LMFDB - Embedded newform 230.2.l.a.33.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			33.2
Character	$\chi$	$=$	230.33
Dual form			230.2.l.a.7.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.997452 - 0.0713392i) q^{2} +(-0.442321 - 2.03332i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.86221 + 1.23780i) q^{5} +(0.296139 + 2.05969i) q^{6} +(1.88657 + 3.45500i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-1.20984 + 0.552516i) q^{9} +(-1.76917 - 1.36750i) q^{10} +(3.04037 + 2.63450i) q^{11} +(-0.148448 - 2.07557i) q^{12} +(-3.08985 - 1.68719i) q^{13} +(-1.63529 - 3.58078i) q^{14} +(1.69315 - 4.33398i) q^{15} +(0.959493 + 0.281733i) q^{16} +(3.08166 - 4.11662i) q^{17} +(1.24618 - 0.464799i) q^{18} +(-0.239698 + 1.66714i) q^{19} +(1.66710 + 1.49023i) q^{20} +(6.19064 - 5.36422i) q^{21} +(-2.84468 - 2.84468i) q^{22} +(-2.44330 - 4.12677i) q^{23} +2.08087i q^{24} +(1.93568 + 4.61011i) q^{25} +(2.96162 + 1.90332i) q^{26} +(-2.08248 - 2.78187i) q^{27} +(1.37567 + 3.68832i) q^{28} +(4.67045 - 0.671509i) q^{29} +(-1.99802 + 4.20215i) q^{30} +(-4.96472 + 3.19063i) q^{31} +(-0.936950 - 0.349464i) q^{32} +(4.01195 - 7.34734i) q^{33} +(-3.36749 + 3.88629i) q^{34} +(-0.763412 + 8.76915i) q^{35} +(-1.27616 + 0.374714i) q^{36} +(-0.192063 + 0.514940i) q^{37} +(0.358020 - 1.64579i) q^{38} +(-2.06388 + 7.02893i) q^{39} +(-1.55654 - 1.60536i) q^{40} +(2.91137 - 6.37502i) q^{41} +(-6.55754 + 4.90892i) q^{42} +(-0.984612 + 0.214189i) q^{43} +(2.63450 + 3.04037i) q^{44} +(-2.93689 - 0.468644i) q^{45} +(2.14268 + 4.29056i) q^{46} +(-8.34469 + 8.34469i) q^{47} +(0.148448 - 2.07557i) q^{48} +(-4.59336 + 7.14741i) q^{49} +(-1.60187 - 4.73646i) q^{50} +(-9.73349 - 4.44514i) q^{51} +(-2.81829 - 2.10975i) q^{52} +(1.94492 - 1.06201i) q^{53} +(1.87872 + 2.92335i) q^{54} +(2.40083 + 8.66939i) q^{55} +(-1.10904 - 3.77706i) q^{56} +(3.49585 - 0.250028i) q^{57} +(-4.70645 + 0.336612i) q^{58} +(-3.42341 - 11.6591i) q^{59} +(2.29271 - 4.04891i) q^{60} +(-1.10856 - 1.72495i) q^{61} +(5.17969 - 2.82833i) q^{62} +(-4.19139 - 3.13764i) q^{63} +(0.909632 + 0.415415i) q^{64} +(-3.66556 - 6.96654i) q^{65} +(-4.52588 + 7.04241i) q^{66} +(0.403696 - 5.64441i) q^{67} +(3.63615 - 3.63615i) q^{68} +(-7.31032 + 6.79338i) q^{69} +(1.38705 - 8.69234i) q^{70} +(8.02440 + 9.26066i) q^{71} +(1.29964 - 0.282719i) q^{72} +(-3.65015 + 2.73247i) q^{73} +(0.228309 - 0.499927i) q^{74} +(8.51764 - 5.97501i) q^{75} +(-0.474517 + 1.61606i) q^{76} +(-3.36630 + 15.4746i) q^{77} +(2.56006 - 6.86379i) q^{78} +(-13.5678 + 3.98387i) q^{79} +(1.43805 + 1.71231i) q^{80} +(-7.34827 + 8.48035i) q^{81} +(-3.35874 + 6.15108i) q^{82} +(11.0747 + 4.13065i) q^{83} +(6.89103 - 4.42860i) q^{84} +(10.8343 - 3.85153i) q^{85} +(0.997384 - 0.143402i) q^{86} +(-3.43123 - 9.19949i) q^{87} +(-2.41089 - 3.22057i) q^{88} +(-5.99039 - 3.84979i) q^{89} +(2.89598 + 0.676965i) q^{90} -13.8584i q^{91} +(-1.83113 - 4.43249i) q^{92} +(8.68358 + 8.68358i) q^{93} +(8.91873 - 7.72812i) q^{94} +(-2.50996 + 2.80787i) q^{95} +(-0.296139 + 2.05969i) q^{96} +(1.81978 - 0.678744i) q^{97} +(5.09155 - 6.80151i) q^{98} +(-5.13397 - 1.50747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.997452	−	0.0713392i	−0.705305	−	0.0504444i
$2$	−0.997452	−	0.0713392i	−0.705305	−	0.0504444i
$3$	−0.442321	−	2.03332i	−0.255374	−	1.17394i	−0.908894	−	0.417028i	$-0.863072\pi$
$3$	−0.442321	−	2.03332i	−0.255374	−	1.17394i	0.653519	−	0.756910i	$-0.273292\pi$
$4$	0.989821	+	0.142315i	0.494911	+	0.0711574i
$5$	1.86221	+	1.23780i	0.832807	+	0.553563i
$5$	1.86221	+	1.23780i	0.832807	+	0.553563i
$6$	0.296139	+	2.05969i	0.120898	+	0.840866i
$7$	1.88657	+	3.45500i	0.713057	+	1.30587i	0.943043	+	0.332672i	$0.107950\pi$
$7$	1.88657	+	3.45500i	0.713057	+	1.30587i	−0.229986	+	0.973194i	$0.573868\pi$
$8$	−0.977147	−	0.212565i	−0.345474	−	0.0751532i
$9$	−1.20984	+	0.552516i	−0.403281	+	0.184172i
$10$	−1.76917	−	1.36750i	−0.559459	−	0.432441i
$11$	3.04037	+	2.63450i	0.916707	+	0.794331i	0.979028	−	0.203725i	$-0.0653049\pi$
$11$	3.04037	+	2.63450i	0.916707	+	0.794331i	−0.0623213	+	0.998056i	$0.519850\pi$
$12$	−0.148448	−	2.07557i	−0.0428532	−	0.599166i
$13$	−3.08985	−	1.68719i	−0.856971	−	0.467942i	−0.0102304	−	0.999948i	$-0.503257\pi$
$13$	−3.08985	−	1.68719i	−0.856971	−	0.467942i	−0.846740	+	0.532006i	$0.821438\pi$
$14$	−1.63529	−	3.58078i	−0.437049	−	0.957004i
$15$	1.69315	−	4.33398i	0.437171	−	1.11903i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	3.08166	−	4.11662i	0.747413	−	0.998427i	−0.252114	−	0.967697i	$-0.581126\pi$
$17$	3.08166	−	4.11662i	0.747413	−	0.998427i	0.999528	−	0.0307298i	$-0.00978315\pi$
$18$	1.24618	−	0.464799i	0.293726	−	0.109554i
$19$	−0.239698	+	1.66714i	−0.0549906	+	0.382468i	0.943677	+	0.330867i	$0.107341\pi$
$19$	−0.239698	+	1.66714i	−0.0549906	+	0.382468i	−0.998668	+	0.0516004i	$0.983568\pi$
$20$	1.66710	+	1.49023i	0.372775	+	0.333225i
$21$	6.19064	−	5.36422i	1.35091	−	1.17057i
$22$	−2.84468	−	2.84468i	−0.606489	−	0.606489i
$23$	−2.44330	−	4.12677i	−0.509464	−	0.860492i
$23$	−2.44330	−	4.12677i	−0.509464	−	0.860492i
$24$			2.08087i			0.424757i
$25$	1.93568	+	4.61011i	0.387136	+	0.922023i
$26$	2.96162	+	1.90332i	0.580821	+	0.373271i
$27$	−2.08248	−	2.78187i	−0.400774	−	0.535371i
$28$	1.37567	+	3.68832i	0.259977	+	0.697026i
$29$	4.67045	−	0.671509i	0.867280	−	0.124696i	0.305710	−	0.952125i	$-0.401106\pi$
$29$	4.67045	−	0.671509i	0.867280	−	0.124696i	0.561571	+	0.827429i	$0.310197\pi$
$30$	−1.99802	+	4.20215i	−0.364787	+	0.767204i
$31$	−4.96472	+	3.19063i	−0.891691	+	0.573055i	−0.904315	−	0.426865i	$-0.859618\pi$
$31$	−4.96472	+	3.19063i	−0.891691	+	0.573055i	0.0126244	+	0.999920i	$0.495981\pi$
$32$	−0.936950	−	0.349464i	−0.165631	−	0.0617771i
$33$	4.01195	−	7.34734i	0.698391	−	1.27901i
$34$	−3.36749	+	3.88629i	−0.577520	+	0.666493i
$35$	−0.763412	+	8.76915i	−0.129040	+	1.48226i
$36$	−1.27616	+	0.374714i	−0.212693	+	0.0624523i
$37$	−0.192063	+	0.514940i	−0.0315749	+	0.0846556i	−0.951781	−	0.306780i	$-0.900749\pi$
$37$	−0.192063	+	0.514940i	−0.0315749	+	0.0846556i	0.920206	+	0.391435i	$0.128021\pi$
$38$	0.358020	−	1.64579i	0.0580785	−	0.266983i
$39$	−2.06388	+	7.02893i	−0.330486	+	1.12553i
$40$	−1.55654	−	1.60536i	−0.246111	−	0.253830i
$41$	2.91137	−	6.37502i	0.454680	−	0.995610i	−0.533988	−	0.845492i	$-0.679307\pi$
$41$	2.91137	−	6.37502i	0.454680	−	0.995610i	0.988668	−	0.150118i	$-0.0479655\pi$
$42$	−6.55754	+	4.90892i	−1.01185	+	0.757462i
$43$	−0.984612	+	0.214189i	−0.150152	+	0.0326636i	−0.287013	−	0.957927i	$-0.592662\pi$
$43$	−0.984612	+	0.214189i	−0.150152	+	0.0326636i	0.136861	+	0.990590i	$0.456299\pi$
$44$	2.63450	+	3.04037i	0.397166	+	0.458353i
$45$	−2.93689	−	0.468644i	−0.437806	−	0.0698613i
$46$	2.14268	+	4.29056i	0.315921	+	0.632609i
$47$	−8.34469	+	8.34469i	−1.21720	+	1.21720i	−0.248589	+	0.968609i	$0.579967\pi$
$47$	−8.34469	+	8.34469i	−1.21720	+	1.21720i	−0.968609	+	0.248589i	$0.920033\pi$
$48$	0.148448	−	2.07557i	0.0214266	−	0.299583i
$49$	−4.59336	+	7.14741i	−0.656195	+	1.02106i
$50$	−1.60187	−	4.73646i	−0.226538	−	0.669836i
$51$	−9.73349	−	4.44514i	−1.36296	−	0.622444i
$52$	−2.81829	−	2.10975i	−0.390827	−	0.292569i
$53$	1.94492	−	1.06201i	0.267155	−	0.145878i	−0.340088	−	0.940393i	$-0.610457\pi$
$53$	1.94492	−	1.06201i	0.267155	−	0.145878i	0.607244	+	0.794516i	$0.292275\pi$
$54$	1.87872	+	2.92335i	0.255661	+	0.397817i
$55$	2.40083	+	8.66939i	0.323728	+	1.16898i
$56$	−1.10904	−	3.77706i	−0.148202	−	0.504731i
$57$	3.49585	−	0.250028i	0.463036	−	0.0331170i
$58$	−4.70645	+	0.336612i	−0.617988	+	0.0441993i
$59$	−3.42341	−	11.6591i	−0.445690	−	1.51788i	−0.809903	−	0.586564i	$-0.800480\pi$
$59$	−3.42341	−	11.6591i	−0.445690	−	1.51788i	0.364213	−	0.931316i	$-0.381338\pi$
$60$	2.29271	−	4.04891i	0.295988	−	0.522712i
$61$	−1.10856	−	1.72495i	−0.141936	−	0.220857i	0.763006	−	0.646391i	$-0.223723\pi$
$61$	−1.10856	−	1.72495i	−0.141936	−	0.220857i	−0.904942	+	0.425534i	$0.860086\pi$
$62$	5.17969	−	2.82833i	0.657822	−	0.359198i
$63$	−4.19139	−	3.13764i	−0.528066	−	0.395305i
$64$	0.909632	+	0.415415i	0.113704	+	0.0519269i
$65$	−3.66556	−	6.96654i	−0.454657	−	0.864092i
$66$	−4.52588	+	7.04241i	−0.557098	+	0.866861i
$67$	0.403696	−	5.64441i	0.0493193	−	0.689574i	−0.911306	−	0.411729i	$-0.864925\pi$
$67$	0.403696	−	5.64441i	0.0493193	−	0.689574i	0.960626	−	0.277845i	$-0.0896203\pi$
$68$	3.63615	−	3.63615i	0.440948	−	0.440948i
$69$	−7.31032	+	6.79338i	−0.880059	+	0.817827i
$70$	1.38705	−	8.69234i	0.165784	−	1.03893i
$71$	8.02440	+	9.26066i	0.952322	+	1.09904i	0.994993	+	0.0999485i	$0.0318678\pi$
$71$	8.02440	+	9.26066i	0.952322	+	1.09904i	−0.0426710	+	0.999089i	$0.513587\pi$
$72$	1.29964	−	0.282719i	0.153164	−	0.0333188i
$73$	−3.65015	+	2.73247i	−0.427217	+	0.319811i	−0.791159	−	0.611611i	$-0.790522\pi$
$73$	−3.65015	+	2.73247i	−0.427217	+	0.319811i	0.363941	+	0.931422i	$0.381431\pi$
$74$	0.228309	−	0.499927i	0.0265404	−	0.0581153i
$75$	8.51764	−	5.97501i	0.983532	−	0.689934i
$76$	−0.474517	+	1.61606i	−0.0544308	+	0.185374i
$77$	−3.36630	+	15.4746i	−0.383626	+	1.76350i
$78$	2.56006	−	6.86379i	0.289870	−	0.777171i
$79$	−13.5678	+	3.98387i	−1.52650	+	0.448221i	−0.933977	−	0.357333i	$-0.883686\pi$
