LMFDB - Embedded newform 125.3.f.b.43.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [125,3,Mod(7,125)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("125.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(125, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([17])) N = Newforms(chi, 3, names="a")

Level:	$N$	$=$	$125 = 5^{3}$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	125.f (of order $20$ , degree $8$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,10,0,-6,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.40600330450$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			43.2
Character	$\chi$	$=$	125.43
Dual form			125.3.f.b.32.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.589367 + 0.0933465i) q^{2} +(0.107372 - 0.210730i) q^{3} +(-3.46559 + 1.12604i) q^{4} +(-0.0436108 + 0.134220i) q^{6} +(7.64532 - 7.64532i) q^{7} +(4.06409 - 2.07076i) q^{8} +(5.25719 + 7.23590i) q^{9} +(7.33868 + 5.33186i) q^{11} +(-0.134818 + 0.851210i) q^{12} +(13.4044 + 2.12306i) q^{13} +(-3.79223 + 5.21956i) q^{14} +(9.59007 - 6.96760i) q^{16} +(0.359196 + 0.704962i) q^{17} +(-3.77386 - 3.77386i) q^{18} +(-13.5696 - 4.40902i) q^{19} +(-0.790204 - 2.43200i) q^{21} +(-4.82288 - 2.45738i) q^{22} +(-2.14764 - 13.5597i) q^{23} -1.07877i q^{24} -8.09832 q^{26} +(4.19167 - 0.663895i) q^{27} +(-17.8866 + 35.1044i) q^{28} +(36.6306 - 11.9020i) q^{29} +(-2.87530 + 8.84925i) q^{31} +(-17.9028 + 17.9028i) q^{32} +(1.91156 - 0.973987i) q^{33} +(-0.277504 - 0.381951i) q^{34} +(-26.3671 - 19.1568i) q^{36} +(-1.44735 + 9.13820i) q^{37} +(8.40902 + 1.33186i) q^{38} +(1.88666 - 2.59677i) q^{39} +(-33.7351 + 24.5100i) q^{41} +(0.692738 + 1.35958i) q^{42} +(-49.4021 - 49.4021i) q^{43} +(-31.4367 - 10.2144i) q^{44} +(2.53150 + 7.79114i) q^{46} +(18.9415 + 9.65116i) q^{47} +(-0.438574 - 2.76905i) q^{48} -67.9017i q^{49} +0.187125 q^{51} +(-48.8449 + 7.73627i) q^{52} +(-28.9788 + 56.8742i) q^{53} +(-2.40846 + 0.782556i) q^{54} +(15.2397 - 46.9029i) q^{56} +(-2.38611 + 2.38611i) q^{57} +(-20.4778 + 10.4340i) q^{58} +(45.6440 + 62.8235i) q^{59} +(11.4153 + 8.29369i) q^{61} +(0.868557 - 5.48385i) q^{62} +(95.5136 + 15.1279i) q^{63} +(-18.9902 + 26.1378i) q^{64} +(-1.03569 + 0.752473i) q^{66} +(-23.8956 - 46.8978i) q^{67} +(-2.03864 - 2.03864i) q^{68} +(-3.08803 - 1.00336i) q^{69} +(-0.846117 - 2.60408i) q^{71} +(36.3495 + 18.5210i) q^{72} +(-9.62940 - 60.7976i) q^{73} -5.52086i q^{74} +51.9912 q^{76} +(96.8703 - 15.3427i) q^{77} +(-0.869536 + 1.70656i) q^{78} +(6.18905 - 2.01094i) q^{79} +(-24.5646 + 75.6022i) q^{81} +(17.5944 - 17.5944i) q^{82} +(100.013 - 50.9593i) q^{83} +(5.47704 + 7.53850i) q^{84} +(33.7274 + 24.5044i) q^{86} +(1.42500 - 8.99712i) q^{87} +(40.8661 + 6.47255i) q^{88} +(-65.5853 + 90.2704i) q^{89} +(118.713 - 86.2498i) q^{91} +(22.7115 + 44.5739i) q^{92} +(1.55608 + 1.55608i) q^{93} +(-12.0644 - 3.91995i) q^{94} +(1.85040 + 5.69493i) q^{96} +(-115.019 - 58.6053i) q^{97} +(6.33839 + 40.0190i) q^{98} +81.1325i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + 10 q^{4} - 6 q^{6} + 10 q^{7} - 30 q^{8} + 10 q^{9} - 6 q^{11} - 80 q^{12} + 10 q^{14} + 2 q^{16} - 140 q^{18} - 90 q^{19} - 6 q^{21} + 150 q^{22} + 160 q^{23} + 4 q^{26} - 210 q^{27} - 160 q^{28}+ \cdots - 170 q^{98}+O(q^{100})$ 32 * q + 10 * q^4 - 6 * q^6 + 10 * q^7 - 30 * q^8 + 10 * q^9 - 6 * q^11 - 80 * q^12 + 10 * q^14 + 2 * q^16 - 140 * q^18 - 90 * q^19 - 6 * q^21 + 150 * q^22 + 160 * q^23 + 4 * q^26 - 210 * q^27 - 160 * q^28 + 110 * q^29 - 6 * q^31 + 290 * q^32 - 50 * q^33 + 260 * q^34 - 58 * q^36 - 150 * q^37 + 630 * q^38 - 390 * q^39 - 86 * q^41 + 120 * q^42 - 230 * q^43 - 340 * q^44 - 6 * q^46 + 150 * q^47 + 400 * q^48 - 16 * q^51 - 700 * q^52 - 10 * q^53 + 660 * q^54 - 70 * q^56 + 650 * q^57 - 120 * q^58 + 260 * q^59 + 114 * q^61 - 120 * q^62 - 40 * q^63 - 340 * q^64 + 138 * q^66 - 330 * q^67 - 710 * q^68 - 340 * q^69 - 66 * q^71 + 290 * q^72 + 320 * q^73 - 80 * q^76 + 210 * q^77 - 590 * q^78 + 210 * q^79 + 62 * q^81 - 30 * q^82 - 30 * q^83 + 10 * q^84 - 6 * q^86 - 200 * q^87 + 30 * q^88 + 10 * q^89 - 6 * q^91 - 270 * q^92 - 520 * q^93 - 790 * q^94 + 174 * q^96 + 90 * q^97 - 170 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$ .

$n$	$2$
$\chi(n)$	$e\left(\frac{19}{20}\right)$

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

)

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

$2$	−0.589367	+	0.0933465i	−0.294683	+	0.0466733i	−0.302026	−	0.953300i	$-0.597663\pi$
$2$	−0.589367	+	0.0933465i	−0.294683	+	0.0466733i	0.00734232	+	0.999973i	$0.497663\pi$
$3$	0.107372	−	0.210730i	0.0357908	−	0.0702435i	−0.872419	−	0.488759i	$-0.837450\pi$
$3$	0.107372	−	0.210730i	0.0357908	−	0.0702435i	0.908209	+	0.418516i	$0.137450\pi$
$4$	−3.46559	+	1.12604i	−0.866397	+	0.281509i
$5$		0			0
$5$		0			0
$6$	−0.0436108	+	0.134220i	−0.00726847	+	0.0223701i
$7$	7.64532	−	7.64532i	1.09219	−	1.09219i	0.0968934	−	0.995295i	$-0.469109\pi$
$7$	7.64532	−	7.64532i	1.09219	−	1.09219i	0.995295	−	0.0968934i	$-0.0308906\pi$
$8$	4.06409	−	2.07076i	0.508011	−	0.258845i
$9$	5.25719	+	7.23590i	0.584132	+	0.803989i
$10$		0			0
$11$	7.33868	+	5.33186i	0.667152	+	0.484715i	0.869071	−	0.494688i	$-0.164718\pi$
$11$	7.33868	+	5.33186i	0.667152	+	0.484715i	−0.201918	+	0.979402i	$0.564718\pi$
$12$	−0.134818	+	0.851210i	−0.0112349	+	0.0709342i
$13$	13.4044	+	2.12306i	1.03111	+	0.163312i	0.648987	−	0.760799i	$-0.275193\pi$
$13$	13.4044	+	2.12306i	1.03111	+	0.163312i	0.382124	+	0.924111i	$0.375193\pi$
$14$	−3.79223	+	5.21956i	−0.270874	+	0.372826i
$15$		0			0
$16$	9.59007	−	6.96760i	0.599380	−	0.435475i
$17$	0.359196	+	0.704962i	0.0211292	+	0.0414683i	0.901330	−	0.433133i	$-0.142592\pi$
$17$	0.359196	+	0.704962i	0.0211292	+	0.0414683i	−0.880201	+	0.474602i	$0.842592\pi$
$18$	−3.77386	−	3.77386i	−0.209659	−	0.209659i
$19$	−13.5696	−	4.40902i	−0.714187	−	0.232054i	−0.0706862	−	0.997499i	$-0.522519\pi$
$19$	−13.5696	−	4.40902i	−0.714187	−	0.232054i	−0.643501	+	0.765445i	$0.722519\pi$
$20$		0			0
$21$	−0.790204	−	2.43200i	−0.0376288	−	0.115809i
$22$	−4.82288	−	2.45738i	−0.219222	−	0.111699i
$23$	−2.14764	−	13.5597i	−0.0933757	−	0.589551i	−0.989363	−	0.145470i	$-0.953530\pi$
$23$	−2.14764	−	13.5597i	−0.0933757	−	0.589551i	0.895987	−	0.444080i	$-0.146470\pi$
$24$		−	1.07877i		−	0.0449488i
$25$		0			0
$26$	−8.09832			−0.311474
$27$	4.19167	−	0.663895i	0.155247	−	0.0245887i
$28$	−17.8866	+	35.1044i	−0.638807	+	1.25373i
$29$	36.6306	−	11.9020i	1.26312	−	0.410413i	0.400517	−	0.916289i	$-0.368831\pi$
$29$	36.6306	−	11.9020i	1.26312	−	0.410413i	0.862606	+	0.505876i	$0.168831\pi$
$30$		0			0
$31$	−2.87530	+	8.84925i	−0.0927515	+	0.285460i	−0.986661	−	0.162787i	$-0.947952\pi$
$31$	−2.87530	+	8.84925i	−0.0927515	+	0.285460i	0.893910	+	0.448247i	$0.147952\pi$
$32$	−17.9028	+	17.9028i	−0.559462	+	0.559462i
$33$	1.91156	−	0.973987i	0.0579260	−	0.0295148i
$34$	−0.277504	−	0.381951i	−0.00816188	−	0.0112339i
$35$		0			0
$36$	−26.3671	−	19.1568i	−0.732420	−	0.532135i
$37$	−1.44735	+	9.13820i	−0.0391175	+	0.246978i	−0.999497	−	0.0317178i	$-0.989902\pi$
$37$	−1.44735	+	9.13820i	−0.0391175	+	0.246978i	0.960379	+	0.278696i	$0.0899022\pi$
$38$	8.40902	+	1.33186i	0.221290	+	0.0350489i
$39$	1.88666	−	2.59677i	0.0483759	−	0.0665838i
$40$		0			0
$41$	−33.7351	+	24.5100i	−0.822807	+	0.597805i	−0.917515	−	0.397701i	$-0.869808\pi$
$41$	−33.7351	+	24.5100i	−0.822807	+	0.597805i	0.0947079	+	0.995505i	$0.469808\pi$
$42$	0.692738	+	1.35958i	0.0164938	+	0.0323708i
$43$	−49.4021	−	49.4021i	−1.14889	−	1.14889i	−0.986772	−	0.162113i	$-0.948169\pi$
$43$	−49.4021	−	49.4021i	−1.14889	−	1.14889i	−0.162113	−	0.986772i	$-0.551831\pi$
$44$	−31.4367	−	10.2144i	−0.714470	−	0.232145i
$45$		0			0
$46$	2.53150	+	7.79114i	0.0550325	+	0.169373i
$47$	18.9415	+	9.65116i	0.403010	+	0.205344i	0.643733	−	0.765250i	$-0.277385\pi$
$47$	18.9415	+	9.65116i	0.403010	+	0.205344i	−0.240723	+	0.970594i	$0.577385\pi$
$48$	−0.438574	−	2.76905i	−0.00913696	−	0.0576885i
$49$		−	67.9017i		−	1.38575i
$50$		0			0
$51$	0.187125			0.00366911
$52$	−48.8449	+	7.73627i	−0.939325	+	0.148775i
