LMFDB - Embedded newform 715.2.z.c.166.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [715,2,Mod(56,715)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(715, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("715.56");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 715 = 5 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	715.z (of order $6$, degree $2$, 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:	$5.70930374452$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			166.19
Character	$\chi$	$=$	715.166
Dual form			715.2.z.c.56.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809271 - 0.467233i) q^{2} +(0.346641 + 0.600400i) q^{3} +(-0.563387 + 0.975815i) q^{4} -1.00000i q^{5} +(0.561053 + 0.323924i) q^{6} +(0.420118 + 0.242555i) q^{7} +2.92186i q^{8} +(1.25968 - 2.18183i) q^{9} +O(q^{10})$	\(q+(0.809271 - 0.467233i) q^{2} +(0.346641 + 0.600400i) q^{3} +(-0.563387 + 0.975815i) q^{4} -1.00000i q^{5} +(0.561053 + 0.323924i) q^{6} +(0.420118 + 0.242555i) q^{7} +2.92186i q^{8} +(1.25968 - 2.18183i) q^{9} +(-0.467233 - 0.809271i) q^{10} +(0.866025 - 0.500000i) q^{11} -0.781172 q^{12} +(3.58349 + 0.398207i) q^{13} +0.453319 q^{14} +(0.600400 - 0.346641i) q^{15} +(0.238416 + 0.412948i) q^{16} +(-2.35798 + 4.08414i) q^{17} -2.35426i q^{18} +(5.42814 + 3.13394i) q^{19} +(0.975815 + 0.563387i) q^{20} +0.336318i q^{21} +(0.467233 - 0.809271i) q^{22} +(-0.823380 - 1.42614i) q^{23} +(-1.75429 + 1.01284i) q^{24} -1.00000 q^{25} +(3.08607 - 1.35207i) q^{26} +3.82647 q^{27} +(-0.473378 + 0.273305i) q^{28} +(5.12779 + 8.88159i) q^{29} +(0.323924 - 0.561053i) q^{30} -1.89308i q^{31} +(-4.67493 - 2.69907i) q^{32} +(0.600400 + 0.346641i) q^{33} +4.40690i q^{34} +(0.242555 - 0.420118i) q^{35} +(1.41937 + 2.45843i) q^{36} +(-1.49068 + 0.860647i) q^{37} +5.85712 q^{38} +(1.00310 + 2.28956i) q^{39} +2.92186 q^{40} +(-2.44072 + 1.40915i) q^{41} +(0.157139 + 0.272173i) q^{42} +(1.07246 - 1.85756i) q^{43} +1.12677i q^{44} +(-2.18183 - 1.25968i) q^{45} +(-1.33267 - 0.769420i) q^{46} +2.90646i q^{47} +(-0.165289 + 0.286290i) q^{48} +(-3.38233 - 5.85837i) q^{49} +(-0.809271 + 0.467233i) q^{50} -3.26949 q^{51} +(-2.40747 + 3.27248i) q^{52} +9.25802 q^{53} +(3.09665 - 1.78785i) q^{54} +(-0.500000 - 0.866025i) q^{55} +(-0.708713 + 1.22753i) q^{56} +4.34541i q^{57} +(8.29954 + 4.79174i) q^{58} +(-8.67319 - 5.00747i) q^{59} +0.781172i q^{60} +(7.15004 - 12.3842i) q^{61} +(-0.884509 - 1.53201i) q^{62} +(1.05843 - 0.611084i) q^{63} -5.99804 q^{64} +(0.398207 - 3.58349i) q^{65} +0.647848 q^{66} +(-6.20047 + 3.57984i) q^{67} +(-2.65691 - 4.60190i) q^{68} +(0.570835 - 0.988714i) q^{69} -0.453319i q^{70} +(4.12383 + 2.38089i) q^{71} +(6.37501 + 3.68061i) q^{72} -8.36628i q^{73} +(-0.804245 + 1.39299i) q^{74} +(-0.346641 - 0.600400i) q^{75} +(-6.11629 + 3.53124i) q^{76} +0.485111 q^{77} +(1.88154 + 1.38420i) q^{78} -13.1974 q^{79} +(0.412948 - 0.238416i) q^{80} +(-2.45263 - 4.24808i) q^{81} +(-1.31680 + 2.28077i) q^{82} -0.355851i q^{83} +(-0.328185 - 0.189477i) q^{84} +(4.08414 + 2.35798i) q^{85} -2.00436i q^{86} +(-3.55500 + 6.15745i) q^{87} +(1.46093 + 2.53041i) q^{88} +(-0.495002 + 0.285789i) q^{89} -2.35426 q^{90} +(1.40890 + 1.03649i) q^{91} +1.85553 q^{92} +(1.13660 - 0.656219i) q^{93} +(1.35799 + 2.35211i) q^{94} +(3.13394 - 5.42814i) q^{95} -3.74244i q^{96} +(-5.73492 - 3.31106i) q^{97} +(-5.47445 - 3.16067i) q^{98} -2.51936i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 34 q^{4} + 18 q^{6} + 6 q^{7} - 46 q^{9}+O(q^{10}) $ 56 * q - 6 * q^3 + 34 * q^4 + 18 * q^6 + 6 * q^7 - 46 * q^9	$ 56 q - 6 q^{3} + 34 q^{4} + 18 q^{6} + 6 q^{7} - 46 q^{9} + 2 q^{10} - 44 q^{12} - 2 q^{13} + 32 q^{14} - 54 q^{16} + 26 q^{17} - 6 q^{19} - 2 q^{22} + 30 q^{23} + 36 q^{24} - 56 q^{25} - 18 q^{28} - 36 q^{29} - 10 q^{30} - 36 q^{32} - 8 q^{35} + 58 q^{36} - 6 q^{37} - 36 q^{38} + 16 q^{39} + 12 q^{40} - 12 q^{41} - 74 q^{42} + 138 q^{46} - 50 q^{48} + 46 q^{49} - 24 q^{51} + 26 q^{52} + 104 q^{53} - 18 q^{54} - 28 q^{55} + 6 q^{58} + 24 q^{59} - 4 q^{61} + 14 q^{62} - 24 q^{63} - 112 q^{64} + 8 q^{65} - 20 q^{66} + 30 q^{67} - 92 q^{68} - 16 q^{69} + 156 q^{72} - 32 q^{74} + 6 q^{75} - 24 q^{76} - 16 q^{77} + 150 q^{78} - 12 q^{79} + 24 q^{80} - 116 q^{81} - 36 q^{82} + 6 q^{84} + 12 q^{85} - 16 q^{87} + 6 q^{88} - 24 q^{89} - 72 q^{90} + 74 q^{91} + 36 q^{92} + 114 q^{93} - 66 q^{94} - 8 q^{95} + 18 q^{97} + 30 q^{98}+O(q^{100}) $ 56 * q - 6 * q^3 + 34 * q^4 + 18 * q^6 + 6 * q^7 - 46 * q^9 + 2 * q^10 - 44 * q^12 - 2 * q^13 + 32 * q^14 - 54 * q^16 + 26 * q^17 - 6 * q^19 - 2 * q^22 + 30 * q^23 + 36 * q^24 - 56 * q^25 - 18 * q^28 - 36 * q^29 - 10 * q^30 - 36 * q^32 - 8 * q^35 + 58 * q^36 - 6 * q^37 - 36 * q^38 + 16 * q^39 + 12 * q^40 - 12 * q^41 - 74 * q^42 + 138 * q^46 - 50 * q^48 + 46 * q^49 - 24 * q^51 + 26 * q^52 + 104 * q^53 - 18 * q^54 - 28 * q^55 + 6 * q^58 + 24 * q^59 - 4 * q^61 + 14 * q^62 - 24 * q^63 - 112 * q^64 + 8 * q^65 - 20 * q^66 + 30 * q^67 - 92 * q^68 - 16 * q^69 + 156 * q^72 - 32 * q^74 + 6 * q^75 - 24 * q^76 - 16 * q^77 + 150 * q^78 - 12 * q^79 + 24 * q^80 - 116 * q^81 - 36 * q^82 + 6 * q^84 + 12 * q^85 - 16 * q^87 + 6 * q^88 - 24 * q^89 - 72 * q^90 + 74 * q^91 + 36 * q^92 + 114 * q^93 - 66 * q^94 - 8 * q^95 + 18 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/715\mathbb{Z}\right)^\times$.

$n$	$287$	$496$	$651$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.809271	−	0.467233i	0.572241	−	0.330383i	−0.185803	−	0.982587i	$-0.559489\pi$
$2$	0.809271	−	0.467233i	0.572241	−	0.330383i	0.758044	+	0.652204i	$0.226155\pi$
$3$	0.346641	+	0.600400i	0.200133	+	0.346641i	0.948571	−	0.316564i	$-0.102529\pi$
$3$	0.346641	+	0.600400i	0.200133	+	0.346641i	−0.748438	+	0.663205i	$0.769196\pi$
$4$	−0.563387	+	0.975815i	−0.281694	+	0.487908i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.561053	+	0.323924i	0.229049	+	0.132241i
$7$	0.420118	+	0.242555i	0.158790	+	0.0916773i	0.577289	−	0.816540i	$-0.304111\pi$
$7$	0.420118	+	0.242555i	0.158790	+	0.0916773i	−0.418500	+	0.908217i	$0.637444\pi$
$8$			2.92186i			1.03303i
$9$	1.25968	−	2.18183i	0.419893	−	0.727277i
$10$	−0.467233	−	0.809271i	−0.147752	−	0.255914i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	−0.781172			−0.225505
$13$	3.58349	+	0.398207i	0.993882	+	0.110443i
$13$	3.58349	+	0.398207i	0.993882	+	0.110443i
$14$	0.453319			0.121155
$15$	0.600400	−	0.346641i	0.155023	−	0.0895023i
$16$	0.238416	+	0.412948i	0.0596040	+	0.103237i
$17$	−2.35798	+	4.08414i	−0.571894	+	0.990549i	0.424477	+	0.905438i	$0.360458\pi$
$17$	−2.35798	+	4.08414i	−0.571894	+	0.990549i	−0.996371	+	0.0851110i	$0.972876\pi$
$18$		−	2.35426i		−	0.554903i
$19$	5.42814	+	3.13394i	1.24530	+	0.718975i	0.970169	−	0.242431i	$-0.0779449\pi$
$19$	5.42814	+	3.13394i	1.24530	+	0.718975i	0.275133	+	0.961406i	$0.411278\pi$
$20$	0.975815	+	0.563387i	0.218199	+	0.125977i
$21$			0.336318i			0.0733907i
$22$	0.467233	−	0.809271i	0.0996144	−	0.172537i
$23$	−0.823380	−	1.42614i	−0.171687	−	0.297370i	0.767323	−	0.641261i	$-0.221588\pi$
$23$	−0.823380	−	1.42614i	−0.171687	−	0.297370i	−0.939010	+	0.343891i	$0.888255\pi$
$24$	−1.75429	+	1.01284i	−0.358092	+	0.206745i
$25$	−1.00000			−0.200000
$26$	3.08607	−	1.35207i	0.605229	−	0.265162i
$27$	3.82647			0.736405
$28$	−0.473378	+	0.273305i	−0.0894601	+	0.0516498i
$29$	5.12779	+	8.88159i	0.952206	+	1.64927i	0.740635	+	0.671907i	$0.234525\pi$
$29$	5.12779	+	8.88159i	0.952206	+	1.64927i	0.211571	+	0.977363i	$0.432142\pi$
$30$	0.323924	−	0.561053i	0.0591402	−	0.102434i
$31$		−	1.89308i		−	0.340007i	−0.985443	−	0.170004i	$-0.945622\pi$
$31$		−	1.89308i		−	0.340007i	0.985443	−	0.170004i	$-0.0543779\pi$
$32$	−4.67493	−	2.69907i	−0.826418	−	0.477133i
$33$	0.600400	+	0.346641i	0.104516	+	0.0603425i
$34$			4.40690i			0.755777i
$35$	0.242555	−	0.420118i	0.0409993	−	0.0710129i
$36$	1.41937	+	2.45843i	0.236562	+	0.409738i
$37$	−1.49068	+	0.860647i	−0.245067	+	0.141489i	−0.617503	−	0.786568i	$-0.711856\pi$
$37$	−1.49068	+	0.860647i	−0.245067	+	0.141489i	0.372436	+	0.928058i	$0.378522\pi$
$38$	5.85712			0.950150
$39$	1.00310	+	2.28956i	0.160625	+	0.366624i
$40$	2.92186			0.461987
$41$	−2.44072	+	1.40915i	−0.381176	+	0.220072i	−0.678330	−	0.734757i	$-0.737296\pi$
$41$	−2.44072	+	1.40915i	−0.381176	+	0.220072i	0.297154	+	0.954830i	$0.403963\pi$
$42$	0.157139	+	0.272173i	0.0242471	+	0.0419972i
$43$	1.07246	−	1.85756i	0.163549	−	0.283275i	−0.772590	−	0.634905i	$-0.781039\pi$
$43$	1.07246	−	1.85756i	0.163549	−	0.283275i	0.936139	+	0.351630i	$0.114372\pi$
$44$			1.12677i			0.169868i
$45$	−2.18183	−	1.25968i	−0.325248	−	0.187782i
$46$	−1.33267	−	0.769420i	−0.196492	−	0.113445i
$47$			2.90646i			0.423951i	0.977275	+	0.211976i	$0.0679897\pi$
$47$			2.90646i			0.423951i	−0.977275	+	0.211976i	$0.932010\pi$
$48$	−0.165289	+	0.286290i	−0.0238575	+	0.0413224i
$49$	−3.38233	−	5.85837i	−0.483191	−	0.836911i
$50$	−0.809271	+	0.467233i	−0.114448	+	0.0660767i
$51$	−3.26949			−0.457820
$52$	−2.40747	+	3.27248i	−0.333856	+	0.453812i
