LMFDB - Embedded newform 650.2.p.a.181.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(181,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("650.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.p (of order $10$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$34$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			181.15
Character	$\chi$	$=$	650.181
Dual form			650.2.p.a.571.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(2.12082 - 1.54087i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-1.15648 + 1.91378i) q^{5} +(-1.54087 + 2.12082i) q^{6} -3.25927i q^{7} +(-0.587785 + 0.809017i) q^{8} +(1.19656 - 3.68265i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(2.12082 - 1.54087i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-1.15648 + 1.91378i) q^{5} +(-1.54087 + 2.12082i) q^{6} -3.25927i q^{7} +(-0.587785 + 0.809017i) q^{8} +(1.19656 - 3.68265i) q^{9} +(0.508489 - 2.17748i) q^{10} +(1.79208 - 0.582281i) q^{11} +(0.810082 - 2.49318i) q^{12} +(-3.22807 - 1.60609i) q^{13} +(1.00717 + 3.09975i) q^{14} +(0.496187 + 5.84077i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.96816 - 3.60958i) q^{17} +3.87216i q^{18} +(4.21823 - 5.80590i) q^{19} +(0.189277 + 2.22804i) q^{20} +(-5.02210 - 6.91233i) q^{21} +(-1.52443 + 1.10756i) q^{22} +(1.72005 + 5.29378i) q^{23} +2.62148i q^{24} +(-2.32510 - 4.42650i) q^{25} +(3.56639 + 0.529955i) q^{26} +(-0.706525 - 2.17446i) q^{27} +(-1.91575 - 2.63680i) q^{28} +(4.98419 - 3.62123i) q^{29} +(-2.27680 - 5.40157i) q^{30} +(1.41436 - 1.94670i) q^{31} +1.00000i q^{32} +(2.90346 - 3.99627i) q^{33} +(5.84043 + 1.89767i) q^{34} +(6.23752 + 3.76929i) q^{35} +(-1.19656 - 3.68265i) q^{36} +(10.4987 + 3.41124i) q^{37} +(-2.21766 + 6.82524i) q^{38} +(-9.32095 + 1.56780i) q^{39} +(-0.868517 - 2.06050i) q^{40} +(-2.67735 - 0.869925i) q^{41} +(6.91233 + 5.02210i) q^{42} -9.33805 q^{43} +(1.10756 - 1.52443i) q^{44} +(5.66397 + 6.54887i) q^{45} +(-3.27173 - 4.50316i) q^{46} +(-0.00698816 - 0.00961837i) q^{47} +(-0.810082 - 2.49318i) q^{48} -3.62283 q^{49} +(3.57916 + 3.49136i) q^{50} -16.0985 q^{51} +(-3.55560 + 0.598058i) q^{52} +(0.327838 - 0.238188i) q^{53} +(1.34389 + 1.84971i) q^{54} +(-0.958148 + 4.10304i) q^{55} +(2.63680 + 1.91575i) q^{56} -18.8130i q^{57} +(-3.62123 + 4.98419i) q^{58} +(-2.62826 - 0.853973i) q^{59} +(3.83454 + 4.43363i) q^{60} +(0.995831 + 3.06485i) q^{61} +(-0.743575 + 2.28849i) q^{62} +(-12.0027 - 3.89993i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(6.80692 - 4.32040i) q^{65} +(-1.52644 + 4.69790i) q^{66} +(1.70284 - 2.34375i) q^{67} -6.14099 q^{68} +(11.8049 + 8.57679i) q^{69} +(-7.09701 - 1.65730i) q^{70} +(5.47411 + 7.53446i) q^{71} +(2.27600 + 3.13265i) q^{72} +(-15.3059 + 4.97320i) q^{73} -11.0390 q^{74} +(-11.7518 - 5.80515i) q^{75} -7.17649i q^{76} +(-1.89781 - 5.84086i) q^{77} +(8.38028 - 4.37140i) q^{78} +(5.90276 - 4.28860i) q^{79} +(1.46274 + 1.69127i) q^{80} +(4.54897 + 3.30502i) q^{81} +2.81514 q^{82} +(-5.49316 + 7.56069i) q^{83} +(-8.12593 - 2.64028i) q^{84} +(12.6535 - 5.33355i) q^{85} +(8.88101 - 2.88562i) q^{86} +(4.99076 - 15.3600i) q^{87} +(-0.582281 + 1.79208i) q^{88} +(10.7046 - 3.47812i) q^{89} +(-7.41047 - 4.47809i) q^{90} +(-5.23469 + 10.5212i) q^{91} +(4.50316 + 3.27173i) q^{92} -6.30796i q^{93} +(0.00961837 + 0.00698816i) q^{94} +(6.23290 + 14.7872i) q^{95} +(1.54087 + 2.12082i) q^{96} +(-3.67422 - 5.05713i) q^{97} +(3.44552 - 1.11952i) q^{98} -7.29632i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q + 34 q^{4} - 30 q^{9}+O(q^{10}) $ 136 * q + 34 * q^4 - 30 * q^9	$ 136 q + 34 q^{4} - 30 q^{9} - 4 q^{10} - 12 q^{13} + 8 q^{14} - 34 q^{16} + 4 q^{23} + 40 q^{25} + 4 q^{26} - 12 q^{27} + 16 q^{29} + 10 q^{30} - 18 q^{35} + 30 q^{36} - 24 q^{38} + 32 q^{39} + 4 q^{40} - 12 q^{42} + 24 q^{43} - 104 q^{49} + 84 q^{51} + 12 q^{52} + 4 q^{53} - 60 q^{55} - 8 q^{56} + 12 q^{61} + 18 q^{62} + 34 q^{64} + 26 q^{65} + 16 q^{66} + 84 q^{69} - 88 q^{74} - 214 q^{75} + 56 q^{78} - 8 q^{79} - 74 q^{81} + 160 q^{82} - 164 q^{87} - 16 q^{90} - 40 q^{91} + 16 q^{92} + 48 q^{94} - 4 q^{95}+O(q^{100}) $ 136 * q + 34 * q^4 - 30 * q^9 - 4 * q^10 - 12 * q^13 + 8 * q^14 - 34 * q^16 + 4 * q^23 + 40 * q^25 + 4 * q^26 - 12 * q^27 + 16 * q^29 + 10 * q^30 - 18 * q^35 + 30 * q^36 - 24 * q^38 + 32 * q^39 + 4 * q^40 - 12 * q^42 + 24 * q^43 - 104 * q^49 + 84 * q^51 + 12 * q^52 + 4 * q^53 - 60 * q^55 - 8 * q^56 + 12 * q^61 + 18 * q^62 + 34 * q^64 + 26 * q^65 + 16 * q^66 + 84 * q^69 - 88 * q^74 - 214 * q^75 + 56 * q^78 - 8 * q^79 - 74 * q^81 + 160 * q^82 - 164 * q^87 - 16 * q^90 - 40 * q^91 + 16 * q^92 + 48 * q^94 - 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$	2.12082	−	1.54087i	1.22446	−	0.889621i	0.227995	−	0.973662i	$-0.426783\pi$
$3$	2.12082	−	1.54087i	1.22446	−	0.889621i	0.996462	+	0.0840416i	$0.0267829\pi$
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−1.15648	+	1.91378i	−0.517194	+	0.855868i
$5$	−1.15648	+	1.91378i	−0.517194	+	0.855868i
$6$	−1.54087	+	2.12082i	−0.629057	+	0.865822i
$7$		−	3.25927i		−	1.23189i	−0.787790	−	0.615944i	$-0.788775\pi$
$7$		−	3.25927i		−	1.23189i	0.787790	−	0.615944i	$-0.211225\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	1.19656	−	3.68265i	0.398855	−	1.22755i
$10$	0.508489	−	2.17748i	0.160798	−	0.688581i
$11$	1.79208	−	0.582281i	0.540332	−	0.175564i	−0.0261209	−	0.999659i	$-0.508315\pi$
$11$	1.79208	−	0.582281i	0.540332	−	0.175564i	0.566452	+	0.824094i	$0.308315\pi$
$12$	0.810082	−	2.49318i	0.233851	−	0.719718i
$13$	−3.22807	−	1.60609i	−0.895307	−	0.445450i
$13$	−3.22807	−	1.60609i	−0.895307	−	0.445450i
$14$	1.00717	+	3.09975i	0.269177	+	0.828443i
$15$	0.496187	+	5.84077i	0.128115	+	1.50808i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−4.96816	−	3.60958i	−1.20496	−	0.875452i	−0.210193	−	0.977660i	$-0.567409\pi$
$17$	−4.96816	−	3.60958i	−1.20496	−	0.875452i	−0.994763	+	0.102208i	$0.967409\pi$
$18$			3.87216i			0.912678i
$19$	4.21823	−	5.80590i	0.967729	−	1.33196i	0.0245431	−	0.999699i	$-0.492187\pi$
$19$	4.21823	−	5.80590i	0.967729	−	1.33196i	0.943186	−	0.332266i	$-0.107813\pi$
$20$	0.189277	+	2.22804i	0.0423237	+	0.498205i
$21$	−5.02210	−	6.91233i	−1.09591	−	1.50839i
$22$	−1.52443	+	1.10756i	−0.325010	+	0.236134i
$23$	1.72005	+	5.29378i	0.358656	+	1.10383i	0.953859	+	0.300254i	$0.0970714\pi$
$23$	1.72005	+	5.29378i	0.358656	+	1.10383i	−0.595204	+	0.803575i	$0.702929\pi$
$24$			2.62148i			0.535108i
$25$	−2.32510	−	4.42650i	−0.465020	−	0.885300i
$26$	3.56639	+	0.529955i	0.699427	+	0.103933i
$27$	−0.706525	−	2.17446i	−0.135971	−	0.418475i
$28$	−1.91575	−	2.63680i	−0.362043	−	0.498309i
$29$	4.98419	−	3.62123i	0.925542	−	0.672445i	−0.0193555	−	0.999813i	$-0.506161\pi$
$29$	4.98419	−	3.62123i	0.925542	−	0.672445i	0.944897	+	0.327367i	$0.106161\pi$
$30$	−2.27680	−	5.40157i	−0.415685	−	0.986188i
$31$	1.41436	−	1.94670i	0.254027	−	0.349639i	−0.662889	−	0.748717i	$-0.730670\pi$
$31$	1.41436	−	1.94670i	0.254027	−	0.349639i	0.916917	+	0.399079i	$0.130670\pi$
$32$			1.00000i			0.176777i
$33$	2.90346	−	3.99627i	0.505428	−	0.695661i
$34$	5.84043	+	1.89767i	1.00162	+	0.325448i
$35$	6.23752	+	3.76929i	1.05433	+	0.637125i
$36$	−1.19656	−	3.68265i	−0.199427	−	0.613774i
$37$	10.4987	+	3.41124i	1.72598	+	0.560804i	0.992859	−	0.119297i	$-0.0380639\pi$
$37$	10.4987	+	3.41124i	1.72598	+	0.560804i	0.733119	+	0.680101i	$0.238064\pi$
$38$	−2.21766	+	6.82524i	−0.359751	+	1.10720i
$39$	−9.32095	+	1.56780i	−1.49255	+	0.251049i
$40$	−0.868517	−	2.06050i	−0.137325	−	0.325794i
$41$	−2.67735	−	0.869925i	−0.418132	−	0.135859i	0.0923921	−	0.995723i	$-0.470549\pi$
$41$	−2.67735	−	0.869925i	−0.418132	−	0.135859i	−0.510524	+	0.859863i	$0.670549\pi$
$42$	6.91233	+	5.02210i	1.06660	+	0.774927i
$43$	−9.33805			−1.42404			−0.712019	−	0.702160i	$-0.752219\pi$
$43$	−9.33805			−1.42404			−0.712019	+	0.702160i	$0.752219\pi$
$44$	1.10756	−	1.52443i	0.166972	−	0.229817i
$45$	5.66397	+	6.54887i	0.844334	+	0.976249i
$46$	−3.27173	−	4.50316i	−0.482391	−	0.663954i
$47$	−0.00698816	−	0.00961837i	−0.00101933	−	0.00140298i	0.808507	−	0.588487i	$-0.200276\pi$
$47$	−0.00698816	−	0.00961837i	−0.00101933	−	0.00140298i	−0.809526	+	0.587084i	$0.800276\pi$
$48$	−0.810082	−	2.49318i	−0.116925	−	0.359859i
$49$	−3.62283			−0.517547
$50$	3.57916	+	3.49136i	0.506170	+	0.493753i
$51$	−16.0985			−2.25424
$52$	−3.55560	+	0.598058i	−0.493074	+	0.0829357i
$53$	0.327838	−	0.238188i	0.0450320	−	0.0327177i	−0.565042	−	0.825062i	$-0.691140\pi$
$53$	0.327838	−	0.238188i	0.0450320	−	0.0327177i	0.610074	+	0.792345i	$0.291140\pi$
$54$	1.34389	+	1.84971i	0.182880	+	0.251713i
$55$	−0.958148	+	4.10304i	−0.129197	+	0.553253i
$56$	2.63680	+	1.91575i	0.352358	+	0.256003i
$57$		−	18.8130i		−	2.49185i
$58$	−3.62123	+	4.98419i	−0.475491	+	0.654457i
$59$	−2.62826	−	0.853973i	−0.342170	−	0.111178i	0.132891	−	0.991131i	$-0.457574\pi$
$59$	−2.62826	−	0.853973i	−0.342170	−	0.111178i	−0.475061	+	0.879953i	$0.657574\pi$
$60$	3.83454	+	4.43363i	0.495037	+	0.572379i
$61$	0.995831	+	3.06485i	0.127503	+	0.392414i	0.994349	−	0.106162i	$-0.0338563\pi$
$61$	0.995831	+	3.06485i	0.127503	+	0.392414i	−0.866846	+	0.498576i	$0.833856\pi$
$62$	−0.743575	+	2.28849i	−0.0944341	+	0.290638i
