LMFDB - Embedded newform 187.2.g.f.69.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(69,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("187.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.g (of order $5$, degree $4$, 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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			69.1
Character	$\chi$	$=$	187.69
Dual form			187.2.g.f.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.14992 + 1.56201i) q^{2} +(0.943884 + 2.90498i) q^{3} +(1.56424 - 4.81425i) q^{4} +(1.58671 + 1.15281i) q^{5} +(-6.56686 - 4.77110i) q^{6} +(-0.547865 + 1.68616i) q^{7} +(2.51450 + 7.73883i) q^{8} +(-5.12092 + 3.72057i) q^{9} +O(q^{10})$	\(q+(-2.14992 + 1.56201i) q^{2} +(0.943884 + 2.90498i) q^{3} +(1.56424 - 4.81425i) q^{4} +(1.58671 + 1.15281i) q^{5} +(-6.56686 - 4.77110i) q^{6} +(-0.547865 + 1.68616i) q^{7} +(2.51450 + 7.73883i) q^{8} +(-5.12092 + 3.72057i) q^{9} -5.21199 q^{10} +(3.30826 - 0.235368i) q^{11} +15.4617 q^{12} +(-0.447400 + 0.325055i) q^{13} +(-1.45592 - 4.48086i) q^{14} +(-1.85122 + 5.69748i) q^{15} +(-9.30357 - 6.75944i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(5.19800 - 15.9978i) q^{18} +(-2.36763 - 7.28683i) q^{19} +(8.03193 - 5.83554i) q^{20} -5.41536 q^{21} +(-6.74484 + 5.67355i) q^{22} +6.15086 q^{23} +(-20.1077 + 14.6091i) q^{24} +(-0.356412 - 1.09692i) q^{25} +(0.454134 - 1.39768i) q^{26} +(-8.22835 - 5.97824i) q^{27} +(7.26058 + 5.27512i) q^{28} +(0.0436695 - 0.134401i) q^{29} +(-4.91952 - 15.1407i) q^{30} +(0.923923 - 0.671269i) q^{31} +14.2860 q^{32} +(3.80635 + 9.38826i) q^{33} +2.65744 q^{34} +(-2.81313 + 2.04386i) q^{35} +(9.90136 + 30.4732i) q^{36} +(0.600286 - 1.84749i) q^{37} +(16.4723 + 11.9678i) q^{38} +(-1.36657 - 0.992871i) q^{39} +(-4.93164 + 15.1780i) q^{40} +(1.47218 + 4.53090i) q^{41} +(11.6426 - 8.45883i) q^{42} -1.62183 q^{43} +(4.04181 - 16.2950i) q^{44} -12.4145 q^{45} +(-13.2238 + 9.60768i) q^{46} +(-1.80698 - 5.56131i) q^{47} +(10.8545 - 33.4068i) q^{48} +(3.12015 + 2.26692i) q^{49} +(2.47966 + 1.80158i) q^{50} +(0.943884 - 2.90498i) q^{51} +(0.865053 + 2.66236i) q^{52} +(-6.67295 + 4.84818i) q^{53} +27.0283 q^{54} +(5.52059 + 3.44035i) q^{55} -14.4265 q^{56} +(18.9333 - 13.7558i) q^{57} +(0.116049 + 0.357162i) q^{58} +(-1.55387 + 4.78231i) q^{59} +(24.5333 + 17.8245i) q^{60} +(7.96278 + 5.78529i) q^{61} +(-0.937830 + 2.88635i) q^{62} +(-3.46788 - 10.6730i) q^{63} +(-12.1066 + 8.79593i) q^{64} -1.08462 q^{65} +(-22.8479 - 14.2384i) q^{66} -3.73972 q^{67} +(-4.09524 + 2.97537i) q^{68} +(5.80570 + 17.8681i) q^{69} +(2.85547 - 8.78823i) q^{70} +(-5.62213 - 4.08471i) q^{71} +(-41.6694 - 30.2746i) q^{72} +(-1.48727 + 4.57734i) q^{73} +(1.59523 + 4.90960i) q^{74} +(2.85012 - 2.07074i) q^{75} -38.7842 q^{76} +(-1.41562 + 5.70720i) q^{77} +4.48888 q^{78} +(8.99061 - 6.53206i) q^{79} +(-6.96971 - 21.4505i) q^{80} +(3.73200 - 11.4859i) q^{81} +(-10.2423 - 7.44150i) q^{82} +(9.64627 + 7.00842i) q^{83} +(-8.47095 + 26.0709i) q^{84} +(-0.606069 - 1.86529i) q^{85} +(3.48681 - 2.53331i) q^{86} +0.431650 q^{87} +(10.1401 + 25.0103i) q^{88} -12.6882 q^{89} +(26.6902 - 19.3916i) q^{90} +(-0.302979 - 0.932472i) q^{91} +(9.62145 - 29.6118i) q^{92} +(2.82210 + 2.05037i) q^{93} +(12.5716 + 9.13384i) q^{94} +(4.64360 - 14.2915i) q^{95} +(13.4843 + 41.5005i) q^{96} +(-0.408714 + 0.296948i) q^{97} -10.2490 q^{98} +(-16.0656 + 13.5139i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−2.14992	+	1.56201i	−1.52022	+	1.10450i	−0.558842	+	0.829274i	$0.688754\pi$
$2$	−2.14992	+	1.56201i	−1.52022	+	1.10450i	−0.961378	+	0.275230i	$0.911246\pi$
$3$	0.943884	+	2.90498i	0.544952	+	1.67719i	0.721105	+	0.692826i	$0.243635\pi$
$3$	0.943884	+	2.90498i	0.544952	+	1.67719i	−0.176153	+	0.984363i	$0.556365\pi$
$4$	1.56424	−	4.81425i	0.782122	−	2.40712i
$5$	1.58671	+	1.15281i	0.709598	+	0.515553i	0.883044	−	0.469290i	$-0.155490\pi$
$5$	1.58671	+	1.15281i	0.709598	+	0.515553i	−0.173446	+	0.984843i	$0.555490\pi$
$6$	−6.56686	−	4.77110i	−2.68091	−	1.94779i
$7$	−0.547865	+	1.68616i	−0.207074	+	0.637307i	0.792548	+	0.609809i	$0.208754\pi$
$7$	−0.547865	+	1.68616i	−0.207074	+	0.637307i	−0.999622	+	0.0274979i	$0.991246\pi$
$8$	2.51450	+	7.73883i	0.889010	+	2.73609i
$9$	−5.12092	+	3.72057i	−1.70697	+	1.24019i
$10$	−5.21199			−1.64818
$11$	3.30826	−	0.235368i	0.997479	−	0.0709661i
$11$	3.30826	−	0.235368i	0.997479	−	0.0709661i
$12$	15.4617			4.46342
$13$	−0.447400	+	0.325055i	−0.124086	+	0.0901540i	−0.648097	−	0.761557i	$-0.724435\pi$
$13$	−0.447400	+	0.325055i	−0.124086	+	0.0901540i	0.524011	+	0.851711i	$0.324435\pi$
$14$	−1.45592	−	4.48086i	−0.389111	−	1.19756i
$15$	−1.85122	+	5.69748i	−0.477984	+	1.47108i
$16$	−9.30357	−	6.75944i	−2.32589	−	1.68986i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	5.19800	−	15.9978i	1.22518	−	3.77072i
$19$	−2.36763	−	7.28683i	−0.543173	−	1.67171i	−0.725295	−	0.688438i	$-0.758297\pi$
$19$	−2.36763	−	7.28683i	−0.543173	−	1.67171i	0.182123	−	0.983276i	$-0.441703\pi$
$20$	8.03193	−	5.83554i	1.79599	−	1.30487i
$21$	−5.41536			−1.18173
$22$	−6.74484	+	5.67355i	−1.43800	+	1.20960i
$23$	6.15086			1.28254			0.641272	−	0.767314i	$-0.278407\pi$
$23$	6.15086			1.28254			0.641272	+	0.767314i	$0.278407\pi$
$24$	−20.1077	+	14.6091i	−4.10447	+	2.98207i
$25$	−0.356412	−	1.09692i	−0.0712824	−	0.219385i
$26$	0.454134	−	1.39768i	0.0890631	−	0.274108i
$27$	−8.22835	−	5.97824i	−1.58355	−	1.15051i
$28$	7.26058	+	5.27512i	1.37212	+	0.996904i
$29$	0.0436695	−	0.134401i	0.00810921	−	0.0249576i	−0.946920	−	0.321469i	$-0.895823\pi$
$29$	0.0436695	−	0.134401i	0.00810921	−	0.0249576i	0.955029	+	0.296512i	$0.0958233\pi$
$30$	−4.91952	−	15.1407i	−0.898177	−	2.76430i
$31$	0.923923	−	0.671269i	0.165941	−	0.120564i	−0.501715	−	0.865033i	$-0.667297\pi$
$31$	0.923923	−	0.671269i	0.165941	−	0.120564i	0.667657	+	0.744469i	$0.267297\pi$
$32$	14.2860			2.52543
$33$	3.80635	+	9.38826i	0.662601	+	1.63429i
$34$	2.65744			0.455748
$35$	−2.81313	+	2.04386i	−0.475505	+	0.345475i
$36$	9.90136	+	30.4732i	1.65023	+	5.07887i
$37$	0.600286	−	1.84749i	0.0986864	−	0.303726i	−0.889510	−	0.456915i	$-0.848954\pi$
$37$	0.600286	−	1.84749i	0.0986864	−	0.303726i	0.988197	+	0.153189i	$0.0489544\pi$
$38$	16.4723	+	11.9678i	2.67216	+	1.94144i
$39$	−1.36657	−	0.992871i	−0.218826	−	0.158987i
$40$	−4.93164	+	15.1780i	−0.779761	+	2.39986i
$41$	1.47218	+	4.53090i	0.229916	+	0.707607i	0.997755	+	0.0669654i	$0.0213317\pi$
$41$	1.47218	+	4.53090i	0.229916	+	0.707607i	−0.767840	+	0.640642i	$0.778668\pi$
$42$	11.6426	−	8.45883i	1.79649	−	1.30523i
$43$	−1.62183			−0.247327			−0.123664	−	0.992324i	$-0.539464\pi$
$43$	−1.62183			−0.247327			−0.123664	+	0.992324i	$0.539464\pi$
$44$	4.04181	−	16.2950i	0.609326	−	2.45656i
$45$	−12.4145			−1.85065
$46$	−13.2238	+	9.60768i	−1.94975	+	1.41658i
$47$	−1.80698	−	5.56131i	−0.263575	−	0.811200i	−0.992018	−	0.126094i	$-0.959756\pi$
$47$	−1.80698	−	5.56131i	−0.263575	−	0.811200i	0.728443	−	0.685106i	$-0.240244\pi$
$48$	10.8545	−	33.4068i	1.56672	−	4.82185i
$49$	3.12015	+	2.26692i	0.445736	+	0.323846i
$50$	2.47966	+	1.80158i	0.350676	+	0.254781i
$51$	0.943884	−	2.90498i	0.132170	−	0.406778i
$52$	0.865053	+	2.66236i	0.119961	+	0.369203i
$53$	−6.67295	+	4.84818i	−0.916600	+	0.665949i	−0.942675	−	0.333711i	$-0.891699\pi$
$53$	−6.67295	+	4.84818i	−0.916600	+	0.665949i	0.0260752	+	0.999660i	$0.491699\pi$
$54$	27.0283			3.67809
$55$	5.52059	+	3.44035i	0.744396	+	0.463896i
$56$	−14.4265			−1.92782
$57$	18.9333	−	13.7558i	2.50778	−	1.82201i
$58$	0.116049	+	0.357162i	0.0152380	+	0.0468977i
$59$	−1.55387	+	4.78231i	−0.202296	+	0.622604i	0.797517	+	0.603296i	$0.206146\pi$
$59$	−1.55387	+	4.78231i	−0.202296	+	0.622604i	−0.999814	+	0.0193077i	$0.993854\pi$
$60$	24.5333	+	17.8245i	3.16724	+	2.30113i
$61$	7.96278	+	5.78529i	1.01953	+	0.740731i	0.966186	−	0.257845i	$-0.0830124\pi$
$61$	7.96278	+	5.78529i	1.01953	+	0.740731i	0.0533426	+	0.998576i	$0.483012\pi$
$62$	−0.937830	+	2.88635i	−0.119105	+	0.366566i
$63$	−3.46788	−	10.6730i	−0.436912	−	1.34468i
$64$	−12.1066	+	8.79593i	−1.51332	+	1.09949i
$65$	−1.08462			−0.134531
$66$	−22.8479	−	14.2384i	−2.81238	−	1.75263i
$67$	−3.73972			−0.456880			−0.228440	−	0.973558i	$-0.573362\pi$
$67$	−3.73972			−0.456880			−0.228440	+	0.973558i	$0.573362\pi$
$68$	−4.09524	+	2.97537i	−0.496621	+	0.360816i
$69$	5.80570	+	17.8681i	0.698924	+	2.15107i
$70$	2.85547	−	8.78823i	0.341294	−	1.05039i
$71$	−5.62213	−	4.08471i	−0.667224	−	0.484766i	0.201871	−	0.979412i	$-0.435298\pi$
$71$	−5.62213	−	4.08471i	−0.667224	−	0.484766i	−0.869095	+	0.494646i	$0.835298\pi$
$72$	−41.6694	−	30.2746i	−4.91078	−	3.56789i
$73$	−1.48727	+	4.57734i	−0.174072	+	0.535737i	−0.999590	−	0.0286381i	$-0.990883\pi$
