LMFDB - Embedded newform 25.3.f.a.23.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,3,Mod(2,25)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("25.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	25.f (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.681200660901$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			23.3
Character	$\chi$	$=$	25.23
Dual form			25.3.f.a.12.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0933465 - 0.589367i) q^{2} +(0.210730 - 0.107372i) q^{3} +(3.46559 + 1.12604i) q^{4} +(-3.31432 - 3.74370i) q^{5} +(-0.0436108 - 0.134220i) q^{6} +(-7.64532 + 7.64532i) q^{7} +(2.07076 - 4.06409i) q^{8} +(-5.25719 + 7.23590i) q^{9} +(-2.51579 + 1.60389i) q^{10} +(7.33868 - 5.33186i) q^{11} +(0.851210 - 0.134818i) q^{12} +(-2.12306 - 13.4044i) q^{13} +(3.79223 + 5.21956i) q^{14} +(-1.10040 - 0.433046i) q^{15} +(9.59007 + 6.96760i) q^{16} +(0.704962 + 0.359196i) q^{17} +(3.77386 + 3.77386i) q^{18} +(13.5696 - 4.40902i) q^{19} +(-7.27050 - 16.7062i) q^{20} +(-0.790204 + 2.43200i) q^{21} +(-2.45738 - 4.82288i) q^{22} +(13.5597 + 2.14764i) q^{23} -1.07877i q^{24} +(-3.03063 + 24.8156i) q^{25} -8.09832 q^{26} +(-0.663895 + 4.19167i) q^{27} +(-35.1044 + 17.8866i) q^{28} +(-36.6306 - 11.9020i) q^{29} +(-0.357941 + 0.608115i) q^{30} +(-2.87530 - 8.84925i) q^{31} +(17.9028 - 17.9028i) q^{32} +(0.973987 - 1.91156i) q^{33} +(0.277504 - 0.381951i) q^{34} +(53.9608 + 3.28280i) q^{35} +(-26.3671 + 19.1568i) q^{36} +(9.13820 - 1.44735i) q^{37} +(-1.33186 - 8.40902i) q^{38} +(-1.88666 - 2.59677i) q^{39} +(-22.0779 + 5.71738i) q^{40} +(-33.7351 - 24.5100i) q^{41} +(1.35958 + 0.692738i) q^{42} +(49.4021 + 49.4021i) q^{43} +(31.4367 - 10.2144i) q^{44} +(44.5130 - 4.30070i) q^{45} +(2.53150 - 7.79114i) q^{46} +(9.65116 + 18.9415i) q^{47} +(2.76905 + 0.438574i) q^{48} -67.9017i q^{49} +(14.3426 + 4.10260i) q^{50} +0.187125 q^{51} +(7.73627 - 48.8449i) q^{52} +(-56.8742 + 28.9788i) q^{53} +(2.40846 + 0.782556i) q^{54} +(-44.2836 - 9.80236i) q^{55} +(15.2397 + 46.9029i) q^{56} +(2.38611 - 2.38611i) q^{57} +(-10.4340 + 20.4778i) q^{58} +(-45.6440 + 62.8235i) q^{59} +(-3.32590 - 2.73985i) q^{60} +(11.4153 - 8.29369i) q^{61} +(-5.48385 + 0.868557i) q^{62} +(-15.1279 - 95.5136i) q^{63} +(18.9902 + 26.1378i) q^{64} +(-43.1458 + 52.3747i) q^{65} +(-1.03569 - 0.752473i) q^{66} +(-46.8978 - 23.8956i) q^{67} +(2.03864 + 2.03864i) q^{68} +(3.08803 - 1.00336i) q^{69} +(6.97183 - 31.4963i) q^{70} +(-0.846117 + 2.60408i) q^{71} +(18.5210 + 36.3495i) q^{72} +(60.7976 + 9.62940i) q^{73} -5.52086i q^{74} +(2.02587 + 5.55481i) q^{75} +51.9912 q^{76} +(-15.3427 + 96.8703i) q^{77} +(-1.70656 + 0.869536i) q^{78} +(-6.18905 - 2.01094i) q^{79} +(-5.69992 - 58.9952i) q^{80} +(-24.5646 - 75.6022i) q^{81} +(-17.5944 + 17.5944i) q^{82} +(50.9593 - 100.013i) q^{83} +(-5.47704 + 7.53850i) q^{84} +(-0.991742 - 3.82966i) q^{85} +(33.7274 - 24.5044i) q^{86} +(-8.99712 + 1.42500i) q^{87} +(-6.47255 - 40.8661i) q^{88} +(65.5853 + 90.2704i) q^{89} +(1.62045 - 26.6360i) q^{90} +(118.713 + 86.2498i) q^{91} +(44.5739 + 22.7115i) q^{92} +(-1.55608 - 1.55608i) q^{93} +(12.0644 - 3.91995i) q^{94} +(-61.4799 - 36.1875i) q^{95} +(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} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19}+ \cdots + 170 q^{98}+O(q^{100}) $ 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

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

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	−0.953300	−	0.302026i	$-0.902337\pi$
$2$	0.0933465	−	0.589367i	0.0466733	−	0.294683i	0.999973	+	0.00734232i	$0.00233715\pi$
$3$	0.210730	−	0.107372i	0.0702435	−	0.0357908i	−0.418516	−	0.908209i	$-0.637450\pi$
$3$	0.210730	−	0.107372i	0.0702435	−	0.0357908i	0.488759	+	0.872419i	$0.337450\pi$
$4$	3.46559	+	1.12604i	0.866397	+	0.281509i
$5$	−3.31432	−	3.74370i	−0.662863	−	0.748741i
$5$	−3.31432	−	3.74370i	−0.662863	−	0.748741i
$6$	−0.0436108	−	0.134220i	−0.00726847	−	0.0223701i
$7$	−7.64532	+	7.64532i	−1.09219	+	1.09219i	−0.0968934	+	0.995295i	$0.530891\pi$
$7$	−7.64532	+	7.64532i	−1.09219	+	1.09219i	−0.995295	+	0.0968934i	$0.969109\pi$
$8$	2.07076	−	4.06409i	0.258845	−	0.508011i
$9$	−5.25719	+	7.23590i	−0.584132	+	0.803989i
$10$	−2.51579	+	1.60389i	−0.251579	+	0.160389i
$11$	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	$-0.875193\pi$
$13$	−2.12306	−	13.4044i	−0.163312	−	1.03111i	0.760799	−	0.648987i	$-0.224807\pi$
$14$	3.79223	+	5.21956i	0.270874	+	0.372826i
$15$	−1.10040	−	0.433046i	−0.0733598	−	0.0288697i
$16$	9.59007	+	6.96760i	0.599380	+	0.435475i
$17$	0.704962	+	0.359196i	0.0414683	+	0.0211292i	0.474602	−	0.880201i	$-0.342592\pi$
$17$	0.704962	+	0.359196i	0.0414683	+	0.0211292i	−0.433133	+	0.901330i	$0.642592\pi$
$18$	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	$0.277481\pi$
$20$	−7.27050	−	16.7062i	−0.363525	−	0.835308i
$21$	−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	0.444080	−	0.895987i	$-0.353530\pi$
$23$	13.5597	+	2.14764i	0.589551	+	0.0933757i	0.145470	+	0.989363i	$0.453530\pi$
$24$		−	1.07877i		−	0.0449488i
$25$	−3.03063	+	24.8156i	−0.121225	+	0.992625i
$26$	−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	$0.831169\pi$
$30$	−0.357941	+	0.608115i	−0.0119314	+	0.0202705i
$31$	−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
$35$	53.9608	+	3.28280i	1.54174	+	0.0937944i
$36$	−26.3671	+	19.1568i	−0.732420	+	0.532135i
$37$	9.13820	−	1.44735i	0.246978	−	0.0391175i	−0.0317178	−	0.999497i	$-0.510098\pi$
$37$	9.13820	−	1.44735i	0.246978	−	0.0391175i	0.278696	+	0.960379i	$0.410098\pi$
$38$	−1.33186	−	8.40902i	−0.0350489	−	0.221290i
$39$	−1.88666	−	2.59677i	−0.0483759	−	0.0665838i
$40$	−22.0779	+	5.71738i	−0.551947	+	0.142934i
$41$	−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	$0.0518308\pi$
$43$	49.4021	+	49.4021i	1.14889	+	1.14889i	0.162113	+	0.986772i	$0.448169\pi$
$44$	31.4367	−	10.2144i	0.714470	−	0.232145i
$45$	44.5130	−	4.30070i	0.989179	−	0.0955711i
