LMFDB - Embedded newform 273.2.cg.b.115.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.10
Character	$\chi$	$=$	273.115
Dual form			273.2.cg.b.19.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.39126 - 0.640737i) q^{2} -1.00000i q^{3} +(3.57554 - 2.06434i) q^{4} +(-1.06950 - 0.286571i) q^{5} +(-0.640737 - 2.39126i) q^{6} +(0.327682 + 2.62538i) q^{7} +(3.72630 - 3.72630i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(2.39126 - 0.640737i) q^{2} -1.00000i q^{3} +(3.57554 - 2.06434i) q^{4} +(-1.06950 - 0.286571i) q^{5} +(-0.640737 - 2.39126i) q^{6} +(0.327682 + 2.62538i) q^{7} +(3.72630 - 3.72630i) q^{8} -1.00000 q^{9} -2.74106 q^{10} +(1.52947 - 1.52947i) q^{11} +(-2.06434 - 3.57554i) q^{12} +(-3.47248 - 0.970511i) q^{13} +(2.46575 + 6.06801i) q^{14} +(-0.286571 + 1.06950i) q^{15} +(2.39431 - 4.14706i) q^{16} +(1.59647 + 2.76517i) q^{17} +(-2.39126 + 0.640737i) q^{18} +(-2.51496 + 2.51496i) q^{19} +(-4.41561 + 1.18316i) q^{20} +(2.62538 - 0.327682i) q^{21} +(2.67738 - 4.63735i) q^{22} +(0.620322 + 0.358143i) q^{23} +(-3.72630 - 3.72630i) q^{24} +(-3.26843 - 1.88703i) q^{25} +(-8.92545 - 0.0958025i) q^{26} +1.00000i q^{27} +(6.59131 + 8.71070i) q^{28} +(1.58131 + 2.73892i) q^{29} +2.74106i q^{30} +(-0.625845 - 2.33568i) q^{31} +(0.340399 - 1.27039i) q^{32} +(-1.52947 - 1.52947i) q^{33} +(5.58933 + 5.58933i) q^{34} +(0.401902 - 2.90174i) q^{35} +(-3.57554 + 2.06434i) q^{36} +(0.726571 + 2.71160i) q^{37} +(-4.40250 + 7.62535i) q^{38} +(-0.970511 + 3.47248i) q^{39} +(-5.05312 + 2.91742i) q^{40} +(4.01046 + 1.07460i) q^{41} +(6.06801 - 2.46575i) q^{42} +(7.32559 + 4.22943i) q^{43} +(2.31134 - 8.62603i) q^{44} +(1.06950 + 0.286571i) q^{45} +(1.71283 + 0.458951i) q^{46} +(2.85863 - 10.6686i) q^{47} +(-4.14706 - 2.39431i) q^{48} +(-6.78525 + 1.72058i) q^{49} +(-9.02475 - 2.41817i) q^{50} +(2.76517 - 1.59647i) q^{51} +(-14.4194 + 3.69827i) q^{52} +(4.54930 - 7.87963i) q^{53} +(0.640737 + 2.39126i) q^{54} +(-2.07407 + 1.19746i) q^{55} +(11.0040 + 8.56192i) q^{56} +(2.51496 + 2.51496i) q^{57} +(5.53626 + 5.53626i) q^{58} +(-2.10905 + 7.87107i) q^{59} +(1.18316 + 4.41561i) q^{60} -13.1295i q^{61} +(-2.99312 - 5.18423i) q^{62} +(-0.327682 - 2.62538i) q^{63} +6.32129i q^{64} +(3.43569 + 2.03307i) q^{65} +(-4.63735 - 2.67738i) q^{66} +(-8.40090 - 8.40090i) q^{67} +(11.4165 + 6.59131i) q^{68} +(0.358143 - 0.620322i) q^{69} +(-0.898198 - 7.19634i) q^{70} +(-14.8017 + 3.96611i) q^{71} +(-3.72630 + 3.72630i) q^{72} +(-4.86210 + 1.30280i) q^{73} +(3.47484 + 6.01860i) q^{74} +(-1.88703 + 3.26843i) q^{75} +(-3.80061 + 14.1841i) q^{76} +(4.51663 + 3.51426i) q^{77} +(-0.0958025 + 8.92545i) q^{78} +(-8.54505 - 14.8005i) q^{79} +(-3.74913 + 3.74913i) q^{80} +1.00000 q^{81} +10.2786 q^{82} +(3.63623 - 3.63623i) q^{83} +(8.71070 - 6.59131i) q^{84} +(-0.915005 - 3.41484i) q^{85} +(20.2274 + 5.41991i) q^{86} +(2.73892 - 1.58131i) q^{87} -11.3985i q^{88} +(-5.24668 + 1.40584i) q^{89} +2.74106 q^{90} +(1.41009 - 9.43460i) q^{91} +2.95732 q^{92} +(-2.33568 + 0.625845i) q^{93} -27.3430i q^{94} +(3.41045 - 1.96903i) q^{95} +(-1.27039 - 0.340399i) q^{96} +(3.61174 + 13.4792i) q^{97} +(-15.1229 + 8.46192i) q^{98} +(-1.52947 + 1.52947i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 - 40 * q^9	$ 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.39126	−	0.640737i	1.69088	−	0.453069i	0.720261	−	0.693703i	$-0.244022\pi$
$2$	2.39126	−	0.640737i	1.69088	−	0.453069i	0.970616	+	0.240634i	$0.0773552\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	3.57554	−	2.06434i	1.78777	−	1.03217i
$5$	−1.06950	−	0.286571i	−0.478294	−	0.128158i	0.0116143	−	0.999933i	$-0.496303\pi$
$5$	−1.06950	−	0.286571i	−0.478294	−	0.128158i	−0.489908	+	0.871774i	$0.662970\pi$
$6$	−0.640737	−	2.39126i	−0.261580	−	0.976229i
$7$	0.327682	+	2.62538i	0.123852	+	0.992301i
$7$	0.327682	+	2.62538i	0.123852	+	0.992301i
$8$	3.72630	−	3.72630i	1.31745	−	1.31745i
$9$	−1.00000			−0.333333
$10$	−2.74106			−0.866801
$11$	1.52947	−	1.52947i	0.461153	−	0.461153i	−0.437880	−	0.899033i	$-0.644271\pi$
$11$	1.52947	−	1.52947i	0.461153	−	0.461153i	0.899033	+	0.437880i	$0.144271\pi$
$12$	−2.06434	−	3.57554i	−0.595923	−	1.03217i
$13$	−3.47248	−	0.970511i	−0.963092	−	0.269171i
$13$	−3.47248	−	0.970511i	−0.963092	−	0.269171i
$14$	2.46575	+	6.06801i	0.659000	+	1.62175i
$15$	−0.286571	+	1.06950i	−0.0739923	+	0.276143i
$16$	2.39431	−	4.14706i	0.598577	−	1.03677i
$17$	1.59647	+	2.76517i	0.387201	+	0.670652i	0.992072	−	0.125671i	$-0.0401085\pi$
$17$	1.59647	+	2.76517i	0.387201	+	0.670652i	−0.604871	+	0.796324i	$0.706775\pi$
$18$	−2.39126	+	0.640737i	−0.563626	+	0.151023i
$19$	−2.51496	+	2.51496i	−0.576971	+	0.576971i	−0.934067	−	0.357097i	$-0.883767\pi$
$19$	−2.51496	+	2.51496i	−0.576971	+	0.576971i	0.357097	+	0.934067i	$0.383767\pi$
$20$	−4.41561	+	1.18316i	−0.987360	+	0.264562i
$21$	2.62538	−	0.327682i	0.572905	−	0.0715062i
$22$	2.67738	−	4.63735i	0.570819	−	0.988687i
$23$	0.620322	+	0.358143i	0.129346	+	0.0746781i	0.563277	−	0.826268i	$-0.309540\pi$
$23$	0.620322	+	0.358143i	0.129346	+	0.0746781i	−0.433931	+	0.900946i	$0.642874\pi$
$24$	−3.72630	−	3.72630i	−0.760628	−	0.760628i
$25$	−3.26843	−	1.88703i	−0.653685	−	0.377405i
$26$	−8.92545	−	0.0958025i	−1.75042	−	0.0187884i
$27$			1.00000i			0.192450i
$28$	6.59131	+	8.71070i	1.24564	+	1.64617i
$29$	1.58131	+	2.73892i	0.293643	+	0.508604i	0.974668	−	0.223656i	$-0.0717991\pi$
$29$	1.58131	+	2.73892i	0.293643	+	0.508604i	−0.681026	+	0.732260i	$0.738466\pi$
$30$			2.74106i			0.500448i
$31$	−0.625845	−	2.33568i	−0.112405	−	0.419501i	0.886675	−	0.462394i	$-0.153009\pi$
$31$	−0.625845	−	2.33568i	−0.112405	−	0.419501i	−0.999080	+	0.0428926i	$0.986343\pi$
$32$	0.340399	−	1.27039i	0.0601747	−	0.224575i
$33$	−1.52947	−	1.52947i	−0.266247	−	0.266247i
$34$	5.58933	+	5.58933i	0.958562	+	0.958562i
$35$	0.401902	−	2.90174i	0.0679339	−	0.490484i
$36$	−3.57554	+	2.06434i	−0.595923	+	0.344056i
$37$	0.726571	+	2.71160i	0.119448	+	0.445784i	0.999581	−	0.0289419i	$-0.00921379\pi$
$37$	0.726571	+	2.71160i	0.119448	+	0.445784i	−0.880134	+	0.474726i	$0.842547\pi$
$38$	−4.40250	+	7.62535i	−0.714179	+	1.23699i
$39$	−0.970511	+	3.47248i	−0.155406	+	0.556042i
$40$	−5.05312	+	2.91742i	−0.798968	+	0.461284i
$41$	4.01046	+	1.07460i	0.626329	+	0.167824i	0.558003	−	0.829839i	$-0.311568\pi$
$41$	4.01046	+	1.07460i	0.626329	+	0.167824i	0.0683255	+	0.997663i	$0.478234\pi$
$42$	6.06801	−	2.46575i	0.936315	−	0.380474i
$43$	7.32559	+	4.22943i	1.11714	+	0.644983i	0.940670	−	0.339323i	$-0.110198\pi$
$43$	7.32559	+	4.22943i	1.11714	+	0.644983i	0.176473	+	0.984306i	$0.443531\pi$
$44$	2.31134	−	8.62603i	0.348447	−	1.30042i
$45$	1.06950	+	0.286571i	0.159431	+	0.0427195i
$46$	1.71283	+	0.458951i	0.252543	+	0.0676687i
$47$	2.85863	−	10.6686i	0.416975	−	1.55617i	−0.363872	−	0.931449i	$-0.618546\pi$
$47$	2.85863	−	10.6686i	0.416975	−	1.55617i	0.780847	−	0.624722i	$-0.214788\pi$
$48$	−4.14706	−	2.39431i	−0.598577	−	0.345589i
$49$	−6.78525	+	1.72058i	−0.969321	+	0.245797i
$50$	−9.02475	−	2.41817i	−1.27629	−	0.341981i
$51$	2.76517	−	1.59647i	0.387201	−	0.223551i
$52$	−14.4194	+	3.69827i	−1.99962	+	0.512858i
$53$	4.54930	−	7.87963i	0.624895	−	1.08235i	−0.363666	−	0.931529i	$-0.618475\pi$
$53$	4.54930	−	7.87963i	0.624895	−	1.08235i	0.988561	−	0.150820i	$-0.0481915\pi$
$54$	0.640737	+	2.39126i	0.0871932	+	0.325410i
$55$	−2.07407	+	1.19746i	−0.279667	+	0.161466i
$56$	11.0040	+	8.56192i	1.47047	+	1.14413i
$57$	2.51496	+	2.51496i	0.333114	+	0.333114i
$58$	5.53626	+	5.53626i	0.726946	+	0.726946i
$59$	−2.10905	+	7.87107i	−0.274575	+	1.02473i	0.681551	+	0.731770i	$0.261306\pi$
$59$	−2.10905	+	7.87107i	−0.274575	+	1.02473i	−0.956126	+	0.292956i	$0.905361\pi$
$60$	1.18316	+	4.41561i	0.152745	+	0.570052i
$61$		−	13.1295i		−	1.68106i	−0.541768	−	0.840528i	$-0.682245\pi$
$61$		−	13.1295i		−	1.68106i	0.541768	−	0.840528i	$-0.317755\pi$
$62$	−2.99312	−	5.18423i	−0.380126	−	0.658398i
$63$	−0.327682	−	2.62538i	−0.0412841	−	0.330767i
$64$			6.32129i			0.790162i
$65$	3.43569	+	2.03307i	0.426144	+	0.252171i
$66$	−4.63735	−	2.67738i	−0.570819	−	0.329562i
$67$	−8.40090	−	8.40090i	−1.02633	−	1.02633i	−0.999644	−	0.0266890i	$-0.991504\pi$
$67$	−8.40090	−	8.40090i	−1.02633	−	1.02633i	−0.0266890	−	0.999644i	$-0.508496\pi$
$68$	11.4165	+	6.59131i	1.38445	+	0.799314i
$69$	0.358143	−	0.620322i	0.0431154	−	0.0746781i
$70$	−0.898198	−	7.19634i	−0.107355	−	0.860127i
$71$	−14.8017	+	3.96611i	−1.75664	+	0.470691i	−0.986024	−	0.166605i	$-0.946720\pi$
$71$	−14.8017	+	3.96611i	−1.75664	+	0.470691i	−0.770619	+	0.637296i	$0.780053\pi$
$72$	−3.72630	+	3.72630i	−0.439149	+	0.439149i
$73$	−4.86210	+	1.30280i	−0.569066	+	0.152481i	−0.531868	−	0.846827i	$-0.678510\pi$
$73$	−4.86210	+	1.30280i	−0.569066	+	0.152481i	−0.0371977	+	0.999308i	$0.511843\pi$
$74$	3.47484	+	6.01860i	0.403942	+	0.699648i
$75$	−1.88703	+	3.26843i	−0.217895	+	0.377405i
$76$	−3.80061	+	14.1841i	−0.435959	+	1.62702i
