LMFDB - Embedded newform 483.2.u.a.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(113,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 13]))

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

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

chi := DirichletCharacter("483.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.u (of order $22$, degree $10$, 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:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.2
Character	$\chi$	$=$	483.113
Dual form			483.2.u.a.218.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.48162 + 2.30545i) q^{2} +(-0.121691 + 1.72777i) q^{3} +(-2.28907 - 5.01236i) q^{4} +(-4.08876 - 1.20057i) q^{5} +(-3.80299 - 2.84046i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(9.52207 + 1.36907i) q^{8} +(-2.97038 - 0.420508i) q^{9} +(8.82585 - 7.64764i) q^{10} +(-2.13484 + 1.37198i) q^{11} +(8.93876 - 3.34502i) q^{12} +(0.776153 + 0.895728i) q^{13} +(2.62949 - 0.772087i) q^{14} +(2.57187 - 6.91834i) q^{15} +(-10.0475 + 11.5954i) q^{16} +(0.184476 - 0.403945i) q^{17} +(5.37045 - 6.22504i) q^{18} +(-1.45894 + 0.666276i) q^{19} +(3.34176 + 23.2425i) q^{20} +(1.22342 - 1.22607i) q^{21} -6.95452i q^{22} +(3.66084 + 3.09810i) q^{23} +(-3.52418 + 16.2854i) q^{24} +(11.0703 + 7.11445i) q^{25} +(-3.21502 + 0.462251i) q^{26} +(1.08801 - 5.08097i) q^{27} +(-1.55243 + 5.28711i) q^{28} +(3.95026 + 1.80402i) q^{29} +(12.1393 + 16.1797i) q^{30} +(0.261035 - 1.81554i) q^{31} +(-6.42553 - 21.8833i) q^{32} +(-2.11067 - 3.85547i) q^{33} +(0.657953 + 1.02379i) q^{34} +(2.30387 + 3.58489i) q^{35} +(4.69167 + 15.8512i) q^{36} +(-1.50060 - 5.11057i) q^{37} +(0.625534 - 4.35068i) q^{38} +(-1.64206 + 1.23201i) q^{39} +(-37.2898 - 17.0297i) q^{40} +(2.51927 - 8.57984i) q^{41} +(1.01400 + 4.63710i) q^{42} +(-3.53154 + 0.507759i) q^{43} +(11.7636 + 7.56003i) q^{44} +(11.6403 + 5.28550i) q^{45} +(-12.5665 + 3.84967i) q^{46} -6.93468i q^{47} +(-18.8115 - 18.7708i) q^{48} +(0.142315 + 0.989821i) q^{49} +(-32.8040 + 14.9811i) q^{50} +(0.675476 + 0.367888i) q^{51} +(2.71304 - 5.94074i) q^{52} +(6.34988 - 7.32816i) q^{53} +(10.1019 + 10.0364i) q^{54} +(10.3760 - 3.04667i) q^{55} +(-6.29975 - 7.27030i) q^{56} +(-0.973632 - 2.60179i) q^{57} +(-10.0119 + 6.43424i) q^{58} +(-2.14873 + 1.86188i) q^{59} +(-40.5643 + 2.94540i) q^{60} +(4.34861 + 0.625235i) q^{61} +(3.79888 + 3.29175i) q^{62} +(1.96949 + 2.26299i) q^{63} +(30.5283 + 8.96393i) q^{64} +(-2.09812 - 4.59424i) q^{65} +(12.0158 + 0.846302i) q^{66} +(0.729030 - 1.13439i) q^{67} -2.44699 q^{68} +(-5.79830 + 5.94808i) q^{69} -11.6783 q^{70} +(-2.40147 + 3.73676i) q^{71} +(-27.7085 - 8.07076i) q^{72} +(-0.0704456 - 0.154254i) q^{73} +(14.0055 + 4.11238i) q^{74} +(-13.6393 + 18.2612i) q^{75} +(6.67922 + 5.78758i) q^{76} +(2.51186 + 0.361151i) q^{77} +(-0.407424 - 5.61108i) q^{78} +(-3.68707 + 3.19487i) q^{79} +(55.0027 - 35.3481i) q^{80} +(8.64635 + 2.49814i) q^{81} +(16.0478 + 18.5201i) q^{82} +(-2.04949 + 0.601784i) q^{83} +(-8.94599 - 3.32564i) q^{84} +(-1.23924 + 1.43016i) q^{85} +(4.06180 - 8.89410i) q^{86} +(-3.59765 + 6.60561i) q^{87} +(-22.2064 + 10.1413i) q^{88} +(-1.35530 - 9.42633i) q^{89} +(-29.4320 + 19.0051i) q^{90} -1.18522i q^{91} +(7.14888 - 25.4412i) q^{92} +(3.10507 + 0.671943i) q^{93} +(15.9876 + 10.2746i) q^{94} +(6.76516 - 0.972683i) q^{95} +(38.5913 - 8.43884i) q^{96} +(4.15665 - 14.1562i) q^{97} +(-2.49284 - 1.13844i) q^{98} +(6.91822 - 3.17758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36}+ \cdots - 132 q^{97}+O(q^{100}) $ 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Character values

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

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−1.48162	+	2.30545i	−1.04767	+	1.63020i	−0.315700	+	0.948859i	$0.602239\pi$
$2$	−1.48162	+	2.30545i	−1.04767	+	1.63020i	−0.731966	+	0.681341i	$0.761397\pi$
$3$	−0.121691	+	1.72777i	−0.0702583	+	0.997529i
$3$	−0.121691	+	1.72777i	−0.0702583	+	0.997529i
$4$	−2.28907	−	5.01236i	−1.14453	−	2.50618i
$5$	−4.08876	−	1.20057i	−1.82855	−	0.536910i	−0.828804	−	0.559540i	$-0.810978\pi$
$5$	−4.08876	−	1.20057i	−1.82855	−	0.536910i	−0.999744	+	0.0226296i	$0.992796\pi$
$6$	−3.80299	−	2.84046i	−1.55256	−	1.15961i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$8$	9.52207	+	1.36907i	3.36656	+	0.484038i
$9$	−2.97038	−	0.420508i	−0.990128	−	0.140169i
$10$	8.82585	−	7.64764i	2.79098	−	2.41840i
$11$	−2.13484	+	1.37198i	−0.643678	+	0.413667i	−0.821351	−	0.570423i	$-0.806779\pi$
$11$	−2.13484	+	1.37198i	−0.643678	+	0.413667i	0.177673	+	0.984090i	$0.443143\pi$
$12$	8.93876	−	3.34502i	2.58040	−	0.965625i
$13$	0.776153	+	0.895728i	0.215266	+	0.248430i	0.853105	−	0.521740i	$-0.174717\pi$
$13$	0.776153	+	0.895728i	0.215266	+	0.248430i	−0.637839	+	0.770170i	$0.720171\pi$
$14$	2.62949	−	0.772087i	0.702760	−	0.206349i
$15$	2.57187	−	6.91834i	0.664054	−	1.78631i
$16$	−10.0475	+	11.5954i	−2.51187	+	2.89885i
$17$	0.184476	−	0.403945i	0.0447419	−	0.0979711i	−0.885941	−	0.463798i	$-0.846486\pi$
$17$	0.184476	−	0.403945i	0.0447419	−	0.0979711i	0.930683	+	0.365827i	$0.119214\pi$
$18$	5.37045	−	6.22504i	1.26583	−	1.46726i
$19$	−1.45894	+	0.666276i	−0.334704	+	0.152854i	−0.575676	−	0.817678i	$-0.695261\pi$
$19$	−1.45894	+	0.666276i	−0.334704	+	0.152854i	0.240972	+	0.970532i	$0.422534\pi$
$20$	3.34176	+	23.2425i	0.747241	+	5.19718i
$21$	1.22342	−	1.22607i	0.266971	−	0.267551i
$22$		−	6.95452i		−	1.48271i
$23$	3.66084	+	3.09810i	0.763338	+	0.645999i
$23$	3.66084	+	3.09810i	0.763338	+	0.645999i
$24$	−3.52418	+	16.2854i	−0.719371	+	3.32423i
$25$	11.0703	+	7.11445i	2.21406	+	1.42289i
$26$	−3.21502	+	0.462251i	−0.630518	+	0.0906548i
$27$	1.08801	−	5.08097i	0.209388	−	0.977833i
$28$	−1.55243	+	5.28711i	−0.293382	+	0.999169i
$29$	3.95026	+	1.80402i	0.733545	+	0.334999i	0.746922	−	0.664912i	$-0.231531\pi$
$29$	3.95026	+	1.80402i	0.733545	+	0.334999i	−0.0133772	+	0.999911i	$0.504258\pi$
$30$	12.1393	+	16.1797i	2.21633	+	2.95399i
$31$	0.261035	−	1.81554i	0.0468833	−	0.326080i	−0.952860	−	0.303411i	$-0.901874\pi$
$31$	0.261035	−	1.81554i	0.0468833	−	0.326080i	0.999743	−	0.0226692i	$-0.00721644\pi$
$32$	−6.42553	−	21.8833i	−1.13588	−	3.86846i
$33$	−2.11067	−	3.85547i	−0.367421	−	0.671151i
$34$	0.657953	+	1.02379i	0.112838	+	0.175579i
$35$	2.30387	+	3.58489i	0.389425	+	0.605958i
$36$	4.69167	+	15.8512i	0.781945	+	2.64186i
$37$	−1.50060	−	5.11057i	−0.246697	−	0.840173i	−0.985992	−	0.166791i	$-0.946659\pi$
$37$	−1.50060	−	5.11057i	−0.246697	−	0.840173i	0.739295	−	0.673381i	$-0.235159\pi$
$38$	0.625534	−	4.35068i	0.101475	−	0.705774i
$39$	−1.64206	+	1.23201i	−0.262941	+	0.197280i
$40$	−37.2898	−	17.0297i	−5.89603	−	2.69263i
$41$	2.51927	−	8.57984i	0.393443	−	1.33995i	−0.490129	−	0.871650i	$-0.663050\pi$
$41$	2.51927	−	8.57984i	0.393443	−	1.33995i	0.883572	−	0.468295i	$-0.155132\pi$
$42$	1.01400	+	4.63710i	0.156464	+	0.715521i
$43$	−3.53154	+	0.507759i	−0.538555	+	0.0774325i	−0.406225	−	0.913773i	$-0.633155\pi$
$43$	−3.53154	+	0.507759i	−0.538555	+	0.0774325i	−0.132330	+	0.991206i	$0.542246\pi$
$44$	11.7636	+	7.56003i	1.77343	+	1.13972i
$45$	11.6403	+	5.28550i	1.73524	+	0.787916i
$46$	−12.5665	+	3.84967i	−1.85283	+	0.567603i
$47$		−	6.93468i		−	1.01153i	−0.862672	−	0.505763i	$-0.831211\pi$
$47$		−	6.93468i		−	1.01153i	0.862672	−	0.505763i	$-0.168789\pi$
$48$	−18.8115	−	18.7708i	−2.71521	−	2.70933i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	−32.8040	+	14.9811i	−4.63919	+	2.11865i
$51$	0.675476	+	0.367888i	0.0945855	+	0.0515146i
$52$	2.71304	−	5.94074i	0.376231	−	0.823832i
$53$	6.34988	−	7.32816i	0.872223	−	1.00660i	−0.127667	−	0.991817i	$-0.540749\pi$
$53$	6.34988	−	7.32816i	0.872223	−	1.00660i	0.999891	−	0.0147825i	$-0.00470558\pi$
$54$	10.1019	+	10.0364i	1.37469	+	1.36579i
$55$	10.3760	−	3.04667i	1.39910	−	0.410812i
$56$	−6.29975	−	7.27030i	−0.841840	−	0.971535i
$57$	−0.973632	−	2.60179i	−0.128961	−	0.344616i
$58$	−10.0119	+	6.43424i	−1.31462	+	0.844858i
$59$	−2.14873	+	1.86188i	−0.279741	+	0.242397i	−0.783418	−	0.621495i	$-0.786526\pi$
$59$	−2.14873	+	1.86188i	−0.279741	+	0.242397i	0.503677	+	0.863892i	$0.331980\pi$
$60$	−40.5643	+	2.94540i	−5.23683	+	0.380250i
$61$	4.34861	+	0.625235i	0.556782	+	0.0800532i	0.414961	−	0.909839i	$-0.363795\pi$
$61$	4.34861	+	0.625235i	0.556782	+	0.0800532i	0.141821	+	0.989892i	$0.454704\pi$
$62$	3.79888	+	3.29175i	0.482458	+	0.418052i
$63$	1.96949	+	2.26299i	0.248133	+	0.285109i
$64$	30.5283	+	8.96393i	3.81604	+	1.12049i
$65$	−2.09812	−	4.59424i	−0.260240	−	0.569845i
$66$	12.0158	+	0.846302i	1.47905	+	0.104173i
$67$	0.729030	−	1.13439i	0.0890652	−	0.138588i	−0.793862	−	0.608098i	$-0.791933\pi$
$67$	0.729030	−	1.13439i	0.0890652	−	0.138588i	0.882927	+	0.469510i	$0.155569\pi$
$68$	−2.44699			−0.296742
$69$	−5.79830	+	5.94808i	−0.698033	+	0.716065i
$70$	−11.6783			−1.39582
$71$	−2.40147	+	3.73676i	−0.285002	+	0.443471i	−0.954006	−	0.299787i	$-0.903084\pi$
$71$	−2.40147	+	3.73676i	−0.285002	+	0.443471i	0.669004	+	0.743258i	$0.266721\pi$
$72$	−27.7085	−	8.07076i	−3.26548	−	0.951148i
$73$	−0.0704456	−	0.154254i	−0.00824503	−	0.0180541i	0.905465	−	0.424422i	$-0.139523\pi$