$63$	−12.0027	−	3.89993i	−1.51220	−	0.491344i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	6.80692	−	4.32040i	0.844294	−	0.535880i
$66$	−1.52644	+	4.69790i	−0.187892	+	0.578271i
$67$	1.70284	−	2.34375i	0.208034	−	0.286335i	−0.692231	−	0.721676i	$-0.743372\pi$
$67$	1.70284	−	2.34375i	0.208034	−	0.286335i	0.900266	+	0.435341i	$0.143372\pi$
$68$	−6.14099			−0.744704
$69$	11.8049	+	8.57679i	1.42115	+	1.03252i
$70$	−7.09701	−	1.65730i	−0.848255	−	0.198086i
$71$	5.47411	+	7.53446i	0.649657	+	0.894176i	0.999084	−	0.0427874i	$-0.0136238\pi$
$71$	5.47411	+	7.53446i	0.649657	+	0.894176i	−0.349427	+	0.936963i	$0.613624\pi$
$72$	2.27600	+	3.13265i	0.268229	+	0.369186i
$73$	−15.3059	+	4.97320i	−1.79142	+	0.582069i	−0.999589	−	0.0286662i	$-0.990874\pi$
$73$	−15.3059	+	4.97320i	−1.79142	+	0.582069i	−0.791835	+	0.610735i	$0.790874\pi$
$74$	−11.0390			−1.28326
$75$	−11.7518	−	5.80515i	−1.35698	−	0.670322i
$76$		−	7.17649i		−	0.823199i
$77$	−1.89781	−	5.84086i	−0.216276	−	0.665628i
$78$	8.38028	−	4.37140i	0.948879	−	0.494963i
$79$	5.90276	−	4.28860i	0.664112	−	0.482506i	−0.203937	−	0.978984i	$-0.565374\pi$
$79$	5.90276	−	4.28860i	0.664112	−	0.482506i	0.868049	+	0.496478i	$0.165374\pi$
$80$	1.46274	+	1.69127i	0.163539	+	0.189090i
$81$	4.54897	+	3.30502i	0.505441	+	0.367225i
$82$	2.81514			0.310880
$83$	−5.49316	+	7.56069i	−0.602953	+	0.829894i	−0.995975	−	0.0896356i	$-0.971430\pi$
$83$	−5.49316	+	7.56069i	−0.602953	+	0.829894i	0.393022	+	0.919529i	$0.371430\pi$
$84$	−8.12593	−	2.64028i	−0.886612	−	0.288078i
$85$	12.6535	−	5.33355i	1.37247	−	0.578505i
$86$	8.88101	−	2.88562i	0.957664	−	0.311164i
$87$	4.99076	−	15.3600i	0.535065	−	1.64676i
$88$	−0.582281	+	1.79208i	−0.0620714	+	0.191036i
$89$	10.7046	−	3.47812i	1.13468	−	0.368680i	0.319327	−	0.947644i	$-0.396543\pi$
$89$	10.7046	−	3.47812i	1.13468	−	0.368680i	0.815353	+	0.578964i	$0.196543\pi$
$90$	−7.41047	−	4.47809i	−0.781132	−	0.472032i
$91$	−5.23469	+	10.5212i	−0.548744	+	1.10292i
$92$	4.50316	+	3.27173i	0.469486	+	0.341102i
$93$		−	6.30796i		−	0.654105i
$94$	0.00961837	+	0.00698816i	0.000992059	+	0.000720773i
$95$	6.23290	+	14.7872i	0.639482	+	1.51713i
$96$	1.54087	+	2.12082i	0.157264	+	0.216456i
$97$	−3.67422	−	5.05713i	−0.373060	−	0.513473i	0.580669	−	0.814140i	$-0.302791\pi$
$97$	−3.67422	−	5.05713i	−0.373060	−	0.513473i	−0.953729	+	0.300666i	$0.902791\pi$
$98$	3.44552	−	1.11952i	0.348050	−	0.113088i
$99$		−	7.29632i		−	0.733308i
$100$	−4.48288	−	2.21446i	−0.448288	−	0.221446i
$101$	−2.73616			−0.272258			−0.136129	−	0.990691i	$-0.543466\pi$
$101$	−2.73616			−0.272258			−0.136129	+	0.990691i	$0.543466\pi$
$102$	15.3106	−	4.97470i	1.51597	−	0.492569i
$103$	9.13074	−	6.63387i	0.899679	−	0.653655i	−0.0387049	−	0.999251i	$-0.512323\pi$
$103$	9.13074	−	6.63387i	0.899679	−	0.653655i	0.938383	+	0.345596i	$0.112323\pi$
$104$	3.19677	−	1.66753i	0.313469	−	0.163515i
$105$	19.0366	−	1.61721i	1.85779	−	0.157823i
$106$	−0.238188	+	0.327838i	−0.0231349	+	0.0318424i
$107$	17.0202			1.64540			0.822700	−	0.568475i	$-0.192467\pi$
$107$	17.0202			1.64540			0.822700	+	0.568475i	$0.192467\pi$
$108$	−1.84971	−	1.34389i	−0.177988	−	0.129316i
$109$	0.328181	+	0.106632i	0.0314340	+	0.0102135i	0.324692	−	0.945820i	$-0.394739\pi$
$109$	0.328181	+	0.106632i	0.0314340	+	0.0102135i	−0.293258	+	0.956033i	$0.594739\pi$
$110$	−0.356656	−	4.19830i	−0.0340058	−	0.400293i
$111$	27.5222	−	8.94250i	2.61229	−	0.848784i
$112$	−3.09975	−	1.00717i	−0.292899	−	0.0951686i
$113$	−0.648974	+	1.99734i	−0.0610503	+	0.187894i	−0.976930	−	0.213559i	$-0.931494\pi$
$113$	−0.648974	+	1.99734i	−0.0610503	+	0.187894i	0.915880	+	0.401452i	$0.131494\pi$
$114$	5.81354	+	17.8922i	0.544488	+	1.67576i
$115$	−12.1203	−	2.83036i	−1.13023	−	0.263932i
$116$	1.90379	−	5.85927i	0.176763	−	0.544020i
$117$	−9.77727	+	9.96606i	−0.903909	+	0.921363i
$118$	2.76351			0.254402
$119$	−11.7646	+	16.1926i	−1.07846	+	1.48437i
$120$	−5.01694	−	3.03170i	−0.457981	−	0.276755i
$121$	−6.02670	+	4.37865i	−0.547882	+	0.398059i
$122$	−1.89418	−	2.60712i	−0.171491	−	0.236037i
$123$	−7.01863	+	2.28049i	−0.632849	+	0.205625i
$124$		−	2.40626i		−	0.216088i
$125$	11.1603	+	0.669443i	0.998206	+	0.0598768i
$126$	12.6204			1.12432
$127$	4.30502	+	13.2495i	0.382009	+	1.17570i	0.938627	+	0.344933i	$0.112098\pi$
$127$	4.30502	+	13.2495i	0.382009	+	1.17570i	−0.556619	+	0.830768i	$0.687902\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	−19.8043	+	14.3887i	−1.74368	+	1.26685i
$130$	−5.13868	+	6.21240i	−0.450692	+	0.544864i
$131$	−5.60081	−	4.06923i	−0.489345	−	0.355530i	0.315587	−	0.948896i	$-0.397798\pi$
$131$	−5.60081	−	4.06923i	−0.489345	−	0.355530i	−0.804932	+	0.593367i	$0.797798\pi$
$132$		−	4.93966i		−	0.429942i
$133$	−18.9230	−	13.7484i	−1.64083	−	1.19213i
$134$	−0.895234	+	2.75525i	−0.0773364	+	0.238017i
$135$	4.97852	+	1.16259i	0.428482	+	0.100060i
$136$	5.84043	−	1.89767i	0.500812	−	0.162724i
$137$	−5.76490	−	1.87313i	−0.492529	−	0.160032i	0.0522134	−	0.998636i	$-0.483372\pi$
$137$	−5.76490	−	1.87313i	−0.492529	−	0.160032i	−0.544742	+	0.838604i	$0.683372\pi$
$138$	−13.8775	−	4.50908i	−1.18133	−	0.383839i
$139$	1.19276	+	3.67093i	0.101168	+	0.311364i	0.988812	−	0.149167i	$-0.0476591\pi$
$139$	1.19276	+	3.67093i	0.101168	+	0.311364i	−0.887644	+	0.460531i	$0.847659\pi$
$140$	7.26179	−	0.616906i	0.613733	−	0.0521381i
$141$	−0.0296413	−	0.00963104i	−0.00249625	−	0.000811080i
$142$	−7.53446	−	5.47411i	−0.632278	−	0.459377i
$143$	−6.72016	−	0.998596i	−0.561968	−	0.0835068i
$144$	−3.13265	−	2.27600i	−0.261054	−	0.189667i
$145$	1.16610	+	13.7265i	0.0968394	+	1.13993i
$146$	13.0200	−	9.45959i	1.07754	−	0.782881i
$147$	−7.68338	+	5.58231i	−0.633715	+	0.460421i
$148$	10.4987	−	3.41124i	0.862989	−	0.280402i
$149$			14.1862i			1.16218i	0.813840	+	0.581089i	$0.197373\pi$
$149$			14.1862i			1.16218i	−0.813840	+	0.581089i	$0.802627\pi$
$150$	12.9705	+	1.88953i	1.05904	+	0.154280i
$151$			15.7021i			1.27782i	0.769283	+	0.638908i	$0.220614\pi$
$151$			15.7021i			1.27782i	−0.769283	+	0.638908i	$0.779386\pi$
$152$	2.21766	+	6.82524i	0.179876	+	0.553600i
$153$	−19.2375	+	13.9769i	−1.55526	+	1.12996i
$154$	3.60985	+	4.96853i	0.290890	+	0.400376i
$155$	2.08988	+	4.95811i	0.167863	+	0.398245i
$156$	−6.61928	+	6.74709i	−0.529967	+	0.540200i
$157$	−10.8303			−0.864354			−0.432177	−	0.901789i	$-0.642254\pi$
$157$	−10.8303			−0.864354			−0.432177	+	0.901789i	$0.642254\pi$
$158$	−4.28860	+	5.90276i	−0.341183	+	0.469598i
$159$	0.328270	−	1.01031i	0.0260335	−	0.0801228i
$160$	−1.91378	−	1.15648i	−0.151298	−	0.0914279i
$161$	17.2538	−	5.60611i	1.35979	−	0.441824i
$162$	−5.34764	−	1.73755i	−0.420150	−	0.136515i
$163$	15.1151	+	4.91119i	1.18390	+	0.384674i	0.833816	−	0.552043i	$-0.186151\pi$
$163$	15.1151	+	4.91119i	1.18390	+	0.384674i	0.350089	+	0.936717i	$0.386151\pi$
$164$	−2.67735	+	0.869925i	−0.209066	+	0.0679297i
$165$	4.29018	+	10.1782i	0.333990	+	0.792371i
$166$	2.88793	−	8.88813i	0.224147	−	0.689852i
$167$	−0.0752439	+	0.103564i	−0.00582255	+	0.00801405i	−0.811918	−	0.583771i	$-0.801577\pi$
$167$	−0.0752439	+	0.103564i	−0.00582255	+	0.00801405i	0.806096	+	0.591785i	$0.201577\pi$
$168$	8.54411			0.659193
$169$	7.84093	+	10.3692i	0.603148	+	0.797629i
$170$	−10.3861	+	8.98266i	−0.796575	+	0.688939i
$171$	−16.3337	−	22.4814i	−1.24907	−	1.71920i
$172$	−7.55464	+	5.48877i	−0.576036	+	0.418514i
$173$	1.45887	+	4.48994i	0.110916	+	0.341364i	0.991073	−	0.133318i	$-0.0425632\pi$
$173$	1.45887	+	4.48994i	0.110916	+	0.341364i	−0.880157	+	0.474682i	$0.842563\pi$
$174$			16.1504i			1.22436i
$175$	−14.4272	+	7.57812i	−1.09059	+	0.572852i
$176$		−	1.88430i		−	0.142035i
$177$	−6.88993	+	2.23867i	−0.517879	+	0.168269i
$178$	−9.10584	+	6.61578i	−0.682511	+	0.495873i
$179$	17.1848	−	12.4855i	1.28445	−	0.933210i	0.284775	−	0.958594i	$-0.408081\pi$
$179$	17.1848	−	12.4855i	1.28445	−	0.933210i	0.999678	+	0.0253846i	$0.00808105\pi$
$180$	8.43158	+	1.96895i	0.628453	+	0.146757i
$181$	14.5331	+	10.5589i	1.08024	+	0.784840i	0.977725	−	0.209891i	$-0.0673109\pi$
$181$	14.5331	+	10.5589i	1.08024	+	0.784840i	0.102515	+	0.994731i	$0.467311\pi$
$182$	1.72727	−	11.6238i	0.128034	−	0.861615i
$183$	6.83451	+	4.96556i	0.505222	+	0.367065i
$184$	−5.29378	−	1.72005i	−0.390262	−	0.126804i
$185$	−18.6699	+	16.1472i	−1.37264	+	1.18716i
$186$	1.94927	+	5.99923i	0.142927	+	0.439885i
$187$	−11.0051	−	3.57578i	−0.804774	−	0.261487i
$188$	−0.0113071	−	0.00367389i	−0.000824653	−	0.000267946i
$189$	−7.08715	+	2.30275i	−0.515514	+	0.167501i
$190$	−10.4973	−	12.1374i	−0.761556	−	0.880538i
$191$	−8.34247	+	25.6755i	−0.603640	+	1.85781i	−0.0977550	+	0.995211i	$0.531166\pi$
$191$	−8.34247	+	25.6755i	−0.603640	+	1.85781i	−0.505885	+	0.862601i	$0.668834\pi$
$192$	−2.12082	−	1.54087i	−0.153057	−	0.111203i
$193$		−	0.881554i		−	0.0634557i	−0.999497	−	0.0317278i	$-0.989899\pi$
$193$		−	0.881554i		−	0.0634557i	0.999497	−	0.0317278i	$-0.0101010\pi$
$194$	5.05713	+	3.67422i	0.363081	+	0.263793i
$195$	7.77909	−	19.6514i	0.557072	−	1.40726i
$196$	−2.93093	+	2.12945i	−0.209352	+	0.152103i
$197$	−8.27733	−	11.3928i	−0.589735	−	0.811701i	0.404985	−	0.914323i	$-0.367277\pi$
$197$	−8.27733	−	11.3928i	−0.589735	−	0.811701i	−0.994720	+	0.102622i	$0.967277\pi$
