LMFDB - Embedded newform 483.2.r.a.181.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(34,483)]

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([0, 11, 9]))

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

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

chi := DirichletCharacter("483.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (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:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			181.16
Character	$\chi$	$=$	483.181
Dual form			483.2.r.a.475.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0528826 - 0.367807i) q^{2} +(0.909632 + 0.415415i) q^{3} +(1.78650 - 0.524564i) q^{4} +(1.16855 - 1.34858i) q^{5} +(0.104689 - 0.356537i) q^{6} +(-2.06795 + 1.65033i) q^{7} +(-0.596140 - 1.30537i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.0528826 - 0.367807i) q^{2} +(0.909632 + 0.415415i) q^{3} +(1.78650 - 0.524564i) q^{4} +(1.16855 - 1.34858i) q^{5} +(0.104689 - 0.356537i) q^{6} +(-2.06795 + 1.65033i) q^{7} +(-0.596140 - 1.30537i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-0.557813 - 0.358485i) q^{10} +(2.52764 + 0.363420i) q^{11} +(1.84297 + 0.264979i) q^{12} +(1.29979 - 2.02252i) q^{13} +(0.716362 + 0.673331i) q^{14} +(1.62317 - 0.741278i) q^{15} +(2.68410 - 1.72497i) q^{16} +(2.41938 + 0.710394i) q^{17} +(0.243339 - 0.280828i) q^{18} +(-4.98600 + 1.46402i) q^{19} +(1.38020 - 3.02222i) q^{20} +(-2.56664 + 0.642140i) q^{21} -0.948903i q^{22} +(2.24432 - 4.23828i) q^{23} -1.43505i q^{24} +(0.258418 + 1.79734i) q^{25} +(-0.812633 - 0.371117i) q^{26} +(0.281733 + 0.959493i) q^{27} +(-2.82868 + 4.03309i) q^{28} +(-0.540320 - 0.158652i) q^{29} +(-0.358485 - 0.557813i) q^{30} +(-6.42522 + 2.93430i) q^{31} +(-2.65591 - 3.06508i) q^{32} +(2.14825 + 1.38060i) q^{33} +(0.133345 - 0.927433i) q^{34} +(-0.190895 + 4.71729i) q^{35} +(1.56635 + 1.00663i) q^{36} +(0.723568 - 0.626975i) q^{37} +(0.802150 + 1.75646i) q^{38} +(2.02252 - 1.29979i) q^{39} +(-2.45701 - 0.721444i) q^{40} +(-0.680684 - 0.589816i) q^{41} +(0.371914 + 0.910071i) q^{42} +(-6.82303 - 3.11597i) q^{43} +(4.70627 - 0.676660i) q^{44} +1.78443 q^{45} +(-1.67755 - 0.601344i) q^{46} +4.33216i q^{47} +(3.15812 - 0.454069i) q^{48} +(1.55280 - 6.82560i) q^{49} +(0.647406 - 0.190096i) q^{50} +(1.90564 + 1.65124i) q^{51} +(1.26114 - 4.29506i) q^{52} +(4.74091 + 7.37701i) q^{53} +(0.338009 - 0.154364i) q^{54} +(3.44378 - 2.98405i) q^{55} +(3.38707 + 1.71560i) q^{56} +(-5.14360 - 0.739538i) q^{57} +(-0.0297799 + 0.207124i) q^{58} +(4.20500 - 6.54311i) q^{59} +(2.51095 - 2.17575i) q^{60} +(4.59307 + 10.0574i) q^{61} +(1.41904 + 2.20807i) q^{62} +(-2.60146 - 0.482111i) q^{63} +(3.19188 - 3.68363i) q^{64} +(-1.20865 - 4.11630i) q^{65} +(0.394189 - 0.863153i) q^{66} +(-9.43925 + 1.35716i) q^{67} +4.69487 q^{68} +(3.80215 - 2.92295i) q^{69} +(1.74515 - 0.179250i) q^{70} +(0.808859 + 5.62574i) q^{71} +(0.596140 - 1.30537i) q^{72} +(-2.02760 - 6.90538i) q^{73} +(-0.268870 - 0.232977i) q^{74} +(-0.511575 + 1.74226i) q^{75} +(-8.13951 + 5.23095i) q^{76} +(-5.82679 + 3.41992i) q^{77} +(-0.585030 - 0.675160i) q^{78} +(-6.76587 + 10.5279i) q^{79} +(0.810253 - 5.63544i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-0.180942 + 0.281551i) q^{82} +(-10.7055 - 12.3548i) q^{83} +(-4.24847 + 2.49355i) q^{84} +(3.78520 - 2.43260i) q^{85} +(-0.785257 + 2.67434i) q^{86} +(-0.425586 - 0.368773i) q^{87} +(-1.03243 - 3.51615i) q^{88} +(-2.99411 + 6.55618i) q^{89} +(-0.0943653 - 0.656325i) q^{90} +(0.649926 + 6.32756i) q^{91} +(1.78623 - 8.74898i) q^{92} -7.06354 q^{93} +(1.59340 - 0.229096i) q^{94} +(-3.85205 + 8.43480i) q^{95} +(-1.14262 - 3.89140i) q^{96} +(0.0261853 - 0.0302194i) q^{97} +(-2.59262 - 0.210176i) q^{98} +(1.38060 + 2.14825i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	−0.0528826	−	0.367807i	−0.0373937	−	0.260079i	0.962545	−	0.271121i	$-0.0873943\pi$
$2$	−0.0528826	−	0.367807i	−0.0373937	−	0.260079i	−0.999939	+	0.0110420i	$0.996485\pi$
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$4$	1.78650	−	0.524564i	0.893250	−	0.262282i
$5$	1.16855	−	1.34858i	0.522592	−	0.603104i	−0.431686	−	0.902024i	$-0.642081\pi$
$5$	1.16855	−	1.34858i	0.522592	−	0.603104i	0.954278	+	0.298920i	$0.0966265\pi$
$6$	0.104689	−	0.356537i	0.0427390	−	0.145556i
$7$	−2.06795	+	1.65033i	−0.781610	+	0.623767i
$7$	−2.06795	+	1.65033i	−0.781610	+	0.623767i
$8$	−0.596140	−	1.30537i	−0.210767	−	0.461516i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	−0.557813	−	0.358485i	−0.176396	−	0.113363i
$11$	2.52764	+	0.363420i	0.762113	+	0.109575i	0.512403	−	0.858745i	$-0.328756\pi$
$11$	2.52764	+	0.363420i	0.762113	+	0.109575i	0.249710	+	0.968321i	$0.419665\pi$
$12$	1.84297	+	0.264979i	0.532020	+	0.0764929i
$13$	1.29979	−	2.02252i	0.360498	−	0.560946i	−0.612873	−	0.790182i	$-0.709986\pi$
$13$	1.29979	−	2.02252i	0.360498	−	0.560946i	0.973371	+	0.229235i	$0.0736226\pi$
$14$	0.716362	+	0.673331i	0.191456	+	0.179955i
$15$	1.62317	−	0.741278i	0.419101	−	0.191397i
$16$	2.68410	−	1.72497i	0.671025	−	0.431241i
$17$	2.41938	+	0.710394i	0.586786	+	0.172296i	0.561631	−	0.827388i	$-0.310174\pi$
$17$	2.41938	+	0.710394i	0.586786	+	0.172296i	0.0251548	+	0.999684i	$0.491992\pi$
$18$	0.243339	−	0.280828i	0.0573556	−	0.0661919i
$19$	−4.98600	+	1.46402i	−1.14387	+	0.335869i	−0.798144	−	0.602467i	$-0.794184\pi$
$19$	−4.98600	+	1.46402i	−1.14387	+	0.335869i	−0.345723	+	0.938337i	$0.612366\pi$
$20$	1.38020	−	3.02222i	0.308622	−	0.675789i
$21$	−2.56664	+	0.642140i	−0.560087	+	0.140126i
$22$		−	0.948903i		−	0.202307i
$23$	2.24432	−	4.23828i	0.467973	−	0.883743i
$23$	2.24432	−	4.23828i	0.467973	−	0.883743i
$24$		−	1.43505i		−	0.292928i
$25$	0.258418	+	1.79734i	0.0516836	+	0.359467i
$26$	−0.812633	−	0.371117i	−0.159370	−	0.0727821i
$27$	0.281733	+	0.959493i	0.0542195	+	0.184655i
$28$	−2.82868	+	4.03309i	−0.534571	+	0.762182i
$29$	−0.540320	−	0.158652i	−0.100335	−	0.0294610i	0.231180	−	0.972911i	$-0.425741\pi$
$29$	−0.540320	−	0.158652i	−0.100335	−	0.0294610i	−0.331515	+	0.943450i	$0.607560\pi$
$30$	−0.358485	−	0.557813i	−0.0654501	−	0.101842i
$31$	−6.42522	+	2.93430i	−1.15400	+	0.527016i	−0.898145	−	0.439698i	$-0.855085\pi$
$31$	−6.42522	+	2.93430i	−1.15400	+	0.527016i	−0.255858	+	0.966714i	$0.582358\pi$
$32$	−2.65591	−	3.06508i	−0.469503	−	0.541835i
$33$	2.14825	+	1.38060i	0.373963	+	0.240331i
$34$	0.133345	−	0.927433i	0.0228684	−	0.159053i
$35$	−0.190895	+	4.71729i	−0.0322672	+	0.797368i
$36$	1.56635	+	1.00663i	0.261058	+	0.167772i
$37$	0.723568	−	0.626975i	0.118954	−	0.103074i	−0.593353	−	0.804943i	$-0.702196\pi$
$37$	0.723568	−	0.626975i	0.118954	−	0.103074i	0.712307	+	0.701868i	$0.247651\pi$
$38$	0.802150	+	1.75646i	0.130126	+	0.284936i
$39$	2.02252	−	1.29979i	0.323862	−	0.208134i
$40$	−2.45701	−	0.721444i	−0.388488	−	0.114070i
$41$	−0.680684	−	0.589816i	−0.106305	−	0.0921138i	0.600087	−	0.799935i	$-0.295133\pi$
$41$	−0.680684	−	0.589816i	−0.106305	−	0.0921138i	−0.706392	+	0.707821i	$0.749678\pi$
$42$	0.371914	+	0.910071i	0.0573876	+	0.140427i
$43$	−6.82303	−	3.11597i	−1.04050	−	0.475182i	−0.179487	−	0.983760i	$-0.557444\pi$
$43$	−6.82303	−	3.11597i	−1.04050	−	0.475182i	−0.861016	+	0.508579i	$0.830171\pi$
$44$	4.70627	−	0.676660i	0.709497	−	0.102010i
$45$	1.78443			0.266007
$46$	−1.67755	−	0.601344i	−0.247342	−	0.0886633i
$47$			4.33216i			0.631911i	0.948774	+	0.315955i	$0.102325\pi$
$47$			4.33216i			0.631911i	−0.948774	+	0.315955i	$0.897675\pi$
$48$	3.15812	−	0.454069i	0.455835	−	0.0655392i
$49$	1.55280	−	6.82560i	0.221829	−	0.975086i
$50$	0.647406	−	0.190096i	0.0915571	−	0.0268836i
$51$	1.90564	+	1.65124i	0.266843	+	0.231221i
$52$	1.26114	−	4.29506i	0.174889	−	0.595617i
$53$	4.74091	+	7.37701i	0.651215	+	1.01331i	0.997179	+	0.0750622i	$0.0239155\pi$
$53$	4.74091	+	7.37701i	0.651215	+	1.01331i	−0.345964	+	0.938248i	$0.612448\pi$
$54$	0.338009	−	0.154364i	0.0459972	−	0.0210062i
$55$	3.44378	−	2.98405i	0.464360	−	0.402370i
$56$	3.38707	+	1.71560i	0.452617	+	0.229256i
$57$	−5.14360	−	0.739538i	−0.681286	−	0.0979542i
$58$	−0.0297799	+	0.207124i	−0.00391029	+	0.0271967i
$59$	4.20500	−	6.54311i	0.547445	−	0.851841i	−0.451743	−	0.892148i	$-0.649197\pi$
$59$	4.20500	−	6.54311i	0.547445	−	0.851841i	0.999187	+	0.0403077i	$0.0128338\pi$
$60$	2.51095	−	2.17575i	0.324162	−	0.280888i
$61$	4.59307	+	10.0574i	0.588083	+	1.28772i	0.936594	+	0.350417i	$0.113960\pi$
$61$	4.59307	+	10.0574i	0.588083	+	1.28772i	−0.348511	+	0.937305i	$0.613313\pi$
$62$	1.41904	+	2.20807i	0.180218	+	0.280425i
$63$	−2.60146	−	0.482111i	−0.327753	−	0.0607403i
$64$	3.19188	−	3.68363i	0.398985	−	0.460454i
$65$	−1.20865	−	4.11630i	−0.149915	−	0.510564i
$66$	0.394189	−	0.863153i	0.0485213	−	0.106247i
$67$	−9.43925	+	1.35716i	−1.15319	+	0.165803i	−0.692270	−	0.721639i	$-0.743389\pi$
$67$	−9.43925	+	1.35716i	−1.15319	+	0.165803i	−0.460919	+	0.887442i	$0.652480\pi$
$68$	4.69487			0.569337
$69$	3.80215	−	2.92295i	0.457725	−	0.351882i
$70$	1.74515	−	0.179250i	0.208585	−	0.0214245i
$71$	0.808859	+	5.62574i	0.0959939	+	0.667652i	0.979827	+	0.199849i	$0.0640452\pi$
$71$	0.808859	+	5.62574i	0.0959939	+	0.667652i	−0.883833	+	0.467803i	$0.845046\pi$
$72$	0.596140	−	1.30537i	0.0702558	−	0.153839i
$73$	−2.02760	−	6.90538i	−0.237313	−	0.808214i	−0.988900	−	0.148580i	$-0.952530\pi$
