LMFDB - Embedded newform 630.2.ca.b.407.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(113,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 0]))

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

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

chi := DirichletCharacter("630.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.ca (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			407.4
Character	$\chi$	$=$	630.407
Dual form			630.2.ca.b.113.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.970129 + 1.43487i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.21913 - 0.274732i) q^{5} +(1.63707 + 0.565701i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.11770 - 2.78402i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.970129 + 1.43487i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.21913 - 0.274732i) q^{5} +(1.63707 + 0.565701i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.11770 - 2.78402i) q^{9} +(-0.839723 - 2.07241i) q^{10} +(2.50570 + 1.44667i) q^{11} +(0.122721 - 1.72770i) q^{12} +(2.57276 + 0.689370i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-1.75863 + 3.45068i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.15464 + 2.15464i) q^{17} +(-2.39987 + 1.80017i) q^{18} -3.49024i q^{19} +(-1.78445 + 1.34749i) q^{20} +(0.565701 - 1.63707i) q^{21} +(0.748850 - 2.79475i) q^{22} +(-0.410109 + 1.53055i) q^{23} +(-1.70059 + 0.328621i) q^{24} +(4.84904 - 1.21933i) q^{25} -2.66352i q^{26} +(5.07901 + 1.09710i) q^{27} +(0.707107 - 0.707107i) q^{28} +(-2.09017 + 3.62028i) q^{29} +(3.78827 + 0.805607i) q^{30} +(5.09198 + 8.81957i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-4.50663 + 2.19190i) q^{33} +(2.63888 + 1.52356i) q^{34} +(-2.07241 + 0.839723i) q^{35} +(2.35997 + 1.85218i) q^{36} +(0.639872 + 0.639872i) q^{37} +(-3.37131 + 0.903340i) q^{38} +(-3.48507 + 3.02280i) q^{39} +(1.76342 + 1.37489i) q^{40} +(10.5356 - 6.08273i) q^{41} +(-1.72770 - 0.122721i) q^{42} +(3.15998 + 11.7932i) q^{43} -2.89334 q^{44} +(-3.24518 - 5.87102i) q^{45} +1.58454 q^{46} +(1.94969 + 7.27636i) q^{47} +(0.757569 + 1.55759i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-2.43281 - 4.36823i) q^{50} +(-1.00135 - 5.18190i) q^{51} +(-2.57276 + 0.689370i) q^{52} +(-1.37865 - 1.37865i) q^{53} +(-0.254828 - 5.18990i) q^{54} +(5.95792 + 2.52194i) q^{55} +(-0.866025 - 0.500000i) q^{56} +(5.00804 + 3.38598i) q^{57} +(4.03789 + 1.08195i) q^{58} +(-5.42618 - 9.39841i) q^{59} +(-0.202320 - 3.86770i) q^{60} +(3.74223 - 6.48173i) q^{61} +(7.20115 - 7.20115i) q^{62} +(1.80017 + 2.39987i) q^{63} +1.00000i q^{64} +(5.89868 + 0.822977i) q^{65} +(3.28362 + 3.78577i) q^{66} +(-1.50066 + 5.60055i) q^{67} +(0.788652 - 2.94329i) q^{68} +(-1.79828 - 2.07328i) q^{69} +(1.34749 + 1.78445i) q^{70} -0.0635062i q^{71} +(1.17826 - 2.75893i) q^{72} +(9.56877 - 9.56877i) q^{73} +(0.452458 - 0.783680i) q^{74} +(-2.95462 + 8.14065i) q^{75} +(1.74512 + 3.02264i) q^{76} +(-2.79475 - 0.748850i) q^{77} +(3.82180 + 2.58396i) q^{78} +(10.3573 + 5.97977i) q^{79} +(0.871638 - 2.05919i) q^{80} +(-6.50149 + 6.22339i) q^{81} +(-8.60228 - 8.60228i) q^{82} +(-11.5162 + 3.08577i) q^{83} +(0.328621 + 1.70059i) q^{84} +(-4.18946 + 5.37336i) q^{85} +(10.5735 - 6.10460i) q^{86} +(-3.16689 - 6.51125i) q^{87} +(0.748850 + 2.79475i) q^{88} -10.6884 q^{89} +(-4.83105 + 4.65413i) q^{90} -2.66352 q^{91} +(-0.410109 - 1.53055i) q^{92} +(-17.5948 - 1.24979i) q^{93} +(6.52380 - 3.76652i) q^{94} +(-0.958882 - 7.74528i) q^{95} +(1.30844 - 1.13489i) q^{96} +(1.36927 - 0.366894i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(1.22692 - 8.59286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{3}+O(q^{10}) $ 72 * q - 4 * q^3	$ 72 q - 4 q^{3} + 12 q^{11} + 4 q^{12} + 36 q^{14} - 20 q^{15} + 36 q^{16} + 24 q^{17} + 12 q^{20} + 4 q^{21} - 8 q^{24} + 12 q^{25} + 32 q^{27} + 32 q^{30} + 44 q^{33} - 12 q^{34} - 4 q^{36} + 24 q^{37} - 36 q^{38} + 40 q^{39} - 48 q^{41} + 4 q^{42} + 48 q^{43} - 68 q^{45} - 48 q^{47} - 8 q^{48} + 16 q^{51} + 4 q^{54} + 24 q^{55} - 84 q^{57} - 48 q^{58} + 4 q^{60} - 8 q^{63} + 24 q^{65} + 8 q^{66} + 12 q^{67} + 12 q^{68} - 64 q^{69} + 16 q^{72} + 84 q^{75} + 24 q^{78} - 72 q^{79} + 48 q^{82} - 60 q^{83} + 24 q^{85} + 72 q^{86} + 4 q^{87} - 48 q^{90} - 24 q^{91} - 64 q^{93} + 132 q^{94} - 60 q^{95} + 36 q^{97} + 40 q^{99}+O(q^{100}) $ 72 * q - 4 * q^3 + 12 * q^11 + 4 * q^12 + 36 * q^14 - 20 * q^15 + 36 * q^16 + 24 * q^17 + 12 * q^20 + 4 * q^21 - 8 * q^24 + 12 * q^25 + 32 * q^27 + 32 * q^30 + 44 * q^33 - 12 * q^34 - 4 * q^36 + 24 * q^37 - 36 * q^38 + 40 * q^39 - 48 * q^41 + 4 * q^42 + 48 * q^43 - 68 * q^45 - 48 * q^47 - 8 * q^48 + 16 * q^51 + 4 * q^54 + 24 * q^55 - 84 * q^57 - 48 * q^58 + 4 * q^60 - 8 * q^63 + 24 * q^65 + 8 * q^66 + 12 * q^67 + 12 * q^68 - 64 * q^69 + 16 * q^72 + 84 * q^75 + 24 * q^78 - 72 * q^79 + 48 * q^82 - 60 * q^83 + 24 * q^85 + 72 * q^86 + 4 * q^87 - 48 * q^90 - 24 * q^91 - 64 * q^93 + 132 * q^94 - 60 * q^95 + 36 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−0.970129	+	1.43487i	−0.560104	+	0.828422i
$3$	−0.970129	+	1.43487i	−0.560104	+	0.828422i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	2.21913	−	0.274732i	0.992424	−	0.122864i
$5$	2.21913	−	0.274732i	0.992424	−	0.122864i
$6$	1.63707	+	0.565701i	0.668329	+	0.230946i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.11770	−	2.78402i	−0.372567	−	0.928005i
$10$	−0.839723	−	2.07241i	−0.265544	−	0.655352i
$11$	2.50570	+	1.44667i	0.755498	+	0.436187i	0.827677	−	0.561205i	$-0.189662\pi$
$11$	2.50570	+	1.44667i	0.755498	+	0.436187i	−0.0721793	+	0.997392i	$0.522995\pi$
$12$	0.122721	−	1.72770i	0.0354266	−	0.498743i
$13$	2.57276	+	0.689370i	0.713556	+	0.191197i	0.597295	−	0.802022i	$-0.296242\pi$
$13$	2.57276	+	0.689370i	0.713556	+	0.191197i	0.116261	+	0.993219i	$0.462909\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$	−1.75863	+	3.45068i	−0.454077	+	0.890962i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.15464	+	2.15464i	−0.522576	+	0.522576i	−0.918349	−	0.395772i	$-0.870477\pi$
$17$	−2.15464	+	2.15464i	−0.522576	+	0.522576i	0.395772	+	0.918349i	$0.370477\pi$
$18$	−2.39987	+	1.80017i	−0.565655	+	0.424305i
$19$		−	3.49024i		−	0.800716i	−0.916359	−	0.400358i	$-0.868886\pi$
$19$		−	3.49024i		−	0.800716i	0.916359	−	0.400358i	$-0.131114\pi$
$20$	−1.78445	+	1.34749i	−0.399016	+	0.301308i
$21$	0.565701	−	1.63707i	0.123446	−	0.357237i
$22$	0.748850	−	2.79475i	0.159655	−	0.595842i
$23$	−0.410109	+	1.53055i	−0.0855136	+	0.319141i	−0.995411	−	0.0956923i	$-0.969494\pi$
$23$	−0.410109	+	1.53055i	−0.0855136	+	0.319141i	0.909897	+	0.414833i	$0.136160\pi$
$24$	−1.70059	+	0.328621i	−0.347132	+	0.0670795i
$25$	4.84904	−	1.21933i	0.969809	−	0.243866i
$26$		−	2.66352i		−	0.522359i
$27$	5.07901	+	1.09710i	0.977456	+	0.211137i
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	−2.09017	+	3.62028i	−0.388134	+	0.672268i	−0.992199	−	0.124667i	$-0.960214\pi$
$29$	−2.09017	+	3.62028i	−0.388134	+	0.672268i	0.604064	+	0.796936i	$0.293547\pi$
$30$	3.78827	+	0.805607i	0.691640	+	0.147083i
$31$	5.09198	+	8.81957i	0.914547	+	1.58404i	0.807564	+	0.589780i	$0.200786\pi$
$31$	5.09198	+	8.81957i	0.914547	+	1.58404i	0.106983	+	0.994261i	$0.465881\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−4.50663	+	2.19190i	−0.784504	+	0.381561i
$34$	2.63888	+	1.52356i	0.452564	+	0.261288i
$35$	−2.07241	+	0.839723i	−0.350300	+	0.141939i
$36$	2.35997	+	1.85218i	0.393328	+	0.308696i
$37$	0.639872	+	0.639872i	0.105194	+	0.105194i	0.757745	−	0.652551i	$-0.226301\pi$
$37$	0.639872	+	0.639872i	0.105194	+	0.105194i	−0.652551	+	0.757745i	$0.726301\pi$
$38$	−3.37131	+	0.903340i	−0.546899	+	0.146541i
$39$	−3.48507	+	3.02280i	−0.558057	+	0.484036i
$40$	1.76342	+	1.37489i	0.278822	+	0.217390i
$41$	10.5356	−	6.08273i	1.64538	−	0.949963i	0.666510	−	0.745496i	$-0.267787\pi$
$41$	10.5356	−	6.08273i	1.64538	−	0.949963i	0.978873	−	0.204467i	$-0.0655461\pi$
$42$	−1.72770	−	0.122721i	−0.266590	−	0.0189363i
$43$	3.15998	+	11.7932i	0.481892	+	1.79844i	0.593667	+	0.804711i	$0.297680\pi$
$43$	3.15998	+	11.7932i	0.481892	+	1.79844i	−0.111775	+	0.993734i	$0.535654\pi$
$44$	−2.89334			−0.436187
$45$	−3.24518	−	5.87102i	−0.483763	−	0.875199i
$46$	1.58454			0.233628
$47$	1.94969	+	7.27636i	0.284392	+	1.06137i	0.949282	+	0.314425i	$0.101812\pi$
$47$	1.94969	+	7.27636i	0.284392	+	1.06137i	−0.664890	+	0.746941i	$0.731522\pi$
$48$	0.757569	+	1.55759i	0.109346	+	0.224819i
$49$	0.866025	−	0.500000i	0.123718	−	0.0714286i
$50$	−2.43281	−	4.36823i	−0.344051	−	0.617761i
$51$	−1.00135	−	5.18190i	−0.140217	−	0.725611i
$52$	−2.57276	+	0.689370i	−0.356778	+	0.0955984i
$53$	−1.37865	−	1.37865i	−0.189372	−	0.189372i	0.606053	−	0.795425i	$-0.292752\pi$
$53$	−1.37865	−	1.37865i	−0.189372	−	0.189372i	−0.795425	+	0.606053i	$0.792752\pi$
$54$	−0.254828	−	5.18990i	−0.0346777	−	0.706256i
$55$	5.95792	+	2.52194i	0.803365	+	0.340058i
$56$	−0.866025	−	0.500000i	−0.115728	−	0.0668153i
$57$	5.00804	+	3.38598i	0.663331	+	0.448484i
$58$	4.03789	+	1.08195i	0.530201	+	0.142067i
$59$	−5.42618	−	9.39841i	−0.706428	−	1.22357i	−0.966174	−	0.257892i	$-0.916972\pi$
$59$	−5.42618	−	9.39841i	−0.706428	−	1.22357i	0.259746	−	0.965677i	$-0.416361\pi$
$60$	−0.202320	−	3.86770i	−0.0261194	−	0.499317i
$61$	3.74223	−	6.48173i	0.479143	−	0.829901i	−0.520571	−	0.853819i	$-0.674281\pi$
$61$	3.74223	−	6.48173i	0.479143	−	0.829901i	0.999714	+	0.0239180i	$0.00761406\pi$
