LMFDB - Embedded newform 192.2.r.a.157.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(13,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.r (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			157.16
Character	$\chi$	$=$	192.157
Dual form			192.2.r.a.181.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41364 - 0.0401896i) q^{2} +(0.980785 + 0.195090i) q^{3} +(1.99677 - 0.113627i) q^{4} +(-1.10999 + 1.66121i) q^{5} +(1.39432 + 0.236371i) q^{6} +(-1.97014 + 0.816058i) q^{7} +(2.81815 - 0.240878i) q^{8} +(0.923880 + 0.382683i) q^{9} +O(q^{10})$	\(q+(1.41364 - 0.0401896i) q^{2} +(0.980785 + 0.195090i) q^{3} +(1.99677 - 0.113627i) q^{4} +(-1.10999 + 1.66121i) q^{5} +(1.39432 + 0.236371i) q^{6} +(-1.97014 + 0.816058i) q^{7} +(2.81815 - 0.240878i) q^{8} +(0.923880 + 0.382683i) q^{9} +(-1.50236 + 2.39297i) q^{10} +(-0.842610 - 4.23609i) q^{11} +(1.98057 + 0.278106i) q^{12} +(0.0329800 + 0.0493581i) q^{13} +(-2.75228 + 1.23279i) q^{14} +(-1.41274 + 1.41274i) q^{15} +(3.97418 - 0.453775i) q^{16} +(-5.58211 - 5.58211i) q^{17} +(1.32142 + 0.503847i) q^{18} +(0.497860 - 0.332660i) q^{19} +(-2.02763 + 3.44318i) q^{20} +(-2.09149 + 0.416023i) q^{21} +(-1.36140 - 5.95445i) q^{22} +(0.591778 - 1.42868i) q^{23} +(2.81099 + 0.313545i) q^{24} +(0.385862 + 0.931552i) q^{25} +(0.0486057 + 0.0684493i) q^{26} +(0.831470 + 0.555570i) q^{27} +(-3.84119 + 1.85334i) q^{28} +(-1.85270 + 9.31417i) q^{29} +(-1.94034 + 2.05389i) q^{30} -2.71983i q^{31} +(5.59983 - 0.801196i) q^{32} -4.31907i q^{33} +(-8.11545 - 7.66677i) q^{34} +(0.831182 - 4.17863i) q^{35} +(1.88826 + 0.659153i) q^{36} +(7.23331 + 4.83314i) q^{37} +(0.690427 - 0.490270i) q^{38} +(0.0227170 + 0.0548438i) q^{39} +(-2.72796 + 4.94892i) q^{40} +(-3.74021 + 9.02966i) q^{41} +(-2.93990 + 0.672164i) q^{42} +(1.17912 - 0.234541i) q^{43} +(-2.16383 - 8.36274i) q^{44} +(-1.66121 + 1.10999i) q^{45} +(0.779145 - 2.04342i) q^{46} +(-6.16559 - 6.16559i) q^{47} +(3.98634 + 0.330268i) q^{48} +(-1.73425 + 1.73425i) q^{49} +(0.582909 + 1.30137i) q^{50} +(-4.38584 - 6.56387i) q^{51} +(0.0714620 + 0.0948093i) q^{52} +(-0.912311 - 4.58650i) q^{53} +(1.19773 + 0.751961i) q^{54} +(7.97232 + 3.30224i) q^{55} +(-5.35558 + 2.77434i) q^{56} +(0.553193 - 0.229140i) q^{57} +(-2.24473 + 13.2414i) q^{58} +(1.50493 - 2.25229i) q^{59} +(-2.66040 + 2.98145i) q^{60} +(-2.18682 - 0.434985i) q^{61} +(-0.109309 - 3.84486i) q^{62} -2.13246 q^{63} +(7.88396 - 1.35766i) q^{64} -0.118602 q^{65} +(-0.173582 - 6.10563i) q^{66} +(14.1219 + 2.80902i) q^{67} +(-11.7805 - 10.5119i) q^{68} +(0.859128 - 1.28578i) q^{69} +(1.00706 - 5.94050i) q^{70} +(-0.535260 + 0.221712i) q^{71} +(2.69581 + 0.855918i) q^{72} +(-2.44344 - 1.01210i) q^{73} +(10.4196 + 6.54163i) q^{74} +(0.196711 + 0.988931i) q^{75} +(0.956313 - 0.720815i) q^{76} +(5.11695 + 7.65806i) q^{77} +(0.0343179 + 0.0766165i) q^{78} +(-6.21967 + 6.21967i) q^{79} +(-3.65747 + 7.10564i) q^{80} +(0.707107 + 0.707107i) q^{81} +(-4.92442 + 12.9150i) q^{82} +(4.16682 - 2.78418i) q^{83} +(-4.12895 + 1.06835i) q^{84} +(15.4691 - 3.07700i) q^{85} +(1.65742 - 0.378945i) q^{86} +(-3.63421 + 8.77375i) q^{87} +(-3.39498 - 11.7350i) q^{88} +(-0.479081 - 1.15660i) q^{89} +(-2.30375 + 1.63589i) q^{90} +(-0.105254 - 0.0703287i) q^{91} +(1.01931 - 2.91998i) q^{92} +(0.530612 - 2.66756i) q^{93} +(-8.96373 - 8.46815i) q^{94} +1.19630i q^{95} +(5.64854 + 0.306671i) q^{96} -0.928685i q^{97} +(-2.38191 + 2.52131i) q^{98} +(0.842610 - 4.23609i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{16}\right)$

Coefficient data

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

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

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

$2$	1.41364	−	0.0401896i	0.999596	−	0.0284183i
$2$	1.41364	−	0.0401896i	0.999596	−	0.0284183i
$3$	0.980785	+	0.195090i	0.566257	+	0.112635i
$3$	0.980785	+	0.195090i	0.566257	+	0.112635i
$4$	1.99677	−	0.113627i	0.998385	−	0.0568137i
$5$	−1.10999	+	1.66121i	−0.496401	+	0.742917i	−0.992083	−	0.125588i	$-0.959918\pi$
$5$	−1.10999	+	1.66121i	−0.496401	+	0.742917i	0.495682	+	0.868504i	$0.334918\pi$
$6$	1.39432	+	0.236371i	0.569229	+	0.0964979i
$7$	−1.97014	+	0.816058i	−0.744643	+	0.308441i	−0.722554	−	0.691315i	$-0.757032\pi$
$7$	−1.97014	+	0.816058i	−0.744643	+	0.308441i	−0.0220891	+	0.999756i	$0.507032\pi$
$8$	2.81815	−	0.240878i	0.996367	−	0.0851631i
$9$	0.923880	+	0.382683i	0.307960	+	0.127561i
$10$	−1.50236	+	2.39297i	−0.475088	+	0.756723i
$11$	−0.842610	−	4.23609i	−0.254056	−	1.27723i	−0.871415	−	0.490546i	$-0.836797\pi$
$11$	−0.842610	−	4.23609i	−0.254056	−	1.27723i	0.617359	−	0.786682i	$-0.288203\pi$
$12$	1.98057	+	0.278106i	0.571741	+	0.0802824i
$13$	0.0329800	+	0.0493581i	0.00914702	+	0.0136895i	0.836015	−	0.548707i	$-0.184880\pi$
$13$	0.0329800	+	0.0493581i	0.00914702	+	0.0136895i	−0.826868	+	0.562396i	$0.809880\pi$
$14$	−2.75228	+	1.23279i	−0.735577	+	0.329478i
$15$	−1.41274	+	1.41274i	−0.364769	+	0.364769i
$16$	3.97418	−	0.453775i	0.993544	−	0.113444i
$17$	−5.58211	−	5.58211i	−1.35386	−	1.35386i	−0.881296	−	0.472565i	$-0.843328\pi$
$17$	−5.58211	−	5.58211i	−1.35386	−	1.35386i	−0.472565	−	0.881296i	$-0.656672\pi$
$18$	1.32142	+	0.503847i	0.311461	+	0.118758i
$19$	0.497860	−	0.332660i	0.114217	−	0.0763173i	−0.497150	−	0.867665i	$-0.665620\pi$
$19$	0.497860	−	0.332660i	0.114217	−	0.0763173i	0.611367	+	0.791347i	$0.290620\pi$
$20$	−2.02763	+	3.44318i	−0.453391	+	0.769919i
$21$	−2.09149	+	0.416023i	−0.456400	+	0.0907837i
$22$	−1.36140	−	5.95445i	−0.290250	−	1.26949i
$23$	0.591778	−	1.42868i	0.123394	−	0.297900i	−0.850096	−	0.526627i	$-0.823456\pi$
$23$	0.591778	−	1.42868i	0.123394	−	0.297900i	0.973491	+	0.228727i	$0.0734564\pi$
$24$	2.81099	+	0.313545i	0.573792	+	0.0640021i
$25$	0.385862	+	0.931552i	0.0771723	+	0.186310i
$26$	0.0486057	+	0.0684493i	0.00953235	+	0.0134240i
$27$	0.831470	+	0.555570i	0.160016	+	0.106920i
$28$	−3.84119	+	1.85334i	−0.725916	+	0.350249i
$29$	−1.85270	+	9.31417i	−0.344038	+	1.72960i	0.290650	+	0.956829i	$0.406128\pi$
$29$	−1.85270	+	9.31417i	−0.344038	+	1.72960i	−0.634689	+	0.772768i	$0.718872\pi$
$30$	−1.94034	+	2.05389i	−0.354256	+	0.374988i
$31$		−	2.71983i		−	0.488495i	−0.969713	−	0.244248i	$-0.921459\pi$
$31$		−	2.71983i		−	0.488495i	0.969713	−	0.244248i	$-0.0785409\pi$
$32$	5.59983	−	0.801196i	0.989919	−	0.141633i
$33$		−	4.31907i		−	0.751854i
$34$	−8.11545	−	7.66677i	−1.39179	−	1.31484i
$35$	0.831182	−	4.17863i	0.140495	−	0.706318i
$36$	1.88826	+	0.659153i	0.314710	+	0.109859i
$37$	7.23331	+	4.83314i	1.18915	+	0.794564i	0.982937	−	0.183943i	$-0.0588863\pi$
$37$	7.23331	+	4.83314i	1.18915	+	0.794564i	0.206212	+	0.978507i	$0.433886\pi$
$38$	0.690427	−	0.490270i	0.112002	−	0.0795324i
$39$	0.0227170	+	0.0548438i	0.00363764	+	0.00878204i
$40$	−2.72796	+	4.94892i	−0.431328	+	0.782493i
$41$	−3.74021	+	9.02966i	−0.584122	+	1.41020i	0.304924	+	0.952377i	$0.401369\pi$
$41$	−3.74021	+	9.02966i	−0.584122	+	1.41020i	−0.889046	+	0.457819i	$0.848631\pi$
$42$	−2.93990	+	0.672164i	−0.453636	+	0.103717i
$43$	1.17912	−	0.234541i	0.179813	−	0.0357671i	−0.104362	−	0.994539i	$-0.533280\pi$
$43$	1.17912	−	0.234541i	0.179813	−	0.0357671i	0.284176	+	0.958772i	$0.408280\pi$
$44$	−2.16383	−	8.36274i	−0.326210	−	1.26073i
$45$	−1.66121	+	1.10999i	−0.247639	+	0.165467i
$46$	0.779145	−	2.04342i	0.114879	−	0.301286i
$47$	−6.16559	−	6.16559i	−0.899344	−	0.899344i	0.0960341	−	0.995378i	$-0.469384\pi$
$47$	−6.16559	−	6.16559i	−0.899344	−	0.899344i	−0.995378	+	0.0960341i	$0.969384\pi$
$48$	3.98634	+	0.330268i	0.575379	+	0.0476700i
$49$	−1.73425	+	1.73425i	−0.247750	+	0.247750i
$50$	0.582909	+	1.30137i	0.0824358	+	0.184042i
$51$	−4.38584	−	6.56387i	−0.614140	−	0.919126i
$52$	0.0714620	+	0.0948093i	0.00990999	+	0.0131477i
$53$	−0.912311	−	4.58650i	−0.125316	−	0.630004i	−0.991482	−	0.130247i	$-0.958423\pi$
$53$	−0.912311	−	4.58650i	−0.125316	−	0.630004i	0.866166	−	0.499756i	$-0.166577\pi$
$54$	1.19773	+	0.751961i	0.162990	+	0.102329i
$55$	7.97232	+	3.30224i	1.07499	+	0.445274i
$56$	−5.35558	+	2.77434i	−0.715670	+	0.370737i
$57$	0.553193	−	0.229140i	0.0732721	−	0.0303503i
$58$	−2.24473	+	13.2414i	−0.294747	+	1.73868i
$59$	1.50493	−	2.25229i	0.195925	−	0.293223i	−0.720479	−	0.693477i	$-0.756078\pi$
$59$	1.50493	−	2.25229i	0.195925	−	0.293223i	0.916404	+	0.400254i	$0.131078\pi$
$60$	−2.66040	+	2.98145i	−0.343456	+	0.384904i
$61$	−2.18682	−	0.434985i	−0.279993	−	0.0556941i	0.0530962	−	0.998589i	$-0.483091\pi$
$61$	−2.18682	−	0.434985i	−0.279993	−	0.0556941i	−0.333089	+	0.942895i	$0.608091\pi$
$62$	−0.109309	−	3.84486i	−0.0138822	−	0.488298i
$63$	−2.13246			−0.268665
$64$	7.88396	−	1.35766i	0.985494	−	0.169707i
$65$	−0.118602			−0.0147107
$66$	−0.173582	−	6.10563i	−0.0213664	−	0.751551i
$67$	14.1219	+	2.80902i	1.72526	+	0.343176i	0.955463	−	0.295111i	$-0.0953566\pi$
$67$	14.1219	+	2.80902i	1.72526	+	0.343176i	0.769799	+	0.638287i	$0.220357\pi$
$68$	−11.7805	−	10.5119i	−1.42859	−	1.27476i
$69$	0.859128	−	1.28578i	0.103427	−	0.154789i
$70$	1.00706	−	5.94050i	0.120366	−	0.710025i
$71$	−0.535260	+	0.221712i	−0.0635237	+	0.0263124i	−0.414219	−	0.910177i	$-0.635945\pi$
$71$	−0.535260	+	0.221712i	−0.0635237	+	0.0263124i	0.350695	+	0.936490i	$0.385945\pi$
$72$	2.69581	+	0.855918i	0.317705	+	0.100871i
