LMFDB - Embedded newform 418.2.s.a.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(107,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.s (of order $30$, degree $8$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			107.2
Character	$\chi$	$=$	418.107
Dual form			418.2.s.a.293.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 - 0.406737i) q^{2} +(-1.85282 - 1.66828i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-0.211376 + 2.01110i) q^{5} +(1.01408 + 2.27766i) q^{6} +(0.508834 + 0.165330i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.336173 + 3.19847i) q^{9} +O(q^{10})$	\(q+(-0.913545 - 0.406737i) q^{2} +(-1.85282 - 1.66828i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-0.211376 + 2.01110i) q^{5} +(1.01408 + 2.27766i) q^{6} +(0.508834 + 0.165330i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.336173 + 3.19847i) q^{9} +(1.01109 - 1.75126i) q^{10} +(1.29424 - 3.05368i) q^{11} -2.49321i q^{12} +(0.0818461 + 0.778714i) q^{13} +(-0.397597 - 0.357998i) q^{14} +(3.74673 - 3.37357i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(5.84843 + 0.614695i) q^{17} +(0.993826 - 3.05868i) q^{18} +(-4.24480 - 0.990781i) q^{19} +(-1.63598 + 1.18861i) q^{20} +(-0.666958 - 1.15520i) q^{21} +(-2.42439 + 2.26326i) q^{22} +(3.60359 - 6.24160i) q^{23} +(-1.01408 + 2.27766i) q^{24} +(0.890880 + 0.189362i) q^{25} +(0.241961 - 0.744680i) q^{26} +(0.316673 - 0.435863i) q^{27} +(0.217612 + 0.488765i) q^{28} +(-4.81582 - 5.34851i) q^{29} +(-4.79496 + 1.55798i) q^{30} +(-5.67483 - 7.81074i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-7.49238 + 3.49875i) q^{33} +(-5.09279 - 2.94032i) q^{34} +(-0.440051 + 0.988371i) q^{35} +(-2.15198 + 2.39002i) q^{36} +(-3.39467 - 1.10299i) q^{37} +(3.47483 + 2.63164i) q^{38} +(1.14747 - 1.57936i) q^{39} +(1.97799 - 0.420435i) q^{40} +(3.12349 - 3.46898i) q^{41} +(0.139432 + 1.32661i) q^{42} +(1.36416 - 0.787597i) q^{43} +(3.13534 - 1.08151i) q^{44} -6.50352 q^{45} +(-5.83073 + 4.23627i) q^{46} +(3.00018 + 0.637708i) q^{47} +(1.85282 - 1.66828i) q^{48} +(-5.43154 - 3.94625i) q^{49} +(-0.736839 - 0.535345i) q^{50} +(-9.81058 - 10.8958i) q^{51} +(-0.523931 + 0.581885i) q^{52} +(8.00440 - 0.841297i) q^{53} +(-0.466577 + 0.269378i) q^{54} +(5.86770 + 3.24831i) q^{55} -0.535019i q^{56} +(6.21193 + 8.91726i) q^{57} +(2.22404 + 6.84488i) q^{58} +(-0.436885 - 2.05538i) q^{59} +(5.01410 + 0.527003i) q^{60} +(1.11934 + 2.51408i) q^{61} +(2.00731 + 9.44363i) q^{62} +(-0.357747 + 1.68307i) q^{63} +(-0.809017 + 0.587785i) q^{64} -1.58337 q^{65} +(8.26770 - 0.148846i) q^{66} +(13.1725 + 7.60516i) q^{67} +(3.45656 + 4.75754i) q^{68} +(-17.0895 + 5.55272i) q^{69} +(0.804013 - 0.723937i) q^{70} +(9.23500 + 0.970637i) q^{71} +(2.93804 - 1.30810i) q^{72} +(-1.85348 - 8.71992i) q^{73} +(2.65256 + 2.38837i) q^{74} +(-1.33473 - 1.83709i) q^{75} +(-2.10403 - 3.81747i) q^{76} +(1.16342 - 1.33984i) q^{77} +(-1.69065 + 0.976095i) q^{78} +(-0.100357 - 0.0446819i) q^{79} +(-1.97799 - 0.420435i) q^{80} +(8.12355 - 1.72671i) q^{81} +(-4.26441 + 1.89864i) q^{82} +(7.58670 - 10.4422i) q^{83} +(0.412202 - 1.26863i) q^{84} +(-2.47243 + 11.6319i) q^{85} +(-1.56656 + 0.164653i) q^{86} +17.9440i q^{87} +(-3.30416 - 0.287252i) q^{88} +(2.70144 + 1.55968i) q^{89} +(5.94126 + 2.64522i) q^{90} +(-0.0870988 + 0.409767i) q^{91} +(7.04968 - 1.49846i) q^{92} +(-2.51610 + 23.9391i) q^{93} +(-2.48142 - 1.80286i) q^{94} +(2.88981 - 8.32731i) q^{95} +(-2.37118 + 0.770444i) q^{96} +(-0.574709 + 1.29082i) q^{97} +(3.35688 + 5.81428i) q^{98} +(10.2022 + 3.11301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9}+O(q^{10}) $ 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9	\( 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9} + 2 q^{10} - q^{11} + 5 q^{13} - 4 q^{14} - 27 q^{15} + 10 q^{16} - 6 q^{17} - 17 q^{18} - 2 q^{19} + 4 q^{20} + 24 q^{21} - 2 q^{22} - 6 q^{23} - 7 q^{24} - 10 q^{26} - 45 q^{27} + 6 q^{28} - 65 q^{29} + 30 q^{30} + 40 q^{32} + 3 q^{33} + 24 q^{34} - 13 q^{35} - q^{36} + 22 q^{38} - 30 q^{39} - 3 q^{40} - 14 q^{41} - 14 q^{42} + 12 q^{43} + 24 q^{44} - 12 q^{45} - 2 q^{46} - q^{47} + 3 q^{48} + 32 q^{49} + 30 q^{50} - 28 q^{51} - 5 q^{52} - q^{53} - 27 q^{54} - 23 q^{55} + 28 q^{57} - 10 q^{58} + 56 q^{59} - 28 q^{60} + 28 q^{61} + 15 q^{62} + 88 q^{63} - 20 q^{64} + 8 q^{65} - 57 q^{66} - 27 q^{67} - 60 q^{69} + 17 q^{70} + 2 q^{71} + 11 q^{72} - q^{73} + 12 q^{74} - 35 q^{75} - 11 q^{76} - 8 q^{77} - 6 q^{79} + 3 q^{80} + 43 q^{81} - 16 q^{82} - 25 q^{83} + 52 q^{84} - 33 q^{85} - 43 q^{86} - 9 q^{88} - 36 q^{89} + 74 q^{90} + 38 q^{91} - 11 q^{92} + 15 q^{93} - 2 q^{94} - 61 q^{95} - 24 q^{97} - 44 q^{98} + 37 q^{99}+O(q^{100}) \) 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9 + 2 * q^10 - q^11 + 5 * q^13 - 4 * q^14 - 27 * q^15 + 10 * q^16 - 6 * q^17 - 17 * q^18 - 2 * q^19 + 4 * q^20 + 24 * q^21 - 2 * q^22 - 6 * q^23 - 7 * q^24 - 10 * q^26 - 45 * q^27 + 6 * q^28 - 65 * q^29 + 30 * q^30 + 40 * q^32 + 3 * q^33 + 24 * q^34 - 13 * q^35 - q^36 + 22 * q^38 - 30 * q^39 - 3 * q^40 - 14 * q^41 - 14 * q^42 + 12 * q^43 + 24 * q^44 - 12 * q^45 - 2 * q^46 - q^47 + 3 * q^48 + 32 * q^49 + 30 * q^50 - 28 * q^51 - 5 * q^52 - q^53 - 27 * q^54 - 23 * q^55 + 28 * q^57 - 10 * q^58 + 56 * q^59 - 28 * q^60 + 28 * q^61 + 15 * q^62 + 88 * q^63 - 20 * q^64 + 8 * q^65 - 57 * q^66 - 27 * q^67 - 60 * q^69 + 17 * q^70 + 2 * q^71 + 11 * q^72 - q^73 + 12 * q^74 - 35 * q^75 - 11 * q^76 - 8 * q^77 - 6 * q^79 + 3 * q^80 + 43 * q^81 - 16 * q^82 - 25 * q^83 + 52 * q^84 - 33 * q^85 - 43 * q^86 - 9 * q^88 - 36 * q^89 + 74 * q^90 + 38 * q^91 - 11 * q^92 + 15 * q^93 - 2 * q^94 - 61 * q^95 - 24 * q^97 - 44 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.913545	−	0.406737i	−0.645974	−	0.287606i
$2$	−0.913545	−	0.406737i	−0.645974	−	0.287606i
$3$	−1.85282	−	1.66828i	−1.06972	−	0.963183i	−0.0703132	−	0.997525i	$-0.522400\pi$
$3$	−1.85282	−	1.66828i	−1.06972	−	0.963183i	−0.999410	+	0.0343418i	$0.989067\pi$
$4$	0.669131	+	0.743145i	0.334565	+	0.371572i
$5$	−0.211376	+	2.01110i	−0.0945300	+	0.899393i	0.839779	+	0.542929i	$0.182685\pi$
$5$	−0.211376	+	2.01110i	−0.0945300	+	0.899393i	−0.934309	+	0.356464i	$0.883982\pi$
$6$	1.01408	+	2.27766i	0.413996	+	0.929851i
$7$	0.508834	+	0.165330i	0.192321	+	0.0624889i	0.403594	−	0.914938i	$-0.367761\pi$
$7$	0.508834	+	0.165330i	0.192321	+	0.0624889i	−0.211273	+	0.977427i	$0.567761\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	0.336173	+	3.19847i	0.112058	+	1.06616i
$10$	1.01109	−	1.75126i	0.319735	−	0.553797i
$11$	1.29424	−	3.05368i	0.390227	−	0.920719i
$11$	1.29424	−	3.05368i	0.390227	−	0.920719i
$12$		−	2.49321i		−	0.719727i
$13$	0.0818461	+	0.778714i	0.0227000	+	0.215976i	0.999992	+	0.00407775i	$0.00129799\pi$
$13$	0.0818461	+	0.778714i	0.0227000	+	0.215976i	−0.977292	+	0.211899i	$0.932035\pi$
$14$	−0.397597	−	0.357998i	−0.106262	−	0.0956790i
$15$	3.74673	−	3.37357i	0.967401	−	0.871052i
$16$	−0.104528	+	0.994522i	−0.0261321	+	0.248630i
$17$	5.84843	+	0.614695i	1.41845	+	0.149085i	0.782504	−	0.622646i	$-0.213942\pi$
$17$	5.84843	+	0.614695i	1.41845	+	0.149085i	0.635949	+	0.771731i	$0.280609\pi$
$18$	0.993826	−	3.05868i	0.234247	−	0.720939i
$19$	−4.24480	−	0.990781i	−0.973825	−	0.227301i
$19$	−4.24480	−	0.990781i	−0.973825	−	0.227301i
$20$	−1.63598	+	1.18861i	−0.365816	+	0.265781i
$21$	−0.666958	−	1.15520i	−0.145542	−	0.252086i
$22$	−2.42439	+	2.26326i	−0.516881	+	0.482529i
$23$	3.60359	−	6.24160i	0.751400	−	1.30146i	−0.195744	−	0.980655i	$-0.562712\pi$
$23$	3.60359	−	6.24160i	0.751400	−	1.30146i	0.947144	−	0.320808i	$-0.103954\pi$
$24$	−1.01408	+	2.27766i	−0.206998	+	0.464925i
$25$	0.890880	+	0.189362i	0.178176	+	0.0378725i
$26$	0.241961	−	0.744680i	0.0474525	−	0.146044i
$27$	0.316673	−	0.435863i	0.0609438	−	0.0838820i
$28$	0.217612	+	0.488765i	0.0411248	+	0.0923678i
$29$	−4.81582	−	5.34851i	−0.894276	−	0.993194i	0.105723	−	0.994396i	$-0.466284\pi$
$29$	−4.81582	−	5.34851i	−0.894276	−	0.993194i	−0.999999	+	0.00120151i	$0.999618\pi$
$30$	−4.79496	+	1.55798i	−0.875436	+	0.284446i
$31$	−5.67483	−	7.81074i	−1.01923	−	1.40285i	−0.912742	−	0.408536i	$-0.866039\pi$
$31$	−5.67483	−	7.81074i	−1.01923	−	1.40285i	−0.106488	−	0.994314i	$-0.533961\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−7.49238	+	3.49875i	−1.30426	+	0.609055i
$34$	−5.09279	−	2.94032i	−0.873406	−	0.504261i
$35$	−0.440051	+	0.988371i	−0.0743822	+	0.167065i
$36$	−2.15198	+	2.39002i	−0.358664	+	0.398337i
$37$	−3.39467	−	1.10299i	−0.558080	−	0.181331i	0.0163770	−	0.999866i	$-0.494787\pi$
$37$	−3.39467	−	1.10299i	−0.558080	−	0.181331i	−0.574457	+	0.818535i	$0.694787\pi$
$38$	3.47483	+	2.63164i	0.563692	+	0.426908i
$39$	1.14747	−	1.57936i	0.183742	−	0.252899i
$40$	1.97799	−	0.420435i	0.312748	−	0.0664766i
$41$	3.12349	−	3.46898i	0.487807	−	0.541764i	−0.448113	−	0.893977i	$-0.647904\pi$
$41$	3.12349	−	3.46898i	0.487807	−	0.541764i	0.935920	+	0.352213i	$0.114571\pi$
$42$	0.139432	+	1.32661i	0.0215148	+	0.204700i
$43$	1.36416	−	0.787597i	0.208032	−	0.120107i	−0.392364	−	0.919810i	$-0.628343\pi$
$43$	1.36416	−	0.787597i	0.208032	−	0.120107i	0.600396	+	0.799702i	$0.295009\pi$
$44$	3.13534	−	1.08151i	0.472670	−	0.163043i
$45$	−6.50352			−0.969487
$46$	−5.83073	+	4.23627i	−0.859694	+	0.624604i
$47$	3.00018	+	0.637708i	0.437621	+	0.0930192i	0.421453	−	0.906850i	$-0.361520\pi$
$47$	3.00018	+	0.637708i	0.437621	+	0.0930192i	0.0161677	+	0.999869i	$0.494853\pi$
$48$	1.85282	−	1.66828i	0.267431	−	0.240796i
$49$	−5.43154	−	3.94625i	−0.775934	−	0.563749i
$50$	−0.736839	−	0.535345i	−0.104205	−	0.0757092i
$51$	−9.81058	−	10.8958i	−1.37376	−	1.52571i
$52$	−0.523931	+	0.581885i	−0.0726562	+	0.0806929i
$53$	8.00440	−	0.841297i	1.09949	−	0.115561i	0.462638	−	0.886547i	$-0.346903\pi$
