LMFDB - Embedded newform 770.2.w.b.139.15

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			139.15
Character	$\chi$	$=$	770.139
Dual form			770.2.w.b.349.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.266549 - 0.820354i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.466255 + 2.18692i) q^{5} +(0.697835 - 0.507006i) q^{6} +(2.50422 + 0.853746i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.82512 + 1.32603i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.266549 - 0.820354i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.466255 + 2.18692i) q^{5} +(0.697835 - 0.507006i) q^{6} +(2.50422 + 0.853746i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.82512 + 1.32603i) q^{9} +(-0.908230 + 2.04331i) q^{10} +(-3.27459 + 0.526346i) q^{11} +0.862571 q^{12} +(1.64268 - 2.26095i) q^{13} +(1.52414 + 2.16264i) q^{14} +(1.91833 + 0.200427i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.88281 - 2.59146i) q^{17} +(0.697133 + 2.14556i) q^{18} +(-0.715313 + 2.20151i) q^{19} +(-1.93580 + 1.11923i) q^{20} +(1.36787 - 1.82678i) q^{21} +(-2.95858 - 1.49893i) q^{22} +5.07812i q^{23} +(0.697835 + 0.507006i) q^{24} +(-4.56521 + 2.03932i) q^{25} +(2.65791 - 0.863607i) q^{26} +(3.66780 - 2.66481i) q^{27} +(-0.0381137 + 2.64548i) q^{28} +(-4.94646 + 1.60720i) q^{29} +(1.43415 + 1.28971i) q^{30} +(2.37730 - 3.27208i) q^{31} -1.00000 q^{32} +(-0.441050 + 2.82662i) q^{33} -3.20322i q^{34} +(-0.699467 + 5.87458i) q^{35} +(-0.697133 + 2.14556i) q^{36} +(4.11787 - 1.33798i) q^{37} +(-1.87271 + 1.36061i) q^{38} +(-1.41693 - 1.95023i) q^{39} +(-2.22396 - 0.232360i) q^{40} +(-0.541521 + 1.66663i) q^{41} +(2.18039 - 0.673883i) q^{42} +9.38054 q^{43} +(-1.51249 - 2.95167i) q^{44} +(-2.04894 + 4.60965i) q^{45} +(-2.98484 + 4.10828i) q^{46} +(2.33266 - 7.17920i) q^{47} +(0.266549 + 0.820354i) q^{48} +(5.54224 + 4.27593i) q^{49} +(-4.89202 - 1.03352i) q^{50} +(-2.62778 + 0.853816i) q^{51} +(2.65791 + 0.863607i) q^{52} +(1.07728 - 1.48275i) q^{53} +4.53365 q^{54} +(-2.67787 - 6.91585i) q^{55} +(-1.58581 + 2.11783i) q^{56} +(1.61535 + 1.17362i) q^{57} +(-4.94646 - 1.60720i) q^{58} +(9.20055 - 2.98944i) q^{59} +(0.402178 + 1.88637i) q^{60} +(-6.40016 + 4.64999i) q^{61} +(3.84656 - 1.24982i) q^{62} +(3.43841 + 4.87885i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(5.71042 + 2.53822i) q^{65} +(-2.01826 + 2.02754i) q^{66} -7.62687i q^{67} +(1.88281 - 2.59146i) q^{68} +(4.16585 + 1.35357i) q^{69} +(-4.01887 + 4.34150i) q^{70} +(-6.31238 + 4.58621i) q^{71} +(-1.82512 + 1.32603i) q^{72} +(-5.53071 + 1.79704i) q^{73} +(4.11787 + 1.33798i) q^{74} +(0.456111 + 4.28867i) q^{75} -2.31480 q^{76} +(-8.64967 - 1.47758i) q^{77} -2.41062i q^{78} +(7.48280 - 10.2992i) q^{79} +(-1.66265 - 1.49520i) q^{80} +(0.882961 + 2.71747i) q^{81} +(-1.41772 + 1.03003i) q^{82} +(-5.00477 - 6.88848i) q^{83} +(2.16007 + 0.736416i) q^{84} +(4.78945 - 5.32583i) q^{85} +(7.58901 + 5.51374i) q^{86} +4.48625i q^{87} +(0.511320 - 3.27697i) q^{88} +10.0985i q^{89} +(-4.36711 + 2.52495i) q^{90} +(6.04390 - 4.25949i) q^{91} +(-4.82958 + 1.56922i) q^{92} +(-2.05059 - 2.82240i) q^{93} +(6.10699 - 4.43699i) q^{94} +(-5.14803 - 0.537868i) q^{95} +(-0.266549 + 0.820354i) q^{96} +(2.05624 + 1.49394i) q^{97} +(1.97043 + 6.71695i) q^{98} +(-6.67447 - 3.38155i) 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
$3$	0.266549	−	0.820354i	0.153892	−	0.473631i	−0.844155	−	0.536100i	$-0.819897\pi$
$3$	0.266549	−	0.820354i	0.153892	−	0.473631i	0.998047	+	0.0624681i	$0.0198972\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.466255	+	2.18692i	0.208515	+	0.978019i
$5$	0.466255	+	2.18692i	0.208515	+	0.978019i
$6$	0.697835	−	0.507006i	0.284890	−	0.206985i
$7$	2.50422	+	0.853746i	0.946506	+	0.322685i
$7$	2.50422	+	0.853746i	0.946506	+	0.322685i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	1.82512	+	1.32603i	0.608373	+	0.442009i
$10$	−0.908230	+	2.04331i	−0.287207	+	0.646152i
$11$	−3.27459	+	0.526346i	−0.987327	+	0.158699i
$11$	−3.27459	+	0.526346i	−0.987327	+	0.158699i
$12$	0.862571			0.249003
$13$	1.64268	−	2.26095i	0.455597	−	0.627075i	−0.517992	−	0.855386i	$-0.673320\pi$
$13$	1.64268	−	2.26095i	0.455597	−	0.627075i	0.973588	+	0.228310i	$0.0733201\pi$
$14$	1.52414	+	2.16264i	0.407343	+	0.577989i
$15$	1.91833	+	0.200427i	0.495309	+	0.0517500i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.88281	−	2.59146i	−0.456648	−	0.628522i	0.517161	−	0.855888i	$-0.326989\pi$
$17$	−1.88281	−	2.59146i	−0.456648	−	0.628522i	−0.973809	+	0.227366i	$0.926989\pi$
$18$	0.697133	+	2.14556i	0.164316	+	0.505712i
$19$	−0.715313	+	2.20151i	−0.164104	+	0.505060i	−0.998969	−	0.0453942i	$-0.985546\pi$
$19$	−0.715313	+	2.20151i	−0.164104	+	0.505060i	0.834865	+	0.550455i	$0.185546\pi$
$20$	−1.93580	+	1.11923i	−0.432858	+	0.250267i
$21$	1.36787	−	1.82678i	0.298494	−	0.398636i
$22$	−2.95858	−	1.49893i	−0.630771	−	0.319574i
$23$			5.07812i			1.05886i	0.848353	+	0.529430i	$0.177594\pi$
$23$			5.07812i			1.05886i	−0.848353	+	0.529430i	$0.822406\pi$
$24$	0.697835	+	0.507006i	0.142445	+	0.103492i
$25$	−4.56521	+	2.03932i	−0.913043	+	0.407864i
$26$	2.65791	−	0.863607i	0.521259	−	0.169367i
$27$	3.66780	−	2.66481i	0.705868	−	0.512843i
$28$	−0.0381137	+	2.64548i	−0.00720281	+	0.499948i
$29$	−4.94646	+	1.60720i	−0.918535	+	0.298450i	−0.729866	−	0.683590i	$-0.760418\pi$
$29$	−4.94646	+	1.60720i	−0.918535	+	0.298450i	−0.188670	+	0.982041i	$0.560418\pi$
$30$	1.43415	+	1.28971i	0.261839	+	0.235468i
$31$	2.37730	−	3.27208i	0.426976	−	0.587682i	−0.540280	−	0.841486i	$-0.681682\pi$
$31$	2.37730	−	3.27208i	0.426976	−	0.587682i	0.967256	+	0.253803i	$0.0816815\pi$
$32$	−1.00000			−0.176777
$33$	−0.441050	+	2.82662i	−0.0767769	+	0.492052i
$34$		−	3.20322i		−	0.549348i
$35$	−0.699467	+	5.87458i	−0.118231	+	0.992986i
$36$	−0.697133	+	2.14556i	−0.116189	+	0.357593i
$37$	4.11787	−	1.33798i	0.676974	−	0.219962i	0.0497042	−	0.998764i	$-0.484172\pi$
$37$	4.11787	−	1.33798i	0.676974	−	0.219962i	0.627270	+	0.778802i	$0.284172\pi$
$38$	−1.87271	+	1.36061i	−0.303794	+	0.220720i
$39$	−1.41693	−	1.95023i	−0.226890	−	0.312287i
$40$	−2.22396	−	0.232360i	−0.351639	−	0.0367394i
$41$	−0.541521	+	1.66663i	−0.0845713	+	0.260284i	−0.984396	−	0.175968i	$-0.943694\pi$
$41$	−0.541521	+	1.66663i	−0.0845713	+	0.260284i	0.899824	+	0.436252i	$0.143694\pi$
$42$	2.18039	−	0.673883i	0.336441	−	0.103982i
$43$	9.38054			1.43052			0.715259	−	0.698859i	$-0.246309\pi$
$43$	9.38054			1.43052			0.715259	+	0.698859i	$0.246309\pi$
$44$	−1.51249	−	2.95167i	−0.228016	−	0.444981i
$45$	−2.04894	+	4.60965i	−0.305438	+	0.687166i
$46$	−2.98484	+	4.10828i	−0.440091	+	0.605733i
$47$	2.33266	−	7.17920i	0.340254	−	1.04719i	−0.623822	−	0.781566i	$-0.714421\pi$
$47$	2.33266	−	7.17920i	0.340254	−	1.04719i	0.964076	−	0.265627i	$-0.0855790\pi$
$48$	0.266549	+	0.820354i	0.0384730	+	0.118408i
$49$	5.54224	+	4.27593i	0.791748	+	0.610848i
$50$	−4.89202	−	1.03352i	−0.691836	−	0.146162i
$51$	−2.62778	+	0.853816i	−0.367962	+	0.119558i
$52$	2.65791	+	0.863607i	0.368586	+	0.119761i
$53$	1.07728	−	1.48275i	0.147976	−	0.203672i	−0.728594	−	0.684946i	$-0.759826\pi$
$53$	1.07728	−	1.48275i	0.147976	−	0.203672i	0.876570	+	0.481274i	$0.159826\pi$
$54$	4.53365			0.616951
$55$	−2.67787	−	6.91585i	−0.361084	−	0.932533i
$56$	−1.58581	+	2.11783i	−0.211912	+	0.283007i
$57$	1.61535	+	1.17362i	0.213958	+	0.155450i
$58$	−4.94646	−	1.60720i	−0.649503	−	0.211036i
$59$	9.20055	−	2.98944i	1.19781	−	0.389192i	0.358855	−	0.933393i	$-0.383167\pi$
$59$	9.20055	−	2.98944i	1.19781	−	0.389192i	0.838954	+	0.544202i	$0.183167\pi$
$60$	0.402178	+	1.88637i	0.0519209	+	0.243529i
$61$	−6.40016	+	4.64999i	−0.819457	+	0.595370i	−0.916557	−	0.399904i	$-0.869043\pi$
$61$	−6.40016	+	4.64999i	−0.819457	+	0.595370i	0.0971000	+	0.995275i	$0.469043\pi$
$62$	3.84656	−	1.24982i	0.488513	−	0.158728i
$63$	3.43841	+	4.87885i	0.433199	+	0.614677i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	5.71042	+	2.53822i	0.708291	+	0.314828i
$66$	−2.01826	+	2.02754i	−0.248431	+	0.249573i
$67$		−	7.62687i		−	0.931770i	−0.884845	−	0.465885i	$-0.845736\pi$
$67$		−	7.62687i		−	0.931770i	0.884845	−	0.465885i	$-0.154264\pi$
$68$	1.88281	−	2.59146i	0.228324	−	0.314261i
$69$	4.16585	+	1.35357i	0.501510	+	0.162950i
$70$	−4.01887	+	4.34150i	−0.480347	+	0.518909i
$71$	−6.31238	+	4.58621i	−0.749141	+	0.544283i	−0.895561	−	0.444940i	$-0.853225\pi$
$71$	−6.31238	+	4.58621i	−0.749141	+	0.544283i	0.146419	+	0.989223i	$0.453225\pi$
$72$	−1.82512	+	1.32603i	−0.215092	+	0.156274i
$73$	−5.53071	+	1.79704i	−0.647320	+	0.210327i	−0.614232	−	0.789125i	$-0.710534\pi$
$73$	−5.53071	+	1.79704i	−0.647320	+	0.210327i	−0.0330882	+	0.999452i	$0.510534\pi$
$74$	4.11787	+	1.33798i	0.478693	+	0.155537i
$75$	0.456111	+	4.28867i	0.0526671	+	0.495213i
$76$	−2.31480			−0.265526
$77$	−8.64967	−	1.47758i	−0.985721	−	0.168386i
$78$		−	2.41062i		−	0.272949i
$79$	7.48280	−	10.2992i	0.841881	−	1.15875i	−0.143713	−	0.989619i	$-0.545904\pi$
$79$	7.48280	−	10.2992i	0.841881	−	1.15875i	0.985594	−	0.169130i	$-0.0540959\pi$