$62$	7.20115	−	7.20115i	0.914547	−	0.914547i
$63$	1.80017	+	2.39987i	0.226800	+	0.302355i
$64$			1.00000i			0.125000i
$65$	5.89868	+	0.822977i	0.731641	+	0.102078i
$66$	3.28362	+	3.78577i	0.404185	+	0.465996i
$67$	−1.50066	+	5.60055i	−0.183335	+	0.684217i	0.811646	+	0.584150i	$0.198572\pi$
$67$	−1.50066	+	5.60055i	−0.183335	+	0.684217i	−0.994981	+	0.100066i	$0.968095\pi$
$68$	0.788652	−	2.94329i	0.0956381	−	0.356926i
$69$	−1.79828	−	2.07328i	−0.216487	−	0.249594i
$70$	1.34749	+	1.78445i	0.161056	+	0.213283i
$71$		−	0.0635062i		−	0.00753680i	−0.999993	−	0.00376840i	$-0.998800\pi$
$71$		−	0.0635062i		−	0.00753680i	0.999993	−	0.00376840i	$-0.00119952\pi$
$72$	1.17826	−	2.75893i	0.138860	−	0.325143i
$73$	9.56877	−	9.56877i	1.11994	−	1.11994i	0.128190	−	0.991750i	$-0.459083\pi$
$73$	9.56877	−	9.56877i	1.11994	−	1.11994i	0.991750	−	0.128190i	$-0.0409166\pi$
$74$	0.452458	−	0.783680i	0.0525971	−	0.0911009i
$75$	−2.95462	+	8.14065i	−0.341170	+	0.940002i
$76$	1.74512	+	3.02264i	0.200179	+	0.346720i
$77$	−2.79475	−	0.748850i	−0.318491	−	0.0853394i
$78$	3.82180	+	2.58396i	0.432734	+	0.292576i
$79$	10.3573	+	5.97977i	1.16528	+	0.672777i	0.952565	−	0.304337i	$-0.0984348\pi$
$79$	10.3573	+	5.97977i	1.16528	+	0.672777i	0.212719	+	0.977113i	$0.431768\pi$
$80$	0.871638	−	2.05919i	0.0974521	−	0.230224i
$81$	−6.50149	+	6.22339i	−0.722388	+	0.691488i
$82$	−8.60228	−	8.60228i	−0.949963	−	0.949963i
$83$	−11.5162	+	3.08577i	−1.26407	+	0.338707i	−0.827757	−	0.561087i	$-0.810383\pi$
$83$	−11.5162	+	3.08577i	−1.26407	+	0.338707i	−0.436315	+	0.899794i	$0.643717\pi$
$84$	0.328621	+	1.70059i	0.0358555	+	0.185550i
$85$	−4.18946	+	5.37336i	−0.454411	+	0.582823i
$86$	10.5735	−	6.10460i	1.14017	−	0.658276i
$87$	−3.16689	−	6.51125i	−0.339526	−	0.698079i
$88$	0.748850	+	2.79475i	0.0798277	+	0.297921i
$89$	−10.6884			−1.13297			−0.566486	−	0.824071i	$-0.691698\pi$
$89$	−10.6884			−1.13297			−0.566486	+	0.824071i	$0.691698\pi$
$90$	−4.83105	+	4.65413i	−0.509238	+	0.490589i
$91$	−2.66352			−0.279213
$92$	−0.410109	−	1.53055i	−0.0427568	−	0.159571i
$93$	−17.5948	−	1.24979i	−1.82450	−	0.129597i
$94$	6.52380	−	3.76652i	0.672879	−	0.388487i
$95$	−0.958882	−	7.74528i	−0.0983792	−	0.794649i
$96$	1.30844	−	1.13489i	0.133543	−	0.115829i
$97$	1.36927	−	0.366894i	0.139028	−	0.0372525i	−0.188634	−	0.982047i	$-0.560406\pi$
$97$	1.36927	−	0.366894i	0.139028	−	0.0372525i	0.327662	+	0.944795i	$0.393739\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$	1.22692	−	8.59286i	0.123310	−	0.863614i
$100$	−3.58973	+	3.48049i	−0.358973	+	0.348049i
$101$	−12.8850	−	7.43918i	−1.28211	−	0.740227i	−0.304876	−	0.952392i	$-0.598615\pi$
$101$	−12.8850	−	7.43918i	−1.28211	−	0.740227i	−0.977234	+	0.212165i	$0.931948\pi$
$102$	−4.74616	+	2.30840i	−0.469940	+	0.228566i
$103$	−8.19286	−	2.19527i	−0.807267	−	0.216307i	−0.168495	−	0.985703i	$-0.553891\pi$
$103$	−8.19286	−	2.19527i	−0.807267	−	0.216307i	−0.638772	+	0.769396i	$0.720557\pi$
$104$	1.33176	+	2.30668i	0.130590	+	0.226188i
$105$	0.805607	−	3.78827i	0.0786192	−	0.369697i
$106$	−0.974852	+	1.68849i	−0.0946860	+	0.164001i
$107$	1.27290	−	1.27290i	0.123056	−	0.123056i	−0.642897	−	0.765953i	$-0.722268\pi$
$107$	1.27290	−	1.27290i	0.123056	−	0.123056i	0.765953	+	0.642897i	$0.222268\pi$
$108$	−4.94710	+	1.58939i	−0.476035	+	0.152939i
$109$		−	5.32096i		−	0.509655i	−0.966986	−	0.254828i	$-0.917981\pi$
$109$		−	5.32096i		−	0.509655i	0.966986	−	0.254828i	$-0.0820187\pi$
$110$	0.893986	−	6.40763i	0.0852382	−	0.610944i
$111$	−1.53889	+	0.297374i	−0.146065	+	0.0282255i
$112$	−0.258819	+	0.965926i	−0.0244561	+	0.0912714i
$113$	−0.426287	+	1.59093i	−0.0401017	+	0.149662i	−0.983074	−	0.183210i	$-0.941351\pi$
$113$	−0.426287	+	1.59093i	−0.0401017	+	0.149662i	0.942972	+	0.332872i	$0.108018\pi$
$114$	1.97443	−	5.71375i	0.184922	−	0.535142i
$115$	−0.489593	+	3.50915i	−0.0456547	+	0.327230i
$116$		−	4.18033i		−	0.388134i
$117$	−0.956362	−	7.93312i	−0.0884157	−	0.733417i
$118$	−7.67377	+	7.67377i	−0.706428	+	0.706428i
$119$	1.52356	−	2.63888i	0.139664	−	0.241906i
$120$	−3.68354	+	1.19646i	−0.336260	+	0.109221i
$121$	−1.31431	−	2.27644i	−0.119482	−	0.206949i
$122$	−7.22943	−	1.93712i	−0.654522	−	0.175379i
$123$	−1.49296	+	21.0182i	−0.134616	+	1.89515i
$124$	−8.81957	−	5.09198i	−0.792021	−	0.457273i
$125$	10.4257	−	4.03804i	0.932499	−	0.361173i
$126$	1.85218	−	2.35997i	0.165005	−	0.210242i
$127$	−4.24532	−	4.24532i	−0.376711	−	0.376711i	0.493203	−	0.869914i	$-0.335826\pi$
$127$	−4.24532	−	4.24532i	−0.376711	−	0.376711i	−0.869914	+	0.493203i	$0.835826\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−19.9873	−	6.90676i	−1.75978	−	0.608106i
$130$	−0.731755	−	5.91069i	−0.0641792	−	0.518402i
$131$	−6.47340	+	3.73742i	−0.565584	+	0.326540i	−0.755384	−	0.655283i	$-0.772549\pi$
$131$	−6.47340	+	3.73742i	−0.565584	+	0.326540i	0.189800	+	0.981823i	$0.439216\pi$
$132$	2.80691	−	4.15156i	0.244310	−	0.361347i
$133$	0.903340	+	3.37131i	0.0783296	+	0.292330i
$134$	5.79812			0.500881
$135$	11.5724	+	1.03923i	0.995992	+	0.0894430i
$136$	−3.04712			−0.261288
$137$	−0.459855	−	1.71620i	−0.0392881	−	0.146625i	0.943496	−	0.331385i	$-0.107516\pi$
$137$	−0.459855	−	1.71620i	−0.0392881	−	0.146625i	−0.982784	+	0.184760i	$0.940849\pi$
$138$	−1.53721	+	2.27361i	−0.130856	+	0.193542i
$139$	10.8454	−	6.26162i	0.919898	−	0.531103i	0.0362954	−	0.999341i	$-0.488444\pi$
$139$	10.8454	−	6.26162i	0.919898	−	0.531103i	0.883602	+	0.468238i	$0.155111\pi$
$140$	1.37489	−	1.76342i	0.116200	−	0.149037i
$141$	−12.3321	−	4.26145i	−1.03855	−	0.358878i
$142$	−0.0613423	+	0.0164366i	−0.00514773	+	0.00137933i
$143$	5.44929	+	5.44929i	0.455692	+	0.455692i
$144$	−2.96988	−	0.424051i	−0.247490	−	0.0353376i
$145$	−3.64374	+	8.60808i	−0.302596	+	0.714863i
$146$	−11.7193	−	6.76614i	−0.969896	−	0.559970i
$147$	−0.122721	+	1.72770i	−0.0101219	+	0.142498i
$148$	−0.874081	−	0.234209i	−0.0718490	−	0.0192519i
$149$	3.43305	+	5.94622i	0.281246	+	0.487133i	0.971692	−	0.236251i	$-0.0759188\pi$
$149$	3.43305	+	5.94622i	0.281246	+	0.487133i	−0.690446	+	0.723384i	$0.742585\pi$
$150$	8.62798	+	0.746983i	0.704472	+	0.0609909i
$151$	2.26044	−	3.91519i	0.183952	−	0.318614i	−0.759271	−	0.650774i	$-0.774444\pi$
$151$	2.26044	−	3.91519i	0.183952	−	0.318614i	0.943223	+	0.332161i	$0.107778\pi$
$152$	2.46797	−	2.46797i	0.200179	−	0.200179i
$153$	8.40678	+	3.59030i	0.679648	+	0.290259i
$154$			2.89334i			0.233152i
$155$	13.7228	+	18.1728i	1.10224	+	1.45967i
$156$	1.50676	−	4.36036i	0.120637	−	0.349108i
$157$	−2.84211	+	10.6069i	−0.226825	+	0.846521i	0.754841	+	0.655908i	$0.227714\pi$
$157$	−2.84211	+	10.6069i	−0.226825	+	0.846521i	−0.981665	+	0.190613i	$0.938952\pi$
$158$	3.09536	−	11.5520i	0.246253	−	0.919030i
$159$	3.31565	−	0.640714i	0.262948	−	0.0508120i
$160$	−2.21462	−	0.308981i	−0.175081	−	0.0244271i
$161$		−	1.58454i		−	0.124879i
$162$	7.69404	+	4.66923i	0.604501	+	0.366849i
$163$	5.13101	−	5.13101i	0.401892	−	0.401892i	−0.477007	−	0.878899i	$-0.658279\pi$
$163$	5.13101	−	5.13101i	0.401892	−	0.401892i	0.878899	+	0.477007i	$0.158279\pi$
$164$	−6.08273	+	10.5356i	−0.474981	+	0.822692i
$165$	−9.39860	+	6.10222i	−0.731680	+	0.475057i
$166$	5.96124	+	10.3252i	0.462682	+	0.801389i
$167$	−22.6752	−	6.07580i	−1.75466	−	0.470159i	−0.769048	−	0.639191i	$-0.779269\pi$
$167$	−22.6752	−	6.07580i	−1.75466	−	0.470159i	−0.985611	+	0.169032i	$0.945936\pi$
$168$	1.55759	−	0.757569i	0.120171	−	0.0584477i
$169$	−5.11445	−	2.95283i	−0.393419	−	0.227141i
$170$	6.27458	+	2.65598i	0.481238	+	0.203705i
$171$	−9.71688	+	3.90104i	−0.743069	+	0.298320i
$172$	−8.63321	−	8.63321i	−0.658276	−	0.658276i
$173$	−5.39137	+	1.44461i	−0.409898	+	0.109832i	−0.457875	−	0.889017i	$-0.651389\pi$
$173$	−5.39137	+	1.44461i	−0.409898	+	0.109832i	0.0479768	+	0.998848i	$0.484723\pi$
$174$	−5.46973	+	4.74422i	−0.414659	+	0.359658i
$175$	−4.36823	+	2.43281i	−0.330207	+	0.183903i
$176$	2.50570	−	1.44667i	0.188874	−	0.109047i
$177$	18.7496	+	1.33182i	1.40930	+	0.100105i
$178$	2.76637	+	10.3242i	0.207348	+	0.773835i
$179$	0.774857			0.0579156			0.0289578	−	0.999581i	$-0.490781\pi$
$179$	0.774857			0.0579156			0.0289578	+	0.999581i	$0.490781\pi$
$180$	5.74591	+	3.46186i	0.428275	+	0.258032i
$181$	15.9309			1.18414			0.592068	−	0.805888i	$-0.298312\pi$
$181$	15.9309			1.18414			0.592068	+	0.805888i	$0.298312\pi$
$182$	0.689370	+	2.57276i	0.0510995	+	0.190706i
$183$	5.66999	+	11.6577i	0.419138	+	0.861764i
$184$	−1.37225	+	0.792270i	−0.101164	+	0.0584069i
$185$	1.59575	+	1.24416i	0.117322	+	0.0914727i
$186$	3.34667	+	17.3187i	0.245389	+	1.26987i
$187$	−8.51592	+	2.28183i	−0.622746	+	0.166864i
$188$	−5.32666	−	5.32666i	−0.388487	−	0.388487i
$189$	−5.18990	+	0.254828i	−0.377510	+	0.0185360i
$190$	−7.23319	+	2.93084i	−0.524751	+	0.212625i
$191$	−5.45782	−	3.15107i	−0.394914	−	0.228004i	0.289373	−	0.957216i	$-0.406553\pi$
$191$	−5.45782	−	3.15107i	−0.394914	−	0.228004i	−0.684287	+	0.729213i	$0.739886\pi$
$192$	−1.43487	−	0.970129i	−0.103553	−	0.0700130i
$193$	−9.17349	−	2.45803i	−0.660322	−	0.176933i	−0.0869308	−	0.996214i	$-0.527706\pi$
$193$	−9.17349	−	2.45803i	−0.660322	−	0.176933i	−0.573391	+	0.819282i	$0.694373\pi$
$194$	−0.708785	−	1.22765i	−0.0508878	−	0.0881403i
$195$	−6.90334	+	7.66544i	−0.494359	+	0.548934i
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	3.38773	−	3.38773i	0.241366	−	0.241366i	−0.576049	−	0.817415i	$-0.695406\pi$
$197$	3.38773	−	3.38773i	0.241366	−	0.241366i	0.817415	+	0.576049i	$0.195406\pi$
