LMFDB - Embedded newform 770.2.w.b.139.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("770.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.16
Character	$\chi$	$=$	770.139
Dual form			770.2.w.b.349.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.403178 - 1.24085i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.07187 + 0.841043i) q^{5} +(1.05553 - 0.766890i) q^{6} +(-2.09063 + 1.62150i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.04989 + 0.762787i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.403178 - 1.24085i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.07187 + 0.841043i) q^{5} +(1.05553 - 0.766890i) q^{6} +(-2.09063 + 1.62150i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.04989 + 0.762787i) q^{9} +(-2.17053 - 0.537397i) q^{10} +(1.69980 - 2.84792i) q^{11} +1.30471 q^{12} +(-0.798552 + 1.09911i) q^{13} +(-2.64445 + 0.0829819i) q^{14} +(0.208279 + 2.90998i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.98538 + 4.10903i) q^{17} +(0.401021 + 1.23421i) q^{18} +(-2.21345 + 6.81229i) q^{19} +(-1.44012 - 1.71057i) q^{20} +(1.16915 + 3.24792i) q^{21} +(3.04914 - 1.30490i) q^{22} +8.11605i q^{23} +(1.05553 + 0.766890i) q^{24} +(3.58529 - 3.48506i) q^{25} +(-1.29208 + 0.419823i) q^{26} +(4.53640 - 3.29588i) q^{27} +(-2.18818 - 1.48723i) q^{28} +(-4.39194 + 1.42703i) q^{29} +(-1.54194 + 2.47664i) q^{30} +(0.995228 - 1.36981i) q^{31} -1.00000 q^{32} +(-2.84854 - 3.25742i) q^{33} +5.07904i q^{34} +(2.96776 - 5.11785i) q^{35} +(-0.401021 + 1.23421i) q^{36} +(-9.02813 + 2.93342i) q^{37} +(-5.79488 + 4.21023i) q^{38} +(1.04188 + 1.43402i) q^{39} +(-0.159636 - 2.23036i) q^{40} +(-1.50051 + 4.61809i) q^{41} +(-0.963215 + 3.31483i) q^{42} +0.645932 q^{43} +(3.23380 + 0.736550i) q^{44} +(-2.81676 - 0.697396i) q^{45} +(-4.77049 + 6.56602i) q^{46} +(2.27230 - 6.99342i) q^{47} +(0.403178 + 1.24085i) q^{48} +(1.74146 - 6.77992i) q^{49} +(4.94903 - 0.712094i) q^{50} +(6.30234 - 2.04775i) q^{51} +(-1.29208 - 0.419823i) q^{52} +(-4.50352 + 6.19856i) q^{53} +5.60729 q^{54} +(-1.12654 + 7.33014i) q^{55} +(-0.896100 - 2.48938i) q^{56} +(7.56064 + 5.49313i) q^{57} +(-4.39194 - 1.42703i) q^{58} +(7.39957 - 2.40427i) q^{59} +(-2.70319 + 1.09732i) q^{60} +(10.7067 - 7.77886i) q^{61} +(1.61031 - 0.523223i) q^{62} +(-3.43178 + 0.107688i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.730095 - 2.94883i) q^{65} +(-0.389848 - 4.30964i) q^{66} -9.00756i q^{67} +(-2.98538 + 4.10903i) q^{68} +(10.0708 + 3.27221i) q^{69} +(5.40917 - 2.39602i) q^{70} +(8.53510 - 6.20112i) q^{71} +(-1.04989 + 0.762787i) q^{72} +(8.11337 - 2.63619i) q^{73} +(-9.02813 - 2.93342i) q^{74} +(-2.87894 - 5.85392i) q^{75} -7.16287 q^{76} +(1.06426 + 8.71019i) q^{77} +1.77255i q^{78} +(-4.85165 + 6.67772i) q^{79} +(1.18183 - 1.89823i) q^{80} +(-1.05767 - 3.25519i) q^{81} +(-3.92838 + 2.85413i) q^{82} +(-7.24004 - 9.96505i) q^{83} +(-2.72767 + 2.11559i) q^{84} +(-9.64119 - 6.00253i) q^{85} +(0.522570 + 0.379669i) q^{86} +6.02510i q^{87} +(2.18327 + 2.49666i) q^{88} +8.78152i q^{89} +(-1.86889 - 2.21986i) q^{90} +(-0.112737 - 3.59269i) q^{91} +(-7.71882 + 2.50800i) q^{92} +(-1.29849 - 1.78721i) q^{93} +(5.94896 - 4.32217i) q^{94} +(-1.14345 - 15.9758i) q^{95} +(-0.403178 + 1.24085i) q^{96} +(7.43468 + 5.40161i) q^{97} +(5.39401 - 4.46147i) q^{98} +(3.95696 - 1.69341i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	0.403178	−	1.24085i	0.232775	−	0.716407i	−0.764634	−	0.644465i	$-0.777080\pi$
$3$	0.403178	−	1.24085i	0.232775	−	0.716407i	0.997409	−	0.0719424i	$-0.0229198\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.07187	+	0.841043i	−0.926569	+	0.376126i
$5$	−2.07187	+	0.841043i	−0.926569	+	0.376126i
$6$	1.05553	−	0.766890i	0.430920	−	0.313081i
$7$	−2.09063	+	1.62150i	−0.790184	+	0.612870i
$7$	−2.09063	+	1.62150i	−0.790184	+	0.612870i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	1.04989	+	0.762787i	0.349962	+	0.254262i
$10$	−2.17053	−	0.537397i	−0.686382	−	0.169940i
$11$	1.69980	−	2.84792i	0.512509	−	0.858682i
$11$	1.69980	−	2.84792i	0.512509	−	0.858682i
$12$	1.30471			0.376638
$13$	−0.798552	+	1.09911i	−0.221478	+	0.304839i	−0.905268	−	0.424840i	$-0.860330\pi$
$13$	−0.798552	+	1.09911i	−0.221478	+	0.304839i	0.683790	+	0.729679i	$0.260330\pi$
$14$	−2.64445	+	0.0829819i	−0.706759	+	0.0221778i
$15$	0.208279	+	2.90998i	0.0537775	+	0.751353i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.98538	+	4.10903i	0.724062	+	0.996585i	0.999379	+	0.0352320i	$0.0112170\pi$
$17$	2.98538	+	4.10903i	0.724062	+	0.996585i	−0.275318	+	0.961353i	$0.588783\pi$
$18$	0.401021	+	1.23421i	0.0945215	+	0.290907i
$19$	−2.21345	+	6.81229i	−0.507800	+	1.56285i	0.288213	+	0.957566i	$0.406939\pi$
$19$	−2.21345	+	6.81229i	−0.507800	+	1.56285i	−0.796012	+	0.605280i	$0.793061\pi$
$20$	−1.44012	−	1.71057i	−0.322021	−	0.382495i
$21$	1.16915	+	3.24792i	0.255130	+	0.708754i
$22$	3.04914	−	1.30490i	0.650078	−	0.278206i
$23$			8.11605i			1.69231i	0.532934	+	0.846157i	$0.321089\pi$
$23$			8.11605i			1.69231i	−0.532934	+	0.846157i	$0.678911\pi$
$24$	1.05553	+	0.766890i	0.215460	+	0.156541i
$25$	3.58529	−	3.48506i	0.717059	−	0.697013i
$26$	−1.29208	+	0.419823i	−0.253398	+	0.0823341i
$27$	4.53640	−	3.29588i	0.873030	−	0.634293i
$28$	−2.18818	−	1.48723i	−0.413527	−	0.281061i
$29$	−4.39194	+	1.42703i	−0.815563	+	0.264992i	−0.686952	−	0.726703i	$-0.741052\pi$
$29$	−4.39194	+	1.42703i	−0.815563	+	0.264992i	−0.128611	+	0.991695i	$0.541052\pi$
$30$	−1.54194	+	2.47664i	−0.281518	+	0.452171i
$31$	0.995228	−	1.36981i	0.178748	−	0.246026i	−0.710236	−	0.703964i	$-0.751412\pi$
$31$	0.995228	−	1.36981i	0.178748	−	0.246026i	0.888984	+	0.457938i	$0.151412\pi$
$32$	−1.00000			−0.176777
$33$	−2.84854	−	3.25742i	−0.495866	−	0.567045i
$34$			5.07904i			0.871048i
$35$	2.96776	−	5.11785i	0.501643	−	0.865075i
$36$	−0.401021	+	1.23421i	−0.0668368	+	0.205702i
$37$	−9.02813	+	2.93342i	−1.48421	+	0.482251i	−0.935369	−	0.353673i	$-0.884933\pi$
$37$	−9.02813	+	2.93342i	−1.48421	+	0.482251i	−0.548846	+	0.835924i	$0.684933\pi$
$38$	−5.79488	+	4.21023i	−0.940054	+	0.682989i
$39$	1.04188	+	1.43402i	0.166834	+	0.229627i
$40$	−0.159636	−	2.23036i	−0.0252407	−	0.352651i
$41$	−1.50051	+	4.61809i	−0.234340	+	0.721224i	0.762868	+	0.646554i	$0.223790\pi$
$41$	−1.50051	+	4.61809i	−0.234340	+	0.721224i	−0.997208	+	0.0746701i	$0.976210\pi$
$42$	−0.963215	+	3.31483i	−0.148627	+	0.511490i
$43$	0.645932			0.0985037			0.0492518	−	0.998786i	$-0.484316\pi$
$43$	0.645932			0.0985037			0.0492518	+	0.998786i	$0.484316\pi$
$44$	3.23380	+	0.736550i	0.487514	+	0.111039i
$45$	−2.81676	−	0.697396i	−0.419898	−	0.103962i
$46$	−4.77049	+	6.56602i	−0.703371	+	0.968107i
$47$	2.27230	−	6.99342i	0.331449	−	1.02009i	−0.636996	−	0.770867i	$-0.719823\pi$
$47$	2.27230	−	6.99342i	0.331449	−	1.02009i	0.968445	−	0.249228i	$-0.0801768\pi$
$48$	0.403178	+	1.24085i	0.0581937	+	0.179102i
$49$	1.74146	−	6.77992i	0.248780	−	0.968560i
$50$	4.94903	−	0.712094i	0.699899	−	0.100705i
$51$	6.30234	−	2.04775i	0.882504	−	0.286743i
$52$	−1.29208	−	0.419823i	−0.179180	−	0.0582190i
$53$	−4.50352	+	6.19856i	−0.618606	+	0.851438i	−0.997250	−	0.0741043i	$-0.976390\pi$
$53$	−4.50352	+	6.19856i	−0.618606	+	0.851438i	0.378645	+	0.925542i	$0.376390\pi$
$54$	5.60729			0.763056
$55$	−1.12654	+	7.33014i	−0.151903	+	0.988395i
$56$	−0.896100	−	2.48938i	−0.119746	−	0.332657i
$57$	7.56064	+	5.49313i	1.00143	+	0.727583i
$58$	−4.39194	−	1.42703i	−0.576690	−	0.187378i
$59$	7.39957	−	2.40427i	0.963342	−	0.313009i	0.215217	−	0.976566i	$-0.430954\pi$
$59$	7.39957	−	2.40427i	0.963342	−	0.313009i	0.748125	+	0.663558i	$0.230954\pi$
$60$	−2.70319	+	1.09732i	−0.348980	+	0.141663i
$61$	10.7067	−	7.77886i	1.37085	−	0.995981i	0.373180	−	0.927759i	$-0.378267\pi$
$61$	10.7067	−	7.77886i	1.37085	−	0.995981i	0.997670	−	0.0682220i	$-0.0217326\pi$
$62$	1.61031	−	0.523223i	0.204510	−	0.0664493i
$63$	−3.43178	+	0.107688i	−0.432364	+	0.0135674i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.730095	−	2.94883i	0.0905571	−	0.365758i
$66$	−0.389848	−	4.30964i	−0.0479869	−	0.530480i
$67$		−	9.00756i		−	1.10045i	−0.835017	−	0.550224i	$-0.814542\pi$
$67$		−	9.00756i		−	1.10045i	0.835017	−	0.550224i	$-0.185458\pi$
$68$	−2.98538	+	4.10903i	−0.362031	+	0.498293i
$69$	10.0708	+	3.27221i	1.21239	+	0.393928i
$70$	5.40917	−	2.39602i	0.646519	−	0.286380i
$71$	8.53510	−	6.20112i	1.01293	−	0.735937i	0.0481088	−	0.998842i	$-0.484681\pi$
$71$	8.53510	−	6.20112i	1.01293	−	0.735937i	0.964822	+	0.262905i	$0.0846806\pi$
$72$	−1.04989	+	0.762787i	−0.123730	+	0.0898953i
$73$	8.11337	−	2.63619i	0.949598	−	0.308543i	0.207046	−	0.978331i	$-0.433615\pi$
$73$	8.11337	−	2.63619i	0.949598	−	0.308543i	0.742552	+	0.669788i	$0.233615\pi$
$74$	−9.02813	−	2.93342i	−1.04950	−	0.341003i
$75$	−2.87894	−	5.85392i	−0.332432	−	0.675953i
$76$	−7.16287			−0.821637
$77$	1.06426	+	8.71019i	0.121284	+	0.992618i
$78$			1.77255i			0.200702i
$79$	−4.85165	+	6.67772i	−0.545853	+	0.751302i	−0.989442	−	0.144928i	$-0.953705\pi$