$53$	8.00440	−	0.841297i	1.09949	−	0.115561i	0.636852	+	0.770986i	$0.280236\pi$
$54$	−0.466577	+	0.269378i	−0.0634931	+	0.0366578i
$55$	5.86770	+	3.24831i	0.791200	+	0.438003i
$56$		−	0.535019i		−	0.0714950i
$57$	6.21193	+	8.91726i	0.822791	+	1.18112i
$58$	2.22404	+	6.84488i	0.292030	+	0.898777i
$59$	−0.436885	−	2.05538i	−0.0568776	−	0.267588i	0.940515	−	0.339752i	$-0.110343\pi$
$59$	−0.436885	−	2.05538i	−0.0568776	−	0.267588i	−0.997393	+	0.0721635i	$0.977010\pi$
$60$	5.01410	+	0.527003i	0.647318	+	0.0680358i
$61$	1.11934	+	2.51408i	0.143317	+	0.321894i	0.970914	−	0.239427i	$-0.0769597\pi$
$61$	1.11934	+	2.51408i	0.143317	+	0.321894i	−0.827598	+	0.561322i	$0.810293\pi$
$62$	2.00731	+	9.44363i	0.254928	+	1.19934i
$63$	−0.357747	+	1.68307i	−0.0450719	+	0.212047i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−1.58337			−0.196393
$66$	8.26770	−	0.148846i	1.01768	−	0.0183216i
$67$	13.1725	+	7.60516i	1.60928	+	0.929118i	0.989531	+	0.144317i	$0.0460985\pi$
$67$	13.1725	+	7.60516i	1.60928	+	0.929118i	0.619748	+	0.784801i	$0.287235\pi$
$68$	3.45656	+	4.75754i	0.419169	+	0.576937i
$69$	−17.0895	+	5.55272i	−2.05734	+	0.668469i
$70$	0.804013	−	0.723937i	0.0960979	−	0.0865270i
$71$	9.23500	+	0.970637i	1.09599	+	0.115193i	0.635225	−	0.772327i	$-0.280907\pi$
$71$	9.23500	+	0.970637i	1.09599	+	0.115193i	0.460768	+	0.887521i	$0.347574\pi$
$72$	2.93804	−	1.30810i	0.346252	−	0.154161i
$73$	−1.85348	−	8.71992i	−0.216933	−	1.02059i	−0.942956	−	0.332918i	$-0.891967\pi$
$73$	−1.85348	−	8.71992i	−0.216933	−	1.02059i	0.726023	−	0.687671i	$-0.241367\pi$
$74$	2.65256	+	2.38837i	0.308353	+	0.277643i
$75$	−1.33473	−	1.83709i	−0.154121	−	0.212129i
$76$	−2.10403	−	3.81747i	−0.241349	−	0.437893i
$77$	1.16342	−	1.33984i	0.132583	−	0.152689i
$78$	−1.69065	+	0.976095i	−0.191428	+	0.110521i
$79$	−0.100357	−	0.0446819i	−0.0112911	−	0.00502710i	0.401083	−	0.916042i	$-0.368634\pi$
$79$	−0.100357	−	0.0446819i	−0.0112911	−	0.00502710i	−0.412374	+	0.911014i	$0.635300\pi$
$80$	−1.97799	−	0.420435i	−0.221146	−	0.0470061i
$81$	8.12355	−	1.72671i	0.902617	−	0.191857i
$82$	−4.26441	+	1.89864i	−0.470925	+	0.209669i
$83$	7.58670	−	10.4422i	0.832748	−	1.14618i	−0.154657	−	0.987968i	$-0.549427\pi$
$83$	7.58670	−	10.4422i	0.832748	−	1.14618i	0.987405	−	0.158211i	$-0.0505728\pi$
$84$	0.412202	−	1.26863i	0.0449750	−	0.138419i
$85$	−2.47243	+	11.6319i	−0.268173	+	1.26165i
$86$	−1.56656	+	0.164653i	−0.168927	+	0.0177549i
$87$			17.9440i			1.92379i
$88$	−3.30416	−	0.287252i	−0.352225	−	0.0306212i
$89$	2.70144	+	1.55968i	0.286352	+	0.165326i	0.636296	−	0.771445i	$-0.280466\pi$
$89$	2.70144	+	1.55968i	0.286352	+	0.165326i	−0.349943	+	0.936771i	$0.613799\pi$
$90$	5.94126	+	2.64522i	0.626264	+	0.278831i
$91$	−0.0870988	+	0.409767i	−0.00913043	+	0.0429553i
$92$	7.04968	−	1.49846i	0.734980	−	0.156225i
$93$	−2.51610	+	23.9391i	−0.260907	+	2.48237i
$94$	−2.48142	−	1.80286i	−0.255939	−	0.185951i
$95$	2.88981	−	8.32731i	0.296488	−	0.854364i
$96$	−2.37118	+	0.770444i	−0.242008	+	0.0786331i
$97$	−0.574709	+	1.29082i	−0.0583529	+	0.131063i	−0.940368	−	0.340158i	$-0.889520\pi$
$97$	−0.574709	+	1.29082i	−0.0583529	+	0.131063i	0.882016	+	0.471220i	$0.156186\pi$
$98$	3.35688	+	5.81428i	0.339096	+	0.587331i
$99$	10.2022	+	3.11301i	1.02536	+	0.312869i
$100$	0.455391	+	0.788761i	0.0455391	+	0.0788761i
$101$	−8.46736	+	0.889955i	−0.842534	+	0.0885539i	−0.515955	−	0.856616i	$-0.672563\pi$
$101$	−8.46736	+	0.889955i	−0.842534	+	0.0885539i	−0.326579	+	0.945170i	$0.605896\pi$
$102$	4.53071	+	13.9441i	0.448607	+	1.38067i
$103$	5.74106	+	1.86538i	0.565683	+	0.183802i	0.577877	−	0.816124i	$-0.303881\pi$
$103$	5.74106	+	1.86538i	0.565683	+	0.183802i	−0.0121936	+	0.999926i	$0.503881\pi$
$104$	0.715309	−	0.318476i	0.0701418	−	0.0312292i
$105$	2.46421	−	1.09714i	0.240483	−	0.107070i
$106$	−7.65457	−	2.48712i	−0.743478	−	0.241571i
$107$	−4.65136	−	14.3154i	−0.449664	−	1.38392i	−0.877287	−	0.479966i	$-0.840649\pi$
$107$	−4.65136	−	14.3154i	−0.449664	−	1.38392i	0.427624	−	0.903957i	$-0.359351\pi$
$108$	0.535805	−	0.0563154i	0.0515579	−	0.00541895i
$109$	2.50894	+	4.34560i	0.240312	+	0.416233i	0.960803	−	0.277231i	$-0.0894168\pi$
$109$	2.50894	+	4.34560i	0.240312	+	0.416233i	−0.720491	+	0.693464i	$0.756083\pi$
$110$	−4.03920	−	5.35409i	−0.385122	−	0.510492i
$111$	4.44959	+	7.70691i	0.422336	+	0.731508i
$112$	−0.217612	+	0.488765i	−0.0205624	+	0.0461839i
$113$	−9.10792	+	2.95934i	−0.856801	+	0.278392i	−0.704292	−	0.709910i	$-0.748735\pi$
$113$	−9.10792	+	2.95934i	−0.856801	+	0.278392i	−0.152509	+	0.988302i	$0.548735\pi$
$114$	−2.04790	−	10.6729i	−0.191804	−	0.999613i
$115$	11.7908	+	8.56651i	1.09950	+	0.798831i
$116$	0.752305	−	7.15771i	0.0698498	−	0.664577i
$117$	−2.46318	+	0.523565i	−0.227721	+	0.0484036i
$118$	−0.436885	+	2.05538i	−0.0402185	+	0.189213i
$119$	2.87425	+	1.27970i	0.263482	+	0.117310i
$120$	−4.36626	−	2.52086i	−0.398583	−	0.230122i
$121$	−7.64991	−	7.90436i	−0.695446	−	0.718578i
$122$		−	2.75200i		−	0.249154i
$123$	−11.5745	+	1.21653i	−1.04364	+	0.109691i
$124$	2.00731	−	9.44363i	0.180261	−	0.848063i
$125$	−3.69358	+	11.3677i	−0.330364	+	1.01676i
$126$	1.01138	−	1.39205i	0.0901013	−	0.124014i
$127$	−6.30397	+	2.80671i	−0.559387	+	0.249055i	−0.666898	−	0.745149i	$-0.732378\pi$
$127$	−6.30397	+	2.80671i	−0.559387	+	0.249055i	0.107512	+	0.994204i	$0.465712\pi$
$128$	0.978148	−	0.207912i	0.0864569	−	0.0183770i
$129$	−3.84147	−	0.816529i	−0.338222	−	0.0718913i
$130$	1.44648	+	0.644016i	0.126865	+	0.0564840i
$131$	−13.1038	+	7.56550i	−1.14489	+	0.661001i	−0.947636	−	0.319352i	$-0.896535\pi$
$131$	−13.1038	+	7.56550i	−1.14489	+	0.661001i	−0.197251	+	0.980353i	$0.563201\pi$
$132$	−7.61346	−	3.22680i	−0.662667	−	0.280857i
$133$	−1.99609	−	1.20594i	−0.173083	−	0.104568i
$134$	−8.94040	−	12.3054i	−0.772333	−	1.06303i
$135$	0.809630	+	0.728994i	0.0696818	+	0.0627418i
$136$	−1.22266	−	5.75214i	−0.104842	−	0.493242i
$137$	7.68561	−	3.42185i	0.656626	−	0.292349i	−0.0512498	−	0.998686i	$-0.516320\pi$
$137$	7.68561	−	3.42185i	0.656626	−	0.292349i	0.707875	+	0.706337i	$0.249654\pi$
$138$	17.8706	+	1.87827i	1.52124	+	0.159889i
$139$	−4.68716	+	4.22034i	−0.397560	+	0.357964i	−0.843529	−	0.537084i	$-0.819526\pi$
$139$	−4.68716	+	4.22034i	−0.397560	+	0.357964i	0.445969	+	0.895048i	$0.352859\pi$
$140$	−1.02895	+	0.334327i	−0.0869625	+	0.0282558i
$141$	−4.49490	−	6.18670i	−0.378539	−	0.521014i
$142$	−8.04180	−	4.64293i	−0.674853	−	0.389626i
$143$	2.48387	+	0.757907i	0.207712	+	0.0633794i
$144$	−3.21609			−0.268007
$145$	11.7744	−	8.55458i	0.977808	−	0.710419i
$146$	−1.85348	+	8.71992i	−0.153395	+	0.721666i
$147$	3.48019	+	16.3730i	0.287041	+	1.35042i
$148$	−1.45179	−	3.26078i	−0.119337	−	0.268034i
$149$	−1.62514	−	0.170810i	−0.133137	−	0.0139933i	0.0377255	−	0.999288i	$-0.487989\pi$
$149$	−1.62514	−	0.170810i	−0.133137	−	0.0139933i	−0.170863	+	0.985295i	$0.554655\pi$
$150$	0.472120	+	2.22115i	0.0385484	+	0.181356i
$151$	−1.38720	−	4.26936i	−0.112889	−	0.347436i	0.878612	−	0.477536i	$-0.158470\pi$
$151$	−1.38720	−	4.26936i	−0.112889	−	0.347436i	−0.991501	+	0.130101i	$0.958470\pi$
$152$	0.369427	+	4.34322i	0.0299645	+	0.352281i
$153$			18.9127i			1.52900i
$154$	−1.60779	+	0.750800i	−0.129560	+	0.0605012i
$155$	16.9077	−	9.76168i	1.35806	−	0.784077i
$156$	1.94150	−	0.204059i	0.155444	−	0.0163378i
$157$	−1.10044	+	1.22216i	−0.0878245	+	0.0975390i	−0.785455	−	0.618919i	$-0.787571\pi$
$157$	−1.10044	+	1.22216i	−0.0878245	+	0.0975390i	0.697631	+	0.716458i	$0.254238\pi$
$158$	0.0735070	+	0.0816378i	0.00584790	+	0.00649476i
$159$	−16.2342	−	11.7948i	−1.28746	−	0.935391i
$160$	1.63598	+	1.18861i	0.129336	+	0.0939677i
$161$	2.86555	−	2.58015i	0.225837	−	0.203345i
$162$	−8.12355	−	1.72671i	−0.638246	−	0.135663i
$163$	−15.5815	+	11.3206i	−1.22043	+	0.886697i	−0.996136	−	0.0878237i	$-0.972009\pi$
$163$	−15.5815	+	11.3206i	−1.22043	+	0.886697i	−0.224298	+	0.974521i	$0.572009\pi$
$164$	4.66798			0.364508
$165$	−5.45265	−	15.8075i	−0.424488	−	1.23061i
$166$	−11.1780	+	6.45363i	−0.867582	+	0.500899i
$167$	1.20042	+	11.4213i	0.0928915	+	0.883803i	0.937398	+	0.348259i	$0.113227\pi$
$167$	1.20042	+	11.4213i	0.0928915	+	0.883803i	−0.844507	+	0.535544i	$0.820106\pi$
$168$	−0.892563	+	0.991292i	−0.0688628	+	0.0764798i
$169$	12.1162	−	2.57538i	0.932017	−	0.198106i
$170$	6.98979	−	9.62061i	0.536092	−	0.737867i
$171$	1.74200	−	13.9100i	0.133214	−	1.06372i
$172$	1.49810	+	0.486762i	0.114229	+	0.0371152i
$173$	2.03298	−	2.25785i	0.154564	−	0.171661i	−0.660889	−	0.750483i	$-0.729821\pi$
$173$	2.03298	−	2.25785i	0.154564	−	0.171661i	0.815454	+	0.578822i	$0.196487\pi$
$174$	7.29847	−	16.3926i	0.553295	−	1.24272i
$175$	0.422002	+	0.243643i	0.0319004	+	0.0184177i
$176$	2.90167	+	1.60634i	0.218721	+	0.121083i
$177$	−2.61949	+	4.53709i	−0.196893	+	0.341029i
$178$	−1.83351	−	2.52361i	−0.137428	−	0.189153i
$179$	21.7886	−	7.07953i	1.62855	−	0.529149i	0.654615	−	0.755962i	$-0.272831\pi$
$179$	21.7886	−	7.07953i	1.62855	−	0.529149i	0.973938	+	0.226813i	$0.0728307\pi$
$180$	−4.35170	−	4.83305i	−0.324357	−	0.360235i
$181$	5.78641	+	12.9965i	0.430101	+	0.966022i	0.990464	+	0.137775i	$0.0439950\pi$
$181$	5.78641	+	12.9965i	0.430101	+	0.966022i	−0.560363	+	0.828247i	$0.689338\pi$
$182$	0.246236	−	0.338915i	0.0182522	−	0.0251220i
$183$	2.12026	−	6.52549i	0.156734	−	0.482378i
$184$	−7.04968	−	1.49846i	−0.519709	−	0.110468i
$185$	2.93579	−	6.59388i	0.215843	−	0.484792i
$186$	12.0355	−	20.8460i	0.882484	−	1.52851i
$187$	9.44633	−	17.0637i	0.690784	−	1.24782i
$188$	1.53360	+	2.65628i	0.111849	+	0.193729i
$189$	0.233195	−	0.169426i	0.0169625	−	0.0123240i
$190$	−6.02700	+	6.43199i	−0.437244	+	0.466625i
$191$	3.93134	−	12.0994i	0.284462	−	0.875483i	−0.702098	−	0.712081i	$-0.747753\pi$
$191$	3.93134	−	12.0994i	0.284462	−	0.875483i	0.986559	−	0.163403i	$-0.0522470\pi$
$192$	2.47955	+	0.260611i	0.178946	+	0.0188080i
