LMFDB - Embedded newform 200.2.o.a.109.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,2,Mod(29,200)] 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("200.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.o (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.15
Character	$\chi$	$=$	200.109
Dual form			200.2.o.a.189.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0166708 + 1.41412i) q^{2} +(-0.423859 - 1.30450i) q^{3} +(-1.99944 + 0.0471489i) q^{4} +(1.11400 - 1.93881i) q^{5} +(1.83765 - 0.621132i) q^{6} +0.927462i q^{7} +(-0.100006 - 2.82666i) q^{8} +(0.904979 - 0.657506i) q^{9} +(2.76028 + 1.54301i) q^{10} +(1.54449 - 2.12581i) q^{11} +(0.908988 + 2.58830i) q^{12} +(2.08531 - 1.51507i) q^{13} +(-1.31154 + 0.0154616i) q^{14} +(-3.00137 - 0.631440i) q^{15} +(3.99555 - 0.188543i) q^{16} +(0.893539 + 0.290328i) q^{17} +(0.944876 + 1.26878i) q^{18} +(0.336558 + 0.109354i) q^{19} +(-2.13598 + 3.92907i) q^{20} +(1.20988 - 0.393113i) q^{21} +(3.03189 + 2.14865i) q^{22} +(-4.22031 + 5.80876i) q^{23} +(-3.64500 + 1.32856i) q^{24} +(-2.51799 - 4.31969i) q^{25} +(2.17724 + 2.92361i) q^{26} +(-4.57033 - 3.32054i) q^{27} +(-0.0437289 - 1.85441i) q^{28} +(1.33062 - 0.432345i) q^{29} +(0.842893 - 4.25481i) q^{30} +(-1.34398 + 4.13636i) q^{31} +(0.333231 + 5.64703i) q^{32} +(-3.42777 - 1.11375i) q^{33} +(-0.395662 + 1.26841i) q^{34} +(1.79818 + 1.03320i) q^{35} +(-1.77845 + 1.35731i) q^{36} +(-7.47195 + 5.42869i) q^{37} +(-0.149029 + 0.477755i) q^{38} +(-2.86029 - 2.07812i) q^{39} +(-5.59177 - 2.95502i) q^{40} +(7.67997 - 5.57982i) q^{41} +(0.576077 + 1.70435i) q^{42} -5.59241 q^{43} +(-2.98790 + 4.32326i) q^{44} +(-0.266630 - 2.48705i) q^{45} +(-8.28461 - 5.87117i) q^{46} +(7.85457 - 2.55210i) q^{47} +(-1.93951 - 5.13230i) q^{48} +6.13981 q^{49} +(6.06656 - 3.63274i) q^{50} -1.28868i q^{51} +(-4.09803 + 3.12761i) q^{52} +(3.01052 + 9.26543i) q^{53} +(4.61944 - 6.51833i) q^{54} +(-2.40098 - 5.36264i) q^{55} +(2.62162 - 0.0927522i) q^{56} -0.485392i q^{57} +(0.633568 + 1.87444i) q^{58} +(-2.55804 - 3.52083i) q^{59} +(6.03084 + 1.12102i) q^{60} +(-2.14775 + 2.95612i) q^{61} +(-5.87169 - 1.83159i) q^{62} +(0.609812 + 0.839334i) q^{63} +(-7.98000 + 0.565368i) q^{64} +(-0.614386 - 5.73082i) q^{65} +(1.51783 - 4.86583i) q^{66} +(0.325879 - 1.00295i) q^{67} +(-1.80027 - 0.538366i) q^{68} +(9.36636 + 3.04331i) q^{69} +(-1.43108 + 2.56005i) q^{70} +(3.56365 + 10.9678i) q^{71} +(-1.94905 - 2.49231i) q^{72} +(-9.25671 + 12.7408i) q^{73} +(-7.80136 - 10.4757i) q^{74} +(-4.56778 + 5.11566i) q^{75} +(-0.678086 - 0.202780i) q^{76} +(1.97161 + 1.43246i) q^{77} +(2.89102 - 4.07942i) q^{78} +(-1.73030 - 5.32530i) q^{79} +(4.08551 - 7.95667i) q^{80} +(-1.35747 + 4.17785i) q^{81} +(8.01855 + 10.7673i) q^{82} +(-2.17829 + 6.70408i) q^{83} +(-2.40055 + 0.843052i) q^{84} +(1.55830 - 1.40898i) q^{85} +(-0.0932301 - 7.90831i) q^{86} +(-1.12799 - 1.55254i) q^{87} +(-6.16340 - 4.15316i) q^{88} +(7.12799 + 5.17879i) q^{89} +(3.51253 - 0.418506i) q^{90} +(1.40517 + 1.93405i) q^{91} +(8.16440 - 11.8133i) q^{92} +5.96555 q^{93} +(3.73991 + 11.0647i) q^{94} +(0.586945 - 0.530702i) q^{95} +(7.22533 - 2.82824i) q^{96} +(1.52791 - 0.496446i) q^{97} +(0.102356 + 8.68240i) q^{98} -2.93933i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28}+ \cdots + 90 q^{98}+O(q^{100}) $ 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	0.0166708	+	1.41412i	0.0117881	+	0.999931i
$2$	0.0166708	+	1.41412i	0.0117881	+	0.999931i
$3$	−0.423859	−	1.30450i	−0.244715	−	0.753155i	−0.995683	−	0.0928169i	$-0.970413\pi$
$3$	−0.423859	−	1.30450i	−0.244715	−	0.753155i	0.750968	−	0.660338i	$-0.229587\pi$
$4$	−1.99944	+	0.0471489i	−0.999722	+	0.0235745i
$5$	1.11400	−	1.93881i	0.498198	−	0.867063i
$5$	1.11400	−	1.93881i	0.498198	−	0.867063i
$6$	1.83765	−	0.621132i	0.750218	−	0.253576i
$7$			0.927462i			0.350548i	0.984520	+	0.175274i	$0.0560811\pi$
$7$			0.927462i			0.350548i	−0.984520	+	0.175274i	$0.943919\pi$
$8$	−0.100006	−	2.82666i	−0.0353576	−	0.999375i
$9$	0.904979	−	0.657506i	0.301660	−	0.219169i
$10$	2.76028	+	1.54301i	0.872876	+	0.487942i
$11$	1.54449	−	2.12581i	0.465682	−	0.640956i	−0.509993	−	0.860179i	$-0.670352\pi$
$11$	1.54449	−	2.12581i	0.465682	−	0.640956i	0.975675	+	0.219222i	$0.0703520\pi$
$12$	0.908988	+	2.58830i	0.262402	+	0.747177i
$13$	2.08531	−	1.51507i	0.578362	−	0.420204i	−0.259771	−	0.965670i	$-0.583647\pi$
$13$	2.08531	−	1.51507i	0.578362	−	0.420204i	0.838133	+	0.545466i	$0.183647\pi$
$14$	−1.31154	+	0.0154616i	−0.350523	+	0.00413228i
$15$	−3.00137	−	0.631440i	−0.774950	−	0.163037i
$16$	3.99555	−	0.188543i	0.998888	−	0.0471358i
$17$	0.893539	+	0.290328i	0.216715	+	0.0704150i	0.415362	−	0.909656i	$-0.363655\pi$
$17$	0.893539	+	0.290328i	0.216715	+	0.0704150i	−0.198647	+	0.980071i	$0.563655\pi$
$18$	0.944876	+	1.26878i	0.222709	+	0.299055i
$19$	0.336558	+	0.109354i	0.0772118	+	0.0250876i	0.347368	−	0.937729i	$-0.387075\pi$
$19$	0.336558	+	0.109354i	0.0772118	+	0.0250876i	−0.270156	+	0.962816i	$0.587075\pi$
$20$	−2.13598	+	3.92907i	−0.477619	+	0.878567i
$21$	1.20988	−	0.393113i	0.264017	−	0.0857843i
$22$	3.03189	+	2.14865i	0.646401	+	0.458094i
$23$	−4.22031	+	5.80876i	−0.879995	+	1.21121i	0.0964270	+	0.995340i	$0.469259\pi$
$23$	−4.22031	+	5.80876i	−0.879995	+	1.21121i	−0.976422	+	0.215869i	$0.930741\pi$
$24$	−3.64500	+	1.32856i	−0.744032	+	0.271192i
$25$	−2.51799	−	4.31969i	−0.503598	−	0.863938i
$26$	2.17724	+	2.92361i	0.426993	+	0.573368i
$27$	−4.57033	−	3.32054i	−0.879561	−	0.639038i
$28$	−0.0437289	−	1.85441i	−0.00826398	−	0.350450i
$29$	1.33062	−	0.432345i	0.247090	−	0.0802844i	−0.182854	−	0.983140i	$-0.558533\pi$
$29$	1.33062	−	0.432345i	0.247090	−	0.0802844i	0.429944	+	0.902856i	$0.358533\pi$
$30$	0.842893	−	4.25481i	0.153891	−	0.776818i
$31$	−1.34398	+	4.13636i	−0.241387	+	0.742911i	0.754823	+	0.655928i	$0.227723\pi$
$31$	−1.34398	+	4.13636i	−0.241387	+	0.742911i	−0.996210	+	0.0869831i	$0.972277\pi$
$32$	0.333231	+	5.64703i	0.0589075	+	0.998263i
$33$	−3.42777	−	1.11375i	−0.596699	−	0.193879i
$34$	−0.395662	+	1.26841i	−0.0678554	+	0.217530i
$35$	1.79818	+	1.03320i	0.303947	+	0.174642i
$36$	−1.77845	+	1.35731i	−0.296409	+	0.226219i
$37$	−7.47195	+	5.42869i	−1.22838	+	0.892471i	−0.996768	−	0.0803370i	$-0.974400\pi$
$37$	−7.47195	+	5.42869i	−1.22838	+	0.892471i	−0.231613	+	0.972808i	$0.574400\pi$
$38$	−0.149029	+	0.477755i	−0.0241757	+	0.0775021i
$39$	−2.86029	−	2.07812i	−0.458013	−	0.332766i
$40$	−5.59177	−	2.95502i	−0.884136	−	0.467229i
$41$	7.67997	−	5.57982i	1.19941	−	0.871422i	0.205183	−	0.978724i	$-0.434221\pi$
$41$	7.67997	−	5.57982i	1.19941	−	0.871422i	0.994227	+	0.107301i	$0.0342210\pi$
$42$	0.576077	+	1.70435i	0.0888906	+	0.262987i
$43$	−5.59241			−0.852834			−0.426417	−	0.904527i	$-0.640224\pi$
$43$	−5.59241			−0.852834			−0.426417	+	0.904527i	$0.640224\pi$
$44$	−2.98790	+	4.32326i	−0.450442	+	0.651756i
$45$	−0.266630	−	2.48705i	−0.0397468	−	0.370747i
$46$	−8.28461	−	5.87117i	−1.22150	−	0.865656i
$47$	7.85457	−	2.55210i	1.14571	−	0.372263i	0.326182	−	0.945307i	$-0.394238\pi$
$47$	7.85457	−	2.55210i	1.14571	−	0.372263i	0.819524	+	0.573044i	$0.194238\pi$
$48$	−1.93951	−	5.13230i	−0.279944	−	0.740783i
$49$	6.13981			0.877116
$50$	6.06656	−	3.63274i	0.857942	−	0.513747i
$51$		−	1.28868i		−	0.180452i
$52$	−4.09803	+	3.12761i	−0.568295	+	0.433722i
$53$	3.01052	+	9.26543i	0.413527	+	1.27270i	0.913562	+	0.406699i	$0.133320\pi$
$53$	3.01052	+	9.26543i	0.413527	+	1.27270i	−0.500035	+	0.866005i	$0.666680\pi$
$54$	4.61944	−	6.51833i	0.628626	−	0.887033i
$55$	−2.40098	−	5.36264i	−0.323748	−	0.723099i
$56$	2.62162	−	0.0927522i	0.350329	−	0.0123945i
$57$		−	0.485392i		−	0.0642918i
$58$	0.633568	+	1.87444i	0.0831915	+	0.246126i
$59$	−2.55804	−	3.52083i	−0.333028	−	0.458374i	0.609361	−	0.792893i	$-0.291426\pi$
$59$	−2.55804	−	3.52083i	−0.333028	−	0.458374i	−0.942389	+	0.334519i	$0.891426\pi$
$60$	6.03084	+	1.12102i	0.778578	+	0.144723i
$61$	−2.14775	+	2.95612i	−0.274991	+	0.378492i	−0.924067	−	0.382231i	$-0.875156\pi$
$61$	−2.14775	+	2.95612i	−0.274991	+	0.378492i	0.649076	+	0.760724i	$0.275156\pi$
$62$	−5.87169	−	1.83159i	−0.745705	−	0.232612i
$63$	0.609812	+	0.839334i	0.0768291	+	0.105746i
$64$	−7.98000	+	0.565368i	−0.997500	+	0.0706710i
$65$	−0.614386	−	5.73082i	−0.0762052	−	0.710821i
$66$	1.51783	−	4.86583i	0.186832	−	0.598943i
$67$	0.325879	−	1.00295i	0.0398124	−	0.122530i	−0.929175	−	0.369640i	$-0.879481\pi$
$67$	0.325879	−	1.00295i	0.0398124	−	0.122530i	0.968987	+	0.247110i	$0.0794809\pi$
$68$	−1.80027	−	0.538366i	−0.218315	−	0.0652865i
$69$	9.36636	+	3.04331i	1.12758	+	0.366372i
$70$	−1.43108	+	2.56005i	−0.171047	+	0.305985i
$71$	3.56365	+	10.9678i	0.422927	+	1.30164i	0.904965	+	0.425486i	$0.139897\pi$
$71$	3.56365	+	10.9678i	0.422927	+	1.30164i	−0.482038	+	0.876151i	$0.660103\pi$
$72$	−1.94905	−	2.49231i	−0.229698	−	0.293722i
$73$	−9.25671	+	12.7408i	−1.08342	+	1.49119i	−0.227712	+	0.973729i	$0.573124\pi$
$73$	−9.25671	+	12.7408i	−1.08342	+	1.49119i	−0.855704	+	0.517466i	$0.826876\pi$
$74$	−7.80136	−	10.4757i	−0.906889	−	1.21778i
$75$	−4.56778	+	5.11566i	−0.527442	+	0.590706i
$76$	−0.678086	−	0.202780i	−0.0777817	−	0.0232604i
$77$	1.97161	+	1.43246i	0.224686	+	0.163244i
$78$	2.89102	−	4.07942i	0.327344	−	0.461904i
