LMFDB - Embedded newform 315.2.cc.a.92.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(92,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("315.92");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.cc (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			92.13
Character	$\chi$	$=$	315.92
Dual form			315.2.cc.a.113.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.270870 - 1.01090i) q^{2} +(1.36595 + 1.06499i) q^{3} +(0.783502 - 0.452355i) q^{4} +(2.05901 - 0.872052i) q^{5} +(0.706600 - 1.66931i) q^{6} +(0.965926 - 0.258819i) q^{7} +(-2.14957 - 2.14957i) q^{8} +(0.731614 + 2.90942i) q^{9} +O(q^{10})$	\(q+(-0.270870 - 1.01090i) q^{2} +(1.36595 + 1.06499i) q^{3} +(0.783502 - 0.452355i) q^{4} +(2.05901 - 0.872052i) q^{5} +(0.706600 - 1.66931i) q^{6} +(0.965926 - 0.258819i) q^{7} +(-2.14957 - 2.14957i) q^{8} +(0.731614 + 2.90942i) q^{9} +(-1.43928 - 1.84524i) q^{10} +(-1.95539 - 1.12894i) q^{11} +(1.55197 + 0.216526i) q^{12} +(-1.24919 - 0.334719i) q^{13} +(-0.523280 - 0.906348i) q^{14} +(3.74122 + 1.00164i) q^{15} +(-0.686039 + 1.18825i) q^{16} +(-4.96756 + 4.96756i) q^{17} +(2.74296 - 1.52766i) q^{18} +5.64097i q^{19} +(1.21876 - 1.61466i) q^{20} +(1.59504 + 0.675164i) q^{21} +(-0.611593 + 2.28250i) q^{22} +(1.93608 - 7.22556i) q^{23} +(-0.646937 - 5.22546i) q^{24} +(3.47905 - 3.59113i) q^{25} +1.35347i q^{26} +(-2.09915 + 4.75327i) q^{27} +(0.639727 - 0.639727i) q^{28} +(-1.34394 + 2.32778i) q^{29} +(-0.000824614 - 4.05331i) q^{30} +(-0.0673239 - 0.116608i) q^{31} +(-4.48571 - 1.20194i) q^{32} +(-1.46864 - 3.62453i) q^{33} +(6.36726 + 3.67614i) q^{34} +(1.76315 - 1.37525i) q^{35} +(1.88931 + 1.94859i) q^{36} +(-0.0224346 - 0.0224346i) q^{37} +(5.70246 - 1.52797i) q^{38} +(-1.34985 - 1.78758i) q^{39} +(-6.30053 - 2.55146i) q^{40} +(5.06234 - 2.92274i) q^{41} +(0.250475 - 1.79531i) q^{42} +(2.31136 + 8.62612i) q^{43} -2.04273 q^{44} +(4.04357 + 5.35253i) q^{45} -7.82875 q^{46} +(-1.19756 - 4.46937i) q^{47} +(-2.20257 + 0.892470i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-4.57264 - 2.54425i) q^{50} +(-12.0758 + 1.49504i) q^{51} +(-1.13015 + 0.302824i) q^{52} +(-9.88439 - 9.88439i) q^{53} +(5.37368 + 0.834510i) q^{54} +(-5.01066 - 0.619308i) q^{55} +(-2.63268 - 1.51998i) q^{56} +(-6.00755 + 7.70526i) q^{57} +(2.71718 + 0.728068i) q^{58} +(3.89858 + 6.75254i) q^{59} +(3.38435 - 0.907572i) q^{60} +(4.12806 - 7.15001i) q^{61} +(-0.0996435 + 0.0996435i) q^{62} +(1.45970 + 2.62093i) q^{63} +7.60433i q^{64} +(-2.86399 + 0.400167i) q^{65} +(-3.26623 + 2.46643i) q^{66} +(-1.71421 + 6.39753i) q^{67} +(-1.64499 + 6.13919i) q^{68} +(10.3397 - 7.80782i) q^{69} +(-1.86782 - 1.40985i) q^{70} +12.1459i q^{71} +(4.68136 - 7.82668i) q^{72} +(-1.60941 + 1.60941i) q^{73} +(-0.0166023 + 0.0287560i) q^{74} +(8.57669 - 1.20015i) q^{75} +(2.55172 + 4.41971i) q^{76} +(-2.18095 - 0.584384i) q^{77} +(-1.44143 + 1.84877i) q^{78} +(1.73195 + 0.999944i) q^{79} +(-0.376343 + 3.04489i) q^{80} +(-7.92948 + 4.25715i) q^{81} +(-4.32584 - 4.32584i) q^{82} +(-9.13794 + 2.44850i) q^{83} +(1.55513 - 0.192532i) q^{84} +(-5.89629 + 14.5602i) q^{85} +(8.09407 - 4.67311i) q^{86} +(-4.31480 + 1.74834i) q^{87} +(1.77650 + 6.62999i) q^{88} +7.69511 q^{89} +(4.31559 - 5.53748i) q^{90} -1.29326 q^{91} +(-1.75159 - 6.53704i) q^{92} +(0.0322255 - 0.230980i) q^{93} +(-4.19370 + 2.42124i) q^{94} +(4.91922 + 11.6148i) q^{95} +(-4.84718 - 6.41900i) q^{96} +(5.23252 - 1.40205i) q^{97} +(-0.740030 - 0.740030i) q^{98} +(1.85398 - 6.51500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 4 q^{3}+O(q^{10}) $ 144 * q + 4 * q^3	$ 144 q + 4 q^{3} - 12 q^{11} - 16 q^{12} + 16 q^{15} + 72 q^{16} - 64 q^{18} - 48 q^{20} - 4 q^{21} - 24 q^{23} - 12 q^{25} - 32 q^{27} - 20 q^{30} - 60 q^{32} - 16 q^{33} - 16 q^{36} - 24 q^{37} + 72 q^{38} + 48 q^{41} - 40 q^{42} + 40 q^{45} - 48 q^{46} + 12 q^{47} + 104 q^{48} - 76 q^{51} - 24 q^{55} - 4 q^{57} - 92 q^{60} + 8 q^{63} - 72 q^{65} - 80 q^{66} - 12 q^{67} - 64 q^{72} - 108 q^{75} - 24 q^{76} + 72 q^{78} + 32 q^{81} - 96 q^{82} + 120 q^{83} - 48 q^{85} - 144 q^{86} + 116 q^{87} - 48 q^{88} + 252 q^{90} + 24 q^{91} + 156 q^{92} - 44 q^{93} + 120 q^{95} - 96 q^{96} - 60 q^{97}+O(q^{100}) $ 144 * q + 4 * q^3 - 12 * q^11 - 16 * q^12 + 16 * q^15 + 72 * q^16 - 64 * q^18 - 48 * q^20 - 4 * q^21 - 24 * q^23 - 12 * q^25 - 32 * q^27 - 20 * q^30 - 60 * q^32 - 16 * q^33 - 16 * q^36 - 24 * q^37 + 72 * q^38 + 48 * q^41 - 40 * q^42 + 40 * q^45 - 48 * q^46 + 12 * q^47 + 104 * q^48 - 76 * q^51 - 24 * q^55 - 4 * q^57 - 92 * q^60 + 8 * q^63 - 72 * q^65 - 80 * q^66 - 12 * q^67 - 64 * q^72 - 108 * q^75 - 24 * q^76 + 72 * q^78 + 32 * q^81 - 96 * q^82 + 120 * q^83 - 48 * q^85 - 144 * q^86 + 116 * q^87 - 48 * q^88 + 252 * q^90 + 24 * q^91 + 156 * q^92 - 44 * q^93 + 120 * q^95 - 96 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.270870	−	1.01090i	−0.191534	−	0.714814i	−0.993137	−	0.116958i	$-0.962686\pi$
$2$	−0.270870	−	1.01090i	−0.191534	−	0.714814i	0.801603	−	0.597857i	$-0.203981\pi$
$3$	1.36595	+	1.06499i	0.788629	+	0.614869i
$3$	1.36595	+	1.06499i	0.788629	+	0.614869i
$4$	0.783502	−	0.452355i	0.391751	−	0.226178i
$5$	2.05901	−	0.872052i	0.920818	−	0.389993i
$5$	2.05901	−	0.872052i	0.920818	−	0.389993i
$6$	0.706600	−	1.66931i	0.288468	−	0.681492i
$7$	0.965926	−	0.258819i	0.365086	−	0.0978244i
$7$	0.965926	−	0.258819i	0.365086	−	0.0978244i
$8$	−2.14957	−	2.14957i	−0.759989	−	0.759989i
$9$	0.731614	+	2.90942i	0.243871	+	0.969808i
$10$	−1.43928	−	1.84524i	−0.455141	−	0.583517i
$11$	−1.95539	−	1.12894i	−0.589571	−	0.340389i	0.175357	−	0.984505i	$-0.443892\pi$
$11$	−1.95539	−	1.12894i	−0.589571	−	0.340389i	−0.764928	+	0.644116i	$0.777225\pi$
$12$	1.55197	+	0.216526i	0.448016	+	0.0625055i
$13$	−1.24919	−	0.334719i	−0.346463	−	0.0928344i	0.0813914	−	0.996682i	$-0.474064\pi$
$13$	−1.24919	−	0.334719i	−0.346463	−	0.0928344i	−0.427854	+	0.903848i	$0.640730\pi$
$14$	−0.523280	−	0.906348i	−0.139853	−	0.242232i
$15$	3.74122	+	1.00164i	0.965978	+	0.258623i
$16$	−0.686039	+	1.18825i	−0.171510	+	0.297064i
$17$	−4.96756	+	4.96756i	−1.20481	+	1.20481i	−0.232123	+	0.972687i	$0.574567\pi$
$17$	−4.96756	+	4.96756i	−1.20481	+	1.20481i	−0.972687	+	0.232123i	$0.925433\pi$
$18$	2.74296	−	1.52766i	0.646523	−	0.360074i
$19$			5.64097i			1.29413i	0.762436	+	0.647064i	$0.224003\pi$
$19$			5.64097i			1.29413i	−0.762436	+	0.647064i	$0.775997\pi$
$20$	1.21876	−	1.61466i	0.272524	−	0.361049i
$21$	1.59504	+	0.675164i	0.348066	+	0.147333i
$22$	−0.611593	+	2.28250i	−0.130392	+	0.486630i
$23$	1.93608	−	7.22556i	0.403701	−	1.50663i	−0.402737	−	0.915316i	$-0.631941\pi$
$23$	1.93608	−	7.22556i	0.403701	−	1.50663i	0.806438	−	0.591318i	$-0.201392\pi$
$24$	−0.646937	−	5.22546i	−0.132055	−	1.06664i
$25$	3.47905	−	3.59113i	0.695810	−	0.718226i
$26$			1.35347i			0.265437i
$27$	−2.09915	+	4.75327i	−0.403981	+	0.914767i
$28$	0.639727	−	0.639727i	0.120897	−	0.120897i
$29$	−1.34394	+	2.32778i	−0.249564	+	0.432258i	−0.963405	−	0.268050i	$-0.913621\pi$
$29$	−1.34394	+	2.32778i	−0.249564	+	0.432258i	0.713841	+	0.700308i	$0.246954\pi$
$30$	−0.000824614	−	4.05331i	−0.000150553	−	0.740030i
$31$	−0.0673239	−	0.116608i	−0.0120917	−	0.0209435i	0.859916	−	0.510435i	$-0.170516\pi$
$31$	−0.0673239	−	0.116608i	−0.0120917	−	0.0209435i	−0.872008	+	0.489492i	$0.837182\pi$
$32$	−4.48571	−	1.20194i	−0.792969	−	0.212475i
$33$	−1.46864	−	3.62453i	−0.255658	−	0.630950i
$34$	6.36726	+	3.67614i	1.09198	+	0.630453i
$35$	1.76315	−	1.37525i	0.298026	−	0.232459i
$36$	1.88931	+	1.94859i	0.314886	+	0.324765i
$37$	−0.0224346	−	0.0224346i	−0.00368822	−	0.00368822i	0.705260	−	0.708948i	$-0.250830\pi$
$37$	−0.0224346	−	0.0224346i	−0.00368822	−	0.00368822i	−0.708948	+	0.705260i	$0.750830\pi$
$38$	5.70246	−	1.52797i	0.925061	−	0.247869i
$39$	−1.34985	−	1.78758i	−0.216149	−	0.286241i
$40$	−6.30053	−	2.55146i	−0.996202	−	0.403421i
$41$	5.06234	−	2.92274i	0.790605	−	0.456456i	−0.0495706	−	0.998771i	$-0.515785\pi$
$41$	5.06234	−	2.92274i	0.790605	−	0.456456i	0.840175	+	0.542315i	$0.182452\pi$
$42$	0.250475	−	1.79531i	0.0386491	−	0.277022i
$43$	2.31136	+	8.62612i	0.352479	+	1.31547i	0.883627	+	0.468192i	$0.155094\pi$
$43$	2.31136	+	8.62612i	0.352479	+	1.31547i	−0.531148	+	0.847279i	$0.678239\pi$
$44$	−2.04273			−0.307954
$45$	4.04357	+	5.35253i	0.602780	+	0.797908i
$46$	−7.82875			−1.15429
$47$	−1.19756	−	4.46937i	−0.174683	−	0.651925i	−0.996605	−	0.0823258i	$-0.973765\pi$
$47$	−1.19756	−	4.46937i	−0.174683	−	0.651925i	0.821923	−	0.569599i	$-0.192901\pi$
$48$	−2.20257	+	0.892470i	−0.317913	+	0.128817i
$49$	0.866025	−	0.500000i	0.123718	−	0.0714286i
$50$	−4.57264	−	2.54425i	−0.646669	−	0.359811i
$51$	−12.0758	+	1.49504i	−1.69095	+	0.209347i
$52$	−1.13015	+	0.302824i	−0.156724	+	0.0419941i
$53$	−9.88439	−	9.88439i	−1.35772	−	1.35772i	−0.876715	−	0.481010i	$-0.840270\pi$
$53$	−9.88439	−	9.88439i	−1.35772	−	1.35772i	−0.481010	−	0.876715i	$-0.659730\pi$
$54$	5.37368	+	0.834510i	0.731265	+	0.113562i
$55$	−5.01066	−	0.619308i	−0.675637	−	0.0835074i
$56$	−2.63268	−	1.51998i	−0.351807	−	0.203116i
$57$	−6.00755	+	7.70526i	−0.795719	+	1.02059i
$58$	2.71718	+	0.728068i	0.356784	+	0.0955999i
$59$	3.89858	+	6.75254i	0.507552	+	0.879106i	0.999962	+	0.00874247i	$0.00278285\pi$
$59$	3.89858	+	6.75254i	0.507552	+	0.879106i	−0.492410	+	0.870364i	$0.663884\pi$
$60$	3.38435	−	0.907572i	0.436918	−	0.117167i
$61$	4.12806	−	7.15001i	0.528544	−	0.915466i	−0.470902	−	0.882186i	$-0.656071\pi$
$61$	4.12806	−	7.15001i	0.528544	−	0.915466i	0.999446	−	0.0332799i	$-0.0105953\pi$