$193$	−0.720392	+	6.85408i	−0.0518550	+	0.493367i	0.937515	+	0.347945i	$0.113121\pi$
$193$	−0.720392	+	6.85408i	−0.0518550	+	0.493367i	−0.989370	+	0.145422i	$0.953546\pi$
$194$	1.05005	−	0.945465i	0.0753889	−	0.0678804i
$195$	2.93370	+	2.64152i	0.210087	+	0.189163i
$196$	−0.701778	−	6.67698i	−0.0501270	−	0.476927i
$197$			13.1821i			0.939189i	0.882882	+	0.469594i	$0.155600\pi$
$197$			13.1821i			0.939189i	−0.882882	+	0.469594i	$0.844400\pi$
$198$	−8.05399	−	6.99348i	−0.572372	−	0.497005i
$199$	−12.4331	+	21.5348i	−0.881360	+	1.52656i	−0.0315301	+	0.999503i	$0.510038\pi$
$199$	−12.4331	+	21.5348i	−0.881360	+	1.52656i	−0.849830	+	0.527057i	$0.823295\pi$
$200$	−0.0952027	−	0.905793i	−0.00673185	−	0.0640493i
$201$	−11.7187	−	36.0664i	−0.826573	−	2.54393i
$202$	8.09730	+	2.63097i	0.569724	+	0.185114i
$203$	−1.56618	−	3.51770i	−0.109924	−	0.246894i
$204$	1.53256	−	14.5814i	0.107301	−	1.02090i
$205$	6.31626	+	7.01491i	0.441147	+	0.489943i
$206$	−4.48600	−	4.03921i	−0.312554	−	0.281425i
$207$	21.1750	+	9.42772i	1.47176	+	0.655272i
$208$	−0.783003			−0.0542915
$209$	−8.51930	+	11.6800i	−0.589292	+	0.807920i
$210$	−2.69742			−0.186140
$211$	−19.2280	−	8.56087i	−1.32371	−	0.589355i	−0.381499	−	0.924369i	$-0.624592\pi$
$211$	−19.2280	−	8.56087i	−1.32371	−	0.589355i	−0.942213	+	0.335014i	$0.891259\pi$
$212$	5.98120	+	5.38549i	0.410790	+	0.369877i
$213$	−15.4914	−	17.2050i	−1.06146	−	1.17887i
$214$	−1.57337	+	14.9696i	−0.107554	+	1.02330i
$215$	1.29559	+	2.90994i	0.0883585	+	0.198456i
$216$	−0.512388	−	0.166485i	−0.0348636	−	0.0113279i
$217$	−1.59620	−	4.91259i	−0.108357	−	0.333488i
$218$	−0.524510	−	4.99038i	−0.0355243	−	0.337991i
$219$	−11.1131	+	19.2485i	−0.750956	+	1.30069i
$220$	1.51229	+	6.53409i	0.101958	+	0.440529i
$221$			4.60456i			0.309737i
$222$	−0.930217	−	8.85042i	−0.0624321	−	0.594002i
$223$	12.6144	+	11.3581i	0.844723	+	0.760592i	0.972916	−	0.231157i	$-0.0742512\pi$
$223$	12.6144	+	11.3581i	0.844723	+	0.760592i	−0.128193	+	0.991749i	$0.540918\pi$
$224$	0.397597	−	0.357998i	0.0265656	−	0.0239197i
$225$	−0.306180	+	2.91311i	−0.0204120	+	0.194207i
$226$	9.52417	+	1.00103i	0.633539	+	0.0665876i
$227$	0.693580	−	2.13462i	0.0460345	−	0.141680i	−0.925397	−	0.378998i	$-0.876269\pi$
$227$	0.693580	−	2.13462i	0.0460345	−	0.141680i	0.971432	+	0.237319i	$0.0762686\pi$
$228$	−2.47022	+	10.5832i	−0.163595	+	0.700888i
$229$	9.77794	−	7.10409i	0.646145	−	0.469452i	−0.215811	−	0.976435i	$-0.569240\pi$
$229$	9.77794	−	7.10409i	0.646145	−	0.469452i	0.861956	+	0.506984i	$0.169240\pi$
$230$	−7.28711	−	12.6216i	−0.480498	−	0.832246i
$231$	−4.39082	+	0.541568i	−0.288895	+	0.0356326i
$232$	−3.59857	+	6.23290i	−0.236258	+	0.409210i
$233$	8.65085	−	19.4301i	0.566736	−	1.27291i	−0.371987	−	0.928238i	$-0.621323\pi$
$233$	8.65085	−	19.4301i	0.566736	−	1.27291i	0.938723	−	0.344672i	$-0.112010\pi$
$234$	2.46318	+	0.523565i	0.161023	+	0.0342265i
$235$	−1.91666	+	5.89887i	−0.125029	+	0.384800i
$236$	1.23511	−	1.69999i	0.0803991	−	0.110660i
$237$	0.111401	+	0.250211i	0.00723629	+	0.0162530i
$238$	−2.10526	−	2.33813i	−0.136464	−	0.151558i
$239$	−21.1210	+	6.86262i	−1.36620	+	0.443906i	−0.898109	−	0.439774i	$-0.855059\pi$
$239$	−21.1210	+	6.86262i	−1.36620	+	0.443906i	−0.468093	+	0.883679i	$0.655059\pi$
$240$	2.96345	+	4.07884i	0.191290	+	0.263288i
$241$	−3.02413	+	5.23795i	−0.194801	+	0.337406i	−0.946835	−	0.321718i	$-0.895740\pi$
$241$	−3.02413	+	5.23795i	−0.194801	+	0.337406i	0.752034	+	0.659124i	$0.229073\pi$
$242$	3.77355	+	10.3325i	0.242573	+	0.664198i
$243$	−19.3318	−	11.1612i	−1.24014	−	0.715993i
$244$	−1.11934	+	2.51408i	−0.0716583	+	0.160947i
$245$	9.08440	−	10.0893i	0.580381	−	0.644579i
$246$	11.0686	+	3.59642i	0.705710	+	0.229299i
$247$	0.424114	−	3.38658i	0.0269858	−	0.215483i
$248$	−5.67483	+	7.81074i	−0.360352	+	0.495982i
$249$	−31.4773	+	6.69070i	−1.99479	+	0.424006i
$250$	7.99790	−	8.88257i	0.505832	−	0.561783i
$251$	1.27198	+	12.1020i	0.0802864	+	0.763874i	0.958401	+	0.285424i	$0.0921345\pi$
$251$	1.27198	+	12.1020i	0.0802864	+	0.763874i	−0.878115	+	0.478450i	$0.841199\pi$
$252$	−1.49014	+	0.860335i	−0.0938703	+	0.0541960i
$253$	−14.3959	−	19.0823i	−0.905065	−	1.19969i
$254$	6.90055			0.432979
$255$	23.9862	−	17.4270i	1.50207	−	1.09132i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	−4.09917	+	3.69091i	−0.255699	+	0.230233i	−0.787004	−	0.616948i	$-0.788369\pi$
$257$	−4.09917	+	3.69091i	−0.255699	+	0.230233i	0.531304	+	0.847181i	$0.321702\pi$
$258$	3.17724	+	2.30840i	0.197806	+	0.143715i
$259$	−1.54496	−	1.12248i	−0.0959994	−	0.0697476i
$260$	−1.05948	−	1.17668i	−0.0657064	−	0.0729744i
$261$	15.4881	−	17.2013i	0.958691	−	1.06473i
$262$	15.0481	−	1.58162i	0.929676	−	0.0977128i
$263$	−1.77102	+	1.02250i	−0.109206	+	0.0630501i	−0.553608	−	0.832777i	$-0.686749\pi$
$263$	−1.77102	+	1.02250i	−0.109206	+	0.0630501i	0.444402	+	0.895827i	$0.353416\pi$
$264$	5.64278	+	6.04450i	0.347289	+	0.372013i
$265$			16.2755i			0.999797i
$266$	1.33302	+	1.91356i	0.0817329	+	0.117328i
$267$	−2.40329	−	7.39657i	−0.147079	−	0.452663i
$268$	3.16240	+	14.8779i	0.193174	+	0.908814i
$269$	5.61904	+	0.590585i	0.342599	+	0.0360086i	0.274266	−	0.961654i	$-0.411565\pi$
$269$	5.61904	+	0.590585i	0.342599	+	0.0360086i	0.0683333	+	0.997663i	$0.478232\pi$
$270$	−0.443125	−	0.995275i	−0.0269677	−	0.0605705i
$271$	0.488508	+	2.29825i	0.0296748	+	0.139609i	0.990491	−	0.137577i	$-0.0439315\pi$
$271$	0.488508	+	2.29825i	0.0296748	+	0.139609i	−0.960816	+	0.277186i	$0.910598\pi$
$272$	−1.22266	+	5.75214i	−0.0741344	+	0.348775i
$273$	0.844986	−	0.613918i	0.0511409	−	0.0371560i
$274$	−8.41294			−0.508245
$275$	1.73126	−	2.47538i	0.104399	−	0.149271i
$276$	−15.5616	−	8.98450i	−0.936698	−	0.540803i
$277$	−14.3404	−	19.7378i	−0.861629	−	1.18593i	−0.981179	−	0.193102i	$-0.938145\pi$
$277$	−14.3404	−	19.7378i	−0.861629	−	1.18593i	0.119550	−	0.992828i	$-0.461855\pi$
$278$	5.99850	−	1.94903i	0.359766	−	0.116895i
$279$	23.0747	−	20.7766i	1.38145	−	1.24386i
$280$	1.07598	+	0.113090i	0.0643021	+	0.00675842i
$281$	1.60919	−	0.716459i	0.0959965	−	0.0427404i	−0.358177	−	0.933654i	$-0.616601\pi$
$281$	1.60919	−	0.716459i	0.0959965	−	0.0427404i	0.454173	+	0.890913i	$0.349935\pi$
$282$	1.58994	+	7.48007i	0.0946795	+	0.445432i
$283$	−14.0304	−	12.6330i	−0.834021	−	0.750956i	0.136842	−	0.990593i	$-0.456305\pi$
$283$	−14.0304	−	12.6330i	−0.834021	−	0.750956i	−0.970863	+	0.239637i	$0.922972\pi$
$284$	5.45810	+	7.51242i	0.323878	+	0.445780i
$285$	−19.2466	+	10.6079i	−1.14007	+	0.628361i
$286$	−1.96086	−	1.70266i	−0.115948	−	0.100681i
$287$	2.16286	−	1.24873i	0.127670	−	0.0737102i
$288$	2.93804	+	1.30810i	0.173126	+	0.0770806i
$289$	17.1978	+	3.65550i	1.01163	+	0.215030i
$290$	−14.2359	+	3.02593i	−0.835959	+	0.177689i
$291$	3.21828	−	1.43287i	0.188659	−	0.0839963i
$292$	5.23994	−	7.21216i	0.306645	−	0.422060i
$293$	−7.11667	+	21.9028i	−0.415760	+	1.27958i	0.495809	+	0.868431i	$0.334872\pi$
$293$	−7.11667	+	21.9028i	−0.415760	+	1.27958i	−0.911569	+	0.411147i	$0.865128\pi$
$294$	3.48019	−	16.3730i	0.202969	−	0.954893i
$295$	4.22593	−	0.444164i	0.246043	−	0.0258602i
$296$			3.56937i			0.207465i
$297$	−0.921137	−	1.53113i	−0.0534498	−	0.0888451i
$298$	1.41517	+	0.817048i	0.0819785	+	0.0473303i
$299$	5.15536	+	2.29531i	0.298142	+	0.132741i
$300$	0.472120	−	2.22115i	0.0272579	−	0.128238i
$301$	0.824343	−	0.175219i	0.0475143	−	0.0100995i
$302$	−0.469236	+	4.46448i	−0.0270015	+	0.256902i
$303$	17.1732	+	12.4770i	0.986572	+	0.716786i
$304$	1.42906	−	4.11798i	0.0819620	−	0.236183i
$305$	−5.29267	+	1.71969i	−0.303057	+	0.0984693i
$306$	7.69248	−	17.2776i	0.439750	−	0.987695i
$307$	5.39487	+	9.34419i	0.307901	+	0.533301i	0.977903	−	0.209059i	$-0.0670400\pi$
$307$	5.39487	+	9.34419i	0.307901	+	0.533301i	−0.670002	+	0.742360i	$0.733707\pi$
$308$	1.77417	−	0.0319409i	0.101093	−	0.00182000i
$309$	−7.52513	−	13.0339i	−0.428090	−	0.741473i
$310$	−19.4164	+	2.04075i	−1.10278	+	0.115907i
$311$	1.74238	+	5.36250i	0.0988014	+	0.304079i	0.988226	−	0.153003i	$-0.0488944\pi$
$311$	1.74238	+	5.36250i	0.0988014	+	0.304079i	−0.889424	+	0.457082i	$0.848894\pi$
$312$	−1.85664	−	0.603260i	−0.105112	−	0.0341529i
$313$	18.8148	−	8.37689i	1.06348	−	0.473490i	0.201001	−	0.979591i	$-0.435580\pi$
$313$	18.8148	−	8.37689i	1.06348	−	0.473490i	0.862474	+	0.506101i	$0.168914\pi$
$314$	1.50240	−	0.668911i	0.0847852	−	0.0377488i
$315$	−3.30921	−	1.07523i	−0.186453	−	0.0605822i
$316$	−0.0339469	−	0.104478i	−0.00190966	−	0.00587734i
$317$	−7.22415	+	0.759289i	−0.405749	+	0.0426459i	−0.305205	−	0.952287i	$-0.598725\pi$
$317$	−7.22415	+	0.759289i	−0.405749	+	0.0426459i	−0.100544	+	0.994933i	$0.532058\pi$
$318$	10.0333	+	17.3782i	0.562639	+	0.974519i
$319$	−22.5655	+	7.78374i	−1.26342	+	0.435806i
$320$	−1.01109	−	1.75126i	−0.0565217	−	0.0978984i
$321$	−15.2640	+	34.2836i	−0.851955	+	1.91352i
$322$	−3.66725	+	1.19156i	−0.204368	+	0.0664032i
$323$	−24.2164	−	8.40378i	−1.34744	−	0.467599i
$324$	6.71892	+	4.88158i	0.373273	+	0.271199i
$325$	−0.0745440	+	0.709239i	−0.00413496	+	0.0393415i
$326$	18.8389	−	4.00432i	1.04339	−	0.221779i
$327$	2.60110	−	12.2372i	0.143841	−	0.676719i
$328$	−4.26441	−	1.89864i	−0.235463	−	0.104835i
$329$	1.42116	+	0.820507i	0.0783511	+	0.0452360i
$330$	−1.44824	+	16.6587i	−0.0797232	+	0.917029i
$331$		−	28.1425i		−	1.54685i	−0.633888	−	0.773425i	$-0.718542\pi$
$331$		−	28.1425i		−	1.54685i	0.633888	−	0.773425i	$-0.281458\pi$
$332$	12.8366	−	1.34918i	0.704497	−	0.0740457i
$333$	2.38670	−	11.2285i	0.130790	−	0.615321i
$334$	3.54880	−	10.9221i	0.194182	−	0.597630i
$335$	−18.0791	+	24.8838i	−0.987767	+	1.35955i
$336$	1.21859	−	0.542552i	0.0664796	−	0.0295986i
$337$	24.3527	−	5.17632i	1.32658	−	0.281972i	0.510480	−	0.859890i	$-0.329468\pi$
$337$	24.3527	−	5.17632i	1.32658	−	0.281972i	0.816095	+	0.577917i	$0.196134\pi$
