LMFDB - Embedded newform 798.2.bu.a.53.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(53,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 12, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.53"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bu (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [162,0,0,0,0,0,0,-81] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.15
Character	$\chi$	$=$	798.53
Dual form			798.2.bu.a.527.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 + 0.984808i) q^{2} +(0.246871 - 1.71437i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.436242 - 1.19856i) q^{5} +(1.73119 - 0.0545760i) q^{6} +(-0.993792 + 2.45201i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.87811 - 0.846456i) q^{9} +(1.25611 + 0.221486i) q^{10} -4.65986i q^{11} +(0.354365 + 1.69541i) q^{12} +(-2.55839 - 0.451112i) q^{13} +(-2.58733 - 0.552907i) q^{14} +(-1.94708 - 1.04377i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-2.81777 - 3.35809i) q^{17} +(0.333818 - 2.98137i) q^{18} +(-3.95809 + 1.82580i) q^{19} +1.27549i q^{20} +(3.95831 + 2.30906i) q^{21} +(4.58906 - 0.809176i) q^{22} +(-4.01982 - 0.708802i) q^{23} +(-1.60812 + 0.643387i) q^{24} +(2.58397 + 2.16821i) q^{25} -2.59785i q^{26} +(-2.16166 + 4.72517i) q^{27} +(0.0952210 - 2.64404i) q^{28} +(2.24287 - 0.816338i) q^{29} +(0.689805 - 2.09875i) q^{30} +(2.93341 - 1.69360i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-7.98870 - 1.15038i) q^{33} +(2.81777 - 3.35809i) q^{34} +(2.50536 + 2.26080i) q^{35} +(2.99404 - 0.188963i) q^{36} +(-3.51420 + 2.02892i) q^{37} +(-2.48538 - 3.58091i) q^{38} +(-1.40496 + 4.27465i) q^{39} +(-1.25611 + 0.221486i) q^{40} +(-1.67805 - 9.51669i) q^{41} +(-1.58662 + 4.29914i) q^{42} +(0.447459 - 0.375463i) q^{43} +(1.59376 + 4.37883i) q^{44} +(-2.27008 + 3.08034i) q^{45} -4.08183i q^{46} +(3.47584 - 4.14235i) q^{47} +(-0.912860 - 1.47197i) q^{48} +(-5.02475 - 4.87359i) q^{49} +(-1.68657 + 2.92122i) q^{50} +(-6.45262 + 4.00168i) q^{51} +(2.55839 - 0.451112i) q^{52} +(-7.31761 + 2.66339i) q^{53} +(-5.02875 - 1.30830i) q^{54} +(-5.58514 - 2.03282i) q^{55} +(2.62040 - 0.365358i) q^{56} +(2.15296 + 7.23635i) q^{57} +(1.19341 + 2.06704i) q^{58} +(-0.978027 + 0.820662i) q^{59} +(2.18665 + 0.314881i) q^{60} +(1.79802 - 10.1971i) q^{61} +(2.17726 + 2.59475i) q^{62} +(4.93577 - 6.21596i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.65676 + 2.86960i) q^{65} +(-0.254316 - 8.06710i) q^{66} +(-8.69655 - 1.53344i) q^{67} +(3.79637 + 2.19184i) q^{68} +(-2.20752 + 6.71646i) q^{69} +(-1.79140 + 2.85989i) q^{70} +(-0.0380509 + 0.0319285i) q^{71} +(0.706002 + 2.91574i) q^{72} +(-3.27177 - 1.19083i) q^{73} +(-2.60834 - 3.10849i) q^{74} +(4.35502 - 3.89461i) q^{75} +(3.09492 - 3.06944i) q^{76} +(11.4260 + 4.63093i) q^{77} +(-4.45367 - 0.641335i) q^{78} +(2.62417 + 3.12736i) q^{79} +(-0.436242 - 1.19856i) q^{80} +(7.56703 + 4.87238i) q^{81} +(9.08072 - 3.30511i) q^{82} +(0.668209 + 0.385791i) q^{83} +(-4.50934 - 0.815981i) q^{84} +(-5.25411 + 1.91234i) q^{85} +(0.447459 + 0.375463i) q^{86} +(-0.845803 - 4.04663i) q^{87} +(-4.03555 + 2.32993i) q^{88} +(5.18621 - 1.88763i) q^{89} +(-3.42774 - 1.70070i) q^{90} +(3.64864 - 5.82489i) q^{91} +(4.01982 - 0.708802i) q^{92} +(-2.17929 - 5.44704i) q^{93} +(4.68299 + 2.70372i) q^{94} +(0.461661 + 5.54051i) q^{95} +(1.29109 - 1.15460i) q^{96} +(2.07068 - 5.68915i) q^{97} +(3.92701 - 5.79471i) q^{98} +(-3.94436 + 13.4116i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q - 81 q^{8} + 15 q^{13} + 6 q^{14} + 27 q^{15} - 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} - 9 q^{27} + 9 q^{28} + 6 q^{29} - 24 q^{33} + 6 q^{34} + 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) $ 162 * q - 81 * q^8 + 15 * q^13 + 6 * q^14 + 27 * q^15 - 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 - 9 * q^27 + 9 * q^28 + 6 * q^29 - 24 * q^33 + 6 * q^34 + 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 - 12 * q^44 - 63 * q^45 + 12 * q^47 - 48 * q^49 + 87 * q^50 - 24 * q^51 - 15 * q^52 - 18 * q^54 - 18 * q^57 - 48 * q^59 + 6 * q^60 + 45 * q^61 + 36 * q^62 - 15 * q^63 - 81 * q^64 + 36 * q^65 + 12 * q^66 + 9 * q^67 + 9 * q^69 - 24 * q^70 + 12 * q^71 + 102 * q^73 + 39 * q^74 - 6 * q^78 - 42 * q^79 + 84 * q^81 - 3 * q^84 - 6 * q^85 - 9 * q^86 + 60 * q^87 + 54 * q^89 + 36 * q^90 - 18 * q^91 - 21 * q^93 - 72 * q^94 - 12 * q^97 - 27 * q^98 - 57 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	0.246871	−	1.71437i	0.142531	−	0.989790i
$3$	0.246871	−	1.71437i	0.142531	−	0.989790i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	0.436242	−	1.19856i	0.195093	−	0.536014i	−0.803117	−	0.595822i	$-0.796826\pi$
$5$	0.436242	−	1.19856i	0.195093	−	0.536014i	0.998210	+	0.0598074i	$0.0190487\pi$
$6$	1.73119	−	0.0545760i	0.706756	−	0.0222806i
$7$	−0.993792	+	2.45201i	−0.375618	+	0.926774i
$7$	−0.993792	+	2.45201i	−0.375618	+	0.926774i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−2.87811	−	0.846456i	−0.959370	−	0.282152i
$10$	1.25611	+	0.221486i	0.397216	+	0.0700400i
$11$		−	4.65986i		−	1.40500i	−0.711684	−	0.702500i	$-0.752067\pi$
$11$		−	4.65986i		−	1.40500i	0.711684	−	0.702500i	$-0.247933\pi$
$12$	0.354365	+	1.69541i	0.102296	+	0.489424i
$13$	−2.55839	−	0.451112i	−0.709568	−	0.125116i	−0.192796	−	0.981239i	$-0.561756\pi$
$13$	−2.55839	−	0.451112i	−0.709568	−	0.125116i	−0.516772	+	0.856123i	$0.672867\pi$
$14$	−2.58733	−	0.552907i	−0.691494	−	0.147771i
$15$	−1.94708	−	1.04377i	−0.502735	−	0.269500i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−2.81777	−	3.35809i	−0.683410	−	0.814456i	0.307132	−	0.951667i	$-0.400631\pi$
$17$	−2.81777	−	3.35809i	−0.683410	−	0.814456i	−0.990542	+	0.137211i	$0.956186\pi$
$18$	0.333818	−	2.98137i	0.0786816	−	0.702716i
$19$	−3.95809	+	1.82580i	−0.908047	+	0.418868i
$19$	−3.95809	+	1.82580i	−0.908047	+	0.418868i
$20$			1.27549i			0.285207i
$21$	3.95831	+	2.30906i	0.863775	+	0.503878i
$22$	4.58906	−	0.809176i	0.978391	−	0.172517i
$23$	−4.01982	−	0.708802i	−0.838190	−	0.147796i	−0.261956	−	0.965080i	$-0.584367\pi$
$23$	−4.01982	−	0.708802i	−0.838190	−	0.147796i	−0.576234	+	0.817284i	$0.695478\pi$
$24$	−1.60812	+	0.643387i	−0.328256	+	0.131331i
$25$	2.58397	+	2.16821i	0.516794	+	0.433642i
$26$		−	2.59785i		−	0.509481i
$27$	−2.16166	+	4.72517i	−0.416011	+	0.909359i
$28$	0.0952210	−	2.64404i	0.0179951	−	0.499676i
$29$	2.24287	−	0.816338i	0.416491	−	0.151590i	−0.125271	−	0.992123i	$-0.539980\pi$
$29$	2.24287	−	0.816338i	0.416491	−	0.151590i	0.541761	+	0.840532i	$0.317758\pi$
$30$	0.689805	−	2.09875i	0.125941	−	0.383178i
$31$	2.93341	−	1.69360i	0.526856	−	0.304180i	−0.212879	−	0.977078i	$-0.568284\pi$
$31$	2.93341	−	1.69360i	0.526856	−	0.304180i	0.739735	+	0.672898i	$0.234951\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−7.98870	−	1.15038i	−1.39066	−	0.200256i
$34$	2.81777	−	3.35809i	0.483244	−	0.575907i
$35$	2.50536	+	2.26080i	0.423484	+	0.382144i
$36$	2.99404	−	0.188963i	0.499007	−	0.0314938i
$37$	−3.51420	+	2.02892i	−0.577731	+	0.333553i	−0.760231	−	0.649653i	$-0.774914\pi$
$37$	−3.51420	+	2.02892i	−0.577731	+	0.333553i	0.182500	+	0.983206i	$0.441581\pi$
$38$	−2.48538	−	3.58091i	−0.403182	−	0.580900i
$39$	−1.40496	+	4.27465i	−0.224974	+	0.684491i
$40$	−1.25611	+	0.221486i	−0.198608	+	0.0350200i
$41$	−1.67805	−	9.51669i	−0.262067	−	1.48626i	−0.777258	−	0.629181i	$-0.783390\pi$
$41$	−1.67805	−	9.51669i	−0.262067	−	1.48626i	0.515191	−	0.857075i	$-0.327721\pi$
$42$	−1.58662	+	4.29914i	−0.244821	+	0.663372i
$43$	0.447459	−	0.375463i	0.0682369	−	0.0572576i	−0.608031	−	0.793913i	$-0.708040\pi$
$43$	0.447459	−	0.375463i	0.0682369	−	0.0572576i	0.676268	+	0.736655i	$0.263596\pi$
$44$	1.59376	+	4.37883i	0.240269	+	0.660134i
$45$	−2.27008	+	3.08034i	−0.338404	+	0.459190i
$46$		−	4.08183i		−	0.601833i
$47$	3.47584	−	4.14235i	0.507003	−	0.604223i	−0.450453	−	0.892800i	$-0.648738\pi$
$47$	3.47584	−	4.14235i	0.507003	−	0.604223i	0.957457	+	0.288577i	$0.0931821\pi$
$48$	−0.912860	−	1.47197i	−0.131760	−	0.212460i
$49$	−5.02475	−	4.87359i	−0.717822	−	0.696227i
$50$	−1.68657	+	2.92122i	−0.238517	+	0.413123i
$51$	−6.45262	+	4.00168i	−0.903548	+	0.560347i
$52$	2.55839	−	0.451112i	0.354784	−	0.0625580i
$53$	−7.31761	+	2.66339i	−1.00515	+	0.365845i	−0.791569	−	0.611080i	$-0.790735\pi$
$53$	−7.31761	+	2.66339i	−1.00515	+	0.365845i	−0.213583	+	0.976925i	$0.568513\pi$
$54$	−5.02875	−	1.30830i	−0.684327	−	0.178037i
$55$	−5.58514	−	2.03282i	−0.753100	−	0.274106i
$56$	2.62040	−	0.365358i	0.350166	−	0.0488230i
$57$	2.15296	+	7.23635i	0.285167	+	0.958478i
$58$	1.19341	+	2.06704i	0.156702	+	0.271416i
$59$	−0.978027	+	0.820662i	−0.127328	+	0.106841i	−0.704228	−	0.709974i	$-0.748707\pi$
$59$	−0.978027	+	0.820662i	−0.127328	+	0.106841i	0.576900	+	0.816815i	$0.304262\pi$
$60$	2.18665	+	0.314881i	0.282295	+	0.0406509i
$61$	1.79802	−	10.1971i	0.230213	−	1.30560i	−0.622253	−	0.782816i	$-0.713782\pi$
$61$	1.79802	−	10.1971i	0.230213	−	1.30560i	0.852465	−	0.522784i	$-0.175107\pi$
$62$	2.17726	+	2.59475i	0.276512	+	0.329534i
$63$	4.93577	−	6.21596i	0.621848	−	0.783138i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.65676	+	2.86960i	−0.205496	+	0.355930i
$66$	−0.254316	−	8.06710i	−0.0313042	−	0.992991i
$67$	−8.69655	−	1.53344i	−1.06245	−	0.187339i	−0.385008	−	0.922913i	$-0.625801\pi$
$67$	−8.69655	−	1.53344i	−1.06245	−	0.187339i	−0.677444	+	0.735574i	$0.736913\pi$
$68$	3.79637	+	2.19184i	0.460378	+	0.265799i