$62$	−0.0996435	+	0.0996435i	−0.0126547	+	0.0126547i
$63$	1.45970	+	2.62093i	0.183905	+	0.330206i
$64$			7.60433i			0.950541i
$65$	−2.86399	+	0.400167i	−0.355234	+	0.0496346i
$66$	−3.26623	+	2.46643i	−0.402045	+	0.303596i
$67$	−1.71421	+	6.39753i	−0.209425	+	0.781583i	0.778631	+	0.627483i	$0.215915\pi$
$67$	−1.71421	+	6.39753i	−0.209425	+	0.781583i	−0.988055	+	0.154101i	$0.950752\pi$
$68$	−1.64499	+	6.13919i	−0.199484	+	0.744486i
$69$	10.3397	−	7.80782i	1.24475	−	0.939951i
$70$	−1.86782	−	1.40985i	−0.223248	−	0.168510i
$71$			12.1459i			1.44146i	0.693218	+	0.720728i	$0.256192\pi$
$71$			12.1459i			1.44146i	−0.693218	+	0.720728i	$0.743808\pi$
$72$	4.68136	−	7.82668i	0.551704	−	0.922383i
$73$	−1.60941	+	1.60941i	−0.188367	+	0.188367i	−0.794990	−	0.606623i	$-0.792524\pi$
$73$	−1.60941	+	1.60941i	−0.188367	+	0.188367i	0.606623	+	0.794990i	$0.292524\pi$
$74$	−0.0166023	+	0.0287560i	−0.00192997	+	0.00334281i
$75$	8.57669	−	1.20015i	0.990351	−	0.138581i
$76$	2.55172	+	4.41971i	0.292703	+	0.506976i
$77$	−2.18095	−	0.584384i	−0.248542	−	0.0665967i
$78$	−1.44143	+	1.84877i	−0.163209	+	0.209332i
$79$	1.73195	+	0.999944i	0.194860	+	0.112503i	0.594256	−	0.804276i	$-0.297447\pi$
$79$	1.73195	+	0.999944i	0.194860	+	0.112503i	−0.399396	+	0.916779i	$0.630780\pi$
$80$	−0.376343	+	3.04489i	−0.0420764	+	0.340429i
$81$	−7.92948	+	4.25715i	−0.881054	+	0.473016i
$82$	−4.32584	−	4.32584i	−0.477709	−	0.477709i
$83$	−9.13794	+	2.44850i	−1.00302	+	0.268758i	−0.722710	−	0.691151i	$-0.757104\pi$
$83$	−9.13794	+	2.44850i	−1.00302	+	0.268758i	−0.280309	+	0.959910i	$0.590437\pi$
$84$	1.55513	−	0.192532i	0.169679	−	0.0210070i
$85$	−5.89629	+	14.5602i	−0.639542	+	1.57928i
$86$	8.09407	−	4.67311i	0.872806	−	0.503915i
$87$	−4.31480	+	1.74834i	−0.462595	+	0.187442i
$88$	1.77650	+	6.62999i	0.189376	+	0.706760i
$89$	7.69511			0.815680			0.407840	−	0.913053i	$-0.366282\pi$
$89$	7.69511			0.815680			0.407840	+	0.913053i	$0.366282\pi$
$90$	4.31559	−	5.53748i	0.454903	−	0.583702i
$91$	−1.29326			−0.135570
$92$	−1.75159	−	6.53704i	−0.182616	−	0.681534i
$93$	0.0322255	−	0.230980i	0.00334162	−	0.0239515i
$94$	−4.19370	+	2.42124i	−0.432548	+	0.249731i
$95$	4.91922	+	11.6148i	0.504701	+	1.19166i
$96$	−4.84718	−	6.41900i	−0.494714	−	0.655137i
$97$	5.23252	−	1.40205i	0.531282	−	0.142357i	0.0168018	−	0.999859i	$-0.494652\pi$
$97$	5.23252	−	1.40205i	0.531282	−	0.142357i	0.514480	+	0.857502i	$0.327985\pi$
$98$	−0.740030	−	0.740030i	−0.0747543	−	0.0747543i
$99$	1.85398	−	6.51500i	0.186332	−	0.654782i
$100$	1.10138	−	4.38742i	0.110138	−	0.438742i
$101$	8.14675	+	4.70353i	0.810632	+	0.468019i	0.847175	−	0.531313i	$-0.178301\pi$
$101$	8.14675	+	4.70353i	0.810632	+	0.468019i	−0.0365433	+	0.999332i	$0.511635\pi$
$102$	4.78230	+	11.8024i	0.473518	+	1.16862i
$103$	−11.1925	−	2.99903i	−1.10283	−	0.295503i	−0.338914	−	0.940817i	$-0.610060\pi$
$103$	−11.1925	−	2.99903i	−1.10283	−	0.295503i	−0.763917	+	0.645314i	$0.776726\pi$
$104$	1.96572	+	3.40473i	0.192755	+	0.333861i
$105$	3.87298		0.000787927i	0.377964		7.68938e-5i
$106$	−7.31475	+	12.6695i	−0.710471	+	1.23057i
$107$	−2.86544	+	2.86544i	−0.277013	+	0.277013i	−0.831915	−	0.554903i	$-0.812755\pi$
$107$	−2.86544	+	2.86544i	−0.277013	+	0.277013i	0.554903	+	0.831915i	$0.312755\pi$
$108$	0.505480	+	4.67376i	0.0486399	+	0.449733i
$109$		−	13.0893i		−	1.25373i	−0.779129	−	0.626864i	$-0.784338\pi$
$109$		−	13.0893i		−	1.25373i	0.779129	−	0.626864i	$-0.215662\pi$
$110$	0.731178	+	5.23303i	0.0697151	+	0.498950i
$111$	−0.00675192	−	0.0545369i	−0.000640864	−	0.00517641i
$112$	−0.355120	+	1.32533i	−0.0335557	+	0.125232i
$113$	0.793347	−	2.96081i	0.0746318	−	0.278530i	−0.918518	−	0.395380i	$-0.870613\pi$
$113$	0.793347	−	2.96081i	0.0746318	−	0.278530i	0.993150	+	0.116850i	$0.0372797\pi$
$114$	9.41651	+	3.98591i	0.881937	+	0.373315i
$115$	−2.31465	−	16.5659i	−0.215842	−	1.54478i
$116$			2.43176i			0.225783i
$117$	0.0599156	−	3.87930i	0.00553920	−	0.358642i
$118$	5.77014	−	5.77014i	0.531184	−	0.531184i
$119$	−3.51259	+	6.08399i	−0.321999	+	0.557718i
$120$	−5.88892	−	10.1951i	−0.537583	−	0.930683i
$121$	−2.95098	−	5.11124i	−0.268271	−	0.464658i
$122$	−8.34612	−	2.23634i	−0.755622	−	0.202468i
$123$	10.0276	+	1.39901i	0.904155	+	0.126144i
$124$	−0.105497	−	0.0609087i	−0.00947390	−	0.00546976i
$125$	4.03176	−	10.4281i	0.360611	−	0.932716i
$126$	2.25411	−	2.18554i	0.200812	−	0.194703i
$127$	−14.9109	−	14.9109i	−1.32313	−	1.32313i	−0.911228	−	0.411902i	$-0.864865\pi$
$127$	−14.9109	−	14.9109i	−1.32313	−	1.32313i	−0.411902	−	0.911228i	$-0.635135\pi$
$128$	−1.28420	+	0.344100i	−0.113508	+	0.0304145i
$129$	−6.02949	+	14.2444i	−0.530867	+	1.25415i
$130$	1.18030	+	2.78681i	0.103519	+	0.244419i
$131$	−0.583600	+	0.336941i	−0.0509893	+	0.0294387i	−0.525278	−	0.850931i	$-0.676039\pi$
$131$	−0.583600	+	0.336941i	−0.0509893	+	0.0294387i	0.474289	+	0.880369i	$0.342705\pi$
$132$	−2.79026	−	2.17548i	−0.242861	−	0.189351i
$133$	1.45999	+	5.44876i	0.126597	+	0.472467i
$134$	6.93160			0.598799
$135$	−0.177069	+	11.6176i	−0.0152397	+	0.999884i
$136$	21.3563			1.83128
$137$	0.545226	+	2.03481i	0.0465818	+	0.173846i	0.985298	−	0.170846i	$-0.0546501\pi$
$137$	0.545226	+	2.03481i	0.0465818	+	0.173846i	−0.938716	+	0.344692i	$0.887983\pi$
$138$	−10.6936	−	8.33750i	−0.910303	−	0.709735i
$139$	0.253465	−	0.146338i	0.0214986	−	0.0124122i	−0.489212	−	0.872165i	$-0.662716\pi$
$139$	0.253465	−	0.146338i	0.0214986	−	0.0124122i	0.510711	+	0.859753i	$0.329382\pi$
$140$	0.759330	−	1.87508i	0.0641751	−	0.158473i
$141$	3.12401	−	7.38031i	0.263089	−	0.621534i
$142$	12.2783	−	3.28996i	1.03037	−	0.276088i
$143$	2.06477	+	2.06477i	0.172665	+	0.172665i
$144$	−3.95905	−	1.12663i	−0.329921	−	0.0938862i
$145$	−0.737251	+	5.96491i	−0.0612254	+	0.495359i
$146$	2.06289	+	1.19101i	0.170726	+	0.0985688i
$147$	1.71544	+	0.239331i	0.141487	+	0.0197397i
$148$	−0.0277259	−	0.00742915i	−0.00227906	−	0.000610672i
$149$	−0.892250	−	1.54542i	−0.0730959	−	0.126606i	0.827161	−	0.561965i	$-0.189955\pi$
$149$	−0.892250	−	1.54542i	−0.0730959	−	0.126606i	−0.900257	+	0.435360i	$0.856621\pi$
$150$	−3.53640	−	8.34510i	−0.288746	−	0.681374i
$151$	−2.82327	+	4.89004i	−0.229754	+	0.397946i	−0.957735	−	0.287651i	$-0.907126\pi$
$151$	−2.82327	+	4.89004i	−0.229754	+	0.397946i	0.727981	+	0.685597i	$0.240459\pi$
$152$	12.1257	−	12.1257i	0.983522	−	0.983522i
$153$	−18.0871	−	10.8184i	−1.46225	−	0.874615i
$154$			2.36301i			0.190417i
$155$	−0.240309	−	0.181388i	−0.0193021	−	0.0145694i
$156$	−1.86623	−	0.789956i	−0.149418	−	0.0632471i
$157$	3.97528	−	14.8360i	0.317262	−	1.18404i	−0.604603	−	0.796527i	$-0.706668\pi$
$157$	3.97528	−	14.8360i	0.317262	−	1.18404i	0.921865	−	0.387511i	$-0.126665\pi$
$158$	0.541710	−	2.02169i	0.0430961	−	0.160837i
$159$	−2.97481	−	24.0283i	−0.235918	−	1.90556i
$160$	−10.2843	+	1.43696i	−0.813044	+	0.113602i
$161$		−	7.48045i		−	0.589542i
$162$	6.45141	+	6.86278i	0.506871	+	0.539191i
$163$	15.0528	−	15.0528i	1.17903	−	1.17903i	0.199034	−	0.979993i	$-0.436220\pi$
$163$	15.0528	−	15.0528i	1.17903	−	1.17903i	0.979993	−	0.199034i	$-0.0637804\pi$
$164$	2.64424	−	4.57995i	0.206480	−	0.357634i
$165$	−6.18473	−	6.18222i	−0.481481	−	0.481285i
$166$	4.95039	+	8.57432i	0.384225	+	0.665496i
$167$	4.88842	+	1.30985i	0.378277	+	0.101359i	0.442947	−	0.896548i	$-0.353933\pi$
$167$	4.88842	+	1.30985i	0.378277	+	0.101359i	−0.0646702	+	0.997907i	$0.520600\pi$
$168$	−1.97734	−	4.87997i	−0.152555	−	0.376498i
$169$	−9.80989	−	5.66374i	−0.754607	−	0.435673i
$170$	16.3161	+	2.01663i	1.25138	+	0.154669i
$171$	−16.4120	+	4.12701i	−1.25505	+	0.315600i
$172$	5.71303	+	5.71303i	0.435614	+	0.435614i
$173$	16.6186	−	4.45293i	1.26349	−	0.338550i	0.435954	−	0.899969i	$-0.356411\pi$
$173$	16.6186	−	4.45293i	1.26349	−	0.338550i	0.827532	+	0.561419i	$0.189744\pi$
$174$	2.93615	+	3.88826i	0.222589	+	0.294768i
$175$	2.43105	−	4.36921i	0.183770	−	0.330281i
$176$	2.68294	−	1.54900i	0.202234	−	0.116760i
$177$	−1.86611	+	13.3755i	−0.140265	+	1.00537i
$178$	−2.08437	−	7.77899i	−0.156230	−	0.583060i
$179$	−11.3181			−0.845955			−0.422978	−	0.906140i	$-0.639015\pi$
$179$	−11.3181			−0.845955			−0.422978	+	0.906140i	$0.639015\pi$
$180$	5.58939	+	2.36459i	0.416608	+	0.176246i
$181$	−3.93433			−0.292436			−0.146218	−	0.989252i	$-0.546710\pi$
$181$	−3.93433			−0.292436			−0.146218	+	0.989252i	$0.546710\pi$
$182$	0.350304	+	1.30735i	0.0259663	+	0.0969074i
$183$	13.2534	−	5.37020i	0.979717	−	0.396977i
$184$	−19.6936	+	11.3701i	−1.45183	+	0.838217i
$185$	−0.0657572	−	0.0266289i	−0.00483456	−	0.00195780i
$186$	−0.242226	+	0.0299887i	−0.0177609	+	0.00219888i
$187$	15.3216	−	4.10540i	1.12042	−	0.300217i
$188$	−2.96004	−	2.96004i	−0.215883	−	0.215883i
$189$	−0.797383	+	5.13461i	−0.0580011	+	0.373488i
$190$	10.4090	−	8.11894i	0.755145	−	0.589010i
$191$	3.54233	+	2.04517i	0.256314	+	0.147983i	0.622652	−	0.782499i	$-0.286055\pi$
$191$	3.54233	+	2.04517i	0.256314	+	0.147983i	−0.366338	+	0.930482i	$0.619389\pi$
$192$	−8.09850	+	10.3871i	−0.584459	+	0.749625i
$193$	16.6258	+	4.45486i	1.19675	+	0.320668i	0.801550	−	0.597928i	$-0.204009\pi$
$193$	16.6258	+	4.45486i	1.19675	+	0.320668i	0.395198	+	0.918596i	$0.370676\pi$
$194$	−2.83467	−	4.90978i	−0.203517	−	0.352502i
$195$	−4.33822	−	2.50350i	−0.310666	−	0.179279i
$196$	0.452355	−	0.783502i	0.0323111	−	0.0559644i
$197$	−3.90457	+	3.90457i	−0.278189	+	0.278189i	−0.832386	−	0.554197i	$-0.813025\pi$
$197$	−3.90457	+	3.90457i	−0.278189	+	0.278189i	0.554197	+	0.832386i	$0.313025\pi$