$53$	−28.9788	+	56.8742i	−0.546771	+	1.07310i	0.437957	+	0.898996i	$0.355702\pi$
$53$	−28.9788	+	56.8742i	−0.546771	+	1.07310i	−0.984728	+	0.174102i	$0.944298\pi$
$54$	−2.40846	+	0.782556i	−0.0446011	+	0.0144918i
$55$		0			0
$56$	15.2397	−	46.9029i	0.272137	−	0.837551i
$57$	−2.38611	+	2.38611i	−0.0418616	+	0.0418616i
$58$	−20.4778	+	10.4340i	−0.353066	+	0.179896i
$59$	45.6440	+	62.8235i	0.773627	+	1.06481i	0.995957	+	0.0898343i	$0.0286338\pi$
$59$	45.6440	+	62.8235i	0.773627	+	1.06481i	−0.222330	+	0.974971i	$0.571366\pi$
$60$		0			0
$61$	11.4153	+	8.29369i	0.187136	+	0.135962i	0.677409	−	0.735607i	$-0.263103\pi$
$61$	11.4153	+	8.29369i	0.187136	+	0.135962i	−0.490273	+	0.871569i	$0.663103\pi$
$62$	0.868557	−	5.48385i	0.0140090	−	0.0884492i
$63$	95.5136	+	15.1279i	1.51609	+	0.240125i
$64$	−18.9902	+	26.1378i	−0.296722	+	0.408403i
$65$		0			0
$66$	−1.03569	+	0.752473i	−0.0156923	+	0.0114011i
$67$	−23.8956	−	46.8978i	−0.356651	−	0.699968i	0.641067	−	0.767485i	$-0.278492\pi$
$67$	−23.8956	−	46.8978i	−0.356651	−	0.699968i	−0.997718	+	0.0675175i	$0.978492\pi$
$68$	−2.03864	−	2.03864i	−0.0299800	−	0.0299800i
$69$	−3.08803	−	1.00336i	−0.0447541	−	0.0145415i
$70$		0			0
$71$	−0.846117	−	2.60408i	−0.0119171	−	0.0366772i	0.944921	−	0.327298i	$-0.106138\pi$
$71$	−0.846117	−	2.60408i	−0.0119171	−	0.0366772i	−0.956838	+	0.290621i	$0.906138\pi$
$72$	36.3495	+	18.5210i	0.504854	+	0.257236i
$73$	−9.62940	−	60.7976i	−0.131910	−	0.832844i	−0.961567	−	0.274571i	$-0.911464\pi$
$73$	−9.62940	−	60.7976i	−0.131910	−	0.832844i	0.829657	−	0.558273i	$-0.188536\pi$
$74$		−	5.52086i		−	0.0746062i
$75$		0			0
$76$	51.9912			0.684095
$77$	96.8703	−	15.3427i	1.25806	−	0.199256i
$78$	−0.869536	+	1.70656i	−0.0111479	+	0.0218790i
$79$	6.18905	−	2.01094i	0.0783423	−	0.0254550i	−0.269584	−	0.962977i	$-0.586886\pi$
$79$	6.18905	−	2.01094i	0.0783423	−	0.0254550i	0.347926	+	0.937522i	$0.386886\pi$
$80$		0			0
$81$	−24.5646	+	75.6022i	−0.303267	+	0.933360i
$82$	17.5944	−	17.5944i	0.214566	−	0.214566i
$83$	100.013	−	50.9593i	1.20498	−	0.613967i	0.268021	−	0.963413i	$-0.413630\pi$
$83$	100.013	−	50.9593i	1.20498	−	0.613967i	0.936957	+	0.349446i	$0.113630\pi$
$84$	5.47704	+	7.53850i	0.0652029	+	0.0897440i
$85$		0			0
$86$	33.7274	+	24.5044i	0.392180	+	0.284935i
$87$	1.42500	−	8.99712i	0.0163794	−	0.103415i
$88$	40.8661	+	6.47255i	0.464387	+	0.0735517i
$89$	−65.5853	+	90.2704i	−0.736914	+	1.01427i	0.261877	+	0.965101i	$0.415659\pi$
$89$	−65.5853	+	90.2704i	−0.736914	+	1.01427i	−0.998790	+	0.0491732i	$0.984341\pi$
$90$		0			0
$91$	118.713	−	86.2498i	1.30454	−	0.947800i
$92$	22.7115	+	44.5739i	0.246864	+	0.484499i
$93$	1.55608	+	1.55608i	0.0167320	+	0.0167320i
$94$	−12.0644	−	3.91995i	−0.128344	−	0.0417016i
$95$		0			0
$96$	1.85040	+	5.69493i	0.0192749	+	0.0593222i
$97$	−115.019	−	58.6053i	−1.18577	−	0.604178i	−0.253989	−	0.967207i	$-0.581743\pi$
$97$	−115.019	−	58.6053i	−1.18577	−	0.604178i	−0.931778	+	0.363029i	$0.881743\pi$
$98$	6.33839	+	40.0190i	0.0646775	+	0.408357i
$99$			81.1325i			0.819521i
$100$		0			0
$101$	−32.5145			−0.321926			−0.160963	−	0.986960i	$-0.551460\pi$
$101$	−32.5145			−0.321926			−0.160963	+	0.986960i	$0.551460\pi$
$102$	−0.110285	+	0.0174674i	−0.00108123	+	0.000171249i
$103$	−23.5856	+	46.2893i	−0.228986	+	0.449411i	−0.976700	−	0.214611i	$-0.931152\pi$
$103$	−23.5856	+	46.2893i	−0.228986	+	0.449411i	0.747713	+	0.664022i	$0.231152\pi$
$104$	58.8732	−	19.1291i	0.566089	−	0.183933i
$105$		0			0
$106$	11.7702	−	36.2248i	0.111039	−	0.341744i
$107$	34.7993	−	34.7993i	0.325227	−	0.325227i	−0.525541	−	0.850768i	$-0.676137\pi$
$107$	34.7993	−	34.7993i	0.325227	−	0.325227i	0.850768	+	0.525541i	$0.176137\pi$
$108$	−13.7790	+	7.02076i	−0.127584	+	0.0650071i
$109$	−76.0086	−	104.617i	−0.697326	−	0.959787i	−0.999978	−	0.00668585i	$-0.997872\pi$
$109$	−76.0086	−	104.617i	−0.697326	−	0.959787i	0.302651	−	0.953101i	$-0.402128\pi$
$110$		0			0
$111$	1.77029	+	1.28619i	0.0159486	+	0.0115873i
$112$	20.0497	−	126.589i	0.179015	−	1.13026i
$113$	−75.5905	−	11.9724i	−0.668942	−	0.105950i	−0.187279	−	0.982307i	$-0.559967\pi$
$113$	−75.5905	−	11.9724i	−0.668942	−	0.105950i	−0.481663	+	0.876357i	$0.659967\pi$
$114$	1.18356	−	1.62903i	0.0103821	−	0.0142897i
$115$		0			0
$116$	−113.544	+	82.4948i	−0.978830	+	0.711162i
$117$	55.1075	+	108.155i	0.471004	+	0.924398i
$118$	−32.7654	−	32.7654i	−0.277673	−	0.277673i
$119$	8.13582	+	2.64349i	0.0683682	+	0.0222142i
$120$		0			0
$121$	−11.9636	−	36.8202i	−0.0988729	−	0.304299i
$122$	−7.50197	−	3.82245i	−0.0614916	−	0.0313315i
$123$	1.54278	+	9.74071i	0.0125429	+	0.0791928i
$124$		−	33.9055i		−	0.273432i
$125$		0			0
$126$	−57.7047			−0.457974
$127$	−60.5024	+	9.58264i	−0.476397	+	0.0754539i	−0.390016	−	0.920808i	$-0.627530\pi$
$127$	−60.5024	+	9.58264i	−0.476397	+	0.0754539i	−0.0863815	+	0.996262i	$0.527530\pi$
$128$	54.7295	−	107.413i	0.427575	−	0.839162i
$129$	−15.7149	+	5.10609i	−0.121821	+	0.0395821i
$130$		0			0
$131$	−1.09573	+	3.37230i	−0.00836432	+	0.0257427i	−0.955152	−	0.296117i	$-0.904308\pi$
$131$	−1.09573	+	3.37230i	−0.00836432	+	0.0257427i	0.946787	+	0.321860i	$0.104308\pi$
$132$	−5.52792	+	5.52792i	−0.0418782	+	0.0418782i
$133$	−137.452	+	70.0353i	−1.03347	+	0.526581i
$134$	18.4610	+	25.4094i	0.137769	+	0.189623i
$135$		0			0
$136$	2.91961	+	2.12122i	0.0214677	+	0.0155972i
$137$	−39.0615	+	246.624i	−0.285120	+	1.80018i	0.264094	+	0.964497i	$0.414927\pi$
$137$	−39.0615	+	246.624i	−0.285120	+	1.80018i	−0.549214	+	0.835682i	$0.685073\pi$
$138$	1.91364	+	0.303091i	0.0138670	+	0.00219631i
$139$	81.3839	−	112.015i	0.585496	−	0.805866i	−0.408789	−	0.912629i	$-0.634049\pi$
$139$	81.3839	−	112.015i	0.585496	−	0.805866i	0.994284	+	0.106763i	$0.0340487\pi$
$140$		0			0
$141$	4.06758	−	2.95527i	0.0288481	−	0.0209594i
$142$	0.741755	+	1.45578i	0.00522363	+	0.0102519i
$143$	87.0511	+	87.0511i	0.608749	+	0.608749i
$144$	100.834	+	32.7628i	0.700234	+	0.227520i
$145$		0			0
$146$	11.3505	+	34.9332i	0.0777431	+	0.239269i
$147$	−14.3090	−	7.29078i	−0.0973399	−	0.0495971i
$148$	−5.27404	−	33.2990i	−0.0356354	−	0.224993i
$149$		−	103.072i		−	0.691761i	−0.938279	−	0.345880i	$-0.887580\pi$
$149$		−	103.072i		−	0.691761i	0.938279	−	0.345880i	$-0.112420\pi$
$150$		0			0
$151$	−47.0940			−0.311880			−0.155940	−	0.987766i	$-0.549841\pi$
$151$	−47.0940			−0.311880			−0.155940	+	0.987766i	$0.549841\pi$
$152$	−64.2780	+	10.1806i	−0.422881	+	0.0669778i
$153$	−3.21267	+	6.30522i	−0.0209978	+	0.0412106i
$154$	−55.6599	+	18.0850i	−0.361428	+	0.117435i
$155$		0			0
$156$	−3.61433	+	11.1238i	−0.0231688	+	0.0713062i
$157$	−94.7590	+	94.7590i	−0.603561	+	0.603561i	−0.941256	−	0.337695i	$-0.890353\pi$
$157$	−94.7590	+	94.7590i	−0.603561	+	0.603561i	0.337695	+	0.941256i	$0.390353\pi$
$158$	−3.45990	+	1.76291i	−0.0218981	+	0.0111577i
$159$	8.87359	+	12.2134i	0.0558087	+	0.0768141i
$160$		0			0
$161$	−120.087	−	87.2486i	−0.745884	−	0.541917i
$162$	7.42038	−	46.8504i	0.0458048	−	0.289200i
$163$	−261.240	−	41.3763i	−1.60270	−	0.253842i	−0.709901	−	0.704302i	$-0.751260\pi$
$163$	−261.240	−	41.3763i	−1.60270	−	0.253842i	−0.892797	+	0.450459i	$0.851260\pi$
$164$	89.3128	−	122.928i	0.544590	−	0.749564i
$165$		0			0
$166$	−54.1876	+	39.3696i	−0.326431	+	0.237166i
$167$	−122.270	−	239.969i	−0.732158	−	1.43694i	−0.893044	−	0.449969i	$-0.851435\pi$
$167$	−122.270	−	239.969i	−0.732158	−	1.43694i	0.160886	−	0.986973i	$-0.448565\pi$
$168$	−8.24754	−	8.24754i	−0.0490925	−	0.0490925i
$169$	14.4433	+	4.69292i	0.0854634	+	0.0277687i
$170$		0			0
$171$	−39.4345	−	121.367i	−0.230611	−	0.709749i
$172$	226.836	+	115.579i	1.31881	+	0.671968i
$173$	29.1468	+	184.026i	0.168479	+	1.06373i	0.916493	+	0.400050i	$0.131007\pi$
$173$	29.1468	+	184.026i	0.168479	+	1.06373i	−0.748014	+	0.663682i	$0.768993\pi$
$174$			5.43562i			0.0312392i
$175$		0			0
$176$	107.529			0.610959
$177$	18.1397	−	2.87305i	0.102484	−	0.0162319i
$178$	30.2274	−	59.3246i	0.169817	−	0.333284i
$179$	−194.558	+	63.2157i	−1.08692	+	0.353161i	−0.797054	−	0.603908i	$-0.793609\pi$
$179$	−194.558	+	63.2157i	−1.08692	+	0.353161i	−0.289862	+	0.957068i	$0.593609\pi$
$180$		0			0