$77$	4.51663	+	3.51426i	0.514717	+	0.400487i
$78$	−0.0958025	+	8.92545i	−0.0108475	+	1.01061i
$79$	−8.54505	−	14.8005i	−0.961393	−	1.66518i	−0.719008	−	0.695001i	$-0.755404\pi$
$79$	−8.54505	−	14.8005i	−0.961393	−	1.66518i	−0.242385	−	0.970180i	$-0.577930\pi$
$80$	−3.74913	+	3.74913i	−0.419166	+	0.419166i
$81$	1.00000			0.111111
$82$	10.2786			1.13508
$83$	3.63623	−	3.63623i	0.399128	−	0.399128i	−0.478797	−	0.877926i	$-0.658927\pi$
$83$	3.63623	−	3.63623i	0.399128	−	0.399128i	0.877926	+	0.478797i	$0.158927\pi$
$84$	8.71070	−	6.59131i	0.950416	−	0.719171i
$85$	−0.915005	−	3.41484i	−0.0992462	−	0.370392i
$86$	20.2274	+	5.41991i	2.18117	+	0.584443i
$87$	2.73892	−	1.58131i	0.293643	−	0.169535i
$88$		−	11.3985i		−	1.21509i
$89$	−5.24668	+	1.40584i	−0.556146	+	0.149019i	−0.525935	−	0.850525i	$-0.676285\pi$
$89$	−5.24668	+	1.40584i	−0.556146	+	0.149019i	−0.0302111	+	0.999544i	$0.509618\pi$
$90$	2.74106			0.288934
$91$	1.41009	−	9.43460i	0.147818	−	0.989015i
$92$	2.95732			0.308321
$93$	−2.33568	+	0.625845i	−0.242199	+	0.0648971i
$94$		−	27.3430i		−	2.82021i
$95$	3.41045	−	1.96903i	0.349905	−	0.202018i
$96$	−1.27039	−	0.340399i	−0.129658	−	0.0347419i
$97$	3.61174	+	13.4792i	0.366717	+	1.36861i	0.865078	+	0.501637i	$0.167269\pi$
$97$	3.61174	+	13.4792i	0.366717	+	1.36861i	−0.498361	+	0.866969i	$0.666065\pi$
$98$	−15.1229	+	8.46192i	−1.52764	+	0.854783i
$99$	−1.52947	+	1.52947i	−0.153718	+	0.153718i
$100$	−15.5818			−1.55818
$101$	18.9217			1.88278			0.941390	−	0.337320i	$-0.109520\pi$
$101$	18.9217			1.88278			0.941390	+	0.337320i	$0.109520\pi$
$102$	5.58933	−	5.58933i	0.553426	−	0.553426i
$103$	−4.50207	−	7.79781i	−0.443602	−	0.768341i	0.554352	−	0.832283i	$-0.312966\pi$
$103$	−4.50207	−	7.79781i	−0.443602	−	0.768341i	−0.997954	+	0.0639412i	$0.979633\pi$
$104$	−16.5559	+	9.32308i	−1.62344	+	0.914204i
$105$	−2.90174	−	0.401902i	−0.283181	−	0.0392217i
$106$	5.82981	−	21.7572i	0.566241	−	2.11324i
$107$	6.49988	−	11.2581i	0.628367	−	1.08836i	−0.359512	−	0.933140i	$-0.617057\pi$
$107$	6.49988	−	11.2581i	0.628367	−	1.08836i	0.987879	−	0.155223i	$-0.0496097\pi$
$108$	2.06434	+	3.57554i	0.198641	+	0.344056i
$109$	−0.626065	+	0.167754i	−0.0599662	+	0.0160679i	−0.288677	−	0.957426i	$-0.593216\pi$
$109$	−0.626065	+	0.167754i	−0.0599662	+	0.0160679i	0.228711	+	0.973494i	$0.426549\pi$
$110$	−4.19238	+	4.19238i	−0.399728	+	0.399728i
$111$	2.71160	−	0.726571i	0.257374	−	0.0689630i
$112$	11.6722	+	4.92705i	1.10292	+	0.465562i
$113$	−2.55967	+	4.43348i	−0.240794	+	0.417067i	−0.960941	−	0.276755i	$-0.910741\pi$
$113$	−2.55967	+	4.43348i	−0.240794	+	0.417067i	0.720147	+	0.693822i	$0.244074\pi$
$114$	7.62535	+	4.40250i	0.714179	+	0.412332i
$115$	−0.560800	−	0.560800i	−0.0522948	−	0.0522948i
$116$	11.3081	+	6.52873i	1.04993	+	0.606178i
$117$	3.47248	+	0.970511i	0.321031	+	0.0897238i
$118$			20.1731i			1.85709i
$119$	−6.73649	+	5.09744i	−0.617533	+	0.467282i
$120$	2.91742	+	5.05312i	0.266323	+	0.461284i
$121$			6.32144i			0.574676i
$122$	−8.41253	−	31.3960i	−0.761635	−	2.84246i
$123$	1.07460	−	4.01046i	0.0968934	−	0.361611i
$124$	−7.05937	−	7.05937i	−0.633950	−	0.633950i
$125$	6.86944	+	6.86944i	0.614421	+	0.614421i
$126$	−2.46575	−	6.06801i	−0.219667	−	0.540582i
$127$	−11.5953	+	6.69453i	−1.02891	+	0.594044i	−0.916673	−	0.399638i	$-0.869136\pi$
$127$	−11.5953	+	6.69453i	−1.02891	+	0.594044i	−0.112240	+	0.993681i	$0.535803\pi$
$128$	4.73108	+	17.6566i	0.418173	+	1.56064i
$129$	4.22943	−	7.32559i	0.372381	−	0.644983i
$130$	9.51829	+	2.66023i	0.834809	+	0.233318i
$131$	2.22446	−	1.28429i	0.194352	−	0.112209i	−0.399666	−	0.916661i	$-0.630874\pi$
$131$	2.22446	−	1.28429i	0.194352	−	0.112209i	0.594018	+	0.804452i	$0.297541\pi$
$132$	−8.62603	−	2.31134i	−0.750799	−	0.201176i
$133$	−7.42683	−	5.77862i	−0.643988	−	0.501069i
$134$	−25.4715	−	14.7060i	−2.20040	−	1.27040i
$135$	0.286571	−	1.06950i	0.0246641	−	0.0920477i
$136$	16.2528	+	4.35492i	1.39367	+	0.373431i
$137$	14.8475	+	3.97837i	1.26851	+	0.339895i	0.829458	−	0.558569i	$-0.188649\pi$
$137$	14.8475	+	3.97837i	1.26851	+	0.339895i	0.439047	+	0.898464i	$0.355316\pi$
$138$	0.458951	−	1.71283i	0.0390685	−	0.145806i
$139$	2.84843	+	1.64454i	0.241601	+	0.139488i	0.615912	−	0.787815i	$-0.288788\pi$
$139$	2.84843	+	1.64454i	0.241601	+	0.139488i	−0.374312	+	0.927303i	$0.622121\pi$
$140$	−4.55316	−	11.2050i	−0.384812	−	0.946991i
$141$	−10.6686	−	2.85863i	−0.898456	−	0.240740i
$142$	−32.8536	+	18.9680i	−2.75701	+	1.59176i
$143$	−6.79543	+	3.82669i	−0.568262	+	0.320004i
$144$	−2.39431	+	4.14706i	−0.199526	+	0.345589i
$145$	−0.906317	−	3.38242i	−0.0752655	−	0.280895i
$146$	−10.7918	+	6.23065i	−0.893136	+	0.515652i
$147$	1.72058	+	6.78525i	0.141911	+	0.559638i
$148$	8.19554	+	8.19554i	0.673669	+	0.673669i
$149$	−2.78449	−	2.78449i	−0.228114	−	0.228114i	0.583790	−	0.811904i	$-0.301569\pi$
$149$	−2.78449	−	2.78449i	−0.228114	−	0.228114i	−0.811904	+	0.583790i	$0.801569\pi$
$150$	−2.41817	+	9.02475i	−0.197443	+	0.736868i
$151$	2.01661	+	7.52610i	0.164110	+	0.612465i	0.998152	+	0.0607650i	$0.0193540\pi$
$151$	2.01661	+	7.52610i	0.164110	+	0.612465i	−0.834043	+	0.551700i	$0.813979\pi$
$152$			18.7430i			1.52026i
$153$	−1.59647	−	2.76517i	−0.129067	−	0.223551i
$154$	13.0522	+	5.50956i	1.05177	+	0.443973i
$155$			2.67736i			0.215050i
$156$	3.69827	+	14.4194i	0.296098	+	1.15448i
$157$	9.33603	+	5.39016i	0.745096	+	0.430181i	0.823919	−	0.566707i	$-0.191783\pi$
$157$	9.33603	+	5.39016i	0.745096	+	0.430181i	−0.0788232	+	0.996889i	$0.525116\pi$
$158$	−29.9166	−	29.9166i	−2.38004	−	2.38004i
$159$	−7.87963	−	4.54930i	−0.624895	−	0.360783i
$160$	−0.728112	+	1.26113i	−0.0575623	+	0.0997009i
$161$	−0.736994	+	1.74594i	−0.0580833	+	0.137599i
$162$	2.39126	−	0.640737i	0.187875	−	0.0503410i
$163$	3.25130	−	3.25130i	0.254662	−	0.254662i	−0.568217	−	0.822879i	$-0.692367\pi$
$163$	3.25130	−	3.25130i	0.254662	−	0.254662i	0.822879	+	0.568217i	$0.192367\pi$
$164$	16.5579	−	4.43667i	1.29295	−	0.346446i
$165$	1.19746	+	2.07407i	0.0932224	+	0.161466i
$166$	6.36532	−	11.0251i	0.494044	−	0.855710i
$167$	2.67718	−	9.99136i	0.207166	−	0.773154i	−0.781612	−	0.623765i	$-0.785602\pi$
$167$	2.67718	−	9.99136i	0.207166	−	0.773154i	0.988778	−	0.149390i	$-0.0477309\pi$
$168$	8.56192	−	11.0040i	0.660566	−	0.848977i
$169$	11.1162	+	6.74016i	0.855093	+	0.518474i
$170$	−4.37603	−	7.57951i	−0.335626	−	0.581322i
$171$	2.51496	−	2.51496i	0.192324	−	0.192324i
$172$	34.9239			2.66292
$173$	7.92507			0.602532			0.301266	−	0.953540i	$-0.402591\pi$
$173$	7.92507			0.602532			0.301266	+	0.953540i	$0.402591\pi$
$174$	5.53626	−	5.53626i	0.419703	−	0.419703i
$175$	3.88316	−	9.19921i	0.293539	−	0.695395i
$176$	−2.68079	−	10.0048i	−0.202072	−	0.754143i
$177$	7.87107	+	2.10905i	0.591626	+	0.158526i
$178$	−11.6454	+	6.72347i	−0.872860	+	0.503946i
$179$			0.776613i			0.0580468i	0.999579	+	0.0290234i	$0.00923973\pi$
$179$			0.776613i			0.0580468i	−0.999579	+	0.0290234i	$0.990760\pi$
$180$	4.41561	−	1.18316i	0.329120	−	0.0881874i
$181$	10.5598			0.784905			0.392452	−	0.919772i	$-0.371627\pi$
$181$	10.5598			0.784905			0.392452	+	0.919772i	$0.371627\pi$
$182$	−2.67319	−	23.4641i	−0.198150	−	1.73927i
$183$	−13.1295			−0.970558
$184$	3.64606	−	0.976958i	0.268791	−	0.0720223i
$185$		−	3.10826i		−	0.228524i
$186$	−5.18423	+	2.99312i	−0.380126	+	0.219466i
$187$	6.67101	+	1.78749i	0.487832	+	0.130714i
$188$	−11.8024	−	44.0471i	−0.860777	−	3.21246i
$189$	−2.62538	+	0.327682i	−0.190968	+	0.0238354i
$190$	6.89366	−	6.89366i	0.500119	−	0.500119i
$191$	−5.45039			−0.394376			−0.197188	−	0.980366i	$-0.563181\pi$
$191$	−5.45039			−0.394376			−0.197188	+	0.980366i	$0.563181\pi$
$192$	6.32129			0.456200
$193$	−10.1470	+	10.1470i	−0.730394	+	0.730394i	−0.970698	−	0.240303i	$-0.922753\pi$
$193$	−10.1470	+	10.1470i	−0.730394	+	0.730394i	0.240303	+	0.970698i	$0.422753\pi$
$194$	17.2732	+	29.9181i	1.24015	+	2.14800i
$195$	2.03307	−	3.43569i	0.145591	−	0.246035i
$196$	−20.7091	+	20.1591i	−1.47922	+	1.43993i
$197$	5.97264	−	22.2902i	0.425533	−	1.58811i	−0.337224	−	0.941424i	$-0.609488\pi$
$197$	5.97264	−	22.2902i	0.425533	−	1.58811i	0.762757	−	0.646686i	$-0.223845\pi$
$198$	−2.67738	+	4.63735i	−0.190273	+	0.329562i
$199$	−4.48268	−	7.76424i	−0.317769	−	0.550392i	0.662253	−	0.749280i	$-0.269600\pi$
$199$	−4.48268	−	7.76424i	−0.317769	−	0.550392i	−0.980022	+	0.198888i	$0.936267\pi$
$200$	−19.2108	+	5.14751i	−1.35841	+	0.363984i
$201$	−8.40090	+	8.40090i	−0.592554	+	0.592554i
$202$	45.2468	−	12.1238i	3.18355	−	0.853030i
$203$	−6.67253	+	5.04905i	−0.468320	+	0.354374i
$204$	6.59131	−	11.4165i	0.461484	−	0.799314i
$205$	−3.98123	−	2.29856i	−0.278061	−	0.160539i
$206$	−15.7620	−	15.7620i	−1.09819	−	1.09819i
$207$	−0.620322	−	0.358143i	−0.0431154	−	0.0248927i
$208$	−12.3390	+	12.0769i	−0.855552	+	0.837381i
$209$			7.69311i			0.532144i
$210$	−7.19634	+	0.898198i	−0.496594	+	0.0619816i
$211$	1.93953	+	3.35936i	0.133523	+	0.231268i	0.925032	−	0.379889i	$-0.124038\pi$
