214i) q^{8} +(0.977169 - 3.00742i) q^{9} +O(q^{10})$	\(q+(1.90211 - 0.618034i) q^{2} +(-2.86980 - 3.94994i) q^{3} +(3.23607 - 2.35114i) q^{4} +(-7.89989 - 5.73960i) q^{6} -32.3828i q^{7} +(4.70228 - 6.47214i) q^{8} +(0.977169 - 3.00742i) q^{9} +(14.5272 + 44.7100i) q^{11} +(-18.5737 - 6.03498i) q^{12} +(-9.48373 - 3.08145i) q^{13} +(-20.0137 - 61.5957i) q^{14} +(4.94427 - 15.2169i) q^{16} +(-26.8671 + 36.9793i) q^{17} -6.32437i q^{18} +(-94.7959 - 68.8733i) q^{19} +(-127.910 + 92.9322i) q^{21} +(55.2646 + 76.0652i) q^{22} +(-8.30148 + 2.69731i) q^{23} -39.0592 q^{24} -19.9436 q^{26} +(-140.056 + 45.5070i) q^{27} +(-76.1365 - 104.793i) q^{28} +(188.929 - 137.265i) q^{29} +(-211.987 - 154.018i) q^{31} -32.0000i q^{32} +(134.912 - 185.690i) q^{33} +(-28.2497 + 86.9436i) q^{34} +(-3.90868 - 12.0297i) q^{36} +(-14.1085 - 4.58412i) q^{37} +(-222.879 - 72.4177i) q^{38} +(15.0449 + 46.3033i) q^{39} +(-79.2986 + 244.056i) q^{41} +(-185.864 + 255.820i) q^{42} -81.5270i q^{43} +(152.130 + 110.529i) q^{44} +(-14.1233 + 10.2612i) q^{46} +(128.690 + 177.126i) q^{47} +(-74.2950 + 24.1399i) q^{48} -705.645 q^{49} +223.169 q^{51} +(-37.9349 + 12.3258i) q^{52} +(190.894 + 262.743i) q^{53} +(-238.278 + 173.119i) q^{54} +(-209.586 - 152.273i) q^{56} +572.091i q^{57} +(274.530 - 377.858i) q^{58} +(162.059 - 498.767i) q^{59} +(77.8088 + 239.471i) q^{61} +(-498.412 - 161.944i) q^{62} +(-97.3885 - 31.6435i) q^{63} +(-19.7771 - 60.8676i) q^{64} +(141.855 - 436.584i) q^{66} +(435.342 - 599.197i) q^{67} +182.836i q^{68} +(34.4778 + 25.0496i) q^{69} +(306.683 - 222.818i) q^{71} +(-14.8695 - 20.4661i) q^{72} +(349.928 - 113.698i) q^{73} -29.6690 q^{74} -468.697 q^{76} +(1447.83 - 470.430i) q^{77} +(57.2341 + 78.7759i) q^{78} +(741.749 - 538.912i) q^{79} +(512.611 + 372.433i) q^{81} +513.232i q^{82} +(258.354 - 355.593i) q^{83} +(-195.429 + 601.470i) q^{84} +(-50.3865 - 155.074i) q^{86} +(-1084.38 - 352.335i) q^{87} +(357.680 + 116.217i) q^{88} +(117.993 + 363.145i) q^{89} +(-99.7859 + 307.110i) q^{91} +(-20.5224 + 28.2466i) q^{92} +1279.34i q^{93} +(354.253 + 257.380i) q^{94} +(-126.398 + 91.8337i) q^{96} +(-395.195 - 543.939i) q^{97} +(-1342.22 + 436.113i) q^{98} +148.657 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 $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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
$3$	−2.86980	−	3.94994i	−0.552294	−	0.760167i	0.438028	−	0.898962i	$-0.355677\pi$
$3$	−2.86980	−	3.94994i	−0.552294	−	0.760167i	−0.990321	+	0.138795i	$0.955677\pi$
$4$	3.23607	−	2.35114i	0.404508	−	0.293893i
$5$		0			0
$5$		0			0
$6$	−7.89989	−	5.73960i	−0.537519	−	0.390531i
$7$		−	32.3828i		−	1.74851i	−0.485470	−	0.874253i	$-0.661352\pi$
$7$		−	32.3828i		−	1.74851i	0.485470	−	0.874253i	$-0.338648\pi$
$8$	4.70228	−	6.47214i	0.207813	−	0.286031i
$9$	0.977169	−	3.00742i	0.0361914	−	0.111386i
$10$		0			0
$11$	14.5272	+	44.7100i	0.398191	+	1.22551i	0.926448	+	0.376422i	$0.122846\pi$
$11$	14.5272	+	44.7100i	0.398191	+	1.22551i	−0.528257	+	0.849084i	$0.677154\pi$
$12$	−18.5737	−	6.03498i	−0.446815	−	0.145179i
$13$	−9.48373	−	3.08145i	−0.202332	−	0.0657416i	0.206098	−	0.978531i	$-0.433923\pi$
$13$	−9.48373	−	3.08145i	−0.202332	−	0.0657416i	−0.408430	+	0.912790i	$0.633923\pi$
$14$	−20.0137	−	61.5957i	−0.382063	−	1.17587i
$15$		0			0
$16$	4.94427	−	15.2169i	0.0772542	−	0.237764i
$17$	−26.8671	+	36.9793i	−0.383307	+	0.527577i	−0.956457	−	0.291874i	$-0.905721\pi$
$17$	−26.8671	+	36.9793i	−0.383307	+	0.527577i	0.573150	+	0.819451i	$0.305721\pi$
$18$		−	6.32437i		−	0.0828149i
$19$	−94.7959	−	68.8733i	−1.14461	−	0.831611i	−0.156859	−	0.987621i	$-0.550137\pi$
$19$	−94.7959	−	68.8733i	−1.14461	−	0.831611i	−0.987756	+	0.156010i	$0.950137\pi$
$20$		0			0
$21$	−127.910	+	92.9322i	−1.32916	+	0.965689i
$22$	55.2646	+	76.0652i	0.535566	+	0.737143i
$23$	−8.30148	+	2.69731i	−0.0752599	+	0.0244534i	−0.346405	−	0.938085i	$-0.612598\pi$
$23$	−8.30148	+	2.69731i	−0.0752599	+	0.0244534i	0.271145	+	0.962538i	$0.412598\pi$
$24$	−39.0592			−0.332205
$25$		0			0
$26$	−19.9436			−0.150433
$27$	−140.056	+	45.5070i	−0.998290	+	0.324364i
$28$	−76.1365	−	104.793i	−0.513873	−	0.707286i
$29$	188.929	−	137.265i	1.20977	−	0.878946i	0.214556	−	0.976712i	$-0.431169\pi$
$29$	188.929	−	137.265i	1.20977	−	0.878946i	0.995210	+	0.0977652i	$0.0311694\pi$
$30$		0			0
$31$	−211.987	−	154.018i	−1.22819	−	0.892336i	−0.231441	−	0.972849i	$-0.574344\pi$
$31$	−211.987	−	154.018i	−1.22819	−	0.892336i	−0.996754	+	0.0805133i	$0.974344\pi$
$32$		−	32.0000i		−	0.176777i
$33$	134.912	−	185.690i	0.711671	−	0.979531i
$34$	−28.2497	+	86.9436i	−0.142494	+	0.438550i
$35$		0			0
$36$	−3.90868	−	12.0297i	−0.0180957	−	0.0556929i
$37$	−14.1085	−	4.58412i	−0.0626869	−	0.0203682i	0.277506	−	0.960724i	$-0.410492\pi$
$37$	−14.1085	−	4.58412i	−0.0626869	−	0.0203682i	−0.340193	+	0.940356i	$0.610492\pi$
$38$	−222.879	−	72.4177i	−0.951465	−	0.309150i
$39$	15.0449	+	46.3033i	0.0617720	+	0.190115i
$40$		0			0
$41$	−79.2986	+	244.056i	−0.302058	+	0.929638i	0.678701	+	0.734415i	$0.262543\pi$
$41$	−79.2986	+	244.056i	−0.302058	+	0.929638i	−0.980759	+	0.195223i	$0.937457\pi$
$42$	−185.864	+	255.820i	−0.682845	+	0.939856i
$43$		−	81.5270i		−	0.289134i	−0.989495	−	0.144567i	$-0.953821\pi$
$43$		−	81.5270i		−	0.289134i	0.989495	−	0.144567i	$-0.0461789\pi$
$44$	152.130	+	110.529i	0.521239	+	0.378702i
$45$		0			0
$46$	−14.1233	+	10.2612i	−0.0452689	+	0.0328898i
$47$	128.690	+	177.126i	0.399390	+	0.549714i	0.960591	−	0.277966i	$-0.0896604\pi$
$47$	128.690	+	177.126i	0.399390	+	0.549714i	−0.561201	+	0.827680i	$0.689660\pi$
$48$	−74.2950	+	24.1399i	−0.223407	+	0.0725895i
$49$	−705.645			−2.05727
$50$		0			0
$51$	223.169			0.612745
$52$	−37.9349	+	12.3258i	−0.101166	+	0.0328708i
$53$	190.894	+	262.743i	0.494741	+	0.680953i	0.981254	−	0.192721i	$-0.0617312\pi$
$53$	190.894	+	262.743i	0.494741	+	0.680953i	−0.486512	+	0.873674i	$0.661731\pi$
$54$	−238.278	+	173.119i	−0.600472	+	0.436269i
$55$		0			0
$56$	−209.586	−	152.273i	−0.500127	−	0.363363i
$57$			572.091i			1.32939i
$58$	274.530	−	377.858i	0.621509	−	0.855434i
$59$	162.059	−	498.767i	0.357599	−	1.10058i	−0.596889	−	0.802324i	$-0.703597\pi$
$59$	162.059	−	498.767i	0.357599	−	1.10058i	0.954487	−	0.298251i	$-0.0964034\pi$
$60$		0			0
$61$	77.8088	+	239.471i	0.163318	+	0.502641i	0.998908	−	0.0467120i	$-0.0148743\pi$
$61$	77.8088	+	239.471i	0.163318	+	0.502641i	−0.835591	+	0.549353i	$0.814874\pi$
$62$	−498.412	−	161.944i	−1.02094	−	0.331724i
$63$	−97.3885	−	31.6435i	−0.194759	−	0.0632810i
$64$	−19.7771	−	60.8676i	−0.0386271	−	0.118882i
$65$		0			0
$66$	141.855	−	436.584i	0.264562	−	0.814239i
$67$	435.342	−	599.197i	0.793813	−	1.09259i	−0.199809	−	0.979835i	$-0.564032\pi$
$67$	435.342	−	599.197i	0.793813	−	1.09259i	0.993623	−	0.112755i	$-0.0359677\pi$
$68$			182.836i			0.326060i
$69$	34.4778	+	25.0496i	0.0601543	+	0.0437046i
$70$		0			0
$71$	306.683	−	222.818i	0.512628	−	0.372446i	−0.301192	−	0.953564i	$-0.597384\pi$
$71$	306.683	−	222.818i	0.512628	−	0.372446i	0.813819	+	0.581118i	$0.197384\pi$
$72$	−14.8695	−	20.4661i	−0.0243387	−	0.0334993i
$73$	349.928	−	113.698i	0.561040	−	0.182293i	−0.0147490	−	0.999891i	$-0.504695\pi$
$73$	349.928	−	113.698i	0.561040	−	0.182293i	0.575789	+	0.817598i	$0.304695\pi$
$74$	−29.6690			−0.0466075
$75$		0			0
$76$	−468.697			−0.707411
$77$	1447.83	−	470.430i	2.14281	−	0.696240i
$78$	57.2341	+	78.7759i	0.0830831	+	0.114354i
$79$	741.749	−	538.912i	1.05637	−	0.767498i	0.0829567	−	0.996553i	$-0.473564\pi$
$79$	741.749	−	538.912i	1.05637	−	0.767498i	0.973413	+	0.229055i	$0.0735637\pi$
$80$		0			0
$81$	512.611	+	372.433i	0.703170	+	0.510883i
$82$			513.232i			0.691182i
$83$	258.354	−	355.593i	0.341663	−	0.470258i	−0.603263	−	0.797542i	$-0.706133\pi$
$83$	258.354	−	355.593i	0.341663	−	0.470258i	0.944926	+	0.327284i	$0.106133\pi$