$198$	−7.08820	−	0.109477i	−0.503736	−	0.00778018i
$199$		−	4.53343i		−	0.321366i	−0.987006	−	0.160683i	$-0.948630\pi$
$199$		−	4.53343i		−	0.321366i	0.987006	−	0.160683i	$-0.0513697\pi$
$200$	−15.1979	+	0.240916i	−1.07465	+	0.0170353i
$201$	−9.15480	+	6.91307i	−0.645730	+	0.487610i
$202$	2.54809	−	9.50960i	0.179283	−	0.669093i
$203$	−0.695676	+	2.59630i	−0.0488269	+	0.182224i
$204$	−8.78511	+	6.63391i	−0.615081	+	0.464466i
$205$	7.87463	−	10.4326i	0.549988	−	0.728643i
$206$			12.1269i			0.844918i
$207$	22.4387	+	0.346564i	1.55960	+	0.0240879i
$208$	1.25472	−	1.25472i	0.0869995	−	0.0869995i
$209$	6.36833	−	11.0303i	0.440507	−	0.762980i
$210$	−1.04987	−	3.91499i	−0.0724480	−	0.270160i
$211$	1.34261	+	2.32547i	0.0924289	+	0.160092i	0.908533	−	0.417814i	$-0.137204\pi$
$211$	1.34261	+	2.32547i	0.0924289	+	0.160092i	−0.816104	+	0.577905i	$0.803870\pi$
$212$	−12.2157	−	3.27318i	−0.838977	−	0.224803i
$213$	−12.9352	+	16.5907i	−0.886307	+	1.13677i
$214$	3.67284	+	2.12051i	0.251070	+	0.144955i
$215$	12.2815	+	15.7456i	0.837594	+	1.07384i
$216$	14.7298	−	5.70523i	1.00223	−	0.388192i
$217$	−0.0952104	−	0.0952104i	−0.00646330	−	0.00646330i
$218$	−13.2320	+	3.54550i	−0.896182	+	0.240131i
$219$	−3.91236	+	0.484368i	−0.264373	+	0.0327306i
$220$	−4.20601	+	1.78137i	−0.283569	+	0.120100i
$221$	7.86815	−	4.54268i	0.529269	−	0.305574i
$222$	−0.0533025	+	0.0215979i	−0.00357743	+	0.00144956i
$223$	6.43461	+	24.0143i	0.430893	+	1.60812i	0.750707	+	0.660635i	$0.229713\pi$
$223$	6.43461	+	24.0143i	0.430893	+	1.60812i	−0.319813	+	0.947481i	$0.603620\pi$
$224$	−4.64395			−0.310287
$225$	12.9934	+	7.49471i	0.866229	+	0.499648i
$226$	−3.20798			−0.213392
$227$	2.04260	+	7.62309i	0.135572	+	0.505962i	0.999995	+	0.00319663i	$0.00101752\pi$
$227$	2.04260	+	7.62309i	0.135572	+	0.505962i	−0.864423	+	0.502766i	$0.832316\pi$
$228$	−1.22141	+	8.75463i	−0.0808901	+	0.579790i
$229$	13.3217	−	7.69130i	0.880324	−	0.508255i	0.00955870	−	0.999954i	$-0.496957\pi$
$229$	13.3217	−	7.69130i	0.880324	−	0.508255i	0.870765	+	0.491699i	$0.163624\pi$
$230$	−16.1195	+	6.82707i	−1.06289	+	0.450164i
$231$	−2.35670	−	3.12092i	−0.155059	−	0.205341i
$232$	7.89264	−	2.11483i	0.518177	−	0.138845i
$233$	14.7010	+	14.7010i	0.963097	+	0.963097i	0.999343	−	0.0362461i	$-0.0115400\pi$
$233$	14.7010	+	14.7010i	0.963097	+	0.963097i	−0.0362461	+	0.999343i	$0.511540\pi$
$234$	−3.93782	+	0.990218i	−0.257423	+	0.0647326i
$235$	−6.36332	−	8.15815i	−0.415097	−	0.532179i
$236$	6.10909	+	3.52709i	0.397668	+	0.229594i
$237$	1.30083	+	3.21037i	0.0844979	+	0.208536i
$238$	7.10176	+	1.90291i	0.460339	+	0.123347i
$239$	12.5103	+	21.6685i	0.809226	+	1.40162i	0.913401	+	0.407061i	$0.133446\pi$
$239$	12.5103	+	21.6685i	0.809226	+	1.40162i	−0.104175	+	0.994559i	$0.533220\pi$
$240$	−3.75683	+	3.75836i	−0.242502	+	0.242601i
$241$	8.56467	−	14.8344i	0.551699	−	0.955570i	−0.446454	−	0.894807i	$-0.647313\pi$
$241$	8.56467	−	14.8344i	0.551699	−	0.955570i	0.998152	−	0.0607633i	$-0.0193535\pi$
$242$	−4.36762	+	4.36762i	−0.280762	+	0.280762i
$243$	−15.3650	−	2.62975i	−0.985668	−	0.168698i
$244$		−	7.46940i		−	0.478179i
$245$	1.34713	−	1.78472i	0.0860650	−	0.114022i
$246$	−1.30191	−	10.5158i	−0.0830065	−	0.670464i
$247$	1.88814	−	7.04664i	0.120140	−	0.448367i
$248$	−0.105941	+	0.395376i	−0.00672724	+	0.0251064i
$249$	−15.0896	−	6.38725i	−0.956261	−	0.404775i
$250$	−11.6338	−	1.25105i	−0.735788	−	0.0791233i
$251$		−	4.09769i		−	0.258644i	−0.991603	−	0.129322i	$-0.958720\pi$
$251$		−	4.09769i		−	0.258644i	0.991603	−	0.129322i	$-0.0412801\pi$
$252$	2.32927	+	1.39320i	0.146730	+	0.0877635i
$253$	−11.9430	+	11.9430i	−0.750852	+	0.750852i
$254$	−11.0345	+	19.1124i	−0.692368	+	1.19922i
$255$	−23.5604	+	13.6090i	−1.47541	+	0.852229i
$256$	8.30003	+	14.3761i	0.518752	+	0.898505i
$257$	−20.0788	−	5.38010i	−1.25248	−	0.335602i	−0.429187	−	0.903215i	$-0.641200\pi$
$257$	−20.0788	−	5.38010i	−1.25248	−	0.335602i	−0.823295	+	0.567614i	$0.807867\pi$
$258$	16.0329	+	2.23684i	0.998162	+	0.139260i
$259$	−0.0274766	−	0.0158636i	−0.00170732	−	0.000985719i
$260$	−2.06292	+	1.60907i	−0.127937	+	0.0997903i
$261$	−7.75574	−	2.20706i	−0.480068	−	0.136614i
$262$	0.498694	+	0.498694i	0.0308094	+	0.0308094i
$263$	23.6905	−	6.34785i	1.46082	−	0.391425i	0.561046	−	0.827785i	$-0.310399\pi$
$263$	23.6905	−	6.34785i	1.46082	−	0.391425i	0.899772	+	0.436359i	$0.143732\pi$
$264$	−4.63424	+	10.9482i	−0.285218	+	0.673812i
$265$	−28.9718	−	11.7324i	−1.77972	−	0.720713i
$266$	5.11268	−	2.95181i	0.313479	−	0.180987i
$267$	10.5111	+	8.19518i	0.643269	+	0.501537i
$268$	1.55087	+	5.78792i	0.0947343	+	0.353553i
$269$	10.9833			0.669661			0.334831	−	0.942278i	$-0.391321\pi$
$269$	10.9833			0.669661			0.334831	+	0.942278i	$0.391321\pi$
$270$	11.7922	−	2.96786i	0.717650	−	0.180618i
$271$	−12.5132			−0.760123			−0.380061	−	0.924961i	$-0.624097\pi$
$271$	−12.5132			−0.760123			−0.380061	+	0.924961i	$0.624097\pi$
$272$	−2.49478	−	9.31066i	−0.151268	−	0.564542i
$273$	−1.76652	−	1.37730i	−0.106914	−	0.0833579i
$274$	1.90931	−	1.10234i	0.115345	−	0.0665947i
$275$	−10.8571	+	3.09439i	−0.654706	+	0.186599i
$276$	4.56927	−	10.7947i	0.275038	−	0.649762i
$277$	−12.0911	+	3.23980i	−0.726485	+	0.194661i	−0.603063	−	0.797693i	$-0.706053\pi$
$277$	−12.0911	+	3.23980i	−0.726485	+	0.194661i	−0.123421	+	0.992354i	$0.539387\pi$
$278$	−0.216589	−	0.216589i	−0.0129901	−	0.0129901i
$279$	0.290008	−	0.281186i	0.0173623	−	0.0168342i
$280$	−6.74621	−	0.833819i	−0.403163	−	0.0498302i
$281$	−17.0639	−	9.85187i	−1.01795	−	0.587713i	−0.104440	−	0.994531i	$-0.533305\pi$
$281$	−17.0639	−	9.85187i	−1.01795	−	0.587713i	−0.913509	+	0.406818i	$0.866638\pi$
$282$	−8.30695	−	1.15896i	−0.494672	−	0.0690148i
$283$	16.7606	+	4.49100i	0.996316	+	0.266962i	0.719901	−	0.694077i	$-0.244187\pi$
$283$	16.7606	+	4.49100i	0.996316	+	0.266962i	0.276414	+	0.961039i	$0.410854\pi$
$284$	5.49427	+	9.51635i	0.326025	+	0.564692i
$285$	−5.65022	+	21.1041i	−0.334690	+	1.25010i
$286$	1.52799	−	2.64656i	0.0903520	−	0.156494i
$287$	4.13338	−	4.13338i	0.243986	−	0.243986i
$288$	0.215151	−	13.9302i	0.0126779	−	0.820844i
$289$		−	32.3532i		−	1.90313i
$290$	6.22963	−	0.870427i	0.365816	−	0.0511132i
$291$	8.64050	+	3.65743i	0.506515	+	0.214403i
$292$	−0.532951	+	1.98900i	−0.0311886	+	0.116397i
$293$	−5.46158	+	20.3829i	−0.319069	+	1.19078i	0.601072	+	0.799195i	$0.294741\pi$
$293$	−5.46158	+	20.3829i	−0.319069	+	1.19078i	−0.920141	+	0.391587i	$0.871926\pi$
$294$	−0.222720	−	1.79896i	−0.0129893	−	0.104918i
$295$	13.9158	+	10.5038i	0.810208	+	0.611554i
$296$			0.0964496i			0.00560602i
$297$	9.47081	−	6.92466i	0.549552	−	0.401810i
$298$	−1.32058	+	1.32058i	−0.0764994	+	0.0764994i
$299$	−4.83707	+	8.37805i	−0.279735	+	0.484515i
$300$	6.17696	−	4.82003i	0.356627	−	0.278284i
$301$	4.46521	+	7.73397i	0.257370	+	0.445779i
$302$	5.70808	+	1.52948i	0.328463	+	0.0880114i
$303$	6.11883	+	15.1009i	0.351518	+	0.867526i
$304$	−6.70291	−	3.86993i	−0.384438	−	0.221955i
$305$	2.26454	−	18.3218i	0.129667	−	1.04911i
$306$	−6.03707	+	21.2146i	−0.345116	+	1.21276i
$307$	11.9815	+	11.9815i	0.683819	+	0.683819i	0.960859	−	0.277039i	$-0.0893532\pi$
$307$	11.9815	+	11.9815i	0.683819	+	0.683819i	−0.277039	+	0.960859i	$0.589353\pi$
$308$	−1.97313	+	0.528698i	−0.112429	+	0.0301254i
$309$	−12.0944	−	16.0164i	−0.688029	−	0.911139i
$310$	−0.118273	+	0.292061i	−0.00671744	+	0.0165880i
$311$	6.35788	−	3.67073i	0.360523	−	0.208148i	−0.308787	−	0.951131i	$-0.599923\pi$
$311$	6.35788	−	3.67073i	0.360523	−	0.208148i	0.669310	+	0.742983i	$0.266590\pi$
$312$	−0.940917	+	6.74413i	−0.0532689	+	0.381811i
$313$	−4.11996	−	15.3759i	−0.232874	−	0.869097i	−0.979096	−	0.203399i	$-0.934801\pi$
$313$	−4.11996	−	15.3759i	−0.232874	−	0.869097i	0.746222	−	0.665697i	$-0.231866\pi$
$314$	−16.0745			−0.907134
$315$	5.29112	+	4.12359i	0.298121	+	0.232338i
$316$	1.80932			0.101782
$317$	0.711062	+	2.65372i	0.0399372	+	0.149048i	0.983015	−	0.183524i	$-0.0587504\pi$
$317$	0.711062	+	2.65372i	0.0399372	+	0.149048i	−0.943078	+	0.332571i	$0.892084\pi$
$318$	−23.4844	+	9.51577i	−1.31694	+	0.533618i
$319$	5.25586	−	3.03447i	0.294271	−	0.169898i
$320$	6.63137	+	15.6574i	0.370705	+	0.875275i
$321$	−6.96569	+	0.862384i	−0.388787	+	0.0481336i
$322$	−7.56199	+	2.02623i	−0.421413	+	0.112917i
$323$	−28.0218	−	28.0218i	−1.55918	−	1.55918i
$324$	−4.28702	+	6.92243i	−0.238168	+	0.384579i
$325$	−5.54801	+	3.32149i	−0.307748	+	0.184243i
$326$	−19.2942	−	11.1395i	−1.06861	−	0.616961i
$327$	13.9399	−	17.8793i	0.770879	−	0.988726i
$328$	−17.1645	−	4.59922i	−0.947752	−	0.253949i
$329$	−2.31352	−	4.00713i	−0.127548	−	0.220920i
$330$	−4.57435	+	7.92672i	−0.251809	+	0.436352i
$331$	5.85956	−	10.1491i	0.322070	−	0.557842i	−0.658845	−	0.752279i	$-0.728955\pi$
$331$	5.85956	−	10.1491i	0.322070	−	0.557842i	0.980915	+	0.194437i	$0.0622879\pi$
$332$	−6.05200	+	6.05200i	−0.332147	+	0.332147i
$333$	0.0488582	−	0.0816851i	0.00267742	−	0.00447632i
$334$		−	5.29650i		−	0.289812i
$335$	2.04939	+	14.6675i	0.111970	+	0.801370i
$336$	−1.89653	+	1.43213i	−0.103464	+	0.0781288i
$337$	6.12298	−	22.8513i	0.333540	−	1.24479i	−0.571903	−	0.820321i	$-0.693795\pi$
$337$	6.12298	−	22.8513i	0.333540	−	1.24479i	0.905443	−	0.424467i	$-0.139539\pi$
$338$	−3.06828	+	11.4510i	−0.166892	+	0.622850i
$339$	4.23689	−	3.19940i	0.230116	−	0.173768i
$340$	1.96664	+	14.0752i	0.106656	+	0.763334i
$341$			0.304019i			0.0164636i
$342$	8.61750	+	15.4730i	0.465981	+	0.836683i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	13.5740	−	23.5109i	0.731863	−	1.26762i