$79$	−13.5678	+	3.98387i	−1.52650	+	0.448221i	−0.592523	+	0.805554i	$0.701868\pi$
$80$	1.43805	+	1.71231i	0.160779	+	0.191442i
$81$	−7.34827	+	8.48035i	−0.816474	+	0.942261i
$82$	−3.35874	+	6.15108i	−0.370911	+	0.679273i
$83$	11.0747	+	4.13065i	1.21561	+	0.453398i	0.873760	−	0.486357i	$-0.161675\pi$
$83$	11.0747	+	4.13065i	1.21561	+	0.453398i	0.341847	+	0.939756i	$0.388947\pi$
$84$	6.89103	−	4.42860i	0.751873	−	0.483200i
$85$	10.8343	−	3.85153i	1.17514	−	0.417757i
$86$	0.997384	−	0.143402i	0.107551	−	0.0154634i
$87$	−3.43123	−	9.19949i	−0.367867	−	0.986289i
$88$	−2.41089	−	3.22057i	−0.257002	−	0.343314i
$89$	−5.99039	−	3.84979i	−0.634980	−	0.408077i	0.183171	−	0.983081i	$-0.441364\pi$
$89$	−5.99039	−	3.84979i	−0.634980	−	0.408077i	−0.818150	+	0.575004i	$0.805000\pi$
$90$	2.89598	+	0.676965i	0.305263	+	0.0713584i
$91$		−	13.8584i		−	1.45276i
$92$	−1.83113	−	4.43249i	−0.190909	−	0.462119i
$93$	8.68358	+	8.68358i	0.900445	+	0.900445i
$94$	8.91873	−	7.72812i	0.919897	−	0.797095i
$95$	−2.50996	+	2.80787i	−0.257517	+	0.288081i
$96$	−0.296139	+	2.05969i	−0.0302246	+	0.210217i
$97$	1.81978	−	0.678744i	0.184771	−	0.0689160i	−0.255376	−	0.966842i	$-0.582199\pi$
$97$	1.81978	−	0.678744i	0.184771	−	0.0689160i	0.440147	+	0.897926i	$0.354926\pi$
$98$	5.09155	−	6.80151i	0.514324	−	0.687057i
$99$	−5.13397	−	1.50747i	−0.515984	−	0.151506i
$100$	1.25989	+	4.83866i	0.125989	+	0.483866i
$101$	−5.46309	−	11.9625i	−0.543598	−	1.19031i	−0.959708	−	0.280999i	$-0.909334\pi$
$101$	−5.46309	−	11.9625i	−0.543598	−	1.19031i	0.416110	−	0.909314i	$-0.363393\pi$
$102$	9.39158	+	5.12819i	0.929905	+	0.507766i
$103$	1.31959	+	18.4503i	0.130023	+	1.81796i	0.475697	+	0.879609i	$0.342196\pi$
$103$	1.31959	+	18.4503i	0.130023	+	1.81796i	−0.345674	+	0.938355i	$0.612350\pi$
$104$	2.66060	+	2.30543i	0.260894	+	0.226066i
$105$	18.1681	−	2.32652i	1.77303	−	0.227045i
$106$	−2.01573	+	0.920551i	−0.195785	+	0.0894118i
$107$	6.92694	+	1.50686i	0.669653	+	0.145674i	0.534523	−	0.845154i	$-0.320491\pi$
$107$	6.92694	+	1.50686i	0.669653	+	0.145674i	0.135130	+	0.990828i	$0.456855\pi$
$108$	−1.66538	−	3.04992i	−0.160252	−	0.293479i
$109$	−0.448085	−	3.11650i	−0.0429188	−	0.298507i	−0.999963	−	0.00856580i	$-0.997273\pi$
$109$	−0.448085	−	3.11650i	−0.0429188	−	0.298507i	0.957045	−	0.289941i	$-0.0936357\pi$
$110$	−1.77625	−	8.81857i	−0.169358	−	0.840818i
$111$	1.13199	+	0.162756i	0.107444	+	0.0154481i
$112$	0.836766	+	3.84655i	0.0790670	+	0.363465i
$113$	−2.32059	−	0.165972i	−0.218302	−	0.0156133i	−0.0382404	−	0.999269i	$-0.512175\pi$
$113$	−2.32059	−	0.165972i	−0.218302	−	0.0156133i	−0.180062	+	0.983655i	$0.557630\pi$
$114$	−3.50478			−0.328253
$115$	0.558183	−	10.7093i	0.0520508	−	0.998644i
$116$	4.71848			0.438099
$117$	4.67043	+	0.334036i	0.431781	+	0.0308816i
$118$	2.58294	+	11.8736i	0.237779	+	1.09305i
$119$	20.0367	+	2.88084i	1.83676	+	0.264086i
$120$	−2.57571	+	3.87503i	−0.235129	+	0.353740i
$121$	0.737824	+	5.13168i	0.0670749	+	0.466516i
$122$	0.982678	+	1.79964i	0.0889675	+	0.162932i
$123$	−14.2502	−	3.09994i	−1.28490	−	0.279512i
$124$	−5.36826	+	2.45160i	−0.482084	+	0.220161i
$125$	−2.10177	+	10.9810i	−0.187988	+	0.982171i
$126$	3.95688	+	3.42865i	0.352507	+	0.305449i
$127$	−0.757790	−	10.5953i	−0.0672430	−	0.940180i	−0.913352	−	0.407170i	$-0.866516\pi$
$127$	−0.757790	−	10.5953i	−0.0672430	−	0.940180i	0.846109	−	0.533009i	$-0.178939\pi$
$128$	−0.877679	−	0.479249i	−0.0775766	−	0.0423600i
$129$	0.871030	+	1.90729i	0.0766899	+	0.167928i
$130$	3.15923	+	7.21028i	0.277083	+	0.632384i
$131$	−13.2034	−	3.87686i	−1.15358	−	0.338723i	−0.351648	−	0.936132i	$-0.614379\pi$
$131$	−13.2034	−	3.87686i	−1.15358	−	0.338723i	−0.801937	+	0.597409i	$0.796197\pi$
$132$	5.01675	−	6.70160i	0.436652	−	0.583299i
$133$	−6.21216	+	2.31702i	−0.538663	+	0.200911i
$134$	−0.805335	+	5.60123i	−0.0695703	+	0.483872i
$135$	−0.434615	−	7.75814i	−0.0374057	−	0.667715i
$136$	−3.88629	+	3.36749i	−0.333247	+	0.288760i
$137$	−3.84645	−	3.84645i	−0.328625	−	0.328625i	0.523439	−	0.852063i	$-0.324649\pi$
$137$	−3.84645	−	3.84645i	−0.328625	−	0.328625i	−0.852063	+	0.523439i	$0.824649\pi$
$138$	7.77633	−	6.25456i	0.661965	−	0.532423i
$139$		−	1.69372i		−	0.143659i	−0.997417	−	0.0718297i	$-0.977116\pi$
$139$		−	1.69372i		−	0.143659i	0.997417	−	0.0718297i	$-0.0228838\pi$
$140$	−2.00362	+	8.57124i	−0.169337	+	0.724402i
$141$	20.6584	+	13.2764i	1.73976	+	1.11807i
$142$	−7.34331	−	9.80952i	−0.616237	−	0.823196i
$143$	−4.94941	−	13.2699i	−0.413891	−	1.10968i
$144$	−1.31650	+	0.189284i	−0.109708	+	0.0157736i
$145$	9.52857	+	4.53061i	0.791305	+	0.376247i
$146$	3.83578	−	2.46511i	0.317451	−	0.204014i
$147$	16.5647	+	6.17832i	1.36623	+	0.509579i
$148$	−0.263391	+	0.482365i	−0.0216506	+	0.0396502i
$149$	11.4940	−	13.2648i	0.941625	−	1.08669i	−0.0544798	−	0.998515i	$-0.517350\pi$
$149$	11.4940	−	13.2648i	0.941625	−	1.08669i	0.996105	−	0.0881782i	$-0.0281045\pi$
$150$	−8.92219	+	5.35214i	−0.728494	+	0.437001i
$151$	2.94415	−	0.864480i	0.239592	−	0.0703504i	−0.159732	−	0.987160i	$-0.551063\pi$
$151$	2.94415	−	0.864480i	0.239592	−	0.0703504i	0.399324	+	0.916810i	$0.369245\pi$
$152$	0.588596	−	1.57809i	0.0477415	−	0.128000i
$153$	−1.45383	+	6.68313i	−0.117535	+	0.540299i
$154$	4.46167	−	15.1951i	0.359532	−	1.22445i
$155$	−13.1948	−	0.203714i	−1.05983	−	0.0163627i
$156$	−3.04320	+	6.66367i	−0.243651	+	0.533521i
$157$	−15.4427	+	11.5603i	−1.23246	+	0.922611i	−0.998764	−	0.0496976i	$-0.984174\pi$
$157$	−15.4427	+	11.5603i	−1.23246	+	0.922611i	−0.233700	+	0.972309i	$0.575083\pi$
$158$	13.8175	−	3.00581i	1.09926	−	0.239129i
$159$	−3.01968	−	3.48489i	−0.239476	−	0.276370i
$160$	−1.31223	−	1.81054i	−0.103741	−	0.143136i
$161$	9.64852	−	16.2271i	0.760410	−	1.27887i
$162$	7.93452	−	7.93452i	0.623395	−	0.623395i
$163$	0.558688	−	7.81148i	0.0437598	−	0.611842i	−0.927500	−	0.373822i	$-0.878047\pi$
$163$	0.558688	−	7.81148i	0.0437598	−	0.611842i	0.971260	−	0.238020i	$-0.0764984\pi$
$164$	3.78900	−	5.89580i	0.295871	−	0.460384i
$165$	16.5657	−	8.71631i	1.28964	−	0.678564i
$166$	−10.7518	−	4.91019i	−0.834503	−	0.381105i
$167$	−17.4031	−	13.0278i	−1.34669	−	1.00812i	−0.997471	−	0.0710806i	$-0.977355\pi$
$167$	−17.4031	−	13.0278i	−1.34669	−	1.00812i	−0.349221	−	0.937040i	$-0.613554\pi$
$168$	−7.18941	+	3.92571i	−0.554675	+	0.302875i
$169$	−0.327742	−	0.509977i	−0.0252109	−	0.0392290i
$170$	−11.0814	+	3.06881i	−0.849908	+	0.235367i
$171$	−0.631124	−	2.14941i	−0.0482633	−	0.164370i
$172$	−1.00507	+	0.0718842i	−0.0766361	+	0.00548112i
$173$	−20.1390	+	1.44037i	−1.53114	+	0.109509i	−0.811300	−	0.584630i	$-0.801240\pi$
$173$	−20.1390	+	1.44037i	−1.53114	+	0.109509i	−0.719841	+	0.694139i	$0.755785\pi$
$174$	2.76621	+	9.42083i	0.209705	+	0.714191i
$175$	−12.2761	+	15.3851i	−0.927988	+	1.16300i
$176$	2.17499	+	3.38435i	0.163946	+	0.255105i
$177$	−22.1923	+	12.1179i	−1.66808	+	0.910840i
$178$	5.70048	+	4.26733i	0.427269	+	0.319850i
$179$	−3.50389	−	1.60017i	−0.261893	−	0.119602i	0.280142	−	0.959959i	$-0.409619\pi$
$179$	−3.50389	−	1.60017i	−0.261893	−	0.119602i	−0.542035	+	0.840356i	$0.682346\pi$
$180$	−2.84030	−	0.881837i	−0.211704	−	0.0657283i
$181$	2.42084	−	3.76691i	0.179940	−	0.279992i	−0.739553	−	0.673098i	$-0.764963\pi$
$181$	2.42084	−	3.76691i	0.179940	−	0.279992i	0.919493	+	0.393106i	$0.128599\pi$
$182$	−0.988649	+	13.8231i	−0.0732835	+	1.02464i
$183$	−3.01704	+	3.01704i	−0.223026	+	0.223026i
$184$	1.51026	+	4.55183i	0.111338	+	0.335565i
$185$	−0.995057	+	0.721193i	−0.0731581	+	0.0530231i
$186$	−8.04198	−	9.28094i	−0.589666	−	0.680511i
$187$	20.2146	−	4.39743i	1.47824	−	0.321572i
$188$	−9.44733	+	7.07218i	−0.689017	+	0.515792i
$189$	5.68260	−	12.4432i	0.413349	−	0.905107i
$190$	2.70388	−	2.62166i	0.196160	−	0.190195i
$191$	−5.03543	+	17.1491i	−0.364351	+	1.24087i	0.549733	+	0.835341i	$0.314730\pi$
$191$	−5.03543	+	17.1491i	−0.364351	+	1.24087i	−0.914084	+	0.405526i	$0.867089\pi$
$192$	0.442321	−	2.03332i	0.0319218	−	0.146742i
$193$	−3.37082	+	9.03751i	−0.242637	+	0.650534i	−0.999997	−	0.00246325i	$-0.999216\pi$
$193$	−3.37082	+	9.03751i	−0.242637	+	0.650534i	0.757360	+	0.652997i	$0.226489\pi$
$194$	−1.86357	+	0.547192i	−0.133796	+	0.0392861i
$195$	−12.5438	+	10.5347i	−0.898283	+	0.754405i
$196$	−5.56379	+	6.42096i	−0.397414	+	0.458640i
$197$	3.22251	−	5.90158i	0.229594	−	0.420470i	−0.737331	−	0.675532i	$-0.763914\pi$
$197$	3.22251	−	5.90158i	0.229594	−	0.420470i	0.966925	+	0.255062i	$0.0820958\pi$
$198$	5.01335	+	1.86988i	0.356283	+	0.132887i
$199$	−0.0437157	+	0.0280944i	−0.00309893	+	0.00199156i	−0.542189	−	0.840256i	$-0.682404\pi$
$199$	−0.0437157	+	0.0280944i	−0.00309893	+	0.00199156i	0.539090	+	0.842248i	$0.318768\pi$
$200$	−0.911494	−	4.91622i	−0.0644524	−	0.347629i
$201$	−11.6554	+	1.67580i	−0.822112	+	0.118202i
$202$	4.59578	+	12.3218i	0.323358	+	0.866956i
$203$	11.1312	+	14.8695i	0.781256	+	1.04364i
$204$	−9.00181	−	5.78511i	−0.630253	−	0.405039i
$205$	13.3126	−	8.26793i	0.929794	−	0.577458i
$206$		−	18.4974i		−	1.28878i
$207$	5.23612	+	3.64278i	0.363936	+	0.253191i
$208$	−2.48936	−	2.48936i	−0.172606	−	0.172606i
$209$	−5.12085	+	4.43724i	−0.354216	+	0.306930i
$210$	−18.2878	+	1.02449i	−1.26198	+	0.0706968i
$211$	−0.0322764	+	0.224487i	−0.00222200	+	0.0154543i	−0.990902	−	0.134583i	$-0.957030\pi$
