LMFDB - Embedded newform 722.2.e.q.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, not 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.6053445140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} + 17x^{6} + 4x^{3} + 1 $ x^12 - 4x^9 + 17x^6 + 4*x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			99.1
Root			$0.107320 + 0.608645i$ of defining polynomial
Character	$\chi$	$=$	722.99
Dual form			722.2.e.q.423.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(-0.214641 - 1.21729i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-2.77157 + 2.32563i) q^{5} +(0.214641 - 1.21729i) q^{6} +(1.61803 - 2.80252i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.38336 - 0.503500i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(-0.214641 - 1.21729i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-2.77157 + 2.32563i) q^{5} +(0.214641 - 1.21729i) q^{6} +(1.61803 - 2.80252i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.38336 - 0.503500i) q^{9} +(-3.39984 + 1.23744i) q^{10} +(1.61803 + 2.80252i) q^{11} +(0.618034 - 1.07047i) q^{12} +(0.239976 - 1.36097i) q^{13} +(2.47897 - 2.08010i) q^{14} +(3.42585 + 2.87463i) q^{15} +(0.173648 + 0.984808i) q^{16} +(3.17801 + 1.15670i) q^{17} +1.47214 q^{18} -3.61803 q^{20} +(-3.75877 - 1.36808i) q^{21} +(0.561937 + 3.18690i) q^{22} +(4.01106 + 3.36568i) q^{23} +(0.946883 - 0.794529i) q^{24} +(1.40484 - 7.96726i) q^{25} +(0.690983 - 1.19682i) q^{26} +(-2.76393 - 4.78727i) q^{27} +(3.04091 - 1.10680i) q^{28} +(8.54197 - 3.10902i) q^{29} +(2.23607 + 3.87298i) q^{30} +(0.618034 - 1.07047i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(3.06418 - 2.57115i) q^{33} +(2.59074 + 2.17389i) q^{34} +(2.03311 + 11.5303i) q^{35} +(1.38336 + 0.503500i) q^{36} +8.38197 q^{37} -1.70820 q^{39} +(-3.39984 - 1.23744i) q^{40} +(0.148313 + 0.841126i) q^{41} +(-3.06418 - 2.57115i) q^{42} +(-7.07524 + 5.93683i) q^{43} +(-0.561937 + 3.18690i) q^{44} +(-2.66312 + 4.61266i) q^{45} +(2.61803 + 4.53457i) q^{46} +(-4.20243 + 1.52956i) q^{47} +(1.16152 - 0.422760i) q^{48} +(-1.73607 - 3.00696i) q^{49} +(4.04508 - 7.00629i) q^{50} +(0.725908 - 4.11683i) q^{51} +(1.05865 - 0.888311i) q^{52} +(-4.66534 - 3.91469i) q^{53} +(-0.959904 - 5.44388i) q^{54} +(-11.0021 - 4.00444i) q^{55} +3.23607 q^{56} +9.09017 q^{58} +(0.443663 + 0.161480i) q^{59} +(0.776578 + 4.40419i) q^{60} +(1.05865 + 0.888311i) q^{61} +(0.946883 - 0.794529i) q^{62} +(0.827248 - 4.69156i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.50000 + 4.33013i) q^{65} +(3.75877 - 1.36808i) q^{66} +(-11.0021 + 4.00444i) q^{67} +(1.69098 + 2.92887i) q^{68} +(3.23607 - 5.60503i) q^{69} +(-2.03311 + 11.5303i) q^{70} +(2.25544 - 1.89254i) q^{71} +(1.12772 + 0.946271i) q^{72} +(-0.975561 - 5.53268i) q^{73} +(7.87647 + 2.86680i) q^{74} -10.0000 q^{75} +10.4721 q^{77} +(-1.60519 - 0.584240i) q^{78} +(-0.479952 - 2.72194i) q^{79} +(-2.77157 - 2.32563i) q^{80} +(-1.85108 + 1.55324i) q^{81} +(-0.148313 + 0.841126i) q^{82} +(0.236068 - 0.408882i) q^{83} +(-2.00000 - 3.46410i) q^{84} +(-11.4981 + 4.18498i) q^{85} +(-8.67906 + 3.15892i) q^{86} +(-5.61803 - 9.73072i) q^{87} +(-1.61803 + 2.80252i) q^{88} +(1.53750 - 8.71959i) q^{89} +(-4.08013 + 3.42364i) q^{90} +(-3.42585 - 2.87463i) q^{91} +(0.909234 + 5.15652i) q^{92} +(-1.43572 - 0.522560i) q^{93} -4.47214 q^{94} +1.23607 q^{96} +(-8.09830 - 2.94754i) q^{97} +(-0.602930 - 3.41939i) q^{98} +(3.64938 + 3.06220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^7 + 6 * q^8	$ 12 q + 6 q^{7} + 6 q^{8} + 6 q^{11} - 6 q^{12} - 36 q^{18} - 30 q^{20} + 15 q^{26} - 60 q^{27} - 6 q^{31} + 114 q^{37} + 60 q^{39} + 15 q^{45} + 18 q^{46} + 6 q^{49} + 15 q^{50} + 12 q^{56} + 42 q^{58} - 6 q^{64} + 30 q^{65} + 27 q^{68} + 12 q^{69} - 120 q^{75} + 72 q^{77} - 24 q^{83} - 24 q^{84} - 54 q^{87} - 6 q^{88} - 12 q^{96}+O(q^{100}) $ 12 * q + 6 * q^7 + 6 * q^8 + 6 * q^11 - 6 * q^12 - 36 * q^18 - 30 * q^20 + 15 * q^26 - 60 * q^27 - 6 * q^31 + 114 * q^37 + 60 * q^39 + 15 * q^45 + 18 * q^46 + 6 * q^49 + 15 * q^50 + 12 * q^56 + 42 * q^58 - 6 * q^64 + 30 * q^65 + 27 * q^68 + 12 * q^69 - 120 * q^75 + 72 * q^77 - 24 * q^83 - 24 * q^84 - 54 * q^87 - 6 * q^88 - 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	−0.214641	−	1.21729i	−0.123923	−	0.702802i	−0.981942	−	0.189184i	$-0.939416\pi$
$3$	−0.214641	−	1.21729i	−0.123923	−	0.702802i	0.858019	−	0.513618i	$-0.171695\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−2.77157	+	2.32563i	−1.23949	+	1.04005i	−0.241922	+	0.970296i	$0.577778\pi$
$5$	−2.77157	+	2.32563i	−1.23949	+	1.04005i	−0.997564	+	0.0697565i	$0.977778\pi$
$6$	0.214641	−	1.21729i	0.0876268	−	0.496956i
$7$	1.61803	−	2.80252i	0.611559	−	1.05925i	−0.379418	−	0.925225i	$-0.623876\pi$
$7$	1.61803	−	2.80252i	0.611559	−	1.05925i	0.990978	−	0.134027i	$-0.0427908\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	1.38336	−	0.503500i	0.461118	−	0.167833i
$10$	−3.39984	+	1.23744i	−1.07512	+	0.391313i
$11$	1.61803	+	2.80252i	0.487856	+	0.844991i	0.999902	−	0.0139668i	$-0.00444592\pi$
$11$	1.61803	+	2.80252i	0.487856	+	0.844991i	−0.512047	+	0.858958i	$0.671113\pi$
$12$	0.618034	−	1.07047i	0.178411	−	0.309017i
$13$	0.239976	−	1.36097i	0.0665573	−	0.377465i	−0.933275	−	0.359162i	$-0.883062\pi$
$13$	0.239976	−	1.36097i	0.0665573	−	0.377465i	0.999832	−	0.0183032i	$-0.00582641\pi$
$14$	2.47897	−	2.08010i	0.662533	−	0.555931i
$15$	3.42585	+	2.87463i	0.884552	+	0.742227i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	3.17801	+	1.15670i	0.770780	+	0.280541i	0.697323	−	0.716757i	$-0.254374\pi$
$17$	3.17801	+	1.15670i	0.770780	+	0.280541i	0.0734575	+	0.997298i	$0.476597\pi$
$18$	1.47214			0.346986
$19$		0			0
$19$		0			0
$20$	−3.61803			−0.809017
$21$	−3.75877	−	1.36808i	−0.820231	−	0.298540i
$22$	0.561937	+	3.18690i	0.119805	+	0.679450i
$23$	4.01106	+	3.36568i	0.836364	+	0.701793i	0.956743	−	0.290935i	$-0.0939664\pi$
$23$	4.01106	+	3.36568i	0.836364	+	0.701793i	−0.120379	+	0.992728i	$0.538411\pi$
$24$	0.946883	−	0.794529i	0.193282	−	0.162183i
$25$	1.40484	−	7.96726i	0.280969	−	1.59345i
$26$	0.690983	−	1.19682i	0.135513	−	0.234715i
$27$	−2.76393	−	4.78727i	−0.531919	−	0.921311i
$28$	3.04091	−	1.10680i	0.574678	−	0.209166i
$29$	8.54197	−	3.10902i	1.58620	−	0.577331i	0.609662	−	0.792661i	$-0.291305\pi$
$29$	8.54197	−	3.10902i	1.58620	−	0.577331i	0.976541	+	0.215331i	$0.0690830\pi$
$30$	2.23607	+	3.87298i	0.408248	+	0.707107i
$31$	0.618034	−	1.07047i	0.111002	−	0.192261i	−0.805172	−	0.593041i	$-0.797927\pi$
$31$	0.618034	−	1.07047i	0.111002	−	0.192261i	0.916175	+	0.400779i	$0.131261\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	3.06418	−	2.57115i	0.533405	−	0.447580i
$34$	2.59074	+	2.17389i	0.444308	+	0.372818i
$35$	2.03311	+	11.5303i	0.343658	+	1.94898i
$36$	1.38336	+	0.503500i	0.230559	+	0.0839167i
$37$	8.38197			1.37799			0.688993	−	0.724768i	$-0.258053\pi$
$37$	8.38197			1.37799			0.688993	+	0.724768i	$0.258053\pi$
$38$		0			0
$39$	−1.70820			−0.273532
$40$	−3.39984	−	1.23744i	−0.537562	−	0.195657i
$41$	0.148313	+	0.841126i	0.0231626	+	0.131362i	0.994196	−	0.107581i	$-0.0343104\pi$
$41$	0.148313	+	0.841126i	0.0231626	+	0.131362i	−0.971034	+	0.238942i	$0.923199\pi$
$42$	−3.06418	−	2.57115i	−0.472813	−	0.396737i
$43$	−7.07524	+	5.93683i	−1.07896	+	0.905358i	−0.995834	−	0.0911807i	$-0.970936\pi$
$43$	−7.07524	+	5.93683i	−1.07896	+	0.905358i	−0.0831294	+	0.996539i	$0.526491\pi$
$44$	−0.561937	+	3.18690i	−0.0847152	+	0.480444i
$45$	−2.66312	+	4.61266i	−0.396994	+	0.687614i
$46$	2.61803	+	4.53457i	0.386008	+	0.668586i
$47$	−4.20243	+	1.52956i	−0.612988	+	0.223109i	−0.629810	−	0.776749i	$-0.716867\pi$
$47$	−4.20243	+	1.52956i	−0.612988	+	0.223109i	0.0168222	+	0.999858i	$0.494645\pi$
$48$	1.16152	−	0.422760i	0.167652	−	0.0610202i
$49$	−1.73607	−	3.00696i	−0.248010	−	0.429565i
$50$	4.04508	−	7.00629i	0.572061	−	0.990839i
$51$	0.725908	−	4.11683i	0.101648	−	0.576472i
$52$	1.05865	−	0.888311i	0.146808	−	0.123187i
$53$	−4.66534	−	3.91469i	−0.640834	−	0.537723i	0.263440	−	0.964676i	$-0.415143\pi$
$53$	−4.66534	−	3.91469i	−0.640834	−	0.537723i	−0.904274	+	0.426952i	$0.859587\pi$
$54$	−0.959904	−	5.44388i	−0.130626	−	0.740819i
$55$	−11.0021	−	4.00444i	−1.48352	−	0.539959i
$56$	3.23607			0.432438
$57$		0			0
$58$	9.09017			1.19360
$59$	0.443663	+	0.161480i	0.0577600	+	0.0210229i	0.370739	−	0.928737i	$-0.379105\pi$
$59$	0.443663	+	0.161480i	0.0577600	+	0.0210229i	−0.312979	+	0.949760i	$0.601327\pi$
$60$	0.776578	+	4.40419i	0.100256	+	0.568579i
$61$	1.05865	+	0.888311i	0.135546	+	0.113737i	0.708040	−	0.706172i	$-0.249580\pi$
$61$	1.05865	+	0.888311i	0.135546	+	0.113737i	−0.572494	+	0.819909i	$0.694024\pi$
$62$	0.946883	−	0.794529i	0.120254	−	0.100905i
$63$	0.827248	−	4.69156i	0.104223	−	0.591081i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.50000	+	4.33013i	0.310087	+	0.537086i
$66$	3.75877	−	1.36808i	0.462673	−	0.168399i
$67$	−11.0021	+	4.00444i	−1.34412	+	0.489220i	−0.911108	−	0.412167i	$-0.864772\pi$
$67$	−11.0021	+	4.00444i	−1.34412	+	0.489220i	−0.433014	+	0.901387i	$0.642550\pi$
$68$	1.69098	+	2.92887i	0.205062	+	0.355177i
