LMFDB - Embedded newform 798.2.bu.b.53.18

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)

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);

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")

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			53.18
Character	$\chi$	$=$	798.53
Dual form			798.2.bu.b.527.18

$q$-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} +(0.912860 - 1.47197i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.436242 + 1.19856i) q^{5} +(-1.60812 - 0.643387i) q^{6} +(-0.993792 + 2.45201i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.33337 - 2.68740i) 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} +(1.36602 + 1.73625i) q^{15} +(0.766044 - 0.642788i) q^{16} +(2.81777 + 3.35809i) q^{17} +(-2.41503 + 1.77978i) q^{18} +(-3.95809 + 1.82580i) q^{19} -1.27549i q^{20} +(2.70209 + 3.70118i) q^{21} +(4.58906 - 0.809176i) q^{22} +(4.01982 + 0.708802i) q^{23} +(1.73119 + 0.0545760i) q^{24} +(2.58397 + 2.16821i) q^{25} +2.59785i q^{26} +(-5.17295 - 0.490534i) q^{27} +(0.0952210 - 2.64404i) q^{28} +(-2.24287 + 0.816338i) q^{29} +(1.47267 - 1.64676i) q^{30} +(2.93341 - 1.69360i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(6.85916 + 4.25379i) q^{33} +(2.81777 - 3.35809i) q^{34} +(-2.50536 - 2.26080i) q^{35} +(2.17211 + 2.06929i) q^{36} +(-3.51420 + 2.02892i) q^{37} +(2.48538 + 3.58091i) q^{38} +(-2.99947 + 3.35406i) q^{39} +(-1.25611 + 0.221486i) q^{40} +(1.67805 + 9.51669i) q^{41} +(3.17573 - 3.30374i) q^{42} +(0.447459 - 0.375463i) q^{43} +(-1.59376 - 4.37883i) q^{44} +(3.80269 - 0.425780i) q^{45} -4.08183i q^{46} +(-3.47584 + 4.14235i) q^{47} +(-0.246871 - 1.71437i) q^{48} +(-5.02475 - 4.87359i) q^{49} +(1.68657 - 2.92122i) q^{50} +(7.51522 - 1.08220i) q^{51} +(2.55839 - 0.451112i) q^{52} +(7.31761 - 2.66339i) q^{53} +(0.415191 + 5.17954i) q^{54} +(-5.58514 - 2.03282i) q^{55} +(-2.62040 + 0.365358i) q^{56} +(-0.925653 + 7.49287i) q^{57} +(1.19341 + 2.06704i) q^{58} +(0.978027 - 0.820662i) q^{59} +(-1.87747 - 1.16434i) q^{60} +(1.79802 - 10.1971i) q^{61} +(-2.17726 - 2.59475i) q^{62} +(7.91464 - 0.598738i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.65676 - 2.86960i) q^{65} +(2.99809 - 7.49361i) q^{66} +(-8.69655 - 1.53344i) q^{67} +(-3.79637 - 2.19184i) q^{68} +(4.71286 - 5.27000i) q^{69} +(-1.79140 + 2.85989i) q^{70} +(0.0380509 - 0.0319285i) q^{71} +(1.66067 - 2.49844i) q^{72} +(-3.27177 - 1.19083i) q^{73} +(2.60834 + 3.10849i) q^{74} +(5.55034 - 1.82425i) q^{75} +(3.09492 - 3.06944i) q^{76} +(-11.4260 - 4.63093i) q^{77} +(3.82395 + 2.37147i) q^{78} +(2.62417 + 3.12736i) q^{79} +(0.436242 + 1.19856i) q^{80} +(-5.44422 + 7.16662i) q^{81} +(9.08072 - 3.30511i) q^{82} +(-0.668209 - 0.385791i) q^{83} +(-3.80501 - 2.55380i) 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} +(-1.07964 - 3.67099i) q^{90} +(3.64864 - 5.82489i) q^{91} +(-4.01982 + 0.708802i) q^{92} +(0.184860 - 5.86390i) q^{93} +(4.68299 + 2.70372i) q^{94} +(-0.461661 - 5.54051i) q^{95} +(-1.64545 + 0.540817i) q^{96} +(2.07068 - 5.68915i) q^{97} +(-3.92701 + 5.79471i) q^{98} +(12.5229 - 6.21333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 81 q^{8} + 15 q^{13} - 6 q^{14} + 3 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 + 39 q^{99}+O(q^{100}) $ 162 * q + 81 * q^8 + 15 * q^13 - 6 * q^14 + 3 * 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 + 45 * 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 + 18 * q^60 + 45 * q^61 - 36 * q^62 - 21 * 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 - 18 * q^78 - 42 * q^79 - 12 * q^81 + 57 * q^84 - 6 * q^85 + 9 * q^86 + 60 * q^87 - 54 * q^89 + 12 * q^90 - 18 * q^91 + 105 * q^93 - 72 * q^94 - 12 * q^97 + 27 * q^98 + 39 * 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
$3$	0.912860	−	1.47197i	0.527040	−	0.849841i
$3$	0.912860	−	1.47197i	0.527040	−	0.849841i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.436242	+	1.19856i	−0.195093	+	0.536014i	−0.998210	−	0.0598074i	$-0.980951\pi$
$5$	−0.436242	+	1.19856i	−0.195093	+	0.536014i	0.803117	+	0.595822i	$0.203174\pi$
$6$	−1.60812	−	0.643387i	−0.656513	−	0.262662i
$7$	−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
$9$	−1.33337	−	2.68740i	−0.444458	−	0.895800i
$10$	1.25611	+	0.221486i	0.397216	+	0.0700400i
$11$			4.65986i			1.40500i	0.711684	+	0.702500i	$0.247933\pi$
$11$			4.65986i			1.40500i	−0.711684	+	0.702500i	$0.752067\pi$
$12$	−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
$15$	1.36602	+	1.73625i	0.352705	+	0.448299i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	2.81777	+	3.35809i	0.683410	+	0.814456i	0.990542	−	0.137211i	$-0.0438138\pi$
$17$	2.81777	+	3.35809i	0.683410	+	0.814456i	−0.307132	+	0.951667i	$0.599369\pi$
$18$	−2.41503	+	1.77978i	−0.569229	+	0.419498i
$19$	−3.95809	+	1.82580i	−0.908047	+	0.418868i
$19$	−3.95809	+	1.82580i	−0.908047	+	0.418868i
$20$		−	1.27549i		−	0.285207i
$21$	2.70209	+	3.70118i	0.589645	+	0.807663i
$22$	4.58906	−	0.809176i	0.978391	−	0.172517i
$23$	4.01982	+	0.708802i	0.838190	+	0.147796i	0.576234	−	0.817284i	$-0.304522\pi$
$23$	4.01982	+	0.708802i	0.838190	+	0.147796i	0.261956	+	0.965080i	$0.415633\pi$
$24$	1.73119	+	0.0545760i	0.353378	+	0.0111403i
$25$	2.58397	+	2.16821i	0.516794	+	0.433642i
$26$			2.59785i			0.509481i
$27$	−5.17295	−	0.490534i	−0.995534	−	0.0944033i
$28$	0.0952210	−	2.64404i	0.0179951	−	0.499676i
$29$	−2.24287	+	0.816338i	−0.416491	+	0.151590i	−0.541761	−	0.840532i	$-0.682242\pi$
$29$	−2.24287	+	0.816338i	−0.416491	+	0.151590i	0.125271	+	0.992123i	$0.460020\pi$
$30$	1.47267	−	1.64676i	0.268872	−	0.300657i
$31$	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
$33$	6.85916	+	4.25379i	1.19403	+	0.740491i
$34$	2.81777	−	3.35809i	0.483244	−	0.575907i
$35$	−2.50536	−	2.26080i	−0.423484	−	0.382144i
$36$	2.17211	+	2.06929i	0.362018	+	0.344881i
$37$	−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
$39$	−2.99947	+	3.35406i	−0.480300	+	0.537079i
$40$	−1.25611	+	0.221486i	−0.198608	+	0.0350200i
$41$	1.67805	+	9.51669i	0.262067	+	1.48626i	0.777258	+	0.629181i	$0.216610\pi$
$41$	1.67805	+	9.51669i	0.262067	+	1.48626i	−0.515191	+	0.857075i	$0.672279\pi$
$42$	3.17573	−	3.30374i	0.490026	−	0.509779i
$43$	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
$45$	3.80269	−	0.425780i	0.566872	−	0.0634715i
$46$		−	4.08183i		−	0.601833i
$47$	−3.47584	+	4.14235i	−0.507003	+	0.604223i	−0.957457	−	0.288577i	$-0.906818\pi$
$47$	−3.47584	+	4.14235i	−0.507003	+	0.604223i	0.450453	+	0.892800i	$0.351262\pi$
$48$	−0.246871	−	1.71437i	−0.0356328	−	0.247448i
$49$	−5.02475	−	4.87359i	−0.717822	−	0.696227i
$50$	1.68657	−	2.92122i	0.238517	−	0.413123i
$51$	7.51522	−	1.08220i	1.05234	−	0.151539i
$52$	2.55839	−	0.451112i	0.354784	−	0.0625580i
$53$	7.31761	−	2.66339i	1.00515	−	0.365845i	0.213583	−	0.976925i	$-0.431487\pi$
$53$	7.31761	−	2.66339i	1.00515	−	0.365845i	0.791569	+	0.611080i	$0.209265\pi$
$54$	0.415191	+	5.17954i	0.0565003	+	0.704846i
$55$	−5.58514	−	2.03282i	−0.753100	−	0.274106i
$56$	−2.62040	+	0.365358i	−0.350166	+	0.0488230i
$57$	−0.925653	+	7.49287i	−0.122606	+	0.992455i
$58$	1.19341	+	2.06704i	0.156702	+	0.271416i
$59$	0.978027	−	0.820662i	0.127328	−	0.106841i	−0.576900	−	0.816815i	$-0.695738\pi$
$59$	0.978027	−	0.820662i	0.127328	−	0.106841i	0.704228	+	0.709974i	$0.251293\pi$
