LMFDB - Embedded newform 770.2.w.a.139.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(139,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 7]))

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

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

chi := DirichletCharacter("770.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.w (of order $10$, degree $4$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.2
Character	$\chi$	$=$	770.139
Dual form			770.2.w.a.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.934488 + 2.87606i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.226592 - 2.22456i) q^{5} +(2.44652 - 1.77750i) q^{6} +(2.25369 - 1.38595i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.97140 - 3.61193i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.934488 + 2.87606i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.226592 - 2.22456i) q^{5} +(2.44652 - 1.77750i) q^{6} +(2.25369 - 1.38595i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.97140 - 3.61193i) q^{9} +(-1.12425 + 1.93289i) q^{10} +(-2.96415 + 1.48789i) q^{11} -3.02407 q^{12} +(-0.321642 + 0.442702i) q^{13} +(-2.63792 - 0.203429i) q^{14} +(6.60971 + 1.42713i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(3.59196 + 4.94391i) q^{17} +(1.89891 + 5.84423i) q^{18} +(-0.0567089 + 0.174532i) q^{19} +(2.04566 - 0.902928i) q^{20} +(1.88003 + 7.77691i) q^{21} +(3.27261 + 0.538560i) q^{22} +8.00171i q^{23} +(2.44652 + 1.77750i) q^{24} +(-4.89731 + 1.00813i) q^{25} +(0.520427 - 0.169097i) q^{26} +(7.69428 - 5.59022i) q^{27} +(2.01455 + 1.71511i) q^{28} +(-4.80026 + 1.55970i) q^{29} +(-4.50852 - 5.03966i) q^{30} +(2.63979 - 3.63336i) q^{31} +1.00000 q^{32} +(-1.50928 - 9.91549i) q^{33} -6.11101i q^{34} +(-3.59380 - 4.69943i) q^{35} +(1.89891 - 5.84423i) q^{36} +(-4.53079 + 1.47214i) q^{37} +(0.148466 - 0.107867i) q^{38} +(-0.972667 - 1.33876i) q^{39} +(-2.18570 - 0.471925i) q^{40} +(-3.44319 + 10.5971i) q^{41} +(3.05018 - 7.39671i) q^{42} +2.20876 q^{43} +(-2.33104 - 2.35929i) q^{44} +(-6.90847 + 11.8776i) q^{45} +(4.70329 - 6.47352i) q^{46} +(0.0177794 - 0.0547195i) q^{47} +(-0.934488 - 2.87606i) q^{48} +(3.15827 - 6.24703i) q^{49} +(4.55457 + 2.06297i) q^{50} +(-17.5756 + 5.71067i) q^{51} +(-0.520427 - 0.169097i) q^{52} +(-7.85350 + 10.8094i) q^{53} -9.51065 q^{54} +(3.98154 + 6.25678i) q^{55} +(-0.621689 - 2.57167i) q^{56} +(-0.448971 - 0.326196i) q^{57} +(4.80026 + 1.55970i) q^{58} +(5.59628 - 1.81834i) q^{59} +(0.685229 + 6.72721i) q^{60} +(-3.98101 + 2.89237i) q^{61} +(-4.27127 + 1.38782i) q^{62} +(-16.2100 - 1.25007i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.05770 + 0.615198i) q^{65} +(-4.60714 + 8.90893i) q^{66} -9.61579i q^{67} +(-3.59196 + 4.94391i) q^{68} +(-23.0134 - 7.47751i) q^{69} +(0.145191 + 5.91430i) q^{70} +(0.266837 - 0.193869i) q^{71} +(-4.97140 + 3.61193i) q^{72} +(-6.98448 + 2.26940i) q^{73} +(4.53079 + 1.47214i) q^{74} +(1.67703 - 15.0270i) q^{75} -0.183514 q^{76} +(-4.61815 + 7.46141i) q^{77} +1.65480i q^{78} +(-2.23926 + 3.08208i) q^{79} +(1.49088 + 1.66652i) q^{80} +(3.19088 + 9.82051i) q^{81} +(9.01440 - 6.54934i) q^{82} +(3.14192 + 4.32448i) q^{83} +(-6.81532 + 4.19121i) q^{84} +(10.1841 - 9.11077i) q^{85} +(-1.78692 - 1.29828i) q^{86} -15.2634i q^{87} +(0.499090 + 3.27886i) q^{88} +1.52742i q^{89} +(12.5705 - 5.54848i) q^{90} +(-0.111318 + 1.44350i) q^{91} +(-7.61008 + 2.47267i) q^{92} +(7.98290 + 10.9875i) q^{93} +(-0.0465472 + 0.0338185i) q^{94} +(0.401106 + 0.0866047i) q^{95} +(-0.934488 + 2.87606i) q^{96} +(8.96753 + 6.51530i) q^{97} +(-6.22700 + 3.19756i) q^{98} +(20.1101 + 3.30945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 24 q^{2} - 24 q^{4} - 3 q^{7} - 24 q^{8} - 18 q^{9}+O(q^{10}) $ 96 * q - 24 * q^2 - 24 * q^4 - 3 * q^7 - 24 * q^8 - 18 * q^9	$ 96 q - 24 q^{2} - 24 q^{4} - 3 q^{7} - 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} - 28 q^{18} + 4 q^{22} - 42 q^{25} + 2 q^{28} - 6 q^{30} + 96 q^{32} + 14 q^{35} - 28 q^{36} + 10 q^{39} + 24 q^{43} - 16 q^{44} + 37 q^{49} + 8 q^{50} - 30 q^{51} - 40 q^{53} + 2 q^{56} + 20 q^{57} - 6 q^{60} - 63 q^{63} - 24 q^{64} + 40 q^{65} + 9 q^{70} - 20 q^{71} - 18 q^{72} + 16 q^{77} - 126 q^{81} + 100 q^{85} - 36 q^{86} + 14 q^{88} - 31 q^{91} + 10 q^{92} - 20 q^{93} - 16 q^{95} - 18 q^{98} + 100 q^{99}+O(q^{100}) $ 96 * q - 24 * q^2 - 24 * q^4 - 3 * q^7 - 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 - 28 * q^18 + 4 * q^22 - 42 * q^25 + 2 * q^28 - 6 * q^30 + 96 * q^32 + 14 * q^35 - 28 * q^36 + 10 * q^39 + 24 * q^43 - 16 * q^44 + 37 * q^49 + 8 * q^50 - 30 * q^51 - 40 * q^53 + 2 * q^56 + 20 * q^57 - 6 * q^60 - 63 * q^63 - 24 * q^64 + 40 * q^65 + 9 * q^70 - 20 * q^71 - 18 * q^72 + 16 * q^77 - 126 * q^81 + 100 * q^85 - 36 * q^86 + 14 * q^88 - 31 * q^91 + 10 * q^92 - 20 * q^93 - 16 * q^95 - 18 * q^98 + 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$-1$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.934488	+	2.87606i	−0.539527	+	1.66049i	0.194132	+	0.980976i	$0.437811\pi$
$3$	−0.934488	+	2.87606i	−0.539527	+	1.66049i	−0.733659	+	0.679518i	$0.762189\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.226592	−	2.22456i	−0.101335	−	0.994852i
$5$	−0.226592	−	2.22456i	−0.101335	−	0.994852i
$6$	2.44652	−	1.77750i	0.998789	−	0.725662i
$7$	2.25369	−	1.38595i	0.851816	−	0.523841i
$7$	2.25369	−	1.38595i	0.851816	−	0.523841i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−4.97140	−	3.61193i	−1.65713	−	1.20398i
$10$	−1.12425	+	1.93289i	−0.355518	+	0.611234i
$11$	−2.96415	+	1.48789i	−0.893725	+	0.448614i
$11$	−2.96415	+	1.48789i	−0.893725	+	0.448614i
$12$	−3.02407			−0.872973
$13$	−0.321642	+	0.442702i	−0.0892074	+	0.122783i	−0.851288	−	0.524699i	$-0.824178\pi$
$13$	−0.321642	+	0.442702i	−0.0892074	+	0.122783i	0.762081	+	0.647482i	$0.224178\pi$
$14$	−2.63792	−	0.203429i	−0.705014	−	0.0543687i
$15$	6.60971	+	1.42713i	1.70662	+	0.368484i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	3.59196	+	4.94391i	0.871178	+	1.19907i	0.978787	+	0.204881i	$0.0656806\pi$
$17$	3.59196	+	4.94391i	0.871178	+	1.19907i	−0.107609	+	0.994193i	$0.534319\pi$
$18$	1.89891	+	5.84423i	0.447576	+	1.37750i
$19$	−0.0567089	+	0.174532i	−0.0130099	+	0.0400404i	−0.957351	−	0.288928i	$-0.906701\pi$
$19$	−0.0567089	+	0.174532i	−0.0130099	+	0.0400404i	0.944341	+	0.328969i	$0.106701\pi$
$20$	2.04566	−	0.902928i	0.457423	−	0.201901i
$21$	1.88003	+	7.77691i	0.410256	+	1.69706i
$22$	3.27261	+	0.538560i	0.697722	+	0.114821i
$23$			8.00171i			1.66847i	0.551407	+	0.834236i	$0.314091\pi$
$23$			8.00171i			1.66847i	−0.551407	+	0.834236i	$0.685909\pi$
$24$	2.44652	+	1.77750i	0.499394	+	0.362831i
$25$	−4.89731	+	1.00813i	−0.979462	+	0.201626i
$26$	0.520427	−	0.169097i	0.102064	−	0.0331627i
$27$	7.69428	−	5.59022i	1.48076	−	1.07584i
$28$	2.01455	+	1.71511i	0.380714	+	0.324125i
$29$	−4.80026	+	1.55970i	−0.891386	+	0.289629i	−0.718677	−	0.695344i	$-0.755252\pi$
$29$	−4.80026	+	1.55970i	−0.891386	+	0.289629i	−0.172709	+	0.984973i	$0.555252\pi$
$30$	−4.50852	−	5.03966i	−0.823139	−	0.920112i
$31$	2.63979	−	3.63336i	0.474120	−	0.652570i	−0.503242	−	0.864146i	$-0.667859\pi$
$31$	2.63979	−	3.63336i	0.474120	−	0.652570i	0.977362	+	0.211576i	$0.0678595\pi$
$32$	1.00000			0.176777
$33$	−1.50928	−	9.91549i	−0.262732	−	1.72607i
$34$		−	6.11101i		−	1.04803i
$35$	−3.59380	−	4.69943i	−0.607463	−	0.794348i
$36$	1.89891	−	5.84423i	0.316484	−	0.974038i
$37$	−4.53079	+	1.47214i	−0.744858	+	0.242019i	−0.656767	−	0.754094i	$-0.728076\pi$
$37$	−4.53079	+	1.47214i	−0.744858	+	0.242019i	−0.0880906	+	0.996112i	$0.528076\pi$
$38$	0.148466	−	0.107867i	0.0240843	−	0.0174983i
$39$	−0.972667	−	1.33876i	−0.155751	−	0.214373i
$40$	−2.18570	−	0.471925i	−0.345590	−	0.0746178i
$41$	−3.44319	+	10.5971i	−0.537736	+	1.65498i	0.199924	+	0.979811i	$0.435930\pi$
$41$	−3.44319	+	10.5971i	−0.537736	+	1.65498i	−0.737661	+	0.675171i	$0.764070\pi$
$42$	3.05018	−	7.39671i	0.470653	−	1.14134i
$43$	2.20876			0.336833			0.168416	−	0.985716i	$-0.446135\pi$
$43$	2.20876			0.336833			0.168416	+	0.985716i	$0.446135\pi$
$44$	−2.33104	−	2.35929i	−0.351417	−	0.355677i
$45$	−6.90847	+	11.8776i	−1.02985	+	1.77061i
$46$	4.70329	−	6.47352i	0.693462	−	0.954469i
$47$	0.0177794	−	0.0547195i	0.00259340	−	0.00798166i	−0.949751	−	0.313005i	$-0.898664\pi$
$47$	0.0177794	−	0.0547195i	0.00259340	−	0.00798166i	0.952345	+	0.305023i	$0.0986643\pi$
$48$	−0.934488	−	2.87606i	−0.134882	−	0.415123i
$49$	3.15827	−	6.24703i	0.451182	−	0.892432i
$50$	4.55457	+	2.06297i	0.644114	+	0.291748i
$51$	−17.5756	+	5.71067i	−2.46108	+	0.799653i
$52$	−0.520427	−	0.169097i	−0.0721703	−	0.0234496i
$53$	−7.85350	+	10.8094i	−1.07876	+	1.48479i	−0.217884	+	0.975975i	$0.569916\pi$
$53$	−7.85350	+	10.8094i	−1.07876	+	1.48479i	−0.860877	+	0.508813i	$0.830084\pi$
$54$	−9.51065			−1.29424
$55$	3.98154	+	6.25678i	0.536871	+	0.843665i
$56$	−0.621689	−	2.57167i	−0.0830767	−	0.343654i
$57$	−0.448971	−	0.326196i	−0.0594676	−	0.0432058i
$58$	4.80026	+	1.55970i	0.630305	+	0.204799i
$59$	5.59628	−	1.81834i	0.728574	−	0.236728i	0.0788372	−	0.996888i	$-0.474879\pi$
$59$	5.59628	−	1.81834i	0.728574	−	0.236728i	0.649736	+	0.760160i	$0.274879\pi$
$60$	0.685229	+	6.72721i	0.0884626	+	0.868479i
$61$	−3.98101	+	2.89237i	−0.509716	+	0.370330i	−0.812716	−	0.582660i	$-0.802012\pi$