$198$	−8.61761	+	1.03888i	−0.612427	+	0.0738299i
$199$		−	15.8487i		−	1.12349i	−0.827311	−	0.561744i	$-0.810131\pi$
$199$		−	15.8487i		−	1.12349i	0.827311	−	0.561744i	$-0.189869\pi$
$200$	4.29099	+	2.56659i	0.303419	+	0.181486i
$201$	−6.58023	−	7.58651i	−0.464133	−	0.535111i
$202$	−3.85081	+	14.3714i	−0.270942	+	1.01117i
$203$	1.08195	−	4.03789i	0.0759380	−	0.283404i
$204$	3.45814	+	3.98698i	0.242118	+	0.279145i
$205$	21.7087	−	16.3928i	1.51620	−	1.14492i
$206$			8.48188i			0.590960i
$207$	4.71945	−	0.568944i	0.328024	−	0.0395443i
$208$	1.88339	−	1.88339i	0.130590	−	0.130590i
$209$	5.04922	−	8.74550i	0.349262	−	0.604939i
$210$	−3.86770	+	0.202320i	−0.266896	+	0.0139614i
$211$	−0.627254	−	1.08643i	−0.0431819	−	0.0747933i	0.843627	−	0.536930i	$-0.180416\pi$
$211$	−0.627254	−	1.08643i	−0.0431819	−	0.0747933i	−0.886809	+	0.462137i	$0.847083\pi$
$212$	1.88327	+	0.504621i	0.129344	+	0.0346575i
$213$	0.0911232	+	0.0616092i	0.00624366	+	0.00422140i
$214$	−1.55898	−	0.900079i	−0.106570	−	0.0615282i
$215$	10.2524	+	25.3024i	0.699205	+	1.72561i
$216$	2.81564	+	4.36717i	0.191580	+	0.297148i
$217$	−7.20115	−	7.20115i	−0.488846	−	0.488846i
$218$	−5.13965	+	1.37717i	−0.348101	+	0.0932734i
$219$	4.44699	+	23.0129i	0.300500	+	1.55507i
$220$	−6.42068	+	0.794893i	−0.432882	+	0.0535917i
$221$	−7.02871	+	4.05803i	−0.472802	+	0.272973i
$222$	0.685536	+	1.40949i	0.0460101	+	0.0945986i
$223$	−7.29914	−	27.2408i	−0.488787	−	1.82418i	−0.562366	−	0.826888i	$-0.690109\pi$
$223$	−7.29914	−	27.2408i	−0.488787	−	1.82418i	0.0735796	−	0.997289i	$-0.476558\pi$
$224$	1.00000			0.0668153
$225$	−8.81442	−	12.1370i	−0.587628	−	0.809131i
$226$	1.64705			0.109560
$227$	−2.08101	−	7.76645i	−0.138122	−	0.515477i	−0.999966	−	0.00830356i	$-0.997357\pi$
$227$	−2.08101	−	7.76645i	−0.138122	−	0.515477i	0.861844	−	0.507174i	$-0.169310\pi$
$228$	−6.03008	−	0.428327i	−0.399352	−	0.0283667i
$229$	19.5597	−	11.2928i	1.29254	−	0.746250i	0.313439	−	0.949608i	$-0.398519\pi$
$229$	19.5597	−	11.2928i	1.29254	−	0.746250i	0.979104	+	0.203358i	$0.0651855\pi$
$230$	3.51629	−	0.435324i	0.231857	−	0.0287044i
$231$	3.78577	−	3.28362i	0.249085	−	0.216046i
$232$	−4.03789	+	1.08195i	−0.265101	+	0.0710335i
$233$	17.3503	+	17.3503i	1.13666	+	1.13666i	0.989045	+	0.147612i	$0.0471586\pi$
$233$	17.3503	+	17.3503i	1.13666	+	1.13666i	0.147612	+	0.989045i	$0.452841\pi$
$234$	−7.41528	+	2.97702i	−0.484752	+	0.194614i
$235$	6.32567	+	15.6115i	0.412641	+	1.01838i
$236$	9.39841	+	5.42618i	0.611784	+	0.353214i
$237$	−18.6281	+	9.06018i	−1.21002	+	0.588522i
$238$	−2.94329	−	0.788652i	−0.190785	−	0.0511207i
$239$	−4.00858	−	6.94307i	−0.259294	−	0.449110i	0.706759	−	0.707454i	$-0.250156\pi$
$239$	−4.00858	−	6.94307i	−0.259294	−	0.449110i	−0.966053	+	0.258344i	$0.916823\pi$
$240$	2.10906	+	3.24836i	0.136139	+	0.209681i
$241$	−9.84102	+	17.0451i	−0.633916	+	1.09797i	0.352828	+	0.935688i	$0.385220\pi$
$241$	−9.84102	+	17.0451i	−0.633916	+	1.09797i	−0.986744	+	0.162286i	$0.948113\pi$
$242$	−1.85871	+	1.85871i	−0.119482	+	0.119482i
$243$	−2.62247	−	15.3663i	−0.168232	−	0.985747i
$244$			7.48446i			0.479143i
$245$	1.78445	−	1.34749i	0.114005	−	0.0860879i
$246$	20.6885	−	3.99783i	1.31905	−	0.254892i
$247$	2.40607	−	8.97956i	0.153094	−	0.571356i
$248$	−2.63580	+	9.83695i	−0.167374	+	0.624647i
$249$	6.74456	−	19.5179i	0.427419	−	1.23690i
$250$	−6.59881	−	9.02528i	−0.417345	−	0.570809i
$251$		−	30.2177i		−	1.90732i	−0.300884	−	0.953661i	$-0.597282\pi$
$251$		−	30.2177i		−	1.90732i	0.300884	−	0.953661i	$-0.402718\pi$
$252$	−2.75893	−	1.17826i	−0.173796	−	0.0742236i
$253$	−3.24180	+	3.24180i	−0.203810	+	0.203810i
$254$	−3.00190	+	5.19944i	−0.188356	+	0.326242i
$255$	−3.64575	−	11.2242i	−0.228306	−	0.702886i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.38735	−	0.907639i	−0.211297	−	0.0566170i	0.151618	−	0.988439i	$-0.451552\pi$
$257$	−3.38735	−	0.907639i	−0.211297	−	0.0566170i	−0.362915	+	0.931822i	$0.618218\pi$
$258$	−1.49833	+	21.0938i	−0.0932820	+	1.31324i
$259$	−0.783680	−	0.452458i	−0.0486955	−	0.0281144i
$260$	−5.51989	+	2.23662i	−0.342329	+	0.138709i
$261$	12.4151	+	1.77268i	0.768474	+	0.109726i
$262$	5.28551	+	5.28551i	0.326540	+	0.326540i
$263$	27.2790	−	7.30940i	1.68210	−	0.450717i	0.713766	−	0.700384i	$-0.246988\pi$
$263$	27.2790	−	7.30940i	1.68210	−	0.450717i	0.968332	+	0.249667i	$0.0803213\pi$
$264$	−4.73658	−	1.63676i	−0.291516	−	0.100736i
$265$	−3.43816	−	2.68064i	−0.211204	−	0.164670i
$266$	3.02264	−	1.74512i	0.185330	−	0.107000i
$267$	10.3692	−	15.3365i	0.634583	−	0.938580i
$268$	−1.50066	−	5.60055i	−0.0916676	−	0.342108i
$269$	3.35621			0.204632			0.102316	−	0.994752i	$-0.467375\pi$
$269$	3.35621			0.204632			0.102316	+	0.994752i	$0.467375\pi$
$270$	−1.99133	−	11.4470i	−0.121188	−	0.696644i
$271$	−3.23357			−0.196425			−0.0982126	−	0.995165i	$-0.531313\pi$
$271$	−3.23357			−0.196425			−0.0982126	+	0.995165i	$0.531313\pi$
$272$	0.788652	+	2.94329i	0.0478190	+	0.178463i
$273$	2.58396	−	3.82180i	0.156388	−	0.231306i
$274$	−1.53871	+	0.888372i	−0.0929566	+	0.0536685i
$275$	13.9142	+	3.95967i	0.839059	+	0.238777i
$276$	2.59399	+	0.896375i	0.156140	+	0.0539554i
$277$	−7.14421	+	1.91428i	−0.429254	+	0.115018i	−0.466976	−	0.884270i	$-0.654657\pi$
$277$	−7.14421	+	1.91428i	−0.429254	+	0.115018i	0.0377221	+	0.999288i	$0.487990\pi$
$278$	−8.85526	−	8.85526i	−0.531103	−	0.531103i
$279$	18.8625	−	24.0338i	1.12927	−	1.43887i
$280$	−2.05919	−	0.871638i	−0.123060	−	0.0520903i
$281$	−2.24180	−	1.29430i	−0.133735	−	0.0772117i	0.431640	−	0.902046i	$-0.357935\pi$
$281$	−2.24180	−	1.29430i	−0.133735	−	0.0772117i	−0.565375	+	0.824834i	$0.691268\pi$
$282$	−0.924465	+	13.0148i	−0.0550511	+	0.775021i
$283$	−14.9725	−	4.01186i	−0.890021	−	0.238480i	−0.215295	−	0.976549i	$-0.569071\pi$
$283$	−14.9725	−	4.01186i	−0.890021	−	0.238480i	−0.674726	+	0.738069i	$0.735738\pi$
$284$	0.0317531	+	0.0549980i	0.00188420	+	0.00326353i
$285$	12.0437	+	6.13805i	0.713408	+	0.363587i
$286$	3.85323	−	6.67399i	0.227846	−	0.394641i
$287$	−8.60228	+	8.60228i	−0.507776	+	0.507776i
$288$	0.359059	+	2.97844i	0.0211578	+	0.175506i
$289$			7.71508i			0.453828i
$290$	9.25784	+	1.29164i	0.543639	+	0.0758479i
$291$	−0.801921	+	2.32065i	−0.0470094	+	0.136039i
$292$	−3.50241	+	13.0712i	−0.204963	+	0.764933i
$293$	2.40605	−	8.97949i	0.140563	−	0.524587i	−0.859350	−	0.511388i	$-0.829132\pi$
$293$	2.40605	−	8.97949i	0.140563	−	0.524587i	0.999913	−	0.0131997i	$-0.00420171\pi$
$294$	1.70059	−	0.328621i	0.0991805	−	0.0191656i
$295$	−14.6234	−	19.3655i	−0.851408	−	1.12750i
$296$			0.904915i			0.0525971i
$297$	11.1394	+	10.0966i	0.646371	+	0.585867i
$298$	4.85507	−	4.85507i	0.281246	−	0.281246i
$299$	−2.11023	+	3.65502i	−0.122038	+	0.211375i
$300$	−1.51156	−	8.52732i	−0.0872697	−	0.492325i
$301$	−6.10460	−	10.5735i	−0.351863	−	0.609445i
$302$	−4.36683	−	1.17009i	−0.251283	−	0.0673310i
$303$	23.1744	−	11.2714i	1.33134	−	0.647525i
$304$	−3.02264	−	1.74512i	−0.173360	−	0.100089i
$305$	6.52374	−	15.4119i	0.373548	−	0.882482i
$306$	1.29213	−	9.04957i	0.0738663	−	0.517329i
$307$	13.3222	+	13.3222i	0.760337	+	0.760337i	0.976383	−	0.216046i	$-0.0693161\pi$
$307$	13.3222	+	13.3222i	0.760337	+	0.760337i	−0.216046	+	0.976383i	$0.569316\pi$
$308$	2.79475	−	0.748850i	0.159246	−	0.0426697i
$309$	11.0981	−	9.62599i	0.631347	−	0.547604i
$310$	14.0019	−	17.9586i	0.795253	−	1.01998i
$311$	−13.8248	+	7.98174i	−0.783932	+	0.452603i	−0.837822	−	0.545944i	$-0.816171\pi$
$311$	−13.8248	+	7.98174i	−0.783932	+	0.452603i	0.0538903	+	0.998547i	$0.482838\pi$
$312$	−4.60176	−	0.326871i	−0.260523	−	0.0185054i
$313$	−3.20099	−	11.9462i	−0.180930	−	0.675242i	−0.995465	−	0.0951269i	$-0.969674\pi$
$313$	−3.20099	−	11.9462i	−0.180930	−	0.675242i	0.814535	−	0.580115i	$-0.196992\pi$
$314$	10.9811			0.619697
$315$	4.65413	+	4.83105i	0.262231	+	0.272199i
$316$	−11.9595			−0.672777
$317$	5.43808	+	20.2952i	0.305433	+	1.13989i	0.932572	+	0.360984i	$0.117559\pi$
$317$	5.43808	+	20.2952i	0.305433	+	1.13989i	−0.627139	+	0.778907i	$0.715774\pi$
$318$	−1.47704	−	3.03684i	−0.0828281	−	0.170298i
$319$	−10.4747	+	6.04755i	−0.586469	+	0.338598i
$320$	0.274732	+	2.21913i	0.0153580	+	0.124053i
$321$	0.591570	+	3.06133i	0.0330182	+	0.170867i
$322$	−1.53055	+	0.410109i	−0.0852941	+	0.0228545i
$323$	7.52020	+	7.52020i	0.418435	+	0.418435i
$324$	2.51876	−	8.64036i	0.139931	−	0.480020i
$325$	13.3160	+	0.205733i	0.738639	+	0.0114120i
$326$	−6.28418	−	3.62817i	−0.348049	−	0.200946i
$327$	7.63488	+	5.16201i	0.422210	+	0.285460i
$328$	11.7509	+	3.14865i	0.648837	+	0.173855i
$329$	−3.76652	−	6.52380i	−0.207655	−	0.359669i
$330$	8.32683	+	7.49898i	0.458377	+	0.412805i
$331$	−16.7522	+	29.0156i	−0.920784	+	1.59484i	−0.122578	+	0.992459i	$0.539116\pi$
$331$	−16.7522	+	29.0156i	−0.920784	+	1.59484i	−0.798205	+	0.602385i	$0.794217\pi$
$332$	8.43047	−	8.43047i	0.462682	−	0.462682i
$333$	1.06623	−	2.49660i	0.0584290	−	0.136813i
$334$			23.4751i			1.28450i
$335$	−1.79151	+	12.8406i	−0.0978806	+	0.701558i
$336$	−1.13489	−	1.30844i	−0.0619133	−	0.0713815i
$337$	4.97434	−	18.5645i	0.270970	−	1.01127i	−0.687525	−	0.726161i	$-0.741303\pi$
$337$	4.97434	−	18.5645i	0.270970	−	1.01127i	0.958494	−	0.285111i	$-0.0920306\pi$
$338$	−1.52850	+	5.70443i	−0.0831393	+	0.310280i
$339$	−1.86922	−	2.15507i	−0.101522	−	0.117047i
$340$	0.941501	−	6.74820i	0.0510601	−	0.365972i
$341$			29.4656i			1.59565i
$342$	6.28303	+	8.37612i	0.339747	+	0.452929i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−6.10460	+	10.5735i	−0.329138	+	0.570084i
