LMFDB - Embedded newform 189.2.ba.a.101.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.6
Character	$\chi$	$=$	189.101
Dual form			189.2.ba.a.131.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07972 + 1.28676i) q^{2} +(-1.69732 + 0.345106i) q^{3} +(-0.142658 - 0.809053i) q^{4} +(2.87107 - 2.40911i) q^{5} +(1.38856 - 2.55666i) q^{6} +(-1.86335 - 1.87828i) q^{7} +(-1.71431 - 0.989760i) q^{8} +(2.76180 - 1.17151i) q^{9} +O(q^{10})$	\(q+(-1.07972 + 1.28676i) q^{2} +(-1.69732 + 0.345106i) q^{3} +(-0.142658 - 0.809053i) q^{4} +(2.87107 - 2.40911i) q^{5} +(1.38856 - 2.55666i) q^{6} +(-1.86335 - 1.87828i) q^{7} +(-1.71431 - 0.989760i) q^{8} +(2.76180 - 1.17151i) q^{9} +6.29553i q^{10} +(3.07307 - 3.66234i) q^{11} +(0.521346 + 1.32399i) q^{12} +(-1.10865 + 3.04598i) q^{13} +(4.42878 - 0.369659i) q^{14} +(-4.04173 + 5.07986i) q^{15} +(4.66853 - 1.69921i) q^{16} +3.86831 q^{17} +(-1.47452 + 4.81867i) q^{18} +1.52130i q^{19} +(-2.35868 - 1.97917i) q^{20} +(3.81090 + 2.54500i) q^{21} +(1.39450 + 7.90859i) q^{22} +(0.124554 - 0.342208i) q^{23} +(3.25131 + 1.08832i) q^{24} +(1.57097 - 8.90940i) q^{25} +(-2.72242 - 4.71536i) q^{26} +(-4.28337 + 2.94155i) q^{27} +(-1.25381 + 1.77550i) q^{28} +(-2.29492 - 6.30525i) q^{29} +(-2.17262 - 10.6855i) q^{30} +(-0.692139 + 0.122043i) q^{31} +(-1.50016 + 4.12165i) q^{32} +(-3.95209 + 7.27671i) q^{33} +(-4.17668 + 4.97757i) q^{34} +(-9.87478 - 0.903668i) q^{35} +(-1.34181 - 2.06732i) q^{36} +(2.75197 - 4.76655i) q^{37} +(-1.95755 - 1.64258i) q^{38} +(0.830544 - 5.55262i) q^{39} +(-7.30635 + 1.28831i) q^{40} +(0.793900 + 0.288956i) q^{41} +(-7.38949 + 2.15583i) q^{42} +(0.0136704 - 0.0775288i) q^{43} +(-3.40143 - 1.96381i) q^{44} +(5.10702 - 10.0170i) q^{45} +(0.305856 + 0.529758i) q^{46} +(0.617436 - 3.50165i) q^{47} +(-7.33760 + 4.49524i) q^{48} +(-0.0558886 + 6.99978i) q^{49} +(9.76803 + 11.6411i) q^{50} +(-6.56576 + 1.33498i) q^{51} +(2.62252 + 0.462421i) q^{52} +(7.25668 + 4.18964i) q^{53} +(0.839774 - 8.68770i) q^{54} -17.9182i q^{55} +(1.33531 + 5.06423i) q^{56} +(-0.525011 - 2.58214i) q^{57} +(10.5912 + 3.85488i) q^{58} +(1.36168 + 0.495612i) q^{59} +(4.68646 + 2.54529i) q^{60} +(2.82040 + 0.497313i) q^{61} +(0.590275 - 1.02239i) q^{62} +(-7.34662 - 3.00451i) q^{63} +(1.28433 + 2.22452i) q^{64} +(4.15511 + 11.4161i) q^{65} +(-5.09621 - 12.9422i) q^{66} +(3.09944 - 2.60074i) q^{67} +(-0.551844 - 3.12967i) q^{68} +(-0.0933094 + 0.623821i) q^{69} +(11.8248 - 11.7307i) q^{70} +(-14.1956 + 8.19580i) q^{71} +(-5.89411 - 0.725182i) q^{72} +(-10.4351 + 6.02468i) q^{73} +(3.16204 + 8.68764i) q^{74} +(0.408251 + 15.6643i) q^{75} +(1.23082 - 0.217026i) q^{76} +(-12.6051 + 1.05212i) q^{77} +(6.24812 + 7.06396i) q^{78} +(1.00589 + 0.844043i) q^{79} +(9.31009 - 16.1256i) q^{80} +(6.25512 - 6.47097i) q^{81} +(-1.22900 + 0.709566i) q^{82} +(-12.7610 + 4.64462i) q^{83} +(1.51538 - 3.44629i) q^{84} +(11.1062 - 9.31918i) q^{85} +(0.0850005 + 0.101300i) q^{86} +(6.07120 + 9.91005i) q^{87} +(-8.89304 + 3.23680i) q^{88} +8.72878 q^{89} +(7.37529 + 17.3870i) q^{90} +(7.78701 - 3.59337i) q^{91} +(-0.294633 - 0.0519517i) q^{92} +(1.13267 - 0.446007i) q^{93} +(3.83912 + 4.57528i) q^{94} +(3.66499 + 4.36777i) q^{95} +(1.12385 - 7.51349i) q^{96} +(-4.18960 - 0.738740i) q^{97} +(-8.94667 - 7.62970i) q^{98} +(4.19674 - 13.7148i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.07972	+	1.28676i	−0.763476	+	0.909875i	−0.998062	−	0.0622204i	$-0.980182\pi$
$2$	−1.07972	+	1.28676i	−0.763476	+	0.909875i	0.234587	+	0.972095i	$0.424626\pi$
$3$	−1.69732	+	0.345106i	−0.979949	+	0.199247i
$3$	−1.69732	+	0.345106i	−0.979949	+	0.199247i
$4$	−0.142658	−	0.809053i	−0.0713289	−	0.404527i
$5$	2.87107	−	2.40911i	1.28398	−	1.07739i	0.291298	−	0.956632i	$-0.405913\pi$
$5$	2.87107	−	2.40911i	1.28398	−	1.07739i	0.992682	−	0.120755i	$-0.0385315\pi$
$6$	1.38856	−	2.55666i	0.566877	−	1.04375i
$7$	−1.86335	−	1.87828i	−0.704278	−	0.709924i
$7$	−1.86335	−	1.87828i	−0.704278	−	0.709924i
$8$	−1.71431	−	0.989760i	−0.606101	−	0.349933i
$9$	2.76180	−	1.17151i	0.920601	−	0.390504i
$10$			6.29553i			1.99082i
$11$	3.07307	−	3.66234i	0.926565	−	1.10424i	−0.0677435	−	0.997703i	$-0.521580\pi$
$11$	3.07307	−	3.66234i	0.926565	−	1.10424i	0.994309	−	0.106535i	$-0.0339756\pi$
$12$	0.521346	+	1.32399i	0.150499	+	0.382203i
$13$	−1.10865	+	3.04598i	−0.307483	+	0.844804i	0.685662	+	0.727920i	$0.259513\pi$
$13$	−1.10865	+	3.04598i	−0.307483	+	0.844804i	−0.993146	+	0.116884i	$0.962709\pi$
$14$	4.42878	−	0.369659i	1.18364	−	0.0987955i
$15$	−4.04173	+	5.07986i	−1.04357	+	1.31161i
$16$	4.66853	−	1.69921i	1.16713	−	0.424802i
$17$	3.86831			0.938202			0.469101	−	0.883144i	$-0.344578\pi$
$17$	3.86831			0.938202			0.469101	+	0.883144i	$0.344578\pi$
$18$	−1.47452	+	4.81867i	−0.347547	+	1.13577i
$19$			1.52130i			0.349011i	0.984656	+	0.174506i	$0.0558327\pi$
$19$			1.52130i			0.349011i	−0.984656	+	0.174506i	$0.944167\pi$
$20$	−2.35868	−	1.97917i	−0.527417	−	0.442555i
$21$	3.81090	+	2.54500i	0.831607	+	0.555364i
$22$	1.39450	+	7.90859i	0.297308	+	1.68612i
$23$	0.124554	−	0.342208i	0.0259712	−	0.0713553i	−0.926029	−	0.377451i	$-0.876801\pi$
$23$	0.124554	−	0.342208i	0.0259712	−	0.0713553i	0.952001	+	0.306096i	$0.0990228\pi$
$24$	3.25131	+	1.08832i	0.663672	+	0.222152i
$25$	1.57097	−	8.90940i	0.314194	−	1.78188i
$26$	−2.72242	−	4.71536i	−0.533910	−	0.924758i
$27$	−4.28337	+	2.94155i	−0.824336	+	0.566101i
$28$	−1.25381	+	1.77550i	−0.236948	+	0.335537i
$29$	−2.29492	−	6.30525i	−0.426157	−	1.17086i	−0.948127	−	0.317892i	$-0.897025\pi$
$29$	−2.29492	−	6.30525i	−0.426157	−	1.17086i	0.521970	−	0.852964i	$-0.325197\pi$
$30$	−2.17262	−	10.6855i	−0.396665	−	1.95090i
$31$	−0.692139	+	0.122043i	−0.124312	+	0.0219195i	−0.235458	−	0.971885i	$-0.575659\pi$
$31$	−0.692139	+	0.122043i	−0.124312	+	0.0219195i	0.111146	+	0.993804i	$0.464548\pi$
$32$	−1.50016	+	4.12165i	−0.265193	+	0.728612i
$33$	−3.95209	+	7.27671i	−0.687971	+	1.26671i
$34$	−4.17668	+	4.97757i	−0.716294	+	0.853647i
$35$	−9.87478	−	0.903668i	−1.66914	−	0.152748i
$36$	−1.34181	−	2.06732i	−0.223635	−	0.344553i
$37$	2.75197	−	4.76655i	0.452421	−	0.783616i	−0.546115	−	0.837710i	$-0.683894\pi$
$37$	2.75197	−	4.76655i	0.452421	−	0.783616i	0.998536	+	0.0540945i	$0.0172272\pi$
$38$	−1.95755	−	1.64258i	−0.317556	−	0.266461i
$39$	0.830544	−	5.55262i	0.132993	−	0.889130i
$40$	−7.30635	+	1.28831i	−1.15524	+	0.203699i
$41$	0.793900	+	0.288956i	0.123986	+	0.0451273i	0.403268	−	0.915082i	$-0.367874\pi$
$41$	0.793900	+	0.288956i	0.123986	+	0.0451273i	−0.279282	+	0.960209i	$0.590096\pi$
$42$	−7.38949	+	2.15583i	−1.14022	+	0.332652i
$43$	0.0136704	−	0.0775288i	0.00208472	−	0.0118230i	−0.983748	−	0.179557i	$-0.942534\pi$
$43$	0.0136704	−	0.0775288i	0.00208472	−	0.0118230i	0.985832	+	0.167734i	$0.0536448\pi$
$44$	−3.40143	−	1.96381i	−0.512784	−	0.296056i
$45$	5.10702	−	10.0170i	0.761309	−	1.49324i
$46$	0.305856	+	0.529758i	0.0450960	+	0.0781086i
$47$	0.617436	−	3.50165i	0.0900622	−	0.510768i	−0.906087	−	0.423092i	$-0.860945\pi$
$47$	0.617436	−	3.50165i	0.0900622	−	0.510768i	0.996149	−	0.0876764i	$-0.0279441\pi$
$48$	−7.33760	+	4.49524i	−1.05909	+	0.648832i
$49$	−0.0558886	+	6.99978i	−0.00798409	+	0.999968i
$50$	9.76803	+	11.6411i	1.38141	+	1.64630i
$51$	−6.56576	+	1.33498i	−0.919391	+	0.186934i
$52$	2.62252	+	0.462421i	0.363678	+	0.0641262i
$53$	7.25668	+	4.18964i	0.996781	+	0.575492i	0.907294	−	0.420496i	$-0.138144\pi$
$53$	7.25668	+	4.18964i	0.996781	+	0.575492i	0.0894868	+	0.995988i	$0.471477\pi$
$54$	0.839774	−	8.68770i	0.114279	−	1.18225i
$55$		−	17.9182i		−	2.41609i
$56$	1.33531	+	5.06423i	0.178438	+	0.676736i
$57$	−0.525011	−	2.58214i	−0.0695394	−	0.342013i
$58$	10.5912	+	3.85488i	1.39069	+	0.506170i
$59$	1.36168	+	0.495612i	0.177276	+	0.0645231i	0.429133	−	0.903241i	$-0.358819\pi$
$59$	1.36168	+	0.495612i	0.177276	+	0.0645231i	−0.251857	+	0.967764i	$0.581041\pi$
$60$	4.68646	+	2.54529i	0.605019	+	0.328595i
$61$	2.82040	+	0.497313i	0.361116	+	0.0636745i	0.351263	−	0.936277i	$-0.385752\pi$
$61$	2.82040	+	0.497313i	0.361116	+	0.0636745i	0.00985324	+	0.999951i	$0.496864\pi$
$62$	0.590275	−	1.02239i	0.0749650	−	0.129843i
$63$	−7.34662	−	3.00451i	−0.925588	−	0.378533i
$64$	1.28433	+	2.22452i	0.160541	+	0.278066i
$65$	4.15511	+	11.4161i	0.515378	+	1.41599i
$66$	−5.09621	−	12.9422i	−0.627301	−	1.59307i
$67$	3.09944	−	2.60074i	0.378657	−	0.317731i	−0.433518	−	0.901145i	$-0.642728\pi$
$67$	3.09944	−	2.60074i	0.378657	−	0.317731i	0.812175	+	0.583414i	$0.198284\pi$
$68$	−0.551844	−	3.12967i	−0.0669210	−	0.379528i
$69$	−0.0933094	+	0.623821i	−0.0112331	+	0.0750993i
$70$	11.8248	−	11.7307i	1.41333	−	1.40209i
$71$	−14.1956	+	8.19580i	−1.68470	+	0.972663i	−0.726240	+	0.687441i	$0.758734\pi$
$71$	−14.1956	+	8.19580i	−1.68470	+	0.972663i	−0.958461	+	0.285222i	$0.907933\pi$
$72$	−5.89411	−	0.725182i	−0.694628	−	0.0854635i
$73$	−10.4351	+	6.02468i	−1.22133	+	0.705136i	−0.965202	−	0.261507i	$-0.915781\pi$
$73$	−10.4351	+	6.02468i	−1.22133	+	0.705136i	−0.256129	+	0.966643i	$0.582447\pi$
$74$	3.16204	+	8.68764i	0.367580	+	1.00992i
$75$	0.408251	+	15.6643i	0.0471407	+	1.80875i