$61$	−3.98101	+	2.89237i	−0.509716	+	0.370330i	0.303000	+	0.952991i	$0.402012\pi$
$62$	−4.27127	+	1.38782i	−0.542451	+	0.176253i
$63$	−16.2100	−	1.25007i	−2.04227	−	0.157494i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.05770	+	0.615198i	0.131191	+	0.0763059i
$66$	−4.60714	+	8.90893i	−0.567100	+	1.09661i
$67$		−	9.61579i		−	1.17476i	−0.809313	−	0.587378i	$-0.800160\pi$
$67$		−	9.61579i		−	1.17476i	0.809313	−	0.587378i	$-0.199840\pi$
$68$	−3.59196	+	4.94391i	−0.435589	+	0.599537i
$69$	−23.0134	−	7.47751i	−2.77049	−	0.900186i
$70$	0.145191	+	5.91430i	0.0173537	+	0.706894i
$71$	0.266837	−	0.193869i	0.0316678	−	0.0230080i	−0.571839	−	0.820366i	$-0.693770\pi$
$71$	0.266837	−	0.193869i	0.0316678	−	0.0230080i	0.603507	+	0.797358i	$0.293770\pi$
$72$	−4.97140	+	3.61193i	−0.585885	+	0.425670i
$73$	−6.98448	+	2.26940i	−0.817472	+	0.265613i	−0.687759	−	0.725939i	$-0.741406\pi$
$73$	−6.98448	+	2.26940i	−0.817472	+	0.265613i	−0.129713	+	0.991552i	$0.541406\pi$
$74$	4.53079	+	1.47214i	0.526694	+	0.171133i
$75$	1.67703	−	15.0270i	0.193647	−	1.73517i
$76$	−0.183514			−0.0210505
$77$	−4.61815	+	7.46141i	−0.526287	+	0.850307i
$78$			1.65480i			0.187369i
$79$	−2.23926	+	3.08208i	−0.251937	+	0.346761i	−0.916188	−	0.400748i	$-0.868750\pi$
$79$	−2.23926	+	3.08208i	−0.251937	+	0.346761i	0.664252	+	0.747509i	$0.268750\pi$
$80$	1.49088	+	1.66652i	0.166685	+	0.186322i
$81$	3.19088	+	9.82051i	0.354542	+	1.09117i
$82$	9.01440	−	6.54934i	0.995474	−	0.723254i
$83$	3.14192	+	4.32448i	0.344870	+	0.474673i	0.945856	−	0.324587i	$-0.105225\pi$
$83$	3.14192	+	4.32448i	0.344870	+	0.474673i	−0.600986	+	0.799260i	$0.705225\pi$
$84$	−6.81532	+	4.19121i	−0.743613	+	0.457299i
$85$	10.1841	−	9.11077i	1.10462	−	0.988202i
$86$	−1.78692	−	1.29828i	−0.192689	−	0.139997i
$87$		−	15.2634i		−	1.63640i
$88$	0.499090	+	3.27886i	0.0532032	+	0.349527i
$89$			1.52742i			0.161907i	0.996718	+	0.0809533i	$0.0257965\pi$
$89$			1.52742i			0.161907i	−0.996718	+	0.0809533i	$0.974204\pi$
$90$	12.5705	−	5.54848i	1.32505	−	0.584861i
$91$	−0.111318	+	1.44350i	−0.0116693	+	0.151319i
$92$	−7.61008	+	2.47267i	−0.793406	+	0.257793i
$93$	7.98290	+	10.9875i	0.827788	+	1.13935i
$94$	−0.0465472	+	0.0338185i	−0.00480098	+	0.00348811i
$95$	0.401106	+	0.0866047i	0.0411526	+	0.00888546i
$96$	−0.934488	+	2.87606i	−0.0953758	+	0.293537i
$97$	8.96753	+	6.51530i	0.910515	+	0.661528i	0.941145	−	0.338003i	$-0.109751\pi$
$97$	8.96753	+	6.51530i	0.910515	+	0.661528i	−0.0306299	+	0.999531i	$0.509751\pi$
$98$	−6.22700	+	3.19756i	−0.629022	+	0.323003i
$99$	20.1101	+	3.30945i	2.02114	+	0.332612i
$100$	−2.47214	−	4.34609i	−0.247214	−	0.434609i
$101$	−10.4062	−	7.56052i	−1.03545	−	0.752300i	−0.0660593	−	0.997816i	$-0.521043\pi$
$101$	−10.4062	−	7.56052i	−1.03545	−	0.752300i	−0.969393	+	0.245516i	$0.921043\pi$
$102$	17.5756	+	5.71067i	1.74025	+	0.565440i
$103$	2.59604	+	7.98980i	0.255796	+	0.787258i	0.993672	+	0.112322i	$0.0358288\pi$
$103$	2.59604	+	7.98980i	0.255796	+	0.787258i	−0.737876	+	0.674936i	$0.764171\pi$
$104$	0.321642	+	0.442702i	0.0315396	+	0.0434105i
$105$	16.8742	−	5.94442i	1.64675	−	0.580116i
$106$	12.7072	−	4.12883i	1.23424	−	0.401027i
$107$	−0.784019	+	2.41296i	−0.0757939	+	0.233270i	−0.981775	−	0.190050i	$-0.939135\pi$
$107$	−0.784019	+	2.41296i	−0.0757939	+	0.233270i	0.905981	+	0.423319i	$0.139135\pi$
$108$	7.69428	+	5.59022i	0.740382	+	0.537919i
$109$		−	13.2256i		−	1.26678i	−0.773833	−	0.633390i	$-0.781663\pi$
$109$		−	13.2256i		−	1.26678i	0.773833	−	0.633390i	$-0.218337\pi$
$110$	0.456513	−	7.40213i	0.0435268	−	0.705766i
$111$		−	14.4065i		−	1.36741i
$112$	−1.00863	+	2.44595i	−0.0953070	+	0.231120i
$113$	3.31407	+	1.07681i	0.311762	+	0.101298i	0.460719	−	0.887546i	$-0.347592\pi$
$113$	3.31407	+	1.07681i	0.311762	+	0.101298i	−0.148957	+	0.988844i	$0.547592\pi$
$114$	0.171492	+	0.527797i	0.0160617	+	0.0494327i
$115$	17.8003	−	1.81312i	1.65988	−	0.169074i
$116$	−2.96673	−	4.08335i	−0.275454	−	0.379129i
$117$	3.19802	−	1.03910i	0.295657	−	0.0960648i
$118$	−5.59628	−	1.81834i	−0.515179	−	0.167392i
$119$	14.9472	+	6.16377i	1.37021	+	0.565032i
$120$	3.39979	−	5.84520i	0.310357	−	0.533591i
$121$	6.57239	−	8.82064i	0.597490	−	0.801876i
$122$	4.92080			0.445508
$123$	−27.2601	−	19.8057i	−2.45796	−	1.78582i
$124$	4.27127	+	1.38782i	0.383571	+	0.124630i
$125$	3.35234	+	10.6659i	0.299842	+	0.953989i
$126$	12.3794	+	10.5393i	1.10284	+	0.938916i
$127$	−15.9399	+	11.5810i	−1.41444	+	1.02765i	−0.421777	+	0.906700i	$0.638593\pi$
$127$	−15.9399	+	11.5810i	−1.41444	+	1.02765i	−0.992659	+	0.120948i	$0.961407\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−2.06406	+	6.35253i	−0.181730	+	0.559309i
$130$	−0.494091	−	1.11940i	−0.0433346	−	0.0981783i
$131$	10.5056			0.917880			0.458940	−	0.888467i	$-0.348229\pi$
$131$	10.5056			0.917880			0.458940	+	0.888467i	$0.348229\pi$
$132$	8.96380	−	4.49947i	0.780198	−	0.391628i
$133$	0.114089	+	0.471938i	0.00989274	+	0.0409222i
$134$	−5.65202	+	7.77934i	−0.488260	+	0.672033i
$135$	−14.1792	−	15.8497i	−1.22035	−	1.36412i
$136$	5.81191	−	1.88841i	0.498367	−	0.161929i
$137$	2.14585	+	2.95350i	0.183332	+	0.252335i	0.890784	−	0.454426i	$-0.150156\pi$
$137$	2.14585	+	2.95350i	0.183332	+	0.252335i	−0.707452	+	0.706761i	$0.750156\pi$
$138$	14.2231	+	19.5764i	1.21075	+	1.66645i
$139$	0.675103	+	2.07775i	0.0572615	+	0.176233i	0.975596	−	0.219571i	$-0.0704659\pi$
$139$	0.675103	+	2.07775i	0.0572615	+	0.176233i	−0.918335	+	0.395804i	$0.870466\pi$
$140$	3.35887	−	4.87011i	0.283877	−	0.411599i
$141$	0.140762	+	0.102269i	0.0118543	+	0.00861264i
$142$	−0.329829			−0.0276786
$143$	0.294705	−	1.79080i	0.0246445	−	0.149754i
$144$	6.14499			0.512082
$145$	4.55734	+	10.3250i	0.378467	+	0.857448i
$146$	6.98448	+	2.26940i	0.578040	+	0.187817i
$147$	15.0154	+	14.9211i	1.23845	+	1.23068i
$148$	−2.80018	−	3.85412i	−0.230174	−	0.316807i
$149$	−3.29150	−	4.53036i	−0.269650	−	0.371141i	0.652622	−	0.757684i	$-0.273669\pi$
$149$	−3.29150	−	4.53036i	−0.269650	−	0.371141i	−0.922272	+	0.386543i	$0.873669\pi$
$150$	−10.1894	+	11.1714i	−0.831963	+	0.912141i
$151$	−0.647227	−	0.210297i	−0.0526706	−	0.0171137i	0.282563	−	0.959249i	$-0.408815\pi$
$151$	−0.647227	−	0.210297i	−0.0526706	−	0.0171137i	−0.335234	+	0.942135i	$0.608815\pi$
$152$	0.148466	+	0.107867i	0.0120422	+	0.00874915i
$153$		−	37.5521i		−	3.03590i
$154$	8.12187	−	3.32193i	0.654479	−	0.267689i
$155$	−8.68076	−	5.04907i	−0.697256	−	0.405551i
$156$	0.972667	−	1.33876i	0.0778757	−	0.107187i
$157$	−7.09516	+	21.8367i	−0.566256	+	1.74276i	0.0979350	+	0.995193i	$0.468776\pi$
$157$	−7.09516	+	21.8367i	−0.566256	+	1.74276i	−0.664191	+	0.747563i	$0.731224\pi$
$158$	3.62321	−	1.17725i	0.288247	−	0.0936570i
$159$	−23.7495	−	32.6884i	−1.88346	−	2.59236i
$160$	−0.226592	−	2.22456i	−0.0179136	−	0.175867i
$161$	11.0900	+	18.0334i	0.874014	+	1.42123i
$162$	3.19088	−	9.82051i	0.250699	−	0.771572i
$163$	9.87785	−	13.5957i	0.773693	−	1.06490i	−0.222257	−	0.974988i	$-0.571342\pi$
$163$	9.87785	−	13.5957i	0.773693	−	1.06490i	0.995950	−	0.0899093i	$-0.0286577\pi$
$164$	−11.1424			−0.870076
$165$	−21.7156	+	5.60425i	−1.69056	+	0.436290i
$166$		−	5.34535i		−	0.414880i
$167$	11.9390	−	16.4326i	0.923868	−	1.27160i	−0.0383353	−	0.999265i	$-0.512206\pi$
$167$	11.9390	−	16.4326i	0.923868	−	1.27160i	0.962204	−	0.272331i	$-0.0877945\pi$
$168$	7.97725	+	0.615183i	0.615458	+	0.0474624i
$169$	3.92469	+	12.0790i	0.301899	+	0.929150i
$170$	−13.5943	+	1.38470i	−1.04263	+	0.106202i
$171$	0.912321	−	0.662840i	0.0697669	−	0.0506886i
$172$	0.682545	+	2.10066i	0.0520435	+	0.160174i
$173$	12.2105	+	3.96744i	0.928349	+	0.301639i	0.733887	−	0.679271i	$-0.237704\pi$
$173$	12.2105	+	3.96744i	0.928349	+	0.301639i	0.194462	+	0.980910i	$0.437704\pi$
$174$	−8.97158	+	12.3483i	−0.680134	+	0.936124i
$175$	−9.63982	+	9.05946i	−0.728702	+	0.684831i
$176$	1.52349	−	2.94601i	0.114838	−	0.222064i
$177$			17.7945i			1.33751i
$178$	0.897797	−	1.23571i	0.0672928	−	0.0926205i
$179$	−1.54764	+	4.76313i	−0.115676	+	0.356013i	−0.992087	−	0.125549i	$-0.959931\pi$
$179$	−1.54764	+	4.76313i	−0.115676	+	0.356013i	0.876412	+	0.481563i	$0.159931\pi$
$180$	−13.4311	−	2.89997i	−1.00110	−	0.216151i
$181$	−8.77710	−	12.0806i	−0.652397	−	0.897947i	0.346803	−	0.937938i	$-0.387267\pi$
$181$	−8.77710	−	12.0806i	−0.652397	−	0.897947i	−0.999200	+	0.0399908i	$0.987267\pi$
$182$	0.938524	−	1.10238i	0.0695680	−	0.0817139i
$183$	−4.59843	−	14.1525i	−0.339925	−	1.04618i
$184$	7.61008	+	2.47267i	0.561023	+	0.182287i
$185$	4.30151	+	9.74543i	0.316253	+	0.716498i
$186$		−	13.5813i		−	0.995831i
$187$	−18.0031	−	9.31007i	−1.31652	−	0.680820i
$188$	0.0575355			0.00419621
$189$	9.59277	−	23.2626i	0.697771	−	1.69210i
$190$	−0.273597	−	0.305829i	−0.0198488	−	0.0221872i
$191$	2.34919	+	7.23006i	0.169981	+	0.523149i	0.999369	−	0.0355249i	$-0.0113103\pi$
$191$	2.34919	+	7.23006i	0.169981	+	0.523149i	−0.829387	+	0.558674i	$0.811310\pi$
$192$	2.44652	−	1.77750i	0.176563	−	0.128280i
$193$	17.6808	−	12.8459i	1.27269	−	0.924666i	0.273387	−	0.961904i	$-0.411856\pi$
$193$	17.6808	−	12.8459i	1.27269	−	0.924666i	0.999306	+	0.0372384i	$0.0118561\pi$
$194$	−3.42529	−	10.5420i	−0.245922	−	0.756869i
$195$	−2.75775	+	2.46711i	−0.197487	+	0.176673i
$196$	6.91723	+	1.07326i	0.494088	+	0.0766613i
$197$	−11.3983			−0.812098			−0.406049	−	0.913851i	$-0.633094\pi$
$197$	−11.3983			−0.812098			−0.406049	+	0.913851i	$0.633094\pi$