$80$	−1.66265	−	1.49520i	−0.185889	−	0.167168i
$81$	0.882961	+	2.71747i	0.0981067	+	0.301941i
$82$	−1.41772	+	1.03003i	−0.156561	+	0.113748i
$83$	−5.00477	−	6.88848i	−0.549345	−	0.756109i	0.440578	−	0.897714i	$-0.354773\pi$
$83$	−5.00477	−	6.88848i	−0.549345	−	0.756109i	−0.989923	+	0.141606i	$0.954773\pi$
$84$	2.16007	+	0.736416i	0.235683	+	0.0803496i
$85$	4.78945	−	5.32583i	0.519488	−	0.577667i
$86$	7.58901	+	5.51374i	0.818344	+	0.594562i
$87$			4.48625i			0.480976i
$88$	0.511320	−	3.27697i	0.0545069	−	0.349326i
$89$			10.0985i			1.07044i	0.844713	+	0.535220i	$0.179771\pi$
$89$			10.0985i			1.07044i	−0.844713	+	0.535220i	$0.820229\pi$
$90$	−4.36711	+	2.52495i	−0.460334	+	0.266153i
$91$	6.04390	−	4.25949i	0.633573	−	0.446516i
$92$	−4.82958	+	1.56922i	−0.503518	+	0.163603i
$93$	−2.05059	−	2.82240i	−0.212637	−	0.292669i
$94$	6.10699	−	4.43699i	0.629888	−	0.457640i
$95$	−5.14803	−	0.537868i	−0.528177	−	0.0551841i
$96$	−0.266549	+	0.820354i	−0.0272046	+	0.0837270i
$97$	2.05624	+	1.49394i	0.208779	+	0.151687i	0.687261	−	0.726410i	$-0.258813\pi$
$97$	2.05624	+	1.49394i	0.208779	+	0.151687i	−0.478482	+	0.878097i	$0.658813\pi$
$98$	1.97043	+	6.71695i	0.199044	+	0.678514i
$99$	−6.67447	−	3.38155i	−0.670810	−	0.339859i
$100$	−3.35024	−	3.71159i	−0.335024	−	0.371159i
$101$	−14.5947	−	10.6037i	−1.45223	−	1.05511i	−0.985304	−	0.170812i	$-0.945361\pi$
$101$	−14.5947	−	10.6037i	−1.45223	−	1.05511i	−0.466928	−	0.884296i	$-0.654639\pi$
$102$	−2.62778	−	0.853816i	−0.260189	−	0.0845404i
$103$	−4.61982	−	14.2183i	−0.455204	−	1.40098i	−0.870895	−	0.491469i	$-0.836460\pi$
$103$	−4.61982	−	14.2183i	−0.455204	−	1.40098i	0.415691	−	0.909506i	$-0.363540\pi$
$104$	1.64268	+	2.26095i	0.161078	+	0.221705i
$105$	4.63280	+	2.13968i	0.452115	+	0.208811i
$106$	1.74308	−	0.566362i	0.169303	−	0.0550099i
$107$	3.71561	−	11.4355i	0.359201	−	1.10551i	−0.594332	−	0.804220i	$-0.702583\pi$
$107$	3.71561	−	11.4355i	0.359201	−	1.10551i	0.953533	−	0.301288i	$-0.0974167\pi$
$108$	3.66780	+	2.66481i	0.352934	+	0.256422i
$109$		−	9.34603i		−	0.895188i	−0.894237	−	0.447594i	$-0.852281\pi$
$109$		−	9.34603i		−	0.895188i	0.894237	−	0.447594i	$-0.147719\pi$
$110$	1.89859	−	7.16905i	0.181024	−	0.683543i
$111$		−	3.73475i		−	0.354487i
$112$	−2.52778	+	0.781249i	−0.238852	+	0.0738211i
$113$	−0.283887	−	0.0922405i	−0.0267058	−	0.00867725i	0.295634	−	0.955301i	$-0.404469\pi$
$113$	−0.283887	−	0.0922405i	−0.0267058	−	0.00867725i	−0.322339	+	0.946624i	$0.604469\pi$
$114$	0.617008	+	1.89896i	0.0577881	+	0.177854i
$115$	−11.1054	+	2.36770i	−1.03559	+	0.220789i
$116$	−3.05708	−	4.20771i	−0.283843	−	0.390676i
$117$	5.99617	−	1.94827i	0.554346	−	0.180118i
$118$	9.20055	+	2.98944i	0.846979	+	0.275200i
$119$	−2.50252	−	8.09703i	−0.229405	−	0.742254i
$120$	−0.783413	+	1.76250i	−0.0715155	+	0.160894i
$121$	10.4459	−	3.44714i	0.949629	−	0.313376i
$122$	−7.91104			−0.716232
$123$	1.22288	+	0.888477i	0.110264	+	0.0801113i
$124$	3.84656	+	1.24982i	0.345431	+	0.112237i
$125$	−6.58838	−	9.03290i	−0.589282	−	0.807927i
$126$	−0.0859834	+	5.96812i	−0.00766001	+	0.531682i
$127$	−11.4465	+	8.31638i	−1.01571	+	0.737959i	−0.965400	−	0.260774i	$-0.916022\pi$
$127$	−11.4465	+	8.31638i	−1.01571	+	0.737959i	−0.0503137	+	0.998733i	$0.516022\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	2.50037	−	7.69536i	0.220146	−	0.677539i
$130$	3.12790	+	5.40996i	0.274335	+	0.474485i
$131$	−6.97684			−0.609570			−0.304785	−	0.952421i	$-0.598585\pi$
$131$	−6.97684			−0.609570			−0.304785	+	0.952421i	$0.598585\pi$
$132$	−2.82457	+	0.454011i	−0.245847	+	0.0395166i
$133$	−3.67083	+	4.90236i	−0.318301	+	0.425089i
$134$	4.48296	−	6.17027i	0.387269	−	0.533030i
$135$	7.53785	+	6.77869i	0.648755	+	0.583417i
$136$	3.04645	−	0.989851i	0.261231	−	0.0848790i
$137$	−0.368589	−	0.507319i	−0.0314907	−	0.0433432i	0.792981	−	0.609246i	$-0.208528\pi$
$137$	−0.368589	−	0.507319i	−0.0314907	−	0.0433432i	−0.824472	+	0.565903i	$0.808528\pi$
$138$	2.57464	+	3.54369i	0.219168	+	0.301659i
$139$	−1.58606	−	4.88139i	−0.134528	−	0.414034i	0.860988	−	0.508625i	$-0.169846\pi$
$139$	−1.58606	−	4.88139i	−0.134528	−	0.414034i	−0.995516	+	0.0945903i	$0.969846\pi$
$140$	−5.80321	+	1.15011i	−0.490461	+	0.0972024i
$141$	−5.26771	−	3.82722i	−0.443621	−	0.322310i
$142$	−7.80253			−0.654774
$143$	−4.18906	+	8.26831i	−0.350307	+	0.691431i
$144$	−2.25597			−0.187998
$145$	−5.82113	−	10.0681i	−0.483419	−	0.836114i
$146$	−5.53071	−	1.79704i	−0.457725	−	0.148724i
$147$	4.98506	−	3.40685i	0.411161	−	0.280992i
$148$	2.54499	+	3.50287i	0.209197	+	0.287934i
$149$	−0.477780	−	0.657608i	−0.0391413	−	0.0538734i	0.788998	−	0.614396i	$-0.210600\pi$
$149$	−0.477780	−	0.657608i	−0.0391413	−	0.0538734i	−0.828139	+	0.560523i	$0.810600\pi$
$150$	−2.15182	+	3.73770i	−0.175695	+	0.305182i
$151$	22.4671	+	7.30000i	1.82835	+	0.594066i	0.999396	+	0.0347436i	$0.0110614\pi$
$151$	22.4671	+	7.30000i	1.82835	+	0.594066i	0.828950	+	0.559322i	$0.188939\pi$
$152$	−1.87271	−	1.36061i	−0.151897	−	0.110360i
$153$		−	7.22638i		−	0.584218i
$154$	−6.12923	−	6.27954i	−0.493907	−	0.506019i
$155$	8.26419	+	3.67334i	0.663796	+	0.295050i
$156$	1.41693	−	1.95023i	0.113445	−	0.156143i
$157$	−6.32923	+	19.4794i	−0.505128	+	1.55462i	0.295428	+	0.955365i	$0.404538\pi$
$157$	−6.32923	+	19.4794i	−0.505128	+	1.55462i	−0.800556	+	0.599258i	$0.795462\pi$
$158$	12.1074	−	3.93394i	0.963215	−	0.312968i
$159$	−0.929234	−	1.27898i	−0.0736930	−	0.101430i
$160$	−0.466255	−	2.18692i	−0.0368607	−	0.172891i
$161$	−4.33542	+	12.7167i	−0.341679	+	1.00222i
$162$	−0.882961	+	2.71747i	−0.0693719	+	0.213505i
$163$	−10.4294	+	14.3549i	−0.816897	+	1.12436i	0.173325	+	0.984865i	$0.444549\pi$
$163$	−10.4294	+	14.3549i	−0.816897	+	1.12436i	−0.990222	+	0.139498i	$0.955451\pi$
$164$	−1.75240			−0.136839
$165$	−6.38723	+	0.353387i	−0.497245	+	0.0275111i
$166$		−	8.51463i		−	0.660863i
$167$	8.81319	−	12.1303i	0.681985	−	0.938672i	−0.317970	−	0.948101i	$-0.603001\pi$
$167$	8.81319	−	12.1303i	0.681985	−	0.938672i	0.999956	+	0.00942838i	$0.00300119\pi$
$168$	1.31468	+	1.86543i	0.101430	+	0.143921i
$169$	1.60371	+	4.93570i	0.123362	+	0.379670i
$170$	7.00519	−	1.49352i	0.537273	−	0.114548i
$171$	−4.22479	+	3.06949i	−0.323078	+	0.234730i
$172$	2.89875	+	8.92142i	0.221027	+	0.680252i
$173$	−9.90285	−	3.21763i	−0.752900	−	0.244632i	−0.0926713	−	0.995697i	$-0.529541\pi$
$173$	−9.90285	−	3.21763i	−0.752900	−	0.244632i	−0.660229	+	0.751065i	$0.729541\pi$
$174$	−2.63695	+	3.62945i	−0.199907	+	0.275148i
$175$	−13.1734	+	1.20938i	−0.995812	+	0.0914203i
$176$	2.33982	−	2.35058i	0.176371	−	0.177182i
$177$		−	8.34453i		−	0.627214i
$178$	−5.93576	+	8.16987i	−0.444904	+	0.612357i
$179$	6.37999	−	19.6356i	0.476863	−	1.46763i	−0.366565	−	0.930392i	$-0.619466\pi$
$179$	6.37999	−	19.6356i	0.476863	−	1.46763i	0.843428	−	0.537242i	$-0.180534\pi$
$180$	−5.01720	−	0.524198i	−0.373960	−	0.0390714i
$181$	−9.18635	−	12.6439i	−0.682816	−	0.939816i	0.317147	−	0.948376i	$-0.397275\pi$
$181$	−9.18635	−	12.6439i	−0.682816	−	0.939816i	−0.999963	+	0.00856029i	$0.997275\pi$
$182$	7.39329	+	0.106516i	0.548027	+	0.00789548i
$183$	2.10868	+	6.48985i	0.155878	+	0.479743i
$184$	−4.82958	−	1.56922i	−0.356041	−	0.115685i
$185$	4.84603	+	8.38161i	0.356287	+	0.616228i
$186$		−	3.48868i		−	0.255802i
$187$	7.52944	+	7.49498i	0.550607	+	0.548087i
$188$	7.54865			0.550542
$189$	11.4600	−	3.54191i	0.833596	−	0.257636i
$190$	−3.84870	−	3.46108i	−0.279214	−	0.251093i
$191$	2.08165	+	6.40667i	0.150623	+	0.463571i	0.997691	−	0.0679140i	$-0.0216343\pi$
$191$	2.08165	+	6.40667i	0.150623	+	0.463571i	−0.847068	+	0.531485i	$0.821634\pi$
$192$	−0.697835	+	0.507006i	−0.0503619	+	0.0365900i
$193$	−6.75164	+	4.90535i	−0.485994	+	0.353095i	−0.803642	−	0.595114i	$-0.797107\pi$
$193$	−6.75164	+	4.90535i	−0.485994	+	0.353095i	0.317648	+	0.948209i	$0.397107\pi$
$194$	0.785413	+	2.41725i	0.0563894	+	0.173549i
$195$	3.60435	−	4.00800i	0.258113	−	0.287019i
$196$	−2.35401	+	6.59232i	−0.168144	+	0.470880i
$197$	−3.95782			−0.281983			−0.140991	−	0.990011i	$-0.545029\pi$
$197$	−3.95782			−0.281983			−0.140991	+	0.990011i	$0.545029\pi$
$198$	−3.41213	−	6.65889i	−0.242490	−	0.473227i
$199$			2.77356i			0.196612i	0.995156	+	0.0983062i	$0.0313425\pi$
$199$			2.77356i			0.196612i	−0.995156	+	0.0983062i	$0.968658\pi$
$200$	−0.528780	−	4.97196i	−0.0373904	−	0.351571i
$201$	−6.25673	−	2.03293i	−0.441316	−	0.143392i
$202$	−5.57470	−	17.1571i	−0.392234	−	1.20717i
$203$	−13.7592	−	0.198230i	−0.965705	−	0.0139130i
$204$	−1.62406	−	2.23532i	−0.113707	−	0.156504i
$205$	−3.89727	−	0.407187i	−0.272197	−	0.0284392i
$206$	4.61982	−	14.2183i	0.321878	−	0.990639i
$207$	−6.73372	+	9.26817i	−0.468026	+	0.644182i
$208$			2.79469i			0.193777i
$209$	1.18360	−	7.58554i	0.0818716	−	0.524703i
$210$	2.49034	+	4.45412i	0.171850	+	0.307364i
$211$	13.8526	−	19.0665i	0.953653	−	1.31259i	0.00376806	−	0.999993i	$-0.498801\pi$
$211$	13.8526	−	19.0665i	0.953653	−	1.31259i	0.949885	−	0.312598i	$-0.101199\pi$
