LMFDB - Embedded newform 350.2.m.a.239.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(29,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("350.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.m (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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			239.2
Character	$\chi$	$=$	350.239
Dual form			350.2.m.a.309.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(0.195447 + 0.0635047i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.0419655 - 2.23567i) q^{5} +(-0.0635047 - 0.195447i) q^{6} -1.00000i q^{7} +(0.951057 - 0.309017i) q^{8} +(-2.39288 - 1.73853i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(0.195447 + 0.0635047i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.0419655 - 2.23567i) q^{5} +(-0.0635047 - 0.195447i) q^{6} -1.00000i q^{7} +(0.951057 - 0.309017i) q^{8} +(-2.39288 - 1.73853i) q^{9} +(-1.83337 + 1.28015i) q^{10} +(0.483397 - 0.351209i) q^{11} +(-0.120793 + 0.166258i) q^{12} +(-1.59798 + 2.19943i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(0.150178 - 0.434292i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.72127 - 0.559274i) q^{17} +2.95777i q^{18} +(-2.23744 - 6.88612i) q^{19} +(2.11328 + 0.730773i) q^{20} +(0.0635047 - 0.195447i) q^{21} +(-0.568268 - 0.184641i) q^{22} +(-0.516806 - 0.711323i) q^{23} +0.205506 q^{24} +(-4.99648 - 0.187642i) q^{25} +2.71865 q^{26} +(-0.719658 - 0.990524i) q^{27} +(0.951057 + 0.309017i) q^{28} +(1.25308 - 3.85659i) q^{29} +(-0.439622 + 0.133774i) q^{30} +(-1.36453 - 4.19959i) q^{31} +1.00000i q^{32} +(0.116782 - 0.0379448i) q^{33} +(-1.46420 - 1.06380i) q^{34} +(-2.23567 - 0.0419655i) q^{35} +(2.39288 - 1.73853i) q^{36} +(-2.27805 + 3.13546i) q^{37} +(-4.25586 + 5.85769i) q^{38} +(-0.451996 + 0.328394i) q^{39} +(-0.650950 - 2.13922i) q^{40} +(4.93070 + 3.58236i) q^{41} +(-0.195447 + 0.0635047i) q^{42} +0.789626i q^{43} +(0.184641 + 0.568268i) q^{44} +(-3.98721 + 5.27675i) q^{45} +(-0.271701 + 0.836210i) q^{46} +(0.430533 + 0.139889i) q^{47} +(-0.120793 - 0.166258i) q^{48} -1.00000 q^{49} +(2.78505 + 4.15253i) q^{50} +0.371934 q^{51} +(-1.59798 - 2.19943i) q^{52} +(9.74573 + 3.16658i) q^{53} +(-0.378346 + 1.16443i) q^{54} +(-0.764902 - 1.09546i) q^{55} +(-0.309017 - 0.951057i) q^{56} -1.48796i q^{57} +(-3.85659 + 1.25308i) q^{58} +(1.21560 + 0.883186i) q^{59} +(0.366629 + 0.277031i) q^{60} +(9.35755 - 6.79866i) q^{61} +(-2.59549 + 3.57238i) q^{62} +(-1.73853 + 2.39288i) q^{63} +(0.809017 - 0.587785i) q^{64} +(4.85016 + 3.66487i) q^{65} +(-0.0993408 - 0.0721753i) q^{66} +(-3.66555 + 1.19101i) q^{67} +1.80985i q^{68} +(-0.0558361 - 0.171846i) q^{69} +(1.28015 + 1.83337i) q^{70} +(-0.329896 + 1.01532i) q^{71} +(-2.81300 - 0.914000i) q^{72} +(4.35351 + 5.99209i) q^{73} +3.87565 q^{74} +(-0.964633 - 0.353974i) q^{75} +7.24050 q^{76} +(-0.351209 - 0.483397i) q^{77} +(0.531353 + 0.172647i) q^{78} +(1.32550 - 4.07947i) q^{79} +(-1.34805 + 1.78403i) q^{80} +(2.66425 + 8.19972i) q^{81} -6.09468i q^{82} +(0.811986 - 0.263830i) q^{83} +(0.166258 + 0.120793i) q^{84} +(-1.17812 - 3.87167i) q^{85} +(0.638821 - 0.464130i) q^{86} +(0.489824 - 0.674185i) q^{87} +(0.351209 - 0.483397i) q^{88} +(9.67930 - 7.03242i) q^{89} +(6.61260 + 0.124124i) q^{90} +(2.19943 + 1.59798i) q^{91} +(0.836210 - 0.271701i) q^{92} -0.907452i q^{93} +(-0.139889 - 0.430533i) q^{94} +(-15.4890 + 4.71320i) q^{95} +(-0.0635047 + 0.195447i) q^{96} +(3.27298 + 1.06346i) q^{97} +(0.587785 + 0.809017i) q^{98} -1.76730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) $ 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9	$ 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) $ 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9 + 2 * q^11 + 10 * q^12 - 6 * q^14 + 20 * q^15 - 6 * q^16 - 22 * q^19 - 2 * q^21 - 10 * q^22 - 10 * q^23 + 8 * q^24 - 10 * q^25 - 4 * q^26 - 30 * q^27 - 12 * q^29 - 10 * q^30 + 20 * q^33 - 8 * q^36 + 10 * q^37 - 10 * q^38 - 48 * q^39 + 10 * q^40 + 42 * q^41 - 2 * q^44 - 40 * q^45 + 10 * q^46 + 30 * q^47 + 10 * q^48 - 24 * q^49 + 20 * q^50 - 52 * q^51 + 10 * q^53 + 4 * q^54 + 10 * q^55 + 6 * q^56 - 20 * q^58 - 10 * q^60 + 46 * q^61 - 20 * q^63 + 6 * q^64 + 10 * q^65 - 10 * q^66 + 10 * q^67 + 32 * q^71 + 30 * q^73 - 28 * q^74 - 10 * q^75 - 48 * q^76 + 20 * q^77 - 20 * q^78 - 44 * q^79 + 76 * q^81 + 50 * q^83 + 2 * q^84 - 50 * q^85 - 6 * q^86 - 20 * q^87 - 20 * q^88 - 4 * q^89 + 50 * q^90 - 6 * q^91 + 30 * q^92 - 6 * q^94 - 60 * q^95 + 2 * q^96 + 30 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	0.195447	+	0.0635047i	0.112842	+	0.0366645i	0.364894	−	0.931049i	$-0.381105\pi$
$3$	0.195447	+	0.0635047i	0.112842	+	0.0366645i	−0.252052	+	0.967714i	$0.581105\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	0.0419655	−	2.23567i	0.0187675	−	0.999824i
$5$	0.0419655	−	2.23567i	0.0187675	−	0.999824i
$6$	−0.0635047	−	0.195447i	−0.0259257	−	0.0797911i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	−2.39288	−	1.73853i	−0.797628	−	0.579511i
$10$	−1.83337	+	1.28015i	−0.579761	+	0.404818i
$11$	0.483397	−	0.351209i	0.145750	−	0.105893i	−0.512521	−	0.858675i	$-0.671288\pi$
$11$	0.483397	−	0.351209i	0.145750	−	0.105893i	0.658271	+	0.752781i	$0.271288\pi$
$12$	−0.120793	+	0.166258i	−0.0348700	+	0.0479944i
$13$	−1.59798	+	2.19943i	−0.443201	+	0.610013i	−0.970920	−	0.239406i	$-0.923047\pi$
$13$	−1.59798	+	2.19943i	−0.443201	+	0.610013i	0.527719	+	0.849419i	$0.323047\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$	0.150178	−	0.434292i	0.0387758	−	0.112134i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.72127	−	0.559274i	0.417469	−	0.135644i	−0.0927479	−	0.995690i	$-0.529565\pi$
$17$	1.72127	−	0.559274i	0.417469	−	0.135644i	0.510217	+	0.860046i	$0.329565\pi$
$18$			2.95777i			0.697152i
$19$	−2.23744	−	6.88612i	−0.513303	−	1.57978i	−0.786348	−	0.617784i	$-0.788031\pi$
$19$	−2.23744	−	6.88612i	−0.513303	−	1.57978i	0.273045	−	0.962001i	$-0.411969\pi$
$20$	2.11328	+	0.730773i	0.472545	+	0.163406i
$21$	0.0635047	−	0.195447i	0.0138579	−	0.0426501i
$22$	−0.568268	−	0.184641i	−0.121155	−	0.0393657i
$23$	−0.516806	−	0.711323i	−0.107762	−	0.148321i	0.751730	−	0.659471i	$-0.229220\pi$
$23$	−0.516806	−	0.711323i	−0.107762	−	0.148321i	−0.859492	+	0.511150i	$0.829220\pi$
$24$	0.205506			0.0419487
$25$	−4.99648	−	0.187642i	−0.999296	−	0.0375285i
$26$	2.71865			0.533171
$27$	−0.719658	−	0.990524i	−0.138498	−	0.190626i
$28$	0.951057	+	0.309017i	0.179733	+	0.0583987i
$29$	1.25308	−	3.85659i	0.232692	−	0.716151i	−0.764728	−	0.644354i	$-0.777126\pi$
$29$	1.25308	−	3.85659i	0.232692	−	0.716151i	0.997419	−	0.0717976i	$-0.0228736\pi$
$30$	−0.439622	+	0.133774i	−0.0802636	+	0.0244236i
$31$	−1.36453	−	4.19959i	−0.245077	−	0.754268i	−0.995624	−	0.0934513i	$-0.970210\pi$
$31$	−1.36453	−	4.19959i	−0.245077	−	0.754268i	0.750547	−	0.660817i	$-0.229790\pi$
$32$			1.00000i			0.176777i
$33$	0.116782	−	0.0379448i	0.0203292	−	0.00660535i
$34$	−1.46420	−	1.06380i	−0.251108	−	0.182441i
$35$	−2.23567	−	0.0419655i	−0.377898	−	0.00709346i
$36$	2.39288	−	1.73853i	0.398814	−	0.289755i
$37$	−2.27805	+	3.13546i	−0.374509	+	0.515467i	−0.954119	−	0.299426i	$-0.903205\pi$
$37$	−2.27805	+	3.13546i	−0.374509	+	0.515467i	0.579611	+	0.814894i	$0.303205\pi$
$38$	−4.25586	+	5.85769i	−0.690391	+	0.950242i
$39$	−0.451996	+	0.328394i	−0.0723773	+	0.0525852i
$40$	−0.650950	−	2.13922i	−0.102924	−	0.338240i
$41$	4.93070	+	3.58236i	0.770046	+	0.559471i	0.901975	−	0.431788i	$-0.142117\pi$
$41$	4.93070	+	3.58236i	0.770046	+	0.559471i	−0.131929	+	0.991259i	$0.542117\pi$
$42$	−0.195447	+	0.0635047i	−0.0301582	+	0.00979899i
$43$			0.789626i			0.120417i	0.998186	+	0.0602084i	$0.0191765\pi$
$43$			0.789626i			0.120417i	−0.998186	+	0.0602084i	$0.980823\pi$
$44$	0.184641	+	0.568268i	0.0278357	+	0.0856696i
$45$	−3.98721	+	5.27675i	−0.594378	+	0.786612i
$46$	−0.271701	+	0.836210i	−0.0400602	+	0.123292i
$47$	0.430533	+	0.139889i	0.0627998	+	0.0204049i	0.340248	−	0.940336i	$-0.389489\pi$
$47$	0.430533	+	0.139889i	0.0627998	+	0.0204049i	−0.277449	+	0.960740i	$0.589489\pi$
$48$	−0.120793	−	0.166258i	−0.0174350	−	0.0239972i
$49$	−1.00000			−0.142857
$50$	2.78505	+	4.15253i	0.393866	+	0.587256i
$51$	0.371934			0.0520812
$52$	−1.59798	−	2.19943i	−0.221600	−	0.305007i
$53$	9.74573	+	3.16658i	1.33868	+	0.434963i	0.888869	−	0.458162i	$-0.151492\pi$
$53$	9.74573	+	3.16658i	1.33868	+	0.434963i	0.449809	+	0.893125i	$0.351492\pi$
$54$	−0.378346	+	1.16443i	−0.0514864	+	0.158459i
$55$	−0.764902	−	1.09546i	−0.103139	−	0.147711i
$56$	−0.309017	−	0.951057i	−0.0412941	−	0.127090i
$57$		−	1.48796i		−	0.197085i
$58$	−3.85659	+	1.25308i	−0.506396	+	0.164538i
$59$	1.21560	+	0.883186i	0.158258	+	0.114981i	0.664096	−	0.747647i	$-0.268817\pi$
$59$	1.21560	+	0.883186i	0.158258	+	0.114981i	−0.505838	+	0.862628i	$0.668817\pi$
$60$	0.366629	+	0.277031i	0.0473315	+	0.0357646i
$61$	9.35755	−	6.79866i	1.19811	−	0.870479i	0.204014	−	0.978968i	$-0.434601\pi$
$61$	9.35755	−	6.79866i	1.19811	−	0.870479i	0.994098	+	0.108489i	$0.0346011\pi$
$62$	−2.59549	+	3.57238i	−0.329627	+	0.453693i
$63$	−1.73853	+	2.39288i	−0.219034	+	0.301475i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	4.85016	+	3.66487i	0.601588	+	0.454571i
$66$	−0.0993408	−	0.0721753i	−0.0122280	−	0.00888417i
