LMFDB - Embedded newform 912.2.cn.a.451.76

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(67,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 0, 34]))

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

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

chi := DirichletCharacter("912.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.cn (of order $36$, degree $12$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$80$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			451.76
Character	$\chi$	$=$	912.451
Dual form			912.2.cn.a.91.76

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38675 + 0.277328i) q^{2} +(-0.819152 + 0.573576i) q^{3} +(1.84618 + 0.769171i) q^{4} +(-2.81369 + 0.246166i) q^{5} +(-1.29503 + 0.568237i) q^{6} +(-2.32408 - 4.02543i) q^{7} +(2.34689 + 1.57865i) q^{8} +(0.342020 - 0.939693i) q^{9} +O(q^{10})$	\(q+(1.38675 + 0.277328i) q^{2} +(-0.819152 + 0.573576i) q^{3} +(1.84618 + 0.769171i) q^{4} +(-2.81369 + 0.246166i) q^{5} +(-1.29503 + 0.568237i) q^{6} +(-2.32408 - 4.02543i) q^{7} +(2.34689 + 1.57865i) q^{8} +(0.342020 - 0.939693i) q^{9} +(-3.97017 - 0.438942i) q^{10} +(2.94767 - 0.789825i) q^{11} +(-1.95348 + 0.428857i) q^{12} +(3.69720 + 2.58881i) q^{13} +(-2.10657 - 6.22682i) q^{14} +(2.16365 - 1.81551i) q^{15} +(2.81675 + 2.84005i) q^{16} +(4.88350 - 1.77745i) q^{17} +(0.734901 - 1.20827i) q^{18} +(2.84188 + 3.30511i) q^{19} +(-5.38392 - 1.70974i) q^{20} +(4.21267 + 1.96440i) q^{21} +(4.30673 - 0.277824i) q^{22} +(3.11698 - 2.61546i) q^{23} +(-2.82793 + 0.0529658i) q^{24} +(2.93222 - 0.517030i) q^{25} +(4.40916 + 4.61537i) q^{26} +(0.258819 + 0.965926i) q^{27} +(-1.19443 - 9.21928i) q^{28} +(3.40902 - 1.58965i) q^{29} +(3.50394 - 1.91764i) q^{30} +(-2.56433 - 4.44155i) q^{31} +(3.11852 + 4.71962i) q^{32} +(-1.96156 + 2.33770i) q^{33} +(7.26515 - 1.11056i) q^{34} +(7.53018 + 10.7542i) q^{35} +(1.35421 - 1.47177i) q^{36} +(-2.40106 - 2.40106i) q^{37} +(3.02439 + 5.37151i) q^{38} -4.51345 q^{39} +(-6.99202 - 3.86410i) q^{40} +(-0.0704889 + 0.399763i) q^{41} +(5.29716 + 3.89243i) q^{42} +(-0.866061 - 9.89912i) q^{43} +(6.04943 + 0.809101i) q^{44} +(-0.731019 + 2.72820i) q^{45} +(5.04783 - 2.76258i) q^{46} +(0.474842 - 1.30462i) q^{47} +(-3.93634 - 0.710813i) q^{48} +(-7.30273 + 12.6487i) q^{49} +(4.20966 + 0.0961922i) q^{50} +(-2.98082 + 4.25706i) q^{51} +(4.83446 + 7.62318i) q^{52} +(4.45895 + 0.390108i) q^{53} +(0.0910408 + 1.41128i) q^{54} +(-8.09939 + 2.94794i) q^{55} +(0.900379 - 13.1161i) q^{56} +(-4.22366 - 1.07735i) q^{57} +(5.16833 - 1.25904i) q^{58} +(-2.70490 + 5.80067i) q^{59} +(5.39092 - 1.68755i) q^{60} +(-5.97662 - 0.522886i) q^{61} +(-2.32433 - 6.87050i) q^{62} +(-4.57755 + 0.807146i) q^{63} +(3.01574 + 7.40981i) q^{64} +(-11.0401 - 6.37398i) q^{65} +(-3.36851 + 2.69782i) q^{66} +(-0.936677 - 2.00871i) q^{67} +(10.3830 + 0.474757i) q^{68} +(-1.05312 + 3.93029i) q^{69} +(7.46007 + 17.0018i) q^{70} +(7.35211 - 8.76191i) q^{71} +(2.28613 - 1.66542i) q^{72} +(-4.34004 - 0.765266i) q^{73} +(-2.66380 - 3.99556i) q^{74} +(-2.10538 + 2.10538i) q^{75} +(2.70442 + 8.28771i) q^{76} +(-10.0300 - 10.0300i) q^{77} +(-6.25904 - 1.25170i) q^{78} +(-1.08843 + 6.17280i) q^{79} +(-8.62460 - 7.29764i) q^{80} +(-0.766044 - 0.642788i) q^{81} +(-0.208616 + 0.534824i) q^{82} +(9.19924 + 2.46493i) q^{83} +(6.26638 + 6.86690i) q^{84} +(-13.3031 + 6.20334i) q^{85} +(1.54428 - 13.9678i) q^{86} +(-1.88072 + 3.25750i) q^{87} +(8.16469 + 2.79970i) q^{88} +(1.51372 + 8.58476i) q^{89} +(-1.77035 + 3.58061i) q^{90} +(1.82846 - 20.8994i) q^{91} +(7.76624 - 2.43111i) q^{92} +(4.64814 + 2.16747i) q^{93} +(1.02030 - 1.67750i) q^{94} +(-8.80977 - 8.59998i) q^{95} +(-5.26161 - 2.07738i) q^{96} +(5.79749 + 15.9285i) q^{97} +(-13.6349 + 15.5154i) q^{98} +(0.265969 - 3.04004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q+O(q^{10}) $ 960 * q	$ 960 q + 48 q^{10} + 12 q^{16} - 60 q^{32} - 120 q^{34} + 12 q^{36} + 108 q^{38} + 60 q^{40} + 180 q^{46} - 480 q^{49} - 108 q^{50} - 24 q^{51} + 48 q^{52} + 12 q^{54} + 72 q^{68} - 144 q^{69} - 72 q^{70} - 48 q^{76} + 72 q^{78} - 120 q^{80} + 120 q^{82} + 96 q^{85} + 84 q^{98}+O(q^{100}) $ 960 * q + 48 * q^10 + 12 * q^16 - 60 * q^32 - 120 * q^34 + 12 * q^36 + 108 * q^38 + 60 * q^40 + 180 * q^46 - 480 * q^49 - 108 * q^50 - 24 * q^51 + 48 * q^52 + 12 * q^54 + 72 * q^68 - 144 * q^69 - 72 * q^70 - 48 * q^76 + 72 * q^78 - 120 * q^80 + 120 * q^82 + 96 * q^85 + 84 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.38675	+	0.277328i	0.980584	+	0.196100i
$2$	1.38675	+	0.277328i	0.980584	+	0.196100i
$3$	−0.819152	+	0.573576i	−0.472938	+	0.331155i
$3$	−0.819152	+	0.573576i	−0.472938	+	0.331155i
$4$	1.84618	+	0.769171i	0.923089	+	0.384585i
$5$	−2.81369	+	0.246166i	−1.25832	+	0.110089i	−0.696734	−	0.717329i	$-0.745364\pi$
$5$	−2.81369	+	0.246166i	−1.25832	+	0.110089i	−0.561587	+	0.827418i	$0.689809\pi$
$6$	−1.29503	+	0.568237i	−0.528694	+	0.231982i
$7$	−2.32408	−	4.02543i	−0.878421	−	1.52147i	−0.853073	−	0.521791i	$-0.825264\pi$
$7$	−2.32408	−	4.02543i	−0.878421	−	1.52147i	−0.0253477	−	0.999679i	$-0.508069\pi$
$8$	2.34689	+	1.57865i	0.829749	+	0.558136i
$9$	0.342020	−	0.939693i	0.114007	−	0.313231i
$10$	−3.97017	−	0.438942i	−1.25548	−	0.138806i
$11$	2.94767	−	0.789825i	0.888755	−	0.238141i	0.214574	−	0.976708i	$-0.431164\pi$
$11$	2.94767	−	0.789825i	0.888755	−	0.238141i	0.674181	+	0.738567i	$0.264497\pi$
$12$	−1.95348	+	0.428857i	−0.563921	+	0.123800i
$13$	3.69720	+	2.58881i	1.02542	+	0.718006i	0.960042	−	0.279855i	$-0.0902864\pi$
$13$	3.69720	+	2.58881i	1.02542	+	0.718006i	0.0653760	+	0.997861i	$0.479175\pi$
$14$	−2.10657	−	6.22682i	−0.563005	−	1.66419i
$15$	2.16365	−	1.81551i	0.558651	−	0.468764i
$16$	2.81675	+	2.84005i	0.704188	+	0.710013i
$17$	4.88350	−	1.77745i	1.18442	−	0.431094i	0.326660	−	0.945142i	$-0.394077\pi$
$17$	4.88350	−	1.77745i	1.18442	−	0.431094i	0.857762	+	0.514048i	$0.171855\pi$
$18$	0.734901	−	1.20827i	0.173218	−	0.284792i
$19$	2.84188	+	3.30511i	0.651971	+	0.758244i
$19$	2.84188	+	3.30511i	0.651971	+	0.758244i
$20$	−5.38392	−	1.70974i	−1.20388	−	0.382310i
$21$	4.21267	+	1.96440i	0.919280	+	0.428667i
$22$	4.30673	−	0.277824i	0.918198	−	0.0592324i
$23$	3.11698	−	2.61546i	0.649936	−	0.545361i	−0.257116	−	0.966381i	$-0.582772\pi$
$23$	3.11698	−	2.61546i	0.649936	−	0.545361i	0.907052	+	0.421020i	$0.138328\pi$
$24$	−2.82793	+	0.0529658i	−0.577249	+	0.0108116i
$25$	2.93222	−	0.517030i	0.586444	−	0.103406i
$26$	4.40916	+	4.61537i	0.864708	+	0.905149i
$27$	0.258819	+	0.965926i	0.0498097	+	0.185893i
$28$	−1.19443	−	9.21928i	−0.225726	−	1.74228i
$29$	3.40902	−	1.58965i	0.633039	−	0.295191i	−0.0794878	−	0.996836i	$-0.525328\pi$
$29$	3.40902	−	1.58965i	0.633039	−	0.295191i	0.712527	+	0.701645i	$0.247551\pi$
$30$	3.50394	−	1.91764i	0.639729	−	0.350111i
$31$	−2.56433	−	4.44155i	−0.460567	−	0.797726i	0.538422	−	0.842675i	$-0.319021\pi$
$31$	−2.56433	−	4.44155i	−0.460567	−	0.797726i	−0.998989	+	0.0449495i	$0.985687\pi$
$32$	3.11852	+	4.71962i	0.551282	+	0.834319i
$33$	−1.96156	+	2.33770i	−0.341464	+	0.406941i
$34$	7.26515	−	1.11056i	1.24596	−	0.190459i
$35$	7.53018	+	10.7542i	1.27283	+	1.81779i
$36$	1.35421	−	1.47177i	0.225702	−	0.245295i
$37$	−2.40106	−	2.40106i	−0.394731	−	0.394731i	0.481639	−	0.876370i	$-0.340042\pi$
$37$	−2.40106	−	2.40106i	−0.394731	−	0.394731i	−0.876370	+	0.481639i	$0.840042\pi$
$38$	3.02439	+	5.37151i	0.490620	+	0.871373i
$39$	−4.51345			−0.722730
$40$	−6.99202	−	3.86410i	−1.10554	−	0.610968i
$41$	−0.0704889	+	0.399763i	−0.0110085	+	0.0624324i	−0.989817	−	0.142345i	$-0.954536\pi$
$41$	−0.0704889	+	0.399763i	−0.0110085	+	0.0624324i	0.978809	+	0.204777i	$0.0656470\pi$
$42$	5.29716	+	3.89243i	0.817369	+	0.600615i
$43$	−0.866061	−	9.89912i	−0.132073	−	1.50960i	−0.716175	−	0.697921i	$-0.754109\pi$
$43$	−0.866061	−	9.89912i	−0.132073	−	1.50960i	0.584102	−	0.811680i	$-0.301447\pi$
$44$	6.04943	+	0.809101i	0.911986	+	0.121977i
$45$	−0.731019	+	2.72820i	−0.108974	+	0.406696i
$46$	5.04783	−	2.76258i	0.744262	−	0.407320i
$47$	0.474842	−	1.30462i	0.0692629	−	0.190298i	−0.900232	−	0.435411i	$-0.856603\pi$
$47$	0.474842	−	1.30462i	0.0692629	−	0.190298i	0.969494	+	0.245113i	$0.0788251\pi$
$48$	−3.93634	−	0.710813i	−0.568161	−	0.102597i
$49$	−7.30273	+	12.6487i	−1.04325	+	1.80696i
$50$	4.20966	+	0.0961922i	0.595336	+	0.0136036i
$51$	−2.98082	+	4.25706i	−0.417399	+	0.596107i
$52$	4.83446	+	7.62318i	0.670418	+	1.05714i
$53$	4.45895	+	0.390108i	0.612484	+	0.0535854i	0.389177	−	0.921163i	$-0.372759\pi$
$53$	4.45895	+	0.390108i	0.612484	+	0.0535854i	0.223307	+	0.974748i	$0.428315\pi$
$54$	0.0910408	+	1.41128i	0.0123891	+	0.192051i
$55$	−8.09939	+	2.94794i	−1.09212	+	0.397500i
$56$	0.900379	−	13.1161i	0.120318	−	1.75272i
$57$	−4.22366	−	1.07735i	−0.559438	−	0.142699i
$58$	5.16833	−	1.25904i	0.678635	−	0.165320i
$59$	−2.70490	+	5.80067i	−0.352148	+	0.755183i	−0.999978	−	0.00660155i	$-0.997899\pi$
$59$	−2.70490	+	5.80067i	−0.352148	+	0.755183i	0.647831	+	0.761784i	$0.275676\pi$
$60$	5.39092	−	1.68755i	0.695964	−	0.217862i
$61$	−5.97662	−	0.522886i	−0.765228	−	0.0669487i	−0.302143	−	0.953263i	$-0.597702\pi$
$61$	−5.97662	−	0.522886i	−0.765228	−	0.0669487i	−0.463085	+	0.886314i	$0.653257\pi$
$62$	−2.32433	−	6.87050i	−0.295191	−	0.872554i
$63$	−4.57755	+	0.807146i	−0.576717	+	0.101691i
$64$	3.01574	+	7.40981i	0.376968	+	0.926226i
$65$	−11.0401	−	6.37398i	−1.36935	−	0.790594i
$66$	−3.36851	+	2.69782i	−0.414635	+	0.332079i