$198$	−14.3242	−	14.4978i	−1.01798	−	1.03032i
$199$			26.1676i			1.85497i	0.373862	+	0.927484i	$0.378033\pi$
$199$			26.1676i			1.85497i	−0.373862	+	0.927484i	$0.621967\pi$
$200$	−0.554562	+	4.96915i	−0.0392134	+	0.351372i
$201$	27.6556	+	8.98585i	1.95068	+	0.633813i
$202$	3.97480	+	12.2332i	0.279666	+	0.860723i
$203$	−8.65665	+	10.1680i	−0.607578	+	0.713655i
$204$	−10.8623	−	14.9507i	−0.760515	−	1.04676i
$205$	24.3540	+	5.25838i	1.70095	+	0.367261i
$206$	2.59604	−	7.98980i	0.180875	−	0.556675i
$207$	28.9016	−	39.7797i	2.00880	−	2.76488i
$208$		−	0.547210i		−	0.0379422i
$209$	−0.0915899	−	0.601716i	−0.00633541	−	0.0416216i
$210$	−17.1456	−	5.10926i	−1.18316	−	0.352573i
$211$	−9.81992	+	13.5160i	−0.676031	+	0.930477i	−0.999878	−	0.0156326i	$-0.995024\pi$
$211$	−9.81992	+	13.5160i	−0.676031	+	0.930477i	0.323847	+	0.946110i	$0.395024\pi$
$212$	−12.7072	−	4.12883i	−0.872736	−	0.283569i
$213$	0.308221	+	0.948608i	0.0211190	+	0.0649975i
$214$	2.05259	−	1.49129i	0.140312	−	0.101943i
$215$	−0.500487	−	4.91352i	−0.0341329	−	0.335099i
$216$	−2.93895	−	9.04517i	−0.199970	−	0.615446i
$217$	0.913614	−	11.8471i	0.0620202	−	0.804233i
$218$	−7.77379	+	10.6997i	−0.526508	+	0.724676i
$219$		−	22.2085i		−	1.50071i
$220$	−4.72019	+	5.72012i	−0.318235	+	0.385650i
$221$	−3.34400			−0.224942
$222$	−8.46794	+	11.6551i	−0.568331	+	0.782241i
$223$	4.14293	−	12.7506i	0.277431	−	0.853846i	−0.711134	−	0.703056i	$-0.751818\pi$
$223$	4.14293	−	12.7506i	0.277431	−	0.853846i	0.988566	−	0.150790i	$-0.0481817\pi$
$224$	2.25369	−	1.38595i	0.150581	−	0.0926028i
$225$	27.9878	+	12.6769i	1.86585	+	0.845129i
$226$	−2.04821	−	2.81912i	−0.136245	−	0.187525i
$227$	−1.47387	+	0.478890i	−0.0978244	+	0.0317851i	−0.357520	−	0.933905i	$-0.616378\pi$
$227$	−1.47387	+	0.478890i	−0.0978244	+	0.0317851i	0.259696	+	0.965690i	$0.416378\pi$
$228$	0.171492	−	0.527797i	0.0113573	−	0.0349542i
$229$	−6.26824	+	8.62749i	−0.414217	+	0.570121i	−0.964241	−	0.265028i	$-0.914619\pi$
$229$	−6.26824	+	8.62749i	−0.414217	+	0.570121i	0.550024	+	0.835149i	$0.314619\pi$
$230$	−15.4664	−	8.99589i	−1.01983	−	0.593171i
$231$	−17.1439	−	20.2547i	−1.12798	−	1.33266i
$232$			5.04730i			0.331371i
$233$	5.49919	+	3.99540i	0.360264	+	0.261747i	0.753162	−	0.657835i	$-0.228527\pi$
$233$	5.49919	+	3.99540i	0.360264	+	0.261747i	−0.392898	+	0.919582i	$0.628527\pi$
$234$	−3.19802	−	1.03910i	−0.209061	−	0.0679281i
$235$	−0.125755	−	0.0271524i	−0.00820337	−	0.00177123i
$236$	3.45869	+	4.76048i	0.225142	+	0.309881i
$237$	−6.77169	−	9.32043i	−0.439868	−	0.605427i
$238$	−8.46957	−	13.7723i	−0.549000	−	0.892728i
$239$	−6.84232	−	2.22320i	−0.442593	−	0.143807i	0.0792388	−	0.996856i	$-0.474751\pi$
$239$	−6.84232	−	2.22320i	−0.442593	−	0.143807i	−0.521832	+	0.853049i	$0.674751\pi$
$240$	−6.18621	+	2.73051i	−0.399318	+	0.176254i
$241$	18.9473			1.22051			0.610253	−	0.792207i	$-0.291068\pi$
$241$	18.9473			1.22051			0.610253	+	0.792207i	$0.291068\pi$
$242$	−10.5018	+	3.27289i	−0.675082	+	0.210389i
$243$	−2.69426			−0.172837
$244$	−3.98101	−	2.89237i	−0.254858	−	0.185165i
$245$	−14.6125	−	5.61023i	−0.933559	−	0.358425i
$246$	10.4125	+	32.0462i	0.663874	+	2.04319i
$247$	−0.0590257	−	0.0812420i	−0.00375572	−	0.00516930i
$248$	−2.63979	−	3.63336i	−0.167627	−	0.230718i
$249$	−15.3735	+	4.99517i	−0.974259	+	0.316556i
$250$	3.55717	−	10.5994i	0.224975	−	0.670363i
$251$	12.5752	−	17.3083i	0.793739	−	1.09249i	−0.199894	−	0.979818i	$-0.564060\pi$
$251$	12.5752	−	17.3083i	0.793739	−	1.09249i	0.993632	−	0.112670i	$-0.0359403\pi$
$252$	−3.82027	−	15.8029i	−0.240655	−	0.995489i
$253$	−11.9056	−	23.7183i	−0.748501	−	1.49116i
$254$	19.7028			1.23626
$255$	16.6862	+	37.8040i	1.04493	+	2.36738i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−8.99513	−	27.6842i	−0.561101	−	1.72689i	−0.679261	−	0.733896i	$-0.737700\pi$
$257$	−8.99513	−	27.6842i	−0.561101	−	1.72689i	0.118160	−	0.992995i	$-0.462300\pi$
$258$	5.40378	−	3.92608i	0.336425	−	0.244427i
$259$	−8.17070	+	9.59722i	−0.507702	+	0.596342i
$260$	−0.258242	+	1.19604i	−0.0160155	+	0.0741751i
$261$	29.4976	+	9.58434i	1.82585	+	0.593255i
$262$	−8.49922	−	6.17505i	−0.525084	−	0.381496i
$263$	7.06518			0.435658			0.217829	−	0.975987i	$-0.430103\pi$
$263$	7.06518			0.435658			0.217829	+	0.975987i	$0.430103\pi$
$264$	−9.89658	−	1.62864i	−0.609093	−	0.100236i
$265$	25.8257	+	15.0212i	1.58646	+	0.922747i
$266$	0.185098	−	0.448865i	0.0113491	−	0.0275217i
$267$	−4.39296	−	1.42736i	−0.268845	−	0.0873530i
$268$	9.14516	−	2.97144i	0.558630	−	0.181510i
$269$	−0.506012	−	0.696466i	−0.0308521	−	0.0424643i	0.793312	−	0.608815i	$-0.208355\pi$
$269$	−0.506012	−	0.696466i	−0.0308521	−	0.0424643i	−0.824164	+	0.566351i	$0.808355\pi$
$270$	2.15503	+	21.1570i	0.131151	+	1.28757i
$271$	4.00444	+	12.3244i	0.243253	+	0.748655i	0.995919	+	0.0902525i	$0.0287674\pi$
$271$	4.00444	+	12.3244i	0.243253	+	0.748655i	−0.752666	+	0.658402i	$0.771233\pi$
$272$	−5.81191	−	1.88841i	−0.352399	−	0.114501i
$273$	−4.04755	−	1.66909i	−0.244969	−	0.101018i
$274$		−	3.65073i		−	0.220549i
$275$	13.0164	−	10.2749i	0.784918	−	0.619600i
$276$		−	24.1977i		−	1.45653i
$277$	−6.92017	−	5.02780i	−0.415793	−	0.302091i	0.360150	−	0.932894i	$-0.382726\pi$
$277$	−6.92017	−	5.02780i	−0.415793	−	0.302091i	−0.775943	+	0.630803i	$0.782726\pi$
$278$	0.675103	−	2.07775i	0.0404900	−	0.124615i
$279$	−26.2469	+	8.52813i	−1.57136	+	0.510566i
$280$	−5.57996	+	1.96570i	−0.333467	+	0.117473i
$281$	−15.8666	−	21.8385i	−0.946521	−	1.30277i	−0.953056	−	0.302795i	$-0.902080\pi$
$281$	−15.8666	−	21.8385i	−0.946521	−	1.30277i	0.00653485	−	0.999979i	$-0.497920\pi$
$282$	−0.0537662	−	0.165475i	−0.00320173	−	0.00985392i
$283$	−2.70732	−	0.879660i	−0.160933	−	0.0522904i	0.227442	−	0.973792i	$-0.426964\pi$
$283$	−2.70732	−	0.879660i	−0.160933	−	0.0522904i	−0.388376	+	0.921501i	$0.626964\pi$
$284$	0.266837	+	0.193869i	0.0158339	+	0.0115040i
$285$	−0.623909	+	1.07267i	−0.0369572	+	0.0635398i
$286$	−1.29103	+	1.27557i	−0.0763401	+	0.0754258i
$287$	6.92712	+	28.6546i	0.408895	+	1.69143i
$288$	−4.97140	−	3.61193i	−0.292942	−	0.212835i
$289$	−6.28677	+	19.3487i	−0.369810	+	1.13816i
$290$	2.38194	−	11.0319i	0.139872	−	0.647814i
$291$	−27.1184	+	19.7027i	−1.58971	+	1.15499i
$292$	−4.31665	−	5.94136i	−0.252613	−	0.347692i
$293$	−10.9571	+	3.56019i	−0.640123	+	0.207989i	−0.611054	−	0.791589i	$-0.709254\pi$
$293$	−10.9571	+	3.56019i	−0.640123	+	0.207989i	−0.0290691	+	0.999577i	$0.509254\pi$
$294$	−3.37732	−	20.8973i	−0.196969	−	1.21876i
$295$	−5.31308	−	12.0372i	−0.309339	−	0.700834i
$296$			4.76396i			0.276899i
$297$	−14.4894	+	28.0185i	−0.840761	+	1.62580i
$298$			5.59983i			0.324389i
$299$	−3.54237	−	2.57369i	−0.204861	−	0.148840i
$300$	14.8098	−	3.04866i	0.855045	−	0.176015i
$301$	4.97787	−	3.06124i	0.286920	−	0.176447i
$302$	0.400008	+	0.550564i	0.0230179	+	0.0316814i
$303$	31.4689	−	22.8635i	1.80784	−	1.31348i
$304$	−0.0567089	−	0.174532i	−0.00325248	−	0.0100101i
$305$	7.33631	+	8.20059i	0.420076	+	0.469565i
$306$	−22.0725	+	30.3803i	−1.26180	+	1.73672i
$307$		−	8.19451i		−	0.467686i	−0.972274	−	0.233843i	$-0.924870\pi$
$307$		−	8.19451i		−	0.467686i	0.972274	−	0.233843i	$-0.0751301\pi$
$308$	−8.52331	−	2.08642i	−0.485661	−	0.118885i
$309$	−25.4051			−1.44525
$310$	4.05512	+	9.18721i	0.230315	+	0.521798i
$311$	14.3278	+	4.65539i	0.812456	+	0.263983i	0.685637	−	0.727943i	$-0.259524\pi$
$311$	14.3278	+	4.65539i	0.812456	+	0.263983i	0.126818	+	0.991926i	$0.459524\pi$
$312$	−1.57381	+	0.511361i	−0.0890993	+	0.0289501i
$313$	14.0535	−	10.2105i	0.794352	−	0.577131i	−0.114900	−	0.993377i	$-0.536655\pi$
$313$	14.0535	−	10.2105i	0.794352	−	0.577131i	0.909252	+	0.416247i	$0.136655\pi$
$314$	18.5754	−	13.4958i	1.04827	−	0.761612i
$315$	0.892198	+	36.3433i	0.0502697	+	2.04771i
$316$	−3.62321	−	1.17725i	−0.203821	−	0.0662255i
$317$	−4.74691	+	6.53356i	−0.266613	+	0.366961i	−0.921243	−	0.388988i	$-0.872825\pi$
$317$	−4.74691	+	6.53356i	−0.266613	+	0.366961i	0.654630	+	0.755950i	$0.272825\pi$
$318$			40.4051i			2.26581i
$319$	11.9081	−	11.7654i	0.666723	−	0.658738i
$320$	−1.12425	+	1.93289i	−0.0628472	+	0.108052i
$321$	−6.20716	−	4.50977i	−0.346450	−	0.251711i
$322$	1.62778	−	21.1079i	0.0907126	−	1.17630i
$323$	−1.06657	+	0.346549i	−0.0593454	+	0.0192825i
$324$	−8.35383	+	6.06941i	−0.464102	+	0.337190i
$325$	1.12888	−	2.49231i	0.0626189	−	0.138248i
$326$	−15.9827	+	5.19310i	−0.885200	+	0.287619i
$327$	38.0375	+	12.3591i	2.10348	+	0.683462i
$328$	9.01440	+	6.54934i	0.497737	+	0.361627i
$329$	−0.0357692	−	0.147962i	−0.00197202	−	0.00815743i
$330$	20.8624	+	8.23017i	1.14844	+	0.453056i
$331$	28.1074			1.54492			0.772460	−	0.635063i	$-0.219026\pi$
$331$	28.1074			1.54492			0.772460	+	0.635063i	$0.219026\pi$
$332$	−3.14192	+	4.32448i	−0.172435	+	0.237337i
$333$	27.8417	+	9.04630i	1.52571	+	0.495734i
$334$	−19.3177	+	6.27671i	−1.05702	+	0.343446i
$335$	−21.3909	+	2.17886i	−1.16871	+	0.119044i
$336$	−6.09213	−	5.18660i	−0.332353	−	0.282952i
$337$	7.35825	+	22.6464i	0.400829	+	1.23363i	0.924328	+	0.381599i	$0.124627\pi$
$337$	7.35825	+	22.6464i	0.400829	+	1.23363i	−0.523499	+	0.852027i	$0.675373\pi$
$338$	3.92469	−	12.0790i	0.213475	−	0.657008i
$339$	−6.19393	+	8.52521i	−0.336408	+	0.463026i
$340$	11.8119	+	6.87027i	0.640591	+	0.372593i
$341$	−2.41871	+	14.6975i	−0.130981	+	0.795915i
$342$	−1.12769			−0.0609785