$84$	−195.429	+	601.470i	−0.253846	+	0.781259i
$85$		0			0
$86$	−50.3865	−	155.074i	−0.0631781	−	0.194442i
$87$	−1084.38	−	352.335i	−1.33629	−	0.434188i
$88$	357.680	+	116.217i	0.433282	+	0.140782i
$89$	117.993	+	363.145i	0.140531	+	0.432509i	0.996409	−	0.0846679i	$-0.0269829\pi$
$89$	117.993	+	363.145i	0.140531	+	0.432509i	−0.855879	+	0.517177i	$0.826983\pi$
$90$		0			0
$91$	−99.7859	+	307.110i	−0.114950	+	0.353778i
$92$	−20.5224	+	28.2466i	−0.0232566	+	0.0320100i
$93$			1279.34i			1.42646i
$94$	354.253	+	257.380i	0.388706	+	0.282412i
$95$		0			0
$96$	−126.398	+	91.8337i	−0.134380	+	0.0976326i
$97$	−395.195	−	543.939i	−0.413669	−	0.569367i	0.550439	−	0.834875i	$-0.314460\pi$
$97$	−395.195	−	543.939i	−0.413669	−	0.569367i	−0.964109	+	0.265508i	$0.914460\pi$
$98$	−1342.22	+	436.113i	−1.38351	+	0.449531i
$99$	148.657			0.150915
$100$		0			0
$101$	1204.04			1.18620			0.593101	−	0.805128i	$-0.297903\pi$
$101$	1204.04			1.18620			0.593101	+	0.805128i	$0.297903\pi$
$102$	424.494	−	137.926i	0.412070	−	0.133890i
$103$	349.429	+	480.948i	0.334275	+	0.460090i	0.942758	−	0.333477i	$-0.108222\pi$
$103$	349.429	+	480.948i	0.334275	+	0.460090i	−0.608484	+	0.793566i	$0.708222\pi$
$104$	−64.5387	+	46.8901i	−0.0608514	+	0.0442111i
$105$		0			0
$106$	525.486	+	381.788i	0.481506	+	0.349835i
$107$		−	856.869i		−	0.774174i	−0.922043	−	0.387087i	$-0.873481\pi$
$107$		−	856.869i		−	0.774174i	0.922043	−	0.387087i	$-0.126519\pi$
$108$	−346.238	+	476.556i	−0.308489	+	0.424598i
$109$	158.978	−	489.285i	0.139700	−	0.429954i	−0.856591	−	0.515996i	$-0.827422\pi$
$109$	158.978	−	489.285i	0.139700	−	0.429954i	0.996292	+	0.0860421i	$0.0274220\pi$
$110$		0			0
$111$	22.3815	+	68.8831i	0.0191384	+	0.0589018i
$112$	−492.766	−	160.109i	−0.415732	−	0.135080i
$113$	−1297.18	−	421.478i	−1.07989	−	0.350879i	−0.285561	−	0.958361i	$-0.592180\pi$
$113$	−1297.18	−	421.478i	−1.07989	−	0.350879i	−0.794334	+	0.607482i	$0.792180\pi$
$114$	353.572	+	1088.18i	0.290483	+	0.894014i
$115$		0			0
$116$	288.658	−	888.397i	0.231045	−	0.711083i
$117$	−18.5344	+	25.5104i	−0.0146454	+	0.0201576i
$118$		−	1048.87i		−	0.818273i
$119$	1197.49	+	870.031i	0.922472	+	0.670215i
$120$		0			0
$121$	−711.143	+	516.676i	−0.534292	+	0.388186i
$122$	296.002	+	407.412i	0.219662	+	0.302339i
$123$	1191.58	−	387.168i	0.873505	−	0.283819i
$124$	−1048.12			−0.759066
$125$		0			0
$126$	−204.801			−0.144802
$127$	1240.00	−	402.900i	0.866394	−	0.281509i	0.158098	−	0.987424i	$-0.449464\pi$
$127$	1240.00	−	402.900i	0.866394	−	0.281509i	0.708297	+	0.705915i	$0.249464\pi$
$128$	−75.2365	−	103.554i	−0.0519534	−	0.0715077i
$129$	−322.027	+	233.966i	−0.219790	+	0.159687i
$130$		0			0
$131$	−1855.99	−	1348.45i	−1.23785	−	0.899350i	−0.240396	−	0.970675i	$-0.577277\pi$
$131$	−1855.99	−	1348.45i	−1.23785	−	0.899350i	−0.997453	+	0.0713254i	$0.977277\pi$
$132$		−	918.103i		−	0.605383i
$133$	−2230.31	+	3069.76i	−1.45408	+	2.00137i
$134$	457.746	−	1408.80i	0.295099	−	0.908220i
$135$		0			0
$136$	112.999	+	347.775i	0.0712468	+	0.219275i
$137$	−449.072	−	145.912i	−0.280050	−	0.0909937i	0.165624	−	0.986189i	$-0.447036\pi$
$137$	−449.072	−	145.912i	−0.280050	−	0.0909937i	−0.445674	+	0.895195i	$0.647036\pi$
$138$	81.0623	+	26.3387i	0.0500035	+	0.0162471i
$139$	679.904	+	2092.53i	0.414883	+	1.27688i	0.912356	+	0.409398i	$0.134261\pi$
$139$	679.904	+	2092.53i	0.414883	+	1.27688i	−0.497473	+	0.867479i	$0.665739\pi$
$140$		0			0
$141$	330.325	−	1016.64i	0.197293	−	0.607207i
$142$	445.636	−	613.366i	0.263359	−	0.362483i
$143$		−	468.782i		−	0.274136i
$144$	−40.9322	−	29.7390i	−0.0236876	−	0.0172101i
$145$		0			0
$146$	595.332	−	432.534i	0.337466	−	0.245184i
$147$	2025.06	+	2787.26i	1.13622	+	1.56387i
$148$	−56.4339	+	18.3365i	−0.0313435	+	0.0101841i
$149$	−1728.16			−0.950177			−0.475088	−	0.879938i	$-0.657584\pi$
$149$	−1728.16			−0.950177			−0.475088	+	0.879938i	$0.657584\pi$
$150$		0			0
$151$	1389.53			0.748861			0.374431	−	0.927255i	$-0.377838\pi$
$151$	1389.53			0.748861			0.374431	+	0.927255i	$0.377838\pi$
$152$	−891.514	+	289.671i	−0.475733	+	0.154575i
$153$	84.9586	+	116.936i	0.0448921	+	0.0617887i
$154$	2463.20	−	1789.62i	1.28890	−	0.936440i
$155$		0			0
$156$	157.552	+	114.468i	0.0808605	+	0.0587486i
$157$		−	2922.98i		−	1.48585i	−0.669372	−	0.742927i	$-0.733437\pi$
$157$		−	2922.98i		−	1.48585i	0.669372	−	0.742927i	$-0.266563\pi$
$158$	1077.82	−	1483.50i	0.542703	−	0.746966i
$159$	489.992	−	1508.04i	0.244395	−	0.752172i
$160$		0			0
$161$	87.3466	+	268.825i	0.0427570	+	0.131592i
$162$	1205.22	+	391.600i	0.584512	+	0.189920i
$163$	3407.69	+	1107.23i	1.63749	+	0.532053i	0.975976	−	0.217878i	$-0.0699134\pi$
$163$	3407.69	+	1107.23i	1.63749	+	0.532053i	0.661516	+	0.749931i	$0.269913\pi$
$164$	317.195	+	976.225i	0.151029	+	0.464819i
$165$		0			0
$166$	271.649	−	836.050i	0.127012	−	0.390904i
$167$	−1215.06	+	1672.38i	−0.563017	+	0.774926i	−0.991706	−	0.128526i	$-0.958976\pi$
$167$	−1215.06	+	1672.38i	−0.563017	+	0.774926i	0.428689	+	0.903452i	$0.358976\pi$
$168$			1264.85i			0.580863i
$169$	−1696.96	−	1232.92i	−0.772401	−	0.561182i
$170$		0			0
$171$	−299.762	+	217.790i	−0.134055	+	0.0973966i
$172$	−191.682	−	263.827i	−0.0849743	−	0.116957i
$173$	1302.66	−	423.260i	0.572482	−	0.186011i	−0.00844803	−	0.999964i	$-0.502689\pi$
$173$	1302.66	−	423.260i	0.572482	−	0.186011i	0.580930	+	0.813954i	$0.302689\pi$
$174$	−2280.36			−0.993528
$175$		0			0
$176$	752.174			0.322143
$177$	−2435.18	+	791.238i	−1.03412	+	0.336006i
$178$	448.872	+	617.819i	0.189013	+	0.260155i
$179$	−1459.45	+	1060.36i	−0.609412	+	0.442764i	−0.849207	−	0.528060i	$-0.822920\pi$
$179$	−1459.45	+	1060.36i	−0.609412	+	0.442764i	0.239795	+	0.970823i	$0.422920\pi$
$180$		0			0
$181$	2641.79	+	1919.37i	1.08488	+	0.788210i	0.978527	−	0.206119i	$-0.0660835\pi$
$181$	2641.79	+	1919.37i	1.08488	+	0.788210i	0.106350	+	0.994329i	$0.466083\pi$
$182$			645.828i			0.263033i
$183$	722.600	−	994.574i	0.291891	−	0.401754i
$184$	−21.5785	+	66.4118i	−0.00864559	+	0.0266084i
$185$		0			0
$186$	790.674	+	2433.45i	0.311694	+	0.959295i
$187$	−2043.65	−	664.021i	−0.799178	−	0.259669i
$188$	832.898	+	270.625i	0.323113	+	0.104986i
$189$	1473.64	+	4535.41i	0.567153	+	1.74552i
$190$		0			0
$191$	−42.3055	+	130.203i	−0.0160268	+	0.0493254i	−0.958750	−	0.284250i	$-0.908255\pi$
$191$	−42.3055	+	130.203i	−0.0160268	+	0.0493254i	0.942723	+	0.333576i	$0.108255\pi$
$192$	−183.667	+	252.796i	−0.0690367	+	0.0950209i
$193$		−	3705.34i		−	1.38195i	−0.722879	−	0.690975i	$-0.757182\pi$
$193$		−	3705.34i		−	1.38195i	0.722879	−	0.690975i	$-0.242818\pi$
$194$	−1087.88	−	790.389i	−0.402603	−	0.292508i
$195$		0			0
$196$	−2283.52	+	1659.07i	−0.832185	+	0.604618i
$197$	942.405	+	1297.11i	0.340830	+	0.469113i	0.944684	−	0.327983i	$-0.106369\pi$
$197$	942.405	+	1297.11i	0.340830	+	0.469113i	−0.603853	+	0.797095i	$0.706369\pi$
$198$	282.763	−	91.8751i	0.101490	−	0.0329762i
$199$	−761.314			−0.271196			−0.135598	−	0.990764i	$-0.543296\pi$
$199$	−761.314			−0.271196			−0.135598	+	0.990764i	$0.543296\pi$
$200$		0			0
$201$	−3616.14			−1.26897
$202$	2290.22	−	744.137i	0.797719	−	0.259195i
$203$	−4445.02	−	6118.04i	−1.53684	−	2.11528i
$204$	722.192	−	524.703i	0.247860	−	0.180081i
$205$		0			0
$206$	961.896	+	698.859i	0.325332	+	0.236368i
$207$			27.6017i			0.00926789i
$208$	−93.7802	+	129.077i	−0.0312620	+	0.0430284i
$209$	1702.21	−	5238.86i	0.563369	−	1.73387i
$210$		0			0
$211$	−1020.62	−	3141.15i	−0.332998	−	1.02486i	−0.967700	−	0.252105i	$-0.918877\pi$
$211$	−1020.62	−	3141.15i	−0.332998	−	1.02486i	0.634702	−	0.772757i	$-0.281123\pi$
$212$	1235.49	+	401.435i	0.400254	+	0.130050i
$213$	−1760.24	−	571.936i	−0.566242	−	0.183983i
$214$	−529.574	−	1629.86i	−0.169163	−	0.520631i
$215$		0			0
$216$	−364.056	+	1120.45i	−0.114680	+	0.352949i
$217$	−4987.52	+	6864.74i	−1.56025	+	2.14751i