$67$	−0.936677	−	2.00871i	−0.114433	−	0.245403i	0.840747	−	0.541429i	$-0.182116\pi$
$67$	−0.936677	−	2.00871i	−0.114433	−	0.245403i	−0.955180	+	0.296026i	$0.904339\pi$
$68$	10.3830	+	0.474757i	1.25912	+	0.0575727i
$69$	−1.05312	+	3.93029i	−0.126780	+	0.473151i
$70$	7.46007	+	17.0018i	0.891649	+	2.03210i
$71$	7.35211	−	8.76191i	0.872535	−	1.03985i	−0.126319	−	0.991990i	$-0.540316\pi$
$71$	7.35211	−	8.76191i	0.872535	−	1.03985i	0.998854	−	0.0478575i	$-0.0152393\pi$
$72$	2.28613	−	1.66542i	0.269422	−	0.196272i
$73$	−4.34004	−	0.765266i	−0.507963	−	0.0895676i	−0.0862077	−	0.996277i	$-0.527475\pi$
$73$	−4.34004	−	0.765266i	−0.507963	−	0.0895676i	−0.421756	+	0.906710i	$0.638586\pi$
$74$	−2.66380	−	3.99556i	−0.309660	−	0.464474i
$75$	−2.10538	+	2.10538i	−0.243108	+	0.243108i
$76$	2.70442	+	8.28771i	0.310218	+	0.950665i
$77$	−10.0300	−	10.0300i	−1.14303	−	1.14303i
$78$	−6.25904	−	1.25170i	−0.708697	−	0.141727i
$79$	−1.08843	+	6.17280i	−0.122458	+	0.694494i	0.860327	+	0.509742i	$0.170259\pi$
$79$	−1.08843	+	6.17280i	−0.122458	+	0.694494i	−0.982785	+	0.184752i	$0.940852\pi$
$80$	−8.62460	−	7.29764i	−0.964259	−	0.815901i
$81$	−0.766044	−	0.642788i	−0.0851160	−	0.0714208i
$82$	−0.208616	+	0.534824i	−0.0230378	+	0.0590615i
$83$	9.19924	+	2.46493i	1.00975	+	0.270561i	0.725524	−	0.688197i	$-0.241597\pi$
$83$	9.19924	+	2.46493i	1.00975	+	0.270561i	0.284224	+	0.958758i	$0.408264\pi$
$84$	6.26638	+	6.86690i	0.683718	+	0.749240i
$85$	−13.3031	+	6.20334i	−1.44292	+	0.672847i
$86$	1.54428	−	13.9678i	0.166524	−	1.50619i
$87$	−1.88072	+	3.25750i	−0.201634	+	0.349241i
$88$	8.16469	+	2.79970i	0.870359	+	0.298449i
$89$	1.51372	+	8.58476i	0.160454	+	0.909983i	0.953628	+	0.300987i	$0.0973161\pi$
$89$	1.51372	+	8.58476i	0.160454	+	0.909983i	−0.793174	+	0.608995i	$0.791573\pi$
$90$	−1.77035	+	3.58061i	−0.186611	+	0.377430i
$91$	1.82846	−	20.8994i	0.191675	−	2.19085i
$92$	7.76624	−	2.43111i	0.809687	−	0.253461i
$93$	4.64814	+	2.16747i	0.481990	+	0.224756i
$94$	1.02030	−	1.67750i	0.105236	−	0.173021i
$95$	−8.80977	−	8.59998i	−0.903863	−	0.882339i
$96$	−5.26161	−	2.07738i	−0.537010	−	0.212021i
$97$	5.79749	+	15.9285i	0.588646	+	1.61729i	0.772982	+	0.634428i	$0.218764\pi$
$97$	5.79749	+	15.9285i	0.588646	+	1.61729i	−0.184336	+	0.982863i	$0.559013\pi$
$98$	−13.6349	+	15.5154i	−1.37734	+	1.56729i
$99$	0.265969	−	3.04004i	0.0267309	−	0.305535i
$100$	5.81109	+	1.30085i	0.581109	+	0.130085i
$101$	−13.9352	−	9.75752i	−1.38660	−	0.970910i	−0.998790	−	0.0491717i	$-0.984342\pi$
$101$	−13.9352	−	9.75752i	−1.38660	−	0.970910i	−0.387813	−	0.921738i	$-0.626769\pi$
$102$	−5.31427	+	5.07683i	−0.526191	+	0.502681i
$103$	−5.53110	−	3.19338i	−0.544996	−	0.314653i	0.202105	−	0.979364i	$-0.435222\pi$
$103$	−5.53110	−	3.19338i	−0.544996	−	0.314653i	−0.747101	+	0.664710i	$0.768555\pi$
$104$	4.59009	+	11.9122i	0.450095	+	1.16809i
$105$	−12.3367	−	4.49020i	−1.20394	−	0.438199i
$106$	6.07528	+	1.77757i	0.590084	+	0.172653i
$107$	17.2116	+	4.61183i	1.66391	+	0.445843i	0.963458	−	0.267859i	$-0.0863163\pi$
$107$	17.2116	+	4.61183i	1.66391	+	0.445843i	0.700449	+	0.713702i	$0.252983\pi$
$108$	−0.265136	+	1.98235i	−0.0255127	+	0.190752i
$109$	−0.557695	+	0.0487920i	−0.0534175	+	0.00467342i	−0.113833	−	0.993500i	$-0.536313\pi$
$109$	−0.557695	+	0.0487920i	−0.0534175	+	0.00467342i	0.0604157	+	0.998173i	$0.480757\pi$
$110$	−12.0494	+	1.84188i	−1.14887	+	0.175617i
$111$	3.34402	+	0.589641i	0.317400	+	0.0559662i
$112$	4.88607	−	17.9392i	0.461690	−	1.69509i
$113$			2.16977i			0.204115i	0.994778	+	0.102058i	$0.0325426\pi$
$113$			2.16977i			0.204115i	−0.994778	+	0.102058i	$0.967457\pi$
$114$	−5.55840	−	2.66536i	−0.520592	−	0.249634i
$115$	−8.12639	+	8.12639i	−0.757790	+	0.757790i
$116$	7.51637	−	0.312664i	0.697878	−	0.0290301i
$117$	3.69720	−	2.58881i	0.341806	−	0.239335i
$118$	−5.35971	+	7.29396i	−0.493402	+	0.671464i
$119$	−18.5046	−	15.5272i	−1.69632	−	1.42338i
$120$	7.94389	−	0.845170i	0.725174	−	0.0771531i
$121$	−1.46137	+	0.843720i	−0.132851	+	0.0767018i
$122$	−8.14309	−	2.38260i	−0.737241	−	0.215710i
$123$	−0.171553	−	0.367897i	−0.0154684	−	0.0331722i
$124$	−1.31790	−	10.1723i	−0.118351	−	0.913500i
$125$	5.51790	−	1.47852i	0.493536	−	0.132243i
$126$	−6.57179	−	0.150168i	−0.585461	−	0.0133780i
$127$	−2.91471	−	16.5301i	−0.258639	−	1.46681i	−0.786557	−	0.617518i	$-0.788138\pi$
$127$	−2.91471	−	16.5301i	−0.258639	−	1.46681i	0.527918	−	0.849295i	$-0.322973\pi$
$128$	2.12715	+	11.1119i	0.188015	+	0.982166i
$129$	6.38734	+	7.61213i	0.562374	+	0.670211i
$130$	−13.5422	−	11.9009i	−1.18773	−	1.04377i
$131$	3.09964	−	6.64719i	0.270817	−	0.580768i	−0.723120	−	0.690722i	$-0.757293\pi$
$131$	3.09964	−	6.64719i	0.270817	−	0.580768i	0.993937	+	0.109954i	$0.0350704\pi$
$132$	−5.41948	+	2.80703i	−0.471705	+	0.244321i
$133$	6.69973	−	19.1211i	0.580940	−	1.65801i
$134$	−0.741871	−	3.04536i	−0.0640879	−	0.263079i
$135$	−0.966015	−	2.65410i	−0.0831413	−	0.228429i
$136$	14.2670	+	3.53785i	1.22338	+	0.303369i
$137$	−9.93202	−	11.8365i	−0.848550	−	1.01126i	−0.999741	−	0.0227575i	$-0.992755\pi$
$137$	−9.93202	−	11.8365i	−0.848550	−	1.01126i	0.151191	−	0.988505i	$-0.451689\pi$
$138$	−2.55039	+	5.15829i	−0.217104	+	0.439103i
$139$	10.3664	−	14.8048i	0.879270	−	1.25573i	−0.0864800	−	0.996254i	$-0.527562\pi$
$139$	10.3664	−	14.8048i	0.879270	−	1.25573i	0.965750	−	0.259474i	$-0.0835492\pi$
$140$	5.63023	+	25.6462i	0.475841	+	2.16750i
$141$	0.359330	+	1.34104i	0.0302611	+	0.112936i
$142$	12.6255	−	10.1117i	1.05951	−	0.848553i
$143$	12.9428	+	4.71080i	1.08233	+	0.393937i
$144$	3.63216	−	1.67553i	0.302680	−	0.139627i
$145$	−9.20061	+	5.31197i	−0.764069	+	0.441135i
$146$	−5.80634	−	2.26485i	−0.480536	−	0.187440i
$147$	−1.27295	−	14.5499i	−0.104991	−	1.20005i
$148$	−2.58596	−	6.27960i	−0.212564	−	0.516180i
$149$	4.36165	+	6.22908i	0.357320	+	0.510306i	0.957060	−	0.289889i	$-0.0936182\pi$
$149$	4.36165	+	6.22908i	0.357320	+	0.510306i	−0.599740	+	0.800195i	$0.704729\pi$
$150$	−3.50352	+	2.33577i	−0.286062	+	0.190714i
$151$			23.3139i			1.89726i	0.316394	+	0.948628i	$0.397528\pi$
$151$			23.3139i			1.89726i	−0.316394	+	0.948628i	$0.602472\pi$
$152$	1.45195	+	12.2430i	0.117769	+	0.993041i
$153$		−	5.19691i		−	0.420145i
$154$	−11.1276	−	16.6908i	−0.896685	−	1.34498i
$155$	8.30859	+	11.8659i	0.667362	+	0.953092i
$156$	−8.33263	−	3.47161i	−0.667144	−	0.277951i
$157$	2.04331	+	23.3552i	0.163074	+	1.86394i	0.433434	+	0.901185i	$0.357302\pi$
$157$	2.04331	+	23.3552i	0.163074	+	1.86394i	−0.270360	+	0.962759i	$0.587143\pi$
$158$	−3.22128	+	8.25831i	−0.256271	+	0.656996i
$159$	−3.87632	+	2.23799i	−0.307412	+	0.177484i
$160$	−9.93637	−	12.5119i	−0.785539	−	0.989151i
$161$	−17.7725	−	6.46865i	−1.40067	−	0.509801i
$162$	−0.884053	−	1.10383i	−0.0694578	−	0.0867254i
$163$	3.26510	+	12.1855i	0.255742	+	0.954443i	0.967676	+	0.252197i	$0.0811530\pi$
$163$	3.26510	+	12.1855i	0.255742	+	0.954443i	−0.711934	+	0.702247i	$0.752180\pi$
$164$	−0.437621	+	0.683815i	−0.0341724	+	0.0533970i
$165$	4.94377	−	7.06043i	0.384872	−	0.549654i
$166$	12.0735	+	5.96946i	0.937086	+	0.463320i
$167$	5.08912	+	6.06497i	0.393808	+	0.469322i	0.926121	−	0.377225i	$-0.123122\pi$
$167$	5.08912	+	6.06497i	0.393808	+	0.469322i	−0.532314	+	0.846547i	$0.678677\pi$
$168$	6.78556	+	11.2605i	0.523517	+	0.868770i
$169$	2.52110	+	6.92666i	0.193930	+	0.532820i
$170$	−20.1685	+	4.91319i	−1.54685	+	0.376825i
$171$	4.07776	−	1.54008i	0.311834	−	0.117773i
$172$	6.01521	−	18.9417i	0.458655	−	1.44429i
$173$	−4.33694	+	9.30060i	−0.329732	+	0.707112i	−0.999367	−	0.0355785i	$-0.988673\pi$
$173$	−4.33694	+	9.30060i	−0.329732	+	0.707112i	0.669635	+	0.742690i	$0.266450\pi$
$174$	−3.51149	+	3.99578i	−0.266205	+	0.302919i
$175$	−8.89599	−	10.6018i	−0.672474	−	0.801423i
$176$	10.5460	+	6.14679i	0.794934	+	0.463332i
$177$	−1.11141	−	6.30309i	−0.0835384	−	0.473770i
$178$	−0.281625	+	12.3248i	−0.0211087	+	0.923779i
$179$	−5.44588	+	1.45922i	−0.407044	+	0.109067i	−0.456531	−	0.889708i	$-0.650908\pi$
$179$	−5.44588	+	1.45922i	−0.407044	+	0.109067i	0.0494866	+	0.998775i	$0.484241\pi$
$180$	−3.44804	+	4.47446i	−0.257002	+	0.333507i
$181$	2.92572	+	6.27423i	0.217467	+	0.466360i	0.984531	−	0.175211i	$-0.0560608\pi$
$181$	2.92572	+	6.27423i	0.217467	+	0.466360i	−0.767064	+	0.641571i	$0.778283\pi$
$182$	8.33161	−	28.4753i	0.617580	−	2.11073i
$183$	5.19567	−	2.99972i	0.384075	−	0.221746i
$184$	11.4441	−	1.21757i	0.843670	−	0.0897601i
$185$	7.34689	+	6.16477i	0.540154	+	0.453243i
$186$	5.84474	+	4.29480i	0.428557	+	0.314910i
$187$	12.9910	−	9.09643i	0.949999	−	0.665197i
$188$	1.88012	−	2.04332i	0.137122	−	0.149025i
$189$	3.28675	−	3.28675i	0.239076	−	0.239076i
$190$	−9.83198	−	14.3693i	−0.713286	−	1.04246i
$191$		−	14.1317i		−	1.02254i	−0.859421	−	0.511268i	$-0.829176\pi$
$191$		−	14.1317i		−	1.02254i	0.859421	−	0.511268i	$-0.170824\pi$
$192$	−6.72044	−	4.34000i	−0.485006	−	0.313213i
$193$	−7.18283	−	1.26653i	−0.517031	−	0.0911666i	−0.0909571	−	0.995855i	$-0.528993\pi$
$193$	−7.18283	−	1.26653i	−0.517031	−	0.0911666i	−0.426074	+	0.904688i	$0.640104\pi$
$194$	3.62229	+	23.6967i	0.260066	+	1.70132i
$195$	12.6994	−	1.11106i	0.909426	−	0.0795645i
$196$	−23.2111	+	17.7347i	−1.65794	+	1.26677i
$197$	3.32868	+	0.891916i	0.237158	+	0.0635464i	0.375441	−	0.926846i	$-0.377491\pi$
$197$	3.32868	+	0.891916i	0.237158	+	0.0635464i	−0.138282	+	0.990393i	$0.544158\pi$
$198$	1.21192	−	4.14202i	0.0861274	−	0.294361i
$199$	−16.5716	−	6.03157i	−1.17473	−	0.427567i	−0.320392	−	0.947285i	$-0.603815\pi$
$199$	−16.5716	−	6.03157i	−1.17473	−	0.427567i	−0.854338	+	0.519718i	$0.826037\pi$