$345$	−4.56020	−	4.10683i	−0.245513	−	0.221104i
$346$	2.79078	+	4.83377i	0.150033	+	0.259865i
$347$	−7.64092	−	2.04738i	−0.410186	−	0.109909i	0.0478247	−	0.998856i	$-0.484771\pi$
$347$	−7.64092	−	2.04738i	−0.410186	−	0.109909i	−0.458010	+	0.888947i	$0.651438\pi$
$348$	5.99823	+	4.05546i	0.321539	+	0.217396i
$349$	23.3704	+	13.4929i	1.25099	+	0.722258i	0.971306	−	0.237834i	$-0.0764375\pi$
$349$	23.3704	+	13.4929i	1.25099	+	0.722258i	0.279682	+	0.960093i	$0.409771\pi$
$350$	3.48049	+	3.58973i	0.186040	+	0.191879i
$351$	12.3108	+	6.32390i	0.657101	+	0.337545i
$352$	−2.04590	−	2.04590i	−0.109047	−	0.109047i
$353$	−13.7322	+	3.67953i	−0.730891	+	0.195842i	−0.605026	−	0.796206i	$-0.706837\pi$
$353$	−13.7322	+	3.67953i	−0.730891	+	0.195842i	−0.125865	+	0.992047i	$0.540171\pi$
$354$	−3.56631	−	18.4554i	−0.189547	−	0.980894i
$355$	−0.0174472	−	0.140928i	−0.000926002	−	0.00747970i
$356$	9.25646	−	5.34422i	0.490592	−	0.283243i
$357$	2.30840	+	4.74616i	0.122174	+	0.251193i
$358$	−0.200548	−	0.748455i	−0.0105993	−	0.0395571i
$359$	−5.35082			−0.282405			−0.141203	−	0.989981i	$-0.545097\pi$
$359$	−5.35082			−0.282405			−0.141203	+	0.989981i	$0.545097\pi$
$360$	1.85675	−	6.44612i	0.0978592	−	0.339740i
$361$	6.81823			0.358854
$362$	−4.12323	−	15.3881i	−0.216712	−	0.808780i
$363$	4.54144	+	0.322587i	0.238364	+	0.0169314i
$364$	2.30668	−	1.33176i	0.120903	−	0.0698032i
$365$	18.6055	−	23.8632i	0.973854	−	1.24905i
$366$	9.79299	−	8.49403i	0.511888	−	0.443990i
$367$	20.3129	−	5.44283i	1.06033	−	0.284113i	0.313813	−	0.949485i	$-0.398393\pi$
$367$	20.3129	−	5.44283i	1.06033	−	0.284113i	0.746512	+	0.665371i	$0.231727\pi$
$368$	1.12044	+	1.12044i	0.0584069	+	0.0584069i
$369$	−28.7101	−	22.5326i	−1.49459	−	1.17300i
$370$	0.788759	−	1.86339i	0.0410056	−	0.0968730i
$371$	1.68849	+	0.974852i	0.0876622	+	0.0506118i
$372$	15.8624	−	7.71505i	0.822429	−	0.400007i
$373$	−5.28527	−	1.41618i	−0.273661	−	0.0733273i	0.119379	−	0.992849i	$-0.461910\pi$
$373$	−5.28527	−	1.41618i	−0.273661	−	0.0733273i	−0.393040	+	0.919522i	$0.628576\pi$
$374$	4.40816	+	7.63517i	0.227941	+	0.394805i
$375$	−4.32016	+	18.8769i	−0.223092	+	0.974797i
$376$	−3.76652	+	6.52380i	−0.194243	+	0.336439i
$377$	−7.87321	+	7.87321i	−0.405491	+	0.405491i
$378$	1.58939	+	4.94710i	0.0817494	+	0.254452i
$379$			17.2012i			0.883568i	0.897121	+	0.441784i	$0.145654\pi$
$379$			17.2012i			0.883568i	−0.897121	+	0.441784i	$0.854346\pi$
$380$	4.70306	+	6.22817i	0.241262	+	0.319498i
$381$	10.2100	−	1.97297i	0.523074	−	0.101078i
$382$	−1.63112	+	6.08741i	−0.0834551	+	0.311459i
$383$	0.732446	−	2.73353i	0.0374263	−	0.139677i	−0.944685	−	0.327980i	$-0.893632\pi$
$383$	0.732446	−	2.73353i	0.0374263	−	0.139677i	0.982111	+	0.188303i	$0.0602988\pi$
$384$	−0.565701	+	1.63707i	−0.0288683	+	0.0835411i
$385$	−6.40763	−	0.893986i	−0.326563	−	0.0455617i
$386$			9.49710i			0.483389i
$387$	29.3005	−	21.9787i	1.48943	−	1.11724i
$388$	−1.00237	+	1.00237i	−0.0508878	+	0.0508878i
$389$	−11.8246	+	20.4808i	−0.599529	+	1.03842i	0.393361	+	0.919384i	$0.371312\pi$
$389$	−11.8246	+	20.4808i	−0.599529	+	1.03842i	−0.992890	+	0.119031i	$0.962021\pi$
$390$	9.19096	+	4.68416i	0.465402	+	0.237191i
$391$	−2.41414	−	4.18141i	−0.122088	−	0.211463i
$392$	0.965926	+	0.258819i	0.0487866	+	0.0130723i
$393$	0.917324	−	12.9143i	0.0462729	−	0.651439i
$394$	−4.14910	−	2.39548i	−0.209029	−	0.120683i
$395$	24.6269	+	10.4244i	1.23911	+	0.524508i
$396$	3.23388	+	8.05509i	0.162509	+	0.404784i
$397$	−17.7179	−	17.7179i	−0.889234	−	0.889234i	0.105216	−	0.994449i	$-0.466447\pi$
$397$	−17.7179	−	17.7179i	−0.889234	−	0.889234i	−0.994449	+	0.105216i	$0.966447\pi$
$398$	−15.3087	+	4.10196i	−0.767356	+	0.205612i
$399$	−5.71375	−	1.97443i	−0.286045	−	0.0988452i
$400$	1.36855	−	4.80906i	0.0684275	−	0.240453i
$401$	−11.4432	+	6.60673i	−0.571445	+	0.329924i	−0.757726	−	0.652572i	$-0.773690\pi$
$401$	−11.4432	+	6.60673i	−0.571445	+	0.329924i	0.186281	+	0.982497i	$0.440357\pi$
$402$	−5.62492	+	8.31954i	−0.280546	+	0.414941i
$403$	7.02051	+	26.2009i	0.349717	+	1.30516i
$404$	14.8784			0.740227
$405$	−12.7179	+	15.5967i	−0.631956	+	0.775004i
$406$	−4.18033			−0.207466
$407$	0.677646	+	2.52901i	0.0335897	+	0.125358i
$408$	2.95610	−	4.37221i	0.146349	−	0.216457i
$409$	3.31959	−	1.91657i	0.164143	−	0.0947681i	−0.415678	−	0.909512i	$-0.636456\pi$
$409$	3.31959	−	1.91657i	0.164143	−	0.0947681i	0.579821	+	0.814744i	$0.303122\pi$
$410$	−21.4529	−	16.7262i	−1.05948	−	0.826049i
$411$	2.90865	+	1.00511i	0.143473	+	0.0495782i
$412$	8.19286	−	2.19527i	0.403633	−	0.108153i
$413$	7.67377	+	7.67377i	0.377602	+	0.377602i
$414$	−1.77104	−	4.41138i	−0.0870419	−	0.216808i
$415$	−24.7082	+	10.0116i	−1.21288	+	0.491450i
$416$	−2.30668	−	1.33176i	−0.113094	−	0.0652949i
$417$	−1.53687	+	21.6364i	−0.0752608	+	1.05954i
$418$	−9.75434	−	2.61367i	−0.477100	−	0.127839i
$419$	3.81141	+	6.60155i	0.186200	+	0.322507i	0.943980	−	0.330002i	$-0.107050\pi$
$419$	3.81141	+	6.60155i	0.186200	+	0.322507i	−0.757781	+	0.652509i	$0.773716\pi$
$420$	1.19646	+	3.68354i	0.0583812	+	0.179738i
$421$	0.940652	−	1.62926i	0.0458446	−	0.0794051i	−0.842193	−	0.539177i	$-0.818735\pi$
$421$	0.940652	−	1.62926i	0.0458446	−	0.0794051i	0.888037	+	0.459772i	$0.152069\pi$
$422$	−0.887070	+	0.887070i	−0.0431819	+	0.0431819i
$423$	18.0783	−	13.5608i	0.878998	−	0.659347i
$424$		−	1.94970i		−	0.0946860i
$425$	−7.82071	+	13.0751i	−0.379360	+	0.634238i
$426$	0.0359255	−	0.103964i	0.00174060	−	0.00503707i
$427$	−1.93712	+	7.22943i	−0.0937438	+	0.349857i
$428$	−0.465915	+	1.73882i	−0.0225209	+	0.0840490i
$429$	−13.1055	+	2.53251i	−0.632741	+	0.122271i
$430$	21.7868	−	16.4518i	1.05065	−	0.793375i
$431$		−	30.4745i		−	1.46790i	−0.679201	−	0.733952i	$-0.737673\pi$
$431$		−	30.4745i		−	1.46790i	0.679201	−	0.733952i	$-0.262327\pi$
$432$	3.48962	−	3.85000i	0.167895	−	0.185233i
$433$	18.1956	−	18.1956i	0.874424	−	0.874424i	−0.118527	−	0.992951i	$-0.537817\pi$
$433$	18.1956	−	18.1956i	0.874424	−	0.874424i	0.992951	+	0.118527i	$0.0378171\pi$
$434$	−5.09198	+	8.81957i	−0.244423	+	0.423353i
$435$	−8.81658	−	13.5792i	−0.422723	−	0.651075i
$436$	2.66048	+	4.60808i	0.127414	+	0.220687i
$437$	5.34198	+	1.43138i	0.255541	+	0.0684721i
$438$	21.0778	−	10.2516i	1.00713	−	0.489842i
$439$	32.3585	+	18.6822i	1.54438	+	0.891651i	0.998554	+	0.0537553i	$0.0171191\pi$
$439$	32.3585	+	18.6822i	1.54438	+	0.891651i	0.545831	+	0.837896i	$0.316214\pi$
$440$	2.42960	+	5.99616i	0.115827	+	0.285856i
$441$	−2.35997	−	1.85218i	−0.112379	−	0.0881990i
$442$	5.73892	+	5.73892i	0.272973	+	0.272973i
$443$	−1.49011	+	0.399274i	−0.0707973	+	0.0189701i	−0.294044	−	0.955792i	$-0.595001\pi$
$443$	−1.49011	+	0.399274i	−0.0707973	+	0.0189701i	0.223247	+	0.974762i	$0.428335\pi$
$444$	1.18403	−	1.02698i	0.0561916	−	0.0487383i
$445$	−23.7190	+	2.93646i	−1.12439	+	0.139202i
$446$	−24.4234	+	14.1009i	−1.15648	+	0.667695i
$447$	−11.8625	−	0.842618i	−0.561079	−	0.0398545i
$448$	−0.258819	−	0.965926i	−0.0122281	−	0.0456357i
$449$	2.98135			0.140699			0.0703494	−	0.997522i	$-0.477589\pi$
$449$	2.98135			0.140699			0.0703494	+	0.997522i	$0.477589\pi$
$450$	−9.44207	+	11.6554i	−0.445104	+	0.549439i
$451$	35.1988			1.65744
$452$	−0.426287	−	1.59093i	−0.0200509	−	0.0748309i
$453$	3.42487	+	7.04167i	0.160915	+	0.330846i
$454$	−6.96321	+	4.02021i	−0.326800	+	0.188678i
$455$	−5.91069	+	0.731755i	−0.277097	+	0.0343052i
$456$	1.14697	+	5.93547i	0.0537116	+	0.277954i
$457$	−38.0371	+	10.1920i	−1.77930	+	0.476762i	−0.990456	−	0.137829i	$-0.955988\pi$
$457$	−38.0371	+	10.1920i	−1.77930	+	0.476762i	−0.788846	+	0.614591i	$0.789321\pi$
$458$	−15.9705	−	15.9705i	−0.746250	−	0.746250i
$459$	−13.3073	+	8.57958i	−0.621131	+	0.400460i
$460$	−1.33057	−	3.28381i	−0.0620384	−	0.153108i
$461$	−26.2642	−	15.1636i	−1.22324	−	0.706240i	−0.257636	−	0.966242i	$-0.582943\pi$
$461$	−26.2642	−	15.1636i	−1.22324	−	0.706240i	−0.965608	+	0.260002i	$0.916277\pi$
$462$	−4.15156	−	2.80691i	−0.193148	−	0.130589i
$463$	−30.6658	−	8.21688i	−1.42516	−	0.381871i	−0.537850	−	0.843041i	$-0.680763\pi$
$463$	−30.6658	−	8.21688i	−1.42516	−	0.381871i	−0.887312	+	0.461170i	$0.847430\pi$
$464$	2.09017	+	3.62028i	0.0970336	+	0.168067i
$465$	−39.3885	+	2.06042i	−1.82660	+	0.0955497i
$466$	12.2685	−	21.2497i	0.568329	−	0.984374i
$467$	5.22469	−	5.22469i	0.241770	−	0.241770i	−0.575812	−	0.817582i	$-0.695314\pi$
$467$	5.22469	−	5.22469i	0.241770	−	0.241770i	0.817582	+	0.575812i	$0.195314\pi$
$468$	4.79479	+	6.39210i	0.221639	+	0.295475i
$469$		−	5.79812i		−	0.267732i
$470$	13.4424	−	10.1507i	0.620050	−	0.468216i
$471$	−12.4623	−	14.3681i	−0.574232	−	0.662047i
$472$	2.80880	−	10.4826i	0.129285	−	0.482499i
$473$	−9.14287	+	34.1216i	−0.420390	+	1.56892i
$474$	13.5728	+	15.6484i	0.623417	+	0.718754i
$475$	−4.25576	−	16.9243i	−0.195268	−	0.776541i
$476$			3.04712i			0.139664i
$477$	−2.29727	+	5.37910i	−0.105185	+	0.246292i
$478$	−5.66899	+	5.66899i	−0.259294	+	0.259294i
$479$	−12.8053	+	22.1795i	−0.585091	+	1.01341i	0.409773	+	0.912187i	$0.365608\pi$
$479$	−12.8053	+	22.1795i	−0.585091	+	1.01341i	−0.994864	+	0.101220i	$0.967725\pi$
$480$	2.59181	−	2.87794i	0.118299	−	0.131359i
$481$	1.20513	+	2.08735i	0.0549492	+	0.0951748i
$482$	19.0114	+	5.09409i	0.865945	+	0.232029i
$483$	2.27361	+	1.53721i	0.103453	+	0.0699453i
$484$	2.27644	+	1.31431i	0.103475	+	0.0597412i
$485$	2.93778	−	1.19037i	0.133398	−	0.0540518i
