LMFDB - Embedded newform 507.2.q.a.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, 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:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			16.3
Character	$\chi$	$=$	507.16
Dual form			507.2.q.a.412.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.21324 - 0.178671i) q^{2} +(0.845190 + 0.534466i) q^{3} +(2.89239 + 0.470059i) q^{4} +(-0.0344706 - 0.0305383i) q^{5} +(-1.77511 - 1.33391i) q^{6} +(3.31537 - 3.45167i) q^{7} +(-2.00573 - 0.494367i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})$	\(q+(-2.21324 - 0.178671i) q^{2} +(0.845190 + 0.534466i) q^{3} +(2.89239 + 0.470059i) q^{4} +(-0.0344706 - 0.0305383i) q^{5} +(-1.77511 - 1.33391i) q^{6} +(3.31537 - 3.45167i) q^{7} +(-2.00573 - 0.494367i) q^{8} +(0.428693 + 0.903450i) q^{9} +(0.0708354 + 0.0737474i) q^{10} +(0.812315 - 1.71192i) q^{11} +(2.19339 + 1.94317i) q^{12} +(-0.437987 - 3.57885i) q^{13} +(-7.95441 + 7.04699i) q^{14} +(-0.0128126 - 0.0442341i) q^{15} +(-1.20825 - 0.403372i) q^{16} +(-2.49687 + 2.59952i) q^{17} +(-0.787377 - 2.07614i) q^{18} +(0.168160 - 0.291261i) q^{19} +(-0.0853477 - 0.104532i) q^{20} +(4.64692 - 1.14536i) q^{21} +(-2.10372 + 3.64374i) q^{22} +(-2.31689 - 4.01298i) q^{23} +(-1.43100 - 1.48983i) q^{24} +(-0.602428 - 4.96144i) q^{25} +(0.329932 + 7.99909i) q^{26} +(-0.120537 + 0.992709i) q^{27} +(11.2118 - 8.42514i) q^{28} +(-1.19073 - 0.0961257i) q^{29} +(0.0204539 + 0.100190i) q^{30} +(-0.826357 + 6.80566i) q^{31} +(6.40296 + 2.72805i) q^{32} +(1.60152 - 1.01274i) q^{33} +(5.99063 - 5.30724i) q^{34} +(-0.219691 + 0.0177353i) q^{35} +(0.815271 + 2.81464i) q^{36} +(-1.65518 + 0.705207i) q^{37} +(-0.424217 + 0.614584i) q^{38} +(1.54259 - 3.25890i) q^{39} +(0.0540415 + 0.0782927i) q^{40} +(-1.56213 - 0.987834i) q^{41} +(-10.4894 + 1.70469i) q^{42} +(7.19726 + 3.06647i) q^{43} +(3.15424 - 4.56970i) q^{44} +(0.0128126 - 0.0442341i) q^{45} +(4.41083 + 9.29563i) q^{46} +(3.31468 - 8.74009i) q^{47} +(-0.805609 - 0.986692i) q^{48} +(-0.640457 - 15.8928i) q^{49} +(0.446850 + 11.0885i) q^{50} +(-3.49969 + 0.862596i) q^{51} +(0.415442 - 10.5573i) q^{52} +(-2.80807 - 0.692126i) q^{53} +(0.444144 - 2.17556i) q^{54} +(-0.0802802 + 0.0342042i) q^{55} +(-8.35611 + 5.28409i) q^{56} +(0.297796 - 0.156295i) q^{57} +(2.61819 + 0.425498i) q^{58} +(6.18543 - 2.06500i) q^{59} +(-0.0162663 - 0.133965i) q^{60} +(-1.27576 + 4.40443i) q^{61} +(3.04489 - 14.9149i) q^{62} +(4.53968 + 1.51557i) q^{63} +(-11.4281 - 5.99791i) q^{64} +(-0.0941944 + 0.136741i) q^{65} +(-3.72550 + 1.95529i) q^{66} +(12.1045 - 1.96717i) q^{67} +(-8.44386 + 6.34515i) q^{68} +(0.186584 - 4.63003i) q^{69} +0.489397 q^{70} +(0.354984 - 8.80884i) q^{71} +(-0.413204 - 2.02401i) q^{72} +(0.400507 + 0.580234i) q^{73} +(3.78931 - 1.26506i) q^{74} +(2.14255 - 4.51534i) q^{75} +(0.623293 - 0.763395i) q^{76} +(-3.21584 - 8.47949i) q^{77} +(-3.99639 + 6.93709i) q^{78} +(1.79760 - 4.73989i) q^{79} +(0.0293307 + 0.0508023i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(3.28088 + 2.46542i) q^{82} +(3.62791 + 1.90407i) q^{83} +(13.9791 - 1.12851i) q^{84} +(0.165454 - 0.0133568i) q^{85} +(-15.3814 - 8.07276i) q^{86} +(-0.955018 - 0.717649i) q^{87} +(-2.47560 + 3.03206i) q^{88} +(3.99080 + 6.91227i) q^{89} +(-0.0362605 + 0.0956112i) q^{90} +(-13.8051 - 10.3534i) q^{91} +(-4.81502 - 12.6962i) q^{92} +(-4.33582 + 5.31042i) q^{93} +(-8.89777 + 18.7516i) q^{94} +(-0.0146912 + 0.00490464i) q^{95} +(3.95367 + 5.72788i) q^{96} +(3.20053 + 15.6772i) q^{97} +(-1.42209 + 35.2889i) q^{98} +1.89487 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) $ 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9} - q^{10} - 2 q^{11} + 30 q^{12} - 19 q^{13} + q^{15} + 15 q^{16} - 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21} + 22 q^{22} + 46 q^{23} + 3 q^{24} + 28 q^{25} + 34 q^{26} + 30 q^{27} - 2 q^{28} + 36 q^{29} + q^{30} - 34 q^{31} - 190 q^{32} + 15 q^{33} - 51 q^{34} - 80 q^{35} + 15 q^{36} + q^{37} - 53 q^{38} + 5 q^{39} - 45 q^{40} + 9 q^{41} + 130 q^{42} + 78 q^{43} + 35 q^{44} - q^{45} - 318 q^{46} - 12 q^{47} - 15 q^{48} - 71 q^{49} + 48 q^{50} - 14 q^{51} - 63 q^{52} - 26 q^{53} - q^{54} - 61 q^{55} - 4 q^{56} - 38 q^{57} - 27 q^{58} + 208 q^{59} - 180 q^{60} - 3 q^{61} - 61 q^{62} + 2 q^{63} + 140 q^{64} + 45 q^{65} - 60 q^{66} - 80 q^{67} - 140 q^{68} + 6 q^{69} - 100 q^{70} + 84 q^{71} - 3 q^{72} + 134 q^{73} - 151 q^{74} - 12 q^{75} + 32 q^{76} + 82 q^{77} - 63 q^{78} + 4 q^{79} - 155 q^{80} + 15 q^{81} - 56 q^{82} + 106 q^{83} + 2 q^{84} - 19 q^{85} + q^{86} - 49 q^{87} + 8 q^{88} - 14 q^{89} + 2 q^{90} - 368 q^{91} + 36 q^{92} - 4 q^{93} - 59 q^{94} + 104 q^{95} + 75 q^{96} - 28 q^{97} + 101 q^{98} + 30 q^{99}+O(q^{100}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9 - q^10 - 2 * q^11 + 30 * q^12 - 19 * q^13 + q^15 + 15 * q^16 - 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 22 * q^22 + 46 * q^23 + 3 * q^24 + 28 * q^25 + 34 * q^26 + 30 * q^27 - 2 * q^28 + 36 * q^29 + q^30 - 34 * q^31 - 190 * q^32 + 15 * q^33 - 51 * q^34 - 80 * q^35 + 15 * q^36 + q^37 - 53 * q^38 + 5 * q^39 - 45 * q^40 + 9 * q^41 + 130 * q^42 + 78 * q^43 + 35 * q^44 - q^45 - 318 * q^46 - 12 * q^47 - 15 * q^48 - 71 * q^49 + 48 * q^50 - 14 * q^51 - 63 * q^52 - 26 * q^53 - q^54 - 61 * q^55 - 4 * q^56 - 38 * q^57 - 27 * q^58 + 208 * q^59 - 180 * q^60 - 3 * q^61 - 61 * q^62 + 2 * q^63 + 140 * q^64 + 45 * q^65 - 60 * q^66 - 80 * q^67 - 140 * q^68 + 6 * q^69 - 100 * q^70 + 84 * q^71 - 3 * q^72 + 134 * q^73 - 151 * q^74 - 12 * q^75 + 32 * q^76 + 82 * q^77 - 63 * q^78 + 4 * q^79 - 155 * q^80 + 15 * q^81 - 56 * q^82 + 106 * q^83 + 2 * q^84 - 19 * q^85 + q^86 - 49 * q^87 + 8 * q^88 - 14 * q^89 + 2 * q^90 - 368 * q^91 + 36 * q^92 - 4 * q^93 - 59 * q^94 + 104 * q^95 + 75 * q^96 - 28 * q^97 + 101 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{39}\right)$

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 $

$2$	−2.21324	−	0.178671i	−1.56499	−	0.126339i	−0.732653	−	0.680603i	$-0.761718\pi$
$2$	−2.21324	−	0.178671i	−1.56499	−	0.126339i	−0.832341	+	0.554263i	$0.813000\pi$
$3$	0.845190	+	0.534466i	0.487971	+	0.308574i
$3$	0.845190	+	0.534466i	0.487971	+	0.308574i
$4$	2.89239	+	0.470059i	1.44619	+	0.235030i
$5$	−0.0344706	−	0.0305383i	−0.0154157	−	0.0136572i	0.655380	−	0.755300i	$-0.272509\pi$
$5$	−0.0344706	−	0.0305383i	−0.0154157	−	0.0136572i	−0.670795	+	0.741642i	$0.734047\pi$
$6$	−1.77511	−	1.33391i	−0.724686	−	0.544566i
$7$	3.31537	−	3.45167i	1.25309	−	1.30461i	0.318921	−	0.947781i	$-0.396679\pi$
$7$	3.31537	−	3.45167i	1.25309	−	1.30461i	0.934171	−	0.356826i	$-0.116141\pi$
$8$	−2.00573	−	0.494367i	−0.709131	−	0.174785i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	0.0708354	+	0.0737474i	0.0224001	+	0.0233210i
$11$	0.812315	−	1.71192i	0.244922	−	0.516163i	−0.743343	−	0.668911i	$-0.766761\pi$
$11$	0.812315	−	1.71192i	0.244922	−	0.516163i	0.988265	+	0.152748i	$0.0488122\pi$
$12$	2.19339	+	1.94317i	0.633177	+	0.560946i
$13$	−0.437987	−	3.57885i	−0.121476	−	0.992594i
$13$	−0.437987	−	3.57885i	−0.121476	−	0.992594i
$14$	−7.95441	+	7.04699i	−2.12591	+	1.88339i
$15$	−0.0128126	−	0.0442341i	−0.00330819	−	0.0114212i
$16$	−1.20825	−	0.403372i	−0.302062	−	0.100843i
$17$	−2.49687	+	2.59952i	−0.605581	+	0.630477i	−0.951449	−	0.307807i	$-0.900405\pi$
$17$	−2.49687	+	2.59952i	−0.605581	+	0.630477i	0.345868	+	0.938283i	$0.387585\pi$
$18$	−0.787377	−	2.07614i	−0.185587	−	0.489352i
$19$	0.168160	−	0.291261i	0.0385785	−	0.0668199i	−0.846091	−	0.533038i	$-0.821050\pi$
$19$	0.168160	−	0.291261i	0.0385785	−	0.0668199i	0.884670	+	0.466218i	$0.154384\pi$
$20$	−0.0853477	−	0.104532i	−0.0190843	−	0.0233741i
$21$	4.64692	−	1.14536i	1.01404	−	0.249938i
$22$	−2.10372	+	3.64374i	−0.448514	+	0.776849i
$23$	−2.31689	−	4.01298i	−0.483106	−	0.836764i	0.516706	−	0.856163i	$-0.327158\pi$
$23$	−2.31689	−	4.01298i	−0.483106	−	0.836764i	−0.999812	+	0.0193990i	$0.993825\pi$
$24$	−1.43100	−	1.48983i	−0.292101	−	0.304109i
$25$	−0.602428	−	4.96144i	−0.120486	−	0.992288i
$26$	0.329932	+	7.99909i	0.0647050	+	1.56875i
$27$	−0.120537	+	0.992709i	−0.0231973	+	0.191047i
$28$	11.2118	−	8.42514i	2.11884	−	1.59220i
$29$	−1.19073	−	0.0961257i	−0.221113	−	0.0178501i	−0.0305865	−	0.999532i	$-0.509737\pi$
$29$	−1.19073	−	0.0961257i	−0.221113	−	0.0178501i	−0.190527	+	0.981682i	$0.561020\pi$
$30$	0.0204539	+	0.100190i	0.00373435	+	0.0182920i
$31$	−0.826357	+	6.80566i	−0.148418	+	1.22233i	0.708061	+	0.706151i	$0.249570\pi$
$31$	−0.826357	+	6.80566i	−0.148418	+	1.22233i	−0.856479	+	0.516181i	$0.827353\pi$
$32$	6.40296	+	2.72805i	1.13189	+	0.482255i
$33$	1.60152	−	1.01274i	0.278789	−	0.176296i
$34$	5.99063	−	5.30724i	1.02738	−	0.910184i
$35$	−0.219691	+	0.0177353i	−0.0371346	+	0.00299781i
$36$	0.815271	+	2.81464i	0.135878	+	0.469107i
$37$	−1.65518	+	0.705207i	−0.272110	+	0.115935i	−0.523712	−	0.851896i	$-0.675453\pi$
$37$	−1.65518	+	0.705207i	−0.272110	+	0.115935i	0.251601	+	0.967831i	$0.419043\pi$
$38$	−0.424217	+	0.614584i	−0.0688170	+	0.0996987i
$39$	1.54259	−	3.25890i	0.247012	−	0.521841i
$40$	0.0540415	+	0.0782927i	0.00854471	+	0.0123792i
$41$	−1.56213	−	0.987834i	−0.243964	−	0.154274i	0.406888	−	0.913478i	$-0.366614\pi$
$41$	−1.56213	−	0.987834i	−0.243964	−	0.154274i	−0.650852	+	0.759204i	$0.725588\pi$
$42$	−10.4894	+	1.70469i	−1.61854	+	0.263039i
$43$	7.19726	+	3.06647i	1.09757	+	0.467632i	0.863378	−	0.504558i	$-0.168344\pi$
$43$	7.19726	+	3.06647i	1.09757	+	0.467632i	0.234195	+	0.972190i	$0.424755\pi$
$44$	3.15424	−	4.56970i	0.475519	−	0.688908i
$45$	0.0128126	−	0.0442341i	0.00190998	−	0.00659403i
$46$	4.41083	+	9.29563i	0.650342	+	1.37057i
$47$	3.31468	−	8.74009i	0.483496	−	1.27487i	−0.442306	−	0.896864i	$-0.645840\pi$
$47$	3.31468	−	8.74009i	0.483496	−	1.27487i	0.925802	−	0.378009i	$-0.123391\pi$
$48$	−0.805609	−	0.986692i	−0.116280	−	0.142417i
$49$	−0.640457	−	15.8928i	−0.0914939	−	2.27040i
$50$	0.446850	+	11.0885i	0.0631942	+	1.56815i
$51$	−3.49969	+	0.862596i	−0.490055	+	0.120788i
