LMFDB - Embedded newform 350.2.r.a.13.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(13,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([19, 10]))

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

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

chi := DirichletCharacter("350.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.r (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.11
Character	$\chi$	$=$	350.13
Dual form			350.2.r.a.27.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.987688 - 0.156434i) q^{2} +(-2.95619 - 1.50625i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.79263 + 1.33659i) q^{5} +(-3.15542 - 1.02526i) q^{6} +(2.61159 - 0.423809i) q^{7} +(0.891007 - 0.453990i) q^{8} +(4.70689 + 6.47848i) q^{9} +O(q^{10})$	\(q+(0.987688 - 0.156434i) q^{2} +(-2.95619 - 1.50625i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.79263 + 1.33659i) q^{5} +(-3.15542 - 1.02526i) q^{6} +(2.61159 - 0.423809i) q^{7} +(0.891007 - 0.453990i) q^{8} +(4.70689 + 6.47848i) q^{9} +(1.97965 + 1.03971i) q^{10} +(-3.03402 - 2.20435i) q^{11} +(-3.27696 - 0.519019i) q^{12} +(0.676747 - 4.27281i) q^{13} +(2.51314 - 0.827134i) q^{14} +(-3.28611 - 6.65137i) q^{15} +(0.809017 - 0.587785i) q^{16} +(3.45448 - 1.76015i) q^{17} +(5.66240 + 5.66240i) q^{18} +(0.207244 - 0.637830i) q^{19} +(2.11792 + 0.717221i) q^{20} +(-8.35870 - 2.68085i) q^{21} +(-3.34151 - 1.70258i) q^{22} +(-0.604943 - 3.81946i) q^{23} -3.31781 q^{24} +(1.42705 + 4.79203i) q^{25} -4.32607i q^{26} +(-2.59917 - 16.4105i) q^{27} +(2.35280 - 1.21009i) q^{28} +(-3.56392 + 1.15799i) q^{29} +(-4.28615 - 6.05542i) q^{30} +(5.04335 + 1.63868i) q^{31} +(0.707107 - 0.707107i) q^{32} +(5.64884 + 11.0865i) q^{33} +(3.13661 - 2.27888i) q^{34} +(5.24807 + 2.73089i) q^{35} +(6.47848 + 4.70689i) q^{36} +(-0.217833 + 1.37534i) q^{37} +(0.104913 - 0.662398i) q^{38} +(-8.43652 + 11.6119i) q^{39} +(2.20405 + 0.377075i) q^{40} +(-1.30332 - 1.79387i) q^{41} +(-8.67517 - 1.34025i) q^{42} +(6.32322 + 6.32322i) q^{43} +(-3.56671 - 1.15889i) q^{44} +(-0.221366 + 17.9047i) q^{45} +(-1.19499 - 3.67780i) q^{46} +(-3.49539 + 6.86008i) q^{47} +(-3.27696 + 0.519019i) q^{48} +(6.64077 - 2.21363i) q^{49} +(2.15912 + 4.50979i) q^{50} -12.8633 q^{51} +(-0.676747 - 4.27281i) q^{52} +(3.62387 - 7.11224i) q^{53} +(-5.13433 - 15.8019i) q^{54} +(-2.49257 - 8.00683i) q^{55} +(2.13454 - 1.56325i) q^{56} +(-1.57338 + 1.57338i) q^{57} +(-3.33889 + 1.70125i) q^{58} +(-6.74241 + 4.89865i) q^{59} +(-5.18066 - 5.31037i) q^{60} +(-7.13087 + 9.81481i) q^{61} +(5.23761 + 0.829556i) q^{62} +(15.0381 + 14.9243i) q^{63} +(0.587785 - 0.809017i) q^{64} +(6.92416 - 6.75504i) q^{65} +(7.31360 + 10.0663i) q^{66} +(-2.04722 - 4.01789i) q^{67} +(2.74149 - 2.74149i) q^{68} +(-3.96475 + 12.2022i) q^{69} +(5.61066 + 1.87629i) q^{70} +(2.06350 + 6.35081i) q^{71} +(7.13504 + 3.63548i) q^{72} +(-5.60808 + 0.888233i) q^{73} +1.39249i q^{74} +(2.99939 - 16.3156i) q^{75} -0.670654i q^{76} +(-8.85784 - 4.47100i) q^{77} +(-6.51616 + 12.7887i) q^{78} +(-3.06230 + 0.995001i) q^{79} +(2.23590 + 0.0276436i) q^{80} +(-9.61105 + 29.5798i) q^{81} +(-1.56790 - 1.56790i) q^{82} +(2.58497 + 5.07329i) q^{83} +(-8.77803 + 0.0333422i) q^{84} +(8.54521 + 1.46194i) q^{85} +(7.23454 + 5.25620i) q^{86} +(12.2798 + 1.94493i) q^{87} +(-3.70409 - 0.586670i) q^{88} +(3.65904 + 2.65845i) q^{89} +(2.58227 + 17.7189i) q^{90} +(-0.0434747 - 11.4456i) q^{91} +(-1.75561 - 3.44559i) q^{92} +(-12.4408 - 12.4408i) q^{93} +(-2.37920 + 7.32242i) q^{94} +(1.22403 - 0.866394i) q^{95} +(-3.15542 + 1.02526i) q^{96} +(1.46631 - 2.87780i) q^{97} +(6.21272 - 3.22522i) q^{98} -30.0315i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{7}+O(q^{10}) $ 160 * q + 8 * q^7	$ 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) $ 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{19}{20}\right)$

Coefficient data

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

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

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

$2$	0.987688	−	0.156434i	0.698401	−	0.110616i
$2$	0.987688	−	0.156434i	0.698401	−	0.110616i
$3$	−2.95619	−	1.50625i	−1.70676	−	0.869635i	−0.983919	−	0.178617i	$-0.942838\pi$
$3$	−2.95619	−	1.50625i	−1.70676	−	0.869635i	−0.722837	−	0.691019i	$-0.757162\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	1.79263	+	1.33659i	0.801689	+	0.597742i
$5$	1.79263	+	1.33659i	0.801689	+	0.597742i
$6$	−3.15542	−	1.02526i	−1.28820	−	0.418560i
$7$	2.61159	−	0.423809i	0.987087	−	0.160185i
$7$	2.61159	−	0.423809i	0.987087	−	0.160185i
$8$	0.891007	−	0.453990i	0.315018	−	0.160510i
$9$	4.70689	+	6.47848i	1.56896	+	2.15949i
$10$	1.97965	+	1.03971i	0.626020	+	0.328784i
$11$	−3.03402	−	2.20435i	−0.914793	−	0.664636i	0.0274296	−	0.999624i	$-0.491268\pi$
$11$	−3.03402	−	2.20435i	−0.914793	−	0.664636i	−0.942222	+	0.334988i	$0.891268\pi$
$12$	−3.27696	−	0.519019i	−0.945977	−	0.149828i
$13$	0.676747	−	4.27281i	0.187696	−	1.18506i	−0.696363	−	0.717689i	$-0.745200\pi$
$13$	0.676747	−	4.27281i	0.187696	−	1.18506i	0.884059	−	0.467375i	$-0.154800\pi$
$14$	2.51314	−	0.827134i	0.671664	−	0.221061i
$15$	−3.28611	−	6.65137i	−0.848469	−	1.71738i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	3.45448	−	1.76015i	0.837835	−	0.426898i	0.0182348	−	0.999834i	$-0.494195\pi$
$17$	3.45448	−	1.76015i	0.837835	−	0.426898i	0.819601	+	0.572935i	$0.194195\pi$
$18$	5.66240	+	5.66240i	1.33464	+	1.33464i
$19$	0.207244	−	0.637830i	0.0475449	−	0.146328i	−0.924466	−	0.381265i	$-0.875488\pi$
$19$	0.207244	−	0.637830i	0.0475449	−	0.146328i	0.972011	+	0.234937i	$0.0754884\pi$
$20$	2.11792	+	0.717221i	0.473582	+	0.160375i
$21$	−8.35870	−	2.68085i	−1.82402	−	0.585009i
$22$	−3.34151	−	1.70258i	−0.712412	−	0.362992i
$23$	−0.604943	−	3.81946i	−0.126139	−	0.796413i	−0.966928	−	0.255049i	$-0.917908\pi$
$23$	−0.604943	−	3.81946i	−0.126139	−	0.796413i	0.840789	−	0.541363i	$-0.182092\pi$
$24$	−3.31781			−0.677244
$25$	1.42705	+	4.79203i	0.285409	+	0.958406i
$26$		−	4.32607i		−	0.848412i
$27$	−2.59917	−	16.4105i	−0.500210	−	3.15820i
$28$	2.35280	−	1.21009i	0.444638	−	0.228686i
$29$	−3.56392	+	1.15799i	−0.661803	+	0.215033i	−0.620611	−	0.784118i	$-0.713115\pi$
$29$	−3.56392	+	1.15799i	−0.661803	+	0.215033i	−0.0411919	+	0.999151i	$0.513115\pi$
$30$	−4.28615	−	6.05542i	−0.782541	−	1.10556i
$31$	5.04335	+	1.63868i	0.905813	+	0.294316i	0.724634	−	0.689134i	$-0.242009\pi$
$31$	5.04335	+	1.63868i	0.905813	+	0.294316i	0.181179	+	0.983450i	$0.442009\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	5.64884	+	11.0865i	0.983337	+	1.92991i
$34$	3.13661	−	2.27888i	0.537923	−	0.390824i
$35$	5.24807	+	2.73089i	0.887086	+	0.461605i
$36$	6.47848	+	4.70689i	1.07975	+	0.784482i
$37$	−0.217833	+	1.37534i	−0.0358116	+	0.226105i	−0.999103	−	0.0423537i	$-0.986514\pi$
$37$	−0.217833	+	1.37534i	−0.0358116	+	0.226105i	0.963291	+	0.268459i	$0.0865144\pi$
$38$	0.104913	−	0.662398i	0.0170192	−	0.107455i
$39$	−8.43652	+	11.6119i	−1.35092	+	1.85939i
$40$	2.20405	+	0.377075i	0.348490	+	0.0596207i
$41$	−1.30332	−	1.79387i	−0.203545	−	0.280155i	0.695025	−	0.718985i	$-0.255393\pi$
$41$	−1.30332	−	1.79387i	−0.203545	−	0.280155i	−0.898570	+	0.438830i	$0.855393\pi$
$42$	−8.67517	−	1.34025i	−1.33861	−	0.206806i
$43$	6.32322	+	6.32322i	0.964282	+	0.964282i	0.999384	−	0.0351018i	$-0.0111755\pi$
$43$	6.32322	+	6.32322i	0.964282	+	0.964282i	−0.0351018	+	0.999384i	$0.511176\pi$
$44$	−3.56671	−	1.15889i	−0.537702	−	0.174710i
$45$	−0.221366	+	17.9047i	−0.0329993	+	2.66908i
$46$	−1.19499	−	3.67780i	−0.176192	−	0.542262i
$47$	−3.49539	+	6.86008i	−0.509854	+	1.00065i	0.482345	+	0.875982i	$0.339785\pi$
$47$	−3.49539	+	6.86008i	−0.509854	+	1.00065i	−0.992199	+	0.124664i	$0.960215\pi$
$48$	−3.27696	+	0.519019i	−0.472988	+	0.0749140i
$49$	6.64077	−	2.21363i	0.948682	−	0.316233i
$50$	2.15912	+	4.50979i	0.305345	+	0.637781i
$51$	−12.8633			−1.80123
$52$	−0.676747	−	4.27281i	−0.0938479	−	0.592532i
$53$	3.62387	−	7.11224i	0.497776	−	0.976941i	−0.496289	−	0.868157i	$-0.665304\pi$
$53$	3.62387	−	7.11224i	0.497776	−	0.976941i	0.994065	−	0.108784i	$-0.0346956\pi$
$54$	−5.13433	−	15.8019i	−0.698694	−	2.15036i
$55$	−2.49257	−	8.00683i	−0.336098	−	1.07964i
$56$	2.13454	−	1.56325i	0.285239	−	0.208898i
$57$	−1.57338	+	1.57338i	−0.208400	+	0.208400i
$58$	−3.33889	+	1.70125i	−0.438418	+	0.223385i
$59$	−6.74241	+	4.89865i	−0.877787	+	0.637750i	−0.932665	−	0.360743i	$-0.882523\pi$
$59$	−6.74241	+	4.89865i	−0.877787	+	0.637750i	0.0548778	+	0.998493i	$0.482523\pi$
$60$	−5.18066	−	5.31037i	−0.668820	−	0.685565i
$61$	−7.13087	+	9.81481i	−0.913015	+	1.25666i	0.0531119	+	0.998589i	$0.483086\pi$
$61$	−7.13087	+	9.81481i	−0.913015	+	1.25666i	−0.966127	+	0.258068i	$0.916914\pi$
$62$	5.23761	+	0.829556i	0.665177	+	0.105354i
$63$	15.0381	+	14.9243i	1.89462	+	1.88028i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	6.92416	−	6.75504i	0.858836	−	0.837859i
$66$	7.31360	+	10.0663i	0.900242	+	1.23908i
$67$	−2.04722	−	4.01789i	−0.250108	−	0.490864i	0.731483	−	0.681859i	$-0.238828\pi$
$67$	−2.04722	−	4.01789i	−0.250108	−	0.490864i	−0.981591	+	0.190995i	$0.938828\pi$
$68$	2.74149	−	2.74149i	0.332455	−	0.332455i
$69$	−3.96475	+	12.2022i	−0.477300	+	1.46898i
