LMFDB - Embedded newform 350.2.r.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(13,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([19, 10]))

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

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

chi := DirichletCharacter("350.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.r (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	350.13
Dual form			350.2.r.a.27.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 + 0.156434i) q^{2} +(-2.12064 - 1.08052i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-2.23074 - 0.154254i) q^{5} +(2.26356 + 0.735475i) q^{6} +(-2.39319 + 1.12812i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.56623 + 2.15573i) q^{9} +O(q^{10})$	\(q+(-0.987688 + 0.156434i) q^{2} +(-2.12064 - 1.08052i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-2.23074 - 0.154254i) q^{5} +(2.26356 + 0.735475i) q^{6} +(-2.39319 + 1.12812i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.56623 + 2.15573i) q^{9} +(2.22741 - 0.196609i) q^{10} +(0.926465 + 0.673116i) q^{11} +(-2.35074 - 0.372321i) q^{12} +(0.0265247 - 0.167470i) q^{13} +(2.18724 - 1.48861i) q^{14} +(4.56392 + 2.73748i) q^{15} +(0.809017 - 0.587785i) q^{16} +(4.69050 - 2.38993i) q^{17} +(-1.88417 - 1.88417i) q^{18} +(-1.34437 + 4.13756i) q^{19} +(-2.16923 + 0.542632i) q^{20} +(6.29404 + 0.193541i) q^{21} +(-1.02036 - 0.519898i) q^{22} +(-0.979337 - 6.18329i) q^{23} +2.38005 q^{24} +(4.95241 + 0.688204i) q^{25} +0.169558i q^{26} +(0.124867 + 0.788382i) q^{27} +(-1.92745 + 1.81244i) q^{28} +(5.60328 - 1.82062i) q^{29} +(-4.93596 - 1.98982i) q^{30} +(6.78079 + 2.20321i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.23738 - 2.42850i) q^{33} +(-4.25889 + 3.09426i) q^{34} +(5.51260 - 2.14739i) q^{35} +(2.15573 + 1.56623i) q^{36} +(-1.59982 + 10.1009i) q^{37} +(0.680566 - 4.29693i) q^{38} +(-0.237204 + 0.326484i) q^{39} +(2.05763 - 0.875294i) q^{40} +(-1.85475 - 2.55284i) q^{41} +(-6.24682 + 0.793446i) q^{42} +(5.30529 + 5.30529i) q^{43} +(1.08912 + 0.353878i) q^{44} +(-3.16132 - 5.05047i) q^{45} +(1.93456 + 5.95396i) q^{46} +(-3.32667 + 6.52895i) q^{47} +(-2.35074 + 0.372321i) q^{48} +(4.45468 - 5.39962i) q^{49} +(-4.99910 + 0.0949972i) q^{50} -12.5292 q^{51} +(-0.0265247 - 0.167470i) q^{52} +(1.02506 - 2.01179i) q^{53} +(-0.246660 - 0.759142i) q^{54} +(-1.96287 - 1.64446i) q^{55} +(1.62019 - 2.09165i) q^{56} +(7.32164 - 7.32164i) q^{57} +(-5.24949 + 2.67475i) q^{58} +(-8.66450 + 6.29513i) q^{59} +(5.18647 + 1.19317i) q^{60} +(2.48396 - 3.41888i) q^{61} +(-7.04197 - 1.11534i) q^{62} +(-6.18020 - 3.39216i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-0.0850028 + 0.369492i) q^{65} +(1.60205 + 2.20503i) q^{66} +(0.600644 + 1.17883i) q^{67} +(3.72240 - 3.72240i) q^{68} +(-4.60434 + 14.1707i) q^{69} +(-5.10880 + 2.98331i) q^{70} +(-3.04903 - 9.38395i) q^{71} +(-2.37420 - 1.20971i) q^{72} +(6.11119 - 0.967917i) q^{73} -10.2268i q^{74} +(-9.75865 - 6.81060i) q^{75} +4.35049i q^{76} +(-2.97656 - 0.565725i) q^{77} +(0.183211 - 0.359571i) q^{78} +(-13.3528 + 4.33859i) q^{79} +(-1.89538 + 1.18640i) q^{80} +(3.05731 - 9.40942i) q^{81} +(2.23127 + 2.23127i) q^{82} +(-0.185637 - 0.364333i) q^{83} +(6.04579 - 1.76090i) q^{84} +(-10.8320 + 4.60778i) q^{85} +(-6.06990 - 4.41004i) q^{86} +(-13.8497 - 2.19358i) q^{87} +(-1.13107 - 0.179145i) q^{88} +(10.2833 + 7.47125i) q^{89} +(3.91246 + 4.49375i) q^{90} +(0.125449 + 0.430711i) q^{91} +(-2.84215 - 5.57803i) q^{92} +(-11.9990 - 11.9990i) q^{93} +(2.26436 - 6.96897i) q^{94} +(3.63719 - 9.02245i) q^{95} +(2.26356 - 0.735475i) q^{96} +(0.0364681 - 0.0715728i) q^{97} +(-3.55514 + 6.03000i) q^{98} +3.05146i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{7}+O(q^{10}) $ 160 * q + 8 * q^7	$ 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) $ 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{19}{20}\right)$

Coefficient data

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

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

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

$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$3$	−2.12064	−	1.08052i	−1.22435	−	0.623838i	−0.282306	−	0.959324i	$-0.591099\pi$
$3$	−2.12064	−	1.08052i	−1.22435	−	0.623838i	−0.942045	+	0.335487i	$0.891099\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	−2.23074	−	0.154254i	−0.997618	−	0.0689847i
$5$	−2.23074	−	0.154254i	−0.997618	−	0.0689847i
$6$	2.26356	+	0.735475i	0.924094	+	0.300256i
$7$	−2.39319	+	1.12812i	−0.904539	+	0.426391i
$7$	−2.39319	+	1.12812i	−0.904539	+	0.426391i
$8$	−0.891007	+	0.453990i	−0.315018	+	0.160510i
$9$	1.56623	+	2.15573i	0.522076	+	0.718576i
$10$	2.22741	−	0.196609i	0.704368	−	0.0621734i
$11$	0.926465	+	0.673116i	0.279340	+	0.202952i	0.718629	−	0.695393i	$-0.244770\pi$
$11$	0.926465	+	0.673116i	0.279340	+	0.202952i	−0.439290	+	0.898345i	$0.644770\pi$
$12$	−2.35074	−	0.372321i	−0.678602	−	0.107480i
$13$	0.0265247	−	0.167470i	0.00735663	−	0.0464479i	−0.983737	−	0.179615i	$-0.942515\pi$
$13$	0.0265247	−	0.167470i	0.00735663	−	0.0464479i	0.991094	+	0.133167i	$0.0425147\pi$
$14$	2.18724	−	1.48861i	0.584566	−	0.397848i
$15$	4.56392	+	2.73748i	1.17840	+	0.706813i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	4.69050	−	2.38993i	1.13761	−	0.579643i	0.219363	−	0.975643i	$-0.429602\pi$
$17$	4.69050	−	2.38993i	1.13761	−	0.579643i	0.918250	+	0.396000i	$0.129602\pi$
$18$	−1.88417	−	1.88417i	−0.444104	−	0.444104i
$19$	−1.34437	+	4.13756i	−0.308421	+	0.949221i	0.669958	+	0.742399i	$0.266312\pi$
$19$	−1.34437	+	4.13756i	−0.308421	+	0.949221i	−0.978379	+	0.206822i	$0.933688\pi$
$20$	−2.16923	+	0.542632i	−0.485054	+	0.121336i
$21$	6.29404	+	0.193541i	1.37347	+	0.0422342i
$22$	−1.02036	−	0.519898i	−0.217541	−	0.110843i
$23$	−0.979337	−	6.18329i	−0.204206	−	1.28931i	−0.850402	−	0.526134i	$-0.823641\pi$
$23$	−0.979337	−	6.18329i	−0.204206	−	1.28931i	0.646196	−	0.763172i	$-0.276359\pi$
$24$	2.38005			0.485825
$25$	4.95241	+	0.688204i	0.990482	+	0.137641i
$26$			0.169558i			0.0332531i
$27$	0.124867	+	0.788382i	0.0240307	+	0.151724i
$28$	−1.92745	+	1.81244i	−0.364253	+	0.342520i
$29$	5.60328	−	1.82062i	1.04050	−	0.338080i	0.261569	−	0.965185i	$-0.415760\pi$
$29$	5.60328	−	1.82062i	1.04050	−	0.338080i	0.778935	+	0.627105i	$0.215760\pi$
$30$	−4.93596	−	1.98982i	−0.901180	−	0.363289i
$31$	6.78079	+	2.20321i	1.21787	+	0.395709i	0.846304	−	0.532700i	$-0.178822\pi$
$31$	6.78079	+	2.20321i	1.21787	+	0.395709i	0.371562	+	0.928408i	$0.378822\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−1.23738	−	2.42850i	−0.215401	−	0.422747i
$34$	−4.25889	+	3.09426i	−0.730393	+	0.530661i
$35$	5.51260	−	2.14739i	0.931799	−	0.362975i
$36$	2.15573	+	1.56623i	0.359288	+	0.261038i
$37$	−1.59982	+	10.1009i	−0.263009	+	1.66058i	0.403425	+	0.915013i	$0.367820\pi$
$37$	−1.59982	+	10.1009i	−0.263009	+	1.66058i	−0.666435	+	0.745564i	$0.732180\pi$
$38$	0.680566	−	4.29693i	0.110402	−	0.697053i
$39$	−0.237204	+	0.326484i	−0.0379831	+	0.0522792i
$40$	2.05763	−	0.875294i	0.325341	−	0.138396i
$41$	−1.85475	−	2.55284i	−0.289663	−	0.398687i	0.639242	−	0.769006i	$-0.279248\pi$
$41$	−1.85475	−	2.55284i	−0.289663	−	0.398687i	−0.928905	+	0.370319i	$0.879248\pi$
$42$	−6.24682	+	0.793446i	−0.963906	+	0.122431i
$43$	5.30529	+	5.30529i	0.809049	+	0.809049i	0.984490	−	0.175441i	$-0.0561350\pi$
$43$	5.30529	+	5.30529i	0.809049	+	0.809049i	−0.175441	+	0.984490i	$0.556135\pi$
$44$	1.08912	+	0.353878i	0.164192	+	0.0533491i
$45$	−3.16132	−	5.05047i	−0.471261	−	0.752879i
$46$	1.93456	+	5.95396i	0.285235	+	0.877864i
$47$	−3.32667	+	6.52895i	−0.485244	+	0.952345i	0.510473	+	0.859894i	$0.329470\pi$
$47$	−3.32667	+	6.52895i	−0.485244	+	0.952345i	−0.995717	+	0.0924514i	$0.970530\pi$
$48$	−2.35074	+	0.372321i	−0.339301	+	0.0537400i
$49$	4.45468	−	5.39962i	0.636382	−	0.771374i
$50$	−4.99910	+	0.0949972i	−0.706979	+	0.0134346i
$51$	−12.5292			−1.75444
$52$	−0.0265247	−	0.167470i	−0.00367832	−	0.0232240i
$53$	1.02506	−	2.01179i	0.140803	−	0.276341i	−0.809827	−	0.586669i	$-0.800439\pi$
$53$	1.02506	−	2.01179i	0.140803	−	0.276341i	0.950630	+	0.310328i	$0.100439\pi$
$54$	−0.246660	−	0.759142i	−0.0335662	−	0.103306i
$55$	−1.96287	−	1.64446i	−0.264674	−	0.221739i
$56$	1.62019	−	2.09165i	0.216507	−	0.279508i
$57$	7.32164	−	7.32164i	0.969775	−	0.969775i
$58$	−5.24949	+	2.67475i	−0.689292	+	0.351212i
$59$	−8.66450	+	6.29513i	−1.12802	+	0.819555i	−0.985406	−	0.170223i	$-0.945551\pi$
$59$	−8.66450	+	6.29513i	−1.12802	+	0.819555i	−0.142616	+	0.989778i	$0.545551\pi$
$60$	5.18647	+	1.19317i	0.669571	+	0.154037i
$61$	2.48396	−	3.41888i	0.318039	−	0.437743i	−0.619828	−	0.784737i	$-0.712798\pi$
$61$	2.48396	−	3.41888i	0.318039	−	0.437743i	0.937867	+	0.346995i	$0.112798\pi$
$62$	−7.04197	−	1.11534i	−0.894331	−	0.141648i
$63$	−6.18020	−	3.39216i	−0.778632	−	0.427372i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	−0.0850028	+	0.369492i	−0.0105433	+	0.0458298i
$66$	1.60205	+	2.20503i	0.197199	+	0.271420i
$67$	0.600644	+	1.17883i	0.0733804	+	0.144017i	0.924782	−	0.380497i	$-0.124247\pi$
$67$	0.600644	+	1.17883i	0.0733804	+	0.144017i	−0.851402	+	0.524514i	$0.824247\pi$
$68$	3.72240	−	3.72240i	0.451408	−	0.451408i
$69$	−4.60434	+	14.1707i	−0.554298	+	1.70595i
$70$	−5.10880	+	2.98331i	−0.610618	+	0.356574i