$69$	−2.20752	+	6.71646i	−0.265755	+	0.808567i
$70$	−1.79140	+	2.85989i	−0.214113	+	0.341822i
$71$	−0.0380509	+	0.0319285i	−0.00451581	+	0.00378922i	−0.645043	−	0.764147i	$-0.723160\pi$
$71$	−0.0380509	+	0.0319285i	−0.00451581	+	0.00378922i	0.640527	+	0.767936i	$0.278716\pi$
$72$	0.706002	+	2.91574i	0.0832032	+	0.343624i
$73$	−3.27177	−	1.19083i	−0.382932	−	0.139376i	0.143379	−	0.989668i	$-0.454203\pi$
$73$	−3.27177	−	1.19083i	−0.382932	−	0.139376i	−0.526311	+	0.850292i	$0.676425\pi$
$74$	−2.60834	−	3.10849i	−0.303213	−	0.361355i
$75$	4.35502	−	3.89461i	0.502874	−	0.449711i
$76$	3.09492	−	3.06944i	0.355012	−	0.352089i
$77$	11.4260	+	4.63093i	1.30212	+	0.527744i
$78$	−4.45367	−	0.641335i	−0.504279	−	0.0726169i
$79$	2.62417	+	3.12736i	0.295242	+	0.351856i	0.893190	−	0.449679i	$-0.148462\pi$
$79$	2.62417	+	3.12736i	0.295242	+	0.351856i	−0.597948	+	0.801535i	$0.704017\pi$
$80$	−0.436242	−	1.19856i	−0.0487733	−	0.134004i
$81$	7.56703	+	4.87238i	0.840781	+	0.541376i
$82$	9.08072	−	3.30511i	1.00280	−	0.364988i
$83$	0.668209	+	0.385791i	0.0733455	+	0.0423461i	0.536224	−	0.844076i	$-0.319850\pi$
$83$	0.668209	+	0.385791i	0.0733455	+	0.0423461i	−0.462879	+	0.886422i	$0.653183\pi$
$84$	−4.50934	−	0.815981i	−0.492010	−	0.0890308i
$85$	−5.25411	+	1.91234i	−0.569889	+	0.207423i
$86$	0.447459	+	0.375463i	0.0482508	+	0.0404872i
$87$	−0.845803	−	4.04663i	−0.0906796	−	0.433845i
$88$	−4.03555	+	2.32993i	−0.430192	+	0.248371i
$89$	5.18621	−	1.88763i	0.549737	−	0.200088i	−0.0521925	−	0.998637i	$-0.516621\pi$
$89$	5.18621	−	1.88763i	0.549737	−	0.200088i	0.601930	+	0.798549i	$0.294399\pi$
$90$	−3.42774	−	1.70070i	−0.361315	−	0.179270i
$91$	3.64864	−	5.82489i	0.382481	−	0.610614i
$92$	4.01982	−	0.708802i	0.419095	−	0.0738978i
$93$	−2.17929	−	5.44704i	−0.225981	−	0.564832i
$94$	4.68299	+	2.70372i	0.483013	+	0.278868i
$95$	0.461661	+	5.54051i	0.0473654	+	0.568445i
$96$	1.29109	−	1.15460i	0.131771	−	0.117840i
$97$	2.07068	−	5.68915i	0.210246	−	0.577646i	−0.789082	−	0.614287i	$-0.789444\pi$
$97$	2.07068	−	5.68915i	0.210246	−	0.577646i	0.999328	+	0.0366411i	$0.0116658\pi$
$98$	3.92701	−	5.79471i	0.396688	−	0.585354i
$99$	−3.94436	+	13.4116i	−0.396423	+	1.34791i
$100$	−3.16971	−	1.15368i	−0.316971	−	0.115368i
$101$	−4.77221	+	5.68729i	−0.474852	+	0.565907i	−0.949298	−	0.314378i	$-0.898204\pi$
$101$	−4.77221	+	5.68729i	−0.474852	+	0.565907i	0.474446	+	0.880285i	$0.342649\pi$
$102$	−5.06137	−	5.65971i	−0.501150	−	0.560395i
$103$	11.6492	+	6.72564i	1.14783	+	0.662697i	0.948356	−	0.317207i	$-0.102745\pi$
$103$	11.6492	+	6.72564i	1.14783	+	0.662697i	0.199469	+	0.979904i	$0.436078\pi$
$104$	0.888518	+	2.44118i	0.0871264	+	0.239378i
$105$	4.49434	−	3.73699i	0.438602	−	0.364693i
$106$	−3.89362	−	6.74395i	−0.378182	−	0.655030i
$107$	−11.9164			−1.15200			−0.576001	−	0.817449i	$-0.695388\pi$
$107$	−11.9164			−1.15200			−0.576001	+	0.817449i	$0.695388\pi$
$108$	0.415191	−	5.17954i	0.0399518	−	0.498401i
$109$	7.55888	−	1.33284i	0.724010	−	0.127662i	0.200514	−	0.979691i	$-0.435739\pi$
$109$	7.55888	−	1.33284i	0.724010	−	0.127662i	0.523496	+	0.852028i	$0.324628\pi$
$110$	1.03209	−	5.85328i	0.0984061	−	0.558089i
$111$	2.61077	+	6.52551i	0.247803	+	0.619374i
$112$	0.814835	+	2.51715i	0.0769947	+	0.237848i
$113$	17.0814			1.60688			0.803442	−	0.595383i	$-0.203000\pi$
$113$	17.0814			1.60688			0.803442	+	0.595383i	$0.203000\pi$
$114$	−6.75256	+	3.37683i	−0.632435	+	0.316269i
$115$	−2.60316	+	4.50880i	−0.242746	+	0.420448i
$116$	−1.82841	+	1.53421i	−0.169763	+	0.142448i
$117$	6.98147	+	3.46391i	0.645437	+	0.320239i
$118$	−0.978027	−	0.820662i	−0.0900347	−	0.0755480i
$119$	11.0344	−	3.57197i	1.01152	−	0.327442i
$120$	0.0696109	+	2.20811i	0.00635458	+	0.201572i
$121$	−10.7143			−0.974024
$122$	10.3544			0.937441
$123$	−16.7294	+	0.527395i	−1.50844	+	0.0475536i
$124$	−2.17726	+	2.59475i	−0.195523	+	0.233016i
$125$	9.24899	−	5.33991i	0.827255	−	0.477616i
$126$	6.97862	+	3.78139i	0.621705	+	0.336873i
$127$	17.0830	+	3.01220i	1.51587	+	0.267289i	0.868809	−	0.495147i	$-0.164886\pi$
$127$	17.0830	+	3.01220i	1.51587	+	0.267289i	0.647064	+	0.762436i	$0.275997\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	−0.533216	−	0.859800i	−0.0469471	−	0.0757012i
$130$	−3.11369	−	1.13329i	−0.273089	−	0.0993963i
$131$	21.6401	−	3.81573i	1.89070	−	0.333382i	0.896693	−	0.442653i	$-0.145963\pi$
$131$	21.6401	−	3.81573i	1.89070	−	0.333382i	0.994012	+	0.109271i	$0.0348516\pi$
$132$	7.90038	−	1.65129i	0.687640	−	0.143726i
$133$	−0.543382	−	11.5198i	−0.0471172	−	0.998889i
$134$		−	8.83071i		−	0.762857i
$135$	4.72042	+	4.65220i	0.406269	+	0.400398i
$136$	−1.49930	+	4.11930i	−0.128564	+	0.353227i
$137$	−1.34330	−	3.69069i	−0.114766	−	0.315317i	0.868989	−	0.494831i	$-0.164770\pi$
$137$	−1.34330	−	3.69069i	−0.114766	−	0.315317i	−0.983756	+	0.179513i	$0.942548\pi$
$138$	−6.99776	−	1.00769i	−0.595688	−	0.0857800i
$139$	−2.96098	+	16.7926i	−0.251147	+	1.42433i	0.554625	+	0.832101i	$0.312862\pi$
$139$	−2.96098	+	16.7926i	−0.251147	+	1.42433i	−0.805772	+	0.592226i	$0.798249\pi$
$140$	−3.12751	−	1.26757i	−0.264323	−	0.107129i
$141$	−6.24342	−	6.98149i	−0.525790	−	0.587948i
$142$	−0.0380509	−	0.0319285i	−0.00319316	−	0.00267938i
$143$	−2.10212	+	11.9217i	−0.175788	+	0.996943i
$144$	−2.74885	+	1.20159i	−0.229071	+	0.100133i
$145$		−	3.04435i		−	0.252819i
$146$	0.604599	−	3.42885i	0.0500370	−	0.283774i
$147$	−9.59559	+	7.41112i	−0.791431	+	0.611259i
$148$	2.60834	−	3.10849i	0.214404	−	0.255517i
$149$	9.38869	+	11.1890i	0.769151	+	0.916639i	0.998389	−	0.0567314i	$-0.0180679\pi$
$149$	9.38869	+	11.1890i	0.769151	+	0.916639i	−0.229238	+	0.973370i	$0.573623\pi$
$150$	4.59168	+	3.61256i	0.374909	+	0.294964i
$151$	17.0223	+	9.82780i	1.38525	+	0.799775i	0.992775	−	0.119987i	$-0.0382852\pi$
$151$	17.0223	+	9.82780i	1.38525	+	0.799775i	0.392476	+	0.919762i	$0.371619\pi$
$152$	3.56024	+	2.51490i	0.288773	+	0.203985i
$153$	5.26738	+	12.0501i	0.425842	+	0.974190i
$154$	−2.57647	+	12.0566i	−0.207618	+	0.971549i
$155$	−0.750219	−	4.25470i	−0.0602590	−	0.341746i
$156$	−0.141780	−	4.49738i	−0.0113515	−	0.360078i
$157$	−1.35177	−	7.66629i	−0.107883	−	0.611837i	−0.990029	−	0.140861i	$-0.955013\pi$
$157$	−1.35177	−	7.66629i	−0.107883	−	0.611837i	0.882146	−	0.470976i	$-0.156098\pi$
$158$	−2.62417	+	3.12736i	−0.208768	+	0.248800i
$159$	2.75953	+	13.2026i	0.218845	+	1.04703i
$160$	1.10460	−	0.637743i	0.0873265	−	0.0504180i
$161$	5.73286	−	9.15225i	0.451813	−	0.721298i
$162$	−3.48436	+	8.29815i	−0.273757	+	0.651964i
$163$	−10.8607	+	18.8113i	−0.850675	+	1.47341i	0.0299253	+	0.999552i	$0.490473\pi$
$163$	−10.8607	+	18.8113i	−0.850675	+	1.47341i	−0.880600	+	0.473860i	$0.842860\pi$
$164$	4.83175	+	8.36883i	0.377296	+	0.653496i
$165$	−4.86382	+	9.07313i	−0.378648	+	0.706342i
$166$	−0.263897	+	0.725050i	−0.0204823	+	0.0562748i
$167$	−1.05217	−	0.882874i	−0.0814192	−	0.0683188i	0.601170	−	0.799121i	$-0.294702\pi$
$167$	−1.05217	−	0.882874i	−0.0814192	−	0.0683188i	−0.682589	+	0.730803i	$0.739146\pi$
$168$	0.0205447	−	4.58253i	0.00158506	−	0.353550i
$169$	−5.87417	−	2.13802i	−0.451859	−	0.164463i
$170$	−2.79566	−	4.84222i	−0.214417	−	0.371381i
$171$	12.9373	−	1.90452i	0.989337	−	0.145642i
$172$	−0.292058	+	0.505860i	−0.0222692	+	0.0385714i
$173$	−3.00010	−	17.0144i	−0.228094	−	1.29358i	−0.856682	−	0.515845i	$-0.827478\pi$
$173$	−3.00010	−	17.0144i	−0.228094	−	1.29358i	0.628588	−	0.777738i	$-0.283633\pi$
$174$	3.83828	−	1.53564i	0.290980	−	0.116417i
$175$	−7.88442	+	4.18119i	−0.596006	+	0.316068i
$176$	−2.99530	−	3.56966i	−0.225779	−	0.269073i
$177$	1.16547	+	1.87929i	0.0876020	+	0.141256i
$178$	2.75953	+	4.77964i	0.206835	+	0.358249i
$179$	−21.6734			−1.61995			−0.809974	−	0.586465i	$-0.800519\pi$
$179$	−21.6734			−1.61995			−0.809974	+	0.586465i	$0.800519\pi$
$180$	1.07964	−	3.67099i	0.0804718	−	0.273619i
$181$	−3.03649	−	8.34269i	−0.225701	−	0.620107i	0.774217	−	0.632920i	$-0.218144\pi$
$181$	−3.03649	−	8.34269i	−0.225701	−	0.620107i	−0.999918	+	0.0128125i	$0.995922\pi$
$182$	6.36997	+	2.58173i	0.472174	+	0.191370i
$183$	−17.0376	−	5.59982i	−1.25946	−	0.413951i
$184$	1.39607	+	3.83567i	0.102920	+	0.282769i
$185$	0.898756	+	5.09710i	0.0660779	+	0.374746i
$186$	4.98586	−	3.09205i	0.365581	−	0.226720i
$187$	−15.6482	+	13.1304i	−1.14431	+	0.960190i
$188$	−1.84946	+	5.08134i	−0.134885	+	0.370595i
$189$	−9.43795	−	9.99626i	−0.686510	−	0.727121i
$190$	−5.37617	+	1.41675i	−0.390029	+	0.102782i
$191$	2.38397	−	1.37639i	0.172498	−	0.0995920i	−0.411265	−	0.911516i	$-0.634913\pi$
$191$	2.38397	−	1.37639i	0.172498	−	0.0995920i	0.583763	+	0.811924i	$0.301580\pi$
$192$	1.36125	+	1.07098i	0.0982397	+	0.0772913i
$193$	4.07189	−	11.1874i	0.293101	−	0.805289i	−0.702508	−	0.711676i	$-0.747936\pi$
$193$	4.07189	−	11.1874i	0.293101	−	0.805289i	0.995609	−	0.0936125i	$-0.0298415\pi$
$194$	5.96229	+	1.05131i	0.428068	+	0.0754799i
$195$	4.51053	+	3.54872i	0.323006	+	0.254129i
$196$	6.38859	+	2.86111i	0.456328	+	0.204365i
$197$	−8.32973	−	4.80917i	−0.593469	−	0.342639i	0.172999	−	0.984922i	$-0.444654\pi$
$197$	−8.32973	−	4.80917i	−0.593469	−	0.342639i	−0.766468	+	0.642283i	$0.777988\pi$
$198$	−13.8928	−	1.55554i	−0.987315	−	0.110548i
$199$	2.93922	−	16.6691i	0.208355	−	1.18164i	−0.683716	−	0.729748i	$-0.739637\pi$
$199$	2.93922	−	16.6691i	0.208355	−	1.18164i	0.892072	−	0.451894i	$-0.149252\pi$
$200$	0.585739	−	3.32189i	0.0414180	−	0.234893i
$201$	−4.77580	+	14.5305i	−0.336859	+	1.02490i
$202$	−6.42958	−	3.71212i	−0.452383	−	0.261184i
