LMFDB - Embedded newform 663.2.ba.a.322.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [663,2,Mod(322,663)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(663, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("663.322");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 663 = 3 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	663.ba (of order $6$, degree $2$, 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:	$5.29408165401$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			322.1
Character	$\chi$	$=$	663.322
Dual form			663.2.ba.a.628.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27119 + 1.31127i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.43887 - 4.22425i) q^{4} +0.0141426 q^{5} +(1.31127 - 2.27119i) q^{6} +(0.545766 - 0.945294i) q^{7} +7.54702i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.27119 + 1.31127i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.43887 - 4.22425i) q^{4} +0.0141426 q^{5} +(1.31127 - 2.27119i) q^{6} +(0.545766 - 0.945294i) q^{7} +7.54702i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.0321205 + 0.0185448i) q^{10} +(-1.64112 - 2.84251i) q^{11} +4.87775i q^{12} +(3.25862 - 1.54318i) q^{13} +2.86259i q^{14} +(-0.0122478 + 0.00707128i) q^{15} +(-5.01845 - 8.69222i) q^{16} +(-1.54294 + 3.82352i) q^{17} +2.62255i q^{18} +(-0.326646 - 0.188589i) q^{19} +(0.0344919 - 0.0597418i) q^{20} +1.09153i q^{21} +(7.45461 + 4.30392i) q^{22} +(3.47973 - 2.00902i) q^{23} +(-3.77351 - 6.53591i) q^{24} -4.99980 q^{25} +(-5.37743 + 7.77779i) q^{26} +1.00000i q^{27} +(-2.66211 - 4.61090i) q^{28} +(-8.88297 + 5.12858i) q^{29} +(0.0185448 - 0.0321205i) q^{30} -6.91262 q^{31} +(9.72392 + 5.61411i) q^{32} +(2.84251 + 1.64112i) q^{33} +(-1.50936 - 10.7072i) q^{34} +(0.00771853 - 0.0133689i) q^{35} +(-2.43887 - 4.22425i) q^{36} +(-2.25533 - 3.90635i) q^{37} +0.989167 q^{38} +(-2.05046 + 2.96574i) q^{39} +0.106734i q^{40} +(-5.04965 - 8.74626i) q^{41} +(-1.43130 - 2.47908i) q^{42} +(1.94386 - 3.36687i) q^{43} -16.0100 q^{44} +(0.00707128 - 0.0122478i) q^{45} +(-5.26875 + 9.12574i) q^{46} +0.540462i q^{47} +(8.69222 + 5.01845i) q^{48} +(2.90428 + 5.03036i) q^{49} +(11.3555 - 6.55610i) q^{50} +(-0.575533 - 4.08274i) q^{51} +(1.42860 - 17.5288i) q^{52} +2.17250 q^{53} +(-1.31127 - 2.27119i) q^{54} +(-0.0232097 - 0.0402004i) q^{55} +(7.13415 + 4.11890i) q^{56} +0.377178 q^{57} +(13.4499 - 23.2960i) q^{58} +(3.92561 + 2.26645i) q^{59} +0.0689838i q^{60} +(-0.600479 - 0.346687i) q^{61} +(15.6999 - 9.06434i) q^{62} +(-0.545766 - 0.945294i) q^{63} -9.37268 q^{64} +(0.0460853 - 0.0218245i) q^{65} -8.60785 q^{66} +(-4.10836 + 2.37196i) q^{67} +(12.3885 + 15.8429i) q^{68} +(-2.00902 + 3.47973i) q^{69} +0.0404844i q^{70} +(6.14996 - 10.6520i) q^{71} +(6.53591 + 3.77351i) q^{72} -6.47605 q^{73} +(10.2446 + 5.91472i) q^{74} +(4.32995 - 2.49990i) q^{75} +(-1.59330 + 0.919890i) q^{76} -3.58268 q^{77} +(0.768095 - 9.42447i) q^{78} -4.58820i q^{79} +(-0.0709738 - 0.122930i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(22.9375 + 13.2429i) q^{82} -13.1412i q^{83} +(4.61090 + 2.66211i) q^{84} +(-0.0218212 + 0.0540744i) q^{85} +10.1957i q^{86} +(5.12858 - 8.88297i) q^{87} +(21.4525 - 12.3856i) q^{88} +(-3.41470 + 1.97148i) q^{89} +0.0370895i q^{90} +(0.319689 - 3.92257i) q^{91} -19.5990i q^{92} +(5.98651 - 3.45631i) q^{93} +(-0.708694 - 1.22749i) q^{94} +(-0.00461961 - 0.00266713i) q^{95} -11.2282 q^{96} +(3.83780 - 6.64726i) q^{97} +(-13.1923 - 7.61661i) q^{98} -3.28225 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 36 q^{4} + 40 q^{9}+O(q^{10}) $ 80 * q + 36 * q^4 + 40 * q^9	$ 80 q + 36 q^{4} + 40 q^{9} - 4 q^{13} - 6 q^{15} - 12 q^{16} - 4 q^{17} + 44 q^{25} - 16 q^{26} - 8 q^{30} - 60 q^{32} - 6 q^{33} - 36 q^{36} + 96 q^{38} + 4 q^{42} + 10 q^{43} - 8 q^{49} + 48 q^{50} + 16 q^{51} + 72 q^{52} - 40 q^{53} + 44 q^{55} + 144 q^{59} - 56 q^{64} - 16 q^{66} - 48 q^{67} + 40 q^{68} - 26 q^{69} - 48 q^{76} - 64 q^{77} - 40 q^{81} + 6 q^{85} - 4 q^{87} - 48 q^{89} - 44 q^{94} + 36 q^{98}+O(q^{100}) $ 80 * q + 36 * q^4 + 40 * q^9 - 4 * q^13 - 6 * q^15 - 12 * q^16 - 4 * q^17 + 44 * q^25 - 16 * q^26 - 8 * q^30 - 60 * q^32 - 6 * q^33 - 36 * q^36 + 96 * q^38 + 4 * q^42 + 10 * q^43 - 8 * q^49 + 48 * q^50 + 16 * q^51 + 72 * q^52 - 40 * q^53 + 44 * q^55 + 144 * q^59 - 56 * q^64 - 16 * q^66 - 48 * q^67 + 40 * q^68 - 26 * q^69 - 48 * q^76 - 64 * q^77 - 40 * q^81 + 6 * q^85 - 4 * q^87 - 48 * q^89 - 44 * q^94 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/663\mathbb{Z}\right)^\times$.

$n$	$443$	$547$	$613$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.27119	+	1.31127i	−1.60597	+	0.927210i	−0.615716	+	0.787968i	$0.711133\pi$
$2$	−2.27119	+	1.31127i	−1.60597	+	0.927210i	−0.990258	+	0.139242i	$0.955533\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	2.43887	−	4.22425i	1.21944	−	2.11213i
$5$	0.0141426			0.00632475			0.00316237	−	0.999995i	$-0.498993\pi$
$5$	0.0141426			0.00632475			0.00316237	+	0.999995i	$0.498993\pi$
$6$	1.31127	−	2.27119i	0.535325	−	0.927210i
$7$	0.545766	−	0.945294i	0.206280	−	0.357288i	−0.744260	−	0.667890i	$-0.767198\pi$
$7$	0.545766	−	0.945294i	0.206280	−	0.357288i	0.950540	+	0.310603i	$0.100531\pi$
$8$			7.54702i			2.66827i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.0321205	+	0.0185448i	−0.0101574	+	0.00586437i
$11$	−1.64112	−	2.84251i	−0.494818	−	0.857049i	0.505165	−	0.863023i	$-0.331432\pi$
$11$	−1.64112	−	2.84251i	−0.494818	−	0.857049i	−0.999982	+	0.00597378i	$0.998098\pi$
$12$			4.87775i			1.40808i
$13$	3.25862	−	1.54318i	0.903779	−	0.428000i
$13$	3.25862	−	1.54318i	0.903779	−	0.428000i
$14$			2.86259i			0.765060i
$15$	−0.0122478	+	0.00707128i	−0.00316237	+	0.00182580i
$16$	−5.01845	−	8.69222i	−1.25461	−	2.17305i
$17$	−1.54294	+	3.82352i	−0.374219	+	0.927340i
$17$	−1.54294	+	3.82352i	−0.374219	+	0.927340i
$18$			2.62255i			0.618140i
$19$	−0.326646	−	0.188589i	−0.0749377	−	0.0432653i	0.462063	−	0.886847i	$-0.347109\pi$
$19$	−0.326646	−	0.188589i	−0.0749377	−	0.0432653i	−0.537001	+	0.843582i	$0.680443\pi$
$20$	0.0344919	−	0.0597418i	0.00771263	−	0.0133587i
$21$			1.09153i			0.238192i
$22$	7.45461	+	4.30392i	1.58933	+	0.917600i
$23$	3.47973	−	2.00902i	0.725573	−	0.418910i	−0.0912275	−	0.995830i	$-0.529079\pi$
$23$	3.47973	−	2.00902i	0.725573	−	0.418910i	0.816800	+	0.576920i	$0.195746\pi$
$24$	−3.77351	−	6.53591i	−0.770264	−	1.33414i
$25$	−4.99980			−0.999960
$26$	−5.37743	+	7.77779i	−1.05460	+	1.52535i
$27$			1.00000i			0.192450i
$28$	−2.66211	−	4.61090i	−0.503091	−	0.871379i
$29$	−8.88297	+	5.12858i	−1.64953	+	0.952354i	−0.672265	+	0.740310i	$0.734679\pi$
$29$	−8.88297	+	5.12858i	−1.64953	+	0.952354i	−0.977260	+	0.212044i	$0.931988\pi$
$30$	0.0185448	−	0.0321205i	0.00338579	−	0.00586437i
$31$	−6.91262			−1.24154			−0.620772	−	0.783991i	$-0.713181\pi$
$31$	−6.91262			−1.24154			−0.620772	+	0.783991i	$0.713181\pi$
$32$	9.72392	+	5.61411i	1.71896	+	0.992443i
$33$	2.84251	+	1.64112i	0.494818	+	0.285683i
$34$	−1.50936	−	10.7072i	−0.258853	−	1.83626i
$35$	0.00771853	−	0.0133689i	0.00130467	−	0.00225975i
$36$	−2.43887	−	4.22425i	−0.406479	−	0.704042i
$37$	−2.25533	−	3.90635i	−0.370775	−	0.642201i	0.618910	−	0.785462i	$-0.287574\pi$
$37$	−2.25533	−	3.90635i	−0.370775	−	0.642201i	−0.989685	+	0.143261i	$0.954241\pi$
$38$	0.989167			0.160464
$39$	−2.05046	+	2.96574i	−0.328337	+	0.474898i
$40$			0.106734i			0.0168762i
$41$	−5.04965	−	8.74626i	−0.788623	−	1.36594i	−0.926810	−	0.375530i	$-0.877461\pi$
$41$	−5.04965	−	8.74626i	−0.788623	−	1.36594i	0.138187	−	0.990406i	$-0.455873\pi$
$42$	−1.43130	−	2.47908i	−0.220854	−	0.382530i
$43$	1.94386	−	3.36687i	0.296436	−	0.513443i	−0.678882	−	0.734248i	$-0.737535\pi$
$43$	1.94386	−	3.36687i	0.296436	−	0.513443i	0.975318	+	0.220805i	$0.0708684\pi$
$44$	−16.0100			−2.41359
$45$	0.00707128	−	0.0122478i	0.00105412	−	0.00182580i
$46$	−5.26875	+	9.12574i	−0.776834	+	1.34552i
$47$			0.540462i			0.0788345i	0.999223	+	0.0394173i	$0.0125502\pi$
$47$			0.540462i			0.0788345i	−0.999223	+	0.0394173i	$0.987450\pi$
$48$	8.69222	+	5.01845i	1.25461	+	0.724351i
$49$	2.90428	+	5.03036i	0.414897	+	0.718623i
$50$	11.3555	−	6.55610i	1.60591	−	0.927173i
$51$	−0.575533	−	4.08274i	−0.0805907	−	0.571698i
$52$	1.42860	−	17.5288i	0.198111	−	2.43081i
$53$	2.17250			0.298416			0.149208	−	0.988806i	$-0.452328\pi$
$53$	2.17250			0.298416			0.149208	+	0.988806i	$0.452328\pi$
$54$	−1.31127	−	2.27119i	−0.178442	−	0.309070i
$55$	−0.0232097	−	0.0402004i	−0.00312960	−	0.00542062i
$56$	7.13415	+	4.11890i	0.953341	+	0.550412i
$57$	0.377178			0.0499585
$58$	13.4499	−	23.2960i	1.76606	−	3.05891i
$59$	3.92561	+	2.26645i	0.511071	+	0.295067i	0.733274	−	0.679933i	$-0.237991\pi$
$59$	3.92561	+	2.26645i	0.511071	+	0.295067i	−0.222203	+	0.975000i	$0.571325\pi$
$60$			0.0689838i			0.00890577i
$61$	−0.600479	−	0.346687i	−0.0768835	−	0.0443887i	0.461065	−	0.887366i	$-0.347467\pi$
