LMFDB - Embedded newform 630.2.ca.a.533.2

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			533.2
Character	$\chi$	$=$	630.533
Dual form			630.2.ca.a.617.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-1.43487 - 0.970129i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.34749 - 1.78445i) q^{5} +(1.63707 + 0.565701i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.11770 + 2.78402i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.43487 - 0.970129i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.34749 - 1.78445i) q^{5} +(1.63707 + 0.565701i) q^{6} +(0.258819 + 0.965926i) 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} +(-1.72770 - 0.122721i) q^{12} +(-0.689370 + 2.57276i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-3.66462 + 1.25322i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.15464 + 2.15464i) q^{17} +(-1.80017 - 2.39987i) q^{18} +3.49024i q^{19} +(0.274732 - 2.21913i) q^{20} +(0.565701 - 1.63707i) q^{21} +(-2.79475 - 0.748850i) q^{22} +(-1.53055 - 0.410109i) q^{23} +(1.70059 - 0.328621i) q^{24} +(-1.36855 - 4.80906i) q^{25} -2.66352i q^{26} +(1.09710 - 5.07901i) q^{27} +(0.707107 + 0.707107i) q^{28} +(2.09017 - 3.62028i) q^{29} +(3.21539 - 2.15899i) q^{30} +(5.09198 + 8.81957i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-2.19190 - 4.50663i) 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} +(-0.903340 - 3.37131i) q^{38} +(3.48507 - 3.02280i) q^{39} +(0.308981 + 2.21462i) q^{40} +(10.5356 - 6.08273i) q^{41} +(-0.122721 + 1.72770i) q^{42} +(-11.7932 + 3.15998i) q^{43} +2.89334 q^{44} +(6.47404 + 1.75694i) q^{45} +1.58454 q^{46} +(7.27636 - 1.94969i) q^{47} +(-1.55759 + 0.757569i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(2.56659 + 4.29099i) q^{50} +(-1.00135 - 5.18190i) q^{51} +(0.689370 + 2.57276i) 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} +(3.38598 - 5.00804i) q^{57} +(-1.08195 + 4.03789i) q^{58} +(5.42618 + 9.39841i) q^{59} +(-2.54704 + 2.91763i) q^{60} +(3.74223 - 6.48173i) q^{61} +(-7.20115 - 7.20115i) q^{62} +(-2.39987 + 1.80017i) q^{63} -1.00000i q^{64} +(3.66206 + 4.69692i) q^{65} +(3.28362 + 3.78577i) q^{66} +(5.60055 + 1.50066i) q^{67} +(2.94329 + 0.788652i) q^{68} +(1.79828 + 2.07328i) q^{69} +(-2.21913 - 0.274732i) q^{70} -0.0635062i q^{71} +(-2.75893 - 1.17826i) q^{72} +(9.56877 + 9.56877i) q^{73} +(-0.452458 + 0.783680i) q^{74} +(-2.70172 + 8.22804i) q^{75} +(1.74512 + 3.02264i) q^{76} +(-0.748850 + 2.79475i) q^{77} +(-2.58396 + 3.82180i) 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} +(-3.08577 - 11.5162i) q^{83} +(-0.328621 - 1.70059i) q^{84} +(6.74820 - 0.941501i) q^{85} +(10.5735 - 6.10460i) q^{86} +(-6.51125 + 3.16689i) q^{87} +(-2.79475 + 0.748850i) q^{88} +10.6884 q^{89} +(-6.70817 - 0.0214746i) q^{90} -2.66352 q^{91} +(-1.53055 + 0.410109i) q^{92} +(1.24979 - 17.5948i) q^{93} +(-6.52380 + 3.76652i) q^{94} +(6.22817 + 4.70306i) q^{95} +(1.30844 - 1.13489i) q^{96} +(-0.366894 - 1.36927i) 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} + 12 q^{15} + 36 q^{16} - 24 q^{17} + 8 q^{18} + 12 q^{20} + 4 q^{21} + 24 q^{23} + 8 q^{24} + 12 q^{25} - 16 q^{27} - 32 q^{30} - 36 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} - 12 q^{45} - 48 q^{47} - 8 q^{48} + 16 q^{51} - 4 q^{54} + 24 q^{55} + 52 q^{57} + 48 q^{58} - 4 q^{60} + 8 q^{66} + 12 q^{67} - 12 q^{68} + 64 q^{69} - 116 q^{75} + 8 q^{78} + 72 q^{79} + 48 q^{82} - 60 q^{83} + 24 q^{85} + 72 q^{86} - 44 q^{87} + 8 q^{90} - 24 q^{91} + 24 q^{92} + 32 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 + 12 * q^15 + 36 * q^16 - 24 * q^17 + 8 * q^18 + 12 * q^20 + 4 * q^21 + 24 * q^23 + 8 * q^24 + 12 * q^25 - 16 * q^27 - 32 * q^30 - 36 * 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 - 12 * q^45 - 48 * q^47 - 8 * q^48 + 16 * q^51 - 4 * q^54 + 24 * q^55 + 52 * q^57 + 48 * q^58 - 4 * q^60 + 8 * q^66 + 12 * q^67 - 12 * q^68 + 64 * q^69 - 116 * q^75 + 8 * q^78 + 72 * q^79 + 48 * q^82 - 60 * q^83 + 24 * q^85 + 72 * q^86 - 44 * q^87 + 8 * q^90 - 24 * q^91 + 24 * q^92 + 32 * 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−1.43487	−	0.970129i	−0.828422	−	0.560104i
$3$	−1.43487	−	0.970129i	−0.828422	−	0.560104i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.34749	−	1.78445i	0.602615	−	0.798032i
$5$	1.34749	−	1.78445i	0.602615	−	0.798032i
$6$	1.63707	+	0.565701i	0.668329	+	0.230946i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$8$	−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	$0.522995\pi$
$12$	−1.72770	−	0.122721i	−0.498743	−	0.0354266i
$13$	−0.689370	+	2.57276i	−0.191197	+	0.713556i	0.802022	+	0.597295i	$0.203758\pi$
$13$	−0.689370	+	2.57276i	−0.191197	+	0.713556i	−0.993219	+	0.116261i	$0.962909\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$	−3.66462	+	1.25322i	−0.946201	+	0.323580i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.15464	+	2.15464i	0.522576	+	0.522576i	0.918349	−	0.395772i	$-0.129523\pi$
$17$	2.15464	+	2.15464i	0.522576	+	0.522576i	−0.395772	+	0.918349i	$0.629523\pi$
$18$	−1.80017	−	2.39987i	−0.424305	−	0.565655i
$19$			3.49024i			0.800716i	0.916359	+	0.400358i	$0.131114\pi$
$19$			3.49024i			0.800716i	−0.916359	+	0.400358i	$0.868886\pi$
$20$	0.274732	−	2.21913i	0.0614320	−	0.496212i
$21$	0.565701	−	1.63707i	0.123446	−	0.357237i
$22$	−2.79475	−	0.748850i	−0.595842	−	0.159655i
$23$	−1.53055	−	0.410109i	−0.319141	−	0.0855136i	0.0956923	−	0.995411i	$-0.469494\pi$
$23$	−1.53055	−	0.410109i	−0.319141	−	0.0855136i	−0.414833	+	0.909897i	$0.636160\pi$
$24$	1.70059	−	0.328621i	0.347132	−	0.0670795i
$25$	−1.36855	−	4.80906i	−0.273710	−	0.961812i
$26$		−	2.66352i		−	0.522359i
$27$	1.09710	−	5.07901i	0.211137	−	0.977456i
$28$	0.707107	+	0.707107i	0.133631	+	0.133631i
$29$	2.09017	−	3.62028i	0.388134	−	0.672268i	−0.604064	−	0.796936i	$-0.706453\pi$
$29$	2.09017	−	3.62028i	0.388134	−	0.672268i	0.992199	+	0.124667i	$0.0397864\pi$
$30$	3.21539	−	2.15899i	0.587048	−	0.394176i
$31$	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	$0.465881\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−2.19190	−	4.50663i	−0.381561	−	0.784504i
$34$	−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	−0.652551	−	0.757745i	$-0.726301\pi$
$37$	0.639872	−	0.639872i	0.105194	−	0.105194i	0.757745	+	0.652551i	$0.226301\pi$
$38$	−0.903340	−	3.37131i	−0.146541	−	0.546899i
$39$	3.48507	−	3.02280i	0.558057	−	0.484036i
$40$	0.308981	+	2.21462i	0.0488542	+	0.350162i
$41$	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	$-0.0655461\pi$
$42$	−0.122721	+	1.72770i	−0.0189363	+	0.266590i
$43$	−11.7932	+	3.15998i	−1.79844	+	0.481892i	−0.993734	−	0.111775i	$-0.964346\pi$
$43$	−11.7932	+	3.15998i	−1.79844	+	0.481892i	−0.804711	+	0.593667i	$0.797680\pi$
$44$	2.89334			0.436187
$45$	6.47404	+	1.75694i	0.965092	+	0.261910i
$46$	1.58454			0.233628
$47$	7.27636	−	1.94969i	1.06137	−	0.284392i	0.314425	−	0.949282i	$-0.398188\pi$
$47$	7.27636	−	1.94969i	1.06137	−	0.284392i	0.746941	+	0.664890i	$0.231522\pi$
$48$	−1.55759	+	0.757569i	−0.224819	+	0.109346i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	2.56659	+	4.29099i	0.362971	+	0.606838i
$51$	−1.00135	−	5.18190i	−0.140217	−	0.725611i
$52$	0.689370	+	2.57276i	0.0955984	+	0.356778i
$53$	1.37865	−	1.37865i	0.189372	−	0.189372i	−0.606053	−	0.795425i	$-0.707248\pi$
$53$	1.37865	−	1.37865i	0.189372	−	0.189372i	0.795425	+	0.606053i	$0.207248\pi$
$54$	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
$57$	3.38598	−	5.00804i	0.448484	−	0.663331i
$58$	−1.08195	+	4.03789i	−0.142067	+	0.530201i
$59$	5.42618	+	9.39841i	0.706428	+	1.22357i	0.966174	+	0.257892i	$0.0830279\pi$
$59$	5.42618	+	9.39841i	0.706428	+	1.22357i	−0.259746	+	0.965677i	$0.583639\pi$
$60$	−2.54704	+	2.91763i	−0.328822	+	0.376665i
$61$	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
$63$	−2.39987	+	1.80017i	−0.302355	+	0.226800i
$64$		−	1.00000i		−	0.125000i
$65$	3.66206	+	4.69692i	0.454222	+	0.582581i
$66$	3.28362	+	3.78577i	0.404185	+	0.465996i
$67$	5.60055	+	1.50066i	0.684217	+	0.183335i	0.584150	−	0.811646i	$-0.301428\pi$
$67$	5.60055	+	1.50066i	0.684217	+	0.183335i	0.100066	+	0.994981i	$0.468095\pi$
$68$	2.94329	+	0.788652i	0.356926	+	0.0956381i
$69$	1.79828	+	2.07328i	0.216487	+	0.249594i
