LMFDB - Embedded newform 507.2.t.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			4.1
Character	$\chi$	$=$	507.4
Dual form			507.2.t.a.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.42393 - 0.0976810i) q^{2} +(0.278217 - 0.960518i) q^{3} +(3.87238 + 0.312611i) q^{4} +(-2.76576 - 1.04892i) q^{5} +(-0.768204 + 2.30105i) q^{6} +(-0.673721 - 1.58128i) q^{7} +(-4.53942 - 0.551185i) q^{8} +(-0.845190 - 0.534466i) q^{9} +O(q^{10})$	\(q+(-2.42393 - 0.0976810i) q^{2} +(0.278217 - 0.960518i) q^{3} +(3.87238 + 0.312611i) q^{4} +(-2.76576 - 1.04892i) q^{5} +(-0.768204 + 2.30105i) q^{6} +(-0.673721 - 1.58128i) q^{7} +(-4.53942 - 0.551185i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(6.60156 + 2.81266i) q^{10} +(-2.00960 - 3.17794i) q^{11} +(1.37763 - 3.63252i) q^{12} +(-1.19549 + 3.40159i) q^{13} +(1.47859 + 3.89872i) q^{14} +(-1.77699 + 2.36474i) q^{15} +(3.28006 + 0.533061i) q^{16} +(1.82380 - 0.777050i) q^{17} +(1.99647 + 1.37807i) q^{18} +(0.437535 - 0.252611i) q^{19} +(-10.3822 - 4.92641i) q^{20} +(-1.70629 + 0.207181i) q^{21} +(4.56072 + 7.89939i) q^{22} +(-1.51770 + 2.62874i) q^{23} +(-1.79237 + 4.20684i) q^{24} +(2.80667 + 2.48650i) q^{25} +(3.23005 - 8.12844i) q^{26} +(-0.748511 + 0.663123i) q^{27} +(-2.11458 - 6.33393i) q^{28} +(-0.0819070 + 2.03250i) q^{29} +(4.53828 - 5.55839i) q^{30} +(-3.69800 - 4.17418i) q^{31} +(1.06214 + 0.216837i) q^{32} +(-3.61157 + 1.04610i) q^{33} +(-4.49667 + 1.70536i) q^{34} +(0.204722 + 5.08013i) q^{35} +(-3.10582 - 2.33387i) q^{36} +(3.77047 - 0.769746i) q^{37} +(-1.08523 + 0.569573i) q^{38} +(2.93468 + 2.09467i) q^{39} +(11.9768 + 6.28592i) q^{40} +(7.45465 + 2.15926i) q^{41} +(4.15616 - 0.335520i) q^{42} +(-0.435464 + 2.13304i) q^{43} +(-6.78849 - 12.9344i) q^{44} +(1.77699 + 2.36474i) q^{45} +(3.93558 - 6.22362i) q^{46} +(-10.5365 + 7.27282i) q^{47} +(1.42458 - 3.00225i) q^{48} +(2.80252 - 2.91773i) q^{49} +(-6.56030 - 6.30125i) q^{50} +(-0.238957 - 1.96799i) q^{51} +(-5.69275 + 12.7985i) q^{52} +(-1.28497 + 10.5827i) q^{53} +(1.87911 - 1.53425i) q^{54} +(2.22471 + 10.8973i) q^{55} +(2.18672 + 7.54944i) q^{56} +(-0.120908 - 0.490541i) q^{57} +(0.397074 - 4.91864i) q^{58} +(1.18870 + 7.31435i) q^{59} +(-7.62041 + 8.60166i) q^{60} +(-5.91488 + 4.44475i) q^{61} +(8.55596 + 10.4791i) q^{62} +(-0.275718 + 1.69656i) q^{63} +(-9.00642 - 2.21988i) q^{64} +(6.87442 - 8.15403i) q^{65} +(8.85638 - 2.18290i) q^{66} +(1.03025 + 12.7620i) q^{67} +(7.30537 - 2.43889i) q^{68} +(2.10270 + 2.18914i) q^{69} -12.3339i q^{70} +(-0.361470 + 0.347196i) q^{71} +(3.54208 + 2.89202i) q^{72} +(-5.73103 + 10.9196i) q^{73} +(-9.21454 + 1.49751i) q^{74} +(3.16919 - 2.00407i) q^{75} +(1.77327 - 0.841428i) q^{76} +(-3.67130 + 5.31879i) q^{77} +(-6.90886 - 5.36399i) q^{78} +(-4.70120 - 6.81087i) q^{79} +(-8.51272 - 4.91482i) q^{80} +(0.428693 + 0.903450i) q^{81} +(-17.8586 - 5.96208i) q^{82} +(1.05909 - 4.29691i) q^{83} +(-6.67217 + 0.268879i) q^{84} +(-5.85927 + 0.236121i) q^{85} +(1.26389 - 5.12781i) q^{86} +(1.92947 + 0.644151i) q^{87} +(7.37080 + 15.5336i) q^{88} +(1.35493 + 0.782267i) q^{89} +(-4.07630 - 5.90554i) q^{90} +(6.18429 - 0.401322i) q^{91} +(-6.69889 + 9.70502i) q^{92} +(-5.03823 + 2.39067i) q^{93} +(26.2501 - 16.5996i) q^{94} +(-1.47509 + 0.239725i) q^{95} +(0.503781 - 0.959875i) q^{96} +(-7.47401 - 6.10234i) q^{97} +(-7.07812 + 6.79863i) q^{98} +3.76002i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9}+O(q^{10}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31} + 65 q^{32} - 13 q^{33} + 65 q^{34} - 82 q^{35} - 12 q^{36} - 73 q^{38} + 24 q^{40} - 132 q^{42} - 72 q^{43} + 39 q^{44} + 8 q^{48} + 68 q^{49} + 52 q^{50} - 8 q^{51} - 65 q^{52} + 37 q^{53} - 53 q^{55} + 14 q^{56} - 26 q^{57} + 26 q^{58} - 208 q^{59} + 78 q^{60} - 12 q^{61} - 49 q^{62} + 14 q^{64} + 52 q^{65} + 64 q^{66} - 26 q^{67} - 33 q^{68} + 4 q^{69} - 78 q^{71} + 52 q^{73} + 205 q^{74} - 8 q^{75} - 26 q^{76} - 114 q^{77} - 65 q^{78} + 28 q^{79} - 468 q^{80} + 14 q^{81} - 45 q^{82} - 78 q^{83} + 13 q^{85} + 13 q^{86} + 46 q^{87} + 26 q^{88} - 8 q^{90} - 260 q^{91} + 8 q^{92} - 25 q^{94} - 90 q^{95} - 65 q^{96} - 26 q^{97} + 104 q^{98}+O(q^{100}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{78}\right)$

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 $

$2$	−2.42393	−	0.0976810i	−1.71398	−	0.0690709i	−0.836285	−	0.548295i	$-0.815277\pi$
$2$	−2.42393	−	0.0976810i	−1.71398	−	0.0690709i	−0.877692	+	0.479225i	$0.840918\pi$
$3$	0.278217	−	0.960518i	0.160629	−	0.554555i
$3$	0.278217	−	0.960518i	0.160629	−	0.554555i
$4$	3.87238	+	0.312611i	1.93619	+	0.156305i
$5$	−2.76576	−	1.04892i	−1.23689	−	0.469090i	−0.352486	−	0.935817i	$-0.614664\pi$
$5$	−2.76576	−	1.04892i	−1.23689	−	0.469090i	−0.884401	+	0.466727i	$0.845433\pi$
$6$	−0.768204	+	2.30105i	−0.313618	+	0.939400i
$7$	−0.673721	−	1.58128i	−0.254642	−	0.597668i	0.742771	−	0.669546i	$-0.233511\pi$
$7$	−0.673721	−	1.58128i	−0.254642	−	0.597668i	−0.997413	+	0.0718777i	$0.977101\pi$
$8$	−4.53942	−	0.551185i	−1.60493	−	0.194873i
$9$	−0.845190	−	0.534466i	−0.281730	−	0.178155i
$10$	6.60156	+	2.81266i	2.08760	+	0.889442i
$11$	−2.00960	−	3.17794i	−0.605919	−	0.958184i	−0.999248	−	0.0387858i	$-0.987651\pi$
$11$	−2.00960	−	3.17794i	−0.605919	−	0.958184i	0.393329	−	0.919398i	$-0.371323\pi$
$12$	1.37763	−	3.63252i	0.397688	−	1.04862i
$13$	−1.19549	+	3.40159i	−0.331568	+	0.943431i
$13$	−1.19549	+	3.40159i	−0.331568	+	0.943431i
$14$	1.47859	+	3.89872i	0.395170	+	1.04198i
$15$	−1.77699	+	2.36474i	−0.458816	+	0.610573i
$16$	3.28006	+	0.533061i	0.820014	+	0.133265i
$17$	1.82380	−	0.777050i	0.442337	−	0.188462i	−0.159303	−	0.987230i	$-0.550925\pi$
$17$	1.82380	−	0.777050i	0.442337	−	0.188462i	0.601640	+	0.798767i	$0.294514\pi$
$18$	1.99647	+	1.37807i	0.470573	+	0.324813i
$19$	0.437535	−	0.252611i	0.100377	−	0.0579530i	−0.448971	−	0.893546i	$-0.648209\pi$
$19$	0.437535	−	0.252611i	0.100377	−	0.0579530i	0.549348	+	0.835593i	$0.314876\pi$
$20$	−10.3822	−	4.92641i	−2.32153	−	1.10158i
$21$	−1.70629	+	0.207181i	−0.372343	+	0.0452106i
$22$	4.56072	+	7.89939i	0.972348	+	1.68416i
$23$	−1.51770	+	2.62874i	−0.316463	+	0.548130i	−0.979747	−	0.200238i	$-0.935829\pi$
$23$	−1.51770	+	2.62874i	−0.316463	+	0.548130i	0.663285	+	0.748367i	$0.269162\pi$
$24$	−1.79237	+	4.20684i	−0.365866	+	0.858718i
$25$	2.80667	+	2.48650i	0.561335	+	0.497299i
$26$	3.23005	−	8.12844i	0.633464	−	1.59412i
$27$	−0.748511	+	0.663123i	−0.144051	+	0.127618i
$28$	−2.11458	−	6.33393i	−0.399617	−	1.19700i
$29$	−0.0819070	+	2.03250i	−0.0152098	+	0.377426i	0.973602	+	0.228254i	$0.0733018\pi$
$29$	−0.0819070	+	2.03250i	−0.0152098	+	0.377426i	−0.988811	+	0.149172i	$0.952339\pi$
$30$	4.53828	−	5.55839i	0.828573	−	1.01482i
$31$	−3.69800	−	4.17418i	−0.664181	−	0.749705i	0.315794	−	0.948828i	$-0.397729\pi$
$31$	−3.69800	−	4.17418i	−0.664181	−	0.749705i	−0.979975	+	0.199123i	$0.936191\pi$
$32$	1.06214	+	0.216837i	0.187761	+	0.0383317i
$33$	−3.61157	+	1.04610i	−0.628694	+	0.182103i
$34$	−4.49667	+	1.70536i	−0.771173	+	0.292467i
$35$	0.204722	+	5.08013i	0.0346043	+	0.858698i
$36$	−3.10582	−	2.33387i	−0.517636	−	0.388978i
$37$	3.77047	−	0.769746i	0.619861	−	0.126546i	0.120176	−	0.992753i	$-0.461654\pi$
$37$	3.77047	−	0.769746i	0.619861	−	0.126546i	0.499685	+	0.866207i	$0.333449\pi$
$38$	−1.08523	+	0.569573i	−0.176048	+	0.0923969i
$39$	2.93468	+	2.09467i	0.469925	+	0.335415i
$40$	11.9768	+	6.28592i	1.89370	+	0.993891i
$41$	7.45465	+	2.15926i	1.16422	+	0.337220i	0.803414	−	0.595420i	$-0.203015\pi$
$41$	7.45465	+	2.15926i	1.16422	+	0.337220i	0.360806	+	0.932641i	$0.382502\pi$
$42$	4.15616	−	0.335520i	0.641310	−	0.0517719i
$43$	−0.435464	+	2.13304i	−0.0664076	+	0.325286i	−0.999401	−	0.0346076i	$-0.988982\pi$
$43$	−0.435464	+	2.13304i	−0.0664076	+	0.325286i	0.932993	+	0.359893i	$0.117187\pi$
$44$	−6.78849	−	12.9344i	−1.02340	−	1.94993i
$45$	1.77699	+	2.36474i	0.264898	+	0.352515i
$46$	3.93558	−	6.22362i	0.580270	−	0.917623i
$47$	−10.5365	+	7.27282i	−1.53691	+	1.06085i	−0.565113	+	0.825014i	$0.691167\pi$
$47$	−10.5365	+	7.27282i	−1.53691	+	1.06085i	−0.971793	+	0.235836i	$0.924217\pi$
$48$	1.42458	−	3.00225i	0.205621	−	0.433337i
$49$	2.80252	−	2.91773i	0.400360	−	0.416819i
$50$	−6.56030	−	6.30125i	−0.927766	−	0.891131i
$51$	−0.238957	−	1.96799i	−0.0334606	−	0.275573i
$52$	−5.69275	+	12.7985i	−0.789442	+	1.77484i
$53$	−1.28497	+	10.5827i	−0.176505	+	1.45365i	0.587913	+	0.808924i	$0.299950\pi$
$53$	−1.28497	+	10.5827i	−0.176505	+	1.45365i	−0.764417	+	0.644722i	$0.776973\pi$
$54$	1.87911	−	1.53425i	0.255715	−	0.208785i
$55$	2.22471	+	10.8973i	0.299979	+	1.46940i
$56$	2.18672	+	7.54944i	0.292213	+	1.00884i
$57$	−0.120908	−	0.490541i	−0.0160146	−	0.0649738i
$58$	0.397074	−	4.91864i	0.0521383	−	0.645849i
$59$	1.18870	+	7.31435i	0.154755	+	0.952248i	0.942001	+	0.335609i	$0.108942\pi$
$59$	1.18870	+	7.31435i	0.154755	+	0.952248i	−0.787246	+	0.616639i	$0.788494\pi$
$60$	−7.62041	+	8.60166i	−0.983791	+	1.11047i
$61$	−5.91488	+	4.44475i	−0.757323	+	0.569091i	−0.907741	−	0.419531i	$-0.862195\pi$
$61$	−5.91488	+	4.44475i	−0.757323	+	0.569091i	0.150418	+	0.988623i	$0.451938\pi$
$62$	8.55596	+	10.4791i	1.08661	+	1.33085i
$63$	−0.275718	+	1.69656i	−0.0347373	+	0.213747i
$64$	−9.00642	−	2.21988i	−1.12580	−	0.277485i
$65$	6.87442	−	8.15403i	0.852666	−	1.01138i
$66$	8.85638	−	2.18290i	1.09015	−	0.268697i
$67$	1.03025	+	12.7620i	0.125866	+	1.55912i	0.684067	+	0.729419i	$0.260210\pi$
$67$	1.03025	+	12.7620i	0.125866	+	1.55912i	−0.558201	+	0.829706i	$0.688508\pi$
