LMFDB - Embedded newform 483.2.j.a.229.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(229,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("483.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.j (of order $6$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.7
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.708878 + 1.22781i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.00501609 - 0.00868813i) q^{4} +(-1.44242 + 2.49834i) q^{5} -1.41776i q^{6} +(-0.0745936 - 2.64470i) q^{7} -2.82129 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.708878 + 1.22781i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.00501609 - 0.00868813i) q^{4} +(-1.44242 + 2.49834i) q^{5} -1.41776i q^{6} +(-0.0745936 - 2.64470i) q^{7} -2.82129 q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.04500 - 3.54204i) q^{10} +(-2.18197 + 1.25976i) q^{11} +(0.00868813 + 0.00501609i) q^{12} +2.09916i q^{13} +(3.30007 + 1.78318i) q^{14} -2.88484i q^{15} +(2.00998 - 3.48139i) q^{16} +(-3.05763 - 5.29598i) q^{17} +(0.708878 + 1.22781i) q^{18} +(1.41088 - 2.44372i) q^{19} +0.0289412 q^{20} +(1.38695 + 2.25308i) q^{21} -3.57208i q^{22} +(-3.33540 + 3.44603i) q^{23} +(2.44331 - 1.41064i) q^{24} +(-1.66114 - 2.87719i) q^{25} +(-2.57737 - 1.48805i) q^{26} +1.00000i q^{27} +(-0.0226033 + 0.0139141i) q^{28} +8.79903 q^{29} +(3.54204 + 2.04500i) q^{30} +(-6.47547 + 3.73862i) q^{31} +(0.0283750 + 0.0491470i) q^{32} +(1.25976 - 2.18197i) q^{33} +8.66996 q^{34} +(6.71496 + 3.62840i) q^{35} -0.0100322 q^{36} +(0.375731 + 0.216929i) q^{37} +(2.00029 + 3.46460i) q^{38} +(-1.04958 - 1.81793i) q^{39} +(4.06948 - 7.04855i) q^{40} -7.73703i q^{41} +(-3.74954 + 0.105756i) q^{42} -5.68029i q^{43} +(0.0218900 + 0.0126382i) q^{44} +(1.44242 + 2.49834i) q^{45} +(-1.86669 - 6.53806i) q^{46} +(-4.09208 - 2.36256i) q^{47} +4.01996i q^{48} +(-6.98887 + 0.394555i) q^{49} +4.71020 q^{50} +(5.29598 + 3.05763i) q^{51} +(0.0182378 - 0.0105296i) q^{52} +(4.31887 - 2.49350i) q^{53} +(-1.22781 - 0.708878i) q^{54} -7.26843i q^{55} +(0.210450 + 7.46146i) q^{56} +2.82176i q^{57} +(-6.23744 + 10.8036i) q^{58} +(-9.85730 + 5.69112i) q^{59} +(-0.0250638 + 0.0144706i) q^{60} +(2.33209 - 4.03929i) q^{61} -10.6009i q^{62} +(-2.32767 - 1.25775i) q^{63} +7.95947 q^{64} +(-5.24442 - 3.02787i) q^{65} +(1.78604 + 3.09351i) q^{66} +(-12.2054 + 7.04681i) q^{67} +(-0.0306748 + 0.0531302i) q^{68} +(1.16552 - 4.65205i) q^{69} +(-9.21509 + 5.67262i) q^{70} +7.71738 q^{71} +(-1.41064 + 2.44331i) q^{72} +(-1.18791 + 0.685840i) q^{73} +(-0.532695 + 0.307552i) q^{74} +(2.87719 + 1.66114i) q^{75} -0.0283085 q^{76} +(3.49446 + 5.67670i) q^{77} +2.97610 q^{78} +(-3.43697 - 1.98433i) q^{79} +(5.79847 + 10.0432i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(9.49963 + 5.48461i) q^{82} -9.38040 q^{83} +(0.0126180 - 0.0233517i) q^{84} +17.6416 q^{85} +(6.97434 + 4.02664i) q^{86} +(-7.62019 + 4.39952i) q^{87} +(6.15598 - 3.55416i) q^{88} +(-8.69055 + 15.0525i) q^{89} -4.09000 q^{90} +(5.55165 - 0.156584i) q^{91} +(0.0466702 + 0.0116928i) q^{92} +(3.73862 - 6.47547i) q^{93} +(5.80157 - 3.34954i) q^{94} +(4.07017 + 7.04974i) q^{95} +(-0.0491470 - 0.0283750i) q^{96} -13.3432 q^{97} +(4.46982 - 8.86072i) q^{98} +2.51953i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9}+O(q^{10}) $ 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9	$ 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50} - 108 q^{52} - 24 q^{58} + 36 q^{59} + 168 q^{64} - 40 q^{70} - 16 q^{71} - 12 q^{72} + 48 q^{73} - 48 q^{75} - 32 q^{78} - 32 q^{81} - 24 q^{82} + 88 q^{85} + 36 q^{87} + 152 q^{92} + 24 q^{93} - 108 q^{94} - 44 q^{95} + 60 q^{96} + 112 q^{98}+O(q^{100}) $ 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.708878	+	1.22781i	−0.501252	+	0.868195i	0.498746	+	0.866748i	$0.333794\pi$
$2$	−0.708878	+	1.22781i	−0.501252	+	0.868195i	−0.999999	+	0.00144681i	$0.999539\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.00501609	−	0.00868813i	−0.00250805	−	0.00434406i
$5$	−1.44242	+	2.49834i	−0.645069	+	1.11729i	0.339216	+	0.940708i	$0.389838\pi$
$5$	−1.44242	+	2.49834i	−0.645069	+	1.11729i	−0.984285	+	0.176584i	$0.943495\pi$
$6$		−	1.41776i		−	0.578796i
$7$	−0.0745936	−	2.64470i	−0.0281937	−	0.999602i
$7$	−0.0745936	−	2.64470i	−0.0281937	−	0.999602i
$8$	−2.82129			−0.997476
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.04500	−	3.54204i	−0.646685	−	1.12009i
$11$	−2.18197	+	1.25976i	−0.657890	+	0.379833i	−0.791473	−	0.611205i	$-0.790685\pi$
$11$	−2.18197	+	1.25976i	−0.657890	+	0.379833i	0.133582	+	0.991038i	$0.457352\pi$
$12$	0.00868813	+	0.00501609i	0.00250805	+	0.00144802i
$13$			2.09916i			0.582202i	0.956692	+	0.291101i	$0.0940216\pi$
$13$			2.09916i			0.582202i	−0.956692	+	0.291101i	$0.905978\pi$
$14$	3.30007	+	1.78318i	0.881982	+	0.476576i
$15$		−	2.88484i		−	0.744862i
$16$	2.00998	−	3.48139i	0.502495	−	0.870348i
$17$	−3.05763	−	5.29598i	−0.741585	−	1.28446i	−0.951773	−	0.306802i	$-0.900741\pi$
$17$	−3.05763	−	5.29598i	−0.741585	−	1.28446i	0.210188	−	0.977661i	$-0.432592\pi$
$18$	0.708878	+	1.22781i	0.167084	+	0.289398i
$19$	1.41088	−	2.44372i	0.323679	−	0.560628i	−0.657565	−	0.753397i	$-0.728414\pi$
$19$	1.41088	−	2.44372i	0.323679	−	0.560628i	0.981244	+	0.192770i	$0.0617470\pi$
$20$	0.0289412			0.00647146
$21$	1.38695	+	2.25308i	0.302657	+	0.491662i
$22$		−	3.57208i		−	0.761569i
$23$	−3.33540	+	3.44603i	−0.695479	+	0.718547i
$23$	−3.33540	+	3.44603i	−0.695479	+	0.718547i
$24$	2.44331	−	1.41064i	0.498738	−	0.287947i
$25$	−1.66114	−	2.87719i	−0.332229	−	0.575437i
$26$	−2.57737	−	1.48805i	−0.505465	−	0.291830i
$27$			1.00000i			0.192450i
$28$	−0.0226033	+	0.0139141i	−0.00427163	+	0.00262953i
$29$	8.79903			1.63394			0.816970	−	0.576680i	$-0.195652\pi$
$29$	8.79903			1.63394			0.816970	+	0.576680i	$0.195652\pi$
$30$	3.54204	+	2.04500i	0.646685	+	0.373364i
$31$	−6.47547	+	3.73862i	−1.16303	+	0.671475i	−0.952028	−	0.306010i	$-0.901006\pi$
$31$	−6.47547	+	3.73862i	−1.16303	+	0.671475i	−0.211001	+	0.977486i	$0.567672\pi$
$32$	0.0283750	+	0.0491470i	0.00501605	+	0.00868805i
$33$	1.25976	−	2.18197i	0.219297	−	0.379833i
$34$	8.66996			1.48689
$35$	6.71496	+	3.62840i	1.13504	+	0.613312i
$36$	−0.0100322			−0.00167203
$37$	0.375731	+	0.216929i	0.0617699	+	0.0356628i	0.530567	−	0.847643i	$-0.321979\pi$
$37$	0.375731	+	0.216929i	0.0617699	+	0.0356628i	−0.468797	+	0.883306i	$0.655312\pi$
$38$	2.00029	+	3.46460i	0.324489	+	0.562032i
$39$	−1.04958	−	1.81793i	−0.168067	−	0.291101i
$40$	4.06948	−	7.04855i	0.643441	−	1.11447i
$41$		−	7.73703i		−	1.20832i	−0.796862	−	0.604161i	$-0.793508\pi$
$41$		−	7.73703i		−	1.20832i	0.796862	−	0.604161i	$-0.206492\pi$
$42$	−3.74954	+	0.105756i	−0.578566	+	0.0163184i
$43$		−	5.68029i		−	0.866237i	−0.901337	−	0.433118i	$-0.857413\pi$
$43$		−	5.68029i		−	0.866237i	0.901337	−	0.433118i	$-0.142587\pi$
$44$	0.0218900	+	0.0126382i	0.00330004	+	0.00190528i
$45$	1.44242	+	2.49834i	0.215023	+	0.372431i
$46$	−1.86669	−	6.53806i	−0.275228	−	0.963984i
$47$	−4.09208	−	2.36256i	−0.596891	−	0.344615i	0.170927	−	0.985284i	$-0.445324\pi$
$47$	−4.09208	−	2.36256i	−0.596891	−	0.344615i	−0.767817	+	0.640669i	$0.778657\pi$
$48$			4.01996i			0.580232i
$49$	−6.98887	+	0.394555i	−0.998410	+	0.0563651i
$50$	4.71020			0.666122
$51$	5.29598	+	3.05763i	0.741585	+	0.428154i
$52$	0.0182378	−	0.0105296i	0.00252912	−	0.00146019i
$53$	4.31887	−	2.49350i	0.593242	−	0.342509i	−0.173136	−	0.984898i	$-0.555390\pi$
$53$	4.31887	−	2.49350i	0.593242	−	0.342509i	0.766379	+	0.642389i	$0.222057\pi$
$54$	−1.22781	−	0.708878i	−0.167084	−	0.0964661i
$55$		−	7.26843i		−	0.980075i
$56$	0.210450	+	7.46146i	0.0281226	+	0.997080i
$57$			2.82176i			0.373752i
$58$	−6.23744	+	10.8036i	−0.819016	+	1.41858i
$59$	−9.85730	+	5.69112i	−1.28331	+	0.740920i	−0.977452	−	0.211156i	$-0.932277\pi$
$59$	−9.85730	+	5.69112i	−1.28331	+	0.740920i	−0.305859	+	0.952077i	$0.598944\pi$
$60$	−0.0250638	+	0.0144706i	−0.00323573	+	0.00186815i
$61$	2.33209	−	4.03929i	0.298593	−	0.517178i	−0.677221	−	0.735779i	$-0.736816\pi$
$61$	2.33209	−	4.03929i	0.298593	−	0.517178i	0.975814	+	0.218601i	$0.0701494\pi$
$62$		−	10.6009i		−	1.34631i
$63$	−2.32767	−	1.25775i	−0.293259	−	0.158462i
$64$	7.95947			0.994934
$65$	−5.24442	−	3.02787i	−0.650490	−	0.375561i
$66$	1.78604	+	3.09351i	0.219846	+	0.380785i
$67$	−12.2054	+	7.04681i	−1.49113	+	0.860905i	−0.999948	−	0.0101508i	$-0.996769\pi$
$67$	−12.2054	+	7.04681i	−1.49113	+	0.860905i	−0.491183	+	0.871056i	$0.663435\pi$
$68$	−0.0306748	+	0.0531302i	−0.00371986	+	0.00644299i
$69$	1.16552	−	4.65205i	0.140313	−	0.560041i
$70$	−9.21509	+	5.67262i	−1.10141	+	0.678008i
$71$	7.71738			0.915884			0.457942	−	0.888982i	$-0.348587\pi$
