LMFDB - Embedded newform 336.2.y.a.293.50

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(125,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("336.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.y (of order $4$, degree $2$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			293.50
Character	$\chi$	$=$	336.293
Dual form			336.2.y.a.125.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18025 + 0.779110i) q^{2} +(1.43440 + 0.970819i) q^{3} +(0.785975 + 1.83909i) q^{4} +(-1.77648 - 1.77648i) q^{5} +(0.936577 + 2.26337i) q^{6} +(2.61801 + 0.382105i) q^{7} +(-0.505204 + 2.78294i) q^{8} +(1.11502 + 2.78509i) q^{9} +O(q^{10})$	\(q+(1.18025 + 0.779110i) q^{2} +(1.43440 + 0.970819i) q^{3} +(0.785975 + 1.83909i) q^{4} +(-1.77648 - 1.77648i) q^{5} +(0.936577 + 2.26337i) q^{6} +(2.61801 + 0.382105i) q^{7} +(-0.505204 + 2.78294i) q^{8} +(1.11502 + 2.78509i) q^{9} +(-0.712616 - 3.48076i) q^{10} +(-0.0741148 + 0.0741148i) q^{11} +(-0.658016 + 3.40103i) q^{12} +(-2.31927 - 2.31927i) q^{13} +(2.79221 + 2.49070i) q^{14} +(-0.823546 - 4.27283i) q^{15} +(-2.76449 + 2.89096i) q^{16} -1.12306 q^{17} +(-0.853890 + 4.15582i) q^{18} +(-0.438173 - 0.438173i) q^{19} +(1.87083 - 4.66337i) q^{20} +(3.38433 + 3.08971i) q^{21} +(-0.145218 + 0.0297304i) q^{22} +5.33792 q^{23} +(-3.42640 + 3.50140i) q^{24} +1.31176i q^{25} +(-0.930352 - 4.54429i) q^{26} +(-1.10443 + 5.07742i) q^{27} +(1.35497 + 5.11508i) q^{28} +(-6.24342 - 6.24342i) q^{29} +(2.35701 - 5.68463i) q^{30} -7.00163i q^{31} +(-5.51515 + 1.25821i) q^{32} +(-0.178263 + 0.0343584i) q^{33} +(-1.32549 - 0.874987i) q^{34} +(-3.97205 - 5.32965i) q^{35} +(-4.24565 + 4.23963i) q^{36} +(2.76432 + 2.76432i) q^{37} +(-0.175768 - 0.858537i) q^{38} +(-1.07518 - 5.57837i) q^{39} +(5.84133 - 4.04636i) q^{40} +5.12996i q^{41} +(1.58713 + 6.28339i) q^{42} +(-6.01001 - 6.01001i) q^{43} +(-0.194556 - 0.0780512i) q^{44} +(2.96685 - 6.92847i) q^{45} +(6.30008 + 4.15883i) q^{46} -9.67990 q^{47} +(-6.77198 + 1.46298i) q^{48} +(6.70799 + 2.00071i) q^{49} +(-1.02201 + 1.54821i) q^{50} +(-1.61092 - 1.09029i) q^{51} +(2.44246 - 6.08824i) q^{52} +(6.64120 - 6.64120i) q^{53} +(-5.25937 + 5.13215i) q^{54} +0.263327 q^{55} +(-2.38601 + 7.09274i) q^{56} +(-0.203129 - 1.05390i) q^{57} +(-2.50448 - 12.2331i) q^{58} +(2.61226 + 2.61226i) q^{59} +(7.21082 - 4.87291i) q^{60} +(8.32252 + 8.32252i) q^{61} +(5.45504 - 8.26367i) q^{62} +(1.85494 + 7.71746i) q^{63} +(-7.48954 - 2.81191i) q^{64} +8.24029i q^{65} +(-0.237163 - 0.0983347i) q^{66} +(3.53606 - 3.53606i) q^{67} +(-0.882697 - 2.06541i) q^{68} +(7.65673 + 5.18216i) q^{69} +(-0.535621 - 9.38498i) q^{70} +13.2577 q^{71} +(-8.31406 + 1.69600i) q^{72} +1.10615 q^{73} +(1.10888 + 5.41630i) q^{74} +(-1.27348 + 1.88159i) q^{75} +(0.461445 - 1.15023i) q^{76} +(-0.222353 + 0.165714i) q^{77} +(3.07719 - 7.42155i) q^{78} -14.8528 q^{79} +(10.0468 - 0.224672i) q^{80} +(-6.51346 + 6.21087i) q^{81} +(-3.99681 + 6.05464i) q^{82} +(-6.51714 + 6.51714i) q^{83} +(-3.02225 + 8.65252i) q^{84} +(1.99509 + 1.99509i) q^{85} +(-2.41085 - 11.7758i) q^{86} +(-2.89435 - 15.0168i) q^{87} +(-0.168814 - 0.243700i) q^{88} +7.27086i q^{89} +(8.89966 - 5.86582i) q^{90} +(-5.18569 - 6.95810i) q^{91} +(4.19548 + 9.81691i) q^{92} +(6.79732 - 10.0432i) q^{93} +(-11.4247 - 7.54171i) q^{94} +1.55681i q^{95} +(-9.13244 - 3.54944i) q^{96} -9.22466i q^{97} +(6.35833 + 7.58760i) q^{98} +(-0.289056 - 0.123777i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 8 q^{4}+O(q^{10}) $ 120 * q - 8 * q^4	$ 120 q - 8 q^{4} - 8 q^{15} + 8 q^{16} - 32 q^{18} - 8 q^{21} + 16 q^{22} - 16 q^{30} - 8 q^{36} - 8 q^{37} - 24 q^{42} - 8 q^{43} - 24 q^{46} - 8 q^{49} - 56 q^{51} + 40 q^{58} - 96 q^{60} + 24 q^{63} - 56 q^{64} + 24 q^{67} - 80 q^{70} - 8 q^{72} + 64 q^{78} - 16 q^{79} - 8 q^{81} - 48 q^{84} - 48 q^{85} - 24 q^{88} - 8 q^{91} + 8 q^{93} - 40 q^{99}+O(q^{100}) $ 120 * q - 8 * q^4 - 8 * q^15 + 8 * q^16 - 32 * q^18 - 8 * q^21 + 16 * q^22 - 16 * q^30 - 8 * q^36 - 8 * q^37 - 24 * q^42 - 8 * q^43 - 24 * q^46 - 8 * q^49 - 56 * q^51 + 40 * q^58 - 96 * q^60 + 24 * q^63 - 56 * q^64 + 24 * q^67 - 80 * q^70 - 8 * q^72 + 64 * q^78 - 16 * q^79 - 8 * q^81 - 48 * q^84 - 48 * q^85 - 24 * q^88 - 8 * q^91 + 8 * q^93 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$-1$

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 $

$2$	1.18025	+	0.779110i	0.834562	+	0.550914i
$2$	1.18025	+	0.779110i	0.834562	+	0.550914i
$3$	1.43440	+	0.970819i	0.828153	+	0.560503i
$3$	1.43440	+	0.970819i	0.828153	+	0.560503i
$4$	0.785975	+	1.83909i	0.392988	+	0.919544i
$5$	−1.77648	−	1.77648i	−0.794466	−	0.794466i	0.187751	−	0.982217i	$-0.439880\pi$
$5$	−1.77648	−	1.77648i	−0.794466	−	0.794466i	−0.982217	+	0.187751i	$0.939880\pi$
$6$	0.936577	+	2.26337i	0.382356	+	0.924015i
$7$	2.61801	+	0.382105i	0.989516	+	0.144422i
$7$	2.61801	+	0.382105i	0.989516	+	0.144422i
$8$	−0.505204	+	2.78294i	−0.178617	+	0.983919i
$9$	1.11502	+	2.78509i	0.371674	+	0.928364i
$10$	−0.712616	−	3.48076i	−0.225349	−	1.10071i
$11$	−0.0741148	+	0.0741148i	−0.0223465	+	0.0223465i	−0.718192	−	0.695845i	$-0.755030\pi$
$11$	−0.0741148	+	0.0741148i	−0.0223465	+	0.0223465i	0.695845	+	0.718192i	$0.255030\pi$
$12$	−0.658016	+	3.40103i	−0.189953	+	0.981793i
$13$	−2.31927	−	2.31927i	−0.643251	−	0.643251i	0.308102	−	0.951353i	$-0.400306\pi$
$13$	−2.31927	−	2.31927i	−0.643251	−	0.643251i	−0.951353	+	0.308102i	$0.900306\pi$
$14$	2.79221	+	2.49070i	0.746249	+	0.665667i
$15$	−0.823546	−	4.27283i	−0.212639	−	1.10324i
$16$	−2.76449	+	2.89096i	−0.691121	+	0.722739i
$17$	−1.12306			−0.272382			−0.136191	−	0.990683i	$-0.543486\pi$
$17$	−1.12306			−0.272382			−0.136191	+	0.990683i	$0.543486\pi$
$18$	−0.853890	+	4.15582i	−0.201264	+	0.979537i
$19$	−0.438173	−	0.438173i	−0.100524	−	0.100524i	0.655056	−	0.755580i	$-0.272645\pi$
$19$	−0.438173	−	0.438173i	−0.100524	−	0.100524i	−0.755580	+	0.655056i	$0.772645\pi$
$20$	1.87083	−	4.66337i	0.418331	−	1.04276i
$21$	3.38433	+	3.08971i	0.738521	+	0.674230i
$22$	−0.145218	+	0.0297304i	−0.0309605	+	0.00633853i
$23$	5.33792			1.11303			0.556517	−	0.830836i	$-0.312137\pi$
$23$	5.33792			1.11303			0.556517	+	0.830836i	$0.312137\pi$
$24$	−3.42640	+	3.50140i	−0.699411	+	0.714720i
$25$			1.31176i			0.262352i
$26$	−0.930352	−	4.54429i	−0.182457	−	0.891209i
$27$	−1.10443	+	5.07742i	−0.212548	+	0.977151i
$28$	1.35497	+	5.11508i	0.256065	+	0.966659i
$29$	−6.24342	−	6.24342i	−1.15937	−	1.15937i	−0.984610	−	0.174764i	$-0.944084\pi$
$29$	−6.24342	−	6.24342i	−1.15937	−	1.15937i	−0.174764	−	0.984610i	$-0.555916\pi$
$30$	2.35701	−	5.68463i	0.430330	−	1.03787i
$31$		−	7.00163i		−	1.25753i	−0.777595	−	0.628765i	$-0.783561\pi$
$31$		−	7.00163i		−	1.25753i	0.777595	−	0.628765i	$-0.216439\pi$
$32$	−5.51515	+	1.25821i	−0.974950	+	0.222422i
$33$	−0.178263	+	0.0343584i	−0.0310315	+	0.00598103i
$34$	−1.32549	−	0.874987i	−0.227320	−	0.150059i
$35$	−3.97205	−	5.32965i	−0.671398	−	0.900875i
$36$	−4.24565	+	4.23963i	−0.707608	+	0.706606i
$37$	2.76432	+	2.76432i	0.454452	+	0.454452i	0.896829	−	0.442377i	$-0.145865\pi$
$37$	2.76432	+	2.76432i	0.454452	+	0.454452i	−0.442377	+	0.896829i	$0.645865\pi$
$38$	−0.175768	−	0.858537i	−0.0285134	−	0.139273i
$39$	−1.07518	−	5.57837i	−0.172166	−	0.893254i
$40$	5.84133	−	4.04636i	0.923595	−	0.639785i
$41$			5.12996i			0.801166i	0.916261	+	0.400583i	$0.131192\pi$
$41$			5.12996i			0.801166i	−0.916261	+	0.400583i	$0.868808\pi$
$42$	1.58713	+	6.28339i	0.244899	+	0.969549i
$43$	−6.01001	−	6.01001i	−0.916519	−	0.916519i	0.0802558	−	0.996774i	$-0.474426\pi$
$43$	−6.01001	−	6.01001i	−0.916519	−	0.916519i	−0.996774	+	0.0802558i	$0.974426\pi$
$44$	−0.194556	−	0.0780512i	−0.0293304	−	0.0117667i
$45$	2.96685	−	6.92847i	0.442271	−	1.03284i
$46$	6.30008	+	4.15883i	0.928896	+	0.613186i
$47$	−9.67990			−1.41196			−0.705980	−	0.708232i	$-0.749493\pi$
$47$	−9.67990			−1.41196			−0.705980	+	0.708232i	$0.749493\pi$
$48$	−6.77198	+	1.46298i	−0.977451	+	0.211163i
$49$	6.70799	+	2.00071i	0.958284	+	0.285816i
$50$	−1.02201	+	1.54821i	−0.144534	+	0.218949i
$51$	−1.61092	−	1.09029i	−0.225574	−	0.152671i
$52$	2.44246	−	6.08824i	0.338708	−	0.844287i
$53$	6.64120	−	6.64120i	0.912239	−	0.912239i	−0.0842090	−	0.996448i	$-0.526836\pi$
$53$	6.64120	−	6.64120i	0.912239	−	0.912239i	0.996448	+	0.0842090i	$0.0268363\pi$
$54$	−5.25937	+	5.13215i	−0.715710	+	0.698397i
$55$	0.263327			0.0355070
$56$	−2.38601	+	7.09274i	−0.318844	+	0.947807i
$57$	−0.203129	−	1.05390i	−0.0269052	−	0.139593i
$58$	−2.50448	−	12.2331i	−0.328854	−	1.60629i
$59$	2.61226	+	2.61226i	0.340087	+	0.340087i	0.856400	−	0.516313i	$-0.172696\pi$
$59$	2.61226	+	2.61226i	0.340087	+	0.340087i	−0.516313	+	0.856400i	$0.672696\pi$
$60$	7.21082	−	4.87291i	0.930912	−	0.629090i
$61$	8.32252	+	8.32252i	1.06559	+	1.06559i	0.997692	+	0.0678974i	$0.0216291\pi$
$61$	8.32252	+	8.32252i	1.06559	+	1.06559i	0.0678974	+	0.997692i	$0.478371\pi$
$62$	5.45504	−	8.26367i	0.692791	−	1.04949i
$63$	1.85494	+	7.71746i	0.233701	+	0.972309i
$64$	−7.48954	−	2.81191i	−0.936192	−	0.351489i
$65$			8.24029i			1.02208i
$66$	−0.237163	−	0.0983347i	−0.0291928	−	0.0121042i