$68$	7.30537	−	2.43889i	0.885906	−	0.295759i
$69$	2.10270	+	2.18914i	0.253135	+	0.263542i
$70$		−	12.3339i		−	1.47418i
$71$	−0.361470	+	0.347196i	−0.0428986	+	0.0412046i	−0.713867	−	0.700281i	$-0.753058\pi$
$71$	−0.361470	+	0.347196i	−0.0428986	+	0.0412046i	0.670969	+	0.741486i	$0.265879\pi$
$72$	3.54208	+	2.89202i	0.417438	+	0.340828i
$73$	−5.73103	+	10.9196i	−0.670766	+	1.27804i	0.277550	+	0.960711i	$0.410478\pi$
$73$	−5.73103	+	10.9196i	−0.670766	+	1.27804i	−0.948316	+	0.317327i	$0.897215\pi$
$74$	−9.21454	+	1.49751i	−1.07117	+	0.174082i
$75$	3.16919	−	2.00407i	0.365947	−	0.231411i
$76$	1.77327	−	0.841428i	0.203408	−	0.0965184i
$77$	−3.67130	+	5.31879i	−0.418383	+	0.606132i
$78$	−6.90886	−	5.36399i	−0.782274	−	0.607352i
$79$	−4.70120	−	6.81087i	−0.528927	−	0.766282i	0.463895	−	0.885890i	$-0.346452\pi$
$79$	−4.70120	−	6.81087i	−0.528927	−	0.766282i	−0.992821	+	0.119608i	$0.961836\pi$
$80$	−8.51272	−	4.91482i	−0.951752	−	0.549494i
$81$	0.428693	+	0.903450i	0.0476325	+	0.100383i
$82$	−17.8586	−	5.96208i	−1.97215	−	0.658402i
$83$	1.05909	−	4.29691i	0.116251	−	0.471647i	−0.883743	−	0.467973i	$-0.844984\pi$
$83$	1.05909	−	4.29691i	0.116251	−	0.471647i	0.999993	−	0.00367408i	$-0.00116950\pi$
$84$	−6.67217	+	0.268879i	−0.727993	+	0.0293371i
$85$	−5.85927	+	0.236121i	−0.635527	+	0.0256109i
$86$	1.26389	−	5.12781i	0.136289	−	0.552946i
$87$	1.92947	+	0.644151i	0.206861	+	0.0690602i
$88$	7.37080	+	15.5336i	0.785730	+	1.65589i
$89$	1.35493	+	0.782267i	0.143622	+	0.0829201i	0.570089	−	0.821583i	$-0.306909\pi$
$89$	1.35493	+	0.782267i	0.143622	+	0.0829201i	−0.426467	+	0.904503i	$0.640242\pi$
$90$	−4.07630	−	5.90554i	−0.429680	−	0.622499i
$91$	6.18429	−	0.401322i	0.648290	−	0.0420700i
$92$	−6.69889	+	9.70502i	−0.698408	+	1.01182i
$93$	−5.03823	+	2.39067i	−0.522440	+	0.247901i
$94$	26.2501	−	16.5996i	2.70750	−	1.71212i
$95$	−1.47509	+	0.239725i	−0.151341	+	0.0245953i
$96$	0.503781	−	0.959875i	0.0514170	−	0.0979668i
$97$	−7.47401	−	6.10234i	−0.758871	−	0.619599i	0.171937	−	0.985108i	$-0.444998\pi$
$97$	−7.47401	−	6.10234i	−0.758871	−	0.619599i	−0.930808	+	0.365509i	$0.880895\pi$
$98$	−7.07812	+	6.79863i	−0.714998	+	0.686765i
$99$			3.76002i			0.377897i
$100$	10.0912	+	10.5060i	1.00912	+	1.05060i
$101$	13.1952	−	4.40520i	1.31297	−	0.438334i	0.427914	−	0.903819i	$-0.359249\pi$
$101$	13.1952	−	4.40520i	1.31297	−	0.438334i	0.885055	+	0.465486i	$0.154120\pi$
$102$	0.386979	+	4.79360i	0.0383167	+	0.474637i
$103$	13.9612	−	3.44113i	1.37564	−	0.339065i	0.518909	−	0.854829i	$-0.326338\pi$
$103$	13.9612	−	3.44113i	1.37564	−	0.339065i	0.856730	+	0.515765i	$0.172492\pi$
$104$	7.30172	−	14.7823i	0.715992	−	1.44952i
$105$	4.93651	+	1.21674i	0.481754	+	0.118742i
$106$	4.14841	−	25.5262i	0.402930	−	2.47933i
$107$	−9.25719	−	11.3380i	−0.894926	−	1.09609i	−0.994877	−	0.101093i	$-0.967766\pi$
$107$	−9.25719	−	11.3380i	−0.894926	−	1.09609i	0.0999508	−	0.994992i	$-0.468131\pi$
$108$	−3.10582	+	2.33387i	−0.298857	+	0.224577i
$109$	4.49911	−	5.07844i	0.430936	−	0.486427i	−0.492427	−	0.870354i	$-0.663890\pi$
$109$	4.49911	−	5.07844i	0.430936	−	0.486427i	0.923363	+	0.383927i	$0.125429\pi$
$110$	−4.32807	−	26.6317i	−0.412665	−	2.53923i
$111$	0.309655	−	3.83576i	0.0293911	−	0.364074i
$112$	−1.36692	−	5.54582i	−0.129162	−	0.524031i
$113$	−3.36146	−	11.6051i	−0.316220	−	1.09172i	−0.948447	−	0.316935i	$-0.897346\pi$
$113$	−3.36146	−	11.6051i	−0.316220	−	1.09172i	0.632227	−	0.774783i	$-0.282141\pi$
$114$	0.245155	+	1.20085i	0.0229609	+	0.112470i
$115$	6.95493	−	5.67853i	0.648551	−	0.529525i
$116$	−0.952557	+	7.84501i	−0.0884427	+	0.728391i
$117$	2.82845	−	2.23604i	0.261490	−	0.206722i
$118$	−2.16685	−	17.8456i	−0.199474	−	1.64282i
$119$	−2.45747	−	2.36043i	−0.225276	−	0.216380i
$120$	9.36990	−	9.75509i	0.855351	−	0.890514i
$121$	−1.34514	+	2.83483i	−0.122286	+	0.257712i
$122$	14.7714	−	10.1960i	1.33734	−	0.923101i
$123$	4.14803	−	6.55958i	0.374015	−	0.591457i
$124$	−13.0152	−	17.3200i	−1.16880	−	1.55539i
$125$	1.71875	+	3.27480i	0.153730	+	0.292907i
$126$	0.834044	−	4.08542i	0.0743025	−	0.363958i
$127$	−20.4417	+	1.65022i	−1.81391	+	0.146434i	−0.940332	−	0.340258i	$-0.889486\pi$
$127$	−20.4417	+	1.65022i	−1.81391	+	0.146434i	−0.873574	+	0.486692i	$0.838204\pi$
$128$	19.5316	+	5.65740i	1.72637	+	0.500048i
$129$	1.92767	+	1.01172i	0.169722	+	0.0890770i
$130$	−17.4596	+	19.0933i	−1.53131	+	1.67459i
$131$	−2.99779	+	1.57336i	−0.261918	+	0.137465i	−0.590571	−	0.806985i	$-0.701098\pi$
$131$	−2.99779	+	1.57336i	−0.261918	+	0.137465i	0.328653	+	0.944451i	$0.393405\pi$
$132$	−14.3124	+	2.92190i	−1.24573	+	0.254318i
$133$	−0.694226	−	0.521677i	−0.0601970	−	0.0452351i
$134$	−1.25066	−	31.0348i	−0.108041	−	2.68100i
$135$	2.76576	−	1.04892i	0.238039	−	0.0902763i
$136$	−8.70731	+	2.52210i	−0.746645	+	0.216268i
$137$	0.637929	+	0.130234i	0.0545020	+	0.0111267i	0.227199	−	0.973848i	$-0.427043\pi$
$137$	0.637929	+	0.130234i	0.0545020	+	0.0111267i	−0.172697	+	0.984975i	$0.555248\pi$
$138$	−4.88296	−	5.51172i	−0.415665	−	0.469189i
$139$	−5.53274	+	6.77638i	−0.469281	+	0.574765i	−0.953963	−	0.299926i	$-0.903038\pi$
$139$	−5.53274	+	6.77638i	−0.469281	+	0.574765i	0.484681	+	0.874691i	$0.338936\pi$
$140$	−0.795340	+	19.7362i	−0.0672185	+	1.66801i
$141$	4.05424	+	12.1439i	0.341428	+	1.02270i
$142$	0.910092	−	0.806271i	0.0763732	−	0.0676608i
$143$	13.2125	−	3.03667i	1.10488	−	0.253939i
$144$	−2.48737	−	2.20362i	−0.207281	−	0.183635i
$145$	2.35846	−	5.53551i	0.195859	−	0.459699i
$146$	14.9582	−	25.9084i	1.23795	−	2.14420i
$147$	−2.02283	−	3.50364i	−0.166840	−	0.288975i
$148$	14.8413	−	1.80206i	1.21995	−	0.148129i
$149$	−20.4446	−	9.70107i	−1.67489	−	0.794743i	−0.998294	−	0.0583840i	$-0.981405\pi$
$149$	−20.4446	−	9.70107i	−1.67489	−	0.794743i	−0.676591	−	0.736359i	$-0.736544\pi$
$150$	−7.87765	+	4.54817i	−0.643208	+	0.371356i
$151$	−9.92385	−	6.84994i	−0.807592	−	0.557440i	0.0911918	−	0.995833i	$-0.470932\pi$
$151$	−9.92385	−	6.84994i	−0.807592	−	0.557440i	−0.898783	+	0.438393i	$0.855548\pi$
$152$	−2.12539	+	0.905544i	−0.172392	+	0.0734493i
$153$	−1.95677	−	0.318006i	−0.158195	−	0.0257092i
$154$	9.41851	−	12.5338i	0.758965	−	1.01000i
$155$	5.84944	+	15.4237i	0.469838	+	1.23886i
$156$	10.7094	+	9.02876i	0.857437	+	0.722879i
$157$	−3.12607	+	8.24276i	−0.249487	+	0.657844i	−0.999995	−	0.00301737i	$-0.999040\pi$
$157$	−3.12607	+	8.24276i	−0.249487	+	0.657844i	0.750508	+	0.660861i	$0.229809\pi$
$158$	10.7301	+	16.9683i	0.853640	+	1.34992i
$159$	9.80738	+	4.17853i	0.777776	+	0.331379i
$160$	−2.71018	−	1.71381i	−0.214259	−	0.135489i
$161$	5.17928	+	0.628878i	0.408184	+	0.0495626i
$162$	−0.950871	−	2.23178i	−0.0747075	−	0.175345i
$163$	−1.81187	+	5.42722i	−0.141917	+	0.425093i	−0.995375	−	0.0960691i	$-0.969373\pi$
$163$	−1.81187	+	5.42722i	−0.141917	+	0.425093i	0.853458	+	0.521162i	$0.174501\pi$
$164$	28.1922	+	10.6919i	2.20144	+	0.834896i
$165$	11.0860	+	0.894957i	0.863046	+	0.0696723i
$166$	−2.98690	+	10.3120i	−0.231828	+	0.800363i
$167$	−11.9915	−	0.483241i	−0.927930	−	0.0373943i	−0.428303	−	0.903635i	$-0.640889\pi$
$167$	−11.9915	−	0.483241i	−0.927930	−	0.0373943i	−0.499627	+	0.866241i	$0.666530\pi$
$168$	7.85976			0.606393
$169$	−10.1416	−	8.13311i	−0.780125	−	0.625624i
$170$	14.2255			1.09105
$171$	−0.504812	−	0.0203432i	−0.0386040	−	0.00155569i
$172$	−2.35309	+	8.12382i	−0.179422	+	0.619435i
$173$	−3.74818	−	0.302584i	−0.284969	−	0.0230050i	−0.0628441	−	0.998023i	$-0.520017\pi$
$173$	−3.74818	−	0.302584i	−0.284969	−	0.0230050i	−0.222124	+	0.975018i	$0.571299\pi$
$174$	−4.61397	−	1.74985i	−0.349784	−	0.132656i
$175$	2.04093	−	6.11334i	0.154280	−	0.462125i
$176$	−4.89758	−	11.4950i	−0.369169	−	0.866472i
$177$	7.35628	+	0.893215i	0.552932	+	0.0671381i
$178$	−3.20783	−	2.02851i	−0.240437	−	0.152043i
$179$	10.0005	+	4.26084i	0.747476	+	0.318470i	0.731903	−	0.681409i	$-0.238632\pi$
$179$	10.0005	+	4.26084i	0.747476	+	0.318470i	0.0155732	+	0.999879i	$0.495043\pi$
$180$	6.14192	+	9.71267i	0.457792	+	0.723940i
$181$	1.75284	−	4.62186i	0.130288	−	0.343540i	−0.853959	−	0.520340i	$-0.825805\pi$
$181$	1.75284	−	4.62186i	0.130288	−	0.343540i	0.984247	+	0.176800i	$0.0565744\pi$
$182$	−15.0295	+	0.368688i	−1.11406	+	0.0273290i
$183$	2.62364	+	6.91796i	0.193945	+	0.511390i
$184$	8.33841	−	11.0964i	0.614715	−	0.818038i
$185$	−11.2356	−	1.82597i	−0.826060	−	0.134248i
$186$	12.4458	−	5.30267i	0.912572	−	0.388811i
$187$	−6.13454	−	4.23437i	−0.448602	−	0.309648i
$188$	−43.0749	+	24.8693i	−3.14156	+	1.81378i
$189$	1.55287	+	0.736846i	0.112955	+	0.0535977i
$190$	3.59892	−	0.436988i	0.261093	−	0.0317025i
$191$	−10.6470	−	18.4412i	−0.770393	−	1.33436i	−0.937348	−	0.348395i	$-0.886727\pi$
$191$	−10.6470	−	18.4412i	−0.770393	−	1.33436i	0.166955	−	0.985965i	$-0.446607\pi$
$192$	−4.63798	+	8.03322i	−0.334717	+	0.579748i
$193$	0.904220	−	2.12228i	0.0650872	−	0.152765i	−0.884259	−	0.466996i	$-0.845336\pi$
$193$	0.904220	−	2.12228i	0.0650872	−	0.152765i	0.949347	+	0.314231i	$0.101747\pi$
$194$	17.5204	+	15.5217i	1.25789	+	1.11439i
$195$	−5.91951	−	8.87159i	−0.423905	−	0.635308i
$196$	11.7645	−	10.4225i	0.840324	−	0.744462i
$197$	8.63804	+	25.8741i	0.615435	+	1.84345i	0.531643	+	0.846968i	$0.321575\pi$
$197$	8.63804	+	25.8741i	0.615435	+	1.84345i	0.0837913	+	0.996483i	$0.473297\pi$
$198$	0.367283	−	9.11403i	0.0261017	−	0.647706i
$199$	−1.14976	+	1.40821i	−0.0815047	+	0.0998251i	−0.813748	−	0.581219i	$-0.802576\pi$
$199$	−1.14976	+	1.40821i	−0.0815047	+	0.0998251i	0.732243	+	0.681044i	$0.238474\pi$