$67$	−3.66555	+	1.19101i	−0.447818	+	0.145505i	−0.524240	−	0.851571i	$-0.675650\pi$
$67$	−3.66555	+	1.19101i	−0.447818	+	0.145505i	0.0764220	+	0.997076i	$0.475650\pi$
$68$			1.80985i			0.219477i
$69$	−0.0558361	−	0.171846i	−0.00672188	−	0.0206878i
$70$	1.28015	+	1.83337i	0.153007	+	0.219129i
$71$	−0.329896	+	1.01532i	−0.0391514	+	0.120496i	−0.968722	−	0.248148i	$-0.920178\pi$
$71$	−0.329896	+	1.01532i	−0.0391514	+	0.120496i	0.929571	+	0.368644i	$0.120178\pi$
$72$	−2.81300	−	0.914000i	−0.331516	−	0.107716i
$73$	4.35351	+	5.99209i	0.509540	+	0.701322i	0.983842	−	0.179041i	$-0.0572994\pi$
$73$	4.35351	+	5.99209i	0.509540	+	0.701322i	−0.474302	+	0.880362i	$0.657299\pi$
$74$	3.87565			0.450535
$75$	−0.964633	−	0.353974i	−0.111386	−	0.0408734i
$76$	7.24050			0.830542
$77$	−0.351209	−	0.483397i	−0.0400239	−	0.0550882i
$78$	0.531353	+	0.172647i	0.0601639	+	0.0195484i
$79$	1.32550	−	4.07947i	0.149130	−	0.458976i	−0.848389	−	0.529374i	$-0.822427\pi$
$79$	1.32550	−	4.07947i	0.149130	−	0.458976i	0.997519	+	0.0703978i	$0.0224269\pi$
$80$	−1.34805	+	1.78403i	−0.150716	+	0.199461i
$81$	2.66425	+	8.19972i	0.296028	+	0.911079i
$82$		−	6.09468i		−	0.673045i
$83$	0.811986	−	0.263830i	0.0891271	−	0.0289591i	−0.264114	−	0.964491i	$-0.585080\pi$
$83$	0.811986	−	0.263830i	0.0891271	−	0.0289591i	0.353241	+	0.935532i	$0.385080\pi$
$84$	0.166258	+	0.120793i	0.0181402	+	0.0131796i
$85$	−1.17812	−	3.87167i	−0.127785	−	0.419941i
$86$	0.638821	−	0.464130i	0.0688858	−	0.0500485i
$87$	0.489824	−	0.674185i	0.0525146	−	0.0722802i
$88$	0.351209	−	0.483397i	0.0374390	−	0.0515303i
$89$	9.67930	−	7.03242i	1.02600	−	0.745435i	0.0584984	−	0.998288i	$-0.481369\pi$
$89$	9.67930	−	7.03242i	1.02600	−	0.745435i	0.967505	+	0.252853i	$0.0813687\pi$
$90$	6.61260	+	0.124124i	0.697030	+	0.0130838i
$91$	2.19943	+	1.59798i	0.230563	+	0.167514i
$92$	0.836210	−	0.271701i	0.0871810	−	0.0283268i
$93$		−	0.907452i		−	0.0940984i
$94$	−0.139889	−	0.430533i	−0.0144284	−	0.0444061i
$95$	−15.4890	+	4.71320i	−1.58914	+	0.483564i
$96$	−0.0635047	+	0.195447i	−0.00648142	+	0.0199478i
$97$	3.27298	+	1.06346i	0.332321	+	0.107978i	0.470425	−	0.882440i	$-0.344101\pi$
$97$	3.27298	+	1.06346i	0.332321	+	0.107978i	−0.138104	+	0.990418i	$0.544101\pi$
$98$	0.587785	+	0.809017i	0.0593753	+	0.0817231i
$99$	−1.76730			−0.177620
$100$	1.72246	−	4.69395i	0.172246	−	0.469395i
$101$	13.8998			1.38308			0.691539	−	0.722339i	$-0.256933\pi$
$101$	13.8998			1.38308			0.691539	+	0.722339i	$0.256933\pi$
$102$	−0.218617	−	0.300901i	−0.0216464	−	0.0297937i
$103$	17.8160	+	5.78877i	1.75546	+	0.570384i	0.996714	−	0.0809992i	$-0.0258111\pi$
$103$	17.8160	+	5.78877i	1.75546	+	0.570384i	0.758749	+	0.651384i	$0.225811\pi$
$104$	−0.840109	+	2.58559i	−0.0823795	+	0.253538i
$105$	−0.434292	−	0.150178i	−0.0423825	−	0.0146559i
$106$	−3.16658	−	9.74573i	−0.307565	−	0.946589i
$107$			15.4645i			1.49501i	0.664255	+	0.747506i	$0.268749\pi$
$107$			15.4645i			1.49501i	−0.664255	+	0.747506i	$0.731251\pi$
$108$	1.16443	−	0.378346i	0.112047	−	0.0364064i
$109$	−5.75790	−	4.18336i	−0.551507	−	0.400693i	0.276834	−	0.960918i	$-0.410715\pi$
$109$	−5.75790	−	4.18336i	−0.551507	−	0.400693i	−0.828341	+	0.560225i	$0.810715\pi$
$110$	−0.436645	+	1.26271i	−0.0416325	+	0.120395i
$111$	−0.644355	+	0.468152i	−0.0611595	+	0.0444350i
$112$	−0.587785	+	0.809017i	−0.0555405	+	0.0764449i
$113$	5.71385	−	7.86444i	0.537514	−	0.739824i	−0.450739	−	0.892656i	$-0.648839\pi$
$113$	5.71385	−	7.86444i	0.537514	−	0.739824i	0.988252	+	0.152832i	$0.0488393\pi$
$114$	−1.20379	+	0.874603i	−0.112745	+	0.0819140i
$115$	−1.61197	+	1.12556i	−0.150317	+	0.104959i
$116$	3.28061	+	2.38351i	0.304597	+	0.221303i
$117$	7.64757	−	2.48485i	0.707019	−	0.229724i
$118$		−	1.50257i		−	0.138322i
$119$	−0.559274	−	1.72127i	−0.0512686	−	0.157789i
$120$	0.00862414	−	0.459444i	0.000787273	−	0.0419413i
$121$	−3.28886	+	10.1221i	−0.298987	+	0.920189i
$122$	−11.0005	−	3.57427i	−0.995935	−	0.323599i
$123$	0.736195	+	1.01329i	0.0663805	+	0.0913649i
$124$	4.41571			0.396542
$125$	−0.629187	+	11.1626i	−0.0562762	+	0.998415i
$126$	2.95777			0.263499
$127$	−12.8753	−	17.7213i	−1.14250	−	1.57251i	−0.761802	−	0.647810i	$-0.775685\pi$
$127$	−12.8753	−	17.7213i	−1.14250	−	1.57251i	−0.380695	−	0.924701i	$-0.624315\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	−0.0501450	+	0.154330i	−0.00441502	+	0.0135880i
$130$	0.114090	−	6.07802i	0.0100063	−	0.533077i
$131$	−0.562324	−	1.73065i	−0.0491305	−	0.151208i	0.923481	−	0.383643i	$-0.125331\pi$
$131$	−0.562324	−	1.73065i	−0.0491305	−	0.151208i	−0.972612	+	0.232435i	$0.925331\pi$
$132$			0.122792i			0.0106877i
$133$	−6.88612	+	2.23744i	−0.597103	+	0.194010i
$134$	3.11810	+	2.26543i	0.269363	+	0.195704i
$135$	−2.24469	+	1.56735i	−0.193192	+	0.134896i
$136$	1.46420	−	1.06380i	0.125554	−	0.0912204i
$137$	−10.7406	+	14.7831i	−0.917630	+	1.26301i	0.0468633	+	0.998901i	$0.485077\pi$
$137$	−10.7406	+	14.7831i	−0.917630	+	1.26301i	−0.964493	+	0.264108i	$0.914923\pi$
$138$	−0.106207	+	0.146181i	−0.00904091	+	0.0124437i
$139$	−0.431646	+	0.313609i	−0.0366117	+	0.0266000i	−0.605941	−	0.795510i	$-0.707203\pi$
$139$	−0.431646	+	0.313609i	−0.0366117	+	0.0266000i	0.569329	+	0.822110i	$0.307203\pi$
$140$	0.730773	−	2.11328i	0.0617616	−	0.178605i
$141$	0.0752631	+	0.0546818i	0.00633829	+	0.00460504i
$142$	1.01532	−	0.329896i	0.0852033	−	0.0276842i
$143$			1.62443i			0.135841i
$144$	0.914000	+	2.81300i	0.0761667	+	0.234417i
$145$	−8.56950	−	2.96333i	−0.711658	−	0.246091i
$146$	2.28878	−	7.04413i	0.189420	−	0.582976i
$147$	−0.195447	−	0.0635047i	−0.0161202	−	0.00523778i
$148$	−2.27805	−	3.13546i	−0.187254	−	0.257734i
$149$	−6.57541			−0.538679			−0.269339	−	0.963045i	$-0.586805\pi$
$149$	−6.57541			−0.538679			−0.269339	+	0.963045i	$0.586805\pi$
$150$	0.280626	+	0.988465i	0.0229130	+	0.0807078i
$151$	−21.8023			−1.77424			−0.887122	−	0.461535i	$-0.847299\pi$
$151$	−21.8023			−1.77424			−0.887122	+	0.461535i	$0.847299\pi$
$152$	−4.25586	−	5.85769i	−0.345196	−	0.475121i
$153$	−5.09112	−	1.65420i	−0.411592	−	0.133734i
$154$	−0.184641	+	0.568268i	−0.0148788	+	0.0457923i
$155$	−9.44617	+	2.87440i	−0.758735	+	0.230878i
$156$	−0.172647	−	0.531353i	−0.0138228	−	0.0425423i
$157$		−	5.49190i		−	0.438301i	−0.975691	−	0.219151i	$-0.929671\pi$
$157$		−	5.49190i		−	0.438301i	0.975691	−	0.219151i	$-0.0703286\pi$
$158$	−4.07947	+	1.32550i	−0.324545	+	0.105451i
$159$	1.70368	+	1.23780i	0.135111	+	0.0981639i
$160$	2.23567	+	0.0419655i	0.176746	+	0.00331766i
$161$	−0.711323	+	0.516806i	−0.0560601	+	0.0407301i
$162$	5.06770	−	6.97509i	0.398156	−	0.548015i
$163$	4.08905	−	5.62809i	0.320279	−	0.440826i	−0.618273	−	0.785963i	$-0.712168\pi$
$163$	4.08905	−	5.62809i	0.320279	−	0.440826i	0.938552	+	0.345137i	$0.112168\pi$
$164$	−4.93070	+	3.58236i	−0.385023	+	0.279735i
$165$	−0.0799314	−	0.262679i	−0.00622265	−	0.0204496i
$166$	−0.690717	−	0.501835i	−0.0536100	−	0.0389500i
$167$	3.03951	−	0.987596i	0.235204	−	0.0764224i	−0.189043	−	0.981969i	$-0.560539\pi$
$167$	3.03951	−	0.987596i	0.235204	−	0.0764224i	0.424247	+	0.905546i	$0.360539\pi$
$168$		−	0.205506i		−	0.0158551i
$169$	1.73326	+	5.33442i	0.133328	+	0.410340i
$170$	−2.43976	+	3.22883i	−0.187121	+	0.247640i
$171$	−6.61782	+	20.3675i	−0.506077	+	1.55755i
$172$	−0.750979	−	0.244008i	−0.0572616	−	0.0186054i
$173$	−5.78976	−	7.96892i	−0.440187	−	0.605866i	0.530067	−	0.847956i	$-0.322167\pi$
$173$	−5.78976	−	7.96892i	−0.440187	−	0.605866i	−0.970254	+	0.242090i	$0.922167\pi$
$174$	−0.833338			−0.0631752
$175$	−0.187642	+	4.99648i	−0.0141844	+	0.377698i
$176$	−0.597512			−0.0450391
$177$	0.181500	+	0.249813i	0.0136424	+	0.0187771i
$178$	−11.3787	−	3.69716i	−0.852869	−	0.277114i
$179$	6.83054	−	21.0222i	0.510538	−	1.57127i	−0.280718	−	0.959790i	$-0.590573\pi$
$179$	6.83054	−	21.0222i	0.510538	−	1.57127i	0.791256	−	0.611485i	$-0.209427\pi$
$180$	−3.78637	−	5.42267i	−0.282220	−	0.404182i
$181$	−6.56272	−	20.1980i	−0.487803	−	1.50130i	−0.827879	−	0.560907i	$-0.810453\pi$
$181$	−6.56272	−	20.1980i	−0.487803	−	1.50130i	0.340076	−	0.940398i	$-0.389547\pi$
$182$		−	2.71865i		−	0.201520i
$183$	2.26066	−	0.734532i	0.167113	−	0.0542982i
$184$	−0.711323	−	0.516806i	−0.0524394	−	0.0380995i
$185$	6.91428	+	5.22455i	0.508348	+	0.384117i
$186$	−0.734144	+	0.533387i	−0.0538301	+	0.0391098i
$187$	0.635635	−	0.874876i	0.0464822	−	0.0639773i
$188$	−0.266084	+	0.366234i	−0.0194062	+	0.0267103i
$189$	−0.990524	+	0.719658i	−0.0720500	+	0.0523474i
$190$	12.9173	+	9.76053i	0.937118	+	0.708103i
$191$	−7.68045	−	5.58017i	−0.555738	−	0.403767i	0.274159	−	0.961684i	$-0.411601\pi$
$191$	−7.68045	−	5.58017i	−0.555738	−	0.403767i	−0.829897	+	0.557917i	$0.811601\pi$
$192$	0.195447	−	0.0635047i	0.0141052	−	0.00458306i
$193$			13.2568i			0.954245i	0.878837	+	0.477122i	$0.158320\pi$
$193$			13.2568i			0.954245i	−0.878837	+	0.477122i	$0.841680\pi$
$194$	−1.06346	−	3.27298i	−0.0763517	−	0.234986i
$195$	0.715215	+	1.02430i	0.0512176	+	0.0733514i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	12.6702	+	4.11680i	0.902714	+	0.293310i	0.723357	−	0.690474i	$-0.242598\pi$
$197$	12.6702	+	4.11680i	0.902714	+	0.293310i	0.179357	+	0.983784i	$0.442598\pi$
$198$	1.03879	+	1.42978i	0.0738238	+	0.101610i
$199$	10.0050			0.709234			0.354617	−	0.935012i	$-0.384611\pi$