$212$	1.74308	+	0.566362i	0.119715	+	0.0388979i
$213$	2.07976	+	6.40083i	0.142503	+	0.438578i
$214$	9.72759	−	7.06751i	0.664964	−	0.483125i
$215$	4.37372	+	20.5145i	0.298285	+	1.39907i
$216$	1.40097	+	4.31176i	0.0953242	+	0.293378i
$217$	8.74681	−	6.16439i	0.593772	−	0.418466i
$218$	5.49346	−	7.56110i	0.372064	−	0.512102i
$219$			5.01614i			0.338959i
$220$	5.74986	−	4.68392i	0.387655	−	0.315790i
$221$	−8.95202			−0.602178
$222$	2.19523	−	3.02148i	0.147334	−	0.202788i
$223$	3.17693	−	9.77759i	0.212743	−	0.654756i	−0.786563	−	0.617510i	$-0.788142\pi$
$223$	3.17693	−	9.77759i	0.212743	−	0.654756i	0.999306	−	0.0372458i	$-0.0118585\pi$
$224$	−2.50422	−	0.853746i	−0.167320	−	0.0570433i
$225$	−11.0363	−	2.33159i	−0.735750	−	0.155439i
$226$	−0.175452	−	0.241489i	−0.0116709	−	0.0160636i
$227$	15.6561	−	5.08698i	1.03913	−	0.337635i	0.260738	−	0.965410i	$-0.416034\pi$
$227$	15.6561	−	5.08698i	1.03913	−	0.337635i	0.778395	+	0.627775i	$0.216034\pi$
$228$	−0.617008	+	1.89896i	−0.0408624	+	0.125761i
$229$	12.8502	−	17.6868i	0.849164	−	1.16877i	−0.134882	−	0.990862i	$-0.543066\pi$
$229$	12.8502	−	17.6868i	0.849164	−	1.16877i	0.984046	−	0.177912i	$-0.0569344\pi$
$230$	−10.3762	−	4.61210i	−0.684184	−	0.304113i
$231$	−3.51770	+	6.70194i	−0.231448	+	0.440955i
$232$		−	5.20102i		−	0.341464i
$233$	−13.0617	−	9.48989i	−0.855701	−	0.621703i	0.0710108	−	0.997476i	$-0.477378\pi$
$233$	−13.0617	−	9.48989i	−0.855701	−	0.621703i	−0.926712	+	0.375772i	$0.877378\pi$
$234$	5.99617	+	1.94827i	0.391982	+	0.127363i
$235$	16.7879	+	1.75401i	1.09512	+	0.114419i
$236$	5.68625	+	7.82645i	0.370143	+	0.509459i
$237$	−6.45445	−	8.88378i	−0.419261	−	0.577064i
$238$	2.73474	−	8.02158i	0.177267	−	0.519962i
$239$	19.1905	+	6.23538i	1.24133	+	0.403333i	0.854807	−	0.518946i	$-0.173675\pi$
$239$	19.1905	+	6.23538i	1.24133	+	0.403333i	0.386525	+	0.922279i	$0.373675\pi$
$240$	−1.66977	+	0.965414i	−0.107783	+	0.0623172i
$241$	6.44405			0.415098			0.207549	−	0.978225i	$-0.433451\pi$
$241$	6.44405			0.415098			0.207549	+	0.978225i	$0.433451\pi$
$242$	10.4771	+	3.35116i	0.673494	+	0.215421i
$243$	16.0656			1.03061
$244$	−6.40016	−	4.64999i	−0.409728	−	0.297685i
$245$	−6.76702	+	14.1141i	−0.432329	+	0.901716i
$246$	0.467100	+	1.43759i	0.0297812	+	0.0916572i
$247$	3.80247	+	5.23366i	0.241946	+	0.333010i
$248$	2.37730	+	3.27208i	0.150959	+	0.207777i
$249$	−6.98501	+	2.26957i	−0.442657	+	0.143828i
$250$	−0.0207026	−	11.1803i	−0.00130935	−	0.707106i
$251$	−1.93104	+	2.65784i	−0.121886	+	0.167761i	−0.865600	−	0.500737i	$-0.833063\pi$
$251$	−1.93104	+	2.65784i	−0.121886	+	0.167761i	0.743714	+	0.668498i	$0.233063\pi$
$252$	−3.57753	+	4.77777i	−0.225364	+	0.300971i
$253$	−2.67285	−	16.6288i	−0.168041	−	1.04544i
$254$	−14.1487			−0.887766
$255$	−3.09244	−	5.34863i	−0.193656	−	0.334944i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	4.54048	+	13.9742i	0.283228	+	0.871685i	0.986924	+	0.161184i	$0.0515314\pi$
$257$	4.54048	+	13.9742i	0.283228	+	0.871685i	−0.703697	+	0.710500i	$0.748469\pi$
$258$	6.54606	−	4.75599i	0.407540	−	0.296095i
$259$	11.4544	+	0.165024i	0.711739	+	0.0102541i
$260$	−0.649374	+	6.21529i	−0.0402725	+	0.385456i
$261$	−11.1591	−	3.62581i	−0.690730	−	0.224432i
$262$	−5.64438	−	4.10088i	−0.348711	−	0.253354i
$263$	−10.4825			−0.646379			−0.323190	−	0.946334i	$-0.604755\pi$
$263$	−10.4825			−0.646379			−0.323190	+	0.946334i	$0.604755\pi$
$264$	−2.55199	−	1.29294i	−0.157064	−	0.0795748i
$265$	3.74495	+	1.66459i	0.230050	+	0.102255i
$266$	−5.85130	+	1.80844i	−0.358766	+	0.110882i
$267$	8.28435	+	2.69175i	0.506994	+	0.164732i
$268$	7.25358	−	2.35683i	0.443083	−	0.143966i
$269$	15.9580	+	21.9643i	0.972977	+	1.33919i	0.940529	+	0.339714i	$0.110330\pi$
$269$	15.9580	+	21.9643i	0.972977	+	1.33919i	0.0324481	+	0.999473i	$0.489670\pi$
$270$	2.11383	+	9.91471i	0.128644	+	0.603390i
$271$	6.92573	+	21.3152i	0.420708	+	1.29481i	0.907045	+	0.421034i	$0.138333\pi$
$271$	6.92573	+	21.3152i	0.420708	+	1.29481i	−0.486337	+	0.873771i	$0.661667\pi$
$272$	3.04645	+	0.989851i	0.184718	+	0.0600185i
$273$	−1.88329	−	6.09350i	−0.113982	−	0.368796i
$274$		−	0.627081i		−	0.0378834i
$275$	13.8758	−	9.08083i	0.836744	−	0.547595i
$276$			4.38024i			0.263659i
$277$	9.21133	+	6.69242i	0.553455	+	0.402109i	0.829058	−	0.559163i	$-0.188877\pi$
$277$	9.21133	+	6.69242i	0.553455	+	0.402109i	−0.275603	+	0.961272i	$0.588877\pi$
$278$	1.58606	−	4.88139i	0.0951256	−	0.292766i
$279$	8.67772	−	2.81956i	0.519522	−	0.168803i
$280$	−5.37092	−	2.48058i	−0.320974	−	0.148243i
$281$	1.42917	+	1.96708i	0.0852569	+	0.117346i	0.849515	−	0.527564i	$-0.176895\pi$
$281$	1.42917	+	1.96708i	0.0852569	+	0.117346i	−0.764258	+	0.644910i	$0.776895\pi$
$282$	−2.01209	−	6.19257i	−0.119818	−	0.368762i
$283$	−18.0132	−	5.85283i	−1.07077	−	0.347915i	−0.279983	−	0.960005i	$-0.590329\pi$
$283$	−18.0132	−	5.85283i	−1.07077	−	0.347915i	−0.790788	+	0.612090i	$0.790329\pi$
$284$	−6.31238	−	4.58621i	−0.374571	−	0.272142i
$285$	−1.81345	+	4.07984i	−0.107419	+	0.241669i
$286$	−8.24901	+	4.22694i	−0.487774	+	0.249944i
$287$	−2.77897	+	3.71129i	−0.164037	+	0.219070i
$288$	−1.82512	−	1.32603i	−0.107546	−	0.0781369i
$289$	2.08258	−	6.40951i	0.122504	−	0.377030i
$290$	1.20851	−	11.5669i	0.0709661	−	0.679230i
$291$	1.77365	−	1.28863i	0.103973	−	0.0755410i
$292$	−3.41817	−	4.70470i	−0.200033	−	0.275322i
$293$	3.98532	−	1.29491i	0.232825	−	0.0756494i	−0.190281	−	0.981730i	$-0.560940\pi$
$293$	3.98532	−	1.29491i	0.232825	−	0.0756494i	0.423106	+	0.906080i	$0.360940\pi$
$294$	6.03549	+	0.173944i	0.351997	+	0.0101446i
$295$	10.8275	+	18.7270i	0.630399	+	1.09033i
$296$			4.32979i			0.251664i
$297$	−10.6079	+	10.6567i	−0.615535	+	0.618365i
$298$		−	0.812848i		−	0.0470870i
$299$	11.4814	+	8.34171i	0.663985	+	0.482413i
$300$	−3.93782	+	1.75906i	−0.227350	+	0.101559i
$301$	23.4909	+	8.00859i	1.35399	+	0.461608i
$302$	13.8854	+	19.1117i	0.799017	+	1.09975i
$303$	−12.5890	+	9.14644i	−0.723219	+	0.525450i
$304$	−0.715313	−	2.20151i	−0.0410260	−	0.126265i
$305$	−13.1532	−	11.8285i	−0.753153	−	0.677301i
$306$	4.24756	−	5.84627i	0.242817	−	0.334209i
$307$		−	19.9426i		−	1.13819i	−0.822273	−	0.569093i	$-0.807294\pi$
$307$		−	19.9426i		−	1.13819i	0.822273	−	0.569093i	$-0.192706\pi$
$308$	−1.26763	−	8.68292i	−0.0722300	−	0.494755i
$309$	−12.8955			−0.733598
$310$	4.52673	+	7.82937i	0.257101	+	0.444678i
$311$	−7.97133	−	2.59004i	−0.452012	−	0.146868i	0.0741587	−	0.997246i	$-0.476373\pi$
$311$	−7.97133	−	2.59004i	−0.452012	−	0.146868i	−0.526171	+	0.850379i	$0.676373\pi$
$312$	2.29263	−	0.744922i	0.129795	−	0.0421729i
$313$	−19.8340	+	14.4103i	−1.12108	+	0.814516i	−0.984373	−	0.176095i	$-0.943653\pi$
$313$	−19.8340	+	14.4103i	−1.12108	+	0.814516i	−0.136712	+	0.990611i	$0.543653\pi$
$314$	−16.5701	+	12.0389i	−0.935107	+	0.679395i
$315$	−9.06647	+	9.79431i	−0.510837	+	0.551847i
$316$	12.1074	+	3.93394i	0.681096	+	0.221302i
$317$	−8.43542	+	11.6104i	−0.473780	+	0.652103i	−0.977295	−	0.211884i	$-0.932040\pi$
$317$	−8.43542	+	11.6104i	−0.473780	+	0.652103i	0.503515	+	0.863987i	$0.332040\pi$
$318$		−	1.58091i		−	0.0886529i
$319$	15.3517	−	7.86649i	0.859531	−	0.440439i
$320$	0.908230	−	2.04331i	0.0507716	−	0.114225i
$321$	−8.39074	−	6.09623i	−0.468325	−	0.340258i
$322$	−10.9821	+	7.73975i	−0.612010	+	0.431319i
$323$	7.05192	−	2.29131i	0.392379	−	0.127492i
$324$	−2.31162	+	1.67949i	−0.128423	+	0.0933050i
$325$	−2.88837	+	13.6717i	−0.160218	+	0.758368i
$326$	−16.8752	+	5.48308i	−0.934631	+	0.303680i
$327$	−7.66705	−	2.49118i	−0.423989	−	0.137762i
$328$	−1.41772	−	1.03003i	−0.0782805	−	0.0568741i
$329$	11.9707	−	15.9868i	0.659966	−	0.881380i
$330$	−5.37509	−	3.46842i	−0.295889	−	0.190930i
$331$	−25.2062			−1.38546			−0.692728	−	0.721199i	$-0.743591\pi$
$331$	−25.2062			−1.38546			−0.692728	+	0.721199i	$0.743591\pi$
$332$	5.00477	−	6.88848i	0.274673	−	0.378054i
$333$	9.28981	+	3.01844i	0.509078	+	0.165410i
$334$	14.2600	−	4.63337i	0.780275	−	0.253527i
$335$	16.6793	−	3.55606i	0.911289	−	0.194288i
$336$	−0.0328757	+	2.28191i	−0.00179352	+	0.124488i
$337$	−2.77031	−	8.52613i	−0.150908	−	0.464448i	0.846815	−	0.531887i	$-0.178517\pi$
$337$	−2.77031	−	8.52613i	−0.150908	−	0.464448i	−0.997723	+	0.0674396i	$0.978517\pi$
$338$	−1.60371	+	4.93570i	−0.0872302	+	0.268467i
$339$	−0.151340	+	0.208301i	−0.00821964	+	0.0113134i
$340$	6.54518	+	2.90926i	0.354962	+	0.157777i
$341$	−6.06245	+	11.9660i	−0.328300	+	0.647996i
$342$	−5.22213			−0.282380
$343$	10.2284	+	15.4395i	0.552283	+	0.833657i
$344$	−2.89875	+	8.92142i	−0.156290	+	0.481011i
$345$	−1.01779	+	9.74148i	−0.0547961	+	0.524464i
$346$	−6.12030	−	8.42387i	−0.329029	−	0.452870i
$347$	−3.50626	+	2.54745i	−0.188226	+	0.136754i	−0.677908	−	0.735147i	$-0.737113\pi$
$347$	−3.50626	+	2.54745i	−0.188226	+	0.136754i	0.489681	+	0.871901i	$0.337113\pi$
$348$	−4.26668	+	1.38633i	−0.228718	+	0.0743149i
$349$	5.73576	−	17.6529i	0.307028	−	0.944935i	−0.671884	−	0.740656i	$-0.734515\pi$
$349$	5.73576	−	17.6529i	0.307028	−	0.944935i	0.978913	−	0.204279i	$-0.0654851\pi$