$73$	−2.44344	−	1.01210i	−0.285983	−	0.118458i	0.235081	−	0.971976i	$-0.424465\pi$
$73$	−2.44344	−	1.01210i	−0.285983	−	0.118458i	−0.521063	+	0.853518i	$0.674465\pi$
$74$	10.4196	+	6.54163i	1.21125	+	0.760449i
$75$	0.196711	+	0.988931i	0.0227142	+	0.114192i
$76$	0.956313	−	0.720815i	0.109697	−	0.0826831i
$77$	5.11695	+	7.65806i	0.583131	+	0.872717i
$78$	0.0343179	+	0.0766165i	0.00388574	+	0.00867511i
$79$	−6.21967	+	6.21967i	−0.699768	+	0.699768i	−0.964360	−	0.264592i	$-0.914763\pi$
$79$	−6.21967	+	6.21967i	−0.699768	+	0.699768i	0.264592	+	0.964360i	$0.414763\pi$
$80$	−3.65747	+	7.10564i	−0.408917	+	0.794434i
$81$	0.707107	+	0.707107i	0.0785674	+	0.0785674i
$82$	−4.92442	+	12.9150i	−0.543811	+	1.42623i
$83$	4.16682	−	2.78418i	0.457368	−	0.305604i	−0.305460	−	0.952205i	$-0.598810\pi$
$83$	4.16682	−	2.78418i	0.457368	−	0.305604i	0.762828	+	0.646601i	$0.223810\pi$
$84$	−4.12895	+	1.06835i	−0.450505	+	0.116567i
$85$	15.4691	−	3.07700i	1.67786	−	0.333748i
$86$	1.65742	−	0.378945i	0.178724	−	0.0408627i
$87$	−3.63421	+	8.77375i	−0.389628	+	0.940645i
$88$	−3.39498	−	11.7350i	−0.361906	−	1.25095i
$89$	−0.479081	−	1.15660i	−0.0507825	−	0.122600i	0.896452	−	0.443140i	$-0.146136\pi$
$89$	−0.479081	−	1.15660i	−0.0507825	−	0.122600i	−0.947235	+	0.320540i	$0.896136\pi$
$90$	−2.30375	+	1.63589i	−0.242837	+	0.172438i
$91$	−0.105254	−	0.0703287i	−0.0110337	−	0.00737245i
$92$	1.01931	−	2.91998i	0.106270	−	0.304429i
$93$	0.530612	−	2.66756i	0.0550219	−	0.276614i
$94$	−8.96373	−	8.46815i	−0.924539	−	0.873423i
$95$			1.19630i			0.122738i
$96$	5.64854	+	0.306671i	0.576501	+	0.0312995i
$97$		−	0.928685i		−	0.0942937i	−0.998888	−	0.0471468i	$-0.984987\pi$
$97$		−	0.928685i		−	0.0942937i	0.998888	−	0.0471468i	$-0.0150129\pi$
$98$	−2.38191	+	2.52131i	−0.240609	+	0.254691i
$99$	0.842610	−	4.23609i	0.0846855	−	0.425743i
$100$	0.876326	+	1.81625i	0.0876326	+	0.181625i
$101$	9.04526	+	6.04385i	0.900037	+	0.601386i	0.917183	−	0.398467i	$-0.130458\pi$
$101$	9.04526	+	6.04385i	0.900037	+	0.601386i	−0.0171452	+	0.999853i	$0.505458\pi$
$102$	−6.46380	−	9.10270i	−0.640012	−	0.901301i
$103$	−1.98179	−	4.78448i	−0.195272	−	0.471428i	0.795668	−	0.605733i	$-0.207120\pi$
$103$	−1.98179	−	4.78448i	−0.195272	−	0.471428i	−0.990940	+	0.134304i	$0.957120\pi$
$104$	0.104832	+	0.131154i	0.0102796	+	0.0128608i
$105$	1.63042	−	3.93619i	0.159113	−	0.384132i
$106$	−1.47401	−	6.44700i	−0.143169	−	0.626188i
$107$	−2.70692	+	0.538439i	−0.261687	+	0.0520529i	−0.324190	−	0.945992i	$-0.605092\pi$
$107$	−2.70692	+	0.538439i	−0.261687	+	0.0520529i	0.0625027	+	0.998045i	$0.480092\pi$
$108$	1.72338	+	1.01487i	0.165832	+	0.0976557i
$109$	6.38579	−	4.26685i	0.611648	−	0.408690i	−0.210801	−	0.977529i	$-0.567607\pi$
$109$	6.38579	−	4.26685i	0.611648	−	0.408690i	0.822449	+	0.568839i	$0.192607\pi$
$110$	11.4027	+	4.34779i	1.08721	+	0.414545i
$111$	6.15143	+	6.15143i	0.583867	+	0.583867i
$112$	−7.45938	+	4.13716i	−0.704845	+	0.390925i
$113$	11.9559	−	11.9559i	1.12471	−	1.12471i	0.133691	−	0.991023i	$-0.457317\pi$
$113$	11.9559	−	11.9559i	1.12471	−	1.12471i	0.991023	−	0.133691i	$-0.0426829\pi$
$114$	0.772807	−	0.346154i	0.0723801	−	0.0324203i
$115$	1.71647	+	2.56888i	0.160062	+	0.239550i
$116$	−2.64108	+	18.8088i	−0.245218	+	1.74635i
$117$	0.0115810	+	0.0582219i	0.00107067	+	0.00538261i
$118$	2.03691	−	3.24441i	0.187513	−	0.298672i
$119$	15.5529	+	6.44221i	1.42573	+	0.590556i
$120$	−3.64103	+	4.32163i	−0.332379	+	0.394509i
$121$	−7.07175	+	2.92922i	−0.642886	+	0.266292i
$122$	−3.10886	−	0.527025i	−0.281463	−	0.0477146i
$123$	−5.42994	+	8.12648i	−0.489601	+	0.732740i
$124$	−0.309046	−	5.43086i	−0.0277532	−	0.487706i
$125$	−11.7735	−	2.34189i	−1.05305	−	0.209465i
$126$	−3.01454	+	0.0857027i	−0.268557	+	0.00763501i
$127$	−18.4252			−1.63497			−0.817486	−	0.575949i	$-0.804633\pi$
$127$	−18.4252			−1.63497			−0.817486	+	0.575949i	$0.804633\pi$
$128$	11.0905	−	2.23610i	0.980274	−	0.197645i
$129$	1.20222			0.105849
$130$	−0.167660	+	0.00476655i	−0.0147048	+	0.000418054i
$131$	12.9302	+	2.57199i	1.12972	+	0.224715i	0.724347	−	0.689436i	$-0.242141\pi$
$131$	12.9302	+	2.57199i	1.12972	+	0.224715i	0.405374	+	0.914151i	$0.367141\pi$
$132$	−0.490765	−	8.62420i	−0.0427156	−	0.750640i
$133$	−0.709384	+	1.06167i	−0.0615114	+	0.0920583i
$134$	20.0762	+	3.40339i	1.73432	+	0.294008i
$135$	−1.84584	+	0.764572i	−0.158865	+	0.0658039i
$136$	−17.0758	−	14.3866i	−1.46424	−	1.23364i
$137$	12.2391	+	5.06960i	1.04566	+	0.433125i	0.838340	−	0.545148i	$-0.183527\pi$
$137$	12.2391	+	5.06960i	1.04566	+	0.433125i	0.207317	+	0.978274i	$0.433527\pi$
$138$	1.16283	−	1.85216i	0.0989863	−	0.157666i
$139$	3.93565	+	19.7858i	0.333817	+	1.67821i	0.674688	+	0.738103i	$0.264278\pi$
$139$	3.93565	+	19.7858i	0.333817	+	1.67821i	−0.340870	+	0.940110i	$0.610722\pi$
$140$	1.18487	−	8.43821i	0.100140	−	0.713159i
$141$	−4.84427	−	7.24997i	−0.407961	−	0.610558i
$142$	−0.747756	+	0.334933i	−0.0627503	+	0.0281070i
$143$	0.181296	−	0.181296i	0.0151607	−	0.0151607i
$144$	3.84531	+	1.10162i	0.320443	+	0.0918015i
$145$	−13.4163	−	13.4163i	−1.11417	−	1.11417i
$146$	−3.49482	−	1.33255i	−0.289234	−	0.110283i
$147$	−2.03926	+	1.36259i	−0.168196	+	0.112385i
$148$	14.9924	+	8.82877i	1.23237	+	0.725721i
$149$	−17.0212	+	3.38574i	−1.39443	+	0.277370i	−0.834428	−	0.551118i	$-0.814202\pi$
$149$	−17.0212	+	3.38574i	−1.39443	+	0.277370i	−0.560007	+	0.828488i	$0.689202\pi$
$150$	0.317823	+	1.39009i	0.0259501	+	0.113500i
$151$	4.42360	−	10.6795i	0.359988	−	0.869087i	−0.635313	−	0.772255i	$-0.719129\pi$
$151$	4.42360	−	10.6795i	0.359988	−	0.869087i	0.995301	−	0.0968323i	$-0.0308711\pi$
$152$	1.32292	−	1.05741i	0.107303	−	0.0857671i
$153$	−3.02102	−	7.29338i	−0.244235	−	0.589635i
$154$	7.54131	+	10.6201i	0.607696	+	0.855793i
$155$	4.51821	+	3.01897i	0.362911	+	0.242489i
$156$	0.0515925	+	0.106929i	0.00413070	+	0.00856118i
$157$	−1.07547	+	5.40676i	−0.0858320	+	0.431507i	0.913844	+	0.406065i	$0.133099\pi$
$157$	−1.07547	+	5.40676i	−0.0858320	+	0.431507i	−0.999676	+	0.0254419i	$0.991901\pi$
$158$	−8.54243	+	9.04236i	−0.679599	+	0.719371i
$159$		−	4.67635i		−	0.370859i
$160$	−4.88478	+	10.1918i	−0.386176	+	0.805734i
$161$			3.29762i			0.259889i
$162$	1.02801	+	0.971178i	0.0807684	+	0.0763029i
$163$	2.42050	−	12.1687i	0.189588	−	0.953125i	−0.762427	−	0.647074i	$-0.775992\pi$
$163$	2.42050	−	12.1687i	0.189588	−	0.953125i	0.952015	−	0.306051i	$-0.0990077\pi$
$164$	−6.44231	+	18.4551i	−0.503060	+	1.44110i
$165$	7.17490	+	4.79411i	0.558565	+	0.373221i
$166$	5.77850	−	4.10330i	0.448499	−	0.318478i
$167$	3.92933	+	9.48624i	0.304061	+	0.734067i	0.999874	+	0.0158452i	$0.00504390\pi$
$167$	3.92933	+	9.48624i	0.304061	+	0.734067i	−0.695814	+	0.718222i	$0.744956\pi$
$168$	−5.79392	+	1.67621i	−0.447011	+	0.129322i
$169$	4.97354	−	12.0072i	0.382580	−	0.923629i
$170$	21.7442	−	4.97148i	1.66770	−	0.381295i
$171$	0.587266	−	0.116814i	0.0449094	−	0.00893303i
$172$	2.32777	−	0.602303i	0.177491	−	0.0459252i
$173$	0.915174	−	0.611500i	0.0695794	−	0.0464915i	−0.520294	−	0.853987i	$-0.674178\pi$
$173$	0.915174	−	0.611500i	0.0695794	−	0.0464915i	0.589873	+	0.807496i	$0.299178\pi$
$174$	−4.78486	+	12.5490i	−0.362739	+	0.951338i
$175$	−1.52040	−	1.52040i	−0.114932	−	0.114932i
$176$	−5.27091	−	16.4526i	−0.397310	−	1.24016i
$177$	1.91541	−	1.91541i	0.143971	−	0.143971i
$178$	−0.723733	−	1.61577i	−0.0542461	−	0.121107i
$179$	−13.3510	−	19.9811i	−0.997898	−	1.49346i	−0.864648	−	0.502378i	$-0.832459\pi$
$179$	−13.3510	−	19.9811i	−0.997898	−	1.49346i	−0.133250	−	0.991082i	$-0.542541\pi$
$180$	−3.19093	+	2.40515i	−0.237838	+	0.179269i
$181$	−3.54131	−	17.8034i	−0.263224	−	1.32332i	−0.855593	−	0.517649i	$-0.826807\pi$
$181$	−3.54131	−	17.8034i	−0.263224	−	1.32332i	0.592369	−	0.805667i	$-0.298193\pi$
$182$	−0.151619	−	0.0951895i	−0.0112387	−	0.00705592i
$183$	−2.05993	−	0.853253i	−0.152275	−	0.0630743i
$184$	1.32358	−	4.16878i	0.0975759	−	0.307326i
$185$	−16.0578	+	6.65134i	−1.18059	+	0.489016i
$186$	0.642887	−	3.79231i	0.0471387	−	0.278065i
$187$	−18.9428	+	28.3498i	−1.38523	+	2.07315i
$188$	−13.0118	−	11.6107i	−0.948986	−	0.846796i
$189$	−2.09149	−	0.416023i	−0.152133	−	0.0302612i
$190$	0.0480787	+	1.69114i	0.00348800	+	0.122688i
$191$	−22.1209			−1.60061			−0.800305	−	0.599593i	$-0.795329\pi$
$191$	−22.1209			−1.60061			−0.800305	+	0.599593i	$0.795329\pi$
$192$	7.99733	+	0.206511i	0.577158	+	0.0149036i
$193$	−22.9272			−1.65033			−0.825167	−	0.564889i	$-0.808919\pi$
$193$	−22.9272			−1.65033			−0.825167	+	0.564889i	$0.808919\pi$
$194$	−0.0373234	−	1.31283i	−0.00267967	−	0.0942556i
$195$	−0.116323	−	0.0231380i	−0.00833005	−	0.00165695i
$196$	−3.26584	+	3.65996i	−0.233274	+	0.261425i
$197$	5.52472	−	8.26833i	0.393620	−	0.589094i	−0.580740	−	0.814089i	$-0.697237\pi$
$197$	5.52472	−	8.26833i	0.393620	−	0.589094i	0.974360	+	0.224995i	$0.0722367\pi$
$198$	1.02090	−	6.02217i	0.0725524	−	0.427977i
$199$	−22.2207	+	9.20412i	−1.57518	+	0.652462i	−0.987641	−	0.156731i	$-0.949904\pi$
$199$	−22.2207	+	9.20412i	−1.57518	+	0.652462i	−0.587542	+	0.809193i	$0.699904\pi$
$200$	1.31181	+	2.53231i	0.0927587	+	0.179061i
$201$	13.3025	+	5.51008i	0.938287	+	0.388651i
$202$	13.0297	+	8.18032i	0.916764	+	0.575565i
$203$	−3.95082	−	19.8621i	−0.277293	−	1.39405i
$204$	−9.50334	−	12.6082i	−0.665367	−	0.882749i
$205$	−10.8486	−	16.2361i	−0.757699	−	1.13398i