$199$	10.0050			0.709234			0.354617	+	0.935012i	$0.384611\pi$
$200$	−4.80992	+	1.36554i	−0.340113	+	0.0965581i
$201$	−0.792056			−0.0558673
$202$	−8.17008	−	11.2451i	−0.574845	−	0.791206i
$203$	−3.85659	−	1.25308i	−0.270680	−	0.0879492i
$204$	−0.114934	+	0.353731i	−0.00804699	+	0.0247661i
$205$	8.21591	−	10.8731i	0.573824	−	0.759410i
$206$	−5.78877	−	17.8160i	−0.403323	−	1.24130i
$207$			2.60060i			0.180754i
$208$	2.58559	−	0.840109i	0.179278	−	0.0582511i
$209$	−3.50004	−	2.54293i	−0.242103	−	0.175898i
$210$	0.133774	+	0.439622i	0.00923127	+	0.0303368i
$211$	−7.03318	+	5.10990i	−0.484184	+	0.351780i	−0.802943	−	0.596056i	$-0.796734\pi$
$211$	−7.03318	+	5.10990i	−0.484184	+	0.351780i	0.318759	+	0.947836i	$0.396734\pi$
$212$	−6.02319	+	8.29021i	−0.413674	+	0.569374i
$213$	−0.128955	+	0.177491i	−0.00883582	+	0.0121615i
$214$	12.5111	−	9.08982i	0.855239	−	0.621368i
$215$	1.76535	+	0.0331370i	0.120396	+	0.00225993i
$216$	−0.990524	−	0.719658i	−0.0673966	−	0.0489665i
$217$	−4.19959	+	1.36453i	−0.285086	+	0.0926302i
$218$			7.11716i			0.482035i
$219$	0.470356	+	1.44761i	0.0317837	+	0.0978203i
$220$	1.27821	−	0.388950i	0.0861769	−	0.0262230i
$221$	−1.52047	+	4.67953i	−0.102278	+	0.314779i
$222$	0.757485	+	0.246122i	0.0508391	+	0.0165186i
$223$	−12.5177	−	17.2291i	−0.838247	−	1.15375i	−0.986331	−	0.164773i	$-0.947311\pi$
$223$	−12.5177	−	17.2291i	−0.838247	−	1.15375i	0.148084	−	0.988975i	$-0.452689\pi$
$224$	1.00000			0.0668153
$225$	11.6298	+	9.13554i	0.775318	+	0.609036i
$226$	−9.72098			−0.646630
$227$	−15.7747	−	21.7121i	−1.04701	−	1.44108i	−0.891376	−	0.453264i	$-0.850259\pi$
$227$	−15.7747	−	21.7121i	−1.04701	−	1.44108i	−0.155630	−	0.987815i	$-0.549741\pi$
$228$	1.41514	+	0.459806i	0.0937197	+	0.0304514i
$229$	6.51678	−	20.0566i	0.430641	−	1.32538i	−0.466848	−	0.884338i	$-0.654610\pi$
$229$	6.51678	−	20.0566i	0.430641	−	1.32538i	0.897488	−	0.441038i	$-0.145390\pi$
$230$	1.85809	+	0.642527i	0.122519	+	0.0423670i
$231$	−0.0379448	−	0.116782i	−0.00249659	−	0.00768370i
$232$		−	4.05506i		−	0.266228i
$233$	7.55691	−	2.45539i	0.495069	−	0.160858i	−0.0508320	−	0.998707i	$-0.516187\pi$
$233$	7.55691	−	2.45539i	0.495069	−	0.160858i	0.545901	+	0.837849i	$0.316187\pi$
$234$	−6.50542	−	4.72646i	−0.425272	−	0.308978i
$235$	0.330813	−	0.956662i	0.0215799	−	0.0624057i
$236$	−1.21560	+	0.883186i	−0.0791289	+	0.0574905i
$237$	0.518131	−	0.713146i	0.0336562	−	0.0463238i
$238$	−1.06380	+	1.46420i	−0.0689561	+	0.0949099i
$239$	−14.5058	+	10.5391i	−0.938303	+	0.681717i	−0.948012	−	0.318236i	$-0.896910\pi$
$239$	−14.5058	+	10.5391i	−0.938303	+	0.681717i	0.00970836	+	0.999953i	$0.496910\pi$
$240$	−0.376767	+	0.263077i	−0.0243202	+	0.0169816i
$241$	15.7279	+	11.4270i	1.01312	+	0.736076i	0.964862	−	0.262758i	$-0.0846322\pi$
$241$	15.7279	+	11.4270i	1.01312	+	0.736076i	0.0482605	+	0.998835i	$0.484632\pi$
$242$	10.1221	−	3.28886i	0.650672	−	0.211416i
$243$			5.44487i			0.349289i
$244$	3.57427	+	11.0005i	0.228819	+	0.704233i
$245$	−0.0419655	+	2.23567i	−0.00268108	+	0.142832i
$246$	0.387041	−	1.19119i	0.0246768	−	0.0759474i
$247$	18.7210	+	6.08281i	1.19119	+	0.387040i
$248$	−2.59549	−	3.57238i	−0.164814	−	0.226846i
$249$	0.175455			0.0111190
$250$	9.40058	−	6.05220i	0.594545	−	0.382775i
$251$	1.64512			0.103839			0.0519195	−	0.998651i	$-0.483466\pi$
$251$	1.64512			0.103839			0.0519195	+	0.998651i	$0.483466\pi$
$252$	−1.73853	−	2.39288i	−0.109517	−	0.150738i
$253$	−0.499646	−	0.162345i	−0.0314124	−	0.0102065i
$254$	−6.76893	+	20.8326i	−0.424721	+	1.30716i
$255$	0.0156084	−	0.831524i	0.000977436	−	0.0520720i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			23.4942i			1.46553i	0.680482	+	0.732765i	$0.261770\pi$
$257$			23.4942i			1.46553i	−0.680482	+	0.732765i	$0.738230\pi$
$258$	0.154330	−	0.0501450i	0.00960819	−	0.00312189i
$259$	3.13546	+	2.27805i	0.194828	+	0.141551i
$260$	−4.98428	+	3.48027i	−0.309112	+	0.215837i
$261$	−9.70329	+	7.04986i	−0.600619	+	0.436375i
$262$	−1.06960	+	1.47218i	−0.0660803	+	0.0909517i
$263$	15.6267	−	21.5083i	0.963582	−	1.32626i	0.0183590	−	0.999831i	$-0.494156\pi$
$263$	15.6267	−	21.5083i	0.963582	−	1.32626i	0.945223	−	0.326425i	$-0.105844\pi$
$264$	0.0993408	−	0.0721753i	0.00611401	−	0.00444209i
$265$	7.48842	−	21.6554i	0.460010	−	1.33028i
$266$	5.85769	+	4.25586i	0.359158	+	0.260943i
$267$	2.33839	−	0.759787i	0.143107	−	0.0464982i
$268$		−	3.85418i		−	0.235432i
$269$	5.31572	+	16.3601i	0.324105	+	0.997493i	0.971843	+	0.235630i	$0.0757153\pi$
$269$	5.31572	+	16.3601i	0.324105	+	0.997493i	−0.647738	+	0.761863i	$0.724285\pi$
$270$	2.58741	+	0.894725i	0.157465	+	0.0544512i
$271$	−9.68797	+	29.8165i	−0.588502	+	1.81122i	−0.00377722	+	0.999993i	$0.501202\pi$
$271$	−9.68797	+	29.8165i	−0.588502	+	1.81122i	−0.584725	+	0.811231i	$0.698798\pi$
$272$	−1.72127	−	0.559274i	−0.104367	−	0.0339110i
$273$	0.328394	+	0.451996i	0.0198753	+	0.0273560i
$274$	18.2730			1.10391
$275$	−2.48119	+	1.66410i	−0.149621	+	0.100349i
$276$	0.180689			0.0108762
$277$	5.27274	+	7.25730i	0.316808	+	0.436049i	0.937489	−	0.348014i	$-0.113144\pi$
$277$	5.27274	+	7.25730i	0.316808	+	0.436049i	−0.620681	+	0.784063i	$0.713144\pi$
$278$	0.507430	+	0.164874i	0.0304336	+	0.00988849i
$279$	−4.03596	+	12.4214i	−0.241626	+	0.743650i
$280$	−2.13922	+	0.650950i	−0.127843	+	0.0389017i
$281$	0.668526	+	2.05751i	0.0398809	+	0.122741i	0.969015	−	0.247003i	$-0.0794456\pi$
$281$	0.668526	+	2.05751i	0.0398809	+	0.122741i	−0.929134	+	0.369743i	$0.879446\pi$
$282$		−	0.0930302i		−	0.00553987i
$283$	7.11838	−	2.31290i	0.423144	−	0.137488i	−0.0897017	−	0.995969i	$-0.528591\pi$
$283$	7.11838	−	2.31290i	0.423144	−	0.137488i	0.512846	+	0.858481i	$0.328591\pi$
$284$	−0.863679	−	0.627499i	−0.0512499	−	0.0372352i
$285$	−3.32660	−	0.0624431i	−0.197051	−	0.00369881i
$286$	1.31419	−	0.954814i	0.0777096	−	0.0564593i
$287$	3.58236	−	4.93070i	0.211460	−	0.291050i
$288$	1.73853	−	2.39288i	0.102444	−	0.141002i
$289$	−11.1033	+	8.06703i	−0.653136	+	0.474531i
$290$	2.63964	+	8.67467i	0.155005	+	0.509394i
$291$	0.572162	+	0.415700i	0.0335407	+	0.0243687i
$292$	−7.04413	+	2.28878i	−0.412226	+	0.133941i
$293$		−	8.18246i		−	0.478025i	−0.971017	−	0.239012i	$-0.923176\pi$
$293$		−	8.18246i		−	0.478025i	0.971017	−	0.239012i	$-0.0768236\pi$
$294$	0.0635047	+	0.195447i	0.00370367	+	0.0113987i
$295$	2.02553	−	2.68063i	0.117931	−	0.156072i
$296$	−1.19764	+	3.68596i	−0.0696115	+	0.214242i
$297$	−0.695761	−	0.226066i	−0.0403721	−	0.0131177i
$298$	3.86493	+	5.31962i	0.223889	+	0.308157i
$299$	2.39036			0.138238
$300$	0.634737	−	0.808036i	0.0366466	−	0.0466520i
$301$	0.789626			0.0455133
$302$	12.8151	+	17.6384i	0.737424	+	1.01498i
$303$	2.71667	+	0.882701i	0.156069	+	0.0507098i
$304$	−2.23744	+	6.88612i	−0.128326	+	0.394946i
$305$	−14.8069	−	21.2057i	−0.847840	−	1.21424i
$306$	1.65420	+	5.09112i	0.0945645	+	0.291040i
$307$		−	10.8094i		−	0.616925i	−0.951237	−	0.308462i	$-0.900186\pi$
$307$		−	10.8094i		−	0.616925i	0.951237	−	0.308462i	$-0.0998144\pi$
$308$	0.568268	−	0.184641i	0.0323800	−	0.0105209i
$309$	3.11448	+	2.26280i	0.177176	+	0.128726i
$310$	7.87776	+	5.95258i	0.447427	+	0.338084i
$311$	18.9746	−	13.7858i	1.07595	−	0.781722i	0.0989763	−	0.995090i	$-0.468443\pi$
$311$	18.9746	−	13.7858i	1.07595	−	0.781722i	0.976972	+	0.213368i	$0.0684432\pi$
$312$	−0.328394	+	0.451996i	−0.0185917	+	0.0255892i
$313$	−3.91222	+	5.38470i	−0.221132	+	0.304361i	−0.905141	−	0.425112i	$-0.860235\pi$
$313$	−3.91222	+	5.38470i	−0.221132	+	0.304361i	0.684009	+	0.729473i	$0.260235\pi$
$314$	−4.44304	+	3.22806i	−0.250735	+	0.182170i
$315$	5.27675	+	3.98721i	0.297311	+	0.224654i
$316$	3.47020	+	2.52125i	0.195214	+	0.141831i
$317$	25.5430	−	8.29941i	1.43464	−	0.466141i	0.514415	−	0.857541i	$-0.328009\pi$
$317$	25.5430	−	8.29941i	1.43464	−	0.466141i	0.920221	+	0.391400i	$0.128009\pi$
$318$		−	2.10587i		−	0.118091i
$319$	−0.748732	−	2.30436i	−0.0419209	−	0.129019i
$320$	−1.28015	−	1.83337i	−0.0715623	−	0.102488i
$321$	−0.982071	+	3.02250i	−0.0548138	+	0.168700i
$322$	0.836210	+	0.271701i	0.0466002	+	0.0151413i
$323$	−7.70246	−	10.6015i	−0.428577	−	0.589885i
$324$	−8.62169			−0.478983
$325$	8.39699	−	10.6896i	0.465781	−	0.592951i
$326$	−6.95670			−0.385296
$327$	−0.859704	−	1.18328i	−0.0475417	−	0.0654356i
$328$	5.79638	+	1.88336i	0.320052	+	0.103991i
$329$	0.139889	−	0.430533i	0.00771232	−	0.0237361i
$330$	−0.165529	+	0.219065i	−0.00911210	+	0.0120591i
$331$	−10.4285	−	32.0956i	−0.573202	−	1.76413i	−0.642221	−	0.766519i	$-0.721987\pi$
$331$	−10.4285	−	32.0956i	−0.573202	−	1.76413i	0.0690191	−	0.997615i	$-0.478013\pi$
$332$			0.853773i			0.0468569i
$333$	10.9022	−	3.54234i	0.597437	−	0.194119i
$334$	−2.58556	−	1.87852i	−0.141475	−	0.102788i
$335$	2.50888	+	8.24495i	0.137075	+	0.450470i
$336$	−0.166258	+	0.120793i	−0.00907009	+	0.00658981i
$337$	−10.9512	+	15.0730i	−0.596547	+	0.821077i	−0.995387	−	0.0959438i	$-0.969413\pi$
$337$	−10.9512	+	15.0730i	−0.596547	+	0.821077i	0.398839	+	0.917021i	$0.369413\pi$
$338$	3.29685	−	4.53773i	0.179325	−	0.246820i
$339$	1.61619	−	1.17423i	0.0877792	−	0.0637753i
$340$	4.04623	+	0.0759513i	0.219438	+	0.00411904i
$341$	−2.13454	−	1.55083i	−0.115592	−	0.0839824i
$342$	20.3675	−	6.61782i	1.10135	−	0.357851i
$343$			1.00000i			0.0539949i
