LMFDB - Embedded newform 220.2.l.c.23.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(23,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	220.l (of order $4$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [28,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.14
Character	$\chi$	$=$	220.23
Dual form			220.2.l.c.67.14

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36901 + 0.354689i) q^{2} +(1.16576 - 1.16576i) q^{3} +(1.74839 + 0.971149i) q^{4} +(-1.42385 - 1.72413i) q^{5} +(2.00942 - 1.18246i) q^{6} +(-1.60129 - 1.60129i) q^{7} +(2.04911 + 1.94965i) q^{8} +0.282018i q^{9} +(-1.33774 - 2.86539i) q^{10} -1.00000i q^{11} +(3.17032 - 0.906076i) q^{12} +(3.94893 + 3.94893i) q^{13} +(-1.62423 - 2.76015i) q^{14} +(-3.66979 - 0.350055i) q^{15} +(2.11374 + 3.39589i) q^{16} +(-4.86073 + 4.86073i) q^{17} +(-0.100029 + 0.386086i) q^{18} -5.54848 q^{19} +(-0.815061 - 4.39723i) q^{20} -3.73344 q^{21} +(0.354689 - 1.36901i) q^{22} +(3.01393 - 3.01393i) q^{23} +(4.66159 - 0.115949i) q^{24} +(-0.945282 + 4.90983i) q^{25} +(4.00550 + 6.80679i) q^{26} +(3.82604 + 3.82604i) q^{27} +(-1.24459 - 4.35478i) q^{28} -6.65635i q^{29} +(-4.89983 - 1.78087i) q^{30} -0.619140i q^{31} +(1.68925 + 5.39874i) q^{32} +(-1.16576 - 1.16576i) q^{33} +(-8.37845 + 4.93035i) q^{34} +(-0.480838 + 5.04085i) q^{35} +(-0.273881 + 0.493077i) q^{36} +(0.294372 - 0.294372i) q^{37} +(-7.59594 - 1.96799i) q^{38} +9.20700 q^{39} +(0.443824 - 6.30896i) q^{40} -2.27347 q^{41} +(-5.11112 - 1.32421i) q^{42} +(2.52940 - 2.52940i) q^{43} +(0.971149 - 1.74839i) q^{44} +(0.486236 - 0.401552i) q^{45} +(5.19511 - 3.05710i) q^{46} +(-8.42819 - 8.42819i) q^{47} +(6.42290 + 1.49468i) q^{48} -1.87173i q^{49} +(-3.03557 + 6.38634i) q^{50} +11.3329i q^{51} +(3.06928 + 10.7393i) q^{52} +(2.22463 + 2.22463i) q^{53} +(3.88084 + 6.59495i) q^{54} +(-1.72413 + 1.42385i) q^{55} +(-0.159268 - 6.40319i) q^{56} +(-6.46819 + 6.46819i) q^{57} +(2.36094 - 9.11263i) q^{58} +1.02645 q^{59} +(-6.07627 - 4.17595i) q^{60} -4.52183 q^{61} +(0.219603 - 0.847611i) q^{62} +(0.451592 - 0.451592i) q^{63} +(0.397727 + 7.99011i) q^{64} +(1.18579 - 12.4312i) q^{65} +(-1.18246 - 2.00942i) q^{66} +(3.45235 + 3.45235i) q^{67} +(-13.2189 + 3.77796i) q^{68} -7.02702i q^{69} +(-2.44621 + 6.73043i) q^{70} -11.6187i q^{71} +(-0.549836 + 0.577886i) q^{72} +(3.57548 + 3.57548i) q^{73} +(0.507410 - 0.298589i) q^{74} +(4.62170 + 6.82564i) q^{75} +(-9.70092 - 5.38840i) q^{76} +(-1.60129 + 1.60129i) q^{77} +(12.6045 + 3.26563i) q^{78} -2.91466 q^{79} +(2.84532 - 8.47963i) q^{80} +8.07441 q^{81} +(-3.11241 - 0.806375i) q^{82} +(-9.90199 + 9.90199i) q^{83} +(-6.52750 - 3.62572i) q^{84} +(15.3015 + 1.45959i) q^{85} +(4.35994 - 2.56563i) q^{86} +(-7.75970 - 7.75970i) q^{87} +(1.94965 - 2.04911i) q^{88} -10.6976i q^{89} +(0.808090 - 0.377266i) q^{90} -12.6468i q^{91} +(8.19649 - 2.34255i) q^{92} +(-0.721768 - 0.721768i) q^{93} +(-8.54891 - 14.5277i) q^{94} +(7.90023 + 9.56633i) q^{95} +(8.26288 + 4.32437i) q^{96} +(-0.328465 + 0.328465i) q^{97} +(0.663883 - 2.56242i) q^{98} +0.282018 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{7} - 14 q^{8} + 6 q^{10} - 8 q^{12} + 6 q^{13} - 20 q^{14} + 8 q^{15} + 8 q^{16} - 14 q^{17} + 34 q^{18} + 4 q^{19} + 8 q^{20} - 16 q^{21}+ \cdots - 20 q^{99}+O(q^{100})$ 28 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 12 * q^6 - 2 * q^7 - 14 * q^8 + 6 * q^10 - 8 * q^12 + 6 * q^13 - 20 * q^14 + 8 * q^15 + 8 * q^16 - 14 * q^17 + 34 * q^18 + 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 - 8 * q^23 + 28 * q^24 - 4 * q^25 + 4 * q^26 + 44 * q^27 - 28 * q^28 - 2 * q^32 + 4 * q^33 - 52 * q^34 - 10 * q^35 - 4 * q^36 + 20 * q^37 + 16 * q^38 + 32 * q^39 - 6 * q^40 + 12 * q^41 - 32 * q^42 + 2 * q^43 - 10 * q^45 + 4 * q^46 - 44 * q^47 - 36 * q^48 + 22 * q^50 + 24 * q^52 - 28 * q^53 - 40 * q^54 - 2 * q^55 + 4 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^59 - 48 * q^60 - 12 * q^61 - 24 * q^62 - 10 * q^63 + 28 * q^64 - 30 * q^65 + 16 * q^67 - 32 * q^68 + 72 * q^70 + 18 * q^72 + 22 * q^73 - 20 * q^74 - 56 * q^75 + 4 * q^76 - 2 * q^77 + 104 * q^78 - 20 * q^79 - 44 * q^80 + 12 * q^81 - 92 * q^82 + 2 * q^83 + 120 * q^84 - 14 * q^85 - 20 * q^86 - 48 * q^87 + 2 * q^88 + 70 * q^90 + 52 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^95 + 40 * q^96 + 16 * q^97 + 18 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$ .

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.36901	+	0.354689i	0.968038	+	0.250803i
$2$	1.36901	+	0.354689i	0.968038	+	0.250803i
$3$	1.16576	−	1.16576i	0.673051	−	0.673051i	−0.285368	−	0.958418i	$-0.592116\pi$
$3$	1.16576	−	1.16576i	0.673051	−	0.673051i	0.958418	+	0.285368i	$0.0921157\pi$
$4$	1.74839	+	0.971149i	0.874195	+	0.485574i
$5$	−1.42385	−	1.72413i	−0.636767	−	0.771057i
$5$	−1.42385	−	1.72413i	−0.636767	−	0.771057i
$6$	2.00942	−	1.18246i	0.820342	−	0.482735i
$7$	−1.60129	−	1.60129i	−0.605231	−	0.605231i	0.336465	−	0.941696i	$-0.390769\pi$
$7$	−1.60129	−	1.60129i	−0.605231	−	0.605231i	−0.941696	+	0.336465i	$0.890769\pi$
$8$	2.04911	+	1.94965i	0.724471	+	0.689306i
$9$			0.282018i			0.0940058i
$10$	−1.33774	−	2.86539i	−0.423031	−	0.906115i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	3.17032	−	0.906076i	0.915194	−	0.261562i
$13$	3.94893	+	3.94893i	1.09524	+	1.09524i	0.994959	+	0.100278i	$0.0319732\pi$
$13$	3.94893	+	3.94893i	1.09524	+	1.09524i	0.100278	+	0.994959i	$0.468027\pi$
$14$	−1.62423	−	2.76015i	−0.434093	−	0.737681i
$15$	−3.66979	−	0.350055i	−0.947536	−	0.0903839i
$16$	2.11374	+	3.39589i	0.528435	+	0.848974i
$17$	−4.86073	+	4.86073i	−1.17890	+	1.17890i	−0.198875	+	0.980025i	$0.563729\pi$
$17$	−4.86073	+	4.86073i	−1.17890	+	1.17890i	−0.980025	+	0.198875i	$0.936271\pi$
$18$	−0.100029	+	0.386086i	−0.0235770	+	0.0910012i
$19$	−5.54848			−1.27291			−0.636455	−	0.771314i	$-0.719600\pi$
$19$	−5.54848			−1.27291			−0.636455	+	0.771314i	$0.719600\pi$
$20$	−0.815061	−	4.39723i	−0.182253	−	0.983252i
$21$	−3.73344			−0.814703
$22$	0.354689	−	1.36901i	0.0756200	−	0.291874i
$23$	3.01393	−	3.01393i	0.628447	−	0.628447i	−0.319230	−	0.947677i	$-0.603424\pi$
$23$	3.01393	−	3.01393i	0.628447	−	0.628447i	0.947677	+	0.319230i	$0.103424\pi$
$24$	4.66159	−	0.115949i	0.951543	−	0.0236680i
$25$	−0.945282	+	4.90983i	−0.189056	+	0.981966i
$26$	4.00550	+	6.80679i	0.785542	+	1.33492i
$27$	3.82604	+	3.82604i	0.736321	+	0.736321i
$28$	−1.24459	−	4.35478i	−0.235206	−	0.822975i
$29$		−	6.65635i		−	1.23605i	−0.786157	−	0.618027i	$-0.787932\pi$
$29$		−	6.65635i		−	1.23605i	0.786157	−	0.618027i	$-0.212068\pi$
$30$	−4.89983	−	1.78087i	−0.894583	−	0.325140i
$31$		−	0.619140i		−	0.111201i	−0.998453	−	0.0556004i	$-0.982293\pi$
$31$		−	0.619140i		−	0.111201i	0.998453	−	0.0556004i	$-0.0177073\pi$
$32$	1.68925	+	5.39874i	0.298620	+	0.954372i
$33$	−1.16576	−	1.16576i	−0.202932	−	0.202932i
$34$	−8.37845	+	4.93035i	−1.43689	+	0.845548i
$35$	−0.480838	+	5.04085i	−0.0812765	+	0.852059i
$36$	−0.273881	+	0.493077i	−0.0456468	+	0.0821795i
$37$	0.294372	−	0.294372i	0.0483945	−	0.0483945i	−0.682495	−	0.730890i	$-0.739105\pi$
$37$	0.294372	−	0.294372i	0.0483945	−	0.0483945i	0.730890	+	0.682495i	$0.239105\pi$
$38$	−7.59594	−	1.96799i	−1.23222	−	0.319250i
$39$	9.20700			1.47430
$40$	0.443824	−	6.30896i	0.0701747	−	0.997535i
$41$	−2.27347			−0.355056			−0.177528	−	0.984116i	$-0.556810\pi$
$41$	−2.27347			−0.355056			−0.177528	+	0.984116i	$0.556810\pi$
$42$	−5.11112	−	1.32421i	−0.788663	−	0.204330i
$43$	2.52940	−	2.52940i	0.385730	−	0.385730i	−0.487431	−	0.873161i	$-0.662066\pi$
$43$	2.52940	−	2.52940i	0.385730	−	0.385730i	0.873161	+	0.487431i	$0.162066\pi$
$44$	0.971149	−	1.74839i	0.146406	−	0.263580i
$45$	0.486236	−	0.401552i	0.0724838	−	0.0598598i
$46$	5.19511	−	3.05710i	0.765977	−	0.450744i
$47$	−8.42819	−	8.42819i	−1.22938	−	1.22938i	−0.964199	−	0.265179i	$-0.914569\pi$
$47$	−8.42819	−	8.42819i	−1.22938	−	1.22938i	−0.265179	−	0.964199i	$-0.585431\pi$
$48$	6.42290	+	1.49468i	0.927066	+	0.215739i
$49$		−	1.87173i		−	0.267390i
$50$	−3.03557	+	6.38634i	−0.429294	+	0.903165i
$51$			11.3329i			1.58692i
$52$	3.06928	+	10.7393i	0.425632	+	1.48927i
$53$	2.22463	+	2.22463i	0.305577	+	0.305577i	0.843191	−	0.537614i	$-0.180674\pi$
$53$	2.22463	+	2.22463i	0.305577	+	0.305577i	−0.537614	+	0.843191i	$0.680674\pi$
$54$	3.88084	+	6.59495i	0.528115	+	0.897459i
$55$	−1.72413	+	1.42385i	−0.232482	+	0.191992i
$56$	−0.159268	−	6.40319i	−0.0212831	−	0.855662i
$57$	−6.46819	+	6.46819i	−0.856732	+	0.856732i