$211$	1.93953	+	3.35936i	0.133523	+	0.231268i	−0.791509	+	0.611157i	$0.790704\pi$
$212$		−	37.5652i		−	2.57999i
$213$	3.96611	+	14.8017i	0.271754	+	1.01420i
$214$	8.32942	−	31.0858i	0.569388	−	2.12498i
$215$	−6.62267	−	6.62267i	−0.451662	−	0.451662i
$216$	3.72630	+	3.72630i	0.253543	+	0.253543i
$217$	5.92698	−	2.40844i	0.402350	−	0.163496i
$218$	−1.38960	+	0.802286i	−0.0941156	+	0.0543377i
$219$	1.30280	+	4.86210i	0.0880348	+	0.328550i
$220$	−4.94394	+	8.56315i	−0.333320	+	0.577328i
$221$	−2.86008	−	11.1514i	−0.192390	−	0.750124i
$222$	6.01860	−	3.47484i	0.403942	−	0.233216i
$223$	19.2784	+	5.16562i	1.29097	+	0.345916i	0.838031	−	0.545623i	$-0.183707\pi$
$223$	19.2784	+	5.16562i	1.29097	+	0.345916i	0.452944	+	0.891539i	$0.350374\pi$
$224$	3.44679	+	0.477394i	0.230299	+	0.0318972i
$225$	3.26843	+	1.88703i	0.217895	+	0.125802i
$226$	−3.28015	+	12.2417i	−0.218192	+	0.814305i
$227$	9.28427	+	2.48771i	0.616219	+	0.165115i	0.553408	−	0.832910i	$-0.313327\pi$
$227$	9.28427	+	2.48771i	0.616219	+	0.165115i	0.0628104	+	0.998025i	$0.479994\pi$
$228$	14.1841	+	3.80061i	0.939362	+	0.251701i
$229$	−6.89824	+	25.7446i	−0.455848	+	1.70125i	0.229733	+	0.973254i	$0.426215\pi$
$229$	−6.89824	+	25.7446i	−0.455848	+	1.70125i	−0.685582	+	0.727996i	$0.740452\pi$
$230$	−1.70034	−	0.981694i	−0.112117	−	0.0647310i
$231$	3.51426	−	4.51663i	0.231222	−	0.297172i
$232$	16.0985	+	4.31357i	1.05692	+	0.283200i
$233$	1.53044	−	0.883603i	0.100263	−	0.0578867i	−0.449030	−	0.893517i	$-0.648230\pi$
$233$	1.53044	−	0.883603i	0.100263	−	0.0578867i	0.549293	+	0.835630i	$0.314897\pi$
$234$	8.92545	+	0.0958025i	0.583475	+	0.00626280i
$235$	−6.11460	+	10.5908i	−0.398873	+	0.690868i
$236$	8.70757	+	32.4971i	0.566815	+	2.11538i
$237$	−14.8005	+	8.54505i	−0.961393	+	0.555061i
$238$	−12.8426	+	16.5056i	−0.832461	+	1.06990i
$239$	21.4837	+	21.4837i	1.38967	+	1.38967i	0.826011	+	0.563654i	$0.190605\pi$
$239$	21.4837	+	21.4837i	1.38967	+	1.38967i	0.563654	+	0.826011i	$0.309395\pi$
$240$	3.74913	+	3.74913i	0.242005	+	0.242005i
$241$	−2.48199	+	9.26292i	−0.159879	+	0.596677i	0.838759	+	0.544503i	$0.183282\pi$
$241$	−2.48199	+	9.26292i	−0.159879	+	0.596677i	−0.998638	+	0.0521742i	$0.983385\pi$
$242$	4.05038	+	15.1162i	0.260368	+	0.971707i
$243$		−	1.00000i		−	0.0641500i
$244$	−27.1037	−	46.9449i	−1.73513	−	3.00534i
$245$	7.74987	+	0.104297i	0.495121	+	0.00666329i
$246$		−	10.2786i		−	0.655339i
$247$	11.1739	−	6.29234i	0.710980	−	0.400372i
$248$	−11.0355	−	6.37138i	−0.700758	−	0.404583i
$249$	−3.63623	−	3.63623i	−0.230437	−	0.230437i
$250$	20.8281	+	12.0251i	1.31729	+	0.760535i
$251$	−7.01379	+	12.1482i	−0.442706	+	0.766790i	−0.997889	−	0.0649385i	$-0.979315\pi$
$251$	−7.01379	+	12.1482i	−0.442706	+	0.766790i	0.555183	+	0.831728i	$0.312648\pi$
$252$	−6.59131	−	8.71070i	−0.415214	−	0.548723i
$253$	1.49654	−	0.400995i	0.0940864	−	0.0252104i
$254$	−23.4379	+	23.4379i	−1.47062	+	1.47062i
$255$	−3.41484	+	0.915005i	−0.213846	+	0.0572998i
$256$	16.3052	+	28.2415i	1.01908	+	1.76509i
$257$	−3.92232	+	6.79366i	−0.244668	+	0.423777i	−0.962038	−	0.272915i	$-0.912012\pi$
$257$	−3.92232	+	6.79366i	−0.244668	+	0.423777i	0.717370	+	0.696692i	$0.245346\pi$
$258$	5.41991	−	20.2274i	0.337429	−	1.25930i
$259$	−6.88090	+	2.79607i	−0.427558	+	0.173739i
$260$	16.4814	+	0.176905i	1.02213	+	0.0109712i
$261$	−1.58131	−	2.73892i	−0.0978809	−	0.169535i
$262$	4.49637	−	4.49637i	0.277787	−	0.277787i
$263$	−30.1387			−1.85843			−0.929217	−	0.369535i	$-0.879517\pi$
$263$	−30.1387			−1.85843			−0.929217	+	0.369535i	$0.879517\pi$
$264$	−11.3985			−0.701532
$265$	−7.12354	+	7.12354i	−0.437595	+	0.437595i
$266$	−21.4621	−	9.05954i	−1.31592	−	0.555476i
$267$	1.40584	+	5.24668i	0.0860362	+	0.321091i
$268$	−47.3800	−	12.6954i	−2.89420	−	0.775497i
$269$	−1.57674	+	0.910328i	−0.0961352	+	0.0555037i	−0.547297	−	0.836939i	$-0.684343\pi$
$269$	−1.57674	+	0.910328i	−0.0961352	+	0.0555037i	0.451162	+	0.892442i	$0.351010\pi$
$270$		−	2.74106i		−	0.166816i
$271$	−4.75330	+	1.27364i	−0.288742	+	0.0773682i	−0.400283	−	0.916392i	$-0.631088\pi$
$271$	−4.75330	+	1.27364i	−0.288742	+	0.0773682i	0.111541	+	0.993760i	$0.464421\pi$
$272$	15.2898			0.927079
$273$	−9.43460	−	1.41009i	−0.571008	−	0.0853426i
$274$	38.0533			2.29888
$275$	−7.88512	+	2.11281i	−0.475490	+	0.127407i
$276$		−	2.95732i		−	0.178009i
$277$	−4.09191	+	2.36247i	−0.245859	+	0.141947i	−0.617867	−	0.786283i	$-0.712003\pi$
$277$	−4.09191	+	2.36247i	−0.245859	+	0.141947i	0.372008	+	0.928230i	$0.378670\pi$
$278$	7.86506	+	2.10744i	0.471715	+	0.126396i
$279$	0.625845	+	2.33568i	0.0374683	+	0.139834i
$280$	−9.31515	−	12.3104i	−0.556687	−	0.735685i
$281$	−12.5689	+	12.5689i	−0.749799	+	0.749799i	−0.974441	−	0.224642i	$-0.927879\pi$
$281$	−12.5689	+	12.5689i	−0.749799	+	0.749799i	0.224642	+	0.974441i	$0.427879\pi$
$282$	−27.3430			−1.62825
$283$	−16.8354			−1.00076			−0.500379	−	0.865806i	$-0.666806\pi$
$283$	−16.8354			−1.00076			−0.500379	+	0.865806i	$0.666806\pi$
$284$	−44.7368	+	44.7368i	−2.65464	+	2.65464i
$285$	−1.96903	−	3.41045i	−0.116635	−	0.202018i
$286$	−13.7977	+	13.5047i	−0.815878	+	0.798549i
$287$	−1.50708	+	10.8811i	−0.0889599	+	0.642292i
$288$	−0.340399	+	1.27039i	−0.0200582	+	0.0748583i
$289$	3.40256	−	5.89340i	0.200150	−	0.346671i
$290$	−4.33448	−	7.50754i	−0.254530	−	0.440858i
$291$	13.4792	−	3.61174i	0.790165	−	0.211724i
$292$	−14.6952	+	14.6952i	−0.859972	+	0.859972i
$293$	2.69125	−	0.721119i	0.157225	−	0.0421282i	−0.179348	−	0.983786i	$-0.557399\pi$
$293$	2.69125	−	0.721119i	0.157225	−	0.0421282i	0.336573	+	0.941657i	$0.390732\pi$
$294$	8.46192	+	15.1229i	0.493509	+	0.881983i
$295$	4.51124	−	7.81370i	0.262655	−	0.454931i
$296$	12.8117	+	7.39681i	0.744662	+	0.429931i
$297$	1.52947	+	1.52947i	0.0887489	+	0.0887489i
$298$	−8.44256	−	4.87432i	−0.489065	−	0.282362i
$299$	−1.80647	−	1.84568i	−0.104471	−	0.106738i
$300$			15.5818i			0.899618i
$301$	−8.70341	+	20.6184i	−0.501656	+	1.18842i
$302$	9.64449	+	16.7047i	0.554978	+	0.961250i
$303$		−	18.9217i		−	1.08702i
$304$	4.40810	+	16.4513i	0.252822	+	0.943545i
$305$	−3.76252	+	14.0419i	−0.215442	+	0.804039i
$306$	−5.58933	−	5.58933i	−0.319521	−	0.319521i
$307$	−11.1210	−	11.1210i	−0.634708	−	0.634708i	0.314537	−	0.949245i	$-0.398151\pi$
$307$	−11.1210	−	11.1210i	−0.634708	−	0.634708i	−0.949245	+	0.314537i	$0.898151\pi$
$308$	23.4040	+	3.24154i	1.33357	+	0.184704i
$309$	−7.79781	+	4.50207i	−0.443602	+	0.256114i
$310$	1.71548	+	6.40226i	0.0974327	+	0.363624i
$311$	12.9496	−	22.4293i	0.734304	−	1.27185i	−0.220725	−	0.975336i	$-0.570842\pi$
$311$	12.9496	−	22.4293i	0.734304	−	1.27185i	0.955028	−	0.296515i	$-0.0958244\pi$
$312$	9.32308	+	16.5559i	0.527816	+	0.937294i
$313$	6.50589	−	3.75618i	0.367734	−	0.212312i	−0.304734	−	0.952438i	$-0.598567\pi$
$313$	6.50589	−	3.75618i	0.367734	−	0.212312i	0.672468	+	0.740126i	$0.265234\pi$
$314$	25.7786	+	6.90734i	1.45477	+	0.389804i
$315$	−0.401902	+	2.90174i	−0.0226446	+	0.163495i
$316$	−61.1063	−	35.2797i	−3.43750	−	1.98464i
$317$	−1.89185	+	7.06048i	−0.106257	+	0.396556i	−0.998485	−	0.0550295i	$-0.982475\pi$
$317$	−1.89185	+	7.06048i	−0.106257	+	0.396556i	0.892228	+	0.451585i	$0.149141\pi$
$318$	−21.7572	−	5.82981i	−1.22008	−	0.326920i
$319$	6.60767	+	1.77052i	0.369958	+	0.0991300i
$320$	1.81150	−	6.76061i	0.101266	−	0.377929i
$321$	−11.2581	−	6.49988i	−0.628367	−	0.362788i
$322$	−0.643658	+	4.64722i	−0.0358696	+	0.258979i
$323$	−10.9693	−	2.93923i	−0.610351	−	0.163543i
$324$	3.57554	−	2.06434i	0.198641	−	0.114685i
$325$	9.51816	+	9.72470i	0.527972	+	0.539429i
$326$	5.69149	−	9.85795i	0.315223	−	0.545981i
$327$	0.167754	+	0.626065i	0.00927680	+	0.0346215i
$328$	18.9485	−	10.9399i	1.04625	−	0.604055i
$329$	28.9458	+	4.00910i	1.59583	+	0.221029i
$330$	4.19238	+	4.19238i	0.230783	+	0.230783i
$331$	23.2409	+	23.2409i	1.27744	+	1.27744i	0.942098	+	0.335339i	$0.108851\pi$
$331$	23.2409	+	23.2409i	1.27744	+	1.27744i	0.335339	+	0.942098i	$0.391149\pi$
$332$	5.49508	−	20.5079i	0.301581	−	1.12552i
$333$	−0.726571	−	2.71160i	−0.0398158	−	0.148595i
$334$		−	25.6073i		−	1.40117i
$335$	6.57728	+	11.3922i	0.359355	+	0.622422i
$336$	4.92705	−	11.6722i	0.268793	−	0.636770i
$337$			6.18416i			0.336873i	0.985713	+	0.168436i	$0.0538718\pi$
$337$			6.18416i			0.336873i	−0.985713	+	0.168436i	$0.946128\pi$
$338$	30.9004	+	8.99492i	1.68076	+	0.489259i
$339$	4.43348	+	2.55967i	0.240794	+	0.139022i
$340$	−10.3210	−	10.3210i	−0.559736	−	0.559736i
$341$	−4.52957	−	2.61515i	−0.245290	−	0.141618i
$342$	4.40250	−	7.62535i	0.238060	−	0.412332i
$343$	−6.74059	−	17.2501i	−0.363958	−	0.931416i
$344$	43.0575	−	11.5372i	2.32151	−	0.622045i
$345$	−0.560800	+	0.560800i	−0.0301924	+	0.0301924i
$346$	18.9509	−	5.07788i	1.01881	−	0.272989i
$347$	−12.5904	−	21.8072i	−0.675889	−	1.17067i	−0.976208	−	0.216835i	$-0.930427\pi$
$347$	−12.5904	−	21.8072i	−0.675889	−	1.17067i	0.300319	−	0.953839i	$-0.402907\pi$
$348$	6.52873	−	11.3081i	0.349977	−	0.606178i