$79$	−1.73030	−	5.32530i	−0.194673	−	0.599143i	−0.999980	−	0.00628500i	$-0.997999\pi$
$79$	−1.73030	−	5.32530i	−0.194673	−	0.599143i	0.805307	−	0.592858i	$-0.202001\pi$
$80$	4.08551	−	7.95667i	0.456774	−	0.889583i
$81$	−1.35747	+	4.17785i	−0.150830	+	0.464206i
$82$	8.01855	+	10.7673i	0.885500	+	1.18905i
$83$	−2.17829	+	6.70408i	−0.239098	+	0.735868i	0.757453	+	0.652889i	$0.226443\pi$
$83$	−2.17829	+	6.70408i	−0.239098	+	0.735868i	−0.996551	+	0.0829787i	$0.973557\pi$
$84$	−2.40055	+	0.843052i	−0.261921	+	0.0919845i
$85$	1.55830	−	1.40898i	0.169021	−	0.152825i
$86$	−0.0932301	−	7.90831i	−0.0100533	−	0.852775i
$87$	−1.12799	−	1.55254i	−0.120933	−	0.166450i
$88$	−6.16340	−	4.15316i	−0.657021	−	0.442728i
$89$	7.12799	+	5.17879i	0.755566	+	0.548951i	0.897547	−	0.440919i	$-0.145347\pi$
$89$	7.12799	+	5.17879i	0.755566	+	0.548951i	−0.141981	+	0.989869i	$0.545347\pi$
$90$	3.51253	−	0.418506i	0.370253	−	0.0441144i
$91$	1.40517	+	1.93405i	0.147302	+	0.202743i
$92$	8.16440	−	11.8133i	0.851197	−	1.23162i
$93$	5.96555			0.618598
$94$	3.73991	+	11.0647i	0.385742	+	1.14124i
$95$	0.586945	−	0.530702i	0.0602193	−	0.0544489i
$96$	7.22533	−	2.82824i	0.737432	−	0.288656i
$97$	1.52791	−	0.496446i	0.155135	−	0.0504065i	−0.230420	−	0.973091i	$-0.574010\pi$
$97$	1.52791	−	0.496446i	0.155135	−	0.0504065i	0.385555	+	0.922685i	$0.374010\pi$
$98$	0.102356	+	8.68240i	0.0103395	+	0.877055i
$99$		−	2.93933i		−	0.295414i
$100$	5.23825	+	8.51826i	0.523825	+	0.851826i
$101$			7.75829i			0.771979i	0.922503	+	0.385989i	$0.126140\pi$
$101$			7.75829i			0.771979i	−0.922503	+	0.385989i	$0.873860\pi$
$102$	1.82235	−	0.0214834i	0.180439	−	0.00212717i
$103$	1.34359	−	0.436559i	0.132388	−	0.0430155i	−0.242074	−	0.970258i	$-0.577828\pi$
$103$	1.34359	−	0.436559i	0.132388	−	0.0430155i	0.374462	+	0.927242i	$0.377828\pi$
$104$	−4.49112	−	5.74295i	−0.440391	−	0.563143i
$105$	0.585636	−	2.78365i	0.0571523	−	0.271657i
$106$	−13.0522	+	4.41168i	−1.26774	+	0.428501i
$107$	16.9717			1.64071			0.820357	−	0.571852i	$-0.193775\pi$
$107$	16.9717			1.64071			0.820357	+	0.571852i	$0.193775\pi$
$108$	9.29468	+	6.42375i	0.894381	+	0.618125i
$109$	−6.86530	−	9.44928i	−0.657577	−	0.905077i	0.341822	−	0.939765i	$-0.388956\pi$
$109$	−6.86530	−	9.44928i	−0.657577	−	0.905077i	−0.999398	+	0.0346883i	$0.988956\pi$
$110$	7.54337	−	3.48466i	0.719232	−	0.332249i
$111$	10.2488	+	7.44618i	0.972772	+	0.706760i
$112$	0.174867	+	3.70573i	0.0165234	+	0.350158i
$113$	−0.532915	−	0.733494i	−0.0501324	−	0.0690013i	0.783215	−	0.621751i	$-0.213578\pi$
$113$	−0.532915	−	0.733494i	−0.0501324	−	0.0690013i	−0.833347	+	0.552750i	$0.813578\pi$
$114$	0.686401	−	0.00809189i	0.0642873	−	0.000757875i
$115$	6.56065	+	14.6534i	0.611784	+	1.36643i
$116$	−2.64012	+	0.927186i	−0.245129	+	0.0860871i
$117$	0.890998	−	2.74221i	0.0823728	−	0.253517i
$118$	4.93622	−	3.67605i	0.454416	−	0.338408i
$119$	−0.269269	+	0.828724i	−0.0246838	+	0.0759690i
$120$	−1.48471	+	8.54699i	−0.135535	+	0.780230i
$121$	1.26557	+	3.89502i	0.115052	+	0.354093i
$122$	−4.21610	−	2.98788i	−0.381708	−	0.270510i
$123$	−10.5341	−	7.65349i	−0.949830	−	0.690092i
$124$	2.49219	−	8.33378i	0.223806	−	0.748395i
$125$	−11.1801	+	0.0697518i	−0.999981	+	0.00623879i
$126$	−1.17675	+	0.876337i	−0.104833	+	0.0780703i
$127$	9.56787	−	13.1690i	0.849012	−	1.16856i	−0.135068	−	0.990836i	$-0.543125\pi$
$127$	9.56787	−	13.1690i	0.849012	−	1.16856i	0.984080	−	0.177728i	$-0.0568747\pi$
$128$	−0.932529	−	11.2752i	−0.0824247	−	0.996597i
$129$	2.37039	+	7.29531i	0.208701	+	0.642317i
$130$	8.09380	−	0.964350i	0.709873	−	0.0845791i
$131$	15.6123	+	5.07274i	1.36405	+	0.443207i	0.897393	−	0.441231i	$-0.145458\pi$
$131$	15.6123	+	5.07274i	1.36405	+	0.443207i	0.466657	+	0.884438i	$0.345458\pi$
$132$	6.90616	+	2.06527i	0.601104	+	0.179758i
$133$	−0.101422	+	0.312145i	−0.00879441	+	0.0270664i
$134$	1.42372	+	0.444110i	0.122991	+	0.0383653i
$135$	−11.5293	+	5.16192i	−0.992282	+	0.444267i
$136$	0.731300	−	2.55476i	0.0627084	−	0.219069i
$137$	−13.1690	−	18.1256i	−1.12510	−	1.54857i	−0.797051	−	0.603913i	$-0.793608\pi$
$137$	−13.1690	−	18.1256i	−1.12510	−	1.54857i	−0.328053	−	0.944659i	$-0.606392\pi$
$138$	−4.14745	+	13.2958i	−0.353054	+	1.13182i
$139$	−6.92525	+	9.53178i	−0.587392	+	0.808475i	−0.994481	−	0.104913i	$-0.966544\pi$
$139$	−6.92525	+	9.53178i	−0.587392	+	0.808475i	0.407090	+	0.913388i	$0.366544\pi$
$140$	−3.64407	−	1.98104i	−0.307980	−	0.167428i
$141$	−6.65845	−	9.16457i	−0.560743	−	0.771796i
$142$	−15.4503	+	5.22225i	−1.29656	+	0.438242i
$143$		−	6.77299i		−	0.566386i
$144$	3.49192	−	2.79773i	0.290994	−	0.233144i
$145$	0.644081	−	3.06146i	0.0534880	−	0.254240i
$146$	−18.1712	−	12.8777i	−1.50386	−	1.06576i
$147$	−2.60241	−	8.00941i	−0.214643	−	0.660605i
$148$	14.6838	−	11.2067i	1.20700	−	0.921181i
$149$		−	13.3102i		−	1.09041i	−0.838302	−	0.545207i	$-0.816451\pi$
$149$		−	13.3102i		−	1.09041i	0.838302	−	0.545207i	$-0.183549\pi$
$150$	−7.31029	−	6.37408i	−0.596882	−	0.520442i
$151$	−21.1864			−1.72412			−0.862062	−	0.506802i	$-0.830827\pi$
$151$	−21.1864			−1.72412			−0.862062	+	0.506802i	$0.830827\pi$
$152$	0.275450	−	0.962272i	0.0223419	−	0.0780505i
$153$	0.999527	−	0.324766i	0.0808069	−	0.0262558i
$154$	−1.99279	+	2.81196i	−0.160584	+	0.226595i
$155$	6.52241	+	7.21365i	0.523893	+	0.579414i
$156$	5.81697	+	4.02023i	0.465730	+	0.321876i
$157$	−3.41079			−0.272211			−0.136105	−	0.990694i	$-0.543459\pi$
$157$	−3.41079			−0.272211			−0.136105	+	0.990694i	$0.543459\pi$
$158$	7.50175	−	2.53561i	0.596807	−	0.201723i
$159$	10.8107	−	7.85446i	0.857348	−	0.622900i
$160$	11.3198	+	5.64474i	0.894905	+	0.446256i
$161$	−5.38740	−	3.91418i	−0.424587	−	0.308480i
$162$	−5.93059	−	1.84997i	−0.465951	−	0.145347i
$163$	15.7109	−	11.4146i	1.23057	−	0.894062i	0.233639	−	0.972324i	$-0.424937\pi$
$163$	15.7109	−	11.4146i	1.23057	−	0.894062i	0.996933	+	0.0782611i	$0.0249368\pi$
$164$	−15.0926	+	11.5187i	−1.17853	+	0.899456i
$165$	−5.97791	+	5.40509i	−0.465380	+	0.420785i
$166$	−9.51665	−	2.96859i	−0.738635	−	0.230407i
$167$	−2.68999	−	0.874029i	−0.208157	−	0.0676344i	0.203082	−	0.979162i	$-0.434904\pi$
$167$	−2.68999	−	0.874029i	−0.208157	−	0.0676344i	−0.411240	+	0.911527i	$0.634904\pi$
$168$	−1.23219	−	3.38060i	−0.0950657	−	0.260819i
$169$	−1.96412	+	6.04495i	−0.151087	+	0.464997i
$170$	2.01843	+	2.18013i	0.154807	+	0.167208i
$171$	0.376479	−	0.122326i	0.0287901	−	0.00935447i
$172$	11.1817	−	0.263676i	0.852597	−	0.0201051i
$173$	−0.694928	−	0.504895i	−0.0528344	−	0.0383864i	0.561055	−	0.827779i	$-0.310396\pi$
$173$	−0.694928	−	0.504895i	−0.0528344	−	0.0383864i	−0.613889	+	0.789392i	$0.710396\pi$
$174$	2.17667	−	1.62099i	0.165013	−	0.122887i
$175$	4.00635	−	2.33534i	0.302852	−	0.176535i
$176$	5.77030	−	8.78500i	0.434952	−	0.662194i
$177$	−3.50869	+	4.82930i	−0.263730	+	0.362993i
$178$	−7.20458	+	10.1661i	−0.540006	+	0.761984i
$179$	−21.7579	+	7.06957i	−1.62626	+	0.528404i	−0.973408	−	0.229079i	$-0.926428\pi$
$179$	−21.7579	+	7.06957i	−1.62626	+	0.528404i	−0.652854	+	0.757484i	$0.726428\pi$
$180$	0.650373	+	4.96014i	0.0484759	+	0.369707i
$181$	−18.5330	−	6.02173i	−1.37754	−	0.447591i	−0.475683	−	0.879617i	$-0.657799\pi$
$181$	−18.5330	−	6.02173i	−1.37754	−	0.447591i	−0.901862	+	0.432025i	$0.857799\pi$
$182$	−2.71154	+	2.01931i	−0.200993	+	0.149681i
$183$	4.76661	+	1.54876i	0.352358	+	0.114488i
$184$	16.8414	+	11.3485i	1.24157	+	0.836620i
$185$	2.20143	+	20.5343i	0.161852	+	1.50971i
$186$	0.0994506	+	8.43597i	0.00729207	+	0.618555i
$187$	1.99725	−	1.45109i	0.146053	−	0.106114i
$188$	−15.5844	+	5.47312i	−1.13661	+	0.399168i
$189$	3.07968	−	4.23881i	0.224013	−	0.308328i
$190$	0.760259	+	0.821161i	0.0551550	+	0.0595733i
$191$	10.2038	−	7.41347i	0.738318	−	0.536420i	−0.153866	−	0.988092i	$-0.549172\pi$
$191$	10.2038	−	7.41347i	0.738318	−	0.536420i	0.892184	+	0.451672i	$0.149172\pi$
$192$	4.11992	+	10.1703i	0.297329	+	0.733978i
$193$			8.48402i			0.610693i	0.952241	+	0.305347i	$0.0987723\pi$
$193$			8.48402i			0.610693i	−0.952241	+	0.305347i	$0.901228\pi$
$194$	0.727504	+	2.15236i	0.0522317	+	0.154530i
$195$	−7.21546	+	3.23053i	−0.516710	+	0.231343i
$196$	−12.2762	+	0.289486i	−0.876872	+	0.0206776i
$197$	4.55285	+	14.0122i	0.324377	+	0.998331i	0.971721	+	0.236132i	$0.0758799\pi$
$197$	4.55285	+	14.0122i	0.324377	+	0.998331i	−0.647344	+	0.762198i	$0.724120\pi$
$198$	4.15655	−	0.0490010i	0.295393	−	0.00348235i
$199$	5.70622			0.404503			0.202252	−	0.979334i	$-0.435174\pi$
$199$	5.70622			0.404503			0.202252	+	0.979334i	$0.435174\pi$
$200$	−11.9585	+	7.54949i	−0.845592	+	0.533830i
$201$	−1.44648			−0.102027
$202$	−10.9711	+	0.129337i	−0.771925	+	0.00910013i
$203$	0.400983	+	1.23410i	0.0281435	+	0.0866168i
$204$	0.0607600	+	2.57665i	0.00425405	+	0.180401i
$205$	−2.26271	−	21.1060i	−0.158035	−	1.47411i
$206$	0.639744	+	1.89272i	0.0445731	+	0.131872i
$207$			8.03168i			0.558240i
$208$	8.04632	−	6.44671i	0.557912	−	0.446999i
$209$	0.752279	−	0.546562i	0.0520362	−	0.0378065i
$210$	3.94617	+	0.781751i	0.272312	+	0.0539460i
$211$	7.99954	−	11.0104i	0.550711	−	0.757989i	−0.439398	−	0.898293i	$-0.644808\pi$
$211$	7.99954	−	11.0104i	0.550711	−	0.757989i	0.990108	+	0.140304i	$0.0448080\pi$
$212$	−6.45622	−	18.3838i	−0.443415	−	1.26260i
$213$	12.7970	−	9.29758i	0.876838	−	0.637060i