$181$	8.53397	−	26.2649i	0.0471490	−	0.145110i	−0.924710	−	0.380671i	$-0.875693\pi$
$181$	8.53397	−	26.2649i	0.0471490	−	0.145110i	0.971859	+	0.235562i	$0.0756929\pi$
$182$	−61.9142	+	61.9142i	−0.340188	+	0.340188i
$183$	2.97342	−	1.51503i	0.0162482	−	0.00827887i
$184$	−36.8070	−	50.6605i	−0.200038	−	0.275329i
$185$		0			0
$186$	−1.06236	−	0.771846i	−0.00571159	−	0.00414971i
$187$	−1.12273	+	7.08867i	−0.00600393	+	0.0379073i
$188$	−76.5108	−	12.1181i	−0.406973	−	0.0644581i
$189$	26.9710	−	37.1223i	0.142703	−	0.196414i
$190$		0			0
$191$	75.2465	−	54.6697i	0.393960	−	0.286229i	−0.373116	−	0.927785i	$-0.621711\pi$
$191$	75.2465	−	54.6697i	0.393960	−	0.286229i	0.767076	+	0.641556i	$0.221711\pi$
$192$	3.46900	+	6.80830i	0.0180677	+	0.0354599i
$193$	172.622	+	172.622i	0.894415	+	0.894415i	0.994935	−	0.100520i	$-0.0320505\pi$
$193$	172.622	+	172.622i	0.894415	+	0.894415i	−0.100520	+	0.994935i	$0.532051\pi$
$194$	73.2592	+	23.8034i	0.377625	+	0.122698i
$195$		0			0
$196$	76.4599	+	235.319i	0.390101	+	1.20061i
$197$	−38.6524	−	19.6944i	−0.196205	−	0.0999715i	0.353128	−	0.935575i	$-0.385118\pi$
$197$	−38.6524	−	19.6944i	−0.196205	−	0.0999715i	−0.549333	+	0.835604i	$0.685118\pi$
$198$	−7.57344	−	47.8168i	−0.0382497	−	0.241499i
$199$			331.210i			1.66437i	0.554496	+	0.832186i	$0.312911\pi$
$199$			331.210i			1.66437i	−0.554496	+	0.832186i	$0.687089\pi$
$200$		0			0
$201$	−12.4485			−0.0619330
$202$	19.1630	−	3.03512i	0.0948663	−	0.0150253i
$203$	189.058	−	371.047i	0.931319	−	1.82782i
$204$	−0.648496	+	0.210709i	−0.00317890	+	0.00103289i
$205$		0			0
$206$	9.57961	−	29.4830i	0.0465030	−	0.143121i
$207$	86.8259	−	86.8259i	0.419449	−	0.419449i
$208$	143.342	−	73.0365i	0.689145	−	0.351137i
$209$	−76.0744	−	104.707i	−0.363992	−	0.500992i
$210$		0			0
$211$	203.359	+	147.749i	0.963785	+	0.700231i	0.954027	−	0.299722i	$-0.0968939\pi$
$211$	203.359	+	147.749i	0.963785	+	0.700231i	0.00975810	+	0.999952i	$0.496894\pi$
$212$	36.3862	−	229.734i	0.171633	−	1.08365i
$213$	−0.639609	−	0.101304i	−0.00300286	−	0.000475606i
$214$	−17.2612	+	23.7580i	−0.0806597	+	0.111019i
$215$		0			0
$216$	15.6606	−	11.3781i	0.0725026	−	0.0526762i
$217$	45.6728	+	89.6379i	0.210474	+	0.413078i
$218$	54.5625	+	54.5625i	0.250287	+	0.250287i
$219$	−13.8458	−	4.49879i	−0.0632230	−	0.0205424i
$220$		0			0
$221$	3.31815	+	10.2122i	0.0150143	+	0.0462091i
$222$	−1.16341	−	0.592788i	−0.00524060	−	0.00267022i
$223$	11.8468	+	74.7975i	0.0531245	+	0.335415i	0.999908	+	0.0135446i	$0.00431151\pi$
$223$	11.8468	+	74.7975i	0.0531245	+	0.335415i	−0.946784	+	0.321870i	$0.895688\pi$
$224$			273.745i			1.22208i
$225$		0			0
$226$	45.6681			0.202071
$227$	338.965	−	53.6868i	1.49324	−	0.236506i	0.644208	−	0.764850i	$-0.277187\pi$
$227$	338.965	−	53.6868i	1.49324	−	0.236506i	0.849030	+	0.528345i	$0.177187\pi$
$228$	5.58243	−	10.9561i	0.0244843	−	0.0480532i
$229$	−22.2341	+	7.22430i	−0.0970921	+	0.0315471i	−0.357160	−	0.934043i	$-0.616255\pi$
$229$	−22.2341	+	7.22430i	−0.0970921	+	0.0315471i	0.260068	+	0.965590i	$0.416255\pi$
$230$		0			0
$231$	7.16802	−	22.0609i	0.0310304	−	0.0955017i
$232$	124.224	−	124.224i	0.535447	−	0.535447i
$233$	−170.566	+	86.9078i	−0.732044	+	0.372995i	−0.779937	−	0.625858i	$-0.784749\pi$
$233$	−170.566	+	86.9078i	−0.732044	+	0.372995i	0.0478936	+	0.998852i	$0.484749\pi$
$234$	−42.5744	−	58.5986i	−0.181942	−	0.250421i
$235$		0			0
$236$	−228.925	−	166.324i	−0.970020	−	0.704761i
$237$	0.240767	−	1.52014i	0.00101589	−	0.00641409i
$238$	−5.04174	−	0.798534i	−0.0211838	−	0.00335518i
$239$	−32.3070	+	44.4668i	−0.135176	+	0.186054i	−0.871239	−	0.490860i	$-0.836683\pi$
$239$	−32.3070	+	44.4668i	−0.135176	+	0.186054i	0.736063	+	0.676913i	$0.236683\pi$
$240$		0			0
$241$	−27.3775	+	19.8909i	−0.113600	+	0.0825349i	−0.643135	−	0.765753i	$-0.722366\pi$
$241$	−27.3775	+	19.8909i	−0.113600	+	0.0825349i	0.529535	+	0.848288i	$0.322366\pi$
$242$	10.4880	+	20.5839i	0.0433388	+	0.0850573i
$243$	40.3022	+	40.3022i	0.165853	+	0.165853i
$244$	−48.8996	−	15.8885i	−0.200408	−	0.0651166i
$245$		0			0
$246$	−1.81852	−	5.59684i	−0.00739237	−	0.0227514i
$247$	−172.532	−	87.9094i	−0.698510	−	0.355908i
$248$	6.63919	+	41.9182i	0.0267709	+	0.169025i
$249$		−	26.5474i		−	0.106616i
$250$		0			0
$251$	221.852			0.883872			0.441936	−	0.897046i	$-0.354292\pi$
$251$	221.852			0.883872			0.441936	+	0.897046i	$0.354292\pi$
$252$	−348.045	+	55.1250i	−1.38113	+	0.218750i
$253$	56.5374	−	110.961i	0.223468	−	0.438581i
$254$	34.7636	−	11.2954i	0.136865	−	0.0444700i
$255$		0			0
$256$	17.7059	−	54.4930i	0.0691635	−	0.212863i
$257$	20.3380	−	20.3380i	0.0791363	−	0.0791363i	−0.666431	−	0.745567i	$-0.732179\pi$
$257$	20.3380	−	20.3380i	0.0791363	−	0.0791363i	0.745567	+	0.666431i	$0.232179\pi$
$258$	8.78523	−	4.47630i	0.0340513	−	0.0173500i
$259$	58.7990	+	80.9299i	0.227023	+	0.312471i
$260$		0			0
$261$	278.695	+	202.484i	1.06780	+	0.775801i
$262$	0.330992	−	2.08980i	0.00126333	−	0.00797634i
$263$	5.35285	+	0.847808i	0.0203530	+	0.00322361i	0.166603	−	0.986024i	$-0.446720\pi$
$263$	5.35285	+	0.847808i	0.0203530	+	0.00322361i	−0.146250	+	0.989248i	$0.546720\pi$
$264$	5.75185	−	7.91675i	0.0217873	−	0.0299877i
$265$		0			0
$266$	74.4721	−	54.1071i	0.279970	−	0.203410i
$267$	11.9807	+	23.5134i	0.0448714	+	0.0880651i
$268$	135.621	+	135.621i	0.506049	+	0.506049i
$269$	59.0391	+	19.1830i	0.219476	+	0.0713122i	0.416691	−	0.909048i	$-0.363190\pi$
$269$	59.0391	+	19.1830i	0.219476	+	0.0713122i	−0.197215	+	0.980360i	$0.563190\pi$
$270$		0			0
$271$	−99.9539	−	307.626i	−0.368833	−	1.13515i	−0.947546	−	0.319621i	$-0.896444\pi$
$271$	−99.9539	−	307.626i	−0.368833	−	1.13515i	0.578712	−	0.815532i	$-0.303556\pi$
$272$	8.35660	+	4.25790i	0.0307228	+	0.0156540i
$273$	−5.42898	−	34.2772i	−0.0198864	−	0.125558i
$274$		−	148.999i		−	0.543790i
$275$		0			0
$276$	11.8317			0.0428684
$277$	−72.0614	+	11.4134i	−0.260150	+	0.0412036i	−0.285147	−	0.958484i	$-0.592042\pi$
$277$	−72.0614	+	11.4134i	−0.260150	+	0.0412036i	0.0249971	+	0.999688i	$0.492042\pi$
$278$	−37.5087	+	73.6150i	−0.134924	+	0.264802i
$279$	−79.1483	+	25.7168i	−0.283686	+	0.0921750i
$280$		0			0
$281$	−84.2374	+	259.256i	−0.299777	+	0.922619i	0.681798	+	0.731541i	$0.261199\pi$
$281$	−84.2374	+	259.256i	−0.299777	+	0.922619i	−0.981575	+	0.191079i	$0.938801\pi$
$282$	−2.12143	+	2.12143i	−0.00752282	+	0.00752282i
$283$	175.869	−	89.6096i	0.621445	−	0.316642i	−0.114768	−	0.993392i	$-0.536612\pi$
$283$	175.869	−	89.6096i	0.621445	−	0.316642i	0.736212	+	0.676750i	$0.236612\pi$
$284$	5.86459	+	8.07191i	0.0206499	+	0.0284222i
$285$		0			0
$286$	−59.4309	−	43.1791i	−0.207800	−	0.150976i
$287$	−70.5289	+	445.302i	−0.245745	+	1.55158i
$288$	−223.661	−	35.4245i	−0.776601	−	0.123002i
$289$	169.502	−	233.299i	0.586512	−	0.807265i
$290$		0			0
$291$	−24.6998	+	17.9455i	−0.0848792	+	0.0616683i
$292$	101.832	+	199.856i	0.348739	+	0.684440i
$293$	−237.228	−	237.228i	−0.809652	−	0.809652i	0.174929	−	0.984581i	$-0.444030\pi$
$293$	−237.228	−	237.228i	−0.809652	−	0.809652i	−0.984581	+	0.174929i	$0.944030\pi$
$294$	9.11379	+	2.96125i	0.0309993	+	0.0100723i
$295$		0			0
$296$	13.0408	+	40.1356i	0.0440569	+	0.135593i
$297$	34.3011	+	17.4773i	0.115492	+	0.0588461i
$298$	9.62145	+	60.7474i	0.0322867	+	0.203850i
$299$		−	186.319i		−	0.623142i
$300$		0			0
$301$	−755.389			−2.50960
$302$	27.7556	−	4.39606i	0.0919060	−	0.0145565i
$303$	−3.49117	+	6.85180i	−0.0115220	+	0.0226132i
$304$	−160.853	+	52.2644i	−0.529123	+	0.171922i
$305$		0			0
$306$	1.30487	−	4.01598i	0.00426428	−	0.0131241i
$307$	79.0993	−	79.0993i	0.257653	−	0.257653i	−0.566446	−	0.824099i	$-0.691682\pi$
$307$	79.0993	−	79.0993i	0.257653	−	0.257653i	0.824099	+	0.566446i	$0.191682\pi$
$308$	−318.436	+	162.251i	−1.03388	+	0.526789i
$309$	7.22212	+	9.94040i	0.0233726	+	0.0321696i
$310$		0			0
$311$	−91.8901	−	66.7620i	−0.295466	−	0.214669i	0.430169	−	0.902748i	$-0.358454\pi$
$311$	−91.8901	−	66.7620i	−0.295466	−	0.214669i	−0.725635	+	0.688080i	$0.758454\pi$
$312$	2.29029	−	14.4603i	0.00734067	−	0.0463472i
$313$	101.510	+	16.0776i	0.324314	+	0.0513662i	0.316469	−	0.948603i	$-0.397503\pi$
$313$	101.510	+	16.0776i	0.324314	+	0.0513662i	0.00784510	+	0.999969i	$0.497503\pi$
