LMFDB - Embedded newform 147.2.m.b.58.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,2,Mod(4,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("147.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	147.m (of order $21$, degree $12$, 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:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			58.5
Character	$\chi$	$=$	147.58
Dual form			147.2.m.b.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60276 + 1.48714i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(0.207780 + 2.77264i) q^{4} +(0.252155 + 0.642481i) q^{5} +(-1.36321 - 1.70941i) q^{6} +(-0.451208 + 2.60699i) q^{7} +(-1.06386 + 1.33404i) q^{8} +(0.955573 + 0.294755i) q^{9} +O(q^{10})$	\(q+(1.60276 + 1.48714i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(0.207780 + 2.77264i) q^{4} +(0.252155 + 0.642481i) q^{5} +(-1.36321 - 1.70941i) q^{6} +(-0.451208 + 2.60699i) q^{7} +(-1.06386 + 1.33404i) q^{8} +(0.955573 + 0.294755i) q^{9} +(-0.551316 + 1.40473i) q^{10} +(0.665733 - 0.205351i) q^{11} +(0.207780 - 2.77264i) q^{12} +(1.27841 - 5.60108i) q^{13} +(-4.60014 + 3.50736i) q^{14} +(-0.153582 - 0.672887i) q^{15} +(1.80969 - 0.272767i) q^{16} +(-4.69720 - 3.20250i) q^{17} +(1.09321 + 1.89349i) q^{18} +(0.410442 - 0.710906i) q^{19} +(-1.72897 + 0.832630i) q^{20} +(0.834720 - 2.51063i) q^{21} +(1.37239 + 0.660910i) q^{22} +(-0.244786 + 0.166892i) q^{23} +(1.25081 - 1.16058i) q^{24} +(3.31606 - 3.07685i) q^{25} +(10.3786 - 7.07599i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(-7.32200 - 0.709354i) q^{28} +(-7.48630 + 3.60521i) q^{29} +(0.754523 - 1.30687i) q^{30} +(1.12729 + 1.95252i) q^{31} +(6.12577 + 4.17648i) q^{32} +(-0.688903 + 0.103835i) q^{33} +(-2.76590 - 12.1182i) q^{34} +(-1.78872 + 0.367474i) q^{35} +(-0.618700 + 2.71070i) q^{36} +(0.0743856 - 0.992607i) q^{37} +(1.71505 - 0.529024i) q^{38} +(-2.09893 + 5.34798i) q^{39} +(-1.12536 - 0.347126i) q^{40} +(-4.21303 + 5.28297i) q^{41} +(5.07151 - 2.78257i) q^{42} +(2.31241 + 2.89967i) q^{43} +(0.707691 + 1.80317i) q^{44} +(0.0515781 + 0.688262i) q^{45} +(-0.640525 - 0.0965436i) q^{46} +(6.01460 + 5.58073i) q^{47} -1.83013 q^{48} +(-6.59282 - 2.35259i) q^{49} +9.89055 q^{50} +(4.16743 + 3.86681i) q^{51} +(15.7954 + 2.38077i) q^{52} +(-0.561174 - 7.48835i) q^{53} +(-0.798787 - 2.03528i) q^{54} +(0.299802 + 0.375940i) q^{55} +(-2.99781 - 3.37541i) q^{56} +(-0.511812 + 0.641792i) q^{57} +(-17.3602 - 5.35490i) q^{58} +(-2.58627 + 6.58970i) q^{59} +(1.83376 - 0.565640i) q^{60} +(-0.172385 + 2.30031i) q^{61} +(-1.09690 + 4.80585i) q^{62} +(-1.19959 + 2.35818i) q^{63} +(2.79262 + 12.2353i) q^{64} +(3.92095 - 0.590988i) q^{65} +(-1.25856 - 0.858073i) q^{66} +(-6.80742 - 11.7908i) q^{67} +(7.90337 - 13.6890i) q^{68} +(0.266926 - 0.128545i) q^{69} +(-3.41336 - 2.07110i) q^{70} +(-11.5600 - 5.56699i) q^{71} +(-1.40981 + 0.961195i) q^{72} +(-0.904509 + 0.839262i) q^{73} +(1.59537 - 1.48029i) q^{74} +(-3.73760 + 2.54825i) q^{75} +(2.05637 + 0.990293i) q^{76} +(0.234966 + 1.82822i) q^{77} +(-11.3173 + 5.45011i) q^{78} +(-3.02406 + 5.23782i) q^{79} +(0.631572 + 1.09391i) q^{80} +(0.826239 + 0.563320i) q^{81} +(-14.6090 + 2.20195i) q^{82} +(-0.767708 - 3.36355i) q^{83} +(7.13449 + 1.79272i) q^{84} +(0.873120 - 3.82539i) q^{85} +(-0.605987 + 8.08634i) q^{86} +(7.94001 - 2.44917i) q^{87} +(-0.434301 + 1.10658i) q^{88} +(-11.1599 - 3.44239i) q^{89} +(-0.940874 + 1.17982i) q^{90} +(14.0251 + 5.86006i) q^{91} +(-0.513594 - 0.644026i) q^{92} +(-0.823689 - 2.09872i) q^{93} +(1.34060 + 17.8891i) q^{94} +(0.560239 + 0.0844424i) q^{95} +(-5.43488 - 5.04283i) q^{96} +16.2259 q^{97} +(-7.06805 - 13.5751i) q^{98} +0.696685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9	\( 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9} - 34 q^{10} - 11 q^{11} + 5 q^{12} - 2 q^{13} + 40 q^{14} - 3 q^{15} - 31 q^{16} - 9 q^{17} - 6 q^{18} - 29 q^{19} - 43 q^{20} - 11 q^{21} + 9 q^{22} - 4 q^{23} - 24 q^{24} + 55 q^{25} + 36 q^{26} - 10 q^{27} - 57 q^{28} + 4 q^{29} - 20 q^{30} - 39 q^{31} - 92 q^{32} - 18 q^{33} - 36 q^{34} - 33 q^{35} - 10 q^{36} - 24 q^{37} + 118 q^{38} - 6 q^{39} + 35 q^{41} + 38 q^{42} + 2 q^{43} + 40 q^{44} + 12 q^{45} - 40 q^{46} - 5 q^{47} + 76 q^{48} + 129 q^{49} - 176 q^{50} + 54 q^{51} - 6 q^{52} + 26 q^{53} + q^{54} + 2 q^{55} + 63 q^{56} - 12 q^{57} + 11 q^{58} - 41 q^{59} + 32 q^{60} + 6 q^{61} + 36 q^{62} - q^{63} + 74 q^{64} - 51 q^{65} - 15 q^{66} - 55 q^{67} - 22 q^{68} + 8 q^{69} - 68 q^{70} - 66 q^{71} - 24 q^{72} + 24 q^{73} + 28 q^{74} + 41 q^{75} + 3 q^{76} - 34 q^{77} - 30 q^{78} - 51 q^{79} - 5 q^{80} + 5 q^{81} - 41 q^{82} + 30 q^{83} - 30 q^{84} + 68 q^{85} + 110 q^{86} + 19 q^{87} + 129 q^{88} + 75 q^{89} - 16 q^{90} + 5 q^{91} - 4 q^{93} + 38 q^{94} + 36 q^{95} - 57 q^{96} - 168 q^{97} + 227 q^{98} + 36 q^{99}+O(q^{100}) \) 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9 - 34 * q^10 - 11 * q^11 + 5 * q^12 - 2 * q^13 + 40 * q^14 - 3 * q^15 - 31 * q^16 - 9 * q^17 - 6 * q^18 - 29 * q^19 - 43 * q^20 - 11 * q^21 + 9 * q^22 - 4 * q^23 - 24 * q^24 + 55 * q^25 + 36 * q^26 - 10 * q^27 - 57 * q^28 + 4 * q^29 - 20 * q^30 - 39 * q^31 - 92 * q^32 - 18 * q^33 - 36 * q^34 - 33 * q^35 - 10 * q^36 - 24 * q^37 + 118 * q^38 - 6 * q^39 + 35 * q^41 + 38 * q^42 + 2 * q^43 + 40 * q^44 + 12 * q^45 - 40 * q^46 - 5 * q^47 + 76 * q^48 + 129 * q^49 - 176 * q^50 + 54 * q^51 - 6 * q^52 + 26 * q^53 + q^54 + 2 * q^55 + 63 * q^56 - 12 * q^57 + 11 * q^58 - 41 * q^59 + 32 * q^60 + 6 * q^61 + 36 * q^62 - q^63 + 74 * q^64 - 51 * q^65 - 15 * q^66 - 55 * q^67 - 22 * q^68 + 8 * q^69 - 68 * q^70 - 66 * q^71 - 24 * q^72 + 24 * q^73 + 28 * q^74 + 41 * q^75 + 3 * q^76 - 34 * q^77 - 30 * q^78 - 51 * q^79 - 5 * q^80 + 5 * q^81 - 41 * q^82 + 30 * q^83 - 30 * q^84 + 68 * q^85 + 110 * q^86 + 19 * q^87 + 129 * q^88 + 75 * q^89 - 16 * q^90 + 5 * q^91 - 4 * q^93 + 38 * q^94 + 36 * q^95 - 57 * q^96 - 168 * q^97 + 227 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{21}\right)$

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 $

$2$	1.60276	+	1.48714i	1.13332	+	1.05157i	0.998153	+	0.0607439i	$0.0193473\pi$
$2$	1.60276	+	1.48714i	1.13332	+	1.05157i	0.135166	+	0.990823i	$0.456843\pi$
$3$	−0.988831	−	0.149042i	−0.570902	−	0.0860496i
$3$	−0.988831	−	0.149042i	−0.570902	−	0.0860496i
$4$	0.207780	+	2.77264i	0.103890	+	1.38632i
$5$	0.252155	+	0.642481i	0.112767	+	0.287326i	0.976105	−	0.217301i	$-0.0697252\pi$
$5$	0.252155	+	0.642481i	0.112767	+	0.287326i	−0.863337	+	0.504627i	$0.831630\pi$
$6$	−1.36321	−	1.70941i	−0.556527	−	0.697863i
$7$	−0.451208	+	2.60699i	−0.170541	+	0.985351i
$7$	−0.451208	+	2.60699i	−0.170541	+	0.985351i
$8$	−1.06386	+	1.33404i	−0.376132	+	0.471655i
$9$	0.955573	+	0.294755i	0.318524	+	0.0982517i
$10$	−0.551316	+	1.40473i	−0.174341	+	0.444215i
$11$	0.665733	−	0.205351i	0.200726	−	0.0619158i	−0.192762	−	0.981246i	$-0.561745\pi$
$11$	0.665733	−	0.205351i	0.200726	−	0.0619158i	0.393488	+	0.919330i	$0.371268\pi$
$12$	0.207780	−	2.77264i	0.0599810	−	0.800391i
$13$	1.27841	−	5.60108i	0.354567	−	1.55346i	−0.411932	−	0.911215i	$-0.635146\pi$
$13$	1.27841	−	5.60108i	0.354567	−	1.55346i	0.766499	−	0.642246i	$-0.221997\pi$
$14$	−4.60014	+	3.50736i	−1.22944	+	0.937382i
$15$	−0.153582	−	0.672887i	−0.0396547	−	0.173739i
$16$	1.80969	−	0.272767i	0.452423	−	0.0681918i
$17$	−4.69720	−	3.20250i	−1.13924	−	0.776719i	−0.161567	−	0.986862i	$-0.551655\pi$
$17$	−4.69720	−	3.20250i	−1.13924	−	0.776719i	−0.977671	+	0.210143i	$0.932607\pi$
$18$	1.09321	+	1.89349i	0.257672	+	0.446300i
$19$	0.410442	−	0.710906i	0.0941618	−	0.163093i	−0.815097	−	0.579325i	$-0.803316\pi$
$19$	0.410442	−	0.710906i	0.0941618	−	0.163093i	0.909258	+	0.416232i	$0.136650\pi$
$20$	−1.72897	+	0.832630i	−0.386610	+	0.186182i
$21$	0.834720	−	2.51063i	0.182151	−	0.547863i
$22$	1.37239	+	0.660910i	0.292595	+	0.140906i
$23$	−0.244786	+	0.166892i	−0.0510414	+	0.0347995i	−0.588572	−	0.808445i	$-0.700310\pi$
$23$	−0.244786	+	0.166892i	−0.0510414	+	0.0347995i	0.537531	+	0.843244i	$0.319357\pi$
$24$	1.25081	−	1.16058i	0.255320	−	0.236903i
$25$	3.31606	−	3.07685i	0.663212	−	0.615371i
$26$	10.3786	−	7.07599i	2.03541	−	1.38772i
$27$	−0.900969	−	0.433884i	−0.173392	−	0.0835010i
$28$	−7.32200	−	0.709354i	−1.38373	−	0.134055i
$29$	−7.48630	+	3.60521i	−1.39017	+	0.669471i	−0.971142	−	0.238502i	$-0.923344\pi$
$29$	−7.48630	+	3.60521i	−1.39017	+	0.669471i	−0.419029	+	0.907973i	$0.637629\pi$
$30$	0.754523	−	1.30687i	0.137756	−	0.238601i
$31$	1.12729	+	1.95252i	0.202467	+	0.350683i	0.949323	−	0.314303i	$-0.101771\pi$
$31$	1.12729	+	1.95252i	0.202467	+	0.350683i	−0.746856	+	0.664986i	$0.768438\pi$
$32$	6.12577	+	4.17648i	1.08289	+	0.738304i
$33$	−0.688903	+	0.103835i	−0.119923	+	0.0180754i
$34$	−2.76590	−	12.1182i	−0.474348	−	2.07826i
$35$	−1.78872	+	0.367474i	−0.302349	+	0.0621145i
$36$	−0.618700	+	2.71070i	−0.103117	+	0.451783i
$37$	0.0743856	−	0.992607i	0.0122289	−	0.163184i	−0.987746	−	0.156071i	$-0.950117\pi$
$37$	0.0743856	−	0.992607i	0.0122289	−	0.163184i	0.999975	−	0.00711229i	$-0.00226393\pi$
$38$	1.71505	−	0.529024i	0.278218	−	0.0858190i
$39$	−2.09893	+	5.34798i	−0.336098	+	0.856363i
$40$	−1.12536	−	0.347126i	−0.177934	−	0.0548855i
$41$	−4.21303	+	5.28297i	−0.657964	+	0.825061i	−0.993120	−	0.117102i	$-0.962640\pi$
$41$	−4.21303	+	5.28297i	−0.657964	+	0.825061i	0.335156	+	0.942163i	$0.391211\pi$
$42$	5.07151	−	2.78257i	0.782550	−	0.429360i
$43$	2.31241	+	2.89967i	0.352639	+	0.442195i	0.926237	−	0.376942i	$-0.123024\pi$
$43$	2.31241	+	2.89967i	0.352639	+	0.442195i	−0.573598	+	0.819137i	$0.694453\pi$
$44$	0.707691	+	1.80317i	0.106688	+	0.271838i
$45$	0.0515781	+	0.688262i	0.00768881	+	0.102600i
$46$	−0.640525	−	0.0965436i	−0.0944402	−	0.0142346i
$47$	6.01460	+	5.58073i	0.877320	+	0.814034i	0.983611	−	0.180301i	$-0.0577072\pi$
$47$	6.01460	+	5.58073i	0.877320	+	0.814034i	−0.106292	+	0.994335i	$0.533898\pi$
$48$	−1.83013			−0.264157