$218$		−	1028.93i		−	0.319669i
$219$	−1453.32	−	1055.90i	−0.448432	−	0.325805i
$220$		0			0
$221$	368.750	−	267.912i	0.112239	−	0.0815463i
$222$	85.1442	+	117.191i	0.0257410	+	0.0354295i
$223$	−968.836	+	314.794i	−0.290933	+	0.0945298i	−0.450847	−	0.892601i	$-0.648878\pi$
$223$	−968.836	+	314.794i	−0.290933	+	0.0945298i	0.159914	+	0.987131i	$0.448878\pi$
$224$	−1036.25			−0.309095
$225$		0			0
$226$	−2727.86			−0.802897
$227$	5345.86	−	1736.97i	1.56307	−	0.507872i	0.605445	−	0.795887i	$-0.292995\pi$
$227$	5345.86	−	1736.97i	1.56307	−	0.507872i	0.957626	+	0.288015i	$0.0929953\pi$
$228$	1345.07	+	1851.33i	0.390698	+	0.537750i
$229$	42.9528	−	31.2070i	0.0123948	−	0.00900533i	−0.581571	−	0.813496i	$-0.697562\pi$
$229$	42.9528	−	31.2070i	0.0123948	−	0.00900533i	0.593965	+	0.804491i	$0.297562\pi$
$230$		0			0
$231$	−6013.17	−	4368.82i	−1.71272	−	1.24436i
$232$		−	1868.23i		−	0.528687i
$233$	−1146.55	+	1578.10i	−0.322374	+	0.443710i	−0.939190	−	0.343397i	$-0.888422\pi$
$233$	−1146.55	+	1578.10i	−0.322374	+	0.443710i	0.616816	+	0.787107i	$0.288422\pi$
$234$	−19.4882	+	59.9786i	−0.00544438	+	0.0167561i
$235$		0			0
$236$	−648.237	−	1995.07i	−0.178799	−	0.550288i
$237$	−4257.34	−	1383.29i	−1.16685	−	0.379133i
$238$	2815.48	+	914.804i	0.766808	+	0.249151i
$239$	480.283	+	1478.16i	0.129987	+	0.400059i	0.994777	−	0.102075i	$-0.0325482\pi$
$239$	480.283	+	1478.16i	0.129987	+	0.400059i	−0.864790	+	0.502135i	$0.832548\pi$
$240$		0			0
$241$	−1073.12	+	3302.73i	−0.286829	+	0.882770i	0.699015	+	0.715107i	$0.253622\pi$
$241$	−1073.12	+	3302.73i	−0.286829	+	0.882770i	−0.985844	+	0.167663i	$0.946378\pi$
$242$	−1033.35	+	1422.29i	−0.274489	+	0.377802i
$243$			882.530i			0.232981i
$244$	814.824	+	592.004i	0.213786	+	0.155325i
$245$		0			0
$246$	2027.24	−	1472.87i	0.525414	−	0.381736i
$247$	686.789	+	945.284i	0.176920	+	0.243510i
$248$	−1993.65	+	647.775i	−0.510471	+	0.165862i
$249$	−2146.00			−0.546173
$250$		0			0
$251$	−1154.53			−0.290333			−0.145166	−	0.989407i	$-0.546372\pi$
$251$	−1154.53			−0.290333			−0.145166	+	0.989407i	$0.546372\pi$
$252$	−389.554	+	126.574i	−0.0973794	+	0.0316405i
$253$	−241.194	−	331.975i	−0.0599357	−	0.0824944i
$254$	2109.61	−	1532.72i	0.521137	−	0.378628i
$255$		0			0
$256$	−207.108	−	150.473i	−0.0505636	−	0.0367366i
$257$			3686.90i			0.894874i	0.894315	+	0.447437i	$0.147663\pi$
$257$			3686.90i			0.894874i	−0.894315	+	0.447437i	$0.852337\pi$
$258$	−467.933	+	644.054i	−0.112916	+	0.155415i
$259$	−148.447	+	456.871i	−0.0356140	+	0.109609i
$260$		0			0
$261$	−228.197	−	702.319i	−0.0541190	−	0.166561i
$262$	−4363.68	−	1417.85i	−1.02897	−	0.334331i
$263$	−7044.09	−	2288.76i	−1.65155	−	0.536620i	−0.672473	−	0.740122i	$-0.734768\pi$
$263$	−7044.09	−	2288.76i	−1.65155	−	0.536620i	−0.979075	+	0.203502i	$0.934768\pi$
$264$	−567.419	−	1746.34i	−0.132281	−	0.407119i
$265$		0			0
$266$	−2345.09	+	7217.43i	−0.540550	+	1.66364i
$267$	1095.79	−	1508.22i	0.251165	−	0.345699i
$268$		−	2962.59i		−	0.675258i
$269$	−4532.74	−	3293.23i	−1.02738	−	0.746438i	−0.0596003	−	0.998222i	$-0.518983\pi$
$269$	−4532.74	−	3293.23i	−1.02738	−	0.746438i	−0.967783	+	0.251784i	$0.918983\pi$
$270$		0			0
$271$	4064.95	−	2953.36i	0.911174	−	0.662006i	−0.0301378	−	0.999546i	$-0.509595\pi$
$271$	4064.95	−	2953.36i	0.911174	−	0.662006i	0.941311	+	0.337539i	$0.109595\pi$
$272$	429.873	+	591.669i	0.0958268	+	0.131894i
$273$	1499.43	−	487.195i	0.332416	−	0.108009i
$274$	−944.365			−0.208216
$275$		0			0
$276$	170.468			0.0371774
$277$	−5011.05	+	1628.19i	−1.08695	+	0.353171i	−0.797067	−	0.603891i	$-0.793616\pi$
$277$	−5011.05	+	1628.19i	−1.08695	+	0.353171i	−0.289883	+	0.957062i	$0.593616\pi$
$278$	2586.51	+	3560.02i	0.558016	+	0.768043i
$279$	−670.343	+	487.033i	−0.143844	+	0.104509i
$280$		0			0
$281$	4852.80	+	3525.77i	1.03023	+	0.748504i	0.968354	−	0.249580i	$-0.0802924\pi$
$281$	4852.80	+	3525.77i	1.03023	+	0.748504i	0.0618736	+	0.998084i	$0.480292\pi$
$282$		−	2137.91i		−	0.451456i
$283$	743.694	−	1023.61i	0.156212	−	0.215008i	−0.723736	−	0.690076i	$-0.757577\pi$
$283$	743.694	−	1023.61i	0.156212	−	0.215008i	0.879949	+	0.475069i	$0.157577\pi$
$284$	468.570	−	1442.11i	0.0979032	−	0.301315i
$285$		0			0
$286$	−289.723	−	891.676i	−0.0599010	−	0.184356i
$287$	7903.22	+	2567.91i	1.62548	+	0.528150i
$288$	−96.2373	−	31.2694i	−0.0196904	−	0.00639780i
$289$	872.568	+	2685.49i	0.177604	+	0.546609i
$290$		0			0
$291$	−1014.40	+	3121.99i	−0.204347	+	0.628916i
$292$	865.069	−	1190.66i	0.173371	−	0.238625i
$293$			5729.80i			1.14245i	0.820793	+	0.571226i	$0.193532\pi$
$293$			5729.80i			1.14245i	−0.820793	+	0.571226i	$0.806468\pi$
$294$	5574.52	+	4050.12i	1.10582	+	0.803429i
$295$		0			0
$296$	−96.0110	+	69.7561i	−0.0188531	+	0.0136976i
$297$	−4069.24	−	5600.82i	−0.795020	−	1.09425i
$298$	−3287.15	+	1068.06i	−0.638992	+	0.207621i
$299$	87.0406			0.0168351
$300$		0			0
$301$	−2640.07			−0.505552
$302$	2643.04	−	858.774i	0.503608	−	0.163632i
$303$	−3455.35	−	4755.89i	−0.655132	−	0.901711i
$304$	−1516.74	+	1101.97i	−0.286154	+	0.207903i
$305$		0			0
$306$	233.871	+	169.917i	0.0436912	+	0.0317435i
$307$		−	5350.98i		−	0.994776i	−0.867528	−	0.497388i	$-0.834292\pi$
$307$		−	5350.98i		−	0.994776i	0.867528	−	0.497388i	$-0.165708\pi$
$308$	3579.24	−	4926.41i	0.662163	−	0.911390i
$309$	896.925	−	2760.45i	0.165127	−	0.508209i
$310$		0			0
$311$	−618.015	−	1902.05i	−0.112683	−	0.346803i	0.878774	−	0.477239i	$-0.158362\pi$
$311$	−618.015	−	1902.05i	−0.112683	−	0.346803i	−0.991457	+	0.130436i	$0.958362\pi$
$312$	370.427	+	120.359i	0.0672156	+	0.0218397i
$313$	7876.42	+	2559.20i	1.42237	+	0.462156i	0.916354	−	0.400369i	$-0.131118\pi$
$313$	7876.42	+	2559.20i	1.42237	+	0.462156i	0.506015	+	0.862525i	$0.331118\pi$
$314$	−1806.50	−	5559.84i	−0.324671	−	0.999235i
$315$		0			0
$316$	1133.29	−	3487.91i	0.201749	−	0.620919i
$317$	2806.32	−	3862.57i	0.497220	−	0.684365i	−0.484479	−	0.874803i	$-0.660991\pi$
$317$	2806.32	−	3862.57i	0.497220	−	0.684365i	0.981699	+	0.190438i	$0.0609908\pi$
$318$		−	3171.29i		−	0.559237i
$319$	8881.71	+	6452.94i	1.55887	+	1.13259i
$320$		0			0
$321$	−3384.58	+	2459.04i	−0.588502	+	0.427571i
$322$	332.286	+	457.353i	0.0575080	+	0.0791530i
$323$	5093.78	−	1655.07i	0.877478	−	0.285110i
$324$	2534.49			0.434583
$325$		0			0
$326$	7166.12			1.21747
$327$	−2388.88	+	776.195i	−0.403992	+	0.131265i
$328$	1206.68	+	1660.85i	0.203133	+	0.279589i
$329$	5735.85	−	4167.34i	0.961178	−	0.698336i
$330$		0			0
$331$	5205.50	+	3782.02i	0.864411	+	0.628031i	0.929081	−	0.369875i	$-0.120600\pi$
$331$	5205.50	+	3782.02i	0.864411	+	0.628031i	−0.0646705	+	0.997907i	$0.520600\pi$
$332$		−	1758.15i		−	0.290636i
$333$	−27.5727	+	37.9506i	−0.00453746	+	0.00624528i
$334$	−1277.59	+	3932.00i	−0.209300	+	0.644161i
$335$		0			0
$336$	781.718	+	2405.88i	0.126923	+	0.390629i
$337$	5637.23	+	1831.65i	0.911215	+	0.296072i	0.726858	−	0.686788i	$-0.240980\pi$
$337$	5637.23	+	1831.65i	0.911215	+	0.296072i	0.184357	+	0.982859i	$0.440980\pi$
$338$	−3989.80	−	1296.37i	−0.642061	−	0.208618i
$339$	2057.82	+	6333.33i	0.329692	+	1.01469i
$340$		0			0
$341$	3806.56	−	11715.4i	0.604507	−	1.86048i
$342$	−435.580	+	599.525i	−0.0688698	+	0.0947912i
$343$			11743.5i			1.84865i
$344$	−527.654	−	383.363i	−0.0827012	−	0.0600859i
$345$		0			0
$346$	2216.22	−	1610.18i	0.344348	−	0.250184i
$347$	783.055	+	1077.78i	0.121143	+	0.166739i	0.865281	−	0.501286i	$-0.167140\pi$
$347$	783.055	+	1077.78i	0.121143	+	0.166739i	−0.744138	+	0.668025i	$0.767140\pi$
$348$	−4337.51	+	1409.34i	−0.668146	+	0.217094i
$349$	−10382.6			−1.59245			−0.796226	−	0.605000i	$-0.793173\pi$
$349$	−10382.6			−1.59245			−0.796226	+	0.605000i	$0.793173\pi$
$350$		0			0
$351$	1468.48			0.223310
$352$	1430.72	−	464.869i	0.216641	−	0.0703909i
$353$	3612.36	+	4971.99i	0.544665	+	0.749667i	0.989276	−	0.146057i	$-0.0466582\pi$