$76$	1.23082	−	0.217026i	0.141184	−	0.0248946i
$77$	−12.6051	+	1.05212i	−1.43648	+	0.119900i
$78$	6.24812	+	7.06396i	0.707460	+	0.799836i
$79$	1.00589	+	0.844043i	0.113172	+	0.0949623i	0.697617	−	0.716471i	$-0.254244\pi$
$79$	1.00589	+	0.844043i	0.113172	+	0.0949623i	−0.584446	+	0.811433i	$0.698688\pi$
$80$	9.31009	−	16.1256i	1.04090	−	1.80289i
$81$	6.25512	−	6.47097i	0.695013	−	0.718997i
$82$	−1.22900	+	0.709566i	−0.135721	+	0.0783584i
$83$	−12.7610	+	4.64462i	−1.40070	+	0.509814i	−0.928386	−	0.371616i	$-0.878804\pi$
$83$	−12.7610	+	4.64462i	−1.40070	+	0.509814i	−0.472315	+	0.881430i	$0.656581\pi$
$84$	1.51538	−	3.44629i	0.165342	−	0.376021i
$85$	11.1062	−	9.31918i	1.20463	−	1.01081i
$86$	0.0850005	+	0.101300i	0.00916584	+	0.0109234i
$87$	6.07120	+	9.91005i	0.650901	+	1.06247i
$88$	−8.89304	+	3.23680i	−0.948002	+	0.345044i
$89$	8.72878			0.925248			0.462624	−	0.886555i	$-0.346908\pi$
$89$	8.72878			0.925248			0.462624	+	0.886555i	$0.346908\pi$
$90$	7.37529	+	17.3870i	0.777423	+	1.83275i
$91$	7.78701	−	3.59337i	0.816300	−	0.376687i
$92$	−0.294633	−	0.0519517i	−0.0307176	−	0.00541634i
$93$	1.13267	−	0.446007i	0.117452	−	0.0462488i
$94$	3.83912	+	4.57528i	0.395975	+	0.471904i
$95$	3.66499	+	4.36777i	0.376020	+	0.448123i
$96$	1.12385	−	7.51349i	0.114702	−	0.766842i
$97$	−4.18960	−	0.738740i	−0.425390	−	0.0750077i	−0.0431451	−	0.999069i	$-0.513738\pi$
$97$	−4.18960	−	0.738740i	−0.425390	−	0.0750077i	−0.382245	+	0.924061i	$0.624849\pi$
$98$	−8.94667	−	7.62970i	−0.903750	−	0.770716i
$99$	4.19674	−	13.7148i	0.421788	−	1.37839i
$100$	−7.43229			−0.743229
$101$	−6.58764	+	2.39771i	−0.655495	+	0.238581i	−0.648290	−	0.761393i	$-0.724516\pi$
$101$	−6.58764	+	2.39771i	−0.655495	+	0.238581i	−0.00720487	+	0.999974i	$0.502293\pi$
$102$	5.37138	−	9.88994i	0.531846	−	0.979250i
$103$	4.60791	+	5.49149i	0.454031	+	0.541093i	0.943694	−	0.330818i	$-0.107325\pi$
$103$	4.60791	+	5.49149i	0.454031	+	0.541093i	−0.489663	+	0.871912i	$0.662880\pi$
$104$	4.91536	−	4.12448i	0.481991	−	0.404438i
$105$	17.0725	−	1.87403i	1.66611	−	0.182887i
$106$	−13.2262	+	4.81395i	−1.28464	+	0.467572i
$107$	15.4107	−	8.89738i	1.48981	−	0.860142i	0.489877	−	0.871792i	$-0.337042\pi$
$107$	15.4107	−	8.89738i	1.48981	−	0.860142i	0.999932	+	0.0116497i	$0.00370831\pi$
$108$	2.99093	+	3.04584i	0.287802	+	0.293086i
$109$	−8.73677	+	15.1325i	−0.836831	+	1.44943i	0.0557007	+	0.998448i	$0.482261\pi$
$109$	−8.73677	+	15.1325i	−0.836831	+	1.44943i	−0.892531	+	0.450986i	$0.851073\pi$
$110$	23.0564	+	19.3466i	2.19834	+	1.84463i
$111$	−3.02601	+	9.04009i	−0.287216	+	0.858047i
$112$	−11.8907	−	5.60261i	−1.12356	−	0.529397i
$113$	11.6574	−	2.05551i	1.09663	−	0.193366i	0.404074	−	0.914726i	$-0.367594\pi$
$113$	11.6574	−	2.05551i	1.09663	−	0.193366i	0.692561	+	0.721360i	$0.256483\pi$
$114$	3.88945	+	2.11242i	0.364281	+	0.197846i
$115$	−0.466816	−	1.28257i	−0.0435308	−	0.119600i
$116$	−4.77389	+	2.75621i	−0.443245	+	0.255908i
$117$	0.506541	+	9.71120i	0.0468297	+	0.897801i
$118$	−2.10796	+	1.21703i	−0.194054	+	0.112037i
$119$	−7.20799	−	7.26577i	−0.660755	−	0.666052i
$120$	11.9566	−	4.70814i	1.09149	−	0.429792i
$121$	−2.05886	−	11.6764i	−0.187169	−	1.06149i
$122$	−3.68516	+	3.09222i	−0.333639	+	0.279956i
$123$	−1.44722	−	0.216472i	−0.130492	−	0.0195186i
$124$	0.197478	+	0.542567i	0.0177341	+	0.0487240i
$125$	−7.58360	−	13.1352i	−0.678298	−	1.17485i
$126$	11.7984	−	6.20930i	1.05108	−	0.553168i
$127$	−0.317649	+	0.550185i	−0.0281868	+	0.0488210i	−0.879775	−	0.475391i	$-0.842307\pi$
$127$	−0.317649	+	0.550185i	−0.0281868	+	0.0488210i	0.851588	+	0.524212i	$0.175640\pi$
$128$	−12.8882	−	2.27254i	−1.13917	−	0.200866i
$129$	0.00355256	+	0.136309i	0.000312785	+	0.0120013i
$130$	−19.1761	−	6.97952i	−1.68185	−	0.612144i
$131$	1.92871	+	0.701993i	0.168512	+	0.0613334i	0.424899	−	0.905241i	$-0.360310\pi$
$131$	1.92871	+	0.701993i	0.168512	+	0.0613334i	−0.256386	+	0.966574i	$0.582532\pi$
$132$	6.45104	+	2.15937i	0.561491	+	0.187949i
$133$	2.85744	−	2.83471i	0.247771	−	0.245801i
$134$			6.79629i			0.587110i
$135$	−5.21133	+	18.7645i	−0.448520	+	1.61499i
$136$	−6.63149	−	3.82869i	−0.568646	−	0.328308i
$137$	−15.4247	−	2.71978i	−1.31782	−	0.232367i	−0.529854	−	0.848089i	$-0.677753\pi$
$137$	−15.4247	−	2.71978i	−1.31782	−	0.232367i	−0.787964	+	0.615722i	$0.788864\pi$
$138$	−0.701959	−	0.793617i	−0.0597547	−	0.0675572i
$139$	14.5992	+	17.3986i	1.23829	+	1.47573i	0.824999	+	0.565133i	$0.191175\pi$
$139$	14.5992	+	17.3986i	1.23829	+	1.47573i	0.413288	+	0.910600i	$0.364380\pi$
$140$	0.677600	+	8.11814i	0.0572676	+	0.686108i
$141$	0.160454	+	6.15651i	0.0135127	+	0.518472i
$142$	4.78117	−	27.1154i	0.401227	−	2.27547i
$143$	7.74848	+	13.4208i	0.647961	+	1.12230i
$144$	10.9029	−	10.1621i	0.908578	−	0.846843i
$145$	−21.7789	−	12.5741i	−1.80864	−	1.04422i
$146$	3.51461	−	19.9323i	0.290871	−	1.64961i
$147$	−2.32080	−	11.9002i	−0.191417	−	0.981509i
$148$	−4.24898	−	1.54650i	−0.349264	−	0.127122i
$149$	−11.5651	+	2.03925i	−0.947454	+	0.167062i	−0.625964	−	0.779852i	$-0.715294\pi$
$149$	−11.5651	+	2.03925i	−0.947454	+	0.167062i	−0.321489	+	0.946913i	$0.604183\pi$
$150$	−20.5969	−	16.3877i	−1.68173	−	1.33805i
$151$	1.20396	+	1.01025i	0.0979771	+	0.0822126i	0.690460	−	0.723370i	$-0.257408\pi$
$151$	1.20396	+	1.01025i	0.0979771	+	0.0822126i	−0.592483	+	0.805583i	$0.701852\pi$
$152$	1.50572	−	2.60799i	0.122130	−	0.211536i
$153$	10.6835	−	4.53177i	0.863710	−	0.366372i
$154$	12.2561	−	17.3557i	0.987627	−	1.39856i
$155$	−1.69316	+	2.01783i	−0.135998	+	0.162076i
$156$	−4.61084	+	0.120170i	−0.369163	+	0.00962132i
$157$	−3.19698	+	8.78364i	−0.255147	+	0.701011i	0.744303	+	0.667842i	$0.232782\pi$
$157$	−3.19698	+	8.78364i	−0.255147	+	0.701011i	−0.999450	+	0.0331683i	$0.989440\pi$
$158$	−2.17216	+	0.383010i	−0.172808	+	0.0304706i
$159$	−13.7628	−	4.60685i	−1.09146	−	0.365347i
$160$	5.62247	+	15.4476i	0.444495	+	1.22124i
$161$	−0.874849	+	0.403705i	−0.0689478	+	0.0318164i
$162$	1.57281	+	15.0356i	0.123572	+	1.18131i
$163$	7.03192	+	12.1796i	0.550783	+	0.953983i	0.998218	+	0.0596673i	$0.0190040\pi$
$163$	7.03192	+	12.1796i	0.550783	+	0.953983i	−0.447436	+	0.894316i	$0.647663\pi$
$164$	0.120525	−	0.683529i	0.00941139	−	0.0533747i
$165$	6.18368	+	30.4129i	0.481399	+	2.36764i
$166$	7.80177	−	21.4352i	0.605535	−	1.66369i
$167$	0.663852	+	3.76489i	0.0513704	+	0.291336i	0.999660	−	0.0260700i	$-0.00829929\pi$
$167$	0.663852	+	3.76489i	0.0513704	+	0.291336i	−0.948290	+	0.317406i	$0.897188\pi$
$168$	−4.01415	−	8.13480i	−0.309698	−	0.627614i
$169$	1.90966	+	1.60240i	0.146897	+	0.123261i
$170$			24.3530i			1.86779i
$171$	1.78223	+	4.20154i	0.136290	+	0.321300i
$172$	−0.0646751			−0.00493143
$173$	−10.8746	+	3.95802i	−0.826777	+	0.300922i	−0.720536	−	0.693418i	$-0.756104\pi$
$173$	−10.8746	+	3.95802i	−0.826777	+	0.300922i	−0.106242	+	0.994340i	$0.533882\pi$
$174$	−19.3070	−	2.88789i	−1.46366	−	0.218930i
$175$	−19.6616	+	13.6506i	−1.48628	+	1.03189i
$176$	8.12365	−	22.3196i	0.612343	−	1.68240i
$177$	−2.48225	−	0.371288i	−0.186577	−	0.0279077i
$178$	−9.42461	+	11.2318i	−0.706404	+	0.841860i
$179$		−	9.11384i		−	0.681200i	−0.940208	−	0.340600i	$-0.889370\pi$
$179$		−	9.11384i		−	0.681200i	0.940208	−	0.340600i	$-0.110630\pi$
$180$	−8.83283	−	2.70285i	−0.658360	−	0.201458i
$181$	6.15516	+	3.55368i	0.457509	+	0.264143i	0.710996	−	0.703196i	$-0.248244\pi$
$181$	6.15516	+	3.55368i	0.457509	+	0.264143i	−0.253487	+	0.967339i	$0.581578\pi$
$182$	−3.78398	+	13.8998i	−0.280487	+	1.03032i
$183$	−4.95876	+	0.129238i	−0.366562	+	0.00955354i
$184$	−0.552227	+	0.463374i	−0.0407107	+	0.0341604i
$185$	−3.58206	−	20.3149i	−0.263358	−	1.49358i
$186$	−0.649055	+	1.93903i	−0.0475910	+	0.142176i
$187$	11.8876	−	14.1671i	0.869306	−	1.03600i
$188$	−2.92110			−0.213043
$189$	13.5065	+	2.56426i	0.982451	+	0.186523i
$190$	−9.57741			−0.694818
$191$	7.87297	−	9.38264i	0.569668	−	0.678904i	−0.401895	−	0.915686i	$-0.631648\pi$
$191$	7.87297	−	9.38264i	0.569668	−	0.678904i	0.971563	+	0.236782i	$0.0760926\pi$
$192$	−2.94762	−	3.33250i	−0.212726	−	0.240503i
$193$	−2.88238	−	16.3468i	−0.207478	−	1.17667i	−0.893493	−	0.449078i	$-0.851753\pi$
$193$	−2.88238	−	16.3468i	−0.207478	−	1.17667i	0.686015	−	0.727588i	$-0.259359\pi$
$194$	5.47417	−	4.59337i	0.393022	−	0.329785i
$195$	−10.9923	−	17.9428i	−0.787176	−	1.28491i
$196$	5.67116	−	0.953357i	0.405083	−	0.0680969i
$197$	7.93030	+	4.57856i	0.565011	+	0.326209i	0.755154	−	0.655547i	$-0.227562\pi$
$197$	7.93030	+	4.57856i	0.565011	+	0.326209i	−0.190144	+	0.981756i	$0.560895\pi$
$198$	13.1163	+	20.2083i	0.932138	+	1.43614i
$199$		−	6.56017i		−	0.465038i	−0.972592	−	0.232519i	$-0.925303\pi$
$199$		−	6.56017i		−	0.465038i	0.972592	−	0.232519i	$-0.0746968\pi$
$200$	−11.5113	+	13.7186i	−0.813971	+	0.970053i
$201$	−4.36322	+	5.48393i	−0.307757	+	0.386806i
$202$	4.02753	−	11.0655i	0.283376	−	0.778569i
$203$	−7.56680	+	16.0594i	−0.531086	+	1.12715i
$204$	2.01672	+	5.12161i	0.141199	+	0.358584i
$205$	2.97547	−	1.08298i	0.207816	−	0.0756387i
$206$	−12.0415			−0.838968
$207$	−0.0569085	−	1.09103i	−0.00395542	−	0.0758316i
$208$			16.1041i			1.11662i