$214$	0.282932	+	23.9999i	0.0193408	+	1.64060i
$215$	−6.22997	+	10.8426i	−0.424880	+	0.739461i
$216$	−8.92897	+	13.2508i	−0.607539	+	0.901606i
$217$	−3.83631	−	1.24649i	−0.260426	−	0.0846175i
$218$	13.2479	−	9.86586i	0.897262	−	0.668200i
$219$	20.5439	+	6.67512i	1.38823	+	0.451063i
$220$	5.05347	+	10.6091i	0.340705	+	0.715266i
$221$	2.30318	−	0.748347i	0.154928	−	0.0503393i
$222$	−10.3589	+	14.6171i	−0.695244	+	0.981036i
$223$	13.3402	−	18.3612i	0.893328	−	1.22956i	−0.0792204	−	0.996857i	$-0.525243\pi$
$223$	13.3402	−	18.3612i	0.893328	−	1.22956i	0.972548	−	0.232703i	$-0.0747569\pi$
$224$	−5.23741	+	0.309059i	−0.349939	+	0.0206499i
$225$	−5.11895	−	2.25364i	−0.341263	−	0.150243i
$226$	1.02836	−	0.765831i	0.0684056	−	0.0509423i
$227$	−11.1188	−	8.07830i	−0.737983	−	0.536176i	0.154096	−	0.988056i	$-0.450753\pi$
$227$	−11.1188	−	8.07830i	−0.737983	−	0.536176i	−0.892079	+	0.451880i	$0.850753\pi$
$228$	0.0228857	+	0.970515i	0.00151564	+	0.0642739i
$229$	−6.28758	+	2.04296i	−0.415495	+	0.135002i	−0.509302	−	0.860588i	$-0.670096\pi$
$229$	−6.28758	+	2.04296i	−0.415495	+	0.135002i	0.0938071	+	0.995590i	$0.470096\pi$
$230$	−20.6122	+	9.52180i	−1.35913	+	0.627849i
$231$	1.03296	−	3.17913i	0.0679639	−	0.209171i
$232$	−1.35516	−	3.71797i	−0.0889707	−	0.244097i
$233$	−13.6940	−	4.44945i	−0.897123	−	0.291493i	−0.176074	−	0.984377i	$-0.556340\pi$
$233$	−13.6940	−	4.44945i	−0.897123	−	0.291493i	−0.721049	+	0.692884i	$0.756340\pi$
$234$	3.89265	+	1.21426i	0.254471	+	0.0793786i
$235$	3.80197	−	18.0716i	0.248013	−	1.17886i
$236$	5.28065	+	6.91910i	0.343741	+	0.450395i
$237$	−6.21347	+	4.51435i	−0.403608	+	0.293239i
$238$	−1.17640	−	0.366961i	−0.0762547	−	0.0237866i
$239$	−0.520809	−	0.378390i	−0.0336883	−	0.0244760i	0.570814	−	0.821080i	$-0.306628\pi$
$239$	−0.520809	−	0.378390i	−0.0336883	−	0.0244760i	−0.604502	+	0.796604i	$0.706628\pi$
$240$	−12.1112	−	1.95706i	−0.781773	−	0.126328i
$241$	−18.0169	+	13.0900i	−1.16057	+	0.843202i	−0.989850	−	0.142118i	$-0.954609\pi$
$241$	−18.0169	+	13.0900i	−1.16057	+	0.843202i	−0.170719	+	0.985320i	$0.554609\pi$
$242$	−5.48691	+	1.85459i	−0.352712	+	0.119218i
$243$	−10.9223			−0.700668
$244$	4.15492	−	6.01186i	0.265992	−	0.384870i
$245$	6.83978	−	11.9039i	0.436977	−	0.760515i
$246$	10.6473	−	15.0241i	0.678847	−	0.957899i
$247$	0.867509	−	0.281871i	0.0551983	−	0.0179350i
$248$	11.8265	+	3.38532i	0.750982	+	0.214968i
$249$	9.66877			0.612734
$250$	−0.285019	−	15.8088i	−0.0180262	−	0.999838i
$251$			5.01412i			0.316488i	0.987400	+	0.158244i	$0.0505833\pi$
$251$			5.01412i			0.316488i	−0.987400	+	0.158244i	$0.949417\pi$
$252$	−1.25886	−	1.64945i	−0.0793006	−	0.103906i
$253$	5.83009	+	17.9432i	0.366534	+	1.12808i
$254$	18.7821	+	13.3105i	1.17849	+	0.835177i
$255$	−2.49851	−	1.43560i	−0.156463	−	0.0899006i
$256$	15.9289	−	1.50667i	0.995556	−	0.0941669i
$257$		−	4.08455i		−	0.254787i	−0.991852	−	0.127394i	$-0.959339\pi$
$257$		−	4.08455i		−	0.254787i	0.991852	−	0.127394i	$-0.0406611\pi$
$258$	−10.2769	+	3.47363i	−0.639812	+	0.216258i
$259$	−5.03490	−	6.92995i	−0.312854	−	0.430606i
$260$	1.49863	+	11.4295i	0.0929412	+	0.708827i
$261$	0.919914	−	1.26615i	0.0569412	−	0.0783729i
$262$	−6.91316	+	22.1621i	−0.427097	+	1.36918i
$263$	−14.0516	−	19.3404i	−0.866458	−	1.19258i	−0.979991	−	0.199043i	$-0.936217\pi$
$263$	−14.0516	−	19.3404i	−0.866458	−	1.19258i	0.113532	−	0.993534i	$-0.463783\pi$
$264$	−2.80540	+	9.80053i	−0.172660	+	0.603181i
$265$	21.3177	+	4.48489i	1.30953	+	0.275505i
$266$	−0.443100	−	0.138219i	−0.0271682	−	0.00847474i
$267$	3.73448	−	11.4936i	0.228547	−	0.703395i
$268$	−0.604288	+	2.02071i	−0.0369128	+	0.123435i
$269$	28.5572	+	9.27879i	1.74116	+	0.565738i	0.994986	−	0.100011i	$-0.0318876\pi$
$269$	28.5572	+	9.27879i	1.74116	+	0.565738i	0.746176	+	0.665749i	$0.231888\pi$
$270$	−7.49175	−	16.2177i	−0.455933	−	0.986976i
$271$	1.45987	+	4.49301i	0.0886807	+	0.272931i	0.985555	−	0.169354i	$-0.0541680\pi$
$271$	1.45987	+	4.49301i	0.0886807	+	0.272931i	−0.896875	+	0.442285i	$0.854168\pi$
$272$	3.62492	+	0.991552i	0.219793	+	0.0601217i
$273$	1.92738	−	2.65281i	0.116650	−	0.160555i
$274$	25.4121	−	18.9246i	1.53520	−	1.14328i
$275$	−13.0719	−	1.31896i	−0.788263	−	0.0795364i
$276$	−18.8710	−	5.64332i	−1.13590	−	0.339688i
$277$	3.00568	+	2.18376i	0.180594	+	0.131209i	0.674410	−	0.738357i	$-0.264398\pi$
$277$	3.00568	+	2.18376i	0.180594	+	0.131209i	−0.493816	+	0.869567i	$0.664398\pi$
$278$	−13.5945	−	9.63419i	−0.815343	−	0.577820i
$279$	1.50340	+	4.62699i	0.0900062	+	0.277011i
$280$	2.74067	−	5.18615i	0.163786	−	0.309932i
$281$	4.25051	−	13.0817i	0.253564	−	0.780389i	−0.740545	−	0.672006i	$-0.765433\pi$
$281$	4.25051	−	13.0817i	0.253564	−	0.780389i	0.994109	−	0.108383i	$-0.0345673\pi$
$282$	12.8488	−	9.56860i	0.765133	−	0.569802i
$283$	0.460617	−	1.41763i	0.0273808	−	0.0842695i	−0.936432	−	0.350848i	$-0.885893\pi$
$283$	0.460617	−	1.41763i	0.0273808	−	0.0842695i	0.963813	+	0.266579i	$0.0858933\pi$
$284$	−7.64244	−	21.7615i	−0.453495	−	1.29130i
$285$	−0.941084	−	0.540729i	−0.0557450	−	0.0320300i
$286$	9.57779	−	0.112911i	0.566347	−	0.00667659i
$287$	5.17508	+	7.12288i	0.305475	+	0.420450i
$288$	4.01452	+	4.89134i	0.236558	+	0.288225i
$289$	−13.0392	−	9.47351i	−0.767010	−	0.557265i
$290$	4.33999	+	0.859768i	0.254853	+	0.0504873i
$291$	−1.29523	−	1.78273i	−0.0759278	−	0.104506i
$292$	17.9076	−	25.9109i	1.04796	−	1.51632i
$293$	−7.33412			−0.428464			−0.214232	−	0.976783i	$-0.568725\pi$
$293$	−7.33412			−0.428464			−0.214232	+	0.976783i	$0.568725\pi$
$294$	11.2828	−	3.81364i	0.658029	−	0.222416i
$295$	−9.67590	+	1.03733i	−0.563353	+	0.0603955i
$296$	16.0923	+	20.5777i	0.935346	+	1.19606i
$297$	−14.1177	+	4.58711i	−0.819191	+	0.266171i
$298$	18.8221	−	0.221892i	1.09034	−	0.0128539i
$299$			18.5071i			1.07029i
$300$	8.89182	−	10.4438i	0.513370	−	0.602976i
$301$		−	5.18675i		−	0.298959i
$302$	−0.353195	−	29.9600i	−0.0203241	−	1.72400i
$303$	10.1207	−	3.28842i	0.581420	−	0.188915i
$304$	1.36536	+	0.373476i	0.0783085	+	0.0214203i
$305$	3.33876	+	7.45721i	0.191177	+	0.426998i
$306$	0.475919	+	1.40803i	0.0272065	+	0.0804918i
$307$	−3.91344			−0.223352			−0.111676	−	0.993745i	$-0.535622\pi$
$307$	−3.91344			−0.223352			−0.111676	+	0.993745i	$0.535622\pi$
$308$	−4.00966	−	2.77116i	−0.228472	−	0.157902i
$309$	−1.13899	−	1.56768i	−0.0647947	−	0.0891822i
$310$	−10.0922	+	9.34370i	−0.573198	+	0.530687i
$311$	5.35582	+	3.89123i	0.303701	+	0.220652i	0.729189	−	0.684312i	$-0.239898\pi$
$311$	5.35582	+	3.89123i	0.303701	+	0.220652i	−0.425488	+	0.904964i	$0.639898\pi$
$312$	−5.58809	+	8.29289i	−0.316363	+	0.469492i
$313$	12.0592	+	16.5981i	0.681628	+	0.938180i	0.999952	−	0.00980162i	$-0.00312000\pi$
$313$	12.0592	+	16.5981i	0.681628	+	0.938180i	−0.318324	+	0.947982i	$0.603120\pi$
$314$	−0.0568607	−	4.82325i	−0.00320884	−	0.272192i
$315$	2.30664	−	0.247289i	0.129965	−	0.0139332i
$316$	3.71071	+	10.5661i	0.208744	+	0.594387i
$317$	1.53918	−	4.73712i	0.0864492	−	0.266063i	−0.898482	−	0.439011i	$-0.855329\pi$
$317$	1.53918	−	4.73712i	0.0864492	−	0.266063i	0.984931	+	0.172947i	$0.0553290\pi$
$318$	11.2873	+	15.1567i	0.632963	+	0.849945i
$319$	1.13605	−	3.49640i	0.0636065	−	0.195761i
$320$	−7.79361	+	16.1015i	−0.435676	+	0.900104i
$321$	−7.19359	−	22.1396i	−0.401507	−	1.23571i
$322$	5.44529	−	7.68366i	0.303454	−	0.428194i
$323$	0.268979	+	0.195425i	0.0149664	+	0.0108737i
$324$	2.51720	−	8.41738i	0.139844	−	0.467632i
$325$	−11.7954	−	5.19298i	−0.654292	−	0.288055i
$326$	16.4035	+	22.0267i	0.908506	+	1.21995i
$327$	−9.41669	+	12.9610i	−0.520744	+	0.716743i
$328$	−16.5403	−	21.1506i	−0.913286	−	1.16785i
$329$	2.36698	+	7.28481i	0.130496	+	0.401625i
$330$	−7.74307	−	8.36335i	−0.426242	−	0.460387i
$331$	18.8854	+	6.13623i	1.03803	+	0.337278i	0.777962	−	0.628311i	$-0.216254\pi$
$331$	18.8854	+	6.13623i	1.03803	+	0.337278i	0.260072	+	0.965589i	$0.416254\pi$
$332$	4.03927	−	13.5071i	0.221684	−	0.741300i
$333$	−3.19256	+	9.82570i	−0.174951	+	0.538445i
$334$	1.19113	−	3.81852i	0.0651760	−	0.208940i
$335$	−1.58151	−	1.74911i	−0.0864069	−	0.0955641i
$336$	4.76001	−	1.79882i	0.259680	−	0.0981336i
$337$	8.18761	+	11.2693i	0.446007	+	0.613876i	0.971534	−	0.236901i	$-0.0761317\pi$
$337$	8.18761	+	11.2693i	0.446007	+	0.613876i	−0.525527	+	0.850777i	$0.676132\pi$
$338$	−8.58101	−	2.67672i	−0.466745	−	0.145595i
$339$	−0.730965	+	1.00609i	−0.0397005	+	0.0546431i
$340$	−3.04930	+	2.89064i	−0.165371	+	0.156767i
$341$	6.71734	+	9.24562i	0.363764	+	0.500679i
$342$	0.179259	+	0.530346i	0.00969320	+	0.0286778i
$343$			12.1867i			0.658019i
$344$	0.559277	+	15.8078i	0.0301542	+	0.852301i
$345$	16.3346	−	14.7693i	0.879424	−	0.795155i
$346$	0.702395	−	0.991126i	0.0377610	−	0.0532832i
$347$	0.983057	+	3.02554i	0.0527733	+	0.162419i	0.973970	−	0.226679i	$-0.0727867\pi$
$347$	0.983057	+	3.02554i	0.0527733	+	0.162419i	−0.921196	+	0.389098i	$0.872787\pi$
$348$	2.32855	+	3.05104i	0.124824	+	0.163553i
$349$			17.7286i			0.948990i	0.880258	+	0.474495i	$0.157369\pi$
$349$			17.7286i			0.948990i	−0.880258	+	0.474495i	$0.842631\pi$
$350$	3.36923	+	5.62651i	0.180093	+	0.300750i
$351$	−14.5614			−0.777231
$352$	12.5192	+	8.01341i	0.667275	+	0.427116i
$353$	23.9311	−	7.77568i	1.27372	−	0.413858i	0.407358	−	0.913269i	$-0.366450\pi$
