LMFDB - Embedded newform 507.2.q.a.490.4

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			490.4
Character	$\chi$	$=$	507.490
Dual form			507.2.q.a.328.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.375533 - 1.83948i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(-1.40271 + 0.597638i) q^{4} +(-4.16091 + 1.02557i) q^{5} +(0.0755962 + 1.87590i) q^{6} +(-0.676651 + 1.42601i) q^{7} +(-0.506888 - 0.734355i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})$	\(q+(-0.375533 - 1.83948i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(-1.40271 + 0.597638i) q^{4} +(-4.16091 + 1.02557i) q^{5} +(0.0755962 + 1.87590i) q^{6} +(-0.676651 + 1.42601i) q^{7} +(-0.506888 - 0.734355i) q^{8} +(0.948536 + 0.316668i) q^{9} +(3.44908 + 7.26877i) q^{10} +(5.23992 - 1.74934i) q^{11} +(1.48041 - 0.364889i) q^{12} +(-1.24007 + 3.38559i) q^{13} +(2.87723 + 0.709173i) q^{14} +(4.27154 - 0.344834i) q^{15} +(-3.27290 + 3.40745i) q^{16} +(0.351146 - 0.740025i) q^{17} +(0.226298 - 1.86373i) q^{18} +(0.108838 + 0.188513i) q^{19} +(5.22362 - 3.92529i) q^{20} +(0.896637 - 1.29900i) q^{21} +(-5.18565 - 8.98180i) q^{22} +(3.79217 - 6.56822i) q^{23} +(0.382526 + 0.806155i) q^{24} +(11.8341 - 6.21100i) q^{25} +(6.69342 + 1.00968i) q^{26} +(-0.885456 - 0.464723i) q^{27} +(0.0969049 - 2.40467i) q^{28} +(2.02203 + 9.90458i) q^{29} +(-2.23842 - 7.72792i) q^{30} +(3.88869 + 2.04094i) q^{31} +(5.98867 + 3.78701i) q^{32} +(-5.45268 + 0.886147i) q^{33} +(-1.49313 - 0.368023i) q^{34} +(1.35301 - 6.62746i) q^{35} +(-1.51977 + 0.122689i) q^{36} +(-6.00433 + 3.79691i) q^{37} +(0.305894 - 0.270999i) q^{38} +(1.76710 - 3.14283i) q^{39} +(2.86225 + 2.53573i) q^{40} +(-5.31467 - 0.863718i) q^{41} +(-2.72621 - 1.16153i) q^{42} +(5.79303 + 3.66329i) q^{43} +(-6.30461 + 5.58539i) q^{44} +(-4.27154 - 0.344834i) q^{45} +(-13.5062 - 4.50903i) q^{46} +(0.413504 + 3.40551i) q^{47} +(3.77710 - 2.83831i) q^{48} +(2.85146 + 3.49241i) q^{49} +(-15.8691 - 19.4361i) q^{50} +(-0.465307 + 0.674114i) q^{51} +(-0.283904 - 5.49011i) q^{52} +(-1.70865 - 2.47541i) q^{53} +(-0.522332 + 1.80330i) q^{54} +(-20.0087 + 12.6528i) q^{55} +(1.39019 - 0.225927i) q^{56} +(-0.0771891 - 0.203531i) q^{57} +(17.4599 - 7.43899i) q^{58} +(0.697083 + 0.725741i) q^{59} +(-5.78563 + 3.03654i) q^{60} +(13.0645 + 1.05467i) q^{61} +(2.29394 - 7.91961i) q^{62} +(-1.09340 + 1.13835i) q^{63} +(1.36640 - 3.60291i) q^{64} +(1.68764 - 15.3589i) q^{65} +(3.67771 + 9.69733i) q^{66} +(4.06299 + 1.73108i) q^{67} +(-0.0502886 + 1.24790i) q^{68} +(-4.79667 + 5.87486i) q^{69} -12.6992 q^{70} +(-6.07261 + 7.43759i) q^{71} +(-0.248255 - 0.857077i) q^{72} +(1.88465 + 1.66966i) q^{73} +(9.23917 + 9.61899i) q^{74} +(-12.6771 + 4.23225i) q^{75} +(-0.265331 - 0.199383i) q^{76} +(-1.05101 + 8.65589i) q^{77} +(-6.44478 - 2.07031i) q^{78} +(-0.586371 - 4.82920i) q^{79} +(10.1236 - 17.5346i) q^{80} +(0.799443 + 0.600742i) q^{81} +(0.407040 + 10.1006i) q^{82} +(1.58070 - 4.16795i) q^{83} +(-0.481386 + 2.35799i) q^{84} +(-0.702138 + 3.43930i) q^{85} +(4.56308 - 12.0319i) q^{86} +(-0.407043 - 10.1007i) q^{87} +(-3.94069 - 2.96124i) q^{88} +(-4.08792 + 7.08048i) q^{89} +(0.969786 + 7.98691i) q^{90} +(-3.98880 - 4.05922i) q^{91} +(-1.39388 + 11.4796i) q^{92} +(-3.51094 - 2.63830i) q^{93} +(6.10909 - 2.03951i) q^{94} +(-0.646199 - 0.672765i) q^{95} +(-5.30364 - 4.69862i) q^{96} +(-0.659267 - 2.27605i) q^{97} +(5.35340 - 6.55673i) q^{98} +5.52422 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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{17}{39}\right)$

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 $

$2$	−0.375533	−	1.83948i	−0.265542	−	1.30071i	−0.865593	−	0.500748i	$-0.833058\pi$
$2$	−0.375533	−	1.83948i	−0.265542	−	1.30071i	0.600051	−	0.799962i	$-0.295147\pi$
$3$	−0.987050	−	0.160411i	−0.569874	−	0.0926135i
$3$	−0.987050	−	0.160411i	−0.569874	−	0.0926135i
$4$	−1.40271	+	0.597638i	−0.701354	+	0.298819i
$5$	−4.16091	+	1.02557i	−1.86081	+	0.458649i	−0.998833	−	0.0482917i	$-0.984622\pi$
$5$	−4.16091	+	1.02557i	−1.86081	+	0.458649i	−0.861981	+	0.506941i	$0.830776\pi$
$6$	0.0755962	+	1.87590i	0.0308620	+	0.765833i
$7$	−0.676651	+	1.42601i	−0.255750	+	0.538982i	−0.990196	−	0.139685i	$-0.955391\pi$
$7$	−0.676651	+	1.42601i	−0.255750	+	0.538982i	0.734446	+	0.678667i	$0.237442\pi$
$8$	−0.506888	−	0.734355i	−0.179212	−	0.259634i
$9$	0.948536	+	0.316668i	0.316179	+	0.105556i
$10$	3.44908	+	7.26877i	1.09069	+	2.29859i
$11$	5.23992	−	1.74934i	1.57990	−	0.527447i	0.614652	−	0.788798i	$-0.289296\pi$
$11$	5.23992	−	1.74934i	1.57990	−	0.527447i	0.965244	+	0.261352i	$0.0841682\pi$
$12$	1.48041	−	0.364889i	0.427358	−	0.105334i
$13$	−1.24007	+	3.38559i	−0.343933	+	0.938994i
$13$	−1.24007	+	3.38559i	−0.343933	+	0.938994i
$14$	2.87723	+	0.709173i	0.768971	+	0.189534i
$15$	4.27154	−	0.344834i	1.10291	−	0.0890358i
$16$	−3.27290	+	3.40745i	−0.818224	+	0.851861i
$17$	0.351146	−	0.740025i	0.0851655	−	0.179482i	−0.856400	−	0.516314i	$-0.827304\pi$
$17$	0.351146	−	0.740025i	0.0851655	−	0.179482i	0.941565	+	0.336831i	$0.109355\pi$
$18$	0.226298	−	1.86373i	0.0533390	−	0.439286i
$19$	0.108838	+	0.188513i	0.0249692	+	0.0432479i	0.878240	−	0.478220i	$-0.158718\pi$
$19$	0.108838	+	0.188513i	0.0249692	+	0.0432479i	−0.853271	+	0.521468i	$0.825385\pi$
$20$	5.22362	−	3.92529i	1.16804	−	0.877722i
$21$	0.896637	−	1.29900i	0.195662	−	0.283466i
$22$	−5.18565	−	8.98180i	−1.10558	−	1.91493i
$23$	3.79217	−	6.56822i	0.790721	−	1.36957i	−0.134800	−	0.990873i	$-0.543039\pi$
$23$	3.79217	−	6.56822i	0.790721	−	1.36957i	0.925521	−	0.378696i	$-0.123627\pi$
$24$	0.382526	+	0.806155i	0.0780827	+	0.164556i
$25$	11.8341	−	6.21100i	2.36681	−	1.24220i
$26$	6.69342	+	1.00968i	1.31269	+	0.198015i
$27$	−0.885456	−	0.464723i	−0.170406	−	0.0894360i
$28$	0.0969049	−	2.40467i	0.0183133	−	0.454440i
$29$	2.02203	+	9.90458i	0.375482	+	1.83923i	0.525816	+	0.850599i	$0.323760\pi$
$29$	2.02203	+	9.90458i	0.375482	+	1.83923i	−0.150333	+	0.988635i	$0.548035\pi$
$30$	−2.23842	−	7.72792i	−0.408677	−	1.41092i
$31$	3.88869	+	2.04094i	0.698429	+	0.366564i	0.776269	−	0.630402i	$-0.217110\pi$
$31$	3.88869	+	2.04094i	0.698429	+	0.366564i	−0.0778398	+	0.996966i	$0.524802\pi$
$32$	5.98867	+	3.78701i	1.05866	+	0.669455i
$33$	−5.45268	+	0.886147i	−0.949190	+	0.154258i
$34$	−1.49313	−	0.368023i	−0.256070	−	0.0631155i
$35$	1.35301	−	6.62746i	0.228700	−	1.12024i
$36$	−1.51977	+	0.122689i	−0.253295	+	0.0204481i
$37$	−6.00433	+	3.79691i	−0.987106	+	0.624208i	−0.927425	−	0.374009i	$-0.877983\pi$
$37$	−6.00433	+	3.79691i	−0.987106	+	0.624208i	−0.0596813	+	0.998217i	$0.519008\pi$
$38$	0.305894	−	0.270999i	0.0496226	−	0.0439618i
$39$	1.76710	−	3.14283i	0.282962	−	0.503255i
$40$	2.86225	+	2.53573i	0.452561	+	0.400934i
$41$	−5.31467	−	0.863718i	−0.830012	−	0.134890i	−0.269462	−	0.963011i	$-0.586846\pi$
$41$	−5.31467	−	0.863718i	−0.830012	−	0.134890i	−0.560549	+	0.828121i	$0.689410\pi$
$42$	−2.72621	−	1.16153i	−0.420663	−	0.179228i
$43$	5.79303	+	3.66329i	0.883428	+	0.558646i	0.897381	−	0.441256i	$-0.145467\pi$
$43$	5.79303	+	3.66329i	0.883428	+	0.558646i	−0.0139527	+	0.999903i	$0.504441\pi$
$44$	−6.30461	+	5.58539i	−0.950455	+	0.842030i
$45$	−4.27154	−	0.344834i	−0.636763	−	0.0514048i
$46$	−13.5062	−	4.50903i	−1.99138	−	0.664821i
$47$	0.413504	+	3.40551i	0.0603157	+	0.496745i	0.991294	+	0.131669i	$0.0420337\pi$
$47$	0.413504	+	3.40551i	0.0603157	+	0.496745i	−0.930978	+	0.365075i	$0.881043\pi$
$48$	3.77710	−	2.83831i	0.545178	−	0.409675i
$49$	2.85146	+	3.49241i	0.407352	+	0.498916i
$50$	−15.8691	−	19.4361i	−2.24423	−	2.74868i
$51$	−0.465307	+	0.674114i	−0.0651561	+	0.0943949i
$52$	−0.283904	−	5.49011i	−0.0393705	−	0.761341i
$53$	−1.70865	−	2.47541i	−0.234702	−	0.340024i	0.687881	−	0.725823i	$-0.258541\pi$
$53$	−1.70865	−	2.47541i	−0.234702	−	0.340024i	−0.922583	+	0.385800i	$0.873926\pi$
$54$	−0.522332	+	1.80330i	−0.0710804	+	0.245398i
$55$	−20.0087	+	12.6528i	−2.69798	+	1.70610i
$56$	1.39019	−	0.225927i	0.185771	−	0.0301908i
$57$	−0.0771891	−	0.203531i	−0.0102239	−	0.0269583i
$58$	17.4599	−	7.43899i	2.29260	−	0.976787i
$59$	0.697083	+	0.725741i	0.0907525	+	0.0944834i	0.765030	−	0.643995i	$-0.222724\pi$
$59$	0.697083	+	0.725741i	0.0907525	+	0.0944834i	−0.674277	+	0.738478i	$0.735545\pi$
$60$	−5.78563	+	3.03654i	−0.746922	+	0.392015i
$61$	13.0645	+	1.05467i	1.67274	+	0.135037i	0.880141	−	0.474712i	$-0.157448\pi$
$61$	13.0645	+	1.05467i	1.67274	+	0.135037i	0.792595	+	0.609749i	$0.208730\pi$
$62$	2.29394	−	7.91961i	0.291331	−	1.00579i
$63$	−1.09340	+	1.13835i	−0.137756	+	0.143419i
$64$	1.36640	−	3.60291i	0.170800	−	0.450364i
$65$	1.68764	−	15.3589i	0.209326	−	1.90504i
$66$	3.67771	+	9.69733i	0.452695	+	1.19366i
$67$	4.06299	+	1.73108i	0.496374	+	0.211485i	0.625621	−	0.780127i	$-0.284846\pi$
$67$	4.06299	+	1.73108i	0.496374	+	0.211485i	−0.129247	+	0.991612i	$0.541256\pi$
$68$	−0.0502886	+	1.24790i	−0.00609838	+	0.151330i
$69$	−4.79667	+	5.87486i	−0.577452	+	0.707250i
$70$	−12.6992			−1.51784
$71$	−6.07261	+	7.43759i	−0.720686	+	0.882680i	−0.996921	−	0.0784100i	$-0.975016\pi$
$71$	−6.07261	+	7.43759i	−0.720686	+	0.882680i	0.276235	+	0.961090i	$0.410913\pi$
$72$	−0.248255	−	0.857077i	−0.0292572	−	0.101008i
$73$	1.88465	+	1.66966i	0.220582	+	0.195418i	0.766175	−	0.642631i	$-0.222157\pi$
$73$	1.88465	+	1.66966i	0.220582	+	0.195418i	−0.545594	+	0.838050i	$0.683696\pi$