$67$	3.53606	−	3.53606i	0.431998	−	0.431998i	−0.457309	−	0.889308i	$-0.651187\pi$
$67$	3.53606	−	3.53606i	0.431998	−	0.431998i	0.889308	+	0.457309i	$0.151187\pi$
$68$	−0.882697	−	2.06541i	−0.107043	−	0.250467i
$69$	7.65673	+	5.18216i	0.921762	+	0.623859i
$70$	−0.535621	−	9.38498i	−0.0640189	−	1.12172i
$71$	13.2577			1.57340			0.786699	−	0.617337i	$-0.211789\pi$
$71$	13.2577			1.57340			0.786699	+	0.617337i	$0.211789\pi$
$72$	−8.31406	+	1.69600i	−0.979821	+	0.199875i
$73$	1.10615			0.129466			0.0647328	−	0.997903i	$-0.479380\pi$
$73$	1.10615			0.129466			0.0647328	+	0.997903i	$0.479380\pi$
$74$	1.10888	+	5.41630i	0.128904	+	0.629632i
$75$	−1.27348	+	1.88159i	−0.147049	+	0.217268i
$76$	0.461445	−	1.15023i	0.0529313	−	0.131940i
$77$	−0.222353	+	0.165714i	−0.0253395	+	0.0188849i
$78$	3.07719	−	7.42155i	0.348423	−	0.840325i
$79$	−14.8528			−1.67108			−0.835538	−	0.549433i	$-0.814844\pi$
$79$	−14.8528			−1.67108			−0.835538	+	0.549433i	$0.814844\pi$
$80$	10.0468	−	0.224672i	1.12326	−	0.0251191i
$81$	−6.51346	+	6.21087i	−0.723718	+	0.690096i
$82$	−3.99681	+	6.05464i	−0.441373	+	0.668623i
$83$	−6.51714	+	6.51714i	−0.715349	+	0.715349i	−0.967649	−	0.252300i	$-0.918813\pi$
$83$	−6.51714	+	6.51714i	−0.715349	+	0.715349i	0.252300	+	0.967649i	$0.418813\pi$
$84$	−3.02225	+	8.65252i	−0.329754	+	0.944067i
$85$	1.99509	+	1.99509i	0.216398	+	0.216398i
$86$	−2.41085	−	11.7758i	−0.259969	−	1.26981i
$87$	−2.89435	−	15.0168i	−0.310306	−	1.60997i
$88$	−0.168814	−	0.243700i	−0.0179957	−	0.0259786i
$89$			7.27086i			0.770710i	0.922768	+	0.385355i	$0.125921\pi$
$89$			7.27086i			0.770710i	−0.922768	+	0.385355i	$0.874079\pi$
$90$	8.89966	−	5.86582i	0.938106	−	0.618312i
$91$	−5.18569	−	6.95810i	−0.543608	−	0.729407i
$92$	4.19548	+	9.81691i	0.437409	+	1.02348i
$93$	6.79732	−	10.0432i	0.704849	−	1.04143i
$94$	−11.4247	−	7.54171i	−1.17837	−	0.777868i
$95$			1.55681i			0.159725i
$96$	−9.13244	−	3.54944i	−0.932076	−	0.362263i
$97$		−	9.22466i		−	0.936623i	−0.883564	−	0.468311i	$-0.844863\pi$
$97$		−	9.22466i		−	0.936623i	0.883564	−	0.468311i	$-0.155137\pi$
$98$	6.35833	+	7.58760i	0.642288	+	0.766464i
$99$	−0.289056	−	0.123777i	−0.0290512	−	0.0124401i
$100$	−2.41244	+	1.03101i	−0.241244	+	0.103101i
$101$	−6.09773	−	6.09773i	−0.606746	−	0.606746i	0.335348	−	0.942094i	$-0.391146\pi$
$101$	−6.09773	−	6.09773i	−0.606746	−	0.606746i	−0.942094	+	0.335348i	$0.891146\pi$
$102$	−1.05183	−	2.54189i	−0.104147	−	0.251685i
$103$	−7.72801			−0.761463			−0.380732	−	0.924686i	$-0.624328\pi$
$103$	−7.72801			−0.761463			−0.380732	+	0.924686i	$0.624328\pi$
$104$	7.62612	−	5.28270i	0.747802	−	0.518011i
$105$	−0.523387	−	11.5010i	−0.0510773	−	1.12238i
$106$	13.0125	−	2.66405i	1.26389	−	0.258755i
$107$	−7.90702	+	7.90702i	−0.764400	+	0.764400i	−0.977114	−	0.212714i	$-0.931770\pi$
$107$	−7.90702	+	7.90702i	−0.764400	+	0.764400i	0.212714	+	0.977114i	$0.431770\pi$
$108$	−10.2059	+	1.95959i	−0.982061	+	0.188561i
$109$	−3.79005	+	3.79005i	−0.363021	+	0.363021i	−0.864924	−	0.501903i	$-0.832633\pi$
$109$	−3.79005	+	3.79005i	−0.363021	+	0.363021i	0.501903	+	0.864924i	$0.332633\pi$
$110$	0.310792	+	0.205161i	0.0296328	+	0.0195613i
$111$	1.28149	+	6.64881i	0.121634	+	0.631077i
$112$	−8.34211	+	6.51224i	−0.788255	+	0.615349i
$113$			15.9062i			1.49633i	0.663510	+	0.748167i	$0.269066\pi$
$113$			15.9062i			1.49633i	−0.663510	+	0.748167i	$0.730934\pi$
$114$	0.581362	−	1.40213i	0.0544496	−	0.131321i
$115$	−9.48272	−	9.48272i	−0.884268	−	0.884268i
$116$	6.57502	−	16.3894i	0.610475	−	1.52172i
$117$	3.87335	−	9.04543i	0.358091	−	0.836250i
$118$	1.04788	+	5.11835i	0.0964650	+	0.471182i
$119$	−2.94019	−	0.429127i	−0.269526	−	0.0393380i
$120$	12.3071	−	0.133231i	1.12348	−	0.0121623i
$121$			10.9890i			0.999001i
$122$	3.33849	+	16.3068i	0.302253	+	1.47635i
$123$	−4.98027	+	7.35843i	−0.449056	+	0.663488i
$124$	12.8766	−	5.50311i	1.15635	−	0.494194i
$125$	−6.55208	+	6.55208i	−0.586036	+	0.586036i
$126$	−3.82346	+	10.5537i	−0.340621	+	0.940201i
$127$	17.0011			1.50861			0.754303	−	0.656526i	$-0.227975\pi$
$127$	17.0011			1.50861			0.754303	+	0.656526i	$0.227975\pi$
$128$	−6.64873	−	9.15393i	−0.587670	−	0.809100i
$129$	−2.78614	−	14.4554i	−0.245306	−	1.27273i
$130$	−6.42009	+	9.72559i	−0.563079	+	0.852991i
$131$	9.03159	−	9.03159i	0.789093	−	0.789093i	−0.192252	−	0.981346i	$-0.561579\pi$
$131$	9.03159	−	9.03159i	0.789093	−	0.789093i	0.981346	+	0.192252i	$0.0615791\pi$
$132$	−0.203298	−	0.300836i	−0.0176948	−	0.0261844i
$133$	−0.979714	−	1.31457i	−0.0849520	−	0.113988i
$134$	6.92841	−	1.41845i	0.598523	−	0.122536i
$135$	10.9819	−	7.05794i	0.945175	−	0.607451i
$136$	0.567375	−	3.12541i	0.0486520	−	0.268002i
$137$	1.35488			0.115755			0.0578777	−	0.998324i	$-0.481567\pi$
$137$	1.35488			0.115755			0.0578777	+	0.998324i	$0.481567\pi$
$138$	4.99938	+	12.0817i	0.425575	+	1.02846i
$139$	7.93580	−	7.93580i	0.673106	−	0.673106i	−0.285325	−	0.958431i	$-0.592101\pi$
$139$	7.93580	−	7.93580i	0.673106	−	0.673106i	0.958431	+	0.285325i	$0.0921015\pi$
$140$	6.67976	−	11.4939i	0.564543	−	0.971413i
$141$	−13.8849	−	9.39744i	−1.16932	−	0.791407i
$142$	15.6474	+	10.3292i	1.31310	+	0.866806i
$143$	0.343785			0.0287488
$144$	−11.1340	−	4.47587i	−0.927836	−	0.372989i
$145$			22.1826i			1.84217i
$146$	1.30554	+	0.861816i	0.108047	+	0.0713244i
$147$	7.67963	+	9.38207i	0.633405	+	0.773820i
$148$	−2.91114	+	7.25652i	−0.239294	+	0.596482i
$149$	−6.09446	+	6.09446i	−0.499277	+	0.499277i	−0.911213	−	0.411936i	$-0.864853\pi$
$149$	−6.09446	+	6.09446i	−0.499277	+	0.499277i	0.411936	+	0.911213i	$0.364853\pi$
$150$	−2.96900	+	1.22857i	−0.242418	+	0.100312i
$151$			7.26102i			0.590893i	0.955359	+	0.295447i	$0.0954684\pi$
$151$			7.26102i			0.590893i	−0.955359	+	0.295447i	$0.904532\pi$
$152$	1.44078	−	0.998042i	0.116862	−	0.0809519i
$153$	−1.25223	−	3.12782i	−0.101237	−	0.252870i
$154$	−0.391542	+	0.0223461i	−0.0315513	+	0.00180070i
$155$	−12.4383	+	12.4383i	−0.999065	+	0.999065i
$156$	9.41405	−	6.36181i	0.753727	−	0.509352i
$157$	2.27650	+	2.27650i	0.181684	+	0.181684i	0.792089	−	0.610405i	$-0.208993\pi$
$157$	2.27650	+	2.27650i	0.181684	+	0.181684i	−0.610405	+	0.792089i	$0.708993\pi$
$158$	−17.5301	−	11.5720i	−1.39462	−	0.920619i
$159$	15.9736	−	3.07875i	1.26679	−	0.244161i
$160$	12.0327	+	7.56237i	0.951272	+	0.597858i
$161$	13.9748	+	2.03965i	1.10137	+	0.160747i
$162$	−12.5265	+	2.25567i	−0.984171	+	0.177222i
$163$	−3.57856	+	3.57856i	−0.280295	+	0.280295i	−0.833227	−	0.552932i	$-0.813509\pi$
$163$	−3.57856	+	3.57856i	−0.280295	+	0.280295i	0.552932	+	0.833227i	$0.313509\pi$
$164$	−9.43445	+	4.03203i	−0.736707	+	0.314848i
$165$	0.377717	+	0.255643i	0.0294052	+	0.0199018i
$166$	−12.7694	+	2.61428i	−0.991098	+	0.202907i
$167$			17.1504i			1.32714i	0.748116	+	0.663568i	$0.230959\pi$
$167$			17.1504i			1.32714i	−0.748116	+	0.663568i	$0.769041\pi$
$168$	−10.3083	+	7.85746i	−0.795300	+	0.606216i
$169$		−	2.24193i		−	0.172456i
$170$	0.800310	+	3.90910i	0.0613810	+	0.299815i
$171$	0.731779	−	1.70892i	0.0559605	−	0.130684i
$172$	6.32922	−	15.7767i	0.482598	−	1.20296i
$173$	−13.3963	+	13.3963i	−1.01850	+	1.01850i	−0.0186756	+	0.999826i	$0.505945\pi$
$173$	−13.3963	+	13.3963i	−1.01850	+	1.01850i	−0.999826	+	0.0186756i	$0.994055\pi$
$174$	8.28370	−	19.9786i	0.627985	−	1.51457i
$175$	−0.501231	+	3.43421i	−0.0378895	+	0.259602i
$176$	−0.00937332	−	0.419152i	−0.000706541	−	0.0315948i
$177$	1.21100	+	6.28306i	0.0910243	+	0.472264i
$178$	−5.66480	+	8.58143i	−0.424595	+	0.643205i
$179$	−4.75096	−	4.75096i	−0.355103	−	0.355103i	0.506901	−	0.862004i	$-0.330791\pi$
$179$	−4.75096	−	4.75096i	−0.355103	−	0.355103i	−0.862004	+	0.506901i	$0.830791\pi$
$180$	15.0739	+	0.0106821i	1.12354	+	0.000796195i
$181$	−7.39355	+	7.39355i	−0.549558	+	0.549558i	−0.926313	−	0.376755i	$-0.877040\pi$
$181$	−7.39355	+	7.39355i	−0.549558	+	0.549558i	0.376755	+	0.926313i	$0.377040\pi$
$182$	−0.699277	−	12.2525i	−0.0518339	−	0.908216i
$183$	3.85818	+	20.0175i	0.285205	+	1.47974i
$184$	−2.69674	+	14.8551i	−0.198807	+	1.09514i
$185$		−	9.82153i		−	0.722093i
$186$	15.8472	−	6.55757i	1.16198	−	0.480824i
$187$	0.0832354	−	0.0832354i	0.00608678	−	0.00608678i
$188$	−7.60817	−	17.8022i	−0.554883	−	1.29836i
$189$	−4.83152	+	12.8708i	−0.351442	+	0.936210i
$190$	−1.21293	+	1.83742i	−0.0879949	+	0.133301i
$191$		−	7.32648i		−	0.530125i	−0.964231	−	0.265063i	$-0.914607\pi$
$191$		−	7.32648i		−	0.530125i	0.964231	−	0.265063i	$-0.0853927\pi$
$192$	−8.01315	−	11.3044i	−0.578300	−	0.815824i
$193$	−6.64143			−0.478061			−0.239030	−	0.971012i	$-0.576830\pi$
$193$	−6.64143			−0.478061			−0.239030	+	0.971012i	$0.576830\pi$
$194$	7.18703	−	10.8874i	0.515998	−	0.781670i
$195$	−7.99983	+	11.8199i	−0.572880	+	0.846440i
$196$	1.59283	+	13.9091i	0.113774	+	0.993507i
$197$	0.265062	−	0.265062i	0.0188849	−	0.0188849i	−0.697601	−	0.716486i	$-0.745749\pi$
$197$	0.265062	−	0.265062i	0.0188849	−	0.0188849i	0.716486	+	0.697601i	$0.245749\pi$
$198$	−0.244722	−	0.371294i	−0.0173917	−	0.0263867i
$199$	5.77400			0.409308			0.204654	−	0.978834i	$-0.434393\pi$
$199$	5.77400			0.409308			0.204654	+	0.978834i	$0.434393\pi$