$79$	−4.85165	+	6.67772i	−0.545853	+	0.751302i	0.443589	+	0.896230i	$0.353705\pi$
$80$	1.18183	−	1.89823i	0.132132	−	0.212229i
$81$	−1.05767	−	3.25519i	−0.117519	−	0.361687i
$82$	−3.92838	+	2.85413i	−0.433817	+	0.315186i
$83$	−7.24004	−	9.96505i	−0.794697	−	1.09381i	−0.993507	−	0.113769i	$-0.963708\pi$
$83$	−7.24004	−	9.96505i	−0.794697	−	1.09381i	0.198810	−	0.980038i	$-0.436292\pi$
$84$	−2.72767	+	2.11559i	−0.297613	+	0.230830i
$85$	−9.64119	−	6.00253i	−1.04573	−	0.651066i
$86$	0.522570	+	0.379669i	0.0563502	+	0.0409408i
$87$			6.02510i			0.645959i
$88$	2.18327	+	2.49666i	0.232737	+	0.266145i
$89$			8.78152i			0.930839i	0.885090	+	0.465420i	$0.154097\pi$
$89$			8.78152i			0.930839i	−0.885090	+	0.465420i	$0.845903\pi$
$90$	−1.86889	−	2.21986i	−0.196998	−	0.233993i
$91$	−0.112737	−	3.59269i	−0.0118181	−	0.376616i
$92$	−7.71882	+	2.50800i	−0.804743	+	0.261477i
$93$	−1.29849	−	1.78721i	−0.134647	−	0.185325i
$94$	5.94896	−	4.32217i	0.613588	−	0.445798i
$95$	−1.14345	−	15.9758i	−0.117316	−	1.63908i
$96$	−0.403178	+	1.24085i	−0.0411492	+	0.126644i
$97$	7.43468	+	5.40161i	0.754877	+	0.548450i	0.897335	−	0.441351i	$-0.145500\pi$
$97$	7.43468	+	5.40161i	0.754877	+	0.548450i	−0.142458	+	0.989801i	$0.545500\pi$
$98$	5.39401	−	4.46147i	0.544877	−	0.450676i
$99$	3.95696	−	1.69341i	0.397689	−	0.170194i
$100$	4.42241	+	2.33287i	0.442241	+	0.233287i
$101$	−6.53637	−	4.74895i	−0.650394	−	0.472539i	0.213012	−	0.977050i	$-0.431673\pi$
$101$	−6.53637	−	4.74895i	−0.650394	−	0.472539i	−0.863405	+	0.504511i	$0.831673\pi$
$102$	6.30234	+	2.04775i	0.624025	+	0.202758i
$103$	−1.11911	−	3.44428i	−0.110270	−	0.339375i	0.880662	−	0.473746i	$-0.157099\pi$
$103$	−1.11911	−	3.44428i	−0.110270	−	0.339375i	−0.990931	+	0.134371i	$0.957099\pi$
$104$	−0.798552	−	1.09911i	−0.0783044	−	0.107777i
$105$	−5.15397	−	5.74596i	−0.502976	−	0.560748i
$106$	−7.28684	+	2.36764i	−0.707761	+	0.229965i
$107$	−4.03835	+	12.4288i	−0.390402	+	1.20153i	0.542084	+	0.840325i	$0.317636\pi$
$107$	−4.03835	+	12.4288i	−0.390402	+	1.20153i	−0.932485	+	0.361208i	$0.882364\pi$
$108$	4.53640	+	3.29588i	0.436515	+	0.317147i
$109$		−	2.38757i		−	0.228688i	−0.993441	−	0.114344i	$-0.963523\pi$
$109$		−	2.38757i		−	0.228688i	0.993441	−	0.114344i	$-0.0364766\pi$
$110$	−5.21994	+	5.26804i	−0.497701	+	0.502288i
$111$			12.3853i			1.17556i
$112$	0.738259	−	2.54066i	0.0697590	−	0.240070i
$113$	−6.62203	−	2.15163i	−0.622948	−	0.202408i	−0.0194993	−	0.999810i	$-0.506207\pi$
$113$	−6.62203	−	2.15163i	−0.622948	−	0.202408i	−0.603449	+	0.797402i	$0.706207\pi$
$114$	2.88791	+	8.88807i	0.270477	+	0.832444i
$115$	−6.82595	−	16.8154i	−0.636523	−	1.56804i
$116$	−2.71437	−	3.73601i	−0.252023	−	0.346880i
$117$	−1.67678	+	0.544818i	−0.155018	+	0.0503684i
$118$	7.39957	+	2.40427i	0.681186	+	0.221331i
$119$	−12.9041	−	3.74965i	−1.18292	−	0.343730i
$120$	−2.83191	−	0.701147i	−0.258517	−	0.0640057i
$121$	−5.22135	−	9.68181i	−0.474668	−	0.880165i
$122$	13.2342			1.19817
$123$	5.12540	+	3.72382i	0.462142	+	0.335765i
$124$	1.61031	+	0.523223i	0.144610	+	0.0469868i
$125$	−4.49717	+	10.2360i	−0.402239	+	0.915535i
$126$	−2.83967	−	1.93003i	−0.252978	−	0.171941i
$127$	15.6540	−	11.3733i	1.38907	−	1.00922i	0.393105	−	0.919494i	$-0.371401\pi$
$127$	15.6540	−	11.3733i	1.38907	−	1.00922i	0.995967	−	0.0897254i	$-0.0285989\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	0.260425	−	0.801507i	0.0229292	−	0.0705688i
$130$	2.32394	−	1.95652i	0.203823	−	0.171598i
$131$	−6.57705			−0.574640			−0.287320	−	0.957835i	$-0.592764\pi$
$131$	−6.57705			−0.574640			−0.287320	+	0.957835i	$0.592764\pi$
$132$	2.21775	−	3.71572i	0.193030	−	0.323412i
$133$	−6.41865	−	17.8311i	−0.556567	−	1.54615i
$134$	5.29451	−	7.28727i	0.457376	−	0.629524i
$135$	−6.62684	+	10.6440i	−0.570348	+	0.916085i
$136$	−4.83045	+	1.56951i	−0.414208	+	0.134584i
$137$	−3.23109	−	4.44722i	−0.276051	−	0.379952i	0.648370	−	0.761325i	$-0.275451\pi$
$137$	−3.23109	−	4.44722i	−0.276051	−	0.379952i	−0.924421	+	0.381374i	$0.875451\pi$
$138$	6.22411	+	8.56676i	0.529832	+	0.729251i
$139$	6.68839	+	20.5848i	0.567302	+	1.74598i	0.661010	+	0.750377i	$0.270128\pi$
$139$	6.68839	+	20.5848i	0.567302	+	1.74598i	−0.0937083	+	0.995600i	$0.529872\pi$
$140$	5.78445	+	1.24100i	0.488876	+	0.104884i
$141$	−7.76167	−	5.63918i	−0.653650	−	0.474905i
$142$	10.5500			0.885334
$143$	1.77281	+	4.14249i	0.148250	+	0.346412i
$144$	−1.29773			−0.108144
$145$	7.89934	−	6.65043i	0.656004	−	0.552288i
$146$	8.11337	+	2.63619i	0.671467	+	0.218173i
$147$	−7.71077	−	4.89441i	−0.635974	−	0.403684i
$148$	−5.57969	−	7.67978i	−0.458648	−	0.631274i
$149$	−5.99675	−	8.25382i	−0.491273	−	0.676179i	0.489349	−	0.872088i	$-0.337234\pi$
$149$	−5.99675	−	8.25382i	−0.491273	−	0.676179i	−0.980622	+	0.195909i	$0.937234\pi$
$150$	1.11174	−	6.42812i	0.0907728	−	0.524854i
$151$	21.3280	+	6.92988i	1.73565	+	0.563946i	0.994246	−	0.107116i	$-0.0341618\pi$
$151$	21.3280	+	6.92988i	1.73565	+	0.563946i	0.741401	+	0.671062i	$0.234162\pi$
$152$	−5.79488	−	4.21023i	−0.470027	−	0.341495i
$153$			6.59122i			0.532868i
$154$	−4.25871	+	7.67225i	−0.343177	+	0.618247i
$155$	−0.909911	+	3.67511i	−0.0730858	+	0.295192i
$156$	−1.04188	+	1.43402i	−0.0834171	+	0.114814i
$157$	−2.23332	+	6.87344i	−0.178238	+	0.548560i	−0.999767	−	0.0216072i	$-0.993122\pi$
$157$	−2.23332	+	6.87344i	−0.178238	+	0.548560i	0.821529	+	0.570167i	$0.193122\pi$
$158$	−7.85013	+	2.55066i	−0.624523	+	0.202920i
$159$	5.87579	+	8.08733i	0.465980	+	0.641367i
$160$	2.07187	−	0.841043i	0.163796	−	0.0664903i
$161$	−13.1602	−	16.9676i	−1.03717	−	1.33724i
$162$	1.05767	−	3.25519i	0.0830987	−	0.255752i
$163$	13.9401	−	19.1870i	1.09188	−	1.50284i	0.246143	−	0.969233i	$-0.420837\pi$
$163$	13.9401	−	19.1870i	1.09188	−	1.50284i	0.845733	−	0.533606i	$-0.179163\pi$
$164$	−4.85574			−0.379170
$165$	8.64143	+	4.35322i	0.672734	+	0.338898i
$166$		−	12.3175i		−	0.956022i
$167$	−1.25806	+	1.73157i	−0.0973515	+	0.133993i	−0.854914	−	0.518770i	$-0.826390\pi$
$167$	−1.25806	+	1.73157i	−0.0973515	+	0.133993i	0.757562	+	0.652763i	$0.226390\pi$
$168$	−3.45024	+	0.108267i	−0.266192	+	0.00835301i
$169$	3.44686	+	10.6083i	0.265143	+	0.816026i
$170$	−4.27169	−	10.5231i	−0.327624	−	0.807085i
$171$	−7.52019	+	5.46374i	−0.575083	+	0.417823i
$172$	0.199604	+	0.614318i	0.0152197	+	0.0468413i
$173$	−6.13548	−	1.99354i	−0.466472	−	0.151566i	0.0663445	−	0.997797i	$-0.478866\pi$
$173$	−6.13548	−	1.99354i	−0.466472	−	0.151566i	−0.532816	+	0.846231i	$0.678866\pi$
$174$	−3.54147	+	4.87441i	−0.268478	+	0.369528i
$175$	−1.84448	+	13.0995i	−0.139429	+	0.990232i
$176$	0.298800	+	3.30314i	0.0225229	+	0.248983i
$177$		−	10.1511i		−	0.763006i
$178$	−5.16165	+	7.10440i	−0.386882	+	0.532497i
$179$	−0.518806	+	1.59672i	−0.0387774	+	0.119345i	−0.968571	−	0.248736i	$-0.919985\pi$
$179$	−0.518806	+	1.59672i	−0.0387774	+	0.119345i	0.929794	+	0.368080i	$0.119985\pi$
$180$	−0.207165	−	2.89441i	−0.0154412	−	0.215736i
$181$	2.16837	+	2.98451i	0.161174	+	0.221837i	0.881964	−	0.471316i	$-0.156221\pi$
$181$	2.16837	+	2.98451i	0.161174	+	0.221837i	−0.720790	+	0.693153i	$0.756221\pi$
$182$	2.02052	−	2.97281i	0.149771	−	0.220359i
$183$	−5.33573	−	16.4217i	−0.394429	−	1.21393i
$184$	−7.71882	−	2.50800i	−0.569039	−	0.184892i
$185$	16.2380	−	13.6707i	1.19384	−	1.00509i
$186$		−	2.20911i		−	0.161980i
$187$	16.7768	−	1.51762i	1.22684	−	0.110979i
$188$	7.35332			0.536296
$189$	−4.13964	+	14.2463i	−0.301114	+	1.03626i
$190$	8.46526	−	13.5968i	0.614134	−	0.986415i
$191$	4.58524	+	14.1119i	0.331776	+	1.02110i	0.968288	+	0.249836i	$0.0803766\pi$
$191$	4.58524	+	14.1119i	0.331776	+	1.02110i	−0.636512	+	0.771267i	$0.719623\pi$
$192$	−1.05553	+	0.766890i	−0.0761765	+	0.0553455i
$193$	0.108963	−	0.0791660i	0.00784330	−	0.00569849i	−0.583857	−	0.811857i	$-0.698457\pi$
$193$	0.108963	−	0.0791660i	0.00784330	−	0.00569849i	0.591700	+	0.806158i	$0.298457\pi$
$194$	2.83979	+	8.73999i	0.203885	+	0.627494i
$195$	−3.36471	−	2.09484i	−0.240952	−	0.150015i
$196$	6.98623	−	0.438883i	0.499016	−	0.0313488i
$197$	−19.1925			−1.36741			−0.683703	−	0.729760i	$-0.739632\pi$
$197$	−19.1925			−1.36741			−0.683703	+	0.729760i	$0.739632\pi$
$198$	4.19661	+	0.955843i	0.298240	+	0.0679288i
$199$		−	11.7730i		−	0.834567i	−0.908776	−	0.417283i	$-0.862982\pi$
$199$		−	11.7730i		−	0.834567i	0.908776	−	0.417283i	$-0.137018\pi$
$200$	2.20658	+	4.48676i	0.156029	+	0.317262i
$201$	−11.1771	−	3.63165i	−0.788369	−	0.256157i
$202$	−2.49667	−	7.68397i	−0.175665	−	0.540642i
$203$	6.86799	−	10.1049i	0.482038	−	0.709227i
$204$	3.89506	+	5.36109i	0.272709	+	0.375351i
$205$	−0.775154	−	10.8301i	−0.0541391	−	0.756405i
$206$	1.11911	−	3.44428i	0.0779723	−	0.239974i
$207$	−6.19081	+	8.52092i	−0.430291	+	0.592245i
$208$		−	1.35858i		−	0.0942004i
$209$	15.6385	+	17.8833i	1.08174	+	1.23701i
$210$	−0.792260	−	7.67801i	−0.0546711	−	0.529833i
$211$	−7.06031	+	9.71768i	−0.486052	+	0.668993i	−0.979654	−	0.200695i	$-0.935680\pi$
$211$	−7.06031	+	9.71768i	−0.486052	+	0.668993i	0.493602	+	0.869688i	$0.335680\pi$