$203$	−0.227275	+	6.31082i	−0.0159516	+	0.442933i
$204$	4.69483	−	5.96727i	0.328704	−	0.417793i
$205$	−12.1384	−	2.14033i	−0.847782	−	0.149487i
$206$	−4.60061	+	12.6401i	−0.320540	+	0.880676i
$207$	10.9695	+	5.44261i	0.762433	+	0.378287i
$208$	−2.24981	+	1.29893i	−0.155996	+	0.0900643i
$209$	8.50798	+	18.4441i	0.588510	+	1.27581i
$210$	4.46065	+	3.77714i	0.307814	+	0.260647i
$211$	1.27357	−	3.49910i	0.0876761	−	0.240888i	−0.888104	−	0.459643i	$-0.847977\pi$
$211$	1.27357	−	3.49910i	0.0876761	−	0.240888i	0.975780	+	0.218755i	$0.0701995\pi$
$212$	5.96537	−	5.00554i	0.409704	−	0.343782i
$213$	0.0453435	+	0.0731154i	0.00310689	+	0.00500979i
$214$	−2.06926	−	11.7354i	−0.141452	−	0.802213i
$215$	−0.254816	−	0.700101i	−0.0173783	−	0.0477465i
$216$	5.17295	−	0.490534i	0.351974	−	0.0333766i
$217$	1.23754	+	8.87585i	0.0840099	+	0.602532i
$218$	2.62517	+	7.21260i	0.177799	+	0.488499i
$219$	−2.84922	+	5.31504i	−0.192533	+	0.359157i
$220$	5.94358			0.400716
$221$	5.69407	+	9.86242i	0.383024	+	0.663418i
$222$	−5.97302	+	3.70425i	−0.400883	+	0.248613i
$223$	−6.66654	−	7.94487i	−0.446424	−	0.532028i	0.495161	−	0.868801i	$-0.335109\pi$
$223$	−6.66654	−	7.94487i	−0.446424	−	0.532028i	−0.941586	+	0.336773i	$0.890664\pi$
$224$	−2.33741	+	1.23955i	−0.156175	+	0.0828212i
$225$	−5.60166	−	8.42756i	−0.373444	−	0.561838i
$226$	2.96616	+	16.8219i	0.197306	+	1.11898i
$227$	6.48864	−	11.2387i	0.430666	−	0.745936i	−0.566265	−	0.824223i	$-0.691612\pi$
$227$	6.48864	−	11.2387i	0.430666	−	0.745936i	0.996931	+	0.0782878i	$0.0249453\pi$
$228$	−4.49810	−	6.06359i	−0.297894	−	0.401571i
$229$	−11.2692	−	19.5189i	−0.744693	−	1.28985i	−0.950338	−	0.311219i	$-0.899263\pi$
$229$	−11.2692	−	19.5189i	−0.744693	−	1.28985i	0.205646	−	0.978626i	$-0.434071\pi$
$230$	−4.89234	−	1.78067i	−0.322591	−	0.117414i
$231$	10.7599	−	18.4452i	0.707948	−	1.21360i
$232$	−1.82841	−	1.53421i	−0.120041	−	0.100726i
$233$	2.65878	−	7.30494i	0.174183	−	0.478563i	−0.821626	−	0.570027i	$-0.806933\pi$
$233$	2.65878	−	7.30494i	0.174183	−	0.478563i	0.995808	+	0.0914645i	$0.0291548\pi$
$234$	−2.19897	+	7.47690i	−0.143751	+	0.488781i
$235$	−3.44856	−	5.97308i	−0.224959	−	0.389641i
$236$	0.638362	−	1.10567i	0.0415538	−	0.0719733i
$237$	6.00928	−	3.72673i	0.390345	−	0.242077i
$238$	5.43380	+	10.2465i	0.352221	+	0.664179i
$239$	6.68292	−	3.85839i	0.432282	−	0.249578i	−0.268036	−	0.963409i	$-0.586375\pi$
$239$	6.68292	−	3.85839i	0.432282	−	0.249578i	0.700319	+	0.713830i	$0.253041\pi$
$240$	−2.16248	+	0.451988i	−0.139587	+	0.0291757i
$241$	2.42878	−	2.89450i	0.156451	−	0.186451i	−0.682125	−	0.731236i	$-0.738944\pi$
$241$	2.42878	−	2.89450i	0.156451	−	0.186451i	0.838576	+	0.544784i	$0.183388\pi$
$242$	−1.86051	−	10.5515i	−0.119598	−	0.678275i
$243$	10.2211	−	11.7698i	0.655686	−	0.755033i
$244$	1.79802	+	10.1971i	0.115106	+	0.652800i
$245$	−8.03332	+	3.89643i	−0.513230	+	0.248934i
$246$	−3.42441	−	16.3836i	−0.218332	−	1.04458i
$247$	10.9500	−	2.88557i	0.696729	−	0.183604i
$248$	−2.93341	−	1.69360i	−0.186272	−	0.107544i
$249$	0.826349	−	1.05032i	0.0523677	−	0.0665611i
$250$	6.86485	+	8.18121i	0.434171	+	0.517425i
$251$	−11.7944	+	14.0560i	−0.744453	+	0.887205i	−0.996759	−	0.0804429i	$-0.974367\pi$
$251$	−11.7944	+	14.0560i	−0.744453	+	0.887205i	0.252306	+	0.967647i	$0.418811\pi$
$252$	−2.51212	+	7.52923i	−0.158249	+	0.474297i
$253$	−3.30292	+	18.7318i	−0.207653	+	1.17766i
$254$			17.3466i			1.08842i
$255$	1.98137	+	9.47958i	0.124078	+	0.593635i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	1.37919	+	1.15728i	0.0860313	+	0.0721888i	0.684789	−	0.728741i	$-0.259894\pi$
$257$	1.37919	+	1.15728i	0.0860313	+	0.0721888i	−0.598758	+	0.800930i	$0.704339\pi$
$258$	0.754146	−	0.674418i	0.0469511	−	0.0419875i
$259$	−1.48257	−	10.6332i	−0.0921222	−	0.660715i
$260$	0.575387	−	3.26318i	0.0356840	−	0.202374i
$261$	−7.14622	+	0.451019i	−0.442340	+	0.0279174i
$262$	7.51553	+	20.6487i	0.464311	+	1.27568i
$263$	−5.77367	+	15.8630i	−0.356020	+	0.978156i	0.624377	+	0.781123i	$0.285353\pi$
$263$	−5.77367	+	15.8630i	−0.356020	+	0.978156i	−0.980397	+	0.197033i	$0.936869\pi$
$264$	2.99809	+	7.49361i	0.184520	+	0.461200i
$265$			9.93252i			0.610150i
$266$	11.2504	−	2.53551i	0.689805	−	0.155462i
$267$	−1.95576	−	9.35707i	−0.119690	−	0.572643i
$268$	8.69655	−	1.53344i	0.531226	−	0.0936696i
$269$	−11.2944	−	4.11081i	−0.688629	−	0.250640i	−0.0260807	−	0.999660i	$-0.508303\pi$
$269$	−11.2944	−	4.11081i	−0.688629	−	0.250640i	−0.662548	+	0.749019i	$0.730525\pi$
$270$	−3.76184	+	5.45655i	−0.228938	+	0.332075i
$271$	16.9070	+	6.15364i	1.02703	+	0.373807i	0.799948	−	0.600069i	$-0.204860\pi$
$271$	16.9070	+	6.15364i	1.02703	+	0.373807i	0.227079	+	0.973876i	$0.427083\pi$
$272$	−4.31707	−	0.761217i	−0.261761	−	0.0461555i
$273$	−9.08525	−	7.69310i	−0.549864	−	0.465608i
$274$	3.40136	−	1.96378i	0.205484	−	0.118636i
$275$	10.1035	−	12.0409i	0.609267	−	0.726096i
$276$	−0.222770	−	7.06643i	−0.0134092	−	0.425349i
$277$	13.1906			0.792547			0.396273	−	0.918133i	$-0.370303\pi$
$277$	13.1906			0.792547			0.396273	+	0.918133i	$0.370303\pi$
$278$	−17.0516			−1.02269
$279$	−9.87623	+	2.39138i	−0.591275	+	0.143168i
$280$	0.705225	−	3.30011i	0.0421452	−	0.197219i
$281$	−19.9046	−	16.7020i	−1.18741	−	0.996356i	−0.999901	−	0.0140931i	$-0.995514\pi$
$281$	−19.9046	−	16.7020i	−1.18741	−	0.996356i	−0.187510	−	0.982263i	$-0.560042\pi$
$282$	5.79127	−	7.36089i	0.344865	−	0.438334i
$283$	−14.4015	+	12.0843i	−0.856083	+	0.718339i	−0.961120	−	0.276129i	$-0.910948\pi$
$283$	−14.4015	+	12.0843i	−0.856083	+	0.718339i	0.105038	+	0.994468i	$0.466504\pi$
$284$	0.0248360	−	0.0430172i	0.00147374	−	0.00255260i
$285$	9.61244	+	0.576336i	0.569392	+	0.0341392i
$286$	−12.1056			−0.715820
$287$	25.0027	+	5.34301i	1.47586	+	0.315388i
$288$	−1.66067	−	2.49844i	−0.0978558	−	0.147222i
$289$	−0.384906	+	2.18291i	−0.0226415	+	0.128406i
$290$	2.99810	−	0.528645i	0.176054	−	0.0310431i
$291$	−9.24211	−	4.95440i	−0.541782	−	0.290432i
$292$	3.48175			0.203754
$293$	15.5152	+	26.8731i	0.906407	+	1.56994i	0.819017	+	0.573769i	$0.194519\pi$
$293$	15.5152	+	26.8731i	0.906407	+	1.56994i	0.0873902	+	0.996174i	$0.472147\pi$
$294$	−8.96479	−	8.16288i	−0.522837	−	0.476069i
$295$	0.556960	+	1.53024i	0.0324275	+	0.0890937i
$296$	3.51420	+	2.02892i	0.204259	+	0.117929i
$297$	22.0186	+	10.0730i	1.27765	+	0.584496i
$298$	−9.38869	+	11.1890i	−0.543872	+	0.648162i
$299$	9.96449	+	3.62678i	0.576262	+	0.209742i
$300$	−2.76034	+	5.14924i	−0.159368	+	0.297291i
$301$	0.475959	+	1.47031i	0.0274338	+	0.0847472i
$302$	−6.72261	+	18.4702i	−0.386843	+	1.06284i
$303$	8.57199	+	9.58534i	0.492448	+	0.550664i
$304$	−1.85847	+	3.94286i	−0.106590	+	0.226138i
$305$	−11.4375	−	6.60343i	−0.654908	−	0.378111i
$306$	−10.9523	+	7.27983i	−0.626103	+	0.416160i
$307$	−16.0743	+	2.83433i	−0.917408	+	0.161764i	−0.612365	−	0.790575i	$-0.709782\pi$
$307$	−16.0743	+	2.83433i	−0.917408	+	0.161764i	−0.305043	+	0.952339i	$0.598671\pi$
$308$	−12.3208	−	0.443716i	−0.702045	−	0.0252831i
$309$	14.4061	−	18.3106i	0.819532	−	1.04165i
$310$	4.05979	−	1.47764i	0.230580	−	0.0839244i
$311$	−6.95931	+	4.01796i	−0.394626	+	0.227837i	−0.684163	−	0.729329i	$-0.739832\pi$
$311$	−6.95931	+	4.01796i	−0.394626	+	0.227837i	0.289537	+	0.957167i	$0.406499\pi$
$312$	4.40443	−	0.920588i	0.249352	−	0.0521180i
$313$	−16.4244	−	13.7817i	−0.928363	−	0.778989i	0.0471600	−	0.998887i	$-0.484983\pi$
$313$	−16.4244	−	13.7817i	−0.928363	−	0.778989i	−0.975523	+	0.219898i	$0.929427\pi$
$314$	7.31509	−	2.66248i	0.412814	−	0.150252i
$315$	−5.29705	−	8.62750i	−0.298455	−	0.486104i
$316$	−3.53553	−	2.04124i	−0.198889	−	0.114829i
$317$	−4.15917	+	1.51381i	−0.233602	+	0.0850242i	−0.456169	−	0.889893i	$-0.650779\pi$
$317$	−4.15917	+	1.51381i	−0.233602	+	0.0850242i	0.222567	+	0.974917i	$0.428556\pi$
$318$	−12.5228	+	5.01021i	−0.702245	+	0.280959i
$319$	−3.80402	−	10.4515i	−0.212984	−	0.585169i
$320$	0.819866	+	0.977079i	0.0458319	+	0.0546204i
$321$	−2.94182	+	20.4291i	−0.164196	+	1.14024i
$322$	10.0087	+	4.05649i	0.557763	+	0.226059i
$323$	17.2842	+	8.14690i	0.961718	+	0.453306i
$324$	−8.77713	−	1.99047i	−0.487618	−	0.110582i
$325$	−5.63269	−	6.71278i	−0.312445	−	0.372358i
$326$	−20.4114	−	7.42915i	−1.13048	−	0.411463i
$327$	−0.418898	−	13.2877i	−0.0231651	−	0.734814i
$328$	−7.40267	+	6.21158i	−0.408744	+	0.342977i
$329$	6.70283	+	12.6394i	0.369539	+	0.696835i
$330$	−9.77988	−	3.21439i	−0.538365	−	0.176946i
$331$	25.4930	+	14.7184i	1.40122	+	0.808996i	0.994518	−	0.104564i	$-0.0333448\pi$
$331$	25.4930	+	14.7184i	1.40122	+	0.808996i	0.406704	+	0.913560i	$0.366678\pi$
$332$	−0.759860	−	0.133984i	−0.0417027	−	0.00735332i
$333$	11.8316	−	2.86485i	0.648370	−	0.156993i
$334$	0.686754	−	1.18949i	0.0375775	−	0.0650861i
$335$	−5.63172	+	9.75443i	−0.307694	+	0.532941i
$336$	4.51648	−	0.775515i	0.246394	−	0.0423078i
$337$	14.7632	+	17.5940i	0.804200	+	0.958409i	0.999752	−	0.0222849i	$-0.00709408\pi$
$337$	14.7632	+	17.5940i	0.804200	+	0.958409i	−0.195551	+	0.980693i	$0.562650\pi$
$338$	1.08550	−	6.15619i	0.0590436	−	0.334853i
$339$	4.21691	−	29.2838i	0.229031	−	1.59048i
$340$	4.28319	−	3.59403i	0.232289	−	0.194913i
$341$	−7.89195	−	13.6693i	−0.427373	−	0.740232i
$342$	4.12212	+	12.4100i	0.222899	+	0.671056i
$343$	16.9437	−	7.47743i	0.914872	−	0.403743i
$344$	−0.548890	−	0.199780i	−0.0295942	−	0.0107714i
$345$	7.08710	+	5.57586i	0.381556	+	0.300194i
$346$	16.2350	−	5.90905i	0.872798	−	0.317672i