$350$	−11.3683	−	6.76470i	−0.607663	−	0.361588i
$351$		−	12.6701i		−	0.676282i
$352$	3.27459	−	0.526346i	0.174536	−	0.0280544i
$353$	−10.9295			−0.581719			−0.290860	−	0.956766i	$-0.593941\pi$
$353$	−10.9295			−0.581719			−0.290860	+	0.956766i	$0.593941\pi$
$354$	4.90479	−	6.75087i	0.260687	−	0.358805i
$355$	−12.9728	−	11.6663i	−0.688527	−	0.619183i
$356$	−9.60425	+	3.12061i	−0.509024	+	0.165392i
$357$	−7.30947	−	0.105308i	−0.386858	−	0.00557351i
$358$	16.7030	−	12.1355i	0.882783	−	0.641380i
$359$	−20.7589	+	6.74498i	−1.09561	+	0.355986i	−0.800413	−	0.599449i	$-0.795386\pi$
$359$	−20.7589	+	6.74498i	−1.09561	+	0.355986i	−0.295200	+	0.955435i	$0.595386\pi$
$360$	−3.75088	−	3.37312i	−0.197689	−	0.177779i
$361$	11.0364	+	8.01839i	0.580861	+	0.422020i
$362$		−	15.6288i		−	0.821429i
$363$	−0.0435247	−	9.48818i	−0.00228445	−	0.498000i
$364$	5.91869	+	4.43184i	0.310224	+	0.232291i
$365$	−6.50869	−	11.2573i	−0.340680	−	0.589235i
$366$	−2.10868	+	6.48985i	−0.110222	+	0.339230i
$367$	5.68237	+	17.4885i	0.296617	+	0.912894i	0.982673	+	0.185345i	$0.0593403\pi$
$367$	5.68237	+	17.4885i	0.296617	+	0.912894i	−0.686056	+	0.727548i	$0.740660\pi$
$368$	−2.98484	−	4.10828i	−0.155596	−	0.214159i
$369$	−3.19834	+	2.32373i	−0.166499	+	0.120968i
$370$	−1.00607	+	9.62929i	−0.0523031	+	0.500603i
$371$	3.96365	−	2.79342i	0.205782	−	0.145027i
$372$	2.05059	−	2.82240i	0.106318	−	0.146335i
$373$	−33.4440			−1.73167			−0.865833	−	0.500334i	$-0.833211\pi$
$373$	−33.4440			−1.73167			−0.865833	+	0.500334i	$0.833211\pi$
$374$	1.68601	+	10.4893i	0.0871813	+	0.542386i
$375$	−9.16630	+	2.99709i	−0.473346	+	0.154769i
$376$	6.10699	+	4.43699i	0.314944	+	0.228820i
$377$	−4.49164	+	13.8238i	−0.231331	+	0.711964i
$378$	11.3533	+	3.87058i	0.583948	+	0.199081i
$379$	−24.7305	+	17.9678i	−1.27032	+	0.922942i	−0.999215	−	0.0396078i	$-0.987389\pi$
$379$	−24.7305	+	17.9678i	−1.27032	+	0.922942i	−0.271105	+	0.962550i	$0.587389\pi$
$380$	−1.07929	−	5.06228i	−0.0553663	−	0.259689i
$381$	3.77131	+	11.6069i	0.193210	+	0.594640i
$382$	−2.08165	+	6.40667i	−0.106507	+	0.327794i
$383$	11.4421	+	8.31318i	0.584664	+	0.424783i	0.840403	−	0.541963i	$-0.182319\pi$
$383$	11.4421	+	8.31318i	0.584664	+	0.424783i	−0.255738	+	0.966746i	$0.582319\pi$
$384$	−0.862571			−0.0440179
$385$	−0.801598	−	19.6050i	−0.0408532	−	0.999165i
$386$	−8.34549			−0.424774
$387$	17.1206	+	12.4388i	0.870289	+	0.632302i
$388$	−0.785413	+	2.41725i	−0.0398733	+	0.122717i
$389$	9.55492	+	29.4070i	0.484453	+	1.49099i	0.832771	+	0.553618i	$0.186753\pi$
$389$	9.55492	+	29.4070i	0.484453	+	1.49099i	−0.348317	+	0.937377i	$0.613247\pi$
$390$	5.27182	−	1.12396i	0.266949	−	0.0569140i
$391$	13.1597	−	9.56112i	0.665517	−	0.483527i
$392$	−5.77930	+	3.94964i	−0.291899	+	0.199487i
$393$	−1.85967	+	5.72348i	−0.0938080	+	0.288711i
$394$	−3.20194	−	2.32635i	−0.161312	−	0.117200i
$395$	26.0124	+	11.5622i	1.30882	+	0.581758i
$396$	1.15352	−	7.39276i	0.0579667	−	0.371500i
$397$	2.38129			0.119513			0.0597566	−	0.998213i	$-0.480968\pi$
$397$	2.38129			0.119513			0.0597566	+	0.998213i	$0.480968\pi$
$398$	−1.63026	+	2.24386i	−0.0817174	+	0.112474i
$399$	3.04322	+	4.31810i	0.152351	+	0.216175i
$400$	2.49465	−	4.33321i	0.124733	−	0.216660i
$401$	−13.3127	+	9.67226i	−0.664806	+	0.483010i	−0.868282	−	0.496070i	$-0.834776\pi$
$401$	−13.3127	+	9.67226i	−0.664806	+	0.483010i	0.203477	+	0.979080i	$0.434776\pi$
$402$	−3.86687	−	5.32229i	−0.192862	−	0.265452i
$403$	−3.49287	−	10.7499i	−0.173992	−	0.535492i
$404$	5.57470	−	17.1571i	0.277351	−	0.853600i
$405$	−5.53120	+	3.19800i	−0.274848	+	0.158910i
$406$	−11.0149	−	8.24781i	−0.546660	−	0.409332i
$407$	−12.7801	+	6.54876i	−0.633487	+	0.324610i
$408$		−	2.76301i		−	0.136789i
$409$	12.2745	+	8.91795i	0.606935	+	0.440964i	0.848334	−	0.529462i	$-0.177606\pi$
$409$	12.2745	+	8.91795i	0.606935	+	0.440964i	−0.241399	+	0.970426i	$0.577606\pi$
$410$	−2.91362	−	2.62018i	−0.143893	−	0.129401i
$411$	−0.514429	+	0.167148i	−0.0253749	+	0.00824480i
$412$	12.0948	−	8.78742i	0.595870	−	0.432925i
$413$	25.5924	+	0.368713i	1.25932	+	0.0181432i
$414$	−10.8954	+	3.54012i	−0.535479	+	0.173988i
$415$	12.7310	−	14.1568i	0.624942	−	0.694930i
$416$	−1.64268	+	2.26095i	−0.0805389	+	0.110852i
$417$	−4.42723			−0.216802
$418$	5.41623	−	5.44113i	0.264916	−	0.266134i
$419$			34.7341i			1.69687i	0.529297	+	0.848437i	$0.322456\pi$
$419$			34.7341i			1.69687i	−0.529297	+	0.848437i	$0.677544\pi$
$420$	−0.603340	+	5.06725i	−0.0294400	+	0.247256i
$421$	−7.57844	+	23.3241i	−0.369351	+	1.13674i	0.577861	+	0.816135i	$0.303888\pi$
$421$	−7.57844	+	23.3241i	−0.369351	+	1.13674i	−0.947212	+	0.320609i	$0.896112\pi$
$422$	22.4140	−	7.28275i	1.09110	−	0.354519i
$423$	13.7772	−	10.0097i	0.669870	−	0.486689i
$424$	1.07728	+	1.48275i	0.0523175	+	0.0720089i
$425$	13.8802	+	7.99093i	0.673291	+	0.387617i
$426$	−2.07976	+	6.40083i	−0.100765	+	0.310121i
$427$	−19.9973	+	6.18049i	−0.967738	+	0.299095i
$428$	12.0240			0.581200
$429$	5.66635	+	5.64042i	0.273574	+	0.272322i
$430$	−8.51968	+	19.1674i	−0.410856	+	0.924332i
$431$	−16.5319	+	22.7542i	−0.796315	+	1.09603i	0.196978	+	0.980408i	$0.436887\pi$
$431$	−16.5319	+	22.7542i	−0.796315	+	1.09603i	−0.993293	+	0.115625i	$0.963113\pi$
$432$	−1.40097	+	4.31176i	−0.0674044	+	0.207449i
$433$	−8.77864	−	27.0179i	−0.421874	−	1.29840i	−0.905956	−	0.423373i	$-0.860846\pi$
$433$	−8.77864	−	27.0179i	−0.421874	−	1.29840i	0.484081	−	0.875023i	$-0.339154\pi$
$434$	10.6997	+	0.154151i	0.513600	+	0.00739949i
$435$	−9.81106	+	2.09173i	−0.470404	+	0.100291i
$436$	8.88861	−	2.88808i	0.425687	−	0.138314i
$437$	−11.1795	−	3.63244i	−0.534789	−	0.173763i
$438$	−2.94841	+	4.05814i	−0.140881	+	0.193905i
$439$	−33.4903			−1.59841			−0.799204	−	0.601060i	$-0.794745\pi$
$439$	−33.4903			−1.59841			−0.799204	+	0.601060i	$0.794745\pi$
$440$	7.40487	−	0.409690i	0.353014	−	0.0195312i
$441$	4.44524	+	15.1532i	0.211678	+	0.721583i
$442$	−7.24234	−	5.26187i	−0.344483	−	0.250281i
$443$	10.4747	+	3.40344i	0.497668	+	0.161702i	0.547087	−	0.837076i	$-0.315737\pi$
$443$	10.4747	+	3.40344i	0.497668	+	0.161702i	−0.0494185	+	0.998778i	$0.515737\pi$
$444$	3.55196	−	1.15410i	0.168569	−	0.0547712i
$445$	−22.0846	+	4.70848i	−1.04691	+	0.223203i
$446$	8.31731	−	6.04288i	0.393836	−	0.286139i
$447$	−0.666823	+	0.216664i	−0.0315397	+	0.0102479i
$448$	−1.52414	−	2.16264i	−0.0720087	−	0.102175i
$449$	−9.61952	−	6.98899i	−0.453973	−	0.329831i	0.337189	−	0.941437i	$-0.390524\pi$
$449$	−9.61952	−	6.98899i	−0.453973	−	0.329831i	−0.791162	+	0.611606i	$0.790524\pi$
$450$	−7.55804	−	8.37324i	−0.356289	−	0.394718i
$451$	0.896036	−	5.74256i	0.0421927	−	0.270407i
$452$		−	0.298496i		−	0.0140401i
$453$	11.9772	−	16.4852i	0.562737	−	0.774540i
$454$	15.6561	+	5.08698i	0.734778	+	0.238744i
$455$	12.1332	+	11.2315i	0.568811	+	0.526541i
$456$	−1.61535	+	1.17362i	−0.0756456	+	0.0549598i
$457$	21.9291	−	15.9324i	1.02580	−	0.745286i	0.0583347	−	0.998297i	$-0.481421\pi$
$457$	21.9291	−	15.9324i	1.02580	−	0.745286i	0.967463	+	0.253011i	$0.0814209\pi$
$458$	20.7920	−	6.75574i	0.971548	−	0.315675i
$459$	−13.8115	−	4.48763i	−0.644667	−	0.209465i
$460$	−5.68358	−	9.83022i	−0.264998	−	0.458337i
$461$	−8.89628			−0.414341			−0.207170	−	0.978305i	$-0.566425\pi$
$461$	−8.89628			−0.414341			−0.207170	+	0.978305i	$0.566425\pi$
$462$	−6.78518	+	3.35433i	−0.315675	+	0.156058i
$463$			16.3872i			0.761576i	0.924662	+	0.380788i	$0.124347\pi$
$463$			16.3872i			0.761576i	−0.924662	+	0.380788i	$0.875653\pi$
$464$	3.05708	−	4.20771i	0.141922	−	0.195338i
$465$	5.21625	−	5.80043i	0.241898	−	0.268989i
$466$	−4.98913	−	15.3550i	−0.231117	−	0.711305i
$467$	−1.83858	+	1.33581i	−0.0850792	+	0.0618137i	−0.629512	−	0.776991i	$-0.716745\pi$
$467$	−1.83858	+	1.33581i	−0.0850792	+	0.0618137i	0.544432	+	0.838805i	$0.316745\pi$
$468$	3.70583	+	5.10064i	0.171302	+	0.235777i
$469$	6.51140	−	19.0994i	0.300669	−	0.881926i
$470$	12.5507	+	11.2867i	0.578922	+	0.520617i
$471$	14.2929	+	10.3844i	0.658583	+	0.478489i
$472$			9.67403i			0.445283i
$473$	−30.7174	+	4.93741i	−1.41239	+	0.227022i
$474$		−	10.9810i		−	0.504372i
$475$	−1.22402	−	11.5091i	−0.0561620	−	0.528074i
$476$	6.92742	−	4.88215i	0.317518	−	0.223773i
$477$	3.93234	−	1.27770i	0.180050	−	0.0585017i
$478$	11.8604	+	16.3244i	0.542482	+	0.746662i
$479$	−18.1327	+	13.1742i	−0.828504	+	0.601943i	−0.919136	−	0.393941i	$-0.871111\pi$
$479$	−18.1327	+	13.1742i	−0.828504	+	0.601943i	0.0906319	+	0.995884i	$0.471111\pi$
$480$	−1.91833	−	0.200427i	−0.0875592	−	0.00914820i
$481$	3.73924	−	11.5082i	0.170494	−	0.524728i
$482$	5.21335	+	3.78772i	0.237461	+	0.172526i
$483$	9.27661	+	6.94621i	0.422100	+	0.316063i
$484$	6.50639	+	8.86943i	0.295745	+	0.403156i
$485$	−2.30840	+	5.19338i	−0.104819	+	0.235819i
$486$	12.9973	+	9.44311i	0.589571	+	0.428348i
$487$	17.9940	+	5.84661i	0.815387	+	0.264935i	0.686878	−	0.726773i	$-0.258981\pi$
$487$	17.9940	+	5.84661i	0.815387	+	0.264935i	0.128509	+	0.991708i	$0.458981\pi$
$488$	−2.44464	−	7.52384i	−0.110664	−	0.340588i