$74$	9.23917	+	9.61899i	1.07403	+	1.11819i
$75$	−12.6771	+	4.23225i	−1.46383	+	0.488698i
$76$	−0.265331	−	0.199383i	−0.0304356	−	0.0228708i
$77$	−1.05101	+	8.65589i	−0.119774	+	0.986430i
$78$	−6.44478	−	2.07031i	−0.729727	−	0.234416i
$79$	−0.586371	−	4.82920i	−0.0659719	−	0.543327i	−0.987800	−	0.155728i	$-0.950228\pi$
$79$	−0.586371	−	4.82920i	−0.0659719	−	0.543327i	0.921828	−	0.387599i	$-0.126695\pi$
$80$	10.1236	−	17.5346i	1.13186	−	1.96043i
$81$	0.799443	+	0.600742i	0.0888270	+	0.0667491i
$82$	0.407040	+	10.1006i	0.0449500	+	1.11542i
$83$	1.58070	−	4.16795i	0.173504	−	0.457492i	−0.819852	−	0.572576i	$-0.805944\pi$
$83$	1.58070	−	4.16795i	0.173504	−	0.457492i	0.993356	+	0.115083i	$0.0367135\pi$
$84$	−0.481386	+	2.35799i	−0.0525236	+	0.257277i
$85$	−0.702138	+	3.43930i	−0.0761576	+	0.373045i
$86$	4.56308	−	12.0319i	0.492050	−	1.29743i
$87$	−0.407043	−	10.1007i	−0.0436396	−	1.08291i
$88$	−3.94069	−	2.96124i	−0.420079	−	0.315669i
$89$	−4.08792	+	7.08048i	−0.433318	+	0.750530i	−0.997157	−	0.0753556i	$-0.975991\pi$
$89$	−4.08792	+	7.08048i	−0.433318	+	0.750530i	0.563838	+	0.825885i	$0.309324\pi$
$90$	0.969786	+	7.98691i	0.102224	+	0.841894i
$91$	−3.98880	−	4.05922i	−0.418140	−	0.425522i
$92$	−1.39388	+	11.4796i	−0.145322	+	1.19684i
$93$	−3.51094	−	2.63830i	−0.364068	−	0.273579i
$94$	6.10909	−	2.03951i	0.630104	−	0.210360i
$95$	−0.646199	−	0.672765i	−0.0662987	−	0.0690242i
$96$	−5.30364	−	4.69862i	−0.541301	−	0.479551i
$97$	−0.659267	−	2.27605i	−0.0669384	−	0.231098i	0.920073	−	0.391746i	$-0.128129\pi$
$97$	−0.659267	−	2.27605i	−0.0669384	−	0.231098i	−0.987012	+	0.160648i	$0.948642\pi$
$98$	5.35340	−	6.55673i	0.540775	−	0.662330i
$99$	5.52422			0.555205
$100$	−12.8878	+	15.7847i	−1.28878	+	1.57847i
$101$	−0.414891	+	10.2954i	−0.0412832	+	1.02443i	0.837271	+	0.546789i	$0.184150\pi$
$101$	−0.414891	+	10.2954i	−0.0412832	+	1.02443i	−0.878554	+	0.477644i	$0.841491\pi$
$102$	1.41476	+	0.602772i	0.140082	+	0.0596834i
$103$	−0.572487	−	1.50952i	−0.0564088	−	0.148738i	0.903850	−	0.427850i	$-0.140729\pi$
$103$	−0.572487	−	1.50952i	−0.0564088	−	0.148738i	−0.960258	+	0.279113i	$0.909960\pi$
$104$	3.11480	−	0.805467i	0.305431	−	0.0789825i
$105$	−2.39860	+	6.32460i	−0.234080	+	0.617217i
$106$	−3.91182	+	4.07263i	−0.379949	+	0.395569i
$107$	−2.94905	+	10.1813i	−0.285095	+	0.984263i	0.682317	+	0.731056i	$0.260972\pi$
$107$	−2.94905	+	10.1813i	−0.285095	+	0.984263i	−0.967412	+	0.253206i	$0.918515\pi$
$108$	1.51977	+	0.122689i	0.146240	+	0.0118057i
$109$	5.96683	−	3.13164i	0.571519	−	0.299956i	−0.154097	−	0.988056i	$-0.549247\pi$
$109$	5.96683	−	3.13164i	0.571519	−	0.299956i	0.725616	+	0.688099i	$0.241555\pi$
$110$	30.7885	+	32.0542i	2.93557	+	3.05625i
$111$	6.53565	−	2.78458i	0.620336	−	0.264300i
$112$	−2.64445	−	6.97284i	−0.249877	−	0.658871i
$113$	−3.01528	+	0.490030i	−0.283653	+	0.0460982i	−0.300573	−	0.953759i	$-0.597178\pi$
$113$	−3.01528	+	0.490030i	−0.283653	+	0.0460982i	0.0169200	+	0.999857i	$0.494614\pi$
$114$	−0.345404	+	0.218421i	−0.0323501	+	0.0204570i
$115$	−9.04266	+	31.2189i	−0.843233	+	2.91118i
$116$	−8.75568	−	12.6848i	−0.812944	−	1.17775i
$117$	−2.24836	+	2.81867i	−0.207861	+	0.260586i
$118$	1.07321	−	1.55481i	0.0987969	−	0.143132i
$119$	0.817681	+	1.00148i	0.0749567	+	0.0918053i
$120$	−2.41842	−	2.96203i	−0.220771	−	0.270395i
$121$	15.6027	−	11.7247i	1.41843	−	1.06588i
$122$	−2.96609	−	24.4279i	−0.268537	−	2.21160i
$123$	5.10729	+	1.70507i	0.460509	+	0.153741i
$124$	−6.67444	−	0.538816i	−0.599382	−	0.0483871i
$125$	−26.8322	+	23.7712i	−2.39994	+	2.12616i
$126$	2.50458	+	1.58380i	0.223126	+	0.141096i
$127$	−0.400843	−	0.170783i	−0.0355690	−	0.0151546i	0.374109	−	0.927385i	$-0.377949\pi$
$127$	−0.400843	−	0.170783i	−0.0355690	−	0.0151546i	−0.409678	+	0.912230i	$0.634359\pi$
$128$	6.84706	+	1.11276i	0.605200	+	0.0983546i
$129$	−5.13038	−	4.54512i	−0.451704	−	0.400175i
$130$	−28.8862	+	2.66339i	−2.53349	+	0.233594i
$131$	6.98482	−	6.18801i	0.610267	−	0.540649i	−0.300388	−	0.953817i	$-0.597116\pi$
$131$	6.98482	−	6.18801i	0.610267	−	0.540649i	0.910655	+	0.413168i	$0.135578\pi$
$132$	7.11892	−	4.50174i	0.619623	−	0.391826i
$133$	−0.342468	+	0.0276469i	−0.0296957	+	0.00239729i
$134$	1.65850	−	8.12388i	0.143273	−	0.701796i
$135$	4.16091	+	1.02557i	0.358114	+	0.0882671i
$136$	−0.721433	+	0.117244i	−0.0618624	+	0.0100536i
$137$	0.984782	+	0.622739i	0.0841356	+	0.0532041i	0.575871	−	0.817540i	$-0.304663\pi$
$137$	0.984782	+	0.622739i	0.0841356	+	0.0532041i	−0.491736	+	0.870745i	$0.663637\pi$
$138$	12.6080	+	6.61719i	1.07326	+	0.563293i
$139$	4.24382	+	14.6514i	0.359956	+	1.24271i	0.912447	+	0.409194i	$0.134190\pi$
$139$	4.24382	+	14.6514i	0.359956	+	1.24271i	−0.552491	+	0.833519i	$0.686323\pi$
$140$	2.06295	+	10.1050i	0.174351	+	0.854028i
$141$	0.138133	−	3.42774i	0.0116329	−	0.288668i
$142$	15.9618	+	8.37739i	1.33948	+	0.703015i
$143$	−0.575301	+	19.9095i	−0.0481091	+	1.66492i
$144$	−4.18349	+	2.19566i	−0.348624	+	0.182972i
$145$	−18.5713	−	39.1383i	−1.54227	−	3.25026i
$146$	2.36355	−	4.09379i	0.195609	−	0.338805i
$147$	−2.25432	−	3.90459i	−0.185933	−	0.322045i
$148$	6.15315	−	8.91438i	0.505786	−	0.732757i
$149$	−2.14627	+	1.61282i	−0.175829	+	0.132127i	−0.685013	−	0.728531i	$-0.740204\pi$
$149$	−2.14627	+	1.61282i	−0.175829	+	0.132127i	0.509184	+	0.860658i	$0.329947\pi$
$150$	12.5458	+	21.7300i	1.02436	+	1.77425i
$151$	2.55239	−	21.0208i	0.207711	−	1.71065i	−0.400019	−	0.916507i	$-0.630996\pi$
$151$	2.55239	−	21.0208i	0.207711	−	1.71065i	0.607729	−	0.794144i	$-0.292080\pi$
$152$	0.0832668	−	0.175481i	0.00675383	−	0.0142334i
$153$	0.567417	−	0.590744i	0.0458730	−	0.0477588i
$154$	16.3170	−	1.31725i	1.31486	−	0.106147i
$155$	−18.2736	−	4.50404i	−1.46777	−	0.361773i
$156$	−0.600448	+	5.46456i	−0.0480743	+	0.437515i
$157$	−22.1977	+	5.47125i	−1.77157	+	0.436653i	−0.983793	−	0.179305i	$-0.942615\pi$
$157$	−22.1977	+	5.47125i	−1.77157	+	0.436653i	−0.787778	+	0.615959i	$0.788769\pi$
$158$	−8.66302	+	2.89214i	−0.689193	+	0.230086i
$159$	1.28944	+	2.71744i	0.102259	+	0.215507i
$160$	−28.8022	−	9.61557i	−2.27701	−	0.760178i
$161$	6.80039	+	9.85207i	0.535946	+	0.776452i
$162$	0.804837	−	1.69616i	0.0632340	−	0.133263i
$163$	0.133464	+	3.31188i	0.0104537	+	0.259407i	0.995962	+	0.0897780i	$0.0286158\pi$
$163$	0.133464	+	3.31188i	0.0104537	+	0.259407i	−0.985508	+	0.169629i	$0.945743\pi$
$164$	7.97112	−	1.96470i	0.622440	−	0.153418i
$165$	21.7793	−	9.27929i	1.69552	−	0.722392i
$166$	−8.26048	−	1.34246i	−0.641137	−	0.104195i
$167$	2.30068	+	11.2695i	0.178032	+	0.872057i	0.966438	+	0.256902i	$0.0827016\pi$
$167$	2.30068	+	11.2695i	0.178032	+	0.872057i	−0.788406	+	0.615155i	$0.789093\pi$
$168$	−1.40842			−0.108662
$169$	−9.92446	−	8.39673i	−0.763420	−	0.645902i
$170$	6.59021			0.505446
$171$	0.0435409	+	0.213277i	0.00332965	+	0.0163097i
$172$	−10.3152	−	1.67639i	−0.786530	−	0.127824i
$173$	15.5535	−	6.62672i	1.18251	−	0.503820i	0.290956	−	0.956736i	$-0.406027\pi$
$173$	15.5535	−	6.62672i	1.18251	−	0.503820i	0.891553	+	0.452916i	$0.149616\pi$
$174$	−18.4271	+	4.54188i	−1.39696	+	0.344319i
$175$	0.849422	+	21.0782i	0.0642103	+	1.59336i
$176$	−11.1889	+	23.5802i	−0.843397	+	1.77742i
$177$	−0.571639	−	0.828163i	−0.0429670	−	0.0622485i
$178$	14.5596	+	4.86070i	1.09129	+	0.364325i
$179$	0.455396	+	0.959726i	0.0340379	+	0.0717333i	0.919757	−	0.392488i	$-0.128386\pi$
$179$	0.455396	+	0.959726i	0.0340379	+	0.0717333i	−0.885719	+	0.464221i	$0.846334\pi$
$180$	6.19781	−	2.06913i	0.461957	−	0.154224i
$181$	22.4520	−	5.53392i	1.66885	−	0.411333i	0.712058	−	0.702121i	$-0.247763\pi$
$181$	22.4520	−	5.53392i	1.66885	−	0.411333i	0.956788	+	0.290788i	$0.0939173\pi$
$182$	−5.96893	+	8.86169i	−0.442446	+	0.656873i
$183$	−12.7261	−	3.13671i	−0.940742	−	0.231872i
$184$	−6.74561	+	0.544562i	−0.497293	+	0.0401456i
$185$	21.0895	−	21.9565i	1.55053	−	1.61427i
$186$	−3.53463	+	7.44908i	−0.259172	+	0.546193i
$187$	0.545421	−	4.49195i	0.0398852	−	0.328484i
$188$	−2.61529	−	4.52981i	−0.190739	−	0.330370i
$189$	1.26185	−	0.948216i	0.0917858	−	0.0689725i
$190$	−0.994869	+	1.44132i	−0.0721754	+	0.104564i
$191$	3.21064	+	5.56099i	0.232314	+	0.402379i	0.958489	−	0.285131i	$-0.0920370\pi$
$191$	3.21064	+	5.56099i	0.232314	+	0.402379i	−0.726175	+	0.687510i	$0.758704\pi$
$192$	−1.92666	+	3.33707i	−0.139044	+	0.240832i
$193$	−5.33568	−	11.2447i	−0.384071	−	0.809411i	−0.999770	−	0.0214307i	$-0.993178\pi$
$193$	−5.33568	−	11.2447i	−0.384071	−	0.809411i	0.615700	−	0.787981i	$-0.288873\pi$
$194$	−3.93918	+	2.06744i	−0.282817	+	0.148434i
$195$	−4.12953	+	14.8893i	−0.295722	+	1.06624i
$196$	−6.08697	−	3.19469i	−0.434783	−	0.228192i
$197$	0.257261	−	6.38386i	0.0183291	−	0.454831i	−0.963800	−	0.266625i	$-0.914092\pi$
$197$	0.257261	−	6.38386i	0.0183291	−	0.454831i	0.982129	−	0.188207i	$-0.0602674\pi$
$198$	−2.07453	−	10.1617i	−0.147430	−	0.722160i
$199$	4.01955	+	13.8771i	0.284938	+	0.983721i	0.967495	+	0.252889i	$0.0813807\pi$
$199$	4.01955	+	13.8771i	0.284938	+	0.983721i	−0.682557	+	0.730832i	$0.739132\pi$
$200$	−10.5596	−	5.54212i	−0.746678	−	0.391887i
$201$	−3.73269	−	2.36041i	−0.263284	−	0.166491i
$202$	19.0940	−	3.10308i	1.34345	−	0.218332i
$203$	−15.4923	−	3.81850i	−1.08734	−	0.268006i
$204$	0.249814	−	1.22367i	0.0174905	−	0.0856741i
$205$	22.9996	−	1.85672i	1.60636	−	0.129679i
$206$	−2.56175	+	1.61995i	−0.178486	+	0.112868i