$46$	2.53150	−	7.79114i	0.0550325	−	0.169373i
$47$	9.65116	+	18.9415i	0.205344	+	0.403010i	0.970594	−	0.240723i	$-0.0773847\pi$
$47$	9.65116	+	18.9415i	0.205344	+	0.403010i	−0.765250	+	0.643733i	$0.777385\pi$
$48$	2.76905	+	0.438574i	0.0576885	+	0.00913696i
$49$		−	67.9017i		−	1.38575i
$50$	14.3426	+	4.10260i	0.286852	+	0.0820521i
$51$	0.187125			0.00366911
$52$	7.73627	−	48.8449i	0.148775	−	0.939325i
$53$	−56.8742	+	28.9788i	−1.07310	+	0.546771i	−0.898996	−	0.437957i	$-0.855702\pi$
$53$	−56.8742	+	28.9788i	−1.07310	+	0.546771i	−0.174102	+	0.984728i	$0.555702\pi$
$54$	2.40846	+	0.782556i	0.0446011	+	0.0144918i
$55$	−44.2836	−	9.80236i	−0.805156	−	0.178225i
$56$	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	$0.971366\pi$
$60$	−3.32590	−	2.73985i	−0.0554316	−	0.0456641i
$61$	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
$65$	−43.1458	+	52.3747i	−0.663781	+	0.805764i
$66$	−1.03569	−	0.752473i	−0.0156923	−	0.0114011i
$67$	−46.8978	−	23.8956i	−0.699968	−	0.356651i	0.0675175	−	0.997718i	$-0.478492\pi$
$67$	−46.8978	−	23.8956i	−0.699968	−	0.356651i	−0.767485	+	0.641067i	$0.778492\pi$
$68$	2.03864	+	2.03864i	0.0299800	+	0.0299800i
$69$	3.08803	−	1.00336i	0.0447541	−	0.0145415i
$70$	6.97183	−	31.4963i	0.0995975	−	0.449947i
$71$	−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	0.558273	−	0.829657i	$-0.311464\pi$
$73$	60.7976	+	9.62940i	0.832844	+	0.131910i	0.274571	+	0.961567i	$0.411464\pi$
$74$		−	5.52086i		−	0.0746062i
$75$	2.02587	+	5.55481i	0.0270116	+	0.0740642i
$76$	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	$0.613114\pi$
$80$	−5.69992	−	58.9952i	−0.0712490	−	0.737440i
$81$	−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	$-0.613630\pi$
$83$	50.9593	−	100.013i	0.613967	−	1.20498i	0.963413	−	0.268021i	$-0.0863698\pi$
$84$	−5.47704	+	7.53850i	−0.0652029	+	0.0897440i
$85$	−0.991742	−	3.82966i	−0.0116676	−	0.0450548i
$86$	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	$0.584341\pi$
$90$	1.62045	−	26.6360i	0.0180050	−	0.295955i
$91$	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
$95$	−61.4799	−	36.1875i	−0.647156	−	0.380921i
$96$	1.85040	−	5.69493i	0.0192749	−	0.0593222i
$97$	−58.6053	−	115.019i	−0.604178	−	1.18577i	−0.967207	−	0.253989i	$-0.918257\pi$
$97$	−58.6053	−	115.019i	−0.604178	−	1.18577i	0.363029	−	0.931778i	$-0.381743\pi$
$98$	−40.0190	−	6.33839i	−0.408357	−	0.0646775i
$99$			81.1325i			0.819521i
$100$	−38.4462	+	82.5881i	−0.384462	+	0.825881i
$101$	−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	−0.664022	−	0.747713i	$-0.731152\pi$
$103$	−46.2893	+	23.5856i	−0.449411	+	0.228986i	0.214611	+	0.976700i	$0.431152\pi$
$104$	−58.8732	−	19.1291i	−0.566089	−	0.183933i
$105$	11.7237	−	5.10212i	0.111654	−	0.0485916i
$106$	11.7702	+	36.2248i	0.111039	+	0.341744i
$107$	−34.7993	+	34.7993i	−0.325227	+	0.325227i	−0.850768	−	0.525541i	$-0.823863\pi$
$107$	−34.7993	+	34.7993i	−0.325227	+	0.325227i	0.525541	+	0.850768i	$0.323863\pi$
$108$	−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	$-0.00212819\pi$
$110$	−9.91090	+	25.1843i	−0.0900991	+	0.228948i
$111$	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	$0.0599670\pi$
$113$	11.9724	+	75.5905i	0.105950	+	0.668942i	−0.876357	+	0.481663i	$0.840033\pi$
$114$	−1.18356	−	1.62903i	−0.0103821	−	0.0142897i
$115$	−36.9009	−	57.8813i	−0.320877	−	0.503316i
$116$	−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
$120$	−4.03859	+	3.57538i	−0.0336550	+	0.0297949i
$121$	−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
$125$	102.947	−	70.9011i	0.823574	−	0.567208i
$126$	−57.7047			−0.457974
$127$	9.58264	−	60.5024i	0.0754539	−	0.476397i	−0.920808	−	0.390016i	$-0.872470\pi$
$127$	9.58264	−	60.5024i	0.0754539	−	0.476397i	0.996262	−	0.0863815i	$-0.0275304\pi$
$128$	107.413	−	54.7295i	0.839162	−	0.427575i
$129$	15.7149	+	5.10609i	0.121821	+	0.0395821i
$130$	26.8404	+	30.3177i	0.206464	+	0.233213i
$131$	−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
$135$	17.8927	−	11.4071i	0.132539	−	0.0844969i
$136$	2.91961	−	2.12122i	0.0214677	−	0.0155972i
$137$	246.624	−	39.0615i	1.80018	−	0.285120i	0.835682	−	0.549214i	$-0.185073\pi$
$137$	246.624	−	39.0615i	1.80018	−	0.285120i	0.964497	+	0.264094i	$0.0850728\pi$
$138$	−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	$0.965951\pi$
$140$	183.309	+	72.1387i	1.30935	+	0.515276i
$141$	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
$145$	76.8477	+	176.581i	0.529984	+	1.21780i
$146$	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	$-0.112420\pi$
$150$	3.46293	−	0.675459i	0.0230862	−	0.00450306i
$151$	−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
$155$	−23.5993	+	40.0935i	−0.152254	+	0.258667i
$156$	−3.61433	−	11.1238i	−0.0231688	−	0.0713062i
$157$	94.7590	−	94.7590i	0.603561	−	0.603561i	−0.337695	−	0.941256i	$-0.609647\pi$
$157$	94.7590	−	94.7590i	0.603561	−	0.603561i	0.941256	+	0.337695i	$0.109647\pi$
$158$	−1.76291	+	3.45990i	−0.0111577	+	0.0218981i
$159$	−8.87359	+	12.2134i	−0.0558087	+	0.0768141i
$160$	−126.358	−	7.68724i	−0.789739	−	0.0480452i
$161$	−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	$0.251260\pi$
$163$	41.3763	+	261.240i	0.253842	+	1.60270i	−0.450459	+	0.892797i	$0.648740\pi$
$164$	−89.3128	−	122.928i	−0.544590	−	0.749564i
$165$	−10.3844	+	2.68919i	−0.0629358	+	0.0162981i
$166$	−54.1876	−	39.3696i	−0.326431	−	0.237166i
$167$	−239.969	−	122.270i	−1.43694	−	0.732158i	−0.449969	−	0.893044i	$-0.648565\pi$
$167$	−239.969	−	122.270i	−1.43694	−	0.732158i	−0.986973	+	0.160886i	$0.948565\pi$
$168$	8.24754	+	8.24754i	0.0490925	+	0.0490925i
$169$	−14.4433	+	4.69292i	−0.0854634	+	0.0277687i
$170$	−2.34965	+	0.227015i	−0.0138215	+	0.00133538i
$171$	−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	−0.400050	−	0.916493i	$-0.631007\pi$
$173$	−184.026	−	29.1468i	−1.06373	−	0.168479i	−0.663682	+	0.748014i	$0.731007\pi$
$174$			5.43562i			0.0312392i
$175$	−166.553	−	212.893i	−0.951733	−	1.21653i
$176$	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	$0.406391\pi$