$53$	9.25802			1.27169			0.635843	−	0.771818i	$-0.280653\pi$
$53$	9.25802			1.27169			0.635843	+	0.771818i	$0.280653\pi$
$54$	3.09665	−	1.78785i	0.421401	−	0.243296i
$55$	−0.500000	−	0.866025i	−0.0674200	−	0.116775i
$56$	−0.708713	+	1.22753i	−0.0947058	+	0.164035i
$57$			4.34541i			0.575563i
$58$	8.29954	+	4.79174i	1.08978	+	0.629187i
$59$	−8.67319	−	5.00747i	−1.12915	−	0.651917i	−0.185432	−	0.982657i	$-0.559368\pi$
$59$	−8.67319	−	5.00747i	−1.12915	−	0.651917i	−0.943722	+	0.330740i	$0.892702\pi$
$60$			0.781172i			0.100849i
$61$	7.15004	−	12.3842i	0.915468	−	1.58564i	0.109254	−	0.994014i	$-0.465154\pi$
$61$	7.15004	−	12.3842i	0.915468	−	1.58564i	0.806214	−	0.591624i	$-0.201513\pi$
$62$	−0.884509	−	1.53201i	−0.112333	−	0.194566i
$63$	1.05843	−	0.611084i	0.133349	−	0.0769894i
$64$	−5.99804			−0.749755
$65$	0.398207	−	3.58349i	0.0493916	−	0.444478i
$66$	0.647848			0.0797446
$67$	−6.20047	+	3.57984i	−0.757508	+	0.437347i	−0.828400	−	0.560137i	$-0.810749\pi$
$67$	−6.20047	+	3.57984i	−0.757508	+	0.437347i	0.0708926	+	0.997484i	$0.477415\pi$
$68$	−2.65691	−	4.60190i	−0.322198	−	0.558063i
$69$	0.570835	−	0.988714i	0.0687204	−	0.119027i
$70$		−	0.453319i		−	0.0541820i
$71$	4.12383	+	2.38089i	0.489408	+	0.282560i	0.724329	−	0.689455i	$-0.242150\pi$
$71$	4.12383	+	2.38089i	0.489408	+	0.282560i	−0.234921	+	0.972015i	$0.575483\pi$
$72$	6.37501	+	3.68061i	0.751302	+	0.433764i
$73$		−	8.36628i		−	0.979199i	−0.871947	−	0.489600i	$-0.837143\pi$
$73$		−	8.36628i		−	0.979199i	0.871947	−	0.489600i	$-0.162857\pi$
$74$	−0.804245	+	1.39299i	−0.0934916	+	0.161932i
$75$	−0.346641	−	0.600400i	−0.0400267	−	0.0693282i
$76$	−6.11629	+	3.53124i	−0.701587	+	0.405061i
$77$	0.485111			0.0552835
$78$	1.88154	+	1.38420i	0.213043	+	0.156729i
$79$	−13.1974			−1.48483			−0.742413	−	0.669942i	$-0.766319\pi$
$79$	−13.1974			−1.48483			−0.742413	+	0.669942i	$0.766319\pi$
$80$	0.412948	−	0.238416i	0.0461690	−	0.0266557i
$81$	−2.45263	−	4.24808i	−0.272514	−	0.472008i
$82$	−1.31680	+	2.28077i	−0.145416	+	0.251869i
$83$		−	0.355851i		−	0.0390598i	−0.999809	−	0.0195299i	$-0.993783\pi$
$83$		−	0.355851i		−	0.0390598i	0.999809	−	0.0195299i	$-0.00621695\pi$
$84$	−0.328185	−	0.189477i	−0.0358079	−	0.0206737i
$85$	4.08414	+	2.35798i	0.442987	+	0.255759i
$86$		−	2.00436i		−	0.216135i
$87$	−3.55500	+	6.15745i	−0.381136	+	0.660148i
$88$	1.46093	+	2.53041i	0.155736	+	0.269742i
$89$	−0.495002	+	0.285789i	−0.0524701	+	0.0302936i	−0.526006	−	0.850481i	$-0.676311\pi$
$89$	−0.495002	+	0.285789i	−0.0524701	+	0.0302936i	0.473535	+	0.880775i	$0.342978\pi$
$90$	−2.35426			−0.248160
$91$	1.40890	+	1.03649i	0.147693	+	0.108654i
$92$	1.85553			0.193452
$93$	1.13660	−	0.656219i	0.117860	−	0.0680467i
$94$	1.35799	+	2.35211i	0.140066	+	0.242602i
$95$	3.13394	−	5.42814i	0.321535	−	0.556916i
$96$		−	3.74244i		−	0.381961i
$97$	−5.73492	−	3.31106i	−0.582293	−	0.336187i	0.179751	−	0.983712i	$-0.442471\pi$
$97$	−5.73492	−	3.31106i	−0.582293	−	0.336187i	−0.762044	+	0.647525i	$0.775804\pi$
$98$	−5.47445	−	3.16067i	−0.553003	−	0.319276i
$99$		−	2.51936i		−	0.253205i
$100$	0.563387	−	0.975815i	0.0563387	−	0.0975815i
$101$	−1.24410	−	2.15484i	−0.123792	−	0.214414i	0.797468	−	0.603361i	$-0.206172\pi$
$101$	−1.24410	−	2.15484i	−0.123792	−	0.214414i	−0.921260	+	0.388947i	$0.872839\pi$
$102$	−2.64590	+	1.52761i	−0.261983	+	0.151256i
$103$	−16.7569			−1.65111			−0.825553	−	0.564325i	$-0.809136\pi$
$103$	−16.7569			−1.65111			−0.825553	+	0.564325i	$0.809136\pi$
$104$	−1.16351	+	10.4705i	−0.114091	+	1.02671i
$105$	0.336318			0.0328213
$106$	7.49224	−	4.32565i	0.727711	−	0.420144i
$107$	4.01644	+	6.95668i	0.388284	+	0.672527i	0.992219	−	0.124506i	$-0.0397347\pi$
$107$	4.01644	+	6.95668i	0.388284	+	0.672527i	−0.603935	+	0.797034i	$0.706401\pi$
$108$	−2.15579	+	3.73393i	−0.207441	+	0.359298i
$109$		−	16.6673i		−	1.59644i	−0.602369	−	0.798218i	$-0.705776\pi$
$109$		−	16.6673i		−	1.59644i	0.602369	−	0.798218i	$-0.294224\pi$
$110$	−0.809271	−	0.467233i	−0.0771610	−	0.0445489i
$111$	−1.03346	−	0.596671i	−0.0980921	−	0.0566335i
$112$			0.231316i			0.0218573i
$113$	2.21313	−	3.83326i	0.208194	−	0.360602i	−0.742952	−	0.669345i	$-0.766575\pi$
$113$	2.21313	−	3.83326i	0.208194	−	0.360602i	0.951146	+	0.308743i	$0.0999082\pi$
$114$	2.03032	+	3.51661i	0.190157	+	0.329361i
$115$	−1.42614	+	0.823380i	−0.132988	+	0.0767806i
$116$	−11.5557			−1.07292
$117$	5.38288	−	7.31696i	0.497647	−	0.676453i
$118$	−9.35862			−0.861531
$119$	−1.98126	+	1.14388i	−0.181622	+	0.104859i
$120$	1.01284	+	1.75429i	0.0924590	+	0.160144i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		−	13.3629i		−	1.20982i
$123$	−1.69211	−	0.976938i	−0.152572	−	0.0880876i
$124$	1.84730	+	1.06654i	0.165892	+	0.0957778i
$125$			1.00000i			0.0894427i
$126$	0.571037	−	0.989065i	0.0508720	−	0.0881129i
$127$	−0.730927	−	1.26600i	−0.0648593	−	0.112340i	0.831772	−	0.555117i	$-0.187327\pi$
$127$	−0.730927	−	1.26600i	−0.0648593	−	0.112340i	−0.896632	+	0.442777i	$0.853993\pi$
$128$	4.49582	−	2.59566i	0.397378	−	0.229426i
$129$	1.48704			0.130926
$130$	−1.35207	−	3.08607i	−0.118584	−	0.270667i
$131$	13.6653			1.19394			0.596970	−	0.802263i	$-0.296371\pi$
$131$	13.6653			1.19394			0.596970	+	0.802263i	$0.296371\pi$
$132$	−0.676515	+	0.390586i	−0.0588831	+	0.0339962i
$133$	1.52031	+	2.63325i	0.131827	+	0.228332i
$134$	−3.34524	+	5.79412i	−0.288985	+	0.500536i
$135$		−	3.82647i		−	0.329330i
$136$	−11.9333	−	6.88969i	−1.02327	−	0.590786i
$137$	10.9715	+	6.33441i	0.937361	+	0.541186i	0.889132	−	0.457651i	$-0.151309\pi$
$137$	10.9715	+	6.33441i	0.937361	+	0.541186i	0.0482288	+	0.998836i	$0.484642\pi$
$138$		−	1.06685i		−	0.0908163i
$139$	−0.979623	+	1.69676i	−0.0830905	+	0.143917i	−0.904576	−	0.426313i	$-0.859812\pi$
$139$	−0.979623	+	1.69676i	−0.0830905	+	0.143917i	0.821485	+	0.570230i	$0.193146\pi$
$140$	0.273305	+	0.473378i	0.0230985	+	0.0400078i
$141$	−1.74504	+	1.00750i	−0.146959	+	0.0848467i
$142$	4.44972			0.373412
$143$	3.30250	−	1.44689i	0.276169	−	0.120995i
$144$	1.20131			0.100109
$145$	8.88159	−	5.12779i	0.737576	−	0.425840i
$146$	−3.90900	−	6.77059i	−0.323511	−	0.560338i
$147$	2.34491	−	4.06151i	0.193405	−	0.334987i
$148$		−	1.93951i		−	0.159427i
$149$	−14.3871	−	8.30641i	−1.17864	−	0.680487i	−0.222939	−	0.974832i	$-0.571565\pi$
$149$	−14.3871	−	8.30641i	−1.17864	−	0.680487i	−0.955699	+	0.294345i	$0.904899\pi$
$150$	−0.561053	−	0.323924i	−0.0458098	−	0.0264483i
$151$		−	9.10563i		−	0.741005i	−0.928831	−	0.370503i	$-0.879185\pi$
$151$		−	9.10563i		−	0.741005i	0.928831	−	0.370503i	$-0.120815\pi$
$152$	−9.15694	+	15.8603i	−0.742726	+	1.28644i
$153$	5.94060	+	10.2894i	0.480269	+	0.831850i
$154$	0.392586	−	0.226660i	0.0316355	−	0.0182647i
$155$	−1.89308			−0.152056
$156$	−2.79933	−	0.311069i	−0.224125	−	0.0249054i
$157$	−15.4020			−1.22922			−0.614609	−	0.788832i	$-0.710686\pi$
$157$	−15.4020			−1.22922			−0.614609	+	0.788832i	$0.710686\pi$
$158$	−10.6803	+	6.16627i	−0.849679	+	0.490562i
$159$	3.20921	+	5.55851i	0.254507	+	0.440819i
$160$	−2.69907	+	4.67493i	−0.213380	+	0.369586i
$161$		−	0.798861i		−	0.0629590i
$162$	−3.96968	−	2.29190i	−0.311888	−	0.180068i
$163$	−1.94879	−	1.12514i	−0.152641	−	0.0881275i	0.421734	−	0.906720i	$-0.361422\pi$
$163$	−1.94879	−	1.12514i	−0.152641	−	0.0881275i	−0.574375	+	0.818592i	$0.694755\pi$
$164$		−	3.17559i		−	0.247972i
$165$	0.346641	−	0.600400i	0.0269860	−	0.0467411i
$166$	−0.166265	−	0.287980i	−0.0129047	−	0.0223516i
$167$	−12.7283	+	7.34867i	−0.984943	+	0.568657i	−0.903759	−	0.428042i	$-0.859204\pi$
$167$	−12.7283	+	7.34867i	−0.984943	+	0.568657i	−0.0811844	+	0.996699i	$0.525870\pi$
$168$	−0.982676			−0.0758151
$169$	12.6829	+	2.85395i	0.975605	+	0.219534i
$170$	4.40690			0.337994
$171$	13.6754	−	7.89552i	1.04579	−	0.603786i
$172$	1.20842	+	2.09305i	0.0921414	+	0.159594i
$173$	−2.52495	+	4.37334i	−0.191968	+	0.332499i	−0.945902	−	0.324451i	$-0.894820\pi$
$173$	−2.52495	+	4.37334i	−0.191968	+	0.332499i	0.753934	+	0.656950i	$0.228154\pi$
$174$			6.64406i			0.503685i
$175$	−0.420118	−	0.242555i	−0.0317579	−	0.0183355i
$176$	0.412948	+	0.238416i	0.0311272	+	0.0179713i
$177$		−	6.94318i		−	0.521881i
$178$	−0.267060	+	0.462562i	−0.0200170	+	0.0346705i
$179$	6.25456	+	10.8332i	0.467488	+	0.809712i	0.999310	−	0.0371437i	$-0.0118259\pi$
$179$	6.25456	+	10.8332i	0.467488	+	0.809712i	−0.531822	+	0.846856i	$0.678493\pi$
$180$	2.45843	−	1.41937i	0.183241	−	0.105794i
$181$	12.2525			0.910721			0.455361	−	0.890307i	$-0.349510\pi$
$181$	12.2525			0.910721			0.455361	+	0.890307i	$0.349510\pi$
$182$	1.62447	+	0.180515i	0.120413	+	0.0133807i
$183$	9.91398			0.732863
$184$	4.16697	−	2.40580i	0.307193	−	0.177358i
$185$	0.860647	+	1.49068i	0.0632760	+	0.109597i
$186$	0.613214	−	1.06212i	0.0449630	−	0.0778783i
$187$			4.71596i			0.344865i
$188$	−2.83617	−	1.63746i	−0.206849	−	0.119424i
$189$	1.60757	+	0.928131i	0.116934	+	0.0675116i
$190$		−	5.85712i		−	0.424920i
$191$	−3.03373	+	5.25457i	−0.219513	+	0.380207i	−0.954659	−	0.297701i	$-0.903780\pi$