$207$	5.67695	−	5.02934i	0.394575	−	0.349563i
$208$	−7.47760	−	15.3062i	−0.518478	−	1.06129i
$209$	0.900078	+	0.797400i	0.0622597	+	0.0551573i
$210$	12.5347	+	2.03709i	0.864979	+	0.140573i
$211$	15.7431	+	6.70750i	1.08380	+	0.461764i	0.858651	−	0.512561i	$-0.171303\pi$
$211$	15.7431	+	6.70750i	1.08380	+	0.461764i	0.225148	+	0.974325i	$0.427713\pi$
$212$	3.87614	+	2.45112i	0.266215	+	0.168344i
$213$	7.18704	−	6.36717i	0.492448	−	0.436271i
$214$	19.8358	+	1.60131i	1.35594	+	0.109463i
$215$	−27.8612	−	9.30144i	−1.90012	−	0.634353i
$216$	0.107556	+	0.885801i	0.00731824	+	0.0602712i
$217$	−5.54169	+	4.16431i	−0.376195	+	0.282692i
$218$	−8.00133	−	9.79985i	−0.541918	−	0.663729i
$219$	−1.59241	−	1.95035i	−0.107605	−	0.131793i
$220$	20.5047	−	29.7061i	1.38242	−	2.00279i
$221$	2.06998	+	2.10652i	0.139242	+	0.141700i
$222$	−7.57653	−	10.9765i	−0.508503	−	0.736694i
$223$	−6.75186	+	23.3101i	−0.452138	+	1.56096i	0.333792	+	0.942647i	$0.391672\pi$
$223$	−6.75186	+	23.3101i	−0.452138	+	1.56096i	−0.785930	+	0.618316i	$0.787815\pi$
$224$	−9.45256	+	5.97744i	−0.631576	+	0.399384i
$225$	13.1919	−	2.14389i	0.879458	−	0.142926i
$226$	2.03374	+	5.36253i	0.135282	+	0.356710i
$227$	−1.53578	+	0.654337i	−0.101934	+	0.0434299i	−0.442331	−	0.896852i	$-0.645849\pi$
$227$	−1.53578	+	0.654337i	−0.101934	+	0.0434299i	0.340398	+	0.940282i	$0.389438\pi$
$228$	0.229912	+	0.239363i	0.0152263	+	0.0158522i
$229$	−5.15786	+	2.70705i	−0.340841	+	0.178887i	−0.626455	−	0.779458i	$-0.715495\pi$
$229$	−5.15786	+	2.70705i	−0.340841	+	0.178887i	0.285614	+	0.958345i	$0.407802\pi$
$230$	60.8224	+	4.91009i	4.01051	+	0.323762i
$231$	2.42591	−	8.37520i	0.159613	−	0.551048i
$232$	6.24853	−	6.50540i	0.410236	−	0.427101i
$233$	7.18898	−	18.9558i	0.470966	−	1.24184i	−0.463600	−	0.886045i	$-0.653442\pi$
$233$	7.18898	−	18.9558i	0.470966	−	1.24184i	0.934566	−	0.355790i	$-0.115788\pi$
$234$	6.02922	+	3.07731i	0.394142	+	0.201170i
$235$	−5.21314	−	13.7459i	−0.340068	−	0.896685i
$236$	−1.41153	−	0.601399i	−0.0918831	−	0.0391477i
$237$	−0.195880	+	4.86072i	−0.0127238	+	0.315738i
$238$	1.53513	−	1.88020i	0.0995079	−	0.121875i
$239$	−8.01789			−0.518634			−0.259317	−	0.965792i	$-0.583497\pi$
$239$	−8.01789			−0.518634			−0.259317	+	0.965792i	$0.583497\pi$
$240$	−12.8053	+	15.6836i	−0.826578	+	1.01237i
$241$	−8.44918	−	29.1699i	−0.544259	−	1.87900i	−0.471963	−	0.881618i	$-0.656454\pi$
$241$	−8.44918	−	29.1699i	−0.544259	−	1.87900i	−0.0722966	−	0.997383i	$-0.523033\pi$
$242$	−27.4267	−	24.2979i	−1.76305	−	1.56193i
$243$	−0.692724	−	0.721202i	−0.0444383	−	0.0462652i
$244$	−18.9560	+	6.32843i	−1.21353	+	0.405137i
$245$	−15.4464	−	11.6072i	−0.986834	−	0.741557i
$246$	1.21848	−	10.0351i	0.0776874	−	0.639813i
$247$	−0.773196	+	0.134712i	−0.0491973	+	0.00857154i
$248$	−0.472356	−	3.89021i	−0.0299947	−	0.247028i
$249$	−2.22881	+	3.86042i	−0.141245	+	0.244644i
$250$	53.8031	+	40.4304i	3.40280	+	2.55704i
$251$	−0.236237	−	5.86217i	−0.0149112	−	0.370017i	−0.989367	−	0.145439i	$-0.953541\pi$
$251$	−0.236237	−	5.86217i	−0.0149112	−	0.370017i	0.974456	−	0.224578i	$-0.0721004\pi$
$252$	0.853400	−	2.25023i	0.0537592	−	0.141751i
$253$	8.38057	−	41.0508i	0.526882	−	2.58084i
$254$	−0.163623	+	0.801478i	−0.0102666	+	0.0502892i
$255$	1.24475	−	3.28213i	0.0779492	−	0.205535i
$256$	−0.834717	−	20.7133i	−0.0521698	−	1.29458i
$257$	−22.1051	−	16.6109i	−1.37888	−	1.03616i	−0.993552	−	0.113376i	$-0.963834\pi$
$257$	−22.1051	−	16.6109i	−1.37888	−	1.03616i	−0.385323	−	0.922782i	$-0.625910\pi$
$258$	−6.43403	+	11.1441i	−0.400565	+	0.693800i
$259$	−1.35160	−	11.1314i	−0.0839844	−	0.691674i
$260$	6.81180	+	22.5527i	0.422450	+	1.39866i
$261$	−1.21849	+	10.0352i	−0.0754226	+	0.621161i
$262$	−14.0058	−	10.5246i	−0.865279	−	0.650215i
$263$	−2.11594	+	0.706405i	−0.130475	+	0.0435588i	−0.381155	−	0.924511i	$-0.624474\pi$
$263$	−2.11594	+	0.706405i	−0.130475	+	0.0435588i	0.250681	+	0.968070i	$0.419346\pi$
$264$	3.41465	+	3.55502i	0.210157	+	0.218797i
$265$	9.64826	+	8.54761i	0.592688	+	0.525075i
$266$	0.179464	+	0.619581i	0.0110036	+	0.0379889i
$267$	5.17077	−	6.33304i	0.316446	−	0.387576i
$268$	−6.73375			−0.411330
$269$	−3.73784	+	4.57802i	−0.227900	+	0.279127i	−0.875878	−	0.482532i	$-0.839717\pi$
$269$	−3.73784	+	4.57802i	−0.227900	+	0.279127i	0.647978	+	0.761659i	$0.275615\pi$
$270$	0.323962	−	8.03905i	0.0197157	−	0.489241i
$271$	−14.1658	−	6.03549i	−0.860512	−	0.366630i	−0.0837977	−	0.996483i	$-0.526705\pi$
$271$	−14.1658	−	6.03549i	−0.860512	−	0.366630i	−0.776715	+	0.629853i	$0.783115\pi$
$272$	1.37233	+	3.61854i	0.0832097	+	0.219406i
$273$	3.28600	+	4.64650i	0.198878	+	0.281219i
$274$	0.775698	−	2.04535i	0.0468616	−	0.123564i
$275$	51.1444	−	53.2470i	3.08412	−	3.21091i
$276$	3.21729	−	11.1074i	0.193658	−	0.668586i
$277$	−12.7705	−	1.03094i	−0.767305	−	0.0619432i	−0.309385	−	0.950937i	$-0.600123\pi$
$277$	−12.7705	−	1.03094i	−0.767305	−	0.0619432i	−0.457920	+	0.888994i	$0.651405\pi$
$278$	25.3572	−	13.3085i	1.52083	−	0.798191i
$279$	3.04226	+	3.16733i	0.182135	+	0.189623i
$280$	−5.55273	+	2.36580i	−0.331839	+	0.141383i
$281$	9.29632	+	24.5124i	0.554572	+	1.46229i	0.860111	+	0.510106i	$0.170394\pi$
$281$	9.29632	+	24.5124i	0.554572	+	1.46229i	−0.305539	+	0.952179i	$0.598837\pi$
$282$	−6.35714	+	1.03314i	−0.378562	+	0.0615223i
$283$	−0.788700	+	0.498744i	−0.0468833	+	0.0296472i	−0.557702	−	0.830041i	$-0.688317\pi$
$283$	−0.788700	+	0.498744i	−0.0468833	+	0.0296472i	0.510819	+	0.859689i	$0.329342\pi$
$284$	4.07311	−	14.0620i	0.241694	−	0.834426i
$285$	0.529912	+	0.767710i	0.0313893	+	0.0454752i
$286$	36.8393	−	6.41843i	2.17835	−	0.379530i
$287$	4.82785	−	6.99434i	0.284979	−	0.412863i
$288$	4.48125	+	5.48854i	0.264060	+	0.323415i
$289$	10.3272	+	12.6486i	0.607485	+	0.744034i
$290$	−65.0200	+	48.8594i	−3.81811	+	2.86912i
$291$	0.285625	+	2.35233i	0.0167436	+	0.137896i
$292$	−3.64147	−	1.21570i	−0.213101	−	0.0711435i
$293$	−5.48132	−	0.442498i	−0.320222	−	0.0258510i	−0.0806893	−	0.996739i	$-0.525712\pi$
$293$	−5.48132	−	0.442498i	−0.320222	−	0.0258510i	−0.239533	+	0.970888i	$0.576994\pi$
$294$	−6.33585	+	5.61307i	−0.369514	+	0.327361i
$295$	−3.64480	−	2.30483i	−0.212208	−	0.134192i
$296$	5.83180	+	2.48470i	0.338967	+	0.144420i
$297$	−5.45268	−	0.886147i	−0.316397	−	0.0514195i
$298$	3.77274	+	3.34236i	0.218549	+	0.193617i
$299$	17.5348	+	20.9838i	1.01406	+	1.21352i
$300$	15.2530	−	13.5129i	0.880630	−	0.780170i
$301$	−9.14375	+	5.78216i	−0.527037	+	0.333278i
$302$	−39.6259	+	3.19894i	−2.28022	+	0.184078i
$303$	2.06102	−	10.0955i	0.118402	−	0.579974i
$304$	−0.998565	−	0.246124i	−0.0572716	−	0.0141162i
$305$	−55.4417	+	9.01016i	−3.17459	+	0.515920i
$306$	−1.29975	−	0.821910i	−0.0743016	−	0.0469855i
$307$	−10.8232	−	5.68043i	−0.617710	−	0.324199i	0.126681	−	0.991944i	$-0.459568\pi$
$307$	−10.8232	−	5.68043i	−0.617710	−	0.324199i	−0.744391	+	0.667744i	$0.767260\pi$
$308$	−3.69882	−	12.7698i	−0.210760	−	0.727627i
$309$	0.322928	+	1.58181i	0.0183708	+	0.0899859i
$310$	−1.42276	+	35.3054i	−0.0808072	+	2.00521i
$311$	−0.607963	−	0.319084i	−0.0344744	−	0.0180936i	0.447398	−	0.894335i	$-0.352351\pi$
$311$	−0.607963	−	0.319084i	−0.0344744	−	0.0180936i	−0.481872	+	0.876241i	$0.660043\pi$
$312$	−3.20367	+	0.295387i	−0.181372	+	0.0167230i
$313$	−5.37319	+	2.82007i	−0.303711	+	0.159400i	−0.609693	−	0.792637i	$-0.708707\pi$
$313$	−5.37319	+	2.82007i	−0.303711	+	0.159400i	0.305982	+	0.952037i	$0.401015\pi$
$314$	18.4002	+	38.7777i	1.03839	+	2.18835i
$315$	3.38208	−	5.85793i	0.190559	−	0.330057i
$316$	3.70862	+	6.42352i	0.208626	+	0.361351i
$317$	1.70979	−	2.47706i	0.0960315	−	0.139126i	−0.772023	−	0.635595i	$-0.780755\pi$
$317$	1.70979	−	2.47706i	0.0960315	−	0.139126i	0.868054	+	0.496469i	$0.165370\pi$
$318$	4.51446	−	3.39239i	0.253158	−	0.190236i
$319$	27.9218	+	48.3620i	1.56332	+	2.70775i
$320$	−1.99044	+	16.3927i	−0.111269	+	0.916380i
$321$	4.54405	−	9.57639i	0.253624	−	0.534502i
$322$	15.5689	−	16.2090i	0.867622	−	0.903291i
$323$	0.177723	−	0.0143473i	0.00988876	−	0.000798303i
$324$	−1.48041	−	0.364889i	−0.0822451	−	0.0202716i
$325$	6.35285	+	47.7674i	0.352393	+	2.64966i
$326$	6.04202	−	1.48922i	0.334637	−	0.0824805i
$327$	−6.39191	+	2.13393i	−0.353474	+	0.118007i
$328$	2.05967	+	4.34066i	0.113726	+	0.239673i
$329$	−5.13610	−	1.71468i	−0.283162	−	0.0945334i
$330$	−25.2479	−	36.5779i	−1.38985	−	2.01355i
$331$	−5.54903	+	11.6943i	−0.305002	+	0.642779i	−0.996854	−	0.0792611i	$-0.974744\pi$
$331$	−5.54903	+	11.6943i	−0.305002	+	0.642779i	0.691852	+	0.722040i	$0.256795\pi$
$332$	0.273672	+	6.79111i	0.0150197	+	0.372710i
$333$	−6.89769	+	1.70013i	−0.377991	+	0.0931664i
$334$	19.8660	−	8.46411i	1.08702	−	0.463135i
$335$	−18.6811	−	3.03597i	−1.02066	−	0.165873i
$336$	1.49168	+	7.30674i	0.0813779	+	0.398616i
$337$	8.59200			0.468036			0.234018	−	0.972232i	$-0.424813\pi$
$337$	8.59200			0.468036			0.234018	+	0.972232i	$0.424813\pi$
$338$	−11.7187	+	21.4091i	−0.637412	+	1.16450i
$339$	3.05484			0.165916
$340$	−1.07056	−	5.24396i	−0.0580594	−	0.284394i
$341$	23.9467	+	3.89172i	1.29679	+	0.210749i
$342$	0.375969	−	0.160185i	0.0203301	−	0.00866183i
$343$	−17.6375	+	4.34724i	−0.952333	+	0.234729i
$344$	−0.246265	−	6.11101i	−0.0132777	−	0.329484i
$345$	13.9334	−	29.3641i	0.750150	−	1.58091i
$346$	−18.0306	−	26.1218i	−0.969330	−	1.40432i
$347$	6.68280	+	2.23105i	0.358751	+	0.119769i	0.490330	−	0.871537i	$-0.336876\pi$