$347$	−17.5501	+	3.09456i	−0.942138	+	0.166124i	−0.623563	−	0.781773i	$-0.714316\pi$
$347$	−17.5501	+	3.09456i	−0.942138	+	0.166124i	−0.318575	+	0.947898i	$0.603204\pi$
$348$	2.17883	+	3.51331i	0.116797	+	0.188333i
$349$	12.6233	−	21.8642i	0.675711	−	1.17037i	−0.300549	−	0.953766i	$-0.597170\pi$
$349$	12.6233	−	21.8642i	0.675711	−	1.17037i	0.976261	−	0.216600i	$-0.0694966\pi$
$350$	−5.48678	−	7.03858i	−0.293281	−	0.376228i
$351$	7.66194	−	11.1137i	0.408964	−	0.593203i
$352$	2.99530	−	3.56966i	0.159650	−	0.190263i
$353$		−	16.9670i		−	0.903064i	−0.892255	−	0.451532i	$-0.850878\pi$
$353$		−	16.9670i		−	0.903064i	0.892255	−	0.451532i	$-0.149122\pi$
$354$	−1.64836	+	1.47410i	−0.0876095	+	0.0783475i
$355$	0.0216690	+	0.0595350i	0.00115007	+	0.00315979i
$356$	−4.22784	+	3.54758i	−0.224075	+	0.188021i
$357$	−3.39961	−	19.7988i	−0.179926	−	1.04786i
$358$	−3.76355	−	21.3442i	−0.198910	−	1.12807i
$359$	−14.4703	+	2.55150i	−0.763713	+	0.134663i	−0.541919	−	0.840430i	$-0.682302\pi$
$359$	−14.4703	+	2.55150i	−0.763713	+	0.134663i	−0.221794	+	0.975094i	$0.571191\pi$
$360$	3.80269	+	0.425780i	0.200420	+	0.0224406i
$361$	12.3329	−	14.4534i	0.649099	−	0.760704i
$362$	7.68867	−	4.43905i	0.404107	−	0.233312i
$363$	−2.64504	+	18.3682i	−0.138829	+	0.964079i
$364$	−1.43637	+	6.72151i	−0.0752862	+	0.352303i
$365$	−2.85457	+	3.40194i	−0.149415	+	0.178066i
$366$	2.55620	−	17.7512i	0.133615	−	0.927870i
$367$	−15.3317	−	12.8648i	−0.800309	−	0.671539i	0.147965	−	0.988993i	$-0.452728\pi$
$367$	−15.3317	−	12.8648i	−0.800309	−	0.671539i	−0.948274	+	0.317454i	$0.897172\pi$
$368$	−3.53497	+	2.04092i	−0.184273	+	0.106390i
$369$	−3.22585	+	28.8105i	−0.167931	+	1.49981i
$370$	−4.86359	+	1.77020i	−0.252846	+	0.0920285i
$371$	0.741509	−	20.5898i	0.0384972	−	1.06897i
$372$	3.91086	+	4.37319i	0.202768	+	0.226739i
$373$		−	11.4340i		−	0.592028i	−0.955184	−	0.296014i	$-0.904342\pi$
$373$		−	11.4340i		−	0.592028i	0.955184	−	0.296014i	$-0.0956576\pi$
$374$	−15.6482	−	13.1304i	−0.809150	−	0.678957i
$375$	−6.87125	−	17.1744i	−0.354830	−	0.886884i
$376$	−5.32530	−	0.938993i	−0.274631	−	0.0484249i
$377$	−6.10639	+	1.07672i	−0.314495	+	0.0554540i
$378$	8.20551	−	11.0304i	0.422046	−	0.567342i
$379$		−	0.746950i		−	0.0383682i	−0.999816	−	0.0191841i	$-0.993893\pi$
$379$		−	0.746950i		−	0.0383682i	0.999816	−	0.0191841i	$-0.00610687\pi$
$380$	−2.32879	−	5.04848i	−0.119464	−	0.258982i
$381$	9.38132	−	28.5430i	0.480620	−	1.46230i
$382$	1.76945	+	2.10875i	0.0905330	+	0.107893i
$383$	−3.11357	+	2.61260i	−0.159096	+	0.133498i	−0.718861	−	0.695154i	$-0.755336\pi$
$383$	−3.11357	+	2.61260i	−0.159096	+	0.133498i	0.559764	+	0.828652i	$0.310892\pi$
$384$	−0.818331	+	1.52654i	−0.0417603	+	0.0779011i
$385$	10.5350	−	11.6746i	0.536913	−	0.594995i
$386$	11.7245	+	2.06735i	0.596764	+	0.105226i
$387$	−1.60565	+	0.701869i	−0.0816197	+	0.0356780i
$388$			6.05427i			0.307359i
$389$	−37.8871	−	6.68052i	−1.92095	−	0.338716i	−0.922114	−	0.386918i	$-0.873540\pi$
$389$	−37.8871	−	6.68052i	−1.92095	−	0.338716i	−0.998838	+	0.0482024i	$0.984651\pi$
$390$	−2.71156	+	5.05824i	−0.137305	+	0.256134i
$391$	8.94670	+	15.4961i	0.452454	+	0.783674i
$392$	−1.70827	+	6.78836i	−0.0862809	+	0.342864i
$393$	−1.19925	−	38.0411i	−0.0604942	−	1.91892i
$394$	3.28967	−	9.03829i	0.165731	−	0.455342i
$395$	4.89312	−	1.78095i	0.246200	−	0.0896093i
$396$	−0.880541	−	13.9518i	−0.0442488	−	0.701105i
$397$	1.35637	+	7.69236i	0.0680743	+	0.386068i	0.999741	+	0.0227546i	$0.00724363\pi$
$397$	1.35637	+	7.69236i	0.0680743	+	0.386068i	−0.931667	+	0.363314i	$0.881645\pi$
$398$	16.9263			0.848437
$399$	−19.8832	−	1.91234i	−0.995407	−	0.0957367i
$400$	3.37314			0.168657
$401$	−5.28461	−	29.9705i	−0.263901	−	1.49666i	−0.772147	−	0.635444i	$-0.780817\pi$
$401$	−5.28461	−	29.9705i	−0.263901	−	1.49666i	0.508246	−	0.861212i	$-0.330294\pi$
$402$	−15.1391	−	2.18005i	−0.755069	−	0.108731i
$403$	−8.26880	+	3.00960i	−0.411898	+	0.149919i
$404$	2.53924	−	6.97650i	0.126332	−	0.347094i
$405$	9.14092	−	6.94403i	0.454216	−	0.345052i
$406$	−6.25441	+	0.872041i	−0.310401	+	0.0432787i
$407$	9.45450	+	16.3757i	0.468642	+	0.811712i
$408$	6.69187	+	3.58730i	0.331297	+	0.177598i
$409$	−2.40910	−	0.424790i	−0.119122	−	0.0210045i	0.113769	−	0.993507i	$-0.463708\pi$
$409$	−2.40910	−	0.424790i	−0.119122	−	0.0210045i	−0.232891	+	0.972503i	$0.574819\pi$
$410$		−	12.3257i		−	0.608721i
$411$	−6.65883	+	1.39179i	−0.328456	+	0.0686519i
$412$	−13.2469	−	2.33579i	−0.652629	−	0.115076i
$413$	−1.04032	−	3.21370i	−0.0511908	−	0.158136i
$414$	−3.45509	+	11.7480i	−0.169808	+	0.577380i
$415$	0.753896	−	0.632594i	0.0370073	−	0.0310528i
$416$	−1.66987	−	1.99007i	−0.0818720	−	0.0975712i
$417$	28.0576	+	9.22181i	1.37399	+	0.451594i
$418$	−16.6865	+	11.5815i	−0.816164	+	0.566470i
$419$		−	9.86310i		−	0.481844i	−0.970545	−	0.240922i	$-0.922550\pi$
$419$		−	9.86310i		−	0.481844i	0.970545	−	0.240922i	$-0.0774498\pi$
$420$	−2.94517	+	5.04877i	−0.143710	+	0.246355i
$421$	2.04157	−	0.359983i	0.0994999	−	0.0175445i	−0.123677	−	0.992323i	$-0.539469\pi$
$421$	2.04157	−	0.359983i	0.0994999	−	0.0175445i	0.223176	+	0.974778i	$0.428357\pi$
$422$	3.66710	+	0.646608i	0.178511	+	0.0314764i
$423$	−13.5102	+	8.97998i	−0.656886	+	0.436621i
$424$	5.96537	+	5.00554i	0.289704	+	0.243091i
$425$		−	14.7867i		−	0.717261i
$426$	−0.0641308	+	0.0573510i	−0.00310715	+	0.00277866i
$427$	23.2165	+	14.5425i	1.12352	+	0.703762i
$428$	11.1978	−	4.07565i	0.541264	−	0.197004i
$429$	19.9192	+	6.54693i	0.961710	+	0.316089i
$430$	0.645217	−	0.372516i	0.0311151	−	0.0179643i
$431$	−31.6457	−	26.5539i	−1.52432	−	1.27906i	−0.826808	−	0.562484i	$-0.809846\pi$
$431$	−31.6457	−	26.5539i	−1.52432	−	1.27906i	−0.697513	−	0.716572i	$-0.745710\pi$
$432$	1.38135	+	5.00918i	0.0664604	+	0.241004i
$433$	11.7215	−	13.9692i	0.563300	−	0.671315i	−0.406941	−	0.913454i	$-0.633405\pi$
$433$	11.7215	−	13.9692i	0.563300	−	0.671315i	0.970241	+	0.242139i	$0.0778491\pi$
$434$	−8.52611	+	2.76002i	−0.409266	+	0.132485i
$435$	−5.21913	−	0.751562i	−0.250238	−	0.0360346i
$436$	−6.64717	+	3.83775i	−0.318342	+	0.183795i
$437$	17.2049	−	4.53390i	0.823023	−	0.216886i
$438$	−5.72905	−	1.88299i	−0.273745	−	0.0899727i
$439$	29.6266	−	5.22397i	1.41400	−	0.249326i	0.586117	−	0.810227i	$-0.300656\pi$
$439$	29.6266	−	5.22397i	1.41400	−	0.249326i	0.827883	+	0.560900i	$0.189545\pi$
$440$	1.03209	+	5.85328i	0.0492031	+	0.279044i
$441$	10.3365	+	18.2799i	0.492215	+	0.870474i
$442$	−8.72382	+	7.32015i	−0.414950	+	0.348184i
$443$	4.93747	+	13.5656i	0.234586	+	0.644521i	1.00000		0.000981425i	$0.000312397\pi$
$443$	4.93747	+	13.5656i	0.234586	+	0.644521i	−0.765413	+	0.643539i	$0.777465\pi$
$444$	−4.68518	−	5.23904i	−0.222349	−	0.248634i
$445$		−	7.03947i		−	0.333703i
$446$	6.66654	−	7.94487i	0.315670	−	0.376201i
$447$	21.4999	−	13.3334i	1.01691	−	0.630649i
$448$	−1.62661	−	2.08666i	−0.0768501	−	0.0985853i
$449$	−17.7125	+	30.6790i	−0.835906	+	1.44783i	0.0573850	+	0.998352i	$0.481724\pi$
$449$	−17.7125	+	30.6790i	−0.835906	+	1.44783i	−0.893291	+	0.449479i	$0.851610\pi$
$450$	7.32681	−	6.97999i	0.345389	−	0.329040i
$451$	−44.3464	+	7.81947i	−2.08819	+	0.368204i
$452$	−16.0513	+	5.84219i	−0.754989	+	0.274793i
$453$	21.0508	−	26.7562i	0.989052	−	1.25712i
$454$	12.1947	+	4.43849i	0.572323	+	0.208309i
$455$	−5.38981	−	6.91419i	−0.252678	−	0.324142i
$456$	5.19038	−	5.48269i	0.243062	−	0.256751i
$457$	−9.37396	−	16.2362i	−0.438495	−	0.759496i	0.559078	−	0.829115i	$-0.311155\pi$
$457$	−9.37396	−	16.2362i	−0.438495	−	0.759496i	−0.997574	+	0.0696187i	$0.977822\pi$
$458$	17.2655	−	14.4875i	0.806763	−	0.676955i
$459$	21.9586	−	6.05541i	1.02494	−	0.282642i
$460$	0.904067	−	5.12722i	0.0421524	−	0.239058i
$461$	16.6219	+	19.8093i	0.774161	+	0.922609i	0.998654	−	0.0518663i	$-0.0165170\pi$
$461$	16.6219	+	19.8093i	0.774161	+	0.922609i	−0.224493	+	0.974476i	$0.572073\pi$
$462$	20.0334	+	7.39344i	0.932038	+	0.343974i
$463$	−19.0360	+	32.9713i	−0.884677	+	1.53231i	−0.0385946	+	0.999255i	$0.512288\pi$
$463$	−19.0360	+	32.9713i	−0.884677	+	1.53231i	−0.846083	+	0.533051i	$0.821045\pi$
$464$	1.19341	−	2.06704i	0.0554025	−	0.0959600i
$465$	−7.47933	+	0.235787i	−0.346845	+	0.0109344i
$466$	7.65566	+	1.34990i	0.354642	+	0.0625329i
$467$	−14.5373	−	8.39312i	−0.672707	−	0.388387i	0.124395	−	0.992233i	$-0.460301\pi$
$467$	−14.5373	−	8.39312i	−0.672707	−	0.388387i	−0.797101	+	0.603845i	$0.793634\pi$
$468$	−7.74516	−	0.867210i	−0.358020	−	0.0400868i
$469$	12.4026	−	19.8002i	0.572698	−	0.914286i
$470$	5.28350	−	4.43339i	0.243710	−	0.204497i
$471$	−13.4766	+	0.424850i	−0.620967	+	0.0195761i
$472$	1.19973	+	0.436665i	0.0552219	+	0.0200991i
$473$	−1.74960	−	2.08510i	−0.0804468	−	0.0958728i
$474$	4.71362	+	5.27085i	0.216504	+	0.242098i
$475$	−14.1863	−	3.86413i	−0.650912	−	0.177299i
$476$	−9.14722	+	7.13053i	−0.419262	+	0.326827i
$477$	23.3153	−	1.47150i	1.06754	−	0.0673754i
$478$	4.96025	+	5.91139i	0.226876	+	0.270381i
$479$	−11.4673	−	31.5062i	−0.523956	−	1.43956i	−0.866082	−	0.499902i	$-0.833369\pi$
$479$	−11.4673	−	31.5062i	−0.523956	−	1.43956i	0.342126	−	0.939654i	$-0.388853\pi$
$480$	−0.820631	−	2.05114i	−0.0374565	−	0.0936211i
$481$	9.90595	−	3.60547i	0.451673	−	0.164395i
$482$	3.27228	+	1.88925i	0.149048	+	0.0860531i
$483$	−14.2750	−	12.0877i	−0.649537	−	0.550007i
$484$	10.0681	−	3.66449i	0.457642	−	0.166568i
$485$	−5.91550	−	4.96369i	−0.268609	−	0.225390i
$486$	13.3659	+	8.02205i	0.606289	+	0.363888i
$487$	11.6731	−	6.73946i	0.528958	−	0.305394i	−0.211634	−	0.977349i	$-0.567879\pi$
