LMFDB - Embedded newform 125.3.f.c.93.2

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)

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")

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);

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 = [32,10,10,-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			93.2
Character	$\chi$	$=$	125.93
Dual form			125.3.f.c.82.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0933465 + 0.589367i) q^{2} +(-0.210730 + 0.107372i) q^{3} +(3.46559 + 1.12604i) q^{4} +(-0.0436108 - 0.134220i) q^{6} +(7.64532 - 7.64532i) q^{7} +(-2.07076 + 4.06409i) q^{8} +(-5.25719 + 7.23590i) q^{9} +(7.33868 - 5.33186i) q^{11} +(-0.851210 + 0.134818i) q^{12} +(2.12306 + 13.4044i) q^{13} +(3.79223 + 5.21956i) q^{14} +(9.59007 + 6.96760i) q^{16} +(-0.704962 - 0.359196i) q^{17} +(-3.77386 - 3.77386i) q^{18} +(13.5696 - 4.40902i) q^{19} +(-0.790204 + 2.43200i) q^{21} +(2.45738 + 4.82288i) q^{22} +(-13.5597 - 2.14764i) q^{23} -1.07877i q^{24} -8.09832 q^{26} +(0.663895 - 4.19167i) q^{27} +(35.1044 - 17.8866i) q^{28} +(-36.6306 - 11.9020i) q^{29} +(-2.87530 - 8.84925i) q^{31} +(-17.9028 + 17.9028i) q^{32} +(-0.973987 + 1.91156i) q^{33} +(0.277504 - 0.381951i) q^{34} +(-26.3671 + 19.1568i) q^{36} +(-9.13820 + 1.44735i) q^{37} +(1.33186 + 8.40902i) q^{38} +(-1.88666 - 2.59677i) q^{39} +(-33.7351 - 24.5100i) q^{41} +(-1.35958 - 0.692738i) q^{42} +(-49.4021 - 49.4021i) q^{43} +(31.4367 - 10.2144i) q^{44} +(2.53150 - 7.79114i) q^{46} +(-9.65116 - 18.9415i) q^{47} +(-2.76905 - 0.438574i) q^{48} -67.9017i q^{49} +0.187125 q^{51} +(-7.73627 + 48.8449i) q^{52} +(56.8742 - 28.9788i) q^{53} +(2.40846 + 0.782556i) q^{54} +(15.2397 + 46.9029i) q^{56} +(-2.38611 + 2.38611i) q^{57} +(10.4340 - 20.4778i) q^{58} +(-45.6440 + 62.8235i) q^{59} +(11.4153 - 8.29369i) q^{61} +(5.48385 - 0.868557i) q^{62} +(15.1279 + 95.5136i) q^{63} +(18.9902 + 26.1378i) q^{64} +(-1.03569 - 0.752473i) q^{66} +(46.8978 + 23.8956i) q^{67} +(-2.03864 - 2.03864i) q^{68} +(3.08803 - 1.00336i) q^{69} +(-0.846117 + 2.60408i) q^{71} +(-18.5210 - 36.3495i) q^{72} +(-60.7976 - 9.62940i) q^{73} -5.52086i q^{74} +51.9912 q^{76} +(15.3427 - 96.8703i) q^{77} +(1.70656 - 0.869536i) q^{78} +(-6.18905 - 2.01094i) q^{79} +(-24.5646 - 75.6022i) q^{81} +(17.5944 - 17.5944i) q^{82} +(-50.9593 + 100.013i) q^{83} +(-5.47704 + 7.53850i) q^{84} +(33.7274 - 24.5044i) q^{86} +(8.99712 - 1.42500i) q^{87} +(6.47255 + 40.8661i) q^{88} +(65.5853 + 90.2704i) q^{89} +(118.713 + 86.2498i) q^{91} +(-44.5739 - 22.7115i) q^{92} +(1.55608 + 1.55608i) q^{93} +(12.0644 - 3.91995i) q^{94} +(1.85040 - 5.69493i) q^{96} +(58.6053 + 115.019i) q^{97} +(40.0190 + 6.33839i) q^{98} +81.1325i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + 10 q^{2} + 10 q^{3} - 10 q^{4} - 6 q^{6} + 10 q^{7} + 10 q^{8} - 10 q^{9} - 6 q^{11} + 10 q^{12} + 10 q^{13} - 10 q^{14} + 2 q^{16} - 60 q^{17} - 140 q^{18} + 90 q^{19} - 6 q^{21} - 70 q^{22} - 10 q^{23}+ \cdots - 170 q^{98}+O(q^{100})$ 32 * q + 10 * q^2 + 10 * q^3 - 10 * q^4 - 6 * q^6 + 10 * q^7 + 10 * q^8 - 10 * q^9 - 6 * q^11 + 10 * q^12 + 10 * q^13 - 10 * q^14 + 2 * q^16 - 60 * q^17 - 140 * q^18 + 90 * q^19 - 6 * q^21 - 70 * q^22 - 10 * q^23 + 4 * q^26 + 100 * q^27 + 250 * q^28 - 110 * q^29 - 6 * q^31 + 290 * q^32 + 190 * q^33 - 260 * q^34 - 58 * q^36 - 50 * q^37 - 320 * q^38 + 390 * q^39 - 86 * q^41 - 690 * q^42 - 230 * q^43 + 340 * q^44 - 6 * q^46 - 70 * q^47 - 160 * q^48 - 16 * q^51 + 320 * q^52 + 190 * q^53 - 660 * q^54 - 70 * q^56 + 650 * q^57 + 640 * q^58 - 260 * q^59 + 114 * q^61 - 60 * q^62 + 20 * q^63 + 340 * q^64 + 138 * q^66 - 270 * q^67 - 710 * q^68 + 340 * q^69 - 66 * q^71 - 360 * q^72 - 30 * q^73 - 80 * q^76 + 250 * q^77 + 500 * q^78 - 210 * q^79 + 62 * q^81 - 30 * q^82 - 10 * q^84 - 6 * q^86 - 300 * q^87 - 190 * q^88 - 10 * q^89 - 6 * q^91 + 30 * q^92 - 520 * q^93 + 790 * q^94 + 174 * q^96 - 270 * q^97 - 170 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{20}\right)$

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

)

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

$2$	−0.0933465	+	0.589367i	−0.0466733	+	0.294683i	−0.999973	−	0.00734232i	$-0.997663\pi$
$2$	−0.0933465	+	0.589367i	−0.0466733	+	0.294683i	0.953300	+	0.302026i	$0.0976628\pi$
$3$	−0.210730	+	0.107372i	−0.0702435	+	0.0357908i	−0.488759	−	0.872419i	$-0.662550\pi$
$3$	−0.210730	+	0.107372i	−0.0702435	+	0.0357908i	0.418516	+	0.908209i	$0.362550\pi$
$4$	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	$-0.0308906\pi$
$8$	−2.07076	+	4.06409i	−0.258845	+	0.508011i
$9$	−5.25719	+	7.23590i	−0.584132	+	0.803989i
$10$		0			0
$11$	7.33868	−	5.33186i	0.667152	−	0.484715i	−0.201918	−	0.979402i	$-0.564718\pi$
$11$	7.33868	−	5.33186i	0.667152	−	0.484715i	0.869071	+	0.494688i	$0.164718\pi$
$12$	−0.851210	+	0.134818i	−0.0709342	+	0.0112349i
$13$	2.12306	+	13.4044i	0.163312	+	1.03111i	0.924111	+	0.382124i	$0.124807\pi$
$13$	2.12306	+	13.4044i	0.163312	+	1.03111i	−0.760799	+	0.648987i	$0.775193\pi$
$14$	3.79223	+	5.21956i	0.270874	+	0.372826i
$15$		0			0
$16$	9.59007	+	6.96760i	0.599380	+	0.435475i
$17$	−0.704962	−	0.359196i	−0.0414683	−	0.0211292i	0.433133	−	0.901330i	$-0.357408\pi$
$17$	−0.704962	−	0.359196i	−0.0414683	−	0.0211292i	−0.474602	+	0.880201i	$0.657408\pi$
$18$	−3.77386	−	3.77386i	−0.209659	−	0.209659i
$19$	13.5696	−	4.40902i	0.714187	−	0.232054i	0.0706862	−	0.997499i	$-0.477481\pi$
$19$	13.5696	−	4.40902i	0.714187	−	0.232054i	0.643501	+	0.765445i	$0.277481\pi$
$20$		0			0
$21$	−0.790204	+	2.43200i	−0.0376288	+	0.115809i
$22$	2.45738	+	4.82288i	0.111699	+	0.219222i
$23$	−13.5597	−	2.14764i	−0.589551	−	0.0933757i	−0.145470	−	0.989363i	$-0.546470\pi$
$23$	−13.5597	−	2.14764i	−0.589551	−	0.0933757i	−0.444080	+	0.895987i	$0.646470\pi$
$24$		−	1.07877i		−	0.0449488i
$25$		0			0
$26$	−8.09832			−0.311474
$27$	0.663895	−	4.19167i	0.0245887	−	0.155247i
$28$	35.1044	−	17.8866i	1.25373	−	0.638807i
$29$	−36.6306	−	11.9020i	−1.26312	−	0.410413i	−0.400517	−	0.916289i	$-0.631169\pi$
$29$	−36.6306	−	11.9020i	−1.26312	−	0.410413i	−0.862606	+	0.505876i	$0.831169\pi$
$30$		0			0
$31$	−2.87530	−	8.84925i	−0.0927515	−	0.285460i	0.893910	−	0.448247i	$-0.147952\pi$
$31$	−2.87530	−	8.84925i	−0.0927515	−	0.285460i	−0.986661	+	0.162787i	$0.947952\pi$
$32$	−17.9028	+	17.9028i	−0.559462	+	0.559462i
$33$	−0.973987	+	1.91156i	−0.0295148	+	0.0579260i
$34$	0.277504	−	0.381951i	0.00816188	−	0.0112339i
$35$		0			0
$36$	−26.3671	+	19.1568i	−0.732420	+	0.532135i
$37$	−9.13820	+	1.44735i	−0.246978	+	0.0391175i	−0.278696	−	0.960379i	$-0.589902\pi$
$37$	−9.13820	+	1.44735i	−0.246978	+	0.0391175i	0.0317178	+	0.999497i	$0.489902\pi$
$38$	1.33186	+	8.40902i	0.0350489	+	0.221290i
$39$	−1.88666	−	2.59677i	−0.0483759	−	0.0665838i
$40$		0			0
$41$	−33.7351	−	24.5100i	−0.822807	−	0.597805i	0.0947079	−	0.995505i	$-0.469808\pi$
$41$	−33.7351	−	24.5100i	−0.822807	−	0.597805i	−0.917515	+	0.397701i	$0.869808\pi$
$42$	−1.35958	−	0.692738i	−0.0323708	−	0.0164938i