$344$	0.244008	+	0.750979i	0.0131560	+	0.0404901i
$345$	−0.386535	+	0.117620i	−0.0208103	+	0.00633244i
$346$	−3.04386	+	9.36802i	−0.163639	+	0.503628i
$347$	18.4628	+	5.99892i	0.991134	+	0.322039i	0.759317	−	0.650721i	$-0.225533\pi$
$347$	18.4628	+	5.99892i	0.991134	+	0.322039i	0.231817	+	0.972759i	$0.425533\pi$
$348$	0.489824	+	0.674185i	0.0262573	+	0.0361401i
$349$	−22.2937			−1.19336			−0.596678	−	0.802481i	$-0.703513\pi$
$349$	−22.2937			−1.19336			−0.596678	+	0.802481i	$0.703513\pi$
$350$	4.15253	−	2.78505i	0.221962	−	0.148867i
$351$	3.32859			0.177667
$352$	0.351209	+	0.483397i	0.0187195	+	0.0257652i
$353$	−24.3446	−	7.91003i	−1.29573	−	0.421008i	−0.421637	−	0.906765i	$-0.638544\pi$
$353$	−24.3446	−	7.91003i	−1.29573	−	0.421008i	−0.874094	+	0.485756i	$0.838544\pi$
$354$	0.0954201	−	0.293673i	0.00507152	−	0.0156085i
$355$	2.25607	+	0.780148i	0.119740	+	0.0414059i
$356$	3.69716	+	11.3787i	0.195949	+	0.603070i
$357$		−	0.371934i		−	0.0196849i
$358$	−21.0222	+	6.83054i	−1.11106	+	0.361005i
$359$	22.0744	+	16.0380i	1.16504	+	0.846452i	0.990407	−	0.138182i	$-0.0441258\pi$
$359$	22.0744	+	16.0380i	1.16504	+	0.846452i	0.174634	+	0.984633i	$0.444126\pi$
$360$	−2.16146	+	6.25060i	−0.113919	+	0.329436i
$361$	−27.0412	+	19.6466i	−1.42322	+	1.03403i
$362$	−12.4830	+	17.1814i	−0.656094	+	0.903036i
$363$	−1.28560	+	1.76948i	−0.0674765	+	0.0928734i
$364$	−2.19943	+	1.59798i	−0.115282	+	0.0837570i
$365$	13.5791	−	9.48157i	0.710761	−	0.496288i
$366$	−1.92303	−	1.39716i	−0.100518	−	0.0730309i
$367$	21.9376	−	7.12795i	1.14513	−	0.372076i	0.325824	−	0.945430i	$-0.394358\pi$
$367$	21.9376	−	7.12795i	1.14513	−	0.372076i	0.819307	+	0.573355i	$0.194358\pi$
$368$			0.879244i			0.0458337i
$369$	−5.57054	−	17.1444i	−0.289991	−	0.892499i
$370$	0.162643	−	8.66468i	0.00845543	−	0.450455i
$371$	3.16658	−	9.74573i	0.164401	−	0.505973i
$372$	0.863038	+	0.280418i	0.0447465	+	0.0145390i
$373$	9.99802	+	13.7611i	0.517678	+	0.712522i	0.985190	−	0.171464i	$-0.0548498\pi$
$373$	9.99802	+	13.7611i	0.517678	+	0.712522i	−0.467513	+	0.883986i	$0.654850\pi$
$374$	−1.08141			−0.0559182
$375$	−0.831852	+	2.14175i	−0.0429567	+	0.110599i
$376$	0.452690			0.0233457
$377$	6.47992	+	8.91884i	0.333733	+	0.459344i
$378$	1.16443	+	0.378346i	0.0598918	+	0.0194600i
$379$	−10.7117	+	32.9671i	−0.550221	+	1.69341i	0.158022	+	0.987436i	$0.449488\pi$
$379$	−10.7117	+	32.9671i	−0.550221	+	1.69341i	−0.708242	+	0.705970i	$0.750512\pi$
$380$	0.303851	−	16.1874i	0.0155872	−	0.830396i
$381$	−1.39105	−	4.28122i	−0.0712659	−	0.219334i
$382$			9.49356i			0.485733i
$383$	−14.5295	+	4.72092i	−0.742422	+	0.241228i	−0.655717	−	0.755006i	$-0.727634\pi$
$383$	−14.5295	+	4.72092i	−0.742422	+	0.241228i	−0.0867049	+	0.996234i	$0.527634\pi$
$384$	−0.166258	−	0.120793i	−0.00848429	−	0.00616420i
$385$	−1.09546	+	0.764902i	−0.0558297	+	0.0389830i
$386$	10.7250	−	7.79215i	0.545887	−	0.396610i
$387$	1.37279	−	1.88948i	0.0697828	−	0.0960478i
$388$	−2.02281	+	2.78417i	−0.102693	+	0.141345i
$389$	19.5191	−	14.1815i	0.989658	−	0.719029i	0.0298121	−	0.999556i	$-0.490509\pi$
$389$	19.5191	−	14.1815i	0.989658	−	0.719029i	0.959846	+	0.280527i	$0.0905091\pi$
$390$	0.408281	−	1.18069i	0.0206741	−	0.0597864i
$391$	−1.28739	−	0.935342i	−0.0651060	−	0.0473023i
$392$	−0.951057	+	0.309017i	−0.0480356	+	0.0156077i
$393$		−	0.373962i		−	0.0188639i
$394$	−4.11680	−	12.6702i	−0.207401	−	0.638315i
$395$	−9.06474	−	3.13458i	−0.456097	−	0.157718i
$396$	0.546126	−	1.68080i	0.0274439	−	0.0844635i
$397$	16.0557	+	5.21680i	0.805811	+	0.261824i	0.682823	−	0.730584i	$-0.260752\pi$
$397$	16.0557	+	5.21680i	0.805811	+	0.261824i	0.122988	+	0.992408i	$0.460752\pi$
$398$	−5.88078	−	8.09420i	−0.294777	−	0.405726i
$399$	−1.48796			−0.0744913
$400$	3.93194	+	3.08866i	0.196597	+	0.154433i
$401$	−16.1334			−0.805665			−0.402832	−	0.915274i	$-0.631974\pi$
$401$	−16.1334			−0.805665			−0.402832	+	0.915274i	$0.631974\pi$
$402$	0.465559	+	0.640787i	0.0232200	+	0.0319595i
$403$	11.4172	+	3.70968i	0.568732	+	0.184792i
$404$	−4.29526	+	13.2195i	−0.213697	+	0.657693i
$405$	18.4437	−	5.61229i	0.916475	−	0.278877i
$406$	1.25308	+	3.85659i	0.0621895	+	0.191400i
$407$			2.31575i			0.114787i
$408$	0.353731	−	0.114934i	0.0175123	−	0.00569008i
$409$	−3.24392	−	2.35685i	−0.160402	−	0.116539i	0.504689	−	0.863301i	$-0.331607\pi$
$409$	−3.24392	−	2.35685i	−0.160402	−	0.116539i	−0.665091	+	0.746763i	$0.731607\pi$
$410$	−13.6257	−	0.255766i	−0.672926	−	0.0126314i
$411$	−3.03802	+	2.20725i	−0.149854	+	0.108876i
$412$	−11.0109	+	15.1552i	−0.542468	+	0.746643i
$413$	0.883186	−	1.21560i	0.0434588	−	0.0598159i
$414$	2.10393	−	1.52859i	0.103402	−	0.0751263i
$415$	−0.555763	−	1.82641i	−0.0272813	−	0.0896549i
$416$	−2.19943	−	1.59798i	−0.107836	−	0.0783475i
$417$	−0.104280	+	0.0338825i	−0.00510660	+	0.00165924i
$418$			4.32628i			0.211605i
$419$	9.44691	+	29.0746i	0.461512	+	1.42039i	0.863317	+	0.504662i	$0.168383\pi$
$419$	9.44691	+	29.0746i	0.461512	+	1.42039i	−0.401805	+	0.915725i	$0.631617\pi$
$420$	0.277031	−	0.366629i	0.0135177	−	0.0178896i
$421$	3.63978	−	11.2021i	0.177392	−	0.545957i	−0.822343	−	0.568993i	$-0.807333\pi$
$421$	3.63978	−	11.2021i	0.177392	−	0.545957i	0.999735	+	0.0230361i	$0.00733325\pi$
$422$	8.26799	+	2.68643i	0.402480	+	0.130774i
$423$	−0.787015	−	1.08323i	−0.0382660	−	0.0526686i
$424$	10.2473			0.497651
$425$	−8.70523	+	2.47142i	−0.422266	+	0.119881i
$426$	0.219391			0.0106295
$427$	−6.79866	−	9.35755i	−0.329010	−	0.452844i
$428$	−14.7076	−	4.77880i	−0.710921	−	0.230992i
$429$	−0.103159	+	0.317490i	−0.00498055	+	0.0153286i
$430$	−1.01084	−	1.44767i	−0.0487468	−	0.0698129i
$431$	−2.65854	−	8.18215i	−0.128057	−	0.394120i	0.866388	−	0.499371i	$-0.166436\pi$
$431$	−2.65854	−	8.18215i	−0.128057	−	0.394120i	−0.994446	+	0.105251i	$0.966436\pi$
$432$			1.22435i			0.0589068i
$433$	−28.7516	+	9.34196i	−1.38171	+	0.448946i	−0.903232	−	0.429152i	$-0.858813\pi$
$433$	−28.7516	+	9.34196i	−1.38171	+	0.448946i	−0.478481	+	0.878098i	$0.658813\pi$
$434$	3.57238	+	2.59549i	0.171480	+	0.124587i
$435$	−1.48670	−	1.12338i	−0.0712819	−	0.0538619i
$436$	5.75790	−	4.18336i	0.275753	−	0.200347i
$437$	−3.74194	+	5.15033i	−0.179001	+	0.246374i
$438$	0.894671	−	1.23141i	0.0427490	−	0.0588390i
$439$	−6.96389	+	5.05957i	−0.332369	+	0.241480i	−0.741435	−	0.671025i	$-0.765854\pi$
$439$	−6.96389	+	5.05957i	−0.332369	+	0.241480i	0.409066	+	0.912505i	$0.365854\pi$
$440$	−1.06598	−	0.805474i	−0.0508186	−	0.0383995i
$441$	2.39288	+	1.73853i	0.113947	+	0.0827872i
$442$	4.67953	−	1.52047i	0.222583	−	0.0723215i
$443$		−	39.6209i		−	1.88245i	−0.337786	−	0.941223i	$-0.609678\pi$
$443$		−	39.6209i		−	1.88245i	0.337786	−	0.941223i	$-0.390322\pi$
$444$	−0.246122	−	0.757485i	−0.0116804	−	0.0359487i
$445$	−15.3160	−	21.9349i	−0.726048	−	1.03981i
$446$	−6.58094	+	20.2541i	−0.311617	+	0.959058i
$447$	−1.28515	−	0.417570i	−0.0607854	−	0.0197504i
$448$	−0.587785	−	0.809017i	−0.0277702	−	0.0382225i
$449$	−33.7067			−1.59072			−0.795360	−	0.606138i	$-0.792718\pi$
$449$	−33.7067			−1.59072			−0.795360	+	0.606138i	$0.792718\pi$
$450$	0.555002	−	14.7784i	0.0261631	−	0.696661i
$451$	3.64164			0.171478
$452$	5.71385	+	7.86444i	0.268757	+	0.369912i
$453$	−4.26120	−	1.38455i	−0.200209	−	0.0650517i
$454$	−8.29327	+	25.5241i	−0.389222	+	1.19790i
$455$	3.66487	−	4.85016i	0.171812	−	0.227379i
$456$	−0.459806	−	1.41514i	−0.0215324	−	0.0662698i
$457$			30.2989i			1.41732i	0.705548	+	0.708662i	$0.250701\pi$
$457$			30.2989i			1.41732i	−0.705548	+	0.708662i	$0.749299\pi$
$458$	−20.0566	+	6.51678i	−0.937182	+	0.304509i
$459$	−1.79270	−	1.30247i	−0.0836760	−	0.0607942i
$460$	−0.572343	−	1.88090i	−0.0266856	−	0.0876972i
$461$	23.7399	−	17.2481i	1.10568	−	0.803322i	0.123700	−	0.992320i	$-0.460524\pi$
$461$	23.7399	−	17.2481i	1.10568	−	0.803322i	0.981978	+	0.188998i	$0.0605239\pi$
$462$	−0.0721753	+	0.0993408i	−0.00335790	+	0.00462175i
$463$	1.96033	−	2.69816i	0.0911043	−	0.125394i	−0.761032	−	0.648715i	$-0.775307\pi$
$463$	1.96033	−	2.69816i	0.0911043	−	0.125394i	0.852136	+	0.523320i	$0.175307\pi$
$464$	−3.28061	+	2.38351i	−0.152299	+	0.110651i
$465$	−2.02877	−	0.0380817i	−0.0940819	−	0.00176600i
$466$	−6.42829	−	4.67043i	−0.297785	−	0.216353i
$467$	2.83618	−	0.921529i	0.131243	−	0.0426433i	−0.242659	−	0.970112i	$-0.578020\pi$
$467$	2.83618	−	0.921529i	0.131243	−	0.0426433i	0.373902	+	0.927468i	$0.378020\pi$
$468$			8.04114i			0.371702i
$469$	1.19101	+	3.66555i	0.0549956	+	0.169259i
$470$	−0.968403	+	0.294678i	−0.0446691	+	0.0135925i
$471$	0.348762	−	1.07338i	0.0160701	−	0.0494586i
$472$	1.42903	+	0.464319i	0.0657762	+	0.0213720i
$473$	0.277323	+	0.381703i	0.0127513	+	0.0175507i
$474$	−0.881497			−0.0404885
$475$	9.88718	+	34.8262i	0.453655	+	1.59794i
$476$	1.80985			0.0829543
$477$	−17.8152	−	24.5205i	−0.815702	−	1.12272i
$478$	17.0526	+	5.54073i	0.779968	+	0.253427i
$479$	0.952326	−	2.93096i	0.0435129	−	0.133919i	−0.926940	−	0.375210i	$-0.877571\pi$
$479$	0.952326	−	2.93096i	0.0435129	−	0.133919i	0.970453	+	0.241291i	$0.0775707\pi$
$480$	0.434292	+	0.150178i	0.0198226	+	0.00685465i
$481$	−3.25597	−	10.0208i	−0.148459	−	0.456911i
$482$		−	19.4407i		−	0.885501i
$483$	−0.171846	+	0.0558361i	−0.00781926	+	0.00254063i
$484$	−8.61035	−	6.25579i	−0.391380	−	0.284354i
$485$	2.51489	−	7.27269i	0.114195	−	0.330236i