$200$	7.69780	+	3.41553i	0.544316	+	0.241515i
$201$	1.91943	+	1.10818i	0.135386	+	0.0781652i
$202$	−16.6187	−	17.3959i	−1.16928	−	1.22397i
$203$	−14.3219	−	10.0283i	−1.00520	−	0.703848i
$204$	−8.77754	+	5.56653i	−0.614551	+	0.389735i
$205$	0.0999261	−	1.14216i	0.00697914	−	0.0797719i
$206$	−6.78467	−	5.96237i	−0.472711	−	0.415418i
$207$	−1.39166	−	3.82355i	−0.0967268	−	0.265755i
$208$	3.06175	+	17.7923i	0.212294	+	1.23367i
$209$	10.9874	+	7.49777i	0.760011	+	0.518632i
$210$	−15.8628	−	9.64812i	−1.09463	−	0.665783i
$211$	−21.2600	−	9.91370i	−1.46360	−	0.682487i	−0.482482	−	0.875906i	$-0.660265\pi$
$211$	−21.2600	−	9.91370i	−1.46360	−	0.682487i	−0.981116	+	0.193418i	$0.938042\pi$
$212$	7.93196	+	4.14990i	0.544769	+	0.285016i
$213$	−0.996875	+	11.3943i	−0.0683048	+	0.780727i
$214$	22.5893	+	11.1687i	1.54417	+	0.763479i
$215$	4.87365	+	27.6399i	0.332380	+	1.88502i
$216$	−0.917438	+	2.67550i	−0.0624237	+	0.182045i
$217$	−11.9194	+	20.6451i	−0.809144	+	1.40148i
$218$	−0.786917	−	0.0870016i	−0.0532968	−	0.00589249i
$219$	3.99409	−	1.86248i	0.269896	−	0.125854i
$220$	−17.2204	−	0.787396i	−1.16100	−	0.0530862i
$221$	22.6567	+	6.07085i	1.52406	+	0.408370i
$222$	4.47381	+	1.74508i	0.300263	+	0.117122i
$223$	−1.53198	−	1.28548i	−0.102589	−	0.0860824i	0.590050	−	0.807366i	$-0.299108\pi$
$223$	−1.53198	−	1.28548i	−0.102589	−	0.0860824i	−0.692639	+	0.721284i	$0.743552\pi$
$224$	11.7508	−	23.5222i	0.785134	−	1.57164i
$225$	0.517030	−	2.93222i	0.0344687	−	0.195481i
$226$	−0.601738	+	3.00895i	−0.0400270	+	0.200152i
$227$	−5.94140	−	5.94140i	−0.394345	−	0.394345i	0.481888	−	0.876233i	$-0.339951\pi$
$227$	−5.94140	−	5.94140i	−0.394345	−	0.394345i	−0.876233	+	0.481888i	$0.839951\pi$
$228$	−6.96896	−	5.23770i	−0.461531	−	0.346875i
$229$	−16.3944	+	16.3944i	−1.08337	+	1.08337i	−0.0871821	+	0.996192i	$0.527786\pi$
$229$	−16.3944	+	16.3944i	−1.08337	+	1.08337i	−0.996192	+	0.0871821i	$0.972214\pi$
$230$	−13.5230	+	9.01564i	−0.891679	+	0.594474i
$231$	13.9691	+	2.46313i	0.919098	+	0.162062i
$232$	10.5101	+	1.65091i	0.690020	+	0.108388i
$233$	−11.9110	+	14.1949i	−0.780313	+	0.929941i	−0.998948	−	0.0458655i	$-0.985395\pi$
$233$	−11.9110	+	14.1949i	−0.780313	+	0.929941i	0.218634	+	0.975807i	$0.429840\pi$
$234$	5.84506	−	2.56470i	0.382103	−	0.167660i
$235$	−1.01491	+	3.78768i	−0.0662052	+	0.247081i
$236$	−9.45543	+	8.62855i	−0.615496	+	0.561670i
$237$	−2.64898	−	5.68076i	−0.172070	−	0.369005i
$238$	−21.3553	−	26.6643i	−1.38426	−	1.72839i
$239$	−12.3009	−	7.10194i	−0.795680	−	0.459386i	0.0462782	−	0.998929i	$-0.485264\pi$
$239$	−12.3009	−	7.10194i	−0.795680	−	0.459386i	−0.841958	+	0.539542i	$0.818597\pi$
$240$	11.2506	+	1.03101i	0.726224	+	0.0665517i
$241$	−5.09396	+	0.898203i	−0.328131	+	0.0578583i	−0.335287	−	0.942116i	$-0.608833\pi$
$241$	−5.09396	+	0.898203i	−0.328131	+	0.0578583i	0.00715598	+	0.999974i	$0.497722\pi$
$242$	−2.26054	+	0.764756i	−0.145313	+	0.0491604i
$243$	0.996195	+	0.0871557i	0.0639059	+	0.00559104i
$244$	−10.6317	−	5.56238i	−0.680626	−	0.356095i
$245$	17.4339	−	37.3872i	1.11381	−	2.38858i
$246$	−0.135874	−	0.557760i	−0.00866303	−	0.0355615i
$247$	1.95069	+	19.5767i	0.124120	+	1.24564i
$248$	0.993453	−	14.4720i	0.0630843	−	0.918972i
$249$	−8.94941	+	3.25732i	−0.567146	+	0.206424i
$250$	8.06201	−	0.520075i	0.509886	−	0.0328924i
$251$	−26.0939	−	2.28292i	−1.64703	−	0.144097i	−0.774475	−	0.632605i	$-0.781986\pi$
$251$	−26.0939	−	2.28292i	−1.64703	−	0.144097i	−0.872559	+	0.488508i	$0.837541\pi$
$252$	−9.07181	−	2.03078i	−0.571470	−	0.127927i
$253$	7.12207	−	10.1714i	0.447761	−	0.639469i
$254$	0.542275	−	23.7316i	0.0340254	−	1.48905i
$255$	7.33918	−	12.7118i	0.459597	−	0.796045i
$256$	−0.131808	+	15.9995i	−0.00823803	+	0.999966i
$257$	−6.59040	+	18.1070i	−0.411098	+	1.12948i	0.545510	+	0.838104i	$0.316336\pi$
$257$	−6.59040	+	18.1070i	−0.411098	+	1.12948i	−0.956608	+	0.291378i	$0.905886\pi$
$258$	6.74662	+	12.3275i	0.420026	+	0.767479i
$259$	−4.08503	+	15.2455i	−0.253832	+	0.947312i
$260$	−15.4792	−	20.2592i	−0.959981	−	1.25642i
$261$	−0.327831	−	3.74712i	−0.0202922	−	0.231941i
$262$	6.14189	−	8.35842i	0.379447	−	0.516385i
$263$	−1.70518	+	9.67054i	−0.105146	+	0.596311i	0.886016	+	0.463654i	$0.153462\pi$
$263$	−1.70518	+	9.67054i	−0.105146	+	0.596311i	−0.991162	+	0.132657i	$0.957649\pi$
$264$	−8.29396	+	2.38970i	−0.510458	+	0.147076i
$265$	−12.6421			−0.776601
$266$	14.5937	−	24.6583i	0.894797	−	1.51190i
$267$	−6.16399	−	6.16399i	−0.377230	−	0.377230i
$268$	−0.184232	−	4.42890i	−0.0112538	−	0.270538i
$269$	6.10036	+	8.71221i	0.371945	+	0.531193i	0.960872	−	0.276994i	$-0.0893381\pi$
$269$	6.10036	+	8.71221i	0.371945	+	0.531193i	−0.588926	+	0.808187i	$0.700449\pi$
$270$	−0.603570	−	3.94850i	−0.0367321	−	0.240298i
$271$	−6.35610	+	7.57491i	−0.386106	+	0.460143i	−0.923731	−	0.383041i	$-0.874877\pi$
$271$	−6.35610	+	7.57491i	−0.386106	+	0.460143i	0.537626	+	0.843184i	$0.319321\pi$
$272$	18.8036	+	8.86276i	1.14014	+	0.537384i
$273$	10.4896	+	18.1686i	0.634861	+	1.09961i
$274$	−10.4907	−	19.1688i	−0.633765	−	1.15803i
$275$	8.23485	−	3.83997i	0.496580	−	0.231559i
$276$	−4.96730	+	6.44599i	−0.298997	+	0.388003i
$277$	−0.366917	−	1.36935i	−0.0220459	−	0.0822764i	0.954026	−	0.299722i	$-0.0968941\pi$
$277$	−0.366917	−	1.36935i	−0.0220459	−	0.0822764i	−0.976072	+	0.217446i	$0.930227\pi$
$278$	18.4815	−	17.6557i	1.10845	−	1.05892i
$279$	−5.05074	+	0.890582i	−0.302380	+	0.0533178i
$280$	0.695359	+	37.1264i	0.0415557	+	2.21873i
$281$	20.8973	−	17.5349i	1.24663	−	1.04605i	0.249654	−	0.968335i	$-0.419683\pi$
$281$	20.8973	−	17.5349i	1.24663	−	1.04605i	0.996976	−	0.0777121i	$-0.0247615\pi$
$282$	0.126396	+	1.95935i	0.00752678	+	0.116677i
$283$	26.7948	+	12.4946i	1.59279	+	0.742729i	0.998123	−	0.0612447i	$-0.0195070\pi$
$283$	26.7948	+	12.4946i	1.59279	+	0.742729i	0.594665	+	0.803974i	$0.297285\pi$
$284$	20.3127	−	10.5210i	1.20534	−	0.624308i
$285$	12.1493	+	1.99162i	0.719662	+	0.117973i
$286$	16.6421	+	10.1221i	0.984066	+	0.598533i
$287$	1.77304	−	0.645333i	0.104659	−	0.0380928i
$288$	5.50159	−	1.31625i	0.324184	−	0.0775605i
$289$	7.66646	−	6.43293i	0.450968	−	0.378407i
$290$	−14.2321	+	4.81482i	−0.835740	+	0.282736i
$291$	−13.8852	−	9.72254i	−0.813966	−	0.569945i
$292$	−7.42387	−	4.75105i	−0.434449	−	0.278034i
$293$	5.36646	−	1.43794i	0.313512	−	0.0840053i	−0.0986320	−	0.995124i	$-0.531447\pi$
$293$	5.36646	−	1.43794i	0.313512	−	0.0840053i	0.412144	+	0.911119i	$0.364780\pi$
$294$	2.26981	−	20.5301i	0.132378	−	1.19734i
$295$	6.18282	−	16.9871i	0.359977	−	0.989030i
$296$	−1.84458	−	9.42543i	−0.107214	−	0.547842i
$297$	1.52582	+	2.64281i	0.0885373	+	0.153351i
$298$	4.32104	+	9.84782i	0.250311	+	0.570469i
$299$	18.2950	−	1.60061i	1.05803	−	0.0925655i
$300$	−5.50630	+	2.26751i	−0.317907	+	0.130915i
$301$	−37.8354	+	26.4926i	−2.18080	+	1.52701i
$302$	−6.46558	+	32.3306i	−0.372052	+	1.86042i
$303$	17.0117			0.977298
$304$	−1.38182	+	17.3808i	−0.0792531	+	0.996855i
$305$	16.9451			0.970272
$306$	1.44125	−	7.20684i	0.0823905	−	0.411988i
$307$	−11.8155	+	8.27332i	−0.674348	+	0.472183i	−0.859908	−	0.510450i	$-0.829479\pi$
$307$	−11.8155	+	8.27332i	−0.674348	+	0.472183i	0.185560	+	0.982633i	$0.440590\pi$
$308$	−10.8024	−	26.2320i	−0.615524	−	1.49471i
$309$	6.36246	−	0.556644i	0.361948	−	0.0316663i
$310$	8.23124	+	18.7593i	0.467503	+	1.06546i
$311$	−11.7892	−	20.4194i	−0.668502	−	1.15788i	−0.978323	−	0.207085i	$-0.933602\pi$
$311$	−11.7892	−	20.4194i	−0.668502	−	1.15788i	0.309821	−	0.950795i	$-0.399731\pi$
$312$	−10.5925	−	7.12514i	−0.599685	−	0.403382i
$313$	5.83215	−	16.0237i	0.329653	−	0.905713i	−0.658547	−	0.752540i	$-0.728829\pi$
$313$	5.83215	−	16.0237i	0.329653	−	0.905713i	0.988199	−	0.153173i	$-0.0489492\pi$
$314$	−3.64346	+	32.9546i	−0.205612	+	1.85973i
$315$	12.6811	−	3.39790i	0.714500	−	0.191450i
$316$	−6.75738	+	10.5589i	−0.380132	+	0.593985i
$317$	−5.32596	−	3.72928i	−0.299136	−	0.209457i	0.414366	−	0.910110i	$-0.364003\pi$
$317$	−5.32596	−	3.72928i	−0.299136	−	0.209457i	−0.713502	+	0.700653i	$0.752892\pi$
$318$	−5.99616	+	2.02854i	−0.336248	+	0.113755i
$319$	8.79310	−	7.37829i	0.492319	−	0.413105i
$320$	−10.3094	−	20.1065i	−0.576314	−	1.12399i
$321$	−16.7441	+	6.09437i	−0.934567	+	0.340155i
$322$	−22.8521	−	13.8992i	−1.27350	−	0.774574i
$323$	19.7529	+	11.0892i	1.09908	+	0.617020i
$324$	−0.919842	−	1.77592i	−0.0511023	−	0.0986622i
$325$	12.1795	+	5.67939i	0.675597	+	0.315036i
$326$	1.14851	+	17.8038i	0.0636103	+	0.986063i
$327$	0.428851	−	0.359849i	0.0237155	−	0.0198997i
$328$	−0.796514	+	0.826920i	−0.0439801	+	0.0456590i
$329$	−6.35523	+	1.12060i	−0.350375	+	0.0617806i
$330$	8.81385	−	8.42005i	0.485186	−	0.463508i
$331$	3.55612	+	13.2716i	0.195462	+	0.729475i	0.992147	+	0.125079i	$0.0399185\pi$
$331$	3.55612	+	13.2716i	0.195462	+	0.729475i	−0.796685	+	0.604395i	$0.793415\pi$
$332$	15.0875	+	11.6265i	0.828034	+	0.638087i
$333$	−3.07747	+	1.43505i	−0.168644	+	0.0786400i
$334$	5.37537	+	9.82198i	0.294127	+	0.537435i
$335$	3.13000	+	5.42131i	0.171010	+	0.296198i
$336$	6.28705	+	17.4974i	0.342987	+	0.954563i
$337$	14.2539	−	16.9871i	0.776459	−	0.925348i	−0.222309	−	0.974976i	$-0.571359\pi$
$337$	14.2539	−	16.9871i	0.776459	−	0.925348i	0.998768	+	0.0496285i	$0.0158037\pi$
$338$	1.57519	+	10.3047i	0.0856791	+	0.560504i
$339$	−1.24453	−	1.77738i	−0.0675937	−	0.0965338i
$340$	−29.3313	+	1.22012i	−1.59072	+	0.0661700i
$341$	−11.0668	−	11.0668i	−0.599303	−	0.599303i
$342$	6.08197	−	1.00483i	0.328875	−	0.0543351i