$209$	5.57154	+	4.67507i	0.385391	+	0.323382i
$210$	−16.0221	+	23.9916i	−1.10563	+	1.65558i
$211$	2.58385	+	14.6538i	0.177880	+	1.00881i	0.934767	+	0.355261i	$0.115608\pi$
$211$	2.58385	+	14.6538i	0.177880	+	1.00881i	−0.756888	+	0.653545i	$0.773281\pi$
$212$	2.35442	−	6.46872i	0.161702	−	0.444274i
$213$	21.2660	−	18.8099i	1.45712	−	1.28883i
$214$	−5.19045	+	29.4365i	−0.354812	+	2.01224i
$215$	−0.147527	−	0.255524i	−0.0100612	−	0.0174266i
$216$	10.2545	−	0.803228i	0.697728	−	0.0546527i
$217$	1.51893	+	1.07262i	0.103111	+	0.0728145i
$218$	−10.0386	−	27.5810i	−0.679903	−	1.86802i
$219$	15.6325	−	13.8270i	1.05635	−	0.934344i
$220$	−14.4968	+	2.55617i	−0.977372	+	0.172337i
$221$	−4.28859	+	11.7828i	−0.288482	+	0.792597i
$222$	−8.36516	−	13.6545i	−0.561433	−	0.916429i
$223$	0.651794	−	0.776778i	0.0436474	−	0.0520169i	−0.743779	−	0.668425i	$-0.766969\pi$
$223$	0.651794	−	0.776778i	0.0436474	−	0.0520169i	0.787426	+	0.616409i	$0.211413\pi$
$224$	10.5369	−	4.86234i	0.704029	−	0.324879i
$225$	−6.09877	−	26.4464i	−0.406585	−	1.76309i
$226$	−9.94174	+	17.2196i	−0.661315	+	1.14543i
$227$	17.6041	+	14.7716i	1.16843	+	0.980428i	0.999986	−	0.00528399i	$-0.00168195\pi$
$227$	17.6041	+	14.7716i	1.16843	+	0.980428i	0.168442	+	0.985712i	$0.446126\pi$
$228$	−2.01419	+	0.793125i	−0.133393	+	0.0525260i
$229$	0.352295	−	0.0621191i	0.0232803	−	0.00410495i	−0.161996	−	0.986791i	$-0.551793\pi$
$229$	0.352295	−	0.0621191i	0.0232803	−	0.00410495i	0.185276	+	0.982686i	$0.440682\pi$
$230$	2.15438	+	0.784130i	0.142056	+	0.0517040i
$231$	21.0318	−	6.13588i	1.38379	−	0.403711i
$232$	−2.30646	+	13.0806i	−0.151427	+	0.858783i
$233$	17.2582	+	9.96402i	1.13062	+	0.652764i	0.944091	−	0.329685i	$-0.106942\pi$
$233$	17.2582	+	9.96402i	1.13062	+	0.652764i	0.186530	+	0.982449i	$0.440276\pi$
$234$	−13.0429	−	9.83356i	−0.852640	−	0.642840i
$235$	−6.66317	−	11.5409i	−0.434657	−	0.752848i
$236$	0.206721	−	1.17238i	0.0134564	−	0.0763152i
$237$	−1.99861	−	1.08547i	−0.129823	−	0.0705091i
$238$	17.1319	−	1.42995i	1.11049	−	0.0926901i
$239$	−8.88553	−	10.5894i	−0.574757	−	0.684969i	0.397843	−	0.917454i	$-0.369759\pi$
$239$	−8.88553	−	10.5894i	−0.574757	−	0.684969i	−0.972600	+	0.232485i	$0.925314\pi$
$240$	−10.2372	+	30.5832i	−0.660808	+	1.97414i
$241$	−3.32597	−	0.586458i	−0.214244	−	0.0377770i	0.0654957	−	0.997853i	$-0.479137\pi$
$241$	−3.32597	−	0.586458i	−0.214244	−	0.0377770i	−0.279740	+	0.960076i	$0.590248\pi$
$242$	17.2477	+	9.95794i	1.10872	+	0.640121i
$243$	−8.38378	+	13.1420i	−0.537819	+	0.843060i
$244$		−	2.35280i		−	0.150623i
$245$	16.7028	+	20.2315i	1.06710	+	1.29254i
$246$	1.84114	−	1.62850i	0.117387	−	0.103829i
$247$	−4.63387	−	1.68659i	−0.294846	−	0.107315i
$248$	1.30734	+	0.475832i	0.0830160	+	0.0302153i
$249$	20.0566	−	12.2873i	1.27104	−	0.778677i
$250$	25.0899	+	4.42403i	1.58683	+	0.279800i
$251$	0.197747	−	0.342507i	0.0124817	−	0.0216189i	−0.859717	−	0.510770i	$-0.829360\pi$
$251$	0.197747	−	0.342507i	0.0124817	−	0.0216189i	0.872199	+	0.489152i	$0.162694\pi$
$252$	−1.38276	+	6.37243i	−0.0871056	+	0.401425i
$253$	−0.870521	−	1.50779i	−0.0547292	−	0.0947937i
$254$	−0.364983	−	1.00278i	−0.0229010	−	0.0629201i
$255$	−15.6346	+	19.6505i	−0.979079	+	1.23056i
$256$	12.9044	−	10.8281i	0.806526	−	0.676756i
$257$	−5.15739	−	29.2490i	−0.321709	−	1.82450i	−0.531857	−	0.846834i	$-0.678505\pi$
$257$	−5.15739	−	29.2490i	−0.321709	−	1.82450i	0.210147	−	0.977670i	$-0.432606\pi$
$258$	−0.179232	−	0.142604i	−0.0111585	−	0.00887814i
$259$	−14.0808	+	3.71275i	−0.874938	+	0.230699i
$260$	8.64345	−	4.99030i	0.536044	−	0.309485i
$261$	−13.7248	−	14.7253i	−0.849544	−	0.911475i
$262$	−2.98576	+	1.72383i	−0.184461	+	0.106498i
$263$	−4.12604	−	11.3362i	−0.254422	−	0.699020i	−0.999487	−	0.0320276i	$-0.989804\pi$
$263$	−4.12604	−	11.3362i	−0.254422	−	0.699020i	0.745065	−	0.666992i	$-0.232419\pi$
$264$	13.9773	−	8.56294i	0.860244	−	0.527013i
$265$	30.9277	−	5.45339i	1.89987	−	0.334999i
$266$	0.562363	+	6.73752i	0.0344807	+	0.413104i
$267$	−14.8155	+	3.01235i	−0.906696	+	0.184353i
$268$	−2.54629	−	2.13659i	−0.155540	−	0.130513i
$269$	−1.78062	+	3.08412i	−0.108566	+	0.188042i	−0.915190	−	0.403024i	$-0.867959\pi$
$269$	−1.78062	+	3.08412i	−0.108566	+	0.188042i	0.806624	+	0.591066i	$0.201293\pi$
$270$	−18.5186	−	26.9661i	−1.12701	−	1.64110i
$271$	6.59196	−	3.80587i	0.400433	−	0.231190i	−0.286238	−	0.958159i	$-0.592405\pi$
$271$	6.59196	−	3.80587i	0.400433	−	0.231190i	0.686671	+	0.726969i	$0.259071\pi$
$272$	18.0593	−	6.57306i	1.09501	−	0.398550i
$273$	−11.9770	+	8.78644i	−0.724879	+	0.531780i
$274$	20.1540	−	16.9112i	1.21755	−	1.02164i
$275$	−27.8016	−	33.1326i	−1.67650	−	1.99797i
$276$	0.518016	−	0.0135008i	0.0311809	−	0.000812653i
$277$	10.1541	−	3.69580i	0.610103	−	0.222059i	−0.0184453	−	0.999830i	$-0.505872\pi$
$277$	10.1541	−	3.69580i	0.610103	−	0.222059i	0.628548	+	0.777771i	$0.283649\pi$
$278$	−38.1508			−2.28814
$279$	−1.76858	+	1.14791i	−0.105882	+	0.0687235i
$280$	16.0341	+	11.3228i	0.958218	+	0.676668i
$281$	3.59151	+	0.633280i	0.214252	+	0.0377783i	0.279744	−	0.960075i	$-0.409751\pi$
$281$	3.59151	+	0.633280i	0.214252	+	0.0377783i	−0.0654920	+	0.997853i	$0.520862\pi$
$282$	−8.09518	−	6.44083i	−0.482061	−	0.383546i
$283$	16.0737	+	19.1559i	0.955484	+	1.13870i	0.990249	+	0.139306i	$0.0444870\pi$
$283$	16.0737	+	19.1559i	0.955484	+	1.13870i	−0.0347657	+	0.999395i	$0.511069\pi$
$284$	8.65595	+	10.3158i	0.513636	+	0.612128i
$285$	−7.72801	−	6.14869i	−0.457768	−	0.364217i
$286$	−25.6354	−	4.52022i	−1.51586	−	0.267286i
$287$	−0.936569	−	2.02959i	−0.0552839	−	0.119803i
$288$	0.685423	+	13.1407i	0.0403889	+	0.774321i
$289$	−2.03620			−0.119777
$290$	39.6949	−	14.4477i	2.33096	−	0.848401i
$291$	7.36605	−	0.191978i	0.431806	−	0.0112539i
$292$	6.36293	+	7.58305i	0.372362	+	0.443764i
$293$	−23.0690	+	19.3572i	−1.34770	+	1.13086i	−0.368131	+	0.929774i	$0.620002\pi$
$293$	−23.0690	+	19.3572i	−1.34770	+	1.13086i	−0.979574	+	0.201084i	$0.935554\pi$
$294$	17.8184	+	9.86250i	1.03919	+	0.575193i
$295$	5.10346	−	1.85751i	0.297135	−	0.108148i
$296$	−9.43547	+	5.44757i	−0.548426	+	0.316634i
$297$	−2.39015	+	24.7268i	−0.138690	+	1.43479i
$298$	9.86307	−	17.0833i	0.571352	−	0.989612i
$299$	0.904274	+	0.758776i	0.0522955	+	0.0438811i
$300$	12.6150	−	2.56493i	0.728327	−	0.148086i
$301$	−0.171094	+	0.118786i	−0.00986168	+	0.00684671i
$302$	−2.59988	+	0.458429i	−0.149606	+	0.0263796i
$303$	10.3539	−	6.34312i	0.594815	−	0.364402i
$304$	2.58501	+	7.10226i	0.148261	+	0.407342i
$305$	9.29565	−	5.36685i	0.532268	−	0.307305i
$306$	−5.70388	+	18.6401i	−0.326069	+	1.06558i
$307$	21.5000	−	12.4130i	1.22707	−	0.708449i	0.260654	−	0.965432i	$-0.416062\pi$
$307$	21.5000	−	12.4130i	1.22707	−	0.708449i	0.966416	+	0.256983i	$0.0827284\pi$
$308$	2.64943	+	10.0481i	0.150966	+	0.572544i
$309$	−9.71626	−	7.73062i	−0.552739	−	0.439779i
$310$	−0.768324	−	4.35738i	−0.0436379	−	0.247483i
$311$	6.04946	−	5.07610i	0.343034	−	0.287839i	−0.454952	−	0.890516i	$-0.650344\pi$
$311$	6.04946	−	5.07610i	0.343034	−	0.287839i	0.797985	+	0.602677i	$0.205899\pi$
$312$	−6.91957	+	8.69689i	−0.391743	+	0.492364i
$313$	6.61039	+	18.1619i	0.373641	+	1.02657i	0.973942	+	0.226797i	$0.0728253\pi$
$313$	6.61039	+	18.1619i	0.373641	+	1.02657i	−0.600301	+	0.799774i	$0.704952\pi$
$314$	−7.85057	−	13.5976i	−0.443033	−	0.767356i
$315$	−28.3309	+	9.07267i	−1.59626	+	0.511187i
$316$	0.539377	−	0.934229i	0.0303424	−	0.0525545i
$317$	13.9204	+	2.45453i	0.781845	+	0.137860i	0.550304	−	0.834965i	$-0.314512\pi$
$317$	13.9204	+	2.45453i	0.781845	+	0.137860i	0.231541	+	0.972825i	$0.425623\pi$
$318$	20.7878	−	12.7353i	1.16572	−	0.714158i
$319$	−30.1444	−	10.9717i	−1.68776	−	0.614296i
$320$	9.04652	+	3.29266i	0.505716	+	0.184066i
$321$	−23.0864	+	20.4200i	−1.28856	+	1.13974i
$322$	0.425120	−	1.56161i	0.0236910	−	0.0870249i
$323$			5.88487i			0.327443i
$324$	−6.12770	−	4.13759i	−0.340428	−	0.229866i
$325$	25.3962	+	14.6625i	1.40873	+	0.813330i
$326$	−23.2647	−	4.10220i	−1.28851	−	0.227200i
$327$	9.60678	−	28.6999i	0.531256	−	1.58711i
$328$	−1.07500	−	1.28113i	−0.0593568	−	0.0707386i
$329$	−7.72758	+	5.36507i	−0.426036	+	0.295786i
$330$	−45.8107	−	24.8805i	−2.52180	−	1.36963i
$331$	−2.53135	+	14.3560i	−0.139135	+	0.789077i	0.832755	+	0.553642i	$0.186762\pi$
$331$	−2.53135	+	14.3560i	−0.139135	+	0.789077i	−0.971890	+	0.235435i	$0.924349\pi$
$332$	5.57820	+	9.66173i	0.306144	+	0.530256i
$333$	2.01632	−	16.3882i	0.110494	−	0.898070i
$334$	−5.56127	−	3.21080i	−0.304299	−	0.175687i
$335$	2.63323	−	14.9338i	0.143869	−	0.815920i
$336$	22.1158	+	5.40589i	1.20652	+	0.294916i
$337$	−25.3341	−	9.22085i	−1.38003	−	0.502291i	−0.457846	−	0.889032i	$-0.651379\pi$
$337$	−25.3341	−	9.22085i	−1.38003	−	0.502291i	−0.922189	+	0.386740i	$0.873601\pi$
$338$	−4.12379	+	0.727136i	−0.224305	+	0.0395510i
$339$	−19.0770	+	7.51190i	−1.03612	+	0.407991i
$340$	−9.12410	−	7.65602i	−0.494824	−	0.415206i
$341$	−1.68003	+	2.90990i	−0.0909787	+	0.157580i
$342$	−7.33067	−	2.24319i	−0.396397	−	0.121298i
$343$	13.2517	−	12.9380i	0.715524	−	0.698588i
$344$	−0.100170	+	0.119378i	−0.00540082	+	0.00643644i
$345$	1.23496	+	2.01583i	0.0664879	+	0.108528i