$486$	−14.1639	+	6.51020i	−0.642490	+	0.295309i
$487$	4.19267	+	4.19267i	0.189988	+	0.189988i	0.795691	−	0.605703i	$-0.207108\pi$
$487$	4.19267	+	4.19267i	0.189988	+	0.189988i	−0.605703	+	0.795691i	$0.707108\pi$
$488$	7.22943	−	1.93712i	0.327261	−	0.0876893i
$489$	2.38459	+	12.3401i	0.107835	+	0.558037i
$490$	−1.76342	−	1.37489i	−0.0796634	−	0.0621114i
$491$	−4.12389	+	2.38093i	−0.186109	+	0.107450i	−0.590160	−	0.807287i	$-0.700935\pi$
$491$	−4.12389	+	2.38093i	−0.186109	+	0.107450i	0.404051	+	0.914737i	$0.367602\pi$
$492$	−9.21617	−	18.9488i	−0.415497	−	0.854278i
$493$	−3.29683	−	12.3039i	−0.148482	−	0.554141i
$494$	−9.29632			−0.418261
$495$	0.361959	−	19.4057i	0.0162689	−	0.872222i
$496$	10.1840			0.457273
$497$	0.0164366	+	0.0613423i	0.000737283	+	0.00275158i
$498$	−20.5985	−	1.46315i	−0.923039	−	0.0655651i
$499$	−8.23352	+	4.75362i	−0.368583	+	0.212801i	−0.672839	−	0.739789i	$-0.734925\pi$
$499$	−8.23352	+	4.75362i	−0.368583	+	0.212801i	0.304256	+	0.952590i	$0.401592\pi$
$500$	−7.00986	+	8.70987i	−0.313490	+	0.389517i
$501$	30.7158	−	26.6416i	1.37228	−	1.19026i
$502$	−29.1880	+	7.82091i	−1.30272	+	0.349064i
$503$	11.4348	+	11.4348i	0.509851	+	0.509851i	0.914481	−	0.404630i	$-0.132600\pi$
$503$	11.4348	+	11.4348i	0.509851	+	0.509851i	−0.404630	+	0.914481i	$0.632600\pi$
$504$	−0.424051	+	2.96988i	−0.0188887	+	0.132289i
$505$	−30.6373	−	12.9686i	−1.36334	−	0.577093i
$506$	3.97038	+	2.29230i	0.176505	+	0.101905i
$507$	9.19860	−	4.47394i	0.408524	−	0.198695i
$508$	5.79922	+	1.55390i	0.257299	+	0.0689430i
$509$	20.6275	+	35.7279i	0.914297	+	1.58361i	0.807927	+	0.589283i	$0.200590\pi$
$509$	20.6275	+	35.7279i	0.914297	+	1.58361i	0.106371	+	0.994327i	$0.466077\pi$
$510$	−9.89814	+	6.42656i	−0.438297	+	0.284573i
$511$	−6.76614	+	11.7193i	−0.299316	+	0.518431i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	3.82914	−	17.7270i	0.169061	−	0.782665i
$514$			3.50685i			0.154680i
$515$	−18.7841	−	2.62074i	−0.827727	−	0.115484i
$516$	20.7629	−	4.01220i	0.914034	−	0.176627i
$517$	−5.64112	+	21.0529i	−0.248096	+	0.925907i
$518$	−0.234209	+	0.874081i	−0.0102906	+	0.0384049i
$519$	3.15749	−	9.13737i	0.138598	−	0.401086i
$520$	3.58906	+	4.75293i	0.157391	+	0.208430i
$521$			31.4346i			1.37717i	0.725154	+	0.688587i	$0.241768\pi$
$521$			31.4346i			1.37717i	−0.725154	+	0.688587i	$0.758232\pi$
$522$	−1.50099	−	12.4509i	−0.0656964	−	0.544959i
$523$	−16.1228	+	16.1228i	−0.705001	+	0.705001i	−0.965480	−	0.260478i	$-0.916120\pi$
$523$	−16.1228	+	16.1228i	−0.705001	+	0.705001i	0.260478	+	0.965480i	$0.416120\pi$
$524$	3.73742	−	6.47340i	0.163270	−	0.282792i
$525$	0.746983	−	8.62798i	0.0326010	−	0.376556i
$526$	−14.1207	−	24.4577i	−0.615691	−	1.06641i
$527$	−29.9743	−	8.03160i	−1.30570	−	0.349862i
$528$	−0.355074	+	4.99881i	−0.0154526	+	0.217545i
$529$	17.7442	+	10.2446i	0.771487	+	0.445418i
$530$	−1.69944	+	4.01480i	−0.0738188	+	0.174392i
$531$	−20.1005	+	25.6112i	−0.872287	+	1.11143i
$532$	−2.46797	−	2.46797i	−0.107000	−	0.107000i
$533$	31.2988	−	8.38650i	1.35570	−	0.363260i
$534$	−17.4977	−	6.04646i	−0.757199	−	0.261656i
$535$	2.47503	−	3.17444i	0.107005	−	0.137243i
$536$	−5.02132	+	2.89906i	−0.216888	+	0.125220i
$537$	−0.751711	+	1.11182i	−0.0324387	+	0.0479785i
$538$	−0.868651	−	3.24185i	−0.0374502	−	0.139766i
$539$	2.89334			0.124625
$540$	−10.5416	+	4.88619i	−0.453638	+	0.210268i
$541$	−3.96847			−0.170618			−0.0853089	−	0.996355i	$-0.527188\pi$
$541$	−3.96847			−0.170618			−0.0853089	+	0.996355i	$0.527188\pi$
$542$	0.836908	+	3.12338i	0.0359483	+	0.134161i
$543$	−15.4550	+	22.8588i	−0.663240	+	0.980965i
$544$	2.63888	−	1.52356i	0.113141	−	0.0653220i
$545$	−1.46184	−	11.8079i	−0.0626183	−	0.505794i
$546$	−4.36036	−	1.50676i	−0.186606	−	0.0644832i
$547$	31.3521	−	8.40078i	1.34052	−	0.359191i	0.483893	−	0.875127i	$-0.339222\pi$
$547$	31.3521	−	8.40078i	1.34052	−	0.359191i	0.856627	+	0.515936i	$0.172556\pi$
$548$	1.25635	+	1.25635i	0.0536685	+	0.0536685i
$549$	−22.2279	−	3.17379i	−0.948665	−	0.135454i
$550$	0.223484	−	14.4650i	0.00952939	−	0.616788i
$551$	12.6356	+	7.29518i	0.538296	+	0.310785i
$552$	0.194457	−	2.73760i	0.00827664	−	0.116520i
$553$	−11.5520	−	3.09536i	−0.491242	−	0.131628i
$554$	3.69811	+	6.40532i	0.157118	+	0.272136i
$555$	−3.33329	+	1.08269i	−0.141490	+	0.0459578i
$556$	−6.26162	+	10.8454i	−0.265552	+	0.459949i
$557$	24.0046	−	24.0046i	1.01711	−	1.01711i	0.0172581	−	0.999851i	$-0.494506\pi$
$557$	24.0046	−	24.0046i	1.01711	−	1.01711i	0.999851	−	0.0172581i	$-0.00549369\pi$
$558$	−28.0968	−	11.9994i	−1.18943	−	0.507974i
$559$			32.5195i			1.37543i
$560$	−0.308981	+	2.21462i	−0.0130568	+	0.0935847i
$561$	4.98741	−	14.4329i	0.210568	−	0.609358i
$562$	−0.669981	+	2.50040i	−0.0282614	+	0.105473i
$563$	9.36965	−	34.9680i	0.394884	−	1.47373i	−0.427095	−	0.904207i	$-0.640463\pi$
$563$	9.36965	−	34.9680i	0.394884	−	1.47373i	0.821978	−	0.569519i	$-0.192870\pi$
$564$	12.8106	−	2.47552i	0.539424	−	0.104238i
$565$	−0.508907	+	3.64758i	−0.0214099	+	0.153455i
$566$			15.5006i			0.651540i
$567$	4.66923	−	7.69404i	0.196089	−	0.323120i
$568$	0.0449057	−	0.0449057i	0.00188420	−	0.00188420i
$569$	−3.03886	+	5.26347i	−0.127396	+	0.220656i	−0.922667	−	0.385598i	$-0.873995\pi$
$569$	−3.03886	+	5.26347i	−0.127396	+	0.220656i	0.795271	+	0.606254i	$0.207329\pi$
$570$	2.81176	−	13.2220i	0.117772	−	0.553808i
$571$	5.43870	+	9.42011i	0.227603	+	0.394219i	0.957097	−	0.289767i	$-0.0935780\pi$
$571$	5.43870	+	9.42011i	0.227603	+	0.394219i	−0.729494	+	0.683987i	$0.760245\pi$
$572$	−7.44387	−	1.99458i	−0.311244	−	0.0833975i
$573$	9.81617	−	4.77431i	0.410076	−	0.199450i
$574$	10.5356	+	6.08273i	0.439747	+	0.253888i
$575$	−0.122391	+	7.92175i	−0.00510407	+	0.330360i
$576$	2.78402	−	1.11770i	0.116001	−	0.0465709i
$577$	−18.6033	−	18.6033i	−0.774466	−	0.774466i	0.204417	−	0.978884i	$-0.434470\pi$
$577$	−18.6033	−	18.6033i	−0.774466	−	0.774466i	−0.978884	+	0.204417i	$0.934470\pi$
$578$	7.45220	−	1.99681i	0.309971	−	0.0830564i
$579$	12.4264	−	10.7782i	0.516424	−	0.447925i
$580$	−1.14847	−	9.27669i	−0.0476877	−	0.385194i
$581$	10.3252	−	5.96124i	0.428361	−	0.247314i
$582$	2.44913	+	0.173966i	0.101520	+	0.00721113i
$583$	−1.46004	−	5.44893i	−0.0604685	−	0.225672i
$584$	13.5323			0.559970
$585$	−4.30177	−	17.3419i	−0.177856	−	0.716998i
$586$	−9.29625			−0.384025
$587$	−8.22656	−	30.7019i	−0.339547	−	1.26720i	−0.898855	−	0.438245i	$-0.855600\pi$
$587$	−8.22656	−	30.7019i	−0.339547	−	1.26720i	0.559309	−	0.828959i	$-0.311067\pi$
$588$	−0.757569	−	1.55759i	−0.0312416	−	0.0642340i
$589$	30.7824	−	17.7722i	1.26837	−	0.732292i
$590$	−14.9208	+	19.1373i	−0.614281	+	0.787870i
$591$	1.57441	+	8.14748i	0.0647627	+	0.335142i
$592$	0.874081	−	0.234209i	0.0359245	−	0.00962594i
$593$	−15.3830	−	15.3830i	−0.631703	−	0.631703i	0.316792	−	0.948495i	$-0.397394\pi$
$593$	−15.3830	−	15.3830i	−0.631703	−	0.631703i	−0.948495	+	0.316792i	$0.897394\pi$
$594$	6.86954	−	13.3730i	0.281861	−	0.548701i
$595$	2.65598	−	6.27458i	0.108885	−	0.257233i
$596$	−5.94622	−	3.43305i	−0.243567	−	0.140623i
$597$	22.7409	+	15.3753i	0.930722	+	0.629270i
$598$	4.07664	+	1.09233i	0.166706	+	0.0446688i
$599$	7.54399	+	13.0666i	0.308239	+	0.533886i	0.977977	−	0.208711i	$-0.0669269\pi$
$599$	7.54399	+	13.0666i	0.308239	+	0.533886i	−0.669738	+	0.742597i	$0.733594\pi$
$600$	−7.84554	+	3.66708i	−0.320293	+	0.149708i
$601$	1.66113	−	2.87717i	0.0677591	−	0.117362i	−0.830155	−	0.557532i	$-0.811748\pi$
$601$	1.66113	−	2.87717i	0.0677591	−	0.117362i	0.897915	+	0.440170i	$0.145082\pi$
$602$	−8.63321	+	8.63321i	−0.351863	+	0.351863i
$603$	17.2693	−	2.08187i	0.703261	−	0.0847803i
$604$			4.52087i			0.183952i
$605$	−3.54202	−	4.69063i	−0.144004	−	0.190701i
$606$	−16.8853	−	19.4675i	−0.685919	−	0.790814i
$607$	7.33369	−	27.3697i	0.297665	−	1.11090i	−0.641412	−	0.767196i	$-0.721651\pi$
$607$	7.33369	−	27.3697i	0.297665	−	1.11090i	0.939078	−	0.343705i	$-0.111682\pi$
$608$	−0.903340	+	3.37131i	−0.0366353	+	0.136725i
$609$	4.74422	+	5.46973i	0.192245	+	0.221645i
$610$	−16.5752	−	2.31256i	−0.671111	−	0.0936327i
$611$			20.0644i			0.811719i
$612$	−9.07564	+	1.09410i	−0.366861	+	0.0442262i
$613$	23.3541	−	23.3541i	0.943261	−	0.943261i	−0.0552131	−	0.998475i	$-0.517584\pi$
$613$	23.3541	−	23.3541i	0.943261	−	0.943261i	0.998475	+	0.0552131i	$0.0175838\pi$
$614$	9.42021	−	16.3163i	0.380169	−	0.658471i
$615$	2.46132	+	47.0523i	0.0992499	+	1.89733i
$616$	−1.44667	−	2.50570i	−0.0582879	−	0.100958i
$617$	−14.4307	−	3.86668i	−0.580956	−	0.155667i	−0.0436396	−	0.999047i	$-0.513895\pi$
$617$	−14.4307	−	3.86668i	−0.580956	−	0.155667i	−0.537317	+	0.843381i	$0.680562\pi$
$618$	−12.1704	−	8.22851i	−0.489565	−	0.330999i
$619$	−24.7406	−	14.2840i	−0.994408	−	0.574122i	−0.0878190	−	0.996136i	$-0.527990\pi$
$619$	−24.7406	−	14.2840i	−0.994408	−	0.574122i	−0.906589	+	0.422015i	$0.861323\pi$
$620$	−20.9707	−	8.87673i	−0.842202	−	0.356498i
$621$	−3.76211	+	7.32374i	−0.150968	+	0.293892i
$622$	11.2879	+	11.2879i	0.452603	+	0.452603i
$623$	10.3242	−	2.76637i	0.413632	−	0.110832i
$624$	0.875289	+	4.52956i	0.0350396	+	0.181327i
$625$	22.0265	−	11.8252i	0.881058	−	0.473007i
$626$	−10.7107	+	6.18383i	−0.428086	+	0.247156i
$627$	7.65026	+	15.7292i	0.305522	+	0.628165i
$628$	−2.84211	−	10.6069i	−0.113412	−	0.423261i
$629$	−2.75738			−0.109944
$630$	3.46186	−	5.74591i	0.137924	−	0.228923i
$631$	−29.7860			−1.18576			−0.592881	−	0.805290i	$-0.702010\pi$
$631$	−29.7860			−1.18576			−0.592881	+	0.805290i	$0.702010\pi$