$61$	−0.600479	−	0.346687i	−0.0768835	−	0.0443887i	−0.537949	+	0.842977i	$0.680801\pi$
$62$	15.6999	−	9.06434i	1.99389	−	1.15117i
$63$	−0.545766	−	0.945294i	−0.0687600	−	0.119096i
$64$	−9.37268			−1.17159
$65$	0.0460853	−	0.0218245i	0.00571617	−	0.00270699i
$66$	−8.60785			−1.05955
$67$	−4.10836	+	2.37196i	−0.501916	+	0.289781i	−0.729504	−	0.683976i	$-0.760249\pi$
$67$	−4.10836	+	2.37196i	−0.501916	+	0.289781i	0.227588	+	0.973757i	$0.426916\pi$
$68$	12.3885	+	15.8429i	1.50232	+	1.92123i
$69$	−2.00902	+	3.47973i	−0.241858	+	0.418910i
$70$			0.0404844i			0.00483881i
$71$	6.14996	−	10.6520i	0.729865	−	1.26416i	−0.227074	−	0.973877i	$-0.572916\pi$
$71$	6.14996	−	10.6520i	0.729865	−	1.26416i	0.956940	−	0.290287i	$-0.0937506\pi$
$72$	6.53591	+	3.77351i	0.770264	+	0.444712i
$73$	−6.47605			−0.757964			−0.378982	−	0.925404i	$-0.623726\pi$
$73$	−6.47605			−0.757964			−0.378982	+	0.925404i	$0.623726\pi$
$74$	10.2446	+	5.91472i	1.19091	+	0.687572i
$75$	4.32995	−	2.49990i	0.499980	−	0.288664i
$76$	−1.59330	+	0.919890i	−0.182764	+	0.105519i
$77$	−3.58268			−0.408284
$78$	0.768095	−	9.42447i	0.0869696	−	1.06711i
$79$		−	4.58820i		−	0.516213i	−0.966117	−	0.258106i	$-0.916902\pi$
$79$		−	4.58820i		−	0.516213i	0.966117	−	0.258106i	$-0.0830985\pi$
$80$	−0.0709738	−	0.122930i	−0.00793511	−	0.0137440i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	22.9375	+	13.2429i	2.53302	+	1.46244i
$83$		−	13.1412i		−	1.44243i	−0.692709	−	0.721217i	$-0.743583\pi$
$83$		−	13.1412i		−	1.44243i	0.692709	−	0.721217i	$-0.256417\pi$
$84$	4.61090	+	2.66211i	0.503091	+	0.290460i
$85$	−0.0218212	+	0.0540744i	−0.00236684	+	0.00586519i
$86$			10.1957i			1.09943i
$87$	5.12858	−	8.88297i	0.549842	−	0.952354i
$88$	21.4525	−	12.3856i	2.28684	−	1.32031i
$89$	−3.41470	+	1.97148i	−0.361957	+	0.208976i	−0.669939	−	0.742416i	$-0.733680\pi$
$89$	−3.41470	+	1.97148i	−0.361957	+	0.208976i	0.307982	+	0.951392i	$0.400346\pi$
$90$			0.0370895i			0.00390958i
$91$	0.319689	−	3.92257i	0.0335125	−	0.411197i
$92$		−	19.5990i		−	2.04333i
$93$	5.98651	−	3.45631i	0.620772	−	0.358403i
$94$	−0.708694	−	1.22749i	−0.0730962	−	0.126606i
$95$	−0.00461961	−	0.00266713i	−0.000473962	−	0.000273642i
$96$	−11.2282			−1.14597
$97$	3.83780	−	6.64726i	0.389669	−	0.674927i	−0.602736	−	0.797941i	$-0.705923\pi$
$97$	3.83780	−	6.64726i	0.389669	−	0.674927i	0.992405	+	0.123014i	$0.0392560\pi$
$98$	−13.1923	−	7.61661i	−1.33263	−	0.769393i
$99$	−3.28225			−0.329878
$100$	−12.1939	+	21.1204i	−1.21939	+	2.11204i
$101$	−5.01375	−	8.68407i	−0.498887	−	0.864098i	0.501112	−	0.865382i	$-0.332924\pi$
$101$	−5.01375	−	8.68407i	−0.498887	−	0.864098i	−0.999999	+	0.00128467i	$0.999591\pi$
$102$	6.66073	+	8.51800i	0.659511	+	0.843408i
$103$	−1.93704			−0.190862			−0.0954309	−	0.995436i	$-0.530423\pi$
$103$	−1.93704			−0.190862			−0.0954309	+	0.995436i	$0.530423\pi$
$104$	11.6464	+	24.5929i	1.14202	+	2.41153i
$105$			0.0154371i			0.00150650i
$106$	−4.93416	+	2.84874i	−0.479248	+	0.276694i
$107$	0.499363	−	0.288307i	0.0482752	−	0.0278717i	−0.475668	−	0.879625i	$-0.657794\pi$
$107$	0.499363	−	0.288307i	0.0482752	−	0.0278717i	0.523943	+	0.851753i	$0.324460\pi$
$108$	4.22425	+	2.43887i	0.406479	+	0.234681i
$109$	−17.9069			−1.71517			−0.857587	−	0.514339i	$-0.828037\pi$
$109$	−17.9069			−1.71517			−0.857587	+	0.514339i	$0.828037\pi$
$110$	0.105427	+	0.0608685i	0.0100521	+	0.00580359i
$111$	3.90635	+	2.25533i	0.370775	+	0.214067i
$112$	−10.9556			−1.03521
$113$	−13.8140	−	7.97551i	−1.29951	−	0.750273i	−0.319191	−	0.947691i	$-0.603411\pi$
$113$	−13.8140	−	7.97551i	−1.29951	−	0.750273i	−0.980319	+	0.197418i	$0.936744\pi$
$114$	−0.856644	+	0.494584i	−0.0802321	+	0.0463220i
$115$	0.0492122	−	0.0284127i	0.00458907	−	0.00264950i
$116$			50.0318i			4.64534i
$117$	0.292881	−	3.59364i	0.0270769	−	0.332232i
$118$	−11.8878			−1.09436
$119$	2.77227	+	3.54528i	0.254133	+	0.324996i
$120$	−0.0533671	−	0.0924345i	−0.00487173	−	0.00843808i
$121$	0.113421	−	0.196451i	0.0103110	−	0.0178592i
$122$	1.81840			0.164631
$123$	8.74626	+	5.04965i	0.788623	+	0.455312i
$124$	−16.8590	+	29.2007i	−1.51398	+	2.62230i
$125$	−0.141423			−0.0126492
$126$	2.47908	+	1.43130i	0.220854	+	0.127510i
$127$	8.33942	+	14.4443i	0.740004	+	1.28172i	0.952493	+	0.304561i	$0.0985099\pi$
$127$	8.33942	+	14.4443i	0.740004	+	1.28172i	−0.212489	+	0.977164i	$0.568157\pi$
$128$	1.83932	−	1.06193i	0.162574	−	0.0938623i
$129$			3.88772i			0.342295i
$130$	−0.0760506	+	0.109998i	−0.00667008	+	0.00964745i
$131$			11.9703i			1.04585i	0.852378	+	0.522925i	$0.175159\pi$
$131$			11.9703i			1.04585i	−0.852378	+	0.522925i	$0.824841\pi$
$132$	13.8650	−	8.00499i	1.20680	−	0.696745i
$133$	−0.356544	+	0.205851i	−0.0309163	+	0.0178495i
$134$	6.22058	−	10.7744i	0.537376	−	0.930763i
$135$			0.0141426i			0.00121720i
$136$	−28.8562	−	11.6446i	−2.47440	−	0.998518i
$137$	−9.24293	−	5.33641i	−0.789677	−	0.455920i	0.0501717	−	0.998741i	$-0.484023\pi$
$137$	−9.24293	−	5.33641i	−0.789677	−	0.455920i	−0.839849	+	0.542820i	$0.817356\pi$
$138$		−	10.5375i		−	0.897011i
$139$	−7.20622	−	4.16051i	−0.611223	−	0.352890i	0.162221	−	0.986754i	$-0.448134\pi$
$139$	−7.20622	−	4.16051i	−0.611223	−	0.352890i	−0.773444	+	0.633865i	$0.781468\pi$
$140$	−0.0376490	−	0.0652100i	−0.00318192	−	0.00551125i
$141$	−0.270231	−	0.468054i	−0.0227576	−	0.0394173i
$142$			32.2571i			2.70695i
$143$	−9.73429	−	6.73012i	−0.814023	−	0.562801i
$144$	−10.0369			−0.836409
$145$	−0.125628	+	0.0725313i	−0.0104328	+	0.00602340i
$146$	14.7084	−	8.49187i	1.21727	−	0.702792i
$147$	−5.03036	−	2.90428i	−0.414897	−	0.239541i
$148$	−22.0019			−1.80854
$149$	−16.3107	−	9.41700i	−1.33623	−	0.771470i	−0.349980	−	0.936757i	$-0.613812\pi$
$149$	−16.3107	−	9.41700i	−1.33623	−	0.771470i	−0.986246	+	0.165287i	$0.947145\pi$
$150$	−6.55610	+	11.3555i	−0.535303	+	0.927173i
$151$			8.23175i			0.669890i	0.942238	+	0.334945i	$0.108718\pi$
$151$			8.23175i			0.669890i	−0.942238	+	0.334945i	$0.891282\pi$
$152$	1.42329	−	2.46520i	0.115444	−	0.199954i
$153$	2.53980	+	3.24799i	0.205330	+	0.262584i
$154$	8.13695	−	4.69787i	0.655694	−	0.378565i
$155$	−0.0977622			−0.00785245
$156$	7.52722	+	15.8947i	0.602660	+	1.27260i
$157$	5.06474			0.404210			0.202105	−	0.979364i	$-0.435222\pi$
$157$	5.06474			0.404210			0.202105	+	0.979364i	$0.435222\pi$
$158$	6.01638	+	10.4207i	0.478637	+	0.829024i
$159$	−1.88144	+	1.08625i	−0.149208	+	0.0861452i
$160$	0.137521	+	0.0793979i	0.0108720	+	0.00627695i
$161$		−	4.38582i		−	0.345651i
$162$	2.27119	+	1.31127i	0.178442	+	0.103023i
$163$	10.3481	−	17.9235i	0.810528	−	1.40388i	−0.101966	−	0.994788i	$-0.532513\pi$
$163$	10.3481	−	17.9235i	0.810528	−	1.40388i	0.912495	−	0.409089i	$-0.134153\pi$
$164$	−49.2619			−3.84670
$165$	0.0402004	+	0.0232097i	0.00312960	+	0.00180687i
$166$	17.2317	+	29.8462i	1.33744	+	2.31651i
$167$	4.27308	+	7.40120i	0.330661	+	0.572722i	0.982642	−	0.185514i	$-0.0593949\pi$
$167$	4.27308	+	7.40120i	0.330661	+	0.572722i	−0.651980	+	0.758236i	$0.726062\pi$
$168$	−8.23781			−0.635561
$169$	8.23722	−	10.0572i	0.633632	−	0.773634i
$170$	−0.0213462	−	0.151427i	−0.00163718	−	0.0116139i
$171$	−0.326646	+	0.188589i	−0.0249792	+	0.0144218i
$172$	−9.48167	−	16.4227i	−0.722970	−	1.25222i
$173$	6.18636	+	3.57169i	0.470340	+	0.271551i	0.716382	−	0.697708i	$-0.245797\pi$
$173$	6.18636	+	3.57169i	0.470340	+	0.271551i	−0.246042	+	0.969259i	$0.579130\pi$
$174$			26.8999i			2.03928i
$175$	−2.72872	+	4.72628i	−0.206272	+	0.357273i
$176$	−16.4718	+	28.5300i	−1.24161	+	2.15053i
$177$	−4.53291			−0.340714
$178$	5.17029	−	8.95520i	0.387530	−	0.671221i
$179$	−10.6603	−	18.4642i	−0.796789	−	1.38008i	−0.921697	−	0.387911i	$-0.873197\pi$
$179$	−10.6603	−	18.4642i	−0.796789	−	1.38008i	0.124907	−	0.992168i	$-0.460137\pi$
$180$	−0.0344919	−	0.0597418i	−0.00257088	−	0.00445289i
$181$			15.0552i			1.11904i	0.828815	+	0.559522i	$0.189015\pi$
$181$			15.0552i			1.11904i	−0.828815	+	0.559522i	$0.810985\pi$
$182$	4.41748	+	9.32810i	0.327445	+	0.691445i
$183$	0.693374			0.0512557
$184$	15.1621	+	26.2616i	1.11777	+	1.93603i
$185$	−0.0318962	−	0.0552459i	−0.00234506	−	0.00406176i
$186$	−9.06434	+	15.6999i	−0.664629	+	1.15117i
$187$	13.4006	−	1.88904i	0.979947	−	0.138140i
$188$	2.28305	+	1.31812i	0.166508	+	0.0961337i
$189$	0.945294	+	0.545766i	0.0687600	+	0.0396986i
$190$	0.0139894			0.00101490
$191$	0.544397	−	0.942923i	0.0393912	−	0.0682275i	−0.845658	−	0.533726i	$-0.820791\pi$
$191$	0.544397	−	0.942923i	0.0393912	−	0.0682275i	0.885049	+	0.465498i	$0.154125\pi$
$192$	8.11698	−	4.68634i	0.585793	−	0.338208i
$193$	9.88333	+	17.1184i	0.711418	+	1.23221i	0.964325	+	0.264721i	$0.0852800\pi$
$193$	9.88333	+	17.1184i	0.711418	+	1.23221i	−0.252907	+	0.967491i	$0.581387\pi$
$194$			20.1296i			1.44522i
$195$	−0.0289988	+	0.0419432i	−0.00207665	+	0.00300361i
$196$	28.3327			2.02376
$197$	−2.68352	−	4.64799i	−0.191193	−	0.331156i	0.754453	−	0.656354i	$-0.227902\pi$