$200$	−3.65056	−	0.662708i	−0.258133	−	0.0468605i
$201$	8.50500	−	1.63926i	0.599897	−	0.115624i
$202$	−2.44604	−	11.9476i	−0.172103	−	0.840633i
$203$	−13.9597	−	18.7310i	−0.979780	−	1.31466i
$204$	0.738991	−	3.81956i	0.0517397	−	0.267423i
$205$	9.11328	−	9.11328i	0.636499	−	0.636499i
$206$	−9.12097	−	6.02097i	−0.635488	−	0.419501i
$207$	5.95190	+	14.8666i	0.413685	+	1.03330i
$208$	13.1165	−	0.293319i	0.909467	−	0.0203380i
$209$	0.0649502			0.00449270
$210$	8.34282	−	13.9818i	0.575709	−	0.964837i
$211$	2.23723	−	2.23723i	0.154018	−	0.154018i	−0.625892	−	0.779910i	$-0.715265\pi$
$211$	2.23723	−	2.23723i	0.154018	−	0.154018i	0.779910	+	0.625892i	$0.215265\pi$
$212$	17.4336	+	6.99393i	1.19734	+	0.480345i
$213$	19.0169	+	12.8708i	1.30301	+	0.881893i
$214$	−15.4927	+	3.17181i	−1.05906	+	0.216821i
$215$			21.3533i			1.45629i
$216$	−13.5722	−	5.63870i	−0.923472	−	0.383665i
$217$	2.67536	−	18.3304i	0.181615	−	1.24435i
$218$	−7.42607	+	1.52034i	−0.502957	+	0.102970i
$219$	1.58667	+	1.07388i	0.107217	+	0.0725658i
$220$	0.206969	+	0.484281i	0.0139538	+	0.0326503i
$221$	2.60468	+	2.60468i	0.175210	+	0.175210i
$222$	−3.66767	+	8.84568i	−0.246158	+	0.593683i
$223$			0.469170i			0.0314179i	0.999877	+	0.0157090i	$0.00500052\pi$
$223$			0.469170i			0.0314179i	−0.999877	+	0.0157090i	$0.994999\pi$
$224$	−14.9195	+	1.18664i	−0.996852	+	0.0792859i
$225$	−3.65338	+	1.46264i	−0.243558	+	0.0975094i
$226$	−12.3927	+	18.7733i	−0.824351	+	1.24878i
$227$	9.61841	−	9.61841i	0.638396	−	0.638396i	−0.311763	−	0.950160i	$-0.600920\pi$
$227$	9.61841	−	9.61841i	0.638396	−	0.638396i	0.950160	+	0.311763i	$0.100920\pi$
$228$	1.77856	−	1.20191i	0.117788	−	0.0795987i
$229$	−11.4717	+	11.4717i	−0.758074	+	0.758074i	−0.975972	−	0.217898i	$-0.930080\pi$
$229$	−11.4717	+	11.4717i	−0.758074	+	0.758074i	0.217898	+	0.975972i	$0.430080\pi$
$230$	−3.80389	−	18.5800i	−0.250821	−	1.22513i
$231$	−0.479822	+	0.0218357i	−0.0315700	+	0.00143669i
$232$	20.5293	−	14.2209i	1.34781	−	0.933646i
$233$	3.56188			0.233346			0.116673	−	0.993170i	$-0.462777\pi$
$233$	3.56188			0.233346			0.116673	+	0.993170i	$0.462777\pi$
$234$	11.6189	−	7.65809i	0.759551	−	0.500625i
$235$	17.1962	+	17.1962i	1.12175	+	1.12175i
$236$	−2.75100	+	6.85734i	−0.179075	+	0.446375i
$237$	−21.3050	−	14.4194i	−1.38391	−	0.936642i
$238$	−3.13581	−	2.79720i	−0.203265	−	0.181316i
$239$		−	7.92785i		−	0.512810i	−0.966569	−	0.256405i	$-0.917462\pi$
$239$		−	7.92785i		−	0.512810i	0.966569	−	0.256405i	$-0.0825380\pi$
$240$	14.6292	+	9.43133i	0.944313	+	0.608790i
$241$			19.5089i			1.25668i	0.777939	+	0.628340i	$0.216265\pi$
$241$			19.5089i			1.25668i	−0.777939	+	0.628340i	$0.783735\pi$
$242$	−8.56165	+	12.9698i	−0.550364	+	0.833729i
$243$	−15.3725	+	2.58549i	−0.986149	+	0.165859i
$244$	−8.76455	+	21.8471i	−0.561093	+	1.39862i
$245$	−8.36239	−	15.4708i	−0.534253	−	0.988396i
$246$	−11.6110	+	4.80461i	−0.740289	+	0.306331i
$247$			2.03248i			0.129324i
$248$	19.4851	+	3.53725i	1.23731	+	0.224616i
$249$	−15.6752	+	3.02124i	−0.993373	+	0.191463i
$250$	−12.8379	+	2.62830i	−0.811939	+	0.166228i
$251$	8.55946	+	8.55946i	0.540268	+	0.540268i	0.923608	−	0.383339i	$-0.125226\pi$
$251$	8.55946	+	8.55946i	0.540268	+	0.540268i	−0.383339	+	0.923608i	$0.625226\pi$
$252$	−12.7351	+	9.47713i	−0.802239	+	0.597003i
$253$	−0.395619	+	0.395619i	−0.0248724	+	0.0248724i
$254$	20.0656	+	13.2458i	1.25903	+	0.831112i
$255$	0.924892	+	4.79864i	0.0579190	+	0.300503i
$256$	−0.715245	−	15.9840i	−0.0447028	−	0.999000i
$257$	28.6292			1.78584			0.892921	−	0.450213i	$-0.148652\pi$
$257$	28.6292			1.78584			0.892921	+	0.450213i	$0.148652\pi$
$258$	7.97402	−	19.2317i	0.496441	−	1.19731i
$259$	6.18077	+	8.29330i	0.384055	+	0.515320i
$260$	−15.1546	+	6.47667i	−0.939849	+	0.401666i
$261$	10.4270	−	24.3500i	0.645412	−	1.50723i
$262$	17.6961	−	3.62292i	1.09327	−	0.223825i
$263$	10.7939			0.665582			0.332791	−	0.943001i	$-0.392010\pi$
$263$	10.7939			0.665582			0.332791	+	0.943001i	$0.392010\pi$
$264$	−0.00555840	−	0.513453i	−0.000342096	−	0.0316008i
$265$	−23.5959			−1.44949
$266$	−0.132112	−	2.31482i	−0.00810031	−	0.141931i
$267$	−7.05869	+	10.4293i	−0.431985	+	0.638265i
$268$	9.28238	+	3.72387i	0.567011	+	0.227471i
$269$	17.9513	−	17.9513i	1.09451	−	1.09451i	0.0994711	−	0.995040i	$-0.468285\pi$
$269$	17.9513	−	17.9513i	1.09451	−	1.09451i	0.995040	−	0.0994711i	$-0.0317151\pi$
$270$	18.4603	+	0.226010i	1.12346	+	0.0137545i
$271$		−	23.0817i		−	1.40211i	−0.713105	−	0.701057i	$-0.752712\pi$
$271$		−	23.0817i		−	1.40211i	0.713105	−	0.701057i	$-0.247288\pi$
$272$	3.10468	−	3.24672i	0.188249	−	0.196861i
$273$	−0.683305	−	15.0151i	−0.0413555	−	0.908754i
$274$	1.59910	+	1.05560i	0.0966051	+	0.0637713i
$275$	−0.0972210	−	0.0972210i	−0.00586265	−	0.00586265i
$276$	−3.51244	+	18.1544i	−0.211424	+	1.09277i
$277$	−10.7260	−	10.7260i	−0.644461	−	0.644461i	0.307188	−	0.951649i	$-0.400612\pi$
$277$	−10.7260	−	10.7260i	−0.644461	−	0.644461i	−0.951649	+	0.307188i	$0.900612\pi$
$278$	15.5491	−	3.18336i	0.932572	−	0.190925i
$279$	19.5002	−	7.80696i	1.16744	−	0.467391i
$280$	16.8388	−	8.36141i	1.00631	−	0.499690i
$281$	28.2692			1.68640			0.843200	−	0.537600i	$-0.180669\pi$
$281$	28.2692			1.68640			0.843200	+	0.537600i	$0.180669\pi$
$282$	−9.06598	−	21.9092i	−0.539871	−	1.30467i
$283$	−2.15511	+	2.15511i	−0.128108	+	0.128108i	−0.768254	−	0.640146i	$-0.778874\pi$
$283$	−2.15511	+	2.15511i	−0.128108	+	0.128108i	0.640146	+	0.768254i	$0.278874\pi$
$284$	10.4202	+	24.3820i	0.618326	+	1.44681i
$285$	−1.51138	+	2.23309i	−0.0895264	+	0.132277i
$286$	0.405752	+	0.267847i	0.0239926	+	0.0158381i
$287$	−1.96019	+	13.4303i	−0.115706	+	0.792767i
$288$	−9.65374	−	13.9573i	−0.568852	−	0.822440i
$289$	−15.7387			−0.925808
$290$	−17.2827	+	26.1810i	−1.01488	+	1.53740i
$291$	8.95548	−	13.2319i	0.524980	−	0.775667i
$292$	0.869410	+	2.03431i	0.0508784	+	0.119049i
$293$	−6.06656	−	6.06656i	−0.354412	−	0.354412i	0.507336	−	0.861748i	$-0.330630\pi$
$293$	−6.06656	−	6.06656i	−0.354412	−	0.354412i	−0.861748	+	0.507336i	$0.830630\pi$
$294$	1.75421	+	17.0565i	0.102308	+	0.994753i
$295$		−	9.28125i		−	0.540375i
$296$	−9.08950	+	6.29640i	−0.528316	+	0.365971i
$297$	−0.294458	−	0.458167i	−0.0170862	−	0.0265856i
$298$	−11.9412	+	2.44472i	−0.691737	+	0.141619i
$299$	−12.3801	−	12.3801i	−0.715960	−	0.715960i
$300$	−4.46134	−	0.863160i	−0.257576	−	0.0498346i
$301$	−13.4378	−	18.0308i	−0.774544	−	1.03928i
$302$	−5.65713	+	8.56981i	−0.325531	+	0.493137i
$303$	−2.82680	−	14.6664i	−0.162396	−	0.842562i
$304$	2.47806	−	0.0554158i	0.142126	−	0.00317831i
$305$		−	29.5696i		−	1.69315i
$306$	0.958969	−	4.66724i	0.0548206	−	0.266808i
$307$	11.8881	+	11.8881i	0.678492	+	0.678492i	0.959659	−	0.281167i	$-0.0907215\pi$
$307$	11.8881	+	11.8881i	0.678492	+	0.678492i	−0.281167	+	0.959659i	$0.590721\pi$
$308$	−0.479527	−	0.278680i	−0.0273236	−	0.0158793i
$309$	−11.0851	−	7.50250i	−0.630608	−	0.426802i
$310$	−24.3710	+	4.98947i	−1.38418	+	0.283383i
$311$		−	24.4490i		−	1.38638i	−0.720756	−	0.693189i	$-0.756205\pi$
$311$		−	24.4490i		−	1.38638i	0.720756	−	0.693189i	$-0.243795\pi$
$312$	16.0675	−	0.173939i	0.909641	−	0.00984735i
$313$	24.0174			1.35754			0.678771	−	0.734350i	$-0.262513\pi$
$313$	24.0174			1.35754			0.678771	+	0.734350i	$0.262513\pi$
$314$	0.913192	+	4.46047i	0.0515344	+	0.251719i
$315$	10.4146	−	17.0052i	0.586799	−	0.958133i
$316$	−11.6740	−	27.3157i	−0.656712	−	1.53663i
$317$	−9.04926	−	9.04926i	−0.508257	−	0.508257i	0.405734	−	0.913991i	$-0.367016\pi$
$317$	−9.04926	−	9.04926i	−0.508257	−	0.508257i	−0.913991	+	0.405734i	$0.867016\pi$
$318$	21.2515	+	8.81147i	1.19172	+	0.494123i
$319$	0.925460			0.0518158
$320$	8.30971	+	18.3003i	0.464527	+	1.02302i
$321$	−19.0181	+	3.66556i	−1.06149	+	0.204592i
$322$	14.9046	+	13.2952i	0.830600	+	0.740911i
$323$	0.492094	+	0.492094i	0.0273808	+	0.0273808i
$324$	−16.5417	−	7.09723i	−0.918986	−	0.394291i
$325$	3.04234	−	3.04234i	0.168758	−	0.168758i
$326$	−7.01169	+	1.43550i	−0.388342	+	0.0795051i
$327$	−9.11591	+	1.75700i	−0.504111	+	0.0971626i
$328$	−14.2764	−	2.59168i	−0.788282	−	0.143102i
$329$	−25.3421	−	3.69874i	−1.39716	−	0.203918i
$330$	0.246626	+	0.596005i	0.0135763	+	0.0328090i
$331$	14.0440	+	14.0440i	0.771927	+	0.771927i	0.978443	−	0.206516i	$-0.0662127\pi$
$331$	14.0440	+	14.0440i	0.771927	+	0.771927i	−0.206516	+	0.978443i	$0.566213\pi$
$332$	−17.1079	−	6.86327i	−0.938918	−	0.376671i
$333$	−4.61661	+	10.7812i	−0.252989	+	0.590804i
$334$	−13.3620	+	20.2417i	−0.731138	+	1.10758i
$335$	−12.5635			−0.686416
$336$	−18.2881	+	1.24249i	−0.997700	+	0.0677834i
$337$	−7.68303			−0.418521			−0.209261	−	0.977860i	$-0.567106\pi$
$337$	−7.68303			−0.418521			−0.209261	+	0.977860i	$0.567106\pi$
$338$	1.74671	−	2.64604i	0.0950085	−	0.143925i
$339$	−15.4421	+	22.8160i	−0.838699	+	1.23919i
$340$	−2.10106	+	5.23725i	−0.113946	+	0.284029i
$341$	0.518925	+	0.518925i	0.0281014	+	0.0281014i
$342$	2.19512	−	1.44682i	0.118698	−	0.0782349i
$343$	16.7971	+	7.80105i	0.906960	+	0.421217i
$344$	19.7618	−	13.6892i	1.06549	−	0.738074i
$345$	−4.39603	−	22.8080i	−0.236674	−	1.22794i