$200$	−11.3701	−	12.8342i	−0.803991	−	0.907518i
$201$	12.5448	+	2.56103i	0.884839	+	0.180641i
$202$	−32.4145	+	9.38897i	−2.28068	+	0.660606i
$203$	3.26914	−	1.23982i	0.229449	−	0.0870184i
$204$	−0.310117	−	7.69548i	−0.0217126	−	0.538792i
$205$	−18.3529	−	13.7913i	−1.28182	−	0.963227i
$206$	−34.1771	+	6.97731i	−2.38123	+	0.486132i
$207$	2.68772	−	1.41062i	0.186809	−	0.0980451i
$208$	−5.73452	+	10.5201i	−0.397617	+	0.729440i
$209$	−1.68205	−	0.882810i	−0.116350	−	0.0610653i
$210$	−11.8469	−	3.43150i	−0.817514	−	0.236796i
$211$	17.3439	−	1.40014i	1.19400	−	0.0963898i	0.532564	−	0.846390i	$-0.321229\pi$
$211$	17.3439	−	1.40014i	1.19400	−	0.0963898i	0.661438	+	0.750000i	$0.269947\pi$
$212$	−8.28417	+	40.5785i	−0.568959	+	2.78695i
$213$	0.232921	+	0.443794i	0.0159595	+	0.0304083i
$214$	21.3313	+	28.3868i	1.45818	+	1.94048i
$215$	3.44177	−	5.44273i	0.234727	−	0.371191i
$216$	3.76331	−	2.59762i	0.256061	−	0.176746i
$217$	−4.10913	+	8.65981i	−0.278946	+	0.587866i
$218$	−11.4016	+	11.8703i	−0.772213	+	0.803959i
$219$	8.89397	+	8.54277i	0.600999	+	0.577267i
$220$	5.20828	+	42.8940i	0.351142	+	2.89192i
$221$	0.462873	+	7.13278i	0.0311362	+	0.479803i
$222$	−1.12526	+	9.26736i	−0.0755226	+	0.621985i
$223$	10.5820	−	8.63998i	0.708626	−	0.578576i	−0.208092	−	0.978109i	$-0.566725\pi$
$223$	10.5820	−	8.63998i	0.708626	−	0.578576i	0.916719	+	0.399534i	$0.130828\pi$
$224$	−0.372704	−	1.82563i	−0.0249023	−	0.121980i
$225$	−1.04323	−	3.60163i	−0.0695484	−	0.240109i
$226$	7.01435	+	28.4583i	0.466588	+	1.89302i
$227$	0.929094	−	11.5089i	0.0616662	−	0.763872i	−0.889846	−	0.456261i	$-0.849188\pi$
$227$	0.929094	−	11.5089i	0.0616662	−	0.763872i	0.951512	−	0.307611i	$-0.0995296\pi$
$228$	−0.314851	−	1.93736i	−0.0208515	−	0.128305i
$229$	−9.98950	+	11.2758i	−0.660125	+	0.745127i	−0.979266	−	0.202580i	$-0.935067\pi$
$229$	−9.98950	+	11.2758i	−0.660125	+	0.745127i	0.319141	+	0.947707i	$0.396606\pi$
$230$	−17.4130	+	13.0850i	−1.14818	+	0.862798i
$231$	4.08738	+	5.00613i	0.268930	+	0.329379i
$232$	1.49210	−	9.18123i	0.0979609	−	0.602777i
$233$	7.47827	+	1.84323i	0.489918	+	0.120754i	0.476533	−	0.879157i	$-0.341893\pi$
$233$	7.47827	+	1.84323i	0.489918	+	0.120754i	0.0133846	+	0.999910i	$0.495739\pi$
$234$	−7.07437	+	5.14373i	−0.462466	+	0.336256i
$235$	36.7700	−	9.06300i	2.39861	−	0.591205i
$236$	2.31654	+	28.6955i	0.150794	+	1.86792i
$237$	−7.84992	+	2.62069i	−0.509907	+	0.170232i
$238$	5.72616	+	5.96157i	0.371172	+	0.386431i
$239$		−	3.41597i		−	0.220961i	−0.993878	−	0.110480i	$-0.964761\pi$
$239$		−	3.41597i		−	0.220961i	0.993878	−	0.110480i	$-0.0352389\pi$
$240$	−7.08917	+	6.80924i	−0.457604	+	0.439534i
$241$	−9.81865	−	8.01668i	−0.632475	−	0.516400i	0.261101	−	0.965311i	$-0.415914\pi$
$241$	−9.81865	−	8.01668i	−0.632475	−	0.516400i	−0.893576	+	0.448912i	$0.851812\pi$
$242$	3.53745	−	6.74004i	0.227396	−	0.433266i
$243$	0.987050	−	0.160411i	0.0633193	−	0.0102904i
$244$	−24.2941	+	15.3627i	−1.55527	+	0.983495i
$245$	−10.8116	+	5.13015i	−0.690726	+	0.327754i
$246$	−10.6953	+	15.4948i	−0.681905	+	0.987910i
$247$	0.336212	+	1.79031i	0.0213926	+	0.113915i
$248$	14.4860	+	20.9866i	0.919864	+	1.33265i
$249$	−3.83260	−	2.21275i	−0.242881	−	0.140228i
$250$	−3.84624	−	8.10578i	−0.243258	−	0.512655i
$251$	−26.1910	−	8.74384i	−1.65316	−	0.551906i	−0.671247	−	0.741234i	$-0.734241\pi$
$251$	−26.1910	−	8.74384i	−1.65316	−	0.551906i	−0.981914	+	0.189328i	$0.939369\pi$
$252$	−1.59805	+	6.48354i	−0.100668	+	0.408425i
$253$	11.4039	−	0.459563i	0.716960	−	0.0288925i
$254$	49.7104	−	2.00326i	3.11911	−	0.125696i
$255$	−1.40335	+	5.69363i	−0.0878814	+	0.356549i
$256$	−29.1934	−	9.74619i	−1.82459	−	0.609137i
$257$	6.76370	+	14.2542i	0.421908	+	0.889153i	0.997449	+	0.0713798i	$0.0227402\pi$
$257$	6.76370	+	14.2542i	0.421908	+	0.889153i	−0.575541	+	0.817773i	$0.695208\pi$
$258$	−4.57371	−	2.64064i	−0.284747	−	0.164399i
$259$	−3.75743	−	5.44357i	−0.233475	−	0.338247i
$260$	29.1694	−	29.4265i	1.80901	−	1.82495i
$261$	1.15553	−	1.67407i	0.0715255	−	0.103623i
$262$	7.42012	−	3.52089i	0.458417	−	0.217521i
$263$	−4.01519	+	2.53905i	−0.247587	+	0.156565i	−0.652495	−	0.757793i	$-0.726278\pi$
$263$	−4.01519	+	2.53905i	−0.247587	+	0.156565i	0.404908	+	0.914357i	$0.367303\pi$
$264$	16.9710	−	2.75806i	1.04449	−	0.169747i
$265$	14.6543	−	27.9214i	0.900207	−	1.71520i
$266$	1.63180	+	1.33232i	0.100052	+	0.0816898i
$267$	1.12835	−	1.08379i	0.0690536	−	0.0663269i
$268$			49.7413i			3.03843i
$269$	−0.680977	−	0.708972i	−0.0415199	−	0.0432268i	0.700119	−	0.714027i	$-0.253130\pi$
$269$	−0.680977	−	0.708972i	−0.0415199	−	0.0432268i	−0.741638	+	0.670800i	$0.765951\pi$
$270$	−6.80648	+	2.27234i	−0.414229	+	0.138290i
$271$	0.960652	+	11.8998i	0.0583555	+	0.722862i	0.958098	+	0.286441i	$0.0924722\pi$
$271$	0.960652	+	11.8998i	0.0583555	+	0.722862i	−0.899742	+	0.436421i	$0.856246\pi$
$272$	6.39639	−	1.57657i	0.387838	−	0.0955935i
$273$	1.33510	−	6.05178i	0.0808040	−	0.366270i
$274$	−1.53357	−	0.377992i	−0.0926466	−	0.0228353i
$275$	2.26162	−	13.9163i	0.136381	−	0.839185i
$276$	7.45810	+	9.13451i	0.448925	+	0.549833i
$277$	−7.72251	+	5.80309i	−0.464001	+	0.348674i	−0.806890	−	0.590702i	$-0.798851\pi$
$277$	−7.72251	+	5.80309i	−0.464001	+	0.348674i	0.342889	+	0.939376i	$0.388594\pi$
$278$	14.0729	−	15.8850i	0.844037	−	0.952721i
$279$	0.894557	+	5.50443i	0.0535557	+	0.329542i
$280$	1.87077	−	23.1737i	0.111800	−	1.38489i
$281$	−2.01126	−	8.15999i	−0.119982	−	0.486784i	−0.999931	−	0.0117175i	$-0.996270\pi$
$281$	−2.01126	−	8.15999i	−0.119982	−	0.486784i	0.879950	−	0.475067i	$-0.157576\pi$
$282$	−8.64095	−	29.8320i	−0.514561	−	1.77647i
$283$	−4.60152	−	22.5397i	−0.273532	−	1.33985i	−0.851742	−	0.523961i	$-0.824454\pi$
$283$	−4.60152	−	22.5397i	−0.273532	−	1.33985i	0.578210	−	0.815888i	$-0.303751\pi$
$284$	−1.50829	+	1.23148i	−0.0895003	+	0.0730747i
$285$	−0.180135	+	1.48354i	−0.0106703	+	0.0878775i
$286$	−32.3228	+	6.07007i	−1.91129	+	0.358931i
$287$	−1.60795	−	13.2426i	−0.0949141	−	0.781688i
$288$	−0.781817	−	0.750945i	−0.0460690	−	0.0442499i
$289$	−9.05386	+	9.42607i	−0.532580	+	0.554475i
$290$	−6.25745	+	13.1873i	−0.367450	+	0.774385i
$291$	−7.94081	+	5.48115i	−0.465499	+	0.321311i
$292$	−25.6063	+	40.4931i	−1.49849	+	2.36968i
$293$	10.2181	+	13.5978i	0.596947	+	0.794393i	0.992263	−	0.124153i	$-0.0396212\pi$
$293$	10.2181	+	13.5978i	0.596947	+	0.794393i	−0.395316	+	0.918545i	$0.629365\pi$
$294$	4.56095	+	8.69016i	0.266000	+	0.506821i
$295$	4.38448	−	21.4766i	0.255274	−	1.25042i
$296$	−17.5400	+	1.41598i	−1.01949	+	0.0823019i
$297$	3.61157	+	1.04610i	0.209565	+	0.0607011i
$298$	48.6086	+	25.5118i	2.81582	+	1.47786i
$299$	−7.12749	−	8.30522i	−0.412194	−	0.480303i
$300$	12.8988	−	6.76981i	0.744712	−	0.390855i
$301$	3.66632	−	0.748484i	0.211323	−	0.0431419i
$302$	23.3856	+	17.5731i	1.34569	+	1.01122i
$303$	−0.560143	−	13.8998i	−0.0321794	−	0.798523i
$304$	1.56980	−	0.595345i	0.0900340	−	0.0341454i
$305$	21.0213	−	6.08891i	1.20368	−	0.348650i
$306$	4.71200	+	0.961962i	0.269367	+	0.0549917i
$307$	−22.0539	−	24.8937i	−1.25868	−	1.42076i	−0.865202	−	0.501423i	$-0.832810\pi$
$307$	−22.0539	−	24.8937i	−1.25868	−	1.42076i	−0.393478	−	0.919334i	$-0.628728\pi$
$308$	−15.8794	+	19.4487i	−0.904810	+	1.10819i
$309$	0.578986	−	14.3674i	0.0329373	−	0.817332i
$310$	−12.6720	−	37.9573i	−0.719722	−	2.15583i
$311$	15.8364	−	14.0298i	0.897998	−	0.795557i	−0.0815703	−	0.996668i	$-0.525994\pi$
$311$	15.8364	−	14.0298i	0.897998	−	0.795557i	0.979569	+	0.201111i	$0.0644551\pi$
$312$	−12.1672	−	11.1261i	−0.688832	−	0.629893i
$313$	2.49039	+	2.20629i	0.140765	+	0.124707i	0.730567	−	0.682841i	$-0.239256\pi$
$313$	2.49039	+	2.20629i	0.140765	+	0.124707i	−0.589802	+	0.807548i	$0.700794\pi$
$314$	8.38252	−	19.6745i	0.473053	−	1.11030i
$315$	2.54212	−	4.40309i	0.143232	−	0.248086i
$316$	−16.0757	−	27.8439i	−0.904328	−	1.56634i
$317$	−31.1484	+	3.78211i	−1.74947	+	0.212424i	−0.931727	−	0.363159i	$-0.881698\pi$
$317$	−31.1484	+	3.78211i	−1.74947	+	0.212424i	−0.817743	+	0.575583i	$0.804775\pi$
$318$	−23.3642	−	11.0865i	−1.31020	−	0.621698i
$319$	6.62376	−	3.82423i	0.370859	−	0.214116i
$320$	22.5812	+	15.5867i	1.26233	+	0.871320i
$321$	−13.4659	+	5.73727i	−0.751591	+	0.320223i
$322$	−12.4928	−	2.03027i	−0.696195	−	0.113143i
$323$	0.601687	−	0.800700i	0.0334788	−	0.0445521i
$324$	1.37763	+	3.63252i	0.0765351	+	0.201806i
$325$	−11.8134	+	6.57458i	−0.655288	+	0.364692i
$326$	4.92199	−	12.9782i	0.272604	−	0.718797i
$327$	−3.62621	−	5.73439i	−0.200530	−	0.317112i
$328$	−32.6496	−	13.9107i	−1.80277	−	0.768090i
$329$	18.5990	+	11.7613i	1.02540	+	0.648422i
$330$	−26.7843	−	3.25221i	−1.47443	−	0.179028i
$331$	11.2345	+	26.3684i	0.617505	+	1.44934i	0.875513	+	0.483194i	$0.160523\pi$
$331$	11.2345	+	26.3684i	0.617505	+	1.44934i	−0.258009	+	0.966143i	$0.583066\pi$
$332$	5.44447	−	16.3082i	0.298804	−	0.895028i
$333$	−3.59816	−	1.36460i	−0.197178	−	0.0747798i
$334$	29.0194	+	2.34268i	1.58787	+	0.128186i
$335$	10.5368	−	36.3773i	0.575688	−	1.98750i
$336$	−5.70716	−	0.229991i	−0.311351	−	0.0125470i
$337$	−7.27443			−0.396263			−0.198132	−	0.980175i	$-0.563487\pi$
$337$	−7.27443			−0.396263			−0.198132	+	0.980175i	$0.563487\pi$
$338$	23.7881	+	20.7047i	1.29390	+	1.12619i
$339$	−12.0821			−0.656212
$340$	−22.7631	−	0.917323i	−1.23450	−	0.0497488i
$341$	−5.83376	+	20.1405i	−0.315916	+	1.09067i
$342$	1.22164	+	0.0986212i	0.0660589	+	0.00533282i
$343$	−17.7518	−	6.73235i	−0.958505	−	0.363513i
$344$	3.15245	−	9.44275i	0.169969	−	0.509119i