$43$	−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
$47$	−9.65116	−	18.9415i	−0.205344	−	0.403010i	0.765250	−	0.643733i	$-0.222615\pi$
$47$	−9.65116	−	18.9415i	−0.205344	−	0.403010i	−0.970594	+	0.240723i	$0.922615\pi$
$48$	−2.76905	−	0.438574i	−0.0576885	−	0.00913696i
$49$		−	67.9017i		−	1.38575i
$50$		0			0
$51$	0.187125			0.00366911
$52$	−7.73627	+	48.8449i	−0.148775	+	0.939325i
$53$	56.8742	−	28.9788i	1.07310	−	0.546771i	0.174102	−	0.984728i	$-0.444298\pi$
$53$	56.8742	−	28.9788i	1.07310	−	0.546771i	0.898996	+	0.437957i	$0.144298\pi$
$54$	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
$58$	10.4340	−	20.4778i	0.179896	−	0.353066i
$59$	−45.6440	+	62.8235i	−0.773627	+	1.06481i	0.222330	+	0.974971i	$0.428634\pi$
$59$	−45.6440	+	62.8235i	−0.773627	+	1.06481i	−0.995957	+	0.0898343i	$0.971366\pi$
$60$		0			0
$61$	11.4153	−	8.29369i	0.187136	−	0.135962i	−0.490273	−	0.871569i	$-0.663103\pi$
$61$	11.4153	−	8.29369i	0.187136	−	0.135962i	0.677409	+	0.735607i	$0.263103\pi$
$62$	5.48385	−	0.868557i	0.0884492	−	0.0140090i
$63$	15.1279	+	95.5136i	0.240125	+	1.51609i
$64$	18.9902	+	26.1378i	0.296722	+	0.408403i
$65$		0			0
$66$	−1.03569	−	0.752473i	−0.0156923	−	0.0114011i
$67$	46.8978	+	23.8956i	0.699968	+	0.356651i	0.767485	−	0.641067i	$-0.221508\pi$
$67$	46.8978	+	23.8956i	0.699968	+	0.356651i	−0.0675175	+	0.997718i	$0.521508\pi$
$68$	−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	−0.956838	−	0.290621i	$-0.906138\pi$
$71$	−0.846117	+	2.60408i	−0.0119171	+	0.0366772i	0.944921	+	0.327298i	$0.106138\pi$
$72$	−18.5210	−	36.3495i	−0.257236	−	0.504854i
$73$	−60.7976	−	9.62940i	−0.832844	−	0.131910i	−0.274571	−	0.961567i	$-0.588536\pi$
$73$	−60.7976	−	9.62940i	−0.832844	−	0.131910i	−0.558273	+	0.829657i	$0.688536\pi$
$74$		−	5.52086i		−	0.0746062i
$75$		0			0
$76$	51.9912			0.684095
$77$	15.3427	−	96.8703i	0.199256	−	1.25806i
$78$	1.70656	−	0.869536i	0.0218790	−	0.0111479i
$79$	−6.18905	−	2.01094i	−0.0783423	−	0.0254550i	0.269584	−	0.962977i	$-0.413114\pi$
$79$	−6.18905	−	2.01094i	−0.0783423	−	0.0254550i	−0.347926	+	0.937522i	$0.613114\pi$
$80$		0			0
$81$	−24.5646	−	75.6022i	−0.303267	−	0.933360i
$82$	17.5944	−	17.5944i	0.214566	−	0.214566i
$83$	−50.9593	+	100.013i	−0.613967	+	1.20498i	0.349446	+	0.936957i	$0.386370\pi$
$83$	−50.9593	+	100.013i	−0.613967	+	1.20498i	−0.963413	+	0.268021i	$0.913630\pi$
$84$	−5.47704	+	7.53850i	−0.0652029	+	0.0897440i
$85$		0			0
$86$	33.7274	−	24.5044i	0.392180	−	0.284935i
$87$	8.99712	−	1.42500i	0.103415	−	0.0163794i
$88$	6.47255	+	40.8661i	0.0735517	+	0.464387i
$89$	65.5853	+	90.2704i	0.736914	+	1.01427i	0.998790	+	0.0491732i	$0.0156586\pi$
$89$	65.5853	+	90.2704i	0.736914	+	1.01427i	−0.261877	+	0.965101i	$0.584341\pi$
$90$		0			0
$91$	118.713	+	86.2498i	1.30454	+	0.947800i
$92$	−44.5739	−	22.7115i	−0.484499	−	0.246864i
$93$	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
$97$	58.6053	+	115.019i	0.604178	+	1.18577i	0.967207	+	0.253989i	$0.0817427\pi$
$97$	58.6053	+	115.019i	0.604178	+	1.18577i	−0.363029	+	0.931778i	$0.618257\pi$
$98$	40.0190	+	6.33839i	0.408357	+	0.0646775i
$99$			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	$0.551460\pi$
$102$	−0.0174674	+	0.110285i	−0.000171249	+	0.00108123i
$103$	46.2893	−	23.5856i	0.449411	−	0.228986i	−0.214611	−	0.976700i	$-0.568848\pi$
$103$	46.2893	−	23.5856i	0.449411	−	0.228986i	0.664022	+	0.747713i	$0.268848\pi$
$104$	−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	$0.176137\pi$
$108$	7.02076	−	13.7790i	0.0650071	−	0.127584i
$109$	76.0086	−	104.617i	0.697326	−	0.959787i	−0.302651	−	0.953101i	$-0.597872\pi$
$109$	76.0086	−	104.617i	0.697326	−	0.959787i	0.999978	−	0.00668585i	$-0.00212819\pi$
$110$		0			0
$111$	1.77029	−	1.28619i	0.0159486	−	0.0115873i
$112$	126.589	−	20.0497i	1.13026	−	0.179015i
$113$	−11.9724	−	75.5905i	−0.105950	−	0.668942i	−0.982307	−	0.187279i	$-0.940033\pi$
$113$	−11.9724	−	75.5905i	−0.105950	−	0.668942i	0.876357	−	0.481663i	$-0.159967\pi$
$114$	−1.18356	−	1.62903i	−0.0103821	−	0.0142897i
$115$		0			0
$116$	−113.544	−	82.4948i	−0.978830	−	0.711162i
$117$	−108.155	−	55.1075i	−0.924398	−	0.471004i
$118$	−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
$122$	3.82245	+	7.50197i	0.0313315	+	0.0614916i
$123$	9.74071	+	1.54278i	0.0791928	+	0.0125429i
$124$		−	33.9055i		−	0.273432i
$125$		0			0
$126$	−57.7047			−0.457974
$127$	−9.58264	+	60.5024i	−0.0754539	+	0.476397i	0.920808	+	0.390016i	$0.127530\pi$
$127$	−9.58264	+	60.5024i	−0.0754539	+	0.476397i	−0.996262	+	0.0863815i	$0.972470\pi$
$128$	−107.413	+	54.7295i	−0.839162	+	0.427575i
$129$	15.7149	+	5.10609i	0.121821	+	0.0395821i
$130$		0			0
$131$	−1.09573	−	3.37230i	−0.00836432	−	0.0257427i	0.946787	−	0.321860i	$-0.104308\pi$
$131$	−1.09573	−	3.37230i	−0.00836432	−	0.0257427i	−0.955152	+	0.296117i	$0.904308\pi$
$132$	−5.52792	+	5.52792i	−0.0418782	+	0.0418782i
$133$	70.0353	−	137.452i	0.526581	−	1.03347i
$134$	−18.4610	+	25.4094i	−0.137769	+	0.189623i
$135$		0			0
$136$	2.91961	−	2.12122i	0.0214677	−	0.0155972i
$137$	−246.624	+	39.0615i	−1.80018	+	0.285120i	−0.964497	−	0.264094i	$-0.914927\pi$
$137$	−246.624	+	39.0615i	−1.80018	+	0.285120i	−0.835682	+	0.549214i	$0.814927\pi$
$138$	0.303091	+	1.91364i	0.00219631	+	0.0138670i
$139$	−81.3839	−	112.015i	−0.585496	−	0.805866i	0.408789	−	0.912629i	$-0.365951\pi$
$139$	−81.3839	−	112.015i	−0.585496	−	0.805866i	−0.994284	+	0.106763i	$0.965951\pi$
$140$		0			0
$141$	4.06758	+	2.95527i	0.0288481	+	0.0209594i
$142$	−1.45578	−	0.741755i	−0.0102519	−	0.00522363i
$143$	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
$147$	7.29078	+	14.3090i	0.0495971	+	0.0973399i
$148$	−33.2990	−	5.27404i	−0.224993	−	0.0356354i
$149$		−	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	$0.549841\pi$
$152$	−10.1806	+	64.2780i	−0.0669778	+	0.422881i
$153$	6.30522	−	3.21267i	0.0412106	−	0.0209978i
$154$	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	$0.390353\pi$
$158$	1.76291	−	3.45990i	0.0111577	−	0.0218981i
$159$	−8.87359	+	12.2134i	−0.0558087	+	0.0768141i
$160$		0			0
$161$	−120.087	+	87.2486i	−0.745884	+	0.541917i
$162$	46.8504	−	7.42038i	0.289200	−	0.0458048i
$163$	−41.3763	−	261.240i	−0.253842	−	1.60270i	−0.704302	−	0.709901i	$-0.748740\pi$
$163$	−41.3763	−	261.240i	−0.253842	−	1.60270i	0.450459	−	0.892797i	$-0.351260\pi$
$164$	−89.3128	−	122.928i	−0.544590	−	0.749564i
$165$		0			0
$166$	−54.1876	−	39.3696i	−0.326431	−	0.237166i
$167$	239.969	+	122.270i	1.43694	+	0.732158i	0.986973	−	0.160886i	$-0.0514351\pi$
$167$	239.969	+	122.270i	1.43694	+	0.732158i	0.449969	+	0.893044i	$0.351435\pi$
$168$	−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
$172$	−115.579	−	226.836i	−0.671968	−	1.31881i
$173$	184.026	+	29.1468i	1.06373	+	0.168479i	0.663682	−	0.748014i	$-0.268993\pi$
$173$	184.026	+	29.1468i	1.06373	+	0.168479i	0.400050	+	0.916493i	$0.368993\pi$
$174$			5.43562i			0.0312392i
$175$		0			0
$176$	107.529			0.610959