$345$	14.4807	−	25.0931i	0.779616	−	1.35097i
$346$	−9.00293	−	15.5935i	−0.484001	−	0.838314i
$347$	−16.3983	−	4.39392i	−0.880308	−	0.235878i	−0.209768	−	0.977751i	$-0.567271\pi$
$347$	−16.3983	−	4.39392i	−0.880308	−	0.235878i	−0.670540	+	0.741873i	$0.733938\pi$
$348$	−2.58979	+	3.32165i	−0.138827	+	0.178059i
$349$	−17.6288	−	10.1780i	−0.943650	−	0.544817i	−0.0525476	−	0.998618i	$-0.516734\pi$
$349$	−17.6288	−	10.1780i	−0.943650	−	0.544817i	−0.891103	+	0.453802i	$0.850067\pi$
$350$	−5.07533	−	1.27407i	−0.271288	−	0.0681017i
$351$	4.21324	−	5.23511i	0.224886	−	0.279429i
$352$	7.41437	+	7.41437i	0.395187	+	0.395187i
$353$	30.9704	−	8.29848i	1.64839	−	0.441684i	0.689225	−	0.724547i	$-0.257951\pi$
$353$	30.9704	−	8.29848i	1.64839	−	0.441684i	0.959160	+	0.282863i	$0.0912843\pi$
$354$	14.0268	−	1.73658i	0.745516	−	0.0922983i
$355$	10.5919	+	25.0086i	0.562158	+	1.32732i
$356$	6.02914	−	3.48092i	0.319544	−	0.184489i
$357$	−11.2774	+	4.56954i	−0.596861	+	0.241846i
$358$	3.06574	+	11.4415i	0.162029	+	0.604701i
$359$	−14.6294			−0.772109			−0.386055	−	0.922476i	$-0.626162\pi$
$359$	−14.6294			−0.772109			−0.386055	+	0.922476i	$0.626162\pi$
$360$	2.81371	−	20.1976i	0.148295	−	1.06451i
$361$	−12.8205			−0.674765
$362$	1.06569	+	3.97721i	0.0560115	+	0.209038i
$363$	1.41252	−	10.1244i	0.0741382	−	0.531394i
$364$	−1.01327	+	0.585011i	−0.0531097	+	0.0306629i
$365$	−1.91030	+	4.71728i	−0.0999898	+	0.246914i
$366$	−9.01868	−	11.9432i	−0.471414	−	0.624281i
$367$	−0.801886	+	0.214865i	−0.0418581	+	0.0112158i	−0.279687	−	0.960091i	$-0.590231\pi$
$367$	−0.801886	+	0.214865i	−0.0418581	+	0.0112158i	0.237829	+	0.971307i	$0.423564\pi$
$368$	7.25758	+	7.25758i	0.378327	+	0.378327i
$369$	12.2072	+	12.5902i	0.635480	+	0.655418i
$370$	−0.00910756	+	0.0736869i	−0.000473480	+	0.00383080i
$371$	−12.1059	−	6.98932i	−0.628504	−	0.362867i
$372$	−0.0792362	−	0.195550i	−0.00410820	−	0.0101388i
$373$	−22.2471	−	5.96109i	−1.15191	−	0.308654i	−0.368180	−	0.929755i	$-0.620019\pi$
$373$	−22.2471	−	5.96109i	−1.15191	−	0.308654i	−0.783731	+	0.621101i	$0.786686\pi$
$374$	−8.30031	−	14.3766i	−0.429199	−	0.743394i
$375$	16.6129	−	9.95043i	0.857887	−	0.513838i
$376$	−7.03299	+	12.1815i	−0.362699	+	0.628213i
$377$	2.45799	−	2.45799i	0.126593	−	0.126593i
$378$	5.40656	−	0.584735i	0.278084	−	0.0300755i
$379$			27.1820i			1.39624i	0.715978	+	0.698122i	$0.245981\pi$
$379$			27.1820i			1.39624i	−0.715978	+	0.698122i	$0.754019\pi$
$380$	9.10824	+	6.87500i	0.467243	+	0.352680i
$381$	−4.48760	−	36.2474i	−0.229907	−	1.85701i
$382$	1.10795	−	4.13492i	0.0566876	−	0.211561i
$383$	5.67181	−	21.1675i	0.289816	−	1.08161i	−0.655432	−	0.755254i	$-0.727513\pi$
$383$	5.67181	−	21.1675i	0.289816	−	1.08161i	0.945248	−	0.326354i	$-0.105820\pi$
$384$	−2.12061	−	0.897631i	−0.108217	−	0.0458071i
$385$	−5.00021	+	0.698648i	−0.254834	+	0.0356064i
$386$		−	18.0137i		−	0.916872i
$387$	−23.4060	+	13.0357i	−1.18979	+	0.662643i
$388$	3.46547	−	3.46547i	0.175932	−	0.175932i
$389$	1.34581	−	2.33102i	0.0682354	−	0.118187i	−0.829889	−	0.557928i	$-0.811596\pi$
$389$	1.34581	−	2.33102i	0.0682354	−	0.118187i	0.898125	+	0.439741i	$0.144930\pi$
$390$	−1.35569	+	5.06363i	−0.0686481	+	0.256407i
$391$	26.2758	+	45.5110i	1.32882	+	2.30159i
$392$	−2.93637	−	0.786799i	−0.148309	−	0.0397393i
$393$	−1.15600	−	0.161281i	−0.0583126	−	0.00813557i
$394$	5.00475	+	2.88950i	0.252136	+	0.145571i
$395$	4.43812	+	0.548543i	0.223306	+	0.0276002i
$396$	−1.49449	−	5.94317i	−0.0751010	−	0.298656i
$397$	25.4716	+	25.4716i	1.27838	+	1.27838i	0.941573	+	0.336808i	$0.109347\pi$
$397$	25.4716	+	25.4716i	1.27838	+	1.27838i	0.336808	+	0.941573i	$0.390653\pi$
$398$	−4.58284	+	1.22797i	−0.229717	+	0.0615525i
$399$	−3.80858	+	8.99757i	−0.190667	+	0.450442i
$400$	1.88041	+	6.59765i	0.0940204	+	0.329883i
$401$	0.533595	−	0.308071i	0.0266465	−	0.0153843i	−0.486618	−	0.873615i	$-0.661769\pi$
$401$	0.533595	−	0.308071i	0.0266465	−	0.0153843i	0.513264	+	0.858231i	$0.328436\pi$
$402$	9.46818	+	7.38205i	0.472230	+	0.368183i
$403$	0.0450692	+	0.168201i	0.00224506	+	0.00837867i
$404$	8.51066			0.423421
$405$	−12.6144	+	15.6804i	−0.626816	+	0.779167i
$406$	2.81304			0.139609
$407$	0.0185409	+	0.0691956i	0.000919039	+	0.00342990i
$408$	29.1715	+	22.7441i	1.44420	+	1.12600i
$409$	−14.5678	+	8.41072i	−0.720331	+	0.415884i	−0.814875	−	0.579637i	$-0.803194\pi$
$409$	−14.5678	+	8.41072i	−0.720331	+	0.415884i	0.0945432	+	0.995521i	$0.469861\pi$
$410$	−12.6793	−	5.13459i	−0.626186	−	0.253579i
$411$	−1.42229	+	3.36010i	−0.0701566	+	0.165741i
$412$	−10.1260	+	2.71325i	−0.498871	+	0.133672i
$413$	5.51343	+	5.51343i	0.271298	+	0.271298i
$414$	−5.72762	−	22.7771i	−0.281497	−	1.11944i
$415$	−16.6799	+	13.0103i	−0.818784	+	0.638648i
$416$	5.20119	+	3.00291i	0.255009	+	0.147230i
$417$	0.502066	+	0.0700464i	0.0245863	+	0.00343019i
$418$	−12.8755	−	3.44998i	−0.629761	−	0.168744i
$419$	−6.31093	−	10.9309i	−0.308309	−	0.534007i	0.669683	−	0.742647i	$-0.266430\pi$
$419$	−6.31093	−	10.9309i	−0.308309	−	0.534007i	−0.977993	+	0.208639i	$0.933096\pi$
$420$	3.03413	−	1.75258i	0.148051	−	0.0855172i
$421$	−2.72983	+	4.72820i	−0.133044	+	0.230439i	−0.924848	−	0.380336i	$-0.875808\pi$
$421$	−2.72983	+	4.72820i	−0.133044	+	0.230439i	0.791805	+	0.610774i	$0.209142\pi$
$422$	1.98714	−	1.98714i	0.0967325	−	0.0967325i
$423$	12.1271	−	6.75408i	0.589642	−	0.328394i
$424$			42.4944i			2.06371i
$425$	0.556744	+	35.1215i	0.0270060	+	1.70364i
$426$	20.2753	+	8.58231i	0.982340	+	0.415814i
$427$	2.13684	−	7.97480i	0.103409	−	0.385928i
$428$	−0.948882	+	3.54128i	−0.0458659	+	0.171174i
$429$	0.621414	+	5.01931i	0.0300021	+	0.242334i
$430$	12.5906	−	16.6804i	0.607172	−	0.804402i
$431$		−	18.6882i		−	0.900181i	−0.892983	−	0.450090i	$-0.851392\pi$
$431$		−	18.6882i		−	0.900181i	0.892983	−	0.450090i	$-0.148608\pi$
$432$	−4.20800	−	5.75525i	−0.202457	−	0.276900i
$433$	−8.48817	+	8.48817i	−0.407915	+	0.407915i	−0.881011	−	0.473096i	$-0.843136\pi$
$433$	−8.48817	+	8.48817i	−0.407915	+	0.407915i	0.473096	+	0.881011i	$0.343136\pi$
$434$	−0.0704586	+	0.122038i	−0.00338212	+	0.00585800i
$435$	−7.35958	+	7.36258i	−0.352865	+	0.353009i
$436$	−5.92101	−	10.2555i	−0.283565	−	0.491149i
$437$	40.7592	+	10.9214i	1.94978	+	0.522441i
$438$	1.54939	+	3.82380i	0.0740326	+	0.182708i
$439$	−10.4728	−	6.04647i	−0.499839	−	0.288582i	0.228808	−	0.973472i	$-0.426517\pi$
$439$	−10.4728	−	6.04647i	−0.499839	−	0.288582i	−0.728647	+	0.684889i	$0.759850\pi$
$440$	9.43953	+	12.1020i	0.450012	+	0.576941i
$441$	2.08831	+	2.15383i	0.0994432	+	0.102563i
$442$	−6.72344	−	6.72344i	−0.319801	−	0.319801i
$443$	26.2233	−	7.02651i	1.24591	−	0.333839i	0.425152	−	0.905122i	$-0.360221\pi$
$443$	26.2233	−	7.02651i	1.24591	−	0.333839i	0.820753	+	0.571283i	$0.193554\pi$
$444$	−0.0299602	−	0.0396755i	−0.00142185	−	0.00188292i
$445$	15.8443	−	6.71054i	0.751093	−	0.318110i
$446$	22.5331	−	13.0095i	1.06697	−	0.616018i
$447$	0.427087	−	3.06119i	0.0202005	−	0.144790i
$448$	1.96815	+	7.34522i	0.0929862	+	0.347029i
$449$	3.85295			0.181832			0.0909159	−	0.995859i	$-0.471021\pi$
$449$	3.85295			0.181832			0.0909159	+	0.995859i	$0.471021\pi$
$450$	4.05688	−	15.1652i	0.191243	−	0.714892i
$451$	−13.1984			−0.621490
$452$	−0.717749	−	2.67868i	−0.0337601	−	0.125994i
$453$	−9.06425	+	3.67279i	−0.425876	+	0.172563i
$454$	7.15291	−	4.12973i	0.335703	−	0.193818i
$455$	−2.66283	+	1.12779i	−0.124835	+	0.0528714i
$456$	29.4767	−	3.64935i	1.38037	−	0.170896i
$457$	−22.3437	+	5.98699i	−1.04520	+	0.280059i	−0.740265	−	0.672315i	$-0.765300\pi$
$457$	−22.3437	+	5.98699i	−1.04520	+	0.280059i	−0.304931	+	0.952375i	$0.598633\pi$
$458$	−11.3836	−	11.3836i	−0.531920	−	0.531920i
$459$	−13.1845	−	34.0398i	−0.615400	−	1.58884i
$460$	−9.30719	−	11.9324i	−0.433950	−	0.556349i
$461$	−9.68201	−	5.58991i	−0.450936	−	0.260348i	0.257289	−	0.966334i	$-0.417171\pi$
$461$	−9.68201	−	5.58991i	−0.450936	−	0.260348i	−0.708225	+	0.705986i	$0.750504\pi$
$462$	−2.51658	+	3.22775i	−0.117082	+	0.150168i
$463$	8.50775	+	2.27964i	0.395389	+	0.105944i	0.451034	−	0.892507i	$-0.351055\pi$
$463$	8.50775	+	2.27964i	0.395389	+	0.105944i	−0.0556460	+	0.998451i	$0.517722\pi$
$464$	−1.84400	−	3.19389i	−0.0856053	−	0.148273i
$465$	−0.135074	−	0.503692i	−0.00626389	−	0.0233582i
$466$	10.8792	−	18.8433i	0.503970	−	0.872901i
$467$	−10.9122	+	10.9122i	−0.504958	+	0.504958i	−0.912975	−	0.408016i	$-0.866221\pi$
$467$	−10.9122	+	10.9122i	−0.504958	+	0.504958i	0.408016	+	0.912975i	$0.366221\pi$
$468$	−1.70788	−	3.06655i	−0.0789468	−	0.141751i
$469$			6.62322i			0.305832i
$470$	−6.52344	+	8.64248i	−0.300904	+	0.398648i
$471$	21.2301	−	16.0315i	0.978231	−	0.738692i
$472$	6.13480	−	22.8954i	0.282377	−	1.05384i
$473$	5.21879	−	19.4768i	0.239960	−	0.895544i
$474$	2.89301	−	2.18460i	0.132880	−	0.100342i
$475$	20.2574	+	19.6252i	0.929475	+	0.900467i
$476$			6.35576i			0.291316i
$477$	21.5263	−	35.9894i	0.985622	−	1.64784i
$478$	18.5160	−	18.5160i	0.846904	−	0.846904i
$479$	5.05441	−	8.75450i	0.230942	−	0.400003i	−0.727144	−	0.686485i	$-0.759153\pi$
$479$	5.05441	−	8.75450i	0.230942	−	0.400003i	0.958086	+	0.286482i	$0.0924859\pi$
$480$	−15.5781	−	8.98980i	−0.711040	−	0.410326i
$481$	0.0205158	+	0.0355343i	0.000935438	+	0.00162023i
$482$	−17.3160	−	4.63982i	−0.788724	−	0.211338i
$483$	7.96657	−	10.2179i	0.362491	−	0.464930i
$484$	−4.62419	−	2.66978i	−0.210191	−	0.121354i
$485$	9.55116	−	7.44987i	0.433696	−	0.338281i
$486$	1.50351	+	16.2448i	0.0682008	+	0.736881i
$487$	−1.14268	−	1.14268i	−0.0517797	−	0.0517797i	0.680743	−	0.732523i	$-0.261657\pi$