$198$	2.25469	+	6.93922i	0.160234	+	0.493149i
$199$	−24.9470			−1.76845			−0.884223	−	0.467065i	$-0.845311\pi$
$199$	−24.9470			−1.76845			−0.884223	+	0.467065i	$0.845311\pi$
$200$	4.94777	+	0.720788i	0.349860	+	0.0509674i
$201$		−	7.59453i		−	0.535677i
$202$	2.60224	−	0.845521i	0.183093	−	0.0594906i
$203$	−11.8026	−	16.2448i	−0.828377	−	1.14016i
$204$	−13.0239	+	9.46245i	−0.911859	+	0.662504i
$205$	4.76115	−	4.11781i	0.332533	−	0.287600i
$206$	−6.63387	+	9.13074i	−0.462204	+	0.636169i
$207$	21.5533			1.49806
$208$	−2.52502	+	2.57377i	−0.175078	+	0.178459i
$209$	4.17873	−	12.8608i	0.289049	−	0.889601i
$210$	−17.6052	+	7.42070i	−1.21487	+	0.512077i
$211$	−3.97859	−	12.2449i	−0.273898	−	0.842970i	−0.989509	−	0.144472i	$-0.953852\pi$
$211$	−3.97859	−	12.2449i	−0.273898	−	0.842970i	0.715611	−	0.698499i	$-0.246148\pi$
$212$	0.125223	−	0.385397i	0.00860035	−	0.0264691i
$213$	23.2192	+	7.54438i	1.59095	+	0.516933i
$214$	−16.1871	+	5.25952i	−1.10653	+	0.359533i
$215$	10.7993	−	17.8710i	0.736505	−	1.21879i
$216$	2.17446	+	0.706525i	0.147953	+	0.0480729i
$217$	−6.34483	−	4.60979i	−0.430715	−	0.312933i
$218$	−0.345070			−0.0233711
$219$	−24.7981	+	34.1317i	−1.67570	+	2.30641i
$220$	1.63655	+	3.88261i	0.110336	+	0.261766i
$221$	10.2403	+	19.6313i	0.688835	+	1.32055i
$222$	−23.4118	+	17.0096i	−1.57129	+	1.14161i
$223$	11.8400	−	3.84706i	0.792867	−	0.257618i	0.115542	−	0.993303i	$-0.463139\pi$
$223$	11.8400	−	3.84706i	0.792867	−	0.257618i	0.677324	+	0.735685i	$0.263139\pi$
$224$	3.25927			0.217769
$225$	−19.0834	+	3.26592i	−1.27222	+	0.217728i
$226$		−	2.10012i		−	0.139698i
$227$	−1.98673	+	0.645526i	−0.131864	+	0.0428451i	−0.374205	−	0.927346i	$-0.622084\pi$
$227$	−1.98673	+	0.645526i	−0.131864	+	0.0428451i	0.242342	+	0.970191i	$0.422084\pi$
$228$	−11.0580	−	15.2201i	−0.732335	−	1.00797i
$229$	8.39918	+	11.5605i	0.555033	+	0.763938i	0.990684	−	0.136178i	$-0.0434818\pi$
$229$	8.39918	+	11.5605i	0.555033	+	0.763938i	−0.435651	+	0.900116i	$0.643482\pi$
$230$	12.4017	−	1.05356i	0.817747	−	0.0694695i
$231$	−13.0249	−	9.46316i	−0.856977	−	0.622630i
$232$			6.16080i			0.404477i
$233$	22.7169	+	16.5048i	1.48824	+	1.08127i	0.974784	+	0.223149i	$0.0716336\pi$
$233$	22.7169	+	16.5048i	1.48824	+	1.08127i	0.513452	+	0.858118i	$0.328366\pi$
$234$	6.21906	−	12.4996i	0.406552	−	0.817127i
$235$	0.0264891	−	0.00225031i	0.00172796	−	0.000146794i
$236$	−2.62826	+	0.853973i	−0.171085	+	0.0555889i
$237$	5.91053	−	18.1907i	0.383930	−	1.18162i
$238$	6.18501	−	19.0355i	0.400915	−	1.23389i
$239$	14.8302	−	4.81864i	0.959288	−	0.311692i	0.212804	−	0.977095i	$-0.431740\pi$
$239$	14.8302	−	4.81864i	0.959288	−	0.311692i	0.746484	+	0.665403i	$0.231740\pi$
$240$	5.70823	+	1.33300i	0.368465	+	0.0860445i
$241$	13.6708	+	4.44191i	0.880613	+	0.286129i	0.714212	−	0.699929i	$-0.246785\pi$
$241$	13.6708	+	4.44191i	0.880613	+	0.286129i	0.166401	+	0.986058i	$0.446785\pi$
$242$	4.37865	−	6.02670i	0.281470	−	0.387411i
$243$	21.5992			1.38559
$244$	2.60712	+	1.89418i	0.166904	+	0.121263i
$245$	4.18974	−	6.93330i	0.267673	−	0.442952i
$246$	5.97040	−	4.33775i	0.380659	−	0.276565i
$247$	−22.9416	+	11.9670i	−1.45974	+	0.761442i
$248$	0.743575	+	2.28849i	0.0472171	+	0.145319i
$249$			24.4991i			1.55257i
$250$	−10.8209	+	2.81204i	−0.684375	+	0.177849i
$251$	−11.3307			−0.715187			−0.357593	−	0.933877i	$-0.616403\pi$
$251$	−11.3307			−0.715187			−0.357593	+	0.933877i	$0.616403\pi$
$252$	−12.0027	+	3.89993i	−0.756101	+	0.245672i
$253$	6.16493	+	8.48530i	0.387586	+	0.533466i
$254$	−8.18863	−	11.2707i	−0.513800	−	0.707186i
$255$	18.6176	−	30.8089i	1.16588	−	1.92933i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	3.28629			0.204993			0.102497	−	0.994733i	$-0.467317\pi$
$257$	3.28629			0.204993			0.102497	+	0.994733i	$0.467317\pi$
$258$	14.3887	−	19.8043i	0.895801	−	1.23296i
$259$	11.1181	−	34.2181i	0.690848	−	2.12621i
$260$	2.96744	−	7.49628i	0.184033	−	0.464900i
$261$	−7.37180	−	22.6881i	−0.456303	−	1.40436i
$262$	6.58414	+	2.13932i	0.406770	+	0.132168i
$263$	5.01427	−	15.4323i	0.309193	−	0.951598i	−0.668886	−	0.743365i	$-0.733229\pi$
$263$	5.01427	−	15.4323i	0.309193	−	0.951598i	0.978079	−	0.208233i	$-0.0667713\pi$
$264$	1.52644	+	4.69790i	0.0939458	+	0.289136i
$265$	0.0767009	+	0.902869i	0.00471170	+	0.0554628i
$266$	22.2453	+	7.22794i	1.36395	+	0.443173i
$267$	17.3431	−	23.8708i	1.06138	−	1.46087i
$268$		−	2.89704i		−	0.176965i
$269$	−18.7417	−	13.6167i	−1.14270	−	0.830223i	−0.155210	−	0.987881i	$-0.549606\pi$
$269$	−18.7417	−	13.6167i	−1.14270	−	0.830223i	−0.987494	+	0.157658i	$0.949606\pi$
$270$	−5.09411	+	0.432757i	−0.310018	+	0.0263367i
$271$	4.50387	+	6.19904i	0.273590	+	0.376565i	0.923598	−	0.383363i	$-0.125234\pi$
$271$	4.50387	+	6.19904i	0.273590	+	0.376565i	−0.650007	+	0.759928i	$0.725234\pi$
$272$	−4.96816	+	3.60958i	−0.301239	+	0.218863i
$273$	5.10987	+	30.3795i	0.309264	+	1.83865i
$274$	6.06157			0.366193
$275$	−6.74423	−	6.57877i	−0.406692	−	0.396715i
$276$	14.5917			0.878317
$277$	−7.60283	−	23.3991i	−0.456810	−	1.40592i	−0.868997	−	0.494817i	$-0.835235\pi$
$277$	−7.60283	−	23.3991i	−0.456810	−	1.40592i	0.412188	−	0.911099i	$-0.364765\pi$
$278$	−2.26876	−	3.12268i	−0.136071	−	0.187286i
$279$	−5.47665	−	7.53796i	−0.327878	−	0.451286i
$280$	−6.71574	+	2.83073i	−0.401342	+	0.169168i
$281$	3.67311	−	5.05561i	0.219120	−	0.301592i	−0.685279	−	0.728280i	$-0.740320\pi$
$281$	3.67311	−	5.05561i	0.219120	−	0.301592i	0.904399	+	0.426688i	$0.140320\pi$
$282$	0.0311667			0.00185595
$283$	10.5341	+	7.65348i	0.626188	+	0.454952i	0.855077	−	0.518500i	$-0.173510\pi$
$283$	10.5341	+	7.65348i	0.626188	+	0.454952i	−0.228890	+	0.973452i	$0.573510\pi$
$284$	8.85729	+	2.87791i	0.525583	+	0.170772i
$285$	36.0040	+	21.7569i	2.13269	+	1.28877i
$286$	6.69983	−	1.12692i	0.396169	−	0.0666363i
$287$	−2.83532	+	8.72621i	−0.167364	+	0.515092i
$288$	3.68265	+	1.19656i	0.217002	+	0.0705082i
$289$	6.40027	+	19.6980i	0.376487	+	1.15871i
$290$	−5.35076	−	12.6944i	−0.314207	−	0.745439i
$291$	−15.5847	−	5.06379i	−0.913593	−	0.296844i
$292$	−9.45959	+	13.0200i	−0.553580	+	0.761938i
$293$			13.6499i			0.797438i	0.917073	+	0.398719i	$0.130545\pi$
$293$			13.6499i			0.797438i	−0.917073	+	0.398719i	$0.869455\pi$
$294$	5.58231	−	7.68338i	0.325567	−	0.448104i
$295$	4.67385	−	4.04230i	0.272122	−	0.235352i
$296$	−8.93074	+	6.48856i	−0.519089	+	0.377140i
$297$	−2.53229	−	3.48540i	−0.146939	−	0.202244i
$298$	−4.38378	−	13.4919i	−0.253945	−	0.781564i
$299$	2.94984	−	19.8513i	0.170594	−	1.14803i
$300$	−12.9196	+	2.21105i	−0.745912	+	0.127655i
$301$			30.4352i			1.75426i
$302$	−4.85221	−	14.9336i	−0.279213	−	0.859330i
$303$	−5.80291	+	4.21606i	−0.333369	+	0.242207i
$304$	−4.21823	−	5.80590i	−0.241932	−	0.332991i
$305$	−7.01711	−	1.63865i	−0.401798	−	0.0938286i
$306$	13.9769	−	19.2375i	0.799006	−	1.09974i
$307$		−	7.39593i		−	0.422108i	−0.977474	−	0.211054i	$-0.932310\pi$
$307$		−	7.39593i		−	0.422108i	0.977474	−	0.211054i	$-0.0676896\pi$
$308$	−4.96853	−	3.60985i	−0.283108	−	0.205690i
$309$	9.14276	−	28.1385i	0.520114	−	1.60075i
$310$	−3.51973	−	4.06963i	−0.199907	−	0.231140i
$311$	−5.24332	−	16.1373i	−0.297321	−	0.915061i	−0.982432	−	0.186622i	$-0.940246\pi$
$311$	−5.24332	−	16.1373i	−0.297321	−	0.915061i	0.685110	−	0.728439i	$-0.259754\pi$
$312$	4.21034	−	8.46234i	0.238364	−	0.479085i
$313$	3.83953	−	11.8169i	0.217023	−	0.667929i	−0.781981	−	0.623303i	$-0.785790\pi$
$313$	3.83953	−	11.8169i	0.217023	−	0.667929i	0.999004	−	0.0446260i	$-0.0142096\pi$
$314$	10.3002	−	3.34675i	0.581277	−	0.188868i
$315$	21.3445	−	18.4604i	1.20263	−	1.04013i
$316$	2.25465	−	6.93911i	0.126834	−	0.390355i
$317$	−4.40541	+	6.06352i	−0.247432	+	0.340561i	−0.914610	−	0.404337i	$-0.867502\pi$
$317$	−4.40541	+	6.06352i	−0.247432	+	0.340561i	0.667178	+	0.744899i	$0.267502\pi$
$318$			1.06230i			0.0595710i
$319$	6.82349	−	9.39173i	0.382042	−	0.525836i
$320$	2.17748	+	0.508489i	0.121725	+	0.0284254i
$321$	36.0967	−	26.2258i	2.01472	−	1.46378i
$322$	−14.6770	+	10.6635i	−0.817917	+	0.594251i
$323$	−41.9137	+	13.6186i	−2.33214	+	0.757759i
$324$	5.62284			0.312380
$325$	0.396220	+	18.0234i	0.0219783	+	0.999758i
$326$	−15.8929			−0.880228
$327$	0.860321	−	0.279535i	0.0475758	−	0.0154583i
$328$	2.27749	−	1.65470i	0.125753	−	0.0913653i
$329$	−0.0313489	+	0.0227763i	−0.00172832	+	0.00125570i
$330$	−7.22544	−	8.35430i	−0.397747	−	0.459889i
$331$	2.76013	−	3.79900i	0.151711	−	0.208812i	−0.726396	−	0.687276i	$-0.758806\pi$
$331$	2.76013	−	3.79900i	0.151711	−	0.208812i	0.878107	+	0.478464i	$0.158806\pi$
$332$			9.34553i			0.512902i
$333$	25.1248	−	34.5813i	1.37683	−	1.89504i
$334$	0.0395581	−	0.121747i	0.00216452	−	0.00666171i
$335$	2.51612	+	5.96936i	0.137471	+	0.326141i
$336$	−8.12593	+	2.64028i	−0.443306	+	0.144039i
$337$	3.53119	−	10.8679i	0.192356	−	0.592011i	−0.807641	−	0.589674i	$-0.799256\pi$
$337$	3.53119	−	10.8679i	0.192356	−	0.592011i	0.999997	−	0.00233688i	$-0.000743853\pi$
$338$	−10.6614	−	7.43869i	−0.579905	−	0.404611i
$339$	1.70127	+	5.23598i	0.0924005	+	0.284379i
$340$	7.10194	−	11.7525i	0.385157	−	0.637368i
$341$	1.40112	−	4.31220i	0.0758749	−	0.233519i
$342$	22.4814	+	16.3337i	1.21565	+	0.883225i
$343$		−	11.0071i		−	0.594327i