$177$	2.87305	−	18.1397i	0.0162319	−	0.102484i
$178$	−59.3246	+	30.2274i	−0.333284	+	0.169817i
$179$	194.558	+	63.2157i	1.08692	+	0.353161i	0.797054	−	0.603908i	$-0.206391\pi$
$179$	194.558	+	63.2157i	1.08692	+	0.353161i	0.289862	+	0.957068i	$0.406391\pi$
$180$		0			0
$181$	8.53397	+	26.2649i	0.0471490	+	0.145110i	0.971859	−	0.235562i	$-0.0756929\pi$
$181$	8.53397	+	26.2649i	0.0471490	+	0.145110i	−0.924710	+	0.380671i	$0.875693\pi$
$182$	−61.9142	+	61.9142i	−0.340188	+	0.340188i
$183$	−1.51503	+	2.97342i	−0.00827887	+	0.0162482i
$184$	36.8070	−	50.6605i	0.200038	−	0.275329i
$185$		0			0
$186$	−1.06236	+	0.771846i	−0.00571159	+	0.00414971i
$187$	−7.08867	+	1.12273i	−0.0379073	+	0.00600393i
$188$	−12.1181	−	76.5108i	−0.0644581	−	0.406973i
$189$	−26.9710	−	37.1223i	−0.142703	−	0.196414i
$190$		0			0
$191$	75.2465	+	54.6697i	0.393960	+	0.286229i	0.767076	−	0.641556i	$-0.221711\pi$
$191$	75.2465	+	54.6697i	0.393960	+	0.286229i	−0.373116	+	0.927785i	$0.621711\pi$
$192$	−6.80830	−	3.46900i	−0.0354599	−	0.0180677i
$193$	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
$197$	19.6944	+	38.6524i	0.0999715	+	0.196205i	0.935575	−	0.353128i	$-0.114882\pi$
$197$	19.6944	+	38.6524i	0.0999715	+	0.196205i	−0.835604	+	0.549333i	$0.814882\pi$
$198$	−47.8168	−	7.57344i	−0.241499	−	0.0382497i
$199$			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
$202$	3.03512	−	19.1630i	0.0150253	−	0.0948663i
$203$	−371.047	+	189.058i	−1.82782	+	0.931319i
$204$	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
$208$	−73.0365	+	143.342i	−0.351137	+	0.689145i
$209$	76.0744	−	104.707i	0.363992	−	0.500992i
$210$		0			0
$211$	203.359	−	147.749i	0.963785	−	0.700231i	0.00975810	−	0.999952i	$-0.496894\pi$
$211$	203.359	−	147.749i	0.963785	−	0.700231i	0.954027	+	0.299722i	$0.0968939\pi$
$212$	229.734	−	36.3862i	1.08365	−	0.171633i
$213$	−0.101304	−	0.639609i	−0.000475606	−	0.00300286i
$214$	17.2612	+	23.7580i	0.0806597	+	0.111019i
$215$		0			0
$216$	15.6606	+	11.3781i	0.0725026	+	0.0526762i
$217$	−89.6379	−	45.6728i	−0.413078	−	0.210474i
$218$	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
$222$	0.592788	+	1.16341i	0.00267022	+	0.00524060i
$223$	74.7975	+	11.8468i	0.335415	+	0.0531245i	0.321870	−	0.946784i	$-0.395688\pi$
$223$	74.7975	+	11.8468i	0.335415	+	0.0531245i	0.0135446	+	0.999908i	$0.495688\pi$
$224$			273.745i			1.22208i
$225$		0			0
$226$	45.6681			0.202071
$227$	53.6868	−	338.965i	0.236506	−	1.49324i	−0.528345	−	0.849030i	$-0.677187\pi$
$227$	53.6868	−	338.965i	0.236506	−	1.49324i	0.764850	−	0.644208i	$-0.222813\pi$
$228$	−10.9561	+	5.58243i	−0.0480532	+	0.0244843i
$229$	22.2341	+	7.22430i	0.0970921	+	0.0315471i	0.357160	−	0.934043i	$-0.383745\pi$
$229$	22.2341	+	7.22430i	0.0970921	+	0.0315471i	−0.260068	+	0.965590i	$0.583745\pi$
$230$		0			0
$231$	7.16802	+	22.0609i	0.0310304	+	0.0955017i
$232$	124.224	−	124.224i	0.535447	−	0.535447i
$233$	86.9078	−	170.566i	0.372995	−	0.732044i	−0.625858	−	0.779937i	$-0.715251\pi$
$233$	86.9078	−	170.566i	0.372995	−	0.732044i	0.998852	+	0.0478936i	$0.0152509\pi$
$234$	42.5744	−	58.5986i	0.181942	−	0.250421i
$235$		0			0
$236$	−228.925	+	166.324i	−0.970020	+	0.704761i
$237$	1.52014	−	0.240767i	0.00641409	−	0.00101589i
$238$	−0.798534	−	5.04174i	−0.00335518	−	0.0211838i
$239$	32.3070	+	44.4668i	0.135176	+	0.186054i	0.871239	−	0.490860i	$-0.163317\pi$
$239$	32.3070	+	44.4668i	0.135176	+	0.186054i	−0.736063	+	0.676913i	$0.763317\pi$
$240$		0			0
$241$	−27.3775	−	19.8909i	−0.113600	−	0.0825349i	0.529535	−	0.848288i	$-0.322366\pi$
$241$	−27.3775	−	19.8909i	−0.113600	−	0.0825349i	−0.643135	+	0.765753i	$0.722366\pi$
$242$	−20.5839	−	10.4880i	−0.0850573	−	0.0433388i
$243$	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
$247$	87.9094	+	172.532i	0.355908	+	0.698510i
$248$	41.9182	+	6.63919i	0.169025	+	0.0267709i
$249$		−	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	$0.354292\pi$
$252$	−55.1250	+	348.045i	−0.218750	+	1.38113i
$253$	−110.961	+	56.5374i	−0.438581	+	0.223468i
$254$	−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	$0.232179\pi$
$258$	−4.47630	+	8.78523i	−0.0173500	+	0.0340513i
$259$	−58.7990	+	80.9299i	−0.227023	+	0.312471i
$260$		0			0
$261$	278.695	−	202.484i	1.06780	−	0.775801i
$262$	2.08980	−	0.330992i	0.00797634	−	0.00126333i
$263$	0.847808	+	5.35285i	0.00322361	+	0.0203530i	0.989248	−	0.146250i	$-0.0467203\pi$
$263$	0.847808	+	5.35285i	0.00322361	+	0.0203530i	−0.986024	+	0.166603i	$0.946720\pi$
$264$	−5.75185	−	7.91675i	−0.0217873	−	0.0299877i
$265$		0			0
$266$	74.4721	+	54.1071i	0.279970	+	0.203410i
$267$	−23.5134	−	11.9807i	−0.0880651	−	0.0448714i
$268$	135.621	+	135.621i	0.506049	+	0.506049i
$269$	−59.0391	+	19.1830i	−0.219476	+	0.0713122i	−0.416691	−	0.909048i	$-0.636810\pi$
$269$	−59.0391	+	19.1830i	−0.219476	+	0.0713122i	0.197215	+	0.980360i	$0.436810\pi$
$270$		0			0
$271$	−99.9539	+	307.626i	−0.368833	+	1.13515i	0.578712	+	0.815532i	$0.303556\pi$
$271$	−99.9539	+	307.626i	−0.368833	+	1.13515i	−0.947546	+	0.319621i	$0.896444\pi$
$272$	−4.25790	−	8.35660i	−0.0156540	−	0.0307228i
$273$	−34.2772	−	5.42898i	−0.125558	−	0.0198864i
$274$		−	148.999i		−	0.543790i
$275$		0			0
$276$	11.8317			0.0428684
$277$	−11.4134	+	72.0614i	−0.0412036	+	0.260150i	−0.999688	−	0.0249971i	$-0.992042\pi$
$277$	−11.4134	+	72.0614i	−0.0412036	+	0.260150i	0.958484	+	0.285147i	$0.0920423\pi$
$278$	73.6150	−	37.5087i	0.264802	−	0.134924i
$279$	79.1483	+	25.7168i	0.283686	+	0.0921750i
$280$		0			0
$281$	−84.2374	−	259.256i	−0.299777	−	0.922619i	−0.981575	−	0.191079i	$-0.938801\pi$
$281$	−84.2374	−	259.256i	−0.299777	−	0.922619i	0.681798	−	0.731541i	$-0.261199\pi$
$282$	−2.12143	+	2.12143i	−0.00752282	+	0.00752282i
$283$	−89.6096	+	175.869i	−0.316642	+	0.621445i	−0.993392	−	0.114768i	$-0.963388\pi$
$283$	−89.6096	+	175.869i	−0.316642	+	0.621445i	0.676750	+	0.736212i	$0.263388\pi$
$284$	−5.86459	+	8.07191i	−0.0206499	+	0.0284222i
$285$		0			0
$286$	−59.4309	+	43.1791i	−0.207800	+	0.150976i
$287$	−445.302	+	70.5289i	−1.55158	+	0.245745i
$288$	−35.4245	−	223.661i	−0.123002	−	0.776601i
$289$	−169.502	−	233.299i	−0.586512	−	0.807265i
$290$		0			0
$291$	−24.6998	−	17.9455i	−0.0848792	−	0.0616683i
$292$	−199.856	−	101.832i	−0.684440	−	0.348739i
$293$	−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
$297$	−17.4773	−	34.3011i	−0.0588461	−	0.115492i
$298$	60.7474	+	9.62145i	0.203850	+	0.0322867i
$299$		−	186.319i		−	0.623142i
$300$		0			0
$301$	−755.389			−2.50960
$302$	4.39606	−	27.7556i	0.0145565	−	0.0919060i
$303$	6.85180	−	3.49117i	0.0226132	−	0.0115220i
$304$	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	$0.191682\pi$
$308$	162.251	−	318.436i	0.526789	−	1.03388i
$309$	−7.22212	+	9.94040i	−0.0233726	+	0.0321696i
$310$		0			0
$311$	−91.8901	+	66.7620i	−0.295466	+	0.214669i	−0.725635	−	0.688080i	$-0.758454\pi$
$311$	−91.8901	+	66.7620i	−0.295466	+	0.214669i	0.430169	+	0.902748i	$0.358454\pi$
$312$	14.4603	−	2.29029i	0.0463472	−	0.00734067i