$206$	−2.99383	−	6.68389i	−0.208590	−	0.465689i
$207$	1.09346	−	1.09346i	0.0760009	−	0.0760009i
$208$	0.153466	+	0.181192i	0.0106410	+	0.0125634i
$209$	−1.82868	−	1.82868i	−0.126492	−	0.126492i
$210$	2.14664	−	5.62989i	0.148132	−	0.388499i
$211$	−11.4336	+	7.63969i	−0.787122	+	0.525938i	−0.882954	−	0.469460i	$-0.844449\pi$
$211$	−11.4336	+	7.63969i	−0.787122	+	0.525938i	0.0958322	+	0.995398i	$0.469449\pi$
$212$	−2.34283	−	9.05451i	−0.160906	−	0.621867i
$213$	−0.568229	+	0.113028i	−0.0389344	+	0.00774454i
$214$	−3.80497	+	0.869950i	−0.260103	+	0.0594686i
$215$	−0.919181	+	2.21910i	−0.0626876	+	0.151341i
$216$	2.47703	+	1.36540i	0.168541	+	0.0929036i
$217$	2.21954	+	5.35843i	0.150672	+	0.363754i
$218$	8.85574	−	6.28844i	0.599787	−	0.425907i
$219$	−2.19904	−	1.46935i	−0.148597	−	0.0992894i
$220$	16.2941	+	5.68795i	1.09855	+	0.383481i
$221$	0.0914243	−	0.459621i	0.00614986	−	0.0309174i
$222$	8.94314	+	8.44869i	0.600224	+	0.567039i
$223$		−	21.1944i		−	1.41928i	−0.704563	−	0.709642i	$-0.748857\pi$
$223$		−	21.1944i		−	1.41928i	0.704563	−	0.709642i	$-0.251143\pi$
$224$	−10.3786	+	6.14826i	−0.693451	+	0.410798i
$225$			1.00830i			0.0672203i
$226$	16.4208	−	17.3818i	1.09230	−	1.15622i
$227$	−4.19059	+	21.0675i	−0.278139	+	1.39830i	0.548774	+	0.835971i	$0.315095\pi$
$227$	−4.19059	+	21.0675i	−0.278139	+	1.39830i	−0.826913	+	0.562330i	$0.809905\pi$
$228$	1.07856	−	0.520397i	0.0714295	−	0.0344642i
$229$	11.7649	+	7.86103i	0.777444	+	0.519472i	0.879839	−	0.475272i	$-0.157650\pi$
$229$	11.7649	+	7.86103i	0.777444	+	0.519472i	−0.102395	+	0.994744i	$0.532650\pi$
$230$	2.52972	+	3.56250i	0.166805	+	0.234904i
$231$	3.52462	+	8.50918i	0.231903	+	0.559863i
$232$	−2.97762	+	26.6950i	−0.195491	+	1.75261i
$233$	−4.03616	+	9.74415i	−0.264418	+	0.638360i	−0.999202	−	0.0399401i	$-0.987283\pi$
$233$	−4.03616	+	9.74415i	−0.264418	+	0.638360i	0.734785	+	0.678301i	$0.237283\pi$
$234$	0.0187114	+	0.0818395i	0.00122320	+	0.00535001i
$235$	17.0861	−	3.39863i	1.11457	−	0.221702i
$236$	2.74908	−	4.66830i	0.178950	−	0.303880i
$237$	−7.31356	+	4.88677i	−0.475067	+	0.317430i
$238$	22.2451	+	8.48192i	1.44194	+	0.549801i
$239$	14.7054	+	14.7054i	0.951215	+	0.951215i	0.998864	−	0.0476488i	$-0.0151728\pi$
$239$	14.7054	+	14.7054i	0.951215	+	0.951215i	−0.0476488	+	0.998864i	$0.515173\pi$
$240$	−4.97343	+	6.25557i	−0.321034	+	0.403795i
$241$	10.5449	−	10.5449i	0.679256	−	0.679256i	−0.280576	−	0.959832i	$-0.590526\pi$
$241$	10.5449	−	10.5449i	0.679256	−	0.679256i	0.959832	+	0.280576i	$0.0905255\pi$
$242$	−9.87920	+	4.42507i	−0.635059	+	0.284454i
$243$	0.555570	+	0.831470i	0.0356398	+	0.0533388i
$244$	−4.41599	−	0.620082i	−0.282705	−	0.0396967i
$245$	−0.955963	−	4.80595i	−0.0610743	−	0.307041i
$246$	−7.34939	+	11.7062i	−0.468580	+	0.746357i
$247$	0.0328389	+	0.0136023i	0.00208949	+	0.000865495i
$248$	−0.655145	−	7.66488i	−0.0416018	−	0.486720i
$249$	4.62992	−	1.91778i	0.293409	−	0.121534i
$250$	−16.7376	−	2.83742i	−1.05858	−	0.179454i
$251$	−4.15564	+	6.21936i	−0.262302	+	0.392562i	−0.939121	−	0.343587i	$-0.888358\pi$
$251$	−4.15564	+	6.21936i	−0.262302	+	0.392562i	0.676819	+	0.736149i	$0.263358\pi$
$252$	−4.25804	+	0.242306i	−0.268231	+	0.0152638i
$253$	−6.55064	−	1.30300i	−0.411835	−	0.0819191i
$254$	−26.0466	+	0.740500i	−1.63431	+	0.0464631i
$255$	15.7722			0.987693
$256$	15.5882	−	3.60677i	0.974261	−	0.225423i
$257$	24.1168			1.50437			0.752184	−	0.658954i	$-0.229001\pi$
$257$	24.1168			1.50437			0.752184	+	0.658954i	$0.229001\pi$
$258$	1.69950	−	0.0483165i	0.105806	−	0.00300806i
$259$	−18.1948	−	3.61916i	−1.13057	−	0.224884i
$260$	−0.236820	+	0.0134764i	−0.0146870	+	0.000835770i
$261$	−5.27605	+	7.89617i	−0.326579	+	0.488761i
$262$	18.3821	+	3.11621i	1.13565	+	0.192520i
$263$	10.3721	−	4.29628i	0.639574	−	0.264920i	−0.0392409	−	0.999230i	$-0.512494\pi$
$263$	10.3721	−	4.29628i	0.639574	−	0.264920i	0.678815	+	0.734310i	$0.262494\pi$
$264$	−1.04037	−	12.1718i	−0.0640303	−	0.749123i
$265$	8.63180	+	3.57541i	0.530247	+	0.219636i
$266$	−0.960148	+	1.52933i	−0.0588704	+	0.0937692i
$267$	−0.244234	−	1.22784i	−0.0149468	−	0.0751429i
$268$	28.5173	+	4.00433i	1.74197	+	0.244603i
$269$	0.548849	+	0.821411i	0.0334639	+	0.0500823i	0.847824	−	0.530277i	$-0.177912\pi$
$269$	0.548849	+	0.821411i	0.0334639	+	0.0500823i	−0.814360	+	0.580359i	$0.802912\pi$
$270$	−2.57863	+	1.15501i	−0.156930	+	0.0702920i
$271$	15.0109	−	15.0109i	0.911848	−	0.911848i	−0.0845699	−	0.996418i	$-0.526952\pi$
$271$	15.0109	−	15.0109i	0.911848	−	0.911848i	0.996418	+	0.0845699i	$0.0269516\pi$
$272$	−24.7173	−	19.6513i	−1.49871	−	1.19153i
$273$	−0.0895115	−	0.0895115i	−0.00541748	−	0.00541748i
$274$	17.5055	+	6.67472i	1.05754	+	0.403235i
$275$	3.62100	−	2.41948i	0.218355	−	0.145900i
$276$	1.56938	−	2.66502i	0.0944657	−	0.160415i
$277$	19.9079	−	3.95994i	1.19615	−	0.237930i	0.443455	−	0.896296i	$-0.353752\pi$
$277$	19.9079	−	3.95994i	1.19615	−	0.237930i	0.752697	+	0.658367i	$0.228752\pi$
$278$	6.35879	+	27.8119i	0.381375	+	1.66805i
$279$	1.04083	−	2.51279i	0.0623130	−	0.150437i
$280$	1.33586	−	11.9762i	0.0798327	−	0.715717i
$281$	−0.479897	−	1.15857i	−0.0286283	−	0.0691147i	0.908919	−	0.416973i	$-0.136909\pi$
$281$	−0.479897	−	1.15857i	−0.0286283	−	0.0691147i	−0.937547	+	0.347858i	$0.886909\pi$
$282$	−7.13944	−	10.0542i	−0.425148	−	0.598717i
$283$	−8.48093	−	5.66677i	−0.504139	−	0.336855i	0.277355	−	0.960767i	$-0.410542\pi$
$283$	−8.48093	−	5.66677i	−0.504139	−	0.336855i	−0.781494	+	0.623913i	$0.785542\pi$
$284$	−1.04360	+	0.503528i	−0.0619262	+	0.0298789i
$285$	−0.233386	+	1.17331i	−0.0138246	+	0.0695010i
$286$	0.249001	−	0.263574i	0.0147238	−	0.0155854i
$287$		−	20.8419i		−	1.23026i
$288$	5.48017	+	1.40275i	0.322922	+	0.0826580i
$289$			45.3199i			2.66588i
$290$	−19.5051	−	18.4267i	−1.14538	−	1.08205i
$291$	0.181177	−	0.910841i	0.0106208	−	0.0533944i
$292$	−4.99398	−	1.74330i	−0.292251	−	0.102019i
$293$	−16.8634	−	11.2678i	−0.985172	−	0.658271i	−0.0450055	−	0.998987i	$-0.514331\pi$
$293$	−16.8634	−	11.2678i	−0.985172	−	0.658271i	−0.940166	+	0.340716i	$0.889331\pi$
$294$	−2.82803	+	2.00817i	−0.164934	+	0.117119i
$295$	2.07107	+	5.00001i	0.120583	+	0.291112i
$296$	21.5488	+	11.8782i	1.25250	+	0.690406i
$297$	1.65284	−	3.99030i	0.0959074	−	0.231541i
$298$	−23.9259	+	5.47030i	−1.38599	+	0.316886i
$299$	0.0900337	−	0.0179088i	0.00520679	−	0.00103569i
$300$	0.505155	+	1.95231i	0.0291651	+	0.112717i
$301$	−2.13162	+	1.42430i	−0.122865	+	0.0820956i
$302$	5.82419	−	15.2748i	0.335144	−	0.878966i
$303$	7.69236	+	7.69236i	0.441915	+	0.441915i
$304$	1.82763	−	1.54796i	0.104822	−	0.0887819i
$305$	3.14994	−	3.14994i	0.180365	−	0.180365i
$306$	−4.56376	−	10.1888i	−0.260893	−	0.582456i
$307$	−2.09175	−	3.13053i	−0.119383	−	0.178669i	0.766965	−	0.641689i	$-0.221766\pi$
$307$	−2.09175	−	3.13053i	−0.119383	−	0.178669i	−0.886348	+	0.463020i	$0.846766\pi$
$308$	11.0875	+	14.7100i	0.631771	+	0.838177i
$309$	−1.01031	−	5.07917i	−0.0574745	−	0.288944i
$310$	6.50846	+	4.08616i	0.369656	+	0.232078i
$311$	22.9718	+	9.51523i	1.30261	+	0.539559i	0.922720	−	0.385472i	$-0.125961\pi$
$311$	22.9718	+	9.51523i	1.30261	+	0.539559i	0.379891	+	0.925031i	$0.375961\pi$
$312$	0.0772307	+	0.149086i	0.00437233	+	0.00844034i
$313$	−2.62201	+	1.08607i	−0.148205	+	0.0613885i	−0.455553	−	0.890209i	$-0.650558\pi$
$313$	−2.62201	+	1.08607i	−0.148205	+	0.0613885i	0.307348	+	0.951597i	$0.400558\pi$
$314$	−1.30304	+	7.68645i	−0.0735347	+	0.433772i
$315$	2.36701	−	3.54247i	0.133366	−	0.199596i
$316$	−11.7125	+	13.1260i	−0.658881	+	0.738394i
$317$	−2.91167	−	0.579168i	−0.163536	−	0.0325293i	0.112643	−	0.993636i	$-0.464068\pi$
$317$	−2.91167	−	0.579168i	−0.163536	−	0.0325293i	−0.276179	+	0.961106i	$0.589068\pi$
$318$	−0.187940	−	6.61069i	−0.0105392	−	0.370709i
$319$	41.0167			2.29649
$320$	−6.49572	+	14.6039i	−0.363122	+	0.816383i
$321$	−2.75995			−0.154045
$322$	0.132530	+	4.66166i	0.00738560	+	0.259784i
$323$	−4.63605	−	0.922168i	−0.257957	−	0.0513108i
$324$	1.49228	+	1.33158i	0.0829042	+	0.0739768i
$325$	−0.0332539	+	0.0497680i	−0.00184460	+	0.00276063i
$326$	2.93267	−	17.2995i	0.162426	−	0.958128i
$327$	7.09551	−	2.93906i	0.392383	−	0.162530i
$328$	−8.36543	+	26.3479i	−0.461903	+	1.45482i
$329$	17.1786	+	7.11559i	0.947084	+	0.392295i
$330$	10.3354	+	6.48881i	0.568946	+	0.357197i
$331$	0.532840	+	2.67877i	0.0292876	+	0.147238i	0.992662	−	0.120921i	$-0.0385847\pi$
$331$	0.532840	+	2.67877i	0.0292876	+	0.147238i	−0.963375	+	0.268159i	$0.913585\pi$
$332$	8.00382	−	6.03283i	0.439267	−	0.331095i
$333$	4.83314	+	7.23331i	0.264855	+	0.396383i
$334$	5.93592	+	13.2522i	0.324799	+	0.725130i
$335$	−20.3415	+	20.3415i	−1.11137	+	1.11137i
$336$	−8.12317	+	2.60241i	−0.443155	+	0.141973i
$337$	2.93868	+	2.93868i	0.160080	+	0.160080i	0.782602	−	0.622522i	$-0.213892\pi$
$337$	2.93868	+	2.93868i	0.160080	+	0.160080i	−0.622522	+	0.782602i	$0.713892\pi$
$338$	6.54824	−	17.1737i	0.356177	−	0.934128i
$339$	14.0586	−	9.39367i	0.763559	−	0.510194i
$340$	30.5387	−	7.90178i	1.65619	−	0.428534i
$341$	−11.5214	+	2.29175i	−0.623919	+	0.124105i
$342$	0.825490	−	0.188736i	0.0446374	−	0.0102057i
$343$	7.71387	−	18.6229i	0.416510	−	1.00554i
$344$	3.26643	−	0.944994i	0.176114	−	0.0509507i
$345$	1.18233	+	2.85439i	0.0636543	+	0.153675i
$346$	1.26915	−	0.901223i	0.0682301	−	0.0484500i