$632$	3.09536	+	11.5520i	0.123127	+	0.459515i
$633$	2.16741	+	0.153955i	0.0861468	+	0.00611916i
$634$	18.1962	−	10.5056i	0.722662	−	0.417229i
$635$	−10.5872	−	8.25458i	−0.420141	−	0.327573i
$636$	−2.55108	+	2.21270i	−0.101157	+	0.0877392i
$637$	2.57276	−	0.689370i	0.101937	−	0.0273138i
$638$	8.55253	+	8.55253i	0.338598	+	0.338598i
$639$	−0.176802	+	0.0709810i	−0.00699420	+	0.00280796i
$640$	2.07241	−	0.839723i	0.0819190	−	0.0331930i
$641$	−41.4340	−	23.9219i	−1.63654	−	0.944858i	−0.982011	−	0.188824i	$-0.939532\pi$
$641$	−41.4340	−	23.9219i	−1.63654	−	0.944858i	−0.654532	−	0.756034i	$-0.727134\pi$
$642$	2.80391	−	1.36374i	0.110662	−	0.0538227i
$643$	−18.5659	−	4.97471i	−0.732166	−	0.196183i	−0.126573	−	0.991957i	$-0.540398\pi$
$643$	−18.5659	−	4.97471i	−0.732166	−	0.196183i	−0.605594	+	0.795774i	$0.707064\pi$
$644$	0.792270	+	1.37225i	0.0312198	+	0.0540743i
$645$	−46.2518	−	9.83582i	−1.82116	−	0.387285i
$646$	5.31758	−	9.21032i	0.209218	−	0.362375i
$647$	26.0435	−	26.0435i	1.02388	−	1.02388i	0.0241677	−	0.999708i	$-0.492306\pi$
$647$	26.0435	−	26.0435i	1.02388	−	1.02388i	0.999708	−	0.0241677i	$-0.00769356\pi$
$648$	−8.99785	−	0.196646i	−0.353469	−	0.00772499i
$649$		−	31.3995i		−	1.23254i
$650$	−3.24771	−	12.9155i	−0.127386	−	0.506589i
$651$	17.3187	−	3.34667i	0.678775	−	0.131166i
$652$	−1.87808	+	7.00909i	−0.0735513	+	0.274497i
$653$	−7.65454	+	28.5671i	−0.299545	+	1.11792i	0.637995	+	0.770041i	$0.279764\pi$
$653$	−7.65454	+	28.5671i	−0.299545	+	1.11792i	−0.937540	+	0.347878i	$0.886902\pi$
$654$	3.01007	−	8.71075i	0.117703	−	0.340617i
$655$	−13.3385	+	10.0723i	−0.521179	+	0.393556i
$656$		−	12.1655i		−	0.474981i
$657$	−37.3346	−	15.9446i	−1.45656	−	0.622057i
$658$	−5.32666	+	5.32666i	−0.207655	+	0.207655i
$659$	−14.3651	+	24.8811i	−0.559585	+	0.969230i	0.437945	+	0.899002i	$0.355706\pi$
$659$	−14.3651	+	24.8811i	−0.559585	+	0.969230i	−0.997531	+	0.0702288i	$0.977627\pi$
$660$	5.08832	−	9.98398i	0.198062	−	0.388626i
$661$	2.28338	+	3.95493i	0.0888131	+	0.153829i	0.907010	−	0.421110i	$-0.138359\pi$
$661$	2.28338	+	3.95493i	0.0888131	+	0.153829i	−0.818197	+	0.574939i	$0.805026\pi$
$662$	32.3628	+	8.67157i	1.25781	+	0.337030i
$663$	0.996014	−	14.0221i	0.0386820	−	0.544573i
$664$	−10.3252	−	5.96124i	−0.400695	−	0.231341i
$665$	2.93084	+	7.23319i	0.113653	+	0.280491i
$666$	−2.68749	−	0.383730i	−0.104138	−	0.0148692i
$667$	−4.68381	−	4.68381i	−0.181358	−	0.181358i
$668$	22.6752	−	6.07580i	0.877329	−	0.235080i
$669$	46.1681	+	15.9537i	1.78496	+	0.616807i
$670$	12.8668	−	1.59293i	0.497086	−	0.0615403i
$671$	18.7538	−	10.8275i	0.723983	−	0.417992i
$672$	−0.970129	+	1.43487i	−0.0374235	+	0.0553513i
$673$	3.59846	+	13.4297i	0.138711	+	0.517675i	0.999955	+	0.00948408i	$0.00301892\pi$
$673$	3.59846	+	13.4297i	0.138711	+	0.517675i	−0.861244	+	0.508191i	$0.830314\pi$
$674$	−19.2194			−0.740303
$675$	25.9661	−	0.873116i	0.999435	−	0.0336062i
$676$	5.90566			0.227141
$677$	6.78010	+	25.3037i	0.260580	+	0.972499i	0.964900	+	0.262616i	$0.0845854\pi$
$677$	6.78010	+	25.3037i	0.260580	+	0.972499i	−0.704320	+	0.709883i	$0.748748\pi$
$678$	−1.59785	+	2.36330i	−0.0613650	+	0.0907619i
$679$	−1.22765	+	0.708785i	−0.0471130	+	0.0272007i
$680$	−6.76194	+	0.837142i	−0.259308	+	0.0321029i
$681$	13.1627	+	4.54847i	0.504396	+	0.174298i
$682$	28.4616	−	7.62626i	1.08985	−	0.292025i
$683$	−17.2386	−	17.2386i	−0.659618	−	0.659618i	0.295671	−	0.955290i	$-0.404457\pi$
$683$	−17.2386	−	17.2386i	−0.659618	−	0.659618i	−0.955290	+	0.295671i	$0.904457\pi$
$684$	6.46455	−	8.23684i	0.247178	−	0.314944i
$685$	−1.49197	−	3.68213i	−0.0570054	−	0.140687i
$686$	0.866025	+	0.500000i	0.0330650	+	0.0190901i
$687$	−2.77174	+	39.0212i	−0.105749	+	1.48875i
$688$	11.7932	+	3.15998i	0.449611	+	0.120473i
$689$	−2.59654	−	4.49734i	−0.0989203	−	0.171335i
$690$	−2.78662	+	5.46774i	−0.106085	+	0.208153i
$691$	−20.9029	+	36.2050i	−0.795186	+	1.37730i	0.127536	+	0.991834i	$0.459293\pi$
$691$	−20.9029	+	36.2050i	−0.795186	+	1.37730i	−0.922721	+	0.385468i	$0.874040\pi$
$692$	3.94676	−	3.94676i	0.150033	−	0.150033i
$693$	1.03888	+	8.61761i	0.0394637	+	0.327356i
$694$			7.91046i			0.300277i
$695$	22.3471	−	16.8749i	0.847675	−	0.640102i
$696$	2.36482	−	6.84348i	0.0896382	−	0.259401i
$697$	−9.59431	+	35.8065i	−0.363410	+	1.35627i
$698$	6.98444	−	26.0663i	0.264365	−	0.986623i
$699$	−41.7275	+	8.06340i	−1.57828	+	0.304986i
$700$	2.56659	−	4.29099i	0.0970081	−	0.162184i
$701$		−	2.87388i		−	0.108545i	−0.998526	−	0.0542724i	$-0.982716\pi$
$701$		−	2.87388i		−	0.108545i	0.998526	−	0.0542724i	$-0.0172839\pi$
$702$	2.92215	−	13.5281i	0.110289	−	0.510583i
$703$	2.23331	−	2.23331i	0.0842307	−	0.0842307i
$704$	−1.44667	+	2.50570i	−0.0545233	+	0.0944372i
$705$	−28.5372	−	6.06867i	−1.07477	−	0.228559i
$706$	7.10831	+	12.3119i	0.267525	+	0.463366i
$707$	14.3714	+	3.85081i	0.540492	+	0.144824i
$708$	−16.9035	+	8.22140i	−0.635273	+	0.308979i
$709$	−26.2628	−	15.1629i	−0.986322	−	0.569453i	−0.0821491	−	0.996620i	$-0.526178\pi$
$709$	−26.2628	−	15.1629i	−0.986322	−	0.569453i	−0.904173	+	0.427167i	$0.859512\pi$
$710$	−0.131611	+	0.0533277i	−0.00493926	+	0.00200135i
$711$	5.07146	−	35.5184i	0.190194	−	1.33204i
$712$	−7.55787	−	7.55787i	−0.283243	−	0.283243i
$713$	−15.5870	+	4.17653i	−0.583739	+	0.156412i
$714$	3.98698	−	3.45814i	0.149209	−	0.129418i
$715$	13.5898	+	10.5956i	0.508228	+	0.396252i
$716$	−0.671046	+	0.387429i	−0.0250782	+	0.0144789i
$717$	13.8512	+	0.983878i	0.517284	+	0.0367436i
$718$	1.38489	+	5.16849i	0.0516838	+	0.192886i
$719$	−45.6824			−1.70366			−0.851832	−	0.523814i	$-0.824509\pi$
$719$	−45.6824			−1.70366			−0.851832	+	0.523814i	$0.824509\pi$
$720$	−6.70704	−	0.125101i	−0.249957	−	0.00466224i
$721$	8.48188			0.315882
$722$	−1.76469	−	6.58590i	−0.0656749	−	0.245102i
$723$	−14.9105	−	30.6566i	−0.554527	−	1.14013i
$724$	−13.7966	+	7.96546i	−0.512746	+	0.296034i
$725$	−5.72099	+	20.1035i	−0.212472	+	0.746625i
$726$	−0.863817	−	4.47019i	−0.0320593	−	0.165904i
$727$	−18.2212	+	4.88235i	−0.675785	+	0.181076i	−0.580360	−	0.814360i	$-0.697088\pi$
$727$	−18.2212	+	4.88235i	−0.675785	+	0.181076i	−0.0954259	+	0.995437i	$0.530421\pi$
$728$	−1.88339	−	1.88339i	−0.0698032	−	0.0698032i
$729$	24.5927	+	11.1444i	0.910842	+	0.412754i
$730$	−27.8655	−	11.7952i	−1.03135	−	0.436562i
$731$	−32.2186	−	18.6014i	−1.19165	−	0.687999i
$732$	−10.7392	−	7.26089i	−0.396933	−	0.268370i
$733$	−29.1168	−	7.80181i	−1.07545	−	0.288167i	−0.322721	−	0.946494i	$-0.604598\pi$
$733$	−29.1168	−	7.80181i	−1.07545	−	0.288167i	−0.752732	+	0.658328i	$0.771264\pi$
$734$	−10.5147	−	18.2121i	−0.388106	−	0.672219i
$735$	0.202320	+	3.86770i	0.00746269	+	0.142662i
$736$	0.792270	−	1.37225i	0.0292034	−	0.0505818i
$737$	−11.8624	+	11.8624i	−0.436955	+	0.436955i
$738$	−14.3341	+	33.5637i	−0.527646	+	1.23550i
$739$			19.4818i			0.716651i	0.933597	+	0.358326i	$0.116652\pi$
$739$			19.4818i			0.716651i	−0.933597	+	0.358326i	$0.883348\pi$
$740$	−2.00404	−	0.279602i	−0.0736700	−	0.0102784i
$741$	10.5503	+	12.1637i	0.387575	+	0.446845i
$742$	0.504621	−	1.88327i	0.0185252	−	0.0691370i
$743$	5.82409	−	21.7358i	0.213665	−	0.797408i	−0.772967	−	0.634446i	$-0.781228\pi$
$743$	5.82409	−	21.7358i	0.213665	−	0.797408i	0.986632	−	0.162963i	$-0.0521050\pi$
$744$	−11.5577	−	13.3251i	−0.423725	−	0.488523i
$745$	9.25199	+	12.2522i	0.338967	+	0.448887i
$746$			5.47172i			0.200334i
$747$	21.4625	+	28.6124i	0.785273	+	1.04687i
$748$	6.23409	−	6.23409i	0.227941	−	0.227941i
$749$	−0.900079	+	1.55898i	−0.0328882	+	0.0569640i
$750$	19.3518	−	0.712735i	0.706628	−	0.0260254i
$751$	−21.1411	−	36.6174i	−0.771448	−	1.33619i	−0.936769	−	0.349948i	$-0.886199\pi$
$751$	−21.1411	−	36.6174i	−0.771448	−	1.33619i	0.165321	−	0.986240i	$-0.447134\pi$
$752$	7.27636	+	1.94969i	0.265341	+	0.0710980i
$753$	43.3584	+	29.3150i	1.58007	+	1.06830i
$754$	9.64268	+	5.56720i	0.351166	+	0.202746i
$755$	3.94056	−	9.30932i	0.143412	−	0.338801i
$756$	4.36717	−	2.81564i	0.158832	−	0.102404i
$757$	9.97956	+	9.97956i	0.362713	+	0.362713i	0.864811	−	0.502098i	$-0.167438\pi$
$757$	9.97956	+	9.97956i	0.362713	+	0.362713i	−0.502098	+	0.864811i	$0.667438\pi$
$758$	16.6151	−	4.45201i	0.603488	−	0.161704i
$759$	−1.50660	−	7.79653i	−0.0546860	−	0.282996i
$760$	4.79871	−	6.15477i	0.174068	−	0.223257i
$761$	21.8324	−	12.6049i	0.791423	−	0.456928i	−0.0490402	−	0.998797i	$-0.515616\pi$
$761$	21.8324	−	12.6049i	0.791423	−	0.456928i	0.840463	+	0.541868i	$0.182283\pi$
$762$	−4.54829	−	9.35145i	−0.164767	−	0.338767i
$763$	1.37717	+	5.13965i	0.0498567	+	0.186068i
$764$	6.30215			0.228004
$765$	19.6421	+	5.65773i	0.710161	+	0.204555i
$766$	−2.82996			−0.102250
$767$	−7.48128	−	27.9205i	−0.270133	−	1.00815i
$768$	1.72770	+	0.122721i	0.0623429	+	0.00442833i
$769$	31.5524	−	18.2168i	1.13781	−	0.656915i	0.191922	−	0.981410i	$-0.438528\pi$
$769$	31.5524	−	18.2168i	1.13781	−	0.656915i	0.945887	+	0.324495i	$0.105194\pi$
$770$	0.794893	+	6.42068i	0.0286460	+	0.231385i
$771$	4.58851	−	3.97988i	0.165251	−	0.143332i
$772$	9.17349	−	2.45803i	0.330161	−	0.0884664i
$773$	−13.2819	−	13.2819i	−0.477718	−	0.477718i	0.426683	−	0.904401i	$-0.359682\pi$
$773$	−13.2819	−	13.2819i	−0.477718	−	0.477718i	−0.904401	+	0.426683i	$0.859682\pi$
$774$	−28.8133	−	22.6136i	−1.03567	−	0.812830i
$775$	35.4452	+	36.5577i	1.27323	+	1.31319i
$776$	1.22765	+	0.708785i	0.0440701	+	0.0254439i
$777$	1.40949	−	0.685536i	0.0505651	−	0.0245935i
$778$	22.8433	+	6.12085i	0.818972	+	0.219443i