$73$	−2.02760	−	6.90538i	−0.237313	−	0.808214i	0.751587	−	0.659634i	$-0.229289\pi$
$74$	−0.268870	−	0.232977i	−0.0312555	−	0.0270831i
$75$	−0.511575	+	1.74226i	−0.0590716	+	0.201179i
$76$	−8.13951	+	5.23095i	−0.933666	+	0.600031i
$77$	−5.82679	+	3.41992i	−0.664025	+	0.389736i
$78$	−0.585030	−	0.675160i	−0.0662416	−	0.0764468i
$79$	−6.76587	+	10.5279i	−0.761220	+	1.18448i	0.216850	+	0.976205i	$0.430422\pi$
$79$	−6.76587	+	10.5279i	−0.761220	+	1.18448i	−0.978070	+	0.208276i	$0.933215\pi$
$80$	0.810253	−	5.63544i	0.0905891	−	0.630061i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−0.180942	+	0.281551i	−0.0199817	+	0.0310921i
$83$	−10.7055	−	12.3548i	−1.17509	−	1.35612i	−0.921296	−	0.388861i	$-0.872869\pi$
$83$	−10.7055	−	12.3548i	−1.17509	−	1.35612i	−0.253789	−	0.967260i	$-0.581677\pi$
$84$	−4.24847	+	2.49355i	−0.463546	+	0.272069i
$85$	3.78520	−	2.43260i	0.410562	−	0.263852i
$86$	−0.785257	+	2.67434i	−0.0846764	+	0.288381i
$87$	−0.425586	−	0.368773i	−0.0456276	−	0.0395366i
$88$	−1.03243	−	3.51615i	−0.110058	−	0.374823i
$89$	−2.99411	+	6.55618i	−0.317375	+	0.694954i	−0.999336	−	0.0364342i	$-0.988400\pi$
$89$	−2.99411	+	6.55618i	−0.317375	+	0.694954i	0.681961	+	0.731388i	$0.261127\pi$
$90$	−0.0943653	−	0.656325i	−0.00994697	−	0.0691827i
$91$	0.649926	+	6.32756i	0.0681307	+	0.663308i
$92$	1.78623	−	8.74898i	0.186227	−	0.912144i
$93$	−7.06354			−0.732455
$94$	1.59340	−	0.229096i	0.164347	−	0.0236295i
$95$	−3.85205	+	8.43480i	−0.395212	+	0.865393i
$96$	−1.14262	−	3.89140i	−0.116618	−	0.397165i
$97$	0.0261853	−	0.0302194i	0.00265871	−	0.00306832i	−0.754419	−	0.656394i	$-0.772081\pi$
$97$	0.0261853	−	0.0302194i	0.00265871	−	0.00306832i	0.757077	+	0.653325i	$0.226627\pi$
$98$	−2.59262	−	0.210176i	−0.261894	−	0.0212310i
$99$	1.38060	+	2.14825i	0.138755	+	0.215908i
$100$	1.40448	+	3.07538i	0.140448	+	0.307538i
$101$	8.11335	−	7.03026i	0.807308	−	0.699537i	−0.149974	−	0.988690i	$-0.547919\pi$
$101$	8.11335	−	7.03026i	0.807308	−	0.699537i	0.957283	+	0.289153i	$0.0933737\pi$
$102$	0.506564	−	0.788229i	0.0501573	−	0.0780463i
$103$	0.300741	−	2.09170i	0.0296329	−	0.206101i	−0.969626	−	0.244592i	$-0.921346\pi$
$103$	0.300741	−	2.09170i	0.0296329	−	0.206101i	0.999259	+	0.0384909i	$0.0122551\pi$
$104$	−3.41499	−	0.491001i	−0.334867	−	0.0481466i
$105$	−2.13328	+	4.21170i	−0.208187	+	0.411020i
$106$	2.46260	−	2.13386i	0.239189	−	0.207258i
$107$	−13.1144	+	5.98915i	−1.26782	+	0.578993i	−0.931838	−	0.362875i	$-0.881795\pi$
$107$	−13.1144	+	5.98915i	−1.26782	+	0.578993i	−0.335981	+	0.941869i	$0.609068\pi$
$108$	1.00663	+	1.56635i	0.0968631	+	0.150722i
$109$	−5.41552	+	18.4436i	−0.518713	+	1.76657i	0.115386	+	0.993321i	$0.463189\pi$
$109$	−5.41552	+	18.4436i	−0.518713	+	1.76657i	−0.634099	+	0.773252i	$0.718629\pi$
$110$	−1.27967	−	1.10884i	−0.122012	−	0.105724i
$111$	0.918636	−	0.269736i	0.0871931	−	0.0256022i
$112$	−2.70381	+	7.99679i	−0.255486	+	0.755626i
$113$	−9.67659	+	1.39128i	−0.910297	+	0.130881i	−0.581525	−	0.813528i	$-0.697544\pi$
$113$	−9.67659	+	1.39128i	−0.910297	+	0.130881i	−0.328772	+	0.944409i	$0.606635\pi$
$114$			1.93096i			0.180851i
$115$	−3.09306	−	7.97930i	−0.288430	−	0.744073i
$116$	−1.04851			−0.0973513
$117$	2.37970	−	0.342150i	0.220004	−	0.0316317i
$118$	−2.62897	−	1.20061i	−0.242017	−	0.110525i
$119$	−6.17554	+	2.52373i	−0.566111	+	0.231350i
$120$	−1.93528	−	1.67693i	−0.176666	−	0.153082i
$121$	−4.29752	−	1.26187i	−0.390684	−	0.114715i
$122$	3.45630	−	2.22123i	0.312918	−	0.201100i
$123$	−0.374153	−	0.819282i	−0.0337363	−	0.0738722i
$124$	−9.93943	+	8.61257i	−0.892587	+	0.773431i
$125$	10.2316	+	6.57545i	0.915143	+	0.588127i
$126$	−0.0397520	+	0.982328i	−0.00354139	+	0.0875128i
$127$	−0.983659	+	6.84150i	−0.0872856	+	0.607085i	0.898487	+	0.439000i	$0.144667\pi$
$127$	−0.983659	+	6.84150i	−0.0872856	+	0.607085i	−0.985773	+	0.168085i	$0.946242\pi$
$128$	−8.34738	−	5.36454i	−0.737811	−	0.474162i
$129$	−4.91203	−	5.66878i	−0.432480	−	0.499108i
$130$	−1.45009	+	0.662232i	−0.127181	+	0.0580816i
$131$	6.97012	+	10.8457i	0.608982	+	0.947595i	0.999634	+	0.0270560i	$0.00861325\pi$
$131$	6.97012	+	10.8457i	0.608982	+	0.947595i	−0.390652	+	0.920538i	$0.627750\pi$
$132$	4.56207	+	1.33954i	0.397077	+	0.116592i
$133$	7.89465	−	11.2561i	0.684553	−	0.976025i
$134$	0.998346	+	3.40005i	0.0862439	+	0.293720i
$135$	1.62317	+	0.741278i	0.139700	+	0.0637991i
$136$	−0.514967	−	3.58167i	−0.0441580	−	0.307126i
$137$		−	15.0547i		−	1.28621i	−0.765779	−	0.643104i	$-0.777646\pi$
$137$		−	15.0547i		−	1.28621i	0.765779	−	0.643104i	$-0.222354\pi$
$138$	−1.27615	−	1.24388i	−0.108633	−	0.105886i
$139$		−	0.0576594i		−	0.00489061i	−0.999997	−	0.00244530i	$-0.999222\pi$
$139$		−	0.0576594i		−	0.00489061i	0.999997	−	0.00244530i	$-0.000778365\pi$
$140$	2.13349	+	8.52758i	0.180312	+	0.720712i
$141$	−1.79965	+	3.94067i	−0.151557	+	0.331865i
$142$	2.02641	−	0.595008i	0.170053	−	0.0499319i
$143$	4.02044	−	4.63984i	0.336206	−	0.388003i
$144$	3.06135	+	0.898894i	0.255113	+	0.0749079i
$145$	−0.845348	+	0.543272i	−0.0702023	+	0.0451163i
$146$	−2.43262	+	1.11094i	−0.201325	+	0.0919422i
$147$	4.24794	−	5.56373i	0.350364	−	0.458888i
$148$	0.963766	−	1.49965i	0.0792211	−	0.123270i
$149$	7.42062	+	1.06692i	0.607921	+	0.0874058i	0.439399	−	0.898292i	$-0.355191\pi$
$149$	7.42062	+	1.06692i	0.607921	+	0.0874058i	0.168522	+	0.985698i	$0.446101\pi$
$150$	0.667870	+	0.0960252i	0.0545314	+	0.00784043i
$151$	−0.981968	−	0.631072i	−0.0799114	−	0.0513559i	0.500075	−	0.865982i	$-0.333306\pi$
$151$	−0.981968	−	0.631072i	−0.0799114	−	0.0513559i	−0.579986	+	0.814626i	$0.696942\pi$
$152$	4.88344	+	5.63579i	0.396099	+	0.457123i
$153$	1.04748	+	2.29366i	0.0846835	+	0.185431i
$154$	1.56601	+	1.96228i	0.126192	+	0.158125i
$155$	−3.55106	+	12.0938i	−0.285228	+	0.971398i
$156$	2.93141	−	3.38302i	0.234700	−	0.270859i
$157$	16.6163	−	4.87899i	1.32613	−	0.389386i	0.459427	−	0.888215i	$-0.348055\pi$
$157$	16.6163	−	4.87899i	1.32613	−	0.389386i	0.866700	+	0.498829i	$0.166237\pi$
$158$	4.23003	+	1.93179i	0.336523	+	0.153685i
$159$	1.24797	+	8.67981i	0.0989703	+	0.688354i
$160$	−7.23708			−0.572141
$161$	2.35345	+	12.4684i	0.185478	+	0.982648i
$162$	0.371589			0.0291948
$163$	−0.0202717	−	0.140992i	−0.00158780	−	0.0110434i	0.989012	−	0.147834i	$-0.0472302\pi$
$163$	−0.0202717	−	0.140992i	−0.00158780	−	0.0110434i	−0.990600	+	0.136791i	$0.956321\pi$
$164$	−1.52544	−	0.696644i	−0.119117	−	0.0543988i
$165$	4.37220	−	1.28379i	0.340375	−	0.0999431i
$166$	−3.97806	+	4.59093i	−0.308757	+	0.356325i
$167$	0.664497	−	2.26307i	0.0514203	−	0.175122i	−0.929779	−	0.368118i	$-0.880002\pi$
$167$	0.664497	−	2.26307i	0.0514203	−	0.175122i	0.981200	+	0.192996i	$0.0618205\pi$
$168$	2.36831	+	2.96760i	0.182719	+	0.228955i
$169$	2.99927	+	6.56750i	0.230713	+	0.505192i
$170$	−1.09490	−	1.26358i	−0.0839748	−	0.0969121i
$171$	−4.37157	−	2.80944i	−0.334302	−	0.214843i
$172$	−13.8239	−	1.98757i	−1.05406	−	0.151551i
$173$	−23.6711	−	3.40340i	−1.79968	−	0.258755i	−0.840555	−	0.541726i	$-0.817771\pi$
$173$	−23.6711	−	3.40340i	−1.79968	−	0.258755i	−0.959129	+	0.282970i	$0.908680\pi$
$174$	−0.113131	+	0.176035i	−0.00857643	+	0.0133452i
$175$	−3.50060	−	3.29032i	−0.264620	−	0.248725i
$176$	7.41133	−	3.38464i	0.558650	−	0.255127i
$177$	6.54311	−	4.20500i	0.491810	−	0.316067i
$178$	2.56975	+	0.754546i	0.192611	+	0.0565556i
$179$	13.9524	−	16.1020i	1.04285	−	1.20352i	0.0642152	−	0.997936i	$-0.479546\pi$
$179$	13.9524	−	16.1020i	1.04285	−	1.20352i	0.978640	−	0.205583i	$-0.0659089\pi$
$180$	3.18788	−	0.936046i	0.237611	−	0.0697688i
$181$	1.66306	−	3.64159i	0.123614	−	0.270677i	−0.837701	−	0.546130i	$-0.816101\pi$
$181$	1.66306	−	3.64159i	0.123614	−	0.270677i	0.961315	+	0.275453i	$0.0888278\pi$
$182$	2.29295	−	0.573665i	0.169965	−	0.0425229i
$183$			11.0566i			0.817326i
$184$	−6.87044	−	0.403044i	−0.506495	−	0.0297128i
$185$		−	1.70844i		−	0.125607i
$186$	0.373539	+	2.59802i	0.0273892	+	0.190496i
$187$	5.85716	+	2.67488i	0.428318	+	0.195606i
$188$	2.27250	+	7.73941i	0.165739	+	0.564455i
$189$	−2.16609	−	1.51923i	−0.157560	−	0.110508i
$190$	3.30608	+	0.970754i	0.239849	+	0.0704259i
$191$	0.910791	+	1.41722i	0.0659025	+	0.102546i	0.872641	−	0.488363i	$-0.162406\pi$
$191$	0.910791	+	1.41722i	0.0659025	+	0.102546i	−0.806738	+	0.590909i	$0.798769\pi$
$192$	4.43367	−	2.02479i	0.319973	−	0.146127i
$193$	−8.44951	−	9.75126i	−0.608209	−	0.701911i	0.365214	−	0.930923i	$-0.380996\pi$
$193$	−8.44951	−	9.75126i	−0.608209	−	0.701911i	−0.973423	+	0.229013i	$0.926450\pi$
$194$	−0.0124997	−	0.00803305i	−0.000897424	−	0.000576739i
$195$	0.610541	−	4.24641i	0.0437218	−	0.304092i
$196$	−0.806379	−	13.0085i	−0.0575985	−	0.929177i
$197$	−10.7390	−	6.90152i	−0.765120	−	0.491713i	0.0989452	−	0.995093i	$-0.468453\pi$
$197$	−10.7390	−	6.90152i	−0.765120	−	0.491713i	−0.864065	+	0.503380i	$0.832090\pi$
$198$	0.717133	−	0.621399i	0.0509644	−	0.0441609i
$199$	−0.240381	−	0.526360i	−0.0170401	−	0.0373127i	0.900921	−	0.433984i	$-0.142893\pi$
$199$	−0.240381	−	0.526360i	−0.0170401	−	0.0373127i	−0.917961	+	0.396671i	$0.870165\pi$
$200$	2.19213	−	1.40879i	0.155007	−	0.0996168i
$201$	−9.15003	−	2.68669i	−0.645394	−	0.189505i
$202$	−3.01483	−	2.61237i	−0.212123	−	0.183805i
$203$	1.37918	−	0.563624i	0.0967997	−	0.0395586i
$204$	4.27061	+	1.95032i	0.299002	+	0.136550i