$487$	11.6731	−	6.73946i	0.528958	−	0.305394i	0.740592	+	0.671955i	$0.234545\pi$
$488$	−9.72993	+	3.54140i	−0.440453	+	0.160312i
$489$	29.5682	+	23.2632i	1.33712	+	1.05200i
$490$	−5.23220	−	7.23467i	−0.236367	−	0.326829i
$491$	−34.8454	+	6.14418i	−1.57255	+	0.277283i	−0.890832	−	0.454333i	$-0.849878\pi$
$491$	−34.8454	+	6.14418i	−1.57255	+	0.277283i	−0.681717	+	0.731616i	$0.738767\pi$
$492$	15.5401	−	6.21737i	0.700601	−	0.280301i
$493$	−9.06123	−	5.23150i	−0.408097	−	0.235615i
$494$	4.74317	+	10.2825i	0.213405	+	0.462633i
$495$	14.3539	+	10.5783i	0.645162	+	0.475458i
$496$	1.15849	−	3.18293i	0.0520179	−	0.142918i
$497$	−0.0404745	−	0.125032i	−0.00181553	−	0.00560844i
$498$	1.17785	+	0.631409i	0.0527809	+	0.0282941i
$499$	−6.50491	−	2.36759i	−0.291200	−	0.105988i	0.192290	−	0.981338i	$-0.438409\pi$
$499$	−6.50491	−	2.36759i	−0.291200	−	0.105988i	−0.483489	+	0.875350i	$0.660631\pi$
$500$	−6.86485	+	8.18121i	−0.307006	+	0.365875i
$501$	−1.77332	+	1.58585i	−0.0792261	+	0.0708504i
$502$	−15.8905	−	9.17438i	−0.709227	−	0.409473i
$503$	−8.05235	−	22.1237i	−0.359037	−	0.986445i	−0.979364	−	0.202102i	$-0.935223\pi$
$503$	−8.05235	−	22.1237i	−0.359037	−	0.986445i	0.620328	−	0.784343i	$-0.287000\pi$
$504$	−7.85107	−	1.16652i	−0.349714	−	0.0519607i
$505$	4.73475	+	8.20083i	0.210694	+	0.364932i
$506$	−19.0207			−0.845575
$507$	−5.11552	+	9.54267i	−0.227188	+	0.423805i
$508$	−17.0830	+	3.01220i	−0.757937	+	0.133645i
$509$	−1.58675	+	8.99888i	−0.0703313	+	0.398868i	0.929237	+	0.369484i	$0.120466\pi$
$509$	−1.58675	+	8.99888i	−0.0703313	+	0.398868i	−0.999568	+	0.0293841i	$0.990645\pi$
$510$	−8.99151	+	3.59738i	−0.398151	+	0.159295i
$511$	6.17139	−	6.83900i	0.273006	−	0.302540i
$512$	1.00000			0.0441942
$513$	−0.0712048	−	22.6494i	−0.00314377	−	0.999995i
$514$	−0.900200	+	1.55919i	−0.0397061	+	0.0687730i
$515$	13.1430	−	11.0283i	0.579148	−	0.485963i
$516$	0.795129	+	0.625577i	0.0350036	+	0.0275395i
$517$	−19.3027	−	16.1969i	−0.848933	−	0.712340i
$518$	10.2142	−	3.30648i	0.448787	−	0.145278i
$519$	−29.9096	+	0.942905i	−1.31289	+	0.0413889i
$520$	3.31352			0.145308
$521$	31.1019			1.36260			0.681300	−	0.732005i	$-0.261415\pi$
$521$	31.1019			1.36260			0.681300	+	0.732005i	$0.261415\pi$
$522$	−1.68510	−	6.95934i	−0.0737546	−	0.304602i
$523$	16.2963	−	19.4211i	0.712586	−	0.849227i	−0.281302	−	0.959619i	$-0.590766\pi$
$523$	16.2963	−	19.4211i	0.712586	−	0.849227i	0.993888	+	0.110392i	$0.0352106\pi$
$524$	−19.0300	+	10.9870i	−0.831329	+	0.479968i
$525$	5.22165	+	14.5490i	0.227892	+	0.634970i
$526$	−16.6246	−	2.93137i	−0.724868	−	0.127814i
$527$	−13.9529	−	5.07846i	−0.607800	−	0.221221i
$528$	−6.85916	+	4.25379i	−0.298506	+	0.185123i
$529$	−5.95640	−	2.16795i	−0.258974	−	0.0942587i
$530$	−9.78162	+	1.72476i	−0.424886	+	0.0749189i
$531$	3.50952	−	1.53410i	0.152300	−	0.0665742i
$532$	4.45060	+	10.6392i	0.192958	+	0.461267i
$533$			25.1043i			1.08739i
$534$	8.87530	−	3.55088i	0.384072	−	0.153662i
$535$	−5.19843	+	14.2826i	−0.224748	+	0.617490i
$536$	3.02028	+	8.29815i	0.130456	+	0.358426i
$537$	−5.35055	+	37.1562i	−0.230893	+	1.60341i
$538$	2.08711	−	11.8366i	0.0899818	−	0.510312i
$539$	−22.7102	+	23.4146i	−0.978198	+	1.00854i
$540$	−6.02689	−	2.75716i	−0.259356	−	0.118649i
$541$	−20.6430	−	17.3215i	−0.887512	−	0.744711i	0.0801975	−	0.996779i	$-0.474445\pi$
$541$	−20.6430	−	17.3215i	−0.887512	−	0.744711i	−0.967710	+	0.252068i	$0.918889\pi$
$542$	−3.12429	+	17.7187i	−0.134200	+	0.761083i
$543$	−15.0521	+	3.14609i	−0.645946	+	0.135012i
$544$		−	4.38367i		−	0.187948i
$545$	1.70001	−	9.64125i	0.0728205	−	0.412986i
$546$	5.99859	−	10.2831i	0.256716	−	0.440077i
$547$	23.1593	−	27.6002i	0.990219	−	1.18010i	0.00657466	−	0.999978i	$-0.497907\pi$
$547$	23.1593	−	27.6002i	0.990219	−	1.18010i	0.983645	−	0.180119i	$-0.0576483\pi$
$548$	2.52458	+	3.00868i	0.107845	+	0.128525i
$549$	−13.8063	+	27.8263i	−0.589237	+	1.18760i
$550$	13.6125	+	7.85916i	0.580438	+	0.335116i
$551$	−7.38700	+	7.32618i	−0.314697	+	0.312106i
$552$	6.92039	−	1.44646i	0.294551	−	0.0615653i
$553$	−10.2762	+	3.32655i	−0.436989	+	0.141459i
$554$	2.29053	+	12.9902i	0.0973151	+	0.551901i
$555$	8.96018	−	0.282471i	0.380338	−	0.0119902i
$556$	−2.96098	−	16.7926i	−0.125574	−	0.712163i
$557$	−12.0940	+	14.4131i	−0.512439	+	0.610701i	−0.958776	−	0.284164i	$-0.908284\pi$
$557$	−12.0940	+	14.4131i	−0.512439	+	0.610701i	0.446337	+	0.894865i	$0.352728\pi$
$558$	−4.07004	−	9.31093i	−0.172298	−	0.394163i
$559$	−1.31415	+	0.758724i	−0.0555826	+	0.0320906i
$560$	3.37243	+	0.121453i	0.142511	+	0.00513233i
$561$	18.6472	+	30.0683i	0.787287	+	1.26948i
$562$	12.9918	−	22.5025i	0.548027	−	0.949211i
$563$	21.5935	+	37.4011i	0.910058	+	1.57627i	0.813980	+	0.580893i	$0.197296\pi$
$563$	21.5935	+	37.4011i	0.910058	+	1.57627i	0.0960779	+	0.995374i	$0.469370\pi$
$564$	8.25470	+	4.42508i	0.347586	+	0.186330i
$565$	7.45163	−	20.4732i	0.313492	−	0.861313i
$566$	−14.4015	−	12.0843i	−0.605342	−	0.507942i
$567$	−19.4672	+	13.7123i	−0.817546	+	0.575863i
$568$	0.0466763	+	0.0169888i	0.00195850	+	0.000712834i
$569$	4.01376	+	6.95204i	0.168266	+	0.291445i	0.937810	−	0.347149i	$-0.112850\pi$
$569$	4.01376	+	6.95204i	0.168266	+	0.291445i	−0.769545	+	0.638593i	$0.779517\pi$
$570$	1.10160	+	9.56649i	0.0461411	+	0.400696i
$571$	−7.54116	+	13.0617i	−0.315588	+	0.546614i	−0.979562	−	0.201141i	$-0.935535\pi$
$571$	−7.54116	+	13.0617i	−0.315588	+	0.546614i	0.663974	+	0.747755i	$0.268868\pi$
$572$	−2.10212	−	11.9217i	−0.0878940	−	0.498472i
$573$	−1.77110	−	4.42680i	−0.0739888	−	0.184932i
$574$	−0.920168	+	25.5506i	−0.0384071	+	1.06646i
$575$	−8.85026	−	10.5473i	−0.369082	−	0.439854i
$576$	2.17211	−	2.06929i	0.0905045	−	0.0862203i
$577$	−7.42687	−	12.8637i	−0.309185	−	0.535524i	0.669000	−	0.743263i	$-0.266723\pi$
$577$	−7.42687	−	12.8637i	−0.309185	−	0.535524i	−0.978184	+	0.207739i	$0.933389\pi$
$578$	−2.21659			−0.0921978
$579$	−18.1741	−	9.74257i	−0.755291	−	0.404887i
$580$	1.04123	+	2.86075i	0.0432346	+	0.118786i
$581$	−1.61003	+	1.25506i	−0.0667952	+	0.0520688i
$582$	3.27426	−	9.96202i	0.135722	−	0.412939i
$583$	12.4110	+	34.0990i	0.514012	+	1.41224i
$584$	0.604599	+	3.42885i	0.0250185	+	0.141887i
$585$	7.19733	−	6.85664i	0.297573	−	0.283487i
$586$	−23.7707	+	19.9459i	−0.981957	+	0.823959i
$587$	−8.79349	+	24.1599i	−0.362946	+	0.997186i	0.615036	+	0.788499i	$0.289141\pi$
$587$	−8.79349	+	24.1599i	−0.362946	+	0.997186i	−0.977982	+	0.208688i	$0.933081\pi$
$588$	6.48215	−	10.2461i	0.267319	−	0.422540i
$589$	−8.51849	+	12.0593i	−0.350998	+	0.496893i
$590$	−1.41027	+	0.814221i	−0.0580600	+	0.0335210i
$591$	−10.3011	+	13.0930i	−0.423729	+	0.538573i
$592$	−1.38787	+	3.81313i	−0.0570410	+	0.156719i
$593$	13.9963	+	2.46792i	0.574758	+	0.101345i	0.453469	−	0.891272i	$-0.350186\pi$
$593$	13.9963	+	2.46792i	0.574758	+	0.101345i	0.121289	+	0.992617i	$0.461297\pi$
$594$	−6.09649	+	23.4333i	−0.250142	+	0.961478i
$595$	0.532410	−	14.7836i	0.0218267	−	0.606070i
$596$	−12.6493	−	7.30310i	−0.518137	−	0.299147i
$597$	−27.8514	−	9.15402i	−1.13988	−	0.374649i
$598$	−1.84136	+	10.4429i	−0.0752990	+	0.427042i
$599$	0.321068	−	1.82087i	0.0131185	−	0.0743986i	−0.977546	−	0.210724i	$-0.932418\pi$
$599$	0.321068	−	1.82087i	0.0131185	−	0.0743986i	0.990664	+	0.136325i	$0.0435291\pi$
$600$	−5.55034	−	1.82425i	−0.226592	−	0.0744747i
$601$	18.7390	+	10.8190i	0.764381	+	0.441316i	0.830867	−	0.556472i	$-0.187845\pi$
$601$	18.7390	+	10.8190i	0.764381	+	0.441316i	−0.0664854	+	0.997787i	$0.521179\pi$
$602$	−1.36532	+	0.724044i	−0.0556464	+	0.0295099i
$603$	23.7316	+	11.7746i	0.966427	+	0.479501i
$604$	−19.3570	−	3.41316i	−0.787625	−	0.138880i
$605$	−4.67401	+	12.8417i	−0.190026	+	0.522091i
$606$	−7.95121	+	10.1062i	−0.322996	+	0.410538i
$607$	−34.3581	+	19.8367i	−1.39455	+	0.805145i	−0.993815	−	0.111048i	$-0.964579\pi$
$607$	−34.3581	+	19.8367i	−1.39455	+	0.805145i	−0.400738	+	0.916193i	$0.631246\pi$
$608$	−4.20567	−	1.14556i	−0.170563	−	0.0464587i
$609$	10.7630	+	1.94759i	0.436137	+	0.0789205i
$610$	4.51701	−	12.4104i	0.182888	−	0.502482i
$611$	−10.7612	+	9.02972i	−0.435352	+	0.365303i
$612$	−9.07108	−	9.52181i	−0.366677	−	0.384896i
$613$	7.30430	+	41.4248i	0.295018	+	1.67313i	0.667129	+	0.744942i	$0.267523\pi$
$613$	7.30430	+	41.4248i	0.295018	+	1.67313i	−0.372111	+	0.928188i	$0.621366\pi$
$614$	−5.58254	−	15.3379i	−0.225293	−	0.618988i
$615$	−6.66593	+	20.2813i	−0.268796	+	0.817820i
$616$	−1.70252	−	12.2107i	−0.0685963	−	0.491983i
$617$	7.69406	+	21.1392i	0.309751	+	0.851034i	0.992705	+	0.120572i	$0.0384729\pi$
$617$	7.69406	+	21.1392i	0.309751	+	0.851034i	−0.682954	+	0.730462i	$0.739305\pi$
$618$	20.5340	+	11.0076i	0.825997	+	0.442791i
$619$	−18.0395			−0.725067			−0.362533	−	0.931971i	$-0.618088\pi$
$619$	−18.0395			−0.725067			−0.362533	+	0.931971i	$0.618088\pi$
$620$	2.16017	+	3.74152i	0.0867544	+	0.150263i
$621$	12.0387	−	17.4621i	0.483096	−	0.700731i
$622$	−5.16539	−	6.15587i	−0.207113	−	0.246828i
$623$	−0.525530	+	14.5926i	−0.0210549	+	0.584639i
$624$	1.67142	+	4.17766i	0.0669105	+	0.167240i
$625$	0.563267	+	3.19445i	0.0225307	+	0.127778i
$626$	10.7203	−	18.5681i	0.428468	−	0.742129i
$627$	33.7204	−	10.0325i	1.34666	−	0.400659i
$628$	3.89228	+	6.74162i	0.155319	+	0.269020i
$629$	16.7155	+	6.08395i	0.666491	+	0.242583i
$630$	7.57660	−	6.71472i	0.301859	−	0.267521i
$631$	−11.3744	−	9.54430i	−0.452810	−	0.379952i	0.387668	−	0.921799i	$-0.373281\pi$