$60$	−1.87747	−	1.16434i	−0.242381	−	0.150316i
$61$	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
$63$	7.91464	−	0.598738i	0.997151	−	0.0754339i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	1.65676	−	2.86960i	0.205496	−	0.355930i
$66$	2.99809	−	7.49361i	0.369039	−	0.922400i
$67$	−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
$69$	4.71286	−	5.27000i	0.567362	−	0.634434i
$70$	−1.79140	+	2.85989i	−0.214113	+	0.341822i
$71$	0.0380509	−	0.0319285i	0.00451581	−	0.00378922i	−0.640527	−	0.767936i	$-0.721284\pi$
$71$	0.0380509	−	0.0319285i	0.00451581	−	0.00378922i	0.645043	+	0.764147i	$0.276840\pi$
$72$	1.66067	−	2.49844i	0.195712	−	0.294443i
$73$	−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
$75$	5.55034	−	1.82425i	0.640898	−	0.210646i
$76$	3.09492	−	3.06944i	0.355012	−	0.352089i
$77$	−11.4260	−	4.63093i	−1.30212	−	0.527744i
$78$	3.82395	+	2.37147i	0.432978	+	0.268517i
$79$	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
$81$	−5.44422	+	7.16662i	−0.604914	+	0.796291i
$82$	9.08072	−	3.30511i	1.00280	−	0.364988i
$83$	−0.668209	−	0.385791i	−0.0733455	−	0.0423461i	0.462879	−	0.886422i	$-0.346817\pi$
$83$	−0.668209	−	0.385791i	−0.0733455	−	0.0423461i	−0.536224	+	0.844076i	$0.680150\pi$
$84$	−3.80501	−	2.55380i	−0.415161	−	0.278642i
$85$	−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	−0.601930	−	0.798549i	$-0.705601\pi$
$89$	−5.18621	+	1.88763i	−0.549737	+	0.200088i	0.0521925	+	0.998637i	$0.483379\pi$
$90$	−1.07964	−	3.67099i	−0.113804	−	0.386956i
$91$	3.64864	−	5.82489i	0.382481	−	0.610614i
$92$	−4.01982	+	0.708802i	−0.419095	+	0.0738978i
$93$	0.184860	−	5.86390i	0.0191691	−	0.608059i
$94$	4.68299	+	2.70372i	0.483013	+	0.278868i
$95$	−0.461661	−	5.54051i	−0.0473654	−	0.568445i
$96$	−1.64545	+	0.540817i	−0.167938	+	0.0551969i
$97$	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
$99$	12.5229	−	6.21333i	1.25860	−	0.624464i
$100$	−3.16971	−	1.15368i	−0.316971	−	0.115368i
$101$	4.77221	−	5.68729i	0.474852	−	0.565907i	−0.474446	−	0.880285i	$-0.657351\pi$
$101$	4.77221	−	5.68729i	0.474852	−	0.565907i	0.949298	+	0.314378i	$0.101796\pi$
$102$	−2.37077	−	7.21313i	−0.234741	−	0.714206i
$103$	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
$105$	−5.61486	+	1.62402i	−0.547955	+	0.158489i
$106$	−3.89362	−	6.74395i	−0.378182	−	0.655030i
$107$	11.9164			1.15200			0.576001	−	0.817449i	$-0.304612\pi$
$107$	11.9164			1.15200			0.576001	+	0.817449i	$0.304612\pi$
$108$	5.02875	−	1.30830i	0.483892	−	0.125891i
$109$	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
$111$	−0.221461	+	7.02491i	−0.0210202	+	0.666775i
$112$	0.814835	+	2.51715i	0.0769947	+	0.237848i
$113$	−17.0814			−1.60688			−0.803442	−	0.595383i	$-0.797000\pi$
$113$	−17.0814			−1.60688			−0.803442	+	0.595383i	$0.797000\pi$
$114$	7.53978	−	0.389534i	0.706165	−	0.0364832i
$115$	−2.60316	+	4.50880i	−0.242746	+	0.420448i
$116$	1.82841	−	1.53421i	0.169763	−	0.142448i
$117$	2.19897	+	7.47690i	0.203295	+	0.691240i
$118$	−0.978027	−	0.820662i	−0.0900347	−	0.0755480i
$119$	−11.0344	+	3.57197i	−1.01152	+	0.327442i
$120$	−0.820631	+	2.05114i	−0.0749130	+	0.187242i
$121$	−10.7143			−0.974024
$122$	−10.3544			−0.937441
$123$	15.5401	+	6.21737i	1.40120	+	0.560601i
$124$	−2.17726	+	2.59475i	−0.195523	+	0.233016i
$125$	−9.24899	+	5.33991i	−0.827255	+	0.477616i
$126$	−1.96400	−	7.69043i	−0.174967	−	0.685118i
$127$	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
$129$	−0.144202	−	1.00139i	−0.0126962	−	0.0881675i
$130$	−3.11369	−	1.13329i	−0.273089	−	0.0993963i
$131$	−21.6401	+	3.81573i	−1.89070	+	0.333382i	−0.994012	−	0.109271i	$-0.965148\pi$
$131$	−21.6401	+	3.81573i	−1.89070	+	0.333382i	−0.896693	+	0.442653i	$0.854037\pi$
$132$	−7.90038	−	1.65129i	−0.687640	−	0.143726i
$133$	−0.543382	−	11.5198i	−0.0471172	−	0.998889i
$134$			8.83071i			0.762857i
$135$	2.84459	−	5.98612i	0.244824	−	0.515203i
$136$	−1.49930	+	4.11930i	−0.128564	+	0.353227i
$137$	1.34330	+	3.69069i	0.114766	+	0.315317i	0.983756	−	0.179513i	$-0.0574523\pi$
$137$	1.34330	+	3.69069i	0.114766	+	0.315317i	−0.868989	+	0.494831i	$0.835230\pi$
$138$	−6.00832	−	3.72614i	−0.511462	−	0.317190i
$139$	−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
$141$	2.92444	+	8.89770i	0.246282	+	0.749322i
$142$	−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
$147$	−11.7607	+	2.94737i	−0.970002	+	0.243095i
$148$	2.60834	−	3.10849i	0.214404	−	0.255517i
$149$	−9.38869	−	11.1890i	−0.769151	−	0.916639i	0.229238	−	0.973370i	$-0.426377\pi$
$149$	−9.38869	−	11.1890i	−0.769151	−	0.916639i	−0.998389	+	0.0567314i	$0.981932\pi$
$150$	−2.76034	−	5.14924i	−0.225381	−	0.420434i
$151$	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
$156$	1.67142	−	4.17766i	0.133821	−	0.334481i
$157$	−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
$162$	8.00312	+	4.11704i	0.628785	+	0.323466i
$163$	−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
$165$	−8.09070	+	6.36546i	−0.629860	+	0.495550i
$166$	−0.263897	+	0.725050i	−0.0204823	+	0.0562748i
$167$	1.05217	+	0.882874i	0.0814192	+	0.0683188i	0.682589	−	0.730803i	$-0.260854\pi$
$167$	1.05217	+	0.882874i	0.0814192	+	0.0683188i	−0.601170	+	0.799121i	$0.705298\pi$
$168$	−1.85427	+	4.19067i	−0.143060	+	0.323317i
$169$	−5.87417	−	2.13802i	−0.451859	−	0.164463i
$170$	2.79566	+	4.84222i	0.214417	+	0.371381i
$171$	10.1843	+	8.20247i	0.778811	+	0.627259i
$172$	−0.292058	+	0.505860i	−0.0222692	+	0.0385714i
$173$	3.00010	+	17.0144i	0.228094	+	1.29358i	0.856682	+	0.515845i	$0.172522\pi$
$173$	3.00010	+	17.0144i	0.228094	+	1.29358i	−0.628588	+	0.777738i	$0.716367\pi$
$174$	4.13203	+	0.130263i	0.313248	+	0.00987520i
$175$	−7.88442	+	4.18119i	−0.596006	+	0.316068i
$176$	2.99530	+	3.56966i	0.225779	+	0.269073i
$177$	−0.315186	−	2.18877i	−0.0236908	−	0.164518i
$178$	2.75953	+	4.77964i	0.206835	+	0.358249i
$179$	21.6734			1.61995			0.809974	−	0.586465i	$-0.199481\pi$
$179$	21.6734			1.61995			0.809974	+	0.586465i	$0.199481\pi$
$180$	−3.42774	+	1.70070i	−0.255489	+	0.126763i
$181$	−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
$183$	−13.3684	−	11.9551i	−0.988221	−	0.883747i
$184$	1.39607	+	3.83567i	0.102920	+	0.282769i
$185$	−0.898756	−	5.09710i	−0.0660779	−	0.374746i
$186$	−5.80692	+	0.836204i	−0.425784	+	0.0613135i
$187$	−15.6482	+	13.1304i	−1.14431	+	0.960190i
$188$	1.84946	−	5.08134i	0.134885	−	0.370595i
$189$	6.34363	−	12.1967i	0.461431	−	0.887176i
$190$	−5.37617	+	1.41675i	−0.390029	+	0.102782i
$191$	−2.38397	+	1.37639i	−0.172498	+	0.0995920i	−0.583763	−	0.811924i	$-0.698420\pi$
$191$	−2.38397	+	1.37639i	−0.172498	+	0.0995920i	0.411265	+	0.911516i	$0.365087\pi$
$192$	0.818331	+	1.52654i	0.0590580	+	0.110169i
$193$	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
$195$	−2.71156	−	5.05824i	−0.194179	−	0.362228i
$196$	6.38859	+	2.86111i	0.456328	+	0.204365i
$197$	8.32973	+	4.80917i	0.593469	+	0.342639i	0.766468	−	0.642283i	$-0.222012\pi$
$197$	8.32973	+	4.80917i	0.593469	+	0.342639i	−0.172999	+	0.984922i	$0.555346\pi$
$198$	−8.29352	−	11.2537i	−0.589395	−	0.799766i
$199$	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
$201$	−10.1959	+	11.4012i	−0.719163	+	0.804181i
$202$	−6.42958	−	3.71212i	−0.452383	−	0.261184i
$203$	0.227275	−	6.31082i	0.0159516	−	0.442933i
