LMFDB - Embedded newform 483.2.u.a.113.9

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			113.9
Character	$\chi$	$=$	483.113
Dual form			483.2.u.a.218.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.07812 + 1.67759i) q^{2} +(1.58707 - 0.693695i) q^{3} +(-0.821124 - 1.79801i) q^{4} +(-1.95772 - 0.574839i) q^{5} +(-0.547316 + 3.41033i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-0.0461173 - 0.00663067i) q^{8} +(2.03757 - 2.20188i) q^{9} +(3.07500 - 2.66450i) q^{10} +(-3.31421 + 2.12992i) q^{11} +(-2.55045 - 2.28396i) q^{12} +(-3.27962 - 3.78489i) q^{13} +(1.91337 - 0.561817i) q^{14} +(-3.50580 + 0.445753i) q^{15} +(2.64969 - 3.05790i) q^{16} +(-0.964591 + 2.11216i) q^{17} +(1.49710 + 5.79210i) q^{18} +(-1.91527 + 0.874676i) q^{19} +(0.573966 + 3.99202i) q^{20} +(-1.65370 - 0.515049i) q^{21} -7.85618i q^{22} +(3.25253 - 3.52435i) q^{23} +(-0.0777911 + 0.0214680i) q^{24} +(-0.704035 - 0.452456i) q^{25} +(9.88530 - 1.42129i) q^{26} +(1.70633 - 4.90800i) q^{27} +(-0.556883 + 1.89657i) q^{28} +(-9.41051 - 4.29763i) q^{29} +(3.03188 - 6.36186i) q^{30} +(0.354302 - 2.46423i) q^{31} +(2.24696 + 7.65245i) q^{32} +(-3.78237 + 5.67938i) q^{33} +(-2.50338 - 3.89534i) q^{34} +(1.10311 + 1.71647i) q^{35} +(-5.63211 - 1.85556i) q^{36} +(0.623786 + 2.12442i) q^{37} +(0.597549 - 4.15604i) q^{38} +(-7.83055 - 3.73182i) q^{39} +(0.0864733 + 0.0394910i) q^{40} +(-1.97370 + 6.72182i) q^{41} +(2.64692 - 2.21894i) q^{42} +(-3.55611 + 0.511291i) q^{43} +(6.55100 + 4.21007i) q^{44} +(-5.25473 + 3.13940i) q^{45} +(2.40578 + 9.25607i) q^{46} -6.97798i q^{47} +(2.08398 - 6.69117i) q^{48} +(0.142315 + 0.989821i) q^{49} +(1.51807 - 0.693278i) q^{50} +(-0.0656770 + 4.02127i) q^{51} +(-4.11229 + 9.00466i) q^{52} +(2.42909 - 2.80331i) q^{53} +(6.39396 + 8.15393i) q^{54} +(7.71267 - 2.26464i) q^{55} +(0.0305110 + 0.0352116i) q^{56} +(-2.43291 + 2.71679i) q^{57} +(17.3553 - 11.1536i) q^{58} +(4.83586 - 4.19029i) q^{59} +(3.68017 + 5.93745i) q^{60} +(11.3602 + 1.63335i) q^{61} +(3.75197 + 3.25110i) q^{62} +(-2.98182 + 0.329746i) q^{63} +(-7.49557 - 2.20090i) q^{64} +(4.24489 + 9.29501i) q^{65} +(-5.44980 - 12.4683i) q^{66} +(1.68271 - 2.61835i) q^{67} +4.58973 q^{68} +(2.71717 - 7.84965i) q^{69} -4.06881 q^{70} +(-7.74611 + 12.0532i) q^{71} +(-0.108567 + 0.0880345i) q^{72} +(2.63075 + 5.76055i) q^{73} +(-4.23641 - 1.24392i) q^{74} +(-1.43122 - 0.229693i) q^{75} +(3.14535 + 2.72547i) q^{76} +(3.89951 + 0.560666i) q^{77} +(14.7027 - 9.11307i) q^{78} +(-3.71086 + 3.21547i) q^{79} +(-6.94515 + 4.46337i) q^{80} +(-0.696585 - 8.97300i) q^{81} +(-9.14854 - 10.5580i) q^{82} +(11.3963 - 3.34627i) q^{83} +(0.431829 + 3.39629i) q^{84} +(3.10255 - 3.58053i) q^{85} +(2.97617 - 6.51691i) q^{86} +(-17.9164 - 0.292617i) q^{87} +(0.166966 - 0.0762506i) q^{88} +(-0.675274 - 4.69663i) q^{89} +(0.398614 - 12.1999i) q^{90} +5.00812i q^{91} +(-9.00755 - 2.95417i) q^{92} +(-1.14712 - 4.15667i) q^{93} +(11.7062 + 7.52310i) q^{94} +(4.25237 - 0.611398i) q^{95} +(8.87455 + 10.5863i) q^{96} +(-3.95894 + 13.4829i) q^{97} +(-1.81394 - 0.828400i) q^{98} +(-2.06313 + 11.6374i) 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 $

$2$	−1.07812	+	1.67759i	−0.762345	+	1.18623i	0.215418	+	0.976522i	$0.430889\pi$
$2$	−1.07812	+	1.67759i	−0.762345	+	1.18623i	−0.977764	+	0.209711i	$0.932748\pi$
$3$	1.58707	−	0.693695i	0.916295	−	0.400505i
$3$	1.58707	−	0.693695i	0.916295	−	0.400505i
$4$	−0.821124	−	1.79801i	−0.410562	−	0.899006i
$5$	−1.95772	−	0.574839i	−0.875520	−	0.257076i	−0.187058	−	0.982349i	$-0.559895\pi$
$5$	−1.95772	−	0.574839i	−0.875520	−	0.257076i	−0.688461	+	0.725273i	$0.741713\pi$
$6$	−0.547316	+	3.41033i	−0.223441	+	1.39226i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$8$	−0.0461173	−	0.00663067i	−0.0163049	−	0.00234430i
$9$	2.03757	−	2.20188i	0.679191	−	0.733961i
$10$	3.07500	−	2.66450i	0.972400	−	0.842589i
$11$	−3.31421	+	2.12992i	−0.999273	+	0.642194i	−0.934596	−	0.355712i	$-0.884238\pi$
$11$	−3.31421	+	2.12992i	−0.999273	+	0.642194i	−0.0646778	+	0.997906i	$0.520602\pi$
$12$	−2.55045	−	2.28396i	−0.736252	−	0.659322i
$13$	−3.27962	−	3.78489i	−0.909604	−	1.04974i	−0.998557	−	0.0537031i	$-0.982898\pi$
$13$	−3.27962	−	3.78489i	−0.909604	−	1.04974i	0.0889530	−	0.996036i	$-0.471648\pi$
$14$	1.91337	−	0.561817i	0.511371	−	0.150152i
$15$	−3.50580	+	0.445753i	−0.905194	+	0.115093i
$16$	2.64969	−	3.05790i	0.662421	−	0.764475i
$17$	−0.964591	+	2.11216i	−0.233948	+	0.512274i	−0.989799	−	0.142469i	$-0.954496\pi$
$17$	−0.964591	+	2.11216i	−0.233948	+	0.512274i	0.755852	+	0.654743i	$0.227223\pi$
$18$	1.49710	+	5.79210i	0.352870	+	1.36521i
$19$	−1.91527	+	0.874676i	−0.439394	+	0.200664i	−0.622814	−	0.782370i	$-0.714011\pi$
$19$	−1.91527	+	0.874676i	−0.439394	+	0.200664i	0.183420	+	0.983035i	$0.441283\pi$
$20$	0.573966	+	3.99202i	0.128343	+	0.892643i
$21$	−1.65370	−	0.515049i	−0.360867	−	0.112393i
$22$		−	7.85618i		−	1.67494i
$23$	3.25253	−	3.52435i	0.678200	−	0.734877i
$23$	3.25253	−	3.52435i	0.678200	−	0.734877i
$24$	−0.0777911	+	0.0214680i	−0.0158790	+	0.00438215i
$25$	−0.704035	−	0.452456i	−0.140807	−	0.0904912i
$26$	9.88530	−	1.42129i	1.93867	−	0.278738i
$27$	1.70633	−	4.90800i	0.328384	−	0.944544i
$28$	−0.556883	+	1.89657i	−0.105241	+	0.358418i
$29$	−9.41051	−	4.29763i	−1.74749	−	0.798051i	−0.989279	−	0.146039i	$-0.953348\pi$
$29$	−9.41051	−	4.29763i	−1.74749	−	0.798051i	−0.758208	−	0.652012i	$-0.773925\pi$
$30$	3.03188	−	6.36186i	0.553543	−	1.16151i
$31$	0.354302	−	2.46423i	0.0636346	−	0.442588i	−0.932950	−	0.360007i	$-0.882774\pi$
$31$	0.354302	−	2.46423i	0.0636346	−	0.442588i	0.996584	−	0.0825815i	$-0.0263165\pi$
$32$	2.24696	+	7.65245i	0.397210	+	1.35277i
$33$	−3.78237	+	5.67938i	−0.658427	+	0.988653i
$34$	−2.50338	−	3.89534i	−0.429327	−	0.668046i
$35$	1.10311	+	1.71647i	0.186459	+	0.290136i
$36$	−5.63211	−	1.85556i	−0.938686	−	0.309260i
$37$	0.623786	+	2.12442i	0.102550	+	0.349252i	0.994743	−	0.102401i	$-0.0326525\pi$
$37$	0.623786	+	2.12442i	0.102550	+	0.349252i	−0.892193	+	0.451653i	$0.850834\pi$
$38$	0.597549	−	4.15604i	0.0969352	−	0.674199i
$39$	−7.83055	−	3.73182i	−1.25389	−	0.597569i
$40$	0.0864733	+	0.0394910i	0.0136726	+	0.00624408i
$41$	−1.97370	+	6.72182i	−0.308241	+	1.04977i	0.649074	+	0.760725i	$0.275156\pi$
$41$	−1.97370	+	6.72182i	−0.308241	+	1.04977i	−0.957315	+	0.289047i	$0.906662\pi$
$42$	2.64692	−	2.21894i	0.408429	−	0.342390i
$43$	−3.55611	+	0.511291i	−0.542302	+	0.0779712i	−0.408022	−	0.912972i	$-0.633781\pi$
$43$	−3.55611	+	0.511291i	−0.542302	+	0.0779712i	−0.134280	+	0.990943i	$0.542872\pi$
$44$	6.55100	+	4.21007i	0.987600	+	0.634692i
$45$	−5.25473	+	3.13940i	−0.783329	+	0.467994i
$46$	2.40578	+	9.25607i	0.354712	+	1.36473i
$47$		−	6.97798i		−	1.01784i	−0.860813	−	0.508922i	$-0.830044\pi$
$47$		−	6.97798i		−	1.01784i	0.860813	−	0.508922i	$-0.169956\pi$
$48$	2.08398	−	6.69117i	0.300797	−	0.965788i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	1.51807	−	0.693278i	0.214687	−	0.0980444i
$51$	−0.0656770	+	4.02127i	−0.00919663	+	0.563091i
$52$	−4.11229	+	9.00466i	−0.570272	+	1.24872i
$53$	2.42909	−	2.80331i	0.333661	−	0.385065i	−0.563983	−	0.825786i	$-0.690732\pi$
$53$	2.42909	−	2.80331i	0.333661	−	0.385065i	0.897644	+	0.440721i	$0.145277\pi$
$54$	6.39396	+	8.15393i	0.870107	+	1.10961i
$55$	7.71267	−	2.26464i	1.03998	−	0.305364i
$56$	0.0305110	+	0.0352116i	0.00407720	+	0.00470534i
$57$	−2.43291	+	2.71679i	−0.322247	+	0.359847i
$58$	17.3553	−	11.1536i	2.27886	−	1.46454i
$59$	4.83586	−	4.19029i	0.629575	−	0.545530i	−0.280563	−	0.959836i	$-0.590521\pi$
$59$	4.83586	−	4.19029i	0.629575	−	0.545530i	0.910138	+	0.414306i	$0.135976\pi$
$60$	3.68017	+	5.93745i	0.475108	+	0.766522i
$61$	11.3602	+	1.63335i	1.45453	+	0.209129i	0.823802	−	0.566878i	$-0.191849\pi$
$61$	11.3602	+	1.63335i	1.45453	+	0.209129i	0.630724	+	0.776007i	$0.282758\pi$
$62$	3.75197	+	3.25110i	0.476501	+	0.412890i
$63$	−2.98182	+	0.329746i	−0.375674	+	0.0415441i
$64$	−7.49557	−	2.20090i	−0.936946	−	0.275112i
$65$	4.24489	+	9.29501i	0.526514	+	1.15290i
$66$	−5.44980	−	12.4683i	−0.670824	−	1.53474i
$67$	1.68271	−	2.61835i	0.205576	−	0.319882i	−0.723122	−	0.690721i	$-0.757293\pi$
$67$	1.68271	−	2.61835i	0.205576	−	0.319882i	0.928697	+	0.370839i	$0.120930\pi$
$68$	4.58973			0.556587
$69$	2.71717	−	7.84965i	0.327109	−	0.944987i
$70$	−4.06881			−0.486315
$71$	−7.74611	+	12.0532i	−0.919294	+	1.43045i	−0.0167455	+	0.999860i	$0.505331\pi$
$71$	−7.74611	+	12.0532i	−0.919294	+	1.43045i	−0.902548	+	0.430589i	$0.858306\pi$
$72$	−0.108567	+	0.0880345i	−0.0127948	+	0.0103750i
$73$	2.63075	+	5.76055i	0.307907	+	0.674221i	0.998812	−	0.0487236i	$-0.0155153\pi$
$73$	2.63075	+	5.76055i	0.307907	+	0.674221i	−0.690906	+	0.722945i	$0.742788\pi$
$74$	−4.23641	−	1.24392i	−0.492473	−	0.144603i
$75$	−1.43122	−	0.229693i	−0.165263	−	0.0265226i
$76$	3.14535	+	2.72547i	0.360797	+	0.312632i
$77$	3.89951	+	0.560666i	0.444391	+	0.0638938i
$78$	14.7027	−	9.11307i	1.66475	−	1.03185i
$79$	−3.71086	+	3.21547i	−0.417504	+	0.361769i	−0.838135	−	0.545463i	$-0.816354\pi$
$79$	−3.71086	+	3.21547i	−0.417504	+	0.361769i	0.420631	+	0.907232i	$0.361809\pi$