$347$	6.68280	+	2.23105i	0.358751	+	0.119769i	−0.131578	+	0.991306i	$0.542005\pi$
$348$	6.60751	+	13.9250i	0.354200	+	0.746460i
$349$	22.1589	−	7.39771i	1.18614	−	0.395991i	0.345932	−	0.938260i	$-0.387563\pi$
$349$	22.1589	−	7.39771i	1.18614	−	0.395991i	0.840205	+	0.542269i	$0.182435\pi$
$350$	38.4540	−	9.47805i	2.05545	−	0.506623i
$351$	2.67139	−	2.42150i	0.142588	−	0.129250i
$352$	38.0050	+	9.36738i	2.02567	+	0.499283i
$353$	23.3939	−	1.88855i	1.24513	−	0.100518i	0.559726	−	0.828678i	$-0.310906\pi$
$353$	23.3939	−	1.88855i	1.24513	−	0.100518i	0.685407	+	0.728160i	$0.259624\pi$
$354$	−1.30872	+	1.36252i	−0.0695577	+	0.0724172i
$355$	17.6398	−	37.1750i	0.936222	−	1.97305i
$356$	1.50259	−	12.3749i	0.0796371	−	0.655871i
$357$	−0.646444	−	1.11967i	−0.0342135	−	0.0592595i
$358$	1.59438	−	1.19810i	0.0842657	−	0.0633216i
$359$	−9.54147	+	13.8232i	−0.503579	+	0.729561i	−0.989514	−	0.144434i	$-0.953864\pi$
$359$	−9.54147	+	13.8232i	−0.503579	+	0.729561i	0.485935	+	0.873995i	$0.338479\pi$
$360$	1.91196	+	3.31161i	0.100769	+	0.174537i
$361$	9.47631	−	16.4134i	0.498753	−	0.863866i
$362$	−18.6110	−	39.2219i	−0.978174	−	2.06146i
$363$	−17.2814	+	9.06999i	−0.907040	+	0.476051i
$364$	8.02107	+	3.31004i	0.420418	+	0.173493i
$365$	−9.55421	−	5.01444i	−0.500090	−	0.262468i
$366$	−0.990839	+	24.5874i	−0.0517920	+	1.28520i
$367$	−0.0597475	−	0.292663i	−0.00311880	−	0.0152769i	0.978201	−	0.207658i	$-0.0665841\pi$
$367$	−0.0597475	−	0.292663i	−0.00311880	−	0.0152769i	−0.981320	+	0.192381i	$0.938379\pi$
$368$	9.96950	+	34.4187i	0.519696	+	1.79420i
$369$	−4.76764	−	2.50225i	−0.248194	−	0.130262i
$370$	−48.3083	−	30.5483i	−2.51143	−	1.58813i
$371$	4.68613	−	0.761570i	0.243292	−	0.0395387i
$372$	6.50157	+	1.60249i	0.337091	+	0.0830855i
$373$	−4.46565	+	21.8742i	−0.231223	+	1.13260i	0.683946	+	0.729533i	$0.260262\pi$
$373$	−4.46565	+	21.8742i	−0.231223	+	1.13260i	−0.915169	+	0.403071i	$0.867943\pi$
$374$	−8.46768	+	0.683582i	−0.437853	+	0.0353472i
$375$	30.2979	−	19.1592i	1.56457	−	0.989377i
$376$	2.29125	−	2.02987i	0.118162	−	0.104683i
$377$	−36.0403	−	5.43657i	−1.85617	−	0.279998i
$378$	−2.21809	−	1.96506i	−0.114086	−	0.101072i
$379$	4.46872	+	0.726237i	0.229543	+	0.0373043i	0.274095	−	0.961703i	$-0.411622\pi$
$379$	4.46872	+	0.726237i	0.229543	+	0.0373043i	−0.0445519	+	0.999007i	$0.514186\pi$
$380$	1.30850	+	0.557499i	0.0671246	+	0.0285991i
$381$	0.368256	+	0.232871i	0.0188663	+	0.0119304i
$382$	9.02364	−	7.99425i	0.461690	−	0.409021i
$383$	23.0955	+	1.86446i	1.18013	+	0.0952696i	0.654915	−	0.755703i	$-0.272704\pi$
$383$	23.0955	+	1.86446i	1.18013	+	0.0952696i	0.525211	+	0.850972i	$0.323987\pi$
$384$	−6.57989	−	2.19669i	−0.335779	−	0.112099i
$385$	−4.50405	−	37.0942i	−0.229548	−	1.89050i
$386$	−18.6807	+	14.0376i	−0.950823	+	0.714497i
$387$	4.33485	+	5.30923i	0.220353	+	0.269883i
$388$	2.28502	+	2.79864i	0.116004	+	0.142079i
$389$	5.38871	−	7.80689i	0.273218	−	0.395825i	−0.662223	−	0.749307i	$-0.730387\pi$
$389$	5.38871	−	7.80689i	0.273218	−	0.395825i	0.935441	+	0.353482i	$0.115002\pi$
$390$	28.9394	+	2.00478i	1.46540	+	0.101516i
$391$	−3.52905	−	5.11271i	−0.178472	−	0.258561i
$392$	1.11929	−	3.86425i	0.0565328	−	0.195174i
$393$	−7.88700	+	4.98744i	−0.397846	+	0.251583i
$394$	−11.8396	+	1.92412i	−0.596471	+	0.0969359i
$395$	7.39252	+	19.4925i	0.371958	+	0.980773i
$396$	−7.74887	+	3.30148i	−0.389395	+	0.165906i
$397$	10.0212	+	10.4332i	0.502950	+	0.523626i	0.923477	−	0.383654i	$-0.125334\pi$
$397$	10.0212	+	10.4332i	0.502950	+	0.523626i	−0.420527	+	0.907280i	$0.638155\pi$
$398$	24.0172	−	12.6052i	1.20387	−	0.631841i
$399$	0.342468	+	0.0276469i	0.0171448	+	0.00138407i
$400$	−17.5680	+	60.6519i	−0.878401	+	3.03259i
$401$	1.10745	−	1.15298i	0.0553036	−	0.0575771i	−0.692976	−	0.720961i	$-0.743701\pi$
$401$	1.10745	−	1.15298i	0.0553036	−	0.0575771i	0.748279	+	0.663384i	$0.230880\pi$
$402$	−2.94019	+	7.75264i	−0.146643	+	0.386666i
$403$	−11.7320	+	10.6346i	−0.584414	+	0.529747i
$404$	−5.57096	−	14.6894i	−0.277166	−	0.730826i
$405$	−3.94251	−	1.67975i	−0.195905	−	0.0834673i
$406$	−1.20621	+	29.9317i	−0.0598630	+	1.48549i
$407$	−24.8201	+	30.3991i	−1.23029	+	1.50683i
$408$	0.730898			0.0361848
$409$	1.06227	−	1.30105i	0.0525260	−	0.0643327i	−0.747674	−	0.664066i	$-0.768829\pi$
$409$	1.06227	−	1.30105i	0.0525260	−	0.0643327i	0.800200	+	0.599733i	$0.204727\pi$
$410$	−12.0525	−	41.6101i	−0.595232	−	2.05498i
$411$	−0.872135	−	0.772644i	−0.0430193	−	0.0381117i
$412$	1.70518	+	1.77528i	0.0840082	+	0.0874618i
$413$	−1.50660	+	0.502976i	−0.0741348	+	0.0247498i
$414$	−11.3833	−	8.55397i	−0.559457	−	0.420405i
$415$	−2.30260	+	18.9636i	−0.113030	+	0.930886i
$416$	−20.2476	+	15.5791i	−0.992721	+	0.763826i
$417$	−1.83862	−	15.1424i	−0.0900376	−	0.741526i
$418$	1.12879	−	1.95513i	0.0552111	−	0.0956284i
$419$	−16.4274	−	12.3444i	−0.802529	−	0.603062i	0.118322	−	0.992975i	$-0.462248\pi$
$419$	−16.4274	−	12.3444i	−0.802529	−	0.603062i	−0.920851	+	0.389914i	$0.872505\pi$
$420$	−0.415280	−	10.3051i	−0.0202636	−	0.502835i
$421$	−7.35232	+	19.3865i	−0.358330	+	0.944839i	0.627727	+	0.778433i	$0.283985\pi$
$421$	−7.35232	+	19.3865i	−0.358330	+	0.944839i	−0.986057	+	0.166406i	$0.946784\pi$
$422$	6.42628	−	31.4780i	0.312827	−	1.53233i
$423$	−0.686192	+	3.36119i	−0.0333638	+	0.163427i
$424$	−0.951733	+	2.50951i	−0.0462202	+	0.121873i
$425$	−0.440806	−	10.9385i	−0.0213822	−	0.530594i
$426$	−14.4113	−	10.8294i	−0.698227	−	0.524684i
$427$	−10.3441	+	17.9165i	−0.500585	+	0.867039i
$428$	−1.94808	−	16.0438i	−0.0941638	−	0.775508i
$429$	3.76157	−	19.5594i	0.181610	−	0.944338i
$430$	−6.64702	+	54.7432i	−0.320548	+	2.63995i
$431$	−6.68051	−	5.02008i	−0.321789	−	0.241809i	0.427556	−	0.903989i	$-0.359375\pi$
$431$	−6.68051	−	5.02008i	−0.321789	−	0.241809i	−0.749344	+	0.662180i	$0.769631\pi$
$432$	4.48152	−	1.49615i	0.215617	−	0.0719837i
$433$	5.52890	+	5.75619i	0.265702	+	0.276625i	0.840666	−	0.541553i	$-0.182164\pi$
$433$	5.52890	+	5.75619i	0.265702	+	0.276625i	−0.574964	+	0.818178i	$0.694984\pi$
$434$	9.74126	+	8.63000i	0.467595	+	0.414253i
$435$	12.0526	+	41.6105i	0.577879	+	1.99507i
$436$	−6.49814	+	7.95878i	−0.311205	+	0.381156i
$437$	1.65093			0.0789747
$438$	−2.98964	+	3.66164i	−0.142850	+	0.174960i
$439$	0.0581666	−	1.44339i	0.00277614	−	0.0688892i	−0.997207	−	0.0746866i	$-0.976204\pi$
$439$	0.0581666	−	1.44339i	0.00277614	−	0.0688892i	0.999983	+	0.00579740i	$0.00184538\pi$
$440$	19.4338	+	8.27998i	0.926471	+	0.394732i
$441$	1.59878	+	4.21564i	0.0761325	+	0.200745i
$442$	3.09756	−	4.59875i	0.147336	−	0.218740i
$443$	−5.73133	+	15.1123i	−0.272304	+	0.718006i	0.727198	+	0.686428i	$0.240822\pi$
$443$	−5.73133	+	15.1123i	−0.272304	+	0.718006i	−0.999501	+	0.0315778i	$0.989947\pi$
$444$	−7.50343	+	7.81190i	−0.356097	+	0.370736i
$445$	9.74791	−	33.6537i	0.462095	−	1.59534i
$446$	45.4141	+	3.66621i	2.15042	+	0.173600i
$447$	2.37719	−	1.24764i	0.112437	−	0.0590116i
$448$	4.21321	+	4.38642i	0.199056	+	0.207239i
$449$	5.82196	−	2.48050i	0.274755	−	0.117062i	−0.250194	−	0.968196i	$-0.580494\pi$
$449$	5.82196	−	2.48050i	0.274755	−	0.117062i	0.524949	+	0.851133i	$0.324084\pi$
$450$	−8.89762	−	23.4611i	−0.419438	−	1.10597i
$451$	−29.3594	+	4.77136i	−1.38248	+	0.224675i
$452$	3.93669	−	2.48941i	0.185167	−	0.117092i
$453$	−5.89132	+	20.3392i	−0.276798	+	0.955618i
$454$	1.78038	+	2.57932i	0.0835573	+	0.121054i
$455$	20.7600	+	12.7992i	0.973246	+	0.600037i
$456$	−0.110338	+	0.159852i	−0.00516703	+	0.00748574i
$457$	17.1678	+	21.0268i	0.803076	+	0.983590i	0.999995	+	0.00317021i	$0.00100911\pi$
$457$	17.1678	+	21.0268i	0.803076	+	0.983590i	−0.196919	+	0.980420i	$0.563093\pi$
$458$	6.91652	+	8.47120i	0.323188	+	0.395833i
$459$	−0.654832	+	0.492074i	−0.0305649	+	0.0229680i
$460$	−5.97338	−	49.1952i	−0.278510	−	2.29374i
$461$	15.5407	+	5.18826i	0.723805	+	0.241641i	0.654615	−	0.755962i	$-0.272831\pi$
$461$	15.5407	+	5.18826i	0.723805	+	0.241641i	0.0691891	+	0.997604i	$0.477959\pi$
$462$	−16.3170	−	1.31725i	−0.759137	−	0.0612839i
$463$	19.0440	−	16.8716i	0.885052	−	0.784088i	−0.0922948	−	0.995732i	$-0.529420\pi$
$463$	19.0440	−	16.8716i	0.885052	−	0.784088i	0.977347	+	0.211644i	$0.0678818\pi$
$464$	−40.3672	−	25.5267i	−1.87400	−	1.18505i
$465$	17.3145	+	7.37700i	0.802939	+	0.342100i
$466$	−37.5685	−	6.10548i	−1.74033	−	0.282831i
$467$	21.4469	+	19.0003i	0.992446	+	0.879230i	0.992681	−	0.120770i	$-0.0385363\pi$
$467$	21.4469	+	19.0003i	0.992446	+	0.879230i	−0.000234891		1.00000i	$0.500075\pi$
$468$	1.46925	−	5.29747i	0.0679160	−	0.244876i
$469$	−5.21777	+	4.62254i	−0.240934	+	0.213449i
$470$	−23.3277	+	14.7515i	−1.07603	+	0.680437i
$471$	22.7879	−	1.83963i	1.05001	−	0.0847658i
$472$	0.179608	−	0.879776i	0.00826711	−	0.0404950i
$473$	36.7634	+	9.06135i	1.69038	+	0.416642i
$474$	9.01477	−	1.46504i	0.414062	−	0.0672916i
$475$	2.45885	+	1.55489i	0.112820	+	0.0713430i
$476$	−1.74549	−	0.916104i	−0.0800044	−	0.0419895i
$477$	−0.836836	−	2.88909i	−0.0383161	−	0.132282i
$478$	3.01098	+	14.7488i	0.137719	+	0.674592i
$479$	−0.0486568	+	1.20741i	−0.00222318	+	0.0551677i	−0.999920	−	0.0126667i	$-0.995968\pi$
$479$	−0.0486568	+	1.20741i	−0.00222318	+	0.0551677i	0.997697	+	0.0678345i	$0.0216090\pi$
$480$	26.8867	+	14.1112i	1.22721	+	0.644087i
$481$	−5.40900	−	25.0366i	−0.246629	−	1.14157i
$482$	−50.4846	+	26.4964i	−2.29951	+	1.20688i