$486$	4.40499	−	3.20041i	0.199814	−	0.145174i
$487$	−5.20244	+	7.16055i	−0.235745	+	0.324475i	−0.910455	−	0.413607i	$-0.864269\pi$
$487$	−5.20244	+	7.16055i	−0.235745	+	0.324475i	0.674710	+	0.738083i	$0.264269\pi$
$488$	6.79866	−	9.35755i	0.307761	−	0.423597i
$489$	1.15660	−	0.840322i	0.0523034	−	0.0380007i
$490$	1.83337	−	1.28015i	0.0828230	−	0.0578311i
$491$	3.53757	+	2.57019i	0.159648	+	0.115991i	0.664741	−	0.747074i	$-0.268542\pi$
$491$	3.53757	+	2.57019i	0.159648	+	0.115991i	−0.505093	+	0.863065i	$0.668542\pi$
$492$	−1.19119	+	0.387041i	−0.0537030	+	0.0174491i
$493$		−	7.33905i		−	0.330534i
$494$	−6.08281	−	18.7210i	−0.273679	−	0.842296i
$495$	−0.0741657	+	3.95111i	−0.00333350	+	0.177589i
$496$	−1.36453	+	4.19959i	−0.0612691	+	0.188567i
$497$	1.01532	+	0.329896i	0.0455431	+	0.0147979i
$498$	−0.103130	−	0.141946i	−0.00462136	−	0.00636076i
$499$	10.6594			0.477182			0.238591	−	0.971120i	$-0.423315\pi$
$499$	10.6594			0.477182			0.238591	+	0.971120i	$0.423315\pi$
$500$	−10.4219	−	4.04783i	−0.466080	−	0.181025i
$501$	0.656781			0.0293428
$502$	−0.966976	−	1.33093i	−0.0431583	−	0.0594022i
$503$	−15.8259	−	5.14215i	−0.705643	−	0.229277i	−0.0658553	−	0.997829i	$-0.520978\pi$
$503$	−15.8259	−	5.14215i	−0.705643	−	0.229277i	−0.639787	+	0.768552i	$0.720978\pi$
$504$	−0.914000	+	2.81300i	−0.0407128	+	0.125301i
$505$	0.583311	−	31.0754i	0.0259570	−	1.38284i
$506$	0.162345	+	0.499646i	0.00721710	+	0.0222120i
$507$			1.15267i			0.0511918i
$508$	20.8326	−	6.76893i	0.924299	−	0.300323i
$509$	23.0243	+	16.7281i	1.02053	+	0.741462i	0.966392	−	0.257071i	$-0.0827576\pi$
$509$	23.0243	+	16.7281i	1.02053	+	0.741462i	0.0541422	+	0.998533i	$0.482758\pi$
$510$	−0.681891	+	0.476130i	−0.0301947	+	0.0210834i
$511$	5.99209	−	4.35351i	0.265075	−	0.192588i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−5.21068	+	7.17188i	−0.230057	+	0.316646i
$514$	19.0072	−	13.8096i	0.838373	−	0.609114i
$515$	13.6895	−	39.5878i	0.603230	−	1.74445i
$516$	−0.131281	−	0.0953814i	−0.00577933	−	0.00419893i
$517$	0.257249	−	0.0835852i	0.0113138	−	0.00367607i
$518$		−	3.87565i		−	0.170286i
$519$	−0.625529	−	1.92518i	−0.0274577	−	0.0845061i
$520$	5.74528	+	1.98672i	0.251947	+	0.0871233i
$521$	3.68129	−	11.3298i	0.161280	−	0.496369i	−0.837463	−	0.546494i	$-0.815962\pi$
$521$	3.68129	−	11.3298i	0.161280	−	0.496369i	0.998743	+	0.0501250i	$0.0159620\pi$
$522$	11.4069	+	3.70633i	0.499267	+	0.162222i
$523$	16.1834	+	22.2745i	0.707649	+	0.973995i	0.999844	+	0.0176365i	$0.00561416\pi$
$523$	16.1834	+	22.2745i	0.707649	+	0.973995i	−0.292196	+	0.956359i	$0.594386\pi$
$524$	1.81972			0.0794947
$525$	−0.353974	+	0.964633i	−0.0154487	+	0.0421000i
$526$	−26.5857			−1.15919
$527$	−4.69744	−	6.46547i	−0.204624	−	0.281640i
$528$	−0.116782	−	0.0379448i	−0.00508229	−	0.00165134i
$529$	6.86850	−	21.1391i	0.298630	−	0.919090i
$530$	−21.9212	+	6.67045i	−0.952194	+	0.289746i
$531$	−1.37335	−	4.22673i	−0.0595982	−	0.183424i
$532$		−	7.24050i		−	0.313915i
$533$	−15.7583	+	5.12019i	−0.682569	+	0.221780i
$534$	−1.98915	−	1.44520i	−0.0860789	−	0.0625400i
$535$	34.5737	+	0.648977i	1.49475	+	0.0280577i
$536$	−3.11810	+	2.26543i	−0.134681	+	0.0978518i
$537$	2.67002	−	3.67497i	0.115220	−	0.158587i
$538$	10.1111	−	13.9167i	0.435921	−	0.599993i
$539$	−0.483397	+	0.351209i	−0.0208214	+	0.0151276i
$540$	−0.796993	−	2.61916i	−0.0342971	−	0.112711i
$541$	14.8582	+	10.7951i	0.638805	+	0.464119i	0.859440	−	0.511237i	$-0.170813\pi$
$541$	14.8582	+	10.7951i	0.638805	+	0.464119i	−0.220634	+	0.975357i	$0.570813\pi$
$542$	29.8165	−	9.68797i	1.28073	−	0.416134i
$543$		−	4.36441i		−	0.187295i
$544$	0.559274	+	1.72127i	0.0239787	+	0.0737988i
$545$	−9.59426	+	12.6972i	−0.410973	+	0.543890i
$546$	0.172647	−	0.531353i	0.00738862	−	0.0227398i
$547$	−0.799842	−	0.259884i	−0.0341988	−	0.0111119i	0.291868	−	0.956459i	$-0.405723\pi$
$547$	−0.799842	−	0.259884i	−0.0341988	−	0.0111119i	−0.326066	+	0.945347i	$0.605723\pi$
$548$	−10.7406	−	14.7831i	−0.458815	−	0.631505i
$549$	−34.2112			−1.46010
$550$	2.80469	+	1.02919i	0.119592	+	0.0438847i
$551$	−29.3607			−1.25081
$552$	−0.106207	−	0.146181i	−0.00452045	−	0.00622187i
$553$	−4.07947	−	1.32550i	−0.173477	−	0.0563660i
$554$	2.77204	−	8.53146i	0.117773	−	0.362467i
$555$	1.01959	+	1.46022i	0.0432794	+	0.0619827i
$556$	−0.164874	−	0.507430i	−0.00699222	−	0.0215198i
$557$			8.98757i			0.380816i	0.981705	+	0.190408i	$0.0609810\pi$
$557$			8.98757i			0.380816i	−0.981705	+	0.190408i	$0.939019\pi$
$558$	12.4214	−	4.03596i	0.525840	−	0.170856i
$559$	−1.73673	−	1.26181i	−0.0734558	−	0.0533688i
$560$	1.78403	+	1.34805i	0.0753891	+	0.0569654i
$561$	0.179792	−	0.130627i	0.00759082	−	0.00551506i
$562$	1.27161	−	1.75022i	0.0536397	−	0.0738287i
$563$	−7.70184	+	10.6007i	−0.324594	+	0.446765i	−0.939863	−	0.341552i	$-0.889047\pi$
$563$	−7.70184	+	10.6007i	−0.324594	+	0.446765i	0.615269	+	0.788317i	$0.289047\pi$
$564$	−0.0752631	+	0.0546818i	−0.00316915	+	0.00230252i
$565$	−17.3425	−	13.1043i	−0.729606	−	0.551304i
$566$	−6.05526	−	4.39940i	−0.254521	−	0.184921i
$567$	8.19972	−	2.66425i	0.344356	−	0.111888i
$568$			1.06757i			0.0447941i
$569$	−10.8277	−	33.3243i	−0.453922	−	1.39703i	−0.872396	−	0.488799i	$-0.837435\pi$
$569$	−10.8277	−	33.3243i	−0.453922	−	1.39703i	0.418474	−	0.908229i	$-0.362565\pi$
$570$	1.90481	+	2.72798i	0.0797837	+	0.114262i
$571$	−5.34991	+	16.4653i	−0.223887	+	0.689053i	0.774516	+	0.632555i	$0.217994\pi$
$571$	−5.34991	+	16.4653i	−0.223887	+	0.689053i	−0.998403	+	0.0564986i	$0.982006\pi$
$572$	−1.54492	−	0.501975i	−0.0645964	−	0.0209886i
$573$	−1.14676	−	1.57838i	−0.0479065	−	0.0659376i
$574$	−6.09468			−0.254387
$575$	2.44874	+	3.65108i	0.102119	+	0.152261i
$576$	−2.95777			−0.123240
$577$	−8.05116	−	11.0815i	−0.335174	−	0.461327i	0.607850	−	0.794052i	$-0.292032\pi$
$577$	−8.05116	−	11.0815i	−0.335174	−	0.461327i	−0.943024	+	0.332724i	$0.892032\pi$
$578$	13.0527	+	4.24109i	0.542922	+	0.176406i
$579$	−0.841869	+	2.59101i	−0.0349869	+	0.107679i
$580$	5.46641	−	7.23436i	0.226981	−	0.300390i
$581$	−0.263830	−	0.811986i	−0.0109455	−	0.0336869i
$582$		−	0.707231i		−	0.0293157i
$583$	5.82319	−	1.89207i	0.241172	−	0.0783614i
$584$	5.99209	+	4.35351i	0.247955	+	0.180150i
$585$	−5.23438	−	17.2018i	−0.216415	−	0.711205i
$586$	−6.61975	+	4.80953i	−0.273459	+	0.198680i
$587$	−4.29522	+	5.91187i	−0.177283	+	0.244009i	−0.888406	−	0.459059i	$-0.848187\pi$
$587$	−4.29522	+	5.91187i	−0.177283	+	0.244009i	0.711123	+	0.703067i	$0.248187\pi$
$588$	0.120793	−	0.166258i	0.00498143	−	0.00685634i
$589$	−25.8658	+	18.7926i	−1.06578	+	0.774336i
$590$	−3.35925	−	0.0630560i	−0.138298	−	0.00259597i
$591$	2.21492	+	1.60924i	0.0911097	+	0.0661951i
$592$	3.68596	−	1.19764i	0.151492	−	0.0492227i
$593$		−	1.85774i		−	0.0762883i	−0.999272	−	0.0381442i	$-0.987855\pi$
$593$		−	1.85774i		−	0.0762883i	0.999272	−	0.0381442i	$-0.0121446\pi$
$594$	0.226066	+	0.695761i	0.00927562	+	0.0285474i
$595$	−3.87167	+	1.17812i	−0.158723	+	0.0482983i
$596$	2.03191	−	6.25359i	0.0832305	−	0.256157i
$597$	1.95545	+	0.635364i	0.0800312	+	0.0260037i
$598$	−1.40502	−	1.93384i	−0.0574554	−	0.0790805i
$599$	9.82175			0.401306			0.200653	−	0.979662i	$-0.435694\pi$
$599$	9.82175			0.401306			0.200653	+	0.979662i	$0.435694\pi$
$600$	−1.02680	−	0.0385616i	−0.0419191	−	0.00157427i
$601$	−18.6184			−0.759461			−0.379731	−	0.925097i	$-0.623983\pi$
$601$	−18.6184			−0.759461			−0.379731	+	0.925097i	$0.623983\pi$
$602$	−0.464130	−	0.638821i	−0.0189165	−	0.0260364i
$603$	10.8418	+	3.52272i	0.441514	+	0.143456i
$604$	6.73727	−	20.7352i	0.274136	−	0.843703i
$605$	22.4916	+	7.77760i	0.914415	+	0.316204i
$606$	−0.882701	−	2.71667i	−0.0358573	−	0.110357i
$607$			25.4476i			1.03289i	0.856322	+	0.516443i	$0.172744\pi$
$607$			25.4476i			1.03289i	−0.856322	+	0.516443i	$0.827256\pi$
$608$	6.88612	−	2.23744i	0.279269	−	0.0907400i
$609$	−0.674185	−	0.489824i	−0.0273193	−	0.0198487i
$610$	−8.45254	+	24.4435i	−0.342233	+	0.989687i
$611$	−0.995661	+	0.723390i	−0.0402801	+	0.0292652i
$612$	3.14648	−	4.33076i	0.127189	−	0.175061i
$613$	−21.9475	+	30.2081i	−0.886450	+	1.22009i	0.0881418	+	0.996108i	$0.471907\pi$
$613$	−21.9475	+	30.2081i	−0.886450	+	1.22009i	−0.974592	+	0.223986i	$0.928093\pi$
$614$	−8.74498	+	6.35360i	−0.352919	+	0.256411i
$615$	2.29627	−	1.60337i	0.0925946	−	0.0646541i
$616$	−0.483397	−	0.351209i	−0.0194766	−	0.0141506i
$617$	−26.6903	+	8.67220i	−1.07451	+	0.349129i	−0.792243	−	0.610206i	$-0.791087\pi$
$617$	−26.6903	+	8.67220i	−1.07451	+	0.349129i	−0.282267	+	0.959336i	$0.591087\pi$
$618$		−	3.84971i		−	0.154858i
$619$	6.94800	+	21.3838i	0.279264	+	0.859486i	0.988060	+	0.154072i	$0.0492388\pi$
$619$	6.94800	+	21.3838i	0.279264	+	0.859486i	−0.708796	+	0.705414i	$0.750761\pi$
$620$	0.185307	−	9.87208i	0.00744212	−	0.396472i
$621$	−0.332659	+	1.02382i	−0.0133491	+	0.0410844i
$622$	−22.3059	−	7.24763i	−0.894386	−	0.290604i
$623$	−7.03242	−	9.67930i	−0.281748	−	0.387793i
$624$	0.558698			0.0223658
$625$	24.9296	+	1.87510i	0.997183	+	0.0750041i
$626$	6.65586			0.266022
$627$	−0.522585	−	0.719277i	−0.0208701	−	0.0287252i
$628$	5.22311	+	1.69709i	0.208425	+	0.0677213i
$629$	−2.16755	+	6.67103i	−0.0864259	+	0.265992i
$630$	0.124124	−	6.61260i	0.00494523	−	0.263452i