$80$	−6.94515	+	4.46337i	−0.776491	+	0.499020i
$81$	−0.696585	−	8.97300i	−0.0773984	−	0.997000i
$82$	−9.14854	−	10.5580i	−1.01029	−	1.16593i
$83$	11.3963	−	3.34627i	1.25091	−	0.367301i	0.411807	−	0.911271i	$-0.364898\pi$
$83$	11.3963	−	3.34627i	1.25091	−	0.367301i	0.839105	+	0.543970i	$0.183080\pi$
$84$	0.431829	+	3.39629i	0.0471164	+	0.370566i
$85$	3.10255	−	3.58053i	0.336519	−	0.388363i
$86$	2.97617	−	6.51691i	0.320929	−	0.702737i
$87$	−17.9164	−	0.292617i	−1.92084	−	0.0313719i
$88$	0.166966	−	0.0762506i	0.0177986	−	0.00812834i
$89$	−0.675274	−	4.69663i	−0.0715789	−	0.497842i	−0.993800	−	0.111180i	$-0.964537\pi$
$89$	−0.675274	−	4.69663i	−0.0715789	−	0.497842i	0.922221	−	0.386662i	$-0.126372\pi$
$90$	0.398614	−	12.1999i	0.0420176	−	1.28598i
$91$			5.00812i			0.524994i
$92$	−9.00755	−	2.95417i	−0.939102	−	0.307993i
$93$	−1.14712	−	4.15667i	−0.118951	−	0.431027i
$94$	11.7062	+	7.52310i	1.20740	+	0.775948i
$95$	4.25237	−	0.611398i	0.436284	−	0.0627282i
$96$	8.87455	+	10.5863i	0.905755	+	1.08046i
$97$	−3.95894	+	13.4829i	−0.401969	+	1.36898i	0.471399	+	0.881920i	$0.343749\pi$
$97$	−3.95894	+	13.4829i	−0.401969	+	1.36898i	−0.873368	+	0.487061i	$0.838069\pi$
$98$	−1.81394	−	0.828400i	−0.183236	−	0.0836810i
$99$	−2.06313	+	11.6374i	−0.207352	+	1.16960i
$100$	−0.235421	+	1.63739i	−0.0235421	+	0.163739i
$101$	−2.94293	−	10.0227i	−0.292833	−	0.997296i	−0.966158	−	0.257950i	$-0.916953\pi$
$101$	−2.94293	−	10.0227i	−0.292833	−	0.997296i	0.673326	−	0.739346i	$-0.264865\pi$
$102$	−6.67522	−	4.44559i	−0.660946	−	0.440179i
$103$	8.63200	+	13.4316i	0.850536	+	1.32346i	0.944711	+	0.327904i	$0.106342\pi$
$103$	8.63200	+	13.4316i	0.850536	+	1.32346i	−0.0941751	+	0.995556i	$0.530021\pi$
$104$	0.126151	+	0.196295i	0.0123701	+	0.0192483i
$105$	2.94141	+	1.95893i	0.287053	+	0.191172i
$106$	2.08396	+	7.09731i	0.202412	+	0.689351i
$107$	0.930543	−	6.47207i	0.0899590	−	0.625679i	−0.894104	−	0.447859i	$-0.852187\pi$
$107$	0.930543	−	6.47207i	0.0899590	−	0.625679i	0.984063	−	0.177819i	$-0.0569043\pi$
$108$	−10.2257	+	0.962068i	−0.983973	+	0.0925750i
$109$	−12.1313	−	5.54020i	−1.16197	−	0.530655i	−0.261344	−	0.965246i	$-0.584166\pi$
$109$	−12.1313	−	5.54020i	−1.16197	−	0.530655i	−0.900628	+	0.434591i	$0.856893\pi$
$110$	−4.51604	+	15.3802i	−0.430587	+	1.46645i
$111$	2.46369	+	2.93888i	0.233843	+	0.278946i
$112$	−4.00500	+	0.575832i	−0.378437	+	0.0544110i
$113$	−10.6364	−	6.83559i	−1.00059	−	0.643038i	−0.0656464	−	0.997843i	$-0.520911\pi$
$113$	−10.6364	−	6.83559i	−1.00059	−	0.643038i	−0.934940	+	0.354805i	$0.884547\pi$
$114$	−1.93468	−	7.01044i	−0.181199	−	0.656588i
$115$	−8.39349	+	5.03001i	−0.782697	+	0.469050i
$116$			20.4491i			1.89865i
$117$	−15.0164	−	0.490637i	−1.38826	−	0.0453594i
$118$	1.81595	+	12.6302i	0.167172	+	1.16270i
$119$	2.11216	−	0.964591i	0.193621	−	0.0884239i
$120$	0.164634	+	0.00268887i	0.0150289	+	0.000245459i
$121$	1.87791	−	4.11205i	0.170719	−	0.373823i
$122$	−14.9877	+	17.2968i	−1.35693	+	1.56598i
$123$	1.53049	+	12.0371i	0.138000	+	1.08535i
$124$	−4.72163	+	1.38640i	−0.424015	+	0.124502i
$125$	7.79901	+	9.00054i	0.697564	+	0.805032i
$126$	2.66158	−	5.35777i	0.237113	−	0.477308i
$127$	−8.75277	+	5.62506i	−0.776683	+	0.499144i	−0.867931	−	0.496684i	$-0.834551\pi$
$127$	−8.75277	+	5.62506i	−0.776683	+	0.499144i	0.0912484	+	0.995828i	$0.470914\pi$
$128$	−0.281673	+	0.244071i	−0.0248966	+	0.0215731i
$129$	−5.28911	+	3.27831i	−0.465680	+	0.288639i
$130$	−20.1697	−	2.89996i	−1.76900	−	0.254343i
$131$	−4.90847	−	4.25322i	−0.428855	−	0.371605i	0.413521	−	0.910494i	$-0.364299\pi$
$131$	−4.90847	−	4.25322i	−0.428855	−	0.371605i	−0.842377	+	0.538889i	$0.818844\pi$
$132$	13.3174	+	2.13727i	1.15913	+	0.186026i
$133$	2.02026	+	0.593201i	0.175179	+	0.0514371i
$134$	2.57834	+	5.64578i	0.222735	+	0.487721i
$135$	−6.16183	+	8.62762i	−0.530326	+	0.742547i
$136$	0.0584894	−	0.0910113i	0.00501542	−	0.00780415i
$137$	−14.1447			−1.20846			−0.604231	−	0.796809i	$-0.706520\pi$
$137$	−14.1447			−1.20846			−0.604231	+	0.796809i	$0.706520\pi$
$138$	10.2390	+	13.0211i	0.871604	+	1.10843i
$139$	−17.7832			−1.50835			−0.754175	−	0.656673i	$-0.771963\pi$
$139$	−17.7832			−1.50835			−0.754175	+	0.656673i	$0.771963\pi$
$140$	2.18044	−	3.39283i	0.184281	−	0.286747i
$141$	−4.84059	−	11.0745i	−0.407652	−	0.932644i
$142$	−11.8690	−	25.9895i	−0.996026	−	2.18099i
$143$	18.9309	+	5.55861i	1.58308	+	0.464834i
$144$	−1.33421	−	12.0650i	−0.111184	−	1.00542i
$145$	15.9527	+	13.8231i	1.32480	+	1.14795i
$146$	−12.5001	−	1.79724i	−1.03451	−	0.148741i
$147$	0.912498	+	1.47219i	0.0752616	+	0.121424i
$148$	3.30752	−	2.86599i	0.271877	−	0.235583i
$149$	5.66513	−	3.64076i	0.464106	−	0.298263i	−0.287613	−	0.957747i	$-0.592862\pi$
$149$	5.66513	−	3.64076i	0.464106	−	0.298263i	0.751719	+	0.659484i	$0.229225\pi$
$150$	1.92835	−	2.15336i	0.157449	−	0.175821i
$151$	−6.22379	−	7.18264i	−0.506485	−	0.584515i	0.443710	−	0.896170i	$-0.353662\pi$
$151$	−6.22379	−	7.18264i	−0.506485	−	0.584515i	−0.950195	+	0.311656i	$0.899116\pi$
$152$	0.0941270	−	0.0276382i	0.00763471	−	0.00224175i
$153$	2.68530	+	6.42760i	0.217094	+	0.519640i
$154$	−5.14471	+	5.93731i	−0.414572	+	0.478442i
$155$	−2.11016	+	4.62060i	−0.169492	+	0.371136i
$156$	−0.279998	+	17.1437i	−0.0224178	+	1.37259i
$157$	17.2378	−	7.87223i	1.37572	−	0.628272i	0.416039	−	0.909347i	$-0.363418\pi$
$157$	17.2378	−	7.87223i	1.37572	−	0.628272i	0.959686	+	0.281075i	$0.0906908\pi$
$158$	−1.39349	−	9.69194i	−0.110860	−	0.771050i
$159$	1.91048	−	6.13410i	0.151511	−	0.486466i
$160$		−	16.2730i		−	1.28649i
$161$	−4.76606	+	0.533567i	−0.375618	+	0.0420510i
$162$	15.8040	+	8.50538i	1.24168	+	0.668246i
$163$	5.66759	+	3.64234i	0.443920	+	0.285290i	0.743443	−	0.668799i	$-0.233191\pi$
$163$	5.66759	+	3.64234i	0.443920	+	0.285290i	−0.299524	+	0.954089i	$0.596828\pi$
$164$	13.7066	−	1.97071i	1.07030	−	0.153886i
$165$	10.6696	−	8.94438i	0.830624	−	0.696319i
$166$	−6.67297	+	22.7260i	−0.517923	+	1.76388i
$167$	2.38105	+	1.08739i	0.184251	+	0.0841448i	0.505405	−	0.862882i	$-0.331343\pi$
$167$	2.38105	+	1.08739i	0.184251	+	0.0841448i	−0.321153	+	0.947027i	$0.604070\pi$
$168$	0.0728491	+	0.0347178i	0.00562043	+	0.00267854i
$169$	−1.71935	+	11.9583i	−0.132258	+	0.919872i
$170$	2.66173	+	9.06504i	0.204146	+	0.695257i
$171$	−1.97658	+	5.99943i	−0.151153	+	0.458788i
$172$	3.83931	+	5.97409i	0.292745	+	0.455520i
$173$	−0.285707	−	0.444569i	−0.0217219	−	0.0337999i	0.830223	−	0.557432i	$-0.188213\pi$
$173$	−0.285707	−	0.444569i	−0.0217219	−	0.0337999i	−0.851945	+	0.523632i	$0.824577\pi$
$174$	19.8069	−	29.7408i	1.50156	−	2.25464i
$175$	0.235779	+	0.802988i	0.0178232	+	0.0607002i
$176$	−2.26856	+	15.7781i	−0.170999	+	1.18932i
$177$	4.76805	−	10.0049i	0.358389	−	0.752014i
$178$	8.60703	+	3.93070i	0.645124	+	0.294618i
$179$	1.75878	−	5.98984i	0.131457	−	0.447702i	−0.867287	−	0.497809i	$-0.834138\pi$
$179$	1.75878	−	5.98984i	0.131457	−	0.447702i	0.998744	+	0.0501070i	$0.0159562\pi$
$180$	9.95946	+	6.87023i	0.742334	+	0.512077i
$181$	6.47822	−	0.931428i	0.481523	−	0.0692325i	0.102721	−	0.994710i	$-0.467245\pi$
$181$	6.47822	−	0.931428i	0.481523	−	0.0692325i	0.378802	+	0.925478i	$0.376336\pi$
$182$	−8.40156	−	5.39935i	−0.622765	−	0.400227i
$183$	19.1625	−	5.28828i	1.41653	−	0.390921i
$184$	−0.173367	+	0.140967i	−0.0127808	+	0.0103922i
$185$		−	4.51760i		−	0.332140i
$186$	8.20991	+	2.55700i	0.601980	+	0.187488i
$187$	−1.30186	−	9.05464i	−0.0952015	−	0.662141i
$188$	−12.5465	+	5.72979i	−0.915047	+	0.417888i
$189$	−4.50361	+	2.59181i	−0.327590	+	0.188526i
$190$	−3.55889	+	7.79288i	−0.258189	+	0.565355i
$191$	−1.57583	+	1.81860i	−0.114023	+	0.131590i	−0.809892	−	0.586580i	$-0.800474\pi$
$191$	−1.57583	+	1.81860i	−0.114023	+	0.131590i	0.695869	+	0.718169i	$0.255020\pi$
$192$	−13.4227	+	1.70666i	−0.968702	+	0.123168i
$193$	−14.7952	+	4.34427i	−1.06498	+	0.312707i	−0.766856	−	0.641819i	$-0.778180\pi$
$193$	−14.7952	+	4.34427i	−1.06498	+	0.312707i	−0.298127	+	0.954526i	$0.596362\pi$
$194$	−18.3505	−	21.1776i	−1.31749	−	1.52047i
$195$	13.1848	+	11.8072i	0.944185	+	0.845528i
$196$	1.66285	−	1.06865i	0.118775	−	0.0763321i
$197$	18.8558	−	16.3387i	1.34342	−	1.16408i	0.371594	−	0.928395i	$-0.378811\pi$
$197$	18.8558	−	16.3387i	1.34342	−	1.16408i	0.971829	−	0.235687i	$-0.0757340\pi$
$198$	−17.2984	−	16.0076i	−1.22934	−	1.13761i
$199$	−0.930788	−	0.133827i	−0.0659818	−	0.00948675i	0.109245	−	0.994015i	$-0.465157\pi$
$199$	−0.930788	−	0.133827i	−0.0659818	−	0.00948675i	−0.175227	+	0.984528i	$0.556066\pi$
$200$	0.0294681	+	0.0255343i	0.00208371	+	0.00180555i
$201$	0.854241	−	5.32279i	0.0602535	−	0.375440i
$202$	19.9868	+	5.86865i	1.40626	+	0.412917i
$203$	4.29763	+	9.41051i	0.301635	+	0.660488i
$204$	7.28422	−	3.18388i	0.509998	−	0.222916i
$205$	7.72792	−	12.0249i	0.539742	−	0.839854i
$206$	−31.8391			−2.21833
$207$	−1.13292	−	14.3428i	−0.0787437	−	0.996895i
$208$	−20.2638			−1.40504
$209$	4.48464	−	6.97824i	0.310209	−	0.482695i
$210$	−6.45747	+	2.82251i	−0.445608	+	0.194772i
$211$	−8.53249	−	18.6836i	−0.587401	−	1.28623i	−0.937000	−	0.349330i	$-0.886409\pi$
$211$	−8.53249	−	18.6836i	−0.587401	−	1.28623i	0.349599	−	0.936900i	$-0.386318\pi$
