LMFDB - Embedded newform 507.2.q.a.16.10

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			16.10
Character	$\chi$	$=$	507.16
Dual form			507.2.q.a.412.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03364 + 0.0834440i) q^{2} +(0.845190 + 0.534466i) q^{3} +(-0.912654 - 0.148321i) q^{4} +(-1.98811 - 1.76131i) q^{5} +(0.829023 + 0.622971i) q^{6} +(-2.70082 + 2.81186i) q^{7} +(-2.94471 - 0.725807i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})$	\(q+(1.03364 + 0.0834440i) q^{2} +(0.845190 + 0.534466i) q^{3} +(-0.912654 - 0.148321i) q^{4} +(-1.98811 - 1.76131i) q^{5} +(0.829023 + 0.622971i) q^{6} +(-2.70082 + 2.81186i) q^{7} +(-2.94471 - 0.725807i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-1.90802 - 1.98646i) q^{10} +(-1.15055 + 2.42473i) q^{11} +(-0.692094 - 0.613142i) q^{12} +(-3.13586 + 1.77944i) q^{13} +(-3.02631 + 2.68108i) q^{14} +(-0.738971 - 2.55122i) q^{15} +(-1.22912 - 0.410341i) q^{16} +(2.30308 - 2.39776i) q^{17} +(0.367726 + 0.969613i) q^{18} +(-1.39301 + 2.41276i) q^{19} +(1.55322 + 1.90235i) q^{20} +(-3.78555 + 0.933055i) q^{21} +(-1.39158 + 2.41029i) q^{22} +(-1.15514 - 2.00075i) q^{23} +(-2.10092 - 2.18729i) q^{24} +(0.247681 + 2.03984i) q^{25} +(-3.38983 + 1.57763i) q^{26} +(-0.120537 + 0.992709i) q^{27} +(2.88197 - 2.16566i) q^{28} +(1.28241 + 0.103527i) q^{29} +(-0.550945 - 2.69871i) q^{30} +(-0.0936485 + 0.771264i) q^{31} +(4.34408 + 1.85084i) q^{32} +(-2.26837 + 1.43443i) q^{33} +(2.58063 - 2.28624i) q^{34} +(10.3221 - 0.833287i) q^{35} +(-0.257248 - 0.888122i) q^{36} +(0.930584 - 0.396485i) q^{37} +(-1.64120 + 2.37768i) q^{38} +(-3.60144 - 0.172048i) q^{39} +(4.57605 + 6.62955i) q^{40} +(-4.18322 - 2.64531i) q^{41} +(-3.99075 + 0.648560i) q^{42} +(-3.78557 - 1.61288i) q^{43} +(1.40969 - 2.04229i) q^{44} +(0.738971 - 2.55122i) q^{45} +(-1.02704 - 2.16445i) q^{46} +(-1.83596 + 4.84103i) q^{47} +(-0.819528 - 1.00374i) q^{48} +(-0.330220 - 8.19434i) q^{49} +(0.0858008 + 2.12913i) q^{50} +(3.22806 - 0.795645i) q^{51} +(3.12588 - 1.15890i) q^{52} +(-0.0869297 - 0.0214262i) q^{53} +(-0.207427 + 1.01604i) q^{54} +(6.55813 - 2.79416i) q^{55} +(9.99402 - 6.31984i) q^{56} +(-2.46689 + 1.29473i) q^{57} +(1.31691 + 0.214018i) q^{58} +(0.241894 - 0.0807559i) q^{59} +(0.296026 + 2.43799i) q^{60} +(2.96219 - 10.2267i) q^{61} +(-0.161156 + 0.789395i) q^{62} +(-3.69820 - 1.23464i) q^{63} +(6.63053 + 3.47997i) q^{64} +(9.36859 + 1.98551i) q^{65} +(-2.46437 + 1.29340i) q^{66} +(-7.16148 + 1.16385i) q^{67} +(-2.45755 + 1.84673i) q^{68} +(0.0930252 - 2.30840i) q^{69} +10.7389 q^{70} +(-0.456272 + 11.3223i) q^{71} +(-0.606647 - 2.97155i) q^{72} +(-7.85264 - 11.3765i) q^{73} +(0.994972 - 0.332170i) q^{74} +(-0.880887 + 1.85643i) q^{75} +(1.62920 - 1.99540i) q^{76} +(-3.71056 - 9.78395i) q^{77} +(-3.70824 - 0.478354i) q^{78} +(-5.11294 + 13.4817i) q^{79} +(1.72089 + 2.98067i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-4.10320 - 3.08336i) q^{82} +(11.5590 + 6.06662i) q^{83} +(3.59329 - 0.290080i) q^{84} +(-8.80199 + 0.710570i) q^{85} +(-3.77833 - 1.98302i) q^{86} +(1.02855 + 0.772902i) q^{87} +(5.14792 - 6.30506i) q^{88} +(3.22667 + 5.58875i) q^{89} +(0.976713 - 2.57538i) q^{90} +(3.46589 - 13.6235i) q^{91} +(0.757486 + 1.99733i) q^{92} +(-0.491365 + 0.601813i) q^{93} +(-2.30168 + 4.85068i) q^{94} +(7.01909 - 2.34332i) q^{95} +(2.68236 + 3.88607i) q^{96} +(1.82464 + 8.93770i) q^{97} +(0.342439 - 8.49754i) q^{98} -2.68385 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 $

$2$	1.03364	+	0.0834440i	0.730893	+	0.0590038i	0.440310	−	0.897846i	$-0.354869\pi$
$2$	1.03364	+	0.0834440i	0.730893	+	0.0590038i	0.290583	+	0.956850i	$0.406151\pi$
$3$	0.845190	+	0.534466i	0.487971	+	0.308574i
$3$	0.845190	+	0.534466i	0.487971	+	0.308574i
$4$	−0.912654	−	0.148321i	−0.456327	−	0.0741604i
$5$	−1.98811	−	1.76131i	−0.889111	−	0.787684i	0.0889425	−	0.996037i	$-0.471651\pi$
$5$	−1.98811	−	1.76131i	−0.889111	−	0.787684i	−0.978054	+	0.208353i	$0.933190\pi$
$6$	0.829023	+	0.622971i	0.338447	+	0.254327i
$7$	−2.70082	+	2.81186i	−1.02082	+	1.06278i	−0.0228048	+	0.999740i	$0.507260\pi$
$7$	−2.70082	+	2.81186i	−1.02082	+	1.06278i	−0.998011	+	0.0630418i	$0.979920\pi$
$8$	−2.94471	−	0.725807i	−1.04111	−	0.256612i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	−1.90802	−	1.98646i	−0.603369	−	0.628174i
$11$	−1.15055	+	2.42473i	−0.346903	+	0.731083i	−0.999649	−	0.0264938i	$-0.991566\pi$
$11$	−1.15055	+	2.42473i	−0.346903	+	0.731083i	0.652746	+	0.757577i	$0.273617\pi$
$12$	−0.692094	−	0.613142i	−0.199790	−	0.176999i
$13$	−3.13586	+	1.77944i	−0.869731	+	0.493527i
$13$	−3.13586	+	1.77944i	−0.869731	+	0.493527i
$14$	−3.02631	+	2.68108i	−0.808815	+	0.716548i
$15$	−0.738971	−	2.55122i	−0.190802	−	0.658723i
$16$	−1.22912	−	0.410341i	−0.307280	−	0.102585i
$17$	2.30308	−	2.39776i	0.558579	−	0.581542i	−0.380699	−	0.924699i	$-0.624317\pi$
$17$	2.30308	−	2.39776i	0.558579	−	0.581542i	0.939278	+	0.343157i	$0.111496\pi$
$18$	0.367726	+	0.969613i	0.0866738	+	0.228540i
$19$	−1.39301	+	2.41276i	−0.319578	+	0.553525i	−0.980400	−	0.197017i	$-0.936874\pi$
$19$	−1.39301	+	2.41276i	−0.319578	+	0.553525i	0.660822	+	0.750543i	$0.270208\pi$
$20$	1.55322	+	1.90235i	0.347311	+	0.425378i
$21$	−3.78555	+	0.933055i	−0.826075	+	0.203609i
$22$	−1.39158	+	2.41029i	−0.296686	+	0.513875i
$23$	−1.15514	−	2.00075i	−0.240862	−	0.417186i	0.720098	−	0.693873i	$-0.244097\pi$
$23$	−1.15514	−	2.00075i	−0.240862	−	0.417186i	−0.960960	+	0.276687i	$0.910764\pi$
$24$	−2.10092	−	2.18729i	−0.428849	−	0.446480i
$25$	0.247681	+	2.03984i	0.0495363	+	0.407968i
$26$	−3.38983	+	1.57763i	−0.664800	+	0.309398i
$27$	−0.120537	+	0.992709i	−0.0231973	+	0.191047i
$28$	2.88197	−	2.16566i	0.544642	−	0.409272i
$29$	1.28241	+	0.103527i	0.238137	+	0.0192244i	0.198959	−	0.980008i	$-0.436244\pi$
$29$	1.28241	+	0.103527i	0.238137	+	0.0192244i	0.0391781	+	0.999232i	$0.487526\pi$
$30$	−0.550945	−	2.69871i	−0.100588	−	0.492714i
$31$	−0.0936485	+	0.771264i	−0.0168198	+	0.138523i	−0.998700	−	0.0509814i	$-0.983765\pi$
$31$	−0.0936485	+	0.771264i	−0.0168198	+	0.138523i	0.981880	+	0.189505i	$0.0606882\pi$
$32$	4.34408	+	1.85084i	0.767932	+	0.327185i
$33$	−2.26837	+	1.43443i	−0.394872	+	0.249702i
$34$	2.58063	−	2.28624i	0.442575	−	0.392087i
$35$	10.3221	−	0.833287i	1.74475	−	0.140851i
$36$	−0.257248	−	0.888122i	−0.0428746	−	0.148020i
$37$	0.930584	−	0.396485i	0.152987	−	0.0651817i	−0.314116	−	0.949385i	$-0.601708\pi$
$37$	0.930584	−	0.396485i	0.152987	−	0.0651817i	0.467103	+	0.884203i	$0.345298\pi$
$38$	−1.64120	+	2.37768i	−0.266237	+	0.385711i
$39$	−3.60144	−	0.172048i	−0.576693	−	0.0275497i
$40$	4.57605	+	6.62955i	0.723537	+	1.04822i
$41$	−4.18322	−	2.64531i	−0.653309	−	0.413128i	0.166281	−	0.986078i	$-0.446824\pi$
$41$	−4.18322	−	2.64531i	−0.653309	−	0.413128i	−0.819590	+	0.572951i	$0.805799\pi$
$42$	−3.99075	+	0.648560i	−0.615786	+	0.100075i
$43$	−3.78557	−	1.61288i	−0.577295	−	0.245962i	0.0835267	−	0.996506i	$-0.473382\pi$
$43$	−3.78557	−	1.61288i	−0.577295	−	0.245962i	−0.660821	+	0.750543i	$0.729792\pi$
$44$	1.40969	−	2.04229i	0.212519	−	0.307887i
$45$	0.738971	−	2.55122i	0.110159	−	0.380314i
$46$	−1.02704	−	2.16445i	−0.151429	−	0.319130i
$47$	−1.83596	+	4.84103i	−0.267802	+	0.706137i	0.731892	+	0.681421i	$0.238638\pi$
$47$	−1.83596	+	4.84103i	−0.267802	+	0.706137i	−0.999695	+	0.0247165i	$0.992132\pi$
$48$	−0.819528	−	1.00374i	−0.118289	−	0.144877i
$49$	−0.330220	−	8.19434i	−0.0471744	−	1.17062i
$50$	0.0858008	+	2.12913i	0.0121341	+	0.301104i
$51$	3.22806	−	0.795645i	0.452019	−	0.111413i
$52$	3.12588	−	1.15890i	0.433482	−	0.160710i
$53$	−0.0869297	−	0.0214262i	−0.0119407	−	0.00294312i	0.233341	−	0.972395i	$-0.425034\pi$
$53$	−0.0869297	−	0.0214262i	−0.0119407	−	0.00294312i	−0.245281	+	0.969452i	$0.578880\pi$
$54$	−0.207427	+	1.01604i	−0.0282272	+	0.138266i
$55$	6.55813	−	2.79416i	0.884298	−	0.376764i
$56$	9.99402	−	6.31984i	1.33551	−	0.844524i
$57$	−2.46689	+	1.29473i	−0.326748	+	0.171491i
$58$	1.31691	+	0.214018i	0.172918	+	0.0281020i
$59$	0.241894	−	0.0807559i	0.0314919	−	0.0105135i	−0.300878	−	0.953663i	$-0.597280\pi$
$59$	0.241894	−	0.0807559i	0.0314919	−	0.0105135i	0.332370	+	0.943149i	$0.392152\pi$
$60$	0.296026	+	2.43799i	0.0382167	+	0.314743i
$61$	2.96219	−	10.2267i	0.379269	−	1.30939i	−0.513195	−	0.858272i	$-0.671538\pi$
$61$	2.96219	−	10.2267i	0.379269	−	1.30939i	0.892464	−	0.451118i	$-0.148975\pi$
$62$	−0.161156	+	0.789395i	−0.0204668	+	0.100253i
$63$	−3.69820	−	1.23464i	−0.465929	−	0.155550i
$64$	6.63053	+	3.47997i	0.828816	+	0.434996i
$65$	9.36859	+	1.98551i	1.16203	+	0.246273i
$66$	−2.46437	+	1.29340i	−0.303343	+	0.159206i
$67$	−7.16148	+	1.16385i	−0.874914	+	0.142187i	−0.581254	−	0.813722i	$-0.697438\pi$
$67$	−7.16148	+	1.16385i	−0.874914	+	0.142187i	−0.293660	+	0.955910i	$0.594873\pi$
$68$	−2.45755	+	1.84673i	−0.298022	+	0.223949i
$69$	0.0930252	−	2.30840i	0.0111989	−	0.277898i
$70$	10.7389			1.28354
$71$	−0.456272	+	11.3223i	−0.0541495	+	1.34371i	0.712514	+	0.701658i	$0.247556\pi$
$71$	−0.456272	+	11.3223i	−0.0541495	+	1.34371i	−0.766664	+	0.642049i	$0.778085\pi$
$72$	−0.606647	−	2.97155i	−0.0714940	−	0.350201i
$73$	−7.85264	−	11.3765i	−0.919082	−	1.33152i	−0.943345	−	0.331814i	$-0.892339\pi$
$73$	−7.85264	−	11.3765i	−0.919082	−	1.33152i	0.0242628	−	0.999706i	$-0.492276\pi$
$74$	0.994972	−	0.332170i	0.115663	−	0.0386140i