$70$	5.61066	+	1.87629i	0.670602	+	0.224260i
$71$	2.06350	+	6.35081i	0.244893	+	0.753703i	0.995654	+	0.0931291i	$0.0296869\pi$
$71$	2.06350	+	6.35081i	0.244893	+	0.753703i	−0.750761	+	0.660574i	$0.770313\pi$
$72$	7.13504	+	3.63548i	0.840873	+	0.428446i
$73$	−5.60808	+	0.888233i	−0.656376	+	0.103960i	−0.475734	−	0.879589i	$-0.657818\pi$
$73$	−5.60808	+	0.888233i	−0.656376	+	0.103960i	−0.180642	+	0.983549i	$0.557818\pi$
$74$			1.39249i			0.161873i
$75$	2.99939	−	16.3156i	0.346340	−	1.88397i
$76$		−	0.670654i		−	0.0769293i
$77$	−8.85784	−	4.47100i	−1.00944	−	0.509517i
$78$	−6.51616	+	12.7887i	−0.737810	+	1.44803i
$79$	−3.06230	+	0.995001i	−0.344535	+	0.111946i	−0.476173	−	0.879352i	$-0.657976\pi$
$79$	−3.06230	+	0.995001i	−0.344535	+	0.111946i	0.131638	+	0.991298i	$0.457976\pi$
$80$	2.23590	+	0.0276436i	0.249981	+	0.00309065i
$81$	−9.61105	+	29.5798i	−1.06789	+	3.28664i
$82$	−1.56790	−	1.56790i	−0.173146	−	0.173146i
$83$	2.58497	+	5.07329i	0.283737	+	0.556866i	0.988254	−	0.152822i	$-0.0488360\pi$
$83$	2.58497	+	5.07329i	0.283737	+	0.556866i	−0.704516	+	0.709688i	$0.748836\pi$
$84$	−8.77803	+	0.0333422i	−0.957761	+	0.00363793i
$85$	8.54521	+	1.46194i	0.926858	+	0.158570i
$86$	7.23454	+	5.25620i	0.780120	+	0.566791i
$87$	12.2798	+	1.94493i	1.31654	+	0.208519i
$88$	−3.70409	−	0.586670i	−0.394857	−	0.0625392i
$89$	3.65904	+	2.65845i	0.387857	+	0.281795i	0.764577	−	0.644533i	$-0.222948\pi$
$89$	3.65904	+	2.65845i	0.387857	+	0.281795i	−0.376720	+	0.926327i	$0.622948\pi$
$90$	2.58227	+	17.7189i	0.272196	+	1.86774i
$91$	−0.0434747	−	11.4456i	−0.00455739	−	1.19983i
$92$	−1.75561	−	3.44559i	−0.183035	−	0.359227i
$93$	−12.4408	−	12.4408i	−1.29005	−	1.29005i
$94$	−2.37920	+	7.32242i	−0.245396	+	0.755250i
$95$	1.22403	−	0.866394i	0.125583	−	0.0888901i
$96$	−3.15542	+	1.02526i	−0.322049	+	0.104640i
$97$	1.46631	−	2.87780i	0.148881	−	0.292196i	−0.804506	−	0.593944i	$-0.797570\pi$
$97$	1.46631	−	2.87780i	0.148881	−	0.292196i	0.953388	+	0.301748i	$0.0975701\pi$
$98$	6.21272	−	3.22522i	0.627580	−	0.325797i
$99$		−	30.0315i		−	3.01828i
$100$	2.83802	+	4.11651i	0.283802	+	0.411651i
$101$		−	7.48726i		−	0.745010i	−0.928030	−	0.372505i	$-0.878499\pi$
$101$		−	7.48726i		−	0.745010i	0.928030	−	0.372505i	$-0.121501\pi$
$102$	−12.7050	+	2.01227i	−1.25798	+	0.199244i
$103$	−1.10739	−	0.564244i	−0.109115	−	0.0555966i	0.398581	−	0.917133i	$-0.369503\pi$
$103$	−1.10739	−	0.564244i	−0.109115	−	0.0555966i	−0.507696	+	0.861536i	$0.669503\pi$
$104$	−1.33683	−	4.11434i	−0.131087	−	0.403444i
$105$	−11.4009	−	15.9779i	−1.11261	−	1.55929i
$106$	2.46665	−	7.59157i	0.239582	−	0.737359i
$107$	3.31249	−	3.31249i	0.320231	−	0.320231i	−0.528625	−	0.848856i	$-0.677292\pi$
$107$	3.31249	−	3.31249i	0.320231	−	0.320231i	0.848856	+	0.528625i	$0.177292\pi$
$108$	−7.54308	−	14.8041i	−0.725833	−	1.42453i
$109$	8.22626	+	11.3225i	0.787932	+	1.08450i	0.994362	+	0.106035i	$0.0338154\pi$
$109$	8.22626	+	11.3225i	0.787932	+	1.08450i	−0.206430	+	0.978461i	$0.566185\pi$
$110$	−3.71443	−	7.51833i	−0.354157	−	0.716845i
$111$	2.71557	−	3.73766i	0.257751	−	0.354763i
$112$	1.86371	−	1.87792i	0.176104	−	0.177447i
$113$	−17.6171	−	2.79028i	−1.65728	−	0.262488i	−0.743512	−	0.668722i	$-0.766842\pi$
$113$	−17.6171	−	2.79028i	−1.65728	−	0.262488i	−0.913769	+	0.406235i	$0.866842\pi$
$114$	−1.30788	+	1.80015i	−0.122494	+	0.168599i
$115$	4.02062	−	7.65544i	0.374925	−	0.713874i
$116$	−3.03165	+	2.20262i	−0.281482	+	0.204508i
$117$	30.8667	−	15.7274i	2.85363	−	1.45400i
$118$	−5.89308	+	5.89308i	−0.542502	+	0.542502i
$119$	8.27572	−	6.06082i	0.758634	−	0.555595i
$120$	−5.94760	−	4.43455i	−0.542939	−	0.404817i
$121$	0.946968	+	2.91447i	0.0860880	+	0.264952i
$122$	−5.50771	+	10.8095i	−0.498644	+	0.978645i
$123$	1.15085	+	7.26615i	0.103768	+	0.655167i
$124$	5.30290			0.476214
$125$	−3.84682	+	10.4977i	−0.344070	+	0.938944i
$126$	17.1876	+	12.3881i	1.53120	+	1.10362i
$127$	−12.3535	+	1.95661i	−1.09620	+	0.173621i	−0.678237	−	0.734843i	$-0.737256\pi$
$127$	−12.3535	+	1.95661i	−1.09620	+	0.173621i	−0.417962	+	0.908464i	$0.637256\pi$
$128$	0.453990	−	0.891007i	0.0401275	−	0.0787546i
$129$	−9.16826	−	28.2170i	−0.807220	−	2.48437i
$130$	5.78219	−	7.75505i	0.507132	−	0.680163i
$131$	−9.78191	−	3.17834i	−0.854650	−	0.277693i	−0.151257	−	0.988494i	$-0.548332\pi$
$131$	−9.78191	−	3.17834i	−0.854650	−	0.277693i	−0.703392	+	0.710802i	$0.748332\pi$
$132$	8.79828	+	8.79828i	0.765792	+	0.765792i
$133$	0.270916	−	1.75358i	0.0234914	−	0.152055i
$134$	−2.65055	−	3.64817i	−0.228973	−	0.315154i
$135$	17.2748	−	32.8920i	1.48678	−	2.83089i
$136$	2.27888	−	3.13661i	0.195412	−	0.268962i
$137$	−2.34567	+	14.8100i	−0.200404	+	1.26530i	0.658271	+	0.752781i	$0.271288\pi$
$137$	−2.34567	+	14.8100i	−0.200404	+	1.26530i	−0.858675	+	0.512520i	$0.828712\pi$
$138$	−2.00708	+	12.6722i	−0.170854	+	1.07873i
$139$	−0.198440	−	0.144175i	−0.0168314	−	0.0122288i	0.579338	−	0.815088i	$-0.303311\pi$
$139$	−0.198440	−	0.144175i	−0.0168314	−	0.0122288i	−0.596169	+	0.802859i	$0.703311\pi$
$140$	5.83510	+	0.975489i	0.493156	+	0.0824439i
$141$	20.6660	−	15.0148i	1.74039	−	1.26447i
$142$	3.03159	+	5.94982i	0.254405	+	0.499298i
$143$	−11.4720	+	11.4720i	−0.959339	+	0.959339i
$144$	7.61591	+	2.47456i	0.634659	+	0.206213i
$145$	−7.93655	−	2.68766i	−0.659094	−	0.223198i
$146$	−5.40009	+	1.75459i	−0.446914	+	0.145211i
$147$	−22.9657	−	3.45877i	−1.89418	−	0.285275i
$148$	0.217833	+	1.37534i	0.0179058	+	0.113053i
$149$			13.1868i			1.08030i	0.841568	+	0.540152i	$0.181633\pi$
$149$			13.1868i			1.08030i	−0.841568	+	0.540152i	$0.818367\pi$
$150$	0.410136	−	16.5840i	0.0334875	−	1.35407i
$151$	20.1966			1.64358			0.821789	−	0.569793i	$-0.192976\pi$
$151$	20.1966			1.64358			0.821789	+	0.569793i	$0.192976\pi$
$152$	−0.104913	−	0.662398i	−0.00850961	−	0.0537275i
$153$	27.6630	+	14.0950i	2.23642	+	1.13951i
$154$	−9.44820	−	3.03028i	−0.761358	−	0.244187i
$155$	6.85061	+	9.67846i	0.550255	+	0.777392i
$156$	−4.43534	+	13.6506i	−0.355112	+	1.09292i
$157$	0.927618	+	0.927618i	0.0740320	+	0.0740320i	0.743153	−	0.669121i	$-0.233329\pi$
$157$	0.927618	+	0.927618i	0.0740320	+	0.0740320i	−0.669121	+	0.743153i	$0.733329\pi$
$158$	−2.86894	+	1.46180i	−0.228241	+	0.116295i
$159$	−21.4257	+	15.5666i	−1.69916	+	1.23452i
$160$	2.21269	−	0.322468i	0.174929	−	0.0254933i
$161$	−3.19858	−	9.71847i	−0.252084	−	0.765923i
$162$	−4.86543	+	30.7191i	−0.382264	+	2.41352i
$163$	−1.11565	−	0.176701i	−0.0873843	−	0.0138403i	0.112589	−	0.993642i	$-0.464086\pi$
$163$	−1.11565	−	0.176701i	−0.0873843	−	0.0138403i	−0.199973	+	0.979801i	$0.564086\pi$
$164$	−1.79387	−	1.30332i	−0.140078	−	0.101772i
$165$	−4.69180	+	27.4241i	−0.365256	+	2.13497i
$166$	3.34678	+	4.60645i	0.259761	+	0.357530i
$167$	−14.7128	+	7.49655i	−1.13851	+	0.580101i	−0.918509	−	0.395399i	$-0.870606\pi$
$167$	−14.7128	+	7.49655i	−1.13851	+	0.580101i	−0.220002	+	0.975499i	$0.570606\pi$
$168$	−8.66474	+	1.40612i	−0.668499	+	0.108484i
$169$	−5.43519	−	1.76600i	−0.418091	−	0.135846i
$170$	8.66870	+	0.107176i	0.664859	+	0.00822002i
$171$	5.10764	−	1.65957i	0.390591	−	0.126911i
$172$	7.96772	+	4.05976i	0.607533	+	0.309554i
$173$	−2.95758	+	0.468435i	−0.224861	+	0.0356145i	−0.267848	−	0.963461i	$-0.586313\pi$
$173$	−2.95758	+	0.468435i	−0.224861	+	0.0356145i	0.0429872	+	0.999076i	$0.486313\pi$
$174$	12.4329			0.942536
$175$	5.75776	+	11.9100i	0.435246	+	0.900312i
$176$	−3.75026			−0.282687
$177$	27.3104	−	4.32555i	2.05278	−	0.325128i
$178$	4.02986	+	2.05332i	0.302051	+	0.153903i
$179$	−13.3756	+	4.34598i	−0.999736	+	0.324834i	−0.762760	−	0.646682i	$-0.776156\pi$
$179$	−13.3756	+	4.34598i	−0.999736	+	0.324834i	−0.236976	+	0.971516i	$0.576156\pi$
$180$	5.32233	+	17.0968i	0.396703	+	1.27432i
$181$	0.900037	+	0.292440i	0.0668993	+	0.0217369i	0.342275	−	0.939600i	$-0.388802\pi$
$181$	0.900037	+	0.292440i	0.0668993	+	0.0217369i	−0.275376	+	0.961337i	$0.588802\pi$
$182$	−1.83343	−	11.2979i	−0.135903	−	0.837457i
$183$	35.8638	−	18.2735i	2.65113	−	1.35082i
$184$	−2.27301	−	3.12853i	−0.167568	−	0.230638i
$185$	−2.22877	+	2.17433i	−0.163862	+	0.159860i
$186$	−14.2338	−	10.3415i	−1.04368	−	0.758274i
$187$	−14.3610	−	2.27455i	−1.05018	−	0.166332i
$188$	−1.20443	+	7.60446i	−0.0878419	+	0.554612i
$189$	−13.7429	−	41.7559i	−0.999647	−	3.03729i
$190$	1.07343	−	1.04721i	0.0778745	−	0.0759724i
$191$	−7.53888	+	5.47731i	−0.545494	+	0.396325i	−0.826121	−	0.563492i	$-0.809457\pi$
$191$	−7.53888	+	5.47731i	−0.545494	+	0.396325i	0.280627	+	0.959817i	$0.409457\pi$
$192$	−2.95619	+	1.50625i	−0.213344	+	0.108704i
$193$	−12.3943	−	12.3943i	−0.892158	−	0.892158i	0.102568	−	0.994726i	$-0.467294\pi$
$193$	−12.3943	−	12.3943i	−0.892158	−	0.892158i	−0.994726	+	0.102568i	$0.967294\pi$
$194$	0.998072	−	3.07175i	0.0716574	−	0.220539i
$195$	−30.6439	+	9.53962i	−2.19446	+	0.683146i
$196$	5.63170	−	4.15740i	0.402264	−	0.296957i
$197$	−12.1712	−	6.20155i	−0.867164	−	0.441842i	−0.0369699	−	0.999316i	$-0.511771\pi$
$197$	−12.1712	−	6.20155i	−0.867164	−	0.441842i	−0.830194	+	0.557474i	$0.811771\pi$
$198$	−4.69796	−	29.6618i	−0.333870	−	2.10797i
$199$	22.8013			1.61634			0.808171	−	0.588948i	$-0.200458\pi$
$199$	22.8013			1.61634			0.808171	+	0.588948i	$0.200458\pi$
$200$	3.44704	+	3.62186i	0.243743	+	0.256104i
$201$			14.9613i			1.05529i
$202$	−1.17127	−	7.39508i	−0.0824099	−	0.520316i