$212$	−7.03497	−	2.06565i	−0.483164	−	0.141870i
$213$	−3.93237	+	24.5027i	−0.269442	+	1.67889i
$214$	9.85422	+	8.53873i	0.673620	+	0.583695i
$215$	7.25578	+	1.04322i	0.494840	+	0.0711473i
$216$	−0.111235	+	0.215030i	−0.00756857	+	0.0146309i
$217$	−1.88149	+	1.63032i	−0.127724	+	0.110673i
$218$	22.3732	−	14.3784i	1.51530	−	0.973826i
$219$	8.17125	+	7.31744i	0.552162	+	0.494467i
$220$	−10.4049	−	12.0079i	−0.701499	−	0.809573i
$221$	11.1578	−	3.27622i	0.750553	−	0.220382i
$222$	−7.58638	+	0.964588i	−0.509164	+	0.0647389i
$223$	9.12603	−	10.5320i	0.611124	−	0.705275i	−0.362872	−	0.931839i	$-0.618204\pi$
$223$	9.12603	−	10.5320i	0.611124	−	0.705275i	0.973996	+	0.226564i	$0.0727492\pi$
$224$	3.31315	−	7.25478i	0.221369	−	0.484731i
$225$	−2.43078	+	0.628291i	−0.162052	+	0.0418861i
$226$	22.9346	−	10.4739i	1.52559	−	0.696712i
$227$	2.00213	+	13.9251i	0.132886	+	0.924244i	0.941766	+	0.336270i	$0.109165\pi$
$227$	2.00213	+	13.9251i	0.132886	+	0.924244i	−0.808879	+	0.587974i	$0.799926\pi$
$228$	6.88254	+	2.14358i	0.455807	+	0.141962i
$229$		−	21.6847i		−	1.43297i	−0.697604	−	0.716483i	$-0.745751\pi$
$229$		−	21.6847i		−	1.43297i	0.697604	−	0.716483i	$-0.254249\pi$
$230$	0.610910	−	19.5037i	0.0402822	−	1.28604i
$231$	6.57773	−	1.81526i	0.432783	−	0.119435i
$232$	0.405491	+	0.260593i	0.0266218	+	0.0171088i
$233$	28.4352	−	4.08836i	1.86285	−	0.267837i	0.883266	−	0.468872i	$-0.155339\pi$
$233$	28.4352	−	4.08836i	1.86285	−	0.267837i	0.979584	+	0.201034i	$0.0644302\pi$
$234$	17.0125	−	24.6623i	1.11214	−	1.61222i
$235$	−4.01122	+	13.6609i	−0.261663	+	0.891142i
$236$	−11.5050	−	5.25417i	−0.748914	−	0.342018i
$237$	−3.65882	+	7.67738i	−0.237666	+	0.498699i
$238$	−0.658975	+	4.58327i	−0.0427150	+	0.297089i
$239$	−4.72877	−	16.1047i	−0.305879	−	1.04173i	−0.958748	−	0.284257i	$-0.908253\pi$
$239$	−4.72877	−	16.1047i	−0.305879	−	1.04173i	0.652869	−	0.757471i	$-0.273565\pi$
$240$	−7.92620	+	11.9015i	−0.511634	+	0.768238i
$241$	6.04221	+	9.40186i	0.389213	+	0.605627i	0.979470	−	0.201588i	$-0.0646102\pi$
$241$	6.04221	+	9.40186i	0.389213	+	0.605627i	−0.590258	+	0.807215i	$0.700974\pi$
$242$	4.87371	+	7.58363i	0.313294	+	0.487494i
$243$	−7.33006	−	13.7576i	−0.470223	−	0.882547i
$244$	−6.39136	−	21.7670i	−0.409165	−	1.39349i
$245$	0.290375	−	2.01960i	0.0185514	−	0.129028i
$246$	−21.8434	−	10.4099i	−1.39268	−	0.663713i
$247$	9.59193	+	4.38049i	0.610320	+	0.278724i
$248$	−0.0326790	+	0.111294i	−0.00207512	+	0.00706720i
$249$	15.7655	−	13.2164i	0.999098	−	0.837552i
$250$	−23.5074	+	3.37986i	−1.48674	+	0.213761i
$251$	−23.3438	−	15.0021i	−1.47345	−	0.946926i	−0.997731	−	0.0673270i	$-0.978553\pi$
$251$	−23.3438	−	15.0021i	−1.47345	−	0.946926i	−0.475715	−	0.879599i	$-0.657811\pi$
$252$	3.04133	+	5.09059i	0.191586	+	0.320677i
$253$	−3.27303	+	18.6081i	−0.205774	+	1.16988i
$254$		−	20.7480i		−	1.30185i
$255$	2.44016	−	7.83478i	0.152809	−	0.490633i
$256$	−2.32930	−	16.2007i	−0.145581	−	1.01254i
$257$	−9.22692	+	4.21379i	−0.575560	+	0.262849i	−0.681857	−	0.731485i	$-0.738828\pi$
$257$	−9.22692	+	4.21379i	−0.575560	+	0.262849i	0.106298	+	0.994334i	$0.466100\pi$
$258$	0.202642	−	12.4073i	0.0126159	−	0.772448i
$259$	0.919773	−	2.01402i	0.0571519	−	0.125145i
$260$	13.2269	−	15.2647i	0.820301	−	0.946677i
$261$	−28.6375	+	11.9641i	−1.77262	+	0.740559i
$262$	12.4271	−	3.64891i	0.767746	−	0.225431i
$263$	−2.41205	−	2.78365i	−0.148733	−	0.171647i	0.676494	−	0.736448i	$-0.263498\pi$
$263$	−2.41205	−	2.78365i	−0.148733	−	0.171647i	−0.825227	+	0.564801i	$0.808953\pi$
$264$	0.212091	−	0.236838i	0.0130533	−	0.0145764i
$265$	−6.36693	+	4.09177i	−0.391117	+	0.251356i
$266$	−3.17323	+	2.74962i	−0.194563	+	0.168590i
$267$	−4.32974	−	6.98544i	−0.264976	−	0.427502i
$268$	−6.08953	−	0.875543i	−0.371978	−	0.0534823i
$269$	16.7393	+	14.5047i	1.02061	+	0.884367i	0.993335	−	0.115261i	$-0.0367703\pi$
$269$	16.7393	+	14.5047i	1.02061	+	0.884367i	0.0272790	+	0.999628i	$0.491316\pi$
$270$	−7.83039	−	19.6386i	−0.476542	−	1.19517i
$271$	−17.9666	−	5.27547i	−1.09139	−	0.320462i	−0.313966	−	0.949434i	$-0.601658\pi$
$271$	−17.9666	−	5.27547i	−1.09139	−	0.320462i	−0.777428	+	0.628972i	$0.783476\pi$
$272$	3.90291	+	8.54618i	0.236649	+	0.518188i
$273$	3.47411	+	7.94824i	0.210263	+	0.481049i
$274$	15.2497	−	23.7289i	0.921265	−	1.43352i
$275$	3.29702			0.198818
$276$	−16.3449	+	1.56003i	−0.983847	+	0.0939027i
$277$	12.1422			0.729555			0.364777	−	0.931095i	$-0.381145\pi$
$277$	12.1422			0.729555			0.364777	+	0.931095i	$0.381145\pi$
$278$	19.1724	−	29.8328i	1.14988	−	1.78925i
$279$	−4.70402	−	5.80118i	−0.281623	−	0.347307i
$280$	−0.0394910	−	0.0864733i	−0.00236004	−	0.00516777i
$281$	24.1583	+	7.09352i	1.44116	+	0.423164i	0.906610	−	0.421970i	$-0.138661\pi$
$281$	24.1583	+	7.09352i	1.44116	+	0.423164i	0.534555	+	0.845134i	$0.320479\pi$
$282$	23.7972	+	3.81916i	1.41710	+	0.227428i
$283$	−1.76062	−	1.52559i	−0.104658	−	0.0906867i	0.600960	−	0.799279i	$-0.294785\pi$
$283$	−1.76062	−	1.52559i	−0.104658	−	0.0906867i	−0.705618	+	0.708592i	$0.749331\pi$
$284$	28.0323	+	4.03043i	1.66341	+	0.239162i
$285$	6.32468	−	3.92018i	0.374642	−	0.232211i
$286$	−29.7348	+	25.7653i	−1.75825	+	1.52354i
$287$	5.89348	−	3.78751i	0.347881	−	0.223570i
$288$	21.4282	+	10.6449i	1.26267	+	0.627256i
$289$	7.60185	+	8.77301i	0.447168	+	0.516059i
$290$	−40.3883	+	11.8591i	−2.37169	+	0.696390i
$291$	3.06992	+	24.1446i	0.179962	+	1.41538i
$292$	8.19736	−	9.46025i	0.479714	−	0.553619i
$293$	−4.32941	+	9.48009i	−0.252927	+	0.553833i	−0.992920	−	0.118781i	$-0.962101\pi$
$293$	−4.32941	+	9.48009i	−0.252927	+	0.553833i	0.739993	+	0.672614i	$0.234829\pi$
$294$	−3.45351	−	0.0564041i	−0.201413	−	0.00328955i
$295$	−11.8760	+	5.42359i	−0.691448	+	0.315774i
$296$	−0.0146810	−	0.102109i	−0.000853317	−	0.00593495i
$297$	4.79847	+	19.9005i	0.278435	+	1.15474i
$298$			13.4289i			0.777917i
$299$	−24.0063	−	0.751944i	−1.38832	−	0.0434861i
$300$	0.762218	+	2.76195i	0.0440067	+	0.159461i
$301$	3.02235	+	1.94235i	0.174205	+	0.111955i
$302$	18.7595	−	2.69721i	1.07949	−	0.155207i
$303$	−11.6233	−	13.8652i	−0.667743	−	0.796536i
$304$	−2.40020	+	8.17433i	−0.137661	+	0.468830i
$305$	−21.3012	−	9.72793i	−1.21970	−	0.557020i
$306$	−13.6779	−	2.42489i	−0.781915	−	0.138621i
$307$	1.96867	−	13.6924i	0.112358	−	0.781467i	−0.853257	−	0.521491i	$-0.825376\pi$
$307$	1.96867	−	13.6924i	0.112358	−	0.781467i	0.965615	−	0.259976i	$-0.0837147\pi$
$308$	−2.19390	−	7.47175i	−0.125009	−	0.425742i
$309$	23.0170	+	15.3290i	1.30939	+	0.872035i
$310$	−5.47646	−	8.52153i	−0.311042	−	0.483990i
$311$	−0.750569	−	1.16791i	−0.0425609	−	0.0662260i	0.819321	−	0.573335i	$-0.194351\pi$
$311$	−0.750569	−	1.16791i	−0.0425609	−	0.0662260i	−0.861882	+	0.507109i	$0.830714\pi$
$312$	0.336380	+	0.224023i	0.0190437	+	0.0126828i
$313$	2.21091	+	7.52966i	0.124968	+	0.425602i	0.998081	−	0.0619154i	$-0.0197209\pi$
$313$	2.21091	+	7.52966i	0.124968	+	0.425602i	−0.873114	+	0.487517i	$0.837903\pi$
$314$	−5.37804	+	37.4051i	−0.303500	+	2.11089i
$315$	6.02713	+	1.06852i	0.339590	+	0.0602041i
$316$	8.82853	+	4.03186i	0.496644	+	0.226810i
$317$	−1.88321	+	6.41362i	−0.105772	+	0.360225i	−0.995322	−	0.0966119i	$-0.969199\pi$
$317$	−1.88321	+	6.41362i	−0.105772	+	0.360225i	0.889551	+	0.456837i	$0.151018\pi$
$318$	8.23075	+	9.81828i	0.461558	+	0.550582i
$319$	40.3420	−	5.80031i	2.25872	−	0.324755i
$320$	13.4091	+	8.61749i	0.749590	+	0.481732i
$321$	−3.01281	−	10.9171i	−0.168159	−	0.609335i
$322$	4.24327	−	8.57072i	0.236468	−	0.477628i
$323$		−	4.88907i		−	0.272035i
$324$	−15.5616	+	8.62042i	−0.864532	+	0.478912i
$325$	0.596476	+	4.14858i	0.0330865	+	0.230122i
$326$	−12.2207	+	5.58099i	−0.676840	+	0.309103i
$327$	−23.0965	−	0.377221i	−1.27724	−	0.0208604i
$328$	0.135592	−	0.296905i	0.00748682	−	0.0163939i
$329$	−4.56961	+	5.27361i	−0.251931	+	0.290743i
$330$	3.50192	+	27.5422i	0.192774	+	1.51615i
$331$	19.4350	−	5.70663i	1.06824	−	0.313665i	0.300077	−	0.953915i	$-0.402987\pi$
$331$	19.4350	−	5.70663i	1.06824	−	0.313665i	0.768167	+	0.640250i	$0.221169\pi$
$332$	−15.3744	−	17.7431i	−0.843783	−	0.973777i
$333$	5.94873	+	2.95516i	0.325989	+	0.161942i
$334$	−4.39125	+	2.82208i	−0.240278	+	0.154418i
$335$	−4.79941	+	4.15871i	−0.262220	+	0.227215i
$336$	−5.95676	+	3.69213i	−0.324968	+	0.201422i
$337$	−9.70171	−	1.39490i	−0.528486	−	0.0759848i	−0.127093	−	0.991891i	$-0.540565\pi$
$337$	−9.70171	−	1.39490i	−0.528486	−	0.0759848i	−0.401393	+	0.915906i	$0.631474\pi$
$338$	−18.2075	−	15.7769i	−0.990356	−	0.858148i
$339$	−21.6225	−	3.47014i	−1.17437	−	0.188472i
$340$	−8.98542	−	2.63836i	−0.487303	−	0.143085i
$341$	4.07436	+	8.92161i	0.220639	+	0.483132i
$342$	−7.93357	−	9.78397i	−0.428998	−	0.529057i
$343$	0.540641	−	0.841254i	0.0291919	−	0.0454234i
$344$	0.167388			0.00902498
$345$	−9.83175	+	13.8055i	−0.529324	+	0.743262i
$346$	1.05383			0.0566542
$347$	0.248919	−	0.387326i	0.0133627	−	0.0207927i	−0.834508	−	0.550996i	$-0.814248\pi$
$347$	0.248919	−	0.387326i	0.0133627	−	0.0207927i	0.847871	+	0.530203i	$0.177884\pi$
$348$	14.1854	+	32.4541i	0.760419	+	1.73972i
$349$	−6.14218	−	13.4495i	−0.328783	−	0.719935i	0.670985	−	0.741471i	$-0.265872\pi$