$343$	35.3514			1.90880
$344$	13.5947	−	24.5993i	0.732976	−	1.32631i
$345$	1.99564	−	11.3179i	0.107442	−	0.609333i
$346$	−8.59359	+	11.6949i	−0.461994	+	0.628722i
$347$	−0.970038	−	11.0876i	−0.0520744	−	0.595213i	−0.976739	−	0.214431i	$-0.931210\pi$
$347$	−0.970038	−	11.0876i	−0.0520744	−	0.595213i	0.924665	−	0.380782i	$-0.124345\pi$
$348$	−5.97772	+	4.56733i	−0.320439	+	0.244835i
$349$	7.00806	−	26.1544i	0.375133	−	1.40002i	−0.478017	−	0.878350i	$-0.658644\pi$
$349$	7.00806	−	26.1544i	0.375133	−	1.40002i	0.853150	−	0.521665i	$-0.174689\pi$
$350$	−9.39638	−	17.1693i	−0.502258	−	0.917735i
$351$	−1.54369	+	4.24125i	−0.0823960	+	0.226381i
$352$	12.9200	+	11.4488i	0.688640	+	0.610222i
$353$	12.0461	−	20.8645i	0.641150	−	1.11050i	−0.344026	−	0.938960i	$-0.611791\pi$
$353$	12.0461	−	20.8645i	0.641150	−	1.11050i	0.985176	−	0.171544i	$-0.0548757\pi$
$354$	0.206775	−	9.04907i	0.0109899	−	0.480953i
$355$	−18.5297	+	26.4631i	−0.983454	+	1.40452i
$356$	−3.80854	+	17.0133i	−0.201852	+	0.901704i
$357$	24.0642	+	2.10534i	1.27361	+	0.111427i
$358$	−7.95678	+	0.513287i	−0.420529	+	0.0271281i
$359$	22.9204	−	8.34236i	1.20969	−	0.440293i	0.343097	−	0.939300i	$-0.388524\pi$
$359$	22.9204	−	8.34236i	1.20969	−	0.440293i	0.866598	+	0.499007i	$0.166302\pi$
$360$	−6.02248	+	5.24875i	−0.317413	+	0.276633i
$361$	−2.84749	+	18.7854i	−0.149868	+	0.988706i
$362$	2.31724	+	9.51220i	0.121792	+	0.499950i
$363$	0.713143	−	1.52934i	0.0374303	−	0.0802696i
$364$	19.4509	−	37.1777i	1.01950	−	1.94864i
$365$	12.3999	+	1.08485i	0.649041	+	0.0567837i
$366$	8.03703	−	2.71898i	0.420102	−	0.142123i
$367$	−20.8471	+	3.67591i	−1.08821	+	0.191881i	−0.688844	−	0.724910i	$-0.741882\pi$
$367$	−20.8471	+	3.67591i	−1.08821	+	0.191881i	−0.399368	+	0.916791i	$0.630770\pi$
$368$	16.2078	+	1.48530i	0.844891	+	0.0774264i
$369$	0.351545	+	0.202965i	0.0183007	+	0.0105659i
$370$	8.47868	+	10.5865i	0.440785	+	0.550367i
$371$	−8.79262	−	18.8558i	−0.456490	−	0.978946i
$372$	6.91415	+	7.57675i	0.358482	+	0.392836i
$373$	4.11648	−	15.3629i	0.213143	−	0.795462i	−0.773669	−	0.633591i	$-0.781580\pi$
$373$	4.11648	−	15.3629i	0.213143	−	0.795462i	0.986812	−	0.161871i	$-0.0517529\pi$
$374$	20.5381	−	9.01174i	1.06200	−	0.465986i
$375$	−3.67196	+	4.37607i	−0.189619	+	0.225979i
$376$	3.17393	−	2.31218i	0.163683	−	0.119242i
$377$	16.7191	+	2.94803i	0.861079	+	0.151831i
$378$	5.46942	−	3.64641i	0.281317	−	0.187551i
$379$	−10.9698	+	10.9698i	−0.563478	+	0.563478i	−0.930294	−	0.366815i	$-0.880448\pi$
$379$	−10.9698	+	10.9698i	−0.563478	+	0.563478i	0.366815	+	0.930294i	$0.380448\pi$
$380$	−9.64955	−	22.6533i	−0.495011	−	1.16209i
$381$	11.8689	+	11.8689i	0.608062	+	0.608062i
$382$	3.91912	−	19.5972i	0.200519	−	1.00268i
$383$	−2.35431	+	13.3520i	−0.120300	+	0.682253i	0.863689	+	0.504024i	$0.168148\pi$
$383$	−2.35431	+	13.3520i	−0.120300	+	0.682253i	−0.983989	+	0.178229i	$0.942963\pi$
$384$	−8.11601	−	7.88228i	−0.414168	−	0.402241i
$385$	30.6904	+	25.7523i	1.56413	+	1.31246i
$386$	−9.60958	−	3.74836i	−0.489115	−	0.190786i
$387$	−9.59834	−	2.57187i	−0.487911	−	0.130735i
$388$	−1.54851	+	33.8661i	−0.0786138	+	1.71929i
$389$	−22.1441	+	10.3260i	−1.12275	+	0.523547i	−0.893160	−	0.449740i	$-0.851517\pi$
$389$	−22.1441	+	10.3260i	−1.12275	+	0.523547i	−0.229591	+	0.973287i	$0.573739\pi$
$390$	17.9191	+	1.98114i	0.907371	+	0.100319i
$391$	10.5729	−	18.3129i	0.534696	−	0.926121i
$392$	−37.1065	+	18.1566i	−1.87416	+	0.917047i
$393$	1.27360	+	7.22294i	0.0642446	+	0.364349i
$394$	4.36871	+	2.16000i	0.220092	+	0.108819i
$395$	1.54298	−	17.6363i	0.0776355	−	0.887378i
$396$	2.82933	−	5.40788i	0.142179	−	0.271756i
$397$	−16.6031	−	7.74217i	−0.833287	−	0.388568i	−0.0413305	−	0.999146i	$-0.513160\pi$
$397$	−16.6031	−	7.74217i	−0.833287	−	0.388568i	−0.791957	+	0.610577i	$0.790937\pi$
$398$	−21.3080	−	12.9601i	−1.06808	−	0.649630i
$399$	5.47933	+	19.5059i	0.274309	+	0.976517i
$400$	9.72773	+	6.87132i	0.486387	+	0.343566i
$401$	2.57323	+	7.06990i	0.128501	+	0.353054i	0.987213	−	0.159404i	$-0.0509573\pi$
$401$	2.57323	+	7.06990i	0.128501	+	0.353054i	−0.858712	+	0.512458i	$0.828735\pi$
$402$	2.35445	+	2.06909i	0.117429	+	0.103197i
$403$	2.01747	−	23.0598i	0.100498	−	1.14869i
$404$	−18.2216	−	28.7327i	−0.906561	−	1.42950i
$405$	2.31364	+	1.62003i	0.114966	+	0.0805000i
$406$	−17.0798	−	17.8786i	−0.847657	−	0.887301i
$407$	−8.97393	−	5.18110i	−0.444821	−	0.256818i
$408$	−13.7160	+	5.28516i	−0.679046	+	0.261654i
$409$	26.9803	+	9.82004i	1.33409	+	0.485570i	0.907947	−	0.419085i	$-0.137649\pi$
$409$	26.9803	+	9.82004i	1.33409	+	0.485570i	0.426145	+	0.904655i	$0.359871\pi$
$410$	0.455326	−	1.55618i	0.0224869	−	0.0768545i
$411$	14.9250	+	3.99914i	0.736195	+	0.197263i
$412$	−7.75515	−	10.1499i	−0.382069	−	0.500051i
$413$	29.6366	−	2.59287i	1.45832	−	0.127587i
$414$	−0.869512	−	5.68827i	−0.0427342	−	0.279563i
$415$	−26.4906	−	4.67101i	−1.30037	−	0.229291i
$416$	−0.688396	+	25.5226i	−0.0337514	+	1.25135i
$417$			18.0733i			0.885055i
$418$	13.1574	+	13.4447i	0.643551	+	0.657600i
$419$	−14.2260	+	14.2260i	−0.694987	+	0.694987i	−0.963325	−	0.268338i	$-0.913526\pi$
$419$	−14.2260	+	14.2260i	−0.694987	+	0.694987i	0.268338	+	0.963325i	$0.413526\pi$
$420$	−19.3221	−	17.7788i	−0.942820	−	0.867514i
$421$	2.82433	−	1.97762i	0.137649	−	0.0963831i	−0.502724	−	0.864447i	$-0.667669\pi$
$421$	2.82433	−	1.97762i	0.137649	−	0.0963831i	0.640373	+	0.768064i	$0.278780\pi$
$422$	−26.7331	−	19.6439i	−1.30135	−	0.956248i
$423$	−1.06354	−	0.892412i	−0.0517108	−	0.0433906i
$424$	9.84880	+	7.95465i	0.478300	+	0.386312i
$425$	13.4005	−	7.73678i	0.650020	−	0.375289i
$426$	−4.54238	+	15.5247i	−0.220079	+	0.752174i
$427$	11.7853	+	25.2737i	0.570331	+	1.22308i
$428$	28.2284	+	21.7529i	1.36447	+	1.05147i
$429$	−13.3041	+	3.56483i	−0.642330	+	0.172112i
$430$	−0.906732	+	39.6813i	−0.0437265	+	1.91360i
$431$	2.66446	+	15.1109i	0.128342	+	0.727866i	0.979266	+	0.202577i	$0.0649316\pi$
$431$	2.66446	+	15.1109i	0.128342	+	0.727866i	−0.850924	+	0.525289i	$0.823957\pi$
$432$	−2.01425	+	3.45583i	−0.0969107	+	0.166269i
$433$	−24.4219	−	29.1048i	−1.17364	−	1.39869i	−0.899456	−	0.437011i	$-0.856037\pi$
$433$	−24.4219	−	29.1048i	−1.17364	−	1.39869i	−0.274183	−	0.961677i	$-0.588407\pi$
$434$	−22.2548	+	25.3241i	−1.06826	+	1.21559i
$435$	4.48987	−	9.62857i	0.215273	−	0.461654i
$436$	−1.06713	−	0.338884i	−0.0511064	−	0.0162296i
$437$	17.5025	+	2.86916i	0.837256	+	0.137250i
$438$	6.05534	−	1.47513i	0.289335	−	0.0704842i
$439$	−10.3353	−	28.3959i	−0.493276	−	1.35526i	−0.897666	−	0.440677i	$-0.854738\pi$
$439$	−10.3353	−	28.3959i	−0.493276	−	1.35526i	0.404390	−	0.914587i	$-0.367484\pi$
$440$	−23.6621	−	5.86762i	−1.12805	−	0.279728i
$441$	9.38821	+	11.1884i	0.447057	+	0.532782i
$442$	29.7357	+	14.7021i	1.41438	+	0.699308i
$443$	−5.07945	+	7.25420i	−0.241332	+	0.344658i	−0.921486	−	0.388412i	$-0.873024\pi$
$443$	−5.07945	+	7.25420i	−0.241332	+	0.344658i	0.680154	+	0.733069i	$0.261913\pi$
$444$	5.72013	+	3.66071i	0.271465	+	0.173729i
$445$	−6.37243	−	23.7822i	−0.302082	−	1.12739i
$446$	−1.76798	−	2.20751i	−0.0837164	−	0.104529i
$447$	−7.14571	−	2.60083i	−0.337981	−	0.123015i
$448$	22.8188	−	29.3607i	1.07809	−	1.38716i
$449$	−15.2235	+	8.78931i	−0.718443	+	0.414793i	−0.814179	−	0.580613i	$-0.802813\pi$
$449$	−15.2235	+	8.78931i	−0.718443	+	0.414793i	0.0957364	+	0.995407i	$0.469479\pi$
$450$	1.53018	−	3.92289i	0.0721333	−	0.184927i
$451$	0.107965	+	1.23404i	0.00508385	+	0.0581087i
$452$	−1.66893	+	4.00579i	−0.0784997	+	0.188417i
$453$	−13.3723	−	19.0976i	−0.628285	−	0.897284i
$454$	−6.59156	−	9.88698i	−0.309357	−	0.464019i
$455$			59.2546i			2.77790i
$456$	−8.21169	−	9.19610i	−0.384547	−	0.430647i
$457$		−	9.50416i		−	0.444586i	−0.974980	−	0.222293i	$-0.928646\pi$
$457$		−	9.50416i		−	0.444586i	0.974980	−	0.222293i	$-0.0713541\pi$
$458$	−27.2817	+	18.1884i	−1.27479	+	0.849890i
$459$	2.98082	+	4.25706i	0.139133	+	0.198702i
$460$	−21.2534	+	8.75219i	−0.990943	+	0.408073i
$461$	2.09614	+	23.9590i	0.0976269	+	1.11588i	0.874105	+	0.485737i	$0.161449\pi$
$461$	2.09614	+	23.9590i	0.0976269	+	1.11588i	−0.776478	+	0.630144i	$0.782996\pi$
$462$	18.6886	+	7.28976i	0.869472	+	0.339150i
$463$	20.8893	−	12.0604i	0.970806	−	0.560495i	0.0713241	−	0.997453i	$-0.477278\pi$
$463$	20.8893	−	12.0604i	0.970806	−	0.560495i	0.899482	+	0.436958i	$0.143944\pi$
$464$	14.1171	+	5.20414i	0.655368	+	0.241596i
$465$	−13.6120	−	4.95436i	−0.631241	−	0.229753i
$466$	−20.4542	+	16.3817i	−0.947524	+	0.758866i
$467$	10.1728	+	37.9653i	0.470740	+	1.75683i	0.637121	+	0.770764i	$0.280125\pi$
$467$	10.1728	+	37.9653i	0.470740	+	1.75683i	−0.166381	+	0.986062i	$0.553208\pi$
$468$	8.81692	−	1.93562i	0.407562	−	0.0894742i
$469$	−5.90901	+	8.43894i	−0.272853	+	0.389674i
$470$	−2.45786	+	4.97113i	−0.113372	+	0.229301i
$471$	−15.0698	−	17.9594i	−0.694378	−	0.827527i
$472$	−15.5053	+	9.34343i	−0.713689	+	0.430066i
$473$	−10.3714	−	28.4953i	−0.476879	−	1.31021i
$474$	−2.09806	−	8.61246i	−0.0963670	−	0.395583i
$475$	10.0418	+	8.22198i	0.460752	+	0.377250i
$476$	−22.2198	−	42.8993i	−1.01844	−	1.96629i
$477$	1.89163	−	4.05662i	0.0866119	−	0.185740i
$478$	−15.0888	−	13.2600i	−0.690145	−	0.606500i
$479$	15.3736	+	18.3215i	0.702438	+	0.837132i	0.992800	−	0.119784i	$-0.0382203\pi$
$479$	15.3736	+	18.3215i	0.702438	+	0.837132i	−0.290362	+	0.956917i	$0.593776\pi$
$480$	15.3159	+	4.54987i	0.699073	+	0.207672i
$481$	−2.66131	−	15.0931i	−0.121345	−	0.688184i
$482$	−7.31317	−	0.167109i	−0.333106	−	0.00761159i
$483$	18.2686	−	4.89506i	0.831251	−	0.222733i