$70$	−2.21913	−	0.274732i	−0.265236	−	0.0328368i
$71$		−	0.0635062i		−	0.00753680i	−0.999993	−	0.00376840i	$-0.998800\pi$
$71$		−	0.0635062i		−	0.00753680i	0.999993	−	0.00376840i	$-0.00119952\pi$
$72$	−2.75893	−	1.17826i	−0.325143	−	0.138860i
$73$	9.56877	+	9.56877i	1.11994	+	1.11994i	0.991750	+	0.128190i	$0.0409166\pi$
$73$	9.56877	+	9.56877i	1.11994	+	1.11994i	0.128190	+	0.991750i	$0.459083\pi$
$74$	−0.452458	+	0.783680i	−0.0525971	+	0.0911009i
$75$	−2.70172	+	8.22804i	−0.311968	+	0.950093i
$76$	1.74512	+	3.02264i	0.200179	+	0.346720i
$77$	−0.748850	+	2.79475i	−0.0853394	+	0.318491i
$78$	−2.58396	+	3.82180i	−0.292576	+	0.432734i
$79$	−10.3573	−	5.97977i	−1.16528	−	0.672777i	−0.212719	−	0.977113i	$-0.568232\pi$
$79$	−10.3573	−	5.97977i	−1.16528	−	0.672777i	−0.952565	+	0.304337i	$0.901565\pi$
$80$	−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
$83$	−3.08577	−	11.5162i	−0.338707	−	1.26407i	−0.899794	−	0.436315i	$-0.856283\pi$
$83$	−3.08577	−	11.5162i	−0.338707	−	1.26407i	0.561087	−	0.827757i	$-0.310383\pi$
$84$	−0.328621	−	1.70059i	−0.0358555	−	0.185550i
$85$	6.74820	−	0.941501i	0.731945	−	0.102120i
$86$	10.5735	−	6.10460i	1.14017	−	0.658276i
$87$	−6.51125	+	3.16689i	−0.698079	+	0.339526i
$88$	−2.79475	+	0.748850i	−0.297921	+	0.0798277i
$89$	10.6884			1.13297			0.566486	−	0.824071i	$-0.308302\pi$
$89$	10.6884			1.13297			0.566486	+	0.824071i	$0.308302\pi$
$90$	−6.70817	−	0.0214746i	−0.707103	−	0.00226362i
$91$	−2.66352			−0.279213
$92$	−1.53055	+	0.410109i	−0.159571	+	0.0427568i
$93$	1.24979	−	17.5948i	0.129597	−	1.82450i
$94$	−6.52380	+	3.76652i	−0.672879	+	0.388487i
$95$	6.22817	+	4.70306i	0.638997	+	0.482524i
$96$	1.30844	−	1.13489i	0.133543	−	0.115829i
$97$	−0.366894	−	1.36927i	−0.0372525	−	0.139028i	0.944795	−	0.327662i	$-0.106261\pi$
$97$	−0.366894	−	1.36927i	−0.0372525	−	0.139028i	−0.982047	+	0.188634i	$0.939594\pi$
$98$	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	$0.931948\pi$
$102$	2.30840	+	4.74616i	0.228566	+	0.469940i
$103$	2.19527	−	8.19286i	0.216307	−	0.807267i	−0.769396	−	0.638772i	$-0.779443\pi$
$103$	2.19527	−	8.19286i	0.216307	−	0.807267i	0.985703	−	0.168495i	$-0.0538907\pi$
$104$	−1.33176	−	2.30668i	−0.130590	−	0.226188i
$105$	−2.15899	−	3.21539i	−0.210696	−	0.313790i
$106$	−0.974852	+	1.68849i	−0.0946860	+	0.164001i
$107$	−1.27290	−	1.27290i	−0.123056	−	0.123056i	0.642897	−	0.765953i	$-0.277732\pi$
$107$	−1.27290	−	1.27290i	−0.123056	−	0.123056i	−0.765953	+	0.642897i	$0.777732\pi$
$108$	−1.58939	−	4.94710i	−0.152939	−	0.476035i
$109$			5.32096i			0.509655i	0.966986	+	0.254828i	$0.0820187\pi$
$109$			5.32096i			0.509655i	−0.966986	+	0.254828i	$0.917981\pi$
$110$	−5.10218	+	3.97803i	−0.486474	+	0.379290i
$111$	−1.53889	+	0.297374i	−0.146065	+	0.0282255i
$112$	0.965926	+	0.258819i	0.0912714	+	0.0244561i
$113$	−1.59093	−	0.426287i	−0.149662	−	0.0401017i	0.183210	−	0.983074i	$-0.441351\pi$
$113$	−1.59093	−	0.426287i	−0.149662	−	0.0401017i	−0.332872	+	0.942972i	$0.608018\pi$
$114$	−1.97443	+	5.71375i	−0.184922	+	0.535142i
$115$	−2.79422	+	2.17857i	−0.260562	+	0.203153i
$116$		−	4.18033i		−	0.388134i
$117$	−7.93312	+	0.956362i	−0.733417	+	0.0884157i
$118$	−7.67377	−	7.67377i	−0.706428	−	0.706428i
$119$	−1.52356	+	2.63888i	−0.139664	+	0.241906i
$120$	1.70512	−	3.47744i	0.155655	−	0.317445i
$121$	−1.31431	−	2.27644i	−0.119482	−	0.206949i
$122$	−1.93712	+	7.22943i	−0.175379	+	0.654522i
$123$	−21.0182	−	1.49296i	−1.89515	−	0.134616i
$124$	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	−0.869914	−	0.493203i	$-0.835826\pi$
$127$	−4.24532	+	4.24532i	−0.376711	+	0.376711i	0.493203	+	0.869914i	$0.335826\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	19.9873	+	6.90676i	1.75978	+	0.608106i
$130$	−4.75293	−	3.58906i	−0.416859	−	0.314782i
$131$	−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	$0.439216\pi$
$132$	−4.15156	−	2.80691i	−0.361347	−	0.244310i
$133$	−3.37131	+	0.903340i	−0.292330	+	0.0783296i
$134$	−5.79812			−0.500881
$135$	−7.58493	−	8.80164i	−0.652807	−	0.757524i
$136$	−3.04712			−0.261288
$137$	−1.71620	+	0.459855i	−0.146625	+	0.0392881i	−0.331385	−	0.943496i	$-0.607516\pi$
$137$	−1.71620	+	0.459855i	−0.146625	+	0.0392881i	0.184760	+	0.982784i	$0.440849\pi$
$138$	−2.27361	−	1.53721i	−0.193542	−	0.130856i
$139$	−10.8454	+	6.26162i	−0.919898	+	0.531103i	−0.883602	−	0.468238i	$-0.844889\pi$
$139$	−10.8454	+	6.26162i	−0.919898	+	0.531103i	−0.0362954	+	0.999341i	$0.511556\pi$
$140$	2.21462	−	0.308981i	0.187169	−	0.0261137i
$141$	−12.3321	−	4.26145i	−1.03855	−	0.358878i
$142$	0.0164366	+	0.0613423i	0.00137933	+	0.00514773i
$143$	−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
$147$	1.72770	+	0.122721i	0.142498	+	0.0101219i
$148$	0.234209	−	0.874081i	0.0192519	−	0.0718490i
$149$	−3.43305	−	5.94622i	−0.281246	−	0.487133i	0.690446	−	0.723384i	$-0.257415\pi$
$149$	−3.43305	−	5.94622i	−0.281246	−	0.487133i	−0.971692	+	0.236251i	$0.924081\pi$
$150$	0.480085	−	8.64694i	0.0391988	−	0.706019i
$151$	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
$153$	−3.59030	+	8.40678i	−0.290259	+	0.679648i
$154$		−	2.89334i		−	0.233152i
$155$	22.5995	+	2.79786i	1.81524	+	0.224730i
$156$	1.50676	−	4.36036i	0.120637	−	0.349108i
$157$	10.6069	+	2.84211i	0.846521	+	0.226825i	0.655908	−	0.754841i	$-0.272286\pi$
$157$	10.6069	+	2.84211i	0.846521	+	0.226825i	0.190613	+	0.981665i	$0.438952\pi$
$158$	11.5520	+	3.09536i	0.919030	+	0.246253i
$159$	−3.31565	+	0.640714i	−0.262948	+	0.0508120i
$160$	1.37489	+	1.76342i	0.108695	+	0.139411i
$161$		−	1.58454i		−	0.124879i
$162$	4.66923	−	7.69404i	0.366849	−	0.604501i
$163$	5.13101	+	5.13101i	0.401892	+	0.401892i	0.878899	−	0.477007i	$-0.158279\pi$
$163$	5.13101	+	5.13101i	0.401892	+	0.401892i	−0.477007	+	0.878899i	$0.658279\pi$
$164$	6.08273	−	10.5356i	0.474981	−	0.822692i
$165$	−10.9954	−	2.16129i	−0.855994	−	0.168256i
$166$	5.96124	+	10.3252i	0.462682	+	0.801389i
$167$	−6.07580	+	22.6752i	−0.470159	+	1.75466i	0.169032	+	0.985611i	$0.445936\pi$
$167$	−6.07580	+	22.6752i	−0.470159	+	1.75466i	−0.639191	+	0.769048i	$0.720731\pi$
$168$	0.757569	+	1.55759i	0.0584477	+	0.120171i
$169$	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
$173$	−1.44461	−	5.39137i	−0.109832	−	0.409898i	0.889017	−	0.457875i	$-0.151389\pi$
$173$	−1.44461	−	5.39137i	−0.109832	−	0.409898i	−0.998848	+	0.0479768i	$0.984723\pi$
$174$	5.46973	−	4.74422i	0.414659	−	0.359658i
$175$	4.29099	−	2.56659i	0.324368	−	0.194016i
$176$	2.50570	−	1.44667i	0.188874	−	0.109047i
$177$	1.33182	−	18.7496i	0.100105	−	1.40930i
$178$	−10.3242	+	2.76637i	−0.773835	+	0.207348i
$179$	−0.774857			−0.0579156			−0.0289578	−	0.999581i	$-0.509219\pi$
$179$	−0.774857			−0.0579156			−0.0289578	+	0.999581i	$0.509219\pi$
$180$	6.48515	−	1.71546i	0.483375	−	0.127863i
$181$	15.9309			1.18414			0.592068	−	0.805888i	$-0.298312\pi$
$181$	15.9309			1.18414			0.592068	+	0.805888i	$0.298312\pi$
$182$	2.57276	−	0.689370i	0.190706	−	0.0510995i
$183$	−11.6577	+	5.66999i	−0.861764	+	0.419138i
$184$	1.37225	−	0.792270i	0.101164	−	0.0584069i
$185$	−0.279602	−	2.00404i	−0.0205567	−	0.147340i
$186$	3.34667	+	17.3187i	0.245389	+	1.26987i
$187$	2.28183	+	8.51592i	0.166864	+	0.622746i
$188$	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	$0.739886\pi$
$192$	−0.970129	+	1.43487i	−0.0700130	+	0.103553i
$193$	2.45803	−	9.17349i	0.176933	−	0.660322i	−0.819282	−	0.573391i	$-0.805627\pi$
$193$	2.45803	−	9.17349i	0.176933	−	0.660322i	0.996214	−	0.0869308i	$-0.0277059\pi$
$194$	0.708785	+	1.22765i	0.0508878	+	0.0881403i
$195$	−0.697962	−	10.2921i	−0.0499821	−	0.737035i
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	−3.38773	−	3.38773i	−0.241366	−	0.241366i	0.576049	−	0.817415i	$-0.304594\pi$
$197$	−3.38773	−	3.38773i	−0.241366	−	0.241366i	−0.817415	+	0.576049i	$0.804594\pi$
$198$	−1.03888	−	8.61761i	−0.0738299	−	0.612427i
$199$			15.8487i			1.12349i	0.827311	+	0.561744i	$0.189869\pi$
$199$			15.8487i			1.12349i	−0.827311	+	0.561744i	$0.810131\pi$
$200$	4.36823	+	2.43281i	0.308881	+	0.172026i
$201$	−6.58023	−	7.58651i	−0.464133	−	0.535111i
$202$	14.3714	+	3.85081i	1.01117	+	0.270942i
$203$	4.03789	+	1.08195i	0.283404	+	0.0759380i
$204$	−3.45814	−	3.98698i	−0.242118	−	0.279145i
$205$	3.34225	−	26.9967i	0.233433	−	1.88553i