$203$	−8.81672	+	4.53461i	−0.618812	+	0.318267i
$204$	−12.2338	+	3.97499i	−0.856534	+	0.278305i
$205$	0.0612955	−	4.95776i	0.00428106	−	0.346265i
$206$	−1.18203	−	0.384063i	−0.0823556	−	0.0267590i
$207$	21.8969	−	21.8969i	1.52194	−	1.52194i
$208$	−1.96400	−	3.85456i	−0.136179	−	0.267266i
$209$	−2.03478	+	1.47836i	−0.140749	+	0.102260i
$210$	−13.7600	−	13.9977i	−0.949530	−	0.965936i
$211$	21.1406	+	15.3595i	1.45538	+	1.05739i	0.984538	+	0.175173i	$0.0560486\pi$
$211$	21.1406	+	15.3595i	1.45538	+	1.05739i	0.470839	+	0.882219i	$0.343951\pi$
$212$	1.24870	−	7.88398i	0.0857610	−	0.541474i
$213$	3.46582	−	21.8824i	0.237474	−	1.49935i
$214$	2.75352	−	3.78990i	0.188227	−	0.259072i
$215$	2.88363	+	19.7868i	0.196662	+	1.34945i
$216$	−9.76608	−	13.4419i	−0.664498	−	0.914603i
$217$	13.8656	+	2.14215i	0.941261	+	0.145418i
$218$	9.89620	+	9.89620i	0.670255	+	0.670255i
$219$	17.9164	+	5.82141i	1.21068	+	0.393374i
$220$	−4.84482	−	6.84470i	−0.326638	−	0.461470i
$221$	−5.18297	−	15.9515i	−0.348644	−	1.07302i
$222$	2.09744	−	4.11646i	0.140771	−	0.276278i
$223$	13.0630	−	2.06898i	0.874766	−	0.138549i	0.297124	−	0.954839i	$-0.403973\pi$
$223$	13.0630	−	2.06898i	0.874766	−	0.138549i	0.577643	+	0.816290i	$0.303973\pi$
$224$	1.54699	−	2.14635i	0.103363	−	0.143409i
$225$	−24.3281	+	31.8007i	−1.62187	+	2.12004i
$226$	−17.8367			−1.18648
$227$	2.14652	+	13.5526i	0.142470	+	0.899518i	0.950578	+	0.310485i	$0.100491\pi$
$227$	2.14652	+	13.5526i	0.142470	+	0.899518i	−0.808109	+	0.589033i	$0.799509\pi$
$228$	−1.01018	+	1.98258i	−0.0669005	+	0.131300i
$229$	2.20096	+	6.77387i	0.145444	+	0.447630i	0.997068	−	0.0765232i	$-0.0243819\pi$
$229$	2.20096	+	6.77387i	0.145444	+	0.447630i	−0.851624	+	0.524153i	$0.824382\pi$
$230$	2.77354	−	8.19015i	0.182882	−	0.540043i
$231$	19.4510	+	26.5593i	1.27978	+	1.74747i
$232$	−2.64976	+	2.64976i	−0.173965	+	0.173965i
$233$	11.7726	−	5.99844i	0.771249	−	0.392971i	−0.0236442	−	0.999720i	$-0.507527\pi$
$233$	11.7726	−	5.99844i	0.771249	−	0.392971i	0.794893	+	0.606749i	$0.207527\pi$
$234$	28.0264	−	20.3624i	1.83214	−	1.33113i
$235$	−15.4351	+	7.62568i	−1.00687	+	0.497445i
$236$	−4.89865	+	6.74241i	−0.318875	+	0.438894i
$237$	10.5514	+	1.67119i	0.685390	+	0.108555i
$238$	7.22571	−	7.28081i	0.468373	−	0.471945i
$239$	−1.69453	+	2.33232i	−0.109610	+	0.150865i	−0.860298	−	0.509792i	$-0.829722\pi$
$239$	−1.69453	+	2.33232i	−0.109610	+	0.150865i	0.750688	+	0.660657i	$0.229722\pi$
$240$	−6.56809	−	3.44955i	−0.423969	−	0.222667i
$241$	−17.9306	−	24.6794i	−1.15501	−	1.58974i	−0.728147	−	0.685421i	$-0.759618\pi$
$241$	−17.9306	−	24.6794i	−1.15501	−	1.58974i	−0.426865	−	0.904315i	$-0.640382\pi$
$242$	1.39123	+	2.73045i	0.0894318	+	0.175520i
$243$	37.7208	−	37.7208i	2.41979	−	2.41979i
$244$	−3.74892	+	11.5380i	−0.240000	+	0.738644i
$245$	14.8632	+	4.90778i	0.949573	+	0.313546i
$246$	2.27335	+	6.99666i	0.144944	+	0.446091i
$247$	−2.58508	−	1.31716i	−0.164484	−	0.0838090i
$248$	5.23761	−	0.829556i	0.332588	−	0.0526768i
$249$		−	18.8912i		−	1.19718i
$250$	−2.15725	+	10.9702i	−0.136437	+	0.693819i
$251$		−	17.6424i		−	1.11358i	−0.830653	−	0.556791i	$-0.812033\pi$
$251$		−	17.6424i		−	1.11358i	0.830653	−	0.556791i	$-0.187967\pi$
$252$	18.9139	+	9.54682i	1.19147	+	0.601393i
$253$	−6.58401	+	12.9218i	−0.413933	+	0.812389i
$254$	−11.8954	+	3.86504i	−0.746382	+	0.242514i
$255$	−23.0592	−	17.1930i	−1.44402	−	1.07667i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	9.35931	+	9.35931i	0.583818	+	0.583818i	0.935950	−	0.352132i	$-0.114543\pi$
$257$	9.35931	+	9.35931i	0.583818	+	0.583818i	−0.352132	+	0.935950i	$0.614543\pi$
$258$	−13.4695	−	26.4354i	−0.838574	−	1.64579i
$259$	0.0139938	+	3.68415i	0.000869531	+	0.228922i
$260$	4.49785	−	8.56410i	0.278945	−	0.531123i
$261$	−24.2770	−	17.6383i	−1.50271	−	1.09178i
$262$	−10.1587	−	1.60898i	−0.627606	−	0.0994030i
$263$	−10.8176	−	1.71333i	−0.667040	−	0.105649i	−0.186274	−	0.982498i	$-0.559641\pi$
$263$	−10.8176	−	1.71333i	−0.667040	−	0.105649i	−0.480766	+	0.876849i	$0.659641\pi$
$264$	10.0663	+	7.31360i	0.619538	+	0.450121i
$265$	16.0024	−	7.90598i	0.983020	−	0.485661i
$266$	−0.00673973	−	1.77437i	−0.000413239	−	0.108794i
$267$	−6.81251	−	13.3703i	−0.416919	−	0.818249i
$268$	−3.18862	−	3.18862i	−0.194776	−	0.194776i
$269$	2.14254	−	6.59405i	0.130633	−	0.402047i	−0.864252	−	0.503058i	$-0.832208\pi$
$269$	2.14254	−	6.59405i	0.130633	−	0.402047i	0.994885	+	0.101012i	$0.0322080\pi$
$270$	11.9167	−	35.1894i	0.725225	−	2.14156i
$271$	−8.45892	+	2.74847i	−0.513843	+	0.166958i	−0.554449	−	0.832218i	$-0.687071\pi$
$271$	−8.45892	+	2.74847i	−0.513843	+	0.166958i	0.0406065	+	0.999175i	$0.487071\pi$
$272$	1.76015	−	3.45448i	0.106725	−	0.209459i
$273$	−17.1115	+	33.9009i	−1.03563	+	2.05178i
$274$			14.9946i			0.905856i
$275$	6.23360	−	17.6848i	0.375901	−	1.06644i
$276$			12.8302i			0.772287i
$277$	23.7077	−	3.75494i	1.42446	−	0.225612i	0.603848	−	0.797099i	$-0.293633\pi$
$277$	23.7077	−	3.75494i	1.42446	−	0.225612i	0.820611	+	0.571487i	$0.193633\pi$
$278$	−0.218551	−	0.111357i	−0.0131078	−	0.00667875i
$279$	13.1223	+	40.3864i	0.785613	+	2.41787i
$280$	5.91586	+	0.0506681i	0.353540	+	0.00302800i
$281$	9.40822	−	28.9555i	0.561247	−	1.72734i	−0.117600	−	0.993061i	$-0.537520\pi$
$281$	9.40822	−	28.9555i	0.561247	−	1.72734i	0.678847	−	0.734280i	$-0.262480\pi$
$282$	18.0628	−	18.0628i	1.07562	−	1.07562i
$283$	−3.68107	−	7.22450i	−0.218817	−	0.429452i	0.755337	−	0.655336i	$-0.227473\pi$
$283$	−3.68107	−	7.22450i	−0.218817	−	0.429452i	−0.974154	+	0.225884i	$0.927473\pi$
$284$	3.92502	+	5.40232i	0.232907	+	0.320569i
$285$	−4.92347	+	0.717524i	−0.291641	+	0.0425025i
$286$	−9.53617	+	13.1254i	−0.563885	+	0.776122i
$287$	−4.16400	−	4.13249i	−0.245793	−	0.243933i
$288$	7.90925	+	1.25270i	0.466057	+	0.0738162i
$289$	−1.15701	+	1.59249i	−0.0680594	+	0.0936758i
$290$	−8.25928	−	1.41302i	−0.485001	−	0.0829755i
$291$	−8.66938	+	6.29867i	−0.508208	+	0.369235i
$292$	−5.05912	+	2.57775i	−0.296063	+	0.150852i
$293$	1.90870	−	1.90870i	0.111507	−	0.111507i	−0.649152	−	0.760659i	$-0.724876\pi$
$293$	1.90870	−	1.90870i	0.111507	−	0.111507i	0.760659	+	0.649152i	$0.224876\pi$
$294$	−23.2240	+	0.176429i	−1.35445	+	0.0102896i
$295$	−18.6341	−	0.230384i	−1.08492	−	0.0134135i
$296$	0.430303	+	1.32434i	0.0250108	+	0.0769754i
$297$	−28.2885	+	55.5193i	−1.64147	+	3.22156i
$298$	2.06287	+	13.0244i	0.119499	+	0.754485i
$299$	−16.7292			−0.967476
$300$	−2.18922	−	16.4439i	−0.126394	−	0.949392i
$301$	19.1935	+	13.8338i	1.10629	+	0.797367i
$302$	19.9480	−	3.15945i	1.14788	−	0.181806i
$303$	−11.2777	+	22.1337i	−0.647887	+	1.27155i
$304$	−0.207244	−	0.637830i	−0.0118862	−	0.0365821i
$305$	−25.9014	+	8.06325i	−1.48311	+	0.461700i
$306$	29.5273	+	9.59401i	1.68796	+	0.548453i
$307$	−10.4888	−	10.4888i	−0.598628	−	0.598628i	0.341319	−	0.939947i	$-0.389126\pi$
$307$	−10.4888	−	10.4888i	−0.598628	−	0.598628i	−0.939947	+	0.341319i	$0.889126\pi$
$308$	−9.80592	−	1.51495i	−0.558744	−	0.0863221i
$309$	2.42376	+	3.33602i	0.137883	+	0.189780i
$310$	8.28032	+	8.48763i	0.470290	+	0.482065i
$311$	−3.57663	+	4.92281i	−0.202812	+	0.279147i	−0.898292	−	0.439398i	$-0.855192\pi$
$311$	−3.57663	+	4.92281i	−0.202812	+	0.279147i	0.695480	+	0.718545i	$0.255192\pi$
$312$	−2.24531	+	14.1764i	−0.127116	+	0.802578i
$313$	−0.200361	+	1.26503i	−0.0113251	+	0.0715038i	−0.992704	−	0.120580i	$-0.961525\pi$
$313$	−0.200361	+	1.26503i	−0.0113251	+	0.0715038i	0.981379	+	0.192084i	$0.0615246\pi$
$314$	1.06131	+	0.771086i	0.0598931	+	0.0435149i
$315$	7.01007	+	46.8535i	0.394973	+	2.63990i
$316$	−2.60495	+	1.89260i	−0.146540	+	0.106467i
$317$	−8.77995	−	17.2316i	−0.493131	−	0.967824i	−0.994711	−	0.102713i	$-0.967248\pi$
$317$	−8.77995	−	17.2316i	−0.493131	−	0.967824i	0.501580	−	0.865111i	$-0.332752\pi$
$318$	−18.7267	+	18.7267i	−1.05014	+	1.05014i
$319$	13.3656	+	4.34275i	0.748331	+	0.243148i
$320$	2.13501	−	0.664640i	0.119351	−	0.0371545i
$321$	−14.7818	+	4.80290i	−0.825039	+	0.268071i
$322$	−4.67951	−	9.09845i	−0.260779	−	0.507037i
$323$	−0.406756	−	2.56815i	−0.0226325	−	0.142896i
$324$			31.1020i			1.72789i
$325$	21.4412	−	2.85451i	1.18934	−	0.158340i
$326$	−1.12955			−0.0625603
$327$	−7.26385	−	45.8622i	−0.401692	−	2.53618i
$328$	−1.97567	−	1.00665i	−0.109088	−	0.0555832i
$329$	−6.22114	+	19.3971i	−0.342982	+	1.06940i
$330$	−0.343960	+	27.8205i	−0.0189344	+	1.53147i
$331$	0.0967457	−	0.297753i	0.00531763	−	0.0163660i	−0.948362	−	0.317189i	$-0.897261\pi$
$331$	0.0967457	−	0.297753i	0.00531763	−	0.0163660i	0.953680	+	0.300823i	$0.0972612\pi$
$332$	4.02619	+	4.02619i	0.220966	+	0.220966i
$333$	−9.93546	+	5.06237i	−0.544460	+	0.277416i
$334$	−13.3590	+	9.70585i	−0.730969	+	0.531080i
$335$	1.70038	−	9.93889i	0.0929015	−	0.543020i
$336$	−8.33810	+	2.74427i	−0.454881	+	0.149712i
$337$	2.21427	−	13.9803i	0.120619	−	0.761557i	−0.851028	−	0.525120i	$-0.824020\pi$
$337$	2.21427	−	13.9803i	0.120619	−	0.761557i	0.971647	−	0.236437i	$-0.0759796\pi$
$338$	−5.64453	−	0.894006i	−0.307022	−	0.0486275i
$339$	47.8767	+	34.7845i	2.60031	+	1.88923i
$340$	8.57874	−	1.25023i	0.465248	−	0.0678031i
$341$	−11.6894	−	16.0891i	−0.633018	−	0.871274i
$342$	4.78515	−	2.43815i	0.258751	−	0.131840i
$343$	16.4048	−	8.59551i	0.885776	−	0.464114i