$191$	−3.03373	+	5.25457i	−0.219513	+	0.380207i	0.735146	+	0.677908i	$0.237113\pi$
$192$	−2.07917	−	3.60122i	−0.150051	−	0.259896i
$193$	0.0673917	−	0.0389086i	0.00485096	−	0.00280070i	−0.497573	−	0.867422i	$-0.665775\pi$
$193$	0.0673917	−	0.0389086i	0.00485096	−	0.00280070i	0.502424	+	0.864622i	$0.332442\pi$
$194$	−6.18814			−0.444283
$195$	2.28956	−	1.00310i	0.163959	−	0.0718337i
$196$	7.62225			0.544447
$197$	−19.1129	+	11.0348i	−1.36174	+	0.786200i	−0.989855	−	0.142080i	$-0.954621\pi$
$197$	−19.1129	+	11.0348i	−1.36174	+	0.786200i	−0.371883	+	0.928280i	$0.621288\pi$
$198$	−1.17713	−	2.03884i	−0.0836548	−	0.144894i
$199$	−10.4885	+	18.1667i	−0.743513	+	1.28780i	0.207374	+	0.978262i	$0.433508\pi$
$199$	−10.4885	+	18.1667i	−0.743513	+	1.28780i	−0.950886	+	0.309540i	$0.899825\pi$
$200$		−	2.92186i		−	0.206607i
$201$	−4.29867	−	2.48184i	−0.303205	−	0.175055i
$202$	−2.01362	−	1.16257i	−0.141678	−	0.0817978i
$203$			4.97509i			0.349183i
$204$	1.84199	−	3.19042i	0.128965	−	0.223374i
$205$	1.40915	+	2.44072i	0.0984193	+	0.170467i
$206$	−13.5609	+	7.82937i	−0.944830	+	0.545498i
$207$	−4.14878			−0.288360
$208$	0.689923	+	1.57474i	0.0478375	+	0.109188i
$209$	6.26788			0.433558
$210$	0.272173	−	0.157139i	0.0187817	−	0.0108436i
$211$	−10.9485	−	18.9633i	−0.753724	−	1.30549i	−0.946006	−	0.324149i	$-0.894922\pi$
$211$	−10.9485	−	18.9633i	−0.753724	−	1.30549i	0.192282	−	0.981340i	$-0.438411\pi$
$212$	−5.21585	+	9.03411i	−0.358226	+	0.620465i
$213$			3.30126i			0.226199i
$214$	6.50077	+	3.75322i	0.444384	+	0.256565i
$215$	−1.85756	−	1.07246i	−0.126684	−	0.0731413i
$216$			11.1804i			0.760732i
$217$	0.459176	−	0.795317i	0.0311709	−	0.0539896i
$218$	−7.78750	−	13.4883i	−0.527436	−	0.913546i
$219$	5.02311	−	2.90010i	0.339431	−	0.195970i
$220$	1.12677			0.0759671
$221$	−10.0761	+	13.6965i	−0.677795	+	0.921328i
$222$	−1.11514			−0.0748431
$223$	−6.33406	+	3.65697i	−0.424160	+	0.244889i	−0.696856	−	0.717212i	$-0.745418\pi$
$223$	−6.33406	+	3.65697i	−0.424160	+	0.244889i	0.272696	+	0.962100i	$0.412085\pi$
$224$	−1.30935	−	2.26786i	−0.0874845	−	0.151528i
$225$	−1.25968	+	2.18183i	−0.0839787	+	0.145455i
$226$		−	4.13619i		−	0.275135i
$227$	15.7935	+	9.11836i	1.04825	+	0.605207i	0.922158	−	0.386812i	$-0.126424\pi$
$227$	15.7935	+	9.11836i	1.04825	+	0.605207i	0.126090	+	0.992019i	$0.459757\pi$
$228$	−4.24031	−	2.44815i	−0.280822	−	0.162132i
$229$		−	2.75048i		−	0.181757i	−0.995862	−	0.0908784i	$-0.971033\pi$
$229$		−	2.75048i		−	0.181757i	0.995862	−	0.0908784i	$-0.0289674\pi$
$230$	−0.769420	+	1.33267i	−0.0507341	+	0.0878740i
$231$	0.168159	+	0.291260i	0.0110641	+	0.0191635i
$232$	−25.9508	+	14.9827i	−1.70375	+	0.983662i
$233$	−14.9838			−0.981619			−0.490810	−	0.871267i	$-0.663299\pi$
$233$	−14.9838			−0.981619			−0.490810	+	0.871267i	$0.663299\pi$
$234$	0.937482	−	8.43646i	0.0612851	−	0.551509i
$235$	2.90646			0.189597
$236$	9.77273	−	5.64229i	0.636151	−	0.367282i
$237$	−4.57477	−	7.92373i	−0.297163	−	0.514702i
$238$	−1.06892	+	1.85142i	−0.0692876	+	0.120010i
$239$		−	13.9019i		−	0.899239i	−0.893220	−	0.449620i	$-0.851560\pi$
$239$		−	13.9019i		−	0.899239i	0.893220	−	0.449620i	$-0.148440\pi$
$240$	0.286290	+	0.165289i	0.0184799	+	0.0106694i
$241$	−15.3550	−	8.86522i	−0.989103	−	0.571059i	−0.0840969	−	0.996458i	$-0.526801\pi$
$241$	−15.3550	−	8.86522i	−0.989103	−	0.571059i	−0.905006	+	0.425399i	$0.860134\pi$
$242$		−	0.934466i		−	0.0600697i
$243$	7.44007	−	12.8866i	0.477281	−	0.826675i
$244$	8.05648	+	13.9542i	0.515763	+	0.893328i
$245$	−5.85837	+	3.38233i	−0.374278	+	0.216089i
$246$	−1.82583			−0.116411
$247$	18.2038	+	13.3920i	1.15828	+	0.852111i
$248$	5.53132			0.351239
$249$	0.213653	−	0.123353i	0.0135397	−	0.00781716i
$250$	0.467233	+	0.809271i	0.0295504	+	0.0511828i
$251$	−9.02122	+	15.6252i	−0.569415	+	0.986255i	0.427209	+	0.904153i	$0.359497\pi$
$251$	−9.02122	+	15.6252i	−0.569415	+	0.986255i	−0.996624	+	0.0821022i	$0.973837\pi$
$252$			1.37711i			0.0867496i
$253$	−1.42614	−	0.823380i	−0.0896604	−	0.0517655i
$254$	−1.18304	−	0.683026i	−0.0742303	−	0.0428569i
$255$			3.26949i			0.204743i
$256$	8.42360	−	14.5901i	0.526475	−	0.911881i
$257$	10.5181	+	18.2178i	0.656098	+	1.13640i	0.981617	+	0.190860i	$0.0611276\pi$
$257$	10.5181	+	18.2178i	0.656098	+	1.13640i	−0.325519	+	0.945535i	$0.605539\pi$
$258$	1.20342	−	0.694793i	0.0749214	−	0.0432559i
$259$	−0.835018			−0.0518855
$260$	3.27248	+	2.40747i	0.202951	+	0.149305i
$261$	25.8375			1.59930
$262$	11.0589	−	6.38487i	0.683222	−	0.394458i
$263$	−2.79553	−	4.84201i	−0.172380	−	0.298571i	0.766871	−	0.641801i	$-0.221812\pi$
$263$	−2.79553	−	4.84201i	−0.172380	−	0.298571i	−0.939251	+	0.343230i	$0.888479\pi$
$264$	−1.01284	+	1.75429i	−0.0623358	+	0.107969i
$265$		−	9.25802i		−	0.568715i
$266$	2.46068	+	1.42067i	0.150874	+	0.0871071i
$267$	−0.343176	−	0.198133i	−0.0210020	−	0.0121255i
$268$		−	8.06734i		−	0.492792i
$269$	10.9002	−	18.8798i	0.664599	−	1.15112i	−0.314794	−	0.949160i	$-0.601936\pi$
$269$	10.9002	−	18.8798i	0.664599	−	1.15112i	0.979394	−	0.201960i	$-0.0647311\pi$
$270$	−1.78785	−	3.09665i	−0.108805	−	0.188456i
$271$	14.2552	−	8.23024i	0.865942	−	0.499952i	−5.58149e−5	−	1.00000i	$-0.500018\pi$
$271$	14.2552	−	8.23024i	0.865942	−	0.499952i	0.865997	+	0.500048i	$0.166684\pi$
$272$	−2.24872			−0.136349
$273$	−0.133924	+	1.20520i	−0.00810548	+	0.0729417i
$274$	11.8386			0.715195
$275$	−0.866025	+	0.500000i	−0.0522233	+	0.0301511i
$276$	0.643202	+	1.11406i	0.0387162	+	0.0670584i
$277$	2.06480	−	3.57635i	0.124062	−	0.214882i	−0.797304	−	0.603578i	$-0.793741\pi$
$277$	2.06480	−	3.57635i	0.124062	−	0.214882i	0.921366	+	0.388696i	$0.127074\pi$
$278$			1.83085i			0.109807i
$279$	−4.13038	−	2.38467i	−0.247279	−	0.142767i
$280$	1.22753	+	0.708713i	0.0733588	+	0.0423537i
$281$		−	25.7497i		−	1.53610i	−0.640391	−	0.768049i	$-0.721228\pi$
$281$		−	25.7497i		−	1.53610i	0.640391	−	0.768049i	$-0.278772\pi$
$282$	−0.941473	+	1.63068i	−0.0560639	+	0.0971055i
$283$	9.97168	+	17.2714i	0.592755	+	1.02668i	0.993860	+	0.110649i	$0.0352929\pi$
$283$	9.97168	+	17.2714i	0.592755	+	1.02668i	−0.401105	+	0.916032i	$0.631374\pi$
$284$	−4.64662	+	2.68273i	−0.275726	+	0.159191i
$285$	4.34541			0.257400
$286$	1.99658	−	2.71396i	0.118060	−	0.160480i
$287$	−1.36719			−0.0807025
$288$	−11.7778	+	6.79993i	−0.694015	+	0.400690i
$289$	−2.62013	−	4.53820i	−0.154125	−	0.266953i
$290$	4.79174	−	8.29954i	0.281381	−	0.487366i
$291$		−	4.59100i		−	0.269129i
$292$	8.16394	+	4.71345i	0.477759	+	0.275834i
$293$	16.8643	+	9.73660i	0.985222	+	0.568818i	0.903843	−	0.427865i	$-0.140734\pi$
$293$	16.8643	+	9.73660i	0.985222	+	0.568818i	0.0813796	+	0.996683i	$0.474067\pi$
$294$		−	4.38248i		−	0.255591i
$295$	−5.00747	+	8.67319i	−0.291546	+	0.504973i
$296$	−2.51469	−	4.35557i	−0.146163	−	0.253163i
$297$	3.31382	−	1.91324i	0.192288	−	0.111017i
$298$	−15.5241			−0.899287
$299$	−2.38268	−	5.43843i	−0.137794	−	0.314512i
$300$	0.781172			0.0451010
$301$	0.901122	−	0.520263i	0.0519398	−	0.0299875i
$302$	−4.25445	−	7.36892i	−0.244816	−	0.424034i
$303$	0.862510	−	1.49391i	0.0495499	−	0.0858229i
$304$			2.98872i			0.171415i
$305$	−12.3842	−	7.15004i	−0.709119	−	0.409410i
$306$	9.61511	+	5.55129i	0.549659	+	0.317346i
$307$		−	21.7876i		−	1.24348i	−0.783222	−	0.621742i	$-0.786425\pi$
$307$		−	21.7876i		−	1.24348i	0.783222	−	0.621742i	$-0.213575\pi$
$308$	−0.273305	+	0.473378i	−0.0155730	+	0.0269732i
$309$	−5.80862	−	10.0608i	−0.330441	−	0.572341i
$310$	−1.53201	+	0.884509i	−0.0870126	+	0.0502367i
$311$	−4.99148			−0.283041			−0.141520	−	0.989935i	$-0.545199\pi$
$311$	−4.99148			−0.283041			−0.141520	+	0.989935i	$0.545199\pi$
$312$	−6.68979	+	2.93093i	−0.378735	+	0.165931i
$313$	−3.04003			−0.171833			−0.0859163	−	0.996302i	$-0.527382\pi$
$313$	−3.04003			−0.171833			−0.0859163	+	0.996302i	$0.527382\pi$
$314$	−12.4644	+	7.19634i	−0.703408	+	0.406113i
$315$	−0.611084	−	1.05843i	−0.0344307	−	0.0596357i
$316$	7.43526	−	12.8782i	0.418266	−	0.724458i
$317$		−	11.2479i		−	0.631743i	−0.948802	−	0.315871i	$-0.897703\pi$
$317$		−	11.2479i		−	0.631743i	0.948802	−	0.315871i	$-0.102297\pi$
$318$	5.19424	+	2.99889i	0.291278	+	0.168170i
$319$	8.88159	+	5.12779i	0.497274	+	0.287101i
$320$			5.99804i			0.335301i
$321$	−2.78452	+	4.82294i	−0.155417	+	0.269190i
$322$	−0.373254	−	0.646495i	−0.0208006	−	0.0360277i
$323$	−25.5989	+	14.7795i	−1.42436	+	0.822355i
$324$	5.52711			0.307062
$325$	−3.58349	−	0.398207i	−0.198776	−	0.0220886i
$326$	−2.10280			−0.116464
$327$	10.0070	−	5.77756i	0.553390	−	0.319500i
$328$	−4.11734	−	7.13145i	−0.227342	−	0.393768i
$329$	−0.704978	+	1.22106i	−0.0388667	+	0.0673191i
$330$		−	0.647848i		−	0.0356629i
$331$	8.43495	+	4.86992i	0.463627	+	0.267675i	0.713568	−	0.700586i	$-0.247078\pi$
$331$	8.43495	+	4.86992i	0.463627	+	0.267675i	−0.249941	+	0.968261i	$0.580411\pi$
$332$	0.347245	+	0.200482i	0.0190576	+	0.0110029i
$333$			4.33656i			0.237642i
$334$	−6.86708	+	11.8941i	−0.375750	+	0.650818i
$335$	3.57984	+	6.20047i	0.195588	+	0.338768i
$336$	−0.138882	+	0.0801837i	−0.00757664	+	0.00437438i