$49$	−6.59282	−	2.35259i	−0.941832	−	0.336084i
$50$	9.89055			1.39873
$51$	4.16743	+	3.86681i	0.583556	+	0.541461i
$52$	15.7954	+	2.38077i	2.19043	+	0.330154i
$53$	−0.561174	−	7.48835i	−0.0770832	−	1.02860i	−0.892889	−	0.450278i	$-0.851325\pi$
$53$	−0.561174	−	7.48835i	−0.0770832	−	1.02860i	0.815805	−	0.578326i	$-0.196294\pi$
$54$	−0.798787	−	2.03528i	−0.108701	−	0.276966i
$55$	0.299802	+	0.375940i	0.0404254	+	0.0506918i
$56$	−2.99781	−	3.37541i	−0.400600	−	0.451059i
$57$	−0.511812	+	0.641792i	−0.0677912	+	0.0850075i
$58$	−17.3602	−	5.35490i	−2.27950	−	0.703133i
$59$	−2.58627	+	6.58970i	−0.336703	+	0.857905i	0.657799	+	0.753193i	$0.271487\pi$
$59$	−2.58627	+	6.58970i	−0.336703	+	0.857905i	−0.994503	+	0.104712i	$0.966608\pi$
$60$	1.83376	−	0.565640i	0.236737	−	0.0730238i
$61$	−0.172385	+	2.30031i	−0.0220716	+	0.294525i	0.975235	+	0.221173i	$0.0709886\pi$
$61$	−0.172385	+	2.30031i	−0.0220716	+	0.294525i	−0.997306	+	0.0733518i	$0.976630\pi$
$62$	−1.09690	+	4.80585i	−0.139307	+	0.610343i
$63$	−1.19959	+	2.35818i	−0.151134	+	0.297102i
$64$	2.79262	+	12.2353i	0.349077	+	1.52941i
$65$	3.92095	−	0.590988i	0.486334	−	0.0733030i
$66$	−1.25856	−	0.858073i	−0.154918	−	0.105621i
$67$	−6.80742	−	11.7908i	−0.831659	−	1.44048i	−0.896722	−	0.442595i	$-0.854058\pi$
$67$	−6.80742	−	11.7908i	−0.831659	−	1.44048i	0.0650627	−	0.997881i	$-0.479275\pi$
$68$	7.90337	−	13.6890i	0.958425	−	1.66004i
$69$	0.266926	−	0.128545i	0.0321341	−	0.0154750i
$70$	−3.41336	−	2.07110i	−0.407975	−	0.247544i
$71$	−11.5600	−	5.56699i	−1.37192	−	0.660680i	−0.404656	−	0.914469i	$-0.632609\pi$
$71$	−11.5600	−	5.56699i	−1.37192	−	0.660680i	−0.967260	+	0.253789i	$0.918323\pi$
$72$	−1.40981	+	0.961195i	−0.166148	+	0.113278i
$73$	−0.904509	+	0.839262i	−0.105865	+	0.0982281i	−0.731330	−	0.682024i	$-0.761100\pi$
$73$	−0.904509	+	0.839262i	−0.105865	+	0.0982281i	0.625465	+	0.780252i	$0.284909\pi$
$74$	1.59537	−	1.48029i	0.185458	−	0.172080i
$75$	−3.73760	+	2.54825i	−0.431581	+	0.294247i
$76$	2.05637	+	0.990293i	0.235881	+	0.113594i
$77$	0.234966	+	1.82822i	0.0267768	+	0.208345i
$78$	−11.3173	+	5.45011i	−1.28143	+	0.617104i
$79$	−3.02406	+	5.23782i	−0.340233	+	0.589301i	−0.984476	−	0.175520i	$-0.943839\pi$
$79$	−3.02406	+	5.23782i	−0.340233	+	0.589301i	0.644243	+	0.764821i	$0.277173\pi$
$80$	0.631572	+	1.09391i	0.0706119	+	0.122303i
$81$	0.826239	+	0.563320i	0.0918043	+	0.0625911i
$82$	−14.6090	+	2.20195i	−1.61329	+	0.243164i
$83$	−0.767708	−	3.36355i	−0.0842669	−	0.369198i	0.915158	−	0.403094i	$-0.132065\pi$
$83$	−0.767708	−	3.36355i	−0.0842669	−	0.369198i	−0.999425	+	0.0338969i	$0.989208\pi$
$84$	7.13449	+	1.79272i	0.778437	+	0.195602i
$85$	0.873120	−	3.82539i	0.0947031	−	0.414922i
$86$	−0.605987	+	8.08634i	−0.0653453	+	0.871972i
$87$	7.94001	−	2.44917i	0.851259	−	0.262579i
$88$	−0.434301	+	1.10658i	−0.0462967	+	0.117962i
$89$	−11.1599	−	3.44239i	−1.18295	−	0.364892i	−0.359972	−	0.932963i	$-0.617214\pi$
$89$	−11.1599	−	3.44239i	−1.18295	−	0.364892i	−0.822980	+	0.568071i	$0.807690\pi$
$90$	−0.940874	+	1.17982i	−0.0991769	+	0.124364i
$91$	14.0251	+	5.86006i	1.47024	+	0.614301i
$92$	−0.513594	−	0.644026i	−0.0535459	−	0.0671444i
$93$	−0.823689	−	2.09872i	−0.0854125	−	0.217628i
$94$	1.34060	+	17.8891i	0.138273	+	1.84512i
$95$	0.560239	+	0.0844424i	0.0574793	+	0.00866360i
$96$	−5.43488	−	5.04283i	−0.554695	−	0.514682i
$97$	16.2259			1.64749			0.823743	−	0.566963i	$-0.191882\pi$
$97$	16.2259			1.64749			0.823743	+	0.566963i	$0.191882\pi$
$98$	−7.06805	−	13.5751i	−0.713981	−	1.37129i
$99$	0.696685			0.0700194
$100$	9.22001	+	8.55492i	0.922001	+	0.855492i
$101$	3.20653	+	0.483306i	0.319061	+	0.0480908i	0.306620	−	0.951832i	$-0.400802\pi$
$101$	3.20653	+	0.483306i	0.319061	+	0.0480908i	0.0124408	+	0.999923i	$0.496040\pi$
$102$	0.928884	+	12.3951i	0.0919732	+	1.22730i
$103$	7.05431	+	17.9741i	0.695082	+	1.77104i	0.634561	+	0.772873i	$0.281181\pi$
$103$	7.05431	+	17.9741i	0.695082	+	1.77104i	0.0605211	+	0.998167i	$0.480724\pi$
$104$	6.11202	+	7.66424i	0.599333	+	0.751540i
$105$	1.82351	−	0.0967754i	0.177956	−	0.00944432i
$106$	10.2368	−	12.8365i	0.994286	−	1.24680i
$107$	10.7156	+	3.30534i	1.03592	+	0.319539i	0.765658	−	0.643248i	$-0.222414\pi$
$107$	10.7156	+	3.30534i	1.03592	+	0.319539i	0.270262	+	0.962787i	$0.412890\pi$
$108$	1.01580	−	2.58821i	0.0977453	−	0.249051i
$109$	12.9774	−	4.00301i	1.24301	−	0.383419i	0.397613	−	0.917553i	$-0.369839\pi$
$109$	12.9774	−	4.00301i	1.24301	−	0.383419i	0.845400	+	0.534134i	$0.179362\pi$
$110$	−0.0785659	+	1.04839i	−0.00749096	+	0.0999600i
$111$	−0.221495	+	0.970434i	−0.0210234	+	0.0921095i
$112$	−0.105445	+	4.84093i	−0.00996364	+	0.457425i
$113$	−1.57596	−	6.90471i	−0.148253	−	0.649541i	−0.993370	−	0.114959i	$-0.963326\pi$
$113$	−1.57596	−	6.90471i	−0.148253	−	0.649541i	0.845117	−	0.534582i	$-0.179531\pi$
$114$	−1.77475	+	0.267500i	−0.166220	+	0.0250537i
$115$	−0.168949	−	0.115188i	−0.0157546	−	0.0107413i
$116$	−11.5515	−	20.0077i	−1.07253	−	1.85767i
$117$	2.87256	−	4.97542i	0.265568	−	0.459978i
$118$	−13.9450	+	6.71554i	−1.28374	+	0.618215i
$119$	10.4683	−	10.8006i	0.959627	−	0.990087i
$120$	1.06105	+	0.510975i	0.0968602	+	0.0466454i
$121$	−8.68760	+	5.92310i	−0.789781	+	0.538464i
$122$	−3.69718	+	3.43048i	−0.334727	+	0.310581i
$123$	4.95336	−	4.59604i	0.446629	−	0.414411i
$124$	−5.17940	+	3.53125i	−0.465124	+	0.317116i
$125$	5.92219	+	2.85198i	0.529697	+	0.255088i
$126$	−5.42958	+	1.99563i	−0.483706	+	0.177785i
$127$	−16.2318	+	7.81682i	−1.44034	+	0.693631i	−0.980888	−	0.194572i	$-0.937668\pi$
$127$	−16.2318	+	7.81682i	−1.44034	+	0.693631i	−0.459451	+	0.888203i	$0.651954\pi$
$128$	−6.30561	+	10.9216i	−0.557342	+	0.965345i
$129$	−1.85441	−	3.21193i	−0.163272	−	0.282795i
$130$	7.16320	+	4.88379i	0.628254	+	0.428337i
$131$	−17.9748	+	2.70927i	−1.57047	+	0.236710i	−0.875818	−	0.482641i	$-0.839678\pi$
$131$	−17.9748	+	2.70927i	−1.57047	+	0.236710i	−0.694648	+	0.719350i	$0.744440\pi$
$132$	−0.431039	−	1.88850i	−0.0375171	−	0.164373i
$133$	1.66813	+	1.39078i	0.144645	+	0.120596i
$134$	6.62394	−	29.0214i	0.572221	−	2.50706i
$135$	0.0515781	−	0.688262i	0.00443913	−	0.0592361i
$136$	9.26944	−	2.85924i	0.794848	−	0.245178i
$137$	1.78265	−	4.54212i	0.152302	−	0.388059i	−0.834277	−	0.551346i	$-0.814114\pi$
$137$	1.78265	−	4.54212i	0.152302	−	0.388059i	0.986579	+	0.163287i	$0.0522096\pi$
$138$	0.618982	+	0.190931i	0.0526912	+	0.0162531i
$139$	10.4267	−	13.0747i	0.884381	−	1.10898i	−0.108992	−	0.994043i	$-0.534762\pi$
$139$	10.4267	−	13.0747i	0.884381	−	1.10898i	0.993373	−	0.114936i	$-0.0366663\pi$
$140$	−1.39053	−	4.88311i	−0.117522	−	0.412698i
$141$	−5.11566	−	6.41483i	−0.430816	−	0.540226i
$142$	−10.2489	−	26.1138i	−0.860070	−	2.19142i
$143$	−0.299110	−	3.99135i	−0.0250128	−	0.333773i
$144$	1.80969	+	0.272767i	0.150808	+	0.0227306i
$145$	−4.20399	−	3.90073i	−0.349122	−	0.323938i
$146$	−2.69781			−0.223272
$147$	6.16855	+	3.30892i	0.508774	+	0.272915i
$148$	2.76760			0.227495
$149$	15.7246	+	14.5903i	1.28821	+	1.19528i	0.968849	+	0.247651i	$0.0796586\pi$
$149$	15.7246	+	14.5903i	1.28821	+	1.19528i	0.319361	+	0.947633i	$0.396532\pi$
$150$	−9.78008	−	1.47411i	−0.798540	−	0.120361i
$151$	−0.418329	−	5.58221i	−0.0340431	−	0.454274i	−0.988013	−	0.154371i	$-0.950665\pi$
$151$	−0.418329	−	5.58221i	−0.0340431	−	0.454274i	0.953970	−	0.299903i	$-0.0969543\pi$
$152$	0.511724	+	1.30385i	0.0415063	+	0.105756i
$153$	−3.54456	−	4.44474i	−0.286561	−	0.359336i
$154$	−2.34222	+	3.27961i	−0.188742	+	0.264279i
$155$	−0.970205	+	1.21660i	−0.0779288	+	0.0977196i
$156$	−15.2641	−	4.70836i	−1.22211	−	0.376971i
$157$	6.57998	−	16.7655i	0.525140	−	1.33803i	−0.384687	−	0.923047i	$-0.625691\pi$
$157$	6.57998	−	16.7655i	0.525140	−	1.33803i	0.909827	−	0.414987i	$-0.136214\pi$
$158$	−12.6362	+	3.89775i	−1.00528	+	0.310088i
$159$	−0.561174	+	7.48835i	−0.0445040	+	0.593865i
$160$	−1.13866	+	4.98881i	−0.0900193	+	0.394400i
$161$	−0.324638	−	0.713459i	−0.0255850	−	0.0562284i
$162$	0.486523	+	2.13160i	0.0382249	+	0.167474i
$163$	2.73345	−	0.412002i	0.214100	−	0.0322705i	−0.0411161	−	0.999154i	$-0.513091\pi$
$163$	2.73345	−	0.412002i	0.214100	−	0.0322705i	0.255217	+	0.966884i	$0.417853\pi$
$164$	−15.5231	−	10.5835i	−1.21215	−	0.826432i
$165$	−0.240423	−	0.416425i	−0.0187169	−	0.0324186i
$166$	3.77162	−	6.53264i	0.292735	−	0.507031i
$167$	−1.26375	+	0.608589i	−0.0977918	+	0.0470941i	−0.482140	−	0.876094i	$-0.660140\pi$
$167$	−1.26375	+	0.608589i	−0.0977918	+	0.0470941i	0.384348	+	0.923188i	$0.374426\pi$
$168$	2.46125	+	3.78451i	0.189890	+	0.291982i
$169$	−18.0252	−	8.68047i	−1.38655	−	0.667728i
$170$	7.08828	−	4.83271i	0.543647	−	0.370652i
$171$	0.601750	−	0.558342i	0.0460170	−	0.0426975i
$172$	−7.55926	+	7.01397i	−0.576388	+	0.534810i
$173$	5.08016	−	3.46359i	0.386237	−	0.263332i	−0.354598	−	0.935019i	$-0.615382\pi$
$173$	5.08016	−	3.46359i	0.386237	−	0.263332i	0.740835	+	0.671687i	$0.234430\pi$
$174$	16.3682	+	7.88249i	1.24087	+	0.597570i
$175$	6.52510	+	10.0332i	0.493251	+	0.758442i
$176$	1.14876	−	0.553213i	0.0865910	−	0.0417000i
$177$	3.53952	−	6.13063i	0.266047	−	0.460807i
$178$	−12.7674	−	22.1137i	−0.956954	−	1.65749i
$179$	9.82971	+	6.70178i	0.734707	+	0.500915i	0.871933	−	0.489625i	$-0.162866\pi$
$179$	9.82971	+	6.70178i	0.734707	+	0.500915i	−0.137226	+	0.990540i	$0.543819\pi$
$180$	−1.89758	+	0.286015i	−0.141437	+	0.0213183i
$181$	3.08318	+	13.5083i	0.229171	+	1.00406i	0.950318	+	0.311282i	$0.100758\pi$
$181$	3.08318	+	13.5083i	0.229171	+	1.00406i	−0.721146	+	0.692783i	$0.756384\pi$
$182$	13.7642	+	30.2496i	1.02027	+	2.24225i
$183$	0.513304	−	2.24893i	0.0379445	−	0.166246i
$184$	0.0377775	−	0.504106i	0.00278499	−	0.0371632i
$185$	0.656488	−	0.202500i	0.0482660	−	0.0148881i
$186$	1.80093	−	4.58868i	0.132050	−	0.336459i
$187$	−3.78472	−	1.16743i	−0.276766	−	0.0853710i
$188$	−14.2236	+	17.8359i	−1.03737	+	1.30081i
$189$	1.53766	−	2.15305i	0.111848	−	0.156611i
$190$	0.772348	+	0.968494i	0.0560320	+	0.0702619i