$180$	159.107	+	35.2189i	0.883925	+	0.195661i
$181$	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
$185$	−35.7053	−	29.4137i	−0.193002	−	0.158993i
$186$	−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
$190$	−27.0667	+	32.8562i	−0.142456	+	0.172927i
$191$	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	0.100520	−	0.994935i	$-0.467949\pi$
$193$	−172.622	−	172.622i	−0.894415	−	0.894415i	−0.994935	+	0.100520i	$0.967949\pi$
$194$	−73.2592	+	23.8034i	−0.377625	+	0.122698i
$195$	−3.46853	+	15.6696i	−0.0177873	+	0.0803569i
$196$	76.4599	−	235.319i	0.390101	−	1.20061i
$197$	−19.6944	−	38.6524i	−0.0999715	−	0.196205i	0.835604	−	0.549333i	$-0.185118\pi$
$197$	−19.6944	−	38.6524i	−0.0999715	−	0.196205i	−0.935575	+	0.353128i	$0.885118\pi$
$198$	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	$0.687089\pi$
$200$	94.5773	+	63.7039i	0.472886	+	0.318519i
$201$	−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
$205$	20.0507	+	207.528i	0.0978081	+	1.01233i
$206$	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
$210$	−1.91266	−	7.38580i	−0.00910789	−	0.0351705i
$211$	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
$215$	21.2126	−	348.681i	0.0986634	−	1.62177i
$216$	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
$220$	−142.431	−	83.8359i	−0.647413	−	0.381072i
$221$	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	−0.0135446	−	0.999908i	$-0.504312\pi$
$223$	−74.7975	−	11.8468i	−0.335415	−	0.0531245i	−0.321870	+	0.946784i	$0.604312\pi$
$224$			273.745i			1.22208i
$225$	−163.631	−	152.390i	−0.727248	−	0.677288i
$226$	45.6681			0.202071
$227$	−53.6868	+	338.965i	−0.236506	+	1.49324i	0.528345	+	0.849030i	$0.322813\pi$
$227$	−53.6868	+	338.965i	−0.236506	+	1.49324i	−0.764850	+	0.644208i	$0.777187\pi$
$228$	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	$0.583745\pi$
$230$	−37.5579	+	16.3451i	−0.163295	+	0.0710658i
$231$	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	−0.998852	−	0.0478936i	$-0.984749\pi$
$233$	−86.9078	+	170.566i	−0.372995	+	0.732044i	0.625858	+	0.779937i	$0.284749\pi$
$234$	42.5744	−	58.5986i	0.181942	−	0.250421i
$235$	38.9242	−	98.9090i	0.165635	−	0.420890i
$236$	−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	$0.763317\pi$
$240$	−7.53561	−	11.8201i	−0.0313984	−	0.0492503i
$241$	−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
$245$	−254.204	+	225.048i	−1.03757	+	0.918562i
$246$	−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
$250$	−32.1770	−	67.2918i	−0.128708	−	0.269167i
$251$	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
$255$	−0.620190	−	0.700539i	−0.00243212	−	0.00274721i
$256$	17.7059	+	54.4930i	0.0691635	+	0.212863i
$257$	−20.3380	+	20.3380i	−0.0791363	+	0.0791363i	−0.745567	−	0.666431i	$-0.767821\pi$
$257$	−20.3380	+	20.3380i	−0.0791363	+	0.0791363i	0.666431	+	0.745567i	$0.267821\pi$
$258$	4.47630	−	8.78523i	0.0173500	−	0.0340513i
$259$	−58.7990	+	80.9299i	−0.227023	+	0.312471i
$260$	−208.501	+	132.925i	−0.801928	+	0.511251i
$261$	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	0.986024	−	0.166603i	$-0.0532797\pi$
$263$	−0.847808	−	5.35285i	−0.00322361	−	0.0203530i	−0.989248	+	0.146250i	$0.953280\pi$
$264$	−5.75185	−	7.91675i	−0.0217873	−	0.0299877i
$265$	296.987	+	116.875i	1.12071	+	0.441038i
$266$	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	$0.436810\pi$
$270$	−5.05274	−	11.6102i	−0.0187138	−	0.0430007i
$271$	−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
$275$	110.073	+	198.273i	0.400264	+	0.720992i
$276$	11.8317			0.0428684
$277$	11.4134	−	72.0614i	0.0412036	−	0.260150i	−0.958484	−	0.285147i	$-0.907958\pi$
$277$	11.4134	−	72.0614i	0.0412036	−	0.260150i	0.999688	+	0.0249971i	$0.00795767\pi$
$278$	−73.6150	+	37.5087i	−0.264802	+	0.134924i
$279$	79.1483	+	25.7168i	0.283686	+	0.0921750i
$280$	125.081	−	212.504i	0.446719	−	0.758942i
$281$	−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	−0.676750	−	0.736212i	$-0.736612\pi$
$283$	89.6096	−	175.869i	0.316642	−	0.621445i	0.993392	+	0.114768i	$0.0366124\pi$
$284$	−5.86459	+	8.07191i	−0.0206499	+	0.0284222i
$285$	−16.8412	−	1.02457i	−0.0590920	−	0.00359497i
$286$	−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
$290$	111.244	−	28.8083i	0.383601	−	0.0993389i
$291$	−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	0.984581	−	0.174929i	$-0.0559695\pi$
$293$	237.228	+	237.228i	0.809652	+	0.809652i	−0.174929	+	0.984581i	$0.555970\pi$
$294$	−9.11379	+	2.96125i	−0.0309993	+	0.0100723i
$295$	386.471	−	37.3396i	1.31007	−	0.126575i
$296$	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
$300$	0.765905	+	21.5319i	0.00255302	+	0.0717730i
$301$	−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
$305$	−68.8829	−	15.2475i	−0.225846	−	0.0499919i
$306$	1.30487	+	4.01598i	0.00426428	+	0.0131241i
$307$	−79.0993	+	79.0993i	−0.257653	+	0.257653i	−0.824099	−	0.566446i	$-0.808318\pi$
$307$	−79.0993	+	79.0993i	−0.257653	+	0.257653i	0.566446	+	0.824099i	$0.308318\pi$
$308$	−162.251	+	318.436i	−0.526789	+	1.03388i
$309$	−7.22212	+	9.94040i	−0.0233726	+	0.0321696i
$310$	21.4268	+	17.6512i	0.0691188	+	0.0569395i
$311$	−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	$-0.997503\pi$
$313$	−16.0776	−	101.510i	−0.0513662	−	0.324314i	0.948603	−	0.316469i	$-0.102497\pi$
$314$	−47.0024	−	64.6933i	−0.149689	−	0.206029i
$315$	−307.436	+	373.197i	−0.975988	+	1.18475i
$316$	−19.1843	−	13.9382i	−0.0607097	−	0.0441082i
$317$	−363.850	−	185.391i	−1.14779	−	0.584829i	−0.226618	−	0.973984i	$-0.572767\pi$
$317$	−363.850	−	185.391i	−1.14779	−	0.584829i	−0.921172	+	0.389155i	$0.872767\pi$
$318$	6.36988	+	6.36988i	0.0200311	+	0.0200311i
$319$	−332.280	+	107.964i	−1.04163	+	0.338446i
$320$	34.9126	−	157.723i	0.109102	−	0.492884i
$321$	−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
$325$	339.074	−	12.0611i	1.04330	−	0.0371111i
$326$	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
$330$	0.615569	+	6.37125i	0.00186536	+	0.0193068i