$69$	3.23607	−	5.60503i	0.389577	−	0.674767i
$70$	−2.03311	+	11.5303i	−0.243003	+	1.37814i
$71$	2.25544	−	1.89254i	0.267672	−	0.224603i	−0.499066	−	0.866564i	$-0.666323\pi$
$71$	2.25544	−	1.89254i	0.267672	−	0.224603i	0.766737	+	0.641961i	$0.221879\pi$
$72$	1.12772	+	0.946271i	0.132903	+	0.111519i
$73$	−0.975561	−	5.53268i	−0.114181	−	0.647552i	−0.987153	−	0.159781i	$-0.948921\pi$
$73$	−0.975561	−	5.53268i	−0.114181	−	0.647552i	0.872972	−	0.487771i	$-0.162190\pi$
$74$	7.87647	+	2.86680i	0.915621	+	0.333259i
$75$	−10.0000			−1.15470
$76$		0			0
$77$	10.4721			1.19341
$78$	−1.60519	−	0.584240i	−0.181752	−	0.0661522i
$79$	−0.479952	−	2.72194i	−0.0539988	−	0.306242i	0.945832	−	0.324658i	$-0.105249\pi$
$79$	−0.479952	−	2.72194i	−0.0539988	−	0.306242i	−0.999830	+	0.0184152i	$0.994138\pi$
$80$	−2.77157	−	2.32563i	−0.309871	−	0.260013i
$81$	−1.85108	+	1.55324i	−0.205675	+	0.172582i
$82$	−0.148313	+	0.841126i	−0.0163785	+	0.0928869i
$83$	0.236068	−	0.408882i	0.0259118	−	0.0448806i	−0.852779	−	0.522272i	$-0.825084\pi$
$83$	0.236068	−	0.408882i	0.0259118	−	0.0448806i	0.878691	+	0.477392i	$0.158418\pi$
$84$	−2.00000	−	3.46410i	−0.218218	−	0.377964i
$85$	−11.4981	+	4.18498i	−1.24715	+	0.453925i
$86$	−8.67906	+	3.15892i	−0.935888	+	0.340635i
$87$	−5.61803	−	9.73072i	−0.602316	−	1.04324i
$88$	−1.61803	+	2.80252i	−0.172483	+	0.298749i
$89$	1.53750	−	8.71959i	0.162975	−	0.924275i	−0.788154	−	0.615478i	$-0.788963\pi$
$89$	1.53750	−	8.71959i	0.162975	−	0.924275i	0.951128	−	0.308796i	$-0.0999261\pi$
$90$	−4.08013	+	3.42364i	−0.430084	+	0.360883i
$91$	−3.42585	−	2.87463i	−0.359127	−	0.301343i
$92$	0.909234	+	5.15652i	0.0947942	+	0.537604i
$93$	−1.43572	−	0.522560i	−0.148877	−	0.0541870i
$94$	−4.47214			−0.461266
$95$		0			0
$96$	1.23607			0.126156
$97$	−8.09830	−	2.94754i	−0.822258	−	0.299277i	−0.103581	−	0.994621i	$-0.533030\pi$
$97$	−8.09830	−	2.94754i	−0.822258	−	0.299277i	−0.718677	+	0.695344i	$0.755252\pi$
$98$	−0.602930	−	3.41939i	−0.0609051	−	0.345410i
$99$	3.64938	+	3.06220i	0.366777	+	0.307762i
$100$	6.19743	−	5.20026i	0.619743	−	0.520026i
$101$	−2.71204	+	15.3808i	−0.269858	+	1.53044i	0.484976	+	0.874527i	$0.338828\pi$
$101$	−2.71204	+	15.3808i	−0.269858	+	1.53044i	−0.754834	+	0.655915i	$0.772283\pi$
$102$	2.09017	−	3.62028i	0.206958	−	0.358461i
$103$	−7.32624	−	12.6894i	−0.721876	−	1.25033i	−0.960247	−	0.279151i	$-0.909947\pi$
$103$	−7.32624	−	12.6894i	−0.721876	−	1.25033i	0.238371	−	0.971174i	$-0.423386\pi$
$104$	1.29862	−	0.472660i	0.127340	−	0.0463481i
$105$	13.5994	−	4.94976i	1.32716	−	0.483047i
$106$	−3.04508	−	5.27424i	−0.295765	−	0.512280i
$107$	−4.70820	+	8.15485i	−0.455159	+	0.788359i	−0.998697	−	0.0510255i	$-0.983751\pi$
$107$	−4.70820	+	8.15485i	−0.455159	+	0.788359i	0.543538	+	0.839385i	$0.317084\pi$
$108$	0.959904	−	5.44388i	0.0923668	−	0.523838i
$109$	−8.45287	+	7.09280i	−0.809638	+	0.679367i	−0.950521	−	0.310659i	$-0.899450\pi$
$109$	−8.45287	+	7.09280i	−0.809638	+	0.679367i	0.140883	+	0.990026i	$0.455006\pi$
$110$	−8.96900	−	7.52589i	−0.855161	−	0.717565i
$111$	−1.79911	−	10.2033i	−0.170764	−	0.968452i
$112$	3.04091	+	1.10680i	0.287339	+	0.104583i
$113$	−9.85410			−0.926996			−0.463498	−	0.886098i	$-0.653406\pi$
$113$	−9.85410			−0.926996			−0.463498	+	0.886098i	$0.653406\pi$
$114$		0			0
$115$	−18.9443			−1.76656
$116$	8.54197	+	3.10902i	0.793102	+	0.288665i
$117$	−0.353277	−	2.00353i	−0.0326605	−	0.185227i
$118$	0.361677	+	0.303483i	0.0332951	+	0.0279379i
$119$	8.38380	−	7.03484i	0.768542	−	0.644883i
$120$	−0.776578	+	4.40419i	−0.0708916	+	0.402046i
$121$	0.263932	−	0.457144i	0.0239938	−	0.0415585i
$122$	0.690983	+	1.19682i	0.0625587	+	0.108355i
$123$	0.992060	−	0.361080i	0.0894510	−	0.0325575i
$124$	1.16152	−	0.422760i	0.104308	−	0.0379650i
$125$	5.59017	+	9.68246i	0.500000	+	0.866025i
$126$	2.38197	−	4.12569i	0.212202	−	0.367545i
$127$	−1.98244	+	11.2430i	−0.175913	+	0.997652i	0.761172	+	0.648550i	$0.224624\pi$
$127$	−1.98244	+	11.2430i	−0.175913	+	0.997652i	−0.937085	+	0.349102i	$0.886487\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	8.74548	+	7.33833i	0.769996	+	0.646104i
$130$	0.868241	+	4.92404i	0.0761498	+	0.431867i
$131$	−4.20243	−	1.52956i	−0.367168	−	0.133638i	0.151845	−	0.988404i	$-0.451478\pi$
$131$	−4.20243	−	1.52956i	−0.367168	−	0.133638i	−0.519014	+	0.854766i	$0.673701\pi$
$132$	4.00000			0.348155
$133$		0			0
$134$	−11.7082			−1.01143
$135$	18.7939	+	6.84040i	1.61752	+	0.588728i
$136$	0.587272	+	3.33059i	0.0503582	+	0.285595i
$137$	1.82469	+	1.53110i	0.155894	+	0.130811i	0.717398	−	0.696663i	$-0.245333\pi$
$137$	1.82469	+	1.53110i	0.155894	+	0.130811i	−0.561504	+	0.827474i	$0.689777\pi$
$138$	4.95794	−	4.16021i	0.422048	−	0.354140i
$139$	−2.43107	+	13.7873i	−0.206201	+	1.16942i	0.689338	+	0.724440i	$0.257902\pi$
$139$	−2.43107	+	13.7873i	−0.206201	+	1.16942i	−0.895539	+	0.444984i	$0.853209\pi$
$140$	−5.85410	+	10.1396i	−0.494762	+	0.856953i
$141$	2.76393	+	4.78727i	0.232765	+	0.403161i
$142$	2.76671	−	1.00700i	0.232177	−	0.0845056i
$143$	4.20243	−	1.52956i	0.351425	−	0.127908i
$144$	0.736068	+	1.27491i	0.0613390	+	0.106242i
$145$	−16.4443	+	28.4823i	−1.36562	+	2.36533i
$146$	0.975561	−	5.53268i	0.0807380	−	0.457888i
$147$	−3.28771	+	2.75871i	−0.271165	+	0.227535i
$148$	6.42096	+	5.38782i	0.527800	+	0.442876i
$149$	−2.27308	−	12.8913i	−0.186218	−	1.05610i	−0.924380	−	0.381473i	$-0.875417\pi$
$149$	−2.27308	−	12.8913i	−0.186218	−	1.05610i	0.738162	−	0.674624i	$-0.235694\pi$
$150$	−9.39693	−	3.42020i	−0.767256	−	0.279258i
$151$	14.4721			1.17773			0.588863	−	0.808233i	$-0.299576\pi$
$151$	14.4721			1.17773			0.588863	+	0.808233i	$0.299576\pi$
$152$		0			0
$153$	4.97871			0.402505
$154$	9.84059	+	3.58168i	0.792977	+	0.288620i
$155$	0.776578	+	4.40419i	0.0623763	+	0.353753i
$156$	−1.30856	−	1.09801i	−0.104769	−	0.0879113i
$157$	7.18700	−	6.03061i	0.573585	−	0.481295i	−0.309248	−	0.950981i	$-0.600077\pi$
$157$	7.18700	−	6.03061i	0.573585	−	0.481295i	0.882833	+	0.469686i	$0.155633\pi$
$158$	0.479952	−	2.72194i	0.0381829	−	0.216546i
$159$	−3.76393	+	6.51932i	−0.298499	+	0.517016i
$160$	−1.80902	−	3.13331i	−0.143015	−	0.247710i
$161$	15.9224	−	5.79528i	1.25486	−	0.456732i
$162$	−2.27068	+	0.826460i	−0.178402	+	0.0649328i
$163$	−5.32624	−	9.22531i	−0.417183	−	0.722582i	0.578472	−	0.815702i	$-0.303649\pi$
$163$	−5.32624	−	9.22531i	−0.417183	−	0.722582i	−0.995655	+	0.0931200i	$0.970316\pi$
$164$	−0.427051	+	0.739674i	−0.0333471	+	0.0577588i
$165$	−2.51306	+	14.2523i	−0.195641	+	1.10954i
$166$	0.361677	−	0.303483i	0.0280716	−	0.0235549i
$167$	−9.55421	−	8.01693i	−0.739327	−	0.620369i	0.193330	−	0.981134i	$-0.438071\pi$
$167$	−9.55421	−	8.01693i	−0.739327	−	0.620369i	−0.932657	+	0.360765i	$0.882516\pi$
$168$	−0.694593	−	3.93923i	−0.0535890	−	0.303918i
$169$	10.4214	+	3.79306i	0.801642	+	0.291774i
$170$	−12.2361			−0.938464
$171$		0			0
$172$	−9.23607			−0.704244
$173$	−1.24626	−	0.453600i	−0.0947511	−	0.0344866i	0.294210	−	0.955741i	$-0.404944\pi$
$173$	−1.24626	−	0.453600i	−0.0947511	−	0.0344866i	−0.388961	+	0.921254i	$0.627166\pi$
$174$	−1.95112	−	11.0654i	−0.147914	−	0.838863i
$175$	−20.0553	−	16.8284i	−1.51604	−	1.27211i
$176$	−2.47897	+	2.08010i	−0.186860	+	0.156794i
$177$	0.101340	−	0.574726i	0.00761716	−	0.0431991i
$178$	4.42705	−	7.66788i	0.331822	−	0.574732i
$179$	11.7082	+	20.2792i	0.875112	+	1.51574i	0.856643	+	0.515909i	$0.172546\pi$
$179$	11.7082	+	20.2792i	0.875112	+	1.51574i	0.0184691	+	0.999829i	$0.494121\pi$
$180$	−5.00503	+	1.82168i	−0.373053	+	0.135780i
$181$	−5.08976	+	1.85252i	−0.378319	+	0.137697i	−0.524178	−	0.851609i	$-0.675627\pi$
$181$	−5.08976	+	1.85252i	−0.378319	+	0.137697i	0.145860	+	0.989305i	$0.453405\pi$
$182$	−2.23607	−	3.87298i	−0.165748	−	0.287085i
$183$	0.854102	−	1.47935i	0.0631370	−	0.109357i
$184$	−0.909234	+	5.15652i	−0.0670296	+	0.380144i
$185$	−23.2312	+	19.4933i	−1.70800	+	1.43318i
$186$	−1.17041	−	0.982092i	−0.0858188	−	0.0720105i
$187$	1.90045	+	10.7780i	0.138975	+	0.788166i
$188$	−4.20243	−	1.52956i	−0.306494	−	0.111555i
$189$	−17.8885			−1.30120
$190$		0			0
$191$	3.52786			0.255267			0.127634	−	0.991821i	$-0.459262\pi$
$191$	3.52786			0.255267			0.127634	+	0.991821i	$0.459262\pi$
$192$	1.16152	+	0.422760i	0.0838258	+	0.0305101i
$193$	−2.00179	−	11.3527i	−0.144092	−	0.817187i	−0.968092	−	0.250597i	$-0.919373\pi$
$193$	−2.00179	−	11.3527i	−0.144092	−	0.817187i	0.823999	−	0.566591i	$-0.191738\pi$
$194$	−6.60180	−	5.53957i	−0.473981	−	0.397718i
$195$	4.73442	−	3.97265i	0.339039	−	0.284487i
$196$	0.602930	−	3.41939i	0.0430664	−	0.244242i
$197$	2.07295	−	3.59045i	0.147692	−	0.255809i	−0.782682	−	0.622421i	$-0.786149\pi$
$197$	2.07295	−	3.59045i	0.147692	−	0.255809i	0.930374	+	0.366612i	$0.119482\pi$
$198$	2.38197	+	4.12569i	0.169279	+	0.293200i
$199$	−9.84059	+	3.58168i	−0.697581	+	0.253899i	−0.666378	−	0.745614i	$-0.732156\pi$
$199$	−9.84059	+	3.58168i	−0.697581	+	0.253899i	−0.0312032	+	0.999513i	$0.509934\pi$
$200$	7.60227	−	2.76700i	0.537562	−	0.195657i
$201$	7.23607	+	12.5332i	0.510393	+	0.884026i
$202$	−7.80902	+	13.5256i	−0.549441	+	0.951659i
$203$	5.10811	−	28.9695i	0.358519	−	2.03326i