$73$	−0.0704456	−	0.154254i	−0.00824503	−	0.0180541i	−0.913710	+	0.406368i	$0.866795\pi$
$74$	14.0055	+	4.11238i	1.62811	+	0.478055i
$75$	−13.6393	+	18.2612i	−1.57493	+	2.10862i
$76$	6.67922	+	5.78758i	0.766159	+	0.663881i
$77$	2.51186	+	0.361151i	0.286253	+	0.0411570i
$78$	−0.407424	−	5.61108i	−0.0461317	−	0.635329i
$79$	−3.68707	+	3.19487i	−0.414828	+	0.359450i	−0.837129	−	0.547005i	$-0.815768\pi$
$79$	−3.68707	+	3.19487i	−0.414828	+	0.359450i	0.422301	+	0.906455i	$0.361222\pi$
$80$	55.0027	−	35.3481i	6.14949	−	3.95204i
$81$	8.64635	+	2.49814i	0.960705	+	0.277571i
$82$	16.0478	+	18.5201i	1.77218	+	2.04521i
$83$	−2.04949	+	0.601784i	−0.224961	+	0.0660544i	−0.392270	−	0.919850i	$-0.628310\pi$
$83$	−2.04949	+	0.601784i	−0.224961	+	0.0660544i	0.167310	+	0.985904i	$0.446492\pi$
$84$	−8.94599	−	3.32564i	−0.976087	−	0.362857i
$85$	−1.23924	+	1.43016i	−0.134414	+	0.155123i
$86$	4.06180	−	8.89410i	0.437995	−	0.959075i
$87$	−3.59765	+	6.60561i	−0.385708	+	0.708195i
$88$	−22.2064	+	10.1413i	−2.36721	+	1.08107i
$89$	−1.35530	−	9.42633i	−0.143662	−	0.999189i	−0.926320	−	0.376738i	$-0.877046\pi$
$89$	−1.35530	−	9.42633i	−0.143662	−	0.999189i	0.782658	−	0.622452i	$-0.213863\pi$
$90$	−29.4320	+	19.0051i	−3.10241	+	2.00331i
$91$		−	1.18522i		−	0.124245i
$92$	7.14888	−	25.4412i	0.745322	−	2.65243i
$93$	3.10507	+	0.671943i	0.321981	+	0.0696772i
$94$	15.9876	+	10.2746i	1.64899	+	1.05974i
$95$	6.76516	−	0.972683i	0.694091	−	0.0997952i
$96$	38.5913	−	8.43884i	3.93871	−	0.861285i
$97$	4.15665	−	14.1562i	0.422043	−	1.43735i	−0.424694	−	0.905337i	$-0.639618\pi$
$97$	4.15665	−	14.1562i	0.422043	−	1.43735i	0.846738	−	0.532011i	$-0.178563\pi$
$98$	−2.49284	−	1.13844i	−0.251815	−	0.115000i
$99$	6.91822	−	3.17758i	0.695307	−	0.319359i
$100$	10.3195	−	71.7737i	1.03195	−	7.17737i
$101$	1.26978	+	4.32446i	0.126347	+	0.430300i	0.998234	−	0.0594084i	$-0.0189214\pi$
$101$	1.26978	+	4.32446i	0.126347	+	0.430300i	−0.871886	+	0.489708i	$0.837103\pi$
$102$	−1.84895	+	1.01221i	−0.183073	+	0.100223i
$103$	−0.779884	−	1.21352i	−0.0768442	−	0.119572i	0.800704	−	0.599060i	$-0.204459\pi$
$103$	−0.779884	−	1.21352i	−0.0768442	−	0.119572i	−0.877549	+	0.479488i	$0.840822\pi$
$104$	6.16427	+	9.59180i	0.604457	+	0.940553i
$105$	−6.47424	+	3.54431i	−0.631821	+	0.345890i
$106$	7.48657	+	25.4969i	0.727160	+	2.47648i
$107$	−1.45001	+	10.0850i	−0.140178	+	0.974956i	0.791370	+	0.611337i	$0.209368\pi$
$107$	−1.45001	+	10.0850i	−0.140178	+	0.974956i	−0.931548	+	0.363619i	$0.881541\pi$
$108$	−27.9581	+	6.17718i	−2.69027	+	0.594399i
$109$	16.6753	+	7.61536i	1.59721	+	0.729420i	0.997491	−	0.0707941i	$-0.0225533\pi$
$109$	16.6753	+	7.61536i	1.59721	+	0.729420i	0.599715	+	0.800214i	$0.295281\pi$
$110$	−8.34937	+	28.4354i	−0.796081	+	2.71120i
$111$	9.01251	−	1.97078i	0.855429	−	0.187058i
$112$	15.1867	−	2.18352i	1.43501	−	0.206324i
$113$	−2.37668	−	1.52740i	−0.223579	−	0.143686i	0.424056	−	0.905636i	$-0.360606\pi$
$113$	−2.37668	−	1.52740i	−0.223579	−	0.143686i	−0.647636	+	0.761950i	$0.724242\pi$
$114$	7.44086	+	1.61022i	0.696901	+	0.150811i
$115$	−11.2488	−	17.0625i	−1.04896	−	1.59108i
$116$		−	23.9296i		−	2.22181i
$117$	−1.92881	−	2.98703i	−0.178319	−	0.276151i
$118$	−1.10888	−	7.71240i	−0.102080	−	0.709984i
$119$	−0.403945	+	0.184476i	−0.0370296	+	0.0169109i
$120$	33.9612	−	62.3558i	3.10022	−	5.69228i
$121$	−1.89435	+	4.14804i	−0.172213	+	0.377095i
$122$	−7.88444	+	9.09913i	−0.713824	+	0.823797i
$123$	14.5174	+	5.39680i	1.30899	+	0.486613i
$124$	−9.69765	+	2.84749i	−0.870875	+	0.255712i
$125$	−22.7694	−	26.2772i	−2.03655	−	2.35031i
$126$	−8.13525	+	1.18767i	−0.724745	+	0.105806i
$127$	14.7235	−	9.46219i	1.30650	−	0.839633i	0.312592	−	0.949888i	$-0.398803\pi$
$127$	14.7235	−	9.46219i	1.30650	−	0.839633i	0.993903	+	0.110254i	$0.0351665\pi$
$128$	−31.4244	+	27.2294i	−2.77755	+	2.40676i
$129$	−0.447534	−	6.16348i	−0.0394032	−	0.542664i
$130$	13.7004	+	1.96982i	1.20161	+	0.172765i
$131$	−1.61494	−	1.39936i	−0.141098	−	0.122262i	0.581452	−	0.813581i	$-0.302485\pi$
$131$	−1.61494	−	1.39936i	−0.141098	−	0.122262i	−0.722550	+	0.691318i	$0.757030\pi$
$132$	−14.4935	+	19.4049i	−1.26150	+	1.68898i
$133$	1.53891	+	0.451865i	0.133441	+	0.0391817i
$134$	1.53514	+	3.36149i	0.132616	+	0.290388i
$135$	−10.5487	+	19.4686i	−0.907883	+	1.67559i
$136$	2.30962	−	3.59384i	0.198048	−	0.308169i
$137$	−9.83263			−0.840058			−0.420029	−	0.907511i	$-0.637980\pi$
$137$	−9.83263			−0.840058			−0.420029	+	0.907511i	$0.637980\pi$
$138$	−5.12212	−	22.1805i	−0.436024	−	1.88813i
$139$	−4.21772			−0.357742			−0.178871	−	0.983873i	$-0.557245\pi$
$139$	−4.21772			−0.357742			−0.178871	+	0.983873i	$0.557245\pi$
$140$	12.6951	−	19.7539i	1.07293	−	1.66951i
$141$	11.9815	+	0.843887i	1.00903	+	0.0710681i
$142$	−5.05684	−	11.0729i	−0.424360	−	0.929220i
$143$	−2.88588	−	0.847371i	−0.241330	−	0.0708608i
$144$	34.7208	−	30.2177i	2.89340	−	2.51814i
$145$	−13.9858	−	12.1188i	−1.16146	−	1.00641i
$146$	0.460000	+	0.0661380i	0.0380698	+	0.00547362i
$147$	−1.72750	+	0.125435i	−0.142482	+	0.0103457i
$148$	−22.1810	+	19.2200i	−1.82327	+	1.57987i
$149$	9.47148	−	6.08695i	0.775934	−	0.498662i	−0.0917481	−	0.995782i	$-0.529245\pi$
$149$	9.47148	−	6.08695i	0.775934	−	0.498662i	0.867682	+	0.497120i	$0.165609\pi$
$150$	−21.8920	−	58.5009i	−1.78747	−	4.77658i
$151$	−9.57722	−	11.0527i	−0.779383	−	0.899456i	0.217681	−	0.976020i	$-0.430151\pi$
$151$	−9.57722	−	11.0527i	−0.779383	−	0.899456i	−0.997065	+	0.0765635i	$0.975605\pi$
$152$	−14.8043	+	4.34694i	−1.20079	+	0.352583i
$153$	−0.717826	+	1.12230i	−0.0580328	+	0.0907325i
$154$	−4.55424	+	5.25588i	−0.366991	+	0.423531i
$155$	−3.24698	+	7.10990i	−0.260804	+	0.571081i
$156$	9.93408	+	5.41045i	0.795363	+	0.433183i
$157$	−8.67175	+	3.96025i	−0.692081	+	0.316063i	−0.730222	−	0.683210i	$-0.760584\pi$
$157$	−8.67175	+	3.96025i	−0.692081	+	0.316063i	0.0381415	+	0.999272i	$0.487856\pi$
$158$	−1.90275	−	13.2339i	−0.151375	−	1.05284i
$159$	11.8886	+	11.8629i	0.942831	+	0.940790i
$160$			97.1899i			7.68354i
$161$	−0.737855	−	4.73873i	−0.0581511	−	0.373464i
$162$	−18.5700	+	16.2324i	−1.45899	+	1.27534i
$163$	8.29759	+	5.33254i	0.649918	+	0.417677i	0.823636	−	0.567119i	$-0.191942\pi$
$163$	8.29759	+	5.33254i	0.649918	+	0.417677i	−0.173719	+	0.984795i	$0.555578\pi$
$164$	−48.7720	+	7.01235i	−3.80845	+	0.547573i
$165$	4.00128	+	18.2981i	0.311499	+	1.42450i
$166$	1.64919	−	5.61661i	0.128002	−	0.435934i
$167$	19.5702	+	8.93741i	1.51439	+	0.691598i	0.987396	−	0.158272i	$-0.0505923\pi$
$167$	19.5702	+	8.93741i	1.51439	+	0.691598i	0.526992	+	0.849870i	$0.323320\pi$
$168$	13.3280	−	9.99980i	1.02828	−	0.771501i
$169$	1.65018	−	11.4772i	0.126937	−	0.882864i
$170$	−1.46107	−	4.97596i	−0.112059	−	0.381639i
$171$	4.61379	−	1.36560i	0.352825	−	0.104430i
$172$	10.6290	+	16.5390i	0.810453	+	1.26109i
$173$	1.28137	+	1.99384i	0.0974205	+	0.151589i	0.886542	−	0.462647i	$-0.153100\pi$
$173$	1.28137	+	1.99384i	0.0974205	+	0.151589i	−0.789122	+	0.614237i	$0.789464\pi$
$174$	−9.89854	−	18.0812i	−0.750407	−	1.37073i
$175$	−3.70740	−	12.6262i	−0.280253	−	0.954455i
$176$	5.54110	−	38.5392i	0.417677	−	2.90500i
$177$	−2.95543	−	3.93909i	−0.222144	−	0.296080i
$178$	23.7400	+	10.8417i	1.77939	+	0.812619i
$179$	−4.97927	+	16.9578i	−0.372168	+	1.26749i	0.534330	+	0.845276i	$0.320564\pi$
$179$	−4.97927	+	16.9578i	−0.372168	+	1.26749i	−0.906498	+	0.422211i	$0.861254\pi$
$180$	−0.152672	−	70.4443i	−0.0113795	−	5.25061i
$181$	−9.42577	+	1.35522i	−0.700612	+	0.100733i	−0.483410	−	0.875394i	$-0.660602\pi$
$181$	−9.42577	+	1.35522i	−0.700612	+	0.100733i	−0.217202	+	0.976127i	$0.569693\pi$
$182$	2.73246	+	1.75605i	0.202544	+	0.130167i
$183$	−1.60945	+	7.43731i	−0.118974	+	0.549782i
$184$	30.6173	+	34.5123i	2.25714	+	2.54428i
$185$			22.6975i			1.66875i
$186$	−6.14967	+	6.16301i	−0.450916	+	0.451894i
$187$	0.160378	+	1.11546i	0.0117280	+	0.0815702i
$188$	−34.7591	+	15.8739i	−2.53507	+	1.15773i
$189$	−4.14959	+	3.12744i	−0.301838	+	0.227488i
$190$	−7.78095	+	17.0379i	−0.564489	+	1.23606i
$191$	14.2693	−	16.4677i	1.03249	−	1.19156i	0.0512669	−	0.998685i	$-0.483674\pi$
$191$	14.2693	−	16.4677i	1.03249	−	1.19156i	0.981224	−	0.192873i	$-0.0617805\pi$
$192$	−19.2026	+	51.6551i	−1.38583	+	3.72789i
$193$	17.2682	−	5.07040i	1.24299	−	0.364975i	0.406853	−	0.913494i	$-0.366626\pi$
$193$	17.2682	−	5.07040i	1.24299	−	0.364975i	0.836138	+	0.548518i	$0.184808\pi$
$194$	26.4779	+	30.5571i	1.90100	+	2.19388i
$195$	8.19311	−	3.06599i	0.586721	−	0.219560i
$196$	4.63557	−	2.97910i	0.331112	−	0.212793i
$197$	0.770289	−	0.667459i	0.0548808	−	0.0475545i	−0.626989	−	0.779028i	$-0.715713\pi$
$197$	0.770289	−	0.667459i	0.0548808	−	0.0475545i	0.681869	+	0.731474i	$0.261167\pi$
$198$	−2.92443	+	20.6576i	−0.207830	+	1.46807i
$199$	−2.86753	−	0.412289i	−0.203274	−	0.0292264i	0.0399256	−	0.999203i	$-0.487288\pi$
$199$	−2.86753	−	0.412289i	−0.203274	−	0.0292264i	−0.243200	+	0.969976i	$0.578197\pi$
$200$	95.6721	+	82.9003i	6.76504	+	5.86194i
$201$	1.87125	+	1.39764i	0.131988	+	0.0985820i
$202$	−11.8512	−	3.47982i	−0.833845	−	0.244839i
$203$	−1.80402	−	3.95026i	−0.126618	−	0.277254i