$353$	23.9311	−	7.77568i	1.27372	−	0.413858i	0.866365	+	0.499411i	$0.166450\pi$
$354$	−6.88768	−	4.88119i	−0.366076	−	0.259432i
$355$	25.2344	+	5.30891i	1.33930	+	0.281768i
$356$	−14.4962	−	10.0186i	−0.768297	−	0.530986i
$357$	1.19520			0.0632569
$358$	−10.3599	−	30.6503i	−0.547538	−	1.61992i
$359$	−24.3831	+	17.7154i	−1.28689	+	0.934983i	−0.999738	−	0.0229013i	$-0.992710\pi$
$359$	−24.3831	+	17.7154i	−1.28689	+	0.934983i	−0.287156	+	0.957884i	$0.592710\pi$
$360$	−7.00337	+	1.00239i	−0.369110	+	0.0528307i
$361$	−15.2700	−	11.0943i	−0.803685	−	0.583911i
$362$	8.20646	−	26.3081i	0.431322	−	1.38273i
$363$	4.54465	−	3.30188i	0.238532	−	0.173304i
$364$	−2.90074	−	3.80077i	−0.152040	−	0.199214i
$365$	14.3899	+	32.1403i	0.753204	+	1.68230i
$366$	−2.11067	+	6.76635i	−0.110326	+	0.353683i
$367$	6.38802	+	2.07559i	0.333452	+	0.108345i	0.470957	−	0.882156i	$-0.343909\pi$
$367$	6.38802	+	2.07559i	0.333452	+	0.108345i	−0.137506	+	0.990501i	$0.543909\pi$
$368$	−15.7673	+	24.0049i	−0.821926	+	1.25134i
$369$	3.28144	−	10.0992i	0.170825	−	0.525746i
$370$	−29.0012	+	3.45539i	−1.50770	+	0.179637i
$371$	−8.59333	+	2.79214i	−0.446144	+	0.144961i
$372$	−11.9278	+	0.281269i	−0.618427	+	0.0145831i
$373$	−19.6096	−	14.2472i	−1.01535	−	0.737692i	−0.0500223	−	0.998748i	$-0.515929\pi$
$373$	−19.6096	−	14.2472i	−1.01535	−	0.737692i	−0.965324	+	0.261056i	$0.915929\pi$
$374$	2.08530	+	2.80015i	0.107828	+	0.144792i
$375$	4.82978	+	14.5549i	0.249409	+	0.751614i
$376$	−7.99943	−	21.9470i	−0.412539	−	1.13183i
$377$	2.11973	−	2.91755i	0.109171	−	0.150262i
$378$	6.04551	+	4.28435i	0.310947	+	0.220363i
$379$	−7.74403	+	2.51619i	−0.397784	+	0.129248i	−0.501076	−	0.865403i	$-0.667062\pi$
$379$	−7.74403	+	2.51619i	−0.397784	+	0.129248i	0.103292	+	0.994651i	$0.467062\pi$
$380$	−1.14854	+	1.08878i	−0.0589190	+	0.0558534i
$381$	−21.2345	−	6.89950i	−1.08788	−	0.353472i
$382$	10.6536	+	14.3057i	0.545086	+	0.731944i
$383$	8.59217	+	2.79177i	0.439040	+	0.142653i	0.520192	−	0.854049i	$-0.325860\pi$
$383$	8.59217	+	2.79177i	0.439040	+	0.142653i	−0.0811529	+	0.996702i	$0.525860\pi$
$384$	−14.3133	+	5.99558i	−0.730422	+	0.305961i
$385$	4.97365	−	2.22682i	0.253481	−	0.113489i
$386$	−11.9974	+	0.141436i	−0.610651	+	0.00719889i
$387$	−5.06101	+	3.67704i	−0.257266	+	0.186914i
$388$	−3.03155	+	1.06466i	−0.153904	+	0.0540497i
$389$	7.45733	−	10.2641i	0.378102	−	0.520412i	−0.576979	−	0.816759i	$-0.695768\pi$
$389$	7.45733	−	10.2641i	0.378102	−	0.520412i	0.955080	+	0.296347i	$0.0957685\pi$
$390$	−4.68863	−	10.1496i	−0.237418	−	0.513947i
$391$	−5.45746	+	3.96507i	−0.275995	+	0.200522i
$392$	−0.614021	−	17.3552i	−0.0310127	−	0.876568i
$393$		−	22.5164i		−	1.13580i
$394$	−19.7390	+	6.67185i	−0.994438	+	0.336123i
$395$	−12.2523	−	2.57769i	−0.616481	−	0.129698i
$396$	0.138586	+	5.87702i	0.00696422	+	0.295331i
$397$	4.22625	+	13.0071i	0.212109	+	0.652805i	0.999346	+	0.0361546i	$0.0115109\pi$
$397$	4.22625	+	13.0071i	0.212109	+	0.652805i	−0.787237	+	0.616651i	$0.788489\pi$
$398$	0.0951275	+	8.06926i	0.00476831	+	0.404475i
$399$	0.450183			0.0225373
$400$	−10.8752	−	16.7848i	−0.543760	−	0.839241i
$401$	34.7894			1.73730			0.868649	−	0.495428i	$-0.164989\pi$
$401$	34.7894			1.73730			0.868649	+	0.495428i	$0.164989\pi$
$402$	−0.0241140	−	2.04549i	−0.00120270	−	0.102020i
$403$	3.46424	+	10.6618i	0.172566	+	0.531103i
$404$	−0.365795	−	15.5123i	−0.0181990	−	0.771764i
$405$	6.58785	+	7.28602i	0.327353	+	0.362045i
$406$	−1.73847	+	0.587610i	−0.0862790	+	0.0291626i
$407$			24.2685i			1.20295i
$408$	−3.64267	+	0.128877i	−0.180339	+	0.00638034i
$409$	−13.3846	+	9.72446i	−0.661824	+	0.480843i	−0.867278	−	0.497823i	$-0.834133\pi$
$409$	−13.3846	+	9.72446i	−0.661824	+	0.480843i	0.205454	+	0.978667i	$0.434133\pi$
$410$	29.8086	−	3.55159i	1.47214	−	0.175401i
$411$	−18.0631	+	24.8617i	−0.890985	+	1.22634i
$412$	−2.66585	+	0.936225i	−0.131337	+	0.0461245i
$413$	3.26544	−	2.37248i	0.160682	−	0.116742i
$414$	−11.3577	+	0.133895i	−0.558202	+	0.00658057i
$415$	10.5713	+	11.6917i	0.518926	+	0.573921i
$416$	9.25053	+	11.2710i	0.453544	+	0.552604i
$417$	15.3696	+	4.99387i	0.752651	+	0.244551i
$418$	0.785443	+	1.05470i	0.0384173	+	0.0515869i
$419$	−2.26155	−	0.734822i	−0.110484	−	0.0358984i	0.253253	−	0.967400i	$-0.418499\pi$
$419$	−2.26155	−	0.734822i	−0.110484	−	0.0358984i	−0.363737	+	0.931502i	$0.618499\pi$
$420$	−1.03970	+	5.59337i	−0.0507322	+	0.272929i
$421$	5.82497	−	1.89265i	0.283892	−	0.0922420i	−0.163610	−	0.986525i	$-0.552314\pi$
$421$	5.82497	−	1.89265i	0.283892	−	0.0922420i	0.447502	+	0.894283i	$0.352314\pi$
$422$	15.7034	+	11.1287i	0.764428	+	0.541737i
$423$	5.43020	−	7.47402i	0.264025	−	0.363399i
$424$	25.8891	−	9.43631i	1.25729	−	0.458268i
$425$	−0.995791	−	4.59086i	−0.0483030	−	0.222689i
$426$	13.3612	+	17.9415i	0.647352	+	0.869267i
$427$	−2.74169	−	1.99195i	−0.132680	−	0.0963974i
$428$	−33.9339	+	0.800197i	−1.64026	+	0.0386790i
$429$	−8.83539	+	2.87079i	−0.426577	+	0.138603i
$430$	−15.4366	−	8.62914i	−0.744418	−	0.416134i
$431$	9.67194	−	29.7672i	0.465881	−	1.43383i	−0.391990	−	0.919970i	$-0.628213\pi$
$431$	9.67194	−	29.7672i	0.465881	−	1.43383i	0.857871	−	0.513865i	$-0.171787\pi$
$432$	−18.8871	−	12.4057i	−0.908705	−	0.596869i
$433$	14.1827	+	4.60823i	0.681575	+	0.221457i	0.629285	−	0.777175i	$-0.283348\pi$
$433$	14.1827	+	4.60823i	0.681575	+	0.221457i	0.0522905	+	0.998632i	$0.483348\pi$
$434$	1.69873	−	5.44577i	0.0815417	−	0.261405i
$435$	−4.26668	+	0.457419i	−0.204572	+	0.0219316i
$436$	14.1723	+	18.5696i	0.678731	+	0.889323i
$437$	−2.05559	+	1.49348i	−0.0983324	+	0.0714426i
$438$	−9.09691	+	29.1627i	−0.434667	+	1.39345i
$439$	−26.3874	−	19.1715i	−1.25940	−	0.915008i	−0.260672	−	0.965427i	$-0.583944\pi$
$439$	−26.3874	−	19.1715i	−1.25940	−	0.915008i	−0.998728	+	0.0504195i	$0.983944\pi$
$440$	−14.9183	+	7.32305i	−0.711200	+	0.349112i
$441$	5.55640	−	4.03696i	0.264591	−	0.192236i
$442$	1.09664	+	3.24448i	0.0521621	+	0.154324i
$443$	−24.4310			−1.16075			−0.580375	−	0.814349i	$-0.697094\pi$
$443$	−24.4310			−1.16075			−0.580375	+	0.814349i	$0.697094\pi$
$444$	−20.8430	−	14.4050i	−0.989163	−	0.683631i
$445$	17.9813	−	8.05065i	0.852396	−	0.381637i
$446$	26.1873	+	18.5585i	1.24001	+	0.878771i
$447$	−17.3632	+	5.64164i	−0.821251	+	0.266841i
$448$	−0.524358	−	7.40115i	−0.0247736	−	0.349671i
$449$	−11.0987			−0.523780			−0.261890	−	0.965098i	$-0.584346\pi$
$449$	−11.0987			−0.523780			−0.261890	+	0.965098i	$0.584346\pi$
$450$	3.10157	−	7.27635i	0.146209	−	0.343011i
$451$		−	24.9442i		−	1.17457i
$452$	1.10012	+	1.44145i	0.0517451	+	0.0678003i
$453$	8.98004	+	27.6377i	0.421919	+	1.29853i
$454$	11.2383	−	15.8580i	0.527439	−	0.744252i
$455$	5.31512	−	0.569820i	0.249177	−	0.0267136i
$456$	−1.37204	+	0.0485423i	−0.0642516	+	0.00227320i
$457$		−	10.7162i		−	0.501281i	−0.968080	−	0.250641i	$-0.919359\pi$
$457$		−	10.7162i		−	0.501281i	0.968080	−	0.250641i	$-0.0806412\pi$
$458$	−2.99380	−	8.85730i	−0.139891	−	0.413874i
$459$	−3.11972	−	4.29393i	−0.145616	−	0.200423i
$460$	−13.8085	−	28.9893i	−0.643827	−	1.35163i
$461$	−9.05653	+	12.4652i	−0.421804	+	0.580564i	−0.966048	−	0.258363i	$-0.916817\pi$
$461$	−9.05653	+	12.4652i	−0.421804	+	0.580564i	0.544243	+	0.838927i	$0.316817\pi$
$462$	4.51288	+	1.40773i	0.209958	+	0.0654935i
$463$	−1.08285	−	1.49042i	−0.0503245	−	0.0692657i	0.783113	−	0.621879i	$-0.213631\pi$
$463$	−1.08285	−	1.49042i	−0.0503245	−	0.0692657i	−0.833438	+	0.552614i	$0.813631\pi$
$464$	5.23505	−	1.97834i	0.243031	−	0.0918419i
$465$	6.64565	−	11.5661i	0.308184	−	0.536364i
$466$	6.06374	−	19.4391i	0.280897	−	0.900497i
$467$	−6.50123	+	20.0087i	−0.300841	+	0.925894i	0.680355	+	0.732883i	$0.261826\pi$
$467$	−6.50123	+	20.0087i	−0.300841	+	0.925894i	−0.981196	+	0.193012i	$0.938174\pi$
$468$	−1.65221	+	5.52490i	−0.0763734	+	0.255389i
$469$	0.930200	+	0.302240i	0.0429527	+	0.0139562i
$470$	25.6187	+	5.07516i	1.18170	+	0.234100i
$471$	1.44569	+	4.44939i	0.0666140	+	0.205017i
$472$	−9.69638	+	7.58280i	−0.446312	+	0.349027i
$473$	−8.63743	+	11.8884i	−0.397150	+	0.546630i
$474$	−6.48740	−	8.71131i	−0.297976	−	0.400124i
$475$	−0.375073	−	1.72918i	−0.0172095	−	0.0793403i
$476$	0.499314	−	1.66968i	0.0228860	−	0.0765298i
$477$	8.81653	+	6.40558i	0.403681	+	0.293292i
$478$	0.526404	−	0.742791i	0.0240772	−	0.0339745i
$479$	0.641151	+	1.97326i	0.0292949	+	0.0901606i	0.964635	−	0.263589i	$-0.0849064\pi$
$479$	0.641151	+	1.97326i	0.0292949	+	0.0901606i	−0.935340	+	0.353750i	$0.884906\pi$
$480$	2.56561	−	17.1592i	0.117103	−	0.783208i
$481$	−7.35651	+	22.6410i	−0.335428	+	1.03234i
$482$	−18.8112	−	25.2597i	−0.856824	−	1.15055i
$483$	−2.82256	+	8.68694i	−0.128431	+	0.395270i
$484$	−2.71408	−	7.72821i	−0.123367	−	0.351282i
$485$	0.739576	−	3.51537i	0.0335824	−	0.159625i
$486$	−0.182084	−	15.4454i	−0.00825951	−	0.700619i
$487$	2.86770	+	3.94704i	0.129948	+	0.178858i	0.869033	−	0.494754i	$-0.164742\pi$
$487$	2.86770	+	3.94704i	0.129948	+	0.178858i	−0.739085	+	0.673612i	$0.764742\pi$
$488$	8.57073	+	5.77531i	0.387979	+	0.261436i
$489$	−21.5496	−	15.6567i	−0.974507	−	0.708021i
$490$	16.9476	+	9.47379i	0.765614	+	0.427982i
$491$	−11.2000	−	15.4154i	−0.505447	−	0.695688i	0.477696	−	0.878525i	$-0.341472\pi$
$491$	−11.2000	−	15.4154i	−0.505447	−	0.695688i	−0.983143	+	0.182837i	$0.941472\pi$