$338$	−12.1162	−	2.57538i	−0.659036	−	0.140082i
$339$	21.8123	+	9.71147i	1.18468	+	0.527455i
$340$	−10.2985	+	5.94587i	−0.558517	+	0.322460i
$341$	−31.1961	+	7.22019i	−1.68936	+	0.390995i
$342$	−7.24908	+	11.9988i	−0.391986	+	0.648823i
$343$	−4.31265	−	5.93586i	−0.232861	−	0.320506i
$344$	−1.17060	−	1.05401i	−0.0631144	−	0.0568284i
$345$	−7.55480	−	35.5425i	−0.406737	−	1.91354i
$346$	−2.77557	+	1.23576i	−0.149216	+	0.0664350i
$347$	−19.7016	−	2.07072i	−1.05764	−	0.111162i	−0.440292	−	0.897855i	$-0.645125\pi$
$347$	−19.7016	−	2.07072i	−1.05764	−	0.111162i	−0.617345	+	0.786693i	$0.711792\pi$
$348$	−13.3350	+	12.0069i	−0.714829	+	0.643635i
$349$	−16.4258	+	5.33708i	−0.879255	+	0.285687i	−0.713648	−	0.700505i	$-0.752958\pi$
$349$	−16.4258	+	5.33708i	−0.879255	+	0.285687i	−0.165607	+	0.986192i	$0.552958\pi$
$350$	−0.286420	−	0.394223i	−0.0153098	−	0.0210721i
$351$	0.365331	+	0.210924i	0.0194999	+	0.0112583i
$352$	−1.99745	−	2.64768i	−0.106464	−	0.141122i
$353$	25.9770			1.38261			0.691307	−	0.722561i	$-0.257035\pi$
$353$	25.9770			1.38261			0.691307	+	0.722561i	$0.257035\pi$
$354$	4.23843	−	3.07940i	0.225270	−	0.163668i
$355$	−3.90410	+	18.3674i	−0.207208	+	0.974839i
$356$	0.648551	+	3.05119i	0.0343731	+	0.161713i
$357$	−3.19056	−	7.16611i	−0.168862	−	0.379271i
$358$	−22.7843	−	2.39473i	−1.20419	−	0.126565i
$359$	7.04198	+	33.1299i	0.371662	+	1.74853i	0.624503	+	0.781022i	$0.285302\pi$
$359$	7.04198	+	33.1299i	0.371662	+	1.74853i	−0.252842	+	0.967508i	$0.581365\pi$
$360$	2.00970	+	6.18521i	0.105920	+	0.325989i
$361$	17.0367	+	8.41134i	0.896669	+	0.442702i
$362$		−	14.2264i		−	0.747725i
$363$	0.987171	+	27.4075i	0.0518130	+	1.43852i
$364$	−0.362797	+	0.209461i	−0.0190157	+	0.0109787i
$365$	17.9284	−	1.88435i	0.938417	−	0.0986316i
$366$	−4.59111	+	5.09894i	−0.239981	+	0.266526i
$367$	−1.22828	−	1.36414i	−0.0641157	−	0.0712077i	0.710234	−	0.703966i	$-0.248589\pi$
$367$	−1.22828	−	1.36414i	−0.0641157	−	0.0712077i	−0.774349	+	0.632758i	$0.781923\pi$
$368$	5.83073	+	4.23627i	0.303948	+	0.220831i
$369$	12.1455	+	8.82421i	0.632268	+	0.459370i
$370$	−5.36395	+	4.82972i	−0.278858	+	0.251085i
$371$	4.21200	+	0.895289i	0.218676	+	0.0464811i
$372$	−19.4738	+	14.1485i	−1.00967	+	0.733568i
$373$	29.2484			1.51442			0.757212	−	0.653170i	$-0.226561\pi$
$373$	29.2484			1.51442			0.757212	+	0.653170i	$0.226561\pi$
$374$	−15.5701	+	11.7463i	−0.805109	+	0.607385i
$375$	25.8080	−	14.9003i	1.33272	−	0.769446i
$376$	−0.320610	−	3.05040i	−0.0165342	−	0.157312i
$377$	3.77081	−	4.18790i	0.194206	−	0.215688i
$378$	−0.281947	+	0.0599296i	−0.0145018	+	0.00308244i
$379$	−4.58067	+	6.30475i	−0.235293	+	0.323853i	−0.910293	−	0.413965i	$-0.864144\pi$
$379$	−4.58067	+	6.30475i	−0.235293	+	0.323853i	0.675000	+	0.737818i	$0.264144\pi$
$380$	8.12206	−	3.42451i	0.416653	−	0.175674i
$381$	16.3625	+	5.31649i	0.838274	+	0.272372i
$382$	−8.51274	+	9.45435i	−0.435549	+	0.483727i
$383$	−7.75086	+	17.4087i	−0.396050	+	0.889543i	0.599937	+	0.800047i	$0.295192\pi$
$383$	−7.75086	+	17.4087i	−0.396050	+	0.889543i	−0.995987	+	0.0894961i	$0.971474\pi$
$384$	−2.15918	−	1.24660i	−0.110185	−	0.0636155i
$385$	2.44864	+	2.62296i	0.124794	+	0.133678i
$386$	3.44592	−	5.96850i	0.175392	−	0.303789i
$387$	2.97770	+	4.09845i	0.151365	+	0.208336i
$388$	−1.34382	+	0.436633i	−0.0682221	+	0.0221667i
$389$	11.2194	+	12.4604i	0.568845	+	0.631766i	0.957090	−	0.289790i	$-0.0935855\pi$
$389$	11.2194	+	12.4604i	0.568845	+	0.631766i	−0.388246	+	0.921556i	$0.626919\pi$
$390$	−1.60567	−	3.60639i	−0.0813061	−	0.182617i
$391$	24.9120	−	34.2884i	1.25985	−	1.73404i
$392$	−2.07466	+	6.38516i	−0.104786	+	0.322499i
$393$	36.9004	+	7.84342i	1.86138	+	0.395648i
$394$	5.36166	−	12.0425i	0.270117	−	0.606692i
$395$	0.111073	−	0.192384i	0.00558868	−	0.00967988i
$396$	4.51318	+	9.66472i	0.226796	+	0.485670i
$397$	4.24553	+	7.35348i	0.213077	+	0.369061i	0.952676	−	0.303987i	$-0.0983181\pi$
$397$	4.24553	+	7.35348i	0.213077	+	0.369061i	−0.739599	+	0.673048i	$0.764985\pi$
$398$	20.1172	−	14.6160i	1.00838	−	0.732634i
$399$	1.68655	+	5.56442i	0.0844330	+	0.278570i
$400$	−0.281447	+	0.866206i	−0.0140724	+	0.0433103i
$401$	1.82530	+	0.191847i	0.0911511	+	0.00958037i	0.149994	−	0.988687i	$-0.452074\pi$
$401$	1.82530	+	0.191847i	0.0911511	+	0.00958037i	−0.0588431	+	0.998267i	$0.518741\pi$
$402$	−3.96398	+	37.7148i	−0.197705	+	1.88104i
$403$	5.61787	−	5.05835i	0.279846	−	0.251974i
$404$	−6.32714	−	5.69698i	−0.314787	−	0.283435i
$405$	1.75548	+	16.7023i	0.0872306	+	0.829943i
$406$			3.85061i			0.191102i
$407$	−7.76169	+	8.93869i	−0.384733	+	0.443075i
$408$	−7.33084	+	12.6974i	−0.362931	+	0.628614i
$409$	−1.27342	−	12.1158i	−0.0629665	−	0.599086i	−0.979823	−	0.199869i	$-0.935949\pi$
$409$	−1.27342	−	12.1158i	−0.0629665	−	0.599086i	0.916856	−	0.399217i	$-0.130718\pi$
$410$	−2.91697	−	8.97750i	−0.144059	−	0.443367i
$411$	−19.9486	−	6.48170i	−0.983993	−	0.319719i
$412$	2.45527	+	5.51462i	0.120962	+	0.271686i
$413$	0.117515	−	1.11808i	0.00578252	−	0.0550170i
$414$	−15.5097	−	17.2253i	−0.762261	−	0.846577i
$415$	19.3967	+	17.4649i	0.952146	+	0.857316i
$416$	0.715309	+	0.318476i	0.0350709	+	0.0156146i
$417$	15.7252			0.770064
$418$	12.5334	−	7.20506i	0.613030	−	0.352411i
$419$	32.6626			1.59567			0.797836	−	0.602874i	$-0.205978\pi$
$419$	32.6626			1.59567			0.797836	+	0.602874i	$0.205978\pi$
$420$	2.46421	+	1.09714i	0.120241	+	0.0535349i
$421$	−13.4486	−	12.1092i	−0.655447	−	0.590167i	0.272828	−	0.962063i	$-0.412041\pi$
$421$	−13.4486	−	12.1092i	−0.655447	−	0.590167i	−0.928274	+	0.371896i	$0.878708\pi$
$422$	14.0837	+	15.6415i	0.685582	+	0.761416i
$423$	−1.03111	+	9.81037i	−0.0501343	+	0.476996i
$424$	−3.27362	−	7.35266i	−0.158981	−	0.357077i
$425$	5.09385	+	1.65509i	0.247088	+	0.0802838i
$426$	7.15424	+	22.0185i	0.346624	+	1.06680i
$427$	0.153905	+	1.46431i	0.00744798	+	0.0708628i
$428$	7.52605	−	13.0355i	0.363786	−	0.630095i
$429$	−3.33775	−	5.54806i	−0.161148	−	0.267863i
$430$		−	3.18533i		−	0.153610i
$431$	−3.80585	−	36.2103i	−0.183322	−	1.74419i	−0.569705	−	0.821849i	$-0.692942\pi$
$431$	−3.80585	−	36.2103i	−0.183322	−	1.74419i	0.386383	−	0.922338i	$-0.373724\pi$
$432$	0.400374	+	0.360499i	0.0192630	+	0.0173445i
$433$	−12.1934	+	10.9790i	−0.585976	+	0.527616i	−0.907920	−	0.419143i	$-0.862330\pi$
$433$	−12.1934	+	10.9790i	−0.585976	+	0.527616i	0.321944	+	0.946759i	$0.395664\pi$
$434$	−0.539931	+	5.13710i	−0.0259175	+	0.246589i
$435$	−36.0872	−	3.79291i	−1.73025	−	0.181856i
$436$	−1.55061	+	4.77228i	−0.0742606	+	0.228551i
$437$	−21.4806	+	22.9240i	−1.02756	+	1.09660i
$438$	17.9814	−	13.0643i	0.859186	−	0.624235i
$439$	15.6820	+	27.1620i	0.748461	+	1.29637i	0.948560	+	0.316597i	$0.102540\pi$
$439$	15.6820	+	27.1620i	0.748461	+	1.29637i	−0.200099	+	0.979776i	$0.564126\pi$
$440$	1.27611	−	6.58429i	0.0608363	−	0.313894i
$441$	10.7960	−	18.6993i	0.514096	−	0.890441i
$442$	1.87285	−	4.20648i	0.0890822	−	0.200082i
$443$	−8.34354	−	1.77347i	−0.396414	−	0.0842603i	0.00539163	−	0.999985i	$-0.498284\pi$
$443$	−8.34354	−	1.77347i	−0.396414	−	0.0842603i	−0.401805	+	0.915725i	$0.631617\pi$
$444$	−2.75000	+	8.46362i	−0.130509	+	0.401665i
$445$	−3.70770	+	5.10321i	−0.175762	+	0.241915i
$446$	−6.90409	−	15.5068i	−0.326918	−	0.734270i
$447$	2.72613	+	3.02768i	0.128942	+	0.143204i
$448$	−0.508834	+	0.165330i	−0.0240401	+	0.00781111i
$449$	12.3501	+	16.9984i	0.582836	+	0.802205i	0.994003	−	0.109355i	$-0.0348786\pi$
$449$	12.3501	+	16.9984i	0.582836	+	0.802205i	−0.411167	+	0.911560i	$0.634879\pi$
$450$	1.46458	−	2.53673i	0.0690409	−	0.119582i
$451$	−6.55064	−	14.0278i	−0.308457	−	0.660544i
$452$	−8.29361	−	4.78832i	−0.390099	−	0.225224i
$453$	−4.55227	+	10.2246i	−0.213884	+	0.480392i
$454$	−1.50185	+	1.66797i	−0.0704851	+	0.0782816i
$455$	−0.805674	−	0.261779i	−0.0377706	−	0.0122724i
$456$	6.56123	−	8.66348i	0.307258	−	0.405705i
$457$	−22.7887	+	31.3660i	−1.06601	+	1.46724i	−0.191964	+	0.981402i	$0.561486\pi$
$457$	−22.7887	+	31.3660i	−1.06601	+	1.46724i	−0.874049	+	0.485838i	$0.838514\pi$
$458$	−11.8221	+	2.51286i	−0.552410	+	0.117418i
$459$	2.11997	−	2.35446i	0.0989515	−	0.109897i
$460$	1.52342	+	14.4944i	0.0710298	+	0.675804i
$461$	−3.89487	+	2.24871i	−0.181402	+	0.104733i	−0.587951	−	0.808896i	$-0.700065\pi$
$461$	−3.89487	+	2.24871i	−0.181402	+	0.104733i	0.406549	+	0.913629i	$0.366732\pi$
$462$	4.23149	+	1.29116i	0.196867	+	0.0600703i
$463$	17.7507			0.824944			0.412472	−	0.910970i	$-0.364665\pi$
$463$	17.7507			0.824944			0.412472	+	0.910970i	$0.364665\pi$
$464$	5.82260	−	4.23037i	0.270308	−	0.196390i
$465$	−47.6121	−	10.1203i	−2.20796	−	0.469316i
$466$	−15.8059	+	14.2317i	−0.732194	+	0.659270i
$467$	−29.6146	−	21.5163i	−1.37040	−	0.995656i	−0.997706	−	0.0677025i	$-0.978433\pi$
$467$	−29.6146	−	21.5163i	−1.37040	−	0.995656i	−0.372697	−	0.927953i	$-0.621567\pi$
$468$	−2.03727	−	1.48017i	−0.0941730	−	0.0684207i
$469$	5.44526	+	6.04757i	0.251439	+	0.279251i
$470$	4.15025	−	4.60931i	0.191437	−	0.212612i
$471$	4.07782	−	0.428596i	0.187896	−	0.0197487i
$472$	−1.81978	+	1.05065i	−0.0837622	+	0.0483601i
$473$	−0.639527	−	5.18503i	−0.0294055	−	0.238408i
$474$		−	0.273890i		−	0.0125802i
$475$	−3.59399	−	1.68647i	−0.164904	−	0.0773807i
$476$	0.972248	+	2.99227i	0.0445629	+	0.137151i
$477$	5.38173	+	25.3190i	0.246412	+	1.15928i
$478$	22.0862	+	2.32136i	1.01020	+	0.106176i
$479$	−7.92532	−	17.8006i	−0.362117	−	0.813328i	−0.999099	−	0.0424492i	$-0.986484\pi$
$479$	−7.92532	−	17.8006i	−0.362117	−	0.813328i	0.636982	−	0.770879i	$-0.280183\pi$
$480$	−1.04823	−	4.93155i	−0.0478451	−	0.225093i
$481$	0.581077	−	2.73375i	0.0264948	−	0.124648i
$482$	4.89314	−	3.55508i	0.222877	−	0.161929i
$483$	−9.61376			−0.437441
$484$	0.755293	−	10.9740i	0.0343315	−	0.498820i
$485$	−2.47449	−	1.42865i	−0.112361	−	0.0648715i
$486$	13.1208	+	18.0592i	0.595172	+	0.819184i