$337$	28.7492			1.56607			0.783034	−	0.621978i	$-0.213671\pi$
$337$	28.7492			1.56607			0.783034	+	0.621978i	$0.213671\pi$
$338$	11.5973	−	3.61623i	0.630812	−	0.196697i
$339$	3.06865			0.166666
$340$	−4.60190	+	2.65691i	−0.249573	+	0.144091i
$341$	−0.946540	−	1.63945i	−0.0512580	−	0.0887815i
$342$	7.37809	−	12.7792i	0.398962	−	0.691022i
$343$		−	6.67739i		−	0.360545i
$344$	5.42753	+	3.13359i	0.292633	+	0.168952i
$345$	−0.988714	−	0.570835i	−0.0532306	−	0.0307327i
$346$			4.71895i			0.253693i
$347$	−11.5630	+	20.0277i	−0.620734	+	1.07514i	0.368616	+	0.929582i	$0.379832\pi$
$347$	−11.5630	+	20.0277i	−0.620734	+	1.07514i	−0.989349	+	0.145561i	$0.953501\pi$
$348$	−4.00569	−	6.93805i	−0.214727	−	0.371919i
$349$	−7.63171	+	4.40617i	−0.408516	+	0.235857i	−0.690152	−	0.723665i	$-0.742456\pi$
$349$	−7.63171	+	4.40617i	−0.408516	+	0.235857i	0.281636	+	0.959521i	$0.409123\pi$
$350$	−0.453319			−0.0242309
$351$	13.7121	+	1.52373i	0.731900	+	0.0813307i
$352$	−5.39814			−0.287722
$353$	11.6787	−	6.74268i	0.621592	−	0.358876i	−0.155896	−	0.987773i	$-0.549827\pi$
$353$	11.6787	−	6.74268i	0.621592	−	0.358876i	0.777489	+	0.628897i	$0.216493\pi$
$354$	−3.24408	−	5.61891i	−0.172421	−	0.298642i
$355$	2.38089	−	4.12383i	0.126365	−	0.218870i
$356$		−	0.644040i		−	0.0341341i
$357$	−1.37357	−	0.793032i	−0.0726971	−	0.0419717i
$358$	10.1233	+	5.84467i	0.535031	+	0.308900i
$359$		−	33.0899i		−	1.74642i	−0.487348	−	0.873208i	$-0.662036\pi$
$359$		−	33.0899i		−	1.74642i	0.487348	−	0.873208i	$-0.337964\pi$
$360$	3.68061	−	6.37501i	0.193985	−	0.335992i
$361$	10.1431	+	17.5684i	0.533850	+	0.924655i
$362$	9.91560	−	5.72477i	0.521152	−	0.300887i
$363$	0.693282			0.0363879
$364$	−1.80518	+	0.790884i	−0.0946172	+	0.0414536i
$365$	−8.36628			−0.437911
$366$	8.02310	−	4.63214i	0.419374	−	0.242126i
$367$	17.0911	+	29.6026i	0.892148	+	1.54525i	0.837295	+	0.546751i	$0.184136\pi$
$367$	17.0911	+	29.6026i	0.892148	+	1.54525i	0.0548529	+	0.998494i	$0.482531\pi$
$368$	0.392614	−	0.680027i	0.0204664	−	0.0354489i
$369$			7.10031i			0.369627i
$370$	1.39299	+	0.804245i	0.0724183	+	0.0418107i
$371$	3.88946	+	2.24558i	0.201931	+	0.116585i
$372$			1.47882i			0.0766733i
$373$	−10.9979	+	19.0489i	−0.569448	+	0.986313i	0.427172	+	0.904170i	$0.359510\pi$
$373$	−10.9979	+	19.0489i	−0.569448	+	0.986313i	−0.996621	+	0.0821431i	$0.973824\pi$
$374$	2.20345	+	3.81649i	0.113938	+	0.197346i
$375$	−0.600400	+	0.346641i	−0.0310045	+	0.0179005i
$376$	−8.49228			−0.437956
$377$	14.8387	+	33.8691i	0.764231	+	1.74434i
$378$	1.73461			0.0892189
$379$	0.323524	−	0.186786i	0.0166183	−	0.00959458i	−0.491668	−	0.870783i	$-0.663613\pi$
$379$	0.323524	−	0.186786i	0.0166183	−	0.00959458i	0.508286	+	0.861188i	$0.330279\pi$
$380$	3.53124	+	6.11629i	0.181149	+	0.313759i
$381$	0.506738	−	0.877697i	0.0259610	−	0.0449658i
$382$			5.66983i			0.290094i
$383$	15.1627	+	8.75419i	0.774778	+	0.447318i	0.834576	−	0.550892i	$-0.185713\pi$
$383$	15.1627	+	8.75419i	0.774778	+	0.447318i	−0.0597986	+	0.998210i	$0.519046\pi$
$384$	3.11687	+	1.79952i	0.159057	+	0.0918316i
$385$		−	0.485111i		−	0.0247235i
$386$	0.0363587	−	0.0629752i	0.00185061	−	0.00320535i
$387$	−2.70192	−	4.67986i	−0.137346	−	0.237891i
$388$	6.46196	−	3.73082i	0.328056	−	0.189404i
$389$	−18.0925			−0.917325			−0.458663	−	0.888610i	$-0.651671\pi$
$389$	−18.0925			−0.917325			−0.458663	+	0.888610i	$0.651671\pi$
$390$	1.38420	−	1.88154i	0.0700915	−	0.0952755i
$391$	7.76605			0.392746
$392$	17.1174	−	9.88272i	0.864557	−	0.499152i
$393$	4.73695	+	8.20463i	0.238947	+	0.413869i
$394$	−10.3117	+	17.8604i	−0.519495	+	0.899792i
$395$			13.1974i			0.664035i
$396$	2.45843	+	1.41937i	0.123541	+	0.0713263i
$397$	−12.3385	−	7.12362i	−0.619251	−	0.357524i	0.157327	−	0.987547i	$-0.449712\pi$
$397$	−12.3385	−	7.12362i	−0.619251	−	0.357524i	−0.776577	+	0.630022i	$0.783046\pi$
$398$			19.6024i			0.982577i
$399$	−1.05400	+	1.82558i	−0.0527661	+	0.0913935i
$400$	−0.238416	−	0.412948i	−0.0119208	−	0.0206474i
$401$	11.9636	−	6.90717i	0.597432	−	0.344928i	−0.170598	−	0.985341i	$-0.554570\pi$
$401$	11.9636	−	6.90717i	0.597432	−	0.344928i	0.768031	+	0.640413i	$0.221237\pi$
$402$	−4.63839			−0.231342
$403$	0.753838	−	6.78384i	0.0375514	−	0.337927i
$404$	2.80363			0.139486
$405$	−4.24808	+	2.45263i	−0.211089	+	0.121872i
$406$	2.32452	+	4.02619i	0.115364	+	0.199817i
$407$	−0.860647	+	1.49068i	−0.0426607	+	0.0738905i
$408$		−	9.55300i		−	0.472944i
$409$	0.614063	+	0.354529i	0.0303634	+	0.0175303i	0.515105	−	0.857127i	$-0.327753\pi$
$409$	0.614063	+	0.354529i	0.0303634	+	0.0175303i	−0.484741	+	0.874657i	$0.661086\pi$
$410$	2.28077	+	1.31680i	0.112639	+	0.0650322i
$411$			8.78307i			0.433237i
$412$	9.44061	−	16.3516i	0.465106	−	0.805587i
$413$	−2.42918	−	4.20746i	−0.119532	−	0.207035i
$414$	−3.35749	+	1.93845i	−0.165012	+	0.0952695i
$415$	−0.355851			−0.0174681
$416$	−15.6778	−	11.5337i	−0.768667	−	0.565486i
$417$	−1.35831			−0.0665167
$418$	5.07241	−	2.92856i	0.248100	−	0.143240i
$419$	−10.2025	−	17.6713i	−0.498426	−	0.863300i	0.501572	−	0.865116i	$-0.332755\pi$
$419$	−10.2025	−	17.6713i	−0.498426	−	0.863300i	−0.999998	+	0.00181615i	$0.999422\pi$
$420$	−0.189477	+	0.328185i	−0.00924555	+	0.0160138i
$421$		−	10.1539i		−	0.494872i	−0.968904	−	0.247436i	$-0.920412\pi$
$421$		−	10.1539i		−	0.494872i	0.968904	−	0.247436i	$-0.0795881\pi$
$422$	−17.7206	−	10.2310i	−0.862623	−	0.498036i
$423$	6.34140	+	3.66121i	0.308330	+	0.178014i
$424$			27.0507i			1.31370i
$425$	2.35798	−	4.08414i	0.114379	−	0.198110i
$426$	1.54246	+	2.67161i	0.0747323	+	0.129440i
$427$	6.00772	−	3.46856i	0.290734	−	0.167855i
$428$	−9.05124			−0.437508
$429$	2.01349	+	1.48127i	0.0972124	+	0.0715164i
$430$	−2.00436			−0.0966587
$431$	18.1356	−	10.4706i	0.873562	−	0.504351i	0.00503187	−	0.999987i	$-0.498398\pi$
$431$	18.1356	−	10.4706i	0.873562	−	0.504351i	0.868530	+	0.495636i	$0.165065\pi$
$432$	0.912292	+	1.58014i	0.0438927	+	0.0760243i
$433$	12.8681	−	22.2882i	0.618400	−	1.07110i	−0.371378	−	0.928482i	$-0.621114\pi$
$433$	12.8681	−	22.2882i	0.618400	−	1.07110i	0.989778	−	0.142619i	$-0.0455522\pi$
$434$		−	0.858169i		−	0.0411934i
$435$	6.15745	+	3.55500i	0.295227	+	0.170449i
$436$	16.2642	+	9.39013i	0.778913	+	0.449706i
$437$		−	10.3217i		−	0.493753i
$438$	2.71004	−	4.69393i	0.129491	−	0.224284i
$439$	20.3015	+	35.1632i	0.968937	+	1.67825i	0.698643	+	0.715471i	$0.253788\pi$
$439$	20.3015	+	35.1632i	0.968937	+	1.67825i	0.270294	+	0.962778i	$0.412879\pi$
$440$	2.53041	−	1.46093i	0.120632	−	0.0696472i
$441$	−17.0426			−0.811554
$442$	−1.75486	+	15.7921i	−0.0834702	+	0.751154i
$443$	−6.46840			−0.307323			−0.153662	−	0.988124i	$-0.549107\pi$
$443$	−6.46840			−0.307323			−0.153662	+	0.988124i	$0.549107\pi$
$444$	1.16448	−	0.672313i	0.0552638	−	0.0319066i
$445$	0.285789	+	0.495002i	0.0135477	+	0.0234653i
$446$	−3.41731	+	5.91896i	−0.161814	+	0.280271i
$447$		−	11.5174i		−	0.544753i
$448$	−2.51989	−	1.45486i	−0.119053	−	0.0687355i
$449$	−24.9420	−	14.4003i	−1.17709	−	0.679591i	−0.221747	−	0.975104i	$-0.571176\pi$
$449$	−24.9420	−	14.4003i	−1.17709	−	0.679591i	−0.955339	+	0.295514i	$0.904509\pi$
$450$			2.35426i			0.110981i
$451$	−1.40915	+	2.44072i	−0.0663543	+	0.114929i
$452$	2.49370	+	4.31921i	0.117294	+	0.203159i
$453$	5.46702	−	3.15638i	0.256863	−	0.148300i
$454$	17.0416			0.799801
$455$	1.03649	−	1.40890i	0.0485914	−	0.0660504i
$456$	−12.6967			−0.594577
$457$	31.2900	−	18.0653i	1.46368	−	0.845059i	0.464506	−	0.885570i	$-0.346232\pi$
$457$	31.2900	−	18.0653i	1.46368	−	0.845059i	0.999179	+	0.0405115i	$0.0128987\pi$
$458$	−1.28511	−	2.22588i	−0.0600494	−	0.104009i
$459$	−9.02274	+	15.6279i	−0.421146	+	0.729446i
$460$		−	1.85553i		−	0.0865144i
$461$	19.3358	+	11.1635i	0.900557	+	0.519937i	0.877381	−	0.479794i	$-0.159289\pi$
$461$	19.3358	+	11.1635i	0.900557	+	0.519937i	0.0231764	+	0.999731i	$0.492622\pi$
$462$	0.272173	+	0.157139i	0.0126626	+	0.00731077i
$463$		−	8.38209i		−	0.389549i	−0.980848	−	0.194774i	$-0.937603\pi$
$463$		−	8.38209i		−	0.389549i	0.980848	−	0.194774i	$-0.0623975\pi$
$464$	−2.44509	+	4.23502i	−0.113511	+	0.196606i
$465$	−0.656219	−	1.13660i	−0.0304314	−	0.0527088i
$466$	−12.1259	+	7.00091i	−0.561723	+	0.324311i
$467$	−36.9610			−1.71035			−0.855176	−	0.518338i	$-0.826551\pi$
$467$	−36.9610			−1.71035			−0.855176	+	0.518338i	$0.826551\pi$
$468$	4.10736	+	9.37497i	0.189863	+	0.433358i
$469$	−3.47324			−0.160379
$470$	2.35211	−	1.35799i	0.108495	−	0.0626396i
$471$	−5.33898	−	9.24739i	−0.246007	−	0.426097i
$472$	14.6311	−	25.3419i	0.673453	−	1.16645i
$473$		−	2.14492i		−	0.0986237i
$474$	−7.40446	−	4.27496i	−0.340098	−	0.196356i
$475$	−5.42814	−	3.13394i	−0.249060	−	0.143795i
$476$		−	2.57779i		−	0.118153i
$477$	11.6621	−	20.1994i	0.533973	−	0.924868i
$478$	−6.49542	−	11.2504i	−0.297094	−	0.514582i
$479$	−11.7974	+	6.81123i	−0.539037	+	0.311213i	−0.744688	−	0.667412i	$-0.767402\pi$
$479$	−11.7974	+	6.81123i	−0.539037	+	0.311213i	0.205652	+	0.978625i	$0.434069\pi$
$480$	−3.74244			−0.170818
$481$	−5.68457	+	2.49052i	−0.259194	+	0.113558i