$212$	−7.28684	−	2.36764i	−0.500463	−	0.162610i
$213$	−4.25351	−	13.0910i	−0.291446	−	0.896978i
$214$	−10.5725	+	7.68139i	−0.722723	+	0.525089i
$215$	−1.33829	+	0.543257i	−0.0912704	+	0.0370498i
$216$	1.73275	+	5.33285i	0.117899	+	0.362855i
$217$	0.140504	+	4.47754i	0.00953800	+	0.303955i
$218$	1.40338	−	1.93159i	0.0950489	−	0.130824i
$219$		−	11.1304i		−	0.752120i
$220$	−7.31949	+	1.19373i	−0.493480	+	0.0804815i
$221$	−6.90026			−0.464162
$222$	−7.27988	+	10.0199i	−0.488594	+	0.672491i
$223$	3.43122	−	10.5602i	0.229772	−	0.707164i	−0.768000	−	0.640449i	$-0.778748\pi$
$223$	3.43122	−	10.5602i	0.229772	−	0.707164i	0.997772	−	0.0667151i	$-0.0212519\pi$
$224$	2.09063	−	1.62150i	0.139686	−	0.108341i
$225$	6.42251	−	0.924106i	0.428167	−	0.0616071i
$226$	−4.09264	−	5.63303i	−0.272238	−	0.374704i
$227$	−2.08529	+	0.677551i	−0.138405	+	0.0449707i	−0.377401	−	0.926050i	$-0.623182\pi$
$227$	−2.08529	+	0.677551i	−0.138405	+	0.0449707i	0.238995	+	0.971021i	$0.423182\pi$
$228$	−2.88791	+	8.88807i	−0.191256	+	0.588627i
$229$	−3.67931	+	5.06414i	−0.243136	+	0.334648i	−0.913093	−	0.407752i	$-0.866313\pi$
$229$	−3.67931	+	5.06414i	−0.243136	+	0.334648i	0.669957	+	0.742400i	$0.266313\pi$
$230$	4.36154	−	17.6161i	0.287591	−	1.16157i
$231$	11.2372	+	2.19116i	0.739350	+	0.144168i
$232$		−	4.61796i		−	0.303184i
$233$	13.8292	+	10.0475i	0.905980	+	0.658233i	0.939995	−	0.341188i	$-0.110829\pi$
$233$	13.8292	+	10.0475i	0.905980	+	0.658233i	−0.0340148	+	0.999421i	$0.510829\pi$
$234$	−1.67678	−	0.544818i	−0.109614	−	0.0356158i
$235$	1.17386	+	16.4006i	0.0765740	+	1.06985i
$236$	4.57319	+	6.29445i	0.297689	+	0.409734i
$237$	6.33000	+	8.71249i	0.411177	+	0.565937i
$238$	−8.23567	−	10.6184i	−0.533839	−	0.688287i
$239$	13.8185	+	4.48990i	0.893844	+	0.290427i	0.719694	−	0.694292i	$-0.244282\pi$
$239$	13.8185	+	4.48990i	0.893844	+	0.290427i	0.174150	+	0.984719i	$0.444282\pi$
$240$	−1.87894	−	2.23180i	−0.121285	−	0.144062i
$241$	−5.26402			−0.339086			−0.169543	−	0.985523i	$-0.554229\pi$
$241$	−5.26402			−0.339086			−0.169543	+	0.985523i	$0.554229\pi$
$242$	1.46667	−	10.9018i	0.0942808	−	0.700793i
$243$	12.3562			0.792653
$244$	10.7067	+	7.77886i	0.685425	+	0.497990i
$245$	2.09412	+	15.5118i	0.133789	+	0.991010i
$246$	1.95773	+	6.02527i	0.124820	+	0.384157i
$247$	−5.71992	−	7.87279i	−0.363950	−	0.500934i
$248$	0.995228	+	1.36981i	0.0631971	+	0.0869833i
$249$	−15.2842	+	4.96614i	−0.968596	+	0.314716i
$250$	−9.65485	+	5.63772i	−0.610626	+	0.356561i
$251$	4.98547	−	6.86190i	0.314680	−	0.433120i	−0.622154	−	0.782895i	$-0.713742\pi$
$251$	4.98547	−	6.86190i	0.314680	−	0.433120i	0.936834	+	0.349776i	$0.113742\pi$
$252$	−1.16290	−	3.23054i	−0.0732556	−	0.203505i
$253$	23.1139	+	13.7957i	1.45316	+	0.867326i
$254$	19.3495			1.21409
$255$	−11.3354	+	9.54322i	−0.709849	+	0.597620i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−4.43343	−	13.6447i	−0.276550	−	0.851133i	−0.988805	−	0.149212i	$-0.952326\pi$
$257$	−4.43343	−	13.6447i	−0.276550	−	0.851133i	0.712255	−	0.701920i	$-0.247674\pi$
$258$	0.681803	−	0.495359i	0.0424472	−	0.0308397i
$259$	14.1179	−	20.7718i	0.877245	−	1.29070i
$260$	3.03012	−	0.216878i	0.187920	−	0.0134502i
$261$	−5.69955	−	1.85190i	−0.352793	−	0.114630i
$262$	−5.32095	−	3.86590i	−0.328729	−	0.238836i
$263$	20.8023			1.28272			0.641361	−	0.767239i	$-0.278370\pi$
$263$	20.8023			1.28272			0.641361	+	0.767239i	$0.278370\pi$
$264$	3.97824	−	1.70252i	0.244844	−	0.104783i
$265$	4.11745	−	16.6303i	0.252933	−	1.02159i
$266$	5.28805	−	18.1984i	0.324231	−	1.11582i
$267$	10.8966	+	3.54051i	0.666860	+	0.216676i
$268$	8.56670	−	2.78349i	0.523295	−	0.170029i
$269$	0.0511561	+	0.0704103i	0.00311904	+	0.00429299i	0.810574	−	0.585637i	$-0.199155\pi$
$269$	0.0511561	+	0.0704103i	0.00311904	+	0.00429299i	−0.807455	+	0.589930i	$0.799155\pi$
$270$	−11.6176	+	4.71598i	−0.707024	+	0.287005i
$271$	1.50500	+	4.63192i	0.0914223	+	0.281369i	0.986305	−	0.164933i	$-0.0527408\pi$
$271$	1.50500	+	4.63192i	0.0914223	+	0.281369i	−0.894882	+	0.446302i	$0.852741\pi$
$272$	−4.83045	−	1.56951i	−0.292889	−	0.0951654i
$273$	−4.50345	−	1.30860i	−0.272561	−	0.0792002i
$274$		−	5.49707i		−	0.332090i
$275$	−3.83092	−	16.1346i	−0.231013	−	0.972951i
$276$			10.5891i			0.637389i
$277$	5.87889	+	4.27126i	0.353228	+	0.256635i	0.750222	−	0.661186i	$-0.229947\pi$
$277$	5.87889	+	4.27126i	0.353228	+	0.256635i	−0.396994	+	0.917821i	$0.629947\pi$
$278$	−6.68839	+	20.5848i	−0.401143	+	1.23459i
$279$	2.08975	−	0.679002i	0.125110	−	0.0406508i
$280$	3.95028	+	4.40401i	0.236074	+	0.263190i
$281$	−1.95404	−	2.68950i	−0.116568	−	0.160442i	0.746746	−	0.665110i	$-0.231615\pi$
$281$	−1.95404	−	2.68950i	−0.116568	−	0.160442i	−0.863314	+	0.504667i	$0.831615\pi$
$282$	−2.96469	−	9.12439i	−0.176545	−	0.543349i
$283$	11.4856	+	3.73189i	0.682747	+	0.221838i	0.629798	−	0.776759i	$-0.283138\pi$
$283$	11.4856	+	3.73189i	0.682747	+	0.221838i	0.0529493	+	0.998597i	$0.483138\pi$
$284$	8.53510	+	6.20112i	0.506465	+	0.367969i
$285$	−20.2846	−	5.02222i	−1.20156	−	0.297491i
$286$	−1.00066	+	4.39337i	−0.0591703	+	0.259786i
$287$	−4.35123	−	12.0878i	−0.256845	−	0.713519i
$288$	−1.04989	−	0.762787i	−0.0618651	−	0.0449476i
$289$	−2.71830	+	8.36607i	−0.159900	+	0.492122i
$290$	10.2997	−	0.737195i	0.604820	−	0.0432896i
$291$	9.70010	−	7.04754i	0.568630	−	0.413134i
$292$	5.01434	+	6.90164i	0.293442	+	0.403888i
$293$	11.3386	−	3.68413i	0.662408	−	0.215229i	0.0415307	−	0.999137i	$-0.486777\pi$
$293$	11.3386	−	3.68413i	0.662408	−	0.215229i	0.620877	+	0.783908i	$0.286777\pi$
$294$	−3.36128	−	8.49194i	−0.196034	−	0.495260i
$295$	−13.3089	+	11.2047i	−0.774872	+	0.652362i
$296$		−	9.49273i		−	0.551754i
$297$	−1.67546	−	18.5217i	−0.0972200	−	1.07474i
$298$		−	10.2023i		−	0.591003i
$299$	−8.92045	−	6.48108i	−0.515883	−	0.374811i
$300$	4.67777	−	4.54700i	0.270071	−	0.262521i
$301$	−1.35040	+	1.04738i	−0.0778360	+	0.0603700i
$302$	13.1814	+	18.1427i	0.758506	+	1.04399i
$303$	−8.52808	+	6.19601i	−0.489925	+	0.355952i
$304$	−2.21345	−	6.81229i	−0.126950	−	0.390712i
$305$	−15.6405	+	25.1216i	−0.895572	+	1.43846i
$306$	−3.87422	+	5.33241i	−0.221474	+	0.304833i
$307$			26.7668i			1.52766i	0.645415	+	0.763832i	$0.276685\pi$
$307$			26.7668i			1.52766i	−0.645415	+	0.763832i	$0.723315\pi$
$308$	−7.95500	+	3.70377i	−0.453278	+	0.211042i
$309$	−4.72504			−0.268798
$310$	−2.89631	+	2.43839i	−0.164499	+	0.138491i
$311$	3.20596	+	1.04168i	0.181793	+	0.0590683i	0.398499	−	0.917169i	$-0.369531\pi$
$311$	3.20596	+	1.04168i	0.181793	+	0.0590683i	−0.216706	+	0.976237i	$0.569531\pi$
$312$	−1.68580	+	0.547748i	−0.0954394	+	0.0310101i
$313$	15.9104	−	11.5596i	0.899307	−	0.653385i	−0.0389809	−	0.999240i	$-0.512411\pi$
$313$	15.9104	−	11.5596i	0.899307	−	0.653385i	0.938288	+	0.345855i	$0.112411\pi$
$314$	−5.84690	+	4.24802i	−0.329960	+	0.239730i
$315$	7.01964	−	3.10939i	0.395512	−	0.175194i
$316$	−7.85013	−	2.55066i	−0.441604	−	0.143486i
$317$	−2.02322	+	2.78473i	−0.113636	+	0.156406i	−0.862046	−	0.506830i	$-0.830817\pi$
$317$	−2.02322	+	2.78473i	−0.113636	+	0.156406i	0.748411	+	0.663236i	$0.230817\pi$
$318$			9.99649i			0.560575i
$319$	−3.40136	+	14.9336i	−0.190439	+	0.836120i
$320$	2.17053	+	0.537397i	0.121336	+	0.0300414i
$321$	13.7941	+	10.0220i	0.769911	+	0.559373i
$322$	−0.673485	−	21.4625i	−0.0375318	−	1.19606i
$323$	−34.5999	+	11.2422i	−1.92519	+	0.625532i
$324$	2.76903	−	2.01182i	0.153835	−	0.111768i
$325$	0.967435	+	6.72364i	0.0536636	+	0.372961i
$326$	22.5556	−	7.32877i	1.24924	−	0.405903i
$327$	−2.96263	−	0.962617i	−0.163834	−	0.0532328i
$328$	−3.92838	−	2.85413i	−0.216908	−	0.157593i
$329$	6.58931	+	18.3052i	0.363280	+	1.00920i
$330$	4.43231	+	8.60113i	0.243990	+	0.473477i
$331$	9.86863			0.542429			0.271214	−	0.962519i	$-0.412575\pi$
$331$	9.86863			0.542429			0.271214	+	0.962519i	$0.412575\pi$
$332$	7.24004	−	9.96505i	0.397349	−	0.546903i
$333$	−11.7161	−	3.80678i	−0.642037	−	0.208610i
$334$	−2.03558	+	0.661400i	−0.111382	+	0.0361902i
$335$	7.57575	+	18.6625i	0.413907	+	1.01964i
$336$	−2.85494	−	1.94041i	−0.155750	−	0.105858i
$337$	−2.86859	−	8.82861i	−0.156262	−	0.480925i	0.842025	−	0.539439i	$-0.181364\pi$
$337$	−2.86859	−	8.82861i	−0.156262	−	0.480925i	−0.998287	+	0.0585141i	$0.981364\pi$
$338$	−3.44686	+	10.6083i	−0.187484	+	0.577018i
$339$	−5.33971	+	7.34948i	−0.290013	+	0.399169i
$340$	2.72946	−	11.0242i	0.148026	−	0.597871i
$341$	−2.20944	−	5.16275i	−0.119648	−	0.279578i
$342$	−9.29547			−0.502641
$343$	7.35291	+	16.9981i	0.397020	+	0.917810i
$344$	−0.199604	+	0.614318i	−0.0107619	+	0.0331218i
$345$	−23.6175	+	1.69041i	−1.27152	+	0.0910084i
$346$	−3.79194	−	5.21915i	−0.203856	−	0.280583i
$347$	6.15841	−	4.47434i	0.330601	−	0.240195i	−0.410085	−	0.912047i	$-0.634501\pi$
$347$	6.15841	−	4.47434i	0.330601	−	0.240195i	0.740685	+	0.671852i	$0.234501\pi$
$348$	−5.73021	+	1.86186i	−0.307172	+	0.0998061i
$349$	−3.14104	+	9.66712i	−0.168136	+	0.517469i	−0.999254	−	0.0386274i	$-0.987701\pi$
$349$	−3.14104	+	9.66712i	−0.168136	+	0.517469i	0.831118	+	0.556096i	$0.187701\pi$