$71$	−3.04903	−	9.38395i	−0.361853	−	1.11367i	−0.951928	−	0.306321i	$-0.900902\pi$
$71$	−3.04903	−	9.38395i	−0.361853	−	1.11367i	0.590075	−	0.807348i	$-0.299098\pi$
$72$	−2.37420	−	1.20971i	−0.279802	−	0.142566i
$73$	6.11119	−	0.967917i	0.715260	−	0.113286i	0.211811	−	0.977311i	$-0.432064\pi$
$73$	6.11119	−	0.967917i	0.715260	−	0.113286i	0.503450	+	0.864025i	$0.332064\pi$
$74$		−	10.2268i		−	1.18884i
$75$	−9.75865	−	6.81060i	−1.12683	−	0.786421i
$76$			4.35049i			0.499035i
$77$	−2.97656	−	0.565725i	−0.339211	−	0.0644704i
$78$	0.183211	−	0.359571i	0.0207445	−	0.0407134i
$79$	−13.3528	+	4.33859i	−1.50231	+	0.488130i	−0.940690	−	0.339267i	$-0.889821\pi$
$79$	−13.3528	+	4.33859i	−1.50231	+	0.488130i	−0.561619	+	0.827396i	$0.689821\pi$
$80$	−1.89538	+	1.18640i	−0.211909	+	0.132644i
$81$	3.05731	−	9.40942i	0.339701	−	1.04549i
$82$	2.23127	+	2.23127i	0.246402	+	0.246402i
$83$	−0.185637	−	0.364333i	−0.0203763	−	0.0399907i	0.880594	−	0.473872i	$-0.157144\pi$
$83$	−0.185637	−	0.364333i	−0.0203763	−	0.0399907i	−0.900970	+	0.433881i	$0.857144\pi$
$84$	6.04579	−	1.76090i	0.659650	−	0.192129i
$85$	−10.8320	+	4.60778i	−1.17489	+	0.499784i
$86$	−6.06990	−	4.41004i	−0.654535	−	0.475547i
$87$	−13.8497	−	2.19358i	−1.48485	−	0.235177i
$88$	−1.13107	−	0.179145i	−0.120573	−	0.0190969i
$89$	10.2833	+	7.47125i	1.09003	+	0.791951i	0.979404	−	0.201912i	$-0.0647154\pi$
$89$	10.2833	+	7.47125i	1.09003	+	0.791951i	0.110623	+	0.993862i	$0.464715\pi$
$90$	3.91246	+	4.49375i	0.412410	+	0.473683i
$91$	0.125449	+	0.430711i	0.0131506	+	0.0451508i
$92$	−2.84215	−	5.57803i	−0.296314	−	0.581550i
$93$	−11.9990	−	11.9990i	−1.24424	−	1.24424i
$94$	2.26436	−	6.96897i	0.233551	−	0.718795i
$95$	3.63719	−	9.02245i	0.373168	−	0.925684i
$96$	2.26356	−	0.735475i	0.231024	−	0.0750641i
$97$	0.0364681	−	0.0715728i	0.00370278	−	0.00726711i	−0.889148	−	0.457620i	$-0.848702\pi$
$97$	0.0364681	−	0.0715728i	0.00370278	−	0.00726711i	0.892851	+	0.450353i	$0.148702\pi$
$98$	−3.55514	+	6.03000i	−0.359124	+	0.609122i
$99$			3.05146i			0.306683i
$100$	4.92269	−	0.875859i	0.492269	−	0.0875859i
$101$			10.5086i			1.04564i	0.852442	+	0.522822i	$0.175121\pi$
$101$			10.5086i			1.04564i	−0.852442	+	0.522822i	$0.824879\pi$
$102$	12.3750	−	1.96000i	1.22530	−	0.194069i
$103$	7.38580	+	3.76325i	0.727744	+	0.370804i	0.778279	−	0.627918i	$-0.216093\pi$
$103$	7.38580	+	3.76325i	0.727744	+	0.370804i	−0.0505353	+	0.998722i	$0.516093\pi$
$104$	0.0523963	+	0.161259i	0.00513788	+	0.0158128i
$105$	−14.0105	−	1.40262i	−1.36729	−	0.136882i
$106$	−0.697726	+	2.14738i	−0.0677691	+	0.208572i
$107$	5.15446	−	5.15446i	0.498301	−	0.498301i	−0.412608	−	0.910909i	$-0.635382\pi$
$107$	5.15446	−	5.15446i	0.498301	−	0.498301i	0.910909	+	0.412608i	$0.135382\pi$
$108$	0.362379	+	0.711209i	0.0348700	+	0.0684362i
$109$	6.89413	+	9.48896i	0.660338	+	0.908878i	0.999493	−	0.0318532i	$-0.0101409\pi$
$109$	6.89413	+	9.48896i	0.660338	+	0.908878i	−0.339154	+	0.940731i	$0.610141\pi$
$110$	2.19596	+	1.31715i	0.209376	+	0.125586i
$111$	14.3068	−	19.6917i	1.35795	−	1.86905i
$112$	−1.27303	+	2.31935i	−0.120290	+	0.219158i
$113$	14.2577	+	2.25820i	1.34125	+	0.212433i	0.785472	−	0.618897i	$-0.212420\pi$
$113$	14.2577	+	2.25820i	1.34125	+	0.212433i	0.555779	+	0.831330i	$0.312420\pi$
$114$	−6.08614	+	8.37686i	−0.570020	+	0.784565i
$115$	1.23085	+	13.9444i	0.114777	+	1.30032i
$116$	4.76644	−	3.46302i	0.442553	−	0.321533i
$117$	0.402564	−	0.205117i	0.0372171	−	0.0189630i
$118$	7.57305	−	7.57305i	0.697156	−	0.697156i
$119$	−8.52910	+	11.0110i	−0.781862	+	1.00938i
$120$	−5.30927	−	0.367133i	−0.484668	−	0.0335145i
$121$	−2.99393	−	9.21438i	−0.272176	−	0.837671i
$122$	−1.91855	+	3.76537i	−0.173697	+	0.340900i
$123$	1.17486	+	7.41774i	0.105933	+	0.668835i
$124$	7.12975			0.640270
$125$	−10.9414	−	2.29914i	−0.978628	−	0.205641i
$126$	6.63476	+	2.38360i	0.591071	+	0.212348i
$127$	1.42424	−	0.225577i	0.126381	−	0.0200167i	−0.0929236	−	0.995673i	$-0.529621\pi$
$127$	1.42424	−	0.225577i	0.126381	−	0.0200167i	0.219304	+	0.975656i	$0.429621\pi$
$128$	−0.453990	+	0.891007i	−0.0401275	+	0.0787546i
$129$	−5.51813	−	16.9831i	−0.485844	−	1.49528i
$130$	0.0261551	−	0.378240i	0.00229395	−	0.0331738i
$131$	4.38379	+	1.42438i	0.383014	+	0.124449i	0.494194	−	0.869352i	$-0.335463\pi$
$131$	4.38379	+	1.42438i	0.383014	+	0.124449i	−0.111180	+	0.993800i	$0.535463\pi$
$132$	−1.92727	−	1.92727i	−0.167747	−	0.167747i
$133$	−1.45034	−	11.4186i	−0.125760	−	0.990115i
$134$	−0.777659	−	1.07036i	−0.0671795	−	0.0924647i
$135$	−0.156935	−	1.77794i	−0.0135068	−	0.153020i
$136$	−3.09426	+	4.25889i	−0.265331	+	0.365196i
$137$	−2.28950	+	14.4553i	−0.195605	+	1.23500i	0.673055	+	0.739592i	$0.264982\pi$
$137$	−2.28950	+	14.4553i	−0.195605	+	1.23500i	−0.868660	+	0.495408i	$0.835018\pi$
$138$	2.33087	−	14.7165i	0.198417	−	1.25275i
$139$	0.971548	+	0.705871i	0.0824056	+	0.0598712i	0.628225	−	0.778031i	$-0.283782\pi$
$139$	0.971548	+	0.705871i	0.0824056	+	0.0598712i	−0.545820	+	0.837903i	$0.683782\pi$
$140$	4.57921	−	3.74578i	0.387014	−	0.316576i
$141$	14.1093	−	10.2510i	1.18822	−	0.863291i
$142$	4.47946	+	8.79144i	0.375908	+	0.737761i
$143$	0.137301	−	0.137301i	0.0114817	−	0.0114817i
$144$	2.53421	+	0.823414i	0.211184	+	0.0686179i
$145$	−12.7803	+	3.19699i	−1.06135	+	0.265496i
$146$	−5.88453	+	1.91200i	−0.487007	+	0.158238i
$147$	−15.2811	+	6.63727i	−1.26037	+	0.547433i
$148$	1.59982	+	10.1009i	0.131505	+	0.830288i
$149$			10.7466i			0.880399i	0.897900	+	0.440199i	$0.145092\pi$
$149$			10.7466i			0.880399i	−0.897900	+	0.440199i	$0.854908\pi$
$150$	10.7039	+	5.20016i	0.873971	+	0.424592i
$151$	−13.5546			−1.10306			−0.551531	−	0.834155i	$-0.685956\pi$
$151$	−13.5546			−1.10306			−0.551531	+	0.834155i	$0.685956\pi$
$152$	−0.680566	−	4.29693i	−0.0552012	−	0.348527i
$153$	12.4984	+	6.36827i	1.01044	+	0.514844i
$154$	3.02841	+	0.0931236i	0.244037	+	0.00750411i
$155$	−14.7863	−	5.96076i	−1.18767	−	0.478780i
$156$	−0.124706	+	0.383805i	−0.00998444	+	0.0307290i
$157$	5.92468	+	5.92468i	0.472841	+	0.472841i	0.902833	−	0.429992i	$-0.141484\pi$
$157$	5.92468	+	5.92468i	0.472841	+	0.472841i	−0.429992	+	0.902833i	$0.641484\pi$
$158$	12.5097	−	6.37402i	0.995219	−	0.507090i
$159$	−4.34756	+	3.15869i	−0.344784	+	0.250500i
$160$	1.68645	−	1.46830i	0.133325	−	0.116079i
$161$	9.31925	+	13.6930i	0.734460	+	1.07916i
$162$	−1.54771	+	9.77184i	−0.121599	+	0.767748i
$163$	12.1417	+	1.92306i	0.951015	+	0.150626i	0.612619	−	0.790378i	$-0.290116\pi$
$163$	12.1417	+	1.92306i	0.951015	+	0.150626i	0.338395	+	0.941004i	$0.390116\pi$
$164$	−2.55284	−	1.85475i	−0.199343	−	0.144832i
$165$	2.38567	+	5.60822i	0.185724	+	0.436600i
$166$	0.240346	+	0.330807i	0.0186544	+	0.0256756i
$167$	19.2652	−	9.81613i	1.49079	−	0.759595i	0.496676	−	0.867936i	$-0.334554\pi$
$167$	19.2652	−	9.81613i	1.49079	−	0.759595i	0.994114	+	0.108341i	$0.0345539\pi$
$168$	−5.69589	+	2.68499i	−0.439448	+	0.207151i
$169$	12.3364	+	4.00834i	0.948953	+	0.308334i
$170$	9.97777	−	6.24554i	0.765260	−	0.479011i
$171$	−11.0250	+	3.58225i	−0.843106	+	0.273942i
$172$	6.68506	+	3.40621i	0.509731	+	0.259721i
$173$	11.5233	−	1.82511i	0.876100	−	0.138761i	0.297842	−	0.954615i	$-0.403733\pi$
$173$	11.5233	−	1.82511i	0.876100	−	0.138761i	0.578257	+	0.815854i	$0.303733\pi$
$174$	14.0224			1.06303
$175$	−12.6284	+	3.93993i	−0.954619	+	0.297831i
$176$	1.14517			0.0863207
$177$	25.1763	−	3.98753i	1.89236	−	0.299721i
$178$	−11.3254	−	5.77060i	−0.848878	−	0.432525i
$179$	9.50844	−	3.08948i	0.710694	−	0.230918i	0.0687102	−	0.997637i	$-0.478112\pi$
$179$	9.50844	−	3.08948i	0.710694	−	0.230918i	0.641984	+	0.766718i	$0.278112\pi$
$180$	−4.56727	−	3.82638i	−0.340424	−	0.285201i
$181$	−17.8613	−	5.80348i	−1.32762	−	0.431369i	−0.442514	−	0.896762i	$-0.645913\pi$
$181$	−17.8613	−	5.80348i	−1.32762	−	0.431369i	−0.885104	+	0.465392i	$0.845913\pi$
$182$	−0.191282	−	0.405784i	−0.0141788	−	0.0300787i
$183$	−8.96175	+	4.56624i	−0.662472	+	0.337546i
$184$	3.67975	+	5.06474i	0.271275	+	0.373378i
$185$	5.12690	−	22.2857i	0.376937	−	1.63848i
$186$	13.7283	+	9.97420i	1.00661	+	0.731344i
$187$	5.95429	+	0.943066i	0.435420	+	0.0689638i
$188$	−1.14629	+	7.23740i	−0.0836019	+	0.527841i
$189$	−1.18822	−	1.74588i	−0.0864305	−	0.126994i
$190$	−2.18099	+	9.48035i	−0.158225	+	0.687777i
$191$	−15.9596	+	11.5953i	−1.15480	+	0.839009i	−0.989111	−	0.147170i	$-0.952984\pi$
$191$	−15.9596	+	11.5953i	−1.15480	+	0.839009i	−0.165685	+	0.986179i	$0.552984\pi$
$192$	−2.12064	+	1.08052i	−0.153044	+	0.0779797i
$193$	−3.01499	−	3.01499i	−0.217024	−	0.217024i	0.590219	−	0.807243i	$-0.299041\pi$
$193$	−3.01499	−	3.01499i	−0.217024	−	0.217024i	−0.807243	+	0.590219i	$0.799041\pi$
$194$	−0.0248227	+	0.0763964i	−0.00178217	+	0.00548495i
$195$	0.579503	−	0.691711i	0.0414991	−	0.0495344i
$196$	2.56807	−	6.51191i	0.183434	−	0.465137i
$197$	−11.1002	−	5.65584i	−0.790858	−	0.402962i	0.0114039	−	0.999935i	$-0.496370\pi$
$197$	−11.1002	−	5.65584i	−0.790858	−	0.402962i	−0.802261	+	0.596973i	$0.796370\pi$
$198$	−0.477353	−	3.01389i	−0.0339240	−	0.214188i
$199$	12.6730			0.898364			0.449182	−	0.893440i	$-0.351716\pi$
$199$	12.6730			0.898364			0.449182	+	0.893440i	$0.351716\pi$
$200$	−4.72507	+	1.63515i	−0.334113	+	0.115623i
$201$		−	3.14888i		−	0.222105i
$202$	−1.64391	−	10.3792i	−0.115665	−	0.730279i
$203$	−11.3558	+	10.6783i	−0.797022	+	0.749468i