$71$	7.71738			0.915884			0.457942	+	0.888982i	$0.348587\pi$
$72$	−1.41064	+	2.44331i	−0.166246	+	0.287947i
$73$	−1.18791	+	0.685840i	−0.139034	+	0.0802715i	−0.567904	−	0.823095i	$-0.692245\pi$
$73$	−1.18791	+	0.685840i	−0.139034	+	0.0802715i	0.428869	+	0.903367i	$0.358912\pi$
$74$	−0.532695	+	0.307552i	−0.0619246	+	0.0357522i
$75$	2.87719	+	1.66114i	0.332229	+	0.191812i
$76$	−0.0283085			−0.00324720
$77$	3.49446	+	5.67670i	0.398230	+	0.646920i
$78$	2.97610			0.336977
$79$	−3.43697	−	1.98433i	−0.386689	−	0.223255i	0.294035	−	0.955795i	$-0.405002\pi$
$79$	−3.43697	−	1.98433i	−0.386689	−	0.223255i	−0.680725	+	0.732539i	$0.738335\pi$
$80$	5.79847	+	10.0432i	0.648289	+	1.12287i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	9.49963	+	5.48461i	1.04906	+	0.605674i
$83$	−9.38040			−1.02963			−0.514816	−	0.857300i	$-0.672140\pi$
$83$	−9.38040			−1.02963			−0.514816	+	0.857300i	$0.672140\pi$
$84$	0.0126180	−	0.0233517i	0.00137673	−	0.00254788i
$85$	17.6416			1.91350
$86$	6.97434	+	4.02664i	0.752062	+	0.434203i
$87$	−7.62019	+	4.39952i	−0.816970	+	0.471678i
$88$	6.15598	−	3.55416i	0.656230	−	0.378874i
$89$	−8.69055	+	15.0525i	−0.921196	+	1.59556i	−0.123629	+	0.992328i	$0.539453\pi$
$89$	−8.69055	+	15.0525i	−0.921196	+	1.59556i	−0.797567	+	0.603230i	$0.793880\pi$
$90$	−4.09000			−0.431123
$91$	5.55165	−	0.156584i	0.581971	−	0.0164145i
$92$	0.0466702	+	0.0116928i	0.00486571	+	0.00121905i
$93$	3.73862	−	6.47547i	0.387676	−	0.671475i
$94$	5.80157	−	3.34954i	0.598386	−	0.345478i
$95$	4.07017	+	7.04974i	0.417590	+	0.723288i
$96$	−0.0491470	−	0.0283750i	−0.00501605	−	0.00289602i
$97$	−13.3432			−1.35480			−0.677400	−	0.735615i	$-0.736893\pi$
$97$	−13.3432			−1.35480			−0.677400	+	0.735615i	$0.736893\pi$
$98$	4.46982	−	8.86072i	0.451520	−	0.895068i
$99$			2.51953i			0.253222i
$100$	−0.0166649	+	0.0288645i	−0.00166649	+	0.00288645i
$101$	0.530141	−	0.306077i	0.0527510	−	0.0304558i	−0.473393	−	0.880852i	$-0.656971\pi$
$101$	0.530141	−	0.306077i	0.0527510	−	0.0304558i	0.526144	+	0.850396i	$0.323637\pi$
$102$	−7.50840	+	4.33498i	−0.743443	+	0.429227i
$103$	−0.399991	+	0.692805i	−0.0394123	+	0.0682641i	−0.885059	−	0.465479i	$-0.845882\pi$
$103$	−0.399991	+	0.692805i	−0.0394123	+	0.0682641i	0.845646	+	0.533744i	$0.179215\pi$
$104$		−	5.92234i		−	0.580733i
$105$	−7.62953	+	0.215190i	−0.744566	+	0.0210004i
$106$			7.07035i			0.686733i
$107$	−4.58225	−	2.64556i	−0.442983	−	0.255756i	0.261879	−	0.965101i	$-0.415658\pi$
$107$	−4.58225	−	2.64556i	−0.442983	−	0.255756i	−0.704862	+	0.709344i	$0.748991\pi$
$108$	0.00868813	−	0.00501609i	0.000836016	−	0.000482674i
$109$	−8.44858	+	4.87779i	−0.809227	+	0.467207i	−0.846687	−	0.532091i	$-0.821406\pi$
$109$	−8.44858	+	4.87779i	−0.809227	+	0.467207i	0.0374605	+	0.999298i	$0.488073\pi$
$110$	8.92427	+	5.15243i	0.850896	+	0.491265i
$111$	−0.433857			−0.0411799
$112$	−9.35716	−	5.05611i	−0.884169	−	0.477757i
$113$			13.6647i			1.28547i	0.766088	+	0.642735i	$0.222200\pi$
$113$			13.6647i			1.28547i	−0.766088	+	0.642735i	$0.777800\pi$
$114$	−3.46460	−	2.00029i	−0.324489	−	0.187344i
$115$	−3.79832	−	13.3036i	−0.354195	−	1.24057i
$116$	−0.0441368	−	0.0764472i	−0.00409800	−	0.00709794i
$117$	1.81793	+	1.04958i	0.168067	+	0.0970337i
$118$		−	16.1372i		−	1.48555i
$119$	−13.7782	+	8.48157i	−1.26304	+	0.777504i
$120$			8.13896i			0.742982i
$121$	−2.32599	+	4.02873i	−0.211454	+	0.366248i
$122$	3.30633	+	5.72673i	0.299341	+	0.518474i
$123$	3.86852	+	6.70047i	0.348812	+	0.604161i
$124$	0.0649632	+	0.0375065i	0.00583387	+	0.00336818i
$125$	−4.83992			−0.432896
$126$	3.19432	−	1.96636i	0.284572	−	0.175177i
$127$	−8.82555			−0.783141			−0.391570	−	0.920148i	$-0.628068\pi$
$127$	−8.82555			−0.783141			−0.391570	+	0.920148i	$0.628068\pi$
$128$	−5.69904	+	9.87103i	−0.503729	+	0.872484i
$129$	2.84015	+	4.91928i	0.250061	+	0.433118i
$130$	7.43531	−	4.29278i	0.652120	−	0.376501i
$131$	−5.63155	−	3.25138i	−0.492031	−	0.284074i	0.233386	−	0.972384i	$-0.425020\pi$
$131$	−5.63155	−	3.25138i	−0.492031	−	0.284074i	−0.725417	+	0.688310i	$0.758353\pi$
$132$	−0.0252764			−0.00220003
$133$	−6.56815	−	3.54907i	−0.569531	−	0.307744i
$134$		−	19.9813i		−	1.72612i
$135$	−2.49834	−	1.44242i	−0.215023	−	0.124144i
$136$	8.62647	+	14.9415i	0.739714	+	1.28122i
$137$	14.1113	−	8.14716i	1.20561	−	0.696059i	0.243813	−	0.969822i	$-0.421602\pi$
$137$	14.1113	−	8.14716i	1.20561	−	0.696059i	0.961797	+	0.273763i	$0.0882684\pi$
$138$	4.88563	+	4.72878i	0.415892	+	0.402541i
$139$			16.0227i			1.35903i	0.733662	+	0.679515i	$0.237810\pi$
$139$			16.0227i			1.35903i	−0.733662	+	0.679515i	$0.762190\pi$
$140$	−0.00215883	−	0.0765409i	−0.000182455	−	0.00646888i
$141$	4.72512			0.397927
$142$	−5.47068	+	9.47549i	−0.459089	+	0.795166i
$143$	−2.64445	−	4.58031i	−0.221140	−	0.383025i
$144$	−2.00998	−	3.48139i	−0.167498	−	0.290116i
$145$	−12.6919	+	21.9830i	−1.05400	+	1.82559i
$146$		−	1.94471i		−	0.160945i
$147$	5.85526	−	3.83613i	0.482934	−	0.316399i
$148$		−	0.00435254i		−	0.000357776i
$149$	4.37058	+	2.52336i	0.358052	+	0.206721i	0.668226	−	0.743958i	$-0.267054\pi$
$149$	4.37058	+	2.52336i	0.358052	+	0.206721i	−0.310174	+	0.950680i	$0.600387\pi$
$150$	−4.07915	+	2.35510i	−0.333061	+	0.192293i
$151$	−1.70315	−	2.94994i	−0.138600	−	0.240063i	0.788367	−	0.615206i	$-0.210927\pi$
$151$	−1.70315	−	2.94994i	−0.138600	−	0.240063i	−0.926967	+	0.375143i	$0.877594\pi$
$152$	−3.98051	+	6.89444i	−0.322862	+	0.559213i
$153$	−6.11527			−0.494390
$154$	−9.44707	+	0.266454i	−0.761266	+	0.0214715i
$155$		−	21.5706i		−	1.73259i
$156$	−0.0105296	+	0.0182378i	−0.000843041	+	0.00146019i
$157$	3.91373	+	6.77879i	0.312350	+	0.541006i	0.978871	−	0.204481i	$-0.0655505\pi$
$157$	3.91373	+	6.77879i	0.312350	+	0.541006i	−0.666521	+	0.745487i	$0.732217\pi$
$158$	4.87278	−	2.81330i	0.387658	−	0.223814i
$159$	−2.49350	+	4.31887i	−0.197747	+	0.342509i
$160$	−0.163715			−0.0129428
$161$	9.36251	+	8.56407i	0.737869	+	0.674944i
$162$	1.41776			0.111389
$163$	5.77328	−	9.99961i	0.452198	−	0.783230i	−0.546324	−	0.837574i	$-0.683973\pi$
$163$	5.77328	−	9.99961i	0.452198	−	0.783230i	0.998522	+	0.0543439i	$0.0173067\pi$
$164$	−0.0672204	+	0.0388097i	−0.00524903	+	0.00303053i
$165$	3.63421	+	6.29464i	0.282923	+	0.490037i
$166$	6.64956	−	11.5174i	0.516106	−	0.893922i
$167$		−	23.4571i		−	1.81516i	−0.419874	−	0.907582i	$-0.637926\pi$
$167$		−	23.4571i		−	1.81516i	0.419874	−	0.907582i	$-0.362074\pi$
$168$	−3.91299	−	6.35659i	−0.301893	−	0.490422i
$169$	8.59353			0.661041
$170$	−12.5057	+	21.6605i	−0.959144	+	1.66129i
$171$	−1.41088	−	2.44372i	−0.107893	−	0.186876i
$172$	−0.0493511	+	0.0284929i	−0.00376299	+	0.00217256i
$173$	−9.81044	−	5.66406i	−0.745874	−	0.430630i	0.0783272	−	0.996928i	$-0.475042\pi$
$173$	−9.81044	−	5.66406i	−0.745874	−	0.430630i	−0.824201	+	0.566297i	$0.808375\pi$
$174$		−	12.4749i		−	0.945719i
$175$	−7.48538	+	4.60785i	−0.565842	+	0.348321i
$176$			10.1284i			0.763458i
$177$	5.69112	−	9.85730i	0.427771	−	0.740920i
$178$	−12.3211	−	21.3407i	−0.923504	−	1.59956i
$179$	−8.15303	−	14.1215i	−0.609386	−	1.05549i	−0.991342	−	0.131307i	$-0.958083\pi$
$179$	−8.15303	−	14.1215i	−0.609386	−	1.05549i	0.381956	−	0.924180i	$-0.375251\pi$
$180$	0.0144706	−	0.0250638i	0.00107858	−	0.00186815i
$181$	−11.9758			−0.890157			−0.445078	−	0.895492i	$-0.646824\pi$
$181$	−11.9758			−0.890157			−0.445078	+	0.895492i	$0.646824\pi$
$182$	−3.74318	+	6.92738i	−0.277463	+	0.513492i
$183$			4.66417i			0.344785i
$184$	9.41012	−	9.72225i	0.693723	−	0.716733i
$185$	−1.08392	+	0.625804i	−0.0796917	+	0.0460100i
$186$	5.30045	+	9.18064i	0.388648	+	0.673157i
$187$	13.3434	+	7.70379i	0.975763	+	0.563357i
$188$			0.0474033i			0.00345724i
$189$	2.64470	−	0.0745936i	0.192374	−	0.00542589i
$190$	−11.5410			−0.837273
$191$	0.120570	+	0.0696114i	0.00872417	+	0.00503690i	0.504356	−	0.863496i	$-0.331730\pi$
$191$	0.120570	+	0.0696114i	0.00872417	+	0.00503690i	−0.495632	+	0.868533i	$0.665063\pi$
$192$	−6.89310	+	3.97973i	−0.497467	+	0.287213i
$193$	−2.51703	−	4.35962i	−0.181180	−	0.313812i	0.761103	−	0.648631i	$-0.224658\pi$
$193$	−2.51703	−	4.35962i	−0.181180	−	0.313812i	−0.942283	+	0.334819i	$0.891325\pi$
$194$	9.45873	−	16.3830i	0.679097	−	1.17623i
$195$	6.05573			0.433660
$196$	0.0384848	+	0.0587411i	0.00274891	+	0.00419579i
$197$	7.92744			0.564807			0.282403	−	0.959296i	$-0.408868\pi$
$197$	7.92744			0.564807			0.282403	+	0.959296i	$0.408868\pi$
$198$	−3.09351	−	1.78604i	−0.219846	−	0.126928i
$199$	7.33880	+	12.7112i	0.520234	+	0.901072i	0.999723	+	0.0235240i	$0.00748861\pi$
$199$	7.33880	+	12.7112i	0.520234	+	0.901072i	−0.479489	+	0.877548i	$0.659178\pi$
$200$	4.68657	+	8.11738i	0.331390	+	0.573985i
$201$	7.04681	−	12.2054i	0.497044	−	0.860905i
$202$			0.867885i			0.0610642i