$487$	−1.14268	−	1.14268i	−0.0517797	−	0.0517797i	−0.732523	+	0.680743i	$0.761657\pi$
$488$	−24.2431	+	6.49591i	−1.09743	+	0.294056i
$489$	36.5923	−	4.53030i	1.65476	−	0.204867i
$490$	−2.16908	−	0.878386i	−0.0979888	−	0.0396814i
$491$	11.6749	−	6.74052i	0.526882	−	0.304195i	−0.212864	−	0.977082i	$-0.568279\pi$
$491$	11.6749	−	6.74052i	0.526882	−	0.304195i	0.739746	+	0.672886i	$0.234946\pi$
$492$	8.48946	−	3.43989i	0.382735	−	0.155082i
$493$	−4.88725	−	18.2395i	−0.220111	−	0.821465i
$494$	−7.63489			−0.343510
$495$	−1.86404	−	15.0312i	−0.0837823	−	0.675603i
$496$	0.184747			0.00829540
$497$	3.14359	+	11.7321i	0.141009	+	0.526255i
$498$	−2.36957	+	16.9841i	−0.106183	+	0.761078i
$499$	−12.7525	+	7.36266i	−0.570880	+	0.329598i	−0.757501	−	0.652834i	$-0.773580\pi$
$499$	−12.7525	+	7.36266i	−0.570880	+	0.329598i	0.186621	+	0.982432i	$0.440247\pi$
$500$	−1.55831	−	9.99421i	−0.0696896	−	0.446955i
$501$	5.28234	+	6.99527i	0.235998	+	0.312526i
$502$	−4.14236	+	1.10994i	−0.184883	+	0.0495391i
$503$	−2.71942	−	2.71942i	−0.121253	−	0.121253i	0.643877	−	0.765129i	$-0.277325\pi$
$503$	−2.71942	−	2.71942i	−0.121253	−	0.121253i	−0.765129	+	0.643877i	$0.777325\pi$
$504$	2.49615	−	8.77161i	0.111188	−	0.390719i
$505$	20.8760	+	2.58023i	0.928968	+	0.114819i
$506$	15.3082	+	8.83821i	0.680534	+	0.392906i
$507$	−7.36798	−	18.1838i	−0.327223	−	0.807569i
$508$	−18.4278	−	4.93771i	−0.817600	−	0.219075i
$509$	−6.52095	−	11.2946i	−0.289036	−	0.500625i	0.684544	−	0.728972i	$-0.260001\pi$
$509$	−6.52095	−	11.2946i	−0.289036	−	0.500625i	−0.973580	+	0.228347i	$0.926668\pi$
$510$	20.1392	+	20.1310i	0.891777	+	0.891414i
$511$	−1.13802	+	1.97111i	−0.0503432	+	0.0871970i
$512$	10.4044	−	10.4044i	0.459812	−	0.459812i
$513$	−26.8131	−	11.8412i	−1.18383	−	0.522803i
$514$			21.7550i			0.959571i
$515$	−25.6608	+	3.58543i	−1.13075	+	0.157993i
$516$	1.71940	+	13.8880i	0.0756922	+	0.611384i
$517$	−2.70396	+	10.0913i	−0.118920	+	0.443816i
$518$	−0.00859397	+	0.0320731i	−0.000377597	+	0.00140921i
$519$	27.4423	+	11.6161i	1.20459	+	0.509888i
$520$	7.01654	+	5.29616i	0.307696	+	0.232252i
$521$			24.9630i			1.09365i	0.837247	+	0.546824i	$0.184164\pi$
$521$			24.9630i			1.09365i	−0.837247	+	0.546824i	$0.815836\pi$
$522$	−0.130326	+	8.43810i	−0.00570422	+	0.369326i
$523$	−30.1029	+	30.1029i	−1.31631	+	1.31631i	−0.399634	+	0.916675i	$0.630863\pi$
$523$	−30.1029	+	30.1029i	−1.31631	+	1.31631i	−0.916675	+	0.399634i	$0.869137\pi$
$524$	−0.304834	+	0.527989i	−0.0133168	+	0.0230653i
$525$	7.97383	−	3.37906i	0.348006	−	0.147474i
$526$	−12.8341	−	22.2293i	−0.559593	−	0.969243i
$527$	0.913694	+	0.244824i	0.0398012	+	0.0106647i
$528$	5.31441	+	0.741448i	0.231280	+	0.0322674i
$529$	−28.5417	−	16.4786i	−1.24094	−	0.716460i
$530$	−4.01267	+	32.4655i	−0.174299	+	1.41021i
$531$	−16.7937	+	16.2829i	−0.728786	+	0.706617i
$532$	3.60868	+	3.60868i	0.156456	+	0.156456i
$533$	−7.30212	+	1.95660i	−0.316290	+	0.0847496i
$534$	5.43737	−	12.8455i	0.235298	−	0.555879i
$535$	−3.40116	+	8.39879i	−0.147045	+	0.363111i
$536$	17.4368	−	10.0671i	0.753155	−	0.434834i
$537$	−15.4599	−	12.0536i	−0.667145	−	0.520152i
$538$	−2.97504	−	11.1030i	−0.128263	−	0.478684i
$539$	−2.25789			−0.0972540
$540$	5.11655	+	9.18251i	0.220181	+	0.395152i
$541$	7.11356			0.305836			0.152918	−	0.988239i	$-0.451133\pi$
$541$	7.11356			0.305836			0.152918	+	0.988239i	$0.451133\pi$
$542$	3.38945	+	12.6496i	0.145589	+	0.543347i
$543$	−5.37408	−	4.19000i	−0.230624	−	0.179810i
$544$	28.2537	−	16.3123i	1.21137	−	0.699384i
$545$	−11.4145	−	26.9510i	−0.488945	−	1.15445i
$546$	−0.913814	+	2.15884i	−0.0391077	+	0.0923898i
$547$	23.3988	−	6.26969i	1.00046	−	0.268073i	0.278822	−	0.960343i	$-0.410056\pi$
$547$	23.3988	−	6.26969i	1.00046	−	0.268073i	0.721638	+	0.692270i	$0.243389\pi$
$548$	1.34764	+	1.34764i	0.0575685	+	0.0575685i
$549$	23.8226	+	6.77923i	1.01672	+	0.289330i
$550$	6.06897	+	10.1372i	0.258782	+	0.432253i
$551$	−13.1309	−	7.58114i	−0.559396	−	0.322968i
$552$	−39.0094	−	5.44245i	−1.66035	−	0.231646i
$553$	1.93174	+	0.517609i	0.0821461	+	0.0220110i
$554$	6.55024	+	11.3453i	0.278293	+	0.482018i
$555$	−0.0614613	−	0.106404i	−0.00260889	−	0.00451660i
$556$	0.132393	−	0.229312i	0.00561473	−	0.00972499i
$557$	12.6979	−	12.6979i	0.538028	−	0.538028i	−0.384922	−	0.922949i	$-0.625772\pi$
$557$	12.6979	−	12.6979i	0.538028	−	0.538028i	0.922949	+	0.384922i	$0.125772\pi$
$558$	−0.362806	−	0.217004i	−0.0153588	−	0.00918653i
$559$		−	11.5493i		−	0.488484i
$560$	0.424557	+	3.03854i	0.0179408	+	0.128402i
$561$	25.3006	+	10.7095i	1.06819	+	0.452155i
$562$	−5.33715	+	19.9185i	−0.225134	+	0.840212i
$563$	−6.36452	+	23.7527i	−0.268232	+	1.00106i	0.692010	+	0.721888i	$0.256726\pi$
$563$	−6.36452	+	23.7527i	−0.268232	+	1.00106i	−0.960242	+	0.279169i	$0.909941\pi$
$564$	−0.890854	−	7.19565i	−0.0375117	−	0.302991i
$565$	−0.948470	−	6.78818i	−0.0399024	−	0.285581i
$566$		−	18.1598i		−	0.763313i
$567$	−6.55746	+	6.16439i	−0.275387	+	0.258880i
$568$	26.1085	−	26.1085i	1.09549	−	1.09549i
$569$	3.26377	−	5.65302i	0.136825	−	0.236987i	−0.789468	−	0.613791i	$-0.789644\pi$
$569$	3.26377	−	5.65302i	0.136825	−	0.236987i	0.926293	+	0.376804i	$0.122977\pi$
$570$	22.8646	−	0.00465162i	0.957693	−	0.000194835i
$571$	−13.1795	−	22.8276i	−0.551545	−	0.955305i	−0.998163	−	0.0605800i	$-0.980705\pi$
$571$	−13.1795	−	22.8276i	−0.551545	−	0.955305i	0.446618	−	0.894725i	$-0.352628\pi$
$572$	2.55176	+	0.683742i	0.106694	+	0.0285887i
$573$	2.66056	+	6.56612i	0.111147	+	0.274304i
$574$	−5.29805	−	3.05883i	−0.221136	−	0.127673i
$575$	−19.2122	−	32.0908i	−0.801203	−	1.33828i
$576$	−22.1242	+	5.56343i	−0.921842	+	0.231810i
$577$	13.6545	+	13.6545i	0.568446	+	0.568446i	0.931693	−	0.363247i	$-0.118332\pi$
$577$	13.6545	+	13.6545i	0.568446	+	0.568446i	−0.363247	+	0.931693i	$0.618332\pi$
$578$	−32.7059	+	8.76351i	−1.36038	+	0.364514i
$579$	17.9655	+	23.7913i	0.746622	+	0.988732i
$580$	2.12062	+	5.00702i	0.0880539	+	0.207905i
$581$	−8.19285	+	4.73015i	−0.339897	+	0.196240i
$582$	1.35685	−	9.72537i	0.0562432	−	0.403130i
$583$	8.16889	+	30.4867i	0.338321	+	1.26263i
$584$	6.91908			0.286314
$585$	−3.25959	−	8.03978i	−0.134767	−	0.332404i
$586$	22.0845			0.912301
$587$	8.47719	+	31.6373i	0.349891	+	1.30581i	0.886793	+	0.462167i	$0.152928\pi$
$587$	8.47719	+	31.6373i	0.349891	+	1.30581i	−0.536902	+	0.843645i	$0.680406\pi$
$588$	1.45231	−	0.588470i	0.0598923	−	0.0242681i
$589$	0.657785	−	0.379772i	0.0271035	−	0.0156482i
$590$	6.84892	−	16.9126i	0.281965	−	0.696282i
$591$	−9.49173	+	1.17512i	−0.390437	+	0.0483380i
$592$	0.0420490	−	0.0112670i	0.00172820	−	0.000463071i
$593$	−25.4874	−	25.4874i	−1.04664	−	1.04664i	−0.998858	−	0.0477841i	$-0.984784\pi$
$593$	−25.4874	−	25.4874i	−1.04664	−	1.04664i	−0.0477841	−	0.998858i	$-0.515216\pi$
$594$	−9.56550	−	7.69836i	−0.392477	−	0.315868i
$595$	−1.92691	+	15.5902i	−0.0789958	+	0.639134i
$596$	−1.39816	−	0.807228i	−0.0572708	−	0.0330653i
$597$	4.82803	−	6.19241i	0.197598	−	0.253439i
$598$	9.77959	+	2.62043i	0.399917	+	0.107157i
$599$	12.6728	+	21.9500i	0.517797	+	0.896851i	0.999786	+	0.0206737i	$0.00658112\pi$
$599$	12.6728	+	21.9500i	0.517797	+	0.896851i	−0.481989	+	0.876177i	$0.660086\pi$
$600$	−21.0160	−	15.8564i	−0.857976	−	0.647336i
$601$	−20.3321	+	35.2163i	−0.829365	+	1.43650i	0.0691722	+	0.997605i	$0.477964\pi$
$601$	−20.3321	+	35.2163i	−0.829365	+	1.43650i	−0.898537	+	0.438897i	$0.855369\pi$
$602$	6.60878	−	6.60878i	0.269354	−	0.269354i
$603$	−19.8673	−	0.306849i	−0.809058	−	0.0124959i
$604$			5.10848i			0.207861i
$605$	−10.5334	−	7.95070i	−0.428242	−	0.323242i
$606$	13.6081	−	10.2759i	0.552792	−	0.417430i
$607$	4.10605	−	15.3240i	0.166660	−	0.621982i	−0.831163	−	0.556029i	$-0.812324\pi$
$607$	4.10605	−	15.3240i	0.166660	−	0.621982i	0.997823	−	0.0659534i	$-0.0210089\pi$
$608$	6.78012	−	25.3038i	0.274970	−	1.02620i
$609$	−3.71528	+	2.80552i	−0.150551	+	0.113685i
$610$	−19.1349	+	2.67361i	−0.774751	+	0.108251i
$611$			5.98394i			0.242084i
$612$	−19.0650	−	0.294458i	−0.770657	−	0.0119028i
$613$	−10.7101	+	10.7101i	−0.432577	+	0.432577i	−0.889504	−	0.456927i	$-0.848950\pi$
$613$	−10.7101	+	10.7101i	−0.432577	+	0.432577i	0.456927	+	0.889504i	$0.348950\pi$
$614$	8.86666	−	15.3575i	0.357829	−	0.619778i
$615$	21.8669	−	5.86398i	0.881757	−	0.236458i
$616$	3.43194	+	5.94429i	0.138277	+	0.239502i
$617$	−28.1131	−	7.53288i	−1.13179	−	0.303263i	−0.356145	−	0.934431i	$-0.615909\pi$
$617$	−28.1131	−	7.53288i	−1.13179	−	0.303263i	−0.775646	+	0.631168i	$0.782576\pi$
$618$	−12.9149	+	16.5646i	−0.519515	+	0.666327i
$619$	−15.1344	−	8.73783i	−0.608302	−	0.351203i	0.163999	−	0.986461i	$-0.447561\pi$
$619$	−15.1344	−	8.73783i	−0.608302	−	0.351203i	−0.772300	+	0.635257i	$0.780894\pi$
$620$	−0.270335	−	0.0334128i	−0.0108569	−	0.00134189i
$621$	30.2809	+	24.3702i	1.21513	+	0.977944i
$622$	−5.43290	−	5.43290i	−0.217839	−	0.217839i
$623$	7.43291	−	1.99164i	0.297793	−	0.0797934i
$624$	3.05015	−	0.377622i	0.122104	−	0.0151170i
$625$	−0.792397	−	24.9874i	−0.0316959	−	0.999498i
$626$	−14.4275	+	8.32973i	−0.576639	+	0.332923i
$627$	20.4459	−	8.28457i	0.816529	−	0.330854i
$628$	−3.59648	−	13.4222i	−0.143515	−	0.535606i
$629$	0.222890			0.00888721
$630$	2.73533	−	6.46575i	0.108978	−	0.257602i
$631$	−17.0736			−0.679689			−0.339845	−	0.940482i	$-0.610375\pi$
$631$	−17.0736			−0.679689			−0.339845	+	0.940482i	$0.610375\pi$
$632$	−1.57351	−	5.87242i	−0.0625908	−	0.233592i
$633$	−0.642656	+	4.60632i	−0.0255433	+	0.183085i