$492$	21.4232	+	14.8060i	0.965834	+	0.667508i
$493$	1.31448			0.0592013
$494$	0.413060	+	1.22206i	0.0185844	+	0.0549830i
$495$	−5.69881	−	3.27442i	−0.256142	−	0.147174i
$496$	−4.59008	+	16.7804i	−0.206100	+	0.753464i
$497$	−10.1722	+	3.30515i	−0.456286	+	0.148256i
$498$	0.161186	+	13.6728i	0.00722294	+	0.612691i
$499$		−	12.8562i		−	0.575522i	−0.957702	−	0.287761i	$-0.907089\pi$
$499$		−	12.8562i		−	0.575522i	0.957702	−	0.287761i	$-0.0929108\pi$
$500$	22.3507	−	0.666596i	0.999556	−	0.0298111i
$501$			3.87956i			0.173326i
$502$	−7.09054	+	0.0835895i	−0.316466	+	0.00373078i
$503$	−23.8717	+	7.75639i	−1.06439	+	0.345840i	−0.788299	−	0.615292i	$-0.789038\pi$
$503$	−23.8717	+	7.75639i	−1.06439	+	0.345840i	−0.276088	+	0.961132i	$0.589038\pi$
$504$	2.31153	−	1.80767i	0.102964	−	0.0805200i
$505$	15.0419	+	8.64277i	0.669354	+	0.384598i
$506$	−25.2765	+	8.54354i	−1.12368	+	0.379807i
$507$	8.71817			0.387188
$508$	−18.5095	+	26.7819i	−0.821227	+	1.18825i
$509$	−7.89183	−	10.8622i	−0.349799	−	0.481457i	0.597472	−	0.801890i	$-0.296172\pi$
$509$	−7.89183	−	10.8622i	−0.349799	−	0.481457i	−0.947271	+	0.320432i	$0.896172\pi$
$510$	1.98845	−	3.55712i	0.0880500	−	0.157512i
$511$	−11.8166	−	8.58525i	−0.522735	−	0.379789i
$512$	2.39615	+	22.5002i	0.105896	+	0.994377i
$513$	−1.17507	−	1.61734i	−0.0518805	−	0.0714074i
$514$	5.77602	−	0.0680928i	0.254769	−	0.00300344i
$515$	0.650360	−	3.09130i	0.0286583	−	0.136219i
$516$	−5.08343	−	14.4748i	−0.223786	−	0.637218i
$517$	6.70603	−	20.6390i	0.294931	−	0.907704i
$518$	9.71581	−	7.23546i	0.426888	−	0.317908i
$519$	−0.364086	+	1.12054i	−0.0159816	+	0.0491862i
$520$	−16.1376	+	2.30978i	−0.707682	+	0.101290i
$521$	−7.91688	−	24.3656i	−0.346845	−	1.06748i	−0.960589	−	0.277973i	$-0.910337\pi$
$521$	−7.91688	−	24.3656i	−0.346845	−	1.06748i	0.613744	−	0.789505i	$-0.289663\pi$
$522$	1.80582	+	1.27976i	0.0790387	+	0.0560134i
$523$	−21.7366	−	15.7926i	−0.950476	−	0.690562i	0.000443114	−	1.00000i	$-0.499859\pi$
$523$	−21.7366	−	15.7926i	−0.950476	−	0.690562i	−0.950919	+	0.309438i	$0.899859\pi$
$524$	−31.4550	−	9.40655i	−1.37412	−	0.410927i
$525$	−4.74458	−	4.23644i	−0.207071	−	0.184894i
$526$	27.1152	−	20.1930i	1.18228	−	0.880456i
$527$	−2.40180	+	3.30580i	−0.104624	+	0.144003i
$528$	−13.9058	−	3.80377i	−0.605174	−	0.165538i
$529$	−8.82326	−	27.1552i	−0.383620	−	1.18066i
$530$	−5.98677	+	30.2204i	−0.260049	+	1.31269i
$531$	−4.62994	−	1.50436i	−0.200922	−	0.0652836i
$532$	0.188071	−	0.628899i	0.00815389	−	0.0272662i
$533$	7.56132	−	23.2714i	0.327517	−	1.00799i
$534$	16.3155	+	5.08939i	0.706040	+	0.220239i
$535$	18.9065	−	32.9049i	0.817400	−	1.42260i
$536$	−2.86759	−	0.820847i	−0.123861	−	0.0354552i
$537$	18.4446	+	25.3867i	0.795941	+	1.09552i
$538$	−12.6452	+	40.5378i	−0.545174	+	1.74771i
$539$	9.48290	−	13.0521i	0.408457	−	0.562193i
$540$	22.8088	−	10.8646i	0.981533	−	0.467536i
$541$	11.1415	+	15.3350i	0.479011	+	0.659302i	0.978314	−	0.207125i	$-0.0664108\pi$
$541$	11.1415	+	15.3350i	0.479011	+	0.659302i	−0.499304	+	0.866427i	$0.666411\pi$
$542$	−6.32930	+	2.13932i	−0.271867	+	0.0918919i
$543$			26.7287i			1.14704i
$544$	−1.34174	+	5.14259i	−0.0575266	+	0.220487i
$545$	−25.9684	+	2.78400i	−1.11236	+	0.119253i
$546$	3.78351	+	2.68131i	0.161919	+	0.114750i
$547$	4.69413	+	14.4470i	0.200706	+	0.617711i	0.999862	+	0.0165870i	$0.00528004\pi$
$547$	4.69413	+	14.4470i	0.200706	+	0.617711i	−0.799156	+	0.601124i	$0.794720\pi$
$548$	27.1853	+	35.6202i	1.16130	+	1.52162i
$549$			4.08738i			0.174445i
$550$	1.64725	−	18.5071i	0.0702388	−	0.789146i
$551$	0.495110			0.0210924
$552$	7.66571	−	26.7798i	0.326274	−	1.13983i
$553$	4.93902	−	1.60478i	0.210028	−	0.0682424i
$554$	−3.03798	+	4.28679i	−0.129071	+	0.182128i
$555$	25.8540	−	11.5754i	1.09744	−	0.491349i
$556$	13.3972	−	19.3848i	0.568169	−	0.822098i
$557$	−1.85471			−0.0785867			−0.0392933	−	0.999228i	$-0.512511\pi$
$557$	−1.85471			−0.0785867			−0.0392933	+	0.999228i	$0.512511\pi$
$558$	−6.51804	+	2.20312i	−0.275931	+	0.0932654i
$559$	−11.6619	+	8.47288i	−0.493247	+	0.358365i
$560$	7.37951	+	3.78916i	0.311841	+	0.160121i
$561$	−2.73950	−	1.99036i	−0.115662	−	0.0840331i
$562$	18.5699	+	5.79262i	0.783324	+	0.244347i
$563$	30.3261	−	22.0332i	1.27809	−	0.928587i	0.278597	−	0.960408i	$-0.410131\pi$
$563$	30.3261	−	22.0332i	1.27809	−	0.928587i	0.999494	+	0.0318207i	$0.0101306\pi$
$564$	13.7453	+	18.0101i	0.578782	+	0.758363i
$565$	−2.01578	+	0.216106i	−0.0848044	+	0.00909164i
$566$	2.01237	+	0.627732i	0.0845864	+	0.0263855i
$567$	−3.87480	−	1.25900i	−0.162726	−	0.0528730i
$568$	30.6458	−	11.1701i	1.28587	−	0.468686i
$569$	−8.05065	+	24.7774i	−0.337501	+	1.03872i	0.627976	+	0.778233i	$0.283884\pi$
$569$	−8.05065	+	24.7774i	−0.337501	+	1.03872i	−0.965477	+	0.260488i	$0.916116\pi$
$570$	0.748965	−	1.33982i	0.0313707	−	0.0561187i
$571$	−31.4963	+	10.2338i	−1.31808	+	0.428270i	−0.881835	−	0.471558i	$-0.843692\pi$
$571$	−31.4963	+	10.2338i	−1.31808	+	0.428270i	−0.436244	+	0.899828i	$0.643692\pi$
$572$	0.319339	+	13.5422i	0.0133523	+	0.566229i
$573$	−13.9958	−	10.1686i	−0.584685	−	0.424798i
$574$	−9.98630	+	7.43690i	−0.416820	+	0.310410i
$575$	35.7187	+	3.60405i	1.48957	+	0.150299i
$576$	−6.85000	+	5.75854i	−0.285417	+	0.239939i
$577$	−10.2228	+	14.0705i	−0.425580	+	0.585761i	−0.966932	−	0.255035i	$-0.917913\pi$
$577$	−10.2228	+	14.0705i	−0.425580	+	0.585761i	0.541351	+	0.840796i	$0.317913\pi$
$578$	13.1793	−	18.5968i	0.548185	−	0.773526i
$579$	11.0674	−	3.59603i	0.459947	−	0.149446i
$580$	−1.14346	+	6.15158i	−0.0474796	+	0.255430i
$581$	−6.21778	−	2.02028i	−0.257957	−	0.0838153i
$582$	2.49940	−	1.86133i	0.103603	−	0.0771545i
$583$	24.3463	+	7.91058i	1.00832	+	0.327623i
$584$	36.9395	+	24.8914i	1.52857	+	1.03001i
$585$	−4.32405	−	4.78231i	−0.178778	−	0.197724i
$586$	−0.122266	−	10.3713i	−0.00505075	−	0.428434i
$587$	27.1271	−	19.7090i	1.11965	−	0.813476i	0.135497	−	0.990778i	$-0.456737\pi$
$587$	27.1271	−	19.7090i	1.11965	−	0.813476i	0.984157	+	0.177301i	$0.0567368\pi$
$588$	5.58102	+	15.8917i	0.230157	+	0.655361i
$589$	−0.904658	+	1.24515i	−0.0372758	+	0.0513057i
$590$	−1.62821	−	13.6655i	−0.0670321	−	0.562602i
$591$	16.3492	−	11.8784i	0.672518	−	0.488613i
$592$	−28.8310	+	23.0994i	−1.18495	+	0.949380i
$593$		−	19.5523i		−	0.802917i	−0.915877	−	0.401458i	$-0.868503\pi$
$593$		−	19.5523i		−	0.802917i	0.915877	−	0.401458i	$-0.131497\pi$
$594$	−6.72206	−	19.8876i	−0.275810	−	0.815997i
$595$	1.30677	+	1.44526i	0.0535725	+	0.0592500i
$596$	0.627562	+	26.6130i	0.0257059	+	1.09011i
$597$	−2.41863	−	7.44379i	−0.0989880	−	0.304654i
$598$	−26.1712	+	0.308529i	−1.07022	+	0.0126167i
$599$	−15.7131			−0.642018			−0.321009	−	0.947076i	$-0.604022\pi$
$599$	−15.7131			−0.642018			−0.321009	+	0.947076i	$0.604022\pi$
$600$	14.9170	+	12.4000i	0.608986	+	0.506226i
$601$	44.4894			1.81476			0.907380	−	0.420310i	$-0.138079\pi$
$601$	44.4894			1.81476			0.907380	+	0.420310i	$0.138079\pi$
$602$	7.33466	−	0.0864674i	0.298938	−	0.00352415i
$603$	−0.364533	−	1.12192i	−0.0148449	−	0.0456880i
$604$	42.3610	−	0.998916i	1.72365	−	0.0406453i
$605$	8.96157	+	1.88537i	0.364340	+	0.0766512i
$606$	4.81892	+	14.2570i	0.195755	+	0.579152i
$607$		−	21.4173i		−	0.869301i	−0.900599	−	0.434651i	$-0.856872\pi$
$607$		−	21.4173i		−	0.869301i	0.900599	−	0.434651i	$-0.143128\pi$
$608$	−0.505376	+	1.93700i	−0.0204957	+	0.0785555i
$609$	1.43993	−	1.04617i	0.0583488	−	0.0423929i
$610$	−10.4897	+	4.84571i	−0.424715	+	0.196197i
$611$	12.5126	−	17.2221i	0.506206	−	0.696733i
$612$	−1.98319	+	0.696478i	−0.0801655	+	0.0281534i
$613$	1.93251	−	1.40405i	0.0780532	−	0.0567090i	−0.548074	−	0.836430i	$-0.684639\pi$
$613$	1.93251	−	1.40405i	0.0780532	−	0.0567090i	0.626128	+	0.779721i	$0.284639\pi$
$614$	−0.0652402	−	5.53405i	−0.00263288	−	0.223336i
$615$	−26.5737	+	11.8977i	−1.07156	+	0.479760i
$616$	3.85190	−	5.71632i	0.155197	−	0.230317i
$617$	9.76545	+	3.17299i	0.393142	+	0.127740i	0.498915	−	0.866651i	$-0.333732\pi$
$617$	9.76545	+	3.17299i	0.393142	+	0.127740i	−0.105773	+	0.994390i	$0.533732\pi$
$618$	2.19789	−	1.63679i	0.0884122	−	0.0658414i
$619$	22.9711	+	7.46375i	0.923285	+	0.299994i	0.731814	−	0.681505i	$-0.238674\pi$
$619$	22.9711	+	7.46375i	0.923285	+	0.299994i	0.191471	+	0.981498i	$0.438674\pi$
$620$	−13.3813	−	14.1158i	−0.537407	−	0.566903i
$621$	38.5764	−	12.5342i	1.54802	−	0.502982i
$622$	−5.41337	+	7.63862i	−0.217056	+	0.306281i
$623$	−4.80313	+	6.61094i	−0.192433	+	0.264862i
$624$	−11.8203	−	7.76396i	−0.473189	−	0.310807i
$625$	−12.3195	+	21.7539i	−0.492779	+	0.870155i
$626$	−23.2706	+	17.3298i	−0.930080	+	0.692640i
$627$	−1.03185	−	0.749685i	−0.0412082	−	0.0299395i
$628$	6.81969	−	0.160815i	0.272135	−	0.00641722i
$629$	−8.25258	+	2.68143i	−0.329052	+	0.106915i
$630$	0.388149	+	3.25774i	0.0154642	+	0.129791i
$631$	5.14314	−	15.8289i	0.204745	−	0.630140i	−0.794979	−	0.606637i	$-0.792518\pi$
$631$	5.14314	−	15.8289i	0.204745	−	0.630140i	0.999724	−	0.0235031i	$-0.00748197\pi$
$632$	−14.8798	+	5.42352i	−0.591885	+	0.215736i
$633$	−17.7538	−	5.76856i	−0.705650	−	0.229280i
$634$	6.72450	+	2.09761i	0.267064	+	0.0833068i
$635$	−14.8737	−	33.2207i	−0.590243	−	1.31832i
$636$	−21.2451	+	16.2143i	−0.842425	+	0.642938i
$637$	12.8034	−	9.30224i	0.507290	−	0.368568i
$638$	4.96325	+	1.54822i	0.196497	+	0.0612945i