$75$	−0.880887	+	1.85643i	−0.101716	+	0.214362i
$76$	1.62920	−	1.99540i	0.186882	−	0.228888i
$77$	−3.71056	−	9.78395i	−0.422858	−	1.11498i
$78$	−3.70824	−	0.478354i	−0.419875	−	0.0541630i
$79$	−5.11294	+	13.4817i	−0.575250	+	1.51681i	0.259254	+	0.965809i	$0.416523\pi$
$79$	−5.11294	+	13.4817i	−0.575250	+	1.51681i	−0.834505	+	0.551001i	$0.814246\pi$
$80$	1.72089	+	2.98067i	0.192402	+	0.333249i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	−4.10320	−	3.08336i	−0.453123	−	0.340500i
$83$	11.5590	+	6.06662i	1.26876	+	0.665898i	0.958592	−	0.284784i	$-0.0919217\pi$
$83$	11.5590	+	6.06662i	1.26876	+	0.665898i	0.310170	+	0.950681i	$0.399614\pi$
$84$	3.59329	−	0.290080i	0.392060	−	0.0316504i
$85$	−8.80199	+	0.710570i	−0.954710	+	0.0770722i
$86$	−3.77833	−	1.98302i	−0.407428	−	0.213835i
$87$	1.02855	+	0.772902i	0.110272	+	0.0828638i
$88$	5.14792	−	6.30506i	0.548770	−	0.672122i
$89$	3.22667	+	5.58875i	0.342026	+	0.592406i	0.984809	−	0.173642i	$-0.0555536\pi$
$89$	3.22667	+	5.58875i	0.342026	+	0.592406i	−0.642783	+	0.766048i	$0.722220\pi$
$90$	0.976713	−	2.57538i	0.102955	−	0.271469i
$91$	3.46589	−	13.6235i	0.363324	−	1.42813i
$92$	0.757486	+	1.99733i	0.0789734	+	0.208236i
$93$	−0.491365	+	0.601813i	−0.0509522	+	0.0624051i
$94$	−2.30168	+	4.85068i	−0.237400	+	0.500309i
$95$	7.01909	−	2.34332i	0.720143	−	0.240419i
$96$	2.68236	+	3.88607i	0.273768	+	0.396621i
$97$	1.82464	+	8.93770i	0.185265	+	0.907486i	0.961026	+	0.276459i	$0.0891611\pi$
$97$	1.82464	+	8.93770i	0.185265	+	0.907486i	−0.775761	+	0.631027i	$0.782634\pi$
$98$	0.342439	−	8.49754i	0.0345916	−	0.858381i
$99$	−2.68385			−0.269738
$100$	0.0765031	−	1.89840i	0.00765031	−	0.189840i
$101$	−11.8994	+	8.94184i	−1.18404	+	0.889746i	−0.995725	−	0.0923629i	$-0.970558\pi$
$101$	−11.8994	+	8.94184i	−1.18404	+	0.889746i	−0.188312	+	0.982109i	$0.560302\pi$
$102$	3.40304	−	0.553048i	0.336951	−	0.0547599i
$103$	−15.8562	+	8.32199i	−1.56236	+	0.819990i	−0.999976	−	0.00688578i	$-0.997808\pi$
$103$	−15.8562	+	8.32199i	−1.56236	+	0.819990i	−0.562384	+	0.826876i	$0.690116\pi$
$104$	10.5257	−	2.96390i	1.03213	−	0.290634i
$105$	9.16951	+	4.81253i	0.894852	+	0.469655i
$106$	−0.0880660	−	0.0294008i	−0.00855373	−	0.00285565i
$107$	1.86111	−	9.11634i	0.179921	−	0.881310i	−0.785147	−	0.619309i	$-0.787413\pi$
$107$	1.86111	−	9.11634i	0.179921	−	0.881310i	0.965068	−	0.262001i	$-0.0843822\pi$
$108$	0.257248	−	0.888122i	0.0247537	−	0.0854595i
$109$	2.07679	+	17.1039i	0.198921	+	1.63826i	0.660261	+	0.751036i	$0.270446\pi$
$109$	2.07679	+	17.1039i	0.198921	+	1.63826i	−0.461340	+	0.887223i	$0.652631\pi$
$110$	7.01190	−	2.34091i	0.668558	−	0.223197i
$111$	0.998428	+	0.162260i	0.0947666	+	0.0154011i
$112$	4.47346	−	2.34785i	0.422702	−	0.221851i
$113$	13.4830	−	8.52612i	1.26837	−	0.802070i	0.280881	−	0.959743i	$-0.409373\pi$
$113$	13.4830	−	8.52612i	1.26837	−	0.802070i	0.987491	+	0.157673i	$0.0503991\pi$
$114$	−2.65791	+	1.13243i	−0.248937	+	0.106062i
$115$	−1.22742	+	6.01228i	−0.114457	+	0.560648i
$116$	−1.15504	−	0.284691i	−0.107243	−	0.0264329i
$117$	−2.95195	−	2.07026i	−0.272908	−	0.191396i
$118$	0.256769	−	0.0632879i	0.0236375	−	0.00582613i
$119$	0.521942	+	12.9519i	0.0478463	+	1.18729i
$120$	0.324363	+	8.04898i	0.0296101	+	0.734768i
$121$	2.40135	+	2.94112i	0.218304	+	0.267374i
$122$	3.91519	−	10.3235i	0.354464	−	0.934645i
$123$	−2.12179	−	4.47158i	−0.191315	−	0.403188i
$124$	0.199863	−	0.690008i	0.0179482	−	0.0619645i
$125$	−4.44378	+	6.43792i	−0.397464	+	0.575825i
$126$	−3.71958	−	1.58476i	−0.331366	−	0.141182i
$127$	−2.95474	+	0.480192i	−0.262191	+	0.0426101i	−0.290085	−	0.957001i	$-0.593684\pi$
$127$	−2.95474	+	0.480192i	−0.262191	+	0.0426101i	0.0278949	+	0.999611i	$0.491120\pi$
$128$	−1.41867	−	0.897111i	−0.125394	−	0.0792941i
$129$	−2.33750	−	3.38645i	−0.205805	−	0.298160i
$130$	9.51806	+	2.83406i	0.834789	+	0.248563i
$131$	−1.79667	+	2.60293i	−0.156976	+	0.227419i	−0.893578	−	0.448907i	$-0.851813\pi$
$131$	−1.79667	+	2.60293i	−0.156976	+	0.227419i	0.736603	+	0.676326i	$0.236429\pi$
$132$	2.28299	−	0.972691i	0.198709	−	0.0846619i
$133$	−3.02207	−	10.4334i	−0.262046	−	0.904689i
$134$	−7.49950	+	0.605422i	−0.647858	+	0.0523005i
$135$	1.98811	−	1.76131i	0.171110	−	0.151590i
$136$	−8.52222	+	5.38913i	−0.730775	+	0.462114i
$137$	17.7471	+	7.56134i	1.51624	+	0.646009i	0.980169	−	0.198165i	$-0.0634982\pi$
$137$	17.7471	+	7.56134i	1.51624	+	0.646009i	0.536069	+	0.844174i	$0.319908\pi$
$138$	0.288776	−	2.37829i	0.0245823	−	0.202453i
$139$	2.67872	+	13.1212i	0.227206	+	1.11293i	0.920038	+	0.391830i	$0.128158\pi$
$139$	2.67872	+	13.1212i	0.227206	+	1.11293i	−0.692831	+	0.721100i	$0.743637\pi$
$140$	−9.54411	−	0.770480i	−0.806624	−	0.0651174i
$141$	−4.13910	+	3.11033i	−0.348575	+	0.261937i
$142$	−1.41640	+	11.6651i	−0.118861	+	0.978911i
$143$	−0.706693	−	9.65094i	−0.0590966	−	0.807052i
$144$	−0.156192	−	1.28636i	−0.0130160	−	0.107197i
$145$	−2.36723	−	2.46454i	−0.196587	−	0.204669i
$146$	−7.16749	−	12.4145i	−0.593186	−	1.02743i
$147$	4.10049	−	7.10226i	0.338203	−	0.585785i
$148$	−0.908108	+	0.223829i	−0.0746460	+	0.0183986i
$149$	−12.3558	−	15.1331i	−1.01223	−	1.23975i	−0.970620	−	0.240617i	$-0.922650\pi$
$149$	−12.3558	−	15.1331i	−1.01223	−	1.23975i	−0.0416053	−	0.999134i	$-0.513247\pi$
$150$	−1.06543	+	1.84537i	−0.0869917	+	0.150674i
$151$	−7.47214	−	19.7024i	−0.608074	−	1.60336i	−0.785249	−	0.619180i	$-0.787465\pi$
$151$	−7.47214	−	19.7024i	−0.608074	−	1.60336i	0.177176	−	0.984179i	$-0.443304\pi$
$152$	5.85321	−	6.09384i	0.474758	−	0.494275i
$153$	3.15357	+	1.05282i	0.254951	+	0.0851152i
$154$	−3.01897	−	10.4227i	−0.243275	−	0.839884i
$155$	1.54462	−	1.36842i	0.124067	−	0.109914i
$156$	3.26135	+	0.691189i	0.261117	+	0.0553394i
$157$	−9.61370	−	8.51699i	−0.767257	−	0.679730i	0.185778	−	0.982592i	$-0.440520\pi$
$157$	−9.61370	−	8.51699i	−0.767257	−	0.679730i	−0.953035	+	0.302862i	$0.902058\pi$
$158$	−6.40990	+	13.5086i	−0.509944	+	1.07468i
$159$	−0.0620205	−	0.0645702i	−0.00491855	−	0.00512075i
$160$	−5.37661	−	11.3310i	−0.425059	−	0.895792i
$161$	8.74565	+	2.15561i	0.689254	+	0.169886i
$162$	−0.718356	+	0.747888i	−0.0564394	+	0.0587596i
$163$	−10.9485	−	8.22726i	−0.857552	−	0.644409i	0.0782499	−	0.996934i	$-0.475067\pi$
$163$	−10.9485	−	8.22726i	−0.857552	−	0.644409i	−0.935802	+	0.352525i	$0.885323\pi$
$164$	3.42548	+	3.03471i	0.267485	+	0.236971i
$165$	7.03625	+	1.14350i	0.547771	+	0.0890215i
$166$	11.4416	+	7.23522i	0.888039	+	0.561562i
$167$	13.2247	+	1.06761i	1.02336	+	0.0826143i	0.580736	−	0.814092i	$-0.302765\pi$
$167$	13.2247	+	1.06761i	1.02336	+	0.0826143i	0.442626	+	0.896706i	$0.354047\pi$
$168$	11.8246			0.912287
$169$	6.66722	−	11.1601i	0.512863	−	0.858470i
$170$	−9.15737			−0.702338
$171$	−2.77698	−	0.224181i	−0.212361	−	0.0171436i
$172$	3.21570	+	2.03348i	0.245194	+	0.155052i
$173$	−0.408570	−	0.0663991i	−0.0310630	−	0.00504823i	0.144860	−	0.989452i	$-0.453727\pi$
$173$	−0.408570	−	0.0663991i	−0.0310630	−	0.00504823i	−0.175923	+	0.984404i	$0.556291\pi$
$174$	0.998651	+	0.884728i	0.0757075	+	0.0670710i
$175$	−6.40468	−	4.81281i	−0.484148	−	0.363814i
$176$	2.40913	−	2.50817i	0.181595	−	0.189060i
$177$	0.247607	+	0.0610297i	0.0186113	+	0.00458728i
$178$	2.86886	+	6.04599i	0.215030	+	0.453166i
$179$	14.0864	+	14.6655i	1.05287	+	1.09615i	0.995205	+	0.0978124i	$0.0311845\pi$
$179$	14.0864	+	14.6655i	1.05287	+	1.09615i	0.0576602	+	0.998336i	$0.481636\pi$
$180$	−1.05282	+	2.21878i	−0.0784729	+	0.165378i
$181$	−12.6384	−	11.1967i	−0.939406	−	0.832241i	0.0466062	−	0.998913i	$-0.485159\pi$
$181$	−12.6384	−	11.1967i	−0.939406	−	0.832241i	−0.986012	+	0.166672i	$0.946698\pi$
$182$	4.71928	−	13.7926i	0.349816	−	1.02238i
$183$	7.96941	−	7.06028i	0.589116	−	0.521911i
$184$	1.94938	+	6.73005i	0.143710	+	0.496146i
$185$	−2.54844	−	0.850794i	−0.187365	−	0.0625517i
$186$	−0.558112	+	0.581056i	−0.0409228	+	0.0426051i
$187$	3.16411	+	8.34308i	0.231383	+	0.610107i
$188$	2.39362	−	4.14588i	0.174573	−	0.302369i
$189$	−2.46581	−	3.02006i	−0.179361	−	0.219677i
$190$	7.45074	−	1.83644i	0.540533	−	0.133229i
$191$	0.401806	−	0.695949i	0.0290737	−	0.0503571i	−0.851122	−	0.524967i	$-0.824078\pi$
$191$	0.401806	−	0.695949i	0.0290737	−	0.0503571i	0.880196	+	0.474610i	$0.157411\pi$
$192$	3.74413	+	6.48503i	0.270210	+	0.468017i
$193$	8.99335	+	9.36307i	0.647355	+	0.673968i	0.961310	−	0.275470i	$-0.0888334\pi$
$193$	8.99335	+	9.36307i	0.647355	+	0.673968i	−0.313954	+	0.949438i	$0.601654\pi$
$194$	1.14023	+	9.39061i	0.0818635	+	0.674207i
$195$	6.85705	+	6.68533i	0.491043	+	0.478746i
$196$	−0.914013	+	7.52757i	−0.0652866	+	0.537684i
$197$	0.168281	−	0.126455i	0.0119895	−	0.00900952i	−0.594731	−	0.803925i	$-0.702741\pi$
$197$	0.168281	−	0.126455i	0.0119895	−	0.00900952i	0.606720	+	0.794916i	$0.292485\pi$
$198$	−2.77414	−	0.223951i	−0.197149	−	0.0159155i
$199$	−0.862225	−	4.22346i	−0.0611215	−	0.299393i	0.937727	−	0.347374i	$-0.112927\pi$
$199$	−0.862225	−	4.22346i	−0.0611215	−	0.299393i	−0.998848	+	0.0479808i	$0.984721\pi$
$200$	0.751179	−	6.18652i	0.0531164	−	0.437453i
$201$	−6.67485	−	2.84389i	−0.470808	−	0.200592i
$202$	−13.0459	+	8.24970i	−0.917903	+	0.580447i
$203$	−3.75466	+	3.32634i	−0.263525	+	0.233463i
$204$	−3.06411	+	0.247361i	−0.214531	+	0.0173187i
$205$	3.65749	+	12.6271i	0.255450	+	0.881917i
$206$	−17.0840	+	7.27883i	−1.19030	+	0.507140i
$207$	1.31238	−	1.90132i	0.0912170	−	0.132151i
