LMFDB - Embedded newform 855.2.i.d.286.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(286,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("855.286");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			286.5
Character	$\chi$	$=$	855.286
Dual form			855.2.i.d.571.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.876140 + 1.51752i) q^{2} +(0.239525 - 1.71541i) q^{3} +(-0.535244 - 0.927070i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.39331 + 1.86642i) q^{6} +(-0.602689 + 1.04389i) q^{7} -1.62877 q^{8} +(-2.88526 - 0.821768i) q^{9} +O(q^{10})$	\(q+(-0.876140 + 1.51752i) q^{2} +(0.239525 - 1.71541i) q^{3} +(-0.535244 - 0.927070i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.39331 + 1.86642i) q^{6} +(-0.602689 + 1.04389i) q^{7} -1.62877 q^{8} +(-2.88526 - 0.821768i) q^{9} -1.75228 q^{10} +(2.67570 - 4.63446i) q^{11} +(-1.71851 + 0.696106i) q^{12} +(0.104894 + 0.181681i) q^{13} +(-1.05608 - 1.82918i) q^{14} +(1.60535 - 0.650269i) q^{15} +(2.49752 - 4.32582i) q^{16} +2.79479 q^{17} +(3.77494 - 3.65845i) q^{18} +1.00000 q^{19} +(0.535244 - 0.927070i) q^{20} +(1.64633 + 1.28390i) q^{21} +(4.68859 + 8.12087i) q^{22} +(-0.481177 - 0.833423i) q^{23} +(-0.390131 + 2.79400i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.367607 q^{26} +(-2.10076 + 4.75256i) q^{27} +1.29034 q^{28} +(3.38420 - 5.86161i) q^{29} +(-0.419716 + 3.00588i) q^{30} +(0.267981 + 0.464157i) q^{31} +(2.74758 + 4.75895i) q^{32} +(-7.30909 - 5.70000i) q^{33} +(-2.44862 + 4.24114i) q^{34} -1.20538 q^{35} +(0.782479 + 3.11468i) q^{36} +10.3143 q^{37} +(-0.876140 + 1.51752i) q^{38} +(0.336783 - 0.136418i) q^{39} +(-0.814383 - 1.41055i) q^{40} +(-3.81234 - 6.60317i) q^{41} +(-3.39076 + 1.37347i) q^{42} +(-1.75761 + 3.04428i) q^{43} -5.72862 q^{44} +(-0.730955 - 2.90959i) q^{45} +1.68631 q^{46} +(2.21220 - 3.83165i) q^{47} +(-6.82234 - 5.32041i) q^{48} +(2.77353 + 4.80390i) q^{49} +(-0.876140 - 1.51752i) q^{50} +(0.669422 - 4.79420i) q^{51} +(0.112288 - 0.194488i) q^{52} +9.46943 q^{53} +(-5.37154 - 7.35185i) q^{54} +5.35141 q^{55} +(0.981639 - 1.70025i) q^{56} +(0.239525 - 1.71541i) q^{57} +(5.93008 + 10.2712i) q^{58} +(-5.24839 - 9.09048i) q^{59} +(-1.46210 - 1.14022i) q^{60} +(-0.0249540 + 0.0432215i) q^{61} -0.939157 q^{62} +(2.59674 - 2.51661i) q^{63} +0.360986 q^{64} +(-0.104894 + 0.181681i) q^{65} +(15.0536 - 6.09769i) q^{66} +(-1.22861 - 2.12802i) q^{67} +(-1.49589 - 2.59096i) q^{68} +(-1.54491 + 0.625789i) q^{69} +(1.05608 - 1.82918i) q^{70} +3.67721 q^{71} +(4.69940 + 1.33847i) q^{72} +14.3659 q^{73} +(-9.03680 + 15.6522i) q^{74} +(1.36582 + 1.06514i) q^{75} +(-0.535244 - 0.927070i) q^{76} +(3.22523 + 5.58627i) q^{77} +(-0.0880512 + 0.630596i) q^{78} +(0.375760 - 0.650835i) q^{79} +4.99503 q^{80} +(7.64939 + 4.74202i) q^{81} +13.3606 q^{82} +(1.29683 - 2.24618i) q^{83} +(0.309070 - 2.21347i) q^{84} +(1.39739 + 2.42036i) q^{85} +(-3.07983 - 5.33443i) q^{86} +(-9.24446 - 7.20930i) q^{87} +(-4.35809 + 7.54844i) q^{88} -5.83021 q^{89} +(5.05578 + 1.43997i) q^{90} -0.252873 q^{91} +(-0.515094 + 0.892169i) q^{92} +(0.860407 - 0.348520i) q^{93} +(3.87640 + 6.71412i) q^{94} +(0.500000 + 0.866025i) q^{95} +(8.82167 - 3.57334i) q^{96} +(-8.41705 + 14.5788i) q^{97} -9.72002 q^{98} +(-11.5285 + 11.1728i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9	\( 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9} + 6 q^{10} - q^{11} + 9 q^{12} - 11 q^{13} - 3 q^{14} + q^{15} - 45 q^{16} - 30 q^{17} - 18 q^{18} + 46 q^{19} + 29 q^{20} - 2 q^{21} - 5 q^{22} + 13 q^{23} - 6 q^{24} - 23 q^{25} - 12 q^{26} + 23 q^{27} + 56 q^{28} + 2 q^{29} + 6 q^{30} - 16 q^{31} + 25 q^{32} + 19 q^{33} - 18 q^{34} - 20 q^{35} - 5 q^{36} + 58 q^{37} + 3 q^{38} + 32 q^{39} - 6 q^{40} + 14 q^{41} - 67 q^{42} - 34 q^{43} + 64 q^{44} - 7 q^{45} - 4 q^{46} + 22 q^{47} + 89 q^{48} - 61 q^{49} + 3 q^{50} - 38 q^{51} - 20 q^{52} - 70 q^{53} - 91 q^{54} - 2 q^{55} - 26 q^{56} + 2 q^{57} - 23 q^{58} - 15 q^{59} + 3 q^{60} - 32 q^{61} + 6 q^{62} - 31 q^{63} + 164 q^{64} + 11 q^{65} + 54 q^{66} - 16 q^{67} + 26 q^{68} - 19 q^{69} + 3 q^{70} + 50 q^{71} + 22 q^{72} + 82 q^{73} + 9 q^{74} - q^{75} - 29 q^{76} + 18 q^{77} - 41 q^{78} - 11 q^{79} - 90 q^{80} + 8 q^{81} + 60 q^{82} + 26 q^{83} + 123 q^{84} - 15 q^{85} - 15 q^{86} - 26 q^{87} - 22 q^{88} + 40 q^{89} - 12 q^{90} + 116 q^{91} + 2 q^{92} + 42 q^{93} - 36 q^{94} + 23 q^{95} - 48 q^{96} - 50 q^{97} - 24 q^{98} - 29 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9 + 6 * q^10 - q^11 + 9 * q^12 - 11 * q^13 - 3 * q^14 + q^15 - 45 * q^16 - 30 * q^17 - 18 * q^18 + 46 * q^19 + 29 * q^20 - 2 * q^21 - 5 * q^22 + 13 * q^23 - 6 * q^24 - 23 * q^25 - 12 * q^26 + 23 * q^27 + 56 * q^28 + 2 * q^29 + 6 * q^30 - 16 * q^31 + 25 * q^32 + 19 * q^33 - 18 * q^34 - 20 * q^35 - 5 * q^36 + 58 * q^37 + 3 * q^38 + 32 * q^39 - 6 * q^40 + 14 * q^41 - 67 * q^42 - 34 * q^43 + 64 * q^44 - 7 * q^45 - 4 * q^46 + 22 * q^47 + 89 * q^48 - 61 * q^49 + 3 * q^50 - 38 * q^51 - 20 * q^52 - 70 * q^53 - 91 * q^54 - 2 * q^55 - 26 * q^56 + 2 * q^57 - 23 * q^58 - 15 * q^59 + 3 * q^60 - 32 * q^61 + 6 * q^62 - 31 * q^63 + 164 * q^64 + 11 * q^65 + 54 * q^66 - 16 * q^67 + 26 * q^68 - 19 * q^69 + 3 * q^70 + 50 * q^71 + 22 * q^72 + 82 * q^73 + 9 * q^74 - q^75 - 29 * q^76 + 18 * q^77 - 41 * q^78 - 11 * q^79 - 90 * q^80 + 8 * q^81 + 60 * q^82 + 26 * q^83 + 123 * q^84 - 15 * q^85 - 15 * q^86 - 26 * q^87 - 22 * q^88 + 40 * q^89 - 12 * q^90 + 116 * q^91 + 2 * q^92 + 42 * q^93 - 36 * q^94 + 23 * q^95 - 48 * q^96 - 50 * q^97 - 24 * q^98 - 29 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.876140	+	1.51752i	−0.619525	+	1.07305i	0.370048	+	0.929013i	$0.379341\pi$
$2$	−0.876140	+	1.51752i	−0.619525	+	1.07305i	−0.989572	+	0.144036i	$0.953992\pi$
$3$	0.239525	−	1.71541i	0.138290	−	0.990392i
$3$	0.239525	−	1.71541i	0.138290	−	0.990392i
$4$	−0.535244	−	0.927070i	−0.267622	−	0.463535i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	2.39331	+	1.86642i	0.977064	+	0.761964i
$7$	−0.602689	+	1.04389i	−0.227795	+	0.394552i	−0.957154	−	0.289578i	$-0.906485\pi$
$7$	−0.602689	+	1.04389i	−0.227795	+	0.394552i	0.729359	+	0.684131i	$0.239818\pi$
$8$	−1.62877			−0.575856
$9$	−2.88526	−	0.821768i	−0.961752	−	0.273923i
$10$	−1.75228			−0.554120
$11$	2.67570	−	4.63446i	0.806755	−	1.39734i	−0.108345	−	0.994113i	$-0.534555\pi$
$11$	2.67570	−	4.63446i	0.806755	−	1.39734i	0.915100	−	0.403228i	$-0.132112\pi$
$12$	−1.71851	+	0.696106i	−0.496091	+	0.200948i
$13$	0.104894	+	0.181681i	0.0290923	+	0.0503894i	0.880205	−	0.474594i	$-0.157405\pi$
$13$	0.104894	+	0.181681i	0.0290923	+	0.0503894i	−0.851113	+	0.524983i	$0.824072\pi$
$14$	−1.05608	−	1.82918i	−0.282249	−	0.488870i
$15$	1.60535	−	0.650269i	0.414500	−	0.167899i
$16$	2.49752	−	4.32582i	0.624379	−	1.08146i
$17$	2.79479			0.677835			0.338918	−	0.940816i	$-0.389939\pi$
$17$	2.79479			0.677835			0.338918	+	0.940816i	$0.389939\pi$
$18$	3.77494	−	3.65845i	0.889761	−	0.862304i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	0.535244	−	0.927070i	0.119684	−	0.207299i
$21$	1.64633	+	1.28390i	0.359260	+	0.280169i
$22$	4.68859	+	8.12087i	0.999610	+	1.73137i
$23$	−0.481177	−	0.833423i	−0.100332	−	0.173781i	0.811489	−	0.584367i	$-0.198657\pi$
$23$	−0.481177	−	0.833423i	−0.100332	−	0.173781i	−0.911822	+	0.410587i	$0.865324\pi$
$24$	−0.390131	+	2.79400i	−0.0796351	+	0.570323i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.367607			−0.0720936
$27$	−2.10076	+	4.75256i	−0.404292	+	0.914630i
$28$	1.29034			0.243852
$29$	3.38420	−	5.86161i	0.628431	−	1.08847i	−0.359436	−	0.933170i	$-0.617031\pi$
$29$	3.38420	−	5.86161i	0.628431	−	1.08847i	0.987867	−	0.155304i	$-0.0496358\pi$
$30$	−0.419716	+	3.00588i	−0.0766293	+	0.548796i
$31$	0.267981	+	0.464157i	0.0481308	+	0.0833651i	0.889087	−	0.457738i	$-0.151340\pi$
$31$	0.267981	+	0.464157i	0.0481308	+	0.0833651i	−0.840956	+	0.541103i	$0.818007\pi$
$32$	2.74758	+	4.75895i	0.485709	+	0.841272i
$33$	−7.30909	−	5.70000i	−1.27235	−	0.992242i
$34$	−2.44862	+	4.24114i	−0.419936	+	0.727350i
$35$	−1.20538			−0.203746
$36$	0.782479	+	3.11468i	0.130413	+	0.519113i
$37$	10.3143			1.69567			0.847833	−	0.530264i	$-0.177907\pi$
$37$	10.3143			1.69567			0.847833	+	0.530264i	$0.177907\pi$
$38$	−0.876140	+	1.51752i	−0.142129	+	0.246174i
$39$	0.336783	−	0.136418i	0.0539284	−	0.0218444i
$40$	−0.814383	−	1.41055i	−0.128765	−	0.223028i
$41$	−3.81234	−	6.60317i	−0.595387	−	1.03124i	−0.993492	−	0.113901i	$-0.963665\pi$
$41$	−3.81234	−	6.60317i	−0.595387	−	1.03124i	0.398105	−	0.917340i	$-0.369668\pi$
$42$	−3.39076	+	1.37347i	−0.523205	+	0.211931i
$43$	−1.75761	+	3.04428i	−0.268033	+	0.464248i	−0.968354	−	0.249581i	$-0.919707\pi$
$43$	−1.75761	+	3.04428i	−0.268033	+	0.464248i	0.700320	+	0.713829i	$0.253040\pi$
$44$	−5.72862			−0.863622
$45$	−0.730955	−	2.90959i	−0.108964	−	0.433736i
$46$	1.68631			0.248633
$47$	2.21220	−	3.83165i	0.322683	−	0.558903i	−0.658358	−	0.752705i	$-0.728749\pi$
$47$	2.21220	−	3.83165i	0.322683	−	0.558903i	0.981041	+	0.193802i	$0.0620819\pi$
$48$	−6.82234	−	5.32041i	−0.984720	−	0.767934i
$49$	2.77353	+	4.80390i	0.396219	+	0.686271i
$50$	−0.876140	−	1.51752i	−0.123905	−	0.214610i
$51$	0.669422	−	4.79420i	0.0937379	−	0.671322i