$58$	2.36094	−	9.11263i	0.310006	−	1.19655i
$59$	1.02645			0.133632			0.0668162	−	0.997765i	$-0.478716\pi$
$59$	1.02645			0.133632			0.0668162	+	0.997765i	$0.478716\pi$
$60$	−6.07627	−	4.17595i	−0.784444	−	0.539112i
$61$	−4.52183			−0.578962			−0.289481	−	0.957184i	$-0.593483\pi$
$61$	−4.52183			−0.578962			−0.289481	+	0.957184i	$0.593483\pi$
$62$	0.219603	−	0.847611i	0.0278895	−	0.107647i
$63$	0.451592	−	0.451592i	0.0568953	−	0.0568953i
$64$	0.397727	+	7.99011i	0.0497158	+	0.998763i
$65$	1.18579	−	12.4312i	0.147079	−	1.54190i
$66$	−1.18246	−	2.00942i	−0.145550	−	0.247342i
$67$	3.45235	+	3.45235i	0.421772	+	0.421772i	0.885814	−	0.464041i	$-0.153601\pi$
$67$	3.45235	+	3.45235i	0.421772	+	0.421772i	−0.464041	+	0.885814i	$0.653601\pi$
$68$	−13.2189	+	3.77796i	−1.60303	+	0.458145i
$69$		−	7.02702i		−	0.845953i
$70$	−2.44621	+	6.73043i	−0.292378	+	0.804441i
$71$		−	11.6187i		−	1.37889i	−0.724339	−	0.689444i	$-0.757855\pi$
$71$		−	11.6187i		−	1.37889i	0.724339	−	0.689444i	$-0.242145\pi$
$72$	−0.549836	+	0.577886i	−0.0647987	+	0.0681045i
$73$	3.57548	+	3.57548i	0.418478	+	0.418478i	0.884679	−	0.466201i	$-0.154377\pi$
$73$	3.57548	+	3.57548i	0.418478	+	0.418478i	−0.466201	+	0.884679i	$0.654377\pi$
$74$	0.507410	−	0.298589i	0.0589853	−	0.0347102i
$75$	4.62170	+	6.82564i	0.533668	+	0.788158i
$76$	−9.70092	−	5.38840i	−1.11277	−	0.618092i
$77$	−1.60129	+	1.60129i	−0.182484	+	0.182484i
$78$	12.6045	+	3.26563i	1.42718	+	0.369759i
$79$	−2.91466			−0.327925			−0.163963	−	0.986467i	$-0.552428\pi$
$79$	−2.91466			−0.327925			−0.163963	+	0.986467i	$0.552428\pi$
$80$	2.84532	−	8.47963i	0.318117	−	0.948052i
$81$	8.07441			0.897157
$82$	−3.11241	−	0.806375i	−0.343708	−	0.0890492i
$83$	−9.90199	+	9.90199i	−1.08689	+	1.08689i	−0.0910377	+	0.995847i	$0.529018\pi$
$83$	−9.90199	+	9.90199i	−1.08689	+	1.08689i	−0.995847	+	0.0910377i	$0.970982\pi$
$84$	−6.52750	−	3.62572i	−0.712209	−	0.395599i
$85$	15.3015	+	1.45959i	1.65968	+	0.158314i
$86$	4.35994	−	2.56563i	0.470144	−	0.276659i
$87$	−7.75970	−	7.75970i	−0.831927	−	0.831927i
$88$	1.94965	−	2.04911i	0.207833	−	0.218436i
$89$		−	10.6976i		−	1.13394i	−0.823737	−	0.566972i	$-0.808115\pi$
$89$		−	10.6976i		−	1.13394i	0.823737	−	0.566972i	$-0.191885\pi$
$90$	0.808090	−	0.377266i	0.0851801	−	0.0397674i
$91$		−	12.6468i		−	1.32574i
$92$	8.19649	−	2.34255i	0.854543	−	0.244228i
$93$	−0.721768	−	0.721768i	−0.0748438	−	0.0748438i
$94$	−8.54891	−	14.5277i	−0.881753	−	1.49842i
$95$	7.90023	+	9.56633i	0.810546	+	0.981485i
$96$	8.26288	+	4.32437i	0.843327	+	0.441354i
$97$	−0.328465	+	0.328465i	−0.0333506	+	0.0333506i	−0.723585	−	0.690235i	$-0.757507\pi$
$97$	−0.328465	+	0.328465i	−0.0333506	+	0.0333506i	0.690235	+	0.723585i	$0.257507\pi$
$98$	0.663883	−	2.56242i	0.0670624	−	0.258844i
$99$	0.282018			0.0283438
$100$	−6.42090	+	7.66629i	−0.642090	+	0.766629i
$101$	14.1852			1.41148			0.705739	−	0.708471i	$-0.250615\pi$
$101$	14.1852			1.41148			0.705739	+	0.708471i	$0.250615\pi$
$102$	−4.01965	+	15.5148i	−0.398004	+	1.53620i
$103$	−4.88657	+	4.88657i	−0.481488	+	0.481488i	−0.905607	−	0.424119i	$-0.860584\pi$
$103$	−4.88657	+	4.88657i	−0.481488	+	0.481488i	0.424119	+	0.905607i	$0.360584\pi$
$104$	0.392771	+	15.7909i	0.0385143	+	1.54842i
$105$	5.31587	+	6.43695i	0.518775	+	0.628182i
$106$	2.25650	+	3.83460i	0.219170	+	0.372450i
$107$	5.44264	+	5.44264i	0.526160	+	0.526160i	0.919425	−	0.393265i	$-0.128655\pi$
$107$	5.44264	+	5.44264i	0.526160	+	0.526160i	−0.393265	+	0.919425i	$0.628655\pi$
$108$	2.97376	+	10.4051i	0.286150	+	1.00123i
$109$		−	1.02824i		−	0.0984878i	−0.998787	−	0.0492439i	$-0.984319\pi$
$109$		−	1.02824i		−	0.0984878i	0.998787	−	0.0492439i	$-0.0156812\pi$
$110$	−2.86539	+	1.33774i	−0.273204	+	0.127549i
$111$		−	0.686334i		−	0.0651439i
$112$	2.05310	−	8.82253i	0.194000	−	0.833651i
$113$	−0.452117	−	0.452117i	−0.0425316	−	0.0425316i	0.685521	−	0.728053i	$-0.259574\pi$
$113$	−0.452117	−	0.452117i	−0.0425316	−	0.0425316i	−0.728053	+	0.685521i	$0.759574\pi$
$114$	−11.1492	+	6.56083i	−1.04422	+	0.614478i
$115$	−9.48780	−	0.905026i	−0.884742	−	0.0843941i
$116$	6.46431	−	11.6379i	0.600196	−	1.08055i
$117$	−1.11367	+	1.11367i	−0.102959	+	0.102959i
$118$	1.40522	+	0.364071i	0.129361	+	0.0335155i
$119$	15.5669			1.42701
$120$	−6.83733	−	7.87211i	−0.624160	−	0.718622i
$121$	−1.00000			−0.0909091
$122$	−6.19045	−	1.60385i	−0.560457	−	0.145205i
$123$	−2.65031	+	2.65031i	−0.238971	+	0.238971i
$124$	0.601277	−	1.08250i	0.0539963	−	0.0972113i
$125$	9.81115	−	5.36109i	0.877536	−	0.479510i
$126$	0.778410	−	0.458060i	0.0693463	−	0.0408073i
$127$	15.4099	+	15.4099i	1.36741	+	1.36741i	0.864120	+	0.503286i	$0.167876\pi$
$127$	15.4099	+	15.4099i	1.36741	+	1.36741i	0.503286	+	0.864120i	$0.332124\pi$
$128$	−2.28951	+	11.0796i	−0.202366	+	0.979310i
$129$		−	5.89734i		−	0.519232i
$130$	6.03258	−	16.5979i	0.529092	−	1.45573i
$131$		−	4.72547i		−	0.412866i	−0.978461	−	0.206433i	$-0.933814\pi$
$131$		−	4.72547i		−	0.412866i	0.978461	−	0.206433i	$-0.0661856\pi$
$132$	−0.906076	−	3.17032i	−0.0788638	−	0.275941i
$133$	8.88474	+	8.88474i	0.770404	+	0.770404i
$134$	3.50180	+	5.95083i	0.302510	+	0.514073i
$135$	1.14889	−	12.0443i	0.0988805	−	1.03661i
$136$	−19.4369	+	0.483460i	−1.66670	+	0.0414563i
$137$	11.8530	−	11.8530i	1.01267	−	1.01267i	0.0127513	−	0.999919i	$-0.495941\pi$
$137$	11.8530	−	11.8530i	1.01267	−	1.01267i	0.999919	−	0.0127513i	$-0.00405896\pi$
$138$	2.49241	−	9.62007i	0.212168	−	0.818915i
$139$	4.55579			0.386417			0.193209	−	0.981158i	$-0.438111\pi$
$139$	4.55579			0.386417			0.193209	+	0.981158i	$0.438111\pi$
$140$	−5.73610	+	8.34640i	−0.484789	+	0.705400i
$141$	−19.6505			−1.65487
$142$	4.12104	−	15.9062i	0.345830	−	1.33482i
$143$	3.94893	−	3.94893i	0.330227	−	0.330227i
$144$	−0.957702	+	0.596112i	−0.0798085	+	0.0496760i
$145$	−11.4765	+	9.47767i	−0.953068	+	0.787078i
$146$	3.62669	+	6.16306i	0.300147	+	0.510059i
$147$	−2.18199	−	2.18199i	−0.179967	−	0.179967i
$148$	0.800557	−	0.228799i	0.0658054	−	0.0188071i
$149$		−	3.61522i		−	0.296170i	−0.988975	−	0.148085i	$-0.952689\pi$
$149$		−	3.61522i		−	0.296170i	0.988975	−	0.148085i	$-0.0473110\pi$
$150$	3.90619	+	10.9837i	0.318939	+	0.896812i
$151$			1.98805i			0.161786i	0.996723	+	0.0808928i	$0.0257771\pi$
$151$			1.98805i			0.161786i	−0.996723	+	0.0808928i	$0.974223\pi$
$152$	−11.3695	−	10.8176i	−0.922185	−	0.877423i
$153$	−1.37081	−	1.37081i	−0.110823	−	0.110823i
$154$	−2.76015	+	1.62423i	−0.222419	+	0.130884i
$155$	−1.06748	+	0.881565i	−0.0857422	+	0.0708090i
$156$	16.0974	+	8.94137i	1.28883	+	0.715882i
$157$	−2.98260	+	2.98260i	−0.238037	+	0.238037i	−0.816037	−	0.578000i	$-0.803833\pi$
$157$	−2.98260	+	2.98260i	−0.238037	+	0.238037i	0.578000	+	0.816037i	$0.303833\pi$
$158$	−3.99021	−	1.03380i	−0.317444	−	0.0822447i
$159$	5.18676			0.411337
$160$	6.90292	−	10.5995i	0.545724	−	0.837965i
$161$	−9.65235			−0.760712
$162$	11.0540	+	2.86391i	0.868482	+	0.225010i
$163$	0.576690	−	0.576690i	0.0451699	−	0.0451699i	−0.684161	−	0.729331i	$-0.739831\pi$
$163$	0.576690	−	0.576690i	0.0451699	−	0.0451699i	0.729331	+	0.684161i	$0.239831\pi$
$164$	−3.97491	−	2.20787i	−0.310388	−	0.172406i
$165$	−0.350055	+	3.66979i	−0.0272518	+	0.285693i
$166$	−17.0681	+	10.0438i	−1.32474	+	0.779552i
$167$	−7.41719	−	7.41719i	−0.573959	−	0.573959i	0.359273	−	0.933232i	$-0.383025\pi$
$167$	−7.41719	−	7.41719i	−0.573959	−	0.573959i	−0.933232	+	0.359273i	$0.883025\pi$
$168$	−7.65023	−	7.27889i	−0.590228	−	0.561579i
$169$			18.1882i			1.39909i
$170$	20.4303	+	7.42548i	1.56693	+	0.569508i
$171$		−	1.56477i		−	0.119661i
$172$	6.87881	−	1.96596i	0.524505	−	0.149903i
$173$	−0.328589	−	0.328589i	−0.0249821	−	0.0249821i	0.694505	−	0.719488i	$-0.255623\pi$
$173$	−0.328589	−	0.328589i	−0.0249821	−	0.0249821i	−0.719488	+	0.694505i	$0.755623\pi$
$174$	−7.87084	−	13.3754i	−0.596687	−	1.01399i
$175$	9.37574	−	6.34840i	0.708740	−	0.479894i
$176$	3.39589	−	2.11374i	0.255975	−	0.159329i
$177$	1.19659	−	1.19659i	0.0899414	−	0.0899414i
$178$	3.79433	−	14.6452i	0.284397	−	1.09770i
$179$	−9.12102			−0.681737			−0.340868	−	0.940111i	$-0.610721\pi$
$179$	−9.12102			−0.681737			−0.340868	+	0.940111i	$0.610721\pi$
$180$	1.24010	−	0.229862i	0.0924314	−	0.0171329i
$181$	3.15434			0.234460			0.117230	−	0.993105i	$-0.462599\pi$
$181$	3.15434			0.234460			0.117230	+	0.993105i	$0.462599\pi$
$182$	4.48568	−	17.3136i	0.332501	−	1.28337i
$183$	−5.27136	+	5.27136i	−0.389670	+	0.389670i
$184$	12.0520	−	0.299772i	0.888484	−	0.0220995i