$349$	−4.81860	+	17.9833i	−0.257934	+	0.962622i	0.708501	+	0.705710i	$0.249372\pi$
$349$	−4.81860	+	17.9833i	−0.257934	+	0.962622i	−0.966435	+	0.256912i	$0.917295\pi$
$350$	3.39138	−	24.4858i	0.181277	−	1.30882i
$351$	0.970511	−	3.47248i	0.0518021	−	0.185347i
$352$	−1.42239	−	2.46365i	−0.0758137	−	0.131313i
$353$	−14.5922	+	14.5922i	−0.776665	+	0.776665i	−0.979262	−	0.202597i	$-0.935062\pi$
$353$	−14.5922	+	14.5922i	−0.776665	+	0.776665i	0.202597	+	0.979262i	$0.435062\pi$
$354$	20.1731			1.07219
$355$	16.9670			0.900514
$356$	−15.8576	+	15.8576i	−0.840449	+	0.840449i
$357$	5.09744	+	6.73649i	0.269785	+	0.356533i
$358$	0.497605	+	1.85709i	0.0262992	+	0.0981500i
$359$	−8.98361	−	2.40715i	−0.474137	−	0.127045i	0.0138345	−	0.999904i	$-0.495596\pi$
$359$	−8.98361	−	2.40715i	−0.474137	−	0.127045i	−0.487971	+	0.872860i	$0.662263\pi$
$360$	5.05312	−	2.91742i	0.266323	−	0.153761i
$361$			6.34997i			0.334209i
$362$	25.2513	−	6.76606i	1.32718	−	0.355616i
$363$	6.32144			0.331789
$364$	−14.4344	−	36.6447i	−0.756566	−	1.92070i
$365$	5.57335			0.291722
$366$	−31.3960	+	8.41253i	−1.64110	+	0.439730i
$367$		−	34.0704i		−	1.77846i	−0.457460	−	0.889230i	$-0.651241\pi$
$367$		−	34.0704i		−	1.77846i	0.457460	−	0.889230i	$-0.348759\pi$
$368$	2.97049	−	1.71501i	0.154847	−	0.0894011i
$369$	−4.01046	−	1.07460i	−0.208776	−	0.0559414i
$370$	−1.99158	−	7.43267i	−0.103537	−	0.386406i
$371$	22.1777	+	9.36164i	1.15141	+	0.486032i
$372$	−7.05937	+	7.05937i	−0.366011	+	0.366011i
$373$	22.0202			1.14016			0.570082	−	0.821588i	$-0.306912\pi$
$373$	22.0202			1.14016			0.570082	+	0.821588i	$0.306912\pi$
$374$	17.0974			0.884087
$375$	6.86944	−	6.86944i	0.354736	−	0.354736i
$376$	−29.1022	−	50.4064i	−1.50083	−	2.59951i
$377$	−2.83293	−	11.0455i	−0.145903	−	0.568873i
$378$	−6.06801	+	2.46575i	−0.312105	+	0.126825i
$379$	−0.321459	+	1.19970i	−0.0165123	+	0.0616246i	−0.973690	−	0.227875i	$-0.926822\pi$
$379$	−0.321459	+	1.19970i	−0.0165123	+	0.0616246i	0.957178	+	0.289500i	$0.0934889\pi$
$380$	8.12947	−	14.0807i	0.417033	−	0.722323i
$381$	6.69453	+	11.5953i	0.342971	+	0.594044i
$382$	−13.0333	+	3.49226i	−0.666842	+	0.178680i
$383$	−10.3254	+	10.3254i	−0.527603	+	0.527603i	−0.919857	−	0.392254i	$-0.871695\pi$
$383$	−10.3254	+	10.3254i	−0.527603	+	0.527603i	0.392254	+	0.919857i	$0.371695\pi$
$384$	17.6566	−	4.73108i	0.901037	−	0.241432i
$385$	−3.82343	−	5.05283i	−0.194860	−	0.257516i
$386$	−17.7625	+	30.7656i	−0.904088	+	1.56593i
$387$	−7.32559	−	4.22943i	−0.372381	−	0.214994i
$388$	40.7396	+	40.7396i	2.06824	+	2.06824i
$389$	14.0217	+	8.09545i	0.710930	+	0.410456i	0.811405	−	0.584484i	$-0.198703\pi$
$389$	14.0217	+	8.09545i	0.710930	+	0.410456i	−0.100475	+	0.994940i	$0.532036\pi$
$390$	2.66023	−	9.51829i	0.134706	−	0.481977i
$391$			2.28706i			0.115662i
$392$	−18.8725	+	31.6953i	−0.953204	+	1.60085i
$393$	−1.28429	−	2.22446i	−0.0647840	−	0.112209i
$394$		−	57.1286i		−	2.87810i
$395$	4.89752	+	18.2778i	0.246421	+	0.919656i
$396$	−2.31134	+	8.62603i	−0.116149	+	0.433474i
$397$	−21.7086	−	21.7086i	−1.08952	−	1.08952i	−0.995577	−	0.0939469i	$-0.970052\pi$
$397$	−21.7086	−	21.7086i	−1.08952	−	1.08952i	−0.0939469	−	0.995577i	$-0.529948\pi$
$398$	−15.6941	−	15.6941i	−0.786674	−	0.786674i
$399$	−5.77862	+	7.42683i	−0.289293	+	0.371807i
$400$	−15.6512	+	9.03624i	−0.782562	+	0.451812i
$401$	1.25827	+	4.69592i	0.0628349	+	0.234503i	0.990200	−	0.139654i	$-0.0445989\pi$
$401$	1.25827	+	4.69592i	0.0628349	+	0.234503i	−0.927366	+	0.374157i	$0.877932\pi$
$402$	−14.7060	+	25.4715i	−0.733468	+	1.27040i
$403$	−0.0935758	+	8.71800i	−0.00466134	+	0.434275i
$404$	67.6553	−	39.0608i	3.36598	−	1.94335i
$405$	−1.06950	−	0.286571i	−0.0531437	−	0.0142398i
$406$	−12.7207	+	16.3489i	−0.631315	+	0.811383i
$407$	5.25858	+	3.03604i	0.260658	+	0.150491i
$408$	4.35492	−	16.2528i	0.215601	−	0.804633i
$409$	−7.01765	−	1.88037i	−0.347000	−	0.0929784i	0.0811095	−	0.996705i	$-0.474154\pi$
$409$	−7.01765	−	1.88037i	−0.347000	−	0.0929784i	−0.428110	+	0.903727i	$0.640820\pi$
$410$	−10.9929	−	2.94555i	−0.542902	−	0.145470i
$411$	3.97837	−	14.8475i	0.196239	−	0.732372i
$412$	−32.1947	−	18.5876i	−1.58612	−	0.915745i
$413$	−21.3557	−	2.95784i	−1.05084	−	0.145546i
$414$	−1.71283	−	0.458951i	−0.0841810	−	0.0225562i
$415$	−4.93098	+	2.84690i	−0.242052	+	0.139749i
$416$	−2.41496	+	4.08103i	−0.118403	+	0.200089i
$417$	1.64454	−	2.84843i	0.0805336	−	0.139488i
$418$	4.92926	+	18.3962i	0.241098	+	0.899790i
$419$	−3.79902	+	2.19337i	−0.185594	+	0.107153i	−0.589918	−	0.807463i	$-0.700840\pi$
$419$	−3.79902	+	2.19337i	−0.185594	+	0.107153i	0.404324	+	0.914616i	$0.367507\pi$
$420$	−11.2050	+	4.55316i	−0.546746	+	0.222171i
$421$	2.39860	+	2.39860i	0.116901	+	0.116901i	0.763137	−	0.646236i	$-0.223658\pi$
$421$	2.39860	+	2.39860i	0.116901	+	0.116901i	−0.646236	+	0.763137i	$0.723658\pi$
$422$	6.79039	+	6.79039i	0.330551	+	0.330551i
$423$	−2.85863	+	10.6686i	−0.138992	+	0.518724i
$424$	−12.4098	−	46.3139i	−0.602672	−	2.24920i
$425$		−	12.0503i		−	0.584527i
$426$	18.9680	+	32.8536i	0.919004	+	1.59176i
$427$	34.4699	−	4.30230i	1.66811	−	0.208203i
$428$		−	53.6718i		−	2.59432i
$429$	3.82669	+	6.79543i	0.184754	+	0.328086i
$430$	−20.0799	−	11.5931i	−0.968340	−	0.559071i
$431$	−19.8131	−	19.8131i	−0.954365	−	0.954365i	0.0446380	−	0.999003i	$-0.485787\pi$
$431$	−19.8131	−	19.8131i	−0.954365	−	0.954365i	−0.999003	+	0.0446380i	$0.985787\pi$
$432$	4.14706	+	2.39431i	0.199526	+	0.115196i
$433$	0.984147	−	1.70459i	0.0472951	−	0.0819175i	−0.841409	−	0.540399i	$-0.818273\pi$
$433$	0.984147	−	1.70459i	0.0472951	−	0.0819175i	0.888704	+	0.458482i	$0.151607\pi$
$434$	12.6298	−	9.55685i	0.606249	−	0.458744i
$435$	−3.38242	+	0.906317i	−0.162175	+	0.0434546i
$436$	−1.89222	+	1.89222i	−0.0906209	+	0.0906209i
$437$	−2.46080	+	0.659370i	−0.117716	+	0.0315419i
$438$	6.23065	+	10.7918i	0.297712	+	0.515652i
$439$	−4.86693	+	8.42976i	−0.232286	+	0.402331i	−0.958480	−	0.285158i	$-0.907954\pi$
$439$	−4.86693	+	8.42976i	−0.232286	+	0.402331i	0.726195	+	0.687489i	$0.241287\pi$
$440$	−3.26649	+	12.1907i	−0.155724	+	0.581169i
$441$	6.78525	−	1.72058i	0.323107	−	0.0819325i
$442$	−13.9843	−	24.8333i	−0.665166	−	1.18120i
$443$	−14.0996	−	24.4213i	−0.669894	−	1.16029i	−0.977933	−	0.208916i	$-0.933006\pi$
$443$	−14.0996	−	24.4213i	−0.669894	−	1.16029i	0.308040	−	0.951373i	$-0.400327\pi$
$444$	8.19554	−	8.19554i	0.388943	−	0.388943i
$445$	6.01418			0.285099
$446$	49.4094			2.33960
$447$	−2.78449	+	2.78449i	−0.131702	+	0.131702i
$448$	−16.5958	+	2.07138i	−0.784078	+	0.0978634i
$449$	−6.46808	−	24.1392i	−0.305247	−	1.13920i	−0.932732	−	0.360570i	$-0.882582\pi$
$449$	−6.46808	−	24.1392i	−0.305247	−	1.13920i	0.627485	−	0.778629i	$-0.284084\pi$
$450$	9.02475	+	2.41817i	0.425431	+	0.113994i
$451$	7.77745	−	4.49031i	0.366226	−	0.211441i
$452$			21.1361i			0.994159i
$453$	7.52610	−	2.01661i	0.353607	−	0.0947487i
$454$	23.7951			1.11676
$455$	−4.21177	+	9.68618i	−0.197451	+	0.454095i
$456$	18.7430			0.877721
$457$	18.3479	−	4.91632i	0.858281	−	0.229976i	0.197267	−	0.980350i	$-0.436793\pi$
$457$	18.3479	−	4.91632i	0.858281	−	0.229976i	0.661013	+	0.750374i	$0.270127\pi$
$458$			65.9820i			3.08313i
$459$	−2.76517	+	1.59647i	−0.129067	+	0.0745169i
$460$	−3.16284	−	0.847481i	−0.147468	−	0.0395140i
$461$	−4.98997	−	18.6228i	−0.232406	−	0.867350i	−0.979301	−	0.202409i	$-0.935123\pi$
$461$	−4.98997	−	18.6228i	−0.232406	−	0.867350i	0.746895	−	0.664942i	$-0.231544\pi$
$462$	5.50956	−	13.0522i	0.256328	−	0.607241i
$463$	−9.73196	+	9.73196i	−0.452283	+	0.452283i	−0.896112	−	0.443829i	$-0.853620\pi$
$463$	−9.73196	+	9.73196i	−0.452283	+	0.452283i	0.443829	+	0.896112i	$0.353620\pi$
$464$	15.1446			0.703071
$465$	2.67736			0.124159
$466$	3.09354	−	3.09354i	0.143305	−	0.143305i
$467$	−15.2510	−	26.4155i	−0.705733	−	1.22237i	−0.966426	−	0.256944i	$-0.917284\pi$
$467$	−15.2510	−	26.4155i	−0.705733	−	1.22237i	0.260693	−	0.965422i	$-0.416049\pi$
$468$	14.4194	−	3.69827i	0.666539	−	0.170953i
$469$	19.3027	−	24.8084i	0.891317	−	1.14554i
$470$	−7.83570	+	29.2432i	−0.361434	+	1.34889i
$471$	5.39016	−	9.33603i	0.248365	−	0.430181i
$472$	21.4710	+	37.1889i	0.988285	+	1.71176i
$473$	17.6731	−	4.73549i	0.812609	−	0.217738i
$474$	−29.9166	+	29.9166i	−1.37412	+	1.37412i
$475$	12.9657	−	3.47416i	0.594909	−	0.159405i
$476$	−13.5637	+	32.1325i	−0.621692	+	1.47279i
$477$	−4.54930	+	7.87963i	−0.208298	+	0.360783i
$478$	65.1385	+	37.6078i	2.97937	+	1.72014i
$479$	7.15853	+	7.15853i	0.327082	+	0.327082i	0.851476	−	0.524394i	$-0.175708\pi$
$479$	7.15853	+	7.15853i	0.327082	+	0.327082i	−0.524394	+	0.851476i	$0.675708\pi$
$480$	1.26113	+	0.728112i	0.0575623	+	0.0332336i
$481$	0.108636	−	10.1211i	0.00495339	−	0.461483i
$482$			23.7404i			1.08134i
$483$	1.74594	+	0.736994i	0.0794430	+	0.0335344i
$484$	13.0496	+	22.6025i	0.593163	+	1.02739i
$485$		−	15.4510i		−	0.701594i
$486$	−0.640737	−	2.39126i	−0.0290644	−	0.108470i
$487$	−6.33502	+	23.6426i	−0.287067	+	1.07135i	0.660249	+	0.751047i	$0.270451\pi$