$208$	4.58453	−	0.900371i	0.317880	−	0.0624295i
$209$	−4.24757	−	6.15366i	−0.293810	−	0.425658i
$210$	9.07638	+	5.73956i	0.626330	+	0.396067i
$211$	4.99037	−	0.811014i	0.343551	−	0.0558325i	0.0138121	−	0.999905i	$-0.495603\pi$
$211$	4.99037	−	0.811014i	0.343551	−	0.0558325i	0.329739	+	0.944072i	$0.393039\pi$
$212$	0.0761588	+	0.0324482i	0.00523061	+	0.00222855i
$213$	−6.43700	+	9.32561i	−0.441056	+	0.638980i
$214$	2.68442	−	9.26771i	0.183503	−	0.633527i
$215$	4.68536	+	9.87418i	0.319539	+	0.673413i
$216$	1.07546	−	2.83576i	0.0731759	−	0.192949i
$217$	−1.91576	−	2.34638i	−0.130050	−	0.159282i
$218$	0.719434	+	17.8526i	0.0487263	+	1.20913i
$219$	−0.556616	−	13.8123i	−0.0376126	−	0.933348i
$220$	−6.39974	+	1.57739i	−0.431470	+	0.106348i
$221$	−2.95547	+	11.6172i	−0.198807	+	0.781459i
$222$	1.01847	+	0.251031i	0.0683555	+	0.0168481i
$223$	1.65039	−	8.08416i	0.110518	−	0.541355i	−0.886401	−	0.462919i	$-0.846802\pi$
$223$	1.65039	−	8.08416i	0.110518	−	0.541355i	0.996919	−	0.0784364i	$-0.0249928\pi$
$224$	−16.9369	+	7.21614i	−1.13164	+	0.482148i
$225$	−1.73672	+	1.09823i	−0.115781	+	0.0732155i
$226$	14.6480	−	7.68786i	0.974370	−	0.511389i
$227$	4.93296	+	0.801685i	0.327412	+	0.0532097i	0.321896	−	0.946775i	$-0.395680\pi$
$227$	4.93296	+	0.801685i	0.327412	+	0.0532097i	0.00551655	+	0.999985i	$0.498244\pi$
$228$	2.44346	−	0.815745i	0.161822	−	0.0540241i
$229$	−0.616768	−	5.07955i	−0.0407572	−	0.335666i	−0.998797	−	0.0490314i	$-0.984387\pi$
$229$	−0.616768	−	5.07955i	−0.0407572	−	0.335666i	0.958040	−	0.286634i	$-0.0925365\pi$
$230$	−1.77039	+	6.11211i	−0.116736	+	0.403020i
$231$	2.09306	−	10.2525i	0.137713	−	0.674562i
$232$	−3.70118	−	1.23564i	−0.242994	−	0.0811235i
$233$	−23.1788	−	12.1652i	−1.51849	−	0.796966i	−0.520125	−	0.854090i	$-0.674115\pi$
$233$	−23.1788	−	12.1652i	−1.51849	−	0.796966i	−0.998367	+	0.0571242i	$0.981807\pi$
$234$	−2.87850	−	2.38623i	−0.188173	−	0.155992i
$235$	12.1767	−	6.39081i	0.794319	−	0.416891i
$236$	−0.232743	+	0.0378244i	−0.0151503	+	0.00246216i
$237$	−11.5269	+	8.66191i	−0.748753	+	0.562652i
$238$	−0.541255	+	13.4311i	−0.0350843	+	0.870609i
$239$	−6.18386			−0.400001			−0.200000	−	0.979796i	$-0.564094\pi$
$239$	−6.18386			−0.400001			−0.200000	+	0.979796i	$0.564094\pi$
$240$	−0.138587	+	3.43899i	−0.00894574	+	0.221986i
$241$	2.46943	+	12.0961i	0.159070	+	0.779175i	0.978541	+	0.206054i	$0.0660624\pi$
$241$	2.46943	+	12.0961i	0.159070	+	0.779175i	−0.819471	+	0.573121i	$0.805732\pi$
$242$	2.23671	+	3.24043i	0.143781	+	0.208303i
$243$	−0.948536	+	0.316668i	−0.0608486	+	0.0203143i
$244$	−4.22028	+	8.89405i	−0.270176	+	0.569383i
$245$	−13.7763	+	16.8729i	−0.880135	+	1.07797i
$246$	−1.82004	−	4.79905i	−0.116041	−	0.305976i
$247$	0.0749241	−	10.0448i	0.00476731	−	0.639138i
$248$	0.835557	−	2.20318i	0.0530579	−	0.139902i
$249$	6.52713	+	11.3053i	0.413640	+	0.716445i
$250$	−5.13047	+	6.28368i	−0.324479	+	0.397415i
$251$	−19.9902	−	15.0217i	−1.26177	−	0.948161i	−0.261916	−	0.965091i	$-0.584354\pi$
$251$	−19.9902	−	15.0217i	−1.26177	−	0.948161i	−0.999857	+	0.0169300i	$0.994611\pi$
$252$	3.19205	+	1.67532i	0.201080	+	0.105535i
$253$	6.18033	−	0.498927i	0.388554	−	0.0313673i
$254$	−3.09420	+	0.249790i	−0.194147	+	0.0156732i
$255$	−7.81913	−	4.10380i	−0.489653	−	0.256990i
$256$	−13.3644	−	10.0427i	−0.835276	−	0.627669i
$257$	0.508961	−	0.623364i	0.0317481	−	0.0388844i	−0.758487	−	0.651688i	$-0.774061\pi$
$257$	0.508961	−	0.623364i	0.0317481	−	0.0388844i	0.790235	+	0.612804i	$0.209958\pi$
$258$	−2.13355	−	3.69542i	−0.132829	−	0.230067i
$259$	−1.39849	+	3.68750i	−0.0868977	+	0.229130i
$260$	−8.25579	−	3.20164i	−0.512002	−	0.198557i
$261$	0.456227	+	1.20297i	0.0282397	+	0.0744621i
$262$	−2.07431	+	2.54056i	−0.128151	+	0.156957i
$263$	−6.00686	+	12.6592i	−0.370399	+	0.780600i	0.629594	+	0.776924i	$0.283221\pi$
$263$	−6.00686	+	12.6592i	−0.370399	+	0.780600i	−0.999993	+	0.00367535i	$0.998830\pi$
$264$	7.72081	−	2.57759i	0.475183	−	0.158639i
$265$	0.135088	+	0.195708i	0.00829837	+	0.0120223i
$266$	−2.25312	−	11.0365i	−0.138148	−	0.676692i
$267$	−0.259849	+	6.44810i	−0.0159025	+	0.394617i
$268$	6.70858			0.409791
$269$	0.230553	−	5.72112i	0.0140571	−	0.348823i	−0.976821	−	0.214059i	$-0.931331\pi$
$269$	0.230553	−	5.72112i	0.0140571	−	0.348823i	0.990878	−	0.134764i	$-0.0430275\pi$
$270$	2.20196	−	1.65467i	0.134007	−	0.100700i
$271$	−5.19639	+	0.844495i	−0.315658	+	0.0512994i	−0.316176	−	0.948700i	$-0.602399\pi$
$271$	−5.19639	+	0.844495i	−0.315658	+	0.0512994i	0.000518243		1.00000i	$0.499835\pi$
$272$	−3.81466	+	2.00209i	−0.231298	+	0.121395i
$273$	10.2106	−	9.66207i	0.617976	−	0.584775i
$274$	17.7132	+	9.29658i	1.07009	+	0.561627i
$275$	−5.23103	−	1.74637i	−0.315443	−	0.105310i
$276$	−0.427283	+	2.09297i	−0.0257194	+	0.125982i
$277$	−8.19464	+	28.2912i	−0.492368	+	1.69985i	0.201277	+	0.979534i	$0.435491\pi$
$277$	−8.19464	+	28.2912i	−0.492368	+	1.69985i	−0.693645	+	0.720317i	$0.743996\pi$
$278$	1.67394	+	13.7862i	0.100396	+	0.826839i
$279$	−0.736946	+	0.246029i	−0.0441198	+	0.0147293i
$280$	−31.0005	−	5.03807i	−1.85263	−	0.301082i
$281$	1.31086	−	0.687990i	0.0781991	−	0.0410421i	−0.425170	−	0.905113i	$-0.639786\pi$
$281$	1.31086	−	0.687990i	0.0781991	−	0.0410421i	0.503369	+	0.864071i	$0.332093\pi$
$282$	−4.53788	+	2.86958i	−0.270227	+	0.170881i
$283$	−4.90852	+	2.09133i	−0.291781	+	0.124316i	−0.532897	−	0.846180i	$-0.678897\pi$
$283$	−4.90852	+	2.09133i	−0.291781	+	0.124316i	0.241116	+	0.970496i	$0.422487\pi$
$284$	2.09575	−	10.2656i	0.124360	−	0.609154i
$285$	7.18488	+	1.77091i	0.425596	+	0.104900i
$286$	0.0748474	−	10.0346i	0.00442582	−	0.593355i
$287$	18.7364	−	4.61810i	1.10597	−	0.272598i
$288$	0.190133	+	4.71810i	0.0112037	+	0.278017i
$289$	0.239444	+	5.94175i	0.0140850	+	0.349515i
$290$	−2.24121	−	2.74498i	−0.131608	−	0.161191i
$291$	−3.23472	+	8.52927i	−0.189623	+	0.499994i
$292$	5.47937	+	11.5475i	0.320656	+	0.675768i
$293$	5.50590	−	19.0086i	0.321658	−	1.11049i	−0.622941	−	0.782269i	$-0.714062\pi$
$293$	5.50590	−	19.0086i	0.321658	−	1.11049i	0.944600	−	0.328225i	$-0.106450\pi$
$294$	4.83107	−	6.99901i	0.281754	−	0.408191i
$295$	−0.623148	−	0.265499i	−0.0362811	−	0.0154579i
$296$	−3.02808	+	0.492110i	−0.176003	+	0.0286033i
$297$	−2.26837	−	1.43443i	−0.131624	−	0.0832340i
$298$	−11.5087	−	16.6732i	−0.666679	−	0.965851i
$299$	7.18255	+	4.21859i	0.415378	+	0.243967i
$300$	1.07929	−	1.56362i	0.0623130	−	0.0902759i
$301$	14.7594	−	6.28838i	0.850716	−	0.362456i
$302$	−6.07944	−	20.9887i	−0.349833	−	1.20776i
$303$	−14.8364	+	1.19772i	−0.852328	+	0.0688070i
$304$	2.70223	−	2.39397i	0.154984	−	0.137303i
$305$	−23.9015	+	15.1144i	−1.36860	+	0.865449i
$306$	3.17180	+	1.35138i	0.181320	+	0.0772532i
$307$	1.58056	−	13.0170i	0.0902070	−	0.742922i	−0.875487	−	0.483241i	$-0.839460\pi$
$307$	1.58056	−	13.0170i	0.0902070	−	0.742922i	0.965694	−	0.259681i	$-0.0836174\pi$
$308$	1.93530	+	9.47971i	0.110274	+	0.540157i
$309$	−17.8493	−	1.44095i	−1.01541	−	0.0819727i
$310$	1.71077	−	1.28556i	0.0971651	−	0.0730149i
$311$	0.779794	−	6.42218i	0.0442181	−	0.364168i	−0.953758	−	0.300576i	$-0.902821\pi$
$311$	0.779794	−	6.42218i	0.0442181	−	0.364168i	0.997976	−	0.0635925i	$-0.0202558\pi$
$312$	10.4804	+	3.12059i	0.593333	+	0.176668i
$313$	−1.63600	−	13.4737i	−0.0924723	−	0.761578i	−0.963008	−	0.269473i	$-0.913151\pi$
$313$	−1.63600	−	13.4737i	−0.0924723	−	0.761578i	0.870536	−	0.492105i	$-0.163772\pi$
$314$	−9.22640	−	9.60570i	−0.520676	−	0.542081i
$315$	5.17784	+	8.96829i	0.291738	+	0.505306i
$316$	6.66596	−	11.5458i	0.374989	−	0.649501i
$317$	−23.1923	+	5.71640i	−1.30261	+	0.321065i	−0.828792	−	0.559557i	$-0.810971\pi$
$317$	−23.1923	+	5.71640i	−1.30261	+	0.321065i	−0.473820	+	0.880622i	$0.657125\pi$
$318$	−0.0587188	−	0.0719175i	−0.00329279	−	0.00403293i
$319$	−1.72649	+	2.99038i	−0.0966651	+	0.167429i
$320$	−7.05292	−	18.5970i	−0.394270	−	1.03961i
$321$	6.44537	−	6.71034i	0.359745	−	0.374535i
$322$	8.85997	+	2.95789i	0.493747	+	0.164837i
$323$	2.57701	+	8.89688i	0.143389	+	0.495035i
$324$	0.692094	−	0.613142i	0.0384497	−	0.0340634i
$325$	−4.40646	−	5.95592i	−0.244426	−	0.330375i
$326$	−10.6303	−	9.41760i	−0.588757	−	0.521593i
$327$	−7.38618	+	15.5660i	−0.408457	+	0.860804i
$328$	10.3984	+	10.8259i	0.574156	+	0.597760i
$329$	−8.65368	−	18.2372i	−0.477093	−	1.00545i
$330$	7.17752	+	1.76910i	0.395110	+	0.0973858i
$331$	−7.33654	+	7.63815i	−0.403253	+	0.419831i	−0.891604	−	0.452817i	$-0.850419\pi$
$331$	−7.33654	+	7.63815i	−0.403253	+	0.419831i	0.488351	+	0.872647i	$0.337599\pi$
$332$	−9.64954	−	7.25116i	−0.529587	−	0.397959i
$333$	0.757139	+	0.670766i	0.0414909	+	0.0367578i
$334$	13.5805	+	2.20705i	0.743094	+	0.120764i
$335$	16.2877	+	10.2997i	0.889894	+	0.562735i
$336$	5.03577	+	0.406530i	0.274724	+	0.0221780i
$337$	21.5044			1.17142			0.585710	−	0.810520i	$-0.300816\pi$
$337$	21.5044			1.17142			0.585710	+	0.810520i	$0.300816\pi$
$338$	7.82274	−	10.9792i	0.425501	−	0.597189i
$339$	15.9526			0.866426
$340$	8.13856	+	0.657013i	0.441376	+	0.0356315i
$341$	−1.76236	−	1.11445i	−0.0954372	−	0.0603508i
$342$	−2.85169	−	0.463445i	−0.154202	−	0.0250602i
$343$	3.50487	+	3.10505i	0.189245	+	0.167657i
$344$	9.97679	+	7.49707i	0.537913	+	0.404215i
$345$	−4.25076	+	4.42551i	−0.228853	+	0.238261i
$346$	−0.416774	−	0.102725i	−0.0224059	−	0.00552256i
$347$	7.04600	+	14.8491i	0.378249	+	0.797143i	0.999904	+	0.0138518i	$0.00440930\pi$
