LMFDB - Embedded newform 483.2.j.a.229.8

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			229.8
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.8

$q$-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} +(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} +(-1.31665 + 4.61155i) 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} +(-4.72878 - 4.88563i) 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} - 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}+ \cdots + 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

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	$-0.610162\pi$
$5$	1.44242	−	2.49834i	0.645069	−	1.11729i	0.984285	−	0.176584i	$-0.0565049\pi$
$6$		−	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	−0.133582	−	0.991038i	$-0.542648\pi$
$11$	2.18197	−	1.25976i	0.657890	−	0.379833i	0.791473	+	0.611205i	$0.209315\pi$
$12$	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	$0.0992590\pi$
$17$	3.05763	+	5.29598i	0.741585	+	1.28446i	−0.210188	+	0.977661i	$0.567408\pi$
$18$	0.708878	+	1.22781i	0.167084	+	0.289398i
$19$	−1.41088	+	2.44372i	−0.323679	+	0.560628i	−0.981244	−	0.192770i	$-0.938253\pi$
$19$	−1.41088	+	2.44372i	−0.323679	+	0.560628i	0.657565	+	0.753397i	$0.271586\pi$
$20$	−0.0289412			−0.00647146
$21$	−1.38695	−	2.25308i	−0.302657	−	0.491662i
$22$			3.57208i			0.761569i
$23$	−1.31665	+	4.61155i	−0.274541	+	0.961576i
$23$	−1.31665	+	4.61155i	−0.274541	+	0.961576i
$24$	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	0.468797	−	0.883306i	$-0.344688\pi$
$37$	−0.375731	−	0.216929i	−0.0617699	−	0.0356628i	−0.530567	+	0.847643i	$0.678021\pi$
$38$	−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	$0.142587\pi$
$43$			5.68029i			0.866237i	−0.901337	+	0.433118i	$0.857413\pi$
$44$	−0.0218900	−	0.0126382i	−0.00330004	−	0.00190528i
$45$	−1.44242	−	2.49834i	−0.215023	−	0.372431i
$46$	−4.72878	−	4.88563i	−0.697221	−	0.720347i
$47$	−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	−0.766379	−	0.642389i	$-0.777943\pi$
$53$	−4.31887	+	2.49350i	−0.593242	+	0.342509i	0.173136	+	0.984898i	$0.444610\pi$
$54$	−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	−0.975814	−	0.218601i	$-0.929851\pi$
$61$	−2.33209	+	4.03929i	−0.298593	+	0.517178i	0.677221	+	0.735779i	$0.263184\pi$
$62$		−	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	0.491183	−	0.871056i	$-0.336565\pi$
$67$	12.2054	−	7.04681i	1.49113	−	0.860905i	0.999948	+	0.0101508i	$0.00323117\pi$
$68$	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	0.680725	−	0.732539i	$-0.261665\pi$
$79$	3.43697	+	1.98433i	0.386689	+	0.223255i	−0.294035	+	0.955795i	$0.594998\pi$
$80$	−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	$-0.327860\pi$
$83$	9.38040			1.02963			0.514816	+	0.857300i	$0.327860\pi$
$84$	−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	$-0.460547\pi$
$89$	8.69055	−	15.0525i	0.921196	−	1.59556i	0.797567	−	0.603230i	$-0.206120\pi$
$90$	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	$-0.263107\pi$
$97$	13.3432			1.35480			0.677400	+	0.735615i	$0.263107\pi$
$98$	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	−0.845646	−	0.533744i	$-0.820785\pi$
$103$	0.399991	−	0.692805i	0.0394123	−	0.0682641i	0.885059	+	0.465479i	$0.154118\pi$
$104$		−	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	0.704862	−	0.709344i	$-0.251009\pi$
$107$	4.58225	+	2.64556i	0.442983	+	0.255756i	−0.261879	+	0.965101i	$0.584342\pi$
$108$	0.00868813	−	0.00501609i	0.000836016	−	0.000482674i
$109$	8.44858	−	4.87779i	0.809227	−	0.467207i	−0.0374605	−	0.999298i	$-0.511927\pi$
$109$	8.44858	−	4.87779i	0.809227	−	0.467207i	0.846687	+	0.532091i	$0.178594\pi$
$110$	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	$-0.777800\pi$
$113$		−	13.6647i		−	1.28547i	0.766088	−	0.642735i	$-0.222200\pi$
$114$	3.46460	+	2.00029i	0.324489	+	0.187344i
$115$	9.62208	+	9.94124i	0.897264	+	0.927025i