$344$	8.50471	+	2.76335i	0.458543	+	0.148990i
$345$	−23.4167	+	16.5749i	−1.26071	+	0.892360i
$346$	−2.84789	+	0.925336i	−0.153104	+	0.0497464i
$347$	−2.31826	−	1.18121i	−0.124451	−	0.0634108i	0.390657	−	0.920536i	$-0.372248\pi$
$347$	−2.31826	−	1.18121i	−0.124451	−	0.0634108i	−0.515107	+	0.857126i	$0.672248\pi$
$348$	12.2798	−	1.94493i	0.658268	−	0.104259i
$349$	19.8451			1.06228			0.531141	−	0.847283i	$-0.321763\pi$
$349$	19.8451			1.06228			0.531141	+	0.847283i	$0.321763\pi$
$350$	7.55001	+	10.8627i	0.403565	+	0.580634i
$351$	−71.8779			−3.83656
$352$	−3.70409	+	0.586670i	−0.197429	+	0.0312696i
$353$	26.4395	+	13.4716i	1.40723	+	0.717021i	0.982144	−	0.188130i	$-0.0602426\pi$
$353$	26.4395	+	13.4716i	1.40723	+	0.717021i	0.425090	+	0.905151i	$0.360243\pi$
$354$	26.2975	−	8.54459i	1.39770	−	0.454140i
$355$	−4.78934	+	14.1427i	−0.254192	+	0.750618i
$356$	4.30146	+	1.39763i	0.227977	+	0.0740741i
$357$	−33.5937	+	5.45160i	−1.77797	+	0.288529i
$358$	−12.5310	+	6.38487i	−0.662285	+	0.337451i
$359$	4.06625	+	5.59671i	0.214608	+	0.295383i	0.902726	−	0.430216i	$-0.141563\pi$
$359$	4.06625	+	5.59671i	0.214608	+	0.295383i	−0.688118	+	0.725599i	$0.741563\pi$
$360$	7.93133	+	16.0537i	0.418018	+	0.846105i
$361$	15.0074	+	10.9035i	0.789866	+	0.573871i
$362$	0.934704	+	0.148043i	0.0491270	+	0.00778095i
$363$	1.59051	−	10.0421i	0.0834802	−	0.527073i
$364$	−3.57824	−	10.8720i	−0.187551	−	0.569848i
$365$	−11.2404	−	5.90344i	−0.588351	−	0.309000i
$366$	32.5636	−	23.6589i	1.70213	−	1.23667i
$367$	−15.6257	+	7.96169i	−0.815654	+	0.415597i	−0.811470	−	0.584395i	$-0.801332\pi$
$367$	−15.6257	+	7.96169i	−0.815654	+	0.415597i	−0.00418472	+	0.999991i	$0.501332\pi$
$368$	−2.73443	−	2.73443i	−0.142542	−	0.142542i
$369$	5.48695	−	16.8871i	0.285639	−	0.879108i
$370$	−1.86119	+	2.49622i	−0.0967586	+	0.129772i
$371$	6.44981	−	20.1101i	0.334857	−	1.04406i
$372$	−15.6764	−	7.98750i	−0.812781	−	0.414133i
$373$	−2.18035	−	13.7662i	−0.112894	−	0.712787i	−0.977594	−	0.210498i	$-0.932491\pi$
$373$	−2.18035	−	13.7662i	−0.112894	−	0.712787i	0.864700	−	0.502289i	$-0.167509\pi$
$374$	−14.5400			−0.751844
$375$	27.1841	−	25.2389i	1.40378	−	1.30333i
$376$			7.69925i			0.397058i
$377$	2.53599	+	16.0116i	0.130610	+	0.824640i
$378$	−20.1057	−	39.0919i	−1.03413	−	2.01067i
$379$	13.3192	−	4.32767i	0.684162	−	0.222298i	0.0537452	−	0.998555i	$-0.482884\pi$
$379$	13.3192	−	4.32767i	0.684162	−	0.222298i	0.630417	+	0.776257i	$0.282884\pi$
$380$	0.896391	−	1.20224i	0.0459839	−	0.0616734i
$381$	39.4665	+	12.8235i	2.02193	+	0.656965i
$382$	−6.58922	+	6.58922i	−0.337134	+	0.337134i
$383$	5.85269	+	11.4866i	0.299059	+	0.586935i	0.990820	−	0.135191i	$-0.0431648\pi$
$383$	5.85269	+	11.4866i	0.299059	+	0.586935i	−0.691761	+	0.722127i	$0.743165\pi$
$384$	−2.68416	+	1.95016i	−0.136976	+	0.0995186i
$385$	−9.90294	−	19.8542i	−0.504700	−	1.01186i
$386$	−14.1806	−	10.3028i	−0.721771	−	0.524397i
$387$	−11.2021	+	70.7276i	−0.569437	+	3.59528i
$388$	0.505256	−	3.19006i	0.0256505	−	0.161951i
$389$	−19.1824	+	26.4023i	−0.972585	+	1.33865i	−0.0318555	+	0.999492i	$0.510142\pi$
$389$	−19.1824	+	26.4023i	−0.972585	+	1.33865i	−0.940730	+	0.339157i	$0.889858\pi$
$390$	−28.7743	+	14.2159i	−1.45704	+	0.719852i
$391$	−8.81258	−	12.1295i	−0.445671	−	0.613414i
$392$	4.91200	−	4.98721i	0.248094	−	0.251892i
$393$	24.1298	+	24.1298i	1.21719	+	1.21719i
$394$	−12.9915	−	4.22120i	−0.654503	−	0.212661i
$395$	−6.81948	−	2.30937i	−0.343125	−	0.116197i
$396$	−9.28024	−	28.5616i	−0.466350	−	1.43528i
$397$	0.894683	−	1.75591i	0.0449028	−	0.0881268i	−0.867465	−	0.497498i	$-0.834252\pi$
$397$	0.894683	−	1.75591i	0.0449028	−	0.0881268i	0.912368	+	0.409372i	$0.134252\pi$
$398$	22.5206	−	3.56691i	1.12885	−	0.178793i
$399$	−3.44222	+	4.77585i	−0.172326	+	0.239091i
$400$	3.97119	+	3.03804i	0.198559	+	0.151902i
$401$	−15.0001			−0.749069			−0.374535	−	0.927213i	$-0.622197\pi$
$401$	−15.0001			−0.749069			−0.374535	+	0.927213i	$0.622197\pi$
$402$	2.34046	+	14.7771i	0.116732	+	0.737014i
$403$	10.4149	−	20.4403i	0.518801	−	1.01820i
$404$	−2.31369	−	7.12081i	−0.115110	−	0.354273i
$405$	−56.7651	+	40.1795i	−2.82068	+	1.99654i
$406$	−7.99880	+	5.85802i	−0.396974	+	0.290729i
$407$	3.69265	−	3.69265i	0.183038	−	0.183038i
$408$	−11.4613	+	5.83983i	−0.567419	+	0.289115i
$409$	16.5114	−	11.9963i	0.816438	−	0.593177i	−0.0992520	−	0.995062i	$-0.531645\pi$
$409$	16.5114	−	11.9963i	0.816438	−	0.593177i	0.915690	+	0.401885i	$0.131645\pi$
$410$	−0.715023	−	4.90631i	−0.0353125	−	0.242305i
$411$	29.2418	−	40.2479i	1.44239	−	1.98528i
$412$	−1.22755	−	0.194425i	−0.0604772	−	0.00957865i
$413$	−15.5323	+	15.6507i	−0.764295	+	0.770123i
$414$	18.2019	−	25.0527i	0.894574	−	1.23128i
$415$	−2.14702	+	12.5496i	−0.105393	+	0.616035i
$416$	−2.54280	−	3.49987i	−0.124671	−	0.171595i
$417$	0.369461	+	0.725109i	0.0180926	+	0.0355087i
$418$	−1.77846	+	1.77846i	−0.0869876	+	0.0869876i
$419$	2.24822	−	6.91932i	0.109833	−	0.338031i	−0.881001	−	0.473114i	$-0.843130\pi$
$419$	2.24822	−	6.91932i	0.109833	−	0.338031i	0.990834	+	0.135083i	$0.0431300\pi$
$420$	−15.7803	−	11.6729i	−0.770001	−	0.569578i
$421$	−3.87271	−	11.9190i	−0.188744	−	0.580895i	0.811249	−	0.584701i	$-0.198788\pi$
$421$	−3.87271	−	11.9190i	−0.188744	−	0.580895i	−0.999993	+	0.00380647i	$0.998788\pi$
$422$	23.2830	+	11.8633i	1.13340	+	0.577497i
$423$	−60.8953	+	9.64487i	−2.96083	+	0.468950i
$424$		−	7.98225i		−	0.387652i
$425$	13.3644	+	14.0422i	0.648268	+	0.681145i
$426$		−	22.1551i		−	1.07342i
$427$	−14.4633	+	28.6543i	−0.699928	+	1.38668i
$428$	2.12675	−	4.17398i	0.102800	−	0.201757i
$429$	51.1932	−	16.6337i	2.47163	−	0.803082i
$430$	5.94346	+	19.0920i	0.286619	+	0.920700i
$431$	−1.09682	+	3.37565i	−0.0528317	+	0.162599i	−0.973991	−	0.226586i	$-0.927244\pi$
$431$	−1.09682	+	3.37565i	−0.0528317	+	0.162599i	0.921159	+	0.389186i	$0.127244\pi$
$432$	−11.7486	−	11.7486i	−0.565256	−	0.565256i
$433$	3.20202	+	6.28432i	0.153879	+	0.302005i	0.955057	−	0.296421i	$-0.0957931\pi$
$433$	3.20202	+	6.28432i	0.153879	+	0.302005i	−0.801178	+	0.598426i	$0.795793\pi$
$434$	14.0300	−	0.0532913i	0.673463	−	0.00255806i
$435$	19.4136	+	19.8997i	0.930812	+	0.954116i
$436$	11.3225	+	8.22626i	0.542248	+	0.393966i
$437$	−2.56154	−	0.405708i	−0.122535	−	0.0194076i
$438$	18.6065	+	2.94699i	0.889055	+	0.140812i
$439$	2.90257	+	2.10884i	0.138532	+	0.100650i	0.654893	−	0.755722i	$-0.272714\pi$
$439$	2.90257	+	2.10884i	0.138532	+	0.100650i	−0.516361	+	0.856371i	$0.672714\pi$
$440$	−5.85592	−	6.00254i	−0.279170	−	0.286160i
$441$	45.5984	+	32.6028i	2.17135	+	1.55251i
$442$	−7.61452	−	14.9443i	−0.362186	−	0.710830i
$443$	17.6360	+	17.6360i	0.837910	+	0.837910i	0.988584	−	0.150673i	$-0.0481442\pi$
$443$	17.6360	+	17.6360i	0.837910	+	0.837910i	−0.150673	+	0.988584i	$0.548144\pi$
$444$	1.42766	−	4.39389i	0.0677538	−	0.208525i
$445$	3.00604	+	9.65625i	0.142500	+	0.457750i
$446$	12.5786	−	4.08702i	0.595612	−	0.193526i
$447$	19.8626	−	38.9826i	0.939470	−	1.84381i
$448$	1.19218	−	2.36193i	0.0563254	−	0.111591i
$449$			3.56590i			0.168285i	0.996454	+	0.0841426i	$0.0268151\pi$
$449$			3.56590i			0.168285i	−0.996454	+	0.0841426i	$0.973185\pi$
$450$	−19.0539	+	35.2149i	−0.898208	+	1.66005i
$451$			8.31562i			0.391567i
$452$	−17.6171	+	2.79028i	−0.828641	+	0.131244i
$453$	−59.7050	−	30.4212i	−2.80518	−	1.42931i
$454$	4.24019	+	13.0500i	0.199002	+	0.612465i
$455$	15.2202	−	20.5759i	0.713534	−	0.964612i
$456$	−0.687594	+	2.11620i	−0.0321996	+	0.0991000i
$457$	−5.57340	+	5.57340i	−0.260713	+	0.260713i	−0.825344	−	0.564631i	$-0.809019\pi$
$457$	−5.57340	+	5.57340i	−0.260713	+	0.260713i	0.564631	+	0.825344i	$0.309019\pi$
$458$	3.23353	+	6.34617i	0.151093	+	0.296537i
$459$	−37.8637	−	52.1149i	−1.76732	−	2.43251i
$460$	1.45817	−	8.52320i	0.0679877	−	0.397396i
$461$	21.5232	−	29.6242i	1.00244	−	1.37974i	0.0786187	−	0.996905i	$-0.474949\pi$
$461$	21.5232	−	29.6242i	1.00244	−	1.37974i	0.923818	−	0.382831i	$-0.125051\pi$
$462$	23.3663	+	23.1895i	1.08710	+	1.07887i
$463$	−36.4489	−	5.77294i	−1.69393	−	0.268291i	−0.766485	−	0.642262i	$-0.777996\pi$
$463$	−36.4489	−	5.77294i	−1.69393	−	0.268291i	−0.927440	+	0.373971i	$0.877996\pi$
$464$	−2.20262	+	3.03165i	−0.102254	+	0.140741i
$465$	−5.67350	−	38.9301i	−0.263102	−	1.80534i
$466$	10.6893	−	7.76623i	0.495172	−	0.359764i
$467$	−34.6748	+	17.6677i	−1.60456	+	0.817562i	−0.604780	+	0.796392i	$0.706739\pi$
$467$	−34.6748	+	17.6677i	−1.60456	+	0.817562i	−0.999776	+	0.0211701i	$0.993261\pi$
$468$	24.4959	−	24.4959i	1.13233	−	1.13233i
$469$	−7.04931	−	9.62545i	−0.325507	−	0.444462i
$470$	−14.0521	+	9.94638i	−0.648175	+	0.458792i
$471$	−1.34499	−	4.13944i	−0.0619737	−	0.190735i
$472$	−3.78359	+	7.42572i	−0.174154	+	0.341796i
$473$	−5.24623	−	33.1234i	−0.241222	−	1.52301i
$474$	10.6830			0.490685
$475$	3.35225	+	0.0829041i	0.153812	+	0.00380390i
$476$	5.99778	−	8.32152i	0.274908	−	0.381416i
$477$	63.1336	−	9.99939i	2.89069	−	0.457840i
$478$	−1.30881	+	2.56869i	−0.0598637	+	0.117489i
$479$	−1.58117	−	4.86633i	−0.0722454	−	0.222348i	0.908414	−	0.418073i	$-0.137294\pi$
$479$	−1.58117	−	4.86633i	−0.0722454	−	0.222348i	−0.980659	+	0.195724i	$0.937294\pi$
$480$	−7.02686	−	2.37960i	−0.320731	−	0.108613i
$481$	5.72917	+	1.86152i	0.261228	+	0.0848780i
$482$	−21.5705	−	21.5705i	−0.982511	−	0.982511i