$197$	−2.68352	−	4.64799i	−0.191193	−	0.331156i	−0.945646	+	0.325198i	$0.894569\pi$
$198$	7.45461	−	4.30392i	0.529776	−	0.305867i
$199$	4.56361	+	2.63480i	0.323506	+	0.186776i	0.652954	−	0.757397i	$-0.273529\pi$
$199$	4.56361	+	2.63480i	0.323506	+	0.186776i	−0.329448	+	0.944174i	$0.606863\pi$
$200$		−	37.7336i		−	2.66817i
$201$	2.37196	−	4.10836i	0.167305	−	0.289781i
$202$	22.7744	+	13.1488i	1.60240	+	0.925146i
$203$			11.1960i			0.785807i
$204$	−18.6502	−	7.52609i	−1.30577	−	0.526931i
$205$	−0.0714151	−	0.123695i	−0.00498784	−	0.00863920i
$206$	4.39938	−	2.53998i	0.306519	−	0.176969i
$207$		−	4.01804i		−	0.279273i
$208$	−29.7669	−	20.5803i	−2.06396	−	1.42699i
$209$			1.23799i			0.0856338i
$210$	−0.0202422	−	0.0350605i	−0.00139684	−	0.00241940i
$211$	−9.36868	+	5.40901i	−0.644967	+	0.372372i	−0.786525	−	0.617558i	$-0.788122\pi$
$211$	−9.36868	+	5.40901i	−0.644967	+	0.372372i	0.141558	+	0.989930i	$0.454789\pi$
$212$	5.29845	−	9.17718i	0.363899	−	0.630292i
$213$			12.2999i			0.842776i
$214$	−0.756099	+	1.30960i	−0.0516859	+	0.0895225i
$215$	0.0274912	−	0.0476162i	0.00187488	−	0.00324739i
$216$	−7.54702			−0.513510
$217$	−3.77267	+	6.53446i	−0.256106	+	0.443588i
$218$	40.6701	−	23.4809i	2.75453	−	1.59033i
$219$	5.60843	−	3.23803i	0.378982	−	0.218806i
$220$	−0.226422			−0.0152654
$221$	0.872497	+	14.8404i	0.0586905	+	0.998276i
$222$	−11.8294			−0.793940
$223$	−18.7962	+	10.8520i	−1.25869	+	0.726702i	−0.972819	−	0.231567i	$-0.925615\pi$
$223$	−18.7962	+	10.8520i	−1.25869	+	0.726702i	−0.285866	+	0.958269i	$0.592281\pi$
$224$	10.6140	−	6.12797i	0.709175	−	0.409442i
$225$	−2.49990	+	4.32995i	−0.166660	+	0.288664i
$226$	41.8323			2.78264
$227$	−9.11552	+	15.7885i	−0.605018	+	1.04792i	0.387030	+	0.922067i	$0.373501\pi$
$227$	−9.11552	+	15.7885i	−0.605018	+	1.04792i	−0.992049	+	0.125855i	$0.959832\pi$
$228$	0.919890	−	1.59330i	0.0609212	−	0.105519i
$229$		−	13.5277i		−	0.893933i	−0.894551	−	0.446966i	$-0.852504\pi$
$229$		−	13.5277i		−	0.893933i	0.894551	−	0.446966i	$-0.147496\pi$
$230$	−0.0745136	+	0.129061i	−0.00491328	+	0.00851005i
$231$	3.10269	−	1.79134i	0.204142	−	0.117861i
$232$	−38.7055	−	67.0399i	−2.54114	−	4.40139i
$233$		−	4.02693i		−	0.263813i	−0.991262	−	0.131906i	$-0.957890\pi$
$233$		−	4.02693i		−	0.263813i	0.991262	−	0.131906i	$-0.0421099\pi$
$234$	4.04705	+	8.54588i	0.264564	+	0.558662i
$235$			0.00764352i			0.000498609i
$236$	19.1481	−	11.0552i	1.24644	−	0.719631i
$237$	2.29410	+	3.97350i	0.149018	+	0.258106i
$238$	−10.9452	−	4.41682i	−0.709471	−	0.286300i
$239$			3.02848i			0.195896i	0.995192	+	0.0979481i	$0.0312279\pi$
$239$			3.02848i			0.195896i	−0.995192	+	0.0979481i	$0.968772\pi$
$240$	0.122930	+	0.0709738i	0.00793511	+	0.00458134i
$241$	−0.411048	+	0.711956i	−0.0264779	+	0.0458611i	−0.878961	−	0.476894i	$-0.841763\pi$
$241$	−0.411048	+	0.711956i	−0.0264779	+	0.0458611i	0.852483	+	0.522755i	$0.175096\pi$
$242$			0.594905i			0.0382419i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−2.92898	+	1.69105i	−0.187509	+	0.108258i
$245$	0.0410740	+	0.0711422i	0.00262412	+	0.00454511i
$246$	−26.4859			−1.68868
$247$	−1.35544	−	0.110469i	−0.0862447	−	0.00702894i
$248$		−	52.1697i		−	3.31278i
$249$	6.57060	+	11.3806i	0.416395	+	0.721217i
$250$	0.321198	−	0.185444i	0.0203144	−	0.0117285i
$251$	9.76067	−	16.9060i	0.616088	−	1.06710i	−0.374104	−	0.927387i	$-0.622050\pi$
$251$	9.76067	−	16.9060i	0.616088	−	1.06710i	0.990193	−	0.139709i	$-0.0446168\pi$
$252$	−5.32421			−0.335394
$253$	−11.4213	−	6.59411i	−0.718053	−	0.414568i
$254$	−37.8809	−	21.8705i	−2.37686	−	1.37228i
$255$	−0.00813951	−	0.0577404i	−0.000509716	−	0.00361584i
$256$	6.58772	−	11.4103i	0.411732	−	0.713142i
$257$	8.87748	+	15.3762i	0.553762	+	0.959144i	0.997999	+	0.0632346i	$0.0201416\pi$
$257$	8.87748	+	15.3762i	0.553762	+	0.959144i	−0.444237	+	0.895910i	$0.646525\pi$
$258$	−5.09787	−	8.82977i	−0.317379	−	0.549717i
$259$	−4.92354			−0.305934
$260$	0.0202041	−	0.247903i	0.00125300	−	0.0153743i
$261$			10.2572i			0.634903i
$262$	−15.6963	−	27.1869i	−0.969723	−	1.67961i
$263$	7.87686	+	13.6431i	0.485708	+	0.841271i	0.999865	−	0.0164253i	$-0.00522855\pi$
$263$	7.87686	+	13.6431i	0.485708	+	0.841271i	−0.514157	+	0.857696i	$0.671895\pi$
$264$	−12.3856	+	21.4525i	−0.762281	+	1.32031i
$265$	0.0307247			0.00188740
$266$	0.539854	−	0.935054i	0.0331005	−	0.0573318i
$267$	1.97148	−	3.41470i	0.120652	−	0.208976i
$268$			23.1397i			1.41348i
$269$	−0.172606	−	0.0996542i	−0.0105240	−	0.00607602i	0.494729	−	0.869047i	$-0.335267\pi$
$269$	−0.172606	−	0.0996542i	−0.0105240	−	0.00607602i	−0.505253	+	0.862971i	$0.668601\pi$
$270$	−0.0185448	−	0.0321205i	−0.00112860	−	0.00195479i
$271$	−16.4010	+	9.46910i	−0.996287	+	0.575207i	−0.907148	−	0.420812i	$-0.861745\pi$
$271$	−16.4010	+	9.46910i	−0.996287	+	0.575207i	−0.0891396	+	0.996019i	$0.528412\pi$
$272$	40.9781	−	5.77657i	2.48466	−	0.350256i
$273$	1.68442	+	3.55689i	0.101946	+	0.215273i
$274$	27.9900			1.69094
$275$	8.20529	+	14.2120i	0.494798	+	0.857015i
$276$	9.79949	+	16.9732i	0.589860	+	1.02167i
$277$	−10.6100	−	6.12571i	−0.637496	−	0.368058i	0.146153	−	0.989262i	$-0.453311\pi$
$277$	−10.6100	−	6.12571i	−0.637496	−	0.368058i	−0.783649	+	0.621204i	$0.786644\pi$
$278$	21.8223			1.30881
$279$	−3.45631	+	5.98651i	−0.206924	+	0.358403i
$280$	0.100895	+	0.0582519i	0.00602964	+	0.00348121i
$281$		−	25.4827i		−	1.52017i	−0.649825	−	0.760084i	$-0.725158\pi$
$281$		−	25.4827i		−	1.52017i	0.649825	−	0.760084i	$-0.274842\pi$
$282$	1.22749	+	0.708694i	0.0730962	+	0.0422021i
$283$	26.9563	−	15.5632i	1.60238	−	0.925136i	0.611374	−	0.791342i	$-0.290617\pi$
$283$	26.9563	−	15.5632i	1.60238	−	0.925136i	0.991009	−	0.133794i	$-0.0427162\pi$
$284$	−29.9979	−	51.9579i	−1.78005	−	3.08314i
$285$	0.00533427			0.000315975
$286$	30.9335	+	2.52108i	1.82913	+	0.149074i
$287$	−11.0237			−0.650709
$288$	9.72392	−	5.61411i	0.572987	−	0.330814i
$289$	−12.2386	−	11.7990i	−0.719921	−	0.694056i
$290$	0.190217	−	0.329465i	0.0111699	−	0.0193469i
$291$			7.67559i			0.449951i
$292$	−15.7943	+	27.3565i	−0.924289	+	1.60092i
$293$	6.40962	+	3.70059i	0.374454	+	0.216191i	0.675402	−	0.737449i	$-0.263970\pi$
$293$	6.40962	+	3.70059i	0.374454	+	0.216191i	−0.300949	+	0.953640i	$0.597303\pi$
$294$	15.2332			0.888419
$295$	0.0555182	+	0.0320535i	0.00323240	+	0.00186622i
$296$	29.4813	−	17.0210i	1.71357	−	0.989328i
$297$	2.84251	−	1.64112i	0.164939	−	0.0952277i
$298$	49.3930			2.86126
$299$	8.23884	−	11.9165i	0.476464	−	0.689147i
$300$		−	24.3878i		−	1.40803i
$301$	−2.12179	−	3.67504i	−0.122298	−	0.211826i
$302$	−10.7941	−	18.6959i	−0.621129	−	1.07583i
$303$	8.68407	+	5.01375i	0.498887	+	0.288033i
$304$			3.78570i			0.217125i
$305$	−0.00849232	−	0.00490304i	−0.000486269	−	0.000280747i
$306$	−10.0274	−	4.04644i	−0.573226	−	0.231320i
$307$		−	16.6582i		−	0.950736i	−0.879787	−	0.475368i	$-0.842315\pi$
$307$		−	16.6582i		−	0.950736i	0.879787	−	0.475368i	$-0.157685\pi$
$308$	−8.73769	+	15.1341i	−0.497876	+	0.862347i
$309$	1.67752	−	0.968518i	0.0954309	−	0.0550971i
$310$	0.222037	−	0.128193i	0.0126108	−	0.00728087i
$311$		−	21.7615i		−	1.23398i	−0.786970	−	0.616991i	$-0.788351\pi$
$311$		−	21.7615i		−	1.23398i	0.786970	−	0.616991i	$-0.211649\pi$
$312$	−22.3825	−	15.4749i	−1.26716	−	0.876092i
$313$			16.3723i			0.925418i	0.886510	+	0.462709i	$0.153122\pi$
$313$			16.3723i			0.925418i	−0.886510	+	0.462709i	$0.846878\pi$
$314$	−11.5030	+	6.64125i	−0.649151	+	0.374787i
$315$	−0.00771853	−	0.0133689i	−0.000434890	−	0.000753251i
$316$	−19.3817	−	11.1900i	−1.09031	−	0.629488i
$317$	30.3084			1.70229			0.851144	−	0.524933i	$-0.175909\pi$
$317$	30.3084			1.70229			0.851144	+	0.524933i	$0.175909\pi$
$318$	2.84874	−	4.93416i	0.159749	−	0.276694i
$319$	29.1561	+	16.8333i	1.63243	+	0.942483i
$320$	−0.132554			−0.00740998
$321$	−0.288307	+	0.499363i	−0.0160917	+	0.0278717i
$322$	5.75100	+	9.96103i	0.320491	+	0.555107i
$323$	1.22507	−	0.957956i	0.0681648	−	0.0533021i
$324$	−4.87775			−0.270986
$325$	−16.2925	+	7.71557i	−0.903743	+	0.427983i
$326$			54.2769i			3.00612i
$327$	15.5079	−	8.95347i	0.857587	−	0.495128i
$328$	66.0082	−	38.1098i	3.64469	−	2.10426i
$329$	0.510896	+	0.294966i	0.0281666	+	0.0162620i
$330$	−0.121737			−0.00670140
$331$	7.52787	+	4.34622i	0.413769	+	0.238890i	0.692408	−	0.721506i	$-0.256550\pi$
$331$	7.52787	+	4.34622i	0.413769	+	0.238890i	−0.278639	+	0.960396i	$0.589883\pi$
$332$	−55.5118	−	32.0497i	−3.04660	−	1.75896i
$333$	−4.51067			−0.247183
$334$	−19.4100	−	11.2064i	−1.06207	−	0.613185i
$335$	−0.0581028	+	0.0335456i	−0.00317449	+	0.00183279i
$336$	9.48783	−	5.47780i	0.517603	−	0.298839i
$337$			26.2207i			1.42833i	0.699976	+	0.714166i	$0.253194\pi$
$337$			26.2207i			1.42833i	−0.699976	+	0.714166i	$0.746806\pi$
$338$	−5.52051	+	33.6432i	−0.300276	+	1.82995i
$339$	15.9510			0.866340
$340$	0.175205	+	0.224059i	0.00950182	+	0.0121513i