$206$			8.48188i			0.590960i
$207$	−0.568944	−	4.71945i	−0.0395443	−	0.328024i
$208$	1.88339	+	1.88339i	0.130590	+	0.130590i
$209$	−5.04922	+	8.74550i	−0.349262	+	0.604939i
$210$	2.91763	+	2.54704i	0.201336	+	0.175763i
$211$	−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	$0.847083\pi$
$212$	0.504621	−	1.88327i	0.0346575	−	0.129344i
$213$	−0.0616092	+	0.0911232i	−0.00422140	+	0.00624366i
$214$	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
$218$	−1.37717	−	5.13965i	−0.0932734	−	0.348101i
$219$	−4.44699	−	23.0129i	−0.300500	−	1.55507i
$220$	3.89874	−	5.16302i	0.262853	−	0.348091i
$221$	−7.02871	+	4.05803i	−0.472802	+	0.272973i
$222$	1.40949	−	0.685536i	0.0945986	−	0.0460101i
$223$	27.2408	−	7.29914i	1.82418	−	0.488787i	0.826888	−	0.562366i	$-0.190109\pi$
$223$	27.2408	−	7.29914i	1.82418	−	0.488787i	0.997289	+	0.0735796i	$0.0234423\pi$
$224$	−1.00000			−0.0668153
$225$	11.8589	−	9.18515i	0.790592	−	0.612344i
$226$	1.64705			0.109560
$227$	−7.76645	+	2.08101i	−0.515477	+	0.138122i	−0.507174	−	0.861844i	$-0.669310\pi$
$227$	−7.76645	+	2.08101i	−0.515477	+	0.138122i	−0.00830356	+	0.999966i	$0.502643\pi$
$228$	0.428327	−	6.03008i	0.0283667	−	0.399352i
$229$	−19.5597	+	11.2928i	−1.29254	+	0.746250i	−0.979104	−	0.203358i	$-0.934815\pi$
$229$	−19.5597	+	11.2928i	−1.29254	+	0.746250i	−0.313439	+	0.949608i	$0.601481\pi$
$230$	2.13515	−	2.82754i	0.140788	−	0.186442i
$231$	3.78577	−	3.28362i	0.249085	−	0.216046i
$232$	1.08195	+	4.03789i	0.0710335	+	0.265101i
$233$	−17.3503	+	17.3503i	−1.13666	+	1.13666i	−0.147612	+	0.989045i	$0.547159\pi$
$233$	−17.3503	+	17.3503i	−1.13666	+	1.13666i	−0.989045	+	0.147612i	$0.952841\pi$
$234$	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
$237$	9.06018	+	18.6281i	0.588522	+	1.21002i
$238$	0.788652	−	2.94329i	0.0511207	−	0.190785i
$239$	4.00858	+	6.94307i	0.259294	+	0.449110i	0.966053	−	0.258344i	$-0.0831769\pi$
$239$	4.00858	+	6.94307i	0.259294	+	0.449110i	−0.706759	+	0.707454i	$0.749844\pi$
$240$	−0.746989	+	3.80026i	−0.0482179	+	0.245306i
$241$	−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
$243$	15.3663	−	2.62247i	0.985747	−	0.168232i
$244$		−	7.48446i		−	0.479143i
$245$	−0.274732	+	2.21913i	−0.0175520	+	0.141775i
$246$	20.6885	−	3.99783i	1.31905	−	0.254892i
$247$	−8.97956	−	2.40607i	−0.571356	−	0.153094i
$248$	−9.83695	−	2.63580i	−0.624647	−	0.167374i
$249$	−6.74456	+	19.5179i	−0.427419	+	1.23690i
$250$	11.1155	+	1.20209i	0.703008	+	0.0760269i
$251$		−	30.2177i		−	1.90732i	−0.300884	−	0.953661i	$-0.597282\pi$
$251$		−	30.2177i		−	1.90732i	0.300884	−	0.953661i	$-0.402718\pi$
$252$	−1.17826	+	2.75893i	−0.0742236	+	0.173796i
$253$	−3.24180	−	3.24180i	−0.203810	−	0.203810i
$254$	3.00190	−	5.19944i	0.188356	−	0.326242i
$255$	−10.5962	−	5.19569i	−0.663557	−	0.325367i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.907639	+	3.38735i	−0.0566170	+	0.211297i	−0.988439	−	0.151618i	$-0.951552\pi$
$257$	−0.907639	+	3.38735i	−0.0566170	+	0.211297i	0.931822	+	0.362915i	$0.118218\pi$
$258$	−21.0938	−	1.49833i	−1.31324	−	0.0932820i
$259$	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
$263$	7.30940	+	27.2790i	0.450717	+	1.68210i	0.700384	+	0.713766i	$0.253012\pi$
$263$	7.30940	+	27.2790i	0.450717	+	1.68210i	−0.249667	+	0.968332i	$0.580321\pi$
$264$	4.73658	+	1.63676i	0.291516	+	0.100736i
$265$	−0.602422	−	4.31785i	−0.0370065	−	0.265243i
$266$	3.02264	−	1.74512i	0.185330	−	0.107000i
$267$	−15.3365	−	10.3692i	−0.938580	−	0.634583i
$268$	5.60055	−	1.50066i	0.342108	−	0.0916676i
$269$	−3.35621			−0.204632			−0.102316	−	0.994752i	$-0.532625\pi$
$269$	−3.35621			−0.204632			−0.102316	+	0.994752i	$0.532625\pi$
$270$	9.60451	+	6.53860i	0.584512	+	0.397927i
$271$	−3.23357			−0.196425			−0.0982126	−	0.995165i	$-0.531313\pi$
$271$	−3.23357			−0.196425			−0.0982126	+	0.995165i	$0.531313\pi$
$272$	2.94329	−	0.788652i	0.178463	−	0.0478190i
$273$	3.82180	+	2.58396i	0.231306	+	0.156388i
$274$	1.53871	−	0.888372i	0.0929566	−	0.0536685i
$275$	3.52794	−	14.0299i	0.212743	−	0.846035i
$276$	2.59399	+	0.896375i	0.156140	+	0.0539554i
$277$	1.91428	+	7.14421i	0.115018	+	0.429254i	0.999288	−	0.0377221i	$-0.0120102\pi$
$277$	1.91428	+	7.14421i	0.115018	+	0.429254i	−0.884270	+	0.466976i	$0.845343\pi$
$278$	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	$0.691268\pi$
$282$	13.0148	+	0.924465i	0.775021	+	0.0550511i
$283$	4.01186	−	14.9725i	0.238480	−	0.890021i	−0.738069	−	0.674726i	$-0.764262\pi$
$283$	4.01186	−	14.9725i	0.238480	−	0.890021i	0.976549	−	0.215295i	$-0.0690713\pi$
$284$	−0.0317531	−	0.0549980i	−0.00188420	−	0.00326353i
$285$	−4.37404	−	12.7904i	−0.259096	−	0.757638i
$286$	3.85323	−	6.67399i	0.227846	−	0.394641i
$287$	8.60228	+	8.60228i	0.507776	+	0.507776i
$288$	−2.97844	+	0.359059i	−0.175506	+	0.0211578i
$289$		−	7.71508i		−	0.453828i
$290$	5.74752	+	7.37170i	0.337506	+	0.432881i
$291$	−0.801921	+	2.32065i	−0.0470094	+	0.136039i
$292$	13.0712	+	3.50241i	0.764933	+	0.204963i
$293$	8.97949	+	2.40605i	0.524587	+	0.140563i	0.511388	−	0.859350i	$-0.329132\pi$
$293$	8.97949	+	2.40605i	0.524587	+	0.140563i	0.0131997	+	0.999913i	$0.495798\pi$
$294$	−1.70059	+	0.328621i	−0.0991805	+	0.0191656i
$295$	24.0827	+	2.98149i	1.40215	+	0.173589i
$296$			0.904915i			0.0525971i
$297$	10.0966	−	11.1394i	0.585867	−	0.646371i
$298$	4.85507	+	4.85507i	0.281246	+	0.281246i
$299$	2.11023	−	3.65502i	0.122038	−	0.211375i
$300$	1.77427	+	8.47655i	0.102437	+	0.489394i
$301$	−6.10460	−	10.5735i	−0.351863	−	0.609445i
$302$	−1.17009	+	4.36683i	−0.0673310	+	0.251283i
$303$	11.2714	+	23.1744i	0.647525	+	1.33134i
$304$	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	−0.216046	−	0.976383i	$-0.569316\pi$
$307$	13.3222	−	13.3222i	0.760337	−	0.760337i	0.976383	+	0.216046i	$0.0693161\pi$
$308$	0.748850	+	2.79475i	0.0426697	+	0.159246i
$309$	−11.0981	+	9.62599i	−0.631347	+	0.547604i
$310$	−22.5536	+	3.14665i	−1.28096	+	0.178718i
$311$	−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	$0.482838\pi$
$312$	−0.326871	+	4.60176i	−0.0185054	+	0.260523i
$313$	11.9462	−	3.20099i	0.675242	−	0.180930i	0.0951269	−	0.995465i	$-0.469674\pi$
$313$	11.9462	−	3.20099i	0.675242	−	0.180930i	0.580115	+	0.814535i	$0.303008\pi$
$314$	−10.9811			−0.619697
$315$	−0.0214746	+	6.70817i	−0.00120996	+	0.377963i
$316$	−11.9595			−0.672777
$317$	20.2952	−	5.43808i	1.13989	−	0.305433i	0.360984	−	0.932572i	$-0.382441\pi$
$317$	20.2952	−	5.43808i	1.13989	−	0.305433i	0.778907	+	0.627139i	$0.215774\pi$
$318$	3.03684	−	1.47704i	0.170298	−	0.0828281i
$319$	10.4747	−	6.04755i	0.586469	−	0.338598i
$320$	−1.78445	−	1.34749i	−0.0997540	−	0.0753269i
$321$	0.591570	+	3.06133i	0.0330182	+	0.170867i
$322$	0.410109	+	1.53055i	0.0228545	+	0.0852941i
$323$	−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
$327$	5.16201	−	7.63488i	0.285460	−	0.422210i
$328$	−3.14865	+	11.7509i	−0.173855	+	0.648837i
$329$	3.76652	+	6.52380i	0.207655	+	0.359669i
$330$	11.1802	−	0.758184i	0.615448	−	0.0417366i
$331$	−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
$333$	2.49660	+	1.06623i	0.136813	+	0.0584290i
$334$		−	23.4751i		−	1.28450i
$335$	10.2245	−	7.97180i	0.558627	−	0.435546i
$336$	−1.13489	−	1.30844i	−0.0619133	−	0.0713815i
$337$	−18.5645	−	4.97434i	−1.01127	−	0.270970i	−0.285111	−	0.958494i	$-0.592031\pi$
$337$	−18.5645	−	4.97434i	−1.01127	−	0.270970i	−0.726161	+	0.687525i	$0.758697\pi$
$338$	−5.70443	−	1.52850i	−0.310280	−	0.0831393i
$339$	1.86922	+	2.15507i	0.101522	+	0.117047i
$340$	5.37336	−	4.18946i	0.291411	−	0.227206i
$341$			29.4656i			1.59565i
$342$	8.37612	−	6.28303i	0.452929	−	0.339747i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	6.10460	−	10.5735i	0.329138	−	0.570084i
$345$	6.12283	−	0.415220i	0.329642	−	0.0223547i
$346$	2.79078	+	4.83377i	0.150033	+	0.259865i
$347$	−2.04738	+	7.64092i	−0.109909	+	0.410186i	−0.998856	−	0.0478247i	$-0.984771\pi$
$347$	−2.04738	+	7.64092i	−0.109909	+	0.410186i	0.888947	+	0.458010i	$0.151438\pi$
$348$	−4.05546	+	5.99823i	−0.217396	+	0.321539i
$349$	−23.3704	−	13.4929i	−1.25099	−	0.722258i	−0.279682	−	0.960093i	$-0.590229\pi$
$349$	−23.3704	−	13.4929i	−1.25099	−	0.722258i	−0.971306	+	0.237834i	$0.923562\pi$
$350$	−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