$489$	8.99614	+	12.3821i	0.406819	+	0.559939i
$490$	−13.7707	+	7.44098i	−0.622096	+	0.336149i
$491$	7.55842	−	2.45588i	0.341107	−	0.110832i	−0.133454	−	0.991055i	$-0.542607\pi$
$491$	7.55842	−	2.45588i	0.341107	−	0.110832i	0.474561	+	0.880223i	$0.342607\pi$
$492$	−0.467100	+	1.43759i	−0.0210585	+	0.0648114i
$493$	13.4783	+	9.79252i	0.607030	+	0.441033i
$494$			6.46915i			0.291061i
$495$	4.28317	−	16.1732i	0.192514	−	0.726930i
$496$			4.04451i			0.181604i
$497$	−19.7230	+	6.09572i	−0.884699	+	0.273430i
$498$	−6.98501	−	2.26957i	−0.313006	−	0.101702i
$499$	−0.395005	−	1.21570i	−0.0176828	−	0.0544222i	0.941826	−	0.336102i	$-0.109109\pi$
$499$	−0.395005	−	1.21570i	−0.0176828	−	0.0544222i	−0.959509	+	0.281679i	$0.909109\pi$
$500$	6.55488	−	9.05724i	0.293143	−	0.405052i
$501$	−7.60200	−	10.4633i	−0.339633	−	0.467464i
$502$	−3.12448	+	1.01521i	−0.139452	+	0.0453108i
$503$	−8.05349	−	2.61674i	−0.359087	−	0.116675i	0.123917	−	0.992293i	$-0.460454\pi$
$503$	−8.05349	−	2.61674i	−0.359087	−	0.116675i	−0.483004	+	0.875618i	$0.660454\pi$
$504$	−5.70259	+	1.76248i	−0.254014	+	0.0785069i
$505$	16.3845	−	36.8615i	0.729103	−	1.64032i
$506$	7.61176	−	15.0240i	0.338384	−	0.667899i
$507$	4.47649			0.198808
$508$	−11.4465	−	8.31638i	−0.507857	−	0.368980i
$509$	−38.8422	−	12.6206i	−1.72165	−	0.559398i	−0.729448	−	0.684036i	$-0.760223\pi$
$509$	−38.8422	−	12.6206i	−1.72165	−	0.559398i	−0.992202	+	0.124638i	$0.960223\pi$
$510$	0.642013	−	6.14483i	0.0284288	−	0.272097i
$511$	−15.3843	−	0.221644i	−0.680562	−	0.00980494i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	3.24298	+	9.98086i	0.143181	+	0.440666i
$514$	−4.54048	+	13.9742i	−0.200272	+	0.616374i
$515$	28.9403	−	16.7325i	1.27526	−	0.737323i
$516$	8.09138			0.356203
$517$	−3.85977	+	24.7367i	−0.169753	+	1.08792i
$518$	9.16977	+	6.86621i	0.402897	+	0.301684i
$519$	−5.27919	+	7.26618i	−0.231731	+	0.318950i
$520$	−4.17861	+	4.64658i	−0.183244	+	0.203766i
$521$	30.9309	−	10.0501i	1.35511	−	0.440302i	0.460702	−	0.887555i	$-0.347598\pi$
$521$	30.9309	−	10.0501i	1.35511	−	0.440302i	0.894407	+	0.447253i	$0.147598\pi$
$522$	−6.89669	−	9.49248i	−0.301860	−	0.415475i
$523$	2.72093	+	3.74504i	0.118978	+	0.163759i	0.864352	−	0.502887i	$-0.167729\pi$
$523$	2.72093	+	3.74504i	0.118978	+	0.163759i	−0.745374	+	0.666647i	$0.767729\pi$
$524$	−2.15596	−	6.63537i	−0.0941837	−	0.289868i
$525$	−2.51923	+	11.1292i	−0.109948	+	0.485717i
$526$	−8.48053	−	6.16146i	−0.369769	−	0.268653i
$527$	−12.9555			−0.564349
$528$	−1.30463	−	2.54603i	−0.0567767	−	0.110802i
$529$	−2.78727			−0.121185
$530$	2.05131	+	3.54791i	0.0891030	+	0.154111i
$531$	20.7562	+	6.74409i	0.900741	+	0.292668i
$532$	−5.79677	−	1.97625i	−0.251322	−	0.0856814i
$533$	2.87863	+	3.96209i	0.124687	+	0.171617i
$534$	5.12001	+	7.04709i	0.221565	+	0.304957i
$535$	26.7408	+	2.79389i	1.15611	+	0.120790i
$536$	7.25358	+	2.35683i	0.313307	+	0.101800i
$537$	−14.4076	−	10.4677i	−0.621732	−	0.451715i
$538$			27.1494i			1.17049i
$539$	−20.3992	−	11.0848i	−0.878655	−	0.477456i
$540$	−4.11759	+	9.26365i	−0.177193	+	0.398644i
$541$	11.5465	−	15.8925i	0.496425	−	0.683270i	−0.485132	−	0.874441i	$-0.661228\pi$
$541$	11.5465	−	15.8925i	0.496425	−	0.683270i	0.981557	+	0.191171i	$0.0612285\pi$
$542$	−6.92573	+	21.3152i	−0.297485	+	0.915566i
$543$	−12.8211	+	4.16583i	−0.550207	+	0.178773i
$544$	1.88281	+	2.59146i	0.0807247	+	0.111108i
$545$	20.4390	−	4.35763i	0.875511	−	0.186660i
$546$	2.05805	−	6.03672i	0.0880766	−	0.258348i
$547$	6.81461	−	20.9732i	0.291372	−	0.896750i	−0.693044	−	0.720895i	$-0.743731\pi$
$547$	6.81461	−	20.9732i	0.291372	−	0.896750i	0.984416	−	0.175855i	$-0.0562690\pi$
$548$	0.368589	−	0.507319i	0.0157453	−	0.0216716i
$549$	−17.8471			−0.761694
$550$	16.5634	+	0.809462i	0.706264	+	0.0345156i
$551$		−	12.0393i		−	0.512893i
$552$	−2.57464	+	3.54369i	−0.109584	+	0.150829i
$553$	27.5315	−	19.4030i	1.17076	−	0.825101i
$554$	3.51842	+	10.8286i	0.149483	+	0.460062i
$555$	8.16759	−	1.74134i	0.346695	−	0.0739160i
$556$	4.15236	−	3.01687i	0.176099	−	0.127944i
$557$	9.82568	+	30.2403i	0.416328	+	1.28132i	0.911058	+	0.412278i	$0.135267\pi$
$557$	9.82568	+	30.2403i	0.416328	+	1.28132i	−0.494730	+	0.869046i	$0.664733\pi$
$558$	8.67772	+	2.81956i	0.367357	+	0.119362i
$559$	15.4092	−	21.2089i	0.651740	−	0.897043i
$560$	−2.88711	−	5.16378i	−0.122003	−	0.218209i
$561$	8.15550	−	4.17902i	0.344325	−	0.176438i
$562$			2.43144i			0.102564i
$563$	−4.85082	+	6.67658i	−0.204438	+	0.281384i	−0.898908	−	0.438137i	$-0.855639\pi$
$563$	−4.85082	+	6.67658i	−0.204438	+	0.281384i	0.694471	+	0.719521i	$0.255639\pi$
$564$	2.01209	−	6.19257i	0.0847241	−	0.260754i
$565$	0.0693587	−	0.663845i	0.00291794	−	0.0279282i
$566$	−11.1327	−	15.3229i	−0.467944	−	0.644070i
$567$	−0.108903	+	7.55898i	−0.00457350	+	0.317447i
$568$	−2.41111	−	7.42065i	−0.101168	−	0.311363i
$569$	24.8820	+	8.08464i	1.04311	+	0.338926i	0.779959	−	0.625830i	$-0.215240\pi$
$569$	24.8820	+	8.08464i	1.04311	+	0.338926i	0.263147	+	0.964756i	$0.415240\pi$
$570$	−3.86518	+	2.23474i	−0.161894	+	0.0936031i
$571$			4.20124i			0.175816i	0.996129	+	0.0879082i	$0.0280182\pi$
$571$			4.20124i			0.175816i	−0.996129	+	0.0879082i	$0.971982\pi$
$572$	−9.15812	−	1.42898i	−0.382920	−	0.0597487i
$573$	5.81060			0.242741
$574$	−4.42967	+	1.36906i	−0.184891	+	0.0571434i
$575$	−10.3559	−	23.1827i	−0.431871	−	0.966785i
$576$	−0.697133	−	2.14556i	−0.0290472	−	0.0893982i
$577$	9.87724	−	7.17623i	0.411195	−	0.298750i	−0.362891	−	0.931832i	$-0.618210\pi$
$577$	9.87724	−	7.17623i	0.411195	−	0.298750i	0.774085	+	0.633081i	$0.218210\pi$
$578$	5.45225	−	3.96129i	0.226784	−	0.164768i
$579$	2.22448	+	6.84625i	0.0924463	+	0.284520i
$580$	7.77654	−	8.64745i	0.322903	−	0.359066i
$581$	−6.65204	−	21.5231i	−0.275973	−	0.892927i
$582$	2.19235			0.0908760
$583$	−2.74722	+	5.42244i	−0.113778	+	0.224575i
$584$		−	5.81533i		−	0.240640i
$585$	7.05645	+	12.2047i	0.291748	+	0.504603i
$586$	3.98532	+	1.29491i	0.164632	+	0.0534922i
$587$	3.64820	+	11.2280i	0.150577	+	0.463430i	0.997686	−	0.0679902i	$-0.0216587\pi$
$587$	3.64820	+	11.2280i	0.150577	+	0.463430i	−0.847109	+	0.531420i	$0.821659\pi$
$588$	4.78057	+	3.68830i	0.197148	+	0.152103i
$589$	5.50299	+	7.57421i	0.226747	+	0.312090i
$590$	−2.24786	+	21.5147i	−0.0925428	+	0.885745i
$591$	−1.05495	+	3.24681i	−0.0433950	+	0.133556i
$592$	−2.54499	+	3.50287i	−0.104598	+	0.143967i
$593$		−	13.8550i		−	0.568958i	−0.958682	−	0.284479i	$-0.908179\pi$
$593$		−	13.8550i		−	0.568958i	0.958682	−	0.284479i	$-0.0918206\pi$
$594$	−14.8459	+	2.38627i	−0.609133	+	0.0979098i
$595$	16.5407	−	9.24807i	0.678104	−	0.379134i
$596$	0.477780	−	0.657608i	0.0195706	−	0.0269367i
$597$	2.27530	+	0.739290i	0.0931219	+	0.0302571i
$598$	4.38550	+	13.4972i	0.179336	+	0.551940i
$599$	7.50680	−	5.45401i	0.306720	−	0.222845i	−0.423768	−	0.905771i	$-0.639293\pi$
$599$	7.50680	−	5.45401i	0.306720	−	0.222845i	0.730488	+	0.682926i	$0.239293\pi$
$600$	−4.21971	−	0.891485i	−0.172269	−	0.0363947i
$601$	−1.98279	−	6.10239i	−0.0808795	−	0.248922i	0.902438	−	0.430820i	$-0.141776\pi$
$601$	−1.98279	−	6.10239i	−0.0808795	−	0.248922i	−0.983317	+	0.181899i	$0.941776\pi$
$602$	14.2972	+	20.2867i	0.582712	+	0.826825i
$603$	10.1134	−	13.9199i	0.411851	−	0.566864i
$604$			23.6233i			0.961219i
$605$	12.4091	+	21.2371i	0.504500	+	0.863411i
$606$	−15.5609			−0.632117
$607$	−10.4609	+	14.3982i	−0.424594	+	0.584403i	−0.966702	−	0.255906i	$-0.917626\pi$
$607$	−10.4609	+	14.3982i	−0.424594	+	0.584403i	0.542108	+	0.840309i	$0.317626\pi$
$608$	0.715313	−	2.20151i	0.0290098	−	0.0892829i
$609$	−3.83012	+	11.2346i	−0.155204	+	0.455247i
$610$	−3.68856	−	17.3008i	−0.149345	−	0.700488i
$611$	−12.4000	−	17.0671i	−0.501650	−	0.690463i
$612$	6.87270	−	2.23307i	0.277812	−	0.0902667i
$613$	0.942644	−	2.90116i	0.0380731	−	0.117177i	−0.930214	−	0.367018i	$-0.880379\pi$
$613$	0.942644	−	2.90116i	0.0380731	−	0.117177i	0.968287	+	0.249842i	$0.0803786\pi$
$614$	11.7220	−	16.1339i	0.473061	−	0.651112i
$615$	−1.37285	+	3.08860i	−0.0553587	+	0.124544i
$616$	4.07816	−	7.76972i	0.164314	−	0.313051i
$617$			26.7836i			1.07827i	0.842220	+	0.539133i	$0.181248\pi$
$617$			26.7836i			1.07827i	−0.842220	+	0.539133i	$0.818752\pi$
$618$	−10.4327	−	7.57977i	−0.419663	−	0.304903i
$619$	−14.4491	−	4.69479i	−0.580758	−	0.188700i	0.00388225	−	0.999992i	$-0.498764\pi$
$619$	−14.4491	−	4.69479i	−0.580758	−	0.188700i	−0.584640	+	0.811293i	$0.698764\pi$
$620$	−0.939783	+	8.99484i	−0.0377426	+	0.361241i
$621$	13.5322	+	18.6255i	0.543029	+	0.747416i
$622$	−4.92655	−	6.78081i	−0.197537	−	0.271886i
$623$	−8.62156	+	25.2889i	−0.345415	+	1.01318i
$624$	2.29263	+	0.744922i	0.0917788	+	0.0298208i
$625$	16.6823	−	18.6199i	0.667294	−	0.744795i
$626$	−24.5162			−0.979864
$627$	−5.90734	−	2.99289i	−0.235916	−	0.119525i
$628$	−20.4818			−0.817314
$629$	−11.2205	−	8.15216i	−0.447390	−	0.325048i
$630$	−13.0919	+	2.59462i	−0.521593	+	0.103372i
$631$	−2.21702	−	6.82330i	−0.0882583	−	0.271631i	0.897180	−	0.441665i	$-0.145612\pi$