$345$	−3.51934	−	8.26020i	−0.189475	−	0.444714i
$346$	9.05576	+	1.09957i	0.486841	+	0.0591132i
$347$	3.50928	+	2.21914i	0.188388	+	0.119129i	0.625330	−	0.780360i	$-0.284964\pi$
$347$	3.50928	+	2.21914i	0.188388	+	0.119129i	−0.436942	+	0.899490i	$0.643939\pi$
$348$	7.27026	+	3.09757i	0.389727	+	0.166047i
$349$	18.6566	+	29.5031i	0.998667	+	1.57927i	0.800707	+	0.599056i	$0.204457\pi$
$349$	18.6566	+	29.5031i	0.998667	+	1.57927i	0.197960	+	0.980210i	$0.436568\pi$
$350$	−5.54424	+	14.6190i	−0.296352	+	0.781416i
$351$	−1.36084	−	3.33888i	−0.0726361	−	0.178216i
$352$	−1.44538	−	3.81116i	−0.0770392	−	0.203136i
$353$	15.7110	−	20.9076i	0.836213	−	1.11280i	−0.155940	−	0.987766i	$-0.549841\pi$
$353$	15.7110	−	20.9076i	0.836213	−	1.11280i	0.992153	−	0.125030i	$-0.0399029\pi$
$354$	−17.7439	−	2.88366i	−0.943076	−	0.153265i
$355$	1.36392	−	0.581112i	0.0723894	−	0.0308422i
$356$	5.00224	+	3.45280i	0.265118	+	0.182998i
$357$	−2.95095	+	1.70373i	−0.156181	+	0.0901710i
$358$	−23.8244	−	11.3048i	−1.25916	−	0.597479i
$359$	−27.4029	+	3.32732i	−1.44627	+	0.175609i	−0.805715	−	0.592303i	$-0.798219\pi$
$359$	−27.4029	+	3.32732i	−1.44627	+	0.175609i	−0.640556	+	0.767912i	$0.721296\pi$
$360$	−6.76308	−	11.7140i	−0.356445	−	0.617382i
$361$	−9.37238	+	16.2334i	−0.493283	+	0.854391i
$362$	−4.70023	+	11.0319i	−0.247039	+	0.579821i
$363$	2.34867	+	2.08074i	0.123273	+	0.109210i
$364$	24.0734	+	0.379205i	1.26179	+	0.0198758i
$365$	27.3044	−	24.1896i	1.42918	−	1.26614i
$366$	−5.68375	−	17.0249i	−0.297095	−	0.889907i
$367$	−1.40736	+	34.9232i	−0.0734633	+	1.82297i	0.372622	+	0.927983i	$0.378459\pi$
$367$	−1.40736	+	34.9232i	−0.0734633	+	1.82297i	−0.446085	+	0.894991i	$0.647182\pi$
$368$	−6.37943	+	7.81338i	−0.332551	+	0.407300i
$369$	−5.14654	−	5.80924i	−0.267918	−	0.302417i
$370$	27.0560	+	5.52352i	1.40657	+	0.287154i
$371$	17.5999	−	5.09788i	0.913743	−	0.264669i
$372$	−20.2573	+	7.68257i	−1.05029	+	0.398323i
$373$	−0.193392	−	4.79898i	−0.0100135	−	0.248482i	−0.996441	−	0.0842873i	$-0.973139\pi$
$373$	−0.193392	−	4.79898i	−0.0100135	−	0.248482i	0.986428	−	0.164194i	$-0.0525024\pi$
$374$	14.4561	+	10.8630i	0.747506	+	0.561714i
$375$	3.62369	−	0.739782i	0.187127	−	0.0382022i
$376$	51.8382	−	27.2068i	2.67335	−	1.40308i
$377$	−6.81582	−	2.70844i	−0.351033	−	0.139492i
$378$	−3.69207	−	1.93775i	−0.189900	−	0.0996671i
$379$	19.7295	+	5.71471i	1.01344	+	0.293545i	0.743071	−	0.669213i	$-0.233369\pi$
$379$	19.7295	+	5.71471i	1.01344	+	0.293545i	0.270365	+	0.962758i	$0.412856\pi$
$380$	−5.78704	+	0.467178i	−0.296869	+	0.0239657i
$381$	−4.10216	+	20.0937i	−0.210160	+	1.02943i
$382$	24.0063	+	45.7402i	1.22827	+	2.34027i
$383$	14.2888	+	19.0149i	0.730122	+	0.971616i	0.999962	+	0.00871069i	$0.00277274\pi$
$383$	14.2888	+	19.0149i	0.730122	+	0.971616i	−0.269840	+	0.962905i	$0.586971\pi$
$384$	10.8681	−	17.1865i	0.554608	−	0.877043i
$385$	15.7329	−	10.8596i	0.801823	−	0.553458i
$386$	−2.39907	+	5.05594i	−0.122110	+	0.257340i
$387$	1.50809	−	1.57009i	0.0766604	−	0.0798119i
$388$	−27.0346	−	25.9670i	−1.37247	−	1.31828i
$389$	2.65696	+	21.8820i	0.134713	+	1.10946i	0.890609	+	0.454771i	$0.150279\pi$
$389$	2.65696	+	21.8820i	0.134713	+	1.10946i	−0.755895	+	0.654693i	$0.772798\pi$
$390$	13.4819	+	22.0823i	0.682682	+	1.11818i
$391$	−0.725330	+	5.97363i	−0.0366815	+	0.302100i
$392$	−14.3300	+	11.7001i	−0.723776	+	0.590945i
$393$	0.677205	+	3.31717i	0.0341605	+	0.167329i
$394$	−18.4106	−	63.5607i	−0.927512	−	3.20214i
$395$	5.85839	+	23.7684i	0.294768	+	1.19592i
$396$	−1.17542	+	14.5602i	−0.0590673	+	0.731680i
$397$	1.05333	+	6.48138i	0.0528649	+	0.325291i	0.999990	+	0.00442700i	$0.00140916\pi$
$397$	1.05333	+	6.48138i	0.0528649	+	0.325291i	−0.947125	+	0.320864i	$0.896027\pi$
$398$	2.92450	−	3.30108i	0.146592	−	0.165468i
$399$	−0.694226	+	0.521677i	−0.0347547	+	0.0261165i
$400$	7.88059	+	9.65197i	0.394030	+	0.482599i
$401$	−5.66167	+	34.8376i	−0.282730	+	1.73971i	0.325134	+	0.945668i	$0.394591\pi$
$401$	−5.66167	+	34.8376i	−0.282730	+	1.73971i	−0.607864	+	0.794041i	$0.707974\pi$
$402$	−30.1574	−	7.43314i	−1.50412	−	0.370731i
$403$	18.6198	−	7.58891i	0.927516	−	0.378030i
$404$	52.4738	−	12.9336i	2.61067	−	0.643473i
$405$	−0.238019	−	2.94839i	−0.0118273	−	0.146507i
$406$	−8.04527	+	2.68591i	−0.399280	+	0.133299i
$407$	−10.0234	−	10.4354i	−0.496839	−	0.517264i
$408$			9.06522i			0.448795i
$409$	−15.9151	+	15.2866i	−0.786950	+	0.755876i	−0.974018	−	0.226471i	$-0.927281\pi$
$409$	−15.9151	+	15.2866i	−0.786950	+	0.755876i	0.187068	+	0.982347i	$0.440102\pi$
$410$	43.1390	+	35.2219i	2.13048	+	1.73949i
$411$	0.302575	−	0.576509i	0.0149249	−	0.0284371i
$412$	55.1388	−	8.96093i	2.71650	−	0.441474i
$413$	10.7652	−	6.80750i	0.529721	−	0.334975i
$414$	−6.65263	+	3.15671i	−0.326959	+	0.155144i
$415$	−7.43630	+	10.7733i	−0.365034	+	0.528843i
$416$	−2.00736	+	3.35373i	−0.0984190	+	0.164430i
$417$	4.96953	+	7.19961i	0.243359	+	0.352566i
$418$	3.99095	+	2.30417i	0.195204	+	0.112701i
$419$	−10.2771	−	21.6585i	−0.502068	−	1.05809i	−0.983384	−	0.181538i	$-0.941892\pi$
$419$	−10.2771	−	21.6585i	−0.502068	−	1.05809i	0.481316	−	0.876547i	$-0.340159\pi$
$420$	18.7357	+	6.25489i	0.914207	+	0.305207i
$421$	−4.06715	+	16.5011i	−0.198221	+	0.804213i	0.784653	+	0.619935i	$0.212841\pi$
$421$	−4.06715	+	16.5011i	−0.198221	+	0.804213i	−0.982874	+	0.184279i	$0.941005\pi$
$422$	−42.1771	+	1.69968i	−2.05315	+	0.0827391i
$423$	12.7924	−	0.515517i	0.621988	−	0.0250653i
$424$	11.6661	−	47.3311i	0.566554	−	2.29860i
$425$	7.05095	+	2.35395i	0.342021	+	0.114184i
$426$	−0.521234	−	1.09848i	−0.0252539	−	0.0532215i
$427$	11.0134	+	6.35857i	0.532974	+	0.307713i
$428$	−32.3030	−	46.7989i	−1.56142	−	2.26211i
$429$	0.759166	−	13.5357i	0.0366529	−	0.653509i
$430$	−8.87426	+	12.8566i	−0.427955	+	0.620000i
$431$	−6.76131	+	3.20828i	−0.325681	+	0.154538i	−0.584512	−	0.811385i	$-0.698714\pi$
$431$	−6.76131	+	3.20828i	−0.325681	+	0.154538i	0.258831	+	0.965923i	$0.416663\pi$
$432$	−2.80864	+	1.77608i	−0.135131	+	0.0854516i
$433$	−18.9789	+	3.08437i	−0.912068	+	0.148225i	−0.598298	−	0.801274i	$-0.704156\pi$
$433$	−18.9789	+	3.08437i	−0.912068	+	0.148225i	−0.313770	+	0.949499i	$0.601592\pi$
$434$	10.8061	−	20.5894i	0.518712	−	0.988322i
$435$	−4.66079	−	3.80542i	−0.223468	−	0.182456i
$436$	19.0098	−	18.2592i	0.910406	−	0.874456i
$437$			1.53355i			0.0733598i
$438$	−20.7239	−	21.5758i	−0.990225	−	1.03093i
$439$	18.7579	−	6.26231i	0.895266	−	0.298884i	0.168445	−	0.985711i	$-0.446125\pi$
$439$	18.7579	−	6.26231i	0.895266	−	0.298884i	0.726821	+	0.686827i	$0.240997\pi$
$440$	−4.09242	−	50.6937i	−0.195099	−	2.41673i
$441$	−3.92809	+	0.968188i	−0.187052	+	0.0461042i
$442$	−0.425235	−	17.3346i	−0.0202263	−	0.824522i
$443$	−32.1750	−	7.93044i	−1.52868	−	0.376786i	−0.616761	−	0.787151i	$-0.711555\pi$
$443$	−32.1750	−	7.93044i	−1.52868	−	0.376786i	−0.911922	+	0.410364i	$0.865402\pi$
$444$	2.39820	−	14.7567i	0.113813	−	0.700323i
$445$	−2.92687	−	3.58477i	−0.138747	−	0.169934i
$446$	−26.4941	+	19.9090i	−1.25453	+	0.942720i
$447$	−15.0061	+	16.9384i	−0.709764	+	0.801158i
$448$	2.55755	+	15.7373i	0.120833	+	0.743516i
$449$	1.61025	−	19.9466i	0.0759926	−	0.941337i	−0.840637	−	0.541599i	$-0.817819\pi$
$449$	1.61025	−	19.9466i	0.0759926	−	0.941337i	0.916630	−	0.399738i	$-0.130899\pi$
$450$	2.17689	+	8.83201i	0.102620	+	0.416345i
$451$	−8.11889	−	28.0297i	−0.382303	−	1.31986i
$452$	−9.38898	−	45.9902i	−0.441620	−	2.16320i
$453$	−9.34048	+	7.62627i	−0.438854	+	0.358313i
$454$	−3.37626	+	27.8060i	−0.158456	+	1.30500i
$455$	−17.5252	−	5.37684i	−0.821596	−	0.252070i
$456$	0.278471	+	2.29341i	0.0130406	+	0.107399i
$457$	−21.5727	−	20.7208i	−1.00913	−	0.969279i	−0.00959699	−	0.999954i	$-0.503055\pi$
$457$	−21.5727	−	20.7208i	−1.00913	−	0.969279i	−0.999529	+	0.0306749i	$0.990234\pi$
$458$	25.3153	−	26.3560i	1.18291	−	1.23154i
$459$	−0.849857	+	1.79104i	−0.0396679	+	0.0835984i
$460$	28.7073	−	19.8152i	1.33848	−	0.923889i
$461$	0.491907	−	0.777889i	0.0229104	−	0.0362299i	−0.833541	−	0.552458i	$-0.813690\pi$
$461$	0.491907	−	0.777889i	0.0229104	−	0.0362299i	0.856451	+	0.516228i	$0.172664\pi$
$462$	−9.41851	−	12.5338i	−0.438189	−	0.583123i
$463$	−18.7704	−	35.7640i	−0.872334	−	1.66209i	−0.741770	−	0.670654i	$-0.766013\pi$
$463$	−18.7704	−	35.7640i	−0.872334	−	1.66209i	−0.130564	−	0.991440i	$-0.541679\pi$
$464$	−1.35211	+	6.62306i	−0.0627700	+	0.307468i
$465$	16.4422	−	1.32735i	0.762487	−	0.0615543i
$466$	−17.9467	−	5.19834i	−0.831367	−	0.240808i
$467$	−11.6378	−	6.10797i	−0.538531	−	0.282643i	0.173449	−	0.984843i	$-0.444509\pi$
$467$	−11.6378	−	6.10797i	−0.538531	−	0.282643i	−0.711980	+	0.702200i	$0.752201\pi$
$468$	11.6518	−	7.77460i	0.538606	−	0.359381i
$469$	19.4862	−	10.2271i	0.899788	−	0.472245i
$470$	−90.0133	+	18.3763i	−4.15200	+	0.847637i
$471$	7.04759	+	5.29592i	0.324736	+	0.244023i
$472$	−1.36443	−	33.8581i	−0.0628032	−	1.55845i
$473$	7.65378	−	2.90270i	0.351921	−	0.133466i
$474$	19.2836	−	5.58557i	0.885727	−	0.256554i
$475$	1.85613	+	0.378933i	0.0851653	+	0.0173866i
$476$	−8.77835	−	9.90871i	−0.402355	−	0.454165i
$477$	6.74214	−	8.25762i	0.308701	−	0.378091i
$478$	−0.333675	+	8.28006i	−0.0152619	+	0.378721i
$479$	−11.7488	−	35.1919i	−0.536816	−	1.60796i	−0.771734	−	0.635945i	$-0.780610\pi$
$479$	−11.7488	−	35.1919i	−0.536816	−	1.60796i	0.234918	−	0.972015i	$-0.424518\pi$
$480$	−2.40017	+	2.12636i	−0.109552	+	0.0970548i
$481$	−1.88918	+	13.7458i	−0.0861392	+	0.626755i
$482$	23.0166	+	20.3910i	1.04838	+	0.928783i
$483$	2.04502	−	4.79983i	0.0930514	−	0.218400i