$779$	−21.2302	−	36.7718i	−0.760650	−	1.31748i
$780$	2.14575	−	10.0901i	0.0768302	−	0.361285i
$781$	0.0918724	−	0.159128i	0.00328745	−	0.00569404i
$782$	−3.41411	+	3.41411i	−0.122088	+	0.122088i
$783$	−14.5878	+	16.0943i	−0.521325	+	0.575163i
$784$		−	1.00000i		−	0.0357143i
$785$	−3.39294	+	24.3188i	−0.121099	+	0.867976i
$786$	−12.7116	+	2.45639i	−0.453409	+	0.0876166i
$787$	−2.05800	+	7.68056i	−0.0733597	+	0.273782i	−0.992856	−	0.119316i	$-0.961930\pi$
$787$	−2.05800	+	7.68056i	−0.0733597	+	0.273782i	0.919497	+	0.393098i	$0.128597\pi$
$788$	−1.23999	+	4.62772i	−0.0441730	+	0.164856i
$789$	−15.9762	+	46.2329i	−0.568766	+	1.64594i
$790$	3.69527	−	26.4858i	0.131472	−	0.942323i
$791$		−	1.64705i		−	0.0585623i
$792$	6.94363	−	5.20850i	0.246731	−	0.185076i
$793$	14.0962	−	14.0962i	0.500570	−	0.500570i
$794$	−12.5284	+	21.6998i	−0.444617	+	0.770099i
$795$	7.18182	−	2.33274i	0.254713	−	0.0827338i
$796$	7.92437	+	13.7254i	0.280872	+	0.486484i
$797$	19.7485	+	5.29158i	0.699526	+	0.187438i	0.591018	−	0.806658i	$-0.298726\pi$
$797$	19.7485	+	5.29158i	0.699526	+	0.187438i	0.108508	+	0.994096i	$0.465393\pi$
$798$	−0.428327	+	6.03008i	−0.0151626	+	0.213462i
$799$	−19.8788	−	11.4770i	−0.703261	−	0.406028i
$800$	−4.99940	−	0.0772410i	−0.176756	−	0.00273088i
$801$	11.9465	+	29.7568i	0.422108	+	1.05140i
$802$	9.34332	+	9.34332i	0.329924	+	0.329924i
$803$	37.8193	−	10.1337i	1.33461	−	0.357609i
$804$	9.49190	+	3.28000i	0.334754	+	0.115677i
$805$	−0.435324	−	3.51629i	−0.0153432	−	0.123933i
$806$	23.4911	−	13.5626i	0.827439	−	0.477722i
$807$	−3.25596	+	4.81572i	−0.114615	+	0.169522i
$808$	−3.85081	−	14.3714i	−0.135471	−	0.505584i
$809$	−19.1740			−0.674122			−0.337061	−	0.941483i	$-0.609433\pi$
$809$	−19.1740			−0.674122			−0.337061	+	0.941483i	$0.609433\pi$
$810$	18.3568	+	8.24780i	0.644994	+	0.289798i
$811$	24.2281			0.850764			0.425382	−	0.905014i	$-0.360140\pi$
$811$	24.2281			0.850764			0.425382	+	0.905014i	$0.360140\pi$
$812$	1.08195	+	4.03789i	0.0379690	+	0.141702i
$813$	3.13698	−	4.63974i	0.110019	−	0.162723i
$814$	2.26745	−	1.30911i	0.0794740	−	0.0458843i
$815$	9.97671	−	12.7960i	0.349469	−	0.448225i
$816$	−4.98833	−	1.72376i	−0.174626	−	0.0603435i
$817$	41.1611	−	11.0291i	1.44004	−	0.385858i
$818$	−2.71043	−	2.71043i	−0.0947681	−	0.0947681i
$819$	2.97702	+	7.41528i	0.104025	+	0.259111i
$820$	−10.6039	+	25.0509i	−0.370303	+	0.874817i
$821$	34.6590	+	20.0104i	1.20961	+	0.698367i	0.962673	−	0.270666i	$-0.0872438\pi$
$821$	34.6590	+	20.0104i	1.20961	+	0.698367i	0.246933	+	0.969033i	$0.420577\pi$
$822$	0.218045	−	3.06968i	0.00760518	−	0.107067i
$823$	−5.10866	−	1.36886i	−0.178077	−	0.0477155i	0.168679	−	0.985671i	$-0.446050\pi$
$823$	−5.10866	−	1.36886i	−0.178077	−	0.0477155i	−0.346755	+	0.937956i	$0.612717\pi$
$824$	−4.24094	−	7.34552i	−0.147740	−	0.255893i
$825$	−19.1802	+	16.1237i	−0.667769	+	0.561355i
$826$	5.42618	−	9.39841i	0.188801	−	0.327013i
$827$	−9.58257	+	9.58257i	−0.333218	+	0.333218i	−0.853807	−	0.520589i	$-0.825712\pi$
$827$	−9.58257	+	9.58257i	−0.333218	+	0.333218i	0.520589	+	0.853807i	$0.325712\pi$
$828$	−3.80269	+	2.85244i	−0.132153	+	0.0991293i
$829$		−	8.07858i		−	0.280581i	−0.990110	−	0.140290i	$-0.955196\pi$
$829$		−	8.07858i		−	0.280581i	0.990110	−	0.140290i	$-0.0448036\pi$
$830$	16.0654	+	21.2751i	0.557639	+	0.738471i
$831$	4.18405	−	12.1081i	0.145143	−	0.420026i
$832$	−0.689370	+	2.57276i	−0.0238996	+	0.0891945i
$833$	−0.788652	+	2.94329i	−0.0273252	+	0.101979i
$834$	21.2969	−	4.11540i	0.737451	−	0.142505i
$835$	−51.9883	−	7.25336i	−1.79913	−	0.251013i
$836$			10.0984i			0.349262i
$837$	16.1863	+	50.3811i	0.559480	+	1.74143i
$838$	5.39015	−	5.39015i	0.186200	−	0.186200i
$839$	10.0382	−	17.3867i	0.346558	−	0.600256i	−0.639077	−	0.769142i	$-0.720684\pi$
$839$	10.0382	−	17.3867i	0.346558	−	0.600256i	0.985636	+	0.168886i	$0.0540170\pi$
$840$	3.24836	−	2.10906i	0.112079	−	0.0727696i
$841$	5.76241	+	9.98078i	0.198704	+	0.344165i
$842$	−1.81720	−	0.486917i	−0.0626248	−	0.0167803i
$843$	4.03199	−	1.96105i	0.138869	−	0.0675421i
$844$	1.08643	+	0.627254i	0.0373966	+	0.0215910i
$845$	−12.1609	−	5.14760i	−0.418346	−	0.177083i
$846$	−17.7777	−	13.9525i	−0.611210	−	0.479698i
$847$	1.85871	+	1.85871i	0.0638660	+	0.0638660i
$848$	−1.88327	+	0.504621i	−0.0646718	+	0.0173287i
$849$	20.2817	−	17.5915i	0.696067	−	0.603739i
$850$	14.6538	+	4.17013i	0.502620	+	0.143034i
$851$	−1.24177	+	0.716937i	−0.0425674	+	0.0245763i
$852$	−0.109720	−	0.00779358i	−0.00375893	−	0.000267004i
$853$	9.01730	+	33.6530i	0.308746	+	1.15226i	0.929672	+	0.368388i	$0.120090\pi$
$853$	9.01730	+	33.6530i	0.308746	+	1.15226i	−0.620926	+	0.783869i	$0.713243\pi$
$854$	7.48446			0.256113
$855$	−20.4912	+	11.3264i	−0.700786	+	0.387356i
$856$	1.80016			0.0615282
$857$	−0.919357	−	3.43109i	−0.0314046	−	0.117204i	0.948444	−	0.316944i	$-0.102657\pi$
$857$	−0.919357	−	3.43109i	−0.0314046	−	0.117204i	−0.979849	+	0.199740i	$0.935990\pi$
$858$	5.83817	+	12.0035i	0.199312	+	0.409793i
$859$	12.9565	−	7.48045i	0.442071	−	0.255230i	−0.262405	−	0.964958i	$-0.584516\pi$
$859$	12.9565	−	7.48045i	0.442071	−	0.255230i	0.704476	+	0.709728i	$0.251182\pi$
$860$	−21.5300	−	16.7864i	−0.734167	−	0.572410i
$861$	−3.99783	−	20.6885i	−0.136246	−	0.705061i
$862$	−29.4361	+	7.88738i	−1.00260	+	0.268645i
$863$	−11.7835	−	11.7835i	−0.401114	−	0.401114i	0.477512	−	0.878625i	$-0.341539\pi$
$863$	−11.7835	−	11.7835i	−0.401114	−	0.401114i	−0.878625	+	0.477512i	$0.841539\pi$
$864$	−4.62200	−	2.37426i	−0.157244	−	0.0807740i
$865$	−11.5672	+	4.68696i	−0.393298	+	0.159362i
$866$	−22.2850	−	12.8662i	−0.757274	−	0.437212i
$867$	−11.0701	−	7.48462i	−0.375961	−	0.254191i
$868$	9.83695	+	2.63580i	0.333888	+	0.0894650i
$869$	17.3015	+	29.9670i	0.586913	+	1.01656i
$870$	−10.8346	+	12.0307i	−0.367329	+	0.407880i
$871$	−7.72170	+	13.3744i	−0.261640	+	0.453174i
$872$	3.76249	−	3.76249i	0.127414	−	0.127414i
$873$	−2.55187	−	3.40199i	−0.0863677	−	0.115140i
$874$		−	5.53042i		−	0.187069i
$875$	−9.02528	+	6.59881i	−0.305110	+	0.223080i
$876$	−15.3576	−	17.7062i	−0.518887	−	0.598238i
$877$	−14.7195	+	54.9338i	−0.497041	+	1.85498i	0.0212463	+	0.999774i	$0.493237\pi$
$877$	−14.7195	+	54.9338i	−0.497041	+	1.85498i	−0.518287	+	0.855207i	$0.673430\pi$
$878$	9.67060	−	36.0912i	0.326367	−	1.21802i
$879$	10.5502	+	12.1636i	0.355850	+	0.410269i
$880$	5.16302	−	3.89874i	0.174045	−	0.131426i
$881$		−	30.3578i		−	1.02278i	−0.859349	−	0.511390i	$-0.829131\pi$
$881$		−	30.3578i		−	1.02278i	0.859349	−	0.511390i	$-0.170869\pi$
$882$	−1.17826	+	2.75893i	−0.0396742	+	0.0928980i
$883$	−23.2297	+	23.2297i	−0.781741	+	0.781741i	−0.980124	−	0.198384i	$-0.936431\pi$
$883$	−23.2297	+	23.2297i	−0.781741	+	0.781741i	0.198384	+	0.980124i	$0.436431\pi$
$884$	4.05803	−	7.02871i	0.136486	−	0.236401i
$885$	41.9736	−	2.19565i	1.41093	−	0.0738059i
$886$	0.771339	+	1.33600i	0.0259136	+	0.0448837i
$887$	41.6259	+	11.1536i	1.39766	+	0.374502i	0.877504	−	0.479569i	$-0.159207\pi$
$887$	41.6259	+	11.1536i	1.39766	+	0.374502i	0.520156	+	0.854071i	$0.325874\pi$
$888$	−1.29844	−	0.877884i	−0.0435726	−	0.0294599i
$889$	5.19944	+	3.00190i	0.174383	+	0.100680i
$890$	8.97533	+	22.1508i	0.300854	+	0.742496i
$891$	−25.2940	+	6.18847i	−0.847380	+	0.207321i
$892$	19.9416	+	19.9416i	0.667695	+	0.667695i
$893$	25.3962	−	6.80490i	0.849852	−	0.227717i
$894$	2.25635	+	11.6764i	0.0754635	+	0.390518i
$895$	1.71951	−	0.212878i	0.0574768	−	0.00711574i
$896$	−0.866025	+	0.500000i	−0.0289319	+	0.0167038i
$897$	−3.19728	−	6.57374i	−0.106754	−	0.219491i
$898$	−0.771631	−	2.87977i	−0.0257497	−	0.0960990i
$899$	−42.5723			−1.41987
$900$	13.7020	+	6.10372i	0.456733	+	0.203457i
$901$	5.94098			0.197923
$902$	−9.11011	−	33.9994i	−0.303333	−	1.13206i
$903$	21.0938	+	1.49833i	0.701958	+	0.0498613i
$904$	−1.42639	+	0.823524i	−0.0474409	+	0.0273900i
$905$	35.3527	−	4.37674i	1.17516	−	0.145488i
$906$	5.91531	−	5.13069i	0.196523	−	0.170456i
$907$	4.89845	−	1.31253i	0.162650	−	0.0435820i	−0.176575	−	0.984287i	$-0.556502\pi$
$907$	4.89845	−	1.31253i	0.162650	−	0.0435820i	0.339225	+	0.940705i	$0.389835\pi$
$908$	5.68544	+	5.68544i	0.188678	+	0.188678i
$909$	−6.30919	+	44.1870i	−0.209263	+	1.46559i
$910$	2.23662	+	5.51989i	0.0741432	+	0.182983i
$911$	19.1430	+	11.0522i	0.634236	+	0.366177i	0.782391	−	0.622788i	$-0.214000\pi$
$911$	19.1430	+	11.0522i	0.634236	+	0.366177i	−0.148155	+	0.988964i	$0.547333\pi$
$912$	5.43637	−	2.64410i	0.180016	−	0.0875548i
$913$	−33.3203	−	8.92816i	−1.10274	−	0.295479i
$914$	19.6895	+	34.1032i	0.651270	+	1.12803i
$915$	15.7852	+	24.3122i	0.521842	+	0.803738i
$916$	−11.2928	+	19.5597i	−0.373125	+	0.646272i
$917$	5.28551	−	5.28551i	0.174543	−	0.174543i
$918$	11.7314	+	10.6333i	0.387194	+	0.350951i
$919$			26.2807i			0.866921i	0.901173	+	0.433461i	$0.142708\pi$
$919$			26.2807i			0.866921i	−0.901173	+	0.433461i	$0.857292\pi$
$920$	−2.82754	+	2.13515i	−0.0932211	+	0.0703938i
$921$	−32.0398	+	6.19136i	−1.05575	+	0.204012i
$922$	−7.84927	+	29.2939i	−0.258502	+	0.964742i
$923$	0.0437793	−	0.163387i	0.00144101	−	0.00537793i
$924$	−1.63676	+	4.73658i	−0.0538455	+	0.155822i
$925$	3.88298	+	2.32255i	0.127672	+	0.0763650i
$926$			31.7476i			1.04329i
$927$	3.04550	+	25.2627i	0.100027	+	0.829737i
$928$	2.95594	−	2.95594i	0.0970336	−	0.0970336i
$929$	12.7254	−	22.0410i	0.417506	−	0.723142i	−0.578182	−	0.815908i	$-0.696238\pi$
$929$	12.7254	−	22.0410i	0.417506	−	0.723142i	0.995688	+	0.0927661i	$0.0295709\pi$