$191$	−4.82414	−	12.2917i	−0.349063	−	0.889398i	−0.992314	−	0.123743i	$-0.960510\pi$
$191$	−4.82414	−	12.2917i	−0.349063	−	0.889398i	0.643252	−	0.765655i	$-0.277585\pi$
$192$	−0.937856	−	12.5148i	−0.0676839	−	0.903179i
$193$	−22.0544	−	3.32417i	−1.58751	−	0.239279i	−0.704875	−	0.709332i	$-0.748997\pi$
$193$	−22.0544	−	3.32417i	−1.58751	−	0.239279i	−0.882638	+	0.470052i	$0.844235\pi$
$194$	26.0061	+	24.1301i	1.86713	+	1.73244i
$195$	−3.96524			−0.283956
$196$	5.15302	−	18.7683i	0.368073	−	1.34059i
$197$	26.9785			1.92214			0.961071	−	0.276302i	$-0.0891089\pi$
$197$	26.9785			1.92214			0.961071	+	0.276302i	$0.0891089\pi$
$198$	1.11662	+	1.03607i	0.0793544	+	0.0736301i
$199$	−2.63999	−	0.397914i	−0.187144	−	0.0282074i	0.0548016	−	0.998497i	$-0.482547\pi$
$199$	−2.63999	−	0.397914i	−0.187144	−	0.0282074i	−0.241945	+	0.970290i	$0.577785\pi$
$200$	0.576819	+	7.69711i	0.0407873	+	0.544268i
$201$	4.97406	+	12.6737i	0.350843	+	0.893934i
$202$	4.42054	+	5.54318i	0.311028	+	0.390017i
$203$	−6.02088	−	21.1434i	−0.422583	−	1.48398i
$204$	−9.85534	+	12.3582i	−0.690012	+	0.865248i
$205$	−4.45654	−	1.37466i	−0.311259	−	0.0960106i
$206$	−15.4237	+	39.2988i	−1.07462	+	2.73808i
$207$	−0.283103	+	0.0873258i	−0.0196770	+	0.00606956i
$208$	0.785738	−	10.4849i	0.0544811	−	0.727000i
$209$	0.127259	−	0.557558i	0.00880269	−	0.0385671i
$210$	3.06656	+	2.55671i	0.211613	+	0.176429i
$211$	5.56789	+	24.3945i	0.383310	+	1.67939i	0.687031	+	0.726628i	$0.258914\pi$
$211$	5.56789	+	24.3945i	0.383310	+	1.67939i	−0.303721	+	0.952761i	$0.598229\pi$
$212$	20.6459	−	3.11187i	1.41796	−	0.213724i
$213$	10.6011	+	7.22773i	0.726378	+	0.495236i
$214$	12.2590	+	21.2333i	0.838011	+	1.45148i
$215$	−1.27990	+	2.21685i	−0.0872882	+	0.151188i
$216$	1.53733	−	0.740338i	0.104602	−	0.0503736i
$217$	−5.59884	+	2.05784i	−0.380074	+	0.139695i
$218$	26.7527	+	12.8834i	1.81192	+	0.872575i
$219$	1.01949	−	0.695078i	0.0688909	−	0.0469690i
$220$	−0.980053	+	0.909356i	−0.0660752	+	0.0613088i
$221$	−23.9424	+	22.2153i	−1.61054	+	1.49436i
$222$	−1.79817	+	1.22597i	−0.120686	+	0.0822820i
$223$	−17.3106	−	8.33633i	−1.15920	−	0.558242i	−0.247416	−	0.968909i	$-0.579581\pi$
$223$	−17.3106	−	8.33633i	−1.15920	−	0.558242i	−0.911785	+	0.410668i	$0.865296\pi$
$224$	−13.6520	+	14.0854i	−0.912166	+	0.941119i
$225$	4.07565	−	1.96273i	0.271710	−	0.130849i
$226$	7.74240	−	13.4102i	0.515017	−	0.892035i
$227$	−0.0135758	−	0.0235139i	−0.000901055	−	0.00156067i	0.865575	−	0.500780i	$-0.166953\pi$
$227$	−0.0135758	−	0.0235139i	−0.000901055	−	0.00156067i	−0.866476	+	0.499219i	$0.833620\pi$
$228$	−1.88580	−	1.28572i	−0.124890	−	0.0851487i
$229$	4.78410	−	0.721087i	0.316142	−	0.0476508i	0.0109456	−	0.999940i	$-0.496516\pi$
$229$	4.78410	−	0.721087i	0.316142	−	0.0476508i	0.305197	+	0.952289i	$0.401278\pi$
$230$	−0.0994843	−	0.435869i	−0.00655980	−	0.0287404i
$231$	0.0401403	−	1.84282i	0.00264104	−	0.121248i
$232$	3.15489	−	13.8225i	0.207129	−	0.907491i
$233$	−0.0820888	+	1.09540i	−0.00537782	+	0.0717620i	−0.999247	−	0.0388007i	$-0.987646\pi$
$233$	−0.0820888	+	1.09540i	−0.00537782	+	0.0717620i	0.993869	+	0.110563i	$0.0352653\pi$
$234$	12.0032	−	3.70249i	0.784671	−	0.242039i
$235$	−2.06890	+	5.27148i	−0.134960	+	0.343873i
$236$	−18.8082	−	5.80157i	−1.22431	−	0.377650i
$237$	3.77094	−	4.72861i	0.244949	−	0.307156i
$238$	32.8401	−	1.74286i	2.12871	−	0.112973i
$239$	−2.46711	−	3.09366i	−0.159584	−	0.200112i	0.695611	−	0.718419i	$-0.255134\pi$
$239$	−2.46711	−	3.09366i	−0.159584	−	0.200112i	−0.855195	+	0.518307i	$0.826563\pi$
$240$	−0.461478	−	1.17583i	−0.0297883	−	0.0758993i
$241$	0.691452	+	9.22678i	0.0445403	+	0.594349i	0.974164	+	0.225840i	$0.0725127\pi$
$241$	0.691452	+	9.22678i	0.0445403	+	0.594349i	−0.929624	+	0.368509i	$0.879868\pi$
$242$	−22.7326	−	3.42638i	−1.46131	−	0.220256i
$243$	−0.733052	−	0.680173i	−0.0470253	−	0.0436331i
$244$	−6.41376			−0.410599
$245$	−0.150919	−	4.82898i	−0.00964189	−	0.308512i
$246$	14.7740			0.941955
$247$	−3.45713	−	3.20775i	−0.219972	−	0.204104i
$248$	−3.80402	−	0.573364i	−0.241556	−	0.0364087i
$249$	0.257823	+	3.44040i	0.0163388	+	0.218027i
$250$	5.25053	+	13.3781i	0.332073	+	0.846108i
$251$	2.52929	+	3.17163i	0.159647	+	0.200191i	0.855221	−	0.518263i	$-0.173421\pi$
$251$	2.52929	+	3.17163i	0.159647	+	0.200191i	−0.695574	+	0.718455i	$0.744850\pi$
$252$	−6.78762	−	2.83604i	−0.427580	−	0.178653i
$253$	−0.128691	+	0.161373i	−0.00809071	+	0.0101454i
$254$	−37.6403	−	11.6105i	−2.36176	−	0.728508i
$255$	−1.43351	+	3.65253i	−0.0897700	+	0.228730i
$256$	−2.36366	+	0.729093i	−0.147729	+	0.0455683i
$257$	−0.371363	+	4.95549i	−0.0231650	+	0.309115i	0.973571	+	0.228385i	$0.0733444\pi$
$257$	−0.371363	+	4.95549i	−0.0231650	+	0.309115i	−0.996736	+	0.0807305i	$0.974275\pi$
$258$	1.80443	−	7.90570i	0.112339	−	0.492188i
$259$	2.55416	+	0.641795i	0.158708	+	0.0398792i
$260$	2.45329	+	10.7486i	0.152147	+	0.666598i
$261$	−8.21636	+	1.23842i	−0.508580	+	0.0766561i
$262$	−32.8383	−	22.3888i	−2.02876	−	1.38318i
$263$	6.15524	+	10.6612i	0.379549	+	0.657398i	0.990997	−	0.133887i	$-0.0427460\pi$
$263$	6.15524	+	10.6612i	0.379549	+	0.657398i	−0.611448	+	0.791285i	$0.709413\pi$
$264$	0.594378	−	1.02949i	0.0365814	−	0.0633609i
$265$	4.66962	−	2.24877i	0.286853	−	0.138141i
$266$	0.605316	+	4.70983i	0.0371143	+	0.288778i
$267$	10.5222	+	5.06724i	0.643950	+	0.310110i
$268$	31.2772	−	21.3244i	1.91056	−	1.30260i
$269$	−3.50671	+	3.25375i	−0.213808	+	0.198385i	−0.779805	−	0.626023i	$-0.784682\pi$
$269$	−3.50671	+	3.25375i	−0.213808	+	0.198385i	0.565997	+	0.824407i	$0.308491\pi$
$270$	1.10621	−	1.02641i	0.0673217	−	0.0624654i
$271$	6.47848	−	4.41695i	0.393540	−	0.268311i	−0.350342	−	0.936622i	$-0.613935\pi$
$271$	6.47848	−	4.41695i	0.393540	−	0.268311i	0.743882	+	0.668311i	$0.232982\pi$
$272$	−9.37402	−	4.51429i	−0.568384	−	0.273719i
$273$	−12.9951	−	7.88495i	−0.786499	−	0.477219i
$274$	9.61192	−	4.62886i	0.580677	−	0.279639i
$275$	1.57577	−	2.72932i	0.0950227	−	0.164584i
$276$	0.411870	+	0.713380i	0.0247917	+	0.0429404i
$277$	−13.5198	−	9.21765i	−0.812326	−	0.553835i	0.0843940	−	0.996432i	$-0.473105\pi$
$277$	−13.5198	−	9.21765i	−0.812326	−	0.553835i	−0.896720	+	0.442598i	$0.854057\pi$
$278$	36.1553	−	5.44954i	2.16845	−	0.326841i
$279$	0.501690	+	2.19805i	0.0300354	+	0.131594i
$280$	1.41272	−	2.77717i	0.0844265	−	0.165968i
$281$	−2.19739	+	9.62741i	−0.131085	+	0.574323i	0.866135	+	0.499811i	$0.166597\pi$
$281$	−2.19739	+	9.62741i	−0.131085	+	0.574323i	−0.997220	+	0.0745121i	$0.976260\pi$
$282$	1.34060	−	17.8891i	0.0798318	−	1.06528i
$283$	−8.69639	+	2.68248i	−0.516947	+	0.159457i	−0.542241	−	0.840223i	$-0.682424\pi$
$283$	−8.69639	+	2.68248i	−0.516947	+	0.159457i	0.0252940	+	0.999680i	$0.491948\pi$
$284$	13.0333	−	33.2083i	0.773384	−	1.97055i
$285$	−0.541396	−	0.166998i	−0.0320695	−	0.00989213i
$286$	5.45629	−	6.84197i	0.322637	−	0.404574i
$287$	−11.8717	−	13.3670i	−0.700765	−	0.789032i
$288$	4.62258	+	5.79653i	0.272388	+	0.341564i
$289$	5.59689	+	14.2607i	0.329229	+	0.838862i
$290$	−0.937034	−	12.5038i	−0.0550245	−	0.734251i
$291$	−16.0446	−	2.41834i	−0.940553	−	0.141765i
$292$	−2.51491	−	2.33349i	−0.147174	−	0.136557i
$293$	−1.43734			−0.0839700			−0.0419850	−	0.999118i	$-0.513368\pi$
$293$	−1.43734			−0.0839700			−0.0419850	+	0.999118i	$0.513368\pi$
$294$	4.96585	+	14.4769i	0.289614	+	0.844310i
$295$	−4.88590			−0.284468
$296$	1.24504	+	1.15523i	0.0723667	+	0.0671465i
$297$	−0.688903	−	0.103835i	−0.0399742	−	0.00602514i
$298$	3.50488	+	46.7694i	0.203032	+	2.70928i
$299$	0.621841	+	1.58442i	0.0359620	+	0.0916296i
$300$	−7.84199	−	9.83354i	−0.452757	−	0.567740i
$301$	−8.60280	+	4.72008i	−0.495857	+	0.272061i
$302$	7.63105	−	9.56904i	0.439118	−	0.550636i
$303$	−3.09868	−	0.955816i	−0.178014	−	0.0549102i
$304$	0.548862	−	1.39848i	0.0314794	−	0.0802081i
$305$	−1.52138	+	0.469283i	−0.0871138	+	0.0268710i
$306$	0.928884	−	12.3951i	0.0531008	−	0.708580i
$307$	−6.56595	+	28.7673i	−0.374738	+	1.64184i	0.338537	+	0.940953i	$0.390068\pi$
$307$	−6.56595	+	28.7673i	−0.374738	+	1.64184i	−0.713276	+	0.700883i	$0.752789\pi$
$308$	−5.02016	+	1.03134i	−0.286050	+	0.0587662i
$309$	−4.29662	−	18.8247i	−0.244426	−	1.07090i
$310$	−3.36426	+	0.507080i	−0.191077	+	0.0288002i
$311$	3.63107	+	2.47562i	0.205899	+	0.140380i	0.661880	−	0.749610i	$-0.269759\pi$
$311$	3.63107	+	2.47562i	0.205899	+	0.140380i	−0.455981	+	0.889990i	$0.650711\pi$
$312$	−4.90146	−	8.48958i	−0.277491	−	0.480628i
$313$	9.73692	−	16.8648i	0.550363	−	0.953257i	−0.447885	−	0.894091i	$-0.647823\pi$
$313$	9.73692	−	16.8648i	0.550363	−	0.953257i	0.998248	−	0.0591658i	$-0.0188441\pi$
$314$	35.4788	−	17.0857i	2.00218	−	0.964201i
$315$	−1.81757	−	0.176085i	−0.102408	−	0.00992129i
$316$	−15.1509	−	7.29630i	−0.852306	−	0.410449i
$317$	1.88025	−	1.28193i	0.105605	−	0.0720003i	−0.509366	−	0.860550i	$-0.670120\pi$
$317$	1.88025	−	1.28193i	0.105605	−	0.0720003i	0.614971	+	0.788550i	$0.289168\pi$
$318$	−12.0357	+	11.1675i	−0.674926	+	0.626240i
$319$	−4.24354	+	3.93743i	−0.237593	+	0.220454i
$320$	−7.15675	+	4.87939i	−0.400074	+	0.272766i
$321$	−10.1033	−	4.86550i	−0.563912	−	0.271566i
$322$	0.540698	−	1.62628i	0.0301319	−	0.0906292i
$323$	−4.20460	+	2.02483i	−0.233950	+	0.112664i
$324$	−1.39021	+	2.40791i	−0.0772337	+	0.133773i
$325$	−12.9944	−	22.5070i	−0.720801	−	1.24846i
$326$	4.99376	+	3.40469i	0.276579	+	0.188568i
$327$	−13.4291	+	2.02411i	−0.742631	+	0.111934i
$328$	−2.56562	−	11.2407i	−0.141663	−	0.620664i
$329$	−17.2628	+	13.1620i	−0.951727	+	0.725642i
$330$	0.233943	−	1.02497i	0.0128781	−	0.0564227i
$331$	−0.0966490	+	1.28969i	−0.00531231	+	0.0708878i	−0.999230	−	0.0392389i	$-0.987507\pi$
$331$	−0.0966490	+	1.28969i	−0.00531231	+	0.0708878i	0.993918	+	0.110127i	$0.0351257\pi$
$332$	9.16639	−	2.82746i	0.503071	−	0.155177i
$333$	0.363657	−	0.926583i	0.0199283	−	0.0507764i
$334$	−2.93054	−	0.903951i	−0.160352	−	0.0494620i
$335$	5.85884	−	7.34675i	0.320103	−	0.401396i