$353$	3612.36	+	4971.99i	0.544665	+	0.749667i	−0.444611	+	0.895724i	$0.646658\pi$
$354$	−4142.98	+	3010.05i	−0.622024	+	0.451927i
$355$		0			0
$356$	1235.64	+	897.744i	0.183957	+	0.133653i
$357$		−	7226.85i		−	1.07139i
$358$	−2120.71	+	2918.91i	−0.313081	+	0.430919i
$359$	−876.677	+	2698.13i	−0.128884	+	0.396663i	−0.994589	−	0.103891i	$-0.966871\pi$
$359$	−876.677	+	2698.13i	−0.128884	+	0.396663i	0.865705	+	0.500555i	$0.166871\pi$
$360$		0			0
$361$	2123.19	+	6534.52i	0.309549	+	0.952693i
$362$	6211.22	+	2018.15i	0.901809	+	0.293015i
$363$	4081.68	+	1326.22i	0.590173	+	0.191759i
$364$	399.144	+	1228.44i	0.0574748	+	0.176889i
$365$		0			0
$366$	759.787	−	2338.38i	0.108510	−	0.333960i
$367$	−1384.81	+	1906.03i	−0.196966	+	0.271100i	−0.896063	−	0.443926i	$-0.853585\pi$
$367$	−1384.81	+	1906.03i	−0.196966	+	0.271100i	0.699098	+	0.715026i	$0.253585\pi$
$368$			139.659i			0.0197832i
$369$	656.490	+	476.968i	0.0926166	+	0.0672899i
$370$		0			0
$371$	8508.35	−	6181.68i	1.19065	−	0.865058i
$372$	3007.90	+	4140.02i	0.419227	+	0.577017i
$373$	2408.61	−	782.604i	0.334351	−	0.108637i	−0.137030	−	0.990567i	$-0.543756\pi$
$373$	2408.61	−	782.604i	0.334351	−	0.108637i	0.471381	+	0.881930i	$0.343756\pi$
$374$	−4297.64			−0.594186
$375$		0			0
$376$	1751.52			0.240234
$377$	−2214.72	+	719.608i	−0.302557	+	0.0983068i
$378$	5606.08	+	7716.10i	0.762819	+	1.04993i
$379$	−2370.58	+	1722.33i	−0.321290	+	0.233431i	−0.736726	−	0.676192i	$-0.763629\pi$
$379$	−2370.58	+	1722.33i	−0.321290	+	0.233431i	0.415436	+	0.909622i	$0.363629\pi$
$380$		0			0
$381$	−5149.98	−	3741.68i	−0.692497	−	0.503129i
$382$			273.807i			0.0366733i
$383$	1751.18	−	2410.29i	0.233632	−	0.321567i	−0.676063	−	0.736844i	$-0.736315\pi$
$383$	1751.18	−	2410.29i	0.233632	−	0.321567i	0.909695	+	0.415277i	$0.136315\pi$
$384$	−193.119	+	594.360i	−0.0256643	+	0.0789865i
$385$		0			0
$386$	−2290.03	−	7047.98i	−0.301967	−	0.929359i
$387$	−245.186	−	79.6657i	−0.0322054	−	0.0104642i
$388$	−2557.75	−	831.064i	−0.334666	−	0.108739i
$389$	−750.758	−	2310.60i	−0.0978534	−	0.301162i	0.890133	−	0.455700i	$-0.150611\pi$
$389$	−750.758	−	2310.60i	−0.0978534	−	0.301162i	−0.987987	+	0.154538i	$0.950611\pi$
$390$		0			0
$391$	123.291	−	379.452i	0.0159466	−	0.0490786i
$392$	−3318.14	+	4567.03i	−0.427529	+	0.588444i
$393$			11200.8i			1.43768i
$394$	2594.22	+	1884.81i	0.331713	+	0.241003i
$395$		0			0
$396$	481.064	−	349.514i	0.0610464	−	0.0443528i
$397$	−164.598	−	226.550i	−0.0208085	−	0.0286404i	0.798486	−	0.602013i	$-0.205635\pi$
$397$	−164.598	−	226.550i	−0.0208085	−	0.0286404i	−0.819294	+	0.573373i	$0.805635\pi$
$398$	−1448.10	+	470.518i	−0.182379	+	0.0592586i
$399$	18525.9			2.32445
$400$		0			0
$401$	6908.71			0.860361			0.430180	−	0.902743i	$-0.358450\pi$
$401$	6908.71			0.860361			0.430180	+	0.902743i	$0.358450\pi$
$402$	−6878.30	+	2234.90i	−0.853380	+	0.277280i
$403$	1535.83	+	2113.89i	0.189839	+	0.261291i
$404$	3896.35	−	2830.87i	0.479829	−	0.348616i
$405$		0			0
$406$	−12236.1	−	8890.04i	−1.49573	−	1.08671i
$407$		−	697.383i		−	0.0849337i
$408$	1049.41	−	1444.38i	0.127337	−	0.175264i
$409$	−3250.62	+	10004.4i	−0.392990	+	1.20950i	0.537526	+	0.843247i	$0.319359\pi$
$409$	−3250.62	+	10004.4i	−0.392990	+	1.20950i	−0.930516	+	0.366251i	$0.880641\pi$
$410$		0			0
$411$	712.402	+	2192.55i	0.0854993	+	0.263140i
$412$	2261.55	+	734.823i	0.270434	+	0.0878693i
$413$	−16151.5	−	5247.93i	−1.92436	−	0.625263i
$414$	17.0588	+	52.5016i	0.00202511	+	0.00623264i
$415$		0			0
$416$	−98.6064	+	303.479i	−0.0116216	+	0.0357675i
$417$	6314.18	−	8690.73i	0.741503	−	1.02059i
$418$		−	11016.9i		−	1.28913i
$419$	−2148.93	−	1561.29i	−0.250554	−	0.182038i	0.455418	−	0.890278i	$-0.349490\pi$
$419$	−2148.93	−	1561.29i	−0.250554	−	0.182038i	−0.705972	+	0.708239i	$0.749490\pi$
$420$		0			0
$421$	−8668.65	+	6298.14i	−1.00353	+	0.729104i	−0.962841	−	0.270068i	$-0.912954\pi$
$421$	−8668.65	+	6298.14i	−1.00353	+	0.729104i	−0.0406843	+	0.999172i	$0.512954\pi$
$422$	−3882.68	−	5344.05i	−0.447881	−	0.616455i
$423$	658.444	−	213.942i	0.0756848	−	0.0245915i
$424$	2598.14			0.297587
$425$		0			0
$426$	−3701.65			−0.420999
$427$	7754.73	−	2519.66i	0.878871	−	0.285562i
$428$	−2014.62	−	2772.89i	−0.227524	−	0.313160i
$429$	−1851.66	+	1345.31i	−0.208390	+	0.151404i
$430$		0			0
$431$	10253.3	+	7449.46i	1.14590	+	0.832547i	0.987931	−	0.154897i	$-0.0495045\pi$
$431$	10253.3	+	7449.46i	1.14590	+	0.832547i	0.157972	+	0.987444i	$0.449504\pi$
$432$			2356.22i			0.262416i
$433$	−2262.19	+	3113.64i	−0.251072	+	0.345570i	−0.915886	−	0.401438i	$-0.868511\pi$
$433$	−2262.19	+	3113.64i	−0.251072	+	0.345570i	0.664815	+	0.747008i	$0.268511\pi$
$434$	−5244.19	+	16140.0i	−0.580022	+	1.78512i
$435$		0			0
$436$	−635.913	−	1957.14i	−0.0698502	−	0.214977i
$437$	972.720	+	316.056i	0.106479	+	0.0345972i
$438$	−3416.97	−	1110.24i	−0.372761	−	0.121117i
$439$	−2291.82	−	7053.49i	−0.249163	−	0.766844i	−0.994924	−	0.100631i	$-0.967914\pi$
$439$	−2291.82	−	7053.49i	−0.249163	−	0.766844i	0.745761	−	0.666213i	$-0.232086\pi$
$440$		0			0
$441$	−689.535	+	2122.17i	−0.0744557	+	0.229151i
$442$	535.825	−	737.500i	0.0576620	−	0.0793649i
$443$		−	14961.3i		−	1.60459i	−0.596928	−	0.802295i	$-0.703612\pi$
$443$		−	14961.3i		−	1.60459i	0.596928	−	0.802295i	$-0.296388\pi$
$444$	234.382	+	170.288i	0.0250524	+	0.0182017i
$445$		0			0
$446$	−1648.28	+	1197.55i	−0.174996	+	0.127142i
$447$	4959.47	+	6826.13i	0.524777	+	0.722293i
$448$	−1971.06	+	640.437i	−0.207866	+	0.0675398i
$449$	14241.7			1.49689			0.748447	−	0.663195i	$-0.230800\pi$
$449$	14241.7			1.49689			0.748447	+	0.663195i	$0.230800\pi$
$450$		0			0
$451$	−12063.7			−1.25955
$452$	−5188.70	+	1685.91i	−0.539947	+	0.175439i
$453$	−3987.66	−	5488.55i	−0.413591	−	0.569259i
$454$	9094.92	−	6607.84i	0.940188	−	0.683087i
$455$		0			0
$456$	3702.65	+	2690.13i	0.380247	+	0.276266i
$457$			7924.89i			0.811183i	0.914054	+	0.405592i	$0.132935\pi$
$457$			7924.89i			0.811183i	−0.914054	+	0.405592i	$0.867065\pi$
$458$	62.4141	−	85.9056i	0.00636773	−	0.00876442i
$459$	2080.08	−	6401.83i	0.211525	−	0.651006i
$460$		0			0
$461$	2758.84	+	8490.84i	0.278724	+	0.857826i	0.988210	+	0.153106i	$0.0489274\pi$
$461$	2758.84	+	8490.84i	0.278724	+	0.857826i	−0.709485	+	0.704720i	$0.751073\pi$
$462$	−14137.8	−	4593.65i	−1.42370	−	0.462589i
$463$	5669.44	+	1842.11i	0.569074	+	0.184903i	0.579400	−	0.815043i	$-0.303287\pi$
$463$	5669.44	+	1842.11i	0.569074	+	0.184903i	−0.0103259	+	0.999947i	$0.503287\pi$
$464$	−1154.63	−	3553.59i	−0.115522	−	0.355541i
$465$		0			0
$466$	−1205.56	+	3710.33i	−0.119842	+	0.368836i
$467$	1949.68	−	2683.51i	0.193192	−	0.265906i	−0.701422	−	0.712747i	$-0.747451\pi$
$467$	1949.68	−	2683.51i	0.193192	−	0.265906i	0.894613	+	0.446841i	$0.147451\pi$
$468$			126.130i			0.0124581i
$469$	−19403.7	−	14097.6i	−1.91040	−	1.38799i
$470$		0			0
$471$	−11545.6	+	8388.37i	−1.12950	+	0.820628i
$472$	−2466.04	−	3394.21i	−0.240485	−	0.330999i
$473$	3645.07	−	1184.36i	0.354335	−	0.115131i
$474$	−8952.87			−0.867551
$475$		0			0
$476$	5920.74			0.570119
$477$	976.713	−	317.353i	0.0937539	−	0.0304625i
$478$	1827.11	+	2514.80i	0.174832	+	0.240636i
$479$	−6937.51	+	5040.40i	−0.661760	+	0.480797i	−0.867257	−	0.497861i	$-0.834119\pi$
$479$	−6937.51	+	5040.40i	−0.661760	+	0.480797i	0.205497	+	0.978658i	$0.434119\pi$
$480$		0			0
$481$	119.675	+	86.9490i	0.0113445	+	0.00824228i
$482$			6945.39i			0.656336i
$483$	811.177	−	1116.49i	0.0764178	−	0.105180i
$484$	−1086.53	+	3344.00i	−0.102041	+	0.314049i
$485$		0			0
$486$	545.433	+	1678.67i	0.0509081	+	0.156679i
$487$	−11776.6	−	3826.46i	−1.09579	−	0.356044i	−0.295310	−	0.955401i	$-0.595423\pi$
$487$	−11776.6	−	3826.46i	−1.09579	−	0.356044i	−0.800482	+	0.599357i	$0.795423\pi$
$488$	1915.77	+	622.470i	0.177710	+	0.0577416i
$489$	−5405.92	−	16637.7i	−0.499927	−	1.53862i
$490$		0			0