$52$	0.112288	−	0.194488i	0.0155715	−	0.0269706i
$53$	9.46943			1.30073			0.650363	−	0.759623i	$-0.274617\pi$
$53$	9.46943			1.30073			0.650363	+	0.759623i	$0.274617\pi$
$54$	−5.37154	−	7.35185i	−0.730974	−	1.00046i
$55$	5.35141			0.721584
$56$	0.981639	−	1.70025i	0.131177	−	0.227205i
$57$	0.239525	−	1.71541i	0.0317259	−	0.227211i
$58$	5.93008	+	10.2712i	0.778657	+	1.34867i
$59$	−5.24839	−	9.09048i	−0.683283	−	1.18348i	−0.973973	−	0.226663i	$-0.927218\pi$
$59$	−5.24839	−	9.09048i	−0.683283	−	1.18348i	0.290691	−	0.956817i	$-0.406115\pi$
$60$	−1.46210	−	1.14022i	−0.188756	−	0.147202i
$61$	−0.0249540	+	0.0432215i	−0.00319503	+	0.00553395i	−0.867618	−	0.497230i	$-0.834350\pi$
$61$	−0.0249540	+	0.0432215i	−0.00319503	+	0.00553395i	0.864423	+	0.502764i	$0.167684\pi$
$62$	−0.939157			−0.119273
$63$	2.59674	−	2.51661i	0.327159	−	0.317063i
$64$	0.360986			0.0451232
$65$	−0.104894	+	0.181681i	−0.0130105	+	0.0225348i
$66$	15.0536	−	6.09769i	1.85298	−	0.750573i
$67$	−1.22861	−	2.12802i	−0.150099	−	0.259979i	0.781165	−	0.624325i	$-0.214626\pi$
$67$	−1.22861	−	2.12802i	−0.150099	−	0.259979i	−0.931264	+	0.364346i	$0.881292\pi$
$68$	−1.49589	−	2.59096i	−0.181404	−	0.314200i
$69$	−1.54491	+	0.625789i	−0.185986	+	0.0753361i
$70$	1.05608	−	1.82918i	0.126226	−	0.218629i
$71$	3.67721			0.436405			0.218202	−	0.975904i	$-0.429981\pi$
$71$	3.67721			0.436405			0.218202	+	0.975904i	$0.429981\pi$
$72$	4.69940	+	1.33847i	0.553830	+	0.157740i
$73$	14.3659			1.68140			0.840700	−	0.541501i	$-0.182144\pi$
$73$	14.3659			1.68140			0.840700	+	0.541501i	$0.182144\pi$
$74$	−9.03680	+	15.6522i	−1.05051	+	1.81953i
$75$	1.36582	+	1.06514i	0.157712	+	0.122992i
$76$	−0.535244	−	0.927070i	−0.0613967	−	0.106342i
$77$	3.22523	+	5.58627i	0.367549	+	0.636614i
$78$	−0.0880512	+	0.630596i	−0.00996983	+	0.0714009i
$79$	0.375760	−	0.650835i	0.0422763	−	0.0732247i	−0.844113	−	0.536165i	$-0.819872\pi$
$79$	0.375760	−	0.650835i	0.0422763	−	0.0732247i	0.886389	+	0.462941i	$0.153206\pi$
$80$	4.99503			0.558461
$81$	7.64939	+	4.74202i	0.849933	+	0.526891i
$82$	13.3606			1.47543
$83$	1.29683	−	2.24618i	0.142346	−	0.246550i	−0.786034	−	0.618184i	$-0.787869\pi$
$83$	1.29683	−	2.24618i	0.142346	−	0.246550i	0.928380	+	0.371633i	$0.121202\pi$
$84$	0.309070	−	2.21347i	0.0337223	−	0.241509i
$85$	1.39739	+	2.42036i	0.151569	+	0.262524i
$86$	−3.07983	−	5.33443i	−0.332107	−	0.575226i
$87$	−9.24446	−	7.20930i	−0.991110	−	0.772918i
$88$	−4.35809	+	7.54844i	−0.464574	+	0.804667i
$89$	−5.83021			−0.618001			−0.309000	−	0.951062i	$-0.599994\pi$
$89$	−5.83021			−0.618001			−0.309000	+	0.951062i	$0.599994\pi$
$90$	5.05578	+	1.43997i	0.532926	+	0.151786i
$91$	−0.252873			−0.0265083
$92$	−0.515094	+	0.892169i	−0.0537023	+	0.0930151i
$93$	0.860407	−	0.348520i	0.0892201	−	0.0361398i
$94$	3.87640	+	6.71412i	0.399820	+	0.692509i
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$	8.82167	−	3.57334i	0.900358	−	0.364702i
$97$	−8.41705	+	14.5788i	−0.854622	+	1.48025i	0.0223733	+	0.999750i	$0.492878\pi$
$97$	−8.41705	+	14.5788i	−0.854622	+	1.48025i	−0.876995	+	0.480499i	$0.840456\pi$
$98$	−9.72002			−0.981870
$99$	−11.5285	+	11.1728i	−1.15866	+	1.12291i
$100$	1.07049			0.107049
$101$	6.21759	−	10.7692i	0.618673	−	1.07157i	−0.371055	−	0.928611i	$-0.621004\pi$
$101$	6.21759	−	10.7692i	0.618673	−	1.07157i	0.989728	−	0.142963i	$-0.0456629\pi$
$102$	6.68879	+	5.21625i	0.662288	+	0.516486i
$103$	−7.03464	−	12.1843i	−0.693143	−	1.20056i	−0.970803	−	0.239880i	$-0.922892\pi$
$103$	−7.03464	−	12.1843i	−0.693143	−	1.20056i	0.277659	−	0.960680i	$-0.410441\pi$
$104$	−0.170847	−	0.295916i	−0.0167530	−	0.0290170i
$105$	−0.288719	+	2.06772i	−0.0281761	+	0.201788i
$106$	−8.29655	+	14.3701i	−0.805833	+	1.39574i
$107$	−7.57630			−0.732429			−0.366215	−	0.930530i	$-0.619346\pi$
$107$	−7.57630			−0.732429			−0.366215	+	0.930530i	$0.619346\pi$
$108$	5.53037	−	0.596226i	0.532161	−	0.0573719i
$109$	10.6151			1.01675			0.508373	−	0.861137i	$-0.330247\pi$
$109$	10.6151			1.01675			0.508373	+	0.861137i	$0.330247\pi$
$110$	−4.68859	+	8.12087i	−0.447039	+	0.774294i
$111$	2.47054	−	17.6933i	0.234494	−	1.67937i
$112$	3.01045	+	5.21425i	0.284461	+	0.492700i
$113$	0.706264	+	1.22329i	0.0664398	+	0.115077i	0.897332	−	0.441357i	$-0.145503\pi$
$113$	0.706264	+	1.22329i	0.0664398	+	0.115077i	−0.830892	+	0.556434i	$0.812169\pi$
$114$	2.39331	+	1.86642i	0.224154	+	0.174807i
$115$	0.481177	−	0.833423i	0.0448700	−	0.0777171i
$116$	−7.24550			−0.672728
$117$	−0.153345	−	0.610396i	−0.0141768	−	0.0564311i
$118$	18.3933			1.69324
$119$	−1.68439	+	2.91744i	−0.154407	+	0.267441i
$120$	−2.61474	+	1.05914i	−0.238692	+	0.0966855i
$121$	−8.81879	−	15.2746i	−0.801708	−	1.38860i
$122$	−0.0437264	−	0.0757363i	−0.00395880	−	0.00685684i
$123$	−12.2403	+	4.95810i	−1.10367	+	0.447056i
$124$	0.286871	−	0.496875i	0.0257618	−	0.0446207i
$125$	−1.00000			−0.0894427
$126$	1.54389	+	6.14552i	0.137541	+	0.547486i
$127$	−18.7096			−1.66021			−0.830103	−	0.557611i	$-0.811718\pi$
$127$	−18.7096			−1.66021			−0.830103	+	0.557611i	$0.811718\pi$
$128$	−5.81144	+	10.0657i	−0.513664	+	0.889692i
$129$	4.80118	+	3.74421i	0.422721	+	0.329659i
$130$	−0.183803	−	0.318357i	−0.0161206	−	0.0279217i
$131$	10.7132	+	18.5558i	0.936015	+	1.62123i	0.772814	+	0.634633i	$0.218849\pi$
$131$	10.7132	+	18.5558i	0.936015	+	1.62123i	0.163201	+	0.986593i	$0.447818\pi$
$132$	−1.37215	+	9.82693i	−0.119430	+	0.855324i
$133$	−0.602689	+	1.04389i	−0.0522597	+	0.0905165i
$134$	4.30574			0.371960
$135$	−5.16622	+	0.556967i	−0.444637	+	0.0479361i
$136$	−4.55205			−0.390335
$137$	−8.62800	+	14.9441i	−0.737140	+	1.27676i	0.216638	+	0.976252i	$0.430491\pi$
$137$	−8.62800	+	14.9441i	−0.737140	+	1.27676i	−0.953778	+	0.300512i	$0.902843\pi$
$138$	0.403915	−	2.89272i	0.0343835	−	0.246244i
$139$	−1.30716	−	2.26407i	−0.110872	−	0.192036i	0.805250	−	0.592935i	$-0.202031\pi$
$139$	−1.30716	−	2.26407i	−0.110872	−	0.192036i	−0.916122	+	0.400900i	$0.868698\pi$
$140$	0.645171	+	1.11747i	0.0545269	+	0.0944434i
$141$	−6.04296	−	4.71261i	−0.508909	−	0.396873i
$142$	−3.22175	+	5.58024i	−0.270363	+	0.468283i
$143$	1.12266			0.0938815
$144$	−10.7608	+	10.4287i	−0.896733	+	0.869061i
$145$	6.76841			0.562086
$146$	−12.5865	+	21.8005i	−1.04167	+	1.80422i
$147$	8.90498	−	3.60709i	0.734471	−	0.297507i
$148$	−5.52068	−	9.56211i	−0.453797	−	0.786000i
$149$	−5.70934	−	9.88886i	−0.467727	−	0.810127i	0.531593	−	0.847000i	$-0.321594\pi$
$149$	−5.70934	−	9.88886i	−0.467727	−	0.810127i	−0.999320	+	0.0368730i	$0.988260\pi$
$150$	−2.81302	+	1.13945i	−0.229683	+	0.0930361i
$151$	−0.306475	+	0.530830i	−0.0249406	+	0.0431984i	−0.878226	−	0.478245i	$-0.841273\pi$
$151$	−0.306475	+	0.530830i	−0.0249406	+	0.0431984i	0.853286	+	0.521444i	$0.174606\pi$
$152$	−1.62877			−0.132110
$153$	−8.06367	−	2.29667i	−0.651909	−	0.185674i
$154$	−11.3030			−0.910824
$155$	−0.267981	+	0.464157i	−0.0215248	+	0.0372820i
$156$	−0.306730	−	0.239204i	−0.0245581	−	0.0191516i
$157$	4.78927	+	8.29527i	0.382226	+	0.662034i	0.991380	−	0.131017i	$-0.0418244\pi$
$157$	4.78927	+	8.29527i	0.382226	+	0.662034i	−0.609154	+	0.793052i	$0.708491\pi$
$158$	0.658437	+	1.14045i	0.0523824	+	0.0907290i
$159$	2.26817	−	16.2440i	0.179878	−	1.28823i
$160$	−2.74758	+	4.75895i	−0.217216	+	0.376228i
$161$	1.16000			0.0914207
$162$	−13.8981	+	7.45343i	−1.09193	+	0.585597i
$163$	18.3614			1.43817			0.719086	−	0.694921i	$-0.244561\pi$
$163$	18.3614			1.43817			0.719086	+	0.694921i	$0.244561\pi$
$164$	−4.08107	+	7.06861i	−0.318678	+	0.551966i
$165$	1.28180	−	9.17985i	0.0997879	−	0.714651i
$166$	2.27241	+	3.93594i	0.176374	+	0.305488i
$167$	−6.00213	−	10.3960i	−0.464459	−	0.804467i	0.534718	−	0.845031i	$-0.320418\pi$
$167$	−6.00213	−	10.3960i	−0.464459	−	0.804467i	−0.999177	+	0.0405640i	$0.987085\pi$
$168$	−2.68149	−	2.09116i	−0.206882	−	0.161337i
$169$	6.47799	−	11.2202i	0.498307	−	0.863094i
$170$	−4.89725			−0.375602
$171$	−2.88526	−	0.821768i	−0.220641	−	0.0628422i
$172$	3.76301			0.286927
$173$	−6.76964	+	11.7254i	−0.514686	+	0.891462i	0.485169	+	0.874421i	$0.338758\pi$
$173$	−6.76964	+	11.7254i	−0.514686	+	0.891462i	−0.999855	+	0.0170417i	$0.994575\pi$
$174$	19.0397	−	7.71229i	1.44340	−	0.584667i
$175$	−0.602689	−	1.04389i	−0.0455590	−	0.0789105i
$176$	−13.3652	−	23.1493i	−1.00744	−	1.74494i
$177$	−16.8510	+	6.82574i	−1.26660	+	0.513054i
$178$	5.10808	−	8.84745i	0.382867	−	0.663145i
$179$	10.8926			0.814148			0.407074	−	0.913395i	$-0.366549\pi$
$179$	10.8926			0.814148			0.407074	+	0.913395i	$0.366549\pi$
$180$	−2.30615	+	2.23499i	−0.171890	+	0.166586i
$181$	−14.6879			−1.09174			−0.545870	−	0.837870i	$-0.683801\pi$
$181$	−14.6879			−1.09174			−0.545870	+	0.837870i	$0.683801\pi$
$182$	0.221552	−	0.383740i	0.0164226	−	0.0284447i
$183$	0.0681655	+	0.0531589i	0.00503894	+	0.00392962i
$184$	0.783724	+	1.35745i	0.0577769	+	0.100073i
$185$	5.15716	+	8.93247i	0.379162	+	0.656728i
$186$	−0.224952	+	1.61104i	−0.0164943	+	0.118127i
$187$	7.47802	−	12.9523i	0.546847	−	0.947167i
$188$	−4.73628			−0.345428
$189$	−3.69503	−	5.05727i	−0.268774	−	0.367862i
$190$	−1.75228			−0.127124
$191$	5.37731	−	9.31378i	0.389089	−	0.673921i	−0.603239	−	0.797561i	$-0.706123\pi$