$336$	0.825771	−	4.77115i	0.0450495	−	0.260287i
$337$	4.55785	+	5.71537i	0.248282	+	0.311336i	0.890319	−	0.455338i	$-0.150482\pi$
$337$	4.55785	+	5.71537i	0.248282	+	0.311336i	−0.642036	+	0.766674i	$0.721910\pi$
$338$	−15.9809	−	40.7186i	−0.869246	−	2.21480i
$339$	0.529259	+	7.06247i	0.0287454	+	0.383581i
$340$	10.7878	+	1.62600i	0.585052	+	0.0881824i
$341$	1.15142	+	1.06837i	0.0623532	+	0.0578553i
$342$	1.79479			0.0970512
$343$	9.10792	−	16.1259i	0.491782	−	0.870719i
$344$	−6.32837			−0.341203
$345$	0.149894	+	0.139082i	0.00807005	+	0.00748791i
$346$	13.2931	+	2.00361i	0.714641	+	0.107715i
$347$	−1.99657	−	26.6423i	−0.107181	−	1.43023i	−0.748589	−	0.663034i	$-0.769268\pi$
$347$	−1.99657	−	26.6423i	−0.107181	−	1.43023i	0.641408	−	0.767200i	$-0.278351\pi$
$348$	8.44044	+	21.5059i	0.452455	+	1.15284i
$349$	4.01375	+	5.03308i	0.214851	+	0.269414i	0.877565	−	0.479458i	$-0.159167\pi$
$349$	4.01375	+	5.03308i	0.214851	+	0.269414i	−0.662714	+	0.748873i	$0.730595\pi$
$350$	−4.46269	+	25.7846i	−0.238541	+	1.37824i
$351$	−3.58203	+	4.49172i	−0.191194	+	0.239750i
$352$	4.93577	+	1.52248i	0.263077	+	0.0811487i
$353$	2.34561	−	5.97652i	0.124844	−	0.318098i	−0.854763	−	0.519018i	$-0.826298\pi$
$353$	2.34561	−	5.97652i	0.124844	−	0.318098i	0.979608	+	0.200920i	$0.0643930\pi$
$354$	14.7901	−	4.56214i	0.786085	−	0.242475i
$355$	0.661777	−	8.83081i	0.0351235	−	0.468690i
$356$	7.22567	−	31.6577i	0.382960	−	1.67786i
$357$	−11.9611	+	9.11972i	−0.633049	+	0.482667i
$358$	5.78814	+	25.3595i	0.305913	+	1.34029i
$359$	20.9748	−	3.16144i	1.10701	−	0.166854i	0.429998	−	0.902830i	$-0.358514\pi$
$359$	20.9748	−	3.16144i	1.10701	−	0.166854i	0.677008	+	0.735976i	$0.263276\pi$
$360$	−0.973042	−	0.663409i	−0.0512838	−	0.0349647i
$361$	9.16308	+	15.8709i	0.482267	+	0.835311i
$362$	−15.1472	+	26.2356i	−0.796117	+	1.37891i
$363$	9.47335	−	4.56213i	0.497222	−	0.239450i
$364$	−13.3337	+	40.1043i	−0.698874	+	2.10203i
$365$	−0.767286	−	0.369506i	−0.0401616	−	0.0193408i
$366$	4.16717	−	2.84113i	0.217822	−	0.148508i
$367$	6.38268	−	5.92226i	0.333173	−	0.309139i	−0.495790	−	0.868442i	$-0.665122\pi$
$367$	6.38268	−	5.92226i	0.333173	−	0.309139i	0.828963	+	0.559303i	$0.188931\pi$
$368$	−0.397465	+	0.368794i	−0.0207193	+	0.0192247i
$369$	−5.58304	+	3.80645i	−0.290641	+	0.198156i
$370$	1.35334	+	0.651732i	0.0703566	+	0.0338819i
$371$	19.7753	+	1.91583i	1.02668	+	0.0994647i
$372$	5.64786	−	2.71986i	0.292828	−	0.141018i
$373$	−9.24794	+	16.0179i	−0.478840	+	0.829376i	−0.999706	−	0.0242630i	$-0.992276\pi$
$373$	−9.24794	+	16.0179i	−0.478840	+	0.829376i	0.520865	+	0.853639i	$0.325609\pi$
$374$	−4.32984	−	7.49951i	−0.223891	−	0.387790i
$375$	−5.43098	−	3.70278i	−0.280454	−	0.191211i
$376$	−13.8436	+	2.08659i	−0.713932	+	0.107608i
$377$	10.6225	+	46.5403i	0.547088	+	2.39695i
$378$	5.66637	−	1.16410i	0.291447	−	0.0598748i
$379$	2.37392	−	10.4008i	0.121940	−	0.534254i	−0.876648	−	0.481132i	$-0.840226\pi$
$379$	2.37392	−	10.4008i	0.121940	−	0.534254i	0.998588	−	0.0531219i	$-0.0169172\pi$
$380$	−0.117721	+	1.57088i	−0.00603898	+	0.0805846i
$381$	17.2155	−	5.31029i	0.881979	−	0.272054i
$382$	10.5476	−	26.8748i	0.539661	−	1.37503i
$383$	8.87562	+	2.73777i	0.453523	+	0.139893i	0.513097	−	0.858331i	$-0.328498\pi$
$383$	8.87562	+	2.73777i	0.453523	+	0.139893i	−0.0595741	+	0.998224i	$0.518974\pi$
$384$	7.86297	−	9.85985i	0.401255	−	0.503158i
$385$	−1.11535	+	0.611956i	−0.0568434	+	0.0311881i
$386$	−30.4044	−	38.1259i	−1.54754	−	1.94056i
$387$	1.35498	+	3.45244i	0.0688777	+	0.175497i
$388$	3.37141	+	44.9884i	0.171158	+	2.28394i
$389$	28.7783	+	4.33764i	1.45912	+	0.219927i	0.830166	−	0.557516i	$-0.188245\pi$
$389$	28.7783	+	4.33764i	1.45912	+	0.219927i	0.628953	+	0.777443i	$0.283484\pi$
$390$	−6.35530	−	5.89686i	−0.321813	−	0.298599i
$391$	1.68428			0.0851778
$392$	10.1523	−	6.29227i	0.512769	−	0.317808i
$393$	18.1778			0.916951
$394$	43.2400	+	40.1209i	2.17840	+	2.02126i
$395$	−4.12773	−	0.622156i	−0.207689	−	0.0313041i
$396$	0.144757	+	1.93165i	0.00727433	+	0.0970692i
$397$	−0.802234	−	2.04406i	−0.0402630	−	0.102588i	0.909328	−	0.416080i	$-0.136596\pi$
$397$	−0.802234	−	2.04406i	−0.0402630	−	0.102588i	−0.949591	+	0.313492i	$0.898501\pi$
$398$	−3.63950	−	4.56379i	−0.182432	−	0.228762i
$399$	−1.44221	−	1.62387i	−0.0722010	−	0.0812953i
$400$	5.16179	−	6.47267i	0.258089	−	0.323634i
$401$	−6.76651	−	2.08719i	−0.337904	−	0.104229i	0.121160	−	0.992633i	$-0.461339\pi$
$401$	−6.76651	−	2.08719i	−0.337904	−	0.104229i	−0.459063	+	0.888404i	$0.651815\pi$
$402$	−10.8754	+	27.7100i	−0.542414	+	1.38205i
$403$	12.3774	−	3.81791i	0.616560	−	0.190184i
$404$	−0.673779	+	8.99096i	−0.0335218	+	0.447317i
$405$	−0.153582	+	0.672887i	−0.00763155	+	0.0334360i
$406$	21.7932	−	42.8417i	1.08158	−	2.12620i
$407$	−0.154312	−	0.676087i	−0.00764898	−	0.0335124i
$408$	−9.59206	+	1.44577i	−0.474877	+	0.0715763i
$409$	−19.0475	−	12.9864i	−0.941839	−	0.642135i	−0.00805306	−	0.999968i	$-0.502563\pi$
$409$	−19.0475	−	12.9864i	−0.941839	−	0.642135i	−0.933786	+	0.357833i	$0.883516\pi$
$410$	−5.09844	−	8.83075i	−0.251794	−	0.436120i
$411$	−2.43971	+	4.22570i	−0.120342	+	0.208438i
$412$	−48.3699	+	23.2937i	−2.38301	+	1.14760i
$413$	−16.0123	−	9.71570i	−0.787916	−	0.478078i
$414$	−0.583611	−	0.281052i	−0.0286829	−	0.0138130i
$415$	1.96744	−	1.34137i	0.0965776	−	0.0658455i
$416$	31.2240	−	28.9717i	1.53088	−	1.42045i
$417$	−12.2589	+	11.3746i	−0.600322	+	0.557017i
$418$	1.03313	−	0.704377i	0.0505321	−	0.0344522i
$419$	−15.2843	−	7.36052i	−0.746686	−	0.359585i	0.0215365	−	0.999768i	$-0.493144\pi$
$419$	−15.2843	−	7.36052i	−0.746686	−	0.359585i	−0.768222	+	0.640183i	$0.778858\pi$
$420$	0.647213	+	5.03582i	0.0315807	+	0.245723i
$421$	28.5313	−	13.7400i	1.39053	−	0.669644i	0.419314	−	0.907841i	$-0.362271\pi$
$421$	28.5313	−	13.7400i	1.39053	−	0.669644i	0.971217	+	0.238197i	$0.0765564\pi$
$422$	−27.3541	+	47.3787i	−1.33158	+	2.30636i
$423$	4.10244	+	7.10563i	0.199467	+	0.345488i
$424$	10.5868	+	7.21795i	0.514140	+	0.350535i
$425$	−25.4298	+	3.83293i	−1.23353	+	0.185924i
$426$	6.24238	+	27.3497i	0.302444	+	1.32510i
$427$	−5.91912	−	1.48733i	−0.286446	−	0.0719768i
$428$	−6.93800	+	30.3974i	−0.335361	+	1.46931i
$429$	−0.299110	+	3.99135i	−0.0144412	+	0.192704i
$430$	−5.34812	+	1.64968i	−0.257909	+	0.0795545i
$431$	4.50740	−	11.4847i	0.217114	−	0.553197i	−0.780273	−	0.625439i	$-0.784920\pi$
$431$	4.50740	−	11.4847i	0.217114	−	0.553197i	0.997387	+	0.0722416i	$0.0230152\pi$
$432$	−1.74883	−	0.539442i	−0.0841405	−	0.0259539i
$433$	6.73179	−	8.44140i	0.323509	−	0.405668i	−0.593308	−	0.804976i	$-0.702178\pi$
$433$	6.73179	−	8.44140i	0.323509	−	0.405668i	0.916817	+	0.399308i	$0.130750\pi$
$434$	−12.0339	−	5.02805i	−0.577644	−	0.241354i
$435$	3.57566	+	4.48374i	0.171440	+	0.214979i
$436$	13.7954	+	35.1500i	0.660677	+	1.68338i
$437$	0.0181743	+	0.242519i	0.000869396	+	0.0116013i
$438$	2.66767	+	0.402087i	0.127466	+	0.0192125i
$439$	−9.81884	−	9.11056i	−0.468628	−	0.434823i	0.410176	−	0.912006i	$-0.365467\pi$
$439$	−9.81884	−	9.11056i	−0.468628	−	0.434823i	−0.878804	+	0.477183i	$0.841658\pi$
$440$	−0.820469			−0.0391143
$441$	−5.60648	−	4.19134i	−0.266975	−	0.199588i
$442$	−71.4110			−3.39668
$443$	−21.1587	−	19.6324i	−1.00528	−	0.932764i	−0.00754171	−	0.999972i	$-0.502401\pi$
$443$	−21.1587	−	19.6324i	−1.00528	−	0.932764i	−0.997739	+	0.0672073i	$0.978591\pi$
$444$	−2.73668	−	0.412489i	−0.129877	−	0.0195759i
$445$	−0.602370	−	8.03807i	−0.0285551	−	0.381041i
$446$	−15.3473	−	39.1043i	−0.726716	−	1.85164i
$447$	−13.3744	−	16.7710i	−0.632588	−	0.793240i
$448$	−33.1573	+	1.75969i	−1.56653	+	0.0831375i
$449$	−10.1857	+	12.7724i	−0.480691	+	0.602768i	−0.961753	−	0.273919i	$-0.911680\pi$
$449$	−10.1857	+	12.7724i	−0.480691	+	0.602768i	0.481062	+	0.876687i	$0.340251\pi$
$450$	9.45114	+	2.91529i	0.445531	+	0.137428i
$451$	−1.71989	+	4.38220i	−0.0809862	+	0.206350i
$452$	18.8168	−	5.80422i	0.885068	−	0.273007i
$453$	−0.418329	+	5.58221i	−0.0196548	+	0.262275i
$454$	0.0132098	−	0.0578761i	0.000619969	−	0.00271626i
$455$	−0.228462	+	10.4885i	−0.0107104	+	0.491710i
$456$	−0.311680	−	1.36556i	−0.0145957	−	0.0639481i
$457$	−24.0137	+	3.61949i	−1.12332	+	0.169313i	−0.684324	−	0.729178i	$-0.739902\pi$
$457$	−24.0137	+	3.61949i	−1.12332	+	0.169313i	−0.438992	+	0.898491i	$0.644664\pi$
$458$	8.74011	+	5.95890i	0.408398	+	0.278441i
$459$	2.84252	+	4.92339i	0.132677	+	0.229804i
$460$	0.284269	−	0.492369i	0.0132541	−	0.0229568i
$461$	26.3733	−	12.7007i	1.22833	−	0.591531i	0.296707	−	0.954968i	$-0.404111\pi$
$461$	26.3733	−	12.7007i	1.22833	−	0.591531i	0.931618	+	0.363438i	$0.118397\pi$
$462$	2.80486	−	2.89389i	0.130494	−	0.134636i
$463$	−13.4752	−	6.48930i	−0.626244	−	0.301583i	0.0937157	−	0.995599i	$-0.470126\pi$
$463$	−13.4752	−	6.48930i	−0.626244	−	0.301583i	−0.719960	+	0.694016i	$0.755840\pi$
$464$	−12.5645	+	8.56635i	−0.583293	+	0.397683i
$465$	1.14069	−	1.05841i	0.0528984	−	0.0490825i
$466$	−1.76058	+	1.63358i	−0.0815573	+	0.0756741i
$467$	10.6247	−	7.24378i	0.491651	−	0.335202i	−0.291984	−	0.956423i	$-0.594315\pi$
$467$	10.6247	−	7.24378i	0.491651	−	0.335202i	0.783635	+	0.621221i	$0.213363\pi$
$468$	14.3919	+	6.93077i	0.665266	+	0.320375i
$469$	33.8101	−	12.4268i	1.56121	−	0.573816i
$470$	−11.1554	+	5.37215i	−0.514559	+	0.247799i
$471$	−9.00526	+	15.5976i	−0.414941	+	0.718698i
$472$	−6.03950	−	10.4607i	−0.277991	−	0.481494i
$473$	2.13490	+	1.45555i	0.0981627	+	0.0669262i
$474$	13.0760	−	1.97089i	0.600600	−	0.0905259i
$475$	−0.826304	−	3.62027i	−0.0379134	−	0.166110i
$476$	32.1212	+	26.7806i	1.47227	+	1.22749i
$477$	1.67099	−	7.32107i	0.0765092	−	0.335209i
$478$	0.646529	−	8.62732i	0.0295715	−	0.394605i
$479$	35.9947	−	11.1029i	1.64464	−	0.507305i	0.672184	−	0.740384i	$-0.265356\pi$
$479$	35.9947	−	11.1029i	1.64464	−	0.507305i	0.972458	+	0.233079i	$0.0748801\pi$
$480$	1.86949	−	4.76338i	0.0853301	−	0.217418i
$481$	−5.46458	−	1.68560i	−0.249163	−	0.0768567i
$482$	−12.6133	+	15.8166i	−0.574520	+	0.720425i