$482$	−16.5685			−0.754674
$483$	0.479636	−	0.276918i	0.0218242	−	0.0126002i
$484$	0.563387	+	0.975815i	0.0256085	+	0.0443552i
$485$	−3.31106	+	5.73492i	−0.150347	+	0.260409i
$486$		−	13.9050i		−	0.630743i
$487$	8.35422	+	4.82331i	0.378566	+	0.218565i	0.677194	−	0.735804i	$-0.263196\pi$
$487$	8.35422	+	4.82331i	0.378566	+	0.218565i	−0.298628	+	0.954369i	$0.596529\pi$
$488$	36.1850	+	20.8914i	1.63802	+	0.945710i
$489$		−	1.56007i		−	0.0705490i
$490$	−3.16067	+	5.47445i	−0.142785	+	0.247310i
$491$	12.1237	+	20.9989i	0.547135	+	0.947666i	0.998469	+	0.0553108i	$0.0176150\pi$
$491$	12.1237	+	20.9989i	0.547135	+	0.947666i	−0.451334	+	0.892355i	$0.649052\pi$
$492$	1.90662	−	1.10079i	0.0859572	−	0.0496274i
$493$	−48.3649			−2.17824
$494$	20.9889	+	2.33235i	0.944337	+	0.104937i
$495$	−2.51936			−0.113237
$496$	0.781744	−	0.451340i	0.0351014	−	0.0202658i
$497$	1.15500	+	2.00051i	0.0518086	+	0.0897352i
$498$	0.115269	−	0.199651i	0.00516532	−	0.00894660i
$499$		−	36.9871i		−	1.65577i	−0.560898	−	0.827885i	$-0.689544\pi$
$499$		−	36.9871i		−	1.65577i	0.560898	−	0.827885i	$-0.310456\pi$
$500$	−0.975815	−	0.563387i	−0.0436398	−	0.0251954i
$501$	−8.82428	−	5.09470i	−0.394240	−	0.227614i
$502$			16.8600i			0.752501i
$503$	−16.3347	+	28.2925i	−0.728326	+	1.26150i	0.229264	+	0.973364i	$0.426368\pi$
$503$	−16.3347	+	28.2925i	−0.728326	+	1.26150i	−0.957590	+	0.288134i	$0.906965\pi$
$504$	1.78550	+	3.09258i	0.0795327	+	0.137755i
$505$	−2.15484	+	1.24410i	−0.0958890	+	0.0553616i
$506$	−1.53884			−0.0684098
$507$	2.68289	+	8.60408i	0.119151	+	0.382121i
$508$	1.64718			0.0730817
$509$	−1.39101	+	0.803099i	−0.0616554	+	0.0355967i	−0.530511	−	0.847678i	$-0.678000\pi$
$509$	−1.39101	+	0.803099i	−0.0616554	+	0.0355967i	0.468855	+	0.883275i	$0.344667\pi$
$510$	1.52761	+	2.64590i	0.0676438	+	0.117163i
$511$	2.02929	−	3.51483i	0.0897703	−	0.155487i
$512$		−	5.36048i		−	0.236902i
$513$	20.7706	+	11.9919i	0.917046	+	0.529457i
$514$	17.0239	+	9.82876i	0.750892	+	0.433528i
$515$			16.7569i			0.738397i
$516$	−0.837778	+	1.45107i	−0.0368811	+	0.0638800i
$517$	1.45323	+	2.51707i	0.0639130	+	0.110701i
$518$	−0.675756	+	0.390148i	−0.0296910	+	0.0171421i
$519$	−3.50100			−0.153677
$520$	10.4705	+	1.16351i	0.459161	+	0.0510232i
$521$	−9.12602			−0.399818			−0.199909	−	0.979814i	$-0.564065\pi$
$521$	−9.12602			−0.399818			−0.199909	+	0.979814i	$0.564065\pi$
$522$	20.9095	−	12.0721i	0.915185	−	0.528382i
$523$	11.0917	+	19.2115i	0.485008	+	0.840059i	0.999852	−	0.0172254i	$-0.00548328\pi$
$523$	11.0917	+	19.2115i	0.485008	+	0.840059i	−0.514843	+	0.857284i	$0.672150\pi$
$524$	−7.69884	+	13.3348i	−0.336325	+	0.582533i
$525$		−	0.336318i		−	0.0146781i
$526$	−4.52469	−	2.61233i	−0.197286	−	0.113903i
$527$	7.73160	+	4.46384i	0.336794	+	0.194448i
$528$			0.330579i			0.0143866i
$529$	10.1441	−	17.5701i	0.441047	−	0.763917i
$530$	−4.32565	−	7.49224i	−0.187894	−	0.325442i
$531$	−21.8509	+	12.6156i	−0.948248	+	0.547471i
$532$	−3.42609			−0.148540
$533$	−9.30744	+	4.07777i	−0.403150	+	0.176628i
$534$	−0.370296			−0.0160243
$535$	6.95668	−	4.01644i	0.300763	−	0.173646i
$536$	−10.4598	−	18.1169i	−0.451795	−	0.782531i
$537$	−4.33617	+	7.51047i	−0.187120	+	0.324101i
$538$		−	20.3718i		−	0.878291i
$539$	−5.85837	−	3.38233i	−0.252338	−	0.145687i
$540$	3.73393	+	2.15579i	0.160683	+	0.0927702i
$541$		−	2.71087i		−	0.116549i	−0.998301	−	0.0582746i	$-0.981440\pi$
$541$		−	2.71087i		−	0.116549i	0.998301	−	0.0582746i	$-0.0185599\pi$
$542$	7.69088	−	13.3210i	0.330352	−	0.572186i
$543$	4.24722	+	7.35640i	0.182266	+	0.315693i
$544$	22.0468	−	12.7287i	0.945247	−	0.545739i
$545$	−16.6673			−0.713948
$546$	0.454726	+	1.03790i	0.0194605	+	0.0444182i
$547$	−1.46672			−0.0627125			−0.0313563	−	0.999508i	$-0.509983\pi$
$547$	−1.46672			−0.0627125			−0.0313563	+	0.999508i	$0.509983\pi$
$548$	−12.3624	+	7.13745i	−0.528097	+	0.304897i
$549$	−18.0135	−	31.2003i	−0.768798	−	1.33160i
$550$	−0.467233	+	0.809271i	−0.0199229	+	0.0345074i
$551$			64.2807i			2.73845i
$552$	2.88889	+	1.66790i	0.122959	+	0.0709905i
$553$	−5.54448	−	3.20111i	−0.235775	−	0.136125i
$554$		−	3.85898i		−	0.163952i
$555$	−0.596671	+	1.03346i	−0.0253273	+	0.0438681i
$556$	−1.10381	−	1.91186i	−0.0468121	−	0.0810810i
$557$	−19.6545	+	11.3475i	−0.832787	+	0.480810i	−0.854806	−	0.518948i	$-0.826324\pi$
$557$	−19.6545	+	11.3475i	−0.832787	+	0.480810i	0.0220188	+	0.999758i	$0.492991\pi$
$558$	−4.45679			−0.188671
$559$	4.58286	−	6.22949i	0.193834	−	0.263479i
$560$	0.231316			0.00977489
$561$	−2.83146	+	1.63474i	−0.119544	+	0.0690190i
$562$	−12.0311	−	20.8385i	−0.507501	−	0.879018i
$563$	9.18955	−	15.9168i	0.387293	−	0.670812i	−0.604791	−	0.796384i	$-0.706743\pi$
$563$	9.18955	−	15.9168i	0.387293	−	0.670812i	0.992084	+	0.125572i	$0.0400768\pi$
$564$		−	2.27045i		−	0.0956031i
$565$	−3.83326	−	2.21313i	−0.161266	−	0.0931071i
$566$	16.1396	+	9.31819i	0.678397	+	0.391673i
$567$		−	2.37959i		−	0.0999334i
$568$	−6.95664	+	12.0493i	−0.291894	+	0.505575i
$569$	−8.44285	−	14.6234i	−0.353943	−	0.613047i	0.632994	−	0.774157i	$-0.281826\pi$
$569$	−8.44285	−	14.6234i	−0.353943	−	0.613047i	−0.986936	+	0.161110i	$0.948493\pi$
$570$	3.51661	−	2.03032i	0.147295	−	0.0850406i
$571$	19.9745			0.835906			0.417953	−	0.908469i	$-0.362748\pi$
$571$	19.9745			0.835906			0.417953	+	0.908469i	$0.362748\pi$
$572$	−0.448690	+	4.03779i	−0.0187607	+	0.168828i
$573$	−4.20646			−0.175727
$574$	−1.10642	+	0.638795i	−0.0461813	+	0.0266628i
$575$	0.823380	+	1.42614i	0.0343373	+	0.0594740i
$576$	−7.55561	+	13.0867i	−0.314817	+	0.545279i
$577$		−	34.4390i		−	1.43371i	−0.697221	−	0.716857i	$-0.745580\pi$
$577$		−	34.4390i		−	1.43371i	0.697221	−	0.716857i	$-0.254420\pi$
$578$	−4.24080	−	2.44842i	−0.176394	−	0.101841i
$579$	0.0467214	+	0.0269746i	0.00194168	+	0.00112103i
$580$			11.5557i			0.479825i
$581$	0.0863136	−	0.149500i	0.00358089	−	0.00620229i
$582$	−2.14506	−	3.71536i	−0.0889158	−	0.154007i
$583$	8.01768	−	4.62901i	0.332058	−	0.191714i
$584$	24.4451			1.01155
$585$	−7.31696	−	5.38288i	−0.302519	−	0.222555i
$586$	18.1970			0.751713
$587$	−16.3914	+	9.46355i	−0.676544	+	0.390603i	−0.798552	−	0.601926i	$-0.794400\pi$
$587$	−16.3914	+	9.46355i	−0.676544	+	0.390603i	0.122008	+	0.992529i	$0.461067\pi$
$588$	2.64219	+	4.57640i	0.108962	+	0.188728i
$589$	5.93280	−	10.2759i	0.244457	−	0.423411i
$590$			9.35862i			0.385288i
$591$	−13.2506	−	7.65026i	−0.545058	−	0.314690i
$592$	−0.710806	−	0.410384i	−0.0292139	−	0.0168667i
$593$			20.2898i			0.833202i	0.909089	+	0.416601i	$0.136779\pi$
$593$			20.2898i			0.833202i	−0.909089	+	0.416601i	$0.863221\pi$
$594$	1.78785	−	3.09665i	0.0733565	−	0.127057i
$595$	1.14388	+	1.98126i	0.0468945	+	0.0812237i
$596$	16.2110	−	9.35944i	0.664030	−	0.383378i
$597$	−14.5430			−0.595206
$598$	−4.46924	−	3.28789i	−0.182761	−	0.134452i
$599$	−2.20289			−0.0900075			−0.0450038	−	0.998987i	$-0.514330\pi$
$599$	−2.20289			−0.0900075			−0.0450038	+	0.998987i	$0.514330\pi$
$600$	1.75429	−	1.01284i	0.0716184	−	0.0413489i
$601$	−0.460431	−	0.797490i	−0.0187814	−	0.0325303i	0.856482	−	0.516177i	$-0.172645\pi$
$601$	−0.460431	−	0.797490i	−0.0187814	−	0.0325303i	−0.875263	+	0.483647i	$0.839312\pi$
$602$	0.486168	−	0.842067i	0.0198147	−	0.0343201i
$603$			18.0378i			0.734557i
$604$	8.88541	+	5.12999i	0.361542	+	0.208736i
$605$	−0.866025	−	0.500000i	−0.0352089	−	0.0203279i
$606$		−	1.61197i		−	0.0654818i
$607$	−20.3314	+	35.2150i	−0.825226	+	1.42933i	0.0765212	+	0.997068i	$0.475619\pi$
$607$	−20.3314	+	35.2150i	−0.825226	+	1.42933i	−0.901747	+	0.432265i	$0.857715\pi$
$608$	−16.9174	−	29.3019i	−0.686093	−	1.18835i
$609$	−2.98704	+	1.72457i	−0.121041	+	0.0698831i
$610$	−13.3629			−0.541049
$611$	−1.15737	+	10.4153i	−0.0468224	+	0.421357i
$612$	−13.3874			−0.541155
$613$	−17.9883	+	10.3856i	−0.726542	+	0.419469i	−0.817156	−	0.576417i	$-0.804450\pi$
$613$	−17.9883	+	10.3856i	−0.726542	+	0.419469i	0.0906138	+	0.995886i	$0.471117\pi$
$614$	−10.1799	−	17.6321i	−0.410827	−	0.711573i
$615$	−0.976938	+	1.69211i	−0.0393940	+	0.0682323i
$616$			1.41743i			0.0571097i
$617$	21.6983	+	12.5275i	0.873540	+	0.504339i	0.868523	−	0.495649i	$-0.165070\pi$
$617$	21.6983	+	12.5275i	0.873540	+	0.504339i	0.00501716	+	0.999987i	$0.498403\pi$
$618$	−9.40150	−	5.42796i	−0.378184	−	0.218345i
$619$			33.8540i			1.36071i	0.732883	+	0.680354i	$0.238174\pi$
$619$			33.8540i			1.36071i	−0.732883	+	0.680354i	$0.761826\pi$
$620$	1.06654	−	1.84730i	0.0428331	−	0.0741892i
$621$	−3.15064	−	5.45707i	−0.126431	−	0.218985i
$622$	−4.03946	+	2.33218i	−0.161968	+	0.0935120i
$623$	−0.277279			−0.0111089
$624$	−0.706317	+	0.960098i	−0.0282753	+	0.0384347i
$625$	1.00000			0.0400000
$626$	−2.46021	+	1.42040i	−0.0983296	+	0.0567706i
$627$	2.17270	+	3.76323i	0.0867694	+	0.150289i
$628$	8.67731	−	15.0295i	0.346263	−	0.599744i
$629$		−	8.11755i		−	0.323668i
$630$	−0.989065	−	0.571037i	−0.0394053	−	0.0227507i
$631$	9.49870	+	5.48408i	0.378137	+	0.218318i	0.677008	−	0.735976i	$-0.263276\pi$
$631$	9.49870	+	5.48408i	0.378137	+	0.218318i	−0.298870	+	0.954294i	$0.596610\pi$
