LMFDB - Embedded newform 798.2.cj.b.241.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(241,798)] 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([0, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.241"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			241.6
Character	$\chi$	$=$	798.241
Dual form			798.2.cj.b.649.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.342020 + 0.939693i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(1.19350 + 1.42236i) q^{5} +(-0.342020 - 0.939693i) q^{6} +(-1.25603 - 2.32860i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-1.74479 + 0.635050i) q^{10} +4.39522 q^{11} +1.00000 q^{12} +(-2.19945 + 0.800533i) q^{13} +(2.61776 - 0.383856i) q^{14} +(-1.82855 - 0.322424i) q^{15} +(0.173648 + 0.984808i) q^{16} +(1.48613 - 0.262046i) q^{17} +(0.866025 + 0.500000i) q^{18} +(3.55738 + 2.51894i) q^{19} -1.85676i q^{20} +(2.45897 + 0.976449i) q^{21} +(-1.50325 + 4.13015i) q^{22} +(4.53192 - 1.64948i) q^{23} +(-0.342020 + 0.939693i) q^{24} +(0.269577 - 1.52885i) q^{25} -2.34060i q^{26} +(0.500000 + 0.866025i) q^{27} +(-0.534619 + 2.59117i) q^{28} +(-2.32748 + 2.77379i) q^{29} +(0.928382 - 1.60800i) q^{30} +(3.92094 + 6.79127i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(-3.36693 + 2.82519i) q^{33} +(-0.262046 + 1.48613i) q^{34} +(1.81304 - 4.56573i) q^{35} +(-0.766044 + 0.642788i) q^{36} +(3.69593 - 2.13384i) q^{37} +(-3.58373 + 2.48131i) q^{38} +(1.17030 - 2.02702i) q^{39} +(1.74479 + 0.635050i) q^{40} +(1.02055 + 0.371449i) q^{41} +(-1.75858 + 1.97671i) q^{42} +(1.02112 + 5.79105i) q^{43} +(-3.36693 - 2.82519i) q^{44} +(1.60800 - 0.928382i) q^{45} +4.82277i q^{46} +(-7.96080 - 1.40370i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(-3.84476 + 5.84960i) q^{49} +(1.34444 + 0.776215i) q^{50} +(-0.970005 + 1.15601i) q^{51} +(2.19945 + 0.800533i) q^{52} +(1.37488 - 1.63852i) q^{53} +(-0.984808 + 0.173648i) q^{54} +(5.24571 + 6.25160i) q^{55} +(-2.25206 - 1.38861i) q^{56} +(-4.34425 + 0.357015i) q^{57} +(-1.81046 - 3.13581i) q^{58} +(1.79842 + 10.1994i) q^{59} +(1.19350 + 1.42236i) q^{60} +(-1.62907 - 4.47582i) q^{61} +(-7.72275 + 1.36173i) q^{62} +(-2.51133 + 0.832593i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-3.76370 - 2.17297i) q^{65} +(-1.50325 - 4.13015i) q^{66} +(2.56080 + 7.03573i) q^{67} +(-1.30688 - 0.754530i) q^{68} +(-2.41139 + 4.17664i) q^{69} +(3.67029 + 3.26527i) q^{70} +(2.88380 - 0.508491i) q^{71} +(-0.342020 - 0.939693i) q^{72} +(0.0555272 + 0.0661747i) q^{73} +(0.741076 + 4.20285i) q^{74} +(0.776215 + 1.34444i) q^{75} +(-1.10596 - 4.21626i) q^{76} +(-5.52054 - 10.2347i) q^{77} +(1.50451 + 1.79301i) q^{78} +(7.34566 - 1.29524i) q^{79} +(-1.19350 + 1.42236i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-0.698095 + 0.831958i) q^{82} +(5.86812 + 3.38796i) q^{83} +(-1.25603 - 2.32860i) q^{84} +(2.14643 + 1.80107i) q^{85} +(-5.79105 - 1.02112i) q^{86} -3.62092i q^{87} +(3.80637 - 2.19761i) q^{88} +(-5.48267 - 4.60050i) q^{89} +(0.322424 + 1.82855i) q^{90} +(4.62670 + 4.11614i) q^{91} +(-4.53192 - 1.64948i) q^{92} +(-7.36896 - 2.68208i) q^{93} +(4.04180 - 7.00061i) q^{94} +(0.662892 + 8.06625i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-7.09820 + 5.95609i) q^{97} +(-4.18184 - 5.61358i) q^{98} +(0.763222 - 4.32845i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 12 q^{7} - 12 q^{10} - 12 q^{11} + 84 q^{12} + 24 q^{13} + 6 q^{14} + 6 q^{19} - 6 q^{21} + 12 q^{22} - 42 q^{23} - 30 q^{25} + 42 q^{27} + 6 q^{28} + 6 q^{31} + 12 q^{33} - 30 q^{34} - 42 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) $ 84 * q + 12 * q^7 - 12 * q^10 - 12 * q^11 + 84 * q^12 + 24 * q^13 + 6 * q^14 + 6 * q^19 - 6 * q^21 + 12 * q^22 - 42 * q^23 - 30 * q^25 + 42 * q^27 + 6 * q^28 + 6 * q^31 + 12 * q^33 - 30 * q^34 - 42 * q^35 - 18 * q^37 + 12 * q^38 + 12 * q^40 + 36 * q^41 + 18 * q^42 + 12 * q^43 + 12 * q^44 - 18 * q^45 + 18 * q^47 - 24 * q^49 + 18 * q^51 - 24 * q^52 + 60 * q^53 - 30 * q^55 - 18 * q^56 + 6 * q^57 + 48 * q^59 - 12 * q^62 - 6 * q^63 + 42 * q^64 + 108 * q^65 + 12 * q^66 + 42 * q^67 + 6 * q^69 + 18 * q^70 + 42 * q^71 - 48 * q^73 - 18 * q^74 - 48 * q^75 + 18 * q^76 - 96 * q^77 - 12 * q^78 - 60 * q^79 - 6 * q^82 + 54 * q^83 + 12 * q^84 - 24 * q^85 - 12 * q^86 - 24 * q^89 + 6 * q^90 + 24 * q^91 + 42 * q^92 - 36 * q^93 + 18 * q^94 - 12 * q^95 - 78 * q^97 + 24 * q^98 + 6 * q^99

Character values

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

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{18}\right)$	$1$

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 $

$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$	1.19350	+	1.42236i	0.533751	+	0.636100i	0.963775	−	0.266718i	$-0.0859391\pi$
$5$	1.19350	+	1.42236i	0.533751	+	0.636100i	−0.430023	+	0.902818i	$0.641495\pi$
$6$	−0.342020	−	0.939693i	−0.139629	−	0.383628i
$7$	−1.25603	−	2.32860i	−0.474736	−	0.880128i
$7$	−1.25603	−	2.32860i	−0.474736	−	0.880128i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	−1.74479	+	0.635050i	−0.551750	+	0.200821i
$11$	4.39522			1.32521			0.662604	−	0.748970i	$-0.269451\pi$
$11$	4.39522			1.32521			0.662604	+	0.748970i	$0.269451\pi$
$12$	1.00000			0.288675
$13$	−2.19945	+	0.800533i	−0.610017	+	0.222028i	−0.628511	−	0.777801i	$-0.716335\pi$
$13$	−2.19945	+	0.800533i	−0.610017	+	0.222028i	0.0184937	+	0.999829i	$0.494113\pi$
$14$	2.61776	−	0.383856i	0.699625	−	0.102590i
$15$	−1.82855	−	0.322424i	−0.472131	−	0.0832494i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	1.48613	−	0.262046i	0.360440	−	0.0635554i	0.00950449	−	0.999955i	$-0.496975\pi$
$17$	1.48613	−	0.262046i	0.360440	−	0.0635554i	0.350936	+	0.936399i	$0.385863\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	3.55738	+	2.51894i	0.816118	+	0.577885i
$19$	3.55738	+	2.51894i	0.816118	+	0.577885i
$20$		−	1.85676i		−	0.415185i
$21$	2.45897	+	0.976449i	0.536592	+	0.213079i
$22$	−1.50325	+	4.13015i	−0.320495	+	0.880552i
$23$	4.53192	−	1.64948i	0.944971	−	0.343941i	0.176844	−	0.984239i	$-0.443411\pi$
$23$	4.53192	−	1.64948i	0.944971	−	0.343941i	0.768127	+	0.640297i	$0.221189\pi$
$24$	−0.342020	+	0.939693i	−0.0698146	+	0.191814i
$25$	0.269577	−	1.52885i	0.0539153	−	0.305769i
$26$		−	2.34060i		−	0.459030i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−0.534619	+	2.59117i	−0.101033	+	0.489686i
$29$	−2.32748	+	2.77379i	−0.432203	+	0.515080i	−0.937557	−	0.347833i	$-0.886918\pi$
$29$	−2.32748	+	2.77379i	−0.432203	+	0.515080i	0.505353	+	0.862912i	$0.331362\pi$
$30$	0.928382	−	1.60800i	0.169499	−	0.293580i
$31$	3.92094	+	6.79127i	0.704222	+	1.21975i	0.966971	+	0.254885i	$0.0820375\pi$
$31$	3.92094	+	6.79127i	0.704222	+	1.21975i	−0.262749	+	0.964864i	$0.584629\pi$
$32$	−0.984808	−	0.173648i	−0.174091	−	0.0306970i
$33$	−3.36693	+	2.82519i	−0.586108	+	0.491803i
$34$	−0.262046	+	1.48613i	−0.0449404	+	0.254870i
$35$	1.81304	−	4.56573i	0.306459	−	0.771749i
$36$	−0.766044	+	0.642788i	−0.127674	+	0.107131i
$37$	3.69593	−	2.13384i	0.607606	−	0.350802i	−0.164422	−	0.986390i	$-0.552576\pi$
$37$	3.69593	−	2.13384i	0.607606	−	0.350802i	0.772028	+	0.635588i	$0.219242\pi$
$38$	−3.58373	+	2.48131i	−0.581357	+	0.402522i
$39$	1.17030	−	2.02702i	0.187398	−	0.324583i
$40$	1.74479	+	0.635050i	0.275875	+	0.100410i
$41$	1.02055	+	0.371449i	0.159383	+	0.0580106i	0.420479	−	0.907302i	$-0.361862\pi$
$41$	1.02055	+	0.371449i	0.159383	+	0.0580106i	−0.261097	+	0.965313i	$0.584084\pi$
$42$	−1.75858	+	1.97671i	−0.271355	+	0.305013i
$43$	1.02112	+	5.79105i	0.155719	+	0.883127i	0.958125	+	0.286349i	$0.0924416\pi$
$43$	1.02112	+	5.79105i	0.155719	+	0.883127i	−0.802406	+	0.596778i	$0.796447\pi$
$44$	−3.36693	−	2.82519i	−0.507584	−	0.425914i
$45$	1.60800	−	0.928382i	0.239707	−	0.138395i
$46$			4.82277i			0.711079i
$47$	−7.96080	−	1.40370i	−1.16120	−	0.204751i	−0.440341	−	0.897831i	$-0.645142\pi$
$47$	−7.96080	−	1.40370i	−1.16120	−	0.204751i	−0.720861	+	0.693079i	$0.756253\pi$
$48$	−0.766044	−	0.642788i	−0.110569	−	0.0927784i
$49$	−3.84476	+	5.84960i	−0.549252	+	0.835657i
$50$	1.34444	+	0.776215i	0.190133	+	0.109773i
$51$	−0.970005	+	1.15601i	−0.135828	+	0.161873i
$52$	2.19945	+	0.800533i	0.305009	+	0.111014i
$53$	1.37488	−	1.63852i	0.188854	−	0.225068i	−0.663307	−	0.748348i	$-0.730847\pi$
$53$	1.37488	−	1.63852i	0.188854	−	0.225068i	0.852161	+	0.523280i	$0.175292\pi$
$54$	−0.984808	+	0.173648i	−0.134015	+	0.0236305i
$55$	5.24571	+	6.25160i	0.707332	+	0.842965i
$56$	−2.25206	−	1.38861i	−0.300944	−	0.185561i
$57$	−4.34425	+	0.357015i	−0.575410	+	0.0472878i
$58$	−1.81046	−	3.13581i	−0.237725	−	0.411752i
$59$	1.79842	+	10.1994i	0.234134	+	1.32784i	0.844429	+	0.535668i	$0.179940\pi$
$59$	1.79842	+	10.1994i	0.234134	+	1.32784i	−0.610294	+	0.792175i	$0.708949\pi$
$60$	1.19350	+	1.42236i	0.154081	+	0.183626i
$61$	−1.62907	−	4.47582i	−0.208581	−	0.573070i	0.790651	−	0.612267i	$-0.209742\pi$
$61$	−1.62907	−	4.47582i	−0.208581	−	0.573070i	−0.999232	+	0.0391968i	$0.987520\pi$
$62$	−7.72275	+	1.36173i	−0.980791	+	0.172940i
$63$	−2.51133	+	0.832593i	−0.316398	+	0.104897i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−3.76370	−	2.17297i	−0.466830	−	0.269524i
$66$	−1.50325	−	4.13015i	−0.185038	−	0.508387i
$67$	2.56080	+	7.03573i	0.312851	+	0.859551i	0.992078	+	0.125623i	$0.0400930\pi$
$67$	2.56080	+	7.03573i	0.312851	+	0.859551i	−0.679227	+	0.733928i	$0.737685\pi$