$344$	5.48877	−	7.55464i	0.295934	−	0.407319i
$345$	−30.0663	+	12.6731i	−1.61871	+	0.682299i
$346$	−2.77494	−	3.81937i	−0.149181	−	0.205331i
$347$	−7.86829	+	5.71665i	−0.422392	+	0.306886i	−0.778600	−	0.627521i	$-0.784070\pi$
$347$	−7.86829	+	5.71665i	−0.422392	+	0.306886i	0.356208	+	0.934407i	$0.384070\pi$
$348$	−4.99076	−	15.3600i	−0.267533	−	0.823381i
$349$			3.46234i			0.185335i	0.995697	+	0.0926673i	$0.0295393\pi$
$349$			3.46234i			0.185335i	−0.995697	+	0.0926673i	$0.970461\pi$
$350$	11.3793	−	11.6655i	0.608248	−	0.623545i
$351$	−1.21167	+	8.15406i	−0.0646741	+	0.435232i
$352$	0.582281	+	1.79208i	0.0310357	+	0.0955180i
$353$	1.77492	+	2.44296i	0.0944693	+	0.130026i	0.853635	−	0.520871i	$-0.174393\pi$
$353$	1.77492	+	2.44296i	0.0944693	+	0.130026i	−0.759166	+	0.650897i	$0.774393\pi$
$354$	5.86092	−	4.25821i	0.311505	−	0.226321i
$355$	−20.7500	+	1.76276i	−1.10130	+	0.0935576i
$356$	6.61578	−	9.10584i	0.350635	−	0.482608i
$357$			52.4693i			2.77697i
$358$	−12.4855	+	17.1848i	−0.659879	+	0.908245i
$359$	−27.8290	−	9.04221i	−1.46876	−	0.477229i	−0.538027	−	0.842927i	$-0.680830\pi$
$359$	−27.8290	−	9.04221i	−1.46876	−	0.477229i	−0.930734	+	0.365698i	$0.880830\pi$
$360$	−8.62735	+	0.732913i	−0.454701	+	0.0386279i
$361$	−10.0437	−	30.9112i	−0.528613	−	1.62690i
$362$	−17.0847	−	5.55117i	−0.897954	−	0.291763i
$363$	−6.03463	+	18.5727i	−0.316736	+	0.974813i
$364$	1.94923	+	11.5887i	0.102168	+	0.607411i
$365$	8.18343	−	35.0436i	0.428340	−	1.83427i
$366$	−8.03445	−	2.61055i	−0.419967	−	0.136456i
$367$	14.1007	+	10.2447i	0.736049	+	0.534771i	0.891471	−	0.453077i	$-0.149674\pi$
$367$	14.1007	+	10.2447i	0.736049	+	0.534771i	−0.155422	+	0.987848i	$0.549674\pi$
$368$	5.56621			0.290159
$369$	−6.40725	+	8.81882i	−0.333548	+	0.459090i
$370$	12.7664	−	21.1262i	0.663694	−	1.09830i
$371$	−0.776319	−	1.06851i	−0.0403045	−	0.0554744i
$372$	−3.70773	−	5.10325i	−0.192237	−	0.264591i
$373$	−5.52804	−	17.0135i	−0.286231	−	0.880928i	−0.986027	−	0.166585i	$-0.946726\pi$
$373$	−5.52804	−	17.0135i	−0.286231	−	0.880928i	0.699796	−	0.714343i	$-0.253274\pi$
$374$	11.5715			0.598347
$375$	24.7005	−	15.7767i	1.27553	−	0.814708i
$376$	0.0118890			0.000613126
$377$	−21.9054	+	3.68452i	−1.12818	+	0.189762i
$378$	6.02869	−	4.38010i	0.310082	−	0.225288i
$379$	5.26534	+	7.24713i	0.270463	+	0.372260i	0.922546	−	0.385888i	$-0.126105\pi$
$379$	5.26534	+	7.24713i	0.270463	+	0.372260i	−0.652083	+	0.758147i	$0.726105\pi$
$380$	13.7342	+	8.29948i	0.704550	+	0.425754i
$381$	29.5459	+	21.4663i	1.51368	+	1.09975i
$382$		−	26.9968i		−	1.38128i
$383$	−9.33995	+	12.8553i	−0.477249	+	0.656877i	−0.977973	−	0.208730i	$-0.933067\pi$
$383$	−9.33995	+	12.8553i	−0.477249	+	0.656877i	0.500724	+	0.865607i	$0.333067\pi$
$384$	2.49318	+	0.810082i	0.127229	+	0.0413393i
$385$	13.3729	+	3.12286i	0.681546	+	0.159156i
$386$	0.272415	+	0.838408i	0.0138656	+	0.0426738i
$387$	−11.1736	+	34.3887i	−0.567985	+	1.74808i
$388$	−5.94501	−	1.93165i	−0.301812	−	0.0980647i
$389$	4.30449	+	13.2479i	0.218246	+	0.671693i	0.998907	+	0.0467383i	$0.0148827\pi$
$389$	4.30449	+	13.2479i	0.218246	+	0.671693i	−0.780661	+	0.624955i	$0.785117\pi$
$390$	−1.32575	+	21.0934i	−0.0671320	+	1.06811i
$391$	10.5628	−	32.5090i	0.534185	−	1.64405i
$392$	2.12945	−	2.93093i	0.107553	−	0.148034i
$393$	−18.1485			−0.915469
$394$	11.3928	+	8.27733i	0.573959	+	0.417006i
$395$	1.38101	+	16.2563i	0.0694860	+	0.817941i
$396$	−4.28867	−	5.90285i	−0.215514	−	0.296629i
$397$	−6.47802	−	8.91623i	−0.325122	−	0.447493i	0.614900	−	0.788605i	$-0.289196\pi$
$397$	−6.47802	−	8.91623i	−0.325122	−	0.447493i	−0.940023	+	0.341112i	$0.889196\pi$
$398$	23.7260	−	7.70905i	1.18928	−	0.386420i
$399$	−61.3167			−3.06967
$400$	−4.92835	+	0.843436i	−0.246417	+	0.0421718i
$401$			15.2165i			0.759877i	0.925012	+	0.379939i	$0.124055\pi$
$401$			15.2165i			0.759877i	−0.925012	+	0.379939i	$0.875945\pi$
$402$	2.34684	+	7.22282i	0.117050	+	0.360242i
$403$	−7.69226	+	4.01251i	−0.383179	+	0.199877i
$404$	−2.21360	+	1.60828i	−0.110131	+	0.0800147i
$405$	−11.5859	+	4.88353i	−0.575707	+	0.242664i
$406$	16.2448	+	11.8026i	0.806217	+	0.585751i
$407$	20.8008			1.03106
$408$	9.46245	−	13.0239i	0.468461	−	0.644781i
$409$	−1.20303	−	0.390889i	−0.0594862	−	0.0193282i	0.279123	−	0.960255i	$-0.409956\pi$
$409$	−1.20303	−	0.390889i	−0.0594862	−	0.0193282i	−0.338609	+	0.940927i	$0.609956\pi$
$410$	−3.25565	+	5.38755i	−0.160785	+	0.266072i
$411$	−15.1126	+	4.91037i	−0.745448	+	0.242211i
$412$	3.48763	−	10.7338i	0.171823	−	0.528818i
$413$	−2.78333	+	8.56620i	−0.136959	+	0.421515i
$414$	−20.4984	+	6.66032i	−1.00744	+	0.327337i
$415$	−8.11675	−	19.2565i	−0.398435	−	0.945265i
$416$	1.60609	−	3.22807i	0.0787452	−	0.158269i
$417$	8.18604	+	5.94750i	0.400872	+	0.291251i
$418$			13.5227i			0.661415i
$419$	−27.9892	−	20.3353i	−1.36736	−	0.993447i	−0.997938	−	0.0641858i	$-0.979555\pi$
$419$	−27.9892	−	20.3353i	−1.36736	−	0.993447i	−0.369424	−	0.929261i	$-0.620445\pi$
$420$	14.4504	−	12.4978i	0.705107	−	0.609831i
$421$	−13.7988	−	18.9924i	−0.672513	−	0.925635i	0.327301	−	0.944920i	$-0.393861\pi$
$421$	−13.7988	−	18.9924i	−0.672513	−	0.925635i	−0.999814	+	0.0192853i	$0.993861\pi$
$422$	7.56773	+	10.4161i	0.368392	+	0.507047i
$423$	−0.0437829	+	0.0142259i	−0.00212880	+	0.000691687i
$424$			0.405230i			0.0196797i
$425$	−4.42635	+	30.3842i	−0.214709	+	1.47385i
$426$	−24.4141			−1.18287
$427$	9.98917	−	3.24568i	0.483410	−	0.157069i
$428$	13.7696	−	10.0042i	0.665578	−	0.483571i
$429$	−15.7910	+	8.23703i	−0.762395	+	0.397688i
$430$	−4.74830	+	20.3335i	−0.228983	+	0.980566i
$431$	4.99648	−	6.87707i	0.240672	−	0.331257i	−0.671545	−	0.740964i	$-0.734369\pi$
$431$	4.99648	−	6.87707i	0.240672	−	0.331257i	0.912217	+	0.409707i	$0.134369\pi$
$432$	−2.28636			−0.110003
$433$	4.85945	+	3.53060i	0.233530	+	0.169670i	0.698396	−	0.715711i	$-0.253897\pi$
$433$	4.85945	+	3.53060i	0.233530	+	0.169670i	−0.464866	+	0.885381i	$0.653897\pi$
$434$	7.45880	+	2.42351i	0.358034	+	0.116332i
$435$	23.6239	+	27.3147i	1.13268	+	1.30964i
$436$	0.328181	−	0.106632i	0.0157170	−	0.00510677i
$437$	37.9907	+	12.3439i	1.81734	+	0.590490i
$438$	13.0371	−	40.1242i	0.622939	−	1.91721i
$439$	−3.01971	−	9.29370i	−0.144123	−	0.443564i	0.852774	−	0.522279i	$-0.174918\pi$
$439$	−3.01971	−	9.29370i	−0.144123	−	0.443564i	−0.996897	+	0.0787154i	$0.974918\pi$
$440$	−2.75624	−	3.18686i	−0.131399	−	0.151928i
$441$	−4.33495	+	13.3416i	−0.206426	+	0.635315i
$442$	−15.8055	−	15.5061i	−0.751791	−	0.737549i
$443$	5.05295			0.240073			0.120036	−	0.992769i	$-0.461699\pi$
$443$	5.05295			0.240073			0.120036	+	0.992769i	$0.461699\pi$
$444$	17.0096	−	23.4118i	0.807242	−	1.11107i
$445$	−5.72327	+	24.5085i	−0.271309	+	1.16182i
$446$	−10.0717	+	7.31754i	−0.476910	+	0.346496i
$447$	21.8591	+	30.0864i	1.03390	+	1.42304i
$448$	−3.09975	+	1.00717i	−0.146449	+	0.0475843i
$449$		−	27.2361i		−	1.28535i	−0.766139	−	0.642675i	$-0.777825\pi$
$449$		−	27.2361i		−	1.28535i	0.766139	−	0.642675i	$-0.222175\pi$
$450$	17.1401	−	9.00316i	0.807994	−	0.424413i
$451$	−5.30456			−0.249782
$452$	0.648974	+	1.99734i	0.0305252	+	0.0939468i
$453$	24.1948	+	33.3013i	1.13677	+	1.56463i
$454$	1.69001	−	1.22786i	0.0793161	−	0.0576265i
$455$	−14.0814	−	22.1856i	−0.660144	−	1.04008i
$456$	15.2201	+	11.0580i	0.712744	+	0.517839i
$457$		−	31.3348i		−	1.46578i	−0.680346	−	0.732891i	$-0.738171\pi$
$457$		−	31.3348i		−	1.46578i	0.680346	−	0.732891i	$-0.261829\pi$
$458$	−11.5605	−	8.39918i	−0.540186	−	0.392468i
$459$	−4.33876	+	13.3533i	−0.202516	+	0.623280i
$460$	−11.4692	+	4.83434i	−0.534754	+	0.225402i
$461$	−30.2330	+	9.82330i	−1.40809	+	0.457517i	−0.911799	−	0.410638i	$-0.865306\pi$
$461$	−30.2330	+	9.82330i	−1.40809	+	0.457517i	−0.496294	+	0.868155i	$0.665306\pi$
$462$	15.3117	+	4.97508i	0.712365	+	0.231461i
$463$	6.28243	+	2.04129i	0.291969	+	0.0948666i	0.451340	−	0.892352i	$-0.350946\pi$
$463$	6.28243	+	2.04129i	0.291969	+	0.0948666i	−0.159370	+	0.987219i	$0.550946\pi$
$464$	−1.90379	−	5.85927i	−0.0883814	−	0.272010i
$465$	12.0720	+	7.29505i	0.559828	+	0.338300i
$466$	−26.7054	−	8.67710i	−1.23710	−	0.401959i
$467$	6.79440	+	4.93642i	0.314407	+	0.228430i	0.733785	−	0.679381i	$-0.237752\pi$
$467$	6.79440	+	4.93642i	0.314407	+	0.228430i	−0.419378	+	0.907812i	$0.637752\pi$
$468$	−2.05207	+	13.8097i	−0.0948572	+	0.638351i
$469$	−7.63892	−	5.55000i	−0.352732	−	0.256275i
$470$	−0.0244973	+	0.0103258i	−0.00112997	+	0.000476292i
$471$	−22.9692	+	16.6881i	−1.05836	+	0.768947i
$472$	2.23573	−	1.62435i	0.102908	−	0.0747669i
$473$	−16.7345	+	5.43737i	−0.769453	+	0.250010i
$474$			19.1269i			0.878526i
$475$	−35.5076	−	5.17272i	−1.62920	−	0.237341i
$476$			20.0151i			0.917392i
$477$	−0.484884	−	1.49232i	−0.0222013	−	0.0683286i
$478$	−12.6154	+	9.16559i	−0.577013	+	0.419224i
$479$	5.55890	+	7.65117i	0.253992	+	0.349591i	0.916905	−	0.399107i	$-0.130680\pi$
$479$	5.55890	+	7.65117i	0.253992	+	0.349591i	−0.662912	+	0.748697i	$0.730680\pi$
$480$	−5.84077	+	0.496187i	−0.266594	+	0.0226477i
$481$	−28.4119	−	27.8736i	−1.29547	−	1.27093i
$482$	−14.3743			−0.654733
$483$	27.9541	−	38.4755i	1.27195	−	1.75069i
$484$	−2.30199	+	7.08481i	−0.104636	+	0.322037i
$485$	13.9274	−	1.18316i	0.632410	−	0.0537247i