$204$	−11.9160	+	3.87174i	−0.834286	+	0.271076i
$205$	3.74368	+	5.98083i	0.261470	+	0.417719i
$206$	−7.88357	−	2.56153i	−0.549274	−	0.178470i
$207$	11.7956	−	11.7956i	0.819853	−	0.819853i
$208$	−0.0769777	−	0.151077i	−0.00533744	−	0.0104753i
$209$	−4.03057	+	2.92838i	−0.278801	+	0.202561i
$210$	14.0574	−	0.806372i	0.970056	−	0.0556449i
$211$	17.4954	+	12.7112i	1.20443	+	0.875073i	0.994714	−	0.102689i	$-0.0327446\pi$
$211$	17.4954	+	12.7112i	1.20443	+	0.875073i	0.209721	+	0.977761i	$0.432745\pi$
$212$	0.353212	−	2.23009i	0.0242587	−	0.153163i
$213$	−3.67365	+	23.1945i	−0.251714	+	1.58926i
$214$	−4.28467	+	5.89734i	−0.292894	+	0.403134i
$215$	−11.0164	−	12.6531i	−0.751310	−	0.862934i
$216$	−0.469175	−	0.645765i	−0.0319233	−	0.0439387i
$217$	−18.7132	+	2.37687i	−1.27033	+	0.161353i
$218$	−8.29366	−	8.29366i	−0.561717	−	0.561717i
$219$	−14.0055	−	4.55065i	−0.946402	−	0.307505i
$220$	−2.37497	−	0.957413i	−0.160120	−	0.0645488i
$221$	−0.275828	−	0.848912i	−0.0185542	−	0.0571040i
$222$	−11.0502	+	21.6873i	−0.741644	+	1.45556i
$223$	16.6679	−	2.63994i	1.11616	−	0.176783i	0.429014	−	0.903298i	$-0.358861\pi$
$223$	16.6679	−	2.63994i	1.11616	−	0.176783i	0.687151	+	0.726515i	$0.258861\pi$
$224$	0.894534	−	2.48994i	0.0597686	−	0.166366i
$225$	6.27302	+	11.7539i	0.418201	+	0.783595i
$226$	−14.4354			−0.960230
$227$	−1.08840	−	6.87186i	−0.0722393	−	0.456101i	−0.997120	−	0.0758432i	$-0.975835\pi$
$227$	−1.08840	−	6.87186i	−0.0722393	−	0.456101i	0.924880	−	0.380258i	$-0.124165\pi$
$228$	4.70078	−	9.22581i	0.311317	−	0.610994i
$229$	−7.79490	−	23.9902i	−0.515101	−	1.58532i	−0.783097	−	0.621899i	$-0.786361\pi$
$229$	−7.79490	−	23.9902i	−0.515101	−	1.58532i	0.267996	−	0.963420i	$-0.413639\pi$
$230$	−3.39708	−	13.5802i	−0.223997	−	0.895450i
$231$	5.70093	+	4.41593i	0.375094	+	0.290547i
$232$	−4.16602	+	4.16602i	−0.273513	+	0.273513i
$233$	−0.218546	+	0.111355i	−0.0143174	+	0.00729508i	−0.461135	−	0.887330i	$-0.652557\pi$
$233$	−0.218546	+	0.111355i	−0.0143174	+	0.00729508i	0.446817	+	0.894625i	$0.352557\pi$
$234$	−0.365521	+	0.265566i	−0.0238948	+	0.0173606i
$235$	8.42805	−	14.0512i	0.549785	−	0.916602i
$236$	−6.29513	+	8.66450i	−0.409778	+	0.564011i
$237$	33.0044	+	5.22738i	2.14387	+	0.339555i
$238$	6.70160	−	12.2097i	0.434400	−	0.791437i
$239$	11.1475	−	15.3432i	0.721069	−	0.992466i	−0.278419	−	0.960460i	$-0.589810\pi$
$239$	11.1475	−	15.3432i	0.721069	−	0.992466i	0.999488	−	0.0320062i	$-0.0101896\pi$
$240$	5.30134	−	0.467940i	0.342200	−	0.0302054i
$241$	−1.91538	−	2.63629i	−0.123380	−	0.169818i	0.742859	−	0.669448i	$-0.233469\pi$
$241$	−1.91538	−	2.63629i	−0.123380	−	0.169818i	−0.866239	+	0.499630i	$0.833469\pi$
$242$	4.39852	+	8.63259i	0.282748	+	0.554924i
$243$	−14.9572	+	14.9572i	−0.959507	+	0.959507i
$244$	1.30590	−	4.01914i	0.0836014	−	0.257299i
$245$	−10.7701	+	11.3580i	−0.688079	+	0.725636i
$246$	−2.32078	−	7.14263i	−0.147968	−	0.455397i
$247$	0.657260	+	0.334891i	0.0418204	+	0.0213086i
$248$	−7.04197	+	1.11534i	−0.447165	+	0.0708240i
$249$			0.973202i			0.0616742i
$250$	11.1663	+	0.559219i	0.706222	+	0.0353681i
$251$		−	10.7220i		−	0.676768i	−0.941008	−	0.338384i	$-0.890120\pi$
$251$		−	10.7220i		−	0.676768i	0.941008	−	0.338384i	$-0.109880\pi$
$252$	−6.92595	−	1.31635i	−0.436294	−	0.0829220i
$253$	3.25475	−	6.38781i	0.204625	−	0.401598i
$254$	−1.37142	+	0.445600i	−0.0860503	+	0.0279594i
$255$	27.9494	+	1.93269i	1.75026	+	0.121030i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	11.3943	+	11.3943i	0.710760	+	0.710760i	0.966694	−	0.255935i	$-0.0823832\pi$
$257$	11.3943	+	11.3943i	0.710760	+	0.710760i	−0.255935	+	0.966694i	$0.582383\pi$
$258$	8.10693	+	15.9108i	0.504716	+	0.990560i
$259$	−7.56638	−	25.9781i	−0.470152	−	1.61420i
$260$	0.0333367	+	0.377675i	0.00206745	+	0.0234224i
$261$	12.7008	+	9.22765i	0.786158	+	0.571177i
$262$	−4.55264	−	0.721068i	−0.281263	−	0.0445477i
$263$	−1.66381	−	0.263522i	−0.102595	−	0.0162495i	0.104926	−	0.994480i	$-0.466539\pi$
$263$	−1.66381	−	0.263522i	−0.102595	−	0.0162495i	−0.207521	+	0.978231i	$0.566539\pi$
$264$	2.20503	+	1.60205i	0.135710	+	0.0985993i
$265$	−2.59697	+	4.32967i	−0.159531	+	0.265970i
$266$	3.21874	+	11.0511i	0.197354	+	0.677587i
$267$	−13.7343	−	26.9551i	−0.840526	−	1.64963i
$268$	0.935526	+	0.935526i	0.0571463	+	0.0571463i
$269$	5.34915	−	16.4630i	0.326143	−	1.00377i	−0.644778	−	0.764370i	$-0.723050\pi$
$269$	5.34915	−	16.4630i	0.326143	−	1.00377i	0.970922	−	0.239397i	$-0.0769497\pi$
$270$	0.433134	+	1.73150i	0.0263597	+	0.105376i
$271$	7.14705	−	2.32222i	0.434152	−	0.141065i	−0.0837837	−	0.996484i	$-0.526700\pi$
$271$	7.14705	−	2.32222i	0.434152	−	0.141065i	0.517936	+	0.855419i	$0.326700\pi$
$272$	2.38993	−	4.69050i	0.144911	−	0.284403i
$273$	0.199360	−	1.04893i	0.0120658	−	0.0634842i
$274$		−	14.6355i		−	0.884163i
$275$	4.12499	+	3.97114i	0.248747	+	0.239469i
$276$			14.9000i			0.896873i
$277$	−21.5541	+	3.41384i	−1.29506	+	0.205118i	−0.765655	−	0.643251i	$-0.777585\pi$
$277$	−21.5541	+	3.41384i	−1.29506	+	0.205118i	−0.529406	+	0.848369i	$0.677585\pi$
$278$	−1.07001	−	0.545197i	−0.0641749	−	0.0326987i
$279$	5.87073	+	18.0683i	0.351472	+	1.08172i
$280$	−3.93686	+	4.41601i	−0.235273	+	0.263907i
$281$	−5.43726	+	16.7342i	−0.324360	+	0.998276i	0.647369	+	0.762176i	$0.275869\pi$
$281$	−5.43726	+	16.7342i	−0.324360	+	0.998276i	−0.971729	+	0.236100i	$0.924131\pi$
$282$	−12.3320	+	12.3320i	−0.734359	+	0.734359i
$283$	9.71826	+	19.0731i	0.577690	+	1.13378i	0.976252	+	0.216639i	$0.0695096\pi$
$283$	9.71826	+	19.0731i	0.577690	+	1.13378i	−0.398561	+	0.917142i	$0.630490\pi$
$284$	−5.79960	−	7.98246i	−0.344143	−	0.473672i
$285$	−17.4621	+	15.2033i	−1.03436	+	0.900565i
$286$	−0.114132	+	0.157090i	−0.00674878	+	0.00928890i
$287$	7.31868	+	4.01704i	0.432008	+	0.237118i
$288$	−2.63182	−	0.416839i	−0.155081	−	0.0245625i
$289$	6.29669	−	8.66665i	0.370393	−	0.509803i
$290$	12.1228	−	5.15692i	0.711878	−	0.302825i
$291$	−0.154671	+	0.112375i	−0.00906700	+	0.00658756i
$292$	5.51298	−	2.80900i	0.322623	−	0.164385i
$293$	−10.9683	+	10.9683i	−0.640774	+	0.640774i	−0.950746	−	0.309972i	$-0.899680\pi$
$293$	−10.9683	+	10.9683i	−0.640774	+	0.640774i	0.309972	+	0.950746i	$0.399680\pi$
$294$	14.0547	−	8.94605i	0.819687	−	0.521744i
$295$	20.2993	−	12.7063i	1.18187	−	0.739787i
$296$	−3.16025	−	9.72626i	−0.183686	−	0.565328i
$297$	−0.414987	+	0.814458i	−0.0240800	+	0.0472597i
$298$	−1.68114	−	10.6143i	−0.0973861	−	0.614872i
$299$	−1.06150			−0.0613879
$300$	−11.3856	−	3.46168i	−0.657349	−	0.199860i
$301$	−18.6816	−	6.71152i	−1.07679	−	0.386846i
$302$	13.3878	−	2.12041i	0.770379	−	0.122016i
$303$	11.3547	−	22.2849i	0.652312	−	1.28023i
$304$	1.34437	+	4.13756i	0.0771052	+	0.237305i
$305$	−6.06845	+	7.24348i	−0.347479	+	0.414760i
$306$	−13.3408	−	4.33468i	−0.762641	−	0.247797i
$307$	−18.6575	−	18.6575i	−1.06484	−	1.06484i	−0.997747	−	0.0670921i	$-0.978628\pi$
$307$	−18.6575	−	18.6575i	−1.06484	−	1.06484i	−0.0670921	−	0.997747i	$-0.521372\pi$
$308$	−3.00570	+	0.381771i	−0.171265	+	0.0217534i
$309$	−11.5963	−	15.9610i	−0.659692	−	0.907989i
$310$	15.5368	+	3.57428i	0.882429	+	0.203006i
$311$	−8.42566	+	11.5969i	−0.477775	+	0.657601i	−0.978075	−	0.208251i	$-0.933223\pi$
$311$	−8.42566	+	11.5969i	−0.477775	+	0.657601i	0.500300	+	0.865852i	$0.333223\pi$
$312$	0.0631301	−	0.398588i	0.00357404	−	0.0225656i
$313$	0.583593	−	3.68466i	0.0329867	−	0.208270i	−0.965690	−	0.259697i	$-0.916377\pi$
$313$	0.583593	−	3.68466i	0.0329867	−	0.208270i	0.998677	+	0.0514278i	$0.0163772\pi$
$314$	−6.77856	−	4.92491i	−0.382536	−	0.277929i
$315$	13.2632	+	8.52035i	0.747295	+	0.480067i
$316$	−11.3586	+	8.25249i	−0.638970	+	0.464239i
$317$	3.61743	+	7.09960i	0.203175	+	0.398753i	0.970001	−	0.243102i	$-0.0781650\pi$
$317$	3.61743	+	7.09960i	0.203175	+	0.398753i	−0.766826	+	0.641855i	$0.778165\pi$
$318$	3.79991	−	3.79991i	0.213088	−	0.213088i
$319$	6.41673	+	2.08492i	0.359268	+	0.116733i
$320$	−1.43599	+	1.71404i	−0.0802743	+	0.0958177i
$321$	−16.5002	+	5.36125i	−0.920954	+	0.299236i
$322$	−11.3466	−	12.0665i	−0.632320	−	0.672441i
$323$	3.58269	+	22.6202i	0.199346	+	1.25862i
$324$		−	9.89365i		−	0.549647i
$325$	0.246615	−	0.811128i	0.0136797	−	0.0449933i
$326$	−12.2931			−0.680851
$327$	−4.36696	−	27.5719i	−0.241493	−	1.52473i
$328$	2.81156	+	1.43256i	0.155242	+	0.0790999i
$329$	0.595869	−	19.3779i	0.0328513	−	1.06834i
$330$	−3.23362	−	5.16598i	−0.178005	−	0.284378i
$331$	−5.76151	+	17.7321i	−0.316681	+	0.974644i	0.658376	+	0.752689i	$0.271244\pi$
$331$	−5.76151	+	17.7321i	−0.316681	+	0.974644i	−0.975057	+	0.221955i	$0.928756\pi$
$332$	−0.289136	−	0.289136i	−0.0158684	−	0.0158684i
$333$	−24.2804	+	12.3715i	−1.33056	+	0.677954i
$334$	−17.4925	+	12.7090i	−0.957146	+	0.695407i
$335$	−1.15804	−	2.72232i	−0.0632706	−	0.148736i
$336$	5.20574	−	3.54296i	0.283997	−	0.193285i
$337$	−3.77213	+	23.8163i	−0.205481	+	1.29736i	0.642072	+	0.766645i	$0.278075\pi$
$337$	−3.77213	+	23.8163i	−0.205481	+	1.29736i	−0.847553	+	0.530711i	$0.821925\pi$
$338$	−12.8116	−	2.02915i	−0.696857	−	0.110371i
$339$	−27.7954	−	20.1945i	−1.50964	−	1.09682i
$340$	−8.87791	+	7.72952i	−0.481472	+	0.419192i
$341$	4.79915	+	6.60546i	0.259888	+	0.357706i
$342$	10.3289	−	5.26285i	0.558524	−	0.284582i
$343$	−4.56943	+	17.9477i	−0.246726	+	0.969085i
$344$	−7.13560	−	2.31850i	−0.384726	−	0.125005i