$204$	3.20233	−	2.68707i	0.224208	−	0.188133i
$205$	−2.36721	−	1.98632i	−0.165333	−	0.138731i
$206$	−2.54438	−	14.4299i	−0.177275	−	1.00538i
$207$	7.24334	+	2.63636i	0.503447	+	0.183240i
$208$	1.38197			0.0958221
$209$		0			0
$210$	14.4721			0.998672
$211$	6.79968	+	2.47488i	0.468109	+	0.170378i	0.565296	−	0.824888i	$-0.308762\pi$
$211$	6.79968	+	2.47488i	0.468109	+	0.170378i	−0.0971864	+	0.995266i	$0.530984\pi$
$212$	−1.05755	−	5.99765i	−0.0726326	−	0.411920i
$213$	−2.78788	−	2.33931i	−0.191022	−	0.160287i
$214$	−7.21339	+	6.05275i	−0.493097	+	0.413757i
$215$	5.80270	−	32.9087i	0.395741	−	2.24436i
$216$	2.76393	−	4.78727i	0.188062	−	0.325733i
$217$	−2.00000	−	3.46410i	−0.135769	−	0.235159i
$218$	−10.3690	+	3.77400i	−0.702276	+	0.255608i
$219$	−6.52548	+	2.37508i	−0.440951	+	0.160493i
$220$	−5.85410	−	10.1396i	−0.394683	−	0.683612i
$221$	2.33688	−	4.04760i	0.157196	−	0.272271i
$222$	1.79911	−	10.2033i	0.120749	−	0.684799i
$223$	21.2257	−	17.8105i	1.42138	−	1.19268i	0.470783	−	0.882249i	$-0.343972\pi$
$223$	21.2257	−	17.8105i	1.42138	−	1.19268i	0.950596	−	0.310429i	$-0.100473\pi$
$224$	2.47897	+	2.08010i	0.165633	+	0.138983i
$225$	−2.06812	−	11.7289i	−0.137875	−	0.781926i
$226$	−9.25983	−	3.37030i	−0.615955	−	0.224189i
$227$	−8.94427			−0.593652			−0.296826	−	0.954932i	$-0.595928\pi$
$227$	−8.94427			−0.593652			−0.296826	+	0.954932i	$0.595928\pi$
$228$		0			0
$229$	4.38197			0.289568			0.144784	−	0.989463i	$-0.453751\pi$
$229$	4.38197			0.289568			0.144784	+	0.989463i	$0.453751\pi$
$230$	−17.8018	−	6.47932i	−1.17382	−	0.427234i
$231$	−2.24775	−	12.7476i	−0.147891	−	0.838732i
$232$	6.96347	+	5.84305i	0.457174	+	0.383615i
$233$	1.19680	−	1.00423i	0.0784047	−	0.0657894i	−0.602743	−	0.797935i	$-0.705926\pi$
$233$	1.19680	−	1.00423i	0.0784047	−	0.0657894i	0.681148	+	0.732146i	$0.261481\pi$
$234$	0.353277	−	2.00353i	0.0230944	−	0.130975i
$235$	8.09017	−	14.0126i	0.527744	−	0.914080i
$236$	0.236068	+	0.408882i	0.0153667	+	0.0266159i
$237$	−3.21037	+	1.16848i	−0.208536	+	0.0759010i
$238$	10.2843	−	3.74316i	0.666629	−	0.242633i
$239$	−15.0902	−	26.1369i	−0.976102	−	1.69066i	−0.676250	−	0.736673i	$-0.736396\pi$
$239$	−15.0902	−	26.1369i	−0.976102	−	1.69066i	−0.299852	−	0.953986i	$-0.596937\pi$
$240$	−2.23607	+	3.87298i	−0.144338	+	0.250000i
$241$	−4.41351	+	25.0303i	−0.284299	+	1.61234i	0.423478	+	0.905906i	$0.360809\pi$
$241$	−4.41351	+	25.0303i	−0.284299	+	1.61234i	−0.707777	+	0.706435i	$0.750302\pi$
$242$	0.404367	−	0.339304i	0.0259937	−	0.0218113i
$243$	−10.4157	−	8.73982i	−0.668168	−	0.560660i
$244$	0.239976	+	1.36097i	0.0153629	+	0.0871272i
$245$	11.8047	+	4.29656i	0.754175	+	0.274497i
$246$	1.05573			0.0673108
$247$		0			0
$248$	1.23607			0.0784904
$249$	−0.548397	−	0.199600i	−0.0347533	−	0.0126492i
$250$	1.94145	+	11.0105i	0.122788	+	0.696364i
$251$	−1.75562	−	1.47314i	−0.110814	−	0.0929837i	0.585697	−	0.810530i	$-0.300821\pi$
$251$	−1.75562	−	1.47314i	−0.110814	−	0.0929837i	−0.696511	+	0.717546i	$0.745265\pi$
$252$	3.64938	−	3.06220i	0.229890	−	0.192900i
$253$	−2.94234	+	16.6869i	−0.184983	+	1.04909i
$254$	−5.70820	+	9.88690i	−0.358165	+	0.620359i
$255$	7.56231	+	13.0983i	0.473570	+	0.820247i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−17.2734	+	6.28700i	−1.07748	+	0.392172i	−0.818971	−	0.573835i	$-0.805455\pi$
$257$	−17.2734	+	6.28700i	−1.07748	+	0.392172i	−0.258514	+	0.966007i	$0.583233\pi$
$258$	5.70820	+	9.88690i	0.355377	+	0.615531i
$259$	13.5623	−	23.4906i	0.842721	−	1.45964i
$260$	−0.868241	+	4.92404i	−0.0538460	+	0.305376i
$261$	10.2512	−	8.60176i	0.634532	−	0.532436i
$262$	−3.42585	−	2.87463i	−0.211650	−	0.177595i
$263$	0.511267	+	2.89954i	0.0315261	+	0.178793i	0.996505	−	0.0835345i	$-0.0266209\pi$
$263$	0.511267	+	2.89954i	0.0315261	+	0.178793i	−0.964979	+	0.262328i	$0.915510\pi$
$264$	3.75877	+	1.36808i	0.231336	+	0.0841995i
$265$	22.0344			1.35357
$266$		0			0
$267$	−10.9443			−0.669779
$268$	−11.0021	−	4.00444i	−0.672061	−	0.244610i
$269$	2.48773	+	14.1086i	0.151679	+	0.860216i	0.961759	+	0.273896i	$0.0883126\pi$
$269$	2.48773	+	14.1086i	0.151679	+	0.860216i	−0.810080	+	0.586319i	$0.800576\pi$
$270$	15.3209	+	12.8558i	0.932400	+	0.782376i
$271$	19.9172	−	16.7125i	1.20988	−	1.01521i	0.210590	−	0.977575i	$-0.432462\pi$
$271$	19.9172	−	16.7125i	1.20988	−	1.01521i	0.999292	−	0.0376362i	$-0.0119828\pi$
$272$	−0.587272	+	3.33059i	−0.0356086	+	0.201946i
$273$	−2.76393	+	4.78727i	−0.167281	+	0.289739i
$274$	1.19098	+	2.06284i	0.0719499	+	0.124621i
$275$	24.6015	−	8.95420i	1.48352	−	0.539959i
$276$	6.08182	−	2.21360i	0.366082	−	0.133243i
$277$	5.04508	+	8.73834i	0.303130	+	0.525036i	0.976843	−	0.213957i	$-0.0686351\pi$
$277$	5.04508	+	8.73834i	0.303130	+	0.525036i	−0.673713	+	0.738993i	$0.735302\pi$
$278$	−7.00000	+	12.1244i	−0.419832	+	0.727171i
$279$	0.315981	−	1.79202i	0.0189173	−	0.107285i
$280$	−8.96900	+	7.52589i	−0.536001	+	0.449758i
$281$	16.0706	+	13.4849i	0.958693	+	0.804439i	0.980740	−	0.195318i	$-0.0625738\pi$
$281$	16.0706	+	13.4849i	0.958693	+	0.804439i	−0.0220468	+	0.999757i	$0.507018\pi$
$282$	0.959904	+	5.44388i	0.0571614	+	0.324179i
$283$	−21.1169	−	7.68592i	−1.25527	−	0.456881i	−0.373090	−	0.927795i	$-0.621702\pi$
$283$	−21.1169	−	7.68592i	−1.25527	−	0.456881i	−0.882179	+	0.470914i	$0.843924\pi$
$284$	2.94427			0.174710
$285$		0			0
$286$	4.47214			0.264443
$287$	2.59725	+	0.945320i	0.153311	+	0.0558005i
$288$	0.255634	+	1.44977i	0.0150634	+	0.0854286i
$289$	−4.26097	−	3.57538i	−0.250646	−	0.210317i
$290$	−25.1941	+	21.1403i	−1.47945	+	1.24140i
$291$	−1.84978	+	10.4906i	−0.108436	+	0.614972i
$292$	2.80902	−	4.86536i	0.164385	−	0.284724i
$293$	−11.4721	−	19.8703i	−0.670209	−	1.16084i	−0.977845	−	0.209332i	$-0.932871\pi$
$293$	−11.4721	−	19.8703i	−0.670209	−	1.16084i	0.307635	−	0.951504i	$-0.400462\pi$
$294$	−4.03297	+	1.46788i	−0.235208	+	0.0856085i
$295$	−1.60519	+	0.584240i	−0.0934576	+	0.0340158i
$296$	4.19098	+	7.25900i	0.243596	+	0.421921i
$297$	8.94427	−	15.4919i	0.518999	−	0.898933i
$298$	2.27308	−	12.8913i	0.131676	−	0.746773i
$299$	5.54315	−	4.65125i	0.320569	−	0.268989i
$300$	−7.66044	−	6.42788i	−0.442276	−	0.371114i
$301$	5.19009	+	29.4345i	0.299152	+	1.69657i
$302$	13.5994	+	4.94976i	0.782555	+	0.284827i
$303$	19.3050			1.10904
$304$		0			0
$305$	−5.00000			−0.286299
$306$	4.67846	+	1.70282i	0.267450	+	0.0973438i
$307$	2.03311	+	11.5303i	0.116036	+	0.658071i	0.986232	+	0.165366i	$0.0528806\pi$
$307$	2.03311	+	11.5303i	0.116036	+	0.658071i	−0.870197	+	0.492705i	$0.836008\pi$
$308$	8.02212	+	6.73136i	0.457103	+	0.383555i
$309$	−13.8742	+	11.6418i	−0.789275	+	0.662280i
$310$	−0.776578	+	4.40419i	−0.0441067	+	0.250141i
$311$	−15.6180	+	27.0512i	−0.885617	+	1.53393i	−0.0406131	+	0.999175i	$0.512931\pi$
$311$	−15.6180	+	27.0512i	−0.885617	+	1.53393i	−0.845004	+	0.534759i	$0.820402\pi$
$312$	−0.854102	−	1.47935i	−0.0483540	−	0.0837516i
$313$	14.5714	−	5.30356i	0.823625	−	0.299775i	0.104385	−	0.994537i	$-0.466712\pi$
$313$	14.5714	−	5.30356i	0.823625	−	0.299775i	0.719240	+	0.694762i	$0.244490\pi$
$314$	8.81616	−	3.20882i	0.497525	−	0.181084i
$315$	8.61803	+	14.9269i	0.485571	+	0.841034i
$316$	1.38197	−	2.39364i	0.0777417	−	0.134653i
$317$	0.230299	−	1.30609i	0.0129349	−	0.0733573i	−0.977657	−	0.210206i	$-0.932586\pi$
$317$	0.230299	−	1.30609i	0.0129349	−	0.0733573i	0.990592	+	0.136849i	$0.0436975\pi$
$318$	−5.76668	+	4.83882i	−0.323379	+	0.271347i
$319$	22.5343	+	18.9085i	1.26168	+	1.05867i
$320$	−0.628265	−	3.56307i	−0.0351211	−	0.199182i
$321$	10.9374	+	3.98088i	0.610465	+	0.222191i
$322$	16.9443			0.944267
$323$		0			0
$324$	−2.41641			−0.134245
$325$	−10.5061	−	3.82390i	−0.582773	−	0.212112i
$326$	−1.84978	−	10.4906i	−0.102450	−	0.581023i
$327$	10.4483	+	8.76719i	0.577794	+	0.484826i
$328$	−0.654280	+	0.549006i	−0.0361266	+	0.0303138i
$329$	−2.51306	+	14.2523i	−0.138549	+	0.785753i
$330$	−7.23607	+	12.5332i	−0.398332	+	0.689932i
$331$	−12.8541	−	22.2640i	−0.706525	−	1.22374i	−0.966138	−	0.258025i	$-0.916928\pi$
$331$	−12.8541	−	22.2640i	−0.706525	−	1.22374i	0.259613	−	0.965713i	$-0.416405\pi$
$332$	0.443663	−	0.161480i	0.0243492	−	0.00886237i
$333$	11.5952	−	4.22032i	0.635415	−	0.231272i
$334$	−6.23607	−	10.8012i	−0.341222	−	0.591015i
$335$	21.1803	−	36.6854i	1.15721	−	2.00434i
$336$	0.694593	−	3.93923i	0.0378931	−	0.214903i
$337$	1.82469	−	1.53110i	0.0993973	−	0.0834042i	−0.591735	−	0.806133i	$-0.701557\pi$
$337$	1.82469	−	1.53110i	0.0993973	−	0.0834042i	0.691132	+	0.722728i	$0.257112\pi$
$338$	8.49556	+	7.12862i	0.462098	+	0.387746i
$339$	2.11509	+	11.9953i	0.114876	+	0.651495i
$340$	−11.4981	−	4.18498i	−0.623574	−	0.226963i
$341$	4.00000			0.216612
$342$		0			0
$343$	11.4164			0.616428
$344$	−8.67906	−	3.15892i	−0.467944	−	0.170318i
$345$	4.06622	+	23.0607i	0.218918	+	1.24154i
$346$	−1.01596	−	0.852489i	−0.0546182	−	0.0458301i
$347$	−2.03191	+	1.70498i	−0.109079	+	0.0915280i	−0.695696	−	0.718336i	$-0.744904\pi$
$347$	−2.03191	+	1.70498i	−0.109079	+	0.0915280i	0.586617	+	0.809865i	$0.300459\pi$
$348$	1.95112	−	11.0654i	0.104591	−	0.593166i
$349$	16.5451	−	28.6569i	0.885638	−	1.53397i	0.0406575	−	0.999173i	$-0.487055\pi$