$631$	−2.21702	−	6.82330i	−0.0882583	−	0.271631i	−0.985438	+	0.170034i	$0.945612\pi$
$632$	7.48280	+	10.2992i	0.297650	+	0.409680i
$633$	−11.9489	−	16.4462i	−0.474925	−	0.653678i
$634$	−13.6488	+	4.43476i	−0.542063	+	0.176127i
$635$	−23.5242	−	21.1550i	−0.933530	−	0.839511i
$636$	0.929234	−	1.27898i	0.0368465	−	0.0507149i
$637$	18.7718	−	5.50675i	0.743765	−	0.218185i
$638$	17.0436	+	2.65938i	0.674763	+	0.105286i
$639$	−17.6023			−0.696335
$640$	1.93580	−	1.11923i	0.0765193	−	0.0442414i
$641$	−2.27829	+	7.01185i	−0.0899869	+	0.276951i	−0.985915	−	0.167248i	$-0.946512\pi$
$641$	−2.27829	+	7.01185i	−0.0899869	+	0.276951i	0.895928	+	0.444200i	$0.146512\pi$
$642$	−3.20498	−	9.86390i	−0.126490	−	0.389297i
$643$	11.2162	−	8.14903i	0.442323	−	0.321366i	−0.344234	−	0.938884i	$-0.611861\pi$
$643$	11.2162	−	8.14903i	0.442323	−	0.321366i	0.786557	+	0.617517i	$0.211861\pi$
$644$	−13.4340	−	0.193546i	−0.529375	−	0.00762677i
$645$	17.9949	+	1.88011i	0.708549	+	0.0740294i
$646$	7.05192	+	2.29131i	0.277454	+	0.0901503i
$647$	−1.70773	−	1.24074i	−0.0671377	−	0.0487784i	0.553710	−	0.832709i	$-0.313212\pi$
$647$	−1.70773	−	1.24074i	−0.0671377	−	0.0487784i	−0.620848	+	0.783931i	$0.713212\pi$
$648$	−2.85732			−0.112246
$649$	−28.5546	+	14.6319i	−1.12086	+	0.574351i
$650$	−10.3727	+	9.36288i	−0.406853	+	0.367242i
$651$	−2.72553	−	8.81859i	−0.106822	−	0.345628i
$652$	−16.8752	−	5.48308i	−0.660884	−	0.214734i
$653$	−44.7435	+	14.5381i	−1.75095	+	0.568918i	−0.996200	−	0.0870955i	$-0.972241\pi$
$653$	−44.7435	+	14.5381i	−1.75095	+	0.568918i	−0.754749	+	0.656013i	$0.772241\pi$
$654$	−4.73850	−	6.52199i	−0.185290	−	0.255030i
$655$	−3.25298	−	15.2578i	−0.127105	−	0.596171i
$656$	−0.541521	−	1.66663i	−0.0211428	−	0.0650710i
$657$	−12.4771	−	4.05406i	−0.486779	−	0.158164i
$658$	19.0813	−	5.89738i	0.743867	−	0.229904i
$659$			4.07489i			0.158735i	0.996845	+	0.0793676i	$0.0252901\pi$
$659$			4.07489i			0.158735i	−0.996845	+	0.0793676i	$0.974710\pi$
$660$	−2.30985	−	5.96541i	−0.0899109	−	0.232203i
$661$			21.7937i			0.847677i	0.905738	+	0.423838i	$0.139318\pi$
$661$			21.7937i			0.847677i	−0.905738	+	0.423838i	$0.860682\pi$
$662$	−20.3922	−	14.8158i	−0.792566	−	0.575833i
$663$	−2.38615	+	7.34382i	−0.0926705	+	0.285210i
$664$	8.09789	−	2.63116i	0.314259	−	0.102109i
$665$	−12.4326	−	5.74205i	−0.482116	−	0.222667i
$666$	5.74142	+	7.90238i	0.222475	+	0.306211i
$667$	−8.16157	−	25.1187i	−0.316017	−	0.972601i
$668$	14.2600	+	4.63337i	0.551738	+	0.179270i
$669$	−7.17427	−	5.21241i	−0.277373	−	0.201524i
$670$	15.5841	+	6.92695i	0.602065	+	0.267611i
$671$	18.5104	−	18.5955i	0.714587	−	0.717872i
$672$	−1.36787	+	1.82678i	−0.0527668	+	0.0704696i
$673$	−5.73674	−	4.16799i	−0.221135	−	0.160664i	0.471702	−	0.881758i	$-0.343640\pi$
$673$	−5.73674	−	4.16799i	−0.221135	−	0.160664i	−0.692838	+	0.721094i	$0.743640\pi$
$674$	2.77031	−	8.52613i	0.106708	−	0.328414i
$675$	−11.3099	+	19.6452i	−0.435317	+	0.756146i
$676$	−4.19856	+	3.05043i	−0.161483	+	0.117324i
$677$	22.7593	+	31.3255i	0.874712	+	1.20394i	0.977858	+	0.209271i	$0.0671090\pi$
$677$	22.7593	+	31.3255i	0.874712	+	1.20394i	−0.103146	+	0.994666i	$0.532891\pi$
$678$	−0.244873	+	0.0795639i	−0.00940428	+	0.00305564i
$679$	3.87382	+	5.49667i	0.148664	+	0.210943i
$680$	3.58514	+	6.20081i	0.137484	+	0.237790i
$681$		−	14.1995i		−	0.544125i
$682$	−11.9381	+	6.11728i	−0.457132	+	0.234243i
$683$		−	6.28478i		−	0.240480i	−0.992745	−	0.120240i	$-0.961634\pi$
$683$		−	6.28478i		−	0.240480i	0.992745	−	0.120240i	$-0.0383665\pi$
$684$	−4.22479	−	3.06949i	−0.161539	−	0.117365i
$685$	0.937609	−	1.04261i	0.0358242	−	0.0398362i
$686$	−0.800166	+	18.5030i	−0.0305505	+	0.706447i
$687$	−11.0842	−	15.2561i	−0.422888	−	0.582056i
$688$	−7.58901	+	5.51374i	−0.289328	+	0.210209i
$689$	−1.58281	−	4.87137i	−0.0603001	−	0.185585i
$690$	−6.54931	+	7.28278i	−0.249328	+	0.277251i
$691$	−10.7047	+	14.7338i	−0.407226	+	0.560499i	−0.962539	−	0.271143i	$-0.912599\pi$
$691$	−10.7047	+	14.7338i	−0.407226	+	0.560499i	0.555313	+	0.831642i	$0.312599\pi$
$692$		−	10.4125i		−	0.395823i
$693$	−13.8274	−	14.1665i	−0.525258	−	0.538139i
$694$	−4.33398			−0.164516
$695$	9.93569	−	5.74456i	0.376882	−	0.217903i
$696$	−4.26668	−	1.38633i	−0.161728	−	0.0525486i
$697$	5.33859	−	1.73461i	0.202213	−	0.0657031i
$698$	15.0164	−	10.9101i	0.568380	−	0.412952i
$699$	−11.2667	+	8.18570i	−0.426144	+	0.309612i
$700$	−5.22098	−	12.1549i	−0.197334	−	0.459412i
$701$	21.0859	+	6.85122i	0.796403	+	0.258767i	0.678828	−	0.734297i	$-0.262488\pi$
$701$	21.0859	+	6.85122i	0.796403	+	0.258767i	0.117574	+	0.993064i	$0.462488\pi$
$702$	7.44732	−	10.2504i	0.281081	−	0.386875i
$703$			10.0226i			0.378010i
$704$	2.95858	+	1.49893i	0.111506	+	0.0564932i
$705$	5.91371	−	13.3045i	0.222723	−	0.501077i
$706$	−8.84216	−	6.42420i	−0.332779	−	0.241778i
$707$	−27.4956	−	39.0142i	−1.03408	−	1.46728i
$708$	7.93612	−	2.57860i	0.298258	−	0.0969098i
$709$	20.7210	−	15.0547i	0.778195	−	0.565392i	−0.126242	−	0.992000i	$-0.540291\pi$
$709$	20.7210	−	15.0547i	0.778195	−	0.565392i	0.904437	+	0.426608i	$0.140291\pi$
$710$	−3.63796	−	17.0635i	−0.136530	−	0.640381i
$711$	27.3140	−	8.87486i	1.02436	−	0.332833i
$712$	−9.60425	−	3.12061i	−0.359935	−	0.116950i
$713$	16.6160	+	12.0722i	0.622274	+	0.452108i
$714$	−5.85159	−	4.38160i	−0.218990	−	0.163977i
$715$	−20.0353	−	5.30598i	−0.749277	−	0.198432i
$716$	20.6461			0.771581
$717$	10.2304	−	14.0810i	0.382063	−	0.525864i
$718$	−20.7589	−	6.74498i	−0.774715	−	0.251720i
$719$	−7.34449	+	2.38637i	−0.273903	+	0.0889966i	−0.442748	−	0.896646i	$-0.645996\pi$
$719$	−7.34449	+	2.38637i	−0.273903	+	0.0889966i	0.168845	+	0.985643i	$0.445996\pi$
$720$	−1.05186	−	4.93362i	−0.0392004	−	0.183865i
$721$	0.569801	−	39.5500i	0.0212205	−	1.47292i
$722$	4.21551	+	12.9740i	0.156885	+	0.482843i
$723$	1.71766	−	5.28640i	0.0638803	−	0.196603i
$724$	9.18635	−	12.6439i	0.341408	−	0.469908i
$725$	19.3041	−	17.4247i	0.716935	−	0.647135i
$726$	5.54180	−	7.70168i	0.205676	−	0.285836i
$727$	44.9203			1.66600			0.833001	−	0.553272i	$-0.186621\pi$
$727$	44.9203			1.66600			0.833001	+	0.553272i	$0.186621\pi$
$728$	2.18335	+	7.06435i	0.0809203	+	0.261822i
$729$	1.63339	−	5.02704i	0.0604958	−	0.186187i
$730$	1.35125	−	12.9331i	0.0500120	−	0.478675i
$731$	−17.6618	−	24.3093i	−0.653243	−	0.899113i
$732$	−5.52059	+	4.01095i	−0.204047	+	0.148249i
$733$	−48.4375	+	15.7383i	−1.78908	+	0.581308i	−0.999478	−	0.0323109i	$-0.989713\pi$
$733$	−48.4375	+	15.7383i	−1.78908	+	0.581308i	−0.789603	+	0.613618i	$0.789713\pi$
$734$	−5.68237	+	17.4885i	−0.209740	+	0.645513i
$735$	9.77480	+	9.31345i	0.360549	+	0.343532i
$736$		−	5.07812i		−	0.187182i
$737$	4.01437	+	24.9749i	0.147871	+	0.919962i
$738$	−3.95336			−0.145525
$739$	21.5089	−	29.6045i	0.791219	−	1.08902i	−0.202736	−	0.979233i	$-0.564983\pi$
$739$	21.5089	−	29.6045i	0.791219	−	1.08902i	0.993955	−	0.109786i	$-0.0350165\pi$
$740$	−6.47388	+	7.19891i	−0.237985	+	0.264637i
$741$	5.30700	−	1.72435i	0.194957	−	0.0633455i
$742$	4.84859	+	0.0698542i	0.177997	+	0.00256443i
$743$	14.0197	−	10.1859i	0.514332	−	0.373684i	−0.300133	−	0.953897i	$-0.597031\pi$
$743$	14.0197	−	10.1859i	0.514332	−	0.373684i	0.814464	+	0.580214i	$0.197031\pi$
$744$	3.31793	−	1.07806i	0.121641	−	0.0395236i
$745$	1.21537	−	1.35148i	0.0445276	−	0.0495143i
$746$	−27.0568	−	19.6579i	−0.990619	−	0.719727i
$747$		−	19.2088i		−	0.702811i
$748$	−4.80142	+	9.47700i	−0.175557	+	0.346513i
$749$	19.0677	−	25.4647i	0.696718	−	0.930461i
$750$	−9.17734	−	2.96312i	−0.335109	−	0.108198i
$751$	7.90135	−	24.3179i	0.288324	−	0.887371i	−0.697058	−	0.717015i	$-0.745508\pi$
$751$	7.90135	−	24.3179i	0.288324	−	0.887371i	0.985382	−	0.170357i	$-0.0544919\pi$
$752$	2.33266	+	7.17920i	0.0850634	+	0.261798i
$753$	1.66565	+	2.29258i	0.0606998	+	0.0835462i
$754$	−11.7593	+	8.54360i	−0.428247	+	0.311140i
$755$	−5.48911	+	52.5373i	−0.199769	+	1.91203i
$756$	6.90990	+	9.80464i	0.251311	+	0.356591i
$757$	18.8993	−	26.0126i	0.686905	−	0.945444i	−0.313086	−	0.949725i	$-0.601363\pi$
$757$	18.8993	−	26.0126i	0.686905	−	0.945444i	0.999991	+	0.00428091i	$0.00136266\pi$
$758$	−30.5686			−1.11030
$759$	−14.3539	−	2.23970i	−0.521014	−	0.0812960i
$760$	2.10237	−	4.72986i	0.0762610	−	0.171570i
$761$	−3.30634	−	2.40220i	−0.119855	−	0.0870795i	0.526243	−	0.850334i	$-0.323600\pi$
$761$	−3.30634	−	2.40220i	−0.119855	−	0.0870795i	−0.646098	+	0.763255i	$0.723600\pi$
$762$	−3.77131	+	11.6069i	−0.136620	+	0.420474i
$763$	7.97913	−	23.4045i	0.288864	−	0.847301i
$764$	−5.44984	+	3.95954i	−0.197168	+	0.143251i
$765$	15.8035	−	3.36933i	0.571377	−	0.121819i
$766$	4.37049	+	13.4510i	0.157912	+	0.486004i
$767$	8.35455	−	25.7127i	0.301665	−	0.928431i
$768$	−0.697835	−	0.507006i	−0.0251809	−	0.0182950i
$769$	−43.4712			−1.56761			−0.783805	−	0.621007i	$-0.786724\pi$
$769$	−43.4712			−1.56761			−0.783805	+	0.621007i	$0.786724\pi$
$770$	10.8750	−	16.3320i	0.391909	−	0.588564i
$771$	12.6740			0.456444
$772$	−6.75164	−	4.90535i	−0.242997	−	0.176548i
$773$	8.69833	−	26.7707i	0.312857	−	0.962876i	−0.663770	−	0.747937i	$-0.731045\pi$