$483$	−5.13195	−	10.8153i	−0.233512	−	0.492115i
$484$	−14.8789	+	25.7711i	−0.676315	+	1.17141i
$485$	5.07740	+	8.79432i	0.230553	+	0.399330i
$486$	−1.06650	+	1.54509i	−0.0483773	+	0.0700867i
$487$	−11.4701	+	8.61921i	−0.519759	+	0.390574i	−0.827994	−	0.560737i	$-0.810518\pi$
$487$	−11.4701	+	8.61921i	−0.519759	+	0.390574i	0.308235	+	0.951310i	$0.400262\pi$
$488$	−5.84773	−	10.1286i	−0.264714	−	0.458499i
$489$	0.399527	−	3.29040i	0.0180672	−	0.148797i
$490$	−15.5506	+	32.7722i	−0.702505	+	1.48050i
$491$	−13.3246	+	13.8724i	−0.601331	+	0.626052i	−0.950394	−	0.311047i	$-0.899320\pi$
$491$	−13.3246	+	13.8724i	−0.601331	+	0.626052i	0.349063	+	0.937099i	$0.386500\pi$
$492$	−8.18306	+	0.660605i	−0.368921	+	0.0297824i
$493$	8.03967	+	1.98160i	0.362088	+	0.0892468i
$494$	0.538161	+	1.37169i	0.0242130	+	0.0617153i
$495$	−22.9858	+	5.66548i	−1.03313	+	0.254644i
$496$	−19.6817	+	6.57071i	−0.883733	+	0.295033i
$497$	−6.49706	−	13.6923i	−0.291433	−	0.614182i
$498$	7.93816	+	2.65015i	0.355717	+	0.118756i
$499$	14.7564	+	21.3783i	0.660586	+	0.957024i	0.999867	+	0.0163391i	$0.00520112\pi$
$499$	14.7564	+	21.3783i	0.660586	+	0.957024i	−0.339280	+	0.940685i	$0.610183\pi$
$500$	23.4311	−	49.3800i	1.04787	−	2.20834i
$501$	−0.463135	−	11.4926i	−0.0206914	−	0.513451i
$502$	−10.6946	+	2.63599i	−0.477325	+	0.117650i
$503$	19.8340	−	8.45047i	0.884353	−	0.376788i	0.0984535	−	0.995142i	$-0.468610\pi$
$503$	19.8340	−	8.45047i	0.884353	−	0.376788i	0.785900	+	0.618354i	$0.212200\pi$
$504$	1.39019	+	0.225927i	0.0619238	+	0.0100636i
$505$	−8.83236	−	43.2638i	−0.393035	−	1.92521i
$506$	−78.6593			−3.49683
$507$	8.44901	+	9.87999i	0.375234	+	0.438786i
$508$	0.664332			0.0294750
$509$	−5.77845	−	28.3047i	−0.256125	−	1.25459i	−0.880720	−	0.473637i	$-0.842941\pi$
$509$	−5.77845	−	28.3047i	−0.256125	−	1.25459i	0.624595	−	0.780949i	$-0.285264\pi$
$510$	−6.50487	−	1.05714i	−0.288040	−	0.0468111i
$511$	−3.65620	+	1.55776i	−0.161741	+	0.0689113i
$512$	−24.3176	+	5.99375i	−1.07470	+	0.264889i
$513$	−0.00876495	−	0.217500i	−0.000386982	−	0.00960285i
$514$	−22.2542	+	46.8998i	−0.981591	+	2.06866i
$515$	3.93019	+	5.69386i	0.173185	+	0.250901i
$516$	9.91276	+	3.30936i	0.436385	+	0.145687i
$517$	8.12413	+	17.1212i	0.357299	+	0.752991i
$518$	−19.9685	+	6.66646i	−0.877365	+	0.292908i
$519$	−16.4151	+	4.04595i	−0.720542	+	0.177598i
$520$	−12.1343	+	6.54592i	−0.532126	+	0.287058i
$521$	−6.87562	−	1.69469i	−0.301226	−	0.0742456i	0.0858057	−	0.996312i	$-0.472654\pi$
$521$	−6.87562	−	1.69469i	−0.301226	−	0.0742456i	−0.387032	+	0.922066i	$0.626500\pi$
$522$	18.9171	−	1.52715i	0.827978	−	0.0668413i
$523$	10.2451	−	10.6663i	0.447988	−	0.466405i	−0.458465	−	0.888713i	$-0.651600\pi$
$523$	10.2451	−	10.6663i	0.447988	−	0.466405i	0.906452	+	0.422308i	$0.138780\pi$
$524$	−6.09948	+	12.8544i	−0.266457	+	0.561546i
$525$	2.54276	−	20.9415i	0.110975	−	0.913962i
$526$	2.09402	+	3.62696i	0.0913038	+	0.158143i
$527$	2.87585	−	2.16106i	0.125274	−	0.0941372i
$528$	14.8266	−	21.4800i	0.645243	−	0.934796i
$529$	−17.2610	−	29.8970i	−0.750480	−	1.29987i
$530$	12.0999	−	20.9577i	0.525587	−	0.910344i
$531$	0.431390	+	0.909136i	0.0187207	+	0.0394531i
$532$	0.463860	−	0.243452i	0.0201109	−	0.0105550i
$533$	9.51475	−	16.9222i	0.412129	−	0.732983i
$534$	−13.5913	−	7.13327i	−0.588154	−	0.308687i
$535$	1.82907	−	45.3879i	0.0790775	−	1.96229i
$536$	−0.788258	−	3.86114i	−0.0340476	−	0.166776i
$537$	−0.295547	−	1.02035i	−0.0127538	−	0.0440313i
$538$	9.82486	+	5.15648i	0.423580	+	0.222312i
$539$	21.0509	+	13.3118i	0.906725	+	0.573378i
$540$	−6.44946	+	1.04814i	−0.277540	+	0.0451047i
$541$	21.2724	+	5.24318i	0.914573	+	0.225422i	0.668398	−	0.743804i	$-0.266980\pi$
$541$	21.2724	+	5.24318i	0.914573	+	0.225422i	0.246175	+	0.969226i	$0.420826\pi$
$542$	−5.78244	+	28.3243i	−0.248377	+	1.21663i
$543$	−23.0490	+	1.86071i	−0.989126	+	0.0798505i
$544$	4.90538	−	3.10198i	0.210317	−	0.132996i
$545$	−21.6157	+	19.1499i	−0.925916	+	0.820290i
$546$	7.31315	−	7.78945i	0.312974	−	0.333358i
$547$	−15.9927	−	14.1683i	−0.683800	−	0.605794i	0.248003	−	0.968759i	$-0.420226\pi$
$547$	−15.9927	−	14.1683i	−0.683800	−	0.605794i	−0.931803	+	0.362966i	$0.881764\pi$
$548$	−1.75353	−	0.284977i	−0.0749073	−	0.0121736i
$549$	12.0582	+	5.13750i	0.514630	+	0.219263i
$550$	−117.153	−	74.0832i	−4.99543	−	3.15892i
$551$	−1.64707	+	1.45918i	−0.0701675	+	0.0621630i
$552$	6.74561	+	0.544562i	0.287112	+	0.0231781i
$553$	7.28326	+	2.43151i	0.309716	+	0.103398i
$554$	2.89934	+	23.8782i	0.123181	+	1.01449i
$555$	−24.3384	+	18.2891i	−1.03311	+	0.776331i
$556$	−14.7091	−	18.0153i	−0.623803	−	0.764020i
$557$	5.72995	+	7.01791i	0.242786	+	0.297359i	0.881595	−	0.472007i	$-0.156470\pi$
$557$	5.72995	+	7.01791i	0.242786	+	0.297359i	−0.638809	+	0.769365i	$0.720573\pi$
$558$	4.68378	−	6.78562i	0.198280	−	0.287258i
$559$	−19.5862	+	15.0701i	−0.828406	+	0.637397i
$560$	18.1545	+	26.3013i	0.767166	+	1.11143i
$561$	−1.25892	+	4.34629i	−0.0531516	+	0.183500i
$562$	41.5990	−	26.3056i	1.75475	−	1.10964i
$563$	−38.8009	+	6.30577i	−1.63526	+	0.265756i	−0.907494	−	0.420065i	$-0.862007\pi$
$563$	−38.8009	+	6.30577i	−1.63526	+	0.265756i	−0.727770	+	0.685821i	$0.759443\pi$
$564$	1.85479	+	4.89067i	0.0781006	+	0.205934i
$565$	12.0437	−	5.13135i	0.506683	−	0.215878i
$566$	1.21361	+	1.26350i	0.0510119	+	0.0531091i
$567$	−1.39761	+	0.733522i	−0.0586941	+	0.0308050i
$568$	8.53997	+	0.689417i	0.358329	+	0.0289273i
$569$	−3.74764	+	12.9384i	−0.157109	+	0.542405i	0.842881	+	0.538100i	$0.180858\pi$
$569$	−3.74764	+	12.9384i	−0.157109	+	0.542405i	−0.999991	+	0.00430514i	$0.998630\pi$
$570$	1.21319	−	1.26306i	0.0508149	−	0.0529039i
$571$	0.0763045	−	0.201199i	0.00319325	−	0.00841990i	−0.933410	−	0.358811i	$-0.883182\pi$
$571$	0.0763045	−	0.201199i	0.00319325	−	0.00841990i	0.936603	+	0.350391i	$0.113951\pi$
$572$	−11.0917	−	28.2711i	−0.463768	−	1.18207i
$573$	−2.27702	−	6.00400i	−0.0951238	−	0.250821i
$574$	−14.6790	−	6.25413i	−0.612689	−	0.261042i
$575$	4.08152	−	101.282i	0.170211	−	4.22375i
$576$	2.43701	−	2.98479i	0.101542	−	0.124366i
$577$	3.63782			0.151444			0.0757222	−	0.997129i	$-0.475874\pi$
$577$	3.63782			0.151444			0.0757222	+	0.997129i	$0.475874\pi$
$578$	19.3886	−	23.7467i	0.806459	−	0.987733i
$579$	3.46281	+	11.9550i	0.143909	+	0.496832i
$580$	49.4407	+	43.8006i	2.05291	+	1.81872i
$581$	4.87397	+	5.07434i	0.202206	+	0.210519i
$582$	4.21981	−	1.40878i	0.174917	−	0.0583958i
$583$	−13.2836	−	9.98194i	−0.550148	−	0.413410i
$584$	0.270811	−	2.23033i	0.0112062	−	0.0922918i
$585$	6.46447	−	14.0341i	0.267273	−	0.580237i
$586$	1.24445	+	10.2490i	0.0514077	+	0.423380i
$587$	−5.16333	+	8.94316i	−0.213114	+	0.369124i	−0.952687	−	0.303952i	$-0.901694\pi$
$587$	−5.16333	+	8.94316i	−0.213114	+	0.369124i	0.739574	+	0.673076i	$0.235027\pi$
$588$	5.49568	+	4.12974i	0.226638	+	0.170307i
$589$	0.0384933	+	0.955202i	0.00158609	+	0.0393584i
$590$	−2.87095	+	7.57008i	−0.118195	+	0.311655i
$591$	−1.27797	+	6.25993i	−0.0525688	+	0.257499i
$592$	6.71379	−	32.8863i	0.275935	−	1.35162i
$593$	−7.15769	+	18.8733i	−0.293931	+	0.775033i	0.703967	+	0.710233i	$0.251410\pi$
$593$	−7.15769	+	18.8733i	−0.293931	+	0.775033i	−0.997898	+	0.0648002i	$0.979359\pi$
$594$	0.417610	+	10.3629i	0.0171347	+	0.425194i
$595$	−4.42938	−	3.32847i	−0.181587	−	0.136454i
$596$	2.04671	−	3.54500i	0.0838364	−	0.145209i
$597$	−1.74145	−	14.3422i	−0.0712730	−	0.586986i
$598$	32.0144	−	40.1350i	1.30916	−	1.64124i
$599$	1.97094	−	16.2322i	0.0805306	−	0.663229i	−0.895418	−	0.445227i	$-0.853123\pi$
$599$	1.97094	−	16.2322i	0.0805306	−	0.663229i	0.975948	−	0.218002i	$-0.0699539\pi$
$600$	9.53386	+	7.16423i	0.389218	+	0.292479i
$601$	−5.16562	+	1.72454i	−0.210710	+	0.0703453i	−0.420064	−	0.907495i	$-0.637992\pi$
$601$	−5.16562	+	1.72454i	−0.210710	+	0.0703453i	0.209354	+	0.977840i	$0.432864\pi$
$602$	14.0700	+	14.6484i	0.573449	+	0.597023i
$603$	3.30572	+	2.92861i	0.134619	+	0.119262i
$604$	8.98259	+	31.0115i	0.365496	+	1.26184i
$605$	−52.8969	+	64.7870i	−2.15057	+	2.63396i
$606$	−19.3445			−0.785818
$607$	10.2062	−	12.5003i	0.414255	−	0.507370i	−0.524758	−	0.851251i	$-0.675844\pi$
$607$	10.2062	−	12.5003i	0.414255	−	0.507370i	0.939013	+	0.343881i	$0.111742\pi$
$608$	−0.0621048	+	1.54112i	−0.00251868	+	0.0625005i
$609$	14.6791	+	6.25418i	0.594828	+	0.253432i
$610$	37.3942	+	98.6005i	1.51405	+	3.99222i
$611$	−12.0424	−	2.82311i	−0.487185	−	0.114211i
$612$	−0.442870	+	1.16775i	−0.0179020	+	0.0472036i
$613$	19.4588	−	20.2587i	0.785932	−	0.818242i	−0.200964	−	0.979599i	$-0.564408\pi$
$613$	19.4588	−	20.2587i	0.785932	−	0.818242i	0.986896	+	0.161357i	$0.0515870\pi$
$614$	−6.38460	+	22.0422i	−0.257661	+	0.889550i
$615$	−22.9996	−	1.85672i	−0.927435	−	0.0748703i
$616$	6.88924	−	3.61575i	0.277575	−	0.145683i
$617$	23.0139	+	23.9600i	0.926505	+	0.964594i	0.999464	−	0.0327413i	$-0.0104238\pi$
$617$	23.0139	+	23.9600i	0.926505	+	0.964594i	−0.0729591	+	0.997335i	$0.523244\pi$
$618$	2.78844	−	1.18804i	0.112167	−	0.0477901i
$619$	−13.1155	−	34.5829i	−0.527158	−	1.39000i	−0.889062	−	0.457787i	$-0.848642\pi$
$619$	−13.1155	−	34.5829i	−0.527158	−	1.39000i	0.361904	−	0.932215i	$-0.382127\pi$
$620$	28.3243	−	4.60315i	1.13753	−	0.184867i
$621$	−6.41020	+	4.05357i	−0.257232	+	0.162664i
$622$	−0.358639	+	1.23816i	−0.0143801	+	0.0496458i
$623$	−7.33076	−	10.6204i	−0.293701	−	0.425499i