$191$	5.37731	−	9.31378i	0.389089	−	0.673921i	0.992327	+	0.123640i	$0.0394567\pi$
$192$	0.0864653	−	0.619238i	0.00624010	−	0.0446897i
$193$	−9.13581	−	15.8237i	−0.657610	−	1.13901i	−0.981233	−	0.192828i	$-0.938234\pi$
$193$	−9.13581	−	15.8237i	−0.657610	−	1.13901i	0.323622	−	0.946186i	$-0.395099\pi$
$194$	−14.7490	−	25.5461i	−1.05892	−	1.83410i
$195$	0.286533	+	0.223453i	0.0205191	+	0.0160018i
$196$	2.96903	−	5.14252i	0.212074	−	0.367323i
$197$	−13.6801			−0.974670			−0.487335	−	0.873215i	$-0.662031\pi$
$197$	−13.6801			−0.974670			−0.487335	+	0.873215i	$0.662031\pi$
$198$	−6.85429	−	27.2837i	−0.487113	−	1.93897i
$199$	−3.66211			−0.259600			−0.129800	−	0.991540i	$-0.541434\pi$
$199$	−3.66211			−0.259600			−0.129800	+	0.991540i	$0.541434\pi$
$200$	0.814383	−	1.41055i	0.0575856	−	0.0997411i
$201$	−3.94470	+	1.59786i	−0.278238	+	0.112704i
$202$	10.8950	+	18.8706i	0.766567	+	1.32773i
$203$	4.07924	+	7.06546i	0.286307	+	0.495898i
$204$	−4.80286	+	1.94547i	−0.336268	+	0.136210i
$205$	3.81234	−	6.60317i	0.266265	−	0.461185i
$206$	24.6533			1.71768
$207$	0.703437	+	2.80005i	0.0488923	+	0.194617i
$208$	1.04790			0.0726585
$209$	2.67570	−	4.63446i	0.185082	−	0.320572i
$210$	−2.88484	−	2.24975i	−0.199073	−	0.155247i
$211$	−5.08135	−	8.80115i	−0.349814	−	0.605896i	0.636402	−	0.771358i	$-0.280422\pi$
$211$	−5.08135	−	8.80115i	−0.349814	−	0.605896i	−0.986216	+	0.165461i	$0.947089\pi$
$212$	−5.06846	−	8.77883i	−0.348103	−	0.602932i
$213$	0.880786	−	6.30792i	0.0603504	−	0.432211i
$214$	6.63791	−	11.4972i	0.453758	−	0.785932i
$215$	−3.51523			−0.239736
$216$	3.42165	−	7.74080i	0.232814	−	0.526695i
$217$	−0.646037			−0.0438558
$218$	−9.30035	+	16.1087i	−0.629899	+	1.09102i
$219$	3.44100	−	24.6434i	0.232521	−	1.66524i
$220$	−2.86431	−	4.96113i	−0.193112	−	0.334479i
$221$	0.293156	+	0.507761i	0.0197198	+	0.0341557i
$222$	24.6854	+	19.2509i	1.65677	+	1.29204i
$223$	−10.4389	+	18.0807i	−0.699039	+	1.21077i	0.269762	+	0.962927i	$0.413055\pi$
$223$	−10.4389	+	18.0807i	−0.699039	+	1.21077i	−0.968800	+	0.247843i	$0.920278\pi$
$224$	−6.62375			−0.442568
$225$	2.15430	−	2.08782i	0.143620	−	0.139188i
$226$	−2.47515			−0.164644
$227$	0.187370	−	0.324534i	0.0124362	−	0.0215401i	−0.859740	−	0.510731i	$-0.829375\pi$
$227$	0.187370	−	0.324534i	0.0124362	−	0.0215401i	0.872177	+	0.489191i	$0.162708\pi$
$228$	−1.71851	+	0.696106i	−0.113811	+	0.0461007i
$229$	11.6938	+	20.2543i	0.772750	+	1.33844i	0.936050	+	0.351866i	$0.114453\pi$
$229$	11.6938	+	20.2543i	0.772750	+	1.33844i	−0.163300	+	0.986576i	$0.552214\pi$
$230$	0.843157	+	1.46039i	0.0555961	+	0.0962953i
$231$	10.3553	−	4.19454i	0.681326	−	0.275981i
$232$	−5.51207	+	9.54719i	−0.361885	+	0.626804i
$233$	5.13063			0.336119			0.168059	−	0.985777i	$-0.446250\pi$
$233$	5.13063			0.336119			0.168059	+	0.985777i	$0.446250\pi$
$234$	1.06064	+	0.302088i	0.0693362	+	0.0197481i
$235$	4.42441			0.288616
$236$	−5.61834	+	9.73126i	−0.365723	+	0.633451i
$237$	−1.02644	−	0.800473i	−0.0666747	−	0.0519963i
$238$	−2.95152	−	5.11218i	−0.191318	−	0.331373i
$239$	−2.02200	−	3.50220i	−0.130792	−	0.226539i	0.793190	−	0.608974i	$-0.208419\pi$
$239$	−2.02200	−	3.50220i	−0.130792	−	0.226539i	−0.923982	+	0.382436i	$0.875085\pi$
$240$	1.19644	−	8.56852i	0.0772297	−	0.553096i
$241$	−4.63757	+	8.03250i	−0.298732	+	0.517419i	−0.975846	−	0.218459i	$-0.929897\pi$
$241$	−4.63757	+	8.03250i	−0.298732	+	0.517419i	0.677114	+	0.735878i	$0.263230\pi$
$242$	30.9060			1.98671
$243$	9.96673	−	11.9860i	0.639366	−	0.768902i
$244$	0.0534259			0.00342024
$245$	−2.77353	+	4.80390i	−0.177195	+	0.306910i
$246$	3.20020	−	22.9189i	0.204037	−	1.46125i
$247$	0.104894	+	0.181681i	0.00667423	+	0.0115601i
$248$	−0.436478	−	0.756003i	−0.0277164	−	0.0480062i
$249$	−3.54249	−	2.76261i	−0.224496	−	0.175074i
$250$	0.876140	−	1.51752i	0.0554120	−	0.0959764i
$251$	−8.04509			−0.507802			−0.253901	−	0.967230i	$-0.581714\pi$
$251$	−8.04509			−0.507802			−0.253901	+	0.967230i	$0.581714\pi$
$252$	−3.72297	−	1.06036i	−0.234525	−	0.0667966i
$253$	−5.14995			−0.323774
$254$	16.3922	−	28.3921i	1.02854	−	1.78148i
$255$	4.48661	−	1.81736i	0.280962	−	0.113808i
$256$	−9.82229	−	17.0127i	−0.613893	−	1.06329i
$257$	−10.1779	−	17.6286i	−0.634878	−	1.09964i	−0.986541	−	0.163514i	$-0.947717\pi$
$257$	−10.1779	−	17.6286i	−0.634878	−	1.09964i	0.351663	−	0.936127i	$-0.385616\pi$
$258$	−9.88842	+	4.00544i	−0.615626	+	0.249368i
$259$	−6.21633	+	10.7670i	−0.386264	+	0.669029i
$260$	0.224575			0.0139276
$261$	−14.5812	+	14.1312i	−0.902552	+	0.874700i
$262$	−37.5450			−2.31954
$263$	−7.85725	+	13.6092i	−0.484499	+	0.839176i	−0.999841	−	0.0178078i	$-0.994331\pi$
$263$	−7.85725	+	13.6092i	−0.484499	+	0.839176i	0.515343	+	0.856984i	$0.327665\pi$
$264$	11.9048	+	9.28396i	0.732689	+	0.571388i
$265$	4.73472	+	8.20077i	0.290851	+	0.503769i
$266$	−1.05608	−	1.82918i	−0.0647524	−	0.112154i
$267$	−1.39648	+	10.0012i	−0.0854634	+	0.612063i
$268$	−1.31521	+	2.27802i	−0.0803395	+	0.139152i
$269$	−5.21208			−0.317786			−0.158893	−	0.987296i	$-0.550792\pi$
$269$	−5.21208			−0.317786			−0.158893	+	0.987296i	$0.550792\pi$
$270$	3.68112	−	8.32782i	0.224026	−	0.506815i
$271$	−5.50043			−0.334128			−0.167064	−	0.985946i	$-0.553429\pi$
$271$	−5.50043			−0.334128			−0.167064	+	0.985946i	$0.553429\pi$
$272$	6.98002	−	12.0898i	0.423226	−	0.733049i
$273$	−0.0605696	+	0.433781i	−0.00366584	+	0.0262536i
$274$	−15.1187	−	26.1863i	−0.913353	−	1.58197i
$275$	2.67570	+	4.63446i	0.161351	+	0.279468i
$276$	1.40706	+	1.09729i	0.0846949	+	0.0660494i
$277$	−4.31394	+	7.47197i	−0.259200	+	0.448947i	−0.966028	−	0.258438i	$-0.916792\pi$
$277$	−4.31394	+	7.47197i	−0.259200	+	0.448947i	0.706828	+	0.707385i	$0.250125\pi$
$278$	4.58102			0.274751
$279$	−0.391765	−	1.55943i	−0.0234543	−	0.0933606i
$280$	1.96328			0.117328
$281$	−12.8549	+	22.2654i	−0.766861	+	1.32824i	0.172396	+	0.985028i	$0.444849\pi$
$281$	−12.8549	+	22.2654i	−0.766861	+	1.32824i	−0.939257	+	0.343214i	$0.888484\pi$
$282$	12.4460	−	5.04141i	0.741146	−	0.300212i
$283$	−8.12385	−	14.0709i	−0.482913	−	0.836429i	0.516895	−	0.856049i	$-0.327088\pi$
$283$	−8.12385	−	14.0709i	−0.482913	−	0.836429i	−0.999808	+	0.0196197i	$0.993754\pi$
$284$	−1.96821	−	3.40903i	−0.116792	−	0.202289i
$285$	1.60535	−	0.650269i	0.0950928	−	0.0385186i
$286$	−0.983607	+	1.70366i	−0.0581619	+	0.100739i
$287$	9.19062			0.542505
$288$	−4.01672	−	15.9887i	−0.236688	−	0.942142i
$289$	−9.18917			−0.540540
$290$	−5.93008	+	10.2712i	−0.348226	+	0.603145i
$291$	22.9924	+	17.9307i	1.34784	+	1.05111i
$292$	−7.68926	−	13.3182i	−0.449980	−	0.779388i
$293$	−1.49857	−	2.59560i	−0.0875473	−	0.151636i	0.818927	−	0.573898i	$-0.194570\pi$
$293$	−1.49857	−	2.59560i	−0.0875473	−	0.151636i	−0.906474	+	0.422262i	$0.861236\pi$
$294$	−2.32819	+	16.6738i	−0.135783	+	0.972436i
$295$	5.24839	−	9.09048i	0.305573	−	0.529268i
$296$	−16.7996			−0.976458
$297$	16.4045	+	22.4523i	0.951886	+	1.30282i
$298$	20.0087			1.15907
$299$	0.100945	−	0.174842i	0.00583779	−	0.0101114i
$300$	0.256409	−	1.83633i	0.0148038	−	0.106020i
$301$	−2.11859	−	3.66950i	−0.122113	−	0.211506i
$302$	−0.537030	−	0.930164i	−0.0309026	−	0.0535249i
$303$	−16.9843	−	13.2452i	−0.975722	−	0.760917i
$304$	2.49752	−	4.32582i	0.143242	−	0.248103i
$305$	−0.0499079			−0.00285772
$306$	10.5501	−	10.2246i	0.603112	−	0.584500i
$307$	−9.12325			−0.520691			−0.260346	−	0.965516i	$-0.583836\pi$
$307$	−9.12325			−0.520691			−0.260346	+	0.965516i	$0.583836\pi$
$308$	3.45258	−	5.98004i	0.196729	−	0.340744i
$309$	−22.5861	+	9.14882i	−1.28488	+	0.520458i
$310$	−0.469578	−	0.813333i	−0.0266703	−	0.0461942i
$311$	1.65814	+	2.87199i	0.0940246	+	0.162855i	0.909201	−	0.416357i	$-0.136693\pi$
$311$	1.65814	+	2.87199i	0.0940246	+	0.162855i	−0.815177	+	0.579213i	$0.803360\pi$
$312$	−0.548540	+	0.222194i	−0.0310550	+	0.0125792i
$313$	5.77700	−	10.0061i	0.326535	−	0.565576i	−0.655287	−	0.755380i	$-0.727452\pi$
$313$	5.77700	−	10.0061i	0.326535	−	0.565576i	0.981822	+	0.189805i	$0.0607855\pi$
$314$	−16.7843			−0.947193
$315$	3.47782	+	0.990541i	0.195953	+	0.0558107i
$316$	−0.804493			−0.0452563
$317$	−2.00410	+	3.47121i	−0.112562	+	0.194962i	−0.916802	−	0.399341i	$-0.869239\pi$
$317$	−2.00410	+	3.47121i	−0.112562	+	0.194962i	0.804241	+	0.594304i	$0.202572\pi$
$318$	22.6633	+	17.6740i	1.27089	+	0.991107i
$319$	−18.1103	−	31.3679i	−1.01398	−	1.75626i
$320$	0.180493	+	0.312623i	0.0100899	+	0.0174762i
$321$	−1.81472	+	12.9965i	−0.101288	+	0.725392i
$322$	−1.01632	+	1.76032i	−0.0566374	+	0.0980989i
$323$	2.79479			0.155506
$324$	0.301893	−	9.62966i	0.0167719	−	0.534981i
$325$	−0.209788			−0.0116369
$326$	−16.0871	+	27.8637i	−0.890983	+	1.54323i
$327$	2.54260	−	18.2093i	0.140606	−	1.00698i
$328$	6.20941	+	10.7550i	0.342857	+	0.593846i
$329$	2.66654	+	4.61858i	0.147011	+	0.254631i
$330$	12.8076	+	9.98800i	0.705034	+	0.549821i
$331$	−11.0826	+	19.1957i	−0.609157	+	1.05509i	0.382223	+	0.924070i	$0.375159\pi$
$331$	−11.0826	+	19.1957i	−0.609157	+	1.05509i	−0.991380	+	0.131021i	$0.958175\pi$
$332$	−2.77649			−0.152380
$333$	−29.7595	−	8.47599i	−1.63081	−	0.464481i
$334$	21.0348			1.15098
$335$	1.22861	−	2.12802i	0.0671262	−	0.116266i
$336$	9.66565	−	3.91521i	0.527304	−	0.213592i
$337$	6.57912	+	11.3954i	0.358387	+	0.620745i	0.987692	−	0.156414i	$-0.0499934\pi$