$68$	−1.30688	−	0.754530i	−0.158483	−	0.0915002i
$69$	−2.41139	+	4.17664i	−0.290297	+	0.502809i
$70$	3.67029	+	3.26527i	0.438683	+	0.390274i
$71$	2.88380	−	0.508491i	0.342244	−	0.0603468i	0.000115191	−	1.00000i	$-0.499963\pi$
$71$	2.88380	−	0.508491i	0.342244	−	0.0603468i	0.342128	+	0.939653i	$0.388852\pi$
$72$	−0.342020	−	0.939693i	−0.0403075	−	0.110744i
$73$	0.0555272	+	0.0661747i	0.00649897	+	0.00774517i	0.769284	−	0.638907i	$-0.220613\pi$
$73$	0.0555272	+	0.0661747i	0.00649897	+	0.00774517i	−0.762785	+	0.646652i	$0.776169\pi$
$74$	0.741076	+	4.20285i	0.0861483	+	0.488572i
$75$	0.776215	+	1.34444i	0.0896296	+	0.155243i
$76$	−1.10596	−	4.21626i	−0.126863	−	0.483638i
$77$	−5.52054	−	10.2347i	−0.629124	−	1.16635i
$78$	1.50451	+	1.79301i	0.170352	+	0.203018i
$79$	7.34566	−	1.29524i	0.826451	−	0.145726i	0.255604	−	0.966782i	$-0.417726\pi$
$79$	7.34566	−	1.29524i	0.826451	−	0.145726i	0.570848	+	0.821056i	$0.306615\pi$
$80$	−1.19350	+	1.42236i	−0.133438	+	0.159025i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	−0.698095	+	0.831958i	−0.0770917	+	0.0918744i
$83$	5.86812	+	3.38796i	0.644109	+	0.371877i	0.786196	−	0.617978i	$-0.212048\pi$
$83$	5.86812	+	3.38796i	0.644109	+	0.371877i	−0.142086	+	0.989854i	$0.545381\pi$
$84$	−1.25603	−	2.32860i	−0.137044	−	0.254071i
$85$	2.14643	+	1.80107i	0.232813	+	0.195353i
$86$	−5.79105	−	1.02112i	−0.624465	−	0.110110i
$87$		−	3.62092i		−	0.388204i
$88$	3.80637	−	2.19761i	0.405761	−	0.234266i
$89$	−5.48267	−	4.60050i	−0.581161	−	0.487652i	0.304167	−	0.952619i	$-0.401622\pi$
$89$	−5.48267	−	4.60050i	−0.581161	−	0.487652i	−0.885328	+	0.464966i	$0.846066\pi$
$90$	0.322424	+	1.82855i	0.0339864	+	0.192747i
$91$	4.62670	+	4.11614i	0.485010	+	0.431489i
$92$	−4.53192	−	1.64948i	−0.472486	−	0.171971i
$93$	−7.36896	−	2.68208i	−0.764126	−	0.278119i
$94$	4.04180	−	7.00061i	0.416880	−	0.722058i
$95$	0.662892	+	8.06625i	0.0680113	+	0.827580i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	−7.09820	+	5.95609i	−0.720713	+	0.604750i	−0.927582	−	0.373619i	$-0.878117\pi$
$97$	−7.09820	+	5.95609i	−0.720713	+	0.604750i	0.206870	+	0.978369i	$0.433672\pi$
$98$	−4.18184	−	5.61358i	−0.422429	−	0.567057i
$99$	0.763222	−	4.32845i	0.0767067	−	0.435025i
$100$	−1.18923	+	0.997883i	−0.118923	+	0.0997883i
$101$	16.2807	+	2.87073i	1.61999	+	0.285648i	0.908763	−	0.417313i	$-0.137028\pi$
$101$	16.2807	+	2.87073i	1.61999	+	0.285648i	0.711229	+	0.702961i	$0.248139\pi$
$102$	−0.754530	−	1.30688i	−0.0747096	−	0.129401i
$103$	2.83605	−	4.91219i	0.279445	−	0.484012i	−0.691802	−	0.722087i	$-0.743183\pi$
$103$	2.83605	−	4.91219i	0.279445	−	0.484012i	0.971247	+	0.238075i	$0.0765163\pi$
$104$	−1.50451	+	1.79301i	−0.147529	+	0.175819i
$105$	1.54593	+	4.66295i	0.150867	+	0.455057i
$106$	1.06947	+	1.85237i	0.103876	+	0.179918i
$107$			3.00843i			0.290836i	0.989370	+	0.145418i	$0.0464526\pi$
$107$			3.00843i			0.290836i	−0.989370	+	0.145418i	$0.953547\pi$
$108$	0.173648	−	0.984808i	0.0167093	−	0.0947632i
$109$	−3.79750	+	10.4335i	−0.363734	+	0.999352i	0.613963	+	0.789335i	$0.289574\pi$
$109$	−3.79750	+	10.4335i	−0.363734	+	0.999352i	−0.977698	+	0.210017i	$0.932648\pi$
$110$	−7.66872	+	2.79119i	−0.731184	+	0.266129i
$111$	−1.45963	+	4.01031i	−0.138542	+	0.380642i
$112$	2.07512	−	1.64131i	0.196080	−	0.155089i
$113$		−	9.76764i		−	0.918863i	−0.888213	−	0.459431i	$-0.848053\pi$
$113$		−	9.76764i		−	0.918863i	0.888213	−	0.459431i	$-0.151947\pi$
$114$	1.15034	−	4.20437i	0.107739	−	0.393775i
$115$	7.75504	+	4.47737i	0.723161	+	0.417517i
$116$	3.56591	−	0.628767i	0.331087	−	0.0583795i
$117$	0.406442	+	2.30504i	0.0375755	+	0.213101i
$118$	−10.1994	−	1.79842i	−0.938927	−	0.165558i
$119$	−2.47683	−	3.13148i	−0.227051	−	0.287062i
$120$	−1.74479	+	0.635050i	−0.159277	+	0.0579719i
$121$	8.31795			0.756177
$122$	4.76307			0.431228
$123$	−1.02055	+	0.371449i	−0.0920197	+	0.0334924i
$124$	1.36173	−	7.72275i	0.122287	−	0.693524i
$125$	10.5363	−	6.08316i	0.942398	−	0.544094i
$126$	0.0765441	−	2.64464i	0.00681909	−	0.235604i
$127$	−3.22571	−	8.86257i	−0.286236	−	0.786426i	−0.996585	−	0.0825765i	$-0.973685\pi$
$127$	−3.22571	−	8.86257i	−0.286236	−	0.786426i	0.710349	−	0.703850i	$-0.248537\pi$
$128$	0.642788	+	0.766044i	0.0568149	+	0.0677094i
$129$	−4.50464	−	3.77984i	−0.396611	−	0.332796i
$130$	3.32919	−	2.79352i	0.291989	−	0.245008i
$131$	1.93440	−	5.31471i	0.169009	−	0.464349i	−0.826054	−	0.563591i	$-0.809420\pi$
$131$	1.93440	−	5.31471i	0.169009	−	0.464349i	0.995063	+	0.0992420i	$0.0316418\pi$
$132$	4.39522			0.382555
$133$	1.39743	−	11.4476i	0.121173	−	0.992631i
$134$	−7.48727			−0.646802
$135$	−0.635050	+	1.74479i	−0.0546564	+	0.150167i
$136$	1.15601	−	0.970005i	0.0991268	−	0.0831773i
$137$	−3.06144	−	2.56885i	−0.261557	−	0.219472i	0.502573	−	0.864535i	$-0.332387\pi$
$137$	−3.06144	−	2.56885i	−0.261557	−	0.219472i	−0.764130	+	0.645063i	$0.776831\pi$
$138$	−3.10002	−	3.69446i	−0.263891	−	0.314493i
$139$	3.67770	+	10.1044i	0.311939	+	0.857044i	0.992265	+	0.124135i	$0.0396157\pi$
$139$	3.67770	+	10.1044i	0.311939	+	0.857044i	−0.680327	+	0.732909i	$0.738162\pi$
$140$	−4.32366	+	2.33216i	−0.365416	+	0.197103i
$141$	7.00061	−	4.04180i	0.589558	−	0.340381i
$142$	−0.508491	+	2.88380i	−0.0426716	+	0.242003i
$143$	−9.66705	+	3.51852i	−0.808400	+	0.294233i
$144$	1.00000			0.0833333
$145$	−6.72320			−0.558331
$146$	−0.0811753	+	0.0295454i	−0.00671812	+	0.00244519i
$147$	−0.814789	−	6.95242i	−0.0672027	−	0.573426i
$148$	−4.20285	−	0.741076i	−0.345472	−	0.0609161i
$149$	−3.51055	−	19.9093i	−0.287595	−	1.63103i	−0.695865	−	0.718173i	$-0.744979\pi$
$149$	−3.51055	−	19.9093i	−0.287595	−	1.63103i	0.408270	−	0.912861i	$-0.366132\pi$
$150$	−1.52885	+	0.269577i	−0.124830	+	0.0220108i
$151$	−11.7108	−	6.76126i	−0.953015	−	0.550224i	−0.0589990	−	0.998258i	$-0.518791\pi$
$151$	−11.7108	−	6.76126i	−0.953015	−	0.550224i	−0.894016	+	0.448034i	$0.852124\pi$
$152$	4.34025	+	0.402781i	0.352041	+	0.0326698i
$153$		−	1.50906i		−	0.122000i
$154$	11.5056	−	1.68713i	0.927149	−	0.135953i
$155$	−4.97999	+	13.6824i	−0.400003	+	1.09900i
$156$	−2.19945	+	0.800533i	−0.176097	+	0.0640940i
$157$	6.56530	−	18.0380i	0.523968	−	1.43959i	−0.342100	−	0.939663i	$-0.611138\pi$
$157$	6.56530	−	18.0380i	0.523968	−	1.43959i	0.866068	−	0.499926i	$-0.166639\pi$
$158$	−1.29524	+	7.34566i	−0.103044	+	0.584389i
$159$			2.13893i			0.169628i
$160$	−0.928382	−	1.60800i	−0.0733950	−	0.127124i
$161$	−9.53324	−	8.48123i	−0.751324	−	0.668415i
$162$	0.642788	−	0.766044i	0.0505022	−	0.0601861i
$163$	1.62040	−	2.80662i	0.126920	−	0.219831i	−0.795562	−	0.605872i	$-0.792824\pi$
$163$	1.62040	−	2.80662i	0.126920	−	0.219831i	0.922482	+	0.386041i	$0.126158\pi$
$164$	−0.543022	−	0.940541i	−0.0424029	−	0.0734440i
$165$	−8.03690	−	1.41712i	−0.625672	−	0.110323i
$166$	−5.19065	+	4.35548i	−0.402873	+	0.338050i
$167$	2.52565	−	14.3237i	0.195441	−	1.10840i	−0.716349	−	0.697742i	$-0.754188\pi$
$167$	2.52565	−	14.3237i	0.195441	−	1.10840i	0.911790	−	0.410658i	$-0.134701\pi$
$168$	2.61776	−	0.383856i	0.201964	−	0.0296152i
$169$	−5.76186	+	4.83478i	−0.443220	+	0.371906i
$170$	−2.42658	+	1.40098i	−0.186110	+	0.107451i
$171$	3.09841	−	3.06592i	0.236941	−	0.234457i
$172$	2.94019	−	5.09256i	0.224188	−	0.388304i
$173$	−4.95890	−	1.80489i	−0.377018	−	0.137223i	0.146558	−	0.989202i	$-0.453180\pi$
$173$	−4.95890	−	1.80489i	−0.377018	−	0.137223i	−0.523577	+	0.851979i	$0.675403\pi$
$174$	3.40256	+	1.23843i	0.257947	+	0.0938850i
$175$	−3.89867	+	1.29254i	−0.294712	+	0.0977071i
$176$	0.763222	+	4.32845i	0.0575300	+	0.326269i
$177$	−7.93369	−	6.65716i	−0.596333	−	0.500382i
$178$	6.19824	−	3.57856i	0.464578	−	0.268224i
$179$		−	17.9546i		−	1.34199i	−0.741462	−	0.670994i	$-0.765867\pi$
$179$		−	17.9546i		−	1.34199i	0.741462	−	0.670994i	$-0.234133\pi$
$180$	−1.82855	−	0.322424i	−0.136292	−	0.0240320i
$181$	4.12716	+	3.46310i	0.306769	+	0.257410i	0.783155	−	0.621826i	$-0.213609\pi$
$181$	4.12716	+	3.46310i	0.306769	+	0.257410i	−0.476386	+	0.879236i	$0.658053\pi$
$182$	−5.45033	+	2.93987i	−0.404005	+	0.217918i
$183$	4.12494	+	2.38154i	0.304924	+	0.176048i
$184$	3.10002	−	3.69446i	0.228536	−	0.272359i
$185$	7.44620	+	2.71020i	0.547456	+	0.199258i
$186$	5.04067	−	6.00723i	0.369600	−	0.440472i
$187$	6.53188	−	1.15175i	0.477659	−	0.0842241i
$188$	5.19604	+	6.19240i	0.378960	+	0.451627i
$189$	1.38861	−	2.25206i	0.101007	−	0.163813i
$190$	−7.80652	−	2.13591i	−0.566344	−	0.154955i
$191$	−2.15055	−	3.72486i	−0.155608	−	0.269522i	0.777672	−	0.628670i	$-0.216400\pi$
$191$	−2.15055	−	3.72486i	−0.155608	−	0.269522i	−0.933280	+	0.359149i	$0.883067\pi$
$192$	0.173648	+	0.984808i	0.0125320	+	0.0710724i
$193$	3.34452	+	3.98584i	0.240744	+	0.286907i	0.872865	−	0.487963i	$-0.162260\pi$
$193$	3.34452	+	3.98584i	0.240744	+	0.286907i	−0.632121	+	0.774870i	$0.717815\pi$
$194$	−3.16917	−	8.70723i	−0.227533	−	0.625142i
$195$	4.27992	−	0.754666i	0.306492	−	0.0540427i
$196$	6.70531	−	2.00969i	0.478951	−	0.143549i
$197$	10.3521	−	17.9304i	0.737558	−	1.27749i	−0.216034	−	0.976386i	$-0.569312\pi$
$197$	10.3521	−	17.9304i	0.737558	−	1.27749i	0.953592	−	0.301102i	$-0.0973544\pi$
$198$	3.80637	+	2.19761i	0.270507	+	0.156177i
$199$	9.12123	+	25.0604i	0.646587	+	1.77648i	0.629969	+	0.776620i	$0.283068\pi$
$199$	9.12123	+	25.0604i	0.646587	+	1.77648i	0.0166175	+	0.999862i	$0.494710\pi$
$200$	−0.530962	−	1.45881i	−0.0375447	−	0.103153i