$203$	−0.656352	−	23.2708i	−0.0460669	−	1.63329i
$204$		−	0.0613495i		−	0.00429533i
$205$	19.3298	+	11.1600i	1.35005	+	0.779451i
$206$	−0.567090	−	0.982228i	−0.0395110	−	0.0684351i
$207$	1.31665	+	4.61155i	0.0915135	+	0.320525i
$208$	7.30799	+	4.21927i	0.506718	+	0.292554i
$209$			7.10951i			0.491775i
$210$	5.14419	−	9.52018i	0.354983	−	0.656955i
$211$	22.9656			1.58101			0.790507	−	0.612453i	$-0.209817\pi$
$211$	22.9656			1.58101			0.790507	+	0.612453i	$0.209817\pi$
$212$	−0.0433277	−	0.0250153i	−0.00297576	−	0.00171806i
$213$	−6.68344	+	3.85869i	−0.457942	+	0.264393i
$214$	6.49651	−	3.75076i	0.444092	−	0.256397i
$215$	14.1913	+	8.19336i	0.967840	+	0.558783i
$216$		−	2.82129i		−	0.191964i
$217$	10.3705	+	16.8468i	0.703999	+	1.14364i
$218$		−	13.8310i		−	0.936755i
$219$	0.685840	−	1.18791i	0.0463448	−	0.0802715i
$220$	−0.0631491	+	0.0364591i	−0.00425751	+	0.00245807i
$221$	11.1171	−	6.41846i	0.747817	−	0.431752i
$222$	0.307552	−	0.532695i	0.0206415	−	0.0357522i
$223$			17.8119i			1.19277i	0.802697	+	0.596387i	$0.203398\pi$
$223$			17.8119i			1.19277i	−0.802697	+	0.596387i	$0.796602\pi$
$224$	0.127863	−	0.0787095i	0.00854317	−	0.00525900i
$225$	−3.32229			−0.221486
$226$	−16.7777	−	9.68663i	−1.11604	−	0.644345i
$227$	−1.92149	−	3.32812i	−0.127534	−	0.220895i	0.795187	−	0.606365i	$-0.207373\pi$
$227$	−1.92149	−	3.32812i	−0.127534	−	0.220895i	−0.922721	+	0.385470i	$0.874039\pi$
$228$	0.0245159	−	0.0141542i	0.00162360	−	0.000937387i
$229$	5.59104	−	9.68397i	0.369467	−	0.639935i	−0.620016	−	0.784589i	$-0.712874\pi$
$229$	5.59104	−	9.68397i	0.369467	−	0.639935i	0.989482	+	0.144655i	$0.0462071\pi$
$230$	19.0269	+	4.76699i	1.25459	+	0.314326i
$231$	−5.86464	−	3.16894i	−0.385865	−	0.208501i
$232$	−24.8246			−1.62982
$233$	0.734054	−	1.27142i	0.0480895	−	0.0832935i	−0.840979	−	0.541068i	$-0.818020\pi$
$233$	0.734054	−	1.27142i	0.0480895	−	0.0832935i	0.889068	+	0.457775i	$0.151353\pi$
$234$	−2.57737	+	1.48805i	−0.168488	+	0.0972767i
$235$	11.8050	−	6.81561i	0.770072	−	0.444601i
$236$	0.0988903	+	0.0570943i	0.00643721	+	0.00371653i
$237$	3.96867			0.257793
$238$	−0.646723	−	22.9294i	−0.0419209	−	1.48629i
$239$	6.69892			0.433317			0.216658	−	0.976247i	$-0.430484\pi$
$239$	6.69892			0.433317			0.216658	+	0.976247i	$0.430484\pi$
$240$	−10.0432	−	5.79847i	−0.648289	−	0.374290i
$241$	6.29844	+	10.9092i	0.405718	+	0.702724i	0.994405	−	0.105637i	$-0.0336882\pi$
$241$	6.29844	+	10.9092i	0.405718	+	0.702724i	−0.588687	+	0.808361i	$0.700355\pi$
$242$	−3.29769	−	5.71176i	−0.211983	−	0.367166i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−0.0467918			−0.00299554
$245$	9.09515	−	18.0297i	0.581068	−	1.15188i
$246$	−10.9692			−0.699372
$247$	5.12976	+	2.96167i	0.326399	+	0.188446i
$248$	18.2692	−	10.5477i	1.16009	−	0.669781i
$249$	8.12367	−	4.69020i	0.514816	−	0.297229i
$250$	3.43092	−	5.94252i	0.216990	−	0.375838i
$251$	26.6710			1.68346			0.841729	−	0.539901i	$-0.181538\pi$
$251$	26.6710			1.68346			0.841729	+	0.539901i	$0.181538\pi$
$252$	0.000748337		0.0265321i	4.71408e−5		0.00167137i
$253$	2.93657	−	11.7210i	0.184621	−	0.736891i
$254$	6.25624	−	10.8361i	0.392551	−	0.679919i
$255$	−15.2780	+	8.82078i	−0.956748	+	0.552379i
$256$	−0.120383	−	0.208510i	−0.00752395	−	0.0130319i
$257$	−13.8881	−	8.01828i	−0.866314	−	0.500167i	−0.000192319	−	1.00000i	$-0.500061\pi$
$257$	−13.8881	−	8.01828i	−0.866314	−	0.500167i	−0.866122	+	0.499833i	$0.833395\pi$
$258$	−8.05327			−0.501375
$259$	0.545684	−	1.00988i	0.0339071	−	0.0627508i
$260$			0.0607523i			0.00376770i
$261$	4.39952	−	7.62019i	0.272323	−	0.471678i
$262$	7.98416	−	4.60966i	0.493263	−	0.284786i
$263$	−28.0220	+	16.1785i	−1.72791	+	0.997611i	−0.829416	+	0.558631i	$0.811327\pi$
$263$	−28.0220	+	16.1785i	−1.72791	+	0.997611i	−0.898497	+	0.438980i	$0.855340\pi$
$264$	−3.55416	+	6.15598i	−0.218743	+	0.378874i
$265$			14.3867i			0.883767i
$266$	9.01361	−	5.54859i	0.552660	−	0.340206i
$267$		−	17.3811i		−	1.06371i
$268$	0.122447	+	0.0706950i	0.00747966	+	0.00431838i
$269$	−5.46259	+	3.15383i	−0.333060	+	0.192292i	−0.657199	−	0.753717i	$-0.728259\pi$
$269$	−5.46259	+	3.15383i	−0.333060	+	0.192292i	0.324139	+	0.946010i	$0.394926\pi$
$270$	3.54204	−	2.04500i	0.215562	−	0.124455i
$271$	−14.8145	−	8.55317i	−0.899918	−	0.519568i	−0.0227443	−	0.999741i	$-0.507240\pi$
$271$	−14.8145	−	8.55317i	−0.899918	−	0.519568i	−0.877174	+	0.480174i	$0.840574\pi$
$272$	−24.5832			−1.49057
$273$	−4.72957	+	2.91143i	−0.286247	+	0.176208i
$274$			23.1014i			1.39561i
$275$	7.24915	+	4.18530i	0.437140	+	0.252383i
$276$	−0.0462640	+	0.0132089i	−0.00278476	+	0.000795081i
$277$	2.73987	+	4.74559i	0.164623	+	0.285135i	0.936521	−	0.350611i	$-0.114026\pi$
$277$	2.73987	+	4.74559i	0.164623	+	0.285135i	−0.771898	+	0.635746i	$0.780693\pi$
$278$	−19.6729	−	11.3582i	−1.17990	−	0.681217i
$279$			7.47723i			0.447650i
$280$	−18.9448	−	10.2368i	−1.13217	−	0.611764i
$281$			20.4793i			1.22169i	0.791749	+	0.610847i	$0.209171\pi$
$281$			20.4793i			1.22169i	−0.791749	+	0.610847i	$0.790829\pi$
$282$	−3.34954	+	5.80157i	−0.199462	+	0.345478i
$283$	9.04218	+	15.6615i	0.537502	+	0.930980i	0.999038	+	0.0438586i	$0.0139651\pi$
$283$	9.04218	+	15.6615i	0.537502	+	0.930980i	−0.461536	+	0.887121i	$0.652702\pi$
$284$	−0.0387111	−	0.0670496i	−0.00229708	−	0.00397866i
$285$	−7.04974	−	4.07017i	−0.417590	−	0.241096i
$286$	7.49836			0.443387
$287$	−20.4621	+	0.577133i	−1.20784	+	0.0340671i
$288$	0.0567501			0.00334403
$289$	−10.1983	+	17.6639i	−0.599897	+	1.03905i
$290$	−17.9940	−	31.1665i	−1.05664	−	1.83016i
$291$	11.5556	−	6.67162i	0.677400	−	0.391097i
$292$	0.0119173	+	0.00688048i	0.000697409	+	0.000402649i
$293$	18.2954			1.06883			0.534415	−	0.845222i	$-0.320532\pi$
$293$	18.2954			1.06883			0.534415	+	0.845222i	$0.320532\pi$
$294$	0.559383	+	9.90851i	0.0326239	+	0.577876i
$295$		−	32.8359i		−	1.91178i
$296$	−1.06005	−	0.612018i	−0.0616140	−	0.0355728i
$297$	−1.25976	−	2.18197i	−0.0730989	−	0.126611i
$298$	−6.19642	+	3.57750i	−0.358949	+	0.207239i
$299$	−7.23377	−	7.00153i	−0.418339	−	0.404909i
$300$		−	0.0333298i		−	0.00192430i
$301$	−15.0227	+	0.423714i	−0.865892	+	0.0244225i
$302$	4.82930			0.277895
$303$	−0.306077	+	0.530141i	−0.0175837	+	0.0304558i
$304$	−5.67170	−	9.82366i	−0.325294	−	0.563426i
$305$	6.72769	+	11.6527i	0.385226	+	0.667232i
$306$	4.33498	−	7.50840i	0.247814	−	0.429227i
$307$		−	5.95059i		−	0.339618i	−0.985477	−	0.169809i	$-0.945685\pi$
$307$		−	5.95059i		−	0.339618i	0.985477	−	0.169809i	$-0.0543151\pi$
$308$	0.0317914	−	0.0588352i	0.00181148	−	0.00335244i
$309$		−	0.799982i		−	0.0455094i
$310$	26.4847	+	15.2909i	1.50423	+	0.868466i
$311$	20.6378	−	11.9152i	1.17026	−	0.675651i	0.216521	−	0.976278i	$-0.430529\pi$
$311$	20.6378	−	11.9152i	1.17026	−	0.675651i	0.953742	+	0.300627i	$0.0971958\pi$
$312$	2.96117	+	5.12889i	0.167643	+	0.290366i
$313$	3.55429	−	6.15621i	0.200900	−	0.347970i	−0.747918	−	0.663791i	$-0.768947\pi$
$313$	3.55429	−	6.15621i	0.200900	−	0.347970i	0.948819	+	0.315821i	$0.102280\pi$
$314$	−11.0974			−0.626265
$315$	6.49977	−	4.00113i	0.366221	−	0.225438i
$316$			0.0398144i			0.00223974i
$317$	−11.2104	+	19.4170i	−0.629639	+	1.09057i	0.357985	+	0.933727i	$0.383464\pi$
$317$	−11.2104	+	19.4170i	−0.629639	+	1.09057i	−0.987624	+	0.156840i	$0.949869\pi$
$318$	−3.53518	−	6.12310i	−0.198243	−	0.343367i
$319$	−19.1993	+	11.0847i	−1.07495	+	0.620624i
$320$	−11.4809	+	19.8855i	−0.641801	+	1.11163i
$321$	5.29112			0.295322
$322$	−17.1520	+	5.42453i	−0.955841	+	0.302297i
$323$	−17.2558			−0.960141
$324$	−0.00501609	+	0.00868813i	−0.000278672	+	0.000482674i
$325$	6.03967	−	3.48701i	0.335021	−	0.193424i
$326$	8.18510	+	14.1770i	0.453331	+	0.785192i
$327$	4.87779	−	8.44858i	0.269742	−	0.467207i
$328$			21.8284i			1.20527i
$329$	−5.94302	+	10.9985i	−0.327649	+	0.606369i
$330$	−10.3049			−0.567264
$331$	7.61357	−	13.1871i	0.418480	−	0.724828i	−0.577307	−	0.816527i	$-0.695896\pi$
$331$	7.61357	−	13.1871i	0.418480	−	0.724828i	0.995787	+	0.0916991i	$0.0292298\pi$
$332$	0.0470530	+	0.0814981i	0.00258237	+	0.00447279i
$333$	0.375731	−	0.216929i	0.0205900	−	0.0118876i
$334$	28.8009	+	16.6282i	1.57592	+	0.909856i
$335$		−	40.6578i		−	2.22137i
$336$	10.6316	−	0.299864i	0.580001	−	0.0163589i
$337$			4.37048i			0.238075i	0.992890	+	0.119038i	$0.0379809\pi$
$337$			4.37048i			0.238075i	−0.992890	+	0.119038i	$0.962019\pi$
$338$	−6.09176	+	10.5512i	−0.331348	+	0.573912i
$339$	−6.83237	−	11.8340i	−0.371083	−	0.642735i
$340$	−0.0884917	−	0.153272i	−0.00479914	−	0.00831235i
$341$	9.41955	−	16.3151i	0.510097	−	0.883514i
$342$	4.00057			0.216326
$343$	1.56481	+	18.4540i	0.0844916	+	0.996424i
$344$			16.0258i			0.864051i
$345$	9.94124	+	9.62208i	0.535218	+	0.518035i
$346$	13.9088	−	8.03026i	0.747742	−	0.431709i