$331$	−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
$335$	65.9760	+	254.769i	0.196943	+	0.760505i
$336$	−24.5233	+	17.8172i	−0.0729860	+	0.0530274i
$337$	−38.2752	+	6.06219i	−0.113576	+	0.0179887i	−0.212964	−	0.977060i	$-0.568312\pi$
$337$	−38.2752	+	6.06219i	−0.113576	+	0.0179887i	0.0993876	+	0.995049i	$0.468312\pi$
$338$	1.41762	+	8.95048i	0.00419413	+	0.0264807i
$339$	10.6393	+	14.6437i	0.0313843	+	0.0431968i
$340$	0.875365	−	14.3887i	0.00257460	−	0.0423198i
$341$	−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
$345$	−13.9910	−	8.23522i	−0.0405536	−	0.0238702i
$346$	−34.3563	+	105.738i	−0.0992958	+	0.305601i
$347$	−106.794	−	209.594i	−0.307762	−	0.604018i	0.684381	−	0.729125i	$-0.260073\pi$
$347$	−106.794	−	209.594i	−0.307762	−	0.604018i	−0.992143	+	0.125107i	$0.960073\pi$
$348$	−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	$0.992287\pi$
$350$	−141.019	+	78.2881i	−0.402913	+	0.223680i
$351$	57.5965			0.164093
$352$	35.9276	−	226.838i	0.102067	−	0.644426i
$353$	−449.055	+	228.805i	−1.27211	+	0.648173i	−0.953979	−	0.299873i	$-0.903056\pi$
$353$	−449.055	+	228.805i	−1.27211	+	0.648173i	−0.318132	+	0.948046i	$0.603056\pi$
$354$	10.4228	+	3.38656i	0.0294429	+	0.00956656i
$355$	12.5532	−	5.46313i	0.0353611	−	0.0153891i
$356$	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	$0.0445245\pi$
$360$	74.6973	−	189.811i	0.207493	−	0.527252i
$361$	−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
$365$	−165.453	−	259.523i	−0.453296	−	0.711022i
$366$	−1.61101	−	1.17047i	−0.00440167	−	0.00319800i
$367$	416.928	+	212.435i	1.13604	+	0.578843i	0.917797	−	0.397050i	$-0.129966\pi$
$367$	416.928	+	212.435i	1.13604	+	0.578843i	0.218247	+	0.975894i	$0.429966\pi$
$368$	115.074	+	115.074i	0.312702	+	0.312702i
$369$	354.704	−	115.250i	0.961256	−	0.312331i
$370$	−20.6684	+	18.2979i	−0.0558607	+	0.0494537i
$371$	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	0.756164	−	0.654382i	$-0.227071\pi$
$373$	474.868	+	75.2117i	1.27310	+	0.201640i	0.516940	+	0.856022i	$0.327071\pi$
$374$		−	4.28263i		−	0.0114509i
$375$	14.0812	−	25.9947i	0.0375498	−	0.0693191i
$376$	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	$0.910804\pi$
$380$	−172.315	−	194.640i	−0.453461	−	0.512210i
$381$	−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	$-0.681906\pi$
$383$	175.227	−	343.902i	0.457511	−	0.897916i	0.998385	−	0.0568121i	$-0.0180936\pi$
$384$	16.7587	−	23.0664i	0.0436424	−	0.0600686i
$385$	413.504	−	263.620i	1.07404	−	0.684727i
$386$	−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	$0.632238\pi$
$390$	8.91137	+	3.50694i	0.0228497	+	0.00899216i
$391$	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
$395$	12.9841	+	29.8348i	0.0328711	+	0.0755313i
$396$	−91.3583	+	281.172i	−0.230703	+	0.710030i
$397$	155.364	+	304.919i	0.391345	+	0.768058i	0.999672	−	0.0256288i	$-0.00815880\pi$
$397$	155.364	+	304.919i	0.391345	+	0.768058i	−0.608326	+	0.793687i	$0.708159\pi$
$398$	195.204	+	30.9173i	0.490463	+	0.0776817i
$399$			36.4852i			0.0914415i
$400$	−201.969	+	216.867i	−0.504923	+	0.542169i
$401$	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
$405$	−201.617	+	342.532i	−0.497820	+	0.845759i
$406$	−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	$0.920681\pi$
$410$	124.182	+	7.55483i	0.302882	+	0.0184264i
$411$	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
$415$	−543.315	+	140.699i	−1.30919	+	0.339033i
$416$	−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	$0.444544\pi$
$420$	46.3745	−	4.48055i	0.110416	−	0.0106680i
$421$	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
$425$	−11.0501	+	16.4055i	−0.0260003	+	0.0386011i
$426$	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
$430$	−203.521	−	45.0501i	−0.473304	−	0.104768i
$431$	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	−0.763285	−	0.646062i	$-0.776415\pi$
$433$	90.0802	−	176.792i	0.208037	−	0.408296i	0.971323	+	0.237765i	$0.0764149\pi$
$434$	35.2854	−	48.5662i	0.0813028	−	0.111904i
$435$	35.1541	+	28.9596i	0.0808140	+	0.0665739i
$436$	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	$0.611439\pi$
$440$	−131.538	+	159.674i	−0.298951	+	0.362896i
$441$	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	0.925118	−	0.379681i	$-0.123966\pi$
$443$	241.629	+	241.629i	0.545437	+	0.545437i	−0.379681	+	0.925118i	$0.623966\pi$
$444$	7.58340	−	2.46399i	0.0170797	−	0.00554954i
$445$	120.575	−	544.717i	0.270956	−	1.22408i
$446$	−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	$-0.125208\pi$
$450$	−105.088	+	82.2135i	−0.233528	+	0.182697i
$451$	−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
$455$	−70.5576	−	730.284i	−0.155072	−	1.60502i
$456$	−4.75632	−	14.6384i	−0.0104305	−	0.0321018i
$457$	−145.902	+	145.902i	−0.319260	+	0.319260i	−0.848483	−	0.529223i	$-0.822484\pi$
$457$	−145.902	+	145.902i	−0.319260	+	0.319260i	0.529223	+	0.848483i	$0.322484\pi$
$458$	6.33324	−	12.4297i	0.0138280	−	0.0271390i
$459$	−1.97365	+	2.71650i	−0.00429989	+	0.00591829i
$460$	−62.7067	−	242.145i	−0.136319	−	0.526401i
$461$	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	0.982555	−	0.185970i	$-0.0595428\pi$
$463$	−4.34214	−	27.4152i	−0.00937827	−	0.0592120i	−0.991934	+	0.126758i	$0.959543\pi$
$464$	−268.362	−	369.368i	−0.578365	−	0.796052i
$465$	−0.668161	+	10.9828i	−0.00143690	+	0.0236190i
$466$	92.4135	+	67.1423i	0.198312	+	0.144082i
$467$	−365.168	−	186.062i	−0.781943	−	0.398420i	0.0169777	−	0.999856i	$-0.494596\pi$
$467$	−365.168	−	186.062i	−0.781943	−	0.398420i	−0.798921	+	0.601436i	$0.794596\pi$
$468$	312.766	+	312.766i	0.668303	+	0.668303i
$469$	541.238	−	175.859i	1.15403	−	0.374966i
$470$	−54.6603	−	32.1735i	−0.116298	−	0.0684542i
$471$	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
$475$	68.2883	+	350.099i	0.143765	+	0.737051i
$476$	−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	$0.380566\pi$
$480$	−27.4529	+	11.9475i	−0.0571936	+	0.0248906i
$481$	−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