$486$	−20.5421	+	6.67454i	−0.931809	+	0.302763i
$487$	−18.5056	−	6.01284i	−0.838569	−	0.272468i	−0.141919	−	0.989878i	$-0.545327\pi$
$487$	−18.5056	−	6.01284i	−0.838569	−	0.272468i	−0.696651	+	0.717411i	$0.745327\pi$
$488$	−3.06485	−	0.995831i	−0.138739	−	0.0450791i
$489$	39.6239	−	12.8746i	1.79185	−	0.582209i
$490$	−1.84217	+	7.88866i	−0.0832208	+	0.356373i
$491$	−8.80255	+	27.0915i	−0.397254	+	1.22262i	0.529939	+	0.848036i	$0.322215\pi$
$491$	−8.80255	+	27.0915i	−0.397254	+	1.22262i	−0.927193	+	0.374585i	$0.877785\pi$
$492$	−4.33775	+	5.97040i	−0.195561	+	0.269167i
$493$	−37.8334			−1.70393
$494$	18.1207	−	18.4706i	0.815290	−	0.831033i
$495$	13.9636	+	8.43807i	0.627615	+	0.379263i
$496$	−1.41436	−	1.94670i	−0.0635068	−	0.0874096i
$497$	24.5568	−	17.8416i	1.10152	−	0.800304i
$498$	−7.57065	−	23.3001i	−0.339249	−	1.04410i
$499$		−	19.2944i		−	0.863738i	−0.901936	−	0.431869i	$-0.857854\pi$
$499$		−	19.2944i		−	0.863738i	0.901936	−	0.431869i	$-0.142146\pi$
$500$	9.42234	−	6.01826i	0.421380	−	0.269145i
$501$			0.335583i			0.0149927i
$502$	10.7761	−	3.50138i	0.480962	−	0.156274i
$503$	12.0859	−	8.78095i	0.538885	−	0.391523i	−0.284786	−	0.958591i	$-0.591922\pi$
$503$	12.0859	−	8.78095i	0.538885	−	0.391523i	0.823671	+	0.567068i	$0.191922\pi$
$504$	10.2101	−	7.41810i	0.454796	−	0.330428i
$505$	3.16432	−	5.23641i	0.140810	−	0.233017i
$506$	−8.48530	−	6.16493i	−0.377218	−	0.274065i
$507$	32.6068	+	9.90935i	1.44812	+	0.440090i
$508$	11.2707	+	8.18863i	0.500056	+	0.363312i
$509$	30.6728	+	9.96619i	1.35955	+	0.441743i	0.895892	−	0.444272i	$-0.146538\pi$
$509$	30.6728	+	9.96619i	1.35955	+	0.441743i	0.463655	+	0.886016i	$0.346538\pi$
$510$	−8.18591	+	35.0542i	−0.362478	+	1.55223i
$511$	16.2090	+	49.8861i	0.717044	+	2.20683i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	−15.6050	−	5.07036i	−0.688976	−	0.223862i
$514$	−3.12545	+	1.01552i	−0.137858	+	0.0447926i
$515$	2.13623	+	25.1462i	0.0941334	+	1.10807i
$516$	−7.56459	+	23.2814i	−0.333012	+	1.02491i
$517$	−0.0181239	−	0.0131678i	−0.000797089	−	0.000579119i
$518$			35.9791i			1.58083i
$519$	10.0124	+	7.27444i	0.439496	+	0.319313i
$520$	−0.505726	+	8.04638i	−0.0221775	+	0.352857i
$521$	12.8903	−	9.36538i	0.564736	−	0.410305i	−0.268453	−	0.963293i	$-0.586512\pi$
$521$	12.8903	−	9.36538i	0.564736	−	0.410305i	0.833189	+	0.552988i	$0.186512\pi$
$522$	14.0220	+	19.2996i	0.613726	+	0.844721i
$523$	−12.1537	−	37.4051i	−0.531442	−	1.63561i	−0.751213	−	0.660060i	$-0.770531\pi$
$523$	−12.1537	−	37.4051i	−0.531442	−	1.63561i	0.219770	−	0.975552i	$-0.429469\pi$
$524$	−6.92298			−0.302432
$525$	−18.9206	+	38.3022i	−0.825761	+	1.67165i
$526$			16.2265i			0.707509i
$527$	−14.0536	+	4.56628i	−0.612184	+	0.198910i
$528$	−2.90346	−	3.99627i	−0.126357	−	0.173915i
$529$	−6.45810	+	4.69209i	−0.280787	+	0.204004i
$530$	−0.351949	−	0.834978i	−0.0152877	−	0.0362691i
$531$	−6.28976	+	8.65711i	−0.272952	+	0.375687i
$532$	−23.3901			−1.01409
$533$	7.24552	+	7.10826i	0.313838	+	0.307893i
$534$	−9.11783	+	28.0618i	−0.394567	+	1.21435i
$535$	−19.6835	+	32.5728i	−0.850992	+	1.40825i
$536$	0.895234	+	2.75525i	0.0386682	+	0.119008i
$537$	17.2074	−	52.9590i	0.742556	−	2.28535i
$538$	22.0322	+	7.15871i	0.949877	+	0.308634i
$539$	−6.49239	+	2.10951i	−0.279647	+	0.0908629i
$540$	4.71106	−	1.98574i	0.202732	−	0.0854528i
$541$	4.56375	+	1.48285i	0.196211	+	0.0637528i	0.405474	−	0.914107i	$-0.367106\pi$
$541$	4.56375	+	1.48285i	0.196211	+	0.0637528i	−0.209263	+	0.977859i	$0.567106\pi$
$542$	−6.19904	−	4.50387i	−0.266272	−	0.193458i
$543$	47.0922			2.02092
$544$	3.60958	−	4.96816i	0.154760	−	0.213008i
$545$	−0.583607	+	0.504747i	−0.0249990	+	0.0216210i
$546$	−14.2476	−	27.3136i	−0.609739	−	1.16891i
$547$	−2.40561	+	1.74778i	−0.102857	+	0.0747296i	−0.638025	−	0.770016i	$-0.720248\pi$
$547$	−2.40561	+	1.74778i	−0.102857	+	0.0747296i	0.535168	+	0.844746i	$0.320248\pi$
$548$	−5.76490	+	1.87313i	−0.246264	+	0.0800161i
$549$	12.4783			0.532563
$550$	8.44709	+	4.17270i	0.360185	+	0.177925i
$551$		−	44.2129i		−	1.88353i
$552$	−13.8775	+	4.50908i	−0.590667	+	0.191919i
$553$	−13.9777	−	19.2387i	−0.594393	−	0.818111i
$554$	14.4614	+	19.9045i	0.614408	+	0.845660i
$555$	−14.7149	+	63.0132i	−0.624614	+	2.67476i
$556$	3.12268	+	2.26876i	0.132431	+	0.0962167i
$557$			11.4540i			0.485319i	0.970111	+	0.242660i	$0.0780199\pi$
$557$			11.4540i			0.485319i	−0.970111	+	0.242660i	$0.921980\pi$
$558$	7.53796	+	5.47665i	0.319107	+	0.231845i
$559$	30.1439	+	14.9978i	1.27495	+	0.634338i
$560$	5.51230	−	4.76746i	0.232937	−	0.201462i
$561$	−28.8497	+	9.37384i	−1.21804	+	0.395764i
$562$	−1.93107	+	5.94322i	−0.0814573	+	0.250700i
$563$	−10.2870	+	31.6600i	−0.433543	+	1.33431i	0.461029	+	0.887385i	$0.347481\pi$
$563$	−10.2870	+	31.6600i	−0.433543	+	1.33431i	−0.894572	+	0.446924i	$0.852519\pi$
$564$	−0.0296413	+	0.00963104i	−0.00124812	+	0.000405540i
$565$	−3.07193	−	3.55188i	−0.129237	−	0.149429i
$566$	−12.3836	−	4.02367i	−0.520521	−	0.169127i
$567$	10.7720	−	14.8263i	0.452379	−	0.622647i
$568$	−9.31311			−0.390769
$569$	3.69032	+	2.68117i	0.154706	+	0.112401i	0.662445	−	0.749110i	$-0.269519\pi$
$569$	3.69032	+	2.68117i	0.154706	+	0.112401i	−0.507739	+	0.861511i	$0.669519\pi$
$570$	−40.9651	−	9.56622i	−1.71584	−	0.400685i
$571$	5.30627	−	3.85523i	0.222061	−	0.161337i	−0.471193	−	0.882030i	$-0.656177\pi$
$571$	5.30627	−	3.85523i	0.222061	−	0.161337i	0.693254	+	0.720694i	$0.256177\pi$
$572$	−6.02368	+	3.14213i	−0.251863	+	0.131379i
$573$	21.8696	+	67.3078i	0.913616	+	2.81182i
$574$		−	9.17528i		−	0.382969i
$575$	19.4336	−	19.9224i	0.810438	−	0.830820i
$576$	−3.87216			−0.161340
$577$	44.0295	−	14.3061i	1.83297	−	0.595569i	0.833929	−	0.551872i	$-0.186086\pi$
$577$	44.0295	−	14.3061i	1.83297	−	0.595569i	0.999045	−	0.0436973i	$-0.0139137\pi$
$578$	−12.1740	−	16.7561i	−0.506373	−	0.696963i
$579$	−1.35836	−	1.86962i	−0.0564515	−	0.0776988i
$580$	9.01165	+	10.4196i	0.374188	+	0.432650i
$581$	24.6423	+	17.9037i	1.02234	+	0.742770i
$582$	16.3868			0.679253
$583$	0.448818	−	0.617745i	0.0185882	−	0.0255844i
$584$	4.97320	−	15.3059i	0.205792	−	0.633364i
$585$	−7.76560	−	30.2371i	−0.321068	−	1.25015i
$586$	−4.21806	−	12.9819i	−0.174247	−	0.536276i
$587$	−38.1772	−	12.4045i	−1.57574	−	0.511990i	−0.614787	−	0.788693i	$-0.710758\pi$
$587$	−38.1772	−	12.4045i	−1.57574	−	0.511990i	−0.960955	+	0.276703i	$0.910758\pi$
$588$	−2.93479	+	9.03236i	−0.121029	+	0.372488i
$589$	−5.33626	−	16.4233i	−0.219877	−	0.676711i
$590$	−3.19595	+	5.28875i	−0.131575	+	0.217735i
$591$	−35.1095	−	11.4078i	−1.44421	−	0.469253i
$592$	6.48856	−	8.93074i	0.266678	−	0.367051i
$593$		−	3.60619i		−	0.148088i	−0.997255	−	0.0740442i	$-0.976409\pi$
$593$		−	3.60619i		−	0.148088i	0.997255	−	0.0740442i	$-0.0235906\pi$
$594$	3.48540	+	2.53229i	0.143008	+	0.103901i
$595$	−17.3835	−	41.2413i	−0.712653	−	1.69073i
$596$	8.33844	+	11.4769i	0.341556	+	0.470111i
$597$	−52.9082	+	38.4400i	−2.16539	+	1.57325i
$598$	3.32891	+	19.7912i	0.136129	+	0.809324i
$599$	−29.5182			−1.20608			−0.603040	−	0.797711i	$-0.706044\pi$
$599$	−29.5182			−1.20608			−0.603040	+	0.797711i	$0.706044\pi$
$600$	11.6040	−	6.09520i	0.473731	−	0.248836i
$601$	0.728658			0.0297226			0.0148613	−	0.999890i	$-0.495269\pi$
$601$	0.728658			0.0297226			0.0148613	+	0.999890i	$0.495269\pi$
$602$	−9.40499	−	28.9456i	−0.383319	−	1.17973i
$603$	−6.59366	−	9.07539i	−0.268515	−	0.369579i
$604$	9.22944	+	12.7032i	0.375541	+	0.516888i
$605$	−1.41000	−	16.5976i	−0.0573249	−	0.674788i
$606$	4.21606	−	5.80291i	0.171266	−	0.235727i
$607$	31.2457			1.26822			0.634111	−	0.773242i	$-0.281366\pi$
$607$	31.2457			1.26822			0.634111	+	0.773242i	$0.281366\pi$
$608$	5.80590	+	4.21823i	0.235460	+	0.171072i
$609$	−50.0623	−	16.2662i	−2.02863	−	0.659140i
$610$	7.18003	−	0.609961i	0.290711	−	0.0246966i
$611$	0.00711029	+	0.0422725i	0.000287652	+	0.00171016i
$612$	−7.34809	+	22.6151i	−0.297029	+	0.914161i
$613$	13.6034	+	4.42002i	0.549437	+	0.178523i	0.570563	−	0.821254i	$-0.306725\pi$
$613$	13.6034	+	4.42002i	0.549437	+	0.178523i	−0.0211260	+	0.999777i	$0.506725\pi$
$614$	2.28547	+	7.03394i	0.0922340	+	0.283867i
$615$	3.75256	−	16.0695i	0.151318	−	0.647983i
$616$	5.84086	+	1.89781i	0.235335	+	0.0764650i
$617$	24.1097	−	33.1842i	0.970622	−	1.33595i	0.0288896	−	0.999583i	$-0.490803\pi$
$617$	24.1097	−	33.1842i	0.970622	−	1.33595i	0.941732	−	0.336364i	$-0.109197\pi$
$618$			29.5866i			1.19015i
$619$	21.6901	−	29.8538i	0.871798	−	1.19993i	−0.106827	−	0.994278i	$-0.534069\pi$
$619$	21.6901	−	29.8538i	0.871798	−	1.19993i	0.978626	−	0.205650i	$-0.0659307\pi$
$620$	4.60505	+	2.78280i	0.184943	+	0.111760i
$621$	10.2958	−	7.48037i	0.413158	−	0.300177i
$622$	9.97339	+	13.7272i	0.399897	+	0.550410i
$623$	−11.3361	−	34.8890i	−0.454172	−	1.39780i
$624$	−1.38927	+	9.34923i	−0.0556152	+	0.374269i
$625$	−14.1878	+	20.5841i	−0.567513	+	0.823364i
$626$			12.4250i			0.496603i
$627$	−10.9545	−	33.7144i	−0.437479	−	1.34642i
$628$	−8.76191	+	6.36590i	−0.349638	+	0.254027i
$629$	−39.8462	−	54.8435i	−1.58877	−	2.18676i
$630$	−14.5953	+	24.1527i	−0.581490	+	0.962267i
$631$	−11.9090	+	16.3914i	−0.474091	+	0.652530i	−0.977356	−	0.211602i	$-0.932132\pi$