$347$	7.98117	+	13.8238i	0.428452	+	0.742100i	0.996736	−	0.0807321i	$-0.0257258\pi$
$347$	7.98117	+	13.8238i	0.428452	+	0.742100i	−0.568284	+	0.822832i	$0.692392\pi$
$348$	0.0764472	+	0.0441368i	0.00409800	+	0.00236598i
$349$		−	20.8327i		−	1.11515i	−0.830127	−	0.557574i	$-0.811732\pi$
$349$		−	20.8327i		−	1.11515i	0.830127	−	0.557574i	$-0.188268\pi$
$350$	−0.351351	−	12.4571i	−0.0187805	−	0.665857i
$351$	−2.09916			−0.112045
$352$	−0.123827	−	0.0714917i	−0.00660002	−	0.00381052i
$353$	−6.20316	+	3.58140i	−0.330161	+	0.190619i	−0.655913	−	0.754837i	$-0.727716\pi$
$353$	−6.20316	+	3.58140i	−0.330161	+	0.190619i	0.325752	+	0.945455i	$0.394383\pi$
$354$	8.06861	+	13.9753i	0.428842	+	0.742776i
$355$	−11.1317	+	19.2807i	−0.590809	+	1.02331i
$356$	0.174370			0.00924162
$357$	7.69148	−	14.2343i	0.407076	−	0.753362i
$358$	23.1180			1.22182
$359$	−32.0458	−	18.5017i	−1.69131	−	0.976481i	−0.953459	−	0.301523i	$-0.902505\pi$
$359$	−32.0458	−	18.5017i	−1.69131	−	0.976481i	−0.737856	−	0.674958i	$-0.764162\pi$
$360$	−4.06948	−	7.04855i	−0.214480	−	0.371491i
$361$	5.51882	+	9.55888i	0.290464	+	0.503099i
$362$	8.48941	−	14.7041i	0.446193	−	0.772830i
$363$		−	4.65198i		−	0.244166i
$364$	−0.0292080	−	0.0474480i	−0.00153092	−	0.00248695i
$365$		−	3.95707i		−	0.207123i
$366$	−5.72673	−	3.30633i	−0.299341	−	0.172825i
$367$	−8.41051	−	14.5674i	−0.439025	−	0.760414i	0.558589	−	0.829444i	$-0.311343\pi$
$367$	−8.41051	−	14.5674i	−0.439025	−	0.760414i	−0.997615	+	0.0690305i	$0.978009\pi$
$368$	5.29289	+	18.5383i	0.275911	+	0.966375i
$369$	−6.70047	−	3.86852i	−0.348812	−	0.201387i
$370$		−	1.77447i		−	0.0922505i
$371$	−6.91672	−	11.2361i	−0.359098	−	0.583350i
$372$	−0.0750130			−0.00388924
$373$	−18.5423	−	10.7054i	−0.960084	−	0.554305i	−0.0638852	−	0.997957i	$-0.520349\pi$
$373$	−18.5423	−	10.7054i	−0.960084	−	0.554305i	−0.896199	+	0.443652i	$0.853682\pi$
$374$	−18.9176	+	10.9221i	−0.978207	+	0.564768i
$375$	4.19150	−	2.41996i	0.216448	−	0.124966i
$376$	11.5449	+	6.66547i	0.595384	+	0.343745i
$377$			18.4706i			0.951283i
$378$	−1.78318	+	3.30007i	−0.0917170	+	0.169737i
$379$			6.88991i			0.353911i	0.984219	+	0.176956i	$0.0566249\pi$
$379$			6.88991i			0.353911i	−0.984219	+	0.176956i	$0.943375\pi$
$380$	0.0408327	−	0.0707243i	0.00209467	−	0.00362808i
$381$	7.64315	−	4.41277i	0.391570	−	0.226073i
$382$	−0.170940	+	0.0986920i	−0.00874603	+	0.00504952i
$383$	13.9631	−	24.1848i	0.713481	−	1.23578i	−0.250062	−	0.968230i	$-0.580451\pi$
$383$	13.9631	−	24.1848i	0.713481	−	1.23578i	0.963543	−	0.267555i	$-0.0862156\pi$
$384$		−	11.3981i		−	0.581656i
$385$	−19.2228	+	0.542178i	−0.979685	+	0.0276320i
$386$	7.13707			0.363267
$387$	−4.91928	−	2.84015i	−0.250061	−	0.144373i
$388$	0.0669309	+	0.115928i	0.00339790	+	0.00588534i
$389$	−5.17774	+	2.98937i	−0.262522	+	0.151567i	−0.625485	−	0.780237i	$-0.715099\pi$
$389$	−5.17774	+	2.98937i	−0.262522	+	0.151567i	0.362962	+	0.931804i	$0.381765\pi$
$390$	−4.29278	+	7.43531i	−0.217373	+	0.376501i
$391$	28.4485	+	7.12749i	1.43870	+	0.360453i
$392$	19.7176	−	1.11315i	0.995890	−	0.0562228i
$393$	6.50275			0.328021
$394$	−5.61959	+	9.73341i	−0.283111	+	0.490362i
$395$	9.91510	−	5.72448i	0.498883	−	0.288030i
$396$	0.0218900	−	0.0126382i	0.00110001	−	0.000635093i
$397$	7.71977	+	4.45701i	0.387444	+	0.223691i	0.681052	−	0.732235i	$-0.261523\pi$
$397$	7.71977	+	4.45701i	0.387444	+	0.223691i	−0.293608	+	0.955926i	$0.594856\pi$
$398$	−20.8093			−1.04307
$399$	7.46272	−	0.210486i	0.373603	−	0.0105375i
$400$	−13.3555			−0.667774
$401$	33.0540	+	19.0838i	1.65064	+	0.952998i	0.976809	+	0.214112i	$0.0686859\pi$
$401$	33.0540	+	19.0838i	1.65064	+	0.952998i	0.673831	+	0.738885i	$0.264647\pi$
$402$	9.99066	+	17.3043i	0.498289	+	0.863062i
$403$	−7.84795	−	13.5931i	−0.390934	−	0.677118i
$404$	−0.00531847	−	0.00307062i	−0.000264604	−	0.000152769i
$405$	2.88484			0.143349
$406$	29.0375	+	15.6903i	1.44111	+	0.778696i
$407$	−1.09312			−0.0541837
$408$	−14.9415	−	8.62647i	−0.739714	−	0.427074i
$409$	11.3464	−	6.55085i	0.561043	−	0.323919i	−0.192521	−	0.981293i	$-0.561666\pi$
$409$	11.3464	−	6.55085i	0.561043	−	0.323919i	0.753564	+	0.657374i	$0.228333\pi$
$410$	−27.4049	+	15.8222i	−1.35343	+	0.781404i
$411$	−8.14716	+	14.1113i	−0.401870	+	0.696059i
$412$	0.00802557			0.000395391
$413$	15.7866	+	25.6451i	0.776807	+	1.26191i
$414$	−6.59547	−	1.65243i	−0.324150	−	0.0812125i
$415$	13.5305	−	23.4355i	0.664185	−	1.15040i
$416$	−0.103167	+	0.0595637i	−0.00505820	+	0.00292035i
$417$	−8.01136	−	13.8761i	−0.392318	−	0.679515i
$418$	−8.72915	−	5.03978i	−0.426957	−	0.246504i
$419$	−22.9395			−1.12067			−0.560334	−	0.828267i	$-0.689327\pi$
$419$	−22.9395			−1.12067			−0.560334	+	0.828267i	$0.689327\pi$
$420$	0.0401400	+	0.0652069i	0.00195863	+	0.00318177i
$421$			38.2820i			1.86575i	0.360200	+	0.932875i	$0.382708\pi$
$421$			38.2820i			1.86575i	−0.360200	+	0.932875i	$0.617292\pi$
$422$	−16.2798	+	28.1974i	−0.792487	+	1.37263i
$423$	−4.09208	+	2.36256i	−0.198964	+	0.114872i
$424$	−12.1848	+	7.03489i	−0.591745	+	0.341644i
$425$	−10.1583	+	17.5948i	−0.492752	+	0.853472i
$426$		−	10.9414i		−	0.530110i
$427$	−10.8567	−	5.86636i	−0.525391	−	0.283893i
$428$			0.0530816i			0.00256579i
$429$	4.58031	+	2.64445i	0.221140	+	0.127675i
$430$	−20.1198	+	11.6162i	−0.970265	+	0.560183i
$431$	−0.0210478	+	0.0121519i	−0.00101384	+	0.000585338i	−0.500507	−	0.865733i	$-0.666853\pi$
$431$	−0.0210478	+	0.0121519i	−0.00101384	+	0.000585338i	0.499493	+	0.866318i	$0.333520\pi$
$432$	3.48139	+	2.00998i	0.167498	+	0.0967053i
$433$	19.2727			0.926185			0.463092	−	0.886310i	$-0.346740\pi$
$433$	19.2727			0.926185			0.463092	+	0.886310i	$0.346740\pi$
$434$	−28.0362	+	0.790759i	−1.34578	+	0.0379576i
$435$		−	25.3838i		−	1.21706i
$436$	0.0847577	+	0.0489349i	0.00405916	+	0.00234356i
$437$	3.71528	+	13.0127i	0.177726	+	0.622483i
$438$	0.972354	+	1.68417i	0.0464609	+	0.0804726i
$439$	11.2511	+	6.49581i	0.536984	+	0.310028i	0.743856	−	0.668340i	$-0.232995\pi$
$439$	11.2511	+	6.49581i	0.536984	+	0.310028i	−0.206872	+	0.978368i	$0.566328\pi$
$440$			20.5063i			0.977601i
$441$	−3.15274	+	6.24982i	−0.150131	+	0.297610i
$442$			18.1996i			0.865668i
$443$	−0.727931	+	1.26081i	−0.0345851	+	0.0599031i	−0.882800	−	0.469749i	$-0.844344\pi$
$443$	−0.727931	+	1.26081i	−0.0345851	+	0.0599031i	0.848215	+	0.529652i	$0.177678\pi$
$444$	0.00217627	+	0.00376941i	0.000103281	+	0.000178888i
$445$	−25.0708	−	43.4239i	−1.18847	−	2.05849i
$446$	−21.8697	−	12.6265i	−1.03556	−	0.597881i
$447$	−5.04671			−0.238701
$448$	−0.593726	−	21.0504i	−0.0280509	−	0.994538i
$449$	−0.839294			−0.0396087			−0.0198044	−	0.999804i	$-0.506304\pi$
$449$	−0.839294			−0.0396087			−0.0198044	+	0.999804i	$0.506304\pi$
$450$	2.35510	−	4.07915i	0.111020	−	0.192293i
$451$	9.74684	+	16.8820i	0.458961	+	0.794943i
$452$	0.118721	−	0.0685436i	0.00558417	−	0.00322402i
$453$	2.94994	+	1.70315i	0.138600	+	0.0800210i
$454$	5.44841			0.255706
$455$	−7.61660	+	14.0958i	−0.357072	+	0.660820i
$456$		−	7.96101i		−	0.372809i
$457$	−17.4011	−	10.0465i	−0.813987	−	0.469956i	0.0343516	−	0.999410i	$-0.489063\pi$
$457$	−17.4011	−	10.0465i	−0.813987	−	0.469956i	−0.848338	+	0.529454i	$0.822397\pi$
$458$	7.92674	+	13.7295i	0.370392	+	0.641538i
$459$	5.29598	−	3.05763i	0.247195	−	0.142718i
$460$	−0.0965305	+	0.0997324i	−0.00450076	+	0.00465005i
$461$			11.4988i			0.535553i	0.963481	+	0.267777i	$0.0862889\pi$
$461$			11.4988i			0.535553i	−0.963481	+	0.267777i	$0.913711\pi$
$462$	8.04817	−	4.95429i	0.374435	−	0.230494i
$463$	−25.2657			−1.17420			−0.587098	−	0.809516i	$-0.699730\pi$
$463$	−25.2657			−1.17420			−0.587098	+	0.809516i	$0.699730\pi$
$464$	17.6859	−	30.6329i	0.821047	−	1.42210i
$465$	10.7853	+	18.6807i	0.500156	+	0.866296i
$466$	1.04071	+	1.80256i	0.0482100	+	0.0835021i
$467$	−7.50819	+	13.0046i	−0.347438	+	0.601780i	−0.985794	−	0.167962i	$-0.946282\pi$
$467$	−7.50819	+	13.0046i	−0.347438	+	0.601780i	0.638356	+	0.769741i	$0.279615\pi$
$468$		−	0.0210592i		−	0.000973460i
$469$	19.5472	+	31.7541i	0.902604	+	1.46627i
$470$			19.3257i			0.891430i
$471$	−6.77879	−	3.91373i	−0.312350	−	0.180335i
$472$	27.8103	−	16.0563i	1.28007	−	0.739050i
$473$	7.15583	+	12.3943i	0.329025	+	0.569889i
$474$	−2.81330	+	4.87278i	−0.129219	+	0.223814i
$475$	−9.37472			−0.430142
$476$	0.142802	+	0.0771623i	0.00654530	+	0.00353673i
$477$		−	4.98700i		−	0.228339i
$478$	−4.74872	+	8.22502i	−0.217201	+	0.376204i
$479$	−1.85472	−	3.21247i	−0.0847445	−	0.146782i	0.820538	−	0.571592i	$-0.193674\pi$
$479$	−1.85472	−	3.21247i	−0.0847445	−	0.146782i	−0.905282	+	0.424810i	$0.860341\pi$
$480$	0.141781	−	0.0818574i	0.00647140	−	0.00373626i
$481$	−0.455368	+	0.788720i	−0.0207630	+	0.0359625i
$482$	−17.8593			−0.813468