$484$	−6.09511	+	10.5570i	−0.277050	+	0.479865i
$485$	14.2705	+	24.7173i	0.647991	+	1.12235i
$486$	−2.40821	+	0.292410i	−0.109239	+	0.0132640i
$487$	26.7731	+	12.7040i	1.21321	+	0.575673i	0.924293	−	0.381683i	$-0.124655\pi$
$487$	26.7731	+	12.7040i	1.21321	+	0.575673i	0.288912	+	0.957356i	$0.406707\pi$
$488$	29.3000	−	16.9164i	1.32635	−	0.765768i
$489$	4.70885	+	3.25028i	0.212942	+	0.146983i
$490$	26.7076	−	11.3790i	1.20653	−	0.514053i
$491$	−5.16516	−	0.839420i	−0.233100	−	0.0378825i	0.0427389	−	0.999086i	$-0.486392\pi$
$491$	−5.16516	−	0.839420i	−0.233100	−	0.0378825i	−0.275839	+	0.961204i	$0.588956\pi$
$492$	18.1133	−	24.1044i	0.816611	−	1.08671i
$493$	1.42997	+	3.77053i	0.0644028	+	0.169816i
$494$	−0.640075	−	4.37242i	−0.0287983	−	0.196725i
$495$	3.94395	−	10.3993i	0.177267	−	0.467416i
$496$	−9.90456	−	15.6628i	−0.444728	−	0.703281i
$497$	0.792545	+	0.337672i	0.0355505	+	0.0151466i
$498$	9.07382	+	5.73793i	0.406607	+	0.257123i
$499$	29.8648	+	3.62625i	1.33693	+	0.162333i	0.757580	−	0.652743i	$-0.226382\pi$
$499$	29.8648	+	3.62625i	1.33693	+	0.162333i	0.579354	+	0.815076i	$0.303305\pi$
$500$	5.63191	+	13.2186i	0.251867	+	0.591153i
$501$	−3.80041	+	11.3836i	−0.169790	+	0.508582i
$502$	62.6310	+	23.7528i	2.79536	+	1.06014i
$503$	23.6906	+	1.91251i	1.05631	+	0.0852744i	0.596398	−	0.802689i	$-0.296598\pi$
$503$	23.6906	+	1.91251i	1.05631	+	0.0852744i	0.459915	+	0.887963i	$0.347880\pi$
$504$	2.18672	−	7.54944i	0.0974043	−	0.336279i
$505$	−41.1154	−	1.65690i	−1.82961	−	0.0737309i
$506$	−27.6872			−1.23085
$507$	−10.6336	+	7.47844i	−0.472254	+	0.332129i
$508$	−79.6738			−3.53495
$509$	−17.6234	−	0.710200i	−0.781145	−	0.0314791i	−0.353510	−	0.935431i	$-0.615012\pi$
$509$	−17.6234	−	0.710200i	−0.781145	−	0.0314791i	−0.427635	+	0.903952i	$0.640653\pi$
$510$	3.95779	−	13.6639i	0.175254	−	0.605047i
$511$	21.1280	+	1.70563i	0.934648	+	0.0754526i
$512$	31.7847	+	12.0543i	1.40470	+	0.532732i
$513$	−0.159988	+	0.479222i	−0.00706363	+	0.0211582i
$514$	−15.0024	−	35.2119i	−0.661726	−	1.55313i
$515$	−42.2229	−	5.12679i	−1.86056	−	0.225913i
$516$	7.14840	+	4.52037i	0.314691	+	0.198998i
$517$	44.2867	+	18.8688i	1.94773	+	0.829850i
$518$	8.57601	+	13.5619i	0.376808	+	0.595874i
$519$	−1.33345	+	3.51601i	−0.0585318	+	0.154336i
$520$	−35.7002	+	33.2255i	−1.56556	+	1.45703i
$521$	−2.86749	−	7.56096i	−0.125627	−	0.331252i	0.857417	−	0.514623i	$-0.172068\pi$
$521$	−2.86749	−	7.56096i	−0.125627	−	0.331252i	−0.983044	+	0.183371i	$0.941299\pi$
$522$	−2.96445	+	3.94496i	−0.129750	+	0.172666i
$523$	−8.96817	−	1.45747i	−0.392151	−	0.0637307i	−0.0388609	−	0.999245i	$-0.512373\pi$
$523$	−8.96817	−	1.45747i	−0.392151	−	0.0637307i	−0.353290	+	0.935514i	$0.614937\pi$
$524$	−12.1004	+	5.15551i	−0.528610	+	0.225220i
$525$	−5.30415	−	3.66119i	−0.231492	−	0.159788i
$526$	9.98055	−	5.76227i	0.435173	−	0.251247i
$527$	−9.98798	−	4.73935i	−0.435083	−	0.206449i
$528$	−12.4038	+	1.50609i	−0.539806	+	0.0655443i
$529$	6.89316	+	11.9393i	0.299703	+	0.519100i
$530$	−38.2484	+	66.2482i	−1.66140	+	2.87764i
$531$	2.90460	−	6.81734i	0.126049	−	0.295847i
$532$	−2.52522	−	2.23715i	−0.109482	−	0.0969928i
$533$	−16.2569	+	22.7763i	−0.704163	+	0.986550i
$534$	−2.84089	+	2.51681i	−0.122938	+	0.108913i
$535$	13.7106	+	41.0682i	0.592761	+	1.77553i
$536$	2.35746	−	58.4999i	0.101827	−	2.52681i
$537$	6.87494	−	8.42027i	0.296675	−	0.363361i
$538$	1.58139	+	1.78502i	0.0681785	+	0.0769576i
$539$	−14.9043	−	3.04274i	−0.641975	−	0.131060i
$540$	11.0380	−	3.19719i	0.474999	−	0.137585i
$541$	9.42309	−	3.57371i	0.405130	−	0.153646i	−0.143618	−	0.989633i	$-0.545874\pi$
$541$	9.42309	−	3.57371i	0.405130	−	0.153646i	0.548748	+	0.835988i	$0.315105\pi$
$542$	−1.16617	−	28.9381i	−0.0500912	−	1.24300i
$543$	−3.95171	−	2.96952i	−0.169584	−	0.127434i
$544$	2.10562	−	0.429866i	0.0902779	−	0.0184304i
$545$	−17.7703	+	9.32659i	−0.761197	+	0.399507i
$546$	−3.82733	+	14.5387i	−0.163795	+	0.622198i
$547$	13.0610	+	6.85494i	0.558448	+	0.293096i	0.720236	−	0.693730i	$-0.244034\pi$
$547$	13.0610	+	6.85494i	0.558448	+	0.293096i	−0.161788	+	0.986826i	$0.551726\pi$
$548$	2.42959	+	0.703739i	0.103787	+	0.0300623i
$549$	7.37477	−	0.595353i	0.314747	−	0.0254090i
$550$	−6.84136	+	33.5112i	−0.291717	+	1.42892i
$551$	0.477595	+	0.909982i	0.0203462	+	0.0387665i
$552$	−8.33841	−	11.0964i	−0.354906	−	0.472294i
$553$	−7.60260	+	12.0225i	−0.323295	+	0.511251i
$554$	19.2857	−	13.3119i	0.819370	−	0.565570i
$555$	−4.87982	+	10.2840i	−0.207137	+	0.436532i
$556$	−23.5433	+	24.5111i	−0.998456	+	1.03950i
$557$	−4.03171	−	3.87251i	−0.170829	−	0.164084i	0.602434	−	0.798168i	$-0.294197\pi$
$557$	−4.03171	−	3.87251i	−0.170829	−	0.164084i	−0.773263	+	0.634085i	$0.781377\pi$
$558$	−1.63067	−	13.4297i	−0.0690316	−	0.568526i
$559$	−6.73514	−	4.03129i	−0.284866	−	0.170505i
$560$	−2.03652	+	16.7722i	−0.0860585	+	0.708756i
$561$	−5.77392	+	4.71426i	−0.243775	+	0.199036i
$562$	4.07807	+	19.9757i	0.172023	+	0.842624i
$563$	−2.35200	−	8.12005i	−0.0991250	−	0.342219i	0.895592	−	0.444877i	$-0.146753\pi$
$563$	−2.35200	−	8.12005i	−0.0991250	−	0.342219i	−0.994717	+	0.102658i	$0.967265\pi$
$564$	11.9032	+	48.2933i	0.501216	+	2.03351i
$565$	−2.87578	+	35.6229i	−0.120985	+	1.49867i
$566$	8.95206	+	55.0842i	0.376283	+	2.31536i
$567$	1.13979	−	1.28656i	0.0478667	−	0.0540303i
$568$	1.83223	−	1.37683i	0.0768787	−	0.0577706i
$569$	−18.1461	−	22.2250i	−0.760726	−	0.931720i	0.238497	−	0.971143i	$-0.423345\pi$
$569$	−18.1461	−	22.2250i	−0.760726	−	0.931720i	−0.999223	+	0.0394235i	$0.987448\pi$
$570$	0.581548	−	3.57841i	0.0243584	−	0.149883i
$571$	−4.55221	−	1.12202i	−0.190504	−	0.0469550i	0.142909	−	0.989736i	$-0.454354\pi$
$571$	−4.55221	−	1.12202i	−0.190504	−	0.0469550i	−0.333413	+	0.942781i	$0.608200\pi$
$572$	52.1130	−	7.62878i	2.17896	−	0.318975i
$573$	−20.6753	+	5.09601i	−0.863724	+	0.212889i
$574$	2.60399	+	32.2563i	0.108689	+	1.34635i
$575$	−10.7960	+	3.60425i	−0.450226	+	0.150308i
$576$	6.42568	+	6.68985i	0.267737	+	0.278744i
$577$		−	8.60420i		−	0.358197i	−0.983831	−	0.179099i	$-0.942682\pi$
$577$		−	8.60420i		−	0.358197i	0.983831	−	0.179099i	$-0.0573182\pi$
$578$	22.8667	−	21.9637i	0.951128	−	0.913571i
$579$	−1.78692	−	1.45898i	−0.0742619	−	0.0606329i
$580$	10.8633	−	20.6983i	0.451074	−	0.859450i
$581$	−7.50816	+	1.22019i	−0.311491	+	0.0506222i
$582$	19.7834	−	12.5102i	0.820047	−	0.518566i
$583$	36.2134	−	17.1835i	1.49981	−	0.711668i
$584$	32.0342	−	46.4096i	1.32559	−	1.92044i
$585$	−10.1682	+	3.21757i	−0.420405	+	0.133030i
$586$	−23.4397	−	33.9583i	−0.968285	−	1.40280i
$587$	35.1315	+	20.2832i	1.45003	+	0.837176i	0.998482	−	0.0550711i	$-0.0175386\pi$
$587$	35.1315	+	20.2832i	1.45003	+	0.837176i	0.451548	+	0.892247i	$0.350872\pi$
$588$	−6.73787	−	14.1998i	−0.277865	−	0.585589i
$589$	−2.67245	−	0.892195i	−0.110116	−	0.0367623i
$590$	−12.7255	+	51.6295i	−0.523902	+	2.12555i
$591$	27.2558	−	1.09837i	1.12115	−	0.0451809i
$592$	12.7777	−	0.514922i	0.525159	−	0.0211632i
$593$	−6.24896	+	25.3530i	−0.256614	+	1.04112i	0.691293	+	0.722575i	$0.257042\pi$
$593$	−6.24896	+	25.3530i	−0.256614	+	1.04112i	−0.947907	+	0.318549i	$0.896805\pi$
$594$	−8.65201	−	2.88847i	−0.354996	−	0.118515i
$595$	4.32089	+	9.10607i	0.177139	+	0.373313i
$596$	−76.1365	−	43.9574i	−3.11867	−	1.80057i
$597$	1.03272	+	1.49616i	0.0422665	+	0.0612336i
$598$	16.4653	+	20.8275i	0.673315	+	0.851699i
$599$	−3.15800	+	4.57516i	−0.129033	+	0.186936i	−0.882175	−	0.470921i	$-0.843922\pi$
$599$	−3.15800	+	4.57516i	−0.129033	+	0.186936i	0.753143	+	0.657857i	$0.228537\pi$
$600$	−15.4909	+	7.35052i	−0.632413	+	0.300084i
$601$	−7.70474	+	4.87218i	−0.314283	+	0.198740i	−0.682288	−	0.731083i	$-0.739015\pi$
$601$	−7.70474	+	4.87218i	−0.314283	+	0.198740i	0.368005	+	0.929824i	$0.380041\pi$
$602$	−8.96001	+	1.45614i	−0.365183	+	0.0593480i
$603$	5.95009	−	11.3369i	0.242306	−	0.461676i
$604$	−36.2875	−	29.6279i	−1.47652	−	1.20554i
$605$	6.69385	−	6.42953i	0.272144	−	0.261398i
$606$			33.7469i			1.37087i
$607$	5.09723	+	5.30678i	0.206890	+	0.215395i	0.816561	−	0.577259i	$-0.195878\pi$
$607$	5.09723	+	5.30678i	0.206890	+	0.215395i	−0.609671	+	0.792655i	$0.708698\pi$
$608$	0.519498	−	0.173434i	0.0210684	−	0.00703368i
$609$	−0.281339	−	3.48501i	−0.0114004	−	0.141220i
$610$	−51.5490	+	12.7057i	−2.08716	+	0.514438i
$611$	−12.1429	−	44.5354i	−0.491249	−	1.80171i
$612$	−7.47793	−	1.84314i	−0.302277	−	0.0745047i
$613$	2.56199	−	15.7645i	0.103478	−	0.636724i	−0.882560	−	0.470200i	$-0.844182\pi$
$613$	2.56199	−	15.7645i	0.103478	−	0.636724i	0.986037	−	0.166524i	$-0.0532543\pi$
$614$	51.0254	+	62.4947i	2.05922	+	2.52208i
$615$	−18.3529	+	13.7913i	−0.740061	+	0.556119i
$616$	19.5972	−	22.1206i	0.789593	−	0.891266i
$617$	−6.21173	−	38.2223i	−0.250075	−	1.53877i	−0.743352	−	0.668900i	$-0.766765\pi$
$617$	−6.21173	−	38.2223i	−0.250075	−	1.53877i	0.493278	−	0.869872i	$-0.335799\pi$
$618$	−2.80684	+	34.7690i	−0.112908	+	1.39861i
$619$	3.71627	+	15.0775i	0.149370	+	0.606017i	0.997135	+	0.0756448i	$0.0241015\pi$
$619$	3.71627	+	15.0775i	0.149370	+	0.606017i	−0.847765	+	0.530372i	$0.822052\pi$
$620$	17.8296	+	61.5550i	0.716055	+	2.47211i
$621$	−0.607159	−	2.97406i	−0.0243644	−	0.119345i
$622$	−39.7567	+	32.4603i	−1.59410	+	1.30154i
$623$	0.324142	−	2.66955i	0.0129865	−	0.106953i
$624$	8.50934	+	8.43499i	0.340646	+	0.337670i
$625$	−3.57853	−	29.4718i	−0.143141	−	1.17887i
$626$	−5.82101	−	5.59116i	−0.232654	−	0.223468i
$627$	−1.31593	+	1.37003i	−0.0525533	+	0.0547137i
$628$	−14.6821	+	30.9418i	−0.585879	+	1.23471i