$631$	−11.9090	+	16.3914i	−0.474091	+	0.652530i	0.503265	+	0.864132i	$0.332132\pi$
$632$			7.29621i			0.290228i
$633$	−27.3056	−	19.8387i	−1.08530	−	0.788516i
$634$	2.31606	−	7.12810i	0.0919825	−	0.283093i
$635$	−30.3353	−	7.08393i	−1.20382	−	0.281117i
$636$	−0.328270	−	1.01031i	−0.0130167	−	0.0400614i
$637$	11.6948	+	5.81860i	0.463364	+	0.230542i
$638$	−3.58732	+	11.0406i	−0.142023	+	0.437103i
$639$	34.2969	−	11.1437i	1.35676	−	0.440839i
$640$	−2.22804	+	0.189277i	−0.0880711	+	0.00748185i
$641$	5.20628	−	16.0233i	0.205636	−	0.632881i	−0.794051	−	0.607851i	$-0.792032\pi$
$641$	5.20628	−	16.0233i	0.205636	−	0.632881i	0.999687	−	0.0250304i	$-0.00796824\pi$
$642$	−26.2258	+	36.0967i	−1.03505	+	1.42462i
$643$			12.3715i			0.487886i	0.969790	+	0.243943i	$0.0784409\pi$
$643$			12.3715i			0.487886i	−0.969790	+	0.243943i	$0.921559\pi$
$644$	10.6635	−	14.6770i	0.420199	−	0.578355i
$645$	−4.63342	−	54.5414i	−0.182441	−	2.14757i
$646$	35.6539	−	25.9041i	1.40279	−	1.01918i
$647$	−25.6142	+	18.6098i	−1.00700	+	0.731627i	−0.963577	−	0.267430i	$-0.913826\pi$
$647$	−25.6142	+	18.6098i	−1.00700	+	0.731627i	−0.0434207	+	0.999057i	$0.513826\pi$
$648$	−5.34764	+	1.73755i	−0.210075	+	0.0682575i
$649$	−5.20729			−0.204404
$650$	−5.94637	−	17.0188i	−0.233236	−	0.667534i
$651$	−20.5594			−0.805784
$652$	15.1151	−	4.91119i	0.591952	−	0.192337i
$653$	−28.9304	+	21.0192i	−1.13213	+	0.822543i	−0.986004	−	0.166722i	$-0.946682\pi$
$653$	−28.9304	+	21.0192i	−1.13213	+	0.822543i	−0.146130	+	0.989265i	$0.546682\pi$
$654$	−0.731832	+	0.531707i	−0.0286169	+	0.0207914i
$655$	14.2648	−	6.01272i	0.557373	−	0.234937i
$656$	−1.65470	+	2.27749i	−0.0646050	+	0.0889211i
$657$			62.3171i			2.43122i
$658$	0.0227763	−	0.0313489i	0.000887912	−	0.00122211i
$659$	−8.13147	+	25.0261i	−0.316757	+	0.974878i	0.658268	+	0.752784i	$0.271289\pi$
$659$	−8.13147	+	25.0261i	−0.316757	+	0.974878i	−0.975025	+	0.222095i	$0.928711\pi$
$660$	9.45342	+	5.71263i	0.367974	+	0.222364i
$661$	9.74022	−	3.16479i	0.378851	−	0.123096i	−0.113400	−	0.993549i	$-0.536174\pi$
$661$	9.74022	−	3.16479i	0.378851	−	0.123096i	0.492251	+	0.870453i	$0.336174\pi$
$662$	−1.45109	+	4.46599i	−0.0563981	+	0.173576i
$663$	51.9671	+	25.8557i	2.01823	+	1.00415i
$664$	−2.88793	−	8.88813i	−0.112073	−	0.344926i
$665$	48.1954	−	20.3147i	1.86894	−	0.787770i
$666$	−13.2089	+	40.6527i	−0.511833	+	1.57526i
$667$	27.7431	+	20.1565i	1.07422	+	0.780463i
$668$			0.128013i			0.00495296i
$669$	19.1828	−	26.4028i	0.741650	−	1.02079i
$670$	−4.23761	−	4.89967i	−0.163713	−	0.189291i
$671$	3.56921	+	4.91260i	0.137788	+	0.189649i
$672$	6.91233	−	5.02210i	0.266649	−	0.193732i
$673$	11.0739	+	34.0818i	0.426866	+	1.31376i	0.901196	+	0.433411i	$0.142690\pi$
$673$	11.0739	+	34.0818i	0.426866	+	1.31376i	−0.474330	+	0.880347i	$0.657310\pi$
$674$			11.4272i			0.440158i
$675$	−7.98251	+	8.18326i	−0.307247	+	0.314974i
$676$	12.4383	+	3.78006i	0.478396	+	0.145387i
$677$	3.21383	+	9.89116i	0.123518	+	0.380148i	0.993628	−	0.112709i	$-0.0359526\pi$
$677$	3.21383	+	9.89116i	0.123518	+	0.380148i	−0.870110	+	0.492857i	$0.835953\pi$
$678$	−3.23601	−	4.45399i	−0.124278	−	0.171055i
$679$	−16.4825	+	11.9753i	−0.632542	+	0.459568i
$680$	−3.12263	+	13.3719i	−0.119747	+	0.512789i
$681$	−3.21882	+	4.43033i	−0.123346	+	0.169771i
$682$			4.53412i			0.173620i
$683$	−4.66454	+	6.42020i	−0.178484	+	0.245662i	−0.888880	−	0.458140i	$-0.848516\pi$
$683$	−4.66454	+	6.42020i	−0.178484	+	0.245662i	0.710396	+	0.703802i	$0.248516\pi$
$684$	−26.4285	−	8.58713i	−1.01052	−	0.328337i
$685$	10.2518	−	8.86650i	0.391700	−	0.338772i
$686$	3.40138	+	10.4684i	0.129865	+	0.399684i
$687$	35.6263	+	11.5757i	1.35923	+	0.441641i
$688$	−2.88562	+	8.88101i	−0.110013	+	0.338585i
$689$	−1.44084	+	0.242351i	−0.0548915	+	0.00923284i
$690$	24.6785	−	21.3439i	0.939495	−	0.812547i
$691$	13.3417	+	4.33498i	0.507542	+	0.164910i	0.551584	−	0.834119i	$-0.314024\pi$
$691$	13.3417	+	4.33498i	0.507542	+	0.164910i	−0.0440422	+	0.999030i	$0.514024\pi$
$692$	3.81937	+	2.77494i	0.145191	+	0.105487i
$693$	−23.7807			−0.903353
$694$	5.71665	−	7.86829i	0.217001	−	0.298676i
$695$	−8.40474	−	1.96269i	−0.318810	−	0.0744490i
$696$	9.49298	+	13.0660i	0.359831	+	0.495264i
$697$	10.1615	+	13.9861i	0.384893	+	0.529759i
$698$	−1.06992	−	3.29288i	−0.0404971	−	0.124637i
$699$	73.6104			2.78420
$700$	−7.21751	+	14.6109i	−0.272796	+	0.552240i
$701$	6.14674			0.232159			0.116080	−	0.993240i	$-0.462967\pi$
$701$	6.14674			0.232159			0.116080	+	0.993240i	$0.462967\pi$
$702$	−1.36738	−	8.12940i	−0.0516083	−	0.306824i
$703$	64.0913	−	46.5651i	2.41725	−	1.75623i
$704$	−1.10756	−	1.52443i	−0.0417429	−	0.0574542i
$705$	0.0527113	−	0.0455887i	0.00198522	−	0.00171697i
$706$	−2.44296	−	1.77492i	−0.0919422	−	0.0667999i
$707$			8.91789i			0.335392i
$708$	−4.25821	+	5.86092i	−0.160033	+	0.220267i
$709$	−9.23460	−	3.00050i	−0.346813	−	0.112686i	0.130431	−	0.991457i	$-0.458364\pi$
$709$	−9.23460	−	3.00050i	−0.346813	−	0.112686i	−0.477243	+	0.878771i	$0.658364\pi$
$710$	19.1897	−	8.08859i	0.720177	−	0.303559i
$711$	−8.73038	−	26.8694i	−0.327415	−	1.00768i
$712$	−3.47812	+	10.7046i	−0.130348	+	0.401170i
$713$	12.7382	+	4.13889i	0.477049	+	0.155003i
$714$	−16.2139	−	49.9012i	−0.606790	−	1.86751i
$715$	9.68283	−	11.7060i	0.362117	−	0.437781i
$716$	6.56401	−	20.2020i	0.245309	−	0.754983i
$717$	24.0274	−	33.0709i	0.897320	−	1.23506i
$718$	29.2612			1.09202
$719$	−5.83791	−	4.24149i	−0.217717	−	0.158181i	0.473581	−	0.880750i	$-0.342961\pi$
$719$	−5.83791	−	4.24149i	−0.217717	−	0.158181i	−0.691298	+	0.722569i	$0.742961\pi$
$720$	7.97861	−	3.36304i	0.297345	−	0.125333i
$721$	−21.6216	−	29.7595i	−0.805229	−	1.10830i
$722$	19.1042	+	26.2946i	0.710983	+	0.978585i
$723$	35.8377	−	11.6444i	1.33282	−	0.433059i
$724$	17.9640			0.667625
$725$	−27.6181	−	13.6428i	−1.02571	−	0.506682i
$726$		−	19.5285i		−	0.724770i
$727$	12.3308	+	37.9504i	0.457326	+	1.40750i	0.868383	+	0.495894i	$0.165160\pi$
$727$	12.3308	+	37.9504i	0.457326	+	1.40750i	−0.411057	+	0.911609i	$0.634840\pi$
$728$	−5.43493	−	10.4191i	−0.201432	−	0.386159i
$729$	32.1613	−	23.3665i	1.19116	−	0.865427i
$730$	3.04616	+	35.8573i	0.112743	+	1.32714i
$731$	46.3929	+	33.7064i	1.71590	+	1.24668i
$732$	8.44792			0.312244
$733$	−30.3036	+	41.7093i	−1.11929	+	1.54057i	−0.312318	+	0.949978i	$0.601105\pi$
$733$	−30.3036	+	41.7093i	−1.11929	+	1.54057i	−0.806971	+	0.590591i	$0.798895\pi$
$734$	−16.5763	−	5.38598i	−0.611844	−	0.198800i
$735$	−1.79760	−	21.1601i	−0.0663056	−	0.780503i
$736$	−5.29378	+	1.72005i	−0.195131	+	0.0634020i
$737$	1.68689	−	5.19171i	0.0621374	−	0.191239i
$738$	3.36849	−	10.3671i	0.123996	−	0.381620i
$739$	−6.89035	+	2.23881i	−0.253465	+	0.0823559i	−0.432994	−	0.901397i	$-0.642543\pi$
$739$	−6.89035	+	2.23881i	−0.253465	+	0.0823559i	0.179528	+	0.983753i	$0.442543\pi$
$740$	−5.61321	+	24.0372i	−0.206346	+	0.883627i
$741$	−30.2155	+	60.7298i	−1.10999	+	2.23097i
$742$	1.06851	+	0.776319i	0.0392263	+	0.0284996i
$743$		−	27.8490i		−	1.02168i	−0.859676	−	0.510840i	$-0.829334\pi$
$743$		−	27.8490i		−	1.02168i	0.859676	−	0.510840i	$-0.170666\pi$
$744$	5.10325	+	3.70773i	0.187094	+	0.135932i
$745$	−27.1493	−	16.4061i	−0.994672	−	0.601072i
$746$	10.5149	+	14.4726i	0.384980	+	0.529879i
$747$	21.2704	+	29.2762i	0.778244	+	1.07116i
$748$	−11.0051	+	3.57578i	−0.402387	+	0.130744i
$749$		−	55.4733i		−	2.02695i
$750$	−18.6163	+	22.6375i	−0.679771	+	0.826603i
$751$	−35.3329			−1.28932			−0.644658	−	0.764471i	$-0.723000\pi$
$751$	−35.3329			−1.28932			−0.644658	+	0.764471i	$0.723000\pi$
$752$	−0.0113071	+	0.00367389i	−0.000412327	+	0.000133973i
$753$	−24.0304	+	17.4591i	−0.875716	+	0.636245i
$754$	19.6947	−	10.2733i	0.717238	−	0.374132i
$755$	−30.0503	−	18.1592i	−1.09364	−	0.660879i
$756$	−4.38010	+	6.02869i	−0.159303	+	0.219261i
$757$	36.7398			1.33533			0.667665	−	0.744462i	$-0.267294\pi$
$757$	36.7398			1.33533			0.667665	+	0.744462i	$0.267294\pi$
$758$	−7.24713	−	5.26534i	−0.263227	−	0.191246i
$759$	26.1495	+	8.49648i	0.949165	+	0.308403i
$760$	−15.6267	−	3.64917i	−0.566839	−	0.132369i
$761$	14.9788	−	4.86690i	0.542980	−	0.176425i	−0.0246689	−	0.999696i	$-0.507853\pi$
$761$	14.9788	−	4.86690i	0.542980	−	0.176425i	0.567649	+	0.823271i	$0.307853\pi$
$762$	−34.7333	−	11.2855i	−1.25825	−	0.408831i
$763$	0.347544	−	1.06963i	0.0125819	−	0.0387232i
$764$	8.34247	+	25.6755i	0.301820	+	0.928906i
$765$	−4.50081	−	52.9804i	−0.162727	−	1.91551i
$766$	4.91030	−	15.1124i	0.177417	−	0.546032i
$767$	7.11265	+	6.97791i	0.256823	+	0.251958i
$768$	−2.62148			−0.0945946
$769$	−20.1766	+	27.7706i	−0.727585	+	1.00144i	0.271652	+	0.962395i	$0.412430\pi$
$769$	−20.1766	+	27.7706i	−0.727585	+	1.00144i	−0.999238	+	0.0390398i	$0.987570\pi$
$770$	−13.6834	+	1.16244i	−0.493116	+	0.0418913i
$771$	6.96964	−	5.06374i	0.251005	−	0.182366i
$772$	−0.518165	−	0.713192i	−0.0186491	−	0.0256684i
$773$	−27.3079	+	8.87288i	−0.982197	+	0.319135i	−0.755730	−	0.654883i	$-0.772718\pi$
$773$	−27.3079	+	8.87288i	−0.982197	+	0.319135i	−0.226468	+	0.974019i	$0.572718\pi$
$774$		−	36.1584i		−	1.29969i
$775$	−11.9056	−	1.73440i	−0.427663	−	0.0623016i
$776$	6.25095			0.224396
$777$	−29.1460	−	89.7022i	−1.04561	−	3.21805i
$778$	−8.18763	−	11.2693i	−0.293541	−	0.404024i