$337$	6.57912	+	11.3954i	0.358387	+	0.620745i	−0.629304	+	0.777159i	$0.716660\pi$
$338$	11.3513	+	19.6610i	0.617427	+	1.06942i
$339$	2.26760	−	0.918524i	0.123159	−	0.0498874i
$340$	1.49589	−	2.59096i	0.0811262	−	0.140515i
$341$	2.86815			0.155319
$342$	3.77494	−	3.65845i	0.204125	−	0.197826i
$343$	−15.1239			−0.816616
$344$	2.86274	−	4.95841i	0.154349	−	0.267340i
$345$	−1.31441	−	1.02504i	−0.0707653	−	0.0551863i
$346$	−11.8623	−	20.5461i	−0.637721	−	1.10457i
$347$	10.8984	+	18.8765i	0.585055	+	1.01334i	0.994869	+	0.101175i	$0.0322604\pi$
$347$	10.8984	+	18.8765i	0.585055	+	1.01334i	−0.409814	+	0.912169i	$0.634406\pi$
$348$	−1.73548	+	12.4290i	−0.0930316	+	0.666264i
$349$	−8.89376	+	15.4044i	−0.476072	+	0.824581i	−0.999624	−	0.0274125i	$-0.991273\pi$
$349$	−8.89376	+	15.4044i	−0.476072	+	0.824581i	0.523552	+	0.851994i	$0.324607\pi$
$350$	2.11216			0.112900
$351$	−1.08381	+	0.116845i	−0.0578494	+	0.00623671i
$352$	29.4069			1.56739
$353$	−2.50307	+	4.33544i	−0.133225	+	0.230752i	−0.924918	−	0.380167i	$-0.875867\pi$
$353$	−2.50307	+	4.33544i	−0.133225	+	0.230752i	0.791693	+	0.610919i	$0.209200\pi$
$354$	4.40567	−	31.5521i	0.234159	−	1.67697i
$355$	1.83861	+	3.18456i	0.0975830	+	0.169019i
$356$	3.12058	+	5.40501i	0.165391	+	0.286465i
$357$	4.60115	+	3.58821i	0.243519	+	0.189908i
$358$	−9.54341	+	16.5297i	−0.504385	+	0.873620i
$359$	28.7335			1.51650			0.758248	−	0.651966i	$-0.226055\pi$
$359$	28.7335			1.51650			0.758248	+	0.651966i	$0.226055\pi$
$360$	1.19055	+	4.73904i	0.0627477	+	0.249769i
$361$	1.00000			0.0526316
$362$	12.8686	−	22.2891i	0.676360	−	1.17149i
$363$	−28.3145	+	11.4692i	−1.48613	+	0.601975i
$364$	0.135349	+	0.234431i	0.00709421	+	0.0122875i
$365$	7.18294	+	12.4412i	0.375973	+	0.651203i
$366$	−0.140392	+	0.0568678i	−0.00733842	+	0.00297253i
$367$	3.69743	−	6.40414i	0.193004	−	0.334293i	−0.753240	−	0.657746i	$-0.771510\pi$
$367$	3.69743	−	6.40414i	0.193004	−	0.334293i	0.946244	+	0.323452i	$0.104844\pi$
$368$	−4.80699			−0.250581
$369$	5.57330	+	22.1847i	0.290134	+	1.15489i
$370$	−18.0736			−0.939602
$371$	−5.70712	+	9.88502i	−0.296299	+	0.513205i
$372$	−0.783630	−	0.611115i	−0.0406293	−	0.0316848i
$373$	−6.52156	−	11.2957i	−0.337674	−	0.584868i	0.646321	−	0.763066i	$-0.276307\pi$
$373$	−6.52156	−	11.2957i	−0.337674	−	0.584868i	−0.983995	+	0.178198i	$0.942973\pi$
$374$	13.1036	+	22.6961i	0.677571	+	1.17359i
$375$	−0.239525	+	1.71541i	−0.0123690	+	0.0885833i
$376$	−3.60316	+	6.24086i	−0.185819	+	0.321848i
$377$	1.41993			0.0731300
$378$	10.9119	−	1.17640i	0.561246	−	0.0605076i
$379$	−18.8921			−0.970421			−0.485210	−	0.874397i	$-0.661257\pi$
$379$	−18.8921			−0.970421			−0.485210	+	0.874397i	$0.661257\pi$
$380$	0.535244	−	0.927070i	0.0274574	−	0.0475577i
$381$	−4.48142	+	32.0945i	−0.229590	+	1.64425i
$382$	9.42256	+	16.3204i	0.482100	+	0.835022i
$383$	2.20533	+	3.81974i	0.112687	+	0.195180i	0.916853	−	0.399225i	$-0.130721\pi$
$383$	2.20533	+	3.81974i	0.112687	+	0.195180i	−0.804166	+	0.594405i	$0.797388\pi$
$384$	15.8748	+	12.3800i	0.810109	+	0.631764i
$385$	−3.22523	+	5.58627i	−0.164373	+	0.284703i
$386$	32.0170			1.62962
$387$	7.57285	−	7.33916i	0.384950	−	0.373070i
$388$	18.0207			0.914863
$389$	2.01211	−	3.48508i	0.102018	−	0.176701i	−0.810498	−	0.585742i	$-0.800803\pi$
$389$	2.01211	−	3.48508i	0.102018	−	0.176701i	0.912516	+	0.409041i	$0.134137\pi$
$390$	−0.590138	+	0.239043i	−0.0298828	+	0.0121044i
$391$	−1.34479	−	2.32924i	−0.0680087	−	0.117795i
$392$	−4.51743	−	7.82443i	−0.228165	−	0.395193i
$393$	34.3968	−	13.9329i	1.73509	−	0.702822i
$394$	11.9857	−	20.7599i	0.603832	−	1.04587i
$395$	0.751520			0.0378131
$396$	16.5285	+	4.70760i	0.830590	+	0.236566i
$397$	34.4917			1.73109			0.865545	−	0.500831i	$-0.166972\pi$
$397$	34.4917			1.73109			0.865545	+	0.500831i	$0.166972\pi$
$398$	3.20852	−	5.55733i	0.160829	−	0.278564i
$399$	1.64633	+	1.28390i	0.0824198	+	0.0642752i
$400$	2.49752	+	4.32582i	0.124876	+	0.216291i
$401$	14.5863	+	25.2642i	0.728406	+	1.26164i	0.957557	+	0.288245i	$0.0930719\pi$
$401$	14.5863	+	25.2642i	0.728406	+	1.26164i	−0.229151	+	0.973391i	$0.573595\pi$
$402$	1.03134	−	7.38611i	0.0514383	−	0.368386i
$403$	−0.0562191	+	0.0973744i	−0.00280047	+	0.00485056i
$404$	−13.3117			−0.662283
$405$	−0.282015	+	8.99558i	−0.0140134	+	0.446994i
$406$	−14.2960			−0.709496
$407$	27.5981	−	47.8013i	1.36799	−	2.36942i
$408$	−1.09033	+	7.80863i	−0.0539795	+	0.386585i
$409$	9.87526	+	17.1045i	0.488300	+	0.845761i	0.999909	−	0.0134573i	$-0.00428372\pi$
$409$	9.87526	+	17.1045i	0.488300	+	0.845761i	−0.511609	+	0.859218i	$0.670950\pi$
$410$	6.68029	+	11.5706i	0.329916	+	0.571431i
$411$	23.5687	+	18.3800i	1.16256	+	0.906621i
$412$	−7.53050	+	13.0432i	−0.371001	+	0.642592i
$413$	12.6526			0.622593
$414$	−4.86545	−	1.38576i	−0.239124	−	0.0681063i
$415$	2.59366			0.127318
$416$	−0.576409	+	0.998370i	−0.0282608	+	0.0489491i
$417$	−4.19690	+	1.70001i	−0.205523	+	0.0832499i
$418$	4.68859	+	8.12087i	0.229326	+	0.397205i
$419$	16.7867	+	29.0754i	0.820083	+	1.42043i	0.905620	+	0.424091i	$0.139406\pi$
$419$	16.7867	+	29.0754i	0.820083	+	1.42043i	−0.0855363	+	0.996335i	$0.527260\pi$
$420$	2.07145	−	0.839070i	0.101077	−	0.0409424i
$421$	9.85600	−	17.0711i	0.480352	−	0.831994i	−0.519394	−	0.854535i	$-0.673842\pi$
$421$	9.85600	−	17.0711i	0.480352	−	0.831994i	0.999746	+	0.0225411i	$0.00717566\pi$
$422$	17.8079			0.866875
$423$	−9.53150	+	9.23736i	−0.463437	+	0.449136i
$424$	−15.4235			−0.749031
$425$	−1.39739	+	2.42036i	−0.0677835	+	0.117404i
$426$	8.80070	+	6.86323i	0.426395	+	0.332525i
$427$	−0.0300790	−	0.0520983i	−0.00145562	−	0.00252121i
$428$	4.05517	+	7.02377i	0.196014	+	0.339507i
$429$	0.268905	−	1.92582i	0.0129829	−	0.0929794i
$430$	3.07983	−	5.33443i	0.148523	−	0.257249i
$431$	−18.9181			−0.911253			−0.455627	−	0.890171i	$-0.650585\pi$
$431$	−18.9181			−0.911253			−0.455627	+	0.890171i	$0.650585\pi$
$432$	15.3120	+	20.9571i	0.736701	+	1.00830i
$433$	−3.15942			−0.151832			−0.0759160	−	0.997114i	$-0.524188\pi$
$433$	−3.15942			−0.151832			−0.0759160	+	0.997114i	$0.524188\pi$
$434$	0.566019	−	0.980374i	0.0271698	−	0.0470594i
$435$	1.62121	−	11.6106i	0.0777309	−	0.556685i
$436$	−5.68169	−	9.84097i	−0.272104	−	0.471297i
$437$	−0.481177	−	0.833423i	−0.0230178	−	0.0398680i
$438$	34.3820	+	26.8128i	1.64284	+	1.28117i
$439$	17.7422	−	30.7304i	0.846788	−	1.46668i	−0.0372705	−	0.999305i	$-0.511866\pi$
$439$	17.7422	−	30.7304i	0.846788	−	1.46668i	0.884059	−	0.467375i	$-0.154800\pi$
$440$	−8.71619			−0.415528
$441$	−4.05466	−	16.1397i	−0.193079	−	0.768556i
$442$	−1.02738			−0.0488676
$443$	10.6958	−	18.5257i	0.508175	−	0.880185i	−0.491780	−	0.870719i	$-0.663654\pi$
$443$	10.6958	−	18.5257i	0.508175	−	0.880185i	0.999955	−	0.00946533i	$-0.00301295\pi$
$444$	−17.7253	+	7.17986i	−0.841204	+	0.340741i
$445$	−2.91510	−	5.04911i	−0.138189	−	0.239351i
$446$	−18.2918	−	31.6824i	−0.866144	−	1.50020i
$447$	−18.3310	+	7.42521i	−0.867025	+	0.351200i
$448$	−0.217562	+	0.376829i	−0.0102788	+	0.0178035i
$449$	32.0526			1.51266			0.756328	−	0.654192i	$-0.226991\pi$
$449$	32.0526			1.51266			0.756328	+	0.654192i	$0.226991\pi$
$450$	1.28084	+	5.09842i	0.0603793	+	0.240342i
$451$	−40.8028			−1.92133
$452$	0.756048	−	1.30951i	0.0355615	−	0.0615943i
$453$	0.837183	+	0.652877i	0.0393343	+	0.0306749i
$454$	0.328325	+	0.568675i	0.0154090	+	0.0266892i
$455$	−0.126437	−	0.218995i	−0.00592744	−	0.0102666i
$456$	−0.390131	+	2.79400i	−0.0182695	+	0.130841i
$457$	−16.2977	+	28.2285i	−0.762376	+	1.32047i	0.179247	+	0.983804i	$0.442634\pi$
$457$	−16.2977	+	28.2285i	−0.762376	+	1.32047i	−0.941623	+	0.336669i	$0.890700\pi$
$458$	−40.9818			−1.91495
$459$	−5.87118	+	13.2824i	−0.274043	+	0.619968i
$460$	−1.03019			−0.0480328
$461$	0.449218	−	0.778069i	0.0209222	−	0.0362383i	−0.855375	−	0.518010i	$-0.826673\pi$
$461$	0.449218	−	0.778069i	0.0209222	−	0.0362383i	0.876297	+	0.481771i	$0.160006\pi$
$462$	−2.70736	+	19.3893i	−0.125958	+	0.902073i
$463$	−7.30576	−	12.6539i	−0.339527	−	0.588079i	0.644817	−	0.764337i	$-0.276934\pi$
$463$	−7.30576	−	12.6539i	−0.339527	−	0.588079i	−0.984344	+	0.176259i	$0.943600\pi$
$464$	−16.9042	−	29.2789i	−0.784758	−	1.35924i
$465$	0.732031	+	0.570875i	0.0339471	+	0.0264737i
$466$	−4.49515	+	7.78583i	−0.208234	+	0.360672i
$467$	28.1038			1.30049			0.650245	−	0.759724i	$-0.274666\pi$
$467$	28.1038			1.30049			0.650245	+	0.759724i	$0.274666\pi$
$468$	−0.483802	+	0.468873i	−0.0223638	+	0.0216736i
$469$	2.96188			0.136767
$470$	−3.87640	+	6.71412i	−0.178805	+	0.309699i
$471$	15.3769	−	6.22864i	0.708531	−	0.287000i
$472$	8.54840	+	14.8063i	0.393472	+	0.681514i
$473$	9.40571	+	16.2912i	0.432475	+	0.749068i
$474$	2.11404	−	0.856323i	0.0971013	−	0.0393322i
$475$	−0.500000	+	0.866025i	−0.0229416	+	0.0397360i
$476$	3.60623			0.165291
$477$	−27.3217	−	7.78168i	−1.25098	−	0.356299i
$478$	7.08621			0.324116
$479$	14.7929	−	25.6220i	0.675904	−	1.17070i	−0.300300	−	0.953845i	$-0.597087\pi$
$479$	14.7929	−	25.6220i	0.675904	−	1.17070i	0.976204	−	0.216855i	$-0.0695800\pi$
$480$	7.50544	+	5.85312i	0.342575	+	0.267157i
$481$	1.08191	+	1.87392i	0.0493308	+	0.0854435i
$482$	−8.12632	−	14.0752i	−0.370144	−	0.641108i