$52$	0.415442	−	10.5573i	0.0576114	−	1.46404i
$53$	−2.80807	−	0.692126i	−0.385718	−	0.0950709i	0.0416883	−	0.999131i	$-0.486726\pi$
$53$	−2.80807	−	0.692126i	−0.385718	−	0.0950709i	−0.427406	+	0.904060i	$0.640573\pi$
$54$	0.444144	−	2.17556i	0.0604404	−	0.296057i
$55$	−0.0802802	+	0.0342042i	−0.0108250	+	0.00461209i
$56$	−8.35611	+	5.28409i	−1.11663	+	0.706116i
$57$	0.297796	−	0.156295i	0.0394440	−	0.0207018i
$58$	2.61819	+	0.425498i	0.343786	+	0.0558706i
$59$	6.18543	−	2.06500i	0.805274	−	0.268840i	0.115914	−	0.993259i	$-0.463020\pi$
$59$	6.18543	−	2.06500i	0.805274	−	0.268840i	0.689360	+	0.724419i	$0.257892\pi$
$60$	−0.0162663	−	0.133965i	−0.00209997	−	0.0172948i
$61$	−1.27576	+	4.40443i	−0.163344	+	0.563929i	0.836528	+	0.547924i	$0.184582\pi$
$61$	−1.27576	+	4.40443i	−0.163344	+	0.563929i	−0.999872	+	0.0160047i	$0.994905\pi$
$62$	3.04489	−	14.9149i	0.386702	−	1.89419i
$63$	4.53968	+	1.51557i	0.571946	+	0.190944i
$64$	−11.4281	−	5.99791i	−1.42851	−	0.749738i
$65$	−0.0941944	+	0.136741i	−0.0116834	+	0.0169606i
$66$	−3.72550	+	1.95529i	−0.458577	+	0.240680i
$67$	12.1045	−	1.96717i	1.47880	−	0.240328i	0.633132	−	0.774044i	$-0.281769\pi$
$67$	12.1045	−	1.96717i	1.47880	−	0.240328i	0.845664	+	0.533716i	$0.179205\pi$
$68$	−8.44386	+	6.34515i	−1.02397	+	0.769463i
$69$	0.186584	−	4.63003i	0.0224621	−	0.557390i
$70$	0.489397			0.0584941
$71$	0.354984	−	8.80884i	0.0421289	−	1.04542i	−0.830496	−	0.557025i	$-0.811943\pi$
$71$	0.354984	−	8.80884i	0.0421289	−	1.04542i	0.872625	−	0.488392i	$-0.162416\pi$
$72$	−0.413204	−	2.02401i	−0.0486965	−	0.238531i
$73$	0.400507	+	0.580234i	0.0468757	+	0.0679112i	0.845721	−	0.533625i	$-0.179171\pi$
$73$	0.400507	+	0.580234i	0.0468757	+	0.0679112i	−0.798845	+	0.601537i	$0.794555\pi$
$74$	3.78931	−	1.26506i	0.440498	−	0.147060i
$75$	2.14255	−	4.51534i	0.247401	−	0.521386i
$76$	0.623293	−	0.763395i	0.0714966	−	0.0875674i
$77$	−3.21584	−	8.47949i	−0.366480	−	0.966327i
$78$	−3.99639	+	6.93709i	−0.452502	+	0.785471i
$79$	1.79760	−	4.73989i	0.202246	−	0.533279i	−0.795068	−	0.606520i	$-0.792565\pi$
$79$	1.79760	−	4.73989i	0.202246	−	0.533279i	0.997314	+	0.0732412i	$0.0233343\pi$
$80$	0.0293307	+	0.0508023i	0.00327927	+	0.00567987i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	3.28088	+	2.46542i	0.362312	+	0.272260i
$83$	3.62791	+	1.90407i	0.398214	+	0.208999i	0.651929	−	0.758280i	$-0.273960\pi$
$83$	3.62791	+	1.90407i	0.398214	+	0.208999i	−0.253715	+	0.967279i	$0.581652\pi$
$84$	13.9791	−	1.12851i	1.52524	−	0.123130i
$85$	0.165454	−	0.0133568i	0.0179460	−	0.00144875i
$86$	−15.3814	−	8.07276i	−1.65861	−	0.870508i
$87$	−0.955018	−	0.717649i	−0.102389	−	0.0769401i
$88$	−2.47560	+	3.03206i	−0.263900	+	0.323218i
$89$	3.99080	+	6.91227i	0.423024	+	0.732699i	0.996234	−	0.0867099i	$-0.0276353\pi$
$89$	3.99080	+	6.91227i	0.423024	+	0.732699i	−0.573210	+	0.819409i	$0.694302\pi$
$90$	−0.0362605	+	0.0956112i	−0.00382220	+	0.0100783i
$91$	−13.8051	−	10.3534i	−1.44717	−	1.08533i
$92$	−4.81502	−	12.6962i	−0.502001	−	1.32367i
$93$	−4.33582	+	5.31042i	−0.449604	+	0.550664i
$94$	−8.89777	+	18.7516i	−0.917734	+	1.93408i
$95$	−0.0146912	+	0.00490464i	−0.00150728	+	0.000503205i
$96$	3.95367	+	5.72788i	0.403520	+	0.584600i
$97$	3.20053	+	15.6772i	0.324965	+	1.59178i	0.733925	+	0.679231i	$0.237686\pi$
$97$	3.20053	+	15.6772i	0.324965	+	1.59178i	−0.408960	+	0.912552i	$0.634108\pi$
$98$	−1.42209	+	35.2889i	−0.143653	+	3.56472i
$99$	1.89487			0.190441
$100$	0.589714	−	14.6336i	0.0589714	−	1.46336i
$101$	−2.36304	+	1.77571i	−0.235131	+	0.176690i	−0.711776	−	0.702406i	$-0.752109\pi$
$101$	−2.36304	+	1.77571i	−0.235131	+	0.176690i	0.476645	+	0.879096i	$0.341853\pi$
$102$	7.89976	−	1.28384i	0.782193	−	0.127119i
$103$	−14.0935	+	7.39686i	−1.38868	+	0.728834i	−0.982727	−	0.185061i	$-0.940752\pi$
$103$	−14.0935	+	7.39686i	−1.38868	+	0.728834i	−0.405950	+	0.913895i	$0.633059\pi$
$104$	−0.890784	+	7.39472i	−0.0873485	+	0.725112i
$105$	−0.195160	−	0.102428i	−0.0190456	−	0.00999592i
$106$	6.09125	+	2.03356i	0.591635	+	0.197517i
$107$	−3.60344	+	17.6508i	−0.348358	+	1.70637i	0.307553	+	0.951531i	$0.400490\pi$
$107$	−3.60344	+	17.6508i	−0.348358	+	1.70637i	−0.655911	+	0.754839i	$0.727715\pi$
$108$	−0.815271	+	2.81464i	−0.0784495	+	0.270839i
$109$	−0.0362570	−	0.298603i	−0.00347279	−	0.0286010i	0.990869	−	0.134825i	$-0.0430471\pi$
$109$	−0.0362570	−	0.298603i	−0.00347279	−	0.0286010i	−0.994342	+	0.106224i	$0.966124\pi$
$110$	0.183790	−	0.0613582i	0.0175237	−	0.00585027i
$111$	−1.77585	−	0.288604i	−0.168556	−	0.0273931i
$112$	−5.39809	+	2.83314i	−0.510072	+	0.267706i
$113$	13.1220	−	8.29787i	1.23442	−	0.780598i	0.252078	−	0.967707i	$-0.418886\pi$
$113$	13.1220	−	8.29787i	1.23442	−	0.780598i	0.982339	+	0.187109i	$0.0599117\pi$
$114$	−0.687018	+	0.292711i	−0.0643451	+	0.0274149i
$115$	−0.0426848	+	0.209084i	−0.00398038	+	0.0194972i
$116$	−3.39887	−	0.837747i	−0.315577	−	0.0777828i
$117$	3.04555	−	1.92993i	0.281561	−	0.178422i
$118$	−14.0588	+	3.46517i	−1.29421	+	0.318995i
$119$	0.694618	+	17.2368i	0.0636755	+	1.58009i
$120$	0.00383061	+	0.0950555i	0.000349685	+	0.00867734i
$121$	4.68609	+	5.73942i	0.426008	+	0.521765i
$122$	3.61050	−	9.52009i	0.326879	−	0.861909i
$123$	−0.792337	−	1.66982i	−0.0714426	−	0.150562i
$124$	−5.58921	+	19.2962i	−0.501926	+	1.73285i
$125$	−0.261551	+	0.378923i	−0.0233939	+	0.0338919i
$126$	−9.77660	−	4.16542i	−0.870969	−	0.371085i
$127$	6.01705	−	0.977866i	0.533927	−	0.0867716i	0.112531	−	0.993648i	$-0.464104\pi$
$127$	6.01705	−	0.977866i	0.533927	−	0.0867716i	0.421396	+	0.906877i	$0.361540\pi$
$128$	12.4565	+	7.87699i	1.10101	+	0.696234i
$129$	4.44413	+	6.43844i	0.391284	+	0.566873i
$130$	0.232906	−	0.285809i	0.0204272	−	0.0250672i
$131$	−3.46332	+	5.01749i	−0.302592	+	0.438380i	−0.944554	−	0.328356i	$-0.893505\pi$
$131$	−3.46332	+	5.01749i	−0.302592	+	0.438380i	0.641962	+	0.766736i	$0.278121\pi$
$132$	5.10828	−	2.17643i	0.444618	−	0.189434i
$133$	−0.447824	−	1.54607i	−0.0388313	−	0.134061i
$134$	−27.1415	+	2.19109i	−2.34467	+	0.189281i
$135$	0.0344706	−	0.0305383i	0.00296676	−	0.00262832i
$136$	6.29316	−	3.97956i	0.539634	−	0.341244i
$137$	11.9651	+	5.09786i	1.02225	+	0.435540i	0.837030	−	0.547157i	$-0.184290\pi$
$137$	11.9651	+	5.09786i	1.02225	+	0.435540i	0.185220	+	0.982697i	$0.440700\pi$
$138$	−1.24021	+	10.2140i	−0.105573	+	0.869475i
$139$	2.30224	+	11.2771i	0.195273	+	0.956512i	0.952775	+	0.303678i	$0.0982148\pi$
$139$	2.30224	+	11.2771i	0.195273	+	0.956512i	−0.757501	+	0.652834i	$0.773580\pi$
$140$	−0.643769	−	0.0519704i	−0.0544084	−	0.00439230i
$141$	7.47281	−	5.61545i	0.629324	−	0.472907i
$142$	−2.35955	+	19.4326i	−0.198009	+	1.63075i
$143$	−6.48248	−	2.15736i	−0.542092	−	0.180407i
$144$	−0.153540	−	1.26451i	−0.0127950	−	0.105376i
$145$	0.0381097	+	0.0396764i	0.00316484	+	0.00329495i
$146$	−0.782745	−	1.35575i	−0.0647804	−	0.112203i
$147$	7.95284	−	13.7747i	0.655939	−	1.13612i
$148$	−5.11892	+	1.26170i	−0.420773	+	0.103711i
$149$	−13.7572	−	16.8495i	−1.12703	−	1.38037i	−0.915171	−	0.403066i	$-0.867944\pi$
$149$	−13.7572	−	16.8495i	−1.12703	−	1.38037i	−0.211863	−	0.977299i	$-0.567953\pi$
$150$	−5.54874	+	9.61069i	−0.453052	+	0.784710i
$151$	4.59024	+	12.1035i	0.373548	+	0.984966i	0.981580	+	0.191053i	$0.0611903\pi$
$151$	4.59024	+	12.1035i	0.373548	+	0.984966i	−0.608031	+	0.793913i	$0.708040\pi$
$152$	−0.481272	+	0.501057i	−0.0390363	+	0.0406411i
$153$	−3.41893	−	1.14141i	−0.276404	−	0.0922773i
$154$	5.60239	+	19.3417i	0.451453	+	1.55860i
$155$	0.236318	−	0.209360i	0.0189816	−	0.0168162i
$156$	5.99365	−	8.70089i	0.479876	−	0.696629i
$157$	10.6331	+	9.42006i	0.848610	+	0.751803i	0.970592	−	0.240729i	$-0.0773866\pi$
$157$	10.6331	+	9.42006i	0.848610	+	0.751803i	−0.121982	+	0.992532i	$0.538925\pi$
$158$	−4.82540	+	10.1693i	−0.383888	+	0.809026i
$159$	−2.00343	−	2.08579i	−0.158883	−	0.165414i
$160$	−0.137404	−	0.289573i	−0.0108628	−	0.0228928i
$161$	−21.5328	−	5.30737i	−1.69702	−	0.418279i
$162$	1.53815	−	1.60138i	0.120848	−	0.125817i
$163$	−14.4266	−	10.8409i	−1.12998	−	0.849127i	−0.139977	−	0.990155i	$-0.544703\pi$
$163$	−14.4266	−	10.8409i	−1.12998	−	0.849127i	−0.990006	+	0.141028i	$0.954959\pi$
$164$	−4.05396	−	3.59150i	−0.316561	−	0.280449i
$165$	−0.0861330	−	0.0139980i	−0.00670544	−	0.00108974i
$166$	−7.68921	−	4.86236i	−0.596798	−	0.377392i
$167$	−12.7649	−	1.03049i	−0.987781	−	0.0797419i	−0.423996	−	0.905664i	$-0.639373\pi$
$167$	−12.7649	−	1.03049i	−0.987781	−	0.0797419i	−0.563784	+	0.825922i	$0.690655\pi$
$168$	−9.88667			−0.762773
$169$	−12.6163	+	3.13498i	−0.970487	+	0.241152i
$170$	−0.368575			−0.0282684
$171$	0.335229	+	0.0270625i	0.0256356	+	0.00206952i
$172$	19.3759	+	12.2526i	1.47740	+	0.934249i
$173$	14.8605	+	2.41507i	1.12983	+	0.183615i	0.696454	−	0.717601i	$-0.254760\pi$
$173$	14.8605	+	2.41507i	1.12983	+	0.183615i	0.433371	+	0.901216i	$0.357324\pi$
$174$	1.98546	+	1.75896i	0.150517	+	0.133346i
$175$	−19.1225	−	14.3696i	−1.44553	−	1.08624i
$176$	−1.67202	+	1.74075i	−0.126033	+	0.131214i
$177$	6.33153	+	1.56058i	0.475907	+	0.117301i
$178$	−7.59756	−	16.0115i	−0.569461	−	1.20011i
$179$	2.81650	+	2.93229i	0.210515	+	0.219169i	0.818086	−	0.575096i	$-0.195035\pi$
$179$	2.81650	+	2.93229i	0.210515	+	0.219169i	−0.607571	+	0.794266i	$0.707856\pi$
$180$	0.0578515	−	0.121919i	0.00431200	−	0.00908734i
$181$	−17.1868	−	15.2262i	−1.27749	−	1.13176i	−0.984452	−	0.175654i	$-0.943796\pi$
$181$	−17.1868	−	15.2262i	−1.27749	−	1.13176i	−0.293036	−	0.956101i	$-0.594666\pi$
$182$	28.7041	+	25.3811i	2.12769	+	1.88138i
$183$	−3.43227	+	3.04073i	−0.253721	+	0.224777i
$184$	2.66317	+	9.19433i	0.196332	+	0.677815i
$185$	0.0785910	+	0.0262375i	0.00577813	+	0.00192902i
$186$	10.5450	−	10.9785i	0.773198	−	0.804984i
$187$	2.42192	+	6.38608i	0.177108	+	0.466996i
$188$	13.6957	−	23.7216i	0.998862	−	1.73008i
$189$	3.02688	+	3.70725i	0.220173	+	0.269663i
$190$	0.0333914	−	0.00823024i	0.00242247	−	0.000597084i
$191$	−2.26484	+	3.92283i	−0.163878	+	0.283846i	−0.936256	−	0.351317i	$-0.885734\pi$