$632$		−	38.5611i		−	1.53388i
$633$	7.59038	−	13.1469i	0.301691	−	0.522543i
$634$	−5.25537	−	9.10257i	−0.208717	−	0.361509i
$635$	−1.26600	+	0.730927i	−0.0502398	+	0.0290059i
$636$	−7.23210			−0.286772
$637$	−9.78773	−	22.3403i	−0.387804	−	0.885156i
$638$	9.58348			0.379414
$639$	10.3894	−	5.99832i	0.410998	−	0.237290i
$640$	−2.59566	−	4.49582i	−0.102602	−	0.177713i
$641$	−13.1251	+	22.7334i	−0.518412	+	0.897916i	0.481359	+	0.876523i	$0.340143\pi$
$641$	−13.1251	+	22.7334i	−0.518412	+	0.897916i	−0.999771	+	0.0213923i	$0.993190\pi$
$642$			5.20409i			0.205389i
$643$	26.7082	+	15.4200i	1.05327	+	0.608105i	0.923563	−	0.383447i	$-0.125263\pi$
$643$	26.7082	+	15.4200i	1.05327	+	0.608105i	0.129706	+	0.991552i	$0.458597\pi$
$644$	0.779540	+	0.450068i	0.0307182	+	0.0177352i
$645$		−	1.48704i		−	0.0585520i
$646$	−13.8110	+	23.9213i	−0.543385	+	0.941170i
$647$	−16.9472	−	29.3535i	−0.666264	−	1.15400i	−0.978941	−	0.204144i	$-0.934559\pi$
$647$	−16.9472	−	29.3535i	−0.666264	−	1.15400i	0.312677	−	0.949860i	$-0.398774\pi$
$648$	12.4123	−	7.16624i	0.487601	−	0.281517i
$649$	−10.0149			−0.393121
$650$	−3.08607	+	1.35207i	−0.121046	+	0.0530325i
$651$	0.636678			0.0249534
$652$	2.19585	−	1.26778i	0.0859962	−	0.0496499i
$653$	−17.3728	−	30.0905i	−0.679848	−	1.17753i	−0.975026	−	0.222090i	$-0.928712\pi$
$653$	−17.3728	−	30.0905i	−0.679848	−	1.17753i	0.295178	−	0.955442i	$-0.404621\pi$
$654$	5.39893	−	9.35123i	0.211115	−	0.365662i
$655$		−	13.6653i		−	0.533947i
$656$	−1.16381	−	0.671927i	−0.0454392	−	0.0262344i
$657$	−18.2538	−	10.5388i	−0.712149	−	0.411159i
$658$			1.31755i			0.0513636i
$659$	0.159673	−	0.276561i	0.00621997	−	0.0107733i	−0.862899	−	0.505377i	$-0.831353\pi$
$659$	0.159673	−	0.276561i	0.00621997	−	0.0107733i	0.869119	+	0.494604i	$0.164687\pi$
$660$	0.390586	+	0.676515i	0.0152035	+	0.0263333i
$661$	−28.1206	+	16.2354i	−1.09376	+	0.631484i	−0.934576	−	0.355764i	$-0.884221\pi$
$661$	−28.1206	+	16.2354i	−1.09376	+	0.631484i	−0.159187	+	0.987248i	$0.550887\pi$
$662$	9.10154			0.353742
$663$	−11.7162	−	1.30193i	−0.455019	−	0.0505630i
$664$	1.03975			0.0403501
$665$	2.63325	−	1.52031i	0.102113	−	0.0589550i
$666$	2.02618	+	3.50945i	0.0785130	+	0.135988i
$667$	8.44424	−	14.6258i	0.326962	−	0.566315i
$668$		−	16.5606i		−	0.640748i
$669$	−4.39129	−	2.53531i	−0.169777	−	0.0980208i
$670$	5.79412	+	3.34524i	0.223846	+	0.129238i
$671$		−	14.3001i		−	0.552048i
$672$	0.907747	−	1.57226i	0.0350171	−	0.0606514i
$673$	7.00842	+	12.1389i	0.270155	+	0.467922i	0.968901	−	0.247448i	$-0.0795918\pi$
$673$	7.00842	+	12.1389i	0.270155	+	0.467922i	−0.698746	+	0.715369i	$0.746258\pi$
$674$	23.2659	−	13.4326i	0.896169	−	0.517403i
$675$	−3.82647			−0.147281
$676$	−9.93029	+	10.7682i	−0.381934	+	0.414163i
$677$	21.7671			0.836578			0.418289	−	0.908314i	$-0.362630\pi$
$677$	21.7671			0.836578			0.418289	+	0.908314i	$0.362630\pi$
$678$	2.48337	−	1.43377i	0.0953731	−	0.0550637i
$679$	−1.60623	−	2.78207i	−0.0616415	−	0.106766i
$680$	−6.88969	+	11.9333i	−0.264208	+	0.457621i
$681$			12.6432i			0.484488i
$682$	−1.53201	−	0.884509i	−0.0586638	−	0.0338696i
$683$	−12.4677	−	7.19822i	−0.477063	−	0.275432i	0.242129	−	0.970244i	$-0.422154\pi$
$683$	−12.4677	−	7.19822i	−0.477063	−	0.275432i	−0.719192	+	0.694812i	$0.755488\pi$
$684$			17.7929i			0.680330i
$685$	6.33441	−	10.9715i	0.242026	−	0.419200i
$686$	−3.11989	−	5.40381i	−0.119118	−	0.206319i
$687$	1.65139	−	0.953429i	0.0630043	−	0.0363756i
$688$	1.02277			0.0389927
$689$	33.1760	+	3.68661i	1.26391	+	0.140449i
$690$	−1.06685			−0.0406143
$691$	−4.85763	+	2.80455i	−0.184793	+	0.106690i	−0.589543	−	0.807737i	$-0.700692\pi$
$691$	−4.85763	+	2.80455i	−0.184793	+	0.106690i	0.404750	+	0.914428i	$0.367359\pi$
$692$	−2.84505	−	4.92776i	−0.108152	−	0.187326i
$693$	0.611084	−	1.05843i	0.0232132	−	0.0402064i
$694$			21.6104i			0.820321i
$695$	1.69676	+	0.979623i	0.0643616	+	0.0371592i
$696$	−17.9912	−	10.3872i	−0.681955	−	0.393727i
$697$		−	13.2910i		−	0.503432i
$698$	−4.11741	+	7.13157i	−0.155846	+	0.269934i
$699$	−5.19399	−	8.99625i	−0.196455	−	0.340270i
$700$	0.473378	−	0.273305i	0.0178920	−	0.0103300i
$701$	−6.30685			−0.238206			−0.119103	−	0.992882i	$-0.538002\pi$
$701$	−6.30685			−0.238206			−0.119103	+	0.992882i	$0.538002\pi$
$702$	11.8088	−	5.17365i	0.445694	−	0.195267i
$703$	−10.7889			−0.406910
$704$	−5.19446	+	2.99902i	−0.195773	+	0.113030i
$705$	1.00750	+	1.74504i	0.0379446	+	0.0657220i
$706$	6.30080	−	10.9133i	0.237134	−	0.410728i
$707$		−	1.20705i		−	0.0453957i
$708$	6.77526	+	3.91170i	0.254630	+	0.147011i
$709$	−8.67075	−	5.00606i	−0.325637	−	0.188007i	0.328265	−	0.944586i	$-0.393536\pi$
$709$	−8.67075	−	5.00606i	−0.325637	−	0.188007i	−0.653902	+	0.756579i	$0.726869\pi$
$710$		−	4.44972i		−	0.166995i
$711$	−16.6245	+	28.7945i	−0.623469	+	1.07988i
$712$	−0.835037	−	1.44633i	−0.0312943	−	0.0542034i
$713$	−2.69979	+	1.55872i	−0.101108	+	0.0583747i
$714$	−1.48212			−0.0554670
$715$	−1.44689	−	3.30250i	−0.0541106	−	0.123507i
$716$	−14.0949			−0.526753
$717$	8.34670	−	4.81897i	0.311713	−	0.179968i
$718$	−15.4607	−	26.7787i	−0.576987	−	0.999371i
$719$	−2.04155	+	3.53606i	−0.0761368	+	0.131873i	−0.901580	−	0.432612i	$-0.857592\pi$
$719$	−2.04155	+	3.53606i	−0.0761368	+	0.131873i	0.825443	+	0.564485i	$0.190925\pi$
$720$		−	1.20131i		−	0.0447702i
$721$	−7.03987	−	4.06447i	−0.262179	−	0.151369i
$722$	16.4171	+	9.47842i	0.610982	+	0.352750i
$723$		−	12.2922i		−	0.457152i
$724$	−6.90290	+	11.9562i	−0.256544	+	0.444348i
$725$	−5.12779	−	8.88159i	−0.190441	−	0.329854i
$726$	0.561053	−	0.323924i	0.0208226	−	0.0120220i
$727$	−32.4256			−1.20260			−0.601299	−	0.799024i	$-0.705350\pi$
$727$	−32.4256			−1.20260			−0.601299	+	0.799024i	$0.705350\pi$
$728$	−3.02848	+	4.11662i	−0.112243	+	0.152572i
$729$	−4.39963			−0.162949
$730$	−6.77059	+	3.90900i	−0.250591	+	0.144679i
$731$	5.05769	+	8.76017i	0.187065	+	0.324007i
$732$	−5.58541	+	9.67421i	−0.206443	+	0.357569i
$733$		−	50.7325i		−	1.87385i	−0.349533	−	0.936924i	$-0.613660\pi$
$733$		−	50.7325i		−	1.87385i	0.349533	−	0.936924i	$-0.386340\pi$
$734$	27.6627	+	15.9710i	1.02105	+	0.589502i
$735$	−4.06151	−	2.34491i	−0.149811	−	0.0864934i
$736$			8.88945i			0.327669i
$737$	−3.57984	+	6.20047i	−0.131865	+	0.228397i
$738$	3.31750	+	5.74608i	0.122119	+	0.211516i
$739$	7.48707	−	4.32266i	0.275416	−	0.159012i	−0.355930	−	0.934513i	$-0.615836\pi$
$739$	7.48707	−	4.32266i	0.275416	−	0.159012i	0.631346	+	0.775501i	$0.282503\pi$
$740$	−1.93951			−0.0712978
$741$	−1.73037	+	15.5717i	−0.0635669	+	0.572042i
$742$	4.19684			0.154071
$743$	−39.8687	+	23.0182i	−1.46264	+	0.844456i	−0.999133	−	0.0416368i	$-0.986743\pi$
$743$	−39.8687	+	23.0182i	−1.46264	+	0.844456i	−0.463508	+	0.886093i	$0.653409\pi$
$744$	1.91738	+	3.32100i	0.0702946	+	0.121754i
$745$	−8.30641	+	14.3871i	−0.304323	+	0.527103i
$746$			20.5543i			0.752545i
$747$	−0.776407	−	0.448259i	−0.0284073	−	0.0164009i
$748$	−4.60190	−	2.65691i	−0.168262	−	0.0971463i
$749$			3.89683i			0.142387i
$750$	−0.323924	+	0.561053i	−0.0118280	+	0.0204868i
$751$	−24.7082	−	42.7958i	−0.901614	−	1.56164i	−0.825398	−	0.564551i	$-0.809049\pi$
$751$	−24.7082	−	42.7958i	−0.901614	−	1.56164i	−0.0762160	−	0.997091i	$-0.524284\pi$
$752$	−1.20022	+	0.692947i	−0.0437675	+	0.0252692i
$753$	−12.5085			−0.455835
$754$	27.8332	+	20.4761i	1.01363	+	0.745696i
$755$	−9.10563			−0.331388
$756$	−1.81137	+	1.04579i	−0.0658789	+	0.0380352i
$757$	−18.8099	−	32.5797i	−0.683658	−	1.18413i	−0.973857	−	0.227163i	$-0.927055\pi$
$757$	−18.8099	−	32.5797i	−0.683658	−	1.18413i	0.290199	−	0.956966i	$-0.406278\pi$
$758$	0.174546	−	0.302322i	0.00633978	−	0.0109808i
$759$		−	1.14167i		−	0.0414400i
$760$	15.8603	+	9.15694i	0.575313	+	0.332157i
$761$	−17.8853	−	10.3261i	−0.648342	−	0.374321i	0.139479	−	0.990225i	$-0.455457\pi$
$761$	−17.8853	−	10.3261i	−0.648342	−	0.374321i	−0.787821	+	0.615905i	$0.788791\pi$
$762$		−	0.947059i		−	0.0343083i
$763$	4.04274	−	7.00222i	0.146357	−	0.253498i
$764$	−3.41833	−	5.92071i	−0.123671	−	0.214204i
$765$	10.2894	−	5.94060i	0.372015	−	0.214783i
$766$	16.3610			0.591146
$767$	−29.0863	−	21.3980i	−1.05025	−	0.772636i
$768$	11.6799			0.421461
$769$	−25.6562	+	14.8126i	−0.925187	+	0.534157i	−0.885286	−	0.465047i	$-0.846038\pi$
$769$	−25.6562	+	14.8126i	−0.925187	+	0.534157i	−0.0399008	+	0.999204i	$0.512704\pi$
$770$	−0.226660	−	0.392586i	−0.00816824	−	0.0141478i
$771$	−7.29198	+	12.6301i	−0.262614	+	0.454861i
$772$			0.0876824i			0.00315576i
$773$	32.5587	+	18.7978i	1.17106	+	0.676109i	0.953929	−	0.300034i	$-0.0969980\pi$
$773$	32.5587	+	18.7978i	1.17106	+	0.676109i	0.217127	+	0.976143i	$0.430331\pi$
$774$	−4.37317	−	2.52485i	−0.157190	−	0.0907539i
$775$			1.89308i			0.0680014i
$776$	9.67446	−	16.7567i	0.347293	−	0.601529i
$777$	−0.289451	−	0.501345i	−0.0103840	−	0.0179856i
$778$	−14.6417	+	8.45340i	−0.524931	+	0.303069i
$779$	−17.6648			−0.632906
$780$	−0.311069	+	2.79933i	−0.0111380	+	0.100232i
$781$	4.76178			0.170390
$782$	6.28484	−	3.62855i	0.224745	−	0.129757i