$204$	0.297777	−	4.22785i	0.0208486	−	0.296008i
$205$	−20.6013	+	32.0563i	−1.43886	+	2.23891i
$206$	3.95321			0.275433
$207$	−9.57133	−	10.7420i	−0.665253	−	0.746618i
$208$	−18.1847			−1.26088
$209$	2.20049	−	3.42403i	0.152211	−	0.236845i
$210$	1.42114	−	20.1774i	0.0980679	−	1.39237i
$211$	−8.98904	−	19.6833i	−0.618831	−	1.35505i	−0.916367	−	0.400340i	$-0.868892\pi$
$211$	−8.98904	−	19.6833i	−0.618831	−	1.35505i	0.297536	−	0.954711i	$-0.403835\pi$
$212$	−51.2666	−	15.0532i	−3.52101	−	1.03386i
$213$	−6.16402	−	4.60391i	−0.422352	−	0.315455i
$214$	−21.1022	−	18.2851i	−1.44251	−	1.24995i
$215$	15.0492	+	2.16375i	1.02635	+	0.147566i
$216$	17.3163	−	46.8918i	1.17822	−	3.19058i
$217$	−1.38620	+	1.20115i	−0.0941015	+	0.0815394i
$218$	−42.2634	+	27.1610i	−2.86244	+	1.83958i
$219$	0.275089	−	0.102942i	0.0185888	−	0.00695621i
$220$	−39.0223	−	45.0341i	−2.63088	−	3.03620i
$221$	0.505007	−	0.148283i	0.0339704	−	0.00997462i
$222$	−8.80960	+	23.6978i	−0.591262	+	1.59050i
$223$	14.0304	−	16.1919i	0.939545	−	1.08429i	−0.0567584	−	0.998388i	$-0.518076\pi$
$223$	14.0304	−	16.1919i	0.939545	−	1.08429i	0.996303	−	0.0859047i	$-0.0273781\pi$
$224$	−9.47445	+	20.7461i	−0.633038	+	1.38616i
$225$	−29.8913	−	25.7878i	−1.99276	−	1.71919i
$226$	7.04270	−	3.21629i	0.468473	−	0.213945i
$227$	−2.51630	−	17.5013i	−0.167013	−	1.16160i	−0.885016	−	0.465560i	$-0.845853\pi$
$227$	−2.51630	−	17.5013i	−0.167013	−	1.16160i	0.718003	−	0.696040i	$-0.245056\pi$
$228$	−10.8124	+	10.8359i	−0.716069	+	0.717623i
$229$			7.77712i			0.513926i	0.966421	+	0.256963i	$0.0827219\pi$
$229$			7.77712i			0.513926i	−0.966421	+	0.256963i	$0.917278\pi$
$230$	56.0032	−	0.653430i	3.69274	−	0.0430859i
$231$	−0.929656	+	4.29597i	−0.0611669	+	0.282654i
$232$	35.1448	+	22.5862i	2.30737	+	1.48286i
$233$	10.1914	−	1.46530i	0.667659	−	0.0959948i	0.199853	−	0.979826i	$-0.435954\pi$
$233$	10.1914	−	1.46530i	0.667659	−	0.0959948i	0.467806	+	0.883831i	$0.345045\pi$
$234$	9.74423	−	0.0211184i	0.637000	−	0.00138055i
$235$	−8.32555	+	28.3542i	−0.543099	+	1.84962i
$236$	14.2510	+	6.50822i	0.927662	+	0.423649i
$237$	−5.07131	−	6.75920i	−0.329417	−	0.439057i
$238$	0.173195	−	1.20460i	0.0112266	−	0.0780826i
$239$	3.13026	+	10.6607i	0.202479	+	0.689582i	0.996642	+	0.0818770i	$0.0260915\pi$
$239$	3.13026	+	10.6607i	0.202479	+	0.689582i	−0.794163	+	0.607705i	$0.792090\pi$
$240$	54.3801	+	99.3336i	3.51022	+	6.41196i
$241$	−14.9170	−	23.2112i	−0.960885	−	1.49517i	−0.866223	−	0.499657i	$-0.833459\pi$
$241$	−14.9170	−	23.2112i	−0.960885	−	1.49517i	−0.0946624	−	0.995509i	$-0.530177\pi$
$242$	−6.75640	−	10.5132i	−0.434318	−	0.675812i
$243$	−5.36839	+	14.6349i	−0.344383	+	0.938829i
$244$	−6.82035	−	23.2280i	−0.436628	−	1.48702i
$245$	0.606456	−	4.21800i	0.0387451	−	0.269478i
$246$	−33.9514	+	25.4732i	−2.16466	+	1.62411i
$247$	−1.72916	−	0.789682i	−0.110024	−	0.0502463i
$248$	4.97119	−	16.9303i	0.315671	−	1.07508i
$249$	−0.790341	−	3.61428i	−0.0500858	−	0.229045i
$250$	94.3165	−	13.5607i	5.96510	−	0.857652i
$251$	−10.8857	−	6.99580i	−0.687098	−	0.441571i	0.149955	−	0.988693i	$-0.452087\pi$
$251$	−10.8857	−	6.99580i	−0.687098	−	0.441571i	−0.837053	+	0.547122i	$0.815724\pi$
$252$	6.83459	−	15.0519i	0.430539	−	0.948182i
$253$	−12.0658	−	1.59136i	−0.758573	−	0.100048i
$254$			47.9636i			3.00950i
$255$	−2.32018	−	2.31516i	−0.145295	−	0.144981i
$256$	−7.16078	−	49.8043i	−0.447549	−	3.11277i
$257$	−6.70324	+	3.06127i	−0.418137	+	0.190957i	−0.613362	−	0.789802i	$-0.710183\pi$
$257$	−6.70324	+	3.06127i	−0.418137	+	0.190957i	0.195225	+	0.980758i	$0.437456\pi$
$258$	14.8727	+	8.10019i	0.925933	+	0.504296i
$259$	−2.21264	+	4.84500i	−0.137486	+	0.301053i
$260$	−18.2252	+	21.0330i	−1.13028	+	1.30441i
$261$	−10.9752	−	7.01975i	−0.679346	−	0.434512i
$262$	5.61889	−	1.64985i	0.347136	−	0.101928i
$263$	1.15476	+	1.33267i	0.0712056	+	0.0821757i	0.790235	−	0.612804i	$-0.209959\pi$
$263$	1.15476	+	1.33267i	0.0712056	+	0.0821757i	−0.719029	+	0.694980i	$0.755413\pi$
$264$	−14.8196	−	39.6017i	−0.912082	−	2.43732i
$265$	−34.7611	+	22.3396i	−2.13536	+	1.37231i
$266$	−3.32184	+	2.87839i	−0.203675	+	0.176485i
$267$	16.4515	−	1.19455i	1.00681	−	0.0731054i
$268$	−7.35478	−	1.05746i	−0.449265	−	0.0645945i
$269$	−21.7703	−	18.8641i	−1.32736	−	1.15016i	−0.976926	−	0.213577i	$-0.931489\pi$
$269$	−21.7703	−	18.8641i	−1.32736	−	1.15016i	−0.350434	−	0.936587i	$-0.613966\pi$
$270$	−29.2548	−	53.1645i	−1.78039	−	3.23549i
$271$	24.4289	+	7.17298i	1.48395	+	0.435728i	0.920606	−	0.390493i	$-0.127696\pi$
$271$	24.4289	+	7.17298i	1.48395	+	0.435728i	0.563346	+	0.826221i	$0.309514\pi$
$272$	2.83039	+	6.19770i	0.171618	+	0.375791i
$273$	2.04779	+	0.144230i	0.123938	+	0.00872921i
$274$	14.5683	−	22.6687i	0.880101	−	1.36946i
$275$	−33.3942			−2.01375
$276$	43.0866	+	15.4476i	2.59351	+	0.929835i
$277$	−14.4299			−0.867010			−0.433505	−	0.901151i	$-0.642723\pi$
$277$	−14.4299			−0.867010			−0.433505	+	0.901151i	$0.642723\pi$
$278$	6.24907	−	9.72374i	0.374794	−	0.583191i
$279$	−1.53882	+	5.28308i	−0.0921269	+	0.316289i
$280$	17.0297	+	37.2898i	1.01772	+	2.22849i
$281$	5.49796	+	1.61435i	0.327981	+	0.0963038i	0.441577	−	0.897223i	$-0.354419\pi$
$281$	5.49796	+	1.61435i	0.327981	+	0.0963038i	−0.113597	+	0.993527i	$0.536237\pi$
$282$	−19.6977	+	26.3725i	−1.17298	+	1.57046i
$283$	−12.6433	−	10.9555i	−0.751565	−	0.651235i	0.192387	−	0.981319i	$-0.438377\pi$
$283$	−12.6433	−	10.9555i	−0.751565	−	0.651235i	−0.943951	+	0.330085i	$0.892923\pi$
$284$	24.2271	+	3.48333i	1.43761	+	0.206697i
$285$	0.857315	+	11.8070i	0.0507830	+	0.699387i
$286$	6.22936	−	5.39777i	0.368350	−	0.319177i
$287$	−7.52253	+	4.83444i	−0.444041	+	0.285368i
$288$	9.88416	+	67.7039i	0.582430	+	3.98949i
$289$	11.0035	+	12.6987i	0.647264	+	0.746983i
$290$	48.6609	−	14.2881i	2.85747	−	0.839028i
$291$	23.9529	+	8.90441i	1.40414	+	0.521986i
$292$	−0.611923	+	0.706197i	−0.0358101	+	0.0413270i
$293$	−9.43789	+	20.6661i	−0.551367	+	1.20733i	0.404773	+	0.914417i	$0.367351\pi$
$293$	−9.43789	+	20.6661i	−0.551367	+	1.20733i	−0.956140	+	0.292909i	$0.905377\pi$
$294$	2.27032	−	4.16852i	0.132408	−	0.243113i
$295$	11.0210	−	5.03310i	0.641665	−	0.293038i
$296$	−7.29210	−	50.7177i	−0.423845	−	2.94790i
$297$	4.64825	+	12.3398i	0.269719	+	0.716027i
$298$			30.8546i			1.78736i
$299$	0.0663161	+	5.68372i	0.00383516	+	0.328698i
$300$	122.753	+	26.5639i	7.08713	+	1.53367i
$301$	3.00147	+	1.92893i	0.173002	+	0.111182i
$302$	39.6713	−	5.70387i	2.28283	−	0.328221i
$303$	−7.62620	+	1.66763i	−0.438114	+	0.0958031i
$304$	6.93293	−	23.6114i	0.397631	−	1.35421i
$305$	−17.0298	−	7.77723i	−0.975121	−	0.445323i
$306$	−1.52386	−	3.31774i	−0.0871132	−	0.189662i
$307$	−1.32818	+	9.23771i	−0.0758034	+	0.527224i	0.916171	+	0.400787i	$0.131263\pi$
$307$	−1.32818	+	9.23771i	−0.0758034	+	0.527224i	−0.991975	+	0.126437i	$0.959646\pi$
$308$	−3.93960	−	13.4170i	−0.224479	−	0.764506i
$309$	2.19159	−	1.19979i	0.124675	−	0.0682534i
$310$	−11.5807	−	18.0200i	−0.657741	−	1.02346i
$311$	13.1131	+	20.4044i	0.743577	+	1.15703i	0.982549	+	0.186002i	$0.0595530\pi$
$311$	13.1131	+	20.4044i	0.743577	+	1.15703i	−0.238973	+	0.971026i	$0.576811\pi$
$312$	−17.3226	+	9.48322i	−0.980697	+	0.536881i
$313$	−5.72670	−	19.5033i	−0.323692	−	1.10239i	−0.947218	−	0.320591i	$-0.896118\pi$
$313$	−5.72670	−	19.5033i	−0.323692	−	1.10239i	0.623526	−	0.781803i	$-0.285700\pi$
$314$	3.71809	−	25.8599i	0.209824	−	1.45936i
$315$	−5.33590	−	11.6173i	−0.300644	−	0.654561i
$316$	24.4538	+	11.1677i	1.37563	+	0.628230i
$317$	7.92260	−	26.9819i	0.444978	−	1.51545i	−0.366133	−	0.930562i	$-0.619319\pi$
$317$	7.92260	−	26.9819i	0.444978	−	1.51545i	0.811111	−	0.584892i	$-0.198863\pi$
$318$	−44.9639	+	9.83233i	−2.52145	+	0.551370i
$319$	−10.9082	+	1.56837i	−0.610745	+	0.0878118i
$320$	−114.061	−	73.3027i	−6.37621	−	4.09774i
$321$	−17.2482	−	3.73254i	−0.962699	−	0.208330i
$322$	12.0181	+	5.31993i	0.669744	+	0.296468i
$323$			0.712244i			0.0396303i
$324$	−7.27050	−	49.0570i	−0.403917	−	2.72539i
$325$	2.21963	+	15.4379i	0.123123	+	0.856340i
$326$	−24.5878	+	11.2289i	−1.36179	+	0.621910i
$327$	−15.1868	+	27.8844i	−0.839834	+	1.54201i
$328$	35.7350	−	78.2488i	1.97314	−	4.32057i
$329$	−4.54125	+	5.24088i	−0.250367	+	0.288939i
$330$	−48.1137	−	17.8861i	−2.64857	−	0.984599i
$331$	13.0203	−	3.82311i	0.715660	−	0.210137i	0.0964228	−	0.995340i	$-0.469260\pi$
$331$	13.0203	−	3.82311i	0.715660	−	0.210137i	0.619238	+	0.785204i	$0.287442\pi$
$332$	7.70777	+	8.89524i	0.423019	+	0.488190i
$333$	2.30832	+	15.8114i	0.126495	+	0.866458i
$334$	−49.6004	+	31.8763i	−2.71402	+	1.74419i
$335$	−4.34274	+	3.76301i	−0.237269	+	0.205595i
$336$	1.92454	+	26.5049i	0.104992	+	1.44596i
$337$	−0.367056	−	0.0527747i	−0.0199948	−	0.00287482i	0.132310	−	0.991208i	$-0.457761\pi$
$337$	−0.367056	−	0.0527747i	−0.0199948	−	0.00287482i	−0.152305	+	0.988334i	$0.548670\pi$
$338$	24.0153	+	20.8093i	1.30626	+	1.13188i
$339$	2.92822	−	3.92049i	0.159039	−	0.212932i
$340$	10.0052	+	2.93778i	0.542606	+	0.159324i
$341$	1.93361	+	4.23402i	0.104711	+	0.229285i
$342$	−3.68757	+	12.6602i	−0.199401	+	0.684583i
$343$	0.540641	−	0.841254i	0.0291919	−	0.0454234i
$344$	−34.3227			−1.85056