$211$	−0.0322764	+	0.224487i	−0.00222200	+	0.0154543i	0.988680	+	0.150038i	$0.0479395\pi$
$212$	2.07626	−	0.774405i	0.142598	−	0.0531864i
$213$	15.2805	−	20.4124i	1.04700	−	1.39863i
$214$	−6.80179	−	1.99719i	−0.464961	−	0.136525i
$215$	−2.09868	−	0.819891i	−0.143129	−	0.0559161i
$216$	1.44356	+	3.16096i	0.0982220	+	0.215076i
$217$	−20.3899	−	11.1337i	−1.38416	−	0.755808i
$218$	0.224615	+	3.14053i	0.0152129	+	0.212703i
$219$	7.17051	+	6.21328i	0.484538	+	0.419855i
$220$	1.14261	+	8.92282i	0.0770349	+	0.601576i
$221$	−16.4674	+	7.52041i	−1.10772	+	0.505877i
$222$	−1.11750	−	0.243096i	−0.0750014	−	0.0163156i
$223$	5.15414	+	9.43910i	0.345147	+	0.632089i	0.991375	−	0.131055i	$-0.0418365\pi$
$223$	5.15414	+	9.43910i	0.345147	+	0.632089i	−0.646228	+	0.763144i	$0.723655\pi$
$224$	−0.560224	−	3.89645i	−0.0374316	−	0.260342i
$225$	−4.88903	−	4.50801i	−0.325935	−	0.300534i
$226$	2.30283	+	0.331097i	0.153182	+	0.0220243i
$227$	3.22899	+	14.8434i	0.214316	+	0.985194i	0.951056	+	0.309018i	$0.100000\pi$
$227$	3.22899	+	14.8434i	0.214316	+	0.985194i	−0.736740	+	0.676176i	$0.763636\pi$
$228$	3.49585	+	0.250028i	0.231518	+	0.0165585i
$229$	23.6433			1.56239			0.781196	−	0.624286i	$-0.214610\pi$
$229$	23.6433			1.56239			0.781196	+	0.624286i	$0.214610\pi$
$230$	−1.32075	+	10.6422i	−0.0870877	+	0.701723i
$231$	32.9539			2.16821
$232$	−4.70645	−	0.336612i	−0.308994	−	0.0220997i
$233$	5.52371	+	25.3921i	0.361870	+	1.66349i	0.693785	+	0.720182i	$0.255942\pi$
$233$	5.52371	+	25.3921i	0.361870	+	1.66349i	−0.331915	+	0.943309i	$0.607695\pi$
$234$	−4.63470	−	0.666369i	−0.302980	−	0.0435619i
$235$	−25.8687	+	5.21050i	−1.68749	+	0.339896i
$236$	−1.72931	−	12.0276i	−0.112568	−	0.782929i
$237$	14.1018	+	25.8256i	0.916012	+	1.67755i
$238$	−19.7801	−	4.30290i	−1.28215	−	0.278916i
$239$	−10.4380	+	4.76688i	−0.675179	+	0.308344i	−0.723336	−	0.690496i	$-0.757392\pi$
$239$	−10.4380	+	4.76688i	−0.675179	+	0.308344i	0.0481574	+	0.998840i	$0.484665\pi$
$240$	2.84559	−	3.68141i	0.183682	−	0.237634i
$241$	−5.81282	−	5.03684i	−0.374437	−	0.324451i	0.447231	−	0.894419i	$-0.352410\pi$
$241$	−5.81282	−	5.03684i	−0.374437	−	0.324451i	−0.821667	+	0.569967i	$0.806956\pi$
$242$	−0.369854	−	5.17124i	−0.0237751	−	0.332420i
$243$	11.3438	+	6.19417i	0.727704	+	0.397356i
$244$	−0.851789	−	1.86516i	−0.0545302	−	0.119405i
$245$	−17.4009	+	7.62432i	−1.11170	+	0.487100i
$246$	13.9927	+	4.10864i	0.892145	+	0.261957i
$247$	3.55341	−	4.74680i	0.226098	−	0.302031i
$248$	5.52948	−	2.06239i	0.351123	−	0.130962i
$249$	3.50035	−	24.3455i	0.221826	−	1.54283i
$250$	2.87979	−	10.8031i	0.182134	−	0.683248i
$251$	1.40073	−	1.21374i	0.0884132	−	0.0766105i	−0.609533	−	0.792761i	$-0.708643\pi$
$251$	1.40073	−	1.21374i	0.0884132	−	0.0766105i	0.697946	+	0.716150i	$0.254098\pi$
$252$	−3.70220	−	3.70220i	−0.233217	−	0.233217i
$253$	3.44342	−	18.9838i	0.216486	−	1.19350i
$254$			10.6224i			0.666506i
$255$	−12.6236	−	20.3259i	−0.790522	−	1.27286i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	5.09830	+	6.81053i	0.318023	+	0.424829i	0.930858	−	0.365382i	$-0.119062\pi$
$257$	5.09830	+	6.81053i	0.318023	+	0.424829i	−0.612834	+	0.790211i	$0.709971\pi$
$258$	−0.732746	−	1.96457i	−0.0456188	−	0.122309i
$259$	−2.14146	+	0.307895i	−0.133064	+	0.0191317i
$260$	−2.63681	−	7.41729i	−0.163528	−	0.460001i
$261$	−5.27948	+	3.39292i	−0.326792	+	0.210016i
$262$	12.8932	+	4.80890i	0.796543	+	0.297095i
$263$	9.88978	−	18.1118i	0.609830	−	1.11682i	−0.372210	−	0.928149i	$-0.621400\pi$
$263$	9.88978	−	18.1118i	0.609830	−	1.11682i	0.982040	−	0.188672i	$-0.0604183\pi$
$264$	−5.48206	+	6.32663i	−0.337397	+	0.389377i
$265$	4.93641	+	0.429747i	0.303241	+	0.0263991i
$266$	6.36163	−	1.86794i	0.390057	−	0.114531i
$267$	−5.17817	+	13.8832i	−0.316899	+	0.849639i
$268$	1.20287	−	5.52950i	0.0734770	−	0.337768i
$269$	−4.12067	+	14.0337i	−0.251242	+	0.855651i	0.733211	+	0.680001i	$0.238021\pi$
$269$	−4.12067	+	14.0337i	−0.251242	+	0.855651i	−0.984453	+	0.175650i	$0.943797\pi$
$270$	−0.119952	+	7.76938i	−0.00730002	+	0.472830i
$271$	4.61184	−	10.0985i	0.280149	−	0.613441i	−0.716286	−	0.697807i	$-0.754159\pi$
$271$	4.61184	−	10.0985i	0.280149	−	0.613441i	0.996435	+	0.0843662i	$0.0268866\pi$
$272$	4.11662	−	3.08166i	0.249607	−	0.186853i
$273$	−28.1786	+	6.12988i	−1.70545	+	0.370997i
$274$	3.56225	+	4.11106i	0.215203	+	0.248358i
$275$	−6.26014	+	19.1160i	−0.377501	+	1.15274i
$276$	−8.20271	+	5.68386i	−0.493745	+	0.342128i
$277$	20.3447	−	20.3447i	1.22239	−	1.22239i	0.255613	−	0.966779i	$-0.417723\pi$
$277$	20.3447	−	20.3447i	1.22239	−	1.22239i	0.966779	−	0.255613i	$-0.0822773\pi$
$278$	−0.120828	+	1.68940i	−0.00724681	+	0.101324i
$279$	4.24365	−	6.60325i	0.254061	−	0.395326i
$280$	2.60998	−	8.40647i	0.155976	−	0.502383i
$281$	−4.91139	−	2.24296i	−0.292989	−	0.133804i	0.263498	−	0.964660i	$-0.415124\pi$
$281$	−4.91139	−	2.24296i	−0.292989	−	0.133804i	−0.556487	+	0.830856i	$0.687851\pi$
$282$	−19.6587	−	14.7163i	−1.17066	−	0.876343i
$283$	7.65315	−	4.17894i	0.454933	−	0.248412i	−0.235408	−	0.971897i	$-0.575643\pi$
$283$	7.65315	−	4.17894i	0.454933	−	0.248412i	0.690340	+	0.723485i	$0.257461\pi$
$284$	6.62480	+	10.3084i	0.393109	+	0.611690i
$285$	6.81950	+	3.86157i	0.403952	+	0.228740i
$286$	3.99014	+	13.5892i	0.235942	+	0.803544i
$287$	27.5182	−	1.96814i	1.62435	−	0.116176i
$288$	1.32665	−	0.0948835i	0.0781733	−	0.00559107i
$289$	−2.66046	−	9.06071i	−0.156498	−	0.532983i
$290$	−9.18108	−	5.19882i	−0.539132	−	0.305286i
$291$	−2.18503	−	3.39997i	−0.128089	−	0.199310i
$292$	−4.00186	+	2.18518i	−0.234191	+	0.127878i
$293$	18.0534	+	13.5146i	1.05469	+	0.789531i	0.978226	−	0.207541i	$-0.0665460\pi$
$293$	18.0534	+	13.5146i	1.05469	+	0.789531i	0.0764641	+	0.997072i	$0.475637\pi$
$294$	−16.0817	−	7.34429i	−0.937907	−	0.428328i
$295$	8.05652	−	25.9492i	0.469068	−	1.51082i
$296$	0.297132	−	0.462346i	0.0172704	−	0.0268733i
$297$	0.997310	−	13.9442i	0.0578698	−	0.809126i
$298$	−12.4110	+	12.4110i	−0.718951	+	0.718951i
$299$	0.586812	+	16.8734i	0.0339362	+	0.975816i
$300$	9.28127	−	4.70200i	0.535854	−	0.271470i
$301$	−2.59756	−	2.99775i	−0.149721	−	0.172787i
$302$	−2.99832	+	0.652245i	−0.172534	+	0.0375325i
$303$	−21.9071	+	16.3995i	−1.25853	+	0.942126i
$304$	−0.699676	+	1.53208i	−0.0401292	+	0.0878706i
$305$	0.0707787	−	4.58441i	0.00405278	−	0.262502i
$306$	1.92689	−	6.56239i	0.110153	−	0.375147i
$307$	5.99337	−	27.5511i	0.342060	−	1.57242i	−0.409218	−	0.912437i	$-0.634198\pi$
$307$	5.99337	−	27.5511i	0.342060	−	1.57242i	0.751277	−	0.659987i	$-0.229438\pi$
$308$	−5.53431	+	14.8381i	−0.315347	+	0.845477i
$309$	36.9317	−	10.8441i	2.10097	−	0.616901i
$310$	13.1466	+	1.14450i	0.746677	+	0.0650031i
$311$	8.00719	−	9.24079i	0.454046	−	0.523997i	−0.481859	−	0.876249i	$-0.660038\pi$
$311$	8.00719	−	9.24079i	0.454046	−	0.523997i	0.935905	+	0.352252i	$0.114584\pi$
$312$	3.51082	−	6.42959i	0.198761	−	0.364004i
$313$	−22.7563	−	8.48767i	−1.28626	−	0.479752i	−0.388996	−	0.921239i	$-0.627178\pi$
$313$	−22.7563	−	8.48767i	−1.28626	−	0.479752i	−0.897267	+	0.441488i	$0.854451\pi$
$314$	16.2281	−	10.4292i	0.915804	−	0.588551i
$315$	−3.92149	−	11.0311i	−0.220951	−	0.621531i
$316$	−13.9967	+	2.01242i	−0.787375	+	0.113208i
$317$	8.85341	+	23.7369i	0.497257	+	1.33320i	0.907051	+	0.421020i	$0.138328\pi$
$317$	8.85341	+	23.7369i	0.497257	+	1.33320i	−0.409794	+	0.912178i	$0.634399\pi$
$318$	2.76337	+	3.69143i	0.154962	+	0.207005i
$319$	15.9690	+	10.2626i	0.894092	+	0.574598i
$320$	1.17973	+	1.89954i	0.0659487	+	0.106187i
$321$		−	14.7512i		−	0.823332i
$322$	−10.7816	+	15.4974i	−0.600833	+	0.863636i
$323$	6.12431	+	6.12431i	0.340766	+	0.340766i
$324$	−8.48035	+	7.34827i	−0.471131	+	0.408237i
$325$	1.79716	−	17.5104i	0.0996883	−	0.971304i
$326$	−1.11453	+	7.75172i	−0.0617281	+	0.429328i
$327$	−6.13865	+	2.28960i	−0.339468	+	0.126615i
$328$	−4.19995	+	5.61047i	−0.231903	+	0.309786i
$329$	−44.5737	−	13.0880i	−2.45743	−	0.721566i
$330$	−17.1453	+	7.51232i	−0.943817	+	0.413540i
$331$	−3.43651	−	7.52492i	−0.188888	−	0.413607i	0.791368	−	0.611340i	$-0.209369\pi$
$331$	−3.43651	−	7.52492i	−0.188888	−	0.413607i	−0.980256	+	0.197733i	$0.936642\pi$
$332$	10.3741	+	5.66470i	0.569354	+	0.310891i
$333$	−0.0521473	−	0.729114i	−0.00285765	−	0.0399552i
$334$	16.4294	+	14.2361i	0.898975	+	0.778966i
$335$	7.73844	−	10.0114i	0.422796	−	0.546981i
$336$	7.45115	−	3.40283i	0.406493	−	0.185639i
$337$	4.05014	+	0.881054i	0.220625	+	0.0479941i	0.321519	−	0.946903i	$-0.395807\pi$
$337$	4.05014	+	0.881054i	0.220625	+	0.0479941i	−0.100894	+	0.994897i	$0.532170\pi$
$338$	0.290526	+	0.532058i	0.0158025	+	0.0289402i
$339$	0.688972	+	4.79190i	0.0374198	+	0.260261i
$340$	11.2721	−	2.27045i	0.611318	−	0.123132i
$341$	−23.5003	−	3.37884i	−1.27261	−	0.182974i
$342$	0.476179	+	2.18896i	0.0257488	+	0.118365i
$343$	−5.87459	−	0.420159i	−0.317198	−	0.0226864i
$344$	1.00764			0.0543283
$345$	−22.0223	+	3.60198i	−1.18564	+	0.193924i
$346$	20.1905			1.08545
$347$	24.6627	+	1.76391i	1.32396	+	0.0946917i	0.715345	−	0.698771i	$-0.246270\pi$
$347$	24.6627	+	1.76391i	1.32396	+	0.0946917i	0.608618	+	0.793463i	$0.291724\pi$
$348$	−2.08708	−	9.59417i	−0.111879	−	0.514301i
$349$	17.4342	+	2.50666i	0.933233	+	0.134179i	0.592126	−	0.805846i	$-0.298289\pi$