$487$	−6.33502	+	23.6426i	−0.287067	+	1.07135i	−0.947316	+	0.320301i	$0.896216\pi$
$488$	−48.9244	−	48.9244i	−2.21470	−	2.21470i
$489$	−3.25130	−	3.25130i	−0.147029	−	0.147029i
$490$	18.5988	−	4.71623i	0.840208	−	0.213057i
$491$	3.99686	−	2.30759i	0.180376	−	0.104140i	−0.407093	−	0.913387i	$-0.633458\pi$
$491$	3.99686	−	2.30759i	0.180376	−	0.104140i	0.587469	+	0.809247i	$0.300124\pi$
$492$	−4.43667	−	16.5579i	−0.200021	−	0.746487i
$493$	−5.04905	+	8.74520i	−0.227398	+	0.393864i
$494$	22.6881	−	22.2062i	1.02078	−	0.999104i
$495$	2.07407	−	1.19746i	0.0932224	−	0.0538220i
$496$	−11.1847	−	2.99693i	−0.502207	−	0.134566i
$497$	−15.2628	−	37.5606i	−0.684631	−	1.68482i
$498$	−11.0251	−	6.36532i	−0.494044	−	0.285237i
$499$	3.12405	−	11.6591i	0.139852	−	0.521934i	−0.860079	−	0.510161i	$-0.829586\pi$
$499$	3.12405	−	11.6591i	0.139852	−	0.521934i	0.999931	−	0.0117728i	$-0.00374750\pi$
$500$	38.7428	+	10.3811i	1.73263	+	0.464257i
$501$	−9.99136	−	2.67718i	−0.446381	−	0.119607i
$502$	−8.98798	+	33.5436i	−0.401153	+	1.49712i
$503$	26.0380	+	15.0331i	1.16098	+	0.670291i	0.951538	−	0.307531i	$-0.0995027\pi$
$503$	26.0380	+	15.0331i	1.16098	+	0.670291i	0.209440	+	0.977822i	$0.432836\pi$
$504$	−11.0040	−	8.56192i	−0.490157	−	0.381378i
$505$	−20.2367	−	5.42241i	−0.900522	−	0.241294i
$506$	3.32168	−	1.91777i	0.147666	−	0.0852553i
$507$	6.74016	−	11.1162i	0.299341	−	0.493688i
$508$	−27.6396	+	47.8731i	−1.22631	+	2.12403i
$509$	5.60832	+	20.9305i	0.248584	+	0.927730i	0.971548	+	0.236843i	$0.0761128\pi$
$509$	5.60832	+	20.9305i	0.248584	+	0.927730i	−0.722963	+	0.690886i	$0.757221\pi$
$510$	−7.57951	+	4.37603i	−0.335626	+	0.193774i
$511$	−5.01356	−	12.3380i	−0.221787	−	0.545799i
$512$	31.2343	+	31.2343i	1.38037	+	1.38037i
$513$	−2.51496	−	2.51496i	−0.111038	−	0.111038i
$514$	−5.02635	+	18.7586i	−0.221703	+	0.827406i
$515$	2.58032	+	9.62990i	0.113703	+	0.424344i
$516$		−	34.9239i		−	1.53744i
$517$	−11.9451	−	20.6895i	−0.525344	−	0.909922i
$518$	−14.6625	+	11.0950i	−0.644232	+	0.487485i
$519$		−	7.92507i		−	0.347872i
$520$	20.3782	−	5.22657i	0.893645	−	0.229200i
$521$	−10.6562	−	6.15238i	−0.466858	−	0.269541i	0.248065	−	0.968743i	$-0.420205\pi$
$521$	−10.6562	−	6.15238i	−0.466858	−	0.269541i	−0.714924	+	0.699203i	$0.753539\pi$
$522$	−5.53626	−	5.53626i	−0.242315	−	0.242315i
$523$	3.57584	+	2.06451i	0.156360	+	0.0902747i	0.576139	−	0.817352i	$-0.304559\pi$
$523$	3.57584	+	2.06451i	0.156360	+	0.0902747i	−0.419778	+	0.907627i	$0.637892\pi$
$524$	5.30242	−	9.18407i	0.231638	−	0.401208i
$525$	−9.19921	−	3.88316i	−0.401486	−	0.169475i
$526$	−72.0696	+	19.3110i	−3.14238	+	0.841999i
$527$	5.45942	−	5.45942i	0.237816	−	0.237816i
$528$	−10.0048	+	2.68079i	−0.435405	+	0.116666i
$529$	−11.2435	−	19.4743i	−0.488846	−	0.846707i
$530$	−12.4699	+	21.5986i	−0.541659	+	0.938181i
$531$	2.10905	−	7.87107i	0.0915249	−	0.341575i
$532$	−38.4839	−	5.33017i	−1.66849	−	0.231092i
$533$	−12.8833	−	7.62372i	−0.558039	−	0.330220i
$534$	6.72347	+	11.6454i	0.290953	+	0.503946i
$535$	−10.1779	+	10.1779i	−0.440027	+	0.440027i
$536$	−62.6085			−2.70428
$537$	0.776613			0.0335133
$538$	−3.18711	+	3.18711i	−0.137406	+	0.137406i
$539$	−7.74626	+	13.0094i	−0.333655	+	0.560356i
$540$	−1.18316	−	4.41561i	−0.0509150	−	0.190017i
$541$	−10.1891	−	2.73015i	−0.438062	−	0.117378i	0.0330459	−	0.999454i	$-0.489479\pi$
$541$	−10.1891	−	2.73015i	−0.438062	−	0.117378i	−0.471108	+	0.882075i	$0.656146\pi$
$542$	−10.5503	+	6.09122i	−0.453175	+	0.261640i
$543$		−	10.5598i		−	0.453165i
$544$	4.05628	−	1.08688i	0.173911	−	0.0465994i
$545$	0.717648			0.0307407
$546$	−23.4641	+	2.67319i	−1.00417	+	0.114402i
$547$	33.3666			1.42665			0.713327	−	0.700831i	$-0.247187\pi$
$547$	33.3666			1.42665			0.713327	+	0.700831i	$0.247187\pi$
$548$	61.3004	−	16.4254i	2.61862	−	0.701658i
$549$			13.1295i			0.560352i
$550$	−17.5016	+	10.1046i	−0.746272	+	0.430860i
$551$	−10.8652	−	2.91132i	−0.462873	−	0.124026i
$552$	−0.976958	−	3.64606i	−0.0415821	−	0.155187i
$553$	36.0568	−	27.2839i	1.53329	−	1.16023i
$554$	−8.27111	+	8.27111i	−0.351406	+	0.351406i
$555$	−3.10826			−0.131938
$556$	13.5796			0.575902
$557$	7.06829	−	7.06829i	0.299493	−	0.299493i	−0.541322	−	0.840815i	$-0.682076\pi$
$557$	7.06829	−	7.06829i	0.299493	−	0.299493i	0.840815	+	0.541322i	$0.182076\pi$
$558$	2.99312	+	5.18423i	0.126709	+	0.219466i
$559$	−21.3333	−	21.7962i	−0.902300	−	0.921881i
$560$	−11.0714	−	8.61438i	−0.467853	−	0.364024i
$561$	1.78749	−	6.67101i	0.0754679	−	0.281650i
$562$	−22.0022	+	38.1090i	−0.928108	+	1.60753i
$563$	1.69542	+	2.93656i	0.0714535	+	0.123761i	0.899539	−	0.436841i	$-0.143903\pi$
$563$	1.69542	+	2.93656i	0.0714535	+	0.123761i	−0.828085	+	0.560603i	$0.810570\pi$
$564$	−44.0471	+	11.8024i	−1.85472	+	0.496970i
$565$	4.00807	−	4.00807i	0.168621	−	0.168621i
$566$	−40.2578	+	10.7870i	−1.69216	+	0.453413i
$567$	0.327682	+	2.62538i	0.0137614	+	0.110256i
$568$	−40.3768	+	69.9347i	−1.69417	+	2.93439i
$569$	−0.943027	−	0.544457i	−0.0395337	−	0.0228248i	0.480103	−	0.877212i	$-0.340599\pi$
$569$	−0.943027	−	0.544457i	−0.0395337	−	0.0228248i	−0.519637	+	0.854387i	$0.673933\pi$
$570$	−6.89366	−	6.89366i	−0.288744	−	0.288744i
$571$	29.1820	+	16.8482i	1.22123	+	0.705076i	0.965180	−	0.261588i	$-0.0842462\pi$
$571$	29.1820	+	16.8482i	1.22123	+	0.705076i	0.256048	+	0.966664i	$0.417579\pi$
$572$	−16.3977	+	27.7105i	−0.685623	+	1.15864i
$573$			5.45039i			0.227693i
$574$	3.36811	+	26.9852i	0.140582	+	1.12634i
$575$	−1.35165	−	2.34113i	−0.0563678	−	0.0976319i
$576$		−	6.32129i		−	0.263387i
$577$	1.97749	+	7.38008i	0.0823239	+	0.307237i	0.994794	−	0.101907i	$-0.0324943\pi$
$577$	1.97749	+	7.38008i	0.0823239	+	0.307237i	−0.912470	+	0.409143i	$0.865828\pi$
$578$	4.36029	−	16.2728i	0.181364	−	0.676859i
$579$	10.1470	+	10.1470i	0.421693	+	0.421693i
$580$	−10.2230	−	10.2230i	−0.424488	−	0.424488i
$581$	10.7380	+	8.35497i	0.445488	+	0.346622i
$582$	29.9181	−	17.2732i	1.24015	−	0.715999i
$583$	−5.09363	−	19.0097i	−0.210957	−	0.787301i
$584$	−13.2630	+	22.9723i	−0.548828	+	0.950599i
$585$	−3.43569	−	2.03307i	−0.142048	−	0.0840571i
$586$	5.97344	−	3.44877i	0.246761	−	0.142467i
$587$	7.85719	+	2.10533i	0.324301	+	0.0868961i	0.417297	−	0.908770i	$-0.362978\pi$
$587$	7.85719	+	2.10533i	0.324301	+	0.0868961i	−0.0929958	+	0.995667i	$0.529644\pi$
$588$	20.1591	+	20.7091i	0.831345	+	0.854027i
$589$	7.44812	+	4.30017i	0.306894	+	0.177186i
$590$	5.78103	−	21.5751i	0.238001	−	0.888233i
$591$	−22.2902	−	5.97264i	−0.916896	−	0.245681i
$592$	12.9848	+	3.47927i	0.533672	+	0.142997i
$593$	−0.989650	+	3.69342i	−0.0406400	+	0.151671i	−0.983264	−	0.182185i	$-0.941683\pi$
$593$	−0.989650	+	3.69342i	−0.0406400	+	0.151671i	0.942624	+	0.333855i	$0.108350\pi$
$594$	4.63735	+	2.67738i	0.190273	+	0.109854i
$595$	8.66543	−	3.52122i	0.355248	−	0.144356i
$596$	−15.7042	−	4.20792i	−0.643268	−	0.172363i
$597$	−7.76424	+	4.48268i	−0.317769	+	0.183464i
$598$	−5.50234	−	3.25602i	−0.225008	−	0.133148i
$599$	−14.5091	+	25.1304i	−0.592824	+	1.02680i	0.401026	+	0.916067i	$0.368654\pi$
$599$	−14.5091	+	25.1304i	−0.592824	+	1.02680i	−0.993850	+	0.110734i	$0.964680\pi$
$600$	5.14751	+	19.2108i	0.210146	+	0.784276i
$601$	−18.8192	+	10.8653i	−0.767653	+	0.443205i	−0.832037	−	0.554721i	$-0.812825\pi$
$601$	−18.8192	+	10.8653i	−0.767653	+	0.443205i	0.0643839	+	0.997925i	$0.479492\pi$
$602$	−7.60117	+	54.8805i	−0.309800	+	2.23676i
$603$	8.40090	+	8.40090i	0.342111	+	0.342111i
$604$	22.7469	+	22.7469i	0.925557	+	0.925557i
$605$	1.81154	−	6.76076i	0.0736496	−	0.274864i
$606$	−12.1238	−	45.2468i	−0.492497	−	1.83802i
$607$		−	41.5379i		−	1.68597i	−0.537936	−	0.842985i	$-0.680796\pi$
$607$		−	41.5379i		−	1.68597i	0.537936	−	0.842985i	$-0.319204\pi$
$608$	2.33888	+	4.05106i	0.0948542	+	0.164292i
$609$	5.04905	+	6.67253i	0.204598	+	0.270384i
$610$			35.9887i			1.45714i
$611$	−20.2805	+	34.2720i	−0.820462	+	1.38650i
$612$	−11.4165	−	6.59131i	−0.461484	−	0.266438i
$613$	4.78251	+	4.78251i	0.193164	+	0.193164i	0.797062	−	0.603898i	$-0.206387\pi$
$613$	4.78251	+	4.78251i	0.193164	+	0.193164i	−0.603898	+	0.797062i	$0.706387\pi$
$614$	−33.7188	−	19.4676i	−1.36078	−	0.785647i
$615$	−2.29856	+	3.98123i	−0.0926870	+	0.160539i
$616$	29.9255	−	3.73510i	1.20573	−	0.150492i
$617$	36.0435	−	9.65782i	1.45106	−	0.388809i	0.554665	−	0.832074i	$-0.312846\pi$
$617$	36.0435	−	9.65782i	1.45106	−	0.388809i	0.896391	+	0.443264i	$0.146180\pi$
$618$	−15.7620	+	15.7620i	−0.634040	+	0.634040i
$619$	−19.8305	+	5.31356i	−0.797054	+	0.213570i	−0.634290	−	0.773095i	$-0.718707\pi$
$619$	−19.8305	+	5.31356i	−0.797054	+	0.213570i	−0.162764	+	0.986665i	$0.552041\pi$
$620$	5.52697	+	9.57299i	0.221968	+	0.384461i
$621$	−0.358143	+	0.620322i	−0.0143718	+	0.0248927i
$622$	16.5945	−	61.9317i	0.665381	−	2.48323i
$623$	−5.41011	−	13.3139i	−0.216752	−	0.533408i
$624$	12.0769	+	12.3390i	0.483462	+	0.493953i
$625$	4.05687	+	7.02671i	0.162275	+	0.281068i
$626$	13.1506	−	13.1506i	0.525602	−	0.525602i
$627$	7.69311			0.307233