$345$	30.8489	−	17.3590i	1.66085	−	0.934578i
$346$	−6.49521			−0.349185
$347$	−4.17350	+	6.49410i	−0.224045	+	0.348622i	−0.935019	−	0.354597i	$-0.884618\pi$
$347$	−4.17350	+	6.49410i	−0.224045	+	0.348622i	0.710974	+	0.703219i	$0.248254\pi$
$348$	41.3449	+	2.91202i	2.21632	+	0.156101i
$349$	−3.74478	−	8.19992i	−0.200453	−	0.438932i	0.782533	−	0.622609i	$-0.213927\pi$
$349$	−3.74478	−	8.19992i	−0.200453	−	0.438932i	−0.982987	+	0.183677i	$0.941200\pi$
$350$	34.6022	+	10.1601i	1.84956	+	0.543081i
$351$	5.39563	−	2.96905i	0.287997	−	0.158476i
$352$	43.7409	+	37.9017i	2.33140	+	2.02017i
$353$	−15.2561	−	2.19349i	−0.811999	−	0.116748i	−0.276208	−	0.961098i	$-0.589078\pi$
$353$	−15.2561	−	2.19349i	−0.811999	−	0.116748i	−0.535792	+	0.844350i	$0.679987\pi$
$354$	13.4602	−	0.977354i	0.715402	−	0.0519458i
$355$	14.3052	−	12.3956i	0.759243	−	0.657888i
$356$	−44.1458	+	28.3708i	−2.33972	+	1.50365i
$357$	−0.269575	−	0.720374i	−0.0142674	−	0.0381262i
$358$	−31.7180	−	36.6046i	−1.67635	−	1.93461i
$359$	−12.4004	+	3.64110i	−0.654471	+	0.192170i	−0.592077	−	0.805882i	$-0.701692\pi$
$359$	−12.4004	+	3.64110i	−0.654471	+	0.192170i	−0.0623939	+	0.998052i	$0.519874\pi$
$360$	103.604	+	66.2653i	5.46040	+	3.49249i
$361$	−10.7578	+	12.4151i	−0.566198	+	0.653428i
$362$	10.8410	−	23.7386i	0.569792	−	1.24767i
$363$	−6.93634	−	3.77778i	−0.364064	−	0.198282i
$364$	−5.94074	+	2.71304i	−0.311379	+	0.142202i
$365$	0.102842	+	0.715283i	0.00538301	+	0.0374396i
$366$	−14.7618	−	14.7298i	−0.771609	−	0.769939i
$367$		−	18.6496i		−	0.973501i	−0.873541	−	0.486750i	$-0.838182\pi$
$367$		−	18.6496i		−	0.973501i	0.873541	−	0.486750i	$-0.161818\pi$
$368$	−72.7059	+	11.3208i	−3.79006	+	0.590140i
$369$	−11.0911	+	24.4260i	−0.577378	+	1.27157i
$370$	−52.3279	−	33.6291i	−2.72040	−	1.74829i
$371$	−9.59784	+	1.37996i	−0.498295	+	0.0716440i
$372$	−3.73969	−	17.1018i	−0.193894	−	0.886688i
$373$	4.81017	−	16.3819i	0.249061	−	0.848224i	−0.736141	−	0.676828i	$-0.763354\pi$
$373$	4.81017	−	16.3819i	0.249061	−	0.848224i	0.985202	−	0.171396i	$-0.0548277\pi$
$374$	−2.80925	−	1.28294i	−0.145263	−	0.0663393i
$375$	48.1719	−	36.1425i	2.48759	−	1.86639i
$376$	9.49404	−	66.0325i	0.489618	−	3.40537i
$377$	1.45009	+	4.93856i	0.0746835	+	0.254349i
$378$	−1.06204	−	14.2004i	−0.0546255	−	0.730388i
$379$	3.97402	+	6.18369i	0.204131	+	0.317635i	0.928192	−	0.372102i	$-0.121363\pi$
$379$	3.97402	+	6.18369i	0.204131	+	0.317635i	−0.724060	+	0.689736i	$0.757726\pi$
$380$	−20.3613	−	31.6829i	−1.04451	−	1.62530i
$381$	14.5568	+	26.5902i	0.745766	+	1.36226i
$382$	16.8236	+	57.2960i	0.860772	+	2.93152i
$383$	3.69700	−	25.7132i	0.188908	−	1.31388i	−0.645935	−	0.763393i	$-0.723532\pi$
$383$	3.69700	−	25.7132i	0.188908	−	1.31388i	0.834842	−	0.550489i	$-0.185559\pi$
$384$	−43.2220	−	57.6076i	−2.20566	−	2.93978i
$385$	−9.83679	−	4.49231i	−0.501329	−	0.228949i
$386$	−13.8954	+	47.3234i	−0.707257	+	2.40870i
$387$	10.7035	−	0.0231975i	0.544092	−	0.00117919i
$388$	−80.4709	+	11.5700i	−4.08529	+	0.587376i
$389$	15.9112	+	10.2255i	0.806730	+	0.518454i	0.877806	−	0.479017i	$-0.159007\pi$
$389$	15.9112	+	10.2255i	0.806730	+	0.518454i	−0.0710756	+	0.997471i	$0.522643\pi$
$390$	−5.07062	+	23.4315i	−0.256761	+	1.18650i
$391$	1.92680	−	0.907256i	0.0974425	−	0.0458819i
$392$			9.61999i			0.485883i
$393$	2.61429	−	2.61996i	0.131874	−	0.132160i
$394$	0.397516	+	2.76479i	0.0200266	+	0.139288i
$395$	18.9112	−	8.63645i	0.951525	−	0.434547i
$396$	−31.7634	−	27.4029i	−1.59617	−	1.37705i
$397$	6.70633	−	14.6848i	0.336581	−	0.737010i	−0.663355	−	0.748305i	$-0.730868\pi$
$397$	6.70633	−	14.6848i	0.336581	−	0.737010i	0.999936	+	0.0112950i	$0.00359538\pi$
$398$	5.19912	−	6.00010i	0.260608	−	0.300758i
$399$	−0.967991	+	2.60390i	−0.0484602	+	0.130358i
$400$	−193.723	+	56.8823i	−9.68617	+	2.84412i
$401$	−12.3040	−	14.1996i	−0.614435	−	0.709095i	0.360206	−	0.932873i	$-0.382707\pi$
$401$	−12.3040	−	14.1996i	−0.614435	−	0.709095i	−0.974640	+	0.223777i	$0.928161\pi$
$402$	−5.99469	+	2.24331i	−0.298988	+	0.111886i
$403$	1.82883	−	1.17532i	0.0911006	−	0.0585468i
$404$	18.7691	−	16.2635i	0.933799	−	0.809142i
$405$	−32.3536	−	20.5948i	−1.60766	−	1.02336i
$406$	11.7800	+	1.69371i	0.584632	+	0.0840574i
$407$	10.2151	+	8.85146i	0.506345	+	0.438751i
$408$	5.92827	+	4.42783i	0.293493	+	0.219210i
$409$	17.0159	+	4.99632i	0.841383	+	0.247052i	0.673900	−	0.738823i	$-0.264618\pi$
$409$	17.0159	+	4.99632i	0.841383	+	0.247052i	0.167483	+	0.985875i	$0.446436\pi$
$410$	−43.3808	−	94.9908i	−2.14243	−	4.69126i
$411$	1.19654	−	16.9885i	0.0590211	−	0.837983i
$412$	−4.29740	+	6.68689i	−0.211718	+	0.329439i
$413$	2.84318			0.139904
$414$	38.9462	−	6.15068i	1.91410	−	0.302289i
$415$	9.10234			0.446816
$416$	14.6143	−	22.7403i	0.716527	−	1.11494i
$417$	0.513258	−	7.28725i	0.0251344	−	0.356858i
$418$	4.63363	+	10.1462i	0.226638	+	0.496269i
$419$	8.02274	+	2.35569i	0.391937	+	0.115083i	0.471762	−	0.881726i	$-0.343618\pi$
$419$	8.02274	+	2.35569i	0.391937	+	0.115083i	−0.0798255	+	0.996809i	$0.525436\pi$
$420$	32.5853	+	24.3380i	1.59000	+	1.18757i
$421$	13.3545	+	11.5718i	0.650860	+	0.563973i	0.916468	−	0.400108i	$-0.131027\pi$
$421$	13.3545	+	11.5718i	0.650860	+	0.563973i	−0.265608	+	0.964081i	$0.585573\pi$
$422$	58.6971	+	8.43937i	2.85733	+	0.410822i
$423$	−2.91609	+	20.5986i	−0.141785	+	1.00154i
$424$	70.4968	−	61.0858i	3.42363	−	2.96659i
$425$	4.91605	−	3.15935i	0.238463	−	0.153251i
$426$	19.7469	−	7.38958i	0.956738	−	0.358026i
$427$	−2.87702	−	3.32025i	−0.139229	−	0.160678i
$428$	53.8689	−	15.8173i	2.60385	−	0.764560i
$429$	1.81525	−	4.88302i	0.0876410	−	0.235755i
$430$	−27.2857	+	31.4893i	−1.31583	+	1.51855i
$431$	6.85805	−	15.0170i	0.330341	−	0.723346i	−0.669469	−	0.742840i	$-0.733478\pi$
$431$	6.85805	−	15.0170i	0.330341	−	0.723346i	0.999810	+	0.0194943i	$0.00620562\pi$
$432$	47.9841	+	63.6668i	2.30864	+	3.06317i
$433$	18.8840	−	8.62406i	0.907509	−	0.414446i	0.0937153	−	0.995599i	$-0.470126\pi$
$433$	18.8840	−	8.62406i	0.907509	−	0.414446i	0.813794	+	0.581153i	$0.197398\pi$
$434$	−0.715365	−	4.97547i	−0.0343386	−	0.238830i
$435$	22.6404	−	22.6895i	1.08552	−	1.08788i
$436$		−	101.015i		−	4.83773i
$437$	−7.40514	−	2.08082i	−0.354236	−	0.0995389i
$438$	−0.170249	+	0.786725i	−0.00813481	+	0.0375912i
$439$	27.2706	+	17.5257i	1.30155	+	0.836458i	0.993380	−	0.114872i	$-0.0366459\pi$
$439$	27.2706	+	17.5257i	1.30155	+	0.836458i	0.308173	+	0.951330i	$0.400282\pi$
$440$	102.972	−	14.8051i	4.90900	−	0.705808i
$441$	−0.00650179	−	2.99999i	−0.000309609	−	0.142857i
$442$	−0.406370	+	1.38397i	−0.0193290	+	0.0658286i
$443$	−4.32439	−	1.97488i	−0.205458	−	0.0938295i	0.310028	−	0.950727i	$-0.399661\pi$
$443$	−4.32439	−	1.97488i	−0.205458	−	0.0938295i	−0.515486	+	0.856898i	$0.672389\pi$
$444$	−30.5085	−	40.6626i	−1.44787	−	1.92976i
$445$	−5.77545	+	40.1691i	−0.273782	+	1.90420i
$446$	16.5420	+	56.3368i	0.783285	+	2.66762i
$447$	9.36426	+	17.1053i	0.442914	+	0.809051i
$448$	−17.2017	−	26.7663i	−0.812702	−	1.26459i
$449$	−10.6873	−	16.6297i	−0.504364	−	0.784806i	0.491947	−	0.870625i	$-0.336285\pi$
$449$	−10.6873	−	16.6297i	−0.504364	−	0.784806i	−0.996311	+	0.0858197i	$0.972649\pi$
$450$	103.740	−	30.7052i	4.89036	−	1.44746i
$451$	6.39312	+	21.7730i	0.301040	+	1.02525i
$452$	−2.21549	+	15.4091i	−0.104208	+	0.724783i
$453$	20.2620	−	15.2022i	0.951992	−	0.714263i
$454$	44.0765	+	20.1291i	2.06861	+	0.944705i
$455$	−1.42293	+	4.84607i	−0.0667082	+	0.227187i
$456$	−5.70896	−	26.1074i	−0.267347	−	1.22259i
$457$	6.36089	−	0.914558i	0.297550	−	0.0427812i	0.00807694	−	0.999967i	$-0.497429\pi$
$457$	6.36089	−	0.914558i	0.297550	−	0.0427812i	0.289473	+	0.957186i	$0.406520\pi$
$458$	−17.9298	−	11.5228i	−0.837803	−	0.538423i
$459$	−1.85172	−	1.37681i	−0.0864310	−	0.0642641i
$460$	−59.7739	+	95.4402i	−2.78697	+	4.44992i
$461$			24.2813i			1.13089i	0.824785	+	0.565447i	$0.191296\pi$
$461$			24.2813i			1.13089i	−0.824785	+	0.565447i	$0.808704\pi$
$462$	−8.52674	−	8.50828i	−0.396700	−	0.395841i
$463$	5.50613	+	38.2960i	0.255891	+	1.77976i	0.561370	+	0.827565i	$0.310274\pi$
$463$	5.50613	+	38.2960i	0.255891	+	1.77976i	−0.305479	+	0.952199i	$0.598816\pi$
$464$	−60.6085	+	27.6790i	−2.81368	+	1.28496i
$465$	−11.8892	−	6.47525i	−0.551346	−	0.300283i
$466$	−11.7216	+	25.6667i	−0.542992	+	1.18899i
$467$	22.6646	−	26.1563i	1.04879	−	1.21037i	0.0717261	−	0.997424i	$-0.477149\pi$
$467$	22.6646	−	26.1563i	1.04879	−	1.21037i	0.977064	−	0.212944i	$-0.0683053\pi$
$468$	−10.5569	+	16.5054i	−0.487993	+	0.762963i
$469$	−1.29383	+	0.379904i	−0.0597437	+	0.0175423i
$470$	−53.0339	−	61.2044i	−2.44627	−	2.82315i
$471$	−5.78714	−	15.4647i	−0.266657	−	0.712577i
$472$	−23.0094	+	14.7872i	−1.05909	+	0.680638i
$473$	6.84264	−	5.92918i	0.314625	−	0.272624i
$474$	23.0968	−	1.67707i	1.06087	−	0.0770305i
$475$	−20.8911	−	3.00369i	−0.958549	−	0.137819i
$476$	1.84932	+	1.60244i	0.0847632	+	0.0734478i
$477$	−21.9431	+	19.0972i	−1.00471	+	0.874403i
$478$	−29.2155	−	8.57845i	−1.33629	−	0.392369i
$479$	8.97689	+	19.6567i	0.410165	+	0.898136i	0.996138	+	0.0878049i	$0.0279852\pi$
$479$	8.97689	+	19.6567i	0.410165	+	0.898136i	−0.585973	+	0.810331i	$0.699288\pi$
$480$	−167.922	−	11.8271i	−7.66455	−	0.539832i