$779$	−16.3444	+	11.8749i	−0.585599	+	0.425462i
$780$	−5.25737	−	20.4707i	−0.188244	−	0.732970i
$781$	14.1972	+	10.3149i	0.508016	+	0.369095i
$782$			34.1820i			1.22235i
$783$	−11.3957	−	8.27944i	−0.407248	−	0.295883i
$784$	−1.11952	+	3.44552i	−0.0399827	+	0.123054i
$785$	12.5251	−	20.7268i	0.447039	−	0.739773i
$786$	17.2602	−	5.60818i	0.615651	−	0.200037i
$787$	−22.4948	−	7.30899i	−0.801852	−	0.260537i	−0.120709	−	0.992688i	$-0.538517\pi$
$787$	−22.4948	−	7.30899i	−0.801852	−	0.260537i	−0.681143	+	0.732151i	$0.738517\pi$
$788$	−13.3930	−	4.35165i	−0.477106	−	0.155021i
$789$	−13.1448	−	40.4556i	−0.467967	−	1.44026i
$790$	−6.33688	−	15.0339i	−0.225456	−	0.534881i
$791$	6.50986	+	2.11518i	0.231464	+	0.0752072i
$792$	5.90285	+	4.28867i	0.209749	+	0.152391i
$793$	1.70782	−	11.4930i	0.0606465	−	0.408127i
$794$	8.91623	+	6.47802i	0.316425	+	0.229896i
$795$	1.55387	+	1.79664i	0.0551101	+	0.0637203i
$796$	−20.1825	+	14.6635i	−0.715351	+	0.519733i
$797$	−12.2806	+	8.92240i	−0.435002	+	0.316047i	−0.783646	−	0.621208i	$-0.786642\pi$
$797$	−12.2806	+	8.92240i	−0.435002	+	0.316047i	0.348644	+	0.937255i	$0.386642\pi$
$798$	58.3156	−	18.9479i	2.06435	−	0.670748i
$799$			0.0730100i			0.00258291i
$800$	4.42650	−	2.32510i	0.156500	−	0.0822047i
$801$		−	43.5829i		−	1.53993i
$802$	−4.70217	−	14.4718i	−0.166039	−	0.511016i
$803$	−24.5336	+	17.8247i	−0.865772	+	0.629021i
$804$	−4.46395	−	6.14410i	−0.157431	−	0.216686i
$805$	−9.22489	+	39.5034i	−0.325135	+	1.39231i
$806$	6.07584	−	6.19316i	0.214012	−	0.218145i
$807$	−60.7294			−2.13778
$808$	1.60828	−	2.21360i	0.0565789	−	0.0778742i
$809$	−10.0587	+	30.9574i	−0.353644	+	1.08840i	0.603148	+	0.797630i	$0.293913\pi$
$809$	−10.0587	+	30.9574i	−0.353644	+	1.08840i	−0.956792	+	0.290775i	$0.906087\pi$
$810$	9.50974	−	8.22475i	0.334138	−	0.288988i
$811$	−9.18568	+	2.98461i	−0.322553	+	0.104804i	−0.465818	−	0.884881i	$-0.654240\pi$
$811$	−9.18568	+	2.98461i	−0.322553	+	0.104804i	0.143265	+	0.989684i	$0.454240\pi$
$812$	−19.0969	−	6.20497i	−0.670171	−	0.217752i
$813$	19.1038	+	6.20720i	0.670000	+	0.217696i
$814$	−19.7827	+	6.42780i	−0.693385	+	0.225294i
$815$	−26.8792	+	23.2472i	−0.941539	+	0.814315i
$816$	−4.97470	+	15.3106i	−0.174149	+	0.535977i
$817$	−39.3901	+	54.2158i	−1.37808	+	1.89677i
$818$	1.26494			0.0442277
$819$	32.4821	+	31.8668i	1.13502	+	1.11351i
$820$	1.43147	−	6.12991i	0.0499890	−	0.214066i
$821$	7.02758	+	9.67264i	0.245264	+	0.337577i	0.913846	−	0.406062i	$-0.133098\pi$
$821$	7.02758	+	9.67264i	0.245264	+	0.337577i	−0.668581	+	0.743639i	$0.733098\pi$
$822$	12.8555	−	9.34009i	0.448388	−	0.325773i
$823$	−2.35339	−	7.24298i	−0.0820339	−	0.252474i	0.901624	−	0.432520i	$-0.142375\pi$
$823$	−2.35339	−	7.24298i	−0.0820339	−	0.252474i	−0.983658	+	0.180046i	$0.942375\pi$
$824$			11.2862i			0.393174i
$825$	−24.4403	−	3.56045i	−0.850903	−	0.123959i
$826$		−	9.00703i		−	0.313395i
$827$	−43.6571	+	14.1850i	−1.51811	+	0.493262i	−0.945237	−	0.326385i	$-0.894169\pi$
$827$	−43.6571	+	14.1850i	−1.51811	+	0.493262i	−0.572868	+	0.819647i	$0.694169\pi$
$828$	17.4370	−	12.6687i	0.605976	−	0.440267i
$829$	15.8554	−	11.5196i	0.550681	−	0.400093i	−0.277356	−	0.960767i	$-0.589458\pi$
$829$	15.8554	−	11.5196i	0.550681	−	0.400093i	0.828036	+	0.560674i	$0.189458\pi$
$830$	13.6701	+	15.8058i	0.474495	+	0.548628i
$831$	−52.1792	−	37.9104i	−1.81008	−	1.31510i
$832$	−0.529955	+	3.56639i	−0.0183729	+	0.123642i
$833$	17.9988	+	13.0769i	0.623622	+	0.453088i
$834$	−9.62326	−	3.12679i	−0.333226	−	0.108272i
$835$	−0.111181	−	0.263771i	−0.00384758	−	0.00912816i
$836$	−4.17873	−	12.8608i	−0.144524	−	0.444801i
$837$	−5.23231	−	1.70008i	−0.180855	−	0.0587634i
$838$	32.9033	+	10.6909i	1.13663	+	0.369312i
$839$	−17.4860	+	5.68154i	−0.603683	+	0.196149i	−0.594882	−	0.803813i	$-0.702801\pi$
$839$	−17.4860	+	5.68154i	−0.603683	+	0.196149i	−0.00880076	+	0.999961i	$0.502801\pi$
$840$	−9.88111	+	16.3515i	−0.340931	+	0.564182i
$841$	2.76740	−	8.51718i	0.0954276	−	0.293696i
$842$	18.9924	+	13.7988i	0.654523	+	0.475539i
$843$		−	16.3818i		−	0.564220i
$844$	−10.4161	−	7.56773i	−0.358537	−	0.260492i
$845$	−28.9122	+	3.01404i	−0.994610	+	0.103686i
$846$	0.0372439	−	0.0270593i	0.00128047	−	0.000930318i
$847$	14.2712	+	19.6426i	0.490364	+	0.674929i
$848$	−0.125223	−	0.385397i	−0.00430017	−	0.0132346i
$849$	34.1340			1.17147
$850$	−5.17953	−	30.2649i	−0.177656	−	1.03808i
$851$			61.4453i			2.10632i
$852$	23.2192	−	7.54438i	0.795477	−	0.258466i
$853$	20.8288	+	28.6684i	0.713164	+	0.981586i	0.999723	+	0.0235237i	$0.00748852\pi$
$853$	20.8288	+	28.6684i	0.713164	+	0.981586i	−0.286559	+	0.958063i	$0.592511\pi$
$854$	−8.49730	+	6.17365i	−0.290772	+	0.211258i
$855$	61.9140	−	5.25974i	2.11742	−	0.179879i
$856$	−10.0042	+	13.7696i	−0.341936	+	0.470635i
$857$	−11.1717			−0.381617			−0.190809	−	0.981627i	$-0.561111\pi$
$857$	−11.1717			−0.381617			−0.190809	+	0.981627i	$0.561111\pi$
$858$	12.4727	−	12.7136i	0.425812	−	0.434034i
$859$	−12.2583	+	37.7272i	−0.418248	+	1.28724i	0.491065	+	0.871123i	$0.336608\pi$
$859$	−12.2583	+	37.7272i	−0.418248	+	1.28724i	−0.909313	+	0.416113i	$0.863392\pi$
$860$	−1.76748	−	20.8056i	−0.0602706	−	0.709464i
$861$	7.43273	+	22.8756i	0.253307	+	0.779598i
$862$	−2.62681	+	8.08448i	−0.0894694	+	0.275358i
$863$	−15.0941	−	4.90436i	−0.513808	−	0.166946i	0.0406254	−	0.999174i	$-0.487065\pi$
$863$	−15.0941	−	4.90436i	−0.513808	−	0.166946i	−0.554433	+	0.832228i	$0.687065\pi$
$864$	2.17446	−	0.706525i	0.0739766	−	0.0240365i
$865$	−10.2799	−	2.40058i	−0.349527	−	0.0816222i
$866$	−5.71263	−	1.85614i	−0.194123	−	0.0630744i
$867$	43.9259	+	31.9140i	1.49180	+	1.08386i
$868$	−7.84265			−0.266197
$869$	8.08102	−	11.1226i	0.274130	−	0.377307i
$870$	−30.9084	−	18.6777i	−1.04789	−	0.633233i
$871$	−9.26116	+	4.83089i	−0.313803	+	0.163689i
$872$	−0.279168	+	0.202827i	−0.00945380	+	0.00686859i
$873$	−23.0201	+	7.47967i	−0.779111	+	0.253148i
$874$	−39.9458			−1.35119
$875$	2.18190	−	36.3743i	0.0737615	−	1.22968i
$876$			42.1891i			1.42544i
$877$	8.79845	−	2.85879i	0.297103	−	0.0965345i	−0.156673	−	0.987651i	$-0.550077\pi$
$877$	8.79845	−	2.85879i	0.297103	−	0.0965345i	0.453775	+	0.891116i	$0.350077\pi$
$878$	5.74382	+	7.90569i	0.193845	+	0.266804i
$879$	21.0327	+	28.9491i	0.709417	+	0.976429i
$880$	3.60614	+	2.17916i	0.121563	+	0.0734595i
$881$	−4.72342	−	3.43176i	−0.159136	−	0.115619i	0.505367	−	0.862904i	$-0.331357\pi$
$881$	−4.72342	−	3.43176i	−0.159136	−	0.115619i	−0.664504	+	0.747285i	$0.731357\pi$
$882$		−	14.0282i		−	0.472354i
$883$	−16.4798	−	11.9733i	−0.554589	−	0.402932i	0.274886	−	0.961477i	$-0.411360\pi$
$883$	−16.4798	−	11.9733i	−0.554589	−	0.402932i	−0.829474	+	0.558545i	$0.811360\pi$
$884$	19.8236	+	9.86300i	0.666739	+	0.331728i
$885$	3.68375	−	15.7748i	0.123828	−	0.530264i
$886$	−4.80564	+	1.56145i	−0.161449	+	0.0524579i
$887$	7.98587	−	24.5780i	0.268139	−	0.825248i	−0.722814	−	0.691043i	$-0.757152\pi$
$887$	7.98587	−	24.5780i	0.268139	−	0.825248i	0.990954	−	0.134206i	$-0.0428483\pi$
$888$	−8.94250	+	27.5222i	−0.300091	+	0.923584i
$889$	43.1836	−	14.0312i	1.44833	−	0.470592i
$890$	−2.13040	−	25.0776i	−0.0714112	−	0.840603i
$891$	10.0766	+	3.27407i	0.337577	+	0.109686i
$892$	7.31754	−	10.0717i	0.245009	−	0.337226i
$893$	−0.0853210			−0.00285516
$894$	−30.0864	−	21.8591i	−1.00624	−	0.731076i
$895$	4.02055	+	47.3272i	0.134392	+	1.58197i
$896$	2.63680	−	1.91575i	0.0880894	−	0.0640007i
$897$	−24.3321	−	46.6463i	−0.812425	−	1.55748i
$898$	8.41641	+	25.9030i	0.280859	+	0.864396i
$899$		−	14.8245i		−	0.494424i
$900$	−13.5191	+	13.8591i	−0.450637	+	0.461970i
$901$	−2.48851			−0.0829043
$902$	5.04494	−	1.63920i	0.167978	−	0.0545794i
$903$	46.8966	+	64.5477i	1.56062	+	2.14801i
$904$	−1.23442	−	1.69904i	−0.0410563	−	0.0565091i
$905$	−37.0148	+	15.6020i	−1.23041	+	0.518628i
$906$	−33.3013	−	24.1948i	−1.10636	−	0.803819i
$907$	−34.3266			−1.13980			−0.569898	−	0.821715i	$-0.693017\pi$
$907$	−34.3266			−1.13980			−0.569898	+	0.821715i	$0.693017\pi$
$908$	−1.22786	+	1.69001i	−0.0407481	+	0.0560850i
$909$	−3.27399	+	10.0763i	−0.108592	+	0.334210i
$910$	20.2479	+	16.7484i	0.671211	+	0.555202i
$911$	−10.0537	−	30.9420i	−0.333092	−	1.02515i	−0.967654	−	0.252281i	$-0.918819\pi$
$911$	−10.0537	−	30.9420i	−0.333092	−	1.02515i	0.634562	−	0.772872i	$-0.281181\pi$
$912$	−17.8922	−	5.81354i	−0.592472	−	0.192506i
$913$	−5.44173	+	16.7479i	−0.180095	+	0.554275i
$914$	9.68300	+	29.8012i	0.320285	+	0.985736i
$915$	−17.4070	+	7.33716i	−0.575457	+	0.242559i
$916$	13.5902	+	4.41571i	0.449031	+	0.145899i
$917$	−13.2627	+	18.2545i	−0.437973	+	0.602818i
$918$		−	14.0405i		−	0.463406i
$919$	37.0882	+	26.9462i	1.22343	+	0.888872i	0.996380	−	0.0850111i	$-0.0270926\pi$
$919$	37.0882	+	26.9462i	1.22343	+	0.888872i	0.227048	+	0.973884i	$0.427093\pi$
$920$	9.41396	−	8.14191i	0.310369	−	0.268431i
$921$	−11.3961	−	15.6855i	−0.375516	−	0.516853i
$922$	25.7177	−	18.6850i	0.846969	−	0.615359i
$923$	−5.56978	−	33.1137i	−0.183331	−	1.08995i
$924$	−16.0997			−0.529641
$925$	−9.31069	−	54.4040i	−0.306134	−	1.78879i
$926$	−6.60574			−0.217078
$927$	−13.5047	−	41.5631i	−0.443552	−	1.36511i
$928$	3.62123	+	4.98419i	0.118873	+	0.163614i
$929$	−5.30159	−	7.29701i	−0.173939	−	0.239407i	0.713142	−	0.701019i	$-0.247271\pi$