$349$	17.4342	+	2.50666i	0.933233	+	0.134179i	0.341107	+	0.940024i	$0.389198\pi$
$350$	13.3424	−	14.4701i	0.713182	−	0.773460i
$351$	1.74103	+	12.1091i	0.0929291	+	0.646336i
$352$	−1.92801	−	3.53089i	−0.102763	−	0.188197i
$353$	−3.01075	−	0.654948i	−0.160246	−	0.0348594i	0.131727	−	0.991286i	$-0.457948\pi$
$353$	−3.01075	−	0.654948i	−0.160246	−	0.0348594i	−0.291972	+	0.956427i	$0.594312\pi$
$354$	23.0003	−	10.5039i	1.22245	−	0.558275i
$355$	3.48027	+	27.1780i	0.184714	+	1.44246i
$356$	−5.38153	−	4.66312i	−0.285221	−	0.247145i
$357$	−3.00499	−	42.0152i	−0.159041	−	2.22368i
$358$	3.38080	+	1.84606i	0.178681	+	0.0975672i
$359$	0.926627	+	2.02903i	0.0489055	+	0.107088i	0.932507	−	0.361151i	$-0.117616\pi$
$359$	0.926627	+	2.02903i	0.0489055	+	0.107088i	−0.883602	+	0.468239i	$0.844889\pi$
$360$	2.77016	+	1.08222i	0.146000	+	0.0570377i
$361$	15.5085	+	4.55370i	0.816235	+	0.239668i
$362$	−2.68340	+	3.58461i	−0.141037	+	0.188403i
$363$	10.1080	−	3.77008i	0.530531	−	0.197878i
$364$	1.97226	−	13.7174i	0.103374	−	0.718985i
$365$	−10.1796	+	0.570267i	−0.532825	+	0.0298492i
$366$	3.22458	−	2.79412i	0.168552	−	0.146051i
$367$	11.5918	+	11.5918i	0.605086	+	0.605086i	0.941658	−	0.336572i	$-0.109267\pi$
$367$	11.5918	+	11.5918i	0.605086	+	0.605086i	−0.336572	+	0.941658i	$0.609267\pi$
$368$	−1.18169	−	4.64797i	−0.0615997	−	0.242292i
$369$			9.32134i			0.485250i
$370$	1.04397	−	0.648368i	0.0542735	−	0.0337071i
$371$	7.33845	+	4.71614i	0.380993	+	0.244850i
$372$	7.35939	+	9.83100i	0.381567	+	0.509713i
$373$	10.8633	+	29.1255i	0.562478	+	1.50806i	0.837397	+	0.546596i	$0.184076\pi$
$373$	10.8633	+	29.1255i	0.562478	+	1.50806i	−0.274918	+	0.961468i	$0.588651\pi$
$374$	−20.4768	+	2.94413i	−1.05883	+	0.152237i
$375$	23.2576	−	0.583572i	1.20101	−	0.0301355i
$376$	9.92778	−	6.38020i	0.511986	−	0.329033i
$377$	−15.5640	−	5.80506i	−0.801585	−	0.298976i
$378$	−6.55581	+	12.0061i	−0.337194	+	0.617525i
$379$	−16.2692	+	18.7757i	−0.835692	+	0.964441i	−0.999758	−	0.0220089i	$-0.992994\pi$
$379$	−16.2692	+	18.7757i	−0.835692	+	0.964441i	0.164065	+	0.986449i	$0.447539\pi$
$380$	−2.88401	+	2.42208i	−0.147947	+	0.124250i
$381$	−21.2084	+	6.22735i	−1.08654	+	0.319037i
$382$	6.24601	−	16.7462i	0.319574	−	0.856810i
$383$	3.35511	−	15.4232i	0.171438	−	0.788089i	−0.808454	−	0.588560i	$-0.799695\pi$
$383$	3.35511	−	15.4232i	0.171438	−	0.788089i	0.979892	−	0.199529i	$-0.0639412\pi$
$384$	−0.586250	+	1.99658i	−0.0299169	+	0.101888i
$385$	−25.4234	+	24.6503i	−1.29569	+	1.25629i
$386$	4.00696	−	8.77401i	0.203949	−	0.446585i
$387$	1.07288	−	0.803149i	0.0545376	−	0.0408264i
$388$	1.89785	−	0.412853i	0.0963490	−	0.0209594i
$389$	−4.58691	−	5.29358i	−0.232566	−	0.268395i	0.627457	−	0.778652i	$-0.284096\pi$
$389$	−4.58691	−	5.29358i	−0.232566	−	0.268395i	−0.860022	+	0.510256i	$0.829551\pi$
$390$	13.2634	−	9.61299i	0.671619	−	0.486773i
$391$	−24.5178	−	2.65917i	−1.23992	−	0.134480i
$392$	6.00768	−	6.00768i	0.303434	−	0.303434i
$393$	−2.04276	+	28.5615i	−0.103044	+	1.44074i
$394$	−3.63531	+	5.65665i	−0.183144	+	0.284978i
$395$	−30.1975	−	9.37549i	−1.51940	−	0.471732i
$396$	−4.86718	−	2.22277i	−0.244585	−	0.111698i
$397$	−15.9640	−	11.9505i	−0.801208	−	0.599777i	0.118242	−	0.992985i	$-0.462274\pi$
$397$	−15.9640	−	11.9505i	−0.801208	−	0.599777i	−0.919449	+	0.393208i	$0.871365\pi$
$398$	0.0456086	−	0.0249042i	0.00228615	−	0.00124833i
$399$	7.45901	+	11.6064i	0.373418	+	0.581049i
$400$	0.558453	+	4.96872i	0.0279226	+	0.248436i
$401$	7.00904	+	23.8706i	0.350015	+	1.19204i	0.926929	+	0.375236i	$0.122438\pi$
$401$	7.00904	+	23.8706i	0.350015	+	1.19204i	−0.576915	+	0.816804i	$0.695743\pi$
$402$	11.7453	−	0.840040i	0.585802	−	0.0418974i
$403$	20.7235	−	1.48217i	1.03231	−	0.0738322i
$404$	−3.70504	−	12.6182i	−0.184333	−	0.627780i
$405$	−24.1811	+	6.69651i	−1.20157	+	0.332752i
$406$	−10.0420	−	15.6257i	−0.498379	−	0.775492i
$407$	−1.94055	+	1.05962i	−0.0961896	+	0.0525235i
$408$	8.56617	+	6.41255i	0.424088	+	0.317469i
$409$	14.3325	+	6.54543i	0.708696	+	0.323651i	0.736947	−	0.675950i	$-0.236267\pi$
$409$	14.3325	+	6.54543i	0.708696	+	0.323651i	−0.0282514	+	0.999601i	$0.508994\pi$
$410$	−13.8685	+	7.29716i	−0.684918	+	0.360381i
$411$	−6.11970	+	9.52244i	−0.301863	+	0.469707i
$412$	−1.31959	+	18.4503i	−0.0650117	+	0.908982i
$413$	33.8235	−	33.8235i	1.66435	−	1.66435i
$414$	−4.96291	−	4.00704i	−0.243914	−	0.196935i
$415$	15.5105	+	21.4005i	0.761382	+	1.05051i
$416$	2.30543	+	2.66060i	0.113033	+	0.130447i
$417$	−3.44387	+	0.749168i	−0.168647	+	0.0366869i
$418$	5.42435	−	4.06062i	0.265313	−	0.198611i
$419$	3.72558	−	8.15789i	0.182007	−	0.398539i	−0.796534	−	0.604594i	$-0.793335\pi$
$419$	3.72558	−	8.15789i	0.182007	−	0.398539i	0.978540	+	0.206055i	$0.0660626\pi$
$420$	18.3143	+	0.282755i	0.893647	+	0.0137970i
$421$	−7.09736	+	24.1714i	−0.345904	+	1.17804i	0.584466	+	0.811418i	$0.301304\pi$
$421$	−7.09736	+	24.1714i	−0.345904	+	1.17804i	−0.930370	+	0.366623i	$0.880514\pi$
$422$	0.0482089	−	0.221613i	0.00234677	−	0.0107879i
$423$	5.48518	−	14.7063i	0.266698	−	0.715046i
$424$	−2.12622	+	0.624314i	−0.103258	+	0.0303193i
$425$	24.9432	+	6.23836i	1.20992	+	0.302605i
$426$	−16.6978	+	19.2703i	−0.809010	+	0.933647i
$427$	3.86833	−	7.08431i	0.187201	−	0.342834i
$428$	6.64199	+	2.47733i	0.321052	+	0.119746i
$429$	−24.7927	+	15.9333i	−1.19700	+	0.769266i
$430$	2.03485	+	0.967520i	0.0981289	+	0.0466580i
$431$	1.09186	−	0.156986i	0.0525932	−	0.00756176i	−0.115968	−	0.993253i	$-0.536997\pi$
$431$	1.09186	−	0.156986i	0.0525932	−	0.00756176i	0.168561	+	0.985691i	$0.446088\pi$
$432$	−1.21438	−	3.25589i	−0.0584271	−	0.156649i
$433$	3.17038	+	4.23513i	0.152359	+	0.203527i	0.870226	−	0.492652i	$-0.163973\pi$
$433$	3.17038	+	4.23513i	0.152359	+	0.203527i	−0.717868	+	0.696180i	$0.754882\pi$
$434$	19.5437	+	12.5600i	0.938128	+	0.602898i
$435$	4.99748	−	21.3786i	0.239611	−	1.02503i
$436$		−	3.14855i		−	0.150788i
$437$	7.46556	−	3.08415i	0.357126	−	0.147535i
$438$	−6.70899	−	6.70899i	−0.320568	−	0.320568i
$439$	−6.75769	+	5.85557i	−0.322527	+	0.279471i	−0.801042	−	0.598608i	$-0.795721\pi$
$439$	−6.75769	+	5.85557i	−0.322527	+	0.279471i	0.478515	+	0.878079i	$0.341175\pi$
$440$	−0.503154	−	8.98160i	−0.0239869	−	0.428181i
$441$	1.60818	−	11.1851i	0.0765800	−	0.532626i
$442$	16.9619	−	6.32648i	0.806797	−	0.300920i
$443$	5.21622	−	6.96805i	0.247830	−	0.331062i	−0.659326	−	0.751858i	$-0.729158\pi$
$443$	5.21622	−	6.96805i	0.247830	−	0.331062i	0.907156	+	0.420796i	$0.138249\pi$
$444$	1.09731	+	0.322198i	0.0520759	+	0.0152909i
$445$	−6.39010	−	14.5841i	−0.302920	−	0.691351i
$446$	−4.46763	−	9.78274i	−0.211548	−	0.463226i
$447$	−32.0556	−	17.5037i	−1.51618	−	0.827895i
$448$	0.280828	+	3.92648i	0.0132679	+	0.185509i
$449$	−15.8364	−	13.7223i	−0.747365	−	0.647595i	0.195526	−	0.980699i	$-0.437359\pi$
$449$	−15.8364	−	13.7223i	−0.747365	−	0.647595i	−0.942890	+	0.333103i	$0.891904\pi$
$450$	4.55497	+	4.84531i	0.214724	+	0.228410i
$451$	25.6466	−	11.7124i	1.20765	−	0.551516i
$452$	−2.27335	−	0.494536i	−0.106929	−	0.0232610i
$453$	−3.06003	−	5.60402i	−0.143773	−	0.263300i
$454$	−2.16185	−	15.0360i	−0.101461	−	0.705674i
$455$	17.1540	−	25.8074i	0.804193	−	1.20987i
$456$	−3.46910	−	0.498782i	−0.162456	−	0.0233576i
$457$	4.52714	+	20.8109i	0.211771	+	0.973495i	0.953171	+	0.302432i	$0.0977984\pi$
$457$	4.52714	+	20.8109i	0.211771	+	0.973495i	−0.741400	+	0.671063i	$0.765838\pi$
$458$	−23.5830	−	1.68669i	−1.10196	−	0.0788139i
$459$	−17.8694			−0.834073
$460$	2.07659	−	10.5208i	0.0968215	−	0.490536i
$461$	−27.4064			−1.27644			−0.638221	−	0.769853i	$-0.720329\pi$
$461$	−27.4064			−1.27644			−0.638221	+	0.769853i	$0.720329\pi$
$462$	−32.8699	−	2.35090i	−1.52925	−	0.109374i
$463$	−1.50660	−	6.92573i	−0.0700177	−	0.321866i	0.928794	−	0.370596i	$-0.120846\pi$
$463$	−1.50660	−	6.92573i	−0.0700177	−	0.321866i	−0.998812	+	0.0487295i	$0.984483\pi$
$464$	4.67045	+	0.671509i	0.216820	+	0.0311740i
$465$	5.42211	+	26.9193i	0.251444	+	1.24835i
$466$	−3.69819	−	25.7215i	−0.171315	−	1.19152i
$467$	−6.66654	−	12.2089i	−0.308491	−	0.564958i	0.676734	−	0.736228i	$-0.263395\pi$
$467$	−6.66654	−	12.2089i	−0.308491	−	0.564958i	−0.985224	+	0.171270i	$0.945213\pi$
$468$	4.57535	+	0.995307i	0.211496	+	0.0460081i
$469$	20.2630	−	9.25381i	0.935659	−	0.427301i
$470$	26.1745	−	3.35177i	1.20734	−	0.154606i
$471$	30.3364	+	26.2866i	1.39783	+	1.21122i
$472$	0.866862	+	12.1203i	0.0399005	+	0.557882i
$473$	−3.55787	−	1.94274i	−0.163591	−	0.0893274i
$474$	−12.2235	−	26.7658i	−0.561445	−	1.22939i
$475$	−8.14968	+	2.12201i	−0.373933	+	0.0973645i
$476$	19.4228	+	5.70304i	0.890240	+	0.261398i
$477$	−1.76627	+	2.35946i	−0.0808719	+	0.108032i
$478$	10.7515	−	4.01010i	0.491761	−	0.183418i
$479$	3.33934	−	23.2256i	0.152578	−	1.06120i	−0.759299	−	0.650742i	$-0.774458\pi$
$479$	3.33934	−	23.2256i	0.152578	−	1.06120i	0.911877	−	0.410463i	$-0.134633\pi$
$480$	−3.10097	+	3.46903i	−0.141539	+	0.158339i
$481$	1.46225	−	1.26704i	0.0666727	−	0.0577722i
$482$	5.43869	+	5.43869i	0.247725	+	0.247725i
$483$	−37.2625	−	12.4409i	−1.69550	−	0.566082i
$484$			5.18445i			0.235657i
$485$	4.22898	+	0.988569i	0.192028	+	0.0448886i
$486$	−10.8730	−	6.98765i	−0.493209	−	0.316966i