$314$	47.0024	−	64.6933i	0.149689	−	0.206029i
$315$		0			0
$316$	−19.1843	+	13.9382i	−0.0607097	+	0.0441082i
$317$	−185.391	−	363.850i	−0.584829	−	1.14779i	−0.973984	−	0.226618i	$-0.927233\pi$
$317$	−185.391	−	363.850i	−0.584829	−	1.14779i	0.389155	−	0.921172i	$-0.372767\pi$
$318$	−6.36988	−	6.36988i	−0.0200311	−	0.0200311i
$319$	332.280	+	107.964i	1.04163	+	0.338446i
$320$		0			0
$321$	−3.59678	−	11.0698i	−0.0112049	−	0.0344852i
$322$	78.9199	+	40.2117i	0.245093	+	0.124881i
$323$	−1.76594	−	11.1497i	−0.00546731	−	0.0345193i
$324$		−	289.667i		−	0.894033i
$325$		0			0
$326$	157.828			0.484136
$327$	−30.2072	+	4.78435i	−0.0923767	+	0.0146310i
$328$	−86.3483	+	169.468i	−0.263257	+	0.516671i
$329$	218.600	−	71.0273i	0.664437	−	0.215889i
$330$		0			0
$331$	−37.2677	+	114.698i	−0.112591	+	0.346520i	−0.991437	−	0.130586i	$-0.958314\pi$
$331$	−37.2677	+	114.698i	−0.112591	+	0.346520i	0.878846	+	0.477106i	$0.158314\pi$
$332$	−289.222	+	289.222i	−0.871151	+	0.871151i
$333$	−73.7321	+	37.5684i	−0.221418	+	0.112818i
$334$	94.4624	+	130.016i	0.282822	+	0.389271i
$335$		0			0
$336$	−24.5233	−	17.8172i	−0.0729860	−	0.0530274i
$337$	6.06219	−	38.2752i	0.0179887	−	0.113576i	−0.977060	−	0.212964i	$-0.931688\pi$
$337$	6.06219	−	38.2752i	0.0179887	−	0.113576i	0.995049	+	0.0993876i	$0.0316884\pi$
$338$	−8.95048	−	1.41762i	−0.0264807	−	0.00419413i
$339$	−10.6393	+	14.6437i	−0.0313843	+	0.0431968i
$340$		0			0
$341$	−68.2838	+	49.6111i	−0.200246	+	0.145487i
$342$	34.5706	+	67.8486i	0.101084	+	0.198388i
$343$	−144.510	−	144.510i	−0.421311	−	0.421311i
$344$	−303.074	−	98.4748i	−0.881030	−	0.286264i
$345$		0			0
$346$	−34.3563	−	105.738i	−0.0992958	−	0.305601i
$347$	−209.594	−	106.794i	−0.604018	−	0.307762i	0.125107	−	0.992143i	$-0.460073\pi$
$347$	−209.594	−	106.794i	−0.604018	−	0.307762i	−0.729125	+	0.684381i	$0.760073\pi$
$348$	5.19262	+	32.7849i	0.0149213	+	0.0942095i
$349$			16.9114i			0.0484568i	0.999706	+	0.0242284i	$0.00771289\pi$
$349$			16.9114i			0.0484568i	−0.999706	+	0.0242284i	$0.992287\pi$
$350$		0			0
$351$	57.5965			0.164093
$352$	−226.838	+	35.9276i	−0.644426	+	0.102067i
$353$	−228.805	+	449.055i	−0.648173	+	1.27211i	0.299873	+	0.953979i	$0.403056\pi$
$353$	−228.805	+	449.055i	−0.648173	+	1.27211i	−0.948046	+	0.318132i	$0.896944\pi$
$354$	−10.4228	+	3.38656i	−0.0294429	+	0.00956656i
$355$		0			0
$356$	125.644	−	386.692i	0.352932	−	1.08621i
$357$	1.43063	−	1.43063i	0.00400736	−	0.00400736i
$358$	108.765	−	55.4186i	0.303813	−	0.154800i
$359$	−198.037	−	272.575i	−0.551636	−	0.759262i	0.438597	−	0.898684i	$-0.355475\pi$
$359$	−198.037	−	272.575i	−0.551636	−	0.759262i	−0.990233	+	0.139422i	$0.955475\pi$
$360$		0			0
$361$	−127.362	−	92.5336i	−0.352802	−	0.256326i
$362$	−2.57791	+	16.2763i	−0.00712129	+	0.0449620i
$363$	−9.04370	−	1.43238i	−0.0249138	−	0.00394596i
$364$	−314.289	+	432.581i	−0.863430	+	1.18841i
$365$		0			0
$366$	−1.61101	+	1.17047i	−0.00440167	+	0.00319800i
$367$	212.435	+	416.928i	0.578843	+	1.13604i	0.975894	+	0.218247i	$0.0700339\pi$
$367$	212.435	+	416.928i	0.578843	+	1.13604i	−0.397050	+	0.917797i	$0.629966\pi$
$368$	−115.074	−	115.074i	−0.312702	−	0.312702i
$369$	−354.704	−	115.250i	−0.961256	−	0.312331i
$370$		0			0
$371$	213.269	+	656.374i	0.574848	+	1.76920i
$372$	−7.14493	−	3.64052i	−0.0192068	−	0.00978635i
$373$	−75.2117	−	474.868i	−0.201640	−	1.27310i	−0.856022	−	0.516940i	$-0.827071\pi$
$373$	−75.2117	−	474.868i	−0.201640	−	1.27310i	0.654382	−	0.756164i	$-0.272929\pi$
$374$		−	4.28263i		−	0.0114509i
$375$		0			0
$376$	96.9651			0.257886
$377$	516.281	−	81.7709i	1.36945	−	0.216899i
$378$	−12.4305	+	24.3963i	−0.0328850	+	0.0645405i
$379$	597.265	−	194.063i	1.57590	−	0.512040i	0.614901	−	0.788604i	$-0.289196\pi$
$379$	597.265	−	194.063i	1.57590	−	0.512040i	0.960995	+	0.276564i	$0.0891958\pi$
$380$		0			0
$381$	−4.47694	+	13.7786i	−0.0117505	+	0.0361643i
$382$	−39.2445	+	39.2445i	−0.102734	+	0.102734i
$383$	343.902	−	175.227i	0.897916	−	0.457511i	0.0568121	−	0.998385i	$-0.481906\pi$
$383$	343.902	−	175.227i	0.897916	−	0.457511i	0.841104	+	0.540874i	$0.181906\pi$
$384$	−16.7587	−	23.0664i	−0.0436424	−	0.0600686i
$385$		0			0
$386$	−117.851	−	85.6241i	−0.305315	−	0.221824i
$387$	97.7524	−	617.184i	0.252590	−	1.59479i
$388$	464.601	+	73.5856i	1.19743	+	0.189654i
$389$	−230.009	+	316.581i	−0.591284	+	0.813833i	−0.994876	−	0.101107i	$-0.967762\pi$
$389$	−230.009	+	316.581i	−0.591284	+	0.813833i	0.403592	+	0.914939i	$0.367762\pi$
$390$		0			0
$391$	8.78762	−	6.38458i	0.0224747	−	0.0163289i
$392$	−140.608	−	275.959i	−0.358694	−	0.703977i
$393$	0.592995	+	0.592995i	0.00150889	+	0.00150889i
$394$	24.6188	+	7.99915i	0.0624844	+	0.0203024i
$395$		0			0
$396$	−91.3583	−	281.172i	−0.230703	−	0.710030i
$397$	304.919	+	155.364i	0.768058	+	0.391345i	0.793687	−	0.608326i	$-0.208159\pi$
$397$	304.919	+	155.364i	0.768058	+	0.391345i	−0.0256288	+	0.999672i	$0.508159\pi$
$398$	−30.9173	−	195.204i	−0.0776817	−	0.490463i
$399$			36.4852i			0.0914415i
$400$		0			0
$401$	665.647			1.65997			0.829983	−	0.557788i	$-0.188350\pi$
$401$	665.647			1.65997			0.829983	+	0.557788i	$0.188350\pi$
$402$	7.33675	−	1.16203i	0.0182506	−	0.00289062i
$403$	−57.3292	+	112.515i	−0.142256	+	0.279193i
$404$	112.682	−	36.6126i	0.278916	−	0.0906252i
$405$		0			0
$406$	−76.7884	+	236.331i	−0.189134	+	0.582095i
$407$	−59.3452	+	59.3452i	−0.145811	+	0.145811i
$408$	0.760491	−	0.387490i	0.00186395	−	0.000949730i
$409$	369.812	+	509.003i	0.904187	+	1.24451i	0.969113	+	0.246616i	$0.0793187\pi$
$409$	369.812	+	509.003i	0.904187	+	1.24451i	−0.0649265	+	0.997890i	$0.520681\pi$
$410$		0			0
$411$	47.7771	+	34.7121i	0.116246	+	0.0844577i
$412$	29.6144	−	186.978i	0.0718796	−	0.453830i
$413$	829.269	+	131.343i	2.00791	+	0.318022i
$414$	−43.0674	+	59.2772i	−0.104028	+	0.143182i
$415$		0			0
$416$	−277.986	+	201.968i	−0.668235	+	0.485501i
$417$	−14.8666	−	29.1774i	−0.0356514	−	0.0699699i
$418$	54.6098	+	54.6098i	0.130645	+	0.130645i
$419$	111.166	+	36.1200i	0.265312	+	0.0862052i	0.438652	−	0.898657i	$-0.355456\pi$
$419$	111.166	+	36.1200i	0.265312	+	0.0862052i	−0.173340	+	0.984862i	$0.555456\pi$
$420$		0			0
$421$	1.06048	+	3.26382i	0.00251896	+	0.00775255i	0.952308	−	0.305138i	$-0.0987026\pi$
$421$	1.06048	+	3.26382i	0.00251896	+	0.00775255i	−0.949789	+	0.312891i	$0.898703\pi$
$422$	−133.645	−	68.0953i	−0.316693	−	0.161363i
$423$	29.7440	+	187.796i	0.0703169	+	0.443963i
$424$			291.150i			0.686675i
$425$		0			0
$426$	0.386421			0.000907090
$427$	150.681	−	23.8656i	0.352884	−	0.0558913i
$428$	−81.4147	+	159.785i	−0.190221	+	0.373330i
$429$	27.6912	−	8.99742i	0.0645482	−	0.0209730i
$430$		0			0
$431$	144.037	−	443.300i	0.334193	−	1.02854i	−0.632926	−	0.774212i	$-0.718146\pi$
$431$	144.037	−	443.300i	0.334193	−	1.02854i	0.967118	−	0.254327i	$-0.0818538\pi$
$432$	35.5727	−	35.5727i	0.0823441	−	0.0823441i
$433$	176.792	−	90.0802i	0.408296	−	0.208037i	−0.237765	−	0.971323i	$-0.576415\pi$
$433$	176.792	−	90.0802i	0.408296	−	0.208037i	0.646062	+	0.763285i	$0.276415\pi$
$434$	−35.2854	−	48.5662i	−0.0813028	−	0.111904i
$435$		0			0
$436$	381.217	+	276.970i	0.874350	+	0.635253i
$437$	−30.6423	+	193.468i	−0.0701196	+	0.442718i
$438$	8.58022	+	1.35897i	0.0195896	+	0.00310268i
$439$	−288.145	+	396.598i	−0.656367	+	0.903412i	−0.999354	−	0.0359283i	$-0.988561\pi$
$439$	−288.145	+	396.598i	−0.656367	+	0.903412i	0.342987	+	0.939340i	$0.388561\pi$
$440$		0			0
$441$	491.330	−	356.972i	1.11413	−	0.809461i
$442$	−2.90888	−	5.70900i	−0.00658118	−	0.0129163i
$443$	−241.629	−	241.629i	−0.545437	−	0.545437i	0.379681	−	0.925118i	$-0.376034\pi$
$443$	−241.629	−	241.629i	−0.545437	−	0.545437i	−0.925118	+	0.379681i	$0.876034\pi$
$444$	−7.58340	−	2.46399i	−0.0170797	−	0.00554954i
$445$		0			0
$446$	−13.9642	−	42.9773i	−0.0313098	−	0.0963617i
$447$	−21.7205	−	11.0671i	−0.0485917	−	0.0247587i
$448$	54.6455	+	345.018i	0.121977	+	0.770130i
$449$		−	344.192i		−	0.766575i	−0.923629	−	0.383288i	$-0.874792\pi$
$449$		−	344.192i		−	0.766575i	0.923629	−	0.383288i	$-0.125208\pi$
$450$		0			0
$451$	−378.255			−0.838703
$452$	275.447	−	43.6265i	0.609395	−	0.0965187i