$204$	−6.69187	+	3.58730i	−0.468524	+	0.251161i
$205$	−12.1384	−	2.14033i	−0.847782	−	0.149487i
$206$	4.60061	−	12.6401i	0.320540	−	0.880676i
$207$	−3.45509	−	11.7480i	−0.240145	−	0.816539i
$208$	−2.24981	+	1.29893i	−0.155996	+	0.0900643i
$209$	−8.50798	−	18.4441i	−0.588510	−	1.27581i
$210$	2.57436	+	5.24755i	0.177648	+	0.362115i
$211$	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
$213$	−0.0122626	−	0.0851559i	−0.000840217	−	0.00583479i
$214$	−2.06926	−	11.7354i	−0.141452	−	0.802213i
$215$	0.254816	+	0.700101i	0.0173783	+	0.0477465i
$216$	−2.16166	−	4.72517i	−0.147082	−	0.321507i
$217$	1.23754	+	8.87585i	0.0840099	+	0.602532i
$218$	−2.62517	−	7.21260i	−0.177799	−	0.488499i
$219$	−4.73953	+	3.72888i	−0.320268	+	0.251975i
$220$	5.94358			0.400716
$221$	−5.69407	−	9.86242i	−0.383024	−	0.663418i
$222$	6.95664	−	1.00177i	0.466899	−	0.0672342i
$223$	−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
$225$	2.38144	−	9.83520i	0.158763	−	0.655680i
$226$	2.96616	+	16.8219i	0.197306	+	1.11898i
$227$	−6.48864	+	11.2387i	−0.430666	+	0.745936i	−0.996931	−	0.0782878i	$-0.975055\pi$
$227$	−6.48864	+	11.2387i	−0.430666	+	0.745936i	0.566265	+	0.824223i	$0.308388\pi$
$228$	−1.69288	−	7.35759i	−0.112114	−	0.487268i
$229$	−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
$231$	−17.2469	+	12.5914i	−1.13477	+	0.828451i
$232$	−1.82841	−	1.53421i	−0.120041	−	0.100726i
$233$	−2.65878	+	7.30494i	−0.174183	+	0.478563i	−0.995808	−	0.0914645i	$-0.970845\pi$
$233$	−2.65878	+	7.30494i	−0.174183	+	0.478563i	0.821626	+	0.570027i	$0.193067\pi$
$234$	6.98147	−	3.46391i	0.456393	−	0.226443i
$235$	−3.44856	−	5.97308i	−0.224959	−	0.389641i
$236$	−0.638362	+	1.10567i	−0.0415538	+	0.0719733i
$237$	6.99888	−	1.00785i	0.454626	−	0.0654667i
$238$	5.43380	+	10.2465i	0.352221	+	0.664179i
$239$	−6.68292	+	3.85839i	−0.432282	+	0.249578i	−0.700319	−	0.713830i	$-0.746959\pi$
$239$	−6.68292	+	3.85839i	−0.432282	+	0.249578i	0.268036	+	0.963409i	$0.413625\pi$
$240$	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
$243$	5.57922	+	14.5558i	0.357907	+	0.933757i
$244$	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
$249$	−1.17785	+	0.631409i	−0.0746434	+	0.0400139i
$250$	6.86485	+	8.18121i	0.434171	+	0.517425i
$251$	11.7944	−	14.0560i	0.744453	−	0.887205i	−0.252306	−	0.967647i	$-0.581189\pi$
$251$	11.7944	−	14.0560i	0.744453	−	0.887205i	0.996759	+	0.0804429i	$0.0256335\pi$
$252$	−7.23255	+	3.26960i	−0.455608	+	0.205965i
$253$	−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	0.598758	−	0.800930i	$-0.295661\pi$
$257$	−1.37919	−	1.15728i	−0.0860313	−	0.0721888i	−0.684789	+	0.728741i	$0.740106\pi$
$258$	−0.961137	+	0.315900i	−0.0598377	+	0.0196671i
$259$	−1.48257	−	10.6332i	−0.0921222	−	0.660715i
$260$	−0.575387	+	3.26318i	−0.0356840	+	0.202374i
$261$	5.18441	+	4.93900i	0.320907	+	0.305717i
$262$	7.51553	+	20.6487i	0.464311	+	1.27568i
$263$	5.77367	−	15.8630i	0.356020	−	0.978156i	−0.624377	−	0.781123i	$-0.714647\pi$
$263$	5.77367	−	15.8630i	0.356020	−	0.978156i	0.980397	−	0.197033i	$-0.0631306\pi$
$264$	−0.254316	+	8.06710i	−0.0156521	+	0.496496i
$265$			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	0.662548	−	0.749019i	$-0.269475\pi$
$269$	11.2944	+	4.11081i	0.688629	+	0.250640i	0.0260807	+	0.999660i	$0.491697\pi$
$270$	−6.38913	−	1.76190i	−0.388830	−	0.107226i
$271$	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
$273$	−5.24335	−	10.6880i	−0.317342	−	0.646866i
$274$	3.40136	−	1.96378i	0.205484	−	0.118636i
$275$	−10.1035	+	12.0409i	−0.609267	+	0.726096i
$276$	−2.62620	+	6.56408i	−0.158078	+	0.395111i
$277$	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
$279$	−8.46272	−	5.62503i	−0.506650	−	0.336762i
$280$	0.705225	−	3.30011i	0.0421452	−	0.197219i
$281$	19.9046	+	16.7020i	1.18741	+	0.996356i	0.999901	+	0.0140931i	$0.00448612\pi$
$281$	19.9046	+	16.7020i	1.18741	+	0.996356i	0.187510	+	0.982263i	$0.439958\pi$
$282$	8.25470	−	4.42508i	0.491560	−	0.263510i
$283$	−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
$285$	−8.57689	−	4.37816i	−0.508051	−	0.259340i
$286$	−12.1056			−0.715820
$287$	−25.0027	−	5.34301i	−1.47586	−	0.315388i
$288$	−0.706002	+	2.91574i	−0.0416016	+	0.171812i
$289$	−0.384906	+	2.18291i	−0.0226415	+	0.128406i
$290$	−2.99810	+	0.528645i	−0.176054	+	0.0310431i
$291$	−6.48401	−	8.24138i	−0.380099	−	0.483118i
$292$	3.48175			0.203754
$293$	−15.5152	−	26.8731i	−0.906407	−	1.56994i	−0.819017	−	0.573769i	$-0.805481\pi$
$293$	−15.5152	−	26.8731i	−0.906407	−	1.56994i	−0.0873902	−	0.996174i	$-0.527853\pi$
$294$	4.94481	+	11.0702i	0.288387	+	0.645626i
$295$	0.556960	+	1.53024i	0.0324275	+	0.0890937i
$296$	−3.51420	−	2.02892i	−0.204259	−	0.117929i
$297$	2.28582	−	24.1052i	0.132637	−	1.39872i
$298$	−9.38869	+	11.1890i	−0.543872	+	0.648162i
$299$	−9.96449	−	3.62678i	−0.576262	−	0.209742i
$300$	−4.59168	+	3.61256i	−0.265101	+	0.208571i
$301$	0.475959	+	1.47031i	0.0274338	+	0.0847472i
$302$	6.72261	−	18.4702i	0.386843	−	1.06284i
$303$	−4.01516	−	12.2162i	−0.230665	−	0.701804i
$304$	−1.85847	+	3.94286i	−0.106590	+	0.226138i
$305$	11.4375	+	6.60343i	0.654908	+	0.378111i
$306$	−12.7817	−	3.09488i	−0.730679	−	0.176923i
$307$	−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
$309$	20.5340	−	11.0076i	1.16814	−	0.626201i
$310$	4.05979	−	1.47764i	0.230580	−	0.0839244i
$311$	6.95931	−	4.01796i	0.394626	−	0.227837i	−0.289537	−	0.957167i	$-0.593501\pi$
$311$	6.95931	−	4.01796i	0.394626	−	0.227837i	0.684163	+	0.729329i	$0.260168\pi$
$312$	−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
$315$	−2.73507	+	9.74740i	−0.154104	+	0.549204i
$316$	−3.53553	−	2.04124i	−0.198889	−	0.114829i
$317$	4.15917	−	1.51381i	0.233602	−	0.0850242i	−0.222567	−	0.974917i	$-0.571444\pi$
$317$	4.15917	−	1.51381i	0.233602	−	0.0850242i	0.456169	+	0.889893i	$0.349221\pi$
$318$	−13.4812	−	0.424997i	−0.755988	−	0.0238326i
$319$	−3.80402	−	10.4515i	−0.212984	−	0.585169i
$320$	−0.819866	−	0.977079i	−0.0458319	−	0.0546204i
$321$	10.8780	−	17.5406i	0.607151	−	0.979018i
$322$	10.0087	+	4.05649i	0.557763	+	0.226059i
$323$	−17.2842	−	8.14690i	−0.961718	−	0.453306i
$324$	2.66477	−	8.59645i	0.148043	−	0.477581i
$325$	−5.63269	−	6.71278i	−0.312445	−	0.372358i
$326$	20.4114	+	7.42915i	1.13048	+	0.411463i
$327$	4.93831	−	12.3431i	0.273089	−	0.682576i
$328$	−7.40267	+	6.21158i	−0.408744	+	0.342977i
$329$	−6.70283	−	12.6394i	−0.369539	−	0.696835i
$330$	7.67369	+	6.86243i	0.422423	+	0.377764i
$331$	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
$333$	10.1383	+	6.73874i	0.555574	+	0.369281i
$334$	0.686754	−	1.18949i	0.0375775	−	0.0650861i
$335$	5.63172	−	9.75443i	0.307694	−	0.532941i
$336$	4.44899	+	1.09839i	0.242712	+	0.0599223i
$337$	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
$339$	−15.5929	+	25.1433i	−0.846892	+	1.36560i
$340$	4.28319	−	3.59403i	0.232289	−	0.194913i
$341$	7.89195	+	13.6693i	0.427373	+	0.740232i
$342$	6.30938	−	11.4539i	0.341172	−	0.619356i
$343$	16.9437	−	7.47743i	0.914872	−	0.403743i
$344$	0.548890	+	0.199780i	0.0295942	+	0.0107714i
$345$	4.26049	+	7.94767i	0.229377	+	0.427888i
$346$	16.2350	−	5.90905i	0.872798	−	0.317672i
$347$	17.5501	−	3.09456i	0.942138	−	0.166124i	0.318575	−	0.947898i	$-0.396796\pi$
$347$	17.5501	−	3.09456i	0.942138	−	0.166124i	0.623563	+	0.781773i	$0.285684\pi$