$350$	−9.19193	+	9.51359i	−0.491329	+	0.508523i
$351$			7.61794i			0.406616i
$352$	−1.69980	+	2.84792i	−0.0905997	+	0.151795i
$353$	−13.5006			−0.718562			−0.359281	−	0.933229i	$-0.616978\pi$
$353$	−13.5006			−0.718562			−0.359281	+	0.933229i	$0.616978\pi$
$354$	5.96668	−	8.21244i	0.317126	−	0.436486i
$355$	−12.4682	+	20.0263i	−0.661745	+	1.06289i
$356$	−8.35172	+	2.71364i	−0.442640	+	0.143823i
$357$	−9.85542	+	14.5004i	−0.521604	+	0.767440i
$358$	−1.35825	+	0.986828i	−0.0717859	+	0.0521555i
$359$	−15.9542	+	5.18385i	−0.842033	+	0.273593i	−0.698105	−	0.715995i	$-0.745973\pi$
$359$	−15.9542	+	5.18385i	−0.842033	+	0.273593i	−0.143928	+	0.989588i	$0.545973\pi$
$360$	1.53369	−	2.46339i	0.0808326	−	0.129832i
$361$	−26.1366	−	18.9894i	−1.37561	−	0.999441i
$362$			3.68905i			0.193892i
$363$	−14.1188	+	2.57544i	−0.741047	+	0.135176i
$364$	3.38201	−	1.21742i	0.177266	−	0.0638102i
$365$	−14.5927	+	12.2855i	−0.763817	+	0.643055i
$366$	5.33573	−	16.4217i	0.278903	−	0.858375i
$367$	2.07810	+	6.39575i	0.108476	+	0.333855i	0.990531	−	0.137292i	$-0.0438399\pi$
$367$	2.07810	+	6.39575i	0.108476	+	0.333855i	−0.882054	+	0.471148i	$0.843840\pi$
$368$	−4.77049	−	6.56602i	−0.248679	−	0.342277i
$369$	−5.09798	+	3.70390i	−0.265390	+	0.192817i
$370$	21.1722	−	1.51539i	1.10069	−	0.0787812i
$371$	−0.635794	−	20.2614i	−0.0330088	−	1.05192i
$372$	1.29849	−	1.78721i	0.0673233	−	0.0926626i
$373$	34.7044			1.79693			0.898463	−	0.439050i	$-0.144685\pi$
$373$	34.7044			1.79693			0.898463	+	0.439050i	$0.144685\pi$
$374$	14.4647	+	8.63335i	0.747952	+	0.446420i
$375$	10.8882	+	9.70725i	0.562264	+	0.501280i
$376$	5.94896	+	4.32217i	0.306794	+	0.222899i
$377$	1.93873	−	5.96679i	0.0998495	−	0.307305i
$378$	−11.7228	+	9.09224i	−0.602954	+	0.467654i
$379$	24.9342	−	18.1157i	1.28078	−	0.930542i	0.281205	−	0.959648i	$-0.409266\pi$
$379$	24.9342	−	18.1157i	1.28078	−	0.930542i	0.999576	+	0.0291053i	$0.00926580\pi$
$380$	14.8405	−	6.02428i	0.761303	−	0.309039i
$381$	−7.80127	−	24.0098i	−0.399671	−	1.23006i
$382$	−4.58524	+	14.1119i	−0.234601	+	0.722028i
$383$	−6.54541	−	4.75552i	−0.334455	−	0.242996i	0.407864	−	0.913043i	$-0.366274\pi$
$383$	−6.54541	−	4.75552i	−0.334455	−	0.242996i	−0.742319	+	0.670047i	$0.766274\pi$
$384$	−1.30471			−0.0665807
$385$	−9.53066	−	17.1513i	−0.485727	−	0.874110i
$386$	0.134685			0.00685530
$387$	0.678155	+	0.492708i	0.0344725	+	0.0250458i
$388$	−2.83979	+	8.73999i	−0.144169	+	0.443706i
$389$	−7.72791	−	23.7841i	−0.391821	−	1.20590i	−0.931410	−	0.363971i	$-0.881421\pi$
$389$	−7.72791	−	23.7841i	−0.391821	−	1.20590i	0.539590	−	0.841928i	$-0.318579\pi$
$390$	−1.49079	−	3.67249i	−0.0754891	−	0.185964i
$391$	−33.3491	+	24.2295i	−1.68653	+	1.22534i
$392$	5.90995	+	3.75134i	0.298497	+	0.189471i
$393$	−2.65172	+	8.16116i	−0.133762	+	0.411676i
$394$	−15.5270	−	11.2810i	−0.782240	−	0.568331i
$395$	4.43573	−	17.9158i	0.223186	−	0.901442i
$396$	2.83330	+	3.24000i	0.142378	+	0.162816i
$397$	−30.7565			−1.54363			−0.771813	−	0.635850i	$-0.780650\pi$
$397$	−30.7565			−1.54363			−0.771813	+	0.635850i	$0.780650\pi$
$398$	6.92000	−	9.52457i	0.346868	−	0.477423i
$399$	−24.7136	+	0.775504i	−1.23723	+	0.0388238i
$400$	−0.852093	+	4.92686i	−0.0426047	+	0.246343i
$401$	−24.5383	+	17.8281i	−1.22539	+	0.890295i	−0.996536	−	0.0831667i	$-0.973497\pi$
$401$	−24.5383	+	17.8281i	−1.22539	+	0.890295i	−0.228850	+	0.973462i	$0.573497\pi$
$402$	−6.90781	−	9.50778i	−0.344530	−	0.474205i
$403$	0.710838	+	2.18773i	0.0354094	+	0.108979i
$404$	2.49667	−	7.68397i	0.124214	−	0.382292i
$405$	4.92912	+	5.85477i	0.244930	+	0.290926i
$406$	11.4958	−	4.13815i	0.570529	−	0.205373i
$407$	−6.99187	+	30.6976i	−0.346574	+	1.52163i
$408$			6.62667i			0.328069i
$409$	−21.4628	−	15.5937i	−1.06127	−	0.771057i	−0.0869462	−	0.996213i	$-0.527711\pi$
$409$	−21.4628	−	15.5937i	−1.06127	−	0.771057i	−0.974323	+	0.225156i	$0.927711\pi$
$410$	5.73864	−	9.21733i	0.283411	−	0.455212i
$411$	−6.82105	+	2.21629i	−0.336458	+	0.109322i
$412$	2.92988	−	2.12868i	0.144345	−	0.104873i
$413$	−11.5712	+	17.0248i	−0.569383	+	0.837738i
$414$	−10.0169	+	3.25470i	−0.492306	+	0.159960i
$415$	23.3815	+	14.5571i	1.14775	+	0.714581i
$416$	0.798552	−	1.09911i	0.0391522	−	0.0538884i
$417$	28.2393			1.38288
$418$	2.14026	+	23.6599i	0.104684	+	1.15725i
$419$			9.42669i			0.460524i	0.973129	+	0.230262i	$0.0739583\pi$
$419$			9.42669i			0.460524i	−0.973129	+	0.230262i	$0.926042\pi$
$420$	3.87207	−	6.67732i	0.188938	−	0.325820i
$421$	0.476388	−	1.46617i	0.0232177	−	0.0714568i	−0.938776	−	0.344527i	$-0.888039\pi$
$421$	0.476388	−	1.46617i	0.0232177	−	0.0714568i	0.961994	+	0.273070i	$0.0880392\pi$
$422$	−11.4238	+	3.71182i	−0.556103	+	0.180689i
$423$	7.72014	−	5.60901i	0.375366	−	0.272719i
$424$	−4.50352	−	6.19856i	−0.218710	−	0.301029i
$425$	25.0237	+	4.32781i	1.21383	+	0.209930i
$426$	4.25351	−	13.0910i	0.206083	−	0.634259i
$427$	−9.77026	+	33.6236i	−0.472816	+	1.62716i
$428$	−13.0684			−0.631683
$429$	5.85498	−	0.529638i	0.282681	−	0.0255712i
$430$	−1.40202	−	0.347122i	−0.0676112	−	0.0167397i
$431$	−10.2729	+	14.1395i	−0.494830	+	0.681075i	−0.981270	−	0.192639i	$-0.938295\pi$
$431$	−10.2729	+	14.1395i	−0.494830	+	0.681075i	0.486440	+	0.873714i	$0.338295\pi$
$432$	−1.73275	+	5.33285i	−0.0833669	+	0.256577i
$433$	−0.443558	−	1.36513i	−0.0213160	−	0.0656039i	0.939833	−	0.341635i	$-0.110981\pi$
$433$	−0.443558	−	1.36513i	−0.0213160	−	0.0656039i	−0.961149	+	0.276031i	$0.910981\pi$
$434$	−2.51816	+	3.70499i	−0.120876	+	0.177845i
$435$	−5.06737	−	12.4832i	−0.242962	−	0.598525i
$436$	2.27072	−	0.737801i	0.108748	−	0.0353343i
$437$	−55.2889	−	17.9644i	−2.64483	−	0.859356i
$438$	6.54226	−	9.00465i	0.312601	−	0.430259i
$439$	35.0071			1.67080			0.835400	−	0.549643i	$-0.185236\pi$
$439$	35.0071			1.67080			0.835400	+	0.549643i	$0.185236\pi$
$440$	−6.62325	−	3.33654i	−0.315751	−	0.159063i
$441$	6.99997	−	5.78978i	0.333332	−	0.275704i
$442$	−5.58243	−	4.05587i	−0.265529	−	0.192918i
$443$	21.1377	+	6.86807i	1.00428	+	0.326312i	0.764576	−	0.644533i	$-0.222948\pi$
$443$	21.1377	+	6.86807i	1.00428	+	0.326312i	0.239708	+	0.970845i	$0.422948\pi$
$444$	−11.7791	+	3.82726i	−0.559011	+	0.181634i
$445$	−7.38564	−	18.1942i	−0.350113	−	0.862486i
$446$	8.98306	−	6.52657i	0.425360	−	0.309042i
$447$	−12.6595	+	4.11333i	−0.598776	+	0.194554i
$448$	2.64445	−	0.0829819i	0.124939	−	0.00392052i
$449$	15.7142	+	11.4170i	0.741599	+	0.538803i	0.893211	−	0.449637i	$-0.148447\pi$
$449$	15.7142	+	11.4170i	0.741599	+	0.538803i	−0.151612	+	0.988440i	$0.548447\pi$
$450$	5.73909	+	3.02744i	0.270544	+	0.142715i
$451$	10.6014	+	12.1232i	0.499200	+	0.570857i
$452$		−	6.96281i		−	0.327503i
$453$	17.1979	−	23.6709i	0.808030	−	1.11216i
$454$	−2.08529	−	0.677551i	−0.0978674	−	0.0317991i
$455$	3.25518	+	7.34877i	0.152605	+	0.344516i
$456$	−7.56064	+	5.49313i	−0.354060	+	0.257239i
$457$	10.7473	−	7.80834i	0.502736	−	0.365259i	−0.307325	−	0.951605i	$-0.599434\pi$
$457$	10.7473	−	7.80834i	0.502736	−	0.365259i	0.810061	+	0.586346i	$0.199434\pi$
$458$	−5.95325	+	1.93433i	−0.278177	+	0.0903853i
$459$	27.0858	+	8.80070i	1.26425	+	0.410781i
$460$	13.8831	−	11.6881i	0.647301	−	0.544961i
$461$	24.4262			1.13764			0.568820	−	0.822462i	$-0.307400\pi$
$461$	24.4262			1.13764			0.568820	+	0.822462i	$0.307400\pi$
$462$	7.80312	+	8.37772i	0.363034	+	0.389767i
$463$		−	35.8500i		−	1.66609i	−0.553206	−	0.833044i	$-0.686596\pi$
$463$		−	35.8500i		−	1.66609i	0.553206	−	0.833044i	$-0.313404\pi$
$464$	2.71437	−	3.73601i	0.126011	−	0.173440i
$465$	4.19341	+	2.61079i	0.194465	+	0.121072i
$466$	5.28228	+	16.2572i	0.244697	+	0.753100i
$467$	20.6535	−	15.0056i	0.955729	−	0.694378i	0.00357383	−	0.999994i	$-0.498862\pi$
$467$	20.6535	−	15.0056i	0.955729	−	0.694378i	0.952155	+	0.305616i	$0.0988624\pi$
$468$	−1.03630	−	1.42635i	−0.0479032	−	0.0659331i
$469$	14.6058	+	18.8315i	0.674432	+	0.869557i
$470$	−8.69034	+	13.9583i	−0.400855	+	0.643849i
$471$	7.62851	+	5.54244i	0.351503	+	0.255382i
$472$			7.78037i			0.358120i
$473$	1.09796	−	1.83957i	0.0504841	−	0.0845833i
$474$			10.7692i			0.494647i
$475$	15.8054	+	32.1381i	0.725202	+	1.47460i
$476$	−0.421468	−	13.4313i	−0.0193180	−	0.615621i
$477$	−9.45636	+	3.07256i	−0.432977	+	0.140683i
$478$	8.54029	+	11.7547i	0.390624	+	0.537648i
$479$	−4.38016	+	3.18238i	−0.200135	+	0.145406i	−0.683339	−	0.730101i	$-0.739473\pi$
$479$	−4.38016	+	3.18238i	−0.200135	+	0.145406i	0.483204	+	0.875508i	$0.339473\pi$
$480$	−0.208279	−	2.90998i	−0.00950661	−	0.132822i
$481$	3.98527	−	12.2654i	0.181713	−	0.559254i
$482$	−4.25868	−	3.09412i	−0.193978	−	0.140933i
$483$	−26.3603	+	9.48889i	−1.19943	+	0.431759i
$484$	7.59446	−	7.95764i	0.345203	−	0.361711i
$485$	−19.9467	−	4.93855i	−0.905732	−	0.224248i
$486$	9.99641	+	7.26282i	0.453446	+	0.329448i
$487$	−11.1909	−	3.63613i	−0.507106	−	0.164769i	0.0442795	−	0.999019i	$-0.485901\pi$
$487$	−11.1909	−	3.63613i	−0.507106	−	0.164769i	−0.551386	+	0.834250i	$0.685901\pi$
$488$	4.08959	+	12.5865i	0.185127	+	0.569762i
$489$	−18.1879	−	25.0334i	−0.822483	−	1.13205i