$483$	−12.3902	−	2.73545i	−0.563774	−	0.124467i
$484$	0.0466695			0.00212134
$485$	19.2465	−	33.3360i	0.873940	−	1.51371i
$486$	−1.22781	+	0.708878i	−0.0556947	+	0.0321554i
$487$	10.0762	+	17.4524i	0.456595	+	0.790845i	0.998778	−	0.0494147i	$-0.0157356\pi$
$487$	10.0762	+	17.4524i	0.456595	+	0.790845i	−0.542184	+	0.840260i	$0.682402\pi$
$488$	−6.57949	+	11.3960i	−0.297839	+	0.515873i
$489$			11.5466i			0.522153i
$490$	15.6898	+	23.9480i	0.708791	+	1.08186i
$491$	−35.5739			−1.60543			−0.802714	−	0.596364i	$-0.796611\pi$
$491$	−35.5739			−1.60543			−0.802714	+	0.596364i	$0.796611\pi$
$492$	0.0388097	−	0.0672204i	0.00174968	−	0.00303053i
$493$	−26.9042	−	46.5995i	−1.21171	−	2.09874i
$494$	−7.27274	+	4.19892i	−0.327216	+	0.188918i
$495$	−6.29464	−	3.63421i	−0.282923	−	0.163346i
$496$			30.0582i			1.34965i
$497$	−0.575667	−	20.4101i	−0.0258222	−	0.915520i
$498$			13.2991i			0.595948i
$499$	−17.5213	+	30.3478i	−0.784362	+	1.35856i	0.145017	+	0.989429i	$0.453676\pi$
$499$	−17.5213	+	30.3478i	−0.784362	+	1.35856i	−0.929379	+	0.369126i	$0.879657\pi$
$500$	0.0242775	+	0.0420499i	0.00108572	+	0.00188053i
$501$	11.7285	+	20.3144i	0.523993	+	0.907582i
$502$	−18.9065	+	32.7470i	−0.843837	+	1.46157i
$503$	4.81854			0.214848			0.107424	−	0.994213i	$-0.465740\pi$
$503$	4.81854			0.214848			0.107424	+	0.994213i	$0.465740\pi$
$504$	6.56704	+	3.54848i	0.292519	+	0.158062i
$505$			1.76597i			0.0785844i
$506$	12.3095	+	11.9143i	0.547223	+	0.529655i
$507$	−7.44221	+	4.29676i	−0.330520	+	0.190826i
$508$	0.0442698	+	0.0766775i	0.00196415	+	0.00340201i
$509$	19.2537	+	11.1161i	0.853405	+	0.492714i	0.861798	−	0.507251i	$-0.169338\pi$
$509$	19.2537	+	11.1161i	0.853405	+	0.492714i	−0.00839299	+	0.999965i	$0.502672\pi$
$510$		−	25.0114i		−	1.10752i
$511$	1.90245	+	3.09051i	0.0841595	+	0.136716i
$512$	−22.4548			−0.992372
$513$	2.44372	+	1.41088i	0.107893	+	0.0622920i
$514$	19.6899	−	11.3680i	0.868484	−	0.501419i
$515$	−1.15391	−	1.99863i	−0.0508473	−	0.0880701i
$516$	0.0284929	−	0.0493511i	0.00125433	−	0.00217256i
$517$	11.9051			0.523585
$518$	0.853118	+	1.38588i	0.0374838	+	0.0608920i
$519$	11.3281			0.497249
$520$	14.7960	+	8.54249i	0.648849	+	0.374613i
$521$	−3.93165	−	6.80981i	−0.172249	−	0.298343i	0.766957	−	0.641698i	$-0.221770\pi$
$521$	−3.93165	−	6.80981i	−0.172249	−	0.298343i	−0.939206	+	0.343355i	$0.888437\pi$
$522$	6.23744	+	10.8036i	0.273005	+	0.472859i
$523$	−7.09281	+	12.2851i	−0.310147	+	0.537190i	−0.978394	−	0.206749i	$-0.933712\pi$
$523$	−7.09281	+	12.2851i	−0.310147	+	0.537190i	0.668247	+	0.743939i	$0.267045\pi$
$524$			0.0652368i			0.00284988i
$525$	4.17861	−	7.73321i	0.182369	−	0.337505i
$526$		−	45.8744i		−	2.00022i
$527$	39.5993	+	22.8626i	1.72497	+	0.995912i
$528$	−5.06420	−	8.77146i	−0.220391	−	0.381729i
$529$	−0.750242	−	22.9878i	−0.0326192	−	0.999468i
$530$	−17.6642	−	10.1984i	−0.767282	−	0.442991i
$531$			11.3822i			0.493947i
$532$	0.00211163	+	0.0748674i	9.15508e−5	+	0.00324591i
$533$	16.2413			0.703488
$534$	21.3407	+	12.3211i	0.923504	+	0.533185i
$535$	13.2190	−	7.63202i	0.571509	−	0.329961i
$536$	34.4351	−	19.8811i	1.48737	−	0.858733i
$537$	14.1215	+	8.15303i	0.609386	+	0.351829i
$538$		−	8.94272i		−	0.385548i
$539$	14.7525	−	9.66524i	0.635435	−	0.416311i
$540$			0.0289412i			0.00124543i
$541$	−1.06464	+	1.84402i	−0.0457726	+	0.0792805i	−0.888004	−	0.459836i	$-0.847908\pi$
$541$	−1.06464	+	1.84402i	−0.0457726	+	0.0792805i	0.842231	+	0.539116i	$0.181242\pi$
$542$	21.0034	−	12.1263i	0.902172	−	0.520869i
$543$	10.3714	−	5.98792i	0.445078	−	0.256966i
$544$	0.173521	−	0.300547i	0.00743965	−	0.0128859i
$545$		−	28.1433i		−	1.20552i
$546$	−0.221998	−	7.87088i	−0.00950063	−	0.336843i
$547$	17.2635			0.738134			0.369067	−	0.929403i	$-0.379677\pi$
$547$	17.2635			0.738134			0.369067	+	0.929403i	$0.379677\pi$
$548$	−0.141567	−	0.0817339i	−0.00604745	−	0.00349150i
$549$	−2.33209	−	4.03929i	−0.0995310	−	0.172393i
$550$	−10.2775	+	5.93373i	−0.438235	+	0.253015i
$551$	12.4144	−	21.5024i	0.528871	−	0.916032i
$552$	−3.28828	+	13.1248i	−0.139959	+	0.558627i
$553$	−4.99159	+	9.23777i	−0.212264	+	0.392830i
$554$	−7.76893			−0.330070
$555$	0.625804	−	1.08392i	0.0265639	−	0.0460100i
$556$	0.139207	−	0.0803715i	0.00590371	−	0.00340851i
$557$	11.1188	−	6.41944i	0.471118	−	0.272000i	−0.245589	−	0.969374i	$-0.578981\pi$
$557$	11.1188	−	6.41944i	0.471118	−	0.272000i	0.716708	+	0.697374i	$0.245648\pi$
$558$	−9.18064	−	5.30045i	−0.388648	−	0.224386i
$559$	11.9238			0.504325
$560$	26.1288	−	16.0844i	1.10415	−	0.679689i
$561$	−15.4076			−0.650509
$562$	−25.1448	−	14.5173i	−1.06067	−	0.612377i
$563$	18.9166	+	32.7646i	0.797241	+	1.38086i	0.921406	+	0.388601i	$0.127042\pi$
$563$	18.9166	+	32.7646i	0.797241	+	1.38086i	−0.124165	+	0.992262i	$0.539625\pi$
$564$	−0.0237017	−	0.0410525i	−0.000998020	−	0.00172862i
$565$	−34.1392	−	19.7103i	−1.43625	−	0.829218i
$566$	−25.6392			−1.07770
$567$	−2.25308	+	1.38695i	−0.0946205	+	0.0582464i
$568$	−21.7729			−0.913573
$569$	−33.2822	−	19.2155i	−1.39526	−	0.805555i	−0.401370	−	0.915916i	$-0.631466\pi$
$569$	−33.2822	−	19.2155i	−1.39526	−	0.805555i	−0.993892	+	0.110361i	$0.964799\pi$
$570$	9.99480	−	5.77050i	0.418636	−	0.241700i
$571$	22.3491	−	12.9032i	0.935280	−	0.539984i	0.0468022	−	0.998904i	$-0.485097\pi$
$571$	22.3491	−	12.9032i	0.935280	−	0.539984i	0.888478	+	0.458920i	$0.151764\pi$
$572$	−0.0265296	+	0.0459506i	−0.00110926	+	0.00192129i
$573$	−0.139223			−0.00581612
$574$	13.7965	−	25.5328i	0.575857	−	1.06572i
$575$	15.4555	+	3.87221i	0.644537	+	0.161482i
$576$	3.97973	−	6.89310i	0.165822	−	0.287213i
$577$	27.7723	−	16.0343i	1.15617	−	0.667518i	0.205790	−	0.978596i	$-0.434024\pi$
$577$	27.7723	−	16.0343i	1.15617	−	0.667518i	0.950384	+	0.311078i	$0.100690\pi$
$578$	−14.4586	−	25.0431i	−0.601400	−	1.04166i
$579$	4.35962	+	2.51703i	0.181180	+	0.104604i
$580$	0.254655			0.0105740
$581$	0.699718	+	24.8083i	0.0290292	+	1.02922i
$582$			18.9175i			0.784154i
$583$	−6.28244	+	10.8815i	−0.260192	+	0.450666i
$584$	3.35144	−	1.93495i	0.138683	−	0.0800689i
$585$	−5.24442	+	3.02787i	−0.216830	+	0.125187i
$586$	−12.9692	+	22.4634i	−0.535754	+	0.927953i
$587$			25.9758i			1.07214i	0.844175	+	0.536068i	$0.180091\pi$
$587$			25.9758i			1.07214i	−0.844175	+	0.536068i	$0.819909\pi$
$588$	−0.0626993	−	0.0316289i	−0.00258568	−	0.00130435i
$589$			21.0990i			0.869369i
$590$	40.3163	+	23.2766i	1.65980	+	0.958284i
$591$	−6.86536	+	3.96372i	−0.282403	+	0.163046i
$592$	1.51043	−	0.872045i	0.0620781	−	0.0358408i
$593$	4.34832	+	2.51050i	0.178564	+	0.103094i	0.586618	−	0.809864i	$-0.300459\pi$
$593$	4.34832	+	2.51050i	0.178564	+	0.103094i	−0.408054	+	0.912958i	$0.633792\pi$
$594$	3.57208			0.146564
$595$	−1.31595	−	46.6566i	−0.0539486	−	1.91273i
$596$		−	0.0506296i		−	0.00207387i
$597$	−12.7112	−	7.33880i	−0.520234	−	0.300357i
$598$	13.7244	−	3.91848i	0.561234	−	0.160238i
$599$	−3.20737	−	5.55533i	−0.131050	−	0.226985i	0.793032	−	0.609180i	$-0.208501\pi$
$599$	−3.20737	−	5.55533i	−0.131050	−	0.226985i	−0.924081	+	0.382195i	$0.875168\pi$
$600$	−8.11738	−	4.68657i	−0.331390	−	0.191328i
$601$			24.8550i			1.01386i	0.861988	+	0.506928i	$0.169219\pi$
$601$			24.8550i			1.01386i	−0.861988	+	0.506928i	$0.830781\pi$
$602$	10.1290	−	18.7454i	0.412827	−	0.764005i
$603$			14.0936i			0.573937i
$604$	−0.0170863	+	0.0295944i	−0.000695233	+	0.00120418i
$605$	−6.71010	−	11.6222i	−0.272805	−	0.472511i
$606$	−0.433943	−	0.751611i	−0.0176277	−	0.0305321i
$607$	−24.6590	−	14.2369i	−1.00088	−	0.577858i	−0.0923714	−	0.995725i	$-0.529445\pi$
$607$	−24.6590	−	14.2369i	−1.00088	−	0.577858i	−0.908509	+	0.417866i	$0.862778\pi$
$608$	0.160135			0.00649435
$609$	12.2038	+	19.8249i	0.494524	+	0.803347i
$610$	−19.0764			−0.772383
$611$	4.95939	−	8.58992i	0.200636	−	0.347511i
$612$	0.0306748	+	0.0531302i	0.00123995	+	0.00214766i
$613$	−10.7843	+	6.22631i	−0.435573	+	0.251478i	−0.701718	−	0.712455i	$-0.747583\pi$
$613$	−10.7843	+	6.22631i	−0.435573	+	0.251478i	0.266145	+	0.963933i	$0.414250\pi$
$614$	7.30622	+	4.21825i	0.294855	+	0.170235i
$615$	−22.3201			−0.900033
$616$	−9.85888	−	16.0156i	−0.397225	−	0.645287i
$617$			10.2735i			0.413594i	0.978384	+	0.206797i	$0.0663039\pi$
$617$			10.2735i			0.413594i	−0.978384	+	0.206797i	$0.933696\pi$
$618$	0.982228	+	0.567090i	0.0395110	+	0.0228117i
$619$	6.08049	+	10.5317i	0.244395	+	0.423305i	0.961961	−	0.273185i	$-0.0880772\pi$
$619$	6.08049	+	10.5317i	0.244395	+	0.423305i	−0.717566	+	0.696490i	$0.754744\pi$
$620$	−0.187408	+	0.108200i	−0.00752650	+	0.00434542i
$621$	−3.44603	−	3.33540i	−0.138284	−	0.133845i
$622$			33.7858i			1.35469i
$623$	40.4575	+	21.8611i	1.62090	+	0.875845i
$624$	−8.43854			−0.337812
$625$	15.2869	−	26.4777i	0.611477	−	1.05911i
$626$	5.03912	+	8.72801i	0.201404	+	0.348841i