$205$	−1.59083	+	0.228727i	−0.111108	+	0.0159750i
$206$	−0.785245			−0.0547106
$207$	4.67280	−	1.07934i	0.324782	−	0.0750195i
$208$		−	7.67074i		−	0.531870i
$209$	−13.1349	+	1.88851i	−0.908558	+	0.130631i
$210$	1.66190	+	0.561909i	0.114682	+	0.0387754i
$211$	24.8927	−	7.30914i	1.71368	−	0.503182i	0.730052	−	0.683391i	$-0.239496\pi$
$211$	24.8927	−	7.30914i	1.71368	−	0.503182i	0.983628	+	0.180209i	$0.0576774\pi$
$212$	12.3394	+	10.6921i	0.847471	+	0.734338i
$213$	−1.60125	+	5.45336i	−0.109716	+	0.373658i
$214$	2.89638	+	4.50685i	0.197992	+	0.308082i
$215$	−12.1752	+	5.56023i	−0.830342	+	0.379205i
$216$	1.08454	−	0.939757i	0.0737934	−	0.0639423i
$217$	8.44444	−	16.6717i	0.573246	−	1.13175i
$218$	7.07005	+	1.01652i	0.478845	+	0.0688474i
$219$	1.02423	−	7.12366i	0.0692109	−	0.481372i
$220$	4.58699	−	7.13750i	0.309255	−	0.481210i
$221$	4.58149	−	3.96988i	0.308184	−	0.267043i
$222$	−0.147791	−	0.323616i	−0.00991905	−	0.0217197i
$223$	−1.25692	−	1.95580i	−0.0841696	−	0.130970i	0.796616	−	0.604486i	$-0.206621\pi$
$223$	−1.25692	−	1.95580i	−0.0841696	−	0.130970i	−0.880786	+	0.473515i	$0.842985\pi$
$224$	10.5507	+	1.95529i	0.704947	+	0.130643i
$225$	−1.18911	+	1.37230i	−0.0792738	+	0.0914869i
$226$	1.02345	+	3.48554i	0.0680787	+	0.231855i
$227$	3.49471	−	7.65235i	0.231952	−	0.507905i	−0.757487	−	0.652850i	$-0.773573\pi$
$227$	3.49471	−	7.65235i	0.231952	−	0.507905i	0.989440	+	0.144945i	$0.0463006\pi$
$228$	−9.57698	+	1.37696i	−0.634251	+	0.0911915i
$229$	2.80899			0.185624			0.0928118	−	0.995684i	$-0.470415\pi$
$229$	2.80899			0.185624			0.0928118	+	0.995684i	$0.470415\pi$
$230$	−2.77127	+	1.55962i	−0.182732	+	0.102838i
$231$	−6.72092	+	0.690330i	−0.442204	+	0.0454204i
$232$	0.115008	+	0.799895i	0.00755061	+	0.0525157i
$233$	5.61198	−	12.2885i	0.367653	−	0.805048i	−0.631897	−	0.775052i	$-0.717724\pi$
$233$	5.61198	−	12.2885i	0.367653	−	0.805048i	0.999550	−	0.0299953i	$-0.00954923\pi$
$234$	−0.251690	−	0.857177i	−0.0164535	−	0.0560354i
$235$	5.84227	+	5.06236i	0.381108	+	0.330232i
$236$	4.07996	−	13.8951i	0.265583	−	0.904492i
$237$	−10.5279	+	6.76587i	−0.683860	+	0.439490i
$238$	1.25482	+	2.13794i	0.0813381	+	0.138582i
$239$	−13.9147	−	16.0585i	−0.900069	−	1.03874i	−0.999047	−	0.0436456i	$-0.986103\pi$
$239$	−13.9147	−	16.0585i	−0.900069	−	1.03874i	0.0989779	−	0.995090i	$-0.468443\pi$
$240$	3.07808	−	4.78958i	0.198689	−	0.309166i
$241$	0.996136	−	6.92828i	0.0641667	−	0.446289i	−0.932257	−	0.361796i	$-0.882164\pi$
$241$	0.996136	−	6.92828i	0.0641667	−	0.446289i	0.996424	−	0.0844935i	$-0.0269272\pi$
$242$	−0.236859	+	1.64739i	−0.0152258	+	0.105898i
$243$	−0.540641	+	0.841254i	−0.0346821	+	0.0539664i
$244$	13.4813	+	15.5582i	0.863051	+	0.996014i
$245$	−7.39034	−	10.0701i	−0.472151	−	0.643358i
$246$	−0.281551	+	0.180942i	−0.0179511	+	0.0115364i
$247$	−3.51976	+	11.9872i	−0.223957	+	0.762728i
$248$	7.66067	+	6.63801i	0.486453	+	0.421514i
$249$	−4.60571	−	15.6856i	−0.291875	−	0.994035i
$250$	1.87742	−	4.11098i	0.118739	−	0.260001i
$251$	−0.699522	−	4.86528i	−0.0441534	−	0.307094i	−0.999916	−	0.0129549i	$-0.995876\pi$
$251$	−0.699522	−	4.86528i	−0.0441534	−	0.307094i	0.955763	−	0.294139i	$-0.0950329\pi$
$252$	−4.90040	+	0.503337i	−0.308696	+	0.0317073i
$253$	7.21311	−	9.89723i	0.453484	−	0.622234i
$254$	2.56837			0.161154
$255$	4.45367	−	0.640342i	0.278900	−	0.0400997i
$256$	2.51790	−	5.51343i	0.157369	−	0.344590i
$257$	6.02898	+	20.5328i	0.376077	+	1.28080i	0.902541	+	0.430604i	$0.141699\pi$
$257$	6.02898	+	20.5328i	0.376077	+	1.28080i	−0.526464	+	0.850198i	$0.676482\pi$
$258$	−1.82526	+	2.10646i	−0.113635	+	0.131142i
$259$	−0.461582	+	2.49068i	−0.0286813	+	0.154763i
$260$	−4.31852	−	6.71975i	−0.267823	−	0.416741i
$261$	−0.233933	−	0.512242i	−0.0144801	−	0.0317070i
$262$	3.62053	−	3.13721i	0.223677	−	0.193817i
$263$	−5.13861	+	7.99583i	−0.316860	+	0.493044i	−0.962752	−	0.270385i	$-0.912849\pi$
$263$	−5.13861	+	7.99583i	−0.316860	+	0.493044i	0.645892	+	0.763428i	$0.276485\pi$
$264$	0.521525	−	3.62729i	0.0320977	−	0.223244i
$265$	15.4885	+	2.22691i	0.951450	+	0.136798i
$266$	−4.55755	−	2.30846i	−0.279441	−	0.141541i
$267$	−5.44708	+	4.71992i	−0.333356	+	0.288854i
$268$	−16.1513	+	7.37606i	−0.986599	+	0.450565i
$269$	−6.73891	−	10.4859i	−0.410878	−	0.639339i	0.572712	−	0.819757i	$-0.305891\pi$
$269$	−6.73891	−	10.4859i	−0.410878	−	0.639339i	−0.983590	+	0.180418i	$0.942255\pi$
$270$	0.186810	−	0.636215i	0.0113689	−	0.0387188i
$271$	15.7013	+	13.6053i	0.953786	+	0.826460i	0.984912	−	0.173055i	$-0.0553639\pi$
$271$	15.7013	+	13.6053i	0.953786	+	0.826460i	−0.0311261	+	0.999515i	$0.509909\pi$
$272$	7.71927	−	2.26658i	0.468049	−	0.137432i
$273$	−2.03737	+	6.02574i	−0.123307	+	0.364694i
$274$	−5.53721	+	0.796131i	−0.334515	+	0.0480960i
$275$			4.63694i			0.279618i
$276$	5.25927	−	7.21633i	0.316571	−	0.434372i
$277$	7.58961			0.456015			0.228008	−	0.973659i	$-0.426779\pi$
$277$	7.58961			0.456015			0.228008	+	0.973659i	$0.426779\pi$
$278$	−0.0212075	+	0.00304918i	−0.00127194	+	0.000182878i
$279$	−6.42522	−	2.93430i	−0.384668	−	0.175672i
$280$	6.27159	−	2.56298i	0.374799	−	0.153167i
$281$	22.1086	+	19.1573i	1.31889	+	1.14283i	0.979336	+	0.202240i	$0.0648220\pi$
$281$	22.1086	+	19.1573i	1.31889	+	1.14283i	0.339555	+	0.940586i	$0.389723\pi$
$282$	1.54458	+	0.453529i	0.0919782	+	0.0270072i
$283$	11.5659	−	7.43297i	0.687523	−	0.441844i	−0.149681	−	0.988734i	$-0.547825\pi$
$283$	11.5659	−	7.43297i	0.687523	−	0.441844i	0.837204	+	0.546890i	$0.184188\pi$
$284$	4.39609	+	9.62608i	0.260860	+	0.571203i
$285$	−7.00789	+	6.07237i	−0.415111	+	0.359696i
$286$	−1.91918	−	1.23338i	−0.113483	−	0.0729312i
$287$	2.38101	+	0.0963527i	0.140547	+	0.00568752i
$288$	0.577184	−	4.01441i	0.0340109	−	0.236551i
$289$	−8.95256	−	5.75346i	−0.526621	−	0.338439i
$290$	0.244523	+	0.282195i	0.0143589	+	0.0165711i
$291$	0.0363726	−	0.0166108i	0.00213220	−	0.000973743i
$292$	−7.24463	−	11.2729i	−0.423960	−	0.659695i
$293$	14.7698	+	4.33681i	0.862861	+	0.253359i	0.683076	−	0.730347i	$-0.260642\pi$
$293$	14.7698	+	4.33681i	0.862861	+	0.253359i	0.179785	+	0.983706i	$0.442460\pi$
$294$	−2.27102	−	1.26820i	−0.132448	−	0.0739627i
$295$	−3.91015	−	13.3167i	−0.227658	−	0.775331i
$296$	−1.24978	−	0.570756i	−0.0726420	−	0.0331745i
$297$	0.363420	+	2.52764i	0.0210878	+	0.146669i
$298$		−	2.78578i		−	0.161376i
$299$	−5.65486	−	10.0481i	−0.327029	−	0.581095i
$300$			3.38091i			0.195197i
$301$	19.2521	−	4.81661i	1.10967	−	0.277625i
$302$	−0.180184	+	0.394547i	−0.0103684	+	0.0227036i
$303$	10.3006	−	3.02454i	0.591756	−	0.173755i
$304$	−10.8575	+	12.5303i	−0.622722	+	0.718659i
$305$	18.9305	+	5.55849i	1.08396	+	0.318278i
$306$	0.788229	−	0.506564i	0.0450601	−	0.0289583i
$307$	17.6123	−	8.04326i	1.00519	−	0.459053i	0.156346	−	0.987702i	$-0.450028\pi$
$307$	17.6123	−	8.04326i	1.00519	−	0.459053i	0.848841	+	0.528649i	$0.177301\pi$
$308$	−8.61560	+	9.16621i	−0.490920	+	0.522293i
$309$	1.14249	−	1.77774i	0.0649938	−	0.101132i
$310$	4.63598	+	0.666553i	0.263306	+	0.0378576i
$311$	0.717999	+	0.103233i	0.0407140	+	0.00585378i	0.162642	−	0.986685i	$-0.447999\pi$
$311$	0.717999	+	0.103233i	0.0407140	+	0.00585378i	−0.121928	+	0.992539i	$0.538908\pi$
$312$	−2.90241	−	1.86527i	−0.164317	−	0.105600i
$313$	7.23714	+	8.35210i	0.409067	+	0.472089i	0.922475	−	0.386056i	$-0.126163\pi$
$313$	7.23714	+	8.35210i	0.409067	+	0.472089i	−0.513408	+	0.858144i	$0.671617\pi$
$314$	−2.67324	−	5.85359i	−0.150860	−	0.330337i
$315$	−3.69010	+	2.94490i	−0.207914	+	0.165926i
$316$	−6.56467	+	22.3572i	−0.369292	+	1.25769i
$317$	17.1951	−	19.8443i	0.965776	−	1.11456i	−0.0275961	−	0.999619i	$-0.508785\pi$
$317$	17.1951	−	19.8443i	0.965776	−	1.11456i	0.993372	−	0.114945i	$-0.0366693\pi$
$318$	3.12650	−	0.918023i	0.175325	−	0.0514801i
$319$	−1.30808	−	0.597380i	−0.0732384	−	0.0334469i
$320$	−1.23779	−	8.60902i	−0.0691946	−	0.481259i
$321$	−14.4173			−0.804694
$322$	4.46151	−	1.52498i	0.248630	−	0.0849836i
$323$	−13.1031			−0.729074
$324$	0.264979	+	1.84297i	0.0147211	+	0.102387i
$325$	3.97104	+	1.81351i	0.220273	+	0.100596i
$326$	−0.0507860	+	0.0149121i	−0.00281278	+	0.000825905i
$327$	−12.5879	+	14.5272i	−0.696110	+	0.803354i
$328$	−0.364142	+	1.24015i	−0.0201064	+	0.0684761i
$329$	−7.14951	−	8.95868i	−0.394165	−	0.493908i
$330$	−0.703401	−	1.54023i	−0.0387209	−	0.0847871i
$331$	17.0796	+	19.7109i	0.938778	+	1.08341i	0.996375	+	0.0850681i	$0.0271108\pi$
$331$	17.0796	+	19.7109i	0.938778	+	1.08341i	−0.0575968	+	0.998340i	$0.518344\pi$
$332$	−25.6064	−	16.4562i	−1.40533	−	0.903151i
$333$	0.947673	+	0.136255i	0.0519322	+	0.00746672i
$334$	−0.867513	−	0.124730i	−0.0474682	−	0.00682490i
$335$	−9.20002	+	14.3155i	−0.502651	+	0.782140i
$336$	−5.78146	+	6.15094i	−0.315404	+	0.335561i
$337$	10.3077	−	4.70736i	0.561495	−	0.256426i	−0.114387	−	0.993436i	$-0.536490\pi$
$337$	10.3077	−	4.70736i	0.561495	−	0.256426i	0.675882	+	0.737010i	$0.263763\pi$
$338$	2.25696	−	1.45046i	0.122762	−	0.0788946i
$339$	−9.38010	−	2.75424i	−0.509457	−	0.149590i
$340$	5.48620	−	6.33141i	0.297531	−	0.343369i
$341$	−17.3070	+	5.08181i	−0.937229	+	0.275195i
$342$	−0.802150	+	1.75646i	−0.0433753	+	0.0949786i
$343$	8.05340	+	16.6776i	0.434843	+	0.900506i
$344$			10.7641i			0.580362i
$345$	0.501169	−	8.54313i	0.0269821	−	0.459947i
$346$			8.88639i			0.477735i