$347$	7.04600	+	14.8491i	0.378249	+	0.797143i	−0.621655	+	0.783291i	$0.713539\pi$
$348$	−0.824069	−	0.857947i	−0.0441747	−	0.0459908i
$349$	−8.88485	+	18.7244i	−0.475595	+	1.00230i	0.513916	+	0.857840i	$0.328194\pi$
$349$	−8.88485	+	18.7244i	−0.475595	+	1.00230i	−0.989511	+	0.144455i	$0.953857\pi$
$350$	−6.21853	−	5.50914i	−0.332394	−	0.294476i
$351$	−1.38848	−	3.32748i	−0.0741113	−	0.177608i
$352$	−9.48586	+	8.40374i	−0.505598	+	0.447921i
$353$	−7.42903	−	25.6480i	−0.395407	−	1.36510i	−0.873512	−	0.486802i	$-0.838163\pi$
$353$	−7.42903	−	25.6480i	−0.395407	−	1.36510i	0.478105	−	0.878303i	$-0.341324\pi$
$354$	0.250844	+	0.0837440i	0.0133322	+	0.00445095i
$355$	20.8492	−	21.7063i	1.10656	−	1.15205i
$356$	−2.11590	−	5.57918i	−0.112143	−	0.295696i
$357$	−6.48118	+	11.2257i	−0.343021	+	0.594129i
$358$	13.3365	+	16.3342i	0.704855	+	0.863291i
$359$	9.08566	−	2.23941i	0.479523	−	0.118192i	0.00785705	−	0.999969i	$-0.497499\pi$
$359$	9.08566	−	2.23941i	0.479523	−	0.118192i	0.471666	+	0.881777i	$0.343653\pi$
$360$	−4.02776	+	6.97628i	−0.212281	+	0.367682i
$361$	5.61906	+	9.73250i	0.295740	+	0.512237i
$362$	−12.1293	−	12.6279i	−0.637500	−	0.663708i
$363$	0.457669	+	3.76924i	0.0240214	+	0.197834i
$364$	−5.18381	+	11.9195i	−0.271705	+	0.624752i
$365$	−4.42568	+	36.4488i	−0.231651	+	1.90782i
$366$	8.82663	−	6.63278i	0.461375	−	0.346701i
$367$	13.8983	+	1.12198i	0.725484	+	0.0585671i	0.437691	−	0.899126i	$-0.355796\pi$
$367$	13.8983	+	1.12198i	0.725484	+	0.0585671i	0.287793	+	0.957693i	$0.407078\pi$
$368$	0.598811	+	2.93317i	0.0312152	+	0.152902i
$369$	0.596589	−	4.91336i	0.0310572	−	0.255779i
$370$	−2.56317	−	1.09207i	−0.133253	−	0.0567738i
$371$	0.295029	−	0.186565i	0.0153172	−	0.00968599i
$372$	0.537708	−	0.476368i	0.0278789	−	0.0246985i
$373$	32.7744	−	2.64583i	1.69700	−	0.136996i	0.806273	−	0.591543i	$-0.201481\pi$
$373$	32.7744	−	2.64583i	1.69700	−	0.136996i	0.890723	+	0.454547i	$0.150199\pi$
$374$	2.57437	+	8.88776i	0.133118	+	0.459575i
$375$	−7.19669	+	3.06622i	−0.371635	+	0.158339i
$376$	8.92004	−	12.9229i	0.460016	−	0.666448i
$377$	−4.20566	+	1.95731i	−0.216603	+	0.100807i
$378$	−2.29675	−	3.32741i	−0.118132	−	0.171144i
$379$	−24.6888	−	15.6122i	−1.26818	−	0.801947i	−0.280713	−	0.959792i	$-0.590571\pi$
$379$	−24.6888	−	15.6122i	−1.26818	−	0.801947i	−0.987464	+	0.157845i	$0.949545\pi$
$380$	−6.75356	+	1.09756i	−0.346450	+	0.0563036i
$381$	−2.75396	−	1.17335i	−0.141090	−	0.0601127i
$382$	0.473395	−	0.685832i	0.0242210	−	0.0350902i
$383$	8.73267	−	30.1487i	0.446219	−	1.54053i	−0.350729	−	0.936477i	$-0.614066\pi$
$383$	8.73267	−	30.1487i	0.446219	−	1.54053i	0.796947	−	0.604049i	$-0.206447\pi$
$384$	−0.719568	−	1.51646i	−0.0367203	−	0.0773864i
$385$	−9.85559	+	25.9871i	−0.502287	+	1.32442i
$386$	8.51458	+	10.4285i	0.433381	+	0.530795i
$387$	−0.165688	−	4.11151i	−0.00842240	−	0.209000i
$388$	−0.339623	−	8.42766i	−0.0172418	−	0.427850i
$389$	−26.2168	+	6.46185i	−1.32924	+	0.327629i	−0.839083	−	0.544004i	$-0.816908\pi$
$389$	−26.2168	+	6.46185i	−1.32924	+	0.327629i	−0.490160	+	0.871633i	$0.663062\pi$
$390$	6.52986	+	7.48239i	0.330652	+	0.378886i
$391$	−7.45769	−	1.83816i	−0.377152	−	0.0929596i
$392$	−4.97510	+	24.3697i	−0.251281	+	1.23085i
$393$	−2.90970	+	1.23971i	−0.146775	+	0.0625350i
$394$	0.184493	−	0.116666i	0.00929463	−	0.00587757i
$395$	33.9106	−	17.7977i	1.70623	−	0.895498i
$396$	2.44943	+	0.398071i	0.123089	+	0.0200038i
$397$	−3.36764	+	1.12428i	−0.169017	+	0.0564261i	−0.399917	−	0.916551i	$-0.630961\pi$
$397$	−3.36764	+	1.12428i	−0.169017	+	0.0564261i	0.230900	+	0.972977i	$0.425833\pi$
$398$	−0.538807	−	4.43748i	−0.0270080	−	0.222431i
$399$	3.02207	−	10.4334i	0.151292	−	0.522322i
$400$	0.532600	−	2.60885i	0.0266300	−	0.130442i
$401$	−35.8726	−	11.9760i	−1.79139	−	0.598054i	−0.791477	−	0.611200i	$-0.790687\pi$
$401$	−35.8726	−	11.9760i	−1.79139	−	0.598054i	−0.999914	+	0.0131456i	$0.995816\pi$
$402$	−6.66208	−	3.49653i	−0.332274	−	0.174391i
$403$	−1.07875	−	2.58522i	−0.0537362	−	0.128779i
$404$	12.1863	−	6.39587i	0.606292	−	0.318207i
$405$	2.62170	−	0.426067i	0.130273	−	0.0211714i
$406$	−4.15852	+	3.12493i	−0.206384	+	0.155087i
$407$	−0.109314	+	2.71259i	−0.00541847	+	0.134458i
$408$	−10.0832			−0.499193
$409$	−1.58941	+	39.4408i	−0.0785913	+	1.95022i	0.178730	+	0.983898i	$0.442801\pi$
$409$	−1.58941	+	39.4408i	−0.0785913	+	1.95022i	−0.257321	+	0.966326i	$0.582840\pi$
$410$	2.72687	+	13.3571i	0.134671	+	0.659660i
$411$	10.9584	+	15.8760i	0.540538	+	0.783105i
$412$	15.7056	−	5.24329i	0.773758	−	0.258318i
$413$	−0.426238	+	0.898278i	−0.0209738	+	0.0442013i
$414$	1.51518	−	1.85576i	0.0744672	−	0.0912058i
$415$	−12.2953	−	32.4201i	−0.603554	−	1.59144i
$416$	−16.9159	+	1.92604i	−0.829369	+	0.0944318i
$417$	−4.74883	+	12.5216i	−0.232551	+	0.613187i
$418$	−3.87697	−	6.71510i	−0.189629	−	0.328446i
$419$	−5.83750	+	7.14964i	−0.285181	+	0.349283i	−0.897251	−	0.441520i	$-0.854439\pi$
$419$	−5.83750	+	7.14964i	−0.285181	+	0.349283i	0.612071	+	0.790803i	$0.290337\pi$
$420$	−7.65479	−	5.75220i	−0.373515	−	0.280679i
$421$	−16.8329	−	8.83459i	−0.820386	−	0.430572i	0.00165606	−	0.999999i	$-0.499473\pi$
$421$	−16.8329	−	8.83459i	−0.820386	−	0.430572i	−0.822042	+	0.569427i	$0.807165\pi$
$422$	5.22591	−	0.421879i	0.254394	−	0.0205368i
$423$	−5.16070	+	0.416614i	−0.250922	+	0.0202565i
$424$	0.240432	+	0.126188i	0.0116764	+	0.00612825i
$425$	5.46148	+	4.10403i	0.264921	+	0.199075i
$426$	−7.43170	+	9.10218i	−0.360067	+	0.441002i
$427$	20.7555	+	35.9497i	1.00443	+	1.73973i
$428$	−3.05070	+	8.04402i	−0.147461	+	0.388823i
$429$	4.56081	−	8.53458i	0.220198	−	0.412053i
$430$	4.01903	+	10.5973i	0.193815	+	0.511047i
$431$	4.12920	−	5.05735i	0.198896	−	0.243604i	−0.665521	−	0.746380i	$-0.731790\pi$
$431$	4.12920	−	5.05735i	0.198896	−	0.243604i	0.864417	+	0.502776i	$0.167688\pi$
$432$	0.555503	−	1.17070i	0.0267267	−	0.0563253i
$433$	17.7660	−	5.93115i	0.853777	−	0.285033i	0.144103	−	0.989563i	$-0.453970\pi$
$433$	17.7660	−	5.93115i	0.853777	−	0.285033i	0.709674	+	0.704530i	$0.248842\pi$
$434$	−1.78441	−	2.58516i	−0.0856544	−	0.124092i
$435$	−0.683542	−	3.34821i	−0.0327733	−	0.160534i
$436$	0.641473	−	15.9180i	0.0307210	−	0.762334i
$437$	6.43645			0.307897
$438$	0.577212	−	14.3234i	0.0275802	−	0.684397i
$439$	12.9583	−	9.73754i	0.618467	−	0.464748i	−0.244747	−	0.969587i	$-0.578705\pi$
$439$	12.9583	−	9.73754i	0.618467	−	0.464748i	0.863213	+	0.504840i	$0.168448\pi$
$440$	−21.3398	+	3.46806i	−1.01734	+	0.165333i
$441$	7.26161	−	3.81119i	0.345791	−	0.181485i
$442$	−4.02428	+	11.7614i	−0.191415	+	0.559432i
$443$	23.4065	+	12.2847i	1.11208	+	0.583664i	0.917704	−	0.397264i	$-0.130040\pi$
$443$	23.4065	+	12.2847i	1.11208	+	0.583664i	0.194374	+	0.980928i	$0.437732\pi$
$444$	−0.887153	−	0.296175i	−0.0421024	−	0.0140558i
$445$	3.42857	−	16.7942i	0.162530	−	0.796123i
$446$	2.38048	−	8.21839i	0.112719	−	0.389152i
$447$	−2.35487	−	19.3941i	−0.111381	−	0.917309i
$448$	−27.6931	+	9.24531i	−1.30838	+	0.436800i
$449$	19.9690	+	3.24528i	0.942395	+	0.153154i	0.612150	−	0.790741i	$-0.290305\pi$
$449$	19.9690	+	3.24528i	0.942395	+	0.153154i	0.330244	+	0.943895i	$0.392869\pi$
$450$	−1.88678	+	0.990257i	−0.0889435	+	0.0466812i
$451$	11.2272	−	7.09962i	0.528666	−	0.334308i
$452$	−13.5699	+	5.78159i	−0.638274	+	0.271943i
$453$	4.21489	−	20.6459i	0.198033	−	0.970028i
$454$	5.03201	+	1.24028i	0.236164	+	0.0582092i
$455$	−30.8859	+	20.9806i	−1.44795	+	0.983585i
$456$	8.20402	−	2.02211i	0.384188	−	0.0946940i
$457$	1.22936	+	30.5064i	0.0575072	+	1.42703i	0.728237	+	0.685325i	$0.240340\pi$
$457$	1.22936	+	30.5064i	0.0575072	+	1.42703i	−0.670730	+	0.741702i	$0.734019\pi$
$458$	−0.213659	−	5.30188i	−0.00998361	−	0.247741i
$459$	2.10267	+	2.57531i	0.0981443	+	0.120205i
$460$	2.01195	−	5.30508i	0.0938077	−	0.247351i
$461$	12.2707	+	25.8600i	0.571505	+	1.20442i	0.959225	+	0.282644i	$0.0912114\pi$
$461$	12.2707	+	25.8600i	0.571505	+	1.20442i	−0.387720	+	0.921777i	$0.626737\pi$
$462$	3.01897	−	10.4227i	0.140455	−	0.484907i
$463$	16.8823	−	24.4583i	0.784588	−	1.13667i	−0.202934	−	0.979192i	$-0.565048\pi$
$463$	16.8823	−	24.4583i	0.784588	−	1.13667i	0.987522	−	0.157480i	$-0.0503370\pi$
$464$	−1.53375	−	0.653471i	−0.0712026	−	0.0303366i
$465$	2.03687	−	0.331024i	0.0944577	−	0.0153509i
$466$	−22.9434	−	14.5085i	−1.06283	−	0.672094i
$467$	−9.53544	−	13.8145i	−0.441248	−	0.639258i	0.537756	−	0.843101i	$-0.319272\pi$
$467$	−9.53544	−	13.8145i	−0.441248	−	0.639258i	−0.979004	+	0.203843i	$0.934657\pi$
$468$	2.38705	+	2.32727i	0.110341	+	0.107578i
$469$	16.0693	−	23.2804i	0.742012	−	1.07499i
$470$	13.1196	−	5.58972i	0.605160	−	0.257835i
$471$	−3.57336	−	12.3367i	−0.164652	−	0.568444i
$472$	−0.770921	+	0.0622352i	−0.0354845	+	0.00286461i
$473$	8.26629	−	7.32329i	0.380084	−	0.336725i
$474$	−12.6375	+	7.99144i	−0.580457	+	0.367059i
$475$	−5.26667	−	2.24392i	−0.241651	−	0.102958i
$476$	1.44468	−	11.8980i	0.0662166	−	0.545343i
$477$	−0.0179086	−	0.0877219i	−0.000819977	−	0.00401651i
$478$	−6.39188	−	0.516006i	−0.292358	−	0.0236016i
$479$	7.07345	−	5.31535i	0.323194	−	0.242865i	−0.426744	−	0.904372i	$-0.640340\pi$
$479$	7.07345	−	5.31535i	0.323194	−	0.242865i	0.749938	+	0.661508i	$0.230083\pi$
$480$	1.51176	−	12.4504i	0.0690019	−	0.568282i
$481$	−2.21266	+	2.89923i	−0.100889	+	0.132194i
$482$	1.54315	+	12.7090i	0.0702887	+	0.578880i
$483$	6.23964	+	6.49615i	0.283913	+	0.295585i