$73$	−1.48727	+	4.57734i	−0.174072	+	0.535737i	0.825518	+	0.564375i	$0.190883\pi$
$74$	1.59523	+	4.90960i	0.185441	+	0.570729i
$75$	2.85012	−	2.07074i	0.329104	−	0.239108i
$76$	−38.7842			−4.44885
$77$	−1.41562	+	5.70720i	−0.161324	+	0.650395i
$78$	4.48888			0.508266
$79$	8.99061	−	6.53206i	1.01152	−	0.734914i	0.0469944	−	0.998895i	$-0.485036\pi$
$79$	8.99061	−	6.53206i	1.01152	−	0.734914i	0.964528	+	0.263981i	$0.0850357\pi$
$80$	−6.96971	−	21.4505i	−0.779237	−	2.39824i
$81$	3.73200	−	11.4859i	0.414667	−	1.27621i
$82$	−10.2423	−	7.44150i	−1.13108	−	0.821776i
$83$	9.64627	+	7.00842i	1.05882	+	0.769274i	0.973869	−	0.227111i	$-0.0729281\pi$
$83$	9.64627	+	7.00842i	1.05882	+	0.769274i	0.0849465	+	0.996386i	$0.472928\pi$
$84$	−8.47095	+	26.0709i	−0.924257	+	2.84457i
$85$	−0.606069	−	1.86529i	−0.0657375	−	0.202319i
$86$	3.48681	−	2.53331i	0.375992	−	0.273174i
$87$	0.431650			0.0462777
$88$	10.1401	+	25.0103i	1.08094	+	2.66610i
$89$	−12.6882			−1.34495			−0.672473	−	0.740122i	$-0.734768\pi$
$89$	−12.6882			−1.34495			−0.672473	+	0.740122i	$0.734768\pi$
$90$	26.6902	−	19.3916i	2.81339	−	2.04405i
$91$	−0.302979	−	0.932472i	−0.0317608	−	0.0977496i
$92$	9.62145	−	29.6118i	1.00311	−	3.08724i
$93$	2.82210	+	2.05037i	0.292638	+	0.212614i
$94$	12.5716	+	9.13384i	1.29667	+	0.942083i
$95$	4.64360	−	14.2915i	0.476423	−	1.46628i
$96$	13.4843	+	41.5005i	1.37624	+	4.23563i
$97$	−0.408714	+	0.296948i	−0.0414986	+	0.0301505i	−0.608341	−	0.793676i	$-0.708165\pi$
$97$	−0.408714	+	0.296948i	−0.0414986	+	0.0301505i	0.566843	+	0.823826i	$0.308165\pi$
$98$	−10.2490			−1.03531
$99$	−16.0656	+	13.5139i	−1.61466	+	1.35820i
$100$	−5.83837			−0.583837
$101$	1.88559	−	1.36996i	0.187623	−	0.136316i	−0.490009	−	0.871718i	$-0.663006\pi$
$101$	1.88559	−	1.36996i	0.187623	−	0.136316i	0.677632	+	0.735401i	$0.263006\pi$
$102$	2.50832	+	7.71981i	0.248360	+	0.764375i
$103$	5.13685	−	15.8096i	0.506149	−	1.55777i	−0.292682	−	0.956210i	$-0.594548\pi$
$103$	5.13685	−	15.8096i	0.506149	−	1.55777i	0.798830	−	0.601556i	$-0.205452\pi$
$104$	−3.64053	−	2.64500i	−0.356984	−	0.259364i
$105$	−8.59262	−	6.24290i	−0.838553	−	0.609245i
$106$	6.77340	−	20.8464i	0.657890	−	2.02478i
$107$	−0.395245	−	1.21644i	−0.0382098	−	0.117598i	0.930132	−	0.367225i	$-0.119692\pi$
$107$	−0.395245	−	1.21644i	−0.0382098	−	0.117598i	−0.968342	+	0.249627i	$0.919692\pi$
$108$	−41.6519	+	30.2619i	−4.00796	+	2.91195i
$109$	1.01538			0.0972562			0.0486281	−	0.998817i	$-0.484515\pi$
$109$	1.01538			0.0972562			0.0486281	+	0.998817i	$0.484515\pi$
$110$	−17.2426	+	1.22674i	−1.64402	+	0.116965i
$111$	5.93352			0.563184
$112$	16.4946	−	11.9840i	1.55859	−	1.13238i
$113$	3.98557	+	12.2663i	0.374931	+	1.15392i	0.943525	+	0.331300i	$0.107487\pi$
$113$	3.98557	+	12.2663i	0.374931	+	1.15392i	−0.568595	+	0.822618i	$0.692513\pi$
$114$	−19.2183	+	59.1478i	−1.79996	+	5.53970i
$115$	9.75964	+	7.09079i	0.910091	+	0.661220i
$116$	−0.578729	−	0.420471i	−0.0537336	−	0.0390398i
$117$	1.08171	−	3.32916i	0.100004	−	0.307781i
$118$	−4.12931	−	12.7087i	−0.380134	−	1.16993i
$119$	1.43433	−	1.04210i	0.131485	−	0.0955293i
$120$	−48.7467			−4.44995
$121$	10.8892	−	1.55732i	0.989928	−	0.141574i
$122$	−26.1560			−2.36805
$123$	−11.7726	+	8.55329i	−1.06150	+	0.771224i
$124$	−1.78642	−	5.49802i	−0.160425	−	0.493737i
$125$	3.72937	−	11.4778i	0.333565	−	1.02661i
$126$	24.1270	+	17.5293i	2.14940	+	1.56163i
$127$	−6.62303	−	4.81191i	−0.587699	−	0.426988i	0.253793	−	0.967259i	$-0.418322\pi$
$127$	−6.62303	−	4.81191i	−0.587699	−	0.426988i	−0.841491	+	0.540271i	$0.818322\pi$
$128$	3.45956	−	10.6474i	0.305785	−	0.941109i
$129$	−1.53082	−	4.71139i	−0.134781	−	0.414815i
$130$	2.33184	−	1.69418i	0.204516	−	0.148590i
$131$	10.9792			0.959257			0.479628	−	0.877472i	$-0.340772\pi$
$131$	10.9792			0.959257			0.479628	+	0.877472i	$0.340772\pi$
$132$	51.1515	−	3.63920i	4.45217	−	0.316751i
$133$	13.5839			1.17787
$134$	8.04009	−	5.84147i	0.694558	−	0.504626i
$135$	−6.16421	−	18.9715i	−0.530531	−	1.63281i
$136$	2.51450	−	7.73883i	0.215616	−	0.663599i
$137$	6.17119	+	4.48363i	0.527240	+	0.383062i	0.819324	−	0.573330i	$-0.194349\pi$
$137$	6.17119	+	4.48363i	0.527240	+	0.383062i	−0.292084	+	0.956393i	$0.594349\pi$
$138$	−40.3919	−	29.3464i	−3.43838	−	2.49813i
$139$	5.11217	−	15.7336i	0.433608	−	1.33451i	−0.460898	−	0.887453i	$-0.652473\pi$
$139$	5.11217	−	15.7336i	0.433608	−	1.33451i	0.894506	−	0.447056i	$-0.147527\pi$
$140$	5.43921	+	16.7402i	0.459697	+	1.41480i
$141$	14.4499	−	10.4985i	1.21690	−	0.884130i
$142$	18.4674			1.54975
$143$	−1.40361	+	1.18067i	−0.117376	+	0.0987326i
$144$	72.7918			6.06598
$145$	0.224230	−	0.162912i	0.0186213	−	0.0135291i
$146$	−3.95233	−	12.1640i	−0.327097	−	1.00670i
$147$	−3.64030	+	11.2037i	−0.300247	+	0.924064i
$148$	−7.95528	−	5.77985i	−0.653920	−	0.475101i
$149$	−2.80270	−	2.03628i	−0.229606	−	0.166819i	0.467034	−	0.884239i	$-0.345323\pi$
$149$	−2.80270	−	2.03628i	−0.229606	−	0.166819i	−0.696640	+	0.717421i	$0.745323\pi$
$150$	−2.89303	+	8.90382i	−0.236215	+	0.726994i
$151$	0.827052	+	2.54541i	0.0673046	+	0.207142i	0.979052	−	0.203608i	$-0.0652668\pi$
$151$	0.827052	+	2.54541i	0.0673046	+	0.207142i	−0.911748	+	0.410750i	$0.865267\pi$
$152$	50.4381	−	36.6455i	4.09107	−	2.97234i
$153$	6.32980			0.511734
$154$	−5.87122	−	14.4812i	−0.473116	−	1.16693i
$155$	2.23985			0.179909
$156$	−6.91758	+	5.02592i	−0.553850	+	0.402395i
$157$	−4.38442	−	13.4939i	−0.349915	−	1.07693i	−0.958900	−	0.283745i	$-0.908423\pi$
$157$	−4.38442	−	13.4939i	−0.349915	−	1.07693i	0.608985	−	0.793182i	$-0.291577\pi$
$158$	−9.12594	+	28.0868i	−0.726021	+	2.23446i
$159$	−20.3823	−	14.8086i	−1.61643	−	1.17440i
$160$	22.6677	+	16.4691i	1.79204	+	1.30200i
$161$	−3.36984	+	10.3713i	−0.265581	+	0.817374i
$162$	9.91758	+	30.5232i	0.779199	+	2.39813i
$163$	−13.0952	+	9.51424i	−1.02570	+	0.745212i	−0.967443	−	0.253089i	$-0.918553\pi$
$163$	−13.0952	+	9.51424i	−1.02570	+	0.745212i	−0.0582541	+	0.998302i	$0.518553\pi$
$164$	24.1157			1.88312
$165$	−4.78333	+	19.2845i	−0.372382	+	1.50129i
$166$	−31.6859			−2.45930
$167$	−17.8311	+	12.9551i	−1.37981	+	1.00249i	−0.382917	+	0.923783i	$0.625080\pi$
$167$	−17.8311	+	12.9551i	−1.37981	+	1.00249i	−0.996897	+	0.0787107i	$0.974920\pi$
$168$	−13.6169	−	41.9086i	−1.05057	−	3.23332i
$169$	−3.92272	+	12.0729i	−0.301747	+	0.928683i
$170$	4.21659	+	3.06353i	0.323398	+	0.234962i
$171$	39.2356	+	28.5063i	3.00042	+	2.17993i
$172$	−2.53694	+	7.80791i	−0.193440	+	0.595348i
$173$	−2.93796	−	9.04210i	−0.223369	−	0.687458i	−0.998453	−	0.0556005i	$-0.982293\pi$
$173$	−2.93796	−	9.04210i	−0.223369	−	0.687458i	0.775084	−	0.631858i	$-0.217707\pi$
$174$	−0.928011	+	0.674240i	−0.0703523	+	0.0511140i
$175$	2.04485			0.154576
$176$	−32.3696	−	20.1722i	−2.43995	−	1.52054i
$177$	−15.3592			−1.15447
$178$	27.2785	−	19.8190i	2.04461	−	1.48550i
$179$	2.45526	+	7.55652i	0.183515	+	0.564801i	0.999920	−	0.0126795i	$-0.00403612\pi$
$179$	2.45526	+	7.55652i	0.183515	+	0.564801i	−0.816405	+	0.577480i	$0.804036\pi$
$180$	−19.4194	+	59.7666i	−1.44743	+	4.45474i
$181$	−17.0888	−	12.4157i	−1.27020	−	0.922853i	−0.270987	−	0.962583i	$-0.587350\pi$
$181$	−17.0888	−	12.4157i	−1.27020	−	0.922853i	−0.999210	+	0.0397304i	$0.987350\pi$
$182$	2.10791	+	1.53148i	0.156248	+	0.113521i
$183$	−9.29021	+	28.5923i	−0.686752	+	2.11361i
$184$	15.4663	+	47.6005i	1.14019	+	3.50915i
$185$	3.08229	−	2.23942i	0.226615	−	0.164645i
$186$	−9.26997			−0.679707
$187$	−2.81479	−	1.75413i	−0.205838	−	0.128275i
$188$	−29.6001			−2.15881
$189$	14.5883	−	10.5990i	1.06114	−	0.770964i
$190$	12.3401	+	37.9789i	0.895245	+	2.75528i
$191$	6.09953	−	18.7724i	0.441346	−	1.35832i	−0.445095	−	0.895483i	$-0.646830\pi$
$191$	6.09953	−	18.7724i	0.441346	−	1.35832i	0.886441	−	0.462841i	$-0.153170\pi$
$192$	−36.9792	−	26.8669i	−2.66874	−	1.93895i
$193$	9.26098	+	6.72849i	0.666620	+	0.484328i	0.868892	−	0.495002i	$-0.164833\pi$
$193$	9.26098	+	6.72849i	0.666620	+	0.484328i	−0.202272	+	0.979329i	$0.564833\pi$
$194$	0.414866	−	1.27683i	0.0297857	−	0.0916708i
$195$	−1.02376	−	3.15080i	−0.0733127	−	0.225633i
$196$	15.7942	−	11.4752i	1.12816	−	0.819655i
$197$	1.51195			0.107722			0.0538611	−	0.998548i	$-0.482847\pi$
$197$	1.51195			0.107722			0.0538611	+	0.998548i	$0.482847\pi$
$198$	13.4310	−	54.1484i	0.954499	−	3.84816i
$199$	1.82999			0.129725			0.0648623	−	0.997894i	$-0.479339\pi$
$199$	1.82999			0.129725			0.0648623	+	0.997894i	$0.479339\pi$
$200$	7.59271	−	5.51642i	0.536885	−	0.390070i
$201$	−3.52986	−	10.8638i	−0.248977	−	0.766274i
$202$	−1.91397	+	5.89060i	−0.134667	+	0.414461i
$203$	0.202696	+	0.147267i	0.0142264	+	0.0103361i
$204$	−12.5088	−	9.08818i	−0.875792	−	0.636300i
$205$	−2.88736	+	8.88637i	−0.201662	+	0.620651i