$347$	−1.17274	−	8.15661i	−0.0629562	−	0.437870i	−0.996783	−	0.0801449i	$-0.974462\pi$
$347$	−1.17274	−	8.15661i	−0.0629562	−	0.437870i	0.933827	−	0.357725i	$-0.116447\pi$
$348$	−0.953755	−	0.435565i	−0.0511266	−	0.0233487i
$349$	−3.19107	−	10.8678i	−0.170814	−	0.581739i	−0.999749	−	0.0223944i	$-0.992871\pi$
$349$	−3.19107	−	10.8678i	−0.170814	−	0.581739i	0.828935	−	0.559345i	$-0.188947\pi$
$350$	−1.02508	+	1.46154i	−0.0547929	+	0.0781228i
$351$	2.30679	+	0.677334i	0.123127	+	0.0361534i
$352$	−5.59928	−	8.71265i	−0.298443	−	0.464386i
$353$	−13.6324	+	6.22573i	−0.725582	+	0.331362i	−0.743736	−	0.668473i	$-0.766948\pi$
$353$	−13.6324	+	6.22573i	−0.725582	+	0.331362i	0.0181545	+	0.999835i	$0.494221\pi$
$354$	−1.89265	−	2.18423i	−0.100593	−	0.116091i
$355$	8.53195	+	5.48315i	0.452829	+	0.291016i
$356$	−1.90984	+	13.2832i	−0.101221	+	0.704010i
$357$	−6.66586	−	0.269748i	−0.352795	−	0.0142766i
$358$	−6.66026	−	4.28029i	−0.352006	−	0.226220i
$359$	0.858571	−	0.743956i	0.0453136	−	0.0392645i	−0.631910	−	0.775042i	$-0.717729\pi$
$359$	0.858571	−	0.743956i	0.0453136	−	0.0392645i	0.677223	+	0.735778i	$0.263183\pi$
$360$	−1.06377	−	2.32933i	−0.0560656	−	0.122766i
$361$	6.73300	−	4.32703i	0.354368	−	0.227739i
$362$	−1.42735	−	0.419107i	−0.0750197	−	0.0220278i
$363$	−3.38496	−	2.93309i	−0.177664	−	0.153947i
$364$	4.48030	+	10.9633i	0.234832	+	0.574631i
$365$	−11.6818	−	5.33491i	−0.611455	−	0.279242i
$366$	4.06669	−	0.584701i	0.212569	−	0.0305628i
$367$	10.9999			0.574193			0.287096	−	0.957902i	$-0.407310\pi$
$367$	10.9999			0.574193			0.287096	+	0.957902i	$0.407310\pi$
$368$	−1.28692	−	15.2473i	−0.0670854	−	0.794823i
$369$		−	0.900674i		−	0.0468872i
$370$	−0.628377	+	0.0903470i	−0.0326678	+	0.00469692i
$371$	−21.9785	−	7.43117i	−1.14107	−	0.385807i
$372$	−12.6190	+	3.70528i	−0.654266	+	0.192110i
$373$	4.01889	+	3.48239i	0.208090	+	0.180311i	0.752670	−	0.658398i	$-0.228765\pi$
$373$	4.01889	+	3.48239i	0.208090	+	0.180311i	−0.544580	+	0.838709i	$0.683311\pi$
$374$	0.674095	−	2.29576i	0.0348566	−	0.118711i
$375$	6.57545	+	10.2316i	0.339555	+	0.528358i
$376$	5.65506	−	2.58258i	0.291637	−	0.133186i
$377$	−1.02318	+	0.886593i	−0.0526966	+	0.0456619i
$378$	−0.444234	+	0.877044i	−0.0228489	+	0.0451103i
$379$	3.63263	+	0.522294i	0.186596	+	0.0268284i	0.234979	−	0.972000i	$-0.424498\pi$
$379$	3.63263	+	0.522294i	0.186596	+	0.0268284i	−0.0483833	+	0.998829i	$0.515407\pi$
$380$	−2.45709	+	17.0894i	−0.126046	+	0.876669i
$381$	−3.73683	+	5.81462i	−0.191444	+	0.297892i
$382$	0.473097	−	0.409941i	0.0242058	−	0.0209744i
$383$	3.90708	+	8.55531i	0.199642	+	0.437156i	0.982801	−	0.184666i	$-0.0591202\pi$
$383$	3.90708	+	8.55531i	0.199642	+	0.437156i	−0.783159	+	0.621822i	$0.786393\pi$
$384$	−5.36454	−	8.34738i	−0.273758	−	0.425975i
$385$	−2.19687	+	11.8543i	−0.111963	+	0.604149i
$386$	−3.13975	+	3.62346i	−0.159809	+	0.184429i
$387$	−2.11324	−	7.19703i	−0.107422	−	0.365846i
$388$	0.0309280	−	0.0677229i	0.00157013	−	0.00343811i
$389$	−26.3967	+	3.79528i	−1.33837	+	0.192428i	−0.774047	−	0.633128i	$-0.781771\pi$
$389$	−26.3967	+	3.79528i	−1.33837	+	0.192428i	−0.564320	+	0.825556i	$0.690862\pi$
$390$	−1.59415			−0.0807227
$391$	8.44071	−	8.65967i	0.426865	−	0.437938i
$392$	−9.83559	+	2.04204i	−0.496772	+	0.103139i
$393$	1.83477	+	12.7611i	0.0925519	+	0.643712i
$394$	−1.97052	+	4.31484i	−0.0992734	+	0.217378i
$395$	6.29145	+	21.4267i	0.316557	+	1.07809i
$396$	3.59334	+	3.11365i	0.180572	+	0.156467i
$397$	5.70211	−	19.4196i	0.286181	−	0.974642i	−0.683436	−	0.730011i	$-0.739515\pi$
$397$	5.70211	−	19.4196i	0.286181	−	0.974642i	0.969616	−	0.244631i	$-0.0786668\pi$
$398$	−0.180887	+	0.116249i	−0.00906704	+	0.00582704i
$399$	11.8572	−	6.95933i	0.593601	−	0.348402i
$400$	3.79396	+	4.37846i	0.189698	+	0.218923i
$401$	15.3838	−	23.9377i	0.768231	−	1.19539i	−0.207887	−	0.978153i	$-0.566659\pi$
$401$	15.3838	−	23.9377i	0.768231	−	1.19539i	0.976119	−	0.217239i	$-0.0697050\pi$
$402$	−0.504306	+	3.50752i	−0.0251525	+	0.174939i
$403$	−2.41679	+	16.8091i	−0.120389	+	0.837322i
$404$	10.8067	−	16.8155i	0.537653	−	0.836604i
$405$	1.16855	+	1.34858i	0.0580658	+	0.0670115i
$406$	−0.280240	−	0.477467i	−0.0139081	−	0.0236963i
$407$	2.05678	−	1.32181i	0.101951	−	0.0655197i
$408$	1.01945	−	3.47193i	0.0504703	−	0.171886i
$409$	1.84276	+	1.59676i	0.0911187	+	0.0789548i	0.699229	−	0.714898i	$-0.253527\pi$
$409$	1.84276	+	1.59676i	0.0911187	+	0.0789548i	−0.608110	+	0.793852i	$0.708072\pi$
$410$	0.168254	+	0.573022i	0.00830950	+	0.0282995i
$411$	6.25394	−	13.6942i	0.308484	−	0.675486i
$412$	−0.559956	−	3.89458i	−0.0275870	−	0.191872i
$413$	2.10259	+	20.4705i	0.103462	+	1.00729i
$414$	−0.644099	−	1.66161i	−0.0316558	−	0.0816636i
$415$	−29.1715			−1.43197
$416$	−9.65133	+	1.38765i	−0.473195	+	0.0680352i
$417$	0.0239526	−	0.0524488i	0.00117296	−	0.00256843i
$418$	1.38921	+	4.73123i	0.0679487	+	0.231412i
$419$	25.0345	−	28.8914i	1.22302	−	1.41144i	0.341104	−	0.940026i	$-0.389199\pi$
$419$	25.0345	−	28.8914i	1.22302	−	1.41144i	0.881913	−	0.471411i	$-0.156255\pi$
$420$	−1.60180	+	8.64324i	−0.0781597	+	0.421747i
$421$	−0.512484	−	0.797441i	−0.0249770	−	0.0388649i	0.828541	−	0.559929i	$-0.189172\pi$
$421$	−0.512484	−	0.797441i	−0.0249770	−	0.0388649i	−0.853518	+	0.521064i	$0.825535\pi$
$422$	−4.00474	−	8.76916i	−0.194948	−	0.426876i
$423$	−3.27403	+	2.83696i	−0.159189	+	0.137938i
$424$	6.80344	−	10.5864i	0.330404	−	0.514119i
$425$	−0.651606	+	4.53202i	−0.0316075	+	0.219835i
$426$	2.09046	+	0.300563i	0.101283	+	0.0145623i
$427$	−26.0963	−	13.2181i	−1.26289	−	0.639669i
$428$	−20.2872	+	17.5790i	−0.980620	+	0.849712i
$429$	5.58458	−	2.55039i	0.269626	−	0.123134i
$430$	2.68895	+	4.18409i	0.129673	+	0.201775i
$431$	−6.36192	+	21.6667i	−0.306443	+	1.04365i	0.651966	+	0.758249i	$0.273945\pi$
$431$	−6.36192	+	21.6667i	−0.306443	+	1.04365i	−0.958408	+	0.285400i	$0.907874\pi$
$432$	2.41129	+	2.08940i	0.116013	+	0.100526i
$433$	17.6227	−	5.17450i	0.846894	−	0.248671i	0.170635	−	0.985334i	$-0.445418\pi$
$433$	17.6227	−	5.17450i	0.846894	−	0.248671i	0.676259	+	0.736664i	$0.263600\pi$
$434$	−6.57854	−	2.22428i	−0.315780	−	0.106769i
$435$	−0.994639	+	0.143007i	−0.0476893	+	0.00685668i
$436$			35.7902i			1.71404i
$437$	−4.98523	+	24.4178i	−0.238476	+	1.16806i
$438$	−2.67429			−0.127783
$439$	−11.4367	+	1.64435i	−0.545844	+	0.0784806i	−0.409720	−	0.912211i	$-0.634374\pi$
$439$	−11.4367	+	1.64435i	−0.545844	+	0.0784806i	−0.136124	+	0.990692i	$0.543465\pi$
$440$	−5.94826	−	2.71648i	−0.283572	−	0.129503i
$441$	6.17531	−	3.29629i	0.294063	−	0.156966i
$442$	−1.70243	−	1.47516i	−0.0809763	−	0.0701664i
$443$	21.5258	+	6.32053i	1.02272	+	0.300298i	0.749747	−	0.661724i	$-0.230175\pi$
$443$	21.5258	+	6.32053i	1.02272	+	0.300298i	0.272972	+	0.962022i	$0.411993\pi$
$444$	1.49965	−	0.963766i	0.0711702	−	0.0457383i
$445$	5.34277	+	11.6990i	0.253272	+	0.554588i
$446$	−0.652889	+	0.565732i	−0.0309152	+	0.0267882i
$447$	6.30682	+	4.05315i	0.298302	+	0.191707i
$448$	−0.521428	+	12.8852i	−0.0246352	+	0.608769i
$449$	1.77506	−	12.3458i	0.0837702	−	0.582634i	−0.904096	−	0.427329i	$-0.859455\pi$
$449$	1.77506	−	12.3458i	0.0837702	−	0.582634i	0.987866	−	0.155306i	$-0.0496362\pi$
$450$	0.567626	+	0.364791i	0.0267581	+	0.0171964i
$451$	−1.50617	−	1.73822i	−0.0709230	−	0.0818495i
$452$	−16.5574	+	7.56152i	−0.778795	+	0.355664i
$453$	−0.631072	−	0.981968i	−0.0296504	−	0.0461369i
$454$	−2.99940	−	0.880703i	−0.140769	−	0.0413334i
$455$	9.29269	+	6.51760i	0.435648	+	0.305550i
$456$	2.10094	+	7.15515i	0.0983855	+	0.335070i
$457$	−36.0433	−	16.4604i	−1.68604	−	0.769987i	−0.999062	−	0.0433046i	$-0.986211\pi$
$457$	−36.0433	−	16.4604i	−1.68604	−	0.769987i	−0.686974	−	0.726682i	$-0.741061\pi$
$458$	−0.148547	−	1.03317i	−0.00694115	−	0.0482767i
$459$			2.52152i			0.117695i
$460$	−9.71141	−	12.6325i	−0.452797	−	0.588994i
$461$		−	30.8822i		−	1.43833i	−0.694842	−	0.719163i	$-0.744526\pi$
$461$		−	30.8822i		−	1.43833i	0.694842	−	0.719163i	$-0.255474\pi$
$462$	0.609328	+	2.43550i	0.0283485	+	0.113309i
$463$	3.02205	−	6.61736i	0.140446	−	0.307535i	−0.826318	−	0.563204i	$-0.809569\pi$
$463$	3.02205	−	6.61736i	0.140446	−	0.307535i	0.966764	+	0.255669i	$0.0822958\pi$
$464$	−1.72394	+	0.506196i	−0.0800321	+	0.0234995i
$465$	−8.25411	+	9.52575i	−0.382775	+	0.441746i
$466$	−4.81658	−	1.41427i	−0.223124	−	0.0655150i
$467$	13.0534	−	8.38891i	0.604039	−	0.388192i	−0.202578	−	0.979266i	$-0.564932\pi$
$467$	13.0534	−	8.38891i	0.604039	−	0.388192i	0.806618	+	0.591074i	$0.201296\pi$
$468$	4.07186	−	1.85956i	0.188222	−	0.0859580i
$469$	17.2801	−	18.3844i	0.797921	−	0.848915i
$470$	1.55301	−	2.41654i	0.0716352	−	0.111467i
$471$	17.1416	+	2.46458i	0.789841	+	0.113562i
$472$	−11.0479	−	1.58845i	−0.508522	−	0.0731144i
$473$	−16.1138	−	10.3557i	−0.740912	−	0.476155i
$474$	3.04528	+	3.51444i	0.139874	+	0.161423i
$475$	−3.91981	−	8.58318i	−0.179853	−	0.393823i
$476$	−9.70875	+	7.74810i	−0.445000	+	0.355134i
$477$	−2.47053	+	8.41386i	−0.113118	+	0.385244i
$478$	−5.17056	+	5.96715i	−0.236496	+	0.272931i
$479$	−30.2691	+	8.88781i	−1.38303	+	0.406094i	−0.886823	−	0.462109i	$-0.847093\pi$
$479$	−30.2691	+	8.88781i	−1.38303	+	0.406094i	−0.496208	+	0.868204i	$0.665275\pi$
$480$	−6.58308	−	3.00639i	−0.300475	−	0.137222i
$481$	−0.327580	−	2.27837i	−0.0149364	−	0.103885i
$482$	−2.60095			−0.118470