$348$	−0.589236	−	4.09187i	−0.0315863	−	0.219347i
$349$	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
$351$	13.0131	+	3.58856i	0.694588	+	0.191543i
$352$	2.99530	−	3.56966i	0.159650	−	0.190263i
$353$			16.9670i			0.903064i	0.892255	+	0.451532i	$0.149122\pi$
$353$			16.9670i			0.903064i	−0.892255	+	0.451532i	$0.850878\pi$
$354$	−2.10079	+	0.690474i	−0.111656	+	0.0366983i
$355$	0.0216690	+	0.0595350i	0.00115007	+	0.00315979i
$356$	4.22784	−	3.54758i	0.224075	−	0.188021i
$357$	−4.81500	+	19.5029i	−0.254837	+	1.03220i
$358$	−3.76355	−	21.3442i	−0.198910	−	1.12807i
$359$	14.4703	−	2.55150i	0.763713	−	0.134663i	0.221794	−	0.975094i	$-0.428809\pi$
$359$	14.4703	−	2.55150i	0.763713	−	0.134663i	0.541919	+	0.840430i	$0.317698\pi$
$360$	2.27008	+	3.08034i	0.119644	+	0.162348i
$361$	12.3329	−	14.4534i	0.649099	−	0.760704i
$362$	−7.68867	+	4.43905i	−0.404107	+	0.233312i
$363$	−9.78062	+	15.7710i	−0.513349	+	0.827765i
$364$	−1.43637	+	6.72151i	−0.0752862	+	0.352303i
$365$	2.85457	−	3.40194i	0.149415	−	0.178066i
$366$	−9.45209	+	15.2413i	−0.494068	+	0.796675i
$367$	−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
$369$	23.3377	−	17.1989i	1.21491	−	0.895339i
$370$	−4.86359	+	1.77020i	−0.252846	+	0.0920285i
$371$	−0.741509	+	20.5898i	−0.0384972	+	1.06897i
$372$	1.83186	+	5.57349i	0.0949776	+	0.288972i
$373$		−	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
$375$	−0.582862	+	18.4888i	−0.0300989	+	0.954757i
$376$	−5.32530	−	0.938993i	−0.274631	−	0.0484249i
$377$	6.10639	−	1.07672i	0.314495	−	0.0554540i
$378$	−13.1129	−	4.12933i	−0.674456	−	0.212390i
$379$		−	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
$381$	20.0283	−	22.3959i	1.02608	−	1.14738i
$382$	1.76945	+	2.10875i	0.0905330	+	0.107893i
$383$	3.11357	−	2.61260i	0.159096	−	0.133498i	−0.559764	−	0.828652i	$-0.689108\pi$
$383$	3.11357	−	2.61260i	0.159096	−	0.133498i	0.718861	+	0.695154i	$0.244664\pi$
$384$	1.36125	−	1.07098i	0.0694660	−	0.0546532i
$385$	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	0.998838	−	0.0482024i	$-0.0153493\pi$
$389$	37.8871	+	6.68052i	1.92095	+	0.338716i	0.922114	+	0.386918i	$0.126460\pi$
$390$	−4.51053	+	3.54872i	−0.228400	+	0.179696i
$391$	8.94670	+	15.4961i	0.452454	+	0.783674i
$392$	1.70827	−	6.78836i	0.0862809	−	0.342864i
$393$	−14.1377	+	35.3368i	−0.713155	+	1.78250i
$394$	3.28967	−	9.03829i	0.165731	−	0.455342i
$395$	−4.89312	+	1.78095i	−0.246200	+	0.0896093i
$396$	−9.64258	+	10.1217i	−0.484558	+	0.508635i
$397$	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
$399$	−17.4527	−	9.71608i	−0.873729	−	0.486412i
$400$	3.37314			0.168657
$401$	5.28461	+	29.9705i	0.263901	+	1.49666i	0.772147	+	0.635444i	$0.219183\pi$
$401$	5.28461	+	29.9705i	0.263901	+	1.49666i	−0.508246	+	0.861212i	$0.669706\pi$
$402$	12.9985	+	8.06120i	0.648307	+	0.402056i
$403$	−8.26880	+	3.00960i	−0.411898	+	0.149919i
$404$	−2.53924	+	6.97650i	−0.126332	+	0.347094i
$405$	−6.21466	−	9.65163i	−0.308809	−	0.479594i
$406$	−6.25441	+	0.872041i	−0.310401	+	0.0432787i
$407$	−9.45450	−	16.3757i	−0.468642	−	0.811712i
$408$	4.69483	+	5.96727i	0.232429	+	0.295424i
$409$	−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
$414$	−10.9695	+	5.44261i	−0.539122	+	0.267490i
$415$	0.753896	−	0.632594i	0.0370073	−	0.0310528i
$416$	1.66987	+	1.99007i	0.0818720	+	0.0975712i
$417$	22.0151	+	19.6877i	1.07809	+	0.964112i
$418$	−16.6865	+	11.5815i	−0.816164	+	0.566470i
$419$			9.86310i			0.481844i	0.970545	+	0.240922i	$0.0774498\pi$
$419$			9.86310i			0.481844i	−0.970545	+	0.240922i	$0.922550\pi$
$420$	4.72080	−	3.44648i	0.230351	−	0.168171i
$421$	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
$423$	15.7667	+	3.81767i	0.766605	+	0.185622i
$424$	5.96537	+	5.00554i	0.289704	+	0.243091i
$425$			14.7867i			0.717261i
$426$	−0.0817328	+	0.0268634i	−0.00395997	+	0.00130154i
$427$	23.2165	+	14.5425i	1.12352	+	0.703762i
$428$	−11.1978	+	4.07565i	−0.541264	+	0.197004i
$429$	−15.6294	−	13.9771i	−0.754596	−	0.674821i
$430$	0.645217	−	0.372516i	0.0311151	−	0.0179643i
$431$	31.6457	+	26.5539i	1.52432	+	1.27906i	0.826808	+	0.562484i	$0.190154\pi$
$431$	31.6457	+	26.5539i	1.52432	+	1.27906i	0.697513	+	0.716572i	$0.254290\pi$
$432$	−4.27802	+	2.94934i	−0.205826	+	0.141900i
$433$	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
$435$	−4.48118	−	2.77906i	−0.214856	−	0.133246i
$436$	−6.64717	+	3.83775i	−0.318342	+	0.183795i
$437$	−17.2049	+	4.53390i	−0.823023	+	0.216886i
$438$	4.49524	+	4.02001i	0.214791	+	0.192084i
$439$	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
$441$	−6.39740	+	20.0018i	−0.304638	+	0.952468i
$442$	−8.72382	+	7.32015i	−0.414950	+	0.348184i
$443$	−4.93747	−	13.5656i	−0.234586	−	0.644521i	−1.00000		0.000981425i	$-0.999688\pi$
$443$	−4.93747	−	13.5656i	−0.234586	−	0.644521i	0.765413	−	0.643539i	$-0.222535\pi$
$444$	−2.19456	−	6.67700i	−0.104149	−	0.316876i
$445$		−	7.03947i		−	0.333703i
$446$	−6.66654	+	7.94487i	−0.315670	+	0.376201i
$447$	−25.0404	+	3.60585i	−1.18437	+	0.170551i
$448$	−1.62661	−	2.08666i	−0.0768501	−	0.0985853i
$449$	17.7125	−	30.6790i	0.835906	−	1.44783i	−0.0573850	−	0.998352i	$-0.518276\pi$
$449$	17.7125	−	30.6790i	0.835906	−	1.44783i	0.893291	−	0.449479i	$-0.148390\pi$
$450$	−10.0993	−	0.637398i	−0.476086	−	0.0300472i
$451$	−44.3464	+	7.81947i	−2.08819	+	0.368204i
$452$	16.0513	−	5.84219i	0.754989	−	0.274793i
$453$	30.0051	−	16.0848i	1.40976	−	0.755730i
$454$	12.1947	+	4.43849i	0.572323	+	0.208309i
$455$	5.38981	+	6.91419i	0.252678	+	0.324142i
$456$	−6.95185	+	2.94480i	−0.325550	+	0.137903i
$457$	−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
$459$	−12.9289	−	18.7534i	−0.603470	−	0.875335i
$460$	0.904067	−	5.12722i	0.0421524	−	0.239058i
$461$	−16.6219	−	19.8093i	−0.774161	−	0.922609i	0.224493	−	0.974476i	$-0.427927\pi$
$461$	−16.6219	−	19.8093i	−0.774161	−	0.922609i	−0.998654	+	0.0518663i	$0.983483\pi$
$462$	15.3950	+	14.7985i	0.716239	+	0.688487i
$463$	−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
$465$	6.94762	+	2.77965i	0.322188	+	0.128903i
$466$	7.65566	+	1.34990i	0.354642	+	0.0625329i
$467$	14.5373	+	8.39312i	0.672707	+	0.388387i	0.797101	−	0.603845i	$-0.206366\pi$
$467$	14.5373	+	8.39312i	0.672707	+	0.388387i	−0.124395	+	0.992233i	$0.539699\pi$
$468$	−4.62361	−	6.27390i	−0.213726	−	0.290011i
$469$	12.4026	−	19.8002i	0.572698	−	0.914286i
$470$	−5.28350	+	4.43339i	−0.243710	+	0.204497i
$471$	−12.5185	−	5.00848i	−0.576823	−	0.230779i
$472$	1.19973	+	0.436665i	0.0552219	+	0.0200991i
$473$	1.74960	+	2.08510i	0.0804468	+	0.0958728i
$474$	−2.20788	−	6.71754i	−0.101411	−	0.308547i
$475$	−14.1863	−	3.86413i	−0.650912	−	0.177299i
$476$	9.14722	−	7.13053i	0.419262	−	0.326827i
$477$	−16.9147	−	16.1140i	−0.774472	−	0.737811i
$478$	4.96025	+	5.91139i	0.226876	+	0.270381i
$479$	11.4673	+	31.5062i	0.523956	+	1.43956i	0.866082	+	0.499902i	$0.166631\pi$
$479$	11.4673	+	31.5062i	0.523956	+	1.43956i	−0.342126	+	0.939654i	$0.611147\pi$
$480$	0.0696109	−	2.20811i	0.00317729	−	0.100786i
$481$	9.90595	−	3.60547i	0.451673	−	0.164395i
$482$	−3.27228	−	1.88925i	−0.149048	−	0.0860531i
$483$	8.23852	+	16.7933i	0.374865	+	0.764122i
$484$	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
$489$	17.7753	+	33.1586i	0.803826	+	1.49948i