$185$	−0.926681	−	0.0883946i	−0.0681309	−	0.00649890i
$186$	−0.732106	−	1.24411i	−0.0536806	−	0.0912227i
$187$	4.86073	+	4.86073i	0.355452	+	0.355452i
$188$	−6.55075	−	22.9208i	−0.477762	−	1.67167i
$189$		−	12.2532i		−	0.891289i
$190$	7.42243	+	15.8986i	0.538480	+	1.15340i
$191$		−	16.3188i		−	1.18079i	−0.807116	−	0.590393i	$-0.798973\pi$
$191$		−	16.3188i		−	1.18079i	0.807116	−	0.590393i	$-0.201027\pi$
$192$	9.77818	+	8.85088i	0.705680	+	0.638757i
$193$	−2.80499	−	2.80499i	−0.201907	−	0.201907i	0.598909	−	0.800817i	$-0.295601\pi$
$193$	−2.80499	−	2.80499i	−0.201907	−	0.201907i	−0.800817	+	0.598909i	$0.795601\pi$
$194$	−0.566176	+	0.333170i	−0.0406491	+	0.0239202i
$195$	−13.1094	−	15.8741i	−0.938785	−	1.13677i
$196$	1.81773	−	3.27252i	0.129838	−	0.233751i
$197$	−16.8299	+	16.8299i	−1.19908	+	1.19908i	−0.224635	+	0.974443i	$0.572119\pi$
$197$	−16.8299	+	16.8299i	−1.19908	+	1.19908i	−0.974443	+	0.224635i	$0.927881\pi$
$198$	0.386086	+	0.100029i	0.0274379	+	0.00710873i
$199$	−9.45275			−0.670088			−0.335044	−	0.942202i	$-0.608751\pi$
$199$	−9.45275			−0.670088			−0.335044	+	0.942202i	$0.608751\pi$
$200$	−11.5094	+	8.21783i	−0.813841	+	0.581088i
$201$	8.04922			0.567748
$202$	19.4197	+	5.03134i	1.36637	+	0.354004i
$203$	−10.6588	+	10.6588i	−0.748098	+	0.748098i
$204$	−11.0059	+	19.8143i	−0.770567	+	1.38728i
$205$	3.23708	+	3.91976i	0.226088	+	0.273768i
$206$	−8.42299	+	4.95656i	−0.586857	+	0.345340i
$207$	0.849980	+	0.849980i	0.0590777	+	0.0590777i
$208$	−5.06314	+	21.7572i	−0.351066	+	1.50859i
$209$			5.54848i			0.383797i
$210$	4.99437	+	10.6977i	0.344644	+	0.738214i
$211$			21.8214i			1.50225i	0.660160	+	0.751125i	$0.270488\pi$
$211$			21.8214i			1.50225i	−0.660160	+	0.751125i	$0.729512\pi$
$212$	1.72908	+	6.04997i	0.118754	+	0.415514i
$213$	−13.5446	−	13.5446i	−0.928062	−	0.928062i
$214$	5.52060	+	9.38149i	0.377380	+	0.641306i
$215$	−7.96253	−	0.759533i	−0.543040	−	0.0517997i
$216$	0.380547	+	15.2994i	0.0258929	+	1.04099i
$217$	−0.991424	+	0.991424i	−0.0673022	+	0.0673022i
$218$	0.364707	−	1.40768i	0.0247011	−	0.0953399i
$219$	8.33629			0.563314
$220$	−4.39723	+	0.815061i	−0.296462	+	0.0549514i
$221$	−38.3894			−2.58235
$222$	0.243435	−	0.939600i	0.0163383	−	0.0630618i
$223$	1.45621	−	1.45621i	0.0975149	−	0.0975149i	−0.656666	−	0.754181i	$-0.728034\pi$
$223$	1.45621	−	1.45621i	0.0975149	−	0.0975149i	0.754181	+	0.656666i	$0.228034\pi$
$224$	5.93998	−	11.3499i	0.396882	−	0.758350i
$225$	−1.38466	−	0.266586i	−0.0923106	−	0.0177724i
$226$	−0.458593	−	0.779315i	−0.0305051	−	0.0518393i
$227$	−1.29454	−	1.29454i	−0.0859214	−	0.0859214i	0.662840	−	0.748761i	$-0.269351\pi$
$227$	−1.29454	−	1.29454i	−0.0859214	−	0.0859214i	−0.748761	+	0.662840i	$0.769351\pi$
$228$	−17.5905	+	5.02735i	−1.16496	+	0.332944i
$229$			15.5616i			1.02834i	0.857688	+	0.514170i	$0.171900\pi$
$229$			15.5616i			1.02834i	−0.857688	+	0.514170i	$0.828100\pi$
$230$	−12.6679	−	4.60422i	−0.835298	−	0.303593i
$231$			3.73344i			0.245642i
$232$	12.9776	−	13.6396i	0.852019	−	0.895485i
$233$	−14.1453	−	14.1453i	−0.926689	−	0.926689i	0.0708013	−	0.997490i	$-0.477444\pi$
$233$	−14.1453	−	14.1453i	−0.926689	−	0.926689i	−0.997490	+	0.0708013i	$0.977444\pi$
$234$	−1.91963	+	1.12962i	−0.125490	+	0.0738456i
$235$	−2.53083	+	26.5318i	−0.165093	+	1.73075i
$236$	1.79464	+	0.996836i	0.116821	+	0.0648885i
$237$	−3.39779	+	3.39779i	−0.220710	+	0.220710i
$238$	21.3113	+	5.52141i	1.38140	+	0.357900i
$239$	−15.8480			−1.02512			−0.512562	−	0.858650i	$-0.671304\pi$
$239$	−15.8480			−1.02512			−0.512562	+	0.858650i	$0.671304\pi$
$240$	−6.56824	−	13.2022i	−0.423978	−	0.852195i
$241$	12.0625			0.777012			0.388506	−	0.921446i	$-0.372991\pi$
$241$	12.0625			0.777012			0.388506	+	0.921446i	$0.372991\pi$
$242$	−1.36901	−	0.354689i	−0.0880035	−	0.0228003i
$243$	−2.06530	+	2.06530i	−0.132489	+	0.132489i
$244$	−7.90593	−	4.39137i	−0.506125	−	0.281129i
$245$	−3.22712	+	2.66507i	−0.206173	+	0.170265i
$246$	−4.56835	+	2.68827i	−0.291267	+	0.171398i
$247$	−21.9106	−	21.9106i	−1.39414	−	1.39414i
$248$	1.20711	−	1.26869i	0.0766514	−	0.0805618i
$249$			23.0867i			1.46306i
$250$	15.3331	−	3.85948i	0.969751	−	0.244095i
$251$			14.4260i			0.910563i	0.890348	+	0.455281i	$0.150461\pi$
$251$			14.4260i			0.910563i	−0.890348	+	0.455281i	$0.849539\pi$
$252$	1.22812	−	0.350997i	0.0773645	−	0.0221107i
$253$	−3.01393	−	3.01393i	−0.189484	−	0.189484i
$254$	15.6306	+	26.5620i	0.980751	+	1.66665i
$255$	19.5394	−	16.1363i	1.22360	−	1.01050i
$256$	−7.06420	+	14.3561i	−0.441512	+	0.897255i
$257$	15.6814	−	15.6814i	0.978180	−	0.978180i	−0.0215873	−	0.999767i	$-0.506872\pi$
$257$	15.6814	−	15.6814i	0.978180	−	0.978180i	0.999767	+	0.0215873i	$0.00687199\pi$
$258$	2.09173	−	8.07354i	0.130225	−	0.502637i
$259$	−0.942752			−0.0585798
$260$	14.1458	−	20.5830i	0.877283	−	1.27650i
$261$	1.87721			0.116196
$262$	1.67607	−	6.46923i	0.103548	−	0.399670i
$263$	0.393645	−	0.393645i	0.0242732	−	0.0242732i	−0.694866	−	0.719139i	$-0.744536\pi$
$263$	0.393645	−	0.393645i	0.0242732	−	0.0242732i	0.719139	+	0.694866i	$0.244536\pi$
$264$	−0.115949	−	4.66159i	−0.00713617	−	0.286901i
$265$	0.668016	−	7.00312i	0.0410359	−	0.430198i
$266$	9.01199	+	15.3146i	0.552561	+	0.939001i
$267$	−12.4708	−	12.4708i	−0.763202	−	0.763202i
$268$	2.68332	+	9.38881i	0.163910	+	0.573513i
$269$			12.5305i			0.764000i	0.924162	+	0.382000i	$0.124765\pi$
$269$			12.5305i			0.764000i	−0.924162	+	0.382000i	$0.875235\pi$
$270$	5.84484	−	16.0813i	0.355705	−	0.978679i
$271$			5.84858i			0.355276i	0.984096	+	0.177638i	$0.0568456\pi$
$271$			5.84858i			0.355276i	−0.984096	+	0.177638i	$0.943154\pi$
$272$	−26.7808	−	6.23220i	−1.62383	−	0.377883i
$273$	−14.7431	−	14.7431i	−0.892293	−	0.892293i
$274$	20.4310	−	12.0228i	1.23428	−	0.726322i
$275$	4.90983	+	0.945282i	0.296074	+	0.0570027i
$276$	6.82428	−	12.2860i	0.410773	−	0.739528i
$277$	4.14441	−	4.14441i	0.249013	−	0.249013i	−0.571552	−	0.820566i	$-0.693659\pi$
$277$	4.14441	−	4.14441i	0.249013	−	0.249013i	0.820566	+	0.571552i	$0.193659\pi$
$278$	6.23693	+	1.61589i	0.374066	+	0.0969147i
$279$	0.174608			0.0104535
$280$	−10.8132	+	9.39180i	−0.646211	+	0.561267i
$281$	−2.26836			−0.135319			−0.0676595	−	0.997708i	$-0.521553\pi$
$281$	−2.26836			−0.135319			−0.0676595	+	0.997708i	$0.521553\pi$
$282$	−26.9017	−	6.96981i	−1.60197	−	0.415046i
$283$	11.1023	−	11.1023i	0.659965	−	0.659965i	−0.295406	−	0.955372i	$-0.595455\pi$
$283$	11.1023	−	11.1023i	0.659965	−	0.659965i	0.955372	+	0.295406i	$0.0954550\pi$
$284$	11.2835	−	20.3141i	0.669553	−	1.20542i
$285$	20.3618	+	1.94228i	1.20613	+	0.115051i
$286$	6.80679	−	4.00550i	0.402494	−	0.236850i
$287$	3.64048	+	3.64048i	0.214891	+	0.214891i
$288$	−1.52254	+	0.476398i	−0.0897165	+	0.0280720i
$289$		−	30.2533i		−	1.77961i
$290$	−19.0730	+	8.90448i	−1.12001	+	0.522889i
$291$			0.765822i			0.0448933i
$292$	2.77902	+	9.72366i	0.162630	+	0.569034i
$293$	6.78722	+	6.78722i	0.396514	+	0.396514i	0.877001	−	0.480488i	$-0.159540\pi$
$293$	6.78722	+	6.78722i	0.396514	+	0.396514i	−0.480488	+	0.877001i	$0.659540\pi$
$294$	−2.21324	−	3.76109i	−0.129079	−	0.219351i
$295$	−1.46152	−	1.76974i	−0.0850927	−	0.103038i
$296$	1.17713	−	0.0292790i	0.0684190	−	0.00170181i
$297$	3.82604	−	3.82604i	0.222009	−	0.222009i
$298$	1.28228	−	4.94928i	0.0742805	−	0.286704i
$299$	23.8036			1.37660
$300$	1.45183	+	16.4223i	0.0838214	+	0.948139i
$301$	−8.10063			−0.466912
$302$	−0.705142	+	2.72167i	−0.0405763	+	0.156615i
$303$	16.5365	−	16.5365i	0.949997	−	0.949997i
$304$	−11.7281	−	18.8421i	−0.672650	−	1.08067i
$305$	6.43843	+	7.79625i	0.368663	+	0.446412i
$306$	−1.39044	−	2.36287i	−0.0794864	−	0.135076i
$307$	−6.25960	−	6.25960i	−0.357254	−	0.357254i	0.505546	−	0.862800i	$-0.331291\pi$
$307$	−6.25960	−	6.25960i	−0.357254	−	0.357254i	−0.862800	+	0.505546i	$0.831291\pi$
$308$	−4.35478	+	1.24459i	−0.248136	+	0.0709172i
$309$			11.3931i			0.648131i
$310$	−1.77408	+	0.828249i	−0.100761	+	0.0470414i
$311$		−	7.82582i		−	0.443762i	−0.975074	−	0.221881i	$-0.928780\pi$
$311$		−	7.82582i		−	0.443762i	0.975074	−	0.221881i	$-0.0712196\pi$
$312$	18.8662	+	17.9504i	1.06809	+	1.01624i
$313$	21.5271	+	21.5271i	1.21678	+	1.21678i	0.968752	+	0.248032i	$0.0797837\pi$
$313$	21.5271	+	21.5271i	1.21678	+	1.21678i	0.248032	+	0.968752i	$0.420216\pi$
$314$	−5.14111	+	3.02532i	−0.290129	+	0.170728i
$315$	−1.42161	−	0.135605i	−0.0800985	−	0.00764046i
$316$	−5.09597	−	2.83057i	−0.286671	−	0.159232i
$317$	0.706237	−	0.706237i	0.0396662	−	0.0396662i	−0.686995	−	0.726662i	$-0.741071\pi$