$453$	−5.05660	+	9.92413i	−0.0111625	+	0.0219076i
$454$	−194.763	+	63.2824i	−0.428994	+	0.139389i
$455$		0			0
$456$	−4.75632	+	14.6384i	−0.0104305	+	0.0321018i
$457$	145.902	−	145.902i	0.319260	−	0.319260i	−0.529223	−	0.848483i	$-0.677516\pi$
$457$	145.902	−	145.902i	0.319260	−	0.319260i	0.848483	+	0.529223i	$0.177516\pi$
$458$	12.4297	−	6.33324i	0.0271390	−	0.0138280i
$459$	1.97365	+	2.71650i	0.00429989	+	0.00591829i
$460$		0			0
$461$	270.507	+	196.534i	0.586782	+	0.426322i	0.841163	−	0.540782i	$-0.181872\pi$
$461$	270.507	+	196.534i	0.586782	+	0.426322i	−0.254381	+	0.967104i	$0.581872\pi$
$462$	−2.16529	+	13.6711i	−0.00468676	+	0.0295911i
$463$	27.4152	+	4.34214i	0.0592120	+	0.00937827i	0.185970	−	0.982555i	$-0.440457\pi$
$463$	27.4152	+	4.34214i	0.0592120	+	0.00937827i	−0.126758	+	0.991934i	$0.540457\pi$
$464$	268.362	−	369.368i	0.578365	−	0.796052i
$465$		0			0
$466$	92.4135	−	67.1423i	0.198312	−	0.144082i
$467$	−186.062	−	365.168i	−0.398420	−	0.781943i	0.601436	−	0.798921i	$-0.294596\pi$
$467$	−186.062	−	365.168i	−0.398420	−	0.781943i	−0.999856	+	0.0169777i	$0.994596\pi$
$468$	−312.766	−	312.766i	−0.668303	−	0.668303i
$469$	−541.238	−	175.859i	−1.15403	−	0.374966i
$470$		0			0
$471$	9.79409	+	30.1431i	0.0207943	+	0.0639981i
$472$	315.594	+	160.803i	0.668631	+	0.340684i
$473$	−99.1408	−	625.951i	−0.209600	−	1.32336i
$474$			0.918395i			0.00193754i
$475$		0			0
$476$	−31.1721			−0.0654875
$477$	−563.883	+	89.3103i	−1.18215	+	0.187233i
$478$	14.8899	−	29.2230i	0.0311504	−	0.0611360i
$479$	−579.516	+	188.296i	−1.20985	+	0.393103i	−0.843374	−	0.537326i	$-0.819434\pi$
$479$	−579.516	+	188.296i	−1.20985	+	0.393103i	−0.366472	+	0.930429i	$0.619434\pi$
$480$		0			0
$481$	−38.8018	+	119.420i	−0.0806691	+	0.248274i
$482$	14.2786	−	14.2786i	0.0296237	−	0.0296237i
$483$	−31.2800	+	15.9380i	−0.0647619	+	0.0329978i
$484$	82.9219	+	114.132i	0.171326	+	0.235810i
$485$		0			0
$486$	−27.5149	−	19.9907i	−0.0566150	−	0.0411332i
$487$	−36.2960	+	229.164i	−0.0745298	+	0.470563i	0.921990	+	0.387213i	$0.126562\pi$
$487$	−36.2960	+	229.164i	−0.0745298	+	0.470563i	−0.996520	+	0.0833503i	$0.973438\pi$
$488$	63.5670	+	10.0680i	0.130260	+	0.0206312i
$489$	−36.7692	+	50.6085i	−0.0751927	+	0.103494i
$490$		0			0
$491$	−288.845	+	209.858i	−0.588279	+	0.427409i	−0.841699	−	0.539947i	$-0.818444\pi$
$491$	−288.845	+	209.858i	−0.588279	+	0.427409i	0.253421	+	0.967356i	$0.418444\pi$
$492$	−16.3150	−	32.0200i	−0.0331606	−	0.0650814i
$493$	21.5480	+	21.5480i	0.0437079	+	0.0437079i
$494$	109.891	+	35.7056i	0.222451	+	0.0722786i
$495$		0			0
$496$	34.0837	+	104.899i	0.0687171	+	0.211490i
$497$	−26.3779	−	13.4402i	−0.0530742	−	0.0270426i
$498$	2.47811	+	15.6462i	0.00497613	+	0.0314180i
$499$		−	752.086i		−	1.50719i	−0.657341	−	0.753593i	$-0.728319\pi$
$499$		−	752.086i		−	1.50719i	0.657341	−	0.753593i	$-0.271681\pi$
$500$		0			0
$501$	−63.6973			−0.127140
$502$	−130.752	+	20.7091i	−0.260463	+	0.0412532i
$503$	−371.326	+	728.768i	−0.738222	+	1.44884i	0.149644	+	0.988740i	$0.452187\pi$
$503$	−371.326	+	728.768i	−0.738222	+	1.44884i	−0.887866	+	0.460102i	$0.847813\pi$
$504$	419.502	−	136.305i	0.832346	−	0.270446i
$505$		0			0
$506$	−22.9635	+	70.6743i	−0.0453823	+	0.139672i
$507$	2.53975	−	2.53975i	0.00500938	−	0.00500938i
$508$	198.886	−	101.337i	0.391508	−	0.199483i
$509$	529.260	+	728.463i	1.03980	+	1.43117i	0.897327	+	0.441367i	$0.145506\pi$
$509$	529.260	+	728.463i	1.03980	+	1.43117i	0.142476	+	0.989798i	$0.454494\pi$
$510$		0			0
$511$	−538.437	−	391.197i	−1.05369	−	0.765552i
$512$	−80.7826	+	510.041i	−0.157778	+	0.996174i
$513$	−59.8062	−	9.47238i	−0.116581	−	0.0184647i
$514$	−10.0881	+	13.8850i	−0.0196266	+	0.0270137i
$515$		0			0
$516$	48.7118	−	35.3912i	0.0944028	−	0.0685876i
$517$	87.5466	+	171.820i	0.169336	+	0.332340i
$518$	−42.2087	−	42.2087i	−0.0814840	−	0.0814840i
$519$	41.9094	+	13.6172i	0.0807503	+	0.0262374i
$520$		0			0
$521$	−145.536	−	447.915i	−0.279340	−	0.859721i	−0.988038	−	0.154209i	$-0.950717\pi$
$521$	−145.536	−	447.915i	−0.279340	−	0.859721i	0.708698	−	0.705512i	$-0.249283\pi$
$522$	−183.155	−	93.3221i	−0.350872	−	0.178778i
$523$	92.2377	+	582.366i	0.176363	+	1.11351i	0.903995	+	0.427543i	$0.140621\pi$
$523$	92.2377	+	582.366i	0.176363	+	1.11351i	−0.727632	+	0.685967i	$0.759379\pi$
$524$		−	12.9208i		−	0.0246580i
$525$		0			0
$526$	−3.23393			−0.00614816
$527$	−7.27118	+	1.15164i	−0.0137973	+	0.00218528i
$528$	11.5456	−	22.6596i	0.0218667	−	0.0429158i
$529$	323.857	−	105.227i	0.612205	−	0.198918i
$530$		0			0
$531$	−214.626	+	660.550i	−0.404192	+	1.24397i
$532$	397.489	−	397.489i	0.747160	−	0.747160i
$533$	−504.236	+	256.921i	−0.946035	+	0.482029i
$534$	−9.25590	−	12.7397i	−0.0173331	−	0.0238570i
$535$		0			0
$536$	−194.228	−	141.115i	−0.362366	−	0.263274i
$537$	−7.56870	+	47.7869i	−0.0140944	+	0.0889887i
$538$	−36.5864	−	5.79471i	−0.0680044	−	0.0107708i
$539$	362.043	−	498.309i	0.671693	−	0.924506i
$540$		0			0
$541$	4.98311	−	3.62044i	0.00921092	−	0.00669212i	−0.583170	−	0.812350i	$-0.698188\pi$
$541$	4.98311	−	3.62044i	0.00921092	−	0.00669212i	0.592381	+	0.805658i	$0.298188\pi$
$542$	87.6253	+	171.974i	0.161670	+	0.317296i
$543$	−4.61849	−	4.61849i	−0.00850551	−	0.00850551i
$544$	−19.0514	−	6.19017i	−0.0350209	−	0.0113790i
$545$		0			0
$546$	6.39932	+	19.6951i	0.0117204	+	0.0360716i
$547$	−270.185	−	137.666i	−0.493940	−	0.251675i	0.189232	−	0.981932i	$-0.439400\pi$
$547$	−270.185	−	137.666i	−0.493940	−	0.251675i	−0.683172	+	0.730257i	$0.739400\pi$
$548$	−142.337	−	898.683i	−0.259740	−	1.63993i
$549$			126.201i			0.229875i
$550$		0			0
$551$	−549.537			−0.997344
$552$	−14.6278	+	2.31681i	−0.0264996	+	0.00419712i
$553$	31.9429	−	62.6915i	0.0577630	−	0.113366i
$554$	41.4052	−	13.4534i	0.0747387	−	0.0242841i
$555$		0			0
$556$	−155.910	+	479.840i	−0.280413	+	0.863022i
$557$	−39.2190	+	39.2190i	−0.0704112	+	0.0704112i	−0.741435	−	0.671024i	$-0.765855\pi$
$557$	−39.2190	+	39.2190i	−0.0704112	+	0.0704112i	0.671024	+	0.741435i	$0.265855\pi$
$558$	44.2468	−	22.5449i	0.0792953	−	0.0404030i
$559$	−557.324	−	767.091i	−0.997002	−	1.37226i
$560$		0			0
$561$	1.37325	+	0.997722i	0.00244786	+	0.00177847i
$562$	25.4461	−	160.660i	0.0452777	−	0.285872i
$563$	−588.334	−	93.1829i	−1.04500	−	0.165511i	−0.389746	−	0.920922i	$-0.627437\pi$
$563$	−588.334	−	93.1829i	−1.04500	−	0.165511i	−0.655251	+	0.755411i	$0.727437\pi$
$564$	−10.7688	+	14.8220i	−0.0190936	+	0.0262802i
$565$		0			0
$566$	−95.2865	+	69.2297i	−0.168351	+	0.122314i
$567$	390.198	+	765.807i	0.688180	+	1.35063i
$568$	−8.83112	−	8.83112i	−0.0155477	−	0.0155477i
$569$	−258.923	−	84.1291i	−0.455049	−	0.147854i	0.0725195	−	0.997367i	$-0.476896\pi$
$569$	−258.923	−	84.1291i	−0.455049	−	0.147854i	−0.527568	+	0.849513i	$0.676896\pi$
$570$		0			0
$571$	−69.9094	−	215.159i	−0.122433	−	0.376811i	0.870991	−	0.491298i	$-0.163477\pi$
$571$	−69.9094	−	215.159i	−0.122433	−	0.376811i	−0.993425	+	0.114487i	$0.963477\pi$
$572$	−399.706	−	203.660i	−0.698786	−	0.356049i
$573$	−3.44118	−	21.7267i	−0.00600555	−	0.0379175i
$574$		−	269.030i		−	0.468693i
$575$		0			0
$576$	−288.966			−0.501677
$577$	−884.446	+	140.082i	−1.53284	+	0.242777i	−0.865092	−	0.501614i	$-0.832740\pi$
$577$	−884.446	+	140.082i	−1.53284	+	0.242777i	−0.667744	+	0.744391i	$0.732740\pi$
$578$	−78.1211	+	153.321i	−0.135158	+	0.265262i
$579$	54.9116	−	17.8419i	0.0948387	−	0.0308150i
$580$		0			0
$581$	375.033	−	1154.23i	0.645495	−	1.98663i
$582$	12.8821	−	12.8821i	0.0221342	−	0.0221342i
$583$	−515.912	+	262.870i	−0.884926	+	0.450892i
$584$	−165.032	−	227.147i	−0.282589	−	0.388950i
$585$		0			0
$586$	161.959	+	117.670i	0.276380	+	0.200802i
$587$	−54.9201	+	346.752i	−0.0935606	+	0.590718i	0.895712	+	0.444635i	$0.146667\pi$
$587$	−54.9201	+	346.752i	−0.0935606	+	0.590718i	−0.989272	+	0.146083i	$0.953333\pi$
$588$	57.7986	+	9.15440i	0.0982970	+	0.0155687i
$589$	78.0330	−	107.403i	0.132484	−	0.182348i
$590$		0			0
$591$	−8.30041	+	6.03060i	−0.0140447	+	0.0102041i
$592$	49.7911	+	97.7205i	0.0841066	+	0.165068i
$593$	355.629	+	355.629i	0.599711	+	0.599711i	0.940236	−	0.340525i	$-0.110605\pi$