$481$	3.41299	−	5.31072i	0.155619	−	0.242148i
$482$	75.6137			3.44411
$483$	8.27723	−	0.698183i	0.376627	−	0.0317684i
$484$	25.1278			1.14217
$485$	−33.9910	+	52.8911i	−1.54345	+	2.40166i
$486$	−25.7861	−	34.0600i	−1.16968	−	1.54499i
$487$	−6.38289	−	13.9766i	−0.289236	−	0.633339i	0.708113	−	0.706099i	$-0.249547\pi$
$487$	−6.38289	−	13.9766i	−0.289236	−	0.633339i	−0.997350	+	0.0727597i	$0.976819\pi$
$488$	40.5518	+	11.9071i	1.83569	+	0.539008i
$489$	−10.2231	+	13.6874i	−0.462307	+	0.618966i
$490$	8.82585	+	7.64764i	0.398711	+	0.345485i
$491$	21.7376	+	3.12539i	0.981004	+	0.141047i	0.614114	−	0.789217i	$-0.289514\pi$
$491$	21.7376	+	3.12539i	0.981004	+	0.141047i	0.366890	+	0.930264i	$0.380423\pi$
$492$	−6.18063	−	85.1201i	−0.278644	−	3.83751i
$493$	1.45745	−	1.26289i	0.0656404	−	0.0568777i
$494$	4.38254	−	2.81649i	0.197180	−	0.126720i
$495$	−32.1018	+	4.68658i	−1.44287	+	0.210646i
$496$	18.4291	+	21.2684i	0.827493	+	0.954978i
$497$	4.26196	−	1.25143i	0.191175	−	0.0561341i
$498$	9.50352	+	3.53290i	0.425863	+	0.158313i
$499$	5.81661	−	6.71272i	0.260387	−	0.300503i	−0.610470	−	0.792040i	$-0.709019\pi$
$499$	5.81661	−	6.71272i	0.260387	−	0.300503i	0.870857	+	0.491537i	$0.163565\pi$
$500$	−79.5903	+	174.279i	−3.55939	+	7.79397i
$501$	−17.8233	+	32.7252i	−0.796287	+	1.46206i
$502$	32.2570	−	14.7313i	1.43970	−	0.657488i
$503$	4.54981	+	31.6446i	0.202866	+	1.41096i	0.795725	+	0.605658i	$0.207090\pi$
$503$	4.54981	+	31.6446i	0.202866	+	1.41096i	−0.592859	+	0.805306i	$0.702001\pi$
$504$	15.6555	+	24.2447i	0.697350	+	1.07994i
$505$		−	19.2061i		−	0.854661i
$506$	21.5458	−	25.4594i	0.957829	−	1.13181i
$507$	19.6292	+	4.24780i	0.871764	+	0.188652i
$508$	−81.1308	−	52.1396i	−3.59960	−	2.31332i
$509$	−21.7738	+	3.13060i	−0.965106	+	0.138761i	−0.606810	−	0.794847i	$-0.707551\pi$
$509$	−21.7738	+	3.13060i	−0.965106	+	0.138761i	−0.358296	+	0.933608i	$0.616642\pi$
$510$	8.77512	−	1.91887i	0.388569	−	0.0849691i
$511$	−0.0477759	+	0.162710i	−0.00211348	+	0.00719785i
$512$	49.7854	+	22.7362i	2.20022	+	1.00481i
$513$	1.79798	+	8.13774i	0.0793829	+	0.359290i
$514$	2.87408	−	19.9896i	0.126770	−	0.881705i
$515$	1.73184	+	5.89810i	0.0763139	+	0.259901i
$516$	−29.8691	+	16.3518i	−1.31491	+	0.719849i
$517$	9.51423	+	14.8044i	0.418435	+	0.651098i
$518$	−7.89161	−	12.2796i	−0.346737	−	0.539534i
$519$	−3.60084	+	1.97127i	−0.158059	+	0.0865293i
$520$	−13.6886	−	46.6191i	−0.600286	−	2.04438i
$521$	4.00072	−	27.8256i	0.175275	−	1.21906i	−0.692246	−	0.721662i	$-0.743379\pi$
$521$	4.00072	−	27.8256i	0.175275	−	1.21906i	0.867520	−	0.497401i	$-0.165712\pi$
$522$	32.4448	−	14.9021i	1.42007	−	0.652247i
$523$	27.6326	+	12.6194i	1.20829	+	0.551808i	0.914704	−	0.404125i	$-0.132424\pi$
$523$	27.6326	+	12.6194i	1.20829	+	0.551808i	0.293587	+	0.955932i	$0.405151\pi$
$524$	−3.31736	+	11.2979i	−0.144920	+	0.493551i
$525$	22.2664	−	4.86904i	0.971786	−	0.212502i
$526$	−4.78332	+	0.687737i	−0.208562	+	0.0299868i
$527$	−0.685224	−	0.440366i	−0.0298488	−	0.0191827i
$528$	65.9127	+	14.2636i	2.86848	+	0.620745i
$529$	3.80353	+	22.6833i	0.165371	+	0.986231i
$530$		−	113.239i		−	4.91878i
$531$	7.16549	−	4.62695i	0.310956	−	0.200793i
$532$	−1.25776	−	8.74792i	−0.0545309	−	0.379270i
$533$	9.64054	−	4.40269i	0.417578	−	0.190702i
$534$	−21.6209	+	39.6979i	−0.935628	+	1.71790i
$535$	18.0365	−	39.4944i	0.779785	−	1.70749i
$536$	8.49494	−	9.80368i	0.366925	−	0.423454i
$537$	−28.6933	−	10.6666i	−1.23821	−	0.460300i
$538$	75.7457	−	22.2409i	3.26563	−	0.958875i
$539$	−1.66183	−	1.91786i	−0.0715802	−	0.0826080i
$540$	121.730	+	8.30865i	5.23843	+	0.357547i
$541$	1.73434	−	1.11459i	0.0745649	−	0.0479200i	−0.502827	−	0.864387i	$-0.667707\pi$
$541$	1.73434	−	1.11459i	0.0745649	−	0.0479200i	0.577392	+	0.816467i	$0.304070\pi$
$542$	−52.7314	+	45.6920i	−2.26501	+	1.96264i
$543$	−1.19448	−	16.4505i	−0.0512601	−	0.705958i
$544$	−10.0250	−	1.44138i	−0.429819	−	0.0617987i
$545$	−59.0386	−	51.1572i	−2.52893	−	2.19133i
$546$	−3.36656	+	4.50737i	−0.144076	+	0.192898i
$547$	−5.67293	−	1.66572i	−0.242557	−	0.0712212i	0.158194	−	0.987408i	$-0.449433\pi$
$547$	−5.67293	−	1.66572i	−0.242557	−	0.0712212i	−0.400751	+	0.916187i	$0.631251\pi$
$548$	22.5075	+	49.2847i	0.961475	+	2.10534i
$549$	−12.6541	−	3.68581i	−0.540064	−	0.157307i
$550$	49.4776	−	76.9887i	2.10973	−	3.28281i
$551$	−6.96517			−0.296726
$552$	−63.3552	+	48.6998i	−2.69658	+	2.07280i
$553$	4.87869			0.207463
$554$	21.3797	−	33.2675i	0.908337	−	1.41340i
$555$	−39.2160	−	2.76207i	−1.66463	−	0.117244i
$556$	9.65464	+	21.1407i	0.409448	+	0.896566i
$557$	−0.471982	−	0.138586i	−0.0199985	−	0.00587209i	0.271718	−	0.962377i	$-0.412408\pi$
$557$	−0.471982	−	0.138586i	−0.0199985	−	0.00587209i	−0.291717	+	0.956505i	$0.594226\pi$
$558$	−9.89992	−	11.3752i	−0.419097	−	0.481551i
$559$	−3.19583	−	2.76920i	−0.135169	−	0.117125i
$560$	−64.7164	−	9.30481i	−2.73477	−	0.393200i
$561$	−1.94677	+	0.141356i	−0.0821926	+	0.00596806i
$562$	−11.8677	+	10.2834i	−0.500609	+	0.433780i
$563$	5.21079	−	3.34877i	0.219609	−	0.141134i	−0.426211	−	0.904624i	$-0.640152\pi$
$563$	5.21079	−	3.34877i	0.219609	−	0.141134i	0.645820	+	0.763490i	$0.276516\pi$
$564$	−23.1967	−	61.9874i	−0.976755	−	2.61014i
$565$	7.88393	+	9.09854i	0.331679	+	0.382778i
$566$	43.9899	−	12.9166i	1.84903	−	0.542925i
$567$	−4.89854	−	7.55012i	−0.205719	−	0.317075i
$568$	−27.9828	+	32.2939i	−1.17413	+	1.35502i
$569$	9.83573	−	21.5372i	0.412335	−	0.902888i	−0.583534	−	0.812089i	$-0.698331\pi$
$569$	9.83573	−	21.5372i	0.412335	−	0.902888i	0.995869	−	0.0907993i	$-0.0289422\pi$
$570$	−28.4907	−	15.5170i	−1.19334	−	0.649938i
$571$	−18.9588	+	8.65819i	−0.793401	+	0.362334i	−0.770530	−	0.637404i	$-0.780008\pi$
$571$	−18.9588	+	8.65819i	−0.793401	+	0.362334i	−0.0228715	+	0.999738i	$0.507281\pi$
$572$	2.35865	+	16.4048i	0.0986200	+	0.685917i
$573$	26.7159	+	26.6580i	1.11607	+	1.11366i
$574$		−	24.5057i		−	1.02285i
$575$	18.4853	+	60.3418i	0.770892	+	2.51643i
$576$	−86.9114	−	39.4637i	−3.62131	−	1.64432i
$577$	−14.9442	−	9.60404i	−0.622135	−	0.399822i	0.191255	−	0.981540i	$-0.438744\pi$
$577$	−14.9442	−	9.60404i	−0.622135	−	0.399822i	−0.813390	+	0.581719i	$0.802380\pi$
$578$	−45.5793	+	6.55331i	−1.89585	+	0.272582i
$579$	6.65910	+	30.4525i	0.276743	+	1.26556i
$580$	−28.7291	+	97.8424i	−1.19291	+	4.06269i
$581$	1.94298	+	0.887331i	0.0806086	+	0.0368127i
$582$	−56.0179	+	42.0292i	−2.32202	+	1.74217i
$583$	−3.50191	+	24.3563i	−0.145034	+	1.00874i
$584$	−0.459604	−	1.56527i	−0.0190185	−	0.0647712i
$585$	4.30030	+	14.5289i	0.177796	+	0.600697i
$586$	−33.6613	−	52.3780i	−1.39053	−	2.16371i
$587$	−15.9400	−	24.8031i	−0.657915	−	1.02374i	−0.996564	−	0.0828225i	$-0.973607\pi$
$587$	−15.9400	−	24.8031i	−0.657915	−	1.02374i	0.338650	−	0.940913i	$-0.390030\pi$
$588$	4.58309	+	8.37173i	0.189004	+	0.345244i
$589$	0.828814	+	2.82268i	0.0341507	+	0.116307i
$590$	−4.72533	+	32.8654i	−0.194539	+	1.35305i
$591$	1.05948	+	1.41211i	0.0435811	+	0.0580863i
$592$	74.3364	+	33.9483i	3.05521	+	1.39527i
$593$	3.53624	−	12.0433i	0.145216	−	0.494560i	−0.854473	−	0.519496i	$-0.826120\pi$
$593$	3.53624	−	12.0433i	0.145216	−	0.494560i	0.999689	+	0.0249355i	$0.00793805\pi$
$594$	−35.3357	−	7.56659i	−1.44984	−	0.310461i
$595$	1.87311	−	0.269313i	0.0767900	−	0.0110407i
$596$	−52.1908	−	33.5410i	−2.13782	−	1.37389i
$597$	1.06129	−	4.90427i	0.0434359	−	0.200718i
$598$	−13.2018	−	8.26825i	−0.539862	−	0.338114i
$599$		−	6.42021i		−	0.262323i	−0.991361	−	0.131161i	$-0.958129\pi$
$599$		−	6.42021i		−	0.262323i	0.991361	−	0.131161i	$-0.0418706\pi$
$600$	−154.875	+	155.211i	−6.32275	+	6.33647i
$601$	−0.478617	−	3.32885i	−0.0195232	−	0.135787i	0.977729	−	0.209873i	$-0.0673051\pi$
$601$	−0.478617	−	3.32885i	−0.0195232	−	0.135787i	−0.997252	+	0.0740863i	$0.976396\pi$
$602$	−8.89410	+	4.06180i	−0.362496	+	0.165547i
$603$	−2.64252	+	3.06302i	−0.107612	+	0.124736i
$604$	−33.4772	+	73.3048i	−1.36217	+	2.98273i
$605$	12.7255	−	14.6861i	0.517367	−	0.597073i
$606$	7.45450	−	20.0526i	0.302818	−	0.814582i
$607$	−10.5457	+	3.09649i	−0.428036	+	0.125683i	−0.488653	−	0.872478i	$-0.662512\pi$
$607$	−10.5457	+	3.09649i	−0.428036	+	0.125683i	0.0606164	+	0.998161i	$0.480693\pi$
$608$	23.9548	+	27.6453i	0.971495	+	1.12117i
$609$	7.04467	−	2.63623i	0.285465	−	0.106825i
$610$	43.1617	−	27.7383i	1.74757	−	1.12309i
$611$	6.21159	−	5.38237i	0.251294	−	0.217747i
$612$	7.26851	+	1.02898i	0.293812	+	0.0415941i
$613$	3.45461	+	0.496699i	0.139531	+	0.0200615i	0.211726	−	0.977329i	$-0.432091\pi$
$613$	3.45461	+	0.496699i	0.139531	+	0.0200615i	−0.0721956	+	0.997390i	$0.523001\pi$
$614$	−19.3292	−	16.7489i	−0.780064	−	0.675929i
$615$	−52.8790	−	39.4954i	−2.13229	−	1.59261i
$616$	23.4237	+	6.87781i	0.943766	+	0.277115i
$617$	−13.9663	−	30.5818i	−0.562260	−	1.23118i	−0.950817	−	0.309753i	$-0.899754\pi$
$617$	−13.9663	−	30.5818i	−0.562260	−	1.23118i	0.388557	−	0.921425i	$-0.372974\pi$
$618$	−0.481070	+	6.83024i	−0.0193515	+	0.274753i
$619$	−11.2064	+	17.4375i	−0.450423	+	0.700871i	−0.990000	−	0.141065i	$-0.954948\pi$
$619$	−11.2064	+	17.4375i	−0.450423	+	0.700871i	0.539578	+	0.841936i	$0.318584\pi$
$620$	43.0699			1.72973