$317$	0.706237	−	0.706237i	0.0396662	−	0.0396662i	0.726662	+	0.686995i	$0.241071\pi$
$318$	7.10074	+	1.83969i	0.398190	+	0.103165i
$319$	−6.65635			−0.372684
$320$	13.2097	−	12.0625i	0.738446	−	0.674313i
$321$	12.6896			0.708265
$322$	−13.2142	−	3.42359i	−0.736398	−	0.190789i
$323$	26.9697	−	26.9697i	1.50063	−	1.50063i
$324$	14.1172	+	7.84146i	0.784291	+	0.435636i
$325$	−23.1215	+	15.6557i	−1.28255	+	0.868424i
$326$	0.994042	−	0.584950i	0.0550549	−	0.0323974i
$327$	−1.19868	−	1.19868i	−0.0662872	−	0.0662872i
$328$	−4.65859	−	4.43247i	−0.257228	−	0.244742i
$329$			26.9920i			1.48812i
$330$	−1.78087	+	4.89983i	−0.0980335	+	0.269727i
$331$		−	0.765243i		−	0.0420616i	−0.999779	−	0.0210308i	$-0.993305\pi$
$331$		−	0.765243i		−	0.0420616i	0.999779	−	0.0210308i	$-0.00669480\pi$
$332$	−26.9289	+	7.69625i	−1.47791	+	0.422386i
$333$	0.0830182	+	0.0830182i	0.00454937	+	0.00454937i
$334$	−7.52343	−	12.7850i	−0.411664	−	0.699565i
$335$	1.03668	−	10.8680i	0.0566398	−	0.593781i
$336$	−7.89152	−	12.6784i	−0.430517	−	0.691661i
$337$	−9.66961	+	9.66961i	−0.526737	+	0.526737i	−0.919598	−	0.392861i	$-0.871485\pi$
$337$	−9.66961	+	9.66961i	−0.526737	+	0.526737i	0.392861	+	0.919598i	$0.371485\pi$
$338$	−6.45115	+	24.8998i	−0.350896	+	1.35437i
$339$	−1.05412			−0.0572519
$340$	25.3355	+	17.4120i	1.37401	+	0.944297i
$341$	−0.619140			−0.0335283
$342$	0.555007	−	2.14219i	0.0300113	−	0.115836i
$343$	−14.2062	+	14.2062i	−0.767064	+	0.767064i
$344$	10.1145	−	0.251581i	0.545337	−	0.0135643i
$345$	−12.1155	+	10.0054i	−0.652278	+	0.538675i
$346$	−0.333295	−	0.566389i	−0.0179181	−	0.0304493i
$347$	24.7289	+	24.7289i	1.32752	+	1.32752i	0.907528	+	0.419991i	$0.137967\pi$
$347$	24.7289	+	24.7289i	1.32752	+	1.32752i	0.419991	+	0.907528i	$0.362033\pi$
$348$	−6.03116	−	21.1028i	−0.323304	−	1.13123i
$349$		−	28.5812i		−	1.52992i	−0.644081	−	0.764958i	$-0.722760\pi$
$349$		−	28.5812i		−	1.52992i	0.644081	−	0.764958i	$-0.277240\pi$
$350$	15.0872	−	5.36556i	0.806446	−	0.286801i
$351$			30.2175i			1.61289i
$352$	5.39874	−	1.68925i	0.287754	−	0.0900373i
$353$	24.0526	+	24.0526i	1.28019	+	1.28019i	0.940559	+	0.339629i	$0.110302\pi$
$353$	24.0526	+	24.0526i	1.28019	+	1.28019i	0.339629	+	0.940559i	$0.389698\pi$
$354$	2.06257	−	1.21373i	0.109624	−	0.0645091i
$355$	−20.0322	+	16.5434i	−1.06320	+	0.878030i
$356$	10.3890	−	18.7036i	0.550614	−	0.991289i
$357$	18.1472	−	18.1472i	0.960452	−	0.960452i
$358$	−12.4868	−	3.23513i	−0.659947	−	0.170982i
$359$	16.6065			0.876459			0.438230	−	0.898863i	$-0.355606\pi$
$359$	16.6065			0.876459			0.438230	+	0.898863i	$0.355606\pi$
$360$	1.77924	+	0.125166i	0.0937741	+	0.00659683i
$361$	11.7857			0.620298
$362$	4.31833	+	1.11881i	0.226966	+	0.0588034i
$363$	−1.16576	+	1.16576i	−0.0611864	+	0.0611864i
$364$	12.2819	−	22.1115i	0.643747	−	1.15896i
$365$	1.07365	−	11.2556i	0.0561974	−	0.589144i
$366$	−9.08626	+	5.34687i	−0.474946	+	0.279485i
$367$	−15.0735	−	15.0735i	−0.786831	−	0.786831i	0.194143	−	0.980973i	$-0.437808\pi$
$367$	−15.0735	−	15.0735i	−0.786831	−	0.786831i	−0.980973	+	0.194143i	$0.937808\pi$
$368$	16.6056	+	3.86432i	0.865629	+	0.201441i
$369$		−	0.641158i		−	0.0333773i
$370$	−1.23729	−	0.449697i	−0.0643234	−	0.0233786i
$371$		−	7.12457i		−	0.369889i
$372$	−0.560988	−	1.96288i	−0.0290859	−	0.101770i
$373$	−3.75667	−	3.75667i	−0.194513	−	0.194513i	0.603130	−	0.797643i	$-0.293920\pi$
$373$	−3.75667	−	3.75667i	−0.194513	−	0.194513i	−0.797643	+	0.603130i	$0.793920\pi$
$374$	4.93035	+	8.37845i	0.254942	+	0.433239i
$375$	5.18770	−	17.6872i	0.267892	−	0.913361i
$376$	−0.838288	−	33.7023i	−0.0432314	−	1.73807i
$377$	26.2855	−	26.2855i	1.35377	−	1.35377i
$378$	4.34608	−	16.7748i	0.223538	−	0.862802i
$379$	3.44738			0.177080			0.0885401	−	0.996073i	$-0.471780\pi$
$379$	3.44738			0.177080			0.0885401	+	0.996073i	$0.471780\pi$
$380$	4.52235	+	24.3980i	0.231992	+	1.25159i
$381$	35.9284			1.84067
$382$	5.78810	−	22.3406i	0.296145	−	1.14305i
$383$	−20.5991	+	20.5991i	−1.05256	+	1.05256i	−0.0540252	+	0.998540i	$0.517205\pi$
$383$	−20.5991	+	20.5991i	−1.05256	+	1.05256i	−0.998540	+	0.0540252i	$0.982795\pi$
$384$	10.2471	+	15.5852i	0.522922	+	0.795328i
$385$	5.04085	+	0.480838i	0.256905	+	0.0245058i
$386$	−2.84516	−	4.83496i	−0.144815	−	0.246093i
$387$	0.713336	+	0.713336i	0.0362609	+	0.0362609i
$388$	−0.893274	+	0.255297i	−0.0453491	+	0.0129607i
$389$		−	0.568161i		−	0.0288069i	−0.999896	−	0.0144034i	$-0.995415\pi$
$389$		−	0.568161i		−	0.0288069i	0.999896	−	0.0144034i	$-0.00458492\pi$
$390$	−12.3166	−	26.3816i	−0.623674	−	1.33589i
$391$			29.2997i			1.48175i
$392$	3.64922	−	3.83539i	0.184314	−	0.193716i
$393$	−5.50875	−	5.50875i	−0.277880	−	0.277880i
$394$	−29.0097	+	17.0709i	−1.46149	+	0.860020i
$395$	4.15005	+	5.02527i	0.208812	+	0.252849i
$396$	0.493077	+	0.273881i	0.0247780	+	0.0137630i
$397$	16.0678	−	16.0678i	0.806418	−	0.806418i	−0.177672	−	0.984090i	$-0.556856\pi$
$397$	16.0678	−	16.0678i	0.806418	−	0.806418i	0.984090	+	0.177672i	$0.0568565\pi$
$398$	−12.9409	−	3.35279i	−0.648671	−	0.168060i
$399$	20.7149			1.03704
$400$	−18.6714	+	7.16803i	−0.933568	+	0.358402i
$401$	−33.2099			−1.65842			−0.829212	−	0.558935i	$-0.811210\pi$
$401$	−33.2099			−1.65842			−0.829212	+	0.558935i	$0.811210\pi$
$402$	11.0195	+	2.85497i	0.549602	+	0.142393i
$403$	2.44494	−	2.44494i	0.121791	−	0.121791i
$404$	24.8013	+	13.7759i	1.23391	+	0.685378i
$405$	−11.4968	−	13.9214i	−0.571280	−	0.691759i
$406$	−18.3725	+	10.8114i	−0.911813	+	0.536562i
$407$	−0.294372	−	0.294372i	−0.0145915	−	0.0145915i
$408$	−22.0951	+	23.2223i	−1.09387	+	1.14968i
$409$		−	11.3143i		−	0.559458i	−0.960079	−	0.279729i	$-0.909755\pi$
$409$		−	11.3143i		−	0.559458i	0.960079	−	0.279729i	$-0.0902446\pi$
$410$	3.04131	+	6.51437i	0.150200	+	0.321722i
$411$		−	27.6354i		−	1.36316i
$412$	−13.2892	+	3.79805i	−0.654713	+	0.187116i
$413$	−1.64365	−	1.64365i	−0.0808786	−	0.0808786i
$414$	0.862154	+	1.46511i	0.0423726	+	0.0720063i
$415$	31.1714	+	2.97339i	1.53014	+	0.145958i
$416$	−14.6486	+	27.9900i	−0.718204	+	1.37232i
$417$	5.31095	−	5.31095i	0.260078	−	0.260078i
$418$	−1.96799	+	7.59594i	−0.0962574	+	0.371530i
$419$	−29.7516			−1.45346			−0.726731	−	0.686922i	$-0.758961\pi$
$419$	−29.7516			−1.45346			−0.726731	+	0.686922i	$0.758961\pi$
$420$	3.04298	+	16.4168i	0.148482	+	0.801058i
$421$	24.8525			1.21124			0.605620	−	0.795754i	$-0.292925\pi$
$421$	24.8525			1.21124			0.605620	+	0.795754i	$0.292925\pi$
$422$	−7.73984	+	29.8738i	−0.376769	+	1.45424i
$423$	2.37690	−	2.37690i	0.115569	−	0.115569i
$424$	0.221267	+	8.89578i	0.0107457	+	0.432017i
$425$	−19.2706	−	28.4601i	−0.934761	−	1.38052i
$426$	−13.7386	−	23.3469i	−0.665638	−	1.13116i
$427$	7.24077	+	7.24077i	0.350406	+	0.350406i
$428$	4.23025	+	14.8015i	0.204477	+	0.715457i
$429$		−	9.20700i		−	0.444518i
$430$	−10.6314	−	3.86404i	−0.512692	−	0.186340i
$431$		−	0.985843i		−	0.0474864i	−0.999718	−	0.0237432i	$-0.992442\pi$
$431$		−	0.985843i		−	0.0474864i	0.999718	−	0.0237432i	$-0.00755841\pi$
$432$	−4.90557	+	21.0801i	−0.236019	+	1.01422i
$433$	−18.2563	−	18.2563i	−0.877340	−	0.877340i	0.115919	−	0.993259i	$-0.463019\pi$
$433$	−18.2563	−	18.2563i	−0.877340	−	0.877340i	−0.993259	+	0.115919i	$0.963019\pi$
$434$	−1.70892	+	1.00562i	−0.0820308	+	0.0482715i
$435$	−2.33009	+	24.4274i	−0.111719	+	1.17121i
$436$	0.998576	−	1.79777i	0.0478231	−	0.0860976i
$437$	−16.7227	+	16.7227i	−0.799956	+	0.799956i
$438$	11.4125	+	2.95679i	0.545310	+	0.141281i
$439$	−37.5469			−1.79201			−0.896007	−	0.444040i	$-0.853545\pi$
$439$	−37.5469			−1.79201			−0.896007	+	0.444040i	$0.853545\pi$
$440$	−6.30896	−	0.443824i	−0.300768	−	0.0211585i
$441$	0.527861			0.0251362
$442$	−52.5556	−	13.6163i	−2.49981	−	0.647662i
$443$	−6.60548	+	6.60548i	−0.313836	+	0.313836i	−0.846394	−	0.532558i	$-0.821231\pi$
$443$	−6.60548	+	6.60548i	−0.313836	+	0.313836i	0.532558	+	0.846394i	$0.321231\pi$
$444$	0.666532	−	1.19998i	0.0316322	−	0.0569485i
$445$	−18.4441	+	15.2318i	−0.874335	+	0.722058i
$446$	2.51007	−	1.47706i	0.118855	−	0.0699410i
$447$	−4.21447	−	4.21447i	−0.199338	−	0.199338i
$448$	12.1576	−	13.4314i	0.574393	−	0.634572i
$449$			18.4122i			0.868925i	0.900690	+	0.434462i	$0.143062\pi$
$449$			18.4122i			0.868925i	−0.900690	+	0.434462i	$0.856938\pi$
$450$	−1.80106	−	0.856084i	−0.0849027	−	0.0403562i
$451$			2.27347i			0.107053i
$452$	−0.351405	−	1.22955i	−0.0165287	−	0.0578332i
$453$	2.31759	+	2.31759i	0.108890	+	0.108890i
$454$	−1.31308	−	2.23139i	−0.0616258	−	0.104725i