$491$	1324.69	−	4076.96i	0.121756	−	0.374726i	−0.871540	−	0.490324i	$-0.836878\pi$
$491$	1324.69	−	4076.96i	0.121756	−	0.374726i	0.993296	+	0.115598i	$0.0368784\pi$
$492$	2945.75	−	4054.47i	0.269928	−	0.371524i
$493$			10674.4i			0.975151i
$494$	1890.57	+	1373.58i	0.172188	+	0.125102i
$495$		0			0
$496$	−3391.80	+	2464.28i	−0.307049	+	0.223084i
$497$	−7215.48	−	9931.25i	−0.651224	−	0.896333i
$498$	−4081.93	+	1326.30i	−0.367300	+	0.119343i
$499$	11697.7			1.04942			0.524709	−	0.851281i	$-0.324174\pi$
$499$	11697.7			1.04942			0.524709	+	0.851281i	$0.324174\pi$
$500$		0			0
$501$	10092.8			0.900024
$502$	−2196.06	+	713.542i	−0.195248	+	0.0634401i
$503$	2134.32	+	2937.64i	0.189194	+	0.260404i	0.893068	−	0.449921i	$-0.148548\pi$
$503$	2134.32	+	2937.64i	0.189194	+	0.260404i	−0.703874	+	0.710325i	$0.748548\pi$
$504$	−662.749	+	481.515i	−0.0585738	+	0.0425564i
$505$		0			0
$506$	−663.950	−	482.388i	−0.0583323	−	0.0423809i
$507$			10241.1i			0.897091i
$508$	3065.44	−	4219.22i	0.267730	−	0.368499i
$509$	6036.88	−	18579.6i	0.525698	−	1.61793i	−0.237235	−	0.971452i	$-0.576241\pi$
$509$	6036.88	−	18579.6i	0.525698	−	1.61793i	0.762932	−	0.646478i	$-0.223759\pi$
$510$		0			0
$511$	−3681.87	−	11331.6i	−0.318740	−	0.980982i
$512$	−486.941	−	158.217i	−0.0420312	−	0.0136568i
$513$	16411.0	+	5332.25i	1.41240	+	0.458917i
$514$	2278.63	+	7012.91i	0.195537	+	0.601802i
$515$		0			0
$516$	−492.014	+	1514.26i	−0.0419762	+	0.129189i
$517$	−6049.82	+	8326.86i	−0.514644	+	0.708346i
$518$			960.766i			0.0814935i
$519$	−5410.22	−	3930.76i	−0.457577	−	0.332449i
$520$		0			0
$521$	7395.10	−	5372.86i	0.621853	−	0.451802i	−0.231715	−	0.972784i	$-0.574434\pi$
$521$	7395.10	−	5372.86i	0.621853	−	0.451802i	0.853568	+	0.520981i	$0.174434\pi$
$522$	−868.114	−	1194.86i	−0.0727899	−	0.100187i
$523$	6361.87	−	2067.10i	0.531903	−	0.172826i	−0.0307374	−	0.999527i	$-0.509786\pi$
$523$	6361.87	−	2067.10i	0.531903	−	0.172826i	0.562640	+	0.826702i	$0.309786\pi$
$524$	−9176.49			−0.765033
$525$		0			0
$526$	−14813.2			−1.22792
$527$	11390.9	−	3701.14i	0.941551	−	0.305929i
$528$	−2158.59	−	2971.04i	−0.177918	−	0.244883i
$529$	−9781.67	+	7106.80i	−0.803951	+	0.584105i
$530$		0			0
$531$	−1341.64	−	974.759i	−0.109646	−	0.0796628i
$532$			15177.7i			1.23691i
$533$	1504.09	−	2070.21i	0.122232	−	0.168238i
$534$	1152.18	−	3546.04i	0.0933700	−	0.287363i
$535$		0			0
$536$	−1830.98	−	5635.19i	−0.147549	−	0.454110i
$537$	8376.69	+	2721.75i	0.673149	+	0.218719i
$538$	−10657.1	−	3462.71i	−0.854017	−	0.277487i
$539$	−10251.0	−	31549.4i	−0.819188	−	2.52120i
$540$		0			0
$541$	−3501.45	+	10776.4i	−0.278261	+	0.856399i	0.710077	+	0.704124i	$0.248660\pi$
$541$	−3501.45	+	10776.4i	−0.278261	+	0.856399i	−0.988338	+	0.152275i	$0.951340\pi$
$542$	5906.72	−	8129.90i	0.468109	−	0.644297i
$543$		−	15943.1i		−	1.26001i
$544$	1183.34	+	859.746i	0.0932633	+	0.0677598i
$545$		0			0
$546$	2550.98	−	1853.40i	0.199949	−	0.145271i
$547$	−6922.84	−	9528.47i	−0.541132	−	0.744804i	0.447644	−	0.894212i	$-0.352263\pi$
$547$	−6922.84	−	9528.47i	−0.541132	−	0.744804i	−0.988776	+	0.149408i	$0.952263\pi$
$548$	−1796.29	+	583.649i	−0.140025	+	0.0454968i
$549$	796.221			0.0618978
$550$		0			0
$551$	−27363.6			−2.11566
$552$	324.249	−	105.355i	0.0250017	−	0.00812356i
$553$	−17451.5	−	24019.9i	−1.34197	−	1.84707i
$554$	−8525.31	+	6194.00i	−0.653801	+	0.475014i
$555$		0			0
$556$	7120.05	+	5173.02i	0.543089	+	0.394577i
$557$			19555.7i			1.48762i	0.668393	+	0.743808i	$0.266982\pi$
$557$			19555.7i			1.48762i	−0.668393	+	0.743808i	$0.733018\pi$
$558$	−974.065	+	1340.69i	−0.0738987	+	0.101713i
$559$	−251.221	+	773.180i	−0.0190081	+	0.0585010i
$560$		0			0
$561$	3242.02	+	9977.90i	0.243989	+	0.750922i
$562$	11409.6	+	3707.21i	0.856381	+	0.278255i
$563$	−6919.70	−	2248.35i	−0.517994	−	0.168307i	0.0383406	−	0.999265i	$-0.487793\pi$
$563$	−6919.70	−	2248.35i	−0.517994	−	0.168307i	−0.556335	+	0.830958i	$0.687793\pi$
$564$	−1321.30	−	4066.54i	−0.0986467	−	0.303603i
$565$		0			0
$566$	781.966	−	2406.64i	0.0580715	−	0.178726i
$567$	12060.4	−	16599.8i	0.893282	−	1.22950i
$568$		−	3032.65i		−	0.224027i
$569$	15812.7	+	11488.6i	1.16503	+	0.846443i	0.990405	−	0.138192i	$-0.0441291\pi$
$569$	15812.7	+	11488.6i	1.16503	+	0.846443i	0.174624	+	0.984635i	$0.444129\pi$
$570$		0			0
$571$	−1528.71	+	1110.67i	−0.112039	+	0.0814012i	−0.642394	−	0.766375i	$-0.722059\pi$
$571$	−1528.71	+	1110.67i	−0.112039	+	0.0814012i	0.530355	+	0.847776i	$0.322059\pi$
$572$	−1102.17	−	1517.01i	−0.0805667	−	0.110891i
$573$	635.703	−	206.552i	0.0463471	−	0.0150591i
$574$	16619.9			1.20854
$575$		0			0
$576$	−202.380			−0.0146397
$577$	−18013.4	+	5852.90i	−1.29967	+	0.422287i	−0.875465	−	0.483282i	$-0.839445\pi$
$577$	−18013.4	+	5852.90i	−1.29967	+	0.422287i	−0.424200	+	0.905568i	$0.639445\pi$
$578$	3319.45	+	4568.83i	0.238877	+	0.328786i
$579$	−14635.9	+	10633.6i	−1.05051	+	0.763242i
$580$		0			0
$581$	−11515.1	−	8366.21i	−0.822250	−	0.597399i
$582$			6565.31i			0.467596i
$583$	−8974.09	+	12351.8i	−0.637511	+	0.877458i
$584$	909.587	−	2799.42i	0.0644503	−	0.198358i
$585$		0			0
$586$	3541.21	+	10898.7i	0.249635	+	0.768297i
$587$	−9482.78	−	3081.14i	−0.666774	−	0.216648i	−0.0439781	−	0.999032i	$-0.514003\pi$
$587$	−9482.78	−	3081.14i	−0.666774	−	0.216648i	−0.622796	+	0.782385i	$0.714003\pi$
$588$	13106.5	+	4258.55i	0.919221	+	0.298673i
$589$	9487.82	+	29200.5i	0.663733	+	2.04276i
$590$		0			0
$591$	2418.99	−	7444.89i	0.168366	−	0.518176i
$592$	−139.512	+	192.022i	−0.00968567	+	0.0133312i
$593$		−	12508.5i		−	0.866212i	−0.901343	−	0.433106i	$-0.857418\pi$
$593$		−	12508.5i		−	0.866212i	0.901343	−	0.433106i	$-0.142582\pi$
$594$	−11201.6	−	8138.47i	−0.773753	−	0.562164i
$595$		0			0
$596$	−5592.44	+	4063.15i	−0.384355	+	0.279250i
$597$	2184.82	+	3007.15i	0.149780	+	0.206155i
$598$	165.561	−	53.7941i	0.0113216	−	0.00367860i
$599$	8434.30			0.575319			0.287660	−	0.957733i	$-0.407123\pi$
$599$	8434.30			0.575319			0.287660	+	0.957733i	$0.407123\pi$
$600$		0			0
$601$	17377.0			1.17940			0.589702	−	0.807621i	$-0.299245\pi$
$601$	17377.0			1.17940			0.589702	+	0.807621i	$0.299245\pi$
$602$	−5021.72	+	1631.66i	−0.339983	+	0.110467i
$603$	−1376.63	−	1894.77i	−0.0929698	−	0.127962i
$604$	4496.60	−	3266.97i	0.302921	−	0.220085i
$605$		0			0
$606$	−9511.77	−	6910.71i	−0.637606	−	0.463248i
$607$			23874.5i			1.59643i	0.602370	+	0.798217i	$0.294223\pi$
$607$			23874.5i			1.59643i	−0.602370	+	0.798217i	$0.705777\pi$
$608$	−2203.94	+	3033.47i	−0.147009	+	0.202341i
$609$	−11409.6	+	35115.2i	−0.759180	+	2.33652i
$610$		0			0
$611$	−674.653	−	2076.37i	−0.0446703	−	0.137481i
$612$	549.864	+	178.662i	0.0363185	+	0.0118006i
$613$	3795.34	+	1233.18i	0.250069	+	0.0812525i	0.431369	−	0.902175i	$-0.358031\pi$
$613$	3795.34	+	1233.18i	0.250069	+	0.0812525i	−0.181300	+	0.983428i	$0.558031\pi$
$614$	−3307.09	−	10178.2i	−0.217367	−	0.668986i
$615$		0			0
$616$	3763.44	−	11582.7i	0.246158	−	0.757596i
$617$	4210.88	−	5795.79i	0.274755	−	0.378168i	−0.649233	−	0.760590i	$-0.724910\pi$
$617$	4210.88	−	5795.79i	0.274755	−	0.378168i	0.923988	+	0.382422i	$0.124910\pi$
$618$		−	5805.02i		−	0.377851i
$619$	−5633.63	−	4093.07i	−0.365807	−	0.265775i	0.389663	−	0.920958i	$-0.372592\pi$
$619$	−5633.63	−	4093.07i	−0.365807	−	0.265775i	−0.755470	+	0.655183i	$0.772592\pi$
$620$		0			0
$621$	1039.93	−	755.551i	0.0671994	−	0.0488232i
$622$	−2351.07	−	3235.97i	−0.151558	−	0.208602i
$623$	11759.7	−	3820.94i	0.756245	−	0.245719i
$624$	778.979			0.0499746
$625$		0			0
$626$	16563.5			1.05753
$627$	−25578.2	+	8310.86i	−1.62918	+	0.529352i
$628$	−6872.34	−	9458.96i	−0.436682	−	0.601041i
$629$	548.571	−	398.560i	0.0347742	−	0.0252649i
$630$		0			0
$631$	−4661.94	−	3387.10i	−0.294119	−	0.213690i	0.430933	−	0.902384i	$-0.358184\pi$
$631$	−4661.94	−	3387.10i	−0.294119	−	0.213690i	−0.725052	+	0.688694i	$0.758184\pi$