$201$	−6.48417	−	3.74363i	−0.457358	−	0.264056i
$202$	−8.26593	+	14.3170i	−0.581589	+	1.00734i
$203$	9.38244	+	1.93581i	0.658518	+	0.135868i
$204$	1.48613	−	0.262046i	0.104050	−	0.0183469i
$205$	0.689693	+	1.89491i	0.0481702	+	0.132347i
$206$	3.64596	+	4.34509i	0.254026	+	0.302737i
$207$	−0.837465	−	4.74950i	−0.0582079	−	0.330113i
$208$	−1.17030	−	2.02702i	−0.0811458	−	0.140549i
$209$	15.6354	+	11.0713i	1.08153	+	0.765818i
$210$	−4.91048	−	0.142124i	−0.338855	−	0.00980751i
$211$	12.1019	+	14.4225i	0.833128	+	0.992884i	0.999976	+	0.00690098i	$0.00219667\pi$
$211$	12.1019	+	14.4225i	0.833128	+	0.992884i	−0.166848	+	0.985983i	$0.553359\pi$
$212$	−2.10644	+	0.371422i	−0.144671	+	0.0255093i
$213$	−1.88226	+	2.24319i	−0.128971	+	0.153701i
$214$	−2.82700	−	1.02894i	−0.193250	−	0.0703371i
$215$	−7.01827	+	8.36405i	−0.478642	+	0.570423i
$216$	0.866025	+	0.500000i	0.0589256	+	0.0340207i
$217$	10.8893	−	17.6604i	0.739216	−	1.19886i
$218$	−8.50550	−	7.13696i	−0.576065	−	0.483376i
$219$	−0.0850726	−	0.0150006i	−0.00574867	−	0.00101365i
$220$		−	8.16088i		−	0.550206i
$221$	−3.05890	+	1.76606i	−0.205764	+	0.118798i
$222$	−3.26924	−	2.74322i	−0.219417	−	0.184113i
$223$	−1.39048	−	7.88583i	−0.0931137	−	0.528074i	−0.995309	−	0.0967465i	$-0.969156\pi$
$223$	−1.39048	−	7.88583i	−0.0931137	−	0.528074i	0.902195	−	0.431328i	$-0.141955\pi$
$224$	0.832593	+	2.51133i	0.0556300	+	0.167795i
$225$	−1.45881	−	0.530962i	−0.0972538	−	0.0353975i
$226$	9.17858	+	3.34073i	0.610550	+	0.222222i
$227$	−9.24499	+	16.0128i	−0.613611	+	1.06281i	0.377015	+	0.926207i	$0.376951\pi$
$227$	−9.24499	+	16.0128i	−0.613611	+	1.06281i	−0.990626	+	0.136599i	$0.956383\pi$
$228$	3.55738	+	2.51894i	0.235593	+	0.166821i
$229$	−12.8730	+	7.43223i	−0.850672	+	0.491136i	−0.860877	−	0.508812i	$-0.830085\pi$
$229$	−12.8730	+	7.43223i	−0.850672	+	0.491136i	0.0102058	+	0.999948i	$0.496751\pi$
$230$	−6.85973	+	5.75600i	−0.452317	+	0.379539i
$231$	10.8077	+	4.29171i	0.711096	+	0.282374i
$232$	−0.628767	+	3.56591i	−0.0412806	+	0.234114i
$233$	20.0912	−	16.8585i	1.31622	−	1.10444i	0.329125	−	0.944286i	$-0.393246\pi$
$233$	20.0912	−	16.8585i	1.31622	−	1.10444i	0.987092	−	0.160152i	$-0.0511983\pi$
$234$	−2.30504	−	0.406442i	−0.150685	−	0.0265699i
$235$	−7.50467	−	12.9985i	−0.489551	−	0.847927i
$236$	5.17835	−	8.96916i	0.337082	−	0.583843i
$237$	−4.79454	+	5.71391i	−0.311439	+	0.371158i
$238$	3.78975	−	1.25643i	0.245653	−	0.0814425i
$239$	−7.43787	−	12.8828i	−0.481116	−	0.833317i	0.518650	−	0.854987i	$-0.326435\pi$
$239$	−7.43787	−	12.8828i	−0.481116	−	0.833317i	−0.999765	+	0.0216702i	$0.993102\pi$
$240$		−	1.85676i		−	0.119854i
$241$	1.86656	−	10.5858i	0.120235	−	0.681889i	−0.863789	−	0.503854i	$-0.831915\pi$
$241$	1.86656	−	10.5858i	0.120235	−	0.681889i	0.984024	−	0.178035i	$-0.0569740\pi$
$242$	−2.84491	+	7.81631i	−0.182877	+	0.502452i
$243$	0.939693	−	0.342020i	0.0602813	−	0.0219406i
$244$	−1.62907	+	4.47582i	−0.104290	+	0.286535i
$245$	−12.9090	+	1.51287i	−0.824725	+	0.0966538i
$246$		−	1.08604i		−	0.0692436i
$247$	−9.84076	−	2.69249i	−0.626153	−	0.171319i
$248$	6.79127	+	3.92094i	0.431246	+	0.248980i
$249$	−6.67298	+	1.17663i	−0.422883	+	0.0745656i
$250$	2.11266	+	11.9815i	0.133616	+	0.757775i
$251$	21.0875	+	3.71830i	1.33103	+	0.234697i	0.793513	−	0.608554i	$-0.208250\pi$
$251$	21.0875	+	3.71830i	1.33103	+	0.234697i	0.537520	+	0.843251i	$0.319361\pi$
$252$	2.45897	+	0.976449i	0.154901	+	0.0615105i
$253$	19.9188	−	7.24985i	1.25228	−	0.455794i
$254$	9.43135			0.591776
$255$	−2.80197			−0.175466
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−2.67676	+	15.1807i	−0.166972	+	0.946944i	0.780036	+	0.625734i	$0.215201\pi$
$257$	−2.67676	+	15.1807i	−0.166972	+	0.946944i	−0.947008	+	0.321210i	$0.895910\pi$
$258$	5.09256	−	2.94019i	0.317049	−	0.183048i
$259$	−9.61107	−	5.92616i	−0.597203	−	0.368234i
$260$	1.48640	+	4.08385i	0.0921827	+	0.253270i
$261$	2.32748	+	2.77379i	0.144068	+	0.171693i
$262$	4.33259	+	3.63548i	0.267668	+	0.224601i
$263$	7.56140	−	6.34477i	0.466256	−	0.391235i	−0.379171	−	0.925327i	$-0.623791\pi$
$263$	7.56140	−	6.34477i	0.466256	−	0.391235i	0.845427	+	0.534092i	$0.179346\pi$
$264$	−1.50325	+	4.13015i	−0.0925188	+	0.254193i
$265$	3.97149			0.243967
$266$	10.2793	+	5.22846i	0.630262	+	0.320578i
$267$	7.15711			0.438008
$268$	2.56080	−	7.03573i	0.156426	−	0.429776i
$269$	−12.8279	+	10.7639i	−0.782133	+	0.656288i	−0.943785	−	0.330560i	$-0.892762\pi$
$269$	−12.8279	+	10.7639i	−0.782133	+	0.656288i	0.161652	+	0.986848i	$0.448318\pi$
$270$	−1.42236	−	1.19350i	−0.0865623	−	0.0726344i
$271$	−2.46212	−	2.93424i	−0.149563	−	0.178242i	0.686061	−	0.727544i	$-0.259338\pi$
$271$	−2.46212	−	2.93424i	−0.149563	−	0.178242i	−0.835624	+	0.549302i	$0.814894\pi$
$272$	0.516129	+	1.41805i	0.0312949	+	0.0859821i
$273$	−6.19006	−	0.179159i	−0.374640	−	0.0108432i
$274$	3.46101	−	1.99821i	0.209087	−	0.120717i
$275$	1.18485	−	6.71961i	0.0714491	−	0.405208i
$276$	4.53192	−	1.64948i	0.272790	−	0.0992873i
$277$	−13.0088			−0.781626			−0.390813	−	0.920470i	$-0.627806\pi$
$277$	−13.0088			−0.781626			−0.390813	+	0.920470i	$0.627806\pi$
$278$	−10.7529			−0.644915
$279$	7.36896	−	2.68208i	0.441168	−	0.160572i
$280$	−0.712730	−	4.86056i	−0.0425938	−	0.290474i
$281$	11.4464	+	2.01830i	0.682833	+	0.120402i	0.504295	−	0.863531i	$-0.331752\pi$
$281$	11.4464	+	2.01830i	0.682833	+	0.120402i	0.178537	+	0.983933i	$0.442863\pi$
$282$	1.40370	+	7.96080i	0.0835893	+	0.474059i
$283$	−23.5853	+	4.15872i	−1.40200	+	0.247210i	−0.822965	−	0.568093i	$-0.807681\pi$
$283$	−23.5853	+	4.15872i	−1.40200	+	0.247210i	−0.579034	+	0.815303i	$0.696570\pi$
$284$	−2.53597	−	1.46414i	−0.150482	−	0.0868808i
$285$	−5.69269	−	5.75301i	−0.337206	−	0.340779i
$286$		−	10.2875i		−	0.608310i
$287$	−0.416885	−	2.84300i	−0.0246079	−	0.167817i
$288$	−0.342020	+	0.939693i	−0.0201537	+	0.0553719i
$289$	−13.8348	+	5.03547i	−0.813815	+	0.296204i
$290$	2.29947	−	6.31774i	0.135029	−	0.370990i
$291$	1.60903	−	9.12527i	0.0943230	−	0.534933i
$292$		−	0.0863850i		−	0.00505530i
$293$	3.39641	+	5.88276i	0.198420	+	0.343674i	0.948016	−	0.318221i	$-0.103086\pi$
$293$	3.39641	+	5.88276i	0.198420	+	0.343674i	−0.749596	+	0.661896i	$0.769752\pi$
$294$	6.81181	+	1.61222i	0.397273	+	0.0940263i
$295$	−12.3608	+	14.7310i	−0.719671	+	0.857671i
$296$	2.13384	−	3.69593i	0.124027	−	0.214821i
$297$	2.19761	+	3.80637i	0.127518	+	0.220868i
$298$	19.9093	+	3.51055i	1.15332	+	0.203361i
$299$	−8.64726	+	7.25591i	−0.500084	+	0.419620i
$300$	0.269577	−	1.52885i	0.0155640	−	0.0882679i
$301$	12.2025	−	9.65153i	0.703340	−	0.556305i
$302$	10.3589	−	8.69211i	0.596085	−	0.500175i
$303$	−14.3170	+	8.26593i	−0.822491	+	0.474866i
$304$	−1.86294	+	3.94074i	−0.106847	+	0.226017i
$305$	4.42195	−	7.65904i	0.253200	−	0.438555i
$306$	1.41805	+	0.516129i	0.0810647	+	0.0295051i
$307$	−5.21665	−	1.89870i	−0.297730	−	0.108365i	0.188836	−	0.982009i	$-0.439528\pi$
$307$	−5.21665	−	1.89870i	−0.297730	−	0.108365i	−0.486566	+	0.873644i	$0.661751\pi$
$308$	−2.34977	+	11.3888i	−0.133890	+	0.648936i
$309$	0.984951	+	5.58594i	0.0560319	+	0.317773i
$310$	−11.1540	−	9.35933i	−0.633505	−	0.531574i
$311$	−24.7226	+	14.2736i	−1.40189	+	0.809382i	−0.994587	−	0.103910i	$-0.966865\pi$
$311$	−24.7226	+	14.2736i	−1.40189	+	0.809382i	−0.407305	+	0.913292i	$0.633531\pi$
$312$		−	2.34060i		−	0.132511i
$313$	−25.8938	−	4.56578i	−1.46360	−	0.258073i	−0.615598	−	0.788060i	$-0.711086\pi$
$313$	−25.8938	−	4.56578i	−1.46360	−	0.258073i	−0.848006	+	0.529987i	$0.822197\pi$
$314$	14.7047	+	12.3387i	0.829835	+	0.696314i
$315$	−4.18154	−	2.57832i	−0.235603	−	0.145272i
$316$	−6.45967	−	3.72949i	−0.363385	−	0.209800i
$317$	−6.01894	+	7.17310i	−0.338058	+	0.402881i	−0.908113	−	0.418725i	$-0.862477\pi$
$317$	−6.01894	+	7.17310i	−0.338058	+	0.402881i	0.570056	+	0.821606i	$0.306922\pi$
$318$	−2.00994	−	0.731558i	−0.112712	−	0.0410237i
$319$	−10.2298	+	12.1914i	−0.572759	+	0.682588i
$320$	1.82855	−	0.322424i	0.102219	−	0.0180240i
$321$	−1.93378	−	2.30459i	−0.107933	−	0.128630i
$322$	11.2303	−	6.05756i	0.625841	−	0.337575i
$323$	5.94682	+	2.81129i	0.330890	+	0.156425i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	0.630972	+	3.57842i	0.0350000	+	0.198495i
$326$	2.08315	+	2.48260i	0.115375	+	0.137499i
$327$	−3.79750	−	10.4335i	−0.210002	−	0.576976i
$328$	1.06954	−	0.188590i	0.0590557	−	0.0104131i
$329$	6.73036	+	20.3006i	0.371057	+	1.11921i
$330$	4.08044	−	7.06753i	0.224621	−	0.389055i
$331$	−20.4176	−	11.7881i	−1.12225	−	0.647934i	−0.180279	−	0.983615i	$-0.557700\pi$
$331$	−20.4176	−	11.7881i	−1.12225	−	0.647934i	−0.941976	+	0.335681i	$0.891033\pi$
$332$	−2.31750	−	6.36728i	−0.127189	−	0.349450i
$333$	−1.45963	−	4.01031i	−0.0799875	−	0.219764i
$334$	12.5960	+	7.27232i	0.689224	+	0.397924i
$335$	−6.95104	+	12.0396i	−0.379776	+	0.657791i
$336$	−0.534619	+	2.59117i	−0.0291658	+	0.141360i
$337$	−27.5295	+	4.85419i	−1.49962	+	0.264424i	−0.862390	−	0.506245i	$-0.831033\pi$
$337$	−27.5295	+	4.85419i	−1.49962	+	0.264424i	−0.637235	+	0.770669i	$0.719922\pi$
$338$	−2.57253	−	7.06797i	−0.139927	−	0.384447i
$339$	6.27852	+	7.48245i	0.341002	+	0.406391i
$340$	−0.486557	−	2.75940i	−0.0263872	−	0.149649i
$341$	17.2334	+	29.8491i	0.933241	+	1.61642i
$342$	1.82131	+	3.96016i	0.0984850	+	0.214141i
$343$	18.4505	+	1.60563i	0.996235	+	0.0866960i
$344$	3.77984	+	4.50464i	0.203795	+	0.242874i