$487$	−19.8862	+	6.46143i	−0.901131	+	0.292795i	−0.722704	−	0.691158i	$-0.757101\pi$
$487$	−19.8862	+	6.46143i	−0.901131	+	0.292795i	−0.178427	+	0.983953i	$0.557101\pi$
$488$	2.04513	−	1.84145i	0.0925788	−	0.0833584i
$489$	47.7555	+	5.01930i	2.15958	+	0.226981i
$490$	−12.4027	+	5.52203i	−0.560296	+	0.249460i
$491$	−8.94165	−	42.0671i	−0.403531	−	1.89846i	−0.437841	−	0.899053i	$-0.644257\pi$
$491$	−8.94165	−	42.0671i	−0.403531	−	1.89846i	0.0343098	−	0.999411i	$-0.489077\pi$
$492$	−8.64890	−	7.78750i	−0.389923	−	0.351088i
$493$	−24.8773	−	34.2407i	−1.12042	−	1.54212i
$494$	−1.76489	+	2.92129i	−0.0794063	+	0.131435i
$495$	−8.41708	+	19.8597i	−0.378320	+	0.892625i
$496$	8.36113	−	4.82730i	0.375426	−	0.216752i
$497$	4.53860	+	2.02072i	0.203584	+	0.0906415i
$498$	31.4773	+	6.69070i	1.41053	+	0.299818i
$499$	0.936023	−	0.198958i	0.0419021	−	0.00890657i	−0.186913	−	0.982376i	$-0.559848\pi$
$499$	0.936023	−	0.198958i	0.0419021	−	0.00890657i	0.228815	+	0.973470i	$0.426515\pi$
$500$	−10.9193	+	4.86159i	−0.488326	+	0.217417i
$501$	16.8297	−	23.1641i	0.751896	−	1.03490i
$502$	3.76034	−	11.5731i	0.167832	−	0.516534i
$503$	−2.87583	+	13.5297i	−0.128227	+	0.603260i	0.866366	+	0.499409i	$0.166450\pi$
$503$	−2.87583	+	13.5297i	−0.128227	+	0.603260i	−0.994593	+	0.103850i	$0.966884\pi$
$504$	1.71124	−	0.179859i	0.0762249	−	0.00801156i
$505$		−	17.2169i		−	0.766140i
$506$	5.38988	+	23.2879i	0.239609	+	1.03527i
$507$	−26.7456	−	15.4416i	−1.18781	−	0.685784i
$508$	−6.30397	−	2.80671i	−0.279693	−	0.124527i
$509$	0.758385	−	3.56792i	0.0336148	−	0.158145i	−0.958139	−	0.286304i	$-0.907573\pi$
$509$	0.758385	−	3.56792i	0.0336148	−	0.158145i	0.991754	+	0.128159i	$0.0409066\pi$
$510$	−29.0007	+	6.16428i	−1.28417	+	0.272959i
$511$	0.498554	−	4.74342i	0.0220547	−	0.209837i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−1.77606	+	1.53640i	−0.0784150	+	0.0678337i
$514$	5.24601	−	1.70453i	0.231391	−	0.0751836i
$515$	−4.96500	+	11.1516i	−0.218784	+	0.491397i
$516$	−1.96364	−	3.40113i	−0.0864446	−	0.149726i
$517$	5.83029	−	8.33624i	0.256416	−	0.366627i
$518$	0.954840	+	1.65383i	0.0419533	+	0.0726652i
$519$	−7.53347	+	0.791799i	−0.330682	+	0.0347561i
$520$	0.489290	+	1.50588i	0.0214568	+	0.0660371i
$521$	16.5740	+	5.38522i	0.726120	+	0.235931i	0.648675	−	0.761066i	$-0.275324\pi$
$521$	16.5740	+	5.38522i	0.726120	+	0.235931i	0.0774456	+	0.996997i	$0.475324\pi$
$522$	−21.1455	+	9.41458i	−0.925513	+	0.412065i
$523$	35.8160	−	15.9463i	1.56612	−	0.697283i	0.573577	−	0.819152i	$-0.305555\pi$
$523$	35.8160	−	15.9463i	1.56612	−	0.697283i	0.992546	+	0.121868i	$0.0388886\pi$
$524$	−14.3904	−	4.67574i	−0.628649	−	0.204261i
$525$	−0.375427	−	1.15544i	−0.0163850	−	0.0504277i
$526$	2.03380	−	0.213761i	0.0886778	−	0.00932042i
$527$	−28.3877	−	49.1689i	−1.23659	−	2.14183i
$528$	−2.69642	−	7.81705i	−0.117347	−	0.340194i
$529$	−14.4717	−	25.0657i	−0.629204	−	1.08981i
$530$	6.61985	−	14.8684i	0.287548	−	0.645843i
$531$	6.42721	−	2.08833i	0.278917	−	0.0906257i
$532$	−0.439461	−	2.29032i	−0.0190531	−	0.0992978i
$533$	2.95699	+	2.14838i	0.128081	+	0.0930567i
$534$	−0.812940	+	7.73461i	−0.0351794	+	0.334709i
$535$	29.7729	−	6.32843i	1.28720	−	0.273602i
$536$	3.16240	−	14.8779i	0.136595	−	0.642629i
$537$	−52.1808	−	23.2324i	−2.25177	−	1.00255i
$538$	−4.89304	−	2.82500i	−0.210954	−	0.121794i
$539$	−19.0803	+	11.4788i	−0.821845	+	0.494427i
$540$			1.08946i			0.0468831i
$541$	33.3929	−	3.50973i	1.43567	−	0.150895i	0.645490	−	0.763769i	$-0.276653\pi$
$541$	33.3929	−	3.50973i	1.43567	−	0.150895i	0.790181	+	0.612874i	$0.209987\pi$
$542$	0.488508	−	2.29825i	0.0209832	−	0.0987183i
$543$	10.9607	−	33.7335i	0.470367	−	1.44764i
$544$	3.45656	−	4.75754i	0.148199	−	0.203978i
$545$	−9.26979	+	4.12718i	−0.397074	+	0.176789i
$546$	−1.02164	+	0.217155i	−0.0437220	+	0.00929339i
$547$	21.2815	+	4.52352i	0.909930	+	0.193412i	0.639018	−	0.769192i	$-0.279341\pi$
$547$	21.2815	+	4.52352i	0.909930	+	0.193412i	0.270913	+	0.962604i	$0.412674\pi$
$548$	7.68561	+	3.42185i	0.328313	+	0.146174i
$549$	−7.66491	+	4.42534i	−0.327130	+	0.188869i
$550$	−2.58841	+	1.55721i	−0.110370	+	0.0663995i
$551$	15.1430	+	27.4748i	0.645114	+	1.17047i
$552$	10.5619	+	14.5372i	0.449545	+	0.618745i
$553$	−0.0436778	−	0.0393277i	−0.00185737	−	0.00167238i
$554$	5.07248	+	23.8641i	0.215509	+	1.01389i
$555$	−16.4399	+	7.31953i	−0.697836	+	0.310697i
$556$	−6.27264	−	0.659282i	−0.266019	−	0.0279598i
$557$	−0.425410	+	0.383041i	−0.0180252	+	0.0162300i	−0.678094	−	0.734975i	$-0.737194\pi$
$557$	−0.425410	+	0.383041i	−0.0180252	+	0.0162300i	0.660069	+	0.751205i	$0.270527\pi$
$558$	−29.5304	+	9.59500i	−1.25012	+	0.406189i
$559$	0.724964	+	0.997827i	0.0306627	+	0.0422036i
$560$	−0.936958	−	0.540953i	−0.0395937	−	0.0228594i
$561$	−45.9693	+	15.8567i	−1.94083	+	0.669470i
$562$	−1.76148			−0.0743036
$563$	−8.47940	+	6.16064i	−0.357364	+	0.259640i	−0.751952	−	0.659218i	$-0.770887\pi$
$563$	−8.47940	+	6.16064i	−0.357364	+	0.259640i	0.394588	+	0.918858i	$0.370887\pi$
$564$	1.58994	−	7.48007i	0.0669485	−	0.314968i
$565$	−4.02635	−	18.9425i	−0.169390	−	0.796917i
$566$	7.67910	+	17.2475i	0.322776	+	0.724968i
$567$	4.41901	+	0.464457i	0.185581	+	0.0195054i
$568$	−1.93064	−	9.08295i	−0.0810079	−	0.381112i
$569$	4.39530	+	13.5274i	0.184261	+	0.567096i	0.999935	−	0.0114155i	$-0.00363375\pi$
$569$	4.39530	+	13.5274i	0.184261	+	0.567096i	−0.815674	+	0.578512i	$0.803634\pi$
$570$	21.8973	−	1.86255i	0.917176	−	0.0780136i
$571$		−	23.9732i		−	1.00325i	−0.865086	−	0.501623i	$-0.832736\pi$
$571$		−	23.9732i		−	1.00325i	0.865086	−	0.501623i	$-0.167264\pi$
$572$	1.09880	+	2.35301i	0.0459431	+	0.0983845i
$573$	−27.4693	+	15.8594i	−1.14755	+	0.662536i
$574$	−2.48378	+	0.261056i	−0.103671	+	0.0108962i
$575$	4.39229	−	4.87813i	0.183171	−	0.203432i
$576$	−2.15198	−	2.39002i	−0.0896660	−	0.0995842i
$577$	−30.7670	−	22.3536i	−1.28085	−	0.930591i	−0.281270	−	0.959629i	$-0.590756\pi$
$577$	−30.7670	−	22.3536i	−1.28085	−	0.930591i	−0.999578	+	0.0290377i	$0.990756\pi$
$578$	−14.2241	−	10.3344i	−0.591646	−	0.429856i
$579$	12.7693	−	11.4975i	0.530674	−	0.477821i
$580$	14.2359	+	3.02593i	0.591113	+	0.125645i
$581$	5.58678	−	4.05903i	0.231779	−	0.168397i
$582$	−3.52284			−0.146027
$583$	7.79053	−	25.5317i	0.322651	−	1.05742i
$584$	−7.72038	+	4.45736i	−0.319472	+	0.184447i
$585$	−0.532288	−	5.06438i	−0.0220074	−	0.209386i
$586$	15.4101	−	17.1146i	0.636585	−	0.706999i
$587$	−8.63930	+	1.83634i	−0.356582	+	0.0757939i	−0.382720	−	0.923864i	$-0.625013\pi$
$587$	−8.63930	+	1.83634i	−0.356582	+	0.0757939i	0.0261376	+	0.999658i	$0.491679\pi$
$588$	−9.83881	+	13.5420i	−0.405746	+	0.558461i
$589$	16.3498	+	38.7776i	0.673682	+	1.59780i
$590$	−4.04124	−	1.31308i	−0.166375	−	0.0540586i
$591$	21.9915	−	24.4241i	0.904611	−	1.00467i
$592$	1.45179	−	3.26078i	0.0596683	−	0.134017i
$593$	4.55510	+	2.62989i	0.187055	+	0.107996i	0.590603	−	0.806962i	$-0.298890\pi$
$593$	4.55510	+	2.62989i	0.187055	+	0.107996i	−0.403548	+	0.914958i	$0.632223\pi$
$594$	0.218735	+	1.77342i	0.00897479	+	0.0727641i
$595$	−3.18115	+	5.50992i	−0.130415	+	0.225885i
$596$	−0.960498	−	1.32201i	−0.0393435	−	0.0541517i
$597$	58.9623	−	19.1580i	2.41317	−	0.784086i
$598$	−3.77607	−	4.19375i	−0.154415	−	0.171495i
$599$	−13.4671	−	30.2477i	−0.550252	−	1.23589i	−0.947964	−	0.318376i	$-0.896863\pi$
$599$	−13.4671	−	30.2477i	−0.550252	−	1.23589i	0.397713	−	0.917510i	$-0.369804\pi$
$600$	−1.33473	+	1.83709i	−0.0544900	+	0.0749990i
$601$	−0.666640	+	2.05171i	−0.0271928	+	0.0836908i	−0.963732	−	0.266872i	$-0.914010\pi$
$601$	−0.666640	+	2.05171i	−0.0271928	+	0.0836908i	0.936539	+	0.350563i	$0.114010\pi$
$602$	−0.824343	−	0.175219i	−0.0335977	−	0.00714141i
$603$	−19.8966	+	44.6886i	−0.810254	+	1.81986i
$604$	2.24453	−	3.88765i	0.0913288	−	0.158186i
$605$	17.5135	−	13.7140i	0.712024	−	0.557552i
$606$	−10.6136	−	18.3833i	−0.431148	−	0.746770i
$607$	−6.12360	+	4.44906i	−0.248549	+	0.180582i	−0.705084	−	0.709124i	$-0.749091\pi$
$607$	−6.12360	+	4.44906i	−0.248549	+	0.180582i	0.456534	+	0.889706i	$0.349091\pi$
$608$	−2.98044	+	3.18072i	−0.120873	+	0.128995i
$609$	−2.96668	+	9.13049i	−0.120216	+	0.369986i
$610$	5.53455	+	0.581705i	0.224088	+	0.0235525i
$611$	−0.251039	+	2.38847i	−0.0101559	+	0.0966273i
$612$	−14.0549	+	12.6551i	−0.568134	+	0.511550i
$613$	22.6479	+	20.3922i	0.914739	+	0.823635i	0.984761	−	0.173911i	$-0.0556404\pi$
$613$	22.6479	+	20.3922i	0.914739	+	0.823635i	−0.0700225	+	0.997545i	$0.522307\pi$
$614$	−1.12783	−	10.7306i	−0.0455157	−	0.433053i
$615$		−	23.5346i		−	0.949008i
$616$	−1.63378	−	0.692441i	−0.0658268	−	0.0278992i
$617$	−3.04717	+	5.27784i	−0.122674	+	0.212478i	−0.920821	−	0.389984i	$-0.872480\pi$
$617$	−3.04717	+	5.27784i	−0.122674	+	0.212478i	0.798147	+	0.602463i	$0.205814\pi$
$618$	1.57318	+	14.9678i	0.0632826	+	0.602094i
$619$	7.00001	+	21.5438i	0.281354	+	0.865919i	0.987468	+	0.157821i	$0.0504468\pi$
$619$	7.00001	+	21.5438i	0.281354	+	0.865919i	−0.706114	+	0.708099i	$0.749553\pi$
$620$	18.5678	+	6.03305i	0.745702	+	0.242293i
$621$	−1.57932	−	3.54722i	−0.0633761	−	0.142345i
$622$	0.589380	−	5.60758i	0.0236320	−	0.224843i
$623$	1.11672	+	1.24025i	0.0447406	+	0.0496895i
$624$	1.45076	+	1.30627i	0.0580769	+	0.0522927i
$625$	−17.9206	−	7.97877i	−0.716825	−	0.319151i
$626$	−20.5954			−0.823156
$627$	35.2702	−	7.42821i	1.40855	−	0.296654i
$628$	−1.64458			−0.0656259
$629$	−19.1755	−	8.53747i	−0.764576	−	0.340411i
$630$	2.58578	+	2.32825i	0.103020	+	0.0927595i
$631$	30.1541	+	33.4895i	1.20042	+	1.33320i	0.928705	+	0.370818i	$0.120923\pi$
$631$	30.1541	+	33.4895i	1.20042	+	1.33320i	0.271711	+	0.962379i	$0.412411\pi$
$632$	−0.0114829	+	0.109253i	−0.000456766	+	0.00434584i
$633$	21.3440	+	47.9395i	0.848350	+	1.90542i
$634$	6.90842	+	2.24468i	0.274368	+	0.0891477i
$635$	−4.31207	−	13.2712i	−0.171119	−	0.526651i