$341$	11.3445	+	19.6492i	0.614338	+	1.06406i
$342$	0.494584	−	0.856644i	0.0267440	−	0.0463220i
$343$	13.9809			0.754900
$344$	25.4098	+	14.6704i	1.37001	+	0.790973i
$345$	−0.0284127	+	0.0492122i	−0.00152969	+	0.00264950i
$346$	−18.7339			−1.00714
$347$	−1.48908	−	0.859720i	−0.0799379	−	0.0461522i	0.459498	−	0.888179i	$-0.348029\pi$
$347$	−1.48908	−	0.859720i	−0.0799379	−	0.0461522i	−0.539436	+	0.842026i	$0.681363\pi$
$348$	−25.0159	−	43.3289i	−1.34099	−	2.32267i
$349$	−9.17325	+	5.29618i	−0.491033	+	0.283498i	−0.725003	−	0.688746i	$-0.758162\pi$
$349$	−9.17325	+	5.29618i	−0.491033	+	0.283498i	0.233970	+	0.972244i	$0.424828\pi$
$350$		−	14.3124i		−	0.765029i
$351$	1.54318	+	3.25862i	0.0823686	+	0.173932i
$352$		−	36.8538i		−	1.96431i
$353$	−6.65973	+	3.84500i	−0.354462	+	0.204648i	−0.666649	−	0.745372i	$-0.732272\pi$
$353$	−6.65973	+	3.84500i	−0.354462	+	0.204648i	0.312187	+	0.950021i	$0.398938\pi$
$354$	10.2951	−	5.94388i	0.547178	−	0.315913i
$355$	0.0869762	−	0.150647i	0.00461621	−	0.00799552i
$356$			19.2327i			1.01933i
$357$	−4.17350	−	1.68417i	−0.220885	−	0.0891358i
$358$	48.4232	+	27.9572i	2.55925	+	1.47758i
$359$		−	17.7855i		−	0.938681i	−0.883017	−	0.469340i	$-0.844492\pi$
$359$		−	17.7855i		−	0.938681i	0.883017	−	0.469340i	$-0.155508\pi$
$360$	0.0924345	+	0.0533671i	0.00487173	+	0.00281269i
$361$	−9.42887	−	16.3313i	−0.496256	−	0.859541i
$362$	−19.7415	−	34.1933i	−1.03759	−	1.79716i
$363$			0.226843i			0.0119061i
$364$	−15.7902	−	10.9171i	−0.827633	−	0.572211i
$365$	−0.0915880			−0.00479393
$366$	−1.57478	+	0.909202i	−0.0823153	+	0.0475247i
$367$	−6.39438	+	3.69180i	−0.333784	+	0.192710i	−0.657520	−	0.753437i	$-0.728394\pi$
$367$	−6.39438	+	3.69180i	−0.333784	+	0.192710i	0.323736	+	0.946148i	$0.395061\pi$
$368$	−34.9257	−	20.1644i	−1.82063	−	1.05114i
$369$	−10.0993			−0.525749
$370$	0.144885	+	0.0836493i	0.00753220	+	0.00434872i
$371$	1.18568	−	2.05365i	0.0615572	−	0.106620i
$372$		−	33.7180i		−	1.74820i
$373$	11.6570	−	20.1905i	0.603578	−	1.04543i	−0.388697	−	0.921366i	$-0.627075\pi$
$373$	11.6570	−	20.1905i	0.603578	−	1.04543i	0.992275	−	0.124061i	$-0.0395919\pi$
$374$	−27.9582	+	21.8622i	−1.44568	+	1.13047i
$375$	0.122476	−	0.0707114i	0.00632462	−	0.00365152i
$376$	−4.07888			−0.210352
$377$	−21.0319	+	30.4201i	−1.08320	+	1.56671i
$378$	−2.86259			−0.147236
$379$	4.46749	+	7.73792i	0.229480	+	0.397470i	0.957654	−	0.287922i	$-0.0929643\pi$
$379$	4.46749	+	7.73792i	0.229480	+	0.397470i	−0.728174	+	0.685392i	$0.759631\pi$
$380$	−0.0225333	+	0.0130096i	−0.00115593	+	0.000667378i
$381$	−14.4443	−	8.33942i	−0.740004	−	0.427242i
$382$			2.85541i			0.146095i
$383$	5.03792	+	2.90864i	0.257426	+	0.148625i	0.623160	−	0.782095i	$-0.285849\pi$
$383$	5.03792	+	2.90864i	0.257426	+	0.148625i	−0.365734	+	0.930719i	$0.619182\pi$
$384$	−1.06193	+	1.83932i	−0.0541914	+	0.0938623i
$385$	−0.0506683			−0.00258229
$386$	−44.8939	−	25.9195i	−2.28504	−	1.31927i
$387$	−1.94386	−	3.36687i	−0.0988121	−	0.171148i
$388$	−18.7198	−	32.4236i	−0.950353	−	1.64606i
$389$	−29.6467			−1.50315			−0.751574	−	0.659649i	$-0.770705\pi$
$389$	−29.6467			−1.50315			−0.751574	+	0.659649i	$0.770705\pi$
$390$	0.0108628	−	0.133286i	0.000550061	−	0.00674921i
$391$	2.31251	+	16.4046i	0.116949	+	0.829617i
$392$	−37.9642	+	21.9186i	−1.91748	+	1.10706i
$393$	−5.98516	−	10.3666i	−0.301911	−	0.522925i
$394$	12.1896	+	7.03765i	0.614101	+	0.354552i
$395$		−	0.0648889i		−	0.00326491i
$396$	−8.00499	+	13.8650i	−0.402266	+	0.696745i
$397$	−3.03405	+	5.25512i	−0.152274	+	0.263747i	−0.932063	−	0.362296i	$-0.881993\pi$
$397$	−3.03405	+	5.25512i	−0.152274	+	0.263747i	0.779789	+	0.626043i	$0.215326\pi$
$398$	−13.8198			−0.692723
$399$	0.205851	−	0.356544i	0.0103054	−	0.0178495i
$400$	25.0913	+	43.4593i	1.25456	+	2.17297i
$401$	17.7410	+	30.7283i	0.885942	+	1.53450i	0.844630	+	0.535350i	$0.179820\pi$
$401$	17.7410	+	30.7283i	0.885942	+	1.53450i	0.0413113	+	0.999146i	$0.486846\pi$
$402$			12.4412i			0.620509i
$403$	−22.5256	+	10.6674i	−1.12208	+	0.531381i
$404$	−48.9116			−2.43344
$405$	−0.00707128	−	0.0122478i	−0.000351375	−	0.000608599i
$406$	−14.6810	−	25.4283i	−0.728608	−	1.26199i
$407$	−7.40257	+	12.8216i	−0.366932	+	0.635544i
$408$	30.8125	−	4.34356i	1.52545	−	0.215038i
$409$	1.43561	+	0.828852i	0.0709865	+	0.0409841i	0.535073	−	0.844806i	$-0.320284\pi$
$409$	1.43561	+	0.828852i	0.0709865	+	0.0409841i	−0.464087	+	0.885790i	$0.653617\pi$
$410$	0.324395	+	0.187289i	0.0160207	+	0.00924956i
$411$	10.6728			0.526451
$412$	−4.72418	+	8.18253i	−0.232744	+	0.403124i
$413$	4.28493	−	2.47391i	0.210848	−	0.121733i
$414$	5.26875	+	9.12574i	0.258945	+	0.448506i
$415$		−	0.185850i		−	0.00912304i
$416$	40.3501	+	3.28853i	1.97833	+	0.161234i
$417$	8.32102			0.407482
$418$	−1.62335	−	2.81172i	−0.0794005	−	0.137526i
$419$	28.7510	−	16.5994i	1.40458	−	0.810934i	0.409721	−	0.912211i	$-0.365626\pi$
$419$	28.7510	−	16.5994i	1.40458	−	0.810934i	0.994858	+	0.101277i	$0.0322928\pi$
$420$	0.0652100	+	0.0376490i	0.00318192	+	0.00183708i
$421$			20.1517i			0.982136i	0.871121	+	0.491068i	$0.163393\pi$
$421$			20.1517i			0.982136i	−0.871121	+	0.491068i	$0.836607\pi$
$422$	14.1854	−	24.5698i	0.690534	−	1.19604i
$423$	0.468054	+	0.270231i	0.0227576	+	0.0131391i
$424$			16.3959i			0.796255i
$425$	7.71441	−	19.1168i	0.374204	−	0.927303i
$426$	−16.1285	−	27.9354i	−0.781430	−	1.35348i
$427$	−0.655442	+	0.378420i	−0.0317191	+	0.0183130i
$428$		−	2.81258i		−	0.135951i
$429$	11.7952	+	0.961310i	0.569478	+	0.0464125i
$430$			0.144194i			0.00695365i
$431$	−0.789723	−	1.36784i	−0.0380396	−	0.0658866i	0.846379	−	0.532581i	$-0.178778\pi$
$431$	−0.789723	−	1.36784i	−0.0380396	−	0.0658866i	−0.884418	+	0.466695i	$0.845445\pi$
$432$	8.69222	−	5.01845i	0.418204	−	0.241450i
$433$	−0.901394	+	1.56126i	−0.0433182	+	0.0750294i	−0.886872	−	0.462016i	$-0.847126\pi$
$433$	−0.901394	+	1.56126i	−0.0433182	+	0.0750294i	0.843553	+	0.537045i	$0.180460\pi$
$434$		−	19.7880i		−	0.949855i
$435$	0.0725313	−	0.125628i	0.00347761	−	0.00602340i
$436$	−43.6727	+	75.6434i	−2.09155	+	3.62266i
$437$	−1.51552			−0.0724970
$438$	−8.49187	+	14.7084i	−0.405757	+	0.702792i
$439$	25.8789	−	14.9412i	1.23513	−	0.713104i	0.267037	−	0.963686i	$-0.413955\pi$
$439$	25.8789	−	14.9412i	1.23513	−	0.713104i	0.968095	+	0.250582i	$0.0806219\pi$
$440$	0.303393	−	0.175164i	0.0144637	−	0.00835062i
$441$	5.80856			0.276598
$442$	−21.4415	−	32.5614i	−1.01987	−	1.54879i
$443$	−13.4890			−0.640883			−0.320441	−	0.947268i	$-0.603831\pi$
$443$	−13.4890			−0.640883			−0.320441	+	0.947268i	$0.603831\pi$
$444$	19.0542	−	11.0009i	0.904272	−	0.522082i
$445$	−0.0482926	+	0.0278817i	−0.00228929	+	0.00132172i
$446$	28.4598	−	49.2938i	1.34761	−	2.33413i
$447$	18.8340			0.890817
$448$	−5.11529	+	8.85994i	−0.241675	+	0.418593i
$449$	−6.01687	+	10.4215i	−0.283954	+	0.491822i	−0.972355	−	0.233508i	$-0.924979\pi$
$449$	−6.01687	+	10.4215i	−0.283954	+	0.491822i	0.688401	+	0.725330i	$0.258313\pi$
$450$		−	13.1122i		−	0.618115i
$451$	−16.5742	+	28.7074i	−0.780450	+	1.35178i
$452$	−67.3811	+	38.9025i	−3.16934	+	1.82982i
$453$	−4.11588	−	7.12890i	−0.193381	−	0.334945i
$454$		−	47.8117i		−	2.24392i
$455$	0.00452123	−	0.0554752i	0.000211958	−	0.00260072i
$456$			2.84657i			0.133303i
$457$	−23.4797	+	13.5560i	−1.09833	+	0.634123i	−0.935783	−	0.352577i	$-0.885305\pi$
$457$	−23.4797	+	13.5560i	−1.09833	+	0.634123i	−0.162551	+	0.986700i	$0.551972\pi$
$458$	17.7384	+	30.7239i	0.828863	+	1.43563i
$459$	−3.82352	−	1.54294i	−0.178467	−	0.0720184i
$460$		−	0.277180i		−	0.0129236i
$461$	26.6537	+	15.3885i	1.24139	+	0.716715i	0.969377	−	0.245579i	$-0.0789781\pi$
$461$	26.6537	+	15.3885i	1.24139	+	0.716715i	0.272011	+	0.962294i	$0.412311\pi$
$462$	−4.69787	+	8.13695i	−0.218565	+	0.378565i
$463$			0.470268i			0.0218552i	0.999940	+	0.0109276i	$0.00347843\pi$
$463$			0.470268i			0.0218552i	−0.999940	+	0.0109276i	$0.996522\pi$
$464$	89.1575	+	51.4751i	4.13903	+	2.38967i
$465$	0.0846646	−	0.0488811i	0.00392623	−	0.00226681i
$466$	5.28040	+	9.14593i	0.244610	+	0.423677i
$467$	12.1147			0.560601			0.280301	−	0.959912i	$-0.409566\pi$
$467$	12.1147			0.560601			0.280301	+	0.959912i	$0.409566\pi$
$468$	−14.4661	−	10.0016i	−0.668697	−	0.462325i
$469$			5.17814i			0.239105i
$470$	−0.0100227	−	0.0173599i	−0.000462315	−	0.000800753i
$471$	−4.38619	+	2.53237i	−0.202105	+	0.116685i
$472$	−17.1050	+	29.6267i	−0.787320	+	1.36368i
$473$	−12.7605			−0.586727
$474$	−10.4207	−	6.01638i	−0.478637	−	0.276341i
$475$	1.63316	+	0.942908i	0.0749347	+	0.0432636i
$476$	21.7374	−	3.06426i	0.996331	−	0.140450i
$477$	1.08625	−	1.88144i	0.0497360	−	0.0861452i
$478$	−3.97117	−	6.87826i	−0.181637	−	0.314604i
$479$	−4.29605	−	7.44097i	−0.196291	−	0.339987i	0.751032	−	0.660266i	$-0.229557\pi$
$479$	−4.29605	−	7.44097i	−0.196291	−	0.339987i	−0.947323	+	0.320279i	$0.896223\pi$
$480$	−0.158796			−0.00724800
$481$	−13.3775	−	9.24895i	−0.609960	−	0.421716i