$347$	−10.2158	−	6.82600i	−0.548414	−	0.366439i	0.250282	−	0.968173i	$-0.419477\pi$
$347$	−10.2158	−	6.82600i	−0.548414	−	0.366439i	−0.798696	+	0.601734i	$0.794477\pi$
$348$	−6.25974	+	17.9321i	−0.335557	+	0.961262i
$349$	−1.81035	+	9.10124i	−0.0969057	+	0.487178i	0.901602	+	0.432567i	$0.142392\pi$
$349$	−1.81035	+	9.10124i	−0.0969057	+	0.487178i	−0.998508	+	0.0546113i	$0.982608\pi$
$350$	−2.21041	−	2.08820i	−0.118151	−	0.111619i
$351$			0.0593625i			0.00316854i
$352$	−8.11241	−	23.0463i	−0.432393	−	1.22837i
$353$		−	15.0241i		−	0.799654i	−0.916591	−	0.399827i	$-0.869070\pi$
$353$		−	15.0241i		−	0.799654i	0.916591	−	0.399827i	$-0.130930\pi$
$354$	2.63073	−	2.78469i	0.139822	−	0.148004i
$355$	0.225821	−	1.13528i	0.0119853	−	0.0602543i
$356$	−1.08804	−	2.25504i	−0.0576658	−	0.119517i
$357$	13.9972	+	9.35264i	0.740811	+	0.494994i
$358$	−19.6765	−	27.7096i	−1.03994	−	1.46450i
$359$	−2.75806	−	6.65854i	−0.145565	−	0.351424i	0.834234	−	0.551411i	$-0.185910\pi$
$359$	−2.75806	−	6.65854i	−0.145565	−	0.351424i	−0.979799	+	0.199986i	$0.935910\pi$
$360$	−4.41418	+	3.52826i	−0.232648	+	0.185956i
$361$	−7.13378	+	17.2225i	−0.375462	+	0.906446i
$362$	−5.72166	−	25.0253i	−0.300724	−	1.31530i
$363$	−7.50733	+	1.49330i	−0.394033	+	0.0783780i
$364$	−0.218160	−	0.128470i	−0.0114347	−	0.00673368i
$365$	4.39350	−	2.93564i	0.229966	−	0.153659i
$366$	−2.94630	−	1.12341i	−0.154006	−	0.0587214i
$367$	−5.72499	−	5.72499i	−0.298842	−	0.298842i	0.541718	−	0.840560i	$-0.317774\pi$
$367$	−5.72499	−	5.72499i	−0.298842	−	0.298842i	−0.840560	+	0.541718i	$0.817774\pi$
$368$	1.70353	−	5.94636i	0.0888028	−	0.309975i
$369$	−6.91100	+	6.91100i	−0.359772	+	0.359772i
$370$	−22.4326	+	10.0480i	−1.16622	+	0.522369i
$371$	5.54023	+	8.29154i	0.287634	+	0.430475i
$372$	0.756401	−	5.38680i	0.0392176	−	0.279293i
$373$	0.694560	+	3.49179i	0.0359630	+	0.180798i	0.994592	−	0.103861i	$-0.0331197\pi$
$373$	0.694560	+	3.49179i	0.0359630	+	0.180798i	−0.958629	+	0.284659i	$0.908120\pi$
$374$	−25.6389	+	40.8378i	−1.32576	+	2.11167i
$375$	−11.0904	−	4.59378i	−0.572704	−	0.237222i
$376$	−18.8607	−	15.8904i	−0.972668	−	0.819486i
$377$	−0.520832	+	0.215736i	−0.0268242	+	0.0111110i
$378$	−2.97334	−	0.504052i	−0.152932	−	0.0259256i
$379$	−0.218377	+	0.326825i	−0.0112173	+	0.0167879i	−0.837036	−	0.547148i	$-0.815713\pi$
$379$	−0.218377	+	0.326825i	−0.0112173	+	0.0167879i	0.825819	+	0.563936i	$0.190713\pi$
$380$	0.135932	+	2.38873i	0.00697318	+	0.122539i
$381$	−18.0712	−	3.59458i	−0.925813	−	0.184156i
$382$	−31.2710	+	0.889028i	−1.59996	+	0.0454866i
$383$	−3.27001			−0.167090			−0.0835448	−	0.996504i	$-0.526624\pi$
$383$	−3.27001			−0.167090			−0.0835448	+	0.996504i	$0.526624\pi$
$384$	11.3137	−	0.0294766i	0.577348	−	0.00150422i
$385$	−18.4014			−0.937822
$386$	−32.4108	+	0.921432i	−1.64967	+	0.0468997i
$387$	1.17912	+	0.234541i	0.0599378	+	0.0119224i
$388$	−0.105524	−	1.85437i	−0.00535717	−	0.0941414i
$389$	6.16101	−	9.22061i	0.312376	−	0.467503i	−0.641748	−	0.766915i	$-0.721791\pi$
$389$	6.16101	−	9.22061i	0.312376	−	0.467503i	0.954124	+	0.299412i	$0.0967906\pi$
$390$	−0.165369	−	0.0280340i	−0.00837377	−	0.00141955i
$391$	−11.2784	+	4.67167i	−0.570374	+	0.236257i
$392$	−4.46964	+	5.30512i	−0.225751	+	0.267949i
$393$	12.1800	+	5.04513i	0.614401	+	0.254493i
$394$	7.47768	−	11.9105i	0.376720	−	0.600042i
$395$	−3.42844	−	17.2359i	−0.172504	−	0.867235i
$396$	1.20116	−	8.55423i	0.0603607	−	0.429866i
$397$	−7.55104	−	11.3009i	−0.378976	−	0.567178i	0.592125	−	0.805846i	$-0.298289\pi$
$397$	−7.55104	−	11.3009i	−0.378976	−	0.567178i	−0.971101	+	0.238668i	$0.923289\pi$
$398$	−31.0422	+	13.9044i	−1.55601	+	0.696963i
$399$	−0.902875	+	0.902875i	−0.0452003	+	0.0452003i
$400$	1.95620	+	3.52706i	0.0978099	+	0.176353i
$401$	3.35262	+	3.35262i	0.167422	+	0.167422i	0.785845	−	0.618423i	$-0.212228\pi$
$401$	3.35262	+	3.35262i	0.167422	+	0.167422i	−0.618423	+	0.785845i	$0.712228\pi$
$402$	19.0264	+	7.25466i	0.948953	+	0.361830i
$403$	0.134245	−	0.0896999i	0.00668724	−	0.00446827i
$404$	18.7481	+	11.0404i	0.932750	+	0.549280i
$405$	−1.95953	+	0.389775i	−0.0973700	+	0.0193681i
$406$	−6.38330	−	27.9192i	−0.316798	−	1.38560i
$407$	14.3788	−	34.7134i	0.712728	−	1.72068i
$408$	−13.9410	−	17.4415i	−0.690184	−	0.863484i
$409$	6.15441	+	14.8581i	0.304316	+	0.734684i	0.999869	+	0.0162089i	$0.00515966\pi$
$409$	6.15441	+	14.8581i	0.304316	+	0.734684i	−0.695552	+	0.718475i	$0.744840\pi$
$410$	−15.9886	−	22.5160i	−0.789619	−	1.11199i
$411$	11.0149	+	7.35992i	0.543325	+	0.363038i
$412$	−4.50083	−	9.32831i	−0.221740	−	0.459573i
$413$	−1.12692	+	5.66543i	−0.0554523	+	0.278777i
$414$	1.50182	−	1.58971i	0.0738104	−	0.0781301i
$415$			10.0124i			0.491488i
$416$	0.224228	+	0.249974i	0.0109937	+	0.0122560i
$417$			20.1735i			0.987899i
$418$	−2.65859	−	2.51160i	−0.130036	−	0.122846i
$419$	−7.72896	+	38.8561i	−0.377584	+	1.89824i	0.0584067	+	0.998293i	$0.481398\pi$
$419$	−7.72896	+	38.8561i	−0.377584	+	1.89824i	−0.435991	+	0.899951i	$0.643602\pi$
$420$	2.80832	−	8.04492i	0.137032	−	0.392552i
$421$	−23.9759	−	16.0202i	−1.16851	−	0.780776i	−0.188966	−	0.981984i	$-0.560514\pi$
$421$	−23.9759	−	16.0202i	−1.16851	−	0.780776i	−0.979549	+	0.201207i	$0.935514\pi$
$422$	−15.8560	+	11.2593i	−0.771858	+	0.548094i
$423$	−3.33679	−	8.05573i	−0.162240	−	0.391683i
$424$	−3.67582	−	12.7057i	−0.178513	−	0.617043i
$425$	3.04611	−	7.35395i	0.147758	−	0.356719i
$426$	−0.798730	+	0.182618i	−0.0386986	+	0.00884786i
$427$	4.66330	−	0.927589i	0.225673	−	0.0448892i
$428$	−5.34391	+	1.38272i	−0.258307	+	0.0668362i
$429$	0.213181	−	0.142443i	0.0102925	−	0.00687722i
$430$	−1.21021	+	3.17395i	−0.0583614	+	0.153062i
$431$	1.96172	+	1.96172i	0.0944925	+	0.0944925i	0.752773	−	0.658280i	$-0.228716\pi$
$431$	1.96172	+	1.96172i	0.0944925	+	0.0944925i	−0.658280	+	0.752773i	$0.728716\pi$
$432$	3.55651	+	1.83063i	0.171113	+	0.0880764i
$433$	6.32579	−	6.32579i	0.303998	−	0.303998i	−0.538578	−	0.842576i	$-0.681038\pi$
$433$	6.32579	−	6.32579i	0.303998	−	0.303998i	0.842576	+	0.538578i	$0.181038\pi$
$434$	3.35298	+	7.48571i	0.160948	+	0.359325i
$435$	−10.5411	−	15.7759i	−0.505409	−	0.756398i
$436$	12.2661	−	9.24552i	0.587441	−	0.442780i
$437$	−0.180641	−	0.908143i	−0.00864122	−	0.0434424i
$438$	−3.16770	−	1.98875i	−0.151359	−	0.0950264i
$439$	−18.1301	−	7.50972i	−0.865301	−	0.358419i	−0.0945226	−	0.995523i	$-0.530132\pi$
$439$	−18.1301	−	7.50972i	−0.865301	−	0.358419i	−0.770778	+	0.637103i	$0.780132\pi$
$440$	23.2626	+	7.38587i	1.10900	+	0.352107i
$441$	−2.26591	+	0.938570i	−0.107900	+	0.0446938i
$442$	0.110769	−	0.653414i	0.00526876	−	0.0310797i
$443$	−8.10192	+	12.1254i	−0.384934	+	0.576094i	−0.972448	−	0.233120i	$-0.925107\pi$
$443$	−8.10192	+	12.1254i	−0.384934	+	0.576094i	0.587514	+	0.809214i	$0.300107\pi$
$444$	12.9819	+	11.5840i	0.616096	+	0.549753i
$445$	2.45314	+	0.487960i	0.116290	+	0.0231315i
$446$	−0.851794	−	29.9613i	−0.0403336	−	1.41871i
$447$	−17.3547			−0.820849
$448$	−14.4246	+	9.10855i	−0.681496	+	0.430338i
$449$	13.4540			0.634933			0.317466	−	0.948270i	$-0.397168\pi$
$449$	13.4540			0.634933			0.317466	+	0.948270i	$0.397168\pi$
$450$	0.0405233	+	1.42538i	0.00191029	+	0.0671932i
$451$	41.4019	+	8.23536i	1.94954	+	0.387788i
$452$	22.5146	−	25.2316i	1.05900	−	1.18680i
$453$	6.42207	−	9.61131i	0.301735	−	0.451579i
$454$	−5.07730	+	29.9504i	−0.238290	+	1.40564i
$455$	0.233662	−	0.0967859i	0.0109542	−	0.00453739i
$456$	1.50379	−	0.779003i	0.0704212	−	0.0364801i
$457$	−6.01939	−	2.49331i	−0.281575	−	0.116632i	0.237426	−	0.971406i	$-0.423696\pi$
$457$	−6.01939	−	2.49331i	−0.281575	−	0.116632i	−0.519002	+	0.854773i	$0.673696\pi$
$458$	16.9472	+	10.6399i	0.791893	+	0.497168i
$459$	−1.54010	−	7.74261i	−0.0718858	−	0.361394i
$460$	3.71930	+	4.93443i	0.173413	+	0.230069i
$461$	13.9820	+	20.9256i	0.651208	+	0.974602i	0.999310	+	0.0371449i	$0.0118263\pi$
$461$	13.9820	+	20.9256i	0.651208	+	0.974602i	−0.348102	+	0.937457i	$0.613174\pi$
$462$	5.32453	+	11.8873i	0.247719	+	0.553046i
$463$	12.9201	−	12.9201i	0.600446	−	0.600446i	−0.339985	−	0.940431i	$-0.610422\pi$
$463$	12.9201	−	12.9201i	0.600446	−	0.600446i	0.940431	+	0.339985i	$0.110422\pi$
$464$	−3.13643	+	37.8569i	−0.145605	+	1.75746i
$465$	3.84242	+	3.84242i	0.178188	+	0.178188i
$466$	−5.31407	+	13.9370i	−0.246170	+	0.645617i
$467$	−22.3190	+	14.9131i	−1.03280	+	0.690094i	−0.951831	−	0.306623i	$-0.900801\pi$
$467$	−22.3190	+	14.9131i	−1.03280	+	0.690094i	−0.0809678	+	0.996717i	$0.525801\pi$
$468$	0.0297403	+	0.114940i	0.00137474	+	0.00531309i
$469$	−30.1144	+	5.99012i	−1.39055	+	0.276598i
$470$	24.0170	−	5.49113i	1.10782	−	0.253287i
$471$	−2.10961	+	5.09306i	−0.0972059	+	0.234676i
$472$	3.69859	−	6.70979i	0.170242	−	0.308843i
$473$	−1.98707	−	4.79721i	−0.0913655	−	0.220576i
$474$	−10.1424	+	7.20207i	−0.465854	+	0.330802i
$475$	0.501995	+	0.335422i	0.0230331	+	0.0153902i
$476$	31.7875	+	11.0964i	1.45698	+	0.508602i
$477$	0.912311	−	4.58650i	0.0417718	−	0.210001i
$478$	21.3792	+	20.1972i	0.977863	+	0.923799i
$479$		−	10.7417i		−	0.490803i	−0.969422	−	0.245401i	$-0.921080\pi$
$479$		−	10.7417i		−	0.490803i	0.969422	−	0.245401i	$-0.0789197\pi$
$480$	−6.77924	+	9.04301i	−0.309429	+	0.412755i
$481$			0.516420i			0.0235467i
$482$	14.4829	−	15.3305i	0.659678	−	0.698285i
$483$	−0.643334	+	3.23426i	−0.0292727	+	0.147164i