$346$	−26.2481	+	5.37378i	−1.41111	+	0.288896i
$347$	24.8807	−	24.8807i	1.33566	−	1.33566i	0.435453	−	0.900212i	$-0.356588\pi$
$347$	24.8807	−	24.8807i	1.33566	−	1.33566i	0.900212	−	0.435453i	$-0.143412\pi$
$348$	25.3423	−	17.1258i	1.35849	−	0.918039i
$349$	4.84630	+	4.84630i	0.259416	+	0.259416i	0.824817	−	0.565400i	$-0.191278\pi$
$349$	4.84630	+	4.84630i	0.259416	+	0.259416i	−0.565400	+	0.824817i	$0.691278\pi$
$350$	−3.26720	+	3.66271i	−0.174639	+	0.195780i
$351$	14.3374	−	9.21446i	0.765275	−	0.491832i
$352$	0.315503	−	0.502007i	0.0168163	−	0.0267570i
$353$	−25.8692			−1.37688			−0.688440	−	0.725293i	$-0.741704\pi$
$353$	−25.8692			−1.37688			−0.688440	+	0.725293i	$0.741704\pi$
$354$	−3.46591	+	8.35907i	−0.184211	+	0.444280i
$355$	−23.5520	−	23.5520i	−1.25001	−	1.25001i
$356$	−13.3718	+	5.71472i	−0.708701	+	0.302880i
$357$	−3.80081	−	3.46993i	−0.201160	−	0.183648i
$358$	−1.90580	−	9.30883i	−0.100724	−	0.491987i
$359$	−28.3861			−1.49816			−0.749081	−	0.662478i	$-0.769505\pi$
$359$	−28.3861			−1.49816			−0.749081	+	0.662478i	$0.769505\pi$
$360$	17.7827	+	11.7569i	0.937229	+	0.619641i
$361$		−	18.6160i		−	0.979790i
$362$	−14.4866	+	2.96584i	−0.761400	+	0.155881i
$363$	−10.6683	+	15.7627i	−0.559943	+	0.827326i
$364$	8.72073	−	15.0058i	0.457090	−	0.786519i
$365$	−1.96506	−	1.96506i	−0.102856	−	0.102856i
$366$	−11.0422	+	26.6316i	−0.577186	+	1.39206i
$367$			2.12026i			0.110677i	0.998468	+	0.0553384i	$0.0176238\pi$
$367$			2.12026i			0.110677i	−0.998468	+	0.0553384i	$0.982376\pi$
$368$	−14.7566	+	15.4317i	−0.769242	+	0.804433i
$369$	−14.2874	+	5.72002i	−0.743773	+	0.297772i
$370$	7.65205	−	11.5918i	0.397811	−	0.602632i
$371$	19.9244	−	14.8491i	1.03442	−	0.770928i
$372$	23.8128	+	4.60719i	1.23463	+	0.238871i
$373$	0.149413	+	0.149413i	0.00773629	+	0.00773629i	0.710964	−	0.703228i	$-0.248259\pi$
$373$	0.149413	+	0.149413i	0.00773629	+	0.00773629i	−0.703228	+	0.710964i	$0.748259\pi$
$374$	0.163088	−	0.0333890i	0.00843308	−	0.00172650i
$375$	−15.7592	+	3.03744i	−0.813802	+	0.156852i
$376$	4.89033	−	26.9386i	0.252200	−	1.38925i
$377$			28.9604i			1.49154i
$378$	−15.7301	+	11.4264i	−0.809071	+	0.587711i
$379$	−11.9869	−	11.9869i	−0.615724	−	0.615724i	0.328707	−	0.944432i	$-0.393387\pi$
$379$	−11.9869	−	11.9869i	−0.615724	−	0.615724i	−0.944432	+	0.328707i	$0.893387\pi$
$380$	−2.86311	+	1.22361i	−0.146874	+	0.0627701i
$381$	24.3865	+	16.5050i	1.24936	+	0.845578i
$382$	5.70813	−	8.64707i	0.292053	−	0.442423i
$383$	10.7829			0.550980			0.275490	−	0.961304i	$-0.411160\pi$
$383$	10.7829			0.550980			0.275490	+	0.961304i	$0.411160\pi$
$384$	−0.650151	−	19.5851i	−0.0331779	−	0.999449i
$385$	0.689394	+	0.100619i	0.0351348	+	0.00512800i
$386$	−7.83855	−	5.17441i	−0.398971	−	0.263370i
$387$	10.0371	−	23.4397i	0.510217	−	1.19151i
$388$	16.9650	−	7.25036i	0.861266	−	0.368081i
$389$	−3.38960	+	3.38960i	−0.171860	+	0.171860i	−0.787796	−	0.615936i	$-0.788778\pi$
$389$	−3.38960	+	3.38960i	−0.171860	+	0.171860i	0.615936	+	0.787796i	$0.288778\pi$
$390$	−18.6508	+	7.71767i	−0.944419	+	0.390799i
$391$	−5.99481			−0.303170
$392$	−8.95677	+	17.6572i	−0.452385	+	0.891823i
$393$	21.7230	−	4.18689i	1.09578	−	0.211201i
$394$	0.519351	−	0.106327i	0.0261646	−	0.00535666i
$395$	26.3858	+	26.3858i	1.32761	+	1.32761i
$396$	0.000445657	−	0.628885i	2.23951e−5	−	0.0316027i
$397$	16.6827	+	16.6827i	0.837283	+	0.837283i	0.988500	−	0.151218i	$-0.0483194\pi$
$397$	16.6827	+	16.6827i	0.837283	+	0.837283i	−0.151218	+	0.988500i	$0.548319\pi$
$398$	6.81475	+	4.49858i	0.341593	+	0.225493i
$399$	−0.129094	−	2.83675i	−0.00646281	−	0.142015i
$400$	−3.79225	−	3.62635i	−0.189612	−	0.181317i
$401$		−	26.7116i		−	1.33391i	−0.745096	−	0.666957i	$-0.767597\pi$
$401$		−	26.7116i		−	1.33391i	0.745096	−	0.666957i	$-0.232403\pi$
$402$	11.3152	+	4.69160i	0.564350	+	0.233996i
$403$	−16.2387	+	16.2387i	−0.808908	+	0.808908i
$404$	6.42159	−	16.0069i	0.319486	−	0.796374i
$405$	22.6045	+	0.537549i	1.12323	+	0.0267110i
$406$	−1.88243	−	32.9834i	−0.0934236	−	1.63694i
$407$	−0.409755			−0.0203108
$408$	3.84805	−	3.93228i	0.190507	−	0.194677i
$409$	5.32043			0.263078			0.131539	−	0.991311i	$-0.458008\pi$
$409$	5.32043			0.263078			0.131539	+	0.991311i	$0.458008\pi$
$410$	17.8562	−	3.65569i	0.881854	−	0.180542i
$411$	1.94345	+	1.31535i	0.0958632	+	0.0648813i
$412$	−6.07403	−	14.2125i	−0.299246	−	0.700199i
$413$	5.84077	+	7.83708i	0.287405	+	0.385638i
$414$	−4.55800	+	22.1835i	−0.224013	+	1.09026i
$415$	23.1551			1.13664
$416$	15.7093	+	9.87302i	0.770211	+	0.484065i
$417$	19.0874	−	3.67891i	0.934712	−	0.180157i
$418$	0.0766574	+	0.0506033i	0.00374944	+	0.00247509i
$419$	6.87876	−	6.87876i	0.336049	−	0.336049i	−0.518829	−	0.854878i	$-0.673632\pi$
$419$	6.87876	−	6.87876i	0.336049	−	0.336049i	0.854878	+	0.518829i	$0.173632\pi$
$420$	20.7400	−	10.0021i	1.01201	−	0.488051i
$421$	1.35486	+	1.35486i	0.0660316	+	0.0660316i	0.739351	−	0.673320i	$-0.235132\pi$
$421$	1.35486	+	1.35486i	0.0660316	+	0.0660316i	−0.673320	+	0.739351i	$0.735132\pi$
$422$	4.38355	−	0.897442i	0.213388	−	0.0436868i
$423$	−10.7933	−	26.9594i	−0.524788	−	1.31081i
$424$	15.1269	+	21.8372i	0.734628	+	1.06051i
$425$		−	1.47319i		−	0.0714601i
$426$	12.4168	+	30.0070i	0.601598	+	1.45384i
$427$	18.6084	+	24.9686i	0.900524	+	1.20831i
$428$	−20.7564	−	8.32697i	−1.00330	−	0.402499i
$429$	0.493127	+	0.333753i	0.0238084	+	0.0161138i
$430$	−16.6366	+	25.2023i	−0.802288	+	1.21536i
$431$		−	1.06779i		−	0.0514336i	−0.999669	−	0.0257168i	$-0.991813\pi$
$431$		−	1.06779i		−	0.0514336i	0.999669	−	0.0257168i	$-0.00818682\pi$
$432$	−11.6254	−	17.2293i	−0.559328	−	0.828946i
$433$		−	20.3147i		−	0.976261i	−0.872771	−	0.488131i	$-0.837679\pi$
$433$		−	20.3147i		−	0.976261i	0.872771	−	0.488131i	$-0.162321\pi$
$434$	17.4390	−	19.5500i	0.837097	−	0.938430i
$435$	−21.5353	+	31.8188i	−1.03254	+	1.52560i
$436$	−9.94913	−	3.99135i	−0.476477	−	0.191151i
$437$	−2.33893	−	2.33893i	−0.111886	−	0.111886i
$438$	1.03600	+	2.50363i	0.0495019	+	0.119628i
$439$	−34.8927			−1.66534			−0.832669	−	0.553771i	$-0.813188\pi$
$439$	−34.8927			−1.66534			−0.832669	+	0.553771i	$0.813188\pi$
$440$	−0.133034	+	0.732824i	−0.00634215	+	0.0349360i
$441$	1.90738	+	20.9132i	0.0908277	+	0.995867i
$442$	1.04484	+	5.10351i	0.0496980	+	0.242749i
$443$	1.54345	−	1.54345i	0.0733314	−	0.0733314i	−0.669490	−	0.742821i	$-0.733487\pi$
$443$	1.54345	−	1.54345i	0.0733314	−	0.0733314i	0.742821	+	0.669490i	$0.233487\pi$
$444$	−11.2205	+	7.58258i	−0.532502	+	0.359853i
$445$	12.9165	−	12.9165i	0.612303	−	0.612303i
$446$	−0.365535	+	0.553737i	−0.0173086	+	0.0262202i
$447$	−14.6585	+	2.82529i	−0.693324	+	0.133632i
$448$	−18.5333	−	10.2234i	−0.875614	−	0.483011i
$449$		−	9.06672i		−	0.427885i	−0.976846	−	0.213942i	$-0.931370\pi$
$449$		−	9.06672i		−	0.427885i	0.976846	−	0.213942i	$-0.0686305\pi$
$450$	−5.45145	−	1.12010i	−0.256984	−	0.0528020i
$451$	−0.380207	−	0.380207i	−0.0179032	−	0.0179032i
$452$	−29.2530	+	12.5019i	−1.37594	+	0.588041i
$453$	−7.04913	+	10.4152i	−0.331197	+	0.489350i
$454$	18.8459	−	3.85832i	0.884483	−	0.181080i
$455$	−3.14866	+	21.5732i	−0.147611	+	1.01137i
$456$	3.03557	−	0.0328617i	0.142154	−	0.00153889i
$457$			24.3672i			1.13985i	0.821698	+	0.569924i	$0.193027\pi$
$457$			24.3672i			1.13985i	−0.821698	+	0.569924i	$0.806973\pi$
$458$	−22.4773	+	4.60176i	−1.05029	+	0.215026i
$459$	1.24034	−	5.70225i	0.0578942	−	0.266158i
$460$	9.98636	−	24.8927i	0.465616	−	1.16063i
$461$	20.1422	−	20.1422i	0.938117	−	0.938117i	−0.0600771	−	0.998194i	$-0.519135\pi$
$461$	20.1422	−	20.1422i	0.938117	−	0.938117i	0.998194	+	0.0600771i	$0.0191347\pi$
$462$	−0.583322	−	0.348063i	−0.0271386	−	0.0161934i
$463$	−24.3558			−1.13191			−0.565955	−	0.824436i	$-0.691492\pi$
$463$	−24.3558			−1.13191			−0.565955	+	0.824436i	$0.691492\pi$
$464$	35.3093	−	0.789607i	1.63919	−	0.0366566i
$465$	−29.9168	+	5.76617i	−1.38736	+	0.267400i
$466$	4.20390	+	2.77509i	0.194742	+	0.128554i
$467$	22.6038	−	22.6038i	1.04598	−	1.04598i	0.0470904	−	0.998891i	$-0.485005\pi$
$467$	22.6038	−	22.6038i	1.04598	−	1.04598i	0.998891	−	0.0470904i	$-0.0149949\pi$
$468$	19.6797	+	0.0139459i	0.909694	+	0.000644651i
$469$	10.6086	−	7.90630i	0.489859	−	0.365079i
$470$	6.89805	+	33.6934i	0.318183	+	1.55416i
$471$	1.05535	+	5.47548i	0.0486278	+	0.252297i
$472$	−8.58949	+	5.95004i	−0.395363	+	0.273873i
$473$	0.890862			0.0409619
$474$	−13.9108	−	33.6174i	−0.638946	−	1.54410i
$475$	0.574778	−	0.574778i	0.0263726	−	0.0263726i
$476$	−1.52171	−	5.74454i	−0.0697476	−	0.263301i
$477$	25.9014	+	11.0913i	1.18594	+	0.507834i
$478$	6.17666	−	9.35683i	0.282514	−	0.427972i
$479$	−15.5142			−0.708862			−0.354431	−	0.935082i	$-0.615325\pi$
$479$	−15.5142			−0.708862			−0.354431	+	0.935082i	$0.615325\pi$
$480$	9.91810	+	22.5291i	0.452697	+	1.02831i
$481$		−	12.8224i		−	0.584653i
$482$	−15.1996	+	23.0254i	−0.692323	+	1.04878i
$483$	18.0653	+	16.4926i	0.822000	+	0.750441i
$484$	−20.2098	+	8.63710i	−0.918625	+	0.392595i
$485$	−16.3874	+	16.3874i	−0.744115	+	0.744115i
$486$	−20.1578	−	8.92538i	−0.914377	−	0.404864i
$487$		−	12.0106i		−	0.544254i	−0.962261	−	0.272127i	$-0.912273\pi$