$455$	−21.8048	+	18.0072i	−1.02222	+	0.844189i
$456$	−25.8647	+	0.643342i	−1.21123	+	0.0301272i
$457$	16.1726	−	16.1726i	0.756521	−	0.756521i	−0.219166	−	0.975688i	$-0.570334\pi$
$457$	16.1726	−	16.1726i	0.756521	−	0.756521i	0.975688	+	0.219166i	$0.0703337\pi$
$458$	−5.51954	+	21.3040i	−0.257911	+	0.995472i
$459$	−37.1946			−1.73610
$460$	−15.7095	−	10.7964i	−0.732458	−	0.503385i
$461$	9.65434			0.449648			0.224824	−	0.974399i	$-0.427819\pi$
$461$	9.65434			0.449648			0.224824	+	0.974399i	$0.427819\pi$
$462$	−1.32421	+	5.11112i	−0.0616078	+	0.237791i
$463$	13.2005	−	13.2005i	0.613477	−	0.613477i	−0.330373	−	0.943850i	$-0.607175\pi$
$463$	13.2005	−	13.2005i	0.613477	−	0.613477i	0.943850	+	0.330373i	$0.107175\pi$
$464$	22.6043	−	14.0698i	1.04938	−	0.653174i
$465$	−0.216733	+	2.27212i	−0.0100508	+	0.105367i
$466$	−14.3479	−	24.3823i	−0.664654	−	1.12949i
$467$	22.5203	+	22.5203i	1.04212	+	1.04212i	0.999073	+	0.0430432i	$0.0137053\pi$
$467$	22.5203	+	22.5203i	1.04212	+	1.04212i	0.0430432	+	0.999073i	$0.486295\pi$
$468$	−3.02867	+	0.865590i	−0.140000	+	0.0400119i
$469$		−	11.0565i		−	0.510539i
$470$	−12.8753	+	35.4248i	−0.593893	+	1.63402i
$471$			6.95397i			0.320422i
$472$	2.10331	+	2.00122i	0.0968128	+	0.0921136i
$473$	−2.52940	−	2.52940i	−0.116302	−	0.116302i
$474$	−5.85678	+	3.44646i	−0.269011	+	0.158301i
$475$	5.24488	−	27.2421i	0.240652	−	1.24995i
$476$	27.2170	+	15.1178i	1.24749	+	0.692921i
$477$	−0.627385	+	0.627385i	−0.0287260	+	0.0287260i
$478$	−21.6962	−	5.62113i	−0.992360	−	0.257105i
$479$	−2.72142			−0.124345			−0.0621724	−	0.998065i	$-0.519803\pi$
$479$	−2.72142			−0.124345			−0.0621724	+	0.998065i	$0.519803\pi$
$480$	−4.30934	−	20.4036i	−0.196693	−	0.931293i
$481$	2.32491			0.106007
$482$	16.5137	+	4.27843i	0.752177	+	0.194877i
$483$	−11.2523	+	11.2523i	−0.511997	+	0.511997i
$484$	−1.74839	−	0.971149i	−0.0794723	−	0.0441431i
$485$	1.03400	+	0.0986320i	0.0469517	+	0.00447865i
$486$	−3.55996	+	2.09488i	−0.161483	+	0.0950258i
$487$	27.4404	+	27.4404i	1.24344	+	1.24344i	0.958562	+	0.284882i	$0.0919546\pi$
$487$	27.4404	+	27.4404i	1.24344	+	1.24344i	0.284882	+	0.958562i	$0.408045\pi$
$488$	−9.26575	−	8.81600i	−0.419441	−	0.399081i
$489$		−	1.34456i		−	0.0608032i
$490$	−5.36324	+	2.50389i	−0.242286	+	0.113114i
$491$		−	36.7028i		−	1.65637i	−0.560453	−	0.828186i	$-0.689373\pi$
$491$		−	36.7028i		−	1.65637i	0.560453	−	0.828186i	$-0.310627\pi$
$492$	−7.20763	+	2.05993i	−0.324945	+	0.0928690i
$493$	32.3547	+	32.3547i	1.45718	+	1.45718i
$494$	−22.2244	−	37.7673i	−0.999924	−	1.69923i
$495$	−0.401552	−	0.486236i	−0.0180484	−	0.0218547i
$496$	2.10254	−	1.30870i	0.0944066	−	0.0587625i
$497$	−18.6050	+	18.6050i	−0.834547	+	0.834547i
$498$	−8.18859	+	31.6059i	−0.366940	+	1.41630i
$499$	−27.2636			−1.22049			−0.610244	−	0.792213i	$-0.708929\pi$
$499$	−27.2636			−1.22049			−0.610244	+	0.792213i	$0.708929\pi$
$500$	22.3601	+	0.154817i	0.999976	+	0.00692361i
$501$	−17.2933			−0.772607
$502$	−5.11676	+	19.7494i	−0.228372	+	0.881459i
$503$	8.17166	−	8.17166i	0.364356	−	0.364356i	−0.501058	−	0.865414i	$-0.667056\pi$
$503$	8.17166	−	8.17166i	0.364356	−	0.364356i	0.865414	+	0.501058i	$0.167056\pi$
$504$	1.80581	−	0.0449165i	0.0804372	−	0.00200074i
$505$	−20.1976	−	24.4572i	−0.898783	−	1.08833i
$506$	−3.05710	−	5.19511i	−0.135904	−	0.230951i
$507$	21.2030	+	21.2030i	0.941658	+	0.941658i
$508$	11.9772	+	41.9078i	0.531403	+	1.85936i
$509$			31.8379i			1.41119i	0.708616	+	0.705594i	$0.249320\pi$
$509$			31.8379i			1.41119i	−0.708616	+	0.705594i	$0.750680\pi$
$510$	32.4730	−	15.1604i	1.43793	−	0.671315i
$511$		−	11.4508i		−	0.506552i
$512$	−14.7629	+	17.1481i	−0.652435	+	0.757844i
$513$	−21.2287	−	21.2287i	−0.937270	−	0.937270i
$514$	27.0301	−	15.9060i	1.19225	−	0.701584i
$515$	15.3829	+	1.46735i	0.677850	+	0.0646590i
$516$	5.72720	−	10.3109i	0.252126	−	0.453910i
$517$	−8.42819	+	8.42819i	−0.370671	+	0.370671i
$518$	−1.29064	−	0.334384i	−0.0567074	−	0.0146920i
$519$	−0.766110			−0.0336285
$520$	26.6663	−	23.1611i	1.16940	−	1.01568i
$521$	35.5122			1.55582			0.777908	−	0.628378i	$-0.216281\pi$
$521$	35.5122			1.55582			0.777908	+	0.628378i	$0.216281\pi$
$522$	2.56992	+	0.665826i	0.112482	+	0.0291424i
$523$	22.1359	−	22.1359i	0.967937	−	0.967937i	−0.0315648	−	0.999502i	$-0.510049\pi$
$523$	22.1359	−	22.1359i	0.967937	−	0.967937i	0.999502	+	0.0315648i	$0.0100491\pi$
$524$	4.58913	−	8.26197i	0.200477	−	0.360926i
$525$	3.52915	−	18.3305i	0.154025	−	0.800010i
$526$	0.678527	−	0.399283i	0.0295852	−	0.0174096i
$527$	3.00947	+	3.00947i	0.131095	+	0.131095i
$528$	1.49468	−	6.42290i	0.0650476	−	0.279521i
$529$			4.83250i			0.210109i
$530$	3.39845	−	9.35041i	0.147619	−	0.406156i
$531$			0.289477i			0.0125622i
$532$	6.90559	+	24.1624i	0.299395	+	1.04757i
$533$	−8.97777	−	8.97777i	−0.388871	−	0.388871i
$534$	−12.6494	−	21.4960i	−0.547395	−	0.930222i
$535$	1.63432	−	17.1334i	0.0706580	−	0.740740i
$536$	0.343380	+	13.8051i	0.0148317	+	0.596292i
$537$	−10.6329	+	10.6329i	−0.458843	+	0.458843i
$538$	−4.44445	+	17.1544i	−0.191614	+	0.739581i
$539$	−1.87173			−0.0806212
$540$	13.7055	−	19.9424i	0.589792	−	0.858186i
$541$	5.51867			0.237266			0.118633	−	0.992938i	$-0.462149\pi$
$541$	5.51867			0.237266			0.118633	+	0.992938i	$0.462149\pi$
$542$	−2.07443	+	8.00678i	−0.0891044	+	0.343921i
$543$	3.67719	−	3.67719i	0.157804	−	0.157804i
$544$	−34.4528	−	18.0308i	−1.47715	−	0.773066i
$545$	−1.77283	+	1.46407i	−0.0759396	+	0.0627137i
$546$	−14.9543	−	25.4127i	−0.639983	−	1.08756i
$547$	−0.759953	−	0.759953i	−0.0324932	−	0.0324932i	0.690673	−	0.723167i	$-0.257314\pi$
$547$	−0.759953	−	0.759953i	−0.0324932	−	0.0324932i	−0.723167	+	0.690673i	$0.757314\pi$
$548$	32.2347	−	9.21265i	1.37700	−	0.393545i
$549$		−	1.27524i		−	0.0544258i
$550$	6.38634	+	3.03557i	0.272314	+	0.129437i
$551$			36.9327i			1.57338i
$552$	13.7002	−	14.3991i	0.583120	−	0.612868i
$553$	4.66722	+	4.66722i	0.198471	+	0.198471i
$554$	7.14372	−	4.20377i	0.303508	−	0.178601i
$555$	−1.18333	+	0.977239i	−0.0502297	+	0.0414815i
$556$	7.96530	+	4.42435i	0.337804	+	0.187634i
$557$	4.30671	−	4.30671i	0.182481	−	0.182481i	−0.609955	−	0.792436i	$-0.708812\pi$
$557$	4.30671	−	4.30671i	0.182481	−	0.182481i	0.792436	+	0.609955i	$0.208812\pi$
$558$	0.239041	+	0.0619318i	0.0101194	+	0.00262178i
$559$	19.9769			0.844933
$560$	−18.1346	+	9.02217i	−0.766325	+	0.381256i
$561$	11.3329			0.478474
$562$	−3.10541	−	0.804563i	−0.130994	−	0.0339385i
$563$	3.33376	−	3.33376i	0.140501	−	0.140501i	−0.633358	−	0.773859i	$-0.718324\pi$
$563$	3.33376	−	3.33376i	0.140501	−	0.140501i	0.773859	+	0.633358i	$0.218324\pi$
$564$	−34.3567	−	19.0835i	−1.44668	−	0.803561i
$565$	−0.135762	+	1.42326i	−0.00571157	+	0.0598770i
$566$	19.1371	−	11.2614i	0.804393	−	0.473350i
$567$	−12.9295	−	12.9295i	−0.542988	−	0.542988i
$568$	22.6524	−	23.8081i	0.950476	−	0.998965i
$569$			27.4686i			1.15154i	0.817611	+	0.575771i	$0.195298\pi$
$569$			27.4686i			1.15154i	−0.817611	+	0.575771i	$0.804702\pi$
$570$	27.1866	+	9.88111i	1.13872	+	0.413874i
$571$			2.56853i			0.107490i	0.998555	+	0.0537448i	$0.0171157\pi$
$571$			2.56853i			0.107490i	−0.998555	+	0.0537448i	$0.982884\pi$
$572$	10.7393	−	3.06928i	0.449032	−	0.128333i
$573$	−19.0237	−	19.0237i	−0.794728	−	0.794728i
$574$	3.69263	+	6.27511i	0.154127	+	0.261918i
$575$	11.9489	+	17.6469i	0.498302	+	0.735926i
$576$	−2.25335	+	0.112166i	−0.0938896	+	0.00467358i
$577$	−17.8713	+	17.8713i	−0.743992	+	0.743992i	−0.973344	−	0.229352i	$-0.926339\pi$
$577$	−17.8713	+	17.8713i	−0.743992	+	0.743992i	0.229352	+	0.973344i	$0.426339\pi$
$578$	10.7305	−	41.4172i	0.446332	−	1.72273i
$579$	−6.53987			−0.271788
$580$	−29.2696	+	5.42534i	−1.21535	+	0.225275i
$581$	31.7120			1.31563
$582$	−0.271629	+	1.04842i	−0.0112594	+	0.0434584i
$583$	2.22463	−	2.22463i	0.0921348	−	0.0921348i
$584$	0.355626	+	14.2975i	0.0147159	+	0.591635i
$585$	3.50582	+	0.334414i	0.144948	+	0.0138263i
$586$	6.88443	+	11.6991i	0.284393	+	0.483287i
$587$	25.7297	+	25.7297i	1.06198	+	1.06198i	0.997948	+	0.0640318i	$0.0203959\pi$
$587$	25.7297	+	25.7297i	1.06198	+	1.06198i	0.0640318	+	0.997948i	$0.479604\pi$
$588$	−1.69593	−	5.93400i	−0.0699390	−	0.244714i
$589$			3.43529i			0.141549i
$590$	−1.37312	−	2.94118i	−0.0565307	−	0.121086i
$591$			39.2391i			1.61408i
$592$	1.62188	+	0.377431i	0.0666591	+	0.0155123i
$593$	−8.52513	−	8.52513i	−0.350085	−	0.350085i	0.510056	−	0.860141i	$-0.329625\pi$
$593$	−8.52513	−	8.52513i	−0.350085	−	0.350085i	−0.860141	+	0.510056i	$0.829625\pi$