$349$	16.5451	−	28.6569i	0.885638	−	1.53397i	0.844981	−	0.534797i	$-0.179612\pi$
$350$	−13.0902	−	22.6728i	−0.699699	−	1.21191i
$351$	−7.17861	+	2.61280i	−0.383166	+	0.139461i
$352$	−3.04091	+	1.10680i	−0.162081	+	0.0589927i
$353$	11.8713	+	20.5617i	0.631847	+	1.09439i	0.987174	+	0.159649i	$0.0510361\pi$
$353$	11.8713	+	20.5617i	0.631847	+	1.09439i	−0.355327	+	0.934742i	$0.615631\pi$
$354$	0.291796	−	0.505406i	0.0155088	−	0.0268620i
$355$	−1.84978	+	10.4906i	−0.0981763	+	0.556785i
$356$	6.78264	−	5.69131i	0.359479	−	0.301639i
$357$	−10.3629	−	8.69554i	−0.548465	−	0.460217i
$358$	4.06622	+	23.0607i	0.214906	+	1.21879i
$359$	−10.8326	−	3.94276i	−0.571725	−	0.208091i	0.0399476	−	0.999202i	$-0.487281\pi$
$359$	−10.8326	−	3.94276i	−0.571725	−	0.208091i	−0.611673	+	0.791111i	$0.709503\pi$
$360$	−5.32624			−0.280717
$361$		0			0
$362$	−5.41641			−0.284680
$363$	−0.613127	−	0.223160i	−0.0321808	−	0.0117129i
$364$	−0.776578	−	4.40419i	−0.0407038	−	0.230842i
$365$	15.5708	+	13.0655i	0.815013	+	0.683877i
$366$	1.30856	−	1.09801i	0.0683995	−	0.0573940i
$367$	3.27028	−	18.5467i	0.170707	−	0.968130i	−0.772275	−	0.635288i	$-0.780881\pi$
$367$	3.27028	−	18.5467i	0.170707	−	0.968130i	0.942983	−	0.332842i	$-0.108008\pi$
$368$	−2.61803	+	4.53457i	−0.136474	+	0.236381i
$369$	0.628677	+	1.08890i	0.0327276	+	0.0566859i
$370$	−28.4973	+	10.3722i	−1.48151	+	0.539224i
$371$	−18.5197	+	6.74060i	−0.961493	+	0.349955i
$372$	−0.763932	−	1.32317i	−0.0396080	−	0.0686031i
$373$	−9.16312	+	15.8710i	−0.474448	+	0.821769i	−0.999572	−	0.0292574i	$-0.990686\pi$
$373$	−9.16312	+	15.8710i	−0.474448	+	0.821769i	0.525124	+	0.851026i	$0.324019\pi$
$374$	−1.90045	+	10.7780i	−0.0982701	+	0.557317i
$375$	10.5865	−	8.88311i	0.546683	−	0.458722i
$376$	−3.42585	−	2.87463i	−0.176675	−	0.148248i
$377$	−2.18142	−	12.3715i	−0.112349	−	0.637162i
$378$	−16.8097	−	6.11824i	−0.864599	−	0.314688i
$379$	−35.4164			−1.81922			−0.909609	−	0.415465i	$-0.863619\pi$
$379$	−35.4164			−1.81922			−0.909609	+	0.415465i	$0.863619\pi$
$380$		0			0
$381$	14.1115			0.722952
$382$	3.31511	+	1.20660i	0.169616	+	0.0617351i
$383$	3.60562	+	20.4485i	0.184239	+	1.04487i	0.926930	+	0.375235i	$0.122438\pi$
$383$	3.60562	+	20.4485i	0.184239	+	1.04487i	−0.742691	+	0.669634i	$0.766451\pi$
$384$	0.946883	+	0.794529i	0.0483204	+	0.0405456i
$385$	−29.0243	+	24.3543i	−1.47922	+	1.24121i
$386$	2.00179	−	11.3527i	0.101889	−	0.577839i
$387$	−6.79837	+	11.7751i	−0.345581	+	0.598563i
$388$	−4.30902	−	7.46344i	−0.218757	−	0.378899i
$389$	−12.0265	+	4.37730i	−0.609770	+	0.221938i	−0.628402	−	0.777888i	$-0.716291\pi$
$389$	−12.0265	+	4.37730i	−0.609770	+	0.221938i	0.0186328	+	0.999826i	$0.494069\pi$
$390$	5.80762	−	2.11380i	0.294080	−	0.107036i
$391$	8.85410	+	15.3358i	0.447771	+	0.775562i
$392$	1.73607	−	3.00696i	0.0876847	−	0.151874i
$393$	−0.959904	+	5.44388i	−0.0484207	+	0.274608i
$394$	3.17594	−	2.66493i	0.160002	−	0.134257i
$395$	7.66044	+	6.42788i	0.385439	+	0.323422i
$396$	0.827248	+	4.69156i	0.0415708	+	0.235760i
$397$	21.0122	+	7.64780i	1.05457	+	0.383832i	0.810386	−	0.585897i	$-0.199258\pi$
$397$	21.0122	+	7.64780i	1.05457	+	0.383832i	0.244185	+	0.969729i	$0.421480\pi$
$398$	−10.4721			−0.524921
$399$		0			0
$400$	8.09017			0.404508
$401$	−17.8018	−	6.47932i	−0.888979	−	0.323562i	−0.143151	−	0.989701i	$-0.545724\pi$
$401$	−17.8018	−	6.47932i	−0.888979	−	0.323562i	−0.745828	+	0.666139i	$0.767946\pi$
$402$	2.51306	+	14.2523i	0.125340	+	0.710839i
$403$	−1.30856	−	1.09801i	−0.0651840	−	0.0546959i
$404$	−11.9641	+	10.0391i	−0.595237	+	0.499463i
$405$	1.51814	−	8.60983i	0.0754372	−	0.427826i
$406$	14.7082	−	25.4754i	0.729956	−	1.26432i
$407$	13.5623	+	23.4906i	0.672259	+	1.16439i
$408$	3.92823	−	1.42976i	0.194477	−	0.0707837i
$409$	−15.2893	+	5.56484i	−0.756006	+	0.275164i	−0.691131	−	0.722730i	$-0.742887\pi$
$409$	−15.2893	+	5.56484i	−0.756006	+	0.275164i	−0.0648753	+	0.997893i	$0.520665\pi$
$410$	−1.54508	−	2.67617i	−0.0763063	−	0.132166i
$411$	1.47214	−	2.54981i	0.0726151	−	0.125773i
$412$	2.54438	−	14.4299i	0.125352	−	0.710909i
$413$	1.17041	−	0.982092i	0.0575922	−	0.0483256i
$414$	5.90483	+	4.95474i	0.290206	+	0.243512i
$415$	0.296626	+	1.68225i	0.0145608	+	0.0825785i
$416$	1.29862	+	0.472660i	0.0636702	+	0.0231741i
$417$	17.3050			0.847427
$418$		0			0
$419$	−6.47214			−0.316185			−0.158092	−	0.987424i	$-0.550534\pi$
$419$	−6.47214			−0.316185			−0.158092	+	0.987424i	$0.550534\pi$
$420$	13.5994	+	4.94976i	0.663581	+	0.241524i
$421$	2.41542	+	13.6985i	0.117720	+	0.667624i	0.985367	+	0.170444i	$0.0545202\pi$
$421$	2.41542	+	13.6985i	0.117720	+	0.667624i	−0.867647	+	0.497180i	$0.834369\pi$
$422$	5.54315	+	4.65125i	0.269836	+	0.226420i
$423$	−5.04332	+	4.23185i	−0.245215	+	0.205760i
$424$	1.05755	−	5.99765i	0.0513590	−	0.291271i
$425$	13.6803	−	23.6950i	0.663594	−	1.14938i
$426$	−1.81966	−	3.15174i	−0.0881628	−	0.152702i
$427$	4.20243	−	1.52956i	0.203370	−	0.0740206i
$428$	−8.84853	+	3.22060i	−0.427710	+	0.155674i
$429$	−2.76393	−	4.78727i	−0.133444	−	0.231132i
$430$	16.7082	−	28.9395i	0.805741	−	1.39558i
$431$	1.15519	−	6.55141i	0.0556436	−	0.315570i	−0.944264	−	0.329190i	$-0.893224\pi$
$431$	1.15519	−	6.55141i	0.0556436	−	0.315570i	0.999907	+	0.0136197i	$0.00433543\pi$
$432$	4.23459	−	3.55324i	0.203737	−	0.170955i
$433$	−19.1775	−	16.0918i	−0.921612	−	0.773324i	0.0526807	−	0.998611i	$-0.483223\pi$
$433$	−19.1775	−	16.0918i	−0.921612	−	0.773324i	−0.974292	+	0.225287i	$0.927668\pi$
$434$	−0.694593	−	3.93923i	−0.0333415	−	0.189089i
$435$	38.2008	+	13.9040i	1.83159	+	0.666644i
$436$	−11.0344			−0.528454
$437$		0			0
$438$	−6.94427			−0.331810
$439$	−27.4729	−	9.99932i	−1.31121	−	0.477242i	−0.410579	−	0.911825i	$-0.634673\pi$
$439$	−27.4729	−	9.99932i	−1.31121	−	0.477242i	−0.900632	+	0.434583i	$0.856896\pi$
$440$	−2.03311	−	11.5303i	−0.0969246	−	0.549687i
$441$	−3.91560	−	3.28558i	−0.186457	−	0.156456i
$442$	3.58031	−	3.00424i	0.170298	−	0.142897i
$443$	1.60383	−	9.09575i	0.0762001	−	0.432152i	−0.922711	−	0.385493i	$-0.874031\pi$
$443$	1.60383	−	9.09575i	0.0762001	−	0.432152i	0.998911	−	0.0466592i	$-0.0148575\pi$
$444$	5.18034	−	8.97261i	0.245848	−	0.425821i
$445$	16.0172	+	27.7426i	0.759289	+	1.31513i
$446$	26.0372	−	9.47676i	1.23290	−	0.448738i
$447$	−15.2045	+	5.53400i	−0.719150	+	0.261749i
$448$	1.61803	+	2.80252i	0.0764449	+	0.132406i
$449$	11.3992	−	19.7440i	0.537961	−	0.931776i	−0.461053	−	0.887373i	$-0.652528\pi$
$449$	11.3992	−	19.7440i	0.537961	−	0.931776i	0.999014	−	0.0444029i	$-0.0141385\pi$
$450$	2.06812	−	11.7289i	0.0974921	−	0.552905i
$451$	−2.11729	+	1.77662i	−0.0996995	+	0.0836578i
$452$	−7.54868	−	6.33409i	−0.355060	−	0.297931i
$453$	−3.10631	−	17.6168i	−0.145947	−	0.827708i
$454$	−8.40487	−	3.05912i	−0.394460	−	0.143572i
$455$	16.1803			0.758546
$456$		0			0
$457$	25.2148			1.17950			0.589749	−	0.807587i	$-0.299227\pi$
$457$	25.2148			1.17950			0.589749	+	0.807587i	$0.299227\pi$
$458$	4.11770	+	1.49872i	0.192408	+	0.0700306i
$459$	−3.24636	−	18.4110i	−0.151527	−	0.859353i
$460$	−14.5122	−	12.1771i	−0.676633	−	0.567762i
$461$	16.4059	−	13.7662i	0.764100	−	0.641156i	−0.175091	−	0.984552i	$-0.556022\pi$
$461$	16.4059	−	13.7662i	0.764100	−	0.641156i	0.939191	+	0.343396i	$0.111577\pi$
$462$	2.24775	−	12.7476i	0.104575	−	0.593073i
$463$	2.52786	−	4.37839i	0.117480	−	0.203481i	−0.801289	−	0.598278i	$-0.795852\pi$
$463$	2.52786	−	4.37839i	0.117480	−	0.203481i	0.918768	+	0.394797i	$0.129185\pi$
$464$	4.54508	+	7.87232i	0.211000	+	0.365463i
$465$	5.19449	−	1.89064i	0.240889	−	0.0876764i
$466$	1.46809	−	0.534340i	0.0680078	−	0.0247528i
$467$	16.6525	+	28.8429i	0.770585	+	1.33469i	0.937243	+	0.348677i	$0.113369\pi$
$467$	16.6525	+	28.8429i	0.770585	+	1.33469i	−0.166658	+	0.986015i	$0.553298\pi$
$468$	1.01722	−	1.76188i	0.0470211	−	0.0814429i
$469$	−6.57928	+	37.3129i	−0.303803	+	1.72295i
$470$	12.3949	−	10.4005i	0.571732	−	0.479740i
$471$	−8.88362	−	7.45425i	−0.409336	−	0.343474i
$472$	0.0819855	+	0.464963i	0.00377369	+	0.0214017i
$473$	−28.0860	−	10.2225i	−1.29140	−	0.470030i
$474$	−3.41641			−0.156921
$475$		0			0
$476$	10.9443			0.501630
$477$	−8.42487	−	3.06640i	−0.385748	−	0.140401i
$478$	−5.24076	−	29.7218i	−0.239707	−	1.35944i
$479$	5.90483	+	4.95474i	0.269798	+	0.226388i	0.767642	−	0.640879i	$-0.221430\pi$
$479$	5.90483	+	4.95474i	0.269798	+	0.226388i	−0.497843	+	0.867267i	$0.665875\pi$
$480$	−3.42585	+	2.87463i	−0.156368	+	0.131208i
$481$	2.01147	−	11.4076i	0.0917151	−	0.520142i
$482$	−12.7082	+	22.0113i	−0.578843	+	1.00259i
$483$	−10.4721	−	18.1383i	−0.476499	−	0.825320i
$484$	0.496030	−	0.180540i	0.0225468	−	0.00820637i
$485$	29.2999	−	10.6643i	1.33044	−	0.484241i
$486$	−6.79837	−	11.7751i	−0.308381	−	0.534131i
$487$	−9.61803	+	16.6589i	−0.435835	+	0.754888i	−0.997363	−	0.0725694i	$-0.976880\pi$
$487$	−9.61803	+	16.6589i	−0.435835	+	0.754888i	0.561529	+	0.827457i	$0.310213\pi$
$488$	−0.239976	+	1.36097i	−0.0108632	+	0.0616083i
$489$	−10.0866	+	8.46370i	−0.456134	+	0.382742i
$490$	9.62328	+	8.07489i	0.434736	+	0.364787i
$491$	−0.265311	−	1.50465i	−0.0119733	−	0.0679040i	0.978236	−	0.207497i	$-0.0665317\pi$