$483$	−5.18286	+	33.5475i	−0.235828	+	1.52646i
$484$	1.80124	+	2.47920i	0.0818746	+	0.112691i
$485$	6.47499	−	3.19897i	0.294014	−	0.145258i
$486$	31.3556	−	43.1573i	1.42232	−	1.95765i
$487$	−1.65694	+	10.4615i	−0.0750831	+	0.474056i	0.921284	+	0.388891i	$0.127142\pi$
$487$	−1.65694	+	10.4615i	−0.0750831	+	0.474056i	−0.996367	+	0.0851649i	$0.972858\pi$
$488$	−1.89783	+	11.9824i	−0.0859106	+	0.542418i
$489$	3.03191	+	2.20281i	0.137108	+	0.0996145i
$490$	15.4479	+	2.52224i	0.697866	+	0.113943i
$491$	17.5530	−	12.7530i	0.792157	−	0.575535i	−0.116446	−	0.993197i	$-0.537150\pi$
$491$	17.5530	−	12.7530i	0.792157	−	0.575535i	0.908603	+	0.417662i	$0.137150\pi$
$492$	3.33988	+	6.55489i	0.150574	+	0.295517i
$493$	−10.2733	+	10.2733i	−0.462685	+	0.462685i
$494$	−2.75930	−	0.896551i	−0.124147	−	0.0403377i
$495$	40.1398	−	53.8354i	1.80415	−	2.41972i
$496$	5.04335	−	1.63868i	0.226453	−	0.0735791i
$497$	8.08056	+	15.7112i	0.362462	+	0.704742i
$498$	−2.95524	−	18.6586i	−0.132427	−	0.836114i
$499$		−	21.9256i		−	0.981527i	−0.871293	−	0.490763i	$-0.836718\pi$
$499$		−	21.9256i		−	0.981527i	0.871293	−	0.490763i	$-0.163282\pi$
$500$	−0.414570	+	11.1727i	−0.0185401	+	0.499656i
$501$	54.7855			2.44764
$502$	−2.75989	−	17.4252i	−0.123180	−	0.777727i
$503$	−13.8267	−	7.04504i	−0.616501	−	0.314123i	0.117706	−	0.993048i	$-0.462446\pi$
$503$	−13.8267	−	7.04504i	−0.616501	−	0.314123i	−0.734207	+	0.678925i	$0.762446\pi$
$504$	20.1745	+	6.47049i	0.898645	+	0.288218i
$505$	10.0074	−	13.4219i	0.445324	−	0.597266i
$506$	−4.48153	+	13.7927i	−0.199228	+	0.613161i
$507$	13.4074	+	13.4074i	0.595443	+	0.595443i
$508$	−11.1443	+	5.67830i	−0.494448	+	0.251934i
$509$	−19.5766	+	14.2232i	−0.867718	+	0.630434i	−0.929974	−	0.367626i	$-0.880171\pi$
$509$	−19.5766	+	14.2232i	−0.867718	+	0.630434i	0.0622559	+	0.998060i	$0.480171\pi$
$510$	−25.4649	−	13.3741i	−1.12760	−	0.592215i
$511$	−14.2696	+	4.69646i	−0.631248	+	0.207759i
$512$	0.156434	−	0.987688i	0.00691349	−	0.0436501i
$513$	−11.0058	−	1.74314i	−0.485917	−	0.0769616i
$514$	10.7082	+	7.77996i	0.472318	+	0.343159i
$515$	−1.23098	−	2.49161i	−0.0542435	−	0.109794i
$516$	−17.4391	−	24.0028i	−0.767712	−	1.05666i
$517$	25.7271	−	13.1086i	1.13148	−	0.576516i
$518$	0.590150	+	3.63660i	0.0259297	+	0.159783i
$519$	9.44875	+	3.07009i	0.414754	+	0.134762i
$520$	3.10275	−	9.16228i	0.136065	−	0.401793i
$521$	13.0757	−	4.24854i	0.572855	−	0.186132i	−0.00824218	−	0.999966i	$-0.502624\pi$
$521$	13.0757	−	4.24854i	0.572855	−	0.186132i	0.581097	+	0.813834i	$0.302624\pi$
$522$	−26.7373	−	13.6233i	−1.17026	−	0.596278i
$523$	−7.66242	+	1.21361i	−0.335054	+	0.0530674i	−0.321695	−	0.946843i	$-0.604253\pi$
$523$	−7.66242	+	1.21361i	−0.335054	+	0.0530674i	−0.0133593	+	0.999911i	$0.504253\pi$
$524$	−10.2853			−0.449316
$525$	0.918451	−	43.8808i	0.0400845	−	1.91512i
$526$	−10.9524			−0.477548
$527$	20.3065	−	3.21623i	0.884565	−	0.140101i
$528$	11.0865	+	5.64884i	0.482477	+	0.245834i
$529$	7.65198	−	2.48628i	0.332695	−	0.108099i
$530$	14.5686	−	10.3120i	0.632821	−	0.447924i
$531$	−63.4716	−	20.6232i	−2.75443	−	0.894970i
$532$	−0.284230	−	1.75147i	−0.0123229	−	0.0759360i
$533$	−8.54689	+	4.35486i	−0.370207	+	0.188630i
$534$	−8.82021	−	12.1400i	−0.381688	−	0.525348i
$535$	10.3655	−	1.51062i	0.448140	−	0.0653100i
$536$	−3.64817	−	2.65055i	−0.157577	−	0.114486i
$537$	46.0868	+	7.29943i	1.98879	+	0.314994i
$538$	1.08462	−	6.84804i	0.0467614	−	0.295240i
$539$	−25.0279	−	7.92236i	−1.07803	−	0.341240i
$540$	6.26512	−	36.6203i	0.269608	−	1.57589i
$541$	−29.2804	+	21.2734i	−1.25886	+	0.914616i	−0.998701	−	0.0509497i	$-0.983775\pi$
$541$	−29.2804	+	21.2734i	−1.25886	+	0.914616i	−0.260160	+	0.965566i	$0.583775\pi$
$542$	−7.92482	+	4.03790i	−0.340400	+	0.173443i
$543$	−2.22019	−	2.22019i	−0.0952775	−	0.0952775i
$544$	1.19808	−	3.68730i	0.0513671	−	0.158092i
$545$	−0.386882	+	31.2921i	−0.0165722	+	1.34041i
$546$	−11.5975	+	36.1604i	−0.496329	+	1.54752i
$547$	−21.0937	−	10.7478i	−0.901900	−	0.459541i	−0.0593978	−	0.998234i	$-0.518918\pi$
$547$	−21.0937	−	10.7478i	−0.901900	−	0.459541i	−0.842502	+	0.538694i	$0.818918\pi$
$548$	2.34567	+	14.8100i	0.100202	+	0.632651i
$549$	−97.1493			−4.14623
$550$	3.39034	−	18.4423i	0.144565	−	0.786381i
$551$			2.51316i			0.107064i
$552$	2.00708	+	12.6722i	0.0854272	+	0.539366i
$553$	−7.57576	+	3.89636i	−0.322154	+	0.165690i
$554$	22.8285	−	7.41741i	0.969888	−	0.315136i
$555$	9.86375	−	3.07064i	0.418693	−	0.130341i
$556$	−0.233280	−	0.0757973i	−0.00989327	−	0.00321452i
$557$	1.11150	−	1.11150i	0.0470958	−	0.0470958i	−0.683167	−	0.730262i	$-0.739398\pi$
$557$	1.11150	−	1.11150i	0.0470958	−	0.0470958i	0.730262	+	0.683167i	$0.239398\pi$
$558$	19.2786	+	37.8364i	0.816128	+	1.60174i
$559$	31.2971	−	22.7387i	1.32373	−	0.961745i
$560$	5.85095	−	0.875401i	0.247248	−	0.0369924i
$561$	39.0277	+	28.3553i	1.64775	+	1.19716i
$562$	4.76275	−	30.0708i	0.200904	−	1.26846i
$563$	5.69646	−	35.9660i	0.240077	−	1.51579i	−0.513306	−	0.858205i	$-0.671580\pi$
$563$	5.69646	−	35.9660i	0.240077	−	1.51579i	0.753383	−	0.657581i	$-0.228420\pi$
$564$	15.0148	−	20.6660i	0.632235	−	0.870197i
$565$	−27.8516	−	28.5489i	−1.17172	−	1.20106i
$566$	−4.76591	−	6.55971i	−0.200326	−	0.275725i
$567$	−12.5639	+	81.3234i	−0.527634	+	3.41526i
$568$	4.72180	+	4.72180i	0.198123	+	0.198123i
$569$	−4.36255	−	1.41748i	−0.182888	−	0.0594238i	0.216141	−	0.976362i	$-0.430653\pi$
$569$	−4.36255	−	1.41748i	−0.182888	−	0.0594238i	−0.399029	+	0.916938i	$0.630653\pi$
$570$	−4.75061	+	1.47889i	−0.198981	+	0.0619439i
$571$	−1.93721	−	5.96213i	−0.0810698	−	0.249507i	0.902304	−	0.431101i	$-0.141875\pi$
$571$	−1.93721	−	5.96213i	−0.0810698	−	0.249507i	−0.983374	+	0.181593i	$0.941875\pi$
$572$	−7.36549	+	14.4556i	−0.307967	+	0.604419i
$573$	30.5366	−	4.83651i	1.27568	−	0.202048i
$574$	−4.75920	−	3.43022i	−0.198645	−	0.143174i
$575$	17.4397	−	8.34945i	0.727285	−	0.348196i
$576$	8.00784			0.333660
$577$	−1.48986	−	9.40660i	−0.0620237	−	0.391602i	−0.999098	−	0.0424713i	$-0.986477\pi$
$577$	−1.48986	−	9.40660i	−0.0620237	−	0.391602i	0.937074	−	0.349131i	$-0.113523\pi$
$578$	−0.893645	+	1.75388i	−0.0371707	+	0.0729517i
$579$	17.9709	+	55.3086i	0.746844	+	2.29855i
$580$	−8.37864	−	0.103590i	−0.347904	−	0.00430133i
$581$	8.90099	+	12.1538i	0.369275	+	0.504225i
$582$	−7.57732	+	7.57732i	−0.314090	+	0.314090i
$583$	−26.6727	+	13.5904i	−1.10467	+	0.562859i
$584$	−4.59359	+	3.33744i	−0.190084	+	0.138104i
$585$	76.3536	+	13.0628i	3.15683	+	0.540081i
$586$	1.58661	−	2.18378i	0.0655423	−	0.0902112i
$587$	20.3767	+	3.22736i	0.841038	+	0.133207i	0.562066	−	0.827092i	$-0.310007\pi$
$587$	20.3767	+	3.22736i	0.841038	+	0.133207i	0.278971	+	0.960299i	$0.410007\pi$
$588$	−22.9105	+	3.80729i	−0.944811	+	0.157010i
$589$	2.09041	−	2.87720i	0.0861337	−	0.118553i
$590$	−18.4408	+	2.68747i	−0.759194	+	0.110642i
$591$	26.6393	+	36.6659i	1.09580	+	1.50823i
$592$	0.632176	+	1.24072i	0.0259823	+	0.0509931i
$593$	5.51258	−	5.51258i	0.226375	−	0.226375i	−0.584802	−	0.811176i	$-0.698828\pi$
$593$	5.51258	−	5.51258i	0.226375	−	0.226375i	0.811176	+	0.584802i	$0.198828\pi$
$594$	−19.2551	+	59.2611i	−0.790046	+	2.43151i
$595$	22.9361	+	0.196443i	0.940290	+	0.00805338i
$596$	4.07494	+	12.5414i	0.166916	+	0.513715i
$597$	−67.4049	−	34.3445i	−2.75870	−	1.40563i
$598$	−16.5233	+	2.61703i	−0.675686	+	0.107018i
$599$		−	1.17000i		−	0.0478047i	−0.999714	−	0.0239024i	$-0.992391\pi$
$599$		−	1.17000i		−	0.0478047i	0.999714	−	0.0239024i	$-0.00760909\pi$
$600$	−4.73466	−	15.8990i	−0.193292	−	0.649075i
$601$			15.7875i			0.643985i	0.946742	+	0.321993i	$0.104353\pi$
$601$			15.7875i			0.643985i	−0.946742	+	0.321993i	$0.895647\pi$
$602$	21.1213	+	10.6610i	0.860838	+	0.434508i
$603$	16.3938	−	32.1747i	0.667608	−	1.31025i
$604$	19.2081	−	6.24110i	0.781567	−	0.253947i
$605$	−2.19789	+	6.49027i	−0.0893569	+	0.263867i
$606$	−7.67638	+	23.6255i	−0.311831	+	0.959719i
$607$	26.4587	+	26.4587i	1.07393	+	1.07393i	0.997040	+	0.0768850i	$0.0244974\pi$
$607$	26.4587	+	26.4587i	1.07393	+	1.07393i	0.0768850	+	0.997040i	$0.475503\pi$
$608$	−0.304471	−	0.597557i	−0.0123479	−	0.0242342i
$609$	32.8941	−	0.124944i	1.33294	−	0.00506299i
$610$	−24.3211	+	12.0159i	−0.984734	+	0.486508i
$611$	26.9463	+	19.5777i	1.09013	+	0.792027i
$612$	30.6646	+	4.85680i	1.23954	+	0.196325i
$613$	18.3794	+	2.91102i	0.742338	+	0.117575i	0.516137	−	0.856506i	$-0.327369\pi$
$613$	18.3794	+	2.91102i	0.742338	+	0.117575i	0.226201	+	0.974081i	$0.427369\pi$
$614$	−12.0005	−	8.71887i	−0.484300	−	0.351865i
$615$	−7.64883	+	14.5637i	−0.308431	+	0.587266i
$616$	−9.92219	+	0.0376882i	−0.399776	+	0.00151850i
$617$	13.4248	+	26.3476i	0.540462	+	1.06072i	0.986201	+	0.165553i	$0.0529408\pi$
$617$	13.4248	+	26.3476i	0.540462	+	1.06072i	−0.445739	+	0.895163i	$0.647059\pi$
$618$	2.91579	+	2.91579i	0.117290	+	0.117290i
$619$	−5.72797	+	17.6289i	−0.230226	+	0.708564i	0.767492	+	0.641058i	$0.221504\pi$
$619$	−5.72797	+	17.6289i	−0.230226	+	0.708564i	−0.997719	+	0.0675061i	$0.978496\pi$
$620$	9.50613	+	7.08780i	0.381775	+	0.284653i
$621$	−61.1069	+	19.8548i	−2.45214	+	0.796747i
$622$	−2.76250	+	5.42171i	−0.110766	+	0.217391i
$623$	10.6826	+	5.39203i	0.427988	+	0.216027i
$624$			14.3531i			0.574583i
$625$	−20.9271	+	13.6769i	−0.837083	+	0.547076i
$626$			1.28080i			0.0511911i