$353$	−3.67953	−	13.7322i	−0.195842	−	0.730891i	−0.992047	−	0.125865i	$-0.959829\pi$
$353$	−3.67953	−	13.7322i	−0.195842	−	0.730891i	0.796206	−	0.605026i	$-0.206837\pi$
$354$	3.56631	+	18.4554i	0.189547	+	0.980894i
$355$	−0.113324	−	0.0855739i	−0.00601461	−	0.00454179i
$356$	9.25646	−	5.34422i	0.490592	−	0.283243i
$357$	4.74616	−	2.30840i	0.251193	−	0.122174i
$358$	0.748455	−	0.200548i	0.0395571	−	0.0105993i
$359$	5.35082			0.282405			0.141203	−	0.989981i	$-0.454903\pi$
$359$	5.35082			0.282405			0.141203	+	0.989981i	$0.454903\pi$
$360$	−5.82018	+	3.33549i	−0.306751	+	0.175796i
$361$	6.81823			0.358854
$362$	−15.3881	+	4.12323i	−0.808780	+	0.216712i
$363$	−0.322587	+	4.54144i	−0.0169314	+	0.238364i
$364$	−2.30668	+	1.33176i	−0.120903	+	0.0698032i
$365$	29.9688	−	4.18122i	1.56864	−	0.218855i
$366$	9.79299	−	8.49403i	0.511888	−	0.443990i
$367$	−5.44283	−	20.3129i	−0.284113	−	1.06033i	−0.949485	−	0.313813i	$-0.898393\pi$
$367$	−5.44283	−	20.3129i	−0.284113	−	1.06033i	0.665371	−	0.746512i	$-0.268273\pi$
$368$	−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
$372$	−7.71505	−	15.8624i	−0.400007	−	0.822429i
$373$	1.41618	−	5.28527i	0.0733273	−	0.273661i	−0.919522	−	0.393040i	$-0.871424\pi$
$373$	1.41618	−	5.28527i	0.0733273	−	0.273661i	0.992849	+	0.119379i	$0.0380902\pi$
$374$	−4.40816	−	7.63517i	−0.227941	−	0.394805i
$375$	11.0420	+	15.9083i	0.570208	+	0.821500i
$376$	−3.76652	+	6.52380i	−0.194243	+	0.336439i
$377$	7.87321	+	7.87321i	0.405491	+	0.405491i
$378$	−4.94710	+	1.58939i	−0.254452	+	0.0817494i
$379$		−	17.2012i		−	0.883568i	−0.897121	−	0.441784i	$-0.854346\pi$
$379$		−	17.2012i		−	0.883568i	0.897121	−	0.441784i	$-0.145654\pi$
$380$	7.74528	+	0.958882i	0.397325	+	0.0491896i
$381$	10.2100	−	1.97297i	0.523074	−	0.101078i
$382$	6.08741	+	1.63112i	0.311459	+	0.0834551i
$383$	2.73353	+	0.732446i	0.139677	+	0.0374263i	0.327980	−	0.944685i	$-0.393632\pi$
$383$	2.73353	+	0.732446i	0.139677	+	0.0374263i	−0.188303	+	0.982111i	$0.560299\pi$
$384$	0.565701	−	1.63707i	0.0288683	−	0.0835411i
$385$	3.97803	+	5.10218i	0.202739	+	0.260031i
$386$			9.49710i			0.483389i
$387$	−21.9787	−	29.3005i	−1.11724	−	1.48943i
$388$	−1.00237	−	1.00237i	−0.0508878	−	0.0508878i
$389$	11.8246	−	20.4808i	0.599529	−	1.03842i	−0.393361	−	0.919384i	$-0.628688\pi$
$389$	11.8246	−	20.4808i	0.599529	−	1.03842i	0.992890	−	0.119031i	$-0.0379789\pi$
$390$	3.33798	+	9.76079i	0.169025	+	0.494257i
$391$	−2.41414	−	4.18141i	−0.122088	−	0.211463i
$392$	0.258819	−	0.965926i	0.0130723	−	0.0487866i
$393$	12.9143	+	0.917324i	0.651439	+	0.0462729i
$394$	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	−0.994449	−	0.105216i	$-0.966447\pi$
$397$	−17.7179	+	17.7179i	−0.889234	+	0.889234i	0.105216	+	0.994449i	$0.466447\pi$
$398$	−4.10196	−	15.3087i	−0.205612	−	0.767356i
$399$	5.71375	+	1.97443i	0.286045	+	0.0988452i
$400$	−4.84904	−	1.21933i	−0.242452	−	0.0609666i
$401$	−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	$0.440357\pi$
$402$	8.31954	+	5.62492i	0.414941	+	0.280546i
$403$	−26.2009	+	7.02051i	−1.30516	+	0.349717i
$404$	−14.8784			−0.740227
$405$	2.34467	+	19.9876i	0.116508	+	0.993190i
$406$	−4.18033			−0.207466
$407$	2.52901	−	0.677646i	0.125358	−	0.0335897i
$408$	4.37221	+	2.95610i	0.216457	+	0.146349i
$409$	−3.31959	+	1.91657i	−0.164143	+	0.0947681i	−0.579821	−	0.814744i	$-0.696878\pi$
$409$	−3.31959	+	1.91657i	−0.164143	+	0.0947681i	0.415678	+	0.909512i	$0.363544\pi$
$410$	3.75890	+	26.9418i	0.185639	+	1.33056i
$411$	2.90865	+	1.00511i	0.143473	+	0.0495782i
$412$	−2.19527	−	8.19286i	−0.108153	−	0.403633i
$413$	−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
$417$	21.6364	+	1.53687i	1.05954	+	0.0752608i
$418$	2.61367	−	9.75434i	0.127839	−	0.477100i
$419$	−3.81141	−	6.60155i	−0.186200	−	0.322507i	0.757781	−	0.652509i	$-0.226284\pi$
$419$	−3.81141	−	6.60155i	−0.186200	−	0.322507i	−0.943980	+	0.330002i	$0.892950\pi$
$420$	−3.47744	−	1.70512i	−0.169682	−	0.0832012i
$421$	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
$423$	13.5608	+	18.0783i	0.659347	+	0.878998i
$424$			1.94970i			0.0946860i
$425$	7.41305	−	13.3105i	0.359586	−	0.645654i
$426$	0.0359255	−	0.103964i	0.00174060	−	0.00503707i
$427$	7.22943	+	1.93712i	0.349857	+	0.0937438i
$428$	−1.73882	−	0.465915i	−0.0840490	−	0.0225209i
$429$	13.1055	−	2.53251i	0.632741	−	0.122271i
$430$	3.35426	−	27.0938i	0.161757	−	1.30658i
$431$		−	30.4745i		−	1.46790i	−0.679201	−	0.733952i	$-0.737673\pi$
$431$		−	30.4745i		−	1.46790i	0.679201	−	0.733952i	$-0.262327\pi$
$432$	−3.85000	−	3.48962i	−0.185233	−	0.167895i
$433$	18.1956	+	18.1956i	0.874424	+	0.874424i	0.992951	−	0.118527i	$-0.0378171\pi$
$433$	18.1956	+	18.1956i	0.874424	+	0.874424i	−0.118527	+	0.992951i	$0.537817\pi$
$434$	5.09198	−	8.81957i	0.244423	−	0.423353i
$435$	−3.12266	+	15.8864i	−0.149720	+	0.761693i
$436$	2.66048	+	4.60808i	0.127414	+	0.220687i
$437$	1.43138	−	5.34198i	0.0684721	−	0.255541i
$438$	10.2516	+	21.0778i	0.489842	+	1.00713i
$439$	−32.3585	−	18.6822i	−1.54438	−	0.891651i	−0.998554	−	0.0537553i	$-0.982881\pi$
$439$	−32.3585	−	18.6822i	−1.54438	−	0.891651i	−0.545831	−	0.837896i	$-0.683786\pi$
$440$	−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
$443$	−0.399274	−	1.49011i	−0.0189701	−	0.0707973i	0.955792	−	0.294044i	$-0.0950012\pi$
$443$	−0.399274	−	1.49011i	−0.0189701	−	0.0707973i	−0.974762	+	0.223247i	$0.928335\pi$
$444$	−1.18403	+	1.02698i	−0.0561916	+	0.0487383i
$445$	14.4026	−	19.0730i	0.682747	−	0.904148i
$446$	−24.4234	+	14.1009i	−1.15648	+	0.667695i
$447$	−0.842618	+	11.8625i	−0.0398545	+	0.561079i
$448$	0.965926	−	0.258819i	0.0456357	−	0.0122281i
$449$	−2.98135			−0.140699			−0.0703494	−	0.997522i	$-0.522411\pi$
$449$	−2.98135			−0.140699			−0.0703494	+	0.997522i	$0.522411\pi$
$450$	−9.07750	+	11.9415i	−0.427918	+	0.562927i
$451$	35.1988			1.65744
$452$	−1.59093	+	0.426287i	−0.0748309	+	0.0200509i
$453$	−7.04167	+	3.42487i	−0.330846	+	0.160915i
$454$	6.96321	−	4.02021i	0.326800	−	0.188678i
$455$	−3.58906	+	4.75293i	−0.168258	+	0.222821i
$456$	1.14697	+	5.93547i	0.0537116	+	0.277954i
$457$	10.1920	+	38.0371i	0.476762	+	1.77930i	0.614591	+	0.788846i	$0.289321\pi$
$457$	10.1920	+	38.0371i	0.476762	+	1.77930i	−0.137829	+	0.990456i	$0.544012\pi$
$458$	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	$0.916277\pi$
$462$	−2.80691	+	4.15156i	−0.130589	+	0.193148i
$463$	8.21688	−	30.6658i	0.381871	−	1.42516i	−0.461170	−	0.887312i	$-0.652570\pi$
$463$	8.21688	−	30.6658i	0.381871	−	1.42516i	0.843041	−	0.537850i	$-0.180763\pi$
$464$	−2.09017	−	3.62028i	−0.0970336	−	0.168067i
$465$	−29.7130	−	25.9390i	−1.37791	−	1.20289i
$466$	12.2685	−	21.2497i	0.568329	−	0.984374i
$467$	−5.22469	−	5.22469i	−0.241770	−	0.241770i	0.575812	−	0.817582i	$-0.304686\pi$
$467$	−5.22469	−	5.22469i	−0.241770	−	0.241770i	−0.817582	+	0.575812i	$0.804686\pi$
$468$	−6.39210	+	4.79479i	−0.295475	+	0.221639i
$469$			5.79812i			0.267732i
$470$	−2.06957	+	16.7168i	−0.0954621	+	0.771087i
$471$	−12.4623	−	14.3681i	−0.574232	−	0.662047i
$472$	−10.4826	−	2.80880i	−0.482499	−	0.129285i
$473$	−34.1216	−	9.14287i	−1.56892	−	0.420390i
$474$	−13.5728	−	15.6484i	−0.623417	−	0.718754i
$475$	16.7848	−	4.77657i	0.770138	−	0.219164i
$476$			3.04712i			0.139664i
$477$	5.37910	+	2.29727i	0.246292	+	0.105185i
$478$	−5.66899	−	5.66899i	−0.259294	−	0.259294i
$479$	12.8053	−	22.1795i	0.585091	−	1.01341i	−0.409773	−	0.912187i	$-0.634392\pi$
$479$	12.8053	−	22.1795i	0.585091	−	1.01341i	0.994864	−	0.101220i	$-0.0322746\pi$
$480$	−0.262045	−	3.86411i	−0.0119607	−	0.176372i
$481$	1.20513	+	2.08735i	0.0549492	+	0.0951748i
$482$	5.09409	−	19.0114i	0.232029	−	0.865945i
$483$	−1.53721	+	2.27361i	−0.0699453	+	0.103453i
$484$	−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	−0.605703	−	0.795691i	$-0.707108\pi$
$487$	4.19267	−	4.19267i	0.189988	−	0.189988i	0.795691	+	0.605703i	$0.207108\pi$
$488$	1.93712	+	7.22943i	0.0876893	+	0.327261i
$489$	−2.38459	−	12.3401i	−0.107835	−	0.558037i
$490$	−0.308981	−	2.21462i	−0.0139583	−	0.100046i
$491$	−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	$0.367602\pi$
$492$	−18.9488	+	9.21617i	−0.854278	+	0.415497i
$493$	12.3039	−	3.29683i	0.554141	−	0.148482i
$494$	9.29632			0.418261