$490$	−7.42340	+	13.7802i	−0.335355	+	0.622525i
$491$	−2.40548	+	0.781588i	−0.108558	+	0.0352726i	−0.362792	−	0.931870i	$-0.618177\pi$
$491$	−2.40548	+	0.781588i	−0.108558	+	0.0352726i	0.254234	+	0.967143i	$0.418177\pi$
$492$	−1.95773	+	6.02527i	−0.0882612	+	0.271640i
$493$	−18.9753	−	13.7864i	−0.854605	−	0.620907i
$494$		−	9.73131i		−	0.437832i
$495$	−6.77407	+	6.83650i	−0.304472	+	0.307278i
$496$			1.69318i			0.0760262i
$497$	−7.78861	+	26.8039i	−0.349367	+	1.20232i
$498$	−15.2842	−	4.96614i	−0.684901	−	0.222538i
$499$	−0.555801	−	1.71058i	−0.0248810	−	0.0765760i	0.937845	−	0.347054i	$-0.112818\pi$
$499$	−0.555801	−	1.71058i	−0.0248810	−	0.0765760i	−0.962726	+	0.270478i	$0.912818\pi$
$500$	−11.1247	−	1.11397i	−0.497512	−	0.0498183i
$501$	1.64140	+	2.25920i	0.0733324	+	0.100933i
$502$	8.06665	−	2.62101i	0.360032	−	0.116982i
$503$	1.55492	+	0.505225i	0.0693306	+	0.0225269i	0.343477	−	0.939161i	$-0.388395\pi$
$503$	1.55492	+	0.505225i	0.0693306	+	0.0225269i	−0.274146	+	0.961688i	$0.588395\pi$
$504$	0.958062	−	3.29710i	0.0426755	−	0.146864i
$505$	17.5366	+	4.34184i	0.780368	+	0.193210i
$506$	10.5906	+	24.7469i	0.470811	+	1.10014i
$507$	14.5531			0.646326
$508$	15.6540	+	11.3733i	0.694536	+	0.504610i
$509$	−5.40863	−	1.75737i	−0.239733	−	0.0778941i	0.186686	−	0.982420i	$-0.440225\pi$
$509$	−5.40863	−	1.75737i	−0.239733	−	0.0778941i	−0.426420	+	0.904525i	$0.640225\pi$
$510$	−14.7799	+	1.05786i	−0.654464	+	0.0468428i
$511$	−12.6875	+	18.6672i	−0.561260	+	0.825786i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	12.4115	+	38.1985i	0.547979	+	1.68651i
$514$	4.43343	−	13.6447i	0.195550	−	0.601842i
$515$	5.21544	+	6.19487i	0.229820	+	0.272979i
$516$	0.842754			0.0371002
$517$	−16.0543	−	18.3588i	−0.706066	−	0.807417i
$518$	23.6310	−	8.50644i	1.03829	−	0.373752i
$519$	−4.94738	+	6.80948i	−0.217166	+	0.298903i
$520$	2.57890	+	1.60560i	0.113092	+	0.0704103i
$521$	−5.30795	+	1.72466i	−0.232545	+	0.0755585i	−0.422972	−	0.906143i	$-0.639013\pi$
$521$	−5.30795	+	1.72466i	−0.232545	+	0.0755585i	0.190426	+	0.981701i	$0.439013\pi$
$522$	−3.52252	−	4.84833i	−0.154176	−	0.212206i
$523$	−13.2461	−	18.2316i	−0.579209	−	0.797213i	0.414399	−	0.910095i	$-0.363992\pi$
$523$	−13.2461	−	18.2316i	−0.579209	−	0.797213i	−0.993608	+	0.112882i	$0.963992\pi$
$524$	−2.03242	−	6.25515i	−0.0887867	−	0.273257i
$525$	15.5110	+	7.57017i	0.676954	+	0.330389i
$526$	16.8294	+	12.2273i	0.733796	+	0.533134i
$527$	8.59974			0.374611
$528$	4.21918	+	0.960985i	0.183616	+	0.0418215i
$529$	−42.8702			−1.86392
$530$	13.1061	−	11.0340i	0.569293	−	0.479286i
$531$	9.60265	+	3.12009i	0.416719	+	0.135400i
$532$	14.9749	−	11.6146i	0.649244	−	0.503557i
$533$	−3.87756	−	5.33701i	−0.167956	−	0.231171i
$534$	6.73446	+	9.26919i	0.291428	+	0.401117i
$535$	−2.08619	−	29.1472i	−0.0901937	−	1.26014i
$536$	8.56670	+	2.78349i	0.370025	+	0.120228i
$537$	1.77213	+	1.28753i	0.0764729	+	0.0555608i
$538$			0.0870320i			0.00375221i
$539$	−16.3486	−	16.4841i	−0.704183	−	0.710019i
$540$	−12.1708	−	3.01334i	−0.523748	−	0.129674i
$541$	14.7631	−	20.3196i	0.634713	−	0.873608i	−0.363606	−	0.931553i	$-0.618455\pi$
$541$	14.7631	−	20.3196i	0.634713	−	0.873608i	0.998320	+	0.0579446i	$0.0184547\pi$
$542$	−1.50500	+	4.63192i	−0.0646454	+	0.198958i
$543$	4.57757	−	1.48734i	0.196442	−	0.0638280i
$544$	−2.98538	−	4.10903i	−0.127997	−	0.176173i
$545$	2.00805	+	4.94674i	0.0860155	+	0.211895i
$546$	−2.87419	−	3.70574i	−0.123004	−	0.158591i
$547$	−0.517579	+	1.59294i	−0.0221301	+	0.0681093i	−0.961512	−	0.274764i	$-0.911400\pi$
$547$	−0.517579	+	1.59294i	−0.0221301	+	0.0681093i	0.939382	+	0.342874i	$0.111400\pi$
$548$	3.23109	−	4.44722i	0.138025	−	0.189976i
$549$	17.1744			0.732986
$550$	6.38438	−	15.3049i	0.272231	−	0.652603i
$551$		−	33.0778i		−	1.40916i
$552$	−6.22411	+	8.56676i	−0.264916	+	0.364625i
$553$	−0.684942	−	21.8276i	−0.0291267	−	0.928204i
$554$	2.24553	+	6.91105i	0.0954036	+	0.293622i
$555$	−10.4165	−	25.6607i	−0.442158	−	1.08923i
$556$	−17.5104	+	12.7221i	−0.742608	+	0.539536i
$557$	−4.82683	−	14.8555i	−0.204520	−	0.629446i	−0.999733	−	0.0231166i	$-0.992641\pi$
$557$	−4.82683	−	14.8555i	−0.204520	−	0.629446i	0.795213	−	0.606330i	$-0.207359\pi$
$558$	2.08975	+	0.679002i	0.0884663	+	0.0287444i
$559$	−0.515810	+	0.709952i	−0.0218164	+	0.0300278i
$560$	0.607230	+	5.88483i	0.0256602	+	0.248680i
$561$	4.88088	−	21.4294i	0.206071	−	0.904749i
$562$		−	3.32441i		−	0.140232i
$563$	−7.84200	+	10.7936i	−0.330501	+	0.454895i	−0.941637	−	0.336630i	$-0.890713\pi$
$563$	−7.84200	+	10.7936i	−0.330501	+	0.454895i	0.611136	+	0.791525i	$0.290713\pi$
$564$	2.96469	−	9.12439i	0.124836	−	0.384206i
$565$	15.5296	−	1.11152i	0.653335	−	0.0467619i
$566$	7.09848	+	9.77022i	0.298371	+	0.410673i
$567$	7.48950	+	5.09037i	0.314529	+	0.213775i
$568$	3.26012	+	10.0336i	0.136792	+	0.421001i
$569$	36.2843	+	11.7895i	1.52112	+	0.494241i	0.946093	−	0.323896i	$-0.104993\pi$
$569$	36.2843	+	11.7895i	1.52112	+	0.494241i	0.575024	+	0.818137i	$0.304993\pi$
$570$	−13.4586	−	15.9861i	−0.563720	−	0.669583i
$571$			0.155764i			0.00651853i	0.999995	+	0.00325927i	$0.00103746\pi$
$571$			0.155764i			0.00651853i	−0.999995	+	0.00325927i	$0.998963\pi$
$572$	−3.39191	+	2.96614i	−0.141823	+	0.124021i
$573$	19.3595			0.808754
$574$	3.58480	−	12.3368i	0.149627	−	0.514929i
$575$	28.2850	+	29.0984i	1.17956	+	1.21349i
$576$	−0.401021	−	1.23421i	−0.0167092	−	0.0514256i
$577$	−9.78395	+	7.10846i	−0.407311	+	0.295929i	−0.772512	−	0.635000i	$-0.781000\pi$
$577$	−9.78395	+	7.10846i	−0.407311	+	0.295929i	0.365201	+	0.930929i	$0.381000\pi$
$578$	−7.11661	+	5.17052i	−0.296012	+	0.215065i
$579$	−0.0543021	−	0.167125i	−0.00225672	−	0.00694546i
$580$	8.76596	+	5.45762i	0.363987	+	0.226615i
$581$	31.2946	+	9.09350i	1.29832	+	0.377262i
$582$	11.9900			0.497001
$583$	9.99795	+	23.3620i	0.414073	+	0.967555i
$584$			8.53090i			0.353011i
$585$	3.01585	−	2.53903i	0.124690	−	0.104976i
$586$	11.3386	+	3.68413i	0.468393	+	0.152190i
$587$	−7.08068	−	21.7921i	−0.292251	−	0.899455i	−0.984131	−	0.177443i	$-0.943217\pi$
$587$	−7.08068	−	21.7921i	−0.292251	−	0.899455i	0.691880	−	0.722012i	$-0.256783\pi$
$588$	2.27210	−	8.84583i	0.0936999	−	0.364796i
$589$	7.12869	+	9.81180i	0.293733	+	0.404288i
$590$	−17.3530	+	1.24203i	−0.714413	+	0.0511336i
$591$	−7.73797	+	23.8150i	−0.318298	+	0.979620i
$592$	5.57969	−	7.67978i	0.229324	−	0.315637i
$593$			14.4885i			0.594972i	0.954726	+	0.297486i	$0.0961481\pi$
$593$			14.4885i			0.594972i	−0.954726	+	0.297486i	$0.903852\pi$
$594$	9.53129	−	15.9692i	0.391073	−	0.655222i
$595$	29.8893	−	3.08414i	1.22534	−	0.126438i
$596$	5.99675	−	8.25382i	0.245637	−	0.338090i
$597$	−14.6086	−	4.74662i	−0.597890	−	0.194266i
$598$	−3.40731	−	10.4866i	−0.139335	−	0.428829i
$599$	−19.5996	+	14.2399i	−0.800818	+	0.581828i	−0.911154	−	0.412066i	$-0.864807\pi$
$599$	−19.5996	+	14.2399i	−0.800818	+	0.581828i	0.110336	+	0.993894i	$0.464807\pi$
$600$	6.45706	−	0.929077i	0.263608	−	0.0379294i
$601$	5.21241	+	16.0421i	0.212619	+	0.654373i	0.999314	+	0.0370316i	$0.0117902\pi$
$601$	5.21241	+	16.0421i	0.212619	+	0.654373i	−0.786695	+	0.617341i	$0.788210\pi$
$602$	−1.70813	+	0.0536006i	−0.0696184	+	0.00218460i
$603$	6.87085	−	9.45691i	0.279803	−	0.385115i
$604$			22.4256i			0.912484i
$605$	18.9608	+	15.6681i	0.770865	+	0.636998i
$606$	−10.5413			−0.428210
$607$	5.55911	−	7.65146i	0.225637	−	0.310563i	−0.681156	−	0.732138i	$-0.738523\pi$
$607$	5.55911	−	7.65146i	0.225637	−	0.310563i	0.906794	+	0.421575i	$0.138523\pi$
$608$	2.21345	−	6.81229i	0.0897672	−	0.276275i
$609$	−9.76971	−	12.5963i	−0.395889	−	0.510426i
$610$	−27.4195	+	11.1305i	−1.11018	+	0.450662i
$611$	5.87200	+	8.08212i	0.237556	+	0.326967i
$612$	−6.26862	+	2.03680i	−0.253394	+	0.0823327i
$613$	4.77607	−	14.6992i	0.192904	−	0.593696i	−0.807091	−	0.590427i	$-0.798959\pi$
$613$	4.77607	−	14.6992i	0.192904	−	0.593696i	0.999995	−	0.00326923i	$-0.00104063\pi$
$614$	−15.7332	+	21.6548i	−0.634938	+	0.873918i
$615$	−13.7511	−	3.40459i	−0.554496	−	0.137286i
$616$	−8.61275	−	1.67942i	−0.347018	−	0.0676658i
$617$		−	8.42209i		−	0.339060i	−0.985525	−	0.169530i	$-0.945775\pi$
$617$		−	8.42209i		−	0.339060i	0.985525	−	0.169530i	$-0.0542250\pi$
$618$	−3.82264	−	2.77731i	−0.153769	−	0.111720i
$619$	−16.1543	−	5.24887i	−0.649298	−	0.210970i	−0.0341934	−	0.999415i	$-0.510886\pi$
$619$	−16.1543	−	5.24887i	−0.649298	−	0.210970i	−0.615105	+	0.788446i	$0.710886\pi$
$620$	−3.77641	+	0.270294i	−0.151664	+	0.0108553i
$621$	26.7496	+	36.8176i	1.07342	+	1.47744i
$622$	1.98139	+	2.72715i	0.0794466	+	0.109349i
$623$	−14.2393	−	18.3589i	−0.570484	−	0.735534i
$624$	−1.68580	−	0.547748i	−0.0674858	−	0.0219275i
$625$	0.708649	−	24.9900i	0.0283460	−	0.999598i
$626$	19.6663			0.786023
$627$	28.4956	−	12.1949i	1.13800	−	0.487018i
$628$	−7.22716			−0.288395
$629$	−39.0059	−	28.3394i	−1.55527	−	1.12997i
$630$	7.50666	+	1.61049i	0.299073	+	0.0641634i
$631$	−5.37792	−	16.5515i	−0.214092	−	0.658906i	−0.999217	−	0.0395692i	$-0.987401\pi$