$484$	−1.75537	−	3.04039i	−0.0797896	−	0.138200i
$485$	12.1145	−	20.9829i	0.550091	−	0.952786i
$486$	−1.00687	+	0.248171i	−0.0456725	+	0.0112573i
$487$	22.2526	+	27.2544i	1.00836	+	1.23502i	0.971830	+	0.235684i	$0.0757332\pi$
$487$	22.2526	+	27.2544i	1.00836	+	1.23502i	0.0365305	+	0.999333i	$0.488369\pi$
$488$	−16.1454	+	27.9646i	−0.730867	+	1.26590i
$489$	−4.85637	−	12.8052i	−0.219613	−	0.579071i
$490$	−15.6476	+	16.2909i	−0.706889	+	0.735949i
$491$	31.6979	+	10.5823i	1.43051	+	0.477573i	0.923243	−	0.384217i	$-0.125529\pi$
$491$	31.6979	+	10.5823i	1.43051	+	0.477573i	0.507264	+	0.861791i	$0.330657\pi$
$492$	1.27323	+	4.39571i	0.0574017	+	0.198174i
$493$	3.20172	−	2.83647i	0.144198	−	0.127748i
$494$	0.915626	−	10.3765i	0.0411960	−	0.466860i
$495$	5.33581	+	4.72711i	0.239827	+	0.212468i
$496$	0.431587	−	0.909550i	0.0193788	−	0.0408400i
$497$	−30.6043	−	31.8624i	−1.37279	−	1.42923i
$498$	5.80333	+	12.2303i	0.260054	+	0.548051i
$499$	12.0115	+	2.96057i	0.537710	+	0.132534i	0.498813	−	0.866710i	$-0.333769\pi$
$499$	12.0115	+	2.96057i	0.537710	+	0.132534i	0.0388968	+	0.999243i	$0.487616\pi$
$500$	5.01051	−	5.21649i	0.224077	−	0.233289i
$501$	10.6068	+	7.97051i	0.473878	+	0.356096i
$502$	−19.4092	−	17.1951i	−0.866276	−	0.767453i
$503$	13.7967	+	2.24218i	0.615165	+	0.0999741i	0.460007	−	0.887915i	$-0.347847\pi$
$503$	13.7967	+	2.24218i	0.615165	+	0.0999741i	0.155159	+	0.987890i	$0.450411\pi$
$504$	9.99402	+	6.31984i	0.445169	+	0.281508i
$505$	39.4068	+	3.18125i	1.75358	+	0.141564i
$506$	6.42986			0.285842
$507$	11.5998	−	5.86902i	0.515164	−	0.260652i
$508$	2.76787			0.122805
$509$	2.94395	+	0.237660i	0.130488	+	0.0105341i	0.145538	−	0.989353i	$-0.453509\pi$
$509$	2.94395	+	0.237660i	0.130488	+	0.0105341i	−0.0150499	+	0.999887i	$0.504791\pi$
$510$	−7.73972	−	4.89430i	−0.342721	−	0.216723i
$511$	53.1977	+	8.64547i	2.35333	+	0.382453i
$512$	−10.4632	−	9.26958i	−0.462412	−	0.409662i
$513$	−2.22726	−	1.67368i	−0.0983359	−	0.0738947i
$514$	0.578098	−	0.601864i	0.0254988	−	0.0265471i
$515$	46.1816	+	11.3827i	2.03501	+	0.501584i
$516$	1.63105	+	3.43736i	0.0718028	+	0.151321i
$517$	−9.62583	−	10.0216i	−0.423344	−	0.440747i
$518$	−1.75323	+	3.69485i	−0.0770325	+	0.162342i
$519$	−0.309832	−	0.274487i	−0.0136001	−	0.0120486i
$520$	−26.1467	−	12.6466i	−1.14661	−	0.554588i
$521$	20.2105	−	17.9049i	0.885436	−	0.784428i	−0.0919780	−	0.995761i	$-0.529319\pi$
$521$	20.2105	−	17.9049i	0.885436	−	0.784428i	0.977414	+	0.211333i	$0.0677805\pi$
$522$	0.371193	+	1.28151i	0.0162467	+	0.0560901i
$523$	−9.86151	−	3.29226i	−0.431214	−	0.143960i	0.0927720	−	0.995687i	$-0.470427\pi$
$523$	−9.86151	−	3.29226i	−0.431214	−	0.143960i	−0.523986	+	0.851727i	$0.675555\pi$
$524$	2.02581	−	2.10909i	0.0884977	−	0.0921359i
$525$	−2.84089	−	7.49082i	−0.123987	−	0.326926i
$526$	−7.26526	+	12.5838i	−0.316780	+	0.548680i
$527$	1.63363	+	2.00083i	0.0711619	+	0.0871575i
$528$	3.37670	−	0.832283i	0.146952	−	0.0362205i
$529$	8.83132	−	15.2963i	0.383971	−	0.665057i
$530$	0.123301	+	0.213564i	0.00535586	+	0.00927663i
$531$	0.176657	+	0.183919i	0.00766626	+	0.00798142i
$532$	1.21061	+	9.97030i	0.0524868	+	0.432267i
$533$	17.8251	+	0.851542i	0.772092	+	0.0368844i
$534$	−0.806645	+	6.64332i	−0.0349070	+	0.287485i
$535$	−19.7569	+	14.8463i	−0.854163	+	0.641862i
$536$	21.9332	+	1.77063i	0.947372	+	0.0764798i
$537$	4.06747	+	19.9238i	0.175524	+	0.859775i
$538$	0.715702	−	5.89433i	0.0308561	−	0.254123i
$539$	20.2490	+	8.62729i	0.872185	+	0.371604i
$540$	−2.07570	+	1.31259i	−0.0893238	+	0.0564850i
$541$	−30.1925	+	26.7482i	−1.29808	+	1.15000i	−0.318722	+	0.947848i	$0.603254\pi$
$541$	−30.1925	+	26.7482i	−1.29808	+	1.15000i	−0.979355	+	0.202148i	$0.935208\pi$
$542$	−5.44166	+	0.439296i	−0.233739	+	0.0188694i
$543$	−4.69763	−	16.2181i	−0.201595	−	0.695986i
$544$	14.4426	−	6.15343i	0.619223	−	0.263826i
$545$	25.9965	−	37.6624i	1.11357	−	1.61328i
$546$	11.3604	−	9.13508i	0.486178	−	0.390945i
$547$	18.1194	+	26.2505i	0.774729	+	1.12239i	0.989331	+	0.145687i	$0.0465394\pi$
$547$	18.1194	+	26.2505i	0.774729	+	1.12239i	−0.214601	+	0.976702i	$0.568845\pi$
$548$	−15.0755	−	9.53315i	−0.643992	−	0.407236i
$549$	10.5091	−	1.70790i	0.448520	−	0.0728915i
$550$	−5.26127	−	2.24162i	−0.224341	−	0.0955829i
$551$	−2.03619	+	2.94993i	−0.0867445	+	0.125671i
$552$	−1.94938	+	6.73005i	−0.0829713	+	0.286450i
$553$	−24.0995	−	50.7886i	−1.02481	−	2.15975i
$554$	−10.8310	+	28.5591i	−0.460166	+	1.21336i
$555$	−1.69920	−	2.08114i	−0.0721269	−	0.0883394i
$556$	−0.498593	−	12.3725i	−0.0211451	−	0.524709i
$557$	1.20388	+	29.8740i	0.0510101	+	1.26580i	0.798690	+	0.601743i	$0.205527\pi$
$557$	1.20388	+	29.8740i	0.0510101	+	1.26580i	−0.747680	+	0.664060i	$0.768832\pi$
$558$	−0.782265	+	0.192811i	−0.0331159	+	0.00816234i
$559$	14.7410	−	1.67841i	0.623480	−	0.0709893i
$560$	−13.0291	−	3.21137i	−0.550578	−	0.135705i
$561$	−1.78482	+	8.74260i	−0.0753549	+	0.369113i
$562$	1.41236	−	0.601751i	0.0595768	−	0.0253833i
$563$	9.71643	−	6.14430i	0.409499	−	0.258951i	−0.313796	−	0.949490i	$-0.601601\pi$
$563$	9.71643	−	6.14430i	0.409499	−	0.258951i	0.723295	+	0.690539i	$0.242627\pi$
$564$	4.23890	−	2.22474i	0.178490	−	0.0936786i
$565$	−41.8229	−	6.79688i	−1.75950	−	0.285947i
$566$	−5.24815	+	1.75209i	−0.220596	+	0.0736458i
$567$	−0.469954	−	3.87042i	−0.0197362	−	0.162542i
$568$	9.56137	−	33.0097i	0.401186	−	1.38506i
$569$	2.69659	−	13.2088i	0.113047	−	0.553741i	−0.883334	−	0.468744i	$-0.844707\pi$
$569$	2.69659	−	13.2088i	0.113047	−	0.553741i	0.996381	−	0.0849972i	$-0.0270881\pi$
$570$	7.27880	+	2.43002i	0.304876	+	0.101782i
$571$	28.8893	+	15.1623i	1.20898	+	0.634522i	0.944068	−	0.329750i	$-0.106965\pi$
$571$	28.8893	+	15.1623i	1.20898	+	0.634522i	0.264913	+	0.964272i	$0.414657\pi$
$572$	−0.786468	+	8.91278i	−0.0328839	+	0.372662i
$573$	0.711564	−	0.373457i	0.0297260	−	0.0156014i
$574$	19.7520	−	3.21001i	0.824432	−	0.133983i
$575$	3.79511	−	2.85184i	0.158267	−	0.118930i
$576$	−0.301522	+	7.48219i	−0.0125634	+	0.311758i
$577$	−41.1127			−1.71154			−0.855771	−	0.517354i	$-0.826917\pi$
$577$	−41.1127			−1.71154			−0.855771	+	0.517354i	$0.826917\pi$
$578$	−0.248304	+	6.16160i	−0.0103281	+	0.256289i
$579$	2.59685	+	12.7202i	0.107921	+	0.528634i
$580$	1.79492	+	2.60038i	0.0745298	+	0.107975i
$581$	−48.2772	+	16.1173i	−2.00288	+	0.668658i
$582$	−4.05525	+	8.54626i	−0.168096	+	0.354254i
$583$	0.151970	−	0.186129i	0.00629394	−	0.00770868i
$584$	14.8666	+	39.2001i	0.615186	+	1.62211i
$585$	2.22243	+	9.31523i	0.0918862	+	0.385137i
$586$	7.27727	−	19.1886i	0.300621	−	0.792673i
$587$	−22.1886	−	38.4317i	−0.915820	−	1.58625i	−0.805696	−	0.592330i	$-0.798208\pi$
$587$	−22.1886	−	38.4317i	−0.915820	−	1.58625i	−0.110125	−	0.993918i	$-0.535125\pi$
$588$	−4.79574	+	5.87372i	−0.197773	+	0.242228i
$589$	−1.73042	−	1.30033i	−0.0713008	−	0.0535791i
$590$	−0.621956	−	0.326428i	−0.0256055	−	0.0134388i
$591$	0.209815	−	0.0169380i	0.00863063	−	0.000696736i
$592$	−1.30649	+	0.105471i	−0.0536966	+	0.00433484i
$593$	−16.4555	−	8.63651i	−0.675746	−	0.354659i	0.0916869	−	0.995788i	$-0.470774\pi$
$593$	−16.4555	−	8.63651i	−0.675746	−	0.354659i	−0.767433	+	0.641129i	$0.778466\pi$
$594$	−2.22498	−	1.67196i	−0.0912920	−	0.0686015i
$595$	21.7746	−	26.6691i	0.892672	−	1.09332i
$596$	9.03201	+	15.6439i	0.369965	+	0.640799i
$597$	1.52855	−	4.03046i	0.0625594	−	0.164956i
$598$	7.07215	+	4.95984i	0.289202	+	0.202823i
$599$	3.44982	+	9.09642i	0.140956	+	0.371670i	0.986841	−	0.161696i	$-0.0516963\pi$
$599$	3.44982	+	9.09642i	0.140956	+	0.371670i	−0.845885	+	0.533365i	$0.820927\pi$
$600$	3.94137	−	4.82730i	0.160906	−	0.197074i
$601$	−14.2511	+	30.0335i	−0.581313	+	1.22509i	0.373430	+	0.927659i	$0.378182\pi$
$601$	−14.2511	+	30.0335i	−0.581313	+	1.22509i	−0.954743	+	0.297433i	$0.903870\pi$
$602$	15.7806	−	5.26833i	0.643168	−	0.214721i
$603$	−4.12156	−	5.97111i	−0.167843	−	0.243162i
$604$	3.89720	+	19.0897i	0.158575	+	0.776751i
$605$	0.406081	−	10.0768i	0.0165096	−	0.409680i
$606$	−15.4354			−0.627021
$607$	−0.207128	+	5.13982i	−0.00840705	+	0.208619i	0.989526	+	0.144355i	$0.0461108\pi$
$607$	−0.207128	+	5.13982i	−0.00840705	+	0.208619i	−0.997933	+	0.0642635i	$0.979530\pi$
$608$	−10.5170	+	7.90299i	−0.426519	+	0.320509i
$609$	−4.95121	+	0.804650i	−0.200633	+	0.0326061i
$610$	−25.9668	+	13.6284i	−1.05136	+	0.551798i
$611$	−2.85699	−	18.4478i	−0.115581	−	0.746317i
$612$	−2.72196	−	1.42860i	−0.110029	−	0.0577476i
$613$	−3.46813	−	1.15783i	−0.140077	−	0.0467644i	0.245765	−	0.969329i	$-0.420961\pi$
$613$	−3.46813	−	1.15783i	−0.140077	−	0.0467644i	−0.385842	+	0.922565i	$0.626089\pi$
$614$	2.71992	−	13.3230i	0.109767	−	0.537674i
$615$	−3.65749	+	12.6271i	−0.147484	+	0.509175i
$616$	3.82529	+	31.5041i	0.154125	+	1.26934i
$617$	32.2068	−	10.7522i	1.29660	−	0.432868i	0.417139	−	0.908843i	$-0.363033\pi$
$617$	32.2068	−	10.7522i	1.29660	−	0.432868i	0.879459	+	0.475974i	$0.157904\pi$
$618$	−18.3295	−	2.97884i	−0.737322	−	0.119827i
$619$	−20.4231	+	10.7189i	−0.820872	+	0.430827i	−0.822218	−	0.569172i	$-0.807264\pi$
$619$	−20.4231	+	10.7189i	−0.820872	+	0.430827i	0.00134610	+	0.999999i	$0.499572\pi$
$620$	−1.61267	+	1.01979i	−0.0647664	+	0.0409558i
$621$	2.12540	−	0.905549i	0.0852894	−	0.0363384i
$622$	1.34192	−	6.57315i	0.0538060	−	0.263559i
$623$	−24.4294	−	6.02131i	−0.978744	−	0.241239i
$624$	4.35601	+	1.68929i	0.174380	+	0.0676256i