$485$	−236.362	+	600.611i	−0.487344	+	1.23837i
$486$	−27.5149	+	19.9907i	−0.0566150	+	0.0411332i
$487$	229.164	−	36.2960i	0.470563	−	0.0745298i	0.0833503	−	0.996520i	$-0.473438\pi$
$487$	229.164	−	36.2960i	0.470563	−	0.0745298i	0.387213	+	0.921990i	$0.373438\pi$
$488$	−10.0680	−	63.5670i	−0.0206312	−	0.130260i
$489$	36.7692	+	50.6085i	0.0751927	+	0.103494i
$490$	108.907	+	170.827i	0.222258	+	0.348626i
$491$	−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
$495$	303.736	−	268.899i	0.613608	−	0.543230i
$496$	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	$-0.271681\pi$
$500$	436.608	−	129.792i	0.873216	−	0.259584i
$501$	−63.6973			−0.127140
$502$	20.7091	−	130.752i	0.0412532	−	0.260463i
$503$	−728.768	+	371.326i	−1.44884	+	0.738222i	−0.988740	−	0.149644i	$-0.952187\pi$
$503$	−728.768	+	371.326i	−1.44884	+	0.738222i	−0.460102	+	0.887866i	$0.652187\pi$
$504$	−419.502	−	136.305i	−0.832346	−	0.270446i
$505$	107.763	+	121.725i	0.213393	+	0.241039i
$506$	−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	$0.854494\pi$
$510$	−0.470767	+	0.300126i	−0.000923072	+	0.000588483i
$511$	−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
$515$	241.715	+	95.1234i	0.469349	+	0.184706i
$516$	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
$520$	123.511	+	283.804i	0.237521	+	0.545776i
$521$	−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	−0.427543	−	0.903995i	$-0.640621\pi$
$523$	−582.366	−	92.2377i	−1.11351	−	0.176363i	−0.685967	+	0.727632i	$0.740621\pi$
$524$		−	12.9208i		−	0.0246580i
$525$	−57.9567	−	26.9799i	−0.110394	−	0.0513902i
$526$	−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
$530$	96.6050	−	164.125i	0.182274	−	0.309669i
$531$	−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
$535$	245.614	+	14.9424i	0.459092	+	0.0279297i
$536$	−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
$540$	74.8536	−	19.3844i	0.138618	−	0.0358970i
$541$	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
$545$	−643.571	+	62.1796i	−1.18086	+	0.114091i
$546$	6.39932	−	19.6951i	0.0117204	−	0.0360716i
$547$	−137.666	−	270.185i	−0.251675	−	0.493940i	0.730257	−	0.683172i	$-0.239400\pi$
$547$	−137.666	−	270.185i	−0.251675	−	0.493940i	−0.981932	+	0.189232i	$0.939400\pi$
$548$	898.683	+	142.337i	1.63993	+	0.259740i
$549$			126.201i			0.229875i
$550$	127.130	−	46.3651i	0.231146	−	0.0843002i
$551$	−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
$555$	−10.6824	−	2.36460i	−0.0192476	−	0.00426054i
$556$	−155.910	−	479.840i	−0.280413	−	0.863022i
$557$	39.2190	−	39.2190i	0.0704112	−	0.0704112i	−0.671024	−	0.741435i	$-0.734145\pi$
$557$	39.2190	−	39.2190i	0.0704112	−	0.0704112i	0.741435	+	0.671024i	$0.234145\pi$
$558$	22.5449	−	44.2468i	0.0404030	−	0.0792953i
$559$	557.324	−	767.091i	0.997002	−	1.37226i
$560$	494.615	+	407.459i	0.883240	+	0.727606i
$561$	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	$0.127437\pi$
$563$	93.1829	+	588.334i	0.165511	+	1.04500i	−0.755411	+	0.655251i	$0.772563\pi$
$564$	10.7688	+	14.8220i	0.0190936	+	0.0262802i
$565$	243.308	−	295.352i	0.430634	−	0.522746i
$566$	−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	$0.323104\pi$
$570$	−2.17592	+	9.83002i	−0.00381739	+	0.0172456i
$571$	−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
$575$	−94.3893	+	329.983i	−0.164155	+	0.573884i
$576$	−288.966			−0.501677
$577$	140.082	−	884.446i	0.242777	−	1.53284i	−0.501614	−	0.865092i	$-0.667260\pi$
$577$	140.082	−	884.446i	0.242777	−	1.53284i	0.744391	−	0.667744i	$-0.232740\pi$
$578$	−153.321	+	78.1211i	−0.265262	+	0.135158i
$579$	−54.9116	−	17.8419i	−0.0948387	−	0.0308150i
$580$	67.4857	+	698.490i	0.116355	+	1.20429i
$581$	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
$585$	−152.152	−	587.542i	−0.260089	−	1.00435i
$586$	161.959	−	117.670i	0.276380	−	0.200802i
$587$	346.752	−	54.9201i	0.590718	−	0.0935606i	0.146083	−	0.989272i	$-0.453333\pi$
$587$	346.752	−	54.9201i	0.590718	−	0.0935606i	0.444635	+	0.895712i	$0.353333\pi$
$588$	−9.15440	−	57.7986i	−0.0155687	−	0.0982970i
$589$	−78.0330	−	107.403i	−0.132484	−	0.182348i
$590$	14.0691	−	231.259i	0.0238459	−	0.391964i
$591$	−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	0.340525	−	0.940236i	$-0.389395\pi$
$593$	−355.629	−	355.629i	−0.599711	−	0.599711i	−0.940236	+	0.340525i	$0.889395\pi$
$594$	21.8474	−	7.09864i	0.0367801	−	0.0119506i
$595$	36.8611	+	21.6967i	0.0619514	+	0.0364651i
$596$	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	$0.684759\pi$
$600$	26.7704	+	3.26935i	0.0446173	+	0.00544891i
$601$	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
$605$	177.495	−	77.2456i	0.293380	−	0.127679i
$606$	1.41799	+	4.36411i	0.00233991	+	0.00720151i
$607$	728.906	−	728.906i	1.20083	−	1.20083i	0.226920	−	0.973913i	$-0.427134\pi$
$607$	728.906	−	728.906i	1.20083	−	1.20083i	0.973913	−	0.226920i	$-0.0728657\pi$
$608$	163.999	−	321.867i	0.269736	−	0.529386i
$609$	57.8912	−	79.6804i	0.0950595	−	0.130838i
$610$	−15.4164	+	39.1740i	−0.0252727	+	0.0642197i
$611$	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	0.966613	−	0.256240i	$-0.0824839\pi$
$613$	−19.5383	−	123.360i	−0.0318732	−	0.201240i	−0.998486	+	0.0550007i	$0.982484\pi$
$614$	39.2349	+	54.0022i	0.0639004	+	0.0879514i
$615$	26.5081	+	41.5796i	0.0431026	+	0.0676091i
$616$	361.919	+	262.949i	0.587530	+	0.426866i
$617$	−639.236	−	325.707i	−1.03604	−	0.527888i	−0.148640	−	0.988891i	$-0.547490\pi$
$617$	−639.236	−	325.707i	−1.03604	−	0.527888i	−0.887399	+	0.461003i	$0.847490\pi$
$618$	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	$0.453388\pi$
$620$	−126.932	+	112.374i	−0.204729	+	0.181248i
$621$	−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
$625$	−606.631	−	150.414i	−0.970609	−	0.240662i
$626$	−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
$630$	191.252	+	216.029i	0.303574	+	0.342904i
$631$	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
$635$	−258.263	+	164.650i	−0.406713	+	0.259291i