$631$	−5.37792	−	16.5515i	−0.214092	−	0.658906i	0.785125	−	0.619337i	$-0.212599\pi$
$632$	−4.85165	−	6.67772i	−0.192988	−	0.265625i
$633$	9.21166	+	12.6788i	0.366131	+	0.503936i
$634$	−3.27365	+	1.06367i	−0.130013	+	0.0422438i
$635$	−22.8677	+	36.7298i	−0.907476	+	1.45758i
$636$	−5.87579	+	8.08733i	−0.232990	+	0.320683i
$637$	6.06124	+	7.32818i	0.240155	+	0.290353i
$638$	−11.5295	+	10.0823i	−0.456457	+	0.399160i
$639$	13.6910			0.541608
$640$	1.44012	+	1.71057i	0.0569258	+	0.0676162i
$641$	−6.51410	+	20.0483i	−0.257291	+	0.791861i	0.736078	+	0.676897i	$0.236676\pi$
$641$	−6.51410	+	20.0483i	−0.257291	+	0.791861i	−0.993370	+	0.114965i	$0.963324\pi$
$642$	5.26887	+	16.2159i	0.207946	+	0.639991i
$643$	−33.8311	+	24.5797i	−1.33417	+	0.969329i	−0.334530	+	0.942385i	$0.608578\pi$
$643$	−33.8311	+	24.5797i	−1.33417	+	0.969329i	−0.999637	+	0.0269440i	$0.991422\pi$
$644$	12.0705	−	17.7594i	0.475643	−	0.699817i
$645$	0.134534	+	1.87965i	0.00529728	+	0.0740110i
$646$	−34.5999	−	11.2422i	−1.36131	−	0.442318i
$647$	25.3621	+	18.4266i	0.997087	+	0.724426i	0.961462	−	0.274939i	$-0.0886577\pi$
$647$	25.3621	+	18.4266i	0.997087	+	0.724426i	0.0356254	+	0.999365i	$0.488658\pi$
$648$	3.42271			0.134457
$649$	5.73063	−	25.1602i	0.224947	−	0.987624i
$650$	−3.16939	+	6.00818i	−0.124314	+	0.235660i
$651$	5.61262	+	1.63090i	0.219976	+	0.0639200i
$652$	22.5556	+	7.32877i	0.883347	+	0.287017i
$653$	−19.8677	+	6.45542i	−0.777485	+	0.252620i	−0.670766	−	0.741669i	$-0.734034\pi$
$653$	−19.8677	+	6.45542i	−0.777485	+	0.252620i	−0.106719	+	0.994289i	$0.534034\pi$
$654$	−1.83101	−	2.52016i	−0.0715980	−	0.0985462i
$655$	13.6268	−	5.53159i	0.532443	−	0.216137i
$656$	−1.50051	−	4.61809i	−0.0585850	−	0.180306i
$657$	10.5290	+	3.42107i	0.410774	+	0.133469i
$658$	−5.42865	+	18.6823i	−0.211631	+	0.728312i
$659$		−	3.57588i		−	0.139297i	−0.997572	−	0.0696483i	$-0.977812\pi$
$659$		−	3.57588i		−	0.139297i	0.997572	−	0.0696483i	$-0.0221877\pi$
$660$	−1.46981	+	9.56371i	−0.0572122	+	0.372267i
$661$			38.8402i			1.51071i	0.655318	+	0.755354i	$0.272535\pi$
$661$			38.8402i			1.51071i	−0.655318	+	0.755354i	$0.727465\pi$
$662$	7.98389	+	5.80063i	0.310303	+	0.225448i
$663$	−2.78203	+	8.56222i	−0.108045	+	0.332529i
$664$	11.7146	−	3.80631i	0.454616	−	0.147714i
$665$	28.2953	+	31.5453i	1.09725	+	1.22328i
$666$	−7.24093	−	9.96629i	−0.280580	−	0.386186i
$667$	−11.5818	−	35.6452i	−0.448450	−	1.38019i
$668$	−2.03558	−	0.661400i	−0.0787590	−	0.0255904i
$669$	−11.7203	−	8.51529i	−0.453133	−	0.329220i
$670$	−4.84063	+	19.5512i	−0.187010	+	0.755329i
$671$	−3.95438	−	43.7143i	−0.152657	−	1.68757i
$672$	−1.16915	−	3.24792i	−0.0451010	−	0.125291i
$673$	−32.7279	−	23.7782i	−1.26157	−	0.916584i	−0.262736	−	0.964868i	$-0.584625\pi$
$673$	−32.7279	−	23.7782i	−1.26157	−	0.916584i	−0.998834	+	0.0482842i	$0.984625\pi$
$674$	2.86859	−	8.82861i	0.110494	−	0.340065i
$675$	4.77794	−	27.6263i	0.183903	−	1.06334i
$676$	−9.02399	+	6.55631i	−0.347077	+	0.252166i
$677$	22.3885	+	30.8151i	0.860458	+	1.18432i	0.981460	+	0.191667i	$0.0613892\pi$
$677$	22.3885	+	30.8151i	0.860458	+	1.18432i	−0.121002	+	0.992652i	$0.538611\pi$
$678$	−8.63983	+	2.80725i	−0.331811	+	0.107812i
$679$	−24.3019	+	0.762584i	−0.932620	+	0.0292653i
$680$	8.68804	−	7.31444i	0.333171	−	0.280496i
$681$			2.86071i			0.109623i
$682$	1.24711	−	5.47543i	0.0477545	−	0.209665i
$683$			3.63338i			0.139027i	0.997581	+	0.0695137i	$0.0221448\pi$
$683$			3.63338i			0.139027i	−0.997581	+	0.0695137i	$0.977855\pi$
$684$	−7.52019	−	5.46374i	−0.287542	−	0.208911i
$685$	10.4347	+	6.49657i	0.398690	+	0.248221i
$686$	−4.04260	+	18.0737i	−0.154347	+	0.690056i
$687$	4.80044	+	6.60724i	0.183148	+	0.252082i
$688$	−0.522570	+	0.379669i	−0.0199228	+	0.0144748i
$689$	−3.21662	−	9.89974i	−0.122543	−	0.377150i
$690$	−20.1006	−	12.5145i	−0.765216	−	0.476417i
$691$	5.19367	−	7.14848i	0.197577	−	0.271941i	−0.698721	−	0.715395i	$-0.746247\pi$
$691$	5.19367	−	7.14848i	0.197577	−	0.271941i	0.896297	+	0.443454i	$0.146247\pi$
$692$		−	6.45123i		−	0.245239i
$693$	−5.52666	+	9.95651i	−0.209940	+	0.378216i
$694$	7.61221			0.288956
$695$	−31.1702	−	37.0237i	−1.18235	−	1.40439i
$696$	−5.73021	−	1.86186i	−0.217203	−	0.0705736i
$697$	−23.4554	+	7.62113i	−0.888438	+	0.288671i
$698$	−8.22334	+	5.97461i	−0.311258	+	0.226142i
$699$	18.0431	−	13.1091i	0.682452	−	0.495831i
$700$	−13.0284	+	2.29378i	−0.492426	+	0.0866966i
$701$	0.999671	+	0.324813i	0.0377570	+	0.0122680i	0.327835	−	0.944735i	$-0.393681\pi$
$701$	0.999671	+	0.324813i	0.0377570	+	0.0122680i	−0.290078	+	0.957003i	$0.593681\pi$
$702$	−4.47771	+	6.16304i	−0.169000	+	0.232609i
$703$		−	67.9952i		−	2.56449i
$704$	−3.04914	+	1.30490i	−0.114919	+	0.0491803i
$705$	20.8240	+	5.15576i	0.784276	+	0.194177i
$706$	−10.9222	−	7.93543i	−0.411062	−	0.298654i
$707$	21.3656	−	0.670444i	0.803535	−	0.0252146i
$708$	9.65430	−	3.13687i	0.362831	−	0.117891i
$709$	34.9153	−	25.3674i	1.31127	−	0.952694i	0.311274	−	0.950320i	$-0.399244\pi$
$709$	34.9153	−	25.3674i	1.31127	−	0.952694i	0.999997	−	0.00237436i	$-0.000755783\pi$
$710$	−21.8582	+	8.87298i	−0.820322	+	0.332997i
$711$	−10.1874	+	3.31007i	−0.382056	+	0.124137i
$712$	−8.35172	−	2.71364i	−0.312994	−	0.101698i
$713$	11.1175	+	8.07732i	0.416353	+	0.302498i
$714$	−16.4963	+	5.93816i	−0.617358	+	0.222230i
$715$	−7.15704	−	7.09169i	−0.267658	−	0.265214i
$716$	−1.67889			−0.0627432
$717$	11.1426	−	15.3365i	0.416129	−	0.572752i
$718$	−15.9542	−	5.18385i	−0.595407	−	0.193460i
$719$	−45.5818	+	14.8104i	−1.69991	+	0.552336i	−0.988604	−	0.150543i	$-0.951898\pi$
$719$	−45.5818	+	14.8104i	−1.69991	+	0.552336i	−0.711310	+	0.702878i	$0.751898\pi$
$720$	2.68873	−	1.09145i	0.100203	−	0.0406758i
$721$	7.92455	+	5.38606i	0.295126	+	0.200587i
$722$	−9.98331	−	30.7255i	−0.371540	−	1.14348i
$723$	−2.12234	+	6.53188i	−0.0789306	+	0.242923i
$724$	−2.16837	+	2.98451i	−0.0805868	+	0.110918i
$725$	−10.7731	+	20.4225i	−0.400103	+	0.758473i
$726$	−12.9362	−	6.21527i	−0.480107	−	0.230670i
$727$	35.5828			1.31969			0.659846	−	0.751401i	$-0.270621\pi$
$727$	35.5828			1.31969			0.659846	+	0.751401i	$0.270621\pi$
$728$	3.45169	+	1.00298i	0.127928	+	0.0371730i
$729$	8.15478	−	25.0978i	0.302029	−	0.929550i
$730$	−19.0270	+	1.36184i	−0.704221	+	0.0504041i
$731$	1.92835	+	2.65415i	0.0713227	+	0.0981673i
$732$	13.9691	−	10.1492i	0.516314	−	0.375124i
$733$	38.2959	−	12.4431i	1.41449	−	0.459596i	0.500644	−	0.865653i	$-0.333097\pi$
$733$	38.2959	−	12.4431i	1.41449	−	0.459596i	0.913848	+	0.406057i	$0.133097\pi$
$734$	−2.07810	+	6.39575i	−0.0767042	+	0.236071i
$735$	20.0921	+	3.65549i	0.741109	+	0.134835i
$736$		−	8.11605i		−	0.299162i
$737$	−25.6529	−	15.3111i	−0.944935	−	0.563990i
$738$	−6.30144			−0.231959
$739$	22.2605	−	30.6389i	0.818865	−	1.12707i	−0.171029	−	0.985266i	$-0.554709\pi$
$739$	22.2605	−	30.6389i	0.818865	−	1.12707i	0.989895	−	0.141806i	$-0.0452908\pi$
$740$	18.0194	+	11.2188i	0.662407	+	0.412410i
$741$	−12.0751	+	3.92345i	−0.443591	+	0.144131i
$742$	11.3950	−	16.7655i	0.418322	−	0.615481i
$743$	6.19747	−	4.50273i	0.227363	−	0.165189i	−0.468272	−	0.883585i	$-0.655123\pi$
$743$	6.19747	−	4.50273i	0.227363	−	0.165189i	0.695635	+	0.718396i	$0.255123\pi$
$744$	2.10099	−	0.682654i	0.0770261	−	0.0250273i
$745$	19.3663	+	12.0573i	0.709527	+	0.441746i
$746$	28.0764	+	20.3987i	1.02795	+	0.746850i
$747$		−	15.9848i		−	0.584852i
$748$	6.62764	+	15.4867i	0.242331	+	0.566249i
$749$	−11.7106	−	32.5321i	−0.427895	−	1.18870i
$750$	3.10296	+	14.2533i	0.113304	+	0.520455i
$751$	−6.36662	+	19.5944i	−0.232321	+	0.715011i	0.765144	+	0.643859i	$0.222668\pi$
$751$	−6.36662	+	19.5944i	−0.232321	+	0.715011i	−0.997465	+	0.0711522i	$0.977332\pi$
$752$	2.27230	+	6.99342i	0.0828622	+	0.255024i
$753$	−6.50459	−	8.95280i	−0.237040	−	0.326258i
$754$	5.07565	−	3.68768i	0.184844	−	0.134297i
$755$	−50.0172	+	3.57994i	−1.82031	+	0.130287i
$756$	−14.8282	+	0.465304i	−0.539297	+	0.0169229i
$757$	16.3185	−	22.4604i	0.593105	−	0.816339i	−0.401950	−	0.915661i	$-0.631668\pi$
$757$	16.3185	−	22.4604i	0.593105	−	0.816339i	0.995055	+	0.0993226i	$0.0316676\pi$
$758$	30.8203			1.11944
$759$	26.4374	−	23.1189i	0.959617	−	0.839161i
$760$	15.5472	+	3.84930i	0.563957	+	0.139629i
$761$	2.79830	+	2.03308i	0.101438	+	0.0736992i	0.637348	−	0.770576i	$-0.280031\pi$
$761$	2.79830	+	2.03308i	0.101438	+	0.0736992i	−0.535910	+	0.844275i	$0.680031\pi$
$762$	7.80127	−	24.0098i	0.282610	−	0.869785i
$763$	3.87146	+	4.99153i	0.140156	+	0.180706i
$764$	−12.0043	+	8.72164i	−0.434301	+	0.315538i
$765$	−5.54350	−	13.6561i	−0.200426	−	0.493739i
$766$	−2.50013	−	7.69460i	−0.0903332	−	0.278017i
$767$	−3.26638	+	10.0529i	−0.117942	+	0.362989i
$768$	−1.05553	−	0.766890i	−0.0380883	−	0.0276727i
$769$	−19.9286			−0.718644			−0.359322	−	0.933214i	$-0.616992\pi$
$769$	−19.9286			−0.718644			−0.359322	+	0.933214i	$0.616992\pi$
$770$	2.37081	−	19.4777i	0.0854381	−	0.701926i
$771$	−18.7185			−0.674131
$772$	0.108963	+	0.0791660i	0.00392165	+	0.00284925i
$773$	6.15882	−	18.9549i	0.221518	−	0.681761i	−0.777109	−	0.629366i	$-0.783315\pi$