$773$	8.69833	−	26.7707i	0.312857	−	0.962876i	0.976627	−	0.214939i	$-0.0689553\pi$
$774$	6.53949	+	20.1265i	0.235057	+	0.723431i
$775$	−4.18008	+	19.7858i	−0.150153	+	0.710727i
$776$	−2.05624	+	1.49394i	−0.0738146	+	0.0536295i
$777$	3.18853	−	9.35264i	0.114388	−	0.335524i
$778$	−9.55492	+	29.4070i	−0.342560	+	1.05429i
$779$	−3.28174	−	2.38432i	−0.117581	−	0.0854273i
$780$	4.92564	+	2.18940i	0.176366	+	0.0783929i
$781$	18.2565	−	18.3405i	0.653270	−	0.656274i
$782$	16.2663			0.581683
$783$	−13.8597	+	19.0763i	−0.495307	+	0.681731i
$784$	−6.99709	−	0.201658i	−0.249896	−	0.00720206i
$785$	−45.5508	−	4.75916i	−1.62578	−	0.169862i
$786$	−4.86868	+	3.53730i	−0.173660	+	0.126171i
$787$	−21.9744	−	30.2451i	−0.783302	−	1.07812i	−0.994910	−	0.100768i	$-0.967870\pi$
$787$	−21.9744	−	30.2451i	−0.783302	−	1.07812i	0.211608	−	0.977355i	$-0.432130\pi$
$788$	−1.22303	−	3.76411i	−0.0435688	−	0.134091i
$789$	−2.79410	+	8.59937i	−0.0994727	+	0.306146i
$790$	14.2483	+	24.6437i	0.506933	+	0.876784i
$791$	−0.632166	−	0.473358i	−0.0224772	−	0.0168307i
$792$	5.27857	−	5.30284i	0.187566	−	0.188428i
$793$			22.1089i			0.785110i
$794$	1.92650	+	1.39968i	0.0683689	+	0.0496729i
$795$	2.36377	−	2.62849i	0.0838341	−	0.0932229i
$796$	−2.63781	+	0.857077i	−0.0934948	+	0.0303783i
$797$	−22.4845	+	16.3360i	−0.796443	+	0.578650i	−0.909868	−	0.414897i	$-0.863818\pi$
$797$	−22.4845	+	16.3360i	−0.796443	+	0.578650i	0.113425	+	0.993547i	$0.463818\pi$
$798$	−0.0761008	+	5.28217i	−0.00269394	+	0.186987i
$799$	−22.9966	+	7.47204i	−0.813560	+	0.264342i
$800$	4.56521	−	2.03932i	0.161405	−	0.0721009i
$801$	−13.3909	+	18.4310i	−0.473144	+	0.651227i
$802$	−16.4554			−0.581062
$803$	17.1650	−	8.79563i	0.605738	−	0.310391i
$804$		−	6.57872i		−	0.232013i
$805$	−29.8318	−	3.55197i	−1.05143	−	0.125191i
$806$	3.49287	−	10.7499i	0.123031	−	0.378650i
$807$	22.2721	−	7.23664i	0.784015	−	0.254742i
$808$	14.5947	−	10.6037i	0.513441	−	0.373037i
$809$	−4.46307	−	6.14288i	−0.156913	−	0.215972i	0.723321	−	0.690512i	$-0.242615\pi$
$809$	−4.46307	−	6.14288i	−0.156913	−	0.215972i	−0.880234	+	0.474539i	$0.842615\pi$
$810$	−6.35457	−	0.663927i	−0.223277	−	0.0233280i
$811$	−9.16191	+	28.1975i	−0.321718	+	0.990147i	0.651182	+	0.758922i	$0.274273\pi$
$811$	−9.16191	+	28.1975i	−0.321718	+	0.990147i	−0.972900	+	0.231225i	$0.925727\pi$
$812$	−4.06329	−	13.1470i	−0.142594	−	0.461370i
$813$	19.3320			0.678004
$814$	−14.1886	−	2.21391i	−0.497310	−	0.0775974i
$815$	−36.2557	−	16.1153i	−1.26998	−	0.564494i
$816$	1.62406	−	2.23532i	0.0568533	−	0.0782519i
$817$	−6.71002	+	20.6513i	−0.234754	+	0.722498i
$818$	4.68844	+	14.4295i	0.163928	+	0.504517i
$819$	16.6790	+	0.240297i	0.582813	+	0.00839665i
$820$	−0.817064	−	3.83235i	−0.0285331	−	0.133831i
$821$	−17.8574	+	5.80223i	−0.623228	+	0.202499i	−0.603573	−	0.797308i	$-0.706257\pi$
$821$	−17.8574	+	5.80223i	−0.623228	+	0.202499i	−0.0196551	+	0.999807i	$0.506257\pi$
$822$	−0.514429	−	0.167148i	−0.0179428	−	0.00582995i
$823$	−20.8596	+	28.7108i	−0.727121	+	1.00080i	0.272136	+	0.962259i	$0.412270\pi$
$823$	−20.8596	+	28.7108i	−0.727121	+	1.00080i	−0.999257	+	0.0385380i	$0.987730\pi$
$824$	14.9501			0.520810
$825$	−3.75090	−	13.8036i	−0.130590	−	0.480579i
$826$	20.4880	+	15.3411i	0.712868	+	0.533786i
$827$	−0.318020	−	0.231055i	−0.0110586	−	0.00803457i	0.582242	−	0.813015i	$-0.302176\pi$
$827$	−0.318020	−	0.231055i	−0.0110586	−	0.00803457i	−0.593301	+	0.804981i	$0.702176\pi$
$828$	−10.8954	−	3.54012i	−0.378641	−	0.123028i
$829$	−5.89445	+	1.91522i	−0.204723	+	0.0665184i	−0.409583	−	0.912273i	$-0.634326\pi$
$829$	−5.89445	+	1.91522i	−0.204723	+	0.0665184i	0.204861	+	0.978791i	$0.434326\pi$
$830$	18.6208	−	3.96998i	0.646337	−	0.137800i
$831$	7.94543	−	5.77269i	0.275624	−	0.200252i
$832$	−2.65791	+	0.863607i	−0.0921464	+	0.0299402i
$833$	0.645955	−	22.4133i	0.0223810	−	0.776574i
$834$	−3.58171	−	2.60226i	−0.124024	−	0.0901090i
$835$	30.6372	+	13.6179i	1.06024	+	0.471267i
$836$	7.58003	−	1.21839i	0.262161	−	0.0421388i
$837$		−	18.3364i		−	0.633798i
$838$	−20.4162	+	28.1005i	−0.705266	+	0.970716i
$839$	32.0522	+	10.4144i	1.10656	+	0.359545i	0.804626	−	0.593783i	$-0.202366\pi$
$839$	32.0522	+	10.4144i	1.10656	+	0.359545i	0.301939	+	0.953327i	$0.402366\pi$
$840$	−3.46656	+	3.74485i	−0.119608	+	0.129210i
$841$	−1.57708	+	1.14582i	−0.0543822	+	0.0395110i
$842$	−19.8406	+	14.4151i	−0.683753	+	0.496776i
$843$	1.99464	−	0.648099i	0.0686991	−	0.0223217i
$844$	22.4140	+	7.28275i	0.771522	+	0.250683i
$845$	−10.0462	+	5.80847i	−0.345601	+	0.199817i
$846$	17.0295			0.585488
$847$	29.1019	+	0.285757i	0.999952	+	0.00981873i
$848$			1.83278i			0.0629381i
$849$	−9.60278	+	13.2171i	−0.329567	+	0.453610i
$850$	6.53240	+	14.6234i	0.224059	+	0.501579i
$851$	6.79441	+	20.9110i	0.232909	+	0.716822i
$852$	−5.44487	+	3.95593i	−0.186538	+	0.135528i
$853$	−22.4411	−	30.8875i	−0.768369	−	1.05757i	−0.996471	−	0.0839319i	$-0.973252\pi$
$853$	−22.4411	−	30.8875i	−0.768369	−	1.05757i	0.228103	−	0.973637i	$-0.426748\pi$
$854$	−19.8110	−	6.75401i	−0.677918	−	0.231118i
$855$	−8.68255	−	7.80810i	−0.296937	−	0.267031i
$856$	9.72759	+	7.06751i	0.332482	+	0.241562i
$857$		−	41.5846i		−	1.42050i	−0.703949	−	0.710251i	$-0.748582\pi$
$857$		−	41.5846i		−	1.42050i	0.703949	−	0.710251i	$-0.251418\pi$
$858$	1.26882	+	7.89380i	0.0433168	+	0.269490i
$859$		−	14.1090i		−	0.481392i	−0.970601	−	0.240696i	$-0.922624\pi$
$859$		−	14.1090i		−	0.481392i	0.970601	−	0.240696i	$-0.0773758\pi$
$860$	−18.1589	+	10.4990i	−0.619212	+	0.358012i
$861$	2.30384	+	3.26897i	0.0785146	+	0.111406i
$862$	−26.7492	+	8.69135i	−0.911082	+	0.296028i
$863$	−17.4175	−	23.9731i	−0.592899	−	0.816055i	0.402136	−	0.915580i	$-0.368268\pi$
$863$	−17.4175	−	23.9731i	−0.592899	−	0.816055i	−0.995035	+	0.0995248i	$0.968268\pi$
$864$	−3.66780	+	2.66481i	−0.124781	+	0.0906587i
$865$	2.41944	−	23.1569i	0.0822635	−	0.787360i
$866$	8.77864	−	27.0179i	0.298310	−	0.918104i
$867$	−4.70295	−	3.41690i	−0.159721	−	0.116044i
$868$	8.56560	+	6.41381i	0.290735	+	0.217699i
$869$	−19.0822	+	37.6642i	−0.647319	+	1.27767i
$870$	−9.16680	−	4.07455i	−0.310784	−	0.138140i
$871$	−17.2440	−	12.5285i	−0.584290	−	0.424512i
$872$	8.88861	+	2.88808i	0.301006	+	0.0978028i
$873$	1.77187	+	5.45325i	0.0599687	+	0.184565i
$874$	−6.90932	−	9.50986i	−0.233711	−	0.321676i
$875$	−8.78695	−	28.2452i	−0.297053	−	0.954861i
$876$	−4.77063	+	1.55007i	−0.161185	+	0.0523721i
$877$	6.83141	−	21.0249i	0.230680	−	0.709961i	−0.766985	−	0.641665i	$-0.778244\pi$
$877$	6.83141	−	21.0249i	0.230680	−	0.709961i	0.997665	−	0.0682956i	$-0.0217561\pi$
$878$	−27.0943	−	19.6851i	−0.914387	−	0.664341i
$879$		−	3.61453i		−	0.121915i
$880$	6.23148	+	4.02103i	0.210063	+	0.135549i
$881$			13.0581i			0.439937i	0.975507	+	0.219969i	$0.0705955\pi$
$881$			13.0581i			0.439937i	−0.975507	+	0.219969i	$0.929405\pi$
$882$	−5.31058	+	14.8721i	−0.178816	+	0.500769i
$883$	38.4463	+	12.4920i	1.29382	+	0.420388i	0.873428	−	0.486953i	$-0.161892\pi$
$883$	38.4463	+	12.4920i	1.29382	+	0.420388i	0.420394	+	0.907342i	$0.361892\pi$
$884$	−2.76633	−	8.51388i	−0.0930416	−	0.286353i
$885$	18.2488	−	3.89068i	0.613427	−	0.130784i
$886$	6.47372	+	8.91031i	0.217489	+	0.299348i
$887$	0.121163	−	0.0393684i	0.00406827	−	0.00132186i	−0.306982	−	0.951715i	$-0.599319\pi$
$887$	0.121163	−	0.0393684i	0.00406827	−	0.00132186i	0.311050	+	0.950393i	$0.399319\pi$
$888$	3.55196	+	1.15410i	0.119196	+	0.0387291i
$889$	−35.7646	+	11.0536i	−1.19951	+	0.370727i
$890$	−20.6344	−	9.17177i	−0.691667	−	0.307438i
$891$	−4.32167	−	8.43388i	−0.144781	−	0.282545i
$892$	10.2808			0.344225
$893$	14.1365	+	10.2707i	0.473059	+	0.343697i
$894$	−0.666823	−	0.216664i	−0.0223019	−	0.00724633i
$895$	45.9161	+	4.79733i	1.53481	+	0.160357i
$896$	0.0381137	−	2.64548i	0.00127329	−	0.0883792i
$897$	9.90350	−	7.19532i	0.330668	−	0.240245i
$898$	−3.67433	−	11.3084i	−0.122614	−	0.377367i
$899$	−6.50035	+	20.0060i	−0.216799	+	0.667238i
$900$	−1.19291	−	11.2166i	−0.0397638	−	0.373887i
$901$	−5.87082			−0.195585
$902$	4.10030	−	4.11915i	0.136525	−	0.137153i
$903$	12.8314	−	17.1362i	0.427001	−	0.570257i
$904$	0.175452	−	0.241489i	0.00583544	−	0.00803179i
$905$	23.3681	−	25.9851i	0.776780	−	0.863774i
$906$	19.3795	−	6.29677i	0.643840	−	0.209196i
$907$	11.4900	+	15.8147i	0.381520	+	0.525117i	0.955986	−	0.293411i	$-0.0947905\pi$
$907$	11.4900	+	15.8147i	0.381520	+	0.525117i	−0.574467	+	0.818528i	$0.694790\pi$
$908$	9.67601	+	13.3179i	0.321110	+	0.441970i
$909$	−12.5764	−	38.7060i	−0.417131	−	1.28380i
$910$	3.21421	+	16.2182i	0.106550	+	0.537627i
$911$	18.8935	+	13.7269i	0.625969	+	0.454793i	0.855001	−	0.518626i	$-0.173556\pi$
$911$	18.8935	+	13.7269i	0.625969	+	0.454793i	−0.229032	+	0.973419i	$0.573556\pi$
$912$	−1.99668			−0.0661167
$913$	20.0143	+	19.9227i	0.662377	+	0.659346i
$914$	27.1058			0.896580
$915$	−13.2096	+	7.63743i	−0.436695	+	0.252486i
$916$	20.7920	+	6.75574i	0.686988	+	0.223216i
$917$	−17.4715	−	5.95645i	−0.576961	−	0.196699i
$918$	−8.53599	−	11.7488i	−0.281730	−	0.387768i