$930$	12.1847	+	37.5130i	0.399552	+	1.23010i
$931$	−1.74512	−	3.02264i	−0.0571940	−	0.0990629i
$932$	−23.7010	−	6.35066i	−0.776351	−	0.208023i
$933$	1.95906	−	27.5801i	0.0641368	−	0.902931i
$934$	−6.39891	−	3.69441i	−0.209379	−	0.120885i
$935$	−18.2710	+	7.40328i	−0.597526	+	0.242113i
$936$	4.93331	−	6.28581i	0.161250	−	0.205458i
$937$	−6.90263	−	6.90263i	−0.225499	−	0.225499i	0.585310	−	0.810809i	$-0.300973\pi$
$937$	−6.90263	−	6.90263i	−0.225499	−	0.225499i	−0.810809	+	0.585310i	$0.800973\pi$
$938$	−5.60055	+	1.50066i	−0.182865	+	0.0489984i
$939$	20.2467	+	6.99640i	0.660725	+	0.228319i
$940$	−13.2839	−	10.3571i	−0.433274	−	0.337812i
$941$	18.9245	−	10.9261i	0.616921	−	0.356180i	−0.158748	−	0.987319i	$-0.550746\pi$
$941$	18.9245	−	10.9261i	0.616921	−	0.356180i	0.775669	+	0.631140i	$0.217412\pi$
$942$	−10.6530	+	15.7564i	−0.347095	+	0.513371i
$943$	4.98916	+	18.6198i	0.162470	+	0.606344i
$944$	−10.8524			−0.353214
$945$	−11.4470	+	1.99133i	−0.372372	+	0.0647779i
$946$	35.3253			1.14853
$947$	−15.2855	−	57.0464i	−0.496714	−	1.85376i	−0.520213	−	0.854037i	$-0.674147\pi$
$947$	−15.2855	−	57.0464i	−0.496714	−	1.85376i	0.0234992	−	0.999724i	$-0.492519\pi$
$948$	11.6023	−	17.1604i	0.376825	−	0.557343i
$949$	31.2146	−	18.0217i	1.01327	−	0.585011i
$950$	−15.2462	+	8.49109i	−0.494651	+	0.275487i
$951$	−34.3966	−	11.8860i	−1.11539	−	0.385430i
$952$	2.94329	−	0.788652i	0.0953925	−	0.0255604i
$953$	24.9451	+	24.9451i	0.808051	+	0.808051i	0.984339	−	0.176288i	$-0.0564090\pi$
$953$	24.9451	+	24.9451i	0.808051	+	0.808051i	−0.176288	+	0.984339i	$0.556409\pi$
$954$	5.79039	+	0.826774i	0.187471	+	0.0267678i
$955$	−12.9773	−	5.49319i	−0.419935	−	0.177755i
$956$	6.94307	+	4.00858i	0.224555	+	0.129647i
$957$	1.48433	−	20.8967i	0.0479815	−	0.675494i
$958$	24.7380	+	6.62853i	0.799249	+	0.214158i
$959$	0.888372	+	1.53871i	0.0286870	+	0.0496874i
$960$	−3.45068	−	1.75863i	−0.111370	−	0.0567596i
$961$	−36.3565	+	62.9713i	−1.17279	+	2.03133i
$962$	1.70431	−	1.70431i	0.0549492	−	0.0549492i
$963$	−4.96651	−	2.12106i	−0.160044	−	0.0683502i
$964$		−	19.6820i		−	0.633916i
$965$	−21.0324	−	2.93442i	−0.677058	−	0.0944624i
$966$	0.896375	−	2.59399i	0.0288404	−	0.0834604i
$967$	−0.901566	+	3.36469i	−0.0289924	+	0.108201i	−0.978906	−	0.204312i	$-0.934504\pi$
$967$	−0.901566	+	3.36469i	−0.0289924	+	0.108201i	0.949913	+	0.312513i	$0.101171\pi$
$968$	0.680335	−	2.53904i	0.0218668	−	0.0816079i
$969$	−18.0861	+	3.49494i	−0.581008	+	0.112274i
$970$	−1.91016	−	2.52959i	−0.0613315	−	0.0812202i
$971$		−	22.8993i		−	0.734873i	−0.930049	−	0.367437i	$-0.880235\pi$
$971$		−	22.8993i		−	0.734873i	0.930049	−	0.367437i	$-0.119765\pi$
$972$	9.95427	+	11.9964i	0.319283	+	0.384783i
$973$	−8.85526	+	8.85526i	−0.283887	+	0.283887i
$974$	2.96467	−	5.13496i	0.0949941	−	0.164535i
$975$	−13.2134	+	18.9072i	−0.423169	+	0.605513i
$976$	−3.74223	−	6.48173i	−0.119786	−	0.207475i
$977$	8.96125	+	2.40116i	0.286696	+	0.0768199i	0.399301	−	0.916820i	$-0.369253\pi$
$977$	8.96125	+	2.40116i	0.286696	+	0.0768199i	−0.112605	+	0.993640i	$0.535920\pi$
$978$	11.3024	−	5.49718i	0.361412	−	0.175781i
$979$	−26.7821	−	15.4626i	−0.855958	−	0.494188i
$980$	−0.871638	+	2.05919i	−0.0278435	+	0.0657783i
$981$	−14.8136	+	5.94724i	−0.472963	+	0.189881i
$982$	3.36715	+	3.36715i	0.107450	+	0.107450i
$983$	18.9443	−	5.07610i	0.604228	−	0.161902i	0.0562802	−	0.998415i	$-0.482076\pi$
$983$	18.9443	−	5.07610i	0.604228	−	0.161902i	0.547948	+	0.836513i	$0.315409\pi$
$984$	−15.9178	+	13.8065i	−0.507442	+	0.440134i
$985$	6.58708	−	8.44851i	0.209882	−	0.269192i
$986$	−11.0314	+	6.36898i	−0.351311	+	0.202830i
$987$	13.0148	+	0.924465i	0.414266	+	0.0294261i
$988$	2.40607	+	8.97956i	0.0765471	+	0.285678i
$989$	−19.3460			−0.615166
$990$	−18.8382	+	4.67294i	−0.598716	+	0.148516i
$991$	38.7636			1.23137			0.615683	−	0.787994i	$-0.288880\pi$
$991$	38.7636			1.23137			0.615683	+	0.787994i	$0.288880\pi$
$992$	−2.63580	−	9.83695i	−0.0836868	−	0.312323i
$993$	−25.3819	−	52.1861i	−0.805470	−	1.65608i
$994$	0.0549980	−	0.0317531i	0.00174443	−	0.00100715i
$995$	−4.35416	−	35.1704i	−0.138036	−	1.11498i
$996$	3.91798	+	20.2753i	0.124146	+	0.642447i
$997$	32.8355	−	8.79825i	1.03991	−	0.278643i	0.301835	−	0.953360i	$-0.402401\pi$
$997$	32.8355	−	8.79825i	1.03991	−	0.278643i	0.738077	+	0.674717i	$0.235734\pi$
$998$	6.72264	+	6.72264i	0.212801	+	0.212801i
$999$	2.54791	+	3.95192i	0.0806124	+	0.125033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.ca.b.407.4	yes	72
5.3	odd	4		630.2.ca.a.533.2	✓	72
9.5	odd	6		630.2.ca.a.617.2	yes	72
45.23	even	12	inner	630.2.ca.b.113.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ca.a.533.2	✓	72	5.3	odd	4
630.2.ca.a.617.2	yes	72	9.5	odd	6
630.2.ca.b.113.4	yes	72	45.23	even	12	inner
630.2.ca.b.407.4	yes	72	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.ca (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.970129 + 1.43487i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.21913 - 0.274732i) q^{5} +(1.63707 + 0.565701i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.11770 - 2.78402i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.970129 + 1.43487i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.21913 - 0.274732i) q^{5} +(1.63707 + 0.565701i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.11770 - 2.78402i) q^{9} +(-0.839723 - 2.07241i) q^{10} +(2.50570 + 1.44667i) q^{11} +(0.122721 - 1.72770i) q^{12} +(2.57276 + 0.689370i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-1.75863 + 3.45068i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.15464 + 2.15464i) q^{17} +(-2.39987 + 1.80017i) q^{18} -3.49024i q^{19} +(-1.78445 + 1.34749i) q^{20} +(0.565701 - 1.63707i) q^{21} +(0.748850 - 2.79475i) q^{22} +(-0.410109 + 1.53055i) q^{23} +(-1.70059 + 0.328621i) q^{24} +(4.84904 - 1.21933i) q^{25} -2.66352i q^{26} +(5.07901 + 1.09710i) q^{27} +(0.707107 - 0.707107i) q^{28} +(-2.09017 + 3.62028i) q^{29} +(3.78827 + 0.805607i) q^{30} +(5.09198 + 8.81957i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-4.50663 + 2.19190i) q^{33} +(2.63888 + 1.52356i) q^{34} +(-2.07241 + 0.839723i) q^{35} +(2.35997 + 1.85218i) q^{36} +(0.639872 + 0.639872i) q^{37} +(-3.37131 + 0.903340i) q^{38} +(-3.48507 + 3.02280i) q^{39} +(1.76342 + 1.37489i) q^{40} +(10.5356 - 6.08273i) q^{41} +(-1.72770 - 0.122721i) q^{42} +(3.15998 + 11.7932i) q^{43} -2.89334 q^{44} +(-3.24518 - 5.87102i) q^{45} +1.58454 q^{46} +(1.94969 + 7.27636i) q^{47} +(0.757569 + 1.55759i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-2.43281 - 4.36823i) q^{50} +(-1.00135 - 5.18190i) q^{51} +(-2.57276 + 0.689370i) q^{52} +(-1.37865 - 1.37865i) q^{53} +(-0.254828 - 5.18990i) q^{54} +(5.95792 + 2.52194i) q^{55} +(-0.866025 - 0.500000i) q^{56} +(5.00804 + 3.38598i) q^{57} +(4.03789 + 1.08195i) q^{58} +(-5.42618 - 9.39841i) q^{59} +(-0.202320 - 3.86770i) q^{60} +(3.74223 - 6.48173i) q^{61} +(7.20115 - 7.20115i) q^{62} +(1.80017 + 2.39987i) q^{63} +1.00000i q^{64} +(5.89868 + 0.822977i) q^{65} +(3.28362 + 3.78577i) q^{66} +(-1.50066 + 5.60055i) q^{67} +(0.788652 - 2.94329i) q^{68} +(-1.79828 - 2.07328i) q^{69} +(1.34749 + 1.78445i) q^{70} -0.0635062i q^{71} +(1.17826 - 2.75893i) q^{72} +(9.56877 - 9.56877i) q^{73} +(0.452458 - 0.783680i) q^{74} +(-2.95462 + 8.14065i) q^{75} +(1.74512 + 3.02264i) q^{76} +(-2.79475 - 0.748850i) q^{77} +(3.82180 + 2.58396i) q^{78} +(10.3573 + 5.97977i) q^{79} +(0.871638 - 2.05919i) q^{80} +(-6.50149 + 6.22339i) q^{81} +(-8.60228 - 8.60228i) q^{82} +(-11.5162 + 3.08577i) q^{83} +(0.328621 + 1.70059i) q^{84} +(-4.18946 + 5.37336i) q^{85} +(10.5735 - 6.10460i) q^{86} +(-3.16689 - 6.51125i) q^{87} +(0.748850 + 2.79475i) q^{88} -10.6884 q^{89} +(-4.83105 + 4.65413i) q^{90} -2.66352 q^{91} +(-0.410109 - 1.53055i) q^{92} +(-17.5948 - 1.24979i) q^{93} +(6.52380 - 3.76652i) q^{94} +(-0.958882 - 7.74528i) q^{95} +(1.30844 - 1.13489i) q^{96} +(1.36927 - 0.366894i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(1.22692 - 8.59286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{3}+O(q^{10}) \) 72 * q - 4 * q^3	\( 72 q - 4 q^{3} + 12 q^{11} + 4 q^{12} + 36 q^{14} - 20 q^{15} + 36 q^{16} + 24 q^{17} + 12 q^{20} + 4 q^{21} - 8 q^{24} + 12 q^{25} + 32 q^{27} + 32 q^{30} + 44 q^{33} - 12 q^{34} - 4 q^{36} + 24 q^{37} - 36 q^{38} + 40 q^{39} - 48 q^{41} + 4 q^{42} + 48 q^{43} - 68 q^{45} - 48 q^{47} - 8 q^{48} + 16 q^{51} + 4 q^{54} + 24 q^{55} - 84 q^{57} - 48 q^{58} + 4 q^{60} - 8 q^{63} + 24 q^{65} + 8 q^{66} + 12 q^{67} + 12 q^{68} - 64 q^{69} + 16 q^{72} + 84 q^{75} + 24 q^{78} - 72 q^{79} + 48 q^{82} - 60 q^{83} + 24 q^{85} + 72 q^{86} + 4 q^{87} - 48 q^{90} - 24 q^{91} - 64 q^{93} + 132 q^{94} - 60 q^{95} + 36 q^{97} + 40 q^{99}+O(q^{100}) \) 72 * q - 4 * q^3 + 12 * q^11 + 4 * q^12 + 36 * q^14 - 20 * q^15 + 36 * q^16 + 24 * q^17 + 12 * q^20 + 4 * q^21 - 8 * q^24 + 12 * q^25 + 32 * q^27 + 32 * q^30 + 44 * q^33 - 12 * q^34 - 4 * q^36 + 24 * q^37 - 36 * q^38 + 40 * q^39 - 48 * q^41 + 4 * q^42 + 48 * q^43 - 68 * q^45 - 48 * q^47 - 8 * q^48 + 16 * q^51 + 4 * q^54 + 24 * q^55 - 84 * q^57 - 48 * q^58 + 4 * q^60 - 8 * q^63 + 24 * q^65 + 8 * q^66 + 12 * q^67 + 12 * q^68 - 64 * q^69 + 16 * q^72 + 84 * q^75 + 24 * q^78 - 72 * q^79 + 48 * q^82 - 60 * q^83 + 24 * q^85 + 72 * q^86 + 4 * q^87 - 48 * q^90 - 24 * q^91 - 64 * q^93 + 132 * q^94 - 60 * q^95 + 36 * q^97 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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