$627$	−3.55476	−	6.15702i	−0.141963	−	0.245888i
$628$	0.0392633	−	0.0680060i	0.00156678	−	0.00271374i
$629$		−	2.65315i		−	0.105788i
$630$	0.305088	+	10.8168i	0.0121550	+	0.430952i
$631$		−	5.19292i		−	0.206727i	−0.994644	−	0.103363i	$-0.967040\pi$
$631$		−	5.19292i		−	0.206727i	0.994644	−	0.103363i	$-0.0329605\pi$
$632$	9.69668	+	5.59838i	0.385713	+	0.222692i
$633$	−19.8888	+	11.4828i	−0.790507	+	0.456400i
$634$	−15.8936	−	27.5286i	−0.631216	−	1.09330i
$635$	12.7301	−	22.0492i	0.505180	−	0.874998i
$636$	0.0500305			0.00198384
$637$	−0.828235	−	14.6708i	−0.0328159	−	0.581277i
$638$		−	31.4308i		−	1.24436i
$639$	3.85869	−	6.68344i	0.152647	−	0.264393i
$640$	−16.4408	−	28.4763i	−0.649880	−	1.12563i
$641$	17.8537	−	10.3078i	0.705178	−	0.407135i	−0.104095	−	0.994567i	$-0.533195\pi$
$641$	17.8537	−	10.3078i	0.705178	−	0.407135i	0.809273	+	0.587433i	$0.199861\pi$
$642$	−3.75076	+	6.49651i	−0.148031	+	0.256397i
$643$	−19.7820			−0.780126			−0.390063	−	0.920788i	$-0.627547\pi$
$643$	−19.7820			−0.780126			−0.390063	+	0.920788i	$0.627547\pi$
$644$	0.0274425	−	0.124301i	0.00108139	−	0.00489814i
$645$	−16.3867			−0.645227
$646$	12.2323	−	21.1869i	0.481273	−	0.833589i
$647$	−23.3883	+	13.5033i	−0.919490	+	0.530868i	−0.883472	−	0.468483i	$-0.844801\pi$
$647$	−23.3883	+	13.5033i	−0.919490	+	0.530868i	−0.0360176	+	0.999351i	$0.511467\pi$
$648$	1.41064	+	2.44331i	0.0554153	+	0.0959822i
$649$	14.3389	−	24.8357i	0.562852	−	0.974888i
$650$			9.88745i			0.387818i
$651$	−17.4046	−	9.40449i	−0.682138	−	0.368591i
$652$	−0.115837			−0.00453653
$653$	17.8749	−	30.9603i	0.699501	−	1.21157i	−0.269139	−	0.963101i	$-0.586739\pi$
$653$	17.8749	−	30.9603i	0.699501	−	1.21157i	0.968640	−	0.248470i	$-0.0799276\pi$
$654$	6.91551	+	11.9780i	0.270418	+	0.468378i
$655$	16.2461	−	9.37969i	0.634788	−	0.366495i
$656$	−26.9356	−	15.5513i	−1.05166	−	0.607176i
$657$			1.37168i			0.0535143i
$658$	−9.29128	−	15.0935i	−0.362212	−	0.588408i
$659$		−	0.324762i		−	0.0126509i	−0.999980	−	0.00632547i	$-0.997987\pi$
$659$		−	0.324762i		−	0.0126509i	0.999980	−	0.00632547i	$-0.00201347\pi$
$660$	0.0364591	−	0.0631491i	0.00141917	−	0.00245807i
$661$	−3.76538	−	6.52183i	−0.146456	−	0.253670i	0.783459	−	0.621443i	$-0.213453\pi$
$661$	−3.76538	−	6.52183i	−0.146456	−	0.253670i	−0.929915	+	0.367774i	$0.880120\pi$
$662$	10.7942	+	18.6961i	0.419528	+	0.726644i
$663$	−6.41846	+	11.1171i	−0.249272	+	0.431752i
$664$	26.4648			1.02703
$665$	18.3408	−	11.2902i	0.711227	−	0.437816i
$666$			0.615104i			0.0238348i
$667$	−29.3483	+	30.3217i	−1.13637	+	1.17406i
$668$	−0.203798	+	0.117663i	−0.00788519	+	0.00455252i
$669$	−8.90596	−	15.4256i	−0.344324	−	0.596387i
$670$	49.9202	+	28.8214i	1.92859	+	1.11347i
$671$			11.7515i			0.453662i
$672$	−0.0713774	+	0.132096i	−0.00275344	+	0.00509570i
$673$	13.4936			0.520139			0.260070	−	0.965590i	$-0.416254\pi$
$673$	13.4936			0.520139			0.260070	+	0.965590i	$0.416254\pi$
$674$	−5.36613	−	3.09814i	−0.206696	−	0.119336i
$675$	2.87719	−	1.66114i	0.110743	−	0.0639375i
$676$	−0.0431060	−	0.0746617i	−0.00165792	−	0.00287160i
$677$	10.2175	−	17.6972i	0.392689	−	0.680157i	−0.600114	−	0.799914i	$-0.704878\pi$
$677$	10.2175	−	17.6972i	0.392689	−	0.680157i	0.992803	+	0.119757i	$0.0382116\pi$
$678$	19.3733			0.744026
$679$	0.995320	+	35.2888i	0.0381969	+	1.35426i
$680$	−49.7719			−1.90867
$681$	3.32812	+	1.92149i	0.127534	+	0.0736317i
$682$	13.3546	+	23.1309i	0.511375	+	0.885727i
$683$	10.2259	+	17.7117i	0.391282	+	0.677721i	0.992619	−	0.121275i	$-0.0386983\pi$
$683$	10.2259	+	17.7117i	0.391282	+	0.677721i	−0.601337	+	0.798996i	$0.705365\pi$
$684$	−0.0141542	+	0.0245159i	−0.000541201	+	0.000937387i
$685$			47.0065i			1.79603i
$686$	−23.7674	−	11.1604i	−0.907442	−	0.426105i
$687$			11.1821i			0.426623i
$688$	−19.7753	−	11.4173i	−0.753927	−	0.435280i
$689$	5.23426	+	9.06600i	0.199409	+	0.345387i
$690$	−18.8612	+	5.38510i	−0.718035	+	0.205007i
$691$	−15.0642	−	8.69732i	−0.573069	−	0.330862i	0.185305	−	0.982681i	$-0.440673\pi$
$691$	−15.0642	−	8.69732i	−0.573069	−	0.330862i	−0.758374	+	0.651819i	$0.774006\pi$
$692$			0.113646i			0.00432017i
$693$	6.66339	−	0.187941i	0.253121	−	0.00713928i
$694$	−22.6307			−0.859050
$695$	−40.0302	−	23.1115i	−1.51843	−	0.876668i
$696$	21.4988	−	12.4123i	0.814908	−	0.470487i
$697$	−40.9752	+	23.6570i	−1.55204	+	0.896074i
$698$	25.5786	+	14.7678i	0.968165	+	0.558970i
$699$			1.46811i			0.0555290i
$700$	0.0775810	+	0.0419206i	0.00293229	+	0.00158445i
$701$		−	7.50897i		−	0.283610i	−0.989895	−	0.141805i	$-0.954709\pi$
$701$		−	7.50897i		−	0.283610i	0.989895	−	0.141805i	$-0.0452906\pi$
$702$	1.48805	−	2.57737i	0.0561628	−	0.0972767i
$703$	1.06023	−	0.612121i	0.0399872	−	0.0230866i
$704$	−17.3674	+	10.0271i	−0.654557	+	0.377909i
$705$	−6.81561	+	11.8050i	−0.256691	+	0.444601i
$706$		−	10.1551i		−	0.382192i
$707$	−0.849027	−	1.37923i	−0.0319310	−	0.0518714i
$708$	−0.114189			−0.00429147
$709$	−19.6605	−	11.3510i	−0.738364	−	0.426295i	0.0831103	−	0.996540i	$-0.473515\pi$
$709$	−19.6605	−	11.3510i	−0.738364	−	0.426295i	−0.821474	+	0.570246i	$0.806848\pi$
$710$	−15.7820	−	27.3353i	−0.592289	−	1.02587i
$711$	−3.43697	+	1.98433i	−0.128896	+	0.0744184i
$712$	24.5185	−	42.4674i	0.918872	−	1.59153i
$713$	8.71490	−	34.7844i	0.326375	−	1.30269i
$714$	12.0248	+	19.5341i	0.450017	+	0.731046i
$715$	15.2576			0.570602
$716$	−0.0817927	+	0.141669i	−0.00305674	+	0.00529442i
$717$	−5.80143	+	3.34946i	−0.216658	+	0.125088i
$718$	45.4332	−	26.2309i	1.69555	−	0.978927i
$719$	4.76820	+	2.75292i	0.177824	+	0.102667i	0.586270	−	0.810116i	$-0.300596\pi$
$719$	4.76820	+	2.75292i	0.177824	+	0.102667i	−0.408446	+	0.912782i	$0.633929\pi$
$720$	11.5969			0.432193
$721$	1.86210	+	1.00618i	0.0693481	+	0.0374720i
$722$	−15.6487			−0.582384
$723$	−10.9092	−	6.29844i	−0.405718	−	0.234241i
$724$	0.0600719	+	0.104048i	0.00223256	+	0.00386690i
$725$	−14.6165	−	25.3165i	−0.542842	−	0.940230i
$726$	5.71176	+	3.29769i	0.211983	+	0.122389i
$727$	−14.9811			−0.555617			−0.277809	−	0.960636i	$-0.589608\pi$
$727$	−14.9811			−0.555617			−0.277809	+	0.960636i	$0.589608\pi$
$728$	−15.6628	+	0.441768i	−0.580502	+	0.0163730i
$729$	−1.00000			−0.0370370
$730$	4.85855	+	2.80508i	0.179823	+	0.103821i
$731$	−30.0827	+	17.3683i	−1.11265	+	0.642388i
$732$	0.0405229	−	0.0233959i	0.00149777	−	0.000864738i
$733$	20.0372	−	34.7055i	0.740091	−	1.28188i	−0.212362	−	0.977191i	$-0.568116\pi$
$733$	20.0372	−	34.7055i	0.740091	−	1.28188i	0.952453	−	0.304685i	$-0.0985511\pi$
$734$	23.8481			0.880250
$735$	1.13823	+	20.1618i	0.0419842	+	0.743678i
$736$	−0.264004	−	0.0661436i	−0.00973132	−	0.00243809i
$737$	17.7546	−	30.7519i	0.654001	−	1.13276i
$738$	9.49963	−	5.48461i	0.349686	−	0.201891i
$739$	−24.1937	−	41.9048i	−0.889981	−	1.54149i	−0.839896	−	0.542748i	$-0.817384\pi$
$739$	−24.1937	−	41.9048i	−0.889981	−	1.54149i	−0.0500853	−	0.998745i	$-0.515949\pi$
$740$	0.0108741	+	0.00627818i	0.000399741	+	0.000230791i
$741$	−5.92333			−0.217599
$742$	18.6990	−	0.527403i	0.686460	−	0.0193616i
$743$			15.6831i			0.575359i	0.957727	+	0.287679i	$0.0928838\pi$
$743$			15.6831i			0.575359i	−0.957727	+	0.287679i	$0.907116\pi$
$744$	−10.5477	+	18.2692i	−0.386698	+	0.669781i
$745$	−12.6084	+	7.27947i	−0.461937	+	0.266699i
$746$	26.2885	−	15.1777i	0.962489	−	0.555693i
$747$	−4.69020	+	8.12367i	−0.171605	+	0.297229i
$748$		−	0.154572i		−	0.00565171i
$749$	−6.65491	+	12.3160i	−0.243165	+	0.450017i
$750$			6.86183i			0.250559i
$751$	−31.6795	−	18.2902i	−1.15600	−	0.667417i	−0.205659	−	0.978624i	$-0.565934\pi$
$751$	−31.6795	−	18.2902i	−1.15600	−	0.667417i	−0.950342	+	0.311206i	$0.899267\pi$
$752$	−16.4500	+	9.49741i	−0.599870	+	0.346335i
$753$	−23.0978	+	13.3355i	−0.841729	+	0.485972i
$754$	−22.6784	−	13.0934i	−0.825899	−	0.476833i
$755$	9.82663			0.357628
$756$	−0.0139141	−	0.0226033i	−0.000506052	−	0.000822075i
$757$		−	47.1206i		−	1.71263i	−0.516457	−	0.856313i	$-0.672749\pi$
$757$		−	47.1206i		−	1.71263i	0.516457	−	0.856313i	$-0.327251\pi$
$758$	−8.45953	−	4.88411i	−0.307264	−	0.177399i
$759$	3.31734	+	11.6189i	0.120412	+	0.421741i
$760$	−11.4831	−	19.8893i	−0.416536	−	0.721462i
$761$	−32.2668	−	18.6292i	−1.16967	−	0.675309i	−0.216067	−	0.976378i	$-0.569323\pi$
$761$	−32.2668	−	18.6292i	−1.16967	−	0.675309i	−0.953602	+	0.301069i	$0.902656\pi$
$762$			12.5125i			0.453279i
$763$	13.5305	+	21.9801i	0.489837	+	0.795733i
$764$		−	0.00139671i		−	5.05312e-5i
$765$	8.82078	−	15.2780i	0.318916	−	0.552379i
$766$	19.7963	+	34.2881i	0.715268	+	1.23888i
$767$	−11.9466	−	20.6921i	−0.431365	−	0.747147i
$768$	0.208510	+	0.120383i	0.00752395	+	0.00434396i
$769$	−47.6922			−1.71983			−0.859913	−	0.510441i	$-0.829482\pi$
$769$	−47.6922			−1.71983			−0.859913	+	0.510441i	$0.829482\pi$