$346$	6.64845	−	18.2665i	0.357423	−	0.982011i
$347$	19.7224	−	3.47759i	1.05875	−	0.186687i	0.382950	−	0.923769i	$-0.374908\pi$
$347$	19.7224	−	3.47759i	1.05875	−	0.186687i	0.675803	+	0.737082i	$0.263797\pi$
$348$	7.15165	−	6.32567i	0.383369	−	0.339092i
$349$	−3.59306	−	9.87186i	−0.192332	−	0.528429i	0.805617	−	0.592437i	$-0.201834\pi$
$349$	−3.59306	−	9.87186i	−0.192332	−	0.528429i	−0.997949	+	0.0640080i	$0.979612\pi$
$350$	3.66403	−	40.0385i	0.195851	−	2.14015i
$351$	−4.21116	−	16.3082i	−0.224775	−	0.870469i
$352$	10.4848	+	18.1602i	0.558842	+	0.967944i
$353$	−0.572625	+	3.24752i	−0.0304778	+	0.172848i	−0.996247	−	0.0865542i	$-0.972414\pi$
$353$	−0.572625	+	3.24752i	−0.0304778	+	0.172848i	0.965769	+	0.259402i	$0.0835255\pi$
$354$	3.15789	−	2.79317i	0.167840	−	0.148455i
$355$	−21.0118	+	57.7294i	−1.11519	+	3.06396i
$356$	−1.24523	−	7.06204i	−0.0659970	−	0.374288i
$357$	14.7417	+	9.84483i	0.780216	+	0.521044i
$358$	11.7273	+	9.84037i	0.619807	+	0.520080i
$359$			11.0679i			0.584139i	0.956397	+	0.292070i	$0.0943439\pi$
$359$			11.0679i			0.584139i	−0.956397	+	0.292070i	$0.905656\pi$
$360$	−18.6694	+	12.1175i	−0.983966	+	0.638650i
$361$	16.6856			0.878191
$362$	−11.2186	+	4.08322i	−0.589634	+	0.214609i
$363$	7.52414	+	19.1081i	0.394915	+	1.00291i
$364$	−4.01810	−	5.78748i	−0.210606	−	0.303346i
$365$	−15.4456	+	42.4365i	−0.808461	+	2.22123i
$366$	5.18776	−	6.52026i	0.271169	−	0.340820i
$367$	12.7217	−	15.1611i	0.664066	−	0.791404i	−0.323897	−	0.946092i	$-0.604993\pi$
$367$	12.7217	−	15.1611i	0.664066	−	0.791404i	0.987963	+	0.154689i	$0.0494375\pi$
$368$		−	1.80925i		−	0.0943138i
$369$	2.53111	−	0.132024i	0.131764	−	0.00687290i
$370$	30.0079	+	17.3251i	1.56004	+	0.900688i
$371$	−5.65236	−	21.4368i	−0.293456	−	1.11295i
$372$	−0.522427	−	0.852760i	−0.0270866	−	0.0442135i
$373$	−3.34599	+	2.80762i	−0.173249	+	0.145373i	−0.725289	−	0.688444i	$-0.758294\pi$
$373$	−3.34599	+	2.80762i	−0.173249	+	0.145373i	0.552040	+	0.833817i	$0.313849\pi$
$374$	5.39435	+	30.5929i	0.278935	+	1.58192i
$375$	17.4048	+	19.6775i	0.898783	+	1.01614i
$376$	−4.52427	+	5.39182i	−0.233321	+	0.278062i
$377$	21.7499			1.12018
$378$	−17.8827	+	14.6109i	−0.919789	+	0.751501i
$379$	−5.24775			−0.269559			−0.134780	−	0.990876i	$-0.543033\pi$
$379$	−5.24775			−0.269559			−0.134780	+	0.990876i	$0.543033\pi$
$380$	3.01091	−	3.58827i	0.154457	−	0.184074i
$381$	0.349281	−	1.04346i	0.0178942	−	0.0534582i
$382$	3.57260	+	20.2612i	0.182790	+	1.03665i
$383$	−3.10858	+	2.60841i	−0.158841	+	0.133283i	−0.718744	−	0.695275i	$-0.755283\pi$
$383$	−3.10858	+	2.60841i	−0.158841	+	0.133283i	0.559903	+	0.828558i	$0.310838\pi$
$384$	22.6597	−	0.590569i	1.15635	−	0.0301374i
$385$	−33.6554	+	33.3878i	−1.71524	+	1.70160i
$386$	24.1465	+	13.9410i	1.22902	+	0.709577i
$387$	−0.0530709	−	0.230134i	−0.00269775	−	0.0116984i
$388$			3.49500i			0.177432i
$389$	−5.26118	+	6.27003i	−0.266753	+	0.317903i	−0.882748	−	0.469846i	$-0.844309\pi$
$389$	−5.26118	+	6.27003i	−0.266753	+	0.317903i	0.615996	+	0.787749i	$0.288754\pi$
$390$	34.9566	+	5.22871i	1.77010	+	0.264766i
$391$	0.481811	−	1.32377i	0.0243662	−	0.0669457i
$392$	7.02391	−	11.9445i	0.354761	−	0.603288i
$393$	−3.51590	−	0.525899i	−0.177354	−	0.0265281i
$394$	−14.4540	+	5.26082i	−0.728181	+	0.265036i
$395$	4.92138			0.247621
$396$	−11.6947	−	1.43886i	−0.587681	−	0.0723053i
$397$		−	6.76990i		−	0.339771i	−0.985464	−	0.169886i	$-0.945660\pi$
$397$		−	6.76990i		−	0.339771i	0.985464	−	0.169886i	$-0.0543399\pi$
$398$	8.44135	+	7.08313i	0.423127	+	0.355045i
$399$	−3.87172	+	5.79754i	−0.193828	+	0.290240i
$400$	−7.80480	−	44.2632i	−0.390240	−	2.21316i
$401$	1.24382	−	3.41736i	0.0621133	−	0.170655i	−0.904754	−	0.425935i	$-0.859945\pi$
$401$	1.24382	−	3.41736i	0.0621133	−	0.170655i	0.966867	+	0.255280i	$0.0821676\pi$
$402$	−2.34544	−	11.5355i	−0.116980	−	0.575338i
$403$	0.395598	−	2.24355i	0.0197061	−	0.111759i
$404$	2.87965	+	4.98770i	0.143268	+	0.248147i
$405$	2.36957	−	33.6479i	0.117745	−	1.67198i
$406$	−12.4945	−	27.0762i	−0.620092	−	1.34377i
$407$	−8.99974	−	24.7266i	−0.446101	−	1.22565i
$408$	12.5771	+	4.20996i	0.622658	+	0.208424i
$409$	−36.1958	+	6.38230i	−1.78977	+	0.315584i	−0.967377	−	0.253340i	$-0.918471\pi$
$409$	−36.1958	+	6.38230i	−1.78977	+	0.315584i	−0.822390	+	0.568925i	$0.807360\pi$
$410$	−1.81913	+	4.99802i	−0.0898404	+	0.246835i
$411$	27.1192	−	0.706796i	1.33769	−	0.0348637i
$412$	3.78556	−	4.51145i	0.186501	−	0.222263i
$413$	−1.60638	−	3.48112i	−0.0790450	−	0.171295i
$414$	1.46533	+	1.10477i	0.0720172	+	0.0542967i
$415$	−25.4483	+	44.0777i	−1.24921	+	2.16369i
$416$	−10.8913	−	9.13892i	−0.533992	−	0.448073i
$417$	−30.7839	−	24.4928i	−1.50749	−	1.19942i
$418$	−12.0314	+	2.12145i	−0.588473	+	0.103764i
$419$	11.4760	+	4.17694i	0.560642	+	0.204057i	0.606768	−	0.794879i	$-0.292466\pi$
$419$	11.4760	+	4.17694i	0.560642	+	0.204057i	−0.0461267	+	0.998936i	$0.514688\pi$
$420$	−3.95172	−	13.5452i	−0.192824	−	0.660940i
$421$	0.755733	−	4.28598i	0.0368322	−	0.208886i	−0.960838	−	0.277112i	$-0.910623\pi$
$421$	0.755733	−	4.28598i	0.0368322	−	0.208886i	0.997670	+	0.0682260i	$0.0217339\pi$
$422$	−21.6457	−	12.4971i	−1.05369	−	0.608350i
$423$	−2.39699	−	10.3942i	−0.116546	−	0.505384i
$424$	−8.29348	−	14.3647i	−0.402767	−	0.697613i
$425$	6.07698	−	34.4643i	0.294777	−	1.67176i
$426$	1.24249	+	47.6735i	0.0601990	+	2.30979i
$427$	−4.32129	−	6.22418i	−0.209122	−	0.301209i
$428$	−9.39691	−	11.1988i	−0.454217	−	0.541314i
$429$	−17.7833	−	20.1053i	−0.858584	−	0.970694i
$430$	0.488085	+	0.0860625i	0.0235375	+	0.00415030i
$431$	−7.21480	−	4.16547i	−0.347525	−	0.200644i	0.316070	−	0.948736i	$-0.397637\pi$
$431$	−7.21480	−	4.16547i	−0.347525	−	0.200644i	−0.663595	+	0.748092i	$0.730970\pi$
$432$	−14.9988	+	21.0111i	−0.721629	+	1.01090i
$433$		−	23.0129i		−	1.10593i	−0.833205	−	0.552965i	$-0.813496\pi$
$433$		−	23.0129i		−	1.10593i	0.833205	−	0.552965i	$-0.186504\pi$
$434$	−3.02022	+	0.796356i	−0.144975	+	0.0382263i
$435$	41.3052	+	13.8262i	1.98043	+	0.662916i
$436$	13.4894	+	4.90973i	0.646024	+	0.235134i
$437$	0.520602	+	0.189484i	0.0249038	+	0.00906424i
$438$	0.913349	+	35.0445i	0.0436415	+	1.67449i
$439$	−17.9478	−	3.16469i	−0.856603	−	0.151042i	−0.271936	−	0.962315i	$-0.587664\pi$
$439$	−17.9478	−	3.16469i	−0.856603	−	0.151042i	−0.584667	+	0.811273i	$0.698775\pi$
$440$	−17.7347	+	30.7174i	−0.845469	+	1.46440i
$441$	8.04597	+	19.3975i	0.383142	+	0.923690i
$442$	−10.5311	−	18.2405i	−0.500915	−	0.867610i
$443$	−5.16749	−	14.1975i	−0.245515	−	0.674546i	−0.999837	−	0.0180420i	$-0.994257\pi$
$443$	−5.16749	−	14.1975i	−0.245515	−	0.674546i	0.754323	−	0.656504i	$-0.227965\pi$
$444$	7.74559	+	1.15856i	0.367590	+	0.0549830i
$445$	25.0609	−	21.0286i	1.18800	−	0.996851i
$446$	0.295771	+	1.67740i	0.0140052	+	0.0794273i
$447$	18.9260	−	7.45246i	0.895170	−	0.352489i
$448$	1.78513	−	6.55739i	0.0843397	−	0.309808i
$449$	−19.1172	+	11.0373i	−0.902197	+	0.520884i	−0.877912	−	0.478821i	$-0.841064\pi$
$449$	−19.1172	+	11.0373i	−0.902197	+	0.520884i	−0.0242848	+	0.999705i	$0.507731\pi$
$450$	40.6151	+	20.7070i	1.91461	+	0.976139i
$451$	3.49797	−	2.01955i	0.164713	−	0.0950970i
$452$	−3.32604	−	9.13821i	−0.156444	−	0.429825i
$453$	−2.39216	−	1.29922i	−0.112393	−	0.0610425i
$454$	−38.0150	+	6.70307i	−1.78413	+	0.314591i
$455$	13.7002	−	29.0766i	0.642276	−	1.36313i
$456$	−1.65567	+	4.94624i	−0.0775337	+	0.231629i
$457$	−29.7824	−	24.9904i	−1.39316	−	1.16900i	−0.964040	−	0.265756i	$-0.914379\pi$
$457$	−29.7824	−	24.9904i	−1.39316	−	1.16900i	−0.429122	−	0.903246i	$-0.641177\pi$
$458$	−0.300447	+	0.520389i	−0.0140390	+	0.0243162i
$459$	−16.5694	+	11.3788i	−0.773394	+	0.531118i
$460$	−0.971069	+	0.560647i	−0.0452763	+	0.0261403i
$461$	6.46360	−	2.35256i	0.301040	−	0.109570i	−0.187084	−	0.982344i	$-0.559904\pi$
$461$	6.46360	−	2.35256i	0.301040	−	0.109570i	0.488124	+	0.872774i	$0.337681\pi$
$462$	−14.8130	+	33.6879i	−0.689165	+	1.56730i
$463$	7.23069	−	6.06727i	0.336039	−	0.281970i	−0.459116	−	0.888376i	$-0.651834\pi$
$463$	7.23069	−	6.06727i	0.336039	−	0.281970i	0.795155	+	0.606406i	$0.207389\pi$
$464$	−21.4279	−	25.5367i	−0.994763	−	1.18551i
$465$	2.17748	−	4.00923i	0.100978	−	0.185924i
$466$	−31.4552	+	11.4488i	−1.45714	+	0.530354i
$467$	−19.3403			−0.894962			−0.447481	−	0.894293i	$-0.647679\pi$
$467$	−19.3403			−0.894962			−0.447481	+	0.894293i	$0.647679\pi$
$468$	7.78462	−	1.79520i	0.359844	−	0.0829831i
$469$	−10.6602	−	0.975548i	−0.492244	−	0.0450466i
$470$	22.0447	+	3.88708i	1.01685	+	0.179298i
$471$	2.39502	−	16.0120i	0.110357	−	0.737792i
$472$	−1.84381	−	2.19737i	−0.0848684	−	0.101142i
$473$	−0.241927	−	0.288317i	−0.0111238	−	0.0132568i
$474$	3.55467	−	1.39972i	0.163271	−	0.0642911i
$475$	13.5539	+	2.38992i	0.621896	+	0.109657i
$476$	−4.85012	+	6.86817i	−0.222305	+	0.314802i
$477$	24.9497	+	3.06969i	1.14237	+	0.140551i
$478$	23.2198			1.06205
$479$	−16.0915	+	5.85683i	−0.735240	+	0.267606i	−0.682381	−	0.730996i	$-0.739056\pi$
$479$	−16.0915	+	5.85683i	−0.735240	+	0.267606i	−0.0528590	+	0.998602i	$0.516833\pi$
$480$	−14.8742	−	24.2792i	−0.678911	−	1.10819i
$481$	11.4679	+	13.6669i	0.522890	+	0.623155i