$632$		−	7334.81i		−	0.461651i
$633$	−9478.39	+	13045.9i	−0.595153	+	0.819158i
$634$	2950.74	−	9081.45i	0.184841	−	0.568881i
$635$		0			0
$636$	−1959.97	−	6032.16i	−0.122198	−	0.376086i
$637$	6692.15	+	2174.41i	0.416252	+	0.135248i
$638$	20882.2	+	6785.02i	1.29582	+	0.421037i
$639$	−370.426	−	1140.05i	−0.0229324	−	0.0705788i
$640$		0			0
$641$	−5163.00	+	15890.1i	−0.318138	+	0.979127i	0.656306	+	0.754495i	$0.272118\pi$
$641$	−5163.00	+	15890.1i	−0.318138	+	0.979127i	−0.974444	+	0.224632i	$0.927882\pi$
$642$	−4918.09	+	6769.17i	−0.302339	+	0.416133i
$643$			25943.2i			1.59113i	0.605867	+	0.795566i	$0.292827\pi$
$643$			25943.2i			1.59113i	−0.605867	+	0.795566i	$0.707173\pi$
$644$	914.705	+	664.572i	0.0559696	+	0.0406643i
$645$		0			0
$646$	8666.05	−	6296.25i	0.527804	−	0.383472i
$647$	4580.76	+	6304.88i	0.278344	+	0.383107i	0.925184	−	0.379518i	$-0.123910\pi$
$647$	4580.76	+	6304.88i	0.278344	+	0.383107i	−0.646841	+	0.762625i	$0.723910\pi$
$648$	4820.88	−	1566.40i	0.292256	−	0.0949598i
$649$	24654.1			1.49115
$650$		0			0
$651$	41428.5			2.49418
$652$	13630.8	−	4428.91i	0.818746	−	0.266027i
$653$	5268.80	+	7251.88i	0.315749	+	0.434591i	0.937163	−	0.348891i	$-0.113442\pi$
$653$	5268.80	+	7251.88i	0.315749	+	0.434591i	−0.621414	+	0.783482i	$0.713442\pi$
$654$	−4064.21	+	2952.82i	−0.243002	+	0.176551i
$655$		0			0
$656$	3321.70	+	2413.36i	0.197699	+	0.143637i
$657$		−	1163.48i		−	0.0690893i
$658$	8334.67	−	11471.7i	0.493798	−	0.679655i
$659$	−6504.36	+	20018.3i	−0.384482	+	1.18331i	0.552373	+	0.833597i	$0.313722\pi$
$659$	−6504.36	+	20018.3i	−0.384482	+	1.18331i	−0.936855	+	0.349717i	$0.886278\pi$
$660$		0			0
$661$	−736.277	−	2266.03i	−0.0433251	−	0.133341i	0.927054	−	0.374927i	$-0.122332\pi$
$661$	−736.277	−	2266.03i	−0.0433251	−	0.133341i	−0.970379	+	0.241586i	$0.922332\pi$
$662$	12238.9	+	3976.65i	0.718545	+	0.233469i
$663$	−2116.48	−	687.685i	−0.123978	−	0.0402828i
$664$	−1086.60	−	3344.20i	−0.0635062	−	0.195452i
$665$		0			0
$666$	−28.9917	+	89.2271i	−0.00168679	+	0.00519141i
$667$	−1198.14	+	1649.10i	−0.0695536	+	0.0957324i
$668$			8268.71i			0.478931i
$669$	4023.78	+	2923.45i	0.232539	+	0.168949i
$670$		0			0
$671$	−9576.39	+	6957.66i	−0.550958	+	0.400294i
$672$	2973.83	+	4093.13i	0.170711	+	0.234964i
$673$	−15023.1	+	4881.30i	−0.860473	+	0.279585i	−0.705826	−	0.708385i	$-0.749424\pi$
$673$	−15023.1	+	4881.30i	−0.860473	+	0.279585i	−0.154647	+	0.987970i	$0.549424\pi$
$674$	11854.7			0.677485
$675$		0			0
$676$	−8390.25			−0.477370
$677$	8644.73	−	2808.84i	0.490759	−	0.159457i	−0.0531749	−	0.998585i	$-0.516934\pi$
$677$	8644.73	−	2808.84i	0.490759	−	0.159457i	0.543934	+	0.839128i	$0.316934\pi$
$678$	7828.43	+	10774.9i	0.443435	+	0.610336i
$679$	−17614.3	+	12797.5i	−0.995542	+	0.723304i
$680$		0			0
$681$	−22202.5	−	16131.1i	−1.24934	−	0.907700i
$682$		−	24636.6i		−	1.38326i
$683$	−2059.68	+	2834.91i	−0.115390	+	0.158821i	−0.862805	−	0.505536i	$-0.831295\pi$
$683$	−2059.68	+	2834.91i	−0.115390	+	0.158821i	0.747415	+	0.664357i	$0.231295\pi$
$684$	−457.996	+	1409.57i	−0.0256022	+	0.0787955i
$685$		0			0
$686$	7257.86	+	22337.4i	0.403945	+	1.24322i
$687$	−246.532	−	80.1031i	−0.0136911	−	0.00444851i
$688$	−1240.59	−	403.092i	−0.0687457	−	0.0223368i
$689$	−1000.76	−	3080.01i	−0.0553349	−	0.170303i
$690$		0			0
$691$	8037.73	−	24737.6i	0.442503	−	1.36188i	−0.442696	−	0.896672i	$-0.645978\pi$
$691$	8037.73	−	24737.6i	0.442503	−	1.36188i	0.885199	−	0.465212i	$-0.154022\pi$
$692$	3220.35	−	4432.43i	0.176907	−	0.243491i
$693$		−	4813.93i		−	0.263876i
$694$	2155.57	+	1566.11i	0.117902	+	0.0856610i
$695$		0			0
$696$	−7379.41	+	5361.45i	−0.401890	+	0.291991i
$697$	−6894.51	−	9489.48i	−0.374675	−	0.515696i
$698$	−19748.8	+	6416.77i	−1.07092	+	0.347963i
$699$	9523.77			0.515339
$700$		0			0
$701$	−6741.69			−0.363238			−0.181619	−	0.983369i	$-0.558134\pi$
$701$	−6741.69			−0.363238			−0.181619	+	0.983369i	$0.558134\pi$
$702$	2793.22	−	907.572i	0.150176	−	0.0487950i
$703$	1021.70	+	1406.25i	0.0548140	+	0.0754449i
$704$	2434.09	−	1768.47i	0.130310	−	0.0946756i
$705$		0			0
$706$	9943.98	+	7224.73i	0.530095	+	0.385136i
$707$		−	38990.2i		−	2.07408i
$708$	−6020.10	+	8285.95i	−0.319561	+	0.439838i
$709$	6512.58	−	20043.6i	0.344972	−	1.06171i	−0.616627	−	0.787255i	$-0.711501\pi$
$709$	6512.58	−	20043.6i	0.344972	−	1.06171i	0.961599	−	0.274458i	$-0.0884986\pi$
$710$		0			0
$711$	−895.919	−	2757.36i	−0.0472568	−	0.145441i
$712$	2905.16	+	943.944i	0.152915	+	0.0496851i
$713$	2175.24	+	706.779i	0.114255	+	0.0371235i
$714$	−4466.44	−	13746.3i	−0.234107	−	0.720507i
$715$		0			0
$716$	−2229.85	+	6862.77i	−0.116387	+	0.358203i
$717$	4460.33	−	6139.12i	0.232321	−	0.319762i
$718$			5673.97i			0.294918i
$719$	6738.80	+	4896.02i	0.349534	+	0.253951i	0.748673	−	0.662939i	$-0.230691\pi$
$719$	6738.80	+	4896.02i	0.349534	+	0.253951i	−0.399140	+	0.916890i	$0.630691\pi$
$720$		0			0
$721$	15574.4	−	11315.5i	0.804470	−	0.584481i
$722$	8077.11	+	11117.2i	0.416342	+	0.573045i
$723$	16125.3	−	5239.41i	0.829467	−	0.269510i
$724$	13061.7			0.670491
$725$		0			0
$726$	8583.47			0.438791
$727$	−9732.63	+	3162.32i	−0.496511	+	0.161326i	−0.546559	−	0.837421i	$-0.684062\pi$
$727$	−9732.63	+	3162.32i	−0.496511	+	0.161326i	0.0500482	+	0.998747i	$0.484062\pi$
$728$	1518.43	+	2089.94i	0.0773034	+	0.106399i
$729$	17326.4	−	12588.4i	0.880274	−	0.639556i
$730$		0			0
$731$	3014.82	+	2190.39i	0.152540	+	0.110827i
$732$		−	4917.44i		−	0.248298i
$733$	16084.9	−	22139.0i	0.810519	−	1.11558i	−0.180724	−	0.983534i	$-0.557844\pi$
$733$	16084.9	−	22139.0i	0.810519	−	1.11558i	0.991243	−	0.132050i	$-0.0421559\pi$
$734$	−1456.07	+	4481.34i	−0.0732217	+	0.225353i
$735$		0			0
$736$	86.3141	+	265.647i	0.00432280	+	0.0133042i
$737$	33114.4	+	10759.5i	1.65507	+	0.537763i
$738$	1543.50	+	501.514i	0.0769879	+	0.0250149i
$739$	−2806.35	−	8637.04i	−0.139693	−	0.429931i	0.856597	−	0.515985i	$-0.172574\pi$
$739$	−2806.35	−	8637.04i	−0.139693	−	0.429931i	−0.996290	+	0.0860546i	$0.972574\pi$
$740$		0			0
$741$	1762.87	−	5425.56i	0.0873963	−	0.268978i
$742$	12363.4	−	17016.7i	0.611689	−	0.841917i
$743$			10384.0i			0.512721i	0.966581	+	0.256361i	$0.0825234\pi$
$743$			10384.0i			0.512721i	−0.966581	+	0.256361i	$0.917477\pi$
$744$	8280.05	+	6015.81i	0.408013	+	0.296438i
$745$		0			0
$746$	4097.77	−	2977.20i	0.201113	−	0.146117i
$747$	−816.962	−	1124.45i	−0.0400148	−	0.0550757i
$748$	−8174.59	+	2656.09i	−0.399589	+	0.129834i
$749$	−27747.8			−1.35365
$750$		0			0
$751$	−9567.90			−0.464897			−0.232448	−	0.972609i	$-0.574674\pi$
$751$	−9567.90			−0.464897			−0.232448	+	0.972609i	$0.574674\pi$
$752$	3331.59	−	1082.50i	0.161557	−	0.0524930i
$753$	3313.29	+	4560.35i	0.160349	+	0.220702i
$754$	−3767.91	+	2737.55i	−0.181989	+	0.132222i
$755$		0			0
$756$	15432.2	+	11212.2i	0.742412	+	0.539394i
$757$		−	25864.4i		−	1.24182i	−0.783882	−	0.620910i	$-0.786763\pi$
$757$		−	25864.4i		−	1.24182i	0.783882	−	0.620910i	$-0.213237\pi$
$758$	−3444.66	+	4741.17i	−0.165060	+	0.227186i
$759$	−619.103	+	1905.40i	−0.0296074	+	0.0911222i
$760$		0			0
$761$	−9032.55	−	27799.3i	−0.430262	−	1.32421i	−0.897864	−	0.440272i	$-0.854882\pi$
$761$	−9032.55	−	27799.3i	−0.430262	−	1.32421i	0.467602	−	0.883939i	$-0.345118\pi$
$762$	−12108.3	−	3934.24i	−0.575641	−	0.187037i
$763$	−15844.4	−	5148.16i	−0.751777	−	0.244267i
$764$	169.222	+	520.812i	0.00801340	+	0.0246627i
$765$		0			0
$766$	1841.30	−	5666.94i	0.0868523	−	0.267304i
$767$	−3073.85	+	4230.79i	−0.144707	+	0.199172i
$768$			1249.89i			0.0587261i
$769$	−18373.7	−	13349.2i	−0.861601	−	0.625990i	0.0667189	−	0.997772i	$-0.478747\pi$
$769$	−18373.7	−	13349.2i	−0.861601	−	0.625990i	−0.928320	+	0.371782i	$0.878747\pi$
$770$		0			0
$771$	14563.1	−	10580.7i	0.680254	−	0.494233i
$772$	−8711.78	−	11990.7i	−0.406145	−	0.559010i