$484$	−13.7878	+	6.65251i	−0.626719	+	0.302387i
$485$	1.54274	+	1.03083i	0.0700523	+	0.0468075i
$486$	0.818794	+	1.15307i	0.0371413	+	0.0523044i
$487$	−7.01036	−	16.9245i	−0.317670	−	0.766923i	−0.999377	−	0.0352976i	$-0.988762\pi$
$487$	−7.01036	−	16.9245i	−0.317670	−	0.766923i	0.681707	−	0.731625i	$-0.261238\pi$
$488$	−6.26755	−	0.699097i	−0.283719	−	0.0316467i
$489$	4.74799	−	11.4627i	0.214711	−	0.518359i
$490$	−1.54454	−	6.75548i	−0.0697752	−	0.305181i
$491$	9.73259	−	1.93593i	0.439225	−	0.0873674i	0.0294760	−	0.999565i	$-0.490616\pi$
$491$	9.73259	−	1.93593i	0.439225	−	0.0873674i	0.409749	+	0.912198i	$0.365616\pi$
$492$	−9.91895	+	16.8437i	−0.447181	+	0.759372i
$493$	62.3347	−	41.6507i	2.80741	−	1.87585i
$494$	0.0469691	+	0.0179090i	0.00211324	+	0.000805765i
$495$	6.10175	+	6.10175i	0.274253	+	0.274253i
$496$	−1.23419	−	10.8091i	−0.0554167	−	0.485342i
$497$	0.873607	−	0.873607i	0.0391866	−	0.0391866i
$498$	6.46798	−	2.89713i	0.289837	−	0.129823i
$499$	−5.49104	−	8.21793i	−0.245813	−	0.367885i	0.687962	−	0.725747i	$-0.258506\pi$
$499$	−5.49104	−	8.21793i	−0.245813	−	0.367885i	−0.933774	+	0.357862i	$0.883506\pi$
$500$	−23.7750	−	3.33843i	−1.06325	−	0.149299i
$501$	2.00316	+	10.0705i	0.0894944	+	0.449919i
$502$	−5.62464	+	8.95896i	−0.251040	+	0.399858i
$503$	−1.79810	−	0.744797i	−0.0801733	−	0.0332089i	0.342236	−	0.939614i	$-0.388816\pi$
$503$	−1.79810	−	0.744797i	−0.0801733	−	0.0332089i	−0.422410	+	0.906405i	$0.638816\pi$
$504$	−6.00960	+	0.513663i	−0.267689	+	0.0228804i
$505$	−20.0802	+	8.31751i	−0.893559	+	0.370124i
$506$	−9.31263	−	1.57871i	−0.413997	−	0.0701824i
$507$	7.22046	−	10.8062i	0.320672	−	0.479919i
$508$	−36.7909	+	2.09360i	−1.63233	+	0.0928887i
$509$	16.9975	+	3.38102i	0.753403	+	0.149861i	0.556828	−	0.830628i	$-0.312018\pi$
$509$	16.9975	+	3.38102i	0.753403	+	0.149861i	0.196575	+	0.980489i	$0.437018\pi$
$510$	22.2962	−	0.633878i	0.987294	−	0.0280686i
$511$	5.63985			0.249492
$512$	21.8912	−	5.72516i	0.967461	−	0.253019i
$513$	0.598771			0.0264364
$514$	34.0926	−	0.969245i	1.50376	−	0.0427516i
$515$	10.1478	+	2.01852i	0.447165	+	0.0889467i
$516$	2.40055	−	0.136605i	0.105678	−	0.00601368i
$517$	−20.9228	+	31.3132i	−0.920183	+	1.37715i
$518$	−25.8663	−	4.38496i	−1.13650	−	0.192664i
$519$	1.01689	−	0.421208i	0.0446364	−	0.0184890i
$520$	−0.334238	+	0.0285685i	−0.0146573	+	0.00125281i
$521$	−28.7153	−	11.8943i	−1.25804	−	0.521097i	−0.348732	−	0.937223i	$-0.613387\pi$
$521$	−28.7153	−	11.8943i	−1.25804	−	0.521097i	−0.909307	+	0.416126i	$0.863387\pi$
$522$	−7.14111	+	11.3744i	−0.312558	+	0.497844i
$523$	−4.23821	−	21.3069i	−0.185324	−	0.931687i	−0.955755	−	0.294164i	$-0.904959\pi$
$523$	−4.23821	−	21.3069i	−0.185324	−	0.931687i	0.770431	−	0.637523i	$-0.220041\pi$
$524$	26.1110	+	3.66643i	1.14066	+	0.160169i
$525$	−1.19457	−	1.78780i	−0.0521354	−	0.0780261i
$526$	14.4898	−	6.49026i	0.631787	−	0.282989i
$527$	−15.1824	+	15.1824i	−0.661354	+	0.661354i
$528$	−1.95989	−	17.1648i	−0.0852932	−	0.747001i
$529$	14.5725	+	14.5725i	0.633588	+	0.633588i
$530$	12.3460	+	4.70744i	0.536275	+	0.204478i
$531$	2.25229	−	1.50493i	0.0977409	−	0.0653084i
$532$	−1.29584	+	2.20051i	−0.0561819	+	0.0954043i
$533$	−0.569039	+	0.113189i	−0.0246478	+	0.00490275i
$534$	−0.394605	−	1.72592i	−0.0170762	−	0.0746878i
$535$	2.11018	−	5.09442i	0.0912310	−	0.220251i
$536$	40.4742	+	4.51459i	1.74822	+	0.195000i
$537$	−9.19631	−	22.2019i	−0.396850	−	0.958081i
$538$	0.808889	+	1.13912i	0.0348737	+	0.0491111i
$539$	8.80773	+	5.88514i	0.379376	+	0.253491i
$540$	−3.59884	+	1.73641i	−0.154869	+	0.0747233i
$541$	−7.80278	+	39.2272i	−0.335468	+	1.68651i	0.333126	+	0.942882i	$0.391897\pi$
$541$	−7.80278	+	39.2272i	−0.335468	+	1.68651i	−0.668594	+	0.743628i	$0.733103\pi$
$542$	20.6168	−	21.8233i	0.885566	−	0.937393i
$543$		−	18.1522i		−	0.778984i
$544$	−35.7312	−	26.7865i	−1.53196	−	1.14846i
$545$			15.3443i			0.657278i
$546$	−0.130135	−	0.122940i	−0.00556925	−	0.00526134i
$547$	2.73797	−	13.7647i	0.117067	−	0.588537i	−0.877065	−	0.480371i	$-0.840502\pi$
$547$	2.73797	−	13.7647i	0.117067	−	0.588537i	0.994133	−	0.108166i	$-0.0344979\pi$
$548$	25.0147	+	8.73213i	1.06858	+	0.373018i
$549$	−1.85389	−	1.23873i	−0.0791222	−	0.0528678i
$550$	5.02157	−	3.56580i	0.214120	−	0.152046i
$551$	2.17606	+	5.25347i	0.0927032	+	0.223805i
$552$	2.11144	−	3.83046i	0.0898688	−	0.163035i
$553$	7.17801	−	17.3292i	0.305240	−	0.736914i
$554$	27.9836	−	6.39803i	1.18891	−	0.271826i
$555$	−17.0468	+	3.39082i	−0.723597	+	0.143932i
$556$	10.1068	+	39.0606i	0.428624	+	1.65654i
$557$	20.8301	−	13.9182i	0.882600	−	0.589735i	−0.0295624	−	0.999563i	$-0.509411\pi$
$557$	20.8301	−	13.9182i	0.882600	−	0.589735i	0.912163	+	0.409828i	$0.134411\pi$
$558$	1.37038	−	3.59402i	0.0580127	−	0.152147i
$559$	0.0504638	+	0.0504638i	0.00213439	+	0.00213439i
$560$	1.40710	−	16.9838i	0.0594610	−	0.717696i
$561$	−24.1096	+	24.1096i	−1.01791	+	1.01791i
$562$	−0.724965	−	1.61852i	−0.0305808	−	0.0682733i
$563$	11.2966	+	16.9065i	0.476093	+	0.712524i	0.989325	−	0.145726i	$-0.0465518\pi$
$563$	11.2966	+	16.9065i	0.476093	+	0.712524i	−0.513232	+	0.858250i	$0.671552\pi$
$564$	−10.4967	−	13.9261i	−0.441991	−	0.586394i
$565$	6.59038	+	33.1321i	0.277260	+	1.39388i
$566$	−12.2167	−	7.66995i	−0.513508	−	0.322392i
$567$	−1.97014	−	0.816058i	−0.0827381	−	0.0342712i
$568$	−1.45504	+	0.753750i	−0.0610521	+	0.0316267i
$569$	−26.1705	+	10.8402i	−1.09712	+	0.454443i	−0.856485	−	0.516172i	$-0.827357\pi$
$569$	−26.1705	+	10.8402i	−1.09712	+	0.454443i	−0.240638	+	0.970615i	$0.577357\pi$
$570$	−0.282770	+	1.66802i	−0.0118439	+	0.0698658i
$571$	4.48111	−	6.70645i	0.187529	−	0.280656i	−0.725778	−	0.687929i	$-0.758520\pi$
$571$	4.48111	−	6.70645i	0.187529	−	0.280656i	0.913307	+	0.407273i	$0.133520\pi$
$572$	0.341406	−	0.382606i	0.0142749	−	0.0159976i
$573$	−21.6958	−	4.31557i	−0.906356	−	0.180285i
$574$	−0.837627	−	29.4630i	−0.0349619	−	1.22976i
$575$	1.55923			0.0650245
$576$	7.80338	+	1.76275i	0.325141	+	0.0734477i
$577$	17.2302			0.717304			0.358652	−	0.933471i	$-0.383237\pi$
$577$	17.2302			0.717304			0.358652	+	0.933471i	$0.383237\pi$
$578$	1.82139	+	64.0662i	0.0757598	+	2.66480i
$579$	−22.4866	−	4.47287i	−0.934512	−	0.185886i
$580$	−28.3138	−	25.2649i	−1.17567	−	1.04907i
$581$	−5.93716	+	8.88559i	−0.246315	+	0.368636i
$582$	0.219514	−	1.29488i	0.00909914	−	0.0536747i
$583$	−18.6601	+	7.72925i	−0.772821	+	0.320113i
$584$	−7.12977	−	2.26369i	−0.295032	−	0.0936724i
$585$	−0.109574	−	0.0453869i	−0.00453031	−	0.00187652i
$586$	−24.2917	−	15.2509i	−1.00348	−	0.630008i
$587$	−3.02984	−	15.2320i	−0.125055	−	0.628693i	−0.991573	−	0.129548i	$-0.958647\pi$
$587$	−3.02984	−	15.2320i	−0.125055	−	0.628693i	0.866518	−	0.499145i	$-0.166353\pi$
$588$	−3.91711	+	2.95250i	−0.161539	+	0.121759i
$589$	−0.904776	−	1.35409i	−0.0372806	−	0.0557944i
$590$	3.12870	+	6.98499i	0.128807	+	0.287568i
$591$	7.03163	−	7.03163i	0.289243	−	0.289243i
$592$	30.9396	+	15.9255i	1.27161	+	0.654533i
$593$	2.08919	+	2.08919i	0.0857928	+	0.0857928i	0.748701	−	0.662908i	$-0.230678\pi$
$593$	2.08919	+	2.08919i	0.0857928	+	0.0857928i	−0.662908	+	0.748701i	$0.730678\pi$
$594$	2.17615	−	5.70729i	0.0892887	−	0.234173i
$595$	−27.9653	+	18.6858i	−1.14647	+	0.766045i
$596$	−33.6028	+	8.69461i	−1.37642	+	0.356145i
$597$	−23.5894	+	4.69222i	−0.965449	+	0.192040i
$598$	0.126556	−	0.0289351i	0.00517525	−	0.00118324i
$599$	−11.0960	+	26.7881i	−0.453370	+	1.09453i	0.517662	+	0.855585i	$0.326802\pi$
$599$	−11.0960	+	26.7881i	−0.453370	+	1.09453i	−0.971032	+	0.238948i	$0.923198\pi$
$600$	0.792571	+	2.73957i	0.0323566	+	0.111843i
$601$	−6.21454	−	15.0032i	−0.253496	−	0.611994i	0.744985	−	0.667081i	$-0.232457\pi$
$601$	−6.21454	−	15.0032i	−0.253496	−	0.611994i	−0.998482	+	0.0550866i	$0.982457\pi$
$602$	−2.95611	+	2.09913i	−0.120482	+	0.0855540i
$603$	11.9719	+	7.99940i	0.487535	+	0.325761i
$604$	7.61943	−	21.8272i	0.310030	−	0.888135i
$605$	2.98350	−	14.9991i	0.121297	−	0.609799i
$606$	11.1834	+	10.5651i	0.454295	+	0.429178i
$607$			29.3341i			1.19063i	0.803491	+	0.595317i	$0.202973\pi$
$607$			29.3341i			1.19063i	−0.803491	+	0.595317i	$0.797027\pi$
$608$	2.52141	−	2.26172i	0.102257	−	0.0917249i
$609$		−	20.2512i		−	0.820622i
$610$	4.32629	−	4.57948i	0.175166	−	0.185418i
$611$	0.100981	−	0.507663i	0.00408524	−	0.0205379i
$612$	−6.86100	−	14.2199i	−0.277340	−	0.574807i
$613$	−0.400066	−	0.267316i	−0.0161585	−	0.0107968i	0.547465	−	0.836829i	$-0.315593\pi$
$613$	−0.400066	−	0.267316i	−0.0161585	−	0.0107968i	−0.563623	+	0.826032i	$0.690593\pi$
$614$	−3.08281	−	4.34139i	−0.124412	−	0.175204i
$615$	−7.47264	−	18.0406i	−0.301326	−	0.727465i
$616$	16.2650	+	20.3490i	0.655335	+	0.819885i
$617$	7.84632	−	18.9427i	0.315881	−	0.762604i	−0.683583	−	0.729873i	$-0.739579\pi$
$617$	7.84632	−	18.9427i	0.315881	−	0.762604i	0.999464	−	0.0327314i	$-0.0104206\pi$
$618$	−1.63235	−	7.13953i	−0.0656626	−	0.287194i
$619$	25.5670	−	5.08560i	1.02763	−	0.204407i	0.347636	−	0.937630i	$-0.386984\pi$
$619$	25.5670	−	5.08560i	1.02763	−	0.204407i	0.679989	+	0.733222i	$0.261984\pi$
$620$	9.36485	+	5.51479i	0.376102	+	0.221479i
$621$	1.28578	−	0.859128i	0.0515964	−	0.0344756i
$622$	32.8563	+	12.5279i	1.31742	+	0.502323i
$623$	1.88771	+	1.88771i	0.0756296	+	0.0756296i
$624$	0.115168	+	0.207651i	0.00461042	+	0.00831268i