$636$	−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
$640$	−560.891	−	220.731i	−0.876392	−	0.344892i
$641$	−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	0.957468	−	0.288539i	$-0.0931694\pi$
$643$	430.122	+	430.122i	0.668929	+	0.668929i	−0.288539	+	0.957468i	$0.593169\pi$
$644$	−514.418	+	167.145i	−0.798786	+	0.259541i
$645$	−32.9686	−	75.7553i	−0.0511141	−	0.117450i
$646$	2.08158	−	6.40643i	0.00322225	−	0.00991707i
$647$	400.518	+	786.060i	0.619038	+	1.21493i	0.961346	+	0.275343i	$0.0887914\pi$
$647$	400.518	+	786.060i	0.619038	+	1.21493i	−0.342308	+	0.939588i	$0.611209\pi$
$648$	−358.122	−	56.7209i	−0.552657	−	0.0875323i
$649$			704.409i			1.08538i
$650$	24.5430	−	200.965i	0.0377584	−	0.309177i
$651$	23.7934			0.0365490
$652$	−150.773	+	951.940i	−0.231246	+	1.46003i
$653$	868.933	−	442.744i	1.33068	−	0.678015i	0.363377	−	0.931642i	$-0.381624\pi$
$653$	868.933	−	442.744i	1.33068	−	0.678015i	0.967302	+	0.253627i	$0.0816237\pi$
$654$	−17.3565	−	5.63947i	−0.0265390	−	0.00862304i
$655$	−8.99330	+	15.2789i	−0.0137302	+	0.0233266i
$656$	−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	$0.0565872\pi$
$660$	−39.0162	−	2.37362i	−0.0591154	−	0.00359639i
$661$	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
$665$	746.698	−	193.368i	1.12285	−	0.290779i
$666$	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
$670$	156.311	−	15.1023i	0.233300	−	0.0225407i
$671$	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	0.681726	−	0.731608i	$-0.261230\pi$
$673$	742.996	+	117.679i	1.10401	+	0.174857i	0.422280	+	0.906465i	$0.361230\pi$
$674$			23.1240i			0.0343086i
$675$	−102.007	−	29.1784i	−0.151121	−	0.0432272i
$676$	−55.3389			−0.0818624
$677$	−104.837	+	661.912i	−0.154855	+	0.977714i	0.780796	+	0.624786i	$0.214814\pi$
$677$	−104.837	+	661.912i	−0.154855	+	0.977714i	−0.935651	+	0.352928i	$0.885186\pi$
$678$	9.62365	−	4.90350i	0.0141942	−	0.00723230i
$679$	1327.42	+	431.304i	1.95496	+	0.635204i
$680$	−17.6177	−	3.89976i	−0.0259084	−	0.00573494i
$681$	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	$-0.570552\pi$
$683$	477.148	−	936.456i	0.698607	−	1.37109i	0.918442	−	0.395556i	$-0.129448\pi$
$684$	−273.328	+	376.203i	−0.399602	+	0.550005i
$685$	−963.626	−	793.827i	−1.40675	−	1.15887i
$686$	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
$690$	−6.15957	+	7.47710i	−0.00892692	+	0.0108364i
$691$	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
$695$	−149.620	+	675.931i	−0.215281	+	0.972563i
$696$	−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
$700$	−337.479	−	925.346i	−0.482112	−	1.32192i
$701$	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
$705$	−2.41759	−	25.0225i	−0.00342921	−	0.0354930i
$706$	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	$0.254552\pi$
$710$	−2.04799	−	7.90841i	−0.00288450	−	0.0111386i
$711$	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
$715$	−37.3787	+	614.408i	−0.0522778	+	0.859312i
$716$	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	$0.429542\pi$
$720$	456.849	+	268.905i	0.634512	+	0.373479i
$721$	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
$725$	406.369	−	872.940i	0.560509	−	1.20405i
$726$	5.46377			0.00752585
$727$	202.138	−	1276.25i	0.278044	−	1.75550i	−0.313837	−	0.949477i	$-0.601615\pi$
$727$	202.138	−	1276.25i	0.278044	−	1.75550i	0.591881	−	0.806025i	$-0.298385\pi$
$728$	596.352	−	303.857i	0.819165	−	0.417386i
$729$	667.599	+	216.916i	0.915774	+	0.297553i
$730$	−168.399	+	73.2869i	−0.230683	+	0.100393i
$731$	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	$0.343009\pi$
$733$	−379.282	+	744.383i	−0.517438	+	1.01553i	−0.990885	+	0.134707i	$0.956991\pi$
$734$	164.121	−	225.893i	0.223598	−	0.307757i
$735$	−29.4046	+	74.7189i	−0.0400062	+	0.101658i
$736$	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	$-0.469781\pi$
$740$	−90.6189	−	142.141i	−0.122458	−	0.192083i
$741$	−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	0.445829	−	0.895118i	$-0.352909\pi$
$743$	−333.821	−	333.821i	−0.449289	−	0.449289i	−0.895118	+	0.445829i	$0.852909\pi$
$744$	−9.54631	+	3.10178i	−0.0128311	+	0.00416906i
$745$	−385.872	+	341.614i	−0.517950	+	0.458543i
$746$	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
$750$	−14.0060	−	10.7255i	−0.0186746	−	0.0143007i
$751$	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
$755$	156.084	+	176.306i	0.206734	+	0.233518i
$756$	−51.6690	−	159.021i	−0.0683453	−	0.210345i
$757$	−465.289	+	465.289i	−0.614648	+	0.614648i	−0.944154	−	0.329505i	$-0.893118\pi$
$757$	−465.289	+	465.289i	−0.614648	+	0.614648i	0.329505	+	0.944154i	$0.393118\pi$
$758$	−170.127	+	333.893i	−0.224442	+	0.440492i
$759$	17.3123	−	23.8283i	0.0228093	−	0.0313944i
$760$	−274.379	+	174.924i	−0.361026	+	0.230163i
$761$	−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
$765$	32.9248	+	12.9571i	0.0430389	+	0.0169373i
$766$	−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	$0.585600\pi$
$770$	−116.770	−	268.314i	−0.151649	−	0.348459i
$771$	−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	−0.0539672	−	0.998543i	$-0.517187\pi$
$773$	−319.914	−	50.6693i	−0.413860	−	0.0655489i	−0.359893	+	0.932994i	$0.617187\pi$
$774$			372.873i			0.481748i
$775$	228.314	−	44.5335i	0.294598	−	0.0574626i
$776$	−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
$780$	−29.6651	+	50.3987i	−0.0380321	+	0.0646137i
$781$	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
$785$	−668.811	−	40.6884i	−0.851989	−	0.0518323i
$786$	−0.404845	+	0.294137i	−0.000515070	+	0.000374221i
$787$	−813.494	+	128.845i	−1.03366	+	0.163716i	−0.650140	−	0.759815i	$-0.725290\pi$
$787$	−813.494	+	128.845i	−1.03366	+	0.163716i	−0.383524	+	0.923531i	$0.625290\pi$
$788$	−24.7285	−	156.130i	−0.0313814	−	0.198134i
$789$	−0.753408	−	1.03698i	−0.000954890	−	0.00131429i
$790$	18.7957	−	4.86740i	0.0237920	−	0.00616127i
$791$	−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
$795$	75.1334	−	7.25914i	0.0945074	−	0.00913099i
$796$	−372.955	+	1147.84i	−0.468536	+	1.44201i