$313$	16.0776	+	101.510i	0.0513662	+	0.324314i	0.999969	+	0.00784510i	$0.00249720\pi$
$313$	16.0776	+	101.510i	0.0513662	+	0.324314i	−0.948603	+	0.316469i	$0.897503\pi$
$314$	−47.0024	−	64.6933i	−0.149689	−	0.206029i
$315$		0			0
$316$	−19.1843	−	13.9382i	−0.0607097	−	0.0441082i
$317$	363.850	+	185.391i	1.14779	+	0.584829i	0.921172	−	0.389155i	$-0.127233\pi$
$317$	363.850	+	185.391i	1.14779	+	0.584829i	0.226618	+	0.973984i	$0.427233\pi$
$318$	−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
$322$	−40.2117	−	78.9199i	−0.124881	−	0.245093i
$323$	−11.1497	−	1.76594i	−0.0345193	−	0.00546731i
$324$		−	289.667i		−	0.894033i
$325$		0			0
$326$	157.828			0.484136
$327$	−4.78435	+	30.2072i	−0.0146310	+	0.0923767i
$328$	169.468	−	86.3483i	0.516671	−	0.263257i
$329$	−218.600	−	71.0273i	−0.664437	−	0.215889i
$330$		0			0
$331$	−37.2677	−	114.698i	−0.112591	−	0.346520i	0.878846	−	0.477106i	$-0.158314\pi$
$331$	−37.2677	−	114.698i	−0.112591	−	0.346520i	−0.991437	+	0.130586i	$0.958314\pi$
$332$	−289.222	+	289.222i	−0.871151	+	0.871151i
$333$	37.5684	−	73.7321i	0.112818	−	0.221418i
$334$	−94.4624	+	130.016i	−0.282822	+	0.389271i
$335$		0			0
$336$	−24.5233	+	17.8172i	−0.0729860	+	0.0530274i
$337$	38.2752	−	6.06219i	0.113576	−	0.0179887i	−0.0993876	−	0.995049i	$-0.531688\pi$
$337$	38.2752	−	6.06219i	0.113576	−	0.0179887i	0.212964	+	0.977060i	$0.431688\pi$
$338$	−1.41762	−	8.95048i	−0.00419413	−	0.0264807i
$339$	10.6393	+	14.6437i	0.0313843	+	0.0431968i
$340$		0			0
$341$	−68.2838	−	49.6111i	−0.200246	−	0.145487i
$342$	−67.8486	−	34.5706i	−0.198388	−	0.101084i
$343$	−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
$347$	106.794	+	209.594i	0.307762	+	0.604018i	0.992143	−	0.125107i	$-0.0399274\pi$
$347$	106.794	+	209.594i	0.307762	+	0.604018i	−0.684381	+	0.729125i	$0.739927\pi$
$348$	32.7849	+	5.19262i	0.0942095	+	0.0149213i
$349$			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
$352$	−35.9276	+	226.838i	−0.102067	+	0.644426i
$353$	449.055	−	228.805i	1.27211	−	0.648173i	0.318132	−	0.948046i	$-0.396944\pi$
$353$	449.055	−	228.805i	1.27211	−	0.648173i	0.953979	+	0.299873i	$0.0969444\pi$
$354$	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
$358$	−55.4186	+	108.765i	−0.154800	+	0.303813i
$359$	198.037	−	272.575i	0.551636	−	0.759262i	−0.438597	−	0.898684i	$-0.644525\pi$
$359$	198.037	−	272.575i	0.551636	−	0.759262i	0.990233	+	0.139422i	$0.0445245\pi$
$360$		0			0
$361$	−127.362	+	92.5336i	−0.352802	+	0.256326i
$362$	−16.2763	+	2.57791i	−0.0449620	+	0.00712129i
$363$	−1.43238	−	9.04370i	−0.00394596	−	0.0249138i
$364$	314.289	+	432.581i	0.863430	+	1.18841i
$365$		0			0
$366$	−1.61101	−	1.17047i	−0.00440167	−	0.00319800i
$367$	−416.928	−	212.435i	−1.13604	−	0.578843i	−0.218247	−	0.975894i	$-0.570034\pi$
$367$	−416.928	−	212.435i	−1.13604	−	0.578843i	−0.917797	+	0.397050i	$0.870034\pi$
$368$	−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
$372$	3.64052	+	7.14493i	0.00978635	+	0.0192068i
$373$	−474.868	−	75.2117i	−1.27310	−	0.201640i	−0.516940	−	0.856022i	$-0.672929\pi$
$373$	−474.868	−	75.2117i	−1.27310	−	0.201640i	−0.756164	+	0.654382i	$0.772929\pi$
$374$		−	4.28263i		−	0.0114509i
$375$		0			0
$376$	96.9651			0.257886
$377$	81.7709	−	516.281i	0.216899	−	1.36945i
$378$	24.3963	−	12.4305i	0.0645405	−	0.0328850i
$379$	−597.265	−	194.063i	−1.57590	−	0.512040i	−0.614901	−	0.788604i	$-0.710804\pi$
$379$	−597.265	−	194.063i	−1.57590	−	0.512040i	−0.960995	+	0.276564i	$0.910804\pi$
$380$		0			0
$381$	−4.47694	−	13.7786i	−0.0117505	−	0.0361643i
$382$	−39.2445	+	39.2445i	−0.102734	+	0.102734i
$383$	−175.227	+	343.902i	−0.457511	+	0.897916i	0.540874	+	0.841104i	$0.318094\pi$
$383$	−175.227	+	343.902i	−0.457511	+	0.897916i	−0.998385	+	0.0568121i	$0.981906\pi$
$384$	16.7587	−	23.0664i	0.0436424	−	0.0600686i
$385$		0			0
$386$	−117.851	+	85.6241i	−0.305315	+	0.221824i
$387$	617.184	−	97.7524i	1.59479	−	0.252590i
$388$	73.5856	+	464.601i	0.189654	+	1.19743i
$389$	230.009	+	316.581i	0.591284	+	0.813833i	0.994876	−	0.101107i	$-0.0322383\pi$
$389$	230.009	+	316.581i	0.591284	+	0.813833i	−0.403592	+	0.914939i	$0.632238\pi$
$390$		0			0
$391$	8.78762	+	6.38458i	0.0224747	+	0.0163289i
$392$	275.959	+	140.608i	0.703977	+	0.358694i
$393$	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
$397$	−155.364	−	304.919i	−0.391345	−	0.768058i	0.608326	−	0.793687i	$-0.291841\pi$
$397$	−155.364	−	304.919i	−0.391345	−	0.768058i	−0.999672	+	0.0256288i	$0.991841\pi$
$398$	−195.204	−	30.9173i	−0.490463	−	0.0776817i
$399$			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	$0.188350\pi$
$402$	1.16203	−	7.33675i	0.00289062	−	0.0182506i
$403$	112.515	−	57.3292i	0.279193	−	0.142256i
$404$	−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
$408$	−0.387490	+	0.760491i	−0.000949730	+	0.00186395i
$409$	−369.812	+	509.003i	−0.904187	+	1.24451i	0.0649265	+	0.997890i	$0.479319\pi$
$409$	−369.812	+	509.003i	−0.904187	+	1.24451i	−0.969113	+	0.246616i	$0.920681\pi$
$410$		0			0
$411$	47.7771	−	34.7121i	0.116246	−	0.0844577i
$412$	186.978	−	29.6144i	0.453830	−	0.0718796i
$413$	131.343	+	829.269i	0.318022	+	2.00791i
$414$	43.0674	+	59.2772i	0.104028	+	0.143182i
$415$		0			0
$416$	−277.986	−	201.968i	−0.668235	−	0.485501i
$417$	29.1774	+	14.8666i	0.0699699	+	0.0356514i
$418$	54.6098	+	54.6098i	0.130645	+	0.130645i
$419$	−111.166	+	36.1200i	−0.265312	+	0.0862052i	−0.438652	−	0.898657i	$-0.644544\pi$
$419$	−111.166	+	36.1200i	−0.265312	+	0.0862052i	0.173340	+	0.984862i	$0.444544\pi$
$420$		0			0
$421$	1.06048	−	3.26382i	0.00251896	−	0.00775255i	−0.949789	−	0.312891i	$-0.898703\pi$
$421$	1.06048	−	3.26382i	0.00251896	−	0.00775255i	0.952308	+	0.305138i	$0.0987026\pi$
$422$	68.0953	+	133.645i	0.161363	+	0.316693i
$423$	187.796	+	29.7440i	0.443963	+	0.0703169i
$424$			291.150i			0.686675i
$425$		0			0
$426$	0.386421			0.000907090
$427$	23.8656	−	150.681i	0.0558913	−	0.352884i
$428$	159.785	−	81.4147i	0.373330	−	0.190221i
$429$	−27.6912	−	8.99742i	−0.0645482	−	0.0209730i
$430$		0			0
$431$	144.037	+	443.300i	0.334193	+	1.02854i	0.967118	+	0.254327i	$0.0818538\pi$
$431$	144.037	+	443.300i	0.334193	+	1.02854i	−0.632926	+	0.774212i	$0.718146\pi$
$432$	35.5727	−	35.5727i	0.0823441	−	0.0823441i
$433$	−90.0802	+	176.792i	−0.208037	+	0.408296i	−0.971323	−	0.237765i	$-0.923585\pi$
$433$	−90.0802	+	176.792i	−0.208037	+	0.408296i	0.763285	+	0.646062i	$0.223585\pi$
$434$	35.2854	−	48.5662i	0.0813028	−	0.111904i
$435$		0			0
$436$	381.217	−	276.970i	0.874350	−	0.635253i
$437$	−193.468	+	30.6423i	−0.442718	+	0.0701196i
$438$	1.35897	+	8.58022i	0.00310268	+	0.0195896i
$439$	288.145	+	396.598i	0.656367	+	0.903412i	0.999354	−	0.0359283i	$-0.0114388\pi$
$439$	288.145	+	396.598i	0.656367	+	0.903412i	−0.342987	+	0.939340i	$0.611439\pi$
$440$		0			0
$441$	491.330	+	356.972i	1.11413	+	0.809461i
$442$	5.70900	+	2.90888i	0.0129163	+	0.00658118i
$443$	−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
$447$	11.0671	+	21.7205i	0.0247587	+	0.0485917i