$625$	13.3939	−	13.3939i	0.535755	−	0.535755i
$626$	−3.66294	+	1.64070i	−0.146401	+	0.0655754i
$627$	−1.43678	−	2.15030i	−0.0573795	−	0.0858745i
$628$	−1.53311	+	10.9183i	−0.0611779	+	0.435686i
$629$	−13.3980	−	67.3563i	−0.534213	−	2.68567i
$630$	3.20373	−	5.10292i	0.127640	−	0.203305i
$631$	41.8450	+	17.3328i	1.66582	+	0.690006i	0.998499	−	0.0547622i	$-0.0174401\pi$
$631$	41.8450	+	17.3328i	1.66582	+	0.690006i	0.667323	+	0.744768i	$0.267440\pi$
$632$	−16.0298	+	19.0262i	−0.637631	+	0.756820i
$633$	−12.7043	+	5.26231i	−0.504952	+	0.209158i
$634$	−4.13934	−	0.701718i	−0.164394	−	0.0278688i
$635$	20.4517	−	30.6081i	0.811601	−	1.21465i
$636$	−0.531361	−	9.33760i	−0.0210698	−	0.370260i
$637$	−0.142795	−	0.0284037i	−0.00565774	−	0.00112539i
$638$	57.9830	−	1.64844i	2.29557	−	0.0652625i
$639$	−0.579361			−0.0229192
$640$	−8.59571	+	20.9058i	−0.339775	+	0.826373i
$641$	−22.6441			−0.894389			−0.447194	−	0.894437i	$-0.647577\pi$
$641$	−22.6441			−0.894389			−0.447194	+	0.894437i	$0.647577\pi$
$642$	−3.90158	+	0.110921i	−0.153983	+	0.00437771i
$643$	−17.8754	−	3.55563i	−0.704935	−	0.140220i	−0.170410	−	0.985373i	$-0.554509\pi$
$643$	−17.8754	−	3.55563i	−0.704935	−	0.140220i	−0.534525	+	0.845153i	$0.679509\pi$
$644$	0.374700	+	6.58459i	0.0147652	+	0.259469i
$645$	−1.33444	+	1.99714i	−0.0525437	+	0.0786371i
$646$	−6.59078	−	1.11730i	−0.259311	−	0.0439594i
$647$	−2.76591	+	1.14568i	−0.108739	+	0.0450412i	−0.436390	−	0.899758i	$-0.643743\pi$
$647$	−2.76591	+	1.14568i	−0.108739	+	0.0450412i	0.327651	+	0.944799i	$0.393743\pi$
$648$	2.16306	+	1.82241i	0.0849730	+	0.0715909i
$649$	−10.8089	−	4.47721i	−0.424288	−	0.175746i
$650$	−0.0450090	+	0.0716906i	−0.00176540	+	0.00281194i
$651$	1.13151	+	5.68848i	0.0443474	+	0.222949i
$652$	3.45049	−	24.5731i	0.135132	−	0.962357i
$653$	−2.94153	−	4.40230i	−0.115111	−	0.172275i	0.769440	−	0.638719i	$-0.220535\pi$
$653$	−2.94153	−	4.40230i	−0.115111	−	0.172275i	−0.884551	+	0.466443i	$0.845535\pi$
$654$	9.91240	−	4.43994i	0.387605	−	0.173615i
$655$	−18.6250	+	18.6250i	−0.727739	+	0.727739i
$656$	−10.7668	+	37.5827i	−0.420373	+	1.46736i
$657$	−1.87013	−	1.87013i	−0.0729605	−	0.0729605i
$658$	24.5703	+	9.36850i	0.957850	+	0.365222i
$659$	−13.9441	+	9.31712i	−0.543183	+	0.362943i	−0.796688	−	0.604391i	$-0.793417\pi$
$659$	−13.9441	+	9.31712i	−0.543183	+	0.362943i	0.253505	+	0.967334i	$0.418417\pi$
$660$	14.8714	+	8.75748i	0.578867	+	0.340884i
$661$	9.70864	−	1.93117i	0.377622	−	0.0751138i	−0.00262998	−	0.999997i	$-0.500837\pi$
$661$	9.70864	−	1.93117i	0.377622	−	0.0751138i	0.380252	+	0.924883i	$0.375837\pi$
$662$	0.860904	+	3.76541i	0.0334600	+	0.146347i
$663$	0.179335	−	0.432953i	0.00696480	−	0.0168145i
$664$	11.0721	−	8.84994i	0.429680	−	0.343444i
$665$	−0.976250	−	2.35688i	−0.0378573	−	0.0913957i
$666$	7.12304	+	10.0311i	0.276012	+	0.388696i
$667$	12.2106	+	8.15884i	0.472795	+	0.315911i
$668$	8.92386	+	18.4954i	0.345275	+	0.715607i
$669$	4.13483	−	20.7872i	0.159862	−	0.803679i
$670$	−27.9380	+	29.5731i	−1.07934	+	1.14251i
$671$			9.63006i			0.371764i
$672$	−11.3787	+	4.00535i	−0.438941	+	0.154510i
$673$			14.7891i			0.570077i	0.958516	+	0.285038i	$0.0920063\pi$
$673$			14.7891i			0.570077i	−0.958516	+	0.285038i	$0.907994\pi$
$674$	4.27234	+	4.03614i	0.164565	+	0.155466i
$675$	−0.196711	+	0.988931i	−0.00757139	+	0.0380640i
$676$	8.56666	−	24.5407i	0.329487	−	0.943873i
$677$	−4.42592	−	2.95731i	−0.170102	−	0.113659i	0.467605	−	0.883938i	$-0.345117\pi$
$677$	−4.42592	−	2.95731i	−0.170102	−	0.113659i	−0.637707	+	0.770279i	$0.720117\pi$
$678$	19.4963	−	13.8443i	0.748752	−	0.531687i
$679$	0.757861	+	1.82964i	0.0290840	+	0.0702151i
$680$	42.8532	−	12.3976i	1.64335	−	0.475427i
$681$	−8.22014	+	19.8452i	−0.314996	+	0.760469i
$682$	−16.1951	+	3.70276i	−0.620141	+	0.141786i
$683$	−20.8250	+	4.14235i	−0.796847	+	0.158503i	−0.576691	−	0.816962i	$-0.695656\pi$
$683$	−20.8250	+	4.14235i	−0.796847	+	0.158503i	−0.220155	+	0.975465i	$0.570656\pi$
$684$	1.15936	−	0.299981i	0.0443293	−	0.0114701i
$685$	−22.0069	+	14.7046i	−0.840841	+	0.561832i
$686$	10.1562	−	26.6362i	0.387766	−	1.01697i
$687$	10.0052	+	10.0052i	0.381722	+	0.381722i
$688$	4.57959	−	1.46716i	0.174595	−	0.0559349i
$689$	0.196293	−	0.196293i	0.00747816	−	0.00747816i
$690$	1.78610	+	3.98757i	0.0679958	+	0.151804i
$691$	8.18634	+	12.2517i	0.311423	+	0.466078i	0.953856	−	0.300264i	$-0.0970748\pi$
$691$	8.18634	+	12.2517i	0.311423	+	0.466078i	−0.642433	+	0.766342i	$0.722075\pi$
$692$	1.75791	−	1.32501i	0.0668257	−	0.0503694i
$693$	1.79683	+	9.03330i	0.0682561	+	0.343147i
$694$	−14.7159	−	9.23895i	−0.558607	−	0.350706i
$695$	−37.2370	−	15.4241i	−1.41248	−	0.585068i
$696$	−8.12835	+	25.6012i	−0.308104	+	0.970410i
$697$	71.2828	−	29.5263i	2.70003	−	1.11839i
$698$	−2.19341	+	12.9387i	−0.0830218	+	0.489735i
$699$	−5.85959	+	8.76950i	−0.221630	+	0.331693i
$700$	−3.20865	−	2.86313i	−0.121276	−	0.108216i
$701$	37.5774	+	7.47461i	1.41928	+	0.282312i	0.844307	−	0.535860i	$-0.180013\pi$
$701$	37.5774	+	7.47461i	1.41928	+	0.282312i	0.574973	+	0.818173i	$0.305013\pi$
$702$	0.00238575	+	0.0839173i	9.00444e−5	+	0.00316726i
$703$	5.20897			0.196460
$704$	−12.3943	−	32.2531i	−0.467126	−	1.21559i
$705$	17.4208			0.656106
$706$	−0.603813	−	21.2387i	−0.0227248	−	0.799331i
$707$	−22.7526	−	4.52577i	−0.855698	−	0.170209i
$708$	3.60699	−	4.04228i	0.135559	−	0.151918i
$709$	10.4955	−	15.7077i	0.394168	−	0.589914i	−0.580310	−	0.814395i	$-0.697069\pi$
$709$	10.4955	−	15.7077i	0.394168	−	0.589914i	0.974478	+	0.224481i	$0.0720687\pi$
$710$	0.273604	−	1.61395i	0.0102682	−	0.0605706i
$711$	−8.12639	+	3.36606i	−0.304764	+	0.126237i
$712$	−1.62872	−	3.14409i	−0.0610390	−	0.117830i
$713$	−3.88576	−	1.60953i	−0.145523	−	0.0602775i
$714$	20.1629	+	12.6587i	0.754579	+	0.473742i
$715$	0.0999349	+	0.502407i	0.00373735	+	0.0187890i
$716$	−28.9292	−	38.3807i	−1.08114	−	1.43435i
$717$	11.5540	+	17.2918i	0.431491	+	0.645773i
$718$	−4.16651	−	9.30195i	−0.155493	−	0.347146i
$719$	−9.69241	+	9.69241i	−0.361466	+	0.361466i	−0.864352	−	0.502887i	$-0.832271\pi$
$719$	−9.69241	+	9.69241i	−0.361466	+	0.361466i	0.502887	+	0.864352i	$0.332271\pi$
$720$	−6.09827	+	5.16510i	−0.227269	+	0.192492i
$721$	7.80882	+	7.80882i	0.290816	+	0.290816i
$722$	−9.39245	+	24.6331i	−0.349551	+	0.916750i
$723$	12.3995	−	8.28506i	0.461141	−	0.308125i
$724$	−9.09414	−	35.1469i	−0.337981	−	1.30622i
$725$	−9.39152	+	1.86809i	−0.348792	+	0.0693791i
$726$	−10.5527	+	2.41271i	−0.391646	+	0.0895441i
$727$	−12.6502	+	30.5402i	−0.469169	+	1.13267i	0.495358	+	0.868689i	$0.335037\pi$
$727$	−12.6502	+	30.5402i	−0.469169	+	1.13267i	−0.964527	+	0.263985i	$0.914963\pi$
$728$	−0.313563	−	0.172844i	−0.0116214	−	0.00640601i
$729$	0.382683	+	0.923880i	0.0141735	+	0.0342178i
$730$	6.09286	−	4.32652i	0.225507	−	0.160132i
$731$	−7.89119	−	5.27272i	−0.291866	−	0.195019i
$732$	−4.21017	−	1.46968i	−0.155612	−	0.0543211i
$733$	2.64172	−	13.2808i	0.0975742	−	0.490538i	−0.900835	−	0.434161i	$-0.857045\pi$
$733$	2.64172	−	13.2808i	0.0975742	−	0.490538i	0.998410	−	0.0563776i	$-0.0179551\pi$
$734$	−8.32318	−	7.86301i	−0.307214	−	0.290229i
$735$		−	4.90011i		−	0.180743i
$736$	2.16920	−	8.47449i	0.0799579	−	0.312374i
$737$		−	62.1884i		−	2.29074i
$738$	−9.49193	+	10.0474i	−0.349403	+	0.369851i
$739$	6.17640	−	31.0509i	0.227203	−	1.14222i	−0.683751	−	0.729716i	$-0.739652\pi$
$739$	6.17640	−	31.0509i	0.227203	−	1.14222i	0.910953	−	0.412509i	$-0.135348\pi$
$740$	−31.3079	+	15.1058i	−1.15090	+	0.555300i
$741$	0.0295542	+	0.0197475i	0.00108570	+	0.000725443i
$742$	8.16514	+	11.4986i	0.299752	+	0.422127i
$743$	9.26915	+	22.3777i	0.340052	+	0.820958i	0.997710	+	0.0676413i	$0.0215473\pi$
$743$	9.26915	+	22.3777i	0.340052	+	0.820958i	−0.657658	+	0.753317i	$0.728453\pi$
$744$	0.852787	−	7.64541i	0.0312647	−	0.280294i
$745$	13.2689	−	32.0340i	0.486136	−	1.17364i
$746$	1.12219	+	4.90823i	0.0410864	+	0.179703i
$747$	4.91510	−	0.977674i	0.179834	−	0.0357712i
$748$	−34.6030	+	58.7605i	−1.26521	+	2.14850i
$749$	4.89360	−	3.26980i	0.178808	−	0.119476i
$750$	−15.8624	−	6.04825i	−0.579214	−	0.220851i
$751$	−11.6558	−	11.6558i	−0.425328	−	0.425328i	0.461706	−	0.887033i	$-0.347238\pi$
$751$	−11.6558	−	11.6558i	−0.425328	−	0.425328i	−0.887033	+	0.461706i	$0.847238\pi$
$752$	−27.3009	−	21.7054i	−0.995563	−	0.791513i
$753$	−5.28913	+	5.28913i	−0.192747	+	0.192747i
$754$	−0.727600	+	0.325905i	−0.0264976	+	0.0118688i
$755$	12.8308	+	19.2027i	0.466961	+	0.698856i
$756$	−4.22349	−	0.593052i	−0.153607	−	0.0215691i
$757$	1.17630	+	5.91368i	0.0427535	+	0.214936i	0.996256	−	0.0864475i	$-0.0275515\pi$
$757$	1.17630	+	5.91368i	0.0427535	+	0.214936i	−0.953503	+	0.301384i	$0.902551\pi$
$758$	−0.295572	+	0.470790i	−0.0107357	+	0.0170999i
$759$	−6.17057	−	2.55593i	−0.223977	−	0.0927745i
$760$	0.288162	+	3.37135i	0.0104527	+	0.122292i
$761$	17.3693	−	7.19458i	0.629635	−	0.260803i	−0.0449630	−	0.998989i	$-0.514317\pi$
$761$	17.3693	−	7.19458i	0.629635	−	0.260803i	0.674598	+	0.738185i	$0.264317\pi$
$762$	−25.6906	−	4.35517i	−0.930673	−	0.157771i
$763$	−9.09890	+	13.6175i	−0.329402	+	0.492985i
$764$	−44.1703	+	2.51354i	−1.59803	+	0.0909365i
$765$	15.4691	+	3.07700i	0.559288	+	0.111249i
$766$	−4.62262	+	0.131420i	−0.167022	+	0.00474840i
$767$	0.160801			0.00580619
$768$	15.9923	−	0.496361i	0.577072	−	0.0179109i