$482$		−	2.15599i		−	0.0982024i
$483$	2.19291	+	3.79823i	0.0997808	+	0.172825i
$484$	−0.553240	−	0.958240i	−0.0251473	−	0.0435564i
$485$	0.0542763	−	0.0940093i	0.00246456	−	0.00426874i
$486$	−2.62255			−0.118961
$487$	11.8072	−	20.4507i	0.535037	−	0.926711i	−0.464125	−	0.885770i	$-0.653631\pi$
$487$	11.8072	−	20.4507i	0.535037	−	0.926711i	0.999162	−	0.0409411i	$-0.0130356\pi$
$488$	2.61645	−	4.53183i	0.118441	−	0.205146i
$489$			20.6963i			0.935918i
$490$	−0.186574	−	0.107718i	−0.00842854	−	0.00486622i
$491$	7.88567	+	13.6584i	0.355875	+	0.616394i	0.987267	−	0.159070i	$-0.0508495\pi$
$491$	7.88567	+	13.6584i	0.355875	+	0.616394i	−0.631392	+	0.775464i	$0.717516\pi$
$492$	42.6620	−	24.6309i	1.92335	−	1.11045i
$493$	−5.90334	−	41.8773i	−0.265873	−	1.88606i
$494$	3.22332	−	1.52646i	0.145024	−	0.0686786i
$495$	−0.0464194			−0.00208640
$496$	34.6907	+	60.0860i	1.55766	+	2.69794i
$497$	−6.71287	−	11.6270i	−0.301113	−	0.521544i
$498$	−29.8462	−	17.2317i	−1.33744	−	0.772171i
$499$	40.4316			1.80997			0.904983	−	0.425448i	$-0.139883\pi$
$499$	40.4316			1.80997			0.904983	+	0.425448i	$0.139883\pi$
$500$	−0.344912	+	0.597406i	−0.0154249	+	0.0267168i
$501$	−7.40120	−	4.27308i	−0.330661	−	0.190907i
$502$			51.1956i			2.28497i
$503$	31.1940	+	18.0099i	1.39087	+	0.803021i	0.993412	−	0.114598i	$-0.0365581\pi$
$503$	31.1940	+	18.0099i	1.39087	+	0.803021i	0.397461	+	0.917619i	$0.369891\pi$
$504$	7.13415	−	4.11890i	0.317780	−	0.183471i
$505$	−0.0709073	−	0.122815i	−0.00315533	−	0.00546520i
$506$	34.5867			1.53757
$507$	−2.10502	+	12.8284i	−0.0934872	+	0.569731i
$508$	81.3552			3.60955
$509$	26.1042	−	15.0712i	1.15705	−	0.668021i	0.206452	−	0.978457i	$-0.433808\pi$
$509$	26.1042	−	15.0712i	1.15705	−	0.668021i	0.950594	+	0.310436i	$0.100475\pi$
$510$	0.0941998	+	0.120466i	0.00417124	+	0.00533434i
$511$	−3.53441	+	6.12177i	−0.156353	+	0.270811i
$512$			38.8009i			1.71477i
$513$	0.188589	−	0.326646i	0.00832641	−	0.0144218i
$514$	−40.3249	−	23.2816i	−1.77866	−	1.02691i
$515$	−0.0273947			−0.00120715
$516$	16.4227	+	9.48167i	0.722970	+	0.417407i
$517$	1.53627	−	0.886966i	0.0675651	−	0.0390087i
$518$	11.1823	−	6.45610i	0.491322	−	0.283665i
$519$	−7.14339			−0.313560
$520$	0.164710	+	0.347806i	0.00722299	+	0.0152523i
$521$			27.1060i			1.18753i	0.804637	+	0.593767i	$0.202360\pi$
$521$			27.1060i			1.18753i	−0.804637	+	0.593767i	$0.797640\pi$
$522$	−13.4499	−	23.2960i	−0.588688	−	1.01964i
$523$	−18.7907	−	32.5465i	−0.821661	−	1.42316i	−0.904445	−	0.426591i	$-0.859715\pi$
$523$	−18.7907	−	32.5465i	−0.821661	−	1.42316i	0.0827841	−	0.996568i	$-0.473619\pi$
$524$	50.5656	+	29.1941i	2.20897	+	1.27535i
$525$		−	5.45744i		−	0.238182i
$526$	−35.7797	−	20.6574i	−1.56007	−	0.900706i
$527$	10.6658	−	26.4306i	0.464609	−	1.15133i
$528$		−	32.9436i		−	1.43369i
$529$	−3.42767	+	5.93690i	−0.149029	+	0.258126i
$530$	−0.0697817	+	0.0402885i	−0.00303112	+	0.00175002i
$531$	3.92561	−	2.26645i	0.170357	−	0.0983557i
$532$			2.00818i			0.0870655i
$533$	−29.9519	−	20.7082i	−1.29736	−	0.896973i
$534$			10.3406i			0.447481i
$535$	0.00706227	−	0.00407740i	0.000305329	−	0.000176282i
$536$	−17.9012	−	31.0059i	−0.773216	−	1.33925i
$537$	18.4642	+	10.6603i	0.796789	+	0.460027i
$538$	0.522695			0.0225350
$539$	9.53257	−	16.5109i	0.410597	−	0.711174i
$540$	0.0597418	+	0.0344919i	0.00257088	+	0.00148430i
$541$	−9.94773			−0.427686			−0.213843	−	0.976868i	$-0.568598\pi$
$541$	−9.94773			−0.427686			−0.213843	+	0.976868i	$0.568598\pi$
$542$	24.8331	−	43.0123i	1.06667	−	1.84753i
$543$	−7.52761	−	13.0382i	−0.323040	−	0.559522i
$544$	−36.4691	+	28.5174i	−1.56360	+	1.22267i
$545$	−0.253250			−0.0108480
$546$	−8.48970	−	5.86963i	−0.363326	−	0.251197i
$547$			28.8530i			1.23366i	0.787095	+	0.616832i	$0.211584\pi$
$547$			28.8530i			1.23366i	−0.787095	+	0.616832i	$0.788416\pi$
$548$	−45.0847	+	26.0296i	−1.92592	+	1.11193i
$549$	−0.600479	+	0.346687i	−0.0256278	+	0.0147962i
$550$	−37.2716	−	21.5188i	−1.58927	−	0.917563i
$551$	3.86878			0.164816
$552$	−26.2616	−	15.1621i	−1.11777	−	0.645342i
$553$	−4.33720	−	2.50408i	−0.184436	−	0.106484i
$554$	32.1299			1.36507
$555$	0.0552459	+	0.0318962i	0.00234506	+	0.00135392i
$556$	−35.1501	+	20.2939i	−1.49070	+	0.860654i
$557$	−7.55918	+	4.36429i	−0.320293	+	0.184921i	−0.651523	−	0.758629i	$-0.725870\pi$
$557$	−7.55918	+	4.36429i	−0.320293	+	0.184921i	0.331230	+	0.943550i	$0.392536\pi$
$558$		−	18.1287i		−	0.767448i
$559$	1.13864	−	13.9711i	0.0481594	−	0.590913i
$560$	−0.154940			−0.00654742
$561$	−10.6607	+	8.33624i	−0.450096	+	0.351956i
$562$	33.4147	+	57.8760i	1.40951	+	2.44135i
$563$	9.92476	−	17.1902i	0.418279	−	0.724480i	−0.577488	−	0.816399i	$-0.695967\pi$
$563$	9.92476	−	17.1902i	0.418279	−	0.724480i	0.995766	+	0.0919192i	$0.0293001\pi$
$564$	−2.63624			−0.111006
$565$	−0.195365	−	0.112794i	−0.00821907	−	0.00474528i
$566$	−40.8152	+	70.6940i	−1.71559	+	2.97149i
$567$	−1.09153			−0.0458400
$568$	80.3911	+	46.4138i	3.37314	+	1.94748i
$569$	16.2025	+	28.0635i	0.679243	+	1.17648i	0.975209	+	0.221285i	$0.0710250\pi$
$569$	16.2025	+	28.0635i	0.679243	+	1.17648i	−0.295967	+	0.955198i	$0.595642\pi$
$570$	−0.0121151	+	0.00699468i	−0.000507448	+	0.000292975i
$571$		−	8.33799i		−	0.348934i	−0.984663	−	0.174467i	$-0.944180\pi$
$571$		−	8.33799i		−	0.348934i	0.984663	−	0.174467i	$-0.0558202\pi$
$572$	−52.1704	+	24.7062i	−2.18136	+	1.03302i
$573$			1.08879i			0.0454850i
$574$	25.0370	−	14.4551i	1.04502	−	0.603344i
$575$	−17.3979	+	10.0447i	−0.725544	+	0.418893i
$576$	−4.68634	+	8.11698i	−0.195264	+	0.338208i
$577$		−	5.33443i		−	0.222075i	−0.993816	−	0.111038i	$-0.964583\pi$
$577$		−	5.33443i		−	0.222075i	0.993816	−	0.111038i	$-0.0354174\pi$
$578$	43.2680	+	10.7495i	1.79971	+	0.447120i
$579$	−17.1184	−	9.88333i	−0.711418	−	0.410737i
$580$			0.707579i			0.0293806i
$581$	−12.4223	−	7.17202i	−0.515364	−	0.297545i
$582$	−10.0648	−	17.4327i	−0.417199	−	0.722610i
$583$	−3.56534	−	6.17535i	−0.147661	−	0.255757i
$584$		−	48.8749i		−	2.02246i
$585$	0.00414209	−	0.0508232i	0.000171255	−	0.00210128i
$586$	−19.4100			−0.801818
$587$	35.0987	−	20.2642i	1.44868	−	0.836394i	0.450274	−	0.892890i	$-0.351326\pi$
$587$	35.0987	−	20.2642i	1.44868	−	0.836394i	0.998403	+	0.0564962i	$0.0179929\pi$
$588$	−24.5368	+	14.1663i	−1.01188	+	0.584210i
$589$	2.25798	+	1.30365i	0.0930385	+	0.0537158i
$590$	−0.168123			−0.00692153
$591$	4.64799	+	2.68352i	0.191193	+	0.110385i
$592$	−22.6366	+	39.2077i	−0.930358	+	1.61143i
$593$			29.0289i			1.19207i	0.802957	+	0.596037i	$0.203259\pi$
$593$			29.0289i			1.19207i	−0.802957	+	0.596037i	$0.796741\pi$
$594$	−4.30392	+	7.45461i	−0.176592	+	0.305867i
$595$	0.0392070	+	0.0501394i	0.00160733	+	0.00205551i
$596$	−79.5595	+	45.9337i	−3.25888	+	1.88152i
$597$	−5.26960			−0.215670
$598$	−3.08624	+	37.8679i	−0.126206	+	1.54853i
$599$	−13.5487			−0.553584			−0.276792	−	0.960930i	$-0.589271\pi$
$599$	−13.5487			−0.553584			−0.276792	+	0.960930i	$0.589271\pi$
$600$	18.8668	+	32.6782i	0.770233	+	1.33408i
$601$	3.50698	−	2.02475i	0.143053	−	0.0825915i	−0.426765	−	0.904362i	$-0.640347\pi$
$601$	3.50698	−	2.02475i	0.143053	−	0.0825915i	0.569818	+	0.821771i	$0.307014\pi$
$602$	9.63797	+	5.56448i	0.392814	+	0.226791i
$603$			4.74393i			0.193188i
$604$	34.7730	+	20.0762i	1.41489	+	0.816889i
$605$	0.00160407	−	0.00277833i	6.52146e−5	−	0.000112955i
$606$	−26.2976			−1.06827
$607$	−15.1441	−	8.74347i	−0.614681	−	0.354886i	0.160114	−	0.987099i	$-0.448814\pi$
$607$	−15.1441	−	8.74347i	−0.614681	−	0.354886i	−0.774795	+	0.632212i	$0.782147\pi$
$608$	−2.11752	−	3.66765i	−0.0858767	−	0.148743i
$609$	−5.59801	−	9.69604i	−0.226843	−	0.392903i
$610$	0.0257169			0.00104125
$611$	0.834028	+	1.76116i	0.0337412	+	0.0712490i
$612$	19.9146	−	2.80730i	0.804999	−	0.113478i
$613$	19.8202	−	11.4432i	0.800530	−	0.462186i	−0.0431264	−	0.999070i	$-0.513732\pi$
$613$	19.8202	−	11.4432i	0.800530	−	0.462186i	0.843656	+	0.536883i	$0.180398\pi$
$614$	21.8435	+	37.8340i	0.881531	+	1.52686i
$615$	0.123695	+	0.0714151i	0.00498784	+	0.00287973i
$616$		−	27.0385i		−	1.08941i
$617$	−19.0657	+	33.0228i	−0.767557	+	1.32945i	0.171326	+	0.985214i	$0.445195\pi$
$617$	−19.0657	+	33.0228i	−0.767557	+	1.32945i	−0.938884	+	0.344234i	$0.888139\pi$
$618$	−2.53998	+	4.39938i	−0.102173	+	0.176969i
$619$	−44.1754			−1.77556			−0.887781	−	0.460267i	$-0.847754\pi$
$619$	−44.1754			−1.77556			−0.887781	+	0.460267i	$0.847754\pi$
$620$	−0.238430	+	0.412972i	−0.00957557	+	0.0165854i
$621$	2.00902	+	3.47973i	0.0806192	+	0.139637i
$622$	28.5353	+	49.4245i	1.14416	+	1.98174i
$623$			4.30386i			0.172430i
$624$	36.0690	+	2.93962i	1.44392	+	0.117679i
$625$	24.9970			0.999880
$626$	−21.4686	−	37.1846i	−0.858057	−	1.48620i
$627$	−0.618996	−	1.07213i	−0.0247203	−	0.0428169i
$628$	12.3522	−	21.3947i	0.492908	−	0.853742i
$629$	18.4159	−	2.59604i	0.734289	−	0.103511i
$630$	0.0350605	+	0.0202422i	0.00139684	+	0.000806468i