$639$	10.4364	+	7.58250i	0.412858	+	0.299959i
$640$	−22.8994	−	10.7526i	−0.905177	−	0.425035i
$641$	−11.9869	+	8.70898i	−0.473454	+	0.343984i	−0.798786	−	0.601616i	$-0.794524\pi$
$641$	−11.9869	+	8.70898i	−0.473454	+	0.343984i	0.325332	+	0.945600i	$0.394524\pi$
$642$	31.1880	−	10.5417i	1.23089	−	0.416046i
$643$	17.1919			0.677981			0.338990	−	0.940790i	$-0.389915\pi$
$643$	17.1919			0.677981			0.338990	+	0.940790i	$0.389915\pi$
$644$	10.9564	+	7.57217i	0.431741	+	0.298385i
$645$	16.7849	+	3.53127i	0.660904	+	0.139044i
$646$	−0.271869	+	0.383626i	−0.0106966	+	0.0150935i
$647$	−7.49201	+	2.43430i	−0.294541	+	0.0957023i	−0.452560	−	0.891734i	$-0.649489\pi$
$647$	−7.49201	+	2.43430i	−0.294541	+	0.0957023i	0.158019	+	0.987436i	$0.449489\pi$
$648$	11.9451	+	3.41928i	0.469248	+	0.134322i
$649$	−11.4355			−0.448882
$650$	7.14684	−	16.7667i	0.280322	−	0.657642i
$651$			5.53282i			0.216848i
$652$	−30.8748	+	23.5637i	−1.20915	+	0.922824i
$653$	−11.8930	−	36.6029i	−0.465409	−	1.43238i	−0.858467	−	0.512869i	$-0.828583\pi$
$653$	−11.8930	−	36.6029i	−0.465409	−	1.43238i	0.393057	−	0.919514i	$-0.371417\pi$
$654$	−18.4853	−	13.1002i	−0.722832	−	0.512259i
$655$	27.2272	−	24.6182i	1.06386	−	0.961914i
$656$	29.6337	−	23.7425i	1.15700	−	0.926989i
$657$			17.6165i			0.687284i
$658$	−10.2621	+	3.46863i	−0.400059	+	0.135221i
$659$	−20.8965	−	28.7616i	−0.814013	−	1.12039i	−0.990692	−	0.136124i	$-0.956535\pi$
$659$	−20.8965	−	28.7616i	−0.814013	−	1.12039i	0.176679	−	0.984269i	$-0.443465\pi$
$660$	11.6977	−	11.0890i	0.455331	−	0.431640i
$661$	17.1104	−	23.5504i	0.665516	−	0.916005i	−0.334132	−	0.942526i	$-0.608443\pi$
$661$	17.1104	−	23.5504i	0.665516	−	0.916005i	0.999648	+	0.0265217i	$0.00844310\pi$
$662$	−8.36251	+	26.8084i	−0.325018	+	1.04194i
$663$	−1.95244	−	2.68731i	−0.0758266	−	0.104366i
$664$	19.1680	+	5.48682i	0.743862	+	0.212930i
$665$	0.492206	+	0.544370i	0.0190869	+	0.0211097i
$666$	−13.9479	−	4.35085i	−0.540470	−	0.168592i
$667$	−3.10424	+	9.55387i	−0.120197	+	0.369927i
$668$	5.41969	+	1.62074i	0.209694	+	0.0627084i
$669$	−29.6067	−	9.61979i	−1.14466	−	0.371923i
$670$	2.44708	−	2.26559i	0.0945389	−	0.0875274i
$671$	2.96697	+	9.13141i	0.114539	+	0.352514i
$672$	2.62309	+	6.70122i	0.101188	+	0.258505i
$673$	−1.94169	+	2.67251i	−0.0748467	+	0.103018i	−0.844799	−	0.535084i	$-0.820280\pi$
$673$	−1.94169	+	2.67251i	−0.0748467	+	0.103018i	0.769952	+	0.638102i	$0.220280\pi$
$674$	−15.7996	+	11.7661i	−0.608576	+	0.453213i
$675$	−2.83567	+	28.1035i	−0.109145	+	1.08170i
$676$	3.64214	−	12.1792i	0.140082	−	0.468429i
$677$	−17.2107	−	12.5043i	−0.661460	−	0.480579i	0.205696	−	0.978616i	$-0.434054\pi$
$677$	−17.2107	−	12.5043i	−0.661460	−	0.480579i	−0.867156	+	0.498037i	$0.834054\pi$
$678$	−1.43491	−	1.01690i	−0.0551073	−	0.0390537i
$679$	0.460435	+	1.41707i	0.0176699	+	0.0543823i
$680$	−4.13854	−	4.26387i	−0.158706	−	0.163512i
$681$	−5.82536	+	17.9286i	−0.223228	+	0.687026i
$682$	−12.9624	+	9.65322i	−0.496356	+	0.369641i
$683$	−3.92453	+	12.0784i	−0.150168	+	0.462169i	−0.997639	−	0.0686719i	$-0.978124\pi$
$683$	−3.92453	+	12.0784i	−0.150168	+	0.462169i	0.847471	+	0.530841i	$0.178124\pi$
$684$	−0.746982	+	0.262334i	−0.0285616	+	0.0100306i
$685$	−49.8124	+	5.34025i	−1.90323	+	0.204041i
$686$	−17.2334	+	0.203162i	−0.657973	+	0.00775676i
$687$	5.33009	+	7.33624i	0.203356	+	0.279895i
$688$	−22.3448	+	1.05441i	−0.851886	+	0.0401991i
$689$	20.3156	+	14.7602i	0.773964	+	0.562318i
$690$	21.1579	+	22.8528i	0.805466	+	0.869990i
$691$	22.6417	+	31.1636i	0.861329	+	1.18552i	0.981251	+	0.192734i	$0.0617355\pi$
$691$	22.6417	+	31.1636i	0.861329	+	1.18552i	−0.119922	+	0.992783i	$0.538264\pi$
$692$	1.41328	+	0.976744i	0.0537247	+	0.0371302i
$693$	2.72612			0.103557
$694$	−4.26207	+	1.44059i	−0.161786	+	0.0546842i
$695$	10.7656	+	24.0452i	0.408362	+	0.912086i
$696$	−4.27571	+	3.34371i	−0.162070	+	0.126743i
$697$	8.48233	−	2.75608i	0.321291	−	0.104394i
$698$	−25.0703	+	0.295550i	−0.948924	+	0.0111867i
$699$			19.7498i			0.747006i
$700$	−7.90037	+	4.85828i	−0.298606	+	0.183626i
$701$			39.6154i			1.49625i	0.663555	+	0.748127i	$0.269047\pi$
$701$			39.6154i			1.49625i	−0.663555	+	0.748127i	$0.730953\pi$
$702$	−0.242751	−	20.5915i	−0.00916204	−	0.777177i
$703$	−3.10840	+	1.00998i	−0.117235	+	0.0380921i
$704$	−11.1232	+	17.8372i	−0.419221	+	0.672264i
$705$	−25.1859	+	2.70012i	−0.948557	+	0.101692i
$706$	11.3947	+	33.7117i	0.428844	+	1.26876i
$707$	−7.19552			−0.270615
$708$	6.78774	−	9.82135i	0.255099	−	0.369109i
$709$	5.04361	+	6.94194i	0.189417	+	0.260710i	0.893154	−	0.449750i	$-0.148487\pi$
$709$	5.04361	+	6.94194i	0.189417	+	0.260710i	−0.703738	+	0.710460i	$0.748487\pi$
$710$	−7.08674	+	35.7729i	−0.265960	+	1.34253i
$711$	−5.06730	−	3.68161i	−0.190039	−	0.138071i
$712$	13.9258	−	20.6663i	0.521892	−	0.774503i
$713$	−18.3551	−	25.2636i	−0.687402	−	0.946128i
$714$	0.0199250	+	1.69016i	0.000745676	+	0.0632525i
$715$	−13.1316	−	7.54514i	−0.491093	−	0.282172i
$716$	43.1704	−	15.1611i	1.61335	−	0.566596i
$717$	−0.272861	+	0.839780i	−0.0101902	+	0.0313622i
$718$	−25.4581	−	34.1853i	−0.950088	−	1.27578i
$719$	2.74075	−	8.43517i	0.102213	−	0.314579i	−0.886853	−	0.462051i	$-0.847114\pi$
$719$	2.74075	−	8.43517i	0.102213	−	0.314579i	0.989066	+	0.147472i	$0.0471137\pi$
$720$	−1.53425	−	9.88687i	−0.0571781	−	0.368462i
$721$	0.404892	+	1.24613i	0.0150790	+	0.0464083i
$722$	15.4341	−	21.7785i	0.574397	−	0.810512i
$723$	24.7126	+	17.9547i	0.919071	+	0.667744i
$724$	37.3396	+	11.1663i	1.38771	+	0.414992i
$725$	−5.21808	−	4.65923i	−0.193795	−	0.173039i
$726$	4.74500	+	6.37161i	0.176103	+	0.236473i
$727$	19.5205	−	26.8677i	0.723976	−	0.996468i	−0.275406	−	0.961328i	$-0.588812\pi$
$727$	19.5205	−	26.8677i	0.723976	−	0.996468i	0.999382	−	0.0351397i	$-0.0111876\pi$
$728$	5.32637	−	4.16535i	0.197408	−	0.154378i
$729$	8.70192	+	26.7818i	0.322293	+	0.991917i
$730$	−45.2102	+	20.8848i	−1.67330	+	0.772983i
$731$	−4.99703	−	1.62364i	−0.184822	−	0.0600523i
$732$	−9.60359	−	2.87193i	−0.354959	−	0.106149i
$733$	−0.186051	+	0.572607i	−0.00687196	+	0.0211497i	−0.954434	−	0.298423i	$-0.903539\pi$
$733$	−0.186051	+	0.572607i	−0.00687196	+	0.0211497i	0.947562	+	0.319573i	$0.103539\pi$
$734$	−2.82863	+	9.06799i	−0.104407	+	0.334706i
$735$	−18.4278	−	3.87692i	−0.679721	−	0.143002i
$736$	−34.2086	−	21.8966i	−1.26094	−	0.807118i
$737$	−1.62877	−	2.24181i	−0.0599965	−	0.0825781i
$738$	14.3362	+	4.47198i	0.527723	+	0.164616i
$739$	21.4919	−	29.5811i	0.790594	−	1.08816i	−0.203440	−	0.979087i	$-0.565212\pi$
$739$	21.4919	−	29.5811i	0.790594	−	1.08816i	0.994034	−	0.109072i	$-0.0347878\pi$
$740$	−5.36980	−	40.9534i	−0.197398	−	1.50548i
$741$	−0.735402	−	1.01219i	−0.0270157	−	0.0371839i
$742$	−4.09167	−	12.1054i	−0.150210	−	0.444404i
$743$		−	0.112858i		−	0.00414038i	−0.999998	−	0.00207019i	$-0.999341\pi$
$743$		−	0.112858i		−	0.00414038i	0.999998	−	0.00207019i	$-0.000658962\pi$
$744$	−0.596593	−	16.8626i	−0.0218722	−	0.618212i
$745$	−25.8060	−	14.8276i	−0.945458	−	0.543242i
$746$	19.8203	−	27.9677i	0.725672	−	1.02397i
$747$	2.43667	+	7.49929i	0.0891529	+	0.274385i
$748$	−3.92497	+	2.99553i	−0.143511	+	0.109528i
$749$			15.7406i			0.575149i
$750$	−20.5018	+	7.07251i	−0.748622	+	0.258252i
$751$	−21.9164			−0.799742			−0.399871	−	0.916571i	$-0.630945\pi$
$751$	−21.9164			−0.799742			−0.399871	+	0.916571i	$0.630945\pi$
$752$	30.9022	−	11.6780i	1.12689	−	0.425853i
$753$	6.54093	−	2.12528i	0.238365	−	0.0774495i
$754$	4.16109	+	2.94890i	0.151538	+	0.107393i
$755$	−23.6017	+	41.0765i	−0.858955	+	1.49493i
$756$	−5.95778	+	8.62047i	−0.216683	+	0.313523i
$757$	−16.3710			−0.595014			−0.297507	−	0.954720i	$-0.596155\pi$
$757$	−16.3710			−0.595014			−0.297507	+	0.954720i	$0.596155\pi$
$758$	−3.68728	−	10.9090i	−0.133928	−	0.396233i
$759$	20.9358	−	15.2107i	0.759921	−	0.552115i
$760$	−1.55881	−	1.60602i	−0.0565441	−	0.0582565i
$761$	−5.84229	−	4.24467i	−0.211783	−	0.153869i	0.476837	−	0.878992i	$-0.341783\pi$
$761$	−5.84229	−	4.24467i	−0.211783	−	0.153869i	−0.688620	+	0.725122i	$0.741783\pi$
$762$	9.40270	−	30.1430i	0.340624	−	1.09197i
$763$	8.76385	−	6.36731i	0.317273	−	0.230512i
$764$	−20.0523	+	15.3039i	−0.725467	+	0.553676i
$765$	0.483817	−	2.29969i	0.0174924	−	0.0831453i
$766$	−3.80464	+	12.1969i	−0.137467	+	0.440691i
$767$	−10.6686	−	3.46644i	−0.385221	−	0.125166i
$768$	−8.71706	−	20.1407i	−0.314550	−	0.726764i
$769$	12.3133	−	37.8964i	0.444028	−	1.36658i	−0.439518	−	0.898234i	$-0.644851\pi$
$769$	12.3133	−	37.8964i	0.444028	−	1.36658i	0.883546	−	0.468344i	$-0.155149\pi$
$770$	3.23189	+	6.99619i	0.116469	+	0.252125i
$771$	−5.32830	+	1.73127i	−0.191894	+	0.0623502i
$772$	−0.400013	−	16.9633i	−0.0143968	−	0.610524i
$773$	−40.6107	−	29.5054i	−1.46066	−	1.06123i	−0.983189	−	0.182590i	$-0.941552\pi$
$773$	−40.6107	−	29.5054i	−1.46066	−	1.06123i	−0.477475	−	0.878645i	$-0.658448\pi$
$774$	−5.28413	−	7.09556i	−0.189934	−	0.255044i
$775$	21.2519	−	4.60970i	0.763391	−	0.165585i
$776$	−1.55609	−	4.26922i	−0.0558602	−	0.153256i
$777$	−6.90605	+	9.50537i	−0.247753	+	0.341003i
$778$	14.6390	+	10.3744i	0.524833	+	0.371941i
$779$	3.19494	−	1.03810i	0.114470	−	0.0371937i
$780$	14.2746	−	6.79946i	0.511113	−	0.243460i
$781$	28.8195	+	9.36401i	1.03124	+	0.335071i
$782$	−5.69805	−	7.65137i	−0.203762	−	0.273613i