$483$	−3.03879	+	12.3193i	−0.138270	+	0.560549i
$484$	−8.33945			−0.379066
$485$	−0.0101545	−	0.0706260i	−0.000461091	−	0.00320696i
$486$	0.338009	+	0.154364i	0.0153324	+	0.00700208i
$487$	4.40411	−	1.29316i	0.199569	−	0.0585988i	−0.180420	−	0.983590i	$-0.557746\pi$
$487$	4.40411	−	1.29316i	0.199569	−	0.0585988i	0.379989	+	0.924991i	$0.375928\pi$
$488$	10.3905	−	11.9913i	0.470356	−	0.542820i
$489$	0.0401306	−	0.136672i	0.00181477	−	0.00618054i
$490$	−3.31305	+	3.25075i	−0.149668	+	0.146854i
$491$	10.8460	+	23.7494i	0.489474	+	1.07180i	0.979749	+	0.200230i	$0.0641689\pi$
$491$	10.8460	+	23.7494i	0.489474	+	1.07180i	−0.490275	+	0.871568i	$0.663104\pi$
$492$	−1.09819	−	1.26738i	−0.0495103	−	0.0571379i
$493$	−1.19454	−	0.767681i	−0.0537992	−	0.0345746i
$494$	4.59511	+	0.660677i	0.206744	+	0.0297253i
$495$	4.51040	+	0.648497i	0.202727	+	0.0291478i
$496$	−12.1844	+	18.9592i	−0.547094	+	0.851295i
$497$	−10.9570	−	10.2988i	−0.491489	−	0.461966i
$498$	−5.52571	+	2.52351i	−0.247613	+	0.113081i
$499$	−35.2736	+	22.6690i	−1.57906	+	1.01480i	−0.602886	+	0.797827i	$0.705983\pi$
$499$	−35.2736	+	22.6690i	−1.57906	+	1.01480i	−0.976177	+	0.216975i	$0.930381\pi$
$500$	21.7280	+	6.37992i	0.971706	+	0.285319i
$501$	1.54456	−	1.78252i	0.0690059	−	0.0796370i
$502$	−1.75249	+	0.514578i	−0.0782176	+	0.0229667i
$503$	8.07258	−	17.6765i	0.359939	−	0.788155i	−0.639868	−	0.768485i	$-0.721011\pi$
$503$	8.07258	−	17.6765i	0.359939	−	0.788155i	0.999807	−	0.0196706i	$-0.00626175\pi$
$504$	0.921501	+	3.68326i	0.0410469	+	0.164065i
$505$		−	19.1567i		−	0.852463i
$506$	−4.02172	−	2.12964i	−0.178787	−	0.0946740i
$507$			7.21995i			0.320649i
$508$	1.83150	+	12.7383i	0.0812595	+	0.565172i
$509$	28.4261	+	12.9818i	1.25996	+	0.575406i	0.929643	−	0.368463i	$-0.120116\pi$
$509$	28.4261	+	12.9818i	1.25996	+	0.575406i	0.330321	+	0.943869i	$0.392843\pi$
$510$	−0.471044	−	1.60423i	−0.0208582	−	0.0710364i
$511$	15.5892	+	10.9337i	0.689624	+	0.483680i
$512$	−21.2023	−	6.22555i	−0.937017	−	0.275133i
$513$	−2.80944	−	4.37157i	−0.124040	−	0.193009i
$514$	7.23328	−	3.30333i	0.319046	−	0.145704i
$515$	−2.46939	−	2.84983i	−0.108814	−	0.125578i
$516$	−11.7490	−	7.55061i	−0.517220	−	0.332397i
$517$	−1.57440	+	10.9502i	−0.0692418	+	0.481587i
$518$	0.940499	+	0.0380593i	0.0413232	+	0.00167223i
$519$	−20.1182	−	12.9292i	−0.883091	−	0.567528i
$520$	−4.65274	+	4.03163i	−0.204036	+	0.176798i
$521$	−12.7799	−	27.9840i	−0.559897	−	1.22600i	−0.952005	−	0.306084i	$-0.900981\pi$
$521$	−12.7799	−	27.9840i	−0.559897	−	1.22600i	0.392108	−	0.919919i	$-0.371746\pi$
$522$	−0.176035	+	0.113131i	−0.00770485	+	0.00495161i
$523$	−39.9177	−	11.7209i	−1.74548	−	0.512519i	−0.755673	−	0.654949i	$-0.772690\pi$
$523$	−39.9177	−	11.7209i	−1.74548	−	0.512519i	−0.989805	+	0.142430i	$0.954508\pi$
$524$	18.1414	+	15.7196i	0.792510	+	0.686714i
$525$	−1.81741	−	4.44718i	−0.0793181	−	0.194091i
$526$	3.21266	+	1.46717i	0.140079	+	0.0639718i
$527$	−17.6296	+	2.53475i	−0.767956	+	0.110415i
$528$	8.14761			0.354579
$529$	−12.9261	−	19.0241i	−0.562003	−	0.827135i
$530$		−	5.81454i		−	0.252567i
$531$	7.69865	−	1.10690i	0.334093	−	0.0480353i
$532$	8.19927	−	24.2502i	0.355484	−	1.05138i
$533$	−2.07766	+	0.610057i	−0.0899936	+	0.0264245i
$534$	2.02407	+	1.75387i	0.0875902	+	0.0758974i
$535$	−7.24802	+	24.6845i	−0.313359	+	1.06720i
$536$	7.39871	+	11.5126i	0.319576	+	0.497269i
$537$	19.3806	−	8.85082i	0.836335	−	0.381941i
$538$	−3.50043	+	3.03314i	−0.150914	+	0.130768i
$539$	6.40549	−	16.6884i	0.275904	−	0.718818i
$540$	3.28865	+	0.472836i	0.141521	+	0.0203476i
$541$	−2.94050	+	20.4516i	−0.126422	+	0.879285i	0.823615	+	0.567149i	$0.191954\pi$
$541$	−2.94050	+	20.4516i	−0.126422	+	0.879285i	−0.950037	+	0.312136i	$0.898956\pi$
$542$	4.17378	−	6.49453i	0.179279	−	0.278964i
$543$	3.02554	−	2.62164i	0.129838	−	0.112506i
$544$	−4.24824	−	9.30235i	−0.182142	−	0.398835i
$545$	18.5443	+	28.8555i	0.794351	+	1.23603i
$546$	2.32405	+	0.430701i	0.0994601	+	0.0184323i
$547$	17.0697	−	19.6995i	0.729847	−	0.842288i	−0.262608	−	0.964903i	$-0.584582\pi$
$547$	17.0697	−	19.6995i	0.729847	−	0.842288i	0.992454	+	0.122615i	$0.0391279\pi$
$548$	−7.89714	−	26.8952i	−0.337349	−	1.14891i
$549$	−4.59307	+	10.0574i	−0.196028	+	0.429240i
$550$	1.70550	−	0.245213i	0.0727226	−	0.0104559i
$551$	2.92631			0.124665
$552$	−6.08214	−	3.22070i	−0.258873	−	0.137082i
$553$	−3.38308	−	32.9371i	−0.143863	−	1.40063i
$554$	−0.401359	−	2.79151i	−0.0170521	−	0.118600i
$555$	0.709713	−	1.55405i	0.0301256	−	0.0659659i
$556$	−0.0302460	−	0.103009i	−0.00128272	−	0.00436854i
$557$	7.32080	+	6.34351i	0.310192	+	0.268783i	0.796018	−	0.605272i	$-0.206936\pi$
$557$	7.32080	+	6.34351i	0.310192	+	0.268783i	−0.485826	+	0.874055i	$0.661481\pi$
$558$	−0.739473	+	2.51841i	−0.0313044	+	0.106613i
$559$	−15.1707	+	9.74959i	−0.641651	+	0.412364i
$560$	7.62478	+	12.9910i	0.322206	+	0.548968i
$561$	4.21668	+	4.86630i	0.178028	+	0.205456i
$562$	5.87700	−	9.14480i	0.247906	−	0.385750i
$563$	−5.47881	+	38.1059i	−0.230904	+	1.60597i	0.463304	+	0.886200i	$0.346664\pi$
$563$	−5.47881	+	38.1059i	−0.230904	+	1.60597i	−0.694208	+	0.719775i	$0.744245\pi$
$564$	−1.14793	+	7.98404i	−0.0483367	+	0.336189i
$565$	−9.43134	+	14.6754i	−0.396779	+	0.617401i
$566$	−3.34554	−	3.86095i	−0.140623	−	0.162288i
$567$	−1.33924	−	2.28176i	−0.0562426	−	0.0958251i
$568$	6.86145	−	4.40959i	0.287900	−	0.185022i
$569$	6.52215	−	22.2124i	0.273423	−	0.931193i	−0.702244	−	0.711936i	$-0.747819\pi$
$569$	6.52215	−	22.2124i	0.273423	−	0.931193i	0.975667	−	0.219257i	$-0.0703632\pi$
$570$	2.60405	+	2.25643i	0.109072	+	0.0945113i
$571$	2.96711	+	10.1051i	0.124170	+	0.422884i	0.997990	−	0.0633649i	$-0.0201832\pi$
$571$	2.96711	+	10.1051i	0.124170	+	0.422884i	−0.873821	+	0.486248i	$0.838365\pi$
$572$	4.74863	−	10.3980i	0.198550	−	0.434764i
$573$	0.239751	+	1.66750i	0.0100157	+	0.0696609i
$574$	−0.0904750	−	0.880847i	−0.00377635	−	0.0367659i
$575$	8.19759	+	2.93854i	0.341863	+	0.122546i
$576$	4.87414			0.203089
$577$	−16.6114	+	2.38836i	−0.691543	+	0.0994289i	−0.479121	−	0.877749i	$-0.659044\pi$
$577$	−16.6114	+	2.38836i	−0.691543	+	0.0994289i	−0.212422	+	0.977178i	$0.568135\pi$
$578$	−1.64273	+	3.59707i	−0.0683285	+	0.149619i
$579$	−3.63513	−	12.3801i	−0.151071	−	0.514500i
$580$	−1.22523	+	1.41399i	−0.0508751	+	0.0587129i
$581$	42.5281	+	7.88146i	1.76436	+	0.326978i
$582$	−0.00803305	−	0.0124997i	−0.000332981	−	0.000518128i
$583$	9.30239	+	20.3694i	0.385265	+	0.843614i
$584$	−7.80531	+	6.76334i	−0.322986	+	0.279869i
$585$	2.31939	−	3.60904i	0.0958950	−	0.149215i
$586$	0.814041	−	5.66178i	0.0336277	−	0.233886i
$587$	−7.90217	−	1.13616i	−0.326157	−	0.0468944i	−0.0227087	−	0.999742i	$-0.507229\pi$
$587$	−7.90217	−	1.13616i	−0.326157	−	0.0468944i	−0.303449	+	0.952848i	$0.598138\pi$
$588$	4.67041	−	12.1679i	0.192604	−	0.501796i
$589$	27.7403	−	24.0371i	1.14302	−	0.990430i
$590$	−4.69121	+	2.14241i	−0.193134	+	0.0882014i
$591$	−6.90152	−	10.7390i	−0.283890	−	0.441742i
$592$	0.860618	−	2.93099i	0.0353712	−	0.120463i
$593$	−22.2131	−	19.2478i	−0.912184	−	0.790412i	0.0660716	−	0.997815i	$-0.478953\pi$
$593$	−22.2131	−	19.2478i	−0.912184	−	0.790412i	−0.978256	+	0.207403i	$0.933499\pi$
$594$	0.910466	−	0.267337i	0.0373569	−	0.0109690i
$595$	−3.81299	+	11.2773i	−0.156317	+	0.462325i
$596$	13.8166	−	1.98653i	0.565951	−	0.0813714i
$597$		−	0.578652i		−	0.0236826i
$598$	−3.39671	+	2.61126i	−0.138902	+	0.106783i
$599$	−15.4770			−0.632373			−0.316187	−	0.948697i	$-0.602403\pi$
$599$	−15.4770			−0.632373			−0.316187	+	0.948697i	$0.602403\pi$
$600$	2.57926	−	0.370842i	0.105298	−	0.0151396i
$601$	−0.0889384	−	0.0406168i	−0.00362787	−	0.00165679i	0.413600	−	0.910459i	$-0.364271\pi$
$601$	−0.0889384	−	0.0406168i	−0.00362787	−	0.00165679i	−0.417228	+	0.908802i	$0.636998\pi$
$602$	−2.78968	−	6.82632i	−0.113699	−	0.278220i
$603$	−7.20707	−	6.24496i	−0.293495	−	0.254315i
$604$	−2.08532	−	0.612306i	−0.0848506	−	0.0249144i
$605$	−6.72360	+	4.32100i	−0.273353	+	0.175673i
$606$	−1.65717	−	3.62870i	−0.0673180	−	0.147406i
$607$	0.800830	−	0.693923i	0.0325047	−	0.0281655i	−0.638457	−	0.769658i	$-0.720427\pi$
$607$	0.800830	−	0.693923i	0.0325047	−	0.0281655i	0.670962	+	0.741492i	$0.265882\pi$
$608$	17.7297	+	11.3942i	0.719034	+	0.462095i
$609$	1.48869	+	0.0602429i	0.0603246	+	0.00244117i
$610$	1.04336	−	7.25671i	0.0422443	−	0.293816i
$611$	8.76188	+	5.63092i	0.354468	+	0.227803i
$612$	3.07449	+	3.54815i	0.124279	+	0.143425i
$613$	−15.9158	+	7.26850i	−0.642833	+	0.293572i	−0.710034	−	0.704167i	$-0.751320\pi$
$613$	−15.9158	+	7.26850i	−0.642833	+	0.293572i	0.0672008	+	0.997739i	$0.478593\pi$
$614$	−3.88975	−	6.05257i	−0.156978	−	0.244262i
$615$	−1.54209	−	0.452797i	−0.0621829	−	0.0182585i
$616$	7.93783	+	5.56734i	0.319824	+	0.224315i
$617$	−5.41310	−	18.4353i	−0.217923	−	0.742178i	−0.993789	−	0.111280i	$-0.964505\pi$
$617$	−5.41310	−	18.4353i	−0.217923	−	0.742178i	0.775866	−	0.630898i	$-0.217313\pi$
$618$	−0.714284	−	0.326202i	−0.0287327	−	0.0131218i
$619$	5.05833	+	35.1815i	0.203311	+	1.41406i	0.794370	+	0.607434i	$0.207801\pi$
$619$	5.05833	+	35.1815i	0.203311	+	1.41406i	−0.591059	+	0.806628i	$0.701290\pi$
$620$			23.4684i			0.942512i
$621$	4.69890	+	0.959345i	0.188560	+	0.0384972i
$622$		−	0.269544i		−	0.0108077i
$623$	−4.62823	−	18.4991i	−0.185426	−	0.741151i