$629$	6.27846	−	4.33371i	0.250339	−	0.172796i
$630$	−6.59203	+	10.4245i	−0.262633	+	0.415320i
$631$	−1.46127	−	1.94459i	−0.0581721	−	0.0774131i	0.769419	−	0.638744i	$-0.220546\pi$
$631$	−1.46127	−	1.94459i	−0.0581721	−	0.0774131i	−0.827591	+	0.561331i	$0.810289\pi$
$632$	17.5867	+	33.5086i	0.699560	+	1.33290i
$633$	3.48051	−	17.0486i	0.138338	−	0.677623i
$634$	75.8711	−	6.12495i	3.01322	−	0.243253i
$635$	58.2678	+	16.8775i	2.31229	+	0.669762i
$636$	36.6716	+	19.2468i	1.45412	+	0.763183i
$637$	6.57456	+	13.0211i	0.260493	+	0.515916i
$638$	−16.4291	+	8.62265i	−0.650434	+	0.341374i
$639$	0.491075	−	0.100254i	0.0194266	−	0.00396598i
$640$	−48.0857	−	36.1340i	−1.90075	−	1.42832i
$641$	0.782164	+	19.4092i	0.0308936	+	0.766617i	0.938189	+	0.346123i	$0.112502\pi$
$641$	0.782164	+	19.4092i	0.0308936	+	0.766617i	−0.907295	+	0.420494i	$0.861857\pi$
$642$	33.2007	−	12.5914i	1.31033	−	0.496942i
$643$	4.25792	−	1.23332i	0.167916	−	0.0486375i	−0.193195	−	0.981160i	$-0.561885\pi$
$643$	4.25792	−	1.23332i	0.167916	−	0.0486375i	0.361111	+	0.932523i	$0.382398\pi$
$644$	19.8595	+	4.05435i	0.782575	+	0.159764i
$645$	−4.27028	−	4.82015i	−0.168142	−	0.189793i
$646$	−1.53666	+	1.88207i	−0.0604591	+	0.0740489i
$647$	−0.760489	+	18.8713i	−0.0298979	+	0.741909i	0.912829	+	0.408343i	$0.133893\pi$
$647$	−0.760489	+	18.8713i	−0.0298979	+	0.741909i	−0.942727	+	0.333566i	$0.891748\pi$
$648$	−1.44805	−	4.33743i	−0.0568846	−	0.170390i
$649$	20.8557	−	18.4766i	0.818659	−	0.725269i
$650$	29.2770	−	14.7824i	1.14834	−	0.579813i
$651$	7.17467	+	6.35621i	0.281198	+	0.249119i
$652$	−8.71287	+	20.4498i	−0.341222	+	0.800878i
$653$	−22.1930	+	38.4395i	−0.868480	+	1.50425i	−0.00493115	+	0.999988i	$0.501570\pi$
$653$	−22.1930	+	38.4395i	−0.868480	+	1.50425i	−0.863549	+	0.504264i	$0.831764\pi$
$654$	8.22953	+	14.2540i	0.321800	+	0.557374i
$655$	9.94151	−	1.20712i	0.388447	−	0.0471660i
$656$	23.3006	+	11.0563i	0.909737	+	0.431676i
$657$	10.6799	−	6.16607i	0.416664	−	0.240561i
$658$	−43.9339	−	30.3254i	−1.71272	−	1.18221i
$659$	−24.9967	+	10.6501i	−0.973733	+	0.414869i	−0.819445	−	0.573157i	$-0.805718\pi$
$659$	−24.9967	+	10.6501i	−0.973733	+	0.414869i	−0.154287	+	0.988026i	$0.549308\pi$
$660$	42.6495	+	6.93122i	1.66013	+	0.269798i
$661$	11.7260	−	15.6045i	0.456089	−	0.606944i	−0.511559	−	0.859248i	$-0.670932\pi$
$661$	11.7260	−	15.6045i	0.456089	−	0.606944i	0.967648	+	0.252304i	$0.0811884\pi$
$662$	−24.6560	−	65.0125i	−0.958282	−	2.52678i
$663$	6.97995	+	1.53987i	0.271079	+	0.0598035i
$664$	−7.17606	+	18.9217i	−0.278485	+	0.734305i
$665$	1.37287	+	2.17102i	0.0532376	+	0.0841885i
$666$	8.58840	+	3.65918i	0.332794	+	0.141790i
$667$	−5.21860	−	3.30005i	−0.202065	−	0.127778i
$668$	−46.2846	−	5.61997i	−1.79080	−	0.217443i
$669$	−5.35474	−	12.5680i	−0.207026	−	0.485909i
$670$	−29.0939	+	87.1468i	−1.12399	+	3.36677i
$671$	26.0117	+	9.86493i	1.00417	+	0.380832i
$672$	−1.85724	−	0.149932i	−0.0716446	−	0.00578375i
$673$	3.33402	−	11.5104i	0.128517	−	0.443693i	−0.870289	−	0.492541i	$-0.836068\pi$
$673$	3.33402	−	11.5104i	0.128517	−	0.443693i	0.998806	+	0.0488486i	$0.0155552\pi$
$674$	17.6327	+	0.710573i	0.679186	+	0.0273703i
$675$	−3.74968			−0.144325
$676$	−36.7297	−	34.6649i	−1.41268	−	1.33326i
$677$	−33.1937			−1.27574			−0.637869	−	0.770145i	$-0.720184\pi$
$677$	−33.1937			−1.27574			−0.637869	+	0.770145i	$0.720184\pi$
$678$	29.2863	+	1.18020i	1.12473	+	0.0453252i
$679$	−4.61412	+	15.9298i	−0.177074	+	0.611329i
$680$	26.7278	+	2.15769i	1.02497	+	0.0827438i
$681$	−10.7960	−	4.09439i	−0.413704	−	0.156897i
$682$	16.1080	−	48.2492i	0.616806	−	1.84756i
$683$	0.244755	+	0.574461i	0.00936528	+	0.0219811i	0.924596	−	0.380948i	$-0.124402\pi$
$683$	0.244755	+	0.574461i	0.00936528	+	0.0219811i	−0.915231	+	0.402929i	$0.867992\pi$
$684$	−1.94847	−	0.236587i	−0.0745014	−	0.00904611i
$685$	−1.62776	−	1.02933i	−0.0621934	−	0.0393287i
$686$	42.3714	+	18.0528i	1.61775	+	0.689258i
$687$	8.05137	+	12.7322i	0.307179	+	0.485765i
$688$	−2.56539	+	6.76437i	−0.0978044	+	0.257889i
$689$	−34.4619	−	17.0224i	−1.31289	−	0.648503i
$690$	7.72378	+	20.3659i	0.294039	+	0.775318i
$691$	23.7182	−	31.5632i	0.902284	−	1.20072i	−0.0767550	−	0.997050i	$-0.524456\pi$
$691$	23.7182	−	31.5632i	0.902284	−	1.20072i	0.979039	−	0.203672i	$-0.0652877\pi$
$692$	−14.4198	−	2.34344i	−0.548157	−	0.0890842i
$693$	5.94565	−	2.53321i	0.225857	−	0.0962286i
$694$	−8.28949	−	5.72182i	−0.314665	−	0.217197i
$695$	22.4101	−	12.9385i	0.850064	−	0.490785i
$696$	−8.40361	−	3.98756i	−0.318538	−	0.151148i
$697$	15.2737	−	1.85456i	0.578531	−	0.0702464i
$698$	−42.3405	−	73.3359i	−1.60261	−	2.77580i
$699$	3.85104	−	6.67019i	0.145660	−	0.252290i
$700$	9.81436	−	23.0352i	0.370948	−	0.870647i
$701$	−13.0988	−	11.6045i	−0.494735	−	0.438297i	0.378496	−	0.925603i	$-0.376441\pi$
$701$	−13.0988	−	11.6045i	−0.494735	−	0.438297i	−0.873231	+	0.487306i	$0.837980\pi$
$702$	2.97243	+	8.22614i	0.112187	+	0.310476i
$703$	1.45527	−	1.28925i	0.0548864	−	0.0486251i
$704$	11.0447	+	33.0829i	0.416263	+	1.24686i
$705$	1.52489	−	37.8398i	0.0574307	−	1.42513i
$706$	−40.1247	+	49.1438i	−1.51011	+	1.84955i
$707$	−15.8557	−	17.8974i	−0.596316	−	0.673101i
$708$	28.2071	+	5.75852i	1.06009	+	0.216418i
$709$	−0.175891	+	0.0509473i	−0.00660571	+	0.00191337i	−0.281519	−	0.959556i	$-0.590838\pi$
$709$	−0.175891	+	0.0509473i	−0.00660571	+	0.00191337i	0.274913	+	0.961469i	$0.411351\pi$
$710$	−3.36281	+	1.27535i	−0.126204	+	0.0478629i
$711$	0.333234	+	8.26911i	0.0124972	+	0.310116i
$712$	−5.71940	−	4.29785i	−0.214344	−	0.161069i
$713$	16.5853	−	3.38591i	0.621124	−	0.126803i
$714$	7.31931	−	3.84147i	0.273918	−	0.143763i
$715$	−39.7278	−	5.46007i	−1.48574	−	0.204195i
$716$	37.3939	+	19.6258i	1.39748	+	0.733452i
$717$	−3.28110	−	0.950382i	−0.122535	−	0.0354927i
$718$	66.7478	−	5.38844i	2.49100	−	0.201095i
$719$	−2.62946	+	12.8800i	−0.0980624	+	0.480341i	0.900868	+	0.434094i	$0.142931\pi$
$719$	−2.62946	+	12.8800i	−0.0980624	+	0.480341i	−0.998930	+	0.0462475i	$0.985274\pi$
$720$	4.56807	+	8.70372i	0.170242	+	0.324369i
$721$	−14.8474	−	19.7582i	−0.552944	−	0.735835i
$722$	24.3037	−	38.4332i	0.904489	−	1.43034i
$723$	−10.4319	+	7.20061i	−0.387966	+	0.267794i
$724$	8.23251	−	17.3496i	0.305959	−	0.644795i
$725$	−5.28369	+	5.50091i	−0.196232	+	0.204299i
$726$	−5.48975	−	5.27298i	−0.203744	−	0.195699i
$727$	0.458996	+	3.78017i	0.0170232	+	0.140199i	0.998742	−	0.0501364i	$-0.0159656\pi$
$727$	0.458996	+	3.78017i	0.0170232	+	0.140199i	−0.981719	+	0.190335i	$0.939043\pi$
$728$	−28.2943	−	1.58692i	−1.04866	−	0.0588152i
$729$	0.120537	−	0.992709i	0.00446432	−	0.0367670i
$730$	−68.5468	+	55.9667i	−2.53703	+	2.07142i
$731$	0.863280	+	4.22863i	0.0319296	+	0.156401i
$732$	7.99708	+	27.6091i	0.295581	+	1.02046i
$733$	−2.38074	−	9.65903i	−0.0879346	−	0.356765i	0.910448	−	0.413624i	$-0.135737\pi$
$733$	−2.38074	−	9.65903i	−0.0879346	−	0.356765i	−0.998382	+	0.0568599i	$0.981891\pi$
$734$	6.82266	−	84.5138i	0.251829	−	3.11946i
$735$	1.91964	+	11.8120i	0.0708069	+	0.435693i
$736$	−2.18202	+	2.46299i	−0.0804302	+	0.0907870i
$737$	38.4864	−	28.9206i	1.41766	−	1.06531i
$738$	11.9074	+	14.5839i	0.438317	+	0.536841i
$739$	1.51359	−	9.31350i	0.0556783	−	0.342603i	−0.944233	−	0.329278i	$-0.893195\pi$
$739$	1.51359	−	9.31350i	0.0556783	−	0.342603i	0.999911	−	0.0133242i	$-0.00424134\pi$
$740$	−42.9378	−	10.5832i	−1.57842	−	0.389047i
$741$	1.81316	+	0.175157i	0.0666082	+	0.00643457i
$742$	−43.1590	+	10.6377i	−1.58442	+	0.390523i
$743$	0.393589	+	4.87548i	0.0144394	+	0.178864i	0.999957	+	0.00928997i	$0.00295713\pi$
$743$	0.393589	+	4.87548i	0.0144394	+	0.178864i	−0.985517	+	0.169574i	$0.945761\pi$
$744$	24.1883	−	8.07524i	0.886787	−	0.296053i
$745$	46.3693	+	48.2755i	1.69884	+	1.76868i
$746$			11.6513i			0.426583i
$747$	−3.19169	+	3.06566i	−0.116778	+	0.112167i
$748$	−22.4315	−	18.3148i	−0.820179	−	0.669655i
$749$	−11.6918	+	22.2769i	−0.427209	+	0.813979i
$750$	−8.85584	+	1.43921i	−0.323370	+	0.0525527i
$751$	−18.7327	+	11.8458i	−0.683565	+	0.432260i	−0.830599	−	0.556871i	$-0.812002\pi$
$751$	−18.7327	+	11.8458i	−0.683565	+	0.432260i	0.147034	+	0.989131i	$0.453027\pi$
$752$	−38.4371	+	18.2387i	−1.40166	+	0.665095i
$753$	−15.6854	+	22.7242i	−0.571608	+	0.828117i
$754$	16.2565	+	7.23085i	0.592027	+	0.263332i
$755$	20.2620	+	29.3546i	0.737410	+	1.06832i
$756$	5.78296	+	3.33879i	0.210324	+	0.121431i
$757$	13.1939	+	27.8055i	0.479539	+	1.01061i	0.988696	+	0.149934i	$0.0479060\pi$
$757$	13.1939	+	27.8055i	0.479539	+	1.01061i	−0.509157	+	0.860674i	$0.670043\pi$
$758$	−47.2647	−	15.7793i	−1.71673	−	0.573129i
$759$	2.73136	−	11.0815i	0.0991420	−	0.402235i
$760$	6.82817	−	0.275166i	0.247684	−	0.00998131i
$761$	−19.7577	+	0.796207i	−0.716215	+	0.0288625i	−0.395699	−	0.918380i	$-0.629498\pi$
$761$	−19.7577	+	0.796207i	−0.716215	+	0.0288625i	−0.320517	+	0.947243i	$0.603857\pi$
$762$	11.9061	−	48.3051i	0.431314	−	1.74991i
$763$	−11.0616	−	3.69290i	−0.400456	−	0.133692i
$764$	−35.4644	−	74.7397i	−1.28306	−	2.70399i
$765$	5.07840	+	2.93201i	0.183610	+	0.106007i
$766$	−32.7776	−	47.4865i	−1.18430	−	1.71576i
$767$	−26.3015	−	4.70075i	−0.949692	−	0.169734i
$768$	−17.4835	+	25.3292i	−0.630882	+	0.913990i
$769$	37.5405	−	17.8132i	1.35375	−	0.642360i	0.392935	−	0.919566i	$-0.371460\pi$
$769$	37.5405	−	17.8132i	1.35375	−	0.642360i	0.960811	+	0.277206i	$0.0894083\pi$
$770$	−39.1962	+	24.7862i	−1.41253	+	0.893232i
$771$	15.5732	−	2.53089i	0.560855	−	0.0911478i
$772$	4.16493	−	7.93561i	0.149899	−	0.285609i