$783$	19.6213	+	33.9852i	0.701210	+	1.21453i
$784$	1.61280	−	2.79346i	0.0576002	−	0.0997664i
$785$			15.4020i			0.549723i
$786$	7.66694	+	4.42651i	0.273471	+	0.157888i
$787$	−35.6957	−	20.6089i	−1.27241	−	0.734629i	−0.296973	−	0.954886i	$-0.595977\pi$
$787$	−35.6957	−	20.6089i	−1.27241	−	0.734629i	−0.975442	+	0.220257i	$0.929310\pi$
$788$		−	24.8676i		−	0.885870i
$789$	1.93809	−	3.35688i	0.0689979	−	0.119508i
$790$	6.16627	+	10.6803i	0.219386	+	0.379988i
$791$	1.85955	−	1.07361i	0.0661181	−	0.0381733i
$792$	7.36122			0.261570
$793$	30.5536	−	41.5316i	1.08499	−	1.47483i
$794$	−13.3136			−0.472481
$795$	5.55851	−	3.20921i	0.197140	−	0.113819i
$796$	−11.8182	−	20.4697i	−0.418885	−	0.725531i
$797$	−5.61098	+	9.71850i	−0.198751	+	0.344247i	−0.948124	−	0.317902i	$-0.897022\pi$
$797$	−5.61098	+	9.71850i	−0.198751	+	0.344247i	0.749373	+	0.662148i	$0.230355\pi$
$798$			1.96986i			0.0697322i
$799$	−11.8704	−	6.85338i	−0.419944	−	0.242455i
$800$	4.67493	+	2.69907i	0.165284	+	0.0954266i
$801$			1.44001i			0.0508803i
$802$	6.45452	−	11.1795i	0.227917	−	0.394764i
$803$	−4.18314	−	7.24541i	−0.147620	−	0.255685i
$804$	4.84363	−	2.79647i	0.170822	−	0.0986240i
$805$	−0.798861			−0.0281561
$806$	−2.55957	−	5.84218i	−0.0901571	−	0.205782i
$807$	15.1139			0.532034
$808$	6.29614	−	3.63508i	0.221497	−	0.127882i
$809$	17.6148	+	30.5097i	0.619302	+	1.07266i	0.989613	+	0.143755i	$0.0459178\pi$
$809$	17.6148	+	30.5097i	0.619302	+	1.07266i	−0.370311	+	0.928908i	$0.620749\pi$
$810$	−2.29190	+	3.96968i	−0.0805290	+	0.139480i
$811$			6.48294i			0.227647i	0.993501	+	0.113823i	$0.0363098\pi$
$811$			6.48294i			0.227647i	−0.993501	+	0.113823i	$0.963690\pi$
$812$	−4.85477	−	2.80290i	−0.170369	−	0.0983625i
$813$	9.88287	+	5.70588i	0.346607	+	0.200114i
$814$			1.60849i			0.0563775i
$815$	−1.12514	+	1.94879i	−0.0394118	+	0.0682633i
$816$	−0.779498	−	1.35013i	−0.0272879	−	0.0472640i
$817$	11.6430	−	6.72206i	0.407335	−	0.235175i
$818$	0.662591			0.0231669
$819$	4.03621	−	1.76834i	0.141037	−	0.0617909i
$820$	−3.17559			−0.110896
$821$	−16.4257	+	9.48337i	−0.573260	+	0.330972i	−0.758450	−	0.651731i	$-0.774043\pi$
$821$	−16.4257	+	9.48337i	−0.573260	+	0.330972i	0.185190	+	0.982703i	$0.440710\pi$
$822$	4.10374	+	7.10788i	0.143134	+	0.247916i
$823$	14.8115	−	25.6542i	0.516295	−	0.894249i	−0.483526	−	0.875330i	$-0.660644\pi$
$823$	14.8115	−	25.6542i	0.516295	−	0.894249i	0.999821	−	0.0189188i	$-0.00602241\pi$
$824$		−	48.9613i		−	1.70565i
$825$	−0.600400	−	0.346641i	−0.0209032	−	0.0120685i
$826$	−3.93173	−	2.26998i	−0.136802	−	0.0789828i
$827$			6.65258i			0.231333i	0.993288	+	0.115666i	$0.0369003\pi$
$827$			6.65258i			0.231333i	−0.993288	+	0.115666i	$0.963100\pi$
$828$	2.33737	−	4.04844i	0.0812292	−	0.140693i
$829$	7.34619	+	12.7240i	0.255144	+	0.441922i	0.964935	−	0.262491i	$-0.0845439\pi$
$829$	7.34619	+	12.7240i	0.255144	+	0.441922i	−0.709791	+	0.704413i	$0.751211\pi$
$830$	−0.287980	+	0.166265i	−0.00999594	+	0.00577116i
$831$	2.86298			0.0993158
$832$	−21.4939	−	2.38846i	−0.745169	−	0.0828051i
$833$	31.9019			1.10534
$834$	−1.09924	+	0.634647i	−0.0380636	+	0.0219760i
$835$	7.34867	+	12.7283i	0.254311	+	0.440480i
$836$	−3.53124	+	6.11629i	−0.122131	+	0.211536i
$837$		−	7.24382i		−	0.250383i
$838$	−16.5132	−	9.53392i	−0.570440	−	0.329344i
$839$	−40.7486	−	23.5262i	−1.40680	−	0.812216i	−0.411721	−	0.911310i	$-0.635072\pi$
$839$	−40.7486	−	23.5262i	−1.40680	−	0.812216i	−0.995078	+	0.0990941i	$0.968406\pi$
$840$			0.982676i			0.0339056i
$841$	−38.0884	+	65.9711i	−1.31339	+	2.27487i
$842$	−4.74425	−	8.21728i	−0.163498	−	0.283186i
$843$	15.4601	−	8.92590i	0.532475	−	0.307424i
$844$	24.6729			0.849277
$845$	2.85395	−	12.6829i	0.0981788	−	0.436304i
$846$	6.84255			0.235252
$847$	0.420118	−	0.242555i	0.0144354	−	0.00833430i
$848$	2.20726	+	3.82308i	0.0757976	+	0.131285i
$849$	−6.91318	+	11.9740i	−0.237260	+	0.410946i
$850$		−	4.40690i		−	0.151155i
$851$	2.45480	+	1.41728i	0.0841494	+	0.0485837i
$852$	−3.22142	−	1.85989i	−0.110364	−	0.0637187i
$853$			12.4589i			0.426584i	0.976989	+	0.213292i	$0.0684185\pi$
$853$			12.4589i			0.426584i	−0.976989	+	0.213292i	$0.931581\pi$
$854$	3.24125	−	5.61401i	0.110913	−	0.192107i
$855$	−7.89552	−	13.6754i	−0.270021	−	0.467690i
$856$	−20.3265	+	11.7355i	−0.694744	+	0.401111i
$857$	42.2785			1.44421			0.722103	−	0.691786i	$-0.243176\pi$
$857$	42.2785			1.44421			0.722103	+	0.691786i	$0.243176\pi$
$858$	2.32156	+	0.257978i	0.0792568	+	0.00880722i
$859$	−1.55124			−0.0529276			−0.0264638	−	0.999650i	$-0.508425\pi$
$859$	−1.55124			−0.0529276			−0.0264638	+	0.999650i	$0.508425\pi$
$860$	2.09305	−	1.20842i	0.0713724	−	0.0412069i
$861$	−0.473923	−	0.820859i	−0.0161513	−	0.0279748i
$862$	9.78442	−	16.9471i	0.333259	−	0.577221i
$863$			34.1869i			1.16373i	0.813284	+	0.581867i	$0.197678\pi$
$863$			34.1869i			1.16373i	−0.813284	+	0.581867i	$0.802322\pi$
$864$	−17.8885	−	10.3279i	−0.608579	−	0.351363i
$865$	4.37334	+	2.52495i	0.148698	+	0.0858508i
$866$		−	24.0495i		−	0.817237i
$867$	1.81649	−	3.14626i	0.0616913	−	0.106852i
$868$	0.517388	+	0.896143i	0.0175613	+	0.0304171i
$869$	−11.4293	+	6.59871i	−0.387713	+	0.223846i
$870$	6.64406			0.225255
$871$	−23.6449	+	10.3593i	−0.801175	+	0.351010i
$872$	48.6995			1.64917
$873$	−14.4483	+	8.34175i	−0.489002	+	0.282326i
$874$	−4.82263	−	8.35304i	−0.163128	−	0.282546i
$875$	−0.242555	+	0.420118i	−0.00819987	+	0.0142026i
$876$			6.53551i			0.220814i
$877$	−25.4674	−	14.7036i	−0.859972	−	0.496505i	0.00403105	−	0.999992i	$-0.498717\pi$
$877$	−25.4674	−	14.7036i	−0.859972	−	0.496505i	−0.864003	+	0.503487i	$0.832050\pi$
$878$	32.8588	+	18.9710i	1.10893	+	0.640242i
$879$			13.5004i			0.455358i
$880$	0.238416	−	0.412948i	0.00803700	−	0.0139205i
$881$	23.7247	+	41.0924i	0.799306	+	1.38444i	0.920069	+	0.391757i	$0.128133\pi$
$881$	23.7247	+	41.0924i	0.799306	+	1.38444i	−0.120763	+	0.992681i	$0.538534\pi$
$882$	−13.7921	+	7.96288i	−0.464404	+	0.268124i
$883$	−16.2877			−0.548124			−0.274062	−	0.961712i	$-0.588367\pi$
$883$	−16.2877			−0.548124			−0.274062	+	0.961712i	$0.588367\pi$
$884$	−7.68851	−	17.5489i	−0.258593	−	0.590233i
$885$	−6.94318			−0.233392
$886$	−5.23469	+	3.02225i	−0.175863	+	0.101534i
$887$	6.36602	+	11.0263i	0.213750	+	0.370226i	0.952885	−	0.303331i	$-0.0980989\pi$
$887$	6.36602	+	11.0263i	0.213750	+	0.370226i	−0.739135	+	0.673557i	$0.764766\pi$
$888$	1.74339	−	3.01964i	0.0585044	−	0.101333i
$889$		−	0.709161i		−	0.0237845i
$890$	0.462562	+	0.267060i	0.0155051	+	0.00895188i
$891$	−4.24808	−	2.45263i	−0.142316	−	0.0821661i
$892$		−	8.24116i		−	0.275934i
$893$	−9.10867	+	15.7767i	−0.304810	+	0.527947i
$894$	−5.38129	−	9.32067i	−0.179977	−	0.311730i
$895$	10.8332	−	6.25456i	0.362114	−	0.209067i
$896$	2.51837			0.0841327
$897$	2.43930	−	3.31574i	0.0814457	−	0.110709i
$898$	−26.9131			−0.898102
$899$	16.8136	−	9.70731i	0.560763	−	0.323757i
$900$	−1.41937	−	2.45843i	−0.0473125	−	0.0819476i
$901$	−21.8302	+	37.8110i	−0.727270	+	1.25967i
$902$			2.63360i			0.0876894i
$903$	0.624731	+	0.360689i	0.0207898	+	0.0120030i
$904$	11.2002	+	6.46646i	0.372515	+	0.215071i
$905$		−	12.2525i		−	0.407287i
$906$	2.94953	−	5.10874i	0.0979916	−	0.169726i
$907$	10.9805	+	19.0188i	0.364601	+	0.631507i	0.988712	−	0.149828i	$-0.0478721\pi$
$907$	10.9805	+	19.0188i	0.364601	+	0.631507i	−0.624111	+	0.781336i	$0.714539\pi$
$908$	−17.7957	+	10.2743i	−0.590570	+	0.340966i
$909$	−6.26865			−0.207918
$910$	0.180515	−	1.62447i	0.00598402	−	0.0538505i
$911$	10.6485			0.352800			0.176400	−	0.984319i	$-0.443555\pi$
$911$	10.6485			0.352800			0.176400	+	0.984319i	$0.443555\pi$
$912$	−1.79443	+	1.03601i	−0.0594195	+	0.0343059i
$913$	−0.177926	−	0.308176i	−0.00588848	−	0.0101991i
$914$	16.8814	−	29.2394i	0.558387	−	0.967154i
$915$		−	9.91398i		−	0.327746i
$916$	2.68396	+	1.54958i	0.0886805	+	0.0511997i
$917$	5.74103	+	3.31459i	0.189586	+	0.109457i
$918$			16.8629i			0.556558i
$919$	17.6691	−	30.6038i	0.582851	−	1.00953i	−0.412289	−	0.911053i	$-0.635270\pi$
$919$	17.6691	−	30.6038i	0.582851	−	1.00953i	0.995140	−	0.0984741i	$-0.0313962\pi$
$920$	−2.40580	−	4.16697i	−0.0793170	−	0.137381i
$921$	13.0813	−	7.55248i	0.431043	−	0.248863i
$922$	20.8639			0.687114
$923$	13.8296	+	10.1740i	0.455207	+	0.334883i
$924$	−0.378955			−0.0124667
$925$	1.49068	−	0.860647i	0.0490134	−	0.0282979i
$926$	−3.91639	−	6.78338i	−0.128700	−	0.222916i
$927$	−21.1083	+	36.5607i	−0.693288	+	1.20081i
$928$		−	55.3611i		−	1.81732i
$929$	−17.9469	−	10.3616i	−0.588818	−	0.339954i	0.175812	−	0.984424i	$-0.443745\pi$
$929$	−17.9469	−	10.3616i	−0.588818	−	0.339954i	−0.764630	+	0.644470i	$0.777078\pi$
$930$	−1.06212	−	0.613214i	−0.0348282	−	0.0201081i
$931$		−	42.4001i		−	1.38961i
$932$	8.44166	−	14.6214i	0.276516	−	0.478939i
$933$	−1.73025	−	2.99688i	−0.0566459	−	0.0981135i
$934$	−29.9115	+	17.2694i	−0.978733	+	0.565072i
$935$	4.71596			0.154228
$936$	21.3792	+	15.7280i	0.698800	+	0.514087i
$937$	21.4701			0.701399			0.350700	−	0.936488i	$-0.385944\pi$
$937$	21.4701			0.701399			0.350700	+	0.936488i	$0.385944\pi$