$783$	−7.51699	−	2.44242i	−0.268635	−	0.0872849i
$784$	24.5320	−	1.15762i	0.876141	−	0.0413436i
$785$	−3.79964	+	6.61288i	−0.135615	+	0.236024i
$786$	31.8408	−	0.375367i	1.13572	−	0.0133889i
$787$	−33.6522	+	24.4497i	−1.19957	+	0.871539i	−0.994242	−	0.107154i	$-0.965826\pi$
$787$	−33.6522	+	24.4497i	−1.19957	+	0.871539i	−0.205329	+	0.978693i	$0.565826\pi$
$788$	−9.76384	−	27.8020i	−0.347822	−	0.990406i
$789$	−19.2737	+	26.5279i	−0.686161	+	0.944419i
$790$	3.44090	−	17.3692i	0.122422	−	0.617967i
$791$	0.680288	−	0.494258i	0.0241883	−	0.0175738i
$792$	−8.30848	+	0.293952i	−0.295229	+	0.0104451i
$793$			9.41841i			0.334458i
$794$	−18.3230	+	6.19324i	−0.650260	+	0.219790i
$795$	−3.18512	−	29.7099i	−0.112965	−	1.05370i
$796$	−11.4093	+	0.269042i	−0.404391	+	0.00953595i
$797$	−10.9651	−	33.7472i	−0.388404	−	1.19539i	−0.933980	−	0.357324i	$-0.883689\pi$
$797$	−10.9651	−	33.7472i	−0.388404	−	1.19539i	0.545576	−	0.838061i	$-0.316311\pi$
$798$	0.00750492	+	0.636611i	0.000265671	+	0.0225358i
$799$	7.75931			0.274505
$800$	23.5544	−	15.6586i	0.832772	−	0.553616i
$801$	9.85577			0.348236
$802$	0.579968	+	49.1962i	0.0204794	+	1.73718i
$803$	12.7876	+	39.3560i	0.451263	+	1.38884i
$804$	2.89216	−	0.0682000i	0.101999	−	0.00240523i
$805$	−13.5904	+	6.08475i	−0.479000	+	0.214459i
$806$	−15.0193	+	5.07657i	−0.529032	+	0.178815i
$807$		−	41.1858i		−	1.44981i
$808$	21.9300	−	0.775879i	0.771496	−	0.0272953i
$809$	15.2356	−	11.0693i	0.535656	−	0.389177i	−0.286813	−	0.957986i	$-0.592596\pi$
$809$	15.2356	−	11.0693i	0.535656	−	0.389177i	0.822469	+	0.568810i	$0.192596\pi$
$810$	−10.1934	+	9.43744i	−0.358161	+	0.331598i
$811$	−30.8789	+	42.5012i	−1.08431	+	1.49242i	−0.229616	+	0.973281i	$0.573747\pi$
$811$	−30.8789	+	42.5012i	−1.08431	+	1.49242i	−0.854690	+	0.519138i	$0.826253\pi$
$812$	−0.859930	−	2.44861i	−0.0301776	−	0.0859293i
$813$	5.24237	−	3.80881i	0.183858	−	0.133581i
$814$	−34.3185	+	0.404576i	−1.20286	+	0.0141804i
$815$	−4.62882	−	43.1764i	−0.162141	−	1.51240i
$816$	−0.242973	−	5.14900i	−0.00850574	−	0.180251i
$817$	−1.88217	−	0.611555i	−0.0658489	−	0.0213956i
$818$	−13.9746	−	18.7652i	−0.488612	−	0.656110i
$819$	2.54330	+	0.826367i	0.0888700	+	0.0288756i
$820$	5.51929	+	42.0935i	0.192742	+	1.46997i
$821$	4.70172	−	1.52768i	0.164091	−	0.0533164i	−0.225819	−	0.974169i	$-0.572506\pi$
$821$	4.70172	−	1.52768i	0.164091	−	0.0533164i	0.389910	+	0.920853i	$0.372506\pi$
$822$	−35.4584	−	25.1288i	−1.23675	−	0.876467i
$823$	−3.18730	+	4.38694i	−0.111102	+	0.152919i	−0.860947	−	0.508695i	$-0.830128\pi$
$823$	−3.18730	+	4.38694i	−0.111102	+	0.152919i	0.749845	+	0.661614i	$0.230128\pi$
$824$	−1.36837	−	3.75422i	−0.0476695	−	0.130784i
$825$	3.82003	+	17.6113i	0.132996	+	0.613148i
$826$	3.40940	+	4.57816i	0.118628	+	0.159295i
$827$	33.7010	+	24.4852i	1.17190	+	0.851435i	0.991235	−	0.132110i	$-0.0421752\pi$
$827$	33.7010	+	24.4852i	1.17190	+	0.851435i	0.180664	+	0.983545i	$0.442175\pi$
$828$	−0.378685	−	16.0589i	−0.0131602	−	0.558085i
$829$	−27.3761	+	8.89503i	−0.950811	+	0.308937i	−0.743045	−	0.669241i	$-0.766619\pi$
$829$	−27.3761	+	8.89503i	−0.950811	+	0.308937i	−0.207766	+	0.978179i	$0.566619\pi$
$830$	−16.3571	+	15.1440i	−0.567764	+	0.525655i
$831$	1.57473	−	4.84653i	0.0546268	−	0.168124i
$832$	−15.7842	+	13.2692i	−0.547219	+	0.460027i
$833$	5.48616	+	1.78256i	0.190084	+	0.0617621i
$834$	−6.80569	+	21.8176i	−0.235662	+	0.755481i
$835$	−4.69124	+	4.24171i	−0.162347	+	0.146790i
$836$	−1.47837	+	1.12829i	−0.0511305	+	0.0390227i
$837$	19.8774	−	14.4418i	0.687063	−	0.499180i
$838$	1.00142	−	3.21034i	0.0345935	−	0.110899i
$839$	43.0983	+	31.3128i	1.48792	+	1.08104i	0.974895	+	0.222663i	$0.0714749\pi$
$839$	43.0983	+	31.3128i	1.48792	+	1.08104i	0.513024	+	0.858374i	$0.328525\pi$
$840$	−7.92701	−	1.37701i	−0.273508	−	0.0475114i
$841$	−21.8779	+	15.8952i	−0.754409	+	0.548110i
$842$	2.77353	+	8.20563i	0.0955821	+	0.282785i
$843$	−18.8667			−0.649805
$844$	−15.4755	+	22.3919i	−0.532689	+	0.770761i
$845$	9.53199	+	10.5422i	0.327910	+	0.362662i
$846$	10.6597	+	7.55432i	0.366487	+	0.259723i
$847$	−3.61249	+	1.17377i	−0.124126	+	0.0403311i
$848$	13.7756	+	36.4529i	0.473057	+	1.25180i
$849$	−2.04454			−0.0701685
$850$	6.47540	−	1.48470i	0.222104	−	0.0509247i
$851$		−	66.3135i		−	2.27320i
$852$	−25.1486	+	19.1934i	−0.861576	+	0.657554i
$853$	16.1501	+	49.7048i	0.552968	+	1.70186i	0.701250	+	0.712915i	$0.252625\pi$
$853$	16.1501	+	49.7048i	0.552968	+	1.70186i	−0.148283	+	0.988945i	$0.547375\pi$
$854$	2.77115	−	3.91027i	0.0948266	−	0.133807i
$855$	0.182233	−	0.866194i	0.00623225	−	0.0296232i
$856$	−1.69728	−	47.9731i	−0.0580117	−	1.63969i
$857$		−	6.32615i		−	0.216097i	−0.994146	−	0.108049i	$-0.965540\pi$
$857$		−	6.32615i		−	0.216097i	0.994146	−	0.108049i	$-0.0344602\pi$
$858$	−4.20692	−	12.4464i	−0.143622	−	0.424913i
$859$	31.4567	+	43.2964i	1.07329	+	1.47726i	0.866701	+	0.498827i	$0.166236\pi$
$859$	31.4567	+	43.2964i	1.07329	+	1.47726i	0.206588	+	0.978428i	$0.433764\pi$
$860$	11.9453	−	21.9730i	0.407330	−	0.749272i
$861$	7.09832	−	9.77000i	0.241910	−	0.332961i
$862$	42.2555	+	13.1810i	1.43923	+	0.448947i
$863$	−25.6168	−	35.2585i	−0.872007	−	1.20021i	−0.978571	−	0.205909i	$-0.933985\pi$
$863$	−25.6168	−	35.2585i	−0.872007	−	1.20021i	0.106564	−	0.994306i	$-0.466015\pi$
$864$	17.2282	−	26.9153i	0.586116	−	0.915677i
$865$	−1.75305	+	0.784880i	−0.0596055	+	0.0266867i
$866$	−6.28013	+	20.1327i	−0.213407	+	0.684139i
$867$	−6.83146	+	21.0251i	−0.232008	+	0.714049i
$868$	7.72927	+	2.31142i	0.262348	+	0.0784546i
$869$	−13.9930	−	4.54661i	−0.474681	−	0.154233i
$870$	−0.717972	−	6.02595i	−0.0243415	−	0.204299i
$871$	−0.839981	−	2.58520i	−0.0284617	−	0.0875961i
$872$	−26.0233	+	20.3509i	−0.881260	+	0.689167i
$873$	1.05631	−	1.45388i	0.0357505	−	0.0492064i
$874$	−2.14622	−	2.88195i	−0.0725968	−	0.0974834i
$875$	−0.0646922	−	10.3691i	−0.00218700	−	0.350541i
$876$	−41.3911	−	12.3779i	−1.39848	−	0.418211i
$877$	−3.02353	−	2.19672i	−0.102097	−	0.0741781i	0.535565	−	0.844494i	$-0.320099\pi$
$877$	−3.02353	−	2.19672i	−0.102097	−	0.0741781i	−0.637663	+	0.770316i	$0.720099\pi$
$878$	26.6709	−	37.6344i	0.900098	−	1.27010i
$879$	3.10863	+	9.56738i	0.104851	+	0.322700i
$880$	−10.6043	−	20.9740i	−0.357472	−	0.707035i
$881$	−13.5548	+	41.7174i	−0.456673	+	1.40549i	0.412487	+	0.910963i	$0.364660\pi$
$881$	−13.5548	+	41.7174i	−0.456673	+	1.40549i	−0.869160	+	0.494531i	$0.835340\pi$
$882$	5.80136	+	7.79009i	0.195342	+	0.262306i
$883$	−6.00720	+	18.4883i	−0.202158	+	0.622179i	0.797660	+	0.603108i	$0.206071\pi$
$883$	−6.00720	+	18.4883i	−0.202158	+	0.622179i	−0.999818	+	0.0190716i	$0.993929\pi$
$884$	−4.56979	+	1.60487i	−0.153699	+	0.0539776i
$885$	5.45441	+	12.1826i	0.183348	+	0.409512i
$886$	−0.407285	−	34.5482i	−0.0136830	−	1.16067i
$887$	−10.5570	−	14.5304i	−0.354468	−	0.487883i	0.594129	−	0.804370i	$-0.297497\pi$
$887$	−10.5570	−	14.5304i	−0.354468	−	0.487883i	−0.948597	+	0.316486i	$0.897497\pi$
$888$	20.0229	−	29.7145i	0.671924	−	0.997153i
$889$	12.2138	+	8.87384i	0.409638	+	0.297619i
$890$	11.6843	+	25.2934i	0.391659	+	0.847838i
$891$	6.78473	+	9.33838i	0.227297	+	0.312847i
$892$	−25.8073	+	37.3413i	−0.864093	+	1.25028i
$893$	2.92260			0.0978012
$894$	−8.26739	−	24.4595i	−0.276503	−	0.818048i
$895$	−10.5318	+	50.0600i	−0.352040	+	1.67332i
$896$	10.4573	−	0.864885i	0.349355	−	0.0288938i
$897$	24.1426	−	7.84441i	0.806098	−	0.261917i
$898$	−0.185025	−	15.6948i	−0.00617435	−	0.523744i
$899$			6.08498i			0.202945i
$900$	10.3413	+	4.26467i	0.344710	+	0.142156i
$901$			9.15306i			0.304933i
$902$	35.2739	−	0.415840i	1.17449	−	0.0138460i
$903$	−6.76613	+	2.19845i	−0.225163	+	0.0731598i
$904$	−2.02004	+	1.57972i	−0.0671856	+	0.0525408i
$905$	−32.3208	+	29.2237i	−1.07438	+	0.971429i
$906$	−38.9332	+	13.1596i	−1.29347	+	0.437197i
$907$	−14.9961			−0.497938			−0.248969	−	0.968511i	$-0.580092\pi$
$907$	−14.9961			−0.497938			−0.248969	+	0.968511i	$0.580092\pi$
$908$	22.6124	+	15.6279i	0.750418	+	0.518629i
$909$	5.10112	+	7.02109i	0.169193	+	0.232875i
$910$	0.894398	+	7.50669i	0.0296490	+	0.248845i
$911$	28.4325	+	20.6574i	0.942011	+	0.684411i	0.948904	−	0.315565i	$-0.102194\pi$
$911$	28.4325	+	20.6574i	0.942011	+	0.684411i	−0.00689309	+	0.999976i	$0.502194\pi$
$912$	−0.0915175	−	1.93941i	−0.00303045	−	0.0642203i
$913$	10.8873	+	14.9850i	0.360316	+	0.495932i
$914$	15.1539	−	0.178647i	0.501246	−	0.00590913i
$915$	8.31278	−	7.51623i	0.274812	−	0.248479i
$916$	12.4753	−	4.38123i	0.412197	−	0.144760i
$917$	−4.70477	+	14.4798i	−0.155365	+	0.478165i
$918$	6.02010	−	4.48323i	0.198693	−	0.147969i
$919$	1.49412	−	4.59844i	0.0492866	−	0.151689i	−0.923384	−	0.383877i	$-0.874589\pi$
$919$	1.49412	−	4.59844i	0.0492866	−	0.151689i	0.972671	+	0.232188i	$0.0745886\pi$
$920$	40.7640	−	20.0101i	1.34395	−	0.659715i
$921$	1.65874	+	5.10509i	0.0546575	+	0.168218i
$922$	−17.7783	−	12.5992i	−0.585496	−	0.414931i
$923$	24.0483	+	17.4721i	0.791558	+	0.575101i
$924$	−1.91546	+	6.40520i	−0.0630139	+	0.210716i
$925$	42.2645	+	18.6071i	1.38965	+	0.611799i
$926$	2.08957	−	1.55613i	0.0686677	−	0.0511375i
$927$	0.928882	−	1.27850i	0.0305085	−	0.0419913i
$928$	2.88487	+	7.36998i	0.0947004	+	0.241931i
$929$	−1.73466	−	5.33873i	−0.0569124	−	0.175158i	0.918559	−	0.395283i	$-0.129354\pi$