$482$	4.34573	−	3.64650i	0.197943	−	0.166094i
$483$	1.34558	−	0.987133i	0.0612260	−	0.0449161i
$484$	−9.15310	+	3.33146i	−0.416050	+	0.151430i
$485$	−13.8083	+	7.97225i	−0.627005	+	0.362001i
$486$	−7.85846	−	24.9775i	−0.356467	−	1.13300i
$487$	−20.1639	+	34.9249i	−0.913713	+	1.58260i	−0.104939	+	0.994479i	$0.533465\pi$
$487$	−20.1639	+	34.9249i	−0.913713	+	1.58260i	−0.808774	+	0.588119i	$0.799869\pi$
$488$	−4.34284	−	3.64407i	−0.196591	−	0.164959i
$489$	−16.1387	−	18.2460i	−0.729817	−	0.825113i
$490$	−44.0673	−	0.351848i	−1.99076	−	0.0158949i
$491$	4.14445	−	0.730778i	0.187036	−	0.0329795i	−0.0793453	−	0.996847i	$-0.525283\pi$
$491$	4.14445	−	0.730778i	0.187036	−	0.0329795i	0.266382	+	0.963868i	$0.414172\pi$
$492$	0.0313210	+	1.20176i	0.00141206	+	0.0541797i
$493$	−8.87747	−	24.3906i	−0.399821	−	1.09850i
$494$	7.17350	−	4.14162i	0.322751	−	0.186340i
$495$	−20.9914	−	49.4865i	−0.943493	−	2.22425i
$496$	−3.02390	+	1.74585i	−0.135777	+	0.0783909i
$497$	41.8452	+	11.3916i	1.87702	+	0.510985i
$498$	−5.84470	+	39.0748i	−0.261907	+	1.75099i
$499$	2.17385	+	12.3285i	0.0973149	+	0.551900i	0.994013	+	0.109258i	$0.0348476\pi$
$499$	2.17385	+	12.3285i	0.0973149	+	0.551900i	−0.896698	+	0.442642i	$0.854041\pi$
$500$	−9.54520	+	8.00938i	−0.426874	+	0.358190i
$501$	−2.42606	−	6.16113i	−0.108388	−	0.275259i
$502$	0.227213	+	0.624263i	0.0101410	+	0.0278622i
$503$	−17.2248	−	29.8343i	−0.768016	−	1.33024i	−0.938637	−	0.344907i	$-0.887911\pi$
$503$	−17.2248	−	29.8343i	−0.768016	−	1.33024i	0.170621	−	0.985337i	$-0.445423\pi$
$504$	9.62067	+	12.4221i	0.428539	+	0.553323i
$505$	−13.1372	+	22.7543i	−0.584599	+	1.01255i
$506$	2.88007	+	0.507834i	0.128035	+	0.0225760i
$507$	−3.79431	−	2.06075i	−0.168511	−	0.0915210i
$508$	0.490444	+	0.178507i	0.0217599	+	0.00791996i
$509$	9.42273	+	3.42959i	0.417655	+	0.152014i	0.542295	−	0.840188i	$-0.317555\pi$
$509$	9.42273	+	3.42959i	0.417655	+	0.152014i	−0.124640	+	0.992202i	$0.539778\pi$
$510$	−8.40438	−	41.3349i	−0.372152	−	1.83034i
$511$	30.7602	+	8.37392i	1.36075	+	0.370440i
$512$			2.12207i			0.0937832i
$513$	−4.47499	−	6.51631i	−0.197576	−	0.287702i
$514$	43.2049	+	24.9444i	1.90569	+	1.10025i
$515$	26.4592	+	4.66548i	1.16593	+	0.205586i
$516$	0.109774	−	0.0223198i	0.00483255	−	0.000982573i
$517$	−10.9268	−	13.0221i	−0.480561	−	0.572710i
$518$	10.4259	−	22.1273i	0.458086	−	0.972217i
$519$	17.0917	−	10.4709i	0.750242	−	0.459622i
$520$	4.17600	−	23.6833i	0.183130	−	1.03858i
$521$	16.0296	+	27.7641i	0.702270	+	1.21637i	0.967668	+	0.252228i	$0.0811634\pi$
$521$	16.0296	+	27.7641i	0.702270	+	1.21637i	−0.265398	+	0.964139i	$0.585503\pi$
$522$	33.7668	−	1.76129i	1.47793	−	0.0770898i
$523$	−3.61939	−	2.08966i	−0.158265	−	0.0913742i	0.418776	−	0.908090i	$-0.362459\pi$
$523$	−3.61939	−	2.08966i	−0.158265	−	0.0913742i	−0.577041	+	0.816715i	$0.695793\pi$
$524$	0.292804	−	1.66057i	0.0127912	−	0.0725425i
$525$	28.6612	−	29.9548i	1.25088	−	1.30733i
$526$	19.0419	+	6.93068i	0.830266	+	0.302192i
$527$	−2.67741	+	0.472099i	−0.116630	+	0.0205650i
$528$	−6.08584	+	40.6870i	−0.264852	+	1.77067i
$529$	17.5174	+	14.6989i	0.761627	+	0.639081i
$530$	−26.3760	+	45.6846i	−1.14570	+	1.98441i
$531$	4.34131	−	0.226445i	0.188397	−	0.00982688i
$532$	−2.70107	−	1.90742i	−0.117106	−	0.0826974i
$533$	−1.76031	+	2.09786i	−0.0762475	+	0.0908682i
$534$	12.1204	−	22.3165i	0.524502	−	0.965729i
$535$	22.8104	−	62.6711i	0.986180	−	2.70951i
$536$	−7.88752	+	1.39078i	−0.340689	+	0.0600726i
$537$	3.14524	+	15.4691i	0.135727	+	0.667541i
$538$	−2.04595	−	5.62119i	−0.0882070	−	0.242347i
$539$	25.4638	+	21.7155i	1.09680	+	0.935352i
$540$	15.9249	+	1.53934i	0.685299	+	0.0662427i
$541$	−1.91792	−	3.32193i	−0.0824578	−	0.142821i	0.821847	−	0.569708i	$-0.192944\pi$
$541$	−1.91792	−	3.32193i	−0.0824578	−	0.142821i	−0.904305	+	0.426887i	$0.859610\pi$
$542$	−2.22022	+	12.5915i	−0.0953667	+	0.540852i
$543$	−11.6737	−	3.90756i	−0.500966	−	0.167689i
$544$	−5.80308	+	15.9438i	−0.248805	+	0.683586i
$545$	11.3721	+	64.4943i	0.487127	+	2.76263i
$546$	1.62572	−	24.8983i	0.0695745	−	1.06555i
$547$	3.29856	+	2.76782i	0.141036	+	0.118344i	0.710576	−	0.703620i	$-0.248434\pi$
$547$	3.29856	+	2.76782i	0.141036	+	0.118344i	−0.569540	+	0.821964i	$0.692879\pi$
$548$			12.8674i			0.549667i
$549$	8.37201	−	1.93066i	0.357309	−	0.0823984i
$550$	72.6515			3.09787
$551$	9.59220	−	3.49128i	0.408641	−	0.148733i
$552$	0.777395	−	0.977072i	0.0330881	−	0.0415869i
$553$	−0.288972	−	3.46209i	−0.0122883	−	0.147223i
$554$	−6.20800	+	17.0563i	−0.263753	+	0.724654i
$555$	13.0907	+	33.2447i	0.555669	+	1.41116i
$556$	11.9937	−	14.2936i	0.508648	−	0.606183i
$557$			33.8656i			1.43493i	0.696594	+	0.717465i	$0.254698\pi$
$557$			33.8656i			1.43493i	−0.696594	+	0.717465i	$0.745302\pi$
$558$	0.432486	−	3.51515i	0.0183086	−	0.148808i
$559$	0.220996	+	0.127592i	0.00934712	+	0.00539656i
$560$	−47.6363	+	12.5605i	−2.01300	+	0.530778i
$561$	−15.2879	+	28.1485i	−0.645456	+	1.18843i
$562$	−4.69270	+	3.93764i	−0.197949	+	0.166099i
$563$	−0.780886	−	4.42862i	−0.0329104	−	0.186644i	0.963921	−	0.266189i	$-0.0857645\pi$
$563$	−0.780886	−	4.42862i	−0.0329104	−	0.186644i	−0.996831	+	0.0795446i	$0.974653\pi$
$564$	4.95805	−	1.00809i	0.208772	−	0.0424483i
$565$	28.5172	−	33.9855i	1.19973	−	1.42978i
$566$	−42.0041			−1.76556
$567$	−23.8098	+	0.308782i	−0.999916	+	0.0129676i
$568$	32.4475			1.36147
$569$	2.17293	−	2.58959i	0.0910938	−	0.108561i	−0.718572	−	0.695453i	$-0.755204\pi$
$569$	2.17293	−	2.58959i	0.0910938	−	0.108561i	0.809666	+	0.586891i	$0.199648\pi$
$570$	16.2559	−	3.30522i	0.680887	−	0.138441i
$571$	3.32678	+	18.8671i	0.139222	+	0.789565i	0.971826	+	0.235697i	$0.0757374\pi$
$571$	3.32678	+	18.8671i	0.139222	+	0.789565i	−0.832605	+	0.553867i	$0.813151\pi$
$572$	9.75273	−	8.18351i	0.407782	−	0.342170i
$573$	−10.1250	+	18.6424i	−0.422976	+	0.778797i
$574$	3.62282	+	0.986250i	0.151214	+	0.0411653i
$575$	−2.85320	−	1.64729i	−0.118987	−	0.0686969i
$576$	6.15312	+	4.63909i	0.256380	+	0.193295i
$577$		−	45.8713i		−	1.90965i	−0.297175	−	0.954823i	$-0.596045\pi$
$577$		−	45.8713i		−	1.90965i	0.297175	−	0.954823i	$-0.403955\pi$
$578$	2.19852	−	2.62010i	0.0914465	−	0.108982i
$579$	10.5337	+	26.7510i	0.437765	+	1.11173i
$580$	−7.06615	+	19.4141i	−0.293406	+	0.806127i
$581$	32.5021	+	15.3142i	1.34841	+	0.635341i
$582$	−7.70623	+	9.68560i	−0.319433	+	0.401481i
$583$	37.6442	−	13.7014i	1.55906	−	0.567452i
$584$	23.8519			0.987001
$585$	24.8497	+	26.6612i	1.02741	+	1.10230i
$586$		−	50.5845i		−	2.08963i
$587$	30.9328	+	25.9557i	1.27673	+	1.07131i	0.993686	+	0.112201i	$0.0357901\pi$
$587$	30.9328	+	25.9557i	1.27673	+	1.07131i	0.283048	+	0.959106i	$0.408654\pi$
$588$	−9.29678	+	3.57531i	−0.383393	+	0.147443i
$589$	−0.185664	−	1.05295i	−0.00765016	−	0.0433862i
$590$	−3.12014	+	8.57250i	−0.128454	+	0.352924i
$591$	−15.0404	−	5.03450i	−0.618678	−	0.207092i
$592$	4.74830	−	26.9290i	0.195154	−	1.10677i
$593$	−2.27065	−	3.93289i	−0.0932446	−	0.161504i	0.815630	−	0.578574i	$-0.196391\pi$
$593$	−2.27065	−	3.93289i	−0.0932446	−	0.161504i	−0.908875	+	0.417069i	$0.863057\pi$
$594$	−29.2367	−	29.7735i	−1.19959	−	1.22162i
$595$	−38.1987	−	3.49567i	−1.56599	−	0.143308i
$596$	3.29972	+	9.06590i	0.135162	+	0.371354i
$597$	2.26396	+	11.1347i	0.0926575	+	0.455714i
$598$	−1.95272	+	0.344317i	−0.0798527	+	0.0140802i
$599$	3.36732	−	9.25164i	0.137585	−	0.378012i	−0.851696	−	0.524036i	$-0.824426\pi$
$599$	3.36732	−	9.25164i	0.137585	−	0.378012i	0.989281	+	0.146025i	$0.0466479\pi$
$600$	14.8040	−	27.2575i	0.604370	−	1.11278i
$601$	−13.1479	+	15.6690i	−0.536313	+	0.639153i	−0.964357	−	0.264605i	$-0.914758\pi$
$601$	−13.1479	+	15.6690i	−0.536313	+	0.639153i	0.428044	+	0.903758i	$0.359203\pi$
$602$	0.0318841	−	0.348411i	0.00129950	−	0.0142002i
$603$	5.51324	−	10.8138i	0.224517	−	0.440370i
$604$	0.645587	−	1.11819i	0.0262686	−	0.0454985i
$605$	−34.0408	−	28.5636i	−1.38396	−	1.16128i
$606$	−3.01723	+	20.1717i	−0.122566	+	0.819420i
$607$	16.5784	−	2.92322i	0.672897	−	0.118650i	0.173249	−	0.984878i	$-0.444574\pi$
$607$	16.5784	−	2.92322i	0.672897	−	0.118650i	0.499649	+	0.866228i	$0.333462\pi$
$608$	−6.27029	−	2.28220i	−0.254294	−	0.0925554i
$609$	7.30112	−	29.8693i	0.295856	−	1.21036i
$610$	−3.13085	+	17.7559i	−0.126764	+	0.718917i
$611$	9.98145	+	5.76279i	0.403806	+	0.233138i
$612$	−5.19053	−	7.99703i	−0.209815	−	0.323261i
$613$	7.28280	+	12.6142i	0.294150	+	0.509482i	0.974787	−	0.223139i	$-0.0716303\pi$
$613$	7.28280	+	12.6142i	0.294150	+	0.509482i	−0.680637	+	0.732621i	$0.738297\pi$
$614$	−7.24137	+	41.0679i	−0.292238	+	1.65736i
$615$	−4.67658	+	2.86502i	−0.188578	+	0.115529i
$616$	22.6504	+	10.6724i	0.912612	+	0.430002i
$617$	6.20042	+	7.38938i	0.249620	+	0.297485i	0.876275	−	0.481811i	$-0.160021\pi$
$617$	6.20042	+	7.38938i	0.249620	+	0.297485i	−0.626655	+	0.779297i	$0.715577\pi$
$618$	20.4382	−	4.15558i	0.822147	−	0.167162i
$619$	−31.9542	−	5.63438i	−1.28435	−	0.226465i	−0.510522	−	0.859865i	$-0.670548\pi$
$619$	−31.9542	−	5.63438i	−1.28435	−	0.226465i	−0.773825	+	0.633400i	$0.781659\pi$
$620$	1.87408	+	1.08200i	0.0752648	+	0.0434541i