$593$	355.629	+	355.629i	0.599711	+	0.599711i	−0.340525	+	0.940236i	$0.610605\pi$
$594$	−21.8474	−	7.09864i	−0.0367801	−	0.0119506i
$595$		0			0
$596$	116.063	+	357.206i	0.194737	+	0.599339i
$597$	69.7960	+	35.5629i	0.116911	+	0.0595693i
$598$	17.3923	+	109.811i	0.0290841	+	0.183630i
$599$			1001.80i			1.67245i	0.548390	+	0.836223i	$0.315241\pi$
$599$			1001.80i			1.67245i	−0.548390	+	0.836223i	$0.684759\pi$
$600$		0			0
$601$	796.655			1.32555			0.662775	−	0.748819i	$-0.269379\pi$
$601$	796.655			1.32555			0.662775	+	0.748819i	$0.269379\pi$
$602$	445.201	−	70.5129i	0.739537	−	0.117131i
$603$	213.724	−	419.457i	0.354435	−	0.695617i
$604$	163.208	−	53.0295i	0.270212	−	0.0877973i
$605$		0			0
$606$	1.41799	−	4.36411i	0.00233991	−	0.00720151i
$607$	−728.906	+	728.906i	−1.20083	+	1.20083i	−0.226920	+	0.973913i	$0.572866\pi$
$607$	−728.906	+	728.906i	−1.20083	+	1.20083i	−0.973913	+	0.226920i	$0.927134\pi$
$608$	321.867	−	163.999i	0.529386	−	0.269736i
$609$	−57.8912	−	79.6804i	−0.0950595	−	0.130838i
$610$		0			0
$611$	233.410	+	169.582i	0.382013	+	0.277549i
$612$	4.03387	−	25.4689i	0.00659130	−	0.0416158i
$613$	123.360	+	19.5383i	0.201240	+	0.0318732i	0.256240	−	0.966613i	$-0.417516\pi$
$613$	123.360	+	19.5383i	0.201240	+	0.0318732i	−0.0550007	+	0.998486i	$0.517516\pi$
$614$	−39.2349	+	54.0022i	−0.0639004	+	0.0879514i
$615$		0			0
$616$	361.919	−	262.949i	0.587530	−	0.426866i
$617$	−325.707	−	639.236i	−0.527888	−	1.03604i	−0.988891	−	0.148640i	$-0.952510\pi$
$617$	−325.707	−	639.236i	−0.527888	−	1.03604i	0.461003	−	0.887399i	$-0.347490\pi$
$618$	−5.18438	−	5.18438i	−0.00838897	−	0.00838897i
$619$	196.553	+	63.8639i	0.317533	+	0.103173i	0.463447	−	0.886125i	$-0.346612\pi$
$619$	196.553	+	63.8639i	0.317533	+	0.103173i	−0.145914	+	0.989297i	$0.546612\pi$
$620$		0			0
$621$	−18.0044	−	55.4118i	−0.0289926	−	0.0892300i
$622$	60.3889	+	30.7697i	0.0970883	+	0.0494690i
$623$	188.726	+	1191.57i	0.302930	+	1.91263i
$624$		−	38.0487i		−	0.0609754i
$625$		0			0
$626$	−61.3275			−0.0979673
$627$	−30.2333	+	4.78849i	−0.0482190	+	0.00763714i
$628$	221.693	−	435.098i	0.353015	−	0.692831i
$629$	−6.96196	+	2.26208i	−0.0110683	+	0.00359631i
$630$		0			0
$631$	68.8404	−	211.869i	0.109097	−	0.335767i	−0.881573	−	0.472048i	$-0.843515\pi$
$631$	68.8404	−	211.869i	0.109097	−	0.335767i	0.990670	+	0.136281i	$0.0435149\pi$
$632$	20.9887	−	20.9887i	0.0332099	−	0.0332099i
$633$	52.9703	−	26.9897i	0.0836813	−	0.0426377i
$634$	143.227	+	197.135i	0.225910	+	0.310939i
$635$		0			0
$636$	−44.5050	−	32.3348i	−0.0699764	−	0.0508408i
$637$	144.159	−	910.185i	0.226310	−	1.42886i
$638$	−205.913	−	32.6134i	−0.322747	−	0.0511181i
$639$	14.3947	−	19.8126i	0.0225269	−	0.0310056i
$640$		0			0
$641$	−709.800	+	515.700i	−1.10733	+	0.804524i	−0.982241	−	0.187622i	$-0.939922\pi$
$641$	−709.800	+	515.700i	−1.10733	+	0.804524i	−0.125090	+	0.992145i	$0.539922\pi$
$642$	3.15315	+	6.18840i	0.00491145	+	0.00963926i
$643$	−430.122	−	430.122i	−0.668929	−	0.668929i	0.288539	−	0.957468i	$-0.406831\pi$
$643$	−430.122	−	430.122i	−0.668929	−	0.668929i	−0.957468	+	0.288539i	$0.906831\pi$
$644$	514.418	+	167.145i	0.798786	+	0.259541i
$645$		0			0
$646$	2.08158	+	6.40643i	0.00322225	+	0.00991707i
$647$	786.060	+	400.518i	1.21493	+	0.619038i	0.939588	−	0.342308i	$-0.111209\pi$
$647$	786.060	+	400.518i	1.21493	+	0.619038i	0.275343	+	0.961346i	$0.411209\pi$
$648$	56.7209	+	358.122i	0.0875323	+	0.552657i
$649$			704.409i			1.08538i
$650$		0			0
$651$	23.7934			0.0365490
$652$	951.940	−	150.773i	1.46003	−	0.231246i
$653$	442.744	−	868.933i	0.678015	−	1.33068i	−0.253627	−	0.967302i	$-0.581624\pi$
$653$	442.744	−	868.933i	0.678015	−	1.33068i	0.931642	−	0.363377i	$-0.118376\pi$
$654$	17.3565	−	5.63947i	0.0265390	−	0.00862304i
$655$		0			0
$656$	−152.746	+	470.105i	−0.232845	+	0.716624i
$657$	389.302	−	389.302i	0.592545	−	0.592545i
$658$	−122.205	+	62.2667i	−0.185722	+	0.0946302i
$659$	−337.348	−	464.320i	−0.511909	−	0.704582i	0.472331	−	0.881421i	$-0.343413\pi$
$659$	−337.348	−	464.320i	−0.511909	−	0.704582i	−0.984240	+	0.176839i	$0.943413\pi$
$660$		0			0
$661$	83.1335	+	60.4000i	0.125769	+	0.0913767i	0.648892	−	0.760881i	$-0.275233\pi$
$661$	83.1335	+	60.4000i	0.125769	+	0.0913767i	−0.523122	+	0.852258i	$0.675233\pi$
$662$	11.2577	−	71.0781i	0.0170055	−	0.107369i
$663$	2.50830	+	0.397276i	0.00378326	+	0.000599210i
$664$	300.938	−	414.206i	0.453220	−	0.623804i
$665$		0			0
$666$	39.9484	−	29.0242i	0.0599825	−	0.0435799i
$667$	−240.056	−	471.137i	−0.359905	−	0.706353i
$668$	693.953	+	693.953i	1.03885	+	1.03885i
$669$	17.0341	+	5.53472i	0.0254621	+	0.00827313i
$670$		0			0
$671$	39.5523	+	121.729i	0.0589453	+	0.181415i
$672$	57.6864	+	29.3927i	0.0858429	+	0.0437391i
$673$	−117.679	−	742.996i	−0.174857	−	1.10401i	−0.906465	−	0.422280i	$-0.861230\pi$
$673$	−117.679	−	742.996i	−0.174857	−	1.10401i	0.731608	−	0.681726i	$-0.238770\pi$
$674$			23.1240i			0.0343086i
$675$		0			0
$676$	−55.3389			−0.0818624
$677$	661.912	−	104.837i	0.977714	−	0.154855i	0.352928	−	0.935651i	$-0.385186\pi$
$677$	661.912	−	104.837i	0.977714	−	0.154855i	0.624786	+	0.780796i	$0.285186\pi$
$678$	4.90350	−	9.62365i	0.00723230	−	0.0141942i
$679$	−1327.42	+	431.304i	−1.95496	+	0.635204i
$680$		0			0
$681$	25.0821	−	77.1947i	0.0368313	−	0.113355i
$682$	35.6132	−	35.6132i	0.0522188	−	0.0522188i
$683$	936.456	−	477.148i	1.37109	−	0.698607i	0.395556	−	0.918442i	$-0.370552\pi$
$683$	936.456	−	477.148i	1.37109	−	0.698607i	0.975537	+	0.219835i	$0.0705520\pi$
$684$	273.328	+	376.203i	0.399602	+	0.550005i
$685$		0			0
$686$	98.6588	+	71.6798i	0.143817	+	0.104489i
$687$	−0.864952	+	5.46109i	−0.00125903	+	0.00794919i
$688$	−817.983	−	129.556i	−1.18893	−	0.188308i
$689$	−509.193	+	700.843i	−0.739031	+	1.01719i
$690$		0			0
$691$	281.760	−	204.711i	0.407757	−	0.296253i	−0.364936	−	0.931033i	$-0.618909\pi$
$691$	281.760	−	204.711i	0.407757	−	0.296253i	0.772693	+	0.634780i	$0.218909\pi$
$692$	−308.231	−	604.937i	−0.445420	−	0.874186i
$693$	620.284	+	620.284i	0.895071	+	0.895071i
$694$	133.497	+	43.3757i	0.192358	+	0.0625010i
$695$		0			0
$696$	−12.8395	−	39.5160i	−0.0184476	−	0.0567758i
$697$	−29.3961	−	14.9781i	−0.0421752	−	0.0214893i
$698$	−1.57862	−	9.96703i	−0.00226164	−	0.0142794i
$699$			45.2750i			0.0647711i
$700$		0			0
$701$	685.412			0.977764			0.488882	−	0.872350i	$-0.337405\pi$
$701$	685.412			0.977764			0.488882	+	0.872350i	$0.337405\pi$
$702$	−33.9455	+	5.37643i	−0.0483554	+	0.00765874i
$703$	59.9304	−	117.620i	0.0852495	−	0.167312i
$704$	−278.726	+	90.5637i	−0.395918	+	0.128642i
$705$		0			0
$706$	92.9324	−	286.016i	0.131632	−	0.405122i
$707$	−248.584	+	248.584i	−0.351604	+	0.351604i
$708$	−59.6297	+	30.3828i	−0.0842227	+	0.0429136i
$709$	142.144	+	195.644i	0.200485	+	0.275944i	0.897408	−	0.441202i	$-0.145448\pi$
$709$	142.144	+	195.644i	0.200485	+	0.275944i	−0.696922	+	0.717146i	$0.745448\pi$
$710$		0			0
$711$	47.0880	+	34.2114i	0.0662278	+	0.0481173i
$712$	−79.6165	+	502.679i	−0.111821	+	0.706009i
$713$	126.168	+	19.9831i	0.176954	+	0.0280267i
$714$	−0.709620	+	0.976708i	−0.000993865	+	0.00136794i
$715$		0			0
$716$	603.074	−	438.159i	0.842283	−	0.611954i
$717$	5.90162	+	11.5826i	0.00823099	+	0.0161542i
$718$	142.161	+	142.161i	0.197995	+	0.197995i
$719$	126.747	+	41.1825i	0.176282	+	0.0572774i	0.395828	−	0.918325i	$-0.370458\pi$
$719$	126.747	+	41.1825i	0.176282	+	0.0572774i	−0.219546	+	0.975602i	$0.570458\pi$
$720$		0			0
$721$	173.577	+	534.216i	0.240745	+	0.740937i
$722$	83.7004	+	42.6475i	0.115928	+	0.0590685i
$723$	1.25203	+	7.90500i	0.00173171	+	0.0109336i
$724$			100.633i			0.138996i
$725$		0			0
$726$	5.46377			0.00752585
$727$	−1276.25	+	202.138i	−1.75550	+	0.278044i	−0.949477	−	0.313837i	$-0.898385\pi$
$727$	−1276.25	+	202.138i	−1.75550	+	0.278044i	−0.806025	+	0.591881i	$0.798385\pi$
$728$	303.857	−	596.352i	0.417386	−	0.819165i
$729$	−667.599	+	216.916i	−0.915774	+	0.297553i
$730$		0			0
$731$	17.0815	−	52.5716i	0.0233674	−	0.0719173i
$732$	−8.59866	+	8.59866i	−0.0117468	+	0.0117468i
$733$	−744.383	+	379.282i	−1.01553	+	0.517438i	−0.880822	−	0.473448i	$-0.843009\pi$