$636$	−2.09753	−	19.9566i	−0.0831724	−	0.791333i
$637$	2.62845	−	4.55260i	0.104143	−	0.180381i
$638$	23.7805	+	2.06739i	0.941479	+	0.0818488i
$639$			29.8642i			1.18141i
$640$	0.211376	+	2.01110i	0.00835535	+	0.0794959i
$641$	−32.5023	−	29.2652i	−1.28376	−	1.15590i	−0.979085	−	0.203449i	$-0.934785\pi$
$641$	−32.5023	−	29.2652i	−1.28376	−	1.15590i	−0.304677	−	0.952456i	$-0.598549\pi$
$642$	27.8888	−	25.1112i	1.10068	−	0.991059i
$643$	−2.58220	+	24.5680i	−0.101832	+	0.968866i	0.817645	+	0.575722i	$0.195279\pi$
$643$	−2.58220	+	24.5680i	−0.101832	+	0.968866i	−0.919477	+	0.393143i	$0.871388\pi$
$644$	3.83486	+	0.403060i	0.151114	+	0.0158828i
$645$	2.45412	−	7.55299i	0.0966307	−	0.297399i
$646$	18.7047	+	17.5269i	0.735925	+	0.689588i
$647$	3.69780	−	2.68661i	0.145376	−	0.105622i	−0.512720	−	0.858556i	$-0.671362\pi$
$647$	3.69780	−	2.68661i	0.145376	−	0.105622i	0.658096	+	0.752934i	$0.271362\pi$
$648$	−4.15252	−	7.19237i	−0.163126	−	0.282543i
$649$	−6.84191	−	1.32604i	−0.268568	−	0.0520517i
$650$	0.356573	−	0.617602i	0.0139859	−	0.0242244i
$651$	−5.23813	+	11.7650i	−0.205298	+	0.461108i
$652$	−18.8389	−	4.00432i	−0.737787	−	0.156821i
$653$	5.33179	−	16.4096i	0.208649	−	0.642156i	−0.790895	−	0.611952i	$-0.790384\pi$
$653$	5.33179	−	16.4096i	0.208649	−	0.642156i	0.999544	−	0.0302036i	$-0.00961557\pi$
$654$	−7.35355	+	10.1213i	−0.287546	+	0.395774i
$655$	−12.4452	−	27.9523i	−0.486273	−	1.09219i
$656$	3.12349	+	3.46898i	0.121952	+	0.135441i
$657$	27.2673	−	8.85969i	1.06380	−	0.345649i
$658$	−0.964564	−	1.32761i	−0.0376026	−	0.0517556i
$659$	−3.83756	+	6.64684i	−0.149490	+	0.258924i	−0.931039	−	0.364919i	$-0.881097\pi$
$659$	−3.83756	+	6.64684i	−0.149490	+	0.258924i	0.781549	+	0.623844i	$0.214430\pi$
$660$	8.09872	−	14.6294i	0.315242	−	0.569448i
$661$	−37.9489	−	21.9098i	−1.47604	−	0.852193i	−0.476408	−	0.879225i	$-0.658061\pi$
$661$	−37.9489	−	21.9098i	−1.47604	−	0.852193i	−0.999635	+	0.0270312i	$0.991395\pi$
$662$	−11.4466	+	25.7094i	−0.444883	+	0.999225i
$663$	7.68171	−	8.53141i	0.298333	−	0.331332i
$664$	−12.2755	−	3.98856i	−0.476383	−	0.154786i
$665$	2.84719	−	3.75944i	0.110409	−	0.145785i
$666$	−6.74742	+	9.28703i	−0.261457	+	0.359865i
$667$	−50.7375	+	10.7846i	−1.96456	+	0.417581i
$668$	−7.68441	+	8.53440i	−0.297319	+	0.330206i
$669$	−4.42371	−	42.0888i	−0.171030	−	1.62725i
$670$	26.6372	−	15.3790i	1.02909	−	0.594143i
$671$	9.12587	−	0.164296i	0.352300	−	0.00634256i
$672$	−1.33392			−0.0514569
$673$	0.167797	−	0.121912i	0.00646811	−	0.00469935i	−0.584547	−	0.811360i	$-0.698728\pi$
$673$	0.167797	−	0.121912i	0.00646811	−	0.00469935i	0.591015	+	0.806661i	$0.298728\pi$
$674$	−24.3527	−	5.17632i	−0.938031	−	0.199385i
$675$	0.364654	−	0.328336i	0.0140355	−	0.0126377i
$676$	10.0212	+	7.28084i	0.385431	+	0.280032i
$677$	39.0396	+	28.3639i	1.50041	+	1.09011i	0.970217	+	0.242238i	$0.0778815\pi$
$677$	39.0396	+	28.3639i	1.50041	+	1.09011i	0.530196	+	0.847875i	$0.322118\pi$
$678$	−15.9765	−	17.7437i	−0.613575	−	0.681444i
$679$	−0.505842	+	0.561795i	−0.0194124	+	0.0215597i
$680$	11.8266	−	1.24302i	0.453529	−	0.0476678i
$681$	−4.84622	+	2.79797i	−0.185708	+	0.107218i
$682$	31.4357	+	6.09261i	1.20374	+	0.233298i
$683$			7.60664i			0.291060i	0.989354	+	0.145530i	$0.0464887\pi$
$683$			7.60664i			0.291060i	−0.989354	+	0.145530i	$0.953511\pi$
$684$	11.5027	−	8.01302i	0.439818	−	0.306385i
$685$	5.25715	+	16.1798i	0.200865	+	0.618200i
$686$	1.52547	+	7.17679i	0.0582429	+	0.274011i
$687$	−29.9684	−	3.14980i	−1.14336	−	0.120172i
$688$	0.640689	+	1.43901i	0.0244260	+	0.0548618i
$689$	1.31026	+	6.16428i	0.0499169	+	0.234840i
$690$	−7.55480	+	35.5425i	−0.287606	+	1.35308i
$691$	11.5270	−	8.37488i	0.438509	−	0.318595i	−0.346533	−	0.938038i	$-0.612641\pi$
$691$	11.5270	−	8.37488i	0.438509	−	0.318595i	0.785042	+	0.619442i	$0.212641\pi$
$692$	3.03824			0.115496
$693$	4.67655	+	3.27073i	0.177647	+	0.124245i
$694$	17.1561	+	9.90505i	0.651235	+	0.375991i
$695$	−7.49679	−	10.3184i	−0.284369	−	0.391401i
$696$	17.0657	−	5.54499i	0.646874	−	0.210182i
$697$	20.3999	−	18.3681i	0.772700	−	0.695742i
$698$	17.1765	+	1.80533i	0.650141	+	0.0683326i
$699$	−48.4434	+	21.5684i	−1.83230	+	0.815791i
$700$	0.101313	+	0.476638i	0.00382925	+	0.0180152i
$701$	15.3813	+	13.8494i	0.580943	+	0.523084i	0.906371	−	0.422483i	$-0.138842\pi$
$701$	15.3813	+	13.8494i	0.580943	+	0.523084i	−0.325427	+	0.945567i	$0.605508\pi$
$702$	−0.247956	−	0.341282i	−0.00935850	−	0.0128809i
$703$	13.3169	+	8.04537i	0.502255	+	0.303437i
$704$	0.747849	+	3.23121i	0.0281856	+	0.121781i
$705$	13.3922	−	7.73199i	0.504380	−	0.291204i
$706$	−23.7311	−	10.5658i	−0.893133	−	0.397649i
$707$	−4.45561	−	0.947070i	−0.167571	−	0.0356182i
$708$	−5.12450	+	1.08925i	−0.192590	+	0.0409364i
$709$	13.4331	−	5.98081i	0.504492	−	0.224614i	−0.138679	−	0.990337i	$-0.544285\pi$
$709$	13.4331	−	5.98081i	0.504492	−	0.224614i	0.643170	+	0.765723i	$0.277619\pi$
$710$	11.0373	−	15.1915i	0.414221	−	0.570126i
$711$	0.109176	−	0.336010i	0.00409443	−	0.0126014i
$712$	0.648551	−	3.05119i	0.0243055	−	0.114348i
$713$	−69.2012	+	7.27334i	−2.59161	+	0.272389i
$714$			7.84428i			0.293565i
$715$	−2.04926	+	4.83512i	−0.0766379	+	0.180823i
$716$	19.8405	+	11.4549i	0.741475	+	0.428091i
$717$	50.5820	+	22.5206i	1.88902	+	0.841046i
$718$	7.04198	−	33.1299i	0.262804	−	1.23640i
$719$	−10.8321	+	2.30243i	−0.403969	+	0.0858663i	−0.405415	−	0.914133i	$-0.632873\pi$
$719$	−10.8321	+	2.30243i	−0.403969	+	0.0858663i	0.00144606	+	0.999999i	$0.499540\pi$
$720$	0.679803	−	6.46789i	0.0253347	−	0.241044i
$721$	2.61284	+	1.89834i	0.0973072	+	0.0706978i
$722$	−12.1426	−	14.6136i	−0.451901	−	0.543862i
$723$	14.3415	−	4.65984i	0.533367	−	0.173301i
$724$	−5.78641	+	12.9965i	−0.215050	+	0.483011i
$725$	−3.27751	−	5.67682i	−0.121724	−	0.210832i
$726$	10.2458	−	25.4395i	0.380258	−	0.944150i
$727$	7.62026	+	13.1987i	0.282620	+	0.489512i	0.972029	−	0.234860i	$-0.0754632\pi$
$727$	7.62026	+	13.1987i	0.282620	+	0.489512i	−0.689409	+	0.724372i	$0.742130\pi$
$728$	0.416627	−	0.0437893i	0.0154412	−	0.00162294i
$729$	9.49901	+	29.2349i	0.351815	+	1.08278i
$730$	−17.1449	−	5.57071i	−0.634560	−	0.206181i
$731$	8.46231	−	3.76766i	0.312990	−	0.139352i
$732$	6.26812	−	2.79074i	0.231676	−	0.103149i
$733$	42.7671	+	13.8959i	1.57964	+	0.513256i	0.961964	−	0.273177i	$-0.0880743\pi$
$733$	42.7671	+	13.8959i	1.57964	+	0.513256i	0.617676	+	0.786433i	$0.288074\pi$
$734$	0.567243	+	1.74579i	0.0209373	+	0.0644384i
$735$	−33.6634	+	3.53817i	−1.24169	+	0.130507i
$736$	−3.60359	−	6.24160i	−0.132830	−	0.230068i
$737$	40.2721	−	30.3818i	1.48344	−	1.11913i
$738$	−7.50632	−	13.0013i	−0.276311	−	0.478585i
$739$	−21.5249	+	48.3457i	−0.791805	+	1.77842i	−0.186457	+	0.982463i	$0.559700\pi$
$739$	−21.5249	+	48.3457i	−0.791805	+	1.77842i	−0.605348	+	0.795961i	$0.706966\pi$
$740$	6.86464	−	2.23046i	0.252349	−	0.0819932i
$741$	−6.43557	+	5.56716i	−0.236417	+	0.204515i
$742$	−3.48371	−	2.53106i	−0.127891	−	0.0929182i
$743$	4.85126	−	46.1567i	0.177975	−	1.69332i	−0.432776	−	0.901501i	$-0.642466\pi$
$743$	4.85126	−	46.1567i	0.177975	−	1.69332i	0.610752	−	0.791822i	$-0.290867\pi$
$744$	23.5449	−	5.00463i	0.863199	−	0.183479i
$745$	0.687032	−	3.23223i	0.0251709	−	0.118420i
$746$	−26.7197	−	11.8964i	−0.978278	−	0.435558i
$747$	35.9495	+	20.7555i	1.31532	+	0.759402i
$748$	19.0016	−	4.39784i	0.694768	−	0.160801i
$749$		−	8.05317i		−	0.294256i
$750$	−29.6373	+	3.11500i	−1.08220	+	0.113744i
$751$	−2.75120	+	12.9434i	−0.100393	+	0.472310i	0.899016	+	0.437916i	$0.144283\pi$
$751$	−2.75120	+	12.9434i	−0.100393	+	0.472310i	−0.999408	+	0.0343938i	$0.989050\pi$
$752$	−0.947818	+	2.91709i	−0.0345634	+	0.106375i
$753$	17.8329	−	24.5449i	0.649867	−	0.894465i
$754$	−5.14818	+	2.29212i	−0.187486	+	0.0834739i
$755$	8.87934	−	1.88736i	0.323152	−	0.0686882i
$756$	0.281947	+	0.0599296i	0.0102543	+	0.00217962i
$757$	−17.7343	−	7.89583i	−0.644565	−	0.286979i	0.0583032	−	0.998299i	$-0.481431\pi$
$757$	−17.7343	−	7.89583i	−0.644565	−	0.286979i	−0.702868	+	0.711320i	$0.748098\pi$
$758$	6.74902	−	3.89655i	0.245135	−	0.141529i
$759$	−5.16163	+	59.3725i	−0.187355	+	2.15508i
$760$	−8.81274	−	0.175093i	−0.319672	−	0.00635129i
$761$	−19.0807	−	26.2623i	−0.691674	−	0.952007i	−1.00000		0.000726411i	$-0.999769\pi$
$761$	−19.0807	−	26.2623i	−0.691674	−	0.952007i	0.308326	−	0.951281i	$-0.400231\pi$
$762$	−12.7854	−	11.5121i	−0.463168	−	0.417038i
$763$	0.558172	+	2.62599i	0.0202072	+	0.0950673i
$764$	11.6222	−	5.17454i	0.420477	−	0.187208i
$765$	−38.0354	−	3.99768i	−1.37517	−	0.144536i
$766$	14.1615	−	12.7511i	0.511677	−	0.460716i
$767$	1.56480	−	0.508434i	0.0565016	−	0.0183585i
$768$	1.46547	+	2.01705i	0.0528806	+	0.0727840i
$769$	24.7311	+	14.2785i	0.891826	+	0.514896i	0.874539	−	0.484955i	$-0.161164\pi$
$769$	24.7311	+	14.2785i	0.891826	+	0.514896i	0.0172865	+	0.999851i	$0.494497\pi$
$770$	−1.17009	−	3.39214i	−0.0421670	−	0.122244i
$771$	13.7525			0.495284
$772$	−5.57561	+	4.05092i	−0.200671	+	0.145796i
$773$	−9.98219	+	46.9625i	−0.359034	+	1.68912i	0.313928	+	0.949447i	$0.398355\pi$
$773$	−9.98219	+	46.9625i	−0.359034	+	1.68912i	−0.672962	+	0.739677i	$0.734978\pi$
$774$	−1.05327	−	4.95526i	−0.0378591	−	0.178113i
$775$	−3.57654	−	8.03303i	−0.128473	−	0.288555i
$776$	1.40524	+	0.147696i	0.0504450	+	0.00530198i
$777$	0.989916	+	4.65719i	0.0355130	+	0.167076i
$778$	−5.18131	−	15.9464i	−0.185759	−	0.571708i
$779$	−16.6956	+	11.6305i	−0.598182	+	0.416704i
$780$			3.94768i			0.141350i
$781$	14.9163	−	26.9445i	0.533746	−	0.964149i
$782$	−36.7046	+	21.1914i	−1.31255	+	0.757804i
$783$	−3.85626	+	0.405310i	−0.137812	+	0.0144846i
$784$	4.49238	−	4.98929i	0.160442	−	0.178189i
$785$	−2.22529	−	2.47143i	−0.0794239	−	0.0882091i
$786$	−30.5200	−	22.1741i	−1.08861	−	0.790922i
$787$	−6.48584	−	4.71224i	−0.231195	−	0.167973i	0.466156	−	0.884702i	$-0.345638\pi$