$625$	30.1495	−	7.43119i	1.20598	−	0.297247i
$626$	−0.566737	−	14.0634i	−0.0226514	−	0.562088i
$627$	−0.301079	−	7.47120i	−0.0120239	−	0.298371i
$628$	7.51073	+	9.19898i	0.299711	+	0.367079i
$629$	1.19253	−	3.14445i	0.0475494	−	0.125378i
$630$	4.60367	+	9.70203i	0.183415	+	0.386538i
$631$	0.448396	−	1.54804i	0.0178504	−	0.0616266i	−0.951099	−	0.308888i	$-0.900043\pi$
$631$	0.448396	−	1.54804i	0.0178504	−	0.0616266i	0.968949	+	0.247261i	$0.0795305\pi$
$632$	24.8413	−	35.9888i	0.988132	−	1.43156i
$633$	4.65127	+	1.98172i	0.184871	+	0.0787663i
$634$	−24.4495	+	3.97343i	−0.971014	+	0.157805i
$635$	6.72012	+	4.24955i	0.266680	+	0.168638i
$636$	0.0470262	+	0.0681292i	0.00186471	+	0.00270150i
$637$	15.6168	+	25.1087i	0.618761	+	0.994842i
$638$	−2.03410	+	2.94690i	−0.0805308	+	0.116669i
$639$	−10.4247	+	4.44155i	−0.412395	+	0.175705i
$640$	1.24038	+	4.28228i	0.0490302	+	0.169272i
$641$	−16.5532	+	1.33632i	−0.653814	+	0.0527813i	−0.402923	−	0.915234i	$-0.632006\pi$
$641$	−16.5532	+	1.33632i	−0.653814	+	0.0527813i	−0.250891	+	0.968015i	$0.580724\pi$
$642$	7.22212	−	6.39824i	0.285034	−	0.252518i
$643$	−0.706290	+	0.446631i	−0.0278534	+	0.0176134i	−0.548320	−	0.836269i	$-0.684732\pi$
$643$	−0.706290	+	0.446631i	−0.0278534	+	0.0176134i	0.520467	+	0.853882i	$0.325758\pi$
$644$	−7.66203	−	3.26449i	−0.301926	−	0.128639i
$645$	−1.31739	+	10.8497i	−0.0518724	+	0.427207i
$646$	1.92131	+	9.41119i	0.0755929	+	0.370278i
$647$	32.9187	+	2.65747i	1.29417	+	0.104476i	0.708289	−	0.705922i	$-0.249467\pi$
$647$	32.9187	+	2.65747i	1.29417	+	0.104476i	0.585879	+	0.810398i	$0.300749\pi$
$648$	2.42458	−	1.82196i	0.0952467	−	0.0715732i
$649$	−0.0824990	+	0.679440i	−0.00323837	+	0.0266704i
$650$	−4.05770	−	6.52396i	−0.159156	−	0.255891i
$651$	−0.365121	−	3.00704i	−0.0143102	−	0.117855i
$652$	8.77192	+	9.13253i	0.343535	+	0.357658i
$653$	−11.0191	−	19.0856i	−0.431210	−	0.746877i	0.565768	−	0.824565i	$-0.308580\pi$
$653$	−11.0191	−	19.0856i	−0.431210	−	0.746877i	−0.996978	+	0.0776871i	$0.975246\pi$
$654$	−8.93354	+	15.4733i	−0.349329	+	0.605055i
$655$	8.15656	−	2.01041i	0.318703	−	0.0785532i
$656$	4.05621	+	4.96795i	0.158368	+	0.193966i
$657$	6.91175	−	11.9715i	0.269653	−	0.467053i
$658$	−7.42299	−	19.5728i	−0.289378	−	0.763028i
$659$	−23.8441	+	24.8243i	−0.928833	+	0.967018i	−0.999535	−	0.0304795i	$-0.990297\pi$
$659$	−23.8441	+	24.8243i	−0.928833	+	0.967018i	0.0707020	+	0.997497i	$0.477476\pi$
$660$	−6.25206	−	2.08724i	−0.243361	−	0.0812458i
$661$	−1.55482	−	5.36787i	−0.0604756	−	0.208786i	0.924591	−	0.380962i	$-0.124407\pi$
$661$	−1.55482	−	5.36787i	−0.0604756	−	0.208786i	−0.985066	+	0.172176i	$0.944920\pi$
$662$	−8.22069	+	7.28290i	−0.319506	+	0.283058i
$663$	−8.70694	+	8.23916i	−0.338150	+	0.319982i
$664$	−29.6347	−	26.2540i	−1.15005	−	1.01885i
$665$	−12.3683	+	26.0655i	−0.479620	+	1.01078i
$666$	0.726637	+	0.756509i	0.0281566	+	0.0293141i
$667$	−1.27422	−	2.68537i	−0.0493381	−	0.103978i
$668$	−11.9113	−	2.93586i	−0.460861	−	0.113592i
$669$	5.71560	−	5.95057i	0.220978	−	0.230062i
$670$	15.9762	+	12.0053i	0.617214	+	0.463806i
$671$	21.3887	+	18.9488i	0.825703	+	0.731509i
$672$	−18.1717	−	2.95318i	−0.700987	−	0.113922i
$673$	1.16102	+	0.734185i	0.0447541	+	0.0283008i	0.556656	−	0.830743i	$-0.312084\pi$
$673$	1.16102	+	0.734185i	0.0447541	+	0.0283008i	−0.511901	+	0.859044i	$0.671059\pi$
$674$	22.2278	+	1.79441i	0.856183	+	0.0691183i
$675$	−2.05482			−0.0790901
$676$	−7.74014	+	9.19644i	−0.297698	+	0.353709i
$677$	−30.7258			−1.18089			−0.590444	−	0.807079i	$-0.701047\pi$
$677$	−30.7258			−1.18089			−0.590444	+	0.807079i	$0.701047\pi$
$678$	16.4892	+	1.33115i	0.633265	+	0.0511224i
$679$	−30.0596	−	19.0085i	−1.15358	−	0.729480i
$680$	26.4351	+	4.29612i	1.01374	+	0.164749i
$681$	3.74082	+	3.31408i	0.143349	+	0.126996i
$682$	−1.72865	−	1.29900i	−0.0661934	−	0.0497411i
$683$	−3.95428	+	4.11685i	−0.151306	+	0.157527i	−0.792542	−	0.609818i	$-0.791243\pi$
$683$	−3.95428	+	4.11685i	−0.151306	+	0.157527i	0.641235	+	0.767344i	$0.278422\pi$
$684$	2.50117	+	0.616484i	0.0956347	+	0.0235718i
$685$	−21.9654	−	46.2910i	−0.839254	−	1.76869i
$686$	3.36368	+	3.50196i	0.128426	+	0.133705i
$687$	2.19356	−	4.62282i	0.0836894	−	0.176372i
$688$	3.99110	+	3.53580i	0.152159	+	0.134801i
$689$	0.310726	−	0.0874961i	0.0118377	−	0.00333334i
$690$	−4.76303	+	4.21968i	−0.181326	+	0.160640i
$691$	−4.54015	−	15.6744i	−0.172716	−	0.596283i	−0.999433	−	0.0336661i	$-0.989282\pi$
$691$	−4.54015	−	15.6744i	−0.172716	−	0.596283i	0.826718	−	0.562617i	$-0.190205\pi$
$692$	0.363035	+	0.121199i	0.0138005	+	0.00460729i
$693$	7.24862	−	7.54661i	0.275352	−	0.286672i
$694$	6.04395	+	15.9366i	0.229425	+	0.604944i
$695$	17.7850	−	30.8046i	0.674625	−	1.16848i
$696$	−2.46780	−	3.02250i	−0.0935416	−	0.114568i
$697$	−15.9771	+	3.93800i	−0.605176	+	0.149162i
$698$	−10.7462	+	18.6129i	−0.406748	+	0.704509i
$699$	−13.0886	−	22.6701i	−0.495057	−	0.857463i
$700$	5.13142	+	5.34237i	0.193949	+	0.201923i
$701$	3.46528	+	28.5392i	0.130882	+	1.07791i	0.899107	+	0.437729i	$0.144217\pi$
$701$	3.46528	+	28.5392i	0.130882	+	1.07791i	−0.768225	+	0.640180i	$0.778860\pi$
$702$	−1.15752	−	3.55527i	−0.0436879	−	0.134185i
$703$	−0.339688	+	2.79758i	−0.0128116	+	0.105513i
$704$	−16.0667	+	12.0734i	−0.605538	+	0.455032i
$705$	13.7073	+	1.10657i	0.516246	+	0.0416757i
$706$	−5.53876	−	27.1307i	−0.208454	−	1.02108i
$707$	6.99510	−	57.6098i	0.263078	−	2.16664i
$708$	−0.216928	−	0.0924243i	−0.00815265	−	0.00347352i
$709$	−8.99562	+	5.68849i	−0.337838	+	0.213636i	−0.692602	−	0.721320i	$-0.743536\pi$
$709$	−8.99562	+	5.68849i	−0.337838	+	0.213636i	0.354764	+	0.934956i	$0.384561\pi$
$710$	23.3618	−	20.6968i	0.876753	−	0.776735i
$711$	−14.3719	+	1.16022i	−0.538989	+	0.0435117i
$712$	−5.44526	−	18.7992i	−0.204070	−	0.704530i
$713$	1.65129	−	0.703547i	0.0618412	−	0.0263481i
$714$	−7.63592	+	11.0625i	−0.285767	+	0.414005i
$715$	−15.5933	+	20.4319i	−0.583158	+	0.764108i
$716$	−10.6808	−	15.4738i	−0.399160	−	0.578283i
$717$	−5.22654	−	3.30506i	−0.195189	−	0.123430i
$718$	9.57816	−	1.55660i	0.357454	−	0.0580919i
$719$	1.24121	+	0.528829i	0.0462892	+	0.0197220i	0.414987	−	0.909827i	$-0.363786\pi$
$719$	1.24121	+	0.528829i	0.0462892	+	0.0197220i	−0.368698	+	0.929549i	$0.620196\pi$
$720$	−1.95516	+	2.83253i	−0.0728644	+	0.105562i
$721$	19.4247	−	67.0617i	0.723412	−	2.49751i
$722$	4.99596	+	10.5288i	0.185930	+	0.391840i
$723$	−4.37779	+	11.5433i	−0.162812	+	0.429300i
$724$	9.87381	+	12.0932i	0.366957	+	0.449441i
$725$	0.106451	+	2.64155i	0.00395348	+	0.0981045i
$726$	0.158544	+	3.93422i	0.00588411	+	0.146013i
$727$	30.6310	−	7.54986i	1.13604	−	0.280009i	0.373931	−	0.927457i	$-0.378010\pi$
$727$	30.6310	−	7.54986i	1.13604	−	0.280009i	0.762110	+	0.647448i	$0.224164\pi$
$728$	−20.0941	+	37.6018i	−0.744737	+	1.39362i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−7.61598	+	37.3056i	−0.281880	+	1.38074i
$731$	−12.5858	+	5.36230i	−0.465502	+	0.198332i
$732$	−8.32050	+	5.26157i	−0.307535	+	0.194473i
$733$	−2.92289	+	1.53405i	−0.107959	+	0.0566615i	−0.517839	−	0.855478i	$-0.673263\pi$
$733$	−2.92289	+	1.53405i	−0.107959	+	0.0566615i	0.409879	+	0.912140i	$0.365571\pi$
$734$	14.2722	+	2.31945i	0.526796	+	0.0856126i
$735$	−20.6616	+	6.89784i	−0.762113	+	0.254431i
$736$	−1.31493	−	10.8294i	−0.0484689	−	0.399177i
$737$	5.41760	−	18.7037i	0.199560	−	0.688960i
$738$	1.02665	−	5.02885i	0.0377914	−	0.185115i
$739$	13.5360	+	4.51899i	0.497931	+	0.166234i	0.554531	−	0.832163i	$-0.312898\pi$
$739$	13.5360	+	4.51899i	0.497931	+	0.166234i	−0.0565997	+	0.998397i	$0.518026\pi$
$740$	2.19965	+	1.15447i	0.0808609	+	0.0424391i
$741$	5.43195	−	8.44976i	0.199548	−	0.310410i
$742$	0.320522	−	0.168223i	0.0117667	−	0.00617565i
$743$	−49.2755	+	8.00804i	−1.80774	+	0.293787i	−0.968323	−	0.249699i	$-0.919668\pi$
$743$	−49.2755	+	8.00804i	−1.80774	+	0.293787i	−0.839418	+	0.543486i	$0.817104\pi$
$744$	1.88373	−	1.41553i	0.0690609	−	0.0518959i
$745$	−2.08943	+	51.8487i	−0.0765509	+	1.89959i
$746$	34.0977			1.24841
$747$	−0.525642	+	13.0437i	−0.0192322	+	0.477243i
$748$	−1.65029	−	8.08365i	−0.0603406	−	0.295568i
$749$	20.6073	+	29.8548i	0.752974	+	1.09087i
$750$	−7.69463	+	2.56885i	−0.280968	+	0.0938010i
$751$	−16.3519	+	34.4609i	−0.596690	+	1.25750i	0.350421	+	0.936592i	$0.386038\pi$
$751$	−16.3519	+	34.4609i	−0.596690	+	1.25750i	−0.947111	+	0.320905i	$0.896013\pi$
$752$	4.24309	−	5.19685i	0.154730	−	0.189509i
$753$	−8.86697	−	23.3803i	−0.323130	−	0.852025i
$754$	−4.51046	+	1.67222i	−0.164261	+	0.0608986i
$755$	−19.8467	+	52.3314i	−0.722295	+	1.90453i
$756$	1.80249	+	3.12200i	0.0655559	+	0.113546i
$757$	8.65668	−	10.6025i	0.314633	−	0.385355i	−0.592943	−	0.805245i	$-0.702034\pi$
$757$	8.65668	−	10.6025i	0.314633	−	0.385355i	0.907575	+	0.419890i	$0.137931\pi$
$758$	−24.2165	−	18.1975i	−0.879584	−	0.660965i
$759$	5.49021	+	2.88148i	0.199282	+	0.104591i
$760$	−22.3700	+	1.80589i	−0.811445	+	0.0655066i
$761$	23.4955	−	1.89675i	0.851711	−	0.0687572i	0.353102	−	0.935585i	$-0.385127\pi$
$761$	23.4955	−	1.89675i	0.851711	−	0.0687572i	0.498608	+	0.866827i	$0.333845\pi$
$762$	−2.74869	−	1.44262i	−0.0995746	−	0.0522608i
$763$	−53.7028	−	40.3551i	−1.94417	−	1.46095i
$764$	−0.469934	+	0.575564i	−0.0170016	+	0.0208232i
$765$	−4.41531	−	7.64755i	−0.159636	−	0.276498i
$766$	11.5422	−	30.4342i	0.417035	−	1.09963i
$767$	−0.614844	+	0.683673i	−0.0222007	+	0.0246860i