$349$	−6.14218	−	13.4495i	−0.328783	−	0.719935i	−0.999768	+	0.0215362i	$0.993144\pi$
$350$	−1.60128	−	0.470178i	−0.0855920	−	0.0251321i
$351$	−24.1723	+	9.63810i	−1.29022	+	0.514444i
$352$	−23.7460	−	20.5760i	−1.26567	−	1.09671i
$353$	7.03252	+	1.01112i	0.374303	+	0.0538167i	0.326900	−	0.945059i	$-0.393996\pi$
$353$	7.03252	+	1.01112i	0.374303	+	0.0538167i	0.0474039	+	0.998876i	$0.484905\pi$
$354$	11.6435	+	18.7853i	0.618848	+	0.998427i
$355$	22.0933	−	19.1440i	1.17259	−	1.01606i
$356$	−7.89011	+	5.07067i	−0.418175	+	0.268745i
$357$	2.68301	−	2.99607i	0.142000	−	0.158569i
$358$	8.15231	+	9.40827i	0.430863	+	0.497242i
$359$	−26.8739	+	7.89088i	−1.41835	+	0.416465i	−0.898944	−	0.438064i	$-0.855664\pi$
$359$	−26.8739	+	7.89088i	−1.41835	+	0.416465i	−0.519405	+	0.854528i	$0.673846\pi$
$360$	0.263150	−	0.109938i	0.0138692	−	0.00579426i
$361$	−9.53914	+	11.0088i	−0.502060	+	0.579408i
$362$	−5.42175	+	11.8720i	−0.284961	+	0.623977i
$363$	0.127863	−	7.82880i	0.00671107	−	0.410905i
$364$	9.00466	−	4.11229i	0.471973	−	0.215543i
$365$	−1.83890	−	12.7898i	−0.0962523	−	0.669449i
$366$	−11.7879	+	37.8481i	−0.616163	+	1.97835i
$367$		−	19.5190i		−	1.01888i	−0.860506	−	0.509441i	$-0.829852\pi$
$367$		−	19.5190i		−	1.01888i	0.860506	−	0.509441i	$-0.170148\pi$
$368$	−2.15891	−	19.2843i	−0.112541	−	1.00527i
$369$	10.7791	+	18.0421i	0.561137	+	0.939233i
$370$	7.57866	+	4.87051i	0.393996	+	0.253206i
$371$	−3.67156	+	0.527891i	−0.190618	+	0.0274067i
$372$	−6.53182	+	5.47568i	−0.338659	+	0.283901i
$373$	10.7111	−	36.4787i	0.554600	−	1.88880i	0.107772	−	0.994176i	$-0.465628\pi$
$373$	10.7111	−	36.4787i	0.554600	−	1.88880i	0.446829	−	0.894620i	$-0.352553\pi$
$374$	16.5935	+	7.57800i	0.858030	+	0.391849i
$375$	18.6212	+	8.87433i	0.961594	+	0.458269i
$376$	−0.0462687	+	0.321806i	−0.00238613	+	0.0165959i
$377$	14.5969	+	49.7123i	0.751776	+	2.56032i
$378$	0.507456	−	10.3495i	0.0261007	−	0.532320i
$379$	−2.22140	−	3.45657i	−0.114106	−	0.177552i	0.779503	−	0.626398i	$-0.215472\pi$
$379$	−2.22140	−	3.45657i	−0.114106	−	0.177552i	−0.893609	+	0.448846i	$0.851835\pi$
$380$	−4.59102	−	7.14377i	−0.235515	−	0.366468i
$381$	−9.98917	+	14.9991i	−0.511761	+	0.768428i
$382$	−1.35193	−	4.60426i	−0.0691709	−	0.235575i
$383$	3.22390	−	22.4227i	0.164733	−	1.14575i	−0.724828	−	0.688930i	$-0.758081\pi$
$383$	3.22390	−	22.4227i	0.164733	−	1.14575i	0.889561	−	0.456816i	$-0.151010\pi$
$384$	−0.277724	+	0.582753i	−0.0141725	+	0.0297385i
$385$	−7.31187	−	3.33922i	−0.372647	−	0.170182i
$386$	8.66312	−	29.5039i	0.440941	−	1.50171i
$387$	−6.12003	+	8.87193i	−0.311099	+	0.450986i
$388$	27.4932	−	3.95292i	1.39576	−	0.200679i
$389$	1.29734	+	0.833752i	0.0657779	+	0.0422729i	0.573116	−	0.819474i	$-0.305734\pi$
$389$	1.29734	+	0.833752i	0.0657779	+	0.0422729i	−0.507339	+	0.861747i	$0.669371\pi$
$390$	−34.0223	+	9.38917i	−1.72279	+	0.475439i
$391$	4.30662	+	10.2694i	0.217795	+	0.519347i
$392$		−	0.0465916i		−	0.00235323i
$393$	−10.7405	−	3.34516i	−0.541788	−	0.168741i
$394$	7.08070	+	49.2473i	0.356720	+	2.48104i
$395$	9.11320	−	4.16186i	0.458535	−	0.209406i
$396$	22.6182	−	5.84620i	1.13661	−	0.293783i
$397$	3.63173	−	7.95239i	0.182272	−	0.399119i	−0.796336	−	0.604854i	$-0.793231\pi$
$397$	3.63173	−	7.95239i	0.182272	−	0.399119i	0.978608	+	0.205735i	$0.0659586\pi$
$398$	1.22801	−	1.41720i	0.0615544	−	0.0710376i
$399$	3.61779	−	0.459992i	0.181116	−	0.0230284i
$400$	−3.24904	+	0.954004i	−0.162452	+	0.0477002i
$401$	−16.5453	−	19.0943i	−0.826231	−	0.953522i	0.173277	−	0.984873i	$-0.444564\pi$
$401$	−16.5453	−	19.0943i	−0.826231	−	0.953522i	−0.999508	+	0.0313513i	$0.990019\pi$
$402$	8.00846	+	7.17166i	0.399426	+	0.357690i
$403$	−10.4888	+	6.74074i	−0.522484	+	0.335780i
$404$	−15.6044	+	13.5213i	−0.776349	+	0.672710i
$405$	−3.79431	+	17.9671i	−0.188541	+	0.892790i
$406$	−20.4203	−	2.93600i	−1.01344	−	0.145711i
$407$	−6.59220	−	5.71217i	−0.326763	−	0.283142i
$408$	0.0296926	−	0.185015i	0.00147000	−	0.00915960i
$409$	−9.39280	−	2.75798i	−0.464444	−	0.136373i	0.0411345	−	0.999154i	$-0.486903\pi$
$409$	−9.39280	−	2.75798i	−0.464444	−	0.136373i	−0.505579	+	0.862781i	$0.668721\pi$
$410$	11.8412	+	25.9285i	0.584793	+	1.28052i
$411$	−22.4486	+	9.81210i	−1.10731	+	0.483995i
$412$	17.0623	−	26.5495i	0.840600	−	1.30800i
$413$	−6.39876			−0.314862
$414$	25.2827	+	13.5627i	1.24258	+	0.666570i
$415$	−24.2344			−1.18962
$416$	21.5945	−	33.6016i	1.05876	−	1.64746i
$417$	−28.2231	+	12.3361i	−1.38209	+	0.604102i
$418$	6.87162	+	15.0467i	0.336102	+	0.735960i
$419$	−11.5518	−	3.39191i	−0.564341	−	0.165705i	−0.0128962	−	0.999917i	$-0.504105\pi$
$419$	−11.5518	−	3.39191i	−0.564341	−	0.165705i	−0.551445	+	0.834211i	$0.685923\pi$
$420$	1.10692	−	6.89722i	0.0540121	−	0.336550i
$421$	−8.86143	−	7.67847i	−0.431880	−	0.374226i	0.411620	−	0.911356i	$-0.364963\pi$
$421$	−8.86143	−	7.67847i	−0.431880	−	0.374226i	−0.843500	+	0.537130i	$0.819509\pi$
$422$	40.5423	+	5.82911i	1.97357	+	0.283756i
$423$	−15.3647	−	14.2182i	−0.747058	−	0.691310i
$424$	−0.130611	+	0.113175i	−0.00634302	+	0.00549626i
$425$	1.63476	−	1.05060i	0.0792977	−	0.0509616i
$426$	−36.8657	−	33.0137i	−1.78615	−	1.59952i
$427$	−7.51585	−	8.67376i	−0.363718	−	0.419753i
$428$	−12.4009	+	3.64125i	−0.599422	+	0.176006i
$429$	33.9006	−	4.31037i	1.63673	−	0.208106i
$430$	−9.57269	+	11.0475i	−0.461636	+	0.532757i
$431$	−6.47755	+	14.1838i	−0.312012	+	0.683212i	−0.999058	−	0.0434028i	$-0.986180\pi$
$431$	−6.47755	+	14.1838i	−0.312012	+	0.683212i	0.687045	+	0.726615i	$0.258907\pi$
$432$	−10.4869	−	18.2224i	−0.504552	−	0.876728i
$433$	−0.917931	+	0.419205i	−0.0441129	+	0.0201457i	−0.437349	−	0.899292i	$-0.644083\pi$
$433$	−0.917931	+	0.419205i	−0.0441129	+	0.0201457i	0.393236	+	0.919437i	$0.371355\pi$
$434$	−0.706532	−	4.91404i	−0.0339146	−	0.235881i
$435$	34.9070	+	10.8719i	1.67366	+	0.521267i
$436$			26.3615i			1.26249i
$437$	−3.14683	+	9.59500i	−0.150533	+	0.458991i
$438$	−21.0852	+	5.81890i	−1.00749	+	0.278038i
$439$	31.1556	+	20.0225i	1.48698	+	0.955623i	0.996449	+	0.0841977i	$0.0268327\pi$
$439$	31.1556	+	20.0225i	1.48698	+	0.955623i	0.490529	+	0.871425i	$0.336804\pi$
$440$	−0.370704	+	0.0532992i	−0.0176726	+	0.00254094i
$441$	2.46945	+	1.70347i	0.117593	+	0.0811178i
$442$	−6.53327	+	22.2503i	−0.310756	+	1.05834i
$443$	−14.2004	−	6.48509i	−0.674680	−	0.308116i	0.0484523	−	0.998825i	$-0.484571\pi$
$443$	−14.2004	−	6.48509i	−0.674680	−	0.308116i	−0.723132	+	0.690709i	$0.757298\pi$
$444$	3.26115	−	6.84293i	0.154767	−	0.324751i
$445$	−1.37781	+	9.58287i	−0.0653144	+	0.454271i
$446$	7.82939	+	26.6645i	0.370732	+	1.26260i
$447$	6.46538	−	9.70801i	0.305802	−	0.459173i
$448$	4.22349	+	6.57188i	0.199541	+	0.310492i
$449$	0.478552	+	0.744641i	0.0225843	+	0.0351418i	0.852362	−	0.522952i	$-0.175169\pi$
$449$	0.478552	+	0.744641i	0.0225843	+	0.0351418i	−0.829778	+	0.558094i	$0.811533\pi$
$450$	1.56666	−	4.75521i	0.0738529	−	0.224163i
$451$	−7.77563	−	26.4814i	−0.366140	−	1.24696i
$452$	−3.55667	+	24.7372i	−0.167292	+	1.16354i
$453$	−14.8601	−	7.08192i	−0.698190	−	0.332738i
$454$	−25.5192	−	11.6542i	−1.19767	−	0.546959i
$455$	2.87886	−	9.80451i	0.134963	−	0.459643i
$456$	0.130214	−	0.109159i	0.00609781	−	0.00511185i
$457$	17.6177	−	2.53305i	0.824122	−	0.118491i	0.282664	−	0.959219i	$-0.408782\pi$
$457$	17.6177	−	2.53305i	0.824122	−	0.118491i	0.541458	+	0.840728i	$0.317873\pi$
$458$	36.3780	+	23.3787i	1.69983	+	1.09242i
$459$	8.72055	+	8.33825i	0.407041	+	0.389196i
$460$	15.9361	+	10.9613i	0.743025	+	0.511074i
$461$			4.55078i			0.211951i	0.994369	+	0.105975i	$0.0337965\pi$
$461$			4.55078i			0.211951i	−0.994369	+	0.105975i	$0.966204\pi$
$462$	−4.04632	+	12.9918i	−0.188252	+	0.604432i
$463$	−3.48582	−	24.2444i	−0.162000	−	1.12673i	−0.894857	−	0.446352i	$-0.852723\pi$
$463$	−3.48582	−	24.2444i	−0.162000	−	1.12673i	0.732857	−	0.680382i	$-0.238186\pi$
$464$	−38.0766	+	17.3890i	−1.76766	+	0.807265i
$465$	−0.143676	+	8.79702i	−0.00666284	+	0.407952i
$466$	−23.7979	+	52.1102i	−1.10242	+	2.41396i
$467$	−7.23406	+	8.34855i	−0.334752	+	0.386325i	−0.898024	−	0.439947i	$-0.854997\pi$
$467$	−7.23406	+	8.34855i	−0.334752	+	0.386325i	0.563271	+	0.826272i	$0.309543\pi$
$468$	11.4481	+	27.4025i	0.529190	+	1.26668i
$469$	−2.98636	+	0.876875i	−0.137897	+	0.0404903i
$470$	−18.5928	−	21.4573i	−0.857624	−	0.989751i
$471$	21.8966	−	24.4515i	1.00894	−	1.12667i
$472$	−0.250801	+	0.161180i	−0.0115441	+	0.00741892i
$473$	10.6967	−	9.26874i	0.491835	−	0.426177i
$474$	−8.93482	−	14.4151i	−0.410390	−	0.662108i
$475$	1.74417	+	0.250774i	0.0800281	+	0.0115063i
$476$	−3.46869	−	3.00564i	−0.158987	−	0.137763i
$477$	−1.22313	−	11.0605i	−0.0560033	−	0.506427i
$478$	32.1152	+	9.42988i	1.46892	+	0.431313i
$479$	−12.3064	−	26.9473i	−0.562295	−	1.23126i	−0.950799	−	0.309808i	$-0.899735\pi$
$479$	−12.3064	−	26.9473i	−0.562295	−	1.23126i	0.388504	−	0.921447i	$-0.372992\pi$
$480$	−11.2885	−	25.8264i	−0.515247	−	1.17881i
$481$	5.99491	−	9.32826i	0.273344	−	0.425332i
$482$	−22.2866			−1.01513
$483$	−7.19393	+	4.15300i	−0.327335	+	0.188968i
$484$	−8.93551			−0.406159
$485$	15.5010	−	24.1200i	0.703864	−	1.09523i
$486$	30.9822	+	2.53548i	1.40538	+	0.115012i
$487$	−10.2794	−	22.5087i	−0.465803	−	1.01997i	−0.986126	−	0.165998i	$-0.946916\pi$