$769$	−37.3656			−1.34744			−0.673719	−	0.738988i	$-0.735304\pi$
$769$	−37.3656			−1.34744			−0.673719	+	0.738988i	$0.735304\pi$
$770$	−26.0130	+	0.739544i	−0.937444	+	0.0266513i
$771$	23.6534	+	4.70496i	0.851858	+	0.169445i
$772$	−45.7803	+	2.60515i	−1.64767	+	0.0937615i
$773$	−21.4342	+	32.0786i	−0.770935	+	1.15379i	0.213312	+	0.976984i	$0.431575\pi$
$773$	−21.4342	+	32.0786i	−0.770935	+	1.15379i	−0.984247	+	0.176802i	$0.943425\pi$
$774$	1.67627	+	0.284169i	0.0602524	+	0.0102142i
$775$	2.53366	−	1.04948i	0.0910117	−	0.0376983i
$776$	−0.223700	−	2.61718i	−0.00803034	−	0.0939511i
$777$	−17.1391	−	7.09924i	−0.614861	−	0.254684i
$778$	8.33890	−	13.2822i	0.298964	−	0.476192i
$779$	1.14170	+	5.73972i	0.0409057	+	0.205647i
$780$	−0.234899	−	0.0329839i	−0.00841073	−	0.00118101i
$781$	1.39021	+	2.08059i	0.0497455	+	0.0744494i
$782$	−15.7559	+	7.05735i	−0.563430	+	0.252370i
$783$	−6.71514	+	6.71514i	−0.239980	+	0.239980i
$784$	−6.10526	+	7.67918i	−0.218045	+	0.274256i
$785$	−7.78802	−	7.78802i	−0.277966	−	0.277966i
$786$	17.4210	+	6.64250i	0.621385	+	0.236930i
$787$	12.0617	−	8.05934i	0.429952	−	0.287284i	−0.321704	−	0.946840i	$-0.604256\pi$
$787$	12.0617	−	8.05934i	0.429952	−	0.287284i	0.751656	+	0.659556i	$0.229256\pi$
$788$	10.0921	−	17.1377i	0.359516	−	0.610505i
$789$	11.0110	−	2.19023i	0.392002	−	0.0779741i
$790$	−5.53930	−	24.2277i	−0.197079	−	0.861982i
$791$	−13.7980	+	33.3114i	−0.490602	+	1.18442i
$792$	1.35422	−	12.1409i	0.0481202	−	0.431408i
$793$	−0.0506512	−	0.122283i	−0.00179868	−	0.00434239i
$794$	−11.1287	−	15.6720i	−0.394941	−	0.556179i
$795$	7.76841	+	5.19069i	0.275517	+	0.184095i
$796$	−43.3238	+	20.9034i	−1.53557	+	0.740901i
$797$	2.06005	−	10.3566i	0.0729706	−	0.366848i	−0.926996	−	0.375072i	$-0.877618\pi$
$797$	2.06005	−	10.3566i	0.0729706	−	0.366848i	0.999966	+	0.00822432i	$0.00261791\pi$
$798$	−1.24006	+	1.31263i	−0.0438975	+	0.0464665i
$799$			68.8340i			2.43517i
$800$	2.90711	+	4.90738i	0.102782	+	0.173502i
$801$		−	1.25190i		−	0.0442337i
$802$	4.87415	+	4.60467i	0.172112	+	0.162596i
$803$	−2.22850	+	11.2034i	−0.0786420	+	0.395360i
$804$	27.1882	+	9.49084i	0.958852	+	0.334716i
$805$	−5.47805	−	3.66031i	−0.193076	−	0.129009i
$806$	0.186170	−	0.132199i	0.00655756	−	0.00465651i
$807$	0.378054	+	0.912703i	0.0133081	+	0.0321287i
$808$	26.9468	+	14.8537i	0.947983	+	0.522551i
$809$	−6.65432	+	16.0649i	−0.233953	+	0.564813i	−0.996636	−	0.0819600i	$-0.973882\pi$
$809$	−6.65432	+	16.0649i	−0.233953	+	0.564813i	0.762682	+	0.646773i	$0.223882\pi$
$810$	−2.75441	+	0.629756i	−0.0967803	+	0.0221274i
$811$	33.1959	−	6.60308i	1.16567	−	0.231865i	0.425926	−	0.904758i	$-0.359948\pi$
$811$	33.1959	−	6.60308i	1.16567	−	0.231865i	0.739740	+	0.672893i	$0.234948\pi$
$812$	−10.1458	−	39.2112i	−0.356046	−	1.37604i
$813$	17.6510	−	11.7940i	0.619046	−	0.413633i
$814$	18.9313	−	49.6502i	0.663542	−	1.74024i
$815$	17.5280	+	17.5280i	0.613981	+	0.613981i
$816$	−20.4086	−	24.0958i	−0.714444	−	0.843522i
$817$	0.509013	−	0.509013i	0.0178081	−	0.0178081i
$818$	9.29728	+	20.7567i	0.325072	+	0.725739i
$819$	−0.0703287	−	0.105254i	−0.00245748	−	0.00367789i
$820$	−23.5070	−	31.1870i	−0.820900	−	1.08910i
$821$	3.06776	+	15.4227i	0.107066	+	0.538255i	0.996671	+	0.0815255i	$0.0259792\pi$
$821$	3.06776	+	15.4227i	0.107066	+	0.538255i	−0.889606	+	0.456729i	$0.849021\pi$
$822$	15.8669	+	9.96161i	0.553422	+	0.347451i
$823$	−29.0389	−	12.0283i	−1.01223	−	0.419281i	−0.185964	−	0.982556i	$-0.559541\pi$
$823$	−29.0389	−	12.0283i	−1.01223	−	0.419281i	−0.826269	+	0.563276i	$0.809541\pi$
$824$	−6.73747	−	13.0060i	−0.234711	−	0.453086i
$825$	4.02344	−	1.66656i	0.140078	−	0.0580223i
$826$	−1.36538	+	8.05418i	−0.0475075	+	0.280241i
$827$	15.8521	−	23.7244i	0.551232	−	0.824977i	−0.446322	−	0.894872i	$-0.647267\pi$
$827$	15.8521	−	23.7244i	0.551232	−	0.824977i	0.997554	+	0.0698954i	$0.0222665\pi$
$828$	2.05915	−	2.30764i	0.0715603	−	0.0801961i
$829$	29.8931	+	5.94610i	1.03823	+	0.206517i	0.684638	−	0.728883i	$-0.259960\pi$
$829$	29.8931	+	5.94610i	1.03823	+	0.206517i	0.353591	+	0.935400i	$0.384960\pi$
$830$	0.402393	+	14.1539i	0.0139673	+	0.491290i
$831$	20.2980			0.704129
$832$	0.327025	+	0.344362i	0.0113375	+	0.0119386i
$833$	19.3616			0.670838
$834$	0.810763	+	28.5181i	0.0280744	+	0.987500i
$835$	−20.1202	−	4.00215i	−0.696287	−	0.138500i
$836$	−3.85923	−	3.44366i	−0.133474	−	0.119101i
$837$	1.51105	−	2.26145i	0.0522297	−	0.0781672i
$838$	−9.36437	+	55.2392i	−0.323487	+	1.90821i
$839$	34.4920	−	14.2870i	1.19080	−	0.493244i	0.302782	−	0.953060i	$-0.402085\pi$
$839$	34.4920	−	14.2870i	1.19080	−	0.493244i	0.888014	+	0.459816i	$0.152085\pi$
$840$	3.64664	−	11.4855i	0.125821	−	0.396287i
$841$	−56.5287	−	23.4149i	−1.94926	−	0.807412i
$842$	−34.5372	−	21.6832i	−1.19023	−	0.747254i
$843$	−0.244649	−	1.22994i	−0.00842617	−	0.0423612i
$844$	−21.9622	+	16.5539i	−0.755970	+	0.569808i
$845$	14.4259	+	21.5899i	0.496266	+	0.742715i
$846$	−5.04079	−	11.2538i	−0.173306	−	0.386914i
$847$	11.5419	−	11.5419i	0.396585	−	0.396585i
$848$	−5.70692	−	17.8136i	−0.195977	−	0.611720i
$849$	−7.21243	−	7.21243i	−0.247530	−	0.247530i
$850$	4.01055	−	10.5183i	0.137561	−	0.360774i
$851$	11.1855	−	7.47393i	0.383435	−	0.256203i
$852$	−1.12178	+	0.290257i	−0.0384315	+	0.00994404i
$853$	35.9611	−	7.15311i	1.23129	−	0.244918i	0.463774	−	0.885954i	$-0.346495\pi$
$853$	35.9611	−	7.15311i	1.23129	−	0.244918i	0.767511	+	0.641036i	$0.221495\pi$
$854$	6.55496	−	1.49869i	0.224306	−	0.0512843i
$855$	−0.457804	+	1.10524i	−0.0156566	+	0.0377983i
$856$	−7.49880	+	2.16944i	−0.256304	+	0.0741499i
$857$	−14.6493	−	35.3666i	−0.500411	−	1.20810i	−0.949260	−	0.314492i	$-0.898166\pi$
$857$	−14.6493	−	35.3666i	−0.500411	−	1.20810i	0.448849	−	0.893608i	$-0.351834\pi$
$858$	0.295638	−	0.209931i	0.0100929	−	0.00716694i
$859$	−33.5022	−	22.3855i	−1.14308	−	0.763783i	−0.168035	−	0.985781i	$-0.553742\pi$
$859$	−33.5022	−	22.3855i	−1.14308	−	0.763783i	−0.975047	+	0.221998i	$0.928742\pi$
$860$	−1.58324	+	4.53547i	−0.0539881	+	0.154658i
$861$	4.06605	−	20.4414i	0.138571	−	0.696642i
$862$	2.85201	+	2.69432i	0.0971397	+	0.0917691i
$863$			3.04970i			0.103813i	0.998652	+	0.0519064i	$0.0165298\pi$
$863$			3.04970i			0.103813i	−0.998652	+	0.0519064i	$0.983470\pi$
$864$	5.10121	+	2.44493i	0.173547	+	0.0831781i
$865$			2.19905i			0.0747701i
$866$	8.68817	−	9.19664i	0.295236	−	0.312514i
$867$	−8.84148	+	44.4491i	−0.300273	+	1.50957i
$868$	5.04077	+	10.4474i	0.171095	+	0.354606i
$869$	31.5878	+	21.1063i	1.07154	+	0.715982i
$870$	−15.5354	−	21.8779i	−0.526701	−	0.741730i
$871$	0.327092	+	0.789671i	0.0110831	+	0.0267570i
$872$	16.9683	−	13.5628i	0.574621	−	0.459295i
$873$	0.355392	−	0.857993i	0.0120282	−	0.0290387i
$874$	−0.291859	−	1.27653i	−0.00987229	−	0.0431792i
$875$	25.1065	−	4.99399i	0.848755	−	0.168828i
$876$	−4.55792	−	2.68408i	−0.153998	−	0.0906866i
$877$	−44.8166	+	29.9455i	−1.51335	+	1.01119i	−0.526384	+	0.850247i	$0.676453\pi$
$877$	−44.8166	+	29.9455i	−1.51335	+	1.01119i	−0.986964	+	0.160940i	$0.948547\pi$
$878$	−25.9312	−	9.88742i	−0.875137	−	0.333684i
$879$	−14.3412	−	14.3412i	−0.483715	−	0.483715i
$880$	33.1819	+	9.50606i	1.11856	+	0.320449i
$881$	−6.73106	+	6.73106i	−0.226775	+	0.226775i	−0.811344	−	0.584569i	$-0.801264\pi$
$881$	−6.73106	+	6.73106i	−0.226775	+	0.226775i	0.584569	+	0.811344i	$0.301264\pi$
$882$	−3.16546	+	1.41787i	−0.106587	+	0.0477421i
$883$	1.34241	+	2.00906i	0.0451757	+	0.0676103i	0.853370	−	0.521306i	$-0.174555\pi$
$883$	1.34241	+	2.00906i	0.0451757	+	0.0676103i	−0.808194	+	0.588916i	$0.799555\pi$
$884$	0.130328	−	0.928145i	0.00438339	−	0.0312169i
$885$	1.05582	+	5.30798i	0.0354911	+	0.178426i
$886$	−10.9659	+	17.4666i	−0.368407	+	0.586801i
$887$	−51.4467	−	21.3099i	−1.72741	−	0.715517i	−0.999556	−	0.0297870i	$-0.990517\pi$
$887$	−51.4467	−	21.3099i	−1.72741	−	0.715517i	−0.727856	−	0.685730i	$-0.759483\pi$
$888$	18.8174	+	15.8539i	0.631470	+	0.532022i
$889$	36.3002	−	15.0360i	1.21747	−	0.504292i
$890$	3.48747	+	0.591210i	0.116900	+	0.0198174i
$891$	2.39955	−	3.59118i	0.0803879	−	0.120309i
$892$	−2.40827	−	42.3204i	−0.0806347	−	1.41699i
$893$	−5.12065	−	1.01856i	−0.171356	−	0.0340848i
$894$	−24.5333	+	0.697478i	−0.820518	+	0.0233272i
$895$	48.0123			1.60487
$896$	−20.0251	+	13.4559i	−0.668992	+	0.449532i
$897$	0.0917976			0.00306503
$898$	19.0191	−	0.540710i	0.634676	−	0.0180437i
$899$	25.3329	+	5.03903i	0.844900	+	0.168061i
$900$	0.114571	+	2.01335i	0.00381903	+	0.0671117i
$901$	−20.5097	+	30.6950i	−0.683278	+	1.02260i
$902$	58.8585	+	9.97792i	1.95977	+	0.332228i
$903$	−2.36853	+	0.981078i	−0.0788198	+	0.0326482i
$904$	30.8136	−	36.5734i	1.02484	−	1.21641i
$905$	33.5060	+	13.8786i	1.11378	+	0.461342i
$906$	8.69224	−	13.8451i	0.288780	−	0.459971i
$907$	2.35080	+	11.8183i	0.0780571	+	0.392420i	0.999987	+	0.00506329i	$0.00161170\pi$
$907$	2.35080	+	11.8183i	0.0780571	+	0.392420i	−0.921930	+	0.387356i	$0.873388\pi$
$908$	−5.97380	+	42.5432i	−0.198247	+	1.41184i
$909$	6.04385	+	9.04526i	0.200462	+	0.300012i
$910$	0.326424	−	0.146211i	0.0108209	−	0.00484686i
$911$	26.7369	−	26.7369i	0.885832	−	0.885832i	−0.108287	−	0.994120i	$-0.534537\pi$
$911$	26.7369	−	26.7369i	0.885832	−	0.885832i	0.994120	+	0.108287i	$0.0345366\pi$
$912$	2.09451	−	1.16167i	0.0693561	−	0.0384667i
$913$	−15.3050	−	15.3050i	−0.506523	−	0.506523i