$484$	−3.34691	+	0.433618i	−0.152132	+	0.0197099i
$485$	−20.2334	−	43.3907i	−0.918751	−	1.97027i
$486$	1.35731	+	0.397136i	0.0615687	+	0.0180145i
$487$	9.21230	−	5.31872i	0.417449	−	0.241014i	−0.276536	−	0.961003i	$-0.589187\pi$
$487$	9.21230	−	5.31872i	0.417449	−	0.241014i	0.693985	+	0.719989i	$0.255853\pi$
$488$	−13.2010	−	10.6621i	−0.597581	−	0.482652i
$489$	−9.66394	−	8.10901i	−0.437018	−	0.366702i
$490$	34.5451	−	47.0120i	1.56059	−	2.12379i
$491$	−14.6408	+	10.2516i	−0.660728	+	0.462647i	−0.855225	−	0.518256i	$-0.826581\pi$
$491$	−14.6408	+	10.2516i	−0.660728	+	0.462647i	0.194497	+	0.980903i	$0.437692\pi$
$492$	−0.0337423	−	0.811158i	−0.00152122	−	0.0365698i
$493$	13.8224	−	13.8224i	0.622530	−	0.622530i
$494$	−2.72403	+	27.6891i	−0.122560	+	1.24579i
$495$			8.61920i			0.387404i
$496$	5.39116	−	19.7936i	0.242070	−	0.888758i
$497$	−52.3574	−	9.23202i	−2.34855	−	0.414113i
$498$	−13.3140	+	2.03518i	−0.596614	+	0.0911988i
$499$	−0.234602	+	0.0205250i	−0.0105022	+	0.000918827i	−0.0924057	−	0.995721i	$-0.529456\pi$
$499$	−0.234602	+	0.0205250i	−0.0105022	+	0.000918827i	0.0819034	+	0.996640i	$0.473900\pi$
$500$	11.3243	+	1.51460i	0.506437	+	0.0677350i
$501$	−7.64749	−	2.04914i	−0.341665	−	0.0915487i
$502$	−35.5528	−	10.4024i	−1.58680	−	0.464283i
$503$	16.6087	+	6.04509i	0.740547	+	0.269537i	0.684622	−	0.728898i	$-0.259967\pi$
$503$	16.6087	+	6.04509i	0.740547	+	0.269537i	0.0559247	+	0.998435i	$0.482189\pi$
$504$	−12.0172	−	5.33206i	−0.535288	−	0.237509i
$505$	41.6113	+	24.0243i	1.85168	+	1.06907i
$506$	12.6974	−	12.1301i	0.564467	−	0.539247i
$507$	−6.03813	−	4.22794i	−0.268163	−	0.187770i
$508$	7.33343	−	32.7595i	0.325368	−	1.45347i
$509$	−0.594259	+	6.79241i	−0.0263401	+	0.301068i	0.971585	+	0.236689i	$0.0760623\pi$
$509$	−0.594259	+	6.79241i	−0.0263401	+	0.301068i	−0.997926	+	0.0643791i	$0.979493\pi$
$510$	13.7030	−	15.5928i	0.606778	−	0.690462i
$511$	7.00609	+	19.2491i	0.309931	+	0.851529i
$512$	−4.61988	+	22.1508i	−0.204172	+	0.978935i
$513$	−2.45696	+	3.60047i	−0.108477	+	0.158964i
$514$	−14.1608	+	23.2823i	−0.624608	+	1.02694i
$515$	16.3489	+	7.62363i	0.720420	+	0.335937i
$516$	5.93714	+	18.9663i	0.261368	+	0.834945i
$517$	0.369257	−	4.22062i	0.0162399	−	0.185623i
$518$	−9.89295	+	20.0089i	−0.434671	+	0.879143i
$519$	−1.78199	−	10.1062i	−0.0782207	−	0.443612i
$520$	−15.8475	−	32.3873i	−0.694958	−	1.42028i
$521$	−7.98746	+	13.8347i	−0.349937	+	0.606109i	−0.986238	−	0.165332i	$-0.947130\pi$
$521$	−7.98746	+	13.8347i	−0.349937	+	0.606109i	0.636301	+	0.771441i	$0.280464\pi$
$522$	0.584560	−	5.28726i	0.0255855	−	0.231417i
$523$	17.8993	−	8.34660i	0.782683	−	0.364971i	0.0101524	−	0.999948i	$-0.496768\pi$
$523$	17.8993	−	8.34660i	0.782683	−	0.364971i	0.772531	+	0.634977i	$0.218991\pi$
$524$	10.8353	−	9.88776i	0.473343	−	0.431949i
$525$	13.3681	+	3.58198i	0.583433	+	0.156330i
$526$	−5.04657	+	12.9378i	−0.220041	+	0.564114i
$527$	−20.4175	−	17.1323i	−0.889401	−	0.746296i
$528$	−12.1644	+	1.01378i	−0.529389	+	0.0441190i
$529$	−1.11895	+	6.34589i	−0.0486501	+	0.275908i
$530$	−17.5316	−	3.50601i	−0.761522	−	0.152292i
$531$	4.52572	+	4.52572i	0.196399	+	0.196399i
$532$	27.0763	−	30.1478i	1.17391	−	1.30707i
$533$	−1.29552	+	1.29552i	−0.0561152	+	0.0561152i
$534$	−6.83850	−	10.2574i	−0.295931	−	0.443880i
$535$	−49.5634	−	8.73936i	−2.14281	−	0.377836i
$536$	0.972772	−	6.19290i	0.0420174	−	0.267492i
$537$	3.62403	−	4.31895i	0.156388	−	0.186376i
$538$	6.04356	+	13.7735i	0.260557	+	0.593818i
$539$	−11.5358	+	43.0520i	−0.496880	+	1.85438i
$540$	0.258023	−	5.64298i	0.0111035	−	0.242835i
$541$	2.63805	+	5.65732i	0.113419	+	0.243227i	0.954821	−	0.297183i	$-0.0960470\pi$
$541$	2.63805	+	5.65732i	0.113419	+	0.243227i	−0.841402	+	0.540410i	$0.818269\pi$
$542$	−10.9151	+	8.74182i	−0.468843	+	0.375493i
$543$	−5.99536	−	3.46142i	−0.257286	−	0.148544i
$544$	23.6182	+	17.5052i	1.01262	+	0.750531i
$545$	1.55717	−	0.274571i	0.0667018	−	0.0117613i
$546$	9.50790	+	28.1044i	0.406900	+	1.20276i
$547$	−9.49180	−	0.830425i	−0.405840	−	0.0355064i	−0.117592	−	0.993062i	$-0.537517\pi$
$547$	−9.49180	−	0.830425i	−0.405840	−	0.0355064i	−0.288248	+	0.957556i	$0.593073\pi$
$548$	−9.23198	−	29.4917i	−0.394371	−	1.25983i
$549$	−2.53548	+	5.43735i	−0.108211	+	0.232060i
$550$	12.4846	−	3.04135i	0.532347	−	0.129684i
$551$	14.9420	+	6.74959i	0.636550	+	0.287542i
$552$	−8.67608	+	7.56143i	−0.369279	+	0.321836i
$553$	27.3778	−	9.96470i	1.16422	−	0.423742i
$554$	−0.129065	−	2.00071i	−0.00548343	−	0.0850022i
$555$	−9.55419	−	0.835883i	−0.405553	−	0.0354813i
$556$	30.5257	−	19.3588i	1.29458	−	0.820995i
$557$	10.0753	−	14.3891i	0.426906	−	0.609685i	−0.546864	−	0.837222i	$-0.684178\pi$
$557$	10.0753	−	14.3891i	0.426906	−	0.609685i	0.973769	+	0.227537i	$0.0730673\pi$
$558$	−7.25113	−	0.165691i	−0.306965	−	0.00701425i
$559$	22.4249	−	38.8411i	0.948472	−	1.64280i
$560$	−9.33188	+	51.6781i	−0.394344	+	2.18380i
$561$	−5.42414	+	14.9027i	−0.229008	+	0.629193i
$562$	33.8424	−	18.5213i	1.42756	−	0.781272i
$563$	5.88969	−	21.9806i	0.248221	−	0.926373i	−0.723516	−	0.690307i	$-0.757475\pi$
$563$	5.88969	−	21.9806i	0.248221	−	0.926373i	0.971737	−	0.236065i	$-0.0758580\pi$
$564$	−0.368100	+	2.75219i	−0.0154998	+	0.115888i
$565$	−0.534125	−	6.10508i	−0.0224708	−	0.256842i
$566$	33.6928	+	24.7579i	1.41621	+	1.04065i
$567$	−0.807146	+	4.57755i	−0.0338969	+	0.192239i
$568$	31.0865	−	8.95680i	1.30436	−	0.375819i
$569$	23.7517			0.995724			0.497862	−	0.867256i	$-0.334119\pi$
$569$	23.7517			0.995724			0.497862	+	0.867256i	$0.334119\pi$
$570$	16.2958	+	6.13122i	0.682554	+	0.256808i
$571$	13.0925	+	13.0925i	0.547906	+	0.547906i	0.925835	−	0.377929i	$-0.123364\pi$
$571$	13.0925	+	13.0925i	0.547906	+	0.547906i	−0.377929	+	0.925835i	$0.623364\pi$
$572$	20.2713	+	18.6522i	0.847587	+	0.779888i
$573$	8.10562	+	11.5760i	0.338617	+	0.483596i
$574$	2.63774	−	0.403207i	0.110097	−	0.0168295i
$575$	7.78741	−	9.28068i	0.324758	−	0.387031i
$576$	7.99439	−	0.299567i	0.333100	−	0.0124820i
$577$	5.29504	+	9.17128i	0.220435	+	0.381805i	0.954940	−	0.296798i	$-0.0959188\pi$
$577$	5.29504	+	9.17128i	0.220435	+	0.381805i	−0.734505	+	0.678604i	$0.762585\pi$
$578$	12.4155	−	6.79477i	0.516418	−	0.282625i
$579$	6.61028	−	3.08242i	0.274714	−	0.128101i
$580$	−21.0718	+	2.73001i	−0.874958	+	0.113358i
$581$	−11.4574	−	42.7596i	−0.475333	−	1.77397i
$582$	−16.5591	−	17.3335i	−0.686396	−	0.718498i
$583$	13.4516	−	2.37188i	0.557109	−	0.0982333i
$584$	−8.97749	−	8.64739i	−0.371491	−	0.357831i
$585$	−9.76550	+	8.19423i	−0.403754	+	0.338790i
$586$	7.84075	−	0.505802i	0.323898	−	0.0208945i
$587$	27.3187	+	12.7389i	1.12756	+	0.525791i	0.894677	−	0.446713i	$-0.147405\pi$
$587$	27.3187	+	12.7389i	1.12756	+	0.525791i	0.232886	+	0.972504i	$0.425183\pi$
$588$	8.84125	−	27.8408i	0.364607	−	1.14813i
$589$	7.39230	−	21.0977i	0.304594	−	0.869316i
$590$	13.2851	−	21.8423i	0.546937	−	0.899235i
$591$	−3.23827	+	1.17864i	−0.133205	+	0.0484826i
$592$	0.0559467	−	13.5823i	0.00229939	−	0.558230i
$593$	1.66251	−	1.39501i	0.0682710	−	0.0572861i	−0.608014	−	0.793927i	$-0.708033\pi$
$593$	1.66251	−	1.39501i	0.0682710	−	0.0572861i	0.676285	+	0.736640i	$0.263589\pi$
$594$	1.38302	+	4.08808i	0.0567461	+	0.167736i
$595$	55.8886	+	39.1336i	2.29121	+	1.60432i
$596$	3.26116	+	14.8549i	0.133582	+	0.608479i
$597$	17.0342	−	4.56431i	0.697165	−	0.186805i
$598$	25.8146	+	2.85406i	1.05564	+	0.116711i
$599$	5.59619	−	15.3754i	0.228654	−	0.628223i	−0.771312	−	0.636457i	$-0.780399\pi$
$599$	5.59619	−	15.3754i	0.228654	−	0.628223i	0.999966	+	0.00823493i	$0.00262129\pi$
$600$	−8.26474	+	1.61743i	−0.337406	+	0.0660314i
$601$	−11.2092	−	19.4149i	−0.457232	−	0.791948i	0.541582	−	0.840648i	$-0.317826\pi$
$601$	−11.2092	−	19.4149i	−0.457232	−	0.791948i	−0.998813	+	0.0486996i	$0.984492\pi$
$602$	−59.8156	+	26.2460i	−2.43790	+	1.06971i
$603$	−2.20793	+	0.193169i	−0.0899140	+	0.00786645i
$604$	−17.9323	+	43.0416i	−0.729657	+	1.75134i
$605$	3.90414	−	2.73371i	0.158726	−	0.111141i
$606$	23.5911	+	4.71782i	0.958323	+	0.191648i
$607$	−46.3874			−1.88281			−0.941404	−	0.337282i	$-0.890492\pi$
$607$	−46.3874			−1.88281			−0.941404	+	0.337282i	$0.890492\pi$
$608$	−6.73641	+	23.7196i	−0.273198	+	0.961958i
$609$	17.4838			0.708479
$610$	23.4987	+	4.69934i	0.951433	+	0.190271i
$611$	5.13299	−	3.59416i	0.207659	−	0.145404i
$612$	3.99731	−	9.59442i	0.161582	−	0.387832i
$613$	−8.58622	+	0.751197i	−0.346794	+	0.0303405i	−0.259222	−	0.965818i	$-0.583466\pi$
$613$	−8.58622	+	0.751197i	−0.346794	+	0.0303405i	−0.0875717	+	0.996158i	$0.527911\pi$
$614$	−18.6797	+	8.19630i	−0.753850	+	0.330776i
$615$	0.573262	+	0.992918i	0.0231161	+	0.0400383i
$616$	−7.70543	−	39.3731i	−0.310461	−	1.58639i
$617$	12.5838	−	34.5737i	0.506604	−	1.39188i	−0.378115	−	0.925759i	$-0.623428\pi$
$617$	12.5838	−	34.5737i	0.506604	−	1.39188i	0.884719	−	0.466125i	$-0.154350\pi$
$618$	8.97755	+	0.992559i	0.361130	+	0.0399266i
$619$	−26.2050	+	7.02161i	−1.05327	+	0.282222i	−0.743601	−	0.668623i	$-0.766884\pi$
$619$	−26.2050	+	7.02161i	−1.05327	+	0.282222i	−0.309666	+	0.950845i	$0.600217\pi$
$620$	6.21224	+	28.2973i	0.249490	+	1.13645i
$621$	3.33307	+	2.33384i	0.133752	+	0.0936539i
$622$	−10.6858	−	31.5862i	−0.428462	−	1.26649i
$623$	31.0393	−	26.0451i	1.24356	−	1.04347i
$624$	−12.7133	−	12.8184i	−0.508938	−	0.513148i
$625$	−29.1512	+	10.6102i	−1.16605	+	0.424406i
$626$	12.5316	−	20.6035i	0.500862	−	0.823483i
$627$	−13.3009	+	0.160273i	−0.531185	+	0.00640069i
$628$	−14.1918	+	44.6895i	−0.566314	+	1.78330i