$487$	−10.2794	−	22.5087i	−0.465803	−	1.01997i	0.520323	−	0.853970i	$-0.325812\pi$
$488$	−0.513072	−	0.150652i	−0.0232257	−	0.00681968i
$489$	11.5215	+	1.84906i	0.521021	+	0.0836174i
$490$	3.07500	+	2.66450i	0.138914	+	0.120370i
$491$	14.6840	+	2.11123i	0.662677	+	0.0952786i	0.465443	−	0.885078i	$-0.345895\pi$
$491$	14.6840	+	2.11123i	0.662677	+	0.0952786i	0.197234	+	0.980356i	$0.436804\pi$
$492$	20.3862	−	12.6358i	0.919080	−	0.569667i
$493$	18.1546	−	15.7310i	0.817641	−	0.708490i
$494$	−17.6899	+	11.3686i	−0.795905	+	0.511497i
$495$	10.7286	−	21.5968i	0.482217	−	0.970703i
$496$	−6.59657	−	7.61285i	−0.296195	−	0.341827i
$497$	13.7473	−	4.03656i	0.616649	−	0.181065i
$498$	5.17449	+	40.6968i	0.231874	+	1.82367i
$499$	−11.1397	+	12.8559i	−0.498681	+	0.575508i	−0.948164	−	0.317780i	$-0.897063\pi$
$499$	−11.1397	+	12.8559i	−0.498681	+	0.575508i	0.449484	+	0.893289i	$0.351608\pi$
$500$	9.77911	−	21.4133i	0.437335	−	0.957630i
$501$	4.53321	+	0.0740382i	0.202529	+	0.00330778i
$502$	50.3347	−	22.9871i	2.24655	−	1.02596i
$503$	−0.348565	−	2.42432i	−0.0155417	−	0.108095i	0.980574	−	0.196150i	$-0.0628440\pi$
$503$	−0.348565	−	2.42432i	−0.0155417	−	0.108095i	−0.996116	+	0.0880549i	$0.971935\pi$
$504$	0.139700	+	0.00456450i	0.00622274	+	0.000203319i
$505$			21.3134i			0.948433i
$506$	−27.6879	−	25.5525i	−1.23088	−	1.13595i
$507$	5.56671	+	20.1714i	0.247226	+	0.895843i
$508$	17.3010	+	11.1187i	0.767610	+	0.493313i
$509$	−0.105490	+	0.0151672i	−0.00467578	+	0.000672275i	−0.144652	−	0.989483i	$-0.546206\pi$
$509$	−0.105490	+	0.0151672i	−0.00467578	+	0.000672275i	0.139977	+	0.990155i	$0.455297\pi$
$510$	10.5127	+	12.5404i	0.465511	+	0.555298i
$511$	1.78417	−	6.07631i	0.0789268	−	0.268800i
$512$	29.0112	+	13.2490i	1.28213	+	0.585527i
$513$	1.02481	+	10.8926i	0.0452466	+	0.480922i
$514$	2.87872	−	20.0219i	0.126975	−	0.883129i
$515$	−9.17801	−	31.2574i	−0.404431	−	1.37737i
$516$	10.2375	+	6.81798i	0.450679	+	0.300145i
$517$	14.8625	+	23.1265i	0.653653	+	1.01710i
$518$	2.38707	+	3.71435i	0.104882	+	0.163199i
$519$	−0.761832	−	0.507367i	−0.0334407	−	0.0222710i
$520$	−0.134131	−	0.456808i	−0.00588202	−	0.0200323i
$521$	−0.411643	+	2.86304i	−0.0180344	+	0.125432i	−0.996850	−	0.0793129i	$-0.974727\pi$
$521$	−0.411643	+	2.86304i	−0.0180344	+	0.125432i	0.978815	+	0.204745i	$0.0656365\pi$
$522$	10.8038	−	60.9406i	0.472871	−	2.66730i
$523$	8.82493	+	4.03021i	0.385887	+	0.176229i	0.598906	−	0.800819i	$-0.295602\pi$
$523$	8.82493	+	4.03021i	0.385887	+	0.176229i	−0.213019	+	0.977048i	$0.568330\pi$
$524$	−3.61686	+	12.3179i	−0.158003	+	0.538110i
$525$	0.931226	+	1.11084i	0.0406420	+	0.0484810i
$526$	7.27029	−	1.04531i	0.317000	−	0.0455777i
$527$	4.86308	+	3.12531i	0.211839	+	0.136141i
$528$	7.34487	+	26.6147i	0.319645	+	1.15826i
$529$	−1.84204	−	22.9261i	−0.0800888	−	0.996788i
$530$		−	15.0925i		−	0.655576i
$531$	0.626875	−	19.1860i	0.0272041	−	0.832603i
$532$	−0.592300	−	4.11954i	−0.0256795	−	0.178605i
$533$	31.9143	−	14.5748i	1.38236	−	0.631304i
$534$	16.3867	+	0.267633i	0.709120	+	0.0115816i
$535$	−5.54214	+	12.1356i	−0.239608	+	0.524667i
$536$	−0.0949635	+	0.109594i	−0.00410180	+	0.00473373i
$537$	−1.36383	−	10.7263i	−0.0588535	−	0.462876i
$538$	−42.3799	+	12.4439i	−1.82713	+	0.536493i
$539$	−2.57990	−	2.97736i	−0.111124	−	0.128244i
$540$	20.5722	+	3.99469i	0.885286	+	0.171904i
$541$	−26.0957	+	16.7707i	−1.12194	+	0.721027i	−0.963863	−	0.266399i	$-0.914166\pi$
$541$	−26.0957	+	16.7707i	−1.12194	+	0.721027i	−0.158078	+	0.987427i	$0.550530\pi$
$542$	28.2202	−	24.4529i	1.21216	−	1.05034i
$543$	9.63526	−	5.97215i	0.413489	−	0.256290i
$544$	−18.3306	−	2.63554i	−0.785917	−	0.112998i
$545$	20.5651	+	17.8197i	0.880910	+	0.763313i
$546$	−17.0794	−	2.74102i	−0.730929	−	0.117305i
$547$	−0.0906448	−	0.0266157i	−0.00387569	−	0.00113801i	0.279794	−	0.960060i	$-0.409734\pi$
$547$	−0.0906448	−	0.0266157i	−0.00387569	−	0.00113801i	−0.283670	+	0.958922i	$0.591552\pi$
$548$	11.6145	+	25.4323i	0.496149	+	1.08641i
$549$	26.7437	−	21.6858i	1.14139	−	0.925527i
$550$	−3.55458	+	5.53103i	−0.151568	+	0.235844i
$551$	21.7827			0.927976
$552$	−0.177357	+	0.343988i	−0.00754882	+	0.0146411i
$553$	4.91016			0.208801
$554$	−13.0907	+	20.3696i	−0.556172	+	0.865421i
$555$	−3.13384	−	7.16974i	−0.133024	−	0.304338i
$556$	14.6022	+	31.9744i	0.619272	+	1.35602i
$557$	−10.2906	−	3.02161i	−0.436029	−	0.128030i	0.0563492	−	0.998411i	$-0.482054\pi$
$557$	−10.2906	−	3.02161i	−0.436029	−	0.128030i	−0.492378	+	0.870382i	$0.663872\pi$
$558$	14.8035	−	1.63705i	0.626681	−	0.0693017i
$559$	13.5979	+	11.7826i	0.575129	+	0.498352i
$560$	8.17168	+	1.17491i	0.345316	+	0.0496490i
$561$	−8.34731	−	13.4672i	−0.352424	−	0.568588i
$562$	−37.9455	+	32.8800i	−1.60064	+	1.38696i
$563$	−21.4288	+	13.7715i	−0.903116	+	0.580397i	−0.907713	−	0.419592i	$-0.862173\pi$
$563$	−21.4288	+	13.7715i	−0.903116	+	0.580397i	0.00459679	+	0.999989i	$0.498537\pi$
$564$	−15.9374	+	17.7970i	−0.671086	+	0.749390i
$565$	16.8937	+	19.4964i	0.710724	+	0.820219i
$566$	4.45746	−	1.30883i	0.187361	−	0.0550142i
$567$	−5.34962	+	7.23751i	−0.224663	+	0.303947i
$568$	0.437150	−	0.504499i	0.0183424	−	0.0211683i
$569$	8.76558	−	19.1939i	0.367472	−	0.804652i	−0.632085	−	0.774899i	$-0.717801\pi$
$569$	8.76558	−	19.1939i	0.367472	−	0.804652i	0.999557	−	0.0297530i	$-0.00947208\pi$
$570$	−0.242318	+	14.8366i	−0.0101496	+	0.621437i
$571$	−22.4759	+	10.2644i	−0.940588	+	0.429552i	−0.825879	−	0.563847i	$-0.809321\pi$
$571$	−22.4759	+	10.2644i	−0.940588	+	0.429552i	−0.114709	+	0.993399i	$0.536593\pi$
$572$	−5.55016	−	38.6022i	−0.232064	−	1.61404i
$573$	−1.23939	+	3.97940i	−0.0517764	+	0.166242i
$574$			13.9702i			0.583105i
$575$	−3.88451	+	1.00964i	−0.161995	+	0.0421047i
$576$	−20.1189	+	12.0199i	−0.838287	+	0.500828i
$577$	17.4832	+	11.2358i	0.727835	+	0.467751i	0.851355	−	0.524591i	$-0.175782\pi$
$577$	17.4832	+	11.2358i	0.727835	+	0.467751i	−0.123519	+	0.992342i	$0.539418\pi$
$578$	−22.9132	+	3.29442i	−0.953062	+	0.137030i
$579$	−20.4674	+	17.1580i	−0.850597	+	0.713063i
$580$	11.7549	−	40.0336i	0.488097	−	1.66231i
$581$	−10.8041	−	4.93408i	−0.448231	−	0.204700i
$582$	−43.8144	−	20.8807i	−1.81616	−	0.865533i
$583$	−2.07969	+	14.4645i	−0.0861318	+	0.599060i
$584$	−0.0831271	−	0.283105i	−0.00343982	−	0.0117150i
$585$	29.1158	+	9.59252i	1.20379	+	0.396602i
$586$	−11.2360	−	17.4836i	−0.464157	−	0.722242i
$587$	−12.0193	−	18.7024i	−0.496089	−	0.771930i	0.499444	−	0.866346i	$-0.333538\pi$
$587$	−12.0193	−	18.7024i	−0.496089	−	0.771930i	−0.995533	+	0.0944167i	$0.969901\pi$
$588$	1.89774	−	2.84953i	0.0782616	−	0.117513i
$589$	1.47681	+	5.02957i	0.0608511	+	0.207240i
$590$	3.70521	−	25.7703i	0.152541	−	1.06095i
$591$	18.5914	−	39.0108i	0.764750	−	1.60469i
$592$	8.14910	+	3.72157i	0.334926	+	0.152956i
$593$	−2.78151	+	9.47295i	−0.114223	+	0.389007i	−0.996683	−	0.0813794i	$-0.974067\pi$
$593$	−2.78151	+	9.47295i	−0.114223	+	0.389007i	0.882460	+	0.470387i	$0.155886\pi$
$594$	−38.5581	−	13.4053i	−1.58206	−	0.550025i
$595$	−4.68950	+	0.674249i	−0.192251	+	0.0276415i
$596$	−11.1979	−	7.19646i	−0.458684	−	0.294778i
$597$	−1.57006	+	0.433290i	−0.0642582	+	0.0177334i
$598$	27.1431	−	39.4620i	1.10997	−	1.61372i
$599$		−	30.4875i		−	1.24569i	−0.782347	−	0.622843i	$-0.785978\pi$
$599$		−	30.4875i		−	1.24569i	0.782347	−	0.622843i	$-0.214022\pi$
$600$	0.0644810	+	0.0200828i	0.00263243	+	0.000819876i
$601$	4.84771	+	33.7166i	0.197742	+	1.37533i	0.810816	+	0.585302i	$0.199024\pi$
$601$	4.84771	+	33.7166i	0.197742	+	1.37533i	−0.613073	+	0.790026i	$0.710067\pi$
$602$	−6.51691	+	2.97617i	−0.265609	+	0.121300i
$603$	−2.33665	−	9.04021i	−0.0951559	−	0.368146i
$604$	−7.80396	+	17.0883i	−0.317538	+	0.695312i
$605$	−6.04019	+	6.97075i	−0.245569	+	0.283401i
$606$	35.7914	−	4.55079i	1.45393	−	0.184863i
$607$	−15.0514	+	4.41948i	−0.610916	+	0.179381i	−0.572533	−	0.819882i	$-0.694039\pi$
$607$	−15.0514	+	4.41948i	−0.610916	+	0.179381i	−0.0383836	+	0.999263i	$0.512221\pi$
$608$	−10.9970	−	12.6912i	−0.445986	−	0.514695i
$609$	13.3487	+	11.9539i	0.540915	+	0.484395i
$610$	39.2847	−	25.2467i	1.59059	−	1.02221i
$611$	−26.4109	+	22.8852i	−1.06847	+	0.925835i
$612$	9.35192	−	10.1061i	0.378029	−	0.408513i
$613$	18.4313	+	2.65003i	0.744435	+	0.107034i	0.504087	−	0.863653i	$-0.331829\pi$
$613$	18.4313	+	2.65003i	0.744435	+	0.107034i	0.240348	+	0.970687i	$0.422738\pi$
$614$	20.8477	+	18.0647i	0.841346	+	0.729030i
$615$	3.92314	−	24.4451i	0.158196	−	0.985723i
$616$	−0.176118	−	0.0517128i	−0.00709598	−	0.00208357i
$617$	15.4717	+	33.8783i	0.622867	+	1.36389i	0.913415	+	0.407029i	$0.133435\pi$
$617$	15.4717	+	33.8783i	0.622867	+	1.36389i	−0.290548	+	0.956860i	$0.593838\pi$
$618$	−50.5308	+	22.0866i	−2.03265	+	0.888454i
$619$	−9.85067	+	15.3279i	−0.395932	+	0.616082i	−0.980793	−	0.195051i	$-0.937513\pi$
$619$	−9.85067	+	15.3279i	−0.395932	+	0.616082i	0.584861	+	0.811133i	$0.301149\pi$
$620$	10.0406			0.403240
$621$	−11.7476	−	21.9771i	−0.471414	−	0.881912i
$622$	2.76847			0.111005
$623$	−2.56530	+	3.99169i	−0.102777	+	0.159924i
$624$	−32.1600	+	14.0569i	−1.28743	+	0.562726i
$625$	−8.35615	−	18.2974i	−0.334246	−	0.731896i