$491$	−0.265311	−	1.50465i	−0.0119733	−	0.0679040i	−0.990209	+	0.139593i	$0.955421\pi$
$492$	0.992060	+	0.361080i	0.0447255	+	0.0162788i
$493$	30.7426			1.38458
$494$		0			0
$495$	−17.2361			−0.774704
$496$	1.16152	+	0.422760i	0.0521540	+	0.0189825i
$497$	−1.65450	−	9.38311i	−0.0742143	−	0.420890i
$498$	−0.447058	−	0.375126i	−0.0200331	−	0.0168098i
$499$	−27.0452	+	22.6936i	−1.21071	+	1.01590i	−0.211450	+	0.977389i	$0.567818\pi$
$499$	−27.0452	+	22.6936i	−1.21071	+	1.01590i	−0.999258	+	0.0385155i	$0.987737\pi$
$500$	−1.94145	+	11.0105i	−0.0868241	+	0.492404i
$501$	−7.70820	+	13.3510i	−0.344377	+	0.596479i
$502$	−1.14590	−	1.98475i	−0.0511439	−	0.0885839i
$503$	−6.35602	+	2.31340i	−0.283401	+	0.103149i	−0.479810	−	0.877373i	$-0.659294\pi$
$503$	−6.35602	+	2.31340i	−0.283401	+	0.103149i	0.196409	+	0.980522i	$0.437072\pi$
$504$	4.47663	−	1.62936i	0.199405	−	0.0725775i
$505$	−28.2533	−	48.9361i	−1.25725	−	2.17763i
$506$	−8.47214	+	14.6742i	−0.376632	+	0.652346i
$507$	2.38040	−	13.4999i	0.105717	−	0.599554i
$508$	−8.74548	+	7.33833i	−0.388018	+	0.325586i
$509$	32.7001	+	27.4386i	1.44941	+	1.21620i	0.933013	+	0.359844i	$0.117170\pi$
$509$	32.7001	+	27.4386i	1.44941	+	1.21620i	0.516393	+	0.856352i	$0.327274\pi$
$510$	2.62636	+	14.8948i	0.116297	+	0.659554i
$511$	−17.0839	−	6.21804i	−0.755749	−	0.275070i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−18.3820			−0.810794
$515$	49.8161	+	18.1316i	2.19516	+	0.798972i
$516$	1.98244	+	11.2430i	0.0872720	+	0.494944i
$517$	−11.0863	−	9.30251i	−0.487575	−	0.409124i
$518$	20.7787	−	17.4354i	0.912962	−	0.766066i
$519$	−0.284665	+	1.61442i	−0.0124954	+	0.0708650i
$520$	−2.50000	+	4.33013i	−0.109632	+	0.189889i
$521$	2.63525	+	4.56440i	0.115453	+	0.199970i	0.917961	−	0.396672i	$-0.129835\pi$
$521$	2.63525	+	4.56440i	0.115453	+	0.199970i	−0.802508	+	0.596641i	$0.796501\pi$
$522$	12.5749	−	4.57690i	0.550390	−	0.200326i
$523$	3.75877	−	1.36808i	0.164360	−	0.0598220i	−0.258530	−	0.966003i	$-0.583238\pi$
$523$	3.75877	−	1.36808i	0.164360	−	0.0598220i	0.422889	+	0.906181i	$0.361016\pi$
$524$	−2.23607	−	3.87298i	−0.0976831	−	0.169192i
$525$	−16.1803	+	28.0252i	−0.706168	+	1.22312i
$526$	−0.511267	+	2.89954i	−0.0222923	+	0.126426i
$527$	3.20233	−	2.68707i	0.139496	−	0.117051i
$528$	3.06418	+	2.57115i	0.133351	+	0.111895i
$529$	0.766901	+	4.34931i	0.0333435	+	0.189101i
$530$	20.7056	+	7.53622i	0.899394	+	0.327353i
$531$	0.695048			0.0301625
$532$		0			0
$533$	1.18034			0.0511262
$534$	−10.2843	−	3.74316i	−0.445043	−	0.161982i
$535$	−5.91600	−	33.5513i	−0.255771	−	1.45055i
$536$	−8.96900	−	7.52589i	−0.387402	−	0.325069i
$537$	22.1726	−	18.6050i	0.956818	−	0.802866i
$538$	−2.48773	+	14.1086i	−0.107253	+	0.608265i
$539$	5.61803	−	9.73072i	0.241986	−	0.419132i
$540$	10.0000	+	17.3205i	0.430331	+	0.745356i
$541$	25.0128	−	9.10390i	1.07538	−	0.391407i	0.257196	−	0.966359i	$-0.417201\pi$
$541$	25.0128	−	9.10390i	1.07538	−	0.391407i	0.818187	+	0.574952i	$0.194979\pi$
$542$	24.4320	−	8.89252i	1.04944	−	0.381967i
$543$	3.34752	+	5.79808i	0.143656	+	0.248820i
$544$	−1.69098	+	2.92887i	−0.0725003	+	0.125574i
$545$	6.93255	−	39.3165i	0.296958	−	1.68413i
$546$	−4.23459	+	3.55324i	−0.181224	+	0.152065i
$547$	3.87291	+	3.24976i	0.165594	+	0.138950i	0.721819	−	0.692082i	$-0.243306\pi$
$547$	3.87291	+	3.24976i	0.165594	+	0.138950i	−0.556225	+	0.831032i	$0.687751\pi$
$548$	0.413624	+	2.34578i	0.0176691	+	0.100207i
$549$	1.91175	+	0.695820i	0.0815915	+	0.0296969i
$550$	26.1803			1.11633
$551$		0			0
$552$	6.47214			0.275472
$553$	−8.40487	−	3.05912i	−0.357411	−	0.130087i
$554$	1.75214	+	9.93688i	0.0744413	+	0.422177i
$555$	28.7154	+	24.0951i	1.21890	+	1.02278i
$556$	−10.7246	+	8.99903i	−0.454825	+	0.381644i
$557$	0.877918	−	4.97892i	0.0371986	−	0.210964i	−0.960543	−	0.278131i	$-0.910285\pi$
$557$	0.877918	−	4.97892i	0.0371986	−	0.210964i	0.997742	+	0.0671674i	$0.0213962\pi$
$558$	0.909830	−	1.57587i	0.0385162	−	0.0667120i
$559$	6.38197	+	11.0539i	0.269928	+	0.467530i
$560$	−11.0021	+	4.00444i	−0.464924	+	0.169219i
$561$	12.7120	−	4.62680i	0.536702	−	0.195344i
$562$	10.4894	+	18.1681i	0.442467	+	0.766375i
$563$	−13.1459	+	22.7694i	−0.554034	+	0.959614i	0.443944	+	0.896054i	$0.353579\pi$
$563$	−13.1459	+	22.7694i	−0.554034	+	0.959614i	−0.997978	+	0.0635600i	$0.979755\pi$
$564$	−0.959904	+	5.44388i	−0.0404192	+	0.229229i
$565$	27.3114	−	22.9170i	1.14900	−	0.964124i
$566$	−17.2147	−	14.4448i	−0.723586	−	0.607161i
$567$	1.35787	+	7.70086i	0.0570252	+	0.323406i
$568$	2.76671	+	1.00700i	0.116089	+	0.0422528i
$569$	7.90983			0.331597			0.165799	−	0.986160i	$-0.446980\pi$
$569$	7.90983			0.331597			0.165799	+	0.986160i	$0.446980\pi$
$570$		0			0
$571$	−32.5410			−1.36180			−0.680900	−	0.732377i	$-0.738411\pi$
$571$	−32.5410			−1.36180			−0.680900	+	0.732377i	$0.738411\pi$
$572$	4.20243	+	1.52956i	0.175713	+	0.0639541i
$573$	−0.757224	−	4.29443i	−0.0316335	−	0.179402i
$574$	2.11729	+	1.77662i	0.0883742	+	0.0741547i
$575$	32.4502	−	27.2289i	1.35327	−	1.13552i
$576$	−0.255634	+	1.44977i	−0.0106514	+	0.0604071i
$577$	−22.9615	+	39.7705i	−0.955899	+	1.65567i	−0.223603	+	0.974680i	$0.571782\pi$
$577$	−22.9615	+	39.7705i	−0.955899	+	1.65567i	−0.732296	+	0.680986i	$0.761551\pi$
$578$	−2.78115	−	4.81710i	−0.115681	−	0.200365i
$579$	−13.3899	+	4.87352i	−0.556465	+	0.202537i
$580$	−30.9051	+	11.2485i	−1.28327	+	0.467070i
$581$	−0.763932	−	1.32317i	−0.0316932	−	0.0548943i
$582$	−5.32624	+	9.22531i	−0.220780	+	0.382402i
$583$	3.42229	−	19.4088i	0.141737	−	0.803830i
$584$	4.30366	−	3.61120i	0.178087	−	0.149433i
$585$	5.63861	+	4.73135i	0.233128	+	0.195617i
$586$	−3.98423	−	22.5957i	−0.164587	−	0.933420i
$587$	−2.70198	−	0.983441i	−0.111523	−	0.0405909i	0.285656	−	0.958332i	$-0.407788\pi$
$587$	−2.70198	−	0.983441i	−0.111523	−	0.0405909i	−0.397179	+	0.917741i	$0.630011\pi$
$588$	−4.29180			−0.176991
$589$		0			0
$590$	−1.70820			−0.0703256
$591$	−4.81556	−	1.75272i	−0.198086	−	0.0720973i
$592$	1.45551	+	8.25463i	0.0598212	+	0.339263i
$593$	−26.7526	−	22.4481i	−1.09860	−	0.921831i	−0.101266	−	0.994859i	$-0.532289\pi$
$593$	−26.7526	−	22.4481i	−1.09860	−	0.921831i	−0.997330	+	0.0730279i	$0.976734\pi$
$594$	13.7034	−	11.4985i	0.562258	−	0.471791i
$595$	−6.87590	+	38.9952i	−0.281885	+	1.59865i
$596$	6.54508	−	11.3364i	0.268097	−	0.464358i
$597$	6.47214	+	11.2101i	0.264887	+	0.458798i
$598$	6.79968	−	2.47488i	0.278060	−	0.101205i
$599$	36.7651	−	13.3814i	1.50218	−	0.546749i	0.545557	−	0.838074i	$-0.316318\pi$
$599$	36.7651	−	13.3814i	1.50218	−	0.546749i	0.956624	+	0.291324i	$0.0940958\pi$
$600$	−5.00000	−	8.66025i	−0.204124	−	0.353553i
$601$	−8.23607	+	14.2653i	−0.335956	+	0.581893i	−0.983668	−	0.179992i	$-0.942393\pi$
$601$	−8.23607	+	14.2653i	−0.335956	+	0.581893i	0.647712	+	0.761885i	$0.275726\pi$
$602$	−5.19009	+	29.4345i	−0.211532	+	1.19966i
$603$	−13.2036	+	11.0791i	−0.537692	+	0.451177i
$604$	11.0863	+	9.30251i	0.451095	+	0.378514i
$605$	0.331639	+	1.88082i	0.0134830	+	0.0764660i
$606$	18.1407	+	6.60268i	0.736916	+	0.268216i
$607$	−47.7771			−1.93921			−0.969606	−	0.244671i	$-0.921320\pi$
$607$	−47.7771			−1.93921			−0.969606	+	0.244671i	$0.921320\pi$
$608$		0			0
$609$	−36.3607			−1.47341
$610$	−4.69846	−	1.71010i	−0.190235	−	0.0692400i
$611$	1.07320	+	6.08645i	0.0434172	+	0.246231i
$612$	3.81392	+	3.20026i	0.154168	+	0.129363i
$613$	6.42096	−	5.38782i	0.259340	−	0.217612i	−0.503842	−	0.863796i	$-0.668081\pi$
$613$	6.42096	−	5.38782i	0.259340	−	0.217612i	0.763182	+	0.646184i	$0.223636\pi$
$614$	−2.03311	+	11.5303i	−0.0820496	+	0.465326i
$615$	−1.90983	+	3.30792i	−0.0770118	+	0.133388i
$616$	5.23607	+	9.06914i	0.210967	+	0.365406i
$617$	−40.3544	+	14.6878i	−1.62461	+	0.591309i	−0.984252	−	0.176770i	$-0.943435\pi$
$617$	−40.3544	+	14.6878i	−1.62461	+	0.591309i	−0.640355	+	0.768079i	$0.721213\pi$
$618$	−17.0192	+	6.19448i	−0.684613	+	0.249179i
$619$	−11.1803	−	19.3649i	−0.449376	−	0.778342i	0.548970	−	0.835842i	$-0.315020\pi$
$619$	−11.1803	−	19.3649i	−0.449376	−	0.778342i	−0.998345	+	0.0575005i	$0.981687\pi$
$620$	−2.23607	+	3.87298i	−0.0898027	+	0.155543i
$621$	5.02612	−	28.5045i	0.201691	−	1.14385i
$622$	−23.9282	+	20.0782i	−0.959434	+	0.805061i
$623$	−21.9491	−	18.4175i	−0.879371	−	0.737880i
$624$	−0.296626	−	1.68225i	−0.0118746	−	0.0673440i
$625$		0			0
$626$	15.5066			0.619767
$627$		0			0
$628$	9.38197			0.374381
$629$	26.6380	+	9.69542i	1.06212	+	0.386582i
$630$	2.99301	+	16.9742i	0.119244	+	0.676269i
$631$	−23.8428	−	20.0065i	−0.949168	−	0.796447i	0.0299890	−	0.999550i	$-0.490453\pi$
$631$	−23.8428	−	20.0065i	−0.949168	−	0.796447i	−0.979157	+	0.203103i	$0.934897\pi$
$632$	2.11729	−	1.77662i	0.0842215	−	0.0706702i
$633$	1.55316	−	8.80839i	0.0617324	−	0.350102i
$634$	0.663119	−	1.14856i	0.0263358	−	0.0456150i
$635$	−20.6525	−	35.7711i	−0.819569	−	1.41953i
$636$	−7.07388	+	2.57468i	−0.280498	+	0.102093i
$637$	−4.50900	+	1.64114i	−0.178653	+	0.0650244i
$638$	14.7082	+	25.4754i	0.582303	+	1.00858i
$639$	2.16718	−	3.75367i	0.0857325	−	0.148493i
$640$	0.628265	−	3.56307i	0.0248344	−	0.140843i
$641$	−10.1658	+	8.53012i	−0.401525	+	0.336919i	−0.821083	−	0.570809i	$-0.806630\pi$