$631$	−22.4498	−	12.9614i	−0.893712	−	0.515985i	−0.0185571	−	0.999828i	$-0.505907\pi$
$631$	−22.4498	−	12.9614i	−0.893712	−	0.515985i	−0.875155	+	0.483843i	$0.839241\pi$
$632$	34.6272			1.37740
$633$	5.40901	−	9.36868i	0.214989	−	0.372372i
$634$	−68.8361	+	39.7425i	−2.73383	+	1.57838i
$635$	0.117941	+	0.204280i	0.00468034	+	0.00810659i
$636$			10.5969i			0.420194i
$637$	17.2267	+	11.9102i	0.682546	+	0.471900i
$638$	−88.2921			−3.49552
$639$	−6.14996	−	10.6520i	−0.243288	−	0.421388i
$640$	0.0260127	−	0.0150184i	0.00102824	−	0.000593656i
$641$	−28.3645	−	16.3762i	−1.12033	−	0.646822i	−0.178844	−	0.983877i	$-0.557236\pi$
$641$	−28.3645	−	16.3762i	−1.12033	−	0.646822i	−0.941485	+	0.337056i	$0.890569\pi$
$642$		−	1.51220i		−	0.0596817i
$643$	12.8009	−	22.1718i	0.504817	−	0.874369i	−0.495167	−	0.868798i	$-0.664893\pi$
$643$	12.8009	−	22.1718i	0.504817	−	0.874369i	0.999984	−	0.00557130i	$-0.00177341\pi$
$644$	−18.5268	−	10.6965i	−0.730058	−	0.421499i
$645$			0.0549824i			0.00216493i
$646$	−1.52623	+	3.78210i	−0.0600487	+	0.148805i
$647$	10.6304	+	18.4124i	0.417925	+	0.723868i	0.995731	−	0.0923066i	$-0.0294240\pi$
$647$	10.6304	+	18.4124i	0.417925	+	0.723868i	−0.577805	+	0.816175i	$0.696091\pi$
$648$	6.53591	−	3.77351i	0.256755	−	0.148237i
$649$		−	14.8781i		−	0.584018i
$650$	26.8861	−	38.8874i	1.05456	−	1.52529i
$651$		−	7.54535i		−	0.295725i
$652$	−50.4756	−	87.4262i	−1.97678	−	3.42388i
$653$	−31.0019	+	17.8989i	−1.21320	+	0.700440i	−0.963454	−	0.267873i	$-0.913679\pi$
$653$	−31.0019	+	17.8989i	−1.21320	+	0.700440i	−0.249743	+	0.968312i	$0.580346\pi$
$654$	−23.4809	+	40.6701i	−0.918175	+	1.59033i
$655$			0.169291i			0.00661474i
$656$	−50.6829	+	87.7854i	−1.97884	+	3.42744i
$657$	−3.23803	+	5.60843i	−0.126327	+	0.218806i
$658$	−1.54712			−0.0603131
$659$	−17.2995	+	29.9637i	−0.673894	+	1.16722i	0.302897	+	0.953023i	$0.402046\pi$
$659$	−17.2995	+	29.9637i	−0.673894	+	1.16722i	−0.976791	+	0.214196i	$0.931287\pi$
$660$	0.196087	−	0.113211i	0.00763269	−	0.00440673i
$661$	21.0547	−	12.1560i	0.818935	−	0.472812i	−0.0311143	−	0.999516i	$-0.509906\pi$
$661$	21.0547	−	12.1560i	0.818935	−	0.472812i	0.850049	+	0.526704i	$0.176572\pi$
$662$	−22.7963			−0.886004
$663$	−8.17583	−	12.4160i	−0.317523	−	0.482196i
$664$	99.1769			3.84881
$665$	−0.00504245	+	0.00291126i	−0.000195538	+	0.000112894i
$666$	10.2446	−	5.91472i	0.396970	−	0.229191i
$667$	−20.6069	+	35.6921i	−0.797901	+	1.38200i
$668$	41.6860			1.61288
$669$	10.8520	−	18.7962i	0.419562	−	0.726702i
$670$	0.0879750	−	0.152377i	0.00339877	−	0.00588684i
$671$			2.27582i			0.0878572i
$672$	−6.12797	+	10.6140i	−0.236392	+	0.409442i
$673$	−23.3867	+	13.5023i	−0.901489	+	0.520475i	−0.877683	−	0.479241i	$-0.840912\pi$
$673$	−23.3867	+	13.5023i	−0.901489	+	0.520475i	−0.0238062	+	0.999717i	$0.507578\pi$
$674$	−34.3825	−	59.5522i	−1.32436	−	2.29387i
$675$		−	4.99980i		−	0.192442i
$676$	−22.3948	−	59.3244i	−0.861339	−	2.28171i
$677$		−	4.18681i		−	0.160912i	−0.996758	−	0.0804562i	$-0.974362\pi$
$677$		−	4.18681i		−	0.160912i	0.996758	−	0.0804562i	$-0.0256377\pi$
$678$	−36.2278	+	20.9161i	−1.39132	+	0.803279i
$679$	−4.18908	−	7.25569i	−0.160762	−	0.278448i
$680$	−0.408101	−	0.164685i	−0.0156499	−	0.00631538i
$681$		−	18.2310i		−	0.698615i
$682$	−51.5310	−	29.7514i	−1.97322	−	1.13924i
$683$	21.6542	−	37.5062i	0.828576	−	1.43514i	−0.0705801	−	0.997506i	$-0.522485\pi$
$683$	21.6542	−	37.5062i	0.828576	−	1.43514i	0.899156	−	0.437629i	$-0.144182\pi$
$684$			1.83978i			0.0703457i
$685$	−0.130719	−	0.0754705i	−0.00499451	−	0.00288358i
$686$	−31.7534	+	18.3328i	−1.21235	+	0.699951i
$687$	6.76383	+	11.7153i	0.258056	+	0.446966i
$688$	−39.0207			−1.48765
$689$	7.07935	−	3.35255i	0.269702	−	0.127722i
$690$		−	0.149027i		−	0.00567337i
$691$	4.71556	+	8.16758i	0.179388	+	0.310710i	0.941671	−	0.336534i	$-0.109255\pi$
$691$	4.71556	+	8.16758i	0.179388	+	0.310710i	−0.762283	+	0.647244i	$0.775922\pi$
$692$	30.1755	−	17.4218i	1.14710	−	0.662278i
$693$	−1.79134	+	3.10269i	−0.0680473	+	0.117861i
$694$	4.50931			0.171171
$695$	−0.101914	−	0.0588403i	−0.00386583	−	0.00223194i
$696$	67.0399	+	38.7055i	2.54114	+	1.46713i
$697$	41.2328	−	5.81248i	1.56181	−	0.220164i
$698$	13.8895	−	24.0573i	0.525724	−	0.910581i
$699$	2.01346	+	3.48742i	0.0761562	+	0.131906i
$700$	13.3100	+	23.0536i	0.503071	+	0.871344i
$701$	45.7847			1.72926			0.864632	−	0.502405i	$-0.167551\pi$
$701$	45.7847			1.72926			0.864632	+	0.502405i	$0.167551\pi$
$702$	−7.77779	−	5.37743i	−0.293554	−	0.202958i
$703$			1.70133i			0.0641667i
$704$	15.3817	+	26.6420i	0.579721	+	1.00411i
$705$	−0.00382176	−	0.00661949i	−0.000143936	−	0.000249304i
$706$	10.0837	−	17.4654i	0.379504	−	0.657320i
$707$	−10.9453			−0.411642
$708$	−11.0552	+	19.1481i	−0.415479	+	0.719631i
$709$	15.6703	−	27.1417i	0.588510	−	1.01933i	−0.405918	−	0.913909i	$-0.633048\pi$
$709$	15.6703	−	27.1417i	0.588510	−	1.01933i	0.994428	−	0.105419i	$-0.0336185\pi$
$710$			0.456198i			0.0171208i
$711$	−3.97350	−	2.29410i	−0.149018	−	0.0860354i
$712$	−14.8788	−	25.7708i	−0.557606	−	0.965801i
$713$	−24.0540	+	13.8876i	−0.900831	+	0.520095i
$714$	11.6872	−	1.64752i	0.437383	−	0.0616567i
$715$	−0.137668	−	0.0951812i	−0.00514849	−	0.00355958i
$716$	−103.997			−3.88654
$717$	−1.51424	−	2.62274i	−0.0565504	−	0.0979481i
$718$	23.3216	+	40.3942i	0.870354	+	1.50750i
$719$	−16.8313	−	9.71753i	−0.627700	−	0.362403i	0.152161	−	0.988356i	$-0.451377\pi$
$719$	−16.8313	−	9.71753i	−0.627700	−	0.362403i	−0.779861	+	0.625953i	$0.784710\pi$
$720$	−0.141948			−0.00529008
$721$	−1.05717	+	1.83107i	−0.0393710	+	0.0681926i
$722$	42.8295	+	24.7276i	1.59395	+	0.920267i
$723$		−	0.822096i		−	0.0305741i
$724$	63.5970	+	36.7177i	2.36356	+	1.36460i
$725$	44.4131	−	25.6419i	1.64946	−	0.952316i
$726$	−0.297452	−	0.515203i	−0.0110395	−	0.0191210i
$727$	−40.1933			−1.49069			−0.745344	−	0.666680i	$-0.767715\pi$
$727$	−40.1933			−1.49069			−0.745344	+	0.666680i	$0.767715\pi$
$728$	29.6037	+	2.41270i	1.09719	+	0.0894206i
$729$	−1.00000			−0.0370370
$730$	0.208014	−	0.120097i	0.00769894	−	0.00444498i
$731$	9.87403	+	12.6273i	0.365204	+	0.467037i
$732$	1.69105	−	2.92898i	0.0625030	−	0.108258i
$733$		−	31.0164i		−	1.14562i	−0.819689	−	0.572808i	$-0.805854\pi$
$733$		−	31.0164i		−	1.14562i	0.819689	−	0.572808i	$-0.194146\pi$
$734$	9.68191	−	16.7696i	0.357366	−	0.618976i
$735$	−0.0711422	−	0.0410740i	−0.00262412	−	0.00151504i
$736$	45.1154			1.66298
$737$	13.4847	+	7.78537i	0.496714	+	0.286778i
$738$	22.9375	−	13.2429i	0.844340	−	0.487480i
$739$	15.2290	−	8.79248i	0.560209	−	0.323437i	−0.193021	−	0.981195i	$-0.561828\pi$
$739$	15.2290	−	8.79248i	0.560209	−	0.323437i	0.753229	+	0.657758i	$0.228495\pi$
$740$	−0.311163			−0.0114386
$741$	1.22908	−	0.582052i	0.0451514	−	0.0213822i
$742$			6.21898i			0.228306i
$743$	14.6695	+	25.4084i	0.538173	+	0.932143i	0.999002	+	0.0446544i	$0.0142187\pi$
$743$	14.6695	+	25.4084i	0.538173	+	0.932143i	−0.460829	+	0.887489i	$0.652448\pi$
$744$	26.0849	+	45.1803i	0.956317	+	1.65639i
$745$	−0.230675	−	0.133180i	−0.00845129	−	0.00487936i
$746$			61.1421i			2.23857i
$747$	−11.3806	−	6.57060i	−0.416395	−	0.240406i
$748$	24.7025	−	61.2145i	0.903212	−	2.23822i
$749$		−	0.629393i		−	0.0229975i
$750$	−0.185444	+	0.321198i	−0.00677145	+	0.0117285i
$751$	14.7361	−	8.50791i	0.537729	−	0.310458i	−0.206429	−	0.978462i	$-0.566184\pi$
$751$	14.7361	−	8.50791i	0.537729	−	0.310458i	0.744158	+	0.668004i	$0.232851\pi$
$752$	4.69782	−	2.71229i	0.171312	−	0.0989069i
$753$			19.5213i			0.711397i
$754$	7.87848	−	96.6684i	0.286917	−	3.52046i
$755$			0.116418i			0.00423689i
$756$	4.61090	−	2.66211i	0.167697	−	0.0968199i
$757$	9.47406	+	16.4095i	0.344340	+	0.596415i	0.985234	−	0.171215i	$-0.0547692\pi$
$757$	9.47406	+	16.4095i	0.344340	+	0.596415i	−0.640893	+	0.767630i	$0.721436\pi$
$758$	−20.2930	−	11.7162i	−0.737077	−	0.425551i
$759$	13.1882			0.478702
$760$	0.0201289	−	0.0348643i	0.000730152	−	0.00126466i
$761$	23.2282	+	13.4108i	0.842021	+	0.486141i	0.857951	−	0.513732i	$-0.171738\pi$
$761$	23.2282	+	13.4108i	0.842021	+	0.486141i	−0.0159299	+	0.999873i	$0.505071\pi$
$762$	43.7410			1.58457
$763$	−9.77300	+	16.9273i	−0.353806	+	0.612810i
$764$	−2.65543	−	4.59934i	−0.0960700	−	0.166398i
$765$	0.0359192	+	0.0459349i	0.00129866	+	0.00166078i
$766$	−15.2561			−0.551225
$767$	16.2896	+	1.32760i	0.588184	+	0.0479370i
$768$			13.1754i			0.475428i
$769$	−21.6469	+	12.4979i	−0.780608	+	0.450684i	−0.836646	−	0.547744i	$-0.815487\pi$
$769$	−21.6469	+	12.4979i	−0.780608	+	0.450684i	0.0560376	+	0.998429i	$0.482153\pi$
$770$	0.115077	−	0.0664399i	0.00414710	−	0.00239433i
$771$	−15.3762	−	8.87748i	−0.553762	−	0.319715i
$772$	96.4168			3.47012
$773$	−6.34402	−	3.66272i	−0.228179	−	0.131739i	0.381553	−	0.924347i	$-0.375389\pi$
$773$	−6.34402	−	3.66272i	−0.228179	−	0.131739i	−0.609732	+	0.792608i	$0.708723\pi$
$774$	8.82977	+	5.09787i	0.317379	+	0.183239i