$490$	−5.23220	−	7.23467i	−0.236367	−	0.326829i
$491$	34.8454	−	6.14418i	1.57255	−	0.277283i	0.681717	−	0.731616i	$-0.261233\pi$
$491$	34.8454	−	6.14418i	1.57255	−	0.277283i	0.890832	+	0.454333i	$0.150122\pi$
$492$	−16.7294	−	0.527395i	−0.754218	−	0.0237768i
$493$	−9.06123	−	5.23150i	−0.408097	−	0.235615i
$494$	−4.74317	−	10.2825i	−0.213405	−	0.462633i
$495$	1.98407	+	17.7200i	0.0891775	+	0.796455i
$496$	1.15849	−	3.18293i	0.0520179	−	0.142918i
$497$	0.0404745	+	0.125032i	0.00181553	+	0.00560844i
$498$	0.826349	+	1.05032i	0.0370296	+	0.0470658i
$499$	−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
$501$	2.26004	−	0.742817i	0.100971	−	0.0331866i
$502$	−15.8905	−	9.17438i	−0.709227	−	0.409473i
$503$	8.05235	+	22.1237i	0.359037	+	0.986445i	0.979364	+	0.202102i	$0.0647774\pi$
$503$	8.05235	+	22.1237i	0.359037	+	0.986445i	−0.620328	+	0.784343i	$0.713000\pi$
$504$	4.47584	+	6.55491i	0.199370	+	0.291979i
$505$	4.73475	+	8.20083i	0.210694	+	0.364932i
$506$	19.0207			0.845575
$507$	−8.50939	+	6.69487i	−0.377915	+	0.297330i
$508$	−17.0830	+	3.01220i	−0.757937	+	0.133645i
$509$	1.58675	−	8.99888i	0.0703313	−	0.398868i	−0.929237	−	0.369484i	$-0.879534\pi$
$509$	1.58675	−	8.99888i	0.0703313	−	0.398868i	0.999568	−	0.0293841i	$-0.00935458\pi$
$510$	9.67963	+	0.305152i	0.428621	+	0.0135123i
$511$	6.17139	−	6.83900i	0.273006	−	0.302540i
$512$	−1.00000			−0.0441942
$513$	21.3706	−	7.50321i	0.943534	−	0.331275i
$514$	−0.900200	+	1.55919i	−0.0397061	+	0.0687730i
$515$	−13.1430	+	11.0283i	−0.579148	+	0.485963i
$516$	0.478001	+	0.891679i	0.0210428	+	0.0392540i
$517$	−19.3027	−	16.1969i	−0.848933	−	0.712340i
$518$	−10.2142	+	3.30648i	−0.448787	+	0.145278i
$519$	27.7834	+	11.1157i	1.21955	+	0.487927i
$520$	3.31352			0.145308
$521$	−31.1019			−1.36260			−0.681300	−	0.732005i	$-0.738585\pi$
$521$	−31.1019			−1.36260			−0.681300	+	0.732005i	$0.738585\pi$
$522$	3.96370	−	5.96330i	0.173487	−	0.261007i
$523$	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
$525$	−1.04279	+	15.4224i	−0.0455113	+	0.673090i
$526$	−16.6246	−	2.93137i	−0.724868	−	0.127814i
$527$	13.9529	+	5.07846i	0.607800	+	0.221221i
$528$	7.98870	−	1.15038i	0.347664	−	0.0500641i
$529$	−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
$534$	9.55453	+	0.301208i	0.413465	+	0.0130345i
$535$	−5.19843	+	14.2826i	−0.224748	+	0.617490i
$536$	−3.02028	−	8.29815i	−0.130456	−	0.358426i
$537$	19.7848	−	31.9026i	0.853777	−	1.37670i
$538$	2.08711	−	11.8366i	0.0899818	−	0.510312i
$539$	22.7102	−	23.4146i	0.978198	−	1.00854i
$540$	−0.625669	+	6.59802i	−0.0269245	+	0.283934i
$541$	−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
$546$	−9.61511	+	7.01964i	−0.411489	+	0.300413i
$547$	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
$549$	−29.8010	+	8.76452i	−1.27188	+	0.374060i
$550$	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
$555$	−8.32320	−	3.33000i	−0.353300	−	0.141350i
$556$	−2.96098	−	16.7926i	−0.125574	−	0.712163i
$557$	12.0940	−	14.4131i	0.512439	−	0.610701i	−0.446337	−	0.894865i	$-0.647272\pi$
$557$	12.0940	−	14.4131i	0.512439	−	0.610701i	0.958776	+	0.284164i	$0.0917161\pi$
$558$	−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
$561$	5.04291	+	35.0199i	0.212912	+	1.47854i
$562$	12.9918	−	22.5025i	0.548027	−	0.949211i
$563$	−21.5935	−	37.4011i	−0.910058	−	1.57627i	−0.813980	−	0.580893i	$-0.802704\pi$
$563$	−21.5935	−	37.4011i	−0.910058	−	1.57627i	−0.0960779	−	0.995374i	$-0.530630\pi$
$564$	−5.79127	−	7.36089i	−0.243856	−	0.309949i
$565$	7.45163	−	20.4732i	0.313492	−	0.861313i
$566$	14.4015	+	12.0843i	0.605342	+	0.507942i
$567$	−12.1622	−	20.4714i	−0.510765	−	0.859720i
$568$	0.0466763	+	0.0169888i	0.00195850	+	0.000712834i
$569$	−4.01376	−	6.95204i	−0.168266	−	0.291445i	0.769545	−	0.638593i	$-0.220483\pi$
$569$	−4.01376	−	6.95204i	−0.168266	−	0.291445i	−0.937810	+	0.347149i	$0.887150\pi$
$570$	−2.82229	+	9.20684i	−0.118213	+	0.385632i
$571$	−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
$573$	−0.150236	+	4.76558i	−0.00627618	+	0.199085i
$574$	−0.920168	+	25.5506i	−0.0384071	+	1.06646i
$575$	8.85026	+	10.5473i	0.369082	+	0.439854i
$576$	2.99404	+	0.188963i	0.124752	+	0.00787346i
$577$	−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
$579$	−12.7505	−	16.2062i	−0.529891	−	0.673508i
$580$	1.04123	+	2.86075i	0.0432346	+	0.118786i
$581$	1.61003	−	1.25506i	0.0667952	−	0.0520688i
$582$	−6.99024	+	7.81660i	−0.289755	+	0.324008i
$583$	12.4110	+	34.0990i	0.514012	+	1.41224i
$584$	−0.604599	−	3.42885i	−0.0250185	−	0.141887i
$585$	−9.92083	−	0.626134i	−0.410176	−	0.0258874i
$586$	−23.7707	+	19.9459i	−0.981957	+	0.823959i
$587$	8.79349	−	24.1599i	0.362946	−	0.997186i	−0.615036	−	0.788499i	$-0.710859\pi$
$587$	8.79349	−	24.1599i	0.362946	−	0.997186i	0.977982	−	0.208688i	$-0.0669192\pi$
$588$	10.0433	−	6.79200i	0.414180	−	0.280097i
$589$	−8.51849	+	12.0593i	−0.350998	+	0.496893i
$590$	1.41027	−	0.814221i	0.0580600	−	0.0335210i
$591$	14.6828	−	7.87099i	0.603970	−	0.323769i
$592$	−1.38787	+	3.81313i	−0.0570410	+	0.156719i
$593$	−13.9963	−	2.46792i	−0.574758	−	0.101345i	−0.121289	−	0.992617i	$-0.538703\pi$
$593$	−13.9963	−	2.46792i	−0.574758	−	0.101345i	−0.453469	+	0.891272i	$0.649814\pi$
$594$	−24.1359	+	1.93473i	−0.990308	+	0.0793830i
$595$	0.532410	−	14.7836i	0.0218267	−	0.606070i
$596$	12.6493	+	7.30310i	0.518137	+	0.299147i
$597$	−21.8533	−	19.5430i	−0.894396	−	0.799841i
$598$	−1.84136	+	10.4429i	−0.0752990	+	0.427042i
$599$	−0.321068	+	1.82087i	−0.0131185	+	0.0743986i	−0.990664	−	0.136325i	$-0.956471\pi$
$599$	−0.321068	+	1.82087i	−0.0131185	+	0.0743986i	0.977546	+	0.210724i	$0.0675820\pi$
$600$	4.35502	+	3.89461i	0.177793	+	0.158997i
$601$	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
$603$	7.47481	+	25.4157i	0.304398	+	1.03501i
$604$	−19.3570	−	3.41316i	−0.787625	−	0.138880i
$605$	4.67401	−	12.8417i	0.190026	−	0.522091i
$606$	−11.3334	+	6.07548i	−0.460389	+	0.246800i
$607$	−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
$609$	−9.08185	−	6.09544i	−0.368015	−	0.247000i
$610$	4.51701	−	12.4104i	0.182888	−	0.502482i
$611$	10.7612	−	9.02972i	0.435352	−	0.365303i
$612$	−0.828352	+	13.1249i	−0.0334841	+	0.530543i
$613$	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
$615$	−14.2311	+	15.9135i	−0.573855	+	0.641694i
$616$	−1.70252	−	12.2107i	−0.0685963	−	0.491983i
$617$	−7.69406	−	21.1392i	−0.309751	−	0.851034i	−0.992705	−	0.120572i	$-0.961527\pi$
$617$	−7.69406	−	21.1392i	−0.309751	−	0.851034i	0.682954	−	0.730462i	$-0.260695\pi$
$618$	−14.4061	−	18.3106i	−0.579497	−	0.736559i
$619$	−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
$621$	−20.4466	−	5.63845i	−0.820494	−	0.226263i
$622$	−5.16539	−	6.15587i	−0.207113	−	0.246828i
$623$	0.525530	−	14.5926i	0.0210549	−	0.584639i
$624$	−0.141780	+	4.49738i	−0.00567576	+	0.180039i
$625$	0.563267	+	3.19445i	0.0225307	+	0.127778i
$626$	−10.7203	+	18.5681i	−0.428468	+	0.742129i
$627$	−34.9157	−	4.31341i	−1.39440	−	0.172261i
$628$	3.89228	+	6.74162i	0.155319	+	0.269020i
$629$	−16.7155	−	6.08395i	−0.666491	−	0.242583i
$630$	10.0743	+	1.00090i	0.401368	+	0.0398768i
$631$	−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
$633$	−3.98797	−	5.06884i	−0.158508	−	0.201468i
$634$	−2.21305	−	3.83311i	−0.0878913	−	0.152232i
$635$	−11.0626	+	19.1611i	−0.439008	+	0.760384i