$770$	12.9609	−	23.9863i	0.467080	−	0.864408i
$771$	16.0366			0.577543
$772$	−0.0252513	+	0.0437365i	−0.000908814	+	0.00157411i
$773$	9.83273	+	17.0308i	0.353659	+	0.612555i	0.986887	−	0.161410i	$-0.0516041\pi$
$773$	9.83273	+	17.0308i	0.353659	+	0.612555i	−0.633229	+	0.773965i	$0.718271\pi$
$774$	6.97434	−	4.02664i	0.250687	−	0.144734i
$775$	21.5134	+	12.4208i	0.772784	+	0.446167i
$776$	37.6451			1.35138
$777$	0.0323630	+	1.14742i	0.00116102	+	0.0411635i
$778$		−	8.47640i		−	0.303894i
$779$	−18.9071	−	10.9160i	−0.677419	−	0.391108i
$780$	−0.0303761	−	0.0526130i	−0.00108764	−	0.00188385i
$781$	−16.8391	+	9.72207i	−0.602551	+	0.347883i
$782$	−28.9178	+	29.8769i	−1.03410	+	1.06840i
$783$			8.79903i			0.314452i
$784$	−12.6739	+	25.1240i	−0.452639	+	0.897287i
$785$	−22.5810			−0.805950
$786$	−4.60966	+	7.98416i	−0.164421	+	0.284786i
$787$	−11.8700	−	20.5594i	−0.423120	−	0.732865i	0.573123	−	0.819469i	$-0.305732\pi$
$787$	−11.8700	−	20.5594i	−0.423120	−	0.732865i	−0.996243	+	0.0866046i	$0.972398\pi$
$788$	−0.0397648	−	0.0688746i	−0.00141656	−	0.00245356i
$789$	16.1785	−	28.0220i	0.575971	−	0.997611i
$790$			16.2318i			0.577503i
$791$	36.1391	−	1.01930i	1.28496	−	0.0362422i
$792$		−	7.10832i		−	0.252583i
$793$	8.47912	+	4.89542i	0.301102	+	0.173841i
$794$	−10.9447	+	6.31895i	−0.388415	+	0.224251i
$795$	−7.19334	−	12.4592i	−0.255122	−	0.441884i
$796$	0.0736243	−	0.127521i	0.00260954	−	0.00451986i
$797$	14.7739			0.523317			0.261659	−	0.965160i	$-0.415731\pi$
$797$	14.7739			0.523317			0.261659	+	0.965160i	$0.415731\pi$
$798$	−5.03172	+	9.31203i	−0.178121	+	0.329642i
$799$			28.8954i			1.02225i
$800$	0.0942701	−	0.163281i	0.00333295	−	0.00577284i
$801$	8.69055	+	15.0525i	0.307065	+	0.531853i
$802$	−46.8626	+	27.0561i	−1.65478	+	0.955385i
$803$	1.72799	−	2.99297i	0.0609795	−	0.105620i
$804$	−0.141390			−0.00498644
$805$	−34.9007	+	11.0378i	−1.23009	+	0.389031i
$806$	22.2530			0.783827
$807$	3.15383	−	5.46259i	0.111020	−	0.192292i
$808$	−1.49568	+	0.863532i	−0.0526179	+	0.0303789i
$809$	−4.37158	−	7.57181i	−0.153697	−	0.266211i	0.778887	−	0.627164i	$-0.215785\pi$
$809$	−4.37158	−	7.57181i	−0.153697	−	0.266211i	−0.932584	+	0.360954i	$0.882451\pi$
$810$	−2.04500	+	3.54204i	−0.0718539	+	0.124455i
$811$		−	30.4296i		−	1.06853i	−0.845318	−	0.534264i	$-0.820589\pi$
$811$		−	30.4296i		−	1.06853i	0.845318	−	0.534264i	$-0.179411\pi$
$812$	−0.198887	+	0.122431i	−0.00697958	+	0.00429649i
$813$	17.1063			0.599945
$814$	0.774885	−	1.34214i	0.0271597	−	0.0470420i
$815$	16.6550	+	28.8473i	0.583398	+	1.01048i
$816$	21.2896	−	12.2916i	0.745286	−	0.430291i
$817$	−13.8810	−	8.01423i	−0.485636	−	0.280382i
$818$			18.5750i			0.649460i
$819$	2.64022	−	4.88616i	0.0922567	−	0.170736i
$820$		−	0.223919i		−	0.00781960i
$821$	10.6069	−	18.3716i	0.370182	−	0.641174i	−0.619411	−	0.785067i	$-0.712629\pi$
$821$	10.6069	−	18.3716i	0.370182	−	0.641174i	0.989593	+	0.143892i	$0.0459619\pi$
$822$	−11.5507	−	20.0064i	−0.402877	−	0.697803i
$823$	−20.7921	−	36.0129i	−0.724766	−	1.25533i	−0.959070	−	0.283169i	$-0.908614\pi$
$823$	−20.7921	−	36.0129i	−0.724766	−	1.25533i	0.234304	−	0.972163i	$-0.424719\pi$
$824$	1.12849	−	1.95460i	0.0393128	−	0.0680918i
$825$	−8.37060			−0.291427
$826$	−42.6781	+	1.20373i	−1.48496	+	0.0418833i
$827$			28.9683i			1.00733i	0.863900	+	0.503663i	$0.168015\pi$
$827$			28.9683i			1.00733i	−0.863900	+	0.503663i	$0.831985\pi$
$828$	0.0334613	−	0.0345712i	0.00116286	−	0.00120143i
$829$	7.53193	−	4.34856i	0.261595	−	0.151032i	−0.363467	−	0.931607i	$-0.618407\pi$
$829$	7.53193	−	4.34856i	0.261595	−	0.151032i	0.625062	+	0.780575i	$0.285074\pi$
$830$	19.1829	+	33.2258i	0.665848	+	1.15328i
$831$	−4.74559	−	2.73987i	−0.164623	−	0.0950450i
$832$			16.7082i			0.579252i
$833$	23.4590	+	35.8065i	0.812805	+	1.24062i
$834$	22.7163			0.786601
$835$	58.6039	+	33.8350i	2.02807	+	1.17091i
$836$	0.0617684	−	0.0356620i	0.00213630	−	0.00123340i
$837$	−3.73862	−	6.47547i	−0.129225	−	0.223825i
$838$	16.2613	−	28.1654i	0.561737	−	0.972958i
$839$	−9.04103			−0.312131			−0.156065	−	0.987747i	$-0.549881\pi$
$839$	−9.04103			−0.312131			−0.156065	+	0.987747i	$0.549881\pi$
$840$	21.5251	−	0.607114i	0.742687	−	0.0209474i
$841$	48.4230			1.66976
$842$	−47.0031	−	27.1373i	−1.61983	−	0.935212i
$843$	−10.2397	−	17.7356i	−0.352673	−	0.610847i
$844$	−0.115197	−	0.199528i	−0.00396526	−	0.00686803i
$845$	−12.3955	+	21.4696i	−0.426417	+	0.738576i
$846$		−	6.69907i		−	0.230319i
$847$	10.8283	+	5.85103i	0.372065	+	0.201044i
$848$		−	20.0476i		−	0.688436i
$849$	−15.6615	−	9.04218i	−0.537502	−	0.310327i
$850$	−14.4021	−	24.9451i	−0.493986	−	0.855610i
$851$	−2.00076	+	0.571238i	−0.0685850	+	0.0195818i
$852$	0.0670496	+	0.0387111i	0.00229708	+	0.00132622i
$853$			10.9928i			0.376385i	0.982132	+	0.188193i	$0.0602629\pi$
$853$			10.9928i			0.376385i	−0.982132	+	0.188193i	$0.939737\pi$
$854$	14.8988	−	9.17142i	0.509828	−	0.313840i
$855$	8.14033			0.278394
$856$	12.9278	+	7.46389i	0.441865	+	0.255111i
$857$	3.77882	−	2.18170i	0.129082	−	0.0745255i	−0.434069	−	0.900880i	$-0.642922\pi$
$857$	3.77882	−	2.18170i	0.129082	−	0.0745255i	0.563151	+	0.826354i	$0.309589\pi$
$858$	−6.49377	+	3.74918i	−0.221694	+	0.127995i
$859$	28.6592	+	16.5464i	0.977839	+	0.564556i	0.901617	−	0.432535i	$-0.142381\pi$
$859$	28.6592	+	16.5464i	0.977839	+	0.564556i	0.0762223	+	0.997091i	$0.475714\pi$
$860$		−	0.164395i		−	0.00560581i
$861$	17.4322	−	10.7309i	0.594086	−	0.365707i
$862$		−	0.0344570i		−	0.00117361i
$863$	−5.08683	+	8.81065i	−0.173158	+	0.299918i	−0.939522	−	0.342488i	$-0.888730\pi$
$863$	−5.08683	+	8.81065i	−0.173158	+	0.299918i	0.766365	+	0.642406i	$0.222064\pi$
$864$	−0.0491470	+	0.0283750i	−0.00167202	+	0.000965339i
$865$	28.3015	−	16.3399i	0.962281	−	0.555573i
$866$	−13.6620	+	23.6632i	−0.464252	+	0.804109i
$867$		−	20.3965i		−	0.692702i
$868$	0.0943476	−	0.174606i	0.00320237	−	0.00592651i
$869$	9.99917			0.339199
$870$	31.1665	+	17.9940i	1.05664	+	0.610054i
$871$	−14.7924	−	25.6212i	−0.501221	−	0.868140i
$872$	23.8359	−	13.7616i	0.807184	−	0.466028i
$873$	−6.67162	+	11.5556i	−0.225800	+	0.391097i
$874$	−18.6109	−	4.66277i	−0.629522	−	0.157720i
$875$	0.361027	+	12.8001i	0.0122050	+	0.432724i
$876$	−0.0137610			−0.000464940
$877$	1.17300	−	2.03169i	0.0396093	−	0.0686053i	−0.845541	−	0.533910i	$-0.820722\pi$
$877$	1.17300	−	2.03169i	0.0396093	−	0.0686053i	0.885150	+	0.465305i	$0.154055\pi$
$878$	−15.9513	+	9.20947i	−0.538329	+	0.310805i
$879$	−15.8443	+	9.14772i	−0.534415	+	0.308545i
$880$	−25.3042	−	14.6094i	−0.853006	−	0.492483i
$881$	31.3940			1.05769			0.528846	−	0.848718i	$-0.322625\pi$
$881$	31.3940			1.05769			0.528846	+	0.848718i	$0.322625\pi$
$882$	−5.43870	−	8.30133i	−0.183130	−	0.279520i
$883$	−29.5722			−0.995184			−0.497592	−	0.867411i	$-0.665782\pi$
$883$	−29.5722			−0.995184			−0.497592	+	0.867411i	$0.665782\pi$
$884$	−0.111529	−	0.0643912i	−0.00375112	−	0.00216571i
$885$	16.4179	+	28.4367i	0.551883	+	0.955890i
$886$	−1.03203	−	1.78753i	−0.0346717	−	0.0600531i
$887$	45.0380	+	26.0027i	1.51223	+	0.873085i	0.999898	+	0.0142958i	$0.00455064\pi$
$887$	45.0380	+	26.0027i	1.51223	+	0.873085i	0.512329	+	0.858789i	$0.328783\pi$
$888$	1.22404			0.0410760
$889$	0.658329	+	23.3409i	0.0220797	+	0.782829i
$890$	71.0886			2.38290
$891$	2.18197	+	1.25976i	0.0730989	+	0.0422037i
$892$	0.154752	−	0.0893463i	0.00518149	−	0.00299154i
$893$	−11.5469	+	6.66659i	−0.386402	+	0.223089i
$894$	3.57750	−	6.19642i	0.119650	−	0.207239i
$895$	47.0403			1.57238
$896$	26.5310	+	14.3359i	0.886339	+	0.478930i
$897$	9.76539	+	2.44662i	0.326057	+	0.0816903i
$898$	0.594957	−	1.03050i	0.0198540	−	0.0343881i
$899$	−56.9779	+	32.8962i	−1.90032	+	1.09715i
$900$	0.0166649	+	0.0288645i	0.000555497	+	0.000962149i
$901$	−26.4110	−	15.2484i	−0.879880	−	0.507999i
$902$	−27.6373			−0.920221
$903$	12.7982	−	7.87828i	0.425896	−	0.262173i
$904$		−	38.5522i		−	1.28223i
$905$	17.2742	−	29.9197i	0.574213	−	0.994566i
$906$	−4.18230	+	2.41465i	−0.138948	+	0.0802214i
$907$	45.8713	−	26.4838i	1.52313	−	0.879381i	0.523506	−	0.852022i	$-0.324624\pi$
$907$	45.8713	−	26.4838i	1.52313	−	0.879381i	0.999626	−	0.0273587i	$-0.00870963\pi$
$908$	−0.0192767	+	0.0333883i	−0.000639721	+	0.00110803i
$909$		−	0.612154i		−	0.0203039i
$910$	−11.9077	−	19.3439i	−0.394737	−	0.641245i
$911$		−	39.6752i		−	1.31450i	−0.753673	−	0.657249i	$-0.771720\pi$
$911$		−	39.6752i		−	1.31450i	0.753673	−	0.657249i	$-0.228280\pi$
$912$	9.82366	+	5.67170i	0.325294	+	0.187809i
$913$	20.4678	−	11.8171i	0.677385	−	0.391089i
$914$	24.6704	−	14.2435i	0.816026	−	0.471133i
$915$	−11.6527	−	6.72769i	−0.385226	−	0.222411i
$916$	−0.112181			−0.00370656
$917$	−8.17884	+	15.1363i	−0.270089	+	0.499844i
$918$			8.66996i			0.286151i