$626$	−15.0153	−	4.40888i	−0.600131	−	0.176214i
$627$	2.27666	−	14.1859i	0.0909212	−	0.566531i
$628$	−28.3087	−	24.5296i	−1.12964	−	0.978839i
$629$	−5.08881	−	0.731660i	−0.202904	−	0.0291732i
$630$	−8.29049	+	8.95904i	−0.330301	+	0.356937i
$631$	−34.0394	+	29.4953i	−1.35509	+	1.17419i	−0.387438	+	0.921896i	$0.626640\pi$
$631$	−34.0394	+	29.4953i	−1.35509	+	1.17419i	−0.967650	+	0.252295i	$0.918815\pi$
$632$	0.192456	−	0.123684i	0.00765547	−	0.00491987i
$633$	−26.5023	−	23.7331i	−1.05337	−	0.943307i
$634$	−8.72907	−	10.0739i	−0.346676	−	0.400085i
$635$	20.3690	−	5.98087i	0.808319	−	0.237344i
$636$	−12.5979	+	1.60179i	−0.499540	+	0.0635152i
$637$	3.27962	−	3.78489i	0.129943	−	0.149963i
$638$	−33.7630	+	73.9307i	−1.33669	+	2.92694i
$639$	10.7564	+	41.6153i	0.425518	+	1.64627i
$640$	0.691739	−	0.315907i	0.0273434	−	0.0124873i
$641$	1.41590	+	9.84783i	0.0559249	+	0.388966i	0.998490	+	0.0549423i	$0.0174975\pi$
$641$	1.41590	+	9.84783i	0.0559249	+	0.388966i	−0.942565	+	0.334024i	$0.891593\pi$
$642$	21.5626	+	6.71572i	0.851008	+	0.265048i
$643$		−	30.3507i		−	1.19691i	−0.801155	−	0.598457i	$-0.795781\pi$
$643$		−	30.3507i		−	1.19691i	0.801155	−	0.598457i	$-0.204219\pi$
$644$	4.87288	+	8.13130i	0.192019	+	0.320418i
$645$	12.2391	−	3.37763i	0.481914	−	0.132994i
$646$	8.20183	+	5.27100i	0.322697	+	0.207385i
$647$	42.4731	−	6.10671i	1.66979	−	0.240079i	0.758449	−	0.651733i	$-0.225958\pi$
$647$	42.4731	−	6.10671i	1.66979	−	0.240079i	0.911341	+	0.411653i	$0.135049\pi$
$648$	−0.0273724	+	0.418430i	−0.00107529	+	0.0164375i
$649$	−7.10209	+	24.1875i	−0.278782	+	0.949443i
$650$	−7.60267	−	3.47202i	−0.298201	−	0.136184i
$651$	−1.85511	+	3.89261i	−0.0727074	+	0.152563i
$652$	1.89517	−	13.1812i	0.0742206	−	0.516216i
$653$	−2.32030	−	7.90223i	−0.0908005	−	0.309238i	0.901553	−	0.432669i	$-0.142428\pi$
$653$	−2.32030	−	7.90223i	−0.0908005	−	0.309238i	−0.992353	+	0.123431i	$0.960610\pi$
$654$	25.5336	−	38.3396i	0.998442	−	1.49920i
$655$	7.16451	+	11.1482i	0.279941	+	0.435596i
$656$	15.3250	+	23.8461i	0.598339	+	0.931034i
$657$	18.0444	+	5.94493i	0.703980	+	0.231934i
$658$	−3.92035	−	13.3515i	−0.152831	−	0.520495i
$659$	−6.62502	+	46.0780i	−0.258074	+	1.79495i	0.288442	+	0.957497i	$0.406863\pi$
$659$	−6.62502	+	46.0780i	−0.258074	+	1.79495i	−0.546516	+	0.837448i	$0.684046\pi$
$660$	−24.8431	−	11.8395i	−0.967018	−	0.460853i
$661$	−41.3008	−	18.8615i	−1.60642	−	0.733626i	−0.608226	−	0.793764i	$-0.708119\pi$
$661$	−41.3008	−	18.8615i	−1.60642	−	0.733626i	−0.998190	+	0.0601382i	$0.980846\pi$
$662$	−11.3799	+	38.7563i	−0.442292	+	1.50631i
$663$	15.4355	−	12.9397i	0.599464	−	0.502536i
$664$	−0.547757	+	0.0787556i	−0.0212571	+	0.00305631i
$665$	−3.61411	−	2.32265i	−0.140149	−	0.0900683i
$666$	−11.3710	+	6.79350i	−0.440616	+	0.263243i
$667$	−45.7544	+	19.1877i	−1.77162	+	0.742950i
$668$		−	5.17404i		−	0.200190i
$669$	7.17764	−	23.0457i	0.277504	−	0.890998i
$670$	−1.80226	−	12.5350i	−0.0696274	−	0.484269i
$671$	−41.1291	+	18.7830i	−1.58777	+	0.725110i
$672$	0.225586	−	13.8122i	0.00870216	−	0.532815i
$673$	20.8970	−	45.7580i	0.805520	−	1.76384i	0.179948	−	0.983676i	$-0.442407\pi$
$673$	20.8970	−	45.7580i	0.805520	−	1.76384i	0.625572	−	0.780167i	$-0.284866\pi$
$674$	12.7997	−	14.7716i	0.493024	−	0.568980i
$675$	−3.42197	+	2.68336i	−0.131712	+	0.103283i
$676$	22.9130	−	6.72787i	0.881270	−	0.258764i
$677$	23.4837	+	27.1016i	0.902551	+	1.04160i	0.998930	+	0.0462544i	$0.0147285\pi$
$677$	23.4837	+	27.1016i	0.902551	+	1.04160i	−0.0963789	+	0.995345i	$0.530726\pi$
$678$	29.1331	−	32.5324i	1.11885	−	1.24940i
$679$	11.8214	−	7.59715i	0.453663	−	0.291552i
$680$	−0.166823	+	0.144553i	−0.00639736	+	0.00554334i
$681$	12.8373	+	20.7113i	0.491927	+	0.793658i
$682$	−19.3594	−	2.78346i	−0.741310	−	0.106584i
$683$	−2.25542	−	1.95434i	−0.0863014	−	0.0747806i	0.610642	−	0.791907i	$-0.290912\pi$
$683$	−2.25542	−	1.95434i	−0.0863014	−	0.0747806i	−0.696943	+	0.717126i	$0.745457\pi$
$684$	12.4101	−	1.37237i	0.474510	−	0.0524738i
$685$	27.6913	+	8.13091i	1.05803	+	0.310666i
$686$	0.828400	+	1.81394i	0.0316285	+	0.0692567i
$687$	−15.0426	−	34.4151i	−0.573910	−	1.31302i
$688$	−7.85909	+	12.2290i	−0.299625	+	0.466226i
$689$	−18.5767			−0.707716
$690$	−12.5601	−	31.3776i	−0.478155	−	1.19452i
$691$	9.28661			0.353279			0.176640	−	0.984276i	$-0.443477\pi$
$691$	9.28661			0.353279			0.176640	+	0.984276i	$0.443477\pi$
$692$	−0.564739	+	0.878750i	−0.0214681	+	0.0334051i
$693$	9.18007	−	7.44388i	0.348722	−	0.282770i
$694$	0.381408	+	0.835166i	0.0144780	+	0.0317025i
$695$	34.8145	+	10.2225i	1.32059	+	0.387760i
$696$	0.824315	+	0.132292i	0.0312456	+	0.00501453i
$697$	−12.2937	−	10.6526i	−0.465658	−	0.403495i
$698$	29.1847	+	4.19612i	1.10466	+	0.158826i
$699$	42.2925	−	26.2139i	1.59965	−	0.991499i
$700$	1.25018	−	1.08329i	0.0472523	−	0.0409444i
$701$	−34.8594	+	22.4028i	−1.31662	+	0.846142i	−0.994917	−	0.100698i	$-0.967892\pi$
$701$	−34.8594	+	22.4028i	−1.31662	+	0.846142i	−0.321705	+	0.946840i	$0.604256\pi$
$702$	9.89192	−	50.9422i	0.373347	−	1.92269i
$703$	−3.05290	−	3.52323i	−0.115142	−	0.132881i
$704$	29.5296	−	8.67069i	1.11294	−	0.326789i
$705$	3.11046	+	24.4634i	0.117147	+	0.921346i
$706$	−9.27815	+	10.7076i	−0.349188	+	0.402984i
$707$	−4.33936	+	9.50186i	−0.163198	+	0.357354i
$708$	−21.9041	−	0.357746i	−0.823206	−	0.0134449i
$709$	−29.5183	+	13.4805i	−1.10858	+	0.506272i	−0.883672	−	0.468108i	$-0.844936\pi$
$709$	−29.5183	+	13.4805i	−1.10858	+	0.506272i	−0.224910	+	0.974380i	$0.572209\pi$
$710$	8.29644	+	57.7030i	0.311360	+	2.16556i
$711$	−0.481040	+	14.7226i	−0.0180404	+	0.552142i
$712$			0.221074i			0.00828509i
$713$	−7.53241	−	9.26366i	−0.282091	−	0.346927i
$714$	2.13356	+	7.73109i	0.0798463	+	0.289329i
$715$	−33.8661	−	21.7644i	−1.26652	−	0.813942i
$716$	−12.2140	+	1.75611i	−0.456458	+	0.0656287i
$717$	−18.6767	−	22.2790i	−0.697493	−	0.832023i
$718$	15.7356	−	53.5905i	0.587247	−	1.99998i
$719$	19.3685	+	8.84530i	0.722323	+	0.329874i	0.742430	−	0.669924i	$-0.233673\pi$
$719$	19.3685	+	8.84530i	0.722323	+	0.329874i	−0.0201065	+	0.999798i	$0.506401\pi$
$720$	−4.32342	+	24.3869i	−0.161124	+	0.908845i
$721$	2.27223	−	15.8037i	0.0846223	−	0.588561i
$722$	−8.18380	−	27.8715i	−0.304570	−	1.03727i
$723$	16.1114	+	10.7299i	0.599190	+	0.399051i
$724$	−6.99415	−	10.8831i	−0.259935	−	0.404467i
$725$	4.68084	+	7.28353i	0.173842	+	0.270503i
$726$	12.9956	+	8.65488i	0.482313	+	0.321213i
$727$	8.28640	+	28.2209i	0.307326	+	1.04666i	0.957874	+	0.287190i	$0.0927211\pi$
$727$	8.28640	+	28.2209i	0.307326	+	1.04666i	−0.650548	+	0.759465i	$0.725461\pi$
$728$	0.0332072	−	0.230961i	0.00123074	−	0.00856000i
$729$	−21.1769	−	16.7494i	−0.784328	−	0.620346i
$730$	23.4386	+	10.7040i	0.867500	+	0.396174i
$731$	2.35026	−	8.00425i	0.0869275	−	0.296048i
$732$	−25.2432	−	30.1120i	−0.933014	−	1.11297i
$733$	2.22315	−	0.319641i	0.0821141	−	0.0118062i	−0.101135	−	0.994873i	$-0.532248\pi$
$733$	2.22315	−	0.319641i	0.0821141	−	0.0118062i	0.183249	+	0.983066i	$0.441338\pi$
$734$	32.7447	+	21.0438i	1.20863	+	0.776740i
$735$	−0.940144	−	3.40668i	−0.0346777	−	0.125657i
$736$	34.2782	+	16.9708i	1.26351	+	0.625551i
$737$			12.2618i			0.451669i
$738$	−41.8883	−	1.36864i	−1.54193	−	0.0503802i
$739$	−1.34493	−	9.35420i	−0.0494741	−	0.344100i	−0.999491	−	0.0319015i	$-0.989844\pi$
$739$	−1.34493	−	9.35420i	−0.0494741	−	0.344100i	0.950017	−	0.312198i	$-0.101065\pi$
$740$	−8.12269	+	3.70951i	−0.298596	+	0.136364i
$741$	18.2618	+	0.298259i	0.670863	+	0.0109568i
$742$	3.07280	−	6.72849i	0.112806	−	0.247011i
$743$	34.0709	−	39.3199i	1.24994	−	1.44251i	0.399246	−	0.916844i	$-0.369272\pi$
$743$	34.0709	−	39.3199i	1.24994	−	1.44251i	0.850693	−	0.525662i	$-0.176182\pi$
$744$	0.0253406	+	0.199301i	0.000929031	+	0.00730673i
$745$	−13.1836	+	3.87106i	−0.483010	+	0.141824i
$746$	49.6483	+	57.2972i	1.81775	+	2.09780i
$747$	15.8528	−	31.9117i	0.580024	−	1.16759i
$748$	−15.2114	+	9.77575i	−0.556182	+	0.357437i
$749$	−4.94156	+	4.28189i	−0.180561	+	0.156457i
$750$	−34.9633	+	21.6711i	−1.27668	+	0.791315i
$751$	2.62425	+	0.377310i	0.0957602	+	0.0137682i	0.190028	−	0.981779i	$-0.439142\pi$
$751$	2.62425	+	0.377310i	0.0957602	+	0.0137682i	−0.0942681	+	0.995547i	$0.530051\pi$
$752$	−21.3380	−	18.4895i	−0.778116	−	0.674241i
$753$	−47.4551	−	7.61595i	−1.72936	−	0.277541i
$754$	−99.1339	−	29.1083i	−3.61024	−	1.06006i
$755$	8.05559	+	17.6393i	0.293173	+	0.641959i
$756$	8.35812	+	5.96936i	0.303982	+	0.217103i
$757$	−18.0261	+	28.0491i	−0.655169	+	1.01946i	0.341655	+	0.939826i	$0.389013\pi$
$757$	−18.0261	+	28.0491i	−0.655169	+	1.01946i	−0.996824	+	0.0796377i	$0.974624\pi$
$758$	8.19364			0.297606
$759$	7.71380	+	31.8028i	0.279993	+	1.15437i
$760$	−0.200162			−0.00726064
$761$	21.1719	−	32.9441i	0.767479	−	1.19422i	−0.208853	−	0.977947i	$-0.566973\pi$
$761$	21.1719	−	32.9441i	0.767479	−	1.19422i	0.976333	−	0.216274i	$-0.0693905\pi$
$762$	−14.3928	−	32.9285i	−0.521396	−	1.19287i
$763$	5.54020	+	12.1313i	0.200569	+	0.439184i
$764$	4.56382	+	1.34006i	0.165113	+	0.0484816i
$765$	−1.56224	−	14.1271i	−0.0564831	−	0.510765i
$766$	34.1402	+	29.5827i	1.23354	+	1.06887i
$767$	−31.7196	−	4.56059i	−1.14533	−	0.164673i