$914$	−8.60947	−	3.28274i	−0.284776	−	0.108583i
$915$	3.70393	−	2.47489i	0.122448	−	0.0818173i
$916$	24.3850	+	14.3599i	0.805701	+	0.474463i
$917$	−27.5733	+	5.48466i	−0.910550	+	0.181120i
$918$	−2.48832	−	10.8834i	−0.0821269	−	0.359205i
$919$	10.3494	−	24.9856i	0.341394	−	0.824198i	−0.656182	−	0.754603i	$-0.727829\pi$
$919$	10.3494	−	24.9856i	0.341394	−	0.824198i	0.997575	−	0.0695946i	$-0.0221706\pi$
$920$	5.45607	+	6.82604i	0.179881	+	0.225048i
$921$	−1.44083	−	3.47846i	−0.0474768	−	0.114619i
$922$	20.6066	+	29.0194i	0.678641	+	0.955702i
$923$	−0.0285962	−	0.0191074i	−0.000941255	−	0.000628927i
$924$	8.00472	+	16.5904i	0.263336	+	0.545783i
$925$	−1.71127	+	8.60313i	−0.0562662	+	0.282869i
$926$	17.7451	−	18.7836i	0.583140	−	0.617267i
$927$		−	5.17868i		−	0.170090i
$928$	−2.91234	+	53.6421i	−0.0956024	+	1.76089i
$929$			22.5285i			0.739137i	0.929204	+	0.369568i	$0.120494\pi$
$929$			22.5285i			0.739137i	−0.929204	+	0.369568i	$0.879506\pi$
$930$	5.58623	+	5.27738i	0.183180	+	0.173052i
$931$	−0.286499	+	1.44033i	−0.00938963	+	0.0472049i
$932$	−6.95208	+	19.9154i	−0.227723	+	0.652352i
$933$	20.6741	+	13.8140i	0.676839	+	0.452249i
$934$	−30.9517	+	21.9787i	−1.01277	+	0.719166i
$935$	−26.0689	−	62.9359i	−0.852544	−	2.05822i
$936$	0.0466615	+	0.161288i	0.00152518	+	0.00527188i
$937$	5.10255	−	12.3187i	0.166693	−	0.402433i	−0.818355	−	0.574713i	$-0.805114\pi$
$937$	5.10255	−	12.3187i	0.166693	−	0.402433i	0.985048	+	0.172281i	$0.0551135\pi$
$938$	−42.3302	+	9.67818i	−1.38213	+	0.316004i
$939$	−2.78351	+	0.553675i	−0.0908365	+	0.0180685i
$940$	33.7308	−	8.72773i	1.10018	−	0.284667i
$941$	−37.4938	+	25.0526i	−1.22226	+	0.816690i	−0.987844	−	0.155446i	$-0.950319\pi$
$941$	−37.4938	+	25.0526i	−1.22226	+	0.816690i	−0.234418	+	0.972136i	$0.575319\pi$
$942$	−2.77755	+	7.28455i	−0.0904975	+	0.237343i
$943$	10.6871	+	10.6871i	0.348020	+	0.348020i
$944$	4.95882	−	9.63388i	0.161396	−	0.313556i
$945$	3.01263	−	3.01263i	0.0980007	−	0.0980007i
$946$	−3.00180	−	6.70168i	−0.0975970	−	0.217890i
$947$	30.2141	+	45.2186i	0.981826	+	1.46941i	0.880211	+	0.474583i	$0.157401\pi$
$947$	30.2141	+	45.2186i	0.981826	+	1.46941i	0.101615	+	0.994824i	$0.467599\pi$
$948$	−14.0482	+	10.5888i	−0.456265	+	0.343907i
$949$	−0.0306291	−	0.153983i	−0.000994261	−	0.00499849i
$950$	0.723122	+	0.453992i	0.0234612	+	0.0147294i
$951$	−2.74274	−	1.13608i	−0.0889394	−	0.0368399i
$952$	45.3821	+	14.4088i	1.47084	+	0.466991i
$953$	−35.8366	+	14.8440i	−1.16086	+	0.480844i	−0.878161	−	0.478365i	$-0.841230\pi$
$953$	−35.8366	+	14.8440i	−1.16086	+	0.480844i	−0.282699	+	0.959209i	$0.591230\pi$
$954$	1.10535	−	6.52033i	0.0357871	−	0.211104i
$955$	24.5539	−	36.7475i	0.794545	−	1.18912i
$956$	31.0343	+	27.6924i	1.00372	+	0.895637i
$957$	40.2286	+	8.00196i	1.30041	+	0.258667i
$958$	−0.431706	−	15.1850i	−0.0139478	−	0.490604i
$959$	−28.2498			−0.912234
$960$	−9.21999	+	13.0560i	−0.297574	+	0.421382i
$961$	23.6026			0.761373
$962$	0.0207547	+	0.730033i	0.000669158	+	0.0235372i
$963$	−2.70692	−	0.538439i	−0.0872292	−	0.0173510i
$964$	19.8575	−	22.2539i	0.639568	−	0.716750i
$965$	25.4488	−	38.0869i	0.819227	−	1.22606i
$966$	−0.779461	+	4.59794i	−0.0250787	+	0.147936i
$967$	−45.6321	+	18.9014i	−1.46743	+	0.607829i	−0.966271	−	0.257527i	$-0.917093\pi$
$967$	−45.6321	+	18.9014i	−1.46743	+	0.607829i	−0.501158	+	0.865356i	$0.667093\pi$
$968$	−19.2237	+	9.95840i	−0.617873	+	0.320075i
$969$	−4.36707	−	1.80890i	−0.140290	−	0.0581102i
$970$	2.22232	+	1.39522i	0.0713542	+	0.0447978i
$971$	2.54720	+	12.8057i	0.0817437	+	0.410953i	0.999892	+	0.0147156i	$0.00468430\pi$
$971$	2.54720	+	12.8057i	0.0817437	+	0.410953i	−0.918148	+	0.396237i	$0.870316\pi$
$972$	1.20382	+	1.59713i	0.0386127	+	0.0512278i
$973$	−23.9002	−	35.7692i	−0.766205	−	1.14671i
$974$	−10.5903	−	23.6435i	−0.339336	−	0.757586i
$975$	−0.0423242	+	0.0423242i	−0.00135546	+	0.00135546i
$976$	−8.88818	−	0.736384i	−0.284504	−	0.0235711i
$977$	35.2322	+	35.2322i	1.12718	+	1.12718i	0.990634	+	0.136544i	$0.0435996\pi$
$977$	35.2322	+	35.2322i	1.12718	+	1.12718i	0.136544	+	0.990634i	$0.456400\pi$
$978$	6.25128	−	16.3949i	0.199894	−	0.524251i
$979$	−4.49580	+	3.00400i	−0.143686	+	0.0960081i
$980$	−2.45493	−	9.48775i	−0.0784197	−	0.303075i
$981$	7.53256	−	1.49832i	0.240496	−	0.0478376i
$982$	13.6806	−	3.12786i	0.436565	−	0.0998141i
$983$	−9.31149	+	22.4799i	−0.296990	+	0.716998i	0.702993	+	0.711197i	$0.251847\pi$
$983$	−9.31149	+	22.4799i	−0.296990	+	0.716998i	−0.999983	+	0.00580137i	$0.998153\pi$
$984$	−13.3449	+	24.2096i	−0.425420	+	0.771774i
$985$	7.60308	+	18.3555i	0.242254	+	0.584854i
$986$	86.4451	−	61.3844i	2.75297	−	1.95488i
$987$	15.4603	+	10.3302i	0.492107	+	0.328815i
$988$	0.0671173	+	0.0234293i	0.00213529	+	0.000745385i
$989$	0.362691	−	1.82337i	0.0115329	−	0.0579799i
$990$	8.87092	+	8.38047i	0.281936	+	0.266349i
$991$		−	2.80403i		−	0.0890728i	−0.999008	−	0.0445364i	$-0.985819\pi$
$991$		−	2.80403i		−	0.0890728i	0.999008	−	0.0445364i	$-0.0141811\pi$
$992$	−2.17911	−	15.2306i	−0.0691869	−	0.483571i
$993$			2.73125i			0.0866736i
$994$	1.19986	−	1.27008i	0.0380572	−	0.0402844i
$995$	9.37469	−	47.1297i	0.297198	−	1.49411i
$996$	9.02698	−	4.35544i	0.286031	−	0.138008i
$997$	−9.49096	−	6.34166i	−0.300582	−	0.200842i	0.396128	−	0.918195i	$-0.370354\pi$
$997$	−9.49096	−	6.34166i	−0.300582	−	0.200842i	−0.696710	+	0.717353i	$0.745354\pi$
$998$	−8.09265	−	11.3965i	−0.256168	−	0.360751i
$999$	3.32913	+	8.03723i	0.105329	+	0.254287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.157.16	✓	128
3.2	odd	2		576.2.bd.b.541.1		128
4.3	odd	2		768.2.r.a.721.4		128
64.11	odd	16		768.2.r.a.49.4		128
64.53	even	16	inner	192.2.r.a.181.16	yes	128
192.53	odd	16		576.2.bd.b.181.1		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.157.16	✓	128	1.1	even	1	trivial
192.2.r.a.181.16	yes	128	64.53	even	16	inner
576.2.bd.b.181.1		128	192.53	odd	16
576.2.bd.b.541.1		128	3.2	odd	2
768.2.r.a.49.4		128	64.11	odd	16
768.2.r.a.721.4		128	4.3	odd	2

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41364 - 0.0401896i) q^{2} +(0.980785 + 0.195090i) q^{3} +(1.99677 - 0.113627i) q^{4} +(-1.10999 + 1.66121i) q^{5} +(1.39432 + 0.236371i) q^{6} +(-1.97014 + 0.816058i) q^{7} +(2.81815 - 0.240878i) q^{8} +(0.923880 + 0.382683i) q^{9} +O(q^{10})\)	\(q+(1.41364 - 0.0401896i) q^{2} +(0.980785 + 0.195090i) q^{3} +(1.99677 - 0.113627i) q^{4} +(-1.10999 + 1.66121i) q^{5} +(1.39432 + 0.236371i) q^{6} +(-1.97014 + 0.816058i) q^{7} +(2.81815 - 0.240878i) q^{8} +(0.923880 + 0.382683i) q^{9} +(-1.50236 + 2.39297i) q^{10} +(-0.842610 - 4.23609i) q^{11} +(1.98057 + 0.278106i) q^{12} +(0.0329800 + 0.0493581i) q^{13} +(-2.75228 + 1.23279i) q^{14} +(-1.41274 + 1.41274i) q^{15} +(3.97418 - 0.453775i) q^{16} +(-5.58211 - 5.58211i) q^{17} +(1.32142 + 0.503847i) q^{18} +(0.497860 - 0.332660i) q^{19} +(-2.02763 + 3.44318i) q^{20} +(-2.09149 + 0.416023i) q^{21} +(-1.36140 - 5.95445i) q^{22} +(0.591778 - 1.42868i) q^{23} +(2.81099 + 0.313545i) q^{24} +(0.385862 + 0.931552i) q^{25} +(0.0486057 + 0.0684493i) q^{26} +(0.831470 + 0.555570i) q^{27} +(-3.84119 + 1.85334i) q^{28} +(-1.85270 + 9.31417i) q^{29} +(-1.94034 + 2.05389i) q^{30} -2.71983i q^{31} +(5.59983 - 0.801196i) q^{32} -4.31907i q^{33} +(-8.11545 - 7.66677i) q^{34} +(0.831182 - 4.17863i) q^{35} +(1.88826 + 0.659153i) q^{36} +(7.23331 + 4.83314i) q^{37} +(0.690427 - 0.490270i) q^{38} +(0.0227170 + 0.0548438i) q^{39} +(-2.72796 + 4.94892i) q^{40} +(-3.74021 + 9.02966i) q^{41} +(-2.93990 + 0.672164i) q^{42} +(1.17912 - 0.234541i) q^{43} +(-2.16383 - 8.36274i) q^{44} +(-1.66121 + 1.10999i) q^{45} +(0.779145 - 2.04342i) q^{46} +(-6.16559 - 6.16559i) q^{47} +(3.98634 + 0.330268i) q^{48} +(-1.73425 + 1.73425i) q^{49} +(0.582909 + 1.30137i) q^{50} +(-4.38584 - 6.56387i) q^{51} +(0.0714620 + 0.0948093i) q^{52} +(-0.912311 - 4.58650i) q^{53} +(1.19773 + 0.751961i) q^{54} +(7.97232 + 3.30224i) q^{55} +(-5.35558 + 2.77434i) q^{56} +(0.553193 - 0.229140i) q^{57} +(-2.24473 + 13.2414i) q^{58} +(1.50493 - 2.25229i) q^{59} +(-2.66040 + 2.98145i) q^{60} +(-2.18682 - 0.434985i) q^{61} +(-0.109309 - 3.84486i) q^{62} -2.13246 q^{63} +(7.88396 - 1.35766i) q^{64} -0.118602 q^{65} +(-0.173582 - 6.10563i) q^{66} +(14.1219 + 2.80902i) q^{67} +(-11.7805 - 10.5119i) q^{68} +(0.859128 - 1.28578i) q^{69} +(1.00706 - 5.94050i) q^{70} +(-0.535260 + 0.221712i) q^{71} +(2.69581 + 0.855918i) q^{72} +(-2.44344 - 1.01210i) q^{73} +(10.4196 + 6.54163i) q^{74} +(0.196711 + 0.988931i) q^{75} +(0.956313 - 0.720815i) q^{76} +(5.11695 + 7.65806i) q^{77} +(0.0343179 + 0.0766165i) q^{78} +(-6.21967 + 6.21967i) q^{79} +(-3.65747 + 7.10564i) q^{80} +(0.707107 + 0.707107i) q^{81} +(-4.92442 + 12.9150i) q^{82} +(4.16682 - 2.78418i) q^{83} +(-4.12895 + 1.06835i) q^{84} +(15.4691 - 3.07700i) q^{85} +(1.65742 - 0.378945i) q^{86} +(-3.63421 + 8.77375i) q^{87} +(-3.39498 - 11.7350i) q^{88} +(-0.479081 - 1.15660i) q^{89} +(-2.30375 + 1.63589i) q^{90} +(-0.105254 - 0.0703287i) q^{91} +(1.01931 - 2.91998i) q^{92} +(0.530612 - 2.66756i) q^{93} +(-8.96373 - 8.46815i) q^{94} +1.19630i q^{95} +(5.64854 + 0.306671i) q^{96} -0.928685i q^{97} +(-2.38191 + 2.52131i) q^{98} +(0.842610 - 4.23609i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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