$487$		−	12.0106i		−	0.544254i	0.962261	−	0.272127i	$-0.0877271\pi$
$488$	−27.3657	+	18.9565i	−1.23879	+	0.858122i
$489$	−8.60724	+	1.65896i	−0.389233	+	0.0750209i
$490$	2.18378	−	24.7747i	0.0986533	−	1.11921i
$491$	1.84022	−	1.84022i	0.0830480	−	0.0830480i	−0.664362	−	0.747411i	$-0.731297\pi$
$491$	1.84022	−	1.84022i	0.0830480	−	0.0830480i	0.747411	+	0.664362i	$0.231297\pi$
$492$	−17.4472	−	3.37560i	−0.786579	−	0.152184i
$493$	7.01173	+	7.01173i	0.315793	+	0.315793i
$494$	−1.58353	+	2.39884i	−0.0712463	+	0.107929i
$495$	0.293615	+	0.733390i	0.0131970	+	0.0329634i
$496$	20.2414	+	19.3559i	0.908866	+	0.869106i
$497$	34.7088	+	5.06583i	1.55690	+	0.227233i
$498$	−20.8545	−	8.64686i	−0.934511	−	0.387475i
$499$	−10.6230	+	10.6230i	−0.475551	+	0.475551i	−0.903706	−	0.428155i	$-0.859164\pi$
$499$	−10.6230	+	10.6230i	−0.475551	+	0.475551i	0.428155	+	0.903706i	$0.359164\pi$
$500$	−17.1996	−	6.90007i	−0.769191	−	0.308581i
$501$	−16.6499	+	24.6005i	−0.743863	+	1.09907i
$502$	3.43353	+	16.7710i	0.153246	+	0.748528i
$503$			2.06584i			0.0921115i	0.998939	+	0.0460557i	$0.0146652\pi$
$503$			2.06584i			0.0921115i	−0.998939	+	0.0460557i	$0.985335\pi$
$504$	−22.4144	+	1.26330i	−0.998415	+	0.0562719i
$505$			21.6650i			0.964079i
$506$	−0.775161	+	0.158698i	−0.0344601	+	0.00705501i
$507$	2.17651	−	3.21583i	0.0966621	−	0.142820i
$508$	13.3625	+	31.2666i	0.592864	+	1.38723i
$509$	−14.4489	+	14.4489i	−0.640435	+	0.640435i	−0.950662	−	0.310227i	$-0.899595\pi$
$509$	−14.4489	+	14.4489i	−0.640435	+	0.640435i	0.310227	+	0.950662i	$0.399595\pi$
$510$	−2.64707	+	6.38418i	−0.117214	+	0.282696i
$511$	2.89593	+	0.422667i	0.128108	+	0.0186977i
$512$	11.6091	−	19.4224i	0.513056	−	0.858355i
$513$	2.70872	−	1.74086i	0.119593	−	0.0768607i
$514$	33.7896	+	22.3053i	1.49040	+	0.983846i
$515$	13.7287	+	13.7287i	0.604957	+	0.604957i
$516$	24.3949	−	16.4856i	1.07393	−	0.725736i
$517$	0.717425	−	0.717425i	0.0315523	−	0.0315523i
$518$	0.833462	+	14.6037i	0.0366202	+	0.641648i
$519$	−32.2210	+	6.21030i	−1.41435	+	0.272602i
$520$	−22.9323	−	4.16303i	−1.00565	−	0.182561i
$521$			20.1909i			0.884578i	0.896873	+	0.442289i	$0.145833\pi$
$521$			20.1909i			0.884578i	−0.896873	+	0.442289i	$0.854167\pi$
$522$	31.2778	−	20.6154i	1.36899	−	0.902310i
$523$	21.9175	−	21.9175i	0.958383	−	0.958383i	−0.0407845	−	0.999168i	$-0.512986\pi$
$523$	21.9175	−	21.9175i	0.958383	−	0.958383i	0.999168	+	0.0407845i	$0.0129857\pi$
$524$	23.7085	+	9.51127i	1.03571	+	0.415502i
$525$	−4.05296	+	4.43944i	−0.176886	+	0.193753i
$526$	12.7395	+	8.40966i	0.555470	+	0.366678i
$527$			7.86325i			0.342529i
$528$	0.393476	−	0.610333i	0.0171238	−	0.0265613i
$529$	5.49344			0.238845
$530$	−27.8491	−	18.3838i	−1.20969	−	0.798542i
$531$	−4.36265	+	10.1881i	−0.189323	+	0.442126i
$532$	1.64758	−	2.83500i	0.0714315	−	0.122913i
$533$	11.8978	−	11.8978i	0.515351	−	0.515351i
$534$	−16.4566	+	6.80972i	−0.712148	+	0.294686i
$535$	28.0933			1.21458
$536$	8.05421	+	11.6271i	0.347889	+	0.502213i
$537$	−2.20247	−	11.4271i	−0.0950434	−	0.493116i
$538$	35.1731	−	7.20098i	1.51642	−	0.310456i
$539$	−0.645444	+	0.348879i	−0.0278013	+	0.0150273i
$540$	21.6117	+	14.6494i	0.930020	+	0.630409i
$541$	−26.1032	+	26.1032i	−1.12226	+	1.12226i	−0.130862	+	0.991401i	$0.541775\pi$
$541$	−26.1032	+	26.1032i	−1.12226	+	1.12226i	−0.991401	+	0.130862i	$0.958225\pi$
$542$	17.9832	−	27.2422i	0.772444	−	1.17015i
$543$	−17.7831	+	3.42753i	−0.763147	+	0.147089i
$544$	6.19385	−	1.41304i	0.265559	−	0.0605838i
$545$	13.4659			0.576816
$546$	10.8919	−	18.2539i	0.466131	−	0.781195i
$547$	31.0388	−	31.0388i	1.32712	−	1.32712i	0.419257	−	0.907868i	$-0.362291\pi$
$547$	31.0388	−	31.0388i	1.32712	−	1.32712i	0.907868	−	0.419257i	$-0.137709\pi$
$548$	1.06491	+	2.49175i	0.0454905	+	0.106442i
$549$	−13.8992	+	32.4588i	−0.593203	+	1.38531i
$550$	−0.0389992	−	0.190491i	−0.00166293	−	0.00812256i
$551$			5.47139i			0.233089i
$552$	−18.2899	+	18.6902i	−0.778468	+	0.795508i
$553$	−38.8850	−	5.67535i	−1.65356	−	0.241340i
$554$	−4.30260	−	21.0160i	−0.182800	−	0.892885i
$555$	9.53493	−	14.0880i	0.404735	−	0.598003i
$556$	20.8320	+	8.35729i	0.883473	+	0.354428i
$557$	19.7191	+	19.7191i	0.835525	+	0.835525i	0.988266	−	0.152741i	$-0.0488101\pi$
$557$	19.7191	+	19.7191i	0.835525	+	0.835525i	−0.152741	+	0.988266i	$0.548810\pi$
$558$	29.0975	+	5.97862i	1.23180	+	0.253095i
$559$			27.8777i			1.17910i
$560$	26.3884	+	3.25073i	1.11512	+	0.137368i
$561$	0.200200	−	0.0385865i	0.00845243	−	0.00162913i
$562$	33.3647	+	22.0248i	1.40741	+	0.929062i
$563$	−12.3298	+	12.3298i	−0.519640	+	0.519640i	−0.917462	−	0.397823i	$-0.869766\pi$
$563$	−12.3298	+	12.3298i	−0.519640	+	0.519640i	0.397823	+	0.917462i	$0.369766\pi$
$564$	6.36953	−	32.9217i	0.268206	−	1.38625i
$565$	28.2571	−	28.2571i	1.18879	−	1.18879i
$566$	−4.22263	+	0.864498i	−0.177490	+	0.0363376i
$567$	−19.4255	+	13.7713i	−0.815795	+	0.578341i
$568$	−6.69784	+	36.8954i	−0.281035	+	1.54810i
$569$	−11.1453			−0.467237			−0.233619	−	0.972328i	$-0.575057\pi$
$569$	−11.1453			−0.467237			−0.233619	+	0.972328i	$0.575057\pi$
$570$	−3.52363	+	1.45807i	−0.147589	+	0.0610719i
$571$	−23.2290	−	23.2290i	−0.972103	−	0.972103i	0.0275185	−	0.999621i	$-0.491239\pi$
$571$	−23.2290	−	23.2290i	−0.972103	−	0.972103i	−0.999621	+	0.0275185i	$0.991239\pi$
$572$	0.270207	+	0.632251i	0.0112979	+	0.0264358i
$573$	7.11269	−	10.5091i	0.297137	−	0.439025i
$574$	−12.7772	+	14.3239i	−0.533310	+	0.597869i
$575$			7.00209i			0.292007i
$576$	−0.519565	−	23.9944i	−0.0216485	−	0.999766i
$577$		−	11.2442i		−	0.468102i	−0.972224	−	0.234051i	$-0.924802\pi$
$577$		−	11.2442i		−	0.468102i	0.972224	−	0.234051i	$-0.0751982\pi$
$578$	−18.5756	−	12.2622i	−0.772644	−	0.510041i
$579$	−9.52649	−	6.44763i	−0.395907	−	0.267954i
$580$	−40.7958	+	17.4350i	−1.69395	+	0.723949i
$581$	−19.5522	+	14.5717i	−0.811161	+	0.604537i
$582$	20.8788	−	8.63961i	0.865453	−	0.358123i
$583$			0.984423i			0.0407706i
$584$	−0.558834	+	3.07836i	−0.0231247	+	0.127384i
$585$	−22.9500	+	9.18809i	−0.948864	+	0.379881i
$586$	−2.43354	−	11.8866i	−0.100528	−	0.491030i
$587$	5.48702	+	5.48702i	0.226474	+	0.226474i	0.811218	−	0.584744i	$-0.198805\pi$
$587$	5.48702	+	5.48702i	0.226474	+	0.226474i	−0.584744	+	0.811218i	$0.698805\pi$
$588$	−11.2185	+	21.4976i	−0.462641	+	0.886546i
$589$	−3.06792	+	3.06792i	−0.126412	+	0.126412i
$590$	7.23111	−	10.9542i	0.297700	−	0.450977i
$591$	0.637533	−	0.122878i	0.0262246	−	0.00505454i
$592$	−15.6335	+	0.349605i	−0.642531	+	0.0143687i
$593$	18.3422			0.753226			0.376613	−	0.926371i	$-0.377089\pi$
$593$	18.3422			0.753226			0.376613	+	0.926371i	$0.377089\pi$
$594$	0.00942915	−	0.770166i	0.000386883	−	0.0316003i
$595$	4.46085	+	5.98552i	0.182877	+	0.245382i
$596$	−15.9983	−	6.41814i	−0.655317	−	0.262897i
$597$	8.28223	+	5.60551i	0.338969	+	0.229418i
$598$	−4.96615	−	24.2571i	−0.203081	−	0.991946i
$599$	−11.1799			−0.456799			−0.228399	−	0.973568i	$-0.573349\pi$
$599$	−11.1799			−0.456799			−0.228399	+	0.973568i	$0.573349\pi$
$600$	−4.59300	−	4.49462i	−0.187508	−	0.183492i
$601$	13.8492			0.564922			0.282461	−	0.959279i	$-0.408849\pi$
$601$	13.8492			0.564922			0.282461	+	0.959279i	$0.408849\pi$
$602$	−1.81206	−	31.7503i	−0.0738540	−	1.29405i
$603$	13.7910	+	5.90547i	0.561614	+	0.240489i
$604$	−13.3536	+	5.70698i	−0.543352	+	0.232214i
$605$	19.5218	−	19.5218i	0.793673	−	0.793673i
$606$	8.09039	−	19.5124i	0.328650	−	0.792636i
$607$		−	8.32297i		−	0.337819i	−0.985632	−	0.168909i	$-0.945975\pi$
$607$		−	8.32297i		−	0.337819i	0.985632	−	0.168909i	$-0.0540245\pi$
$608$	2.96790	+	1.86528i	0.120364	+	0.0756469i
$609$	−1.83944	−	40.4202i	−0.0745378	−	1.63791i
$610$	23.0380	−	34.8995i	0.932780	−	1.41304i
$611$	22.4504	+	22.4504i	0.908244	+	0.908244i
$612$	4.76811	−	4.76136i	0.192740	−	0.192467i
$613$	16.4993	+	16.4993i	0.666399	+	0.666399i	0.956880	−	0.290482i	$-0.0938156\pi$
$613$	16.4993	+	16.4993i	0.666399	+	0.666399i	−0.290482	+	0.956880i	$0.593816\pi$
$614$	4.76880	+	23.2931i	0.192453	+	0.940034i
$615$	21.9195	−	4.22476i	0.883878	−	0.170359i
$616$	−0.348839	−	0.702516i	−0.0140551	−	0.0283052i
$617$	−29.4789			−1.18677			−0.593387	−	0.804917i	$-0.702210\pi$
$617$	−29.4789			−1.18677			−0.593387	+	0.804917i	$0.702210\pi$
$618$	−7.23788	−	17.4913i	−0.291150	−	0.703604i
$619$	−21.0776	+	21.0776i	−0.847181	+	0.847181i	−0.989780	−	0.142600i	$-0.954454\pi$
$619$	−21.0776	+	21.0776i	−0.847181	+	0.847181i	0.142600	+	0.989780i	$0.454454\pi$
$620$	−32.6512	−	13.0989i	−1.31130	−	0.526064i
$621$	−5.89537	+	27.1029i	−0.236573	+	1.08760i
$622$	19.0485	−	28.8559i	0.763775	−	1.15702i
$623$	−2.77823	+	19.0352i	−0.111308	+	0.762630i
$624$	19.0991	+	12.3130i	0.764577	+	0.492916i
$625$	29.8381			1.19352
$626$	28.3465	+	18.7122i	1.13295	+	0.747889i
$627$	0.0931647	+	0.0630549i	0.00372064	+	0.00251817i
$628$	−2.39741	+	5.97595i	−0.0956669	+	0.238466i
$629$	−3.10450	−	3.10450i	−0.123785	−	0.123785i
$630$	25.5408	−	11.9562i	1.01757	−	0.476346i
$631$		−	30.3005i		−	1.20624i	−0.797649	−	0.603122i	$-0.793923\pi$
$631$		−	30.3005i		−	1.20624i	0.797649	−	0.603122i	$-0.206077\pi$
$632$	7.50372	−	41.3346i	0.298482	−	1.64420i