$345$	12.4570	−	30.9010i	0.670662	−	1.66365i
$346$	−11.0959	+	3.60528i	−0.596520	+	0.193821i
$347$	−31.0767	−	15.8344i	−1.66828	−	0.850033i	−0.993730	−	0.111809i	$-0.964336\pi$
$347$	−31.0767	−	15.8344i	−1.66828	−	0.850033i	−0.674555	−	0.738225i	$-0.735664\pi$
$348$	−13.8497	+	2.19358i	−0.742424	+	0.117588i
$349$	−26.4358			−1.41508			−0.707538	−	0.706675i	$-0.750194\pi$
$349$	−26.4358			−1.41508			−0.707538	+	0.706675i	$0.750194\pi$
$350$	11.8566	−	5.86694i	0.633762	−	0.313601i
$351$	0.135343			0.00722406
$352$	−1.13107	+	0.179145i	−0.0602865	+	0.00954844i
$353$	−30.8175	−	15.7023i	−1.64025	−	0.835750i	−0.997574	−	0.0696133i	$-0.977823\pi$
$353$	−30.8175	−	15.7023i	−1.64025	−	0.835750i	−0.642678	−	0.766137i	$-0.722177\pi$
$354$	−24.2425	+	7.87687i	−1.28847	+	0.418651i
$355$	5.35408	+	21.4035i	0.284165	+	1.13598i
$356$	12.0887	+	3.92787i	0.640702	+	0.208177i
$357$	29.9847	−	14.1345i	1.58696	−	0.748077i
$358$	−8.90807	+	4.53889i	−0.470806	+	0.239888i
$359$	13.6118	+	18.7350i	0.718401	+	0.988794i	0.999575	+	0.0291375i	$0.00927607\pi$
$359$	13.6118	+	18.7350i	0.718401	+	0.988794i	−0.281174	+	0.959657i	$0.590724\pi$
$360$	5.10962	+	3.06479i	0.269300	+	0.161529i
$361$	0.0592679	+	0.0430606i	0.00311936	+	0.00226635i
$362$	18.5492	+	2.93791i	0.974926	+	0.154413i
$363$	−3.60726	+	22.7754i	−0.189332	+	1.19540i
$364$	0.252406	+	0.370865i	0.0132297	+	0.0194386i
$365$	−13.7818	+	1.21649i	−0.721372	+	0.0636742i
$366$	8.13710	−	5.91195i	0.425333	−	0.309022i
$367$	−8.01487	+	4.08378i	−0.418373	+	0.213171i	−0.650488	−	0.759517i	$-0.725435\pi$
$367$	−8.01487	+	4.08378i	−0.418373	+	0.213171i	0.232115	+	0.972688i	$0.425435\pi$
$368$	−4.42675	−	4.42675i	−0.230760	−	0.230760i
$369$	2.59827	−	7.99666i	0.135261	−	0.416290i
$370$	−1.57753	+	22.8133i	−0.0820119	+	1.18601i
$371$	−0.183608	+	5.97099i	−0.00953244	+	0.309998i
$372$	−15.1196	−	7.70382i	−0.783915	−	0.399425i
$373$	−2.71728	−	17.1562i	−0.140695	−	0.888316i	−0.952534	−	0.304434i	$-0.901533\pi$
$373$	−2.71728	−	17.1562i	−0.140695	−	0.888316i	0.811838	−	0.583883i	$-0.198467\pi$
$374$	−6.02851			−0.311727
$375$	20.7185	+	16.6980i	1.06990	+	0.862281i
$376$		−	7.32761i		−	0.377893i
$377$	−0.156274	−	0.986676i	−0.00804853	−	0.0508164i
$378$	1.44671	+	1.53850i	0.0744107	+	0.0791321i
$379$	16.7832	−	5.45319i	0.862095	−	0.280112i	0.155592	−	0.987821i	$-0.450272\pi$
$379$	16.7832	−	5.45319i	0.862095	−	0.280112i	0.706503	+	0.707710i	$0.250272\pi$
$380$	0.671082	−	9.70481i	0.0344258	−	0.497846i
$381$	−3.26404	−	1.06055i	−0.167222	−	0.0543336i
$382$	13.9492	−	13.9492i	0.713703	−	0.713703i
$383$	−7.29382	−	14.3149i	−0.372697	−	0.731459i	0.626138	−	0.779712i	$-0.284635\pi$
$383$	−7.29382	−	14.3149i	−0.372697	−	0.731459i	−0.998835	+	0.0482532i	$0.984635\pi$
$384$	1.92550	−	1.39896i	0.0982602	−	0.0713902i
$385$	6.55267	+	1.72113i	0.333955	+	0.0877171i
$386$	3.44952	+	2.50623i	0.175576	+	0.127564i
$387$	−3.12747	+	19.7460i	−0.158978	+	1.00375i
$388$	0.0125661	−	0.0793390i	0.000637945	−	0.00402783i
$389$	−9.18626	+	12.6438i	−0.465762	+	0.641066i	−0.975691	−	0.219150i	$-0.929672\pi$
$389$	−9.18626	+	12.6438i	−0.465762	+	0.641066i	0.509929	+	0.860216i	$0.329672\pi$
$390$	−0.464161	+	0.773849i	−0.0235037	+	0.0391854i
$391$	−19.3712	−	26.6622i	−0.979645	−	1.34837i
$392$	−1.51777	+	6.83347i	−0.0766590	+	0.345143i
$393$	−7.75737	−	7.75737i	−0.391307	−	0.391307i
$394$	11.8483	+	3.84975i	0.596910	+	0.193948i
$395$	30.4559	−	7.61854i	1.53240	−	0.383331i
$396$	0.942952	+	2.90211i	0.0473851	+	0.145836i
$397$	5.76715	−	11.3187i	0.289445	−	0.568068i	−0.699800	−	0.714339i	$-0.746727\pi$
$397$	5.76715	−	11.3187i	0.289445	−	0.568068i	0.989244	+	0.146272i	$0.0467273\pi$
$398$	−12.5170	+	1.98249i	−0.627418	+	0.0993733i
$399$	−9.26233	+	25.7818i	−0.463697	+	1.29070i
$400$	4.41110	−	2.35419i	0.220555	−	0.117709i
$401$	28.6619			1.43131			0.715654	−	0.698455i	$-0.246129\pi$
$401$	28.6619			1.43131			0.715654	+	0.698455i	$0.246129\pi$
$402$	0.492593	+	3.11011i	0.0245683	+	0.155118i
$403$	0.548831	−	1.07714i	0.0273392	−	0.0536563i
$404$	3.24733	+	9.99426i	0.161561	+	0.497233i
$405$	−8.27150	+	20.5184i	−0.411014	+	1.01957i
$406$	9.54556	−	12.3232i	0.473738	−	0.611592i
$407$	−8.28125	+	8.28125i	−0.410487	+	0.410487i
$408$	11.1636	−	5.68815i	0.552681	−	0.281605i
$409$	13.7627	−	9.99921i	0.680523	−	0.494429i	−0.193008	−	0.981197i	$-0.561824\pi$
$409$	13.7627	−	9.99921i	0.680523	−	0.494429i	0.873531	+	0.486768i	$0.161824\pi$
$410$	−4.63319	−	5.32156i	−0.228817	−	0.262813i
$411$	20.4744	−	28.1806i	1.00993	−	1.39005i
$412$	8.18722	+	1.29673i	0.403355	+	0.0638852i
$413$	13.6341	−	24.8400i	0.670889	−	1.22230i
$414$	−9.80516	+	13.4956i	−0.481897	+	0.663275i
$415$	0.357908	+	0.841368i	0.0175690	+	0.0413011i
$416$	0.0996637	+	0.137175i	0.00488641	+	0.00672557i
$417$	−1.29759	−	2.54667i	−0.0635435	−	0.124711i
$418$	3.52285	−	3.52285i	0.172308	−	0.172308i
$419$	−9.37990	+	28.8683i	−0.458238	+	1.41031i	0.409054	+	0.912510i	$0.365859\pi$
$419$	−9.37990	+	28.8683i	−0.458238	+	1.41031i	−0.867291	+	0.497801i	$0.834141\pi$
$420$	−13.7582	+	2.99551i	−0.671333	+	0.146166i
$421$	0.308315	+	0.948895i	0.0150263	+	0.0462463i	0.958289	−	0.285802i	$-0.0922601\pi$
$421$	0.308315	+	0.948895i	0.0150263	+	0.0462463i	−0.943262	+	0.332049i	$0.892260\pi$
$422$	−19.2685	−	9.81778i	−0.937975	−	0.477922i
$423$	−19.2849	+	3.05444i	−0.937666	+	0.148512i
$424$			2.25789i			0.109653i
$425$	24.8740	−	8.60789i	1.20657	−	0.417544i
$426$		−	23.4836i		−	1.13778i
$427$	−2.08766	+	10.9842i	−0.101029	+	0.531564i
$428$	3.30937	−	6.49500i	0.159964	−	0.313948i
$429$	−0.439523	+	0.142810i	−0.0212204	+	0.00689491i
$430$	12.8601	+	10.7740i	0.620170	+	0.519567i
$431$	3.98936	−	12.2780i	0.192161	−	0.591410i	−0.807837	−	0.589406i	$-0.799362\pi$
$431$	3.98936	−	12.2780i	0.192161	−	0.591410i	0.999998	−	0.00200427i	$-0.000637978\pi$
$432$	0.564419	+	0.564419i	0.0271556	+	0.0271556i
$433$	15.8495	+	31.1065i	0.761680	+	1.49488i	0.865840	+	0.500321i	$0.166785\pi$
$433$	15.8495	+	31.1065i	0.761680	+	1.49488i	−0.104160	+	0.994561i	$0.533215\pi$
$434$	18.1110	−	5.27500i	0.869354	−	0.253208i
$435$	30.5568	+	7.02970i	1.46509	+	0.337049i
$436$	9.48896	+	6.89413i	0.454439	+	0.330169i
$437$	26.9003	+	4.26060i	1.28682	+	0.203812i
$438$	14.5449	+	2.30369i	0.694983	+	0.110074i
$439$	33.0245	+	23.9937i	1.57617	+	1.14516i	0.920923	+	0.389745i	$0.127437\pi$
$439$	33.0245	+	23.9937i	1.57617	+	1.14516i	0.655250	+	0.755412i	$0.272563\pi$
$440$	2.49550	+	0.574099i	0.118968	+	0.0273691i
$441$	18.6171	+	1.14604i	0.886530	+	0.0545731i
$442$	0.405232	+	0.795312i	0.0192749	+	0.0378291i
$443$	14.7687	+	14.7687i	0.701680	+	0.701680i	0.964771	−	0.263091i	$-0.0847419\pi$
$443$	14.7687	+	14.7687i	0.701680	+	0.701680i	−0.263091	+	0.964771i	$0.584742\pi$
$444$	7.52156	−	23.1490i	0.356957	−	1.09860i
$445$	−21.7869	−	18.2527i	−1.03280	−	0.865259i
$446$	−16.0497	+	5.21487i	−0.759976	+	0.246931i
$447$	11.6119	−	22.7897i	0.549226	−	1.07792i
$448$	−0.494008	+	2.59922i	−0.0233397	+	0.122802i
$449$			15.8729i			0.749088i	0.927209	+	0.374544i	$0.122201\pi$
$449$			15.8729i			0.749088i	−0.927209	+	0.374544i	$0.877799\pi$
$450$	−8.03451	−	10.6279i	−0.378750	−	0.501004i
$451$		−	3.61358i		−	0.170157i
$452$	14.2577	−	2.25820i	0.670626	−	0.106217i
$453$	28.7445	+	14.6461i	1.35053	+	0.688131i
$454$	2.14999	+	6.61699i	0.100904	+	0.310551i
$455$	−0.213405	−	0.980156i	−0.0100046	−	0.0459504i
$456$	−3.19967	+	9.84759i	−0.149839	+	0.461156i
$457$	4.63576	−	4.63576i	0.216852	−	0.216852i	−0.590319	−	0.807170i	$-0.700998\pi$
$457$	4.63576	−	4.63576i	0.216852	−	0.216852i	0.807170	+	0.590319i	$0.200998\pi$
$458$	11.4518	+	22.4755i	0.535109	+	1.05021i
$459$	2.46987	+	3.39948i	0.115284	+	0.158674i
$460$	5.47966	+	12.8816i	0.255490	+	0.600605i
$461$	−10.0823	+	13.8771i	−0.469581	+	0.646322i	−0.976461	−	0.215694i	$-0.930799\pi$
$461$	−10.0823	+	13.8771i	−0.469581	+	0.646322i	0.506880	+	0.862016i	$0.330799\pi$
$462$	−6.32155	−	3.46974i	−0.294105	−	0.161427i
$463$	−7.35355	−	1.16469i	−0.341749	−	0.0541277i	−0.0167987	−	0.999859i	$-0.505347\pi$
$463$	−7.35355	−	1.16469i	−0.341749	−	0.0541277i	−0.324950	+	0.945731i	$0.605347\pi$
$464$	3.46302	−	4.76644i	0.160767	−	0.221276i
$465$	24.9157	+	28.6175i	1.15544	+	1.32711i
$466$	0.198435	−	0.144172i	0.00919234	−	0.00667863i
$467$	13.8313	−	7.04737i	0.640034	−	0.326114i	−0.103681	−	0.994611i	$-0.533062\pi$
$467$	13.8313	−	7.04737i	0.640034	−	0.326114i	0.743715	+	0.668497i	$0.233062\pi$
$468$	0.319477	−	0.319477i	0.0147678	−	0.0147678i
$469$	−2.76732	−	2.14356i	−0.127783	−	0.0989804i
$470$	−6.12619	+	15.1967i	−0.282580	+	0.700971i
$471$	−6.16237	−	18.9658i	−0.283947	−	0.873899i
$472$	4.86220	−	9.54260i	0.223801	−	0.439234i
$473$	1.34409	+	8.48624i	0.0618013	+	0.390198i
$474$	−33.4158			−1.53484
$475$	−9.50538	+	19.5657i	−0.436137	+	0.897736i
$476$	−4.70907	+	13.1077i	−0.215840	+	0.600792i
$477$	5.94235	−	0.941176i	0.272082	−	0.0430935i
$478$	−8.61001	+	16.8981i	−0.393813	+	0.772901i
$479$	−0.881304	−	2.71237i	−0.0402678	−	0.123932i	0.928902	−	0.370326i	$-0.120754\pi$
$479$	−0.881304	−	2.71237i	−0.0402678	−	0.123932i	−0.969170	+	0.246395i	$0.920754\pi$
$480$	−5.16287	+	1.29149i	−0.235651	+	0.0589482i
$481$	1.64917	+	0.535846i	0.0751955	+	0.0244325i
$482$	2.30420	+	2.30420i	0.104953	+	0.104953i
$483$	−4.96726	−	39.1074i	−0.226018	−	1.77945i