$621$	19.7244	−	15.2299i	0.791512	−	0.611153i
$622$	−66.4701			−2.66521
$623$	−5.14867	+	8.01148i	−0.206277	+	0.320973i
$624$	2.21291	−	31.4190i	0.0885874	−	1.25777i
$625$	34.2179	+	74.9269i	1.36872	+	2.99707i
$626$	53.4488	+	15.6940i	2.13624	+	0.627258i
$627$	5.64815	+	4.21861i	0.225565	+	0.168475i
$628$	39.7004	+	34.4006i	1.58422	+	1.37273i
$629$	−2.34122	−	0.336616i	−0.0933504	−	0.0134218i
$630$	34.6889	+	4.91080i	1.38204	+	0.195651i
$631$	−33.0089	+	28.6024i	−1.31407	+	1.13864i	−0.333436	+	0.942773i	$0.608208\pi$
$631$	−33.0089	+	28.6024i	−1.31407	+	1.13864i	−0.980630	+	0.195871i	$0.937247\pi$
$632$	−39.4826	+	25.3739i	−1.57053	+	1.00932i
$633$	35.1020	−	13.1357i	1.39518	−	0.522098i
$634$	50.4672	+	58.2422i	2.00431	+	2.31309i
$635$	−71.5606	+	21.0121i	−2.83980	+	0.833839i
$636$	32.2472	−	86.7451i	1.27869	−	3.43967i
$637$	−0.776153	+	0.895728i	−0.0307523	+	0.0354900i
$638$	12.5461	−	27.4722i	0.496706	−	1.08763i
$639$	8.70461	−	10.0898i	0.344349	−	0.399145i
$640$	161.177	−	73.6072i	6.37109	−	2.90958i
$641$	2.96038	+	20.5899i	0.116928	+	0.813252i	0.960906	+	0.276875i	$0.0892987\pi$
$641$	2.96038	+	20.5899i	0.116928	+	0.813252i	−0.843978	+	0.536378i	$0.819792\pi$
$642$	34.1605	−	34.2346i	1.34821	−	1.35113i
$643$			24.6527i			0.972207i	0.873901	+	0.486103i	$0.161582\pi$
$643$			24.6527i			0.972207i	−0.873901	+	0.486103i	$0.838418\pi$
$644$	−22.0632	+	14.5457i	−0.869412	+	0.573179i
$645$	−5.56981	+	25.7383i	−0.219311	+	1.01344i
$646$	−1.64204	−	1.05528i	−0.0646053	−	0.0415193i
$647$	18.4095	−	2.64688i	0.723751	−	0.104060i	0.229413	−	0.973329i	$-0.426319\pi$
$647$	18.4095	−	2.64688i	0.723751	−	0.104060i	0.494338	+	0.869270i	$0.335410\pi$
$648$	78.9110	+	35.6249i	3.09992	+	1.39948i
$649$	2.03273	−	6.92284i	0.0797916	−	0.271745i
$650$	−38.8799	−	17.7559i	−1.52500	−	0.696443i
$651$	−1.90662	−	2.54121i	−0.0747265	−	0.0995978i
$652$	7.73484	−	53.7970i	0.302920	−	2.10685i
$653$	8.16450	+	27.8057i	0.319501	+	1.08812i	0.950083	+	0.311999i	$0.100998\pi$
$653$	8.16450	+	27.8057i	0.319501	+	1.08812i	−0.630581	+	0.776123i	$0.717183\pi$
$654$	−41.7850	−	76.3267i	−1.63392	−	2.98461i
$655$	4.92309	+	7.66048i	0.192361	+	0.299320i
$656$	74.1744	+	115.418i	2.89602	+	4.50630i
$657$	0.144385	+	0.487817i	0.00563300	+	0.0190316i
$658$	−5.35417	−	18.2346i	−0.208727	−	0.710860i
$659$	2.42862	−	16.8914i	0.0946055	−	0.657996i	−0.886243	−	0.463221i	$-0.846693\pi$
$659$	2.42862	−	16.8914i	0.0946055	−	0.657996i	0.980848	−	0.194774i	$-0.0623975\pi$
$660$	82.5573	−	61.9414i	3.21354	−	2.41106i
$661$	40.8276	+	18.6453i	1.58801	+	0.725220i	0.996696	−	0.0812214i	$-0.0258821\pi$
$661$	40.8276	+	18.6453i	1.58801	+	0.725220i	0.591314	+	0.806441i	$0.298609\pi$
$662$	−10.4772	+	35.6821i	−0.407208	+	1.38682i
$663$	0.194745	+	0.890580i	0.00756326	+	0.0345873i
$664$	−20.3393	+	2.92434i	−0.789316	+	0.113487i
$665$	−5.74974	−	3.69513i	−0.222965	−	0.143291i
$666$	−39.8724	−	18.1048i	−1.54502	−	0.701546i
$667$	8.87223	+	18.8425i	0.343534	+	0.729586i
$668$		−	118.551i		−	4.58688i
$669$	26.2686	+	26.2117i	1.01560	+	1.01340i
$670$	−2.24112	−	15.5873i	−0.0865820	−	0.602191i
$671$	−10.1414	+	4.63142i	−0.391504	+	0.178794i
$672$	−34.6916	−	18.8943i	−1.33826	−	0.728863i
$673$	10.2844	−	22.5197i	0.396434	−	0.868069i	−0.601185	−	0.799110i	$-0.705305\pi$
$673$	10.2844	−	22.5197i	0.396434	−	0.868069i	0.997619	−	0.0689598i	$-0.0219680\pi$
$674$	0.665508	−	0.768037i	0.0256344	−	0.0295837i
$675$	48.1929	−	48.5073i	1.85495	−	1.86705i
$676$	−61.3053	+	18.0009i	−2.35790	+	0.692341i
$677$	3.78430	+	4.36731i	0.145442	+	0.167849i	0.823796	−	0.566886i	$-0.191852\pi$
$677$	3.78430	+	4.36731i	0.145442	+	0.167849i	−0.678354	+	0.734735i	$0.737306\pi$
$678$	4.69998	+	12.5596i	0.180502	+	0.482347i
$679$	−12.4117	+	7.97654i	−0.476319	+	0.306112i
$680$	−13.7581	+	11.9215i	−0.527600	+	0.457168i
$681$	30.5444	−	2.21785i	1.17046	−	0.0849882i
$682$	−12.6262	−	1.81537i	−0.483482	−	0.0695143i
$683$	−9.94424	−	8.61674i	−0.380506	−	0.329710i	0.443518	−	0.896266i	$-0.353730\pi$
$683$	−9.94424	−	8.61674i	−0.380506	−	0.329710i	−0.824024	+	0.566555i	$0.808276\pi$
$684$	−17.4061	−	20.0000i	−0.665540	−	0.764719i
$685$	40.2032	+	11.8047i	1.53609	+	0.451036i
$686$	1.13844	+	2.49284i	0.0434659	+	0.0951771i
$687$	−13.4371	−	0.946404i	−0.512656	−	0.0361076i
$688$	29.5954	−	46.0513i	1.12831	−	1.75569i
$689$	11.4925			0.437830
$690$	−5.68610	+	96.8402i	−0.216466	+	3.68664i
$691$	9.66167			0.367547			0.183774	−	0.982969i	$-0.441169\pi$
$691$	9.66167			0.367547			0.183774	+	0.982969i	$0.441169\pi$
$692$	7.06073	−	10.9867i	0.268409	−	0.417652i
$693$	−7.30932	−	2.12901i	−0.277658	−	0.0808745i
$694$	−8.78827	−	19.2436i	−0.333598	−	0.730478i
$695$	17.2452	+	5.06366i	0.654149	+	0.192075i
$696$	−43.3006	+	57.9737i	−1.64130	+	2.19749i
$697$	−3.00104	−	2.60042i	−0.113673	−	0.0984978i
$698$	24.4529	+	3.51579i	0.925555	+	0.133075i
$699$	1.29150	+	17.7867i	0.0488491	+	0.672753i
$700$	−54.8008	+	47.4851i	−2.07127	+	1.79477i
$701$	17.7040	−	11.3777i	0.668671	−	0.429729i	−0.161775	−	0.986828i	$-0.551722\pi$
$701$	17.7040	−	11.3777i	0.668671	−	0.429729i	0.830446	+	0.557099i	$0.188086\pi$
$702$	−1.14930	+	16.8384i	−0.0433774	+	0.635523i
$703$	5.59433	+	6.45621i	0.210994	+	0.243500i
$704$	−77.4714	+	22.7477i	−2.91981	+	0.857335i
$705$	−47.9764	−	17.8351i	−1.80690	−	0.671708i
$706$	27.6608	−	31.9222i	1.04103	−	1.20141i
$707$	1.87229	−	4.09974i	0.0704146	−	0.154186i
$708$	−12.9789	+	23.8305i	−0.487778	+	0.895605i
$709$	−35.1156	+	16.0368i	−1.31880	+	0.602274i	−0.945556	−	0.325461i	$-0.894481\pi$
$709$	−35.1156	+	16.0368i	−1.31880	+	0.602274i	−0.373240	+	0.927735i	$0.621753\pi$
$710$	7.38238	+	51.3456i	0.277056	+	1.92697i
$711$	12.2955	−	7.93953i	0.461116	−	0.297756i
$712$		−	91.6138i		−	3.43337i
$713$	6.58033	−	5.83769i	0.246435	−	0.218623i
$714$	2.06020	+	0.445831i	0.0771009	+	0.0166848i
$715$	10.7823	+	6.92939i	0.403237	+	0.259145i
$716$	96.3965	−	13.8597i	3.60251	−	0.517962i
$717$	−18.8001	+	4.11106i	−0.702104	+	0.153530i
$718$	9.97841	−	33.9834i	0.372391	−	1.26825i
$719$	−26.6366	−	12.1645i	−0.993377	−	0.453660i	−0.148669	−	0.988887i	$-0.547499\pi$
$719$	−26.6366	−	12.1645i	−0.993377	−	0.453660i	−0.844708	+	0.535227i	$0.820226\pi$
$720$	−178.243	+	81.8683i	−6.64273	+	3.05105i
$721$	−0.205292	+	1.42783i	−0.00764546	+	0.0531753i
$722$	−12.6835	−	43.1961i	−0.472031	−	1.60759i
$723$	41.9189	−	22.9485i	1.55898	−	0.853463i
$724$	28.3691	+	44.1431i	1.05433	+	1.64057i
$725$	30.8959	+	48.0750i	1.14745	+	1.78546i
$726$	18.9865	−	10.3942i	0.704656	−	0.385763i
$727$	−9.45629	−	32.2052i	−0.350714	−	1.19442i	−0.926333	−	0.376705i	$-0.877057\pi$
$727$	−9.45629	−	32.2052i	−0.350714	−	1.19442i	0.575619	−	0.817718i	$-0.304761\pi$
$728$	1.62264	−	11.2857i	0.0601392	−	0.418277i
$729$	−24.6325	−	11.0563i	−0.912314	−	0.409492i
$730$	−1.80142	−	0.822683i	−0.0666737	−	0.0304488i
$731$	−0.446376	+	1.52022i	−0.0165098	+	0.0562273i
$732$	40.9626	−	8.95736i	1.51402	−	0.331074i
$733$	−38.8260	+	5.58234i	−1.43407	+	0.206188i	−0.815144	−	0.579259i	$-0.803342\pi$
$733$	−38.8260	+	5.58234i	−1.43407	+	0.206188i	−0.618928	+	0.785447i	$0.712433\pi$
$734$	42.9957	+	27.6317i	1.58700	+	1.01990i
$735$	7.21393	+	1.56111i	0.266090	+	0.0575824i
$736$	44.2740	−	100.018i	1.63196	−	3.68673i
$737$			3.42196i			0.126050i
$738$	−39.8802	−	61.7601i	−1.46801	−	2.27342i
$739$	−3.25362	−	22.6294i	−0.119686	−	0.832437i	−0.957902	−	0.287097i	$-0.907310\pi$
$739$	−3.25362	−	22.6294i	−0.119686	−	0.832437i	0.838215	−	0.545340i	$-0.183599\pi$
$740$	113.768	−	51.9560i	4.18218	−	1.90994i
$741$	1.57481	−	2.89150i	0.0578522	−	0.106222i
$742$	11.0390	−	24.1719i	0.405253	−	0.887380i
$743$	20.7467	−	23.9429i	0.761121	−	0.878380i	−0.234476	−	0.972122i	$-0.575337\pi$
$743$	20.7467	−	23.9429i	0.761121	−	0.878380i	0.995597	+	0.0937415i	$0.0298827\pi$
$744$	28.6467	+	10.6493i	1.05024	+	0.390424i
$745$	−46.0344	+	13.5169i	−1.68657	+	0.495221i
$746$	30.6409	+	35.3614i	1.12184	+	1.29467i
$747$	6.34082	−	0.925703i	0.231998	−	0.0338697i
$748$	5.22394	−	3.35722i	0.191006	−	0.122752i
$749$	7.70013	−	6.67220i	0.281357	−	0.243797i
$750$	11.9523	+	164.608i	0.436435	+	6.01062i
$751$	−29.4443	−	4.23345i	−1.07444	−	0.154481i	−0.417688	−	0.908590i	$-0.637160\pi$
$751$	−29.4443	−	4.23345i	−1.07444	−	0.154481i	−0.656748	+	0.754110i	$0.728069\pi$
$752$	80.4104	+	69.6760i	2.93226	+	2.54082i
$753$	13.4118	−	17.9566i	0.488754	−	0.654376i
$754$	−13.5341	−	3.97397i	−0.492882	−	0.144723i
$755$	25.8894	+	56.6899i	0.942212	+	2.06316i
$756$	25.1745	+	13.6403i	0.915590	+	0.496093i
$757$	28.3483	−	44.1108i	1.03034	−	1.60323i	0.259985	−	0.965613i	$-0.416282\pi$
$757$	28.3483	−	44.1108i	1.03034	−	1.60323i	0.770350	−	0.637621i	$-0.220081\pi$
$758$	−20.1442			−0.731670
$759$	4.21780	−	20.6534i	0.153096	−	0.749669i
$760$	65.7500			2.38500
$761$	2.53820	−	3.94952i	0.0920098	−	0.143170i	−0.792197	−	0.610265i	$-0.791063\pi$
$761$	2.53820	−	3.94952i	0.0920098	−	0.143170i	0.884207	+	0.467095i	$0.154699\pi$
$762$	−82.8701	−	5.83673i	−3.00207	−	0.211443i
$763$	−7.61536	−	16.6753i	−0.275695	−	0.603687i
$764$	−115.205	−	33.8273i	−4.16798	−	1.22383i
$765$	4.28241	−	3.72701i	0.154831	−	0.134750i