$627$	8.24197	−	1.30540i	0.329153	−	0.0521327i
$628$	1.16887	+	0.595568i	0.0466429	+	0.0237657i
$629$	1.66831	+	5.13452i	0.0665198	+	0.204727i
$630$	14.2533	+	45.1801i	0.567864	+	1.80002i
$631$	−9.76887	+	30.0655i	−0.388892	+	1.19689i	0.544724	+	0.838615i	$0.316634\pi$
$631$	−9.76887	+	30.0655i	−0.388892	+	1.19689i	−0.933617	+	0.358273i	$0.883366\pi$
$632$	−2.27681	+	2.27681i	−0.0905665	+	0.0905665i
$633$	−39.3601	−	77.2486i	−1.56443	−	3.07036i
$634$	−11.3675	−	15.6460i	−0.451460	−	0.621381i
$635$	−24.7605	−	13.0042i	−0.982591	−	0.516054i
$636$	−15.5666	+	21.4257i	−0.617258	+	0.849582i
$637$	−4.96430	−	29.8728i	−0.196693	−	1.18360i
$638$	13.8804	+	2.19844i	0.549531	+	0.0870372i
$639$	−31.4309	+	43.2610i	−1.24339	+	1.71138i
$640$	2.00475	−	0.990445i	0.0792447	−	0.0391508i
$641$	−5.02959	+	3.65421i	−0.198657	+	0.144333i	−0.682667	−	0.730730i	$-0.739180\pi$
$641$	−5.02959	+	3.65421i	−0.198657	+	0.144333i	0.484010	+	0.875063i	$0.339180\pi$
$642$	−13.8485	+	7.05615i	−0.546555	+	0.278484i
$643$	−26.6992	+	26.6992i	−1.05291	+	1.05291i	−0.0543928	+	0.998520i	$0.517322\pi$
$643$	−26.6992	+	26.6992i	−1.05291	+	1.05291i	−0.998520	+	0.0543928i	$0.982678\pi$
$644$	−6.04521	−	8.25440i	−0.238215	−	0.325269i
$645$	21.2793	−	62.8368i	0.837872	−	2.47420i
$646$	−0.803495	−	2.47290i	−0.0316131	−	0.0972951i
$647$	17.9786	−	35.2850i	0.706812	−	1.38720i	−0.205892	−	0.978575i	$-0.566010\pi$
$647$	17.9786	−	35.2850i	0.706812	−	1.38720i	0.912704	−	0.408622i	$-0.133990\pi$
$648$	4.86543	+	30.7191i	0.191132	+	1.20676i
$649$	31.2550			1.22686
$650$	20.7307	−	6.17350i	0.813123	−	0.242145i
$651$	−37.7628	−	27.2178i	−1.48004	−	1.06675i
$652$	−1.11565	+	0.176701i	−0.0436922	+	0.00692016i
$653$	19.3610	−	37.9980i	0.757653	−	1.48698i	−0.112211	−	0.993684i	$-0.535793\pi$
$653$	19.3610	−	37.9980i	0.757653	−	1.48698i	0.869864	−	0.493292i	$-0.164207\pi$
$654$	−14.3488	−	44.1612i	−0.561084	−	1.72684i
$655$	−13.2872	−	18.7720i	−0.519175	−	0.733483i
$656$	−2.10882	−	0.685197i	−0.0823356	−	0.0267525i
$657$	−32.1510	−	32.1510i	−1.25433	−	1.25433i
$658$	−3.11017	+	20.1315i	−0.121247	+	0.784806i
$659$	23.4345	+	32.2548i	0.912879	+	1.25647i	0.966174	+	0.257891i	$0.0830275\pi$
$659$	23.4345	+	32.2548i	0.912879	+	1.25647i	−0.0532956	+	0.998579i	$0.516973\pi$
$660$	4.01235	+	27.5318i	0.156181	+	1.07167i
$661$	−9.55953	+	13.1576i	−0.371823	+	0.511770i	−0.953395	−	0.301725i	$-0.902438\pi$
$661$	−9.55953	+	13.1576i	−0.371823	+	0.511770i	0.581572	+	0.813495i	$0.302438\pi$
$662$	0.0489758	−	0.309221i	0.00190350	−	0.0120182i
$663$	−8.70522	+	54.9626i	−0.338083	+	2.13457i
$664$	4.60645	+	3.34678i	0.178765	+	0.129880i
$665$	2.82947	−	2.78142i	0.109722	−	0.107859i
$666$	−9.02121	+	6.55429i	−0.349565	+	0.253974i
$667$	6.57886	+	12.9117i	0.254734	+	0.499944i
$668$	−11.6762	+	11.6762i	−0.451764	+	0.451764i
$669$	−41.7332	−	13.5600i	−1.61350	−	0.524258i
$670$	0.124656	−	10.0825i	0.00481588	−	0.389522i
$671$	43.2705	−	14.0594i	1.67044	−	0.542758i
$672$	−7.80614	+	4.01485i	−0.301129	+	0.154876i
$673$	−6.80752	−	42.9810i	−0.262411	−	1.65680i	−0.669058	−	0.743210i	$-0.733302\pi$
$673$	−6.80752	−	42.9810i	−0.262411	−	1.65680i	0.406647	−	0.913585i	$-0.366698\pi$
$674$		−	14.1546i		−	0.545214i
$675$	74.9304	−	35.8738i	2.88407	−	1.38078i
$676$	−5.71489			−0.219804
$677$	0.856063	+	5.40497i	0.0329012	+	0.207730i	0.998663	−	0.0517021i	$-0.0164646\pi$
$677$	0.856063	+	5.40497i	0.0329012	+	0.207730i	−0.965761	+	0.259432i	$0.916465\pi$
$678$	52.7287	+	26.8666i	2.02504	+	1.03181i
$679$	2.60976	−	8.13705i	0.100153	−	0.312271i
$680$	8.27754	−	2.57685i	0.317429	−	0.0988175i
$681$	14.0681	−	43.2972i	0.539092	−	1.65915i
$682$	−14.0624	−	14.0624i	−0.538477	−	0.538477i
$683$	1.33296	−	0.679175i	0.0510042	−	0.0259879i	−0.428302	−	0.903635i	$-0.640888\pi$
$683$	1.33296	−	0.679175i	0.0510042	−	0.0259879i	0.479307	+	0.877648i	$0.340888\pi$
$684$	4.34482	−	3.15670i	0.166128	−	0.120699i
$685$	−23.9998	+	23.4136i	−0.916985	+	0.894588i
$686$	14.8582	−	11.0560i	0.567288	−	0.422118i
$687$	3.69670	−	23.3400i	0.141038	−	0.890478i
$688$	8.83229	+	1.39890i	0.336728	+	0.0533324i
$689$	−27.9368	−	20.2973i	−1.06431	−	0.773265i
$690$	−20.5356	+	20.0340i	−0.781775	+	0.762680i
$691$	15.0450	+	20.7077i	0.572340	+	0.787759i	0.992830	−	0.119539i	$-0.0381416\pi$
$691$	15.0450	+	20.7077i	0.572340	+	0.787759i	−0.420489	+	0.907297i	$0.638142\pi$
$692$	−2.66807	+	1.35945i	−0.101425	+	0.0516786i
$693$	−12.7276	−	78.4299i	−0.483483	−	2.97930i
$694$	−2.47450	−	0.804014i	−0.0939308	−	0.0305200i
$695$	−0.163026	−	0.523685i	−0.00618393	−	0.0198645i
$696$	11.8244	−	3.84198i	0.448203	−	0.145630i
$697$	−7.65978	−	3.90285i	−0.290135	−	0.147831i
$698$	19.6007	−	3.10445i	0.741899	−	0.117505i
$699$	−43.8372			−1.65808
$700$	9.15635	+	9.54784i	0.346078	+	0.360874i
$701$	−14.8472			−0.560770			−0.280385	−	0.959888i	$-0.590462\pi$
$701$	−14.8472			−0.560770			−0.280385	+	0.959888i	$0.590462\pi$
$702$	−70.9930	+	11.2442i	−2.67946	+	0.424384i
$703$	0.832092	+	0.423972i	0.0313829	+	0.0159904i
$704$	−3.56671	+	1.15889i	−0.134425	+	0.0436775i
$705$	57.1151	+	0.706146i	2.15108	+	0.0265950i
$706$	28.2214	+	9.16970i	1.06213	+	0.345106i
$707$	−3.17317	−	19.5536i	−0.119339	−	0.735390i
$708$	24.6371	−	12.5532i	0.925919	−	0.471779i
$709$	−28.4023	−	39.0923i	−1.06667	−	1.46814i	−0.873403	−	0.486997i	$-0.838092\pi$
$709$	−28.4023	−	39.0923i	−1.06667	−	1.46814i	−0.193265	−	0.981147i	$-0.561908\pi$
$710$	−2.51797	+	14.7178i	−0.0944977	+	0.552350i
$711$	−20.8600	−	15.1557i	−0.782311	−	0.568382i
$712$	4.46714	+	0.707525i	0.167413	+	0.0265156i
$713$	3.20795	−	20.2542i	0.120139	−	0.758526i
$714$	−32.3273	+	10.6397i	−1.20982	+	0.398181i
$715$	−35.8985	+	5.23169i	−1.34253	+	0.195654i
$716$	−11.3779	+	8.26654i	−0.425213	+	0.308935i
$717$	8.52242	−	4.34239i	0.318276	−	0.162170i
$718$	4.89170	+	4.89170i	0.182557	+	0.182557i
$719$	16.1592	−	49.7328i	0.602635	−	1.85472i	0.0903402	−	0.995911i	$-0.471205\pi$
$719$	16.1592	−	49.7328i	0.602635	−	1.85472i	0.512295	−	0.858810i	$-0.328795\pi$
$720$	10.3450	+	14.6153i	0.385537	+	0.544681i
$721$	−3.13118	−	1.00425i	−0.116611	−	0.0374002i
$722$	16.5284	+	8.42162i	0.615122	+	0.313420i
$723$	15.8329	+	99.9648i	0.588831	+	3.71773i
$724$	0.946355			0.0351710
$725$	−10.6350	−	15.4259i	−0.394973	−	0.572904i
$726$		−	10.1673i		−	0.377343i
$727$	−4.53579	−	28.6378i	−0.168223	−	1.06212i	−0.916881	−	0.399161i	$-0.869301\pi$
$727$	−4.53579	−	28.6378i	−0.168223	−	1.06212i	0.748658	−	0.662957i	$-0.230699\pi$
$728$	−5.23494	−	10.1784i	−0.194020	−	0.377236i
$729$	−79.5877	+	25.8596i	−2.94769	+	0.957763i
$730$	−12.0255	−	4.07237i	−0.445085	−	0.150725i
$731$	32.9733	+	10.7137i	1.21956	+	0.396259i
$732$	28.4617	−	28.4617i	1.05197	−	1.05197i
$733$	5.60581	+	11.0020i	0.207055	+	0.406369i	0.971058	−	0.238844i	$-0.0767686\pi$
$733$	5.60581	+	11.0020i	0.207055	+	0.406369i	−0.764003	+	0.645213i	$0.776769\pi$
$734$	−14.1878	+	10.3081i	−0.523682	+	0.380477i
$735$	−36.5460	−	36.8960i	−1.34802	−	1.36093i
$736$	−3.12853	−	2.27301i	−0.115319	−	0.0837842i
$737$	−2.64552	+	16.7032i	−0.0974491	+	0.615269i
$738$	2.77767	−	17.5375i	0.102248	−	0.645566i
$739$	28.1170	−	38.6997i	1.03430	−	1.42359i	0.132632	−	0.991165i	$-0.457657\pi$
$739$	28.1170	−	38.6997i	1.03430	−	1.42359i	0.901669	−	0.432428i	$-0.142343\pi$
$740$	−1.44778	+	2.75664i	−0.0532214	+	0.101336i
$741$	5.65799	+	7.78756i	0.207852	+	0.286083i
$742$	3.22449	−	20.8714i	0.118375	−	0.766215i
$743$	−34.4186	−	34.4186i	−1.26269	−	1.26269i	−0.949782	−	0.312913i	$-0.898695\pi$
$743$	−34.4186	−	34.4186i	−1.26269	−	1.26269i	−0.312913	−	0.949782i	$-0.601305\pi$
$744$	−16.7329	−	5.43684i	−0.613457	−	0.199324i
$745$	−17.6253	+	23.6390i	−0.645743	+	0.866067i
$746$	−4.30702	−	13.2556i	−0.157691	−	0.485324i
$747$	−20.7000	+	40.6261i	−0.757375	+	1.48643i
$748$	−14.3610	+	2.27455i	−0.525089	+	0.0831659i
$749$	7.24699	−	10.0547i	0.264799	−	0.367392i
$750$	22.9012	−	29.1807i	0.836234	−	1.06553i
$751$	15.6187			0.569936			0.284968	−	0.958537i	$-0.408017\pi$
$751$	15.6187			0.569936			0.284968	+	0.958537i	$0.408017\pi$
$752$	1.20443	+	7.60446i	0.0439210	+	0.277306i
$753$	−26.5740	+	52.1544i	−0.968410	+	1.90061i
$754$	5.00954	+	15.4178i	0.182437	+	0.561482i
$755$	36.2051	+	26.9946i	1.31764	+	0.982435i
$756$	−25.9735	−	35.4654i	−0.944648	−	1.28986i
$757$	−27.5658	+	27.5658i	−1.00189	+	1.00189i	−0.00189648	+	0.999998i	$0.500604\pi$
$757$	−27.5658	+	27.5658i	−1.00189	+	1.00189i	−0.999998	+	0.00189648i	$0.999396\pi$
$758$	12.4782	−	6.35797i	0.453230	−	0.230932i
$759$	38.9271	−	28.2822i	1.41296	−	1.02658i
$760$	0.697284	−	1.32766i	0.0252931	−	0.0481593i
$761$	−23.1037	+	31.7995i	−0.837507	+	1.15273i	0.148972	+	0.988841i	$0.452404\pi$
$761$	−23.1037	+	31.7995i	−0.837507	+	1.15273i	−0.986479	+	0.163888i	$0.947596\pi$
$762$	40.9867	+	6.49165i	1.48479	+	0.235168i
$763$	26.2822	+	26.0832i	0.951478	+	0.944277i
$764$	−5.47731	+	7.53888i	−0.198162	+	0.272747i
$765$	30.7502	+	62.2412i	1.11178	+	2.25033i
$766$	7.57753	+	10.4296i	0.273787	+	0.376836i
$767$	16.3681	+	32.1242i	0.591018	+	1.15994i
$768$	−2.34604	+	2.34604i	−0.0846556	+	0.0846556i
$769$	7.09478	−	21.8355i	0.255844	−	0.787408i	−0.737818	−	0.675000i	$-0.764144\pi$
$769$	7.09478	−	21.8355i	0.255844	−	0.787408i	0.993662	−	0.112408i	$-0.0358564\pi$