$343$	−1.54030	−	18.4561i	−0.0831685	−	0.996535i
$344$	0.682545	−	2.10066i	0.0368003	−	0.113260i
$345$	−11.4195	+	52.8890i	−0.614805	+	2.84745i
$346$	−7.54652	−	10.3869i	−0.405704	−	0.558403i
$347$	−29.0544	+	21.1093i	−1.55972	+	1.13320i	−0.623485	+	0.781835i	$0.714284\pi$
$347$	−29.0544	+	21.1093i	−1.55972	+	1.13320i	−0.936237	+	0.351369i	$0.885716\pi$
$348$	14.5163	−	4.71664i	0.778156	−	0.252838i
$349$	2.44948	−	7.53871i	0.131117	−	0.403538i	−0.863848	−	0.503752i	$-0.831953\pi$
$349$	2.44948	−	7.53871i	0.131117	−	0.403538i	0.994966	+	0.100214i	$0.0319527\pi$
$350$	13.1238	−	1.66312i	0.701496	−	0.0888973i
$351$			5.20432i			0.277786i
$352$	−2.96415	+	1.48789i	−0.157990	+	0.0793046i
$353$	3.28664			0.174930			0.0874652	−	0.996168i	$-0.472123\pi$
$353$	3.28664			0.174930			0.0874652	+	0.996168i	$0.472123\pi$
$354$	10.4593	−	14.3960i	0.555906	−	0.765140i
$355$	−0.491735	−	0.549666i	−0.0260986	−	0.0291732i
$356$	−1.45267	+	0.472000i	−0.0769912	+	0.0250160i
$357$	−31.6954	+	37.2291i	−1.67750	+	1.97037i
$358$	4.05176	−	2.94378i	0.214142	−	0.155584i
$359$	−19.1842	+	6.23332i	−1.01250	+	0.328982i	−0.767851	−	0.640629i	$-0.778674\pi$
$359$	−19.1842	+	6.23332i	−1.01250	+	0.328982i	−0.244652	+	0.969611i	$0.578674\pi$
$360$	9.16143	+	10.2407i	0.482850	+	0.539734i
$361$	15.3441	+	11.1481i	0.807583	+	0.586743i
$362$			14.9325i			0.784834i
$363$	19.2269	+	27.1454i	1.00915	+	1.42476i
$364$	−1.40724	+	0.340195i	−0.0737597	+	0.0178310i
$365$	6.63103	+	15.0232i	0.347084	+	0.786348i
$366$	−4.59843	+	14.1525i	−0.240364	+	0.739763i
$367$	6.38721	+	19.6578i	0.333410	+	1.02613i	0.967500	+	0.252870i	$0.0813746\pi$
$367$	6.38721	+	19.6578i	0.333410	+	1.02613i	−0.634091	+	0.773259i	$0.718625\pi$
$368$	−4.70329	−	6.47352i	−0.245176	−	0.337456i
$369$	55.3934	−	40.2456i	2.88366	−	2.09510i
$370$	2.24823	−	10.4126i	0.116880	−	0.541324i
$371$	−2.71805	+	35.2457i	−0.141114	+	1.82987i
$372$	−7.98290	+	10.9875i	−0.413894	+	0.569676i
$373$	−9.53934			−0.493928			−0.246964	−	0.969025i	$-0.579433\pi$
$373$	−9.53934			−0.493928			−0.246964	+	0.969025i	$0.579433\pi$
$374$	9.09248	+	18.1140i	0.470161	+	0.936650i
$375$	−33.8085	−	0.325651i	−1.74587	−	0.0168166i
$376$	−0.0465472	−	0.0338185i	−0.00240049	−	0.00174406i
$377$	0.853483	−	2.62675i	0.0439566	−	0.135285i
$378$	−21.4341	+	13.1813i	−1.10245	+	0.677974i
$379$	15.6278	−	11.3542i	0.802744	−	0.583227i	−0.108974	−	0.994045i	$-0.534757\pi$
$379$	15.6278	−	11.3542i	0.802744	−	0.583227i	0.911718	+	0.410817i	$0.134757\pi$
$380$	0.0415827	+	0.408237i	0.00213315	+	0.0209421i
$381$	−18.4120	−	56.6663i	−0.943276	−	2.90310i
$382$	2.34919	−	7.23006i	0.120195	−	0.369922i
$383$	−8.21622	−	5.96944i	−0.419829	−	0.305024i	0.357740	−	0.933821i	$-0.383547\pi$
$383$	−8.21622	−	5.96944i	−0.419829	−	0.305024i	−0.777569	+	0.628797i	$0.783547\pi$
$384$	−3.02407			−0.154321
$385$	17.6448	+	8.58265i	0.899261	+	0.437412i
$386$	−21.8547			−1.11237
$387$	−10.9806	−	7.97789i	−0.558177	−	0.405539i
$388$	−3.42529	+	10.5420i	−0.173893	+	0.535187i
$389$	−5.65907	−	17.4168i	−0.286926	−	0.883068i	−0.985815	−	0.167837i	$-0.946322\pi$
$389$	−5.65907	−	17.4168i	−0.286926	−	0.883068i	0.698889	−	0.715230i	$-0.253678\pi$
$390$	3.68120	−	0.374964i	0.186405	−	0.0189870i
$391$	−39.5597	+	28.7418i	−2.00062	+	1.45354i
$392$	−4.96531	−	4.93413i	−0.250786	−	0.249211i
$393$	−9.81738	+	30.2148i	−0.495221	+	1.52413i
$394$	9.22145	+	6.69978i	0.464570	+	0.337530i
$395$	7.36367	+	4.28300i	0.370506	+	0.215501i
$396$	3.06690	+	20.1485i	0.154118	+	1.01250i
$397$	14.0720			0.706255			0.353127	−	0.935575i	$-0.385118\pi$
$397$	14.0720			0.706255			0.353127	+	0.935575i	$0.385118\pi$
$398$	15.3809	−	21.1700i	0.770975	−	1.06116i
$399$	−1.46394	−	0.112895i	−0.0732884	−	0.00565180i
$400$	3.36944	−	3.69416i	0.168472	−	0.184708i
$401$	12.3390	−	8.96478i	0.616178	−	0.447680i	−0.235406	−	0.971897i	$-0.575642\pi$
$401$	12.3390	−	8.96478i	0.616178	−	0.447680i	0.851584	+	0.524217i	$0.175642\pi$
$402$	−17.0921	−	23.5253i	−0.852476	−	1.17333i
$403$	0.759428	+	2.33728i	0.0378298	+	0.116428i
$404$	3.97480	−	12.2332i	0.197754	−	0.608623i
$405$	21.1233	−	9.32354i	1.04962	−	0.463290i
$406$	12.9800	−	3.13785i	0.644186	−	0.155729i
$407$	11.2396	−	11.1050i	0.557125	−	0.550452i
$408$			18.4801i			0.914901i
$409$	−13.6177	−	9.89386i	−0.673353	−	0.489220i	0.197793	−	0.980244i	$-0.436623\pi$
$409$	−13.6177	−	9.89386i	−0.673353	−	0.489220i	−0.871146	+	0.491024i	$0.836623\pi$
$410$	−16.6120	−	18.5690i	−0.820407	−	0.917058i
$411$	−10.4997	+	3.41157i	−0.517913	+	0.168280i
$412$	−6.79653	+	4.93796i	−0.334841	+	0.243276i
$413$	10.0922	−	11.8542i	0.496603	−	0.583305i
$414$	−46.7639	+	15.1945i	−2.29832	+	0.746769i
$415$	8.90812	−	7.96927i	0.437282	−	0.391196i
$416$	−0.321642	+	0.442702i	−0.0157698	+	0.0217053i
$417$	−6.60662			−0.323528
$418$	−0.279582	+	0.540634i	−0.0136748	+	0.0264433i
$419$		−	29.0361i		−	1.41851i	−0.704954	−	0.709253i	$-0.749032\pi$
$419$		−	29.0361i		−	1.41851i	0.704954	−	0.709253i	$-0.250968\pi$
$420$	10.8679	+	14.2114i	0.530299	+	0.693445i
$421$	6.74259	−	20.7516i	0.328614	−	1.01137i	−0.641169	−	0.767400i	$-0.721550\pi$
$421$	6.74259	−	20.7516i	0.328614	−	1.01137i	0.969783	−	0.243970i	$-0.0784498\pi$
$422$	15.8890	−	5.16264i	0.773463	−	0.251313i
$423$	−0.286032	+	0.207814i	−0.0139073	+	0.0101043i
$424$	7.85350	+	10.8094i	0.381400	+	0.524952i
$425$	−22.5751	−	20.5907i	−1.09505	−	0.998795i
$426$	0.308221	−	0.948608i	0.0149334	−	0.0459602i
$427$	−4.96328	+	12.0360i	−0.240190	+	0.582463i
$428$	−2.53714			−0.122637
$429$	4.87506	+	2.52107i	0.235370	+	0.121719i
$430$	−2.48319	+	4.26930i	−0.119750	+	0.205884i
$431$	14.2378	−	19.5966i	0.685810	−	0.943936i	−0.314176	−	0.949365i	$-0.601728\pi$
$431$	14.2378	−	19.5966i	0.685810	−	0.943936i	0.999985	+	0.00542877i	$0.00172804\pi$
$432$	−2.93895	+	9.04517i	−0.141400	+	0.435186i
$433$	−2.20106	−	6.77417i	−0.105776	−	0.325546i	0.884136	−	0.467230i	$-0.154748\pi$
$433$	−2.20106	−	6.77417i	−0.105776	−	0.325546i	−0.989912	+	0.141685i	$0.954748\pi$
$434$	−7.70268	+	9.04749i	−0.369740	+	0.434293i
$435$	−33.9542	+	3.45855i	−1.62798	+	0.165825i
$436$	12.5783	−	4.08693i	0.602390	−	0.195728i
$437$	−1.39656	−	0.453768i	−0.0668063	−	0.0217067i
$438$	−13.0538	+	17.9671i	−0.623736	+	0.858500i
$439$	15.6962			0.749141			0.374571	−	0.927198i	$-0.377790\pi$
$439$	15.6962			0.749141			0.374571	+	0.927198i	$0.377790\pi$
$440$	7.18092	−	1.85322i	0.342337	−	0.0883486i
$441$	−38.2649	+	19.6490i	−1.82214	+	0.935666i
$442$	2.70536	+	1.96556i	0.128681	+	0.0934919i
$443$	37.1947	+	12.0853i	1.76717	+	0.574190i	0.997903	−	0.0647331i	$-0.0206196\pi$
$443$	37.1947	+	12.0853i	1.76717	+	0.574190i	0.769271	+	0.638923i	$0.220620\pi$
$444$	13.7014	−	4.45186i	0.650241	−	0.211276i
$445$	3.39784	−	0.346102i	0.161073	−	0.0164068i
$446$	−10.8463	+	7.88033i	−0.513589	+	0.373144i
$447$	16.1054	−	5.23298i	0.761761	−	0.247511i
$448$	−2.63792	−	0.203429i	−0.124630	−	0.00961111i
$449$	−26.4877	−	19.2444i	−1.25003	−	0.908200i	−0.251806	−	0.967778i	$-0.581025\pi$
$449$	−26.4877	−	19.2444i	−1.25003	−	0.908200i	−0.998224	+	0.0595777i	$0.981025\pi$
$450$	−15.1913	−	26.7067i	−0.716124	−	1.25896i
$451$	−5.56106	−	36.5344i	−0.261860	−	1.72034i
$452$			3.48462i			0.163903i
$453$	1.20965	−	1.66494i	0.0568344	−	0.0782258i
$454$	1.47387	+	0.478890i	0.0691723	+	0.0224754i
$455$	3.23636	−	0.0794501i	0.151723	−	0.00372468i
$456$	−0.448971	+	0.326196i	−0.0210250	+	0.0152755i
$457$	6.62484	−	4.81323i	0.309897	−	0.225153i	−0.421955	−	0.906617i	$-0.638656\pi$
$457$	6.62484	−	4.81323i	0.309897	−	0.225153i	0.731852	+	0.681463i	$0.238656\pi$
$458$	10.1422	−	3.29541i	0.473915	−	0.153984i
$459$	55.2751	+	17.9600i	2.58002	+	0.838299i
$460$	7.22497	+	16.3688i	0.336866	+	0.763198i
$461$	21.4665			0.999797			0.499898	−	0.866084i	$-0.333371\pi$
$461$	21.4665			0.999797			0.499898	+	0.866084i	$0.333371\pi$
$462$	1.96427	+	26.4633i	0.0913859	+	1.23118i
$463$			10.7819i			0.501076i	0.968107	+	0.250538i	$0.0806074\pi$
$463$			10.7819i			0.501076i	−0.968107	+	0.250538i	$0.919393\pi$
$464$	2.96673	−	4.08335i	0.137727	−	0.189565i
$465$	22.6335	−	20.2481i	1.04960	−	0.938983i
$466$	−2.10051	−	6.46469i	−0.0973040	−	0.299471i
$467$	−14.7633	+	10.7262i	−0.683164	+	0.496347i	−0.874406	−	0.485195i	$-0.838748\pi$
$467$	−14.7633	+	10.7262i	−0.683164	+	0.496347i	0.191242	+	0.981543i	$0.438748\pi$
$468$	1.97648	+	2.72040i	0.0913630	+	0.125750i
$469$	−13.3270	−	21.6711i	−0.615385	−	1.00068i
$470$	0.0857784	+	0.0958839i	0.00395666	+	0.00442279i
$471$	−56.1732	−	40.8122i	−2.58832	−	1.88053i
$472$		−	5.88428i		−	0.270846i
$473$	−6.54710	+	3.28638i	−0.301036	+	0.151108i
$474$			11.5207i			0.529162i
$475$	0.101770	−	0.911908i	0.00466952	−	0.0418412i
$476$	−1.24316	+	16.1203i	−0.0569799	+	0.738875i
$477$	78.0858	−	25.3716i	3.57530	−	1.16169i
$478$	4.22878	+	5.82042i	0.193420	+	0.266220i
$479$	−12.8918	+	9.36643i	−0.589041	+	0.427963i	−0.841972	−	0.539521i	$-0.818605\pi$
$479$	−12.8918	+	9.36643i	−0.589041	+	0.427963i	0.252931	+	0.967484i	$0.418605\pi$
$480$	6.60971	+	1.42713i	0.301690	+	0.0651394i
$481$	0.805571	−	2.47929i	0.0367309	−	0.113046i
$482$	−15.3287	−	11.1370i	−0.698204	−	0.507275i
$483$	−62.2286	+	15.0435i	−2.83150	+	0.684502i
$484$	10.4199	+	3.52499i	0.473632	+	0.160227i
$485$	12.4617	−	21.4251i	0.565856	−	0.972864i
$486$	2.17971	+	1.58365i	0.0988734	+	0.0718358i