$191$	−2.26484	+	3.92283i	−0.163878	+	0.283846i	0.772378	+	0.635163i	$0.219067\pi$
$192$	−6.45320	−	11.1773i	−0.465720	−	0.806651i
$193$	7.85051	+	8.17324i	0.565092	+	0.588323i	0.941031	−	0.338322i	$-0.109859\pi$
$193$	7.85051	+	8.17324i	0.565092	+	0.588323i	−0.375939	+	0.926645i	$0.622680\pi$
$194$	−4.28247	−	35.2693i	−0.307463	−	2.53219i
$195$	−0.152695	+	0.0652282i	−0.0109347	+	0.00467108i
$196$	5.61809	−	46.2692i	0.401292	−	3.30494i
$197$	21.6742	−	16.2871i	1.54422	−	1.16041i	0.616376	−	0.787452i	$-0.288600\pi$
$197$	21.6742	−	16.2871i	1.54422	−	1.16041i	0.927849	−	0.372957i	$-0.121656\pi$
$198$	−4.19379	−	0.338558i	−0.298040	−	0.0240602i
$199$	0.410761	+	2.01204i	0.0291181	+	0.142630i	0.991751	−	0.128180i	$-0.0409136\pi$
$199$	0.410761	+	2.01204i	0.0291181	+	0.142630i	−0.962633	+	0.270810i	$0.912708\pi$
$200$	−1.24447	+	10.2491i	−0.0879971	+	0.724721i
$201$	11.2820	+	4.80679i	0.795768	+	0.339045i
$202$	5.54723	−	3.50786i	0.390302	−	0.246812i
$203$	−4.27951	+	3.79131i	−0.300362	+	0.266098i
$204$	−10.5279	+	0.849903i	−0.737103	+	0.0595051i
$205$	0.0236810	+	0.0817562i	0.00165395	+	0.00571010i
$206$	32.5139	−	13.8529i	2.26535	−	0.965177i
$207$	2.63229	−	3.81353i	0.182957	−	0.265059i
$208$	−0.914411	+	4.50080i	−0.0634030	+	0.312075i
$209$	−0.362016	−	0.524471i	−0.0250412	−	0.0362784i
$210$	0.413633	+	0.261566i	0.0285434	+	0.0180498i
$211$	−22.1082	+	3.59293i	−1.52199	+	0.247348i	−0.863155	−	0.504939i	$-0.831515\pi$
$211$	−22.1082	+	3.59293i	−1.52199	+	0.247348i	−0.658836	+	0.752287i	$0.728951\pi$
$212$	−7.79668	−	3.32186i	−0.535478	−	0.228146i
$213$	5.00805	−	7.25542i	0.343146	−	0.497133i
$214$	11.1290	−	38.4216i	0.760760	−	2.62645i
$215$	−0.154450	−	0.325496i	−0.0105334	−	0.0221986i
$216$	0.732526	−	1.93151i	0.0498421	−	0.131423i
$217$	20.7512	+	25.4156i	1.40868	+	1.72532i
$218$	0.0268936	+	0.667357i	0.00182146	+	0.0451991i
$219$	0.0283890	+	0.704465i	0.00191835	+	0.0476033i
$220$	−0.248279	+	0.0611954i	−0.0167390	+	0.00412579i
$221$	10.3969	+	7.79738i	0.699371	+	0.524509i
$222$	3.87881	+	0.956042i	0.260329	+	0.0641653i
$223$	−0.180385	+	0.883583i	−0.0120795	+	0.0591691i	−0.985384	−	0.170350i	$-0.945510\pi$
$223$	−0.180385	+	0.883583i	−0.0120795	+	0.0591691i	0.973304	+	0.229519i	$0.0737153\pi$
$224$	30.6445	−	13.0564i	2.04752	−	0.872368i
$225$	4.22416	−	2.67120i	0.281611	−	0.178080i
$226$	−30.5247	+	16.0206i	−2.03048	+	1.06568i
$227$	29.3953	+	4.77720i	1.95103	+	0.317074i	0.999967	+	0.00809020i	$0.00257522\pi$
$227$	29.3953	+	4.77720i	1.95103	+	0.317074i	0.951067	+	0.308984i	$0.0999889\pi$
$228$	0.934810	−	0.312085i	0.0619093	−	0.0206684i
$229$	−3.22021	−	26.5208i	−0.212797	−	1.75254i	−0.572895	−	0.819629i	$-0.694180\pi$
$229$	−3.22021	−	26.5208i	−0.212797	−	1.75254i	0.360097	−	0.932915i	$-0.382743\pi$
$230$	0.131829	−	0.455126i	0.00869253	−	0.0300101i
$231$	1.81400	−	8.88554i	0.119352	−	0.584625i
$232$	2.34076	+	0.781460i	0.153678	+	0.0513053i
$233$	3.58037	+	1.87912i	0.234558	+	0.123105i	0.577908	−	0.816102i	$-0.303869\pi$
$233$	3.58037	+	1.87912i	0.234558	+	0.123105i	−0.343350	+	0.939208i	$0.611562\pi$
$234$	−7.08535	+	3.72723i	−0.463184	+	0.243657i
$235$	−0.381167	+	0.200052i	−0.0248646	+	0.0130499i
$236$	18.8613	−	3.06526i	1.22777	−	0.199532i
$237$	4.05262	−	3.04535i	0.263246	−	0.197817i
$238$	1.54235	−	38.2731i	0.0999760	−	2.48088i
$239$	−16.2465			−1.05090			−0.525449	−	0.850825i	$-0.676103\pi$
$239$	−16.2465			−1.05090			−0.525449	+	0.850825i	$0.676103\pi$
$240$	−0.00236206	+	0.0586139i	−0.000152470	+	0.00378351i
$241$	−3.29962	−	16.1626i	−0.212547	−	1.04113i	−0.936336	−	0.351104i	$-0.885806\pi$
$241$	−3.29962	−	16.1626i	−0.212547	−	1.04113i	0.723789	−	0.690021i	$-0.242399\pi$
$242$	−9.34596	−	13.5400i	−0.600781	−	0.870381i
$243$	−0.948536	+	0.316668i	−0.0608486	+	0.0203143i
$244$	−5.76033	+	12.1396i	−0.368767	+	0.777160i
$245$	−0.463262	+	0.567393i	−0.0295967	+	0.0362494i
$246$	1.45528	+	3.83726i	0.0927854	+	0.244655i
$247$	−1.11603	−	0.474249i	−0.0710114	−	0.0301758i
$248$	5.02194	−	13.2418i	0.318893	−	0.840853i
$249$	2.04861	+	3.54829i	0.129825	+	0.224864i
$250$	0.646577	−	0.791914i	0.0408931	−	0.0500850i
$251$	5.76390	+	4.33129i	0.363814	+	0.273389i	0.766891	−	0.641778i	$-0.221803\pi$
$251$	5.76390	+	4.33129i	0.363814	+	0.273389i	−0.403077	+	0.915166i	$0.632059\pi$
$252$	12.4181	+	6.51754i	0.782268	+	0.410566i
$253$	−8.75194	+	0.706530i	−0.550230	+	0.0444192i
$254$	−13.4919	+	1.08918i	−0.846556	+	0.0683410i
$255$	0.146979	+	0.0771404i	0.00920417	+	0.00483072i
$256$	−5.52583	−	4.15239i	−0.345364	−	0.259524i
$257$	−0.849358	+	1.04027i	−0.0529815	+	0.0648906i	−0.800416	−	0.599445i	$-0.795388\pi$
$257$	−0.849358	+	1.04027i	−0.0529815	+	0.0648906i	0.747434	+	0.664336i	$0.231285\pi$
$258$	−8.68556	−	15.0438i	−0.540739	−	0.936588i
$259$	−3.05340	+	8.05116i	−0.189729	+	0.500275i
$260$	−0.336723	+	0.351230i	−0.0208827	+	0.0217824i
$261$	−0.423612	−	1.11697i	−0.0262210	−	0.0691390i
$262$	8.56163	−	10.4861i	0.528939	−	0.647833i
$263$	−6.32485	+	13.3293i	−0.390007	+	0.821923i	0.609567	+	0.792735i	$0.291343\pi$
$263$	−6.32485	+	13.3293i	−0.390007	+	0.821923i	−0.999574	+	0.0291880i	$0.990708\pi$
$264$	−3.71288	+	1.23954i	−0.228512	+	0.0762885i
$265$	0.0756595	+	0.109612i	0.00464773	+	0.00673339i
$266$	0.714903	+	3.50183i	0.0438335	+	0.214711i
$267$	−0.321387	+	7.97512i	−0.0196685	+	0.488070i
$268$	35.9355			2.19511
$269$	−0.561876	+	13.9428i	−0.0342582	+	0.850108i	0.887143	+	0.461495i	$0.152687\pi$
$269$	−0.561876	+	13.9428i	−0.0342582	+	0.850108i	−0.921401	+	0.388613i	$0.872954\pi$
$270$	−0.0817480	+	0.0614296i	−0.00497502	+	0.00373849i
$271$	8.14076	−	1.32300i	0.494516	−	0.0803666i	0.0919611	−	0.995763i	$-0.470686\pi$
$271$	8.14076	−	1.32300i	0.494516	−	0.0803666i	0.402555	+	0.915396i	$0.368122\pi$
$272$	4.06541	−	2.13369i	0.246502	−	0.129374i
$273$	−6.13437	−	16.1290i	−0.371269	−	0.976169i
$274$	−25.5708	−	13.4206i	−1.54479	−	0.810768i
$275$	−8.98294	−	2.99895i	−0.541692	−	0.180843i
$276$	2.71606	−	13.3041i	0.163488	−	0.800816i
$277$	−7.05260	+	24.3484i	−0.423750	+	1.46295i	0.410650	+	0.911793i	$0.365302\pi$
$277$	−7.05260	+	24.3484i	−0.423750	+	1.46295i	−0.834400	+	0.551160i	$0.814185\pi$
$278$	−3.08050	−	25.3702i	−0.184756	−	1.52161i
$279$	−6.50283	+	2.17096i	−0.389314	+	0.129972i
$280$	0.449408	+	0.0730359i	0.0268572	+	0.00436473i
$281$	−19.6541	+	10.3153i	−1.17247	+	0.615358i	−0.934516	−	0.355920i	$-0.884168\pi$
$281$	−19.6541	+	10.3153i	−1.17247	+	0.615358i	−0.237950	+	0.971278i	$0.576475\pi$
$282$	−17.5424	+	11.0932i	−1.04464	+	0.660588i
$283$	−12.2748	+	5.22980i	−0.729661	+	0.310880i	−0.724659	−	0.689108i	$-0.758003\pi$
$283$	−12.2748	+	5.22980i	−0.729661	+	0.310880i	−0.00500243	+	0.999987i	$0.501592\pi$
$284$	5.16743	−	25.3117i	0.306630	−	1.50197i
$285$	−0.0150382	−	0.00370659i	−0.000890787	−	0.000219559i
$286$	13.9618	+	5.93297i	0.825579	+	0.350824i
$287$	−8.58873	+	2.11693i	−0.506977	+	0.124959i
$288$	0.280247	+	6.95425i	0.0165137	+	0.409783i
$289$	0.161390	+	4.00485i	0.00949353	+	0.235579i
$290$	−0.0772568	−	0.0946224i	−0.00453667	−	0.00555642i
$291$	−5.67389	+	14.9608i	−0.332609	+	0.877019i
$292$	0.885677	+	1.86652i	0.0518303	+	0.109230i
$293$	−3.92390	+	13.5469i	−0.229237	+	0.791416i	0.760602	+	0.649219i	$0.224904\pi$
$293$	−3.92390	+	13.5469i	−0.229237	+	0.791416i	−0.989838	+	0.142198i	$0.954583\pi$
$294$	−20.0627	+	29.0658i	−1.17008	+	1.69515i
$295$	−0.276277	−	0.117711i	−0.0160855	−	0.00685338i
$296$	3.66847	−	0.596185i	0.213226	−	0.0346525i
$297$	1.60152	+	1.01274i	0.0929298	+	0.0587652i
$298$	27.4374	+	39.7500i	1.58941	+	2.30265i
$299$	−13.3471	+	10.0495i	−0.771882	+	0.581175i
$300$	8.31957	−	12.0530i	0.480331	−	0.695879i
$301$	34.4460	−	14.6761i	1.98544	−	0.845915i
$302$	−7.99675	−	27.6080i	−0.460161	−	1.58866i
$303$	−2.94628	+	0.237848i	−0.169259	+	0.0136640i
$304$	−0.320665	+	0.284084i	−0.0183914	+	0.0162933i
$305$	0.178480	−	0.112864i	0.0102197	−	0.00646257i
$306$	7.36296	+	3.13707i	0.420913	+	0.179334i
$307$	−0.131020	+	1.07905i	−0.00747771	+	0.0615845i	−0.995970	−	0.0896864i	$-0.971414\pi$
$307$	−0.131020	+	1.07905i	−0.00747771	+	0.0615845i	0.988492	+	0.151271i	$0.0483366\pi$
$308$	−5.31562	−	26.0376i	−0.302885	−	1.48363i
$309$	−15.8651	−	1.28076i	−0.902533	−	0.0728600i
$310$	−0.560435	+	0.421140i	−0.0318306	+	0.0239191i
$311$	0.110655	−	0.911329i	0.00627469	−	0.0516767i	−0.989235	−	0.146334i	$-0.953253\pi$
$311$	0.110655	−	0.911329i	0.00627469	−	0.0516767i	0.995510	+	0.0946575i	$0.0301756\pi$
$312$	−4.70511	+	5.77385i	−0.266374	+	0.326880i
$313$	−0.619103	−	5.09878i	−0.0349938	−	0.288200i	−0.999691	−	0.0248399i	$-0.992092\pi$
$313$	−0.619103	−	5.09878i	−0.0349938	−	0.288200i	0.964698	−	0.263360i	$-0.0848307\pi$
$314$	−21.8504	−	22.7486i	−1.23309	−	1.28378i
$315$	−0.110203	−	0.190877i	−0.00620923	−	0.0107547i
$316$	7.42739	−	12.8646i	0.417823	−	0.723691i
$317$	22.1267	−	5.45373i	1.24276	−	0.306312i	0.437489	−	0.899224i	$-0.355868\pi$
$317$	22.1267	−	5.45373i	1.24276	−	0.306312i	0.805268	+	0.592912i	$0.202022\pi$
$318$	4.06140	+	4.97431i	0.227752	+	0.278945i
$319$	−1.13181	+	1.96035i	−0.0633691	+	0.109758i
$320$	0.210766	+	0.555745i	0.0117822	+	0.0310671i
$321$	−12.4794	+	12.9924i	−0.696530	+	0.725164i
$322$	46.7090	+	15.5937i	2.60299	+	0.869005i
$323$	0.337266	+	1.16438i	0.0187660	+	0.0647877i
$324$	−2.19339	+	1.94317i	−0.121855	+	0.107954i
$325$	−17.4924	+	4.32904i	−0.970303	+	0.240132i
$326$	29.9926	+	26.5711i	1.66114	+	1.47164i
$327$	0.128949	−	0.271755i	0.00713090	−	0.0150281i
$328$	2.64486	+	2.75359i	0.146038	+	0.152042i
$329$	−19.1785	−	40.4178i	−1.05734	−	2.22831i
$330$	0.188132	+	0.0463703i	0.0103563	+	0.00255260i
$331$	7.30921	−	7.60969i	0.401750	−	0.418266i	−0.489339	−	0.872093i	$-0.662762\pi$
$331$	7.30921	−	7.60969i	0.401750	−	0.418266i	0.891090	+	0.453827i	$0.149942\pi$
$332$	9.59829	+	7.21265i	0.526775	+	0.395845i
$333$	−1.34668	−	1.19306i	−0.0737978	−	0.0653792i
$334$	28.0677	+	4.56145i	1.53580	+	0.249591i
$335$	−0.477323	−	0.301841i	−0.0260789	−	0.0164913i
$336$	−6.07663	−	0.490556i	−0.331507	−	0.0267620i