$797$	−393.451	−	772.191i	−0.493665	−	0.968872i	−0.994639	−	0.103410i	$-0.967025\pi$
$797$	−393.451	−	772.191i	−0.493665	−	0.968872i	0.500974	−	0.865462i	$-0.332975\pi$
$798$	21.5031	+	3.40576i	0.0269463	+	0.00426787i
$799$			16.8197i			0.0210509i
$800$	390.012	+	498.526i	0.487516	+	0.623157i
$801$	−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
$805$	724.640	+	160.402i	0.900174	+	0.199257i
$806$	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	$0.175690\pi$
$810$	183.057	+	150.801i	0.225996	+	0.186174i
$811$	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
$815$	840.870	−	1020.73i	1.03174	−	1.25243i
$816$	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
$820$	−164.197	+	741.784i	−0.200240	+	0.904615i
$821$	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	−0.321885	−	0.946779i	$-0.604316\pi$
$823$	−757.643	−	119.999i	−0.920587	−	0.145807i	−0.598702	+	0.800972i	$0.704316\pi$
$824$			236.964i			0.287578i
$825$	44.4847	+	29.9633i	0.0539208	+	0.0363192i
$826$	−501.004			−0.606542
$827$	−36.5445	+	230.733i	−0.0441892	+	0.279000i	−0.999882	−	0.0153664i	$-0.995109\pi$
$827$	−36.5445	+	230.733i	−0.0441892	+	0.279000i	0.955693	+	0.294366i	$0.0951085\pi$
$828$	−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	$0.889461\pi$
$830$	32.2067	+	333.345i	0.0388033	+	0.401621i
$831$	−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
$835$	337.590	+	1303.62i	0.404299	+	1.56122i
$836$	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	$-0.414119\pi$
$840$	3.54139	−	58.2113i	0.00421594	−	0.0692991i
$841$	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
$845$	65.4386	+	38.5177i	0.0774421	+	0.0455830i
$846$	−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
$850$	8.63735	+	8.04398i	0.0101616	+	0.00946351i
$851$	127.019			0.149259
$852$	−0.369145	+	2.33069i	−0.000433269	+	0.00273555i
$853$	32.3156	−	16.4656i	0.0378846	−	0.0193032i	−0.434946	−	0.900457i	$-0.643232\pi$
$853$	32.3156	−	16.4656i	0.0378846	−	0.0193032i	0.472830	+	0.881154i	$0.343232\pi$
$854$	86.5788	+	28.1311i	0.101380	+	0.0329405i
$855$	585.061	−	254.617i	0.684281	−	0.297798i
$856$	69.3667	+	213.489i	0.0810358	+	0.249403i
$857$	687.485	−	687.485i	0.802199	−	0.802199i	−0.181240	−	0.983439i	$-0.558011\pi$
$857$	687.485	−	687.485i	0.802199	−	0.802199i	0.983439	+	0.181240i	$0.0580110\pi$
$858$	−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	$-0.139792\pi$
$860$	466.142	−	1184.50i	0.542025	−	1.37732i
$861$	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	$0.225086\pi$
$863$	205.361	+	1296.60i	0.237962	+	1.50243i	−0.522269	+	0.852781i	$0.674914\pi$
$864$	63.1570	+	86.9282i	0.0730984	+	0.100611i
$865$	500.802	+	785.540i	0.578962	+	0.908138i
$866$	−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
$870$	20.3494	−	18.0154i	0.0233901	−	0.0207073i
$871$	−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
$875$	−245.000	+	1329.12i	−0.280000	+	1.51900i
$876$	53.0498			0.0605591
$877$	−58.9645	+	372.287i	−0.0672343	+	0.424501i	0.930996	+	0.365030i	$0.118941\pi$
$877$	−58.9645	+	372.287i	−0.0672343	+	0.424501i	−0.998230	+	0.0594706i	$0.981059\pi$
$878$	260.639	−	132.802i	0.296855	−	0.151255i
$879$	75.4629	+	24.5194i	0.0858509	+	0.0278947i
$880$	−356.384	−	402.556i	−0.404982	−	0.457449i
$881$	−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	−0.881666	−	0.471875i	$-0.843577\pi$
$883$	16.1759	−	31.7470i	0.0183192	−	0.0359535i	0.899985	+	0.435921i	$0.143577\pi$
$884$	22.9987	−	31.6549i	0.0260166	−	0.0358088i
$885$	77.4320	−	49.3650i	0.0874938	−	0.0557796i
$886$	164.963	−	119.853i	0.186189	−	0.135274i
$887$	−296.686	+	46.9904i	−0.334482	+	0.0529768i	−0.321417	−	0.946938i	$-0.604159\pi$
$887$	−296.686	+	46.9904i	−0.334482	+	0.0529768i	−0.0130655	+	0.999915i	$0.504159\pi$
$888$	−1.56136	−	9.85802i	−0.00175828	−	0.0111014i
$889$	389.298	+	535.823i	0.437905	+	0.602725i
$890$	−309.783	−	121.910i	−0.348070	−	0.136978i
$891$	−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
$895$	−408.166	−	937.884i	−0.456051	−	1.04792i
$896$	−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
$900$	−395.480	−	712.374i	−0.439422	−	0.791527i
$901$	−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
$905$	70.0436	−	118.999i	0.0773962	−	0.131490i
$906$	2.05381	+	6.32097i	0.00226689	+	0.00697678i
$907$	−505.478	+	505.478i	−0.557307	+	0.557307i	−0.928540	−	0.371233i	$-0.878935\pi$
$907$	−505.478	+	505.478i	−0.557307	+	0.557307i	0.371233	+	0.928540i	$0.378935\pi$
$908$	−567.744	+	1114.26i	−0.625268	+	1.22716i
$909$	170.935	−	235.272i	0.188047	−	0.258825i
$910$	−436.992	−	26.5852i	−0.480210	−	0.0292145i
$911$	−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
$915$	−16.1529	+	4.18302i	−0.0176534	+	0.00457160i
$916$	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	$0.148476\pi$
$920$	−311.648	+	30.1104i	−0.338748	+	0.0327287i
$921$	−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
$925$	8.22240	+	231.157i	0.00888909	+	0.249899i
$926$	−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	$0.678332\pi$
$930$	6.41054	+	1.41900i	0.00689306	+	0.00152581i
$931$	−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
$935$	−27.6973	−	22.8168i	−0.0296227	−	0.0244030i
$936$	447.924	−	325.436i	0.478551	−	0.347688i
$937$	−517.916	+	82.0298i	−0.552738	+	0.0875451i	−0.426555	−	0.904462i	$-0.640273\pi$
$937$	−517.916	+	82.0298i	−0.552738	+	0.0875451i	−0.126184	+	0.992007i	$0.540273\pi$
$938$	−53.1227	−	335.404i	−0.0566341	−	0.357573i
$939$	−14.2874	−	19.6650i	−0.0152156	−	0.0209425i
$940$	246.271	−	298.948i	0.261990	−	0.318029i
$941$	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
$945$	−49.5847	+	224.006i	−0.0524706	+	0.237044i
$946$	116.861	−	359.660i	0.123531	−	0.380190i
$947$	561.219	+	1101.45i	0.592628	+	1.16310i	0.971365	+	0.237594i	$0.0763588\pi$
$947$	561.219	+	1101.45i	0.592628	+	1.16310i	−0.378736	+	0.925505i	$0.623641\pi$
$948$	−5.53929	−	0.877337i	−0.00584313	−	0.000925461i
$949$		−	835.402i		−	0.880297i
$950$	212.711	−	7.56630i	0.223907	−	0.00796452i