$631$	−11.3744	−	9.54430i	−0.452810	−	0.379952i	−0.840477	+	0.541847i	$0.817725\pi$
$632$	1.39629	−	3.83628i	0.0555415	−	0.152599i
$633$	−5.68434	−	3.04719i	−0.225932	−	0.121115i
$634$	−2.21305	−	3.83311i	−0.0878913	−	0.152232i
$635$	11.0626	−	19.1611i	0.439008	−	0.760384i
$636$	−7.10866	−	11.4626i	−0.281877	−	0.454520i
$637$	10.6567	+	14.7352i	0.422235	+	0.583832i
$638$	9.63211	−	5.56110i	0.381339	−	0.220166i
$639$	0.136541	−	0.0596853i	0.00540147	−	0.00236111i
$640$	−0.819866	+	0.977079i	−0.0324081	+	0.0386224i
$641$	6.11830	+	34.6986i	0.241658	+	1.37051i	0.828127	+	0.560540i	$0.189406\pi$
$641$	6.11830	+	34.6986i	0.241658	+	1.37051i	−0.586469	+	0.809972i	$0.699482\pi$
$642$	−20.6296	+	0.650350i	−0.814184	+	0.0256673i
$643$	2.41812	+	13.7139i	0.0953615	+	0.540822i	0.994636	+	0.103437i	$0.0329841\pi$
$643$	2.41812	+	13.7139i	0.0953615	+	0.540822i	−0.899275	+	0.437385i	$0.855905\pi$
$644$	−2.25687	+	10.5611i	−0.0889332	+	0.416164i
$645$	−1.26314	+	0.264013i	−0.0497360	+	0.0103955i
$646$	−5.02177	+	18.4363i	−0.197579	+	0.725366i
$647$	18.4453	+	10.6494i	0.725160	+	0.418671i	0.816649	−	0.577135i	$-0.195829\pi$
$647$	18.4453	+	10.6494i	0.725160	+	0.418671i	−0.0914890	+	0.995806i	$0.529163\pi$
$648$	0.436096	−	8.98943i	0.0171315	−	0.353138i
$649$	3.82417	+	4.55746i	0.150112	+	0.178896i
$650$	5.63269	−	6.71278i	0.220932	−	0.263297i
$651$	15.5220	+	0.0695892i	0.608354	+	0.00272742i
$652$	3.77188	−	21.3914i	0.147718	−	0.837751i
$653$		−	34.1870i		−	1.33784i	−0.743335	−	0.668920i	$-0.766757\pi$
$653$		−	34.1870i		−	1.33784i	0.743335	−	0.668920i	$-0.233243\pi$
$654$	13.0131	−	2.71993i	0.508854	−	0.106358i
$655$	4.86692	−	27.6016i	0.190166	−	1.07849i
$656$	−7.40267	−	6.21158i	−0.289026	−	0.242521i
$657$	8.40854	+	6.19674i	0.328048	+	0.241758i
$658$	−11.2835	+	8.79581i	−0.439876	+	0.342896i
$659$	2.42072	−	13.7286i	0.0942977	−	0.534789i	−0.900663	−	0.434519i	$-0.856918\pi$
$659$	2.42072	−	13.7286i	0.0942977	−	0.534789i	0.994960	−	0.100270i	$-0.0319706\pi$
$660$	1.46730	−	10.1895i	0.0571145	−	0.396625i
$661$	6.04221	+	16.6008i	0.235015	+	0.645698i	0.999999	+	0.00164828i	$0.000524664\pi$
$661$	6.04221	+	16.6008i	0.235015	+	0.645698i	−0.764984	+	0.644049i	$0.777253\pi$
$662$	−10.0680	+	27.6615i	−0.391303	+	1.07510i
$663$	18.3135	−	7.32698i	0.711237	−	0.284556i
$664$		−	0.771582i		−	0.0299432i
$665$	−14.0442	−	4.37412i	−0.544611	−	0.169621i
$666$	4.87587	+	11.1544i	0.188936	+	0.432225i
$667$	−9.59455	+	1.69178i	−0.371503	+	0.0655059i
$668$	1.29067	+	0.469767i	0.0499377	+	0.0181758i
$669$	−15.2662	+	9.46753i	−0.590225	+	0.366036i
$670$	−10.5842	−	3.85233i	−0.408902	−	0.148828i
$671$	−47.5169	−	8.37850i	−1.83437	−	0.323449i
$672$	1.54801	+	4.31320i	0.0597158	+	0.166385i
$673$	−18.4063	+	10.6269i	−0.709510	+	0.409636i	−0.810880	−	0.585213i	$-0.801011\pi$
$673$	−18.4063	+	10.6269i	−0.709510	+	0.409636i	0.101369	+	0.994849i	$0.467678\pi$
$674$	−14.7632	+	17.5940i	−0.568655	+	0.677697i
$675$	−15.8308	+	7.52278i	−0.609329	+	0.289552i
$676$	6.25116			0.240429
$677$	23.2595			0.893936			0.446968	−	0.894550i	$-0.352504\pi$
$677$	23.2595			0.893936			0.446968	+	0.894550i	$0.352504\pi$
$678$	29.5712	−	0.932236i	1.13567	−	0.0358023i
$679$	11.8921	+	10.7312i	0.456375	+	0.411825i
$680$	4.28319	+	3.59403i	0.164253	+	0.137825i
$681$	−17.6653	−	13.8984i	−0.676937	−	0.532588i
$682$	12.0912	−	10.1457i	0.462995	−	0.388499i
$683$	13.8249	−	23.9455i	0.528997	−	0.916250i	−0.470431	−	0.882437i	$-0.655902\pi$
$683$	13.8249	−	23.9455i	0.528997	−	0.916250i	0.999428	−	0.0338129i	$-0.0107650\pi$
$684$	−11.5057	+	6.21447i	−0.439930	+	0.237616i
$685$	−5.00954			−0.191405
$686$	10.3061	+	15.3878i	0.393488	+	0.587510i
$687$	−36.2446	+	14.5010i	−1.38282	+	0.553246i
$688$	0.101431	−	0.575243i	0.00386701	−	0.0219309i
$689$	19.9228	−	3.51292i	0.758997	−	0.133832i
$690$	−4.26049	+	7.94767i	−0.162194	+	0.302562i
$691$	31.7923			1.20943			0.604717	−	0.796440i	$-0.293286\pi$
$691$	31.7923			1.20943			0.604717	+	0.796440i	$0.293286\pi$
$692$	8.63845	+	14.9622i	0.328385	+	0.568779i
$693$	−28.9655	−	23.0000i	−1.10031	−	0.873696i
$694$	−6.09508	−	16.7461i	−0.231366	−	0.635673i
$695$	18.8353	+	10.8745i	0.714462	+	0.412495i
$696$	−3.08159	+	2.75580i	−0.116807	+	0.104458i
$697$	−27.2295	+	32.4509i	−1.03139	+	1.22916i
$698$	23.7241	+	8.63486i	0.897970	+	0.326834i
$699$	−11.8670	−	6.36151i	−0.448850	−	0.240614i
$700$	5.97888	−	6.62566i	0.225980	−	0.250426i
$701$	6.65409	−	18.2820i	0.251322	−	0.690500i	−0.748310	−	0.663349i	$-0.769134\pi$
$701$	6.65409	−	18.2820i	0.251322	−	0.690500i	0.999631	−	0.0271509i	$-0.00864346\pi$
$702$	12.2753	+	5.61567i	0.463301	+	0.211950i
$703$	10.2051	−	14.4469i	0.384892	−	0.544875i
$704$	4.03555	+	2.32993i	0.152096	+	0.0878125i
$705$	−11.0914	+	4.43752i	−0.417727	+	0.167127i
$706$	16.7093	−	2.94629i	0.628862	−	0.110885i
$707$	−9.20275	−	17.3535i	−0.346105	−	0.652646i
$708$	−1.73794	−	1.36735i	−0.0653158	−	0.0513880i
$709$	19.8694	−	7.23185i	0.746209	−	0.271598i	0.0591995	−	0.998246i	$-0.481145\pi$
$709$	19.8694	−	7.23185i	0.746209	−	0.271598i	0.687010	+	0.726648i	$0.258923\pi$
$710$	−0.0548678	+	0.0316779i	−0.00205915	+	0.00118885i
$711$	−4.90547	−	11.2221i	−0.183970	−	0.420863i
$712$	−4.22784	−	3.54758i	−0.158445	−	0.132951i
$713$	−12.9922	+	4.72877i	−0.486562	+	0.177094i
$714$	18.9076	−	6.78598i	0.707601	−	0.253959i
$715$	13.3719	+	7.72027i	0.500081	+	0.288722i
$716$	20.3664	−	7.41275i	0.761127	−	0.277027i
$717$	−4.96487	−	12.4095i	−0.185417	−	0.463442i
$718$	−5.02548	−	13.8074i	−0.187549	−	0.515287i
$719$	−6.08252	−	7.24887i	−0.226840	−	0.270337i	0.640605	−	0.767871i	$-0.278684\pi$
$719$	−6.08252	−	7.24887i	−0.226840	−	0.270337i	−0.867445	+	0.497533i	$0.834239\pi$
$720$	0.241020	+	3.81886i	0.00898227	+	0.142320i
$721$	−28.0682	+	21.8800i	−1.04531	+	0.814854i
$722$	16.3754	+	9.63571i	0.609428	+	0.358604i
$723$	−4.36265	−	4.87838i	−0.162249	−	0.181429i
$724$	5.70674	+	6.80103i	0.212089	+	0.252758i
$725$	7.56551	+	2.75362i	0.280976	+	0.102267i
$726$	−18.5484	+	0.584742i	−0.688397	+	0.0217018i
$727$	−38.1734	+	32.0313i	−1.41577	+	1.18798i	−0.462216	+	0.886768i	$0.652945\pi$
$727$	−38.1734	+	32.0313i	−1.41577	+	1.18798i	−0.953558	+	0.301208i	$0.902610\pi$
$728$	−6.86882	−	0.247370i	−0.254575	−	0.00916815i
$729$	−17.6545	−	20.4284i	−0.653869	−	0.756608i
$730$	−3.84595	−	2.22046i	−0.142345	−	0.0821829i
$731$	−2.52167	−	0.444639i	−0.0932675	−	0.0164456i
$732$	17.9254	−	0.565100i	0.662541	−	0.0208867i
$733$	7.14075	−	12.3681i	0.263750	−	0.456828i	−0.703486	−	0.710709i	$-0.748374\pi$
$733$	7.14075	−	12.3681i	0.263750	−	0.456828i	0.967235	+	0.253882i	$0.0817074\pi$
$734$	10.0071	−	17.3328i	0.369368	−	0.639764i
$735$	4.69671	+	14.7340i	0.173241	+	0.543471i
$736$	−2.62375	−	3.12686i	−0.0967127	−	0.115258i
$737$	−7.14560	+	40.5247i	−0.263211	+	1.49275i
$738$	−28.9329	+	1.82604i	−1.06504	+	0.0672176i
$739$	2.35647	−	1.97731i	0.0866841	−	0.0727366i	−0.598416	−	0.801186i	$-0.704203\pi$
$739$	2.35647	−	1.97731i	0.0866841	−	0.0727366i	0.685100	+	0.728449i	$0.259758\pi$
$740$	−2.58786	−	4.48231i	−0.0951318	−	0.164773i
$741$	−2.24370	−	19.4846i	−0.0824242	−	0.715785i
$742$	20.4057	−	2.84513i	0.749117	−	0.104448i
$743$	40.7763	+	14.8414i	1.49594	+	0.544477i	0.955005	−	0.296589i	$-0.0958491\pi$
$743$	40.7763	+	14.8414i	1.49594	+	0.544477i	0.540933	+	0.841066i	$0.318071\pi$
$744$	−3.62763	+	4.61084i	−0.132996	+	0.169041i
$745$	17.5065	−	6.37184i	0.641388	−	0.233446i
$746$	11.2603	−	1.98549i	0.412267	−	0.0726939i
$747$	−1.59662	−	1.67596i	−0.0584175	−	0.0613201i
$748$	10.2136	−	17.6905i	0.373448	−	0.646830i
$749$	11.8424	−	29.2192i	0.432713	−	1.06765i
$750$	15.7203	−	9.74917i	0.574026	−	0.355989i
$751$	34.3751	−	40.9666i	1.25436	−	1.49489i	0.459411	−	0.888224i	$-0.348060\pi$
$751$	34.3751	−	40.9666i	1.25436	−	1.49489i	0.794954	−	0.606670i	$-0.207495\pi$
$752$		−	5.40745i		−	0.197189i
$753$	21.1854	+	23.6899i	0.772039	+	0.863307i
$754$	−2.12073	−	5.82665i	−0.0772323	−	0.212194i
$755$	19.2051	−	16.1150i	0.698944	−	0.586484i
$756$	12.2877	+	6.16544i	0.446899	+	0.224235i
$757$	−2.71304	−	15.3864i	−0.0986073	−	0.559230i	−0.993582	−	0.113113i	$-0.963918\pi$
$757$	−2.71304	−	15.3864i	−0.0986073	−	0.559230i	0.894975	−	0.446117i	$-0.147193\pi$
$758$	0.735602	−	0.129706i	0.0267183	−	0.00471115i
$759$	31.2977	+	10.2867i	1.13604	+	0.373385i
$760$	4.56739	−	3.17007i	0.165677	−	0.114990i
$761$	25.3716	−	14.6483i	0.919719	−	0.531000i	0.0361733	−	0.999346i	$-0.488483\pi$
$761$	25.3716	−	14.6483i	0.919719	−	0.531000i	0.883545	+	0.468346i	$0.155150\pi$
$762$	29.7384	+	4.28237i	1.07731	+	0.155134i
$763$	−4.24383	+	19.8591i	−0.153637	+	0.718946i
$764$	−1.76945	+	2.10875i	−0.0640165	+	0.0762919i
$765$	16.7406	−	1.05655i	0.605259	−	0.0381997i
$766$	−3.11357	−	2.61260i	−0.112498	−	0.0943970i
$767$	2.87238	−	1.65837i	0.103716	−	0.0598803i
$768$	−1.64545	−	0.540817i	−0.0593752	−	0.0195151i
$769$	29.0847	−	10.5860i	1.04882	−	0.381740i	0.240604	−	0.970623i	$-0.422654\pi$
$769$	29.0847	−	10.5860i	1.04882	−	0.381740i	0.808218	+	0.588883i	$0.200432\pi$
$770$	13.3267	+	8.34766i	0.480259	+	0.300829i
$771$	2.32448	−	2.07873i	0.0837140	−	0.0748638i
$772$			11.9054i			0.428485i
$773$	−38.2939	−	32.1324i	−1.37734	−	1.15572i	−0.970186	−	0.242363i	$-0.922078\pi$
$773$	−38.2939	−	32.1324i	−1.37734	−	1.15572i	−0.407152	−	0.913361i	$-0.633478\pi$
$774$	−0.970024	−	1.45938i	−0.0348668	−	0.0524562i
$775$	11.2519	+	1.98402i	0.404181	+	0.0712681i
$776$	−5.96229	+	1.05131i	−0.214034	+	0.0377399i