$628$	44.5084			1.77608
$629$	−6.33808	+	6.33808i	−0.252716	+	0.252716i
$630$	0.898198	+	7.19634i	0.0357851	+	0.286709i
$631$	11.1735	+	41.7002i	0.444812	+	1.66006i	0.716433	+	0.697656i	$0.245773\pi$
$631$	11.1735	+	41.7002i	0.444812	+	1.66006i	−0.271622	+	0.962404i	$0.587560\pi$
$632$	−86.9924	−	23.3095i	−3.46037	−	0.927204i
$633$	3.35936	−	1.93953i	0.133523	−	0.0770894i
$634$			18.0956i			0.718669i
$635$	14.3196	−	3.83692i	0.568255	−	0.152263i
$636$	−37.5652			−1.48956
$637$	25.2315	+	0.610476i	0.999707	+	0.0241880i
$638$	16.9351			0.670467
$639$	14.8017	−	3.96611i	0.585548	−	0.156897i
$640$		−	20.2395i		−	0.800037i
$641$	22.8765	−	13.2078i	0.903567	−	0.521675i	0.0252115	−	0.999682i	$-0.491974\pi$
$641$	22.8765	−	13.2078i	0.903567	−	0.521675i	0.878356	+	0.478007i	$0.158641\pi$
$642$	−31.0858	−	8.32942i	−1.22686	−	0.328736i
$643$	2.34913	+	8.76709i	0.0926408	+	0.345740i	0.996651	−	0.0817702i	$-0.0260574\pi$
$643$	2.34913	+	8.76709i	0.0926408	+	0.345740i	−0.904010	+	0.427510i	$0.859391\pi$
$644$	0.969060	+	7.76408i	0.0381863	+	0.305948i
$645$	−6.62267	+	6.62267i	−0.260767	+	0.260767i
$646$	−28.1138			−1.10612
$647$	−9.91733			−0.389891			−0.194945	−	0.980814i	$-0.562453\pi$
$647$	−9.91733			−0.389891			−0.194945	+	0.980814i	$0.562453\pi$
$648$	3.72630	−	3.72630i	0.146383	−	0.146383i
$649$	8.81285	+	15.2643i	0.345935	+	0.599176i
$650$	28.9914	+	17.1557i	1.13714	+	0.672901i
$651$	−2.40844	−	5.92698i	−0.0943943	−	0.232297i
$652$	4.91337	−	18.3370i	0.192423	−	0.718131i
$653$	21.8886	−	37.9122i	0.856567	−	1.48362i	−0.0186158	−	0.999827i	$-0.505926\pi$
$653$	21.8886	−	37.9122i	0.856567	−	1.48362i	0.875183	−	0.483792i	$-0.160741\pi$
$654$	0.802286	+	1.38960i	0.0313719	+	0.0543377i
$655$	−2.74709	+	0.736081i	−0.107338	+	0.0287611i
$656$	14.0587	−	14.0587i	0.548900	−	0.548900i
$657$	4.86210	−	1.30280i	0.189689	−	0.0508269i
$658$	71.7857	−	8.95981i	2.79850	−	0.349290i
$659$	2.58887	−	4.48406i	0.100848	−	0.174674i	−0.811186	−	0.584788i	$-0.801178\pi$
$659$	2.58887	−	4.48406i	0.100848	−	0.174674i	0.912034	+	0.410114i	$0.134511\pi$
$660$	8.56315	+	4.94394i	0.333320	+	0.192443i
$661$	−22.6178	−	22.6178i	−0.879730	−	0.879730i	0.113776	−	0.993506i	$-0.463705\pi$
$661$	−22.6178	−	22.6178i	−0.879730	−	0.879730i	−0.993506	+	0.113776i	$0.963705\pi$
$662$	70.4664	+	40.6838i	2.73876	+	1.58122i
$663$	−11.1514	+	2.86008i	−0.433084	+	0.111076i
$664$		−	27.0994i		−	1.05166i
$665$	6.28699	+	8.30853i	0.243799	+	0.322191i
$666$	−3.47484	−	6.01860i	−0.134647	−	0.233216i
$667$			2.26535i			0.0877146i
$668$	−11.0532	−	41.2511i	−0.427661	−	1.59605i
$669$	5.16562	−	19.2784i	0.199714	−	0.745345i
$670$	23.0274	+	23.0274i	0.889626	+	0.889626i
$671$	−20.0811	−	20.0811i	−0.775224	−	0.775224i
$672$	0.477394	−	3.44679i	0.0184159	−	0.132963i
$673$	30.4851	−	17.6006i	1.17511	−	0.678452i	0.220234	−	0.975447i	$-0.429318\pi$
$673$	30.4851	−	17.6006i	1.17511	−	0.678452i	0.954879	+	0.296995i	$0.0959846\pi$
$674$	3.96242	+	14.7880i	0.152627	+	0.569611i
$675$	1.88703	−	3.26843i	0.0726317	−	0.125802i
$676$	53.6604	+	1.15208i	2.06386	+	0.0443106i
$677$	−33.9514	+	19.6018i	−1.30486	+	0.753360i	−0.981233	−	0.192825i	$-0.938235\pi$
$677$	−33.9514	+	19.6018i	−1.30486	+	0.753360i	−0.323625	+	0.946185i	$0.604902\pi$
$678$	12.2417	+	3.28015i	0.470139	+	0.125973i
$679$	−34.2046	+	13.8991i	−1.31265	+	0.533399i
$680$	−16.1343	−	9.31515i	−0.618723	−	0.357220i
$681$	2.48771	−	9.28427i	0.0953293	−	0.355774i
$682$	−12.5070	−	3.35124i	−0.478918	−	0.128326i
$683$	−10.6441	−	2.85209i	−0.407286	−	0.109132i	0.0493586	−	0.998781i	$-0.484282\pi$
$683$	−10.6441	−	2.85209i	−0.407286	−	0.109132i	−0.456645	+	0.889649i	$0.650949\pi$
$684$	3.80061	−	14.1841i	0.145320	−	0.542341i
$685$	−14.7393	−	8.50971i	−0.563158	−	0.325139i
$686$	−27.1713	−	36.9305i	−1.03740	−	1.41001i
$687$	25.7446	+	6.89824i	0.982217	+	0.263184i
$688$	35.0794	−	20.2531i	1.33739	−	0.772143i
$689$	−23.4446	+	22.9467i	−0.893169	+	0.874199i
$690$	−0.981694	+	1.70034i	−0.0373724	+	0.0647310i
$691$	1.35724	+	5.06530i	0.0516320	+	0.192693i	0.986925	−	0.161182i	$-0.0515305\pi$
$691$	1.35724	+	5.06530i	0.0516320	+	0.192693i	−0.935293	+	0.353875i	$0.884864\pi$
$692$	28.3364	−	16.3600i	1.07719	−	0.621915i
$693$	−4.51663	−	3.51426i	−0.171572	−	0.133496i
$694$	−44.0797	−	44.0797i	−1.67324	−	1.67324i
$695$	−2.57511	−	2.57511i	−0.0976795	−	0.0976795i
$696$	4.31357	−	16.0985i	0.163506	−	0.610211i
$697$	3.43114	+	12.8052i	0.129964	+	0.485031i
$698$			46.0901i			1.74454i
$699$	−0.883603	−	1.53044i	−0.0334209	−	0.0578867i
$700$	−5.10590	−	40.9083i	−0.192985	−	1.54619i
$701$		−	51.3651i		−	1.94003i	−0.243039	−	0.970017i	$-0.578144\pi$
$701$		−	51.3651i		−	1.94003i	0.243039	−	0.970017i	$-0.421856\pi$
$702$	0.0958025	−	8.92545i	0.00361583	−	0.336869i
$703$	−8.64685	−	4.99226i	−0.326122	−	0.188287i
$704$	9.66824	+	9.66824i	0.364385	+	0.364385i
$705$	10.5908	+	6.11460i	0.398873	+	0.230289i
$706$	−25.5440	+	44.2436i	−0.961362	+	1.66513i
$707$	6.20031	+	49.6767i	0.233187	+	1.86828i
$708$	32.4971	−	8.70757i	1.22132	−	0.327251i
$709$	−20.8652	+	20.8652i	−0.783609	+	0.783609i	−0.980438	−	0.196829i	$-0.936936\pi$
$709$	−20.8652	+	20.8652i	−0.783609	+	0.783609i	0.196829	+	0.980438i	$0.436936\pi$
$710$	40.5725	−	10.8714i	1.52266	−	0.407995i
$711$	8.54505	+	14.8005i	0.320464	+	0.555061i
$712$	−14.3121	+	24.7893i	−0.536369	+	0.929018i
$713$	0.448284	−	1.67302i	0.0167884	−	0.0626551i
$714$	16.5056	+	12.8426i	0.617708	+	0.480622i
$715$	8.36430	−	2.14526i	0.312807	−	0.0802282i
$716$	1.60319	+	2.77681i	0.0599141	+	0.103774i
$717$	21.4837	−	21.4837i	0.802323	−	0.802323i
$718$	−23.0245			−0.859267
$719$	−42.9826			−1.60298			−0.801491	−	0.598007i	$-0.795959\pi$
$719$	−42.9826			−1.60298			−0.801491	+	0.598007i	$0.795959\pi$
$720$	3.74913	−	3.74913i	0.139722	−	0.139722i
$721$	18.9970	−	14.3749i	0.707485	−	0.535348i
$722$	4.06866	+	15.1844i	0.151420	+	0.565107i
$723$	9.26292	+	2.48199i	0.344492	+	0.0923063i
$724$	37.7570	−	21.7990i	1.40323	−	0.810155i
$725$		−	11.9359i		−	0.443289i
$726$	15.1162	−	4.05038i	0.561015	−	0.150324i
$727$	3.84403			0.142567			0.0712836	−	0.997456i	$-0.477290\pi$
$727$	3.84403			0.142567			0.0712836	+	0.997456i	$0.477290\pi$
$728$	−29.9017	−	40.4106i	−1.10823	−	1.49772i
$729$	−1.00000			−0.0370370
$730$	13.3273	−	3.57105i	0.493267	−	0.132170i
$731$			27.0087i			0.998952i
$732$	−46.9449	+	27.1037i	−1.73513	+	1.00178i
$733$	13.8365	+	3.70749i	0.511064	+	0.136939i	0.505130	−	0.863043i	$-0.331444\pi$
$733$	13.8365	+	3.70749i	0.511064	+	0.136939i	0.00593416	+	0.999982i	$0.498111\pi$
$734$	−21.8302	−	81.4713i	−0.805766	−	3.00716i
$735$	0.104297	−	7.74987i	0.00384706	−	0.285858i
$736$	0.666138	−	0.666138i	0.0245542	−	0.0245542i
$737$	−25.6979			−0.946593
$738$	−10.2786			−0.378360
$739$	−5.58487	+	5.58487i	−0.205443	+	0.205443i	−0.802327	−	0.596885i	$-0.796405\pi$
$739$	−5.58487	+	5.58487i	−0.205443	+	0.205443i	0.596885	+	0.802327i	$0.296405\pi$
$740$	−6.41650	−	11.1137i	−0.235875	−	0.408548i
$741$	−6.29234	−	11.1739i	−0.231155	−	0.410485i
$742$	59.0311	+	8.17604i	2.16710	+	0.300152i
$743$	11.2562	−	42.0089i	0.412952	−	1.54116i	−0.375952	−	0.926639i	$-0.622684\pi$
$743$	11.2562	−	42.0089i	0.412952	−	1.54116i	0.788903	−	0.614517i	$-0.210649\pi$
$744$	−6.37138	+	11.0355i	−0.233586	+	0.404583i
$745$	2.18005	+	3.77596i	0.0798708	+	0.138340i
$746$	52.6561	−	14.1092i	1.92788	−	0.516573i
$747$	−3.63623	+	3.63623i	−0.133043	+	0.133043i
$748$	27.5424	−	7.37997i	1.00705	−	0.269838i
$749$	31.6867	+	13.3756i	1.15781	+	0.488733i
$750$	12.0251	−	20.8281i	0.439095	−	0.760535i
$751$	2.13841	+	1.23461i	0.0780318	+	0.0450517i	0.538508	−	0.842620i	$-0.318988\pi$
$751$	2.13841	+	1.23461i	0.0780318	+	0.0450517i	−0.460476	+	0.887672i	$0.652321\pi$
$752$	−37.3988	−	37.3988i	−1.36379	−	1.36379i
$753$	12.1482	+	7.01379i	0.442706	+	0.255597i
$754$	−13.8515	−	24.5975i	−0.504443	−	0.895790i
$755$		−	8.62704i		−	0.313970i
$756$	−8.71070	+	6.59131i	−0.316805	+	0.239724i
$757$	1.03968	+	1.80079i	0.0377880	+	0.0654507i	0.884301	−	0.466918i	$-0.154636\pi$
$757$	1.03968	+	1.80079i	0.0377880	+	0.0654507i	−0.846513	+	0.532368i	$0.821302\pi$
$758$			3.07477i			0.111681i
$759$	−0.400995	−	1.49654i	−0.0145552	−	0.0543208i
$760$	5.37119	−	20.0456i	0.194834	−	0.727129i
$761$	15.8414	+	15.8414i	0.574249	+	0.574249i	0.933313	−	0.359064i	$-0.116904\pi$
$761$	15.8414	+	15.8414i	0.574249	+	0.574249i	−0.359064	+	0.933313i	$0.616904\pi$
$762$	23.4379	+	23.4379i	0.849065	+	0.849065i
$763$	−0.645568	−	1.58869i	−0.0233711	−	0.0575144i
$764$	−19.4881	+	11.2514i	−0.705054	+	0.407063i
$765$	0.915005	+	3.41484i	0.0330821	+	0.123464i
$766$	−18.0749	+	31.3066i	−0.653071	+	1.13115i
$767$	14.9626	−	25.2853i	0.540268	−	0.912998i
$768$	28.2415	−	16.3052i	1.01908	−	0.588364i
$769$	−48.4921	−	12.9934i	−1.74867	−	0.468555i	−0.764330	−	0.644826i	$-0.776930\pi$
$769$	−48.4921	−	12.9934i	−1.74867	−	0.468555i	−0.984342	+	0.176271i	$0.943597\pi$
$770$	−12.3804	−	9.63282i	−0.446157	−	0.347143i