$641$	−10.1658	+	8.53012i	−0.401525	+	0.336919i	0.419558	+	0.907729i	$0.362185\pi$
$642$	8.91624	+	7.48161i	0.351896	+	0.295276i
$643$	−6.74325	−	38.2429i	−0.265928	−	1.50815i	−0.766380	−	0.642387i	$-0.777944\pi$
$643$	−6.74325	−	38.2429i	−0.265928	−	1.50815i	0.500453	−	0.865764i	$-0.333167\pi$
$644$	15.9224	+	5.79528i	0.627431	+	0.228366i
$645$	−41.3050			−1.62638
$646$		0			0
$647$	26.0689			1.02487			0.512437	−	0.858725i	$-0.328743\pi$
$647$	26.0689			1.02487			0.512437	+	0.858725i	$0.328743\pi$
$648$	−2.27068	−	0.826460i	−0.0892008	−	0.0324664i
$649$	0.265311	+	1.50465i	0.0104144	+	0.0590628i
$650$	−8.56464	−	7.18658i	−0.335933	−	0.281881i
$651$	−3.78753	+	3.17812i	−0.148445	+	0.124560i
$652$	1.84978	−	10.4906i	0.0724431	−	0.410845i
$653$	17.6976	−	30.6531i	0.692559	−	1.19955i	−0.278438	−	0.960454i	$-0.589817\pi$
$653$	17.6976	−	30.6531i	0.692559	−	1.19955i	0.970997	−	0.239093i	$-0.0768501\pi$
$654$	6.81966	+	11.8120i	0.266670	+	0.461886i
$655$	15.2045	−	5.53400i	0.594091	−	0.216231i
$656$	−0.802593	+	0.292120i	−0.0313360	+	0.0114054i
$657$	−4.13525	−	7.16247i	−0.161332	−	0.279435i
$658$	−7.23607	+	12.5332i	−0.282091	+	0.488596i
$659$	−8.42906	+	47.8036i	−0.328350	+	1.86216i	0.156658	+	0.987653i	$0.449928\pi$
$659$	−8.42906	+	47.8036i	−0.328350	+	1.86216i	−0.485008	+	0.874510i	$0.661183\pi$
$660$	−11.0863	+	9.30251i	−0.431534	+	0.362100i
$661$	−16.4059	−	13.7662i	−0.638116	−	0.535443i	0.265323	−	0.964160i	$-0.414521\pi$
$661$	−16.4059	−	13.7662i	−0.638116	−	0.535443i	−0.903439	+	0.428716i	$0.858966\pi$
$662$	−4.46418	−	25.3176i	−0.173505	−	0.983998i
$663$	−5.42869	−	1.97588i	−0.210833	−	0.0767368i
$664$	0.472136			0.0183224
$665$		0			0
$666$	12.3394			0.478142
$667$	44.7263	+	16.2790i	1.73181	+	0.630327i
$668$	−2.16576	−	12.2827i	−0.0837959	−	0.475230i
$669$	−26.2364	−	22.0150i	−1.01436	−	0.851148i
$670$	32.4502	−	27.2289i	1.25366	−	1.05194i
$671$	−0.776578	+	4.40419i	−0.0299795	+	0.170022i
$672$	2.00000	−	3.46410i	0.0771517	−	0.133631i
$673$	−15.1910	−	26.3116i	−0.585569	−	1.01424i	−0.994804	−	0.101807i	$-0.967538\pi$
$673$	−15.1910	−	26.3116i	−0.585569	−	1.01424i	0.409235	−	0.912429i	$-0.365796\pi$
$674$	2.23832	−	0.814680i	0.0862167	−	0.0313803i
$675$	−42.0243	+	15.2956i	−1.61752	+	0.588728i
$676$	5.54508	+	9.60437i	0.213272	+	0.369399i
$677$	3.30902	−	5.73139i	0.127176	−	0.220275i	−0.795406	−	0.606078i	$-0.792742\pi$
$677$	3.30902	−	5.73139i	0.127176	−	0.220275i	0.922581	+	0.385803i	$0.126075\pi$
$678$	−2.11509	+	11.9953i	−0.0812297	+	0.460676i
$679$	−21.3639	+	17.9264i	−0.819870	+	0.687952i
$680$	−9.37337	−	7.86519i	−0.359452	−	0.301616i
$681$	1.91981	+	10.8878i	0.0735672	+	0.417220i
$682$	3.75877	+	1.36808i	0.143931	+	0.0523865i
$683$	−20.1803			−0.772179			−0.386090	−	0.922461i	$-0.626174\pi$
$683$	−20.1803			−0.772179			−0.386090	+	0.922461i	$0.626174\pi$
$684$		0			0
$685$	−8.61803			−0.329278
$686$	10.7279	+	3.90464i	0.409594	+	0.149080i
$687$	−0.940549	−	5.33412i	−0.0358842	−	0.203509i
$688$	−7.07524	−	5.93683i	−0.269741	−	0.226340i
$689$	−6.44734	+	5.40996i	−0.245624	+	0.206103i
$690$	−4.06622	+	23.0607i	−0.154798	+	0.877904i
$691$	11.1803	−	19.3649i	0.425320	−	0.736676i	−0.571130	−	0.820860i	$-0.693495\pi$
$691$	11.1803	−	19.3649i	0.425320	−	0.736676i	0.996450	+	0.0841834i	$0.0268282\pi$
$692$	−0.663119	−	1.14856i	−0.0252080	−	0.0436615i
$693$	14.4867	−	5.27272i	0.550304	−	0.200294i
$694$	−2.49251	+	0.907200i	−0.0946145	+	0.0344368i
$695$	−25.3262	−	43.8663i	−0.960679	−	1.66394i
$696$	5.61803	−	9.73072i	0.212951	−	0.368842i
$697$	−0.501590	+	2.84466i	−0.0189991	+	0.107749i
$698$	25.3485	−	21.2700i	0.959456	−	0.805080i
$699$	−1.47932	−	1.24130i	−0.0559531	−	0.0469502i
$700$	−4.54617	−	25.7826i	−0.171829	−	0.974491i
$701$	−36.3014	−	13.2126i	−1.37109	−	0.499035i	−0.451623	−	0.892209i	$-0.649155\pi$
$701$	−36.3014	−	13.2126i	−1.37109	−	0.499035i	−0.919464	+	0.393174i	$0.871377\pi$
$702$	−7.63932			−0.288328
$703$		0			0
$704$	−3.23607			−0.121964
$705$	−18.7939	−	6.84040i	−0.707817	−	0.257624i
$706$	4.12287	+	23.3819i	0.155166	+	0.879991i
$707$	38.7167	+	32.4871i	1.45609	+	1.22180i
$708$	0.447058	−	0.375126i	0.0168015	−	0.0140981i
$709$	1.19988	−	6.80485i	0.0450624	−	0.255562i	−0.953951	−	0.299961i	$-0.903026\pi$
$709$	1.19988	−	6.80485i	0.0450624	−	0.255562i	0.999014	+	0.0443994i	$0.0141374\pi$
$710$	−5.32624	+	9.22531i	−0.199890	+	0.346220i
$711$	−2.03444	−	3.52376i	−0.0762975	−	0.132151i
$712$	8.32013	−	3.02828i	0.311810	−	0.113490i
$713$	6.08182	−	2.21360i	0.227766	−	0.0829000i
$714$	−6.76393	−	11.7155i	−0.253134	−	0.438441i
$715$	−8.09017	+	14.0126i	−0.302555	+	0.524041i
$716$	−4.06622	+	23.0607i	−0.151962	+	0.861817i
$717$	−28.5773	+	23.9792i	−1.06724	+	0.895518i
$718$	−8.83086	−	7.40997i	−0.329565	−	0.276538i
$719$	2.13445	+	12.1051i	0.0796015	+	0.451442i	0.998391	+	0.0566958i	$0.0180565\pi$
$719$	2.13445	+	12.1051i	0.0796015	+	0.451442i	−0.918790	+	0.394747i	$0.870832\pi$
$720$	−5.00503	−	1.82168i	−0.186526	−	0.0678900i
$721$	−47.4164			−1.76588
$722$		0			0
$723$	31.4164			1.16839
$724$	−5.08976	−	1.85252i	−0.189159	−	0.0688484i
$725$	−12.7703	−	72.4238i	−0.474276	−	2.68975i
$726$	−0.499825	−	0.419403i	−0.0185503	−	0.0155655i
$727$	−23.7047	+	19.8906i	−0.879158	+	0.737701i	−0.966006	−	0.258520i	$-0.916765\pi$
$727$	−23.7047	+	19.8906i	−0.879158	+	0.737701i	0.0868476	+	0.996222i	$0.472321\pi$
$728$	0.776578	−	4.40419i	0.0287819	−	0.163230i
$729$	−12.0279	+	20.8329i	−0.445476	+	0.771588i
$730$	10.1631	+	17.6030i	0.376154	+	0.651518i
$731$	−29.3523	+	10.6834i	−1.08563	+	0.395139i
$732$	1.60519	−	0.584240i	0.0593294	−	0.0215941i
$733$	0.545085	+	0.944115i	0.0201332	+	0.0348717i	0.875916	−	0.482463i	$-0.160258\pi$
$733$	0.545085	+	0.944115i	0.0201332	+	0.0348717i	−0.855783	+	0.517334i	$0.826924\pi$
$734$	9.41641	−	16.3097i	0.347566	−	0.602002i
$735$	2.69639	−	15.2920i	0.0994577	−	0.564052i
$736$	−4.01106	+	3.36568i	−0.147850	+	0.124061i
$737$	−29.0243	−	24.3543i	−1.06912	−	0.897102i
$738$	0.218337	+	1.23825i	0.00803711	+	0.0455807i
$739$	−8.57433	−	3.12080i	−0.315412	−	0.114801i	0.179463	−	0.983765i	$-0.442564\pi$
$739$	−8.57433	−	3.12080i	−0.315412	−	0.114801i	−0.494875	+	0.868964i	$0.664786\pi$
$740$	−30.3262			−1.11481
$741$		0			0
$742$	−19.7082			−0.723511
$743$	−5.74289	−	2.09024i	−0.210686	−	0.0766835i	0.234521	−	0.972111i	$-0.424648\pi$
$743$	−5.74289	−	2.09024i	−0.210686	−	0.0766835i	−0.445207	+	0.895428i	$0.646870\pi$
$744$	−0.265311	−	1.50465i	−0.00972677	−	0.0551632i
$745$	36.2804	+	30.4429i	1.32921	+	1.11534i
$746$	−14.0387	+	11.7799i	−0.513994	+	0.431292i
$747$	0.120694	−	0.684489i	0.00441596	−	0.0250441i
$748$	−5.47214	+	9.47802i	−0.200081	+	0.346551i
$749$	15.2361	+	26.3896i	0.556714	+	0.964257i
$750$	12.9862	−	4.72660i	0.474190	−	0.172591i
$751$	22.6174	−	8.23204i	0.825319	−	0.300392i	0.105383	−	0.994432i	$-0.466393\pi$
$751$	22.6174	−	8.23204i	0.825319	−	0.300392i	0.719936	+	0.694040i	$0.244171\pi$
$752$	−2.23607	−	3.87298i	−0.0815410	−	0.141233i
$753$	−1.41641	+	2.45329i	−0.0516168	+	0.0894029i
$754$	2.18142	−	12.3715i	0.0794427	−	0.450542i
$755$	−40.1106	+	33.6568i	−1.45977	+	1.22490i
$756$	−13.7034	−	11.4985i	−0.498389	−	0.418198i
$757$	0.770597	+	4.37028i	0.0280078	+	0.158840i	0.995604	−	0.0936624i	$-0.0298574\pi$
$757$	0.770597	+	4.37028i	0.0280078	+	0.158840i	−0.967596	+	0.252503i	$0.918746\pi$
$758$	−33.2805	−	12.1131i	−1.20880	−	0.439969i
$759$	20.9443			0.760229
$760$		0			0
$761$	26.3607			0.955574			0.477787	−	0.878476i	$-0.341439\pi$
$761$	26.3607			0.955574			0.477787	+	0.878476i	$0.341439\pi$
$762$	13.2604	+	4.82640i	0.480375	+	0.174842i
$763$	6.20066	+	35.1657i	0.224479	+	1.27308i
$764$	2.70250	+	2.26767i	0.0977730	+	0.0820413i
$765$	−13.7989	+	11.5786i	−0.498899	+	0.418626i
$766$	−3.60562	+	20.4485i	−0.130276	+	0.738834i
$767$	0.326238	−	0.565061i	0.0117798	−	0.0204032i
$768$	0.618034	+	1.07047i	0.0223014	+	0.0386271i
$769$	−36.4062	+	13.2508i	−1.31284	+	0.477835i	−0.901157	−	0.433492i	$-0.857281\pi$
$769$	−36.4062	+	13.2508i	−1.31284	+	0.477835i	−0.411683	+	0.911327i	$0.635059\pi$
$770$	−35.6036	+	12.9586i	−1.28306	+	0.466997i
$771$	11.3607	+	19.6773i	0.409145	+	0.708660i
$772$	5.76393	−	9.98342i	0.207448	−	0.359311i
$773$	−1.41452	+	8.02214i	−0.0508768	+	0.288536i	−0.999622	−	0.0275066i	$-0.991243\pi$
$773$	−1.41452	+	8.02214i	−0.0508768	+	0.288536i	0.948745	+	0.316043i	$0.102354\pi$
$774$	−10.4157	+	8.73982i	−0.374385	+	0.314146i
$775$	−7.66044	−	6.42788i	−0.275171	−	0.230896i
$776$	−1.49651	−	8.48711i	−0.0537214	−	0.304669i
$777$	−31.5059	−	11.4672i	−1.13027	−	0.411384i
$778$	−12.7984			−0.458844
$779$		0			0
$780$	6.18034			0.221292
$781$	8.95326	+	3.25872i	0.320373	+	0.116606i
$782$	3.07500	+	17.4392i	0.109962	+	0.623624i
$783$	−38.4931	−	32.2996i	−1.37563	−	1.15429i
$784$	2.65981	−	2.23185i	0.0949932	−	0.0797088i
$785$	−5.89436	+	33.4286i	−0.210379	+	1.19312i
$786$	−2.76393	+	4.78727i	−0.0985862	+	0.170756i
$787$	−14.2361	−	24.6576i	−0.507461	−	0.878948i	−0.999963	−	0.00863678i	$-0.997251\pi$
$787$	−14.2361	−	24.6576i	−0.507461	−	0.878948i	0.492502	−	0.870311i	$-0.336083\pi$