$483$	0.277849	−	1.98987i	0.0126426	−	0.0905423i
$484$	−9.44041	+	16.3513i	−0.429109	+	0.743239i
$485$	−16.8341			−0.764397
$486$	9.45674	+	25.6261i	0.428966	+	1.16243i
$487$	42.0449			1.90524			0.952618	−	0.304171i	$-0.0983793\pi$
$487$	42.0449			1.90524			0.952618	+	0.304171i	$0.0983793\pi$
$488$	0.0406442	−	0.0703978i	0.00183987	−	0.00318676i
$489$	4.39801	−	31.4972i	0.198885	−	1.42435i
$490$	−4.86001	−	8.41778i	−0.219553	−	0.380277i
$491$	−7.36174	−	12.7509i	−0.332230	−	0.575440i	0.650718	−	0.759319i	$-0.274468\pi$
$491$	−7.36174	−	12.7509i	−0.332230	−	0.575440i	−0.982949	+	0.183879i	$0.941135\pi$
$492$	11.1480	+	8.69381i	0.502593	+	0.391947i
$493$	9.45812	−	16.3820i	0.425972	−	0.737806i
$494$	−0.367607			−0.0165394
$495$	−15.4402	−	4.39762i	−0.693984	−	0.197658i
$496$	2.67715			0.120208
$497$	−2.21621	+	3.83859i	−0.0994107	+	0.172184i
$498$	7.29604	−	2.95536i	0.326944	−	0.132433i
$499$	19.8857	+	34.4431i	0.890208	+	1.54188i	0.839626	+	0.543165i	$0.182774\pi$
$499$	19.8857	+	34.4431i	0.890208	+	1.54188i	0.0505814	+	0.998720i	$0.483893\pi$
$500$	0.535244	+	0.927070i	0.0239368	+	0.0414598i
$501$	−19.2711	+	7.80601i	−0.860967	+	0.348747i
$502$	7.04863	−	12.2086i	0.314596	−	0.544896i
$503$	−31.2174			−1.39192			−0.695958	−	0.718083i	$-0.745020\pi$
$503$	−31.2174			−1.39192			−0.695958	+	0.718083i	$0.745020\pi$
$504$	−4.22949	+	4.09897i	−0.188396	+	0.182583i
$505$	12.4352			0.553358
$506$	4.51208	−	7.81515i	0.200586	−	0.347426i
$507$	−17.6956	−	13.7999i	−0.785890	−	0.612877i
$508$	10.0142	+	17.3451i	0.444308	+	0.769563i
$509$	13.4412	+	23.2809i	0.595771	+	1.03191i	0.993438	+	0.114376i	$0.0364868\pi$
$509$	13.4412	+	23.2809i	0.595771	+	1.03191i	−0.397666	+	0.917530i	$0.630180\pi$
$510$	−1.17302	+	8.40079i	−0.0519420	+	0.371993i
$511$	−8.65816	+	14.9964i	−0.383014	+	0.663400i
$512$	11.1771			0.493961
$513$	−2.10076	+	4.75256i	−0.0927508	+	0.209831i
$514$	35.6690			1.57329
$515$	7.03464	−	12.1843i	0.309983	−	0.536906i
$516$	0.901336	−	6.45510i	0.0396791	−	0.284170i
$517$	−11.8384	−	20.5047i	−0.520652	−	0.901796i
$518$	−10.8928	−	18.8668i	−0.478600	−	0.828960i
$519$	18.4923	+	14.4212i	0.811721	+	0.633021i
$520$	0.170847	−	0.295916i	0.00749215	−	0.0129768i
$521$	34.3142			1.50333			0.751666	−	0.659544i	$-0.229250\pi$
$521$	34.3142			1.50333			0.751666	+	0.659544i	$0.229250\pi$
$522$	−8.66924	−	34.5082i	−0.379442	−	1.51038i
$523$	17.3682			0.759460			0.379730	−	0.925097i	$-0.376017\pi$
$523$	17.3682			0.759460			0.379730	+	0.925097i	$0.376017\pi$
$524$	11.4683	−	19.8637i	0.500997	−	0.867752i
$525$	−1.93505	+	0.783820i	−0.0844526	+	0.0342087i
$526$	−13.7681	−	23.8471i	−0.600318	−	1.03978i
$527$	0.748950	+	1.29722i	0.0326248	+	0.0565078i
$528$	−42.9117	+	17.3820i	−1.86749	+	0.756454i
$529$	11.0369	−	19.1165i	0.479867	−	0.831154i
$530$	−16.5931			−0.720759
$531$	7.67268	+	30.5413i	0.332966	+	1.32538i
$532$	1.29034			0.0559434
$533$	0.799782	−	1.38526i	0.0346424	−	0.0600024i
$534$	−13.9535	−	10.8816i	−0.603826	−	0.470894i
$535$	−3.78815	−	6.56127i	−0.163776	−	0.283669i
$536$	2.00112	+	3.46604i	0.0864352	+	0.149710i
$537$	2.60904	−	18.6852i	0.112589	−	0.806325i
$538$	4.56651	−	7.90943i	0.196876	−	0.341000i
$539$	29.6846			1.27861
$540$	3.28153	+	4.49133i	0.141215	+	0.193276i
$541$	−5.40850			−0.232530			−0.116265	−	0.993218i	$-0.537092\pi$
$541$	−5.40850			−0.232530			−0.116265	+	0.993218i	$0.537092\pi$
$542$	4.81915	−	8.34702i	0.207000	−	0.358535i
$543$	−3.51812	+	25.1957i	−0.150977	+	1.08125i
$544$	7.67891	+	13.3003i	0.329230	+	0.570244i
$545$	5.30757	+	9.19298i	0.227351	+	0.393784i
$546$	−0.605204	−	0.471969i	−0.0259003	−	0.0201984i
$547$	−6.45963	+	11.1884i	−0.276194	+	0.478382i	−0.970436	−	0.241360i	$-0.922406\pi$
$547$	−6.45963	+	11.1884i	−0.276194	+	0.478382i	0.694242	+	0.719742i	$0.255740\pi$
$548$	18.4723			0.789100
$549$	0.107517	−	0.104199i	0.00458870	−	0.00444710i
$550$	−9.37717			−0.399844
$551$	3.38420	−	5.86161i	0.144172	−	0.249713i
$552$	2.51630	−	1.01926i	0.107101	−	0.0433827i
$553$	0.452933	+	0.784502i	0.0192606	+	0.0333604i
$554$	−7.55924	−	13.0930i	−0.321161	−	0.556268i
$555$	16.5581	−	6.70709i	0.702853	−	0.284700i
$556$	−1.39930	+	2.42366i	−0.0593435	+	0.102786i
$557$	−25.0560			−1.06166			−0.530828	−	0.847479i	$-0.678119\pi$
$557$	−25.0560			−1.06166			−0.530828	+	0.847479i	$0.678119\pi$
$558$	2.70971	+	0.771769i	0.114711	+	0.0326716i
$559$	−0.737451			−0.0311908
$560$	−3.01045	+	5.21425i	−0.127215	+	0.220342i
$561$	−20.4273	−	15.9303i	−0.862443	−	0.672577i
$562$	−22.5255	−	39.0152i	−0.950179	−	1.64576i
$563$	−6.98953	−	12.1062i	−0.294574	−	0.510216i	0.680312	−	0.732923i	$-0.261844\pi$
$563$	−6.98953	−	12.1062i	−0.294574	−	0.510216i	−0.974886	+	0.222706i	$0.928511\pi$
$564$	−1.13446	+	8.12465i	−0.0477693	+	0.342109i
$565$	−0.706264	+	1.22329i	−0.0297128	+	0.0514640i
$566$	28.4705			1.19671
$567$	−9.56034	+	5.12714i	−0.401497	+	0.215320i
$568$	−5.98931			−0.251306
$569$	−11.6654	+	20.2051i	−0.489039	+	0.847040i	−0.999920	−	0.0126110i	$-0.995986\pi$
$569$	−11.6654	+	20.2051i	−0.489039	+	0.847040i	0.510882	+	0.859651i	$0.329319\pi$
$570$	−0.419716	+	3.00588i	−0.0175800	+	0.125902i
$571$	2.16664	+	3.75273i	0.0906712	+	0.157047i	0.907794	−	0.419417i	$-0.137765\pi$
$571$	2.16664	+	3.75273i	0.0906712	+	0.157047i	−0.817123	+	0.576464i	$0.804432\pi$
$572$	−0.600897	−	1.04078i	−0.0251248	−	0.0435174i
$573$	−14.6889	−	11.4552i	−0.613639	−	0.478547i
$574$	−8.05227	+	13.9469i	−0.336095	+	0.582134i
$575$	0.962353			0.0401329
$576$	−1.04154	−	0.296647i	−0.0433973	−	0.0123603i
$577$	21.3945			0.890665			0.445333	−	0.895365i	$-0.353085\pi$
$577$	21.3945			0.890665			0.445333	+	0.895365i	$0.353085\pi$
$578$	8.05101	−	13.9448i	0.334878	−	0.580025i
$579$	−29.3324	+	11.8815i	−1.21901	+	0.493777i
$580$	−3.62275	−	6.27479i	−0.150427	−	0.260546i
$581$	1.56317	+	2.70749i	0.0648513	+	0.112326i
$582$	−47.3547	+	19.1817i	−1.96292	+	0.795107i
$583$	25.3374	−	43.8857i	1.04937	−	1.81756i
$584$	−23.3987			−0.968244
$585$	0.451945	−	0.437999i	0.0186856	−	0.0181090i
$586$	5.25183			0.216951
$587$	−3.59062	+	6.21914i	−0.148201	+	0.256691i	−0.930563	−	0.366133i	$-0.880682\pi$
$587$	−3.59062	+	6.21914i	−0.148201	+	0.256691i	0.782362	+	0.622824i	$0.214015\pi$
$588$	−8.11036	−	6.32487i	−0.334466	−	0.260833i
$589$	0.267981	+	0.464157i	0.0110420	+	0.0191253i
$590$	9.19666	+	15.9291i	0.378621	+	0.655790i
$591$	−3.27674	+	23.4670i	−0.134787	+	0.965305i
$592$	25.7602	−	44.6180i	1.05874	−	1.83379i
$593$	−33.4300			−1.37281			−0.686403	−	0.727221i	$-0.740812\pi$
$593$	−33.4300			−1.37281			−0.686403	+	0.727221i	$0.740812\pi$
$594$	−48.4445	+	5.22277i	−1.98770	+	0.214293i
$595$	−3.36877			−0.138106
$596$	−6.11178	+	10.5859i	−0.250348	+	0.433616i
$597$	−0.877169	+	6.28202i	−0.0359001	+	0.257106i
$598$	0.176884	+	0.306372i	0.00723332	+	0.0125285i
$599$	−4.95025	−	8.57408i	−0.202262	−	0.350328i	0.746995	−	0.664830i	$-0.231496\pi$
$599$	−4.95025	−	8.57408i	−0.202262	−	0.350328i	−0.949257	+	0.314502i	$0.898162\pi$
$600$	−2.22461	−	1.73486i	−0.0908193	−	0.0708255i
$601$	−21.9334	+	37.9897i	−0.894682	+	1.54963i	−0.0604834	+	0.998169i	$0.519264\pi$
$601$	−21.9334	+	37.9897i	−0.894682	+	1.54963i	−0.834198	+	0.551465i	$0.814069\pi$
$602$	7.42472			0.302609
$603$	1.79612	+	7.14950i	0.0731436	+	0.291150i
$604$	0.656156			0.0266986
$605$	8.81879	−	15.2746i	0.358535	−	0.621000i
$606$	34.9805	−	14.1693i	1.42098	−	0.575589i
$607$	6.42139	+	11.1222i	0.260636	+	0.451435i	0.966411	−	0.257001i	$-0.0827343\pi$
$607$	6.42139	+	11.1222i	0.260636	+	0.451435i	−0.705775	+	0.708436i	$0.749401\pi$
$608$	2.74758	+	4.75895i	0.111429	+	0.193001i
$609$	13.0972	−	5.30521i	0.530726	−	0.214978i
$610$	0.0437264	−	0.0757363i	0.00177043	−	0.00306647i
$611$	0.928186			0.0375504
$612$	2.18686	+	8.70487i	0.0883987	+	0.351873i
$613$	41.6575			1.68253			0.841265	−	0.540623i	$-0.181811\pi$
$613$	41.6575			1.68253			0.841265	+	0.540623i	$0.181811\pi$
$614$	7.99324	−	13.8447i	0.322581	−	0.558727i
$615$	−10.4140	−	8.12135i	−0.419932	−	0.327484i
$616$	−5.25315	−	9.09872i	−0.211655	−	0.366598i
$617$	−6.43865	−	11.1521i	−0.259210	−	0.448966i	0.706820	−	0.707393i	$-0.250129\pi$
$617$	−6.43865	−	11.1521i	−0.259210	−	0.448966i	−0.966031	+	0.258428i	$0.916796\pi$
$618$	5.90510	−	42.2905i	0.237538	−	1.70117i
$619$	3.29224	−	5.70232i	0.132326	−	0.229196i	−0.792247	−	0.610201i	$-0.791089\pi$
$619$	3.29224	−	5.70232i	0.132326	−	0.229196i	0.924573	+	0.381005i	$0.124422\pi$
$620$	0.573741			0.0230420
$621$	4.97173	−	0.535999i	0.199508	−	0.0215089i
$622$	−5.81106			−0.233002
$623$	3.51380	−	6.08608i	0.140777	−	0.243834i
$624$	0.250998	−	1.79757i	0.0100479	−	0.0719604i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	10.1229	+	17.5334i	0.404593	+	0.700776i
$627$	−7.30909	−	5.70000i	−0.291897	−	0.227636i
$628$	5.12686	−	8.87999i	0.204584	−	0.354350i
$629$	28.8263			1.14938
$630$	−4.55023	+	4.40981i	−0.181285	+	0.175691i
$631$	6.65273			0.264841			0.132421	−	0.991194i	$-0.457725\pi$
$631$	6.65273			0.264841			0.132421	+	0.991194i	$0.457725\pi$
$632$	−0.612025	+	1.06006i	−0.0243450	+	0.0421668i
$633$	−16.3147	+	6.60849i	−0.648450	+	0.262664i
$634$	−3.51175	−	6.08253i	−0.139469	−	0.241568i
$635$	−9.35478	−	16.2030i	−0.371233	−	0.642995i