$768$	−14.9351	−	24.0957i	−0.538923	−	0.869480i
$769$	−25.2008	+	21.8366i	−0.908765	+	0.787450i	−0.977664	−	0.210174i	$-0.932597\pi$
$769$	−25.2008	+	21.8366i	−0.908765	+	0.787450i	0.0688987	+	0.997624i	$0.478051\pi$
$770$	13.4849	−	8.66622i	0.485962	−	0.312309i
$771$	−11.7207	+	13.0883i	−0.422110	+	0.471362i
$772$	19.9597	+	23.0348i	0.718367	+	0.829040i
$773$	−9.72357	+	2.85510i	−0.349733	+	0.102691i	−0.451881	−	0.892078i	$-0.649247\pi$
$773$	−9.72357	+	2.85510i	−0.349733	+	0.102691i	0.102148	+	0.994769i	$0.467428\pi$
$774$	−8.28531	−	19.8319i	−0.297809	−	0.712842i
$775$	−1.36440	+	1.57460i	−0.0490105	+	0.0565612i
$776$	0.271976	−	0.595545i	0.00976339	−	0.0213788i
$777$	0.0626255	−	3.83443i	0.00224668	−	0.137560i
$778$	−2.79738	+	1.27752i	−0.100291	+	0.0458013i
$779$	−2.09923	−	14.6005i	−0.0752128	−	0.523116i
$780$	10.4030	−	33.4016i	0.372488	−	1.19597i
$781$		−	56.4454i		−	2.01977i
$782$	−21.8709	−	3.84694i	−0.782101	−	0.137566i
$783$	−37.1502	+	38.8535i	−1.32764	+	1.38851i
$784$	3.40387	+	2.18753i	0.121567	+	0.0781261i
$785$	−38.2720	+	5.50269i	−1.36599	+	0.196399i
$786$	17.1914	−	14.4117i	0.613195	−	0.514047i
$787$	−1.20570	+	4.10625i	−0.0429787	+	0.146372i	−0.978187	−	0.207726i	$-0.933394\pi$
$787$	−1.20570	+	4.10625i	−0.0429787	+	0.146372i	0.935208	+	0.354098i	$0.115212\pi$
$788$	−44.8601	−	20.4869i	−1.59808	−	0.729816i
$789$	−5.75909	−	2.74462i	−0.205029	−	0.0977111i
$790$	−2.84324	+	19.7752i	−0.101158	+	0.703568i
$791$	3.56208	+	12.1313i	0.126653	+	0.431341i
$792$	0.172310	−	0.523005i	0.00612276	−	0.0185842i
$793$	−31.0752	−	48.3539i	−1.10351	−	1.71710i
$794$	9.42538	+	14.6662i	0.334494	+	0.520483i
$795$	−7.26630	+	10.9106i	−0.257709	+	0.386960i
$796$	0.523670	+	1.78346i	0.0185610	+	0.0632129i
$797$	−4.05851	+	28.2276i	−0.143760	+	0.999872i	0.782410	+	0.622764i	$0.213990\pi$
$797$	−4.05851	+	28.2276i	−0.143760	+	0.999872i	−0.926169	+	0.377107i	$0.876919\pi$
$798$	−3.12873	+	6.56508i	−0.110756	+	0.232401i
$799$	14.7386	+	6.73090i	0.521415	+	0.238122i
$800$	1.88046	−	6.40425i	0.0664842	−	0.226424i
$801$	−11.7174	−	8.08286i	−0.414012	−	0.285594i
$802$	49.8700	−	7.17023i	1.76097	−	0.253190i
$803$	−20.9884	−	13.4884i	−0.740664	−	0.475996i
$804$	−10.2719	+	2.83473i	−0.362261	+	0.0999734i
$805$	9.63733	+	1.69514i	0.339671	+	0.0597458i
$806$		−	24.8632i		−	0.875768i
$807$	36.6283	+	11.4080i	1.28938	+	0.401580i
$808$	0.0692629	+	0.481734i	0.00243666	+	0.0169473i
$809$	6.77283	−	3.09305i	0.238120	−	0.108746i	−0.292781	−	0.956179i	$-0.594581\pi$
$809$	6.77283	−	3.09305i	0.238120	−	0.108746i	0.530901	+	0.847434i	$0.321854\pi$
$810$	−26.0506	−	25.7359i	−0.915324	−	0.904268i
$811$	6.55486	−	14.3531i	0.230172	−	0.504007i	−0.758942	−	0.651159i	$-0.774283\pi$
$811$	6.55486	−	14.3531i	0.230172	−	0.504007i	0.989114	+	0.147152i	$0.0470105\pi$
$812$	13.3913	−	15.4544i	0.469943	−	0.542343i
$813$	−32.1738	+	4.09081i	−1.12838	+	0.143471i
$814$	16.6898	−	4.90058i	0.584978	−	0.171765i
$815$	−9.00180	−	10.3886i	−0.315319	−	0.363898i
$816$	12.1226	+	10.8559i	0.424377	+	0.380034i
$817$	6.36371	−	4.08971i	0.222638	−	0.143081i
$818$	14.7533	−	12.7838i	0.515837	−	0.446975i
$819$	11.0273	+	10.2044i	0.385325	+	0.356571i
$820$	−27.9665	−	4.02097i	−0.976631	−	0.140418i
$821$	24.9163	+	21.5901i	0.869586	+	0.753501i	0.970425	−	0.241402i	$-0.0776073\pi$
$821$	24.9163	+	21.5901i	0.869586	+	0.753501i	−0.100839	+	0.994903i	$0.532153\pi$
$822$	7.74161	−	48.2380i	0.270019	−	1.68249i
$823$	−16.2548	−	4.77284i	−0.566607	−	0.166371i	−0.0141317	−	0.999900i	$-0.504498\pi$
$823$	−16.2548	−	4.77284i	−0.566607	−	0.166371i	−0.552475	+	0.833529i	$0.686317\pi$
$824$	−0.309024	−	0.676668i	−0.0107654	−	0.0235728i
$825$	5.23259	−	2.28713i	0.182176	−	0.0796275i
$826$	6.89862	−	10.7345i	0.240034	−	0.373500i
$827$	−8.25538			−0.287068			−0.143534	−	0.989645i	$-0.545847\pi$
$827$	−8.25538			−0.287068			−0.143534	+	0.989645i	$0.545847\pi$
$828$	−24.8583	+	13.8142i	−0.863885	+	0.480078i
$829$	−5.22695			−0.181540			−0.0907698	−	0.995872i	$-0.528933\pi$
$829$	−5.22695			−0.181540			−0.0907698	+	0.995872i	$0.528933\pi$
$830$	26.1276	−	40.6554i	0.906903	−	1.41117i
$831$	19.2705	−	8.42299i	0.668487	−	0.292190i
$832$	16.2525	+	35.5880i	0.563454	+	1.23379i
$833$	−2.22794	−	0.654181i	−0.0771934	−	0.0226660i
$834$	9.73302	−	60.6466i	0.337027	−	2.10002i
$835$	−4.03636	−	3.49753i	−0.139684	−	0.121037i
$836$	−16.2294	−	2.33343i	−0.561305	−	0.0807035i
$837$	−11.4899	−	5.94371i	−0.397148	−	0.205445i
$838$	18.1444	−	15.7222i	0.626788	−	0.543115i
$839$	−7.14641	+	4.59272i	−0.246721	+	0.158558i	−0.658157	−	0.752880i	$-0.728664\pi$
$839$	−7.14641	+	4.59272i	−0.246721	+	0.158558i	0.411436	+	0.911439i	$0.365027\pi$
$840$	−0.122661	−	0.109844i	−0.00423221	−	0.00378999i
$841$	51.0970	+	58.9691i	1.76197	+	2.03342i
$842$	22.4350	−	6.58750i	0.773160	−	0.227020i
$843$	43.2617	−	5.50060i	1.49001	−	0.189451i
$844$	−26.5870	+	30.6830i	−0.915162	+	1.05615i
$845$	10.2401	−	22.4227i	0.352271	−	0.771365i
$846$	40.4172	−	10.4468i	1.38957	−	0.359167i
$847$	−4.11205	+	1.87791i	−0.141292	+	0.0645257i
$848$	−2.13594	−	14.8558i	−0.0733486	−	0.510150i
$849$	−3.85252	−	1.19988i	−0.132218	−	0.0411797i
$850$			3.87513i			0.132916i
$851$	9.51608	+	4.71131i	0.326207	+	0.161502i
$852$	47.2850	−	13.0493i	1.61996	−	0.447061i
$853$	−15.4856	−	9.95199i	−0.530217	−	0.340750i	0.247985	−	0.968764i	$-0.420232\pi$
$853$	−15.4856	−	9.95199i	−0.530217	−	0.340750i	−0.778202	+	0.628014i	$0.783868\pi$
$854$	22.6540	−	3.25715i	0.775203	−	0.111457i
$855$	7.31829	−	10.6090i	0.250280	−	0.362820i
$856$	−0.0858283	+	0.292304i	−0.00293355	+	0.00999076i
$857$	47.2292	+	21.5689i	1.61332	+	0.736778i	0.998647	−	0.0520038i	$-0.0165608\pi$
$857$	47.2292	+	21.5689i	1.61332	+	0.736778i	0.614673	+	0.788782i	$0.289288\pi$
$858$	−29.3178	+	61.5182i	−1.00089	+	2.10020i
$859$	−0.251497	+	1.74920i	−0.00858097	+	0.0596819i	−0.993662	−	0.112409i	$-0.964143\pi$
$859$	−0.251497	+	1.74920i	−0.00858097	+	0.0596819i	0.985081	+	0.172091i	$0.0550524\pi$
$860$	−4.08217	−	13.9026i	−0.139201	−	0.474074i
$861$	6.72598	−	10.0993i	0.229221	−	0.344184i
$862$	−16.8111	−	26.1585i	−0.572587	−	0.890963i
$863$	−0.157206	−	0.244617i	−0.00535135	−	0.00832687i	0.838568	−	0.544798i	$-0.183394\pi$
$863$	−0.157206	−	0.244617i	−0.00535135	−	0.00832687i	−0.843919	+	0.536471i	$0.819757\pi$
$864$	41.3923	+	2.02955i	1.40819	+	0.0690467i
$865$	0.303779	+	1.03458i	0.0103288	+	0.0351767i
$866$	0.286386	−	1.99186i	0.00973180	−	0.0676862i
$867$	18.1505	+	8.64999i	0.616422	+	0.293769i
$868$	4.47627	+	2.04424i	0.151934	+	0.0693861i
$869$	5.44988	−	18.5606i	0.184874	−	0.629625i
$870$	−55.8725	+	46.8384i	−1.89425	+	1.58797i
$871$	−15.4288	+	2.21833i	−0.522785	+	0.0751652i
$872$	0.522730	+	0.335938i	0.0177019	+	0.0113763i
$873$	21.6212	+	36.1895i	0.731766	+	1.22483i
$874$	−12.7038	−	15.6236i	−0.429712	−	0.528477i
$875$		−	11.9094i		−	0.402612i
$876$	6.44723	−	20.7005i	0.217832	−	0.699406i
$877$	0.368646	+	2.56399i	0.0124483	+	0.0865798i	0.995098	−	0.0988887i	$-0.0315288\pi$
$877$	0.368646	+	2.56399i	0.0124483	+	0.0865798i	−0.982650	+	0.185469i	$0.940620\pi$
$878$	−67.1790	+	30.6796i	−2.26718	+	1.03539i
$879$	−0.294781	+	18.0488i	−0.00994272	+	0.608773i
$880$	13.5111	−	29.5852i	0.455459	−	0.997316i
$881$	14.8277	−	17.1120i	0.499556	−	0.576519i	−0.448838	−	0.893613i	$-0.648162\pi$
$881$	14.8277	−	17.1120i	0.499556	−	0.576519i	0.948394	+	0.317095i	$0.102707\pi$
$882$	−5.52008	+	2.30617i	−0.185871	+	0.0776526i
$883$	−17.1515	+	5.03613i	−0.577193	+	0.169479i	−0.557283	−	0.830323i	$-0.688156\pi$
$883$	−17.1515	+	5.03613i	−0.577193	+	0.169479i	−0.0199100	+	0.999802i	$0.506338\pi$
$884$	−15.0526	−	17.3716i	−0.506274	−	0.584271i
$885$	−15.0857	+	16.8459i	−0.507101	+	0.566270i
$886$	26.1890	−	16.8306i	0.879837	−	0.565437i
$887$	−10.4215	+	9.03027i	−0.349919	+	0.303207i	−0.812030	−	0.583615i	$-0.801638\pi$
$887$	−10.4215	+	9.03027i	−0.349919	+	0.303207i	0.462111	+	0.886822i	$0.347092\pi$
$888$	−0.0941321	−	0.151869i	−0.00315887	−	0.00509640i
$889$	10.2985	+	1.48071i	0.345402	+	0.0496613i
$890$	−14.5906	−	12.6429i	−0.489079	−	0.423790i
$891$	21.4204	+	28.2548i	0.717610	+	0.946571i
$892$	−26.4303	−	7.76063i	−0.884951	−	0.259845i
$893$	6.10348	+	13.3647i	0.204245	+	0.447234i
$894$	9.31558	+	21.3126i	0.311560	+	0.712801i
$895$	−6.88639	+	10.7154i	−0.230187	+	0.358177i
$896$	0.372707			0.0124513
$897$	−38.6213	+	15.4597i	−1.28953	+	0.516184i
$898$	−1.76514			−0.0589033
$899$	−13.9245	+	21.6670i	−0.464408	+	0.722634i
$900$	3.12565	+	3.85466i	0.104188	+	0.128489i
$901$	3.57797	+	7.83466i	0.119200	+	0.261011i
$902$	52.8078	+	15.5058i	1.75831	+	0.516286i
$903$	6.14408	+	0.986048i	0.204462	+	0.0328136i
$904$	0.445197	+	0.385766i	0.0148070	+	0.0128304i
$905$	−13.2180	−	1.90046i	−0.439380	−	0.0631734i
$906$	27.9015	−	17.2940i	0.926967	−	0.574555i
$907$	7.75137	−	6.71660i	0.257380	−	0.223021i	−0.516607	−	0.856223i	$-0.672805\pi$
$907$	7.75137	−	6.71660i	0.257380	−	0.223021i	0.773987	+	0.633202i	$0.218260\pi$
$908$	23.3936	−	15.0341i	0.776343	−	0.498925i
$909$	−28.0653	−	13.9420i	−0.930866	−	0.462427i
$910$	13.3442	+	15.4000i	0.442354	+	0.510504i