$773$	6.15882	−	18.9549i	0.221518	−	0.681761i	0.998626	−	0.0523947i	$-0.0166854\pi$
$774$	0.259032	+	0.797219i	0.00931072	+	0.0286554i
$775$	−1.20571	−	8.37962i	−0.0433103	−	0.301005i
$776$	−7.43468	+	5.40161i	−0.266889	+	0.193906i
$777$	−20.0827	−	25.8930i	−0.720464	−	0.928907i
$778$	7.72791	−	23.7841i	0.277059	−	0.852700i
$779$	−28.1385	−	20.4438i	−1.00816	−	0.732475i
$780$	0.952562	−	3.84737i	0.0341072	−	0.137758i
$781$	−3.15233	−	34.8480i	−0.112799	−	1.24696i
$782$	−41.2217			−1.47409
$783$	−15.2203	+	20.9489i	−0.543928	+	0.748652i
$784$	2.57627	+	6.50868i	0.0920095	+	0.232453i
$785$	−1.15372	−	16.1192i	−0.0411780	−	0.575319i
$786$	−6.94230	+	5.04387i	−0.247624	+	0.179909i
$787$	−6.62981	−	9.12514i	−0.236327	−	0.325276i	0.674337	−	0.738424i	$-0.264429\pi$
$787$	−6.62981	−	9.12514i	−0.236327	−	0.325276i	−0.910664	+	0.413147i	$0.864429\pi$
$788$	−5.93080	−	18.2531i	−0.211276	−	0.650240i
$789$	8.38701	−	25.8126i	0.298586	−	0.918952i
$790$	14.1192	−	11.8869i	0.502340	−	0.422918i
$791$	17.3331	−	6.23938i	0.616293	−	0.221847i
$792$	0.387762	+	4.28658i	0.0137785	+	0.152317i
$793$			17.9797i			0.638477i
$794$	−24.8825	−	18.0782i	−0.883048	−	0.641572i
$795$	−18.9757	−	11.8141i	−0.672997	−	0.419003i
$796$	11.1968	−	3.63806i	0.396860	−	0.128948i
$797$	17.5531	−	12.7530i	0.621761	−	0.451736i	−0.231775	−	0.972769i	$-0.574453\pi$
$797$	17.5531	−	12.7530i	0.621761	−	0.451736i	0.853536	+	0.521034i	$0.174453\pi$
$798$	−20.4496	−	13.8989i	−0.723907	−	0.492016i
$799$	35.5198	−	11.5411i	1.25660	−	0.408294i
$800$	−3.58529	+	3.48506i	−0.126759	+	0.123216i
$801$	−6.69843	+	9.21959i	−0.236677	+	0.325758i
$802$	−30.3310			−1.07103
$803$	6.28344	−	27.5873i	0.221738	−	0.973534i
$804$		−	11.7523i		−	0.414470i
$805$	41.5367	+	24.0865i	1.46398	+	0.848937i
$806$	−0.710838	+	2.18773i	−0.0250382	+	0.0770597i
$807$	0.107994	−	0.0350893i	0.00380157	−	0.00123520i
$808$	6.53637	−	4.74895i	0.229949	−	0.167068i
$809$	20.1055	+	27.6729i	0.706872	+	0.972926i	0.999859	+	0.0168095i	$0.00535087\pi$
$809$	20.1055	+	27.6729i	0.706872	+	0.972926i	−0.292987	+	0.956117i	$0.594649\pi$
$810$	0.546389	+	7.63387i	0.0191981	+	0.268227i
$811$	−0.602577	+	1.85454i	−0.0211593	+	0.0651217i	−0.961079	−	0.276275i	$-0.910900\pi$
$811$	−0.602577	+	1.85454i	−0.0211593	+	0.0651217i	0.939919	+	0.341397i	$0.110900\pi$
$812$	11.7327	+	3.40925i	0.411736	+	0.119641i
$813$	6.35432			0.222856
$814$	−23.7002	+	20.7252i	−0.830691	+	0.726418i
$815$	−12.7451	+	51.4772i	−0.446442	+	1.80317i
$816$	−3.89506	+	5.36109i	−0.136354	+	0.187676i
$817$	−1.42974	+	4.40028i	−0.0500202	+	0.153946i
$818$	−8.19807	−	25.2311i	−0.286639	−	0.882184i
$819$	2.62209	−	3.85791i	0.0916234	−	0.134806i
$820$	10.0605	−	4.08389i	0.351327	−	0.142616i
$821$	−18.5178	+	6.01679i	−0.646275	+	0.209988i	−0.613771	−	0.789484i	$-0.710348\pi$
$821$	−18.5178	+	6.01679i	−0.646275	+	0.209988i	−0.0325042	+	0.999472i	$0.510348\pi$
$822$	−6.82105	−	2.21629i	−0.237912	−	0.0773021i
$823$	−5.17003	+	7.11594i	−0.180216	+	0.248046i	−0.889562	−	0.456814i	$-0.848990\pi$
$823$	−5.17003	+	7.11594i	−0.180216	+	0.248046i	0.709346	+	0.704860i	$0.248990\pi$
$824$	3.62153			0.126162
$825$	−21.5652	−	1.75149i	−0.750803	−	0.0609791i
$826$	−19.3683	+	6.97199i	−0.673909	+	0.242587i
$827$	−17.8102	−	12.9399i	−0.619322	−	0.449964i	0.233363	−	0.972390i	$-0.425027\pi$
$827$	−17.8102	−	12.9399i	−0.619322	−	0.449964i	−0.852685	+	0.522426i	$0.825027\pi$
$828$	−10.0169	−	3.25470i	−0.348113	−	0.113109i
$829$	51.9680	−	16.8854i	1.80492	−	0.586455i	0.804947	−	0.593347i	$-0.202194\pi$
$829$	51.9680	−	16.8854i	1.80492	−	0.586455i	0.999976	+	0.00689198i	$0.00219380\pi$
$830$	10.3595	+	25.5202i	0.359585	+	0.885820i
$831$	7.67025	−	5.57276i	0.266078	−	0.193317i
$832$	1.29208	−	0.419823i	0.0447949	−	0.0145548i
$833$	33.0578	−	13.0849i	1.14538	−	0.453366i
$834$	22.8461	+	16.5986i	0.791094	+	0.574764i
$835$	1.15021	−	4.64567i	0.0398046	−	0.160770i
$836$	−12.1755	+	20.3993i	−0.421097	+	0.705525i
$837$		−	9.49418i		−	0.328167i
$838$	−5.54087	+	7.62635i	−0.191406	+	0.263448i
$839$	−13.2581	−	4.30782i	−0.457721	−	0.148723i	0.0710761	−	0.997471i	$-0.477357\pi$
$839$	−13.2581	−	4.30782i	−0.457721	−	0.148723i	−0.528797	+	0.848748i	$0.677357\pi$
$840$	7.05740	−	3.12612i	0.243503	−	0.107861i
$841$	−6.20876	+	4.51093i	−0.214095	+	0.155549i
$842$	1.24720	−	0.906144i	0.0429814	−	0.0312278i
$843$	−4.12510	+	1.34033i	−0.142076	+	0.0461633i
$844$	−11.4238	−	3.71182i	−0.393224	−	0.127766i
$845$	−16.0635	−	19.0801i	−0.552602	−	0.656377i
$846$	9.54262			0.328082
$847$	26.6150	+	11.7746i	0.914502	+	0.404582i
$848$		−	7.66184i		−	0.263109i
$849$	9.26146	−	12.7473i	0.317853	−	0.437486i
$850$	17.7008	+	18.2098i	0.607131	+	0.624592i
$851$	−23.8077	−	73.2727i	−0.816119	−	2.51176i
$852$	11.1358	−	8.09066i	0.381508	−	0.277182i
$853$	0.690114	+	0.949861i	0.0236291	+	0.0325226i	0.820668	−	0.571405i	$-0.193602\pi$
$853$	0.690114	+	0.949861i	0.0236291	+	0.0325226i	−0.797039	+	0.603928i	$0.793602\pi$
$854$	−27.6678	+	21.4593i	−0.946772	+	0.734321i
$855$	10.9856	−	17.6450i	0.375700	−	0.603445i
$856$	−10.5725	−	7.68139i	−0.361362	−	0.262545i
$857$			55.3626i			1.89115i	0.325405	+	0.945575i	$0.394499\pi$
$857$			55.3626i			1.89115i	−0.325405	+	0.945575i	$0.605501\pi$
$858$	5.04809	+	3.01298i	0.172339	+	0.102862i
$859$		−	53.9684i		−	1.84138i	−0.390297	−	0.920689i	$-0.627628\pi$
$859$		−	53.9684i		−	1.84138i	0.390297	−	0.920689i	$-0.372372\pi$
$860$	−0.930221	−	1.10491i	−0.0317203	−	0.0376772i
$861$	−16.7535	+	0.525718i	−0.570957	+	0.0179164i
$862$	−16.6220	+	5.40080i	−0.566146	+	0.183952i
$863$	8.88779	+	12.2330i	0.302544	+	0.416416i	0.933038	−	0.359778i	$-0.117148\pi$
$863$	8.88779	+	12.2330i	0.302544	+	0.416416i	−0.630494	+	0.776194i	$0.717148\pi$
$864$	−4.53640	+	3.29588i	−0.154331	+	0.112128i
$865$	14.3886	−	1.02985i	0.489226	−	0.0350160i
$866$	0.443558	−	1.36513i	0.0150727	−	0.0463890i
$867$	9.28511	+	6.74603i	0.315339	+	0.229107i
$868$	−4.21497	+	1.51726i	−0.143066	+	0.0514992i
$869$	10.7708	+	25.1679i	0.365375	+	0.853763i
$870$	3.23787	−	13.0777i	0.109774	−	0.443374i
$871$	9.90032	+	7.19300i	0.335460	+	0.243726i
$872$	2.27072	+	0.737801i	0.0768962	+	0.0249851i
$873$	3.68529	+	11.3421i	0.124728	+	0.383873i
$874$	−34.1704	−	47.0315i	−1.15583	−	1.59087i
$875$	−7.19576	−	28.6918i	−0.243261	−	0.969961i
$876$	10.5856	−	3.43947i	0.357654	−	0.116209i
$877$	−2.42757	+	7.47128i	−0.0819731	+	0.252287i	−0.983640	−	0.180143i	$-0.942344\pi$
$877$	−2.42757	+	7.47128i	−0.0819731	+	0.252287i	0.901667	+	0.432430i	$0.142344\pi$
$878$	28.3214	+	20.5767i	0.955800	+	0.694429i
$879$		−	15.5549i		−	0.524654i
$880$	−3.39716	−	6.59237i	−0.114518	−	0.222229i
$881$		−	18.5617i		−	0.625359i	−0.949859	−	0.312679i	$-0.898773\pi$
$881$		−	18.5617i		−	0.625359i	0.949859	−	0.312679i	$-0.101227\pi$
$882$	9.06624	−	0.569551i	0.305276	−	0.0191778i
$883$	−37.1976	−	12.0862i	−1.25180	−	0.406734i	−0.393233	−	0.919439i	$-0.628644\pi$
$883$	−37.1976	−	12.0862i	−1.25180	−	0.406734i	−0.858565	+	0.512705i	$0.828644\pi$
$884$	−2.13230	−	6.56254i	−0.0717170	−	0.220722i
$885$	8.53754	+	21.0318i	0.286986	+	0.706977i
$886$	13.0638	+	17.9808i	0.438888	+	0.604078i
$887$	37.2367	−	12.0989i	1.25029	−	0.406243i	0.392263	−	0.919853i	$-0.371692\pi$
$887$	37.2367	−	12.0989i	1.25029	−	0.406243i	0.858023	+	0.513611i	$0.171692\pi$
$888$	−11.7791	−	3.82726i	−0.395280	−	0.128434i
$889$	−14.2849	+	49.1605i	−0.479101	+	1.64879i
$890$	4.71916	−	19.0606i	0.158187	−	0.638912i
$891$	−11.0684	−	2.52099i	−0.370804	−	0.0844565i
$892$	11.1037			0.371778
$893$	42.6116	+	30.9591i	1.42594	+	1.03601i
$894$	−12.6595	−	4.11333i	−0.423398	−	0.137570i
$895$	−0.268012	−	3.74454i	−0.00895867	−	0.125166i
$896$	2.18818	+	1.48723i	0.0731020	+	0.0496850i
$897$	−11.6386	+	8.45594i	−0.388602	+	0.282336i
$898$	6.00229	+	18.4732i	0.200299	+	0.616457i
$899$	−2.41622	+	7.43636i	−0.0805855	+	0.248017i
$900$	2.86354	+	5.82260i	0.0954514	+	0.194087i
$901$	−38.9148			−1.29644
$902$	1.45090	+	16.0392i	0.0483096	+	0.534047i
$903$	0.755192	+	2.09793i	0.0251312	+	0.0698149i
$904$	4.09264	−	5.63303i	0.136119	−	0.187352i
$905$	−7.00268	−	4.35982i	−0.232777	−	0.144925i
$906$	27.8269	−	9.04149i	0.924485	−	0.300384i
$907$	−2.01621	−	2.77507i	−0.0669471	−	0.0921448i	0.774231	−	0.632904i	$-0.218137\pi$
$907$	−2.01621	−	2.77507i	−0.0669471	−	0.0921448i	−0.841178	+	0.540759i	$0.818137\pi$
$908$	−1.28878	−	1.77385i	−0.0427696	−	0.0588674i
$909$	−3.24001	−	9.97172i	−0.107464	−	0.330741i
$910$	−1.68600	+	7.85863i	−0.0558903	+	0.260511i
$911$	−27.8259	−	20.2167i	−0.921912	−	0.669809i	0.0220869	−	0.999756i	$-0.492969\pi$
$911$	−27.8259	−	20.2167i	−0.921912	−	0.669809i	−0.943999	+	0.329948i	$0.892969\pi$
$912$	−9.34547			−0.309459
$913$	−40.6863	+	3.68046i	−1.34652	+	0.121806i
$914$	13.2843			0.439407
$915$	24.8663	+	29.5360i	0.822054	+	0.976431i
$916$	−5.95325	−	1.93433i	−0.196701	−	0.0639120i
$917$	13.7502	−	10.6647i	0.454071	−	0.352180i
$918$	16.7399	+	23.0405i	0.552500	+	0.760450i