$929$	−1.73466	−	5.33873i	−0.0569124	−	0.175158i	−0.975472	+	0.220125i	$0.929354\pi$
$930$	16.4666	+	9.20489i	0.539960	+	0.301840i
$931$	2.06641	+	0.671416i	0.0677237	+	0.0220048i
$932$	27.5902	+	8.25077i	0.903746	+	0.270263i
$933$	2.80601	−	8.63602i	0.0918648	−	0.282731i
$934$	−28.4030	−	8.85993i	−0.929376	−	0.289906i
$935$	−0.588440	−	5.48880i	−0.0192440	−	0.179503i
$936$	−7.84040	−	2.24431i	−0.256271	−	0.0733575i
$937$	−20.3931	−	28.0687i	−0.666213	−	0.916964i	0.333454	−	0.942767i	$-0.391786\pi$
$937$	−20.3931	−	28.0687i	−0.666213	−	0.916964i	−0.999667	+	0.0258024i	$0.991786\pi$
$938$	−0.411895	+	1.32045i	−0.0134489	+	0.0431142i
$939$	16.5409	−	22.7666i	0.539791	−	0.742958i
$940$	−6.74977	+	36.3124i	−0.220153	+	1.18438i
$941$	−27.7263	−	38.1620i	−0.903853	−	1.24405i	−0.969223	−	0.246185i	$-0.920823\pi$
$941$	−27.7263	−	38.1620i	−0.903853	−	1.24405i	0.0653703	−	0.997861i	$-0.479177\pi$
$942$	−6.26785	+	2.11855i	−0.204217	+	0.0690262i
$943$			68.1597i			2.21958i
$944$	−10.8846	−	13.5854i	−0.354264	−	0.442167i
$945$	−4.78749	−	10.6930i	−0.155737	−	0.347842i
$946$	−16.9556	−	12.0161i	−0.551273	−	0.390678i
$947$	1.10237	+	3.39273i	0.0358221	+	0.110249i	0.967369	−	0.253373i	$-0.0815400\pi$
$947$	1.10237	+	3.39273i	0.0358221	+	0.110249i	−0.931547	+	0.363622i	$0.881540\pi$
$948$	12.2106	−	9.31915i	0.396583	−	0.302672i
$949$			40.5930i			1.31771i
$950$	2.43901	−	0.559223i	0.0791319	−	0.0181436i
$951$	−6.83199			−0.221542
$952$	2.36945	+	0.678253i	0.0767942	+	0.0219823i
$953$	26.4322	−	8.58834i	0.856222	−	0.278204i	0.152172	−	0.988354i	$-0.451373\pi$
$953$	26.4322	−	8.58834i	0.856222	−	0.278204i	0.704050	+	0.710150i	$0.251373\pi$
$954$	−8.91125	+	12.5744i	−0.288513	+	0.407110i
$955$	−3.00629	−	28.0418i	−0.0972812	−	0.907412i
$956$	1.05917	+	0.732013i	0.0342560	+	0.0236750i
$957$	−5.04259			−0.163004
$958$	−2.77973	+	0.939558i	−0.0898090	+	0.0303557i
$959$	16.8108	−	12.2137i	0.542848	−	0.394402i
$960$	24.3079	+	3.34201i	0.784534	+	0.107863i
$961$	9.77638	+	7.10296i	0.315367	+	0.229128i
$962$	−32.1397	−	10.0255i	−1.03622	−	0.323236i
$963$	15.3590	−	11.1590i	0.494937	−	0.359593i
$964$	35.4065	−	27.0222i	1.14037	−	0.870328i
$965$	16.4489	+	9.45124i	0.529510	+	0.304246i
$966$	−12.3314	−	3.84660i	−0.396756	−	0.123762i
$967$	−23.8022	−	7.73379i	−0.765426	−	0.248702i	−0.0998201	−	0.995006i	$-0.531827\pi$
$967$	−23.8022	−	7.73379i	−0.765426	−	0.248702i	−0.665606	+	0.746304i	$0.731827\pi$
$968$	10.8833	−	3.96686i	0.349804	−	0.127500i
$969$	0.140923	−	0.433717i	0.00452710	−	0.0139330i
$970$	4.98346	+	0.987242i	0.160009	+	0.0316984i
$971$	−23.8687	+	7.75540i	−0.765982	+	0.248883i	−0.665844	−	0.746091i	$-0.731928\pi$
$971$	−23.8687	+	7.75540i	−0.765982	+	0.248883i	−0.100138	+	0.994974i	$0.531928\pi$
$972$	21.8386	−	0.514976i	0.700473	−	0.0165179i
$973$	−8.84037	−	6.42290i	−0.283409	−	0.205909i
$974$	−5.53377	+	4.12105i	−0.177313	+	0.132047i
$975$	−1.77467	+	17.5883i	−0.0568349	+	0.563275i
$976$	−8.02408	+	12.2163i	−0.256844	+	0.391033i
$977$	20.3216	−	27.9703i	0.650146	−	0.894850i	−0.348959	−	0.937138i	$-0.613465\pi$
$977$	20.3216	−	27.9703i	0.650146	−	0.894850i	0.999105	+	0.0422882i	$0.0134648\pi$
$978$	21.7811	−	30.7346i	0.696484	−	0.982785i
$979$	22.0183	−	7.15417i	0.703707	−	0.228648i
$980$	−13.1145	+	24.1238i	−0.418927	+	0.770605i
$981$	−12.4259	−	4.03742i	−0.396729	−	0.128905i
$982$	21.6125	−	16.0950i	0.689682	−	0.513613i
$983$	16.4679	+	5.35074i	0.525244	+	0.170662i	0.559624	−	0.828747i	$-0.310946\pi$
$983$	16.4679	+	5.35074i	0.525244	+	0.170662i	−0.0343798	+	0.999409i	$0.510946\pi$
$984$	−20.5803	+	30.5418i	−0.656076	+	0.973636i
$985$	32.2390	+	6.78257i	1.02722	+	0.216111i
$986$	0.0219135	+	1.85883i	0.000697868	+	0.0591972i
$987$	8.49980	−	6.17546i	0.270552	−	0.196567i
$988$	−1.72125	+	0.604487i	−0.0547601	+	0.0192313i
$989$	23.6017	−	32.4849i	0.750490	−	1.03296i
$990$	4.53541	−	8.11335i	0.144145	−	0.257859i
$991$	−45.0802	+	32.7527i	−1.43202	+	1.04042i	−0.442385	+	0.896825i	$0.645868\pi$
$991$	−45.0802	+	32.7527i	−1.43202	+	1.04042i	−0.989636	+	0.143599i	$0.954132\pi$
$992$	−23.8060	−	6.21115i	−0.755841	−	0.197204i
$993$		−	27.2369i		−	0.864338i
$994$	−4.84344	−	14.3296i	−0.153625	−	0.454506i
$995$	6.35676	−	11.0633i	0.201523	−	0.350730i
$996$	−19.3322	+	0.455872i	−0.612563	+	0.0144449i
$997$	−5.97548	−	18.3906i	−0.189245	−	0.582438i	0.810750	−	0.585392i	$-0.199060\pi$
$997$	−5.97548	−	18.3906i	−0.189245	−	0.582438i	−0.999996	+	0.00295465i	$0.999060\pi$
$998$	18.1801	−	0.214323i	0.575482	−	0.00678428i
$999$	52.1755			1.65076

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.o.a.109.15	yes	112
4.3	odd	2		800.2.be.a.209.20		112
5.2	odd	4		1000.2.t.b.701.2		224
5.3	odd	4		1000.2.t.b.701.55		224
5.4	even	2		1000.2.o.a.549.14		112
8.3	odd	2		800.2.be.a.209.9		112
8.5	even	2	inner	200.2.o.a.109.2	✓	112
25.2	odd	20		1000.2.t.b.301.25		224
25.11	even	5		1000.2.o.a.949.27		112
25.14	even	10	inner	200.2.o.a.189.2	yes	112
25.23	odd	20		1000.2.t.b.301.32		224
40.13	odd	4		1000.2.t.b.701.32		224
40.29	even	2		1000.2.o.a.549.27		112
40.37	odd	4		1000.2.t.b.701.25		224
100.39	odd	10		800.2.be.a.689.9		112
200.61	even	10		1000.2.o.a.949.14		112
200.77	odd	20		1000.2.t.b.301.2		224
200.139	odd	10		800.2.be.a.689.20		112
200.173	odd	20		1000.2.t.b.301.55		224
200.189	even	10	inner	200.2.o.a.189.15	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.2	✓	112	8.5	even	2	inner
200.2.o.a.109.15	yes	112	1.1	even	1	trivial
200.2.o.a.189.2	yes	112	25.14	even	10	inner
200.2.o.a.189.15	yes	112	200.189	even	10	inner
800.2.be.a.209.9		112	8.3	odd	2
800.2.be.a.209.20		112	4.3	odd	2
800.2.be.a.689.9		112	100.39	odd	10
800.2.be.a.689.20		112	200.139	odd	10
1000.2.o.a.549.14		112	5.4	even	2
1000.2.o.a.549.27		112	40.29	even	2
1000.2.o.a.949.14		112	200.61	even	10
1000.2.o.a.949.27		112	25.11	even	5
1000.2.t.b.301.2		224	200.77	odd	20
1000.2.t.b.301.25		224	25.2	odd	20
1000.2.t.b.301.32		224	25.23	odd	20
1000.2.t.b.301.55		224	200.173	odd	20
1000.2.t.b.701.2		224	5.2	odd	4
1000.2.t.b.701.25		224	40.37	odd	4
1000.2.t.b.701.32		224	40.13	odd	4
1000.2.t.b.701.55		224	5.3	odd	4

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0166708 + 1.41412i) q^{2} +(-0.423859 - 1.30450i) q^{3} +(-1.99944 + 0.0471489i) q^{4} +(1.11400 - 1.93881i) q^{5} +(1.83765 - 0.621132i) q^{6} +0.927462i q^{7} +(-0.100006 - 2.82666i) q^{8} +(0.904979 - 0.657506i) q^{9} +(2.76028 + 1.54301i) q^{10} +(1.54449 - 2.12581i) q^{11} +(0.908988 + 2.58830i) q^{12} +(2.08531 - 1.51507i) q^{13} +(-1.31154 + 0.0154616i) q^{14} +(-3.00137 - 0.631440i) q^{15} +(3.99555 - 0.188543i) q^{16} +(0.893539 + 0.290328i) q^{17} +(0.944876 + 1.26878i) q^{18} +(0.336558 + 0.109354i) q^{19} +(-2.13598 + 3.92907i) q^{20} +(1.20988 - 0.393113i) q^{21} +(3.03189 + 2.14865i) q^{22} +(-4.22031 + 5.80876i) q^{23} +(-3.64500 + 1.32856i) q^{24} +(-2.51799 - 4.31969i) q^{25} +(2.17724 + 2.92361i) q^{26} +(-4.57033 - 3.32054i) q^{27} +(-0.0437289 - 1.85441i) q^{28} +(1.33062 - 0.432345i) q^{29} +(0.842893 - 4.25481i) q^{30} +(-1.34398 + 4.13636i) q^{31} +(0.333231 + 5.64703i) q^{32} +(-3.42777 - 1.11375i) q^{33} +(-0.395662 + 1.26841i) q^{34} +(1.79818 + 1.03320i) q^{35} +(-1.77845 + 1.35731i) q^{36} +(-7.47195 + 5.42869i) q^{37} +(-0.149029 + 0.477755i) q^{38} +(-2.86029 - 2.07812i) q^{39} +(-5.59177 - 2.95502i) q^{40} +(7.67997 - 5.57982i) q^{41} +(0.576077 + 1.70435i) q^{42} -5.59241 q^{43} +(-2.98790 + 4.32326i) q^{44} +(-0.266630 - 2.48705i) q^{45} +(-8.28461 - 5.87117i) q^{46} +(7.85457 - 2.55210i) q^{47} +(-1.93951 - 5.13230i) q^{48} +6.13981 q^{49} +(6.06656 - 3.63274i) q^{50} -1.28868i q^{51} +(-4.09803 + 3.12761i) q^{52} +(3.01052 + 9.26543i) q^{53} +(4.61944 - 6.51833i) q^{54} +(-2.40098 - 5.36264i) q^{55} +(2.62162 - 0.0927522i) q^{56} -0.485392i q^{57} +(0.633568 + 1.87444i) q^{58} +(-2.55804 - 3.52083i) q^{59} +(6.03084 + 1.12102i) q^{60} +(-2.14775 + 2.95612i) q^{61} +(-5.87169 - 1.83159i) q^{62} +(0.609812 + 0.839334i) q^{63} +(-7.98000 + 0.565368i) q^{64} +(-0.614386 - 5.73082i) q^{65} +(1.51783 - 4.86583i) q^{66} +(0.325879 - 1.00295i) q^{67} +(-1.80027 - 0.538366i) q^{68} +(9.36636 + 3.04331i) q^{69} +(-1.43108 + 2.56005i) q^{70} +(3.56365 + 10.9678i) q^{71} +(-1.94905 - 2.49231i) q^{72} +(-9.25671 + 12.7408i) q^{73} +(-7.80136 - 10.4757i) q^{74} +(-4.56778 + 5.11566i) q^{75} +(-0.678086 - 0.202780i) q^{76} +(1.97161 + 1.43246i) q^{77} +(2.89102 - 4.07942i) q^{78} +(-1.73030 - 5.32530i) q^{79} +(4.08551 - 7.95667i) q^{80} +(-1.35747 + 4.17785i) q^{81} +(8.01855 + 10.7673i) q^{82} +(-2.17829 + 6.70408i) q^{83} +(-2.40055 + 0.843052i) q^{84} +(1.55830 - 1.40898i) q^{85} +(-0.0932301 - 7.90831i) q^{86} +(-1.12799 - 1.55254i) q^{87} +(-6.16340 - 4.15316i) q^{88} +(7.12799 + 5.17879i) q^{89} +(3.51253 - 0.418506i) q^{90} +(1.40517 + 1.93405i) q^{91} +(8.16440 - 11.8133i) q^{92} +5.96555 q^{93} +(3.73991 + 11.0647i) q^{94} +(0.586945 - 0.530702i) q^{95} +(7.22533 - 2.82824i) q^{96} +(1.52791 - 0.496446i) q^{97} +(0.102356 + 8.68240i) q^{98} -2.93933i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28}+ \cdots + 90 q^{98}+O(q^{100}) \) 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

Introduction

L-functions

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