$624$	3.18654	−	6.97756i	0.127564	−	0.279326i
$625$	12.1124	−	3.55651i	0.484495	−	0.142260i
$626$	2.68924	−	3.10355i	0.107484	−	0.124043i
$627$	−12.7324	−	3.73858i	−0.508484	−	0.149304i
$628$	27.1257	−	17.4327i	1.08243	−	0.695639i
$629$	2.19599	−	1.00287i	0.0875598	−	0.0399872i
$630$	1.27830	+	1.20151i	0.0509286	+	0.0478693i
$631$	16.1381	−	25.1113i	0.642447	−	0.999667i	−0.355441	−	0.934699i	$-0.615669\pi$
$631$	16.1381	−	25.1113i	0.642447	−	0.999667i	0.997887	−	0.0649677i	$-0.0206944\pi$
$632$	17.7762	+	2.55583i	0.707098	+	0.101665i
$633$	25.6795	+	3.69215i	1.02067	+	0.146750i
$634$	−8.20818	−	5.27508i	−0.325988	−	0.209500i
$635$	8.07686	+	9.32119i	0.320520	+	0.369900i
$636$	6.78261	+	14.8518i	0.268948	+	0.588914i
$637$	−11.7866	−	12.0125i	−0.467001	−	0.475951i
$638$	−0.150546	+	0.512712i	−0.00596016	+	0.0202984i
$639$	−3.72196	+	4.29537i	−0.147238	+	0.169922i
$640$	−16.9889	+	4.98838i	−0.671543	+	0.197183i
$641$	7.26388	+	3.31730i	0.286906	+	0.131026i	0.553670	−	0.832736i	$-0.313227\pi$
$641$	7.26388	+	3.31730i	0.286906	+	0.131026i	−0.266764	+	0.963762i	$0.585954\pi$
$642$	0.762424	+	5.30277i	0.0300905	+	0.209284i
$643$	−49.9189			−1.96861			−0.984305	−	0.176475i	$-0.943530\pi$
$643$	−49.9189			−1.96861			−0.984305	+	0.176475i	$0.943530\pi$
$644$	10.7449	+	21.0403i	0.423409	+	0.829104i
$645$	−13.3848			−0.527024
$646$	0.692925	+	4.81940i	0.0272628	+	0.189617i
$647$	31.2141	+	14.2550i	1.22715	+	0.560422i	0.920255	−	0.391320i	$-0.127981\pi$
$647$	31.2141	+	14.2550i	1.22715	+	0.560422i	0.306899	+	0.951742i	$0.400709\pi$
$648$	1.37692	−	0.404300i	0.0540905	−	0.0158824i
$649$	13.0066	−	15.0105i	0.510555	−	0.589212i
$650$	0.457023	−	1.55648i	0.0179259	−	0.0610501i
$651$	14.6070	−	11.6572i	0.572494	−	0.456881i
$652$	−0.110175	−	0.241249i	−0.00431478	−	0.00944806i
$653$	18.8137	+	21.7122i	0.736237	+	0.849663i	0.993159	−	0.116769i	$-0.0372537\pi$
$653$	18.8137	+	21.7122i	0.736237	+	0.849663i	−0.256922	+	0.966432i	$0.582708\pi$
$654$	6.00887	+	3.86167i	0.234965	+	0.151003i
$655$	22.7713	+	3.27401i	0.889747	+	0.127926i
$656$	−2.84444	−	0.408968i	−0.111057	−	0.0159675i
$657$	3.89094	−	6.05443i	0.151800	−	0.236206i
$658$	−2.91698	+	3.10340i	−0.113716	+	0.120983i
$659$	−16.2536	+	7.42277i	−0.633151	+	0.289150i	−0.706021	−	0.708191i	$-0.749511\pi$
$659$	−16.2536	+	7.42277i	−0.633151	+	0.289150i	0.0728700	+	0.997341i	$0.476784\pi$
$660$	7.13750	−	4.58699i	0.277827	−	0.178548i
$661$	−16.7127	−	4.90728i	−0.650047	−	0.190871i	−0.0599474	−	0.998202i	$-0.519093\pi$
$661$	−16.7127	−	4.90728i	−0.650047	−	0.190871i	−0.590099	+	0.807331i	$0.700911\pi$
$662$	6.34658	−	7.32435i	0.246667	−	0.284669i
$663$	5.81661	−	1.70791i	0.225899	−	0.0663298i
$664$	−9.74559	+	21.3399i	−0.378202	+	0.828147i
$665$	−5.95441	−	23.7999i	−0.230902	−	0.922920i
$666$		−	0.355766i		−	0.0137857i
$667$	−1.88506	+	1.93396i	−0.0729900	+	0.0748834i
$668$		−	4.39155i		−	0.169914i
$669$	−0.330863	−	2.30121i	−0.0127919	−	0.0889698i
$670$	5.75186	+	2.62679i	0.222214	+	0.101482i
$671$	7.95457	+	27.0908i	0.307083	+	1.04583i
$672$	8.78498	+	6.16151i	0.338888	+	0.237685i
$673$	47.4059	+	13.9196i	1.82736	+	0.536563i	0.999696	−	0.0246546i	$-0.00784859\pi$
$673$	47.4059	+	13.9196i	1.82736	+	0.536563i	0.827669	+	0.561217i	$0.189667\pi$
$674$	−2.27650	−	3.54230i	−0.0876873	−	0.136444i
$675$	−1.65173	+	0.754318i	−0.0635750	+	0.0290337i
$676$	8.80328	+	10.1595i	0.338588	+	0.390751i
$677$	−11.0679	−	7.11292i	−0.425375	−	0.273372i	0.310389	−	0.950609i	$-0.399541\pi$
$677$	−11.0679	−	7.11292i	−0.425375	−	0.273372i	−0.735764	+	0.677238i	$0.763177\pi$
$678$	−0.516986	+	3.59572i	−0.0198547	+	0.138093i
$679$	−0.00427765	+	0.105707i	−0.000164161	+	0.00405665i
$680$	−5.43194	−	3.49089i	−0.208305	−	0.133870i
$681$	6.35781	−	5.50907i	0.243632	−	0.211108i
$682$	2.78437	+	6.09691i	0.106619	+	0.233463i
$683$	15.8821	−	10.2068i	0.607711	−	0.390552i	−0.200287	−	0.979737i	$-0.564188\pi$
$683$	15.8821	−	10.2068i	0.607711	−	0.390552i	0.807998	+	0.589185i	$0.200551\pi$
$684$	−9.28354	−	2.72589i	−0.354965	−	0.104227i
$685$	−20.3024	−	17.5922i	−0.775717	−	0.672162i
$686$	5.70826	−	3.84405i	0.217942	−	0.146767i
$687$	2.55515	+	1.16690i	0.0974851	+	0.0445199i
$688$	−23.6886	+	3.40591i	−0.903121	+	0.129849i
$689$	21.0824			0.803174
$690$	−3.16872	+	0.267450i	−0.120631	+	0.0101816i
$691$			33.6433i			1.27985i	0.768437	+	0.639925i	$0.221035\pi$
$691$			33.6433i			1.27985i	−0.768437	+	0.639925i	$0.778965\pi$
$692$	−44.0738	+	6.33686i	−1.67544	+	0.240891i
$693$	−6.40034	−	2.16403i	−0.243129	−	0.0822046i
$694$	−2.93804	+	0.862686i	−0.111526	+	0.0327471i
$695$	−0.0777583	−	0.0673780i	−0.00294954	−	0.00255579i
$696$	−0.227674	+	0.775386i	−0.00862995	+	0.0293909i
$697$	−1.22783	−	1.91054i	−0.0465075	−	0.0723670i
$698$	−3.82849	+	1.74841i	−0.144911	+	0.0661784i
$699$	10.2097	−	8.84673i	0.386165	−	0.334614i
$700$	−7.97980	−	4.04187i	−0.301608	−	0.152768i
$701$	2.11726	+	0.304416i	0.0799678	+	0.0114976i	0.182183	−	0.983265i	$-0.441684\pi$
$701$	2.11726	+	0.304416i	0.0799678	+	0.0114976i	−0.102215	+	0.994762i	$0.532593\pi$
$702$	0.127139	−	0.884272i	0.00479856	−	0.0333747i
$703$	−2.68980	+	4.18542i	−0.101448	+	0.157856i
$704$	9.40665	−	8.15091i	0.354526	−	0.307199i
$705$	3.21134	+	7.03185i	0.120946	+	0.264835i
$706$	3.01079	+	4.68487i	0.113312	+	0.176318i
$707$	−5.17571	+	27.9279i	−0.194652	+	1.05034i
$708$	9.48348	−	10.9445i	0.356411	−	0.411320i
$709$	−9.68905	−	32.9979i	−0.363880	−	1.23926i	−0.914528	−	0.404523i	$-0.867437\pi$
$709$	−9.68905	−	32.9979i	−0.363880	−	1.23926i	0.550648	−	0.834738i	$-0.314381\pi$
$710$	1.56555	−	3.42807i	0.0587540	−	0.128653i
$711$	−12.3872	+	1.78100i	−0.464555	+	0.0667929i
$712$	10.3431			0.387625
$713$	−1.98385	+	33.8174i	−0.0742956	+	1.26647i
$714$	0.253293	+	2.46601i	0.00947925	+	0.0922883i
$715$	−1.55910	−	10.8438i	−0.0583070	−	0.405534i
$716$	16.4795	−	36.0852i	0.615869	−	1.34857i
$717$	−5.98636	−	20.3877i	−0.223565	−	0.761392i
$718$	−0.319036	−	0.276446i	−0.0119063	−	0.0103169i
$719$	−5.62214	+	19.1473i	−0.209670	+	0.714072i	0.785756	+	0.618537i	$0.212274\pi$
$719$	−5.62214	+	19.1473i	−0.209670	+	0.714072i	−0.995426	+	0.0955349i	$0.969544\pi$
$720$	4.78958	−	3.07808i	0.178497	−	0.114713i
$721$	2.83008	+	4.82184i	0.105398	+	0.179575i
$722$	−1.94757	−	2.24762i	−0.0724811	−	0.0836476i
$723$	3.78423	−	5.88837i	0.140737	−	0.218991i
$724$	1.06081	−	7.37807i	0.0394246	−	0.274204i
$725$	0.145523	−	1.01214i	0.00540459	−	0.0375898i
$726$	−0.899804	+	1.40012i	−0.0333949	+	0.0519634i
$727$	−15.5015	−	17.8897i	−0.574918	−	0.663490i	0.391586	−	0.920141i	$-0.371926\pi$
$727$	−15.5015	−	17.8897i	−0.574918	−	0.663490i	−0.966504	+	0.256651i	$0.917381\pi$
$728$	7.87233	−	4.62050i	0.291768	−	0.171247i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	−1.34445	+	4.57878i	−0.0497604	+	0.169468i
$731$	−14.2939	−	12.3858i	−0.528681	−	0.458104i
$732$	5.79989	+	19.7526i	0.214370	+	0.730077i
$733$	8.72201	−	19.0985i	0.322155	−	0.705420i	−0.677389	−	0.735625i	$-0.736889\pi$
$733$	8.72201	−	19.0985i	0.322155	−	0.705420i	0.999544	+	0.0302045i	$0.00961587\pi$
$734$	−0.581706	−	4.04586i	−0.0214712	−	0.149335i
$735$	−2.53920	−	12.2302i	−0.0936598	−	0.451117i
$736$	−18.9514	+	4.37747i	−0.698558	+	0.161356i
$737$	−24.3523			−0.897028
$738$	−0.331274	+	0.0476300i	−0.0121944	+	0.00175329i
$739$	13.5382	−	29.6445i	0.498011	−	1.09049i	−0.479100	−	0.877760i	$-0.659037\pi$
$739$	13.5382	−	29.6445i	0.498011	−	1.09049i	0.977111	−	0.212731i	$-0.0682359\pi$
$740$	−0.896188	−	3.05213i	−0.0329445	−	0.112199i
$741$	−8.18135	+	9.44178i	−0.300549	+	0.346853i
$742$	−1.57095	+	8.47681i	−0.0576716	+	0.311194i
$743$	11.7472	+	18.2789i	0.430962	+	0.670589i	0.987028	−	0.160549i	$-0.0513263\pi$
$743$	11.7472	+	18.2789i	0.430962	+	0.670589i	−0.556066	+	0.831138i	$0.687690\pi$
$744$	4.21086	+	9.22050i	0.154378	+	0.338040i
$745$	10.1102	−	8.76055i	0.370410	−	0.320962i
$746$	1.06832	−	1.66233i	0.0391138	−	0.0608623i
$747$	2.32654	−	16.1814i	0.0851235	−	0.592047i
$748$	11.8670	+	1.70621i	0.433899	+	0.0623853i
$749$	17.2358	−	34.0284i	0.629783	−	1.24337i
$750$	3.41553	−	2.95957i	0.124717	−	0.108068i
$751$	−9.81327	+	4.48157i	−0.358091	+	0.163535i	−0.586334	−	0.810069i	$-0.699429\pi$
$751$	−9.81327	+	4.48157i	−0.358091	+	0.163535i	0.228243	+	0.973604i	$0.426702\pi$
$752$	7.47283	+	11.6280i	0.272506	+	0.424028i
$753$	1.38480	−	4.71621i	0.0504651	−	0.171868i
$754$	0.380204	+	0.329448i	0.0138462	+	0.0119978i
$755$	−1.99853	+	0.586822i	−0.0727340	+	0.0213566i
$756$	−4.66665	−	1.57785i	−0.169725	−	0.0573858i
$757$	2.93346	−	0.421767i	0.106618	−	0.0153294i	−0.0887992	−	0.996050i	$-0.528303\pi$
$757$	2.93346	−	0.421767i	0.106618	−	0.0153294i	0.195417	+	0.980720i	$0.437394\pi$
$758$		−	1.36373i		−	0.0495328i
$759$	10.6727	−	6.00641i	0.387396	−	0.218019i
$760$	13.3069			0.482691
$761$	32.8714	−	4.72619i	1.19159	−	0.171324i	0.482147	−	0.876090i	$-0.339857\pi$
$761$	32.8714	−	4.72619i	1.19159	−	0.171324i	0.709440	+	0.704766i	$0.248948\pi$
$762$	2.33627	+	1.06694i	0.0846341	+	0.0386511i
$763$	−19.2390	−	47.0777i	−0.696499	−	1.70433i
$764$	2.37055	+	2.05409i	0.0857635	+	0.0743145i
$765$	4.31721	+	1.26765i	0.156089	+	0.0458319i
$766$	2.94009	−	1.88948i	0.106230	−	0.0682696i
$767$	−7.76793	−	17.0094i	−0.280484	−	0.614174i
$768$	4.58073	−	3.96922i	0.165293	−	0.143227i