$788$	3.89587	−	1.41798i	0.138785	−	0.0505135i
$789$	3.41984	−	1.24472i	0.121750	−	0.0443132i
$790$	5.00000	+	8.66025i	0.177892	+	0.308118i
$791$	−15.9443	+	27.6163i	−0.566913	+	0.981922i
$792$	−0.827248	+	4.69156i	−0.0293950	+	0.166707i
$793$	1.46301	−	1.22762i	0.0519532	−	0.0435939i
$794$	17.1293	+	14.3732i	0.607895	+	0.510085i
$795$	−4.72949	−	26.8223i	−0.167738	−	0.951289i
$796$	−9.84059	−	3.58168i	−0.348790	−	0.126949i
$797$	28.4377			1.00731			0.503657	−	0.863903i	$-0.331987\pi$
$797$	28.4377			1.00731			0.503657	+	0.863903i	$0.331987\pi$
$798$		0			0
$799$	−15.1246			−0.535070
$800$	7.60227	+	2.76700i	0.268781	+	0.0978283i
$801$	−2.26341	−	12.8364i	−0.0799736	−	0.453553i
$802$	−14.5122	−	12.1771i	−0.512442	−	0.429990i
$803$	13.9269	−	11.6861i	0.491471	−	0.412393i
$804$	−2.51306	+	14.2523i	−0.0886288	+	0.502639i
$805$	−30.6525	+	53.0916i	−1.08036	+	1.87123i
$806$	−0.854102	−	1.47935i	−0.0300845	−	0.0521078i
$807$	16.6403	−	6.05656i	0.585765	−	0.213201i
$808$	−14.6762	+	5.34168i	−0.516305	+	0.187920i
$809$	−1.37132	−	2.37520i	−0.0482131	−	0.0835076i	0.840912	−	0.541172i	$-0.182019\pi$
$809$	−1.37132	−	2.37520i	−0.0482131	−	0.0835076i	−0.889125	+	0.457665i	$0.848686\pi$
$810$	4.37132	−	7.57135i	0.153593	−	0.266030i
$811$	0.971865	−	5.51172i	0.0341268	−	0.193543i	−0.962978	−	0.269579i	$-0.913115\pi$
$811$	0.971865	−	5.51172i	0.0341268	−	0.193543i	0.997105	+	0.0760364i	$0.0242265\pi$
$812$	22.5343	−	18.9085i	0.790798	−	0.663558i
$813$	−24.6190	−	20.6578i	−0.863425	−	0.724499i
$814$	4.71014	+	26.7125i	0.165090	+	0.936274i
$815$	36.2167	+	13.1818i	1.26862	+	0.461738i
$816$	4.18034			0.146341
$817$		0			0
$818$	−16.2705			−0.568885
$819$	−6.18655	−	2.25172i	−0.216176	−	0.0786815i
$820$	−0.536602	−	3.04322i	−0.0187390	−	0.106274i
$821$	14.7621	+	12.3868i	0.515200	+	0.432304i	0.862954	−	0.505282i	$-0.168611\pi$
$821$	14.7621	+	12.3868i	0.515200	+	0.432304i	−0.347755	+	0.937586i	$0.613056\pi$
$822$	2.25544	−	1.89254i	0.0786676	−	0.0660100i
$823$	−3.61758	+	20.5163i	−0.126101	+	0.715154i	0.854547	+	0.519374i	$0.173835\pi$
$823$	−3.61758	+	20.5163i	−0.126101	+	0.715154i	−0.980648	+	0.195780i	$0.937276\pi$
$824$	7.32624	−	12.6894i	0.255222	−	0.442057i
$825$	−16.1803	−	28.0252i	−0.563327	−	0.975711i
$826$	1.43572	−	0.522560i	0.0499552	−	0.0181822i
$827$	28.6992	−	10.4456i	0.997968	−	0.363231i	0.209167	−	0.977880i	$-0.432925\pi$
$827$	28.6992	−	10.4456i	0.997968	−	0.363231i	0.788801	+	0.614649i	$0.210702\pi$
$828$	3.85410	+	6.67550i	0.133939	+	0.231990i
$829$	4.86475	−	8.42599i	0.168960	−	0.292647i	−0.769095	−	0.639135i	$-0.779293\pi$
$829$	4.86475	−	8.42599i	0.168960	−	0.292647i	0.938054	+	0.346488i	$0.112626\pi$
$830$	−0.296626	+	1.68225i	−0.0102961	+	0.0583918i
$831$	9.55421	−	8.01693i	0.331432	−	0.278104i
$832$	1.05865	+	0.888311i	0.0367020	+	0.0307966i
$833$	−2.03909	−	11.5642i	−0.0706502	−	0.400677i
$834$	16.2613	+	5.91864i	0.563084	+	0.204946i
$835$	45.1246			1.56160
$836$		0			0
$837$	−6.83282			−0.236177
$838$	−6.08182	−	2.21360i	−0.210093	−	0.0764676i
$839$	3.82026	+	21.6658i	0.131890	+	0.747985i	0.976975	+	0.213354i	$0.0684386\pi$
$839$	3.82026	+	21.6658i	0.131890	+	0.747985i	−0.845085	+	0.534632i	$0.820450\pi$
$840$	11.0863	+	9.30251i	0.382514	+	0.320967i
$841$	41.0839	−	34.4735i	1.41669	−	1.18874i
$842$	−2.41542	+	13.6985i	−0.0832408	+	0.472082i
$843$	12.9656	−	22.4570i	0.446558	−	0.773460i
$844$	3.61803	+	6.26662i	0.124538	+	0.215706i
$845$	−37.7048	+	13.7234i	−1.29708	+	0.472100i
$846$	−6.18655	+	2.25172i	−0.212698	+	0.0774158i
$847$	−0.854102	−	1.47935i	−0.0293473	−	0.0508310i
$848$	3.04508	−	5.27424i	0.104569	−	0.181118i
$849$	−4.82344	+	27.3551i	−0.165540	+	0.938824i
$850$	20.9595	−	17.5871i	0.718905	−	0.603233i
$851$	33.6206	+	28.2110i	1.15250	+	0.967061i
$852$	−0.631961	−	3.58403i	−0.0216506	−	0.122787i
$853$	27.3358	+	9.94942i	0.935961	+	0.340662i	0.764570	−	0.644541i	$-0.222952\pi$
$853$	27.3358	+	9.94942i	0.935961	+	0.340662i	0.171391	+	0.985203i	$0.445174\pi$
$854$	4.47214			0.153033
$855$		0			0
$856$	−9.41641			−0.321846
$857$	−5.22686	−	1.90242i	−0.178546	−	0.0649855i	0.251200	−	0.967935i	$-0.419175\pi$
$857$	−5.22686	−	1.90242i	−0.178546	−	0.0649855i	−0.429746	+	0.902950i	$0.641397\pi$
$858$	−0.959904	−	5.44388i	−0.0327706	−	0.185851i
$859$	21.5020	+	18.0423i	0.733639	+	0.615596i	0.931121	−	0.364710i	$-0.118832\pi$
$859$	21.5020	+	18.0423i	0.733639	+	0.615596i	−0.197482	+	0.980307i	$0.563276\pi$
$860$	25.5985	−	21.4797i	0.872900	−	0.732450i
$861$	0.593253	−	3.36450i	0.0202180	−	0.114662i
$862$	3.32624	−	5.76121i	0.113292	−	0.196228i
$863$	12.9443	+	22.4201i	0.440628	+	0.763190i	0.997736	−	0.0672497i	$-0.0214224\pi$
$863$	12.9443	+	22.4201i	0.440628	+	0.763190i	−0.557108	+	0.830440i	$0.688089\pi$
$864$	5.19449	−	1.89064i	0.176720	−	0.0643209i
$865$	4.50900	−	1.64114i	0.153310	−	0.0558005i
$866$	−12.5172	−	21.6805i	−0.425352	−	0.736732i
$867$	−3.43769	+	5.95426i	−0.116750	+	0.202217i
$868$	0.694593	−	3.93923i	0.0235760	−	0.133706i
$869$	6.85171	−	5.74927i	0.232428	−	0.195031i
$870$	31.1416	+	26.1309i	1.05580	+	0.885921i
$871$	2.80969	+	15.9345i	0.0952026	+	0.539921i
$872$	−10.3690	−	3.77400i	−0.351138	−	0.127804i
$873$	−12.6869			−0.429387
$874$		0			0
$875$	36.1803			1.22312
$876$	−6.52548	−	2.37508i	−0.220476	−	0.0802465i
$877$	0.302607	+	1.71617i	0.0102183	+	0.0579510i	0.989491	−	0.144598i	$-0.0461887\pi$
$877$	0.302607	+	1.71617i	0.0102183	+	0.0579510i	−0.979272	+	0.202548i	$0.935078\pi$
$878$	−22.3961	−	18.7926i	−0.755833	−	0.634219i
$879$	−21.7255	+	18.2299i	−0.732784	+	0.614879i
$880$	2.03311	−	11.5303i	0.0685361	−	0.388687i
$881$	−2.60739	+	4.51613i	−0.0878452	+	0.152152i	−0.906600	−	0.421991i	$-0.861331\pi$
$881$	−2.60739	+	4.51613i	−0.0878452	+	0.152152i	0.818755	+	0.574143i	$0.194665\pi$
$882$	−2.55573	−	4.42665i	−0.0860558	−	0.149053i
$883$	16.7450	−	6.09468i	0.563514	−	0.205102i	−0.0445266	−	0.999008i	$-0.514178\pi$
$883$	16.7450	−	6.09468i	0.563514	−	0.205102i	0.608041	+	0.793906i	$0.291956\pi$
$884$	4.39190	−	1.59852i	0.147716	−	0.0537641i
$885$	1.05573	+	1.82857i	0.0354879	+	0.0614669i
$886$	4.61803	−	7.99867i	0.155146	−	0.268721i
$887$	1.20586	−	6.83877i	0.0404888	−	0.229624i	−0.957848	−	0.287276i	$-0.907250\pi$
$887$	1.20586	−	6.83877i	0.0404888	−	0.229624i	0.998337	+	0.0576523i	$0.0183615\pi$
$888$	7.93674	−	6.65972i	0.266340	−	0.223485i
$889$	28.3010	+	23.7473i	0.949184	+	0.796460i
$890$	5.56272	+	31.5478i	0.186463	+	1.05748i
$891$	−7.34808	−	2.67448i	−0.246170	−	0.0895985i
$892$	27.7082			0.927739
$893$		0			0
$894$	−16.1803			−0.541152
$895$	−79.6120	−	28.9764i	−2.66114	−	0.968575i
$896$	0.561937	+	3.18690i	0.0187730	+	0.106467i
$897$	−6.85171	−	5.74927i	−0.228772	−	0.191962i
$898$	17.4646	−	14.6545i	0.582800	−	0.489027i
$899$	1.95112	−	11.0654i	0.0650736	−	0.369051i
$900$	5.95492	−	10.3142i	0.198497	−	0.343807i
$901$	−10.2984	−	17.8373i	−0.343089	−	0.594247i
$902$	−2.59725	+	0.945320i	−0.0864788	+	0.0314757i
$903$	34.7163	−	12.6357i	1.15528	−	0.420489i
$904$	−4.92705	−	8.53390i	−0.163871	−	0.283833i
$905$	9.79837	−	16.9713i	0.325709	−	0.564144i
$906$	3.10631	−	17.6168i	0.103200	−	0.585278i
$907$	−0.223529	+	0.187563i	−0.00742215	+	0.00622792i	−0.646491	−	0.762921i	$-0.723764\pi$
$907$	−0.223529	+	0.187563i	−0.00742215	+	0.00622792i	0.639069	+	0.769149i	$0.279320\pi$
$908$	−6.85171	−	5.74927i	−0.227382	−	0.190796i
$909$	3.99250	+	22.6426i	0.132423	+	0.751007i
$910$	15.2045	+	5.53400i	0.504026	+	0.183450i
$911$	12.0689			0.399860			0.199930	−	0.979810i	$-0.435929\pi$
$911$	12.0689			0.399860			0.199930	+	0.979810i	$0.435929\pi$
$912$		0			0
$913$	1.52786			0.0505649
$914$	23.6941	+	8.62396i	0.783733	+	0.285255i
$915$	1.07320	+	6.08645i	0.0354791	+	0.201212i
$916$	3.35678	+	2.81667i	0.110911	+	0.0930655i
$917$	−11.0863	+	9.30251i	−0.366102	+	0.307196i
$918$	3.24636	−	18.4110i	0.107146	−	0.607654i
$919$	−22.9443	+	39.7406i	−0.756862	+	1.31092i	0.187582	+	0.982249i	$0.439935\pi$
$919$	−22.9443	+	39.7406i	−0.756862	+	1.31092i	−0.944443	+	0.328674i	$0.893398\pi$
$920$	−9.47214	−	16.4062i	−0.312287	−	0.540897i
$921$	13.5994	−	4.94976i	0.448114	−	0.163100i
$922$	20.1248	−	7.32484i	0.662776	−	0.241231i
$923$	−2.03444	−	3.52376i	−0.0669645	−	0.115986i
$924$	6.47214	−	11.2101i	0.212918	−	0.368784i
$925$	11.7753	−	66.7813i	0.387171	−	2.19576i
$926$	3.87291	−	3.24976i	0.127272	−	0.106794i
$927$	−16.5239	−	13.8652i	−0.542717	−	0.455393i
$928$	1.57849	+	8.95207i	0.0518165	+	0.293866i
$929$	55.5913	+	20.2336i	1.82389	+	0.663842i	0.994445	+	0.105257i	$0.0335667\pi$
$929$	55.5913	+	20.2336i	1.82389	+	0.663842i	0.829447	+	0.558585i	$0.188656\pi$
$930$	5.52786			0.181266
$931$		0			0
$932$	1.56231			0.0511750
$933$	36.2814	+	13.2054i	1.18780	+	0.432324i
$934$	5.78334	+	32.7990i	0.189237	+	1.07322i
$935$	−30.3329	−	25.4523i	−0.991991	−	0.832379i
$936$	1.55847	−	1.30771i	0.0509403	−	0.0427440i
$937$	2.75902	−	15.6472i	0.0901331	−	0.511170i	−0.905997	−	0.423283i	$-0.860877\pi$
$937$	2.75902	−	15.6472i	0.0901331	−	0.511170i	0.996130	−	0.0878870i	$-0.0280114\pi$
$938$	−18.9443	+	32.8124i	−0.618552	+	1.07136i
$939$	−9.58359	−	16.5993i	−0.312749	−	0.541697i