$631$	10.9001	+	33.5471i	0.433927	+	1.33549i	0.894182	+	0.447703i	$0.147758\pi$
$631$	10.9001	+	33.5471i	0.433927	+	1.33549i	−0.460255	+	0.887787i	$0.652242\pi$
$632$		−	4.28941i		−	0.170624i
$633$	−1.69912	+	0.552077i	−0.0675339	+	0.0219431i
$634$	−21.7281	−	15.7864i	−0.862935	−	0.626959i
$635$	−40.1594	+	28.0412i	−1.59368	+	1.11278i
$636$	−1.70368	+	1.23780i	−0.0675555	+	0.0490819i
$637$	1.59798	−	2.19943i	0.0633144	−	0.0871448i
$638$	−1.42417	+	1.96021i	−0.0563835	+	0.0776053i
$639$	2.55456	−	1.85600i	0.101057	−	0.0734221i
$640$	−0.730773	+	2.11328i	−0.0288863	+	0.0835349i
$641$	23.5630	+	17.1195i	0.930684	+	0.676181i	0.946160	−	0.323699i	$-0.104927\pi$
$641$	23.5630	+	17.1195i	0.930684	+	0.676181i	−0.0154765	+	0.999880i	$0.504927\pi$
$642$	3.02250	−	0.982071i	0.119289	−	0.0387592i
$643$			25.7756i			1.01649i	0.861212	+	0.508245i	$0.169706\pi$
$643$			25.7756i			1.01649i	−0.861212	+	0.508245i	$0.830294\pi$
$644$	−0.271701	−	0.836210i	−0.0107065	−	0.0329513i
$645$	0.342928	+	0.118584i	0.0135028	+	0.00466925i
$646$	−4.04942	+	12.4628i	−0.159322	+	0.490344i
$647$	−25.8145	−	8.38764i	−1.01487	−	0.329752i	−0.246080	−	0.969250i	$-0.579143\pi$
$647$	−25.8145	−	8.38764i	−1.01487	−	0.329752i	−0.768793	+	0.639497i	$0.779143\pi$
$648$	5.06770	+	6.97509i	0.199078	+	0.274008i
$649$	0.897801			0.0352418
$650$	−13.5837	−	0.510134i	−0.532796	−	0.0200091i
$651$	−0.907452			−0.0355659
$652$	4.08905	+	5.62809i	0.160139	+	0.220413i
$653$	−42.2646	−	13.7326i	−1.65394	−	0.537398i	−0.674353	−	0.738409i	$-0.735577\pi$
$653$	−42.2646	−	13.7326i	−1.65394	−	0.537398i	−0.979589	+	0.201011i	$0.935577\pi$
$654$	−0.451973	+	1.39103i	−0.0176735	+	0.0543936i
$655$	−3.89278	+	1.18454i	−0.152103	+	0.0462840i
$656$	−1.88336	−	5.79638i	−0.0735328	−	0.226311i
$657$		−	21.9071i		−	0.854678i
$658$	−0.430533	+	0.139889i	−0.0167839	+	0.00545343i
$659$	28.9491	+	21.0328i	1.12770	+	0.819320i	0.985358	−	0.170498i	$-0.0545375\pi$
$659$	28.9491	+	21.0328i	1.12770	+	0.819320i	0.142339	+	0.989818i	$0.454538\pi$
$660$	0.274523	+	0.00515303i	0.0106858	+	0.000200581i
$661$	34.4791	−	25.0505i	1.34108	−	0.974351i	0.341676	−	0.939818i	$-0.389005\pi$
$661$	34.4791	−	25.0505i	1.34108	−	0.974351i	0.999404	−	0.0345336i	$-0.0109946\pi$
$662$	−19.8362	+	27.3022i	−0.770955	+	1.06113i
$663$	−0.594345	+	0.818045i	−0.0230824	+	0.0317702i
$664$	0.690717	−	0.501835i	0.0268050	−	0.0194750i
$665$	4.71320	+	15.4890i	0.182770	+	0.600638i
$666$	−9.27397	−	6.73794i	−0.359359	−	0.261090i
$667$	−3.39089	+	1.10177i	−0.131296	+	0.0426605i
$668$			3.19593i			0.123654i
$669$	−1.35242	−	4.16232i	−0.0522876	−	0.160925i
$670$	5.19562	−	6.87598i	0.200724	−	0.265642i
$671$	2.13567	−	6.57291i	0.0824465	−	0.253744i
$672$	0.195447	+	0.0635047i	0.00753955	+	0.00244975i
$673$	6.89644	+	9.49213i	0.265838	+	0.365895i	0.920979	−	0.389612i	$-0.127391\pi$
$673$	6.89644	+	9.49213i	0.265838	+	0.365895i	−0.655141	+	0.755507i	$0.727391\pi$
$674$	18.6312			0.717648
$675$	3.40989	+	5.08417i	0.131247	+	0.195690i
$676$	−5.60894			−0.215728
$677$	−12.7545	−	17.5551i	−0.490196	−	0.674696i	0.490228	−	0.871594i	$-0.336913\pi$
$677$	−12.7545	−	17.5551i	−0.490196	−	0.674696i	−0.980424	+	0.196898i	$0.936913\pi$
$678$	−1.89994	−	0.617328i	−0.0729668	−	0.0237083i
$679$	1.06346	−	3.27298i	0.0408117	−	0.125606i
$680$	−2.31687	−	3.31812i	−0.0888480	−	0.127244i
$681$	−1.70431	−	5.24534i	−0.0653094	−	0.201002i
$682$			2.63844i			0.101031i
$683$	46.9711	−	15.2618i	1.79730	−	0.583978i	0.797488	−	0.603335i	$-0.206162\pi$
$683$	46.9711	−	15.2618i	1.79730	−	0.583978i	0.999813	+	0.0193572i	$0.00616199\pi$
$684$	−17.3257	−	12.5878i	−0.662464	−	0.481308i
$685$	32.5996	+	24.6328i	1.24557	+	0.941172i
$686$	0.809017	−	0.587785i	0.0308884	−	0.0224417i
$687$	2.54738	−	3.50616i	0.0971884	−	0.133768i
$688$	0.464130	−	0.638821i	0.0176948	−	0.0243548i
$689$	−22.5382	+	16.3749i	−0.858636	+	0.623836i
$690$	0.322356	+	0.243578i	0.0122719	+	0.00927285i
$691$	−32.0004	−	23.2496i	−1.21735	−	0.884457i	−0.221474	−	0.975166i	$-0.571087\pi$
$691$	−32.0004	−	23.2496i	−1.21735	−	0.884457i	−0.995877	+	0.0907091i	$0.971087\pi$
$692$	9.36802	−	3.04386i	0.356119	−	0.115710i
$693$			1.76730i			0.0671342i
$694$	−5.99892	−	18.4628i	−0.227716	−	0.700838i
$695$	0.683014	+	0.978180i	0.0259082	+	0.0371045i
$696$	0.257516	−	0.792552i	0.00976110	−	0.0300416i
$697$	10.4906	+	3.40860i	0.397359	+	0.129110i
$698$	13.1039	+	18.0360i	0.495991	+	0.682673i
$699$	1.63291			0.0617622
$700$	−4.69395	−	1.72246i	−0.177415	−	0.0651027i
$701$	37.2403			1.40655			0.703273	−	0.710920i	$-0.251721\pi$
$701$	37.2403			1.40655			0.703273	+	0.710920i	$0.251721\pi$
$702$	−1.95650	−	2.69289i	−0.0738432	−	0.101636i
$703$	26.6882	+	8.67152i	1.00656	+	0.327052i
$704$	0.184641	−	0.568268i	0.00695893	−	0.0214174i
$705$	0.125409	−	0.165969i	0.00472318	−	0.00625075i
$706$	7.91003	+	24.3446i	0.297698	+	0.916220i
$707$		−	13.8998i		−	0.522755i
$708$	−0.293673	+	0.0954201i	−0.0110369	+	0.00358611i
$709$	12.4344	+	9.03409i	0.466982	+	0.339282i	0.796264	−	0.604949i	$-0.206807\pi$
$709$	12.4344	+	9.03409i	0.466982	+	0.339282i	−0.329282	+	0.944232i	$0.606807\pi$
$710$	−0.694931	−	2.28376i	−0.0260803	−	0.0857079i
$711$	−10.2641	+	7.45727i	−0.384932	+	0.279670i
$712$	7.03242	−	9.67930i	0.263551	−	0.362747i
$713$	−2.28207	+	3.14099i	−0.0854640	+	0.117631i
$714$	−0.300901	+	0.218617i	−0.0112609	+	0.00818155i
$715$	3.63169	+	0.0681698i	0.135817	+	0.00254941i
$716$	17.8826	+	12.9925i	0.668303	+	0.485551i
$717$	−3.50441	+	1.13865i	−0.130874	+	0.0425237i
$718$		−	27.2854i		−	1.01828i
$719$	4.74104	+	14.5914i	0.176811	+	0.544168i	0.999712	−	0.0240172i	$-0.00764565\pi$
$719$	4.74104	+	14.5914i	0.176811	+	0.544168i	−0.822901	+	0.568185i	$0.807646\pi$
$720$	6.32732	−	1.92536i	0.235805	−	0.0717539i
$721$	5.78877	−	17.8160i	0.215585	−	0.663503i
$722$	31.7889	+	10.3288i	1.18306	+	0.384399i
$723$	2.34831	+	3.23217i	0.0873345	+	0.120206i
$724$	21.2374			0.789283
$725$	−6.98466	+	19.0343i	−0.259404	+	0.706914i
$726$	2.18719			0.0811743
$727$	−1.17714	−	1.62019i	−0.0436576	−	0.0600896i	0.786630	−	0.617425i	$-0.211824\pi$
$727$	−1.17714	−	1.62019i	−0.0436576	−	0.0600896i	−0.830288	+	0.557335i	$0.811824\pi$
$728$	2.58559	+	0.840109i	0.0958284	+	0.0311365i
$729$	7.64697	−	23.5350i	0.283221	−	0.871665i
$730$	−15.6523	−	5.41257i	−0.579319	−	0.200328i
$731$	0.441617	+	1.35916i	0.0163338	+	0.0502703i
$732$			2.37700i			0.0878563i
$733$	−8.55268	+	2.77893i	−0.315900	+	0.102642i	−0.462676	−	0.886528i	$-0.653111\pi$
$733$	−8.55268	+	2.77893i	−0.315900	+	0.102642i	0.146775	+	0.989170i	$0.453111\pi$
$734$	−18.6612	−	13.5582i	−0.688798	−	0.500441i
$735$	−0.150178	+	0.434292i	−0.00553940	+	0.0160191i
$736$	0.711323	−	0.516806i	0.0262197	−	0.0190497i
$737$	−1.35362	+	1.86310i	−0.0498613	+	0.0686282i
$738$	−10.5958	+	14.5839i	−0.390036	+	0.536839i
$739$	10.2900	−	7.47610i	0.378523	−	0.275013i	−0.382214	−	0.924074i	$-0.624838\pi$
$739$	10.2900	−	7.47610i	0.378523	−	0.275013i	0.760736	+	0.649061i	$0.224838\pi$
$740$	−7.10548	+	4.96139i	−0.261202	+	0.182384i
$741$	3.27268	+	2.37774i	0.120225	+	0.0873484i
$742$	−9.74573	+	3.16658i	−0.357777	+	0.116249i
$743$			11.6518i			0.427462i	0.976893	+	0.213731i	$0.0685616\pi$
$743$			11.6518i			0.427462i	−0.976893	+	0.213731i	$0.931438\pi$
$744$	−0.280418	−	0.863038i	−0.0102806	−	0.0316405i
$745$	−0.275940	+	14.7005i	−0.0101097	+	0.538584i
$746$	5.25627	−	16.1771i	0.192446	−	0.592287i
$747$	−2.40167	−	0.780349i	−0.0878724	−	0.0285515i
$748$	0.635635	+	0.874876i	0.0232411	+	0.0319887i
$749$	15.4645			0.565062
$750$	2.22166	−	0.585906i	0.0811236	−	0.0213943i
$751$	−6.28867			−0.229477			−0.114738	−	0.993396i	$-0.536603\pi$
$751$	−6.28867			−0.229477			−0.114738	+	0.993396i	$0.536603\pi$
$752$	−0.266084	−	0.366234i	−0.00970310	−	0.0133552i
$753$	0.321534	+	0.104473i	0.0117174	+	0.00380720i
$754$	3.40670	−	10.4847i	0.124065	−	0.381831i
$755$	−0.914943	+	48.7428i	−0.0332982	+	1.77393i
$756$	−0.378346	−	1.16443i	−0.0137603	−	0.0423499i
$757$		−	18.9570i		−	0.689003i	−0.938786	−	0.344502i	$-0.888048\pi$
$757$		−	18.9570i		−	0.689003i	0.938786	−	0.344502i	$-0.111952\pi$
$758$	32.9671	−	10.7117i	1.19742	−	0.389065i
$759$	−0.0873448	−	0.0634597i	−0.00317042	−	0.00230344i
$760$	−13.2745	+	9.26889i	−0.481516	+	0.336218i
$761$	−0.844541	+	0.613595i	−0.0306146	+	0.0222428i	−0.602987	−	0.797751i	$-0.706023\pi$
$761$	−0.844541	+	0.613595i	−0.0306146	+	0.0222428i	0.572373	+	0.819994i	$0.306023\pi$
$762$	−2.64594	+	3.64183i	−0.0958524	+	0.131929i
$763$	−4.18336	+	5.75790i	−0.151448	+	0.208450i
$764$	7.68045	−	5.58017i	0.277869	−	0.201884i
$765$	−3.91191	+	11.3127i	−0.141435	+	0.409010i
$766$	12.3595	+	8.97972i	0.446568	+	0.324450i
$767$	−3.88502	+	1.26232i	−0.140280	+	0.0455797i
$768$			0.205506i			0.00741554i
$769$	9.34609	+	28.7643i	0.337028	+	1.03727i	0.965714	+	0.259608i	$0.0835932\pi$
$769$	9.34609	+	28.7643i	0.337028	+	1.03727i	−0.628686	+	0.777659i	$0.716407\pi$
$770$	1.26271	+	0.436645i	0.0455050	+	0.0157356i
$771$	−1.49199	+	4.59189i	−0.0537329	+	0.165373i
$772$	−12.6080	−	4.09657i	−0.453770	−	0.147439i
$773$	−5.38935	−	7.41780i	−0.193841	−	0.266800i	0.701022	−	0.713139i	$-0.252727\pi$
$773$	−5.38935	−	7.41780i	−0.193841	−	0.266800i	−0.894864	+	0.446340i	$0.852727\pi$
$774$	−2.33553			−0.0839489