$769$	30.4788	+	19.5875i	1.09909	+	0.706344i	0.958890	−	0.283779i	$-0.0915882\pi$
$769$	30.4788	+	19.5875i	1.09909	+	0.706344i	0.140203	+	0.990123i	$0.455225\pi$
$770$	4.47625	+	0.181141i	0.161313	+	0.00652787i
$771$	−3.04549	+	21.1818i	−0.109681	+	0.762845i
$772$	−20.2102	−	12.9883i	−0.727381	−	0.467460i
$773$	24.0284	+	27.7302i	0.864240	+	0.997387i	0.999978	+	0.00664174i	$0.00211415\pi$
$773$	24.0284	+	27.7302i	0.864240	+	0.997387i	−0.135738	+	0.990745i	$0.543340\pi$
$774$	−2.53536	+	1.15786i	−0.0911318	+	0.0416185i
$775$	−6.93431	−	10.7900i	−0.249088	−	0.387588i
$776$	−0.0550575	−	0.0161664i	−0.00197645	−	0.000580338i
$777$	−1.45454	+	2.07385i	−0.0521812	+	0.0743991i
$778$	2.79186	+	9.50819i	0.100093	+	0.340885i
$779$	4.25739	+	1.94429i	0.152537	+	0.0696613i
$780$	−1.13678	−	7.90648i	−0.0407033	−	0.283097i
$781$			14.5138i			0.519345i
$782$	−3.63145	−	2.64661i	−0.129861	−	0.0946424i
$783$		−	0.563131i		−	0.0201247i
$784$	−7.60605	−	20.9991i	−0.271645	−	0.749968i
$785$	12.8373	−	28.1098i	0.458184	−	1.00328i
$786$	4.59659	−	1.34968i	0.163955	−	0.0481415i
$787$	−26.1210	+	30.1453i	−0.931114	+	1.07456i	0.0659377	+	0.997824i	$0.478996\pi$
$787$	−26.1210	+	30.1453i	−0.931114	+	1.07456i	−0.997051	+	0.0767386i	$0.975549\pi$
$788$	−22.8055	−	6.69629i	−0.812411	−	0.238545i
$789$	−7.99583	+	5.13861i	−0.284659	+	0.182939i
$790$	7.54818	−	3.44714i	0.268552	−	0.122644i
$791$	17.7146	−	18.8467i	0.629858	−	0.670111i
$792$	1.98123	−	3.08285i	0.0703998	−	0.109544i
$793$	26.3114	+	3.78301i	0.934345	+	0.134338i
$794$	−7.44421	−	1.07032i	−0.264185	−	0.0379841i
$795$	13.1637	+	8.45982i	0.466870	+	0.300039i
$796$	−0.705550	−	0.814248i	−0.0250076	−	0.0288603i
$797$	1.15278	+	2.52424i	0.0408336	+	0.0894131i	0.928950	−	0.370206i	$-0.120713\pi$
$797$	1.15278	+	2.52424i	0.0408336	+	0.0894131i	−0.888116	+	0.459620i	$0.847986\pi$
$798$	−3.18673	−	3.99312i	−0.112809	−	0.141355i
$799$	−3.07754	+	10.4812i	−0.108876	+	0.370797i
$800$	4.82265	−	5.56563i	0.170506	−	0.196775i
$801$	−6.91556	+	2.03059i	−0.244349	+	0.0717474i
$802$	−9.61799	−	4.39239i	−0.339623	−	0.155101i
$803$	−2.61550	−	18.1912i	−0.0922991	−	0.641954i
$804$	−17.7559			−0.626202
$805$	19.5648	+	11.3962i	0.689568	+	0.401662i
$806$	6.31032			0.222271
$807$	−1.77391	−	12.3378i	−0.0624445	−	0.434311i
$808$	−14.0138	−	6.39987i	−0.493002	−	0.225146i
$809$	43.2081	−	12.6870i	1.51911	−	0.446052i	0.587416	−	0.809285i	$-0.300145\pi$
$809$	43.2081	−	12.6870i	1.51911	−	0.446052i	0.931698	+	0.363233i	$0.118327\pi$
$810$	0.434221	−	0.501118i	0.0152570	−	0.0176075i
$811$	−13.4991	+	45.9737i	−0.474017	+	1.61435i	0.281732	+	0.959493i	$0.409091\pi$
$811$	−13.4991	+	45.9737i	−0.474017	+	1.61435i	−0.755749	+	0.654861i	$0.772727\pi$
$812$	2.16825	−	1.73038i	0.0760908	−	0.0607246i
$813$	8.63058	+	18.8983i	0.302688	+	0.662793i
$814$	−0.594939	−	0.686596i	−0.0208526	−	0.0240652i
$815$	−0.213828	−	0.137419i	−0.00749008	−	0.00481358i
$816$	7.96326	+	1.14494i	0.278770	+	0.0400811i
$817$	38.5815	+	5.54718i	1.34979	+	0.194071i
$818$	0.489850	−	0.762222i	0.0171272	−	0.0266505i
$819$	−4.35644	+	4.63485i	−0.152226	+	0.161955i
$820$	−2.72203	+	1.24311i	−0.0950576	+	0.0434113i
$821$	−30.9829	+	19.9115i	−1.08131	+	0.694915i	−0.954860	−	0.297058i	$-0.903995\pi$
$821$	−30.9829	+	19.9115i	−1.08131	+	0.694915i	−0.126450	+	0.991973i	$0.540358\pi$
$822$	−5.36755	−	1.57606i	−0.187215	−	0.0549713i
$823$	7.66525	−	8.84618i	0.267194	−	0.308358i	−0.606259	−	0.795268i	$-0.707330\pi$
$823$	7.66525	−	8.84618i	0.267194	−	0.308358i	0.873453	+	0.486909i	$0.161876\pi$
$824$	−2.90971	+	0.854369i	−0.101365	+	0.0297634i
$825$	−1.92625	+	4.21791i	−0.0670635	+	0.146849i
$826$	7.41798	−	1.85588i	0.258105	−	0.0645743i
$827$			23.3448i			0.811778i	0.913922	+	0.405889i	$0.133038\pi$
$827$			23.3448i			0.811778i	−0.913922	+	0.405889i	$0.866962\pi$
$828$	7.78177	−	4.37943i	0.270435	−	0.152196i
$829$			34.7750i			1.20779i	0.797065	+	0.603893i	$0.206385\pi$
$829$			34.7750i			1.20779i	−0.797065	+	0.603893i	$0.793615\pi$
$830$	1.54266	+	10.7295i	0.0535467	+	0.372425i
$831$	6.90375	+	3.15284i	0.239488	+	0.109371i
$832$	−3.30142	−	11.2436i	−0.114456	−	0.389802i
$833$	8.60569	−	15.4106i	0.298170	−	0.533946i
$834$	−0.0205577	−	0.00603629i	−0.000711856	−	0.000209020i
$835$	−2.27543	−	3.54064i	−0.0787446	−	0.122529i
$836$	−22.4748	+	10.2639i	−0.777308	+	0.354985i
$837$	−4.62563	−	5.33827i	−0.159885	−	0.184517i
$838$	−11.9503	−	7.68002i	−0.412818	−	0.265302i
$839$	8.19921	−	57.0267i	0.283068	−	1.96878i	0.0379919	−	0.999278i	$-0.487904\pi$
$839$	8.19921	−	57.0267i	0.283068	−	1.96878i	0.245076	−	0.969504i	$-0.421187\pi$
$840$	6.76954	+	0.273944i	0.233571	+	0.00945196i
$841$	−24.1296	−	15.5071i	−0.832054	−	0.534729i
$842$	−0.266203	+	0.230666i	−0.00917395	+	0.00794928i
$843$	12.1525	+	26.6103i	0.418555	+	0.916508i
$844$	40.6366	−	26.1156i	1.39877	−	0.898935i
$845$	12.3616	+	3.62969i	0.425252	+	0.124865i
$846$	1.21659	+	1.05418i	0.0418274	+	0.0362436i
$847$	10.9695	−	4.48287i	0.376918	−	0.154033i
$848$	25.4502	+	11.6227i	0.873962	+	0.399125i
$849$	13.6085	−	1.95661i	0.467043	−	0.0671506i
$850$	1.70137			0.0583564
$851$	−1.03338	−	4.47382i	−0.0354239	−	0.153361i
$852$			10.5824i			0.362547i
$853$	12.5992	−	1.81149i	0.431387	−	0.0620241i	0.0767988	−	0.997047i	$-0.475530\pi$
$853$	12.5992	−	1.81149i	0.431387	−	0.0620241i	0.354588	+	0.935023i	$0.384621\pi$
$854$	−3.48167	+	10.2974i	−0.119140	+	0.352370i
$855$	−8.89715	+	2.61244i	−0.304276	+	0.0893435i
$856$	15.6361	+	13.5487i	0.534430	+	0.463086i
$857$	2.78650	−	9.48995i	0.0951851	−	0.324171i	−0.898111	−	0.439769i	$-0.855060\pi$
$857$	2.78650	−	9.48995i	0.0951851	−	0.324171i	0.993296	+	0.115598i	$0.0368785\pi$
$858$	−1.23338	−	1.91918i	−0.0421069	−	0.0655196i
$859$	−28.5675	+	13.0464i	−0.974712	+	0.445136i	−0.838117	−	0.545491i	$-0.816343\pi$
$859$	−28.5675	+	13.0464i	−0.974712	+	0.445136i	−0.136595	+	0.990627i	$0.543616\pi$
$860$	−18.8343	+	16.3200i	−0.642245	+	0.556508i
$861$	2.12582	+	1.07675i	0.0724477	+	0.0366956i
$862$	8.30560	+	1.19417i	0.282890	+	0.0406734i
$863$	−0.954534	+	6.63893i	−0.0324927	+	0.225992i	−0.999597	−	0.0283886i	$-0.990962\pi$
$863$	−0.954534	+	6.63893i	−0.0324927	+	0.225992i	0.967104	+	0.254380i	$0.0818715\pi$
$864$	2.19267	−	3.41186i	0.0745961	−	0.116074i
$865$	−32.2507	+	27.9454i	−1.09656	+	0.950172i
$866$	−2.83515	−	6.20812i	−0.0963424	−	0.210960i
$867$	−5.75346	−	8.95256i	−0.195398	−	0.304045i
$868$	6.34061	−	34.2137i	0.215214	−	1.16129i
$869$	−20.9278	+	24.1519i	−0.709925	+	0.819297i
$870$	0.105198	+	0.358272i	0.00356656	+	0.0121466i
$871$	−9.52421	+	20.8551i	−0.322716	+	0.706648i
$872$	27.3040	−	3.92572i	0.924630	−	0.132942i
$873$	0.0399861			0.00135332
$874$	9.24466	+	0.542324i	0.312705	+	0.0183444i
$875$	−32.0101	+	3.28787i	−1.08214	+	0.111150i
$876$	−1.90703	−	13.2637i	−0.0644326	−	0.448139i
$877$	−22.5424	+	49.3610i	−0.761203	+	1.66680i	−0.0160851	+	0.999871i	$0.505120\pi$
$877$	−22.5424	+	49.3610i	−0.761203	+	1.66680i	−0.745118	+	0.666932i	$0.767607\pi$
$878$	1.20961	+	4.11954i	0.0408222	+	0.139028i
$879$	11.6335	+	10.0805i	0.392389	+	0.340007i
$880$	4.09606	−	13.9499i	0.138078	−	0.470251i
$881$	−34.1473	+	21.9451i	−1.15045	+	0.739350i	−0.969729	−	0.244184i	$-0.921480\pi$
$881$	−34.1473	+	21.9451i	−1.15045	+	0.739350i	−0.180723	+	0.983534i	$0.557844\pi$
$882$	−1.53896	−	2.09701i	−0.0518196	−	0.0706099i
$883$	−30.4986	−	35.1973i	−1.02636	−	1.18448i	−0.982656	−	0.185440i	$-0.940629\pi$
$883$	−30.4986	−	35.1973i	−1.02636	−	1.18448i	−0.0437056	−	0.999044i	$-0.513916\pi$
$884$	6.10237	−	9.49547i	0.205245	−	0.319367i
$885$	1.97518	−	13.7377i	0.0663949	−	0.461787i
$886$	1.18640	−	8.25157i	0.0398578	−	0.277217i
$887$	12.8127	−	19.9370i	0.430209	−	0.669419i	−0.556696	−	0.830716i	$-0.687931\pi$
$887$	12.8127	−	19.9370i	0.430209	−	0.669419i	0.986906	+	0.161297i	$0.0515677\pi$
$888$	−0.899740	−	1.03836i	−0.0301933	−	0.0348449i
$889$	−9.25660	−	15.7712i	−0.310456	−	0.528950i
$890$	4.02045	−	2.58378i	0.134766	−	0.0866086i
$891$	−0.719442	+	2.45019i	−0.0241022	+	0.0820846i
$892$	−3.27143	−	2.83471i	−0.109536	−	0.0949132i
$893$	−6.34238	−	21.6001i	−0.212240	−	0.722821i
$894$	1.15725	−	2.53403i	0.0387044	−	0.0847507i
$895$	−5.41066	−	37.6320i	−0.180859	−	1.25790i
$896$	26.1152	−	2.68238i	0.872448	−	0.0896122i
$897$	−0.969719	−	11.4892i	−0.0323780	−	0.383612i
$898$	−4.63474			−0.154663
$899$	3.93721	−	0.566086i	0.131313	−	0.0188800i
$900$	−1.40448	+	3.07538i	−0.0468160	+	0.102513i
$901$	6.22950	+	21.2157i	0.207535	+	0.706798i
$902$	−0.559678	+	0.645903i	−0.0186352	+	0.0215062i
$903$	19.5132	+	3.61625i	0.649358	+	0.120341i
$904$	7.58474	+	11.8021i	0.252265	+	0.392532i
$905$	−2.96760	−	6.49815i	−0.0986465	−	0.216006i
$906$	−0.327802	+	0.284042i	−0.0108905	+	0.00943666i
$907$	−21.9707	+	34.1870i	−0.729524	+	1.13516i	0.256172	+	0.966631i	$0.417538\pi$
$907$	−21.9707	+	34.1870i	−0.729524	+	1.13516i	−0.985696	+	0.168530i	$0.946098\pi$
$908$	2.22916	−	15.5041i	0.0739772	−	0.514523i
$909$	10.6262	+	1.52782i	0.352450	+	0.0506746i
$910$	1.90580	−	3.76258i	0.0631765	−	0.124728i
$911$	6.18321	−	5.35778i	0.204859	−	0.177511i	−0.546389	−	0.837532i	$-0.683998\pi$
$911$	6.18321	−	5.35778i	0.204859	−	0.177511i	0.751248	+	0.660021i	$0.229452\pi$
$912$	−15.0816	+	6.88754i	−0.499402	+	0.228069i