$206$	13.6509	+	42.0131i	0.951102	+	2.92719i
$207$	−31.4981	+	22.8847i	−2.18927	+	1.59060i
$208$	6.35960			0.440959
$209$	−9.54784	−	23.5495i	−0.660438	−	1.62895i
$210$	28.2248			1.94770
$211$	−14.1967	+	10.3145i	−0.977344	+	0.710082i	−0.957114	−	0.289713i	$-0.906440\pi$
$211$	−14.1967	+	10.3145i	−0.977344	+	0.710082i	−0.0202309	+	0.999795i	$0.506440\pi$
$212$	12.9022	+	39.7090i	0.886129	+	2.72722i
$213$	6.55936	−	20.1876i	0.449440	−	1.38323i
$214$	2.74983	+	1.99787i	0.187974	+	0.136571i
$215$	−2.57338	−	1.86967i	−0.175503	−	0.127510i
$216$	25.5745	−	78.7101i	1.74012	−	5.35554i
$217$	0.625679	+	1.92564i	0.0424739	+	0.130721i
$218$	−2.18299	+	1.58604i	−0.147851	+	0.107420i
$219$	−14.7009			−0.993393
$220$	25.1982	−	21.1959i	1.69886	−	1.42903i
$221$	0.553017			0.0371999
$222$	−12.7566	+	9.26819i	−0.856164	+	0.622040i
$223$	−4.21646	−	12.9769i	−0.282355	−	0.869000i	−0.987179	−	0.159617i	$-0.948974\pi$
$223$	−4.21646	−	12.9769i	−0.282355	−	0.869000i	0.704824	−	0.709382i	$-0.251026\pi$
$224$	−7.82680	+	24.0884i	−0.522950	+	1.60948i
$225$	5.90633	+	4.29120i	0.393755	+	0.286080i
$226$	−27.7287	−	20.1461i	−1.84449	−	1.34010i
$227$	−2.61862	+	8.05928i	−0.173804	+	0.534913i	−0.999577	−	0.0290895i	$-0.990739\pi$
$227$	−2.61862	+	8.05928i	−0.173804	+	0.534913i	0.825773	+	0.564003i	$0.190739\pi$
$228$	−36.6078	−	112.667i	−2.42441	−	7.46156i
$229$	−8.40190	+	6.10434i	−0.555213	+	0.403386i	−0.829704	−	0.558204i	$-0.811491\pi$
$229$	−8.40190	+	6.10434i	−0.555213	+	0.403386i	0.274491	+	0.961590i	$0.411491\pi$
$230$	−32.0583			−2.11386
$231$	−17.9154	+	1.27460i	−1.17875	+	0.0838627i
$232$	1.14991			0.0754954
$233$	6.27740	−	4.56080i	0.411246	−	0.298788i	−0.362860	−	0.931844i	$-0.618200\pi$
$233$	6.27740	−	4.56080i	0.411246	−	0.298788i	0.774106	+	0.633056i	$0.218200\pi$
$234$	2.87458	+	8.84705i	0.187917	+	0.578350i
$235$	3.54399	−	10.9073i	0.231185	−	0.711513i
$236$	20.5926	+	14.9614i	1.34046	+	0.973904i
$237$	27.4616	+	19.9520i	1.78382	+	1.29602i
$238$	−1.45592	+	4.48086i	−0.0943733	+	0.290451i
$239$	−4.78435	−	14.7247i	−0.309474	−	0.952462i	−0.977970	−	0.208746i	$-0.933062\pi$
$239$	−4.78435	−	14.7247i	−0.309474	−	0.952462i	0.668496	−	0.743716i	$-0.266938\pi$
$240$	55.7347	−	40.4937i	3.59766	−	2.61385i
$241$	3.11780			0.200835			0.100417	−	0.994945i	$-0.467982\pi$
$241$	3.11780			0.200835			0.100417	+	0.994945i	$0.467982\pi$
$242$	−20.9783	+	20.3571i	−1.34854	+	1.30860i
$243$	6.37651			0.409053
$244$	40.3076	−	29.2852i	2.58043	−	1.87479i
$245$	2.33744	+	7.19390i	0.149334	+	0.459602i
$246$	11.9498	−	36.7777i	0.761891	−	2.34486i
$247$	3.42790	+	2.49051i	0.218112	+	0.158468i
$248$	7.51804	+	5.46218i	0.477396	+	0.346849i
$249$	−11.2543	+	34.6373i	−0.713215	+	2.19505i
$250$	9.91059	+	30.5017i	0.626801	+	1.92909i
$251$	6.39050	−	4.64297i	0.403365	−	0.293062i	−0.367545	−	0.930006i	$-0.619802\pi$
$251$	6.39050	−	4.64297i	0.403365	−	0.293062i	0.770910	+	0.636944i	$0.219802\pi$
$252$	−56.8073			−3.57852
$253$	20.3487	−	1.44772i	1.27931	−	0.0910171i
$254$	21.7552			1.36504
$255$	4.84656	−	3.52123i	0.303504	−	0.220508i
$256$	−0.0550024	−	0.169280i	−0.00343765	−	0.0105800i
$257$	4.79418	−	14.7550i	0.299053	−	0.920390i	−0.682777	−	0.730627i	$-0.739228\pi$
$257$	4.79418	−	14.7550i	0.299053	−	0.920390i	0.981830	−	0.189763i	$-0.0607720\pi$
$258$	10.6504	+	7.73794i	0.663062	+	0.481743i
$259$	2.78628	+	2.02435i	0.173131	+	0.125787i
$260$	−1.69661	+	5.22164i	−0.105219	+	0.323832i
$261$	0.276419	+	0.850730i	0.0171099	+	0.0526589i
$262$	−23.6043	+	17.1496i	−1.45828	+	1.05950i
$263$	−18.4641			−1.13854			−0.569271	−	0.822150i	$-0.692775\pi$
$263$	−18.4641			−1.13854			−0.569271	+	0.822150i	$0.692775\pi$
$264$	−63.0831	+	53.0635i	−3.88250	+	3.26583i
$265$	−16.1771			−0.993751
$266$	−29.2042	+	21.2181i	−1.79062	+	1.30096i
$267$	−11.9762	−	36.8589i	−0.732930	−	2.25573i
$268$	−5.84984	+	18.0040i	−0.357336	+	1.09977i
$269$	2.56803	+	1.86578i	0.156576	+	0.113759i	0.663315	−	0.748341i	$-0.269149\pi$
$269$	2.56803	+	1.86578i	0.156576	+	0.113759i	−0.506739	+	0.862100i	$0.669149\pi$
$270$	42.8861	+	31.1586i	2.60996	+	1.89625i
$271$	9.61565	−	29.5939i	0.584109	−	1.79770i	−0.0187090	−	0.999825i	$-0.505956\pi$
$271$	9.61565	−	29.5939i	0.584109	−	1.79770i	0.602818	−	0.797879i	$-0.294044\pi$
$272$	3.55365	+	10.9370i	0.215472	+	0.663153i
$273$	2.42283	−	1.76029i	0.146637	−	0.106538i
$274$	−20.2710			−1.22461
$275$	−1.43728	−	3.54502i	−0.0866715	−	0.213773i
$276$	95.1031			5.72453
$277$	0.255418	−	0.185572i	0.0153466	−	0.0111500i	−0.580086	−	0.814556i	$-0.696981\pi$
$277$	0.255418	−	0.185572i	0.0153466	−	0.0111500i	0.595432	+	0.803406i	$0.296981\pi$
$278$	13.5853	+	41.8112i	0.814791	+	2.50767i
$279$	−2.23383	+	6.87503i	−0.133736	+	0.411597i
$280$	−22.8907	−	16.6310i	−1.36798	−	0.993894i
$281$	−21.2061	−	15.4071i	−1.26505	−	0.919111i	−0.266054	−	0.963958i	$-0.585720\pi$
$281$	−21.2061	−	15.4071i	−1.26505	−	0.919111i	−0.998994	+	0.0448469i	$0.985720\pi$
$282$	−14.6674	+	45.1416i	−0.873431	+	2.68814i
$283$	−5.74770	−	17.6896i	−0.341665	−	1.05154i	−0.963345	−	0.268266i	$-0.913549\pi$
$283$	−5.74770	−	17.6896i	−0.341665	−	1.05154i	0.621680	−	0.783272i	$-0.286451\pi$
$284$	−28.4592	+	20.6768i	−1.68874	+	1.22694i
$285$	45.8996			2.71886
$286$	1.17343	−	4.73079i	0.0693862	−	0.279737i
$287$	−8.44636			−0.498573
$288$	−73.1574	+	53.1520i	−4.31084	+	3.13201i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	−0.227605	+	0.700496i	−0.0133654	+	0.0411345i
$291$	−1.24841	−	0.907020i	−0.0731829	−	0.0531705i
$292$	19.7100	+	14.3202i	1.15344	+	0.838024i
$293$	0.312767	−	0.962597i	0.0182720	−	0.0562355i	−0.941505	−	0.337000i	$-0.890588\pi$
$293$	0.312767	−	0.962597i	0.0182720	−	0.0562355i	0.959777	+	0.280764i	$0.0905879\pi$
$294$	−9.67388	−	29.7731i	−0.564192	−	1.73641i
$295$	−7.97864	+	5.79682i	−0.464535	+	0.337504i
$296$	15.8068			0.918754
$297$	−28.6286	−	17.8409i	−1.66120	−	1.03523i
$298$	9.20626			0.533305
$299$	−2.75189	+	1.99937i	−0.159146	+	0.115626i
$300$	−5.51075	−	16.9603i	−0.318163	−	0.979206i
$301$	0.888546	−	2.73466i	0.0512150	−	0.157623i
$302$	−5.75403	−	4.18055i	−0.331107	−	0.240563i
$303$	5.75948	+	4.18451i	0.330874	+	0.240394i
$304$	−27.2274	+	83.7974i	−1.56160	+	4.80611i
$305$	5.96526	+	18.3592i	0.341570	+	1.05124i
$306$	−13.6085	+	9.88719i	−0.777949	+	0.565213i
$307$	16.5842			0.946510			0.473255	−	0.880925i	$-0.343079\pi$
$307$	16.5842			0.946510			0.473255	+	0.880925i	$0.343079\pi$
$308$	25.2615	+	15.7426i	1.43941	+	0.897016i
$309$	50.7751			2.88849
$310$	−4.81548	+	3.49865i	−0.273501	+	0.198710i
$311$	4.01353	+	12.3524i	0.227586	+	0.700438i	0.998019	+	0.0629167i	$0.0200402\pi$
$311$	4.01353	+	12.3524i	0.227586	+	0.700438i	−0.770433	+	0.637521i	$0.779960\pi$
$312$	4.24743	−	13.0722i	0.240463	−	0.740069i
$313$	14.3050	+	10.3932i	0.808567	+	0.587459i	0.913415	−	0.407030i	$-0.133435\pi$
$313$	14.3050	+	10.3932i	0.808567	+	0.587459i	−0.104847	+	0.994488i	$0.533435\pi$
$314$	30.5036	+	22.1622i	1.72142	+	1.25068i
$315$	6.80149	−	20.9328i	0.383221	−	1.17943i
$316$	−17.3834	−	53.5007i	−0.977895	−	3.00965i
$317$	−0.574876	+	0.417672i	−0.0322882	+	0.0234588i	−0.603812	−	0.797127i	$-0.706352\pi$
$317$	−0.574876	+	0.417672i	−0.0322882	+	0.0234588i	0.571524	+	0.820585i	$0.306352\pi$
$318$	66.9515			3.75445
$319$	0.112836	−	0.454911i	0.00631763	−	0.0254701i
$320$	−29.3497			−1.64070
$321$	3.16066	−	2.29635i	0.176411	−	0.128170i
$322$	−8.95517	−	27.5612i	−0.499052	−	1.53592i
$323$	−2.36763	+	7.28683i	−0.131739	+	0.405450i
$324$	−49.4583	−	35.9336i	−2.74768	−	1.99631i
$325$	0.516019	+	0.374910i	0.0286236	+	0.0207962i
$326$	13.2923	−	40.9096i	0.736195	−	2.26577i
$327$	0.958405	+	2.94967i	0.0529999	+	0.163117i
$328$	−31.3621	+	22.7859i	−1.73168	+	1.25814i
$329$	10.3672			0.571563
$330$	−19.8387	−	48.9316i	−1.09208	−	2.69359i
$331$	10.8674			0.597327			0.298664	−	0.954358i	$-0.403459\pi$
$331$	10.8674			0.597327			0.298664	+	0.954358i	$0.403459\pi$
$332$	48.8294	−	35.4766i	2.67986	−	1.94703i
$333$	3.79969	+	11.6943i	0.208222	+	0.640841i
$334$	18.0995	−	55.7046i	0.990362	−	3.04802i
$335$	−5.93386	−	4.31120i	−0.324201	−	0.235546i
$336$	50.3822	+	36.6048i	2.74858	+	1.99696i
$337$	−4.12822	+	12.7054i	−0.224879	+	0.692105i	0.773425	+	0.633887i	$0.218542\pi$
$337$	−4.12822	+	12.7054i	−0.224879	+	0.692105i	−0.998304	+	0.0582176i	$0.981458\pi$
$338$	−10.4244	−	32.0830i	−0.567012	−	1.74508i
$339$	−31.8714	+	23.1560i	−1.73102	+	1.25766i
$340$	−9.92801			−0.538422
$341$	2.89858	−	2.43820i	0.156967	−	0.132036i
$342$	−128.880			−6.96905
$343$	−15.5721	+	11.3138i	−0.840816	+	0.610888i
$344$	−4.07810	−	12.5511i	−0.219876	−	0.676710i
$345$	−11.3866	+	35.0444i	−0.613035	+	1.88673i
$346$	20.4402	+	14.8507i	1.09887	+	0.798376i