$484$	−5.69480	−	7.83822i	−0.258855	−	0.356283i
$485$	−0.0923914	+	0.154035i	−0.00419528	+	0.00699436i
$486$	12.4333	−	17.1129i	0.563984	−	0.776258i
$487$	−1.11708	+	7.05297i	−0.0506198	+	0.319601i	0.949365	+	0.314174i	$0.101727\pi$
$487$	−1.11708	+	7.05297i	−0.0506198	+	0.319601i	−0.999985	+	0.00542695i	$0.998273\pi$
$488$	−0.661087	+	4.17394i	−0.0299260	+	0.188945i
$489$	−23.6703	−	17.1975i	−1.07041	−	0.777698i
$490$	8.86076	−	12.9030i	0.400288	−	0.582897i
$491$	14.9356	−	10.8514i	0.674035	−	0.489715i	−0.197339	−	0.980335i	$-0.563230\pi$
$491$	14.9356	−	10.8514i	0.674035	−	0.489715i	0.871373	+	0.490620i	$0.163230\pi$
$492$	3.40956	+	6.69164i	0.153715	+	0.301683i
$493$	21.9311	−	21.9311i	0.987725	−	0.987725i
$494$	−0.701556	−	0.227949i	−0.0315645	−	0.0102559i
$495$	0.470701	−	6.80701i	0.0211564	−	0.305953i
$496$	6.78079	−	2.20321i	0.304466	−	0.0989272i
$497$	17.8831	+	19.0178i	0.802169	+	0.853067i
$498$	−0.152242	−	0.961221i	−0.00682214	−	0.0430733i
$499$		−	1.40848i		−	0.0630524i	−0.999503	−	0.0315262i	$-0.989963\pi$
$499$		−	1.40848i		−	0.0630524i	0.999503	−	0.0315262i	$-0.0100368\pi$
$500$	−11.1164	+	1.19447i	−0.497138	+	0.0534182i
$501$	−51.4611			−2.29911
$502$	1.67729	+	10.5900i	0.0748613	+	0.472656i
$503$	−21.3603	−	10.8836i	−0.952410	−	0.485277i	−0.0924943	−	0.995713i	$-0.529484\pi$
$503$	−21.3603	−	10.8836i	−0.952410	−	0.485277i	−0.859916	+	0.510436i	$0.829484\pi$
$504$	7.04660	+	0.216683i	0.313881	+	0.00965182i
$505$	1.62100	−	23.4419i	0.0721334	−	1.04315i
$506$	−2.21541	+	6.81832i	−0.0984869	+	0.303111i
$507$	−21.8299	−	21.8299i	−0.969501	−	0.969501i
$508$	1.28482	−	0.654651i	0.0570049	−	0.0290454i
$509$	15.3918	−	11.1828i	0.682229	−	0.495669i	−0.191867	−	0.981421i	$-0.561454\pi$
$509$	15.3918	−	11.1828i	0.682229	−	0.495669i	0.874097	+	0.485752i	$0.161454\pi$
$510$	−27.9077	+	2.46336i	−1.23577	+	0.109080i
$511$	−13.5333	+	9.21058i	−0.598677	+	0.407452i
$512$	−0.156434	+	0.987688i	−0.00691349	+	0.0436501i
$513$	−3.42984	−	0.543234i	−0.151431	−	0.0239844i
$514$	−13.0365	−	9.47159i	−0.575017	−	0.417774i
$515$	−15.8953	−	9.53413i	−0.700431	−	0.420124i
$516$	−10.4961	−	14.4467i	−0.462066	−	0.635979i
$517$	−7.47678	+	3.80961i	−0.328828	+	0.167546i
$518$	11.5371	+	24.4746i	0.506911	+	1.07535i
$519$	−26.4088	−	8.58074i	−1.15922	−	0.376653i
$520$	−0.0920076	−	0.367810i	−0.00403480	−	0.0161295i
$521$	9.11092	−	2.96032i	0.399157	−	0.129694i	−0.102558	−	0.994727i	$-0.532703\pi$
$521$	9.11092	−	2.96032i	0.399157	−	0.129694i	0.501715	+	0.865033i	$0.332703\pi$
$522$	−13.9879	−	7.12720i	−0.612235	−	0.311949i
$523$	−12.9558	+	2.05199i	−0.566517	+	0.0897275i	−0.433122	−	0.901335i	$-0.642588\pi$
$523$	−12.9558	+	2.05199i	−0.566517	+	0.0897275i	−0.133395	+	0.991063i	$0.542588\pi$
$524$	4.60939			0.201362
$525$	31.0375	+	5.29008i	1.35459	+	0.230878i
$526$	1.68455			0.0734499
$527$	37.0708	−	5.87144i	1.61483	−	0.255764i
$528$	−2.42850	−	1.23738i	−0.105687	−	0.0538501i
$529$	−15.3997	+	5.00367i	−0.669553	+	0.217551i
$530$	1.88769	−	4.68262i	0.0819960	−	0.203400i
$531$	−27.1411	−	8.81869i	−1.17783	−	0.382699i
$532$	−4.90789	−	10.4115i	−0.212784	−	0.451397i
$533$	−0.476722	+	0.242902i	−0.0206491	+	0.0105213i
$534$	17.7819	+	24.4747i	0.769499	+	1.05912i
$535$	−12.2934	+	10.7032i	−0.531489	+	0.462739i
$536$	−1.07036	−	0.777659i	−0.0462323	−	0.0335898i
$537$	−23.5022	−	3.72238i	−1.01419	−	0.160633i
$538$	−2.70791	+	17.0971i	−0.116746	+	0.737108i
$539$	7.76167	−	2.00404i	0.334319	−	0.0863202i
$540$	−0.698667	−	1.64242i	−0.0300658	−	0.0706786i
$541$	17.2094	−	12.5034i	0.739889	−	0.537561i	−0.152787	−	0.988259i	$-0.548825\pi$
$541$	17.2094	−	12.5034i	0.739889	−	0.537561i	0.892676	+	0.450698i	$0.148825\pi$
$542$	−6.69578	+	3.41167i	−0.287609	+	0.146544i
$543$	31.6065	+	31.6065i	1.35637	+	1.35637i
$544$	−1.62675	+	5.00662i	−0.0697463	+	0.214657i
$545$	−13.9153	−	22.2309i	−0.596066	−	0.952266i
$546$	−0.0328165	+	1.06720i	−0.00140442	+	0.0456721i
$547$	23.1307	+	11.7857i	0.988995	+	0.503918i	0.872154	−	0.489232i	$-0.162723\pi$
$547$	23.1307	+	11.7857i	0.988995	+	0.503918i	0.116842	+	0.993151i	$0.462723\pi$
$548$	2.28950	+	14.4553i	0.0978024	+	0.617500i
$549$	11.2606			0.480592
$550$	−4.69543	−	3.27696i	−0.200214	−	0.139730i
$551$			25.6315i			1.09194i
$552$	−2.33087	−	14.7165i	−0.0992084	−	0.626377i
$553$	27.0613	−	25.4467i	1.15076	−	1.08210i
$554$	20.7547	−	6.74361i	0.881783	−	0.286509i
$555$	−34.9524	+	41.7202i	−1.48365	+	1.77092i
$556$	1.14212	+	0.371098i	0.0484368	+	0.0157381i
$557$	−6.45103	+	6.45103i	−0.273339	+	0.273339i	−0.830443	−	0.557104i	$-0.811913\pi$
$557$	−6.45103	+	6.45103i	−0.273339	+	0.273339i	0.557104	+	0.830443i	$0.311913\pi$
$558$	−8.62495	−	16.9274i	−0.365123	−	0.716595i
$559$	1.02920	−	0.747758i	0.0435306	−	0.0316268i
$560$	3.19758	−	4.97750i	0.135122	−	0.210338i
$561$	−11.6079	−	8.43362i	−0.490085	−	0.356068i
$562$	2.75252	−	17.3787i	0.116108	−	0.733076i
$563$	−5.04759	+	31.8692i	−0.212730	+	1.34313i	0.617880	+	0.786273i	$0.287992\pi$
$563$	−5.04759	+	31.8692i	−0.212730	+	1.34313i	−0.830610	+	0.556854i	$0.812008\pi$
$564$	10.2510	−	14.1093i	0.431645	−	0.594109i
$565$	−31.4569	−	7.23677i	−1.32340	−	0.304453i
$566$	−12.5823	−	17.3181i	−0.528874	−	0.727932i
$567$	3.29829	+	25.9675i	0.138515	+	1.09053i
$568$	6.97693	+	6.97693i	0.292745	+	0.292745i
$569$	−24.7377	−	8.03778i	−1.03706	−	0.336961i	−0.259482	−	0.965748i	$-0.583552\pi$
$569$	−24.7377	−	8.03778i	−1.03706	−	0.336961i	−0.777578	+	0.628787i	$0.783552\pi$
$570$	14.8688	−	17.7478i	0.622785	−	0.743373i
$571$	−1.48427	−	4.56811i	−0.0621147	−	0.191169i	0.915184	−	0.403037i	$-0.132045\pi$
$571$	−1.48427	−	4.56811i	−0.0621147	−	0.191169i	−0.977298	+	0.211868i	$0.932045\pi$
$572$	0.0881529	−	0.173010i	0.00368586	−	0.00723390i
$573$	46.3735	−	7.34484i	1.93728	−	0.306835i
$574$	−7.85698	−	2.82269i	−0.327944	−	0.117817i
$575$	−0.594718	−	31.2962i	−0.0248014	−	1.30514i
$576$	2.66462			0.111026
$577$	−1.86021	−	11.7449i	−0.0774415	−	0.488947i	−0.995675	−	0.0929066i	$-0.970384\pi$
$577$	−1.86021	−	11.7449i	−0.0774415	−	0.488947i	0.918233	−	0.396040i	$-0.129616\pi$
$578$	−4.86340	+	9.54496i	−0.202291	+	0.397018i
$579$	3.13595	+	9.65147i	0.130326	+	0.401101i
$580$	−11.1669	+	6.98986i	−0.463679	+	0.290238i
$581$	0.855276	+	0.662495i	0.0354828	+	0.0274849i
$582$	0.135188	−	0.135188i	0.00560371	−	0.00560371i
$583$	2.30385	−	1.17387i	0.0954159	−	0.0486168i
$584$	−5.00568	+	3.63684i	−0.207137	+	0.150494i
$585$	−0.929657	+	0.395465i	−0.0384366	+	0.0163505i
$586$	9.11743	−	12.5491i	0.376638	−	0.518397i
$587$	37.2716	+	5.90324i	1.53836	+	0.243653i	0.867315	−	0.497760i	$-0.165844\pi$
$587$	37.2716	+	5.90324i	1.53836	+	0.243653i	0.671049	+	0.741413i	$0.265844\pi$
$588$	−12.4822	+	11.0346i	−0.514757	+	0.455057i
$589$	−18.2318	+	25.0940i	−0.751230	+	1.03398i
$590$	−18.0617	+	15.7253i	−0.743588	+	0.647402i
$591$	17.4283	+	23.9880i	0.716904	+	0.986734i
$592$	4.64287	+	9.11215i	0.190821	+	0.374507i
$593$	−25.6397	+	25.6397i	−1.05290	+	1.05290i	−0.0543752	+	0.998521i	$0.517317\pi$
$593$	−25.6397	+	25.6397i	−1.05290	+	1.05290i	−0.998521	+	0.0543752i	$0.982683\pi$
$594$	0.282469	−	0.869349i	0.0115898	−	0.0356698i
$595$	20.7247	−	23.2471i	0.849631	−	0.953036i
$596$	3.32089	+	10.2207i	0.136029	+	0.418655i
$597$	−26.8748	−	13.6934i	−1.09991	−	0.560433i
$598$	1.04843	−	0.166054i	0.0428734	−	0.00679047i
$599$			31.4188i			1.28374i	0.766814	+	0.641869i	$0.221841\pi$
$599$			31.4188i			1.28374i	−0.766814	+	0.641869i	$0.778159\pi$
$600$	11.7870	+	1.63796i	0.481201	+	0.0668693i
$601$			8.23773i			0.336024i	0.985785	+	0.168012i	$0.0537347\pi$
$601$			8.23773i			0.336024i	−0.985785	+	0.168012i	$0.946265\pi$
$602$	19.5015	+	3.70645i	0.794821	+	0.151064i
$603$	−1.60049	+	3.14114i	−0.0651771	+	0.127917i
$604$	−12.8912	+	4.18862i	−0.524537	+	0.170432i
$605$	5.25733	+	21.0167i	0.213741	+	0.854452i
$606$	−7.72880	+	23.7868i	−0.313961	+	0.966273i
$607$	−28.5542	−	28.5542i	−1.15898	−	1.15898i	−0.984695	−	0.174285i	$-0.944238\pi$
$607$	−28.5542	−	28.5542i	−1.15898	−	1.15898i	−0.174285	−	0.984695i	$-0.555762\pi$
$608$	−1.97508	−	3.87631i	−0.0801001	−	0.157205i
$609$	35.6197	−	10.3746i	1.44338	−	0.420399i
$610$	4.86061	−	8.10361i	0.196800	−	0.328106i
$611$	1.00517	+	0.730297i	0.0406647	+	0.0295446i
$612$	13.8546	+	2.19435i	0.560039	+	0.0887015i
$613$	−2.71054	−	0.429307i	−0.109478	−	0.0173396i	0.101455	−	0.994840i	$-0.467650\pi$
$613$	−2.71054	−	0.429307i	−0.109478	−	0.0173396i	−0.210933	+	0.977501i	$0.567650\pi$
$614$	21.3465	+	15.5091i	0.861473	+	0.625897i
$615$	−1.47658	−	16.7283i	−0.0595413	−	0.674550i
$616$	2.90897	−	0.847265i	0.117206	−	0.0341373i
$617$	−7.63814	−	14.9907i	−0.307500	−	0.603502i	0.684605	−	0.728914i	$-0.259975\pi$
$617$	−7.63814	−	14.9907i	−0.307500	−	0.603502i	−0.992105	+	0.125412i	$0.959975\pi$
$618$	13.9504	+	13.9504i	0.561168	+	0.561168i
$619$	11.4902	−	35.3630i	0.461828	−	1.42136i	−0.401100	−	0.916034i	$-0.631372\pi$
$619$	11.4902	−	35.3630i	0.461828	−	1.42136i	0.862928	−	0.505327i	$-0.168628\pi$
$620$	−15.9046	−	1.09979i	−0.638745	−	0.0441688i
$621$	4.75251	−	1.54418i	0.190712	−	0.0619659i
$622$	6.50777	−	12.7722i	0.260938	−	0.512119i
$623$	−33.0383	−	6.27926i	−1.32365	−	0.251573i
$624$			0.403556i			0.0161552i
$625$	24.0528	+	6.81653i	0.962110	+	0.272661i
$626$			3.73059i			0.149105i