$773$	−18295.9	+	5944.69i	−0.851302	+	0.276605i	−0.701991	−	0.712185i	$-0.747706\pi$
$773$	−18295.9	+	5944.69i	−0.851302	+	0.276605i	−0.149311	+	0.988790i	$0.547706\pi$
$774$	−515.607			−0.0239446
$775$		0			0
$776$	−5378.76			−0.248823
$777$	2230.63	−	724.775i	0.102990	−	0.0334635i
$778$	−2856.05	−	3931.02i	−0.131612	−	0.181149i
$779$	24326.1	−	17674.0i	1.11884	−	0.812883i
$780$		0			0
$781$	14417.4	+	10474.9i	0.660559	+	0.479924i
$782$		−	797.959i		−	0.0364897i
$783$	−20214.1	+	27822.4i	−0.922599	+	1.26985i
$784$	−3488.90	+	10737.7i	−0.158933	+	0.489146i
$785$		0			0
$786$	6922.49	+	21305.2i	0.314144	+	0.966835i
$787$	−20688.1	−	6721.96i	−0.937039	−	0.304462i	−0.199601	−	0.979877i	$-0.563965\pi$
$787$	−20688.1	−	6721.96i	−0.937039	−	0.304462i	−0.737438	+	0.675415i	$0.763965\pi$
$788$	6099.37	+	1981.81i	0.275738	+	0.0895925i
$789$	11174.6	+	34392.0i	0.504218	+	1.55182i
$790$		0			0
$791$	−13648.6	+	42006.2i	−0.613514	+	1.88820i
$792$	699.027	−	962.129i	0.0313622	−	0.0431664i
$793$		−	2510.84i		−	0.112437i
$794$	−453.101	−	329.197i	−0.0202518	−	0.0147138i
$795$		0			0
$796$	−2463.66	+	1789.96i	−0.109701	+	0.0797026i
$797$	−18091.0	−	24900.1i	−0.804035	−	1.10666i	−0.992216	−	0.124525i	$-0.960259\pi$
$797$	−18091.0	−	24900.1i	−0.804035	−	1.10666i	0.188181	−	0.982134i	$-0.439741\pi$
$798$	35238.4	−	11449.6i	1.56319	−	0.507911i
$799$	−10007.5			−0.443105
$800$		0			0
$801$	1207.43			0.0532614
$802$	13141.2	−	4269.82i	0.578591	−	0.187996i
$803$	10166.9	+	13993.5i	0.446802	+	0.614971i
$804$	−11702.1	+	8502.05i	−0.513309	+	0.372941i
$805$		0			0
$806$	4227.78	+	3071.66i	0.184761	+	0.134237i
$807$			27355.0i			1.19324i
$808$	5661.73	−	7792.71i	0.246509	−	0.339290i
$809$	−7128.84	+	21940.3i	−0.309811	+	0.953499i	0.668028	+	0.744136i	$0.267139\pi$
$809$	−7128.84	+	21940.3i	−0.309811	+	0.953499i	−0.977838	+	0.209362i	$0.932861\pi$
$810$		0			0
$811$	8602.28	+	26475.1i	0.372462	+	1.14632i	0.945175	+	0.326565i	$0.105891\pi$
$811$	8602.28	+	26475.1i	0.372462	+	1.14632i	−0.572713	+	0.819756i	$0.694109\pi$
$812$	−28768.8	−	9347.54i	−1.24333	−	0.403983i
$813$	−23331.2	−	7580.76i	−1.00647	−	0.327022i
$814$	−431.007	−	1326.50i	−0.0185587	−	0.0571178i
$815$		0			0
$816$	1103.41	−	3395.95i	0.0473371	−	0.145689i
$817$	−5615.04	+	7728.43i	−0.240447	+	0.330947i
$818$			21038.5i			0.899257i
$819$	826.099	+	600.196i	0.0352457	+	0.0256075i
$820$		0			0
$821$	7550.19	−	5485.54i	0.320954	−	0.233187i	−0.415628	−	0.909535i	$-0.636438\pi$
$821$	7550.19	−	5485.54i	0.320954	−	0.233187i	0.736583	+	0.676348i	$0.236438\pi$
$822$	2710.14	+	3730.19i	0.114996	+	0.158279i
$823$	−31628.3	+	10276.7i	−1.33960	+	0.435263i	−0.889182	−	0.457553i	$-0.848726\pi$
$823$	−31628.3	+	10276.7i	−1.33960	+	0.435263i	−0.450421	+	0.892816i	$0.648726\pi$
$824$	4755.88			0.201067
$825$		0			0
$826$	−33965.3			−1.43076
$827$	−13015.2	+	4228.89i	−0.547258	+	0.177815i	−0.569580	−	0.821936i	$-0.692894\pi$
$827$	−13015.2	+	4228.89i	−0.547258	+	0.177815i	0.0223222	+	0.999751i	$0.492894\pi$
$828$	64.8956	+	89.3211i	0.00272377	+	0.00374894i
$829$	5102.46	−	3707.16i	0.213771	−	0.155313i	−0.475747	−	0.879582i	$-0.657822\pi$
$829$	5102.46	−	3707.16i	0.213771	−	0.155313i	0.689518	+	0.724268i	$0.257822\pi$
$830$		0			0
$831$	20812.0	+	15120.8i	0.868784	+	0.631209i
$832$			638.194i			0.0265930i
$833$	18958.6	−	26094.3i	0.788568	−	1.08537i
$834$	6639.12	−	20433.1i	0.275652	−	0.848371i
$835$		0			0
$836$	−6808.83	−	20955.4i	−0.281685	−	0.866936i
$837$	36699.0	+	11924.2i	1.51554	+	0.492427i
$838$	−5052.44	−	1641.64i	−0.208274	−	0.0676723i
$839$	10713.7	+	32973.3i	0.440854	+	1.35681i	0.886967	+	0.461833i	$0.152808\pi$
$839$	10713.7	+	32973.3i	0.440854	+	1.35681i	−0.446113	+	0.894977i	$0.647192\pi$
$840$		0			0
$841$	9315.86	−	28671.3i	0.381970	−	1.17558i
$842$	−12596.3	+	17337.3i	−0.515554	+	0.709600i
$843$		−	29286.6i		−	1.19654i
$844$	−10688.1	−	7765.35i	−0.435900	−	0.316700i
$845$		0			0
$846$	1120.21	−	813.882i	0.0455245	−	0.0330755i
$847$	16731.4	+	23028.8i	0.678746	+	0.934214i
$848$	4941.96	−	1605.74i	0.200127	−	0.0650252i
$849$	−6177.45			−0.249717
$850$		0			0
$851$	129.486			0.00521589
$852$	−7040.95	+	2287.74i	−0.283121	+	0.0919916i
$853$	8415.27	+	11582.6i	0.337788	+	0.464926i	0.943794	−	0.330535i	$-0.107229\pi$
$853$	8415.27	+	11582.6i	0.337788	+	0.464926i	−0.606006	+	0.795460i	$0.707229\pi$
$854$	13193.1	−	9585.37i	0.528641	−	0.384081i
$855$		0			0
$856$	−5545.77	−	4029.24i	−0.221438	−	0.160884i
$857$			22693.5i			0.904546i	0.891880	+	0.452273i	$0.149387\pi$
$857$			22693.5i			0.904546i	−0.891880	+	0.452273i	$0.850613\pi$
$858$	−2690.62	+	3703.32i	−0.107059	+	0.147354i
$859$	4345.99	−	13375.6i	0.172623	−	0.531279i	−0.826894	−	0.562358i	$-0.809894\pi$
$859$	4345.99	−	13375.6i	0.172623	−	0.531279i	0.999517	+	0.0310789i	$0.00989431\pi$
$860$		0			0
$861$	−12537.6	−	38586.7i	−0.496259	−	1.52733i
$862$	24107.0	+	7832.82i	0.952536	+	0.309498i
$863$	−13885.0	−	4511.52i	−0.547684	−	0.177953i	0.0220880	−	0.999756i	$-0.492969\pi$
$863$	−13885.0	−	4511.52i	−0.547684	−	0.177953i	−0.569772	+	0.821803i	$0.692969\pi$
$864$	1456.22	+	4481.80i	0.0573400	+	0.176474i
$865$		0			0
$866$	−2378.61	+	7320.61i	−0.0933354	+	0.287257i
$867$	8103.43	−	11153.4i	0.317424	−	0.436897i
$868$			33941.1i			1.32723i
$869$	34870.2	+	25334.7i	1.36121	+	0.988977i
$870$		0			0
$871$	−5975.06	+	4341.13i	−0.232442	+	0.168879i
$872$	−2419.16	−	3329.68i	−0.0939484	−	0.129309i
$873$	−2022.02	+	656.995i	−0.0783907	+	0.0254707i
$874$	2045.56			0.0791670
$875$		0			0
$876$	−7185.63			−0.277146
$877$	40494.7	−	13157.5i	1.55919	−	0.506611i	0.602598	−	0.798045i	$-0.294132\pi$
$877$	40494.7	−	13157.5i	1.55919	−	0.506611i	0.956591	+	0.291433i	$0.0941322\pi$
$878$	−8718.59	−	12000.1i	−0.335123	−	0.461257i
$879$	22632.4	−	16443.4i	0.868454	−	0.630969i
$880$		0			0
$881$	−41286.1	−	29996.1i	−1.57885	−	1.14710i	−0.918001	−	0.396577i	$-0.870198\pi$
$881$	−41286.1	−	29996.1i	−1.57885	−	1.14710i	−0.660845	−	0.750522i	$-0.729802\pi$
$882$			4462.76i			0.170373i
$883$	16820.9	−	23151.9i	0.641072	−	0.882360i	−0.357600	−	0.933875i	$-0.616405\pi$
$883$	16820.9	−	23151.9i	0.641072	−	0.882360i	0.998672	+	0.0515145i	$0.0164048\pi$
$884$	563.400	−	1733.97i	0.0214357	−	0.0659724i
$885$		0			0
$886$	−9246.59	−	28458.1i	−0.350616	−	1.07908i
$887$	−39115.5	−	12709.4i	−1.48069	−	0.481104i	−0.546369	−	0.837545i	$-0.683990\pi$
$887$	−39115.5	−	12709.4i	−1.48069	−	0.481104i	−0.934318	+	0.356440i	$0.883990\pi$
$888$	551.065	+	179.052i	0.0208249	+	0.00676643i
$889$	−13047.0	−	40154.6i	−0.492219	−	1.51490i
$890$		0			0
$891$	−9204.72	+	28329.2i	−0.346094	+	1.06517i
$892$	−2395.09	+	3296.56i	−0.0899032	+	0.123741i
$893$		−	25654.2i		−	0.961348i
$894$	13652.3	+	9918.95i	0.510738	+	0.371073i
$895$		0			0
$896$	−3353.37	+	2436.37i	−0.125032	+	0.0908408i
$897$	−249.789	−	343.805i	−0.00929791	−	0.0127975i
$898$	27089.2	−	8801.83i	1.00666	−	0.327083i
$899$	−61191.7			−2.27014
$900$		0			0
$901$	−14844.8			−0.548893
$902$	−22946.6	+	7455.80i	−0.847048	+	0.275223i
$903$	7576.49	+	10428.1i	0.279213	+	0.384304i
$904$	−8827.55	+	6413.59i	−0.324779	+	0.235966i
$905$		0			0
$906$	−10977.1	−	7975.33i	−0.402527	−	0.292453i
$907$			25369.4i			0.928750i	0.885639	+	0.464375i	$0.153721\pi$
$907$			25369.4i			0.928750i	−0.885639	+	0.464375i	$0.846279\pi$
$908$	13215.7	−	18189.8i	0.483015	−	0.664814i
$909$	1176.55	−	3621.05i	0.0429304	−	0.132126i
$910$		0			0
$911$	−4540.55	−	13974.4i	−0.165132	−	0.508223i	0.833914	−	0.551894i	$-0.186095\pi$
$911$	−4540.55	−	13974.4i	−0.165132	−	0.508223i	−0.999046	+	0.0436709i	$0.986095\pi$
$912$	8705.46	+	2828.57i	0.316082	+	0.102701i
$913$	19651.7	+	6385.23i	0.712352	+	0.231457i
$914$	4897.85	+	15074.0i	0.177250	+	0.545520i
$915$		0			0
$916$	65.6261	−	201.976i	0.00236719	−	0.00728546i
$917$	−43666.6	+	60102.0i	−1.57252	+	2.16439i