$629$	−15.9933	−	7.45780i	−0.637695	−	0.297362i
$630$	18.5279	−	1.19523i	0.738171	−	0.0476189i
$631$	4.02054	−	3.37363i	0.160055	−	0.134302i	−0.559243	−	0.829004i	$-0.688908\pi$
$631$	4.02054	−	3.37363i	0.160055	−	0.134302i	0.719298	+	0.694702i	$0.244464\pi$
$632$	−12.2991	+	12.7686i	−0.489232	+	0.507908i
$633$	23.1014	−	4.07341i	0.918200	−	0.161903i
$634$	−6.35157	−	6.64863i	−0.252253	−	0.264051i
$635$	12.2703	+	45.7932i	0.486930	+	1.81725i
$636$	−8.87777	+	1.15018i	−0.352026	+	0.0456078i
$637$	−59.7447	+	27.8594i	−2.36717	+	1.10383i
$638$	14.2401	−	7.79331i	0.563770	−	0.308540i
$639$	−5.71893	−	9.90548i	−0.226237	−	0.391855i
$640$	−8.72053	−	30.7419i	−0.344709	−	1.21518i
$641$	−7.09436	+	8.45472i	−0.280210	+	0.333942i	−0.887731	−	0.460362i	$-0.847720\pi$
$641$	−7.09436	+	8.45472i	−0.280210	+	0.333942i	0.607521	+	0.794304i	$0.292164\pi$
$642$	−24.9102	+	3.80779i	−0.983126	+	0.150281i
$643$	21.7835	+	31.1101i	0.859058	+	1.22686i	0.972403	+	0.233307i	$0.0749546\pi$
$643$	21.7835	+	31.1101i	0.859058	+	1.22686i	−0.113345	+	0.993556i	$0.536157\pi$
$644$	−27.8357	−	25.6124i	−1.09688	−	1.00927i
$645$	−19.8458	−	19.8458i	−0.781429	−	0.781429i
$646$	24.3172	+	20.8560i	0.956746	+	0.820570i
$647$	−3.20936			−0.126173			−0.0630865	−	0.998008i	$-0.520094\pi$
$647$	−3.20936			−0.126173			−0.0630865	+	0.998008i	$0.520094\pi$
$648$	−0.783083	−	2.71786i	−0.0307624	−	0.106768i
$649$	−3.39162	+	19.2348i	−0.133133	+	0.755033i
$650$	15.3149	+	11.2536i	0.600701	+	0.441404i
$651$	−2.07769	−	23.7482i	−0.0814313	−	0.930764i
$652$	−3.34479	+	25.0081i	−0.130992	+	0.979391i
$653$	−6.80312	+	25.3896i	−0.266227	+	0.993571i	0.695269	+	0.718750i	$0.255285\pi$
$653$	−6.80312	+	25.3896i	−0.266227	+	0.993571i	−0.961495	+	0.274821i	$0.911381\pi$
$654$	0.694507	−	0.380090i	0.0271574	−	0.0148627i
$655$	−7.08511	+	19.4662i	−0.276838	+	0.760607i
$656$	−1.33390	+	0.925840i	−0.0520799	+	0.0361480i
$657$	−2.20350	+	3.81657i	−0.0859666	+	0.148898i
$658$	−9.12391	−	0.208485i	−0.355687	−	0.00812758i
$659$	25.0661	−	35.7980i	0.976435	−	1.39449i	0.0582674	−	0.998301i	$-0.481442\pi$
$659$	25.0661	−	35.7980i	0.976435	−	1.39449i	0.918167	−	0.396192i	$-0.129669\pi$
$660$	14.5578	−	9.23222i	0.566660	−	0.359364i
$661$	24.9149	+	2.17977i	0.969078	+	0.0847834i	0.560691	−	0.828025i	$-0.310536\pi$
$661$	24.9149	+	2.17977i	0.969078	+	0.0847834i	0.408388	+	0.912809i	$0.366091\pi$
$662$	1.25088	+	19.3907i	0.0486169	+	0.753641i
$663$	−22.0414	+	8.02241i	−0.856017	+	0.311565i
$664$	17.6983	+	20.3073i	0.686828	+	0.788075i
$665$	−14.1440	+	55.4502i	−0.548481	+	2.15027i
$666$	−4.66567	+	1.13659i	−0.180791	+	0.0440420i
$667$	6.46819	−	13.8711i	0.250449	−	0.537090i
$668$	4.73042	+	15.1114i	0.183025	+	0.584679i
$669$	1.99225	+	0.174299i	0.0770248	+	0.00673880i
$670$	2.83706	+	8.38607i	0.109605	+	0.323982i
$671$	−18.0301	+	3.17919i	−0.696043	+	0.122731i
$672$	3.86607	+	26.0082i	0.149137	+	1.00329i
$673$	−8.76355	−	5.05964i	−0.337810	−	0.195035i	0.321493	−	0.946912i	$-0.395815\pi$
$673$	−8.76355	−	5.05964i	−0.337810	−	0.195035i	−0.659303	+	0.751877i	$0.729149\pi$
$674$	24.4777	−	19.6040i	0.942844	−	0.755117i
$675$	1.25833	+	2.69849i	0.0484330	+	0.103865i
$676$	−0.673386	+	14.7270i	−0.0258995	+	0.566423i
$677$	−13.1419	+	49.0463i	−0.505084	+	1.88500i	−0.0411044	+	0.999155i	$0.513088\pi$
$677$	−13.1419	+	49.0463i	−0.505084	+	1.88500i	−0.463980	+	0.885846i	$0.653579\pi$
$678$	−1.23295	−	2.80993i	−0.0473510	−	0.107915i
$679$	50.6451	−	60.3565i	1.94358	−	2.31627i
$680$	−41.0137	−	6.44239i	−1.57281	−	0.247054i
$681$	8.27476	+	1.45906i	0.317090	+	0.0559114i
$682$	−12.2779	−	18.4161i	−0.470143	−	0.705190i
$683$	14.8725	−	14.8725i	0.569080	−	0.569080i	−0.362790	−	0.931871i	$-0.618176\pi$
$683$	14.8725	−	14.8725i	0.569080	−	0.569080i	0.931871	+	0.362790i	$0.118176\pi$
$684$	8.71286	+	0.293242i	0.333145	+	0.0112124i
$685$	30.8594	+	30.8594i	1.17908	+	1.17908i
$686$	49.0238	+	9.80393i	1.87174	+	0.374316i
$687$	4.02607	−	22.8330i	0.153604	−	0.871133i
$688$	25.6745	−	30.3430i	0.978833	−	1.15682i
$689$	15.4757	+	12.9857i	0.589578	+	0.494714i
$690$	5.90622	−	15.1416i	0.224846	−	0.576433i
$691$	15.4237	+	4.13277i	0.586745	+	0.157218i	0.539965	−	0.841687i	$-0.318437\pi$
$691$	15.4237	+	4.13277i	0.586745	+	0.157218i	0.0467798	+	0.998905i	$0.485104\pi$
$692$	−15.1605	+	13.8347i	−0.576316	+	0.525917i
$693$	−12.8556	+	5.99466i	−0.488343	+	0.227718i
$694$	1.72969	−	15.6448i	0.0656581	−	0.593868i
$695$	−25.5235	+	44.2080i	−0.968162	+	1.67691i
$696$	−9.55627	+	4.67599i	−0.362230	+	0.177243i
$697$	0.366324	+	2.07753i	0.0138755	+	0.0786920i
$698$	16.9718	−	34.3263i	0.642393	−	1.29927i
$699$	1.61501	−	18.4597i	0.0610853	−	0.698209i
$700$	−8.26898	−	26.4154i	−0.312538	−	0.998409i
$701$	3.05224	+	1.42328i	0.115282	+	0.0537567i	0.479403	−	0.877595i	$-0.340853\pi$
$701$	3.05224	+	1.42328i	0.115282	+	0.0537567i	−0.364122	+	0.931351i	$0.618631\pi$
$702$	−3.31693	+	5.45347i	−0.125190	+	0.205828i
$703$	1.11225	−	14.7593i	0.0419493	−	0.556656i
$704$	14.7419	+	19.4597i	0.555605	+	0.733417i
$705$	−1.34116	−	3.68482i	−0.0505111	−	0.138778i
$706$	22.4913	−	25.5932i	0.846472	−	0.963213i
$707$	−6.89169	+	78.7724i	−0.259189	+	2.96254i
$708$	2.79630	−	12.4915i	0.105091	−	0.469459i
$709$	−12.2283	−	8.56232i	−0.459242	−	0.321565i	0.320959	−	0.947093i	$-0.395995\pi$
$709$	−12.2283	−	8.56232i	−0.459242	−	0.321565i	−0.780202	+	0.625528i	$0.784884\pi$
$710$	−33.0351	+	31.5591i	−1.23979	+	1.18439i
$711$	5.42827	+	3.13401i	0.203576	+	0.117535i
$712$	−9.99977	+	22.5371i	−0.374757	+	0.844613i
$713$	−19.6097	−	7.13733i	−0.734388	−	0.267295i
$714$	32.7872	+	9.59325i	1.22703	+	0.359019i
$715$	−37.5767	−	10.0686i	−1.40529	−	0.376546i
$716$	−11.1765	−	1.49483i	−0.417684	−	0.0558645i
$717$	14.1498	−	1.23795i	0.528435	−	0.0462321i
$718$	34.0986	−	5.21234i	1.27255	−	0.194523i
$719$	−47.4615	−	8.36875i	−1.77002	−	0.312102i	−0.808839	−	0.588030i	$-0.799904\pi$
$719$	−47.4615	−	8.36875i	−1.77002	−	0.312102i	−0.961178	+	0.275929i	$0.911015\pi$
$720$	−9.80733	+	5.60853i	−0.365498	+	0.209018i
$721$			29.6868i			1.10559i
$722$	−9.15848	+	25.2611i	−0.340843	+	0.940120i
$723$	3.65754	−	3.65754i	0.136025	−	0.136025i
$724$	0.575451	+	13.8337i	0.0213865	+	0.514126i
$725$	9.17410	−	6.42378i	0.340718	−	0.238573i
$726$	1.41308	−	1.92305i	0.0524444	−	0.0713709i
$727$	−9.39115	−	7.88011i	−0.348298	−	0.292257i	0.451808	−	0.892115i	$-0.350779\pi$
$727$	−9.39115	−	7.88011i	−0.348298	−	0.292257i	−0.800106	+	0.599858i	$0.795224\pi$
$728$	37.2840	−	46.1620i	1.38184	−	1.71088i
$729$	−0.866025	+	0.500000i	−0.0320750	+	0.0185185i
$730$	16.8948	+	4.94326i	0.625304	+	0.182958i
$731$	−21.8246	−	46.8029i	−0.807211	−	1.73107i
$732$	11.8994	−	1.54167i	0.439816	−	0.0569816i
$733$	13.9245	−	3.73107i	0.514315	−	0.137810i	0.00767911	−	0.999971i	$-0.497556\pi$
$733$	13.9245	−	3.73107i	0.514315	−	0.137810i	0.506636	+	0.862160i	$0.330889\pi$
$734$	−29.9293	−	0.683896i	−1.10471	−	0.0252430i
$735$	7.16337	+	40.6255i	0.264225	+	1.49849i
$736$	22.0644	+	6.55462i	0.813303	+	0.241606i
$737$	−4.34754	−	5.18120i	−0.160144	−	0.190852i
$738$	0.431219	+	0.378956i	0.0158734	+	0.0139495i
$739$	−7.01944	+	15.0532i	−0.258214	+	0.553743i	−0.992088	−	0.125543i	$-0.959933\pi$
$739$	−7.01944	+	15.0532i	−0.258214	+	0.553743i	0.733874	+	0.679286i	$0.237710\pi$
$740$	8.82191	+	17.0323i	0.324300	+	0.626119i
$741$	−12.8267	−	14.9174i	−0.471199	−	0.548005i
$742$	−6.96397	−	28.5869i	−0.255655	−	1.04946i
$743$	11.7304	+	32.2289i	0.430346	+	1.18236i	0.945601	+	0.325328i	$0.105475\pi$
$743$	11.7304	+	32.2289i	0.430346	+	1.18236i	−0.515256	+	0.857037i	$0.672303\pi$
$744$	7.48700	+	12.4246i	0.274487	+	0.455507i
$745$	−13.8057	−	16.4530i	−0.505803	−	0.602792i
$746$	9.96911	−	20.1630i	0.364995	−	0.738220i
$747$	5.46260	−	7.80141i	0.199866	−	0.285439i
$748$	30.9805	−	6.80130i	1.13276	−	0.248680i
$749$	−21.4366	−	80.0024i	−0.783275	−	2.92322i
$750$	−6.30571	+	5.05020i	−0.230252	+	0.184407i
$751$	−10.4325	−	3.79711i	−0.380687	−	0.138559i	0.144587	−	0.989492i	$-0.453815\pi$
$751$	−10.4325	−	3.79711i	−0.380687	−	0.138559i	−0.525273	+	0.850933i	$0.676037\pi$
$752$	5.04270	−	2.32621i	0.183888	−	0.0848282i
$753$	22.6843	−	13.0968i	0.826663	−	0.477274i
$754$	22.3678	+	8.72487i	0.814586	+	0.317741i
$755$	−5.73908	−	65.5980i	−0.208867	−	2.38736i
$756$	8.59600	−	3.53986i	0.312634	−	0.128743i
$757$	21.2323	+	30.3228i	0.771700	+	1.10210i	0.991946	+	0.126658i	$0.0404250\pi$
$757$	21.2323	+	30.3228i	0.771700	+	1.10210i	−0.220246	+	0.975444i	$0.570686\pi$
$758$	−18.2546	+	12.1701i	−0.663036	+	0.442040i
$759$			12.4170i			0.450707i
$760$	−7.09917	−	34.0907i	−0.257514	−	1.23660i
$761$		−	2.92996i		−	0.106211i	−0.998589	−	0.0531054i	$-0.983088\pi$
$761$		−	2.92996i		−	0.106211i	0.998589	−	0.0531054i	$-0.0169119\pi$
$762$	13.1677	+	19.7508i	0.477015	+	0.715497i
$763$	1.49254	+	2.13156i	0.0540335	+	0.0771678i
$764$	10.8697	−	26.0897i	0.393252	−	0.943892i
$765$	1.27930	+	14.6225i	0.0462533	+	0.528677i
$766$	−6.96772	+	17.8630i	−0.251754	+	0.645415i
$767$	−25.0173	+	14.4438i	−0.903324	+	0.521534i
$768$	−9.06894	−	13.1816i	−0.327247	−	0.475650i
$769$	4.73001	+	1.72158i	0.170569	+	0.0620819i	0.425893	−	0.904774i	$-0.359960\pi$
$769$	4.73001	+	1.72158i	0.170569	+	0.0620819i	−0.255324	+	0.966855i	$0.582182\pi$
$770$	35.4182	+	44.2234i	1.27638	+	1.59370i
$771$	−4.98720	−	18.6125i	−0.179610	−	0.670312i
$772$	−12.2866	−	7.86306i	−0.442205	−	0.282998i
$773$	−13.8086	+	19.7208i	−0.496662	+	0.709306i	−0.986729	−	0.162378i	$-0.948083\pi$