$487$	−8.13714	−	10.8699i	−0.368729	−	0.492564i	0.577352	−	0.816496i	$-0.304086\pi$
$487$	−8.13714	−	10.8699i	−0.368729	−	0.492564i	−0.946081	+	0.323932i	$0.894995\pi$
$488$	0.716560	+	1.92117i	0.0324372	+	0.0869674i
$489$	−16.1304	+	2.31919i	−0.729440	+	0.104878i
$490$	17.9005	−	6.36353i	0.808662	−	0.287475i
$491$	25.3922	−	16.3185i	1.14593	−	0.736446i	0.177107	−	0.984192i	$-0.443326\pi$
$491$	25.3922	−	16.3185i	1.14593	−	0.736446i	0.968825	+	0.247746i	$0.0796898\pi$
$492$	−13.6640	−	5.09641i	−0.616020	−	0.229764i
$493$	11.6284	−	21.2958i	0.523717	−	0.959116i
$494$	−3.88299	+	4.48120i	−0.174704	+	0.201619i
$495$	−7.69460	−	9.16209i	−0.345847	−	0.411805i
$496$	−5.66252	+	1.66267i	−0.254255	+	0.0746559i
$497$	−16.8569	+	45.1952i	−0.756136	+	2.02728i
$498$	−5.22822	+	24.0337i	−0.234282	+	1.07698i
$499$	−0.908955	+	3.09562i	−0.0406904	+	0.138579i	−0.977333	−	0.211708i	$-0.932098\pi$
$499$	−0.908955	+	3.09562i	−0.0406904	+	0.138579i	0.936643	+	0.350286i	$0.113916\pi$
$500$	−3.64314	+	10.5701i	−0.162926	+	0.472710i
$501$	−18.7919	+	41.1485i	−0.839560	+	1.83838i
$502$	−1.48375	+	1.11072i	−0.0662228	+	0.0495738i
$503$	−27.8706	+	6.06289i	−1.24269	+	0.270331i	−0.785401	−	0.618987i	$-0.787543\pi$
$503$	−27.8706	+	6.06289i	−1.24269	+	0.270331i	−0.457290	+	0.889318i	$0.651180\pi$
$504$	3.42865	+	3.95688i	0.152724	+	0.176253i
$505$	4.63379	−	29.0390i	0.206201	−	1.29222i
$506$	−4.78894	+	18.6898i	−0.212894	+	0.830863i
$507$	−0.891978	+	0.891978i	−0.0396141	+	0.0396141i
$508$	0.757790	−	10.5953i	0.0336215	−	0.470090i
$509$	15.1441	−	23.5647i	0.671250	−	1.04448i	−0.323898	−	0.946092i	$-0.604993\pi$
$509$	15.1441	−	23.5647i	0.671250	−	1.04448i	0.995148	−	0.0983929i	$-0.0313702\pi$
$510$	11.1414	+	21.1747i	0.493351	+	0.937632i
$511$	−16.3269	−	7.45625i	−0.722260	−	0.329845i
$512$	−0.800541	−	0.599278i	−0.0353793	−	0.0264846i
$513$	5.13693	−	2.80498i	0.226801	−	0.123843i
$514$	−4.59945	−	7.15689i	−0.202873	−	0.315677i
$515$	−20.3805	+	35.9918i	−0.898073	+	1.58599i
$516$	0.590729	+	2.01184i	0.0260054	+	0.0885662i
$517$	−47.3550	+	3.38690i	−2.08267	+	0.148956i
$518$	2.15796	−	0.154341i	0.0948155	−	0.00678134i
$519$	11.8366	+	40.3119i	0.519571	+	1.76950i
$520$	2.10094	+	7.58650i	0.0921325	+	0.332690i
$521$	−8.44469	−	13.1402i	−0.369969	−	0.575683i	0.605493	−	0.795850i	$-0.292976\pi$
$521$	−8.44469	−	13.1402i	−0.369969	−	0.575683i	−0.975462	+	0.220168i	$0.929340\pi$
$522$	5.50808	−	3.00764i	0.241082	−	0.131641i
$523$	6.13209	+	4.59043i	0.268138	+	0.200725i	0.724883	−	0.688872i	$-0.241894\pi$
$523$	6.13209	+	4.59043i	0.268138	+	0.200725i	−0.456745	+	0.889598i	$0.650985\pi$
$524$	−12.5173	−	5.71644i	−0.546819	−	0.249724i
$525$	36.7127	+	18.1561i	1.60228	+	0.792398i
$526$	−11.1567	+	17.3601i	−0.486454	+	0.756937i
$527$	−2.16498	+	30.2704i	−0.0943079	+	1.31860i
$528$	5.91943	−	5.91943i	0.257610	−	0.257610i
$529$	−11.0605	+	20.1659i	−0.480892	+	0.876780i
$530$	−4.89317	−	0.780811i	−0.212546	−	0.0339163i
$531$	10.5836	+	12.2141i	0.459289	+	0.530048i
$532$	−6.47868	+	1.40935i	−0.280886	+	0.0611031i
$533$	−19.7516	+	14.7858i	−0.855535	+	0.640445i
$534$	6.15539	−	13.4784i	0.266370	−	0.583269i
$535$	11.0342	+	11.3803i	0.477052	+	0.492013i
$536$	−1.59428	+	5.42960i	−0.0688622	+	0.234523i
$537$	−1.70381	+	7.83231i	−0.0735250	+	0.337989i
$538$	5.11133	−	13.7040i	0.220365	−	0.590821i
$539$	−32.7954	+	9.62959i	−1.41260	+	0.414776i
$540$	0.673907	−	7.74103i	0.0290004	−	0.333121i
$541$	14.3767	−	16.5916i	0.618102	−	0.713328i	−0.357243	−	0.934011i	$-0.616283\pi$
$541$	14.3767	−	16.5916i	0.618102	−	0.713328i	0.975345	+	0.220684i	$0.0708288\pi$
$542$	−5.32050	+	9.74378i	−0.228535	+	0.418531i
$543$	−8.73012	−	3.25617i	−0.374645	−	0.139735i
$544$	−4.32598	+	2.78014i	−0.185475	+	0.119197i
$545$	3.02319	−	6.35824i	0.129499	−	0.272357i
$546$	28.5441	−	4.10402i	1.22157	−	0.175636i
$547$	7.37685	+	19.7781i	0.315411	+	0.845651i	0.993824	+	0.110969i	$0.0353956\pi$
$547$	7.37685	+	19.7781i	0.315411	+	0.845651i	−0.678412	+	0.734681i	$0.737332\pi$
$548$	−3.25990	−	4.35471i	−0.139256	−	0.186024i
$549$	2.29424	+	1.47442i	0.0979160	+	0.0629268i
$550$	7.60791	−	18.6207i	0.324403	−	0.793990i
$551$			7.94724i			0.338564i
$552$	8.58729	−	5.08421i	0.365499	−	0.216398i
$553$	−39.3609	−	39.3609i	−1.67380	−	1.67380i
$554$	−21.7442	+	18.8415i	−0.923822	+	0.800497i
$555$	1.90655	+	1.70427i	0.0809285	+	0.0723422i
$556$	0.241041	−	1.67648i	0.0102224	−	0.0710985i
$557$	−27.8877	+	10.4016i	−1.18164	+	0.440729i	−0.862048	−	0.506827i	$-0.830818\pi$
$557$	−27.8877	+	10.4016i	−1.18164	+	0.440729i	−0.319591	+	0.947556i	$0.603546\pi$
$558$	−4.70391	+	6.28369i	−0.199132	+	0.266010i
$559$	3.40368	+	0.999412i	0.143960	+	0.0422706i
$560$	−3.20304	+	8.19886i	−0.135353	+	0.346465i
$561$	−17.8827	−	39.1577i	−0.755010	−	1.65324i
$562$	4.73887	+	2.58762i	0.199897	+	0.109152i
$563$	−2.93551	−	41.0438i	−0.123717	−	1.72979i	−0.558714	−	0.829360i	$-0.688705\pi$
$563$	−2.93551	−	41.0438i	−0.123717	−	1.72979i	0.434997	−	0.900432i	$-0.356749\pi$
$564$	18.5588	+	16.0812i	0.781464	+	0.677143i
$565$	−4.11599	−	3.18151i	−0.173161	−	0.133847i
$566$	−7.93178	+	3.62232i	−0.333397	+	0.152257i
$567$	−43.1626	−	9.38945i	−1.81266	−	0.394320i
$568$	−5.87253	−	10.7547i	−0.246406	−	0.451258i
$569$	1.69512	+	11.7898i	0.0710633	+	0.494256i	0.994007	+	0.109320i	$0.0348674\pi$
$569$	1.69512	+	11.7898i	0.0710633	+	0.494256i	−0.922943	+	0.384936i	$0.874224\pi$
$570$	−6.52665	−	4.33823i	−0.273371	−	0.181708i
$571$	−6.50808	−	0.935720i	−0.272354	−	0.0391587i	0.00478432	−	0.999989i	$-0.498477\pi$
$571$	−6.50808	−	0.935720i	−0.272354	−	0.0391587i	−0.277139	+	0.960830i	$0.589386\pi$
$572$	−3.01053	−	13.8392i	−0.125877	−	0.578646i
$573$	37.0969	+	2.65322i	1.54975	+	0.110840i
$574$	−27.5885			−1.15152
$575$	14.2954	−	19.2520i	0.596161	−	0.802865i
$576$	−1.33003			−0.0554181
$577$	28.5765	+	2.04383i	1.18966	+	0.0850860i	0.652094	−	0.758138i	$-0.273891\pi$
$577$	28.5765	+	2.04383i	1.18966	+	0.0850860i	0.537563	+	0.843224i	$0.319345\pi$
$578$	2.00730	+	9.22741i	0.0834927	+	0.383810i
$579$	19.8671	+	2.85646i	0.825649	+	0.118710i
$580$	8.78681	+	5.84055i	0.364852	+	0.242516i
$581$	6.62183	+	46.0558i	0.274720	+	1.91072i
$582$	1.93691	+	3.54719i	0.0802876	+	0.147036i
$583$	8.71113	+	1.89499i	0.360778	+	0.0784825i
$584$	4.14756	−	1.89413i	0.171627	−	0.0783795i
$585$	8.28387	+	6.40313i	0.342496	+	0.264737i
$586$	−17.0433	−	14.7681i	−0.704051	−	0.610064i
$587$	0.999739	+	13.9782i	0.0412636	+	0.576941i	0.975459	+	0.220180i	$0.0706645\pi$
$587$	0.999739	+	13.9782i	0.0412636	+	0.576941i	−0.934196	+	0.356761i	$0.883881\pi$
$588$	15.5168	+	8.47284i	0.639904	+	0.349414i
$589$	−4.12919	−	9.04167i	−0.170140	−	0.372556i
$590$	−9.88718	+	25.3083i	−0.407049	+	1.04193i
$591$	−13.4252	−	3.94199i	−0.552238	−	0.162152i
$592$	−0.329358	+	0.439971i	−0.0135365	+	0.0180827i
$593$	40.5748	−	15.1336i	1.66621	−	0.621463i	0.673193	−	0.739467i	$-0.264922\pi$
$593$	40.5748	−	15.1336i	1.66621	−	0.621463i	0.993013	+	0.118004i	$0.0376497\pi$
$594$	−1.98954	+	13.8375i	−0.0816318	+	0.567761i
$595$	33.7467	+	30.1662i	1.38348	+	1.23670i
$596$	13.2648	−	11.4940i	0.543347	−	0.470812i
$597$	0.0764613	+	0.0764613i	0.00312935	+	0.00312935i
$598$	0.618420	−	16.8723i	0.0252891	−	0.689960i
$599$			5.43966i			0.222258i	0.993806	+	0.111129i	$0.0354467\pi$
$599$			5.43966i			0.222258i	−0.993806	+	0.111129i	$0.964553\pi$
$600$	−9.59306	+	4.02791i	−0.391635	+	0.164439i
$601$	3.68318	+	2.36703i	0.150240	+	0.0965533i	0.613601	−	0.789616i	$-0.289720\pi$
$601$	3.68318	+	2.36703i	0.150240	+	0.0965533i	−0.463361	+	0.886170i	$0.653357\pi$
$602$	2.37709	+	3.17542i	0.0968829	+	0.129420i
$603$	2.63022	+	7.05189i	0.107111	+	0.287175i
$604$	3.03721	−	0.436685i	0.123582	−	0.0177685i
$605$	−4.97803	+	10.4696i	−0.202386	+	0.425648i
$606$	23.0213	−	14.7949i	0.935175	−	0.601000i
$607$	−5.49822	−	2.05073i	−0.223166	−	0.0832366i	0.235394	−	0.971900i	$-0.424362\pi$
$607$	−5.49822	−	2.05073i	−0.223166	−	0.0832366i	−0.458560	+	0.888663i	$0.651635\pi$
$608$	0.807190	−	1.47826i	0.0327359	−	0.0599513i
$609$	25.3109	−	29.2104i	1.02565	−	1.18366i
$610$	−0.397646	+	4.56768i	−0.0161002	+	0.184940i
$611$	39.8629	−	11.7048i	1.61268	−	0.473526i
$612$	−2.39014	+	6.40820i	−0.0966155	+	0.259036i
$613$	4.95769	−	22.7901i	0.200239	−	0.920485i	−0.761851	−	0.647753i	$-0.775709\pi$
$613$	4.95769	−	22.7901i	0.200239	−	0.920485i	0.962090	−	0.272732i	$-0.0879273\pi$
$614$	−7.94357	+	27.0533i	−0.320577	+	1.09178i
$615$	−22.6998	−	23.4117i	−0.915345	−	0.944052i
$616$	6.57874	−	14.4054i	0.265065	−	0.580412i
$617$	−8.31801	+	6.22678i	−0.334870	+	0.250681i	−0.753459	−	0.657495i	$-0.771616\pi$
$617$	−8.31801	+	6.22678i	−0.334870	+	0.250681i	0.418588	+	0.908176i	$0.362525\pi$
$618$	−37.6112	+	8.18182i	−1.51294	+	0.329121i
$619$	−16.5092	−	19.0527i	−0.663563	−	0.765792i	0.319792	−	0.947488i	$-0.396387\pi$
$619$	−16.5092	−	19.0527i	−0.663563	−	0.765792i	−0.983355	+	0.181696i	$0.941841\pi$
$620$	−13.0315	−	2.07945i	−0.523356	−	0.0835127i
$621$	−6.39201	+	15.3909i	−0.256503	+	0.617615i
$622$	−8.64601	+	8.64601i	−0.346674	+	0.346674i
$623$	1.99971	−	27.9597i	0.0801169	−	1.12018i
$624$	−3.96056	+	6.16275i	−0.158549	+	0.246707i
$625$	−17.5063	+	17.8474i	−0.700251	+	0.713896i