$634$	2.49004	−	1.43762i	0.0988921	−	0.0570954i
$635$	−43.7048	−	17.6987i	−1.73437	−	0.702350i
$636$	−13.2001	−	17.4805i	−0.523417	−	0.693148i
$637$	−1.24919	+	0.334719i	−0.0494947	+	0.0132621i
$638$	−4.49120	−	4.49120i	−0.177808	−	0.177808i
$639$	−35.3376	+	8.88612i	−1.39793	+	0.351530i
$640$	−2.34411	+	1.82839i	−0.0926590	+	0.0722737i
$641$	17.6035	+	10.1634i	0.695296	+	0.401429i	0.805593	−	0.592469i	$-0.201847\pi$
$641$	17.6035	+	10.1634i	0.695296	+	0.401429i	−0.110297	+	0.993899i	$0.535180\pi$
$642$	2.75858	+	6.80802i	0.108872	+	0.268691i
$643$	19.1350	+	5.12722i	0.754612	+	0.202198i	0.615563	−	0.788088i	$-0.288929\pi$
$643$	19.1350	+	5.12722i	0.754612	+	0.202198i	0.139049	+	0.990285i	$0.455595\pi$
$644$	−3.38382	−	5.86095i	−0.133341	−	0.230954i
$645$	0.00703652	+	34.5874i	0.000277063	+	1.36188i
$646$	−20.7370	+	35.9175i	−0.815886	+	1.41316i
$647$	−28.0375	+	28.0375i	−1.10227	+	1.10227i	−0.108133	+	0.994136i	$0.534487\pi$
$647$	−28.0375	+	28.0375i	−1.10227	+	1.10227i	−0.994136	+	0.108133i	$0.965513\pi$
$648$	26.1961	+	7.89395i	1.02908	+	0.310104i
$649$		−	17.6051i		−	0.691061i
$650$	4.86049	+	4.70879i	0.190644	+	0.184694i
$651$	−0.0286546	−	0.231450i	−0.00112306	−	0.00907124i
$652$	4.98469	−	18.6031i	0.195216	−	0.728554i
$653$	−2.77432	+	10.3539i	−0.108568	+	0.405180i	−0.998725	−	0.0504723i	$-0.983927\pi$
$653$	−2.77432	+	10.3539i	−0.108568	+	0.405180i	0.890158	+	0.455652i	$0.150594\pi$
$654$	−21.8501	−	9.24890i	−0.854405	−	0.361661i
$655$	−0.907808	+	1.20270i	−0.0354710	+	0.0469932i
$656$			8.02047i			0.313147i
$657$	−5.85991	−	3.50498i	−0.228617	−	0.136742i
$658$	−3.42415	+	3.42415i	−0.133487	+	0.133487i
$659$	14.7622	−	25.5689i	0.575055	−	0.996024i	−0.420981	−	0.907069i	$-0.638314\pi$
$659$	14.7622	−	25.5689i	0.575055	−	0.996024i	0.996036	−	0.0889543i	$-0.0283525\pi$
$660$	−7.64231	−	2.04608i	−0.297476	−	0.0796437i
$661$	1.71447	+	2.96956i	0.0666853	+	0.115502i	0.897440	−	0.441136i	$-0.145424\pi$
$661$	1.71447	+	2.96956i	0.0666853	+	0.115502i	−0.830755	+	0.556638i	$0.812091\pi$
$662$	−11.8469	−	3.17436i	−0.460441	−	0.123375i
$663$	15.5854	+	2.17441i	0.605285	+	0.0844471i
$664$	24.9059	+	14.3794i	0.966537	+	0.558030i
$665$	7.75773	+	9.94587i	0.300832	+	0.385684i
$666$	−0.0958098	−	0.0272648i	−0.00371255	−	0.00105649i
$667$	14.2175	+	14.2175i	0.550504	+	0.550504i
$668$	4.42260	−	1.18503i	0.171116	−	0.0458503i
$669$	−16.7855	+	39.6550i	−0.648966	+	1.53315i
$670$	14.2722	−	6.04471i	0.551385	−	0.233528i
$671$	−16.1439	+	9.32069i	−0.623229	+	0.359821i
$672$	−6.34338	−	4.94574i	−0.244701	−	0.190786i
$673$	−6.80391	−	25.3925i	−0.262271	−	0.978810i	−0.963899	−	0.266267i	$-0.914210\pi$
$673$	−6.80391	−	25.3925i	−0.262271	−	0.978810i	0.701628	−	0.712544i	$-0.252457\pi$
$674$	−24.7589			−0.953677
$675$	9.76656	+	24.0752i	0.375915	+	0.926654i
$676$	−10.2481			−0.394158
$677$	−7.36350	−	27.4810i	−0.283002	−	1.05618i	−0.950287	−	0.311376i	$-0.899210\pi$
$677$	−7.36350	−	27.4810i	−0.283002	−	1.05618i	0.667285	−	0.744803i	$-0.267456\pi$
$678$	−4.38192	−	3.41645i	−0.168287	−	0.131208i
$679$	4.69135	−	2.70855i	0.180038	−	0.103945i
$680$	43.9728	−	18.6238i	1.68628	−	0.714188i
$681$	−5.32840	+	12.5881i	−0.204185	+	0.482376i
$682$	0.307333	−	0.0823497i	0.0117684	−	0.00315333i
$683$	20.5087	+	20.5087i	0.784743	+	0.784743i	0.980627	−	0.195884i	$-0.0627577\pi$
$683$	20.5087	+	20.5087i	0.784743	+	0.784743i	−0.195884	+	0.980627i	$0.562758\pi$
$684$	−10.9919	+	10.6576i	−0.420287	+	0.407502i
$685$	2.89709	+	3.71423i	0.110692	+	0.141914i
$686$	−0.906348	−	0.523280i	−0.0346045	−	0.0199789i
$687$	26.3879	+	3.68154i	1.00676	+	0.140459i
$688$	−11.8357	−	3.17137i	−0.451232	−	0.120907i
$689$	9.03897	+	15.6560i	0.344357	+	0.596445i
$690$	−29.2891	−	7.84159i	−1.11502	−	0.298524i
$691$	3.29934	−	5.71463i	0.125513	−	0.217395i	−0.796420	−	0.604743i	$-0.793276\pi$
$691$	3.29934	−	5.71463i	0.125513	−	0.217395i	0.921933	+	0.387349i	$0.126609\pi$
$692$	11.0064	−	11.0064i	0.418399	−	0.418399i
$693$	0.104606	−	6.77285i	0.00397366	−	0.257279i
$694$			17.7673i			0.674436i
$695$	0.394272	−	0.522345i	0.0149556	−	0.0198137i
$696$	13.0332	+	5.51680i	0.494021	+	0.209114i
$697$	−10.6286	+	39.6663i	−0.402586	+	1.50247i
$698$	−5.51384	+	20.5779i	−0.208702	+	0.778886i
$699$	4.42443	+	35.7372i	0.167347	+	1.35170i
$700$	−0.0716980	−	4.52298i	−0.00270993	−	0.170953i
$701$			48.8079i			1.84345i	0.387846	+	0.921724i	$0.373219\pi$
$701$			48.8079i			1.84345i	−0.387846	+	0.921724i	$0.626781\pi$
$702$	−6.43341	−	2.84113i	−0.242814	−	0.107232i
$703$	0.126553	−	0.126553i	0.00477303	−	0.00477303i
$704$	8.58486	−	14.8694i	0.323554	−	0.560412i
$705$	−0.00364577	−	17.9204i	−0.000137308	−	0.674922i
$706$	−16.7779	−	29.0601i	−0.631444	−	1.09369i
$707$	9.08652	+	2.43473i	0.341734	+	0.0915673i
$708$	4.58839	+	11.3239i	0.172442	+	0.425578i
$709$	18.0831	+	10.4403i	0.679123	+	0.392092i	0.799525	−	0.600633i	$-0.205085\pi$
$709$	18.0831	+	10.4403i	0.679123	+	0.392092i	−0.120401	+	0.992725i	$0.538418\pi$
$710$	22.4122	−	17.4814i	0.841113	−	0.656065i
$711$	−1.64214	+	5.77056i	−0.0615850	+	0.216413i
$712$	−16.5412	−	16.5412i	−0.619908	−	0.619908i
$713$	−0.972906	+	0.260689i	−0.0364356	+	0.00976290i
$714$	7.67405	+	10.1625i	0.287194	+	0.380324i
$715$	6.05196	+	2.45080i	0.226331	+	0.0916546i
$716$	−8.86776	+	5.11981i	−0.331404	+	0.191336i
$717$	−5.98823	+	42.9213i	−0.223634	+	1.60293i
$718$	3.96266	+	14.7888i	0.147885	+	0.551915i
$719$	−36.8394			−1.37388			−0.686938	−	0.726716i	$-0.741046\pi$
$719$	−36.8394			−1.37388			−0.686938	+	0.726716i	$0.741046\pi$
$720$	−9.13421	+	1.13274i	−0.340412	+	0.0422149i
$721$	−11.5873			−0.431535
$722$	3.47270	+	12.9603i	0.129240	+	0.482332i
$723$	27.4973	−	11.1418i	1.02264	−	0.414368i
$724$	−3.08256	+	1.77971i	−0.114562	+	0.0661426i
$725$	3.68370	+	12.9247i	0.136809	+	0.480013i
$726$	−10.6174	+	1.31448i	−0.394048	+	0.0487850i
$727$	1.19144	−	0.319245i	0.0441880	−	0.0118401i	−0.236657	−	0.971593i	$-0.576052\pi$
$727$	1.19144	−	0.319245i	0.0441880	−	0.0118401i	0.280845	+	0.959753i	$0.409385\pi$
$728$	2.77995	+	2.77995i	0.103032	+	0.103032i
$729$	−18.1872	−	19.9556i	−0.673599	−	0.739097i
$730$	5.28614	+	0.653356i	0.195649	+	0.0241818i
$731$	−54.3326	−	31.3689i	−2.00956	−	1.16022i
$732$	7.95480	−	10.2028i	0.294018	−	0.377106i
$733$	12.5193	+	3.35454i	0.462412	+	0.123903i	0.482501	−	0.875895i	$-0.339728\pi$
$733$	12.5193	+	3.35454i	0.462412	+	0.123903i	−0.0200895	+	0.999798i	$0.506395\pi$
$734$	0.434414	+	0.752426i	0.0160345	+	0.0277726i
$735$	3.74081	−	1.00316i	0.137982	−	0.0370022i
$736$	−17.3694	+	30.0847i	−0.640245	+	1.10894i
$737$	10.5744	−	10.5744i	0.389513	−	0.389513i
$738$	9.42085	−	15.7505i	0.346786	−	0.579785i
$739$			22.0941i			0.812746i	0.913707	+	0.406373i	$0.133207\pi$
$739$			22.0941i			0.812746i	−0.913707	+	0.406373i	$0.866793\pi$
$740$	−0.0635666	+	0.00888177i	−0.00233676	+	0.000326500i
$741$	10.0837	−	7.61448i	0.370433	−	0.279725i
$742$	−3.78639	+	14.1310i	−0.139003	+	0.518765i
$743$	−3.29064	+	12.2808i	−0.120722	+	0.450541i	−0.999651	−	0.0264117i	$-0.991592\pi$
$743$	−3.29064	+	12.2808i	−0.120722	+	0.450541i	0.878929	+	0.476952i	$0.158259\pi$
$744$	−0.565779	+	0.427237i	−0.0207425	+	0.0156633i
$745$	−3.18484	−	2.40395i	−0.116683	−	0.0880740i
$746$			24.1043i			0.882520i
$747$	−13.8092	−	24.7948i	−0.505251	−	0.907193i
$748$	10.1474	−	10.1474i	0.371025	−	0.371025i
$749$	−2.02617	+	3.50943i	−0.0740347	+	0.128232i
$750$	−14.5588	−	14.0987i	−0.531613	−	0.514813i
$751$	5.09999	+	8.83345i	0.186101	+	0.322337i	0.943947	−	0.330097i	$-0.107081\pi$
$751$	5.09999	+	8.83345i	0.186101	+	0.322337i	−0.757846	+	0.652434i	$0.773748\pi$
$752$	6.13233	+	1.64315i	0.223623	+	0.0599196i
$753$	4.36398	−	5.59723i	0.159032	−	0.203974i
$754$	−3.15058	−	1.81899i	−0.114737	−	0.0662436i
$755$	−1.54877	+	12.5307i	−0.0563654	+	0.456038i
$756$	1.69791	+	4.38368i	0.0617525	+	0.159433i
$757$	−15.2261	−	15.2261i	−0.553400	−	0.553400i	0.374020	−	0.927421i	$-0.377979\pi$
$757$	−15.2261	−	15.2261i	−0.553400	−	0.553400i	−0.927421	+	0.374020i	$0.877979\pi$
$758$	27.4783	−	7.36278i	0.998056	−	0.267428i
$759$	−29.0327	+	3.59438i	−1.05382	+	0.130468i
$760$	14.3927	−	35.5411i	0.522078	−	1.28921i
$761$	−10.3237	+	5.96040i	−0.374234	+	0.216064i	−0.675307	−	0.737537i	$-0.735989\pi$
$761$	−10.3237	+	5.96040i	−0.374234	+	0.216064i	0.301072	+	0.953601i	$0.402655\pi$
$762$	−35.4270	+	14.3548i	−1.28338	+	0.520021i
$763$	−3.38776	−	12.6433i	−0.122645	−	0.457718i
$764$	3.70057			0.133882
$765$	−46.6756	−	6.50233i	−1.68756	−	0.235092i
$766$	−22.9345			−0.828658
$767$	−2.60986	−	9.74013i	−0.0942366	−	0.351696i
$768$	−3.97292	+	28.4764i	−0.143360	+	1.02755i
$769$	20.0270	−	11.5626i	0.722193	−	0.416958i	−0.0933665	−	0.995632i	$-0.529763\pi$
$769$	20.0270	−	11.5626i	0.722193	−	0.416958i	0.815559	+	0.578674i	$0.196429\pi$
$770$	2.06067	+	4.86547i	0.0742614	+	0.175339i
$771$	−21.6968	−	28.7326i	−0.781393	−	1.03478i
$772$	15.0415	−	4.03036i	0.541355	−	0.145056i
$773$	34.0111	+	34.0111i	1.22329	+	1.22329i	0.966454	+	0.256840i	$0.0826815\pi$
$773$	34.0111	+	34.0111i	1.22329	+	1.22329i	0.256840	+	0.966454i	$0.417319\pi$
$774$	19.5178	+	20.1302i	0.701553	+	0.723563i
$775$	−0.652979	−	0.163918i	−0.0234557	−	0.00588811i
$776$	−14.2615	−	8.23388i	−0.511958	−	0.295579i
$777$	−0.0206370	−	0.0509311i	−0.000740350	−	0.00182714i
$778$	−2.72097	−	0.729081i	−0.0975513	−	0.0261388i
$779$	16.4871	+	28.5565i	0.590712	+	1.02314i
$780$	−4.53147		0.000921892i	−0.162253		3.30090e-5i
$781$	13.7120	−	23.7500i	0.490656	−	0.849840i
$782$	38.8897	−	38.8897i	1.39069	−	1.39069i