$337$	−11.6792			−0.636206			−0.318103	−	0.948056i	$-0.603046\pi$
$337$	−11.6792			−0.636206			−0.318103	+	0.948056i	$0.603046\pi$
$338$	28.4831	−	4.68428i	1.54927	−	0.254791i
$339$	15.5255			0.843232
$340$	0.484836	+	0.0391400i	0.0262939	+	0.00212266i
$341$	10.9795	+	6.94300i	0.594572	+	0.375984i
$342$	−0.737105	−	0.119791i	−0.0398581	−	0.00647757i
$343$	−31.9034	−	28.2639i	−1.72262	−	1.52611i
$344$	−12.9198	−	9.70858i	−0.696588	−	0.523452i
$345$	−0.147825	+	0.153902i	−0.00795863	+	0.00828581i
$346$	−32.4584	−	8.00027i	−1.74497	−	0.430097i
$347$	−14.1586	−	29.8386i	−0.760073	−	1.60182i	−0.798087	−	0.602543i	$-0.794154\pi$
$347$	−14.1586	−	29.8386i	−0.760073	−	1.60182i	0.0380137	−	0.999277i	$-0.487897\pi$
$348$	−2.42495	−	2.52464i	−0.129991	−	0.135335i
$349$	−4.16571	+	8.77905i	−0.222985	+	0.469932i	−0.983854	−	0.178975i	$-0.942722\pi$
$349$	−4.16571	+	8.77905i	−0.222985	+	0.469932i	0.760868	+	0.648906i	$0.224773\pi$
$350$	39.7552	+	35.2200i	2.12500	+	1.88259i
$351$	3.60555	−	0.00341085i	0.192450	−	0.000182057i
$352$	9.87142	−	8.74532i	0.526149	−	0.466127i
$353$	−1.89984	−	6.55902i	−0.101119	−	0.349102i	0.893966	−	0.448136i	$-0.147912\pi$
$353$	−1.89984	−	6.55902i	−0.101119	−	0.349102i	−0.995084	+	0.0990342i	$0.968425\pi$
$354$	−13.7343	−	4.58520i	−0.729972	−	0.243701i
$355$	−0.281244	+	0.292806i	−0.0149269	+	0.0155405i
$356$	8.29377	+	21.8689i	0.439569	+	1.15905i
$357$	−8.62537	+	14.9396i	−0.456503	+	0.790687i
$358$	−5.70967	−	6.99307i	−0.301765	−	0.369595i
$359$	−18.9613	+	4.67354i	−1.00074	+	0.246660i	−0.705459	−	0.708751i	$-0.749259\pi$
$359$	−18.9613	+	4.67354i	−1.00074	+	0.246660i	−0.295280	+	0.955411i	$0.595413\pi$
$360$	−0.0475663	+	0.0823873i	−0.00250697	+	0.00434219i
$361$	9.44344	+	16.3565i	0.497023	+	0.860870i
$362$	35.3181	+	36.7700i	1.85628	+	1.93259i
$363$	0.893114	+	7.35546i	0.0468763	+	0.386061i
$364$	−35.0630	−	36.4354i	−1.83780	−	1.90973i
$365$	0.00391365	−	0.0322318i	0.000204850	−	0.00168709i
$366$	8.13972	−	6.11660i	0.425470	−	0.319720i
$367$	−3.45048	−	0.278551i	−0.180113	−	0.0145403i	−0.00991923	−	0.999951i	$-0.503157\pi$
$367$	−3.45048	−	0.278551i	−0.180113	−	0.0145403i	−0.170194	+	0.985411i	$0.554439\pi$
$368$	1.18066	+	5.78324i	0.0615460	+	0.301472i
$369$	0.222784	−	1.83479i	0.0115977	−	0.0955153i
$370$	−0.169253	−	0.0721118i	−0.00879902	−	0.00374891i
$371$	−11.6988	+	7.39786i	−0.607370	+	0.384078i
$372$	−15.0371	+	13.3217i	−0.779637	+	0.690698i
$373$	21.4955	−	1.73529i	1.11299	−	0.0898501i	0.489739	−	0.871869i	$-0.337092\pi$
$373$	21.4955	−	1.73529i	1.11299	−	0.0898501i	0.623255	+	0.782019i	$0.285810\pi$
$374$	−4.21927	−	14.5666i	−0.218173	−	0.753222i
$375$	−0.423582	+	0.180471i	−0.0218737	+	0.00931950i
$376$	−10.9691	+	15.8916i	−0.565691	+	0.819544i
$377$	0.177505	+	4.30355i	0.00914197	+	0.221644i
$378$	−6.03681	−	8.74583i	−0.310500	−	0.449837i
$379$	10.1908	+	6.44429i	0.523468	+	0.331021i	0.769927	−	0.638132i	$-0.220293\pi$
$379$	10.1908	+	6.44429i	0.523468	+	0.331021i	−0.246459	+	0.969153i	$0.579267\pi$
$380$	−0.0447981	+	0.00728040i	−0.00229809	+	0.000373477i
$381$	5.60819	+	2.38943i	0.287316	+	0.122414i
$382$	5.71353	−	8.27748i	0.292330	−	0.423513i
$383$	−7.01537	+	24.2199i	−0.358468	+	1.23758i	0.555406	+	0.831579i	$0.312563\pi$
$383$	−7.01537	+	24.2199i	−0.358468	+	1.23758i	−0.913874	+	0.405997i	$0.866924\pi$
$384$	6.31810	+	13.3151i	0.322419	+	0.679484i
$385$	−0.148097	+	0.390500i	−0.00754772	+	0.0199017i
$386$	−15.9147	−	19.4920i	−0.810037	−	0.992115i
$387$	0.315012	+	7.81694i	0.0160130	+	0.397358i
$388$	1.88796	+	46.8491i	0.0958464	+	2.37840i
$389$	24.5246	−	6.04476i	1.24344	−	0.306482i	0.437904	−	0.899022i	$-0.355721\pi$
$389$	24.5246	−	6.04476i	1.24344	−	0.306482i	0.805541	+	0.592540i	$0.201875\pi$
$390$	0.349605	−	0.117083i	0.0177029	−	0.00592873i
$391$	16.2168	+	3.99709i	0.820120	+	0.202141i
$392$	−6.57229	+	32.1932i	−0.331951	+	1.62600i
$393$	−5.60884	+	2.38970i	−0.282929	+	0.120545i
$394$	−50.8802	+	32.1747i	−2.56331	+	1.62094i
$395$	−0.206713	+	0.108491i	−0.0104008	+	0.00545878i
$396$	5.48069	+	0.890699i	0.275415	+	0.0447593i
$397$	32.4430	−	10.8311i	1.62827	−	0.543595i	0.651638	−	0.758530i	$-0.274082\pi$
$397$	32.4430	−	10.8311i	1.62827	−	0.543595i	0.976628	+	0.214935i	$0.0689538\pi$
$398$	−0.549618	−	4.52651i	−0.0275499	−	0.226894i
$399$	0.447824	−	1.54607i	0.0224193	−	0.0774003i
$400$	−1.27342	+	6.23764i	−0.0636712	+	0.311882i
$401$	−33.2048	−	11.0854i	−1.65817	−	0.553579i	−0.675247	−	0.737592i	$-0.735963\pi$
$401$	−33.2048	−	11.0854i	−1.65817	−	0.553579i	−0.982924	+	0.184013i	$0.941091\pi$
$402$	−24.1108	−	12.6543i	−1.20254	−	0.631141i
$403$	24.7184	−	0.0233835i	1.23131	−	0.00116482i
$404$	−7.66952	+	4.02528i	−0.381573	+	0.200265i
$405$	0.0454559	−	0.00738731i	0.00225872	−	0.000367078i
$406$	10.1490	−	7.62644i	0.503684	−	0.378494i
$407$	−0.137273	+	3.40639i	−0.00680435	+	0.168848i
$408$	7.44586			0.368625
$409$	0.467055	−	11.5898i	0.0230944	−	0.573081i	−0.945674	−	0.325115i	$-0.894597\pi$
$409$	0.467055	−	11.5898i	0.0230944	−	0.573081i	0.968769	−	0.247966i	$-0.0797620\pi$
$410$	−0.0378041	−	0.185177i	−0.00186701	−	0.00914524i
$411$	7.38817	+	10.7036i	0.364432	+	0.527970i
$412$	−44.2410	+	14.7698i	−2.17960	+	0.727656i
$413$	13.3793	−	28.1963i	0.658352	−	1.38745i
$414$	−6.50725	+	7.96994i	−0.319814	+	0.391701i
$415$	−0.0669091	−	0.176425i	−0.00328444	−	0.00866035i
$416$	6.95886	−	24.1101i	0.341186	−	1.18209i
$417$	−4.08140	+	10.7618i	−0.199867	+	0.527006i
$418$	0.707520	+	1.22546i	0.0346059	+	0.0599392i
$419$	−11.6950	+	14.3238i	−0.571338	+	0.699762i	−0.976752	−	0.214371i	$-0.931230\pi$
$419$	−11.6950	+	14.3238i	−0.571338	+	0.699762i	0.405414	+	0.914133i	$0.367127\pi$
$420$	−0.516331	−	0.387997i	−0.0251943	−	0.0189323i
$421$	7.79048	+	4.08876i	0.379685	+	0.199274i	0.643759	−	0.765228i	$-0.277374\pi$
$421$	7.79048	+	4.08876i	0.379685	+	0.199274i	−0.264074	+	0.964502i	$0.585066\pi$
$422$	49.5726	−	4.00191i	2.41316	−	0.194810i
$423$	9.31722	−	0.752163i	0.453019	−	0.0365714i
$424$	5.29005	+	2.77643i	0.256907	+	0.134835i
$425$	14.4016	+	10.8221i	0.698578	+	0.524947i
$426$	−12.3803	+	15.1632i	−0.599829	+	0.734657i
$427$	10.9730	+	19.0058i	0.531021	+	0.919755i
$428$	−18.7195	+	49.3592i	−0.904840	+	2.38587i
$429$	−4.32590	−	5.28804i	−0.208856	−	0.255309i
$430$	0.283677	+	0.747994i	0.0136801	+	0.0360715i
$431$	0.383979	−	0.470288i	0.0184956	−	0.0226530i	−0.765274	−	0.643704i	$-0.777397\pi$
$431$	0.383979	−	0.470288i	0.0184956	−	0.0226530i	0.783770	+	0.621051i	$0.213294\pi$
$432$	0.546069	−	1.15082i	0.0262728	−	0.0553687i
$433$	−9.62447	+	3.21312i	−0.462522	+	0.154413i	−0.538373	−	0.842707i	$-0.680961\pi$
$433$	−9.62447	+	3.21312i	−0.462522	+	0.154413i	0.0758508	+	0.997119i	$0.475833\pi$
$434$	−41.3862	−	59.9583i	−1.98660	−	2.87809i
$435$	0.0110043	+	0.0539025i	0.000527614	+	0.00258443i
$436$	0.0354918	−	0.880720i	0.00169975	−	0.0421788i
$437$	−1.55843			−0.0745499
$438$	0.0630359	−	1.56422i	0.00301197	−	0.0747413i
$439$	6.40093	−	4.80999i	0.305500	−	0.229568i	−0.436924	−	0.899498i	$-0.643932\pi$
$439$	6.40093	−	4.80999i	0.305500	−	0.229568i	0.742424	+	0.669930i	$0.233676\pi$
$440$	0.177929	−	0.0289163i	0.00848245	−	0.00137853i
$441$	14.0838	−	7.39174i	0.670656	−	0.351988i
$442$	−21.6176	−	19.1151i	−1.02825	−	0.909211i
$443$	−21.7669	−	11.4242i	−1.03418	−	0.542778i	−0.139841	−	0.990174i	$-0.544659\pi$
$443$	−21.7669	−	11.4242i	−1.03418	−	0.542778i	−0.894336	+	0.447396i	$0.852351\pi$
$444$	−5.00079	−	1.66951i	−0.237327	−	0.0792315i
$445$	0.0735236	−	0.360143i	0.00348535	−	0.0170724i
$446$	0.557105	−	1.92335i	0.0263797	−	0.0910732i
$447$	−2.62196	−	21.5938i	−0.124015	−	1.02135i
$448$	−58.5910	+	19.5606i	−2.76817	+	0.924149i
$449$	−0.645849	−	0.104961i	−0.0304795	−	0.00495340i	0.145152	−	0.989409i	$-0.453633\pi$
$449$	−0.645849	−	0.104961i	−0.0304795	−	0.00495340i	−0.175632	+	0.984456i	$0.556197\pi$
$450$	−9.82632	+	5.15725i	−0.463217	+	0.243115i
$451$	−2.96004	+	1.87181i	−0.139383	+	0.0881403i
$452$	41.8545	−	17.8325i	1.96867	−	0.838773i
$453$	−2.58926	+	12.6831i	−0.121654	+	0.595902i
$454$	−64.2052	−	15.8252i	−3.01330	−	0.742711i
$455$	0.159694	+	0.778473i	0.00748656	+	0.0364954i
$456$	−0.674564	+	0.166265i	−0.0315894	+	0.00778608i
$457$	0.766206	+	19.0132i	0.0358416	+	0.889400i	0.912695	+	0.408642i	$0.133997\pi$
$457$	0.766206	+	19.0132i	0.0358416	+	0.889400i	−0.876853	+	0.480758i	$0.840361\pi$
$458$	2.38859	+	59.2721i	0.111611	+	2.76961i
$459$	−2.27960	−	2.79201i	−0.106403	−	0.130320i
$460$	−0.221743	+	0.584688i	−0.0103388	+	0.0272612i
$461$	14.1351	+	29.7891i	0.658338	+	1.38742i	0.907953	+	0.419073i	$0.137645\pi$
$461$	14.1351	+	29.7891i	0.658338	+	1.38742i	−0.249614	+	0.968345i	$0.580304\pi$
$462$	−5.60239	+	19.3417i	−0.260647	+	0.899856i
$463$	2.93298	−	4.24915i	0.136307	−	0.197475i	−0.748886	−	0.662699i	$-0.769411\pi$
$463$	2.93298	−	4.24915i	0.136307	−	0.197475i	0.885193	+	0.465224i	$0.154026\pi$
$464$	1.39992	+	0.596451i	0.0649897	+	0.0276895i
$465$	0.311630	−	0.0506448i	0.0144515	−	0.00234859i
$466$	−7.58846	−	4.79865i	−0.351529	−	0.222293i
$467$	16.4570	+	23.8421i	0.761541	+	1.10328i	0.991503	+	0.130083i	$0.0415243\pi$
$467$	16.4570	+	23.8421i	0.761541	+	1.10328i	−0.229962	+	0.973200i	$0.573860\pi$
$468$	9.71610	−	4.15051i	0.449127	−	0.191857i
$469$	33.3408	−	48.3025i	1.53953	−	2.23040i
$470$	0.879355	−	0.374658i	0.0405616	−	0.0172817i
$471$	3.95225	+	13.6447i	0.182110	+	0.628717i
$472$	−13.4271	+	1.08395i	−0.618034	+	0.0498929i
$473$	11.0960	−	9.83019i	0.510194	−	0.451993i
$474$	−9.51352	+	6.01599i	−0.436971	+	0.276323i
$475$	−1.54638	−	0.658850i	−0.0709527	−	0.0302301i
$476$	−6.09319	+	50.1819i	−0.279281	+	2.30008i
$477$	−0.578496	−	2.83366i	−0.0264875	−	0.129744i
$478$	35.9573	+	2.90277i	1.64465	+	0.132770i
$479$	−22.6920	+	17.0519i	−1.03682	+	0.779123i	−0.975723	−	0.219009i	$-0.929718\pi$
$479$	−22.6920	+	17.0519i	−1.03682	+	0.779123i	−0.0611011	+	0.998132i	$0.519461\pi$
$480$	0.0386343	−	0.318182i	0.00176341	−	0.0145230i