$766$	53.8029	+	46.6205i	1.94398	+	1.68447i
$767$	−3.33549	−	0.479570i	−0.120437	−	0.0173163i
$768$	86.9219	−	6.31146i	3.13652	−	0.227745i
$769$	−28.3047	+	24.5262i	−1.02069	+	0.884436i	−0.993343	−	0.115190i	$-0.963252\pi$
$769$	−28.3047	+	24.5262i	−1.02069	+	0.884436i	−0.0273500	+	0.999626i	$0.508707\pi$
$770$	24.9312	−	16.0223i	0.898459	−	0.577405i
$771$	−4.47345	−	11.9542i	−0.161107	−	0.430520i
$772$	−64.9427	−	74.9478i	−2.33734	−	2.69743i
$773$	25.2053	−	7.40095i	0.906572	−	0.266194i	0.204975	−	0.978767i	$-0.434289\pi$
$773$	25.2053	−	7.40095i	0.906572	−	0.266194i	0.701597	+	0.712574i	$0.252471\pi$
$774$	−15.8051	+	24.7109i	−0.568104	+	0.888213i
$775$	15.8063	−	18.2414i	0.567779	−	0.655252i
$776$	58.9607	−	129.106i	2.11657	−	4.63463i
$777$	−8.10179	−	4.41252i	−0.290650	−	0.158298i
$778$	−47.1488	+	21.5321i	−1.69037	+	0.771965i
$779$	2.04108	+	14.1960i	0.0731291	+	0.508624i
$780$	−34.1224	−	34.0485i	−1.22178	−	1.21913i
$781$		−	11.2721i		−	0.403349i
$782$	−0.763158	+	5.78635i	−0.0272905	+	0.206920i
$783$	13.4641	−	18.1083i	0.481168	−	0.647139i
$784$	−12.9073	−	8.29500i	−0.460974	−	0.296250i
$785$	40.2112	−	5.78150i	1.43520	−	0.206351i
$786$	2.16680	+	9.90892i	0.0772872	+	0.353439i
$787$	2.06808	−	7.04325i	0.0737192	−	0.251065i	−0.914386	−	0.404843i	$-0.867326\pi$
$787$	2.06808	−	7.04325i	0.0737192	−	0.251065i	0.988105	+	0.153779i	$0.0491443\pi$
$788$	−5.10878	−	2.33310i	−0.181993	−	0.0831134i
$789$	−2.44306	+	1.83299i	−0.0869754	+	0.0652561i
$790$	−8.10835	+	56.3948i	−0.288482	+	2.00644i
$791$	0.795942	+	2.71073i	0.0283004	+	0.0963824i
$792$	70.2261	−	20.7857i	2.49538	−	0.738587i
$793$	2.81514	+	4.38045i	0.0999686	+	0.155554i
$794$	23.9189	+	37.2185i	0.848849	+	1.32083i
$795$	−34.3676	−	62.7777i	−1.21889	−	2.22649i
$796$	4.49743	+	15.3169i	0.159407	+	0.542892i
$797$	−0.316928	+	2.20429i	−0.0112262	+	0.0780798i	−0.994664	−	0.103164i	$-0.967103\pi$
$797$	−0.316928	+	2.20429i	−0.0112262	+	0.0780798i	0.983438	+	0.181244i	$0.0580124\pi$
$798$	−4.56896	−	6.08965i	−0.161739	−	0.215571i
$799$	−2.80123	−	1.27928i	−0.0991004	−	0.0452576i
$800$	84.5554	−	287.969i	2.98948	−	10.1812i
$801$	0.0619183	+	28.5697i	0.00218778	+	1.00946i
$802$	50.9665	−	7.32788i	1.79969	−	0.258756i
$803$	0.362024	+	0.232658i	0.0127755	+	0.00821034i
$804$	2.72205	−	12.5787i	0.0959994	−	0.443616i
$805$	−2.67226	+	20.2614i	−0.0941847	+	0.714119i
$806$			5.95766i			0.209850i
$807$	35.2421	−	35.3185i	1.24058	−	1.24327i
$808$	6.17042	+	42.9162i	0.217075	+	1.50979i
$809$	−25.4209	+	11.6094i	−0.893752	+	0.408163i	−0.808705	−	0.588214i	$-0.799831\pi$
$809$	−25.4209	+	11.6094i	−0.893752	+	0.408163i	−0.0850471	+	0.996377i	$0.527104\pi$
$810$	95.4162	−	44.0759i	3.35258	−	1.54867i
$811$	−12.6235	+	27.6417i	−0.443272	+	0.970630i	0.547714	+	0.836665i	$0.315498\pi$
$811$	−12.6235	+	27.6417i	−0.443272	+	0.970630i	−0.990986	+	0.133965i	$0.957229\pi$
$812$	−15.6706	+	18.0848i	−0.549929	+	0.634652i
$813$	−15.3660	+	41.3347i	−0.538911	+	1.44967i
$814$	−35.5416	+	10.4360i	−1.24573	+	0.365780i
$815$	−27.5248	−	31.7653i	−0.964150	−	1.11269i
$816$	−11.0526	+	4.13607i	−0.386920	+	0.144791i
$817$	4.81400	−	3.09377i	0.168420	−	0.108237i
$818$	−36.7299	+	31.8267i	−1.28423	+	1.11279i
$819$	−0.498394	+	3.52055i	−0.0174153	+	0.123018i
$820$	207.836	+	29.8822i	7.25793	+	1.04353i
$821$	−8.05090	−	6.97615i	−0.280978	−	0.243469i	0.502957	−	0.864311i	$-0.332245\pi$
$821$	−8.05090	−	6.97615i	−0.280978	−	0.243469i	−0.783936	+	0.620842i	$0.786791\pi$
$822$	37.3934	+	27.9292i	1.30424	+	0.974142i
$823$	1.25715	+	0.369132i	0.0438214	+	0.0128671i	0.303570	−	0.952809i	$-0.401821\pi$
$823$	1.25715	+	0.369132i	0.0438214	+	0.0128671i	−0.259748	+	0.965676i	$0.583640\pi$
$824$	−5.76471	−	12.6230i	−0.200823	−	0.439742i
$825$	4.06377	−	57.6975i	0.141482	−	2.00877i
$826$	−4.21252	+	6.55480i	−0.146572	+	0.228071i
$827$	3.11705			0.108390			0.0541952	−	0.998530i	$-0.482741\pi$
$827$	3.11705			0.108390			0.0541952	+	0.998530i	$0.482741\pi$
$828$	−31.9331	+	72.5640i	−1.10975	+	2.52177i
$829$	45.3122			1.57376			0.786879	−	0.617107i	$-0.211696\pi$
$829$	45.3122			1.57376			0.786879	+	0.617107i	$0.211696\pi$
$830$	−13.4862	+	20.9850i	−0.468114	+	0.728400i
$831$	1.75599	−	24.9316i	0.0609146	−	0.864868i
$832$	15.6654	+	34.3025i	0.543101	+	1.18922i
$833$	0.426087	+	0.125111i	0.0147631	+	0.00433482i
$834$	16.0399	+	11.9803i	0.555418	+	0.414842i
$835$	−69.2878	−	60.0383i	−2.39780	−	2.07771i
$836$	−22.1995	−	3.19181i	−0.767786	−	0.110391i
$837$	−8.94068	−	3.30163i	−0.309035	−	0.114121i
$838$	−17.3176	+	15.0058i	−0.598227	+	0.518366i
$839$	12.2522	−	7.87399i	0.422992	−	0.271840i	−0.311781	−	0.950154i	$-0.600925\pi$
$839$	12.2522	−	7.87399i	0.422992	−	0.271840i	0.734772	+	0.678314i	$0.237289\pi$
$840$	−66.5005	+	24.8855i	−2.29449	+	0.858633i
$841$	−6.64092	−	7.66403i	−0.228997	−	0.264277i
$842$	−46.4645	+	13.6432i	−1.60127	+	0.470176i
$843$	−3.45827	+	9.30276i	−0.119109	+	0.320404i
$844$	−78.0829	+	90.1125i	−2.68773	+	3.10180i
$845$	−20.5264	+	44.9465i	−0.706128	+	1.54621i
$846$	−43.1686	−	37.2423i	−1.48417	−	1.28042i
$847$	4.14804	−	1.89435i	0.142528	−	0.0650906i
$848$	21.1726	+	147.259i	0.727071	+	5.05689i
$849$	20.4671	−	20.5115i	0.702429	−	0.703953i
$850$			16.0147i			0.549299i
$851$	10.3396	−	23.3580i	0.354437	−	0.800702i
$852$	−8.96660	+	41.4349i	−0.307191	+	1.41954i
$853$	−8.45614	−	5.43443i	−0.289533	−	0.186071i	0.387809	−	0.921740i	$-0.373232\pi$
$853$	−8.45614	−	5.43443i	−0.289533	−	0.186071i	−0.677342	+	0.735668i	$0.736868\pi$
$854$	11.9173	−	1.71345i	0.407803	−	0.0586332i
$855$	−20.5041	+	0.0444380i	−0.701227	+	0.00151975i
$856$	−27.6142	+	94.0452i	−0.943833	+	3.21440i
$857$	−49.2020	−	22.4698i	−1.68071	−	0.767554i	−0.999367	−	0.0355891i	$-0.988669\pi$
$857$	−49.2020	−	22.4698i	−1.68071	−	0.767554i	−0.681342	−	0.731965i	$-0.738603\pi$
$858$	8.56806	+	11.4198i	0.292509	+	0.389865i
$859$	−3.15577	+	21.9489i	−0.107674	+	0.748886i	0.862427	+	0.506182i	$0.168944\pi$
$859$	−3.15577	+	21.9489i	−0.107674	+	0.748886i	−0.970100	+	0.242704i	$0.921966\pi$
$860$	−23.6031	−	80.3849i	−0.804861	−	2.74110i
$861$	−7.43738	−	13.5855i	−0.253465	−	0.462993i
$862$	24.4600	+	38.0605i	0.833111	+	1.29635i
$863$	9.86175	+	15.3452i	0.335698	+	0.522356i	0.967532	−	0.252747i	$-0.0813341\pi$
$863$	9.86175	+	15.3452i	0.335698	+	0.522356i	−0.631834	+	0.775103i	$0.717698\pi$
$864$	−118.180	+	8.83862i	−4.02055	+	0.300696i
$865$	−2.84545	−	9.69071i	−0.0967482	−	0.329494i
$866$	−8.09671	+	56.3138i	−0.275137	+	1.91362i
$867$	−23.2795	+	17.4662i	−0.790612	+	0.593183i
$868$	9.19370	+	4.19862i	0.312055	+	0.142511i
$869$	3.48802	−	11.8791i	0.118323	−	0.402971i
$870$	18.7650	+	85.8136i	0.636194	+	2.90935i
$871$	1.58195	−	0.227450i	0.0536022	−	0.00770683i
$872$	148.358	+	95.3437i	5.02402	+	3.22874i
$873$	−18.2996	+	40.3015i	−0.619349	+	1.36400i
$874$	15.7688	−	13.9892i	0.533389	−	0.473192i
$875$			34.7698i			1.17543i
$876$	−1.14568	−	1.14320i	−0.0387090	−	0.0386252i
$877$	−4.80934	−	33.4497i	−0.162400	−	1.12952i	−0.894093	−	0.447881i	$-0.852179\pi$
$877$	−4.80934	−	33.4497i	−0.162400	−	1.12952i	0.731693	−	0.681634i	$-0.238730\pi$
$878$	−80.8095	+	36.9044i	−2.72719	+	1.24546i
$879$	−34.5578	−	18.8214i	−1.16560	−	0.634830i
$880$	−68.9252	+	150.925i	−2.32347	+	5.08768i
$881$	−20.5357	+	23.6994i	−0.691864	+	0.798454i	−0.987629	−	0.156807i	$-0.949880\pi$
$881$	−20.5357	+	23.6994i	−0.691864	+	0.798454i	0.295765	+	0.955261i	$0.404425\pi$
$882$	6.92597	+	4.42987i	0.233210	+	0.149161i
$883$	14.2084	−	4.17195i	0.478149	−	0.140397i	−0.0337722	−	0.999430i	$-0.510752\pi$
$883$	14.2084	−	4.17195i	0.478149	−	0.140397i	0.511921	+	0.859032i	$0.328934\pi$
$884$	−1.89924	−	2.19184i	−0.0638784	−	0.0737196i
$885$	7.35489	+	19.6542i	0.247232	+	0.660667i
$886$	10.9601	−	7.04364i	0.368212	−	0.236636i
$887$	10.4438	−	9.04957i	0.350667	−	0.303855i	−0.461660	−	0.887057i	$-0.652746\pi$
$887$	10.4438	−	9.04957i	0.350667	−	0.303855i	0.812327	+	0.583202i	$0.198200\pi$
$888$	88.5159	−	6.42720i	2.97040	−	0.215683i
$889$	−17.3237	−	2.49077i	−0.581017	−	0.0835376i
$890$	−84.0509	−	72.8305i	−2.81739	−	2.44128i
$891$	−21.8860	+	6.52947i	−0.733207	+	0.218746i
$892$	−113.276	−	33.2609i	−3.79277	−	1.11366i
$893$	4.62041	+	10.1173i	0.154616	+	0.338562i
$894$	−53.3097	−	3.75472i	−1.78294	−	0.125577i
$895$	40.7180	−	63.3585i	1.36105	−	2.11784i
$896$	41.5804			1.38910
$897$	−9.82824	−	0.577078i	−0.328155	−	0.0192681i
$898$	54.1736			1.80779
$899$	4.30643	−	6.70093i	0.143627	−	0.223489i
$900$	−60.8343	+	208.856i	−2.02781	+	6.96187i
$901$	−1.78878	−	3.91687i	−0.0595928	−	0.130490i
$902$	−59.6687	−	17.5203i	−1.98675	−	0.583362i
$903$	−3.69800	+	4.95112i	−0.123062	+	0.164763i
$904$	−20.5398	−	17.7979i	−0.683145	−	0.591948i
$905$	40.1667	+	5.77510i	1.33519	+	0.191971i
$906$	5.02735	+	69.2370i	0.167022	+	2.30025i
$907$	−19.7193	+	17.0869i	−0.654769	+	0.567360i	−0.917612	−	0.397478i	$-0.869885\pi$
$907$	−19.7193	+	17.0869i	−0.654769	+	0.567360i	0.262843	+	0.964839i	$0.415340\pi$
$908$	−81.9626	+	52.6742i	−2.72003	+	1.74805i
$909$	−1.95325	−	13.3793i	−0.0647853	−	0.443762i
$910$	−9.06412	−	10.4606i	−0.300473	−	0.346764i
$911$	−19.3097	+	5.66984i	−0.639759	+	0.187850i	−0.585495	−	0.810676i	$-0.699100\pi$