$775$	34.5617			1.24149
$776$	50.1670	+	28.9639i	1.80089	+	1.03974i
$777$	4.26391	−	2.46177i	0.152967	−	0.0883154i
$778$	67.3334	−	38.8749i	2.41402	−	1.39373i
$779$			3.80924i			0.136480i
$780$	0.106454	+	0.224792i	0.00381167	+	0.00804885i
$781$	−40.3714			−1.44460
$782$	−26.7631	−	34.2257i	−0.957046	−	1.22391i
$783$	−5.12858	−	8.88297i	−0.183281	−	0.317451i
$784$	29.1500	−	50.4893i	1.04107	−	1.80319i
$785$	0.0716284			0.00255653
$786$	27.1869	+	15.6963i	0.969723	+	0.559870i
$787$	3.77317	−	6.53533i	0.134499	−	0.232959i	−0.790907	−	0.611936i	$-0.790391\pi$
$787$	3.77317	−	6.53533i	0.134499	−	0.232959i	0.925406	+	0.378977i	$0.123724\pi$
$788$	−26.1790			−0.932589
$789$	−13.6431	−	7.87686i	−0.485708	−	0.280424i
$790$	0.0850870	+	0.147375i	0.00302726	+	0.00524337i
$791$	−15.0784	+	8.70552i	−0.536126	+	0.309533i
$792$		−	24.7712i		−	0.880206i
$793$	−2.49173	−	0.203076i	−0.0884840	−	0.00721145i
$794$		−	15.9139i		−	0.564762i
$795$	−0.0266084	+	0.0153624i	−0.000943702	+	0.000544847i
$796$	22.2601	−	12.8519i	0.788989	−	0.455523i
$797$	11.6448	−	20.1693i	0.412479	−	0.714434i	−0.582681	−	0.812701i	$-0.697996\pi$
$797$	11.6448	−	20.1693i	0.412479	−	0.714434i	0.995160	+	0.0982665i	$0.0313298\pi$
$798$			1.07971i			0.0382212i
$799$	−2.06647	−	0.833903i	−0.0731064	−	0.0295014i
$800$	−48.6176	−	28.0694i	−1.71889	−	0.992403i
$801$			3.94295i			0.139317i
$802$	−80.5863	−	46.5265i	−2.84560	−	1.64291i
$803$	10.6280	+	18.4082i	0.375054	+	0.649613i
$804$	−11.5698	−	20.0395i	−0.408037	−	0.706740i
$805$		−	0.0620267i		−	0.00218615i
$806$	37.1721	−	53.7649i	1.30933	−	1.89379i
$807$	0.199308			0.00701599
$808$	65.5389	−	37.8389i	2.30565	−	1.33117i
$809$	−22.8456	+	13.1899i	−0.803207	+	0.463732i	−0.844591	−	0.535411i	$-0.820157\pi$
$809$	−22.8456	+	13.1899i	−0.803207	+	0.463732i	0.0413841	+	0.999143i	$0.486823\pi$
$810$	0.0321205	+	0.0185448i	0.00112860	+	0.000651597i
$811$	−39.0171			−1.37008			−0.685038	−	0.728508i	$-0.740214\pi$
$811$	−39.0171			−1.37008			−0.685038	+	0.728508i	$0.740214\pi$
$812$	47.2948	+	27.3057i	1.65972	+	0.958241i
$813$	9.46910	−	16.4010i	0.332096	−	0.575207i
$814$		−	38.8271i		−	1.36089i
$815$	0.146349	−	0.253484i	0.00512639	−	0.00887916i
$816$	−32.5998	+	25.4917i	−1.14122	+	0.892388i
$817$	−1.26991	+	0.733183i	−0.0444285	+	0.0256508i
$818$	−4.34741			−0.152003
$819$	−3.23720	−	2.23814i	−0.113117	−	0.0782070i
$820$	−0.696689			−0.0243294
$821$	−9.43570	−	16.3431i	−0.329308	−	0.570378i	0.653067	−	0.757300i	$-0.273482\pi$
$821$	−9.43570	−	16.3431i	−0.329308	−	0.570378i	−0.982375	+	0.186922i	$0.940149\pi$
$822$	−24.2400	+	13.9950i	−0.845468	+	0.488131i
$823$	−34.6040	−	19.9786i	−1.20622	−	0.696411i	−0.244288	−	0.969703i	$-0.578554\pi$
$823$	−34.6040	−	19.9786i	−1.20622	−	0.696411i	−0.961931	+	0.273292i	$0.911887\pi$
$824$		−	14.6188i		−	0.509272i
$825$	−14.2120	−	8.20529i	−0.494798	−	0.285672i
$826$	−6.48793	+	11.2374i	−0.225744	+	0.391000i
$827$	13.0048			0.452220			0.226110	−	0.974102i	$-0.427399\pi$
$827$	13.0048			0.452220			0.226110	+	0.974102i	$0.427399\pi$
$828$	−16.9732	−	9.79949i	−0.589860	−	0.340556i
$829$	−24.8586	−	43.0563i	−0.863374	−	1.49541i	−0.868652	−	0.495422i	$-0.835013\pi$
$829$	−24.8586	−	43.0563i	−0.863374	−	1.49541i	0.00527773	−	0.999986i	$-0.498320\pi$
$830$	0.243701	+	0.422102i	0.00845897	+	0.0146514i
$831$	12.2514			0.424997
$832$	−30.5420	+	14.4637i	−1.05885	+	0.501438i
$833$	−23.7148	+	3.34302i	−0.821670	+	0.115829i
$834$	−18.8986	+	10.9111i	−0.654406	+	0.377821i
$835$	0.0604324	+	0.104672i	0.00209135	+	0.00362232i
$836$	5.22959	+	3.01931i	0.180869	+	0.104425i
$837$		−	6.91262i		−	0.238935i
$838$	−43.5327	+	75.4009i	−1.50381	+	2.60468i
$839$	21.6780	−	37.5473i	0.748407	−	1.29628i	−0.200180	−	0.979759i	$-0.564153\pi$
$839$	21.6780	−	37.5473i	0.748407	−	1.29628i	0.948586	−	0.316519i	$-0.102514\pi$
$840$	−0.116504			−0.00401976
$841$	38.1047	−	65.9993i	1.31396	−	2.27584i
$842$	−26.4244	−	45.7685i	−0.910646	−	1.57729i
$843$	12.7413	+	22.0686i	0.438835	+	0.760084i
$844$			52.7676i			1.81633i
$845$	0.116495	−	0.142235i	0.00400756	−	0.00489304i
$846$	−1.41739			−0.0487308
$847$	−0.123803	−	0.214433i	−0.00425392	−	0.00736800i
$848$	−10.9026	−	18.8838i	−0.374396	−	0.648474i
$849$	−15.5632	+	26.9563i	−0.534128	+	0.925136i
$850$	7.54650	+	53.5337i	0.258843	+	1.83619i
$851$	−15.6959	−	9.06202i	−0.538048	−	0.310642i
$852$	51.9579	+	29.9979i	1.78005	+	1.02771i
$853$	−16.5896			−0.568016			−0.284008	−	0.958822i	$-0.591664\pi$
$853$	−16.5896			−0.568016			−0.284008	+	0.958822i	$0.591664\pi$
$854$	0.992423	−	1.71893i	0.0339600	−	0.0588204i
$855$	−0.00461961	+	0.00266713i	−0.000157987	+	9.12141e-5i
$856$	2.17586	+	3.76870i	0.0743694	+	0.128811i
$857$			23.8561i			0.814909i	0.913226	+	0.407454i	$0.133583\pi$
$857$			23.8561i			0.814909i	−0.913226	+	0.407454i	$0.866417\pi$
$858$	−28.0497	+	13.2834i	−0.957601	+	0.453488i
$859$	28.7789			0.981923			0.490961	−	0.871181i	$-0.336646\pi$
$859$	28.7789			0.981923			0.490961	+	0.871181i	$0.336646\pi$
$860$	−0.134095	−	0.232259i	−0.00457260	−	0.00791998i
$861$	9.54682	−	5.51186i	0.325355	−	0.187844i
$862$	3.58722	+	2.07108i	0.122181	+	0.0705414i
$863$		−	19.4810i		−	0.663140i	−0.943431	−	0.331570i	$-0.892422\pi$
$863$		−	19.4810i		−	0.663140i	0.943431	−	0.331570i	$-0.107578\pi$
$864$	−5.61411	+	9.72392i	−0.190996	+	0.330814i
$865$	0.0874909	+	0.0505129i	0.00297478	+	0.00171749i
$866$		−	4.72789i		−	0.160660i
$867$	16.4985	+	4.09887i	0.560317	+	0.139205i
$868$	18.4021	+	31.8734i	0.624609	+	1.08186i
$869$	−13.0420	+	7.52980i	−0.442420	+	0.255431i
$870$			0.380433i			0.0128979i
$871$	−9.72723	+	14.0692i	−0.329595	+	0.476718i
$872$		−	135.144i		−	4.57655i
$873$	−3.83780	−	6.64726i	−0.129890	−	0.224976i
$874$	3.44203	−	1.98726i	0.116428	−	0.0672200i
$875$	−0.0771837	+	0.133686i	−0.00260929	+	0.00451942i
$876$		−	31.5885i		−	1.06728i
$877$	−8.78207	+	15.2110i	−0.296549	+	0.513639i	−0.975344	−	0.220689i	$-0.929169\pi$
$877$	−8.78207	+	15.2110i	−0.296549	+	0.513639i	0.678795	+	0.734328i	$0.262503\pi$
$878$	−39.1840	+	67.8686i	−1.32239	+	2.29045i
$879$	−7.40119			−0.249636
$880$	−0.232954	+	0.403488i	−0.00785287	+	0.0136016i
$881$	23.7072	−	13.6874i	0.798716	−	0.461139i	−0.0443058	−	0.999018i	$-0.514108\pi$
$881$	23.7072	−	13.6874i	0.798716	−	0.461139i	0.843022	+	0.537879i	$0.180774\pi$
$882$	−13.1923	+	7.61661i	−0.444209	+	0.256464i
$883$	44.0339			1.48186			0.740930	−	0.671583i	$-0.234385\pi$
$883$	44.0339			1.48186			0.740930	+	0.671583i	$0.234385\pi$
$884$	64.8177	+	32.5083i	2.18005	+	1.09337i
$885$	−0.0641069			−0.00215493
$886$	30.6361	−	17.6878i	1.02924	−	0.594233i
$887$	−42.7750	+	24.6961i	−1.43624	+	0.829215i	−0.997586	−	0.0694399i	$-0.977879\pi$
$887$	−42.7750	+	24.6961i	−1.43624	+	0.829215i	−0.438656	+	0.898655i	$0.644545\pi$
$888$	−17.0210	+	29.4813i	−0.571189	+	0.989328i
$889$	18.2055			0.610592
$890$	0.0731212	−	0.126650i	0.00245103	−	0.00424530i
$891$	−1.64112	+	2.84251i	−0.0549797	+	0.0952277i
$892$			105.866i			3.54467i
$893$	0.101925	−	0.176540i	0.00341080	−	0.00590768i
$894$	−42.7756	+	24.6965i	−1.43063	+	0.825975i
$895$	−0.150764	−	0.261131i	−0.00503949	−	0.00872866i
$896$		−	2.31826i		−	0.0774477i
$897$	−1.17681	+	14.4394i	−0.0392925	+	0.482117i
$898$		−	31.5590i		−	1.05314i
$899$	61.4046	−	35.4520i	2.04796	−	1.18239i
$900$	12.1939	+	21.1204i	0.406463	+	0.704014i
$901$	−3.35204	+	8.30660i	−0.111673	+	0.276733i
$902$		−	86.9333i		−	2.89456i
$903$	3.67504	+	2.12179i	0.122298	+	0.0706086i
$904$	60.1913	−	104.254i	2.00193	−	3.46745i
$905$			0.212919i			0.00707768i
$906$	18.6959	+	10.7941i	0.621129	+	0.358609i
$907$	−7.11033	+	4.10515i	−0.236095	+	0.136309i	−0.613380	−	0.789788i	$-0.710191\pi$
$907$	−7.11033	+	4.10515i	−0.236095	+	0.136309i	0.377286	+	0.926097i	$0.376857\pi$
$908$	44.4632	+	77.0125i	1.47556	+	2.55575i
$909$	−10.0275			−0.332591
$910$	0.0624745	+	0.131923i	0.00207101	+	0.00437321i
$911$			15.4756i			0.512729i	0.966580	+	0.256364i	$0.0825247\pi$
$911$			15.4756i			0.512729i	−0.966580	+	0.256364i	$0.917475\pi$
$912$	−1.89285	−	3.27852i	−0.0626786	−	0.108562i
$913$	−37.3540	+	21.5664i	−1.23624	+	0.713742i
$914$	35.5512	−	61.5766i	1.17593	−	2.03677i
$915$	0.00980608			0.000324179
$916$	−57.1442	−	32.9922i	−1.88810	−	1.09009i
$917$	11.3155	+	6.53299i	0.373670	+	0.215738i
$918$	10.7072	−	1.50936i	0.353389	−	0.0498163i
$919$	−27.8872	+	48.3021i	−0.919914	+	1.59334i	−0.120371	+	0.992729i	$0.538409\pi$
$919$	−27.8872	+	48.3021i	−0.919914	+	1.59334i	−0.799543	+	0.600609i	$0.794925\pi$
$920$	0.214431	+	0.371406i	0.00706959	+	0.0122449i
$921$	8.32912	+	14.4265i	0.274454	+	0.475368i
$922$	−80.7142			−2.65818
$923$	3.60242	−	44.2014i	0.118575	−	1.45491i
$924$		−	17.4754i		−	0.574898i
$925$	11.2762	+	19.5310i	0.370760	+	0.642175i
$926$	−0.616649	−	1.06807i	−0.0202644	−	0.0350989i
$927$	−0.968518	+	1.67752i	−0.0318103	+	0.0550971i
$928$	−115.170			−3.78063