$345$	−8.81870	+	1.55498i	−0.474783	+	0.0837170i
$346$	3.39209	−	4.04253i	0.182360	−	0.217328i
$347$	−22.6602	−	8.24765i	−1.21646	−	0.442757i	−0.347523	−	0.937671i	$-0.612977\pi$
$347$	−22.6602	−	8.24765i	−1.21646	−	0.442757i	−0.868942	+	0.494914i	$0.835199\pi$
$348$	−2.32748	+	2.77379i	−0.124766	+	0.148691i
$349$	−22.2982	−	12.8738i	−1.19359	−	0.689121i	−0.234473	−	0.972123i	$-0.575337\pi$
$349$	−22.2982	−	12.8738i	−1.19359	−	0.689121i	−0.959119	+	0.283002i	$0.908670\pi$
$350$	0.118829	−	4.10563i	0.00635170	−	0.219455i
$351$	−1.79301	−	1.50451i	−0.0957036	−	0.0803048i
$352$	−4.32845	−	0.763222i	−0.230707	−	0.0406799i
$353$			9.18449i			0.488841i	0.969669	+	0.244421i	$0.0785978\pi$
$353$			9.18449i			0.488841i	−0.969669	+	0.244421i	$0.921402\pi$
$354$	8.96916	−	5.17835i	0.476706	−	0.275226i
$355$	4.16508	+	3.49492i	0.221060	+	0.185491i
$356$	1.24282	+	7.04838i	0.0658693	+	0.373563i
$357$	3.91024	+	0.806772i	0.206952	+	0.0426989i
$358$	16.8718	+	6.14083i	0.891702	+	0.324553i
$359$	−19.5477	−	7.11476i	−1.03169	−	0.375503i	−0.229963	−	0.973199i	$-0.573861\pi$
$359$	−19.5477	−	7.11476i	−1.03169	−	0.375503i	−0.801722	+	0.597697i	$0.796083\pi$
$360$	0.928382	−	1.60800i	0.0489300	−	0.0847493i
$361$	6.30985	+	17.9217i	0.332097	+	0.943245i
$362$	−4.66582	+	2.69381i	−0.245230	+	0.141584i
$363$	−6.37192	+	5.34667i	−0.334439	+	0.280628i
$364$	−0.898455	−	6.12713i	−0.0470919	−	0.321149i
$365$	−0.0278526	+	0.157960i	−0.00145787	+	0.00826799i
$366$	−3.64872	+	3.06164i	−0.190722	+	0.160035i
$367$	32.8299	+	5.78879i	1.71371	+	0.302173i	0.942449	−	0.334351i	$-0.108517\pi$
$367$	32.8299	+	5.78879i	1.71371	+	0.302173i	0.771257	+	0.636524i	$0.219628\pi$
$368$	2.41139	+	4.17664i	0.125702	+	0.217723i
$369$	0.543022	−	0.940541i	0.0282686	−	0.0489626i
$370$	−5.09350	+	6.07020i	−0.264799	+	0.315575i
$371$	−5.54234	−	1.14351i	−0.287744	−	0.0593683i
$372$	3.92094	+	6.79127i	0.203291	+	0.352111i
$373$		−	34.5581i		−	1.78935i	−0.446719	−	0.894674i	$-0.647408\pi$
$373$		−	34.5581i		−	1.78935i	0.446719	−	0.894674i	$-0.352592\pi$
$374$	−1.15175	+	6.53188i	−0.0595554	+	0.337756i
$375$	−4.16112	+	11.4326i	−0.214880	+	0.590377i
$376$	−7.59611	+	2.76476i	−0.391739	+	0.142581i
$377$	2.89867	−	7.96403i	0.149289	−	0.410169i
$378$	1.64131	+	2.07512i	0.0844198	+	0.106732i
$379$		−	16.1669i		−	0.830439i	−0.909721	−	0.415220i	$-0.863705\pi$
$379$		−	16.1669i		−	0.830439i	0.909721	−	0.415220i	$-0.136295\pi$
$380$	4.67708	−	6.60521i	0.239929	−	0.338840i
$381$	8.16779	+	4.71568i	0.418449	+	0.241591i
$382$	4.23576	−	0.746878i	0.216720	−	0.0382136i
$383$	−0.129878	−	0.736573i	−0.00663644	−	0.0376371i	0.981310	−	0.192435i	$-0.0616385\pi$
$383$	−0.129878	−	0.736573i	−0.00663644	−	0.0376371i	−0.987946	+	0.154798i	$0.950527\pi$
$384$	−0.984808	−	0.173648i	−0.0502558	−	0.00886145i
$385$	7.96869	−	20.0674i	0.406122	−	1.02273i
$386$	−4.88936	+	1.77958i	−0.248862	+	0.0905783i
$387$	5.88039			0.298917
$388$	9.26604			0.470412
$389$	−31.4905	+	11.4616i	−1.59663	+	0.581127i	−0.978734	−	0.205132i	$-0.934238\pi$
$389$	−31.4905	+	11.4616i	−1.59663	+	0.581127i	−0.617898	+	0.786258i	$0.712015\pi$
$390$	−0.754666	+	4.27992i	−0.0382140	+	0.216722i
$391$	6.30281	−	3.63893i	0.318747	−	0.184028i
$392$	−0.404864	+	6.98828i	−0.0204487	+	0.352962i
$393$	1.93440	+	5.31471i	0.0975774	+	0.268092i
$394$	13.3084	+	15.8604i	0.670469	+	0.799034i
$395$	10.6094	+	8.90233i	0.533816	+	0.447925i
$396$	−3.36693	+	2.82519i	−0.169195	+	0.141971i
$397$	−3.69446	+	10.1504i	−0.185420	+	0.509436i	−0.997221	−	0.0744972i	$-0.976265\pi$
$397$	−3.69446	+	10.1504i	−0.185420	+	0.509436i	0.811802	+	0.583933i	$0.198487\pi$
$398$	−26.6687			−1.33678
$399$	6.28787	+	9.66761i	0.314787	+	0.483986i
$400$	1.55243			0.0776215
$401$	0.601823	−	1.65349i	0.0300536	−	0.0825716i	−0.923758	−	0.382976i	$-0.874899\pi$
$401$	0.601823	−	1.65349i	0.0300536	−	0.0825716i	0.953812	+	0.300404i	$0.0971215\pi$
$402$	5.73558	−	4.81272i	0.286065	−	0.240037i
$403$	−14.0606	−	11.7982i	−0.700406	−	0.587710i
$404$	−10.6265	−	12.6641i	−0.528687	−	0.630065i
$405$	−0.635050	−	1.74479i	−0.0315559	−	0.0866991i
$406$	−5.02805	+	8.15452i	−0.249538	+	0.404702i
$407$	16.2444	−	9.37871i	0.805205	−	0.464885i
$408$	−0.262046	+	1.48613i	−0.0129732	+	0.0735746i
$409$	−13.8253	+	5.03200i	−0.683617	+	0.248816i	−0.660400	−	0.750914i	$-0.729613\pi$
$409$	−13.8253	+	5.03200i	−0.683617	+	0.248816i	−0.0232171	+	0.999730i	$0.507391\pi$
$410$	−2.01653			−0.0995891
$411$	3.99643			0.197129
$412$	−5.33004	+	1.93998i	−0.262592	+	0.0955757i
$413$	21.4913	−	16.9985i	1.05752	−	0.836443i
$414$	4.74950	+	0.837465i	0.233425	+	0.0411592i
$415$	2.18472	+	12.3901i	0.107243	+	0.608208i
$416$	2.30504	−	0.406442i	0.113014	−	0.0199274i
$417$	−9.31227	−	5.37644i	−0.456024	−	0.263285i
$418$	−15.7513	+	10.9059i	−0.770419	+	0.533425i
$419$		−	20.1418i		−	0.983991i	−0.870598	−	0.491996i	$-0.836268\pi$
$419$		−	20.1418i		−	0.983991i	0.870598	−	0.491996i	$-0.163732\pi$
$420$	1.81304	−	4.56573i	0.0884671	−	0.222785i
$421$	−13.9332	+	38.2812i	−0.679064	+	1.86571i	−0.226389	+	0.974037i	$0.572692\pi$
$421$	−13.9332	+	38.2812i	−0.679064	+	1.86571i	−0.452675	+	0.891676i	$0.649530\pi$
$422$	−17.6918	+	6.43928i	−0.861222	+	0.313459i
$423$	−2.76476	+	7.59611i	−0.134427	+	0.369335i
$424$	0.371422	−	2.10644i	0.0180378	−	0.102298i
$425$		−	2.34271i		−	0.113638i
$426$	−1.46414	−	2.53597i	−0.0709379	−	0.122868i
$427$	−8.37624	+	9.41522i	−0.405355	+	0.455635i
$428$	1.93378	−	2.30459i	0.0934728	−	0.111397i
$429$	5.14373	−	8.90920i	0.248342	−	0.430140i
$430$	−5.45924	−	9.45569i	−0.263268	−	0.455994i
$431$	34.1077	+	6.01410i	1.64291	+	0.289689i	0.917234	−	0.398348i	$-0.130417\pi$
$431$	34.1077	+	6.01410i	1.64291	+	0.289689i	0.725675	+	0.688038i	$0.241528\pi$
$432$	−0.766044	+	0.642788i	−0.0368563	+	0.0309261i
$433$	0.210985	−	1.19656i	0.0101393	−	0.0575029i	−0.979318	−	0.202326i	$-0.935150\pi$
$433$	0.210985	−	1.19656i	0.0101393	−	0.0575029i	0.989458	+	0.144823i	$0.0462612\pi$
$434$	12.8710	+	16.2728i	0.617826	+	0.781121i
$435$	5.15027	−	4.32159i	0.246936	−	0.207204i
$436$	9.61560	−	5.55157i	0.460504	−	0.265872i
$437$	20.2767	+	5.54782i	0.969967	+	0.265388i
$438$	0.0431925	−	0.0748116i	0.00206382	−	0.00357464i
$439$	26.2750	+	9.56334i	1.25404	+	0.456433i	0.881765	−	0.471689i	$-0.156356\pi$
$439$	26.2750	+	9.56334i	1.25404	+	0.456433i	0.372275	+	0.928123i	$0.378578\pi$
$440$	7.66872	+	2.79119i	0.365592	+	0.133065i
$441$	5.09309	+	4.80212i	0.242528	+	0.228673i
$442$	−0.613345	−	3.47845i	−0.0291738	−	0.165453i
$443$	1.72918	+	1.45095i	0.0821556	+	0.0689368i	0.682941	−	0.730474i	$-0.260701\pi$
$443$	1.72918	+	1.45095i	0.0821556	+	0.0689368i	−0.600785	+	0.799411i	$0.705145\pi$
$444$	3.69593	−	2.13384i	0.175401	−	0.101268i
$445$		−	13.2891i		−	0.629962i
$446$	7.88583	+	1.39048i	0.373405	+	0.0658414i
$447$	15.4867	+	12.9949i	0.732495	+	0.614637i
$448$	−2.64464	−	0.0765441i	−0.124948	−	0.00361637i
$449$	1.77237	+	1.02328i	0.0836431	+	0.0482914i	0.541238	−	0.840869i	$-0.317956\pi$
$449$	1.77237	+	1.02328i	0.0836431	+	0.0482914i	−0.457595	+	0.889161i	$0.651289\pi$
$450$	0.997883	−	1.18923i	0.0470407	−	0.0560609i
$451$	4.48553	+	1.63260i	0.211215	+	0.0768761i
$452$	−6.27852	+	7.48245i	−0.295317	+	0.351945i
$453$	13.3171	−	2.34816i	0.625691	−	0.110326i
$454$	−11.8851	−	14.1641i	−0.557797	−	0.664756i
$455$	−0.332657	+	11.4935i	−0.0155952	+	0.538823i
$456$	−3.58373	+	2.48131i	−0.167823	+	0.116198i
$457$	−0.654151	−	1.13302i	−0.0305999	−	0.0530006i	0.850320	−	0.526266i	$-0.176408\pi$
$457$	−0.654151	−	1.13302i	−0.0305999	−	0.0530006i	−0.880920	+	0.473266i	$0.843075\pi$
$458$	−2.58119	−	14.6386i	−0.120611	−	0.684018i
$459$	0.970005	+	1.15601i	0.0452760	+	0.0539578i
$460$	−3.06270	−	8.41471i	−0.142799	−	0.392338i
$461$	−40.4940	+	7.14018i	−1.88599	+	0.332551i	−0.993057	−	0.117634i	$-0.962469\pi$
$461$	−40.4940	+	7.14018i	−1.88599	+	0.332551i	−0.892935	+	0.450185i	$0.851358\pi$
$462$	−7.72935	+	8.68809i	−0.359602	+	0.404206i
$463$	−18.9498	+	32.8220i	−0.880671	+	1.52537i	−0.0300743	+	0.999548i	$0.509574\pi$
$463$	−18.9498	+	32.8220i	−0.880671	+	1.52537i	−0.850597	+	0.525819i	$0.823759\pi$
$464$	−3.13581	−	1.81046i	−0.145576	−	0.0840486i
$465$	−4.97999	−	13.6824i	−0.230942	−	0.634507i
$466$	8.97023	+	24.6455i	0.415538	+	1.14168i
$467$	7.27126	+	4.19807i	0.336474	+	0.194263i	0.658712	−	0.752395i	$-0.271102\pi$
$467$	7.27126	+	4.19807i	0.336474	+	0.194263i	−0.322238	+	0.946659i	$0.604435\pi$
$468$	1.17030	−	2.02702i	0.0540972	−	0.0936991i
$469$	13.1670	−	14.8002i	0.607994	−	0.683409i
$470$	14.7813	−	2.60635i	0.681811	−	0.120222i
$471$	6.56530	+	18.0380i	0.302513	+	0.831147i
$472$	6.65716	+	7.93369i	0.306420	+	0.365178i
$473$	4.48804	+	25.4529i	0.206360	+	1.17033i
$474$	−3.72949	−	6.45967i	−0.171301	−	0.296702i
$475$	4.81006	−	4.75963i	0.220701	−	0.218387i
$476$	−0.115510	+	3.99093i	−0.00529438	+	0.182924i
$477$	−1.37488	−	1.63852i	−0.0629514	−	0.0750225i
$478$	14.6497	−	2.58314i	0.670063	−	0.118150i
$479$	−0.708046	+	0.843816i	−0.0323514	+	0.0385549i	−0.781978	−	0.623307i	$-0.785789\pi$
$479$	−0.708046	+	0.843816i	−0.0323514	+	0.0385549i	0.749626	+	0.661862i	$0.230233\pi$
$480$	1.74479	+	0.635050i	0.0796383	+	0.0289860i
$481$	−6.42078	+	7.65199i	−0.292762	+	0.348901i
$482$	9.30896	+	5.37453i	0.424012	+	0.244803i
$483$	12.7545	+	0.369155i	0.580350	+	0.0167971i
$484$	−6.37192	−	5.34667i	−0.289633	−	0.243031i