$495$	13.6803	+	13.7682i	0.614883	+	0.618833i
$496$	10.1840			0.457273
$497$	0.0613423	−	0.0164366i	0.00275158	−	0.000737283i
$498$	1.46315	−	20.5985i	0.0655651	−	0.923039i
$499$	8.23352	−	4.75362i	0.368583	−	0.212801i	−0.304256	−	0.952590i	$-0.598408\pi$
$499$	8.23352	−	4.75362i	0.368583	−	0.212801i	0.672839	+	0.739789i	$0.265075\pi$
$500$	−11.0479	+	1.71578i	−0.494077	+	0.0767320i
$501$	30.7158	−	26.6416i	1.37228	−	1.19026i
$502$	7.82091	+	29.1880i	0.349064	+	1.30272i
$503$	−11.4348	+	11.4348i	−0.509851	+	0.509851i	−0.914481	−	0.404630i	$-0.867400\pi$
$503$	−11.4348	+	11.4348i	−0.509851	+	0.509851i	0.404630	+	0.914481i	$0.367400\pi$
$504$	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
$507$	−4.47394	−	9.19860i	−0.198695	−	0.408524i
$508$	−1.55390	+	5.79922i	−0.0689430	+	0.257299i
$509$	−20.6275	−	35.7279i	−0.914297	−	1.58361i	−0.807927	−	0.589283i	$-0.799410\pi$
$509$	−20.6275	−	35.7279i	−0.914297	−	1.58361i	−0.106371	−	0.994327i	$-0.533923\pi$
$510$	11.5798	+	2.27616i	0.512764	+	0.100790i
$511$	−6.76614	+	11.7193i	−0.299316	+	0.518431i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	17.7270	+	3.82914i	0.782665	+	0.169061i
$514$		−	3.50685i		−	0.154680i
$515$	−11.6617	−	14.9571i	−0.513875	−	0.659091i
$516$	20.7629	−	4.01220i	0.914034	−	0.176627i
$517$	21.0529	+	5.64112i	0.925907	+	0.248096i
$518$	−0.874081	−	0.234209i	−0.0384049	−	0.0102906i
$519$	−3.15749	+	9.13737i	−0.138598	+	0.401086i
$520$	−5.91069	−	0.731755i	−0.259201	−	0.0320896i
$521$			31.4346i			1.37717i	0.725154	+	0.688587i	$0.241768\pi$
$521$			31.4346i			1.37717i	−0.725154	+	0.688587i	$0.758232\pi$
$522$	−12.4509	+	1.50099i	−0.544959	+	0.0656964i
$523$	−16.1228	−	16.1228i	−0.705001	−	0.705001i	0.260478	−	0.965480i	$-0.416120\pi$
$523$	−16.1228	−	16.1228i	−0.705001	−	0.705001i	−0.965480	+	0.260478i	$0.916120\pi$
$524$	−3.73742	+	6.47340i	−0.163270	+	0.282792i
$525$	−8.64694	−	0.480085i	−0.377383	−	0.0209526i
$526$	−14.1207	−	24.4577i	−0.615691	−	1.06641i
$527$	−8.03160	+	29.9743i	−0.349862	+	1.30570i
$528$	−4.99881	−	0.355074i	−0.217545	−	0.0154526i
$529$	−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
$533$	8.38650	+	31.2988i	0.363260	+	1.35570i
$534$	17.4977	+	6.04646i	0.757199	+	0.261656i
$535$	−3.98666	+	0.556215i	−0.172358	+	0.0240473i
$536$	−5.02132	+	2.89906i	−0.216888	+	0.125220i
$537$	1.11182	+	0.751711i	0.0479785	+	0.0324387i
$538$	3.24185	−	0.868651i	0.139766	−	0.0374502i
$539$	−2.89334			−0.124625
$540$	−10.9696	−	3.82997i	−0.472055	−	0.164816i
$541$	−3.96847			−0.170618			−0.0853089	−	0.996355i	$-0.527188\pi$
$541$	−3.96847			−0.170618			−0.0853089	+	0.996355i	$0.527188\pi$
$542$	3.12338	−	0.836908i	0.134161	−	0.0359483i
$543$	−22.8588	−	15.4550i	−0.980965	−	0.663240i
$544$	−2.63888	+	1.52356i	−0.113141	+	0.0653220i
$545$	9.49500	+	7.16993i	0.406721	+	0.307126i
$546$	−4.36036	−	1.50676i	−0.186606	−	0.0644832i
$547$	−8.40078	−	31.3521i	−0.359191	−	1.34052i	−0.875127	−	0.483893i	$-0.839222\pi$
$547$	−8.40078	−	31.3521i	−0.359191	−	1.34052i	0.515936	−	0.856627i	$-0.327444\pi$
$548$	−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
$552$	−2.73760	−	0.194457i	−0.116520	−	0.00827664i
$553$	3.09536	−	11.5520i	0.131628	−	0.491242i
$554$	−3.69811	−	6.40532i	−0.157118	−	0.272136i
$555$	−1.54299	+	3.14679i	−0.0654961	+	0.133574i
$556$	−6.26162	+	10.8454i	−0.265552	+	0.459949i
$557$	−24.0046	−	24.0046i	−1.01711	−	1.01711i	−0.999851	−	0.0172581i	$-0.994506\pi$
$557$	−24.0046	−	24.0046i	−1.01711	−	1.01711i	−0.0172581	−	0.999851i	$-0.505494\pi$
$558$	11.9994	−	28.0968i	0.507974	−	1.18943i
$559$		−	32.5195i		−	1.37543i
$560$	1.76342	−	1.37489i	0.0745183	−	0.0580999i
$561$	4.98741	−	14.4329i	0.210568	−	0.609358i
$562$	2.50040	+	0.669981i	0.105473	+	0.0282614i
$563$	34.9680	+	9.36965i	1.47373	+	0.394884i	0.904207	−	0.427095i	$-0.140463\pi$
$563$	34.9680	+	9.36965i	1.47373	+	0.394884i	0.569519	+	0.821978i	$0.307130\pi$
$564$	−12.8106	+	2.47552i	−0.539424	+	0.104238i
$565$	−2.90444	+	2.26452i	−0.122191	+	0.0952689i
$566$			15.5006i			0.651540i
$567$	−7.69404	−	4.66923i	−0.323120	−	0.196089i
$568$	0.0449057	+	0.0449057i	0.00188420	+	0.00188420i
$569$	3.03886	−	5.26347i	0.127396	−	0.220656i	−0.795271	−	0.606254i	$-0.792671\pi$
$569$	3.03886	−	5.26347i	0.127396	−	0.220656i	0.922667	+	0.385598i	$0.126005\pi$
$570$	7.53540	+	11.2225i	0.315623	+	0.470059i
$571$	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	$0.760245\pi$
$572$	−1.99458	+	7.44387i	−0.0833975	+	0.311244i
$573$	4.77431	+	9.81617i	0.199450	+	0.410076i
$574$	−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	−0.978884	−	0.204417i	$-0.934470\pi$
$577$	−18.6033	+	18.6033i	−0.774466	+	0.774466i	0.204417	+	0.978884i	$0.434470\pi$
$578$	1.99681	+	7.45220i	0.0830564	+	0.309971i
$579$	−12.4264	+	10.7782i	−0.516424	+	0.447925i
$580$	−7.45961	−	5.63295i	−0.309744	−	0.233896i
$581$	10.3252	−	5.96124i	0.428361	−	0.247314i
$582$	0.173966	−	2.44913i	0.00721113	−	0.101520i
$583$	5.44893	−	1.46004i	0.225672	−	0.0604685i
$584$	−13.5323			−0.559970
$585$	−8.98321	+	15.4450i	−0.371410	+	0.638571i
$586$	−9.29625			−0.384025
$587$	−30.7019	+	8.22656i	−1.26720	+	0.339547i	−0.828959	−	0.559309i	$-0.811067\pi$
$587$	−30.7019	+	8.22656i	−1.26720	+	0.339547i	−0.438245	+	0.898855i	$0.644400\pi$
$588$	1.55759	−	0.757569i	0.0642340	−	0.0312416i
$589$	−30.7824	+	17.7722i	−1.26837	+	0.732292i
$590$	−24.0338	+	3.35317i	−0.989456	+	0.138048i
$591$	1.57441	+	8.14748i	0.0647627	+	0.335142i
$592$	−0.234209	−	0.874081i	−0.00962594	−	0.0359245i
$593$	15.3830	−	15.3830i	0.631703	−	0.631703i	−0.316792	−	0.948495i	$-0.602606\pi$
$593$	15.3830	−	15.3830i	0.631703	−	0.631703i	0.948495	+	0.316792i	$0.102606\pi$
$594$	−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
$597$	15.3753	−	22.7409i	0.629270	−	0.930722i
$598$	−1.09233	+	4.07664i	−0.0446688	+	0.166706i
$599$	−7.54399	−	13.0666i	−0.308239	−	0.533886i	0.669738	−	0.742597i	$-0.266406\pi$
$599$	−7.54399	−	13.0666i	−0.308239	−	0.533886i	−0.977977	+	0.208711i	$0.933073\pi$
$600$	−3.90770	−	7.72851i	−0.159531	−	0.315515i
$601$	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
$603$	2.08187	+	17.2693i	0.0847803	+	0.703261i
$604$		−	4.52087i		−	0.183952i
$605$	−5.83322	−	0.722164i	−0.237154	−	0.0293602i
$606$	−16.8853	−	19.4675i	−0.685919	−	0.790814i
$607$	−27.3697	−	7.33369i	−1.11090	−	0.297665i	−0.343705	−	0.939078i	$-0.611682\pi$
$607$	−27.3697	−	7.33369i	−1.11090	−	0.297665i	−0.767196	+	0.641412i	$0.778349\pi$
$608$	−3.37131	−	0.903340i	−0.136725	−	0.0366353i
$609$	−4.74422	−	5.46973i	−0.192245	−	0.221645i
$610$	10.2903	+	13.1983i	0.416644	+	0.534383i
$611$			20.0644i			0.811719i
$612$	1.09410	+	9.07564i	0.0442262	+	0.366861i
$613$	23.3541	+	23.3541i	0.943261	+	0.943261i	0.998475	−	0.0552131i	$-0.0175838\pi$
$613$	23.3541	+	23.3541i	0.943261	+	0.943261i	−0.0552131	+	0.998475i	$0.517584\pi$
$614$	−9.42021	+	16.3163i	−0.380169	+	0.658471i
$615$	−30.9860	+	35.4943i	−1.24947	+	1.43127i
$616$	−1.44667	−	2.50570i	−0.0582879	−	0.100958i
$617$	−3.86668	+	14.4307i	−0.155667	+	0.580956i	0.843381	+	0.537317i	$0.180562\pi$
$617$	−3.86668	+	14.4307i	−0.155667	+	0.580956i	−0.999047	+	0.0436396i	$0.986105\pi$
$618$	8.22851	−	12.1704i	0.330999	−	0.489565i
$619$	24.7406	+	14.2840i	0.994408	+	0.574122i	0.906589	−	0.422015i	$-0.138677\pi$
$619$	24.7406	+	14.2840i	0.994408	+	0.574122i	0.0878190	+	0.996136i	$0.472010\pi$
$620$	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
$623$	2.76637	+	10.3242i	0.110832	+	0.413632i
$624$	−0.875289	−	4.52956i	−0.0350396	−	0.181327i
$625$	−21.2541	+	13.1629i	−0.850166	+	0.526515i
$626$	−10.7107	+	6.18383i	−0.428086	+	0.247156i
$627$	15.7292	−	7.65026i	0.628165	−	0.305522i
$628$	10.6069	−	2.84211i	0.423261	−	0.113412i
$629$	2.75738			0.109944
$630$	−1.71546	−	6.48515i	−0.0683455	−	0.258375i
$631$	−29.7860			−1.18576			−0.592881	−	0.805290i	$-0.702010\pi$
$631$	−29.7860			−1.18576			−0.592881	+	0.805290i	$0.702010\pi$
$632$	11.5520	−	3.09536i	0.459515	−	0.123127i
$633$	−0.153955	+	2.16741i	−0.00611916	+	0.0861468i
$634$	−18.1962	+	10.5056i	−0.722662	+	0.417229i
$635$	1.85506	+	13.2961i	0.0736157	+	0.527640i
$636$	−2.55108	+	2.21270i	−0.101157	+	0.0877392i
$637$	−0.689370	−	2.57276i	−0.0273138	−	0.101937i