$633$	5.38105	−	1.03714i	0.213877	−	0.0412228i
$634$	−3.63001	−	17.7307i	−0.144166	−	0.704178i
$635$	−30.2022	−	30.2022i	−1.19854	−	1.19854i
$636$	18.2169	+	26.9569i	0.722348	+	1.06891i
$637$	−10.9175	−	20.1979i	−0.432566	−	0.800269i
$638$	1.09227	+	0.721035i	0.0432435	+	0.0285461i
$639$	14.7826	+	36.9238i	0.584790	+	1.46068i
$640$	−4.45043	+	28.0731i	−0.175919	+	1.10969i
$641$			9.09705i			0.359312i	0.983730	+	0.179656i	$0.0574984\pi$
$641$			9.09705i			0.359312i	−0.983730	+	0.179656i	$0.942502\pi$
$642$	−25.3020	−	10.4909i	−0.998590	−	0.414044i
$643$	25.8392	+	25.8392i	1.01900	+	1.01900i	0.999816	+	0.0191830i	$0.00610651\pi$
$643$	25.8392	+	25.8392i	1.01900	+	1.01900i	0.0191830	+	0.999816i	$0.493893\pi$
$644$	7.23273	+	27.3039i	0.285009	+	1.07593i
$645$	−20.7302	+	30.6293i	−0.816252	+	1.20603i
$646$	0.197398	+	0.964189i	0.00776653	+	0.0379355i
$647$		−	8.90215i		−	0.349980i	−0.984570	−	0.174990i	$-0.944011\pi$
$647$		−	8.90215i		−	0.349980i	0.984570	−	0.174990i	$-0.0559893\pi$
$648$	−13.9939	−	21.2643i	−0.549731	−	0.835342i
$649$	−0.387214			−0.0151995
$650$	5.96103	−	1.22040i	0.233811	−	0.0478680i
$651$	21.6330	−	23.6958i	0.847864	−	0.928713i
$652$	−9.39396	−	3.76863i	−0.367896	−	0.147591i
$653$	29.9144	+	29.9144i	1.17064	+	1.17064i	0.982057	+	0.188584i	$0.0603899\pi$
$653$	29.9144	+	29.9144i	1.17064	+	1.17064i	0.188584	+	0.982057i	$0.439610\pi$
$654$	−12.1279	−	5.02860i	−0.474240	−	0.196634i
$655$	−32.0889			−1.25382
$656$	−14.8305	−	14.1817i	−0.579034	−	0.553703i
$657$	1.23338	+	3.08074i	0.0481189	+	0.120191i
$658$	−27.0283	−	24.1097i	−1.05367	−	0.939895i
$659$	−17.8386	−	17.8386i	−0.694892	−	0.694892i	0.268412	−	0.963304i	$-0.413501\pi$
$659$	−17.8386	−	17.8386i	−0.694892	−	0.694892i	−0.963304	+	0.268412i	$0.913501\pi$
$660$	−0.173273	+	0.895584i	−0.00674466	+	0.0348605i
$661$	−15.0300	+	15.0300i	−0.584599	+	0.584599i	−0.936164	−	0.351565i	$-0.885650\pi$
$661$	−15.0300	+	15.0300i	−0.584599	+	0.584599i	0.351565	+	0.936164i	$0.385650\pi$
$662$	5.63359	+	27.5172i	0.218956	+	1.06949i
$663$	1.20749	+	6.26484i	0.0468949	+	0.243306i
$664$	−14.8443	−	21.4293i	−0.576072	−	0.831618i
$665$	−0.594865	+	4.07575i	−0.0230679	+	0.158051i
$666$	−13.8485	+	9.12761i	−0.536617	+	0.353688i
$667$	−33.3269	−	33.3269i	−1.29042	−	1.29042i
$668$	−31.5410	+	13.4798i	−1.22036	+	0.521548i
$669$	−0.455479	+	0.672978i	−0.0176098	+	0.0260188i
$670$	−14.8280	−	9.78833i	−0.572857	−	0.378156i
$671$	−1.23364			−0.0476243
$672$	−22.5526	−	12.7820i	−0.869985	−	0.493077i
$673$	23.7256			0.914554			0.457277	−	0.889324i	$-0.348825\pi$
$673$	23.7256			0.914554			0.457277	+	0.889324i	$0.348825\pi$
$674$	−9.06789	−	5.98592i	−0.349282	−	0.230569i
$675$	−6.66037	−	1.44875i	−0.256358	−	0.0557624i
$676$	4.12311	−	1.76210i	0.158581	−	0.0677732i
$677$	−30.7121	−	30.7121i	−1.18036	−	1.18036i	−0.979650	−	0.200713i	$-0.935674\pi$
$677$	−30.7121	−	30.7121i	−1.18036	−	1.18036i	−0.200713	−	0.979650i	$-0.564326\pi$
$678$	−36.0017	+	14.8974i	−1.38264	+	0.572132i
$679$	3.52479	−	24.1503i	0.135269	−	0.926803i
$680$	−6.56016	+	4.54430i	−0.251571	+	0.174266i
$681$	23.1344	−	4.45894i	0.886513	−	0.170867i
$682$	0.208161	+	1.01676i	0.00797090	+	0.0389337i
$683$	11.9207	−	11.9207i	0.456134	−	0.456134i	−0.441250	−	0.897384i	$-0.645465\pi$
$683$	11.9207	−	11.9207i	0.456134	−	0.456134i	0.897384	+	0.441250i	$0.145465\pi$
$684$	3.71802	+	0.00263476i	0.142162	+	0.000100742i
$685$	−2.40692	−	2.40692i	−0.0919638	−	0.0919638i
$686$	13.7469	+	22.2940i	0.524860	+	0.851189i
$687$	−27.5921	+	5.31811i	−1.05270	+	0.202898i
$688$	33.9893	−	0.760088i	1.29583	−	0.0289781i
$689$	−30.8055			−1.17360
$690$	12.5816	−	30.3441i	0.478972	−	1.15518i
$691$	−11.8519	−	11.8519i	−0.450869	−	0.450869i	0.444774	−	0.895643i	$-0.353284\pi$
$691$	−11.8519	−	11.8519i	−0.450869	−	0.450869i	−0.895643	+	0.444774i	$0.853284\pi$
$692$	−35.1661	−	14.1078i	−1.33681	−	0.536298i
$693$	−0.709457	−	0.434500i	−0.0269500	−	0.0165053i
$694$	48.7502	−	9.98061i	1.85053	−	0.378859i
$695$	−28.1956			−1.06952
$696$	43.2532	−	0.468238i	1.63951	−	0.0177485i
$697$		−	5.76126i		−	0.218223i
$698$	1.94404	+	9.49564i	0.0735830	+	0.359415i
$699$	5.10917	+	3.45794i	0.193246	+	0.130791i
$700$	−6.70977	+	1.77740i	−0.253605	+	0.0671793i
$701$	4.68572	+	4.68572i	0.176977	+	0.176977i	0.790037	−	0.613060i	$-0.210061\pi$
$701$	4.68572	+	4.68572i	0.176977	+	0.176977i	−0.613060	+	0.790037i	$0.710061\pi$
$702$	24.1008	+	0.295066i	0.909626	+	0.0111366i
$703$		−	2.42250i		−	0.0913663i
$704$	0.763490	−	0.346682i	0.0287751	−	0.0130661i
$705$	7.97185	+	41.3606i	0.300237	+	1.55773i
$706$	−30.5321	−	20.1550i	−1.14909	−	0.758542i
$707$	−13.6340	−	18.2939i	−0.512758	−	0.688013i
$708$	−10.6033	+	7.16546i	−0.398496	+	0.269295i
$709$	−1.48771	−	1.48771i	−0.0558719	−	0.0558719i	0.678619	−	0.734491i	$-0.262579\pi$
$709$	−1.48771	−	1.48771i	−0.0558719	−	0.0558719i	−0.734491	+	0.678619i	$0.762579\pi$
$710$	−9.44763	−	46.1468i	−0.354563	−	1.73186i
$711$	−16.5612	−	41.3665i	−0.621095	−	1.55137i
$712$	−20.2344	−	3.67327i	−0.758316	−	0.137662i
$713$		−	37.3742i		−	1.39967i
$714$	−1.78244	−	7.05663i	−0.0667062	−	0.264088i
$715$	−0.610728	−	0.610728i	−0.0228399	−	0.0228399i
$716$	5.00329	−	12.4716i	0.186982	−	0.466084i
$717$	7.69650	−	11.3717i	0.287431	−	0.424685i
$718$	−33.5027	−	22.1159i	−1.25031	−	0.825359i
$719$	12.3272			0.459727			0.229863	−	0.973223i	$-0.426172\pi$
$719$	12.3272			0.459727			0.229863	+	0.973223i	$0.426172\pi$
$720$	11.8281	+	27.7307i	0.440807	+	1.03346i
$721$	−20.2320	−	2.95291i	−0.753480	−	0.109972i
$722$	14.5039	−	21.9715i	0.539780	−	0.817696i
$723$	−18.9396	+	27.9837i	−0.704373	+	1.04072i
$724$	−19.4085	−	7.78623i	−0.721312	−	0.289373i
$725$	8.18988	−	8.18988i	0.304165	−	0.304165i
$726$	−24.8722	+	10.2921i	−0.923092	+	0.381974i
$727$	−7.55402			−0.280163			−0.140082	−	0.990140i	$-0.544736\pi$
$727$	−7.55402			−0.280163			−0.140082	+	0.990140i	$0.544736\pi$
$728$	21.9838	−	10.9162i	0.814775	−	0.404581i
$729$	−24.5605	−	11.2153i	−0.909647	−	0.415383i
$730$	−0.788263	−	3.85026i	−0.0291749	−	0.142504i
$731$	6.74960	+	6.74960i	0.249643	+	0.249643i
$732$	−33.7815	+	22.8288i	−1.24860	+	0.843777i
$733$	−23.4188	−	23.4188i	−0.864992	−	0.864992i	0.126921	−	0.991913i	$-0.459491\pi$
$733$	−23.4188	−	23.4188i	−0.864992	−	0.864992i	−0.991913	+	0.126921i	$0.959491\pi$
$734$	−1.65192	+	2.50244i	−0.0609734	+	0.0923667i
$735$	3.02436	−	30.3098i	0.111555	−	1.11799i
$736$	−29.4395	+	6.71623i	−1.08515	+	0.247563i
$737$			0.524149i			0.0193073i
$738$	−21.3192	−	4.38042i	−0.784772	−	0.161246i
$739$	−13.9721	+	13.9721i	−0.513971	+	0.513971i	−0.915741	−	0.401769i	$-0.868395\pi$
$739$	−13.9721	+	13.9721i	−0.513971	+	0.513971i	0.401769	+	0.915741i	$0.368395\pi$
$740$	18.0627	−	7.71948i	0.663996	−	0.283774i
$741$	−1.97318	+	2.91540i	−0.0724864	+	0.107100i
$742$	35.0848	−	2.00237i	1.28800	−	0.0735092i
$743$	4.89157			0.179454			0.0897272	−	0.995966i	$-0.471400\pi$
$743$	4.89157			0.179454			0.0897272	+	0.995966i	$0.471400\pi$
$744$	24.5155	+	23.9904i	0.898781	+	0.879530i
$745$	21.6534			0.793318
$746$	0.0599352	+	0.292753i	0.00219438	+	0.0107184i
$747$	−25.4176	−	10.8841i	−0.929980	−	0.398227i
$748$	0.218498	+	0.0876562i	0.00798908	+	0.00320503i
$749$	−23.7220	+	17.6794i	−0.866783	+	0.645990i
$750$	−20.9663	−	8.69322i	−0.765580	−	0.317432i
$751$	−5.43041			−0.198159			−0.0990793	−	0.995080i	$-0.531590\pi$
$751$	−5.43041			−0.198159			−0.0990793	+	0.995080i	$0.531590\pi$
$752$	26.7599	−	27.9842i	0.975835	−	1.02048i
$753$	3.96802	+	20.5874i	0.144603	+	0.750246i
$754$	−22.5633	+	34.1805i	−0.821709	+	1.24478i
$755$	12.8991	−	12.8991i	0.469445	−	0.469445i
$756$	−27.4679	+	1.23050i	−0.998998	+	0.0447530i
$757$	15.3545	+	15.3545i	0.558070	+	0.558070i	0.928758	−	0.370687i	$-0.120878\pi$
$757$	15.3545	+	15.3545i	0.558070	+	0.558070i	−0.370687	+	0.928758i	$0.620878\pi$
$758$	−4.80840	−	23.4866i	−0.174649	−	0.853071i
$759$	−0.951552	+	0.183403i	−0.0345392	+	0.00665709i
$760$	−4.33251	−	0.786507i	−0.157157	−	0.0285296i
$761$		−	16.6239i		−	0.602616i	−0.953527	−	0.301308i	$-0.902577\pi$
$761$		−	16.6239i		−	0.602616i	0.953527	−	0.301308i	$-0.0974233\pi$
$762$	15.9229	+	38.4798i	0.576825	+	1.39398i
$763$	−11.3706	+	8.47421i	−0.411644	+	0.306787i
$764$	13.4740	−	5.75843i	0.487473	−	0.208333i
$765$	−3.33195	+	7.78108i	−0.120467	+	0.281326i
$766$	12.7265	+	8.40105i	0.459827	+	0.303542i
$767$		−	12.1171i		−	0.437523i
$768$	14.4916	−	23.6219i	0.522922	−	0.852381i
$769$		−	22.5828i		−	0.814358i	−0.913348	−	0.407179i	$-0.866513\pi$
$769$		−	22.5828i		−	0.814358i	0.913348	−	0.407179i	$-0.133487\pi$
$770$	0.735263	+	0.655869i	0.0264971	+	0.0236359i
$771$	41.0658	+	27.7938i	1.47895	+	1.00097i
$772$	−5.22000	−	12.2142i	−0.187872	−	0.439598i
$773$	31.8455	+	31.8455i	1.14540	+	1.14540i	0.987446	+	0.157958i	$0.0504912\pi$
$773$	31.8455	+	31.8455i	1.14540	+	1.14540i	0.157958	+	0.987446i	$0.449509\pi$
$774$	30.1084	−	19.8447i	1.08223	−	0.713302i
$775$	9.18447			0.329916
$776$	25.6717	+	4.66034i	0.921561	+	0.167296i
$777$	0.814425	+	17.8963i	0.0292173	+	0.642028i
$778$	−6.64144	+	1.35970i	−0.238107	+	0.0487476i