$487$	6.36839	+	2.06922i	0.288579	+	0.0937651i	0.449730	−	0.893165i	$-0.351520\pi$
$487$	6.36839	+	2.06922i	0.288579	+	0.0937651i	−0.161150	+	0.986930i	$0.551520\pi$
$488$	1.52061	+	4.67995i	0.0688347	+	0.211852i
$489$	29.8713	+	41.1143i	1.35083	+	1.85925i
$490$	8.52415	+	13.1278i	0.385082	+	0.593053i
$491$	−9.33984	+	3.03470i	−0.421501	+	0.136954i	−0.512085	−	0.858935i	$-0.671127\pi$
$491$	−9.33984	+	3.03470i	−0.421501	+	0.136954i	0.0905840	+	0.995889i	$0.471127\pi$
$492$	10.4125	−	32.0462i	0.469430	−	1.44476i
$493$	−24.9534	−	18.1297i	−1.12384	−	0.816520i
$494$			0.100421i			0.00451814i
$495$	2.80526	−	45.4860i	0.126087	−	2.04444i
$496$			4.49108i			0.201655i
$497$	0.332677	−	0.806744i	0.0149226	−	0.0361874i
$498$	15.3735	+	4.99517i	0.688905	+	0.223839i
$499$	6.65825	+	20.4920i	0.298064	+	0.917347i	0.982175	+	0.187969i	$0.0601904\pi$
$499$	6.65825	+	20.4920i	0.298064	+	0.917347i	−0.684111	+	0.729378i	$0.739810\pi$
$500$	−9.10796	+	6.48421i	−0.407320	+	0.289983i
$501$	36.1044	+	49.6934i	1.61302	+	2.22014i
$502$	−20.3471	+	6.61117i	−0.908135	+	0.295071i
$503$	−31.0787	−	10.0981i	−1.38573	−	0.450252i	−0.481183	−	0.876620i	$-0.659793\pi$
$503$	−31.0787	−	10.0981i	−1.38573	−	0.450252i	−0.904550	+	0.426368i	$0.859793\pi$
$504$	−6.19804	+	15.0303i	−0.276083	+	0.669503i
$505$	−14.4609	+	24.8623i	−0.643500	+	1.10636i
$506$	−4.30940	+	26.1865i	−0.191576	+	1.16413i
$507$	−38.4074			−1.70573
$508$	−15.9399	−	11.5810i	−0.707218	−	0.513824i
$509$	−7.58289	−	2.46383i	−0.336106	−	0.109207i	0.136102	−	0.990695i	$-0.456543\pi$
$509$	−7.58289	−	2.46383i	−0.336106	−	0.109207i	−0.472207	+	0.881488i	$0.656543\pi$
$510$	8.72121	−	40.3920i	0.386182	−	1.78859i
$511$	−12.5956	+	14.7947i	−0.557197	+	0.654478i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	0.539339	+	1.65991i	0.0238124	+	0.0732870i
$514$	−8.99513	+	27.6842i	−0.396758	+	1.22110i
$515$	17.1855	−	7.58547i	0.757284	−	0.334256i
$516$	−6.67944			−0.294046
$517$	0.0287154	+	0.188651i	0.00126290	+	0.00829685i
$518$	12.2513	−	2.96170i	0.538293	−	0.130130i
$519$	−22.8212	+	31.4107i	−1.00174	+	1.37878i
$520$	0.911935	−	0.815823i	0.0399910	−	0.0357762i
$521$	−19.2169	+	6.24394i	−0.841906	+	0.273552i	−0.698052	−	0.716047i	$-0.745950\pi$
$521$	−19.2169	+	6.24394i	−0.841906	+	0.273552i	−0.143854	+	0.989599i	$0.545950\pi$
$522$	−18.2305	−	25.0921i	−0.797927	−	1.09825i
$523$	−14.1000	−	19.4069i	−0.616548	−	0.848606i	0.380548	−	0.924761i	$-0.375735\pi$
$523$	−14.1000	−	19.4069i	−0.616548	−	0.848606i	−0.997096	+	0.0761555i	$0.975735\pi$
$524$	3.24641	+	9.99144i	0.141820	+	0.436478i
$525$	−17.0473	−	36.1907i	−0.744003	−	1.57949i
$526$	−5.71585	−	4.15281i	−0.249223	−	0.181071i
$527$	27.4450			1.19552
$528$	7.04921	+	7.13467i	0.306778	+	0.310496i
$529$	−41.0274			−1.78380
$530$	−12.0642	−	27.3324i	−0.524034	−	1.18724i
$531$	−34.3891	−	11.1737i	−1.49236	−	0.484897i
$532$	−0.413584	+	0.254341i	−0.0179311	+	0.0110271i
$533$	−3.58386	−	4.93277i	−0.155234	−	0.213662i
$534$	2.71500	+	3.73688i	0.117490	+	0.161711i
$535$	5.54542	+	1.19734i	0.239750	+	0.0517654i
$536$	−9.14516	−	2.97144i	−0.395011	−	0.128347i
$537$	−12.2528	−	8.90219i	−0.528748	−	0.384158i
$538$			0.860880i			0.0371152i
$539$	−0.0667388	+	23.2163i	−0.00287464	+	0.999996i
$540$	10.6923	−	18.3831i	0.460124	−	0.791081i
$541$	8.10276	−	11.1525i	0.348365	−	0.479483i	−0.598496	−	0.801126i	$-0.704235\pi$
$541$	8.10276	−	11.1525i	0.348365	−	0.479483i	0.946861	+	0.321642i	$0.104235\pi$
$542$	4.00444	−	12.3244i	0.172006	−	0.529379i
$543$	42.9467	−	13.9542i	1.84302	−	0.598834i
$544$	3.59196	+	4.94391i	0.154004	+	0.211968i
$545$	−29.4210	+	2.99680i	−1.26026	+	0.128369i
$546$	2.29347	+	3.72941i	0.0981516	+	0.159604i
$547$	1.52982	−	4.70831i	0.0654105	−	0.201313i	−0.913010	−	0.407938i	$-0.866248\pi$
$547$	1.52982	−	4.70831i	0.0654105	−	0.201313i	0.978420	+	0.206625i	$0.0662480\pi$
$548$	−2.14585	+	2.95350i	−0.0916660	+	0.126167i
$549$	30.2382			1.29054
$550$	−16.5699	+	0.661723i	−0.706544	+	0.0282160i
$551$		−	0.926249i		−	0.0394595i
$552$	−14.2231	+	19.5764i	−0.605374	+	0.833226i
$553$	−0.774996	+	10.0496i	−0.0329562	+	0.427352i
$554$	2.64327	+	8.13515i	0.112302	+	0.345629i
$555$	−32.0481	+	3.26440i	−1.36037	+	0.138566i
$556$	−1.76744	+	1.28412i	−0.0749563	+	0.0544589i
$557$	13.0157	+	40.0583i	0.551494	+	1.69732i	0.705026	+	0.709181i	$0.250935\pi$
$557$	13.0157	+	40.0583i	0.551494	+	1.69732i	−0.153532	+	0.988144i	$0.549065\pi$
$558$	26.2469	+	8.52813i	1.11112	+	0.361024i
$559$	−0.710430	+	0.977823i	−0.0300480	+	0.0413575i
$560$	5.66970	+	1.68953i	0.239588	+	0.0713958i
$561$	43.6000	−	43.0778i	1.84079	−	1.81875i
$562$			26.9938i			1.13867i
$563$	17.1541	−	23.6105i	0.722958	−	0.995066i	−0.276463	−	0.961025i	$-0.589162\pi$
$563$	17.1541	−	23.6105i	0.722958	−	0.995066i	0.999420	−	0.0340412i	$-0.0108377\pi$
$564$	−0.0537662	+	0.165475i	−0.00226397	+	0.00696778i
$565$	1.64448	−	7.61634i	0.0691838	−	0.320422i
$566$	1.67321	+	2.30298i	0.0703304	+	0.0968015i
$567$	20.8020	+	17.7100i	0.873603	+	0.743751i
$568$	−0.101923	−	0.313686i	−0.00427658	−	0.0131620i
$569$	14.6092	+	4.74682i	0.612449	+	0.198997i	0.598785	−	0.800910i	$-0.295650\pi$
$569$	14.6092	+	4.74682i	0.612449	+	0.198997i	0.0136643	+	0.999907i	$0.495650\pi$
$570$	1.13526	−	0.501087i	0.0475506	−	0.0209882i
$571$		−	21.3041i		−	0.891548i	−0.895146	−	0.445774i	$-0.852928\pi$
$571$		−	21.3041i		−	0.891548i	0.895146	−	0.445774i	$-0.147072\pi$
$572$	1.79422	−	0.273107i	0.0750202	−	0.0114192i
$573$	−22.9894			−0.960395
$574$	11.2386	−	27.2537i	0.469091	−	1.13755i
$575$	−8.06679	−	39.1869i	−0.336408	−	1.63421i
$576$	1.89891	+	5.84423i	0.0791211	+	0.243510i
$577$	−3.60275	+	2.61755i	−0.149984	+	0.108970i	−0.660247	−	0.751049i	$-0.729548\pi$
$577$	−3.60275	+	2.61755i	−0.149984	+	0.108970i	0.510262	+	0.860019i	$0.329548\pi$
$578$	16.4590	−	11.9581i	0.684603	−	0.497393i
$579$	20.4230	+	62.8554i	0.848749	+	2.61218i
$580$	−8.41141	+	7.52490i	−0.349265	+	0.312455i
$581$	13.0744	+	5.39150i	0.542419	+	0.223677i
$582$	33.5202			1.38946
$583$	7.19580	−	43.7259i	0.298019	−	1.81094i
$584$			7.34392i			0.303894i
$585$	−3.03618	−	6.87873i	−0.125531	−	0.284400i
$586$	10.9571	+	3.56019i	0.452636	+	0.147070i
$587$	−7.52973	−	23.1741i	−0.310785	−	0.956499i	−0.977455	−	0.211145i	$-0.932281\pi$
$587$	−7.52973	−	23.1741i	−0.310785	−	0.956499i	0.666669	−	0.745354i	$-0.267719\pi$
$588$	−9.55083	+	18.8914i	−0.393869	+	0.779069i
$589$	0.484438	+	0.666771i	0.0199609	+	0.0274738i
$590$	−2.77693	+	12.8613i	−0.114325	+	0.529490i
$591$	10.6516	−	32.7823i	0.438149	−	1.34848i
$592$	2.80018	−	3.85412i	0.115087	−	0.158403i
$593$			28.1425i			1.15567i	0.816153	+	0.577836i	$0.196103\pi$
$593$			28.1425i			1.15567i	−0.816153	+	0.577836i	$0.803897\pi$
$594$	28.1910	−	14.1508i	1.15669	−	0.580613i
$595$	10.3248	−	34.6476i	0.423274	−	1.42041i
$596$	3.29150	−	4.53036i	0.134825	−	0.185571i
$597$	−75.2594	−	24.4533i	−3.08016	−	1.00081i
$598$	1.35307	+	4.16431i	0.0553310	+	0.170291i
$599$	13.6082	−	9.88694i	0.556016	−	0.403970i	−0.273982	−	0.961735i	$-0.588341\pi$
$599$	13.6082	−	9.88694i	0.556016	−	0.403970i	0.829999	+	0.557765i	$0.188341\pi$
$600$	−13.7733	−	6.23857i	−0.562294	−	0.254688i
$601$	−2.49492	−	7.67857i	−0.101770	−	0.313215i	0.887189	−	0.461406i	$-0.152655\pi$
$601$	−2.49492	−	7.67857i	−0.101770	−	0.313215i	−0.988959	+	0.148191i	$0.952655\pi$
$602$	−5.82653	−	0.449326i	−0.237472	−	0.0183131i
$603$	−34.7316	+	47.8039i	−1.41438	+	1.94673i
$604$		−	0.680534i		−	0.0276905i
$605$	−21.1113	−	12.6220i	−0.858295	−	0.513157i
$606$	−38.8978			−1.58011
$607$	−2.15762	+	2.96971i	−0.0875752	+	0.120537i	−0.850557	−	0.525884i	$-0.823735\pi$
$607$	−2.15762	+	2.96971i	−0.0875752	+	0.120537i	0.762981	+	0.646420i	$0.223735\pi$
$608$	−0.0567089	+	0.174532i	−0.00229985	+	0.00707821i
$609$	−21.1543	−	34.3989i	−0.857215	−	1.39392i
$610$	−1.11501	−	10.9466i	−0.0451455	−	0.443215i
$611$	0.0185058	+	0.0254711i	0.000748665	+	0.00103045i
$612$	35.7141	−	11.6042i	1.44366	−	0.469073i
$613$	−13.8611	+	42.6600i	−0.559843	+	1.72302i	0.122953	+	0.992412i	$0.460763\pi$
$613$	−13.8611	+	42.6600i	−0.559843	+	1.72302i	−0.682797	+	0.730608i	$0.739237\pi$
$614$	−4.81661	+	6.62950i	−0.194383	+	0.267545i
$615$	−37.8819	+	65.1296i	−1.52755	+	2.62628i
$616$	5.66914	+	6.69783i	0.228416	+	0.269863i
$617$		−	38.2963i		−	1.54175i	−0.636987	−	0.770875i	$-0.719819\pi$
$617$		−	38.2963i		−	1.54175i	0.636987	−	0.770875i	$-0.280181\pi$
$618$	20.5532	+	14.9327i	0.826769	+	0.600683i
$619$	−0.797554	−	0.259141i	−0.0320564	−	0.0104158i	0.292945	−	0.956129i	$-0.405365\pi$
$619$	−0.797554	−	0.259141i	−0.0320564	−	0.0104158i	−0.325001	+	0.945714i	$0.605365\pi$
$620$	2.11945	−	9.81615i	0.0851191	−	0.394226i
$621$	44.7314	+	61.5674i	1.79501	+	2.47062i
$622$	−8.85507	−	12.1880i	−0.355056	−	0.488693i
$623$	2.11694	+	3.44235i	0.0848133	+	0.137915i
$624$	1.57381	+	0.511361i	0.0630027	+	0.0204708i
$625$	22.9673	−	9.87428i	0.918694	−	0.394971i
$626$	−17.3711			−0.694289
$627$	1.81616	+	0.298878i	0.0725305	+	0.0119361i
$628$	−22.9604			−0.916221
$629$	−23.5526	−	17.1119i	−0.939102	−	0.682298i
$630$	20.6402	−	29.9268i	0.822327	−	1.19231i
$631$	5.38408	+	16.5705i	0.214337	+	0.659661i	0.999200	+	0.0399916i	$0.0127331\pi$
$631$	5.38408	+	16.5705i	0.214337	+	0.659661i	−0.784863	+	0.619669i	$0.787267\pi$
$632$	2.23926	+	3.08208i	0.0890731	+	0.122599i