$485$	−16.9435	−	2.98759i	−0.769363	−	0.135659i
$486$			1.00000i			0.0453609i
$487$	−14.2418	+	8.22250i	−0.645357	+	0.372597i	−0.786675	−	0.617367i	$-0.788199\pi$
$487$	−14.2418	+	8.22250i	−0.645357	+	0.372597i	0.141318	+	0.989964i	$0.454866\pi$
$488$	−3.64872	−	3.06164i	−0.165170	−	0.138594i
$489$	0.562760	+	3.19157i	0.0254489	+	0.144328i
$490$	2.99350	−	12.6479i	0.135233	−	0.571375i
$491$	30.0538	+	10.9387i	1.35631	+	0.493657i	0.914912	−	0.403654i	$-0.132260\pi$
$491$	30.0538	+	10.9387i	1.35631	+	0.493657i	0.441399	+	0.897311i	$0.354482\pi$
$492$	1.02055	+	0.371449i	0.0460098	+	0.0167462i
$493$	−2.73210	+	4.73213i	−0.123047	+	0.213124i
$494$	5.89585	−	8.32641i	0.265267	−	0.374623i
$495$	7.06753	−	4.08044i	0.317662	−	0.183402i
$496$	−6.00723	+	5.04067i	−0.269733	+	0.226333i
$497$	−4.80621	−	6.07653i	−0.215588	−	0.272570i
$498$	1.17663	−	6.67298i	0.0527259	−	0.299023i
$499$	21.0023	−	17.6231i	0.940194	−	0.788916i	−0.0374253	−	0.999299i	$-0.511916\pi$
$499$	21.0023	−	17.6231i	0.940194	−	0.788916i	0.977619	+	0.210383i	$0.0674712\pi$
$500$	−11.9815	−	2.11266i	−0.535828	−	0.0944809i
$501$	7.27232	+	12.5960i	0.324903	+	0.562749i
$502$	−10.7064	+	18.5441i	−0.477851	+	0.827662i
$503$	0.842235	−	1.00374i	0.0375534	−	0.0447544i	−0.746941	−	0.664891i	$-0.768478\pi$
$503$	0.842235	−	1.00374i	0.0375534	−	0.0447544i	0.784494	+	0.620136i	$0.212923\pi$
$504$	−1.75858	+	1.97671i	−0.0783334	+	0.0880498i
$505$	15.3479	+	26.5833i	0.682972	+	1.18294i
$506$			21.1971i			0.942328i
$507$	1.30611	−	7.40731i	0.0580063	−	0.328970i
$508$	−3.22571	+	8.86257i	−0.143118	+	0.393213i
$509$	21.1249	−	7.68885i	0.936346	−	0.340802i	0.171624	−	0.985163i	$-0.445099\pi$
$509$	21.1249	−	7.68885i	0.936346	−	0.340802i	0.764722	+	0.644360i	$0.222876\pi$
$510$	0.958329	−	2.63299i	0.0424355	−	0.116591i
$511$	0.0843506	−	0.212418i	0.00373145	−	0.00939683i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.402781	+	4.34025i	−0.0177832	+	0.191627i
$514$	−13.3497	−	7.70743i	−0.588828	−	0.339960i
$515$	10.3718	−	1.82882i	0.457034	−	0.0805875i
$516$	1.02112	+	5.79105i	0.0449522	+	0.254937i
$517$	−34.9895	−	6.16958i	−1.53883	−	0.271338i
$518$	8.85595	−	7.00459i	0.389108	−	0.307764i
$519$	4.95890	−	1.80489i	0.217672	−	0.0792260i
$520$	−4.34595			−0.190582
$521$	21.4508			0.939777			0.469888	−	0.882726i	$-0.344294\pi$
$521$	21.4508			0.939777			0.469888	+	0.882726i	$0.344294\pi$
$522$	−3.40256	+	1.23843i	−0.148926	+	0.0542046i
$523$	5.27357	−	29.9079i	0.230597	−	1.30778i	−0.621093	−	0.783737i	$-0.713311\pi$
$523$	5.27357	−	29.9079i	0.230597	−	1.30778i	0.851690	−	0.524045i	$-0.175578\pi$
$524$	−4.89806	+	2.82790i	−0.213973	+	0.123537i
$525$	2.15572	−	3.49616i	0.0940834	−	0.152585i
$526$	3.37598	+	9.27543i	0.147200	+	0.404428i
$527$	7.60667	+	9.06528i	0.331352	+	0.394890i
$528$	−3.36693	−	2.82519i	−0.146527	−	0.122951i
$529$	0.198500	−	0.166561i	0.00863042	−	0.00724178i
$530$	−1.35833	+	3.73198i	−0.0590021	+	0.162107i
$531$	10.3567			0.449442
$532$	−8.42886	+	7.87111i	−0.365437	+	0.341256i
$533$	−2.54200			−0.110106
$534$	−2.44788	+	6.72549i	−0.105930	+	0.291040i
$535$	−4.27908	+	3.59057i	−0.185001	+	0.155234i
$536$	5.73558	+	4.81272i	0.247739	+	0.207878i
$537$	11.5410	+	13.7540i	0.498030	+	0.593529i
$538$	−5.72736	−	15.7358i	−0.246924	−	0.678418i
$539$	−16.8986	+	25.7103i	−0.727873	+	1.10742i
$540$	1.60800	−	0.928382i	0.0691975	−	0.0399512i
$541$	6.65825	−	37.7608i	0.286260	−	1.62346i	−0.414488	−	0.910055i	$-0.636039\pi$
$541$	6.65825	−	37.7608i	0.286260	−	1.62346i	0.700749	−	0.713408i	$-0.252850\pi$
$542$	3.59938	−	1.31007i	0.154606	−	0.0562721i
$543$	−5.38763			−0.231205
$544$	−1.50906			−0.0647004
$545$	−19.3726	+	7.05105i	−0.829832	+	0.302034i
$546$	2.28548	−	5.75548i	0.0978095	−	0.246312i
$547$	−9.20561	−	1.62320i	−0.393604	−	0.0694029i	−0.0266563	−	0.999645i	$-0.508486\pi$
$547$	−9.20561	−	1.62320i	−0.393604	−	0.0694029i	−0.366947	+	0.930242i	$0.619597\pi$
$548$	0.693972	+	3.93571i	0.0296450	+	0.168125i
$549$	−4.69071	+	0.827098i	−0.200195	+	0.0352997i
$550$	5.90913	+	3.41164i	0.251966	+	0.145473i
$551$	−15.2668	+	4.00461i	−0.650386	+	0.170602i
$552$			4.82277i			0.205271i
$553$	−12.2425	−	15.4783i	−0.520603	−	0.658202i
$554$	4.44929	−	12.2243i	0.189032	−	0.519361i
$555$	−7.44620	+	2.71020i	−0.316074	+	0.115041i
$556$	3.67770	−	10.1044i	0.155969	−	0.428522i
$557$	2.84598	−	16.1403i	0.120588	−	0.683888i	−0.863243	−	0.504789i	$-0.831570\pi$
$557$	2.84598	−	16.1403i	0.120588	−	0.683888i	0.983831	−	0.179100i	$-0.0573185\pi$
$558$			7.84189i			0.331974i
$559$	−6.88183	−	11.9197i	−0.291070	−	0.504148i
$560$	4.81120	+	0.992661i	0.203310	+	0.0419476i
$561$	−4.26338	+	5.08090i	−0.180000	+	0.214516i
$562$	−5.81147	+	10.0658i	−0.245142	+	0.424598i
$563$	−14.3475	−	24.8506i	−0.604674	−	1.04733i	−0.992103	−	0.125426i	$-0.959970\pi$
$563$	−14.3475	−	24.8506i	−0.604674	−	1.04733i	0.387429	−	0.921900i	$-0.373363\pi$
$564$	−7.96080	−	1.40370i	−0.335210	−	0.0591066i
$565$	13.8931	−	11.6577i	0.584489	−	0.490444i
$566$	4.15872	−	23.5853i	0.174804	−	0.991363i
$567$	0.383856	+	2.61776i	0.0161205	+	0.109935i
$568$	2.24319	−	1.88226i	0.0941224	−	0.0789780i
$569$	−16.5826	+	9.57395i	−0.695178	+	0.401361i	−0.805549	−	0.592529i	$-0.798129\pi$
$569$	−16.5826	+	9.57395i	−0.695178	+	0.401361i	0.110371	+	0.993890i	$0.464796\pi$
$570$	7.35307	−	3.38173i	0.307986	−	0.141645i
$571$	−11.4930	+	19.9064i	−0.480965	+	0.833056i	−0.999761	−	0.0218416i	$-0.993047\pi$
$571$	−11.4930	+	19.9064i	−0.480965	+	0.833056i	0.518796	+	0.854898i	$0.326380\pi$
$572$	9.66705	+	3.51852i	0.404200	+	0.147117i
$573$	4.04171	+	1.47106i	0.168845	+	0.0614545i
$574$	2.81413	+	0.580619i	0.117459	+	0.0242346i
$575$	−1.30011	−	7.37327i	−0.0542182	−	0.307487i
$576$	−0.766044	−	0.642788i	−0.0319185	−	0.0267828i
$577$	−9.41749	+	5.43719i	−0.392055	+	0.226353i	−0.683050	−	0.730371i	$-0.739347\pi$
$577$	−9.41749	+	5.43719i	−0.392055	+	0.226353i	0.290995	+	0.956725i	$0.406014\pi$
$578$		−	14.7227i		−	0.612385i
$579$	−5.12410	−	0.903517i	−0.212950	−	0.0375489i
$580$	5.15027	+	4.32159i	0.213853	+	0.179444i
$581$	0.518657	−	17.9199i	0.0215175	−	0.743442i
$582$	8.02462	+	4.63302i	0.332631	+	0.192045i
$583$	6.04289	−	7.20164i	0.250271	−	0.298261i
$584$	0.0811753	+	0.0295454i	0.00335906	+	0.00122260i
$585$	−2.79352	+	3.32919i	−0.115498	+	0.137645i
$586$	−6.68962	+	1.17956i	−0.276346	+	0.0487272i
$587$	17.4307	+	20.7731i	0.719444	+	0.857399i	0.994577	−	0.104007i	$-0.0331663\pi$
$587$	17.4307	+	20.7731i	0.719444	+	0.857399i	−0.275133	+	0.961406i	$0.588722\pi$
$588$	−3.84476	+	5.84960i	−0.158555	+	0.241233i
$589$	−3.15856	+	34.0358i	−0.130146	+	1.40242i
$590$	−9.61496	−	16.6536i	−0.395842	−	0.685618i
$591$	3.59525	+	20.3897i	0.147889	+	0.838720i
$592$	2.74322	+	3.26924i	0.112746	+	0.134365i
$593$	−5.72850	−	15.7389i	−0.235241	−	0.646320i	−0.999998	−	0.00200076i	$-0.999363\pi$
$593$	−5.72850	−	15.7389i	−0.235241	−	0.646320i	0.764757	−	0.644319i	$-0.222859\pi$
$594$	−4.32845	+	0.763222i	−0.177598	+	0.0313154i
$595$	1.49798	−	7.26039i	0.0614114	−	0.297647i
$596$	−10.1082	+	17.5079i	−0.414049	+	0.717154i
$597$	−23.0958	−	13.3343i	−0.945246	−	0.545738i
$598$	−3.86079	−	10.6074i	−0.157879	−	0.433770i
$599$	−7.37277	−	20.2565i	−0.301243	−	0.827659i	−0.994285	−	0.106761i	$-0.965952\pi$
$599$	−7.37277	−	20.2565i	−0.301243	−	0.827659i	0.693042	−	0.720898i	$-0.256270\pi$
$600$	1.34444	+	0.776215i	0.0548867	+	0.0316889i
$601$	8.56431	−	14.8338i	0.349345	−	0.605084i	−0.636788	−	0.771039i	$-0.719737\pi$
$601$	8.56431	−	14.8338i	0.349345	−	0.605084i	0.986133	+	0.165955i	$0.0530706\pi$
$602$	4.89597	+	14.7676i	0.199545	+	0.601883i
$603$	7.37352	−	1.30015i	0.300273	−	0.0529462i
$604$	4.62498	+	12.7070i	0.188188	+	0.517041i
$605$	9.92750	+	11.8311i	0.403610	+	0.481004i
$606$	−2.87073	−	16.2807i	−0.116615	−	0.661359i
$607$	8.32844	+	14.4253i	0.338041	+	0.585504i	0.984064	−	0.177814i	$-0.0569025\pi$
$607$	8.32844	+	14.4253i	0.338041	+	0.585504i	−0.646023	+	0.763318i	$0.723569\pi$
$608$	−3.06592	−	3.09841i	−0.124340	−	0.125657i
$609$	−8.43169	+	4.54800i	−0.341669	+	0.184294i
$610$	5.68475	+	6.77482i	0.230169	+	0.274304i
$611$	18.6331	−	3.28551i	0.753813	−	0.132918i
$612$	−0.970005	+	1.15601i	−0.0392101	+	0.0467288i
$613$	−17.3283	−	6.30700i	−0.699885	−	0.254737i	−0.0325234	−	0.999471i	$-0.510354\pi$
$613$	−17.3283	−	6.30700i	−0.699885	−	0.254737i	−0.667362	+	0.744734i	$0.732577\pi$
$614$	3.56840	−	4.25265i	0.144009	−	0.171623i
$615$	−1.74636	−	1.00826i	−0.0704201	−	0.0406571i
$616$	−9.89828	−	6.10325i	−0.398813	−	0.245907i
$617$	−26.6664	−	22.3757i	−1.07355	−	0.900813i	−0.0781785	−	0.996939i	$-0.524910\pi$
$617$	−26.6664	−	22.3757i	−1.07355	−	0.900813i	−0.995369	+	0.0961259i	$0.969355\pi$
$618$	−5.58594	−	0.984951i	−0.224699	−	0.0396206i
$619$		−	43.2785i		−	1.73951i	−0.493484	−	0.869755i	$-0.664277\pi$
$619$		−	43.2785i		−	1.73951i	0.493484	−	0.869755i	$-0.335723\pi$
$620$	12.6098	−	7.28026i	0.506421	−	0.292382i
$621$	3.69446	+	3.10002i	0.148253	+	0.124399i
$622$	−4.95717	−	28.1135i	−0.198765	−	1.12725i
$623$	−3.82633	+	18.5453i	−0.153299	+	0.743003i
$624$	2.19945	+	0.800533i	0.0880484	+	0.0320470i
$625$	13.9336	+	5.07141i	0.557343	+	0.202856i
$626$	13.1466	−	22.7706i	0.525445	−	0.910097i
$627$	−19.0939	+	1.56916i	−0.762539	+	0.0626661i
$628$	−16.6239	+	9.59782i	−0.663366	+	0.382995i