$116$	−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	−0.961797	−	0.273763i	$-0.911732\pi$
$137$	−14.1113	+	8.14716i	−1.20561	+	0.696059i	−0.243813	+	0.969822i	$0.578398\pi$
$138$	6.53806	+	1.86669i	0.556557	+	0.158903i
$139$			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	0.310174	−	0.950680i	$-0.399613\pi$
$149$	−4.37058	−	2.52336i	−0.358052	−	0.206721i	−0.668226	+	0.743958i	$0.732946\pi$
$150$	−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	0.666521	−	0.745487i	$-0.267783\pi$
$157$	−3.91373	−	6.77879i	−0.312350	−	0.541006i	−0.978871	+	0.204481i	$0.934449\pi$
$158$	−4.87278	+	2.81330i	−0.387658	+	0.223814i
$159$	2.49350	−	4.31887i	0.197747	−	0.342509i
$160$	0.163715			0.0129428
$161$	−12.2944	−	3.13815i	−0.968934	−	0.247321i
$162$	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	$-0.353176\pi$
$181$	11.9758			0.890157			0.445078	+	0.895492i	$0.353176\pi$
$182$	3.74318	−	6.92738i	0.277463	−	0.513492i
$183$		−	4.66417i		−	0.344785i
$184$	3.71465	−	13.0105i	0.273848	−	0.959149i
$185$	−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	0.495632	−	0.868533i	$-0.334937\pi$
$191$	−0.120570	−	0.0696114i	−0.00872417	−	0.00503690i	−0.504356	+	0.863496i	$0.668270\pi$
$192$	−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	$-0.992511\pi$
$199$	−7.33880	−	12.7112i	−0.520234	−	0.901072i	0.479489	−	0.877548i	$-0.340822\pi$
$200$	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
$207$	3.33540	+	3.44603i	0.231826	+	0.239516i
$208$	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	0.922721	−	0.385470i	$-0.125961\pi$
$227$	1.92149	+	3.32812i	0.127534	+	0.220895i	−0.795187	+	0.606365i	$0.792627\pi$
$228$	−0.0245159	+	0.0141542i	−0.00162360	+	0.000937387i
$229$	−5.59104	+	9.68397i	−0.369467	+	0.639935i	−0.989482	−	0.144655i	$-0.953793\pi$
$229$	−5.59104	+	9.68397i	−0.369467	+	0.639935i	0.620016	+	0.784589i	$0.287126\pi$
$230$	−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	0.588687	−	0.808361i	$-0.299645\pi$
$241$	−6.29844	−	10.9092i	−0.405718	−	0.702724i	−0.994405	+	0.105637i	$0.966312\pi$
$242$	−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	$-0.818462\pi$
$251$	−26.6710			−1.68346			−0.841729	+	0.539901i	$0.818462\pi$
$252$	−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	$-0.188673\pi$
$263$	28.0220	−	16.1785i	1.72791	−	0.997611i	0.898497	−	0.438980i	$-0.144660\pi$
$264$	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
$276$	−0.0345712	+	0.0334613i	−0.00208094	+	0.00201414i
$277$	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	$-0.790829\pi$
$281$		−	20.4793i		−	1.22169i	0.791749	−	0.610847i	$-0.209171\pi$
$282$	−3.34954	+	5.80157i	−0.199462	+	0.345478i
$283$	−9.04218	−	15.6615i	−0.537502	−	0.930980i	−0.999038	−	0.0438586i	$-0.986035\pi$
$283$	−9.04218	−	15.6615i	−0.537502	−	0.930980i	0.461536	−	0.887121i	$-0.347298\pi$
$284$	−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	$-0.679468\pi$
$293$	−18.2954			−1.06883			−0.534415	+	0.845222i	$0.679468\pi$
$294$	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
$299$	−9.68039	−	2.76386i	−0.559831	−	0.159838i
$300$		−	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	−0.948819	−	0.315821i	$-0.897720\pi$
$313$	−3.55429	+	6.15621i	−0.200900	+	0.347970i	0.747918	+	0.663791i	$0.231053\pi$
$314$	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
$322$	12.5683	−	12.8706i	0.700403	−	0.717253i
$323$	−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	$-0.962019\pi$
$337$		−	4.37048i		−	0.238075i	0.992890	−	0.119038i	$-0.0379809\pi$
$338$	−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
$345$	−13.3036	−	3.79832i	−0.716241	−	0.204495i
$346$	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	$0.0974949\pi$
$359$	32.0458	+	18.5017i	1.69131	+	0.976481i	0.737856	+	0.674958i	$0.235838\pi$
$360$	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	0.997615	−	0.0690305i	$-0.0219906\pi$
$367$	8.41051	+	14.5674i	0.439025	+	0.760414i	−0.558589	+	0.829444i	$0.688657\pi$