$483$	0.214676	+	0.753875i	0.00976811	+	0.0343025i
$484$	−18.2277	−	22.8568i	−0.828533	−	1.03895i
$485$	4.09143	+	10.4248i	0.185782	+	0.473366i
$486$	−0.163391	−	2.18030i	−0.00741157	−	0.0989005i
$487$	2.37547	+	0.358044i	0.107643	+	0.0162245i	0.202643	−	0.979253i	$-0.435047\pi$
$487$	2.37547	+	0.358044i	0.107643	+	0.0162245i	−0.0949999	+	0.995477i	$0.530285\pi$
$488$	−2.88532	−	2.67719i	−0.130612	−	0.121191i
$489$	−2.76433			−0.125007
$490$	6.93949	−	7.96412i	0.313494	−	0.359782i
$491$	−19.0628			−0.860291			−0.430145	−	0.902760i	$-0.641538\pi$
$491$	−19.0628			−0.860291			−0.430145	+	0.902760i	$0.641538\pi$
$492$	13.7724	+	12.7789i	0.620906	+	0.576117i
$493$	46.7103	+	7.04045i	2.10373	+	0.317086i
$494$	−0.770564	−	10.2825i	−0.0346693	−	0.462630i
$495$	0.175673	+	0.447607i	0.00789590	+	0.0201184i
$496$	2.57263	+	3.22597i	0.115514	+	0.144850i
$497$	19.7290	−	27.6249i	0.884968	−	1.23915i
$498$	−4.70313	+	5.89754i	−0.210752	+	0.264275i
$499$	−5.09302	−	1.57099i	−0.227995	−	0.0703271i	0.178653	−	0.983912i	$-0.442826\pi$
$499$	−5.09302	−	1.57099i	−0.227995	−	0.0703271i	−0.406648	+	0.913585i	$0.633302\pi$
$500$	−6.67698	+	17.0127i	−0.298604	+	0.760829i
$501$	1.34034	−	0.413440i	0.0598819	−	0.0184711i
$502$	−0.662823	+	8.84475i	−0.0295832	+	0.394761i
$503$	−4.02465	+	17.6332i	−0.179450	+	0.786224i	0.802434	+	0.596741i	$0.203538\pi$
$503$	−4.02465	+	17.6332i	−0.179450	+	0.786224i	−0.981884	+	0.189482i	$0.939319\pi$
$504$	−1.86971	−	4.10907i	−0.0832835	−	0.183033i
$505$	0.498028	+	2.18200i	0.0221619	+	0.0970978i
$506$	−0.446244	+	0.0672604i	−0.0198380	+	0.00299009i
$507$	16.5301	+	11.2700i	0.734127	+	0.500519i
$508$	−25.0459	−	43.3807i	−1.11123	−	1.92471i
$509$	12.7563	−	22.0945i	0.565412	−	0.979323i	−0.431599	−	0.902066i	$-0.642050\pi$
$509$	12.7563	−	22.0945i	0.565412	−	0.979323i	0.997011	−	0.0772570i	$-0.0246162\pi$
$510$	−7.72939	+	3.72228i	−0.342263	+	0.164825i
$511$	−1.77983	−	2.73673i	−0.0787349	−	0.121066i
$512$	17.8520	+	8.59707i	0.788954	+	0.379940i
$513$	−0.678246	+	0.462420i	−0.0299453	+	0.0204163i
$514$	−7.96472	+	7.39018i	−0.351309	+	0.325967i
$515$	−9.76923	+	9.06452i	−0.430484	+	0.399431i
$516$	8.52020	−	5.80898i	0.375081	−	0.255726i
$517$	5.15013	+	2.48017i	0.226502	+	0.109078i
$518$	3.13925	+	4.82703i	0.137931	+	0.212088i
$519$	−5.53964	+	2.66775i	−0.243163	+	0.117101i
$520$	−3.38295	+	5.85944i	−0.148352	+	0.256953i
$521$	10.7844	+	18.6791i	0.472472	+	0.818345i	0.999504	−	0.0315002i	$-0.0100285\pi$
$521$	10.7844	+	18.6791i	0.472472	+	0.818345i	−0.527032	+	0.849846i	$0.676695\pi$
$522$	−15.0105	−	10.2340i	−0.656992	−	0.447930i
$523$	24.0162	−	3.61986i	1.05016	−	0.158285i	0.398784	−	0.917045i	$-0.369432\pi$
$523$	24.0162	−	3.61986i	1.05016	−	0.158285i	0.651371	+	0.758759i	$0.274194\pi$
$524$	−11.2466	−	49.2747i	−0.491311	−	2.15257i
$525$	−4.95685	−	10.8937i	−0.216334	−	0.475440i
$526$	−5.98934	+	26.2410i	−0.261148	+	1.14416i
$527$	0.957841	−	12.7815i	0.0417242	−	0.556771i
$528$	−1.21838	+	0.375821i	−0.0530232	+	0.0163555i
$529$	−8.37078	+	21.3284i	−0.363947	+	0.927321i
$530$	10.8285	+	3.34015i	0.470360	+	0.145087i
$531$	−4.41371	+	5.53462i	−0.191539	+	0.240182i
$532$	−3.50954	+	4.91410i	−0.152158	+	0.213053i
$533$	24.2044	+	30.3513i	1.04841	+	1.31466i
$534$	9.32888	+	23.7696i	0.403700	+	1.02861i
$535$	0.578388	+	7.71805i	0.0250059	+	0.333680i
$536$	22.9716	+	3.46241i	0.992222	+	0.149553i
$537$	−8.72107	−	8.09197i	−0.376342	−	0.349194i
$538$	−10.4592			−0.450927
$539$	−4.87217	−	0.212352i	−0.209859	−	0.00914665i
$540$	1.91902			0.0825813
$541$	−5.93408	−	5.50602i	−0.255126	−	0.236722i	0.542232	−	0.840229i	$-0.317579\pi$
$541$	−5.93408	−	5.50602i	−0.255126	−	0.236722i	−0.797358	+	0.603506i	$0.793770\pi$
$542$	16.9521	+	2.55511i	0.728153	+	0.109751i
$543$	−1.03544	−	13.8170i	−0.0444349	−	0.592942i
$544$	−15.3988	−	39.2355i	−0.660218	−	1.68221i
$545$	5.84419	+	7.32838i	0.250337	+	0.313913i
$546$	−9.10196	−	31.9632i	−0.389528	−	1.36790i
$547$	3.17296	−	3.97877i	0.135666	−	0.170120i	−0.709358	−	0.704849i	$-0.751015\pi$
$547$	3.17296	−	3.97877i	0.135666	−	0.170120i	0.845024	+	0.534729i	$0.179586\pi$
$548$	12.9640	+	3.99888i	0.553797	+	0.170824i
$549$	−0.842756	+	2.14731i	−0.0359679	+	0.0916448i
$550$	6.58446	−	2.03104i	0.280762	−	0.0866037i
$551$	−0.509723	+	6.80178i	−0.0217149	+	0.289766i
$552$	−0.112489	+	0.492845i	−0.00478783	+	0.0209769i
$553$	−12.2905	−	10.2470i	−0.522645	−	0.435749i
$554$	−7.96101	−	34.8795i	−0.338231	−	1.48189i
$555$	−0.679337	+	0.102394i	−0.0288362	+	0.00434636i
$556$	38.4178	+	26.1928i	1.62928	+	1.11082i
$557$	10.4722	+	18.1384i	0.443723	+	0.768550i	0.997962	−	0.0638070i	$-0.0203242\pi$
$557$	10.4722	+	18.1384i	0.443723	+	0.768550i	−0.554240	+	0.832357i	$0.686991\pi$
$558$	−2.46472	+	4.26902i	−0.104340	+	0.180722i
$559$	19.1975	−	9.24502i	0.811967	−	0.391023i
$560$	−3.13680	+	1.15292i	−0.132554	+	0.0487198i
$561$	3.56845	+	1.71847i	0.150660	+	0.0725540i
$562$	−17.8392	+	12.1625i	−0.752501	+	0.513046i
$563$	−5.48255	+	5.08707i	−0.231062	+	0.214394i	−0.787203	−	0.616693i	$-0.788472\pi$
$563$	−5.48255	+	5.08707i	−0.231062	+	0.214394i	0.556141	+	0.831088i	$0.312281\pi$
$564$	16.7231	−	15.5167i	0.704168	−	0.653373i
$565$	4.03876	−	2.75358i	0.169912	−	0.115844i
$566$	−17.9274	−	8.63339i	−0.753546	−	0.362888i
$567$	−1.84138	+	1.89982i	−0.0773306	+	0.0797851i
$568$	19.7248	−	9.49897i	0.827635	−	0.398568i
$569$	−16.6322	+	28.8078i	−0.697257	+	1.20769i	0.272156	+	0.962253i	$0.412263\pi$
$569$	−16.6322	+	28.8078i	−0.697257	+	1.20769i	−0.969414	+	0.245432i	$0.921070\pi$
$570$	−0.619375	−	1.07279i	−0.0259428	−	0.0449342i
$571$	−27.1777	−	18.5294i	−1.13735	−	0.775433i	−0.160012	−	0.987115i	$-0.551153\pi$
$571$	−27.1777	−	18.5294i	−1.13735	−	0.775433i	−0.977339	+	0.211682i	$0.932106\pi$
$572$	11.0044	−	1.65865i	0.460117	−	0.0693515i
$573$	2.93828	+	12.8734i	0.122748	+	0.537795i
$574$	0.851220	−	39.0790i	0.0355292	−	1.63113i
$575$	−0.298222	+	1.30660i	−0.0124367	+	0.0544888i
$576$	−0.937856	+	12.5148i	−0.0390773	+	0.521451i
$577$	12.7144	−	3.92188i	0.529309	−	0.163270i	−0.0185706	−	0.999828i	$-0.505912\pi$
$577$	12.7144	−	3.92188i	0.529309	−	0.163270i	0.547879	+	0.836557i	$0.315435\pi$
$578$	−12.2371	+	31.1797i	−0.508998	+	1.29690i
$579$	21.3127	+	6.57409i	0.885724	+	0.273210i
$580$	9.94181	−	12.4666i	0.412811	−	0.517649i
$581$	9.11515	−	0.483750i	0.378160	−	0.0200693i
$582$	−22.1192	−	27.7366i	−0.916871	−	1.14972i
$583$	−1.91134	−	4.87000i	−0.0791594	−	0.201695i
$584$	−0.157337	−	2.09951i	−0.00651064	−	0.0868784i
$585$	3.92095	+	0.590988i	0.162111	+	0.0244343i
$586$	−2.30370	−	2.13752i	−0.0951648	−	0.0883001i
$587$	−38.0655			−1.57113			−0.785565	−	0.618779i	$-0.787628\pi$
$587$	−38.0655			−1.57113			−0.785565	+	0.618779i	$0.787628\pi$
$588$	−7.89274	+	17.7907i	−0.325491	+	0.733675i
$589$	1.85074			0.0762585
$590$	−7.83090	−	7.26601i	−0.322393	−	0.299137i
$591$	−26.6772	−	4.02094i	−1.09735	−	0.165400i
$592$	−0.136136	−	1.81660i	−0.00559514	−	0.0746620i
$593$	−15.0534	−	38.3555i	−0.618169	−	1.57507i	−0.805386	−	0.592751i	$-0.798042\pi$
$593$	−15.0534	−	38.3555i	−0.618169	−	1.57507i	0.187216	−	0.982319i	$-0.440053\pi$
$594$	−0.949726	−	1.19092i	−0.0389677	−	0.0488640i
$595$	9.57880	+	4.00226i	0.392692	+	0.164077i
$596$	−37.1863	+	46.6302i	−1.52321	+	1.91005i
$597$	2.55119	+	0.786939i	0.104413	+	0.0322073i
$598$	−1.35960	+	3.46421i	−0.0555982	+	0.141662i
$599$	24.9427	−	7.69379i	1.01913	−	0.314360i	0.260216	−	0.965551i	$-0.416206\pi$
$599$	24.9427	−	7.69379i	1.01913	−	0.314360i	0.758914	+	0.651191i	$0.225730\pi$
$600$	0.576819	−	7.69711i	0.0235485	−	0.314233i
$601$	−7.87265	+	34.4924i	−0.321132	+	1.40697i	0.514409	+	0.857545i	$0.328011\pi$
$601$	−7.87265	+	34.4924i	−0.321132	+	1.40697i	−0.835541	+	0.549427i	$0.814846\pi$
$602$	−20.8076	−	5.22842i	−0.848055	−	0.213095i
$603$	−3.02959	−	13.2735i	−0.123374	−	0.540538i
$604$	15.3905	−	2.31975i	0.626232	−	0.0943893i
$605$	−5.99610	−	4.08808i	−0.243776	−	0.166204i
$606$	−3.54499	−	6.14011i	−0.144006	−	0.249425i
$607$	1.58531	−	2.74584i	0.0643457	−	0.111450i	−0.832058	−	0.554689i	$-0.812837\pi$
$607$	1.58531	−	2.74584i	0.0643457	−	0.111450i	0.896404	+	0.443239i	$0.146171\pi$
$608$	5.48335	−	2.64064i	0.222379	−	0.107092i
$609$	2.80237	+	21.8046i	0.113558	+	0.883569i
$610$	−3.13628	−	1.51035i	−0.126984	−	0.0611525i
$611$	38.9473	−	26.5538i	1.57564	−	1.07425i
$612$	11.5872	−	10.7513i	0.468383	−	0.434596i
$613$	−3.96550	+	3.67944i	−0.160165	+	0.148611i	−0.756184	−	0.654359i	$-0.772939\pi$
$613$	−3.96550	+	3.67944i	−0.160165	+	0.148611i	0.596019	+	0.802970i	$0.296748\pi$
$614$	−53.3046	+	36.3425i	−2.15120	+	1.46666i
$615$	4.20189	+	2.02352i	0.169436	+	0.0815963i
$616$	−2.68889	−	1.63152i	−0.108338	−	0.0657357i
$617$	9.92557	−	4.77990i	0.399588	−	0.192432i	−0.223287	−	0.974753i	$-0.571679\pi$
$617$	9.92557	−	4.77990i	0.399588	−	0.192432i	0.622875	+	0.782321i	$0.285964\pi$
$618$	21.1086	−	36.5611i	0.849111	−	1.47070i
$619$	−4.28616	−	7.42385i	−0.172275	−	0.298390i	0.766940	−	0.641719i	$-0.221779\pi$
$619$	−4.28616	−	7.42385i	−0.172275	−	0.298390i	−0.939215	+	0.343329i	$0.888445\pi$
$620$	−3.57478	−	2.43724i	−0.143567	−	0.0978820i
$621$	0.292957	−	0.0441561i	0.0117559	−	0.00177192i
$622$	2.13812	+	9.36773i	0.0857309	+	0.375612i
$623$	14.0097	−	27.5407i	0.561288	−	1.10339i
$624$	−2.33966	+	10.2507i	−0.0936615	+	0.410358i
$625$	1.35123	−	18.0309i	0.0540492	−	0.721236i
$626$	40.6863	−	12.5501i	1.62615	−	0.501601i
$627$	−0.208937	+	0.532364i	−0.00834415	+	0.0212606i
$628$	47.8519	+	14.7604i	1.90950	+	0.589002i
$629$	−3.52822	+	4.42425i	−0.140680	+	0.176407i
$630$	−2.65125	−	2.98520i	−0.105628	−	0.118933i
$631$	26.2164	+	32.8743i	1.04366	+	1.30870i	0.949711	+	0.313128i	$0.101377\pi$
$631$	26.2164	+	32.8743i	1.04366	+	1.30870i	0.0939461	+	0.995577i	$0.470052\pi$
$632$	−3.77029	−	9.60655i	−0.149974	−	0.382128i
$633$	−1.86989	−	24.9519i	−0.0743214	−	0.991750i
$634$	4.91998	+	0.741568i	0.195398	+	0.0294514i