$629$	4.93348	−	4.13968i	0.196711	−	0.165060i
$630$	3.85300	−	3.04752i	0.153507	−	0.121416i
$631$	5.13971	−	29.1487i	0.204609	−	1.16039i	−0.693446	−	0.720508i	$-0.743908\pi$
$631$	5.13971	−	29.1487i	0.204609	−	1.16039i	0.898055	−	0.439884i	$-0.144980\pi$
$632$	5.71391	−	4.79454i	0.227287	−	0.190717i
$633$	−18.5412	−	3.26931i	−0.736945	−	0.129943i
$634$	−4.68191	−	8.10930i	−0.185942	−	0.322061i
$635$	8.75589	−	15.1657i	0.347467	−	0.601831i
$636$	1.37488	−	1.63852i	0.0545175	−	0.0649714i
$637$	3.77356	−	15.9437i	0.149514	−	0.631714i
$638$	−7.95738	−	13.7826i	−0.315035	−	0.545657i
$639$		−	2.92828i		−	0.115841i
$640$	−0.322424	+	1.82855i	−0.0127449	+	0.0722800i
$641$	−1.21611	+	3.34122i	−0.0480333	+	0.131970i	−0.961390	−	0.275191i	$-0.911259\pi$
$641$	−1.21611	+	3.34122i	−0.0480333	+	0.131970i	0.913356	+	0.407161i	$0.133481\pi$
$642$	2.82700	−	1.02894i	0.111573	−	0.0406091i
$643$	15.8188	−	43.4617i	0.623831	−	1.71396i	−0.0735796	−	0.997289i	$-0.523442\pi$
$643$	15.8188	−	43.4617i	0.623831	−	1.71396i	0.697410	−	0.716672i	$-0.254335\pi$
$644$	1.85125	+	12.6248i	0.0729495	+	0.497489i
$645$		−	10.9185i		−	0.429915i
$646$	−4.67568	+	4.62666i	−0.183962	+	0.182034i
$647$	6.68208	+	3.85790i	0.262700	+	0.151670i	0.625565	−	0.780172i	$-0.284868\pi$
$647$	6.68208	+	3.85790i	0.262700	+	0.151670i	−0.362866	+	0.931841i	$0.618202\pi$
$648$	−0.984808	+	0.173648i	−0.0386869	+	0.00682154i
$649$	7.90445	+	44.8284i	0.310277	+	1.75967i
$650$	−3.57842	−	0.630972i	−0.140357	−	0.0247488i
$651$	3.01016	+	20.5282i	0.117977	+	0.804562i
$652$	−3.04536	+	1.10842i	−0.119266	+	0.0434091i
$653$	16.4950			0.645499			0.322750	−	0.946484i	$-0.395393\pi$
$653$	16.4950			0.645499			0.322750	+	0.946484i	$0.395393\pi$
$654$	11.1031			0.434167
$655$	9.86816	−	3.59172i	0.385581	−	0.140340i
$656$	−0.188590	+	1.06954i	−0.00736318	+	0.0417587i
$657$	0.0748116	−	0.0431925i	0.00291868	−	0.00168510i
$658$	−21.3783	−	0.618753i	−0.833411	−	0.0241215i
$659$	−11.8454	−	32.5450i	−0.461431	−	1.26777i	−0.924409	−	0.381402i	$-0.875441\pi$
$659$	−11.8454	−	32.5450i	−0.461431	−	1.26777i	0.462978	−	0.886370i	$-0.346781\pi$
$660$	5.24571	+	6.25160i	0.204189	+	0.243343i
$661$	−20.1576	−	16.9143i	−0.784041	−	0.657888i	0.160222	−	0.987081i	$-0.448779\pi$
$661$	−20.1576	−	16.9143i	−0.784041	−	0.657888i	−0.944263	+	0.329193i	$0.893223\pi$
$662$	18.0605	−	15.1545i	0.701940	−	0.588997i
$663$	1.20805	−	3.31910i	0.0469169	−	0.128903i
$664$	6.77592			0.262957
$665$	17.9505	−	11.6751i	0.696089	−	0.452740i
$666$	4.26769			0.165370
$667$	−5.97266	+	16.4097i	−0.231262	+	0.635388i
$668$	−11.1418	+	9.34912i	−0.431091	+	0.361728i
$669$	6.13409	+	5.14711i	0.237158	+	0.198999i
$670$	−8.93609	−	10.6496i	−0.345231	−	0.411431i
$671$	−7.16010	−	19.6722i	−0.276413	−	0.759437i
$672$	−2.25206	−	1.38861i	−0.0868750	−	0.0535668i
$673$	−19.1598	+	11.0619i	−0.738556	+	0.426405i	−0.821544	−	0.570145i	$-0.806887\pi$
$673$	−19.1598	+	11.0619i	−0.738556	+	0.426405i	0.0829882	+	0.996551i	$0.473554\pi$
$674$	4.85419	−	27.5295i	0.186976	−	1.06039i
$675$	1.45881	−	0.530962i	0.0561495	−	0.0204368i
$676$	7.52158			0.289291
$677$	−49.3406			−1.89631			−0.948157	−	0.317803i	$-0.897055\pi$
$677$	−49.3406			−1.89631			−0.948157	+	0.317803i	$0.897055\pi$
$678$	−9.17858	+	3.34073i	−0.352501	+	0.128300i
$679$	22.7849	+	9.04782i	0.874405	+	0.347223i
$680$	2.75940	+	0.486557i	0.105818	+	0.0186586i
$681$	−3.21075	−	18.2091i	−0.123036	−	0.697773i
$682$	−33.9432	+	5.98510i	−1.29975	+	0.229181i
$683$	33.2789	+	19.2136i	1.27338	+	0.735187i	0.975623	−	0.219455i	$-0.0704278\pi$
$683$	33.2789	+	19.2136i	1.27338	+	0.735187i	0.297758	+	0.954641i	$0.403761\pi$
$684$	−4.34425	+	0.357015i	−0.166107	+	0.0136508i
$685$		−	7.42042i		−	0.283520i
$686$	−7.81925	+	16.7887i	−0.298540	+	0.640994i
$687$	5.08394	−	13.9680i	0.193965	−	0.532913i
$688$	−5.52576	+	2.01121i	−0.210667	+	0.0766767i
$689$	−1.71229	+	4.70447i	−0.0652329	+	0.179226i
$690$	1.55498	−	8.81870i	0.0591969	−	0.335722i
$691$			25.3032i			0.962577i	0.876562	+	0.481289i	$0.159831\pi$
$691$			25.3032i			0.962577i	−0.876562	+	0.481289i	$0.840169\pi$
$692$	2.63858	+	4.57015i	0.100304	+	0.173731i
$693$	−11.0379	+	3.65943i	−0.419293	+	0.139010i
$694$	15.5005	−	18.4728i	0.588391	−	0.701217i
$695$	−9.98278	+	17.2907i	−0.378668	+	0.655873i
$696$	−1.81046	−	3.13581i	−0.0686254	−	0.118863i
$697$	1.61401	+	0.284593i	0.0611349	+	0.0107797i
$698$	19.7239	−	16.5503i	0.746560	−	0.626438i
$699$	−4.55430	+	25.8287i	−0.172260	+	0.976933i
$700$	3.81738	+	1.51587i	0.144284	+	0.0572945i
$701$	38.8224	−	32.5758i	1.46630	−	1.23037i	0.546812	−	0.837255i	$-0.315841\pi$
$701$	38.8224	−	32.5758i	1.46630	−	1.23037i	0.919488	−	0.393117i	$-0.128603\pi$
$702$	2.02702	−	1.17030i	0.0765050	−	0.0441702i
$703$	18.5228	+	1.71894i	0.698602	+	0.0648311i
$704$	2.19761	−	3.80637i	0.0828255	−	0.143458i
$705$	14.1042	+	5.13350i	0.531194	+	0.193339i
$706$	−8.63060	−	3.14128i	−0.324817	−	0.118224i
$707$	−13.7643	−	41.5170i	−0.517661	−	1.56141i
$708$	1.79842	+	10.1994i	0.0675888	+	0.383315i
$709$	22.9062	+	19.2206i	0.860260	+	0.721844i	0.962024	−	0.272965i	$-0.0880042\pi$
$709$	22.9062	+	19.2206i	0.860260	+	0.721844i	−0.101764	+	0.994809i	$0.532449\pi$
$710$	−4.70869	+	2.71856i	−0.176714	+	0.102026i
$711$		−	7.45898i		−	0.279734i
$712$	−7.04838	−	1.24282i	−0.264149	−	0.0465766i
$713$	28.9715	+	24.3100i	1.08499	+	0.910416i
$714$	−2.09550	+	3.39849i	−0.0784220	+	0.127185i
$715$	−16.5423	−	9.55069i	−0.618646	−	0.357176i
$716$	−11.5410	+	13.7540i	−0.431307	+	0.514012i
$717$	13.9786	+	5.08780i	0.522041	+	0.190007i
$718$	13.3714	−	15.9354i	0.499015	−	0.594703i
$719$	−5.17001	+	0.911612i	−0.192809	+	0.0339974i	−0.269219	−	0.963079i	$-0.586765\pi$
$719$	−5.17001	+	0.911612i	−0.192809	+	0.0339974i	0.0764098	+	0.997076i	$0.475654\pi$
$720$	1.19350	+	1.42236i	0.0444793	+	0.0530083i
$721$	−15.0007	−	0.434167i	−0.558656	−	0.0161692i
$722$	−18.9989	−	0.200249i	−0.707068	−	0.00745248i
$723$	5.37453	+	9.30896i	0.199881	+	0.346204i
$724$	−0.935552	−	5.30578i	−0.0347695	−	0.197188i
$725$	3.61326	+	4.30611i	0.134193	+	0.159925i
$726$	−2.84491	−	7.81631i	−0.105584	−	0.290091i
$727$	−38.6060	+	6.80727i	−1.43182	+	0.252468i	−0.835150	−	0.550022i	$-0.814619\pi$
$727$	−38.6060	+	6.80727i	−1.43182	+	0.252468i	−0.596666	+	0.802490i	$0.703508\pi$
$728$	6.06491	+	1.25133i	0.224781	+	0.0463774i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−0.138907	−	0.0801982i	−0.00514119	−	0.00296827i
$731$	3.03504	+	8.33870i	0.112255	+	0.308418i
$732$	−1.62907	−	4.47582i	−0.0602120	−	0.165431i
$733$	−25.2200	−	14.5608i	−0.931523	−	0.537815i	−0.0442302	−	0.999021i	$-0.514083\pi$
$733$	−25.2200	−	14.5608i	−0.931523	−	0.537815i	−0.887293	+	0.461206i	$0.847417\pi$
$734$	−16.6682	+	28.8701i	−0.615233	+	1.06562i
$735$	8.91641	−	9.45667i	0.328887	−	0.348814i
$736$	−4.74950	+	0.837465i	−0.175069	+	0.0308694i
$737$	11.2553	+	30.9236i	0.414593	+	1.13908i
$738$	0.698095	+	0.831958i	0.0256972	+	0.0306248i
$739$	7.91756	+	44.9027i	0.291252	+	1.65177i	0.682057	+	0.731299i	$0.261085\pi$
$739$	7.91756	+	44.9027i	0.291252	+	1.65177i	−0.390805	+	0.920473i	$0.627803\pi$
$740$	−3.96204	−	6.86246i	−0.145648	−	0.252269i
$741$	9.26916	−	4.26296i	0.340511	−	0.156604i
$742$	2.97014	−	4.81700i	0.109037	−	0.176837i
$743$	−2.47774	−	2.95285i	−0.0908993	−	0.108330i	0.718677	−	0.695344i	$-0.244748\pi$
$743$	−2.47774	−	2.95285i	−0.0908993	−	0.108330i	−0.809577	+	0.587014i	$0.800303\pi$
$744$	−7.72275	+	1.36173i	−0.283130	+	0.0499234i
$745$	24.1284	−	28.7551i	0.883997	−	1.05351i
$746$	32.4740	+	11.8196i	1.18896	+	0.432745i
$747$	4.35548	−	5.19065i	0.159359	−	0.189916i
$748$	−5.74404	−	3.31632i	−0.210023	−	0.121257i
$749$	7.00543	−	3.77868i	0.255973	−	0.138070i
$750$	−9.31994	−	7.82035i	−0.340316	−	0.285559i
$751$	35.0718	+	6.18410i	1.27979	+	0.225661i	0.771890	−	0.635756i	$-0.219312\pi$
$751$	35.0718	+	6.18410i	1.27979	+	0.225661i	0.507898	+	0.861417i	$0.330423\pi$
$752$		−	8.08361i		−	0.294779i
$753$	−18.5441	+	10.7064i	−0.675783	+	0.390164i
$754$	6.49234	+	5.44772i	0.236437	+	0.198394i
$755$	−4.35998	−	24.7267i	−0.158676	−	0.899896i
$756$	−2.51133	+	0.832593i	−0.0913363	+	0.0302811i
$757$	−16.8881	−	6.14677i	−0.613809	−	0.223408i	0.0163601	−	0.999866i	$-0.494792\pi$
$757$	−16.8881	−	6.14677i	−0.613809	−	0.223408i	−0.630169	+	0.776458i	$0.717014\pi$
$758$	15.1919	+	5.52941i	0.551796	+	0.200837i
$759$	−10.5986	+	18.3573i	−0.384704	+	0.666326i
$760$	4.60721	+	6.65413i	0.167121	+	0.241371i
$761$	3.93526	−	2.27202i	0.142653	−	0.0823608i	−0.426975	−	0.904264i	$-0.640421\pi$
$761$	3.93526	−	2.27202i	0.142653	−	0.0823608i	0.569628	+	0.821903i	$0.307087\pi$
$762$	−7.22483	+	6.06236i	−0.261728	+	0.219616i
$763$	29.0653	−	4.26201i	1.05224	−	0.154295i
$764$	−0.746878	+	4.23576i	−0.0270211	+	0.153244i
$765$	2.14643	−	1.80107i	0.0776044	−	0.0651178i
$766$	0.736573	+	0.129878i	0.0266135	+	0.00469267i
$767$	−12.1205	−	20.9932i	−0.437644	−	0.758022i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	9.90387	−	11.8030i	0.357143	−	0.425626i	−0.557319	−	0.830298i	$-0.688170\pi$
$769$	9.90387	−	11.8030i	0.357143	−	0.425626i	0.914462	+	0.404672i	$0.132614\pi$
$770$	16.1317	+	14.3516i	0.581347	+	0.517194i
$771$	−7.70743	−	13.3497i	−0.277576	−	0.480776i
$772$		−	5.20315i		−	0.187265i
$773$	−3.22153	+	18.2702i	−0.115870	+	0.657134i	0.870445	+	0.492265i	$0.163831\pi$