$368$	13.4082	+	13.8529i	0.698950	+	0.722133i
$369$	−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	0.896199	−	0.443652i	$-0.146318\pi$
$373$	18.5423	+	10.7054i	0.960084	+	0.554305i	0.0638852	+	0.997957i	$0.479651\pi$
$374$	−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	$-0.943375\pi$
$379$		−	6.88991i		−	0.353911i	0.984219	−	0.176956i	$-0.0566249\pi$
$380$	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	$0.419549\pi$
$383$	−13.9631	+	24.1848i	−0.713481	+	1.23578i	−0.963543	+	0.267555i	$0.913784\pi$
$384$		−	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	−0.362962	−	0.931804i	$-0.618235\pi$
$389$	5.17774	−	2.98937i	0.262522	−	0.151567i	0.625485	+	0.780237i	$0.284901\pi$
$390$	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	$-0.931314\pi$
$401$	−33.0540	−	19.0838i	−1.65064	−	0.952998i	−0.673831	−	0.738885i	$-0.735353\pi$
$402$	−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	$-0.310673\pi$
$419$	22.9395			1.12067			0.560334	+	0.828267i	$0.310673\pi$
$420$	0.0401400	+	0.0652069i	0.00195863	+	0.00318177i
$421$		−	38.2820i		−	1.86575i	−0.360200	−	0.932875i	$-0.617292\pi$
$421$		−	38.2820i		−	1.86575i	0.360200	−	0.932875i	$-0.382708\pi$
$422$	−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	−0.499493	−	0.866318i	$-0.666480\pi$
$431$	0.0210478	−	0.0121519i	0.00101384	−	0.000585338i	0.500507	+	0.865733i	$0.333147\pi$
$432$	3.48139	+	2.00998i	0.167498	+	0.0967053i
$433$	−19.2727			−0.926185			−0.463092	−	0.886310i	$-0.653260\pi$
$433$	−19.2727			−0.926185			−0.463092	+	0.886310i	$0.653260\pi$
$434$	28.0362	−	0.790759i	1.34578	−	0.0379576i
$435$			25.3838i			1.21706i
$436$	−0.0847577	−	0.0489349i	−0.00405916	−	0.00234356i
$437$	−9.41171	−	9.72388i	−0.450223	−	0.465156i
$438$	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	0.848338	−	0.529454i	$-0.177603\pi$
$457$	17.4011	+	10.0465i	0.813987	+	0.469956i	−0.0343516	+	0.999410i	$0.510937\pi$
$458$	−7.92674	−	13.7295i	−0.370392	−	0.641538i
$459$	−5.29598	+	3.05763i	−0.247195	+	0.142718i
$460$	0.0381055	−	0.133464i	0.00177668	−	0.00622279i
$461$			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	−0.638356	−	0.769741i	$-0.720385\pi$
$467$	7.50819	−	13.0046i	0.347438	−	0.601780i	0.985794	+	0.167962i	$0.0537185\pi$
$468$		−	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	0.905282	−	0.424810i	$-0.139659\pi$
$479$	1.85472	+	3.21247i	0.0847445	+	0.146782i	−0.820538	+	0.571592i	$0.806326\pi$
$480$	−0.141781	+	0.0818574i	−0.00647140	+	0.00373626i
$481$	0.455368	−	0.788720i	0.0207630	−	0.0359625i
$482$	17.8593			0.813468
$483$	12.2163	−	3.42947i	0.555862	−	0.156047i
$484$	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	$-0.534260\pi$
$503$	−4.81854			−0.214848			−0.107424	+	0.994213i	$0.534260\pi$
$504$	−6.56704	−	3.54848i	−0.292519	−	0.158062i
$505$		−	1.76597i		−	0.0785844i
$506$	−16.4728	−	4.70317i	−0.732306	−	0.209082i
$507$	−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	0.939206	−	0.343355i	$-0.111563\pi$
$521$	3.93165	+	6.80981i	0.172249	+	0.298343i	−0.766957	+	0.641698i	$0.778230\pi$
$522$	6.23744	+	10.8036i	0.273005	+	0.472859i
$523$	7.09281	−	12.2851i	0.310147	−	0.537190i	−0.668247	−	0.743939i	$-0.732955\pi$
$523$	7.09281	−	12.2851i	0.310147	−	0.537190i	0.978394	+	0.206749i	$0.0662884\pi$
$524$			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
$529$	−19.5329	−	12.1436i	−0.849255	−	0.527983i
$530$	−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	−0.716708	−	0.697374i	$-0.754352\pi$
$557$	−11.1188	+	6.41944i	−0.471118	+	0.272000i	0.245589	+	0.969374i	$0.421019\pi$
$558$	−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	$-0.872958\pi$
$563$	−18.9166	−	32.7646i	−0.797241	−	1.38086i	0.124165	−	0.992262i	$-0.460375\pi$
$564$	−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	0.993892	−	0.110361i	$-0.0352007\pi$
$569$	33.2822	+	19.2155i	1.39526	+	0.805555i	0.401370	+	0.915916i	$0.368534\pi$
$570$	9.99480	−	5.77050i	0.418636	−	0.241700i