$768$	−5.92799	−	15.6308i	−0.213908	−	0.564029i
$769$	−11.2256	+	13.7489i	−0.404807	+	0.495798i	−0.936269	−	0.351284i	$-0.885745\pi$
$769$	−11.2256	+	13.7489i	−0.404807	+	0.495798i	0.531462	+	0.847082i	$0.321643\pi$
$770$	−12.3556	+	26.0388i	−0.445264	+	0.938375i
$771$	0.763336	−	0.254839i	0.0274909	−	0.00917780i
$772$	−6.81908	−	9.87914i	−0.245424	−	0.355558i
$773$	0.828175	+	4.05667i	0.0297874	+	0.145908i	0.991965	−	0.126516i	$-0.0403796\pi$
$773$	0.828175	+	4.05667i	0.0297874	+	0.145908i	−0.962177	+	0.272425i	$0.912174\pi$
$774$	0.171819	−	4.26364i	0.00617590	−	0.153253i
$775$	−1.59645			−0.0573462
$776$	1.11399	−	27.6433i	0.0399898	−	0.992337i
$777$	−3.15283	+	2.36920i	−0.113107	+	0.0849945i
$778$	−27.6379	+	4.49159i	−0.990866	+	0.161031i
$779$	12.2098	−	6.40817i	0.437460	−	0.229597i
$780$	−5.26654	−	7.11843i	−0.188572	−	0.254881i
$781$	−26.9285	−	14.1332i	−0.963577	−	0.505724i
$782$	−7.55518	−	2.52229i	−0.270173	−	0.0901969i
$783$	−0.257349	+	1.26058i	−0.00919689	+	0.0450494i
$784$	−2.95659	+	10.2073i	−0.105593	+	0.364548i
$785$	4.11202	+	33.8655i	0.146764	+	1.20871i
$786$	−3.11103	+	1.03861i	−0.110967	+	0.0370461i
$787$	−19.3602	−	3.14634i	−0.690116	−	0.112155i	−0.194768	−	0.980849i	$-0.562395\pi$
$787$	−19.3602	−	3.14634i	−0.690116	−	0.112155i	−0.495348	+	0.868695i	$0.664960\pi$
$788$	−0.172338	+	0.0904498i	−0.00613928	+	0.00322214i
$789$	−11.8428	+	7.48896i	−0.421617	+	0.266614i
$790$	36.5364	−	15.5667i	1.29991	−	0.553839i
$791$	−12.4409	+	60.9398i	−0.442349	+	2.16677i
$792$	7.90319	+	1.94796i	0.280827	+	0.0692178i
$793$	8.90868	+	37.3404i	0.316356	+	1.32600i
$794$	−3.57474	+	0.881094i	−0.126863	+	0.0312688i
$795$	0.00957538	+	0.237610i	0.000339604	+	0.00842718i
$796$	0.160487	+	3.98244i	0.00568831	+	0.141154i
$797$	−11.8967	−	14.5708i	−0.421403	−	0.516125i	0.519652	−	0.854378i	$-0.326061\pi$
$797$	−11.8967	−	14.5708i	−0.421403	−	0.516125i	−0.941055	+	0.338253i	$0.890164\pi$
$798$	3.99433	−	10.5322i	0.141398	−	0.372835i
$799$	7.37927	+	15.5515i	0.261060	+	0.550172i
$800$	−2.69947	+	9.31965i	−0.0954406	+	0.329499i
$801$	−3.66591	+	5.31099i	−0.129529	+	0.187655i
$802$	−36.0799	−	15.3722i	−1.27403	−	0.542812i
$803$	36.6198	−	5.95130i	1.29228	−	0.210017i
$804$	5.67002	+	3.58550i	0.199966	+	0.126451i
$805$	−13.5906	−	19.6894i	−0.479007	−	0.693961i
$806$	−0.899314	−	2.76220i	−0.0316770	−	0.0972942i
$807$	3.25260	−	4.71221i	0.114497	−	0.165878i
$808$	41.5305	−	17.6945i	1.46104	−	0.622490i
$809$	2.77606	+	9.58407i	0.0976010	+	0.336958i	0.994427	−	0.105425i	$-0.0336204\pi$
$809$	2.77606	+	9.58407i	0.0976010	+	0.336958i	−0.896826	+	0.442383i	$0.854133\pi$
$810$	2.74544	−	0.221635i	0.0964649	−	0.00778745i
$811$	−33.7217	+	29.8749i	−1.18413	+	1.04905i	−0.186348	+	0.982484i	$0.559665\pi$
$811$	−33.7217	+	29.8749i	−1.18413	+	1.04905i	−0.997782	+	0.0665642i	$0.978796\pi$
$812$	3.92007	−	2.47890i	0.137567	−	0.0869923i
$813$	−4.84329	−	2.06353i	−0.169862	−	0.0723713i
$814$	−0.339340	+	2.79472i	−0.0118939	+	0.0979548i
$815$	7.27605	+	35.6405i	0.254869	+	1.24843i
$816$	−4.29416	−	0.346661i	−0.150326	−	0.0121356i
$817$	9.16483	−	6.88692i	0.320637	−	0.240943i
$818$	−4.93398	+	40.6350i	−0.172512	+	1.42077i
$819$	13.7940	−	2.70905i	0.482001	−	0.0946618i
$820$	−1.46516	−	12.0667i	−0.0511656	−	0.421387i
$821$	22.9633	+	23.9073i	0.801423	+	0.834370i	0.989005	−	0.147879i	$-0.0472446\pi$
$821$	22.9633	+	23.9073i	0.801423	+	0.834370i	−0.187582	+	0.982249i	$0.560065\pi$
$822$	10.0023	+	17.3245i	0.348870	+	0.604260i
$823$	−26.2827	+	45.5230i	−0.916157	+	1.58683i	−0.110960	+	0.993825i	$0.535392\pi$
$823$	−26.2827	+	45.5230i	−0.916157	+	1.58683i	−0.805198	+	0.593006i	$0.797941\pi$
$824$	52.7322	−	12.9973i	1.83701	−	0.452783i
$825$	−3.48784	−	4.27183i	−0.121431	−	0.148726i
$826$	−0.515532	+	0.892928i	−0.0179377	+	0.0310689i
$827$	−7.87676	−	20.7693i	−0.273902	−	0.722220i	−0.999421	−	0.0340181i	$-0.989170\pi$
$827$	−7.87676	−	20.7693i	−0.273902	−	0.722220i	0.725519	−	0.688202i	$-0.241600\pi$
$828$	−1.47976	+	1.54059i	−0.0514251	+	0.0535392i
$829$	2.87789	+	0.960779i	0.0999531	+	0.0333692i	0.366205	−	0.930534i	$-0.380657\pi$
$829$	2.87789	+	0.960779i	0.0999531	+	0.0333692i	−0.266252	+	0.963904i	$0.585785\pi$
$830$	−10.0037	−	34.5366i	−0.347232	−	1.19878i
$831$	−22.0467	+	19.5317i	−0.764791	+	0.677546i
$832$	−26.9848	+	0.885905i	−0.935529	+	0.0307132i
$833$	−20.4086	−	18.0804i	−0.707115	−	0.626449i
$834$	−5.95343	+	12.5466i	−0.206150	+	0.434453i
$835$	−24.4119	−	25.4155i	−0.844809	−	0.879539i
$836$	2.96384	+	6.24617i	0.102507	+	0.216028i
$837$	−0.754353	−	0.185931i	−0.0260743	−	0.00642673i
$838$	−6.63046	+	6.90304i	−0.229045	+	0.238462i
$839$	12.2176	+	9.18091i	0.421797	+	0.316960i	0.790360	−	0.612643i	$-0.209894\pi$
$839$	12.2176	+	9.18091i	0.421797	+	0.316960i	−0.368563	+	0.929603i	$0.620150\pi$
$840$	−23.5086	−	20.8268i	−0.811124	−	0.718593i
$841$	−26.9906	−	4.38640i	−0.930711	−	0.151255i
$842$	−16.6620	−	10.5364i	−0.574209	−	0.363108i
$843$	1.47563	+	0.119125i	0.0508234	+	0.00410289i
$844$	−4.67477			−0.160912
$845$	−32.9117	+	10.4445i	−1.13220	+	0.359302i
$846$	−5.36906			−0.184592
$847$	−14.7556	−	1.19120i	−0.507009	−	0.0409300i
$848$	0.0980551	+	0.0620063i	0.00336723	+	0.00212930i
$849$	−5.26638	−	0.855870i	−0.180742	−	0.0293734i
$850$	5.30274	+	4.69782i	0.181882	+	0.161134i
$851$	−1.86822	−	1.40388i	−0.0640417	−	0.0481242i
$852$	7.25794	−	7.55631i	0.248653	−	0.258875i
$853$	−39.5248	−	9.74199i	−1.35330	−	0.333559i	−0.505022	−	0.863106i	$-0.668516\pi$
$853$	−39.5248	−	9.74199i	−1.35330	−	0.333559i	−0.848281	+	0.529547i	$0.822362\pi$
$854$	18.4540	+	38.8909i	0.631481	+	1.33082i
$855$	5.12610	+	5.33683i	0.175309	+	0.182516i
$856$	−12.0972	+	25.4942i	−0.413472	+	0.871374i
$857$	24.9602	+	22.1128i	0.852626	+	0.755360i	0.971372	−	0.237564i	$-0.0763491\pi$
$857$	24.9602	+	22.1128i	0.852626	+	0.755360i	−0.118746	+	0.992925i	$0.537888\pi$
$858$	5.42639	−	8.44110i	0.185254	−	0.288174i
$859$	−22.7793	+	20.1807i	−0.777219	+	0.688556i	−0.955358	−	0.295449i	$-0.904531\pi$
$859$	−22.7793	+	20.1807i	−0.777219	+	0.688556i	0.178140	+	0.984005i	$0.442992\pi$
$860$	−2.81156	−	9.70664i	−0.0958735	−	0.330994i
$861$	18.3040	+	6.11078i	0.623799	+	0.208255i
$862$	4.69010	−	4.88291i	0.159746	−	0.166313i
$863$	7.24352	+	19.0996i	0.246572	+	0.650157i	0.999973	−	0.00740466i	$-0.00235700\pi$
$863$	7.24352	+	19.0996i	0.246572	+	0.650157i	−0.753400	+	0.657562i	$0.771588\pi$
$864$	−2.36097	+	4.08931i	−0.0803217	+	0.139121i
$865$	0.695334	+	0.851630i	0.0236421	+	0.0289563i
$866$	18.8585	−	4.64820i	0.640838	−	0.157952i
$867$	−2.97329	+	5.14988i	−0.100978	+	0.174899i
$868$	1.40041	+	2.42558i	0.0475329	+	0.0823294i
$869$	−26.8068	−	27.9088i	−0.909359	−	0.946743i
$870$	−0.427148	−	3.51788i	−0.0144817	−	0.119267i
$871$	20.3864	−	16.3931i	0.690766	−	0.555458i
$872$	6.29859	−	51.8735i	0.213297	−	1.75666i
$873$	−7.29256	+	5.48000i	−0.246816	+	0.185470i
$874$	6.65297	+	0.537083i	0.225040	+	0.0181671i
$875$	−6.10065	−	29.8830i	−0.206240	−	1.01023i
$876$	−1.54065	+	12.6884i	−0.0520537	+	0.428701i
$877$	12.6781	+	5.40163i	0.428109	+	0.182400i	0.595263	−	0.803531i	$-0.297048\pi$
$877$	12.6781	+	5.40163i	0.428109	+	0.182400i	−0.167155	+	0.985931i	$0.553458\pi$
$878$	14.2068	−	8.98381i	0.479455	−	0.303189i
$879$	14.8130	−	13.1232i	0.499629	−	0.442633i
$880$	−9.20730	+	0.743290i	−0.310378	+	0.0250563i
$881$	8.36485	+	28.8788i	0.281819	+	0.972952i	0.969122	+	0.246581i	$0.0793073\pi$
$881$	8.36485	+	28.8788i	0.281819	+	0.972952i	−0.687303	+	0.726371i	$0.741206\pi$
$882$	7.82391	−	3.33346i	0.263445	−	0.112243i
$883$	−8.28927	+	12.0091i	−0.278956	+	0.404138i	−0.937269	−	0.348607i	$-0.886655\pi$
$883$	−8.28927	+	12.0091i	−0.278956	+	0.404138i	0.658313	+	0.752744i	$0.271270\pi$
$884$	4.42040	−	10.1641i	0.148674	−	0.341857i
$885$	−0.384779	−	0.557448i	−0.0129342	−	0.0187384i
$886$	23.1688	+	14.6511i	0.778372	+	0.492213i
$887$	52.7586	−	8.57411i	1.77146	−	0.287891i	0.814939	−	0.579547i	$-0.196770\pi$
$887$	52.7586	−	8.57411i	1.77146	−	0.287891i	0.956523	+	0.291656i	$0.0942064\pi$
$888$	−2.82232	−	1.20248i	−0.0947107	−	0.0403525i
$889$	6.63000	−	9.60521i	0.222363	−	0.322148i
$890$	4.94528	−	17.0731i	0.165766	−	0.572291i
$891$	−1.15055	−	2.42473i	−0.0385448	−	0.0812315i
$892$	−2.70529	+	7.13325i	−0.0905797	+	0.238839i
$893$	−9.12274	−	11.1733i	−0.305281	−	0.373901i
$894$	−0.815764	−	20.2430i	−0.0272832	−	0.677027i
$895$	−2.17480	−	53.9671i	−0.0726956	−	1.80392i
$896$	6.35412	−	1.56615i	0.212276	−	0.0523214i
$897$	3.81593	+	7.40434i	0.127410	+	0.247224i
$898$	20.3699	+	5.02073i	0.679753	+	0.167544i
$899$	−0.199942	+	0.979379i	−0.00666843	+	0.0326641i
$900$	1.74791	−	0.744715i	0.0582637	−	0.0248238i
$901$	−0.251581	+	0.159090i	−0.00838138	+	0.00530006i
$902$	12.1972	−	6.40161i	0.406124	−	0.213150i
$903$	15.8354	+	2.57350i	0.526969	+	0.0856408i
$904$	−45.8919	+	15.3210i	−1.52634	+	0.509567i
$905$	5.40576	+	44.5205i	0.179694	+	1.47991i
$906$	6.07944	−	20.9887i	0.201976	−	0.697302i
$907$	−2.87491	+	14.0822i	−0.0954597	+	0.467593i	0.903758	+	0.428044i	$0.140797\pi$
$907$	−2.87491	+	14.0822i	−0.0954597	+	0.467593i	−0.999218	+	0.0395487i	$0.987408\pi$
$908$	−4.38318	−	1.46332i	−0.145461	−	0.0485620i
$909$	−13.1797	−	6.91724i	−0.437143	−	0.229430i
$910$	−33.6756	+	19.1091i	−1.11633	+	0.633461i
$911$	−0.320302	+	0.168108i	−0.0106121	+	0.00556965i	−0.470021	−	0.882655i	$-0.655754\pi$