$733$	−744.383	+	379.282i	−1.01553	+	0.517438i	−0.134707	+	0.990885i	$0.543009\pi$
$734$	−164.121	−	225.893i	−0.223598	−	0.307757i
$735$		0			0
$736$	281.205	+	204.307i	0.382072	+	0.277591i
$737$	74.6903	−	471.576i	0.101344	−	0.639859i
$738$	219.809	+	34.8143i	0.297844	+	0.0471738i
$739$	651.261	−	896.383i	0.881273	−	1.21297i	−0.0947939	−	0.995497i	$-0.530219\pi$
$739$	651.261	−	896.383i	0.881273	−	1.21297i	0.976067	−	0.217471i	$-0.0697808\pi$
$740$		0			0
$741$	−37.0504	+	26.9187i	−0.0500005	+	0.0363275i
$742$	−186.964	−	366.937i	−0.251973	−	0.494524i
$743$	333.821	+	333.821i	0.449289	+	0.449289i	0.895118	−	0.445829i	$-0.147091\pi$
$743$	333.821	+	333.821i	0.449289	+	0.449289i	−0.445829	+	0.895118i	$0.647091\pi$
$744$	9.54631	+	3.10178i	0.0128311	+	0.00416906i
$745$		0			0
$746$	88.6545	+	272.851i	0.118840	+	0.365751i
$747$	894.524	+	455.783i	1.19749	+	0.610151i
$748$	−4.09117	−	25.8306i	−0.00546948	−	0.0345329i
$749$		−	532.104i		−	0.710419i
$750$		0			0
$751$	698.285			0.929807			0.464904	−	0.885361i	$-0.346089\pi$
$751$	698.285			0.929807			0.464904	+	0.885361i	$0.346089\pi$
$752$	248.895	−	39.4212i	0.330978	−	0.0524217i
$753$	23.8208	−	46.7510i	0.0316345	−	0.0620863i
$754$	−296.646	+	96.3861i	−0.393430	+	0.127833i
$755$		0			0
$756$	−51.6690	+	159.021i	−0.0683453	+	0.210345i
$757$	465.289	−	465.289i	0.614648	−	0.614648i	−0.329505	−	0.944154i	$-0.606882\pi$
$757$	465.289	−	465.289i	0.614648	−	0.614648i	0.944154	+	0.329505i	$0.106882\pi$
$758$	−333.893	+	170.127i	−0.440492	+	0.224442i
$759$	−17.3123	−	23.8283i	−0.0228093	−	0.0313944i
$760$		0			0
$761$	−1146.83	−	833.219i	−1.50700	−	1.09490i	−0.967486	−	0.252924i	$-0.918608\pi$
$761$	−1146.83	−	833.219i	−1.50700	−	1.09490i	−0.539515	−	0.841976i	$-0.681392\pi$
$762$	1.35238	−	8.53856i	0.00177477	−	0.0112055i
$763$	−1380.94	−	218.719i	−1.80988	−	0.286657i
$764$	−199.213	+	274.193i	−0.260750	+	0.358891i
$765$		0			0
$766$	−186.327	+	135.375i	−0.243247	+	0.176730i
$767$	478.454	+	939.020i	0.623800	+	1.22428i
$768$	−9.58222	−	9.58222i	−0.0124768	−	0.0124768i
$769$	805.374	+	261.682i	1.04730	+	0.340288i	0.781608	−	0.623770i	$-0.214400\pi$
$769$	805.374	+	261.682i	1.04730	+	0.340288i	0.265692	+	0.964058i	$0.414400\pi$
$770$		0			0
$771$	−2.10210	−	6.46959i	−0.00272645	−	0.00839116i
$772$	−792.616	−	403.858i	−1.02670	−	0.523132i
$773$	50.6693	+	319.914i	0.0655489	+	0.413860i	0.998543	+	0.0539672i	$0.0171866\pi$
$773$	50.6693	+	319.914i	0.0655489	+	0.413860i	−0.932994	+	0.359893i	$0.882813\pi$
$774$			372.873i			0.481748i
$775$		0			0
$776$	−588.807			−0.758772
$777$	23.3678	−	3.70109i	0.0300744	−	0.00476331i
$778$	106.008	−	208.053i	0.136257	−	0.267420i
$779$	565.836	−	183.851i	0.726361	−	0.236009i
$780$		0			0
$781$	7.67522	−	23.6219i	0.00982742	−	0.0302457i
$782$	−4.58315	+	4.58315i	−0.00586081	+	0.00586081i
$783$	145.642	−	74.2081i	0.186005	−	0.0947740i
$784$	−473.112	−	651.183i	−0.603459	−	0.830590i
$785$		0			0
$786$	−0.404845	−	0.294137i	−0.000515070	−	0.000374221i
$787$	128.845	−	813.494i	0.163716	−	1.03366i	−0.759815	−	0.650140i	$-0.774710\pi$
$787$	128.845	−	813.494i	0.163716	−	1.03366i	0.923531	−	0.383524i	$-0.125290\pi$
$788$	156.130	+	24.7285i	0.198134	+	0.0313814i
$789$	0.753408	−	1.03698i	0.000954890	−	0.00131429i
$790$		0			0
$791$	−669.446	+	486.381i	−0.846328	+	0.614893i
$792$	168.006	+	329.730i	0.212129	+	0.416326i
$793$	135.408	+	135.408i	0.170754	+	0.170754i
$794$	−194.212	−	63.1033i	−0.244599	−	0.0794751i
$795$		0			0
$796$	−372.955	−	1147.84i	−0.468536	−	1.44201i
$797$	−772.191	−	393.451i	−0.968872	−	0.493665i	−0.103410	−	0.994639i	$-0.532975\pi$
$797$	−772.191	−	393.451i	−0.968872	−	0.493665i	−0.865462	+	0.500974i	$0.832975\pi$
$798$	−3.40576	−	21.5031i	−0.00426787	−	0.0269463i
$799$			16.8197i			0.0210509i
$800$		0			0
$801$	−997.982			−1.24592
$802$	−392.310	+	62.1358i	−0.489165	+	0.0774761i
$803$	253.497	−	497.517i	0.315688	−	0.619573i
$804$	43.1415	−	14.0175i	0.0536585	−	0.0174347i
$805$		0			0
$806$	23.2851	−	71.6640i	0.0288896	−	0.0889132i
$807$	10.3816	−	10.3816i	0.0128645	−	0.0128645i
$808$	−132.142	+	67.3298i	−0.163542	+	0.0833289i
$809$	−72.5617	−	99.8726i	−0.0896931	−	0.123452i	0.761812	−	0.647798i	$-0.224310\pi$
$809$	−72.5617	−	99.8726i	−0.0896931	−	0.123452i	−0.851505	+	0.524346i	$0.824310\pi$
$810$		0			0
$811$	378.763	+	275.188i	0.467033	+	0.339319i	0.796284	−	0.604923i	$-0.206796\pi$
$811$	378.763	+	275.188i	0.467033	+	0.339319i	−0.329251	+	0.944242i	$0.606796\pi$
$812$	−237.384	+	1498.78i	−0.292344	+	1.84579i
$813$	−75.5585	−	11.9673i	−0.0929379	−	0.0147199i
$814$	29.4364	−	40.5158i	0.0361627	−	0.0497737i
$815$		0			0
$816$	1.79454	−	1.30381i	0.00219919	−	0.00159780i
$817$	452.550	+	888.179i	0.553916	+	1.08712i
$818$	−265.469	−	265.469i	−0.324534	−	0.324534i
$819$	1248.19	+	405.562i	1.52404	+	0.495191i
$820$		0			0
$821$	285.639	+	879.107i	0.347916	+	1.07078i	0.960004	+	0.279986i	$0.0903298\pi$
$821$	285.639	+	879.107i	0.347916	+	1.07078i	−0.612088	+	0.790790i	$0.709670\pi$
$822$	−31.3985	−	15.9983i	−0.0381977	−	0.0194627i
$823$	119.999	+	757.643i	0.145807	+	0.920587i	0.946779	+	0.321885i	$0.104316\pi$
$823$	119.999	+	757.643i	0.145807	+	0.920587i	−0.800972	+	0.598702i	$0.795684\pi$
$824$			236.964i			0.287578i
$825$		0			0
$826$	−501.004			−0.606542
$827$	230.733	−	36.5445i	0.279000	−	0.0441892i	−0.0153664	−	0.999882i	$-0.504891\pi$
$827$	230.733	−	36.5445i	0.279000	−	0.0441892i	0.294366	+	0.955693i	$0.404891\pi$
$828$	−203.133	+	398.672i	−0.245330	+	0.481488i
$829$	1244.32	−	404.304i	1.50099	−	0.487701i	0.560682	−	0.828031i	$-0.310539\pi$
$829$	1244.32	−	404.304i	1.50099	−	0.487701i	0.940306	+	0.340330i	$0.110539\pi$
$830$		0			0
$831$	−5.33226	+	16.4110i	−0.00641668	+	0.0197485i
$832$	−310.046	+	310.046i	−0.372651	+	0.372651i
$833$	47.8681	−	24.3900i	0.0574647	−	0.0292797i
$834$	11.4855	+	15.8085i	0.0137716	+	0.0189550i
$835$		0			0
$836$	381.547	+	277.210i	0.456396	+	0.331591i
$837$	−6.17731	+	39.0020i	−0.00738030	+	0.0465974i
$838$	−68.8892	−	10.9110i	−0.0822067	−	0.0130203i
$839$	614.547	−	845.852i	0.732476	−	1.00817i	−0.266541	−	0.963824i	$-0.585881\pi$
$839$	614.547	−	845.852i	0.732476	−	1.00817i	0.999016	−	0.0443428i	$-0.0141194\pi$
$840$		0			0
$841$	519.757	−	377.626i	0.618023	−	0.449020i
$842$	−0.929679	−	1.82460i	−0.00110413	−	0.00216698i
$843$	45.5884	+	45.5884i	0.0540787	+	0.0540787i
$844$	−871.127	−	283.046i	−1.03214	−	0.335363i
$845$		0			0
$846$	−35.0603	−	107.905i	−0.0414424	−	0.127547i
$847$	−372.968	−	190.037i	−0.440340	−	0.224364i
$848$	118.367	+	747.341i	0.139584	+	0.881298i
$849$		−	46.6825i		−	0.0549853i
$850$		0			0
$851$	127.019			0.149259
$852$	2.33069	−	0.369145i	0.00273555	−	0.000433269i
$853$	16.4656	−	32.3156i	0.0193032	−	0.0378846i	−0.881154	−	0.472830i	$-0.843232\pi$
$853$	16.4656	−	32.3156i	0.0193032	−	0.0378846i	0.900457	+	0.434946i	$0.143232\pi$
$854$	−86.5788	+	28.1311i	−0.101380	+	0.0329405i
$855$		0			0
$856$	69.3667	−	213.489i	0.0810358	−	0.249403i
$857$	−687.485	+	687.485i	−0.802199	+	0.802199i	−0.983439	−	0.181240i	$-0.941989\pi$
$857$	−687.485	+	687.485i	−0.802199	+	0.802199i	0.181240	+	0.983439i	$0.441989\pi$
$858$	−15.4804	+	7.88766i	−0.0180424	+	0.00919307i
$859$	−884.589	−	1217.53i	−1.02979	−	1.41738i	−0.905106	−	0.425187i	$-0.860208\pi$
$859$	−884.589	−	1217.53i	−1.02979	−	1.41738i	−0.124684	−	0.992197i	$-0.539792\pi$
$860$		0			0
$861$	86.2658	+	62.6758i	0.100193	+	0.0727942i
$862$	−43.5101	+	274.712i	−0.0504757	+	0.318691i
$863$	−1296.60	−	205.361i	−1.50243	−	0.237962i	−0.649653	−	0.760231i	$-0.725086\pi$
$863$	−1296.60	−	205.361i	−1.50243	−	0.237962i	−0.852781	+	0.522269i	$0.825086\pi$
$864$	−63.1570	+	86.9282i	−0.0730984	+	0.100611i
$865$		0			0
$866$	−95.7869	+	69.5932i	−0.110608	+	0.0803617i
$867$	−30.9634	−	60.7692i	−0.0357133	−	0.0700913i
$868$	−259.219	−	259.219i	−0.298639	−	0.298639i
$869$	56.1415	+	18.2415i	0.0646047	+	0.0209913i
$870$		0			0
$871$	−220.741	−	679.371i	−0.253434	−	0.779990i
$872$	−525.542	−	267.777i	−0.602686	−	0.307084i
$873$	−180.617	−	1140.37i	−0.206892	−	1.30626i
$874$		−	116.884i		−	0.133734i
$875$		0			0
$876$	53.0498			0.0605591