$571$	−22.3491	+	12.9032i	−0.935280	+	0.539984i	−0.888478	−	0.458920i	$-0.848236\pi$
$571$	−22.3491	+	12.9032i	−0.935280	+	0.539984i	−0.0468022	+	0.998904i	$0.514903\pi$
$572$	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
$598$	10.2557	−	9.92646i	0.419387	−	0.405923i
$599$	−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	−0.266145	−	0.963933i	$-0.585750\pi$
$613$	10.7843	−	6.22631i	0.435573	−	0.251478i	0.701718	+	0.712455i	$0.252417\pi$
$614$	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	$-0.933696\pi$
$617$		−	10.2735i		−	0.413594i	0.978384	−	0.206797i	$-0.0663039\pi$
$618$	−0.982228	−	0.567090i	−0.0395110	−	0.0228117i
$619$	−6.08049	−	10.5317i	−0.244395	−	0.423305i	0.717566	−	0.696490i	$-0.245256\pi$
$619$	−6.08049	−	10.5317i	−0.244395	−	0.423305i	−0.961961	+	0.273185i	$0.911923\pi$
$620$	0.187408	−	0.108200i	0.00752650	−	0.00434542i
$621$	−4.61155	−	1.31665i	−0.185055	−	0.0528354i
$622$			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	$0.0329605\pi$
$631$			5.19292i			0.206727i	−0.994644	+	0.103363i	$0.967040\pi$
$632$	−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	−0.809273	−	0.587433i	$-0.800139\pi$
$641$	−17.8537	+	10.3078i	−0.705178	+	0.407135i	0.104095	+	0.994567i	$0.466805\pi$
$642$	3.75076	−	6.49651i	0.148031	−	0.256397i
$643$	19.7820			0.780126			0.390063	−	0.920788i	$-0.372453\pi$
$643$	19.7820			0.780126			0.390063	+	0.920788i	$0.372453\pi$
$644$	0.0344051	+	0.122557i	0.00135575	+	0.00482940i
$645$	−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	$0.00201347\pi$
$659$			0.324762i			0.0126509i	−0.999980	+	0.00632547i	$0.997987\pi$
$660$	0.0364591	−	0.0631491i	0.00141917	−	0.00245807i
$661$	3.76538	+	6.52183i	0.146456	+	0.253670i	0.929915	−	0.367774i	$-0.119880\pi$
$661$	3.76538	+	6.52183i	0.146456	+	0.253670i	−0.783459	+	0.621443i	$0.786547\pi$
$662$	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
$667$	−11.5853	+	40.5772i	−0.448583	+	1.57116i
$668$	−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	−0.992803	−	0.119757i	$-0.961788\pi$
$677$	−10.2175	+	17.6972i	−0.392689	+	0.680157i	0.600114	+	0.799914i	$0.295122\pi$
$678$	−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
$690$	14.0942	−	13.6418i	0.536559	−	0.519333i
$691$	−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	$0.0452906\pi$
$701$			7.50897i			0.283610i	−0.989895	+	0.141805i	$0.954709\pi$
$702$	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	0.821474	−	0.570246i	$-0.193152\pi$
$709$	19.6605	+	11.3510i	0.738364	+	0.426295i	−0.0831103	+	0.996540i	$0.526485\pi$
$710$	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	$-0.410392\pi$
$727$	14.9811			0.555617			0.277809	+	0.960636i	$0.410392\pi$
$728$	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	$0.431884\pi$
$733$	−20.0372	+	34.7055i	−0.740091	+	1.28188i	−0.952453	+	0.304685i	$0.901449\pi$
$734$	−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	$-0.907116\pi$
$743$		−	15.6831i		−	0.575359i	0.957727	−	0.287679i	$-0.0928838\pi$
$744$	−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	0.950342	−	0.311206i	$-0.100733\pi$
$751$	31.6795	+	18.2902i	1.15600	+	0.667417i	0.205659	+	0.978624i	$0.434066\pi$
$752$	−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	$0.327251\pi$
$757$			47.1206i			1.71263i	−0.516457	+	0.856313i	$0.672749\pi$
$758$	8.45953	+	4.88411i	0.307264	+	0.177399i
$759$	−8.40363	−	8.68237i	−0.305032	−	0.315150i
$760$	−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	$-0.170518\pi$
$769$	47.6922			1.71983			0.859913	+	0.510441i	$0.170518\pi$
$770$	−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	−

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} +(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} +(-1.31665 + 4.61155i) 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} +(-4.72878 - 4.88563i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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