$594$	6.59495	−	3.88084i	0.270594	−	0.159233i
$595$	−22.1650	−	26.8394i	−0.908675	−	1.10031i
$596$	3.51092	−	6.32082i	0.143813	−	0.258911i
$597$	−11.0196	+	11.0196i	−0.451003	+	0.451003i
$598$	32.5874	+	8.44288i	1.33260	+	0.345255i
$599$	−19.9545			−0.815318			−0.407659	−	0.913134i	$-0.633655\pi$
$599$	−19.9545			−0.815318			−0.407659	+	0.913134i	$0.633655\pi$
$600$	−3.83723	+	22.9972i	−0.156654	+	0.938858i
$601$	−37.8106			−1.54233			−0.771163	−	0.636638i	$-0.780325\pi$
$601$	−37.8106			−1.54233			−0.771163	+	0.636638i	$0.780325\pi$
$602$	−11.0899	−	2.87321i	−0.451989	−	0.117103i
$603$	−0.973624	+	0.973624i	−0.0396491	+	0.0396491i
$604$	−1.93070	+	3.47589i	−0.0785589	+	0.141432i
$605$	1.42385	+	1.72413i	0.0578879	+	0.0700961i
$606$	28.5040	−	16.7733i	1.15790	−	0.681371i
$607$	−17.3630	−	17.3630i	−0.704743	−	0.704743i	0.260682	−	0.965425i	$-0.416053\pi$
$607$	−17.3630	−	17.3630i	−0.704743	−	0.704743i	−0.965425	+	0.260682i	$0.916053\pi$
$608$	−9.37277	−	29.9548i	−0.380116	−	1.21483i
$609$			24.8511i			1.00702i
$610$	6.04904	+	12.9568i	0.244919	+	0.524606i
$611$		−	66.5648i		−	2.69292i
$612$	−1.06545	−	3.72797i	−0.0430683	−	0.150694i
$613$	0.792766	+	0.792766i	0.0320195	+	0.0320195i	0.722935	−	0.690916i	$-0.242792\pi$
$613$	0.792766	+	0.792766i	0.0320195	+	0.0320195i	−0.690916	+	0.722935i	$0.742792\pi$
$614$	−6.34926	−	10.7897i	−0.256235	−	0.435436i
$615$	8.34315	+	0.795840i	0.336428	+	0.0320913i
$616$	−6.40319	+	0.159268i	−0.257992	+	0.00641710i
$617$	−18.6131	+	18.6131i	−0.749336	+	0.749336i	−0.974355	−	0.225018i	$-0.927756\pi$
$617$	−18.6131	+	18.6131i	−0.749336	+	0.749336i	0.225018	+	0.974355i	$0.427756\pi$
$618$	−4.04102	+	15.5973i	−0.162553	+	0.627416i
$619$	35.9346			1.44434			0.722168	−	0.691718i	$-0.243146\pi$
$619$	35.9346			1.44434			0.722168	+	0.691718i	$0.243146\pi$
$620$	−2.72251	+	0.504637i	−0.109338	+	0.0202667i
$621$	23.0628			0.925478
$622$	2.77574	−	10.7136i	0.111297	−	0.429578i
$623$	−17.1300	+	17.1300i	−0.686299	+	0.686299i
$624$	19.4612	+	31.2660i	0.779072	+	1.25164i
$625$	−23.2129	−	9.28235i	−0.928515	−	0.371294i
$626$	21.8354	+	37.1063i	0.872720	+	1.48307i
$627$	6.46819	+	6.46819i	0.258314	+	0.258314i
$628$	−8.11129	+	2.31820i	−0.323676	+	0.0925062i
$629$			2.86173i			0.114105i
$630$	−1.89810	−	0.689874i	−0.0756221	−	0.0274852i
$631$		−	24.0989i		−	0.959361i	−0.877443	−	0.479680i	$-0.840753\pi$
$631$		−	24.0989i		−	0.959361i	0.877443	−	0.479680i	$-0.159247\pi$
$632$	−5.97247	−	5.68257i	−0.237572	−	0.226041i
$633$	25.4385	+	25.4385i	1.01109	+	1.01109i
$634$	1.21734	−	0.716352i	0.0483468	−	0.0284500i
$635$	4.62730	−	48.5101i	0.183629	−	1.92507i
$636$	9.06849	+	5.03712i	0.359589	+	0.199735i
$637$	7.39135	−	7.39135i	0.292856	−	0.292856i
$638$	−9.11263	−	2.36094i	−0.360773	−	0.0934705i
$639$	3.27668			0.129624
$640$	22.3627	−	11.8283i	0.883963	−	0.467556i
$641$	4.03351			0.159314			0.0796571	−	0.996822i	$-0.474617\pi$
$641$	4.03351			0.159314			0.0796571	+	0.996822i	$0.474617\pi$
$642$	17.3722	+	4.50087i	0.685627	+	0.177635i
$643$	24.3073	−	24.3073i	0.958584	−	0.958584i	−0.0405914	−	0.999176i	$-0.512924\pi$
$643$	24.3073	−	24.3073i	0.958584	−	0.958584i	0.999176	+	0.0405914i	$0.0129242\pi$
$644$	−16.8761	−	9.37386i	−0.665011	−	0.369382i
$645$	−10.1678	+	8.39695i	−0.400357	+	0.330630i
$646$	46.4877	−	27.3559i	1.82903	−	1.07631i
$647$	−31.2430	−	31.2430i	−1.22829	−	1.22829i	−0.964611	−	0.263677i	$-0.915065\pi$
$647$	−31.2430	−	31.2430i	−1.22829	−	1.22829i	−0.263677	−	0.964611i	$-0.584935\pi$
$648$	16.5454	+	15.7423i	0.649964	+	0.618415i
$649$		−	1.02645i		−	0.0402917i
$650$	−37.2065	+	13.2320i	−1.45936	+	0.519001i
$651$			2.31152i			0.0905956i
$652$	1.56833	−	0.448228i	0.0614206	−	0.0175540i
$653$	3.01068	+	3.01068i	0.117817	+	0.117817i	0.763557	−	0.645740i	$-0.223451\pi$
$653$	3.01068	+	3.01068i	0.117817	+	0.117817i	−0.645740	+	0.763557i	$0.723451\pi$
$654$	−1.21585	−	2.06617i	−0.0475435	−	0.0807936i
$655$	−8.14735	+	6.72838i	−0.318343	+	0.262899i
$656$	−4.80552	−	7.72046i	−0.187624	−	0.301433i
$657$	−1.00835	+	1.00835i	−0.0393394	+	0.0393394i
$658$	−9.57377	+	36.9524i	−0.373224	+	1.44055i
$659$	8.72762			0.339980			0.169990	−	0.985446i	$-0.445626\pi$
$659$	8.72762			0.339980			0.169990	+	0.985446i	$0.445626\pi$
$660$	−4.17595	+	6.07627i	−0.162549	+	0.236519i
$661$	20.0803			0.781033			0.390517	−	0.920596i	$-0.372296\pi$
$661$	20.0803			0.781033			0.390517	+	0.920596i	$0.372296\pi$
$662$	0.271424	−	1.04763i	0.0105492	−	0.0407172i
$663$	−44.7527	+	44.7527i	−1.73805	+	1.73805i
$664$	−39.5957	+	0.984876i	−1.53661	+	0.0382206i
$665$	2.66792	−	27.9690i	0.103458	−	1.08459i
$666$	0.0842073	+	0.143099i	0.00326296	+	0.00554496i
$667$	−20.0618	−	20.0618i	−0.776794	−	0.776794i
$668$	−5.76495	−	20.1713i	−0.223053	−	0.780453i
$669$		−	3.39517i		−	0.131265i
$670$	5.27398	−	14.5107i	0.203752	−	0.560597i
$671$			4.52183i			0.174563i
$672$	−6.30671	−	20.1559i	−0.243286	−	0.777529i
$673$	6.56936	+	6.56936i	0.253230	+	0.253230i	0.822294	−	0.569063i	$-0.192694\pi$
$673$	6.56936	+	6.56936i	0.253230	+	0.253230i	−0.569063	+	0.822294i	$0.692694\pi$
$674$	−16.6675	+	9.80811i	−0.642009	+	0.377794i
$675$	−22.4019	+	15.1685i	−0.862249	+	0.583836i
$676$	−17.6634	+	31.8000i	−0.679362	+	1.22308i
$677$	23.2815	−	23.2815i	0.894781	−	0.894781i	−0.100187	−	0.994969i	$-0.531944\pi$
$677$	23.2815	−	23.2815i	0.894781	−	0.894781i	0.994969	+	0.100187i	$0.0319441\pi$
$678$	−1.44310	−	0.373885i	−0.0554220	−	0.0143590i
$679$	1.05194			0.0403696
$680$	28.5088	+	32.8235i	1.09326	+	1.25872i
$681$	−3.01823			−0.115659
$682$	−0.847611	−	0.219603i	−0.0324567	−	0.00840901i
$683$	−4.71657	+	4.71657i	−0.180474	+	0.180474i	−0.791563	−	0.611088i	$-0.790732\pi$
$683$	−4.71657	+	4.71657i	−0.180474	+	0.180474i	0.611088	+	0.791563i	$0.290732\pi$
$684$	1.51962	−	2.73583i	0.0581042	−	0.104607i
$685$	−37.3131	−	3.55924i	−1.42566	−	0.135991i
$686$	−24.4873	+	14.4097i	−0.934930	+	0.550165i
$687$	18.1411	+	18.1411i	0.692125	+	0.692125i
$688$	13.9361	+	3.24308i	0.531309	+	0.123641i
$689$			17.5699i			0.669358i
$690$	−20.1351	+	9.40033i	−0.766531	+	0.357864i
$691$		−	23.7358i		−	0.902954i	−0.892283	−	0.451477i	$-0.850897\pi$
$691$		−	23.7358i		−	0.902954i	0.892283	−	0.451477i	$-0.149103\pi$
$692$	−0.255393	−	0.893610i	−0.00970859	−	0.0339700i
$693$	−0.451592	−	0.451592i	−0.0171546	−	0.0171546i
$694$	25.0831	+	42.6253i	0.952143	+	1.61804i
$695$	−6.48678	−	7.85480i	−0.246057	−	0.297949i
$696$	−0.771798	−	31.0292i	−0.0292549	−	1.17616i
$697$	11.0507	−	11.0507i	0.418575	−	0.418575i
$698$	10.1374	−	39.1280i	0.383708	−	1.48102i
$699$	−32.9800			−1.24742
$700$	22.5577	−	1.99424i	0.852601	−	0.0753752i
$701$	−15.2215			−0.574910			−0.287455	−	0.957794i	$-0.592809\pi$
$701$	−15.2215			−0.574910			−0.287455	+	0.957794i	$0.592809\pi$
$702$	−10.7178	+	41.3682i	−0.404519	+	1.56134i
$703$	−1.63332	+	1.63332i	−0.0616018	+	0.0616018i
$704$	7.99011	−	0.397727i	0.301138	−	0.0149899i
$705$	27.9794	+	33.8800i	1.05376	+	1.27600i
$706$	24.3971	+	41.4594i	0.918196	+	1.56035i
$707$	−22.7146	−	22.7146i	−0.854271	−	0.854271i
$708$	3.25418	−	0.930042i	0.122300	−	0.0349531i
$709$		−	41.2498i		−	1.54917i	−0.632471	−	0.774584i	$-0.717959\pi$
$709$		−	41.2498i		−	1.54917i	0.632471	−	0.774584i	$-0.282041\pi$
$710$	−33.2922	+	15.5428i	−1.24943	+	0.583312i
$711$		−	0.821986i		−	0.0308269i
$712$	20.8566	−	21.9206i	0.781634	−	0.821510i
$713$	−1.86604	−	1.86604i	−0.0698839	−	0.0698839i
$714$	31.2804	−	18.4071i	1.17064	−	0.688870i
$715$	−12.4312	−	1.18579i	−0.464901	−	0.0443461i
$716$	−15.9471	−	8.85786i	−0.595971	−	0.331034i
$717$	−18.4750	+	18.4750i	−0.689961	+	0.689961i
$718$	22.7345	+	5.89016i	0.848446	+	0.219819i
$719$	39.9285			1.48908			0.744541	−	0.667577i	$-0.232669\pi$
$719$	39.9285			1.48908			0.744541	+	0.667577i	$0.232669\pi$
$720$	2.39140	+	0.802431i	0.0891224	+	0.0299048i
$721$	15.6496			0.582823
$722$	16.1347	+	4.18025i	0.600472	+	0.155573i
$723$	14.0619	−	14.0619i	0.522968	−	0.522968i
$724$	5.51502	+	3.06333i	0.204964	+	0.113848i
$725$	32.6816	+	6.29213i	1.21376	+	0.233684i
$726$	−2.00942	+	1.18246i	−0.0745765	+	0.0438850i
$727$	20.9135	+	20.9135i	0.775638	+	0.775638i	0.979086	−	0.203448i	$-0.0652148\pi$
$727$	20.9135	+	20.9135i	0.775638	+	0.775638i	−0.203448	+	0.979086i	$0.565215\pi$
$728$	24.6568	−	25.9147i	0.913843	−	0.960463i
$729$			29.0385i			1.07550i
$730$	5.46207	−	15.0282i	0.202160	−	0.556219i
$731$			24.5895i			0.909475i
$732$	−14.3357	+	4.09713i	−0.529862	+	0.151434i