$636$	−16.2733	+	6.59173i	−0.645279	+	0.261379i
$637$	−0.581853	+	1.00780i	−0.0230538	+	0.0399304i
$638$	63.4685			2.51274
$639$	−10.6097	−	3.02181i	−0.419713	−	0.119541i
$640$	−11.6229			−0.459435
$641$	−9.92817	+	17.1961i	−0.392139	+	0.679205i	−0.992731	−	0.120351i	$-0.961598\pi$
$641$	−9.92817	+	17.1961i	−0.392139	+	0.679205i	0.600592	+	0.799555i	$0.294931\pi$
$642$	−18.1324	−	14.1406i	−0.715630	−	0.558085i
$643$	1.17082	+	2.02792i	0.0461726	+	0.0799732i	0.888188	−	0.459480i	$-0.151964\pi$
$643$	1.17082	+	2.02792i	0.0461726	+	0.0799732i	−0.842015	+	0.539453i	$0.818631\pi$
$644$	−0.620883	−	1.07540i	−0.0244662	−	0.0423767i
$645$	−0.841986	+	6.03005i	−0.0331532	+	0.237433i
$646$	−2.44862	+	4.24114i	−0.0963399	+	0.166866i
$647$	−7.44852			−0.292831			−0.146416	−	0.989223i	$-0.546774\pi$
$647$	−7.44852			−0.292831			−0.146416	+	0.989223i	$0.546774\pi$
$648$	−12.4591	−	7.72364i	−0.489438	−	0.303413i
$649$	−56.1726			−2.20497
$650$	0.183803	−	0.318357i	0.00720936	−	0.0124870i
$651$	−0.154742	+	1.10822i	−0.00606483	+	0.0434345i
$652$	−9.82781	−	17.0223i	−0.384887	−	0.666643i
$653$	15.5952	+	27.0117i	0.610287	+	1.05705i	0.991192	+	0.132434i	$0.0422792\pi$
$653$	15.5952	+	27.0117i	0.610287	+	1.05705i	−0.380905	+	0.924614i	$0.624387\pi$
$654$	25.4053	+	19.8123i	0.993426	+	0.774724i
$655$	−10.7132	+	18.5558i	−0.418599	+	0.725034i
$656$	−38.0855			−1.48699
$657$	−41.4493	−	11.8054i	−1.61709	−	0.460574i
$658$	−9.34505			−0.364308
$659$	4.90159	−	8.48979i	0.190939	−	0.330715i	−0.754623	−	0.656159i	$-0.772180\pi$
$659$	4.90159	−	8.48979i	0.190939	−	0.330715i	0.945562	+	0.325443i	$0.105514\pi$
$660$	−9.19644	+	3.72515i	−0.357971	+	0.145001i
$661$	−22.2543	−	38.5456i	−0.865593	−	1.49925i	−0.866457	−	0.499252i	$-0.833608\pi$
$661$	−22.2543	−	38.5456i	−0.865593	−	1.49925i	0.000863182	−	1.00000i	$-0.499725\pi$
$662$	−19.4199	−	33.6363i	−0.754776	−	1.30731i
$663$	0.941235	−	0.381260i	0.0365545	−	0.0148069i
$664$	−2.11224	+	3.65850i	−0.0819706	+	0.141977i
$665$	−1.20538			−0.0467425
$666$	38.9360	−	37.7344i	1.50874	−	1.46218i
$667$	−6.51360			−0.252208
$668$	−6.42521	+	11.1288i	−0.248599	+	0.430586i
$669$	28.5153	+	22.2377i	1.10247	+	0.859760i
$670$	2.15287	+	3.72888i	0.0831727	+	0.144059i
$671$	0.133539	+	0.231296i	0.00515521	+	0.00892909i
$672$	−1.58656	+	11.3624i	−0.0612028	+	0.438316i
$673$	21.6966	−	37.5796i	0.836341	−	1.44859i	−0.0565926	−	0.998397i	$-0.518024\pi$
$673$	21.6966	−	37.5796i	0.836341	−	1.44859i	0.892934	−	0.450188i	$-0.148643\pi$
$674$	−23.0569			−0.888120
$675$	−3.06546	−	4.19559i	−0.117989	−	0.161488i
$676$	−13.8692			−0.533432
$677$	19.3645	−	33.5402i	0.744236	−	1.28906i	−0.206314	−	0.978486i	$-0.566147\pi$
$677$	19.3645	−	33.5402i	0.744236	−	1.28906i	0.950551	−	0.310569i	$-0.100520\pi$
$678$	−0.592861	+	4.24589i	−0.0227687	+	0.163062i
$679$	−10.1457	−	17.5729i	−0.389357	−	0.674386i
$680$	−2.27603	−	3.94219i	−0.0872816	−	0.151176i
$681$	−0.511829	−	0.399150i	−0.0196133	−	0.0152955i
$682$	−2.51291	+	4.35248i	−0.0962241	+	0.166665i
$683$	−18.9876			−0.726542			−0.363271	−	0.931683i	$-0.618340\pi$
$683$	−18.9876			−0.726542			−0.363271	+	0.931683i	$0.618340\pi$
$684$	0.782479	+	3.11468i	0.0299188	+	0.119093i
$685$	−17.2560			−0.659318
$686$	13.2507	−	22.9509i	0.505914	−	0.876269i
$687$	37.5454	−	15.2083i	1.43245	−	0.580232i
$688$	8.77933	+	15.2062i	0.334709	+	0.579733i
$689$	0.993285	+	1.72042i	0.0378411	+	0.0655428i
$690$	2.70712	−	1.09656i	0.103058	−	0.0417452i
$691$	−9.10007	+	15.7618i	−0.346183	+	0.599607i	−0.985568	−	0.169280i	$-0.945856\pi$
$691$	−9.10007	+	15.7618i	−0.346183	+	0.599607i	0.639385	+	0.768887i	$0.279189\pi$
$692$	14.4936			0.550965
$693$	−4.71500	−	18.7682i	−0.179108	−	0.712945i
$694$	−38.1940			−1.44982
$695$	1.30716	−	2.26407i	0.0495834	−	0.0858809i
$696$	15.0571	+	11.7423i	0.570736	+	0.445089i
$697$	−10.6547	−	18.4544i	−0.403575	−	0.699012i
$698$	−15.5844	−	26.9929i	−0.589877	−	1.02170i
$699$	1.22892	−	8.80113i	0.0464819	−	0.332889i
$700$	−0.645171	+	1.11747i	−0.0243852	+	0.0422364i
$701$	1.40888			0.0532125			0.0266063	−	0.999646i	$-0.491530\pi$
$701$	1.40888			0.0532125			0.0266063	+	0.999646i	$0.491530\pi$
$702$	0.772254	−	1.74707i	0.0291468	−	0.0659390i
$703$	10.3143			0.389012
$704$	0.965891	−	1.67297i	0.0364034	−	0.0630525i
$705$	1.05976	−	7.58967i	0.0399128	−	0.285843i
$706$	−4.38608	−	7.59691i	−0.165072	−	0.285914i
$707$	7.49454	+	12.9809i	0.281861	+	0.488198i
$708$	15.3473	+	11.9686i	0.576789	+	0.449809i
$709$	−16.9733	+	29.3986i	−0.637445	+	1.10409i	0.348546	+	0.937292i	$0.386676\pi$
$709$	−16.9733	+	29.3986i	−0.637445	+	1.10409i	−0.985991	+	0.166796i	$0.946658\pi$
$710$	−6.44351			−0.241820
$711$	−1.61900	+	1.56904i	−0.0607172	+	0.0588435i
$712$	9.49604			0.355879
$713$	0.257893	−	0.446683i	0.00965815	−	0.0167284i
$714$	−9.47644	+	3.83856i	−0.354647	+	0.143655i
$715$	0.561330	+	0.972251i	0.0209925	+	0.0363601i
$716$	−5.83018	−	10.0982i	−0.217884	−	0.377386i
$717$	−6.49202	+	2.62968i	−0.242449	+	0.0982074i
$718$	−25.1746	+	43.6037i	−0.939507	+	1.62727i
$719$	27.2031			1.01450			0.507251	−	0.861798i	$-0.330662\pi$
$719$	27.2031			1.01450			0.507251	+	0.861798i	$0.330662\pi$
$720$	−14.4119	−	4.10476i	−0.537101	−	0.152975i
$721$	16.9588			0.631578
$722$	−0.876140	+	1.51752i	−0.0326066	+	0.0564762i
$723$	12.6682	+	9.87931i	0.471136	+	0.367415i
$724$	7.86159	+	13.6167i	0.292174	+	0.506060i
$725$	3.38420	+	5.86161i	0.125686	+	0.217695i
$726$	7.40277	−	53.0164i	0.274743	−	1.96762i
$727$	−11.3896	+	19.7274i	−0.422418	+	0.731650i	−0.996175	−	0.0873755i	$-0.972152\pi$
$727$	−11.3896	+	19.7274i	−0.422418	+	0.731650i	0.573757	+	0.819026i	$0.305485\pi$
$728$	0.411871			0.0152650
$729$	−18.1736	−	19.9680i	−0.673097	−	0.739555i
$730$	−25.1731			−0.931697
$731$	−4.91215	+	8.50810i	−0.181683	+	0.314683i
$732$	0.0127969	−	0.0916472i	0.000472985	−	0.00338738i
$733$	−3.92563	−	6.79940i	−0.144997	−	0.251141i	0.784375	−	0.620287i	$-0.212984\pi$
$733$	−3.92563	−	6.79940i	−0.144997	−	0.251141i	−0.929372	+	0.369145i	$0.879650\pi$
$734$	6.47894	+	11.2218i	0.239142	+	0.414206i
$735$	7.57632	+	5.90840i	0.279457	+	0.217935i
$736$	2.64415	−	4.57980i	0.0974645	−	0.168814i
$737$	−13.1496			−0.484372
$738$	−38.5487	−	10.9793i	−1.41900	−	0.404154i
$739$	31.7734			1.16880			0.584402	−	0.811464i	$-0.301329\pi$
$739$	31.7734			1.16880			0.584402	+	0.811464i	$0.301329\pi$
$740$	5.52068	−	9.56211i	0.202944	−	0.351510i
$741$	0.336783	−	0.136418i	0.0123720	−	0.00501146i
$742$	−10.0005	−	17.3213i	−0.367129	−	0.635886i
$743$	−0.707164	−	1.22484i	−0.0259433	−	0.0449351i	0.852762	−	0.522299i	$-0.174926\pi$
$743$	−0.707164	−	1.22484i	−0.0259433	−	0.0449351i	−0.878706	+	0.477364i	$0.841592\pi$
$744$	−1.40140	+	0.567657i	−0.0513779	+	0.0208113i
$745$	5.70934	−	9.88886i	0.209174	−	0.362300i
$746$	22.8552			0.836789
$747$	−5.58753	+	5.41511i	−0.204437	+	0.198128i
$748$	−16.0103			−0.585393
$749$	4.56615	−	7.90881i	0.166844	−	0.288982i
$750$	−2.39331	−	1.86642i	−0.0873913	−	0.0681522i
$751$	3.29735	+	5.71118i	0.120322	+	0.208404i	0.919895	−	0.392165i	$-0.128274\pi$
$751$	3.29735	+	5.71118i	0.120322	+	0.208404i	−0.799573	+	0.600569i	$0.794941\pi$
$752$	−11.0500	−	19.1392i	−0.402953	−	0.697935i
$753$	−1.92701	+	13.8006i	−0.0702240	+	0.502923i
$754$	−1.24406	+	2.15477i	−0.0453059	+	0.0784720i
$755$	−0.612950			−0.0223075
$756$	−2.71070	+	6.13243i	−0.0985872	+	0.223034i
$757$	37.8891			1.37710			0.688552	−	0.725187i	$-0.258247\pi$
$757$	37.8891			1.37710			0.688552	+	0.725187i	$0.258247\pi$
$758$	16.5521	−	28.6691i	0.601200	−	1.04131i
$759$	−1.23354	+	8.83426i	−0.0447748	+	0.320663i
$760$	−0.814383	−	1.41055i	−0.0295408	−	0.0511661i
$761$	10.6466	+	18.4405i	0.385939	+	0.668467i	0.991899	−	0.127029i	$-0.0405440\pi$
$761$	10.6466	+	18.4405i	0.385939	+	0.668467i	−0.605960	+	0.795495i	$0.707211\pi$
$762$	−44.7778	−	34.9200i	−1.62213	−	1.26502i
$763$	−6.39762	+	11.0810i	−0.231609	+	0.401159i
$764$	−11.5127			−0.416515
$765$	−2.04286	−	8.13168i	−0.0738599	−	0.294001i
$766$	−7.72872			−0.279250
$767$	1.10105	−	1.90707i	0.0397565	−	0.0688603i
$768$	−31.5364	+	12.7743i	−1.13797	+	0.460952i
$769$	14.1125	+	24.4435i	0.508909	+	0.881456i	0.999947	+	0.0103180i	$0.00328439\pi$
$769$	14.1125	+	24.4435i	0.508909	+	0.881456i	−0.491038	+	0.871138i	$0.663382\pi$
$770$	−5.65152	−	9.78871i	−0.203666	−	0.352761i
$771$	−32.6781	+	13.2367i	−1.17687	+	0.476709i
$772$	−9.77978	+	16.9391i	−0.351982	+	0.609651i
$773$	1.59397			0.0573310			0.0286655	−	0.999589i	$-0.490874\pi$
$773$	1.59397			0.0573310			0.0286655	+	0.999589i	$0.490874\pi$
$774$	4.50244	+	17.9221i	0.161837	+	0.644196i
$775$	−0.535962			−0.0192523
$776$	13.7094	−	23.7454i	0.492139	−	0.852409i
$777$	16.9808	+	13.2425i	0.609184	+	0.475073i
$778$	3.52578	+	6.10684i	0.126405	+	0.218941i
$779$	−3.81234	−	6.60317i	−0.136591	−	0.236583i
$780$	0.0537915	−	0.385238i	0.00192604	−	0.0137937i
$781$	9.83913	−	17.0419i	0.352072	−	0.609806i
$782$	4.71289			0.168532
$783$	20.7482	+	28.3975i	0.741482	+	1.01484i
$784$	27.7078			0.989563
$785$	−4.78927	+	8.29527i	−0.170937	+	0.296071i
$786$	−8.99299	+	64.4050i	−0.320769	+	2.29725i
$787$	1.10922	+	1.92123i	0.0395394	+	0.0684843i	0.885118	−	0.465367i	$-0.154078\pi$