$773$	−3.22153	+	18.2702i	−0.115870	+	0.657134i	−0.986316	+	0.164868i	$0.947280\pi$
$774$	−2.01121	+	5.52576i	−0.0722915	+	0.198619i
$775$	11.4398	−	4.16375i	0.410930	−	0.149566i
$776$	−3.16917	+	8.70723i	−0.113767	+	0.312571i
$777$	11.1718	−	1.63818i	0.400785	−	0.0587693i
$778$		−	33.5115i		−	1.20145i
$779$	2.69481	+	3.89208i	0.0965517	+	0.139448i
$780$	−3.76370	−	2.17297i	−0.134762	−	0.0778049i
$781$	12.6749	−	2.23493i	0.453544	−	0.0799720i
$782$	1.26379	+	7.16729i	0.0451929	+	0.256302i
$783$	−3.56591	−	0.628767i	−0.127435	−	0.0224703i
$784$	−6.42837	−	2.77058i	−0.229584	−	0.0989493i
$785$	33.4923	−	12.1902i	1.19539	−	0.435087i
$786$	−5.65580			−0.201736
$787$	−11.4104			−0.406738			−0.203369	−	0.979102i	$-0.565189\pi$
$787$	−11.4104			−0.406738			−0.203369	+	0.979102i	$0.565189\pi$
$788$	−19.4556	+	7.08126i	−0.693078	+	0.252260i
$789$	−1.71403	+	9.72075i	−0.0610211	+	0.346068i
$790$	−11.9941	+	6.92478i	−0.426730	+	0.246373i
$791$	−22.7449	+	12.2685i	−0.808717	+	0.436217i
$792$	−1.50325	−	4.13015i	−0.0534158	−	0.146759i
$793$	7.16609	+	8.54021i	0.254475	+	0.303272i
$794$	−8.27472	−	6.94331i	−0.293659	−	0.246409i
$795$	−3.04234	+	2.55282i	−0.107901	+	0.0905394i
$796$	9.12123	−	25.0604i	0.323293	−	0.888241i
$797$	29.8104			1.05594			0.527969	−	0.849264i	$-0.322954\pi$
$797$	29.8104			1.05594			0.527969	+	0.849264i	$0.322954\pi$
$798$	−11.2352	+	2.60215i	−0.397720	+	0.0921150i
$799$	−12.1987			−0.431557
$800$	−0.530962	+	1.45881i	−0.0187724	+	0.0515766i
$801$	−5.48267	+	4.60050i	−0.193720	+	0.162551i
$802$	1.34794	+	1.13106i	0.0475975	+	0.0399390i
$803$	0.244054	+	0.290852i	0.00861248	+	0.0102640i
$804$	2.56080	+	7.03573i	0.0903124	+	0.248131i
$805$	0.685433	−	23.6821i	0.0241583	−	0.834685i
$806$	15.8957	−	9.17737i	0.559901	−	0.323259i
$807$	2.90786	−	16.4913i	0.102361	−	0.580521i
$808$	15.5349	−	5.65423i	0.546515	−	0.198915i
$809$	6.37968			0.224298			0.112149	−	0.993691i	$-0.464227\pi$
$809$	6.37968			0.224298			0.112149	+	0.993691i	$0.464227\pi$
$810$	1.85676			0.0652400
$811$	−1.18515	+	0.431360i	−0.0416163	+	0.0151471i	−0.362744	−	0.931889i	$-0.618160\pi$
$811$	−1.18515	+	0.431360i	−0.0416163	+	0.0151471i	0.321128	+	0.947036i	$0.395938\pi$
$812$	−5.94305	−	7.51384i	−0.208560	−	0.263684i
$813$	3.77218	+	0.665138i	0.132296	+	0.0233274i
$814$	3.25719	+	18.4725i	0.114165	+	0.647459i
$815$	5.92599	−	1.04491i	0.207578	−	0.0366017i
$816$	−1.30688	−	0.754530i	−0.0457501	−	0.0264138i
$817$	−10.9548	+	23.1731i	−0.383261	+	0.810724i
$818$		−	14.7126i		−	0.514413i
$819$	4.85702	−	3.84165i	0.169718	−	0.134238i
$820$	0.689693	−	1.89491i	0.0240851	−	0.0661733i
$821$	4.37570	−	1.59263i	0.152713	−	0.0555830i	−0.264533	−	0.964377i	$-0.585218\pi$
$821$	4.37570	−	1.59263i	0.152713	−	0.0555830i	0.417246	+	0.908794i	$0.362995\pi$
$822$	−1.36686	+	3.75541i	−0.0476747	+	0.130985i
$823$	5.20694	−	29.5300i	0.181503	−	1.02935i	−0.748865	−	0.662723i	$-0.769401\pi$
$823$	5.20694	−	29.5300i	0.181503	−	1.02935i	0.930367	−	0.366629i	$-0.119488\pi$
$824$		−	5.67211i		−	0.197597i
$825$	3.41164	+	5.90913i	0.118778	+	0.205729i
$826$	8.62292	+	26.0091i	0.300030	+	0.904972i
$827$	−19.3083	+	23.0107i	−0.671414	+	0.800160i	−0.988976	−	0.148077i	$-0.952692\pi$
$827$	−19.3083	+	23.0107i	−0.671414	+	0.800160i	0.317562	+	0.948238i	$0.397136\pi$
$828$	−2.41139	+	4.17664i	−0.0838014	+	0.145148i
$829$	2.69483	+	4.66757i	0.0935952	+	0.162112i	0.909021	−	0.416749i	$-0.136831\pi$
$829$	2.69483	+	4.66757i	0.0935952	+	0.162112i	−0.815426	+	0.578861i	$0.803497\pi$
$830$	−12.3901	−	2.18472i	−0.430068	−	0.0758326i
$831$	9.96535	−	8.36192i	0.345694	−	0.290072i
$832$	−0.406442	+	2.30504i	−0.0140908	+	0.0799130i
$833$	−4.18097	+	9.70079i	−0.144862	+	0.336112i
$834$	8.23718	−	6.91182i	0.285230	−	0.239337i
$835$	23.3879	−	13.5030i	0.809370	−	0.467290i
$836$	−4.86095	−	18.5314i	−0.168119	−	0.640921i
$837$	−3.92094	+	6.79127i	−0.135528	+	0.234741i
$838$	18.9271	+	6.88890i	0.653826	+	0.237973i
$839$	−27.4808	−	10.0022i	−0.948743	−	0.345314i	−0.179130	−	0.983825i	$-0.557328\pi$
$839$	−27.4808	−	10.0022i	−0.948743	−	0.345314i	−0.769613	+	0.638511i	$0.779551\pi$
$840$	3.67029	+	3.26527i	0.126637	+	0.112662i
$841$	2.75908	+	15.6475i	0.0951407	+	0.539570i
$842$	−31.2071	−	26.1859i	−1.07547	−	0.902426i
$843$	−10.0658	+	5.81147i	−0.346683	+	0.200158i
$844$		−	18.8272i		−	0.648059i
$845$	−13.7536	−	2.42513i	−0.473139	−	0.0834271i
$846$	−6.19240	−	5.19604i	−0.212899	−	0.178644i
$847$	−10.4476	−	19.3692i	−0.358984	−	0.665533i
$848$	1.85237	+	1.06947i	0.0636106	+	0.0367256i
$849$	15.3942	−	18.3461i	0.528327	−	0.629636i
$850$	2.20143	+	0.801254i	0.0755084	+	0.0274828i
$851$	13.2299	−	15.7668i	0.453515	−	0.540479i
$852$	2.88380	−	0.508491i	0.0987972	−	0.0174206i
$853$	−16.5839	−	19.7639i	−0.567821	−	0.676703i	0.403361	−	0.915041i	$-0.367842\pi$
$853$	−16.5839	−	19.7639i	−0.567821	−	0.676703i	−0.971182	+	0.238338i	$0.923397\pi$
$854$	−5.98257	−	11.0913i	−0.204719	−	0.379536i
$855$	8.05882	+	0.747869i	0.275606	+	0.0255766i
$856$	1.50421	+	2.60537i	0.0514130	+	0.0890499i
$857$	−5.30233	−	30.0710i	−0.181124	−	1.02721i	−0.930835	−	0.365440i	$-0.880919\pi$
$857$	−5.30233	−	30.0710i	−0.181124	−	1.02721i	0.749711	−	0.661766i	$-0.230193\pi$
$858$	6.61265	+	7.88065i	0.225752	+	0.269041i
$859$	−12.2210	−	33.5768i	−0.416974	−	1.14563i	−0.953408	−	0.301684i	$-0.902451\pi$
$859$	−12.2210	−	33.5768i	−0.416974	−	1.14563i	0.536434	−	0.843942i	$-0.319771\pi$
$860$	10.7526	−	1.89598i	0.366661	−	0.0646522i
$861$	2.14680	+	1.90990i	0.0731626	+	0.0650891i
$862$	−17.3169	+	29.9938i	−0.589817	+	1.02159i
$863$	−9.94728	−	5.74307i	−0.338609	−	0.195496i	0.321047	−	0.947063i	$-0.395965\pi$
$863$	−9.94728	−	5.74307i	−0.338609	−	0.195496i	−0.659657	+	0.751567i	$0.729298\pi$
$864$	−0.342020	−	0.939693i	−0.0116358	−	0.0319690i
$865$	−3.35126	−	9.20751i	−0.113946	−	0.313065i
$866$	1.05224	+	0.607508i	0.0357564	+	0.0206440i
$867$	7.36137	−	12.7503i	0.250005	−	0.433022i
$868$	−19.6936	+	6.52911i	−0.668444	+	0.221612i
$869$	32.2858	−	5.69286i	1.09522	−	0.193117i
$870$	2.29947	+	6.31774i	0.0779593	+	0.214191i
$871$	−11.2647	−	13.4247i	−0.381689	−	0.454879i
$872$	1.92804	+	10.9345i	0.0652917	+	0.370288i
$873$	4.63302	+	8.02462i	0.156804	+	0.271592i
$874$	−12.1483	+	17.1564i	−0.410922	+	0.580324i
$875$	−27.3992	−	16.8943i	−0.926263	−	0.571131i
$876$	0.0555272	+	0.0661747i	0.00187609	+	0.00223584i
$877$	−35.9420	+	6.33755i	−1.21368	+	0.214004i	−0.743601	−	0.668623i	$-0.766884\pi$
$877$	−35.9420	+	6.33755i	−1.21368	+	0.214004i	−0.470074	+	0.882627i	$0.655773\pi$
$878$	−17.9732	+	21.4196i	−0.606566	+	0.722877i
$879$	−6.38317	−	2.32328i	−0.215299	−	0.0783624i
$880$	−5.24571	+	6.25160i	−0.176833	+	0.210741i
$881$	41.6703	+	24.0584i	1.40391	+	0.810547i	0.994791	−	0.101935i	$-0.0325034\pi$
$881$	41.6703	+	24.0584i	1.40391	+	0.810547i	0.409117	+	0.912482i	$0.365837\pi$
$882$	−6.25446	+	3.14352i	−0.210599	+	0.105848i
$883$	0.246188	+	0.206577i	0.00828490	+	0.00695186i	0.646921	−	0.762557i	$-0.276056\pi$
$883$	0.246188	+	0.206577i	0.00828490	+	0.00695186i	−0.638636	+	0.769509i	$0.720501\pi$
$884$	3.47845	+	0.613345i	0.116993	+	0.0206290i
$885$		−	19.2299i		−	0.646407i
$886$	−1.95486	+	1.12864i	−0.0656748	+	0.0379174i
$887$	−38.2048	−	32.0576i	−1.28279	−	1.07639i	−0.992853	−	0.119345i	$-0.961920\pi$
$887$	−38.2048	−	32.0576i	−1.28279	−	1.07639i	−0.289939	−	0.957045i	$-0.593635\pi$
$888$	0.741076	+	4.20285i	0.0248689	+	0.141038i
$889$	−16.5858	+	18.6431i	−0.556270	+	0.625269i
$890$	12.4876	+	4.54513i	0.418586	+	0.152353i
$891$	−4.13015	−	1.50325i	−0.138365	−	0.0503609i
$892$	−4.00374	+	6.93468i	−0.134055	+	0.232190i
$893$	−24.7837	−	25.0463i	−0.829355	−	0.838143i
$894$	−17.5079	+	10.1082i	−0.585553	+	0.338069i
$895$	25.5379	−	21.4289i	0.853639	−	0.716288i
$896$	0.976449	−	2.45897i	0.0326209	−	0.0821485i
$897$	1.96017	−	11.1167i	0.0654483	−	0.371176i
$898$	−1.56775	+	1.31550i	−0.0523165	+	0.0438987i
$899$	−27.9635	−	4.93072i	−0.932635	−	0.164449i
$900$	0.776215	+	1.34444i	0.0258738	+	0.0448148i
$901$	1.61389	−	2.79534i	0.0537664	−	0.0931262i
$902$	−3.06828	+	3.65664i	−0.102163	+	0.121753i
$903$	−3.14377	+	15.2371i	−0.104618	+	0.507059i
$904$	−4.88382	−	8.45903i	−0.162433	−	0.281343i
$905$			10.0035i			0.332529i
$906$	−2.34816	+	13.3171i	−0.0780124	+	0.442431i
$907$	−18.0032	+	49.4634i	−0.597787	+	1.64240i	0.157888	+	0.987457i	$0.449532\pi$
$907$	−18.0032	+	49.4634i	−0.597787	+	1.64240i	−0.755674	+	0.654948i	$0.772691\pi$
$908$	17.3749	−	6.32394i	0.576606	−	0.209867i
$909$	5.65423	−	15.5349i	0.187539	−	0.515259i
$910$	−10.6866	−	4.24360i	−0.354256	−	0.140674i
$911$		−	32.7712i		−	1.08576i	−0.839811	−	0.542879i	$-0.817334\pi$
$911$		−	32.7712i		−	1.08576i	0.839811	−	0.542879i	$-0.182666\pi$
$912$	−1.10596	−	4.21626i	−0.0366221	−	0.139614i
$913$	25.7917	+	14.8908i	0.853579	+	0.492814i
$914$	1.28843	−	0.227184i	0.0426174	−	0.00751459i
$915$	1.53573	+	8.70954i	0.0507695	+	0.287928i
$916$	14.6386	+	2.58119i	0.483674	+	0.0852848i
$917$	−14.8055	+	2.17101i	−0.488921	+	0.0716932i
$918$	−1.41805	+	0.516129i	−0.0468027	+	0.0170348i
$919$	29.1331			0.961012			0.480506	−	0.876992i	$-0.340453\pi$
$919$	29.1331			0.961012			0.480506	+	0.876992i	$0.340453\pi$
$920$	8.95474			0.295229
$921$	5.21665	−	1.89870i	0.171894	−	0.0625644i
$922$	7.14018	−	40.4940i	0.235149	−	1.33360i
$923$	−5.93569	+	3.42697i	−0.195376	+	0.112800i