$919$	0.533492	+	0.734289i	0.0175983	+	0.0242220i	0.817725	−	0.575608i	$-0.195235\pi$
$919$	0.533492	+	0.734289i	0.0175983	+	0.0242220i	−0.800127	+	0.599830i	$0.795235\pi$
$920$	18.1017	−	1.29562i	0.596796	−	0.0427152i
$921$	33.2137	+	10.7918i	1.09443	+	0.355602i
$922$	19.7612	+	14.3573i	0.650800	+	0.472834i
$923$			14.3329i			0.471775i
$924$	1.38855	+	11.3643i	0.0456801	+	0.373857i
$925$	−22.1453	+	41.9808i	−0.728134	+	1.38032i
$926$	21.0721	−	29.0032i	0.692471	−	0.953105i
$927$	1.45231	−	4.46974i	0.0477000	−	0.146806i
$928$	4.39194	−	1.42703i	0.144172	−	0.0468445i
$929$	−1.76241	−	2.42575i	−0.0578227	−	0.0795861i	0.779126	−	0.626867i	$-0.215663\pi$
$929$	−1.76241	−	2.42575i	−0.0578227	−	0.0795861i	−0.836949	+	0.547281i	$0.815663\pi$
$930$	1.85796	+	4.57700i	0.0609249	+	0.150086i
$931$	42.3322	+	26.8703i	1.38738	+	0.880640i
$932$	−5.28228	+	16.2572i	−0.173027	+	0.532522i
$933$	2.58515	−	3.55815i	0.0846339	−	0.116489i
$934$	25.5291			0.835337
$935$	−33.4829	+	17.2543i	−1.09501	+	0.564275i
$936$		−	1.76307i		−	0.0576276i
$937$	0.834019	−	1.14793i	0.0272462	−	0.0375012i	−0.795177	−	0.606378i	$-0.792622\pi$
$937$	0.834019	−	1.14793i	0.0272462	−	0.0375012i	0.822423	+	0.568877i	$0.192622\pi$
$938$	0.747464	+	23.8200i	0.0244056	+	0.777752i
$939$	−7.92901	−	24.4030i	−0.258754	−	0.796361i
$940$	−15.2351	+	6.18446i	−0.496915	+	0.201715i
$941$	−29.8760	+	21.7062i	−0.973930	+	0.707601i	−0.956344	−	0.292244i	$-0.905598\pi$
$941$	−29.8760	+	21.7062i	−0.973930	+	0.707601i	−0.0175860	+	0.999845i	$0.505598\pi$
$942$	2.91383	+	8.96785i	0.0949378	+	0.292188i
$943$	−37.4806	−	12.1782i	−1.22054	−	0.396576i
$944$	−4.57319	+	6.29445i	−0.148845	+	0.204867i
$945$	−3.40492	−	32.9980i	−0.110762	−	1.07342i
$946$	1.96953	−	0.842877i	0.0640351	−	0.0274043i
$947$			39.1324i			1.27163i	0.771841	+	0.635816i	$0.219336\pi$
$947$			39.1324i			1.27163i	−0.771841	+	0.635816i	$0.780664\pi$
$948$	−6.33000	+	8.71249i	−0.205589	+	0.282969i
$949$	−3.58147	+	11.0226i	−0.116260	+	0.357810i
$950$	−6.10343	+	35.2904i	−0.198021	+	1.14497i
$951$	2.63972	+	3.63327i	0.0855989	+	0.117817i
$952$	7.55372	−	11.1138i	0.244817	−	0.360202i
$953$	−2.90738	−	8.94799i	−0.0941792	−	0.289854i	0.892860	−	0.450335i	$-0.148695\pi$
$953$	−2.90738	−	8.94799i	−0.0941792	−	0.289854i	−0.987039	+	0.160481i	$0.948695\pi$
$954$	−9.45636	−	3.07256i	−0.306161	−	0.0994777i
$955$	−21.3687	−	25.3817i	−0.691477	−	0.821332i
$956$			14.5296i			0.469921i
$957$	17.1590	+	10.2415i	0.554673	+	0.331060i
$958$	−5.41418			−0.174924
$959$	13.9662	+	4.05826i	0.450992	+	0.131048i
$960$	1.54194	−	2.47664i	0.0497659	−	0.0799334i
$961$	8.69361	+	26.7562i	0.280439	+	0.863103i
$962$	10.4336	−	7.58044i	0.336392	−	0.244403i
$963$	−13.7203	+	9.96837i	−0.442130	+	0.321226i
$964$	−1.62667	−	5.00638i	−0.0523916	−	0.161245i
$965$	−0.159174	+	0.255664i	−0.00512401	+	0.00823012i
$966$	−26.9033	−	7.81750i	−0.865600	−	0.251524i
$967$	−4.75150			−0.152798			−0.0763989	−	0.997077i	$-0.524342\pi$
$967$	−4.75150			−0.152798			−0.0763989	+	0.997077i	$0.524342\pi$
$968$	10.8214	−	1.97396i	0.347814	−	0.0634453i
$969$			47.4660i			1.52483i
$970$	−13.2344	−	15.7197i	−0.424931	−	0.504730i
$971$	28.1213	+	9.13716i	0.902455	+	0.293225i	0.723250	−	0.690587i	$-0.242648\pi$
$971$	28.1213	+	9.13716i	0.902455	+	0.293225i	0.179205	+	0.983812i	$0.442648\pi$
$972$	3.81829	+	11.7515i	0.122472	+	0.376929i
$973$	−47.3612	−	32.1899i	−1.51833	−	1.03196i
$974$	−6.91633	−	9.51952i	−0.221614	−	0.305025i
$975$	8.73310	+	1.51038i	0.279683	+	0.0483708i
$976$	−4.08959	+	12.5865i	−0.130905	+	0.402883i
$977$	−18.1766	+	25.0179i	−0.581521	+	0.800395i	−0.993861	−	0.110635i	$-0.964711\pi$
$977$	−18.1766	+	25.0179i	−0.581521	+	0.800395i	0.412340	+	0.911030i	$0.364711\pi$
$978$		−	30.9430i		−	0.989449i
$979$	25.0091	+	14.9268i	0.799295	+	0.477064i
$980$	−14.1054	+	6.78503i	−0.450582	+	0.216740i
$981$	1.82121	−	2.50668i	0.0581467	−	0.0800321i
$982$	−2.40548	−	0.781588i	−0.0767619	−	0.0249415i
$983$	8.29640	+	25.5337i	0.264614	+	0.814398i	0.991782	+	0.127939i	$0.0408361\pi$
$983$	8.29640	+	25.5337i	0.264614	+	0.814398i	−0.727168	+	0.686459i	$0.759164\pi$
$984$	−5.12540	+	3.72382i	−0.163392	+	0.118711i
$985$	39.7643	−	16.1417i	1.26700	−	0.514317i
$986$	−7.24793	−	22.3068i	−0.230821	−	0.710394i
$987$	25.3707	−	0.796124i	0.807559	−	0.0253409i
$988$	5.71992	−	7.87279i	0.181975	−	0.250467i
$989$			5.24241i			0.166699i
$990$	−9.49873	+	1.54914i	−0.301889	+	0.0492350i
$991$	0.319071			0.0101356			0.00506782	−	0.999987i	$-0.498387\pi$
$991$	0.319071			0.0101356			0.00506782	+	0.999987i	$0.498387\pi$
$992$	−0.995228	+	1.36981i	−0.0315985	+	0.0434917i
$993$	3.97881	−	12.2455i	0.126264	−	0.388600i
$994$	−22.0561	+	17.1068i	−0.699576	+	0.542595i
$995$	9.90161	+	24.3922i	0.313902	+	0.773283i
$996$	−9.44615	−	13.0015i	−0.299313	−	0.411969i
$997$	−31.7835	+	10.3271i	−1.00659	+	0.327062i	−0.765497	−	0.643439i	$-0.777507\pi$
$997$	−31.7835	+	10.3271i	−1.00659	+	0.327062i	−0.241096	+	0.970501i	$0.577507\pi$
$998$	0.555801	−	1.71058i	0.0175936	−	0.0541474i
$999$	−31.2870	+	43.0628i	−0.989876	+	1.36245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.w.b.139.16	yes	96
5.4	even	2		770.2.w.a.139.9	✓	96
7.6	odd	2	inner	770.2.w.b.139.9	yes	96
11.8	odd	10		770.2.w.a.349.16	yes	96
35.34	odd	2		770.2.w.a.139.16	yes	96
55.19	odd	10	inner	770.2.w.b.349.9	yes	96
77.41	even	10		770.2.w.a.349.9	yes	96
385.349	even	10	inner	770.2.w.b.349.16	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.w.a.139.9	✓	96	5.4	even	2
770.2.w.a.139.16	yes	96	35.34	odd	2
770.2.w.a.349.9	yes	96	77.41	even	10
770.2.w.a.349.16	yes	96	11.8	odd	10
770.2.w.b.139.9	yes	96	7.6	odd	2	inner
770.2.w.b.139.16	yes	96	1.1	even	1	trivial
770.2.w.b.349.9	yes	96	55.19	odd	10	inner
770.2.w.b.349.16	yes	96	385.349	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.403178 - 1.24085i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.07187 + 0.841043i) q^{5} +(1.05553 - 0.766890i) q^{6} +(-2.09063 + 1.62150i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.04989 + 0.762787i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.403178 - 1.24085i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.07187 + 0.841043i) q^{5} +(1.05553 - 0.766890i) q^{6} +(-2.09063 + 1.62150i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.04989 + 0.762787i) q^{9} +(-2.17053 - 0.537397i) q^{10} +(1.69980 - 2.84792i) q^{11} +1.30471 q^{12} +(-0.798552 + 1.09911i) q^{13} +(-2.64445 + 0.0829819i) q^{14} +(0.208279 + 2.90998i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.98538 + 4.10903i) q^{17} +(0.401021 + 1.23421i) q^{18} +(-2.21345 + 6.81229i) q^{19} +(-1.44012 - 1.71057i) q^{20} +(1.16915 + 3.24792i) q^{21} +(3.04914 - 1.30490i) q^{22} +8.11605i q^{23} +(1.05553 + 0.766890i) q^{24} +(3.58529 - 3.48506i) q^{25} +(-1.29208 + 0.419823i) q^{26} +(4.53640 - 3.29588i) q^{27} +(-2.18818 - 1.48723i) q^{28} +(-4.39194 + 1.42703i) q^{29} +(-1.54194 + 2.47664i) q^{30} +(0.995228 - 1.36981i) q^{31} -1.00000 q^{32} +(-2.84854 - 3.25742i) q^{33} +5.07904i q^{34} +(2.96776 - 5.11785i) q^{35} +(-0.401021 + 1.23421i) q^{36} +(-9.02813 + 2.93342i) q^{37} +(-5.79488 + 4.21023i) q^{38} +(1.04188 + 1.43402i) q^{39} +(-0.159636 - 2.23036i) q^{40} +(-1.50051 + 4.61809i) q^{41} +(-0.963215 + 3.31483i) q^{42} +0.645932 q^{43} +(3.23380 + 0.736550i) q^{44} +(-2.81676 - 0.697396i) q^{45} +(-4.77049 + 6.56602i) q^{46} +(2.27230 - 6.99342i) q^{47} +(0.403178 + 1.24085i) q^{48} +(1.74146 - 6.77992i) q^{49} +(4.94903 - 0.712094i) q^{50} +(6.30234 - 2.04775i) q^{51} +(-1.29208 - 0.419823i) q^{52} +(-4.50352 + 6.19856i) q^{53} +5.60729 q^{54} +(-1.12654 + 7.33014i) q^{55} +(-0.896100 - 2.48938i) q^{56} +(7.56064 + 5.49313i) q^{57} +(-4.39194 - 1.42703i) q^{58} +(7.39957 - 2.40427i) q^{59} +(-2.70319 + 1.09732i) q^{60} +(10.7067 - 7.77886i) q^{61} +(1.61031 - 0.523223i) q^{62} +(-3.43178 + 0.107688i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.730095 - 2.94883i) q^{65} +(-0.389848 - 4.30964i) q^{66} -9.00756i q^{67} +(-2.98538 + 4.10903i) q^{68} +(10.0708 + 3.27221i) q^{69} +(5.40917 - 2.39602i) q^{70} +(8.53510 - 6.20112i) q^{71} +(-1.04989 + 0.762787i) q^{72} +(8.11337 - 2.63619i) q^{73} +(-9.02813 - 2.93342i) q^{74} +(-2.87894 - 5.85392i) q^{75} -7.16287 q^{76} +(1.06426 + 8.71019i) q^{77} +1.77255i q^{78} +(-4.85165 + 6.67772i) q^{79} +(1.18183 - 1.89823i) q^{80} +(-1.05767 - 3.25519i) q^{81} +(-3.92838 + 2.85413i) q^{82} +(-7.24004 - 9.96505i) q^{83} +(-2.72767 + 2.11559i) q^{84} +(-9.64119 - 6.00253i) q^{85} +(0.522570 + 0.379669i) q^{86} +6.02510i q^{87} +(2.18327 + 2.49666i) q^{88} +8.78152i q^{89} +(-1.86889 - 2.21986i) q^{90} +(-0.112737 - 3.59269i) q^{91} +(-7.71882 + 2.50800i) q^{92} +(-1.29849 - 1.78721i) q^{93} +(5.94896 - 4.32217i) q^{94} +(-1.14345 - 15.9758i) q^{95} +(-0.403178 + 1.24085i) q^{96} +(7.43468 + 5.40161i) q^{97} +(5.39401 - 4.46147i) q^{98} +(3.95696 - 1.69341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

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