$621$	0.473112	+	1.83218i	0.0189853	+	0.0735231i
$622$			13.2649i			0.531876i
$623$	−16.2647	−	16.3951i	−0.651632	−	0.656856i
$624$	−5.55762	−	27.3338i	−0.222483	−	1.09423i
$625$	−10.9109	−	3.97124i	−0.436436	−	0.158850i
$626$	−30.5073	−	11.1037i	−1.21932	−	0.443795i
$627$	−11.0701	−	6.01233i	−0.442097	−	0.240109i
$628$	7.56251	+	1.33347i	0.301777	+	0.0532114i
$629$	10.6455	−	18.4385i	0.424462	−	0.735190i
$630$	18.9150	−	46.2509i	0.753592	−	1.84268i
$631$	1.22037	+	2.11374i	0.0485821	+	0.0841467i	0.889294	−	0.457336i	$-0.151196\pi$
$631$	1.22037	+	2.11374i	0.0485821	+	0.0841467i	−0.840712	+	0.541483i	$0.817863\pi$
$632$	−0.889014	−	2.44255i	−0.0353631	−	0.0971593i
$633$	−9.44273	−	23.9804i	−0.375315	−	0.953137i
$634$	−18.1884	+	15.2619i	−0.722355	+	0.606128i
$635$	0.413464	+	2.34487i	0.0164078	+	0.0930533i
$636$	−1.76382	+	11.7920i	−0.0699399	+	0.467584i
$637$	−21.2592	−	7.93052i	−0.842322	−	0.314219i
$638$	46.6654	−	26.9423i	1.84750	−	1.06665i
$639$	−29.6038	+	39.2655i	−1.17111	+	1.55332i
$640$	−42.4777	+	24.5245i	−1.67908	+	0.969417i
$641$	−6.48762	−	17.8246i	−0.256245	−	0.704029i	−0.999391	−	0.0348986i	$-0.988889\pi$
$641$	−6.48762	−	17.8246i	−0.256245	−	0.704029i	0.743145	−	0.669130i	$-0.233333\pi$
$642$	−1.34885	−	51.7545i	−0.0532350	−	2.04259i
$643$	−30.7254	+	5.41772i	−1.21169	+	0.213654i	−0.742746	−	0.669573i	$-0.766477\pi$
$643$	−30.7254	+	5.41772i	−1.21169	+	0.213654i	−0.468946	+	0.883227i	$0.655366\pi$
$644$	0.451423	+	0.650208i	0.0177886	+	0.0256218i
$645$	0.338583	+	0.382794i	0.0133317	+	0.0150725i
$646$	−7.57240	−	6.35400i	−0.297932	−	0.249995i
$647$	−18.3923	+	31.8564i	−0.723076	+	1.25240i	0.236685	+	0.971587i	$0.423939\pi$
$647$	−18.3923	+	31.8564i	−0.723076	+	1.25240i	−0.959761	+	0.280818i	$0.909394\pi$
$648$	−17.1279	+	4.90222i	−0.672849	+	0.192577i
$649$	5.99964	−	3.46390i	0.235507	−	0.135970i
$650$	−46.2879	+	16.8474i	−1.81556	+	0.660810i
$651$	−2.94827	−	1.29640i	−0.115552	−	0.0508099i
$652$	8.85082	−	7.42672i	0.346625	−	0.290853i
$653$	10.1406	+	12.0851i	0.396832	+	0.472926i	0.927051	−	0.374935i	$-0.122335\pi$
$653$	10.1406	+	12.0851i	0.396832	+	0.472926i	−0.530220	+	0.847860i	$0.677890\pi$
$654$	26.5572	+	43.3494i	1.03847	+	1.69509i
$655$	7.22864	−	2.63101i	0.282446	−	0.102802i
$656$	4.19735			0.163879
$657$	−21.7616	+	28.8638i	−0.849000	+	1.12608i
$658$	1.44007	−	15.7363i	0.0561398	−	0.613464i
$659$	−14.0350	−	2.47474i	−0.546725	−	0.0964023i	−0.106538	−	0.994309i	$-0.533977\pi$
$659$	−14.0350	−	2.47474i	−0.546725	−	0.0964023i	−0.440187	+	0.897906i	$0.645088\pi$
$660$	23.7235	−	9.34157i	0.923438	−	0.363620i
$661$	−15.3589	−	18.3041i	−0.597394	−	0.711946i	0.379615	−	0.925144i	$-0.376056\pi$
$661$	−15.3589	−	18.3041i	−0.597394	−	0.711946i	−0.977009	+	0.213198i	$0.931612\pi$
$662$	−15.7395	−	18.7576i	−0.611734	−	0.729037i
$663$	3.21280	−	21.4792i	0.124775	−	0.834184i
$664$	26.4734	+	4.66798i	1.02737	+	0.181153i
$665$	1.37475	−	15.0225i	0.0533107	−	0.582549i
$666$	18.9106	+	20.2892i	0.732771	+	0.786190i
$667$	−2.44355			−0.0946145
$668$	2.95129	−	1.07418i	0.114189	−	0.0415614i
$669$	−0.838234	+	1.54338i	−0.0324080	+	0.0596706i
$670$	16.3730	+	19.5126i	0.632545	+	0.753837i
$671$	10.4886	−	8.80101i	0.404909	−	0.339759i
$672$	−16.2066	+	11.8893i	−0.625182	+	0.458641i
$673$	−2.30855	+	0.840244i	−0.0889881	+	0.0323890i	−0.386131	−	0.922444i	$-0.626189\pi$
$673$	−2.30855	+	0.840244i	−0.0889881	+	0.0323890i	0.297142	+	0.954833i	$0.403966\pi$
$674$	39.2186	−	22.6429i	1.51064	−	0.872171i
$675$	19.4784	+	42.7834i	0.749724	+	1.64673i
$676$	1.02400	−	1.77361i	0.0393845	−	0.0682159i
$677$	−2.08260	−	1.74751i	−0.0800409	−	0.0671623i	0.601889	−	0.798579i	$-0.294415\pi$
$677$	−2.08260	−	1.74751i	−0.0800409	−	0.0671623i	−0.681930	+	0.731417i	$0.738859\pi$
$678$	10.9317	−	32.6582i	0.419831	−	1.25423i
$679$	6.41912	+	9.24579i	0.246343	+	0.354821i
$680$	−28.2632	+	4.98357i	−1.08384	+	0.191111i
$681$	−34.9777	−	18.9969i	−1.34035	−	0.727963i
$682$	−1.93037	−	5.30366i	−0.0739178	−	0.203088i
$683$	18.8189	−	10.8651i	0.720086	−	0.415742i	−0.0946982	−	0.995506i	$-0.530189\pi$
$683$	18.8189	−	10.8651i	0.720086	−	0.415742i	0.814784	+	0.579764i	$0.196855\pi$
$684$	3.14502	−	2.04130i	0.120253	−	0.0780510i
$685$	−50.8375	+	29.3510i	−1.94240	+	1.12145i
$686$	2.34001	+	31.0211i	0.0893420	+	1.18439i
$687$	−0.576520	+	0.227015i	−0.0219956	+	0.00866117i
$688$	−0.0679167	−	0.385175i	−0.00258930	−	0.0146846i
$689$	−20.8067	+	17.4589i	−0.792671	+	0.665130i
$690$	−3.92728	−	0.587431i	−0.149509	−	0.0223631i
$691$	4.34469	+	11.9369i	0.165280	+	0.454103i	0.994490	−	0.104835i	$-0.0334314\pi$
$691$	4.34469	+	11.9369i	0.165280	+	0.454103i	−0.829210	+	0.558937i	$0.811209\pi$
$692$	4.75359	+	8.23345i	0.180704	+	0.312989i
$693$	−33.5803	+	17.6728i	−1.27561	+	0.671333i
$694$	−16.8198	+	29.1327i	−0.638471	+	1.10586i
$695$	83.8305	+	14.7816i	3.17987	+	0.560698i
$696$	−0.599385	−	22.9980i	−0.0227196	−	0.871735i
$697$	3.07105	+	1.11777i	0.116324	+	0.0423386i
$698$	16.5822	+	6.03542i	0.627645	+	0.228444i
$699$	−32.7313	−	10.9562i	−1.23801	−	0.414403i
$700$	13.8489	+	13.9599i	0.523440	+	0.527636i
$701$		−	23.3250i		−	0.880973i	−0.897759	−	0.440487i	$-0.854806\pi$
$701$		−	23.3250i		−	0.880973i	0.897759	−	0.440487i	$-0.145194\pi$
$702$	25.5316	+	12.1895i	0.963628	+	0.460064i
$703$	7.25137	+	4.18658i	0.273490	+	0.157900i
$704$	12.0938	+	2.13246i	0.455802	+	0.0803703i
$705$	15.2924	+	17.2892i	0.575945	+	0.651149i
$706$	−3.56050	−	4.24323i	−0.134001	−	0.159696i
$707$	16.7786	+	7.90570i	0.631025	+	0.297324i
$708$	0.0537211	+	2.06124i	0.00201896	+	0.0774661i
$709$	−3.99399	+	22.6510i	−0.149997	+	0.850677i	0.813221	+	0.581955i	$0.197712\pi$
$709$	−3.99399	+	22.6510i	−0.149997	+	0.850677i	−0.963218	+	0.268721i	$0.913399\pi$
$710$	−51.5969	−	89.3684i	−1.93640	−	3.35394i
$711$	3.76688	+	1.15267i	0.141269	+	0.0432284i
$712$	−14.9639	−	8.63939i	−0.560794	−	0.323775i
$713$	−0.0444444	+	0.252056i	−0.00166445	+	0.00943959i
$714$	−28.5848	+	8.33941i	−1.06976	+	0.312094i
$715$	54.5785	+	19.8650i	2.04112	+	0.742907i
$716$	−7.37358	+	1.30016i	−0.275563	+	0.0485893i
$717$	18.7361	+	14.9071i	0.699711	+	0.556716i
$718$	−14.2417	−	11.9502i	−0.531494	−	0.445976i
$719$	9.22441	−	15.9772i	0.344013	−	0.595847i	−0.641161	−	0.767406i	$-0.721547\pi$
$719$	9.22441	−	15.9772i	0.344013	−	0.595847i	0.985174	+	0.171559i	$0.0548804\pi$
$720$	6.82136	−	55.4425i	0.254217	−	2.06622i
$721$	1.72845	−	18.8875i	0.0643708	−	0.703408i
$722$	−18.0158	+	21.4704i	−0.670478	+	0.799044i
$723$	5.84762	−	0.152404i	0.217476	−	0.00566796i
$724$	1.99704	−	5.48681i	0.0742193	−	0.203916i
$725$	−59.7812	+	10.5410i	−2.22022	+	0.391485i
$726$	−32.7114	−	10.9496i	−1.21403	−	0.406376i
$727$	−0.912501	−	2.50708i	−0.0338428	−	0.0929823i	0.921620	−	0.388092i	$-0.126866\pi$
$727$	−0.912501	−	2.50708i	−0.0338428	−	0.0929823i	−0.955463	+	0.295110i	$0.904644\pi$
$728$	−16.9059	−	1.54711i	−0.626576	−	0.0573397i
$729$	9.69458	−	25.1995i	0.359059	−	0.933315i
$730$	−37.9285	−	65.6942i	−1.40380	−	2.43145i
$731$	0.0528814	−	0.299905i	0.00195589	−	0.0110924i
$732$	0.811967	+	3.99346i	0.0300111	+	0.147603i
$733$	11.9877	−	32.9359i	0.442775	−	1.21651i	−0.494884	−	0.868959i	$-0.664790\pi$
$733$	11.9877	−	32.9359i	0.442775	−	1.21651i	0.937659	−	0.347556i	$-0.112988\pi$
$734$	5.77285	+	32.7394i	0.213080	+	1.20843i
$735$	−35.3320	−	28.5751i	−1.30324	−	1.05401i
$736$	1.22361	+	1.02673i	0.0451030	+	0.0378459i
$737$		−	19.3435i		−	0.712525i
$738$	−2.56300	+	3.39947i	−0.0943454	+	0.125136i
$739$	−6.84534			−0.251810			−0.125905	−	0.992042i	$-0.540183\pi$
$739$	−6.84534			−0.251810			−0.125905	+	0.992042i	$0.540183\pi$
$740$	−15.9248	+	5.79615i	−0.585407	+	0.213071i
$741$	8.44721	+	1.26351i	0.310316	+	0.0464162i
$742$	33.6870	+	15.8725i	1.23669	+	0.582698i
$743$	7.09106	−	19.4825i	0.260146	−	0.714744i	−0.739011	−	0.673693i	$-0.764707\pi$
$743$	7.09106	−	19.4825i	0.260146	−	0.714744i	0.999157	−	0.0410513i	$-0.0130707\pi$
$744$	−2.38318	−	0.356470i	−0.0873718	−	0.0130688i
$745$	−28.2915	+	33.7165i	−1.03652	+	1.23528i
$746$		−	7.33692i		−	0.268624i
$747$	−29.8021	+	27.7772i	−1.09040	+	1.01631i
$748$	−13.1578	−	7.59664i	−0.481095	−	0.277761i
$749$	−45.4273	−	12.3668i	−1.65988	−	0.451872i
$750$	−44.1125	+	1.14968i	−1.61076	+	0.0419805i
$751$	22.5351	−	18.9092i	0.822316	−	0.690005i	−0.131197	−	0.991356i	$-0.541882\pi$
$751$	22.5351	−	18.9092i	0.822316	−	0.690005i	0.953513	+	0.301351i	$0.0974376\pi$
$752$	−3.06751	−	17.3967i	−0.111861	−	0.634393i
$753$	−0.217438	+	0.649589i	−0.00792390	+	0.0236723i
$754$	−23.4838	+	27.9869i	−0.855229	+	1.01922i
$755$	5.89045			0.214376
$756$	0.147822	−	11.2933i	0.00537623	−	0.410732i
$757$	−41.4656			−1.50709			−0.753546	−	0.657396i	$-0.771658\pi$
$757$	−41.4656			−1.50709			−0.753546	+	0.657396i	$0.771658\pi$
$758$	5.66609	−	6.75259i	0.205802	−	0.245265i
$759$	1.99790	+	2.25878i	0.0725192	+	0.0819884i
$760$	−1.95991	−	11.1152i	−0.0710933	−	0.403190i
$761$	35.0006	−	29.3690i	1.26877	−	1.06463i	0.274082	−	0.961706i	$-0.411626\pi$
$761$	35.0006	−	29.3690i	1.26877	−	1.06463i	0.994690	−	0.102920i	$-0.0328185\pi$
$762$	0.965559	+	1.57608i	0.0349785	+	0.0570955i