$951$	−96.5800			−0.101556
$952$	−6.10394	+	38.5387i	−0.00641170	+	0.0404819i
$953$	90.7422	−	46.2355i	0.0952174	−	0.0485157i	−0.405733	−	0.913992i	$-0.632984\pi$
$953$	90.7422	−	46.2355i	0.0952174	−	0.0485157i	0.500951	+	0.865476i	$0.332984\pi$
$954$	−323.997	−	105.273i	−0.339620	−	0.110349i
$955$	−44.7232	−	462.893i	−0.0468306	−	0.484705i
$956$	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
$960$	−9.57794	−	36.9856i	−0.00997702	−	0.0385267i
$961$	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
$965$	−74.1218	+	1218.37i	−0.0768102	+	1.26256i
$966$	16.9476	+	12.3132i	0.0175441	+	0.0127466i
$967$	−421.887	−	214.962i	−0.436284	−	0.222298i	0.222032	−	0.975039i	$-0.428731\pi$
$967$	−421.887	−	214.962i	−0.436284	−	0.222298i	−0.658316	+	0.752741i	$0.728731\pi$
$968$	124.867	+	124.867i	0.128995	+	0.128995i
$969$	2.53920	−	0.825036i	0.00262043	−	0.000851430i
$970$	331.917	+	195.369i	0.342182	+	0.201411i
$971$	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
$975$	70.1582	−	38.9489i	0.0719571	−	0.0399475i
$976$	167.260			0.171373
$977$	17.9443	−	113.296i	0.0183667	−	0.115963i	−0.976802	−	0.214146i	$-0.931303\pi$
$977$	17.9443	−	113.296i	0.0183667	−	0.115963i	0.995168	+	0.0981833i	$0.0313032\pi$
$978$	33.2592	−	16.9464i	0.0340074	−	0.0173276i
$979$	962.619	+	312.774i	0.983267	+	0.319483i
$980$	−1134.38	+	493.679i	−1.15753	+	0.503755i
$981$	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	$-0.623125\pi$
$983$	583.651	−	1145.48i	0.593744	−	1.16529i	0.970978	−	0.239170i	$-0.0768755\pi$
$984$	−26.4406	+	36.3924i	−0.0268706	+	0.0369842i
$985$	−79.4297	+	201.836i	−0.0806393	+	0.204910i
$986$	−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
$990$	−130.127	−	204.113i	−0.131442	−	0.206174i
$991$	−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
$995$	1239.95	−	1097.73i	1.24618	−	1.10325i
$996$	29.8934	−	92.0024i	0.0300135	−	0.0923719i
$997$	589.304	+	1156.57i	0.591077	+	1.16005i	0.971897	+	0.235405i	$0.0756417\pi$
$997$	589.304	+	1156.57i	0.591077	+	1.16005i	−0.380820	+	0.924649i	$0.624358\pi$
$998$	−443.254	−	70.2046i	−0.444143	−	0.0703453i
$999$			39.2652i			0.0393045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.3.f.a.23.3	yes	32
3.2	odd	2		225.3.r.a.73.2		32
4.3	odd	2		400.3.bg.c.273.2		32
5.2	odd	4		125.3.f.a.32.3		32
5.3	odd	4		125.3.f.b.32.2		32
5.4	even	2		125.3.f.c.93.2		32
25.9	even	10		125.3.f.b.43.2		32
25.12	odd	20	inner	25.3.f.a.12.3	✓	32
25.13	odd	20		125.3.f.c.82.2		32
25.16	even	5		125.3.f.a.43.3		32
75.62	even	20		225.3.r.a.37.2		32
100.87	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	25.12	odd	20	inner
25.3.f.a.23.3	yes	32	1.1	even	1	trivial
125.3.f.a.32.3		32	5.2	odd	4
125.3.f.a.43.3		32	25.16	even	5
125.3.f.b.32.2		32	5.3	odd	4
125.3.f.b.43.2		32	25.9	even	10
125.3.f.c.82.2		32	25.13	odd	20
125.3.f.c.93.2		32	5.4	even	2
225.3.r.a.37.2		32	75.62	even	20
225.3.r.a.73.2		32	3.2	odd	2
400.3.bg.c.273.2		32	4.3	odd	2
400.3.bg.c.337.2		32	100.87	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0933465 - 0.589367i) q^{2} +(0.210730 - 0.107372i) q^{3} +(3.46559 + 1.12604i) q^{4} +(-3.31432 - 3.74370i) q^{5} +(-0.0436108 - 0.134220i) q^{6} +(-7.64532 + 7.64532i) q^{7} +(2.07076 - 4.06409i) q^{8} +(-5.25719 + 7.23590i) q^{9} +(-2.51579 + 1.60389i) q^{10} +(7.33868 - 5.33186i) q^{11} +(0.851210 - 0.134818i) q^{12} +(-2.12306 - 13.4044i) q^{13} +(3.79223 + 5.21956i) q^{14} +(-1.10040 - 0.433046i) q^{15} +(9.59007 + 6.96760i) q^{16} +(0.704962 + 0.359196i) q^{17} +(3.77386 + 3.77386i) q^{18} +(13.5696 - 4.40902i) q^{19} +(-7.27050 - 16.7062i) q^{20} +(-0.790204 + 2.43200i) q^{21} +(-2.45738 - 4.82288i) q^{22} +(13.5597 + 2.14764i) q^{23} -1.07877i q^{24} +(-3.03063 + 24.8156i) q^{25} -8.09832 q^{26} +(-0.663895 + 4.19167i) q^{27} +(-35.1044 + 17.8866i) q^{28} +(-36.6306 - 11.9020i) q^{29} +(-0.357941 + 0.608115i) q^{30} +(-2.87530 - 8.84925i) q^{31} +(17.9028 - 17.9028i) q^{32} +(0.973987 - 1.91156i) q^{33} +(0.277504 - 0.381951i) q^{34} +(53.9608 + 3.28280i) q^{35} +(-26.3671 + 19.1568i) q^{36} +(9.13820 - 1.44735i) q^{37} +(-1.33186 - 8.40902i) q^{38} +(-1.88666 - 2.59677i) q^{39} +(-22.0779 + 5.71738i) q^{40} +(-33.7351 - 24.5100i) q^{41} +(1.35958 + 0.692738i) q^{42} +(49.4021 + 49.4021i) q^{43} +(31.4367 - 10.2144i) q^{44} +(44.5130 - 4.30070i) q^{45} +(2.53150 - 7.79114i) q^{46} +(9.65116 + 18.9415i) q^{47} +(2.76905 + 0.438574i) q^{48} -67.9017i q^{49} +(14.3426 + 4.10260i) q^{50} +0.187125 q^{51} +(7.73627 - 48.8449i) q^{52} +(-56.8742 + 28.9788i) q^{53} +(2.40846 + 0.782556i) q^{54} +(-44.2836 - 9.80236i) q^{55} +(15.2397 + 46.9029i) q^{56} +(2.38611 - 2.38611i) q^{57} +(-10.4340 + 20.4778i) q^{58} +(-45.6440 + 62.8235i) q^{59} +(-3.32590 - 2.73985i) q^{60} +(11.4153 - 8.29369i) q^{61} +(-5.48385 + 0.868557i) q^{62} +(-15.1279 - 95.5136i) q^{63} +(18.9902 + 26.1378i) q^{64} +(-43.1458 + 52.3747i) q^{65} +(-1.03569 - 0.752473i) q^{66} +(-46.8978 - 23.8956i) q^{67} +(2.03864 + 2.03864i) q^{68} +(3.08803 - 1.00336i) q^{69} +(6.97183 - 31.4963i) q^{70} +(-0.846117 + 2.60408i) q^{71} +(18.5210 + 36.3495i) q^{72} +(60.7976 + 9.62940i) q^{73} -5.52086i q^{74} +(2.02587 + 5.55481i) q^{75} +51.9912 q^{76} +(-15.3427 + 96.8703i) q^{77} +(-1.70656 + 0.869536i) q^{78} +(-6.18905 - 2.01094i) q^{79} +(-5.69992 - 58.9952i) q^{80} +(-24.5646 - 75.6022i) q^{81} +(-17.5944 + 17.5944i) q^{82} +(50.9593 - 100.013i) q^{83} +(-5.47704 + 7.53850i) q^{84} +(-0.991742 - 3.82966i) q^{85} +(33.7274 - 24.5044i) q^{86} +(-8.99712 + 1.42500i) q^{87} +(-6.47255 - 40.8661i) q^{88} +(65.5853 + 90.2704i) q^{89} +(1.62045 - 26.6360i) q^{90} +(118.713 + 86.2498i) q^{91} +(44.5739 + 22.7115i) q^{92} +(-1.55608 - 1.55608i) q^{93} +(12.0644 - 3.91995i) q^{94} +(-61.4799 - 36.1875i) q^{95} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19}+ \cdots + 170 q^{98}+O(q^{100}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

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