$938$	−2.81079	+	1.62281i	−0.0917756	+	0.0529866i
$939$	−1.05380	−	1.82523i	−0.0343894	−	0.0595642i
$940$	−1.63746	+	2.83617i	−0.0534082	+	0.0925056i
$941$		−	24.4222i		−	0.796141i	−0.917355	−	0.398070i	$-0.869680\pi$
$941$		−	24.4222i		−	0.796141i	0.917355	−	0.398070i	$-0.130320\pi$
$942$	−8.64136	−	4.98909i	−0.281551	−	0.162553i
$943$	4.01928	+	2.32053i	0.130886	+	0.0755669i
$944$		−	4.77544i		−	0.155427i
$945$	0.928131	−	1.60757i	0.0301921	−	0.0522943i
$946$	−1.00218	−	1.73583i	−0.0325837	−	0.0564365i
$947$	25.6746	−	14.8233i	0.834313	−	0.481691i	−0.0210138	−	0.999779i	$-0.506689\pi$
$947$	25.6746	−	14.8233i	0.834313	−	0.481691i	0.855327	+	0.518088i	$0.173356\pi$
$948$	10.3095			0.334836
$949$	3.33151	−	29.9805i	0.108146	−	0.973209i
$950$	−5.85712			−0.190030
$951$	6.75321	−	3.89897i	0.218988	−	0.126433i
$952$	−3.34226	−	5.78897i	−0.108323	−	0.187622i
$953$	21.6645	−	37.5240i	0.701782	−	1.21552i	−0.266059	−	0.963957i	$-0.585721\pi$
$953$	21.6645	−	37.5240i	0.701782	−	1.21552i	0.967840	−	0.251565i	$-0.0809452\pi$
$954$		−	21.7957i		−	0.705663i
$955$	5.25457	+	3.03373i	0.170034	+	0.0981691i
$956$	13.5657	+	7.83215i	0.438746	+	0.253310i
$957$			7.11001i			0.229834i
$958$	−6.36486	+	11.0243i	−0.205639	+	0.356177i
$959$	3.07289	+	5.32240i	0.0992288	+	0.171869i
$960$	−3.60122	+	2.07917i	−0.116229	+	0.0671048i
$961$	27.4163			0.884395
$962$	−3.43671	+	4.67153i	−0.110804	+	0.150616i
$963$	20.2377			0.652151
$964$	17.3016	−	9.98910i	0.557248	−	0.321727i
$965$	−0.0389086	−	0.0673917i	−0.00125251	−	0.00216941i
$966$	0.258770	−	0.448203i	0.00832580	−	0.0144207i
$967$		−	6.77238i		−	0.217785i	−0.994054	−	0.108893i	$-0.965270\pi$
$967$		−	6.77238i		−	0.217785i	0.994054	−	0.108893i	$-0.0347304\pi$
$968$	2.53041	+	1.46093i	0.0813304	+	0.0469561i
$969$	−17.7473	−	10.2464i	−0.570124	−	0.329161i
$970$			6.18814i			0.198689i
$971$	−11.5246	+	19.9611i	−0.369841	+	0.640584i	−0.989540	−	0.144256i	$-0.953921\pi$
$971$	−11.5246	+	19.9611i	−0.369841	+	0.640584i	0.619699	+	0.784839i	$0.287255\pi$
$972$	8.38328	+	14.5203i	0.268894	+	0.465738i
$973$	−0.823115	+	0.475225i	−0.0263878	+	0.0152350i
$974$	9.01443			0.288841
$975$	−1.00310	−	2.28956i	−0.0321250	−	0.0733247i
$976$	6.81873			0.218262
$977$	42.5886	−	24.5885i	1.36253	−	0.786656i	0.372569	−	0.928005i	$-0.378477\pi$
$977$	42.5886	−	24.5885i	1.36253	−	0.786656i	0.989960	+	0.141348i	$0.0451438\pi$
$978$	−0.728918	−	1.26252i	−0.0233082	−	0.0403710i
$979$	−0.285789	+	0.495002i	−0.00913387	+	0.0158203i
$980$		−	7.62225i		−	0.243484i
$981$	−36.3652	−	20.9954i	−1.16105	−	0.670333i
$982$	19.6227	+	11.3292i	0.626186	+	0.361529i
$983$			35.9873i			1.14782i	0.818920	+	0.573908i	$0.194573\pi$
$983$			35.9873i			1.14782i	−0.818920	+	0.573908i	$0.805427\pi$
$984$	2.85448	−	4.94410i	0.0909975	−	0.157612i
$985$	11.0348	+	19.1129i	0.351599	+	0.608988i
$986$	−39.1403	+	22.5977i	−1.24648	+	0.719656i
$987$	−0.977497			−0.0311141
$988$	−23.3239	+	10.2186i	−0.742031	+	0.325098i
$989$	−3.53218			−0.112317
$990$	−2.03884	+	1.17713i	−0.0647987	+	0.0374116i
$991$	23.2079	+	40.1972i	0.737222	+	1.27691i	0.953742	+	0.300627i	$0.0971961\pi$
$991$	23.2079	+	40.1972i	0.737222	+	1.27691i	−0.216520	+	0.976278i	$0.569471\pi$
$992$	−5.10956	+	8.85001i	−0.162229	+	0.280988i
$993$			6.75246i			0.214283i
$994$	1.86941	+	1.07930i	0.0592941	+	0.0342334i
$995$	18.1667	+	10.4885i	0.575922	+	0.332509i
$996$			0.277981i			0.00880817i
$997$	−19.2208	+	33.2913i	−0.608727	+	1.05435i	0.382723	+	0.923863i	$0.374986\pi$
$997$	−19.2208	+	33.2913i	−0.608727	+	1.05435i	−0.991450	+	0.130484i	$0.958347\pi$
$998$	−17.2816	−	29.9326i	−0.547039	−	0.947499i
$999$	−5.70406	+	3.29324i	−0.180469	+	0.104194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	715.2.z.c.166.19	yes	56
13.2	odd	12		9295.2.a.bj.1.20		28
13.4	even	6	inner	715.2.z.c.56.19	✓	56
13.11	odd	12		9295.2.a.bk.1.9		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
715.2.z.c.56.19	✓	56	13.4	even	6	inner
715.2.z.c.166.19	yes	56	1.1	even	1	trivial
9295.2.a.bj.1.20		28	13.2	odd	12
9295.2.a.bk.1.9		28	13.11	odd	12

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:	\( N \)	\(=\)	\( 715 = 5 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	715.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809271 - 0.467233i) q^{2} +(0.346641 + 0.600400i) q^{3} +(-0.563387 + 0.975815i) q^{4} -1.00000i q^{5} +(0.561053 + 0.323924i) q^{6} +(0.420118 + 0.242555i) q^{7} +2.92186i q^{8} +(1.25968 - 2.18183i) q^{9} +O(q^{10})\)	\(q+(0.809271 - 0.467233i) q^{2} +(0.346641 + 0.600400i) q^{3} +(-0.563387 + 0.975815i) q^{4} -1.00000i q^{5} +(0.561053 + 0.323924i) q^{6} +(0.420118 + 0.242555i) q^{7} +2.92186i q^{8} +(1.25968 - 2.18183i) q^{9} +(-0.467233 - 0.809271i) q^{10} +(0.866025 - 0.500000i) q^{11} -0.781172 q^{12} +(3.58349 + 0.398207i) q^{13} +0.453319 q^{14} +(0.600400 - 0.346641i) q^{15} +(0.238416 + 0.412948i) q^{16} +(-2.35798 + 4.08414i) q^{17} -2.35426i q^{18} +(5.42814 + 3.13394i) q^{19} +(0.975815 + 0.563387i) q^{20} +0.336318i q^{21} +(0.467233 - 0.809271i) q^{22} +(-0.823380 - 1.42614i) q^{23} +(-1.75429 + 1.01284i) q^{24} -1.00000 q^{25} +(3.08607 - 1.35207i) q^{26} +3.82647 q^{27} +(-0.473378 + 0.273305i) q^{28} +(5.12779 + 8.88159i) q^{29} +(0.323924 - 0.561053i) q^{30} -1.89308i q^{31} +(-4.67493 - 2.69907i) q^{32} +(0.600400 + 0.346641i) q^{33} +4.40690i q^{34} +(0.242555 - 0.420118i) q^{35} +(1.41937 + 2.45843i) q^{36} +(-1.49068 + 0.860647i) q^{37} +5.85712 q^{38} +(1.00310 + 2.28956i) q^{39} +2.92186 q^{40} +(-2.44072 + 1.40915i) q^{41} +(0.157139 + 0.272173i) q^{42} +(1.07246 - 1.85756i) q^{43} +1.12677i q^{44} +(-2.18183 - 1.25968i) q^{45} +(-1.33267 - 0.769420i) q^{46} +2.90646i q^{47} +(-0.165289 + 0.286290i) q^{48} +(-3.38233 - 5.85837i) q^{49} +(-0.809271 + 0.467233i) q^{50} -3.26949 q^{51} +(-2.40747 + 3.27248i) q^{52} +9.25802 q^{53} +(3.09665 - 1.78785i) q^{54} +(-0.500000 - 0.866025i) q^{55} +(-0.708713 + 1.22753i) q^{56} +4.34541i q^{57} +(8.29954 + 4.79174i) q^{58} +(-8.67319 - 5.00747i) q^{59} +0.781172i q^{60} +(7.15004 - 12.3842i) q^{61} +(-0.884509 - 1.53201i) q^{62} +(1.05843 - 0.611084i) q^{63} -5.99804 q^{64} +(0.398207 - 3.58349i) q^{65} +0.647848 q^{66} +(-6.20047 + 3.57984i) q^{67} +(-2.65691 - 4.60190i) q^{68} +(0.570835 - 0.988714i) q^{69} -0.453319i q^{70} +(4.12383 + 2.38089i) q^{71} +(6.37501 + 3.68061i) q^{72} -8.36628i q^{73} +(-0.804245 + 1.39299i) q^{74} +(-0.346641 - 0.600400i) q^{75} +(-6.11629 + 3.53124i) q^{76} +0.485111 q^{77} +(1.88154 + 1.38420i) q^{78} -13.1974 q^{79} +(0.412948 - 0.238416i) q^{80} +(-2.45263 - 4.24808i) q^{81} +(-1.31680 + 2.28077i) q^{82} -0.355851i q^{83} +(-0.328185 - 0.189477i) q^{84} +(4.08414 + 2.35798i) q^{85} -2.00436i q^{86} +(-3.55500 + 6.15745i) q^{87} +(1.46093 + 2.53041i) q^{88} +(-0.495002 + 0.285789i) q^{89} -2.35426 q^{90} +(1.40890 + 1.03649i) q^{91} +1.85553 q^{92} +(1.13660 - 0.656219i) q^{93} +(1.35799 + 2.35211i) q^{94} +(3.13394 - 5.42814i) q^{95} -3.74244i q^{96} +(-5.73492 - 3.31106i) q^{97} +(-5.47445 - 3.16067i) q^{98} -2.51936i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 34 q^{4} + 18 q^{6} + 6 q^{7} - 46 q^{9}+O(q^{10}) \) 56 * q - 6 * q^3 + 34 * q^4 + 18 * q^6 + 6 * q^7 - 46 * q^9	\( 56 q - 6 q^{3} + 34 q^{4} + 18 q^{6} + 6 q^{7} - 46 q^{9} + 2 q^{10} - 44 q^{12} - 2 q^{13} + 32 q^{14} - 54 q^{16} + 26 q^{17} - 6 q^{19} - 2 q^{22} + 30 q^{23} + 36 q^{24} - 56 q^{25} - 18 q^{28} - 36 q^{29} - 10 q^{30} - 36 q^{32} - 8 q^{35} + 58 q^{36} - 6 q^{37} - 36 q^{38} + 16 q^{39} + 12 q^{40} - 12 q^{41} - 74 q^{42} + 138 q^{46} - 50 q^{48} + 46 q^{49} - 24 q^{51} + 26 q^{52} + 104 q^{53} - 18 q^{54} - 28 q^{55} + 6 q^{58} + 24 q^{59} - 4 q^{61} + 14 q^{62} - 24 q^{63} - 112 q^{64} + 8 q^{65} - 20 q^{66} + 30 q^{67} - 92 q^{68} - 16 q^{69} + 156 q^{72} - 32 q^{74} + 6 q^{75} - 24 q^{76} - 16 q^{77} + 150 q^{78} - 12 q^{79} + 24 q^{80} - 116 q^{81} - 36 q^{82} + 6 q^{84} + 12 q^{85} - 16 q^{87} + 6 q^{88} - 24 q^{89} - 72 q^{90} + 74 q^{91} + 36 q^{92} + 114 q^{93} - 66 q^{94} - 8 q^{95} + 18 q^{97} + 30 q^{98}+O(q^{100}) \) 56 * q - 6 * q^3 + 34 * q^4 + 18 * q^6 + 6 * q^7 - 46 * q^9 + 2 * q^10 - 44 * q^12 - 2 * q^13 + 32 * q^14 - 54 * q^16 + 26 * q^17 - 6 * q^19 - 2 * q^22 + 30 * q^23 + 36 * q^24 - 56 * q^25 - 18 * q^28 - 36 * q^29 - 10 * q^30 - 36 * q^32 - 8 * q^35 + 58 * q^36 - 6 * q^37 - 36 * q^38 + 16 * q^39 + 12 * q^40 - 12 * q^41 - 74 * q^42 + 138 * q^46 - 50 * q^48 + 46 * q^49 - 24 * q^51 + 26 * q^52 + 104 * q^53 - 18 * q^54 - 28 * q^55 + 6 * q^58 + 24 * q^59 - 4 * q^61 + 14 * q^62 - 24 * q^63 - 112 * q^64 + 8 * q^65 - 20 * q^66 + 30 * q^67 - 92 * q^68 - 16 * q^69 + 156 * q^72 - 32 * q^74 + 6 * q^75 - 24 * q^76 - 16 * q^77 + 150 * q^78 - 12 * q^79 + 24 * q^80 - 116 * q^81 - 36 * q^82 + 6 * q^84 + 12 * q^85 - 16 * q^87 + 6 * q^88 - 24 * q^89 - 72 * q^90 + 74 * q^91 + 36 * q^92 + 114 * q^93 - 66 * q^94 - 8 * q^95 + 18 * q^97 + 30 * q^98

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