$783$	−8.24342	−	11.2745i	−0.294596	−	0.402917i
$784$			1.37208i			0.0490028i
$785$	−4.75257	−	34.0141i	−0.169627	−	1.21401i
$786$	0.150087	+	1.21229i	0.00535343	+	0.0432409i
$787$	6.26573	−	23.3840i	0.223349	−	0.833551i	−0.759710	−	0.650262i	$-0.774659\pi$
$787$	6.26573	−	23.3840i	0.223349	−	0.833551i	0.983059	−	0.183289i	$-0.0586743\pi$
$788$	−1.29298	+	4.82549i	−0.0460607	+	0.171901i
$789$	39.1203	+	16.5592i	1.39272	+	0.589523i
$790$	−0.647630	−	4.63508i	−0.0230416	−	0.164909i
$791$		−	3.06526i		−	0.108988i
$792$	−17.9897	+	10.0192i	−0.639237	+	0.356016i
$793$	−7.54998	+	7.54998i	−0.268108	+	0.268108i
$794$	18.8497	−	32.6487i	0.668952	−	1.15866i
$795$	−27.0790	−	46.8803i	−0.960395	−	1.66267i
$796$	−2.05072	−	3.55195i	−0.0726858	−	0.125896i
$797$	41.2116	+	11.0426i	1.45979	+	0.391149i	0.899417	−	0.437092i	$-0.143991\pi$
$797$	41.2116	+	11.0426i	1.45979	+	0.391149i	0.560372	+	0.828241i	$0.310658\pi$
$798$	10.1273	+	1.41292i	0.358502	+	0.0500169i
$799$	28.1508	+	16.2529i	0.995904	+	0.574986i
$800$	−19.9223	+	11.9271i	−0.704361	+	0.421688i
$801$	5.62985	+	22.3883i	0.198921	+	0.791053i
$802$	−0.455964	−	0.455964i	−0.0161006	−	0.0161006i
$803$	4.96394	−	1.33008i	0.175174	−	0.0469377i
$804$	−4.04564	+	9.55763i	−0.142679	+	0.337072i
$805$	−6.52334	−	15.4023i	−0.229918	−	0.542861i
$806$	0.157826	−	0.0911210i	0.00555919	−	0.00320960i
$807$	15.0025	+	11.6970i	0.528114	+	0.411754i
$808$	−7.40146	−	27.6226i	−0.260382	−	0.971760i
$809$	14.6957			0.516675			0.258337	−	0.966055i	$-0.416825\pi$
$809$	14.6957			0.516675			0.258337	+	0.966055i	$0.416825\pi$
$810$	19.2682	+	8.50458i	0.677016	+	0.298820i
$811$	35.7614			1.25575			0.627876	−	0.778314i	$-0.283925\pi$
$811$	35.7614			1.25575			0.627876	+	0.778314i	$0.283925\pi$
$812$	0.629385	+	2.34890i	0.0220871	+	0.0824302i
$813$	−17.0923	−	13.3264i	−0.599455	−	0.467376i
$814$	0.0649277	−	0.0374860i	0.00227571	−	0.00131388i
$815$	17.8671	−	44.1207i	0.625856	−	1.54548i
$816$	6.50797	−	15.3748i	0.227825	−	0.538224i
$817$	−48.6597	+	13.0383i	−1.70239	+	0.456153i
$818$	12.4484	+	12.4484i	0.435247	+	0.435247i
$819$	−0.946164	−	3.76263i	−0.0330616	−	0.131477i
$820$	1.45056	−	11.7361i	0.0506557	−	0.409842i
$821$	−33.2479	−	19.1957i	−1.16036	−	0.669935i	−0.208971	−	0.977922i	$-0.567011\pi$
$821$	−33.2479	−	19.1957i	−1.16036	−	0.669935i	−0.951391	+	0.307987i	$0.900345\pi$
$822$	3.78198	+	0.527648i	0.131912	+	0.0184038i
$823$	10.8679	+	2.91204i	0.378830	+	0.101507i	0.443209	−	0.896418i	$-0.353840\pi$
$823$	10.8679	+	2.91204i	0.378830	+	0.101507i	−0.0643790	+	0.997926i	$0.520507\pi$
$824$	17.6125	+	30.5058i	0.613561	+	1.06272i
$825$	−18.1256	−	7.33584i	−0.631054	−	0.255401i
$826$	4.08010	−	7.06695i	0.141965	−	0.245890i
$827$	−25.3158	+	25.3158i	−0.880315	+	0.880315i	−0.993566	−	0.113251i	$-0.963873\pi$
$827$	−25.3158	+	25.3158i	−0.880315	+	0.880315i	0.113251	+	0.993566i	$0.463873\pi$
$828$	17.7375	−	9.87872i	0.616422	−	0.343309i
$829$			39.0123i			1.35495i	0.735544	+	0.677477i	$0.236927\pi$
$829$			39.0123i			1.35495i	−0.735544	+	0.677477i	$0.763073\pi$
$830$	17.6702	+	13.3376i	0.613340	+	0.462956i
$831$	−19.9661	−	8.45146i	−0.692618	−	0.293178i
$832$	2.54532	−	9.49925i	0.0882429	−	0.329327i
$833$	−1.81825	+	6.78581i	−0.0629987	+	0.235114i
$834$	−0.0651847	−	0.526512i	−0.00225716	−	0.0182316i
$835$	11.2076	−	1.56596i	0.387854	−	0.0541924i
$836$		−	11.5230i		−	0.398531i
$837$	0.695594	−	0.0752305i	0.0240433	−	0.00260035i
$838$	−9.34056	+	9.34056i	−0.322664	+	0.322664i
$839$	−21.4411	+	37.1371i	−0.740230	+	1.28212i	0.212161	+	0.977235i	$0.431950\pi$
$839$	−21.4411	+	37.1371i	−0.740230	+	1.28212i	−0.952391	+	0.304881i	$0.901383\pi$
$840$	−8.32696	−	8.32357i	−0.287307	−	0.287190i
$841$	10.8876	+	18.8579i	0.375436	+	0.650274i
$842$	5.51917	+	1.47886i	0.190203	+	0.0509648i
$843$	−12.8163	−	31.6299i	−0.441417	−	1.08939i
$844$	2.10387	+	1.21467i	0.0724183	+	0.0418107i
$845$	−25.1378	−	3.10698i	−0.864765	−	0.106883i
$846$	−10.1126	−	10.4298i	−0.347677	−	0.358586i
$847$	−4.17331	−	4.17331i	−0.143397	−	0.143397i
$848$	18.5262	−	4.96409i	0.636194	−	0.170468i
$849$	18.1113	+	23.9843i	0.621577	+	0.823138i
$850$	35.3535	−	10.0762i	1.21262	−	0.345610i
$851$	−0.205538	+	0.118667i	−0.00704574	+	0.00406786i
$852$	−2.62990	+	18.8501i	−0.0900989	+	0.645795i
$853$	−4.10602	−	15.3239i	−0.140588	−	0.524680i	−0.999912	−	0.0132495i	$-0.995782\pi$
$853$	−4.10602	−	15.3239i	−0.140588	−	0.524680i	0.859325	−	0.511430i	$-0.170884\pi$
$854$	−8.64054			−0.295673
$855$	−30.1934	+	22.8096i	−1.03259	+	0.780073i
$856$	12.3190			0.421053
$857$	−2.90660	−	10.8476i	−0.0992875	−	0.370546i	0.898347	−	0.439286i	$-0.144769\pi$
$857$	−2.90660	−	10.8476i	−0.0992875	−	0.370546i	−0.997635	+	0.0687403i	$0.978102\pi$
$858$	4.90570	−	1.98777i	0.167478	−	0.0678612i
$859$	37.6358	−	21.7291i	1.28412	−	0.741386i	0.306520	−	0.951864i	$-0.400835\pi$
$859$	37.6358	−	21.7291i	1.28412	−	0.741386i	0.977599	+	0.210478i	$0.0675020\pi$
$860$	16.7452	+	6.78113i	0.571008	+	0.231235i
$861$	10.0480	−	1.24398i	0.342434	−	0.0423949i
$862$	−18.8919	+	5.06208i	−0.643462	+	0.172415i
$863$	−30.9036	−	30.9036i	−1.05197	−	1.05197i	−0.998573	−	0.0533972i	$-0.982995\pi$
$863$	−30.9036	−	30.9036i	−1.05197	−	1.05197i	−0.0533972	−	0.998573i	$-0.517005\pi$
$864$	15.1293	−	18.7987i	0.514710	−	0.639546i
$865$	30.3346	−	23.6609i	1.03141	−	0.804494i
$866$	10.8799	+	6.28150i	0.369713	+	0.213454i
$867$	34.4557	−	44.1927i	1.17018	−	1.50086i
$868$	−0.117666	−	0.0315286i	−0.00399386	−	0.00107015i
$869$	−2.25776	−	3.91055i	−0.0765892	−	0.132656i
$870$	9.43632	+	5.44550i	0.319921	+	0.184620i
$871$	4.28276	−	7.41795i	0.145116	−	0.251348i
$872$	−28.1364	+	28.1364i	−0.952819	+	0.952819i
$873$	7.90734	+	14.1979i	0.267623	+	0.480525i
$874$		−	44.1617i		−	1.49379i
$875$	1.19539	−	11.1163i	0.0404116	−	0.375798i
$876$	−2.84624	+	2.14928i	−0.0961654	+	0.0726174i
$877$	−13.5221	+	50.4653i	−0.456610	+	1.70409i	0.226702	+	0.973964i	$0.427206\pi$
$877$	−13.5221	+	50.4653i	−0.456610	+	1.70409i	−0.683312	+	0.730127i	$0.739461\pi$
$878$	−3.27561	+	12.2247i	−0.110547	+	0.412565i
$879$	−29.1677	+	22.0254i	−0.983803	+	0.742900i
$880$	4.17340	−	5.52907i	0.140685	−	0.186385i
$881$			41.9224i			1.41240i	0.708012	+	0.706201i	$0.249592\pi$
$881$			41.9224i			1.41240i	−0.708012	+	0.706201i	$0.750408\pi$
$882$	1.61164	−	2.69448i	0.0542669	−	0.0907278i
$883$	32.9720	−	32.9720i	1.10960	−	1.10960i	0.116394	−	0.993203i	$-0.462867\pi$
$883$	32.9720	−	32.9720i	1.10960	−	1.10960i	0.993203	−	0.116394i	$-0.0371334\pi$
$884$	4.10981	−	7.11840i	0.138228	−	0.239418i
$885$	7.82182	+	29.1677i	0.262928	+	0.980462i
$886$	−14.2062	−	24.6058i	−0.477266	−	0.826650i
$887$	13.9565	+	3.73963i	0.468613	+	0.125565i	0.485396	−	0.874295i	$-0.338676\pi$
$887$	13.9565	+	3.73963i	0.468613	+	0.125565i	−0.0167823	+	0.999859i	$0.505342\pi$
$888$	−0.102717	+	0.131745i	−0.00344697	+	0.00442107i
$889$	−18.2621	−	10.5436i	−0.612490	−	0.353621i
$890$	−11.0754	−	14.1993i	−0.371249	−	0.475963i
$891$	20.3113	+	0.627563i	0.680453	+	0.0210241i
$892$	15.9045	+	15.9045i	0.532523	+	0.532523i
$893$	25.2116	−	6.75542i	0.843674	−	0.226062i
$894$	−3.21025	+	0.397443i	−0.107367	+	0.0132925i
$895$	−23.3041	+	9.86998i	−0.778971	+	0.329917i
$896$	−1.15138	+	0.664751i	−0.0384650	+	0.0222078i
$897$	−15.5297	+	6.29255i	−0.518520	+	0.210102i
$898$	−1.04365	−	3.89495i	−0.0348270	−	0.129976i
$899$	0.361918			0.0120706
$900$	13.5707	−	0.00552168i	0.452355	−	0.000184056i
$901$	98.2025			3.27160
$902$	3.57506	+	13.3423i	0.119036	+	0.444250i
$903$	−2.13733	+	15.3196i	−0.0711258	+	0.509803i
$904$	−8.06984	+	4.65912i	−0.268399	+	0.154960i
$905$	−8.10083	+	3.43094i	−0.269281	+	0.114048i
$906$	6.16806	+	8.16820i	0.204920	+	0.271370i
$907$	−46.6425	+	12.4978i	−1.54874	+	0.414983i	−0.929077	−	0.369885i	$-0.879397\pi$
$907$	−46.6425	+	12.4978i	−1.54874	+	0.414983i	−0.619662	+	0.784869i	$0.712730\pi$
$908$	5.04873	+	5.04873i	0.167548	+	0.167548i
$909$	−7.72428	+	27.1435i	−0.256198	+	0.900293i
$910$	1.86136	+	2.38637i	0.0617034	+	0.0791074i
$911$	−0.649435	−	0.374951i	−0.0215167	−	0.0124227i	0.489203	−	0.872170i	$-0.337288\pi$
$911$	−0.649435	−	0.374951i	−0.0215167	−	0.0124227i	−0.510720	+	0.859747i	$0.670621\pi$
$912$	−5.03439	−	12.4246i	−0.166705	−	0.411420i
$913$	20.6324	+	5.52844i	0.682834	+	0.182965i
$914$	12.1045	+	20.9656i	0.400381	+	0.693480i
$915$	22.6057	−	22.6149i	0.747322	−	0.747627i
$916$	6.95840	−	12.0523i	0.229912	−	0.398219i
$917$	−0.476507	+	0.476507i	−0.0157357	+	0.0157357i
$918$	−30.8395	+	22.5486i	−1.01786	+	0.744214i
$919$		−	59.7851i		−	1.97213i	−0.166365	−	0.986064i	$-0.553203\pi$
$919$		−	59.7851i		−	1.97213i	0.166365	−	0.986064i	$-0.446797\pi$
$920$	−30.6341	+	40.5851i	−1.00998	+	1.33805i
$921$	3.60595	+	29.1262i	0.118820	+	0.959739i
$922$	−3.02828	+	11.3017i	−0.0997310	+	0.372201i
$923$	4.06547	−	15.1725i	0.133817	−	0.499410i
$924$	−3.25824	−	1.37918i	−0.107188	−	0.0453717i
$925$	−0.158617	+	0.00251438i	−0.00521528	+	8.26722e-5i
$926$		−	9.21797i		−	0.302921i
$927$	0.536834	−	34.7579i	0.0176319	−	1.14160i
$928$	8.82639	−	8.82639i	0.289741	−	0.289741i
$929$	−7.79379	+	13.4992i	−0.255706	+	0.442896i	−0.965087	−	0.261929i	$-0.915641\pi$
$929$	−7.79379	+	13.4992i	−0.255706	+	0.442896i	0.709381	+	0.704825i	$0.248975\pi$
$930$	−0.472595	+	0.272981i	−0.0154970	+	0.00895140i
$931$	2.82048	+	4.88522i	0.0924377	+	0.160107i
$932$	18.1684	+	4.86820i	0.595125	+	0.159463i
$933$	12.5938	+	1.75704i	0.412302	+	0.0575229i
$934$	13.9870	+	8.07539i	0.457668	+	0.264235i