$448$	345.018	+	54.6455i	0.770130	+	0.121977i
$449$		−	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
$452$	43.6265	−	275.447i	0.0965187	−	0.609395i
$453$	9.92413	−	5.05660i	0.0219076	−	0.0111625i
$454$	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	$0.177516\pi$
$458$	−6.33324	+	12.4297i	−0.0138280	+	0.0271390i
$459$	−1.97365	+	2.71650i	−0.00429989	+	0.00591829i
$460$		0			0
$461$	270.507	−	196.534i	0.586782	−	0.426322i	−0.254381	−	0.967104i	$-0.581872\pi$
$461$	270.507	−	196.534i	0.586782	−	0.426322i	0.841163	+	0.540782i	$0.181872\pi$
$462$	−13.6711	+	2.16529i	−0.0295911	+	0.00468676i
$463$	4.34214	+	27.4152i	0.00937827	+	0.0592120i	0.991934	−	0.126758i	$-0.0404572\pi$
$463$	4.34214	+	27.4152i	0.00937827	+	0.0592120i	−0.982555	+	0.185970i	$0.940457\pi$
$464$	−268.362	−	369.368i	−0.578365	−	0.796052i
$465$		0			0
$466$	92.4135	+	67.1423i	0.198312	+	0.144082i
$467$	365.168	+	186.062i	0.781943	+	0.398420i	0.798921	−	0.601436i	$-0.205404\pi$
$467$	365.168	+	186.062i	0.781943	+	0.398420i	−0.0169777	+	0.999856i	$0.505404\pi$
$468$	−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
$472$	−160.803	−	315.594i	−0.340684	−	0.668631i
$473$	−625.951	−	99.1408i	−1.32336	−	0.209600i
$474$			0.918395i			0.00193754i
$475$		0			0
$476$	−31.1721			−0.0654875
$477$	−89.3103	+	563.883i	−0.187233	+	1.18215i
$478$	−29.2230	+	14.8899i	−0.0611360	+	0.0311504i
$479$	579.516	+	188.296i	1.20985	+	0.393103i	0.843374	−	0.537326i	$-0.180566\pi$
$479$	579.516	+	188.296i	1.20985	+	0.393103i	0.366472	+	0.930429i	$0.380566\pi$
$480$		0			0
$481$	−38.8018	−	119.420i	−0.0806691	−	0.248274i
$482$	14.2786	−	14.2786i	0.0296237	−	0.0296237i
$483$	15.9380	−	31.2800i	0.0329978	−	0.0647619i
$484$	−82.9219	+	114.132i	−0.171326	+	0.235810i
$485$		0			0
$486$	−27.5149	+	19.9907i	−0.0566150	+	0.0411332i
$487$	−229.164	+	36.2960i	−0.470563	+	0.0745298i	−0.387213	−	0.921990i	$-0.626562\pi$
$487$	−229.164	+	36.2960i	−0.470563	+	0.0745298i	−0.0833503	+	0.996520i	$0.526562\pi$
$488$	10.0680	+	63.5670i	0.0206312	+	0.130260i
$489$	36.7692	+	50.6085i	0.0751927	+	0.103494i
$490$		0			0
$491$	−288.845	−	209.858i	−0.588279	−	0.427409i	0.253421	−	0.967356i	$-0.418444\pi$
$491$	−288.845	−	209.858i	−0.588279	−	0.427409i	−0.841699	+	0.539947i	$0.818444\pi$
$492$	32.0200	+	16.3150i	0.0650814	+	0.0331606i
$493$	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
$497$	13.4402	+	26.3779i	0.0270426	+	0.0530742i
$498$	15.6462	+	2.47811i	0.0314180	+	0.00497613i
$499$		−	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
$502$	−20.7091	+	130.752i	−0.0412532	+	0.260463i
$503$	728.768	−	371.326i	1.44884	−	0.738222i	0.460102	−	0.887866i	$-0.347813\pi$
$503$	728.768	−	371.326i	1.44884	−	0.738222i	0.988740	+	0.149644i	$0.0478127\pi$
$504$	−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
$508$	−101.337	+	198.886i	−0.199483	+	0.391508i
$509$	−529.260	+	728.463i	−1.03980	+	1.43117i	−0.142476	+	0.989798i	$0.545506\pi$
$509$	−529.260	+	728.463i	−1.03980	+	1.43117i	−0.897327	+	0.441367i	$0.854494\pi$
$510$		0			0
$511$	−538.437	+	391.197i	−1.05369	+	0.765552i
$512$	−510.041	+	80.7826i	−0.996174	+	0.157778i
$513$	−9.47238	−	59.8062i	−0.0184647	−	0.116581i
$514$	10.0881	+	13.8850i	0.0196266	+	0.0270137i
$515$		0			0
$516$	48.7118	+	35.3912i	0.0944028	+	0.0685876i
$517$	−171.820	−	87.5466i	−0.332340	−	0.169336i
$518$	−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	0.708698	+	0.705512i	$0.249283\pi$
$521$	−145.536	+	447.915i	−0.279340	+	0.859721i	−0.988038	+	0.154209i	$0.950717\pi$
$522$	93.3221	+	183.155i	0.178778	+	0.350872i
$523$	582.366	+	92.2377i	1.11351	+	0.176363i	0.685967	−	0.727632i	$-0.259379\pi$
$523$	582.366	+	92.2377i	1.11351	+	0.176363i	0.427543	+	0.903995i	$0.359379\pi$
$524$		−	12.9208i		−	0.0246580i
$525$		0			0
$526$	−3.23393			−0.00614816
$527$	−1.15164	+	7.27118i	−0.00218528	+	0.0137973i
$528$	−22.6596	+	11.5456i	−0.0429158	+	0.0218667i
$529$	−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
$533$	256.921	−	504.236i	0.482029	−	0.946035i
$534$	9.25590	−	12.7397i	0.0173331	−	0.0238570i
$535$		0			0
$536$	−194.228	+	141.115i	−0.362366	+	0.263274i
$537$	−47.7869	+	7.56870i	−0.0889887	+	0.0140944i
$538$	−5.79471	−	36.5864i	−0.0107708	−	0.0680044i
$539$	−362.043	−	498.309i	−0.671693	−	0.924506i
$540$		0			0
$541$	4.98311	+	3.62044i	0.00921092	+	0.00669212i	0.592381	−	0.805658i	$-0.298188\pi$
$541$	4.98311	+	3.62044i	0.00921092	+	0.00669212i	−0.583170	+	0.812350i	$0.698188\pi$
$542$	−171.974	−	87.6253i	−0.317296	−	0.161670i
$543$	−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
$547$	137.666	+	270.185i	0.251675	+	0.493940i	0.981932	−	0.189232i	$-0.0605998\pi$
$547$	137.666	+	270.185i	0.251675	+	0.493940i	−0.730257	+	0.683172i	$0.760600\pi$
$548$	−898.683	−	142.337i	−1.63993	−	0.259740i
$549$			126.201i			0.229875i
$550$		0			0
$551$	−549.537			−0.997344
$552$	−2.31681	+	14.6278i	−0.00419712	+	0.0264996i
$553$	−62.6915	+	31.9429i	−0.113366	+	0.0577630i
$554$	−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	$0.265855\pi$
$558$	−22.5449	+	44.2468i	−0.0404030	+	0.0792953i
$559$	557.324	−	767.091i	0.997002	−	1.37226i
$560$		0			0
$561$	1.37325	−	0.997722i	0.00244786	−	0.00177847i
$562$	160.660	−	25.4461i	0.285872	−	0.0452777i
$563$	−93.1829	−	588.334i	−0.165511	−	1.04500i	−0.920922	−	0.389746i	$-0.872563\pi$
$563$	−93.1829	−	588.334i	−0.165511	−	1.04500i	0.755411	−	0.655251i	$-0.227437\pi$
$564$	10.7688	+	14.8220i	0.0190936	+	0.0262802i
$565$		0			0
$566$	−95.2865	−	69.2297i	−0.168351	−	0.122314i
$567$	−765.807	−	390.198i	−1.35063	−	0.688180i
$568$	−8.83112	−	8.83112i	−0.0155477	−	0.0155477i
$569$	258.923	−	84.1291i	0.455049	−	0.147854i	−0.0725195	−	0.997367i	$-0.523104\pi$
$569$	258.923	−	84.1291i	0.455049	−	0.147854i	0.527568	+	0.849513i	$0.323104\pi$
$570$		0			0
$571$	−69.9094	+	215.159i	−0.122433	+	0.376811i	−0.993425	−	0.114487i	$-0.963477\pi$
$571$	−69.9094	+	215.159i	−0.122433	+	0.376811i	0.870991	+	0.491298i	$0.163477\pi$
$572$	203.660	+	399.706i	0.356049	+	0.698786i
$573$	−21.7267	−	3.44118i	−0.0379175	−	0.00600555i
$574$		−	269.030i		−	0.468693i
$575$		0			0
$576$	−288.966			−0.501677
$577$	−140.082	+	884.446i	−0.242777	+	1.53284i	0.501614	+	0.865092i	$0.332740\pi$
$577$	−140.082	+	884.446i	−0.242777	+	1.53284i	−0.744391	+	0.667744i	$0.767260\pi$
$578$	153.321	−	78.1211i	0.265262	−	0.135158i
$579$	−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
$583$	262.870	−	515.912i	0.450892	−	0.884926i
$584$	165.032	−	227.147i	0.282589	−	0.388950i
$585$		0			0
$586$	161.959	−	117.670i	0.276380	−	0.200802i
$587$	−346.752	+	54.9201i	−0.590718	+	0.0935606i	−0.444635	−	0.895712i	$-0.646667\pi$
$587$	−346.752	+	54.9201i	−0.590718	+	0.0935606i	−0.146083	+	0.989272i	$0.546667\pi$
$588$	9.15440	+	57.7986i	0.0155687	+	0.0982970i
$589$	−78.0330	−	107.403i	−0.132484	−	0.182348i
$590$		0			0
$591$	−8.30041	−	6.03060i	−0.0140447	−	0.0102041i
$592$	−97.7205	−	49.7911i	−0.165068	−	0.0841066i