$787$	−6.48584	−	4.71224i	−0.231195	−	0.167973i	−0.697352	+	0.716729i	$0.745638\pi$
$788$	−9.79624	+	8.82057i	−0.348977	+	0.314220i
$789$	4.98720	+	1.06006i	0.177549	+	0.0377392i
$790$	−0.179720	+	0.130574i	−0.00639414	+	0.00464561i
$791$	−5.12369			−0.182177
$792$	−0.192002	−	10.6648i	−0.00682250	−	0.378958i
$793$	−1.86613	+	1.07741i	−0.0662683	+	0.0382600i
$794$	−0.887558	−	8.44455i	−0.0314983	−	0.299686i
$795$	27.1522	−	30.1555i	0.962988	−	1.06951i
$796$	−24.3228	+	5.16998i	−0.862100	+	0.183245i
$797$	22.9925	−	31.6465i	0.814436	−	1.12098i	−0.176187	−	0.984357i	$-0.556376\pi$
$797$	22.9925	−	31.6465i	0.814436	−	1.12098i	0.990624	−	0.136619i	$-0.0436236\pi$
$798$	0.722516	−	5.76934i	0.0255768	−	0.204232i
$799$	17.1543	+	5.57378i	0.606877	+	0.197186i
$800$	0.609432	−	0.676843i	0.0215467	−	0.0239300i
$801$	−4.08044	+	9.16481i	−0.144175	+	0.323823i
$802$	−1.58946	−	0.917677i	−0.0561259	−	0.0324043i
$803$	−29.0267	−	5.62570i	−1.02433	−	0.198527i
$804$	18.9612	−	32.8418i	0.668712	−	1.15824i
$805$	4.58325	+	6.30830i	0.161538	+	0.222338i
$806$	−7.18959	+	2.33604i	−0.253243	+	0.0822835i
$807$	−9.42579	−	10.4684i	−0.331803	−	0.368505i
$808$	3.46296	+	7.77793i	0.121826	+	0.273627i
$809$	14.4770	−	19.9259i	0.508986	−	0.700559i	−0.474762	−	0.880114i	$-0.657466\pi$
$809$	14.4770	−	19.9259i	0.508986	−	0.700559i	0.983748	+	0.179555i	$0.0574659\pi$
$810$	5.18972	−	15.9723i	0.182348	−	0.561210i
$811$	−16.3944	−	3.48473i	−0.575684	−	0.122365i	−0.0891365	−	0.996019i	$-0.528411\pi$
$811$	−16.3944	−	3.48473i	−0.575684	−	0.122365i	−0.486548	+	0.873654i	$0.661744\pi$
$812$	1.56618	−	3.51770i	0.0549622	−	0.123447i
$813$	2.92901	−	5.07320i	0.102725	−	0.177925i
$814$	10.7264	−	5.00894i	0.375958	−	0.175563i
$815$	−19.4733	−	33.7288i	−0.682121	−	1.18147i
$816$	11.8615	−	8.61792i	0.415237	−	0.301687i
$817$	−6.57092	+	1.99161i	−0.229887	+	0.0696777i
$818$	−3.76460	+	11.5862i	−0.131626	+	0.405104i
$819$	−1.33991	−	0.140830i	−0.0468202	−	0.00492101i
$820$	−0.986696	+	9.38779i	−0.0344569	+	0.327836i
$821$	−36.1123	+	32.5156i	−1.26033	+	1.13480i	−0.275493	+	0.961303i	$0.588841\pi$
$821$	−36.1123	+	32.5156i	−1.26033	+	1.13480i	−0.984834	+	0.173501i	$0.944492\pi$
$822$	15.5876	+	14.0352i	0.543681	+	0.489533i
$823$	0.0966811	+	0.919860i	0.00337009	+	0.0320643i	0.996078	−	0.0884827i	$-0.0282018\pi$
$823$	0.0966811	+	0.919860i	0.00337009	+	0.0320643i	−0.992708	+	0.120547i	$0.961535\pi$
$824$		−	6.03650i		−	0.210292i
$825$	−7.33734	+	1.69819i	−0.255453	+	0.0591235i
$826$	−0.562118	+	0.973618i	−0.0195586	+	0.0338765i
$827$	5.34526	+	50.8567i	0.185873	+	1.76846i	0.548139	+	0.836387i	$0.315337\pi$
$827$	5.34526	+	50.8567i	0.185873	+	1.76846i	−0.362266	+	0.932075i	$0.617997\pi$
$828$	7.16268	+	22.0445i	0.248920	+	0.766098i
$829$	9.60727	+	3.12159i	0.333674	+	0.108417i	0.471062	−	0.882100i	$-0.343871\pi$
$829$	9.60727	+	3.12159i	0.333674	+	0.108417i	−0.137388	+	0.990517i	$0.543871\pi$
$830$	−10.6162	−	23.8443i	−0.368492	−	0.827647i
$831$	−6.35821	+	60.4943i	−0.220564	+	2.09852i
$832$	−0.523931	−	0.581885i	−0.0181641	−	0.0201732i
$833$	−29.3403	−	26.4181i	−1.01658	−	0.915333i
$834$	−14.3656	−	6.39600i	−0.497442	−	0.221475i
$835$	−23.2231			−0.803667
$836$	−14.3804	+	1.48434i	−0.497358	+	0.0513371i
$837$	−5.20148			−0.179790
$838$	−29.8388	−	13.2851i	−1.03076	−	0.458925i
$839$	8.33636	+	7.50609i	0.287803	+	0.259139i	0.800367	−	0.599510i	$-0.204638\pi$
$839$	8.33636	+	7.50609i	0.287803	+	0.259139i	−0.512564	+	0.858649i	$0.671304\pi$
$840$	−1.80493	−	2.00457i	−0.0622758	−	0.0691643i
$841$	−2.38312	+	22.6739i	−0.0821765	+	0.781857i
$842$	7.36069	+	16.5324i	0.253666	+	0.569743i
$843$	−4.17680	−	1.35712i	−0.143856	−	0.0467418i
$844$	−6.50410	−	20.0176i	−0.223880	−	0.689033i
$845$	2.61829	+	24.9114i	0.0900719	+	0.856977i
$846$	4.93220	−	8.54283i	0.169573	−	0.293708i
$847$	−2.58570	−	5.28676i	−0.0888458	−	0.181655i
$848$			8.04849i			0.276386i
$849$	4.92028	+	46.8134i	0.168864	+	1.60663i
$850$	−3.98028	−	3.58386i	−0.136522	−	0.122925i
$851$	−19.1174	+	17.2134i	−0.655337	+	0.590068i
$852$	2.42000	−	23.0248i	0.0829079	−	0.788816i
$853$	−43.5019	−	4.57224i	−1.48948	−	0.156550i	−0.675463	−	0.737394i	$-0.736056\pi$
$853$	−43.5019	−	4.57224i	−1.48948	−	0.156550i	−0.814015	+	0.580844i	$0.802723\pi$
$854$	0.454988	−	1.40031i	0.0155694	−	0.0479176i
$855$	27.6061	+	6.44356i	0.944110	+	0.220365i
$856$	−12.1774	+	8.84741i	−0.416215	+	0.302398i
$857$	−1.86715	−	3.23400i	−0.0637807	−	0.110471i	0.832372	−	0.554218i	$-0.186982\pi$
$857$	−1.86715	−	3.23400i	−0.0637807	−	0.110471i	−0.896152	+	0.443746i	$0.853649\pi$
$858$	0.792587	+	6.42599i	0.0270585	+	0.219380i
$859$	−6.13625	+	10.6283i	−0.209366	+	0.362633i	−0.951515	−	0.307602i	$-0.900473\pi$
$859$	−6.13625	+	10.6283i	−0.209366	+	0.362633i	0.742149	+	0.670235i	$0.233807\pi$
$860$	−1.29559	+	2.90994i	−0.0441792	+	0.0992282i
$861$	−6.09062	−	1.29460i	−0.207568	−	0.0441199i
$862$	−11.2512	+	34.6277i	−0.383218	+	1.17942i
$863$	−23.7001	+	32.6204i	−0.806762	+	1.11041i	0.185053	+	0.982729i	$0.440754\pi$
$863$	−23.7001	+	32.6204i	−0.806762	+	1.11041i	−0.991815	+	0.127684i	$0.959246\pi$
$864$	−0.219132	−	0.492179i	−0.00745503	−	0.0167443i
$865$	4.11105	+	4.56578i	0.139780	+	0.155241i
$866$	15.6048	−	5.07029i	0.530271	−	0.172296i
$867$	−25.7659	−	35.4637i	−0.875056	−	1.20441i
$868$	2.58270	−	4.47337i	0.0876626	−	0.151836i
$869$	−0.266330	+	0.248630i	−0.00903462	+	0.00843418i
$870$	31.4245	+	18.1430i	1.06539	+	0.615104i
$871$	−4.84412	+	10.8801i	−0.164137	+	0.368657i
$872$	3.35761	−	3.72901i	0.113703	−	0.126280i
$873$	−4.32184	−	1.40425i	−0.146272	−	0.0475267i
$874$	28.9475	−	12.2052i	0.979164	−	0.412846i
$875$	−3.75884	+	5.17359i	−0.127072	+	0.174899i
$876$	−21.7406	+	4.62110i	−0.734546	+	0.156133i
$877$	1.63705	−	1.81813i	0.0552793	−	0.0613938i	−0.714871	−	0.699256i	$-0.753515\pi$
$877$	1.63705	−	1.81813i	0.0552793	−	0.0613938i	0.770150	+	0.637863i	$0.220181\pi$
$878$	−3.27843	−	31.1922i	−0.110642	−	1.05269i
$879$	49.7260	−	28.7093i	1.67722	−	0.968341i
$880$	−3.84386	+	5.49601i	−0.129577	+	0.185270i
$881$	17.9420			0.604480			0.302240	−	0.953232i	$-0.402266\pi$
$881$	17.9420			0.604480			0.302240	+	0.953232i	$0.402266\pi$
$882$	−17.4683	+	12.6915i	−0.588189	+	0.427344i
$883$	27.1006	+	5.76042i	0.912009	+	0.193854i	0.639941	−	0.768424i	$-0.278959\pi$
$883$	27.1006	+	5.76042i	0.912009	+	0.193854i	0.272069	+	0.962278i	$0.412292\pi$
$884$	−3.42186	+	3.08106i	−0.115090	+	0.103627i
$885$	−8.57086	−	6.22710i	−0.288106	−	0.209322i
$886$	6.90087	+	5.01377i	0.231839	+	0.168441i
$887$	16.2042	+	17.9965i	0.544082	+	0.604264i	0.950996	−	0.309202i	$-0.100062\pi$
$887$	16.2042	+	17.9965i	0.544082	+	0.604264i	−0.406914	+	0.913466i	$0.633395\pi$
$888$	5.95471	−	6.61337i	0.199827	−	0.221930i
$889$	−3.67170	+	0.385912i	−0.123145	+	0.0129431i
$890$	5.46281	−	3.15395i	0.183114	−	0.105721i
$891$	5.24096	−	27.0415i	0.175579	−	0.905924i
$892$			16.9744i			0.568343i
$893$	−12.1033	−	5.67946i	−0.405023	−	0.190056i
$894$	−1.25898	−	3.87474i	−0.0421066	−	0.129591i
$895$	9.63210	+	45.3155i	0.321966	+	1.51473i
$896$	0.532089	+	0.0559248i	0.0177758	+	0.00186831i
$897$	−5.72269	−	12.8534i	−0.191075	−	0.429162i
$898$	−4.36847	−	20.5521i	−0.145778	−	0.685831i
$899$	−14.4468	+	67.9671i	−0.481829	+	2.26683i
$900$	−2.36974	+	1.72172i	−0.0789913	+	0.0573905i
$901$	47.3303			1.57680
$902$	0.278681	+	15.4794i	0.00927905	+	0.515408i
$903$	−1.81967	−	1.05059i	−0.0605548	−	0.0349614i
$904$	5.62901	+	7.74766i	0.187218	+	0.257683i
$905$	−27.3604	+	8.88994i	−0.909491	+	0.295511i
$906$	8.31742	−	7.48904i	0.276328	−	0.248807i
$907$	−26.3812	−	2.77277i	−0.875972	−	0.0920684i	−0.344140	−	0.938918i	$-0.611829\pi$
$907$	−26.3812	−	2.77277i	−0.875972	−	0.0920684i	−0.531832	+	0.846850i	$0.678496\pi$
$908$	2.05043	−	0.912909i	0.0680458	−	0.0302960i
$909$	−5.69299	−	26.7834i	−0.188825	−	0.888350i
$910$	0.629545	+	0.566845i	0.0208692	+	0.0187907i
$911$	−22.0211	−	30.3094i	−0.729591	−	1.00420i	−0.999150	−	0.0412119i	$-0.986878\pi$
$911$	−22.0211	−	30.3094i	−0.729591	−	1.00420i	0.269560	−	0.962984i	$-0.413122\pi$
$912$	−9.51774	+	5.24579i	−0.315164	+	0.173706i
$913$	−22.0681	−	36.6820i	−0.730349	−	1.21400i
$914$	33.5763	−	19.3853i	1.11060	−	0.641208i
$915$	12.6753	+	5.64339i	0.419031	+	0.186565i
$916$	11.8221	+	2.51286i	0.390613	+	0.0830273i
$917$	−7.91848	+	1.68312i	−0.261491	+	0.0555817i
$918$	−2.89433	+	1.28864i	−0.0955271	+	0.0425314i
$919$	17.3242	−	23.8448i	0.571474	−	0.786567i	−0.421254	−	0.906943i	$-0.638410\pi$
$919$	17.3242	−	23.8448i	0.571474	−	0.786567i	0.992728	+	0.120376i	$0.0384100\pi$
$920$	4.50368	−	13.8609i	0.148482	−	0.456980i
$921$	5.59305	−	26.3132i	0.184297	−	0.867050i
$922$	4.47277	−	0.470107i	0.147303	−	0.0154822i
$923$			7.27086i			0.239323i
$924$	−3.34050	−	2.90064i	−0.109894	−	0.0954240i
$925$	−2.81538	−	1.62546i	−0.0925690	−	0.0534447i
$926$	−16.2161	−	7.21985i	−0.532893	−	0.237259i
$927$	−4.03638	+	18.9897i	−0.132572	+	0.623703i
$928$	−7.03986	+	1.49637i	−0.231095	+	0.0491207i
$929$	−2.79563	+	26.5987i	−0.0917217	+	0.872674i	0.847830	+	0.530268i	$0.177909\pi$
$929$	−2.79563	+	26.5987i	−0.0917217	+	0.872674i	−0.939552	+	0.342406i	$0.888758\pi$
$930$	39.3796	+	28.6109i	1.29131	+	0.938189i
$931$	19.1460	+	22.1325i	0.627483	+	0.725364i
$932$	20.2280	−	6.57246i	0.662589	−	0.215288i
$933$	5.71785	−	12.8425i	0.187194	−	0.420445i
$934$	18.3029	+	31.7015i	0.598888	+	1.03730i
$935$	32.3201	+	22.6044i	1.05698	+	0.739242i
$936$	1.25910	+	2.18083i	0.0411551	+	0.0712827i
$937$	−2.83883	+	0.298373i	−0.0927406	+	0.00974743i	−0.150785	−	0.988567i	$-0.548180\pi$
$937$	−2.83883	+	0.298373i	−0.0927406	+	0.00974743i	0.0580445	+	0.998314i	$0.481513\pi$
$938$	−2.51472	−	7.73952i	−0.0821086	−	0.252704i
$939$	−48.8354	−	15.8676i	−1.59368	−	0.517819i
$940$	−5.66621	+	2.52276i	−0.184812	+	0.0822834i