$775$	6.02981	+	21.2392i	0.216597	+	0.762934i
$776$	3.44142			0.123540
$777$	0.468152	+	0.644355i	0.0167948	+	0.0231161i
$778$	−22.9461	−	7.45564i	−0.822657	−	0.267298i
$779$	13.6365	−	41.9687i	0.488577	−	1.50368i
$780$	−1.19518	+	0.363684i	−0.0427942	+	0.0130220i
$781$	0.197117	+	0.606663i	0.00705339	+	0.0217081i
$782$			1.59130i			0.0569047i
$783$	−4.72184	+	1.53422i	−0.168745	+	0.0548285i
$784$	0.809017	+	0.587785i	0.0288935	+	0.0209923i
$785$	−12.2781	−	0.230470i	−0.438224	−	0.00822584i
$786$	−0.302542	+	0.219809i	−0.0107913	+	0.00784034i
$787$	17.4778	−	24.0562i	0.623018	−	0.857510i	−0.374551	−	0.927206i	$-0.622203\pi$
$787$	17.4778	−	24.0562i	0.623018	−	0.857510i	0.997568	+	0.0696962i	$0.0222030\pi$
$788$	−7.83061	+	10.7779i	−0.278954	+	0.383947i
$789$	4.42007	−	3.21137i	0.157359	−	0.114328i
$790$	2.79219	+	9.17599i	0.0993416	+	0.326467i
$791$	−7.86444	−	5.71385i	−0.279627	−	0.203161i
$792$	−1.68080	+	0.546126i	−0.0597247	+	0.0194057i
$793$			31.4455i			1.11666i
$794$	−5.21680	−	16.0557i	−0.185137	−	0.569794i
$795$	2.83881	−	3.75694i	0.100682	−	0.133245i
$796$	−3.09171	+	9.51530i	−0.109583	+	0.337261i
$797$	−8.42383	−	2.73707i	−0.298387	−	0.0969520i	0.155997	−	0.987757i	$-0.450141\pi$
$797$	−8.42383	−	2.73707i	−0.298387	−	0.0969520i	−0.454385	+	0.890806i	$0.650141\pi$
$798$	0.874603	+	1.20379i	0.0309606	+	0.0426136i
$799$	0.819300			0.0289848
$800$	0.187642	−	4.99648i	0.00663416	−	0.176652i
$801$	−35.3875			−1.25036
$802$	9.48299	+	13.0522i	0.334856	+	0.460890i
$803$	4.20895	+	1.36757i	0.148531	+	0.0482605i
$804$	0.244759	−	0.753290i	0.00863198	−	0.0265665i
$805$	1.12556	+	1.61197i	0.0396708	+	0.0568146i
$806$	−3.70968	−	11.4172i	−0.130668	−	0.402154i
$807$			3.53511i			0.124442i
$808$	13.2195	−	4.29526i	0.465059	−	0.151107i
$809$	23.5136	+	17.0837i	0.826695	+	0.600629i	0.918622	−	0.395136i	$-0.129303\pi$
$809$	23.5136	+	17.0837i	0.826695	+	0.600629i	−0.0919272	+	0.995766i	$0.529303\pi$
$810$	−15.3814	−	11.6224i	−0.540446	−	0.408371i
$811$	19.7179	−	14.3259i	0.692388	−	0.503049i	−0.185056	−	0.982728i	$-0.559247\pi$
$811$	19.7179	−	14.3259i	0.692388	−	0.503049i	0.877444	+	0.479679i	$0.159247\pi$
$812$	2.38351	−	3.28061i	0.0836447	−	0.115127i
$813$	−3.78698	+	5.21233i	−0.132815	+	0.182804i
$814$	1.87348	−	1.36116i	0.0656653	−	0.0477087i
$815$	−12.4110	−	9.37796i	−0.434738	−	0.328496i
$816$	−0.300901	−	0.218617i	−0.0105336	−	0.00765314i
$817$	5.43746	−	1.76674i	0.190233	−	0.0618103i
$818$			4.00971i			0.140196i
$819$	−2.48485	−	7.64757i	−0.0868276	−	0.267228i
$820$	7.80207	+	11.1738i	0.272460	+	0.390205i
$821$	0.946848	−	2.91410i	0.0330452	−	0.101703i	−0.933173	−	0.359426i	$-0.882972\pi$
$821$	0.946848	−	2.91410i	0.0330452	−	0.101703i	0.966219	+	0.257724i	$0.0829724\pi$
$822$	3.57141	+	1.16042i	0.124567	+	0.0404743i
$823$	30.0822	+	41.4045i	1.04860	+	1.44327i	0.890018	+	0.455925i	$0.150692\pi$
$823$	30.0822	+	41.4045i	1.04860	+	1.44327i	0.158580	+	0.987346i	$0.449308\pi$
$824$	18.7329			0.652590
$825$	−0.590620	+	0.167677i	−0.0205627	+	0.00583777i
$826$	−1.50257			−0.0522810
$827$	−12.7684	−	17.5742i	−0.444000	−	0.611114i	0.527095	−	0.849806i	$-0.323281\pi$
$827$	−12.7684	−	17.5742i	−0.444000	−	0.611114i	−0.971095	+	0.238693i	$0.923281\pi$
$828$	−2.47332	−	0.803629i	−0.0859537	−	0.0279280i
$829$	−5.99653	+	18.4554i	−0.208268	+	0.640983i	0.791295	+	0.611434i	$0.209407\pi$
$829$	−5.99653	+	18.4554i	−0.208268	+	0.640983i	−0.999563	+	0.0295490i	$0.990593\pi$
$830$	−1.15093	+	1.52316i	−0.0399492	+	0.0528696i
$831$	0.569670	+	1.75326i	0.0197616	+	0.0608200i
$832$			2.71865i			0.0942522i
$833$	−1.72127	+	0.559274i	−0.0596385	+	0.0193777i
$834$	0.0887057	+	0.0644484i	0.00307163	+	0.00223167i
$835$	−2.08039	−	6.83679i	−0.0719948	−	0.236597i
$836$	3.50004	−	2.54293i	0.121051	−	0.0879489i
$837$	−3.17780	+	4.37386i	−0.109841	+	0.151183i
$838$	17.9691	−	24.7323i	0.620732	−	0.854364i
$839$	44.8182	−	32.5623i	1.54730	−	1.12418i	0.601753	−	0.798682i	$-0.294469\pi$
$839$	44.8182	−	32.5623i	1.54730	−	1.12418i	0.945544	−	0.325495i	$-0.105531\pi$
$840$	−0.459444	−	0.00862414i	−0.0158523	−	0.000297561i
$841$	10.1584	+	7.38051i	0.350290	+	0.254500i
$842$	−11.2021	+	3.63978i	−0.386050	+	0.125435i
$843$			0.444590i			0.0153125i
$844$	−2.68643	−	8.26799i	−0.0924709	−	0.284596i
$845$	11.9988	−	3.65114i	0.412770	−	0.125603i
$846$	−0.413758	+	1.27342i	−0.0142253	+	0.0437810i
$847$	10.1221	+	3.28886i	0.347799	+	0.113007i
$848$	−6.02319	−	8.29021i	−0.206837	−	0.284687i
$849$	1.53815			0.0527892
$850$	7.11623	+	5.59001i	0.244085	+	0.191736i
$851$	3.40764			0.116812
$852$	−0.128955	−	0.177491i	−0.00441791	−	0.00608073i
$853$	−6.28413	−	2.04184i	−0.215164	−	0.0699111i	0.199451	−	0.979908i	$-0.436084\pi$
$853$	−6.28413	−	2.04184i	−0.215164	−	0.0699111i	−0.414616	+	0.909997i	$0.636084\pi$
$854$	−3.57427	+	11.0005i	−0.122309	+	0.376428i
$855$	45.2575	+	15.6500i	1.54777	+	0.535219i
$856$	4.77880	+	14.7076i	0.163336	+	0.502697i
$857$			41.4918i			1.41733i	0.705544	+	0.708666i	$0.250703\pi$
$857$			41.4918i			1.41733i	−0.705544	+	0.708666i	$0.749297\pi$
$858$	0.317490	−	0.103159i	0.0108389	−	0.00352178i
$859$	2.95601	+	2.14767i	0.100858	+	0.0732774i	0.637071	−	0.770805i	$-0.280146\pi$
$859$	2.95601	+	2.14767i	0.100858	+	0.0732774i	−0.536213	+	0.844082i	$0.680146\pi$
$860$	−0.577037	+	1.66870i	−0.0196768	+	0.0569023i
$861$	1.01329	−	0.736195i	0.0345327	−	0.0250895i
$862$	−5.05685	+	6.96015i	−0.172237	+	0.237064i
$863$	15.7847	−	21.7257i	0.537316	−	0.739552i	−0.450907	−	0.892571i	$-0.648899\pi$
$863$	15.7847	−	21.7257i	0.537316	−	0.739552i	0.988223	+	0.153019i	$0.0488995\pi$
$864$	0.990524	−	0.719658i	0.0336983	−	0.0244832i
$865$	−18.0589	+	12.6096i	−0.614020	+	0.428739i
$866$	24.4576	+	17.7695i	0.831102	+	0.603831i
$867$	−2.68241	+	0.871567i	−0.0910993	+	0.0296000i
$868$		−	4.41571i		−	0.149879i
$869$	−0.792002	−	2.43753i	−0.0268668	−	0.0826876i
$870$	−0.0349714	+	1.86307i	−0.00118564	+	0.0631641i
$871$	3.23793	−	9.96534i	0.109713	−	0.337663i
$872$	−6.76882	−	2.19932i	−0.229221	−	0.0744784i
$873$	−5.98302	−	8.23491i	−0.202494	−	0.278710i
$874$	6.36616			0.215339
$875$	11.1626	+	0.629187i	0.377365	+	0.0212704i
$876$	−1.52211			−0.0514272
$877$	−29.1169	−	40.0759i	−0.983206	−	1.35327i	−0.935084	−	0.354426i	$-0.884676\pi$
$877$	−29.1169	−	40.0759i	−0.983206	−	1.35327i	−0.0481225	−	0.998841i	$-0.515324\pi$
$878$	8.18655	+	2.65997i	0.276283	+	0.0897697i
$879$	0.519625	−	1.59924i	0.0175265	−	0.0539411i
$880$	−0.0250749	+	1.33584i	−0.000845274	+	0.0450312i
$881$	3.04297	+	9.36530i	0.102520	+	0.315525i	0.989140	−	0.146973i	$-0.0469532\pi$
$881$	3.04297	+	9.36530i	0.102520	+	0.315525i	−0.886620	+	0.462498i	$0.846953\pi$
$882$		−	2.95777i		−	0.0995932i
$883$	−7.57933	+	2.46267i	−0.255065	+	0.0828756i	−0.433758	−	0.901029i	$-0.642813\pi$
$883$	−7.57933	+	2.46267i	−0.255065	+	0.0828756i	0.178694	+	0.983905i	$0.442813\pi$
$884$	−3.98065	−	2.89211i	−0.133884	−	0.0972721i
$885$	0.566117	−	0.395291i	0.0190298	−	0.0132876i
$886$	−32.0540	+	23.2886i	−1.07687	+	0.782395i
$887$	−23.5866	+	32.4642i	−0.791962	+	1.09004i	0.201900	+	0.979406i	$0.435289\pi$
$887$	−23.5866	+	32.4642i	−0.791962	+	1.09004i	−0.993861	+	0.110635i	$0.964711\pi$
$888$	−0.468152	+	0.644355i	−0.0157101	+	0.0216232i
$889$	−17.7213	+	12.8753i	−0.594353	+	0.431823i
$890$	−8.74316	+	25.2839i	−0.293071	+	0.847518i
$891$	4.16770	+	3.02801i	0.139623	+	0.101442i
$892$	20.2541	−	6.58094i	0.678156	−	0.220346i
$893$		−	3.27770i		−	0.109684i
$894$	0.417570	+	1.28515i	0.0139656	+	0.0429818i
$895$	−46.7122	−	16.1531i	−1.56142	−	0.539937i
$896$	−0.309017	+	0.951057i	−0.0103235	+	0.0317726i
$897$	0.467189	+	0.151799i	0.0155990	+	0.00506842i
$898$	19.8123	+	27.2693i	0.661146	+	0.909989i
$899$	−17.9060			−0.597197
$900$	−12.2822	+	8.23753i	−0.409407	+	0.274584i
$901$	18.5460			0.617857
$902$	−2.14050	−	2.94615i	−0.0712710	−	0.0980961i
$903$	0.154330	+	0.0501450i	0.00513579	+	0.00166872i
$904$	3.00395	−	9.24520i	0.0999098	−	0.307491i
$905$	−45.4315	+	13.8245i	−1.51020	+	0.459542i
$906$	1.38455	+	4.26120i	0.0459985	+	0.141569i
$907$		−	23.5477i		−	0.781888i	−0.920414	−	0.390944i	$-0.872149\pi$
$907$		−	23.5477i		−	0.781888i	0.920414	−	0.390944i	$-0.127851\pi$
$908$	25.5241	−	8.29327i	0.847045	−	0.275222i
$909$	−33.2605	−	24.1652i	−1.10318	−	0.801509i
$910$	−6.07802	−	0.114090i	−0.201484	−	0.00378203i
$911$	44.1085	−	32.0467i	1.46138	−	1.06176i	0.478380	−	0.878153i	$-0.341224\pi$
$911$	44.1085	−	32.0467i	1.46138	−	1.06176i	0.983001	−	0.183602i	$-0.0587758\pi$
$912$	−0.874603	+	1.20379i	−0.0289610	+	0.0398614i
$913$	0.299852	−	0.412711i	0.00992367	−	0.0136588i
$914$	24.5123	−	17.8093i	0.810796	−	0.589078i
$915$	−1.54730	−	5.08492i	−0.0511523	−	0.168102i
$916$	17.0611	+	12.3956i	0.563716	+	0.409564i
$917$	−1.73065	+	0.562324i	−0.0571512	+	0.0185696i
$918$			2.21590i			0.0731355i
$919$	3.75109	+	11.5447i	0.123737	+	0.380824i	0.993669	−	0.112348i	$-0.0358372\pi$
$919$	3.75109	+	11.5447i	0.123737	+	0.380824i	−0.869932	+	0.493172i	$0.835837\pi$
$920$	−1.18526	+	1.56860i	−0.0390769	+	0.0517152i
$921$	0.686448	−	2.11267i	0.0226192	−	0.0696148i
$922$	−27.9079	−	9.06784i	−0.919099	−	0.298633i
$923$	−1.70595	−	2.34804i	−0.0561521	−	0.0772867i
$924$	0.122792			0.00403956
$925$	11.9706	−	15.2388i	0.393590	−	0.501049i