$593$	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
$597$	−35.5629	−	69.7960i	−0.0595693	−	0.116911i
$598$	109.811	+	17.3923i	0.183630	+	0.0290841i
$599$			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	$0.269379\pi$
$602$	70.5129	−	445.201i	0.117131	−	0.739537i
$603$	−419.457	+	213.724i	−0.695617	+	0.354435i
$604$	−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	$0.927134\pi$
$608$	−163.999	+	321.867i	−0.269736	+	0.529386i
$609$	57.8912	−	79.6804i	0.0950595	−	0.130838i
$610$		0			0
$611$	233.410	−	169.582i	0.382013	−	0.277549i
$612$	25.4689	−	4.03387i	0.0416158	−	0.00659130i
$613$	19.5383	+	123.360i	0.0318732	+	0.201240i	0.998486	−	0.0550007i	$-0.0175161\pi$
$613$	19.5383	+	123.360i	0.0318732	+	0.201240i	−0.966613	+	0.256240i	$0.917516\pi$
$614$	39.2349	+	54.0022i	0.0639004	+	0.0879514i
$615$		0			0
$616$	361.919	+	262.949i	0.587530	+	0.426866i
$617$	639.236	+	325.707i	1.03604	+	0.527888i	0.887399	−	0.461003i	$-0.152510\pi$
$617$	639.236	+	325.707i	1.03604	+	0.527888i	0.148640	+	0.988891i	$0.452510\pi$
$618$	−5.18438	−	5.18438i	−0.00838897	−	0.00838897i
$619$	−196.553	+	63.8639i	−0.317533	+	0.103173i	−0.463447	−	0.886125i	$-0.653388\pi$
$619$	−196.553	+	63.8639i	−0.317533	+	0.103173i	0.145914	+	0.989297i	$0.453388\pi$
$620$		0			0
$621$	−18.0044	+	55.4118i	−0.0289926	+	0.0892300i
$622$	−30.7697	−	60.3889i	−0.0494690	−	0.0970883i
$623$	1191.57	+	188.726i	1.91263	+	0.302930i
$624$		−	38.0487i		−	0.0609754i
$625$		0			0
$626$	−61.3275			−0.0979673
$627$	−4.78849	+	30.2333i	−0.00763714	+	0.0482190i
$628$	−435.098	+	221.693i	−0.692831	+	0.353015i
$629$	6.96196	+	2.26208i	0.0110683	+	0.00359631i
$630$		0			0
$631$	68.8404	+	211.869i	0.109097	+	0.335767i	0.990670	−	0.136281i	$-0.0435149\pi$
$631$	68.8404	+	211.869i	0.109097	+	0.335767i	−0.881573	+	0.472048i	$0.843515\pi$
$632$	20.9887	−	20.9887i	0.0332099	−	0.0332099i
$633$	−26.9897	+	52.9703i	−0.0426377	+	0.0836813i
$634$	−143.227	+	197.135i	−0.225910	+	0.310939i
$635$		0			0
$636$	−44.5050	+	32.3348i	−0.0699764	+	0.0508408i
$637$	910.185	−	144.159i	1.42886	−	0.226310i
$638$	−32.6134	−	205.913i	−0.0511181	−	0.322747i
$639$	−14.3947	−	19.8126i	−0.0225269	−	0.0310056i
$640$		0			0
$641$	−709.800	−	515.700i	−1.10733	−	0.804524i	−0.125090	−	0.992145i	$-0.539922\pi$
$641$	−709.800	−	515.700i	−1.10733	−	0.804524i	−0.982241	+	0.187622i	$0.939922\pi$
$642$	−6.18840	−	3.15315i	−0.00963926	−	0.00491145i
$643$	−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
$647$	−400.518	−	786.060i	−0.619038	−	1.21493i	−0.961346	−	0.275343i	$-0.911209\pi$
$647$	−400.518	−	786.060i	−0.619038	−	1.21493i	0.342308	−	0.939588i	$-0.388791\pi$
$648$	358.122	+	56.7209i	0.552657	+	0.0875323i
$649$			704.409i			1.08538i
$650$		0			0
$651$	23.7934			0.0365490
$652$	150.773	−	951.940i	0.231246	−	1.46003i
$653$	−868.933	+	442.744i	−1.33068	+	0.678015i	−0.967302	−	0.253627i	$-0.918376\pi$
$653$	−868.933	+	442.744i	−1.33068	+	0.678015i	−0.363377	+	0.931642i	$0.618376\pi$
$654$	−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
$658$	62.2667	−	122.205i	0.0946302	−	0.185722i
$659$	337.348	−	464.320i	0.511909	−	0.704582i	−0.472331	−	0.881421i	$-0.656587\pi$
$659$	337.348	−	464.320i	0.511909	−	0.704582i	0.984240	+	0.176839i	$0.0565872\pi$
$660$		0			0
$661$	83.1335	−	60.4000i	0.125769	−	0.0913767i	−0.523122	−	0.852258i	$-0.675233\pi$
$661$	83.1335	−	60.4000i	0.125769	−	0.0913767i	0.648892	+	0.760881i	$0.275233\pi$
$662$	71.0781	−	11.2577i	0.107369	−	0.0170055i
$663$	0.397276	+	2.50830i	0.000599210	+	0.00378326i
$664$	−300.938	−	414.206i	−0.453220	−	0.623804i
$665$		0			0
$666$	39.9484	+	29.0242i	0.0599825	+	0.0435799i
$667$	471.137	+	240.056i	0.706353	+	0.359905i
$668$	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
$672$	−29.3927	−	57.6864i	−0.0437391	−	0.0858429i
$673$	−742.996	−	117.679i	−1.10401	−	0.174857i	−0.422280	−	0.906465i	$-0.638770\pi$
$673$	−742.996	−	117.679i	−1.10401	−	0.174857i	−0.681726	+	0.731608i	$0.738770\pi$
$674$			23.1240i			0.0343086i
$675$		0			0
$676$	−55.3389			−0.0818624
$677$	104.837	−	661.912i	0.154855	−	0.977714i	−0.780796	−	0.624786i	$-0.785186\pi$
$677$	104.837	−	661.912i	0.154855	−	0.977714i	0.935651	−	0.352928i	$-0.114814\pi$
$678$	−9.62365	+	4.90350i	−0.0141942	+	0.00723230i
$679$	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
$683$	−477.148	+	936.456i	−0.698607	+	1.37109i	0.219835	+	0.975537i	$0.429448\pi$
$683$	−477.148	+	936.456i	−0.698607	+	1.37109i	−0.918442	+	0.395556i	$0.870552\pi$
$684$	−273.328	+	376.203i	−0.399602	+	0.550005i
$685$		0			0
$686$	98.6588	−	71.6798i	0.143817	−	0.104489i
$687$	−5.46109	+	0.864952i	−0.00794919	+	0.00125903i
$688$	−129.556	−	817.983i	−0.188308	−	1.18893i
$689$	509.193	+	700.843i	0.739031	+	1.01719i
$690$		0			0
$691$	281.760	+	204.711i	0.407757	+	0.296253i	0.772693	−	0.634780i	$-0.218909\pi$
$691$	281.760	+	204.711i	0.407757	+	0.296253i	−0.364936	+	0.931033i	$0.618909\pi$
$692$	604.937	+	308.231i	0.874186	+	0.445420i
$693$	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
$697$	14.9781	+	29.3961i	0.0214893	+	0.0421752i
$698$	−9.96703	−	1.57862i	−0.0142794	−	0.00226164i
$699$			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	$0.337405\pi$
$702$	−5.37643	+	33.9455i	−0.00765874	+	0.0483554i
$703$	−117.620	+	59.9304i	−0.167312	+	0.0852495i
$704$	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
$708$	30.3828	−	59.6297i	0.0429136	−	0.0842227i
$709$	−142.144	+	195.644i	−0.200485	+	0.275944i	−0.897408	−	0.441202i	$-0.854552\pi$
$709$	−142.144	+	195.644i	−0.200485	+	0.275944i	0.696922	+	0.717146i	$0.254552\pi$
$710$		0			0
$711$	47.0880	−	34.2114i	0.0662278	−	0.0481173i
$712$	−502.679	+	79.6165i	−0.706009	+	0.111821i
$713$	19.9831	+	126.168i	0.0280267	+	0.176954i
$714$	0.709620	+	0.976708i	0.000993865	+	0.00136794i
$715$		0			0
$716$	603.074	+	438.159i	0.842283	+	0.611954i
$717$	−11.5826	−	5.90162i	−0.0161542	−	0.00823099i
$718$	142.161	+	142.161i	0.197995	+	0.197995i
$719$	−126.747	+	41.1825i	−0.176282	+	0.0572774i	−0.395828	−	0.918325i	$-0.629542\pi$
$719$	−126.747	+	41.1825i	−0.176282	+	0.0572774i	0.219546	+	0.975602i	$0.429542\pi$
$720$		0			0
$721$	173.577	−	534.216i	0.240745	−	0.740937i
$722$	−42.6475	−	83.7004i	−0.0590685	−	0.115928i
$723$	7.90500	+	1.25203i	0.0109336	+	0.00173171i
$724$			100.633i			0.138996i
$725$		0			0
$726$	5.46377			0.00752585
$727$	−202.138	+	1276.25i	−0.278044	+	1.75550i	0.313837	+	0.949477i	$0.398385\pi$
$727$	−202.138	+	1276.25i	−0.278044	+	1.75550i	−0.591881	+	0.806025i	$0.701615\pi$
$728$	−596.352	+	303.857i	−0.819165	+	0.417386i
$729$	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
$733$	379.282	−	744.383i	0.517438	−	1.01553i	−0.473448	−	0.880822i	$-0.656991\pi$
$733$	379.282	−	744.383i	0.517438	−	1.01553i	0.990885	−	0.134707i	$-0.0430093\pi$
$734$	164.121	−	225.893i	0.223598	−	0.307757i
$735$		0			0
$736$	281.205	−	204.307i	0.382072	−	0.277591i
$737$	471.576	−	74.6903i	0.639859	−	0.101344i
$738$	34.8143	+	219.809i	0.0471738	+	0.297844i