$924$	−5.52054	−	10.2347i	−0.181612	−	0.336697i
$925$	−2.26598	−	6.22573i	−0.0745050	−	0.204701i
$926$	−24.3614	−	29.0327i	−0.800564	−	0.954075i
$927$	−4.34509	−	3.64596i	−0.142711	−	0.119749i
$928$	2.77379	−	2.32748i	0.0910541	−	0.0764034i
$929$	−1.78006	+	4.89068i	−0.0584020	+	0.160458i	−0.965462	−	0.260542i	$-0.916099\pi$
$929$	−1.78006	+	4.89068i	−0.0584020	+	0.160458i	0.907060	+	0.421000i	$0.138321\pi$
$930$	14.5605			0.477459
$931$	−28.4121	+	11.1245i	−0.931168	+	0.364590i
$932$	−26.2272			−0.859100
$933$	9.76373	−	26.8256i	0.319650	−	0.878231i
$934$	−6.43181	+	5.39693i	−0.210455	+	0.176593i
$935$	9.43404	+	7.91610i	0.308526	+	0.258884i
$936$	1.50451	+	1.79301i	0.0491765	+	0.0586062i
$937$	9.44743	+	25.9566i	0.308634	+	0.847965i	0.992924	+	0.118755i	$0.0378902\pi$
$937$	9.44743	+	25.9566i	0.308634	+	0.847965i	−0.684290	+	0.729210i	$0.739888\pi$
$938$	9.40426	+	17.4349i	0.307060	+	0.569268i
$939$	22.7706	−	13.1466i	0.743091	−	0.429024i
$940$	−2.60635	+	14.7813i	−0.0850096	+	0.482113i
$941$	−18.6905	+	6.80279i	−0.609293	+	0.221764i	−0.628194	−	0.778057i	$-0.716206\pi$
$941$	−18.6905	+	6.80279i	−0.609293	+	0.221764i	0.0189009	+	0.999821i	$0.493983\pi$
$942$	−19.1956			−0.625428
$943$	5.23774			0.170564
$944$	−9.73211	+	3.54220i	−0.316753	+	0.115289i
$945$	4.86056	−	0.712730i	0.158114	−	0.0231851i
$946$	−25.4529	−	4.48804i	−0.827546	−	0.145919i
$947$	8.58880	+	48.7095i	0.279098	+	1.58285i	0.725634	+	0.688080i	$0.241546\pi$
$947$	8.58880	+	48.7095i	0.279098	+	1.58285i	−0.446536	+	0.894766i	$0.647342\pi$
$948$	7.34566	−	1.29524i	0.238576	−	0.0420674i
$949$	−0.175104	−	0.101096i	−0.00568412	−	0.00328173i
$950$	2.82745	+	6.14787i	0.0917346	+	0.199463i
$951$		−	9.36381i		−	0.303642i
$952$	−3.71074	−	1.47352i	−0.120266	−	0.0477571i
$953$	−6.66732	+	18.3183i	−0.215976	+	0.593388i	−0.999613	−	0.0278308i	$-0.991140\pi$
$953$	−6.66732	+	18.3183i	−0.215976	+	0.593388i	0.783637	+	0.621219i	$0.213362\pi$
$954$	2.00994	−	0.731558i	0.0650742	−	0.0236851i
$955$	2.73142	−	7.50450i	0.0883865	−	0.242840i
$956$	−2.58314	+	14.6497i	−0.0835449	+	0.473806i
$957$		−	15.9148i		−	0.514451i
$958$	−0.550762	−	0.953947i	−0.0177943	−	0.0308206i
$959$	−2.13657	+	10.3554i	−0.0689933	+	0.334395i
$960$	−1.19350	+	1.42236i	−0.0385202	+	0.0459066i
$961$	−15.2476	+	26.4096i	−0.491858	+	0.851923i
$962$	−4.99448	−	8.65070i	−0.161029	−	0.278910i
$963$	2.96272	+	0.522408i	0.0954724	+	0.0168344i
$964$	−8.23426	+	6.90937i	−0.265208	+	0.222536i
$965$	−1.67762	+	9.51424i	−0.0540044	+	0.306274i
$966$	−4.70919	+	11.8591i	−0.151516	+	0.381559i
$967$	2.27589	−	1.90970i	0.0731877	−	0.0614118i	−0.605460	−	0.795876i	$-0.707011\pi$
$967$	2.27589	−	1.90970i	0.0731877	−	0.0614118i	0.678648	+	0.734464i	$0.262566\pi$
$968$	7.20355	−	4.15897i	0.231531	−	0.133674i
$969$	−6.36259	+	1.66896i	−0.204396	+	0.0536149i
$970$	8.60242	−	14.8998i	0.276207	−	0.478405i
$971$	20.8433	+	7.58633i	0.668892	+	0.243457i	0.654071	−	0.756433i	$-0.273060\pi$
$971$	20.8433	+	7.58633i	0.668892	+	0.243457i	0.0148214	+	0.999890i	$0.495282\pi$
$972$	−0.939693	−	0.342020i	−0.0301407	−	0.0109703i
$973$	18.9098	−	21.2554i	0.606221	−	0.681416i
$974$	−2.85564	−	16.1952i	−0.0915008	−	0.518927i
$975$	−2.78352	−	2.33565i	−0.0891439	−	0.0748006i
$976$	4.12494	−	2.38154i	0.132036	−	0.0762311i
$977$			30.8231i			0.986118i	0.869996	+	0.493059i	$0.164121\pi$
$977$			30.8231i			0.986118i	−0.869996	+	0.493059i	$0.835879\pi$
$978$	−3.19157	−	0.562760i	−0.102055	−	0.0179951i
$979$	−24.0975	−	20.2202i	−0.770160	−	0.646241i
$980$	10.8613	+	7.13882i	0.346952	+	0.228041i
$981$	9.61560	+	5.55157i	0.307003	+	0.177248i
$982$	−20.5580	+	24.5001i	−0.656033	+	0.781830i
$983$	−48.2392	−	17.5577i	−1.53859	−	0.560002i	−0.572886	−	0.819635i	$-0.694176\pi$
$983$	−48.2392	−	17.5577i	−1.53859	−	0.560002i	−0.965707	+	0.259633i	$0.916398\pi$
$984$	−0.698095	+	0.831958i	−0.0222545	+	0.0265218i
$985$	37.8588	−	6.67553i	1.20628	−	0.212700i
$986$	−3.51231	−	4.18581i	−0.111855	−	0.133303i
$987$	−18.2047	−	11.2250i	−0.579463	−	0.357295i
$988$	5.80776	+	8.38808i	0.184770	+	0.266860i
$989$	14.1799	+	24.5603i	0.450894	+	0.780971i
$990$	1.41712	+	8.03690i	0.0450391	+	0.255429i
$991$	39.6982	+	47.3105i	1.26106	+	1.50287i	0.779430	+	0.626490i	$0.215509\pi$
$991$	39.6982	+	47.3105i	1.26106	+	1.50287i	0.481625	+	0.876377i	$0.340047\pi$
$992$	−2.68208	−	7.36896i	−0.0851562	−	0.233965i
$993$	23.2181	−	4.09397i	0.736804	−	0.129918i
$994$	7.35389	−	2.43807i	0.233251	−	0.0773309i
$995$	−24.7587	+	42.8834i	−0.784904	+	1.35949i
$996$	5.86812	+	3.38796i	0.185938	+	0.107352i
$997$	5.60220	+	15.3919i	0.177423	+	0.487467i	0.996245	−	0.0865816i	$-0.0275943\pi$
$997$	5.60220	+	15.3919i	0.177423	+	0.487467i	−0.818821	+	0.574048i	$0.805372\pi$
$998$	9.37703	+	25.7632i	0.296825	+	0.815519i
$999$	3.69593	+	2.13384i	0.116934	+	0.0675118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.cj.b.241.6	yes	84
7.5	odd	6		798.2.ca.b.355.9	✓	84
19.3	odd	18		798.2.ca.b.535.9	yes	84
133.117	even	18	inner	798.2.cj.b.649.6	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.ca.b.355.9	✓	84	7.5	odd	6
798.2.ca.b.535.9	yes	84	19.3	odd	18
798.2.cj.b.241.6	yes	84	1.1	even	1	trivial
798.2.cj.b.649.6	yes	84	133.117	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.342020 + 0.939693i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(1.19350 + 1.42236i) q^{5} +(-0.342020 - 0.939693i) q^{6} +(-1.25603 - 2.32860i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-1.74479 + 0.635050i) q^{10} +4.39522 q^{11} +1.00000 q^{12} +(-2.19945 + 0.800533i) q^{13} +(2.61776 - 0.383856i) q^{14} +(-1.82855 - 0.322424i) q^{15} +(0.173648 + 0.984808i) q^{16} +(1.48613 - 0.262046i) q^{17} +(0.866025 + 0.500000i) q^{18} +(3.55738 + 2.51894i) q^{19} -1.85676i q^{20} +(2.45897 + 0.976449i) q^{21} +(-1.50325 + 4.13015i) q^{22} +(4.53192 - 1.64948i) q^{23} +(-0.342020 + 0.939693i) q^{24} +(0.269577 - 1.52885i) q^{25} -2.34060i q^{26} +(0.500000 + 0.866025i) q^{27} +(-0.534619 + 2.59117i) q^{28} +(-2.32748 + 2.77379i) q^{29} +(0.928382 - 1.60800i) q^{30} +(3.92094 + 6.79127i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(-3.36693 + 2.82519i) q^{33} +(-0.262046 + 1.48613i) q^{34} +(1.81304 - 4.56573i) q^{35} +(-0.766044 + 0.642788i) q^{36} +(3.69593 - 2.13384i) q^{37} +(-3.58373 + 2.48131i) q^{38} +(1.17030 - 2.02702i) q^{39} +(1.74479 + 0.635050i) q^{40} +(1.02055 + 0.371449i) q^{41} +(-1.75858 + 1.97671i) q^{42} +(1.02112 + 5.79105i) q^{43} +(-3.36693 - 2.82519i) q^{44} +(1.60800 - 0.928382i) q^{45} +4.82277i q^{46} +(-7.96080 - 1.40370i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(-3.84476 + 5.84960i) q^{49} +(1.34444 + 0.776215i) q^{50} +(-0.970005 + 1.15601i) q^{51} +(2.19945 + 0.800533i) q^{52} +(1.37488 - 1.63852i) q^{53} +(-0.984808 + 0.173648i) q^{54} +(5.24571 + 6.25160i) q^{55} +(-2.25206 - 1.38861i) q^{56} +(-4.34425 + 0.357015i) q^{57} +(-1.81046 - 3.13581i) q^{58} +(1.79842 + 10.1994i) q^{59} +(1.19350 + 1.42236i) q^{60} +(-1.62907 - 4.47582i) q^{61} +(-7.72275 + 1.36173i) q^{62} +(-2.51133 + 0.832593i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-3.76370 - 2.17297i) q^{65} +(-1.50325 - 4.13015i) q^{66} +(2.56080 + 7.03573i) q^{67} +(-1.30688 - 0.754530i) q^{68} +(-2.41139 + 4.17664i) q^{69} +(3.67029 + 3.26527i) q^{70} +(2.88380 - 0.508491i) q^{71} +(-0.342020 - 0.939693i) q^{72} +(0.0555272 + 0.0661747i) q^{73} +(0.741076 + 4.20285i) q^{74} +(0.776215 + 1.34444i) q^{75} +(-1.10596 - 4.21626i) q^{76} +(-5.52054 - 10.2347i) q^{77} +(1.50451 + 1.79301i) q^{78} +(7.34566 - 1.29524i) q^{79} +(-1.19350 + 1.42236i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-0.698095 + 0.831958i) q^{82} +(5.86812 + 3.38796i) q^{83} +(-1.25603 - 2.32860i) q^{84} +(2.14643 + 1.80107i) q^{85} +(-5.79105 - 1.02112i) q^{86} -3.62092i q^{87} +(3.80637 - 2.19761i) q^{88} +(-5.48267 - 4.60050i) q^{89} +(0.322424 + 1.82855i) q^{90} +(4.62670 + 4.11614i) q^{91} +(-4.53192 - 1.64948i) q^{92} +(-7.36896 - 2.68208i) q^{93} +(4.04180 - 7.00061i) q^{94} +(0.662892 + 8.06625i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-7.09820 + 5.95609i) q^{97} +(-4.18184 - 5.61358i) q^{98} +(0.763222 - 4.32845i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 12 q^{7} - 12 q^{10} - 12 q^{11} + 84 q^{12} + 24 q^{13} + 6 q^{14} + 6 q^{19} - 6 q^{21} + 12 q^{22} - 42 q^{23} - 30 q^{25} + 42 q^{27} + 6 q^{28} + 6 q^{31} + 12 q^{33} - 30 q^{34} - 42 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) \) 84 * q + 12 * q^7 - 12 * q^10 - 12 * q^11 + 84 * q^12 + 24 * q^13 + 6 * q^14 + 6 * q^19 - 6 * q^21 + 12 * q^22 - 42 * q^23 - 30 * q^25 + 42 * q^27 + 6 * q^28 + 6 * q^31 + 12 * q^33 - 30 * q^34 - 42 * q^35 - 18 * q^37 + 12 * q^38 + 12 * q^40 + 36 * q^41 + 18 * q^42 + 12 * q^43 + 12 * q^44 - 18 * q^45 + 18 * q^47 - 24 * q^49 + 18 * q^51 - 24 * q^52 + 60 * q^53 - 30 * q^55 - 18 * q^56 + 6 * q^57 + 48 * q^59 - 12 * q^62 - 6 * q^63 + 42 * q^64 + 108 * q^65 + 12 * q^66 + 42 * q^67 + 6 * q^69 + 18 * q^70 + 42 * q^71 - 48 * q^73 - 18 * q^74 - 48 * q^75 + 18 * q^76 - 96 * q^77 - 12 * q^78 - 60 * q^79 - 6 * q^82 + 54 * q^83 + 12 * q^84 - 24 * q^85 - 12 * q^86 - 24 * q^89 + 6 * q^90 + 24 * q^91 + 42 * q^92 - 36 * q^93 + 18 * q^94 - 12 * q^95 - 78 * q^97 + 24 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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