$638$	−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	$-0.727134\pi$
$642$	−1.36374	−	2.80391i	−0.0538227	−	0.110662i
$643$	4.97471	−	18.5659i	0.196183	−	0.732166i	−0.795774	−	0.605594i	$-0.792936\pi$
$643$	4.97471	−	18.5659i	0.196183	−	0.732166i	0.991957	−	0.126573i	$-0.0403976\pi$
$644$	−0.792270	−	1.37225i	−0.0312198	−	0.0540743i
$645$	39.2574	−	26.3596i	1.54576	−	1.03791i
$646$	5.31758	−	9.21032i	0.209218	−	0.362375i
$647$	−26.0435	−	26.0435i	−1.02388	−	1.02388i	−0.999708	−	0.0241677i	$-0.992306\pi$
$647$	−26.0435	−	26.0435i	−1.02388	−	1.02388i	−0.0241677	−	0.999708i	$-0.507694\pi$
$648$	0.196646	−	8.99785i	0.00772499	−	0.353469i
$649$			31.3995i			1.23254i
$650$	−12.8090	+	3.64516i	−0.502412	+	0.142975i
$651$	17.3187	−	3.34667i	0.678775	−	0.131166i
$652$	7.00909	+	1.87808i	0.274497	+	0.0735513i
$653$	−28.5671	−	7.65454i	−1.11792	−	0.299545i	−0.347878	−	0.937540i	$-0.613098\pi$
$653$	−28.5671	−	7.65454i	−1.11792	−	0.299545i	−0.770041	+	0.637995i	$0.779764\pi$
$654$	−3.01007	+	8.71075i	−0.117703	+	0.340617i
$655$	−2.05358	+	16.5876i	−0.0802401	+	0.648132i
$656$		−	12.1655i		−	0.474981i
$657$	−15.9446	+	37.3346i	−0.622057	+	1.45656i
$658$	−5.32666	−	5.32666i	−0.207655	−	0.207655i
$659$	14.3651	−	24.8811i	0.559585	−	0.969230i	−0.437945	−	0.899002i	$-0.644294\pi$
$659$	14.3651	−	24.8811i	0.559585	−	0.969230i	0.997531	−	0.0702288i	$-0.0223730\pi$
$660$	−10.6030	+	3.62599i	−0.412720	+	0.141141i
$661$	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	$0.805026\pi$
$662$	8.67157	−	32.3628i	0.337030	−	1.25781i
$663$	14.0221	+	0.996014i	0.544573	+	0.0386820i
$664$	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
$668$	6.07580	+	22.6752i	0.235080	+	0.877329i
$669$	−46.1681	−	15.9537i	−1.78496	−	0.616807i
$670$	−7.81290	+	10.3465i	−0.301839	+	0.399719i
$671$	18.7538	−	10.8275i	0.723983	−	0.417992i
$672$	1.43487	+	0.970129i	0.0553513	+	0.0374235i
$673$	−13.4297	+	3.59846i	−0.517675	+	0.138711i	−0.508191	−	0.861244i	$-0.669686\pi$
$673$	−13.4297	+	3.59846i	−0.517675	+	0.138711i	−0.00948408	+	0.999955i	$0.503019\pi$
$674$	19.2194			0.740303
$675$	−25.9267	+	1.67486i	−0.997920	+	0.0644654i
$676$	5.90566			0.227141
$677$	25.3037	−	6.78010i	0.972499	−	0.260580i	0.262616	−	0.964900i	$-0.415415\pi$
$677$	25.3037	−	6.78010i	0.972499	−	0.260580i	0.709883	+	0.704320i	$0.248748\pi$
$678$	−2.36330	−	1.59785i	−0.0907619	−	0.0613650i
$679$	1.22765	−	0.708785i	0.0471130	−	0.0272007i
$680$	−4.10595	+	5.43744i	−0.157456	+	0.208516i
$681$	13.1627	+	4.54847i	0.504396	+	0.174298i
$682$	−7.62626	−	28.4616i	−0.292025	−	1.08985i
$683$	17.2386	−	17.2386i	0.659618	−	0.659618i	−0.295671	−	0.955290i	$-0.595543\pi$
$683$	17.2386	−	17.2386i	0.659618	−	0.659618i	0.955290	+	0.295671i	$0.0955434\pi$
$684$	−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
$687$	39.0212	+	2.77174i	1.48875	+	0.105749i
$688$	−3.15998	+	11.7932i	−0.120473	+	0.449611i
$689$	2.59654	+	4.49734i	0.0989203	+	0.171335i
$690$	−5.80673	+	1.98578i	−0.221059	+	0.0755973i
$691$	−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
$693$	−8.61761	+	1.03888i	−0.327356	+	0.0394637i
$694$		−	7.91046i		−	0.300277i
$695$	−3.44054	+	27.7906i	−0.130507	+	1.05416i
$696$	2.36482	−	6.84348i	0.0896382	−	0.259401i
$697$	35.8065	+	9.59431i	1.35627	+	0.363410i
$698$	26.0663	+	6.98444i	0.986623	+	0.264365i
$699$	41.7275	−	8.06340i	1.57828	−	0.304986i
$700$	2.43281	−	4.36823i	0.0919515	−	0.165104i
$701$		−	2.87388i		−	0.108545i	−0.998526	−	0.0542724i	$-0.982716\pi$
$701$		−	2.87388i		−	0.108545i	0.998526	−	0.0542724i	$-0.0172839\pi$
$702$	−13.5281	−	2.92215i	−0.510583	−	0.110289i
$703$	2.23331	+	2.23331i	0.0842307	+	0.0842307i
$704$	1.44667	−	2.50570i	0.0545233	−	0.0944372i
$705$	−24.2217	+	16.2638i	−0.912241	+	0.612529i
$706$	7.10831	+	12.3119i	0.267525	+	0.463366i
$707$	3.85081	−	14.3714i	0.144824	−	0.540492i
$708$	−8.22140	−	16.9035i	−0.308979	−	0.635273i
$709$	26.2628	+	15.1629i	0.986322	+	0.569453i	0.904173	−	0.427167i	$-0.140488\pi$
$709$	26.2628	+	15.1629i	0.986322	+	0.569453i	0.0821491	+	0.996620i	$0.473822\pi$
$710$	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
$713$	−4.17653	−	15.5870i	−0.156412	−	0.583739i
$714$	−3.98698	+	3.45814i	−0.149209	+	0.129418i
$715$	2.38115	+	17.0669i	0.0890499	+	0.638264i
$716$	−0.671046	+	0.387429i	−0.0250782	+	0.0144789i
$717$	0.983878	−	13.8512i	0.0367436	−	0.517284i
$718$	−5.16849	+	1.38489i	−0.192886	+	0.0516838i
$719$	45.6824			1.70366			0.851832	−	0.523814i	$-0.175491\pi$
$719$	45.6824			1.70366			0.851832	+	0.523814i	$0.175491\pi$
$720$	4.75858	−	4.72821i	0.177342	−	0.176210i
$721$	8.48188			0.315882
$722$	−6.58590	+	1.76469i	−0.245102	+	0.0656749i
$723$	30.6566	−	14.9105i	1.14013	−	0.554527i
$724$	13.7966	−	7.96546i	0.512746	−	0.296034i
$725$	−20.2706	−	5.09721i	−0.752832	−	0.189306i
$726$	−0.863817	−	4.47019i	−0.0320593	−	0.165904i
$727$	4.88235	+	18.2212i	0.181076	+	0.675785i	0.995437	+	0.0954259i	$0.0304213\pi$
$727$	4.88235	+	18.2212i	0.181076	+	0.675785i	−0.814360	+	0.580360i	$0.802912\pi$
$728$	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
$732$	−7.26089	+	10.7392i	−0.268370	+	0.396933i
$733$	7.80181	−	29.1168i	0.288167	−	1.07545i	−0.658328	−	0.752732i	$-0.728736\pi$
$733$	7.80181	−	29.1168i	0.288167	−	1.07545i	0.946494	−	0.322721i	$-0.104598\pi$
$734$	10.5147	+	18.2121i	0.388106	+	0.672219i
$735$	2.54704	−	2.91763i	0.0939491	−	0.107618i
$736$	0.792270	−	1.37225i	0.0292034	−	0.0505818i
$737$	11.8624	+	11.8624i	0.436955	+	0.436955i
$738$	−33.5637	−	14.3341i	−1.23550	−	0.527646i
$739$		−	19.4818i		−	0.716651i	−0.933597	−	0.358326i	$-0.883348\pi$
$739$		−	19.4818i		−	0.716651i	0.933597	−	0.358326i	$-0.116652\pi$
$740$	−1.24416	−	1.59575i	−0.0457363	−	0.0586609i
$741$	10.5503	+	12.1637i	0.387575	+	0.446845i
$742$	−1.88327	−	0.504621i	−0.0691370	−	0.0185252i
$743$	21.7358	+	5.82409i	0.797408	+	0.213665i	0.634446	−	0.772967i	$-0.281228\pi$
$743$	21.7358	+	5.82409i	0.797408	+	0.213665i	0.162963	+	0.986632i	$0.447895\pi$
$744$	11.5577	+	13.3251i	0.423725	+	0.488523i
$745$	−15.2367	−	1.88634i	−0.558231	−	0.0691102i
$746$			5.47172i			0.200334i
$747$	28.6124	−	21.4625i	1.04687	−	0.785273i
$748$	6.23409	+	6.23409i	0.227941	+	0.227941i
$749$	0.900079	−	1.55898i	0.0328882	−	0.0569640i
$750$	−14.7831	−	12.5083i	−0.539804	−	0.456740i
$751$	−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	$-0.447134\pi$
$752$	1.94969	−	7.27636i	0.0710980	−	0.265341i
$753$	−29.3150	+	43.3584i	−1.06830	+	1.58007i
$754$	−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	−0.502098	−	0.864811i	$-0.667438\pi$
$757$	9.97956	−	9.97956i	0.362713	−	0.362713i	0.864811	+	0.502098i	$0.167438\pi$
$758$	4.45201	+	16.6151i	0.161704	+	0.603488i
$759$	1.50660	+	7.79653i	0.0546860	+	0.282996i
$760$	−7.72955	+	1.07842i	−0.280380	+	0.0391183i
$761$	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	$0.182283\pi$
$762$	−9.35145	+	4.54829i	−0.338767	+	0.164767i
$763$	−5.13965	+	1.37717i	−0.186068	+	0.0498567i
$764$	−6.30215			−0.228004
$765$	10.1636	+	17.7348i	0.367466	+	0.641202i
$766$	−2.82996			−0.102250
$767$	−27.9205	+	7.48128i	−1.00815	+	0.270133i
$768$	−0.122721	+	1.72770i	−0.00442833	+	0.0623429i
$769$	−31.5524	+	18.2168i	−1.13781	+	0.656915i	−0.945887	−	0.324495i	$-0.894806\pi$
$769$	−31.5524	+	18.2168i	−1.13781	+	0.656915i	−0.191922	+	0.981410i	$0.561472\pi$
$770$	−5.16302	−	3.89874i	−0.186062	−	0.140501i
$771$	4.58851	−	3.97988i	0.165251	−	0.143332i
$772$	−2.45803	−	9.17349i	−0.0884664	−	0.330161i
$773$	13.2819	−	13.2819i	0.477718	−	0.477718i	−0.426683	−	0.904401i	$-0.640318\pi$
$773$	13.2819	−	13.2819i	0.477718	−	0.477718i	0.904401	+	0.426683i	$0.140318\pi$
$774$	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
$777$	−0.685536	−	1.40949i	−0.0245935	−	0.0505651i
$778$	−6.12085	+	22.8433i	−0.219443	+	0.818972i
$779$	21.2302	+	36.7718i	0.760650	+	1.31748i
$780$	−5.75052	−	8.56427i	−0.205902	−	0.306650i
$781$	0.0918724	−	0.159128i	0.00328745	−	0.00569404i
$782$	3.41411	+	3.41411i	0.122088	+	0.122088i
$783$	−16.0943	−	14.5878i	−0.575163	−	0.521325i
$784$			1.00000i			0.0357143i
$785$	19.3643	−	15.0978i	0.691140	−	0.538863i
$786$	−12.7116	+	2.45639i	−0.453409	+	0.0876166i
$787$	7.68056	+	2.05800i	0.273782	+	0.0733597i	0.393098	−	0.919497i	$-0.371403\pi$