$633$	−29.6961	−	40.8732i	−1.18031	−	1.62456i
$634$	7.68066	−	2.49560i	0.305038	−	0.0991129i
$635$	29.3744	+	32.8350i	1.16569	+	1.30302i
$636$	23.7495	−	32.6884i	0.941730	−	1.29618i
$637$	1.74974	+	3.40748i	0.0693272	+	0.135009i
$638$	−16.5494	+	2.51905i	−0.655196	+	0.0997303i
$639$	−2.02680			−0.0801788
$640$	2.04566	−	0.902928i	0.0808618	−	0.0356913i
$641$	10.2392	−	31.5129i	0.404422	−	1.24468i	−0.516954	−	0.856013i	$-0.672934\pi$
$641$	10.2392	−	31.5129i	0.404422	−	1.24468i	0.921377	−	0.388671i	$-0.127066\pi$
$642$	2.37093	+	7.29696i	0.0935730	+	0.287988i
$643$	7.87175	−	5.71916i	0.310431	−	0.225542i	−0.421650	−	0.906759i	$-0.638549\pi$
$643$	7.87175	−	5.71916i	0.310431	−	0.225542i	0.732082	+	0.681217i	$0.238549\pi$
$644$	−13.7238	+	16.1198i	−0.540793	+	0.635211i
$645$	14.5993	+	3.15219i	0.574845	+	0.124117i
$646$	1.06657	+	0.346549i	0.0419635	+	0.0136348i
$647$	2.75076	+	1.99855i	0.108144	+	0.0785710i	0.640543	−	0.767922i	$-0.278709\pi$
$647$	2.75076	+	1.99855i	0.108144	+	0.0785710i	−0.532399	+	0.846493i	$0.678709\pi$
$648$	10.3259			0.405640
$649$	−13.8827	+	13.7165i	−0.544945	+	0.538418i
$650$	−2.37822	+	1.35278i	−0.0932816	+	0.0530604i
$651$	33.2192	+	13.6986i	1.30196	+	0.536890i
$652$	15.9827	+	5.19310i	0.625931	+	0.203377i
$653$	21.7037	−	7.05197i	0.849333	−	0.275965i	0.148166	−	0.988962i	$-0.452663\pi$
$653$	21.7037	−	7.05197i	0.849333	−	0.275965i	0.701167	+	0.712997i	$0.252663\pi$
$654$	−23.5085	−	32.3566i	−0.919254	−	1.26525i
$655$	−2.38049	−	23.3704i	−0.0930133	−	0.913155i
$656$	−3.44319	−	10.5971i	−0.134434	−	0.413746i
$657$	42.9196	+	13.9454i	1.67445	+	0.544062i
$658$	−0.0580323	+	0.140729i	−0.00226233	+	0.00548618i
$659$			17.6702i			0.688333i	0.938909	+	0.344166i	$0.111838\pi$
$659$			17.6702i			0.688333i	−0.938909	+	0.344166i	$0.888162\pi$
$660$	−12.0404	−	18.9209i	−0.468674	−	0.736497i
$661$		−	17.8056i		−	0.692556i	−0.938132	−	0.346278i	$-0.887445\pi$
$661$		−	17.8056i		−	0.692556i	0.938132	−	0.346278i	$-0.112555\pi$
$662$	−22.7393	−	16.5211i	−0.883789	−	0.642111i
$663$	3.12493	−	9.61755i	0.121362	−	0.373515i
$664$	5.08373	−	1.65180i	0.197287	−	0.0641024i
$665$	1.02400	−	0.360734i	0.0397091	−	0.0139887i
$666$	−17.2071	−	23.6835i	−0.666761	−	0.917718i
$667$	−12.4803	−	38.4103i	−0.483238	−	1.48725i
$668$	19.3177	+	6.27671i	0.747425	+	0.242853i
$669$	32.8001	+	23.8307i	1.26812	+	0.921346i
$670$	18.5863	+	10.8105i	0.718051	+	0.417647i
$671$	7.49679	−	14.4967i	0.289410	−	0.559639i
$672$	1.88003	+	7.77691i	0.0725238	+	0.300001i
$673$	−23.3139	−	16.9385i	−0.898685	−	0.652933i	0.0394428	−	0.999222i	$-0.487442\pi$
$673$	−23.3139	−	16.9385i	−0.898685	−	0.652933i	−0.938128	+	0.346289i	$0.887442\pi$
$674$	7.35825	−	22.6464i	0.283429	−	0.872305i
$675$	−32.0456	+	35.1339i	−1.23344	+	1.35230i
$676$	−10.2750	+	7.46520i	−0.395191	+	0.287123i
$677$	−8.05683	−	11.0893i	−0.309649	−	0.426196i	0.625623	−	0.780126i	$-0.284845\pi$
$677$	−8.05683	−	11.0893i	−0.309649	−	0.426196i	−0.935272	+	0.353930i	$0.884845\pi$
$678$	10.0220	−	3.25634i	0.384892	−	0.125059i
$679$	29.2400	+	2.25490i	1.12213	+	0.0865353i
$680$	−5.51780	−	12.5010i	−0.211598	−	0.479393i
$681$		−	4.68646i		−	0.179586i
$682$	10.5958	−	10.4689i	0.405733	−	0.400873i
$683$			20.0456i			0.767024i	0.923536	+	0.383512i	$0.125285\pi$
$683$			20.0456i			0.767024i	−0.923536	+	0.383512i	$0.874715\pi$
$684$	0.912321	+	0.662840i	0.0348834	+	0.0253443i
$685$	6.08401	−	5.44280i	0.232458	−	0.207959i
$686$	−9.60209	+	15.8367i	−0.366609	+	0.604647i
$687$	−18.9556	−	26.0901i	−0.723201	−	0.995400i
$688$	−1.78692	+	1.29828i	−0.0681259	+	0.0494963i
$689$	−2.25934	−	6.95352i	−0.0860738	−	0.264908i
$690$	40.3259	−	36.0759i	1.53518	−	1.37338i
$691$	−10.7938	+	14.8563i	−0.410614	+	0.565162i	−0.963368	−	0.268183i	$-0.913577\pi$
$691$	−10.7938	+	14.8563i	−0.410614	+	0.565162i	0.552754	+	0.833344i	$0.313577\pi$
$692$			12.8389i			0.488062i
$693$	49.9088	−	20.4132i	1.89588	−	0.775433i
$694$	35.9132			1.36325
$695$	4.46911	−	1.97261i	0.169523	−	0.0748253i
$696$	−14.5163	−	4.71664i	−0.550240	−	0.178784i
$697$	−64.7587	+	21.0414i	−2.45291	+	0.796999i
$698$	−6.41281	+	4.65918i	−0.242728	+	0.176353i
$699$	−16.6299	+	12.0824i	−0.629002	+	0.456997i
$700$	−11.5949	−	6.36848i	−0.438247	−	0.240706i
$701$	−16.9802	−	5.51720i	−0.641334	−	0.208382i	−0.0297445	−	0.999558i	$-0.509469\pi$
$701$	−16.9802	−	5.51720i	−0.641334	−	0.208382i	−0.611589	+	0.791176i	$0.709469\pi$
$702$	3.05902	−	4.21039i	0.115455	−	0.158911i
$703$		−	0.874252i		−	0.0329730i
$704$	3.27261	+	0.538560i	0.123341	+	0.0202978i
$705$	0.195609	−	0.336306i	0.00736706	−	0.0126660i
$706$	−2.65895	−	1.93184i	−0.100071	−	0.0727058i
$707$	−33.9308	−	2.61665i	−1.27610	−	0.0984092i
$708$	−16.9235	+	5.49879i	−0.636025	+	0.206657i
$709$	−22.6592	+	16.4629i	−0.850986	+	0.618277i	−0.925418	−	0.378949i	$-0.876286\pi$
$709$	−22.6592	+	16.4629i	−0.850986	+	0.618277i	0.0744319	+	0.997226i	$0.476286\pi$
$710$	0.0747365	+	0.733724i	0.00280481	+	0.0275362i
$711$	22.2645	−	7.23419i	0.834986	−	0.271303i
$712$	1.45267	+	0.472000i	0.0544410	+	0.0176889i
$713$	29.0731	+	21.1228i	1.08880	+	0.791056i
$714$	47.5248	−	11.4889i	1.77857	−	0.429961i
$715$	−4.05052	−	0.249808i	−0.151481	−	0.00934230i
$716$	−5.00826			−0.187167
$717$	12.7881	−	17.6014i	0.477582	−	0.657335i
$718$	19.1842	+	6.23332i	0.715948	+	0.232626i
$719$	22.7280	−	7.38477i	0.847611	−	0.275405i	0.147166	−	0.989112i	$-0.452985\pi$
$719$	22.7280	−	7.38477i	0.847611	−	0.275405i	0.700445	+	0.713707i	$0.252985\pi$
$720$	−1.39240	−	13.6699i	−0.0518918	−	0.509446i
$721$	16.9242	+	14.4086i	0.630289	+	0.536603i
$722$	−5.86092	−	18.0380i	−0.218121	−	0.671307i
$723$	−17.7061	+	54.4937i	−0.658496	+	2.02664i
$724$	8.77710	−	12.0806i	0.326198	−	0.448974i
$725$	21.9360	−	12.4776i	0.814683	−	0.463408i
$726$	0.400803	−	33.2623i	0.0148752	−	1.23448i
$727$	31.6705			1.17460			0.587298	−	0.809371i	$-0.300192\pi$
$727$	31.6705			1.17460			0.587298	+	0.809371i	$0.300192\pi$
$728$	1.33845	+	0.551934i	0.0496061	+	0.0204561i
$729$	−7.05488	+	21.7127i	−0.261292	+	0.804173i
$730$	3.46578	−	16.0516i	0.128274	−	0.594097i
$731$	7.93378	+	10.9199i	0.293441	+	0.403888i
$732$	12.0388	−	8.74673i	0.444968	−	0.323288i
$733$	−33.4533	+	10.8696i	−1.23562	+	0.401479i	−0.852749	−	0.522321i	$-0.825066\pi$
$733$	−33.4533	+	10.8696i	−1.23562	+	0.401479i	−0.382876	+	0.923800i	$0.625066\pi$
$734$	6.38721	−	19.6578i	0.235756	−	0.725583i
$735$	29.7906	−	36.7837i	1.09884	−	1.35679i
$736$			8.00171i			0.294947i
$737$	14.3072	+	28.5027i	0.527012	+	1.04991i
$738$	−68.4699			−2.52041
$739$	4.38429	−	6.03445i	0.161279	−	0.221981i	−0.720728	−	0.693218i	$-0.756192\pi$
$739$	4.38429	−	6.03445i	0.161279	−	0.221981i	0.882007	+	0.471237i	$0.156192\pi$
$740$	−7.93922	+	7.10248i	−0.291851	+	0.261092i
$741$	0.288816	−	0.0938419i	0.0106099	−	0.00344737i
$742$	22.9158	−	26.9167i	0.841267	−	0.988144i
$743$	−16.3919	+	11.9094i	−0.601362	+	0.436915i	−0.846362	−	0.532608i	$-0.821212\pi$
$743$	−16.3919	+	11.9094i	−0.601362	+	0.436915i	0.245000	+	0.969523i	$0.421212\pi$
$744$	12.9166	−	4.19686i	0.473546	−	0.153864i
$745$	−9.33222	+	8.34867i	−0.341906	+	0.305871i
$746$	7.71749	+	5.60708i	0.282557	+	0.205290i
$747$		−	32.8471i		−	1.20181i
$748$	3.29115	−	19.9989i	0.120336	−	0.731233i
$749$	1.57731	+	6.52469i	0.0576337	+	0.238407i
$750$	27.1603	+	20.1356i	0.991753	+	0.735249i
$751$	−3.90941	+	12.0319i	−0.142656	+	0.439051i	−0.996702	−	0.0811465i	$-0.974142\pi$
$751$	−3.90941	+	12.0319i	−0.142656	+	0.439051i	0.854046	+	0.520198i	$0.174142\pi$
$752$	0.0177794	+	0.0547195i	0.000648350	+	0.00199541i
$753$	38.0282	+	52.3414i	1.38583	+	1.90743i
$754$	−2.23445	+	1.62342i	−0.0813738	+	0.0591215i
$755$	−0.321161	+	1.48744i	−0.0116882	+	0.0541336i
$756$	25.0883	+	1.93474i	0.912454	+	0.0703659i
$757$	−3.72903	+	5.13257i	−0.135534	+	0.186547i	−0.871389	−	0.490592i	$-0.836780\pi$
$757$	−3.72903	+	5.13257i	−0.135534	+	0.186547i	0.735855	+	0.677139i	$0.236780\pi$
$758$	−19.3170			−0.701624
$759$	79.3409	−	12.0768i	2.87989	−	0.438361i
$760$	0.206315	−	0.354712i	0.00748382	−	0.0128668i
$761$	11.5375	+	8.38248i	0.418234	+	0.303865i	0.776927	−	0.629591i	$-0.216777\pi$
$761$	11.5375	+	8.38248i	0.418234	+	0.303865i	−0.358693	+	0.933456i	$0.616777\pi$
$762$	−18.4120	+	56.6663i	−0.666997	+	2.05281i
$763$	−18.3300	−	29.8064i	−0.663591	−	1.07906i
$764$	−6.15026	+	4.46843i	−0.222509	+	0.161662i
$765$	−83.5367	+	8.50898i	−3.02028	+	0.307643i
$766$	3.13832	+	9.65875i	0.113392	+	0.348985i
$767$	−0.995014	+	3.06234i	−0.0359279	+	0.110575i
$768$	2.44652	+	1.77750i	0.0882813	+	0.0641401i
$769$	43.4506			1.56687			0.783435	−	0.621474i	$-0.213466\pi$
$769$	43.4506			1.56687			0.783435	+	0.621474i	$0.213466\pi$
$770$	−9.23017	−	17.3148i	−0.332632	−	0.623984i
$771$	88.0272			3.17022
$772$	17.6808	+	12.8459i	0.636347	+	0.462333i
$773$	−10.1745	+	31.3138i	−0.365950	+	1.12628i	0.583434	+	0.812160i	$0.301709\pi$
$773$	−10.1745	+	31.3138i	−0.365950	+	1.12628i	−0.949384	+	0.314117i	$0.898291\pi$
$774$	4.19423	+	12.9085i	0.150758	+	0.463987i
$775$	−9.26496	+	20.4549i	−0.332807	+	0.734763i
$776$	8.96753	−	6.51530i	0.321916	−	0.233885i
$777$	−19.9668	−	32.4679i	−0.716304	−	1.16478i
$778$	−5.65907	+	17.4168i	−0.202887	+	0.624423i
$779$	−1.65427	−	1.20190i	−0.0592703	−	0.0430624i
$780$	−3.19855	−	1.86040i	−0.114526	−	0.0666130i
$781$	−0.502492	+	0.971680i	−0.0179806	+	0.0347694i