$624$	4.92549	+	16.3074i	0.197177	+	0.652820i
$625$	49.3063	−	71.4324i	1.97225	−	2.85730i
$626$	7.20528	+	8.82486i	0.287981	+	0.352712i
$627$	−0.760510	−	0.931456i	−0.0303719	−	0.0371988i
$628$	27.8671	−	20.9408i	1.11202	−	0.835628i
$629$	0.701410	+	5.77663i	0.0279670	+	0.230329i
$630$	−12.0456	−	4.02142i	−0.479910	−	0.160217i
$631$	9.22709	+	0.744887i	0.367325	+	0.0296535i	0.262751	−	0.964864i	$-0.415370\pi$
$631$	9.22709	+	0.744887i	0.367325	+	0.0296535i	0.104573	+	0.994517i	$0.466652\pi$
$632$	−3.24912	+	2.87847i	−0.129243	+	0.114499i
$633$	−14.4633	−	9.14601i	−0.574863	−	0.363521i
$634$	−5.19859	−	2.21491i	−0.206462	−	0.0879654i
$635$	1.84302	+	0.299520i	0.0731380	+	0.0118861i
$636$	−3.43276	−	3.04116i	−0.136118	−	0.120590i
$637$	−15.3599	+	5.32307i	−0.608581	+	0.210908i
$638$	78.4754	−	69.5232i	3.10687	−	2.75245i
$639$	−8.11534	+	5.13183i	−0.321038	+	0.203012i
$640$	−29.6312	+	2.39208i	−1.17128	+	0.0945551i
$641$	1.10476	−	5.41146i	0.0436353	−	0.213740i	−0.952127	−	0.305702i	$-0.901109\pi$
$641$	1.10476	−	5.41146i	0.0436353	−	0.213740i	0.995762	+	0.0919624i	$0.0293139\pi$
$642$	−19.3220	−	4.76245i	−0.762579	−	0.187959i
$643$	23.1461	−	3.76161i	0.912795	−	0.148344i	0.314164	−	0.949369i	$-0.398276\pi$
$643$	23.1461	−	3.76161i	0.912795	−	0.148344i	0.598631	+	0.801025i	$0.295712\pi$
$644$	−15.4269	−	9.75540i	−0.607907	−	0.384417i
$645$	26.0084	+	13.6502i	1.02408	+	0.537478i
$646$	−0.0931322	−	0.321530i	−0.00366424	−	0.0126504i
$647$	2.97858	+	14.5900i	0.117100	+	0.573593i	0.995426	+	0.0955319i	$0.0304552\pi$
$647$	2.97858	+	14.5900i	0.117100	+	0.573593i	−0.878326	+	0.478061i	$0.841340\pi$
$648$	0.0359296	−	0.891584i	0.00141145	−	0.0350247i
$649$	4.92223	+	2.58339i	0.193215	+	0.101407i
$650$	85.4815	−	29.6242i	3.35286	−	1.16196i
$651$	6.13793	−	3.22143i	0.240564	−	0.126258i
$652$	−2.16652	−	4.56584i	−0.0848474	−	0.178812i
$653$	−11.8179	+	20.4692i	−0.462470	+	0.801021i	−0.999083	−	0.0428071i	$-0.986370\pi$
$653$	−11.8179	+	20.4692i	−0.462470	+	0.801021i	0.536614	+	0.843828i	$0.319703\pi$
$654$	6.32571	+	10.9564i	0.247355	+	0.428431i
$655$	−22.7169	+	32.9112i	−0.887624	+	1.28595i
$656$	20.3374	−	15.2826i	0.794043	−	0.596685i
$657$	1.25893	+	2.18054i	0.0491157	+	0.0850709i
$658$	−1.22535	+	10.0917i	−0.0477691	+	0.393414i
$659$	−8.30710	+	17.5068i	−0.323599	+	0.681970i	−0.998431	−	0.0560017i	$-0.982165\pi$
$659$	−8.30710	+	17.5068i	−0.323599	+	0.681970i	0.674832	+	0.737971i	$0.264216\pi$
$660$	−25.0043	+	26.0323i	−0.973292	+	1.01330i
$661$	−16.3034	+	1.31615i	−0.634129	+	0.0511922i	−0.393352	−	0.919388i	$-0.628684\pi$
$661$	−16.3034	+	1.31615i	−0.634129	+	0.0511922i	−0.240778	+	0.970580i	$0.577402\pi$
$662$	23.5953	+	5.81573i	0.917059	+	0.226035i
$663$	−1.70526	−	2.41129i	−0.0662269	−	0.0936467i
$664$	−3.86199	+	0.951896i	−0.149874	+	0.0369407i
$665$	1.39662	−	0.466261i	0.0541587	−	0.0180808i
$666$	5.71766	+	12.0497i	0.221555	+	0.466917i
$667$	72.7234	+	24.2786i	2.81586	+	0.940072i
$668$	−9.96224	−	14.4328i	−0.385451	−	0.558422i
$669$	10.4036	−	21.9252i	0.402228	−	0.847677i
$670$	1.43075	+	35.5036i	0.0552746	+	1.37162i
$671$	70.3019	−	17.3279i	2.71397	−	0.668934i
$672$	10.2890	−	4.38373i	0.396907	−	0.169106i
$673$	−12.8787	−	2.09299i	−0.496437	−	0.0806789i	−0.0929623	−	0.995670i	$-0.529634\pi$
$673$	−12.8787	−	2.09299i	−0.496437	−	0.0806789i	−0.403475	+	0.914991i	$0.632198\pi$
$674$	−3.22658	−	15.8048i	−0.124283	−	0.608779i
$675$	−13.3649			−0.514417
$676$	18.9393	+	5.84693i	0.728436	+	0.224882i
$677$	−51.0381			−1.96156			−0.980778	−	0.195128i	$-0.937488\pi$
$677$	−51.0381			−1.96156			−0.980778	+	0.195128i	$0.937488\pi$
$678$	−1.14719	−	5.61932i	−0.0440576	−	0.215809i
$679$	3.69177	+	0.599972i	0.141677	+	0.0230248i
$680$	2.88157	−	1.22772i	0.110503	−	0.0470810i
$681$	1.62086	−	0.399506i	0.0621115	−	0.0153091i
$682$	−1.83403	−	45.5110i	−0.0702287	−	1.74271i
$683$	−5.64955	+	11.9062i	−0.216174	+	0.455577i	−0.982350	−	0.187054i	$-0.940106\pi$
$683$	−5.64955	+	11.9062i	−0.216174	+	0.455577i	0.766176	+	0.642631i	$0.222157\pi$
$684$	−0.188538	−	0.273144i	−0.00720892	−	0.0104439i
$685$	−4.73625	−	1.58119i	−0.180963	−	0.0604143i
$686$	14.6201	+	30.8112i	0.558198	+	1.17638i
$687$	5.52531	−	1.84462i	0.210804	−	0.0703766i
$688$	−31.4424	+	7.74986i	−1.19873	+	0.295461i
$689$	10.4996	−	2.71512i	0.400002	−	0.103438i
$690$	−59.2471	−	14.6031i	−2.25550	−	0.555931i
$691$	35.1703	−	2.83924i	1.33794	−	0.108010i	0.609320	−	0.792925i	$-0.291443\pi$
$691$	35.1703	−	2.83924i	1.33794	−	0.108010i	0.728623	+	0.684915i	$0.240161\pi$
$692$	−17.8566	+	18.5907i	−0.678807	+	0.706713i
$693$	−3.73797	+	7.87760i	−0.141994	+	0.299245i
$694$	1.59436	−	13.1307i	0.0605210	−	0.498435i
$695$	−32.6842	−	56.6106i	−1.23978	−	2.14736i
$696$	−7.21115	+	5.41883i	−0.273338	+	0.205400i
$697$	−2.50540	+	3.62970i	−0.0948987	+	0.137485i
$698$	−21.9293	−	37.9827i	−0.830038	−	1.43767i
$699$	−10.1366	+	17.5571i	−0.383402	+	0.664071i
$700$	−13.7886	−	29.0589i	−0.521161	−	1.09832i
$701$	−33.1442	+	17.3954i	−1.25184	+	0.657015i	−0.954629	−	0.297797i	$-0.903748\pi$
$701$	−33.1442	+	17.3954i	−1.25184	+	0.657015i	−0.297209	+	0.954813i	$0.596056\pi$
$702$	−5.45751	−	4.00462i	−0.205980	−	0.151144i
$703$	−1.36927	−	0.718648i	−0.0516430	−	0.0271043i
$704$	0.857122	−	21.2693i	0.0323040	−	0.801616i
$705$	2.94063	+	14.4042i	0.110751	+	0.542492i
$706$	−12.2591	−	42.3235i	−0.461379	−	1.59287i
$707$	−14.4007	−	7.55805i	−0.541592	−	0.284250i
$708$	1.29678	+	0.820037i	0.0487362	+	0.0308189i
$709$	−34.9774	+	5.68437i	−1.31360	+	0.213481i	−0.776543	−	0.630064i	$-0.783029\pi$
$709$	−34.9774	+	5.68437i	−1.31360	+	0.213481i	−0.537059	+	0.843545i	$0.680465\pi$
$710$	−75.0071	−	18.4876i	−2.81497	−	0.693827i
$711$	0.973058	−	4.76635i	0.0364925	−	0.178752i
$712$	7.27170	−	0.587033i	0.272519	−	0.0220000i
$713$	28.1519	−	17.8022i	1.05430	−	0.666697i
$714$	−1.81686	+	1.60960i	−0.0679942	+	0.0602376i
$715$	−18.0249	−	83.4317i	−0.674092	−	3.12017i
$716$	−1.21236	−	1.07405i	−0.0453079	−	0.0401393i
$717$	7.91406	+	1.28616i	0.295556	+	0.0480325i
$718$	29.0107	+	12.3603i	1.08267	+	0.461282i
$719$	10.4345	+	6.59837i	0.389140	+	0.246078i	0.714681	−	0.699451i	$-0.246572\pi$
$719$	10.4345	+	6.59837i	0.389140	+	0.246078i	−0.325541	+	0.945528i	$0.605546\pi$
$720$	15.1553	−	13.4264i	0.564805	−	0.500373i
$721$	2.53997	+	0.205048i	0.0945935	+	0.00763638i
$722$	−33.7509	−	11.2677i	−1.25608	−	0.419341i
$723$	3.66058	+	30.1475i	0.136138	+	1.12120i
$724$	−28.1863	+	21.1807i	−1.04754	+	0.787173i
$725$	85.4462	+	104.653i	3.17339	+	3.88670i
$726$	23.1738	+	28.3828i	0.860061	+	1.05338i
$727$	9.15624	−	13.2651i	0.339586	−	0.491976i	−0.615568	−	0.788084i	$-0.711073\pi$
$727$	9.15624	−	13.2651i	0.339586	−	0.491976i	0.955154	+	0.296108i	$0.0956888\pi$
$728$	−0.959028	+	4.98676i	−0.0355439	+	0.184822i
$729$	0.568065	+	0.822984i	0.0210394	+	0.0304809i
$730$	−5.63604	+	19.4579i	−0.208599	+	0.720168i
$731$	4.74513	−	3.00064i	0.175505	−	0.110983i
$732$	19.7257	−	3.20573i	0.729081	−	0.118487i
$733$	−1.35124	−	3.56294i	−0.0499093	−	0.131600i	0.907743	−	0.419526i	$-0.137804\pi$
$733$	−1.35124	−	3.56294i	−0.0499093	−	0.131600i	−0.957653	+	0.287926i	$0.907034\pi$
$734$	−0.515911	+	0.219809i	−0.0190426	+	0.00811330i
$735$	13.3844	+	13.9347i	0.493692	+	0.513988i
$736$	47.5839	−	24.9740i	1.75397	−	0.920553i
$737$	24.3180	+	1.96315i	0.895766	+	0.0723137i
$738$	−2.81244	+	9.70967i	−0.103527	+	0.357418i
$739$	−28.1448	+	29.3019i	−1.03532	+	1.07789i	−0.0384195	+	0.999262i	$0.512232\pi$
$739$	−28.1448	+	29.3019i	−1.03532	+	1.07789i	−0.996904	+	0.0786246i	$0.974947\pi$
$740$	−16.4603	+	43.4024i	−0.605094	+	1.59550i
$741$	0.784793	−	0.00893849i	0.0288301	−	0.000328364i
$742$	−3.16069	−	8.33405i	−0.116033	−	0.305953i
$743$	9.74312	+	4.15115i	0.357440	+	0.152291i	0.563219	−	0.826307i	$-0.309563\pi$
$743$	9.74312	+	4.15115i	0.357440	+	0.152291i	−0.205779	+	0.978598i	$0.565973\pi$
$744$	−0.157793	+	3.91560i	−0.00578498	+	0.143553i
$745$	7.27636	−	8.91193i	0.266585	−	0.326508i
$746$	41.9142			1.53459
$747$	2.81921	−	3.45290i	0.103149	−	0.126335i
$748$	1.91949	+	6.62686i	0.0701836	+	0.242302i
$749$	−12.5232	−	11.0946i	−0.457587	−	0.405386i
$750$	−46.6208	−	48.5374i	−1.70235	−	1.77234i
$751$	24.8628	−	8.30041i	0.907255	−	0.302886i	0.175521	−	0.984476i	$-0.443839\pi$
$751$	24.8628	−	8.30041i	0.907255	−	0.302886i	0.731735	+	0.681589i	$0.238711\pi$
$752$	−12.9574	−	9.73688i	−0.472509	−	0.355068i
$753$	−0.707180	+	5.82415i	−0.0257711	+	0.212244i
$754$	3.53385	+	68.3371i	0.128695	+	2.48869i
$755$	10.9381	+	90.0834i	0.398078	+	3.27847i
$756$	−1.20331	+	2.08420i	−0.0437640	+	0.0758015i
$757$	22.9188	+	17.2224i	0.832999	+	0.625958i	0.929272	−	0.369397i	$-0.120436\pi$
$757$	22.9188	+	17.2224i	0.832999	+	0.625958i	−0.0962725	+	0.995355i	$0.530692\pi$
$758$	−0.342250	−	8.49285i	−0.0124311	−	0.308474i
$759$	−14.8571	+	39.1748i	−0.539277	+	1.42196i
$760$	−0.166497	+	0.815556i	−0.00603948	+	0.0295833i
$761$	5.54141	−	27.1436i	0.200876	−	0.983955i	−0.746880	−	0.664959i	$-0.768449\pi$
$761$	5.54141	−	27.1436i	0.200876	−	0.983955i	0.947756	−	0.318996i	$-0.103346\pi$
$762$	0.290070	−	0.764852i	0.0105081	−	0.0277077i
$763$	0.428286	+	10.6278i	0.0155050	+	0.384752i
$764$	−7.82705	−	5.88165i	−0.283173	−	0.212791i
$765$	−1.75512	+	3.03996i	−0.0634565	+	0.109910i
$766$	−5.24348	−	43.1839i	−0.189455	−	1.56030i
$767$	−3.32149	+	1.46007i	−0.119932	+	0.0527201i