$787$	7.68056	+	2.05800i	0.273782	+	0.0733597i	−0.119316	+	0.992856i	$0.538070\pi$
$788$	−4.62772	−	1.23999i	−0.164856	−	0.0441730i
$789$	15.9762	−	46.2329i	0.568766	−	1.64594i
$790$	21.0897	−	16.4431i	0.750340	−	0.585019i
$791$		−	1.64705i		−	0.0585623i
$792$	−5.20850	−	6.94363i	−0.185076	−	0.246731i
$793$	14.0962	+	14.0962i	0.500570	+	0.500570i
$794$	12.5284	−	21.6998i	0.444617	−	0.770099i
$795$	−3.32447	+	6.77998i	−0.117907	+	0.240461i
$796$	7.92437	+	13.7254i	0.280872	+	0.486484i
$797$	5.29158	−	19.7485i	0.187438	−	0.699526i	−0.806658	−	0.591018i	$-0.798726\pi$
$797$	5.29158	−	19.7485i	0.187438	−	0.699526i	0.994096	−	0.108508i	$-0.0346073\pi$
$798$	−6.03008	−	0.428327i	−0.213462	−	0.0151626i
$799$	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
$803$	10.1337	+	37.8193i	0.357609	+	1.33461i
$804$	−9.49190	−	3.28000i	−0.334754	−	0.115677i
$805$	−2.82754	−	2.13515i	−0.0996576	−	0.0752541i
$806$	23.4911	−	13.5626i	0.827439	−	0.477722i
$807$	4.81572	+	3.25596i	0.169522	+	0.114615i
$808$	14.3714	−	3.85081i	0.505584	−	0.135471i
$809$	19.1740			0.674122			0.337061	−	0.941483i	$-0.390567\pi$
$809$	19.1740			0.674122			0.337061	+	0.941483i	$0.390567\pi$
$810$	−7.43794	−	18.6997i	−0.261343	−	0.657039i
$811$	24.2281			0.850764			0.425382	−	0.905014i	$-0.360140\pi$
$811$	24.2281			0.850764			0.425382	+	0.905014i	$0.360140\pi$
$812$	4.03789	−	1.08195i	0.141702	−	0.0379690i
$813$	4.63974	+	3.13698i	0.162723	+	0.110019i
$814$	−2.26745	+	1.30911i	−0.0794740	+	0.0458843i
$815$	16.0700	−	2.24207i	0.562909	−	0.0785364i
$816$	−4.98833	−	1.72376i	−0.174626	−	0.0603435i
$817$	−11.0291	−	41.1611i	−0.385858	−	1.44004i
$818$	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	$0.420577\pi$
$822$	−3.06968	−	0.218045i	−0.107067	−	0.00760518i
$823$	1.36886	−	5.10866i	0.0477155	−	0.178077i	−0.937956	−	0.346755i	$-0.887283\pi$
$823$	1.36886	−	5.10866i	0.0477155	−	0.178077i	0.985671	+	0.168679i	$0.0539500\pi$
$824$	4.24094	+	7.34552i	0.147740	+	0.255893i
$825$	−18.6729	+	16.7085i	−0.650109	+	0.581717i
$826$	5.42618	−	9.39841i	0.188801	−	0.327013i
$827$	9.58257	+	9.58257i	0.333218	+	0.333218i	0.853807	−	0.520589i	$-0.174288\pi$
$827$	9.58257	+	9.58257i	0.333218	+	0.333218i	−0.520589	+	0.853807i	$0.674288\pi$
$828$	−2.85244	−	3.80269i	−0.0991293	−	0.132153i
$829$			8.07858i			0.280581i	0.990110	+	0.140290i	$0.0448036\pi$
$829$			8.07858i			0.280581i	−0.990110	+	0.140290i	$0.955196\pi$
$830$	26.4575	+	3.27549i	0.918354	+	0.113694i
$831$	4.18405	−	12.1081i	0.145143	−	0.420026i
$832$	2.57276	+	0.689370i	0.0891945	+	0.0238996i
$833$	−2.94329	−	0.788652i	−0.101979	−	0.0273252i
$834$	−21.2969	+	4.11540i	−0.737451	+	0.142505i
$835$	32.2758	+	41.3965i	1.11695	+	1.43259i
$836$			10.0984i			0.349262i
$837$	50.3811	−	16.1863i	1.74143	−	0.559480i
$838$	5.39015	+	5.39015i	0.186200	+	0.186200i
$839$	−10.0382	+	17.3867i	−0.346558	+	0.600256i	−0.985636	−	0.168886i	$-0.945983\pi$
$839$	−10.0382	+	17.3867i	−0.346558	+	0.600256i	0.639077	+	0.769142i	$0.279316\pi$
$840$	3.80026	+	0.746989i	0.131122	+	0.0257736i
$841$	5.76241	+	9.98078i	0.198704	+	0.344165i
$842$	−0.486917	+	1.81720i	−0.0167803	+	0.0626248i
$843$	1.96105	+	4.03199i	0.0675421	+	0.138869i
$844$	−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
$848$	−0.504621	−	1.88327i	−0.0173287	−	0.0646718i
$849$	−20.2817	+	17.5915i	−0.696067	+	0.603739i
$850$	−3.71545	+	14.7756i	−0.127439	+	0.506799i
$851$	−1.24177	+	0.716937i	−0.0425674	+	0.0245763i
$852$	−0.00779358	+	0.109720i	−0.000267004	+	0.00375893i
$853$	−33.6530	+	9.01730i	−1.15226	+	0.308746i	−0.783869	−	0.620926i	$-0.786757\pi$
$853$	−33.6530	+	9.01730i	−1.15226	+	0.308746i	−0.368388	+	0.929672i	$0.620090\pi$
$854$	−7.48446			−0.256113
$855$	−6.13216	+	22.5959i	−0.209715	+	0.772765i
$856$	1.80016			0.0615282
$857$	−3.43109	+	0.919357i	−0.117204	+	0.0314046i	−0.316944	−	0.948444i	$-0.602657\pi$
$857$	−3.43109	+	0.919357i	−0.117204	+	0.0314046i	0.199740	+	0.979849i	$0.435990\pi$
$858$	−12.0035	+	5.83817i	−0.409793	+	0.199312i
$859$	−12.9565	+	7.48045i	−0.442071	+	0.255230i	−0.704476	−	0.709728i	$-0.748818\pi$
$859$	−12.9565	+	7.48045i	−0.442071	+	0.255230i	0.262405	+	0.964958i	$0.415484\pi$
$860$	3.77241	+	27.0387i	0.128638	+	0.922013i
$861$	−3.99783	−	20.6885i	−0.136246	−	0.705061i
$862$	7.88738	+	29.4361i	0.268645	+	1.00260i
$863$	11.7835	−	11.7835i	0.401114	−	0.401114i	−0.477512	−	0.878625i	$-0.658461\pi$
$863$	11.7835	−	11.7835i	0.401114	−	0.401114i	0.878625	+	0.477512i	$0.158461\pi$
$864$	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
$867$	−7.48462	+	11.0701i	−0.254191	+	0.375961i
$868$	−2.63580	+	9.83695i	−0.0894650	+	0.333888i
$869$	−17.3015	−	29.9670i	−0.586913	−	1.01656i
$870$	−1.09544	−	16.1533i	−0.0371387	−	0.547647i
$871$	−7.72170	+	13.3744i	−0.261640	+	0.453174i
$872$	−3.76249	−	3.76249i	−0.127414	−	0.127414i
$873$	3.40199	−	2.55187i	0.115140	−	0.0863677i
$874$			5.53042i			0.187069i
$875$	1.20209	−	11.1155i	0.0406381	−	0.375773i
$876$	−15.3576	−	17.7062i	−0.518887	−	0.598238i
$877$	54.9338	+	14.7195i	1.85498	+	0.497041i	0.999774	−	0.0212463i	$-0.00676342\pi$
$877$	54.9338	+	14.7195i	1.85498	+	0.497041i	0.855207	+	0.518287i	$0.173430\pi$
$878$	36.0912	+	9.67060i	1.21802	+	0.326367i
$879$	−10.5502	−	12.1636i	−0.355850	−	0.410269i
$880$	0.794893	−	6.42068i	0.0267958	−	0.216441i
$881$		−	30.3578i		−	1.02278i	−0.859349	−	0.511390i	$-0.829131\pi$
$881$		−	30.3578i		−	1.02278i	0.859349	−	0.511390i	$-0.170869\pi$
$882$	2.75893	+	1.17826i	0.0928980	+	0.0396742i
$883$	−23.2297	−	23.2297i	−0.781741	−	0.781741i	0.198384	−	0.980124i	$-0.436431\pi$
$883$	−23.2297	−	23.2297i	−0.781741	−	0.781741i	−0.980124	+	0.198384i	$0.936431\pi$
$884$	−4.05803	+	7.02871i	−0.136486	+	0.236401i
$885$	−31.6632	−	27.6414i	−1.06435	−	0.929156i
$886$	0.771339	+	1.33600i	0.0259136	+	0.0448837i
$887$	11.1536	−	41.6259i	0.374502	−	1.39766i	−0.479569	−	0.877504i	$-0.659207\pi$
$887$	11.1536	−	41.6259i	0.374502	−	1.39766i	0.854071	−	0.520156i	$-0.174126\pi$
$888$	0.877884	−	1.29844i	0.0294599	−	0.0435726i
$889$	−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
$893$	6.80490	+	25.3962i	0.227717	+	0.849852i
$894$	−2.25635	−	11.6764i	−0.0754635	−	0.390518i
$895$	−1.04411	+	1.38270i	−0.0349008	+	0.0462185i
$896$	−0.866025	+	0.500000i	−0.0289319	+	0.0167038i
$897$	−6.57374	+	3.19728i	−0.219491	+	0.106754i
$898$	2.87977	−	0.771631i	0.0960990	−	0.0257497i
$899$	42.5723			1.41987
$900$	5.67751	−	13.8840i	0.189250	−	0.462801i
$901$	5.94098			0.197923
$902$	−33.9994	+	9.11011i	−1.13206	+	0.303333i
$903$	−1.49833	+	21.0938i	−0.0498613	+	0.701958i
$904$	1.42639	−	0.823524i	0.0474409	−	0.0273900i
$905$	21.4667	−	28.4280i	0.713578	−	0.944979i
$906$	5.91531	−	5.13069i	0.196523	−	0.170456i
$907$	−1.31253	−	4.89845i	−0.0435820	−	0.162650i	0.940705	−	0.339225i	$-0.110165\pi$
$907$	−1.31253	−	4.89845i	−0.0435820	−	0.162650i	−0.984287	+	0.176575i	$0.943498\pi$
$908$	−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	$0.547333\pi$
$912$	−2.64410	−	5.43637i	−0.0875548	−	0.180016i
$913$	8.92816	−	33.3203i	0.295479	−	1.10274i
$914$	−19.6895	−	34.1032i	−0.651270	−	1.12803i
$915$	−5.59081	+	28.4429i	−0.184826	+	0.940294i
$916$	−11.2928	+	19.5597i	−0.373125	+	0.646272i
$917$	−5.28551	−	5.28551i	−0.174543	−	0.174543i
$918$	−10.6333	+	11.7314i	−0.350951	+	0.387194i
$919$		−	26.2807i		−	0.866921i	−0.901173	−	0.433461i	$-0.857292\pi$
$919$		−	26.2807i		−	0.866921i	0.901173	−	0.433461i	$-0.142708\pi$
$920$	0.435324	−	3.51629i	0.0143522	−	0.115929i
$921$	−32.0398	+	6.19136i	−1.05575	+	0.204012i
$922$	29.2939	+	7.84927i	0.964742	+	0.258502i
$923$	0.163387	+	0.0437793i	0.00537793	+	0.00144101i
$924$	1.63676	−	4.73658i	0.0538455	−	0.155822i
$925$	−3.95288	−	2.20149i	−0.129970	−	0.0723844i
$926$			31.7476i			1.04329i
$927$	25.2627	−	3.04550i	0.829737	−	0.100027i
$928$	2.95594	+	2.95594i	0.0970336	+	0.0970336i
$929$	−12.7254	+	22.0410i	−0.417506	+	0.723142i	−0.995688	−	0.0927661i	$-0.970429\pi$
$929$	−12.7254	+	22.0410i	−0.417506	+	0.723142i	0.578182	+	0.815908i	$0.303762\pi$
$930$	35.4141	+	17.3648i	1.16127	+	0.569415i
$931$	−1.74512	−	3.02264i	−0.0571940	−	0.0990629i
$932$	−6.35066	+	23.7010i	−0.208023	+	0.776351i
$933$	27.5801	+	1.95906i	0.902931	+	0.0641368i