$636$	1.92245	+	13.3502i	0.0762299	+	0.529369i
$637$	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	$-0.810594\pi$
$641$	−6.11830	−	34.6986i	−0.241658	−	1.37051i	0.586469	−	0.809972i	$-0.300518\pi$
$642$	−19.1630	−	7.66686i	−0.756304	−	0.302587i
$643$	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	0.0914890	−	0.995806i	$-0.470837\pi$
$647$	−18.4453	−	10.6494i	−0.725160	−	0.418671i	−0.816649	+	0.577135i	$0.804171\pi$
$648$	−8.92859	−	1.13153i	−0.350748	−	0.0444506i
$649$	3.82417	+	4.55746i	0.150112	+	0.178896i
$650$	−5.63269	+	6.71278i	−0.220932	+	0.263297i
$651$	14.1947	+	6.28078i	0.556333	+	0.246163i
$652$	3.77188	−	21.3914i	0.147718	−	0.837751i
$653$			34.1870i			1.33784i	0.743335	+	0.668920i	$0.233243\pi$
$653$			34.1870i			1.33784i	−0.743335	+	0.668920i	$0.766757\pi$
$654$	−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
$657$	1.16227	+	10.3804i	0.0453445	+	0.404977i
$658$	−11.2835	+	8.79581i	−0.439876	+	0.342896i
$659$	−2.42072	+	13.7286i	−0.0942977	+	0.534789i	0.900663	+	0.434519i	$0.143082\pi$
$659$	−2.42072	+	13.7286i	−0.0942977	+	0.534789i	−0.994960	+	0.100270i	$0.968029\pi$
$660$	5.42565	−	8.74876i	0.211193	−	0.340545i
$661$	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
$663$	−19.7150	−	0.621519i	−0.765669	−	0.0241378i
$664$		−	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
$669$	−17.7802	+	2.56037i	−0.687422	+	0.0989898i
$670$	−10.5842	−	3.85233i	−0.408902	−	0.148828i
$671$	47.5169	+	8.37850i	1.83437	+	0.323449i
$672$	0.309147	−	4.57214i	0.0119256	−	0.176374i
$673$	−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
$675$	−12.3032	−	12.4836i	−0.473549	−	0.480492i
$676$	6.25116			0.240429
$677$	−23.2595			−0.893936			−0.446968	−	0.894550i	$-0.647496\pi$
$677$	−23.2595			−0.893936			−0.446968	+	0.894550i	$0.647496\pi$
$678$	27.4690	+	10.9900i	1.05494	+	0.422067i
$679$	11.8921	+	10.7312i	0.456375	+	0.411825i
$680$	−4.28319	−	3.59403i	−0.164253	−	0.137825i
$681$	10.6197	+	19.8104i	0.406948	+	0.759135i
$682$	12.0912	−	10.1457i	0.462995	−	0.388499i
$683$	−13.8249	+	23.9455i	−0.528997	+	0.916250i	0.470431	+	0.882437i	$0.344098\pi$
$683$	−13.8249	+	23.9455i	−0.528997	+	0.916250i	−0.999428	+	0.0338129i	$0.989235\pi$
$684$	−12.3755	−	4.22458i	−0.473189	−	0.161531i
$685$	−5.00954			−0.191405
$686$	−10.3061	−	15.3878i	−0.393488	−	0.587510i
$687$	−39.0184	−	1.23006i	−1.48865	−	0.0469298i
$688$	0.101431	−	0.575243i	0.00386701	−	0.0219309i
$689$	−19.9228	+	3.51292i	−0.758997	+	0.133832i
$690$	7.08710	−	5.57586i	0.269801	−	0.212269i
$691$	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
$693$	2.79003	+	36.8811i	0.105985	+	1.40100i
$694$	−6.09508	−	16.7461i	−0.231366	−	0.635673i
$695$	−18.8353	−	10.8745i	−0.714462	−	0.412495i
$696$	−3.92739	+	1.29083i	−0.148867	+	0.0489288i
$697$	−27.2295	+	32.4509i	−1.03139	+	1.22916i
$698$	−23.7241	−	8.63486i	−0.897970	−	0.326834i
$699$	8.32554	+	10.5820i	0.314901	+	0.400249i
$700$	5.97888	−	6.62566i	0.225980	−	0.250426i
$701$	−6.65409	+	18.2820i	−0.251322	+	0.690500i	0.748310	+	0.663349i	$0.230866\pi$
$701$	−6.65409	+	18.2820i	−0.251322	+	0.690500i	−0.999631	+	0.0271509i	$0.991357\pi$
$702$	1.27434	−	13.4386i	0.0480967	−	0.507206i
$703$	10.2051	−	14.4469i	0.384892	−	0.544875i
$704$	−4.03555	−	2.32993i	−0.152096	−	0.0878125i
$705$	−11.9402	−	0.376418i	−0.449695	−	0.0141767i
$706$	16.7093	−	2.94629i	0.628862	−	0.110885i
$707$	9.20275	+	17.3535i	0.346105	+	0.652646i
$708$	1.04478	+	1.94897i	0.0392653	+	0.0732469i
$709$	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
$714$	20.0427	+	1.35520i	0.750081	+	0.0507170i
$715$	13.3719	+	7.72027i	0.500081	+	0.288722i
$716$	−20.3664	+	7.41275i	−0.761127	+	0.277027i
$717$	−0.421151	+	13.3592i	−0.0157282	+	0.498909i
$718$	−5.02548	−	13.8074i	−0.187549	−	0.515287i
$719$	6.08252	+	7.24887i	0.226840	+	0.270337i	0.867445	−	0.497533i	$-0.165761\pi$
$719$	6.08252	+	7.24887i	0.226840	+	0.270337i	−0.640605	+	0.767871i	$0.721316\pi$
$720$	2.63935	−	2.77049i	0.0983627	−	0.103250i
$721$	−28.0682	+	21.8800i	−1.04531	+	0.814854i
$722$	−16.3754	−	9.63571i	−0.609428	−	0.358604i
$723$	−2.04348	−	6.21735i	−0.0759979	−	0.231226i
$724$	5.70674	+	6.80103i	0.212089	+	0.252758i
$725$	−7.56551	−	2.75362i	−0.280976	−	0.102267i
$726$	17.2298	+	6.89342i	0.639459	+	0.255839i
$727$	−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
$729$	26.5188	+	5.07501i	0.982176	+	0.187963i
$730$	−3.84595	−	2.22046i	−0.142345	−	0.0821829i
$731$	2.52167	+	0.444639i	0.0932675	+	0.0164456i
$732$	16.6511	+	6.66187i	0.615442	+	0.246230i
$733$	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
$735$	1.59788	−	15.3817i	0.0589386	−	0.567361i
$736$	−2.62375	−	3.12686i	−0.0967127	−	0.115258i
$737$	7.14560	−	40.5247i	0.263211	−	1.49275i
$738$	−20.9901	−	19.9966i	−0.772658	−	0.736083i
$739$	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
$741$	5.74831	−	18.7521i	0.211169	−	0.688875i
$742$	20.4057	−	2.84513i	0.749117	−	0.104448i
$743$	−40.7763	−	14.8414i	−1.49594	−	0.544477i	−0.540933	−	0.841066i	$-0.681929\pi$
$743$	−40.7763	−	14.8414i	−1.49594	−	0.544477i	−0.955005	+	0.296589i	$0.904151\pi$
$744$	5.17072	−	2.77186i	0.189568	−	0.101621i
$745$	17.5065	−	6.37184i	0.641388	−	0.233446i
$746$	−11.2603	+	1.98549i	−0.412267	+	0.0726939i
$747$	−0.145800	+	2.31015i	−0.00533456	+	0.0845239i
$748$	10.2136	−	17.6905i	0.373448	−	0.646830i
$749$	−11.8424	+	29.2192i	−0.432713	+	1.06765i
$750$	18.3091	−	2.63654i	0.668555	−	0.0962728i
$751$	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
$753$	−9.92333	−	30.1920i	−0.361626	−	1.10026i
$754$	−2.12073	−	5.82665i	−0.0772323	−	0.212194i
$755$	−19.2051	+	16.1150i	−0.698944	+	0.586484i
$756$	−1.78956	+	13.6308i	−0.0650858	+	0.495746i
$757$	−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
$759$	24.5575	+	21.9613i	0.891379	+	0.797143i
$760$	4.56739	−	3.17007i	0.165677	−	0.114990i
$761$	−25.3716	+	14.6483i	−0.919719	+	0.531000i	−0.883545	−	0.468346i	$-0.844850\pi$
$761$	−25.3716	+	14.6483i	−0.919719	+	0.531000i	−0.0361733	+	0.999346i	$0.511517\pi$
$762$	−25.5336	−	15.8350i	−0.924983	−	0.573641i
$763$	−4.24383	+	19.8591i	−0.153637	+	0.718946i
$764$	1.76945	−	2.10875i	0.0640165	−	0.0762919i
$765$	12.1449	+	11.5700i	0.439101	+	0.418315i
$766$	−3.11357	−	2.61260i	−0.112498	−	0.0943970i
$767$	−2.87238	+	1.65837i	−0.103716	+	0.0598803i
$768$	−1.29109	−	1.15460i	−0.0465881	−	0.0416629i
$769$	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
$771$	−2.96247	+	0.973688i	−0.106691	+	0.0350665i
$772$			11.9054i			0.428485i
$773$	38.2939	+	32.1324i	1.37734	+	1.15572i	0.970186	+	0.242363i	$0.0779224\pi$
$773$	38.2939	+	32.1324i	1.37734	+	1.15572i	0.407152	+	0.913361i	$0.366522\pi$
$774$	−0.412388	+	1.70313i	−0.0148230	+	0.0612179i
$775$	11.2519	+	1.98402i	0.404181	+	0.0712681i
$776$	5.96229	−	1.05131i	0.214034	−	0.0377399i
$777$	−17.0051	−	7.52433i	−0.610055	−	0.269934i
$778$		−	38.4716i		−	1.37927i
$779$	−24.0175	−	34.6041i	−0.860515	−	1.23982i
$780$	4.27805	+	3.82578i	0.153179	+	0.136985i
$781$	0.148782	+	0.177312i	0.00532385	+	0.00634471i
$782$	13.7071	−	11.5017i	0.490166	−	0.411299i
$783$	12.0027	−	3.12267i	0.428941	−	0.111595i
$784$	−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
$789$	−18.0793	−	22.9794i	−0.643640	−	0.818087i