$911$	−0.320302	+	0.168108i	−0.0106121	+	0.00556965i	0.459409	+	0.888225i	$0.348061\pi$
$912$	3.56339	−	0.579108i	0.117996	−	0.0191762i
$913$	−28.0091	+	21.0474i	−0.926964	+	0.696569i
$914$	−1.27485	+	31.6351i	−0.0421684	+	1.04640i
$915$	−28.2795			−0.934890
$916$	−0.190506	+	4.72735i	−0.00629448	+	0.156196i
$917$	−2.46656	−	12.0820i	−0.0814531	−	0.398984i
$918$	1.95851	+	2.83739i	0.0646405	+	0.0936479i
$919$	28.9325	−	9.65909i	0.954396	−	0.318624i	0.203522	−	0.979070i	$-0.434761\pi$
$919$	28.9325	−	9.65909i	0.954396	−	0.318624i	0.750873	+	0.660446i	$0.229633\pi$
$920$	7.97815	−	16.8136i	0.263032	−	0.554327i
$921$	8.29303	−	10.1571i	0.273265	−	0.334689i
$922$	10.5256	+	27.7538i	0.346644	+	0.914024i
$923$	−18.7164	−	36.3169i	−0.616059	−	1.19539i
$924$	−3.43089	+	9.04651i	−0.112868	+	0.297608i
$925$	1.03925	+	1.80004i	0.0341705	+	0.0591850i
$926$	19.4911	−	23.8723i	0.640518	−	0.784492i
$927$	−14.3160	−	10.7577i	−0.470198	−	0.353331i
$928$	5.37927	+	2.82326i	0.176583	+	0.0926779i
$929$	38.6642	−	3.12130i	1.26853	−	0.102406i	0.572192	−	0.820119i	$-0.306093\pi$
$929$	38.6642	−	3.12130i	1.26853	−	0.102406i	0.696339	+	0.717713i	$0.254811\pi$
$930$	2.13301	−	0.172195i	0.0699442	−	0.00564648i
$931$	20.2310	+	10.6180i	0.663043	+	0.347992i
$932$	19.3499	+	14.5405i	0.633826	+	0.476289i
$933$	4.09151	−	5.01119i	0.133950	−	0.164059i
$934$	−8.70347	−	15.0749i	−0.284786	−	0.493264i
$935$	8.40418	−	22.1600i	0.274846	−	0.724709i
$936$	7.19004	+	8.23888i	0.235014	+	0.269296i
$937$	−6.69086	−	17.6423i	−0.218581	−	0.576350i	0.780210	−	0.625518i	$-0.215112\pi$
$937$	−6.69086	−	17.6423i	−0.218581	−	0.576350i	−0.998791	+	0.0491678i	$0.984343\pi$
$938$	18.5525	−	22.7227i	0.605760	−	0.741921i
$939$	5.81849	−	12.2622i	0.189879	−	0.400162i
$940$	−12.0610	+	4.02655i	−0.393386	+	0.131332i
$941$	4.45910	+	6.46013i	0.145363	+	0.210594i	0.888901	−	0.458099i	$-0.151469\pi$
$941$	4.45910	+	6.46013i	0.145363	+	0.210594i	−0.743539	+	0.668693i	$0.766854\pi$
$942$	−2.66414	−	13.0498i	−0.0868025	−	0.425187i
$943$	−0.460423	+	11.4253i	−0.0149934	+	0.372058i
$944$	−0.330454			−0.0107554
$945$	−0.416981	+	10.3473i	−0.0135644	+	0.336597i
$946$	9.15544	−	6.87987i	0.297669	−	0.223684i
$947$	−18.0975	+	2.94112i	−0.588088	+	0.0955737i	−0.447172	−	0.894448i	$-0.647569\pi$
$947$	−18.0975	+	2.94112i	−0.588088	+	0.0955737i	−0.140916	+	0.990022i	$0.545005\pi$
$948$	11.8048	−	6.19565i	0.383403	−	0.201225i
$949$	44.8685	+	21.7019i	1.45649	+	0.704472i
$950$	−5.25659	−	2.75887i	−0.170546	−	0.0895096i
$951$	−22.6572	−	7.56407i	−0.734709	−	0.245282i
$952$	7.86358	−	38.5184i	0.254860	−	1.24839i
$953$	−4.93120	+	17.0245i	−0.159737	+	0.551477i	0.840220	+	0.542245i	$0.182426\pi$
$953$	−4.93120	+	17.0245i	−0.159737	+	0.551477i	−0.999957	+	0.00923142i	$0.997062\pi$
$954$	−0.0111911	−	0.0921672i	−0.000362326	−	0.00298402i
$955$	−2.02462	+	0.675918i	−0.0655152	+	0.0218722i
$956$	5.64373	+	0.917195i	0.182531	+	0.0296642i
$957$	−3.05747	+	1.60468i	−0.0988340	+	0.0518721i
$958$	7.75493	−	4.90392i	0.250550	−	0.158438i
$959$	−69.1932	+	29.4805i	−2.23437	+	0.951974i
$960$	3.97842	−	19.4876i	0.128403	−	0.628959i
$961$	29.5131	+	7.27433i	0.952036	+	0.234656i
$962$	−2.52902	+	2.81213i	−0.0815387	+	0.0906667i
$963$	9.03401	−	2.22668i	0.291117	−	0.0717539i
$964$	−0.459637	−	11.4058i	−0.0148039	−	0.367355i
$965$	−1.38849	−	34.4549i	−0.0446970	−	1.10914i
$966$	5.90747	+	7.23533i	0.190070	+	0.232793i
$967$	−6.61451	+	17.4410i	−0.212708	+	0.560866i	−0.998325	−	0.0578471i	$-0.981576\pi$
$967$	−6.61451	+	17.4410i	−0.212708	+	0.560866i	0.785617	+	0.618713i	$0.212346\pi$
$968$	−4.93660	−	10.4037i	−0.158668	−	0.334386i
$969$	−2.57701	+	8.89688i	−0.0827855	+	0.285809i
$970$	14.2729	−	20.6779i	0.458276	−	0.663927i
$971$	−15.3358	−	6.53399i	−0.492150	−	0.209686i	0.131610	−	0.991302i	$-0.457985\pi$
$971$	−15.3358	−	6.53399i	−0.492150	−	0.209686i	−0.623760	+	0.781616i	$0.714396\pi$
$972$	0.912654	−	0.148321i	0.0292734	−	0.00475739i
$973$	−44.1298	−	27.9060i	−1.41474	−	0.894625i
$974$	20.7269	+	30.0281i	0.664133	+	0.962162i
$975$	−0.541060	−	7.38898i	−0.0173278	−	0.236637i
$976$	−7.83731	+	11.3543i	−0.250866	+	0.363442i
$977$	16.2439	−	6.92089i	0.519689	−	0.221419i	−0.116163	−	0.993230i	$-0.537059\pi$
$977$	16.2439	−	6.92089i	0.519689	−	0.221419i	0.635851	+	0.771811i	$0.280649\pi$
$978$	−3.95122	−	13.6412i	−0.126346	−	0.436197i
$979$	−17.2636	+	1.39367i	−0.551748	+	0.0445417i
$980$	15.0756	−	13.3558i	0.481572	−	0.426635i
$981$	−14.5622	+	9.20861i	−0.464937	+	0.294008i
$982$	31.8812	+	13.5833i	1.01737	+	0.433460i
$983$	−1.36976	+	11.2810i	−0.0436886	+	0.359808i	0.954427	+	0.298445i	$0.0964678\pi$
$983$	−1.36976	+	11.2810i	−0.0436886	+	0.359808i	−0.998116	+	0.0613631i	$0.980455\pi$
$984$	3.00256	+	14.7075i	0.0957182	+	0.468859i
$985$	−0.557287	−	0.0449889i	−0.0177566	−	0.00143346i
$986$	3.54610	−	2.66472i	0.112931	−	0.0848621i
$987$	2.43318	−	20.0390i	0.0774489	−	0.637849i
$988$	−1.55824	+	9.15635i	−0.0495742	+	0.291302i
$989$	1.14587	+	9.43710i	0.0364366	+	0.300082i
$990$	5.12085	+	5.33137i	0.162751	+	0.169442i
$991$	18.0859	+	31.3257i	0.574518	+	0.995094i	0.996094	+	0.0883013i	$0.0281438\pi$
$991$	18.0859	+	31.3257i	0.574518	+	0.995094i	−0.421576	+	0.906793i	$0.638523\pi$
$992$	−1.83430	+	3.17711i	−0.0582392	+	0.100873i
$993$	−10.2831	+	2.53456i	−0.326324	+	0.0804317i
$994$	−28.9751	−	35.4880i	−0.919033	−	1.12561i
$995$	−5.72464	+	9.91536i	−0.181483	+	0.314338i
$996$	−4.28020	−	11.2860i	−0.135623	−	0.357609i
$997$	4.00096	−	4.16544i	0.126712	−	0.131921i	−0.654824	−	0.755781i	$-0.727257\pi$
$997$	4.00096	−	4.16544i	0.126712	−	0.131921i	0.781536	+	0.623861i	$0.214437\pi$
$998$	12.1685	+	4.06245i	0.385188	+	0.128595i
$999$	0.281424	+	0.971590i	0.00890388	+	0.0307397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.a.16.10	✓	360
169.74	even	39	inner	507.2.q.a.412.10	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.a.16.10	✓	360	1.1	even	1	trivial
507.2.q.a.412.10	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)

\(f(q)\)	\(=\)	\(q+(1.03364 + 0.0834440i) q^{2} +(0.845190 + 0.534466i) q^{3} +(-0.912654 - 0.148321i) q^{4} +(-1.98811 - 1.76131i) q^{5} +(0.829023 + 0.622971i) q^{6} +(-2.70082 + 2.81186i) q^{7} +(-2.94471 - 0.725807i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\)	\(q+(1.03364 + 0.0834440i) q^{2} +(0.845190 + 0.534466i) q^{3} +(-0.912654 - 0.148321i) q^{4} +(-1.98811 - 1.76131i) q^{5} +(0.829023 + 0.622971i) q^{6} +(-2.70082 + 2.81186i) q^{7} +(-2.94471 - 0.725807i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-1.90802 - 1.98646i) q^{10} +(-1.15055 + 2.42473i) q^{11} +(-0.692094 - 0.613142i) q^{12} +(-3.13586 + 1.77944i) q^{13} +(-3.02631 + 2.68108i) q^{14} +(-0.738971 - 2.55122i) q^{15} +(-1.22912 - 0.410341i) q^{16} +(2.30308 - 2.39776i) q^{17} +(0.367726 + 0.969613i) q^{18} +(-1.39301 + 2.41276i) q^{19} +(1.55322 + 1.90235i) q^{20} +(-3.78555 + 0.933055i) q^{21} +(-1.39158 + 2.41029i) q^{22} +(-1.15514 - 2.00075i) q^{23} +(-2.10092 - 2.18729i) q^{24} +(0.247681 + 2.03984i) q^{25} +(-3.38983 + 1.57763i) q^{26} +(-0.120537 + 0.992709i) q^{27} +(2.88197 - 2.16566i) q^{28} +(1.28241 + 0.103527i) q^{29} +(-0.550945 - 2.69871i) q^{30} +(-0.0936485 + 0.771264i) q^{31} +(4.34408 + 1.85084i) q^{32} +(-2.26837 + 1.43443i) q^{33} +(2.58063 - 2.28624i) q^{34} +(10.3221 - 0.833287i) q^{35} +(-0.257248 - 0.888122i) q^{36} +(0.930584 - 0.396485i) q^{37} +(-1.64120 + 2.37768i) q^{38} +(-3.60144 - 0.172048i) q^{39} +(4.57605 + 6.62955i) q^{40} +(-4.18322 - 2.64531i) q^{41} +(-3.99075 + 0.648560i) q^{42} +(-3.78557 - 1.61288i) q^{43} +(1.40969 - 2.04229i) q^{44} +(0.738971 - 2.55122i) q^{45} +(-1.02704 - 2.16445i) q^{46} +(-1.83596 + 4.84103i) q^{47} +(-0.819528 - 1.00374i) q^{48} +(-0.330220 - 8.19434i) q^{49} +(0.0858008 + 2.12913i) q^{50} +(3.22806 - 0.795645i) q^{51} +(3.12588 - 1.15890i) q^{52} +(-0.0869297 - 0.0214262i) q^{53} +(-0.207427 + 1.01604i) q^{54} +(6.55813 - 2.79416i) q^{55} +(9.99402 - 6.31984i) q^{56} +(-2.46689 + 1.29473i) q^{57} +(1.31691 + 0.214018i) q^{58} +(0.241894 - 0.0807559i) q^{59} +(0.296026 + 2.43799i) q^{60} +(2.96219 - 10.2267i) q^{61} +(-0.161156 + 0.789395i) q^{62} +(-3.69820 - 1.23464i) q^{63} +(6.63053 + 3.47997i) q^{64} +(9.36859 + 1.98551i) q^{65} +(-2.46437 + 1.29340i) q^{66} +(-7.16148 + 1.16385i) q^{67} +(-2.45755 + 1.84673i) q^{68} +(0.0930252 - 2.30840i) q^{69} +10.7389 q^{70} +(-0.456272 + 11.3223i) q^{71} +(-0.606647 - 2.97155i) q^{72} +(-7.85264 - 11.3765i) q^{73} +(0.994972 - 0.332170i) q^{74} +(-0.880887 + 1.85643i) q^{75} +(1.62920 - 1.99540i) q^{76} +(-3.71056 - 9.78395i) q^{77} +(-3.70824 - 0.478354i) q^{78} +(-5.11294 + 13.4817i) q^{79} +(1.72089 + 2.98067i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-4.10320 - 3.08336i) q^{82} +(11.5590 + 6.06662i) q^{83} +(3.59329 - 0.290080i) q^{84} +(-8.80199 + 0.710570i) q^{85} +(-3.77833 - 1.98302i) q^{86} +(1.02855 + 0.772902i) q^{87} +(5.14792 - 6.30506i) q^{88} +(3.22667 + 5.58875i) q^{89} +(0.976713 - 2.57538i) q^{90} +(3.46589 - 13.6235i) q^{91} +(0.757486 + 1.99733i) q^{92} +(-0.491365 + 0.601813i) q^{93} +(-2.30168 + 4.85068i) q^{94} +(7.01909 - 2.34332i) q^{95} +(2.68236 + 3.88607i) q^{96} +(1.82464 + 8.93770i) q^{97} +(0.342439 - 8.49754i) q^{98} -2.68385 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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