$627$	11.7116	−	1.85493i	0.467715	−	0.0740787i
$628$	7.46553	+	3.80388i	0.297907	+	0.151791i
$629$	16.6364	+	51.2017i	0.663338	+	2.04155i
$630$	−14.4328	−	6.34063i	−0.575015	−	0.252617i
$631$	−5.59309	+	17.2138i	−0.222657	+	0.685269i	0.775864	+	0.630901i	$0.217314\pi$
$631$	−5.59309	+	17.2138i	−0.222657	+	0.685269i	−0.998521	+	0.0543682i	$0.982686\pi$
$632$	9.92776	−	9.92776i	0.394905	−	0.394905i
$633$	−23.3668	−	45.8599i	−0.928746	−	1.82277i
$634$	−4.68351	−	6.44630i	−0.186006	−	0.256015i
$635$	−3.21190	+	0.283509i	−0.127461	+	0.0112507i
$636$	−3.15869	+	4.34756i	−0.125250	+	0.172392i
$637$	−0.786117	−	0.889250i	−0.0311471	−	0.0352334i
$638$	−6.66389	−	1.05546i	−0.263826	−	0.0417859i
$639$	15.4538	−	21.2703i	0.611341	−	0.841439i
$640$	1.15018	−	1.91757i	0.0454647	−	0.0757988i
$641$	11.3277	−	8.23008i	0.447418	−	0.325068i	−0.341157	−	0.940006i	$-0.610819\pi$
$641$	11.3277	−	8.23008i	0.447418	−	0.325068i	0.788576	+	0.614938i	$0.210819\pi$
$642$	15.4584	−	7.87646i	0.610095	−	0.310859i
$643$	31.9694	−	31.9694i	1.26075	−	1.26075i	0.310019	−	0.950730i	$-0.399665\pi$
$643$	31.9694	−	31.9694i	1.26075	−	1.26075i	0.950730	−	0.310019i	$-0.100335\pi$
$644$	13.0945	+	10.1430i	0.515995	+	0.399689i
$645$	9.68981	+	38.7360i	0.381536	+	1.52523i
$646$	−7.07715	−	21.7812i	−0.278447	−	0.856971i
$647$	−7.11079	+	13.9557i	−0.279554	+	0.548656i	−0.987502	−	0.157609i	$-0.949621\pi$
$647$	−7.11079	+	13.9557i	−0.279554	+	0.548656i	0.707947	+	0.706265i	$0.249621\pi$
$648$	1.54771	+	9.77184i	0.0607997	+	0.383874i
$649$	−12.2647			−0.481432
$650$	−0.116690	+	0.839721i	−0.00457697	+	0.0329366i
$651$	42.2521	+	15.1795i	1.65599	+	0.594930i
$652$	12.1417	−	1.92306i	0.475507	−	0.0753130i
$653$	−14.7108	+	28.8715i	−0.575677	+	1.12983i	0.401193	+	0.915994i	$0.368596\pi$
$653$	−14.7108	+	28.8715i	−0.575677	+	1.12983i	−0.976870	+	0.213835i	$0.931404\pi$
$654$	8.62639	+	26.5493i	0.337318	+	1.03816i
$655$	−9.55939	−	3.85364i	−0.373516	−	0.150574i
$656$	−3.00105	−	0.975099i	−0.117171	−	0.0380712i
$657$	11.6581	+	11.6581i	0.454825	+	0.454825i
$658$	2.44284	+	19.2325i	0.0952316	+	0.749762i
$659$	−7.44509	−	10.2473i	−0.290020	−	0.399178i	0.639001	−	0.769206i	$-0.279348\pi$
$659$	−7.44509	−	10.2473i	−0.290020	−	0.399178i	−0.929021	+	0.370028i	$0.879348\pi$
$660$	4.00194	+	4.59652i	0.155775	+	0.178919i
$661$	−28.6212	+	39.3937i	−1.11324	+	1.53224i	−0.296677	+	0.954978i	$0.595879\pi$
$661$	−28.6212	+	39.3937i	−1.11324	+	1.53224i	−0.816560	+	0.577261i	$0.804121\pi$
$662$	2.91666	−	18.4151i	0.113359	−	0.715723i
$663$	−0.332334	+	2.09827i	−0.0129068	+	0.0814902i
$664$	0.330807	+	0.240346i	0.0128378	+	0.00932722i
$665$	1.47397	+	25.6956i	0.0571580	+	0.996432i
$666$	22.0462	−	16.0175i	0.854272	−	0.620665i
$667$	−16.7449	−	32.8638i	−0.648366	−	1.27249i
$668$	15.2890	−	15.2890i	0.591549	−	0.591549i
$669$	−38.1991	−	12.4116i	−1.47686	−	0.479861i
$670$	1.56965	+	2.50764i	0.0606408	+	0.0968788i
$671$	4.60261	−	1.49548i	0.177682	−	0.0577323i
$672$	−4.58741	+	4.31370i	−0.176963	+	0.166405i
$673$	−2.23840	−	14.1327i	−0.0862840	−	0.544775i	−0.992528	−	0.122020i	$-0.961063\pi$
$673$	−2.23840	−	14.1327i	−0.0862840	−	0.544775i	0.906244	−	0.422756i	$-0.138937\pi$
$674$		−	24.1132i		−	0.928804i
$675$	0.0758276	+	3.99032i	0.00291861	+	0.153588i
$676$	12.9713			0.498894
$677$	0.304936	+	1.92529i	0.0117196	+	0.0739949i	0.992855	−	0.119327i	$-0.0380738\pi$
$677$	0.304936	+	1.92529i	0.0117196	+	0.0739949i	−0.981135	+	0.193322i	$0.938074\pi$
$678$	30.6123	+	15.5977i	1.17566	+	0.599028i
$679$	−0.00653213	+	0.212427i	−0.000250680	+	0.00815222i
$680$	7.55945	−	9.02317i	0.289892	−	0.346023i
$681$	−5.11708	+	15.7488i	−0.196087	+	0.603494i
$682$	−5.77338	−	5.77338i	−0.221074	−	0.221074i
$683$	−10.7217	+	5.46299i	−0.410255	+	0.209035i	−0.646923	−	0.762555i	$-0.723945\pi$
$683$	−10.7217	+	5.46299i	−0.410255	+	0.209035i	0.236668	+	0.971591i	$0.423945\pi$
$684$	−9.37846	+	6.81385i	−0.358594	+	0.260534i
$685$	7.33707	−	31.8929i	0.280335	−	1.21856i
$686$	1.70553	−	18.4416i	0.0651176	−	0.704102i
$687$	−9.39174	+	59.2971i	−0.358317	+	2.26233i
$688$	7.41044	+	1.17370i	0.282520	+	0.0447468i
$689$	−0.309727	−	0.225030i	−0.0117996	−	0.00857294i
$690$	−7.46966	+	32.4692i	−0.284365	+	1.23608i
$691$	−20.4274	−	28.1159i	−0.777095	−	1.06958i	−0.995596	−	0.0937430i	$-0.970117\pi$
$691$	−20.4274	−	28.1159i	−0.777095	−	1.06958i	0.218501	−	0.975837i	$-0.429883\pi$
$692$	10.3953	−	5.29668i	0.395170	−	0.201349i
$693$	−3.44242	−	7.30271i	−0.130767	−	0.277407i
$694$	33.1711	+	10.7780i	1.25916	+	0.409126i
$695$	−2.05839	−	1.72448i	−0.0780791	−	0.0654133i
$696$	13.3361	−	4.33316i	0.505503	−	0.164248i
$697$	−14.8008	−	7.54139i	−0.560621	−	0.285651i
$698$	26.1103	−	4.13547i	0.988291	−	0.156530i
$699$	0.583777			0.0220805
$700$	−10.7928	+	7.64949i	−0.407931	+	0.289124i
$701$	−52.2678			−1.97413			−0.987064	−	0.160324i	$-0.948746\pi$
$701$	−52.2678			−1.97413			−0.987064	+	0.160324i	$0.948746\pi$
$702$	−0.133676	+	0.0211723i	−0.00504529	+	0.000799095i
$703$	−39.6423	−	20.1987i	−1.49514	−	0.761810i
$704$	1.08912	−	0.353878i	0.0410479	−	0.0133373i
$705$	−33.0555	+	20.6909i	−1.24494	+	0.779265i
$706$	32.8945	+	10.6881i	1.23800	+	0.402251i
$707$	−11.8550	−	25.1490i	−0.445853	−	0.945826i
$708$	22.7118	−	11.5723i	0.853563	−	0.434912i
$709$	−24.5770	−	33.8273i	−0.923008	−	1.27041i	−0.962525	−	0.271192i	$-0.912582\pi$
$709$	−24.5770	−	33.8273i	−0.923008	−	1.27041i	0.0395174	−	0.999219i	$-0.487418\pi$
$710$	−8.63640	−	20.3024i	−0.324118	−	0.761936i
$711$	−30.2664	−	21.9898i	−1.13508	−	0.824682i
$712$	−12.5544	−	1.98841i	−0.470494	−	0.0745190i
$713$	6.98243	−	44.0853i	0.261494	−	1.65101i
$714$	−27.4045	+	18.6511i	−1.02559	+	0.698001i
$715$	−0.327463	+	0.285104i	−0.0122464	+	0.0106623i
$716$	8.08836	−	5.87654i	0.302276	−	0.219617i
$717$	−40.2183	+	20.4922i	−1.50198	+	0.765296i
$718$	−16.3750	−	16.3750i	−0.611108	−	0.611108i
$719$	−0.461478	+	1.42028i	−0.0172102	+	0.0529676i	−0.959293	−	0.282413i	$-0.908865\pi$
$719$	−0.461478	+	1.42028i	−0.0172102	+	0.0529676i	0.942083	+	0.335381i	$0.108865\pi$
$720$	−5.52615	−	2.22774i	−0.205947	−	0.0830229i
$721$	−21.9210	−	0.674069i	−0.816380	−	0.0251037i
$722$	−0.0652744	−	0.0332589i	−0.00242926	−	0.00123777i
$723$	1.21326	+	7.66021i	0.0451216	+	0.284886i
$724$	−18.7805			−0.697970
$725$	29.0027	−	5.16025i	1.07713	−	0.191647i
$726$		−	23.0593i		−	0.855810i
$727$	6.81639	+	43.0370i	0.252806	+	1.59615i	0.708298	+	0.705914i	$0.249463\pi$
$727$	6.81639	+	43.0370i	0.252806	+	1.59615i	−0.455492	+	0.890240i	$0.650537\pi$
$728$	−0.307314	−	0.326814i	−0.0113898	−	0.0121125i
$729$	19.6522	−	6.38538i	0.727859	−	0.236496i
$730$	13.4218	−	3.35746i	0.496763	−	0.124265i
$731$	37.5637	+	12.2052i	1.38935	+	0.451426i
$732$	−7.11208	+	7.11208i	−0.262870	+	0.262870i
$733$	16.0417	+	31.4835i	0.592512	+	1.16287i	0.971405	+	0.237430i	$0.0763050\pi$
$733$	16.0417	+	31.4835i	0.592512	+	1.16287i	−0.378893	+	0.925441i	$0.623695\pi$
$734$	7.27735	−	5.28730i	0.268612	−	0.195158i
$735$	35.1121	−	12.4488i	1.29513	−	0.459183i
$736$	5.06474	+	3.67975i	0.186689	+	0.135637i
$737$	−0.237014	+	1.49645i	−0.00873053	+	0.0551224i
$738$	−1.31533	+	8.30467i	−0.0484180	+	0.305699i
$739$	22.4847	−	30.9475i	0.827113	−	1.13842i	−0.161340	−	0.986899i	$-0.551582\pi$
$739$	22.4847	−	30.9475i	0.827113	−	1.13842i	0.988453	−	0.151525i	$-0.0484184\pi$
$740$	−2.01069	−	22.7793i	−0.0739143	−	0.837382i
$741$	−1.03195	−	1.42036i	−0.0379098	−	0.0521783i
$742$	−0.752721	−	5.92620i	−0.0276333	−	0.217558i
$743$	−28.9588	−	28.9588i	−1.06240	−	1.06240i	−0.997919	−	0.0644778i	$-0.979462\pi$
$743$	−28.9588	−	28.9588i	−1.06240	−	1.06240i	−0.0644778	−	0.997919i	$-0.520538\pi$
$744$	16.1386	+	5.24375i	0.591670	+	0.192245i
$745$	1.65772	−	23.9730i	0.0607340	−	0.878302i
$746$	5.36765	+	16.5199i	0.196524	+	0.604838i
$747$	0.494653	−	0.970811i	0.0180984	−	0.0355201i
$748$	5.95429	−	0.943066i	0.217710	−	0.0344819i
$749$	−6.52072	+	18.1505i	−0.238262	+	0.663203i
$750$	−23.0755	−	13.2513i	−0.842599	−	0.483871i
$751$	12.8419			0.468606			0.234303	−	0.972164i	$-0.424719\pi$
$751$	12.8419			0.468606			0.234303	+	0.972164i	$0.424719\pi$
$752$	1.14629	+	7.23740i	0.0418009	+	0.263921i
$753$	−11.5854	+	22.7375i	−0.422194	+	0.828602i
$754$	0.308700	+	0.950082i	0.0112422	+	0.0345999i
$755$	30.2369	+	2.09086i	1.10043	+	0.0760944i
$756$	−1.66957	−	1.29325i	−0.0607218	−	0.0470350i
$757$	17.1512	−	17.1512i	0.623372	−	0.623372i	−0.323020	−	0.946392i	$-0.604698\pi$
$757$	17.1512	−	17.1512i	0.623372	−	0.623372i	0.946392	+	0.323020i	$0.104698\pi$
$758$	−15.7235	+	8.01152i	−0.571103	+	0.290992i
$759$	−13.8043	+	10.0294i	−0.501064	+	0.364045i
$760$	0.855347	+	9.69031i	0.0310267	+	0.351504i
$761$	−13.6816	+	18.8311i	−0.495957	+	0.682626i	−0.981473	−	0.191602i	$-0.938632\pi$
$761$	−13.6816	+	18.8311i	−0.495957	+	0.682626i	0.485516	+	0.874228i	$0.338632\pi$
$762$	3.38976	+	0.536885i	0.122798	+	0.0194493i
$763$	−27.2037	−	14.9314i	−0.984839	−	0.540553i
$764$	−11.5953	+	15.9596i	−0.419504	+	0.577398i
$765$	−26.8984	−	16.1339i	−0.972514	−	0.583322i
$766$	9.44337	+	12.9977i	0.341203	+	0.469626i
$767$	0.824424	+	1.61802i	0.0297682	+	0.0584234i
$768$	−1.68295	+	1.68295i	−0.0607281	+	0.0607281i
$769$	3.83202	−	11.7938i	0.138186	−	0.425294i	−0.857886	−	0.513840i	$-0.828222\pi$
$769$	3.83202	−	11.7938i	0.138186	−	0.425294i	0.996072	+	0.0885469i	$0.0282223\pi$