$790$	2.60357	+	4.50952i	0.0926310	+	0.160442i
$791$	16.9754	−	41.8839i	0.603575	−	1.48922i
$792$	11.6424	+	7.73848i	0.413693	+	0.274975i
$793$	−9.20004	+	25.2769i	−0.326703	+	0.897609i
$794$	7.33996	−	2.67153i	0.260486	−	0.0948090i
$795$	14.6203	+	9.06699i	0.518530	+	0.321573i
$796$	2.93922	+	16.6691i	0.104178	+	0.590821i
$797$	−14.7557			−0.522675			−0.261338	−	0.965247i	$-0.584164\pi$
$797$	−14.7557			−0.522675			−0.261338	+	0.965247i	$0.584164\pi$
$798$	−6.53783	+	18.8748i	−0.231437	+	0.668159i
$799$	−23.7045			−0.838604
$800$	−0.585739	−	3.32189i	−0.0207090	−	0.117447i
$801$	11.9880	+	11.4205i	0.423574	+	0.403524i
$802$	28.5975	−	10.4087i	1.00981	−	0.367542i
$803$	5.54909	−	15.2460i	0.195823	−	0.538019i
$804$	5.68156	−	14.2009i	0.200373	−	0.500825i
$805$	−8.46865	−	10.8638i	−0.298481	−	0.382898i
$806$	4.39973	+	7.62056i	0.154974	+	0.268423i
$807$	16.3611	−	12.8723i	0.575939	−	0.453127i
$808$	7.31144	+	1.28921i	0.257216	+	0.0453541i
$809$			51.5589i			1.81272i	0.422511	+	0.906358i	$0.361149\pi$
$809$			51.5589i			1.81272i	−0.422511	+	0.906358i	$0.638851\pi$
$810$	−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
$813$	24.4917	−	19.2691i	0.858960	−	0.675798i
$814$	−14.4851	+	12.1545i	−0.507704	+	0.426014i
$815$	−17.8086	−	21.2235i	−0.623809	−	0.743427i
$816$	5.06137	−	5.65971i	0.177183	−	0.198129i
$817$	−1.08556	+	2.30309i	−0.0379790	+	0.0805748i
$818$			2.44627i			0.0855317i
$819$	−20.5188	−	2.03859i	−0.716985	−	0.0712341i
$820$	12.1384	−	2.14033i	0.423891	−	0.0747435i
$821$	−54.5610	−	9.62058i	−1.90419	−	0.335761i	−0.907713	−	0.419593i	$-0.862173\pi$
$821$	−54.5610	−	9.62058i	−1.90419	−	0.335761i	−0.996480	+	0.0838321i	$0.973284\pi$
$822$	0.214350	−	6.79935i	0.00747633	−	0.237154i
$823$	−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
$825$	8.50075	+	25.8638i	0.295958	+	0.900461i
$826$	2.98423	−	1.58257i	0.103835	−	0.0550646i
$827$	6.48447	−	2.36015i	0.225487	−	0.0820705i	−0.226806	−	0.973940i	$-0.572828\pi$
$827$	6.48447	−	2.36015i	0.225487	−	0.0820705i	0.452293	+	0.891869i	$0.350606\pi$
$828$	7.26476	+	9.85775i	0.252468	+	0.342581i
$829$	−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
$831$	12.0412	−	19.4161i	0.417704	−	0.673539i
$832$	1.66987	−	1.99007i	0.0578922	−	0.0689933i
$833$	2.20734	−	30.6062i	0.0764797	−	1.06044i
$834$	15.5657	−	25.0994i	0.538997	−	0.869122i
$835$	−1.51718	+	0.875945i	−0.0525042	+	0.0303133i
$836$	14.3031	+	14.4219i	0.494685	+	0.498792i
$837$	−16.0051	+	7.32199i	−0.553218	+	0.253085i
$838$	9.71325	−	1.71271i	0.335539	−	0.0591645i
$839$	8.02514	+	45.5128i	0.277058	+	1.57128i	0.732346	+	0.680932i	$0.238425\pi$
$839$	8.02514	+	45.5128i	0.277058	+	1.57128i	−0.455288	+	0.890344i	$0.650464\pi$
$840$	−4.21388	−	4.05060i	−0.145393	−	0.139759i
$841$	−17.8512	+	14.9790i	−0.615560	+	0.516516i
$842$	−0.709029	−	1.94804i	−0.0244348	−	0.0671339i
$843$	42.7549	−	14.0524i	1.47256	−	0.483991i
$844$			3.72367i			0.128174i
$845$	5.12512	−	6.10788i	0.176309	−	0.210117i
$846$	1.02181	−	16.1901i	0.0351305	−	0.556628i
$847$	10.6478	−	26.2715i	0.365861	−	0.902701i
$848$	3.89362	−	6.74395i	0.133707	−	0.231588i
$849$	4.64115	+	32.2299i	0.159284	+	1.10613i
$850$	14.5621	−	2.56769i	0.499475	−	0.0880710i
$851$	−15.5646	+	5.66503i	−0.533546	+	0.194195i
$852$	0.0406481	+	0.0758263i	0.00139258	+	0.00259777i
$853$	−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
$855$	−14.2740	+	8.62825i	−0.488161	+	0.295080i
$856$	5.95820	+	10.3199i	0.203647	+	0.352727i
$857$	44.1696	−	37.0627i	1.50881	−	1.26604i	0.642765	−	0.766064i	$-0.277787\pi$
$857$	44.1696	−	37.0627i	1.50881	−	1.26604i	0.866040	−	0.499974i	$-0.166657\pi$
$858$	−11.0507	+	17.8191i	−0.377266	+	0.608333i
$859$	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
$861$	−30.6887	+	31.9257i	−1.04587	+	1.08803i
$862$	20.6553	−	35.7760i	0.703521	−	1.21853i
$863$	−9.53883	+	16.5217i	−0.324706	+	0.562407i	−0.981453	−	0.191704i	$-0.938599\pi$
$863$	−9.53883	+	16.5217i	−0.324706	+	0.562407i	0.656747	+	0.754111i	$0.271932\pi$
$864$	3.64740	+	3.70088i	0.124087	+	0.125906i
$865$	−21.7017	−	3.82659i	−0.737879	−	0.130108i
$866$	−15.7924	−	9.11772i	−0.536646	−	0.309833i
$867$	2.86181	+	2.55926i	0.0971921	+	0.0869170i
$868$	−4.19863	−	7.91731i	−0.142511	−	0.268731i
$869$	−14.5731	+	12.2283i	−0.494357	+	0.414815i
$870$	−1.95869	+	4.89568i	−0.0664059	+	0.165979i
$871$	21.5574	+	7.84625i	0.730444	+	0.265860i
$872$	4.93371	+	5.87977i	0.167077	+	0.199114i
$873$	−18.0500	+	2.02102i	−0.610901	+	0.0684013i
$874$	7.45262	+	16.1562i	0.252089	+	0.546493i
$875$	−3.90195	−	27.9854i	−0.131910	−	0.946080i
$876$	3.17835	−	5.12502i	0.107386	−	0.173158i
$877$	−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
$879$	−53.7195	−	1.69352i	−1.81191	−	0.0571208i
$880$	−5.58514	+	2.03282i	−0.188275	+	0.0685265i
$881$	48.9450	+	28.2584i	1.64900	+	0.952050i	0.977471	+	0.211071i	$0.0676951\pi$
$881$	48.9450	+	28.2584i	1.64900	+	0.952050i	0.671528	+	0.740979i	$0.265638\pi$
$882$	20.8089	+	2.82692i	0.700671	+	0.0951874i
$883$	−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	−0.372200	−	0.928152i	$-0.621397\pi$
$887$	−1.80832	+	0.658174i	−0.0607174	+	0.0220993i	0.311483	+	0.950252i	$0.399174\pi$
$888$	−6.19448	+	3.32066i	−0.207873	+	0.111434i
$889$	−24.3629	+	38.8943i	−0.817107	+	1.30447i
$890$	−6.93253	+	1.22239i	−0.232379	+	0.0409746i
$891$	−33.3954	−	25.3693i	−1.11879	−	0.849904i
$892$	8.98180	+	5.18565i	0.300733	+	0.173628i
$893$	6.19456	−	22.7420i	0.207293	−	0.761031i
$894$	7.89929	+	24.0338i	0.264192	+	0.803812i
$895$	−9.45486	+	25.9770i	−0.316041	+	0.868316i
$896$	−1.77250	+	1.96424i	−0.0592150	+	0.0656208i
$897$	−14.4347	+	11.3567i	−0.481960	+	0.379188i
$898$	−33.2887	−	12.1161i	−1.11086	−	0.404319i
$899$	−5.19670	+	6.19319i	−0.173320	+	0.206554i
$900$	1.12601	+	10.0566i	0.0375338	+	0.335219i
$901$	29.5633	+	17.0684i	0.984895	+	0.568629i
$902$	15.4013	+	42.3148i	0.512809	+	1.40893i
$903$	2.59873	+	0.641590i	0.0864803	+	0.0213508i
$904$	−8.54071	−	14.7929i	−0.284060	−	0.492006i
$905$	11.3239			0.376419
$906$	−21.0508	−	26.7562i	−0.699365	−	0.888915i
$907$	−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
$909$	−21.6472	−	5.24153i	−0.717991	−	0.173851i
$910$	5.87321	−	6.50857i	0.194695	−	0.215757i
$911$	−37.2878			−1.23540			−0.617700	−	0.786414i	$-0.711935\pi$
$911$	−37.2878			−1.23540			−0.617700	+	0.786414i	$0.711935\pi$
$912$	4.10724	+	6.33487i	0.136004	+	0.209769i
$913$	1.79773	−	3.11376i	0.0594962	−	0.103050i
$914$	−14.3617	+	12.0509i	−0.475044	+	0.398609i
$915$	20.1608	−	10.8076i	0.666496	−	0.357288i
$916$	17.2655	+	14.4875i	0.570468	+	0.478679i
$917$	12.1495	−	56.8539i	0.401213	−	1.87748i
$918$	−16.2234	+	15.9890i	−0.535453	+	0.527716i
$919$	−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
$921$	−10.5015	+	26.2482i	−0.346037	+	0.864907i
$922$	−16.6219	+	19.8093i	−0.547415	+	0.652383i
$923$	−0.111752	+	0.0645202i	−0.00367837	+	0.00212371i
$924$	11.9003	−	17.7308i	0.391492	−	0.583301i
$925$	−13.4797	−	2.37684i	−0.443211	−	0.0781500i
$926$	35.7760	+	13.0214i	1.17567	+	0.427909i
$927$	2.54180	−	40.2737i	0.0834835	−	1.32276i
$928$	2.24287	+	0.816338i	0.0736258	+	0.0267976i
$929$	38.9022	−	6.85950i	1.27634	−	0.225053i	0.505914	−	0.862584i	$-0.331155\pi$
$929$	38.9022	−	6.85950i	1.27634	−	0.225053i	0.770425	+	0.637531i	$0.220044\pi$