$773$	−13.8086	+	19.7208i	−0.496662	+	0.709306i	0.490067	+	0.871685i	$0.336972\pi$
$774$	−12.5973	−	6.22843i	−0.452800	−	0.223876i
$775$	−9.81560	−	11.6978i	−0.352587	−	0.420196i
$776$	−11.5394	+	46.5345i	−0.414240	+	1.67049i
$777$	−5.39822	−	14.8315i	−0.193660	−	0.532077i
$778$	−33.5721	+	8.17841i	−1.20362	+	0.293210i
$779$	−1.52158	+	0.903102i	−0.0545162	+	0.0323570i
$780$	24.3000	+	7.71683i	0.870081	+	0.276307i
$781$	14.7512	−	31.6341i	0.527840	−	1.13196i
$782$	19.7407	−	22.4633i	0.705927	−	0.803285i
$783$	2.41780	+	2.88143i	0.0864053	+	0.102974i
$784$	−56.4930	+	14.8881i	−2.01761	+	0.531718i
$785$	−11.4985	−	65.2112i	−0.410399	−	2.32749i
$786$	−0.236950	+	10.3697i	−0.00845174	+	0.369873i
$787$	47.7983	−	12.8075i	1.70383	−	0.456539i	0.729929	−	0.683523i	$-0.239553\pi$
$787$	47.7983	−	12.8075i	1.70383	−	0.456539i	0.973898	+	0.226984i	$0.0728866\pi$
$788$	5.45930	+	4.20696i	0.194479	+	0.149867i
$789$	−4.14999	−	8.89969i	−0.147744	−	0.316837i
$790$	7.03076	−	24.0293i	0.250143	−	0.854924i
$791$	8.73428	−	5.04274i	0.310555	−	0.179299i
$792$	5.42334	−	6.71475i	0.192710	−	0.238598i
$793$	−20.7431	−	17.4055i	−0.736609	−	0.618088i
$794$	−20.8774	−	15.3410i	−0.740910	−	0.544431i
$795$	10.3558	−	7.25123i	0.367284	−	0.257175i
$796$	−25.9548	−	23.8818i	−0.919945	−	0.846466i
$797$	36.7749	−	36.7749i	1.30264	−	1.30264i	0.376026	−	0.926609i	$-0.377290\pi$
$797$	36.7749	−	36.7749i	1.30264	−	1.30264i	0.926609	−	0.376026i	$-0.122710\pi$
$798$	2.18896	+	28.5695i	0.0774883	+	1.01135i
$799$		−	7.21511i		−	0.255252i
$800$	11.5844	+	12.2266i	0.409570	+	0.432276i
$801$	8.58476	+	1.51372i	0.303328	+	0.0534848i
$802$	1.60777	+	10.5178i	0.0567722	+	0.371398i
$803$	−13.3974	+	1.17212i	−0.472785	+	0.0413633i
$804$	2.69123	+	3.52227i	0.0949123	+	0.124221i
$805$	51.5986	+	13.8258i	1.81861	+	0.487296i
$806$	9.19287	−	31.4189i	0.323805	−	1.10668i
$807$	−9.99424	−	3.63761i	−0.351814	−	0.128050i
$808$	−17.3006	−	44.8985i	−0.608633	−	1.57953i
$809$	4.84633	+	2.79803i	0.170388	+	0.0983735i	0.582769	−	0.812638i	$-0.301969\pi$
$809$	4.84633	+	2.79803i	0.170388	+	0.0983735i	−0.412381	+	0.911012i	$0.635303\pi$
$810$	2.75918	+	2.88822i	0.0969477	+	0.101482i
$811$	−45.1104	−	31.5866i	−1.58404	−	1.10916i	−0.938419	−	0.345499i	$-0.887710\pi$
$811$	−45.1104	−	31.5866i	−1.58404	−	1.10916i	−0.645621	−	0.763658i	$-0.723401\pi$
$812$	−18.7273	−	29.5300i	−0.657199	−	1.03630i
$813$	0.861825	−	9.85071i	0.0302255	−	0.345479i
$814$	−11.0078	−	9.67363i	−0.385822	−	0.339061i
$815$	−12.1866	−	33.4825i	−0.426879	−	1.17284i
$816$	−20.4865	+	3.52538i	−0.717172	+	0.123413i
$817$	30.2564	−	30.9945i	1.05854	−	1.08436i
$818$	34.6918	+	21.1004i	1.21297	+	0.737758i
$819$	−19.0137	−	8.86621i	−0.664391	−	0.309811i
$820$	1.06300	−	2.03177i	0.0371215	−	0.0709526i
$821$	−2.10156	+	24.0210i	−0.0733451	+	0.838338i	0.867043	+	0.498234i	$0.166018\pi$
$821$	−2.10156	+	24.0210i	−0.0733451	+	0.838338i	−0.940388	+	0.340104i	$0.889538\pi$
$822$	19.5882	+	9.68493i	0.683218	+	0.337801i
$823$	3.02831	+	17.1744i	0.105560	+	0.598662i	0.990995	+	0.133898i	$0.0427496\pi$
$823$	3.02831	+	17.1744i	0.105560	+	0.598662i	−0.885435	+	0.464764i	$0.846139\pi$
$824$	−7.93964	−	16.2262i	−0.276590	−	0.565265i
$825$	−4.54307	+	7.86884i	−0.158170	+	0.273958i
$826$	41.8178	+	4.62337i	1.45503	+	0.160868i
$827$	−33.5915	+	15.6640i	−1.16809	+	0.544690i	−0.907209	−	0.420680i	$-0.861791\pi$
$827$	−33.5915	+	15.6640i	−1.16809	+	0.544690i	−0.260883	+	0.965370i	$0.584014\pi$
$828$	0.371712	−	8.12937i	0.0129179	−	0.282515i
$829$	−11.8228	−	3.16790i	−0.410621	−	0.110026i	0.0475943	−	0.998867i	$-0.484845\pi$
$829$	−11.8228	−	3.16790i	−0.410621	−	0.110026i	−0.458216	+	0.888841i	$0.651511\pi$
$830$	−35.4406	−	13.8241i	−1.23016	−	0.479842i
$831$	1.08599	+	0.911253i	0.0376726	+	0.0316110i
$832$	−8.03276	+	35.2027i	−0.278486	+	1.22043i
$833$	−13.1805	+	74.7501i	−0.456676	+	2.58994i
$834$	−5.01223	+	25.0633i	−0.173559	+	0.867871i
$835$	−15.8122	−	15.8122i	−0.547204	−	0.547204i
$836$	14.5176	+	22.2934i	0.502100	+	0.771033i
$837$	3.62651	−	3.62651i	0.125351	−	0.125351i
$838$	−23.6733	+	15.7827i	−0.817780	+	0.545206i
$839$	−7.59455	−	1.33912i	−0.262193	−	0.0462317i	0.0410062	−	0.999159i	$-0.486944\pi$
$839$	−7.59455	−	1.33912i	−0.262193	−	0.0462317i	−0.303199	+	0.952927i	$0.598055\pi$
$840$	−21.8644	−	30.0133i	−0.754394	−	1.03556i
$841$	−9.54642	+	11.3770i	−0.329187	+	0.392310i
$842$	4.46510	−	1.95920i	0.153877	−	0.0675186i
$843$	−7.06046	+	26.3500i	−0.243175	+	0.907542i
$844$	−31.6244	−	34.6550i	−1.08856	−	1.19288i
$845$	−8.79869	−	18.8689i	−0.302684	−	0.649109i
$846$	−1.22737	−	1.53250i	−0.0421979	−	0.0526886i
$847$	6.79267	+	3.92175i	0.233399	+	0.134753i
$848$	11.4518	+	13.7625i	0.393258	+	0.472606i
$849$	−29.1157	+	5.13388i	−0.999247	+	0.176194i
$850$	20.7288	−	7.01269i	0.710993	−	0.240533i
$851$	−13.7639	−	1.20419i	−0.471821	−	0.0412790i
$852$	−10.6046	+	20.2692i	−0.363308	+	0.694412i
$853$	11.4347	−	24.5219i	0.391518	−	0.839612i	−0.607458	−	0.794352i	$-0.707811\pi$
$853$	11.4347	−	24.5219i	0.391518	−	0.839612i	0.998975	−	0.0452602i	$-0.0144117\pi$
$854$	9.33426	+	38.3168i	0.319412	+	1.31117i
$855$	−11.0945	+	5.33711i	−0.379422	+	0.182525i
$856$	33.1132	+	37.9945i	1.13179	+	1.29862i
$857$	−45.5947	+	16.5951i	−1.55749	+	0.566878i	−0.970159	−	0.242471i	$-0.922042\pi$
$857$	−45.5947	+	16.5951i	−1.55749	+	0.566878i	−0.587327	+	0.809350i	$0.699820\pi$
$858$	−19.4382	+	1.25395i	−0.663609	+	0.0428090i
$859$	−42.6959	−	3.73541i	−1.45677	−	0.127451i	−0.668926	−	0.743329i	$-0.733246\pi$
$859$	−42.6959	−	3.73541i	−1.45677	−	0.127451i	−0.787841	+	0.615879i	$0.788801\pi$
$860$	−12.2621	+	54.7768i	−0.418135	+	1.86787i
$861$	−1.08224	+	1.54560i	−0.0368826	+	0.0526739i
$862$	−0.495716	+	21.6940i	−0.0168842	+	0.738901i
$863$	−6.49176	+	11.2441i	−0.220982	+	0.382752i	−0.955106	−	0.296263i	$-0.904260\pi$
$863$	−6.49176	+	11.2441i	−0.220982	+	0.382752i	0.734124	+	0.679015i	$0.237593\pi$
$864$	−3.75167	+	4.23379i	−0.127634	+	0.144036i
$865$	9.91332	−	27.2366i	0.337063	−	0.926073i
$866$	−25.7956	−	47.1341i	−0.876569	−	1.60168i
$867$	−2.59022	+	9.66685i	−0.0879686	+	0.328303i
$868$	−37.8850	+	28.9464i	−1.28590	+	0.982505i
$869$	1.66710	+	19.0550i	0.0565525	+	0.646397i
$870$	8.89662	−	12.1073i	0.301624	−	0.410476i
$871$	1.73708	−	9.85148i	0.0588587	−	0.333805i
$872$	−1.38587	−	0.765894i	−0.0469315	−	0.0259365i
$873$	16.9507			0.573695
$874$	23.4759	+	8.83273i	0.794085	+	0.298772i
$875$	−18.7757	−	18.7757i	−0.634736	−	0.634736i
$876$	8.80637	−	0.366324i	0.297540	−	0.0123770i
$877$	13.0027	+	18.5697i	0.439068	+	0.627055i	0.976311	−	0.216373i	$-0.0694228\pi$
$877$	13.0027	+	18.5697i	0.439068	+	0.627055i	−0.537242	+	0.843428i	$0.680534\pi$
$878$	−6.45752	−	42.2444i	−0.217931	−	1.42568i
$879$	−3.57118	+	4.25597i	−0.120453	+	0.143550i
$880$	−31.1863	−	14.6991i	−1.05129	−	0.495507i
$881$	−16.1507	−	27.9738i	−0.544130	−	0.942461i	−0.998661	−	0.0517299i	$-0.983527\pi$
$881$	−16.1507	−	27.9738i	−0.544130	−	0.942461i	0.454531	−	0.890731i	$-0.349807\pi$
$882$	9.91628	+	18.1192i	0.333899	+	0.610106i
$883$	−30.7889	+	14.3571i	−1.03613	+	0.483155i	−0.864830	−	0.502065i	$-0.832574\pi$
$883$	−30.7889	+	14.3571i	−1.03613	+	0.483155i	−0.171298	+	0.985219i	$0.554796\pi$
$884$	37.1588	+	28.6348i	1.24979	+	0.963091i
$885$	4.67876	+	17.4614i	0.157275	+	0.586958i
$886$	−9.05574	+	8.65113i	−0.304233	+	0.290640i
$887$	−1.70722	+	0.301029i	−0.0573229	+	0.0101076i	−0.202236	−	0.979337i	$-0.564821\pi$
$887$	−1.70722	+	0.301029i	−0.0573229	+	0.0101076i	0.144913	+	0.989444i	$0.453710\pi$
$888$	6.91720	+	6.66285i	0.232126	+	0.223591i
$889$	−59.7669	+	50.1504i	−2.00452	+	1.68199i
$890$	−2.24153	−	34.7474i	−0.0751363	−	1.16473i
$891$	−2.76573	−	1.28968i	−0.0926555	−	0.0432060i
$892$	−1.83955	−	3.55159i	−0.0615928	−	0.118916i
$893$	5.66135	−	2.13816i	0.189450	−	0.0715508i
$894$	−9.18807	−	5.58841i	−0.307295	−	0.186904i
$895$	14.9638	−	5.44638i	0.500185	−	0.182053i
$896$	39.7867	−	34.3878i	1.32918	−	1.14882i
$897$	−14.0683	+	11.8047i	−0.469728	+	0.394149i
$898$	−23.5488	+	7.96672i	−0.785835	+	0.265853i
$899$	−15.8024	−	11.0649i	−0.527038	−	0.369036i
$900$	3.20991	−	5.01572i	0.106997	−	0.167191i
$901$	22.4687	−	6.02046i	0.748540	−	0.200571i
$902$	−0.192513	+	1.74125i	−0.00640998	+	0.0579774i
$903$	15.7974	−	43.4030i	0.525705	−	1.44436i
$904$	−3.42531	+	5.09221i	−0.113924	+	0.169364i
$905$	−9.77658	−	16.9335i	−0.324984	−	0.562890i
$906$	−13.2478	−	30.1922i	−0.440128	−	1.00307i
$907$	−22.5137	+	1.96970i	−0.747556	+	0.0654027i	−0.454566	−	0.890713i	$-0.650206\pi$
$907$	−22.5137	+	1.96970i	−0.747556	+	0.0654027i	−0.292990	+	0.956116i	$0.594650\pi$
$908$	−6.39894	−	15.5388i	−0.212356	−	0.515675i
$909$	−13.9352	+	9.75752i	−0.462201	+	0.323637i
$910$	−16.4329	+	82.1716i	−0.544747	+	2.72396i
$911$	−17.5046			−0.579954			−0.289977	−	0.957034i	$-0.593648\pi$
$911$	−17.5046			−0.579954			−0.289977	+	0.957034i	$0.593648\pi$
$912$	−8.83727	−	15.0301i	−0.292631	−	0.497695i
$913$	29.0632			0.961850
$914$	2.63576	−	13.1799i	0.0871833	−	0.435954i
$915$	−13.8806	+	9.71930i	−0.458878	+	0.321310i
$916$	−42.8772	+	17.6569i	−1.41670	+	0.583402i
$917$	−33.9616	+	2.97126i	−1.12151	+	0.0981196i
$918$	2.95307	+	6.73016i	0.0974659	+	0.222128i
$919$	22.3505	+	38.7122i	0.737276	+	1.27700i	0.953718	+	0.300704i	$0.0972215\pi$
$919$	22.3505	+	38.7122i	0.737276	+	1.27700i	−0.216442	+	0.976296i	$0.569445\pi$
$920$	−31.9004	+	6.24300i	−1.05173	+	0.205826i
$921$	4.93333	−	13.5542i	0.162559	−	0.446627i
$922$	−3.73765	+	33.8065i	−0.123093	+	1.11336i