$763$	44.7028	−	11.7870i	1.61835	−	0.426718i
$764$	−8.71420	−	5.03115i	−0.315269	−	0.182020i
$765$	19.7555	−	38.7488i	0.714262	−	1.40096i
$766$		−	6.81633i		−	0.246284i
$767$	−3.01925	+	3.59820i	−0.109019	+	0.129924i
$768$	−18.1661	+	22.8322i	−0.655513	+	0.823884i
$769$	−3.17805	+	8.73163i	−0.114604	+	0.314871i	−0.983712	−	0.179750i	$-0.942471\pi$
$769$	−3.17805	+	8.73163i	−0.114604	+	0.314871i	0.869109	+	0.494621i	$0.164693\pi$
$770$	−6.62362	−	79.3557i	−0.238699	−	2.85978i
$771$	18.8478	+	47.8652i	0.678786	+	1.72382i
$772$	−12.8142	+	4.66399i	−0.461193	+	0.167861i
$773$	3.25512			0.117079			0.0585393	−	0.998285i	$-0.481356\pi$
$773$	3.25512			0.117079			0.0585393	+	0.998285i	$0.481356\pi$
$774$	0.353429	+	0.180191i	0.0127037	+	0.00647682i
$775$			6.35827i			0.228396i
$776$	6.45112	+	5.41313i	0.231582	+	0.194320i
$777$	22.6183	−	11.1611i	0.811428	−	0.400402i
$778$	−2.38742	−	13.5397i	−0.0855931	−	0.485423i
$779$	−0.439590	+	1.20776i	−0.0157499	+	0.0432726i
$780$	−12.9485	+	11.4531i	−0.463632	+	0.410085i
$781$	−13.6081	+	77.1752i	−0.486935	+	2.76155i
$782$	1.18314	+	2.04927i	0.0423092	+	0.0732816i
$783$	28.3772	+	20.2571i	1.01412	+	0.723930i
$784$	11.6332	+	32.7737i	0.415470	+	1.17049i
$785$	11.9820	+	32.9203i	0.427656	+	1.17498i
$786$	4.47289	−	3.95629i	0.159543	−	0.141116i
$787$	36.7086	−	6.47272i	1.30852	−	0.230728i	0.524472	−	0.851427i	$-0.324263\pi$
$787$	36.7086	−	6.47272i	1.30852	−	0.230728i	0.784048	+	0.620700i	$0.213151\pi$
$788$	2.57298	−	7.06920i	0.0916586	−	0.251830i
$789$	10.9154	+	17.8173i	0.388599	+	0.634311i
$790$	−5.31370	+	6.33262i	−0.189053	+	0.225304i
$791$	−25.5826	−	18.0657i	−0.909612	−	0.642344i
$792$	−20.7689	+	19.3577i	−0.737990	+	0.687847i
$793$	−4.64164	+	8.03956i	−0.164830	+	0.285493i
$794$	8.71122	+	7.30958i	0.309149	+	0.259407i
$795$	−50.6123	+	19.9295i	−1.79503	+	0.706827i
$796$	−5.30753	+	0.935860i	−0.188120	+	0.0331707i
$797$	−24.8403	−	9.04114i	−0.879889	−	0.320253i	−0.137724	−	0.990471i	$-0.543979\pi$
$797$	−24.8403	−	9.04114i	−0.879889	−	0.320253i	−0.742165	+	0.670217i	$0.766201\pi$
$798$	−3.27967	−	11.2417i	−0.116099	−	0.397951i
$799$	2.38843	−	13.5455i	0.0844966	−	0.479204i
$800$	34.3648	+	19.8405i	1.21498	+	0.701468i
$801$	24.1072	−	10.2259i	0.851785	−	0.361313i
$802$	3.05434	+	5.29028i	0.107853	+	0.186806i
$803$	−10.0032	+	56.7310i	−0.353006	+	2.00199i
$804$	5.05923	+	2.74775i	0.178425	+	0.0969056i
$805$	−1.53918	+	3.26667i	−0.0542490	+	0.115135i
$806$	2.45977	+	2.93144i	0.0866416	+	0.103255i
$807$	1.95793	−	5.84924i	0.0689224	−	0.205903i
$808$	13.6664	+	2.40976i	0.480784	+	0.0847751i
$809$	−5.51222	−	3.18248i	−0.193799	−	0.111890i	0.399961	−	0.916532i	$-0.369024\pi$
$809$	−5.51222	−	3.18248i	−0.193799	−	0.111890i	−0.593760	+	0.804642i	$0.702357\pi$
$810$	40.7382	+	39.3793i	1.43139	+	1.38365i
$811$		−	37.5618i		−	1.31897i	−0.751716	−	0.659487i	$-0.770773\pi$
$811$		−	37.5618i		−	1.31897i	0.751716	−	0.659487i	$-0.229227\pi$
$812$	14.0723	+	3.83095i	0.493843	+	0.134440i
$813$	−9.87524	+	8.73471i	−0.346340	+	0.306340i
$814$	41.5343	+	15.1172i	1.45578	+	0.529859i
$815$	49.5312	+	18.0279i	1.73500	+	0.631490i
$816$	−28.3841	+	17.3890i	−0.993642	+	0.608736i
$817$	0.117945	+	0.0207969i	0.00412637	+	0.000727590i
$818$	30.8688	−	53.4663i	1.07930	−	1.86940i
$819$	17.2965	−	19.0467i	0.604389	−	0.665547i
$820$	−1.30066	−	2.25282i	−0.0454211	−	0.0786717i
$821$	−14.9344	−	41.0321i	−0.521216	−	1.43203i	−0.869168	−	0.494517i	$-0.835345\pi$
$821$	−14.9344	−	41.0321i	−0.521216	−	1.43203i	0.347952	−	0.937512i	$-0.386877\pi$
$822$	−28.3716	+	35.6590i	−0.989574	+	1.24375i
$823$	18.2144	−	15.2837i	0.634914	−	0.532756i	−0.267538	−	0.963547i	$-0.586210\pi$
$823$	18.2144	−	15.2837i	0.634914	−	0.532756i	0.902452	+	0.430791i	$0.141766\pi$
$824$	−2.46415	−	13.9749i	−0.0858426	−	0.486838i
$825$	58.6225	+	46.6422i	2.04097	+	1.62387i
$826$	6.21380	+	1.69160i	0.216206	+	0.0588582i
$827$	1.91398	−	1.10504i	0.0665558	−	0.0384260i	−0.466353	−	0.884599i	$-0.654432\pi$
$827$	1.91398	−	1.10504i	0.0665558	−	0.0384260i	0.532909	+	0.846173i	$0.321099\pi$
$828$	−0.874581	+	0.201686i	−0.0303938	+	0.00700906i
$829$	7.55608	−	4.36250i	0.262433	−	0.151516i	−0.363011	−	0.931785i	$-0.618251\pi$
$829$	7.55608	−	4.36250i	0.262433	−	0.151516i	0.625444	+	0.780269i	$0.284918\pi$
$830$	−29.2403	−	80.3372i	−1.01495	−	2.78854i
$831$	−15.9594	+	9.77722i	−0.553625	+	0.339168i
$832$	−8.19973	+	1.44583i	−0.284275	+	0.0501253i
$833$	−0.216194	+	27.0773i	−0.00749069	+	0.938172i
$834$	64.7543	−	13.1661i	2.24226	−	0.455904i
$835$	10.9760	+	9.20996i	0.379840	+	0.318724i
$836$	2.98756	−	5.17460i	0.103327	−	0.178967i
$837$	2.60570	−	2.55872i	0.0900660	−	0.0884422i
$838$	−17.7656	+	10.2570i	−0.613702	+	0.354321i
$839$	−22.6010	+	8.22611i	−0.780275	+	0.283997i	−0.701287	−	0.712879i	$-0.747391\pi$
$839$	−22.6010	+	8.22611i	−0.780275	+	0.283997i	−0.0789874	+	0.996876i	$0.525169\pi$
$840$	−31.1225	−	13.6850i	−1.07383	−	0.472179i
$841$	−12.2742	+	10.2993i	−0.423249	+	0.355148i
$842$	4.69903	+	5.60009i	0.161939	+	0.192992i
$843$	−6.31450	+	0.164572i	−0.217483	+	0.00566816i
$844$	11.4871	−	4.18095i	0.395401	−	0.143914i
$845$	9.34312			0.321413
$846$	15.9629	+	8.13846i	0.548816	+	0.279806i
$847$	−18.0952	+	25.6243i	−0.621757	+	0.880460i
$848$	40.9971	+	7.22890i	1.40785	+	0.248241i
$849$	−33.8931	−	26.9666i	−1.16321	−	0.925492i
$850$	37.7858	+	45.0313i	1.29604	+	1.54456i
$851$	−1.28838	−	1.53544i	−0.0441652	−	0.0526341i
$852$	−18.2520	−	14.5219i	−0.625302	−	0.497514i
$853$	13.6366	+	2.40451i	0.466910	+	0.0823287i	0.402153	−	0.915572i	$-0.368262\pi$
$853$	13.6366	+	2.40451i	0.466910	+	0.0823287i	0.0647563	+	0.997901i	$0.479373\pi$
$854$	12.6748	+	1.15990i	0.433722	+	0.0396911i
$855$	15.2389	+	7.76933i	0.521158	+	0.265705i
$856$	−35.2250			−1.20397
$857$	−9.93166	+	3.61483i	−0.339259	+	0.123480i	−0.506031	−	0.862515i	$-0.668888\pi$
$857$	−9.93166	+	3.61483i	−0.339259	+	0.123480i	0.166772	+	0.985996i	$0.446666\pi$
$858$	45.0715	−	1.17468i	1.53872	−	0.0401029i
$859$	−29.2486	−	34.8571i	−0.997950	−	1.18931i	−0.981892	−	0.189439i	$-0.939333\pi$
$859$	−29.2486	−	34.8571i	−0.997950	−	1.18931i	−0.0160572	−	0.999871i	$-0.505111\pi$
$860$	−0.185687	+	0.155810i	−0.00633186	+	0.00531306i
$861$	2.29008	+	3.12166i	0.0780459	+	0.106386i
$862$	13.1499	−	4.78617i	0.447887	−	0.163018i
$863$	−42.6896	+	24.6469i	−1.45317	+	0.838989i	−0.998660	−	0.0517521i	$-0.983519\pi$
$863$	−42.6896	+	24.6469i	−1.45317	+	0.838989i	−0.454511	+	0.890741i	$0.650186\pi$
$864$	−5.69830	−	22.0674i	−0.193860	−	0.750748i
$865$	−21.6863	+	37.5618i	−0.737356	+	1.27714i
$866$	29.6120	+	24.8474i	1.00626	+	0.844350i
$867$	3.45609	−	0.702706i	0.117375	−	0.0238651i
$868$	0.651124	−	1.38191i	0.0221006	−	0.0469051i
$869$	6.18235	−	1.09012i	0.209722	−	0.0369796i
$870$	−62.3890	+	38.2214i	−2.11518	+	1.29583i
$871$	4.48562	+	12.3241i	0.151989	+	0.417588i
$872$	29.9551	−	17.2946i	1.01441	−	0.585669i
$873$	−12.4363	+	2.86792i	−0.420905	+	0.0970643i
$874$	−0.805923	+	0.465300i	−0.0272608	+	0.0157390i
$875$	−10.5407	+	38.7195i	−0.356341	+	1.30896i
$876$	−13.4169	−	10.6750i	−0.453315	−	0.360674i
$877$	6.82630	+	38.7139i	0.230508	+	1.30727i	0.851871	+	0.523752i	$0.175468\pi$
$877$	6.82630	+	38.7139i	0.230508	+	1.30727i	−0.621363	+	0.783523i	$0.713421\pi$
$878$	23.4508	−	19.6775i	0.791425	−	0.664085i
$879$	32.4752	−	40.8166i	1.09536	−	1.37671i
$880$	−30.4467	−	83.6517i	−1.02636	−	2.81990i
$881$	20.9452	+	36.2781i	0.705660	+	1.22224i	0.966453	+	0.256845i	$0.0826829\pi$
$881$	20.9452	+	36.2781i	0.705660	+	1.22224i	−0.260792	+	0.965395i	$0.583984\pi$
$882$	−33.6472	−	10.5906i	−1.13296	−	0.356604i
$883$	3.31527	−	5.74221i	0.111568	−	0.193241i	−0.804835	−	0.593499i	$-0.797746\pi$
$883$	3.31527	−	5.74221i	0.111568	−	0.193241i	0.916402	+	0.400258i	$0.131080\pi$
$884$	10.1447	+	1.78879i	0.341204	+	0.0601634i
$885$	−8.02118	+	4.91403i	−0.269629	+	0.165183i
$886$	23.8482	+	8.68004i	0.801197	+	0.291612i
$887$	−37.6426	−	13.7008i	−1.26392	−	0.460028i	−0.378835	−	0.925464i	$-0.623675\pi$
$887$	−37.6426	−	13.7008i	−1.26392	−	0.460028i	−0.885081	+	0.465436i	$0.845897\pi$
$888$	14.1350	−	12.5025i	0.474341	−	0.419557i
$889$	1.62529	−	0.428549i	0.0545105	−	0.0143731i
$890$			54.9522i			1.84200i
$891$	−4.47651	−	42.7941i	−0.149969	−	1.43366i
$892$	−0.721438	−	0.416523i	−0.0241555	−	0.0139462i
$893$	5.32707	+	0.939307i	0.178264	+	0.0314327i
$894$	−10.8452	+	32.3997i	−0.362719	+	1.08361i
$895$	−21.9562	−	26.1664i	−0.733916	−	0.874647i
$896$	19.7467	+	28.4422i	0.659691	+	0.950188i
$897$	−1.79670	−	0.975817i	−0.0599901	−	0.0325816i
$898$	6.43883	−	36.5164i	0.214867	−	1.21857i
$899$	2.35792	+	4.08403i	0.0786409	+	0.136210i
$900$	−20.5265	+	8.70702i	−0.684217	+	0.290234i
$901$	28.0710	+	16.2068i	0.935182	+	0.539928i
$902$	−1.17814	+	6.68158i	−0.0392279	+	0.222472i
$903$	0.249407	−	0.260664i	0.00829975	−	0.00867434i
$904$	−22.0189	−	8.01422i	−0.732337	−	0.266549i
$905$	26.2331	−	4.62560i	0.872017	−	0.153760i
$906$	4.25463	−	1.67534i	0.141351	−	0.0556593i
$907$	35.7631	+	30.0088i	1.18749	+	0.996426i	0.999899	+	0.0141799i	$0.00451377\pi$