$770$	−6.74124	−	0.674881i	−0.242937	−	0.0243210i
$771$	−11.8515	−	36.4751i	−0.426820	−	1.31362i
$772$	−3.79911	−	1.93575i	−0.136733	−	0.0696690i
$773$	−20.6955	+	3.27785i	−0.744366	+	0.117896i	−0.517086	−	0.855933i	$-0.672983\pi$
$773$	−20.6955	+	3.27785i	−0.744366	+	0.117896i	−0.227280	+	0.973829i	$0.572983\pi$
$774$		−	19.9922i		−	0.718604i
$775$	32.0650	+	15.5778i	1.15181	+	0.559570i
$776$			0.0803280i			0.00288361i
$777$	−12.0243	+	63.2658i	−0.431369	+	2.26965i
$778$	7.09524	−	13.9252i	0.254377	−	0.499242i
$779$	13.0560	−	4.24216i	0.467780	−	0.151991i
$780$	0.337390	−	0.836932i	0.0120805	−	0.0299670i
$781$	3.49167	−	10.7463i	0.124942	−	0.384531i
$782$	23.3036	+	23.3036i	0.833335	+	0.833335i
$783$	2.13501	+	4.19019i	0.0762990	+	0.149745i
$784$	0.430093	−	6.98677i	0.0153605	−	0.249528i
$785$	−12.3025	−	14.1303i	−0.439096	−	0.504333i
$786$	8.87538	+	6.44834i	0.316574	+	0.230005i
$787$	−18.4983	−	2.92984i	−0.659392	−	0.104437i	−0.182234	−	0.983255i	$-0.558333\pi$
$787$	−18.4983	−	2.92984i	−0.659392	−	0.104437i	−0.477158	+	0.878818i	$0.658333\pi$
$788$	−12.3047	−	1.94887i	−0.438336	−	0.0694256i
$789$	3.24360	+	2.35661i	0.115475	+	0.0838977i
$790$	−28.8891	+	12.2891i	−1.02783	+	0.437227i
$791$	−36.6688	+	10.6802i	−1.30379	+	0.379743i
$792$	−1.38533	−	2.71887i	−0.0492257	−	0.0966108i
$793$	−0.506675	−	0.506675i	−0.0179926	−	0.0179926i
$794$	−3.92552	+	12.0815i	−0.139311	+	0.428756i
$795$	10.1855	−	6.37559i	0.361243	−	0.226119i
$796$	12.0527	−	3.91617i	0.427197	−	0.138805i
$797$	20.2027	−	39.6499i	0.715615	−	1.40447i	−0.190605	−	0.981667i	$-0.561045\pi$
$797$	20.2027	−	39.6499i	0.715615	−	1.40447i	0.906220	−	0.422806i	$-0.138955\pi$
$798$	5.11514	−	26.9133i	0.181074	−	0.952720i
$799$			38.5745i			1.36467i
$800$	−3.98852	+	3.01525i	−0.141015	+	0.106605i
$801$			33.8696i			1.19672i
$802$	−28.3091	+	4.48371i	−0.999628	+	0.158325i
$803$	6.31332	+	3.21680i	0.222792	+	0.113518i
$804$	−0.973058	−	2.99476i	−0.0343171	−	0.105617i
$805$	−18.6766	−	31.9830i	−0.658265	−	1.12725i
$806$	−0.373572	+	1.14974i	−0.0131585	+	0.0404978i
$807$	−29.1322	+	29.1322i	−1.02550	+	1.02550i
$808$	−4.77080	−	9.36322i	−0.167836	−	0.329397i
$809$	−3.13901	−	4.32048i	−0.110362	−	0.151900i	0.750263	−	0.661139i	$-0.229927\pi$
$809$	−3.13901	−	4.32048i	−0.110362	−	0.151900i	−0.860625	+	0.509239i	$0.829927\pi$
$810$	4.95989	−	21.5597i	0.174273	−	0.757531i
$811$	25.2686	−	34.7792i	0.887300	−	1.22126i	−0.0870448	−	0.996204i	$-0.527742\pi$
$811$	25.2686	−	34.7792i	0.887300	−	1.22126i	0.974345	−	0.225060i	$-0.0722577\pi$
$812$	−7.50026	+	13.6648i	−0.263207	+	0.479540i
$813$	−17.6655	−	2.79794i	−0.619556	−	0.0981281i
$814$	6.88383	−	9.47477i	0.241278	−	0.332091i
$815$	−26.7884	−	6.16277i	−0.938358	−	0.215873i
$816$	−10.1363	+	7.36449i	−0.354843	+	0.257809i
$817$	−29.0833	+	14.8187i	−1.01749	+	0.518439i
$818$	−12.0291	+	12.0291i	−0.420587	+	0.420587i
$819$	−0.732014	+	0.945024i	−0.0255786	+	0.0330218i
$820$	5.40863	+	4.53125i	0.188877	+	0.158238i
$821$	12.5384	+	38.5891i	0.437592	+	1.34677i	0.890407	+	0.455165i	$0.150420\pi$
$821$	12.5384	+	38.5891i	0.437592	+	1.34677i	−0.452815	+	0.891605i	$0.649580\pi$
$822$	−15.8139	+	31.0366i	−0.551574	+	1.08253i
$823$	−8.81248	−	55.6398i	−0.307184	−	1.93948i	−0.341026	−	0.940054i	$-0.610774\pi$
$823$	−8.81248	−	55.6398i	−0.307184	−	1.93948i	0.0338424	−	0.999427i	$-0.489226\pi$
$824$	−8.28927			−0.288770
$825$	−4.45672	−	12.8785i	−0.155163	−	0.448372i
$826$	−9.58038	+	26.6670i	−0.333344	+	0.927865i
$827$	4.62124	−	0.731933i	0.160696	−	0.0254518i	−0.0755678	−	0.997141i	$-0.524077\pi$
$827$	4.62124	−	0.731933i	0.160696	−	0.0254518i	0.236264	+	0.971689i	$0.424077\pi$
$828$	7.57326	−	14.8634i	0.263189	−	0.516537i
$829$	12.3790	+	38.0988i	0.429942	+	1.32323i	0.898182	+	0.439624i	$0.144888\pi$
$829$	12.3790	+	38.0988i	0.429942	+	1.32323i	−0.468240	+	0.883601i	$0.655112\pi$
$830$	−0.485120	−	0.775020i	−0.0168388	−	0.0269013i
$831$	49.3972	+	16.0501i	1.71357	+	0.556772i
$832$	−0.119896	−	0.119896i	−0.00415663	−	0.00415663i
$833$	7.98995	−	35.9733i	0.276835	−	1.24640i
$834$	1.68001	+	2.31233i	0.0581739	+	0.0800695i
$835$	−44.4900	+	18.9255i	−1.53964	+	0.654944i
$836$	−2.92838	+	4.03057i	−0.101280	+	0.139400i
$837$	−0.890273	+	5.62096i	−0.0307723	+	0.194289i
$838$	4.74841	−	29.9803i	0.164031	−	1.03565i
$839$	6.85766	+	4.98238i	0.236753	+	0.172011i	0.699835	−	0.714304i	$-0.253257\pi$
$839$	6.85766	+	4.98238i	0.236753	+	0.172011i	−0.463083	+	0.886315i	$0.653257\pi$
$840$	13.1202	−	5.11089i	0.452691	−	0.176343i
$841$	4.62066	−	3.35710i	0.159333	−	0.115762i
$842$	−0.452959	−	0.888981i	−0.0156100	−	0.0306363i
$843$	29.6120	−	29.6120i	1.01989	−	1.01989i
$844$	20.5671	+	6.68265i	0.707949	+	0.230026i
$845$	−26.9010	−	10.8445i	−0.925422	−	0.373062i
$846$	18.5697	−	6.03366i	0.638439	−	0.207442i
$847$	17.5600	+	18.6742i	0.603369	+	0.641653i
$848$	−0.353212	−	2.23009i	−0.0121293	−	0.0765816i
$849$		−	50.9480i		−	1.74853i
$850$	−23.2212	+	12.3931i	−0.796482	+	0.425079i
$851$	64.0235			2.19470
$852$	3.67365	+	23.1945i	0.125857	+	0.794630i
$853$	21.0001	+	10.7001i	0.719031	+	0.366365i	0.774909	−	0.632073i	$-0.217796\pi$
$853$	21.0001	+	10.7001i	0.719031	+	0.366365i	−0.0558778	+	0.998438i	$0.517796\pi$
$854$	0.343649	−	11.1756i	0.0117594	−	0.382421i
$855$	25.1466	−	6.29042i	0.859995	−	0.215128i
$856$	−2.25258	+	6.93274i	−0.0769917	+	0.236956i
$857$	17.3480	+	17.3480i	0.592596	+	0.592596i	0.938332	−	0.345736i	$-0.112371\pi$
$857$	17.3480	+	17.3480i	0.592596	+	0.592596i	−0.345736	+	0.938332i	$0.612371\pi$
$858$	0.411771	−	0.209808i	0.0140576	−	0.00716273i
$859$	20.3780	−	14.8055i	0.695288	−	0.505156i	−0.183107	−	0.983093i	$-0.558615\pi$
$859$	20.3780	−	14.8055i	0.695288	−	0.505156i	0.878394	+	0.477937i	$0.158615\pi$
$860$	−14.3872	−	8.62956i	−0.490600	−	0.294266i
$861$	−11.1798	−	16.4267i	−0.381006	−	0.559819i
$862$	−2.01954	+	12.7509i	−0.0687859	+	0.434297i
$863$	−20.7456	−	3.28578i	−0.706188	−	0.111849i	−0.206998	−	0.978341i	$-0.566369\pi$
$863$	−20.7456	−	3.28578i	−0.706188	−	0.111849i	−0.499191	+	0.866492i	$0.666369\pi$
$864$	−0.645765	−	0.469175i	−0.0219694	−	0.0159617i
$865$	−25.9870	+	2.29383i	−0.883585	+	0.0779925i
$866$	−20.5205	−	28.2441i	−0.697316	−	0.959773i
$867$	−22.7175	+	11.5751i	−0.771526	+	0.393112i
$868$	−17.0628	+	8.04323i	−0.579149	+	0.273005i
$869$	−15.2913	−	4.96844i	−0.518722	−	0.168543i
$870$	−31.2803	−	2.16302i	−1.06050	−	0.0733331i
$871$	0.213351	−	0.0693220i	0.00722913	−	0.00234889i
$872$	−10.4506	−	5.32485i	−0.353903	−	0.180322i
$873$	0.211409	−	0.0334838i	0.00715510	−	0.00113326i
$874$	−27.2357			−0.921260
$875$	28.7785	−	6.84098i	0.972890	−	0.231267i
$876$	−14.7262			−0.497553
$877$	1.81189	−	0.286975i	0.0611831	−	0.00969045i	−0.125768	−	0.992060i	$-0.540139\pi$
$877$	1.81189	−	0.286975i	0.0611831	−	0.00969045i	0.186951	+	0.982369i	$0.440139\pi$
$878$	−36.3713	−	18.5321i	−1.22747	−	0.625429i
$879$	35.1112	−	11.4083i	1.18427	−	0.384793i
$880$	−2.55459	−	0.176648i	−0.0861151	−	0.00595481i
$881$	−15.3733	−	4.99508i	−0.517939	−	0.168289i	0.0383708	−	0.999264i	$-0.487783\pi$
$881$	−15.3733	−	4.99508i	−0.517939	−	0.168289i	−0.556310	+	0.830975i	$0.687783\pi$
$882$	−18.5672	+	1.78044i	−0.625190	+	0.0599504i
$883$	24.6818	−	12.5760i	0.830610	−	0.423217i	0.0136467	−	0.999907i	$-0.495656\pi$
$883$	24.6818	−	12.5760i	0.830610	−	0.423217i	0.816963	+	0.576690i	$0.195656\pi$
$884$	−0.524657	−	0.722128i	−0.0176461	−	0.0242878i
$885$	−56.7768	+	5.01159i	−1.90853	+	0.168463i
$886$	−16.8972	−	12.2765i	−0.567671	−	0.412437i
$887$	−32.5433	−	5.15435i	−1.09270	−	0.173066i	−0.416026	−	0.909353i	$-0.636577\pi$
$887$	−32.5433	−	5.15435i	−1.09270	−	0.173066i	−0.676670	+	0.736287i	$0.736577\pi$
$888$	−3.80766	+	24.0406i	−0.127777	+	0.806750i
$889$	−3.15399	+	2.14657i	−0.105781	+	0.0719935i
$890$	24.3740	+	14.6197i	0.817018	+	0.490054i
$891$	9.16612	−	6.65958i	0.307077	−	0.223104i
$892$	15.0363	−	7.66139i	0.503453	−	0.256522i
$893$	−22.5416	−	22.5416i	−0.754327	−	0.754327i
$894$	−7.90388	+	24.3257i	−0.264345	+	0.813572i
$895$	−21.6874	+	5.42511i	−0.724931	+	0.181341i
$896$	0.0813183	−	2.64450i	0.00271665	−	0.0883466i
$897$	2.25105	+	1.14697i	0.0751603	+	0.0382961i
$898$	−2.48307	−	15.6775i	−0.0828611	−	0.523164i
$899$	42.0059			1.40098
$900$	9.59816	+	9.24018i	0.319939	+	0.308006i
$901$		−	11.8861i		−	0.395985i
$902$	0.565288	+	3.56909i	0.0188220	+	0.118838i
$903$	32.3649	+	34.4185i	1.07704	+	1.14538i
$904$	−13.7289	+	4.46079i	−0.456616	+	0.148364i
$905$	38.9487	+	15.7012i	1.29470	+	0.521927i
$906$	−30.6817	−	9.96910i	−1.01933	−	0.331201i
$907$	−8.52550	+	8.52550i	−0.283084	+	0.283084i	−0.834338	−	0.551253i	$-0.814150\pi$
$907$	−8.52550	+	8.52550i	−0.283084	+	0.283084i	0.551253	+	0.834338i	$0.314150\pi$
$908$	−3.15865	−	6.19919i	−0.104823	−	0.205727i
$909$	−22.6536	+	16.4588i	−0.751374	+	0.545905i
$910$	0.364107	+	0.934705i	0.0120700	+	0.0309852i
$911$	12.4440	+	9.04106i	0.412286	+	0.299544i	0.774527	−	0.632541i	$-0.217988\pi$
$911$	12.4440	+	9.04106i	0.412286	+	0.299544i	−0.362240	+	0.932085i	$0.617988\pi$
$912$	1.61978	−	10.2269i	0.0536363	−	0.338646i
$913$	0.0732523	−	0.462497i	0.00242430	−	0.0153064i
$914$	−3.85350	+	5.30388i	−0.127462	+	0.175437i
$915$	20.6957	−	8.80371i	0.684179	−	0.291042i
$916$	−14.8268	−	20.4073i	−0.489891	−	0.674276i