$911$	−19.3097	+	5.66984i	−0.639759	+	0.187850i	−0.0542647	+	0.998527i	$0.517281\pi$
$912$	39.9514	+	14.8518i	1.32292	+	0.491792i
$913$	3.54969	−	4.09656i	0.117478	−	0.135577i
$914$	−7.31598	+	16.0198i	−0.241991	+	0.529887i
$915$	15.5096	−	28.4771i	0.512733	−	0.941424i
$916$	38.9817	−	17.8023i	1.28799	−	0.588206i
$917$	0.304109	+	2.11513i	0.0100426	+	0.0698476i
$918$	5.91773	−	2.22914i	0.195314	−	0.0735725i
$919$			21.9093i			0.722723i	0.932426	+	0.361361i	$0.117688\pi$
$919$			21.9093i			0.722723i	−0.932426	+	0.361361i	$0.882312\pi$
$920$	−83.7523	−	177.870i	−2.76123	−	5.86422i
$921$	−15.7990	−	3.41894i	−0.520595	−	0.112658i
$922$	−55.9794	−	35.9758i	−1.84358	−	1.18480i
$923$	−5.21102	+	0.749232i	−0.171523	+	0.0246613i
$924$	23.6610	−	5.17399i	0.778388	−	0.170212i
$925$	19.7468	−	67.2515i	0.649272	−	2.21122i
$926$	−96.4474	−	44.0461i	−3.16946	−	1.44744i
$927$	1.80626	+	3.93257i	0.0593253	+	0.129163i
$928$	14.0955	−	98.0366i	0.462709	−	3.21821i
$929$	−0.399246	−	1.35971i	−0.0130989	−	0.0446106i	0.952684	−	0.303962i	$-0.0983095\pi$
$929$	−0.399246	−	1.35971i	−0.0130989	−	0.0446106i	−0.965783	+	0.259351i	$0.916491\pi$
$930$	32.5436	−	17.8160i	1.06715	−	0.584209i
$931$	−0.867123	−	1.34927i	−0.0284188	−	0.0442205i
$932$	−30.6733	−	47.7286i	−1.00474	−	1.56340i
$933$	−36.8499	+	20.1734i	−1.20641	+	0.660448i
$934$	26.7217	+	91.0058i	0.874361	+	2.97780i
$935$	0.683431	−	4.75337i	0.0223506	−	0.155452i
$936$	−14.2768	−	31.0834i	−0.466653	−	1.01599i
$937$	2.35988	+	1.07772i	0.0770938	+	0.0352076i	0.453589	−	0.891211i	$-0.350144\pi$
$937$	2.35988	+	1.07772i	0.0770938	+	0.0352076i	−0.376495	+	0.926419i	$0.622871\pi$
$938$	1.04112	−	3.54574i	0.0339939	−	0.115773i
$939$	34.3942	−	7.52104i	1.12241	−	0.245440i
$940$	161.179	−	23.1741i	5.25708	−	0.755854i
$941$	−27.2018	−	17.4816i	−0.886755	−	0.569883i	0.0160798	−	0.999871i	$-0.494881\pi$
$941$	−27.2018	−	17.4816i	−0.886755	−	0.569883i	−0.902835	+	0.429988i	$0.858518\pi$
$942$	44.2275	+	9.57092i	1.44101	+	0.311838i
$943$	35.8039	−	23.6045i	1.16593	−	0.768668i
$944$		−	43.6226i		−	1.41980i
$945$	20.7214	−	7.80550i	0.674066	−	0.253913i
$946$	3.53122	+	24.5602i	0.114810	+	0.798520i
$947$	−6.81540	+	3.11249i	−0.221471	+	0.101142i	−0.523061	−	0.852295i	$-0.675210\pi$
$947$	−6.81540	+	3.11249i	−0.221471	+	0.101142i	0.301590	+	0.953438i	$0.402483\pi$
$948$	−22.2709	+	40.8915i	−0.723327	+	1.32809i
$949$	0.0834934	−	0.182825i	0.00271031	−	0.00593475i
$950$	37.8776	−	43.7131i	1.22891	−	1.41824i
$951$	45.6544	+	16.9719i	1.48045	+	0.550351i
$952$	−4.09896	+	1.20356i	−0.132848	+	0.0390077i
$953$	34.7380	+	40.0898i	1.12527	+	1.29864i	0.949346	+	0.314232i	$0.101747\pi$
$953$	34.7380	+	40.0898i	1.12527	+	1.29864i	0.175928	+	0.984403i	$0.443708\pi$
$954$	−11.5163	−	78.8837i	−0.372855	−	2.55396i
$955$	−78.1142	+	50.2010i	−2.52772	+	1.62447i
$956$	46.2697	−	40.0930i	1.49647	−	1.29670i
$957$	−1.38235	−	19.0378i	−0.0446850	−	0.615405i
$958$	−58.6178	−	8.42797i	−1.89386	−	0.272295i
$959$	7.43101	+	6.43900i	0.239960	+	0.207926i
$960$	140.530	−	188.151i	4.53560	−	6.07256i
$961$	26.5162	+	7.78587i	0.855363	+	0.251157i
$962$	7.18683	+	15.7370i	0.231713	+	0.507380i
$963$	8.54791	−	29.3467i	0.275453	−	0.945683i
$964$	−82.1971	+	127.901i	−2.64739	+	4.11942i
$965$	−76.6928			−2.46883
$966$	−10.6541	+	20.1172i	−0.342790	+	0.647260i
$967$	−48.1790			−1.54933			−0.774666	−	0.632370i	$-0.782082\pi$
$967$	−48.1790			−1.54933			−0.774666	+	0.632370i	$0.782082\pi$
$968$	−23.7171	+	36.9045i	−0.762296	+	1.18616i
$969$	−1.23059	−	0.0866736i	−0.0395324	−	0.00278436i
$970$	−71.5759	−	156.729i	−2.29816	−	5.03227i
$971$	−1.84691	−	0.542303i	−0.0592703	−	0.0174033i	0.251963	−	0.967737i	$-0.418924\pi$
$971$	−1.84691	−	0.542303i	−0.0592703	−	0.0174033i	−0.311233	+	0.950334i	$0.600742\pi$
$972$	85.6439	−	6.59197i	2.74703	−	0.211437i
$973$	3.18754	+	2.76202i	0.102188	+	0.0885462i
$974$	41.6794	+	5.99259i	1.33549	+	0.192015i
$975$	−26.9432	+	1.95637i	−0.862874	+	0.0626539i
$976$	−50.9423	+	44.1418i	−1.63062	+	1.41294i
$977$	32.1341	−	20.6514i	1.02806	−	0.660696i	0.0860559	−	0.996290i	$-0.472574\pi$
$977$	32.1341	−	20.6514i	1.02806	−	0.660696i	0.942006	+	0.335595i	$0.108937\pi$
$978$	−16.4088	−	43.8486i	−0.524696	−	1.40212i
$979$	15.8261	+	18.2643i	0.505804	+	0.583729i
$980$	−22.5303	+	6.61550i	−0.719705	+	0.211324i
$981$	−46.3298	−	29.6326i	−1.47920	−	0.946098i
$982$	−39.4124	+	45.4843i	−1.25770	+	1.45146i
$983$	−5.85554	+	12.8218i	−0.186763	+	0.408953i	−0.979733	−	0.200307i	$-0.935806\pi$
$983$	−5.85554	+	12.8218i	−0.186763	+	0.408953i	0.792971	+	0.609260i	$0.208533\pi$
$984$	130.847	+	71.2641i	4.17126	+	2.27182i
$985$	−3.95085	+	1.80429i	−0.125885	+	0.0574896i
$986$	0.752135	+	5.23121i	0.0239529	+	0.166596i
$987$	−8.50241	−	8.48400i	−0.270635	−	0.270049i
$988$			10.4748i			0.333248i
$989$	−14.5015	−	9.08225i	−0.461121	−	0.288799i
$990$	36.7581	−	80.9529i	1.16825	−	2.57285i
$991$	−2.45275	−	1.57629i	−0.0779143	−	0.0500725i	0.501104	−	0.865387i	$-0.332928\pi$
$991$	−2.45275	−	1.57629i	−0.0779143	−	0.0500725i	−0.579018	+	0.815315i	$0.696564\pi$
$992$	−41.4073	+	5.95347i	−1.31468	+	0.189023i
$993$	5.02100	+	22.9613i	0.159337	+	0.728656i
$994$	−3.42952	+	11.6799i	−0.108778	+	0.370464i
$995$	11.2297	+	5.12842i	0.356004	+	0.162582i
$996$	−16.3069	+	12.2348i	−0.516704	+	0.387674i
$997$	7.32092	−	50.9181i	0.231856	−	1.61259i	−0.458208	−	0.888845i	$-0.651508\pi$
$997$	7.32092	−	50.9181i	0.231856	−	1.61259i	0.690064	−	0.723749i	$-0.257582\pi$
$998$	6.85783	+	23.3556i	0.217081	+	0.739309i
$999$	−27.5993	+	2.06415i	−0.873204	+	0.0653067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.u.a.113.2	✓	480
3.2	odd	2	inner	483.2.u.a.113.47	yes	480
23.11	odd	22	inner	483.2.u.a.218.47	yes	480
69.11	even	22	inner	483.2.u.a.218.2	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.u.a.113.2	✓	480	1.1	even	1	trivial
483.2.u.a.113.47	yes	480	3.2	odd	2	inner
483.2.u.a.218.2	yes	480	69.11	even	22	inner
483.2.u.a.218.47	yes	480	23.11	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.48162 + 2.30545i) q^{2} +(-0.121691 + 1.72777i) q^{3} +(-2.28907 - 5.01236i) q^{4} +(-4.08876 - 1.20057i) q^{5} +(-3.80299 - 2.84046i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(9.52207 + 1.36907i) q^{8} +(-2.97038 - 0.420508i) q^{9} +(8.82585 - 7.64764i) q^{10} +(-2.13484 + 1.37198i) q^{11} +(8.93876 - 3.34502i) q^{12} +(0.776153 + 0.895728i) q^{13} +(2.62949 - 0.772087i) q^{14} +(2.57187 - 6.91834i) q^{15} +(-10.0475 + 11.5954i) q^{16} +(0.184476 - 0.403945i) q^{17} +(5.37045 - 6.22504i) q^{18} +(-1.45894 + 0.666276i) q^{19} +(3.34176 + 23.2425i) q^{20} +(1.22342 - 1.22607i) q^{21} -6.95452i q^{22} +(3.66084 + 3.09810i) q^{23} +(-3.52418 + 16.2854i) q^{24} +(11.0703 + 7.11445i) q^{25} +(-3.21502 + 0.462251i) q^{26} +(1.08801 - 5.08097i) q^{27} +(-1.55243 + 5.28711i) q^{28} +(3.95026 + 1.80402i) q^{29} +(12.1393 + 16.1797i) q^{30} +(0.261035 - 1.81554i) q^{31} +(-6.42553 - 21.8833i) q^{32} +(-2.11067 - 3.85547i) q^{33} +(0.657953 + 1.02379i) q^{34} +(2.30387 + 3.58489i) q^{35} +(4.69167 + 15.8512i) q^{36} +(-1.50060 - 5.11057i) q^{37} +(0.625534 - 4.35068i) q^{38} +(-1.64206 + 1.23201i) q^{39} +(-37.2898 - 17.0297i) q^{40} +(2.51927 - 8.57984i) q^{41} +(1.01400 + 4.63710i) q^{42} +(-3.53154 + 0.507759i) q^{43} +(11.7636 + 7.56003i) q^{44} +(11.6403 + 5.28550i) q^{45} +(-12.5665 + 3.84967i) q^{46} -6.93468i q^{47} +(-18.8115 - 18.7708i) q^{48} +(0.142315 + 0.989821i) q^{49} +(-32.8040 + 14.9811i) q^{50} +(0.675476 + 0.367888i) q^{51} +(2.71304 - 5.94074i) q^{52} +(6.34988 - 7.32816i) q^{53} +(10.1019 + 10.0364i) q^{54} +(10.3760 - 3.04667i) q^{55} +(-6.29975 - 7.27030i) q^{56} +(-0.973632 - 2.60179i) q^{57} +(-10.0119 + 6.43424i) q^{58} +(-2.14873 + 1.86188i) q^{59} +(-40.5643 + 2.94540i) q^{60} +(4.34861 + 0.625235i) q^{61} +(3.79888 + 3.29175i) q^{62} +(1.96949 + 2.26299i) q^{63} +(30.5283 + 8.96393i) q^{64} +(-2.09812 - 4.59424i) q^{65} +(12.0158 + 0.846302i) q^{66} +(0.729030 - 1.13439i) q^{67} -2.44699 q^{68} +(-5.79830 + 5.94808i) q^{69} -11.6783 q^{70} +(-2.40147 + 3.73676i) q^{71} +(-27.7085 - 8.07076i) q^{72} +(-0.0704456 - 0.154254i) q^{73} +(14.0055 + 4.11238i) q^{74} +(-13.6393 + 18.2612i) q^{75} +(6.67922 + 5.78758i) q^{76} +(2.51186 + 0.361151i) q^{77} +(-0.407424 - 5.61108i) q^{78} +(-3.68707 + 3.19487i) q^{79} +(55.0027 - 35.3481i) q^{80} +(8.64635 + 2.49814i) q^{81} +(16.0478 + 18.5201i) q^{82} +(-2.04949 + 0.601784i) q^{83} +(-8.94599 - 3.32564i) q^{84} +(-1.23924 + 1.43016i) q^{85} +(4.06180 - 8.89410i) q^{86} +(-3.59765 + 6.60561i) q^{87} +(-22.2064 + 10.1413i) q^{88} +(-1.35530 - 9.42633i) q^{89} +(-29.4320 + 19.0051i) q^{90} -1.18522i q^{91} +(7.14888 - 25.4412i) q^{92} +(3.10507 + 0.671943i) q^{93} +(15.9876 + 10.2746i) q^{94} +(6.76516 - 0.972683i) q^{95} +(38.5913 - 8.43884i) q^{96} +(4.15665 - 14.1562i) q^{97} +(-2.49284 - 1.13844i) q^{98} +(6.91822 - 3.17758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36}+ \cdots - 132 q^{97}+O(q^{100}) \) 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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