$777$	−18.5952	−	0.0833674i	−0.667100	−	0.00299079i
$778$		−	38.4716i		−	1.37927i
$779$	24.0175	+	34.6041i	0.860515	+	1.23982i
$780$	−5.45225	−	1.79201i	−0.195222	−	0.0641643i
$781$	0.148782	+	0.177312i	0.00532385	+	0.00634471i
$782$	−13.7071	+	11.5017i	−0.490166	+	0.411299i
$783$	−0.990983	+	12.3626i	−0.0354149	+	0.441803i
$784$	−6.98187	−	0.503536i	−0.249352	−	0.0179834i
$785$	−9.77825	−	1.72417i	−0.349001	−	0.0615382i
$786$	37.2549	−	7.78680i	1.32884	−	0.277746i
$787$			5.24986i			0.187137i	0.995613	+	0.0935686i	$0.0298274\pi$
$787$			5.24986i			0.187137i	−0.995613	+	0.0935686i	$0.970173\pi$
$788$	9.47222	+	1.67021i	0.337434	+	0.0594987i
$789$	25.7697	+	13.8143i	0.917425	+	0.491803i
$790$	2.60357	+	4.50952i	0.0926310	+	0.160442i
$791$	−16.9754	+	41.8839i	−0.603575	+	1.48922i
$792$	13.5869	−	3.28987i	0.482791	−	0.116900i
$793$	−9.20004	+	25.2769i	−0.326703	+	0.897609i
$794$	−7.33996	+	2.67153i	−0.260486	+	0.0948090i
$795$	17.0280	+	2.45205i	0.603920	+	0.0869653i
$796$	2.93922	+	16.6691i	0.104178	+	0.590821i
$797$	14.7557			0.522675			0.261338	−	0.965247i	$-0.415836\pi$
$797$	14.7557			0.522675			0.261338	+	0.965247i	$0.415836\pi$
$798$	−1.56940	−	19.9132i	−0.0555562	−	0.704921i
$799$	−23.7045			−0.838604
$800$	0.585739	+	3.32189i	0.0207090	+	0.117447i
$801$	−16.5243	+	1.04290i	−0.583857	+	0.0368489i
$802$	28.5975	−	10.4087i	1.00981	−	0.367542i
$803$	−5.54909	+	15.2460i	−0.195823	+	0.538019i
$804$	−0.481945	−	15.2876i	−0.0169969	−	0.539154i
$805$	−8.46865	−	10.8638i	−0.298481	−	0.382898i
$806$	−4.39973	−	7.62056i	−0.154974	−	0.268423i
$807$	−9.83568	+	18.3478i	−0.346232	+	0.645874i
$808$	7.31144	+	1.28921i	0.257216	+	0.0453541i
$809$		−	51.5589i		−	1.81272i	−0.422511	−	0.906358i	$-0.638851\pi$
$809$		−	51.5589i		−	1.81272i	0.422511	−	0.906358i	$-0.361149\pi$
$810$	8.42584	+	7.79623i	0.296054	+	0.273932i
$811$	44.4643	+	7.84026i	1.56135	+	0.275309i	0.886530	−	0.462670i	$-0.153109\pi$
$811$	44.4643	+	7.84026i	1.56135	+	0.275309i	0.674823	+	0.737979i	$0.264220\pi$
$812$	−1.94486	−	6.00797i	−0.0682512	−	0.210838i
$813$	14.7234	−	27.4656i	0.516374	−	0.963262i
$814$	−14.4851	+	12.1545i	−0.507704	+	0.426014i
$815$	17.8086	+	21.2235i	0.623809	+	0.743427i
$816$	−2.37077	+	7.21313i	−0.0829934	+	0.252510i
$817$	−1.08556	+	2.30309i	−0.0379790	+	0.0805748i
$818$		−	2.44627i		−	0.0855317i
$819$	−15.4317	+	13.6762i	−0.539227	+	0.477887i
$820$	12.1384	−	2.14033i	0.423891	−	0.0747435i
$821$	54.5610	+	9.62058i	1.90419	+	0.335761i	0.996480	−	0.0838321i	$-0.0267159\pi$
$821$	54.5610	+	9.62058i	1.90419	+	0.335761i	0.907713	+	0.419593i	$0.137827\pi$
$822$	−2.52694	−	6.31598i	−0.0881371	−	0.220295i
$823$	−10.4235	−	8.74635i	−0.363340	−	0.304878i	0.442780	−	0.896630i	$-0.353992\pi$
$823$	−10.4235	−	8.74635i	−0.363340	−	0.304878i	−0.806120	+	0.591752i	$0.798437\pi$
$824$		−	13.4513i		−	0.468598i
$825$	−18.1483	−	20.2938i	−0.631843	−	0.706538i
$826$	2.98423	−	1.58257i	0.103835	−	0.0550646i
$827$	−6.48447	+	2.36015i	−0.225487	+	0.0820705i	−0.452293	−	0.891869i	$-0.649394\pi$
$827$	−6.48447	+	2.36015i	−0.225487	+	0.0820705i	0.226806	+	0.973940i	$0.427172\pi$
$828$	−12.1694	−	1.36259i	−0.422917	−	0.0473532i
$829$	−21.6021	+	12.4720i	−0.750271	+	0.433169i	−0.825792	−	0.563975i	$-0.809271\pi$
$829$	−21.6021	+	12.4720i	−0.750271	+	0.433169i	0.0755208	+	0.997144i	$0.475938\pi$
$830$	0.753896	+	0.632594i	0.0261681	+	0.0219577i
$831$	3.25638	−	22.6135i	0.112963	−	0.784455i
$832$	1.66987	−	1.99007i	0.0578922	−	0.0689933i
$833$	−2.20734	+	30.6062i	−0.0764797	+	1.06044i
$834$	−4.20955	+	29.2327i	−0.145765	+	1.01225i
$835$	−1.51718	+	0.875945i	−0.0525042	+	0.0303133i
$836$	−14.3031	−	14.4219i	−0.494685	−	0.498792i
$837$	1.66154	+	17.5218i	0.0574313	+	0.605644i
$838$	9.71325	−	1.71271i	0.335539	−	0.0591645i
$839$	−8.02514	−	45.5128i	−0.277058	−	1.57128i	−0.732346	−	0.680932i	$-0.761575\pi$
$839$	−8.02514	−	45.5128i	−0.277058	−	1.57128i	0.455288	−	0.890344i	$-0.349536\pi$
$840$	−5.48350	−	2.02372i	−0.189199	−	0.0698248i
$841$	−17.8512	+	14.9790i	−0.615560	+	0.516516i
$842$	0.709029	+	1.94804i	0.0244348	+	0.0671339i
$843$	−33.5472	+	30.0006i	−1.15543	+	1.03328i
$844$			3.72367i			0.128174i
$845$	−5.12512	+	6.10788i	−0.176309	+	0.210117i
$846$	−11.1896	−	11.7456i	−0.384705	−	0.403820i
$847$	10.6478	−	26.2715i	0.365861	−	0.902701i
$848$	−3.89362	+	6.74395i	−0.133707	+	0.231588i
$849$	17.1617	+	27.6728i	0.588986	+	0.949728i
$850$	14.5621	−	2.56769i	0.499475	−	0.0880710i
$851$	15.5646	−	5.66503i	0.533546	−	0.194195i
$852$	−0.0676159	−	0.0531977i	−0.00231648	−	0.00182252i
$853$	−35.0338	−	12.7513i	−1.19954	−	0.436595i	−0.336474	−	0.941693i	$-0.609234\pi$
$853$	−35.0338	−	12.7513i	−1.19954	−	0.436595i	−0.863062	+	0.505098i	$0.831457\pi$
$854$	−10.2901	+	25.3891i	−0.352120	+	0.868796i
$855$	3.36109	−	16.3370i	0.114947	−	0.558713i
$856$	5.95820	+	10.3199i	0.203647	+	0.352727i
$857$	−44.1696	+	37.0627i	−1.50881	+	1.26604i	−0.642765	+	0.766064i	$0.722213\pi$
$857$	−44.1696	+	37.0627i	−1.50881	+	1.26604i	−0.866040	+	0.499974i	$0.833343\pi$
$858$	−2.98853	+	20.7535i	−0.102027	+	0.708512i
$859$	7.16798	−	40.6517i	0.244568	−	1.38702i	−0.576924	−	0.816798i	$-0.695747\pi$
$859$	7.16798	−	40.6517i	0.244568	−	1.38702i	0.821493	−	0.570219i	$-0.193142\pi$
$860$	0.478898	+	0.570728i	0.0163303	+	0.0194617i
$861$	15.3323	−	41.5447i	0.522524	−	1.41584i
$862$	20.6553	−	35.7760i	0.703521	−	1.21853i
$863$	9.53883	−	16.5217i	0.324706	−	0.562407i	−0.656747	−	0.754111i	$-0.728068\pi$
$863$	9.53883	−	16.5217i	0.324706	−	0.562407i	0.981453	+	0.191704i	$0.0614014\pi$
$864$	−4.69321	+	2.23020i	−0.159666	+	0.0758731i
$865$	−21.7017	−	3.82659i	−0.737879	−	0.130108i
$866$	15.7924	+	9.11772i	0.536646	+	0.309833i
$867$	3.64729	+	1.19877i	0.123868	+	0.0407123i
$868$	−4.19863	−	7.91731i	−0.142511	−	0.268731i
$869$	14.5731	−	12.2283i	0.494357	−	0.414815i
$870$	−0.166148	−	5.27034i	−0.00563296	−	0.178681i
$871$	21.5574	+	7.84625i	0.730444	+	0.265860i
$872$	−4.93371	−	5.87977i	−0.167077	−	0.199114i
$873$	−10.7753	+	14.6213i	−0.364688	+	0.494855i
$874$	7.45262	+	16.1562i	0.252089	+	0.546493i
$875$	3.90195	+	27.9854i	0.131910	+	0.946080i
$876$	0.859543	−	5.96899i	0.0290413	−	0.201674i
$877$	−16.7679	−	19.9832i	−0.566211	−	0.674784i	0.404638	−	0.914477i	$-0.367398\pi$
$877$	−16.7679	−	19.9832i	−0.566211	−	0.674784i	−0.970849	+	0.239693i	$0.922953\pi$
$878$	10.2892	+	28.2694i	0.347244	+	0.954045i
$879$	49.9006	−	19.9645i	1.68311	−	0.673387i
$880$	−5.58514	+	2.03282i	−0.188275	+	0.0685265i
$881$	−48.9450	−	28.2584i	−1.64900	−	0.952050i	−0.977471	−	0.211071i	$-0.932305\pi$
$881$	−48.9450	−	28.2584i	−1.64900	−	0.952050i	−0.671528	−	0.740979i	$-0.734362\pi$
$882$	−16.2073	+	13.3538i	−0.545729	+	0.449644i
$883$	−20.1624	+	7.33853i	−0.678520	+	0.246961i	−0.658212	−	0.752833i	$-0.728687\pi$
$883$	−20.1624	+	7.33853i	−0.678520	+	0.246961i	−0.0203083	+	0.999794i	$0.506465\pi$
$884$	−8.72382	−	7.32015i	−0.293414	−	0.246203i
$885$	2.76088	−	0.577063i	0.0928060	−	0.0193978i
$886$	−12.5021	+	7.21810i	−0.420017	+	0.242497i
$887$	1.80832	−	0.658174i	0.0607174	−	0.0220993i	−0.311483	−	0.950252i	$-0.600826\pi$
$887$	1.80832	−	0.658174i	0.0607174	−	0.0220993i	0.372200	+	0.928152i	$0.378603\pi$
$888$	4.34588	−	5.52375i	0.145838	−	0.185365i
$889$	−24.3629	+	38.8943i	−0.817107	+	1.30447i
$890$	6.93253	−	1.22239i	0.232379	−	0.0409746i
$891$	22.7046	−	35.2613i	0.760633	−	1.18130i
$892$	8.98180	+	5.18565i	0.300733	+	0.173628i
$893$	−6.19456	+	22.7420i	−0.207293	+	0.761031i
$894$	16.8643	+	18.8579i	0.564025	+	0.630703i
$895$	−9.45486	+	25.9770i	−0.316041	+	0.868316i
$896$	1.77250	−	1.96424i	0.0592150	−	0.0656208i
$897$	8.67758	−	16.1875i	0.289736	−	0.540483i
$898$	−33.2887	−	12.1161i	−1.11086	−	0.404319i
$899$	5.19670	−	6.19319i	0.173320	−	0.206554i
$900$	8.14623	+	6.00344i	0.271541	+	0.200115i
$901$	29.5633	+	17.0684i	0.984895	+	0.568629i
$902$	−15.4013	−	42.3148i	−0.512809	−	1.40893i
$903$	2.63815	−	0.452991i	0.0877921	−	0.0150746i
$904$	−8.54071	−	14.7929i	−0.284060	−	0.492006i
$905$	−11.3239			−0.376419
$906$	30.0051	+	16.0848i	0.996854	+	0.534382i
$907$	−1.45440	+	0.256450i	−0.0482926	+	0.00851530i	−0.197742	−	0.980254i	$-0.563361\pi$
$907$	−1.45440	+	0.256450i	−0.0482926	+	0.00851530i	0.149450	+	0.988769i	$0.452250\pi$
$908$	−2.25348	+	12.7801i	−0.0747844	+	0.424123i
$909$	18.5490	−	12.3292i	0.615231	−	0.408934i
$910$	5.87321	−	6.50857i	0.194695	−	0.215757i
$911$	37.2878			1.23540			0.617700	−	0.786414i	$-0.288065\pi$
$911$	37.2878			1.23540			0.617700	+	0.786414i	$0.288065\pi$
$912$	6.30070	+	4.15947i	0.208637	+	0.137734i
$913$	1.79773	−	3.11376i	0.0594962	−	0.103050i
$914$	14.3617	−	12.0509i	0.475044	−	0.398609i
$915$	−14.1443	+	17.9778i	−0.467595	+	0.594329i
$916$	17.2655	+	14.4875i	0.570468	+	0.478679i
$917$	−12.1495	+	56.8539i	−0.401213	+	1.87748i
$918$	9.77648	+	20.5735i	0.322672	+	0.679026i
$919$	−4.88953			−0.161291			−0.0806453	−	0.996743i	$-0.525698\pi$
$919$	−4.88953			−0.161291			−0.0806453	+	0.996743i	$0.525698\pi$
$920$	5.20632			0.171647
$921$	0.890804	+	28.2569i	0.0293530	+	0.931098i
$922$	−16.6219	+	19.8093i	−0.547415	+	0.652383i
$923$	0.111752	−	0.0645202i	0.00367837	−	0.00212371i
$924$	−3.80235	+	21.0129i	−0.125088	+	0.691273i
$925$	−13.4797	−	2.37684i	−0.443211	−	0.0781500i
$926$	−35.7760	−	13.0214i	−1.17567	−	0.427909i
$927$	−27.8346	−	29.2176i	−0.914207	−	0.959633i
$928$	2.24287	+	0.816338i	0.0736258	+	0.0267976i