$917$	−12.0981	+	1.53665i	−0.399515	+	0.0507447i
$918$	−2.97125	−	2.97125i	−0.0980660	−	0.0980660i
$919$	30.0043	+	9.74898i	0.989750	+	0.321589i	0.758762	−	0.651368i	$-0.225804\pi$
$919$	30.0043	+	9.74898i	0.989750	+	0.321589i	0.230987	+	0.972957i	$0.425804\pi$
$920$	−7.42732	−	11.8658i	−0.244871	−	0.391202i
$921$	19.4060	+	59.7255i	0.639449	+	1.96802i
$922$	7.78733	−	15.2835i	0.256462	−	0.503335i
$923$	−1.65241	+	0.261716i	−0.0543897	+	0.00861448i
$924$	6.78650	+	2.43811i	0.223260	+	0.0802080i
$925$	−14.8745	+	48.9228i	−0.489069	+	1.60857i
$926$	7.44522			0.244665
$927$	3.45529	+	21.8159i	0.113487	+	0.716527i
$928$	−2.67475	+	5.24949i	−0.0878030	+	0.172323i
$929$	−4.68633	−	14.4230i	−0.153753	−	0.473204i	0.844279	−	0.535904i	$-0.180029\pi$
$929$	−4.68633	−	14.4230i	−0.153753	−	0.473204i	−0.998032	+	0.0626995i	$0.980029\pi$
$930$	−29.0857	−	24.3675i	−0.953759	−	0.799042i
$931$	16.3525	+	25.6906i	0.535931	+	0.841975i
$932$	−0.173439	+	0.173439i	−0.00568118	+	0.00568118i
$933$	30.3985	−	15.4888i	0.995201	−	0.507080i
$934$	−12.5585	+	9.12429i	−0.410927	+	0.298556i
$935$	−13.1370	−	3.02221i	−0.429626	−	0.0988369i
$936$	−0.265566	+	0.365521i	−0.00868031	+	0.0119474i
$937$	−17.1310	−	2.71328i	−0.559645	−	0.0886391i	−0.129798	−	0.991541i	$-0.541433\pi$
$937$	−17.1310	−	2.71328i	−0.559645	−	0.0886391i	−0.429848	+	0.902901i	$0.641433\pi$
$938$	3.06858	+	1.68427i	0.100193	+	0.0549932i
$939$	−5.21894	+	7.18325i	−0.170314	+	0.234417i
$940$	3.67348	−	15.9679i	0.119816	−	0.520817i
$941$	−3.24176	−	4.46189i	−0.105678	−	0.145454i	0.752902	−	0.658132i	$-0.228653\pi$
$941$	−3.24176	−	4.46189i	−0.105678	−	0.145454i	−0.858581	+	0.512679i	$0.828653\pi$
$942$	9.05341	+	17.7683i	0.294976	+	0.578923i
$943$	−13.9685	+	13.9685i	−0.454878	+	0.454878i
$944$	−3.30954	+	10.1857i	−0.107716	+	0.331517i
$945$	2.38131	+	4.07789i	0.0774639	+	0.132654i
$946$	−2.65508	−	8.17150i	−0.0863242	−	0.265678i
$947$	−43.8360	−	22.3356i	−1.42448	−	0.725808i	−0.439461	−	0.898261i	$-0.644831\pi$
$947$	−43.8360	−	22.3356i	−1.42448	−	0.725808i	−0.985018	+	0.172453i	$0.944831\pi$
$948$	33.0044	−	5.22738i	1.07193	−	0.169778i
$949$		−	1.04912i		−	0.0340558i
$950$	6.32760	−	20.8118i	0.205295	−	0.675223i
$951$		−	18.9644i		−	0.614962i
$952$	2.60059	−	13.6830i	0.0842857	−	0.443469i
$953$	0.248126	−	0.486974i	0.00803758	−	0.0157746i	−0.886953	−	0.461860i	$-0.847182\pi$
$953$	0.248126	−	0.486974i	0.00803758	−	0.0157746i	0.894990	+	0.446085i	$0.147182\pi$
$954$	−5.72196	+	1.85918i	−0.185255	+	0.0601931i
$955$	37.3904	−	23.4043i	1.20992	−	0.757347i
$956$	5.86056	−	18.0370i	0.189544	−	0.583357i
$957$	−11.3548	−	11.3548i	−0.367048	−	0.367048i
$958$	1.29476	+	2.54111i	0.0418319	+	0.0820997i
$959$	−10.8282	−	37.1771i	−0.349660	−	1.20051i
$960$	4.89727	−	2.08324i	0.158059	−	0.0672363i
$961$	16.0454	+	11.6577i	0.517595	+	0.376055i
$962$	−1.71269	−	0.271263i	−0.0552192	−	0.00874587i
$963$	19.1847	+	3.03855i	0.618218	+	0.0979160i
$964$	−2.63629	−	1.91538i	−0.0849092	−	0.0616901i
$965$	6.26059	+	7.19075i	0.201536	+	0.231478i
$966$	11.0239	+	37.8489i	0.354687	+	1.21777i
$967$	8.92455	+	17.5154i	0.286994	+	0.563258i	0.988824	−	0.149087i	$-0.0476333\pi$
$967$	8.92455	+	17.5154i	0.286994	+	0.563258i	−0.701830	+	0.712345i	$0.747633\pi$
$968$	6.85086	+	6.85086i	0.220195	+	0.220195i
$969$	16.8440	−	51.8404i	0.541106	−	1.66535i
$970$	0.0671575	−	0.166592i	0.00215630	−	0.00534894i
$971$	−11.1249	+	3.61470i	−0.357016	+	0.116001i	−0.482033	−	0.876153i	$-0.660101\pi$
$971$	−11.1249	+	3.61470i	−0.357016	+	0.116001i	0.125017	+	0.992155i	$0.460101\pi$
$972$	−9.60314	+	18.8472i	−0.308021	+	0.604525i
$973$	−3.12141	−	0.593254i	−0.100068	−	0.0190189i
$974$		−	7.14089i		−	0.228809i
$975$	−1.39942	+	1.45364i	−0.0448173	+	0.0465536i
$976$		−	4.22597i		−	0.135270i
$977$	0.685175	−	0.108521i	0.0219207	−	0.00347190i	−0.145464	−	0.989363i	$-0.546468\pi$
$977$	0.685175	−	0.108521i	0.0219207	−	0.00347190i	0.167385	+	0.985892i	$0.446468\pi$
$978$	26.0692	+	13.2829i	0.833601	+	0.424741i
$979$	4.49809	+	13.8437i	0.143760	+	0.442447i
$980$	−6.73320	+	14.1303i	−0.215084	+	0.451374i
$981$	−9.65783	+	29.7237i	−0.308351	+	0.949006i
$982$	−13.0542	+	13.0542i	−0.416576	+	0.416576i
$983$	8.27228	+	16.2353i	0.263845	+	0.517824i	0.984482	−	0.175488i	$-0.0561504\pi$
$983$	8.27228	+	16.2353i	0.263845	+	0.517824i	−0.720637	+	0.693313i	$0.756150\pi$
$984$	−4.41439	−	6.07588i	−0.140726	−	0.193692i
$985$	23.8893	+	14.3290i	0.761175	+	0.456559i
$986$	−18.2303	+	25.0918i	−0.580570	+	0.799087i
$987$	−22.2018	+	40.4496i	−0.706691	+	1.28753i
$988$	0.728578	+	0.115395i	0.0231792	+	0.00367122i
$989$	27.6085	−	37.9998i	0.877899	−	1.20832i
$990$	0.599946	+	6.79684i	0.0190675	+	0.216018i
$991$	26.5478	−	19.2881i	0.843319	−	0.612707i	−0.0799765	−	0.996797i	$-0.525485\pi$
$991$	26.5478	−	19.2881i	0.843319	−	0.612707i	0.923296	+	0.384089i	$0.125485\pi$
$992$	−6.35265	+	3.23684i	−0.201697	+	0.102770i
$993$	31.3779	−	31.3779i	0.995749	−	0.995749i
$994$	−20.6380	−	15.9862i	−0.654598	−	0.507050i
$995$	−28.2701	−	1.95486i	−0.896223	−	0.0619733i
$996$	0.300736	+	0.925570i	0.00952919	+	0.0293278i
$997$	−22.3008	+	43.7678i	−0.706273	+	1.38614i	0.206816	+	0.978380i	$0.433690\pi$
$997$	−22.3008	+	43.7678i	−0.706273	+	1.38614i	−0.913089	+	0.407760i	$0.866310\pi$
$998$	0.220336	+	1.39114i	0.00697460	+	0.0440359i
$999$	−8.16312			−0.258270

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.r.a.13.2	✓	160
7.6	odd	2	inner	350.2.r.a.13.9	yes	160
25.2	odd	20	inner	350.2.r.a.27.9	yes	160
175.27	even	20	inner	350.2.r.a.27.2	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.r.a.13.2	✓	160	1.1	even	1	trivial
350.2.r.a.13.9	yes	160	7.6	odd	2	inner
350.2.r.a.27.2	yes	160	175.27	even	20	inner
350.2.r.a.27.9	yes	160	25.2	odd	20	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.r (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 + 0.156434i) q^{2} +(-2.12064 - 1.08052i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-2.23074 - 0.154254i) q^{5} +(2.26356 + 0.735475i) q^{6} +(-2.39319 + 1.12812i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.56623 + 2.15573i) q^{9} +O(q^{10})\)	\(q+(-0.987688 + 0.156434i) q^{2} +(-2.12064 - 1.08052i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-2.23074 - 0.154254i) q^{5} +(2.26356 + 0.735475i) q^{6} +(-2.39319 + 1.12812i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(1.56623 + 2.15573i) q^{9} +(2.22741 - 0.196609i) q^{10} +(0.926465 + 0.673116i) q^{11} +(-2.35074 - 0.372321i) q^{12} +(0.0265247 - 0.167470i) q^{13} +(2.18724 - 1.48861i) q^{14} +(4.56392 + 2.73748i) q^{15} +(0.809017 - 0.587785i) q^{16} +(4.69050 - 2.38993i) q^{17} +(-1.88417 - 1.88417i) q^{18} +(-1.34437 + 4.13756i) q^{19} +(-2.16923 + 0.542632i) q^{20} +(6.29404 + 0.193541i) q^{21} +(-1.02036 - 0.519898i) q^{22} +(-0.979337 - 6.18329i) q^{23} +2.38005 q^{24} +(4.95241 + 0.688204i) q^{25} +0.169558i q^{26} +(0.124867 + 0.788382i) q^{27} +(-1.92745 + 1.81244i) q^{28} +(5.60328 - 1.82062i) q^{29} +(-4.93596 - 1.98982i) q^{30} +(6.78079 + 2.20321i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.23738 - 2.42850i) q^{33} +(-4.25889 + 3.09426i) q^{34} +(5.51260 - 2.14739i) q^{35} +(2.15573 + 1.56623i) q^{36} +(-1.59982 + 10.1009i) q^{37} +(0.680566 - 4.29693i) q^{38} +(-0.237204 + 0.326484i) q^{39} +(2.05763 - 0.875294i) q^{40} +(-1.85475 - 2.55284i) q^{41} +(-6.24682 + 0.793446i) q^{42} +(5.30529 + 5.30529i) q^{43} +(1.08912 + 0.353878i) q^{44} +(-3.16132 - 5.05047i) q^{45} +(1.93456 + 5.95396i) q^{46} +(-3.32667 + 6.52895i) q^{47} +(-2.35074 + 0.372321i) q^{48} +(4.45468 - 5.39962i) q^{49} +(-4.99910 + 0.0949972i) q^{50} -12.5292 q^{51} +(-0.0265247 - 0.167470i) q^{52} +(1.02506 - 2.01179i) q^{53} +(-0.246660 - 0.759142i) q^{54} +(-1.96287 - 1.64446i) q^{55} +(1.62019 - 2.09165i) q^{56} +(7.32164 - 7.32164i) q^{57} +(-5.24949 + 2.67475i) q^{58} +(-8.66450 + 6.29513i) q^{59} +(5.18647 + 1.19317i) q^{60} +(2.48396 - 3.41888i) q^{61} +(-7.04197 - 1.11534i) q^{62} +(-6.18020 - 3.39216i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-0.0850028 + 0.369492i) q^{65} +(1.60205 + 2.20503i) q^{66} +(0.600644 + 1.17883i) q^{67} +(3.72240 - 3.72240i) q^{68} +(-4.60434 + 14.1707i) q^{69} +(-5.10880 + 2.98331i) q^{70} +(-3.04903 - 9.38395i) q^{71} +(-2.37420 - 1.20971i) q^{72} +(6.11119 - 0.967917i) q^{73} -10.2268i q^{74} +(-9.75865 - 6.81060i) q^{75} +4.35049i q^{76} +(-2.97656 - 0.565725i) q^{77} +(0.183211 - 0.359571i) q^{78} +(-13.3528 + 4.33859i) q^{79} +(-1.89538 + 1.18640i) q^{80} +(3.05731 - 9.40942i) q^{81} +(2.23127 + 2.23127i) q^{82} +(-0.185637 - 0.364333i) q^{83} +(6.04579 - 1.76090i) q^{84} +(-10.8320 + 4.60778i) q^{85} +(-6.06990 - 4.41004i) q^{86} +(-13.8497 - 2.19358i) q^{87} +(-1.13107 - 0.179145i) q^{88} +(10.2833 + 7.47125i) q^{89} +(3.91246 + 4.49375i) q^{90} +(0.125449 + 0.430711i) q^{91} +(-2.84215 - 5.57803i) q^{92} +(-11.9990 - 11.9990i) q^{93} +(2.26436 - 6.96897i) q^{94} +(3.63719 - 9.02245i) q^{95} +(2.26356 - 0.735475i) q^{96} +(0.0364681 - 0.0715728i) q^{97} +(-3.55514 + 6.03000i) q^{98} +3.05146i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{7}+O(q^{10}) \) 160 * q + 8 * q^7	\( 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) \) 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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