$481$	3.24878	+	5.61478i	0.148132	+	0.256012i
$482$	4.41505	+	36.3612i	0.201100	+	1.65621i
$483$	−15.3627	−	15.9943i	−0.699028	−	0.727766i
$484$	10.8561	+	18.8034i	0.493461	+	0.854699i
$485$	0.368432	−	0.638143i	0.0167296	−	0.0289766i
$486$	2.15591	−	0.531385i	0.0977943	−	0.0241041i
$487$	20.0237	+	24.5246i	0.907361	+	1.11131i	0.993363	+	0.115020i	$0.0366932\pi$
$487$	20.0237	+	24.5246i	0.907361	+	1.11131i	−0.0860026	+	0.996295i	$0.527409\pi$
$488$	4.73622	−	8.20338i	0.214399	−	0.371350i
$489$	−6.39916	−	16.8732i	−0.289380	−	0.763032i
$490$	1.12668	−	1.17300i	0.0508984	−	0.0529909i
$491$	11.3252	+	3.78089i	0.511097	+	0.170629i	0.560508	−	0.828149i	$-0.310606\pi$
$491$	11.3252	+	3.78089i	0.511097	+	0.170629i	−0.0494106	+	0.998779i	$0.515734\pi$
$492$	−1.50684	−	5.20220i	−0.0679334	−	0.234533i
$493$	3.22299	−	2.85532i	0.145156	−	0.128597i
$494$	2.38531	+	1.24903i	0.107320	+	0.0561964i
$495$	−0.0653173	−	0.0578661i	−0.00293579	−	0.00260089i
$496$	3.74365	−	7.88958i	0.168095	−	0.354253i
$497$	−29.2283	−	30.4298i	−1.31107	−	1.36497i
$498$	−3.90008	−	8.21924i	−0.174767	−	0.368313i
$499$	5.42208	+	1.33642i	0.242726	+	0.0598265i	0.358802	−	0.933414i	$-0.383185\pi$
$499$	5.42208	+	1.33642i	0.242726	+	0.0598265i	−0.116076	+	0.993240i	$0.537032\pi$
$500$	−0.934624	+	0.973047i	−0.0417977	+	0.0435160i
$501$	−10.2380	−	7.69339i	−0.457402	−	0.343715i
$502$	−11.9830	−	10.6160i	−0.534828	−	0.473816i
$503$	−8.76003	−	1.42364i	−0.390590	−	0.0634771i	−0.0380551	−	0.999276i	$-0.512116\pi$
$503$	−8.76003	−	1.42364i	−0.390590	−	0.0634771i	−0.352535	+	0.935799i	$0.614680\pi$
$504$	−8.35611	−	5.28409i	−0.372211	−	0.235372i
$505$	0.135683	+	0.0109534i	0.00603780	+	0.000487422i
$506$	19.4964			0.866718
$507$	−12.3387	−	4.09335i	−0.547983	−	0.181792i
$508$	17.8633			0.792557
$509$	12.4689	+	1.00659i	0.552673	+	0.0446164i	0.353649	−	0.935378i	$-0.384941\pi$
$509$	12.4689	+	1.00659i	0.552673	+	0.0446164i	0.199024	+	0.979995i	$0.436223\pi$
$510$	−0.311516	−	0.196991i	−0.0137942	−	0.00872290i
$511$	3.33060	+	0.541275i	0.147337	+	0.0239446i
$512$	−10.5751	−	9.36876i	−0.467360	−	0.414044i
$513$	0.268868	+	0.202041i	0.0118708	+	0.00892034i
$514$	2.06570	−	2.15062i	0.0911140	−	0.0948597i
$515$	0.711701	+	0.175419i	0.0313613	+	0.00772986i
$516$	9.82772	+	20.7115i	0.432641	+	0.911772i
$517$	−12.2698	−	12.7742i	−0.539623	−	0.561807i
$518$	8.19640	−	17.2736i	0.360129	−	0.758956i
$519$	11.2692	+	9.98364i	0.494663	+	0.438233i
$520$	0.256528	−	0.227698i	0.0112495	−	0.00998520i
$521$	−11.4488	+	10.1428i	−0.501583	+	0.444364i	−0.875585	−	0.483064i	$-0.839524\pi$
$521$	−11.4488	+	10.1428i	−0.501583	+	0.444364i	0.374002	+	0.927428i	$0.377985\pi$
$522$	0.737984	+	2.54781i	0.0323007	+	0.111515i
$523$	9.34736	+	3.12061i	0.408731	+	0.136455i	0.513596	−	0.858032i	$-0.328313\pi$
$523$	9.34736	+	3.12061i	0.408731	+	0.136455i	−0.104865	+	0.994486i	$0.533441\pi$
$524$	−12.3758	+	12.8846i	−0.540639	+	0.562865i
$525$	−8.48207	−	22.3654i	−0.370188	−	0.976106i
$526$	16.3800	−	28.3709i	0.714200	−	1.23703i
$527$	−15.6282	−	19.1410i	−0.680773	−	0.833795i
$528$	−2.34355	+	0.577632i	−0.101990	+	0.0251382i
$529$	0.763999	−	1.32329i	0.0332174	−	0.0575342i
$530$	−0.147868	−	0.256115i	−0.00642297	−	0.0111249i
$531$	4.51727	+	4.70298i	0.196033	+	0.204092i
$532$	−0.568539	−	4.68234i	−0.0246493	−	0.203005i
$533$	−2.85112	+	6.02330i	−0.123496	+	0.260898i
$534$	2.13623	−	17.5934i	0.0924436	−	0.761341i
$535$	0.663239	−	0.498392i	0.0286743	−	0.0215474i
$536$	−25.2508	−	2.03845i	−1.09067	−	0.0880477i
$537$	0.813271	+	3.98366i	0.0350952	+	0.171908i
$538$	3.73474	−	30.7583i	0.161016	−	1.32609i
$539$	−27.7274	−	11.8135i	−1.19430	−	0.508845i
$540$	0.114057	−	0.0721255i	0.00490825	−	0.00310379i
$541$	−9.22042	+	8.16858i	−0.396417	+	0.351195i	−0.837659	−	0.546193i	$-0.816076\pi$
$541$	−9.22042	+	8.16858i	−0.396417	+	0.351195i	0.441242	+	0.897388i	$0.354538\pi$
$542$	−18.2538	+	1.47360i	−0.784068	+	0.0632965i
$543$	−6.38826	−	22.0548i	−0.274146	−	0.946463i
$544$	−23.0790	+	9.83305i	−0.989505	+	0.421589i
$545$	−0.00786904	+	0.0114003i	−0.000337073	+	0.000488334i
$546$	10.6950	+	36.7932i	0.457705	+	1.57460i
$547$	−4.15972	−	6.02640i	−0.177857	−	0.257670i	0.723909	−	0.689896i	$-0.242344\pi$
$547$	−4.15972	−	6.02640i	−0.177857	−	0.257670i	−0.901765	+	0.432226i	$0.857728\pi$
$548$	32.2115	+	20.3693i	1.37601	+	0.870134i
$549$	−4.52609	+	0.735561i	−0.193169	+	0.0313930i
$550$	19.3455	+	8.24237i	0.824897	+	0.351456i
$551$	−0.228230	+	0.330649i	−0.00972294	+	0.0140861i
$552$	−2.66317	+	9.19433i	−0.113352	+	0.391337i
$553$	−10.4008	−	21.9192i	−0.442286	−	0.932099i
$554$	19.9594	−	52.6286i	0.847994	−	2.23598i
$555$	0.0524013	+	0.0641799i	0.00222431	+	0.00272429i
$556$	1.35806	+	33.7000i	0.0575947	+	1.42920i
$557$	0.255113	+	6.33058i	0.0108095	+	0.268235i	0.995552	+	0.0942160i	$0.0300344\pi$
$557$	0.255113	+	6.33058i	0.0108095	+	0.268235i	−0.984742	+	0.174019i	$0.944325\pi$
$558$	14.7802	−	3.64299i	0.625695	−	0.154220i
$559$	7.82212	−	27.1010i	0.330840	−	1.14625i
$560$	0.272595	+	0.0671886i	0.0115192	+	0.00283924i
$561$	−1.36616	+	6.69188i	−0.0576792	+	0.282532i
$562$	45.3422	−	19.3185i	1.91265	−	0.814902i
$563$	17.2234	−	10.8914i	0.725879	−	0.459018i	−0.119740	−	0.992805i	$-0.538206\pi$
$563$	17.2234	−	10.8914i	0.725879	−	0.459018i	0.845619	+	0.533787i	$0.179232\pi$
$564$	24.2539	−	12.7294i	1.02127	−	0.536005i
$565$	−0.705728	−	0.114692i	−0.0296902	−	0.00482513i
$566$	28.1014	−	9.38164i	1.18119	−	0.394340i
$567$	0.576887	+	4.75109i	0.0242270	+	0.199527i
$568$	−5.06680	+	17.4926i	−0.212598	+	0.733974i
$569$	0.454205	−	2.22484i	0.0190413	−	0.0932703i	−0.969160	−	0.246434i	$-0.920741\pi$
$569$	0.454205	−	2.22484i	0.0190413	−	0.0932703i	0.988201	+	0.153164i	$0.0489462\pi$
$570$	0.0326209	+	0.0108904i	0.00136634	+	0.000456150i
$571$	31.7233	+	16.6497i	1.32758	+	0.696767i	0.971355	−	0.237634i	$-0.0763720\pi$
$571$	31.7233	+	16.6497i	1.32758	+	0.696767i	0.356223	+	0.934401i	$0.384064\pi$
$572$	−17.7358	−	9.28707i	−0.741570	−	0.388312i
$573$	−4.01084	+	2.10505i	−0.167555	+	0.0879398i
$574$	19.3871	−	3.15071i	0.809203	−	0.131508i
$575$	−18.5144	+	13.9127i	−0.772103	+	0.580198i
$576$	0.519689	−	12.8959i	0.0216537	−	0.537331i
$577$	36.3669			1.51398			0.756988	−	0.653429i	$-0.226670\pi$
$577$	36.3669			1.51398			0.756988	+	0.653429i	$0.226670\pi$
$578$	0.358356	−	8.89251i	0.0149056	−	0.369880i
$579$	2.26685	+	11.1038i	0.0942071	+	0.461457i
$580$	0.0915779	+	0.132673i	0.00380257	+	0.00550897i
$581$	18.6001	−	6.20962i	0.771661	−	0.257618i
$582$	15.2307	−	32.0981i	0.631334	−	1.33051i
$583$	−3.46590	+	4.24496i	−0.143543	+	0.175808i
$584$	−0.516458	−	1.36179i	−0.0213712	−	0.0563512i
$585$	−0.163919	−	0.0264803i	−0.00677721	−	0.00109482i
$586$	11.1049	−	29.2813i	0.458741	−	1.20960i
$587$	−3.92458	−	6.79757i	−0.161985	−	0.280566i	0.773596	−	0.633679i	$-0.218456\pi$
$587$	−3.92458	−	6.79757i	−0.161985	−	0.280566i	−0.935580	+	0.353114i	$0.885123\pi$
$588$	29.4776	−	36.1036i	1.21564	−	1.48889i
$589$	1.84326	+	1.38512i	0.0759503	+	0.0570730i
$590$	0.590435	+	0.309884i	0.0243078	+	0.0127577i
$591$	27.0237	−	2.18158i	1.11161	−	0.0897383i
$592$	2.28433	−	0.184410i	0.0938853	−	0.00757920i
$593$	−22.8286	−	11.9814i	−0.937458	−	0.492016i	−0.0744601	−	0.997224i	$-0.523723\pi$
$593$	−22.8286	−	11.9814i	−0.937458	−	0.492016i	−0.862997	+	0.505208i	$0.831416\pi$
$594$	−3.36360	−	2.52758i	−0.138010	−	0.103708i
$595$	0.502438	−	0.615375i	0.0205979	−	0.0252279i
$596$	−31.8709	−	55.2020i	−1.30548	−	2.26116i
$597$	−0.728196	+	1.92009i	−0.0298031	+	0.0785842i
$598$	31.3358	−	19.8571i	1.28142	−	0.812016i
$599$	15.4691	+	40.7888i	0.632052	+	1.66658i	0.740148	+	0.672444i	$0.234755\pi$
$599$	15.4691	+	40.7888i	0.632052	+	1.66658i	−0.108096	+	0.994140i	$0.534475\pi$
$600$	−6.52961	+	7.99732i	−0.266570	+	0.326489i
$601$	18.2869	−	38.5388i	0.745938	−	1.57203i	−0.0724542	−	0.997372i	$-0.523083\pi$
$601$	18.2869	−	38.5388i	0.745938	−	1.57203i	0.818392	−	0.574660i	$-0.194866\pi$
$602$	−78.8594	+	26.3271i	−3.21407	+	1.07301i
$603$	6.96633	+	10.0925i	0.283691	+	0.410997i
$604$	7.58742	+	37.1656i	0.308728	+	1.51225i
$605$	0.0137397	−	0.340947i	0.000558598	−	0.0138615i
$606$	6.56330			0.266616
$607$	0.441720	−	10.9612i	0.0179288	−	0.444900i	−0.965148	−	0.261705i	$-0.915715\pi$
$607$	0.441720	−	10.9612i	0.0179288	−	0.444900i	0.983077	−	0.183194i	$-0.0586438\pi$
$608$	1.87129	−	1.40619i	0.0758910	−	0.0570284i
$609$	−5.64332	+	0.917129i	−0.228679	+	0.0371640i
$610$	−0.415184	+	0.217905i	−0.0168103	+	0.00882273i
$611$	−32.7313	−	8.03469i	−1.32416	−	0.325049i
$612$	−9.35235	−	4.90849i	−0.378046	−	0.198414i
$613$	−37.2066	−	12.4214i	−1.50276	−	0.501695i	−0.558108	−	0.829768i	$-0.688472\pi$
$613$	−37.2066	−	12.4214i	−1.50276	−	0.501695i	−0.944652	+	0.328073i	$0.893601\pi$
$614$	0.482773	−	2.36478i	0.0194831	−	0.0954346i
$615$	−0.0236810	+	0.0817562i	−0.000954909	+	0.00329673i
$616$	2.25812	+	18.5973i	0.0909824	+	0.749308i
$617$	−35.6794	+	11.9115i	−1.43640	+	0.479540i	−0.925054	−	0.379836i	$-0.875981\pi$
$617$	−35.6794	+	11.9115i	−1.43640	+	0.479540i	−0.511344	+	0.859376i	$0.670852\pi$
$618$	34.8843	+	5.66926i	1.40325	+	0.228051i
$619$	−21.7563	+	11.4186i	−0.874459	+	0.458951i	−0.841344	−	0.540500i	$-0.818235\pi$
$619$	−21.7563	+	11.4186i	−0.874459	+	0.458951i	−0.0331148	+	0.999452i	$0.510543\pi$
$620$	0.781936	−	0.494467i	0.0314033	−	0.0198583i
$621$	4.26299	−	1.81629i	0.171068	−	0.0728852i
$622$	−0.407734	+	1.99722i	−0.0163487	+	0.0800810i
$623$	37.0898	+	9.14182i	1.48597	+	0.366259i
$624$	−3.17838	+	3.31531i	−0.127237	+	0.132719i
$625$	−24.2427	+	5.97528i	−0.969706	+	0.239011i
$626$	0.459219	+	11.3954i	0.0183541	+	0.455452i
$627$	−0.0256607	−	0.636763i	−0.00102479	−	0.0254299i
$628$	26.3269	+	32.2447i	1.05056	+	1.28670i
$629$	2.29958	−	6.06349i	0.0916903	−	0.241767i
$630$	0.209801	+	0.442146i	0.00835866	+	0.0176155i
$631$	2.26163	−	7.80804i	0.0900339	−	0.310833i	−0.902844	−	0.429968i	$-0.858525\pi$
$631$	2.26163	−	7.80804i	0.0900339	−	0.310833i	0.992878	+	0.119135i	$0.0380120\pi$