$930$	1.53098	−	7.32475i	0.0502027	−	0.240188i
$931$	28.7866	+	10.1159i	0.943443	+	0.331534i
$932$		−	7.77376i		−	0.254638i
$933$	0.438568	−	13.9117i	0.0143581	−	0.455449i
$934$	5.74123	−	15.7739i	0.187859	−	0.516138i
$935$	−8.91124	−	24.4834i	−0.291429	−	0.800693i
$936$	−5.37570	+	5.64281i	−0.175710	+	0.184441i
$937$	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
$939$	−35.2794	+	11.5954i	−1.15130	+	0.378402i
$940$	5.28350	+	4.43339i	0.172329	+	0.144601i
$941$	−2.09985	+	11.9089i	−0.0684532	+	0.388218i	0.931262	+	0.364350i	$0.118709\pi$
$941$	−2.09985	+	11.9089i	−0.0684532	+	0.388218i	−0.999715	+	0.0238671i	$0.992402\pi$
$942$	−2.75857	+	13.1980i	−0.0898792	+	0.430015i
$943$			39.4447i			1.28450i
$944$	0.221701	−	1.25733i	0.00721574	−	0.0409225i
$945$	11.8511	+	12.9239i	0.385517	+	0.420416i
$946$	1.74960	−	2.08510i	0.0568845	−	0.0677923i
$947$	15.4642	+	18.4295i	0.502517	+	0.598877i	0.956355	−	0.292207i	$-0.0943898\pi$
$947$	15.4642	+	18.4295i	0.502517	+	0.598877i	−0.453837	+	0.891084i	$0.649945\pi$
$948$	−6.23209	+	3.34082i	−0.202409	+	0.108505i
$949$	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	$-0.871122\pi$
$953$	−5.87027	−	33.2920i	−0.190157	−	1.07843i	0.728992	−	0.684522i	$-0.239989\pi$
$954$	−12.9320	+	19.4559i	−0.418690	+	0.629909i
$955$	−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
$960$	−2.18665	+	0.314881i	−0.0705739	+	0.0101627i
$961$	−9.76341	+	16.9107i	−0.314949	+	0.545507i
$962$	−5.27085	−	9.12938i	−0.169939	−	0.294343i
$963$	−15.8890	−	32.0241i	−0.512017	−	1.03196i
$964$	−1.29233	+	3.55063i	−0.0416230	+	0.114358i
$965$	11.6325	+	9.76085i	0.374464	+	0.314213i
$966$	15.1076	−	11.0295i	0.486078	−	0.354868i
$967$	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
$969$	−27.7700	+	18.0048i	−0.892101	+	0.578397i
$970$	3.86107	−	6.68757i	0.123971	−	0.214725i
$971$	2.36180	+	13.3945i	0.0757939	+	0.429848i	0.998966	+	0.0454618i	$0.0144759\pi$
$971$	2.36180	+	13.3945i	0.0757939	+	0.429848i	−0.923172	+	0.384387i	$0.874413\pi$
$972$	−10.2211	−	11.7698i	−0.327843	−	0.377517i
$973$	−38.2330	−	23.9487i	−1.22569	−	0.767760i
$974$	−8.66408	−	10.3254i	−0.277615	−	0.330849i
$975$	−15.0228	+	2.16331i	−0.481116	+	0.0692814i
$976$	−5.17719	−	8.96715i	−0.165718	−	0.287031i
$977$	−12.3868			−0.396289			−0.198144	−	0.980173i	$-0.563491\pi$
$977$	−12.3868			−0.396289			−0.198144	+	0.980173i	$0.563491\pi$
$978$	29.5682	−	23.2632i	0.945488	−	0.743874i
$979$	−8.79607	−	24.1670i	−0.281124	−	0.772381i
$980$	−6.21619	+	6.40900i	−0.198569	+	0.204728i
$981$	−13.6607	−	18.5366i	−0.436152	−	0.591827i
$982$	−12.1017	−	33.2491i	−0.386180	−	1.06102i
$983$	0.225565	+	1.27924i	0.00719440	+	0.0408015i	0.988194	−	0.153210i	$-0.0489612\pi$
$983$	0.225565	+	1.27924i	0.00719440	+	0.0408015i	−0.980999	+	0.194012i	$0.937850\pi$
$984$	2.38564	+	16.5668i	0.0760514	+	0.528130i
$985$	−9.39788	+	7.88576i	−0.299441	+	0.251261i
$986$	−3.57856	+	9.83201i	−0.113965	+	0.313115i
$987$	−24.7236	−	1.67170i	−0.786960	−	0.0532106i
$988$	−9.30267	+	6.45665i	−0.295957	+	0.205413i
$989$	2.06483	−	1.19213i	0.0656579	−	0.0379076i
$990$	17.1063	−	5.03098i	0.543673	−	0.159895i
$991$	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
$993$	44.9365	−	24.0890i	1.42602	−	0.764442i
$994$	0.116104	−	0.0615711i	0.00368259	−	0.00195292i
$995$	18.6968	+	10.7946i	0.592729	+	0.342212i
$996$	0.890865	−	0.996180i	0.0282281	−	0.0315652i
$997$	−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
$999$	19.1740	−	8.77168i	0.606639	−	0.277524i

Twists

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

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

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} +(0.912860 - 1.47197i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.436242 + 1.19856i) q^{5} +(-1.60812 - 0.643387i) q^{6} +(-0.993792 + 2.45201i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.33337 - 2.68740i) 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} +(1.36602 + 1.73625i) q^{15} +(0.766044 - 0.642788i) q^{16} +(2.81777 + 3.35809i) q^{17} +(-2.41503 + 1.77978i) q^{18} +(-3.95809 + 1.82580i) q^{19} -1.27549i q^{20} +(2.70209 + 3.70118i) q^{21} +(4.58906 - 0.809176i) q^{22} +(4.01982 + 0.708802i) q^{23} +(1.73119 + 0.0545760i) q^{24} +(2.58397 + 2.16821i) q^{25} +2.59785i q^{26} +(-5.17295 - 0.490534i) q^{27} +(0.0952210 - 2.64404i) q^{28} +(-2.24287 + 0.816338i) q^{29} +(1.47267 - 1.64676i) q^{30} +(2.93341 - 1.69360i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(6.85916 + 4.25379i) q^{33} +(2.81777 - 3.35809i) q^{34} +(-2.50536 - 2.26080i) q^{35} +(2.17211 + 2.06929i) q^{36} +(-3.51420 + 2.02892i) q^{37} +(2.48538 + 3.58091i) q^{38} +(-2.99947 + 3.35406i) q^{39} +(-1.25611 + 0.221486i) q^{40} +(1.67805 + 9.51669i) q^{41} +(3.17573 - 3.30374i) q^{42} +(0.447459 - 0.375463i) q^{43} +(-1.59376 - 4.37883i) q^{44} +(3.80269 - 0.425780i) q^{45} -4.08183i q^{46} +(-3.47584 + 4.14235i) q^{47} +(-0.246871 - 1.71437i) q^{48} +(-5.02475 - 4.87359i) q^{49} +(1.68657 - 2.92122i) q^{50} +(7.51522 - 1.08220i) q^{51} +(2.55839 - 0.451112i) q^{52} +(7.31761 - 2.66339i) q^{53} +(0.415191 + 5.17954i) q^{54} +(-5.58514 - 2.03282i) q^{55} +(-2.62040 + 0.365358i) q^{56} +(-0.925653 + 7.49287i) q^{57} +(1.19341 + 2.06704i) q^{58} +(0.978027 - 0.820662i) q^{59} +(-1.87747 - 1.16434i) q^{60} +(1.79802 - 10.1971i) q^{61} +(-2.17726 - 2.59475i) q^{62} +(7.91464 - 0.598738i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.65676 - 2.86960i) q^{65} +(2.99809 - 7.49361i) q^{66} +(-8.69655 - 1.53344i) q^{67} +(-3.79637 - 2.19184i) q^{68} +(4.71286 - 5.27000i) q^{69} +(-1.79140 + 2.85989i) q^{70} +(0.0380509 - 0.0319285i) q^{71} +(1.66067 - 2.49844i) q^{72} +(-3.27177 - 1.19083i) q^{73} +(2.60834 + 3.10849i) q^{74} +(5.55034 - 1.82425i) q^{75} +(3.09492 - 3.06944i) q^{76} +(-11.4260 - 4.63093i) q^{77} +(3.82395 + 2.37147i) q^{78} +(2.62417 + 3.12736i) q^{79} +(0.436242 + 1.19856i) q^{80} +(-5.44422 + 7.16662i) q^{81} +(9.08072 - 3.30511i) q^{82} +(-0.668209 - 0.385791i) q^{83} +(-3.80501 - 2.55380i) 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} +(-1.07964 - 3.67099i) q^{90} +(3.64864 - 5.82489i) q^{91} +(-4.01982 + 0.708802i) q^{92} +(0.184860 - 5.86390i) q^{93} +(4.68299 + 2.70372i) q^{94} +(-0.461661 - 5.54051i) q^{95} +(-1.64545 + 0.540817i) q^{96} +(2.07068 - 5.68915i) q^{97} +(-3.92701 + 5.79471i) q^{98} +(12.5229 - 6.21333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 81 q^{8} + 15 q^{13} - 6 q^{14} + 3 q^{15} + 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} + 9 q^{27} + 9 q^{28} - 6 q^{29} + 24 q^{33} + 6 q^{34} - 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots + 39 q^{99}+O(q^{100}) \) 162 * q + 81 * q^8 + 15 * q^13 - 6 * q^14 + 3 * 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 + 45 * 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 + 18 * q^60 + 45 * q^61 - 36 * q^62 - 21 * 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 - 18 * q^78 - 42 * q^79 - 12 * q^81 + 57 * q^84 - 6 * q^85 + 9 * q^86 + 60 * q^87 - 54 * q^89 + 12 * q^90 - 18 * q^91 + 105 * q^93 - 72 * q^94 - 12 * q^97 + 27 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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