$929$	−5.30159	−	7.29701i	−0.173939	−	0.239407i	−0.887082	+	0.461612i	$0.847271\pi$
$930$	−13.7355	−	3.20753i	−0.450405	−	0.105179i
$931$	−15.2819	+	21.0338i	−0.500846	+	0.689355i
$932$	28.0797			0.919781
$933$	−35.9856	−	26.1451i	−1.17812	−	0.855951i
$934$	−7.98729	−	2.59523i	−0.261352	−	0.0849185i
$935$	19.5705	−	16.9260i	0.640023	−	0.553541i
$936$	−2.31578	−	13.7679i	−0.0756936	−	0.450017i
$937$	−12.0403	+	37.0563i	−0.393340	+	1.21058i	0.536907	+	0.843642i	$0.319593\pi$
$937$	−12.0403	+	37.0563i	−0.393340	+	1.21058i	−0.930247	+	0.366935i	$0.880407\pi$
$938$	8.98009	+	2.91781i	0.293210	+	0.0952698i
$939$	−10.0653	−	30.9777i	−0.328468	−	1.01092i
$940$	0.0201074	−	0.0173905i	0.000655833	−	0.000567214i
$941$	31.3716	+	10.1932i	1.02268	+	0.332290i	0.771894	−	0.635751i	$-0.219310\pi$
$941$	31.3716	+	10.1932i	1.02268	+	0.332290i	0.250790	+	0.968042i	$0.419310\pi$
$942$	16.6881	−	22.9692i	0.543728	−	0.748377i
$943$		−	15.6696i		−	0.510273i
$944$	−1.62435	+	2.23573i	−0.0528682	+	0.0727668i
$945$	3.78920	−	16.2263i	0.123263	−	0.527842i
$946$	14.2352	−	10.3425i	0.462827	−	0.336263i
$947$	11.1406	+	15.3338i	0.362022	+	0.498281i	0.950711	−	0.310079i	$-0.100356\pi$
$947$	11.1406	+	15.3338i	0.362022	+	0.498281i	−0.588689	+	0.808360i	$0.700356\pi$
$948$	−5.91053	−	18.1907i	−0.191965	−	0.590808i
$949$	57.3961	+	8.52889i	1.86316	+	0.276860i
$950$	35.3682	−	6.05291i	1.14750	−	0.196382i
$951$			19.6478i			0.637124i
$952$	−6.18501	−	19.0355i	−0.200457	−	0.616945i
$953$	28.6374	−	20.8063i	0.927656	−	0.673981i	−0.0177621	−	0.999842i	$-0.505654\pi$
$953$	28.6374	−	20.8063i	0.927656	−	0.673981i	0.945418	+	0.325861i	$0.105654\pi$
$954$	0.922304	+	1.26944i	0.0298607	+	0.0410997i
$955$	−39.4893	−	45.6588i	−1.27784	−	1.47749i
$956$	9.16559	−	12.6154i	0.296436	−	0.408010i
$957$		−	30.4323i		−	0.983736i
$958$	−7.65117	−	5.55890i	−0.247198	−	0.179600i
$959$	−6.10503	+	18.7894i	−0.197142	+	0.606740i
$960$	5.40157	−	2.27680i	0.174335	−	0.0734834i
$961$	7.79029	+	23.9761i	0.251300	+	0.773421i
$962$	35.6347	+	17.7297i	1.14891	+	0.571627i
$963$	20.3657	−	62.6792i	0.656276	−	2.01981i
$964$	13.6708	−	4.44191i	0.440307	−	0.143064i
$965$	1.68710	+	1.01950i	0.0543097	+	0.0328189i
$966$	−14.6963	+	45.2306i	−0.472846	+	1.45527i
$967$	−2.59324	+	3.56929i	−0.0833930	+	0.114781i	−0.848675	−	0.528914i	$-0.822599\pi$
$967$	−2.59324	+	3.56929i	−0.0833930	+	0.114781i	0.765282	+	0.643695i	$0.222599\pi$
$968$		−	7.44941i		−	0.239433i
$969$	−67.9071	+	93.4662i	−2.18149	+	3.00257i
$970$	−12.8801	+	5.42906i	−0.413556	+	0.174317i
$971$	29.6283	−	21.5262i	0.950818	−	0.690809i	−0.000182536	−	1.00000i	$-0.500058\pi$
$971$	29.6283	−	21.5262i	0.950818	−	0.690809i	0.951000	+	0.309191i	$0.100058\pi$
$972$	17.4742	−	12.6957i	0.560484	−	0.407215i
$973$	11.9645	−	3.88751i	0.383565	−	0.124628i
$974$	19.4580			0.623473
$975$	28.6120	+	37.6139i	0.916317	+	1.20461i
$976$	3.22258			0.103152
$977$	−46.8272	+	15.2151i	−1.49814	+	0.486774i	−0.939473	−	0.342622i	$-0.888685\pi$
$977$	−46.8272	+	15.2151i	−1.49814	+	0.486774i	−0.558662	+	0.829396i	$0.688685\pi$
$978$	−33.7061	+	24.4889i	−1.07780	+	0.783069i
$979$	17.1581	−	12.4661i	0.548377	−	0.398419i
$980$	−0.685720	−	8.07182i	−0.0219045	−	0.257845i
$981$	0.785380	−	1.08098i	0.0250752	−	0.0345131i
$982$		−	28.4857i		−	0.909014i
$983$	−17.5695	+	24.1824i	−0.560381	+	0.771299i	−0.991375	−	0.131056i	$-0.958163\pi$
$983$	−17.5695	+	24.1824i	−0.560381	+	0.771299i	0.430994	+	0.902355i	$0.358163\pi$
$984$	2.28049	−	7.01863i	0.0726994	−	0.223746i
$985$	31.3758	−	2.66545i	0.999717	−	0.0849283i
$986$	35.9817	−	11.6912i	1.14589	−	0.372323i
$987$	−0.0313901	+	0.0966089i	−0.000999159	+	0.00307510i
$988$	−11.5261	+	23.1662i	−0.366694	+	0.737016i
$989$	−16.0619	−	49.4335i	−0.510740	−	1.57189i
$990$	−15.8876	−	3.71010i	−0.504942	−	0.117915i
$991$	−1.10023	+	3.38615i	−0.0349498	+	0.107564i	−0.967010	−	0.254740i	$-0.918010\pi$
$991$	−1.10023	+	3.38615i	−0.0349498	+	0.107564i	0.932060	+	0.362305i	$0.118010\pi$
$992$	1.94670	+	1.41436i	0.0618079	+	0.0449061i
$993$		−	12.3100i		−	0.390646i
$994$	−17.8416	+	24.5568i	−0.565901	+	0.778895i
$995$	28.8507	−	47.7430i	0.914630	−	1.51356i
$996$	14.4002	+	19.8202i	0.456289	+	0.628027i
$997$	−1.11173	+	0.807718i	−0.0352088	+	0.0255807i	−0.605250	−	0.796035i	$-0.706927\pi$
$997$	−1.11173	+	0.807718i	−0.0352088	+	0.0255807i	0.570042	+	0.821616i	$0.306927\pi$
$998$	5.96231	+	18.3501i	0.188734	+	0.580862i
$999$		−	25.2391i		−	0.798531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.p.a.181.15	✓	136
13.12	even	2	inner	650.2.p.a.181.32	yes	136
25.21	even	5	inner	650.2.p.a.571.32	yes	136
325.246	even	10	inner	650.2.p.a.571.15	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.p.a.181.15	✓	136	1.1	even	1	trivial
650.2.p.a.181.32	yes	136	13.12	even	2	inner
650.2.p.a.571.15	yes	136	325.246	even	10	inner
650.2.p.a.571.32	yes	136	25.21	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(2.12082 - 1.54087i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-1.15648 + 1.91378i) q^{5} +(-1.54087 + 2.12082i) q^{6} -3.25927i q^{7} +(-0.587785 + 0.809017i) q^{8} +(1.19656 - 3.68265i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(2.12082 - 1.54087i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-1.15648 + 1.91378i) q^{5} +(-1.54087 + 2.12082i) q^{6} -3.25927i q^{7} +(-0.587785 + 0.809017i) q^{8} +(1.19656 - 3.68265i) q^{9} +(0.508489 - 2.17748i) q^{10} +(1.79208 - 0.582281i) q^{11} +(0.810082 - 2.49318i) q^{12} +(-3.22807 - 1.60609i) q^{13} +(1.00717 + 3.09975i) q^{14} +(0.496187 + 5.84077i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.96816 - 3.60958i) q^{17} +3.87216i q^{18} +(4.21823 - 5.80590i) q^{19} +(0.189277 + 2.22804i) q^{20} +(-5.02210 - 6.91233i) q^{21} +(-1.52443 + 1.10756i) q^{22} +(1.72005 + 5.29378i) q^{23} +2.62148i q^{24} +(-2.32510 - 4.42650i) q^{25} +(3.56639 + 0.529955i) q^{26} +(-0.706525 - 2.17446i) q^{27} +(-1.91575 - 2.63680i) q^{28} +(4.98419 - 3.62123i) q^{29} +(-2.27680 - 5.40157i) q^{30} +(1.41436 - 1.94670i) q^{31} +1.00000i q^{32} +(2.90346 - 3.99627i) q^{33} +(5.84043 + 1.89767i) q^{34} +(6.23752 + 3.76929i) q^{35} +(-1.19656 - 3.68265i) q^{36} +(10.4987 + 3.41124i) q^{37} +(-2.21766 + 6.82524i) q^{38} +(-9.32095 + 1.56780i) q^{39} +(-0.868517 - 2.06050i) q^{40} +(-2.67735 - 0.869925i) q^{41} +(6.91233 + 5.02210i) q^{42} -9.33805 q^{43} +(1.10756 - 1.52443i) q^{44} +(5.66397 + 6.54887i) q^{45} +(-3.27173 - 4.50316i) q^{46} +(-0.00698816 - 0.00961837i) q^{47} +(-0.810082 - 2.49318i) q^{48} -3.62283 q^{49} +(3.57916 + 3.49136i) q^{50} -16.0985 q^{51} +(-3.55560 + 0.598058i) q^{52} +(0.327838 - 0.238188i) q^{53} +(1.34389 + 1.84971i) q^{54} +(-0.958148 + 4.10304i) q^{55} +(2.63680 + 1.91575i) q^{56} -18.8130i q^{57} +(-3.62123 + 4.98419i) q^{58} +(-2.62826 - 0.853973i) q^{59} +(3.83454 + 4.43363i) q^{60} +(0.995831 + 3.06485i) q^{61} +(-0.743575 + 2.28849i) q^{62} +(-12.0027 - 3.89993i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(6.80692 - 4.32040i) q^{65} +(-1.52644 + 4.69790i) q^{66} +(1.70284 - 2.34375i) q^{67} -6.14099 q^{68} +(11.8049 + 8.57679i) q^{69} +(-7.09701 - 1.65730i) q^{70} +(5.47411 + 7.53446i) q^{71} +(2.27600 + 3.13265i) q^{72} +(-15.3059 + 4.97320i) q^{73} -11.0390 q^{74} +(-11.7518 - 5.80515i) q^{75} -7.17649i q^{76} +(-1.89781 - 5.84086i) q^{77} +(8.38028 - 4.37140i) q^{78} +(5.90276 - 4.28860i) q^{79} +(1.46274 + 1.69127i) q^{80} +(4.54897 + 3.30502i) q^{81} +2.81514 q^{82} +(-5.49316 + 7.56069i) q^{83} +(-8.12593 - 2.64028i) q^{84} +(12.6535 - 5.33355i) q^{85} +(8.88101 - 2.88562i) q^{86} +(4.99076 - 15.3600i) q^{87} +(-0.582281 + 1.79208i) q^{88} +(10.7046 - 3.47812i) q^{89} +(-7.41047 - 4.47809i) q^{90} +(-5.23469 + 10.5212i) q^{91} +(4.50316 + 3.27173i) q^{92} -6.30796i q^{93} +(0.00961837 + 0.00698816i) q^{94} +(6.23290 + 14.7872i) q^{95} +(1.54087 + 2.12082i) q^{96} +(-3.67422 - 5.05713i) q^{97} +(3.44552 - 1.11952i) q^{98} -7.29632i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q + 34 q^{4} - 30 q^{9}+O(q^{10}) \) 136 * q + 34 * q^4 - 30 * q^9	\( 136 q + 34 q^{4} - 30 q^{9} - 4 q^{10} - 12 q^{13} + 8 q^{14} - 34 q^{16} + 4 q^{23} + 40 q^{25} + 4 q^{26} - 12 q^{27} + 16 q^{29} + 10 q^{30} - 18 q^{35} + 30 q^{36} - 24 q^{38} + 32 q^{39} + 4 q^{40} - 12 q^{42} + 24 q^{43} - 104 q^{49} + 84 q^{51} + 12 q^{52} + 4 q^{53} - 60 q^{55} - 8 q^{56} + 12 q^{61} + 18 q^{62} + 34 q^{64} + 26 q^{65} + 16 q^{66} + 84 q^{69} - 88 q^{74} - 214 q^{75} + 56 q^{78} - 8 q^{79} - 74 q^{81} + 160 q^{82} - 164 q^{87} - 16 q^{90} - 40 q^{91} + 16 q^{92} + 48 q^{94} - 4 q^{95}+O(q^{100}) \) 136 * q + 34 * q^4 - 30 * q^9 - 4 * q^10 - 12 * q^13 + 8 * q^14 - 34 * q^16 + 4 * q^23 + 40 * q^25 + 4 * q^26 - 12 * q^27 + 16 * q^29 + 10 * q^30 - 18 * q^35 + 30 * q^36 - 24 * q^38 + 32 * q^39 + 4 * q^40 - 12 * q^42 + 24 * q^43 - 104 * q^49 + 84 * q^51 + 12 * q^52 + 4 * q^53 - 60 * q^55 - 8 * q^56 + 12 * q^61 + 18 * q^62 + 34 * q^64 + 26 * q^65 + 16 * q^66 + 84 * q^69 - 88 * q^74 - 214 * q^75 + 56 * q^78 - 8 * q^79 - 74 * q^81 + 160 * q^82 - 164 * q^87 - 16 * q^90 - 40 * q^91 + 16 * q^92 + 48 * q^94 - 4 * q^95

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