$779$	2.24781	−	2.24781i	0.0805361	−	0.0805361i
$780$	−28.0255	−	5.42224i	−1.00347	−	0.194147i
$781$	−0.982591	+	0.982591i	−0.0351599	+	0.0351599i
$782$	−7.07537	−	4.67061i	−0.253015	−	0.167021i
$783$	38.5959	−	24.8051i	1.37931	−	0.886461i
$784$	−24.3281	+	13.8616i	−0.868861	+	0.495056i
$785$		−	8.08830i		−	0.288684i
$786$	28.9006	+	11.9830i	1.03085	+	0.427420i
$787$	10.3868	+	10.3868i	0.370248	+	0.370248i	0.867568	−	0.497319i	$-0.165682\pi$
$787$	10.3868	+	10.3868i	0.370248	+	0.370248i	−0.497319	+	0.867568i	$0.665682\pi$
$788$	0.695804	+	0.279140i	0.0247870	+	0.00994395i
$789$	15.4828	+	10.4790i	0.551204	+	0.373061i
$790$	10.5844	+	51.6992i	0.376575	+	1.83938i
$791$	−6.07786	+	41.6428i	−0.216104	+	1.48065i
$792$	0.490497	−	0.741894i	0.0174290	−	0.0263621i
$793$		−	38.6044i		−	1.37088i
$794$	6.69210	+	32.6875i	0.237494	+	1.16004i
$795$	−33.8460	−	22.9074i	−1.20040	−	0.812441i
$796$	4.53822	+	10.6189i	0.160853	+	0.376376i
$797$	−1.56909	+	1.56909i	−0.0555800	+	0.0555800i	−0.734350	−	0.678771i	$-0.762513\pi$
$797$	−1.56909	+	1.56909i	−0.0555800	+	0.0555800i	0.678771	+	0.734350i	$0.262513\pi$
$798$	2.05777	−	3.44865i	0.0728444	−	0.122081i
$799$	10.8711			0.384592
$800$	−1.65047	−	7.23457i	−0.0583530	−	0.255781i
$801$	−20.2500	+	8.10716i	−0.715499	+	0.286452i
$802$	20.8113	−	31.5263i	0.734872	−	1.11323i
$803$	−0.0819825	+	0.0819825i	−0.00289310	+	0.00289310i
$804$	9.69946	+	14.3530i	0.342074	+	0.506192i
$805$	−21.2025	−	28.4493i	−0.747289	−	1.00271i
$806$	−31.8175	+	6.51398i	−1.12072	+	0.229445i
$807$	43.1769	−	8.32193i	1.51990	−	0.292946i
$808$	20.0502	−	13.8890i	0.705364	−	0.488614i
$809$	24.4462			0.859483			0.429741	−	0.902952i	$-0.358605\pi$
$809$	24.4462			0.859483			0.429741	+	0.902952i	$0.358605\pi$
$810$	26.2601	+	18.2458i	0.922687	+	0.641093i
$811$	−6.77672	+	6.77672i	−0.237963	+	0.237963i	−0.816006	−	0.578043i	$-0.803816\pi$
$811$	−6.77672	+	6.77672i	−0.237963	+	0.237963i	0.578043	+	0.816006i	$0.303816\pi$
$812$	23.4760	−	40.3953i	0.823845	−	1.41760i
$813$	22.4082	−	33.1085i	0.785889	−	1.16116i
$814$	−0.483613	−	0.319244i	−0.0169506	−	0.0111895i
$815$	12.7145			0.445369
$816$	7.60534	−	1.64301i	0.266240	−	0.0575169i
$817$			5.26685i			0.184264i
$818$	6.27943	+	4.14520i	0.219555	+	0.144934i
$819$	13.5968	−	22.2010i	0.475110	−	0.775767i
$820$	23.9229	+	9.59730i	0.835425	+	0.335152i
$821$	−37.4556	+	37.4556i	−1.30721	+	1.30721i	−0.383791	+	0.923420i	$0.625382\pi$
$821$	−37.4556	+	37.4556i	−1.30721	+	1.30721i	−0.923420	+	0.383791i	$0.874618\pi$
$822$	1.26895	+	3.06660i	0.0442598	+	0.106960i
$823$			53.8645i			1.87760i	0.344464	+	0.938799i	$0.388061\pi$
$823$			53.8645i			1.87760i	−0.344464	+	0.938799i	$0.611939\pi$
$824$	3.90422	−	21.5066i	0.136010	−	0.749218i
$825$	−0.0450700	−	0.233838i	−0.00156914	−	0.00814120i
$826$	0.787613	+	13.8003i	0.0274046	+	0.480174i
$827$	23.9206	−	23.9206i	0.831802	−	0.831802i	−0.155961	−	0.987763i	$-0.549848\pi$
$827$	23.9206	−	23.9206i	0.831802	−	0.831802i	0.987763	+	0.155961i	$0.0498476\pi$
$828$	−22.6629	+	22.6308i	−0.787592	+	0.786476i
$829$	−12.7297	−	12.7297i	−0.442120	−	0.442120i	0.450604	−	0.892724i	$-0.351209\pi$
$829$	−12.7297	−	12.7297i	−0.442120	−	0.442120i	−0.892724	+	0.450604i	$0.851209\pi$
$830$	27.3288	+	18.0404i	0.948597	+	0.626191i
$831$	−4.97238	−	25.7983i	−0.172490	−	0.894934i
$832$	10.8487	+	23.8919i	0.376111	+	0.828302i
$833$	−7.53348	−	2.24692i	−0.261019	−	0.0778512i
$834$	25.3941	+	10.5291i	0.879326	+	0.364594i
$835$	30.4673	−	30.4673i	1.05436	−	1.05436i
$836$	0.0510492	+	0.119449i	0.00176558	+	0.00413123i
$837$	35.5502	+	7.73282i	1.22880	+	0.267285i
$838$	13.4780	−	2.75934i	0.465588	−	0.0953197i
$839$		−	42.9461i		−	1.48266i	−0.671139	−	0.741332i	$-0.734195\pi$
$839$		−	42.9461i		−	1.48266i	0.671139	−	0.741332i	$-0.265805\pi$
$840$	32.2710	+	4.35380i	1.11346	+	0.150220i
$841$			48.9606i			1.68830i
$842$	0.543486	+	2.65465i	0.0187297	+	0.0914852i
$843$	40.5494	+	27.4443i	1.39660	+	0.945232i
$844$	5.87288	+	2.35606i	0.202153	+	0.0810989i
$845$	−3.98274	+	3.98274i	−0.137011	+	0.137011i
$846$	8.26557	−	40.2280i	0.284176	−	1.38307i
$847$	−4.19896	+	28.7694i	−0.144278	+	0.988528i
$848$	0.839914	+	37.5589i	0.0288428	+	1.28978i
$849$	−5.18351	+	0.999072i	−0.177898	+	0.0342881i
$850$	1.14777	−	1.73873i	0.0393683	−	0.0596379i
$851$	14.7557	+	14.7557i	0.505821	+	0.505821i
$852$	−8.72377	+	45.0898i	−0.298871	+	1.54475i
$853$	−16.4082	+	16.4082i	−0.561806	+	0.561806i	−0.929820	−	0.368014i	$-0.880038\pi$
$853$	−16.4082	+	16.4082i	−0.561806	+	0.561806i	0.368014	+	0.929820i	$0.380038\pi$
$854$	2.50930	+	43.9671i	0.0858664	+	1.50452i
$855$	−4.33586	+	1.73587i	−0.148283	+	0.0593657i
$856$	−18.0101	−	25.9994i	−0.615573	−	0.888642i
$857$			34.7603i			1.18739i	0.804691	+	0.593694i	$0.202331\pi$
$857$			34.7603i			1.18739i	−0.804691	+	0.593694i	$0.797669\pi$
$858$	0.321982	+	0.778112i	0.0109923	+	0.0265643i
$859$	−15.3523	+	15.3523i	−0.523813	+	0.523813i	−0.918721	−	0.394908i	$-0.870776\pi$
$859$	−15.3523	+	15.3523i	−0.523813	+	0.523813i	0.394908	+	0.918721i	$0.370776\pi$
$860$	−39.2707	+	16.7832i	−1.33912	+	0.572302i
$861$	−15.8501	+	17.3615i	−0.540170	+	0.591678i
$862$	0.831925	−	1.26026i	0.0283355	−	0.0429245i
$863$		−	2.02419i		−	0.0689044i	−0.999406	−	0.0344522i	$-0.989031\pi$
$863$		−	2.02419i		−	0.0689044i	0.999406	−	0.0344522i	$-0.0109686\pi$
$864$	−0.297357	−	29.3924i	−0.0101163	−	0.999949i
$865$	47.5965			1.61833
$866$	15.8274	−	23.9764i	0.537836	−	0.814751i
$867$	−22.5757	−	15.2795i	−0.766710	−	0.518918i
$868$	35.8139	−	9.48700i	1.21560	−	0.322010i
$869$	1.10082	−	1.10082i	0.0373426	−	0.0373426i
$870$	−50.2074	+	20.7757i	−1.70219	+	0.704364i
$871$	−16.4022			−0.555767
$872$	−8.63275	−	12.4622i	−0.292342	−	0.422025i
$873$	25.6915	−	10.2857i	0.869526	−	0.348118i
$874$	−0.938237	−	4.58281i	−0.0317363	−	0.155016i
$875$	−19.6570	+	14.6499i	−0.664529	+	0.495255i
$876$	−0.727867	+	3.76207i	−0.0245924	+	0.127108i
$877$	−30.6182	+	30.6182i	−1.03390	+	1.03390i	−0.0344969	+	0.999405i	$0.510983\pi$
$877$	−30.6182	+	30.6182i	−1.03390	+	1.03390i	−0.999405	+	0.0344969i	$0.989017\pi$
$878$	−41.1821	−	27.1853i	−1.38983	−	0.917458i
$879$	−2.81236	−	14.5914i	−0.0948584	−	0.492157i
$880$	−0.727964	+	0.761267i	−0.0245397	+	0.0256623i
$881$	−20.1872			−0.680123			−0.340062	−	0.940403i	$-0.610448\pi$
$881$	−20.1872			−0.680123			−0.340062	+	0.940403i	$0.610448\pi$
$882$	−14.0425	+	26.1688i	−0.472835	+	0.881151i
$883$	−23.9564	+	23.9564i	−0.806197	+	0.806197i	−0.984056	−	0.177859i	$-0.943083\pi$
$883$	−23.9564	+	23.9564i	−0.806197	+	0.806197i	0.177859	+	0.984056i	$0.443083\pi$
$884$	−2.74302	+	6.83746i	−0.0922579	+	0.229969i
$885$	9.01041	−	13.3130i	0.302882	−	0.447513i
$886$	3.02417	−	0.619137i	0.101599	−	0.0208003i
$887$			46.3486i			1.55623i	0.628119	+	0.778117i	$0.283825\pi$
$887$			46.3486i			1.55623i	−0.628119	+	0.778117i	$0.716175\pi$
$888$	−19.1507	+	0.207316i	−0.642654	+	0.00695707i
$889$	44.5092	+	6.49622i	1.49279	+	0.217876i
$890$	25.3081	−	5.18133i	0.848331	−	0.173679i
$891$	0.0224266	−	0.943061i	0.000751319	−	0.0315937i
$892$	−0.862844	+	0.368756i	−0.0288902	+	0.0123469i
$893$	4.24147	+	4.24147i	0.141935	+	0.141935i
$894$	−19.5019	−	8.08605i	−0.652242	−	0.270438i
$895$			16.8800i			0.564235i
$896$	−13.9087	−	26.5056i	−0.464657	−	0.885491i
$897$	−5.73921	−	29.7769i	−0.191627	−	0.994222i
$898$	7.06397	−	10.7010i	0.235728	−	0.357096i
$899$	−43.7141	+	43.7141i	−1.45795	+	1.45795i
$900$	−5.56139	−	5.56928i	−0.185380	−	0.185643i
$901$	−7.45847	+	7.45847i	−0.248478	+	0.248478i
$902$	−0.152516	−	0.744961i	−0.00507822	−	0.0248045i
$903$	−1.77067	−	38.9091i	−0.0589242	−	1.29481i
$904$	−44.2662	−	8.03591i	−1.47227	−	0.267270i
$905$	26.2690			0.873210
$906$	−16.4343	+	6.80050i	−0.545994	+	0.225932i
$907$	21.8696	+	21.8696i	0.726167	+	0.726167i	0.969854	−	0.243687i	$-0.0783569\pi$
$907$	21.8696	+	21.8696i	0.726167	+	0.726167i	−0.243687	+	0.969854i	$0.578357\pi$
$908$	25.2489	+	10.1293i	0.837915	+	0.336151i
$909$	10.1836	−	23.7818i	0.337770	−	0.788793i
$910$	−20.5241	+	23.0086i	−0.680367	+	0.762727i
$911$		−	25.9735i		−	0.860539i	−0.902700	−	0.430270i	$-0.858418\pi$
$911$		−	25.9735i		−	0.860539i	0.902700	−	0.430270i	$-0.141582\pi$
$912$	3.60833	+	2.32626i	0.119484	+	0.0770301i
$913$		−	0.966033i		−	0.0319710i
$914$	−18.9847	+	28.7593i	−0.627958	+	0.951273i
$915$	28.7067	−	42.4147i	0.949015	−	1.40219i
$916$	−30.1140	−	12.0810i	−0.994996	−	0.399168i
$917$	27.0958	−	20.1938i	0.894783	−	0.666858i
$918$	5.90659	−	5.76371i	0.194947	−	0.190231i
$919$			14.2479i			0.469995i	0.971996	+	0.234997i	$0.0755082\pi$
$919$			14.2479i			0.469995i	−0.971996	+	0.234997i	$0.924492\pi$
$920$	31.1806	−	21.5991i	1.02799	−	0.712103i
$921$	5.51114	+	28.5936i	0.181598	+	0.942191i
$922$	39.4658	−	8.07983i	1.29974	−	0.266095i
$923$	−30.7482	−	30.7482i	−1.01209	−	1.01209i
$924$	−0.417287	−	0.865273i	−0.0137277	−	0.0284654i
$925$	−3.62613	+	3.62613i	−0.119227	+	0.119227i
$926$	−28.7459	−	18.9758i	−0.944649	−	0.623585i
$927$	−8.61689	−	21.5232i	−0.283016	−	0.706915i
$928$	42.2890	+	26.5779i	1.38820	+	0.872462i