$877$	372.287	−	58.9645i	0.424501	−	0.0672343i	0.0594706	−	0.998230i	$-0.481059\pi$
$877$	372.287	−	58.9645i	0.424501	−	0.0672343i	0.365030	+	0.930996i	$0.381059\pi$
$878$	132.802	−	260.639i	0.151255	−	0.296855i
$879$	−75.4629	+	24.5194i	−0.0858509	+	0.0278947i
$880$		0			0
$881$	−297.148	+	914.528i	−0.337285	+	1.03806i	0.628300	+	0.777971i	$0.283751\pi$
$881$	−297.148	+	914.528i	−0.337285	+	1.03806i	−0.965585	+	0.260086i	$0.916249\pi$
$882$	−256.252	+	256.252i	−0.290535	+	0.290535i
$883$	31.7470	−	16.1759i	0.0359535	−	0.0183192i	−0.435921	−	0.899985i	$-0.643577\pi$
$883$	31.7470	−	16.1759i	0.0359535	−	0.0183192i	0.471875	+	0.881666i	$0.343577\pi$
$884$	−22.9987	−	31.6549i	−0.0260166	−	0.0358088i
$885$		0			0
$886$	164.963	+	119.853i	0.186189	+	0.135274i
$887$	46.9904	−	296.686i	0.0529768	−	0.334482i	−0.946938	−	0.321417i	$-0.895841\pi$
$887$	46.9904	−	296.686i	0.0529768	−	0.334482i	0.999915	−	0.0130655i	$-0.00415898\pi$
$888$	9.85802	+	1.56136i	0.0111014	+	0.00175828i
$889$	−389.298	+	535.823i	−0.437905	+	0.602725i
$890$		0			0
$891$	−583.372	+	423.845i	−0.654739	+	0.475696i
$892$	−125.281	−	245.877i	−0.140449	−	0.275647i
$893$	−214.475	−	214.475i	−0.240174	−	0.240174i
$894$	13.8344	+	4.49507i	0.0154747	+	0.00502805i
$895$		0			0
$896$	−402.780	−	1239.63i	−0.449531	−	1.38352i
$897$	−39.2632	−	20.0056i	−0.0437717	−	0.0223028i
$898$	32.1291	+	202.855i	0.0357786	+	0.225897i
$899$			358.375i			0.398637i
$900$		0			0
$901$	−50.5032			−0.0560524
$902$	222.931	−	35.3088i	0.247152	−	0.0391450i
$903$	−81.1080	+	159.183i	−0.0898206	+	0.176283i
$904$	−331.998	+	107.873i	−0.367255	+	0.119328i
$905$		0			0
$906$	2.05381	−	6.32097i	0.00226689	−	0.00697678i
$907$	505.478	−	505.478i	0.557307	−	0.557307i	−0.371233	−	0.928540i	$-0.621065\pi$
$907$	505.478	−	505.478i	0.557307	−	0.557307i	0.928540	+	0.371233i	$0.121065\pi$
$908$	−1114.26	+	567.744i	−1.22716	+	0.625268i
$909$	−170.935	−	235.272i	−0.188047	−	0.258825i
$910$		0			0
$911$	−1112.30	−	808.135i	−1.22097	−	0.887086i	−0.224788	−	0.974408i	$-0.572169\pi$
$911$	−1112.30	−	808.135i	−1.22097	−	0.887086i	−0.996180	+	0.0873220i	$0.972169\pi$
$912$	−6.25752	+	39.5084i	−0.00686132	+	0.0433207i
$913$	1005.67	+	159.283i	1.10150	+	0.174461i
$914$	−72.3704	+	99.6093i	−0.0791798	+	0.108982i
$915$		0			0
$916$	68.9194	−	50.0728i	0.0752395	−	0.0546647i
$917$	17.4051	+	34.1594i	0.0189805	+	0.0372513i
$918$	−1.41678	−	1.41678i	−0.00154333	−	0.00154333i
$919$	−1241.96	−	403.536i	−1.35142	−	0.439104i	−0.458252	−	0.888822i	$-0.651524\pi$
$919$	−1241.96	−	403.536i	−1.35142	−	0.439104i	−0.893170	+	0.449718i	$0.851524\pi$
$920$		0			0
$921$	−8.17554	−	25.1617i	−0.00887681	−	0.0273200i
$922$	−177.773	−	90.5801i	−0.192813	−	0.0982430i
$923$	−5.81312	−	36.7026i	−0.00629808	−	0.0397645i
$924$			84.5254i			0.0914777i
$925$		0			0
$926$	−16.5629			−0.0178865
$927$	−458.939	+	72.6888i	−0.495080	+	0.0784129i
$928$	−442.711	+	868.868i	−0.477059	+	0.936281i
$929$	430.474	−	139.870i	0.463374	−	0.150559i	−0.0680204	−	0.997684i	$-0.521668\pi$
$929$	430.474	−	139.870i	0.463374	−	0.150559i	0.531394	+	0.847125i	$0.321668\pi$
$930$		0			0
$931$	−299.380	+	921.397i	−0.321568	+	0.989685i
$932$	493.250	−	493.250i	0.529239	−	0.529239i
$933$	−23.9353	+	12.1956i	−0.0256541	+	0.0130714i
$934$	143.746	+	197.849i	0.153904	+	0.211830i
$935$		0			0
$936$	447.924	+	325.436i	0.478551	+	0.347688i
$937$	82.0298	−	517.916i	0.0875451	−	0.552738i	−0.904462	−	0.426555i	$-0.859727\pi$
$937$	82.0298	−	517.916i	0.0875451	−	0.552738i	0.992007	−	0.126184i	$-0.0402728\pi$
$938$	335.404	+	53.1227i	0.357573	+	0.0566341i
$939$	14.2874	−	19.6650i	0.0152156	−	0.0209425i
$940$		0			0
$941$	983.490	−	714.547i	1.04515	−	0.759349i	0.0738692	−	0.997268i	$-0.476465\pi$
$941$	983.490	−	714.547i	1.04515	−	0.759349i	0.971285	+	0.237919i	$0.0764653\pi$
$942$	−8.58607	−	16.8511i	−0.00911472	−	0.0178887i
$943$	404.798	+	404.798i	0.429266	+	0.429266i
$944$	875.458	+	284.454i	0.927392	+	0.301328i
$945$		0			0
$946$	116.861	+	359.660i	0.123531	+	0.380190i
$947$	1101.45	+	561.219i	1.16310	+	0.592628i	0.925505	−	0.378736i	$-0.123641\pi$
$947$	1101.45	+	561.219i	1.16310	+	0.592628i	0.237594	+	0.971365i	$0.423641\pi$
$948$	0.877337	+	5.53929i	0.000925461	+	0.00584313i
$949$		−	835.402i		−	0.880297i
$950$		0			0
$951$	−96.5800			−0.101556
$952$	38.5387	−	6.10394i	0.0404819	−	0.00641170i
$953$	46.2355	−	90.7422i	0.0485157	−	0.0952174i	−0.865476	−	0.500951i	$-0.832984\pi$
$953$	46.2355	−	90.7422i	0.0485157	−	0.0952174i	0.913992	+	0.405733i	$0.132984\pi$
$954$	323.997	−	105.273i	0.339620	−	0.110349i
$955$		0			0
$956$	61.8915	−	190.483i	0.0647401	−	0.199250i
$957$	58.4290	−	58.4290i	0.0610544	−	0.0610544i
$958$	323.971	−	165.071i	0.338174	−	0.172308i
$959$	1586.89	+	2184.16i	1.65473	+	2.27754i
$960$		0			0
$961$	707.423	+	513.973i	0.736133	+	0.534832i
$962$	11.7211	−	74.0040i	0.0121841	−	0.0769273i
$963$	434.751	+	68.8578i	0.451455	+	0.0715034i
$964$	72.4811	−	99.7617i	0.0751879	−	0.103487i
$965$		0			0
$966$	16.9476	−	12.3132i	0.0175441	−	0.0127466i
$967$	−214.962	−	421.887i	−0.222298	−	0.436284i	0.752741	−	0.658316i	$-0.228731\pi$
$967$	−214.962	−	421.887i	−0.222298	−	0.436284i	−0.975039	+	0.222032i	$0.928731\pi$
$968$	−124.867	−	124.867i	−0.128995	−	0.128995i
$969$	−2.53920	−	0.825036i	−0.00262043	−	0.000851430i
$970$		0			0
$971$	520.392	+	1601.60i	0.535934	+	1.64943i	0.741623	+	0.670817i	$0.234056\pi$
$971$	520.392	+	1601.60i	0.535934	+	1.64943i	−0.205690	+	0.978617i	$0.565944\pi$
$972$	−185.053	−	94.2891i	−0.190383	−	0.0970052i
$973$	−234.187	−	1478.60i	−0.240686	−	1.51963i
$974$		−	138.450i		−	0.142146i
$975$		0			0
$976$	167.260			0.171373
$977$	−113.296	+	17.9443i	−0.115963	+	0.0183667i	−0.214146	−	0.976802i	$-0.568697\pi$
$977$	−113.296	+	17.9443i	−0.115963	+	0.0183667i	0.0981833	+	0.995168i	$0.468697\pi$
$978$	16.9464	−	33.2592i	0.0173276	−	0.0340074i
$979$	−962.619	+	312.774i	−0.983267	+	0.319483i
$980$		0			0
$981$	357.405	−	1099.98i	0.364328	−	1.12128i
$982$	150.646	−	150.646i	0.153407	−	0.153407i
$983$	1145.48	−	583.651i	1.16529	−	0.593744i	0.239170	−	0.970978i	$-0.423125\pi$
$983$	1145.48	−	583.651i	1.16529	−	0.593744i	0.926118	+	0.377233i	$0.123125\pi$
$984$	26.4406	+	36.3924i	0.0268706	+	0.0369842i
$985$		0			0
$986$	−14.7111	−	10.6882i	−0.0149200	−	0.0108400i
$987$	8.50397	−	53.6920i	0.00861598	−	0.0543992i
$988$	696.913	+	110.380i	0.705378	+	0.111721i
$989$	−563.778	+	775.973i	−0.570048	+	0.784604i
$990$		0			0
$991$	−392.287	+	285.013i	−0.395850	+	0.287602i	−0.767848	−	0.640631i	$-0.778673\pi$
$991$	−392.287	+	285.013i	−0.395850	+	0.287602i	0.371999	+	0.928233i	$0.378673\pi$
$992$	−106.950	−	209.902i	−0.107813	−	0.211595i
$993$	20.1689	+	20.1689i	0.0203110	+	0.0203110i
$994$	16.8008	+	5.45892i	0.0169022	+	0.00549187i
$995$		0			0
$996$	29.8934	+	92.0024i	0.0300135	+	0.0923719i
$997$	1156.57	+	589.304i	1.16005	+	0.591077i	0.924649	−	0.380820i	$-0.124358\pi$
$997$	1156.57	+	589.304i	1.16005	+	0.591077i	0.235405	+	0.971897i	$0.424358\pi$
$998$	70.2046	+	443.254i	0.0703453	+	0.444143i
$999$			39.2652i			0.0393045i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.3.f.b.43.2		32
5.2	odd	4		125.3.f.c.82.2		32
5.3	odd	4		25.3.f.a.12.3	✓	32
5.4	even	2		125.3.f.a.43.3		32
15.8	even	4		225.3.r.a.37.2		32
20.3	even	4		400.3.bg.c.337.2		32
25.2	odd	20	inner	125.3.f.b.32.2		32
25.11	even	5		125.3.f.c.93.2		32
25.14	even	10		25.3.f.a.23.3	yes	32
25.23	odd	20		125.3.f.a.32.3		32
75.14	odd	10		225.3.r.a.73.2		32
100.39	odd	10		400.3.bg.c.273.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.12.3	✓	32	5.3	odd	4
25.3.f.a.23.3	yes	32	25.14	even	10
125.3.f.a.32.3		32	25.23	odd	20
125.3.f.a.43.3		32	5.4	even	2
125.3.f.b.32.2		32	25.2	odd	20	inner
125.3.f.b.43.2		32	1.1	even	1	trivial
125.3.f.c.82.2		32	5.2	odd	4
125.3.f.c.93.2		32	25.11	even	5
225.3.r.a.37.2		32	15.8	even	4
225.3.r.a.73.2		32	75.14	odd	10
400.3.bg.c.273.2		32	100.39	odd	10
400.3.bg.c.337.2		32	20.3	even	4

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	125.3.f.b.43.2

Level	$125$
Weight	$3$
Character	125.43
Analytic conductor	$3.406$
Analytic rank	$0$
Dimension	$32$
Inner twists	$2$