$632$	−5.94874	+	8.61824i	−0.236628	+	0.342815i
$633$	−20.6059	−	8.77936i	−0.819012	−	0.348948i
$634$	−49.9459	+	8.11700i	−1.98361	+	0.322367i
$635$	−0.237274	−	0.150043i	−0.00941593	−	0.00595428i
$636$	−4.81426	−	6.97466i	−0.190898	−	0.276563i
$637$	−56.5974	+	9.25293i	−2.24247	+	0.366614i
$638$	2.85522	−	4.13649i	0.113039	−	0.163765i
$639$	8.11053	−	3.45557i	0.320848	−	0.136700i
$640$	−0.188832	−	0.651924i	−0.00746425	−	0.0257696i
$641$	16.1638	−	1.30488i	0.638431	−	0.0515395i	0.242987	−	0.970030i	$-0.421873\pi$
$641$	16.1638	−	1.30488i	0.638431	−	0.0515395i	0.395444	+	0.918490i	$0.370591\pi$
$642$	29.9411	−	26.5255i	1.18168	−	1.04688i
$643$	−22.9135	+	14.4896i	−0.903619	+	0.571414i	−0.903501	−	0.428586i	$-0.859012\pi$
$643$	−22.9135	+	14.4896i	−0.903619	+	0.571414i	−0.000118136		1.00000i	$0.500038\pi$
$644$	−59.7866	−	25.4727i	−2.35592	−	1.00376i
$645$	0.0434270	−	0.357654i	0.00170994	−	0.0140826i
$646$	−0.538409	−	2.63730i	−0.0211834	−	0.103763i
$647$	−14.2757	−	1.15245i	−0.561234	−	0.0453075i	−0.203405	−	0.979095i	$-0.565201\pi$
$647$	−14.2757	−	1.15245i	−0.561234	−	0.0453075i	−0.357829	+	0.933787i	$0.616483\pi$
$648$	1.65145	−	1.24099i	0.0648751	−	0.0487505i
$649$	1.48941	−	12.2664i	0.0584644	−	0.481497i
$650$	39.4883	−	6.45582i	1.54886	−	0.253218i
$651$	3.95493	+	32.5718i	0.155006	+	1.27659i
$652$	−36.6316	−	38.1375i	−1.43460	−	1.49358i
$653$	−7.49800	−	12.9869i	−0.293419	−	0.508217i	0.681197	−	0.732100i	$-0.261460\pi$
$653$	−7.49800	−	12.9869i	−0.293419	−	0.508217i	−0.974616	+	0.223883i	$0.928127\pi$
$654$	−0.333950	+	0.578418i	−0.0130585	+	0.0226179i
$655$	0.272609	−	0.0671920i	0.0106517	−	0.00262541i
$656$	1.48898	+	1.82367i	0.0581349	+	0.0712023i
$657$	−0.352518	+	0.610580i	−0.0137531	+	0.0238210i
$658$	35.2250	+	92.8808i	1.37321	+	3.62087i
$659$	−18.8833	+	19.6596i	−0.735588	+	0.765828i	−0.978948	−	0.204108i	$-0.934571\pi$
$659$	−18.8833	+	19.6596i	−0.735588	+	0.765828i	0.243360	+	0.969936i	$0.421750\pi$
$660$	−0.242550	−	0.0809751i	−0.00944125	−	0.00315195i
$661$	−5.70206	−	19.6858i	−0.221784	−	0.765689i	−0.991815	−	0.127682i	$-0.959246\pi$
$661$	−5.70206	−	19.6858i	−0.221784	−	0.765689i	0.770031	−	0.638007i	$-0.220241\pi$
$662$	−17.5366	+	15.5361i	−0.681580	+	0.603828i
$663$	4.61992	+	12.1471i	0.179423	+	0.471753i
$664$	−6.33527	−	5.61256i	−0.245856	−	0.217810i
$665$	−0.0317776	+	0.0669698i	−0.00123228	+	0.00259698i
$666$	2.76736	+	2.88113i	0.107233	+	0.111642i
$667$	2.37305	+	5.00109i	0.0918847	+	0.193643i
$668$	−36.4368	−	8.98086i	−1.40978	−	0.347480i
$669$	−0.624704	+	0.650386i	−0.0241525	+	0.0251454i
$670$	1.00250	+	0.753328i	0.0387299	+	0.0291036i
$671$	6.50370	+	5.76178i	0.251073	+	0.222431i
$672$	32.8786	+	5.34330i	1.26832	+	0.206122i
$673$	−33.7947	−	21.3705i	−1.30269	−	0.823770i	−0.310750	−	0.950492i	$-0.600580\pi$
$673$	−33.7947	−	21.3705i	−1.30269	−	0.823770i	−0.991938	+	0.126721i	$0.959555\pi$
$674$	25.8488	+	2.08673i	0.995659	+	0.0803779i
$675$	4.99788			0.192368
$676$	−37.9650	+	3.13716i	−1.46019	+	0.120660i
$677$	35.9209			1.38055			0.690276	−	0.723546i	$-0.257489\pi$
$677$	35.9209			1.38055			0.690276	+	0.723546i	$0.257489\pi$
$678$	−34.3617	−	2.77396i	−1.31965	−	0.106533i
$679$	64.7236	+	40.9287i	2.48386	+	1.57070i
$680$	−0.338458	−	0.0550048i	−0.0129793	−	0.00210934i
$681$	22.2914	+	19.7484i	0.854207	+	0.756761i
$682$	−23.0596	−	17.3282i	−0.883000	−	0.663531i
$683$	35.1361	−	36.5806i	1.34445	−	1.39972i	0.498065	−	0.867140i	$-0.334044\pi$
$683$	35.1361	−	36.5806i	1.34445	−	1.39972i	0.846381	−	0.532577i	$-0.178777\pi$
$684$	0.956891	+	0.235852i	0.0365876	+	0.00901804i
$685$	−0.256765	−	0.541121i	−0.00981050	−	0.0206752i
$686$	65.5598	+	68.2550i	2.50308	+	2.60599i
$687$	11.4528	−	24.1362i	0.436951	−	0.920854i
$688$	−7.45914	−	6.60822i	−0.284377	−	0.251936i
$689$	−1.24712	+	10.3528i	−0.0475115	+	0.394410i
$690$	0.354670	−	0.314210i	0.0135020	−	0.0119618i
$691$	−3.34035	−	11.5322i	−0.127073	−	0.438706i	0.871600	−	0.490219i	$-0.163083\pi$
$691$	−3.34035	−	11.5322i	−0.127073	−	0.438706i	−0.998672	+	0.0515122i	$0.983596\pi$
$692$	41.8472	+	13.9707i	1.59079	+	0.531085i
$693$	6.28219	−	6.54045i	0.238641	−	0.248451i
$694$	26.0050	+	68.5696i	0.987137	+	2.60287i
$695$	0.265024	−	0.459036i	0.0100529	−	0.0174122i
$696$	1.56072	+	1.91154i	0.0591590	+	0.0724566i
$697$	6.46835	−	1.59431i	0.245006	−	0.0603886i
$698$	10.7883	−	18.6858i	0.408342	−	0.707269i
$699$	2.02177	+	3.50180i	0.0764702	+	0.132450i
$700$	−48.5552	−	50.5513i	−1.83521	−	1.91066i
$701$	−0.420050	−	3.45942i	−0.0158651	−	0.130661i	0.982624	−	0.185606i	$-0.0594247\pi$
$701$	−0.420050	−	3.45942i	−0.0158651	−	0.130661i	−0.998489	+	0.0549451i	$0.982502\pi$
$702$	−7.98054	−	0.636658i	−0.301206	−	0.0240291i
$703$	−0.0729354	+	0.600677i	−0.00275081	+	0.0226550i
$704$	−19.5511	+	14.6917i	−0.736860	+	0.553715i
$705$	−0.429079	−	0.0346389i	−0.0161601	−	0.00130457i
$706$	3.03290	+	14.8561i	0.114145	+	0.559117i
$707$	−1.70520	+	14.0436i	−0.0641306	+	0.528163i
$708$	17.5797	+	7.49001i	0.660685	+	0.281492i
$709$	34.4407	−	21.7790i	1.29345	−	0.817928i	0.302628	−	0.953109i	$-0.402136\pi$
$709$	34.4407	−	21.7790i	1.29345	−	0.817928i	0.990821	+	0.135181i	$0.0431616\pi$
$710$	0.674774	−	0.597798i	0.0253238	−	0.0224350i
$711$	5.05287	−	0.407910i	0.189497	−	0.0152978i
$712$	−4.58725	−	15.8370i	−0.171915	−	0.593518i
$713$	29.2255	−	12.4518i	1.09451	−	0.466325i
$714$	21.7593	−	31.5237i	0.814320	−	1.17975i
$715$	0.157573	+	0.272330i	0.00589291	+	0.0101846i
$716$	6.76807	+	9.80524i	0.252935	+	0.366439i
$717$	−13.7314	−	8.68319i	−0.512808	−	0.324280i
$718$	42.8008	−	6.95582i	1.59731	−	0.259589i
$719$	−4.19732	−	1.78831i	−0.156534	−	0.0666927i	0.312279	−	0.949991i	$-0.398908\pi$
$719$	−4.19732	−	1.78831i	−0.156534	−	0.0666927i	−0.468812	+	0.883298i	$0.655318\pi$
$720$	−0.0333235	+	0.0482774i	−0.00124189	+	0.00179919i
$721$	−21.1938	+	73.1695i	−0.789299	+	2.72498i
$722$	−17.9781	−	37.8881i	−0.669077	−	1.41005i
$723$	5.84956	−	15.4240i	0.217547	−	0.573625i
$724$	−42.5538	−	52.1190i	−1.58150	−	1.93699i
$725$	0.240407	+	5.96565i	0.00892850	+	0.221558i
$726$	−0.662466	−	16.4389i	−0.0245864	−	0.610106i
$727$	−24.8189	+	6.11732i	−0.920483	+	0.226879i	−0.670963	−	0.741491i	$-0.734119\pi$
$727$	−24.8189	+	6.11732i	−0.920483	+	0.226879i	−0.249520	+	0.968370i	$0.580273\pi$
$728$	22.5708	+	27.5909i	0.836530	+	1.02259i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−0.0144207	+	0.0706374i	−0.000533735	+	0.00261441i
$731$	−25.9420	+	11.0529i	−0.959500	+	0.408805i
$732$	−11.3568	+	7.18160i	−0.419759	+	0.265440i
$733$	5.57235	−	2.92460i	0.205820	−	0.108022i	−0.358664	−	0.933467i	$-0.616768\pi$
$733$	5.57235	−	2.92460i	0.205820	−	0.108022i	0.564484	+	0.825444i	$0.309075\pi$
$734$	7.58695	+	1.23300i	0.280039	+	0.0455108i
$735$	−0.694796	+	0.231957i	−0.0256280	+	0.00855587i
$736$	−3.88739	−	32.0156i	−0.143291	−	1.18011i
$737$	6.46502	−	22.3198i	0.238142	−	0.822161i
$738$	−0.820896	+	4.02101i	−0.0302176	+	0.148016i
$739$	−11.3417	−	3.78642i	−0.417211	−	0.139286i	0.100309	−	0.994956i	$-0.468017\pi$
$739$	−11.3417	−	3.78642i	−0.417211	−	0.139286i	−0.517521	+	0.855671i	$0.673145\pi$
$740$	0.214983	+	0.112832i	0.00790292	+	0.00414777i
$741$	−0.689788	−	0.997311i	−0.0253400	−	0.0366372i
$742$	27.2139	−	14.2830i	0.999055	−	0.524344i
$743$	−49.6880	+	8.07508i	−1.82287	+	0.296246i	−0.973011	−	0.230758i	$-0.925879\pi$
$743$	−49.6880	+	8.07508i	−1.82287	+	0.296246i	−0.849863	+	0.527004i	$0.823315\pi$
$744$	11.3218	−	8.50775i	0.415076	−	0.311909i
$745$	−0.0403363	+	1.00094i	−0.00147781	+	0.0366714i
$746$	−47.8846			−1.75318
$747$	−0.164978	+	4.09389i	−0.00603624	+	0.149788i
$748$	4.00330	+	19.6095i	0.146375	+	0.716993i
$749$	48.9780	+	70.9569i	1.78962	+	2.59271i
$750$	0.969731	−	0.323744i	0.0354096	−	0.0118215i
$751$	4.48582	−	9.45366i	0.163690	−	0.344969i	−0.804988	−	0.593292i	$-0.797828\pi$
$751$	4.48582	−	9.45366i	0.163690	−	0.344969i	0.968677	+	0.248323i	$0.0798794\pi$
$752$	−7.53046	+	9.22313i	−0.274607	+	0.336333i
$753$	2.55667	+	6.74137i	0.0931701	+	0.245669i
$754$	0.376058	−	9.55648i	0.0136952	−	0.348026i
$755$	0.211391	−	0.557392i	0.00769331	−	0.0202856i
$756$	7.01228	+	12.1456i	0.255034	+	0.441732i
$757$	−3.01856	+	3.69707i	−0.109712	+	0.134372i	−0.826541	−	0.562876i	$-0.809695\pi$
$757$	−3.01856	+	3.69707i	−0.109712	+	0.134372i	0.716830	+	0.697248i	$0.245592\pi$
$758$	−21.4033	−	16.0835i	−0.777403	−	0.584181i
$759$	−7.77467	−	4.08046i	−0.282203	−	0.148111i
$760$	0.0318912	−	0.00257452i	0.00115682	−	9.33878e-5i
$761$	43.5136	−	3.51278i	1.57737	−	0.127338i	0.739478	−	0.673180i	$-0.235072\pi$
$761$	43.5136	−	3.51278i	1.57737	−	0.127338i	0.837888	+	0.545842i	$0.183790\pi$
$762$	−11.9853	−	6.29038i	−0.434183	−	0.227877i
$763$	−1.15088	−	0.864833i	−0.0416648	−	0.0313091i
$764$	−8.39477	+	10.2817i	−0.303712	+	0.371980i
$765$	0.0829961	+	0.143753i	0.00300073	+	0.00519742i
$766$	19.8540	−	52.3508i	0.717356	−	1.89151i
$767$	−10.0995	−	21.2323i	−0.364670	−	0.766653i
$768$	−2.45107	−	6.46293i	−0.0884452	−	0.233211i
$769$	−32.6159	+	39.9473i	−1.17616	+	1.44053i	−0.303075	+	0.952967i	$0.598013\pi$
$769$	−32.6159	+	39.9473i	−1.17616	+	1.44053i	−0.873085	+	0.487568i	$0.837884\pi$
$770$	0.397545	−	0.837808i	0.0143265	−	0.0301925i
$771$	−1.27386	+	0.425277i	−0.0458770	+	0.0153160i
$772$	18.8648	+	27.3304i	0.678960	+	0.983643i
$773$	−4.87618	−	23.8851i	−0.175384	−	0.859087i	−0.968307	−	0.249765i	$-0.919647\pi$
$773$	−4.87618	−	23.8851i	−0.175384	−	0.859087i	0.792923	−	0.609322i	$-0.208558\pi$
$774$	0.699464	−	17.3570i	0.0251417	−	0.623885i
$775$	34.2637			1.23079
$776$	1.33092	−	33.0265i	0.0477773	−	1.18558i
$777$	−6.88377	+	5.17282i	−0.246954	+	0.185574i
$778$	−55.3587	+	8.99666i	−1.98470	+	0.322546i
$779$	−0.550405	+	0.288875i	−0.0197203	+	0.0103500i
$780$	−0.472316	+	0.116889i	−0.0169116	+	0.00418531i
$781$	−14.7917	−	7.76326i	−0.529287	−	0.277791i
$782$	−35.1775	−	11.7440i	−1.25794	−	0.419964i
$783$	0.238952	−	1.17046i	0.00853943	−	0.0418289i
$784$	−5.63687	+	19.4607i	−0.201317	+	0.695026i