$635$	−9.11509	−	8.45757i	−0.361721	−	0.335628i
$636$	−20.8791			−0.827909
$637$	−21.6054	+	33.9194i	−0.856037	+	1.34393i
$638$	−12.6569			−0.501090
$639$	−9.40549	−	8.72702i	−0.372075	−	0.345236i
$640$	−8.60694	−	1.29729i	−0.340219	−	0.0512798i
$641$	2.61290	+	34.8667i	0.103203	+	1.37715i	0.772905	+	0.634522i	$0.218803\pi$
$641$	2.61290	+	34.8667i	0.103203	+	1.37715i	−0.669701	+	0.742631i	$0.733578\pi$
$642$	−8.95747	−	22.8233i	−0.353523	−	0.900762i
$643$	−12.3286	−	15.4596i	−0.486194	−	0.609668i	0.476859	−	0.878980i	$-0.341775\pi$
$643$	−12.3286	−	15.4596i	−0.486194	−	0.609668i	−0.963053	+	0.269312i	$0.913204\pi$
$644$	1.91071	−	1.04835i	0.0752925	−	0.0413106i
$645$	1.59601	−	2.00133i	0.0628427	−	0.0788022i
$646$	−9.75014	−	3.00752i	−0.383614	−	0.118329i
$647$	−8.18512	+	20.8553i	−0.321790	+	0.819908i	0.674846	+	0.737958i	$0.264210\pi$
$647$	−8.18512	+	20.8553i	−0.321790	+	0.819908i	−0.996636	+	0.0819499i	$0.973885\pi$
$648$	−1.63050	+	0.502942i	−0.0640520	+	0.0197574i
$649$	−0.368558	+	4.91807i	−0.0144672	+	0.193051i
$650$	12.6442	−	55.3977i	0.495945	−	2.17288i
$651$	5.84301	−	1.20039i	0.229006	−	0.0470470i
$652$	1.71029	+	7.49326i	0.0669801	+	0.293459i
$653$	−15.2976	+	2.30574i	−0.598640	+	0.0902305i	−0.441370	−	0.897325i	$-0.645507\pi$
$653$	−15.2976	+	2.30574i	−0.598640	+	0.0902305i	−0.157270	+	0.987556i	$0.550269\pi$
$654$	−24.5337	−	16.7268i	−0.959344	−	0.654070i
$655$	−6.27309	−	10.8653i	−0.245110	−	0.424543i
$656$	−6.18327	+	10.7097i	−0.241416	+	0.418145i
$657$	−1.11170	+	0.535367i	−0.0433716	+	0.0208867i
$658$	−47.2417	−	4.57676i	−1.84167	−	0.178421i
$659$	−17.3346	−	8.34789i	−0.675259	−	0.325188i	0.0646370	−	0.997909i	$-0.479411\pi$
$659$	−17.3346	−	8.34789i	−0.675259	−	0.325188i	−0.739896	+	0.672721i	$0.765125\pi$
$660$	1.10464	−	0.753130i	0.0429980	−	0.0293156i
$661$	−1.40622	+	1.30478i	−0.0546955	+	0.0507500i	−0.707047	−	0.707167i	$-0.749973\pi$
$661$	−1.40622	+	1.30478i	−0.0546955	+	0.0507500i	0.652352	+	0.757917i	$0.273783\pi$
$662$	−2.07286	+	1.92333i	−0.0805639	+	0.0747523i
$663$	26.9860	−	18.3987i	1.04805	−	0.714547i
$664$	5.30385	+	2.55420i	0.205829	+	0.0991222i
$665$	−0.472925	+	1.42244i	−0.0183392	+	0.0551597i
$666$	1.96081	−	0.944277i	0.0759799	−	0.0365900i
$667$	1.23086	−	2.13191i	0.0476591	−	0.0825480i
$668$	−1.94998	−	3.37746i	−0.0754470	−	0.130678i
$669$	15.8747	+	10.8232i	0.613753	+	0.418450i
$670$	20.3159	−	3.06214i	0.784873	−	0.118301i
$671$	0.357611	+	1.56679i	0.0138054	+	0.0604854i
$672$	15.5989	−	11.8933i	0.601740	−	0.458795i
$673$	−5.80122	+	25.4168i	−0.223620	+	0.979745i	0.731107	+	0.682263i	$0.239004\pi$
$673$	−5.80122	+	25.4168i	−0.223620	+	0.979745i	−0.954727	+	0.297482i	$0.903853\pi$
$674$	−1.19443	+	15.9385i	−0.0460076	+	0.613928i
$675$	−4.32266	+	1.33337i	−0.166379	+	0.0513212i
$676$	20.3225	−	51.7809i	0.781635	−	1.99157i
$677$	−9.71012	−	2.99518i	−0.373190	−	0.115114i	0.102486	−	0.994734i	$-0.467320\pi$
$677$	−9.71012	−	2.99518i	−0.373190	−	0.115114i	−0.475676	+	0.879620i	$0.657797\pi$
$678$	−9.65462	+	12.1065i	−0.370783	+	0.464948i
$679$	−7.32123	+	42.3007i	−0.280963	+	1.62335i
$680$	4.17435	+	5.23447i	0.160079	+	0.200733i
$681$	0.00991957	+	0.0252746i	0.000380119	+	0.000968526i
$682$	0.256643	+	3.42466i	0.00982736	+	0.131137i
$683$	−32.7937	−	4.94285i	−1.25482	−	0.189133i	−0.512209	−	0.858861i	$-0.671173\pi$
$683$	−32.7937	−	4.94285i	−1.25482	−	0.189133i	−0.742607	+	0.669728i	$0.766411\pi$
$684$	1.67311	+	1.55242i	0.0639731	+	0.0593583i
$685$	3.36773			0.128674
$686$	38.5793	−	12.3012i	1.47296	−	0.469661i
$687$	−4.83814			−0.184587
$688$	4.97569	+	4.61676i	0.189696	+	0.176012i
$689$	−42.6603	−	6.43000i	−1.62523	−	0.244964i
$690$	0.0334102	+	0.445828i	0.00127190	+	0.0169724i
$691$	9.28188	+	23.6498i	0.353099	+	0.899682i	0.991515	+	0.129991i	$0.0414948\pi$
$691$	9.28188	+	23.6498i	0.353099	+	0.899682i	−0.638416	+	0.769692i	$0.720410\pi$
$692$	10.6588	+	13.3658i	0.405188	+	0.508090i
$693$	−0.314350	+	1.81625i	−0.0119412	+	0.0689937i
$694$	36.4208	−	45.6703i	1.38252	−	1.73362i
$695$	11.0294	+	3.40211i	0.418368	+	0.129049i
$696$	−5.17979	+	13.1979i	−0.196339	+	0.500265i
$697$	36.7081	−	11.3230i	1.39042	−	0.428887i
$698$	−1.05184	+	14.0358i	−0.0398126	+	0.531263i
$699$	0.244433	−	1.07093i	0.00924530	−	0.0405063i
$700$	−26.4628	+	20.1765i	−1.00020	+	0.762598i
$701$	−1.83588	−	8.04351i	−0.0693402	−	0.303799i	0.928352	−	0.371703i	$-0.121226\pi$
$701$	−1.83588	−	8.04351i	−0.0693402	−	0.303799i	−0.997692	+	0.0679038i	$0.978369\pi$
$702$	−12.4209	+	1.87215i	−0.468798	+	0.0706599i
$703$	−0.675119	−	0.460289i	−0.0254626	−	0.0173601i
$704$	4.37166	+	7.57194i	0.164763	+	0.285378i
$705$	2.83147	−	4.90425i	0.106639	−	0.184705i
$706$	12.6474	−	6.09065i	0.475990	−	0.229225i
$707$	−2.70679	+	8.14132i	−0.101799	+	0.306186i
$708$	17.7335	+	8.53999i	0.666464	+	0.320952i
$709$	11.2958	−	7.70134i	0.424222	−	0.289230i	−0.332330	−	0.943163i	$-0.607835\pi$
$709$	11.2958	−	7.70134i	0.424222	−	0.289230i	0.756552	+	0.653933i	$0.226882\pi$
$710$	14.1933	−	13.1695i	0.532665	−	0.494241i
$711$	−4.43358	+	4.11376i	−0.166272	+	0.154278i
$712$	16.4649	−	11.2256i	0.617050	−	0.420697i
$713$	−0.601805	−	0.289814i	−0.0225378	−	0.0108536i
$714$	−32.7330	−	3.17117i	−1.22500	−	0.118678i
$715$	2.48894	−	1.19861i	0.0930812	−	0.0448255i
$716$	−16.5392	+	28.6467i	−0.618099	+	1.07058i
$717$	1.97847	+	3.42681i	0.0738873	+	0.127977i
$718$	38.3189	+	26.1254i	1.43005	+	0.974991i
$719$	11.2512	−	1.69585i	0.419600	−	0.0632445i	0.0641510	−	0.997940i	$-0.479566\pi$
$719$	11.2512	−	1.69585i	0.419600	−	0.0632445i	0.355449	+	0.934696i	$0.384328\pi$
$720$	0.281076	+	1.23147i	0.0104751	+	0.0458943i
$721$	−50.0413	+	10.2805i	−1.86363	+	0.382865i
$722$	−8.91610	+	39.0640i	−0.331823	+	1.45381i
$723$	0.691452	−	9.22678i	0.0257154	−	0.343148i
$724$	−36.8130	+	11.3553i	−1.36814	+	0.422017i
$725$	−13.7323	+	34.9893i	−0.510005	+	1.29947i
$726$	21.9680	+	6.77623i	0.815309	+	0.251489i
$727$	24.4353	−	30.6409i	0.906255	−	1.13641i	−0.0839053	−	0.996474i	$-0.526739\pi$
$727$	24.4353	−	30.6409i	0.906255	−	1.13641i	0.990161	−	0.139935i	$-0.0446892\pi$
$728$	−22.7384	+	12.4758i	−0.842741	+	0.462385i
$729$	0.623490	+	0.781831i	0.0230922	+	0.0289567i
$730$	−0.680266	−	1.73329i	−0.0251778	−	0.0641519i
$731$	−1.57567	−	21.0258i	−0.0582781	−	0.777667i
$732$	6.34212	+	0.955921i	0.234412	+	0.0353318i
$733$	5.91960	+	5.49259i	0.218645	+	0.202873i	0.781889	−	0.623418i	$-0.214256\pi$
$733$	5.91960	+	5.49259i	0.218645	+	0.202873i	−0.563244	+	0.826291i	$0.690447\pi$
$734$	19.0371			0.702672
$735$	−0.570489	+	4.79754i	−0.0210428	+	0.176960i
$736$	−2.19653			−0.0809650
$737$	−6.95318	−	6.45161i	−0.256124	−	0.237648i
$738$	−14.6090	−	2.20195i	−0.537764	−	0.0810548i
$739$	−1.67910	−	22.4061i	−0.0617668	−	0.824221i	−0.938948	−	0.344060i	$-0.888198\pi$
$739$	−1.67910	−	22.4061i	−0.0617668	−	0.824221i	0.877181	−	0.480160i	$-0.159422\pi$
$740$	0.697864	+	1.77813i	0.0256540	+	0.0653653i
$741$	2.94042	+	3.68718i	0.108019	+	0.135452i
$742$	28.8458	+	32.4792i	1.05896	+	1.19235i
$743$	−8.75745	+	10.9815i	−0.321280	+	0.402872i	−0.916076	−	0.401004i	$-0.868661\pi$
$743$	−8.75745	+	10.9815i	−0.321280	+	0.402872i	0.594796	+	0.803876i	$0.297233\pi$
$744$	3.67608	+	1.13392i	0.134772	+	0.0415715i
$745$	−5.40895	+	13.7818i	−0.198169	+	0.504926i
$746$	−38.6431	+	11.9198i	−1.41482	+	0.436415i
$747$	0.257823	−	3.44040i	0.00943323	−	0.125878i
$748$	2.45047	−	10.7362i	0.0895981	−	0.392555i
$749$	−13.4520	+	26.4442i	−0.491524	+	0.966250i
$750$	−3.19798	−	14.0113i	−0.116774	−	0.511619i
$751$	−44.0912	+	6.64568i	−1.60891	+	0.242504i	−0.891124	−	0.453759i	$-0.850083\pi$
$751$	−44.0912	+	6.64568i	−1.60891	+	0.242504i	−0.717786	+	0.696264i	$0.754844\pi$
$752$	12.4068	+	8.45883i	0.452430	+	0.308462i
$753$	−2.02833	−	3.51317i	−0.0739165	−	0.128027i
$754$	−52.1866	+	90.3899i	−1.90053	+	3.29181i
$755$	3.48098	−	1.67635i	0.126686	−	0.0610087i
$756$	6.28911	+	3.81600i	0.228733	+	0.138787i
$757$	5.83541	+	2.81019i	0.212092	+	0.102138i	0.536914	−	0.843637i	$-0.319590\pi$
$757$	5.83541	+	2.81019i	0.212092	+	0.102138i	−0.324822	+	0.945775i	$0.605304\pi$
$758$	19.2723	−	13.1396i	0.700001	−	0.477253i
$759$	0.151305	−	0.140390i	0.00549201	−	0.00509584i
$760$	−0.708667	+	0.657547i	−0.0257060	+	0.0238517i
$761$	−6.28065	+	4.28208i	−0.227673	+	0.155225i	−0.671785	−	0.740747i	$-0.734472\pi$
$761$	−6.28065	+	4.28208i	−0.227673	+	0.155225i	0.444111	+	0.895972i	$0.353520\pi$
$762$	35.4894	+	17.0908i	1.28565	+	0.619135i
$763$	4.58029	+	35.6383i	0.165818	+	1.29019i
$764$	33.0781	−	15.9296i	1.19672	−	0.576312i
$765$	1.96188	−	3.39808i	0.0709320	−	0.122858i
$766$	10.1540	+	17.5873i	0.366879	+	0.635454i
$767$	33.6031	+	22.9102i	1.21334	+	0.827240i
$768$	2.44593	−	0.368664i	0.0882598	−	0.0133030i
$769$	−6.36795	−	27.8998i	−0.229634	−	1.00609i	−0.949939	−	0.312435i	$-0.898855\pi$
$769$	−6.36795	−	27.8998i	−0.229634	−	1.00609i	0.720305	−	0.693658i	$-0.244002\pi$
$770$	−2.69769	−	0.677862i	−0.0972181	−	0.0244285i
$771$	1.10579	−	4.84480i	0.0398242	−	0.174481i
$772$	4.63424	−	61.8397i	0.166790	−	2.22566i
$773$	−40.5910	+	12.5207i	−1.45996	+	0.450337i	−0.920189	−	0.391475i	$-0.871965\pi$
$773$	−40.5910	+	12.5207i	−1.45996	+	0.450337i	−0.539770	+	0.841813i	$0.681489\pi$
$774$	−2.96256	+	7.54847i	−0.106487	+	0.271324i
$775$	9.74577	+	3.00617i	0.350078	+	0.107985i
$776$	−17.2621	+	21.6460i	−0.619673	+	0.777045i
$777$	−2.42997	−	1.01530i	−0.0871748	−	0.0364238i
$778$	39.6740	+	49.7496i	1.42238	+	1.78361i
$779$	2.02649	+	5.16341i	0.0726066	+	0.184999i
$780$	−0.823898	−	10.9942i	−0.0295003	−	0.393654i
$781$	−8.83904	−	1.33227i	−0.316286	−	0.0476724i
$782$	2.69949	+	2.50476i	0.0965336	+	0.0895701i
$783$	8.30917			0.296945
$784$	−12.5727	−	2.45916i	−0.449025	−	0.0878272i
$785$	12.4307			0.443671
$786$	29.1346	+	27.0330i	1.03920	+	0.964235i
$787$	20.5450	+	3.09667i	0.732352	+	0.110384i	0.504622	−	0.863340i	$-0.331632\pi$