$918$		−	13462.6i		−	0.484020i
$919$	5211.63	+	3786.47i	0.187068	+	0.135913i	0.677378	−	0.735635i	$-0.263116\pi$
$919$	5211.63	+	3786.47i	0.187068	+	0.135913i	−0.490309	+	0.871548i	$0.663116\pi$
$920$		0			0
$921$	−21136.1	+	15356.2i	−0.756196	+	0.549409i
$922$	10495.3	+	14445.5i	0.374884	+	0.515983i
$923$	−3595.10	+	1168.12i	−0.128206	+	0.0416567i
$924$	−29730.7			−1.05852
$925$		0			0
$926$	11922.4			0.423104
$927$	1787.86	−	580.912i	0.0633453	−	0.0205821i
$928$	−4392.48	−	6045.72i	−0.155377	−	0.213858i
$929$	−14965.0	+	10872.7i	−0.528512	+	0.383986i	−0.819801	−	0.572649i	$-0.805916\pi$
$929$	−14965.0	+	10872.7i	−0.528512	+	0.383986i	0.291289	+	0.956635i	$0.405916\pi$
$930$		0			0
$931$	66892.3	+	48600.1i	2.35479	+	1.71085i
$932$			7802.54i			0.274228i
$933$	−5739.43	+	7899.64i	−0.201394	+	0.277195i
$934$	2050.02	−	6309.31i	0.0718187	−	0.221035i
$935$		0			0
$936$	77.9529	+	239.914i	0.00272219	+	0.00837804i
$937$	10023.4	+	3256.80i	0.349466	+	0.113549i	0.478490	−	0.878093i	$-0.341184\pi$
$937$	10023.4	+	3256.80i	0.349466	+	0.113549i	−0.129024	+	0.991642i	$0.541184\pi$
$938$	−45620.8	−	14823.1i	−1.58803	−	0.515982i
$939$	−12495.0	−	38455.8i	−0.434250	−	1.33648i
$940$		0			0
$941$	−273.793	+	842.648i	−0.00948501	+	0.0291919i	−0.955687	−	0.294385i	$-0.904885\pi$
$941$	−273.793	+	842.648i	−0.00948501	+	0.0291919i	0.946202	+	0.323577i	$0.104885\pi$
$942$	−16776.7	+	23091.2i	−0.580272	+	0.798675i
$943$		−	2239.92i		−	0.0773508i
$944$	−6788.43	−	4932.08i	−0.234051	−	0.170048i
$945$		0			0
$946$	6201.37	−	4505.56i	0.213133	−	0.154850i
$947$	6111.55	+	8411.83i	0.209714	+	0.288646i	0.900897	−	0.434034i	$-0.142910\pi$
$947$	6111.55	+	8411.83i	0.209714	+	0.288646i	−0.691183	+	0.722680i	$0.742910\pi$
$948$	−17029.4	+	5533.18i	−0.583426	+	0.189567i
$949$	−3668.97			−0.125500
$950$		0			0
$951$	−23310.5			−0.794843
$952$	11261.9	−	3659.22i	0.383404	−	0.124576i
$953$	6031.58	+	8301.75i	0.205018	+	0.282183i	0.899128	−	0.437686i	$-0.144202\pi$
$953$	6031.58	+	8301.75i	0.205018	+	0.282183i	−0.694110	+	0.719869i	$0.744202\pi$
$954$	1661.68	−	1207.28i	0.0563931	−	0.0409720i
$955$		0			0
$956$	5029.59	+	3654.21i	0.170155	+	0.123625i
$957$		−	53600.9i		−	1.81052i
$958$	−10080.8	+	13875.0i	−0.339974	+	0.467935i
$959$	−4725.05	+	14542.2i	−0.159103	+	0.489669i
$960$		0			0
$961$	12011.2	+	36966.7i	0.403182	+	1.24087i
$962$	281.373	+	91.4236i	0.00943018	+	0.00306405i
$963$	−2576.96	−	837.306i	−0.0862320	−	0.0280185i
$964$	4292.49	+	13210.9i	0.143415	+	0.441385i
$965$		0			0
$966$	852.922	−	2625.02i	0.0284082	−	0.0874314i
$967$	−799.016	+	1099.75i	−0.0265715	+	0.0365725i	−0.822096	−	0.569349i	$-0.807195\pi$
$967$	−799.016	+	1099.75i	−0.0265715	+	0.0365725i	0.795525	+	0.605921i	$0.207195\pi$
$968$			7032.17i			0.233494i
$969$	−21155.6	−	15370.4i	−0.701356	−	0.509565i
$970$		0			0
$971$	14283.3	−	10377.4i	0.472062	−	0.342973i	−0.326182	−	0.945307i	$-0.605762\pi$
$971$	14283.3	−	10377.4i	0.472062	−	0.342973i	0.798244	+	0.602334i	$0.205762\pi$
$972$	2074.95	+	2855.93i	0.0684713	+	0.0942427i
$973$	67761.9	−	22017.2i	2.23263	−	0.725425i
$974$	−24765.4			−0.814717
$975$		0			0
$976$	4028.71			0.132127
$977$	−7051.30	+	2291.11i	−0.230902	+	0.0750245i	−0.422183	−	0.906511i	$-0.638736\pi$
$977$	−7051.30	+	2291.11i	−0.230902	+	0.0750245i	0.191281	+	0.981535i	$0.438736\pi$
$978$	−20565.4	−	28305.8i	−0.672400	−	0.925480i
$979$	−14522.1	+	10550.9i	−0.474084	+	0.344442i
$980$		0			0
$981$	−1316.13	−	956.227i	−0.0428348	−	0.0311213i
$982$		−	8573.54i		−	0.278608i
$983$	1766.61	−	2431.54i	0.0573207	−	0.0788952i	−0.779394	−	0.626534i	$-0.784473\pi$
$983$	1766.61	−	2431.54i	0.0573207	−	0.0788952i	0.836715	+	0.547639i	$0.184473\pi$
$984$	3097.34	−	9532.63i	0.100345	−	0.308831i
$985$		0			0
$986$	6597.12	+	20303.9i	0.213078	+	0.655788i
$987$	−32921.5	−	10696.8i	−1.06170	−	0.344969i
$988$	4444.99	+	1444.27i	0.143132	+	0.0465063i
$989$	219.904	+	676.795i	0.00707032	+	0.0217602i
$990$		0			0
$991$	−5760.26	+	17728.3i	−0.184643	+	0.568271i	−0.999942	−	0.0107682i	$-0.996572\pi$
$991$	−5760.26	+	17728.3i	−0.184643	+	0.568271i	0.815299	+	0.579040i	$0.196572\pi$
$992$	−4928.57	+	6783.59i	−0.157744	+	0.217116i
$993$		−	31415.1i		−	1.00395i
$994$	−19862.5	−	14431.0i	−0.633803	−	0.460485i
$995$		0			0
$996$	−6944.59	+	5045.54i	−0.220932	+	0.160516i
$997$	7472.36	+	10284.8i	0.237364	+	0.326704i	0.911036	−	0.412327i	$-0.135284\pi$
$997$	7472.36	+	10284.8i	0.237364	+	0.326704i	−0.673672	+	0.739031i	$0.735284\pi$
$998$	22250.3	−	7229.56i	0.705733	−	0.229306i
$999$	2184.59			0.0691865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.4.e.b.99.6		32
5.2	odd	4		250.4.d.c.151.3		32
5.3	odd	4		250.4.d.d.151.6		32
5.4	even	2		50.4.e.a.19.3	✓	32
25.2	odd	20		1250.4.a.n.1.11		16
25.3	odd	20		250.4.d.d.101.6		32
25.4	even	10	inner	250.4.e.b.149.6		32
25.21	even	5		50.4.e.a.29.3	yes	32
25.22	odd	20		250.4.d.c.101.3		32
25.23	odd	20		1250.4.a.m.1.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.e.a.19.3	✓	32	5.4	even	2
50.4.e.a.29.3	yes	32	25.21	even	5
250.4.d.c.101.3		32	25.22	odd	20
250.4.d.c.151.3		32	5.2	odd	4
250.4.d.d.101.6		32	25.3	odd	20
250.4.d.d.151.6		32	5.3	odd	4
250.4.e.b.99.6		32	1.1	even	1	trivial
250.4.e.b.149.6		32	25.4	even	10	inner
1250.4.a.m.1.6		16	25.23	odd	20
1250.4.a.n.1.11		16	25.2	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)

\(f(q)\)	\(=\)	\(q+(1.90211 - 0.618034i) q^{2} +(-2.86980 - 3.94994i) q^{3} +(3.23607 - 2.35114i) q^{4} +(-7.89989 - 5.73960i) q^{6} -32.3828i q^{7} +(4.70228 - 6.47214i) q^{8} +(0.977169 - 3.00742i) q^{9} +O(q^{10})\)	\(q+(1.90211 - 0.618034i) q^{2} +(-2.86980 - 3.94994i) q^{3} +(3.23607 - 2.35114i) q^{4} +(-7.89989 - 5.73960i) q^{6} -32.3828i q^{7} +(4.70228 - 6.47214i) q^{8} +(0.977169 - 3.00742i) q^{9} +(14.5272 + 44.7100i) q^{11} +(-18.5737 - 6.03498i) q^{12} +(-9.48373 - 3.08145i) q^{13} +(-20.0137 - 61.5957i) q^{14} +(4.94427 - 15.2169i) q^{16} +(-26.8671 + 36.9793i) q^{17} -6.32437i q^{18} +(-94.7959 - 68.8733i) q^{19} +(-127.910 + 92.9322i) q^{21} +(55.2646 + 76.0652i) q^{22} +(-8.30148 + 2.69731i) q^{23} -39.0592 q^{24} -19.9436 q^{26} +(-140.056 + 45.5070i) q^{27} +(-76.1365 - 104.793i) q^{28} +(188.929 - 137.265i) q^{29} +(-211.987 - 154.018i) q^{31} -32.0000i q^{32} +(134.912 - 185.690i) q^{33} +(-28.2497 + 86.9436i) q^{34} +(-3.90868 - 12.0297i) q^{36} +(-14.1085 - 4.58412i) q^{37} +(-222.879 - 72.4177i) q^{38} +(15.0449 + 46.3033i) q^{39} +(-79.2986 + 244.056i) q^{41} +(-185.864 + 255.820i) q^{42} -81.5270i q^{43} +(152.130 + 110.529i) q^{44} +(-14.1233 + 10.2612i) q^{46} +(128.690 + 177.126i) q^{47} +(-74.2950 + 24.1399i) q^{48} -705.645 q^{49} +223.169 q^{51} +(-37.9349 + 12.3258i) q^{52} +(190.894 + 262.743i) q^{53} +(-238.278 + 173.119i) q^{54} +(-209.586 - 152.273i) q^{56} +572.091i q^{57} +(274.530 - 377.858i) q^{58} +(162.059 - 498.767i) q^{59} +(77.8088 + 239.471i) q^{61} +(-498.412 - 161.944i) q^{62} +(-97.3885 - 31.6435i) q^{63} +(-19.7771 - 60.8676i) q^{64} +(141.855 - 436.584i) q^{66} +(435.342 - 599.197i) q^{67} +182.836i q^{68} +(34.4778 + 25.0496i) q^{69} +(306.683 - 222.818i) q^{71} +(-14.8695 - 20.4661i) q^{72} +(349.928 - 113.698i) q^{73} -29.6690 q^{74} -468.697 q^{76} +(1447.83 - 470.430i) q^{77} +(57.2341 + 78.7759i) q^{78} +(741.749 - 538.912i) q^{79} +(512.611 + 372.433i) q^{81} +513.232i q^{82} +(258.354 - 355.593i) q^{83} +(-195.429 + 601.470i) q^{84} +(-50.3865 - 155.074i) q^{86} +(-1084.38 - 352.335i) q^{87} +(357.680 + 116.217i) q^{88} +(117.993 + 363.145i) q^{89} +(-99.7859 + 307.110i) q^{91} +(-20.5224 + 28.2466i) q^{92} +1279.34i q^{93} +(354.253 + 257.380i) q^{94} +(-126.398 + 91.8337i) q^{96} +(-395.195 - 543.939i) q^{97} +(-1342.22 + 436.113i) q^{98} +148.657 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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