$782$	48.8985			1.74861
$783$	−28.2155	+	38.8353i	−1.00834	+	1.38786i
$784$	1.11681	+	6.91033i	0.0398862	+	0.246798i
$785$	50.1846	+	10.8356i	1.79117	+	0.386739i
$786$	25.7022	−	18.6738i	0.916768	−	0.666071i
$787$	5.30992	+	7.30848i	0.189278	+	0.260519i	0.893101	−	0.449857i	$-0.148525\pi$
$787$	5.30992	+	7.30848i	0.189278	+	0.260519i	−0.703823	+	0.710376i	$0.748525\pi$
$788$	−3.52228	−	10.8405i	−0.125476	−	0.386176i
$789$	−6.60233	+	20.3199i	−0.235049	+	0.723407i
$790$	−3.43985	−	7.79327i	−0.122384	−	0.277272i
$791$	8.96131	−	2.16635i	0.318628	−	0.0770267i
$792$	9.36184	−	18.1032i	0.332658	−	0.643269i
$793$		−	2.69271i		−	0.0956208i
$794$	−11.3845	−	8.27133i	−0.404021	−	0.293539i
$795$	−67.3358	+	60.2391i	−2.38815	+	2.13646i
$796$	−24.8868	+	8.08622i	−0.882090	+	0.286608i
$797$	−25.5287	+	18.5477i	−0.904273	+	0.656993i	−0.939560	−	0.342385i	$-0.888765\pi$
$797$	−25.5287	+	18.5477i	−0.904273	+	0.656993i	0.0352872	+	0.999377i	$0.488765\pi$
$798$	1.11799	+	0.951813i	0.0395764	+	0.0336938i
$799$	0.334391	−	0.108650i	0.0118299	−	0.00384377i
$800$	−4.89731	+	1.00813i	−0.173146	+	0.0356429i
$801$	5.51695	−	7.59343i	0.194932	−	0.268301i
$802$	−15.2518			−0.538559
$803$	17.3265	−	17.1189i	0.611438	−	0.604114i
$804$			29.0788i			1.02553i
$805$	37.6035	−	28.7566i	1.32535	−	1.01354i
$806$	0.759428	−	2.33728i	0.0267497	−	0.0823271i
$807$	2.47594	−	0.804482i	0.0871573	−	0.0283191i
$808$	−10.4062	+	7.56052i	−0.366088	+	0.265978i
$809$	−16.2603	−	22.3803i	−0.571680	−	0.786851i	0.421072	−	0.907027i	$-0.361654\pi$
$809$	−16.2603	−	22.3803i	−0.571680	−	0.786851i	−0.992753	+	0.120177i	$0.961654\pi$
$810$	−22.5693	−	4.87305i	−0.793005	−	0.171221i
$811$	7.43466	−	22.8815i	0.261066	−	0.803479i	−0.731507	−	0.681834i	$-0.761183\pi$
$811$	7.43466	−	22.8815i	0.261066	−	0.803479i	0.992574	−	0.121646i	$-0.0388172\pi$
$812$	−12.3454	−	5.09087i	−0.433239	−	0.178655i
$813$	−39.1879			−1.37438
$814$	−15.6203	+	2.37764i	−0.547492	+	0.0833363i
$815$	−32.4827	−	18.8932i	−1.13782	−	0.661799i
$816$	10.8623	−	14.9507i	0.380258	−	0.523380i
$817$	−0.125256	+	0.385500i	−0.00438217	+	0.0134869i
$818$	5.20151	+	16.0086i	0.181866	+	0.559727i
$819$	5.76721	−	6.77412i	0.201523	−	0.236707i
$820$	2.52478	+	24.7869i	0.0881690	+	0.865597i
$821$	−44.0036	+	14.2976i	−1.53574	+	0.498991i	−0.950196	−	0.311653i	$-0.899117\pi$
$821$	−44.0036	+	14.2976i	−1.53574	+	0.498991i	−0.585539	+	0.810644i	$0.699117\pi$
$822$	10.4997	+	3.41157i	0.366220	+	0.118992i
$823$	18.5911	−	25.5884i	0.648044	−	0.891957i	−0.350968	−	0.936387i	$-0.614147\pi$
$823$	18.5911	−	25.5884i	0.648044	−	0.891957i	0.999012	+	0.0444309i	$0.0141475\pi$
$824$	8.40097			0.292662
$825$	17.3875	+	47.0377i	0.605357	+	1.63764i
$826$	−15.1324	+	3.65819i	−0.526525	+	0.127285i
$827$	31.7845	+	23.0928i	1.10526	+	0.803016i	0.981910	−	0.189348i	$-0.0606375\pi$
$827$	31.7845	+	23.0928i	1.10526	+	0.803016i	0.123346	+	0.992364i	$0.460637\pi$
$828$	46.7639	+	15.1945i	1.62516	+	0.528045i
$829$	28.6276	−	9.30168i	0.994279	−	0.323061i	0.233702	−	0.972308i	$-0.424916\pi$
$829$	28.6276	−	9.30168i	0.994279	−	0.323061i	0.760577	+	0.649247i	$0.224916\pi$
$830$	−11.8910	+	1.21121i	−0.412744	+	0.0420418i
$831$	20.9271	−	15.2044i	0.725952	−	0.527435i
$832$	0.520427	−	0.169097i	0.0180426	−	0.00586239i
$833$	42.2291	−	6.82486i	1.46315	−	0.236467i
$834$	5.34487	+	3.88327i	0.185078	+	0.134467i
$835$	−39.2606	−	22.8355i	−1.35867	−	0.790256i
$836$	0.543963	−	0.273048i	0.0188134	−	0.00944355i
$837$		−	42.7131i		−	1.47638i
$838$	−17.0670	+	23.4907i	−0.589569	+	0.811473i
$839$	25.3742	+	8.24459i	0.876016	+	0.284635i	0.712302	−	0.701873i	$-0.247653\pi$
$839$	25.3742	+	8.24459i	0.876016	+	0.284635i	0.163714	+	0.986508i	$0.447653\pi$
$840$	−0.439068	−	17.8852i	−0.0151493	−	0.617099i
$841$	−2.85163	+	2.07183i	−0.0983322	+	0.0714425i
$842$	−17.6523	+	12.8252i	−0.608340	+	0.441985i
$843$	77.6359	−	25.2254i	2.67392	−	0.868810i
$844$	−15.8890	−	5.16264i	−0.546921	−	0.177705i
$845$	25.9810	−	11.4677i	0.893774	−	0.394500i
$846$	0.353555			0.0121555
$847$	2.58718	−	28.9880i	0.0888965	−	0.996041i
$848$		−	13.3612i		−	0.458825i
$849$	5.05991	−	6.96437i	0.173656	−	0.239016i
$850$	6.16070	+	29.9275i	0.211310	+	1.02651i
$851$	−11.7797	−	36.2541i	−0.403802	−	1.24277i
$852$	−0.806934	+	0.586272i	−0.0276451	+	0.0200853i
$853$	27.2399	+	37.4925i	0.932677	+	1.28372i	0.958806	+	0.284061i	$0.0916817\pi$
$853$	27.2399	+	37.4925i	0.932677	+	1.28372i	−0.0261297	+	0.999659i	$0.508318\pi$
$854$	11.0900	−	6.81999i	0.379491	−	0.233375i
$855$	−1.68125	−	1.87932i	−0.0574975	−	0.0642712i
$856$	2.05259	+	1.49129i	0.0701560	+	0.0509713i
$857$			48.0294i			1.64065i	0.571896	+	0.820326i	$0.306208\pi$
$857$			48.0294i			1.64065i	−0.571896	+	0.820326i	$0.693792\pi$
$858$	−2.46215	−	4.90508i	−0.0840565	−	0.167457i
$859$		−	33.2791i		−	1.13547i	−0.823212	−	0.567735i	$-0.807820\pi$
$859$		−	33.2791i		−	1.13547i	0.823212	−	0.567735i	$-0.192180\pi$
$860$	4.51837	−	1.99435i	0.154075	−	0.0680068i
$861$	−88.8857	−	6.85462i	−3.02922	−	0.233605i
$862$	−23.0372	+	7.48524i	−0.784651	+	0.254948i
$863$	−19.3754	−	26.6680i	−0.659547	−	0.907789i	0.339919	−	0.940455i	$-0.389600\pi$
$863$	−19.3754	−	26.6680i	−0.659547	−	0.907789i	−0.999466	+	0.0326659i	$0.989600\pi$
$864$	7.69428	−	5.59022i	0.261765	−	0.190183i
$865$	6.05900	−	28.0620i	0.206012	−	0.954137i
$866$	−2.20106	+	6.77417i	−0.0747951	+	0.230196i
$867$	−49.7731	−	36.1622i	−1.69038	−	1.22813i
$868$	11.5496	−	2.79205i	0.392018	−	0.0947685i
$869$	2.05173	−	12.4675i	0.0696003	−	0.422932i
$870$	29.5024	+	17.1598i	1.00023	+	0.581771i
$871$	4.25693	+	3.09284i	0.144241	+	0.104797i
$872$	−12.5783	−	4.08693i	−0.425954	−	0.138401i
$873$	−21.0484	−	64.7803i	−0.712380	−	2.19248i
$874$	0.863119	+	1.18798i	0.0291954	+	0.0401841i
$875$	22.3376	+	19.3915i	0.755149	+	0.655553i
$876$	21.1216	−	6.86281i	0.713631	−	0.231873i
$877$	−10.3587	+	31.8809i	−0.349790	+	1.07654i	0.609180	+	0.793032i	$0.291499\pi$
$877$	−10.3587	+	31.8809i	−0.349790	+	1.07654i	−0.958969	+	0.283510i	$0.908501\pi$
$878$	−12.6985	−	9.22602i	−0.428555	−	0.311363i
$879$		−	34.8404i		−	1.17514i
$880$	−6.89878	−	2.72155i	−0.232558	−	0.0917436i
$881$			53.5219i			1.80320i	0.432571	+	0.901600i	$0.357606\pi$
$881$			53.5219i			1.80320i	−0.432571	+	0.901600i	$0.642394\pi$
$882$	42.5063	+	6.59515i	1.43126	+	0.222070i
$883$	6.84493	+	2.22405i	0.230350	+	0.0748453i	0.421918	−	0.906634i	$-0.361357\pi$
$883$	6.84493	+	2.22405i	0.230350	+	0.0748453i	−0.191568	+	0.981479i	$0.561357\pi$
$884$	−1.03335	−	3.18034i	−0.0347554	−	0.106966i
$885$	39.5848	−	4.03207i	1.33063	−	0.135537i
$886$	−22.9876	−	31.6397i	−0.772283	−	1.06296i
$887$	35.5279	−	11.5437i	1.19291	−	0.387600i	0.355761	−	0.934577i	$-0.384222\pi$
$887$	35.5279	−	11.5437i	1.19291	−	0.387600i	0.837147	+	0.546977i	$0.184222\pi$
$888$	−13.7014	−	4.45186i	−0.459790	−	0.149395i
$889$	−19.8729	+	48.1919i	−0.666515	+	1.61631i
$890$	−2.95235	−	1.71720i	−0.0989629	−	0.0575607i
$891$	−24.0700	−	24.3618i	−0.806377	−	0.816152i
$892$	13.4068			0.448893
$893$	0.00854205	+	0.00620617i	0.000285849	+	0.000207681i
$894$	−16.1054	−	5.23298i	−0.538647	−	0.175017i
$895$	10.9465	+	2.36352i	0.365903	+	0.0790037i
$896$	2.01455	+	1.71511i	0.0673014	+	0.0572977i
$897$	10.7124	−	7.78300i	0.357676	−	0.259867i
$898$	10.1174	+	31.1381i	0.337622	+	1.03909i
$899$	−7.00473	+	21.5583i	−0.233621	+	0.719011i
$900$	−3.40778	+	30.5354i	−0.113593	+	1.01785i
$901$	−81.6502			−2.72016
$902$	−16.9754	+	32.8256i	−0.565218	+	1.09297i
$903$	4.15254	+	17.1773i	0.138188	+	0.571626i
$904$	2.04821	−	2.81912i	0.0681224	−	0.0937625i
$905$	−24.8853	+	22.2625i	−0.827214	+	0.740032i
$906$	−1.95726	+	0.635951i	−0.0650255	+	0.0211281i
$907$	12.1152	+	16.6752i	0.402279	+	0.553690i	0.961314	−	0.275454i	$-0.0888282\pi$
$907$	12.1152	+	16.6752i	0.402279	+	0.553690i	−0.559035	+	0.829144i	$0.688828\pi$
$908$	−0.910903	−	1.25375i	−0.0302294	−	0.0416072i
$909$	24.4251	+	75.1727i	0.810129	+	2.49332i
$910$	−2.66497	−	1.83801i	−0.0883429	−	0.0609294i
$911$	34.6498	+	25.1745i	1.14800	+	0.834069i	0.988213	−	0.153083i	$-0.0489200\pi$
$911$	34.6498	+	25.1745i	1.14800	+	0.834069i	0.159785	+	0.987152i	$0.448920\pi$
$912$	0.554958			0.0183765
$913$	−15.7474	−	8.14360i	−0.521165	−	0.269514i
$914$	−8.18875			−0.270860
$915$	−30.4411	+	13.4363i	−1.00635	+	0.444190i
$916$	−10.1422	−	3.29541i	−0.335109	−	0.108883i
$917$	23.6764	−	14.5603i	0.781865	−	0.480823i
$918$	−34.1619	−	47.0198i	−1.12751	−	1.55188i
$919$	−20.7012	−	28.4927i	−0.682869	−	0.939889i	0.317095	−	0.948394i	$-0.397293\pi$
$919$	−20.7012	−	28.4927i	−0.682869	−	0.939889i	−0.999964	+	0.00850529i	$0.997293\pi$
$920$	3.77621	−	17.4894i	0.124498	−	0.576607i
$921$	23.5679	+	7.65768i	0.776589	+	0.252329i
$922$	−17.3668	−	12.6177i	−0.571945	−	0.415542i
$923$			0.180486i			0.00594076i
$924$	13.9656	−	22.5638i	0.459435	−	0.742295i
$925$	20.7046	−	11.7772i	0.680763	−	0.387231i
$926$	6.33742	−	8.72271i	0.208261	−	0.286646i
$927$	15.9526	−	49.0972i	0.523954	−	1.61256i
$928$	−4.80026	+	1.55970i	−0.157576	+	0.0511997i
$929$	−23.5594	−	32.4267i	−0.772957	−	1.06388i	−0.996024	−	0.0890815i	$-0.971607\pi$
$929$	−23.5594	−	32.4267i	−0.772957	−	1.06388i	0.223067	−	0.974803i	$-0.428393\pi$
$930$	−30.2124	+	3.07741i	−0.990704	+	0.100912i
$931$	0.911204	+	0.905482i	0.0298635	+	0.0296760i