$787$	20.5450	+	3.09667i	0.732352	+	0.110384i	0.227729	+	0.973724i	$0.426870\pi$
$788$	5.60561	+	74.8017i	0.199692	+	2.66470i
$789$	−4.49753	−	11.4595i	−0.160116	−	0.407969i
$790$	−5.69052	−	7.13568i	−0.202460	−	0.253876i
$791$	18.7116	−	0.993044i	0.665308	−	0.0353086i
$792$	−0.741177	+	0.929407i	−0.0263366	+	0.0330250i
$793$	12.6639	+	3.90629i	0.449707	+	0.138716i
$794$	1.75402	−	4.46916i	0.0622478	−	0.158605i
$795$	−4.95263	+	1.52768i	−0.175652	+	0.0541813i
$796$	0.554733	−	7.40240i	0.0196620	−	0.262371i
$797$	10.4895	−	45.9577i	0.371559	−	1.62791i	−0.350845	−	0.936434i	$-0.614106\pi$
$797$	10.4895	−	45.9577i	0.371559	−	1.62791i	0.722404	−	0.691472i	$-0.243037\pi$
$798$	0.103409	−	4.74745i	0.00366064	−	0.168058i
$799$	−10.3795	−	45.4755i	−0.367200	−	1.60881i
$800$	33.1638	−	4.99864i	1.17252	−	0.176729i
$801$	−9.64948	−	6.57890i	−0.340948	−	0.232454i
$802$	−7.74112	−	13.4080i	−0.273348	−	0.473453i
$803$	−0.429818	+	0.744466i	−0.0151679	+	0.0262716i
$804$	−34.1061	+	16.4246i	−1.20283	+	0.579252i
$805$	0.376525	−	0.388476i	0.0132708	−	0.0136920i
$806$	25.5156	+	12.2877i	0.898750	+	0.432815i
$807$	3.95249	−	2.69476i	0.139134	−	0.0948601i
$808$	−4.05606	+	3.76347i	−0.142692	+	0.132398i
$809$	26.7020	−	24.7759i	0.938793	−	0.871073i	−0.0530428	−	0.998592i	$-0.516892\pi$
$809$	26.7020	−	24.7759i	0.938793	−	0.871073i	0.991836	+	0.127519i	$0.0407015\pi$
$810$	−1.24683	+	0.850075i	−0.0438092	+	0.0298686i
$811$	−29.1508	−	14.0383i	−1.02362	−	0.492951i	−0.154734	−	0.987956i	$-0.549452\pi$
$811$	−29.1508	−	14.0383i	−1.02362	−	0.492951i	−0.868890	+	0.495005i	$0.835166\pi$
$812$	57.3720	−	21.0869i	2.01336	−	0.740006i
$813$	−7.06443	+	3.40205i	−0.247761	+	0.119315i
$814$	0.758110	−	1.31309i	0.0265718	−	0.0460236i
$815$	0.953958	+	1.65230i	0.0334157	+	0.0578777i
$816$	8.59650	+	5.86100i	0.300938	+	0.205176i
$817$	3.01050	−	0.453760i	0.105324	−	0.0158751i
$818$	−11.2160	−	49.1403i	−0.392157	−	1.71815i
$819$	11.6748	+	9.73370i	0.407949	+	0.340123i
$820$	2.88546	−	12.6420i	0.100764	−	0.441478i
$821$	0.288943	−	3.85567i	0.0100842	−	0.134564i	−0.989889	−	0.141842i	$-0.954698\pi$
$821$	0.288943	−	3.85567i	0.0100842	−	0.134564i	0.999974	+	0.00727786i	$0.00231664\pi$
$822$	−10.1945	+	3.14457i	−0.355573	+	0.109680i
$823$	−10.4588	+	26.6485i	−0.364570	+	0.928910i	0.624441	+	0.781072i	$0.285327\pi$
$823$	−10.4588	+	26.6485i	−0.364570	+	0.928910i	−0.989012	+	0.147838i	$0.952769\pi$
$824$	−31.4830	−	9.71122i	−1.09676	−	0.338307i
$825$	−1.96496	+	2.46398i	−0.0684110	+	0.0857847i
$826$	−11.2153	−	39.3845i	−0.390230	−	1.37036i
$827$	8.91929	+	11.1844i	0.310154	+	0.388921i	0.912339	−	0.409436i	$-0.134274\pi$
$827$	8.91929	+	11.1844i	0.310154	+	0.388921i	−0.602185	+	0.798357i	$0.705703\pi$
$828$	−0.300946	−	0.766798i	−0.0104586	−	0.0266481i
$829$	−0.216207	−	2.88508i	−0.00750917	−	0.100203i	0.992190	−	0.124737i	$-0.0398088\pi$
$829$	−0.216207	−	2.88508i	−0.00750917	−	0.100203i	−0.999699	+	0.0245343i	$0.992190\pi$
$830$	5.14813	+	0.775956i	0.178694	+	0.0269338i
$831$	11.9950	+	11.1297i	0.416101	+	0.386086i
$832$	72.1007			2.49964
$833$	23.4336	+	32.1641i	0.811927	+	1.11442i
$834$	−36.5637			−1.26610
$835$	−0.709668	−	0.658476i	−0.0245591	−	0.0227875i
$836$	1.57235	+	0.236993i	0.0543808	+	0.00819659i
$837$	−0.168485	−	2.24827i	−0.00582368	−	0.0777116i
$838$	−13.5508	−	34.5270i	−0.468106	−	1.19271i
$839$	−18.5992	−	23.3227i	−0.642116	−	0.805187i	0.349150	−	0.937067i	$-0.386470\pi$
$839$	−18.5992	−	23.3227i	−0.642116	−	0.805187i	−0.991266	+	0.131879i	$0.957899\pi$
$840$	−1.81086	+	2.53559i	−0.0624807	+	0.0874863i
$841$	24.9659	−	31.3063i	0.860894	−	1.07953i
$842$	66.1620	+	20.4083i	2.28009	+	0.703315i
$843$	3.60774	−	9.19237i	0.124257	−	0.316602i
$844$	−66.4803	+	20.5065i	−2.28835	+	0.705861i
$845$	1.03189	−	13.7697i	0.0354982	−	0.473691i
$846$	−3.99186	+	17.4895i	−0.137243	+	0.601301i
$847$	−11.5216	−	25.3210i	−0.395886	−	0.870042i
$848$	−3.05813	−	13.3985i	−0.105017	−	0.460108i
$849$	8.99906	−	1.35639i	0.308847	−	0.0465512i
$850$	−46.4579	−	31.6744i	−1.59349	−	1.08642i
$851$	0.147450	+	0.255391i	0.00505452	+	0.00875469i
$852$	−17.8372	+	30.8949i	−0.611091	+	1.05844i
$853$	−26.7627	+	12.8882i	−0.916338	+	0.441285i	−0.831762	−	0.555132i	$-0.812668\pi$
$853$	−26.7627	+	12.8882i	−0.916338	+	0.441285i	−0.0845758	+	0.996417i	$0.526954\pi$
$854$	−7.27505	−	11.1864i	−0.248947	−	0.382790i
$855$	0.510459	+	0.245824i	0.0174573	+	0.00840700i
$856$	−15.8094	+	10.7787i	−0.540355	+	0.368408i
$857$	−12.3346	+	11.4448i	−0.421341	+	0.390947i	−0.862150	−	0.506654i	$-0.830882\pi$
$857$	−12.3346	+	11.4448i	−0.421341	+	0.390947i	0.440809	+	0.897601i	$0.354692\pi$
$858$	−6.41509	+	5.95234i	−0.219008	+	0.203209i
$859$	−4.54751	+	3.10044i	−0.155159	+	0.105786i	−0.638411	−	0.769696i	$-0.720408\pi$
$859$	−4.54751	+	3.10044i	−0.155159	+	0.105786i	0.483252	+	0.875481i	$0.339456\pi$
$860$	−6.41245	−	3.08807i	−0.218663	−	0.105302i
$861$	9.74686	+	14.9871i	0.332172	+	0.510760i
$862$	24.3036	−	11.7040i	0.827783	−	0.398639i
$863$	22.9564	−	39.7617i	0.781446	−	1.35350i	−0.149653	−	0.988739i	$-0.547816\pi$
$863$	22.9564	−	39.7617i	0.781446	−	1.35350i	0.931099	−	0.364766i	$-0.118851\pi$
$864$	−3.70702	−	6.42075i	−0.126115	−	0.218438i
$865$	3.50628	+	2.39054i	0.119217	+	0.0812809i
$866$	23.3430	−	3.51838i	0.793226	−	0.119560i
$867$	−3.40894	−	14.9355i	−0.115774	−	0.507238i
$868$	−6.86897	−	15.0960i	−0.233148	−	0.512391i
$869$	−0.937621	+	4.10798i	−0.0318066	+	0.139354i
$870$	−0.937034	+	12.5038i	−0.0317684	+	0.423920i
$871$	−74.7439	+	23.0554i	−2.53260	+	0.781204i
$872$	−8.46603	+	21.5711i	−0.286696	+	0.730490i
$873$	15.5050	+	4.78265i	0.524764	+	0.161868i
$874$	−0.331531	+	0.415727i	−0.0112142	+	0.0140622i
$875$	−10.1072	+	14.1523i	−0.341686	+	0.478434i
$876$	2.13903	+	2.68226i	0.0722711	+	0.0906251i
$877$	−0.463978	−	1.18220i	−0.0156674	−	0.0399199i	0.922826	−	0.385217i	$-0.125873\pi$
$877$	−0.463978	−	1.18220i	−0.0156674	−	0.0399199i	−0.938493	+	0.345297i	$0.887778\pi$
$878$	−2.18854	−	29.2040i	−0.0738595	−	0.985587i
$879$	1.42128	+	0.214224i	0.0479386	+	0.00722559i
$880$	0.645095	+	0.598560i	0.0217461	+	0.0201775i
$881$	18.1649			0.611991			0.305995	−	0.952033i	$-0.401011\pi$
$881$	18.1649			0.611991			0.305995	+	0.952033i	$0.401011\pi$
$882$	−2.75271	−	15.0553i	−0.0926887	−	0.506939i
$883$	19.7422			0.664379			0.332190	−	0.943213i	$-0.392213\pi$
$883$	19.7422			0.664379			0.332190	+	0.943213i	$0.392213\pi$
$884$	−66.5697	−	61.7676i	−2.23898	−	2.07747i
$885$	4.83133	+	0.728205i	0.162403	+	0.0244783i
$886$	−4.71610	−	62.9319i	−0.158440	−	2.11424i
$887$	5.93625	+	15.1253i	0.199320	+	0.507859i	0.995230	−	0.0975560i	$-0.0311025\pi$
$887$	5.93625	+	15.1253i	0.199320	+	0.507859i	−0.795910	+	0.605415i	$0.793007\pi$
$888$	−1.05896	−	1.32789i	−0.0355364	−	0.0445612i
$889$	−13.0545	−	45.8432i	−0.437833	−	1.53753i
$890$	10.9883	−	13.7789i	0.368328	−	0.461869i
$891$	0.665733	+	0.205351i	0.0223029	+	0.00687953i
$892$	19.5168	−	49.7280i	0.653471	−	1.66502i
$893$	6.43602	−	1.98525i	0.215373	−	0.0664338i
$894$	3.50488	−	46.7694i	0.117221	−	1.56420i
$895$	−1.82716	+	8.00530i	−0.0610751	+	0.267588i
$896$	−25.6275	−	21.3666i	−0.856154	−	0.713808i
$897$	−0.378749	−	1.65941i	−0.0126461	−	0.0554060i
$898$	−35.3195	+	5.32356i	−1.17863	+	0.177649i
$899$	−15.4785	−	10.5530i	−0.516235	−	0.351963i
$900$	6.28878	+	10.8925i	0.209626	+	0.363083i
$901$	−21.3455	+	36.9714i	−0.711120	+	1.23170i
$902$	−9.27350	+	4.46588i	−0.308774	+	0.148698i
$903$	9.21020	−	3.38518i	0.306496	−	0.112652i
$904$	10.8878	+	5.24328i	0.362122	+	0.174389i
$905$	−7.90139	+	5.38708i	−0.262651	+	0.179073i
$906$	−8.97201	+	8.32481i	−0.298075	+	0.276573i
$907$	19.1062	−	17.7279i	0.634409	−	0.588646i	−0.295991	−	0.955191i	$-0.595650\pi$
$907$	19.1062	−	17.7279i	0.634409	−	0.588646i	0.930400	+	0.366545i	$0.119459\pi$
$908$	0.0623748	−	0.0425264i	0.00206998	−	0.00141129i
$909$	2.92161	+	1.40697i	0.0969038	+	0.0466664i
$910$	−15.9641	+	16.4708i	−0.529205	+	0.546002i
$911$	0.251008	−	0.120879i	0.00831628	−	0.00400491i	−0.429721	−	0.902962i	$-0.641388\pi$
$911$	0.251008	−	0.120879i	0.00831628	−	0.00400491i	0.438037	+	0.898957i	$0.355674\pi$
$912$	−0.751163	+	1.30105i	−0.0248735	+	0.0430822i
$913$	−1.20180	−	2.08158i	−0.0397737	−	0.0688901i
$914$	−43.8709	−	29.9106i	−1.45112	−	0.989356i
$915$	1.57433	−	0.237292i	0.0520457	−	0.00784462i
$916$	2.99336	+	13.1148i	0.0989033	+	0.433324i
$917$	1.04734	−	48.0826i	0.0345861	−	1.58783i
$918$	−2.76590	+	12.1182i	−0.0912884	+	0.399960i
$919$	0.596204	−	7.95579i	0.0196670	−	0.262437i	−0.978699	−	0.205299i	$-0.934183\pi$
$919$	0.596204	−	7.95579i	0.0196670	−	0.262437i	0.998366	−	0.0571383i	$-0.0181976\pi$
$920$	0.333404	−	0.102842i	0.0109920	−	0.00339059i
$921$	10.7802	−	27.4674i	0.355218	−	0.905081i
$922$	61.1576	+	18.8646i	2.01412	+	0.621274i
$923$	−45.9595	+	57.6314i	−1.51278	+	1.89696i
$924$	5.11780	−	0.271607i	0.168363	−	0.00893521i
$925$	−2.80744	−	3.52042i	−0.0923081	−	0.115751i
$926$	−11.9469	−	30.4402i	−0.392600	−	1.00033i
$927$	1.44295	+	19.2548i	0.0473927	+	0.632412i
$928$	−60.9164	−	9.18167i	−1.99968	−	0.301403i
$929$	−39.0054	−	36.1917i	−1.27973	−	1.18741i	−0.971749	−	0.236018i	$-0.924158\pi$
$929$	−39.0054	−	36.1917i	−1.27973	−	1.18741i	−0.307977	−	0.951394i	$-0.599652\pi$
$930$	3.40226			0.111564
$931$	−4.37844	+	3.72127i	−0.143498	+	0.121960i
$932$	−3.05420			−0.100044
$933$	−3.22154	−	2.98915i	−0.105469	−	0.0978605i
$934$	27.8013	+	4.19037i	0.909685	+	0.137113i
$935$	−0.204284	−	2.72598i	−0.00668081	−	0.0891492i
$936$	3.58141	+	9.12529i	0.117062	+	0.298269i
$937$	−0.158463	−	0.198707i	−0.00517677	−	0.00649147i	0.779236	−	0.626730i	$-0.215607\pi$
$937$	−0.158463	−	0.198707i	−0.00517677	−	0.00649147i	−0.784413	+	0.620239i	$0.787036\pi$
$938$	72.6697	+	30.3632i	2.37275	+	0.991395i
$939$	−12.1417	+	15.2253i	−0.396231	+	0.496858i
$940$	−15.0458	−	4.64101i	−0.490739	−	0.151373i
$941$	21.2919	−	54.2508i	0.694096	−	1.76853i	0.0561803	−	0.998421i	$-0.482108\pi$