$785$	−0.0788552	−	0.649431i	−0.00281446	−	0.0231792i
$786$	12.8407	−	4.28684i	0.458011	−	0.152907i
$787$	−6.90253	−	1.12177i	−0.246048	−	0.0399868i	0.0361362	−	0.999347i	$-0.488495\pi$
$787$	−6.90253	−	1.12177i	−0.246048	−	0.0399868i	−0.282185	+	0.959360i	$0.591059\pi$
$788$	70.3462	−	36.9205i	2.50598	−	1.31524i
$789$	−12.4698	+	7.88541i	−0.443936	+	0.280728i
$790$	0.476888	−	0.203183i	0.0169669	−	0.00722893i
$791$	14.8629	−	72.8034i	0.528465	−	2.58859i
$792$	−3.80058	−	0.936760i	−0.135048	−	0.0332863i
$793$	16.3215	+	2.63666i	0.579595	+	0.0936307i
$794$	−73.7392	+	18.1751i	−2.61691	+	0.645009i
$795$	0.00536295	+	0.133080i	0.000190204	+	0.00471987i
$796$	0.242303	+	6.01269i	0.00858820	+	0.213114i
$797$	28.4725	+	34.8724i	1.00855	+	1.23525i	0.971772	+	0.235922i	$0.0758109\pi$
$797$	28.4725	+	34.8724i	1.00855	+	1.23525i	0.0367745	+	0.999324i	$0.488292\pi$
$798$	−1.26738	+	3.34180i	−0.0448647	+	0.118299i
$799$	14.4437	+	30.4395i	0.510982	+	1.07687i
$800$	9.67772	−	33.4114i	0.342159	−	1.18127i
$801$	−4.53406	+	6.56873i	−0.160203	+	0.232095i
$802$	71.5095	+	30.4674i	2.52509	+	1.07584i
$803$	1.31865	−	0.214302i	0.0465342	−	0.00756254i
$804$	30.3724	+	19.2063i	1.07115	+	0.677354i
$805$	0.580172	+	0.840525i	0.0204484	+	0.0296246i
$806$	−54.7117	−	4.36470i	−1.92714	−	0.153740i
$807$	−7.92685	+	11.4840i	−0.279038	+	0.404257i
$808$	5.61746	−	2.39338i	0.197622	−	0.0841987i
$809$	1.67006	+	5.76573i	0.0587163	+	0.202712i	0.984514	−	0.175308i	$-0.0560921\pi$
$809$	1.67006	+	5.76573i	0.0587163	+	0.202712i	−0.925797	+	0.378020i	$0.876605\pi$
$810$	−0.101925	+	0.00822820i	−0.00358127	+	0.000289110i
$811$	−13.6906	+	12.1288i	−0.480743	+	0.425901i	−0.868371	−	0.495915i	$-0.834833\pi$
$811$	−13.6906	+	12.1288i	−0.480743	+	0.425901i	0.387628	+	0.921816i	$0.373294\pi$
$812$	−14.1601	+	8.95433i	−0.496923	+	0.314235i
$813$	7.58759	+	3.23277i	0.266108	+	0.113378i
$814$	0.912439	−	7.51461i	0.0319810	−	0.263387i
$815$	0.166232	+	0.814259i	0.00582286	+	0.0285223i
$816$	4.57643	+	0.369448i	0.160207	+	0.0129333i
$817$	2.10343	−	1.58063i	0.0735898	−	0.0552991i
$818$	−3.10447	+	25.5676i	−0.108545	+	0.893950i
$819$	3.43567	−	16.9106i	0.120052	−	0.590906i
$820$	0.0300644	+	0.247602i	0.00104989	+	0.00864665i
$821$	10.1297	+	10.5461i	0.353529	+	0.368062i	0.874092	−	0.485761i	$-0.161457\pi$
$821$	10.1297	+	10.5461i	0.353529	+	0.368062i	−0.520563	+	0.853823i	$0.674278\pi$
$822$	−14.4393	−	25.0097i	−0.503630	−	0.872312i
$823$	−5.65587	+	9.79625i	−0.197151	+	0.341476i	−0.947604	−	0.319449i	$-0.896502\pi$
$823$	−5.65587	+	9.79625i	−0.197151	+	0.341476i	0.750452	+	0.660925i	$0.229836\pi$
$824$	31.9245	−	7.86869i	1.11214	−	0.274119i
$825$	−5.98946	−	7.33575i	−0.208526	−	0.255398i
$826$	−34.6494	+	60.0145i	−1.20561	+	2.08817i
$827$	6.40578	+	16.8907i	0.222751	+	0.587346i	0.999076	−	0.0429875i	$-0.0136876\pi$
$827$	6.40578	+	16.8907i	0.222751	+	0.587346i	−0.776325	+	0.630333i	$0.782918\pi$
$828$	9.40620	−	9.79289i	0.326888	−	0.340327i
$829$	7.88506	+	2.63242i	0.273860	+	0.0914278i	0.450281	−	0.892887i	$-0.351324\pi$
$829$	7.88506	+	2.63242i	0.273860	+	0.0914278i	−0.176421	+	0.984315i	$0.556452\pi$
$830$	0.116564	+	0.402424i	0.00404598	+	0.0139683i
$831$	−18.9742	+	16.8096i	−0.658207	+	0.583120i
$832$	−16.4603	+	43.5263i	−0.570657	+	1.50900i
$833$	42.9128	+	38.0174i	1.48684	+	1.31722i
$834$	10.9559	−	23.0891i	0.379372	−	0.799510i
$835$	0.408546	+	0.425342i	0.0141383	+	0.0147196i
$836$	−0.800560	−	1.68714i	−0.0276879	−	0.0583511i
$837$	−6.65643	−	1.64066i	−0.230080	−	0.0567096i
$838$	28.4430	−	29.6123i	0.982548	−	1.02294i
$839$	−34.7950	−	26.1468i	−1.20126	−	0.902686i	−0.204169	−	0.978936i	$-0.565449\pi$
$839$	−34.7950	−	26.1468i	−1.20126	−	0.902686i	−0.997089	+	0.0762493i	$0.975706\pi$
$840$	0.340800	+	0.301922i	0.0117587	+	0.0104173i
$841$	−27.2159	−	4.42301i	−0.938478	−	0.152518i
$842$	−16.5116	−	10.4413i	−0.569028	−	0.359832i
$843$	−22.1246	−	1.78608i	−0.762012	−	0.0615160i
$844$	−65.6344			−2.25923
$845$	0.530630	+	0.277217i	0.0182542	+	0.00953655i
$846$	−20.7556			−0.713592
$847$	35.3467	+	2.85348i	1.21453	+	0.0980467i
$848$	3.11365	+	1.96895i	0.106923	+	0.0676142i
$849$	−13.1697	−	2.14028i	−0.451983	−	0.0734543i
$850$	−29.9405	−	26.5249i	−1.02695	−	0.909798i
$851$	6.66486	+	5.00832i	0.228469	+	0.171683i
$852$	17.8957	−	18.6314i	0.613097	−	0.638302i
$853$	−14.3900	−	3.54681i	−0.492703	−	0.121440i	−0.0148669	−	0.999889i	$-0.504732\pi$
$853$	−14.3900	−	3.54681i	−0.492703	−	0.121440i	−0.477836	+	0.878449i	$0.658579\pi$
$854$	−20.8901	−	44.0249i	−0.714843	−	1.50650i
$855$	−0.0107291	−	0.0111702i	−0.000366928	−	0.000382012i
$856$	15.9535	−	33.6213i	0.545279	−	1.14915i
$857$	5.87655	+	5.20617i	0.200739	+	0.177839i	0.757503	−	0.652831i	$-0.226419\pi$
$857$	5.87655	+	5.20617i	0.200739	+	0.177839i	−0.556764	+	0.830670i	$0.687957\pi$
$858$	8.62941	+	12.4766i	0.294603	+	0.425944i
$859$	−16.4018	+	14.5308i	−0.559623	+	0.495783i	−0.894858	−	0.446352i	$-0.852723\pi$
$859$	−16.4018	+	14.5308i	−0.559623	+	0.495783i	0.335234	+	0.942135i	$0.391185\pi$
$860$	−0.293726	−	1.01406i	−0.0100160	−	0.0345792i
$861$	−8.39054	−	2.80117i	−0.285949	−	0.0954637i
$862$	−0.933862	+	0.972253i	−0.0318075	+	0.0331151i
$863$	12.7596	+	33.6444i	0.434343	+	1.14527i	0.956324	+	0.292310i	$0.0944239\pi$
$863$	12.7596	+	33.6444i	0.434343	+	1.14527i	−0.521981	+	0.852957i	$0.674807\pi$
$864$	−3.47995	+	6.02745i	−0.118390	+	0.205058i
$865$	−0.438500	−	0.537065i	−0.0149094	−	0.0182608i
$866$	21.8753	−	5.39178i	0.743353	−	0.183220i
$867$	−2.00405	+	3.47112i	−0.0680611	+	0.117885i
$868$	48.0737	+	83.2661i	1.63173	+	2.82623i
$869$	−6.65408	−	6.92763i	−0.225724	−	0.235004i
$870$	−0.0147242	−	0.121265i	−0.000499198	−	0.00411127i
$871$	−12.3418	−	42.4585i	−0.418186	−	1.43865i
$872$	−0.0748980	+	0.616840i	−0.00253637	+	0.0208889i
$873$	−12.7916	+	9.61224i	−0.432929	+	0.325325i
$874$	3.44918	+	0.278446i	0.116670	+	0.00941859i
$875$	0.440775	+	2.15906i	0.0149009	+	0.0729894i
$876$	−0.249028	+	2.05093i	−0.00841388	+	0.0692946i
$877$	−5.99177	−	2.55286i	−0.202328	−	0.0862038i	0.288426	−	0.957502i	$-0.406868\pi$
$877$	−5.99177	−	2.55286i	−0.202328	−	0.0862038i	−0.490753	+	0.871298i	$0.663278\pi$
$878$	−15.0262	+	9.50198i	−0.507109	+	0.320676i
$879$	−10.5568	+	9.35249i	−0.356071	+	0.315452i
$880$	0.110795	−	0.00894431i	0.00373491	−	0.000301513i
$881$	−13.7343	−	47.4163i	−0.462720	−	1.59749i	−0.764837	−	0.644224i	$-0.777181\pi$
$881$	−13.7343	−	47.4163i	−0.462720	−	1.59749i	0.302117	−	0.953271i	$-0.402307\pi$
$882$	−32.4914	+	13.8433i	−1.09404	+	0.466128i
$883$	13.7203	−	19.8773i	0.461726	−	0.668926i	−0.521092	−	0.853500i	$-0.674475\pi$
$883$	13.7203	−	19.8773i	0.461726	−	0.668926i	0.982819	+	0.184575i	$0.0590907\pi$
$884$	26.4066	+	27.4402i	0.888152	+	0.922915i
$885$	−0.170594	−	0.247149i	−0.00573447	−	0.00830781i
$886$	46.1341	+	29.1735i	1.54991	+	0.980101i
$887$	−44.2512	+	7.19152i	−1.48581	+	0.241468i	−0.848523	−	0.529158i	$-0.822508\pi$
$887$	−44.2512	+	7.19152i	−1.48581	+	0.241468i	−0.637288	+	0.770626i	$0.719944\pi$
$888$	3.41920	+	1.45678i	0.114741	+	0.0488864i
$889$	16.5735	−	24.0108i	0.555857	−	0.805298i
$890$	−0.227072	+	0.783944i	−0.00761147	+	0.0262779i
$891$	0.812315	+	1.71192i	0.0272136	+	0.0573514i
$892$	−0.937079	+	2.47088i	−0.0313757	+	0.0827310i
$893$	−1.98825	−	2.43517i	−0.0665343	−	0.0814897i
$894$	1.94484	+	48.2606i	0.0650451	+	1.61408i
$895$	−0.00753943	−	0.187089i	−0.000252015	−	0.00625370i
$896$	68.4865	−	16.8804i	2.28797	−	0.563935i
$897$	−16.6519	+	1.36014i	−0.555991	+	0.0454137i
$898$	1.41066	+	0.347697i	0.0470744	+	0.0116028i
$899$	1.63817	−	8.02427i	0.0546359	−	0.267624i
$900$	13.4735	−	5.74053i	0.449118	−	0.191351i
$901$	8.81059	−	5.57148i	0.293523	−	0.185613i
$902$	6.88570	−	3.61389i	0.229269	−	0.120330i
$903$	36.9573	+	6.00615i	1.22986	+	0.199872i
$904$	−30.4214	+	10.1562i	−1.01180	+	0.337789i
$905$	0.127458	+	1.04971i	0.00423686	+	0.0348937i
$906$	7.99675	−	27.6080i	0.265674	−	0.917213i
$907$	4.65877	−	22.8201i	0.154692	−	0.757730i	−0.826231	−	0.563332i	$-0.809519\pi$
$907$	4.65877	−	22.8201i	0.154692	−	0.757730i	0.980923	−	0.194399i	$-0.0622755\pi$
$908$	82.7771	+	27.6351i	2.74705	+	0.917101i
$909$	−2.61728	−	1.37366i	−0.0868098	−	0.0455613i
$910$	−0.214349	−	1.75148i	−0.00710562	−	0.0580609i
$911$	37.3216	−	19.5879i	1.23652	−	0.648976i	0.285582	−	0.958354i	$-0.407813\pi$
$911$	37.3216	−	19.5879i	1.23652	−	0.648976i	0.950939	+	0.309378i	$0.100121\pi$
$912$	−0.422856	+	0.0687208i	−0.0140022	+	0.00227557i
$913$	6.20662	−	4.66397i	0.205409	−	0.154355i
$914$	1.70131	−	42.2176i	0.0562744	−	1.39643i
$915$	0.211171			0.00698111
$916$	3.15225	−	78.2222i	0.104153	−	2.58453i
$917$	5.83650	+	28.5891i	0.192738	+	0.944094i
$918$	4.54645	+	6.58667i	0.150055	+	0.217393i
$919$	20.1292	−	6.72012i	0.664002	−	0.221676i	0.0353638	−	0.999375i	$-0.488741\pi$
$919$	20.1292	−	6.72012i	0.664002	−	0.221676i	0.628638	+	0.777698i	$0.283613\pi$
$920$	0.188978	−	0.398263i	0.00623043	−	0.0131304i
$921$	−0.687451	+	0.841974i	−0.0226523	+	0.0277440i
$922$	−25.9619	−	68.4559i	−0.855010	−	2.25448i
$923$	−31.6810	+	2.58772i	−1.04279	+	0.0851759i
$924$	9.42351	−	24.8477i	0.310011	−	0.817431i
$925$	4.49597	+	7.78725i	0.147827	+	0.256043i
$926$	−7.25057	+	8.88034i	−0.238268	+	0.291826i
$927$	−12.7245	−	9.56183i	−0.417927	−	0.314052i
$928$	−7.36197	−	3.86386i	−0.241668	−	0.126837i
$929$	−2.32233	+	0.187478i	−0.0761933	+	0.00615096i	−0.118504	−	0.992954i	$-0.537810\pi$
$929$	−2.32233	+	0.187478i	−0.0761933	+	0.00615096i	0.0423111	+	0.999104i	$0.486528\pi$
$930$	−0.698759	+	0.0564096i	−0.0229132	+	0.00184974i
$931$	−4.73665	−	2.48598i	−0.155237	−	0.0814748i
$932$	9.47253	+	7.11814i	0.310283	+	0.233163i
$933$	0.580599	−	0.711105i	0.0190080	−	0.0232805i
$934$	−32.1634	−	55.7087i	−1.05242	−	1.82284i
$935$	0.111535	−	0.294094i	0.00364758	−	0.00961789i
$936$	−7.06263	+	2.36528i	−0.230849	+	0.0773117i
$937$	−4.86739	−	12.8343i	−0.159011	−	0.419277i	0.831707	−	0.555216i	$-0.187364\pi$