$929$	−38.9022	+	6.85950i	−1.27634	+	0.225053i	−0.770425	−	0.637531i	$-0.779956\pi$
$929$	−38.9022	+	6.85950i	−1.27634	+	0.225053i	−0.505914	+	0.862584i	$0.668845\pi$
$930$	−1.53098	−	7.32475i	−0.0502027	−	0.240188i
$931$	28.7866	+	10.1159i	0.943443	+	0.331534i
$932$			7.77376i			0.254638i
$933$	5.17020	+	12.9227i	0.169265	+	0.423071i
$934$	5.74123	−	15.7739i	0.187859	−	0.516138i
$935$	8.91124	+	24.4834i	0.291429	+	0.800693i
$936$	−0.490898	−	7.77808i	−0.0160455	−	0.254235i
$937$	1.26826	−	7.19267i	0.0414323	−	0.234974i	−0.957058	−	0.289895i	$-0.906380\pi$
$937$	1.26826	−	7.19267i	0.0414323	−	0.234974i	0.998491	+	0.0549209i	$0.0174907\pi$
$938$	21.6530	+	8.77589i	0.706997	+	0.286543i
$939$	−27.6816	+	24.7552i	−0.903356	+	0.807854i
$940$	5.28350	+	4.43339i	0.172329	+	0.144601i
$941$	2.09985	−	11.9089i	0.0684532	−	0.388218i	−0.931262	−	0.364350i	$-0.881291\pi$
$941$	2.09985	−	11.9089i	0.0684532	−	0.388218i	0.999715	−	0.0238671i	$-0.00759786\pi$
$942$	−2.75857	−	13.1980i	−0.0898792	−	0.430015i
$943$			39.4447i			1.28450i
$944$	−0.221701	+	1.25733i	−0.00721574	+	0.0409225i
$945$	−16.0984	+	6.95120i	−0.523681	+	0.226123i
$946$	1.74960	−	2.08510i	0.0568845	−	0.0677923i
$947$	−15.4642	−	18.4295i	−0.502517	−	0.598877i	0.453837	−	0.891084i	$-0.350055\pi$
$947$	−15.4642	−	18.4295i	−0.502517	−	0.598877i	−0.956355	+	0.292207i	$0.905610\pi$
$948$	−4.37226	+	5.55728i	−0.142004	+	0.180492i
$949$	7.83326	+	4.52253i	0.254278	+	0.146808i
$950$	1.34200	−	14.6418i	0.0435403	−	0.475042i
$951$	1.56845	+	7.50406i	0.0508606	+	0.243336i
$952$	−8.61060	−	7.77005i	−0.279071	−	0.251829i
$953$	5.87027	+	33.2920i	0.190157	+	1.07843i	0.919149	+	0.393911i	$0.128878\pi$
$953$	5.87027	+	33.2920i	0.190157	+	1.07843i	−0.728992	+	0.684522i	$0.760011\pi$
$954$	5.49781	+	22.7056i	0.177998	+	0.735121i
$955$	−0.609701	−	3.45779i	−0.0197295	−	0.111891i
$956$	−4.96025	+	5.91139i	−0.160426	+	0.191188i
$957$	−18.8567	+	3.94132i	−0.609552	+	0.127405i
$958$	29.0363	−	16.7641i	0.938120	−	0.541624i
$959$	10.3846	+	0.373986i	0.335336	+	0.0120766i
$960$	1.87747	−	1.16434i	0.0605952	−	0.0375789i
$961$	−9.76341	+	16.9107i	−0.314949	+	0.545507i
$962$	5.27085	+	9.12938i	0.169939	+	0.294343i
$963$	34.2967	+	10.0867i	1.10520	+	0.325040i
$964$	−1.29233	+	3.55063i	−0.0416230	+	0.114358i
$965$	−11.6325	−	9.76085i	−0.374464	−	0.314213i
$966$	9.42518	−	16.1572i	0.303250	−	0.519848i
$967$	38.6273	+	14.0592i	1.24217	+	0.452113i	0.877749	−	0.479121i	$-0.159045\pi$
$967$	38.6273	+	14.0592i	1.24217	+	0.452113i	0.364421	+	0.931234i	$0.381267\pi$
$968$	5.35713	+	9.27882i	0.172185	+	0.298233i
$969$	18.2338	−	27.6202i	0.585752	−	0.887289i
$970$	3.86107	−	6.68757i	0.123971	−	0.214725i
$971$	−2.36180	−	13.3945i	−0.0757939	−	0.429848i	−0.998966	−	0.0454618i	$-0.985524\pi$
$971$	−2.36180	−	13.3945i	−0.0757939	−	0.429848i	0.923172	−	0.384387i	$-0.125587\pi$
$972$	−5.57922	+	14.5558i	−0.178953	+	0.466879i
$973$	−38.2330	−	23.9487i	−1.22569	−	0.767760i
$974$	8.66408	+	10.3254i	0.277615	+	0.330849i
$975$	−12.8987	+	7.99931i	−0.413090	+	0.256183i
$976$	−5.17719	−	8.96715i	−0.165718	−	0.287031i
$977$	12.3868			0.396289			0.198144	−	0.980173i	$-0.436509\pi$
$977$	12.3868			0.396289			0.198144	+	0.980173i	$0.436509\pi$
$978$	−17.7753	+	33.1586i	−0.568391	+	1.06030i
$979$	−8.79607	−	24.1670i	−0.281124	−	0.772381i
$980$	6.21619	−	6.40900i	0.198569	−	0.204728i
$981$	−22.8835	−	2.56222i	−0.730613	−	0.0818053i
$982$	−12.1017	−	33.2491i	−0.386180	−	1.06102i
$983$	−0.225565	−	1.27924i	−0.00719440	−	0.0408015i	0.980999	−	0.194012i	$-0.0621500\pi$
$983$	−0.225565	−	1.27924i	−0.00719440	−	0.0408015i	−0.988194	+	0.153210i	$0.951039\pi$
$984$	8.82142	+	14.2243i	0.281216	+	0.453456i
$985$	−9.39788	+	7.88576i	−0.299441	+	0.251261i
$986$	3.57856	−	9.83201i	0.113965	−	0.313115i
$987$	23.3234	−	8.37079i	0.742391	−	0.266445i
$988$	−9.30267	+	6.45665i	−0.295957	+	0.205413i
$989$	−2.06483	+	1.19213i	−0.0656579	+	0.0379076i
$990$	−7.92502	+	15.9728i	−0.251874	+	0.507648i
$991$	5.98367	−	16.4400i	0.190077	−	0.522233i	−0.807646	−	0.589667i	$-0.799259\pi$
$991$	5.98367	−	16.4400i	0.190077	−	0.522233i	0.997724	+	0.0674338i	$0.0214811\pi$
$992$	3.33575	+	0.588183i	0.105910	+	0.0186748i
$993$	31.5262	−	40.0708i	1.00045	−	1.27161i
$994$	0.116104	−	0.0615711i	0.00368259	−	0.00195292i
$995$	−18.6968	−	10.7946i	−0.592729	−	0.342212i
$996$	−0.417285	+	1.26960i	−0.0132222	+	0.0402289i
$997$	−6.54320	+	37.1083i	−0.207225	+	1.17523i	0.686675	+	0.726965i	$0.259070\pi$
$997$	−6.54320	+	37.1083i	−0.207225	+	1.17523i	−0.893900	+	0.448267i	$0.852041\pi$
$998$	1.20206	−	6.81721i	0.0380505	−	0.215795i
$999$	−1.99051	−	20.9910i	−0.0629771	−	0.664127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bu.a.53.15	✓	162
3.2	odd	2		798.2.bu.b.53.18	yes	162
7.2	even	3		798.2.cc.a.737.21	yes	162
19.14	odd	18		798.2.cc.b.641.19	yes	162
21.2	odd	6		798.2.cc.b.737.19	yes	162
57.14	even	18		798.2.cc.a.641.21	yes	162
133.128	odd	18		798.2.bu.b.527.18	yes	162
399.128	even	18	inner	798.2.bu.a.527.15	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.53.15	✓	162	1.1	even	1	trivial
798.2.bu.a.527.15	yes	162	399.128	even	18	inner
798.2.bu.b.53.18	yes	162	3.2	odd	2
798.2.bu.b.527.18	yes	162	133.128	odd	18
798.2.cc.a.641.21	yes	162	57.14	even	18
798.2.cc.a.737.21	yes	162	7.2	even	3
798.2.cc.b.641.19	yes	162	19.14	odd	18
798.2.cc.b.737.19	yes	162	21.2	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bu (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.246871 - 1.71437i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.436242 - 1.19856i) q^{5} +(1.73119 - 0.0545760i) q^{6} +(-0.993792 + 2.45201i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.87811 - 0.846456i) q^{9} +(1.25611 + 0.221486i) q^{10} -4.65986i q^{11} +(0.354365 + 1.69541i) q^{12} +(-2.55839 - 0.451112i) q^{13} +(-2.58733 - 0.552907i) q^{14} +(-1.94708 - 1.04377i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-2.81777 - 3.35809i) q^{17} +(0.333818 - 2.98137i) q^{18} +(-3.95809 + 1.82580i) q^{19} +1.27549i q^{20} +(3.95831 + 2.30906i) q^{21} +(4.58906 - 0.809176i) q^{22} +(-4.01982 - 0.708802i) q^{23} +(-1.60812 + 0.643387i) q^{24} +(2.58397 + 2.16821i) q^{25} -2.59785i q^{26} +(-2.16166 + 4.72517i) q^{27} +(0.0952210 - 2.64404i) q^{28} +(2.24287 - 0.816338i) q^{29} +(0.689805 - 2.09875i) q^{30} +(2.93341 - 1.69360i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-7.98870 - 1.15038i) q^{33} +(2.81777 - 3.35809i) q^{34} +(2.50536 + 2.26080i) q^{35} +(2.99404 - 0.188963i) q^{36} +(-3.51420 + 2.02892i) q^{37} +(-2.48538 - 3.58091i) q^{38} +(-1.40496 + 4.27465i) q^{39} +(-1.25611 + 0.221486i) q^{40} +(-1.67805 - 9.51669i) q^{41} +(-1.58662 + 4.29914i) q^{42} +(0.447459 - 0.375463i) q^{43} +(1.59376 + 4.37883i) q^{44} +(-2.27008 + 3.08034i) q^{45} -4.08183i q^{46} +(3.47584 - 4.14235i) q^{47} +(-0.912860 - 1.47197i) q^{48} +(-5.02475 - 4.87359i) q^{49} +(-1.68657 + 2.92122i) q^{50} +(-6.45262 + 4.00168i) q^{51} +(2.55839 - 0.451112i) q^{52} +(-7.31761 + 2.66339i) q^{53} +(-5.02875 - 1.30830i) q^{54} +(-5.58514 - 2.03282i) q^{55} +(2.62040 - 0.365358i) q^{56} +(2.15296 + 7.23635i) q^{57} +(1.19341 + 2.06704i) q^{58} +(-0.978027 + 0.820662i) q^{59} +(2.18665 + 0.314881i) q^{60} +(1.79802 - 10.1971i) q^{61} +(2.17726 + 2.59475i) q^{62} +(4.93577 - 6.21596i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.65676 + 2.86960i) q^{65} +(-0.254316 - 8.06710i) q^{66} +(-8.69655 - 1.53344i) q^{67} +(3.79637 + 2.19184i) q^{68} +(-2.20752 + 6.71646i) q^{69} +(-1.79140 + 2.85989i) q^{70} +(-0.0380509 + 0.0319285i) q^{71} +(0.706002 + 2.91574i) q^{72} +(-3.27177 - 1.19083i) q^{73} +(-2.60834 - 3.10849i) q^{74} +(4.35502 - 3.89461i) q^{75} +(3.09492 - 3.06944i) q^{76} +(11.4260 + 4.63093i) q^{77} +(-4.45367 - 0.641335i) q^{78} +(2.62417 + 3.12736i) q^{79} +(-0.436242 - 1.19856i) q^{80} +(7.56703 + 4.87238i) q^{81} +(9.08072 - 3.30511i) q^{82} +(0.668209 + 0.385791i) q^{83} +(-4.50934 - 0.815981i) q^{84} +(-5.25411 + 1.91234i) q^{85} +(0.447459 + 0.375463i) q^{86} +(-0.845803 - 4.04663i) q^{87} +(-4.03555 + 2.32993i) q^{88} +(5.18621 - 1.88763i) q^{89} +(-3.42774 - 1.70070i) q^{90} +(3.64864 - 5.82489i) q^{91} +(4.01982 - 0.708802i) q^{92} +(-2.17929 - 5.44704i) q^{93} +(4.68299 + 2.70372i) q^{94} +(0.461661 + 5.54051i) q^{95} +(1.29109 - 1.15460i) q^{96} +(2.07068 - 5.68915i) q^{97} +(3.92701 - 5.79471i) q^{98} +(-3.94436 + 13.4116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q - 81 q^{8} + 15 q^{13} + 6 q^{14} + 27 q^{15} - 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} - 9 q^{27} + 9 q^{28} + 6 q^{29} - 24 q^{33} + 6 q^{34} + 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) \) 162 * q - 81 * q^8 + 15 * q^13 + 6 * q^14 + 27 * q^15 - 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 - 9 * q^27 + 9 * q^28 + 6 * q^29 - 24 * q^33 + 6 * q^34 + 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 - 12 * q^44 - 63 * q^45 + 12 * q^47 - 48 * q^49 + 87 * q^50 - 24 * q^51 - 15 * q^52 - 18 * q^54 - 18 * q^57 - 48 * q^59 + 6 * q^60 + 45 * q^61 + 36 * q^62 - 15 * q^63 - 81 * q^64 + 36 * q^65 + 12 * q^66 + 9 * q^67 + 9 * q^69 - 24 * q^70 + 12 * q^71 + 102 * q^73 + 39 * q^74 - 6 * q^78 - 42 * q^79 + 84 * q^81 - 3 * q^84 - 6 * q^85 - 9 * q^86 + 60 * q^87 + 54 * q^89 + 36 * q^90 - 18 * q^91 - 21 * q^93 - 72 * q^94 - 12 * q^97 - 27 * q^98 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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