$787$	1.10922	+	1.92123i	0.0395394	+	0.0684843i	−0.845578	+	0.533851i	$0.820744\pi$
$788$	7.32222	+	12.6825i	0.260843	+	0.451794i
$789$	21.4633	+	16.7381i	0.764112	+	0.595893i
$790$	−0.658437	+	1.14045i	−0.0234261	+	0.0405753i
$791$	−1.70263			−0.0605386
$792$	18.7773	−	18.1978i	0.667222	−	0.646632i
$793$	−0.0104701			−0.000371803
$794$	−30.2196	+	52.3419i	−1.07245	+	1.85754i
$795$	15.2018	−	6.15768i	0.539151	−	0.218390i
$796$	1.96012	+	3.39503i	0.0694747	+	0.120334i
$797$	−8.31026	−	14.3938i	−0.294364	−	0.509854i	0.680472	−	0.732774i	$-0.261775\pi$
$797$	−8.31026	−	14.3938i	−0.294364	−	0.509854i	−0.974837	+	0.222920i	$0.928441\pi$
$798$	−3.39076	+	1.37347i	−0.120031	+	0.0486204i
$799$	6.18263	−	10.7086i	0.218726	−	0.378844i
$800$	−5.49517			−0.194284
$801$	16.8216	+	4.79108i	0.594363	+	0.169284i
$802$	−51.1187			−1.80506
$803$	38.4389	−	66.5781i	1.35648	−	2.34949i
$804$	3.59270	+	2.80177i	0.126705	+	0.0988109i
$805$	0.580000	+	1.00459i	0.0204423	+	0.0354071i
$806$	−0.0985117	−	0.170627i	−0.00346993	−	0.00601009i
$807$	−1.24843	+	8.94084i	−0.0439466	+	0.314733i
$808$	−10.1270	+	17.5405i	−0.356267	+	0.617072i
$809$	2.32653			0.0817966			0.0408983	−	0.999163i	$-0.486978\pi$
$809$	2.32653			0.0817966			0.0408983	+	0.999163i	$0.486978\pi$
$810$	−13.4039	−	8.30935i	−0.470965	−	0.291961i
$811$	24.5385			0.861665			0.430832	−	0.902432i	$-0.358220\pi$
$811$	24.5385			0.861665			0.430832	+	0.902432i	$0.358220\pi$
$812$	4.36678	−	7.56349i	0.153244	−	0.265426i
$813$	−1.31749	+	9.43549i	−0.0462065	+	0.330917i
$814$	48.3596	+	83.7613i	1.69500	+	2.93583i
$815$	9.18068	+	15.9014i	0.321585	+	0.557002i
$816$	−19.0670	−	14.8694i	−0.667478	−	0.520533i
$817$	−1.75761	+	3.04428i	−0.0614911	+	0.106506i
$818$	−34.6085			−1.21006
$819$	0.729604	+	0.207803i	0.0254944	+	0.00726123i
$820$	−8.16213			−0.285034
$821$	−12.4731	+	21.6041i	−0.435316	+	0.753989i	−0.997321	−	0.0731445i	$-0.976697\pi$
$821$	−12.4731	+	21.6041i	−0.435316	+	0.753989i	0.562006	+	0.827133i	$0.310030\pi$
$822$	−48.5416	+	19.6624i	−1.69308	+	0.685806i
$823$	−9.49847	−	16.4518i	−0.331096	−	0.573475i	0.651631	−	0.758536i	$-0.274085\pi$
$823$	−9.49847	−	16.4518i	−0.331096	−	0.573475i	−0.982727	+	0.185061i	$0.940752\pi$
$824$	11.4578	+	19.8454i	0.399150	+	0.691349i
$825$	8.59089	−	3.47986i	0.299096	−	0.121153i
$826$	−11.0854	+	19.2006i	−0.385712	+	0.668073i
$827$	−46.7695			−1.62633			−0.813167	−	0.582031i	$-0.802258\pi$
$827$	−46.7695			−1.62633			−0.813167	+	0.582031i	$0.802258\pi$
$828$	2.21933	−	2.15085i	0.0771272	−	0.0747471i
$829$	−4.43099			−0.153895			−0.0769474	−	0.997035i	$-0.524517\pi$
$829$	−4.43099			−0.153895			−0.0769474	+	0.997035i	$0.524517\pi$
$830$	−2.27241	+	3.93594i	−0.0788767	+	0.136618i
$831$	11.7842	+	9.18991i	0.408789	+	0.318794i
$832$	0.0378652	+	0.0655844i	0.00131274	+	0.00227373i
$833$	7.75143	+	13.4259i	0.268571	+	0.465179i
$834$	1.09727	−	7.85832i	0.0379954	−	0.272111i
$835$	6.00213	−	10.3960i	0.207712	−	0.359768i
$836$	−5.72862			−0.198128
$837$	−2.76890	+	0.298513i	−0.0957071	+	0.0103181i
$838$	−58.8300			−2.03225
$839$	−13.4901	+	23.3655i	−0.465728	+	0.806665i	−0.999234	−	0.0391314i	$-0.987541\pi$
$839$	−13.4901	+	23.3655i	−0.465728	+	0.806665i	0.533506	+	0.845796i	$0.320874\pi$
$840$	0.470255	−	3.36782i	0.0162253	−	0.116201i
$841$	−8.40567	−	14.5590i	−0.289851	−	0.502036i
$842$	17.2705	+	29.9133i	0.595180	+	1.03088i
$843$	35.1152	+	27.3846i	1.20943	+	0.943175i
$844$	−5.43952	+	9.42153i	−0.187236	+	0.324302i
$845$	12.9560			0.445700
$846$	−5.66695	−	22.5575i	−0.194834	−	0.775542i
$847$	21.2599			0.730500
$848$	23.6501	−	40.9631i	0.812146	−	1.40668i
$849$	−26.0832	+	10.5654i	−0.895175	+	0.362603i
$850$	−2.44862	−	4.24114i	−0.0839871	−	0.145470i
$851$	−4.96301	−	8.59619i	−0.170130	−	0.294674i
$852$	−6.31932	+	2.55973i	−0.216496	+	0.0876948i
$853$	−21.1611	+	36.6521i	−0.724543	+	1.25494i	0.234619	+	0.972087i	$0.424616\pi$
$853$	−21.1611	+	36.6521i	−0.724543	+	1.25494i	−0.959162	+	0.282857i	$0.908718\pi$
$854$	0.105414			0.00360718
$855$	−0.730955	−	2.90959i	−0.0249981	−	0.0995058i
$856$	12.3400			0.421773
$857$	−4.66914	+	8.08718i	−0.159495	+	0.276253i	−0.934687	−	0.355473i	$-0.884320\pi$
$857$	−4.66914	+	8.08718i	−0.159495	+	0.276253i	0.775192	+	0.631726i	$0.217653\pi$
$858$	2.68687	+	2.09536i	0.0917282	+	0.0715343i
$859$	−16.3447	−	28.3098i	−0.557673	−	0.965918i	−0.997690	−	0.0679286i	$-0.978361\pi$
$859$	−16.3447	−	28.3098i	−0.557673	−	0.965918i	0.440017	−	0.897989i	$-0.354972\pi$
$860$	1.88150	+	3.25886i	0.0641588	+	0.111126i
$861$	2.20139	−	15.7657i	0.0750231	−	0.537292i
$862$	16.5749	−	28.7086i	0.564544	−	0.977819i
$863$	32.7824			1.11593			0.557963	−	0.829866i	$-0.311583\pi$
$863$	32.7824			1.11593			0.557963	+	0.829866i	$0.311583\pi$
$864$	−28.3892	+	3.06063i	−0.965821	+	0.104125i
$865$	−13.5393			−0.460349
$866$	2.76810	−	4.79448i	0.0940637	−	0.162923i
$867$	−2.20104	+	15.7632i	−0.0747513	+	0.535346i
$868$	0.345787	+	0.598922i	0.0117368	+	0.0203287i
$869$	−2.01084	−	3.48289i	−0.0682132	−	0.118149i
$870$	16.1989	+	12.6327i	0.549194	+	0.428289i
$871$	0.257747	−	0.446431i	0.00873343	−	0.0151268i
$872$	−17.2896			−0.585498
$873$	36.2657	−	35.1466i	1.22741	−	1.18953i
$874$	1.68631			0.0570404
$875$	0.602689	−	1.04389i	0.0203746	−	0.0352898i
$876$	−24.6879	+	10.0002i	−0.834127	+	0.337875i
$877$	11.3539	+	19.6655i	0.383393	+	0.664056i	0.991545	−	0.129765i	$-0.0414221\pi$
$877$	11.3539	+	19.6655i	0.383393	+	0.664056i	−0.608152	+	0.793821i	$0.708089\pi$
$878$	31.0893	+	53.8482i	1.04921	+	1.81729i
$879$	−4.81145	+	1.94895i	−0.162286	+	0.0657363i
$880$	13.3652	−	23.1493i	0.450542	−	0.780361i
$881$	−40.6307			−1.36888			−0.684442	−	0.729068i	$-0.739954\pi$
$881$	−40.6307			−1.36888			−0.684442	+	0.729068i	$0.739954\pi$
$882$	28.0447	+	7.98760i	0.944315	+	0.268957i
$883$	23.0339			0.775152			0.387576	−	0.921838i	$-0.373312\pi$
$883$	23.0339			0.775152			0.387576	+	0.921838i	$0.373312\pi$
$884$	0.313820	−	0.543552i	0.0105549	−	0.0182816i
$885$	−14.3368	−	11.1805i	−0.481925	−	0.375830i
$886$	18.7421	+	32.4623i	0.629654	+	1.09059i
$887$	−17.2468	−	29.8723i	−0.579090	−	1.00301i	−0.995584	−	0.0938751i	$-0.970075\pi$
$887$	−17.2468	−	29.8723i	−0.579090	−	1.00301i	0.416494	−	0.909139i	$-0.363259\pi$
$888$	−4.02394	+	28.8182i	−0.135034	+	0.967076i
$889$	11.2760	−	19.5307i	0.378186	−	0.655038i
$890$	10.2162			0.342446
$891$	42.4442	−	22.7625i	1.42193	−	0.762573i
$892$	22.3494			0.748313
$893$	2.21220	−	3.83165i	0.0740286	−	0.128221i
$894$	4.79260	−	34.3231i	0.160288	−	1.14794i
$895$	5.44628	+	9.43323i	0.182049	+	0.315318i
$896$	−7.00498	−	12.1330i	−0.234020	−	0.405334i
$897$	−0.275746	−	0.215041i	−0.00920690	−	0.00718000i
$898$	−28.0826	+	48.6405i	−0.937128	+	1.62315i
$899$	3.62761			0.120988
$900$	−3.08863	−	0.879693i	−0.102954	−	0.0293231i
$901$	26.4650			0.881678
$902$	35.7490	−	61.9190i	1.19031	−	2.06168i
$903$	−6.80215	+	2.75530i	−0.226361	+	0.0916908i
$904$	−1.15034	−	1.99245i	−0.0382597	−	0.0662677i
$905$	−7.34393	−	12.7201i	−0.244121	−	0.422829i
$906$	−1.72424	+	0.698429i	−0.0572842	+	0.0232037i
$907$	21.5166	−	37.2678i	0.714446	−	1.23746i	−0.248726	−	0.968574i	$-0.580012\pi$
$907$	21.5166	−	37.2678i	0.714446	−	1.23746i	0.963173	−	0.268883i	$-0.0866546\pi$
$908$	−0.401154			−0.0133128
$909$	−26.7891	+	25.9624i	−0.888539	+	0.861119i
$910$	0.443105			0.0146888
$911$	−11.9458	+	20.6907i	−0.395782	+	0.685514i	−0.993201	−	0.116415i	$-0.962860\pi$
$911$	−11.9458	+	20.6907i	−0.395782	+	0.685514i	0.597419	+	0.801929i	$0.296193\pi$
$912$	−6.82234	−	5.32041i	−0.225910	−	0.176176i
$913$	−6.93988	−	12.0202i	−0.229676	−	0.397811i
$914$	−28.5582	−	49.4643i	−0.944621	−	1.63613i
$915$	−0.0119542	+	0.0856125i	−0.000395194	+	0.00283026i
$916$	12.5181	−	21.6820i	0.413610	−	0.716394i
$917$	−25.8269			−0.852878
$918$	−15.0123	−	20.5469i	−0.495480	−	0.678147i
$919$	−44.8510			−1.47950			−0.739748	−	0.672884i	$-0.765055\pi$
$919$	−44.8510			−1.47950			−0.739748	+	0.672884i	$0.765055\pi$
$920$	−0.783724	+	1.35745i	−0.0258386	+	0.0447538i
$921$	−2.18525	+	15.6501i	−0.0720064	+	0.515688i
$922$	0.787156	+	1.36339i	0.0259236	+	0.0449010i
$923$	0.385717	+	0.668081i	0.0126960	+	0.0219901i
$924$	−9.43123	−	7.35495i	−0.310265	−	0.241960i
$925$	−5.15716	+	8.93247i	−0.169567	+	0.293698i
$926$	25.6035			0.841383
$927$	10.2840	+	40.9358i	0.337771	+	1.34451i
$928$	37.1935			1.22094
$929$	−19.4021	+	33.6055i	−0.636563	+	1.10256i	0.349618	+	0.936892i	$0.386311\pi$
$929$	−19.4021	+	33.6055i	−0.636563	+	1.10256i	−0.986182	+	0.165668i	$0.947022\pi$
$930$	−1.50768	+	0.610705i	−0.0494386	+	0.0200258i
$931$	2.77353	+	4.80390i	0.0908989	+	0.157441i
$932$	−2.74614	−	4.75645i	−0.0899528	−	0.155803i
$933$	5.32380	−	2.15648i	0.174293	−	0.0705999i
$934$	−24.6229	+	42.6481i	−0.805686	+	1.39549i
$935$	14.9560			0.489115
$936$	0.249764	+	0.994191i	0.00816378	+	0.0324962i
$937$	−20.8689			−0.681757			−0.340878	−	0.940107i	$-0.610724\pi$
$937$	−20.8689			−0.681757			−0.340878	+	0.940107i	$0.610724\pi$
$938$	−2.59502	+	4.49471i	−0.0847305	+	0.146758i
$939$	−15.7807	−	12.3066i	−0.514985	−	0.401611i
$940$	−2.36814	−	4.10174i	−0.0772401	−	0.133784i
$941$	15.7170	+	27.2226i	0.512358	+	0.887430i	0.999897	+	0.0143293i	$0.00456131\pi$