$770$	−12.8869	−	18.0606i	−0.464411	−	0.650857i
$771$	−13.5704	−	41.7654i	−0.488726	−	1.50414i
$772$	−15.6177	−	7.95760i	−0.562092	−	0.286400i
$773$	32.3677	−	5.12653i	1.16418	−	0.184389i	0.455712	−	0.890127i	$-0.349385\pi$
$773$	32.3677	−	5.12653i	1.16418	−	0.184389i	0.708472	+	0.705739i	$0.249385\pi$
$774$			71.6092i			2.57394i
$775$	−0.655526	+	26.5064i	−0.0235472	+	0.952137i
$776$		−	3.22983i		−	0.115944i
$777$	5.50789	−	10.9121i	0.197595	−	0.391470i
$778$	−14.8160	+	29.0780i	−0.531179	+	1.04250i
$779$	−1.41429	+	0.459531i	−0.0506722	+	0.0164644i
$780$	−26.1962	+	18.5422i	−0.937974	+	0.663917i
$781$	7.73868	−	23.8172i	0.276912	−	0.852247i
$782$	−10.6016	−	10.6016i	−0.379111	−	0.379111i
$783$	28.2664	+	55.4759i	1.01016	+	1.98255i
$784$	4.07136	−	5.69421i	0.145406	−	0.203365i
$785$	0.423030	+	2.90272i	0.0150986	+	0.103603i
$786$	27.6074	+	20.0580i	0.984725	+	0.715445i
$787$	−13.9361	−	2.20726i	−0.496767	−	0.0786802i	−0.0969764	−	0.995287i	$-0.530917\pi$
$787$	−13.9361	−	2.20726i	−0.496767	−	0.0786802i	−0.399791	+	0.916607i	$0.630917\pi$
$788$	−13.4919	−	2.13691i	−0.480629	−	0.0761242i
$789$	29.3981	+	21.3589i	1.04660	+	0.760398i
$790$	−7.09678	−	1.21414i	−0.252492	−	0.0431971i
$791$	−47.1912	+	0.179250i	−1.67793	+	0.00637339i
$792$	−13.6340	−	26.7583i	−0.484464	−	0.950813i
$793$	37.1110	+	37.1110i	1.31785	+	1.31785i
$794$	0.608982	−	1.87425i	0.0216120	−	0.0665148i
$795$	−59.2145	−	0.732102i	−2.10012	−	0.0259650i
$796$	21.6853	−	7.04599i	0.768616	−	0.249738i
$797$	−4.43748	+	8.70904i	−0.157184	+	0.308490i	−0.956146	−	0.292891i	$-0.905383\pi$
$797$	−4.43748	+	8.70904i	−0.157184	+	0.308490i	0.798962	+	0.601381i	$0.205383\pi$
$798$	−2.65273	+	5.25553i	−0.0939056	+	0.186044i
$799$			29.8504i			1.05603i
$800$	4.39755	+	2.37940i	0.155477	+	0.0841246i
$801$			36.2180i			1.27970i
$802$	−14.8154	+	2.34653i	−0.523151	+	0.0828589i
$803$	18.9730	+	9.66724i	0.669544	+	0.341150i
$804$	4.62329	+	14.2290i	0.163051	+	0.501819i
$805$	7.25575	−	21.6968i	0.255731	−	0.764713i
$806$	7.08907	−	21.8179i	0.249702	−	0.768503i
$807$	−16.2661	+	16.2661i	−0.572592	+	0.572592i
$808$	−3.39914	−	6.67120i	−0.119581	−	0.234692i
$809$	14.3776	+	19.7891i	0.505491	+	0.695748i	0.983151	−	0.182796i	$-0.0585149\pi$
$809$	14.3776	+	19.7891i	0.505491	+	0.695748i	−0.477660	+	0.878545i	$0.658515\pi$
$810$	−49.7808	+	48.5649i	−1.74912	+	1.70640i
$811$	−16.6372	+	22.8991i	−0.584210	+	0.804096i	−0.994149	−	0.108017i	$-0.965550\pi$
$811$	−16.6372	+	22.8991i	−0.584210	+	0.804096i	0.409939	+	0.912113i	$0.365550\pi$
$812$	−6.98393	+	7.03718i	−0.245088	+	0.246957i
$813$	29.1460	+	4.61628i	1.02220	+	0.161900i
$814$	3.06953	−	4.22484i	0.107587	−	0.148081i
$815$	−1.76377	−	1.80793i	−0.0617821	−	0.0633289i
$816$	−10.4067	+	7.56088i	−0.364306	+	0.264684i
$817$	5.34359	−	2.72269i	0.186948	−	0.0952550i
$818$	14.4315	−	14.4315i	0.504586	−	0.504586i
$819$	73.9456	−	54.1550i	2.58387	−	1.89233i
$820$	−1.47374	−	4.73405i	−0.0514651	−	0.165320i
$821$	8.64032	+	26.5922i	0.301549	+	0.928073i	0.980942	+	0.194299i	$0.0622431\pi$
$821$	8.64032	+	26.5922i	0.301549	+	0.928073i	−0.679393	+	0.733774i	$0.737757\pi$
$822$	22.5856	−	44.3268i	0.787764	−	1.54607i
$823$	−7.52630	−	47.5192i	−0.262350	−	1.65641i	−0.669321	−	0.742973i	$-0.733415\pi$
$823$	−7.52630	−	47.5192i	−0.262350	−	1.65641i	0.406971	−	0.913441i	$-0.366585\pi$
$824$	−1.24285			−0.0432969
$825$	−45.0655	+	42.8903i	−1.56898	+	1.49325i
$826$	−12.8928	+	17.8878i	−0.448596	+	0.622398i
$827$	16.2905	−	2.58016i	0.566477	−	0.0897211i	0.133374	−	0.991066i	$-0.457419\pi$
$827$	16.2905	−	2.58016i	0.566477	−	0.0897211i	0.433103	+	0.901345i	$0.357419\pi$
$828$	14.0587	−	27.5917i	0.488573	−	0.958878i
$829$	6.16320	+	18.9684i	0.214057	+	0.658799i	0.999219	+	0.0395093i	$0.0125795\pi$
$829$	6.16320	+	18.9684i	0.214057	+	0.658799i	−0.785162	+	0.619290i	$0.787421\pi$
$830$	−0.157400	+	12.7309i	−0.00546343	+	0.441898i
$831$	−75.7404	−	24.6095i	−2.62741	−	0.853696i
$832$	−3.05899	−	3.05899i	−0.106052	−	0.106052i
$833$	19.0441	−	19.3357i	0.659840	−	0.669942i
$834$	0.478345	+	0.658385i	0.0165637	+	0.0227980i
$835$	−36.3945	−	6.22647i	−1.25948	−	0.215476i
$836$	−1.47836	+	2.03478i	−0.0511300	+	0.0703744i
$837$	13.7831	−	87.0231i	0.476414	−	3.00796i
$838$	1.13812	−	7.18583i	0.0393158	−	0.248230i
$839$	6.40511	+	4.65358i	0.221129	+	0.160659i	0.692835	−	0.721096i	$-0.256362\pi$
$839$	6.40511	+	4.65358i	0.221129	+	0.160659i	−0.471706	+	0.881756i	$0.656362\pi$
$840$	−17.4121	−	9.06057i	−0.600774	−	0.312619i
$841$	−12.1009	+	8.79183i	−0.417273	+	0.303166i
$842$	−5.68957	−	11.1664i	−0.196075	−	0.384820i
$843$	−71.4268	+	71.4268i	−2.46007	+	2.46007i
$844$	24.8522	+	8.07498i	0.855449	+	0.277952i
$845$	−7.38286	−	10.4304i	−0.253978	−	0.358817i
$846$	−58.6368	+	19.0522i	−2.01597	+	0.655030i
$847$	3.70827	+	7.21005i	0.127418	+	0.247740i
$848$	−1.24870	−	7.88398i	−0.0428805	−	0.270737i
$849$			26.9016i			0.923260i
$850$	15.3965	+	11.7786i	0.528097	+	0.404004i
$851$	5.38485			0.184590
$852$	−3.46582	−	21.8824i	−0.118737	−	0.749677i
$853$	−0.688486	−	0.350801i	−0.0235733	−	0.0120112i	0.442164	−	0.896934i	$-0.354211\pi$
$853$	−0.688486	−	0.350801i	−0.0235733	−	0.0120112i	−0.465737	+	0.884923i	$0.654211\pi$
$854$	−9.80269	+	30.5641i	−0.335441	+	1.04588i
$855$	11.3743	+	3.85183i	0.388993	+	0.131730i
$856$	1.44761	−	4.45529i	0.0494783	−	0.152279i
$857$	3.44644	+	3.44644i	0.117728	+	0.117728i	0.763516	−	0.645788i	$-0.223471\pi$
$857$	3.44644	+	3.44644i	0.117728	+	0.117728i	−0.645788	+	0.763516i	$0.723471\pi$
$858$	47.9609	−	24.4373i	1.63736	−	0.834275i
$859$	−34.8497	+	25.3198i	−1.18906	+	0.863901i	−0.993164	−	0.116725i	$-0.962760\pi$
$859$	−34.8497	+	25.3198i	−1.18906	+	0.863901i	−0.195893	+	0.980625i	$0.562760\pi$
$860$	8.85694	+	17.9272i	0.302019	+	0.611314i
$861$	6.08500	+	18.4884i	0.207376	+	0.630084i
$862$	−0.555244	+	3.50567i	−0.0189117	+	0.119404i
$863$	39.1514	+	6.20097i	1.33273	+	0.211083i	0.781831	−	0.623490i	$-0.214286\pi$
$863$	39.1514	+	6.20097i	1.33273	+	0.211083i	0.550896	+	0.834574i	$0.314286\pi$
$864$	−13.4419	−	9.76608i	−0.457301	−	0.332249i
$865$	−5.92796	−	3.11335i	−0.201557	−	0.105857i
$866$	4.14568	+	5.70604i	0.140876	+	0.193899i
$867$	5.81903	−	2.96494i	0.197625	−	0.100695i
$868$	13.8490	−	2.24742i	0.470065	−	0.0762823i
$869$	11.4844	+	3.73151i	0.389582	+	0.126583i
$870$	22.2876	+	16.6177i	0.755620	+	0.563393i
$871$	−18.5531	+	6.02828i	−0.628649	+	0.204261i
$872$	12.4699	+	6.35375i	0.422286	+	0.215165i
$873$	25.5455	−	4.04601i	0.864585	−	0.136937i
$874$	−2.59347			−0.0877254
$875$	−5.59727	+	29.0460i	−0.189222	+	0.981934i
$876$	18.8385			0.636493
$877$	0.827094	−	0.130999i	0.0279290	−	0.00442352i	−0.142454	−	0.989801i	$-0.545499\pi$
$877$	0.827094	−	0.130999i	0.0279290	−	0.00442352i	0.170383	+	0.985378i	$0.445499\pi$
$878$	3.19673	+	1.62882i	0.107884	+	0.0549699i
$879$	−8.51744	+	2.76748i	−0.287286	+	0.0933449i
$880$	−6.72283	−	5.01257i	−0.226627	−	0.168974i
$881$	−20.3327	−	6.60650i	−0.685027	−	0.222579i	−0.0542319	−	0.998528i	$-0.517271\pi$
$881$	−20.3327	−	6.60650i	−0.685027	−	0.222579i	−0.630795	+	0.775950i	$0.717271\pi$
$882$	50.1372	+	25.0682i	1.68821	+	0.844092i
$883$	−23.4972	+	11.9724i	−0.790743	+	0.402904i	−0.802219	−	0.597030i	$-0.796347\pi$
$883$	−23.4972	+	11.9724i	−0.790743	+	0.402904i	0.0114754	+	0.999934i	$0.496347\pi$
$884$	−9.85859	−	13.5692i	−0.331580	−	0.456381i
$885$	54.7390	+	28.7488i	1.84003	+	0.966380i
$886$	20.1777	+	14.6600i	0.677884	+	0.492511i
$887$	−1.86847	−	0.295937i	−0.0627372	−	0.00993660i	0.124987	−	0.992158i	$-0.460111\pi$
$887$	−1.86847	−	0.295937i	−0.0627372	−	0.00993660i	−0.187724	+	0.982222i	$0.560111\pi$
$888$	0.722728	−	4.56313i	0.0242532	−	0.153129i
$889$	−31.4331	+	10.3454i	−1.05423	+	0.346974i
$890$	4.47961	+	9.06712i	0.150157	+	0.303930i
$891$	94.3643	−	68.5597i	3.16132	−	2.29684i
$892$	11.7843	−	6.00442i	0.394569	−	0.201043i
$893$	3.65117	+	3.65117i	0.122182	+	0.122182i
$894$	13.5199	−	41.6099i	0.452172	−	1.39164i
$895$	−29.7862	−	10.0869i	−0.995643	−	0.337168i
$896$	0.808019	−	2.51935i	0.0269940	−	0.0841655i
$897$	49.4547	+	25.1984i	1.65125	+	0.841351i
$898$	0.557830	+	3.52200i	0.0186150	+	0.117531i
$899$	−19.8717			−0.662758
$900$	−13.3105	+	37.7620i	−0.443682	+	1.25873i
$901$		−	30.9476i		−	1.03102i
$902$	1.30085	+	8.21324i	0.0433136	+	0.273471i
$903$	−35.9023	−	69.8055i	−1.19475	−	2.32298i
$904$	−16.9637	+	5.51186i	−0.564206	+	0.183322i
$905$	1.22256	+	1.72722i	0.0406393	+	0.0574147i
$906$	−63.7288	−	20.7068i	−2.11725	−	0.687936i
$907$	−1.78490	+	1.78490i	−0.0592667	+	0.0592667i	−0.736119	−	0.676852i	$-0.763344\pi$
$907$	−1.78490	+	1.78490i	−0.0592667	+	0.0592667i	0.676852	+	0.736119i	$0.263344\pi$
$908$	6.22945	+	12.2260i	0.206731	+	0.405733i
$909$	48.5061	−	35.2417i	1.60884	−	1.16889i
$910$	11.8140	−	22.7035i	0.391631	−	0.752614i
$911$	1.33110	+	0.967102i	0.0441014	+	0.0320415i	0.609618	−	0.792696i	$-0.291323\pi$
$911$	1.33110	+	0.967102i	0.0441014	+	0.0320415i	−0.565516	+	0.824737i	$0.691323\pi$
$912$	−0.348083	+	2.19771i	−0.0115262	+	0.0727734i
$913$	3.34043	−	21.0907i	0.110552	−	0.697999i
$914$	−4.63291	+	6.37666i	−0.153243	+	0.210921i
$915$	88.7147	+	15.1776i	2.93282	+	0.501755i
$916$	4.18648	+	5.76220i	0.138325	+	0.190388i
$917$	−26.8933	−	4.15483i	−0.888096	−	0.137205i