$347$	7.64947	+	5.55767i	0.410645	+	0.298351i	0.773863	−	0.633353i	$-0.218322\pi$
$347$	7.64947	+	5.55767i	0.410645	+	0.298351i	−0.363218	+	0.931704i	$0.618322\pi$
$348$	0.675206	−	2.07807i	0.0361948	−	0.111396i
$349$	−0.873411	−	2.68808i	−0.0467526	−	0.143890i	0.924955	−	0.380076i	$-0.124102\pi$
$349$	−0.873411	−	2.68808i	−0.0467526	−	0.143890i	−0.971708	+	0.236187i	$0.924102\pi$
$350$	−4.39625	+	3.19407i	−0.234990	+	0.170730i
$351$	5.62462			0.300220
$352$	47.2618	−	3.36246i	2.51906	−	0.179220i
$353$	−14.6533			−0.779916			−0.389958	−	0.920833i	$-0.627510\pi$
$353$	−14.6533			−0.779916			−0.389958	+	0.920833i	$0.627510\pi$
$354$	33.0209	−	23.9911i	1.75504	−	1.27511i
$355$	−4.21178	−	12.9625i	−0.223538	−	0.687979i
$356$	−19.8474	+	61.0841i	−1.05191	+	3.23745i
$357$	4.38112	+	3.18307i	0.231874	+	0.168466i
$358$	−17.0819	−	12.4107i	−0.902808	−	0.655928i
$359$	−0.395062	+	1.21588i	−0.0208506	+	0.0641715i	−0.960940	−	0.276755i	$-0.910741\pi$
$359$	−0.395062	+	1.21588i	−0.0208506	+	0.0641715i	0.940090	+	0.340927i	$0.110741\pi$
$360$	−31.2163	−	96.0740i	−1.64524	−	5.06354i
$361$	−32.1209	+	23.3372i	−1.69057	+	1.22827i
$362$	56.1328			2.95027
$363$	14.8021	+	30.1630i	0.776910	+	1.58314i
$364$	−4.96308			−0.260136
$365$	−7.63668	+	5.54838i	−0.399722	+	0.290415i
$366$	−24.6882	−	75.9824i	−1.29047	−	3.97167i
$367$	6.33958	−	19.5112i	0.330924	−	1.01848i	−0.637772	−	0.770225i	$-0.720144\pi$
$367$	6.33958	−	19.5112i	0.330924	−	1.01848i	0.968695	−	0.248253i	$-0.0798563\pi$
$368$	−57.2250	−	41.5764i	−2.98306	−	2.16732i
$369$	−24.3964	−	17.7250i	−1.27003	−	0.922728i
$370$	−3.12869	+	9.62911i	−0.162653	+	0.500594i
$371$	−4.51891	−	13.9078i	−0.234610	−	0.722056i
$372$	14.2855	−	10.3790i	0.740666	−	0.538126i
$373$	14.5005			0.750808			0.375404	−	0.926861i	$-0.377504\pi$
$373$	14.5005			0.750808			0.375404	+	0.926861i	$0.377504\pi$
$374$	8.79152	−	0.625476i	0.454599	−	0.0323426i
$375$	36.8629			1.90359
$376$	38.4944	−	27.9678i	1.98520	−	1.44233i
$377$	0.0241499	+	0.0743258i	0.00124378	+	0.00382798i
$378$	−14.8079	+	45.5739i	−0.761635	+	2.34407i
$379$	24.8161	+	18.0299i	1.27472	+	0.926135i	0.999380	−	0.0352125i	$-0.0112108\pi$
$379$	24.8161	+	18.0299i	1.27472	+	0.926135i	0.275336	+	0.961348i	$0.411211\pi$
$380$	−61.5393	−	44.7109i	−3.15690	−	2.29362i
$381$	7.72712	−	23.7816i	0.395872	−	1.21837i
$382$	16.2091	+	49.8866i	0.829332	+	2.55242i
$383$	21.6344	−	15.7183i	1.10547	−	0.803169i	0.123524	−	0.992342i	$-0.460580\pi$
$383$	21.6344	−	15.7183i	1.10547	−	0.803169i	0.981944	+	0.189172i	$0.0605804\pi$
$384$	34.1960			1.74506
$385$	−8.82550	+	7.42373i	−0.449789	+	0.378348i
$386$	−30.4203			−1.54835
$387$	8.30528	−	6.03414i	0.422181	−	0.306732i
$388$	0.790254	+	2.43215i	0.0401190	+	0.123474i
$389$	1.50267	−	4.62474i	0.0761884	−	0.234484i	−0.905708	−	0.423902i	$-0.860660\pi$
$389$	1.50267	−	4.62474i	0.0761884	−	0.234484i	0.981897	+	0.189418i	$0.0606601\pi$
$390$	7.12256	+	5.17484i	0.360665	+	0.262038i
$391$	−4.97615	−	3.61539i	−0.251655	−	0.182838i
$392$	−9.69772	+	29.8465i	−0.489809	+	1.50748i
$393$	10.3631	+	31.8943i	0.522749	+	1.60885i
$394$	−3.25057	+	2.36168i	−0.163761	+	0.118980i
$395$	21.7957			1.09666
$396$	39.9287	+	98.4831i	2.00649	+	4.94896i
$397$	−9.00862			−0.452130			−0.226065	−	0.974112i	$-0.572586\pi$
$397$	−9.00862			−0.452130			−0.226065	+	0.974112i	$0.572586\pi$
$398$	−3.93433	+	2.85846i	−0.197210	+	0.143281i
$399$	12.8216	+	39.4608i	0.641883	+	1.97551i
$400$	−4.09868	+	12.6144i	−0.204934	+	0.630722i
$401$	−26.4773	−	19.2369i	−1.32221	−	0.960645i	−0.999902	−	0.0140110i	$-0.995540\pi$
$401$	−26.4773	−	19.2369i	−1.32221	−	0.960645i	−0.322312	−	0.946634i	$-0.604460\pi$
$402$	24.5582	+	17.8426i	1.22485	+	0.889908i
$403$	−0.195163	+	0.600651i	−0.00972178	+	0.0299206i
$404$	−3.64581	−	11.2206i	−0.181386	−	0.558248i
$405$	19.1627	−	13.9225i	0.952203	−	0.691816i
$406$	−0.665811			−0.0330436
$407$	1.55106	−	6.25327i	0.0768834	−	0.309963i
$408$	24.8545			1.23048
$409$	−13.6731	+	9.93412i	−0.676093	+	0.491211i	−0.872059	−	0.489400i	$-0.837216\pi$
$409$	−13.6731	+	9.93412i	−0.676093	+	0.491211i	0.195966	+	0.980611i	$0.437216\pi$
$410$	−7.67298	−	23.6150i	−0.378942	−	1.16626i
$411$	−7.19995	+	22.1592i	−0.355147	+	1.09303i
$412$	−68.0761	−	49.4601i	−3.35387	−	2.43673i
$413$	−7.21241	−	5.24012i	−0.354900	−	0.257850i
$414$	31.9722	−	98.4003i	1.57135	−	4.83611i
$415$	7.22643	+	22.2407i	0.354732	+	1.09175i
$416$	−6.39155	+	4.64373i	−0.313372	+	0.227678i
$417$	50.5311			2.47452
$418$	57.3115	+	35.7156i	2.80320	+	1.74691i
$419$	−24.1505			−1.17983			−0.589913	−	0.807467i	$-0.700838\pi$
$419$	−24.1505			−1.17983			−0.589913	+	0.807467i	$0.700838\pi$
$420$	−43.4958	+	31.6016i	−2.12238	+	1.54200i
$421$	8.87521	+	27.3151i	0.432551	+	1.33126i	0.895575	+	0.444910i	$0.146765\pi$
$421$	8.87521	+	27.3151i	0.432551	+	1.33126i	−0.463024	+	0.886346i	$0.653235\pi$
$422$	14.4104	−	44.3508i	0.701490	−	2.15896i
$423$	29.9446	+	21.7560i	1.45596	+	1.05781i
$424$	−54.2984	−	39.4501i	−2.63696	−	1.91587i
$425$	−0.356412	+	1.09692i	−0.0172885	+	0.0532086i
$426$	17.4311	+	53.6475i	0.844541	+	2.59923i
$427$	−14.1174	+	10.2569i	−0.683191	+	0.496367i
$428$	−6.47450			−0.312957
$429$	−4.75466	−	2.96303i	−0.229557	−	0.143057i
$430$	8.45299			0.407639
$431$	−12.4491	+	9.04479i	−0.599651	+	0.435672i	−0.845755	−	0.533571i	$-0.820850\pi$
$431$	−12.4491	+	9.04479i	−0.599651	+	0.435672i	0.246104	+	0.969243i	$0.420850\pi$
$432$	36.1434	+	111.238i	1.73895	+	5.35194i
$433$	2.98034	−	9.17255i	0.143226	−	0.440805i	−0.853553	−	0.521007i	$-0.825557\pi$
$433$	2.98034	−	9.17255i	0.143226	−	0.440805i	0.996779	+	0.0802022i	$0.0255566\pi$
$434$	−4.35302	−	3.16266i	−0.208952	−	0.151812i
$435$	0.684903	+	0.497611i	0.0328386	+	0.0238586i
$436$	1.58831	−	4.88831i	0.0760662	−	0.234108i
$437$	−14.5630	−	44.8203i	−0.696643	−	2.14405i
$438$	31.6057	−	22.9629i	1.51018	−	1.09721i
$439$	11.4999			0.548862			0.274431	−	0.961607i	$-0.411510\pi$
$439$	11.4999			0.548862			0.274431	+	0.961607i	$0.411510\pi$
$440$	−12.7427	+	51.3737i	−0.607487	+	2.44914i
$441$	−24.4123			−1.16249
$442$	−1.18894	+	0.863815i	−0.0565521	+	0.0410875i
$443$	−3.31220	−	10.1939i	−0.157368	−	0.484327i	0.841026	−	0.540995i	$-0.181952\pi$
$443$	−3.31220	−	10.1939i	−0.157368	−	0.484327i	−0.998393	+	0.0566679i	$0.981952\pi$
$444$	9.28147	−	28.5654i	0.440479	−	1.35565i
$445$	−20.1325	−	14.6271i	−0.954371	−	0.693391i
$446$	29.3351	+	21.3132i	1.38906	+	1.00921i
$447$	3.26993	−	10.0638i	0.154662	−	0.476002i
$448$	−8.19855	−	25.2325i	−0.387345	−	1.19213i
$449$	26.5719	−	19.3056i	1.25401	−	0.911089i	0.255559	−	0.966793i	$-0.417740\pi$
$449$	26.5719	−	19.3056i	1.25401	−	0.911089i	0.998447	+	0.0557045i	$0.0177405\pi$
$450$	−19.4010			−0.914572
$451$	5.93678	+	14.6429i	0.279552	+	0.689507i
$452$	65.2875			3.07087
$453$	−6.61370	+	4.80513i	−0.310739	+	0.225765i
$454$	−6.95883	−	21.4171i	−0.326594	−	1.00515i
$455$	0.594226	−	1.82884i	0.0278578	−	0.0857374i
$456$	154.062	+	111.933i	7.21461	+	5.24172i
$457$	−22.8203	−	16.5799i	−1.06749	−	0.775576i	−0.0920293	−	0.995756i	$-0.529335\pi$
$457$	−22.8203	−	16.5799i	−1.06749	−	0.775576i	−0.975459	+	0.220181i	$0.929335\pi$
$458$	8.52837	−	26.2476i	0.398505	−	1.22647i
$459$	3.14295	+	9.67300i	0.146700	+	0.451497i
$460$	49.4033	−	35.8936i	2.30344	−	1.67355i
$461$	−32.0603			−1.49320			−0.746598	−	0.665275i	$-0.768314\pi$
$461$	−32.0603			−1.49320			−0.746598	+	0.665275i	$0.768314\pi$
$462$	36.5258	−	30.7243i	1.69933	−	1.42942i
$463$	7.77545			0.361356			0.180678	−	0.983542i	$-0.442171\pi$
$463$	7.77545			0.361356			0.180678	+	0.983542i	$0.442171\pi$
$464$	−1.31476	+	0.955226i	−0.0610360	+	0.0443452i
$465$	2.11415	+	6.50670i	0.0980416	+	0.301741i
$466$	−6.37189	+	19.6107i	−0.295172	+	0.908446i
$467$	15.3909	+	11.1822i	0.712207	+	0.517449i	0.883885	−	0.467705i	$-0.154919\pi$
$467$	15.3909	+	11.1822i	0.712207	+	0.517449i	−0.171678	+	0.985153i	$0.554919\pi$
$468$	−14.3353	−	10.4152i	−0.662652	−	0.481445i
$469$	2.04886	−	6.30575i	0.0946077	−	0.291173i
$470$	9.41796	+	28.9855i	0.434418	+	1.33700i
$471$	35.0609	−	25.4733i	1.61552	−	1.17375i
$472$	−40.9167			−1.88334
$473$	−5.36545	+	0.381727i	−0.246704	+	0.0175518i
$474$	−90.2052			−4.14326
$475$	−7.14924	+	5.19423i	−0.328030	+	0.238327i
$476$	−2.77329	−	8.53532i	−0.127114	−	0.391216i
$477$	16.1337	−	49.6543i	0.738710	−	2.27351i
$478$	33.2860	+	24.1837i	1.52247	+	1.10614i
$479$	−4.48218	−	3.25649i	−0.204796	−	0.148793i	0.480660	−	0.876907i	$-0.340397\pi$
$479$	−4.48218	−	3.25649i	−0.204796	−	0.148793i	−0.685456	+	0.728114i	$0.740397\pi$
$480$	−26.4466	+	81.3942i	−1.20712	+	3.71512i
$481$	0.331968	+	1.02169i	0.0151364	+	0.0465852i
$482$	−6.70300	+	4.87001i	−0.305313	+	0.221823i
$483$	−33.3092			−1.51562
$484$	9.53606	−	54.8594i	0.433457	−	2.49361i