$941$	15.7170	+	27.2226i	0.512358	+	0.887430i	−0.487539	+	0.873101i	$0.662105\pi$
$942$	−4.02027	+	28.7920i	−0.130987	+	0.938092i
$943$	−3.66882	+	6.35458i	−0.119473	+	0.206934i
$944$	−52.4318			−1.70651
$945$	2.53221	−	5.72863i	0.0823728	−	0.186352i
$946$	−32.9629			−1.07172
$947$	−26.6133	+	46.0957i	−0.864818	+	1.49791i	0.00241048	+	0.999997i	$0.499233\pi$
$947$	−26.6133	+	46.0957i	−0.864818	+	1.49791i	−0.867228	+	0.497911i	$0.834101\pi$
$948$	−0.192697	+	1.38003i	−0.00625850	+	0.0448214i
$949$	1.50689	+	2.61001i	0.0489158	+	0.0847247i
$950$	−0.876140	−	1.51752i	−0.0284258	−	0.0492348i
$951$	5.47451	+	4.26930i	0.177523	+	0.138441i
$952$	2.74347	−	4.75183i	0.0889164	−	0.154008i
$953$	−21.3832			−0.692671			−0.346336	−	0.938111i	$-0.612574\pi$
$953$	−21.3832			−0.692671			−0.346336	+	0.938111i	$0.612574\pi$
$954$	35.7465	−	34.6434i	1.15734	−	1.12162i
$955$	10.7546			0.348011
$956$	−2.16452	+	3.74906i	−0.0700057	+	0.121253i
$957$	−58.1466	+	23.5531i	−1.87961	+	0.761363i
$958$	25.9213	+	44.8970i	0.837479	+	1.45056i
$959$	−10.4000	−	18.0133i	−0.335833	−	0.581681i
$960$	0.579509	−	0.234738i	0.0187036	−	0.00757614i
$961$	15.3564	−	26.5980i	0.495367	−	0.858001i
$962$	−3.79162			−0.122247
$963$	21.8596	+	6.22597i	0.704415	+	0.200629i
$964$	9.92892			0.319789
$965$	9.13581	−	15.8237i	0.294092	−	0.509383i
$966$	2.77624	+	2.16505i	0.0893239	+	0.0696593i
$967$	2.38738	+	4.13506i	0.0767730	+	0.132975i	0.901856	−	0.432037i	$-0.142205\pi$
$967$	2.38738	+	4.13506i	0.0767730	+	0.132975i	−0.825083	+	0.565012i	$0.808872\pi$
$968$	14.3637	+	24.8787i	0.461668	+	0.799632i
$969$	0.669422	−	4.79420i	0.0215049	−	0.154012i
$970$	14.7490	−	25.5461i	0.473563	−	0.820235i
$971$	−38.3955			−1.23217			−0.616086	−	0.787679i	$-0.711283\pi$
$971$	−38.3955			−1.23217			−0.616086	+	0.787679i	$0.711283\pi$
$972$	−16.4465	−	2.82442i	−0.527522	−	0.0905933i
$973$	3.15124			0.101024
$974$	−36.8372	+	63.8039i	−1.18034	+	2.04441i
$975$	−0.0502495	+	0.359871i	−0.00160927	+	0.0115251i
$976$	0.124646	+	0.215893i	0.00398982	+	0.00691057i
$977$	8.72630	+	15.1144i	0.279179	+	0.483552i	0.971181	−	0.238343i	$-0.0766043\pi$
$977$	8.72630	+	15.1144i	0.279179	+	0.483552i	−0.692002	+	0.721896i	$0.743271\pi$
$978$	43.9444	+	34.2701i	1.40519	+	1.09584i
$979$	−15.5999	+	27.0198i	−0.498575	+	0.863558i
$980$	5.93807			0.189685
$981$	−30.6274	−	8.72318i	−0.977857	−	0.278510i
$982$	25.7997			0.823300
$983$	15.2161	−	26.3551i	0.485320	−	0.840598i	−0.514538	−	0.857468i	$-0.672037\pi$
$983$	15.2161	−	26.3551i	0.485320	−	0.840598i	0.999858	+	0.0168693i	$0.00536993\pi$
$984$	19.9365	−	8.07557i	0.635554	−	0.257440i
$985$	−6.84007	−	11.8474i	−0.217943	−	0.377488i
$986$	16.5733	+	28.7058i	0.527801	+	0.914178i
$987$	8.56146	−	3.46794i	0.272514	−	0.110386i
$988$	0.112288	−	0.194488i	0.00357234	−	0.00618748i
$989$	3.38289			0.107570
$990$	20.2012	−	19.5778i	0.642037	−	0.622225i
$991$	22.6162			0.718427			0.359214	−	0.933255i	$-0.383045\pi$
$991$	22.6162			0.718427			0.359214	+	0.933255i	$0.383045\pi$
$992$	−1.47260	+	2.55062i	−0.0467551	+	0.0809823i
$993$	30.2739	+	23.6091i	0.960713	+	0.749213i
$994$	−3.88343	−	6.72629i	−0.123175	−	0.213345i
$995$	−1.83106	−	3.17148i	−0.0580484	−	0.100543i
$996$	−0.665040	+	4.76281i	−0.0210726	+	0.150915i
$997$	−9.12057	+	15.7973i	−0.288851	+	0.500305i	−0.973536	−	0.228534i	$-0.926607\pi$
$997$	−9.12057	+	15.7973i	−0.288851	+	0.500305i	0.684684	+	0.728840i	$0.259940\pi$
$998$	−69.6908			−2.20602
$999$	−21.6679	+	49.0194i	−0.685543	+	1.55091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.i.d.286.5	✓	46
9.2	odd	6		7695.2.a.x.1.5		23
9.4	even	3	inner	855.2.i.d.571.5	yes	46
9.7	even	3		7695.2.a.w.1.19		23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.i.d.286.5	✓	46	1.1	even	1	trivial
855.2.i.d.571.5	yes	46	9.4	even	3	inner
7695.2.a.w.1.19		23	9.7	even	3
7695.2.a.x.1.5		23	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.876140 + 1.51752i) q^{2} +(0.239525 - 1.71541i) q^{3} +(-0.535244 - 0.927070i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.39331 + 1.86642i) q^{6} +(-0.602689 + 1.04389i) q^{7} -1.62877 q^{8} +(-2.88526 - 0.821768i) q^{9} +O(q^{10})\)	\(q+(-0.876140 + 1.51752i) q^{2} +(0.239525 - 1.71541i) q^{3} +(-0.535244 - 0.927070i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.39331 + 1.86642i) q^{6} +(-0.602689 + 1.04389i) q^{7} -1.62877 q^{8} +(-2.88526 - 0.821768i) q^{9} -1.75228 q^{10} +(2.67570 - 4.63446i) q^{11} +(-1.71851 + 0.696106i) q^{12} +(0.104894 + 0.181681i) q^{13} +(-1.05608 - 1.82918i) q^{14} +(1.60535 - 0.650269i) q^{15} +(2.49752 - 4.32582i) q^{16} +2.79479 q^{17} +(3.77494 - 3.65845i) q^{18} +1.00000 q^{19} +(0.535244 - 0.927070i) q^{20} +(1.64633 + 1.28390i) q^{21} +(4.68859 + 8.12087i) q^{22} +(-0.481177 - 0.833423i) q^{23} +(-0.390131 + 2.79400i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.367607 q^{26} +(-2.10076 + 4.75256i) q^{27} +1.29034 q^{28} +(3.38420 - 5.86161i) q^{29} +(-0.419716 + 3.00588i) q^{30} +(0.267981 + 0.464157i) q^{31} +(2.74758 + 4.75895i) q^{32} +(-7.30909 - 5.70000i) q^{33} +(-2.44862 + 4.24114i) q^{34} -1.20538 q^{35} +(0.782479 + 3.11468i) q^{36} +10.3143 q^{37} +(-0.876140 + 1.51752i) q^{38} +(0.336783 - 0.136418i) q^{39} +(-0.814383 - 1.41055i) q^{40} +(-3.81234 - 6.60317i) q^{41} +(-3.39076 + 1.37347i) q^{42} +(-1.75761 + 3.04428i) q^{43} -5.72862 q^{44} +(-0.730955 - 2.90959i) q^{45} +1.68631 q^{46} +(2.21220 - 3.83165i) q^{47} +(-6.82234 - 5.32041i) q^{48} +(2.77353 + 4.80390i) q^{49} +(-0.876140 - 1.51752i) q^{50} +(0.669422 - 4.79420i) q^{51} +(0.112288 - 0.194488i) q^{52} +9.46943 q^{53} +(-5.37154 - 7.35185i) q^{54} +5.35141 q^{55} +(0.981639 - 1.70025i) q^{56} +(0.239525 - 1.71541i) q^{57} +(5.93008 + 10.2712i) q^{58} +(-5.24839 - 9.09048i) q^{59} +(-1.46210 - 1.14022i) q^{60} +(-0.0249540 + 0.0432215i) q^{61} -0.939157 q^{62} +(2.59674 - 2.51661i) q^{63} +0.360986 q^{64} +(-0.104894 + 0.181681i) q^{65} +(15.0536 - 6.09769i) q^{66} +(-1.22861 - 2.12802i) q^{67} +(-1.49589 - 2.59096i) q^{68} +(-1.54491 + 0.625789i) q^{69} +(1.05608 - 1.82918i) q^{70} +3.67721 q^{71} +(4.69940 + 1.33847i) q^{72} +14.3659 q^{73} +(-9.03680 + 15.6522i) q^{74} +(1.36582 + 1.06514i) q^{75} +(-0.535244 - 0.927070i) q^{76} +(3.22523 + 5.58627i) q^{77} +(-0.0880512 + 0.630596i) q^{78} +(0.375760 - 0.650835i) q^{79} +4.99503 q^{80} +(7.64939 + 4.74202i) q^{81} +13.3606 q^{82} +(1.29683 - 2.24618i) q^{83} +(0.309070 - 2.21347i) q^{84} +(1.39739 + 2.42036i) q^{85} +(-3.07983 - 5.33443i) q^{86} +(-9.24446 - 7.20930i) q^{87} +(-4.35809 + 7.54844i) q^{88} -5.83021 q^{89} +(5.05578 + 1.43997i) q^{90} -0.252873 q^{91} +(-0.515094 + 0.892169i) q^{92} +(0.860407 - 0.348520i) q^{93} +(3.87640 + 6.71412i) q^{94} +(0.500000 + 0.866025i) q^{95} +(8.82167 - 3.57334i) q^{96} +(-8.41705 + 14.5788i) q^{97} -9.72002 q^{98} +(-11.5285 + 11.1728i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9	\( 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9} + 6 q^{10} - q^{11} + 9 q^{12} - 11 q^{13} - 3 q^{14} + q^{15} - 45 q^{16} - 30 q^{17} - 18 q^{18} + 46 q^{19} + 29 q^{20} - 2 q^{21} - 5 q^{22} + 13 q^{23} - 6 q^{24} - 23 q^{25} - 12 q^{26} + 23 q^{27} + 56 q^{28} + 2 q^{29} + 6 q^{30} - 16 q^{31} + 25 q^{32} + 19 q^{33} - 18 q^{34} - 20 q^{35} - 5 q^{36} + 58 q^{37} + 3 q^{38} + 32 q^{39} - 6 q^{40} + 14 q^{41} - 67 q^{42} - 34 q^{43} + 64 q^{44} - 7 q^{45} - 4 q^{46} + 22 q^{47} + 89 q^{48} - 61 q^{49} + 3 q^{50} - 38 q^{51} - 20 q^{52} - 70 q^{53} - 91 q^{54} - 2 q^{55} - 26 q^{56} + 2 q^{57} - 23 q^{58} - 15 q^{59} + 3 q^{60} - 32 q^{61} + 6 q^{62} - 31 q^{63} + 164 q^{64} + 11 q^{65} + 54 q^{66} - 16 q^{67} + 26 q^{68} - 19 q^{69} + 3 q^{70} + 50 q^{71} + 22 q^{72} + 82 q^{73} + 9 q^{74} - q^{75} - 29 q^{76} + 18 q^{77} - 41 q^{78} - 11 q^{79} - 90 q^{80} + 8 q^{81} + 60 q^{82} + 26 q^{83} + 123 q^{84} - 15 q^{85} - 15 q^{86} - 26 q^{87} - 22 q^{88} + 40 q^{89} - 12 q^{90} + 116 q^{91} + 2 q^{92} + 42 q^{93} - 36 q^{94} + 23 q^{95} - 48 q^{96} - 50 q^{97} - 24 q^{98} - 29 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9 + 6 * q^10 - q^11 + 9 * q^12 - 11 * q^13 - 3 * q^14 + q^15 - 45 * q^16 - 30 * q^17 - 18 * q^18 + 46 * q^19 + 29 * q^20 - 2 * q^21 - 5 * q^22 + 13 * q^23 - 6 * q^24 - 23 * q^25 - 12 * q^26 + 23 * q^27 + 56 * q^28 + 2 * q^29 + 6 * q^30 - 16 * q^31 + 25 * q^32 + 19 * q^33 - 18 * q^34 - 20 * q^35 - 5 * q^36 + 58 * q^37 + 3 * q^38 + 32 * q^39 - 6 * q^40 + 14 * q^41 - 67 * q^42 - 34 * q^43 + 64 * q^44 - 7 * q^45 - 4 * q^46 + 22 * q^47 + 89 * q^48 - 61 * q^49 + 3 * q^50 - 38 * q^51 - 20 * q^52 - 70 * q^53 - 91 * q^54 - 2 * q^55 - 26 * q^56 + 2 * q^57 - 23 * q^58 - 15 * q^59 + 3 * q^60 - 32 * q^61 + 6 * q^62 - 31 * q^63 + 164 * q^64 + 11 * q^65 + 54 * q^66 - 16 * q^67 + 26 * q^68 - 19 * q^69 + 3 * q^70 + 50 * q^71 + 22 * q^72 + 82 * q^73 + 9 * q^74 - q^75 - 29 * q^76 + 18 * q^77 - 41 * q^78 - 11 * q^79 - 90 * q^80 + 8 * q^81 + 60 * q^82 + 26 * q^83 + 123 * q^84 - 15 * q^85 - 15 * q^86 - 26 * q^87 - 22 * q^88 + 40 * q^89 - 12 * q^90 + 116 * q^91 + 2 * q^92 + 42 * q^93 - 36 * q^94 + 23 * q^95 - 48 * q^96 - 50 * q^97 - 24 * q^98 - 29 * q^99

Introduction

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