$941$	11.7050	−	5.21140i	0.381572	−	0.169887i	−0.206982	−	0.978345i	$-0.566364\pi$
$941$	11.7050	−	5.21140i	0.381572	−	0.169887i	0.588554	+	0.808458i	$0.299697\pi$
$942$	−3.89960	−	1.26706i	−0.127056	−	0.0412829i
$943$	−10.3962	−	31.9963i	−0.338548	−	1.04194i
$944$	2.08979	−	0.219646i	0.0680169	−	0.00714886i
$945$	0.291442	+	0.504793i	0.00948062	+	0.0164209i
$946$	−1.52471	+	4.99688i	−0.0495725	+	0.162463i
$947$	−19.2529	−	33.3470i	−0.625635	−	1.08363i	−0.988418	−	0.151758i	$-0.951506\pi$
$947$	−19.2529	−	33.3470i	−0.625635	−	1.08363i	0.362782	−	0.931874i	$-0.381827\pi$
$948$	−0.111401	+	0.250211i	−0.00361814	+	0.00812648i
$949$	6.63862	−	2.15702i	0.215499	−	0.0700198i
$950$	2.59733	+	3.00248i	0.0842684	+	0.0974133i
$951$	14.6517	+	10.6451i	0.475115	+	0.345191i
$952$	0.328874	−	3.12902i	0.0106589	−	0.101412i
$953$	30.3282	−	6.44646i	0.982427	−	0.208821i	0.311420	−	0.950272i	$-0.399195\pi$
$953$	30.3282	−	6.44646i	0.982427	−	0.208821i	0.671007	+	0.741451i	$0.265862\pi$
$954$	5.38173	−	25.3190i	0.174240	−	0.819734i
$955$	23.5022	+	10.4639i	0.760513	+	0.338602i
$956$	−19.2326	−	11.1039i	−0.622027	−	0.359127i
$957$	54.7951	+	23.2237i	1.77127	+	0.750716i
$958$			19.4851i			0.629536i
$959$	4.47643	−	0.470492i	0.144551	−	0.0151930i
$960$	−1.04823	+	4.93155i	−0.0338316	+	0.159165i
$961$	−19.2244	+	59.1665i	−0.620141	+	1.90860i
$962$	−1.64276	+	2.26106i	−0.0529646	+	0.0728995i
$963$	44.2238	−	19.6897i	1.42509	−	0.634491i
$964$	−5.91609	+	1.25750i	−0.190544	+	0.0405015i
$965$	−13.6320	−	2.89757i	−0.438829	−	0.0932760i
$966$	8.78261	+	3.91027i	0.282576	+	0.125811i
$967$	−18.1969	+	10.5060i	−0.585174	+	0.337851i	−0.763187	−	0.646178i	$-0.776367\pi$
$967$	−18.1969	+	10.5060i	−0.585174	+	0.337851i	0.178013	+	0.984028i	$0.443033\pi$
$968$	−5.15354	+	9.71808i	−0.165641	+	0.312351i
$969$	30.8487	+	55.9705i	0.991002	+	1.79803i
$970$	1.67947	+	2.31160i	0.0539247	+	0.0742210i
$971$	39.8624	+	35.8923i	1.27925	+	1.15184i	0.980288	+	0.197573i	$0.0633059\pi$
$971$	39.8624	+	35.8923i	1.27925	+	1.15184i	0.298959	+	0.954266i	$0.403361\pi$
$972$	−4.64110	−	21.8347i	−0.148863	−	0.700347i
$973$	−3.08273	+	1.37252i	−0.0988279	+	0.0440010i
$974$	20.7951	+	2.18565i	0.666317	+	0.0700327i
$975$	1.32133	−	1.18973i	0.0423163	−	0.0381018i
$976$	−2.61731	+	0.850414i	−0.0837779	+	0.0272211i
$977$	35.0999	+	48.3109i	1.12295	+	1.54560i	0.800820	+	0.598906i	$0.204398\pi$
$977$	35.0999	+	48.3109i	1.12295	+	1.54560i	0.322126	+	0.946697i	$0.395602\pi$
$978$	−41.5853	−	24.0093i	−1.32975	−	0.767732i
$979$	8.25906	−	6.23075i	0.263961	−	0.199136i
$980$	13.5764			0.433683
$981$	−13.0559	+	9.48563i	−0.416841	+	0.302853i
$982$	−8.94165	+	42.0671i	−0.285339	+	1.34242i
$983$	6.45248	+	30.3566i	0.205802	+	0.968224i	0.952847	+	0.303450i	$0.0981386\pi$
$983$	6.45248	+	30.3566i	0.205802	+	0.968224i	−0.747045	+	0.664773i	$0.768528\pi$
$984$	4.73370	+	10.6321i	0.150905	+	0.338938i
$985$	−26.5107	−	2.78638i	−0.844700	−	0.0887815i
$986$	8.79961	+	41.3989i	0.280237	+	1.31841i
$987$	−1.26431	−	3.89114i	−0.0402434	−	0.123856i
$988$	2.80051	−	1.95088i	0.0890960	−	0.0620659i
$989$		−	11.3527i		−	0.360995i
$990$	15.7670	−	14.7192i	0.501109	−	0.467806i
$991$	−42.6689	+	24.6349i	−1.35542	+	0.782553i	−0.989003	−	0.147897i	$-0.952750\pi$
$991$	−42.6689	+	24.6349i	−1.35542	+	0.782553i	−0.366419	+	0.930450i	$0.619416\pi$
$992$	−9.60172	+	1.00918i	−0.304855	+	0.0320415i
$993$	−46.9496	+	52.1428i	−1.48990	+	1.65470i
$994$	−3.32432	−	3.69203i	−0.105441	−	0.117104i
$995$	−40.6806	−	29.5562i	−1.28966	−	0.936995i
$996$	−26.0346	−	18.9152i	−0.824937	−	0.599352i
$997$	44.7176	−	40.2639i	1.41622	−	1.27517i	0.505083	−	0.863071i	$-0.331462\pi$
$997$	44.7176	−	40.2639i	1.41622	−	1.27517i	0.911138	−	0.412101i	$-0.135205\pi$
$998$	−0.936023	−	0.198958i	−0.0296293	−	0.00629790i
$999$	−1.55576	+	1.13032i	−0.0492219	+	0.0357618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.s.a.107.2	✓	80
11.7	odd	10		418.2.s.b.183.9	yes	80
19.8	odd	6		418.2.s.b.217.9	yes	80
209.84	even	30	inner	418.2.s.a.293.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.s.a.107.2	✓	80	1.1	even	1	trivial
418.2.s.a.293.2	yes	80	209.84	even	30	inner
418.2.s.b.183.9	yes	80	11.7	odd	10
418.2.s.b.217.9	yes	80	19.8	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.s (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913545 - 0.406737i) q^{2} +(-1.85282 - 1.66828i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-0.211376 + 2.01110i) q^{5} +(1.01408 + 2.27766i) q^{6} +(0.508834 + 0.165330i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.336173 + 3.19847i) q^{9} +O(q^{10})\)	\(q+(-0.913545 - 0.406737i) q^{2} +(-1.85282 - 1.66828i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-0.211376 + 2.01110i) q^{5} +(1.01408 + 2.27766i) q^{6} +(0.508834 + 0.165330i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.336173 + 3.19847i) q^{9} +(1.01109 - 1.75126i) q^{10} +(1.29424 - 3.05368i) q^{11} -2.49321i q^{12} +(0.0818461 + 0.778714i) q^{13} +(-0.397597 - 0.357998i) q^{14} +(3.74673 - 3.37357i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(5.84843 + 0.614695i) q^{17} +(0.993826 - 3.05868i) q^{18} +(-4.24480 - 0.990781i) q^{19} +(-1.63598 + 1.18861i) q^{20} +(-0.666958 - 1.15520i) q^{21} +(-2.42439 + 2.26326i) q^{22} +(3.60359 - 6.24160i) q^{23} +(-1.01408 + 2.27766i) q^{24} +(0.890880 + 0.189362i) q^{25} +(0.241961 - 0.744680i) q^{26} +(0.316673 - 0.435863i) q^{27} +(0.217612 + 0.488765i) q^{28} +(-4.81582 - 5.34851i) q^{29} +(-4.79496 + 1.55798i) q^{30} +(-5.67483 - 7.81074i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-7.49238 + 3.49875i) q^{33} +(-5.09279 - 2.94032i) q^{34} +(-0.440051 + 0.988371i) q^{35} +(-2.15198 + 2.39002i) q^{36} +(-3.39467 - 1.10299i) q^{37} +(3.47483 + 2.63164i) q^{38} +(1.14747 - 1.57936i) q^{39} +(1.97799 - 0.420435i) q^{40} +(3.12349 - 3.46898i) q^{41} +(0.139432 + 1.32661i) q^{42} +(1.36416 - 0.787597i) q^{43} +(3.13534 - 1.08151i) q^{44} -6.50352 q^{45} +(-5.83073 + 4.23627i) q^{46} +(3.00018 + 0.637708i) q^{47} +(1.85282 - 1.66828i) q^{48} +(-5.43154 - 3.94625i) q^{49} +(-0.736839 - 0.535345i) q^{50} +(-9.81058 - 10.8958i) q^{51} +(-0.523931 + 0.581885i) q^{52} +(8.00440 - 0.841297i) q^{53} +(-0.466577 + 0.269378i) q^{54} +(5.86770 + 3.24831i) q^{55} -0.535019i q^{56} +(6.21193 + 8.91726i) q^{57} +(2.22404 + 6.84488i) q^{58} +(-0.436885 - 2.05538i) q^{59} +(5.01410 + 0.527003i) q^{60} +(1.11934 + 2.51408i) q^{61} +(2.00731 + 9.44363i) q^{62} +(-0.357747 + 1.68307i) q^{63} +(-0.809017 + 0.587785i) q^{64} -1.58337 q^{65} +(8.26770 - 0.148846i) q^{66} +(13.1725 + 7.60516i) q^{67} +(3.45656 + 4.75754i) q^{68} +(-17.0895 + 5.55272i) q^{69} +(0.804013 - 0.723937i) q^{70} +(9.23500 + 0.970637i) q^{71} +(2.93804 - 1.30810i) q^{72} +(-1.85348 - 8.71992i) q^{73} +(2.65256 + 2.38837i) q^{74} +(-1.33473 - 1.83709i) q^{75} +(-2.10403 - 3.81747i) q^{76} +(1.16342 - 1.33984i) q^{77} +(-1.69065 + 0.976095i) q^{78} +(-0.100357 - 0.0446819i) q^{79} +(-1.97799 - 0.420435i) q^{80} +(8.12355 - 1.72671i) q^{81} +(-4.26441 + 1.89864i) q^{82} +(7.58670 - 10.4422i) q^{83} +(0.412202 - 1.26863i) q^{84} +(-2.47243 + 11.6319i) q^{85} +(-1.56656 + 0.164653i) q^{86} +17.9440i q^{87} +(-3.30416 - 0.287252i) q^{88} +(2.70144 + 1.55968i) q^{89} +(5.94126 + 2.64522i) q^{90} +(-0.0870988 + 0.409767i) q^{91} +(7.04968 - 1.49846i) q^{92} +(-2.51610 + 23.9391i) q^{93} +(-2.48142 - 1.80286i) q^{94} +(2.88981 - 8.32731i) q^{95} +(-2.37118 + 0.770444i) q^{96} +(-0.574709 + 1.29082i) q^{97} +(3.35688 + 5.81428i) q^{98} +(10.2022 + 3.11301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9}+O(q^{10}) \) 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9	\( 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9} + 2 q^{10} - q^{11} + 5 q^{13} - 4 q^{14} - 27 q^{15} + 10 q^{16} - 6 q^{17} - 17 q^{18} - 2 q^{19} + 4 q^{20} + 24 q^{21} - 2 q^{22} - 6 q^{23} - 7 q^{24} - 10 q^{26} - 45 q^{27} + 6 q^{28} - 65 q^{29} + 30 q^{30} + 40 q^{32} + 3 q^{33} + 24 q^{34} - 13 q^{35} - q^{36} + 22 q^{38} - 30 q^{39} - 3 q^{40} - 14 q^{41} - 14 q^{42} + 12 q^{43} + 24 q^{44} - 12 q^{45} - 2 q^{46} - q^{47} + 3 q^{48} + 32 q^{49} + 30 q^{50} - 28 q^{51} - 5 q^{52} - q^{53} - 27 q^{54} - 23 q^{55} + 28 q^{57} - 10 q^{58} + 56 q^{59} - 28 q^{60} + 28 q^{61} + 15 q^{62} + 88 q^{63} - 20 q^{64} + 8 q^{65} - 57 q^{66} - 27 q^{67} - 60 q^{69} + 17 q^{70} + 2 q^{71} + 11 q^{72} - q^{73} + 12 q^{74} - 35 q^{75} - 11 q^{76} - 8 q^{77} - 6 q^{79} + 3 q^{80} + 43 q^{81} - 16 q^{82} - 25 q^{83} + 52 q^{84} - 33 q^{85} - 43 q^{86} - 9 q^{88} - 36 q^{89} + 74 q^{90} + 38 q^{91} - 11 q^{92} + 15 q^{93} - 2 q^{94} - 61 q^{95} - 24 q^{97} - 44 q^{98} + 37 q^{99}+O(q^{100}) \) 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9 + 2 * q^10 - q^11 + 5 * q^13 - 4 * q^14 - 27 * q^15 + 10 * q^16 - 6 * q^17 - 17 * q^18 - 2 * q^19 + 4 * q^20 + 24 * q^21 - 2 * q^22 - 6 * q^23 - 7 * q^24 - 10 * q^26 - 45 * q^27 + 6 * q^28 - 65 * q^29 + 30 * q^30 + 40 * q^32 + 3 * q^33 + 24 * q^34 - 13 * q^35 - q^36 + 22 * q^38 - 30 * q^39 - 3 * q^40 - 14 * q^41 - 14 * q^42 + 12 * q^43 + 24 * q^44 - 12 * q^45 - 2 * q^46 - q^47 + 3 * q^48 + 32 * q^49 + 30 * q^50 - 28 * q^51 - 5 * q^52 - q^53 - 27 * q^54 - 23 * q^55 + 28 * q^57 - 10 * q^58 + 56 * q^59 - 28 * q^60 + 28 * q^61 + 15 * q^62 + 88 * q^63 - 20 * q^64 + 8 * q^65 - 57 * q^66 - 27 * q^67 - 60 * q^69 + 17 * q^70 + 2 * q^71 + 11 * q^72 - q^73 + 12 * q^74 - 35 * q^75 - 11 * q^76 - 8 * q^77 - 6 * q^79 + 3 * q^80 + 43 * q^81 - 16 * q^82 - 25 * q^83 + 52 * q^84 - 33 * q^85 - 43 * q^86 - 9 * q^88 - 36 * q^89 + 74 * q^90 + 38 * q^91 - 11 * q^92 + 15 * q^93 - 2 * q^94 - 61 * q^95 - 24 * q^97 - 44 * q^98 + 37 * q^99

Introduction

L-functions

Modular forms

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