$935$	27.9672	−	21.8143i	0.914624	−	0.713403i
$936$	−8.46764	+	8.21006i	−0.276774	+	0.268354i
$937$	−16.0209	−	16.0209i	−0.523380	−	0.523380i	0.395211	−	0.918590i	$-0.370672\pi$
$937$	−16.0209	−	16.0209i	−0.523380	−	0.523380i	−0.918590	+	0.395211i	$0.870672\pi$
$938$	6.69541	−	1.79403i	0.218613	−	0.0585771i
$939$	10.7475	−	25.3903i	0.350730	−	0.828582i
$940$	−8.67606	−	3.51344i	−0.282982	−	0.114596i
$941$	−12.7639	+	7.36924i	−0.416091	+	0.240230i	−0.693404	−	0.720549i	$-0.743890\pi$
$941$	−12.7639	+	7.36924i	−0.416091	+	0.240230i	0.277312	+	0.960780i	$0.410556\pi$
$942$	−21.9568	−	17.1191i	−0.715392	−	0.557769i
$943$	−11.3174	−	42.2369i	−0.368544	−	1.37542i
$944$	−10.6983			−0.348201
$945$	2.83582	+	11.2676i	0.0922493	+	0.366534i
$946$	−21.1027			−0.686108
$947$	0.666806	+	2.48855i	0.0216683	+	0.0808671i	0.975913	−	0.218159i	$-0.0700050\pi$
$947$	0.666806	+	2.48855i	0.0216683	+	0.0808671i	−0.954245	+	0.299026i	$0.903338\pi$
$948$	2.47143	+	1.92690i	0.0802684	+	0.0625828i
$949$	2.54915	−	1.47176i	0.0827491	−	0.0477752i
$950$	14.3520	−	25.7941i	0.465641	−	0.836872i
$951$	−1.85490	+	4.38210i	−0.0601492	+	0.142099i
$952$	20.6286	−	5.52740i	0.668575	−	0.179144i
$953$	−3.59743	−	3.59743i	−0.116532	−	0.116532i	0.646436	−	0.762968i	$-0.276259\pi$
$953$	−3.59743	−	3.59743i	−0.116532	−	0.116532i	−0.762968	+	0.646436i	$0.776259\pi$
$954$	−42.2125	−	12.0125i	−1.36668	−	0.388919i
$955$	9.07720	+	1.12192i	0.293731	+	0.0363046i
$956$	19.6037	+	11.3182i	0.634030	+	0.366057i
$957$	10.4109	+	1.45249i	0.336536	+	0.0469523i
$958$	−10.2190	−	2.73818i	−0.330161	−	0.0884664i
$959$	1.05330	+	1.82436i	0.0340127	+	0.0589117i
$960$	−7.61681	+	28.4495i	−0.245831	+	0.918203i
$961$	15.4909	−	26.8311i	0.499708	−	0.865519i
$962$	0.0303646	−	0.0303646i	0.000978993	−	0.000978993i
$963$	−10.4332	−	6.24038i	−0.336204	−	0.201094i
$964$		−	15.4971i		−	0.499127i
$965$	38.1175	−	5.32592i	1.22705	−	0.171447i
$966$	−12.4872	−	5.28569i	−0.401768	−	0.170064i
$967$	−9.29218	+	34.6789i	−0.298817	+	1.11520i	0.639322	+	0.768939i	$0.279215\pi$
$967$	−9.29218	+	34.6789i	−0.298817	+	1.11520i	−0.938139	+	0.346260i	$0.887452\pi$
$968$	−4.64365	+	17.3303i	−0.149253	+	0.557018i
$969$	−8.43346	−	68.1191i	−0.270922	−	2.18830i
$970$	−10.1182	−	7.63732i	−0.324876	−	0.245220i
$971$		−	18.0216i		−	0.578340i	−0.957278	−	0.289170i	$-0.906621\pi$
$971$		−	18.0216i		−	0.578340i	0.957278	−	0.289170i	$-0.0933793\pi$
$972$	−13.2281	+	4.89004i	−0.424292	+	0.156848i
$973$	0.206953	−	0.206953i	0.00663461	−	0.00663461i
$974$	−0.845616	+	1.46465i	−0.0270953	+	0.0469304i
$975$	−11.1156	−	1.37157i	−0.355985	−	0.0439255i
$976$	5.66403	+	9.81038i	0.181301	+	0.314023i
$977$	−11.1486	−	2.98725i	−0.356674	−	0.0955705i	0.0760326	−	0.997105i	$-0.475775\pi$
$977$	−11.1486	−	2.98725i	−0.356674	−	0.0955705i	−0.432707	+	0.901535i	$0.642441\pi$
$978$	−14.4914	−	35.7641i	−0.463385	−	1.14361i
$979$	−15.0469	−	8.68734i	−0.480902	−	0.277649i
$980$	0.248150	−	2.00772i	0.00792686	−	0.0641342i
$981$	38.0823	−	9.57631i	1.21587	−	0.305748i
$982$	−9.97638	−	9.97638i	−0.318359	−	0.318359i
$983$	−36.0098	+	9.64881i	−1.14854	+	0.307749i	−0.782378	−	0.622804i	$-0.785994\pi$
$983$	−36.0098	+	9.64881i	−1.14854	+	0.307749i	−0.366157	+	0.930553i	$0.619327\pi$
$984$	−18.5477	−	24.5622i	−0.591279	−	0.783016i
$985$	−4.63456	+	11.4445i	−0.147669	+	0.364653i
$986$	−17.1145	+	9.88105i	−0.545036	+	0.314677i
$987$	1.10739	−	7.93738i	0.0352487	−	0.252650i
$988$	−1.70822	−	6.37517i	−0.0543457	−	0.202821i
$989$	66.8036			2.12423
$990$	−14.6901	+	5.95586i	−0.466884	+	0.189290i
$991$	−31.1009			−0.987952			−0.493976	−	0.869476i	$-0.664457\pi$
$991$	−31.1009			−0.987952			−0.493976	+	0.869476i	$0.664457\pi$
$992$	0.161839	+	0.603991i	0.00513839	+	0.0191767i
$993$	18.8124	−	7.62271i	0.596994	−	0.241899i
$994$	11.0084	−	6.35572i	0.349166	−	0.201591i
$995$	−3.95338	−	9.33438i	−0.125331	−	0.295920i
$996$	−14.7120	+	1.82141i	−0.466168	+	0.0577137i
$997$	−43.8121	+	11.7394i	−1.38754	+	0.371791i	−0.873855	−	0.486186i	$-0.838388\pi$
$997$	−43.8121	+	11.7394i	−1.38754	+	0.371791i	−0.513688	+	0.857977i	$0.671721\pi$
$998$	10.8972	+	10.8972i	0.344944	+	0.344944i
$999$	0.153731	−	0.0595442i	0.00486384	−	0.00188389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.cc.a.92.13	✓	144
3.2	odd	2		945.2.cf.a.197.24		144
5.3	odd	4	inner	315.2.cc.a.218.13	yes	144
9.4	even	3		945.2.cf.a.827.24		144
9.5	odd	6	inner	315.2.cc.a.302.13	yes	144
15.8	even	4		945.2.cf.a.8.24		144
45.13	odd	12		945.2.cf.a.638.24		144
45.23	even	12	inner	315.2.cc.a.113.13	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.cc.a.92.13	✓	144	1.1	even	1	trivial
315.2.cc.a.113.13	yes	144	45.23	even	12	inner
315.2.cc.a.218.13	yes	144	5.3	odd	4	inner
315.2.cc.a.302.13	yes	144	9.5	odd	6	inner
945.2.cf.a.8.24		144	15.8	even	4
945.2.cf.a.197.24		144	3.2	odd	2
945.2.cf.a.638.24		144	45.13	odd	12
945.2.cf.a.827.24		144	9.4	even	3

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.270870 - 1.01090i) q^{2} +(1.36595 + 1.06499i) q^{3} +(0.783502 - 0.452355i) q^{4} +(2.05901 - 0.872052i) q^{5} +(0.706600 - 1.66931i) q^{6} +(0.965926 - 0.258819i) q^{7} +(-2.14957 - 2.14957i) q^{8} +(0.731614 + 2.90942i) q^{9} +O(q^{10})\)	\(q+(-0.270870 - 1.01090i) q^{2} +(1.36595 + 1.06499i) q^{3} +(0.783502 - 0.452355i) q^{4} +(2.05901 - 0.872052i) q^{5} +(0.706600 - 1.66931i) q^{6} +(0.965926 - 0.258819i) q^{7} +(-2.14957 - 2.14957i) q^{8} +(0.731614 + 2.90942i) q^{9} +(-1.43928 - 1.84524i) q^{10} +(-1.95539 - 1.12894i) q^{11} +(1.55197 + 0.216526i) q^{12} +(-1.24919 - 0.334719i) q^{13} +(-0.523280 - 0.906348i) q^{14} +(3.74122 + 1.00164i) q^{15} +(-0.686039 + 1.18825i) q^{16} +(-4.96756 + 4.96756i) q^{17} +(2.74296 - 1.52766i) q^{18} +5.64097i q^{19} +(1.21876 - 1.61466i) q^{20} +(1.59504 + 0.675164i) q^{21} +(-0.611593 + 2.28250i) q^{22} +(1.93608 - 7.22556i) q^{23} +(-0.646937 - 5.22546i) q^{24} +(3.47905 - 3.59113i) q^{25} +1.35347i q^{26} +(-2.09915 + 4.75327i) q^{27} +(0.639727 - 0.639727i) q^{28} +(-1.34394 + 2.32778i) q^{29} +(-0.000824614 - 4.05331i) q^{30} +(-0.0673239 - 0.116608i) q^{31} +(-4.48571 - 1.20194i) q^{32} +(-1.46864 - 3.62453i) q^{33} +(6.36726 + 3.67614i) q^{34} +(1.76315 - 1.37525i) q^{35} +(1.88931 + 1.94859i) q^{36} +(-0.0224346 - 0.0224346i) q^{37} +(5.70246 - 1.52797i) q^{38} +(-1.34985 - 1.78758i) q^{39} +(-6.30053 - 2.55146i) q^{40} +(5.06234 - 2.92274i) q^{41} +(0.250475 - 1.79531i) q^{42} +(2.31136 + 8.62612i) q^{43} -2.04273 q^{44} +(4.04357 + 5.35253i) q^{45} -7.82875 q^{46} +(-1.19756 - 4.46937i) q^{47} +(-2.20257 + 0.892470i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-4.57264 - 2.54425i) q^{50} +(-12.0758 + 1.49504i) q^{51} +(-1.13015 + 0.302824i) q^{52} +(-9.88439 - 9.88439i) q^{53} +(5.37368 + 0.834510i) q^{54} +(-5.01066 - 0.619308i) q^{55} +(-2.63268 - 1.51998i) q^{56} +(-6.00755 + 7.70526i) q^{57} +(2.71718 + 0.728068i) q^{58} +(3.89858 + 6.75254i) q^{59} +(3.38435 - 0.907572i) q^{60} +(4.12806 - 7.15001i) q^{61} +(-0.0996435 + 0.0996435i) q^{62} +(1.45970 + 2.62093i) q^{63} +7.60433i q^{64} +(-2.86399 + 0.400167i) q^{65} +(-3.26623 + 2.46643i) q^{66} +(-1.71421 + 6.39753i) q^{67} +(-1.64499 + 6.13919i) q^{68} +(10.3397 - 7.80782i) q^{69} +(-1.86782 - 1.40985i) q^{70} +12.1459i q^{71} +(4.68136 - 7.82668i) q^{72} +(-1.60941 + 1.60941i) q^{73} +(-0.0166023 + 0.0287560i) q^{74} +(8.57669 - 1.20015i) q^{75} +(2.55172 + 4.41971i) q^{76} +(-2.18095 - 0.584384i) q^{77} +(-1.44143 + 1.84877i) q^{78} +(1.73195 + 0.999944i) q^{79} +(-0.376343 + 3.04489i) q^{80} +(-7.92948 + 4.25715i) q^{81} +(-4.32584 - 4.32584i) q^{82} +(-9.13794 + 2.44850i) q^{83} +(1.55513 - 0.192532i) q^{84} +(-5.89629 + 14.5602i) q^{85} +(8.09407 - 4.67311i) q^{86} +(-4.31480 + 1.74834i) q^{87} +(1.77650 + 6.62999i) q^{88} +7.69511 q^{89} +(4.31559 - 5.53748i) q^{90} -1.29326 q^{91} +(-1.75159 - 6.53704i) q^{92} +(0.0322255 - 0.230980i) q^{93} +(-4.19370 + 2.42124i) q^{94} +(4.91922 + 11.6148i) q^{95} +(-4.84718 - 6.41900i) q^{96} +(5.23252 - 1.40205i) q^{97} +(-0.740030 - 0.740030i) q^{98} +(1.85398 - 6.51500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 4 q^{3}+O(q^{10}) \) 144 * q + 4 * q^3	\( 144 q + 4 q^{3} - 12 q^{11} - 16 q^{12} + 16 q^{15} + 72 q^{16} - 64 q^{18} - 48 q^{20} - 4 q^{21} - 24 q^{23} - 12 q^{25} - 32 q^{27} - 20 q^{30} - 60 q^{32} - 16 q^{33} - 16 q^{36} - 24 q^{37} + 72 q^{38} + 48 q^{41} - 40 q^{42} + 40 q^{45} - 48 q^{46} + 12 q^{47} + 104 q^{48} - 76 q^{51} - 24 q^{55} - 4 q^{57} - 92 q^{60} + 8 q^{63} - 72 q^{65} - 80 q^{66} - 12 q^{67} - 64 q^{72} - 108 q^{75} - 24 q^{76} + 72 q^{78} + 32 q^{81} - 96 q^{82} + 120 q^{83} - 48 q^{85} - 144 q^{86} + 116 q^{87} - 48 q^{88} + 252 q^{90} + 24 q^{91} + 156 q^{92} - 44 q^{93} + 120 q^{95} - 96 q^{96} - 60 q^{97}+O(q^{100}) \) 144 * q + 4 * q^3 - 12 * q^11 - 16 * q^12 + 16 * q^15 + 72 * q^16 - 64 * q^18 - 48 * q^20 - 4 * q^21 - 24 * q^23 - 12 * q^25 - 32 * q^27 - 20 * q^30 - 60 * q^32 - 16 * q^33 - 16 * q^36 - 24 * q^37 + 72 * q^38 + 48 * q^41 - 40 * q^42 + 40 * q^45 - 48 * q^46 + 12 * q^47 + 104 * q^48 - 76 * q^51 - 24 * q^55 - 4 * q^57 - 92 * q^60 + 8 * q^63 - 72 * q^65 - 80 * q^66 - 12 * q^67 - 64 * q^72 - 108 * q^75 - 24 * q^76 + 72 * q^78 + 32 * q^81 - 96 * q^82 + 120 * q^83 - 48 * q^85 - 144 * q^86 + 116 * q^87 - 48 * q^88 + 252 * q^90 + 24 * q^91 + 156 * q^92 - 44 * q^93 + 120 * q^95 - 96 * q^96 - 60 * q^97

Introduction

L-functions

Modular forms

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