$733$	−22.5039	−	22.5039i	−0.831202	−	0.831202i	0.156479	−	0.987681i	$-0.449986\pi$
$733$	−22.5039	−	22.5039i	−0.831202	−	0.831202i	−0.987681	+	0.156479i	$0.949986\pi$
$734$	−15.2894	−	25.9822i	−0.564342	−	0.959022i
$735$	−0.655210	+	6.86887i	−0.0241678	+	0.253362i
$736$	21.3627	+	11.1801i	0.787439	+	0.412105i
$737$	3.45235	−	3.45235i	0.127169	−	0.127169i
$738$	0.227412	−	0.877753i	0.00837115	−	0.0323105i
$739$	−47.7709			−1.75728			−0.878641	−	0.477483i	$-0.841549\pi$
$739$	−47.7709			−1.75728			−0.878641	+	0.477483i	$0.841549\pi$
$740$	−1.53436	−	1.05449i	−0.0564041	−	0.0387639i
$741$	−51.0849			−1.87665
$742$	2.52701	−	9.75362i	0.0927694	−	0.358067i
$743$	−31.2753	+	31.2753i	−1.14738	+	1.14738i	−0.160311	+	0.987066i	$0.551250\pi$
$743$	−31.2753	+	31.2753i	−1.14738	+	1.14738i	−0.987066	+	0.160311i	$0.948750\pi$
$744$	−0.0717888	−	2.88618i	−0.00263190	−	0.105812i
$745$	−6.23313	+	5.14754i	−0.228364	+	0.188591i
$746$	−3.81048	−	6.47538i	−0.139511	−	0.237080i
$747$	−2.79254	−	2.79254i	−0.102174	−	0.102174i
$748$	3.77796	+	13.2189i	0.138136	+	0.483332i
$749$		−	17.4305i		−	0.636897i
$750$	13.3755	−	22.3739i	0.488403	−	0.816980i
$751$			20.3844i			0.743836i	0.928266	+	0.371918i	$0.121300\pi$
$751$			20.3844i			0.743836i	−0.928266	+	0.371918i	$0.878700\pi$
$752$	10.8062	−	46.4363i	0.394063	−	1.69336i
$753$	16.8173	+	16.8173i	0.612855	+	0.612855i
$754$	45.3084	−	26.6620i	1.65003	−	0.970973i
$755$	3.42767	−	2.83070i	0.124746	−	0.103020i
$756$	11.8997	−	21.4234i	0.432787	−	0.779161i
$757$	7.90318	−	7.90318i	0.287246	−	0.287246i	−0.548744	−	0.835990i	$-0.684894\pi$
$757$	7.90318	−	7.90318i	0.287246	−	0.287246i	0.835990	+	0.548744i	$0.184894\pi$
$758$	4.71951	+	1.22275i	0.171420	+	0.0444123i
$759$	−7.02702			−0.255065
$760$	−2.46255	+	35.0052i	−0.0893260	+	1.26977i
$761$	−34.4458			−1.24866			−0.624329	−	0.781161i	$-0.714628\pi$
$761$	−34.4458			−1.24866			−0.624329	+	0.781161i	$0.714628\pi$
$762$	49.1864	+	12.7434i	1.78184	+	0.461645i
$763$	−1.64652	+	1.64652i	−0.0596079	+	0.0596079i
$764$	15.8480	−	28.5316i	0.573359	−	1.03224i
$765$	−0.411629	+	4.31529i	−0.0148825	+	0.156020i
$766$	−35.5067	+	20.8941i	−1.28291	+	0.754936i
$767$	4.05339	+	4.05339i	0.146359	+	0.146359i
$768$	8.50057	+	24.9709i	0.306738	+	0.901058i
$769$		−	16.4727i		−	0.594021i	−0.954874	−	0.297011i	$-0.904010\pi$
$769$		−	16.4727i		−	0.594021i	0.954874	−	0.297011i	$-0.0959897\pi$
$770$	6.73043	+	2.44621i	0.242548	+	0.0881552i
$771$		−	36.5615i		−	1.31673i
$772$	−2.18016	−	7.62828i	−0.0784655	−	0.274548i
$773$	−7.75097	−	7.75097i	−0.278783	−	0.278783i	0.553840	−	0.832623i	$-0.313162\pi$
$773$	−7.75097	−	7.75097i	−0.278783	−	0.278783i	−0.832623	+	0.553840i	$0.813162\pi$
$774$	0.723553	+	1.22958i	0.0260076	+	0.0441963i
$775$	3.03987	+	0.585262i	0.109196	+	0.0210232i
$776$	−1.31345	+	0.0326700i	−0.0471503	+	0.00117278i
$777$	−1.09902	+	1.09902i	−0.0394271	+	0.0394271i
$778$	0.201521	−	0.777819i	0.00722486	−	0.0278862i
$779$	12.6143			0.451954
$780$	−7.50427	−	40.4854i	−0.268696	−	1.44961i
$781$	−11.6187			−0.415751
$782$	−10.3923	+	40.1117i	−0.371628	+	1.43439i
$783$	25.4675	−	25.4675i	0.910133	−	0.910133i
$784$	6.35620	−	3.95636i	0.227007	−	0.141298i
$785$	9.38918	+	0.895618i	0.335114	+	0.0319660i
$786$	−5.58766	−	9.49545i	−0.199305	−	0.338691i
$787$	−17.3842	−	17.3842i	−0.619682	−	0.619682i	0.325768	−	0.945450i	$-0.394377\pi$
$787$	−17.3842	−	17.3842i	−0.619682	−	0.619682i	−0.945450	+	0.325768i	$0.894377\pi$
$788$	−45.7695	+	13.0809i	−1.63047	+	0.465987i
$789$		−	0.917790i		−	0.0326742i
$790$	3.89906	+	8.35164i	0.138722	+	0.297138i
$791$			1.44794i			0.0514829i
$792$	0.577886	+	0.549836i	0.0205343	+	0.0195376i
$793$	−17.8564	−	17.8564i	−0.634100	−	0.634100i
$794$	27.6960	−	16.2979i	0.982896	−	0.578391i
$795$	−7.38519	−	8.94268i	−0.261926	−	0.317164i
$796$	−16.5271	−	9.18003i	−0.585788	−	0.325377i
$797$	−13.0904	+	13.0904i	−0.463687	+	0.463687i	−0.899862	−	0.436175i	$-0.856333\pi$
$797$	−13.0904	+	13.0904i	−0.463687	+	0.463687i	0.436175	+	0.899862i	$0.356333\pi$
$798$	28.3590	+	7.34736i	1.00390	+	0.260094i
$799$	81.9343			2.89863
$800$	−28.1037	+	3.19059i	−0.993617	+	0.112804i
$801$	3.01691			0.106597
$802$	−45.4648	−	11.7792i	−1.60542	−	0.415938i
$803$	3.57548	−	3.57548i	0.126176	−	0.126176i
$804$	14.0732	+	7.81699i	0.496323	+	0.275684i
$805$	13.7435	+	16.6420i	0.484396	+	0.586552i
$806$	4.21436	−	2.47996i	0.148444	−	0.0873530i
$807$	14.6076	+	14.6076i	0.514210	+	0.514210i
$808$	29.0670	+	27.6562i	1.02258	+	0.972940i
$809$			4.48181i			0.157572i	0.996892	+	0.0787860i	$0.0251044\pi$
$809$			4.48181i			0.157572i	−0.996892	+	0.0787860i	$0.974896\pi$
$810$	−10.8015	−	23.1363i	−0.379525	−	0.812928i
$811$			30.4210i			1.06822i	0.845414	+	0.534112i	$0.179354\pi$
$811$			30.4210i			1.06822i	−0.845414	+	0.534112i	$0.820646\pi$
$812$	−28.9869	+	8.28444i	−1.01724	+	0.290727i
$813$	6.81803	+	6.81803i	0.239119	+	0.239119i
$814$	−0.298589	−	0.507410i	−0.0104655	−	0.0177847i
$815$	−1.81541	−	0.173169i	−0.0635912	−	0.00606586i
$816$	−38.4852	+	23.9547i	−1.34725	+	0.838583i
$817$	−14.0344	+	14.0344i	−0.491000	+	0.491000i
$818$	4.01308	−	15.4895i	0.140314	−	0.541577i
$819$	3.56662			0.124628
$820$	1.85301	+	9.99697i	0.0647101	+	0.349109i
$821$	30.7984			1.07487			0.537436	−	0.843304i	$-0.319393\pi$
$821$	30.7984			1.07487			0.537436	+	0.843304i	$0.319393\pi$
$822$	9.80200	−	37.8333i	0.341884	−	1.31959i
$823$	0.0108587	−	0.0108587i	0.000378511	−	0.000378511i	−0.706918	−	0.707296i	$-0.749915\pi$
$823$	0.0108587	−	0.0108587i	0.000378511	−	0.000378511i	0.707296	+	0.706918i	$0.249915\pi$
$824$	−19.5402	+	0.486030i	−0.680716	+	0.0169317i
$825$	6.82564	−	4.62170i	0.237638	−	0.160907i
$826$	−1.66719	−	2.83316i	−0.0580089	−	0.0985781i
$827$	36.1314	+	36.1314i	1.25641	+	1.25641i	0.952794	+	0.303617i	$0.0981943\pi$
$827$	36.1314	+	36.1314i	1.25641	+	1.25641i	0.303617	+	0.952794i	$0.401806\pi$
$828$	0.660640	+	2.31155i	0.0229588	+	0.0803321i
$829$			40.0091i			1.38957i	0.719216	+	0.694786i	$0.244501\pi$
$829$			40.0091i			1.38957i	−0.719216	+	0.694786i	$0.755499\pi$
$830$	41.6194	+	15.1268i	1.44463	+	0.525057i
$831$		−	9.66275i		−	0.335197i
$832$	−29.9818	+	33.1230i	−1.03943	+	1.14833i
$833$	9.09798	+	9.09798i	0.315226	+	0.315226i
$834$	9.15449	−	5.38702i	0.316994	−	0.186537i
$835$	−2.22724	+	23.3492i	−0.0770770	+	0.808033i
$836$	−5.38840	+	9.70092i	−0.186362	+	0.335513i
$837$	2.36885	−	2.36885i	0.0818796	−	0.0818796i
$838$	−40.7304	−	10.5526i	−1.40701	−	0.364533i
$839$	−18.2627			−0.630499			−0.315250	−	0.949009i	$-0.602088\pi$
$839$	−18.2627			−0.630499			−0.315250	+	0.949009i	$0.602088\pi$
$840$	−1.65699	+	23.5541i	−0.0571715	+	0.812694i
$841$	−15.3071			−0.527829
$842$	34.0235	+	8.81494i	1.17253	+	0.303783i
$843$	−2.64436	+	2.64436i	−0.0910765	+	0.0910765i
$844$	−21.1919	+	38.1524i	−0.729454	+	1.31326i
$845$	31.3589	−	25.8973i	1.07878	−	0.890894i
$846$	4.09706	−	2.41094i	0.140860	−	0.0828899i
$847$	1.60129	+	1.60129i	0.0550210	+	0.0550210i
$848$	−2.85232	+	12.2569i	−0.0979491	+	0.420904i
$849$		−	25.8853i		−	0.888380i
$850$	−16.2872	−	45.7973i	−0.558646	−	1.57084i
$851$		−	1.77443i		−	0.0608268i
$852$	−10.5274	−	36.8351i	−0.360664	−	1.26195i
$853$	−39.8875	−	39.8875i	−1.36572	−	1.36572i	−0.866441	−	0.499280i	$-0.833598\pi$
$853$	−39.8875	−	39.8875i	−1.36572	−	1.36572i	−0.499280	−	0.866441i	$-0.666402\pi$
$854$	7.34448	+	12.4809i	0.251323	+	0.427089i
$855$	−2.69787	+	2.22800i	−0.0922653	+	0.0761961i
$856$	0.541338	+	21.7638i	0.0185026	+	0.743873i
$857$	−7.72584	+	7.72584i	−0.263910	+	0.263910i	−0.826640	−	0.562731i	$-0.809751\pi$
$857$	−7.72584	+	7.72584i	−0.263910	+	0.263910i	0.562731	+	0.826640i	$0.309751\pi$
$858$	3.26563	−	12.6045i	0.111487	−	0.430311i
$859$	27.5101			0.938633			0.469316	−	0.883030i	$-0.344500\pi$
$859$	27.5101			0.938633			0.469316	+	0.883030i	$0.344500\pi$
$860$	−13.1840	−	9.06076i	−0.449571	−	0.308969i
$861$	8.48784			0.289265
$862$	0.349668	−	1.34963i	0.0119097	−	0.0459686i
$863$	−20.6962	+	20.6962i	−0.704506	+	0.704506i	−0.965374	−	0.260869i	$-0.915991\pi$
$863$	−20.6962	+	20.6962i	−0.704506	+	0.704506i	0.260869	+	0.965374i	$0.415991\pi$
$864$	−14.1927	+	27.1189i	−0.482844	+	0.922605i
$865$	−0.0986691	+	1.03439i	−0.00335485	+	0.0351704i
$866$	−18.5178	−	31.4684i	−0.629259	−	1.06934i
$867$	−35.2681	−	35.2681i	−1.19777	−	1.19777i
$868$	−2.69622	+	0.770577i	−0.0915156	+	0.0261551i
$869$			2.91466i			0.0988732i
$870$	−11.8541	+	32.6150i	−0.401891	+	1.10575i
$871$			27.2662i			0.923882i