$911$	−33.9316	+	9.96322i	−1.12420	+	0.330096i	−0.790427	−	0.612556i	$-0.790141\pi$
$911$	−33.9316	+	9.96322i	−1.12420	+	0.330096i	−0.333777	+	0.942652i	$0.608323\pi$
$912$	1.86121	+	14.6382i	0.0616309	+	0.484720i
$913$	−30.6427	+	35.3635i	−1.01412	+	1.17036i
$914$	−14.7446	+	32.2862i	−0.487708	+	1.06793i
$915$	−40.5547	−	0.662356i	−1.34070	−	0.0218968i
$916$	−38.9894	+	17.8058i	−1.28824	+	0.588322i
$917$	0.924312	+	6.42873i	0.0305235	+	0.212295i
$918$	−23.3899	+	5.63985i	−0.771983	+	0.186143i
$919$		−	43.3277i		−	1.42925i	−0.699509	−	0.714624i	$-0.746598\pi$
$919$		−	43.3277i		−	1.42925i	0.699509	−	0.714624i	$-0.253402\pi$
$920$	0.420438	−	0.176316i	0.0138614	−	0.00581297i
$921$	−6.37394	−	23.0964i	−0.210028	−	0.761054i
$922$	−7.63432	−	4.90628i	−0.251423	−	0.161580i
$923$	71.0242	−	10.2117i	2.33779	−	0.336124i
$924$	−8.66499	−	10.3363i	−0.285057	−	0.340039i
$925$	0.522039	−	1.77790i	0.0171645	−	0.0584571i
$926$	44.4303	+	20.2906i	1.46007	+	0.666791i
$927$	47.1633	+	8.36132i	1.54904	+	0.274622i
$928$	11.7424	−	81.6700i	0.385463	−	2.68095i
$929$	−5.64730	−	19.2329i	−0.185282	−	0.631012i	−0.998777	−	0.0494403i	$-0.984256\pi$
$929$	−5.64730	−	19.2329i	−0.185282	−	0.631012i	0.813495	−	0.581571i	$-0.197562\pi$
$930$	−14.6029	−	9.72526i	−0.478846	−	0.318904i
$931$	−1.13835	−	1.77130i	−0.0373078	−	0.0580520i
$932$	−30.6997	−	47.7697i	−1.00560	−	1.56475i
$933$	−2.00138	−	1.33288i	−0.0655221	−	0.0436367i
$934$	−6.20624	−	21.1365i	−0.203074	−	0.691607i
$935$	−2.65628	+	18.4748i	−0.0868696	+	0.604192i
$936$	0.689261	+	0.122195i	0.0225292	+	0.00399408i
$937$	51.5865	+	23.5587i	1.68526	+	0.769631i	0.999111	+	0.0421662i	$0.0134259\pi$
$937$	51.5865	+	23.5587i	1.68526	+	0.769631i	0.686145	+	0.727464i	$0.259301\pi$
$938$	1.74862	−	5.95525i	0.0570945	−	0.194446i
$939$	8.73215	+	10.4164i	0.284963	+	0.339926i
$940$	27.8562	−	4.00512i	0.908570	−	0.130633i
$941$	−29.4403	−	18.9201i	−0.959726	−	0.616779i	−0.0358041	−	0.999359i	$-0.511399\pi$
$941$	−29.4403	−	18.9201i	−0.959726	−	0.616779i	−0.923922	+	0.382580i	$0.875036\pi$
$942$	17.4124	+	63.0951i	0.567327	+	2.05575i
$943$	17.2705	+	28.8190i	0.562404	+	0.938475i
$944$		−	25.8905i		−	0.842665i
$945$	10.3067	−	2.48518i	0.335277	−	0.0808429i
$946$	4.01680	+	27.9374i	0.130597	+	0.908325i
$947$	24.1037	−	11.0078i	0.783266	−	0.357706i	0.0166913	−	0.999861i	$-0.494687\pi$
$947$	24.1037	−	11.0078i	0.783266	−	0.357706i	0.766575	+	0.642155i	$0.221959\pi$
$948$	16.8084	+	0.274521i	0.545910	+	0.00891603i
$949$	13.1751	−	28.8495i	0.427683	−	0.936496i
$950$	−2.30112	+	2.65564i	−0.0746582	+	0.0861602i
$951$	1.46032	+	11.4852i	0.0473540	+	0.372434i
$952$	−0.103803	+	0.0304793i	−0.00336428	+	0.000987840i
$953$	−8.18986	−	9.45160i	−0.265296	−	0.306167i	0.607435	−	0.794369i	$-0.292198\pi$
$953$	−8.18986	−	9.45160i	−0.265296	−	0.306167i	−0.872731	+	0.488202i	$0.837653\pi$
$954$	19.8737	+	9.87265i	0.643434	+	0.319639i
$955$	4.13044	−	2.65447i	0.133658	−	0.0858967i
$956$	−25.0736	+	21.7264i	−0.810937	+	0.702681i
$957$	60.0019	−	37.1906i	1.93959	−	1.20220i
$958$	58.4743	+	8.40733i	1.88922	+	0.271629i
$959$	10.6898	+	9.26280i	0.345193	+	0.299111i
$960$	27.2590	+	4.37473i	0.879781	+	0.141194i
$961$	23.7974	+	6.98755i	0.767658	+	0.225405i
$962$	9.18573	+	20.1139i	0.296160	+	0.648499i
$963$	−12.3547	−	15.2363i	−0.398124	−	0.490982i
$964$	11.9432	−	18.5841i	0.384666	−	0.598552i
$965$	31.4621			1.01280
$966$	0.788899	−	16.5459i	0.0253824	−	0.532354i
$967$	−32.0005			−1.02907			−0.514534	−	0.857470i	$-0.672035\pi$
$967$	−32.0005			−1.02907			−0.514534	+	0.857470i	$0.672035\pi$
$968$	−0.113870	+	0.177185i	−0.00365992	+	0.00569494i
$969$	−3.39152	−	7.75928i	−0.108951	−	0.249264i
$970$	23.7515	+	52.0085i	0.762614	+	1.66989i
$971$	26.0493	+	7.64876i	0.835962	+	0.245460i	0.671576	−	0.740936i	$-0.265618\pi$
$971$	26.0493	+	7.64876i	0.835962	+	0.245460i	0.164386	+	0.986396i	$0.447436\pi$
$972$	−18.7173	+	24.4762i	−0.600359	+	0.785074i
$973$	13.4396	+	11.6455i	0.430855	+	0.373338i
$974$	48.8427	+	7.02252i	1.56502	+	0.225016i
$975$	3.82450	+	6.17031i	0.122482	+	0.197608i
$976$	35.0956	−	30.4105i	1.12338	−	0.973417i
$977$	−25.4835	+	16.3773i	−0.815290	+	0.523955i	−0.880572	−	0.473912i	$-0.842842\pi$
$977$	−25.4835	+	16.3773i	−0.815290	+	0.523955i	0.0652823	+	0.997867i	$0.479205\pi$
$978$	−15.5235	+	17.3348i	−0.496388	+	0.554307i
$979$	12.2414	+	14.1274i	0.391238	+	0.451513i
$980$	−3.86970	+	1.13625i	−0.123613	+	0.0362961i
$981$	−36.9174	+	15.4232i	−1.17868	+	0.492426i
$982$	−19.3728	+	22.3574i	−0.618212	+	0.713454i
$983$	−11.8628	+	25.9758i	−0.378363	+	0.828500i	0.620650	+	0.784088i	$0.286869\pi$
$983$	−11.8628	+	25.9758i	−0.378363	+	0.828500i	−0.999013	+	0.0444124i	$0.985858\pi$
$984$	0.00923220	−	0.565269i	0.000294312	−	0.0180201i
$985$	−46.3066	+	21.1475i	−1.47545	+	0.673815i
$986$	6.81736	+	47.4158i	0.217109	+	1.51003i
$987$	−3.59400	+	11.5395i	−0.114398	+	0.367306i
$988$		−	20.8433i		−	0.663114i
$989$	−9.76440	+	14.1960i	−0.310490	+	0.451405i
$990$	24.6637	+	41.2821i	0.783864	+	1.31203i
$991$	−21.0500	−	13.5280i	−0.668674	−	0.429731i	0.161773	−	0.986828i	$-0.448279\pi$
$991$	−21.0500	−	13.5280i	−0.668674	−	0.429731i	−0.830447	+	0.557097i	$0.811915\pi$
$992$	19.6535	−	2.82574i	0.623998	−	0.0897174i
$993$	26.8860	−	22.5388i	0.853202	−	0.715246i
$994$	−8.04951	+	27.4141i	−0.255315	+	0.869523i
$995$	1.74529	+	0.797049i	0.0553295	+	0.0252682i
$996$	−36.7086	−	17.4943i	−1.16316	−	0.554327i
$997$	8.75982	−	60.9259i	0.277426	−	1.92954i	−0.0825609	−	0.996586i	$-0.526310\pi$
$997$	8.75982	−	60.9259i	0.277426	−	1.92954i	0.359987	−	0.932957i	$-0.382781\pi$
$998$	−9.55694	−	32.5479i	−0.302520	−	1.03029i
$999$	11.4910	+	0.563429i	0.363560	+	0.0178261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.u.a.113.9	✓	480
3.2	odd	2	inner	483.2.u.a.113.40	yes	480
23.11	odd	22	inner	483.2.u.a.218.40	yes	480
69.11	even	22	inner	483.2.u.a.218.9	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.u.a.113.9	✓	480	1.1	even	1	trivial
483.2.u.a.113.40	yes	480	3.2	odd	2	inner
483.2.u.a.218.9	yes	480	69.11	even	22	inner
483.2.u.a.218.40	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+(-1.07812 + 1.67759i) q^{2} +(1.58707 - 0.693695i) q^{3} +(-0.821124 - 1.79801i) q^{4} +(-1.95772 - 0.574839i) q^{5} +(-0.547316 + 3.41033i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-0.0461173 - 0.00663067i) q^{8} +(2.03757 - 2.20188i) q^{9} +(3.07500 - 2.66450i) q^{10} +(-3.31421 + 2.12992i) q^{11} +(-2.55045 - 2.28396i) q^{12} +(-3.27962 - 3.78489i) q^{13} +(1.91337 - 0.561817i) q^{14} +(-3.50580 + 0.445753i) q^{15} +(2.64969 - 3.05790i) q^{16} +(-0.964591 + 2.11216i) q^{17} +(1.49710 + 5.79210i) q^{18} +(-1.91527 + 0.874676i) q^{19} +(0.573966 + 3.99202i) q^{20} +(-1.65370 - 0.515049i) q^{21} -7.85618i q^{22} +(3.25253 - 3.52435i) q^{23} +(-0.0777911 + 0.0214680i) q^{24} +(-0.704035 - 0.452456i) q^{25} +(9.88530 - 1.42129i) q^{26} +(1.70633 - 4.90800i) q^{27} +(-0.556883 + 1.89657i) q^{28} +(-9.41051 - 4.29763i) q^{29} +(3.03188 - 6.36186i) q^{30} +(0.354302 - 2.46423i) q^{31} +(2.24696 + 7.65245i) q^{32} +(-3.78237 + 5.67938i) q^{33} +(-2.50338 - 3.89534i) q^{34} +(1.10311 + 1.71647i) q^{35} +(-5.63211 - 1.85556i) q^{36} +(0.623786 + 2.12442i) q^{37} +(0.597549 - 4.15604i) q^{38} +(-7.83055 - 3.73182i) q^{39} +(0.0864733 + 0.0394910i) q^{40} +(-1.97370 + 6.72182i) q^{41} +(2.64692 - 2.21894i) q^{42} +(-3.55611 + 0.511291i) q^{43} +(6.55100 + 4.21007i) q^{44} +(-5.25473 + 3.13940i) q^{45} +(2.40578 + 9.25607i) q^{46} -6.97798i q^{47} +(2.08398 - 6.69117i) q^{48} +(0.142315 + 0.989821i) q^{49} +(1.51807 - 0.693278i) q^{50} +(-0.0656770 + 4.02127i) q^{51} +(-4.11229 + 9.00466i) q^{52} +(2.42909 - 2.80331i) q^{53} +(6.39396 + 8.15393i) q^{54} +(7.71267 - 2.26464i) q^{55} +(0.0305110 + 0.0352116i) q^{56} +(-2.43291 + 2.71679i) q^{57} +(17.3553 - 11.1536i) q^{58} +(4.83586 - 4.19029i) q^{59} +(3.68017 + 5.93745i) q^{60} +(11.3602 + 1.63335i) q^{61} +(3.75197 + 3.25110i) q^{62} +(-2.98182 + 0.329746i) q^{63} +(-7.49557 - 2.20090i) q^{64} +(4.24489 + 9.29501i) q^{65} +(-5.44980 - 12.4683i) q^{66} +(1.68271 - 2.61835i) q^{67} +4.58973 q^{68} +(2.71717 - 7.84965i) q^{69} -4.06881 q^{70} +(-7.74611 + 12.0532i) q^{71} +(-0.108567 + 0.0880345i) q^{72} +(2.63075 + 5.76055i) q^{73} +(-4.23641 - 1.24392i) q^{74} +(-1.43122 - 0.229693i) q^{75} +(3.14535 + 2.72547i) q^{76} +(3.89951 + 0.560666i) q^{77} +(14.7027 - 9.11307i) q^{78} +(-3.71086 + 3.21547i) q^{79} +(-6.94515 + 4.46337i) q^{80} +(-0.696585 - 8.97300i) q^{81} +(-9.14854 - 10.5580i) q^{82} +(11.3963 - 3.34627i) q^{83} +(0.431829 + 3.39629i) q^{84} +(3.10255 - 3.58053i) q^{85} +(2.97617 - 6.51691i) q^{86} +(-17.9164 - 0.292617i) q^{87} +(0.166966 - 0.0762506i) q^{88} +(-0.675274 - 4.69663i) q^{89} +(0.398614 - 12.1999i) q^{90} +5.00812i q^{91} +(-9.00755 - 2.95417i) q^{92} +(-1.14712 - 4.15667i) q^{93} +(11.7062 + 7.52310i) q^{94} +(4.25237 - 0.611398i) q^{95} +(8.87455 + 10.5863i) q^{96} +(-3.95894 + 13.4829i) q^{97} +(-1.81394 - 0.828400i) q^{98} +(-2.06313 + 11.6374i) 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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