$771$	6.79366	+	3.92232i	0.244668	+	0.141259i
$772$	−15.3341	+	57.2276i	−0.551886	+	2.05967i
$773$	26.9533	+	7.22211i	0.969443	+	0.259761i	0.708592	−	0.705618i	$-0.249331\pi$
$773$	26.9533	+	7.22211i	0.969443	+	0.259761i	0.260850	+	0.965379i	$0.415997\pi$
$774$	−20.2274	−	5.41991i	−0.727058	−	0.194814i
$775$	−2.36197	+	8.81499i	−0.0848445	+	0.316644i
$776$	63.6860	+	36.7692i	2.28620	+	1.31994i
$777$	2.79607	+	6.88090i	0.100308	+	0.246851i
$778$	38.7167	+	10.3741i	1.38806	+	0.371930i
$779$	−12.7887	+	7.38357i	−0.458203	+	0.264544i
$780$	0.176905	−	16.4814i	0.00633421	−	0.590128i
$781$	−16.5728	+	28.7049i	−0.593020	+	1.02714i
$782$	1.46540	+	5.46897i	0.0524028	+	0.195570i
$783$	−2.73892	+	1.58131i	−0.0978809	+	0.0565115i
$784$	−9.11061	+	32.2585i	−0.325379	+	1.15209i
$785$	−8.44019	−	8.44019i	−0.301243	−	0.301243i
$786$	−4.49637	−	4.49637i	−0.160380	−	0.160380i
$787$	2.90188	−	10.8300i	0.103441	−	0.386047i	−0.894723	−	0.446622i	$-0.852627\pi$
$787$	2.90188	−	10.8300i	0.103441	−	0.386047i	0.998164	+	0.0605752i	$0.0192935\pi$
$788$	−24.6591	−	92.0290i	−0.878444	−	3.27840i
$789$			30.1387i			1.07297i
$790$	23.4225	+	40.5690i	0.833336	+	1.44338i
$791$	−12.4783	−	5.26734i	−0.443678	−	0.187285i
$792$			11.3985i			0.405030i
$793$	−12.7423	+	45.5918i	−0.452492	+	1.61901i
$794$	−65.8205	−	38.0015i	−2.33588	−	1.34862i
$795$	7.12354	+	7.12354i	0.252646	+	0.252646i
$796$	−32.0560	−	18.5076i	−1.13620	−	0.655983i
$797$	−5.68925	+	9.85408i	−0.201524	+	0.349049i	−0.949020	−	0.315217i	$-0.897923\pi$
$797$	−5.68925	+	9.85408i	−0.201524	+	0.349049i	0.747496	+	0.664266i	$0.231256\pi$
$798$	−9.05954	+	21.4621i	−0.320704	+	0.759749i
$799$	34.0641	−	9.12746i	1.20510	−	0.322906i
$800$	−3.50983	+	3.50983i	−0.124091	+	0.124091i
$801$	5.24668	−	1.40584i	0.185382	−	0.0496730i
$802$	6.01770	+	10.4230i	0.212492	+	0.368047i
$803$	−5.44385	+	9.42903i	−0.192109	+	0.332743i
$804$	−12.6954	+	47.3800i	−0.447734	+	1.67096i
$805$	1.28855	−	1.65608i	0.0454154	−	0.0583690i
$806$	5.36218	+	20.9070i	0.188875	+	0.736417i
$807$	0.910328	+	1.57674i	0.0320451	+	0.0555037i
$808$	70.5080	−	70.5080i	2.48046	−	2.48046i
$809$	−14.6689			−0.515730			−0.257865	−	0.966181i	$-0.583019\pi$
$809$	−14.6689			−0.515730			−0.257865	+	0.966181i	$0.583019\pi$
$810$	−2.74106			−0.0963112
$811$	3.00038	−	3.00038i	0.105358	−	0.105358i	−0.652463	−	0.757821i	$-0.726264\pi$
$811$	3.00038	−	3.00038i	0.105358	−	0.105358i	0.757821	+	0.652463i	$0.226264\pi$
$812$	−13.4349	+	31.8274i	−0.471474	+	1.11692i
$813$	1.27364	+	4.75330i	0.0446686	+	0.166705i
$814$	14.5199	+	3.89061i	0.508924	+	0.136366i
$815$	−4.40899	+	2.54553i	−0.154440	+	0.0891661i
$816$		−	15.2898i		−	0.535249i
$817$	−29.0604	+	7.78671i	−1.01669	+	0.272423i
$818$	−17.9859			−0.628861
$819$	−1.41009	+	9.43460i	−0.0492726	+	0.329672i
$820$	−18.9800			−0.662812
$821$	0.618781	−	0.165802i	0.0215956	−	0.00578653i	−0.248005	−	0.968759i	$-0.579775\pi$
$821$	0.618781	−	0.165802i	0.0215956	−	0.00578653i	0.269601	+	0.962972i	$0.413108\pi$
$822$		−	38.0533i		−	1.32726i
$823$	−40.5425	+	23.4072i	−1.41322	+	0.815925i	−0.995691	−	0.0927374i	$-0.970438\pi$
$823$	−40.5425	+	23.4072i	−1.41322	+	0.815925i	−0.417532	+	0.908662i	$0.637105\pi$
$824$	−45.8331	−	12.2809i	−1.59667	−	0.427827i
$825$	2.11281	+	7.88512i	0.0735586	+	0.274524i
$826$	−52.9622	+	6.61038i	−1.84279	+	0.230005i
$827$	3.71960	−	3.71960i	0.129343	−	0.129343i	−0.639472	−	0.768815i	$-0.720847\pi$
$827$	3.71960	−	3.71960i	0.129343	−	0.129343i	0.768815	+	0.639472i	$0.220847\pi$
$828$	−2.95732			−0.102774
$829$	−34.9744			−1.21471			−0.607356	−	0.794430i	$-0.707770\pi$
$829$	−34.9744			−1.21471			−0.607356	+	0.794430i	$0.707770\pi$
$830$	−9.96715	+	9.96715i	−0.345965	+	0.345965i
$831$	2.36247	+	4.09191i	0.0819530	+	0.141947i
$832$	6.13489	−	21.9506i	0.212689	−	0.760999i
$833$	−15.5902	−	16.0155i	−0.540167	−	0.554904i
$834$	2.10744	−	7.86506i	0.0729746	−	0.272345i
$835$	−5.72646	+	9.91853i	−0.198172	+	0.343245i
$836$	15.8812	+	27.5070i	0.549262	+	0.951350i
$837$	2.33568	−	0.625845i	0.0807330	−	0.0216324i
$838$	−7.67908	+	7.67908i	−0.265270	+	0.265270i
$839$	−13.1988	+	3.53660i	−0.455673	+	0.122097i	−0.479352	−	0.877622i	$-0.659128\pi$
$839$	−13.1988	+	3.53660i	−0.455673	+	0.122097i	0.0236798	+	0.999720i	$0.492462\pi$
$840$	−12.3104	+	9.31515i	−0.424748	+	0.321403i
$841$	9.49889	−	16.4526i	0.327548	−	0.567330i
$842$	7.27256	+	4.19882i	0.250629	+	0.144701i
$843$	12.5689	+	12.5689i	0.432897	+	0.432897i
$844$	13.8697	+	8.00769i	0.477416	+	0.275636i
$845$	−9.95723	−	10.3942i	−0.342539	−	0.357570i
$846$			27.3430i			0.940071i
$847$	−16.5962	+	2.07142i	−0.570251	+	0.0711749i
$848$	−21.7849	−	37.7325i	−0.748095	−	1.29574i
$849$			16.8354i			0.577788i
$850$	−7.72109	−	28.8155i	−0.264831	−	0.988364i
$851$	−0.520433	+	1.94228i	−0.0178402	+	0.0665806i
$852$	44.7368	+	44.7368i	1.53266	+	1.53266i
$853$	−15.3692	−	15.3692i	−0.526232	−	0.526232i	0.393215	−	0.919447i	$-0.371363\pi$
$853$	−15.3692	−	15.3692i	−0.526232	−	0.526232i	−0.919447	+	0.393215i	$0.871363\pi$
$854$	79.6698	−	32.3740i	2.72625	−	1.10782i
$855$	−3.41045	+	1.96903i	−0.116635	+	0.0673393i
$856$	−17.7306	−	66.1717i	−0.606021	−	2.26170i
$857$	−15.8211	+	27.4030i	−0.540439	+	0.936068i	0.458440	+	0.888725i	$0.348408\pi$
$857$	−15.8211	+	27.4030i	−0.540439	+	0.936068i	−0.998879	+	0.0473423i	$0.984925\pi$
$858$	13.5047	+	13.7977i	0.461042	+	0.471047i
$859$	−10.4333	+	6.02368i	−0.355980	+	0.205525i	−0.667316	−	0.744775i	$-0.732557\pi$
$859$	−10.4333	+	6.02368i	−0.355980	+	0.205525i	0.311336	+	0.950300i	$0.399224\pi$
$860$	−37.3510	−	10.0082i	−1.27366	−	0.341276i
$861$	10.8811	+	1.50708i	0.370827	+	0.0513610i
$862$	−60.0734	−	34.6834i	−2.04611	−	1.18132i
$863$	−7.52533	+	28.0849i	−0.256165	+	0.956021i	0.711273	+	0.702915i	$0.248119\pi$
$863$	−7.52533	+	28.0849i	−0.256165	+	0.956021i	−0.967439	+	0.253106i	$0.918548\pi$
$864$	1.27039	+	0.340399i	0.0432195	+	0.0115806i
$865$	−8.47584	−	2.27109i	−0.288187	−	0.0772195i
$866$	1.26116	−	4.70671i	0.0428559	−	0.159940i
$867$	−5.89340	−	3.40256i	−0.200150	−	0.115557i
$868$	16.2203	−	20.8468i	0.550553	−	0.707586i
$869$	−35.7063	−	9.56747i	−1.21125	−	0.324554i
$870$	−7.50754	+	4.33448i	−0.254530	+	0.146953i
$871$	21.0188	+	37.3251i	0.712194	+	1.26471i
$872$	−1.70781	+	2.95801i	−0.0578336	+	0.100171i
$873$	−3.61174	−	13.4792i	−0.122239	−	0.456202i
$874$	−5.46194	+	3.15345i	−0.184753	+	0.106667i
$875$	−15.7839	+	20.2859i	−0.533593	+	0.685788i
$876$	14.6952	+	14.6952i	0.496505	+	0.496505i
$877$	−10.3979	−	10.3979i	−0.351110	−	0.351110i	0.509412	−	0.860523i	$-0.329863\pi$
$877$	−10.3979	−	10.3979i	−0.351110	−	0.351110i	−0.860523	+	0.509412i	$0.829863\pi$
$878$	−6.23684	+	23.2762i	−0.210483	+	0.785533i
$879$	−0.721119	−	2.69125i	−0.0243227	−	0.0907737i
$880$			11.4684i			0.386599i
$881$	21.1447	+	36.6236i	0.712382	+	1.23388i	0.963961	+	0.266045i	$0.0857170\pi$
$881$	21.1447	+	36.6236i	0.712382	+	1.23388i	−0.251578	+	0.967837i	$0.580950\pi$
$882$	15.1229	−	8.46192i	0.509213	−	0.284928i
$883$			18.1723i			0.611547i	0.952104	+	0.305773i	$0.0989150\pi$
$883$			18.1723i			0.611547i	−0.952104	+	0.305773i	$0.901085\pi$
$884$	−33.2466	−	33.9680i	−1.11820	−	1.14247i
$885$	−7.81370	−	4.51124i	−0.262655	−	0.151644i
$886$	−49.3635	−	49.3635i	−1.65840	−	1.65840i
$887$	37.9692	+	21.9215i	1.27488	+	0.736053i	0.975903	−	0.218206i	$-0.0700205\pi$
$887$	37.9692	+	21.9215i	1.27488	+	0.736053i	0.298979	+	0.954260i	$0.403354\pi$
$888$	7.39681	−	12.8117i	0.248221	−	0.429931i
$889$	−21.3753	−	28.2483i	−0.716903	−	0.947418i
$890$	14.3815	−	3.85350i	0.482068	−	0.129170i
$891$	1.52947	−	1.52947i	0.0512392	−	0.0512392i
$892$	79.5941	−	21.3272i	2.66501	−	0.714087i
$893$	19.6417	+	34.0204i	0.657283	+	1.13845i
$894$	−4.87432	+	8.44256i	−0.163022	+	0.282362i
$895$	0.222555	−	0.830586i	0.00743919	−	0.0277634i
$896$	−44.8051	+	18.2067i	−1.49683	+	0.608242i
$897$	−1.84568	+	1.80647i	−0.0616253	+	0.0603164i
$898$	−30.9337	−	53.5788i	−1.03227	−	1.78795i
$899$	5.40758	−	5.40758i	0.180353	−	0.180353i
$900$	15.5818			0.519395
$901$	29.0513			0.967840
$902$	15.7208	−	15.7208i	0.523446	−	0.523446i
$903$	20.6184	+	8.70341i	0.686137	+	0.289631i
$904$	6.98238	+	26.0586i	0.232230	+	0.866696i
$905$	−11.2937	−	3.02614i	−0.375415	−	0.100592i
$906$	16.7047	−	9.64449i	0.554978	−	0.320417i
$907$		−	21.0681i		−	0.699555i	−0.936833	−	0.349778i	$-0.886257\pi$
$907$		−	21.0681i		−	0.699555i	0.936833	−	0.349778i	$-0.113743\pi$
$908$	38.3317	−	10.2710i	1.27208	−	0.340854i
$909$	−18.9217			−0.627593
$910$	−3.86515	+	25.8608i	−0.128129	+	0.857278i
$911$	−50.4372			−1.67106			−0.835530	−	0.549445i	$-0.814839\pi$
$911$	−50.4372			−1.67106			−0.835530	+	0.549445i	$0.814839\pi$
$912$	16.4513	−	4.40810i	0.544756	−	0.145967i
$913$		−	11.1230i		−	0.368118i
$914$	40.7247	−	23.5124i	1.34705	−	0.777721i
$915$	14.0419	+	3.76252i	0.464212	+	0.124385i
$916$	28.4806	+	106.291i	0.941025	+	3.51195i
$917$	4.10067	+	5.41921i	0.135416	+	0.178958i