$626$	22.0928	+	10.0895i	0.883008	+	0.403256i
$627$	11.2874	+	8.44963i	0.450775	+	0.337446i
$628$	−16.9307	+	9.24489i	−0.675610	+	0.368911i
$629$	1.52794	+	2.37752i	0.0609230	+	0.0947980i
$630$	3.12455	+	11.2827i	0.124485	+	0.449515i
$631$	11.0746	+	37.7166i	0.440873	+	1.50147i	0.817948	+	0.575292i	$0.195112\pi$
$631$	11.0746	+	37.7166i	0.440873	+	1.50147i	−0.377075	+	0.926183i	$0.623070\pi$
$632$	14.1046	−	1.00878i	0.561051	−	0.0401271i
$633$	0.470731	−	0.0336673i	0.0187099	−	0.00133816i
$634$	−7.13748	−	24.3080i	−0.283466	−	0.965395i
$635$	11.7037	−	20.6687i	0.464448	−	0.820212i
$636$	−2.49299	−	3.87917i	−0.0988534	−	0.153819i
$637$	26.2518	−	14.3346i	1.04014	−	0.567957i
$638$	−15.1962	−	11.3757i	−0.601622	−	0.450369i
$639$	−14.8249	−	6.77031i	−0.586465	−	0.267829i
$640$	−1.04121	−	1.97886i	−0.0411574	−	0.0782213i
$641$	17.3946	−	27.0665i	0.687044	−	1.06906i	−0.306081	−	0.952006i	$-0.599018\pi$
$641$	17.3946	−	27.0665i	0.687044	−	1.06906i	0.993125	−	0.117057i	$-0.0373459\pi$
$642$	−1.05234	+	14.7136i	−0.0415325	+	0.580700i
$643$	−22.3539	+	22.3539i	−0.881551	+	0.881551i	−0.993692	−	0.112141i	$-0.964229\pi$
$643$	−22.3539	+	22.3539i	−0.881551	+	0.881551i	0.112141	+	0.993692i	$0.464229\pi$
$644$	11.8597	−	14.6888i	0.467336	−	0.578818i
$645$	−0.738808	+	4.62995i	−0.0290905	+	0.182304i
$646$	−5.67180	−	6.54561i	−0.223154	−	0.257533i
$647$	32.0766	−	6.97783i	1.26106	−	0.274327i	0.468141	−	0.883654i	$-0.344924\pi$
$647$	32.0766	−	6.97783i	1.26106	−	0.274327i	0.792919	+	0.609327i	$0.208560\pi$
$648$	8.98296	−	6.72456i	0.352884	−	0.264166i
$649$	20.3073	−	44.4668i	0.797132	−	1.74548i
$650$	−3.04176	+	17.3376i	−0.119308	+	0.680037i
$651$	−13.6195	+	46.3839i	−0.533792	+	1.81793i
$652$	1.66469	−	7.65246i	0.0651943	−	0.299694i
$653$	−10.7997	+	28.9551i	−0.422624	+	1.13310i	0.534943	+	0.844888i	$0.320333\pi$
$653$	−10.7997	+	28.9551i	−0.422624	+	1.13310i	−0.957567	+	0.288211i	$0.906940\pi$
$654$	6.28634	−	1.84584i	0.245816	−	0.0721779i
$655$	−19.7887	−	23.5627i	−0.773209	−	0.920673i
$656$	4.58949	−	5.29656i	0.179190	−	0.206796i
$657$	2.90637	−	5.32262i	0.113388	−	0.207655i
$658$	43.5265	+	16.2345i	1.69684	+	0.632888i
$659$	9.29389	−	5.97282i	0.362038	−	0.232668i	−0.346957	−	0.937881i	$-0.612785\pi$
$659$	9.29389	−	5.97282i	0.362038	−	0.232668i	0.708995	+	0.705213i	$0.249149\pi$
$660$	17.6375	−	6.27005i	0.686540	−	0.244061i
$661$	43.4654	−	6.24939i	1.69061	−	0.243073i	0.771262	−	0.636518i	$-0.219626\pi$
$661$	43.4654	−	6.24939i	1.69061	−	0.243073i	0.919348	+	0.393445i	$0.128717\pi$
$662$	2.89094	+	7.75090i	0.112359	+	0.301247i
$663$	22.5753	+	30.1570i	0.876751	+	1.17120i
$664$	−9.94358	−	6.39035i	−0.385886	−	0.247994i
$665$	−14.4364	−	3.37466i	−0.559819	−	0.130864i
$666$			0.730976i			0.0283248i
$667$	−14.1825	−	17.6332i	−0.549148	−	0.682759i
$668$	−15.3719	−	15.3719i	−0.594757	−	0.594757i
$669$	16.9129	−	14.6551i	0.653891	−	0.566600i
$670$	−8.43293	+	9.43384i	−0.325792	+	0.364461i
$671$	1.17395	−	8.16499i	0.0453198	−	0.315206i
$672$	−7.67492	+	2.86260i	−0.296066	+	0.110427i
$673$	7.07657	−	9.45319i	0.272782	−	0.364394i	−0.643141	−	0.765747i	$-0.722369\pi$
$673$	7.07657	−	9.45319i	0.272782	−	0.364394i	0.915923	+	0.401354i	$0.131460\pi$
$674$	−3.97697	−	1.16774i	−0.153187	−	0.0449798i
$675$	8.79372	−	14.9853i	0.338470	−	0.576784i
$676$	−0.251829	−	0.551429i	−0.00968573	−	0.0212088i
$677$	−17.4489	−	9.52784i	−0.670617	−	0.366184i	0.107588	−	0.994196i	$-0.465687\pi$
$677$	−17.4489	−	9.52784i	−0.670617	−	0.366184i	−0.778204	+	0.628011i	$0.783869\pi$
$678$	−0.345366	−	4.82885i	−0.0132637	−	0.185451i
$679$	5.77820	+	5.00684i	0.221747	+	0.192145i
$680$	−11.4054	+	1.46052i	−0.437377	+	0.0560083i
$681$	28.7532	−	13.1312i	1.10183	−	0.503187i
$682$	23.1994	+	5.04672i	0.888351	+	0.193249i
$683$	−11.6172	−	21.2753i	−0.444519	−	0.814076i	0.555327	−	0.831632i	$-0.312593\pi$
$683$	−11.6172	−	21.2753i	−0.444519	−	0.814076i	−0.999846	+	0.0175561i	$0.994411\pi$
$684$	−0.318807	−	2.21735i	−0.0121899	−	0.0847825i
$685$	−2.40176	−	11.9241i	−0.0917666	−	0.455596i
$686$	5.82965	+	0.838177i	0.222577	+	0.0320017i
$687$	−10.4579	−	48.0743i	−0.398995	−	1.83415i
$688$	−1.00507	−	0.0718842i	−0.0383180	−	0.00274056i
$689$	−7.80131			−0.297206
$690$	22.2231	−	2.02175i	0.846019	−	0.0769667i
$691$	9.04069			0.343924			0.171962	−	0.985104i	$-0.444989\pi$
$691$	9.04069			0.343924			0.171962	+	0.985104i	$0.444989\pi$
$692$	−20.1390	−	1.44037i	−0.765570	−	0.0547547i
$693$	−4.47730	−	20.5818i	−0.170078	−	0.781838i
$694$	−24.4740	−	3.51883i	−0.929021	−	0.133573i
$695$	2.09649	−	3.15407i	0.0795245	−	0.119641i
$696$	1.39733	+	9.71861i	0.0529655	+	0.368383i
$697$	−17.2717	−	31.6307i	−0.654211	−	1.19810i
$698$	−17.2110	−	3.74402i	−0.651445	−	0.141713i
$699$	49.1870	−	22.4629i	1.86042	−	0.849626i
$700$	−14.3407	+	13.4814i	−0.542027	+	0.509549i
$701$	−11.7573	−	10.1878i	−0.444068	−	0.384787i	0.403927	−	0.914791i	$-0.367645\pi$
$701$	−11.7573	−	10.1878i	−0.444068	−	0.384787i	−0.847995	+	0.530004i	$0.822190\pi$
$702$	−0.872737	−	12.2025i	−0.0329393	−	0.460552i
$703$	−0.812440	−	0.443626i	−0.0306417	−	0.0167317i
$704$	1.67121	+	3.65944i	0.0629861	+	0.137920i
$705$	22.0369	+	50.2946i	0.829957	+	1.89420i
$706$	2.95635	+	0.868063i	0.111264	+	0.0326700i
$707$	31.0239	−	41.4431i	1.16677	−	1.55863i
$708$	−23.6910	+	8.83629i	−0.890363	+	0.332088i
$709$	−1.47941	+	10.2895i	−0.0555605	+	0.386432i	0.943000	+	0.332793i	$0.107991\pi$
$709$	−1.47941	+	10.2895i	−0.0555605	+	0.386432i	−0.998560	+	0.0536387i	$0.982918\pi$
$710$	−1.53255	−	27.3570i	−0.0575157	−	1.02669i
$711$	14.2138	−	12.3163i	0.533058	−	0.461897i
$712$	5.03516	+	5.03516i	0.188700	+	0.188700i
$713$	25.2974	+	12.6926i	0.947394	+	0.475342i
$714$			42.1226i			1.57640i
$715$	7.20866	−	30.8378i	0.269589	−	1.15327i
$716$	−3.24049	−	2.08254i	−0.121103	−	0.0778281i
$717$	14.3095	+	19.1153i	0.534400	+	0.713874i
$718$	−0.779517	−	2.08996i	−0.0290913	−	0.0779968i
$719$	30.9741	−	4.45341i	1.15514	−	0.166084i	0.461995	−	0.886883i	$-0.347134\pi$
$719$	30.9741	−	4.45341i	1.15514	−	0.166084i	0.693145	+	0.720799i	$0.256225\pi$
$720$	−2.68589	−	1.27708i	−0.100097	−	0.0475939i
$721$	−61.2563	+	39.3670i	−2.28130	+	1.46610i
$722$	−15.1441	−	5.64846i	−0.563605	−	0.210214i
$723$	−7.67036	+	14.0472i	−0.285264	+	0.522422i
$724$	2.93229	−	3.38404i	0.108978	−	0.125767i
$725$	12.1362	+	20.2315i	0.450728	+	0.751378i
$726$	−10.3512	+	3.03938i	−0.384168	+	0.112802i
$727$	7.92393	−	21.2449i	0.293882	−	0.787929i	−0.703157	−	0.711035i	$-0.748227\pi$
$727$	7.92393	−	21.2449i	0.293882	−	0.787929i	0.997039	−	0.0768945i	$-0.0245005\pi$
$728$	−2.94582	+	13.5417i	−0.109179	+	0.501889i
$729$	−1.90693	+	6.49439i	−0.0706269	+	0.240533i
$730$	10.1944	+	0.157391i	0.377310	+	0.00582530i
$731$	−2.15251	+	4.71333i	−0.0796134	+	0.174329i
$732$	−3.41570	+	2.55696i	−0.126248	+	0.0945079i
$733$	24.8488	−	5.40552i	0.917811	−	0.199658i	0.271240	−	0.962512i	$-0.412566\pi$
$733$	24.8488	−	5.40552i	0.917811	−	0.199658i	0.646571	+	0.762854i	$0.276203\pi$
$734$	−10.7353	−	12.3892i	−0.396247	−	0.457294i
$735$	23.1995	+	32.0092i	0.855726	+	1.18068i
$736$	0.847094	+	4.72043i	0.0312243	+	0.173997i
$737$	16.0976	−	16.0976i	0.592962	−	0.592962i
$738$	0.664977	−	9.29759i	0.0244781	−	0.342249i
$739$	−19.6936	+	30.6438i	−0.724440	+	1.12725i	0.262307	+	0.964984i	$0.415517\pi$
$739$	−19.6936	+	30.6438i	−0.724440	+	1.12725i	−0.986747	+	0.162266i	$0.948120\pi$
$740$	−1.08757	+	0.572240i	−0.0399797	+	0.0210360i
$741$	−11.2235	−	5.12560i	−0.412306	−	0.188294i
$742$	−6.98331	−	5.22764i	−0.256365	−	0.191913i
$743$	13.0750	−	7.13951i	0.479677	−	0.261923i	−0.221170	−	0.975235i	$-0.570988\pi$
$743$	13.0750	−	7.13951i	0.479677	−	0.261923i	0.700847	+	0.713312i	$0.252806\pi$
$744$	−6.63931	−	10.3310i	−0.243409	−	0.378751i
$745$	37.8235	−	10.4745i	1.38575	−	0.383757i
$746$	−8.75779	−	29.8263i	−0.320646	−	1.09202i
$747$	−15.6809	+	1.12152i	−0.573734	+	0.0410343i
$748$	20.6347	−	1.47582i	0.754479	−	0.0539614i
$749$	7.86195	+	26.7754i	0.287270	+	0.978350i
$750$	−23.2399	−	1.07709i	−0.848602	−	0.0393297i
$751$	3.07898	+	4.79099i	0.112354	+	0.174826i	0.892877	−	0.450301i	$-0.148683\pi$
$751$	3.07898	+	4.79099i	0.112354	+	0.174826i	−0.780523	+	0.625127i	$0.785047\pi$
$752$	−10.3576	+	5.65570i	−0.377704	+	0.206242i
$753$	−3.08749	−	2.31127i	−0.112514	−	0.0842272i
$754$	15.1102	+	6.90059i	0.550280	+	0.251304i
$755$	6.55269	+	2.03443i	0.238477	+	0.0740407i
$756$	7.39561	−	11.5078i	0.268976	−	0.418534i
$757$	−1.40768	+	19.6819i	−0.0511629	+	0.715350i	0.905536	+	0.424270i	$0.139469\pi$
$757$	−1.40768	+	19.6819i	−0.0511629	+	0.715350i	−0.956699	+	0.291080i	$0.905985\pi$
$758$	17.5672	−	17.5672i	0.638069	−	0.638069i
$759$	−40.1232	+	1.39538i	−1.45638	+	0.0506490i
$760$	3.04946	−	2.21017i	0.110615	−	0.0801713i
$761$	7.86088	+	9.07194i	0.284957	+	0.328857i	0.880124	−	0.474745i	$-0.157460\pi$
$761$	7.86088	+	9.07194i	0.284957	+	0.328857i	−0.595167	+	0.803602i	$0.702914\pi$
$762$	21.5986	−	4.69849i	0.782436	−	0.170208i
$763$	9.92216	−	7.42764i	0.359206	−	0.268898i
$764$	−7.42475	+	16.2579i	−0.268618	+	0.588192i
$765$	−10.9797	+	10.6459i	−0.396973	+	0.384902i
$766$	−4.44684	+	15.1446i	−0.160671	+	0.547195i
$767$	−9.09319	+	41.8007i	−0.328336	+	1.50934i