$773$	38.1074	+	31.1137i	1.37063	+	1.11908i	0.980103	+	0.198491i	$0.0636041\pi$
$773$	38.1074	+	31.1137i	1.37063	+	1.11908i	0.390526	+	0.920592i	$0.372293\pi$
$774$	−3.80887	+	3.65847i	−0.136907	+	0.131501i
$775$		−	20.9106i		−	0.751132i
$776$	30.5642	+	31.8207i	1.09719	+	1.14229i
$777$	−6.27403	+	2.09458i	−0.225080	+	0.0751426i
$778$	−4.30283	−	53.3001i	−0.154264	−	1.91090i
$779$	3.80712	−	0.938372i	0.136404	−	0.0336207i
$780$	−20.1492	−	36.2047i	−0.721458	−	1.29634i
$781$	1.82978	+	0.451000i	0.0654747	+	0.0161381i
$782$	2.34166	−	14.4088i	0.0837376	−	0.515258i
$783$	−1.28649	−	1.57566i	−0.0459754	−	0.0563096i
$784$	10.7478	−	8.07642i	0.383848	−	0.288443i
$785$	17.2919	−	19.5185i	0.617175	−	0.696647i
$786$	−1.31747	−	8.10674i	−0.0469927	−	0.289158i
$787$	−1.96339	+	24.3210i	−0.0699874	+	0.866950i	0.862572	+	0.505934i	$0.168852\pi$
$787$	−1.96339	+	24.3210i	−0.0699874	+	0.866950i	−0.932560	+	0.361016i	$0.882430\pi$
$788$	25.3612	+	102.895i	0.903457	+	3.66547i
$789$	1.32171	+	4.56307i	0.0470541	+	0.162450i
$790$	−11.8786	−	58.1852i	−0.422622	−	2.07014i
$791$	−16.0863	+	13.1340i	−0.571962	+	0.466992i
$792$	2.07247	−	17.0683i	0.0736420	−	0.606496i
$793$	−8.04804	−	25.4336i	−0.285794	−	0.903175i
$794$	−1.92008	−	15.8133i	−0.0681411	−	0.561193i
$795$	−22.7420	−	21.8440i	−0.806574	−	0.774725i
$796$	−4.89254	+	5.09368i	−0.173412	+	0.180541i
$797$	8.11212	−	17.0959i	0.287346	−	0.605569i	−0.707529	−	0.706685i	$-0.750190\pi$
$797$	8.11212	−	17.0959i	0.287346	−	0.605569i	0.994875	+	0.101116i	$0.0322413\pi$
$798$	1.73371	−	1.19669i	0.0613727	−	0.0423625i
$799$	−13.5652	+	21.4516i	−0.479901	+	0.758902i
$800$	2.44191	+	3.24959i	0.0863346	+	0.114890i
$801$	−0.727075	−	1.38533i	−0.0256899	−	0.0489481i
$802$	17.1265	−	83.8910i	0.604756	−	2.96229i
$803$	46.2188	−	3.73117i	1.63103	−	0.131670i
$804$	47.7774	+	13.8389i	1.68498	+	0.488060i
$805$	−13.6650	−	7.17196i	−0.481629	−	0.252778i
$806$	−45.8743	+	16.5762i	−1.61585	+	0.583871i
$807$	−0.870440	+	0.456842i	−0.0306410	+	0.0160816i
$808$	−62.3265	+	12.7240i	−2.19264	+	0.447630i
$809$	−6.69407	−	5.03027i	−0.235351	−	0.176855i	0.476523	−	0.879162i	$-0.341897\pi$
$809$	−6.69407	−	5.03027i	−0.235351	−	0.176855i	−0.711874	+	0.702307i	$0.752153\pi$
$810$	0.288939	+	7.16995i	0.0101523	+	0.251926i
$811$	−1.51036	+	0.572803i	−0.0530358	+	0.0201138i	−0.380980	−	0.924583i	$-0.624413\pi$
$811$	−1.51036	+	0.572803i	−0.0530358	+	0.0201138i	0.327944	+	0.944697i	$0.393644\pi$
$812$	13.0469	−	3.77909i	0.457857	−	0.132620i
$813$	11.6973	+	2.38801i	0.410241	+	0.0837512i
$814$	23.2766	+	26.2738i	0.815843	+	0.920896i
$815$	10.7039	−	13.1099i	0.374942	−	0.459220i
$816$	0.265265	−	6.58248i	0.00928613	−	0.230433i
$817$	0.348299	+	1.04328i	0.0121855	+	0.0364999i
$818$	40.0702	−	35.4991i	1.40102	−	1.24120i
$819$	−5.44140	−	2.96610i	−0.190138	−	0.103644i
$820$	−66.7581	−	59.1425i	−2.33129	−	2.06535i
$821$	12.9833	−	30.4730i	0.453122	−	1.06352i	−0.524169	−	0.851614i	$-0.675624\pi$
$821$	12.9833	−	30.4730i	0.453122	−	1.06352i	0.977291	−	0.211902i	$-0.0679657\pi$
$822$	−0.789735	+	1.36786i	−0.0275452	+	0.0477096i
$823$	−16.0870	−	27.8635i	−0.560758	−	0.971262i	−0.997430	−	0.0716412i	$-0.977176\pi$
$823$	−16.0870	−	27.8635i	−0.560758	−	0.971262i	0.436672	−	0.899621i	$-0.356157\pi$
$824$	−65.2725	+	7.92552i	−2.27388	+	0.276098i
$825$	−12.7376	−	6.04408i	−0.443468	−	0.210428i
$826$	−26.7590	+	15.4493i	−0.931066	+	0.537551i
$827$	17.5135	+	12.0887i	0.609004	+	0.420365i	0.832253	−	0.554396i	$-0.187051\pi$
$827$	17.5135	+	12.0887i	0.609004	+	0.420365i	−0.223248	+	0.974762i	$0.571666\pi$
$828$	10.8488	−	4.62226i	0.377023	−	0.160635i
$829$	−16.6624	−	2.70790i	−0.578708	−	0.0940493i	−0.135990	−	0.990710i	$-0.543422\pi$
$829$	−16.6624	−	2.70790i	−0.578708	−	0.0940493i	−0.442718	+	0.896661i	$0.645986\pi$
$830$	19.0774	−	25.3874i	0.662187	−	0.881211i
$831$	3.42544	+	9.03213i	0.118827	+	0.313321i
$832$	18.3182	−	27.9823i	0.635069	−	0.970112i
$833$	2.84402	−	7.49907i	0.0985396	−	0.259827i
$834$	−11.3425	−	17.9368i	−0.392760	−	0.621100i
$835$	32.6588	+	13.9146i	1.13020	+	0.481535i
$836$	−6.23758	−	3.94440i	−0.215731	−	0.136420i
$837$	5.53599	+	0.672191i	0.191352	+	0.0232343i
$838$	22.7953	+	53.5025i	0.787450	+	1.84821i
$839$	12.6185	−	37.7970i	0.435638	−	1.30490i	−0.470681	−	0.882303i	$-0.655992\pi$
$839$	12.6185	−	37.7970i	0.435638	−	1.30490i	0.906320	−	0.422593i	$-0.138880\pi$
$840$	−21.7382	−	8.24423i	−0.750040	−	0.284453i
$841$	24.7816	+	2.00058i	0.854538	+	0.0689854i
$842$	11.4703	−	39.6002i	0.395294	−	1.36471i
$843$	−8.39738	−	0.338403i	−0.289221	−	0.0116552i
$844$	67.5997			2.32688
$845$	19.5184	+	33.1320i	0.671453	+	1.13977i
$846$	−31.0583			−1.06781
$847$	5.38892	+	0.217166i	0.185165	+	0.00746191i
$848$	−9.85601	+	34.0269i	−0.338457	+	1.16849i
$849$	−22.9301	−	1.85111i	−0.786958	−	0.0635298i
$850$	−16.8611	−	6.39456i	−0.578330	−	0.219332i
$851$	−3.69899	+	11.0798i	−0.126800	+	0.379811i
$852$	0.763224	+	1.79135i	0.0261476	+	0.0613708i
$853$	−28.9404	−	3.51400i	−0.990900	−	0.120317i	−0.390999	−	0.920391i	$-0.627870\pi$
$853$	−28.9404	−	3.51400i	−0.990900	−	0.120317i	−0.599901	+	0.800074i	$0.704794\pi$
$854$	−26.0745	−	16.4885i	−0.892252	−	0.564226i
$855$	1.37485	+	0.585770i	0.0470190	+	0.0200329i
$856$	35.7729	+	56.5703i	1.22269	+	1.93353i
$857$	−6.45432	+	17.0187i	−0.220475	+	0.581346i	−0.998925	−	0.0463615i	$-0.985237\pi$
$857$	−6.45432	+	17.0187i	−0.220475	+	0.581346i	0.778449	+	0.627708i	$0.216007\pi$
$858$	−3.16235	+	32.7354i	−0.107961	+	1.11757i
$859$	16.7901	+	44.2720i	0.572872	+	1.51054i	0.837637	+	0.546227i	$0.183936\pi$
$859$	16.7901	+	44.2720i	0.572872	+	1.51054i	−0.264765	+	0.964313i	$0.585294\pi$
$860$	15.0293	−	20.0004i	0.512495	−	0.682007i
$861$	−13.1671	−	2.13987i	−0.448735	−	0.0729265i
$862$	16.7023	−	7.11620i	0.568884	−	0.242379i
$863$	1.69046	+	1.16684i	0.0575440	+	0.0397197i	0.596489	−	0.802621i	$-0.296562\pi$
$863$	1.69046	+	1.16684i	0.0575440	+	0.0397197i	−0.538945	+	0.842341i	$0.681177\pi$
$864$	−0.938811	+	0.542023i	−0.0319390	+	0.0184400i
$865$	10.0492	+	4.76840i	0.341683	+	0.162130i
$866$	46.3048	−	5.62242i	1.57350	−	0.191058i
$867$	6.53497	+	11.3189i	0.221939	+	0.384410i
$868$	−18.6193	+	32.2495i	−0.631979	+	1.09462i
$869$	−12.1969	+	28.6273i	−0.413753	+	0.971114i
$870$	10.9257	+	9.67934i	0.370416	+	0.328160i
$871$	−44.6427	−	11.7523i	−1.51266	−	0.398211i
$872$	−23.2225	+	20.5733i	−0.786413	+	0.696701i
$873$	3.05547	+	9.15224i	0.103412	+	0.309757i
$874$	0.149799	−	3.71723i	0.00506703	−	0.125737i
$875$	4.02043	−	4.92413i	0.135915	−	0.166466i
$876$	31.7702	+	35.8612i	1.07342	+	1.21164i
$877$	−55.2792	−	11.2853i	−1.86665	−	0.381079i	−0.872454	−	0.488695i	$-0.837473\pi$
$877$	−55.2792	−	11.2853i	−1.86665	−	0.381079i	−0.994192	+	0.107617i	$0.965678\pi$
$878$	−46.0796	+	13.3471i	−1.55511	+	0.450443i
$879$	15.9038	−	6.03151i	0.536422	−	0.203438i
$880$	1.48822	+	36.9297i	0.0501678	+	1.24490i
$881$	38.3160	+	28.7926i	1.29090	+	0.970046i	0.999911	+	0.0133192i	$0.00423976\pi$
$881$	38.3160	+	28.7926i	1.29090	+	0.970046i	0.290986	+	0.956727i	$0.406017\pi$
$882$	9.61599	−	1.96312i	0.323787	−	0.0661017i
$883$	22.7440	−	11.9370i	0.765397	−	0.401711i	−0.0363775	−	0.999338i	$-0.511582\pi$
$883$	22.7440	−	11.9370i	0.765397	−	0.401711i	0.801774	+	0.597627i	$0.203890\pi$
$884$	−0.437364	+	27.7655i	−0.0147102	+	0.933856i
$885$	−19.4088	−	10.1865i	−0.652421	−	0.342417i
$886$	77.2154	+	22.3657i	2.59410	+	0.751391i
$887$	7.41224	−	0.598378i	0.248879	−	0.0200916i	0.0446023	−	0.999005i	$-0.485798\pi$
$887$	7.41224	−	0.598378i	0.248879	−	0.0200916i	0.204276	+	0.978913i	$0.434516\pi$
$888$	−3.51986	+	17.2414i	−0.118119	+	0.578585i
$889$	16.3815	+	31.2122i	0.549416	+	1.04683i
$890$	6.74437	+	8.97512i	0.226072	+	0.300847i
$891$	2.00960	−	3.17794i	0.0673243	−	0.106465i
$892$	43.6786	−	30.1492i	1.46247	−	1.00947i
$893$	−2.77289	+	5.84375i	−0.0927913	+	0.195554i
$894$	38.0283	−	39.5916i	1.27186	−	1.32414i
$895$	−23.1899	−	22.2742i	−0.775153	−	0.744545i
$896$	−4.21291	−	34.6964i	−0.140743	−	1.15913i
$897$	−9.96031	+	4.53543i	−0.332565	+	0.151434i
$898$	−5.85154	+	48.1918i	−0.195269	+	1.60818i
$899$	8.78693	−	7.17430i	0.293060	−	0.239276i
$900$	−2.91386	−	14.2730i	−0.0971285	−	0.475767i
$901$	5.87975	+	20.2993i	0.195883	+	0.676267i
$902$	16.9416	+	68.7350i	0.564095	+	2.28862i
$903$	0.301101	−	3.72981i	0.0100200	−	0.124120i
$904$	8.86252	+	54.5333i	0.294763	+	1.81375i
$905$	−9.69589	+	10.9444i	−0.322302	+	0.363804i
$906$	23.3856	−	17.5731i	0.776935	−	0.583829i
$907$	−0.419652	−	0.513980i	−0.0139343	−	0.0170664i	0.767591	−	0.640940i	$-0.221455\pi$
$907$	−0.419652	−	0.513980i	−0.0139343	−	0.0170664i	−0.781525	+	0.623874i	$0.785558\pi$
$908$	7.19561	−	44.2764i	0.238795	−	1.46936i
$909$	−13.5069	−	3.32914i	−0.447994	−	0.110421i
$910$	41.9547	+	14.7450i	1.39079	+	0.488791i
$911$	−50.3474	+	12.4095i	−1.66808	+	0.411146i	−0.956565	−	0.291520i	$-0.905839\pi$
$911$	−50.3474	+	12.4095i	−1.66808	+	0.411146i	−0.711520	+	0.702666i	$0.751993\pi$
$912$	−0.135095	−	1.67345i	−0.00447345	−	0.0554136i
$913$	−15.7837	+	5.26936i	−0.522363	+	0.174390i
$914$	50.2666	+	52.3330i	1.66267	+	1.73102i
$915$		−	21.8854i		−	0.723510i
$916$	−42.2081	+	40.5414i	−1.39459	+	1.33953i
$917$	4.50760	+	3.68034i	0.148854	+	0.121536i
$918$	2.23494	−	4.25833i	0.0737641	−	0.140546i
$919$	−48.9435	+	7.95410i	−1.61450	+	0.262381i	−0.899557	−	0.436804i	$-0.856110\pi$
$919$	−48.9435	+	7.95410i	−1.61450	+	0.262381i	−0.714941	+	0.699185i	$0.753546\pi$
$920$	−34.7013	+	21.9437i	−1.14407	+	0.723464i