$929$	11.9301			0.391414			0.195707	−	0.980662i	$-0.437300\pi$
$929$	11.9301			0.391414			0.195707	+	0.980662i	$0.437300\pi$
$930$	−39.8017	−	16.5029i	−1.30515	−	0.541152i
$931$	−2.06260	−	3.81591i	−0.0675990	−	0.125062i
$932$	2.79955	+	6.55060i	0.0917022	+	0.214572i
$933$	23.7356	−	35.0697i	0.777068	−	1.14813i
$934$	44.2890	−	9.06728i	1.44918	−	0.296691i
$935$	−0.295732			−0.00967147
$936$	23.2161	+	15.3491i	0.758841	+	0.501701i
$937$	−14.8621			−0.485524			−0.242762	−	0.970086i	$-0.578053\pi$
$937$	−14.8621			−0.485524			−0.242762	+	0.970086i	$0.578053\pi$
$938$	18.6807	−	1.06615i	0.609945	−	0.0348109i
$939$	34.4506	+	23.3165i	1.12425	+	0.760906i
$940$	−18.1095	+	45.1410i	−0.590666	+	1.47234i
$941$	−15.2750	+	15.2750i	−0.497949	+	0.497949i	−0.910799	−	0.412850i	$-0.864533\pi$
$941$	−15.2750	+	15.2750i	−0.497949	+	0.497949i	0.412850	+	0.910799i	$0.364533\pi$
$942$	−3.02043	+	7.28466i	−0.0984109	+	0.237347i
$943$			27.3834i			0.891725i
$944$	−14.7735	+	0.330373i	−0.480835	+	0.0107527i
$945$	31.4477	−	14.2815i	1.02300	−	0.464578i
$946$	1.05144	+	0.694080i	0.0341852	+	0.0225665i
$947$	4.36999	+	4.36999i	0.142006	+	0.142006i	0.774536	−	0.632530i	$-0.217984\pi$
$947$	4.36999	+	4.36999i	0.142006	+	0.142006i	−0.632530	+	0.774536i	$0.717984\pi$
$948$	9.77341	−	50.5150i	0.317426	−	1.64065i
$949$	−2.56548	−	2.56548i	−0.0832789	−	0.0832789i
$950$	1.12620	−	0.230566i	0.0365386	−	0.00748055i
$951$	−4.19509	−	21.7655i	−0.136035	−	0.705794i
$952$	2.67963	−	7.96557i	0.0868473	−	0.258166i
$953$	−13.2376			−0.428806			−0.214403	−	0.976745i	$-0.568781\pi$
$953$	−13.2376			−0.428806			−0.214403	+	0.976745i	$0.568781\pi$
$954$	21.9288	+	33.2705i	0.709971	+	1.07717i
$955$	−13.0153	+	13.0153i	−0.421167	+	0.421167i
$956$	14.5800	−	6.23109i	0.471551	−	0.201528i
$957$	1.32748	+	0.898455i	0.0429114	+	0.0290429i
$958$	−18.3106	−	12.0873i	−0.591589	−	0.390522i
$959$	3.54710	+	0.517708i	0.114542	+	0.0167177i
$960$	−5.84682	+	34.3172i	−0.188705	+	1.10758i
$961$	−18.0228			−0.581382
$962$	9.99010	−	15.1337i	0.322094	−	0.487930i
$963$	−30.8382	−	13.2053i	−0.993749	−	0.425534i
$964$	−35.8786	+	15.3335i	−1.15557	+	0.493860i
$965$	11.7984	+	11.7984i	0.379803	+	0.379803i
$966$	8.47197	+	33.5403i	0.272581	+	1.07914i
$967$		−	21.4429i		−	0.689558i	−0.938684	−	0.344779i	$-0.887954\pi$
$967$		−	21.4429i		−	0.689558i	0.938684	−	0.344779i	$-0.112046\pi$
$968$	−30.5818	−	5.55170i	−0.982936	−	0.178438i
$969$	0.228127	+	1.18359i	0.00732848	+	0.0380225i
$970$	−32.1089	+	6.57364i	−1.03095	+	0.211067i
$971$	12.0600	+	12.0600i	0.387022	+	0.387022i	0.873624	−	0.486602i	$-0.161764\pi$
$971$	12.0600	+	12.0600i	0.387022	+	0.387022i	−0.486602	+	0.873624i	$0.661764\pi$
$972$	−16.8374	−	26.2393i	−0.540060	−	0.841627i
$973$	23.8084	−	17.7437i	0.763261	−	0.568838i
$974$	9.35761	−	14.1756i	0.299837	−	0.454214i
$975$	7.31749	−	1.41038i	0.234347	−	0.0451682i
$976$	−47.0675	+	1.05255i	−1.50659	+	0.0336914i
$977$		−	8.13680i		−	0.260319i	−0.991493	−	0.130160i	$-0.958451\pi$
$977$		−	8.13680i		−	0.260319i	0.991493	−	0.130160i	$-0.0415490\pi$
$978$	−11.4512	−	4.74800i	−0.366169	−	0.151824i
$979$	−0.538879	−	0.538879i	−0.0172226	−	0.0172226i
$980$	21.8796	−	27.5389i	0.698918	−	0.879697i
$981$	−14.7816	−	6.32965i	−0.471941	−	0.202090i
$982$	3.60565	−	0.738185i	0.115061	−	0.0235564i
$983$		−	31.9183i		−	1.01804i	−0.860756	−	0.509018i	$-0.830009\pi$
$983$		−	31.9183i		−	1.01804i	0.860756	−	0.509018i	$-0.169991\pi$
$984$	−17.9620	−	17.5773i	−0.572609	−	0.560344i
$985$	−0.941754			−0.0300068
$986$	2.81268	+	13.7385i	0.0895740	+	0.437523i
$987$	−32.7600	−	29.9081i	−1.04276	−	0.951985i
$988$	−3.73792	+	1.59748i	−0.118919	+	0.0508227i
$989$	−32.0810	−	32.0810i	−1.02012	−	1.02012i
$990$	−0.224852	+	1.09434i	−0.00714627	+	0.0347804i
$991$	45.0234			1.43022			0.715108	−	0.699014i	$-0.246377\pi$
$991$	45.0234			1.43022			0.715108	+	0.699014i	$0.246377\pi$
$992$	8.80952	+	38.6151i	0.279702	+	1.22603i
$993$	6.51055	+	33.7789i	0.206606	+	1.07194i
$994$	37.0182	+	33.0209i	1.17415	+	1.04736i
$995$	−10.2574	−	10.2574i	−0.325181	−	0.325181i
$996$	−17.8766	−	26.4534i	−0.566442	−	0.838207i
$997$	42.7837	−	42.7837i	1.35497	−	1.35497i	0.474970	−	0.880002i	$-0.342459\pi$
$997$	42.7837	−	42.7837i	1.35497	−	1.35497i	0.880002	−	0.474970i	$-0.157541\pi$
$998$	−20.8143	+	4.26130i	−0.658864	+	0.134889i
$999$	−17.0886	+	10.9826i	−0.540661	+	0.347475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.y.a.293.50	yes	120
3.2	odd	2	inner	336.2.y.a.293.12	yes	120
7.6	odd	2	inner	336.2.y.a.293.49	yes	120
16.13	even	4	inner	336.2.y.a.125.11	✓	120
21.20	even	2	inner	336.2.y.a.293.11	yes	120
48.29	odd	4	inner	336.2.y.a.125.49	yes	120
112.13	odd	4	inner	336.2.y.a.125.12	yes	120
336.125	even	4	inner	336.2.y.a.125.50	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.y.a.125.11	✓	120	16.13	even	4	inner
336.2.y.a.125.12	yes	120	112.13	odd	4	inner
336.2.y.a.125.49	yes	120	48.29	odd	4	inner
336.2.y.a.125.50	yes	120	336.125	even	4	inner
336.2.y.a.293.11	yes	120	21.20	even	2	inner
336.2.y.a.293.12	yes	120	3.2	odd	2	inner
336.2.y.a.293.49	yes	120	7.6	odd	2	inner
336.2.y.a.293.50	yes	120	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18025 + 0.779110i) q^{2} +(1.43440 + 0.970819i) q^{3} +(0.785975 + 1.83909i) q^{4} +(-1.77648 - 1.77648i) q^{5} +(0.936577 + 2.26337i) q^{6} +(2.61801 + 0.382105i) q^{7} +(-0.505204 + 2.78294i) q^{8} +(1.11502 + 2.78509i) q^{9} +O(q^{10})\)	\(q+(1.18025 + 0.779110i) q^{2} +(1.43440 + 0.970819i) q^{3} +(0.785975 + 1.83909i) q^{4} +(-1.77648 - 1.77648i) q^{5} +(0.936577 + 2.26337i) q^{6} +(2.61801 + 0.382105i) q^{7} +(-0.505204 + 2.78294i) q^{8} +(1.11502 + 2.78509i) q^{9} +(-0.712616 - 3.48076i) q^{10} +(-0.0741148 + 0.0741148i) q^{11} +(-0.658016 + 3.40103i) q^{12} +(-2.31927 - 2.31927i) q^{13} +(2.79221 + 2.49070i) q^{14} +(-0.823546 - 4.27283i) q^{15} +(-2.76449 + 2.89096i) q^{16} -1.12306 q^{17} +(-0.853890 + 4.15582i) q^{18} +(-0.438173 - 0.438173i) q^{19} +(1.87083 - 4.66337i) q^{20} +(3.38433 + 3.08971i) q^{21} +(-0.145218 + 0.0297304i) q^{22} +5.33792 q^{23} +(-3.42640 + 3.50140i) q^{24} +1.31176i q^{25} +(-0.930352 - 4.54429i) q^{26} +(-1.10443 + 5.07742i) q^{27} +(1.35497 + 5.11508i) q^{28} +(-6.24342 - 6.24342i) q^{29} +(2.35701 - 5.68463i) q^{30} -7.00163i q^{31} +(-5.51515 + 1.25821i) q^{32} +(-0.178263 + 0.0343584i) q^{33} +(-1.32549 - 0.874987i) q^{34} +(-3.97205 - 5.32965i) q^{35} +(-4.24565 + 4.23963i) q^{36} +(2.76432 + 2.76432i) q^{37} +(-0.175768 - 0.858537i) q^{38} +(-1.07518 - 5.57837i) q^{39} +(5.84133 - 4.04636i) q^{40} +5.12996i q^{41} +(1.58713 + 6.28339i) q^{42} +(-6.01001 - 6.01001i) q^{43} +(-0.194556 - 0.0780512i) q^{44} +(2.96685 - 6.92847i) q^{45} +(6.30008 + 4.15883i) q^{46} -9.67990 q^{47} +(-6.77198 + 1.46298i) q^{48} +(6.70799 + 2.00071i) q^{49} +(-1.02201 + 1.54821i) q^{50} +(-1.61092 - 1.09029i) q^{51} +(2.44246 - 6.08824i) q^{52} +(6.64120 - 6.64120i) q^{53} +(-5.25937 + 5.13215i) q^{54} +0.263327 q^{55} +(-2.38601 + 7.09274i) q^{56} +(-0.203129 - 1.05390i) q^{57} +(-2.50448 - 12.2331i) q^{58} +(2.61226 + 2.61226i) q^{59} +(7.21082 - 4.87291i) q^{60} +(8.32252 + 8.32252i) q^{61} +(5.45504 - 8.26367i) q^{62} +(1.85494 + 7.71746i) q^{63} +(-7.48954 - 2.81191i) q^{64} +8.24029i q^{65} +(-0.237163 - 0.0983347i) q^{66} +(3.53606 - 3.53606i) q^{67} +(-0.882697 - 2.06541i) q^{68} +(7.65673 + 5.18216i) q^{69} +(-0.535621 - 9.38498i) q^{70} +13.2577 q^{71} +(-8.31406 + 1.69600i) q^{72} +1.10615 q^{73} +(1.10888 + 5.41630i) q^{74} +(-1.27348 + 1.88159i) q^{75} +(0.461445 - 1.15023i) q^{76} +(-0.222353 + 0.165714i) q^{77} +(3.07719 - 7.42155i) q^{78} -14.8528 q^{79} +(10.0468 - 0.224672i) q^{80} +(-6.51346 + 6.21087i) q^{81} +(-3.99681 + 6.05464i) q^{82} +(-6.51714 + 6.51714i) q^{83} +(-3.02225 + 8.65252i) q^{84} +(1.99509 + 1.99509i) q^{85} +(-2.41085 - 11.7758i) q^{86} +(-2.89435 - 15.0168i) q^{87} +(-0.168814 - 0.243700i) q^{88} +7.27086i q^{89} +(8.89966 - 5.86582i) q^{90} +(-5.18569 - 6.95810i) q^{91} +(4.19548 + 9.81691i) q^{92} +(6.79732 - 10.0432i) q^{93} +(-11.4247 - 7.54171i) q^{94} +1.55681i q^{95} +(-9.13244 - 3.54944i) q^{96} -9.22466i q^{97} +(6.35833 + 7.58760i) q^{98} +(-0.289056 - 0.123777i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 8 q^{4}+O(q^{10}) \) 120 * q - 8 * q^4	\( 120 q - 8 q^{4} - 8 q^{15} + 8 q^{16} - 32 q^{18} - 8 q^{21} + 16 q^{22} - 16 q^{30} - 8 q^{36} - 8 q^{37} - 24 q^{42} - 8 q^{43} - 24 q^{46} - 8 q^{49} - 56 q^{51} + 40 q^{58} - 96 q^{60} + 24 q^{63} - 56 q^{64} + 24 q^{67} - 80 q^{70} - 8 q^{72} + 64 q^{78} - 16 q^{79} - 8 q^{81} - 48 q^{84} - 48 q^{85} - 24 q^{88} - 8 q^{91} + 8 q^{93} - 40 q^{99}+O(q^{100}) \) 120 * q - 8 * q^4 - 8 * q^15 + 8 * q^16 - 32 * q^18 - 8 * q^21 + 16 * q^22 - 16 * q^30 - 8 * q^36 - 8 * q^37 - 24 * q^42 - 8 * q^43 - 24 * q^46 - 8 * q^49 - 56 * q^51 + 40 * q^58 - 96 * q^60 + 24 * q^63 - 56 * q^64 + 24 * q^67 - 80 * q^70 - 8 * q^72 + 64 * q^78 - 16 * q^79 - 8 * q^81 - 48 * q^84 - 48 * q^85 - 24 * q^88 - 8 * q^91 + 8 * q^93 - 40 * q^99

Introduction

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