$872$	2.00471	−	2.10698i	0.0678882	−	0.0713515i
$873$	−0.0926330	−	0.0926330i	−0.00313515	−	0.00313515i
$874$	−28.8250	+	16.9622i	−0.975019	+	0.573756i
$875$	−24.2952	−	7.12586i	−0.821327	−	0.240898i
$876$	14.5751	+	8.09578i	0.492447	+	0.273531i
$877$	−2.55821	+	2.55821i	−0.0863846	+	0.0863846i	−0.748979	−	0.662594i	$-0.769455\pi$
$877$	−2.55821	+	2.55821i	−0.0863846	+	0.0863846i	0.662594	+	0.748979i	$0.269455\pi$
$878$	−51.4021	−	13.3175i	−1.73474	−	0.449443i
$879$	15.8245			0.533747
$880$	−8.47963	−	2.84532i	−0.285848	−	0.0959158i
$881$	−9.02131			−0.303936			−0.151968	−	0.988385i	$-0.548561\pi$
$881$	−9.02131			−0.303936			−0.151968	+	0.988385i	$0.548561\pi$
$882$	0.722648	+	0.187227i	0.0243328	+	0.00630425i
$883$	17.4534	−	17.4534i	0.587355	−	0.587355i	−0.349560	−	0.936914i	$-0.613669\pi$
$883$	17.4534	−	17.4534i	0.587355	−	0.587355i	0.936914	+	0.349560i	$0.113669\pi$
$884$	−67.1197	−	37.2818i	−2.25748	−	1.25392i
$885$	−3.76686	−	0.359315i	−0.126622	−	0.0120782i
$886$	−11.3859	+	6.70010i	−0.382516	+	0.225094i
$887$	−36.0890	−	36.0890i	−1.21175	−	1.21175i	−0.970451	−	0.241299i	$-0.922426\pi$
$887$	−36.0890	−	36.0890i	−1.21175	−	1.21175i	−0.241299	−	0.970451i	$-0.577574\pi$
$888$	1.33811	−	1.40638i	0.0449041	−	0.0471949i
$889$		−	49.3514i		−	1.65519i
$890$	−30.6528	+	14.3106i	−1.02748	+	0.479693i
$891$		−	8.07441i		−	0.270503i
$892$	3.96021	−	1.13183i	0.132598	−	0.0378963i
$893$	46.7637	+	46.7637i	1.56489	+	1.56489i
$894$	−4.27484	−	7.26449i	−0.142972	−	0.242961i
$895$	12.9870	+	15.7259i	0.434107	+	0.525658i
$896$	21.4079	−	14.0755i	0.715187	−	0.470231i
$897$	27.7492	−	27.7492i	0.926520	−	0.926520i
$898$	−6.53061	+	25.2065i	−0.217929	+	0.841152i
$899$	−4.12122			−0.137450
$900$	−2.16203	−	1.81081i	−0.0720676	−	0.0603602i
$901$	−21.6267			−0.720488
$902$	−0.806375	+	3.11241i	−0.0268493	+	0.103632i
$903$	−9.44337	+	9.44337i	−0.314256	+	0.314256i
$904$	−0.0449687	−	1.80791i	−0.00149564	−	0.0601302i
$905$	−4.49132	−	5.43851i	−0.149296	−	0.180782i
$906$	2.35078	+	3.99483i	0.0780996	+	0.132719i
$907$	−1.07824	−	1.07824i	−0.0358024	−	0.0358024i	0.688979	−	0.724781i	$-0.258059\pi$
$907$	−1.07824	−	1.07824i	−0.0358024	−	0.0358024i	−0.724781	+	0.688979i	$0.758059\pi$
$908$	−1.00617	−	3.52054i	−0.0333909	−	0.116833i
$909$			4.00047i			0.132687i
$910$	−36.2380	+	16.9181i	−1.20128	+	0.560831i
$911$			20.9099i			0.692774i	0.938092	+	0.346387i	$0.112592\pi$
$911$			20.9099i			0.692774i	−0.938092	+	0.346387i	$0.887408\pi$
$912$	−35.6373	−	8.29321i	−1.18007	−	0.274616i
$913$	9.90199	+	9.90199i	0.327708	+	0.327708i
$914$	27.8767	−	16.4042i	0.922079	−	0.542603i
$915$	16.5942	+	1.58289i	0.548587	+	0.0523288i
$916$	−15.1126	+	27.2078i	−0.499336	+	0.898970i
$917$	−7.56685	+	7.56685i	−0.249880	+	0.249880i
$918$	−50.9199	−	13.1925i	−1.68061	−	0.435419i
$919$	31.7187			1.04630			0.523151	−	0.852240i	$-0.324756\pi$
$919$	31.7187			1.04630			0.523151	+	0.852240i	$0.324756\pi$
$920$	−17.6771	−	20.3524i	−0.582797	−	0.670999i
$921$	−14.5944			−0.480900
$922$	13.2169	+	3.42429i	0.435276	+	0.112773i
$923$	45.8816	−	45.8816i	1.51021	−	1.51021i
$924$	−3.62572	+	6.52750i	−0.119277	+	0.214739i
$925$	1.16705	+	1.72358i	0.0383725	+	0.0566711i
$926$	22.7537	−	13.3895i	0.747731	−	0.440007i
$927$	−1.37810	−	1.37810i	−0.0452627	−	0.0452627i
$928$	35.9360	−	11.2442i	1.17966	−	0.369110i
$929$		−	44.0057i		−	1.44378i	−0.692008	−	0.721890i	$-0.743274\pi$
$929$		−	44.0057i		−	1.44378i	0.692008	−	0.721890i	$-0.256726\pi$
$930$	−1.10261	+	3.03368i	−0.0361559	+	0.0994784i
$931$			10.3853i			0.340363i
$932$	−10.9943	−	38.4687i	−0.360131	−	1.26008i
$933$	−9.12301	−	9.12301i	−0.298674	−	0.298674i
$934$	22.8429	+	38.8183i	0.747442	+	1.27017i
$935$	1.45959	−	15.3015i	0.0477336	−	0.500413i
$936$	−4.45330	+	0.110768i	−0.145561	+	0.00362057i
$937$	0.232674	−	0.232674i	0.00760114	−	0.00760114i	−0.703296	−	0.710897i	$-0.748289\pi$
$937$	0.232674	−	0.232674i	0.00760114	−	0.00760114i	0.710897	+	0.703296i	$0.248289\pi$
$938$	3.92161	−	15.1364i	0.128045	−	0.494222i
$939$	50.1908			1.63791
$940$	−30.1912	+	43.9302i	−0.984730	+	1.43285i
$941$	−11.3789			−0.370941			−0.185471	−	0.982650i	$-0.559381\pi$
$941$	−11.3789			−0.370941			−0.185471	+	0.982650i	$0.559381\pi$
$942$	−2.46650	+	9.52007i	−0.0803629	+	0.310181i
$943$	−6.85206	+	6.85206i	−0.223134	+	0.223134i
$944$	2.16965	+	3.48572i	0.0706161	+	0.113450i
$945$	−21.1262	+	17.4468i	−0.687234	+	0.567543i
$946$	−2.56563	−	4.35994i	−0.0834159	−	0.141754i
$947$	24.4851	+	24.4851i	0.795658	+	0.795658i	0.982408	−	0.186750i	$-0.0597953\pi$
$947$	24.4851	+	24.4851i	0.795658	+	0.795658i	−0.186750	+	0.982408i	$0.559795\pi$
$948$	−9.24043	+	2.64091i	−0.300115	+	0.0857727i
$949$			28.2387i			0.916667i
$950$	16.8428	−	35.4345i	0.546453	−	1.14965i
$951$		−	1.64660i		−	0.0533947i
$952$	31.8983	+	30.3500i	1.03383	+	0.983648i
$953$	19.6436	+	19.6436i	0.636318	+	0.636318i	0.949645	−	0.313327i	$-0.101444\pi$
$953$	19.6436	+	19.6436i	0.636318	+	0.636318i	−0.313327	+	0.949645i	$0.601444\pi$
$954$	−1.08142	+	0.636371i	−0.0350124	+	0.0206033i
$955$	−28.1358	+	23.2355i	−0.910452	+	0.751885i
$956$	−27.7086	−	15.3908i	−0.896159	−	0.497774i
$957$	−7.75970	+	7.75970i	−0.250835	+	0.250835i
$958$	−3.72566	−	0.965258i	−0.120370	−	0.0311861i
$959$	−37.9602			−1.22580
$960$	1.33741	−	29.4613i	0.0431646	−	0.950858i
$961$	30.6167			0.987634
$962$	3.18284	+	0.824623i	0.102619	+	0.0265869i
$963$	−1.53492	+	1.53492i	−0.0494621	+	0.0494621i
$964$	21.0899	+	11.7144i	0.679260	+	0.377297i
$965$	−0.842286	+	8.83007i	−0.0271141	+	0.284250i
$966$	−19.3956	+	11.4135i	−0.624044	+	0.367222i
$967$	12.5781	+	12.5781i	0.404486	+	0.404486i	0.879810	−	0.475325i	$-0.157669\pi$
$967$	12.5781	+	12.5781i	0.404486	+	0.404486i	−0.475325	+	0.879810i	$0.657669\pi$
$968$	−2.04911	−	1.94965i	−0.0658610	−	0.0626641i
$969$		−	62.8802i		−	2.02000i
$970$	1.38058	+	0.501779i	0.0443278	+	0.0161112i
$971$			29.3778i			0.942779i	0.881925	+	0.471390i	$0.156247\pi$
$971$			29.3778i			0.942779i	−0.881925	+	0.471390i	$0.843753\pi$
$972$	−5.61667	+	1.60524i	−0.180155	+	0.0514881i
$973$	−7.29515	−	7.29515i	−0.233872	−	0.233872i
$974$	27.8335	+	47.2991i	0.891842	+	1.51556i
$975$	−8.70322	+	45.2048i	−0.278726	+	1.44771i
$976$	−9.55798	−	15.3557i	−0.305944	−	0.491523i
$977$	8.15488	−	8.15488i	0.260898	−	0.260898i	−0.564521	−	0.825419i	$-0.690939\pi$
$977$	8.15488	−	8.15488i	0.260898	−	0.260898i	0.825419	+	0.564521i	$0.190939\pi$
$978$	0.476902	−	1.84072i	0.0152496	−	0.0588598i
$979$	−10.6976			−0.341897
$980$	−8.23044	+	1.52558i	−0.262912	+	0.0487327i
$981$	0.289982			0.00925842
$982$	13.0181	−	50.2465i	0.415424	−	1.60343i
$983$	−18.8089	+	18.8089i	−0.599912	+	0.599912i	−0.940289	−	0.340377i	$-0.889445\pi$
$983$	−18.8089	+	18.8089i	−0.599912	+	0.599912i	0.340377	+	0.940289i	$0.389445\pi$
$984$	−10.5980	+	0.263607i	−0.337851	+	0.00840347i
$985$	52.9802	+	5.05369i	1.68809	+	0.161024i
$986$	32.8181	+	55.7699i	1.04514	+	1.77608i
$987$	31.4661	+	31.4661i	1.00158	+	1.00158i
$988$	−17.0298	−	59.5867i	−0.541791	−	1.89571i
$989$		−	15.2469i		−	0.484822i
$990$	−0.377266	−	0.808090i	−0.0119903	−	0.0256828i
$991$		−	3.31013i		−	0.105150i	−0.998617	−	0.0525748i	$-0.983257\pi$
$991$		−	3.31013i		−	0.105150i	0.998617	−	0.0525748i	$-0.0167428\pi$
$992$	3.34258	−	1.04588i	0.106127	−	0.0332068i
$993$	−0.892088	−	0.892088i	−0.0283096	−	0.0283096i
$994$	−32.0694	+	18.8714i	−1.01718	+	0.598566i
$995$	13.4593	+	16.2978i	0.426690	+	0.516676i
$996$	−22.4206	+	40.3645i	−0.710423	+	1.27900i
$997$	19.6314	−	19.6314i	0.621734	−	0.621734i	−0.324241	−	0.945975i	$-0.605109\pi$
$997$	19.6314	−	19.6314i	0.621734	−	0.621734i	0.945975	+	0.324241i	$0.105109\pi$
$998$	−37.3243	−	9.67012i	−1.18148	−	0.306102i
$999$	2.25256			0.0712678

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.l.c.23.14	✓	28
4.3	odd	2		220.2.l.d.23.5	yes	28
5.2	odd	4		220.2.l.d.67.5	yes	28
20.7	even	4	inner	220.2.l.c.67.14	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.14	✓	28	1.1	even	1	trivial
220.2.l.c.67.14	yes	28	20.7	even	4	inner
220.2.l.d.23.5	yes	28	4.3	odd	2
220.2.l.d.67.5	yes	28	5.2	odd	4

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Classical	Maass
Hilbert	Bianchi

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

Introduction

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Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	220.2.l.c.23.14

Level	$220$
Weight	$2$
Character	220.23
Analytic conductor	$1.757$
Analytic rank	$0$
Dimension	$28$
Inner twists	$2$