$919$	11.5830	+	6.68745i	0.382088	+	0.220599i	0.678726	−	0.734391i	$-0.262532\pi$
$919$	11.5830	+	6.68745i	0.382088	+	0.220599i	−0.296638	+	0.954990i	$0.595866\pi$
$920$	10.7162	+	37.5333i	0.353302	+	1.23743i
$921$	2.97530	+	5.15337i	0.0980394	+	0.169809i
$922$	−14.1184	−	8.15126i	−0.464965	−	0.268447i
$923$			16.2000i			0.533230i
$924$	0.00188546	+	0.0668484i	6.20270e−5	+	0.00219915i
$925$		−	1.44140i		−	0.0473929i
$926$	17.9103	−	31.0215i	0.588568	−	1.01943i
$927$	0.399991	+	0.692805i	0.0131374	+	0.0227547i
$928$	0.249673	+	0.432446i	0.00819592	+	0.0141957i
$929$	48.0953	+	27.7678i	1.57796	+	0.911033i	0.995144	+	0.0984252i	$0.0313805\pi$
$929$	48.0953	+	27.7678i	1.57796	+	0.911033i	0.582811	+	0.812608i	$0.301953\pi$
$930$	−30.5819			−1.00282
$931$	−8.89629	+	17.6355i	−0.291564	+	0.577981i
$932$	−0.0147283			−0.000482443
$933$	−11.9152	+	20.6378i	−0.390087	+	0.675651i
$934$	−10.6448	−	18.4373i	−0.348308	−	0.603287i
$935$	−38.4934	+	22.2242i	−1.25887	+	0.726809i
$936$	−5.12889	−	2.96117i	−0.167643	−	0.0967888i
$937$	−42.2026			−1.37870			−0.689350	−	0.724429i	$-0.742104\pi$
$937$	−42.2026			−1.37870			−0.689350	+	0.724429i	$0.742104\pi$
$938$	−52.8446	+	1.49048i	−1.72544	+	0.0486659i
$939$			7.10858i			0.231980i
$940$	−0.118430	−	0.0683755i	−0.00386275	−	0.00223016i
$941$	−17.8644	−	30.9420i	−0.582362	−	1.00868i	−0.995199	−	0.0978761i	$-0.968795\pi$
$941$	−17.8644	−	30.9420i	−0.582362	−	1.00868i	0.412836	−	0.910805i	$-0.364538\pi$
$942$	9.61066	−	5.54872i	0.313132	−	0.180787i
$943$	26.6621	+	25.8061i	0.868236	+	0.840362i
$944$			45.7562i			1.48924i
$945$	−3.62840	+	6.71496i	−0.118032	+	0.218438i
$946$	−20.2904			−0.659699
$947$	−11.4215	+	19.7825i	−0.371148	+	0.642846i	−0.989742	−	0.142864i	$-0.954369\pi$
$947$	−11.4215	+	19.7825i	−0.371148	+	0.642846i	0.618595	+	0.785710i	$0.287702\pi$
$948$	−0.0199072	−	0.0344803i	−0.000646556	−	0.00111987i
$949$	−1.43969	−	2.49361i	−0.0467342	−	0.0809461i
$950$	6.64553	−	11.5104i	0.215610	−	0.373447i
$951$		−	22.4208i		−	0.727045i
$952$	38.8723	−	23.9290i	1.25986	−	0.775542i
$953$			42.1543i			1.36551i	0.730646	+	0.682756i	$0.239219\pi$
$953$			42.1543i			1.36551i	−0.730646	+	0.682756i	$0.760781\pi$
$954$	6.12310	+	3.53518i	0.198243	+	0.114456i
$955$	−0.347826	+	0.200818i	−0.0112554	+	0.00649831i
$956$	−0.0336024	−	0.0582011i	−0.00108678	−	0.00188236i
$957$	11.0847	−	19.1993i	0.358318	−	0.620624i
$958$	5.25909			0.169913
$959$	−22.5994	−	36.7124i	−0.729773	−	1.18551i
$960$		−	22.9618i		−	0.741088i
$961$	12.4545	−	21.5718i	0.401758	−	0.695866i
$962$	−0.645600	−	1.11821i	−0.0208150	−	0.0360526i
$963$	−4.58225	+	2.64556i	−0.147661	+	0.0852520i
$964$	0.0631871	−	0.109443i	0.00203512	−	0.00352493i
$965$	14.5224			0.467494
$966$	12.1418	−	13.2738i	0.390655	−	0.427076i
$967$	−47.4256			−1.52510			−0.762552	−	0.646927i	$-0.776054\pi$
$967$	−47.4256			−1.52510			−0.762552	+	0.646927i	$0.776054\pi$
$968$	6.56229	−	11.3662i	0.210920	−	0.365324i
$969$	14.9440	−	8.62792i	0.480070	−	0.277169i
$970$	27.2869	+	47.2623i	0.876129	+	1.51750i
$971$	−11.4639	+	19.8560i	−0.367893	+	0.637209i	−0.989236	−	0.146330i	$-0.953254\pi$
$971$	−11.4639	+	19.8560i	−0.367893	+	0.637209i	0.621343	+	0.783538i	$0.286587\pi$
$972$		−	0.0100322i		−	0.000321783i
$973$	42.3753	−	1.19519i	1.35849	−	0.0383161i
$974$	−28.5711			−0.915477
$975$	−3.48701	+	6.03967i	−0.111674	+	0.193424i
$976$	−9.37490	−	16.2378i	−0.300083	−	0.519759i
$977$	−36.3899	+	21.0097i	−1.16421	+	0.672160i	−0.952311	−	0.305131i	$-0.901300\pi$
$977$	−36.3899	+	21.0097i	−1.16421	+	0.672160i	−0.211904	+	0.977290i	$0.567967\pi$
$978$	−14.1770	−	8.18510i	−0.453331	−	0.261731i
$979$		−	43.7922i		−	1.39960i
$980$	−0.202267	+	0.0114189i	−0.00646117	+	0.000364764i
$981$			9.75557i			0.311472i
$982$	25.2176	−	43.6781i	0.804725	−	1.39382i
$983$	11.1649	+	19.3381i	0.356104	+	0.616790i	0.987306	−	0.158828i	$-0.0507717\pi$
$983$	11.1649	+	19.3381i	0.356104	+	0.616790i	−0.631203	+	0.775618i	$0.717438\pi$
$984$	−10.9142	−	18.9040i	−0.347932	−	0.602636i
$985$	−11.4347	+	19.8055i	−0.364339	+	0.631054i
$986$	76.2873			2.42948
$987$	−0.352464	−	12.4965i	−0.0112191	−	0.397769i
$988$		−	0.0594240i		−	0.00189053i
$989$	19.5745	+	18.9460i	0.622432	+	0.602449i
$990$	8.92427	−	5.15243i	0.283632	−	0.163755i
$991$	−6.89659	−	11.9452i	−0.219077	−	0.379453i	0.735449	−	0.677580i	$-0.236971\pi$
$991$	−6.89659	−	11.9452i	−0.219077	−	0.379453i	−0.954526	+	0.298127i	$0.903638\pi$
$992$	−0.367484	−	0.212167i	−0.0116676	−	0.00673630i
$993$			15.2271i			0.483219i
$994$	25.4679	+	13.7615i	0.807793	+	0.436488i
$995$	−42.3425			−1.34235
$996$	−0.0814981	−	0.0470530i	−0.00258237	−	0.00149093i
$997$	−50.1189	+	28.9361i	−1.58728	+	0.916417i	−0.593527	+	0.804814i	$0.702265\pi$
$997$	−50.1189	+	28.9361i	−1.58728	+	0.916417i	−0.993753	+	0.111603i	$0.964402\pi$
$998$	−24.8410	−	43.0258i	−0.786327	−	1.36196i
$999$	−0.216929	+	0.375731i	−0.00686332	+	0.0118876i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.j.a.229.7	✓	64
7.3	odd	6	inner	483.2.j.a.367.8	yes	64
23.22	odd	2	inner	483.2.j.a.229.8	yes	64
161.45	even	6	inner	483.2.j.a.367.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.j.a.229.7	✓	64	1.1	even	1	trivial
483.2.j.a.229.8	yes	64	23.22	odd	2	inner
483.2.j.a.367.7	yes	64	161.45	even	6	inner
483.2.j.a.367.8	yes	64	7.3	odd	6	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.708878 + 1.22781i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.00501609 - 0.00868813i) q^{4} +(-1.44242 + 2.49834i) q^{5} -1.41776i q^{6} +(-0.0745936 - 2.64470i) q^{7} -2.82129 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.708878 + 1.22781i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.00501609 - 0.00868813i) q^{4} +(-1.44242 + 2.49834i) q^{5} -1.41776i q^{6} +(-0.0745936 - 2.64470i) q^{7} -2.82129 q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.04500 - 3.54204i) q^{10} +(-2.18197 + 1.25976i) q^{11} +(0.00868813 + 0.00501609i) q^{12} +2.09916i q^{13} +(3.30007 + 1.78318i) q^{14} -2.88484i q^{15} +(2.00998 - 3.48139i) q^{16} +(-3.05763 - 5.29598i) q^{17} +(0.708878 + 1.22781i) q^{18} +(1.41088 - 2.44372i) q^{19} +0.0289412 q^{20} +(1.38695 + 2.25308i) q^{21} -3.57208i q^{22} +(-3.33540 + 3.44603i) q^{23} +(2.44331 - 1.41064i) q^{24} +(-1.66114 - 2.87719i) q^{25} +(-2.57737 - 1.48805i) q^{26} +1.00000i q^{27} +(-0.0226033 + 0.0139141i) q^{28} +8.79903 q^{29} +(3.54204 + 2.04500i) q^{30} +(-6.47547 + 3.73862i) q^{31} +(0.0283750 + 0.0491470i) q^{32} +(1.25976 - 2.18197i) q^{33} +8.66996 q^{34} +(6.71496 + 3.62840i) q^{35} -0.0100322 q^{36} +(0.375731 + 0.216929i) q^{37} +(2.00029 + 3.46460i) q^{38} +(-1.04958 - 1.81793i) q^{39} +(4.06948 - 7.04855i) q^{40} -7.73703i q^{41} +(-3.74954 + 0.105756i) q^{42} -5.68029i q^{43} +(0.0218900 + 0.0126382i) q^{44} +(1.44242 + 2.49834i) q^{45} +(-1.86669 - 6.53806i) q^{46} +(-4.09208 - 2.36256i) q^{47} +4.01996i q^{48} +(-6.98887 + 0.394555i) q^{49} +4.71020 q^{50} +(5.29598 + 3.05763i) q^{51} +(0.0182378 - 0.0105296i) q^{52} +(4.31887 - 2.49350i) q^{53} +(-1.22781 - 0.708878i) q^{54} -7.26843i q^{55} +(0.210450 + 7.46146i) q^{56} +2.82176i q^{57} +(-6.23744 + 10.8036i) q^{58} +(-9.85730 + 5.69112i) q^{59} +(-0.0250638 + 0.0144706i) q^{60} +(2.33209 - 4.03929i) q^{61} -10.6009i q^{62} +(-2.32767 - 1.25775i) q^{63} +7.95947 q^{64} +(-5.24442 - 3.02787i) q^{65} +(1.78604 + 3.09351i) q^{66} +(-12.2054 + 7.04681i) q^{67} +(-0.0306748 + 0.0531302i) q^{68} +(1.16552 - 4.65205i) q^{69} +(-9.21509 + 5.67262i) q^{70} +7.71738 q^{71} +(-1.41064 + 2.44331i) q^{72} +(-1.18791 + 0.685840i) q^{73} +(-0.532695 + 0.307552i) q^{74} +(2.87719 + 1.66114i) q^{75} -0.0283085 q^{76} +(3.49446 + 5.67670i) q^{77} +2.97610 q^{78} +(-3.43697 - 1.98433i) q^{79} +(5.79847 + 10.0432i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(9.49963 + 5.48461i) q^{82} -9.38040 q^{83} +(0.0126180 - 0.0233517i) q^{84} +17.6416 q^{85} +(6.97434 + 4.02664i) q^{86} +(-7.62019 + 4.39952i) q^{87} +(6.15598 - 3.55416i) q^{88} +(-8.69055 + 15.0525i) q^{89} -4.09000 q^{90} +(5.55165 - 0.156584i) q^{91} +(0.0466702 + 0.0116928i) q^{92} +(3.73862 - 6.47547i) q^{93} +(5.80157 - 3.34954i) q^{94} +(4.07017 + 7.04974i) q^{95} +(-0.0491470 - 0.0283750i) q^{96} -13.3432 q^{97} +(4.46982 - 8.86072i) q^{98} +2.51953i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50} - 108 q^{52} - 24 q^{58} + 36 q^{59} + 168 q^{64} - 40 q^{70} - 16 q^{71} - 12 q^{72} + 48 q^{73} - 48 q^{75} - 32 q^{78} - 32 q^{81} - 24 q^{82} + 88 q^{85} + 36 q^{87} + 152 q^{92} + 24 q^{93} - 108 q^{94} - 44 q^{95} + 60 q^{96} + 112 q^{98}+O(q^{100}) \) 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

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