$940$	15.2045	−	5.53400i	0.495918	−	0.180499i
$941$	−24.4320	+	8.89252i	−0.796461	+	0.289888i	−0.708019	−	0.706193i	$-0.750411\pi$
$941$	−24.4320	+	8.89252i	−0.796461	+	0.289888i	−0.0884417	+	0.996081i	$0.528189\pi$
$942$	−5.79837	−	10.0431i	−0.188921	−	0.327221i
$943$	−2.23607	+	3.87298i	−0.0728164	+	0.126122i
$944$	−0.0819855	+	0.464963i	−0.00266840	+	0.0151333i
$945$	49.5794	−	41.6021i	1.61282	−	1.35332i
$946$	−22.8960	−	19.2120i	−0.744412	−	0.624636i
$947$	1.42050	+	8.05606i	0.0461601	+	0.261787i	0.999150	−	0.0412141i	$-0.0131226\pi$
$947$	1.42050	+	8.05606i	0.0461601	+	0.261787i	−0.952990	+	0.303001i	$0.902011\pi$
$948$	−3.21037	−	1.16848i	−0.104268	−	0.0379505i
$949$	−7.76393			−0.252028
$950$		0			0
$951$	−1.63932			−0.0531586
$952$	10.2843	+	3.74316i	0.333315	+	0.121317i
$953$	8.30238	+	47.0852i	0.268941	+	1.52524i	0.757574	+	0.652749i	$0.226384\pi$
$953$	8.30238	+	47.0852i	0.268941	+	1.52524i	−0.488634	+	0.872489i	$0.662505\pi$
$954$	−6.86802	−	5.76295i	−0.222360	−	0.186582i
$955$	−9.77774	+	8.20450i	−0.316400	+	0.265491i
$956$	5.24076	−	29.7218i	0.169498	−	0.961273i
$957$	18.1803	−	31.4893i	0.587687	−	1.01790i
$958$	3.85410	+	6.67550i	0.124520	+	0.215676i
$959$	7.24334	−	2.63636i	0.233900	−	0.0851325i
$960$	−4.20243	+	1.52956i	−0.135633	+	0.0493664i
$961$	14.7361	+	25.5236i	0.475357	+	0.823343i
$962$	5.79180	−	10.0317i	0.186735	−	0.323435i
$963$	−2.40715	+	13.6516i	−0.0775694	+	0.439918i
$964$	−19.4701	+	16.3374i	−0.627090	+	0.526191i
$965$	31.9503	+	26.8095i	1.02852	+	0.863029i
$966$	−3.63693	−	20.6261i	−0.117016	−	0.663633i
$967$	−8.30013	−	3.02100i	−0.266914	−	0.0971488i	0.205096	−	0.978742i	$-0.434249\pi$
$967$	−8.30013	−	3.02100i	−0.266914	−	0.0971488i	−0.472010	+	0.881593i	$0.656472\pi$
$968$	0.527864			0.0169662
$969$		0			0
$970$	31.1803			1.00114
$971$	−56.8899	−	20.7062i	−1.82569	−	0.664495i	−0.994017	−	0.109222i	$-0.965164\pi$
$971$	−56.8899	−	20.7062i	−1.82569	−	0.664495i	−0.831668	−	0.555273i	$-0.812614\pi$
$972$	−2.36105	−	13.3902i	−0.0757307	−	0.429490i
$973$	34.7056	+	29.1215i	1.11261	+	0.933591i
$974$	−14.7357	+	12.3647i	−0.472162	+	0.396191i
$975$	−2.39976	+	13.6097i	−0.0768538	+	0.435859i
$976$	−0.690983	+	1.19682i	−0.0221178	+	0.0383092i
$977$	4.51722	+	7.82406i	0.144519	+	0.250314i	0.929193	−	0.369594i	$-0.120503\pi$
$977$	4.51722	+	7.82406i	0.144519	+	0.250314i	−0.784675	+	0.619908i	$0.787170\pi$
$978$	−12.3731	+	4.50344i	−0.395648	+	0.144004i
$979$	26.9245	−	9.79972i	0.860511	−	0.313201i
$980$	6.28115	+	10.8793i	0.200644	+	0.347526i
$981$	−8.12210	+	14.0679i	−0.259319	+	0.449153i
$982$	0.265311	−	1.50465i	0.00846641	−	0.0480154i
$983$	15.0120	−	12.5965i	0.478808	−	0.401767i	−0.371187	−	0.928558i	$-0.621049\pi$
$983$	15.0120	−	12.5965i	0.478808	−	0.401767i	0.849995	+	0.526791i	$0.176605\pi$
$984$	0.808735	+	0.678609i	0.0257815	+	0.0216333i
$985$	2.60472	+	14.7721i	0.0829934	+	0.470679i
$986$	28.8886	+	10.5146i	0.920002	+	0.334853i
$987$	17.8885			0.569399
$988$		0			0
$989$	−48.3607			−1.53778
$990$	−16.1966	−	5.89508i	−0.514762	−	0.187358i
$991$	−5.32275	−	30.1868i	−0.169083	−	0.958915i	−0.944754	−	0.327779i	$-0.893700\pi$
$991$	−5.32275	−	30.1868i	−0.169083	−	0.958915i	0.775672	−	0.631136i	$-0.217411\pi$
$992$	0.946883	+	0.794529i	0.0300636	+	0.0252263i
$993$	−24.3427	+	20.4259i	−0.772491	+	0.648197i
$994$	1.65450	−	9.38311i	0.0524774	−	0.297614i
$995$	18.9443	−	32.8124i	0.600574	−	1.04022i
$996$	−0.291796	−	0.505406i	−0.00924591	−	0.0160144i
$997$	12.6920	−	4.61952i	0.401961	−	0.146302i	−0.133126	−	0.991099i	$-0.542501\pi$
$997$	12.6920	−	4.61952i	0.401961	−	0.146302i	0.535086	+	0.844797i	$0.320279\pi$
$998$	−33.1758	+	12.0750i	−1.05016	+	0.382228i
$999$	−23.1672	−	40.1267i	−0.732977	−	1.26955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.q.99.1		12
19.2	odd	18		722.2.e.p.415.1		12
19.3	odd	18		722.2.e.p.245.2		12
19.4	even	9		722.2.c.i.653.2		4
19.5	even	9	inner	722.2.e.q.423.1		12
19.6	even	9		722.2.c.i.429.2		4
19.7	even	3	inner	722.2.e.q.595.2		12
19.8	odd	6		722.2.e.p.389.2		12
19.9	even	9		722.2.a.h.1.1	✓	2
19.10	odd	18		722.2.a.i.1.2	yes	2
19.11	even	3	inner	722.2.e.q.389.1		12
19.12	odd	6		722.2.e.p.595.1		12
19.13	odd	18		722.2.c.h.429.1		4
19.14	odd	18		722.2.e.p.423.2		12
19.15	odd	18		722.2.c.h.653.1		4
19.16	even	9	inner	722.2.e.q.245.1		12
19.17	even	9	inner	722.2.e.q.415.2		12
19.18	odd	2		722.2.e.p.99.2		12
57.29	even	18		6498.2.a.be.1.2		2
57.47	odd	18		6498.2.a.bk.1.2		2
76.47	odd	18		5776.2.a.t.1.2		2
76.67	even	18		5776.2.a.be.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.h.1.1	✓	2	19.9	even	9
722.2.a.i.1.2	yes	2	19.10	odd	18
722.2.c.h.429.1		4	19.13	odd	18
722.2.c.h.653.1		4	19.15	odd	18
722.2.c.i.429.2		4	19.6	even	9
722.2.c.i.653.2		4	19.4	even	9
722.2.e.p.99.2		12	19.18	odd	2
722.2.e.p.245.2		12	19.3	odd	18
722.2.e.p.389.2		12	19.8	odd	6
722.2.e.p.415.1		12	19.2	odd	18
722.2.e.p.423.2		12	19.14	odd	18
722.2.e.p.595.1		12	19.12	odd	6
722.2.e.q.99.1		12	1.1	even	1	trivial
722.2.e.q.245.1		12	19.16	even	9	inner
722.2.e.q.389.1		12	19.11	even	3	inner
722.2.e.q.415.2		12	19.17	even	9	inner
722.2.e.q.423.1		12	19.5	even	9	inner
722.2.e.q.595.2		12	19.7	even	3	inner
5776.2.a.t.1.2		2	76.47	odd	18
5776.2.a.be.1.1		2	76.67	even	18
6498.2.a.be.1.2		2	57.29	even	18
6498.2.a.bk.1.2		2	57.47	odd	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.214641 - 1.21729i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-2.77157 + 2.32563i) q^{5} +(0.214641 - 1.21729i) q^{6} +(1.61803 - 2.80252i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.38336 - 0.503500i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.214641 - 1.21729i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-2.77157 + 2.32563i) q^{5} +(0.214641 - 1.21729i) q^{6} +(1.61803 - 2.80252i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.38336 - 0.503500i) q^{9} +(-3.39984 + 1.23744i) q^{10} +(1.61803 + 2.80252i) q^{11} +(0.618034 - 1.07047i) q^{12} +(0.239976 - 1.36097i) q^{13} +(2.47897 - 2.08010i) q^{14} +(3.42585 + 2.87463i) q^{15} +(0.173648 + 0.984808i) q^{16} +(3.17801 + 1.15670i) q^{17} +1.47214 q^{18} -3.61803 q^{20} +(-3.75877 - 1.36808i) q^{21} +(0.561937 + 3.18690i) q^{22} +(4.01106 + 3.36568i) q^{23} +(0.946883 - 0.794529i) q^{24} +(1.40484 - 7.96726i) q^{25} +(0.690983 - 1.19682i) q^{26} +(-2.76393 - 4.78727i) q^{27} +(3.04091 - 1.10680i) q^{28} +(8.54197 - 3.10902i) q^{29} +(2.23607 + 3.87298i) q^{30} +(0.618034 - 1.07047i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(3.06418 - 2.57115i) q^{33} +(2.59074 + 2.17389i) q^{34} +(2.03311 + 11.5303i) q^{35} +(1.38336 + 0.503500i) q^{36} +8.38197 q^{37} -1.70820 q^{39} +(-3.39984 - 1.23744i) q^{40} +(0.148313 + 0.841126i) q^{41} +(-3.06418 - 2.57115i) q^{42} +(-7.07524 + 5.93683i) q^{43} +(-0.561937 + 3.18690i) q^{44} +(-2.66312 + 4.61266i) q^{45} +(2.61803 + 4.53457i) q^{46} +(-4.20243 + 1.52956i) q^{47} +(1.16152 - 0.422760i) q^{48} +(-1.73607 - 3.00696i) q^{49} +(4.04508 - 7.00629i) q^{50} +(0.725908 - 4.11683i) q^{51} +(1.05865 - 0.888311i) q^{52} +(-4.66534 - 3.91469i) q^{53} +(-0.959904 - 5.44388i) q^{54} +(-11.0021 - 4.00444i) q^{55} +3.23607 q^{56} +9.09017 q^{58} +(0.443663 + 0.161480i) q^{59} +(0.776578 + 4.40419i) q^{60} +(1.05865 + 0.888311i) q^{61} +(0.946883 - 0.794529i) q^{62} +(0.827248 - 4.69156i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.50000 + 4.33013i) q^{65} +(3.75877 - 1.36808i) q^{66} +(-11.0021 + 4.00444i) q^{67} +(1.69098 + 2.92887i) q^{68} +(3.23607 - 5.60503i) q^{69} +(-2.03311 + 11.5303i) q^{70} +(2.25544 - 1.89254i) q^{71} +(1.12772 + 0.946271i) q^{72} +(-0.975561 - 5.53268i) q^{73} +(7.87647 + 2.86680i) q^{74} -10.0000 q^{75} +10.4721 q^{77} +(-1.60519 - 0.584240i) q^{78} +(-0.479952 - 2.72194i) q^{79} +(-2.77157 - 2.32563i) q^{80} +(-1.85108 + 1.55324i) q^{81} +(-0.148313 + 0.841126i) q^{82} +(0.236068 - 0.408882i) q^{83} +(-2.00000 - 3.46410i) q^{84} +(-11.4981 + 4.18498i) q^{85} +(-8.67906 + 3.15892i) q^{86} +(-5.61803 - 9.73072i) q^{87} +(-1.61803 + 2.80252i) q^{88} +(1.53750 - 8.71959i) q^{89} +(-4.08013 + 3.42364i) q^{90} +(-3.42585 - 2.87463i) q^{91} +(0.909234 + 5.15652i) q^{92} +(-1.43572 - 0.522560i) q^{93} -4.47214 q^{94} +1.23607 q^{96} +(-8.09830 - 2.94754i) q^{97} +(-0.602930 - 3.41939i) q^{98} +(3.64938 + 3.06220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^7 + 6 * q^8	\( 12 q + 6 q^{7} + 6 q^{8} + 6 q^{11} - 6 q^{12} - 36 q^{18} - 30 q^{20} + 15 q^{26} - 60 q^{27} - 6 q^{31} + 114 q^{37} + 60 q^{39} + 15 q^{45} + 18 q^{46} + 6 q^{49} + 15 q^{50} + 12 q^{56} + 42 q^{58} - 6 q^{64} + 30 q^{65} + 27 q^{68} + 12 q^{69} - 120 q^{75} + 72 q^{77} - 24 q^{83} - 24 q^{84} - 54 q^{87} - 6 q^{88} - 12 q^{96}+O(q^{100}) \) 12 * q + 6 * q^7 + 6 * q^8 + 6 * q^11 - 6 * q^12 - 36 * q^18 - 30 * q^20 + 15 * q^26 - 60 * q^27 - 6 * q^31 + 114 * q^37 + 60 * q^39 + 15 * q^45 + 18 * q^46 + 6 * q^49 + 15 * q^50 + 12 * q^56 + 42 * q^58 - 6 * q^64 + 30 * q^65 + 27 * q^68 + 12 * q^69 - 120 * q^75 + 72 * q^77 - 24 * q^83 - 24 * q^84 - 54 * q^87 - 6 * q^88 - 12 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more