$923$	49.8651	−	13.3613i	1.64133	−	0.439793i
$924$	23.8949	+	15.2920i	0.786083	+	0.503069i
$925$	−8.28185	−	5.79901i	−0.272305	−	0.190670i
$926$	32.3130	−	10.9317i	1.06187	−	0.359237i
$927$	−4.89255	+	4.10534i	−0.160692	+	0.134837i
$928$	18.1337	+	11.1319i	0.595266	+	0.365423i
$929$	−40.1222	+	14.6033i	−1.31637	+	0.479118i	−0.902292	−	0.431125i	$-0.858117\pi$
$929$	−40.1222	+	14.6033i	−1.31637	+	0.479118i	−0.414075	+	0.910243i	$0.635895\pi$
$930$	−17.5025	−	10.6455i	−0.573930	−	0.349079i
$931$	−62.5588	+	11.8097i	−2.05028	+	0.387048i
$932$	−32.9081	+	17.0448i	−1.07794	+	0.558322i
$933$	21.3692	+	9.96464i	0.699597	+	0.326228i
$934$	3.57832	+	55.4698i	0.117086	+	1.81503i
$935$	−34.3136	+	28.7925i	−1.12217	+	0.941615i
$936$	12.7637	−	0.239058i	0.417195	−	0.00781386i
$937$	32.1030	−	5.66063i	1.04876	−	0.184925i	0.377396	−	0.926052i	$-0.376820\pi$
$937$	32.1030	−	5.66063i	1.04876	−	0.184925i	0.671364	+	0.741127i	$0.265709\pi$
$938$	−10.5347	+	10.0640i	−0.343970	+	0.328602i
$939$	4.41340	+	16.4710i	0.144026	+	0.537512i
$940$	−4.78708	+	6.21211i	−0.156137	+	0.202617i
$941$	33.7905	−	15.7568i	1.10154	−	0.513656i	0.215142	−	0.976583i	$-0.430978\pi$
$941$	33.7905	−	15.7568i	1.10154	−	0.513656i	0.886397	+	0.462927i	$0.153201\pi$
$942$	−15.9174	−	29.0846i	−0.518617	−	0.947627i
$943$	0.825850	+	1.43041i	0.0268934	+	0.0465807i
$944$	−24.0932	+	8.65700i	−0.784168	+	0.281761i
$945$	−8.43881	+	10.0570i	−0.274515	+	0.327154i
$946$	−6.48011	−	42.3922i	−0.210686	−	1.37829i
$947$	−30.7590	−	43.9285i	−0.999534	−	1.42748i	−0.901741	−	0.432276i	$-0.857711\pi$
$947$	−30.7590	−	43.9285i	−0.999534	−	1.42748i	−0.0977930	−	0.995207i	$-0.531178\pi$
$948$	−0.521020	−	12.5252i	−0.0169219	−	0.406800i
$949$	−14.0649	−	14.0649i	−0.456565	−	0.456565i
$950$	11.6454	+	14.1867i	0.377827	+	0.460279i
$951$	6.50180			0.210835
$952$	−18.9162	−	65.6530i	−0.613079	−	2.12782i
$953$	−4.90659	+	27.8266i	−0.158940	+	0.901393i	0.796155	+	0.605093i	$0.206864\pi$
$953$	−4.90659	+	27.8266i	−0.158940	+	0.901393i	−0.955095	+	0.296300i	$0.904247\pi$
$954$	3.74824	−	5.10093i	0.121354	−	0.165149i
$955$	3.47875	+	39.7623i	0.112570	+	1.28668i
$956$	−17.2471	−	22.5730i	−0.557811	−	0.730062i
$957$	−2.97088	+	11.0875i	−0.0960348	+	0.358407i
$958$	16.2383	+	29.6710i	0.524637	+	0.958627i
$959$	−24.5642	+	67.4897i	−0.793221	+	2.17936i
$960$	19.9776	+	10.5571i	0.644775	+	0.340728i
$961$	2.34842	−	4.06759i	0.0757556	−	0.131213i
$962$	0.495131	−	21.6684i	0.0159637	−	0.698618i
$963$	10.2204	−	14.5963i	0.329348	−	0.470358i
$964$	−10.0952	−	2.25988i	−0.325146	−	0.0727860i
$965$	20.5220	+	1.79545i	0.660628	+	0.0577974i
$966$	26.6916	−	1.72186i	0.858790	−	0.0554000i
$967$	−8.95213	+	3.25831i	−0.287881	+	0.104780i	−0.481924	−	0.876213i	$-0.660062\pi$
$967$	−8.95213	+	3.25831i	−0.287881	+	0.104780i	0.194043	+	0.980993i	$0.437840\pi$
$968$	−4.76160	−	0.326868i	−0.153044	−	0.0105059i
$969$	−22.5412	+	2.24608i	−0.724127	+	0.0721545i
$970$	−16.0253	−	65.7835i	−0.514543	−	2.11218i
$971$	−13.5971	+	29.1591i	−0.436352	+	0.935760i	0.558021	+	0.829827i	$0.311561\pi$
$971$	−13.5971	+	29.1591i	−0.436352	+	0.935760i	−0.994373	+	0.105933i	$0.966217\pi$
$972$	1.77212	+	0.927149i	0.0568406	+	0.0297383i
$973$	−83.6882	−	7.32177i	−2.68292	−	0.234725i
$974$	14.2502	−	4.82094i	0.456607	−	0.154473i
$975$	−13.2344	+	2.33359i	−0.423841	+	0.0747346i
$976$	−15.3496	−	18.4468i	−0.491330	−	0.590466i
$977$	27.8853	+	16.0996i	0.892131	+	0.515072i	0.874639	−	0.484775i	$-0.161099\pi$
$977$	27.8853	+	16.0996i	0.892131	+	0.515072i	0.0174919	+	0.999847i	$0.494432\pi$
$978$	−11.1527	−	13.9253i	−0.356623	−	0.445281i
$979$	11.2424	+	24.1094i	0.359309	+	0.770541i
$980$	60.9433	−	55.6138i	1.94676	−	1.77652i
$981$	−0.144893	+	0.540749i	−0.00462609	+	0.0172648i
$982$	−23.1462	+	10.1561i	−0.738625	+	0.324095i
$983$	−19.0718	+	22.7288i	−0.608295	+	0.724937i	−0.979011	−	0.203809i	$-0.934668\pi$
$983$	−19.0718	+	22.7288i	−0.608295	+	0.724937i	0.370716	+	0.928746i	$0.379112\pi$
$984$	0.178164	−	1.13423i	0.00567966	−	0.0361581i
$985$	−9.58543	−	1.69017i	−0.305417	−	0.0538533i
$986$	23.0016	−	15.3350i	0.732521	−	0.488365i
$987$	4.56315	−	4.56315i	0.145247	−	0.145247i
$988$	−11.4565	+	37.6425i	−0.364480	+	1.19757i
$989$	−28.5902	−	28.5902i	−0.909117	−	0.909117i
$990$	−2.39034	+	11.9527i	−0.0759700	+	0.379882i
$991$	−2.89357	+	16.4103i	−0.0919173	+	0.521289i	0.903731	+	0.428100i	$0.140817\pi$
$991$	−2.89357	+	16.4103i	−0.0919173	+	0.521289i	−0.995648	+	0.0931885i	$0.970294\pi$
$992$	12.9655	−	25.9537i	0.411656	−	0.824032i
$993$	−10.5253	−	8.83177i	−0.334010	−	0.280268i
$994$	−70.0466	−	27.3227i	−2.22174	−	0.866623i
$995$	48.1121	+	12.8916i	1.52526	+	0.408692i
$996$	−19.0276	−	0.870031i	−0.602914	−	0.0275680i
$997$	−42.9897	+	20.0464i	−1.36150	+	0.634876i	−0.959745	−	0.280872i	$-0.909376\pi$
$997$	−42.9897	+	20.0464i	−1.36150	+	0.634876i	−0.401752	+	0.915749i	$0.631598\pi$
$998$	−0.331028	−	0.0365985i	−0.0104785	−	0.00115850i
$999$	1.69780	−	2.94068i	0.0537161	−	0.0930391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.cn.a.451.76	yes	960
16.11	odd	4	inner	912.2.cn.a.907.22	yes	960
19.15	odd	18	inner	912.2.cn.a.547.22	yes	960
304.91	even	36	inner	912.2.cn.a.91.76	✓	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.cn.a.91.76	✓	960	304.91	even	36	inner
912.2.cn.a.451.76	yes	960	1.1	even	1	trivial
912.2.cn.a.547.22	yes	960	19.15	odd	18	inner
912.2.cn.a.907.22	yes	960	16.11	odd	4	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.cn (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38675 + 0.277328i) q^{2} +(-0.819152 + 0.573576i) q^{3} +(1.84618 + 0.769171i) q^{4} +(-2.81369 + 0.246166i) q^{5} +(-1.29503 + 0.568237i) q^{6} +(-2.32408 - 4.02543i) q^{7} +(2.34689 + 1.57865i) q^{8} +(0.342020 - 0.939693i) q^{9} +O(q^{10})\)	\(q+(1.38675 + 0.277328i) q^{2} +(-0.819152 + 0.573576i) q^{3} +(1.84618 + 0.769171i) q^{4} +(-2.81369 + 0.246166i) q^{5} +(-1.29503 + 0.568237i) q^{6} +(-2.32408 - 4.02543i) q^{7} +(2.34689 + 1.57865i) q^{8} +(0.342020 - 0.939693i) q^{9} +(-3.97017 - 0.438942i) q^{10} +(2.94767 - 0.789825i) q^{11} +(-1.95348 + 0.428857i) q^{12} +(3.69720 + 2.58881i) q^{13} +(-2.10657 - 6.22682i) q^{14} +(2.16365 - 1.81551i) q^{15} +(2.81675 + 2.84005i) q^{16} +(4.88350 - 1.77745i) q^{17} +(0.734901 - 1.20827i) q^{18} +(2.84188 + 3.30511i) q^{19} +(-5.38392 - 1.70974i) q^{20} +(4.21267 + 1.96440i) q^{21} +(4.30673 - 0.277824i) q^{22} +(3.11698 - 2.61546i) q^{23} +(-2.82793 + 0.0529658i) q^{24} +(2.93222 - 0.517030i) q^{25} +(4.40916 + 4.61537i) q^{26} +(0.258819 + 0.965926i) q^{27} +(-1.19443 - 9.21928i) q^{28} +(3.40902 - 1.58965i) q^{29} +(3.50394 - 1.91764i) q^{30} +(-2.56433 - 4.44155i) q^{31} +(3.11852 + 4.71962i) q^{32} +(-1.96156 + 2.33770i) q^{33} +(7.26515 - 1.11056i) q^{34} +(7.53018 + 10.7542i) q^{35} +(1.35421 - 1.47177i) q^{36} +(-2.40106 - 2.40106i) q^{37} +(3.02439 + 5.37151i) q^{38} -4.51345 q^{39} +(-6.99202 - 3.86410i) q^{40} +(-0.0704889 + 0.399763i) q^{41} +(5.29716 + 3.89243i) q^{42} +(-0.866061 - 9.89912i) q^{43} +(6.04943 + 0.809101i) q^{44} +(-0.731019 + 2.72820i) q^{45} +(5.04783 - 2.76258i) q^{46} +(0.474842 - 1.30462i) q^{47} +(-3.93634 - 0.710813i) q^{48} +(-7.30273 + 12.6487i) q^{49} +(4.20966 + 0.0961922i) q^{50} +(-2.98082 + 4.25706i) q^{51} +(4.83446 + 7.62318i) q^{52} +(4.45895 + 0.390108i) q^{53} +(0.0910408 + 1.41128i) q^{54} +(-8.09939 + 2.94794i) q^{55} +(0.900379 - 13.1161i) q^{56} +(-4.22366 - 1.07735i) q^{57} +(5.16833 - 1.25904i) q^{58} +(-2.70490 + 5.80067i) q^{59} +(5.39092 - 1.68755i) q^{60} +(-5.97662 - 0.522886i) q^{61} +(-2.32433 - 6.87050i) q^{62} +(-4.57755 + 0.807146i) q^{63} +(3.01574 + 7.40981i) q^{64} +(-11.0401 - 6.37398i) q^{65} +(-3.36851 + 2.69782i) q^{66} +(-0.936677 - 2.00871i) q^{67} +(10.3830 + 0.474757i) q^{68} +(-1.05312 + 3.93029i) q^{69} +(7.46007 + 17.0018i) q^{70} +(7.35211 - 8.76191i) q^{71} +(2.28613 - 1.66542i) q^{72} +(-4.34004 - 0.765266i) q^{73} +(-2.66380 - 3.99556i) q^{74} +(-2.10538 + 2.10538i) q^{75} +(2.70442 + 8.28771i) q^{76} +(-10.0300 - 10.0300i) q^{77} +(-6.25904 - 1.25170i) q^{78} +(-1.08843 + 6.17280i) q^{79} +(-8.62460 - 7.29764i) q^{80} +(-0.766044 - 0.642788i) q^{81} +(-0.208616 + 0.534824i) q^{82} +(9.19924 + 2.46493i) q^{83} +(6.26638 + 6.86690i) q^{84} +(-13.3031 + 6.20334i) q^{85} +(1.54428 - 13.9678i) q^{86} +(-1.88072 + 3.25750i) q^{87} +(8.16469 + 2.79970i) q^{88} +(1.51372 + 8.58476i) q^{89} +(-1.77035 + 3.58061i) q^{90} +(1.82846 - 20.8994i) q^{91} +(7.76624 - 2.43111i) q^{92} +(4.64814 + 2.16747i) q^{93} +(1.02030 - 1.67750i) q^{94} +(-8.80977 - 8.59998i) q^{95} +(-5.26161 - 2.07738i) q^{96} +(5.79749 + 15.9285i) q^{97} +(-13.6349 + 15.5154i) q^{98} +(0.265969 - 3.04004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q+O(q^{10}) \) 960 * q	\( 960 q + 48 q^{10} + 12 q^{16} - 60 q^{32} - 120 q^{34} + 12 q^{36} + 108 q^{38} + 60 q^{40} + 180 q^{46} - 480 q^{49} - 108 q^{50} - 24 q^{51} + 48 q^{52} + 12 q^{54} + 72 q^{68} - 144 q^{69} - 72 q^{70} - 48 q^{76} + 72 q^{78} - 120 q^{80} + 120 q^{82} + 96 q^{85} + 84 q^{98}+O(q^{100}) \) 960 * q + 48 * q^10 + 12 * q^16 - 60 * q^32 - 120 * q^34 + 12 * q^36 + 108 * q^38 + 60 * q^40 + 180 * q^46 - 480 * q^49 - 108 * q^50 - 24 * q^51 + 48 * q^52 + 12 * q^54 + 72 * q^68 - 144 * q^69 - 72 * q^70 - 48 * q^76 + 72 * q^78 - 120 * q^80 + 120 * q^82 + 96 * q^85 + 84 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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