$913$	−22.5698	−	35.1192i	−0.746950	−	1.16228i
$914$	−4.14820	+	14.1275i	−0.137210	+	0.467295i
$915$	14.9107	+	12.9202i	0.492932	+	0.427128i
$916$	5.01827	−	1.47350i	0.165808	−	0.0486857i
$917$	−32.3129	−	10.9253i	−1.06706	−	0.360787i
$918$	0.927433	−	0.133345i	0.0306098	−	0.00440103i
$919$		−	25.3955i		−	0.837720i	−0.908051	−	0.418860i	$-0.862430\pi$
$919$		−	25.3955i		−	0.837720i	0.908051	−	0.418860i	$-0.137570\pi$
$920$	−8.57200	+	8.79436i	−0.282610	+	0.289941i
$921$	19.3620			0.637999
$922$	−11.3587	+	1.63313i	−0.374078	+	0.0537843i
$923$	12.4295	+	5.67637i	0.409122	+	0.186840i
$924$	−11.6448	+	4.75883i	−0.383086	+	0.156554i
$925$	1.31387	+	1.13847i	0.0431997	+	0.0374328i
$926$	−2.59372	−	0.761586i	−0.0852351	−	0.0250273i
$927$	1.77774	−	1.14249i	0.0583887	−	0.0375242i
$928$	0.948760	+	2.07749i	0.0311446	+	0.0681971i
$929$	−35.8330	+	31.0495i	−1.17564	+	1.01870i	−0.176234	+	0.984348i	$0.556391\pi$
$929$	−35.8330	+	31.0495i	−1.17564	+	1.01870i	−0.999410	+	0.0343526i	$0.989063\pi$
$930$	3.94014	+	2.53217i	0.129202	+	0.0830332i
$931$	2.25055	+	36.3058i	0.0737587	+	1.18987i
$932$	3.57969	−	24.8973i	0.117257	−	0.815538i
$933$	0.610230	+	0.392171i	0.0199780	+	0.0128391i
$934$	−3.77580	−	4.35750i	−0.123548	−	0.142582i
$935$	10.4517	−	4.77312i	0.341806	−	0.156098i
$936$	−1.86527	−	2.90241i	−0.0609682	−	0.0948683i
$937$	−22.5848	−	6.63149i	−0.737813	−	0.216641i	−0.108830	−	0.994060i	$-0.534710\pi$
$937$	−22.5848	−	6.63149i	−0.737813	−	0.216641i	−0.628983	+	0.777419i	$0.716528\pi$
$938$	−7.67574	−	5.38352i	−0.250622	−	0.175778i
$939$	3.11354	+	10.6038i	0.101607	+	0.346040i
$940$	13.0927	+	5.97926i	0.427038	+	0.195022i
$941$	2.25615	+	15.6918i	0.0735482	+	0.511539i	0.992979	+	0.118288i	$0.0377406\pi$
$941$	2.25615	+	15.6918i	0.0735482	+	0.511539i	−0.919431	+	0.393251i	$0.871350\pi$
$942$		−	6.43511i		−	0.209667i
$943$	−4.02748	+	1.56120i	−0.131153	+	0.0508395i
$944$		−	24.8158i		−	0.807687i
$945$	−4.57999	+	1.14585i	−0.148987	+	0.0372746i
$946$	−2.95676	+	6.47440i	−0.0961325	+	0.210501i
$947$	54.7477	−	16.0754i	1.77906	−	0.522380i	0.783922	−	0.620859i	$-0.213216\pi$
$947$	54.7477	−	16.0754i	1.77906	−	0.522380i	0.995139	+	0.0984796i	$0.0313979\pi$
$948$	−15.2590	+	17.6098i	−0.495588	+	0.571939i
$949$	−16.6017	−	4.87471i	−0.538915	−	0.158240i
$950$	−2.94966	+	1.89563i	−0.0956997	+	0.0615025i
$951$	23.8849	−	10.9078i	0.774520	−	0.353711i
$952$	6.97587	+	6.55684i	0.226089	+	0.212508i
$953$	−8.08530	+	12.5810i	−0.261908	+	0.407538i	−0.947156	−	0.320772i	$-0.896058\pi$
$953$	−8.08530	+	12.5810i	−0.261908	+	0.407538i	0.685248	+	0.728310i	$0.259694\pi$
$954$	3.22532	+	0.463731i	0.104424	+	0.0150139i
$955$	2.97554	+	0.427818i	0.0962861	+	0.0138439i
$956$	−33.2824	−	21.3893i	−1.07643	−	0.691779i
$957$	−0.941710	−	1.08679i	−0.0304412	−	0.0351310i
$958$	4.86971	+	10.6632i	0.157333	+	0.344511i
$959$	24.8452	+	31.1323i	0.802294	+	1.00531i
$960$	2.45038	−	8.34524i	0.0790858	−	0.269341i
$961$	12.3727	−	14.2788i	0.399118	−	0.460607i
$962$	−0.820677	+	0.240973i	−0.0264597	+	0.00776927i
$963$	−13.1144	−	5.98915i	−0.422606	−	0.192998i
$964$	−1.85473	−	12.8999i	−0.0597367	−	0.415478i
$965$	−23.0240			−0.741170
$966$	4.69183	+	0.466211i	0.150957	+	0.0150001i
$967$	−14.4238			−0.463838			−0.231919	−	0.972735i	$-0.574500\pi$
$967$	−14.4238			−0.463838			−0.231919	+	0.972735i	$0.574500\pi$
$968$	0.914729	+	6.36208i	0.0294005	+	0.204485i
$969$	−11.9190	−	5.44321i	−0.382892	−	0.174861i
$970$	−0.0254397	+	0.00746978i	−0.000816820	+	0.000239840i
$971$	33.7872	−	38.9925i	1.08428	−	1.25133i	0.118229	−	0.992986i	$-0.462278\pi$
$971$	33.7872	−	38.9925i	1.08428	−	1.25133i	0.966054	−	0.258342i	$-0.0831761\pi$
$972$	−0.524564	+	1.78650i	−0.0168254	+	0.0573020i
$973$	0.0951572	+	0.119237i	0.00305060	+	0.00382255i
$974$	−0.708535	−	1.55147i	−0.0227029	−	0.0497125i
$975$	2.85882	+	3.29926i	0.0915556	+	0.105661i
$976$	29.6770	+	19.0722i	0.949937	+	0.610487i
$977$	−56.4151	−	8.11127i	−1.80488	−	0.259502i	−0.843975	−	0.536383i	$-0.819790\pi$
$977$	−56.4151	−	8.11127i	−1.80488	−	0.259502i	−0.960904	+	0.276880i	$0.910699\pi$
$978$	−0.0523913	−	0.00753273i	−0.00167529	−	0.000240870i
$979$	−9.95069	+	15.4836i	−0.318025	+	0.494857i
$980$	−18.4853	−	14.1136i	−0.590491	−	0.450843i
$981$	−17.4851	+	7.98519i	−0.558257	+	0.254947i
$982$	8.16164	−	5.24517i	0.260449	−	0.167380i
$983$	3.89741	+	1.14438i	0.124308	+	0.0365001i	0.343295	−	0.939228i	$-0.388457\pi$
$983$	3.89741	+	1.14438i	0.124308	+	0.0365001i	−0.218987	+	0.975728i	$0.570275\pi$
$984$	−0.846414	+	0.976814i	−0.0269827	+	0.0311397i
$985$	−21.8563	+	6.41759i	−0.696399	+	0.204481i
$986$	−0.219188	+	0.479955i	−0.00698038	+	0.0152849i
$987$	−2.78185	−	11.1191i	−0.0885474	−	0.353925i
$988$			23.2615i			0.740047i
$989$	−28.5194	+	21.9247i	−0.906865	+	0.697165i
$990$		−	1.69325i		−	0.0538150i
$991$	4.65331	+	32.3645i	0.147817	+	1.02809i	0.919783	+	0.392428i	$0.128365\pi$
$991$	4.65331	+	32.3645i	0.147817	+	1.02809i	−0.771966	+	0.635664i	$0.780726\pi$
$992$	26.0587	+	11.9006i	0.827364	+	0.377844i
$993$	7.34793	+	25.0248i	0.233180	+	0.794137i
$994$	−3.20855	+	4.57470i	−0.101769	+	0.145101i
$995$	−0.990736	−	0.290906i	−0.0314085	−	0.00922236i
$996$	−16.4562	−	25.6064i	−0.521435	−	0.811368i
$997$	−33.5013	+	15.2995i	−1.06100	+	0.484541i	−0.867952	−	0.496648i	$-0.834564\pi$
$997$	−33.5013	+	15.2995i	−1.06100	+	0.484541i	−0.193046	+	0.981190i	$0.561837\pi$
$998$	10.2032	+	11.7751i	0.322976	+	0.372734i
$999$	0.805431	+	0.517619i	0.0254827	+	0.0163767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.181.16	yes	320
7.6	odd	2	inner	483.2.r.a.181.15	✓	320
23.15	odd	22	inner	483.2.r.a.475.15	yes	320
161.153	even	22	inner	483.2.r.a.475.16	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.181.15	✓	320	7.6	odd	2	inner
483.2.r.a.181.16	yes	320	1.1	even	1	trivial
483.2.r.a.475.15	yes	320	23.15	odd	22	inner
483.2.r.a.475.16	yes	320	161.153	even	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.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0528826 - 0.367807i) q^{2} +(0.909632 + 0.415415i) q^{3} +(1.78650 - 0.524564i) q^{4} +(1.16855 - 1.34858i) q^{5} +(0.104689 - 0.356537i) q^{6} +(-2.06795 + 1.65033i) q^{7} +(-0.596140 - 1.30537i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.0528826 - 0.367807i) q^{2} +(0.909632 + 0.415415i) q^{3} +(1.78650 - 0.524564i) q^{4} +(1.16855 - 1.34858i) q^{5} +(0.104689 - 0.356537i) q^{6} +(-2.06795 + 1.65033i) q^{7} +(-0.596140 - 1.30537i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-0.557813 - 0.358485i) q^{10} +(2.52764 + 0.363420i) q^{11} +(1.84297 + 0.264979i) q^{12} +(1.29979 - 2.02252i) q^{13} +(0.716362 + 0.673331i) q^{14} +(1.62317 - 0.741278i) q^{15} +(2.68410 - 1.72497i) q^{16} +(2.41938 + 0.710394i) q^{17} +(0.243339 - 0.280828i) q^{18} +(-4.98600 + 1.46402i) q^{19} +(1.38020 - 3.02222i) q^{20} +(-2.56664 + 0.642140i) q^{21} -0.948903i q^{22} +(2.24432 - 4.23828i) q^{23} -1.43505i q^{24} +(0.258418 + 1.79734i) q^{25} +(-0.812633 - 0.371117i) q^{26} +(0.281733 + 0.959493i) q^{27} +(-2.82868 + 4.03309i) q^{28} +(-0.540320 - 0.158652i) q^{29} +(-0.358485 - 0.557813i) q^{30} +(-6.42522 + 2.93430i) q^{31} +(-2.65591 - 3.06508i) q^{32} +(2.14825 + 1.38060i) q^{33} +(0.133345 - 0.927433i) q^{34} +(-0.190895 + 4.71729i) q^{35} +(1.56635 + 1.00663i) q^{36} +(0.723568 - 0.626975i) q^{37} +(0.802150 + 1.75646i) q^{38} +(2.02252 - 1.29979i) q^{39} +(-2.45701 - 0.721444i) q^{40} +(-0.680684 - 0.589816i) q^{41} +(0.371914 + 0.910071i) q^{42} +(-6.82303 - 3.11597i) q^{43} +(4.70627 - 0.676660i) q^{44} +1.78443 q^{45} +(-1.67755 - 0.601344i) q^{46} +4.33216i q^{47} +(3.15812 - 0.454069i) q^{48} +(1.55280 - 6.82560i) q^{49} +(0.647406 - 0.190096i) q^{50} +(1.90564 + 1.65124i) q^{51} +(1.26114 - 4.29506i) q^{52} +(4.74091 + 7.37701i) q^{53} +(0.338009 - 0.154364i) q^{54} +(3.44378 - 2.98405i) q^{55} +(3.38707 + 1.71560i) q^{56} +(-5.14360 - 0.739538i) q^{57} +(-0.0297799 + 0.207124i) q^{58} +(4.20500 - 6.54311i) q^{59} +(2.51095 - 2.17575i) q^{60} +(4.59307 + 10.0574i) q^{61} +(1.41904 + 2.20807i) q^{62} +(-2.60146 - 0.482111i) q^{63} +(3.19188 - 3.68363i) q^{64} +(-1.20865 - 4.11630i) q^{65} +(0.394189 - 0.863153i) q^{66} +(-9.43925 + 1.35716i) q^{67} +4.69487 q^{68} +(3.80215 - 2.92295i) q^{69} +(1.74515 - 0.179250i) q^{70} +(0.808859 + 5.62574i) q^{71} +(0.596140 - 1.30537i) q^{72} +(-2.02760 - 6.90538i) q^{73} +(-0.268870 - 0.232977i) q^{74} +(-0.511575 + 1.74226i) q^{75} +(-8.13951 + 5.23095i) q^{76} +(-5.82679 + 3.41992i) q^{77} +(-0.585030 - 0.675160i) q^{78} +(-6.76587 + 10.5279i) q^{79} +(0.810253 - 5.63544i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-0.180942 + 0.281551i) q^{82} +(-10.7055 - 12.3548i) q^{83} +(-4.24847 + 2.49355i) q^{84} +(3.78520 - 2.43260i) q^{85} +(-0.785257 + 2.67434i) q^{86} +(-0.425586 - 0.368773i) q^{87} +(-1.03243 - 3.51615i) q^{88} +(-2.99411 + 6.55618i) q^{89} +(-0.0943653 - 0.656325i) q^{90} +(0.649926 + 6.32756i) q^{91} +(1.78623 - 8.74898i) q^{92} -7.06354 q^{93} +(1.59340 - 0.229096i) q^{94} +(-3.85205 + 8.43480i) q^{95} +(-1.14262 - 3.89140i) q^{96} +(0.0261853 - 0.0302194i) q^{97} +(-2.59262 - 0.210176i) q^{98} +(1.38060 + 2.14825i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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