$929$	−0.123312	+	0.213582i	−0.00404573	+	0.00700740i	−0.868041	−	0.496492i	$-0.834621\pi$
$929$	−0.123312	+	0.213582i	−0.00404573	+	0.00700740i	0.863995	+	0.503500i	$0.167954\pi$
$930$	−0.128193	+	0.222037i	−0.00420361	+	0.00728087i
$931$		−	2.19086i		−	0.0718026i
$932$	−17.0108	−	9.82117i	−0.557206	−	0.321703i
$933$	10.8808	+	18.8460i	0.356220	+	0.616991i
$934$	−27.5148	+	15.8857i	−0.900312	+	0.519795i
$935$	0.189518	−	0.0267159i	0.00619791	−	0.000873703i
$936$	27.1212	+	2.21038i	0.886485	+	0.0722486i
$937$	19.9464			0.651620			0.325810	−	0.945435i	$-0.394363\pi$
$937$	19.9464			0.651620			0.325810	+	0.945435i	$0.394363\pi$
$938$	−6.78996	−	11.7606i	−0.221700	−	0.383996i
$939$	−8.18616	−	14.1788i	−0.267145	−	0.462709i
$940$	0.0322882	+	0.0186416i	0.00105312	+	0.000608021i
$941$	44.3381			1.44538			0.722690	−	0.691173i	$-0.242906\pi$
$941$	44.3381			1.44538			0.722690	+	0.691173i	$0.242906\pi$
$942$	6.64125	−	11.5030i	0.216384	−	0.374787i
$943$	−35.1428	−	20.2897i	−1.14441	−	0.660724i
$944$		−	45.4964i		−	1.48078i
$945$	0.0133689	+	0.00771853i	0.000434890	+	0.000251084i
$946$	28.9815	−	16.7325i	0.942269	−	0.544020i
$947$	14.1518	+	24.5116i	0.459871	+	0.796520i	0.998954	−	0.0457331i	$-0.0145624\pi$
$947$	14.1518	+	24.5116i	0.459871	+	0.796520i	−0.539083	+	0.842253i	$0.681229\pi$
$948$	22.3801			0.726870
$949$	−21.1030	+	9.99368i	−0.685032	+	0.324409i
$950$	−4.94564			−0.160458
$951$	−26.2478	+	15.1542i	−0.851144	+	0.491408i
$952$	−26.7563	+	20.9223i	−0.867177	+	0.678097i
$953$	25.0471	−	43.3828i	0.811354	−	1.40531i	−0.100563	−	0.994931i	$-0.532064\pi$
$953$	25.0471	−	43.3828i	0.811354	−	1.40531i	0.911917	−	0.410375i	$-0.134602\pi$
$954$			5.69748i			0.184463i
$955$	0.00769917	−	0.0133353i	0.000249139	−	0.000431522i
$956$	12.7931	+	7.38608i	0.413757	+	0.238883i
$957$	−33.6666			−1.08829
$958$	19.5143	+	11.2666i	0.630478	+	0.364007i
$959$	−10.0890	+	5.82486i	−0.325789	+	0.188095i
$960$	0.114795	−	0.0662769i	0.00370499	−	0.00213908i
$961$	16.7844			0.541432
$962$	42.5107	+	3.46462i	1.37060	+	0.111704i
$963$		−	0.576614i		−	0.0185811i
$964$	2.00499	+	3.47274i	0.0645763	+	0.111849i
$965$	0.139776	+	0.242099i	0.00449954	+	0.00779343i
$966$	−9.96103	−	5.75100i	−0.320491	−	0.185036i
$967$			23.2103i			0.746392i	0.927753	+	0.373196i	$0.121738\pi$
$967$			23.2103i			0.746392i	−0.927753	+	0.373196i	$0.878262\pi$
$968$	1.48262	+	0.855992i	0.0476533	+	0.0275126i
$969$	−0.581965	+	1.44215i	−0.0186954	+	0.0463285i
$970$			0.284684i			0.00914065i
$971$	14.0077	−	24.2620i	0.449528	−	0.778606i	−0.548827	−	0.835936i	$-0.684925\pi$
$971$	14.0077	−	24.2620i	0.449528	−	0.778606i	0.998355	+	0.0573301i	$0.0182587\pi$
$972$	4.22425	−	2.43887i	0.135493	−	0.0782269i
$973$	−7.86581	+	4.54133i	−0.252166	+	0.145588i
$974$			61.9300i			1.98437i
$975$	10.2519	−	14.8281i	0.328323	−	0.474879i
$976$			6.95933i			0.222763i
$977$	−31.9239	+	18.4312i	−1.02133	+	0.589668i	−0.914490	−	0.404608i	$-0.867408\pi$
$977$	−31.9239	+	18.4312i	−1.02133	+	0.589668i	−0.106844	+	0.994276i	$0.534075\pi$
$978$	−27.1385	−	47.0052i	−0.867792	−	1.50306i
$979$	11.2079	+	6.47088i	0.358206	+	0.206810i
$980$	0.400697			0.0127998
$981$	−8.95347	+	15.5079i	−0.285862	+	0.495128i
$982$	−35.8197	−	20.6805i	−1.14305	−	0.659942i
$983$	−45.2598			−1.44356			−0.721782	−	0.692121i	$-0.756677\pi$
$983$	−45.2598			−1.44356			−0.721782	+	0.692121i	$0.756677\pi$
$984$	−38.1098	+	66.0082i	−1.21490	+	2.10426i
$985$	−0.0379518	−	0.0657345i	−0.00120925	−	0.00209448i
$986$	68.3202	+	87.3706i	2.17576	+	2.78245i
$987$	−0.589932			−0.0187777
$988$	−3.77240	+	5.45631i	−0.120016	+	0.173588i
$989$		−	15.6210i		−	0.496720i
$990$	0.105427	−	0.0608685i	0.00335070	−	0.00193453i
$991$	31.9954	−	18.4725i	1.01637	−	0.586800i	0.103317	−	0.994648i	$-0.467054\pi$
$991$	31.9954	−	18.4725i	1.01637	−	0.586800i	0.913050	+	0.407849i	$0.133721\pi$
$992$	−67.2178	−	38.8082i	−2.13417	−	1.23216i
$993$	−8.69244			−0.275846
$994$	30.4924	+	17.6048i	0.967161	+	0.558391i
$995$	0.0645411	+	0.0372628i	0.00204609	+	0.00118131i
$996$	64.0994			2.03107
$997$	37.8859	+	21.8734i	1.19986	+	0.692739i	0.960524	−	0.278198i	$-0.0897372\pi$
$997$	37.8859	+	21.8734i	1.19986	+	0.692739i	0.239335	+	0.970937i	$0.423071\pi$
$998$	−91.8278	+	53.0168i	−2.90676	+	1.67822i
$999$	3.90635	−	2.25533i	0.123592	−	0.0713556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	663.2.ba.a.322.1	✓	80
13.4	even	6	inner	663.2.ba.a.628.2	yes	80
17.16	even	2	inner	663.2.ba.a.322.2	yes	80
221.186	even	6	inner	663.2.ba.a.628.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
663.2.ba.a.322.1	✓	80	1.1	even	1	trivial
663.2.ba.a.322.2	yes	80	17.16	even	2	inner
663.2.ba.a.628.1	yes	80	221.186	even	6	inner
663.2.ba.a.628.2	yes	80	13.4	even	6	inner

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:	\( N \)	\(=\)	\( 663 = 3 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	663.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.27119 + 1.31127i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.43887 - 4.22425i) q^{4} +0.0141426 q^{5} +(1.31127 - 2.27119i) q^{6} +(0.545766 - 0.945294i) q^{7} +7.54702i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.27119 + 1.31127i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.43887 - 4.22425i) q^{4} +0.0141426 q^{5} +(1.31127 - 2.27119i) q^{6} +(0.545766 - 0.945294i) q^{7} +7.54702i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.0321205 + 0.0185448i) q^{10} +(-1.64112 - 2.84251i) q^{11} +4.87775i q^{12} +(3.25862 - 1.54318i) q^{13} +2.86259i q^{14} +(-0.0122478 + 0.00707128i) q^{15} +(-5.01845 - 8.69222i) q^{16} +(-1.54294 + 3.82352i) q^{17} +2.62255i q^{18} +(-0.326646 - 0.188589i) q^{19} +(0.0344919 - 0.0597418i) q^{20} +1.09153i q^{21} +(7.45461 + 4.30392i) q^{22} +(3.47973 - 2.00902i) q^{23} +(-3.77351 - 6.53591i) q^{24} -4.99980 q^{25} +(-5.37743 + 7.77779i) q^{26} +1.00000i q^{27} +(-2.66211 - 4.61090i) q^{28} +(-8.88297 + 5.12858i) q^{29} +(0.0185448 - 0.0321205i) q^{30} -6.91262 q^{31} +(9.72392 + 5.61411i) q^{32} +(2.84251 + 1.64112i) q^{33} +(-1.50936 - 10.7072i) q^{34} +(0.00771853 - 0.0133689i) q^{35} +(-2.43887 - 4.22425i) q^{36} +(-2.25533 - 3.90635i) q^{37} +0.989167 q^{38} +(-2.05046 + 2.96574i) q^{39} +0.106734i q^{40} +(-5.04965 - 8.74626i) q^{41} +(-1.43130 - 2.47908i) q^{42} +(1.94386 - 3.36687i) q^{43} -16.0100 q^{44} +(0.00707128 - 0.0122478i) q^{45} +(-5.26875 + 9.12574i) q^{46} +0.540462i q^{47} +(8.69222 + 5.01845i) q^{48} +(2.90428 + 5.03036i) q^{49} +(11.3555 - 6.55610i) q^{50} +(-0.575533 - 4.08274i) q^{51} +(1.42860 - 17.5288i) q^{52} +2.17250 q^{53} +(-1.31127 - 2.27119i) q^{54} +(-0.0232097 - 0.0402004i) q^{55} +(7.13415 + 4.11890i) q^{56} +0.377178 q^{57} +(13.4499 - 23.2960i) q^{58} +(3.92561 + 2.26645i) q^{59} +0.0689838i q^{60} +(-0.600479 - 0.346687i) q^{61} +(15.6999 - 9.06434i) q^{62} +(-0.545766 - 0.945294i) q^{63} -9.37268 q^{64} +(0.0460853 - 0.0218245i) q^{65} -8.60785 q^{66} +(-4.10836 + 2.37196i) q^{67} +(12.3885 + 15.8429i) q^{68} +(-2.00902 + 3.47973i) q^{69} +0.0404844i q^{70} +(6.14996 - 10.6520i) q^{71} +(6.53591 + 3.77351i) q^{72} -6.47605 q^{73} +(10.2446 + 5.91472i) q^{74} +(4.32995 - 2.49990i) q^{75} +(-1.59330 + 0.919890i) q^{76} -3.58268 q^{77} +(0.768095 - 9.42447i) q^{78} -4.58820i q^{79} +(-0.0709738 - 0.122930i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(22.9375 + 13.2429i) q^{82} -13.1412i q^{83} +(4.61090 + 2.66211i) q^{84} +(-0.0218212 + 0.0540744i) q^{85} +10.1957i q^{86} +(5.12858 - 8.88297i) q^{87} +(21.4525 - 12.3856i) q^{88} +(-3.41470 + 1.97148i) q^{89} +0.0370895i q^{90} +(0.319689 - 3.92257i) q^{91} -19.5990i q^{92} +(5.98651 - 3.45631i) q^{93} +(-0.708694 - 1.22749i) q^{94} +(-0.00461961 - 0.00266713i) q^{95} -11.2282 q^{96} +(3.83780 - 6.64726i) q^{97} +(-13.1923 - 7.61661i) q^{98} -3.28225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 36 q^{4} + 40 q^{9}+O(q^{10}) \) 80 * q + 36 * q^4 + 40 * q^9	\( 80 q + 36 q^{4} + 40 q^{9} - 4 q^{13} - 6 q^{15} - 12 q^{16} - 4 q^{17} + 44 q^{25} - 16 q^{26} - 8 q^{30} - 60 q^{32} - 6 q^{33} - 36 q^{36} + 96 q^{38} + 4 q^{42} + 10 q^{43} - 8 q^{49} + 48 q^{50} + 16 q^{51} + 72 q^{52} - 40 q^{53} + 44 q^{55} + 144 q^{59} - 56 q^{64} - 16 q^{66} - 48 q^{67} + 40 q^{68} - 26 q^{69} - 48 q^{76} - 64 q^{77} - 40 q^{81} + 6 q^{85} - 4 q^{87} - 48 q^{89} - 44 q^{94} + 36 q^{98}+O(q^{100}) \) 80 * q + 36 * q^4 + 40 * q^9 - 4 * q^13 - 6 * q^15 - 12 * q^16 - 4 * q^17 + 44 * q^25 - 16 * q^26 - 8 * q^30 - 60 * q^32 - 6 * q^33 - 36 * q^36 + 96 * q^38 + 4 * q^42 + 10 * q^43 - 8 * q^49 + 48 * q^50 + 16 * q^51 + 72 * q^52 - 40 * q^53 + 44 * q^55 + 144 * q^59 - 56 * q^64 - 16 * q^66 - 48 * q^67 + 40 * q^68 - 26 * q^69 - 48 * q^76 - 64 * q^77 - 40 * q^81 + 6 * q^85 - 4 * q^87 - 48 * q^89 - 44 * q^94 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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