$918$	−45.5501	−	45.5501i	−1.50338	−	1.50338i
$919$	−42.9318	−	13.9494i	−1.41619	−	0.460148i	−0.501801	−	0.864983i	$-0.667329\pi$
$919$	−42.9318	−	13.9494i	−1.41619	−	0.460148i	−0.914390	+	0.404835i	$0.867329\pi$
$920$	0.106900	−	8.64637i	0.00352439	−	0.285062i
$921$	15.2081	+	46.8057i	0.501124	+	1.54230i
$922$	16.6240	−	32.6264i	0.547482	−	1.07449i
$923$	28.5323	−	4.51907i	0.939152	−	0.148747i
$924$	26.7063	+	19.2487i	0.878571	+	0.633235i
$925$	−6.90155	+	0.918817i	−0.226922	+	0.0302105i
$926$	−36.9033			−1.21272
$927$	−1.55693	−	9.83005i	−0.0511362	−	0.322861i
$928$	−1.70125	+	3.33889i	−0.0558463	+	0.109605i
$929$	0.615487	+	1.89427i	0.0201935	+	0.0621491i	0.960645	−	0.277777i	$-0.0895978\pi$
$929$	0.615487	+	1.89427i	0.0201935	+	0.0621491i	−0.940452	+	0.339927i	$0.889598\pi$
$930$	−11.6937	−	37.5633i	−0.383450	−	1.23175i
$931$	−0.0356630	−	4.69445i	−0.00116881	−	0.153854i
$932$	9.34279	−	9.34279i	0.306033	−	0.306033i
$933$	17.9882	−	9.16543i	0.588906	−	0.300063i
$934$	−31.4840	+	22.8745i	−1.03019	+	0.748476i
$935$	−22.7038	−	23.2722i	−0.742492	−	0.761082i
$936$	20.3624	−	28.0264i	0.665564	−	0.916071i
$937$	19.5867	+	3.10223i	0.639869	+	0.101345i	0.467935	−	0.883763i	$-0.344998\pi$
$937$	19.5867	+	3.10223i	0.639869	+	0.101345i	0.171934	+	0.985108i	$0.444998\pi$
$938$	−8.46828	−	8.40419i	−0.276499	−	0.274406i
$939$	2.49776	−	3.43788i	0.0815114	−	0.112191i
$940$	−12.3231	+	12.0222i	−0.401937	+	0.392119i
$941$	−14.0657	−	19.3597i	−0.458528	−	0.631110i	0.515675	−	0.856784i	$-0.327541\pi$
$941$	−14.0657	−	19.3597i	−0.458528	−	0.631110i	−0.974203	+	0.225675i	$0.927541\pi$
$942$	−1.97598	−	3.87808i	−0.0643809	−	0.126355i
$943$	−6.06318	+	6.06318i	−0.197444	+	0.197444i
$944$	−2.57537	+	7.92618i	−0.0838212	+	0.257975i
$945$	31.1747	−	93.2215i	1.01411	−	3.03249i
$946$	−10.3633	−	31.8949i	−0.336939	−	1.03699i
$947$	20.3537	+	10.3707i	0.661407	+	0.337004i	0.752266	−	0.658860i	$-0.228961\pi$
$947$	20.3537	+	10.3707i	0.661407	+	0.337004i	−0.0908582	+	0.995864i	$0.528961\pi$
$948$	10.5514	−	1.67119i	0.342695	−	0.0542776i
$949$			24.5634i			0.797361i
$950$	3.32394	−	0.442524i	0.107843	−	0.0143574i
$951$			64.1647i			2.08068i
$952$	4.62216	−	9.15733i	0.149805	−	0.296791i
$953$	−11.8915	+	23.3384i	−0.385203	+	0.756004i	−0.999452	−	0.0331086i	$-0.989459\pi$
$953$	−11.8915	+	23.3384i	−0.385203	+	0.756004i	0.614248	+	0.789113i	$0.289459\pi$
$954$	60.7921	−	19.7526i	1.96822	−	0.639513i
$955$	−20.8353	−	0.257599i	−0.674216	−	0.00833571i
$956$	−0.890868	+	2.74181i	−0.0288127	+	0.0886764i
$957$	−32.9700	−	32.9700i	−1.06577	−	1.06577i
$958$	−2.32296	−	4.55907i	−0.0750515	−	0.147297i
$959$	0.150688	+	39.6716i	0.00486596	+	1.28106i
$960$	−7.31260	−	1.25106i	−0.236013	−	0.0403778i
$961$	−2.32941	−	1.69241i	−0.0751421	−	0.0545939i
$962$	5.94984	+	0.942362i	0.191830	+	0.0303830i
$963$	37.0514	+	5.86837i	1.19397	+	0.189106i
$964$	−24.6794	−	17.9306i	−0.794868	−	0.577506i
$965$	−5.65226	−	38.7844i	−0.181953	−	1.24851i
$966$	0.128937	+	33.9453i	0.00414847	+	1.09217i
$967$	16.2495	+	31.8914i	0.522548	+	1.02556i	0.989937	+	0.141506i	$0.0451945\pi$
$967$	16.2495	+	31.8914i	0.522548	+	1.02556i	−0.467390	+	0.884051i	$0.654805\pi$
$968$	2.16690	+	2.16690i	0.0696467	+	0.0696467i
$969$	−2.66584	+	8.20462i	−0.0856392	+	0.263570i
$970$	5.89485	−	4.17250i	0.189272	−	0.133971i
$971$	13.6349	−	4.43024i	0.437564	−	0.142173i	−0.0819472	−	0.996637i	$-0.526114\pi$
$971$	13.6349	−	4.43024i	0.437564	−	0.142173i	0.519512	+	0.854463i	$0.326114\pi$
$972$	24.2183	−	47.5310i	0.776801	−	1.52456i
$973$	−0.579345	−	0.292425i	−0.0185730	−	0.00937471i
$974$			10.5919i			0.339387i
$975$	−67.6838	−	23.8574i	−2.16762	−	0.764047i
$976$			12.1318i			0.388328i
$977$	−43.2239	+	6.84599i	−1.38285	+	0.219023i	−0.803137	−	0.595795i	$-0.796837\pi$
$977$	−43.2239	+	6.84599i	−1.38285	+	0.219023i	−0.579718	+	0.814817i	$0.696837\pi$
$978$	3.33918	+	1.70140i	0.106775	+	0.0544046i
$979$	−5.24147	−	16.1316i	−0.167518	−	0.515568i
$980$	15.6523	+	0.0746028i	0.499994	+	0.00238310i
$981$	−34.6323	+	106.587i	−1.10572	+	3.40307i
$982$	15.3419	−	15.3419i	0.489580	−	0.489580i
$983$	−12.4958	−	24.5243i	−0.398553	−	0.782205i	0.601305	−	0.799019i	$-0.294648\pi$
$983$	−12.4958	−	24.5243i	−0.398553	−	0.782205i	−0.999859	+	0.0168145i	$0.994648\pi$
$984$	4.32417	+	5.95171i	0.137850	+	0.189734i
$985$	−13.5296	−	27.3850i	−0.431088	−	0.872560i
$986$	−8.53970	+	11.7539i	−0.271959	+	0.374320i
$987$	47.6077	−	47.9708i	1.51537	−	1.52693i
$988$	−2.86558	−	0.453863i	−0.0911662	−	0.0144393i
$989$	20.3261	−	27.9765i	0.646332	−	0.889600i
$990$	31.2239	−	59.4518i	0.992362	−	1.88950i
$991$	25.9207	−	18.8325i	0.823399	−	0.598235i	−0.0942848	−	0.995545i	$-0.530056\pi$
$991$	25.9207	−	18.8325i	0.823399	−	0.598235i	0.917684	+	0.397311i	$0.130056\pi$
$992$	4.72491	−	2.40746i	0.150016	−	0.0764371i
$993$	−0.734490	+	0.734490i	−0.0233083	+	0.0233083i
$994$	10.4388	+	14.2537i	0.331100	+	0.452099i
$995$	40.8743	+	30.4760i	1.29580	+	0.966155i
$996$	−5.83771	−	17.9666i	−0.184975	−	0.569294i
$997$	−14.9043	+	29.2512i	−0.472022	+	0.926396i	0.525133	+	0.851020i	$0.324016\pi$
$997$	−14.9043	+	29.2512i	−0.472022	+	0.926396i	−0.997155	+	0.0753759i	$0.975984\pi$
$998$	−3.42993	−	21.6557i	−0.108572	−	0.685499i
$999$	23.1363			0.731999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.r.a.13.11	✓	160
7.6	odd	2	inner	350.2.r.a.13.20	yes	160
25.2	odd	20	inner	350.2.r.a.27.20	yes	160
175.27	even	20	inner	350.2.r.a.27.11	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.r.a.13.11	✓	160	1.1	even	1	trivial
350.2.r.a.13.20	yes	160	7.6	odd	2	inner
350.2.r.a.27.11	yes	160	175.27	even	20	inner
350.2.r.a.27.20	yes	160	25.2	odd	20	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.r (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.987688 - 0.156434i) q^{2} +(-2.95619 - 1.50625i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.79263 + 1.33659i) q^{5} +(-3.15542 - 1.02526i) q^{6} +(2.61159 - 0.423809i) q^{7} +(0.891007 - 0.453990i) q^{8} +(4.70689 + 6.47848i) q^{9} +O(q^{10})\)	\(q+(0.987688 - 0.156434i) q^{2} +(-2.95619 - 1.50625i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.79263 + 1.33659i) q^{5} +(-3.15542 - 1.02526i) q^{6} +(2.61159 - 0.423809i) q^{7} +(0.891007 - 0.453990i) q^{8} +(4.70689 + 6.47848i) q^{9} +(1.97965 + 1.03971i) q^{10} +(-3.03402 - 2.20435i) q^{11} +(-3.27696 - 0.519019i) q^{12} +(0.676747 - 4.27281i) q^{13} +(2.51314 - 0.827134i) q^{14} +(-3.28611 - 6.65137i) q^{15} +(0.809017 - 0.587785i) q^{16} +(3.45448 - 1.76015i) q^{17} +(5.66240 + 5.66240i) q^{18} +(0.207244 - 0.637830i) q^{19} +(2.11792 + 0.717221i) q^{20} +(-8.35870 - 2.68085i) q^{21} +(-3.34151 - 1.70258i) q^{22} +(-0.604943 - 3.81946i) q^{23} -3.31781 q^{24} +(1.42705 + 4.79203i) q^{25} -4.32607i q^{26} +(-2.59917 - 16.4105i) q^{27} +(2.35280 - 1.21009i) q^{28} +(-3.56392 + 1.15799i) q^{29} +(-4.28615 - 6.05542i) q^{30} +(5.04335 + 1.63868i) q^{31} +(0.707107 - 0.707107i) q^{32} +(5.64884 + 11.0865i) q^{33} +(3.13661 - 2.27888i) q^{34} +(5.24807 + 2.73089i) q^{35} +(6.47848 + 4.70689i) q^{36} +(-0.217833 + 1.37534i) q^{37} +(0.104913 - 0.662398i) q^{38} +(-8.43652 + 11.6119i) q^{39} +(2.20405 + 0.377075i) q^{40} +(-1.30332 - 1.79387i) q^{41} +(-8.67517 - 1.34025i) q^{42} +(6.32322 + 6.32322i) q^{43} +(-3.56671 - 1.15889i) q^{44} +(-0.221366 + 17.9047i) q^{45} +(-1.19499 - 3.67780i) q^{46} +(-3.49539 + 6.86008i) q^{47} +(-3.27696 + 0.519019i) q^{48} +(6.64077 - 2.21363i) q^{49} +(2.15912 + 4.50979i) q^{50} -12.8633 q^{51} +(-0.676747 - 4.27281i) q^{52} +(3.62387 - 7.11224i) q^{53} +(-5.13433 - 15.8019i) q^{54} +(-2.49257 - 8.00683i) q^{55} +(2.13454 - 1.56325i) q^{56} +(-1.57338 + 1.57338i) q^{57} +(-3.33889 + 1.70125i) q^{58} +(-6.74241 + 4.89865i) q^{59} +(-5.18066 - 5.31037i) q^{60} +(-7.13087 + 9.81481i) q^{61} +(5.23761 + 0.829556i) q^{62} +(15.0381 + 14.9243i) q^{63} +(0.587785 - 0.809017i) q^{64} +(6.92416 - 6.75504i) q^{65} +(7.31360 + 10.0663i) q^{66} +(-2.04722 - 4.01789i) q^{67} +(2.74149 - 2.74149i) q^{68} +(-3.96475 + 12.2022i) q^{69} +(5.61066 + 1.87629i) q^{70} +(2.06350 + 6.35081i) q^{71} +(7.13504 + 3.63548i) q^{72} +(-5.60808 + 0.888233i) q^{73} +1.39249i q^{74} +(2.99939 - 16.3156i) q^{75} -0.670654i q^{76} +(-8.85784 - 4.47100i) q^{77} +(-6.51616 + 12.7887i) q^{78} +(-3.06230 + 0.995001i) q^{79} +(2.23590 + 0.0276436i) q^{80} +(-9.61105 + 29.5798i) q^{81} +(-1.56790 - 1.56790i) q^{82} +(2.58497 + 5.07329i) q^{83} +(-8.77803 + 0.0333422i) q^{84} +(8.54521 + 1.46194i) q^{85} +(7.23454 + 5.25620i) q^{86} +(12.2798 + 1.94493i) q^{87} +(-3.70409 - 0.586670i) q^{88} +(3.65904 + 2.65845i) q^{89} +(2.58227 + 17.7189i) q^{90} +(-0.0434747 - 11.4456i) q^{91} +(-1.75561 - 3.44559i) q^{92} +(-12.4408 - 12.4408i) q^{93} +(-2.37920 + 7.32242i) q^{94} +(1.22403 - 0.866394i) q^{95} +(-3.15542 + 1.02526i) q^{96} +(1.46631 - 2.87780i) q^{97} +(6.21272 - 3.22522i) q^{98} -30.0315i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{7}+O(q^{10}) \) 160 * q + 8 * q^7	\( 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) \) 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

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Database

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