$768$	−2.49874	+	20.5790i	−0.0901654	+	0.742579i
$769$	−5.40229	−	4.05956i	−0.194811	−	0.146391i	0.498861	−	0.866682i	$-0.333752\pi$
$769$	−5.40229	−	4.05956i	−0.194811	−	0.146391i	−0.693672	+	0.720291i	$0.744008\pi$
$770$	−66.5427	+	22.2152i	−2.39803	+	0.800581i
$771$	19.1542	+	19.9417i	0.689823	+	0.718181i
$772$	14.2047	+	12.5842i	0.511237	+	0.452916i
$773$	0.0170469	+	0.0588526i	0.000613134	+	0.00211678i	0.960824	−	0.277159i	$-0.0893928\pi$
$773$	0.0170469	+	0.0588526i	0.000613134	+	0.00211678i	−0.960211	+	0.279276i	$0.909906\pi$
$774$	8.13835	−	9.96767i	0.292527	−	0.358280i
$775$	58.6953			2.10840
$776$	−1.33726	+	1.63784i	−0.0480047	+	0.0587951i
$777$	−0.451510	+	11.2041i	−0.0161978	+	0.401945i
$778$	−16.3843	−	6.98068i	−0.587404	−	0.250270i
$779$	−0.415617	−	1.09589i	−0.0148910	−	0.0392644i
$780$	−3.10589	−	23.3533i	−0.111209	−	0.836182i
$781$	−18.8091	+	49.5955i	−0.673042	+	1.77467i
$782$	−8.07945	+	8.41160i	−0.288921	+	0.300798i
$783$	2.81246	−	9.70975i	0.100509	−	0.346998i
$784$	−21.2327	−	1.71408i	−0.758312	−	0.0612173i
$785$	86.7515	−	45.5307i	3.09629	−	1.62506i
$786$	12.1361	+	12.6350i	0.432881	+	0.450677i
$787$	1.95194	−	0.831646i	0.0695793	−	0.0296450i	−0.356897	−	0.934144i	$-0.616165\pi$
$787$	1.95194	−	0.831646i	0.0695793	−	0.0296450i	0.426476	+	0.904499i	$0.359755\pi$
$788$	3.45438	+	9.10845i	0.123057	+	0.324475i
$789$	2.20186	−	0.357836i	0.0783882	−	0.0127393i
$790$	33.0799	−	20.9185i	1.17693	−	0.744246i
$791$	1.34150	−	4.63140i	0.0476983	−	0.164674i
$792$	−2.80016	−	4.05673i	−0.0994994	−	0.144150i
$793$	−19.7716	+	42.9231i	−0.702108	+	1.52425i
$794$	15.4283	−	22.3518i	0.547532	−	0.793236i
$795$	−8.15218	−	9.98461i	−0.289128	−	0.354118i
$796$	−13.9317	−	17.0633i	−0.493797	−	0.604792i
$797$	28.5595	−	21.4610i	1.01163	−	0.760189i	0.0406051	−	0.999175i	$-0.487071\pi$
$797$	28.5595	−	21.4610i	1.01163	−	0.760189i	0.971023	+	0.238986i	$0.0768150\pi$
$798$	−0.0777520	−	0.640345i	−0.00275239	−	0.0226680i
$799$	2.66536	+	0.889829i	0.0942938	+	0.0314799i
$800$	94.3914	+	7.62007i	3.33724	+	0.269410i
$801$	−6.11970	+	5.42158i	−0.216229	+	0.191562i
$802$	−2.53677	−	1.60416i	−0.0895765	−	0.0566448i
$803$	12.7962	+	5.45196i	0.451569	+	0.192396i
$804$	6.64655	+	1.08017i	0.234406	+	0.0380947i
$805$	−38.3998	−	34.0193i	−1.35341	−	1.19902i
$806$	23.9679	+	17.5872i	0.844234	+	0.619483i
$807$	4.42380	−	3.91914i	0.155725	−	0.137960i
$808$	7.77079	−	4.91395i	0.273375	−	0.172872i
$809$	3.83418	−	0.309527i	0.134803	−	0.0108824i	−0.0128811	−	0.999917i	$-0.504100\pi$
$809$	3.83418	−	0.309527i	0.134803	−	0.0108824i	0.147684	+	0.989035i	$0.452818\pi$
$810$	−1.60932	+	7.88298i	−0.0565458	+	0.276980i
$811$	−43.7433	−	10.7818i	−1.53604	−	0.378599i	−0.621601	−	0.783334i	$-0.713518\pi$
$811$	−43.7433	−	10.7818i	−1.53604	−	0.378599i	−0.914434	+	0.404735i	$0.867364\pi$
$812$	24.0132	−	3.90253i	0.842698	−	0.136952i
$813$	13.0142	+	8.22969i	0.456428	+	0.288628i
$814$	65.2394	+	34.2403i	2.28664	+	1.20012i
$815$	−3.95190	−	13.6435i	−0.138429	−	0.477913i
$816$	−0.774105	−	3.79182i	−0.0270991	−	0.132740i
$817$	−0.0600759	+	1.49077i	−0.00210179	+	0.0521554i
$818$	−2.79217	−	1.46545i	−0.0976260	−	0.0512381i
$819$	−2.49810	−	5.11344i	−0.0872906	−	0.178678i
$820$	−31.1521	+	16.3499i	−1.08788	+	0.570963i
$821$	−8.48217	−	17.8758i	−0.296030	−	0.623869i	0.699876	−	0.714264i	$-0.253238\pi$
$821$	−8.48217	−	17.8758i	−0.296030	−	0.623869i	−0.995906	+	0.0903947i	$0.971187\pi$
$822$	−1.09375	+	1.89443i	−0.0381489	+	0.0660758i
$823$	−8.27940	−	14.3403i	−0.288602	−	0.499873i	0.684874	−	0.728661i	$-0.259857\pi$
$823$	−8.27940	−	14.3403i	−0.288602	−	0.499873i	−0.973476	+	0.228788i	$0.926524\pi$
$824$	−0.818338	+	1.18557i	−0.0285082	+	0.0413012i
$825$	−59.0235	+	44.3533i	−2.05494	+	1.54418i
$826$	1.49099	+	2.58247i	0.0518782	+	0.0898558i
$827$	6.25065	−	51.4787i	0.217356	−	1.79009i	−0.320699	−	0.947181i	$-0.603918\pi$
$827$	6.25065	−	51.4787i	0.217356	−	1.79009i	0.538055	−	0.842909i	$-0.319159\pi$
$828$	−4.95738	+	10.4475i	−0.172281	+	0.363074i
$829$	1.42266	−	1.48115i	0.0494110	−	0.0514423i	−0.696038	−	0.718005i	$-0.745056\pi$
$829$	1.42266	−	1.48115i	0.0494110	−	0.0514423i	0.745449	+	0.666562i	$0.232235\pi$
$830$	35.7479	−	2.88587i	1.24083	−	0.100170i
$831$	12.4397	+	3.06612i	0.431530	+	0.106363i
$832$	10.5035	+	9.09394i	0.364145	+	0.315275i
$833$	3.58575	−	0.883808i	0.124239	−	0.0306221i
$834$	−27.1637	+	9.06857i	−0.940602	+	0.314019i
$835$	−21.1305	−	44.5317i	−0.731252	−	1.54108i
$836$	−1.73910	−	0.580598i	−0.0601481	−	0.0200804i
$837$	−2.49479	−	3.61433i	−0.0862326	−	0.124929i
$838$	−16.5382	+	34.8535i	−0.571303	+	1.20400i
$839$	−2.05430	−	50.9768i	−0.0709222	−	1.75992i	−0.508803	−	0.860883i	$-0.669912\pi$
$839$	−2.05430	−	50.9768i	−0.0709222	−	1.75992i	0.437881	−	0.899033i	$-0.355729\pi$
$840$	5.86032	−	1.44444i	0.202200	−	0.0498379i
$841$	−67.3326	+	28.6878i	−2.32182	+	0.989233i
$842$	38.4221	+	6.24420i	1.32411	+	0.215189i
$843$	−5.24387	−	25.6862i	−0.180609	−	0.884679i
$844$	−26.0916			−0.898111
$845$	49.9062	+	24.7598i	1.71683	+	0.851762i
$846$	6.44054			0.221430
$847$	6.16194	+	30.1832i	0.211727	+	1.03711i
$848$	14.0271	+	2.27962i	0.481692	+	0.0782825i
$849$	0.858491	−	0.365769i	0.0294633	−	0.0125531i
$850$	−19.9556	+	4.91861i	−0.684471	+	0.168707i
$851$	2.16953	+	53.8363i	0.0743705	+	1.84548i
$852$	−6.27606	+	13.2265i	−0.215014	+	0.453133i
$853$	−21.2370	−	30.7672i	−0.727142	−	1.05345i	−0.995920	−	0.0902453i	$-0.971235\pi$
$853$	−21.2370	−	30.7672i	−0.727142	−	1.05345i	0.268777	−	0.963202i	$-0.413380\pi$
$854$	36.8416	+	12.2995i	1.26069	+	0.420881i
$855$	−0.399901	−	0.842773i	−0.0136763	−	0.0288222i
$856$	8.97151	−	2.99513i	0.306640	−	0.102371i
$857$	12.3779	−	3.05088i	0.422822	−	0.104216i	−0.0221631	−	0.999754i	$-0.507055\pi$
$857$	12.3779	−	3.05088i	0.422822	−	0.104216i	0.444985	+	0.895538i	$0.353209\pi$
$858$	−37.3918	+	0.425878i	−1.27654	+	0.0145392i
$859$	9.45954	+	2.33157i	0.322755	+	0.0795520i	0.397365	−	0.917661i	$-0.369925\pi$
$859$	9.45954	+	2.33157i	0.322755	+	0.0795520i	−0.0746093	+	0.997213i	$0.523771\pi$
$860$	44.6400	−	3.60372i	1.52221	−	0.122886i
$861$	−5.88730	+	6.12933i	−0.200639	+	0.208887i
$862$	−6.72559	+	14.1739i	−0.229075	+	0.482764i
$863$	−3.09587	+	25.4968i	−0.105385	+	0.867920i	0.840140	+	0.542370i	$0.182473\pi$
$863$	−3.09587	+	25.4968i	−0.105385	+	0.867920i	−0.945525	+	0.325551i	$0.894450\pi$
$864$	−3.54280	−	6.13630i	−0.120528	−	0.208761i
$865$	−57.9204	+	43.5244i	−1.96935	+	1.47987i
$866$	8.51213	−	12.3319i	0.289254	−	0.419057i
$867$	−8.16453	−	14.1414i	−0.277282	−	0.480266i
$868$	5.28463	−	9.15324i	0.179372	−	0.310681i
$869$	−11.5205	−	24.2789i	−0.390805	−	0.823604i
$870$	72.0156	−	37.7967i	2.44156	−	1.28143i
$871$	−10.8991	+	11.6090i	−0.369303	+	0.393355i
$872$	−5.32425	−	2.79438i	−0.180302	−	0.0946297i
$873$	0.0954146	−	2.36769i	0.00322930	−	0.0801341i
$874$	−0.619978	−	3.03685i	−0.0209711	−	0.102723i
$875$	−15.7420	−	54.3478i	−0.532178	−	1.83729i
$876$	3.39930	+	1.78409i	0.114852	+	0.0602788i
$877$	13.1410	+	8.30989i	0.443741	+	0.280605i	0.737592	−	0.675246i	$-0.235963\pi$
$877$	13.1410	+	8.30989i	0.443741	+	0.280605i	−0.293851	+	0.955851i	$0.594937\pi$
$878$	−2.67693	+	0.435044i	−0.0903421	+	0.0146820i
$879$	5.33935	+	1.31603i	0.180092	+	0.0443887i
$880$	22.3729	−	109.590i	0.754192	−	3.69427i
$881$	1.50451	−	0.121457i	0.0506883	−	0.00409198i	−0.0550964	−	0.998481i	$-0.517547\pi$
$881$	1.50451	−	0.121457i	0.0506883	−	0.00409198i	0.105785	+	0.994389i	$0.466265\pi$
$882$	7.15420	−	4.52404i	0.240895	−	0.152333i
$883$	−42.3969	+	37.5603i	−1.42677	+	1.26401i	−0.512626	+	0.858612i	$0.671327\pi$
$883$	−42.3969	+	37.5603i	−1.42677	+	1.26401i	−0.914142	+	0.405394i	$0.867134\pi$
$884$	−4.16251	−	1.71774i	−0.140000	−	0.0577737i
$885$	3.22788	+	2.85965i	0.108504	+	0.0961261i
$886$	29.9511	+	4.86752i	1.00623	+	0.163528i
$887$	−2.34700	−	0.999963i	−0.0788045	−	0.0335755i	0.352205	−	0.935923i	$-0.385432\pi$
$887$	−2.34700	−	0.999963i	−0.0788045	−	0.0335755i	−0.431009	+	0.902348i	$0.641842\pi$
$888$	−5.35771	−	3.38801i	−0.179793	−	0.113694i
$889$	0.514770	−	0.456046i	0.0172648	−	0.0152953i
$890$	−65.5660	−	5.29303i	−2.19778	−	0.177423i
$891$	5.23992	+	1.74934i	0.175544	+	0.0586052i
$892$	−4.46013	−	36.7325i	−0.149336	−	1.22990i
$893$	−0.596979	+	0.448600i	−0.0199771	+	0.0150118i
$894$	−3.18773	−	3.90426i	−0.106614	−	0.130578i
$895$	−2.87913	−	3.52629i	−0.0962385	−	0.117871i
$896$	−6.21987	+	9.01104i	−0.207791	+	0.301038i
$897$	−13.9417	−	23.5248i	−0.465499	−	0.785471i
$898$	−6.74918	−	9.77787i	−0.225223	−	0.326292i
$899$	−12.3516	+	42.6427i	−0.411949	+	1.42221i
$900$	−17.2231	+	10.8912i	−0.574102	+	0.363040i
$901$	−2.43185	+	0.395215i	−0.0810168	+	0.0131665i
$902$	19.8022	+	52.2142i	0.659343	+	1.73854i
$903$	9.95287	−	4.24052i	0.331211	−	0.141116i
$904$	1.88827	+	1.96589i	0.0628028	+	0.0653846i
$905$	−87.7453	+	46.0523i	−2.91675	+	1.53083i
$906$	39.6259	+	3.19894i	1.31648	+	0.106278i
$907$	13.9895	−	48.2973i	0.464513	−	1.60369i	−0.296556	−	0.955016i	$-0.595838\pi$
$907$	13.9895	−	48.2973i	0.464513	−	1.60369i	0.761069	−	0.648671i	$-0.224675\pi$
$908$	1.76320	−	1.83569i	0.0585139	−	0.0609194i
$909$	−3.65377	+	9.63420i	−0.121188	+	0.319546i
$910$	15.7479	−	42.9942i	0.522036	−	1.42525i
$911$	−16.4278	−	43.3165i	−0.544276	−	1.43514i	−0.871596	−	0.490225i	$-0.836915\pi$