$941$	21.2919	−	54.2508i	0.694096	−	1.76853i	0.637915	−	0.770106i	$-0.279797\pi$
$942$	−37.6290	+	11.6070i	−1.22602	+	0.378177i
$943$	0.149603	−	1.99632i	0.00487176	−	0.0650091i
$944$	−2.88289	+	12.6308i	−0.0938302	+	0.411097i
$945$	1.77102	+	0.445013i	0.0576113	+	0.0144763i
$946$	1.25712	+	5.50778i	0.0408723	+	0.179073i
$947$	−11.7746	+	1.77473i	−0.382622	+	0.0576710i	−0.337537	−	0.941312i	$-0.609594\pi$
$947$	−11.7746	+	1.77473i	−0.382622	+	0.0576710i	−0.0450849	+	0.998983i	$0.514356\pi$
$948$	13.8942	+	9.47293i	0.451264	+	0.307667i
$949$	3.54444	+	6.13915i	0.115057	+	0.199285i
$950$	4.05949	−	7.03125i	0.131707	−	0.228124i
$951$	−2.05031	+	0.987376i	−0.0664857	+	0.0320178i
$952$	3.27158	+	25.4555i	0.106033	+	0.825017i
$953$	−30.9504	−	14.9049i	−1.00258	−	0.482817i	−0.140767	−	0.990043i	$-0.544957\pi$
$953$	−30.9504	−	14.9049i	−1.00258	−	0.482817i	−0.861814	+	0.507225i	$0.830671\pi$
$954$	13.5656	−	9.24890i	0.439204	−	0.299444i
$955$	6.68076	−	6.19884i	0.216184	−	0.200590i
$956$	8.06498	−	7.48321i	0.260840	−	0.242024i
$957$	4.78299	−	3.26099i	0.154612	−	0.105413i
$958$	74.2024	+	35.7340i	2.39737	+	1.15451i
$959$	11.0369	+	6.69680i	0.356401	+	0.216251i
$960$	7.80405	−	3.75823i	0.251875	−	0.121296i
$961$	12.9584	−	22.4447i	0.418014	−	0.724022i
$962$	−6.25166	−	10.8282i	−0.201562	−	0.349115i
$963$	9.26530	+	6.31698i	0.298570	+	0.203562i
$964$	−25.4389	+	3.83429i	−0.819330	+	0.123494i
$965$	−3.42543	−	15.0078i	−0.110268	−	0.483117i
$966$	−0.777044	+	1.52753i	−0.0250010	+	0.0491475i
$967$	−4.97106	+	21.7796i	−0.159859	+	0.700386i	0.829933	+	0.557863i	$0.188379\pi$
$967$	−4.97106	+	21.7796i	−0.159859	+	0.700386i	−0.989791	+	0.142523i	$0.954479\pi$
$968$	1.34074	−	17.8910i	0.0430932	−	0.575038i
$969$	4.45942	−	1.37555i	0.143257	−	0.0441890i
$970$	−8.94558	+	22.7930i	−0.287225	+	0.731838i
$971$	−19.5585	−	6.03300i	−0.627662	−	0.193608i	−0.0354257	−	0.999372i	$-0.511279\pi$
$971$	−19.5585	−	6.03300i	−0.627662	−	0.193608i	−0.592237	+	0.805764i	$0.701755\pi$
$972$	1.73356	−	2.17381i	0.0556039	−	0.0697251i
$973$	29.3809	+	33.0817i	0.941910	+	1.06055i
$974$	3.27483	+	4.10651i	0.104932	+	0.131581i
$975$	9.49479	+	24.1923i	0.304077	+	0.774775i
$976$	0.315487	+	4.20989i	0.0100985	+	0.134755i
$977$	−17.3867	−	2.62062i	−0.556249	−	0.0838410i	−0.135099	−	0.990832i	$-0.543135\pi$
$977$	−17.3867	−	2.62062i	−0.556249	−	0.0838410i	−0.421150	+	0.906991i	$0.638373\pi$
$978$	−4.43054	−	4.11094i	−0.141673	−	0.131453i
$979$	−8.13644			−0.260042
$980$	13.3577	−	1.42181i	0.426695	−	0.0454182i
$981$	13.5808			0.433601
$982$	−30.5530	−	28.3490i	−0.974984	−	0.904653i
$983$	−11.0269	−	1.66204i	−0.351703	−	0.0530108i	−0.0291852	−	0.999574i	$-0.509291\pi$
$983$	−11.0269	−	1.66204i	−0.351703	−	0.0530108i	−0.322518	+	0.946563i	$0.604529\pi$
$984$	0.861622	+	11.4975i	0.0274675	+	0.366528i
$985$	6.80278	+	17.3332i	0.216755	+	0.552282i
$986$	64.3951	+	80.7489i	2.05076	+	2.57157i
$987$	19.0316	−	10.4421i	0.605784	−	0.332374i
$988$	8.17559	−	10.2519i	0.260100	−	0.326155i
$989$	−1.04998	−	0.323875i	−0.0333874	−	0.0102986i
$990$	−0.384093	+	0.978654i	−0.0122073	+	0.0311037i
$991$	1.70837	−	0.526962i	0.0542681	−	0.0167395i	−0.267502	−	0.963557i	$-0.586198\pi$
$991$	1.70837	−	0.526962i	0.0542681	−	0.0167395i	0.321770	+	0.946818i	$0.395722\pi$
$992$	−1.24915	+	16.6688i	−0.0396606	+	0.529234i
$993$	0.287788	−	1.26088i	0.00913268	−	0.0400129i
$994$	72.7029	−	14.9361i	2.30600	−	0.473744i
$995$	−0.410034	−	1.79648i	−0.0129990	−	0.0569522i
$996$	−9.48542	+	1.42970i	−0.300557	+	0.0453017i
$997$	31.6896	+	21.6056i	1.00362	+	0.684257i	0.949334	−	0.314268i	$-0.101759\pi$
$997$	31.6896	+	21.6056i	1.00362	+	0.684257i	0.0542866	+	0.998525i	$0.482712\pi$
$998$	−5.82659	−	10.0919i	−0.184437	−	0.319455i
$999$	−0.497695	+	0.862034i	−0.0157464	+	0.0272735i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.2.m.b.58.5	✓	60
3.2	odd	2		441.2.bb.e.352.1		60
49.11	even	21	inner	147.2.m.b.109.5	yes	60
49.16	even	21		7203.2.a.n.1.4		30
49.33	odd	42		7203.2.a.m.1.4		30
147.11	odd	42		441.2.bb.e.109.1		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.58.5	✓	60	1.1	even	1	trivial
147.2.m.b.109.5	yes	60	49.11	even	21	inner
441.2.bb.e.109.1		60	147.11	odd	42
441.2.bb.e.352.1		60	3.2	odd	2
7203.2.a.m.1.4		30	49.33	odd	42
7203.2.a.n.1.4		30	49.16	even	21

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60276 + 1.48714i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(0.207780 + 2.77264i) q^{4} +(0.252155 + 0.642481i) q^{5} +(-1.36321 - 1.70941i) q^{6} +(-0.451208 + 2.60699i) q^{7} +(-1.06386 + 1.33404i) q^{8} +(0.955573 + 0.294755i) q^{9} +O(q^{10})\)	\(q+(1.60276 + 1.48714i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(0.207780 + 2.77264i) q^{4} +(0.252155 + 0.642481i) q^{5} +(-1.36321 - 1.70941i) q^{6} +(-0.451208 + 2.60699i) q^{7} +(-1.06386 + 1.33404i) q^{8} +(0.955573 + 0.294755i) q^{9} +(-0.551316 + 1.40473i) q^{10} +(0.665733 - 0.205351i) q^{11} +(0.207780 - 2.77264i) q^{12} +(1.27841 - 5.60108i) q^{13} +(-4.60014 + 3.50736i) q^{14} +(-0.153582 - 0.672887i) q^{15} +(1.80969 - 0.272767i) q^{16} +(-4.69720 - 3.20250i) q^{17} +(1.09321 + 1.89349i) q^{18} +(0.410442 - 0.710906i) q^{19} +(-1.72897 + 0.832630i) q^{20} +(0.834720 - 2.51063i) q^{21} +(1.37239 + 0.660910i) q^{22} +(-0.244786 + 0.166892i) q^{23} +(1.25081 - 1.16058i) q^{24} +(3.31606 - 3.07685i) q^{25} +(10.3786 - 7.07599i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(-7.32200 - 0.709354i) q^{28} +(-7.48630 + 3.60521i) q^{29} +(0.754523 - 1.30687i) q^{30} +(1.12729 + 1.95252i) q^{31} +(6.12577 + 4.17648i) q^{32} +(-0.688903 + 0.103835i) q^{33} +(-2.76590 - 12.1182i) q^{34} +(-1.78872 + 0.367474i) q^{35} +(-0.618700 + 2.71070i) q^{36} +(0.0743856 - 0.992607i) q^{37} +(1.71505 - 0.529024i) q^{38} +(-2.09893 + 5.34798i) q^{39} +(-1.12536 - 0.347126i) q^{40} +(-4.21303 + 5.28297i) q^{41} +(5.07151 - 2.78257i) q^{42} +(2.31241 + 2.89967i) q^{43} +(0.707691 + 1.80317i) q^{44} +(0.0515781 + 0.688262i) q^{45} +(-0.640525 - 0.0965436i) q^{46} +(6.01460 + 5.58073i) q^{47} -1.83013 q^{48} +(-6.59282 - 2.35259i) q^{49} +9.89055 q^{50} +(4.16743 + 3.86681i) q^{51} +(15.7954 + 2.38077i) q^{52} +(-0.561174 - 7.48835i) q^{53} +(-0.798787 - 2.03528i) q^{54} +(0.299802 + 0.375940i) q^{55} +(-2.99781 - 3.37541i) q^{56} +(-0.511812 + 0.641792i) q^{57} +(-17.3602 - 5.35490i) q^{58} +(-2.58627 + 6.58970i) q^{59} +(1.83376 - 0.565640i) q^{60} +(-0.172385 + 2.30031i) q^{61} +(-1.09690 + 4.80585i) q^{62} +(-1.19959 + 2.35818i) q^{63} +(2.79262 + 12.2353i) q^{64} +(3.92095 - 0.590988i) q^{65} +(-1.25856 - 0.858073i) q^{66} +(-6.80742 - 11.7908i) q^{67} +(7.90337 - 13.6890i) q^{68} +(0.266926 - 0.128545i) q^{69} +(-3.41336 - 2.07110i) q^{70} +(-11.5600 - 5.56699i) q^{71} +(-1.40981 + 0.961195i) q^{72} +(-0.904509 + 0.839262i) q^{73} +(1.59537 - 1.48029i) q^{74} +(-3.73760 + 2.54825i) q^{75} +(2.05637 + 0.990293i) q^{76} +(0.234966 + 1.82822i) q^{77} +(-11.3173 + 5.45011i) q^{78} +(-3.02406 + 5.23782i) q^{79} +(0.631572 + 1.09391i) q^{80} +(0.826239 + 0.563320i) q^{81} +(-14.6090 + 2.20195i) q^{82} +(-0.767708 - 3.36355i) q^{83} +(7.13449 + 1.79272i) q^{84} +(0.873120 - 3.82539i) q^{85} +(-0.605987 + 8.08634i) q^{86} +(7.94001 - 2.44917i) q^{87} +(-0.434301 + 1.10658i) q^{88} +(-11.1599 - 3.44239i) q^{89} +(-0.940874 + 1.17982i) q^{90} +(14.0251 + 5.86006i) q^{91} +(-0.513594 - 0.644026i) q^{92} +(-0.823689 - 2.09872i) q^{93} +(1.34060 + 17.8891i) q^{94} +(0.560239 + 0.0844424i) q^{95} +(-5.43488 - 5.04283i) q^{96} +16.2259 q^{97} +(-7.06805 - 13.5751i) q^{98} +0.696685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9	\( 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9} - 34 q^{10} - 11 q^{11} + 5 q^{12} - 2 q^{13} + 40 q^{14} - 3 q^{15} - 31 q^{16} - 9 q^{17} - 6 q^{18} - 29 q^{19} - 43 q^{20} - 11 q^{21} + 9 q^{22} - 4 q^{23} - 24 q^{24} + 55 q^{25} + 36 q^{26} - 10 q^{27} - 57 q^{28} + 4 q^{29} - 20 q^{30} - 39 q^{31} - 92 q^{32} - 18 q^{33} - 36 q^{34} - 33 q^{35} - 10 q^{36} - 24 q^{37} + 118 q^{38} - 6 q^{39} + 35 q^{41} + 38 q^{42} + 2 q^{43} + 40 q^{44} + 12 q^{45} - 40 q^{46} - 5 q^{47} + 76 q^{48} + 129 q^{49} - 176 q^{50} + 54 q^{51} - 6 q^{52} + 26 q^{53} + q^{54} + 2 q^{55} + 63 q^{56} - 12 q^{57} + 11 q^{58} - 41 q^{59} + 32 q^{60} + 6 q^{61} + 36 q^{62} - q^{63} + 74 q^{64} - 51 q^{65} - 15 q^{66} - 55 q^{67} - 22 q^{68} + 8 q^{69} - 68 q^{70} - 66 q^{71} - 24 q^{72} + 24 q^{73} + 28 q^{74} + 41 q^{75} + 3 q^{76} - 34 q^{77} - 30 q^{78} - 51 q^{79} - 5 q^{80} + 5 q^{81} - 41 q^{82} + 30 q^{83} - 30 q^{84} + 68 q^{85} + 110 q^{86} + 19 q^{87} + 129 q^{88} + 75 q^{89} - 16 q^{90} + 5 q^{91} - 4 q^{93} + 38 q^{94} + 36 q^{95} - 57 q^{96} - 168 q^{97} + 227 q^{98} + 36 q^{99}+O(q^{100}) \) 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9 - 34 * q^10 - 11 * q^11 + 5 * q^12 - 2 * q^13 + 40 * q^14 - 3 * q^15 - 31 * q^16 - 9 * q^17 - 6 * q^18 - 29 * q^19 - 43 * q^20 - 11 * q^21 + 9 * q^22 - 4 * q^23 - 24 * q^24 + 55 * q^25 + 36 * q^26 - 10 * q^27 - 57 * q^28 + 4 * q^29 - 20 * q^30 - 39 * q^31 - 92 * q^32 - 18 * q^33 - 36 * q^34 - 33 * q^35 - 10 * q^36 - 24 * q^37 + 118 * q^38 - 6 * q^39 + 35 * q^41 + 38 * q^42 + 2 * q^43 + 40 * q^44 + 12 * q^45 - 40 * q^46 - 5 * q^47 + 76 * q^48 + 129 * q^49 - 176 * q^50 + 54 * q^51 - 6 * q^52 + 26 * q^53 + q^54 + 2 * q^55 + 63 * q^56 - 12 * q^57 + 11 * q^58 - 41 * q^59 + 32 * q^60 + 6 * q^61 + 36 * q^62 - q^63 + 74 * q^64 - 51 * q^65 - 15 * q^66 - 55 * q^67 - 22 * q^68 + 8 * q^69 - 68 * q^70 - 66 * q^71 - 24 * q^72 + 24 * q^73 + 28 * q^74 + 41 * q^75 + 3 * q^76 - 34 * q^77 - 30 * q^78 - 51 * q^79 - 5 * q^80 + 5 * q^81 - 41 * q^82 + 30 * q^83 - 30 * q^84 + 68 * q^85 + 110 * q^86 + 19 * q^87 + 129 * q^88 + 75 * q^89 - 16 * q^90 + 5 * q^91 - 4 * q^93 + 38 * q^94 + 36 * q^95 - 57 * q^96 - 168 * q^97 + 227 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

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