$934$	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	−0.810809	−	0.585310i	$-0.800973\pi$
$937$	−6.90263	+	6.90263i	−0.225499	+	0.225499i	0.585310	+	0.810809i	$0.300973\pi$
$938$	−1.50066	−	5.60055i	−0.0489984	−	0.182865i
$939$	−20.2467	−	6.99640i	−0.660725	−	0.228319i
$940$	−2.32757	−	16.6828i	−0.0759168	−	0.544133i
$941$	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	$0.217412\pi$
$942$	15.7564	+	10.6530i	0.513371	+	0.347095i
$943$	−18.6198	+	4.98916i	−0.606344	+	0.162470i
$944$	10.8524			0.353214
$945$	6.53860	−	9.60451i	0.212701	−	0.312435i
$946$	35.3253			1.14853
$947$	−57.0464	+	15.2855i	−1.85376	+	0.496714i	−0.999724	−	0.0234992i	$-0.992519\pi$
$947$	−57.0464	+	15.2855i	−1.85376	+	0.496714i	−0.854037	+	0.520213i	$0.825853\pi$
$948$	17.1604	+	11.6023i	0.557343	+	0.376825i
$949$	−31.2146	+	18.0217i	−1.01327	+	0.585011i
$950$	−14.9766	+	8.95803i	−0.485904	+	0.290637i
$951$	−34.3966	−	11.8860i	−1.11539	−	0.385430i
$952$	−0.788652	−	2.94329i	−0.0255604	−	0.0953925i
$953$	−24.9451	+	24.9451i	−0.808051	+	0.808051i	−0.984339	−	0.176288i	$-0.943591\pi$
$953$	−24.9451	+	24.9451i	−0.808051	+	0.808051i	0.176288	+	0.984339i	$0.443591\pi$
$954$	−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
$957$	−20.8967	−	1.48433i	−0.675494	−	0.0479815i
$958$	−6.62853	+	24.7380i	−0.214158	+	0.799249i
$959$	−0.888372	−	1.53871i	−0.0286870	−	0.0496874i
$960$	1.25322	+	3.66462i	0.0404475	+	0.118275i
$961$	−36.3565	+	62.9713i	−1.17279	+	2.03133i
$962$	−1.70431	−	1.70431i	−0.0549492	−	0.0549492i
$963$	2.12106	−	4.96651i	0.0683502	−	0.160044i
$964$			19.6820i			0.633916i
$965$	−13.0575	−	16.7474i	−0.420336	−	0.539118i
$966$	0.896375	−	2.59399i	0.0288404	−	0.0834604i
$967$	3.36469	+	0.901566i	0.108201	+	0.0289924i	0.312513	−	0.949913i	$-0.398829\pi$
$967$	3.36469	+	0.901566i	0.108201	+	0.0289924i	−0.204312	+	0.978906i	$0.565496\pi$
$968$	2.53904	+	0.680335i	0.0816079	+	0.0218668i
$969$	18.0861	−	3.49494i	0.581008	−	0.112274i
$970$	3.14577	+	0.389452i	0.101005	+	0.0125046i
$971$		−	22.8993i		−	0.734873i	−0.930049	−	0.367437i	$-0.880235\pi$
$971$		−	22.8993i		−	0.734873i	0.930049	−	0.367437i	$-0.119765\pi$
$972$	11.9964	−	9.95427i	0.384783	−	0.319283i
$973$	−8.85526	−	8.85526i	−0.283887	−	0.283887i
$974$	−2.96467	+	5.13496i	−0.0949941	+	0.164535i
$975$	−19.3063	−	12.6230i	−0.618297	−	0.404261i
$976$	−3.74223	−	6.48173i	−0.119786	−	0.207475i
$977$	2.40116	−	8.96125i	0.0768199	−	0.286696i	−0.916820	−	0.399301i	$-0.869253\pi$
$977$	2.40116	−	8.96125i	0.0768199	−	0.286696i	0.993640	+	0.112605i	$0.0359195\pi$
$978$	5.49718	+	11.3024i	0.175781	+	0.361412i
$979$	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
$983$	5.07610	+	18.9443i	0.161902	+	0.604228i	0.998415	+	0.0562802i	$0.0179240\pi$
$983$	5.07610	+	18.9443i	0.161902	+	0.604228i	−0.836513	+	0.547948i	$0.815409\pi$
$984$	15.9178	−	13.8065i	0.507442	−	0.440134i
$985$	−10.6102	+	1.48032i	−0.338068	+	0.0471669i
$986$	−11.0314	+	6.36898i	−0.351311	+	0.202830i
$987$	0.924465	−	13.0148i	0.0294261	−	0.414266i
$988$	−8.97956	+	2.40607i	−0.285678	+	0.0765471i
$989$	19.3460			0.615166
$990$	−16.7776	−	9.75830i	−0.533227	−	0.310139i
$991$	38.7636			1.23137			0.615683	−	0.787994i	$-0.288880\pi$
$991$	38.7636			1.23137			0.615683	+	0.787994i	$0.288880\pi$
$992$	−9.83695	+	2.63580i	−0.312323	+	0.0836868i
$993$	52.1861	−	25.3819i	1.65608	−	0.805470i
$994$	−0.0549980	+	0.0317531i	−0.00174443	+	0.00100715i
$995$	28.2813	+	21.3560i	0.896579	+	0.677030i
$996$	3.91798	+	20.2753i	0.124146	+	0.642447i
$997$	−8.79825	−	32.8355i	−0.278643	−	1.03991i	−0.953360	−	0.301835i	$-0.902401\pi$
$997$	−8.79825	−	32.8355i	−0.278643	−	1.03991i	0.674717	−	0.738077i	$-0.264266\pi$
$998$	−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.a.533.2	✓	72
5.2	odd	4		630.2.ca.b.407.4	yes	72
9.5	odd	6		630.2.ca.b.113.4	yes	72
45.32	even	12	inner	630.2.ca.a.617.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ca.a.533.2	✓	72	1.1	even	1	trivial
630.2.ca.a.617.2	yes	72	45.32	even	12	inner
630.2.ca.b.113.4	yes	72	9.5	odd	6
630.2.ca.b.407.4	yes	72	5.2	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.43487 - 0.970129i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.34749 - 1.78445i) q^{5} +(1.63707 + 0.565701i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.11770 + 2.78402i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.43487 - 0.970129i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.34749 - 1.78445i) q^{5} +(1.63707 + 0.565701i) q^{6} +(0.258819 + 0.965926i) 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} +(-1.72770 - 0.122721i) q^{12} +(-0.689370 + 2.57276i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-3.66462 + 1.25322i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.15464 + 2.15464i) q^{17} +(-1.80017 - 2.39987i) q^{18} +3.49024i q^{19} +(0.274732 - 2.21913i) q^{20} +(0.565701 - 1.63707i) q^{21} +(-2.79475 - 0.748850i) q^{22} +(-1.53055 - 0.410109i) q^{23} +(1.70059 - 0.328621i) q^{24} +(-1.36855 - 4.80906i) q^{25} -2.66352i q^{26} +(1.09710 - 5.07901i) q^{27} +(0.707107 + 0.707107i) q^{28} +(2.09017 - 3.62028i) q^{29} +(3.21539 - 2.15899i) q^{30} +(5.09198 + 8.81957i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-2.19190 - 4.50663i) 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} +(-0.903340 - 3.37131i) q^{38} +(3.48507 - 3.02280i) q^{39} +(0.308981 + 2.21462i) q^{40} +(10.5356 - 6.08273i) q^{41} +(-0.122721 + 1.72770i) q^{42} +(-11.7932 + 3.15998i) q^{43} +2.89334 q^{44} +(6.47404 + 1.75694i) q^{45} +1.58454 q^{46} +(7.27636 - 1.94969i) q^{47} +(-1.55759 + 0.757569i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(2.56659 + 4.29099i) q^{50} +(-1.00135 - 5.18190i) q^{51} +(0.689370 + 2.57276i) 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} +(3.38598 - 5.00804i) q^{57} +(-1.08195 + 4.03789i) q^{58} +(5.42618 + 9.39841i) q^{59} +(-2.54704 + 2.91763i) q^{60} +(3.74223 - 6.48173i) q^{61} +(-7.20115 - 7.20115i) q^{62} +(-2.39987 + 1.80017i) q^{63} -1.00000i q^{64} +(3.66206 + 4.69692i) q^{65} +(3.28362 + 3.78577i) q^{66} +(5.60055 + 1.50066i) q^{67} +(2.94329 + 0.788652i) q^{68} +(1.79828 + 2.07328i) q^{69} +(-2.21913 - 0.274732i) q^{70} -0.0635062i q^{71} +(-2.75893 - 1.17826i) q^{72} +(9.56877 + 9.56877i) q^{73} +(-0.452458 + 0.783680i) q^{74} +(-2.70172 + 8.22804i) q^{75} +(1.74512 + 3.02264i) q^{76} +(-0.748850 + 2.79475i) q^{77} +(-2.58396 + 3.82180i) 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} +(-3.08577 - 11.5162i) q^{83} +(-0.328621 - 1.70059i) q^{84} +(6.74820 - 0.941501i) q^{85} +(10.5735 - 6.10460i) q^{86} +(-6.51125 + 3.16689i) q^{87} +(-2.79475 + 0.748850i) q^{88} +10.6884 q^{89} +(-6.70817 - 0.0214746i) q^{90} -2.66352 q^{91} +(-1.53055 + 0.410109i) q^{92} +(1.24979 - 17.5948i) q^{93} +(-6.52380 + 3.76652i) q^{94} +(6.22817 + 4.70306i) q^{95} +(1.30844 - 1.13489i) q^{96} +(-0.366894 - 1.36927i) 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	\( 72 q - 4 q^{3} + 12 q^{11} + 4 q^{12} - 36 q^{14} + 12 q^{15} + 36 q^{16} - 24 q^{17} + 8 q^{18} + 12 q^{20} + 4 q^{21} + 24 q^{23} + 8 q^{24} + 12 q^{25} - 16 q^{27} - 32 q^{30} - 36 q^{33} + 12 q^{34} - 4 q^{36} + 24 q^{37} - 36 q^{38} - 40 q^{39} - 48 q^{41} - 4 q^{42} - 48 q^{43} - 12 q^{45} - 48 q^{47} - 8 q^{48} + 16 q^{51} - 4 q^{54} + 24 q^{55} + 52 q^{57} + 48 q^{58} - 4 q^{60} + 8 q^{66} + 12 q^{67} - 12 q^{68} + 64 q^{69} - 116 q^{75} + 8 q^{78} + 72 q^{79} + 48 q^{82} - 60 q^{83} + 24 q^{85} + 72 q^{86} - 44 q^{87} + 8 q^{90} - 24 q^{91} + 24 q^{92} + 32 q^{93} - 132 q^{94} - 60 q^{95} + 36 q^{97} - 40 q^{99}+O(q^{100}) \) 72 * q - 4 * q^3 + 12 * q^11 + 4 * q^12 - 36 * q^14 + 12 * q^15 + 36 * q^16 - 24 * q^17 + 8 * q^18 + 12 * q^20 + 4 * q^21 + 24 * q^23 + 8 * q^24 + 12 * q^25 - 16 * q^27 - 32 * q^30 - 36 * 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 - 12 * q^45 - 48 * q^47 - 8 * q^48 + 16 * q^51 - 4 * q^54 + 24 * q^55 + 52 * q^57 + 48 * q^58 - 4 * q^60 + 8 * q^66 + 12 * q^67 - 12 * q^68 + 64 * q^69 - 116 * q^75 + 8 * q^78 + 72 * q^79 + 48 * q^82 - 60 * q^83 + 24 * q^85 + 72 * q^86 - 44 * q^87 + 8 * q^90 - 24 * q^91 + 24 * q^92 + 32 * 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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