$926$	−3.33511			−0.109599
$927$	−32.5677	−	44.8255i	−1.06966	−	1.47226i
$928$	3.85659	+	1.25308i	0.126599	+	0.0411345i
$929$	10.5876	−	32.5854i	0.347369	−	1.06909i	−0.612935	−	0.790133i	$-0.710011\pi$
$929$	10.5876	−	32.5854i	0.347369	−	1.06909i	0.960303	−	0.278957i	$-0.0899888\pi$
$930$	1.16167	+	1.66369i	0.0380927	+	0.0545546i
$931$	2.23744	+	6.88612i	0.0733290	+	0.225684i
$932$			7.94580i			0.260273i
$933$	4.58399	−	1.48943i	0.150073	−	0.0487617i
$934$	−2.41260	−	1.75285i	−0.0789425	−	0.0573551i
$935$	−1.92926	−	1.45779i	−0.0630937	−	0.0476747i
$936$	6.50542	−	4.72646i	0.212636	−	0.154489i
$937$	1.78871	−	2.46195i	0.0584348	−	0.0804285i	−0.778800	−	0.627273i	$-0.784171\pi$
$937$	1.78871	−	2.46195i	0.0584348	−	0.0804285i	0.837234	+	0.546844i	$0.184171\pi$
$938$	2.26543	−	3.11810i	0.0739690	−	0.101810i
$939$	−1.10659	+	0.803982i	−0.0361121	+	0.0262370i
$940$	0.807613	+	0.610247i	0.0263414	+	0.0199041i
$941$	20.3221	+	14.7649i	0.662482	+	0.481322i	0.867500	−	0.497437i	$-0.165725\pi$
$941$	20.3221	+	14.7649i	0.662482	+	0.481322i	−0.205018	+	0.978758i	$0.565725\pi$
$942$	−1.07338	+	0.348762i	−0.0349725	+	0.0113633i
$943$		−	5.35871i		−	0.174503i
$944$	−0.464319	−	1.42903i	−0.0151123	−	0.0465108i
$945$	1.56735	+	2.24469i	0.0509860	+	0.0730197i
$946$	0.145798	−	0.448719i	0.00474029	−	0.0145891i
$947$	−32.3340	−	10.5060i	−1.05071	−	0.341398i	−0.267766	−	0.963484i	$-0.586285\pi$
$947$	−32.3340	−	10.5060i	−1.05071	−	0.341398i	−0.782949	+	0.622086i	$0.786285\pi$
$948$	0.518131	+	0.713146i	0.0168281	+	0.0231619i
$949$	−20.1361			−0.653644
$950$	22.3634	−	28.4692i	0.725566	−	0.923663i
$951$	5.51936			0.178977
$952$	−1.06380	−	1.46420i	−0.0344781	−	0.0474550i
$953$	17.8597	+	5.80296i	0.578532	+	0.187976i	0.583643	−	0.812011i	$-0.301627\pi$
$953$	17.8597	+	5.80296i	0.578532	+	0.187976i	−0.00511108	+	0.999987i	$0.501627\pi$
$954$	−9.36600	+	28.8256i	−0.303236	+	0.933263i
$955$	−12.7978	+	16.9368i	−0.414126	+	0.548062i
$956$	−5.54073	−	17.0526i	−0.179200	−	0.551521i
$957$		−	0.497929i		−	0.0160958i
$958$	−2.93096	+	0.952326i	−0.0946950	+	0.0307683i
$959$	14.7831	+	10.7406i	0.477373	+	0.346831i
$960$	−0.133774	−	0.439622i	−0.00431753	−	0.0141887i
$961$	9.30494	−	6.76044i	0.300159	−	0.218079i
$962$	−6.19322	+	8.52423i	−0.199677	+	0.274832i
$963$	26.8856	−	37.0048i	0.866376	−	1.19246i
$964$	−15.7279	+	11.4270i	−0.506561	+	0.368038i
$965$	29.6379	+	0.556328i	0.954077	+	0.0179088i
$966$	0.146181	+	0.106207i	0.00470329	+	0.00341714i
$967$	−41.0932	+	13.3520i	−1.32147	+	0.429371i	−0.882999	−	0.469376i	$-0.844479\pi$
$967$	−41.0932	+	13.3520i	−1.32147	+	0.429371i	−0.438469	+	0.898746i	$0.644479\pi$
$968$			10.6430i			0.342078i
$969$	−0.832179	−	2.56119i	−0.0267335	−	0.0822771i
$970$	−7.36195	+	2.24019i	−0.236378	+	0.0719282i
$971$	3.39734	−	10.4560i	0.109026	−	0.335547i	−0.881628	−	0.471944i	$-0.843552\pi$
$971$	3.39734	−	10.4560i	0.109026	−	0.335547i	0.990654	+	0.136397i	$0.0435523\pi$
$972$	−5.17838	−	1.68256i	−0.166097	−	0.0539680i
$973$	0.313609	+	0.431646i	0.0100538	+	0.0138379i
$974$	8.85093			0.283602
$975$	2.32001	−	1.55600i	0.0742998	−	0.0498319i
$976$	−11.5666			−0.370237
$977$	16.8687	+	23.2178i	0.539678	+	0.742802i	0.988567	−	0.150785i	$-0.0481801\pi$
$977$	16.8687	+	23.2178i	0.539678	+	0.742802i	−0.448889	+	0.893588i	$0.648180\pi$
$978$	−1.35967	−	0.441783i	−0.0434774	−	0.0141267i
$979$	2.20910	−	6.79890i	0.0706031	−	0.217294i
$980$	−2.11328	−	0.730773i	−0.0675064	−	0.0233437i
$981$	6.50508	+	20.0206i	0.207691	+	0.639208i
$982$		−	4.37268i		−	0.139538i
$983$	−18.4987	+	6.01061i	−0.590018	+	0.191709i	−0.588784	−	0.808291i	$-0.700393\pi$
$983$	−18.4987	+	6.01061i	−0.590018	+	0.191709i	−0.00123459	+	0.999999i	$0.500393\pi$
$984$	1.01329	+	0.736195i	0.0323024	+	0.0234691i
$985$	9.73553	−	28.1537i	0.310200	−	0.897051i
$986$	−5.93742	+	4.31379i	−0.189086	+	0.137379i
$987$	0.0546818	−	0.0752631i	0.00174054	−	0.00239565i
$988$	−11.5702	+	15.9250i	−0.368097	+	0.506642i
$989$	0.561679	−	0.408084i	0.0178604	−	0.0129763i
$990$	3.24011	−	2.26240i	0.102977	−	0.0719039i
$991$	−25.8093	−	18.7516i	−0.819861	−	0.595664i	0.0968120	−	0.995303i	$-0.469135\pi$
$991$	−25.8093	−	18.7516i	−0.819861	−	0.595664i	−0.916673	+	0.399639i	$0.869135\pi$
$992$	4.19959	−	1.36453i	0.133337	−	0.0433238i
$993$		−	6.93527i		−	0.220084i
$994$	−0.329896	−	1.01532i	−0.0104637	−	0.0322038i
$995$	0.419864	−	22.3679i	0.0133106	−	0.709110i
$996$	−0.0542186	+	0.166868i	−0.00171798	+	0.00528741i
$997$	−53.6265	−	17.4243i	−1.69837	−	0.551833i	−0.710038	−	0.704163i	$-0.751322\pi$
$997$	−53.6265	−	17.4243i	−1.69837	−	0.551833i	−0.988330	+	0.152330i	$0.951322\pi$
$998$	−6.26546	−	8.62366i	−0.198330	−	0.272977i
$999$	4.74517			0.150130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.m.a.239.2	✓	24
25.3	odd	20		8750.2.a.bb.1.7		12
25.9	even	10	inner	350.2.m.a.309.2	yes	24
25.22	odd	20		8750.2.a.z.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.m.a.239.2	✓	24	1.1	even	1	trivial
350.2.m.a.309.2	yes	24	25.9	even	10	inner
8750.2.a.z.1.6		12	25.22	odd	20
8750.2.a.bb.1.7		12	25.3	odd	20

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.195447 + 0.0635047i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.0419655 - 2.23567i) q^{5} +(-0.0635047 - 0.195447i) q^{6} -1.00000i q^{7} +(0.951057 - 0.309017i) q^{8} +(-2.39288 - 1.73853i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.195447 + 0.0635047i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.0419655 - 2.23567i) q^{5} +(-0.0635047 - 0.195447i) q^{6} -1.00000i q^{7} +(0.951057 - 0.309017i) q^{8} +(-2.39288 - 1.73853i) q^{9} +(-1.83337 + 1.28015i) q^{10} +(0.483397 - 0.351209i) q^{11} +(-0.120793 + 0.166258i) q^{12} +(-1.59798 + 2.19943i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(0.150178 - 0.434292i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.72127 - 0.559274i) q^{17} +2.95777i q^{18} +(-2.23744 - 6.88612i) q^{19} +(2.11328 + 0.730773i) q^{20} +(0.0635047 - 0.195447i) q^{21} +(-0.568268 - 0.184641i) q^{22} +(-0.516806 - 0.711323i) q^{23} +0.205506 q^{24} +(-4.99648 - 0.187642i) q^{25} +2.71865 q^{26} +(-0.719658 - 0.990524i) q^{27} +(0.951057 + 0.309017i) q^{28} +(1.25308 - 3.85659i) q^{29} +(-0.439622 + 0.133774i) q^{30} +(-1.36453 - 4.19959i) q^{31} +1.00000i q^{32} +(0.116782 - 0.0379448i) q^{33} +(-1.46420 - 1.06380i) q^{34} +(-2.23567 - 0.0419655i) q^{35} +(2.39288 - 1.73853i) q^{36} +(-2.27805 + 3.13546i) q^{37} +(-4.25586 + 5.85769i) q^{38} +(-0.451996 + 0.328394i) q^{39} +(-0.650950 - 2.13922i) q^{40} +(4.93070 + 3.58236i) q^{41} +(-0.195447 + 0.0635047i) q^{42} +0.789626i q^{43} +(0.184641 + 0.568268i) q^{44} +(-3.98721 + 5.27675i) q^{45} +(-0.271701 + 0.836210i) q^{46} +(0.430533 + 0.139889i) q^{47} +(-0.120793 - 0.166258i) q^{48} -1.00000 q^{49} +(2.78505 + 4.15253i) q^{50} +0.371934 q^{51} +(-1.59798 - 2.19943i) q^{52} +(9.74573 + 3.16658i) q^{53} +(-0.378346 + 1.16443i) q^{54} +(-0.764902 - 1.09546i) q^{55} +(-0.309017 - 0.951057i) q^{56} -1.48796i q^{57} +(-3.85659 + 1.25308i) q^{58} +(1.21560 + 0.883186i) q^{59} +(0.366629 + 0.277031i) q^{60} +(9.35755 - 6.79866i) q^{61} +(-2.59549 + 3.57238i) q^{62} +(-1.73853 + 2.39288i) q^{63} +(0.809017 - 0.587785i) q^{64} +(4.85016 + 3.66487i) q^{65} +(-0.0993408 - 0.0721753i) q^{66} +(-3.66555 + 1.19101i) q^{67} +1.80985i q^{68} +(-0.0558361 - 0.171846i) q^{69} +(1.28015 + 1.83337i) q^{70} +(-0.329896 + 1.01532i) q^{71} +(-2.81300 - 0.914000i) q^{72} +(4.35351 + 5.99209i) q^{73} +3.87565 q^{74} +(-0.964633 - 0.353974i) q^{75} +7.24050 q^{76} +(-0.351209 - 0.483397i) q^{77} +(0.531353 + 0.172647i) q^{78} +(1.32550 - 4.07947i) q^{79} +(-1.34805 + 1.78403i) q^{80} +(2.66425 + 8.19972i) q^{81} -6.09468i q^{82} +(0.811986 - 0.263830i) q^{83} +(0.166258 + 0.120793i) q^{84} +(-1.17812 - 3.87167i) q^{85} +(0.638821 - 0.464130i) q^{86} +(0.489824 - 0.674185i) q^{87} +(0.351209 - 0.483397i) q^{88} +(9.67930 - 7.03242i) q^{89} +(6.61260 + 0.124124i) q^{90} +(2.19943 + 1.59798i) q^{91} +(0.836210 - 0.271701i) q^{92} -0.907452i q^{93} +(-0.139889 - 0.430533i) q^{94} +(-15.4890 + 4.71320i) q^{95} +(-0.0635047 + 0.195447i) q^{96} +(3.27298 + 1.06346i) q^{97} +(0.587785 + 0.809017i) q^{98} -1.76730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) \) 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9	\( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) \) 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9 + 2 * q^11 + 10 * q^12 - 6 * q^14 + 20 * q^15 - 6 * q^16 - 22 * q^19 - 2 * q^21 - 10 * q^22 - 10 * q^23 + 8 * q^24 - 10 * q^25 - 4 * q^26 - 30 * q^27 - 12 * q^29 - 10 * q^30 + 20 * q^33 - 8 * q^36 + 10 * q^37 - 10 * q^38 - 48 * q^39 + 10 * q^40 + 42 * q^41 - 2 * q^44 - 40 * q^45 + 10 * q^46 + 30 * q^47 + 10 * q^48 - 24 * q^49 + 20 * q^50 - 52 * q^51 + 10 * q^53 + 4 * q^54 + 10 * q^55 + 6 * q^56 - 20 * q^58 - 10 * q^60 + 46 * q^61 - 20 * q^63 + 6 * q^64 + 10 * q^65 - 10 * q^66 + 10 * q^67 + 32 * q^71 + 30 * q^73 - 28 * q^74 - 10 * q^75 - 48 * q^76 + 20 * q^77 - 20 * q^78 - 44 * q^79 + 76 * q^81 + 50 * q^83 + 2 * q^84 - 50 * q^85 - 6 * q^86 - 20 * q^87 - 20 * q^88 - 4 * q^89 + 50 * q^90 - 6 * q^91 + 30 * q^92 - 6 * q^94 - 60 * q^95 + 2 * q^96 + 30 * q^97 + 56 * q^99

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