$921$	−30.0466	+	14.2573i	−0.990069	+	0.469793i
$922$	−1.26833	+	1.83750i	−0.0417703	+	0.0605148i
$923$	−0.748888	−	1.64464i	−0.0246499	−	0.0541340i
$924$	14.2629	+	20.6634i	0.469215	+	0.679775i
$925$	12.4964	+	7.21482i	0.410881	+	0.237222i
$926$	42.0047	+	88.5229i	1.38036	+	2.90904i
$927$	−13.6390	−	4.55338i	−0.447965	−	0.149553i
$928$	−0.527718	+	2.14104i	−0.0173232	+	0.0702830i
$929$	12.1553	−	0.489842i	0.398803	−	0.0160712i	0.159945	−	0.987126i	$-0.448868\pi$
$929$	12.1553	−	0.489842i	0.398803	−	0.0160712i	0.238857	+	0.971055i	$0.423227\pi$
$930$	−39.9843	+	1.61131i	−1.31114	+	0.0528370i
$931$	0.489150	−	1.98456i	0.0160312	−	0.0650413i
$932$	28.3825	+	9.47546i	0.929699	+	0.310379i
$933$	−9.06992	−	19.1145i	−0.296936	−	0.625779i
$934$	27.6125	+	15.9421i	0.903508	+	0.521640i
$935$	12.5252	+	18.1459i	0.409618	+	0.593434i
$936$	−14.0720	+	8.59134i	−0.459957	+	0.280817i
$937$	9.14279	−	13.2456i	0.298682	−	0.432715i	−0.644694	−	0.764441i	$-0.723015\pi$
$937$	9.14279	−	13.2456i	0.298682	−	0.432715i	0.943376	+	0.331725i	$0.107631\pi$
$938$	−48.2321	+	22.8864i	−1.57483	+	0.747268i
$939$	2.81205	−	1.77823i	0.0917678	−	0.0580304i
$940$	145.221	−	23.6007i	4.73658	−	0.769769i
$941$	17.1318	−	32.6418i	0.558479	−	1.06409i	−0.428545	−	0.903520i	$-0.640974\pi$
$941$	17.1318	−	32.6418i	0.558479	−	1.06409i	0.987024	−	0.160573i	$-0.0513341\pi$
$942$	−16.5656	−	13.5254i	−0.539735	−	0.440680i
$943$	−16.9901	+	16.3192i	−0.553273	+	0.531426i
$944$			24.6251i			0.801480i
$945$	−3.52198	−	3.66677i	−0.114570	−	0.119280i
$946$	−18.8358	+	6.28830i	−0.612403	+	0.204450i
$947$	−1.79832	−	22.2762i	−0.0584377	−	0.723880i	−0.957941	−	0.286966i	$-0.907353\pi$
$947$	−1.79832	−	22.2762i	−0.0584377	−	0.723880i	0.899503	−	0.436914i	$-0.143929\pi$
$948$	−31.2171	+	7.69433i	−1.01388	+	0.249900i
$949$	−30.2925	−	32.5488i	−0.983337	−	1.05658i
$950$	−4.46213	−	1.09982i	−0.144770	−	0.0356827i
$951$	−5.03326	+	30.9709i	−0.163215	+	1.00430i
$952$	9.85444	+	12.0695i	0.319384	+	0.391175i
$953$	24.7492	−	18.5978i	0.801707	−	0.602443i	−0.118913	−	0.992905i	$-0.537941\pi$
$953$	24.7492	−	18.5978i	0.801707	−	0.602443i	0.920619	+	0.390461i	$0.127684\pi$
$954$	−17.1491	+	19.3573i	−0.555222	+	0.626716i
$955$	10.1039	+	62.1719i	0.326955	+	2.01184i
$956$	1.06787	−	13.2279i	0.0345373	−	0.427821i
$957$	−1.83040	−	7.42621i	−0.0591683	−	0.240055i
$958$	25.0407	+	86.4504i	0.809027	+	2.79309i
$959$	−0.223849	−	1.09649i	−0.00722847	−	0.0354074i
$960$	21.2537	−	17.3531i	0.685961	−	0.560070i
$961$	−0.0119339	+	0.0982844i	−0.000384964	+	0.00317046i
$962$	5.92195	−	33.1343i	0.190931	−	1.06829i
$963$	1.76431	+	14.5304i	0.0568541	+	0.468236i
$964$	−35.5154	−	34.1130i	−1.14388	−	1.09871i
$965$	−4.72695	+	4.92128i	−0.152166	+	0.158422i
$966$	−5.42582	+	11.4347i	−0.174573	+	0.367905i
$967$	23.4908	−	16.2145i	0.755414	−	0.521425i	−0.126997	−	0.991903i	$-0.540534\pi$
$967$	23.4908	−	16.2145i	0.755414	−	0.521425i	0.882412	+	0.470478i	$0.155919\pi$
$968$	7.66869	−	12.1271i	0.246481	−	0.389779i
$969$	−0.601687	−	0.800700i	−0.0193290	−	0.0257222i
$970$	−32.1763	−	61.3068i	−1.03312	−	1.96844i
$971$	−7.88345	+	38.6157i	−0.252992	+	1.23924i	0.632492	+	0.774567i	$0.282032\pi$
$971$	−7.88345	+	38.6157i	−0.252992	+	1.23924i	−0.885484	+	0.464670i	$0.846173\pi$
$972$	3.87238	−	0.312611i	0.124207	−	0.0100270i
$973$	14.4429	+	4.18343i	0.463018	+	0.134115i
$974$	−63.6552	−	33.4088i	−2.03964	−	1.07049i
$975$	3.02832	+	13.1761i	0.0969837	+	0.421974i
$976$	−21.7705	+	11.4260i	−0.696856	+	0.365738i
$977$	−18.5375	+	3.78446i	−0.593068	+	0.121076i	−0.487179	−	0.873302i	$-0.661974\pi$
$977$	−18.5375	+	3.78446i	−0.593068	+	0.121076i	−0.105889	+	0.994378i	$0.533769\pi$
$978$	−11.0964	−	8.33843i	−0.354825	−	0.266634i
$979$	−0.236872	−	5.87791i	−0.00757045	−	0.187859i
$980$	−43.4702	+	16.4861i	−1.38861	+	0.526629i
$981$	−6.51686	+	1.88763i	−0.208067	+	0.0602674i
$982$	12.4380	+	2.53923i	0.396912	+	0.0810302i
$983$	−17.7606	−	20.0476i	−0.566477	−	0.639420i	0.393559	−	0.919300i	$-0.371244\pi$
$983$	−17.7606	−	20.0476i	−0.566477	−	0.639420i	−0.960035	+	0.279880i	$0.909705\pi$
$984$	−22.4452	+	27.4903i	−0.715526	+	0.876360i
$985$	3.24896	−	80.6222i	0.103521	−	2.56884i
$986$	−3.09785	−	9.27918i	−0.0986555	−	0.295509i
$987$	16.4715	−	14.5925i	0.524294	−	0.464484i
$988$	0.742270	+	7.03786i	0.0236148	+	0.223904i
$989$	−4.94630	−	4.38204i	−0.157283	−	0.139341i
$990$	−10.5757	+	24.8220i	−0.336117	+	0.788896i
$991$	−6.20773	+	10.7521i	−0.197195	+	0.341552i	−0.947618	−	0.319406i	$-0.896517\pi$
$991$	−6.20773	+	10.7521i	−0.197195	+	0.341552i	0.750423	+	0.660958i	$0.229850\pi$
$992$	−3.02267	−	5.23542i	−0.0959699	−	0.166225i
$993$	28.4529	−	3.45481i	0.902927	−	0.109635i
$994$	−1.88809	−	0.895909i	−0.0598865	−	0.0284165i
$995$	4.65707	−	2.68876i	0.147639	−	0.0852394i
$996$	−14.1496	−	9.76674i	−0.448346	−	0.309471i
$997$	−13.7044	+	5.83891i	−0.434023	+	0.184920i	−0.597917	−	0.801558i	$-0.704005\pi$
$997$	−13.7044	+	5.83891i	−0.434023	+	0.184920i	0.163894	+	0.986478i	$0.447595\pi$
$998$	−72.0361	−	11.7070i	−2.28026	−	0.370579i
$999$	−2.31180	+	3.07645i	−0.0731421	+	0.0973344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.a.4.1	✓	336
169.127	even	78	inner	507.2.t.a.127.1	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.a.4.1	✓	336	1.1	even	1	trivial
507.2.t.a.127.1	yes	336	169.127	even	78	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.42393 - 0.0976810i) q^{2} +(0.278217 - 0.960518i) q^{3} +(3.87238 + 0.312611i) q^{4} +(-2.76576 - 1.04892i) q^{5} +(-0.768204 + 2.30105i) q^{6} +(-0.673721 - 1.58128i) q^{7} +(-4.53942 - 0.551185i) q^{8} +(-0.845190 - 0.534466i) q^{9} +O(q^{10})\)	\(q+(-2.42393 - 0.0976810i) q^{2} +(0.278217 - 0.960518i) q^{3} +(3.87238 + 0.312611i) q^{4} +(-2.76576 - 1.04892i) q^{5} +(-0.768204 + 2.30105i) q^{6} +(-0.673721 - 1.58128i) q^{7} +(-4.53942 - 0.551185i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(6.60156 + 2.81266i) q^{10} +(-2.00960 - 3.17794i) q^{11} +(1.37763 - 3.63252i) q^{12} +(-1.19549 + 3.40159i) q^{13} +(1.47859 + 3.89872i) q^{14} +(-1.77699 + 2.36474i) q^{15} +(3.28006 + 0.533061i) q^{16} +(1.82380 - 0.777050i) q^{17} +(1.99647 + 1.37807i) q^{18} +(0.437535 - 0.252611i) q^{19} +(-10.3822 - 4.92641i) q^{20} +(-1.70629 + 0.207181i) q^{21} +(4.56072 + 7.89939i) q^{22} +(-1.51770 + 2.62874i) q^{23} +(-1.79237 + 4.20684i) q^{24} +(2.80667 + 2.48650i) q^{25} +(3.23005 - 8.12844i) q^{26} +(-0.748511 + 0.663123i) q^{27} +(-2.11458 - 6.33393i) q^{28} +(-0.0819070 + 2.03250i) q^{29} +(4.53828 - 5.55839i) q^{30} +(-3.69800 - 4.17418i) q^{31} +(1.06214 + 0.216837i) q^{32} +(-3.61157 + 1.04610i) q^{33} +(-4.49667 + 1.70536i) q^{34} +(0.204722 + 5.08013i) q^{35} +(-3.10582 - 2.33387i) q^{36} +(3.77047 - 0.769746i) q^{37} +(-1.08523 + 0.569573i) q^{38} +(2.93468 + 2.09467i) q^{39} +(11.9768 + 6.28592i) q^{40} +(7.45465 + 2.15926i) q^{41} +(4.15616 - 0.335520i) q^{42} +(-0.435464 + 2.13304i) q^{43} +(-6.78849 - 12.9344i) q^{44} +(1.77699 + 2.36474i) q^{45} +(3.93558 - 6.22362i) q^{46} +(-10.5365 + 7.27282i) q^{47} +(1.42458 - 3.00225i) q^{48} +(2.80252 - 2.91773i) q^{49} +(-6.56030 - 6.30125i) q^{50} +(-0.238957 - 1.96799i) q^{51} +(-5.69275 + 12.7985i) q^{52} +(-1.28497 + 10.5827i) q^{53} +(1.87911 - 1.53425i) q^{54} +(2.22471 + 10.8973i) q^{55} +(2.18672 + 7.54944i) q^{56} +(-0.120908 - 0.490541i) q^{57} +(0.397074 - 4.91864i) q^{58} +(1.18870 + 7.31435i) q^{59} +(-7.62041 + 8.60166i) q^{60} +(-5.91488 + 4.44475i) q^{61} +(8.55596 + 10.4791i) q^{62} +(-0.275718 + 1.69656i) q^{63} +(-9.00642 - 2.21988i) q^{64} +(6.87442 - 8.15403i) q^{65} +(8.85638 - 2.18290i) q^{66} +(1.03025 + 12.7620i) q^{67} +(7.30537 - 2.43889i) q^{68} +(2.10270 + 2.18914i) q^{69} -12.3339i q^{70} +(-0.361470 + 0.347196i) q^{71} +(3.54208 + 2.89202i) q^{72} +(-5.73103 + 10.9196i) q^{73} +(-9.21454 + 1.49751i) q^{74} +(3.16919 - 2.00407i) q^{75} +(1.77327 - 0.841428i) q^{76} +(-3.67130 + 5.31879i) q^{77} +(-6.90886 - 5.36399i) q^{78} +(-4.70120 - 6.81087i) q^{79} +(-8.51272 - 4.91482i) q^{80} +(0.428693 + 0.903450i) q^{81} +(-17.8586 - 5.96208i) q^{82} +(1.05909 - 4.29691i) q^{83} +(-6.67217 + 0.268879i) q^{84} +(-5.85927 + 0.236121i) q^{85} +(1.26389 - 5.12781i) q^{86} +(1.92947 + 0.644151i) q^{87} +(7.37080 + 15.5336i) q^{88} +(1.35493 + 0.782267i) q^{89} +(-4.07630 - 5.90554i) q^{90} +(6.18429 - 0.401322i) q^{91} +(-6.69889 + 9.70502i) q^{92} +(-5.03823 + 2.39067i) q^{93} +(26.2501 - 16.5996i) q^{94} +(-1.47509 + 0.239725i) q^{95} +(0.503781 - 0.959875i) q^{96} +(-7.47401 - 6.10234i) q^{97} +(-7.07812 + 6.79863i) q^{98} +3.76002i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9}+O(q^{10}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31} + 65 q^{32} - 13 q^{33} + 65 q^{34} - 82 q^{35} - 12 q^{36} - 73 q^{38} + 24 q^{40} - 132 q^{42} - 72 q^{43} + 39 q^{44} + 8 q^{48} + 68 q^{49} + 52 q^{50} - 8 q^{51} - 65 q^{52} + 37 q^{53} - 53 q^{55} + 14 q^{56} - 26 q^{57} + 26 q^{58} - 208 q^{59} + 78 q^{60} - 12 q^{61} - 49 q^{62} + 14 q^{64} + 52 q^{65} + 64 q^{66} - 26 q^{67} - 33 q^{68} + 4 q^{69} - 78 q^{71} + 52 q^{73} + 205 q^{74} - 8 q^{75} - 26 q^{76} - 114 q^{77} - 65 q^{78} + 28 q^{79} - 468 q^{80} + 14 q^{81} - 45 q^{82} - 78 q^{83} + 13 q^{85} + 13 q^{86} + 46 q^{87} + 26 q^{88} - 8 q^{90} - 260 q^{91} + 8 q^{92} - 25 q^{94} - 90 q^{95} - 65 q^{96} - 26 q^{97} + 104 q^{98}+O(q^{100}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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