$739$	−651.261	−	896.383i	−0.881273	−	1.21297i	−0.976067	−	0.217471i	$-0.930219\pi$
$739$	−651.261	−	896.383i	−0.881273	−	1.21297i	0.0947939	−	0.995497i	$-0.469781\pi$
$740$		0			0
$741$	−37.0504	−	26.9187i	−0.0500005	−	0.0363275i
$742$	366.937	+	186.964i	0.494524	+	0.251973i
$743$	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
$747$	−455.783	−	894.524i	−0.610151	−	1.19749i
$748$	−25.8306	−	4.09117i	−0.0345329	−	0.00546948i
$749$		−	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	$0.346089\pi$
$752$	39.4212	−	248.895i	0.0524217	−	0.330978i
$753$	−46.7510	+	23.8208i	−0.0620863	+	0.0316345i
$754$	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	$0.106882\pi$
$758$	170.127	−	333.893i	0.224442	−	0.440492i
$759$	17.3123	−	23.8283i	0.0228093	−	0.0313944i
$760$		0			0
$761$	−1146.83	+	833.219i	−1.50700	+	1.09490i	−0.539515	+	0.841976i	$0.681392\pi$
$761$	−1146.83	+	833.219i	−1.50700	+	1.09490i	−0.967486	+	0.252924i	$0.918608\pi$
$762$	8.53856	−	1.35238i	0.0112055	−	0.00177477i
$763$	−218.719	−	1380.94i	−0.286657	−	1.80988i
$764$	199.213	+	274.193i	0.260750	+	0.358891i
$765$		0			0
$766$	−186.327	−	135.375i	−0.243247	−	0.176730i
$767$	−939.020	−	478.454i	−1.22428	−	0.623800i
$768$	−9.58222	−	9.58222i	−0.0124768	−	0.0124768i
$769$	−805.374	+	261.682i	−1.04730	+	0.340288i	−0.781608	−	0.623770i	$-0.785600\pi$
$769$	−805.374	+	261.682i	−1.04730	+	0.340288i	−0.265692	+	0.964058i	$0.585600\pi$
$770$		0			0
$771$	−2.10210	+	6.46959i	−0.00272645	+	0.00839116i
$772$	403.858	+	792.616i	0.523132	+	1.02670i
$773$	319.914	+	50.6693i	0.413860	+	0.0655489i	0.359893	−	0.932994i	$-0.382813\pi$
$773$	319.914	+	50.6693i	0.413860	+	0.0655489i	0.0539672	+	0.998543i	$0.482813\pi$
$774$			372.873i			0.481748i
$775$		0			0
$776$	−588.807			−0.758772
$777$	3.70109	−	23.3678i	0.00476331	−	0.0300744i
$778$	−208.053	+	106.008i	−0.267420	+	0.136257i
$779$	−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
$783$	−74.2081	+	145.642i	−0.0947740	+	0.186005i
$784$	473.112	−	651.183i	0.603459	−	0.830590i
$785$		0			0
$786$	−0.404845	+	0.294137i	−0.000515070	+	0.000374221i
$787$	813.494	−	128.845i	1.03366	−	0.163716i	0.383524	−	0.923531i	$-0.374710\pi$
$787$	813.494	−	128.845i	1.03366	−	0.163716i	0.650140	+	0.759815i	$0.274710\pi$
$788$	24.7285	+	156.130i	0.0313814	+	0.198134i
$789$	−0.753408	−	1.03698i	−0.000954890	−	0.00131429i
$790$		0			0
$791$	−669.446	−	486.381i	−0.846328	−	0.614893i
$792$	−329.730	−	168.006i	−0.416326	−	0.212129i
$793$	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
$797$	393.451	+	772.191i	0.493665	+	0.968872i	0.994639	+	0.103410i	$0.0329752\pi$
$797$	393.451	+	772.191i	0.493665	+	0.968872i	−0.500974	+	0.865462i	$0.667025\pi$
$798$	−21.5031	−	3.40576i	−0.0269463	−	0.00426787i
$799$			16.8197i			0.0210509i
$800$		0			0
$801$	−997.982			−1.24592
$802$	−62.1358	+	392.310i	−0.0774761	+	0.489165i
$803$	−497.517	+	253.497i	−0.619573	+	0.315688i
$804$	−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
$808$	67.3298	−	132.142i	0.0833289	−	0.163542i
$809$	72.5617	−	99.8726i	0.0896931	−	0.123452i	−0.761812	−	0.647798i	$-0.775690\pi$
$809$	72.5617	−	99.8726i	0.0896931	−	0.123452i	0.851505	+	0.524346i	$0.175690\pi$
$810$		0			0
$811$	378.763	−	275.188i	0.467033	−	0.339319i	−0.329251	−	0.944242i	$-0.606796\pi$
$811$	378.763	−	275.188i	0.467033	−	0.339319i	0.796284	+	0.604923i	$0.206796\pi$
$812$	−1498.78	+	237.384i	−1.84579	+	0.292344i
$813$	−11.9673	−	75.5585i	−0.0147199	−	0.0929379i
$814$	−29.4364	−	40.5158i	−0.0361627	−	0.0497737i
$815$		0			0
$816$	1.79454	+	1.30381i	0.00219919	+	0.00159780i
$817$	−888.179	−	452.550i	−1.08712	−	0.553916i
$818$	−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	−0.612088	−	0.790790i	$-0.709670\pi$
$821$	285.639	−	879.107i	0.347916	−	1.07078i	0.960004	−	0.279986i	$-0.0903298\pi$
$822$	15.9983	+	31.3985i	0.0194627	+	0.0381977i
$823$	757.643	+	119.999i	0.920587	+	0.145807i	0.598702	−	0.800972i	$-0.295684\pi$
$823$	757.643	+	119.999i	0.920587	+	0.145807i	0.321885	+	0.946779i	$0.395684\pi$
$824$			236.964i			0.287578i
$825$		0			0
$826$	−501.004			−0.606542
$827$	36.5445	−	230.733i	0.0441892	−	0.279000i	−0.955693	−	0.294366i	$-0.904891\pi$
$827$	36.5445	−	230.733i	0.0441892	−	0.279000i	0.999882	+	0.0153664i	$0.00489148\pi$
$828$	398.672	−	203.133i	0.481488	−	0.245330i
$829$	−1244.32	−	404.304i	−1.50099	−	0.487701i	−0.560682	−	0.828031i	$-0.689461\pi$
$829$	−1244.32	−	404.304i	−1.50099	−	0.487701i	−0.940306	+	0.340330i	$0.889461\pi$
$830$		0			0
$831$	−5.33226	−	16.4110i	−0.00641668	−	0.0197485i
$832$	−310.046	+	310.046i	−0.372651	+	0.372651i
$833$	−24.3900	+	47.8681i	−0.0292797	+	0.0574647i
$834$	−11.4855	+	15.8085i	−0.0137716	+	0.0189550i
$835$		0			0
$836$	381.547	−	277.210i	0.456396	−	0.331591i
$837$	−39.0020	+	6.17731i	−0.0465974	+	0.00738030i
$838$	−10.9110	−	68.8892i	−0.0130203	−	0.0822067i
$839$	−614.547	−	845.852i	−0.732476	−	1.00817i	−0.999016	−	0.0443428i	$-0.985881\pi$
$839$	−614.547	−	845.852i	−0.732476	−	1.00817i	0.266541	−	0.963824i	$-0.414119\pi$
$840$		0			0
$841$	519.757	+	377.626i	0.618023	+	0.449020i
$842$	1.82460	+	0.929679i	0.00216698	+	0.00110413i
$843$	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
$847$	190.037	+	372.968i	0.224364	+	0.440340i
$848$	747.341	+	118.367i	0.881298	+	0.139584i
$849$		−	46.6825i		−	0.0549853i
$850$		0			0
$851$	127.019			0.149259
$852$	0.369145	−	2.33069i	0.000433269	−	0.00273555i
$853$	−32.3156	+	16.4656i	−0.0378846	+	0.0193032i	−0.472830	−	0.881154i	$-0.656768\pi$
$853$	−32.3156	+	16.4656i	−0.0378846	+	0.0193032i	0.434946	+	0.900457i	$0.356768\pi$
$854$	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	$0.441989\pi$
$858$	7.88766	−	15.4804i	0.00919307	−	0.0180424i
$859$	884.589	−	1217.53i	1.02979	−	1.41738i	0.124684	−	0.992197i	$-0.460208\pi$
$859$	884.589	−	1217.53i	1.02979	−	1.41738i	0.905106	−	0.425187i	$-0.139792\pi$
$860$		0			0
$861$	86.2658	−	62.6758i	0.100193	−	0.0727942i
$862$	−274.712	+	43.5101i	−0.318691	+	0.0504757i
$863$	−205.361	−	1296.60i	−0.237962	−	1.50243i	−0.760231	−	0.649653i	$-0.774914\pi$
$863$	−205.361	−	1296.60i	−0.237962	−	1.50243i	0.522269	−	0.852781i	$-0.325086\pi$
$864$	63.1570	+	86.9282i	0.0730984	+	0.100611i
$865$		0			0
$866$	−95.7869	−	69.5932i	−0.110608	−	0.0803617i
$867$	60.7692	+	30.9634i	0.0700913	+	0.0357133i
$868$	−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
$872$	267.777	+	525.542i	0.307084	+	0.602686i
$873$	−1140.37	−	180.617i	−1.30626	−	0.206892i
$874$		−	116.884i		−	0.133734i
$875$		0			0
$876$	53.0498			0.0605591
$877$	58.9645	−	372.287i	0.0672343	−	0.424501i	−0.930996	−	0.365030i	$-0.881059\pi$
$877$	58.9645	−	372.287i	0.0672343	−	0.424501i	0.998230	−	0.0594706i	$-0.0189413\pi$
$878$	−260.639	+	132.802i	−0.296855	+	0.151255i
$879$	75.4629	+	24.5194i	0.0858509	+	0.0278947i
$880$		0			0
$881$	−297.148	−	914.528i	−0.337285	−	1.03806i	−0.965585	−	0.260086i	$-0.916249\pi$
$881$	−297.148	−	914.528i	−0.337285	−	1.03806i	0.628300	−	0.777971i	$-0.283751\pi$