$485$	−0.990836			−0.0449916
$486$	−13.7090	+	9.96014i	−0.621851	+	0.451801i
$487$	2.45779	+	7.56429i	0.111373	+	0.342771i	0.991173	−	0.132573i	$-0.0423238\pi$
$487$	2.45779	+	7.56429i	0.111373	+	0.342771i	−0.879800	+	0.475344i	$0.842324\pi$
$488$	−24.7490	+	76.1697i	−1.12034	+	3.44804i
$489$	−39.9990	−	29.0610i	−1.80882	−	1.31418i
$490$	−16.2622	−	11.8152i	−0.734652	−	0.533756i
$491$	1.19470	−	3.67692i	0.0539162	−	0.165937i	−0.920472	−	0.390807i	$-0.872196\pi$
$491$	1.19470	−	3.67692i	0.0539162	−	0.165937i	0.974389	+	0.224870i	$0.0721958\pi$
$492$	22.7624	+	70.0556i	1.02621	+	3.15835i
$493$	−0.114328	+	0.0830642i	−0.00514908	+	0.00374103i
$494$	−11.2599			−0.506607
$495$	−41.0705	+	2.92198i	−1.84598	+	0.131333i
$496$	−13.1332			−0.589697
$497$	9.96763	−	7.24191i	0.447109	−	0.324844i
$498$	−29.9078	−	92.0467i	−1.34020	−	4.12471i
$499$	−9.11218	+	28.0444i	−0.407917	+	1.25544i	0.510518	+	0.859867i	$0.329454\pi$
$499$	−9.11218	+	28.0444i	−0.407917	+	1.25544i	−0.918435	+	0.395572i	$0.870546\pi$
$500$	−49.4235	−	35.9082i	−2.21028	−	1.60587i
$501$	−54.4647	−	39.5709i	−2.43330	−	1.76790i
$502$	−6.48670	+	19.9640i	−0.289515	+	0.891037i
$503$	8.32807	+	25.6312i	0.371330	+	1.14284i	0.945921	+	0.324397i	$0.105161\pi$
$503$	8.32807	+	25.6312i	0.371330	+	1.14284i	−0.574591	+	0.818441i	$0.694839\pi$
$504$	73.8769	−	53.6747i	3.29074	−	2.39086i
$505$	4.57119			0.203415
$506$	−41.4866	+	34.8972i	−1.84430	+	1.55137i
$507$	−38.7740			−1.72201
$508$	−33.5258	+	24.3579i	−1.48747	+	1.08071i
$509$	12.3981	+	38.1574i	0.549536	+	1.69130i	0.709953	+	0.704249i	$0.248716\pi$
$509$	12.3981	+	38.1574i	0.549536	+	1.69130i	−0.160417	+	0.987049i	$0.551284\pi$
$510$	−4.91952	+	15.1407i	−0.217840	+	0.670442i
$511$	−6.90329	−	5.01553i	−0.305384	−	0.221874i
$512$	18.4972	+	13.4390i	0.817467	+	0.593925i
$513$	−24.0807	+	74.1129i	−1.06319	+	3.27216i
$514$	12.7403	+	39.2105i	0.561949	+	1.72950i
$515$	26.3762	−	19.1634i	1.16227	−	0.844442i
$516$	−25.0764			−1.10393
$517$	−7.28691	−	17.9730i	−0.320478	−	0.790450i
$518$	−9.15232			−0.402130
$519$	23.4940	−	17.0694i	1.03127	−	0.749263i
$520$	−2.72728	−	8.39370i	−0.119599	−	0.368088i
$521$	−4.26622	+	13.1301i	−0.186907	+	0.575240i	−0.999976	−	0.00692723i	$-0.997795\pi$
$521$	−4.26622	+	13.1301i	−0.186907	+	0.575240i	0.813069	+	0.582167i	$0.197795\pi$
$522$	−1.92312	−	1.39723i	−0.0841728	−	0.0611551i
$523$	1.41158	+	1.02557i	0.0617240	+	0.0448451i	0.618219	−	0.786006i	$-0.287854\pi$
$523$	1.41158	+	1.02557i	0.0617240	+	0.0448451i	−0.556495	+	0.830851i	$0.687854\pi$
$524$	17.1741	−	52.8566i	0.750256	−	2.30905i
$525$	1.93010	+	5.94024i	0.0842365	+	0.259253i
$526$	39.6962	−	28.8410i	1.73084	−	1.25753i
$527$	−1.14203			−0.0497477
$528$	28.0467	−	113.073i	1.22058	−	4.92088i
$529$	14.8331			0.644918
$530$	34.7794	−	25.2687i	1.51072	−	1.09760i
$531$	−9.83567	−	30.2711i	−0.426832	−	1.31365i
$532$	21.2485	−	65.3962i	0.921239	−	2.83528i
$533$	−2.13144	−	1.54858i	−0.0923231	−	0.0670766i
$534$	83.3215	+	60.5366i	3.60568	+	2.61968i
$535$	0.775187	−	2.38578i	0.0335142	−	0.103146i
$536$	−9.40353	−	28.9411i	−0.406170	−	1.25006i
$537$	−19.6340	+	14.2650i	−0.847270	+	0.615578i
$538$	−8.43542			−0.363677
$539$	10.8558	+	6.76520i	0.467594	+	0.291398i
$540$	−100.976			−4.34531
$541$	−5.28964	+	3.84315i	−0.227420	+	0.165230i	−0.695660	−	0.718371i	$-0.744888\pi$
$541$	−5.28964	+	3.84315i	−0.227420	+	0.165230i	0.468241	+	0.883601i	$0.344888\pi$
$542$	25.5530	+	78.6442i	1.09760	+	3.37806i
$543$	19.9375	−	61.3614i	0.855602	−	2.63327i
$544$	−11.5576	−	8.39710i	−0.495529	−	0.360023i
$545$	1.61112	+	1.17055i	0.0690129	+	0.0501408i
$546$	−2.45930	+	7.56896i	−0.105248	+	0.323921i
$547$	−1.21135	−	3.72815i	−0.0517935	−	0.159404i	0.921814	−	0.387632i	$-0.126707\pi$
$547$	−1.21135	−	3.72815i	−0.0517935	−	0.159404i	−0.973608	+	0.228228i	$0.926707\pi$
$548$	31.2385	−	22.6961i	1.33444	−	0.969531i
$549$	−62.3013			−2.65895
$550$	8.62738	+	5.37645i	0.367873	+	0.229253i
$551$	−1.08275			−0.0461267
$552$	−123.680	+	89.8587i	−5.26416	+	3.82464i
$553$	6.08843	+	18.7383i	0.258906	+	0.796832i
$554$	−0.259263	+	0.797929i	−0.0110150	+	0.0339008i
$555$	9.41477	+	6.84023i	0.399635	+	0.290352i
$556$	−67.7489	−	49.2225i	−2.87319	−	2.08750i
$557$	−13.1862	+	40.5831i	−0.558719	+	1.71956i	0.127196	+	0.991878i	$0.459402\pi$
$557$	−13.1862	+	40.5831i	−0.558719	+	1.71956i	−0.685915	+	0.727682i	$0.740598\pi$
$558$	−5.93628	−	18.2700i	−0.251303	−	0.773431i
$559$	0.725608	−	0.527185i	0.0306899	−	0.0222976i
$560$	39.9874			1.68978
$561$	2.43888	−	9.83258i	0.102970	−	0.415132i
$562$	69.6573			2.93831
$563$	19.1723	−	13.9295i	0.808014	−	0.587057i	−0.105240	−	0.994447i	$-0.533561\pi$
$563$	19.1723	−	13.9295i	0.808014	−	0.587057i	0.913254	+	0.407390i	$0.133561\pi$
$564$	−27.9390	−	85.9875i	−1.17645	−	3.62073i
$565$	−7.81682	+	24.0577i	−0.328856	+	1.01212i
$566$	39.9883	+	29.0532i	1.68083	+	1.22120i
$567$	17.3224	+	12.5855i	0.727473	+	0.528540i
$568$	17.4741	−	53.7797i	0.733196	−	2.25655i
$569$	−9.17109	−	28.2257i	−0.384472	−	1.18328i	−0.936863	−	0.349698i	$-0.886284\pi$
$569$	−9.17109	−	28.2257i	−0.384472	−	1.18328i	0.552390	−	0.833585i	$-0.313716\pi$
$570$	−98.6802	+	71.6954i	−4.13326	+	3.00299i
$571$	42.3068			1.77048			0.885242	−	0.465131i	$-0.153993\pi$
$571$	42.3068			1.77048			0.885242	+	0.465131i	$0.153993\pi$
$572$	3.48846	+	8.60418i	0.145860	+	0.359759i
$573$	60.2907			2.51868
$574$	18.1590	−	13.1933i	0.757940	−	0.550676i
$575$	−2.19224	−	6.74702i	−0.0914228	−	0.281370i
$576$	29.2709	−	90.0865i	1.21962	−	3.75360i
$577$	8.55417	+	6.21497i	0.356115	+	0.258732i	0.751430	−	0.659813i	$-0.229365\pi$
$577$	8.55417	+	6.21497i	0.356115	+	0.258732i	−0.395315	+	0.918546i	$0.629365\pi$
$578$	−2.14992	−	1.56201i	−0.0894247	−	0.0649709i
$579$	−10.8048	+	33.2538i	−0.449033	+	1.38198i
$580$	−0.433551	−	1.33433i	−0.0180022	−	0.0554051i
$581$	−17.1021	+	12.4254i	−0.709517	+	0.515494i
$582$	4.10074			0.169981
$583$	−20.9348	+	17.6097i	−0.867030	+	0.729318i
$584$	−39.1630			−1.62058
$585$	5.55426	−	4.03540i	0.229640	−	0.166843i
$586$	0.831160	+	2.55805i	0.0343349	+	0.105672i
$587$	−1.58053	+	4.86438i	−0.0652356	+	0.200775i	−0.978361	−	0.206903i	$-0.933661\pi$
$587$	−1.58053	+	4.86438i	−0.0652356	+	0.200775i	0.913126	+	0.407678i	$0.133661\pi$
$588$	48.2430	+	35.0506i	1.98951	+	1.44546i
$589$	−7.07894	−	5.14315i	−0.291683	−	0.211920i
$590$	8.09874	−	24.9254i	0.333420	−	1.02616i
$591$	1.42711	+	4.39219i	0.0587034	+	0.180670i
$592$	−18.0728	+	13.1307i	−0.742788	+	0.539667i
$593$	−16.2886			−0.668891			−0.334446	−	0.942415i	$-0.608549\pi$
$593$	−16.2886			−0.668891			−0.334446	+	0.942415i	$0.608549\pi$
$594$	89.4167	−	6.36159i	3.66881	−	0.261019i
$595$	3.47721			0.142552
$596$	−14.1873	+	10.3077i	−0.581134	+	0.422218i
$597$	1.72730	+	5.31608i	0.0706936	+	0.217573i
$598$	2.79332	−	8.59695i	0.114227	−	0.351555i
$599$	5.42082	+	3.93845i	0.221489	+	0.160921i	0.692996	−	0.720941i	$-0.256290\pi$
$599$	5.42082	+	3.93845i	0.221489	+	0.160921i	−0.471508	+	0.881862i	$0.656290\pi$
$600$	23.1917	+	16.8498i	0.946798	+	0.687889i
$601$	−6.66629	+	20.5167i	−0.271924	+	0.836895i	0.718093	+	0.695947i	$0.245015\pi$
$601$	−6.66629	+	20.5167i	−0.271924	+	0.836895i	−0.990017	+	0.140948i	$0.954985\pi$
$602$	2.36126	+	7.26721i	0.0962378	+	0.296190i
$603$	19.1508	−	13.9139i	0.779881	−	0.566617i
$604$	13.5479			0.551257
$605$	19.0733	+	10.0822i	0.775440	+	0.409900i
$606$	−18.9186			−0.768517
$607$	−27.7574	+	20.1669i	−1.12664	+	0.818551i	−0.985202	−	0.171397i	$-0.945172\pi$
$607$	−27.7574	+	20.1669i	−1.12664	+	0.818551i	−0.141436	+	0.989947i	$0.545172\pi$
$608$	−33.8240	−	104.100i	−1.37175	−	4.22180i
$609$	−0.236486	+	0.727829i	−0.00958290	+	0.0294931i
$610$	−41.5019	−	30.1529i	−1.68036	−	1.22086i
$611$	2.61617	+	1.90076i	0.105839	+	0.0768966i
$612$	9.90136	−	30.4732i	0.400239	−	1.23181i
$613$	−8.34210	−	25.6743i	−0.336934	−	1.03698i	−0.965761	−	0.259432i	$-0.916465\pi$
$613$	−8.34210	−	25.6743i	−0.336934	−	1.03698i	0.628827	−	0.777545i	$-0.283535\pi$
$614$	−35.6546	+	25.9046i	−1.43890	+	1.04542i
$615$	−28.5400			−1.15084
$616$	−47.7266	+	3.39553i	−1.92296	+	0.136810i
$617$	−16.8730			−0.679283			−0.339641	−	0.940555i	$-0.610306\pi$
$617$	−16.8730			−0.679283			−0.339641	+	0.940555i	$0.610306\pi$
$618$	−109.162	+	79.3110i	−4.39115	+	3.19036i
$619$	−10.3048	−	31.7149i	−0.414185	−	1.27473i	−0.912978	−	0.408010i	$-0.866223\pi$
$619$	−10.3048	−	31.7149i	−0.414185	−	1.27473i	0.498792	−	0.866722i	$-0.333777\pi$
$620$	3.50367	−	10.7832i	0.140711	−	0.433063i
$621$	−50.6114	−	36.7714i	−2.03097	−	1.47558i
$622$	−27.9232	−	20.2874i	−1.11962	−	0.813450i
$623$	6.95142	−	21.3943i	0.278503	−	0.857143i
$624$	6.00273	+	18.4745i	0.240301	+	0.739572i