$911$	−16.4278	−	43.3165i	−0.544276	−	1.43514i	0.327319	−	0.944914i	$-0.393855\pi$
$912$	0.946153	+	0.403118i	0.0313302	+	0.0133486i
$913$	0.991545	−	24.6049i	0.0328153	−	0.814304i
$914$	32.2312	−	39.4761i	1.06611	−	1.30575i
$915$	56.1691			1.85689
$916$	5.61713	−	6.87974i	0.185595	−	0.227313i
$917$	4.09789	+	14.1476i	0.135324	+	0.467194i
$918$	1.15107	+	1.01976i	0.0379910	+	0.0336571i
$919$	−31.2163	−	32.4996i	−1.02973	−	1.07206i	−0.997362	−	0.0725862i	$-0.976875\pi$
$919$	−31.2163	−	32.4996i	−1.02973	−	1.07206i	−0.0323676	−	0.999476i	$-0.510305\pi$
$920$	27.5094	−	9.18397i	0.906957	−	0.302787i
$921$	9.77179	+	7.34303i	0.321992	+	0.241961i
$922$	3.70765	−	30.5353i	0.122105	−	1.00563i
$923$	−17.6502	−	29.7825i	−0.580964	−	0.980303i
$924$	1.60250	+	13.1978i	0.0527184	+	0.434175i
$925$	−47.4731	+	82.2258i	−1.56091	+	2.70357i
$926$	−38.1866	−	28.6954i	−1.25489	−	0.942988i
$927$	−0.0650067	−	1.61313i	−0.00213510	−	0.0529820i
$928$	−25.3994	+	66.9727i	−0.833776	+	2.19849i
$929$	5.62482	−	27.5522i	0.184544	−	0.903957i	−0.777041	−	0.629450i	$-0.783280\pi$
$929$	5.62482	−	27.5522i	0.184544	−	0.903957i	0.961585	−	0.274507i	$-0.0885147\pi$
$930$	7.06771	−	34.6199i	0.231759	−	1.13523i
$931$	−0.348017	+	0.917646i	−0.0114058	+	0.0300746i
$932$	1.24466	+	30.8859i	0.0407701	+	1.01170i
$933$	0.548906	+	0.412476i	0.0179704	+	0.0135039i
$934$	26.8967	−	46.5865i	0.880087	−	1.52436i
$935$	2.33737	+	19.2500i	0.0764401	+	0.629541i
$936$	3.20957	+	0.222343i	0.104908	+	0.00726751i
$937$	−0.815712	+	6.71799i	−0.0266481	+	0.219467i	−0.999949	−	0.0100644i	$-0.996796\pi$
$937$	−0.815712	+	6.71799i	−0.0266481	+	0.219467i	0.973301	+	0.229532i	$0.0737194\pi$
$938$	10.4625	+	7.86208i	0.341614	+	0.256706i
$939$	5.75598	−	1.92163i	0.187839	−	0.0627100i
$940$	15.5276	+	16.1660i	0.506455	+	0.527275i
$941$	−13.2694	−	11.7556i	−0.432569	−	0.383223i	0.418552	−	0.908193i	$-0.362538\pi$
$941$	−13.2694	−	11.7556i	−0.432569	−	0.383223i	−0.851120	+	0.524970i	$0.824076\pi$
$942$	−11.9416	−	41.2271i	−0.389078	−	1.34325i
$943$	−25.8272	+	31.6326i	−0.841049	+	1.03010i
$944$	−4.75440			−0.154743
$945$	−4.27796	+	5.23955i	−0.139162	+	0.170443i
$946$	2.86234	−	71.0284i	0.0930629	−	2.30933i
$947$	34.1009	+	14.5290i	1.10813	+	0.472130i	0.866972	−	0.498356i	$-0.166063\pi$
$947$	34.1009	+	14.5290i	1.10813	+	0.472130i	0.241157	+	0.970486i	$0.422473\pi$
$948$	−2.63019	−	6.93524i	−0.0854246	−	0.225246i
$949$	−7.98987	+	4.31017i	−0.259362	+	0.139914i
$950$	1.93680	−	5.10693i	0.0628381	−	0.165691i
$951$	−2.08500	+	2.17071i	−0.0676107	+	0.0703902i
$952$	0.320967	−	1.10811i	0.0104026	−	0.0359139i
$953$	−14.8626	−	1.19983i	−0.481448	−	0.0388665i	−0.162639	−	0.986686i	$-0.552001\pi$
$953$	−14.8626	−	1.19983i	−0.481448	−	0.0388665i	−0.318808	+	0.947819i	$0.603283\pi$
$954$	−5.00017	+	2.62429i	−0.161887	+	0.0849647i
$955$	−19.0624	−	19.8460i	−0.616844	−	0.642202i
$956$	11.2468	−	4.79180i	0.363746	−	0.154978i
$957$	−19.8024	−	52.2147i	−0.640121	−	1.68786i
$958$	2.23927	−	0.363917i	0.0723476	−	0.0117576i
$959$	−1.55439	+	0.982935i	−0.0501938	+	0.0317406i
$960$	4.59424	−	15.8611i	0.148278	−	0.511916i
$961$	−6.65355	−	9.63933i	−0.214631	−	0.310946i
$962$	−44.0232	+	19.3518i	−1.41936	+	0.623928i
$963$	−6.02137	+	8.72346i	−0.194036	+	0.281109i
$964$	29.2848	+	35.8674i	0.943200	+	1.15521i
$965$	33.7335	+	41.3160i	1.08592	+	1.33001i
$966$	−17.9674	+	13.5016i	−0.578092	+	0.434408i
$967$	3.86054	+	31.7944i	0.124147	+	1.02244i	0.913029	+	0.407895i	$0.133737\pi$
$967$	3.86054	+	31.7944i	0.124147	+	1.02244i	−0.788882	+	0.614545i	$0.789340\pi$
$968$	−16.5189	−	5.51482i	−0.530938	−	0.177253i
$969$	−0.177723	−	0.0143473i	−0.00570928	−	0.000460900i
$970$	14.2703	−	12.6423i	0.458190	−	0.405921i
$971$	−14.3509	−	9.07499i	−0.460544	−	0.291230i	0.283975	−	0.958832i	$-0.408347\pi$
$971$	−14.3509	−	9.07499i	−0.460544	−	0.291230i	−0.744519	+	0.667601i	$0.767321\pi$
$972$	1.40271	+	0.597638i	0.0449919	+	0.0191693i
$973$	−23.7646	−	3.86213i	−0.761859	−	0.123814i
$974$	20.1623	+	17.8622i	0.646041	+	0.572342i
$975$	1.39185	−	48.1679i	0.0445748	−	1.54261i
$976$	−46.3524	+	41.0647i	−1.48371	+	1.31445i
$977$	0.895125	−	0.566042i	0.0286376	−	0.0181093i	−0.520070	−	0.854123i	$-0.674094\pi$
$977$	0.895125	−	0.566042i	0.0286376	−	0.0181093i	0.548708	+	0.836014i	$0.315120\pi$
$978$	−6.20267	+	0.500731i	−0.198339	+	0.0160116i
$979$	−9.03418	+	44.2523i	−0.288734	+	1.41431i
$980$	28.6037	+	7.05018i	0.913711	+	0.225210i
$981$	6.65145	−	1.08097i	0.212364	−	0.0345126i
$982$	30.5218	+	19.3008i	0.973990	+	0.615914i
$983$	−7.74740	−	4.06615i	−0.247104	−	0.129690i	0.336625	−	0.941639i	$-0.390715\pi$
$983$	−7.74740	−	4.06615i	−0.247104	−	0.129690i	−0.583729	+	0.811949i	$0.698407\pi$
$984$	−1.33671	−	4.61484i	−0.0426126	−	0.147116i
$985$	5.47667	+	26.8265i	0.174501	+	0.854763i
$986$	0.625957	−	15.5330i	0.0199345	−	0.494671i
$987$	4.79453	+	2.51636i	0.152612	+	0.0800967i
$988$	1.00406	−	0.651053i	0.0319434	−	0.0207128i
$989$	46.0294	−	24.1581i	1.46365	−	0.768183i
$990$	19.0534	+	40.1543i	0.605558	+	1.27619i
$991$	25.4744	−	44.1229i	0.809220	−	1.40161i	−0.104185	−	0.994558i	$-0.533223\pi$
$991$	25.4744	−	44.1229i	0.809220	−	1.40161i	0.913405	−	0.407052i	$-0.133443\pi$
$992$	15.5590	+	26.9490i	0.494000	+	0.855632i
$993$	7.35307	−	10.6528i	0.233343	−	0.338055i
$994$	−22.7468	+	17.0931i	−0.721485	+	0.542161i
$995$	−30.9569	−	53.6189i	−0.981400	−	1.69983i
$996$	0.819242	−	6.74706i	0.0259587	−	0.213789i
$997$	17.7681	−	37.4454i	0.562721	−	1.18591i	−0.400276	−	0.916395i	$-0.631086\pi$
$997$	17.7681	−	37.4454i	0.562721	−	1.18591i	0.962996	−	0.269514i	$-0.0868630\pi$
$998$	33.7835	−	35.1723i	1.06940	−	1.11336i
$999$	7.08108	−	0.571644i	0.224036	−	0.0180860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.a.490.4	yes	360
169.159	even	39	inner	507.2.q.a.328.4	✓	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.a.328.4	✓	360	169.159	even	39	inner
507.2.q.a.490.4	yes	360	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.375533 - 1.83948i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(-1.40271 + 0.597638i) q^{4} +(-4.16091 + 1.02557i) q^{5} +(0.0755962 + 1.87590i) q^{6} +(-0.676651 + 1.42601i) q^{7} +(-0.506888 - 0.734355i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})\)	\(q+(-0.375533 - 1.83948i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(-1.40271 + 0.597638i) q^{4} +(-4.16091 + 1.02557i) q^{5} +(0.0755962 + 1.87590i) q^{6} +(-0.676651 + 1.42601i) q^{7} +(-0.506888 - 0.734355i) q^{8} +(0.948536 + 0.316668i) q^{9} +(3.44908 + 7.26877i) q^{10} +(5.23992 - 1.74934i) q^{11} +(1.48041 - 0.364889i) q^{12} +(-1.24007 + 3.38559i) q^{13} +(2.87723 + 0.709173i) q^{14} +(4.27154 - 0.344834i) q^{15} +(-3.27290 + 3.40745i) q^{16} +(0.351146 - 0.740025i) q^{17} +(0.226298 - 1.86373i) q^{18} +(0.108838 + 0.188513i) q^{19} +(5.22362 - 3.92529i) q^{20} +(0.896637 - 1.29900i) q^{21} +(-5.18565 - 8.98180i) q^{22} +(3.79217 - 6.56822i) q^{23} +(0.382526 + 0.806155i) q^{24} +(11.8341 - 6.21100i) q^{25} +(6.69342 + 1.00968i) q^{26} +(-0.885456 - 0.464723i) q^{27} +(0.0969049 - 2.40467i) q^{28} +(2.02203 + 9.90458i) q^{29} +(-2.23842 - 7.72792i) q^{30} +(3.88869 + 2.04094i) q^{31} +(5.98867 + 3.78701i) q^{32} +(-5.45268 + 0.886147i) q^{33} +(-1.49313 - 0.368023i) q^{34} +(1.35301 - 6.62746i) q^{35} +(-1.51977 + 0.122689i) q^{36} +(-6.00433 + 3.79691i) q^{37} +(0.305894 - 0.270999i) q^{38} +(1.76710 - 3.14283i) q^{39} +(2.86225 + 2.53573i) q^{40} +(-5.31467 - 0.863718i) q^{41} +(-2.72621 - 1.16153i) q^{42} +(5.79303 + 3.66329i) q^{43} +(-6.30461 + 5.58539i) q^{44} +(-4.27154 - 0.344834i) q^{45} +(-13.5062 - 4.50903i) q^{46} +(0.413504 + 3.40551i) q^{47} +(3.77710 - 2.83831i) q^{48} +(2.85146 + 3.49241i) q^{49} +(-15.8691 - 19.4361i) q^{50} +(-0.465307 + 0.674114i) q^{51} +(-0.283904 - 5.49011i) q^{52} +(-1.70865 - 2.47541i) q^{53} +(-0.522332 + 1.80330i) q^{54} +(-20.0087 + 12.6528i) q^{55} +(1.39019 - 0.225927i) q^{56} +(-0.0771891 - 0.203531i) q^{57} +(17.4599 - 7.43899i) q^{58} +(0.697083 + 0.725741i) q^{59} +(-5.78563 + 3.03654i) q^{60} +(13.0645 + 1.05467i) q^{61} +(2.29394 - 7.91961i) q^{62} +(-1.09340 + 1.13835i) q^{63} +(1.36640 - 3.60291i) q^{64} +(1.68764 - 15.3589i) q^{65} +(3.67771 + 9.69733i) q^{66} +(4.06299 + 1.73108i) q^{67} +(-0.0502886 + 1.24790i) q^{68} +(-4.79667 + 5.87486i) q^{69} -12.6992 q^{70} +(-6.07261 + 7.43759i) q^{71} +(-0.248255 - 0.857077i) q^{72} +(1.88465 + 1.66966i) q^{73} +(9.23917 + 9.61899i) q^{74} +(-12.6771 + 4.23225i) q^{75} +(-0.265331 - 0.199383i) q^{76} +(-1.05101 + 8.65589i) q^{77} +(-6.44478 - 2.07031i) q^{78} +(-0.586371 - 4.82920i) q^{79} +(10.1236 - 17.5346i) q^{80} +(0.799443 + 0.600742i) q^{81} +(0.407040 + 10.1006i) q^{82} +(1.58070 - 4.16795i) q^{83} +(-0.481386 + 2.35799i) q^{84} +(-0.702138 + 3.43930i) q^{85} +(4.56308 - 12.0319i) q^{86} +(-0.407043 - 10.1007i) q^{87} +(-3.94069 - 2.96124i) q^{88} +(-4.08792 + 7.08048i) q^{89} +(0.969786 + 7.98691i) q^{90} +(-3.98880 - 4.05922i) q^{91} +(-1.39388 + 11.4796i) q^{92} +(-3.51094 - 2.63830i) q^{93} +(6.10909 - 2.03951i) q^{94} +(-0.646199 - 0.672765i) q^{95} +(-5.30364 - 4.69862i) q^{96} +(-0.659267 - 2.27605i) q^{97} +(5.35340 - 6.55673i) q^{98} +5.52422 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

Modular forms

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