$882$	−256.252	+	256.252i	−0.290535	+	0.290535i
$883$	−16.1759	+	31.7470i	−0.0183192	+	0.0359535i	−0.899985	−	0.435921i	$-0.856423\pi$
$883$	−16.1759	+	31.7470i	−0.0183192	+	0.0359535i	0.881666	+	0.471875i	$0.156423\pi$
$884$	22.9987	−	31.6549i	0.0260166	−	0.0358088i
$885$		0			0
$886$	164.963	−	119.853i	0.186189	−	0.135274i
$887$	296.686	−	46.9904i	0.334482	−	0.0529768i	0.0130655	−	0.999915i	$-0.495841\pi$
$887$	296.686	−	46.9904i	0.334482	−	0.0529768i	0.321417	+	0.946938i	$0.395841\pi$
$888$	1.56136	+	9.85802i	0.00175828	+	0.0111014i
$889$	389.298	+	535.823i	0.437905	+	0.602725i
$890$		0			0
$891$	−583.372	−	423.845i	−0.654739	−	0.475696i
$892$	245.877	+	125.281i	0.275647	+	0.140449i
$893$	−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
$897$	20.0056	+	39.2632i	0.0223028	+	0.0437717i
$898$	202.855	+	32.1291i	0.225897	+	0.0357786i
$899$			358.375i			0.398637i
$900$		0			0
$901$	−50.5032			−0.0560524
$902$	35.3088	−	222.931i	0.0391450	−	0.247152i
$903$	159.183	−	81.1080i	0.176283	−	0.0898206i
$904$	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	$0.121065\pi$
$908$	567.744	−	1114.26i	0.625268	−	1.22716i
$909$	170.935	−	235.272i	0.188047	−	0.258825i
$910$		0			0
$911$	−1112.30	+	808.135i	−1.22097	+	0.887086i	−0.996180	−	0.0873220i	$-0.972169\pi$
$911$	−1112.30	+	808.135i	−1.22097	+	0.887086i	−0.224788	+	0.974408i	$0.572169\pi$
$912$	−39.5084	+	6.25752i	−0.0433207	+	0.00686132i
$913$	159.283	+	1005.67i	0.174461	+	1.10150i
$914$	72.3704	+	99.6093i	0.0791798	+	0.108982i
$915$		0			0
$916$	68.9194	+	50.0728i	0.0752395	+	0.0546647i
$917$	−34.1594	−	17.4051i	−0.0372513	−	0.0189805i
$918$	−1.41678	−	1.41678i	−0.00154333	−	0.00154333i
$919$	1241.96	−	403.536i	1.35142	−	0.439104i	0.458252	−	0.888822i	$-0.348476\pi$
$919$	1241.96	−	403.536i	1.35142	−	0.439104i	0.893170	+	0.449718i	$0.148476\pi$
$920$		0			0
$921$	−8.17554	+	25.1617i	−0.00887681	+	0.0273200i
$922$	90.5801	+	177.773i	0.0982430	+	0.192813i
$923$	−36.7026	−	5.81312i	−0.0397645	−	0.00629808i
$924$			84.5254i			0.0914777i
$925$		0			0
$926$	−16.5629			−0.0178865
$927$	−72.6888	+	458.939i	−0.0784129	+	0.495080i
$928$	868.868	−	442.711i	0.936281	−	0.477059i
$929$	−430.474	−	139.870i	−0.463374	−	0.150559i	0.0680204	−	0.997684i	$-0.478332\pi$
$929$	−430.474	−	139.870i	−0.463374	−	0.150559i	−0.531394	+	0.847125i	$0.678332\pi$
$930$		0			0
$931$	−299.380	−	921.397i	−0.321568	−	0.989685i
$932$	493.250	−	493.250i	0.529239	−	0.529239i
$933$	12.1956	−	23.9353i	0.0130714	−	0.0256541i
$934$	−143.746	+	197.849i	−0.153904	+	0.211830i
$935$		0			0
$936$	447.924	−	325.436i	0.478551	−	0.347688i
$937$	517.916	−	82.0298i	0.552738	−	0.0875451i	0.126184	−	0.992007i	$-0.459727\pi$
$937$	517.916	−	82.0298i	0.552738	−	0.0875451i	0.426555	+	0.904462i	$0.359727\pi$
$938$	53.1227	+	335.404i	0.0566341	+	0.357573i
$939$	−14.2874	−	19.6650i	−0.0152156	−	0.0209425i
$940$		0			0
$941$	983.490	+	714.547i	1.04515	+	0.759349i	0.971285	−	0.237919i	$-0.0764653\pi$
$941$	983.490	+	714.547i	1.04515	+	0.759349i	0.0738692	+	0.997268i	$0.476465\pi$
$942$	16.8511	+	8.58607i	0.0178887	+	0.00911472i
$943$	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
$947$	−561.219	−	1101.45i	−0.592628	−	1.16310i	−0.971365	−	0.237594i	$-0.923641\pi$
$947$	−561.219	−	1101.45i	−0.592628	−	1.16310i	0.378736	−	0.925505i	$-0.376359\pi$
$948$	5.53929	+	0.877337i	0.00584313	+	0.000925461i
$949$		−	835.402i		−	0.880297i
$950$		0			0
$951$	−96.5800			−0.101556
$952$	6.10394	−	38.5387i	0.00641170	−	0.0404819i
$953$	−90.7422	+	46.2355i	−0.0952174	+	0.0485157i	−0.500951	−	0.865476i	$-0.667016\pi$
$953$	−90.7422	+	46.2355i	−0.0952174	+	0.0485157i	0.405733	+	0.913992i	$0.367016\pi$
$954$	−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
$958$	−165.071	+	323.971i	−0.172308	+	0.338174i
$959$	−1586.89	+	2184.16i	−1.65473	+	2.27754i
$960$		0			0
$961$	707.423	−	513.973i	0.736133	−	0.534832i
$962$	74.0040	−	11.7211i	0.0769273	−	0.0121841i
$963$	68.8578	+	434.751i	0.0715034	+	0.451455i
$964$	−72.4811	−	99.7617i	−0.0751879	−	0.103487i
$965$		0			0
$966$	16.9476	+	12.3132i	0.0175441	+	0.0127466i
$967$	421.887	+	214.962i	0.436284	+	0.222298i	0.658316	−	0.752741i	$-0.271269\pi$
$967$	421.887	+	214.962i	0.436284	+	0.222298i	−0.222032	+	0.975039i	$0.571269\pi$
$968$	−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	−0.205690	−	0.978617i	$-0.565944\pi$
$971$	520.392	−	1601.60i	0.535934	−	1.64943i	0.741623	−	0.670817i	$-0.234056\pi$
$972$	94.2891	+	185.053i	0.0970052	+	0.190383i
$973$	−1478.60	−	234.187i	−1.51963	−	0.240686i
$974$		−	138.450i		−	0.142146i
$975$		0			0
$976$	167.260			0.171373
$977$	−17.9443	+	113.296i	−0.0183667	+	0.115963i	−0.995168	−	0.0981833i	$-0.968697\pi$
$977$	−17.9443	+	113.296i	−0.0183667	+	0.115963i	0.976802	+	0.214146i	$0.0686968\pi$
$978$	−33.2592	+	16.9464i	−0.0340074	+	0.0173276i
$979$	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
$983$	−583.651	+	1145.48i	−0.593744	+	1.16529i	0.377233	+	0.926118i	$0.376875\pi$
$983$	−583.651	+	1145.48i	−0.593744	+	1.16529i	−0.970978	+	0.239170i	$0.923125\pi$
$984$	−26.4406	+	36.3924i	−0.0268706	+	0.0369842i
$985$		0			0
$986$	−14.7111	+	10.6882i	−0.0149200	+	0.0108400i
$987$	53.6920	−	8.50397i	0.0543992	−	0.00861598i
$988$	110.380	+	696.913i	0.111721	+	0.705378i
$989$	563.778	+	775.973i	0.570048	+	0.784604i
$990$		0			0
$991$	−392.287	−	285.013i	−0.395850	−	0.287602i	0.371999	−	0.928233i	$-0.378673\pi$
$991$	−392.287	−	285.013i	−0.395850	−	0.287602i	−0.767848	+	0.640631i	$0.778673\pi$
$992$	209.902	+	106.950i	0.211595	+	0.107813i
$993$	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
$997$	−589.304	−	1156.57i	−0.591077	−	1.16005i	−0.971897	−	0.235405i	$-0.924358\pi$
$997$	−589.304	−	1156.57i	−0.591077	−	1.16005i	0.380820	−	0.924649i	$-0.375642\pi$
$998$	443.254	+	70.2046i	0.444143	+	0.0703453i
$999$			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.c.93.2		32
5.2	odd	4		125.3.f.b.32.2		32
5.3	odd	4		125.3.f.a.32.3		32
5.4	even	2		25.3.f.a.23.3	yes	32
15.14	odd	2		225.3.r.a.73.2		32
20.19	odd	2		400.3.bg.c.273.2		32
25.9	even	10		125.3.f.a.43.3		32
25.12	odd	20	inner	125.3.f.c.82.2		32
25.13	odd	20		25.3.f.a.12.3	✓	32
25.16	even	5		125.3.f.b.43.2		32
75.38	even	20		225.3.r.a.37.2		32
100.63	even	20		400.3.bg.c.337.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.12.3	✓	32	25.13	odd	20
25.3.f.a.23.3	yes	32	5.4	even	2
125.3.f.a.32.3		32	5.3	odd	4
125.3.f.a.43.3		32	25.9	even	10
125.3.f.b.32.2		32	5.2	odd	4
125.3.f.b.43.2		32	25.16	even	5
125.3.f.c.82.2		32	25.12	odd	20	inner
125.3.f.c.93.2		32	1.1	even	1	trivial
225.3.r.a.37.2		32	75.38	even	20
225.3.r.a.73.2		32	15.14	odd	2
400.3.bg.c.273.2		32	20.19	odd	2
400.3.bg.c.337.2		32	100.63	even	20

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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.c.93.2

Level	$125$
Weight	$3$
Character	125.93
Analytic conductor	$3.406$
Analytic rank	$0$
Dimension	$32$
Inner twists	$2$