$625$	14.4837	−	10.5230i	0.579349	−	0.420922i
$626$	−46.9888			−1.87805
$627$	59.3986	−	49.9642i	2.37215	−	1.99538i
$628$	−71.8211			−2.86597
$629$	−1.57157	+	1.14181i	−0.0626626	+	0.0455270i
$630$	18.0746	+	55.6278i	0.720108	+	2.21626i
$631$	−12.5635	+	38.6665i	−0.500145	+	1.53929i	0.308637	+	0.951180i	$0.400127\pi$
$631$	−12.5635	+	38.6665i	−0.500145	+	1.53929i	−0.808782	+	0.588109i	$0.799873\pi$
$632$	73.1574	+	53.1519i	2.91004	+	2.11427i
$633$	−43.3636	−	31.5055i	−1.72355	−	1.25223i
$634$	0.583529	−	1.79592i	0.0231749	−	0.0713250i
$635$	−4.96159	−	15.2702i	−0.196895	−	0.605980i
$636$	−103.175	+	74.9613i	−4.09117	+	2.97241i
$637$	−2.13283			−0.0845058
$638$	0.467985	+	1.15427i	0.0185277	+	0.0456981i
$639$	43.9879			1.74013
$640$	17.7638	−	12.9062i	0.702177	−	0.510161i
$641$	14.8515	+	45.7082i	0.586599	+	1.80537i	0.592752	+	0.805385i	$0.298041\pi$
$641$	14.8515	+	45.7082i	0.586599	+	1.80537i	−0.00615322	+	0.999981i	$0.501959\pi$
$642$	−3.20824	+	9.87394i	−0.126619	+	0.389693i
$643$	−32.4217	−	23.5558i	−1.27859	−	0.928949i	−0.279079	−	0.960268i	$-0.590029\pi$
$643$	−32.4217	−	23.5558i	−1.27859	−	0.928949i	−0.999509	+	0.0313195i	$0.990029\pi$
$644$	44.6588	+	32.4465i	1.75980	+	1.27857i
$645$	3.00238	−	9.24036i	0.118218	−	0.363839i
$646$	−6.29185	−	19.3643i	−0.247550	−	0.761880i
$647$	31.8866	−	23.1670i	1.25359	−	0.910787i	0.255166	−	0.966897i	$-0.417870\pi$
$647$	31.8866	−	23.1670i	1.25359	−	0.910787i	0.998425	+	0.0561101i	$0.0178698\pi$
$648$	98.2717			3.86048
$649$	−4.01500	+	16.1869i	−0.157602	+	0.635390i
$650$	−1.69501			−0.0664837
$651$	−5.00338	+	3.63517i	−0.196098	+	0.142473i
$652$	25.3198	+	77.9262i	0.991599	+	3.05183i
$653$	−13.2922	+	40.9092i	−0.520164	+	1.60090i	0.253521	+	0.967330i	$0.418411\pi$
$653$	−13.2922	+	40.9092i	−0.520164	+	1.60090i	−0.773685	+	0.633571i	$0.781589\pi$
$654$	−6.66789	−	4.84450i	−0.260735	−	0.189435i
$655$	17.4208	+	12.6570i	0.680687	+	0.494548i
$656$	16.9298	−	52.1046i	0.660999	−	2.03434i
$657$	−9.41412	−	28.9737i	−0.367280	−	1.13037i
$658$	−22.2886	+	16.1936i	−0.868902	+	0.631294i
$659$	39.1188			1.52385			0.761925	−	0.647665i	$-0.224254\pi$
$659$	39.1188			1.52385			0.761925	+	0.647665i	$0.224254\pi$
$660$	85.3579	+	53.1937i	3.32255	+	2.07056i
$661$	−2.42316			−0.0942502			−0.0471251	−	0.998889i	$-0.515006\pi$
$661$	−2.42316			−0.0942502			−0.0471251	+	0.998889i	$0.515006\pi$
$662$	−23.3640	+	16.9750i	−0.908069	+	0.659750i
$663$	0.521983	+	1.60650i	0.0202722	+	0.0623913i
$664$	−29.9815	+	92.2735i	−1.16351	+	3.58091i
$665$	21.5537	+	15.6597i	0.835816	+	0.607256i
$666$	−26.4355	−	19.2065i	−1.02436	−	0.744238i
$667$	0.268605	−	0.826681i	0.0104004	−	0.0320092i
$668$	34.4767	+	106.108i	1.33394	+	4.10546i
$669$	33.7178	−	24.4974i	1.30361	−	0.947126i
$670$	19.4914			0.753019
$671$	27.7046	+	17.2651i	1.06953	+	0.666512i
$672$	−77.3639			−2.98438
$673$	−16.0654	+	11.6722i	−0.619276	+	0.449931i	−0.852669	−	0.522452i	$-0.825017\pi$
$673$	−16.0654	+	11.6722i	−0.619276	+	0.449931i	0.233392	+	0.972383i	$0.425017\pi$
$674$	−10.9705	−	33.7638i	−0.422568	−	1.30053i
$675$	−3.62499	+	11.1566i	−0.139526	+	0.429417i
$676$	51.9857	+	37.7698i	1.99945	+	1.45269i
$677$	−16.9357	−	12.3045i	−0.650892	−	0.472900i	0.212683	−	0.977121i	$-0.431780\pi$
$677$	−16.9357	−	12.3045i	−0.650892	−	0.472900i	−0.863575	+	0.504221i	$0.831780\pi$
$678$	32.3512	−	99.5668i	1.24244	−	3.82384i
$679$	−0.276781	−	0.851843i	−0.0106219	−	0.0326907i
$680$	12.9112	−	9.38054i	0.495122	−	0.359727i
$681$	−25.8837			−0.991865
$682$	−2.42324	+	9.76952i	−0.0927905	+	0.374094i
$683$	−39.3056			−1.50399			−0.751994	−	0.659170i	$-0.770908\pi$
$683$	−39.3056			−1.50399			−0.751994	+	0.659170i	$0.770908\pi$
$684$	198.611	−	144.299i	7.59407	−	5.51741i
$685$	4.62310	+	14.2284i	0.176640	+	0.543641i
$686$	15.8065	−	48.6475i	0.603496	−	1.85737i
$687$	−25.6634	−	18.6455i	−0.979119	−	0.711372i
$688$	15.0888	+	10.9627i	0.575257	+	0.417948i
$689$	1.40955	−	4.33815i	0.0536996	−	0.165270i
$690$	−30.2593	−	93.1285i	−1.15195	−	3.54534i
$691$	24.6514	−	17.9103i	0.937785	−	0.681341i	−0.0101017	−	0.999949i	$-0.503216\pi$
$691$	24.6514	−	17.9103i	0.937785	−	0.681341i	0.947886	+	0.318608i	$0.103216\pi$
$692$	−48.1266			−1.82950
$693$	−13.9847	−	34.4930i	−0.531237	−	1.31028i
$694$	−25.1268			−0.953801
$695$	26.2495	−	19.0713i	0.995699	−	0.723417i
$696$	1.08538	+	3.34047i	0.0411413	+	0.126620i
$697$	1.47218	−	4.53090i	0.0557627	−	0.171620i
$698$	6.07656	+	4.41488i	0.230001	+	0.167106i
$699$	19.1741	+	13.9308i	0.725233	+	0.526912i
$700$	3.19864	−	9.84441i	0.120897	−	0.372084i
$701$	5.05231	+	15.5494i	0.190823	+	0.587294i	1.00000		0.000271742i	$-8.64980e-5\pi$
$701$	5.05231	+	15.5494i	0.190823	+	0.587294i	−0.809177	+	0.587565i	$0.800086\pi$
$702$	−12.0925	+	8.78568i	−0.456400	+	0.331594i
$703$	−14.8836			−0.561346
$704$	−37.9814	+	31.9487i	−1.43148	+	1.20411i
$705$	35.0306			1.31933
$706$	31.5033	−	22.8885i	1.18564	−	0.861421i
$707$	1.27692	+	3.92995i	0.0480235	+	0.147801i
$708$	−24.0255	+	73.9428i	−0.902933	+	2.77894i
$709$	25.3200	+	18.3960i	0.950911	+	0.690877i	0.951022	−	0.309123i	$-0.100035\pi$
$709$	25.3200	+	18.3960i	0.950911	+	0.690877i	−0.000111143		1.00000i	$0.500035\pi$
$710$	29.3025	+	21.2895i	1.09970	+	0.798981i
$711$	−21.7372	+	66.9003i	−0.815209	+	2.50896i
$712$	−31.9044	−	98.1917i	−1.19567	−	3.67989i
$713$	5.68292	−	4.12888i	0.212827	−	0.154628i
$714$	−14.3910			−0.538570
$715$	−3.58821	+	0.255285i	−0.134192	+	0.00954712i
$716$	40.2196			1.50308
$717$	38.2590	−	27.7968i	1.42881	−	1.03809i
$718$	−1.04986	−	3.23112i	−0.0391803	−	0.120584i
$719$	4.46963	−	13.7561i	0.166689	−	0.513016i	−0.832468	−	0.554073i	$-0.813073\pi$
$719$	4.46963	−	13.7561i	0.166689	−	0.513016i	0.999157	+	0.0410576i	$0.0130727\pi$
$720$	115.499	+	83.9153i	4.30441	+	3.12734i
$721$	23.8432	+	17.3231i	0.887965	+	0.645145i
$722$	32.6044	−	100.346i	1.21341	−	3.73449i
$723$	2.94284	+	9.05712i	0.109445	+	0.336838i
$724$	−86.5033	+	62.8483i	−3.21487	+	2.33574i
$725$	−0.162992			−0.00605336
$726$	−78.9380	−	41.7268i	−2.92966	−	1.54863i
$727$	30.6616			1.13718			0.568589	−	0.822622i	$-0.307490\pi$
$727$	30.6616			1.13718			0.568589	+	0.822622i	$0.307490\pi$
$728$	6.45441	−	4.68940i	0.239216	−	0.173801i
$729$	−5.17732	−	15.9342i	−0.191753	−	0.590154i
$730$	7.75164	−	23.8571i	0.286901	−	0.882990i
$731$	1.31209	+	0.953290i	0.0485294	+	0.0352587i
$732$	123.118	+	89.4507i	4.55059	+	3.30619i
$733$	11.6560	−	35.8733i	0.430523	−	1.32501i	−0.467083	−	0.884213i	$-0.654695\pi$
$733$	11.6560	−	35.8733i	0.430523	−	1.32501i	0.897606	−	0.440799i	$-0.145305\pi$
$734$	16.8471	+	51.8500i	0.621837	+	1.91382i
$735$	−18.6918	+	13.5804i	−0.689459	+	0.500921i
$736$	87.8712			3.23898
$737$	−12.3720	+	0.880210i	−0.455728	+	0.0324230i
$738$	80.1368			2.94988
$739$	7.83895	−	5.69533i	0.288360	−	0.209506i	−0.434195	−	0.900819i	$-0.642967\pi$
$739$	7.83895	−	5.69533i	0.288360	−	0.209506i	0.722556	+	0.691313i	$0.242967\pi$
$740$	−5.95965	−	18.3419i	−0.219081	−	0.674262i
$741$	−3.99935	+	12.3087i	−0.146920	+	0.452172i
$742$	31.4393	+	22.8420i	1.15417	+	0.838556i
$743$	21.7728	+	15.8189i	0.798766	+	0.580338i	0.910552	−	0.413395i	$-0.135657\pi$
$743$	21.7728	+	15.8189i	0.798766	+	0.580338i	−0.111786	+	0.993732i	$0.535657\pi$
$744$	−8.77134	+	26.9954i	−0.321573	+	0.989699i
$745$	−2.09963	−	6.46198i	−0.0769243	−	0.236749i
$746$	−31.1749	+	22.6499i	−1.14139	+	0.829271i
$747$	−75.4731			−2.76141
$748$	−12.8478	+	10.8072i	−0.469763	+	0.395150i
$749$	2.26765			0.0828580
$750$	−79.2522	+	57.5801i	−2.89388	+	2.10253i
$751$	−7.92293	−	24.3843i	−0.289112	−	0.889795i	−0.985136	−	0.171777i	$-0.945049\pi$
$751$	−7.92293	−	24.3843i	−0.289112	−	0.889795i	0.696024	−	0.718019i	$-0.254951\pi$
$752$	−20.7800	+	63.9542i	−0.757768	+	2.33217i
$753$	19.5196	+	14.1818i	0.711334	+	0.516815i
$754$	−0.168018	−	0.122072i	−0.00611884	−	0.00444560i
$755$	−1.62208	+	4.99226i	−0.0590336	+	0.181687i
$756$	−28.2066	−	86.8110i	−1.02586	−	3.15729i
$757$	9.04750	−	6.57339i	0.328837	−	0.238914i	−0.411100	−	0.911590i	$-0.634855\pi$
$757$	9.04750	−	6.57339i	0.328837	−	0.238914i	0.739937	+	0.672676i	$0.234855\pi$
$758$	−81.5153			−2.96077
$759$	23.4124	+	57.7459i	0.849815	+	2.09604i
$760$	122.276			4.43542
$761$	−43.8175	+	31.8353i	−1.58838	+	1.15403i	−0.682184	+	0.731180i	$0.738970\pi$
$761$	−43.8175	+	31.8353i	−1.58838	+	1.15403i	−0.906200	+	0.422849i	$0.861030\pi$
$762$	20.5344	+	63.1983i	0.743882	+	2.28943i
$763$	−0.556294	+	1.71210i	−0.0201392	+	0.0619821i
$764$	−80.8339	−	58.7293i	−2.92447	−	2.12475i
$765$	10.0436	+	7.29708i	0.363126	+	0.263826i
$766$	−21.9601	+	67.5862i	−0.793450	+	2.44199i
$767$	−0.859314	−	2.64470i	−0.0310280	−	0.0954944i
$768$	0.439838	−	0.319561i	0.0158713	−	0.0115312i