$937$	−4.86739	−	12.8343i	−0.159011	−	0.419277i	−0.990717	+	0.135939i	$0.956595\pi$
$938$	−82.4213	+	100.948i	−2.69115	+	3.29606i
$939$	2.20186	−	4.64032i	0.0718550	−	0.151431i
$940$	−1.19652	+	0.399457i	−0.0390261	+	0.0130288i
$941$	26.6902	+	38.6674i	0.870076	+	1.26052i	0.964257	+	0.264967i	$0.0853611\pi$
$941$	26.6902	+	38.6674i	0.870076	+	1.26052i	−0.0941819	+	0.995555i	$0.530024\pi$
$942$	−6.30934	−	30.9052i	−0.205569	−	1.00695i
$943$	−0.344856	+	8.55752i	−0.0112301	+	0.278671i
$944$	−8.30648			−0.270353
$945$	0.00887484	−	0.220227i	0.000288699	−	0.00716398i
$946$	−26.3144	+	19.7740i	−0.855556	+	0.642908i
$947$	43.5779	−	7.08210i	1.41609	−	0.230137i	0.596283	−	0.802774i	$-0.296643\pi$
$947$	43.5779	−	7.08210i	1.41609	−	0.230137i	0.819809	+	0.572637i	$0.194079\pi$
$948$	13.1533	−	6.90336i	0.427198	−	0.224211i
$949$	1.90115	−	1.68749i	0.0617141	−	0.0547782i
$950$	3.30478	+	1.73448i	0.107221	+	0.0562741i
$951$	21.6161	+	7.21650i	0.700949	+	0.234011i
$952$	7.12807	−	34.9156i	0.231022	−	1.13162i
$953$	13.7939	−	47.6221i	0.446828	−	1.54263i	−0.349009	−	0.937119i	$-0.613482\pi$
$953$	13.7939	−	47.6221i	0.446828	−	1.54263i	0.795837	−	0.605511i	$-0.207031\pi$
$954$	0.774055	+	6.37492i	0.0250610	+	0.206396i
$955$	0.197867	−	0.0660578i	0.00640283	−	0.00213758i
$956$	−46.9912	−	7.63681i	−1.51980	−	0.246992i
$957$	−2.00433	+	1.05195i	−0.0647909	+	0.0340049i
$958$	53.2694	−	33.6856i	1.72106	−	1.08833i
$959$	57.2649	−	24.3983i	1.84918	−	0.787863i
$960$	−0.118889	+	0.582358i	−0.00383713	+	0.0187955i
$961$	−15.5349	−	3.82901i	−0.501127	−	0.123517i
$962$	−6.18712	−	13.0073i	−0.199481	−	0.419372i
$963$	−17.4914	+	4.31125i	−0.563653	+	0.138928i
$964$	−1.94641	−	48.2996i	−0.0626896	−	1.55563i
$965$	−0.0210149	−	0.521478i	−0.000676492	−	0.0167870i
$966$	31.1436	+	38.1440i	1.00203	+	1.22726i
$967$	7.24948	−	19.1153i	0.233128	−	0.614707i	−0.766493	−	0.642253i	$-0.778000\pi$
$967$	7.24948	−	19.1153i	0.233128	−	0.614707i	0.999621	+	0.0275458i	$0.00876921\pi$
$968$	−6.56163	−	13.8283i	−0.210899	−	0.444460i
$969$	−0.337266	+	1.16438i	−0.0108345	+	0.0374052i
$970$	−0.929445	+	1.34653i	−0.0298427	+	0.0432346i
$971$	−43.5702	−	18.5635i	−1.39823	−	0.595732i	−0.444335	−	0.895861i	$-0.646560\pi$
$971$	−43.5702	−	18.5635i	−1.39823	−	0.595732i	−0.953899	+	0.300129i	$0.902970\pi$
$972$	−2.89239	+	0.470059i	−0.0927734	+	0.0150772i
$973$	46.5576	+	29.4412i	1.49257	+	0.943842i
$974$	−39.9353	−	57.8563i	−1.27961	−	1.85384i
$975$	−17.0981	−	5.69022i	−0.547578	−	0.182233i
$976$	3.31805	−	4.80703i	0.106208	−	0.153869i
$977$	−35.4119	+	15.0876i	−1.13293	+	0.482695i	−0.875315	−	0.483554i	$-0.839346\pi$
$977$	−35.4119	+	15.0876i	−1.13293	+	0.482695i	−0.257612	+	0.966248i	$0.582936\pi$
$978$	11.1481	+	38.4877i	0.356477	+	1.23070i
$979$	15.0750	−	1.21698i	0.481800	−	0.0388949i
$980$	−1.60664	+	1.42336i	−0.0513223	+	0.0454676i
$981$	0.254230	−	0.160765i	0.00811694	−	0.00513284i
$982$	−24.3897	−	10.3915i	−0.778306	−	0.331605i
$983$	4.55750	−	37.5344i	0.145362	−	1.19716i	−0.719261	−	0.694740i	$-0.755519\pi$
$983$	4.55750	−	37.5344i	0.145362	−	1.19716i	0.864623	−	0.502422i	$-0.167557\pi$
$984$	0.763710	+	3.74090i	0.0243462	+	0.119255i
$985$	−1.24451	−	0.100467i	−0.0396532	−	0.00320114i
$986$	−7.64339	+	5.74363i	−0.243415	+	0.182915i
$987$	5.39247	−	44.4110i	0.171644	−	1.41362i
$988$	−3.00507	−	1.89631i	−0.0956041	−	0.0603298i
$989$	−4.36963	−	35.9872i	−0.138946	−	1.14432i
$990$	0.134224	+	0.139742i	0.00426591	+	0.00444128i
$991$	−29.4721	−	51.0472i	−0.936213	−	1.62157i	−0.772456	−	0.635068i	$-0.780972\pi$
$991$	−29.4721	−	51.0472i	−0.936213	−	1.62157i	−0.163757	−	0.986501i	$-0.552361\pi$
$992$	−23.8573	+	41.3220i	−0.757470	+	1.31198i
$993$	10.2448	−	2.52511i	0.325109	−	0.0801321i
$994$	59.2521	+	72.5707i	1.87936	+	2.30180i
$995$	0.0472852	−	0.0819003i	0.00149904	−	0.00259641i
$996$	4.25747	+	11.2260i	0.134903	+	0.355710i
$997$	−5.97474	+	6.22036i	−0.189222	+	0.197001i	−0.809055	−	0.587733i	$-0.800021\pi$
$997$	−5.97474	+	6.22036i	−0.189222	+	0.197001i	0.619833	+	0.784733i	$0.287200\pi$
$998$	−11.7616	−	3.92659i	−0.372306	−	0.124294i
$999$	−0.500555	−	1.72812i	−0.0158369	−	0.0546752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.a.16.3	✓	360
169.74	even	39	inner	507.2.q.a.412.3	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.a.16.3	✓	360	1.1	even	1	trivial
507.2.q.a.412.3	yes	360	169.74	even	39	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.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.21324 - 0.178671i) q^{2} +(0.845190 + 0.534466i) q^{3} +(2.89239 + 0.470059i) q^{4} +(-0.0344706 - 0.0305383i) q^{5} +(-1.77511 - 1.33391i) q^{6} +(3.31537 - 3.45167i) q^{7} +(-2.00573 - 0.494367i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\)	\(q+(-2.21324 - 0.178671i) q^{2} +(0.845190 + 0.534466i) q^{3} +(2.89239 + 0.470059i) q^{4} +(-0.0344706 - 0.0305383i) q^{5} +(-1.77511 - 1.33391i) q^{6} +(3.31537 - 3.45167i) q^{7} +(-2.00573 - 0.494367i) q^{8} +(0.428693 + 0.903450i) q^{9} +(0.0708354 + 0.0737474i) q^{10} +(0.812315 - 1.71192i) q^{11} +(2.19339 + 1.94317i) q^{12} +(-0.437987 - 3.57885i) q^{13} +(-7.95441 + 7.04699i) q^{14} +(-0.0128126 - 0.0442341i) q^{15} +(-1.20825 - 0.403372i) q^{16} +(-2.49687 + 2.59952i) q^{17} +(-0.787377 - 2.07614i) q^{18} +(0.168160 - 0.291261i) q^{19} +(-0.0853477 - 0.104532i) q^{20} +(4.64692 - 1.14536i) q^{21} +(-2.10372 + 3.64374i) q^{22} +(-2.31689 - 4.01298i) q^{23} +(-1.43100 - 1.48983i) q^{24} +(-0.602428 - 4.96144i) q^{25} +(0.329932 + 7.99909i) q^{26} +(-0.120537 + 0.992709i) q^{27} +(11.2118 - 8.42514i) q^{28} +(-1.19073 - 0.0961257i) q^{29} +(0.0204539 + 0.100190i) q^{30} +(-0.826357 + 6.80566i) q^{31} +(6.40296 + 2.72805i) q^{32} +(1.60152 - 1.01274i) q^{33} +(5.99063 - 5.30724i) q^{34} +(-0.219691 + 0.0177353i) q^{35} +(0.815271 + 2.81464i) q^{36} +(-1.65518 + 0.705207i) q^{37} +(-0.424217 + 0.614584i) q^{38} +(1.54259 - 3.25890i) q^{39} +(0.0540415 + 0.0782927i) q^{40} +(-1.56213 - 0.987834i) q^{41} +(-10.4894 + 1.70469i) q^{42} +(7.19726 + 3.06647i) q^{43} +(3.15424 - 4.56970i) q^{44} +(0.0128126 - 0.0442341i) q^{45} +(4.41083 + 9.29563i) q^{46} +(3.31468 - 8.74009i) q^{47} +(-0.805609 - 0.986692i) q^{48} +(-0.640457 - 15.8928i) q^{49} +(0.446850 + 11.0885i) q^{50} +(-3.49969 + 0.862596i) q^{51} +(0.415442 - 10.5573i) q^{52} +(-2.80807 - 0.692126i) q^{53} +(0.444144 - 2.17556i) q^{54} +(-0.0802802 + 0.0342042i) q^{55} +(-8.35611 + 5.28409i) q^{56} +(0.297796 - 0.156295i) q^{57} +(2.61819 + 0.425498i) q^{58} +(6.18543 - 2.06500i) q^{59} +(-0.0162663 - 0.133965i) q^{60} +(-1.27576 + 4.40443i) q^{61} +(3.04489 - 14.9149i) q^{62} +(4.53968 + 1.51557i) q^{63} +(-11.4281 - 5.99791i) q^{64} +(-0.0941944 + 0.136741i) q^{65} +(-3.72550 + 1.95529i) q^{66} +(12.1045 - 1.96717i) q^{67} +(-8.44386 + 6.34515i) q^{68} +(0.186584 - 4.63003i) q^{69} +0.489397 q^{70} +(0.354984 - 8.80884i) q^{71} +(-0.413204 - 2.02401i) q^{72} +(0.400507 + 0.580234i) q^{73} +(3.78931 - 1.26506i) q^{74} +(2.14255 - 4.51534i) q^{75} +(0.623293 - 0.763395i) q^{76} +(-3.21584 - 8.47949i) q^{77} +(-3.99639 + 6.93709i) q^{78} +(1.79760 - 4.73989i) q^{79} +(0.0293307 + 0.0508023i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(3.28088 + 2.46542i) q^{82} +(3.62791 + 1.90407i) q^{83} +(13.9791 - 1.12851i) q^{84} +(0.165454 - 0.0133568i) q^{85} +(-15.3814 - 8.07276i) q^{86} +(-0.955018 - 0.717649i) q^{87} +(-2.47560 + 3.03206i) q^{88} +(3.99080 + 6.91227i) q^{89} +(-0.0362605 + 0.0956112i) q^{90} +(-13.8051 - 10.3534i) q^{91} +(-4.81502 - 12.6962i) q^{92} +(-4.33582 + 5.31042i) q^{93} +(-8.89777 + 18.7516i) q^{94} +(-0.0146912 + 0.00490464i) q^{95} +(3.95367 + 5.72788i) q^{96} +(3.20053 + 15.6772i) q^{97} +(-1.42209 + 35.2889i) q^{98} +1.89487 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9} - q^{10} - 2 q^{11} + 30 q^{12} - 19 q^{13} + q^{15} + 15 q^{16} - 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21} + 22 q^{22} + 46 q^{23} + 3 q^{24} + 28 q^{25} + 34 q^{26} + 30 q^{27} - 2 q^{28} + 36 q^{29} + q^{30} - 34 q^{31} - 190 q^{32} + 15 q^{33} - 51 q^{34} - 80 q^{35} + 15 q^{36} + q^{37} - 53 q^{38} + 5 q^{39} - 45 q^{40} + 9 q^{41} + 130 q^{42} + 78 q^{43} + 35 q^{44} - q^{45} - 318 q^{46} - 12 q^{47} - 15 q^{48} - 71 q^{49} + 48 q^{50} - 14 q^{51} - 63 q^{52} - 26 q^{53} - q^{54} - 61 q^{55} - 4 q^{56} - 38 q^{57} - 27 q^{58} + 208 q^{59} - 180 q^{60} - 3 q^{61} - 61 q^{62} + 2 q^{63} + 140 q^{64} + 45 q^{65} - 60 q^{66} - 80 q^{67} - 140 q^{68} + 6 q^{69} - 100 q^{70} + 84 q^{71} - 3 q^{72} + 134 q^{73} - 151 q^{74} - 12 q^{75} + 32 q^{76} + 82 q^{77} - 63 q^{78} + 4 q^{79} - 155 q^{80} + 15 q^{81} - 56 q^{82} + 106 q^{83} + 2 q^{84} - 19 q^{85} + q^{86} - 49 q^{87} + 8 q^{88} - 14 q^{89} + 2 q^{90} - 368 q^{91} + 36 q^{92} - 4 q^{93} - 59 q^{94} + 104 q^{95} + 75 q^{96} - 28 q^{97} + 101 q^{98} + 30 q^{99}+O(q^{100}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9 - q^10 - 2 * q^11 + 30 * q^12 - 19 * q^13 + q^15 + 15 * q^16 - 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 22 * q^22 + 46 * q^23 + 3 * q^24 + 28 * q^25 + 34 * q^26 + 30 * q^27 - 2 * q^28 + 36 * q^29 + q^30 - 34 * q^31 - 190 * q^32 + 15 * q^33 - 51 * q^34 - 80 * q^35 + 15 * q^36 + q^37 - 53 * q^38 + 5 * q^39 - 45 * q^40 + 9 * q^41 + 130 * q^42 + 78 * q^43 + 35 * q^44 - q^45 - 318 * q^46 - 12 * q^47 - 15 * q^48 - 71 * q^49 + 48 * q^50 - 14 * q^51 - 63 * q^52 - 26 * q^53 - q^54 - 61 * q^55 - 4 * q^56 - 38 * q^57 - 27 * q^58 + 208 * q^59 - 180 * q^60 - 3 * q^61 - 61 * q^62 + 2 * q^63 + 140 * q^64 + 45 * q^65 - 60 * q^66 - 80 * q^67 - 140 * q^68 + 6 * q^69 - 100 * q^70 + 84 * q^71 - 3 * q^72 + 134 * q^73 - 151 * q^74 - 12 * q^75 + 32 * q^76 + 82 * q^77 - 63 * q^78 + 4 * q^79 - 155 * q^80 + 15 * q^81 - 56 * q^82 + 106 * q^83 + 2 * q^84 - 19 * q^85 + q^86 - 49 * q^87 + 8 * q^88 - 14 * q^89 + 2 * q^90 - 368 * q^91 + 36 * q^92 - 4 * q^93 - 59 * q^94 + 104 * q^95 + 75 * q^96 - 28 * q^97 + 101 * q^98 + 30 * q^99

Introduction

L-functions

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