$919$	23.2717	+	32.0308i	0.767663	+	1.05660i	0.996538	+	0.0831417i	$0.0264954\pi$
$919$	23.2717	+	32.0308i	0.767663	+	1.05660i	−0.228875	+	0.973456i	$0.573505\pi$
$920$	1.17995	−	11.2935i	0.0389019	−	0.372337i
$921$	−16.3600	−	5.31569i	−0.539081	−	0.175158i
$922$	−7.19724	−	5.22910i	−0.237028	−	0.172211i
$923$			21.8056i			0.717742i
$924$	−7.46095	−	1.27452i	−0.245447	−	0.0419286i
$925$	−16.0704	+	14.5058i	−0.528392	+	0.476949i
$926$	−9.63214	+	13.2575i	−0.316532	+	0.435668i
$927$	10.4222	−	32.0762i	0.342309	−	1.05352i
$928$	4.94646	−	1.60720i	0.162376	−	0.0527591i
$929$	−5.75046	−	7.91483i	−0.188666	−	0.259677i	0.704197	−	0.710005i	$-0.251307\pi$
$929$	−5.75046	−	7.91483i	−0.188666	−	0.259677i	−0.892863	+	0.450328i	$0.851307\pi$
$930$	7.62945	−	1.62661i	0.250179	−	0.0533387i
$931$	−13.3779	+	9.14265i	−0.438444	+	0.299638i
$932$	4.98913	−	15.3550i	0.163424	−	0.502969i
$933$	−4.24950	+	5.84893i	−0.139122	+	0.191486i
$934$	−2.27261			−0.0743620
$935$	−12.8803	+	19.9608i	−0.421229	+	0.652789i
$936$			6.30474i			0.206077i
$937$	−19.1984	+	26.4243i	−0.627184	+	0.863244i	−0.997851	−	0.0655213i	$-0.979129\pi$
$937$	−19.1984	+	26.4243i	−0.627184	+	0.863244i	0.370667	+	0.928766i	$0.379129\pi$
$938$	16.4942	−	11.6244i	0.538553	−	0.379550i
$939$	6.53477	+	20.1120i	0.213254	+	0.656329i
$940$	3.51959	+	16.5083i	0.114797	+	0.538441i
$941$	−17.6290	+	12.8082i	−0.574689	+	0.417536i	−0.836806	−	0.547500i	$-0.815580\pi$
$941$	−17.6290	+	12.8082i	−0.574689	+	0.417536i	0.262116	+	0.965036i	$0.415580\pi$
$942$	5.45941	+	16.8023i	0.177877	+	0.547450i
$943$	−8.46334	−	2.74991i	−0.275604	−	0.0895493i
$944$	−5.68625	+	7.82645i	−0.185072	+	0.254729i
$945$	13.0892	+	23.4107i	0.425790	+	0.761551i
$946$	−27.7531	−	14.0608i	−0.902330	−	0.457156i
$947$		−	46.0261i		−	1.49565i	−0.663897	−	0.747824i	$-0.731099\pi$
$947$		−	46.0261i		−	1.49565i	0.663897	−	0.747824i	$-0.268901\pi$
$948$	6.45445	−	8.88378i	0.209631	−	0.288532i
$949$	−5.02216	+	15.4566i	−0.163026	+	0.501743i
$950$	5.77463	−	10.0305i	0.187354	−	0.325433i
$951$	7.27615	+	10.0148i	0.235945	+	0.324751i
$952$	8.47406	+	0.122087i	0.274646	+	0.00395685i
$953$	5.98906	+	18.4324i	0.194005	+	0.597085i	0.999987	+	0.00514514i	$0.00163776\pi$
$953$	5.98906	+	18.4324i	0.194005	+	0.597085i	−0.805982	+	0.591940i	$0.798362\pi$
$954$	3.93234	+	1.27770i	0.127314	+	0.0413669i
$955$	−13.0403	+	7.53955i	−0.421974	+	0.243974i
$956$			20.1781i			0.652607i
$957$	−2.36132	−	14.6906i	−0.0763307	−	0.474881i
$958$	−22.4132			−0.724139
$959$	−0.489907	−	1.58512i	−0.0158199	−	0.0511862i
$960$	−1.43415	−	1.28971i	−0.0462870	−	0.0416253i
$961$	4.52461	+	13.9253i	0.145955	+	0.449204i
$962$	9.78945	−	7.11245i	0.315624	−	0.229315i
$963$	21.9452	−	15.9441i	0.707173	−	0.513791i
$964$	1.99132	+	6.12866i	0.0641361	+	0.197391i
$965$	−13.8756	−	12.4781i	−0.446671	−	0.401685i
$966$	3.42205	+	11.0723i	0.110103	+	0.356244i
$967$	−41.3208			−1.32879			−0.664393	−	0.747383i	$-0.731310\pi$
$967$	−41.3208			−1.32879			−0.664393	+	0.747383i	$0.731310\pi$
$968$	0.0504592	+	10.9999i	0.00162182	+	0.353550i
$969$		−	6.39582i		−	0.205463i
$970$	−4.92013	+	2.84469i	−0.157976	+	0.0913374i
$971$	−48.8798	−	15.8820i	−1.56863	−	0.509678i	−0.609532	−	0.792761i	$-0.708643\pi$
$971$	−48.8798	−	15.8820i	−1.56863	−	0.509678i	−0.959095	+	0.283083i	$0.908643\pi$
$972$	4.96454	+	15.2793i	0.159238	+	0.490083i
$973$	0.195622	−	13.5782i	0.00627136	−	0.435296i
$974$	11.1209	+	15.3066i	0.356337	+	0.490456i
$975$	10.4457	+	6.01366i	0.334531	+	0.192591i
$976$	2.44464	−	7.52384i	0.0782512	−	0.240832i
$977$	6.89083	−	9.48441i	0.220457	−	0.303433i	−0.684435	−	0.729074i	$-0.739951\pi$
$977$	6.89083	−	9.48441i	0.220457	−	0.303433i	0.904892	+	0.425640i	$0.139951\pi$
$978$			15.3051i			0.489404i
$979$	−5.31532	−	33.0685i	−0.169878	−	1.05687i
$980$	−15.5144	−	2.07432i	−0.495590	−	0.0662619i
$981$	12.3931	−	17.0576i	0.395681	−	0.544608i
$982$	7.55842	+	2.45588i	0.241199	+	0.0783703i
$983$	8.02450	+	24.6969i	0.255942	+	0.787707i	0.993643	+	0.112580i	$0.0359114\pi$
$983$	8.02450	+	24.6969i	0.255942	+	0.787707i	−0.737701	+	0.675128i	$0.764089\pi$
$984$	−1.22288	+	0.888477i	−0.0389841	+	0.0283236i
$985$	−1.84535	−	8.65542i	−0.0587978	−	0.275785i
$986$	5.14823	+	15.8446i	0.163953	+	0.504596i
$987$	−9.92404	−	14.0815i	−0.315886	−	0.448218i
$988$	−3.80247	+	5.23366i	−0.120973	+	0.166505i
$989$			47.6355i			1.51472i
$990$	12.9715	−	10.5668i	0.412262	−	0.335835i
$991$	22.9032			0.727544			0.363772	−	0.931488i	$-0.381489\pi$
$991$	22.9032			0.727544			0.363772	+	0.931488i	$0.381489\pi$
$992$	−2.37730	+	3.27208i	−0.0754795	+	0.103889i
$993$	−6.71868	+	20.6780i	−0.213211	+	0.656195i
$994$	−19.5392	−	6.66137i	−0.619747	−	0.211286i
$995$	−6.06555	+	1.29319i	−0.192291	+	0.0409967i
$996$	−4.31697	−	5.94180i	−0.136788	−	0.188273i
$997$	42.9490	−	13.9550i	1.36021	−	0.441958i	0.464095	−	0.885786i	$-0.346380\pi$
$997$	42.9490	−	13.9550i	1.36021	−	0.441958i	0.896112	+	0.443828i	$0.146380\pi$
$998$	0.395005	−	1.21570i	0.0125037	−	0.0384823i
$999$	11.5381	−	15.8808i	0.365049	−	0.502446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.w.b.139.15	yes	96
5.4	even	2		770.2.w.a.139.10	✓	96
7.6	odd	2	inner	770.2.w.b.139.10	yes	96
11.8	odd	10		770.2.w.a.349.15	yes	96
35.34	odd	2		770.2.w.a.139.15	yes	96
55.19	odd	10	inner	770.2.w.b.349.10	yes	96
77.41	even	10		770.2.w.a.349.10	yes	96
385.349	even	10	inner	770.2.w.b.349.15	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.w.a.139.10	✓	96	5.4	even	2
770.2.w.a.139.15	yes	96	35.34	odd	2
770.2.w.a.349.10	yes	96	77.41	even	10
770.2.w.a.349.15	yes	96	11.8	odd	10
770.2.w.b.139.10	yes	96	7.6	odd	2	inner
770.2.w.b.139.15	yes	96	1.1	even	1	trivial
770.2.w.b.349.10	yes	96	55.19	odd	10	inner
770.2.w.b.349.15	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)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.266549 - 0.820354i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.466255 + 2.18692i) q^{5} +(0.697835 - 0.507006i) q^{6} +(2.50422 + 0.853746i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.82512 + 1.32603i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.266549 - 0.820354i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.466255 + 2.18692i) q^{5} +(0.697835 - 0.507006i) q^{6} +(2.50422 + 0.853746i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.82512 + 1.32603i) q^{9} +(-0.908230 + 2.04331i) q^{10} +(-3.27459 + 0.526346i) q^{11} +0.862571 q^{12} +(1.64268 - 2.26095i) q^{13} +(1.52414 + 2.16264i) q^{14} +(1.91833 + 0.200427i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.88281 - 2.59146i) q^{17} +(0.697133 + 2.14556i) q^{18} +(-0.715313 + 2.20151i) q^{19} +(-1.93580 + 1.11923i) q^{20} +(1.36787 - 1.82678i) q^{21} +(-2.95858 - 1.49893i) q^{22} +5.07812i q^{23} +(0.697835 + 0.507006i) q^{24} +(-4.56521 + 2.03932i) q^{25} +(2.65791 - 0.863607i) q^{26} +(3.66780 - 2.66481i) q^{27} +(-0.0381137 + 2.64548i) q^{28} +(-4.94646 + 1.60720i) q^{29} +(1.43415 + 1.28971i) q^{30} +(2.37730 - 3.27208i) q^{31} -1.00000 q^{32} +(-0.441050 + 2.82662i) q^{33} -3.20322i q^{34} +(-0.699467 + 5.87458i) q^{35} +(-0.697133 + 2.14556i) q^{36} +(4.11787 - 1.33798i) q^{37} +(-1.87271 + 1.36061i) q^{38} +(-1.41693 - 1.95023i) q^{39} +(-2.22396 - 0.232360i) q^{40} +(-0.541521 + 1.66663i) q^{41} +(2.18039 - 0.673883i) q^{42} +9.38054 q^{43} +(-1.51249 - 2.95167i) q^{44} +(-2.04894 + 4.60965i) q^{45} +(-2.98484 + 4.10828i) q^{46} +(2.33266 - 7.17920i) q^{47} +(0.266549 + 0.820354i) q^{48} +(5.54224 + 4.27593i) q^{49} +(-4.89202 - 1.03352i) q^{50} +(-2.62778 + 0.853816i) q^{51} +(2.65791 + 0.863607i) q^{52} +(1.07728 - 1.48275i) q^{53} +4.53365 q^{54} +(-2.67787 - 6.91585i) q^{55} +(-1.58581 + 2.11783i) q^{56} +(1.61535 + 1.17362i) q^{57} +(-4.94646 - 1.60720i) q^{58} +(9.20055 - 2.98944i) q^{59} +(0.402178 + 1.88637i) q^{60} +(-6.40016 + 4.64999i) q^{61} +(3.84656 - 1.24982i) q^{62} +(3.43841 + 4.87885i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(5.71042 + 2.53822i) q^{65} +(-2.01826 + 2.02754i) q^{66} -7.62687i q^{67} +(1.88281 - 2.59146i) q^{68} +(4.16585 + 1.35357i) q^{69} +(-4.01887 + 4.34150i) q^{70} +(-6.31238 + 4.58621i) q^{71} +(-1.82512 + 1.32603i) q^{72} +(-5.53071 + 1.79704i) q^{73} +(4.11787 + 1.33798i) q^{74} +(0.456111 + 4.28867i) q^{75} -2.31480 q^{76} +(-8.64967 - 1.47758i) q^{77} -2.41062i q^{78} +(7.48280 - 10.2992i) q^{79} +(-1.66265 - 1.49520i) q^{80} +(0.882961 + 2.71747i) q^{81} +(-1.41772 + 1.03003i) q^{82} +(-5.00477 - 6.88848i) q^{83} +(2.16007 + 0.736416i) q^{84} +(4.78945 - 5.32583i) q^{85} +(7.58901 + 5.51374i) q^{86} +4.48625i q^{87} +(0.511320 - 3.27697i) q^{88} +10.0985i q^{89} +(-4.36711 + 2.52495i) q^{90} +(6.04390 - 4.25949i) q^{91} +(-4.82958 + 1.56922i) q^{92} +(-2.05059 - 2.82240i) q^{93} +(6.10699 - 4.43699i) q^{94} +(-5.14803 - 0.537868i) q^{95} +(-0.266549 + 0.820354i) q^{96} +(2.05624 + 1.49394i) q^{97} +(1.97043 + 6.71695i) q^{98} +(-6.67447 - 3.38155i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more