$769$	−6.37955			−0.230052			−0.115026	−	0.993362i	$-0.536695\pi$
$769$	−6.37955			−0.230052			−0.115026	+	0.993362i	$0.536695\pi$
$770$	7.37818	−	29.7459i	0.265891	−	1.07197i
$771$	47.3880			1.70664
$772$	46.8791	−	34.0596i	1.68721	−	1.22583i
$773$	−0.190385	−	0.585943i	−0.00684766	−	0.0210749i	0.947574	−	0.319535i	$-0.103527\pi$
$773$	−0.190385	−	0.585943i	−0.00684766	−	0.0210749i	−0.954422	+	0.298461i	$0.903527\pi$
$774$	−8.43030	+	25.9458i	−0.303021	+	0.932602i
$775$	−1.06563	−	0.774224i	−0.0382785	−	0.0278109i
$776$	−3.32574	−	2.41629i	−0.119387	−	0.0867399i
$777$	−3.25077	+	10.0048i	−0.116621	+	0.358921i
$778$	3.99326	+	12.2900i	0.143165	+	0.440617i
$779$	29.5303	−	21.4550i	1.05803	−	0.768706i
$780$	−16.7701			−0.600467
$781$	−19.5609	−	12.1900i	−0.699943	−	0.436194i
$782$	16.3456			0.584516
$783$	−1.16281	+	0.844829i	−0.0415554	+	0.0301917i
$784$	−13.7054	−	42.1810i	−0.489480	−	1.50646i
$785$	8.59908	−	26.4653i	0.306914	−	0.944585i
$786$	−72.0988	−	52.3829i	−2.57168	−	1.86843i
$787$	−26.7186	−	19.4122i	−0.952415	−	0.691970i	−0.00103836	−	0.999999i	$-0.500331\pi$
$787$	−26.7186	−	19.4122i	−0.952415	−	0.691970i	−0.951377	+	0.308029i	$0.900331\pi$
$788$	2.36506	−	7.27892i	0.0842519	−	0.259301i
$789$	−17.4279	−	53.6377i	−0.620451	−	1.90955i
$790$	−46.8590	+	34.0450i	−1.66717	+	1.21127i
$791$	−22.8665			−0.813038
$792$	−144.979	−	90.3486i	−5.15160	−	3.21040i
$793$	−5.44308			−0.193290
$794$	19.3678	−	14.0715i	0.687337	−	0.499380i
$795$	−15.2693	−	46.9941i	−0.541546	−	1.66671i
$796$	2.86255	−	8.81003i	0.101460	−	0.312263i
$797$	27.7773	+	20.1814i	0.983923	+	0.714862i	0.958582	−	0.284817i	$-0.0919328\pi$
$797$	27.7773	+	20.1814i	0.983923	+	0.714862i	0.0253413	+	0.999679i	$0.491933\pi$
$798$	−89.2034	−	64.8101i	−3.15777	−	2.29425i
$799$	−1.80698	+	5.56131i	−0.0639263	+	0.196745i
$800$	−5.09170	−	15.6706i	−0.180019	−	0.554041i
$801$	64.9752	−	47.2072i	2.29579	−	1.66799i
$802$	86.9721			3.07109
$803$	−3.84292	+	15.4931i	−0.135614	+	0.546740i
$804$	−57.8226			−2.03925
$805$	−17.3031	+	12.5715i	−0.609856	+	0.443086i
$806$	−0.518636	−	1.59620i	−0.0182682	−	0.0562236i
$807$	−2.99613	+	9.22115i	−0.105469	+	0.324600i
$808$	15.3432	+	11.1475i	0.539772	+	0.392167i
$809$	−21.7670	−	15.8146i	−0.765286	−	0.556013i	0.135241	−	0.990813i	$-0.456819\pi$
$809$	−21.7670	−	15.8146i	−0.765286	−	0.556013i	−0.900527	+	0.434800i	$0.856819\pi$
$810$	−19.4512	+	59.8645i	−0.683444	+	2.10343i
$811$	1.80708	+	5.56162i	0.0634552	+	0.195295i	0.977758	−	0.209736i	$-0.0672606\pi$
$811$	1.80708	+	5.56162i	0.0634552	+	0.195295i	−0.914303	+	0.405031i	$0.867261\pi$
$812$	1.02605	−	0.745466i	0.0360071	−	0.0261607i
$813$	95.0457			3.33340
$814$	6.43299	+	15.8668i	0.225476	+	0.556130i
$815$	−31.7465			−1.11203
$816$	−28.4175	+	20.6465i	−0.994812	+	0.722773i
$817$	3.83991	+	11.8180i	0.134341	+	0.413460i
$818$	13.8790	−	42.7150i	0.485266	−	1.49350i
$819$	5.02085	+	3.64786i	0.175443	+	0.127467i
$820$	38.2647	+	27.8009i	1.33626	+	0.970850i
$821$	17.4795	−	53.7964i	0.610040	−	1.87751i	0.152544	−	0.988297i	$-0.451253\pi$
$821$	17.4795	−	53.7964i	0.610040	−	1.87751i	0.457495	−	0.889212i	$-0.348747\pi$
$822$	−19.1335	−	58.8867i	−0.667356	−	2.05391i
$823$	−4.38824	+	3.18824i	−0.152964	+	0.111135i	−0.661635	−	0.749826i	$-0.730137\pi$
$823$	−4.38824	+	3.18824i	−0.152964	+	0.111135i	0.508671	+	0.860961i	$0.330137\pi$
$824$	135.264			4.71216
$825$	8.94157	−	7.52137i	0.311306	−	0.261860i
$826$	23.6912			0.824322
$827$	−6.07106	+	4.41088i	−0.211111	+	0.153381i	−0.688316	−	0.725411i	$-0.741650\pi$
$827$	−6.07106	+	4.41088i	−0.211111	+	0.153381i	0.477205	+	0.878792i	$0.341650\pi$
$828$	60.9019	+	187.437i	2.11649	+	6.51388i
$829$	3.15272	−	9.70306i	0.109498	−	0.337001i	−0.881262	−	0.472629i	$-0.843305\pi$
$829$	3.15272	−	9.70306i	0.109498	−	0.337001i	0.990760	+	0.135628i	$0.0433051\pi$
$830$	−50.2763	−	36.5279i	−1.74512	−	1.26790i
$831$	0.780168	+	0.566825i	0.0270637	+	0.0196630i
$832$	2.55731	−	7.87059i	0.0886588	−	0.272864i
$833$	−1.19179	−	3.66796i	−0.0412932	−	0.127087i
$834$	−108.638	+	78.9299i	−3.76181	+	2.73312i
$835$	−43.2276			−1.49595
$836$	−128.308	+	9.12855i	−4.43763	+	0.315717i
$837$	−11.6154			−0.401486
$838$	51.9214	−	37.7231i	1.79360	−	1.30312i
$839$	−13.5380	−	41.6655i	−0.467382	−	1.43845i	−0.855962	−	0.517039i	$-0.827034\pi$
$839$	−13.5380	−	41.6655i	−0.467382	−	1.43845i	0.388580	−	0.921415i	$-0.372966\pi$
$840$	26.7066	−	82.1946i	0.921466	−	2.83598i
$841$	23.4453	+	17.0340i	0.808460	+	0.587380i
$842$	−61.7473	−	44.8620i	−2.12795	−	1.54605i
$843$	24.7412	−	76.1457i	0.852133	−	2.62260i
$844$	27.4496	+	84.4811i	0.944854	+	2.90796i
$845$	−20.1420	+	14.6340i	−0.692905	+	0.503425i
$846$	−98.3614			−3.38174
$847$	−3.33994	+	19.2141i	−0.114762	+	0.660204i
$848$	94.8533			3.25727
$849$	45.9627	−	33.3939i	1.57744	−	1.14607i
$850$	−0.947144	−	2.91501i	−0.0324868	−	0.0999840i
$851$	3.69228	−	11.3637i	0.126570	−	0.389541i
$852$	−86.9279	−	63.1568i	−2.97810	−	2.16372i
$853$	24.0550	+	17.4770i	0.823628	+	0.598401i	0.917749	−	0.397160i	$-0.130004\pi$
$853$	24.0550	+	17.4770i	0.823628	+	0.598401i	−0.0941214	+	0.995561i	$0.530004\pi$
$854$	14.3299	−	44.1030i	0.490361	−	1.50917i
$855$	29.3931	+	90.4626i	1.00522	+	3.09376i
$856$	8.41997	−	6.11747i	0.287789	−	0.209091i
$857$	−2.25119			−0.0768993			−0.0384497	−	0.999261i	$-0.512242\pi$
$857$	−2.25119			−0.0768993			−0.0384497	+	0.999261i	$0.512242\pi$
$858$	14.8504	−	1.05654i	0.506984	−	0.0360696i
$859$	−19.3299			−0.659527			−0.329763	−	0.944064i	$-0.606969\pi$
$859$	−19.3299			−0.659527			−0.329763	+	0.944064i	$0.606969\pi$
$860$	−13.0265	+	9.46427i	−0.444198	+	0.322729i
$861$	−7.97238	−	24.5365i	−0.271698	−	0.836201i
$862$	12.6365	−	38.8911i	0.430400	−	1.32464i
$863$	−31.8531	−	23.1426i	−1.08429	−	0.787784i	−0.105865	−	0.994380i	$-0.533761\pi$
$863$	−31.8531	−	23.1426i	−1.08429	−	0.787784i	−0.978426	+	0.206597i	$0.933761\pi$
$864$	−117.550	−	85.4052i	−3.99914	−	2.90554i
$865$	5.76216	−	17.7341i	0.195919	−	0.602978i
$866$	7.92009	+	24.3755i	0.269136	+	0.828314i
$867$	−2.47112	+	1.79537i	−0.0839236	+	0.0609741i
$868$	10.2492			0.347882
$869$	28.2059	−	23.7259i	0.956818	−	0.804845i
$870$	−2.24976			−0.0762739
$871$	1.67315	−	1.21562i	0.0566925	−	0.0411895i
$872$	2.55318	+	7.85789i	0.0864617	+	0.266102i
$873$	0.988177	−	3.04129i	0.0334447	−	0.102932i
$874$	101.319	+	73.6124i	3.42716	+	2.48998i
$875$	17.3102	+	12.5766i	0.585192	+	0.425167i
$876$	−22.9958	+	70.7737i	−0.776955	+	2.39122i
$877$	−7.36027	−	22.6526i	−0.248539	−	0.764924i	−0.995034	−	0.0995332i	$-0.968265\pi$
$877$	−7.36027	−	22.6526i	−0.248539	−	0.764924i	0.746495	−	0.665391i	$-0.231735\pi$
$878$	−24.7239	+	17.9630i	−0.834392	+	0.606221i
$879$	3.09154			0.104275
$880$	−28.1064	−	69.3236i	−0.947466	−	2.33690i
$881$	11.2330			0.378451			0.189225	−	0.981934i	$-0.439402\pi$
$881$	11.2330			0.378451			0.189225	+	0.981934i	$0.439402\pi$
$882$	52.4844	−	38.1321i	1.76724	−	1.28398i
$883$	16.4106	+	50.5067i	0.552261	+	1.69968i	0.703069	+	0.711121i	$0.251812\pi$
$883$	16.4106	+	50.5067i	0.552261	+	1.69968i	−0.150808	+	0.988563i	$0.548188\pi$
$884$	0.865053	−	2.66236i	0.0290949	−	0.0895448i
$885$	−24.3705	−	17.7062i	−0.819207	−	0.595189i
$886$	23.0439	+	16.7424i	0.774175	+	0.562471i
$887$	1.72097	−	5.29660i	0.0577845	−	0.177842i	−0.917998	−	0.396585i	$-0.870195\pi$
$887$	1.72097	−	5.29660i	0.0577845	−	0.177842i	0.975783	+	0.218742i	$0.0701954\pi$
$888$	14.9198	+	45.9185i	0.500676	+	1.54092i
$889$	11.7422	−	8.53118i	0.393819	−	0.286127i
$890$	66.1308			2.21671
$891$	9.64302	−	38.8768i	0.323053	−	1.30242i
$892$	−69.0698			−2.31263
$893$	−36.2461	+	26.3343i	−1.21293	+	0.881244i
$894$	8.68964	+	26.7440i	0.290625	+	0.894452i
$895$	−4.81546	+	14.8205i	−0.160963	+	0.495393i
$896$	16.0579	+	11.6667i	0.536456	+	0.389758i
$897$	−8.40559	−	6.10702i	−0.280654	−	0.203907i
$898$	−26.9719	+	83.0110i	−0.900064	+	2.77011i
$899$	−0.0498719	−	0.153490i	−0.00166332	−	0.00511917i
$900$	29.8978	−	21.7221i	0.996595	−	0.724069i
$901$	8.24822			0.274788
$902$	−35.6359	−	22.2077i	−1.18654	−	0.739436i
$903$	8.78282			0.292274
$904$	−84.9053	+	61.6873i	−2.82391	+	2.05169i
$905$	−12.8019	−	39.4003i	−0.425550	−	1.30971i
$906$	6.71325	−	20.6613i	0.223033	−	0.686425i
$907$	−0.184632	−	0.134143i	−0.00613061	−	0.00445415i	0.584716	−	0.811238i	$-0.301206\pi$
$907$	−0.184632	−	0.134143i	−0.00613061	−	0.00445415i	−0.590846	+	0.806784i	$0.701206\pi$
$908$	34.7032	+	25.2134i	1.15167	+	0.836735i
$909$	−4.55892	+	14.0309i	−0.151210	+	0.465376i
$910$	1.57912	+	4.86004i	0.0523474	+	0.161109i
$911$	23.3499	−	16.9647i	0.773616	−	0.562065i	−0.129440	−	0.991587i	$-0.541318\pi$
$911$	23.3499	−	16.9647i	0.773616	−	0.562065i	0.903056	+	0.429522i	$0.141318\pi$