$932$	−2.10051	+	6.46469i	−0.0688043	+	0.211758i
$933$	−26.7783	+	36.8572i	−0.876684	+	1.20665i
$934$	18.2484			0.597107
$935$	−16.6314	+	42.1585i	−0.543906	+	1.37873i
$936$		−	3.36260i		−	0.109910i
$937$	18.4145	−	25.3454i	0.601577	−	0.827999i	−0.394275	−	0.918993i	$-0.629004\pi$
$937$	18.4145	−	25.3454i	0.601577	−	0.827999i	0.995851	+	0.0909934i	$0.0290042\pi$
$938$	−1.95613	+	25.3657i	−0.0638699	+	0.828219i
$939$	16.2331	+	49.9603i	0.529747	+	1.63039i
$940$	−0.0130371	−	0.127991i	−0.000425222	−	0.00417461i
$941$	−17.1985	+	12.4954i	−0.560654	+	0.407339i	−0.831698	−	0.555228i	$-0.812631\pi$
$941$	−17.1985	+	12.4954i	−0.560654	+	0.407339i	0.271044	+	0.962567i	$0.412631\pi$
$942$	21.4563	+	66.0356i	0.699083	+	2.15156i
$943$	−84.7946	−	27.5514i	−2.76129	−	0.897199i
$944$	−3.45869	+	4.76048i	−0.112571	+	0.154940i
$945$	−53.9225	−	16.0686i	−1.75410	−	0.522710i
$946$	7.22840	+	1.18955i	0.235016	+	0.0386756i
$947$			11.2484i			0.365523i	0.983157	+	0.182761i	$0.0585036\pi$
$947$			11.2484i			0.365523i	−0.983157	+	0.182761i	$0.941496\pi$
$948$	6.77169	−	9.32043i	0.219934	−	0.302713i
$949$	1.24184	−	3.82198i	0.0403117	−	0.124067i
$950$	−0.618340	+	0.677930i	−0.0200616	+	0.0219950i
$951$	−14.3550	−	19.7579i	−0.465492	−	0.640695i
$952$	10.4810	−	12.3109i	0.339692	−	0.398999i
$953$	−9.11957	−	28.0672i	−0.295412	−	0.909184i	−0.983083	−	0.183162i	$-0.941367\pi$
$953$	−9.11957	−	28.0672i	−0.295412	−	0.909184i	0.687671	−	0.726023i	$-0.258633\pi$
$954$	−78.0858	−	25.3716i	−2.52812	−	0.821436i
$955$	15.5514	−	6.86418i	0.503231	−	0.222120i
$956$		−	7.19444i		−	0.232685i
$957$	22.7101	+	45.2429i	0.734114	+	1.46250i
$958$	15.9351			0.514841
$959$	8.92950	+	3.68225i	0.288348	+	0.118906i
$960$	−4.50852	−	5.03966i	−0.145512	−	0.162654i
$961$	3.34673	+	10.3002i	0.107959	+	0.332264i
$962$	−2.10901	+	1.53229i	−0.0679973	+	0.0494029i
$963$	12.6131	−	9.16397i	0.406452	−	0.295305i
$964$	5.85505	+	18.0200i	0.188578	+	0.580385i
$965$	−32.5827	−	36.4212i	−1.04887	−	1.17244i
$966$	59.1864	+	24.4067i	1.90429	+	0.785271i
$967$	9.31716			0.299620			0.149810	−	0.988715i	$-0.452134\pi$
$967$	9.31716			0.299620			0.149810	+	0.988715i	$0.452134\pi$
$968$	−6.35794	−	8.97644i	−0.204352	−	0.288514i
$969$		−	3.39135i		−	0.108946i
$970$	−22.6751	+	10.0085i	−0.728053	+	0.321353i
$971$	20.1278	+	6.53990i	0.645930	+	0.209876i	0.613619	−	0.789602i	$-0.289713\pi$
$971$	20.1278	+	6.53990i	0.645930	+	0.209876i	0.0323115	+	0.999478i	$0.489713\pi$
$972$	−0.832573	−	2.56240i	−0.0267048	−	0.0821889i
$973$	4.40114	+	3.74696i	0.141094	+	0.120122i
$974$	−3.93588	−	5.41728i	−0.126114	−	0.173581i
$975$	6.11310	+	5.57575i	0.195776	+	0.178567i
$976$	1.52061	−	4.67995i	0.0486735	−	0.149802i
$977$	8.87118	−	12.2101i	0.283814	−	0.390637i	−0.643178	−	0.765716i	$-0.722385\pi$
$977$	8.87118	−	12.2101i	0.283814	−	0.390637i	0.926993	+	0.375080i	$0.122385\pi$
$978$		−	50.8201i		−	1.62505i
$979$	−2.27263	−	4.52752i	−0.0726336	−	0.144700i
$980$	0.820136	−	15.6310i	0.0261983	−	0.499313i
$981$	−47.7699	+	65.7496i	−1.52517	+	2.09922i
$982$	9.33984	+	3.03470i	0.298046	+	0.0968411i
$983$	7.77647	+	23.9335i	0.248031	+	0.763360i	0.995123	+	0.0986401i	$0.0314492\pi$
$983$	7.77647	+	23.9335i	0.248031	+	0.763360i	−0.747092	+	0.664720i	$0.768551\pi$
$984$	−27.2601	+	19.8057i	−0.869022	+	0.631381i
$985$	2.58277	+	25.3563i	0.0822939	+	0.807918i
$986$	9.53134	+	29.3344i	0.303540	+	0.934199i
$987$	0.458975	+	0.0353948i	0.0146093	+	0.00112663i
$988$	0.0590257	−	0.0812420i	0.00187786	−	0.00258465i
$989$			17.6739i			0.561996i
$990$	−29.0055	+	35.1501i	−0.921856	+	1.11714i
$991$	−12.9027			−0.409866			−0.204933	−	0.978776i	$-0.565698\pi$
$991$	−12.9027			−0.409866			−0.204933	+	0.978776i	$0.565698\pi$
$992$	2.63979	−	3.63336i	0.0838134	−	0.115359i
$993$	−26.2660	+	80.8385i	−0.833526	+	2.56533i
$994$	−0.743334	+	0.457127i	−0.0235771	+	0.0144992i
$995$	58.2112	−	5.92935i	1.84542	−	0.187973i
$996$	−9.50137	−	13.0775i	−0.301062	−	0.414377i
$997$	−2.86579	+	0.931152i	−0.0907605	+	0.0294899i	−0.354045	−	0.935228i	$-0.615194\pi$
$997$	−2.86579	+	0.931152i	−0.0907605	+	0.0294899i	0.263285	+	0.964718i	$0.415194\pi$
$998$	6.65825	−	20.4920i	0.210763	−	0.648662i
$999$	−26.6316	+	36.6552i	−0.842586	+	1.15972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.w.a.139.2	✓	96
5.4	even	2		770.2.w.b.139.23	yes	96
7.6	odd	2	inner	770.2.w.a.139.23	yes	96
11.8	odd	10		770.2.w.b.349.2	yes	96
35.34	odd	2		770.2.w.b.139.2	yes	96
55.19	odd	10	inner	770.2.w.a.349.23	yes	96
77.41	even	10		770.2.w.b.349.23	yes	96
385.349	even	10	inner	770.2.w.a.349.2	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.w.a.139.2	✓	96	1.1	even	1	trivial
770.2.w.a.139.23	yes	96	7.6	odd	2	inner
770.2.w.a.349.2	yes	96	385.349	even	10	inner
770.2.w.a.349.23	yes	96	55.19	odd	10	inner
770.2.w.b.139.2	yes	96	35.34	odd	2
770.2.w.b.139.23	yes	96	5.4	even	2
770.2.w.b.349.2	yes	96	11.8	odd	10
770.2.w.b.349.23	yes	96	77.41	even	10

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.934488 + 2.87606i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.226592 - 2.22456i) q^{5} +(2.44652 - 1.77750i) q^{6} +(2.25369 - 1.38595i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.97140 - 3.61193i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.934488 + 2.87606i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.226592 - 2.22456i) q^{5} +(2.44652 - 1.77750i) q^{6} +(2.25369 - 1.38595i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.97140 - 3.61193i) q^{9} +(-1.12425 + 1.93289i) q^{10} +(-2.96415 + 1.48789i) q^{11} -3.02407 q^{12} +(-0.321642 + 0.442702i) q^{13} +(-2.63792 - 0.203429i) q^{14} +(6.60971 + 1.42713i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(3.59196 + 4.94391i) q^{17} +(1.89891 + 5.84423i) q^{18} +(-0.0567089 + 0.174532i) q^{19} +(2.04566 - 0.902928i) q^{20} +(1.88003 + 7.77691i) q^{21} +(3.27261 + 0.538560i) q^{22} +8.00171i q^{23} +(2.44652 + 1.77750i) q^{24} +(-4.89731 + 1.00813i) q^{25} +(0.520427 - 0.169097i) q^{26} +(7.69428 - 5.59022i) q^{27} +(2.01455 + 1.71511i) q^{28} +(-4.80026 + 1.55970i) q^{29} +(-4.50852 - 5.03966i) q^{30} +(2.63979 - 3.63336i) q^{31} +1.00000 q^{32} +(-1.50928 - 9.91549i) q^{33} -6.11101i q^{34} +(-3.59380 - 4.69943i) q^{35} +(1.89891 - 5.84423i) q^{36} +(-4.53079 + 1.47214i) q^{37} +(0.148466 - 0.107867i) q^{38} +(-0.972667 - 1.33876i) q^{39} +(-2.18570 - 0.471925i) q^{40} +(-3.44319 + 10.5971i) q^{41} +(3.05018 - 7.39671i) q^{42} +2.20876 q^{43} +(-2.33104 - 2.35929i) q^{44} +(-6.90847 + 11.8776i) q^{45} +(4.70329 - 6.47352i) q^{46} +(0.0177794 - 0.0547195i) q^{47} +(-0.934488 - 2.87606i) q^{48} +(3.15827 - 6.24703i) q^{49} +(4.55457 + 2.06297i) q^{50} +(-17.5756 + 5.71067i) q^{51} +(-0.520427 - 0.169097i) q^{52} +(-7.85350 + 10.8094i) q^{53} -9.51065 q^{54} +(3.98154 + 6.25678i) q^{55} +(-0.621689 - 2.57167i) q^{56} +(-0.448971 - 0.326196i) q^{57} +(4.80026 + 1.55970i) q^{58} +(5.59628 - 1.81834i) q^{59} +(0.685229 + 6.72721i) q^{60} +(-3.98101 + 2.89237i) q^{61} +(-4.27127 + 1.38782i) q^{62} +(-16.2100 - 1.25007i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.05770 + 0.615198i) q^{65} +(-4.60714 + 8.90893i) q^{66} -9.61579i q^{67} +(-3.59196 + 4.94391i) q^{68} +(-23.0134 - 7.47751i) q^{69} +(0.145191 + 5.91430i) q^{70} +(0.266837 - 0.193869i) q^{71} +(-4.97140 + 3.61193i) q^{72} +(-6.98448 + 2.26940i) q^{73} +(4.53079 + 1.47214i) q^{74} +(1.67703 - 15.0270i) q^{75} -0.183514 q^{76} +(-4.61815 + 7.46141i) q^{77} +1.65480i q^{78} +(-2.23926 + 3.08208i) q^{79} +(1.49088 + 1.66652i) q^{80} +(3.19088 + 9.82051i) q^{81} +(9.01440 - 6.54934i) q^{82} +(3.14192 + 4.32448i) q^{83} +(-6.81532 + 4.19121i) q^{84} +(10.1841 - 9.11077i) q^{85} +(-1.78692 - 1.29828i) q^{86} -15.2634i q^{87} +(0.499090 + 3.27886i) q^{88} +1.52742i q^{89} +(12.5705 - 5.54848i) q^{90} +(-0.111318 + 1.44350i) q^{91} +(-7.61008 + 2.47267i) q^{92} +(7.98290 + 10.9875i) q^{93} +(-0.0465472 + 0.0338185i) q^{94} +(0.401106 + 0.0866047i) q^{95} +(-0.934488 + 2.87606i) q^{96} +(8.96753 + 6.51530i) q^{97} +(-6.22700 + 3.19756i) q^{98} +(20.1101 + 3.30945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 24 q^{2} - 24 q^{4} - 3 q^{7} - 24 q^{8} - 18 q^{9}+O(q^{10}) \) 96 * q - 24 * q^2 - 24 * q^4 - 3 * q^7 - 24 * q^8 - 18 * q^9	\( 96 q - 24 q^{2} - 24 q^{4} - 3 q^{7} - 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} - 28 q^{18} + 4 q^{22} - 42 q^{25} + 2 q^{28} - 6 q^{30} + 96 q^{32} + 14 q^{35} - 28 q^{36} + 10 q^{39} + 24 q^{43} - 16 q^{44} + 37 q^{49} + 8 q^{50} - 30 q^{51} - 40 q^{53} + 2 q^{56} + 20 q^{57} - 6 q^{60} - 63 q^{63} - 24 q^{64} + 40 q^{65} + 9 q^{70} - 20 q^{71} - 18 q^{72} + 16 q^{77} - 126 q^{81} + 100 q^{85} - 36 q^{86} + 14 q^{88} - 31 q^{91} + 10 q^{92} - 20 q^{93} - 16 q^{95} - 18 q^{98} + 100 q^{99}+O(q^{100}) \) 96 * q - 24 * q^2 - 24 * q^4 - 3 * q^7 - 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 - 28 * q^18 + 4 * q^22 - 42 * q^25 + 2 * q^28 - 6 * q^30 + 96 * q^32 + 14 * q^35 - 28 * q^36 + 10 * q^39 + 24 * q^43 - 16 * q^44 + 37 * q^49 + 8 * q^50 - 30 * q^51 - 40 * q^53 + 2 * q^56 + 20 * q^57 - 6 * q^60 - 63 * q^63 - 24 * q^64 + 40 * q^65 + 9 * q^70 - 20 * q^71 - 18 * q^72 + 16 * q^77 - 126 * q^81 + 100 * q^85 - 36 * q^86 + 14 * q^88 - 31 * q^91 + 10 * q^92 - 20 * q^93 - 16 * q^95 - 18 * q^98 + 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more