$768$	0.727191	−	1.94967i	0.0262402	−	0.0703528i
$769$	−23.4533	+	6.88650i	−0.845746	+	0.248333i	−0.675768	−	0.737114i	$-0.736188\pi$
$769$	−23.4533	+	6.88650i	−0.845746	+	0.248333i	−0.169978	+	0.985448i	$0.554370\pi$
$770$	27.1171	−	22.7738i	0.977233	−	0.820710i
$771$	11.5929	−	13.3789i	0.417508	−	0.481830i
$772$	−4.62268	+	8.46580i	−0.166374	+	0.304691i
$773$	35.6847	+	13.3097i	1.28349	+	0.478717i	0.896368	−	0.443311i	$-0.146196\pi$
$773$	35.6847	+	13.3097i	1.28349	+	0.478717i	0.387123	+	0.922028i	$0.373469\pi$
$774$	−1.12744	+	0.724564i	−0.0405251	+	0.0260439i
$775$	−24.3193	−	16.7119i	−0.873575	−	0.600309i
$776$	−1.92247	+	0.276410i	−0.0690127	+	0.00992253i
$777$	1.57326	+	4.21807i	0.0564404	+	0.151323i
$778$	4.19759	+	5.60732i	0.150491	+	0.201032i
$779$	9.93019	+	6.38174i	0.355786	+	0.228650i
$780$	−13.9154	+	8.64230i	−0.498251	+	0.309444i
$781$			49.2961i			1.76395i
$782$	24.2656	+	4.40147i	0.867737	+	0.157396i
$783$	−11.5942	−	11.5942i	−0.414342	−	0.414342i
$784$	−6.42096	+	5.56379i	−0.229320	+	0.198707i
$785$	−43.0670	+	2.41264i	−1.53713	+	0.0861108i
$786$	4.07511	−	28.3430i	0.145354	−	1.01096i
$787$	−42.7534	+	15.9462i	−1.52399	+	0.568421i	−0.965344	−	0.260982i	$-0.915954\pi$
$787$	−42.7534	+	15.9462i	−1.52399	+	0.568421i	−0.558651	+	0.829403i	$0.688681\pi$
$788$	4.02959	−	5.38290i	0.143548	−	0.191758i
$789$	−41.2015	−	12.0979i	−1.46681	−	0.430695i
$790$	29.4517	+	11.5059i	1.04784	+	0.409360i
$791$	−3.80452	−	8.33073i	−0.135273	−	0.296207i
$792$	4.69621	+	2.56432i	0.166873	+	0.0911193i
$793$	0.514968	+	7.20019i	0.0182870	+	0.255686i
$794$	15.0707	+	13.0589i	0.534841	+	0.463442i
$795$	−1.30967	−	10.2274i	−0.0464491	−	0.362728i
$796$	−0.0472690	+	0.0215870i	−0.00167541	+	0.000765132i
$797$	3.46437	+	0.753629i	0.122714	+	0.0266949i	0.273503	−	0.961871i	$-0.411818\pi$
$797$	3.46437	+	0.753629i	0.122714	+	0.0266949i	−0.150789	+	0.988566i	$0.548181\pi$
$798$	−6.61201	−	12.1090i	−0.234063	−	0.428654i
$799$	8.63640	+	60.0675i	0.305534	+	2.12503i
$800$	−0.202566	−	4.99590i	−0.00716178	−	0.176632i
$801$	9.37449	+	1.34785i	0.331231	+	0.0476239i
$802$	−5.28827	−	24.3098i	−0.186735	−	0.858409i
$803$	−18.2965	−	1.30859i	−0.645669	−	0.0461792i
$804$	−11.7753			−0.415283
$805$	38.0535	−	18.2753i	1.34121	−	0.644119i
$806$	−20.7764			−0.731817
$807$	30.3577	+	2.17122i	1.06864	+	0.0764307i
$808$	2.79543	+	12.8504i	0.0983429	+	0.452075i
$809$	−23.9519	−	3.44376i	−0.842103	−	0.121076i	−0.292255	−	0.956341i	$-0.594406\pi$
$809$	−23.9519	−	3.44376i	−0.842103	−	0.121076i	−0.549849	+	0.835264i	$0.685315\pi$
$810$	24.5972	−	4.95439i	0.864256	−	0.174080i
$811$	4.17912	+	29.0664i	0.146749	+	1.02066i	0.921496	+	0.388389i	$0.126968\pi$
$811$	4.17912	+	29.0664i	0.146749	+	1.02066i	−0.774747	+	0.632272i	$0.782123\pi$
$812$	8.90174	+	16.3023i	0.312390	+	0.572099i
$813$	−22.5734	−	4.91054i	−0.791684	−	0.172220i
$814$	2.01120	−	0.918484i	0.0704925	−	0.0321928i
$815$	10.7095	−	13.8551i	0.375137	−	0.485323i
$816$	−8.08688	−	7.00732i	−0.283097	−	0.245305i
$817$	−0.121073	−	1.69283i	−0.00423582	−	0.0592245i
$818$	−13.8290	−	7.55122i	−0.483520	−	0.264022i
$819$	7.65700	+	16.7665i	0.267557	+	0.585869i
$820$	14.3538	−	6.28919i	0.501255	−	0.219628i
$821$	14.4503	+	4.24299i	0.504318	+	0.148081i	0.523989	−	0.851725i	$-0.324443\pi$
$821$	14.4503	+	4.24299i	0.504318	+	0.148081i	−0.0196702	+	0.999807i	$0.506262\pi$
$822$	6.78343	−	9.06160i	0.236599	−	0.316060i
$823$	−20.5474	+	7.66379i	−0.716238	+	0.267143i	−0.681049	−	0.732238i	$-0.738476\pi$
$823$	−20.5474	+	7.66379i	−0.716238	+	0.267143i	−0.0351890	+	0.999381i	$0.511203\pi$
$824$	2.63246	−	18.3092i	0.0917061	−	0.637830i
$825$	41.6379	+	4.27345i	1.44965	+	0.148782i
$826$	−36.1503	+	31.3244i	−1.25783	+	1.08991i
$827$	15.1528	+	15.1528i	0.526913	+	0.526913i	0.919651	−	0.392737i	$-0.128472\pi$
$827$	15.1528	+	15.1528i	0.526913	+	0.526913i	−0.392737	+	0.919651i	$0.628472\pi$
$828$	4.66440	+	4.35088i	0.162099	+	0.151203i
$829$			11.4324i			0.397065i	0.980094	+	0.198532i	$0.0636175\pi$
$829$			11.4324i			0.397065i	−0.980094	+	0.198532i	$0.936382\pi$
$830$	−13.9443	−	22.4525i	−0.484015	−	0.779336i
$831$	−50.3661	−	32.3683i	−1.74718	−	1.12284i
$832$	−2.10975	−	2.81829i	−0.0731423	−	0.0977066i
$833$	15.2680	+	40.9351i	0.529004	+	1.41832i
$834$	3.48854	−	0.501576i	0.120798	−	0.0173682i
$835$	−16.2824	−	45.8022i	−0.563476	−	1.58505i
$836$	−5.70021	+	3.66330i	−0.197146	+	0.126698i
$837$	19.2149	+	7.16678i	0.664164	+	0.247720i
$838$	−4.29807	+	7.87133i	−0.148474	+	0.271910i
$839$	4.52450	−	5.22155i	0.156203	−	0.180268i	−0.672254	−	0.740321i	$-0.734674\pi$
$839$	4.52450	−	5.22155i	0.156203	−	0.180268i	0.828457	+	0.560053i	$0.189219\pi$
$840$	−18.2475	−	1.58856i	−0.629598	−	0.0548106i
$841$	−6.46313	+	1.89775i	−0.222867	+	0.0654396i
$842$	8.80364	−	23.6035i	0.303394	−	0.813430i
$843$	−2.38823	+	10.9785i	−0.0822551	+	0.378121i
$844$	−0.0638957	+	0.217609i	−0.00219938	+	0.00749041i
$845$	0.0209255	−	1.35537i	0.000719860	−	0.0466260i
$846$	−6.52034	+	14.2775i	−0.224174	+	0.490872i
$847$	−16.3380	+	12.2304i	−0.561379	+	0.420243i
$848$	2.16534	−	0.471040i	0.0743580	−	0.0161756i
$849$	−11.8823	−	13.7129i	−0.407798	−	0.470624i
$850$	−24.4346	−	8.00189i	−0.838100	−	0.274463i
$851$	2.59431	−	0.465556i	0.0889318	−	0.0159591i
$852$	18.0299	−	18.0299i	0.617696	−	0.617696i
$853$	−2.36408	+	33.0541i	−0.0809444	+	1.13175i	0.780926	+	0.624623i	$0.214747\pi$
$853$	−2.36408	+	33.0541i	−0.0809444	+	1.13175i	−0.861871	+	0.507128i	$0.830707\pi$
$854$	−4.36386	+	6.79030i	−0.149328	+	0.232359i
$855$	1.48526	−	4.78387i	0.0507949	−	0.163605i
$856$	−6.44833	−	2.94485i	−0.220399	−	0.100653i
$857$	16.5184	+	12.3655i	0.564258	+	0.422398i	0.842957	−	0.537980i	$-0.180813\pi$
$857$	16.5184	+	12.3655i	0.564258	+	0.422398i	−0.278700	+	0.960378i	$0.589903\pi$
$858$	25.8662	−	14.1240i	0.883057	−	0.482186i
$859$	26.0451	+	40.5269i	0.888646	+	1.38276i	0.923595	+	0.383371i	$0.125237\pi$
$859$	26.0451	+	40.5269i	0.888646	+	1.38276i	−0.0349488	+	0.999389i	$0.511127\pi$
$860$	−1.96064	−	1.11022i	−0.0668572	−	0.0378582i
$861$	−16.1737	−	55.0827i	−0.551199	−	1.87721i
$862$	−1.10028	+	0.0786936i	−0.0374757	+	0.00268032i
$863$	−24.7687	+	1.77149i	−0.843136	+	0.0603023i	−0.486223	−	0.873835i	$-0.661626\pi$
$863$	−24.7687	+	1.77149i	−0.843136	+	0.0603023i	−0.356914	+	0.934137i	$0.616171\pi$
$864$	0.979017	+	3.33423i	0.0333068	+	0.113433i
$865$	−39.2860	−	22.2459i	−1.33577	−	0.756383i
$866$	−2.86017	−	4.45051i	−0.0971924	−	0.151234i
$867$	−17.2465	+	9.41731i	−0.585723	+	0.319829i
$868$	−18.5979	−	13.9222i	−0.631254	−	0.472551i
$869$	−51.7468	−	23.6320i	−1.75539	−	0.801659i
$870$	−6.50988	+	20.9676i	−0.220706	+	0.710869i
$871$	−10.7705	+	16.7593i	−0.364946	+	0.567866i
$872$	−0.224615	+	3.14053i	−0.00760643	+	0.106352i
$873$	−1.82663	+	1.82663i	−0.0618221	+	0.0618221i
$874$	−7.66656	+	2.54370i	−0.259325	+	0.0860420i
$875$	−41.9045	+	13.4548i	−1.41663	+	0.454857i
$876$	6.21328	+	7.17051i	0.209927	+	0.242269i
$877$	8.36009	−	1.81863i	0.282300	−	0.0614106i	−0.0691859	−	0.997604i	$-0.522040\pi$
$877$	8.36009	−	1.81863i	0.282300	−	0.0614106i	0.351486	+	0.936193i	$0.385677\pi$
$878$	7.15820	−	5.35856i	0.241578	−	0.180843i
$879$	19.4941	−	42.6861i	0.657519	−	1.43977i
$880$	−0.138868	+	8.99461i	−0.00468124	+	0.303208i
$881$	7.52581	−	25.6305i	0.253551	−	0.863515i	−0.730086	−	0.683355i	$-0.760520\pi$
$881$	7.52581	−	25.6305i	0.253551	−	0.863515i	0.983637	−	0.180160i	$-0.0576616\pi$
$882$	−2.40202	+	11.0419i	−0.0808803	+	0.371801i
$883$	−0.391435	+	1.04948i	−0.0131728	+	0.0353177i	−0.943370	−	0.331743i	$-0.892363\pi$
$883$	−0.391435	+	1.04948i	−0.0131728	+	0.0353177i	0.930197	+	0.367061i	$0.119636\pi$
$884$	−17.3700	+	5.10031i	−0.584218	+	0.171542i
$885$	−56.3265	−	4.90359i	−1.89339	−	0.164832i
$886$	−5.70002	+	6.57818i	−0.191496	+	0.220998i
$887$	−10.3731	+	18.9968i	−0.348293	+	0.637851i	−0.991830	−	0.127564i	$-0.959284\pi$
$887$	−10.3731	+	18.9968i	−0.348293	+	0.637851i	0.643537	+	0.765415i	$0.277466\pi$
$888$	−1.07153	−	0.399658i	−0.0359580	−	0.0134117i
$889$	35.1771	−	22.6069i	1.17980	−	0.758212i
$890$	5.33340	+	15.0028i	0.178776	+	0.502894i
$891$	−44.6829	+	6.42444i	−1.49693	+	0.215227i
$892$	3.75835	+	10.0765i	0.125839	+	0.337387i
$893$	−11.9115	−	15.9120i	−0.398605	−	0.532473i
$894$	30.7252	+	19.7459i	1.02760	+	0.660401i
$895$	−4.54429	−	7.31699i	−0.151899	−	0.244580i
$896$		−	3.93651i		−	0.131510i
$897$	34.0495	−	8.65666i	1.13688	−	0.289037i
$898$	14.8171	+	14.8171i	0.494453	+	0.494453i
$899$	−21.0449	+	18.2355i	−0.701888	+	0.608190i
$900$	−4.19771	−	5.15791i	−0.139924	−	0.171930i
$901$	1.62171	−	11.2792i	0.0540270	−	0.375766i
$902$	−26.4168	+	9.85297i	−0.879584	+	0.328068i
$903$	−4.94642	+	6.60764i	−0.164607	+	0.219889i
$904$	2.23227	+	0.655455i	0.0742443	+	0.0218001i
$905$	9.17083	−	4.01826i	0.304849	−	0.133571i
$906$	2.65244	+	5.80804i	0.0881215	+	0.192959i
$907$	−28.0353	−	15.3084i	−0.930897	−	0.508308i	−0.0591416	−	0.998250i	$-0.518836\pi$
$907$	−28.0353	−	15.3084i	−0.930897	−	0.508308i	−0.871755	+	0.489941i	$0.837018\pi$
$908$	1.08369	+	15.1519i	0.0359634	+	0.502833i
$909$	13.2190	+	11.4543i	0.438445	+	0.379915i
$910$	−18.9514	+	24.5178i	−0.628232	+	0.812759i