$912$	−269.129			−8.91175
$913$	33.5619	+	20.9153i	1.11074	+	0.692195i
$914$	74.9596			2.47944
$915$	−47.7025	+	34.6579i	−1.57699	+	1.14575i
$916$	16.2452	+	49.9975i	0.536756	+	1.65196i
$917$	−6.01512	+	18.5126i	−0.198637	+	0.611341i
$918$	−21.8664	−	15.8868i	−0.721697	−	0.524344i
$919$	−40.5966	−	29.4951i	−1.33916	−	0.972955i	−0.999475	−	0.0324146i	$-0.989680\pi$
$919$	−40.5966	−	29.4951i	−1.33916	−	0.972955i	−0.339683	−	0.940540i	$-0.610320\pi$
$920$	−30.3338	+	93.3580i	−1.00008	+	3.07792i
$921$	15.6536	+	48.1767i	0.515802	+	1.58748i
$922$	68.9269	−	50.0783i	2.26999	−	1.64924i
$923$	3.84309			0.126497
$924$	−21.8879	+	88.2432i	−0.720058	+	2.90299i
$925$	−2.24050			−0.0736673
$926$	−16.7166	+	12.1453i	−0.549341	+	0.399119i
$927$	32.5153	+	100.072i	1.06794	+	3.28679i
$928$	0.623862	−	1.92005i	0.0204793	−	0.0630287i
$929$	−41.1090	−	29.8674i	−1.34874	−	0.979919i	−0.999073	−	0.0430454i	$-0.986294\pi$
$929$	−41.1090	−	29.8674i	−1.34874	−	0.979919i	−0.349669	−	0.936873i	$-0.613706\pi$
$930$	−14.7088	−	10.6865i	−0.482319	−	0.350425i
$931$	9.13131	−	28.1033i	0.299267	−	0.921048i
$932$	−12.1374	−	37.3552i	−0.397575	−	1.22361i
$933$	−32.0950	+	23.3184i	−1.05074	+	0.763410i
$934$	−50.5558			−1.65424
$935$	−2.44407	−	6.02822i	−0.0799295	−	0.197144i
$936$	28.4838			0.931021
$937$	1.16057	−	0.843202i	0.0379141	−	0.0275462i	−0.568667	−	0.822568i	$-0.692541\pi$
$937$	1.16057	−	0.843202i	0.0379141	−	0.0275462i	0.606581	+	0.795022i	$0.292541\pi$
$938$	5.44474	+	16.7572i	0.177777	+	0.547141i
$939$	−16.6897	+	51.3657i	−0.544649	+	1.67626i
$940$	−46.9668	−	34.1233i	−1.53189	−	1.11298i
$941$	23.8381	+	17.3194i	0.777101	+	0.564597i	0.904108	−	0.427305i	$-0.140537\pi$
$941$	23.8381	+	17.3194i	0.777101	+	0.564597i	−0.127007	+	0.991902i	$0.540537\pi$
$942$	−35.5887	+	109.531i	−1.15954	+	3.56871i
$943$	9.05517	+	27.8689i	0.294877	+	0.907537i
$944$	46.7822	−	33.9893i	1.52263	−	1.10626i
$945$	35.3660			1.15046
$946$	10.9390	−	9.20155i	0.355658	−	0.299168i
$947$	20.4456			0.664392			0.332196	−	0.943210i	$-0.392210\pi$
$947$	20.4456			0.664392			0.332196	+	0.943210i	$0.392210\pi$
$948$	139.010	−	100.997i	4.51485	−	3.28023i
$949$	−0.822484	−	2.53135i	−0.0266990	−	0.0821710i
$950$	7.25685	−	22.3343i	0.235443	−	0.724620i
$951$	−1.75594	−	1.27577i	−0.0569403	−	0.0413696i
$952$	11.6713	+	8.47967i	0.378268	+	0.274828i
$953$	8.72407	−	26.8499i	0.282600	−	0.869754i	−0.704507	−	0.709697i	$-0.748832\pi$
$953$	8.72407	−	26.8499i	0.282600	−	0.869754i	0.987108	−	0.160058i	$-0.0511680\pi$
$954$	42.8743	+	131.953i	1.38811	+	4.27215i
$955$	31.3193	−	22.7548i	1.01347	−	0.736327i
$956$	−78.3723			−2.53474
$957$	1.42801	−	0.101597i	0.0461611	−	0.00328415i
$958$	14.7230			0.475677
$959$	−10.9411	+	7.94916i	−0.353306	+	0.256692i
$960$	−27.7027	−	85.2601i	−0.894100	−	2.75176i
$961$	−9.17650	+	28.2424i	−0.296016	+	0.911044i
$962$	−2.30959	−	1.67802i	−0.0744643	−	0.0541015i
$963$	6.54986	+	4.75875i	0.211066	+	0.153349i
$964$	4.87699	−	15.0098i	0.157077	−	0.483435i
$965$	6.93780	+	21.3523i	0.223336	+	0.687356i
$966$	71.6119	−	52.0291i	2.30408	−	1.67401i
$967$	−0.0798391			−0.00256745			−0.00128373	−	0.999999i	$-0.500409\pi$
$967$	−0.0798391			−0.00256745			−0.00128373	+	0.999999i	$0.500409\pi$
$968$	39.4327	+	80.3538i	1.26742	+	2.58267i
$969$	−23.4028			−0.751808
$970$	2.13022	−	1.54769i	0.0683971	−	0.0496934i
$971$	−9.03855	−	27.8178i	−0.290061	−	0.892715i	−0.984836	−	0.173488i	$-0.944496\pi$
$971$	−9.03855	−	27.8178i	−0.290061	−	0.892715i	0.694775	−	0.719227i	$-0.255504\pi$
$972$	9.97441	−	30.6981i	0.319929	−	0.984642i
$973$	23.7286	+	17.2398i	0.760703	+	0.552683i
$974$	−17.0995	−	12.4235i	−0.547903	−	0.398075i
$975$	−0.602042	+	1.85289i	−0.0192808	+	0.0593401i
$976$	−34.9769	−	107.648i	−1.11958	−	3.44572i
$977$	−38.9011	+	28.2633i	−1.24456	+	0.904222i	−0.997893	−	0.0648790i	$-0.979334\pi$
$977$	−38.9011	+	28.2633i	−1.24456	+	0.904222i	−0.246662	+	0.969101i	$0.579334\pi$
$978$	131.388			4.20132
$979$	−41.9759	+	2.98639i	−1.34155	+	0.0954455i
$980$	38.2896			1.22312
$981$	−5.19970	+	3.77780i	−0.166014	+	0.120616i
$982$	3.17486	+	9.77121i	0.101314	+	0.311812i
$983$	8.77821	−	27.0166i	0.279982	−	0.861694i	−0.707877	−	0.706336i	$-0.750347\pi$
$983$	8.77821	−	27.0166i	0.279982	−	0.861694i	0.987858	−	0.155358i	$-0.0496532\pi$
$984$	−95.7946	−	69.5988i	−3.05382	−	2.21873i
$985$	2.39903	+	1.74300i	0.0764395	+	0.0555366i
$986$	0.116049	−	0.357162i	0.00369575	−	0.0113744i
$987$	9.78545	+	30.1165i	0.311474	+	0.958619i
$988$	17.3520	−	12.6070i	0.552042	−	0.401082i
$989$	−9.97568			−0.317208
$990$	83.7340	−	70.4344i	2.66124	−	2.23855i
$991$	−39.0075			−1.23911			−0.619557	−	0.784951i	$-0.712688\pi$
$991$	−39.0075			−1.23911			−0.619557	+	0.784951i	$0.712688\pi$
$992$	13.1992	−	9.58975i	0.419074	−	0.304475i
$993$	10.2576	+	31.5696i	0.325514	+	1.00183i
$994$	−10.1177	+	31.1390i	−0.320913	+	0.987669i
$995$	2.90367	+	2.10964i	0.0920524	+	0.0668800i
$996$	149.148	+	108.362i	4.72594	+	3.43359i
$997$	5.06312	−	15.5827i	0.160351	−	0.493508i	−0.838313	−	0.545189i	$-0.816458\pi$
$997$	5.06312	−	15.5827i	0.160351	−	0.493508i	0.998664	+	0.0516808i	$0.0164578\pi$
$998$	−24.2151	−	74.5264i	−0.766515	−	2.35909i
$999$	−15.9841	+	11.6131i	−0.505715	+	0.367423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.f.69.1	✓	36
11.2	odd	10		2057.2.a.be.1.1		18
11.4	even	5	inner	187.2.g.f.103.1	yes	36
11.9	even	5		2057.2.a.bd.1.18		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.f.69.1	✓	36	1.1	even	1	trivial
187.2.g.f.103.1	yes	36	11.4	even	5	inner
2057.2.a.bd.1.18		18	11.9	even	5
2057.2.a.be.1.1		18	11.2	odd	10

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.14992 + 1.56201i) q^{2} +(0.943884 + 2.90498i) q^{3} +(1.56424 - 4.81425i) q^{4} +(1.58671 + 1.15281i) q^{5} +(-6.56686 - 4.77110i) q^{6} +(-0.547865 + 1.68616i) q^{7} +(2.51450 + 7.73883i) q^{8} +(-5.12092 + 3.72057i) q^{9} +O(q^{10})\)	\(q+(-2.14992 + 1.56201i) q^{2} +(0.943884 + 2.90498i) q^{3} +(1.56424 - 4.81425i) q^{4} +(1.58671 + 1.15281i) q^{5} +(-6.56686 - 4.77110i) q^{6} +(-0.547865 + 1.68616i) q^{7} +(2.51450 + 7.73883i) q^{8} +(-5.12092 + 3.72057i) q^{9} -5.21199 q^{10} +(3.30826 - 0.235368i) q^{11} +15.4617 q^{12} +(-0.447400 + 0.325055i) q^{13} +(-1.45592 - 4.48086i) q^{14} +(-1.85122 + 5.69748i) q^{15} +(-9.30357 - 6.75944i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(5.19800 - 15.9978i) q^{18} +(-2.36763 - 7.28683i) q^{19} +(8.03193 - 5.83554i) q^{20} -5.41536 q^{21} +(-6.74484 + 5.67355i) q^{22} +6.15086 q^{23} +(-20.1077 + 14.6091i) q^{24} +(-0.356412 - 1.09692i) q^{25} +(0.454134 - 1.39768i) q^{26} +(-8.22835 - 5.97824i) q^{27} +(7.26058 + 5.27512i) q^{28} +(0.0436695 - 0.134401i) q^{29} +(-4.91952 - 15.1407i) q^{30} +(0.923923 - 0.671269i) q^{31} +14.2860 q^{32} +(3.80635 + 9.38826i) q^{33} +2.65744 q^{34} +(-2.81313 + 2.04386i) q^{35} +(9.90136 + 30.4732i) q^{36} +(0.600286 - 1.84749i) q^{37} +(16.4723 + 11.9678i) q^{38} +(-1.36657 - 0.992871i) q^{39} +(-4.93164 + 15.1780i) q^{40} +(1.47218 + 4.53090i) q^{41} +(11.6426 - 8.45883i) q^{42} -1.62183 q^{43} +(4.04181 - 16.2950i) q^{44} -12.4145 q^{45} +(-13.2238 + 9.60768i) q^{46} +(-1.80698 - 5.56131i) q^{47} +(10.8545 - 33.4068i) q^{48} +(3.12015 + 2.26692i) q^{49} +(2.47966 + 1.80158i) q^{50} +(0.943884 - 2.90498i) q^{51} +(0.865053 + 2.66236i) q^{52} +(-6.67295 + 4.84818i) q^{53} +27.0283 q^{54} +(5.52059 + 3.44035i) q^{55} -14.4265 q^{56} +(18.9333 - 13.7558i) q^{57} +(0.116049 + 0.357162i) q^{58} +(-1.55387 + 4.78231i) q^{59} +(24.5333 + 17.8245i) q^{60} +(7.96278 + 5.78529i) q^{61} +(-0.937830 + 2.88635i) q^{62} +(-3.46788 - 10.6730i) q^{63} +(-12.1066 + 8.79593i) q^{64} -1.08462 q^{65} +(-22.8479 - 14.2384i) q^{66} -3.73972 q^{67} +(-4.09524 + 2.97537i) q^{68} +(5.80570 + 17.8681i) q^{69} +(2.85547 - 8.78823i) q^{70} +(-5.62213 - 4.08471i) q^{71} +(-41.6694 - 30.2746i) q^{72} +(-1.48727 + 4.57734i) q^{73} +(1.59523 + 4.90960i) q^{74} +(2.85012 - 2.07074i) q^{75} -38.7842 q^{76} +(-1.41562 + 5.70720i) q^{77} +4.48888 q^{78} +(8.99061 - 6.53206i) q^{79} +(-6.96971 - 21.4505i) q^{80} +(3.73200 - 11.4859i) q^{81} +(-10.2423 - 7.44150i) q^{82} +(9.64627 + 7.00842i) q^{83} +(-8.47095 + 26.0709i) q^{84} +(-0.606069 - 1.86529i) q^{85} +(3.48681 - 2.53331i) q^{86} +0.431650 q^{87} +(10.1401 + 25.0103i) q^{88} -12.6882 q^{89} +(26.6902 - 19.3916i) q^{90} +(-0.302979 - 0.932472i) q^{91} +(9.62145 - 29.6118i) q^{92} +(2.82210 + 2.05037i) q^{93} +(12.5716 + 9.13384i) q^{94} +(4.64360 - 14.2915i) q^{95} +(13.4843 + 41.5005i) q^{96} +(-0.408714 + 0.296948i) q^{97} -10.2490 q^{98} +(-16.0656 + 13.5139i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

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