$918$	−5.58933	+	5.58933i	−0.184475	+	0.184475i
$919$	16.0192			0.528423			0.264212	−	0.964465i	$-0.414888\pi$
$919$	16.0192			0.528423			0.264212	+	0.964465i	$0.414888\pi$
$920$	−4.17942			−0.137791
$921$	−11.1210	+	11.1210i	−0.366449	+	0.366449i
$922$	−23.8646	−	41.3347i	−0.785940	−	1.36129i
$923$	55.2479	+	0.593010i	1.81851	+	0.0195192i
$924$	3.24154	−	23.4040i	0.106639	−	0.769935i
$925$	2.74212	−	10.2337i	0.0901602	−	0.336483i
$926$	−17.0360	+	29.5073i	−0.559839	+	0.969670i
$927$	4.50207	+	7.79781i	0.147867	+	0.256114i
$928$	4.01776	−	1.07656i	0.131890	−	0.0353397i
$929$	14.3914	−	14.3914i	0.472166	−	0.472166i	−0.430449	−	0.902615i	$-0.641645\pi$
$929$	14.3914	−	14.3914i	0.472166	−	0.472166i	0.902615	+	0.430449i	$0.141645\pi$
$930$	6.40226	−	1.71548i	0.209938	−	0.0562528i
$931$	12.7374	−	21.3918i	0.417452	−	0.701088i
$932$	3.64811	−	6.31871i	0.119498	−	0.206976i
$933$	−22.4293	−	12.9496i	−0.734304	−	0.423950i
$934$	−53.3946	−	53.3946i	−1.74712	−	1.74712i
$935$	−6.62238	−	3.82343i	−0.216575	−	0.125040i
$936$	16.5559	−	9.32308i	0.541147	−	0.304735i
$937$		−	51.5507i		−	1.68409i	−0.539410	−	0.842043i	$-0.681353\pi$
$937$		−	51.5507i		−	1.68409i	0.539410	−	0.842043i	$-0.318647\pi$
$938$	30.2622	−	71.6913i	0.988097	−	2.34080i
$939$	−3.75618	−	6.50589i	−0.122578	−	0.212312i
$940$			50.4904i			1.64682i
$941$	−3.60461	−	13.4526i	−0.117507	−	0.438542i	0.881955	−	0.471333i	$-0.156227\pi$
$941$	−3.60461	−	13.4526i	−0.117507	−	0.438542i	−0.999462	+	0.0327912i	$0.989560\pi$
$942$	6.90734	−	25.7786i	0.225053	−	0.839911i
$943$	2.10292	+	2.10292i	0.0684804	+	0.0684804i
$944$	27.5921	+	27.5921i	0.898047	+	0.898047i
$945$	2.90174	+	0.401902i	0.0943937	+	0.0130739i
$946$	39.2268	−	22.6476i	1.27537	−	0.736336i
$947$	1.46661	+	5.47346i	0.0476584	+	0.177864i	0.985652	−	0.168788i	$-0.0539853\pi$
$947$	1.46661	+	5.47346i	0.0476584	+	0.177864i	−0.937994	+	0.346652i	$0.887319\pi$
$948$	−35.2797	+	61.1063i	−1.14583	+	1.98464i
$949$	18.1479	+	0.194793i	0.589106	+	0.00632325i
$950$	28.7785	−	16.6153i	0.933697	−	0.539070i
$951$	7.06048	+	1.89185i	0.228952	+	0.0613474i
$952$	−6.10758	+	44.0968i	−0.197948	+	1.42919i
$953$	28.3739	+	16.3817i	0.919121	+	0.530654i	0.883354	−	0.468706i	$-0.155280\pi$
$953$	28.3739	+	16.3817i	0.919121	+	0.530654i	0.0357662	+	0.999360i	$0.488613\pi$
$954$	−5.82981	+	21.7572i	−0.188747	+	0.704414i
$955$	5.82917	+	1.56192i	0.188628	+	0.0505426i
$956$	121.165	+	32.4662i	3.91877	+	1.05003i
$957$	1.77052	−	6.60767i	0.0572327	−	0.213596i
$958$	21.7046	+	12.5312i	0.701245	+	0.404864i
$959$	−5.57948	+	40.2839i	−0.180171	+	1.30084i
$960$	−6.76061	−	1.81150i	−0.218198	−	0.0584659i
$961$	21.7830	−	12.5764i	0.702679	−	0.405692i
$962$	−6.22519	−	24.2718i	−0.200708	−	0.782556i
$963$	−6.49988	+	11.2581i	−0.209456	+	0.362788i
$964$	10.2473	+	38.2436i	0.330045	+	1.23174i
$965$	13.7600	−	7.94432i	0.442949	−	0.255737i
$966$	4.64722	+	0.643658i	0.149522	+	0.0207093i
$967$	−29.4635	−	29.4635i	−0.947483	−	0.947483i	0.0512055	−	0.998688i	$-0.483694\pi$
$967$	−29.4635	−	29.4635i	−0.947483	−	0.947483i	−0.998688	+	0.0512055i	$0.983694\pi$
$968$	23.5556	+	23.5556i	0.757105	+	0.757105i
$969$	−2.93923	+	10.9693i	−0.0944216	+	0.352386i
$970$	−9.90002	−	36.9474i	−0.317870	−	1.18631i
$971$			18.5931i			0.596681i	0.954460	+	0.298340i	$0.0964330\pi$
$971$			18.5931i			0.596681i	−0.954460	+	0.298340i	$0.903567\pi$
$972$	−2.06434	−	3.57554i	−0.0662137	−	0.114685i
$973$	−3.38417	+	8.01710i	−0.108491	+	0.257016i
$974$			60.5947i			1.94158i
$975$	9.72470	−	9.51816i	0.311440	−	0.304825i
$976$	−54.4487	−	31.4360i	−1.74286	−	1.00624i
$977$	−6.71191	−	6.71191i	−0.214733	−	0.214733i	0.591542	−	0.806274i	$-0.298520\pi$
$977$	−6.71191	−	6.71191i	−0.214733	−	0.214733i	−0.806274	+	0.591542i	$0.798520\pi$
$978$	−9.85795	−	5.69149i	−0.315223	−	0.181994i
$979$	−5.87444	+	10.1748i	−0.187748	+	0.325189i
$980$	27.9253	−	15.6254i	0.892040	−	0.499136i
$981$	0.626065	−	0.167754i	0.0199887	−	0.00535596i
$982$	8.07898	−	8.07898i	0.257811	−	0.257811i
$983$	41.4077	−	11.0952i	1.32070	−	0.353881i	0.471461	−	0.881887i	$-0.343727\pi$
$983$	41.4077	−	11.0952i	1.32070	−	0.353881i	0.849241	+	0.528006i	$0.177060\pi$
$984$	−10.9399	−	18.9485i	−0.348751	−	0.604055i
$985$	−12.7754	+	22.1277i	−0.407059	+	0.705047i
$986$	−6.47022	+	24.1472i	−0.206054	+	0.769003i
$987$	4.00910	−	28.9458i	0.127611	−	0.921354i
$988$	26.9633	−	45.5653i	0.857817	−	1.44962i
$989$	3.02949	+	5.24723i	0.0963321	+	0.166852i
$990$	4.19238	−	4.19238i	0.133243	−	0.133243i
$991$	16.4509			0.522580			0.261290	−	0.965260i	$-0.415852\pi$
$991$	16.4509			0.522580			0.261290	+	0.965260i	$0.415852\pi$
$992$	−3.18026			−0.100973
$993$	23.2409	−	23.2409i	0.737528	−	0.737528i
$994$	−60.5638	−	80.0377i	−1.92097	−	2.53864i
$995$	2.56921	+	9.58844i	0.0814496	+	0.303974i
$996$	−20.5079	−	5.49508i	−0.649818	−	0.174118i
$997$	−12.7995	+	7.38978i	−0.405364	+	0.234037i	−0.688796	−	0.724956i	$-0.741860\pi$
$997$	−12.7995	+	7.38978i	−0.405364	+	0.234037i	0.283432	+	0.958992i	$0.408527\pi$
$998$		−	29.8817i		−	0.945889i
$999$	−2.71160	+	0.726571i	−0.0857912	+	0.0229877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.b.115.10	yes	40
3.2	odd	2		819.2.gh.d.388.1		40
7.5	odd	6		273.2.bt.b.271.1	yes	40
13.6	odd	12		273.2.bt.b.136.1	✓	40
21.5	even	6		819.2.et.d.271.10		40
39.32	even	12		819.2.et.d.136.10		40
91.19	even	12	inner	273.2.cg.b.19.10	yes	40
273.110	odd	12		819.2.gh.d.19.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.136.1	✓	40	13.6	odd	12
273.2.bt.b.271.1	yes	40	7.5	odd	6
273.2.cg.b.19.10	yes	40	91.19	even	12	inner
273.2.cg.b.115.10	yes	40	1.1	even	1	trivial
819.2.et.d.136.10		40	39.32	even	12
819.2.et.d.271.10		40	21.5	even	6
819.2.gh.d.19.1		40	273.110	odd	12
819.2.gh.d.388.1		40	3.2	odd	2

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.39126 - 0.640737i) q^{2} -1.00000i q^{3} +(3.57554 - 2.06434i) q^{4} +(-1.06950 - 0.286571i) q^{5} +(-0.640737 - 2.39126i) q^{6} +(0.327682 + 2.62538i) q^{7} +(3.72630 - 3.72630i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(2.39126 - 0.640737i) q^{2} -1.00000i q^{3} +(3.57554 - 2.06434i) q^{4} +(-1.06950 - 0.286571i) q^{5} +(-0.640737 - 2.39126i) q^{6} +(0.327682 + 2.62538i) q^{7} +(3.72630 - 3.72630i) q^{8} -1.00000 q^{9} -2.74106 q^{10} +(1.52947 - 1.52947i) q^{11} +(-2.06434 - 3.57554i) q^{12} +(-3.47248 - 0.970511i) q^{13} +(2.46575 + 6.06801i) q^{14} +(-0.286571 + 1.06950i) q^{15} +(2.39431 - 4.14706i) q^{16} +(1.59647 + 2.76517i) q^{17} +(-2.39126 + 0.640737i) q^{18} +(-2.51496 + 2.51496i) q^{19} +(-4.41561 + 1.18316i) q^{20} +(2.62538 - 0.327682i) q^{21} +(2.67738 - 4.63735i) q^{22} +(0.620322 + 0.358143i) q^{23} +(-3.72630 - 3.72630i) q^{24} +(-3.26843 - 1.88703i) q^{25} +(-8.92545 - 0.0958025i) q^{26} +1.00000i q^{27} +(6.59131 + 8.71070i) q^{28} +(1.58131 + 2.73892i) q^{29} +2.74106i q^{30} +(-0.625845 - 2.33568i) q^{31} +(0.340399 - 1.27039i) q^{32} +(-1.52947 - 1.52947i) q^{33} +(5.58933 + 5.58933i) q^{34} +(0.401902 - 2.90174i) q^{35} +(-3.57554 + 2.06434i) q^{36} +(0.726571 + 2.71160i) q^{37} +(-4.40250 + 7.62535i) q^{38} +(-0.970511 + 3.47248i) q^{39} +(-5.05312 + 2.91742i) q^{40} +(4.01046 + 1.07460i) q^{41} +(6.06801 - 2.46575i) q^{42} +(7.32559 + 4.22943i) q^{43} +(2.31134 - 8.62603i) q^{44} +(1.06950 + 0.286571i) q^{45} +(1.71283 + 0.458951i) q^{46} +(2.85863 - 10.6686i) q^{47} +(-4.14706 - 2.39431i) q^{48} +(-6.78525 + 1.72058i) q^{49} +(-9.02475 - 2.41817i) q^{50} +(2.76517 - 1.59647i) q^{51} +(-14.4194 + 3.69827i) q^{52} +(4.54930 - 7.87963i) q^{53} +(0.640737 + 2.39126i) q^{54} +(-2.07407 + 1.19746i) q^{55} +(11.0040 + 8.56192i) q^{56} +(2.51496 + 2.51496i) q^{57} +(5.53626 + 5.53626i) q^{58} +(-2.10905 + 7.87107i) q^{59} +(1.18316 + 4.41561i) q^{60} -13.1295i q^{61} +(-2.99312 - 5.18423i) q^{62} +(-0.327682 - 2.62538i) q^{63} +6.32129i q^{64} +(3.43569 + 2.03307i) q^{65} +(-4.63735 - 2.67738i) q^{66} +(-8.40090 - 8.40090i) q^{67} +(11.4165 + 6.59131i) q^{68} +(0.358143 - 0.620322i) q^{69} +(-0.898198 - 7.19634i) q^{70} +(-14.8017 + 3.96611i) q^{71} +(-3.72630 + 3.72630i) q^{72} +(-4.86210 + 1.30280i) q^{73} +(3.47484 + 6.01860i) q^{74} +(-1.88703 + 3.26843i) q^{75} +(-3.80061 + 14.1841i) q^{76} +(4.51663 + 3.51426i) q^{77} +(-0.0958025 + 8.92545i) q^{78} +(-8.54505 - 14.8005i) q^{79} +(-3.74913 + 3.74913i) q^{80} +1.00000 q^{81} +10.2786 q^{82} +(3.63623 - 3.63623i) q^{83} +(8.71070 - 6.59131i) q^{84} +(-0.915005 - 3.41484i) q^{85} +(20.2274 + 5.41991i) q^{86} +(2.73892 - 1.58131i) q^{87} -11.3985i q^{88} +(-5.24668 + 1.40584i) q^{89} +2.74106 q^{90} +(1.41009 - 9.43460i) q^{91} +2.95732 q^{92} +(-2.33568 + 0.625845i) q^{93} -27.3430i q^{94} +(3.41045 - 1.96903i) q^{95} +(-1.27039 - 0.340399i) q^{96} +(3.61174 + 13.4792i) q^{97} +(-15.1229 + 8.46192i) q^{98} +(-1.52947 + 1.52947i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 - 40 * q^9	\( 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more