$911$	4.58077	−	2.09197i	0.151768	−	0.0693099i	−0.338083	−	0.941116i	$-0.609779\pi$
$911$	4.58077	−	2.09197i	0.151768	−	0.0693099i	0.489851	+	0.871806i	$0.337051\pi$
$912$	3.42468	+	0.744994i	0.113403	+	0.0246692i
$913$	22.7890	+	41.7350i	0.754207	+	1.38123i
$914$	−3.03097	−	21.0809i	−0.100256	−	0.697294i
$915$	−9.35287	+	1.88387i	−0.309196	+	0.0622787i
$916$	23.4026	+	3.36479i	0.773244	+	0.111176i
$917$	−11.5146	−	52.9316i	−0.380244	−	1.74796i
$918$	17.8239	+	1.27479i	0.588276	+	0.0420743i
$919$	22.4511			0.740594			0.370297	−	0.928913i	$-0.379256\pi$
$919$	22.4511			0.740594			0.370297	+	0.928913i	$0.379256\pi$
$920$	−2.82185	+	10.3459i	−0.0930335	+	0.341093i
$921$	−58.6711			−1.93328
$922$	27.3366	+	1.95515i	0.900281	+	0.0643894i
$923$	−9.16977	−	42.1527i	−0.301827	−	1.38747i
$924$	32.6184	+	4.68982i	1.07307	+	0.154284i
$925$	−2.74570	+	0.111329i	−0.0902782	+	0.00366046i
$926$	1.00869	+	7.01557i	0.0331475	+	0.230546i
$927$	−11.7906	−	21.5929i	−0.387254	−	0.709203i
$928$	−4.61064	−	1.00298i	−0.151352	−	0.0329246i
$929$	−30.5308	+	13.9430i	−1.00168	+	0.457454i	−0.847618	−	0.530607i	$-0.821964\pi$
$929$	−30.5308	+	13.9430i	−1.00168	+	0.457454i	−0.154066	+	0.988061i	$0.549237\pi$
$930$	−3.48790	−	27.2375i	−0.114373	−	0.893152i
$931$	−10.8147	−	9.37099i	−0.354438	−	0.307122i
$932$	1.85382	+	25.9197i	0.0607238	+	0.849029i
$933$	−22.3312	−	12.1938i	−0.731091	−	0.399206i
$934$	5.77858	+	12.6533i	0.189081	+	0.414030i
$935$	43.0871	+	16.8328i	1.40910	+	0.550492i
$936$	−4.49269	−	1.31917i	−0.146848	−	0.0431185i
$937$	−2.31990	+	3.09902i	−0.0757879	+	0.101241i	−0.836833	−	0.547458i	$-0.815596\pi$
$937$	−2.31990	+	3.09902i	−0.0757879	+	0.101241i	0.761045	+	0.648699i	$0.224686\pi$
$938$	−20.8715	+	7.78468i	−0.681480	+	0.254179i
$939$	−7.19253	+	50.0252i	−0.234719	+	1.63251i
$940$	−26.3469	+	1.47597i	−0.859342	+	0.0481408i
$941$	27.4073	−	23.7486i	0.893452	−	0.774181i	−0.0814819	−	0.996675i	$-0.525965\pi$
$941$	27.4073	−	23.7486i	0.893452	−	0.774181i	0.974934	+	0.222494i	$0.0714198\pi$
$942$	−28.3838	−	28.3838i	−0.924795	−	0.924795i
$943$	−33.4216	+	3.56153i	−1.08836	+	0.115980i
$944$		−	12.1513i		−	0.395490i
$945$	25.9844	−	16.1379i	0.845273	−	0.524965i
$946$	3.41021	+	2.19161i	0.110875	+	0.0712554i
$947$	5.53287	+	7.39105i	0.179794	+	0.240177i	0.881380	−	0.472408i	$-0.156615\pi$
$947$	5.53287	+	7.39105i	0.179794	+	0.240177i	−0.701586	+	0.712585i	$0.747524\pi$
$948$	10.2829	+	27.5696i	0.333974	+	0.895419i
$949$	15.8886	−	2.28444i	0.515766	−	0.0741559i
$950$	8.28029	−	1.53521i	0.268648	−	0.0498089i
$951$	44.3487	−	28.5012i	1.43810	−	0.924213i
$952$	−18.9664	−	7.07411i	−0.614705	−	0.229273i
$953$	5.00827	−	9.17197i	0.162234	−	0.297109i	−0.783899	−	0.620889i	$-0.786772\pi$
$953$	5.00827	−	9.17197i	0.162234	−	0.297109i	0.946133	+	0.323780i	$0.104954\pi$
$954$	1.93009	−	2.22744i	0.0624890	−	0.0721161i
$955$	−30.6043	+	25.7024i	−0.990332	+	0.831711i
$956$	−11.0102	+	3.23288i	−0.356094	+	0.104559i
$957$	13.8038	−	37.0094i	0.446214	−	1.19635i
$958$	−4.98772	+	22.9282i	−0.161146	+	0.740776i
$959$	6.03288	−	20.5461i	0.194812	−	0.663468i
$960$	3.34055	−	3.23897i	0.107816	−	0.104537i
$961$	1.59047	−	3.48265i	0.0513055	−	0.112343i
$962$	−1.54891	+	1.15950i	−0.0499389	+	0.0373838i
$963$	−9.21307	+	2.00418i	−0.296887	+	0.0645838i
$964$	−5.03684	−	5.81282i	−0.162226	−	0.187218i
$965$	−17.4638	+	12.6574i	−0.562181	+	0.407455i
$966$	36.2801	+	15.0675i	1.16729	+	0.484790i
$967$	−0.509421	+	0.509421i	−0.0163819	+	0.0163819i	−0.715250	−	0.698868i	$-0.753687\pi$
$967$	−0.509421	+	0.509421i	−0.0163819	+	0.0163819i	0.698868	+	0.715250i	$0.253687\pi$
$968$	0.369854	−	5.17124i	0.0118876	−	0.166210i
$969$	9.74376	−	15.1616i	0.313015	−	0.487060i
$970$	−4.14768	−	1.28774i	−0.133174	−	0.0413469i
$971$	−15.9441	−	7.28145i	−0.511672	−	0.233673i	0.142810	−	0.989750i	$-0.454386\pi$
$971$	−15.9441	−	7.28145i	−0.511672	−	0.233673i	−0.654482	+	0.756077i	$0.727113\pi$
$972$	10.3468	+	7.74551i	0.331874	+	0.248437i
$973$	5.85179	−	3.19532i	0.187600	−	0.102437i
$974$	7.34095	+	11.4227i	0.235219	+	0.366008i
$975$	−36.3992	+	4.09104i	−1.16571	+	0.131018i
$976$	−0.577680	−	1.96740i	−0.0184911	−	0.0629748i
$977$	−23.7739	+	1.70034i	−0.760595	+	0.0543989i	−0.446248	−	0.894909i	$-0.647240\pi$
$977$	−23.7739	+	1.70034i	−0.760595	+	0.0543989i	−0.314347	+	0.949308i	$0.601786\pi$
$978$	16.2547	−	1.16256i	0.519768	−	0.0371745i
$979$	−8.07075	−	27.4865i	−0.257942	−	0.878471i
$980$	−18.3089	+	5.07031i	−0.584855	+	0.161965i
$981$	2.26403	+	3.52290i	0.0722849	+	0.112478i
$982$	−26.4916	+	14.4655i	−0.845381	+	0.461613i
$983$	18.3630	+	13.7464i	0.585689	+	0.438441i	0.850586	−	0.525835i	$-0.176247\pi$
$983$	18.3630	+	13.7464i	0.585689	+	0.438441i	−0.264897	+	0.964277i	$0.585338\pi$
$984$	13.2656	+	6.05820i	0.422892	+	0.193128i
$985$	13.3060	−	7.00117i	0.423964	−	0.223076i
$986$	−13.1180	+	20.4120i	−0.417762	+	0.650051i
$987$	−6.89621	+	96.4217i	−0.219509	+	3.06914i
$988$	4.19278	−	4.19278i	0.133390	−	0.133390i
$989$	3.28962	+	3.53994i	0.104604	+	0.112564i
$990$	7.02138	+	9.68767i	0.223154	+	0.307894i
$991$	18.2595	+	21.0726i	0.580032	+	0.669392i	0.967612	−	0.252444i	$-0.0812343\pi$
$991$	18.2595	+	21.0726i	0.580032	+	0.669392i	−0.387580	+	0.921836i	$0.626689\pi$
$992$	5.76671	−	1.25447i	0.183093	−	0.0398295i
$993$	−13.7805	+	10.3160i	−0.437311	+	0.327367i
$994$	20.0382	−	43.8775i	0.635572	−	1.39171i
$995$	−0.116183	−	0.00179376i	−0.00368326	−	5.68659e-5i
$996$	6.92945	−	23.5995i	0.219568	−	0.747780i
$997$	9.65479	−	44.3823i	0.305770	−	1.40560i	−0.526001	−	0.850484i	$-0.676309\pi$
$997$	9.65479	−	44.3823i	0.305770	−	1.40560i	0.831771	−	0.555119i	$-0.187327\pi$
$998$	1.12748	−	3.02289i	0.0356897	−	0.0956878i
$999$	1.83246	−	0.538060i	0.0579766	−	0.0170235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.33.2	yes	240
5.2	odd	4	inner	230.2.l.a.217.8	yes	240
23.7	odd	22	inner	230.2.l.a.53.8	yes	240
115.7	even	44	inner	230.2.l.a.7.2	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.2	✓	240	115.7	even	44	inner
230.2.l.a.33.2	yes	240	1.1	even	1	trivial
230.2.l.a.53.8	yes	240	23.7	odd	22	inner
230.2.l.a.217.8	yes	240	5.2	odd	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.997452 - 0.0713392i) q^{2} +(-0.442321 - 2.03332i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.86221 + 1.23780i) q^{5} +(0.296139 + 2.05969i) q^{6} +(1.88657 + 3.45500i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-1.20984 + 0.552516i) q^{9} +(-1.76917 - 1.36750i) q^{10} +(3.04037 + 2.63450i) q^{11} +(-0.148448 - 2.07557i) q^{12} +(-3.08985 - 1.68719i) q^{13} +(-1.63529 - 3.58078i) q^{14} +(1.69315 - 4.33398i) q^{15} +(0.959493 + 0.281733i) q^{16} +(3.08166 - 4.11662i) q^{17} +(1.24618 - 0.464799i) q^{18} +(-0.239698 + 1.66714i) q^{19} +(1.66710 + 1.49023i) q^{20} +(6.19064 - 5.36422i) q^{21} +(-2.84468 - 2.84468i) q^{22} +(-2.44330 - 4.12677i) q^{23} +2.08087i q^{24} +(1.93568 + 4.61011i) q^{25} +(2.96162 + 1.90332i) q^{26} +(-2.08248 - 2.78187i) q^{27} +(1.37567 + 3.68832i) q^{28} +(4.67045 - 0.671509i) q^{29} +(-1.99802 + 4.20215i) q^{30} +(-4.96472 + 3.19063i) q^{31} +(-0.936950 - 0.349464i) q^{32} +(4.01195 - 7.34734i) q^{33} +(-3.36749 + 3.88629i) q^{34} +(-0.763412 + 8.76915i) q^{35} +(-1.27616 + 0.374714i) q^{36} +(-0.192063 + 0.514940i) q^{37} +(0.358020 - 1.64579i) q^{38} +(-2.06388 + 7.02893i) q^{39} +(-1.55654 - 1.60536i) q^{40} +(2.91137 - 6.37502i) q^{41} +(-6.55754 + 4.90892i) q^{42} +(-0.984612 + 0.214189i) q^{43} +(2.63450 + 3.04037i) q^{44} +(-2.93689 - 0.468644i) q^{45} +(2.14268 + 4.29056i) q^{46} +(-8.34469 + 8.34469i) q^{47} +(0.148448 - 2.07557i) q^{48} +(-4.59336 + 7.14741i) q^{49} +(-1.60187 - 4.73646i) q^{50} +(-9.73349 - 4.44514i) q^{51} +(-2.81829 - 2.10975i) q^{52} +(1.94492 - 1.06201i) q^{53} +(1.87872 + 2.92335i) q^{54} +(2.40083 + 8.66939i) q^{55} +(-1.10904 - 3.77706i) q^{56} +(3.49585 - 0.250028i) q^{57} +(-4.70645 + 0.336612i) q^{58} +(-3.42341 - 11.6591i) q^{59} +(2.29271 - 4.04891i) q^{60} +(-1.10856 - 1.72495i) q^{61} +(5.17969 - 2.82833i) q^{62} +(-4.19139 - 3.13764i) q^{63} +(0.909632 + 0.415415i) q^{64} +(-3.66556 - 6.96654i) q^{65} +(-4.52588 + 7.04241i) q^{66} +(0.403696 - 5.64441i) q^{67} +(3.63615 - 3.63615i) q^{68} +(-7.31032 + 6.79338i) q^{69} +(1.38705 - 8.69234i) q^{70} +(8.02440 + 9.26066i) q^{71} +(1.29964 - 0.282719i) q^{72} +(-3.65015 + 2.73247i) q^{73} +(0.228309 - 0.499927i) q^{74} +(8.51764 - 5.97501i) q^{75} +(-0.474517 + 1.61606i) q^{76} +(-3.36630 + 15.4746i) q^{77} +(2.56006 - 6.86379i) q^{78} +(-13.5678 + 3.98387i) q^{79} +(1.43805 + 1.71231i) q^{80} +(-7.34827 + 8.48035i) q^{81} +(-3.35874 + 6.15108i) q^{82} +(11.0747 + 4.13065i) q^{83} +(6.89103 - 4.42860i) q^{84} +(10.8343 - 3.85153i) q^{85} +(0.997384 - 0.143402i) q^{86} +(-3.43123 - 9.19949i) q^{87} +(-2.41089 - 3.22057i) q^{88} +(-5.99039 - 3.84979i) q^{89} +(2.89598 + 0.676965i) q^{90} -13.8584i q^{91} +(-1.83113 - 4.43249i) q^{92} +(8.68358 + 8.68358i) q^{93} +(8.91873 - 7.72812i) q^{94} +(-2.50996 + 2.80787i) q^{95} +(-0.296139 + 2.05969i) q^{96} +(1.81978 - 0.678744i) q^{97} +(5.09155 - 6.80151i) q^{98} +(-5.13397 - 1.50747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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