$907$	35.7631	+	30.0088i	1.18749	+	0.996426i	0.187595	+	0.982246i	$0.439931\pi$
$908$	9.43966	−	16.3500i	0.313266	−	0.542593i
$909$	−15.3848	+	14.3395i	−0.510283	+	0.475611i
$910$	22.6221	+	49.0233i	0.749916	+	1.62511i
$911$	−11.2903	+	13.4553i	−0.374066	+	0.445794i	−0.919932	−	0.392078i	$-0.871756\pi$
$911$	−11.2903	+	13.4553i	−0.374066	+	0.445794i	0.545866	+	0.837872i	$0.316201\pi$
$912$	−6.83863	−	11.1627i	−0.226450	−	0.369634i
$913$	−22.2052	+	61.0084i	−0.734886	+	2.01908i
$914$	64.3132	−	11.3402i	2.12729	−	0.375099i
$915$	−13.9256	+	12.3173i	−0.460366	+	0.407196i
$916$	−0.100515	−	0.276164i	−0.00332112	−	0.00912470i
$917$	−2.27531	−	4.93072i	−0.0751374	−	0.162827i
$918$	3.24850	−	33.6067i	0.107217	−	1.10919i
$919$	−0.970359	−	1.68071i	−0.0320092	−	0.0554416i	0.849577	−	0.527465i	$-0.176857\pi$
$919$	−0.970359	−	1.68071i	−0.0320092	−	0.0554416i	−0.881586	+	0.472023i	$0.843524\pi$
$920$	−0.469163	+	2.66075i	−0.0154678	+	0.0877225i
$921$	−32.2086	+	28.4887i	−1.06131	+	0.938735i
$922$	−3.95169	+	10.8572i	−0.130142	+	0.357562i
$923$	−9.22643	−	52.3257i	−0.303692	−	1.72232i
$924$	−7.96461	−	16.1405i	−0.262016	−	0.530985i
$925$	−38.1438	−	32.0065i	−1.25416	−	1.05237i
$926$			15.8551i			0.521030i
$927$	19.1595	+	9.76820i	0.629281	+	0.320830i
$928$	29.4308			0.966114
$929$	4.71446	−	1.71592i	0.154676	−	0.0562976i	−0.263522	−	0.964653i	$-0.584884\pi$
$929$	4.71446	−	1.71592i	0.154676	−	0.0562976i	0.418198	+	0.908356i	$0.362662\pi$
$930$	2.80785	+	7.13072i	0.0920731	+	0.233826i
$931$	−10.6488	−	0.0850236i	−0.349000	−	0.00278654i
$932$	5.59940	−	15.3842i	0.183415	−	0.503927i
$933$	−8.51609	+	10.7035i	−0.278804	+	0.350416i
$934$	20.8820	−	24.8863i	0.683282	−	0.814303i
$935$		−	69.3131i		−	2.26678i
$936$	8.74338	−	17.1494i	0.285786	−	0.560546i
$937$	25.9158	+	14.9625i	0.846632	+	0.488803i	0.859513	−	0.511114i	$-0.170767\pi$
$937$	25.9158	+	14.9625i	0.846632	+	0.488803i	−0.0128808	+	0.999917i	$0.504100\pi$
$938$	12.7653	−	12.6638i	0.416803	−	0.413489i
$939$	−17.4877	−	28.5453i	−0.570691	−	0.931541i
$940$	−8.38668	+	7.03726i	−0.273543	+	0.229530i
$941$	−7.13638	−	40.4724i	−0.232639	−	1.31936i	−0.847529	−	0.530750i	$-0.821910\pi$
$941$	−7.13638	−	40.4724i	−0.232639	−	1.31936i	0.614889	−	0.788613i	$-0.289201\pi$
$942$	18.0176	+	20.3702i	0.587044	+	0.663697i
$943$	0.197766	−	0.235688i	0.00644015	−	0.00767507i
$944$	7.19920			0.234314
$945$	44.9556	−	25.1764i	1.46240	−	0.818988i
$946$	0.632207			0.0205548
$947$	−12.6597	+	15.0873i	−0.411386	+	0.490270i	−0.931456	−	0.363853i	$-0.881461\pi$
$947$	−12.6597	+	15.0873i	−0.411386	+	0.490270i	0.520071	+	0.854123i	$0.325906\pi$
$948$	−0.593089	+	1.77183i	−0.0192626	+	0.0575464i
$949$	−6.78229	−	38.4643i	−0.220162	−	1.24860i
$950$	−17.7096	+	14.8601i	−0.574576	+	0.482127i
$951$	−24.4744	+	0.637865i	−0.793637	+	0.0206842i
$952$	5.16539	+	19.5900i	0.167411	+	0.634915i
$953$	−11.1121	−	6.41558i	−0.359956	−	0.207821i	0.309105	−	0.951028i	$-0.399970\pi$
$953$	−11.1121	−	6.41558i	−0.359956	−	0.207821i	−0.669062	+	0.743207i	$0.733304\pi$
$954$	−30.8886	+	28.7899i	−1.00006	+	0.932106i
$955$		−	45.9051i		−	1.48545i
$956$	−7.29977	+	8.69952i	−0.236091	+	0.281363i
$957$	54.9512	+	8.21944i	1.77632	+	0.265697i
$958$	9.83797	−	27.0296i	0.317850	−	0.873287i
$959$	23.6329	+	34.0398i	0.763148	+	1.09920i
$960$	−16.4912	−	2.46670i	−0.532251	−	0.0796125i
$961$	−28.6663	+	10.4337i	−0.924720	+	0.336570i
$962$	−29.9680			−0.966207
$963$	32.1380	−	42.6266i	1.03563	−	1.37362i
$964$			2.77455i			0.0893621i
$965$	−47.6567	−	39.9887i	−1.53412	−	1.28728i
$966$	−0.182646	+	2.79726i	−0.00587653	+	0.0900004i
$967$	10.1442	+	57.5307i	0.326216	+	1.85006i	0.500987	+	0.865455i	$0.332971\pi$
$967$	10.1442	+	57.5307i	0.326216	+	1.85006i	−0.174771	+	0.984609i	$0.555918\pi$
$968$	−8.02728	+	22.0548i	−0.258006	+	0.708867i
$969$	−2.03090	−	9.98852i	−0.0652421	−	0.320877i
$970$	4.65076	−	26.3758i	0.149327	−	0.846875i
$971$	−28.5180	−	49.3946i	−0.915186	−	1.58515i	−0.806629	−	0.591059i	$-0.798710\pi$
$971$	−28.5180	−	49.3946i	−0.915186	−	1.58515i	−0.108558	−	0.994090i	$-0.534623\pi$
$972$	11.8286	+	4.90811i	0.379402	+	0.157428i
$973$	5.47622	−	59.8411i	0.175560	−	1.91842i
$974$	−23.1685	−	63.6551i	−0.742368	−	2.03964i
$975$	−48.1657	−	16.1226i	−1.54254	−	0.516337i
$976$	14.0122	−	2.47073i	0.448519	−	0.0790861i
$977$	7.13483	−	19.6028i	0.228263	−	0.627148i	−0.771698	−	0.635990i	$-0.780592\pi$
$977$	7.13483	−	19.6028i	0.228263	−	0.627148i	0.999961	+	0.00884128i	$0.00281430\pi$
$978$	40.9034	−	1.06605i	1.30795	−	0.0340884i
$979$	26.8241	−	31.9678i	0.857303	−	1.02169i
$980$	13.9856	−	16.3996i	0.446752	−	0.523867i
$981$	−6.40130	+	52.0283i	−0.204378	+	1.66114i
$982$	−3.53450	+	6.12193i	−0.112790	+	0.195359i
$983$	−29.7422	−	24.9567i	−0.948630	−	0.795995i	0.0304360	−	0.999537i	$-0.490310\pi$
$983$	−29.7422	−	24.9567i	−0.948630	−	0.795995i	−0.979066	+	0.203541i	$0.934755\pi$
$984$	2.26674	+	1.80350i	0.0722611	+	0.0574936i
$985$	33.7987	−	5.95962i	1.07692	−	0.189889i
$986$	40.9700	+	14.9119i	1.30475	+	0.474890i
$987$	11.2647	−	11.7731i	0.358559	−	0.374741i
$988$	−0.703483	+	3.98965i	−0.0223808	+	0.126928i
$989$	−0.0248283	−	0.0143346i	−0.000789493	−	0.000455814i
$990$	86.3419	+	26.4207i	2.74413	+	0.839704i
$991$	−30.3659	−	52.5952i	−0.964603	−	1.67074i	−0.710677	−	0.703518i	$-0.751611\pi$
$991$	−30.3659	−	52.5952i	−0.964603	−	1.67074i	−0.253926	−	0.967224i	$-0.581722\pi$
$992$	0.535301	−	3.03584i	0.0169958	−	0.0963881i
$993$	−0.657827	−	25.2403i	−0.0208755	−	0.800977i
$994$	−59.8393	+	41.5449i	−1.89799	+	1.31772i
$995$	−15.8042	−	18.8347i	−0.501026	−	0.597100i
$996$	−12.8023	−	14.4740i	−0.405657	−	0.458626i
$997$	45.0811	+	7.94902i	1.42773	+	0.251748i	0.833489	−	0.552536i	$-0.186340\pi$
$997$	45.0811	+	7.94902i	1.42773	+	0.251748i	0.594245	+	0.804284i	$0.297451\pi$
$998$	−18.2110	−	10.5141i	−0.576458	−	0.332818i
$999$	2.23333	+	28.5120i	0.0706593	+	0.902078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.101.6	✓	132
3.2	odd	2		567.2.ba.a.143.17		132
7.5	odd	6		189.2.bd.a.47.17	yes	132
21.5	even	6		567.2.bd.a.467.6		132
27.4	even	9		567.2.bd.a.17.6		132
27.23	odd	18		189.2.bd.a.185.17	yes	132
189.131	even	18	inner	189.2.ba.a.131.6	yes	132
189.166	odd	18		567.2.ba.a.341.17		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.6	✓	132	1.1	even	1	trivial
189.2.ba.a.131.6	yes	132	189.131	even	18	inner
189.2.bd.a.47.17	yes	132	7.5	odd	6
189.2.bd.a.185.17	yes	132	27.23	odd	18
567.2.ba.a.143.17		132	3.2	odd	2
567.2.ba.a.341.17		132	189.166	odd	18
567.2.bd.a.17.6		132	27.4	even	9
567.2.bd.a.467.6		132	21.5	even	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07972 + 1.28676i) q^{2} +(-1.69732 + 0.345106i) q^{3} +(-0.142658 - 0.809053i) q^{4} +(2.87107 - 2.40911i) q^{5} +(1.38856 - 2.55666i) q^{6} +(-1.86335 - 1.87828i) q^{7} +(-1.71431 - 0.989760i) q^{8} +(2.76180 - 1.17151i) q^{9} +O(q^{10})\)	\(q+(-1.07972 + 1.28676i) q^{2} +(-1.69732 + 0.345106i) q^{3} +(-0.142658 - 0.809053i) q^{4} +(2.87107 - 2.40911i) q^{5} +(1.38856 - 2.55666i) q^{6} +(-1.86335 - 1.87828i) q^{7} +(-1.71431 - 0.989760i) q^{8} +(2.76180 - 1.17151i) q^{9} +6.29553i q^{10} +(3.07307 - 3.66234i) q^{11} +(0.521346 + 1.32399i) q^{12} +(-1.10865 + 3.04598i) q^{13} +(4.42878 - 0.369659i) q^{14} +(-4.04173 + 5.07986i) q^{15} +(4.66853 - 1.69921i) q^{16} +3.86831 q^{17} +(-1.47452 + 4.81867i) q^{18} +1.52130i q^{19} +(-2.35868 - 1.97917i) q^{20} +(3.81090 + 2.54500i) q^{21} +(1.39450 + 7.90859i) q^{22} +(0.124554 - 0.342208i) q^{23} +(3.25131 + 1.08832i) q^{24} +(1.57097 - 8.90940i) q^{25} +(-2.72242 - 4.71536i) q^{26} +(-4.28337 + 2.94155i) q^{27} +(-1.25381 + 1.77550i) q^{28} +(-2.29492 - 6.30525i) q^{29} +(-2.17262 - 10.6855i) q^{30} +(-0.692139 + 0.122043i) q^{31} +(-1.50016 + 4.12165i) q^{32} +(-3.95209 + 7.27671i) q^{33} +(-4.17668 + 4.97757i) q^{34} +(-9.87478 - 0.903668i) q^{35} +(-1.34181 - 2.06732i) q^{36} +(2.75197 - 4.76655i) q^{37} +(-1.95755 - 1.64258i) q^{38} +(0.830544 - 5.55262i) q^{39} +(-7.30635 + 1.28831i) q^{40} +(0.793900 + 0.288956i) q^{41} +(-7.38949 + 2.15583i) q^{42} +(0.0136704 - 0.0775288i) q^{43} +(-3.40143 - 1.96381i) q^{44} +(5.10702 - 10.0170i) q^{45} +(0.305856 + 0.529758i) q^{46} +(0.617436 - 3.50165i) q^{47} +(-7.33760 + 4.49524i) q^{48} +(-0.0558886 + 6.99978i) q^{49} +(9.76803 + 11.6411i) q^{50} +(-6.56576 + 1.33498i) q^{51} +(2.62252 + 0.462421i) q^{52} +(7.25668 + 4.18964i) q^{53} +(0.839774 - 8.68770i) q^{54} -17.9182i q^{55} +(1.33531 + 5.06423i) q^{56} +(-0.525011 - 2.58214i) q^{57} +(10.5912 + 3.85488i) q^{58} +(1.36168 + 0.495612i) q^{59} +(4.68646 + 2.54529i) q^{60} +(2.82040 + 0.497313i) q^{61} +(0.590275 - 1.02239i) q^{62} +(-7.34662 - 3.00451i) q^{63} +(1.28433 + 2.22452i) q^{64} +(4.15511 + 11.4161i) q^{65} +(-5.09621 - 12.9422i) q^{66} +(3.09944 - 2.60074i) q^{67} +(-0.551844 - 3.12967i) q^{68} +(-0.0933094 + 0.623821i) q^{69} +(11.8248 - 11.7307i) q^{70} +(-14.1956 + 8.19580i) q^{71} +(-5.89411 - 0.725182i) q^{72} +(-10.4351 + 6.02468i) q^{73} +(3.16204 + 8.68764i) q^{74} +(0.408251 + 15.6643i) q^{75} +(1.23082 - 0.217026i) q^{76} +(-12.6051 + 1.05212i) q^{77} +(6.24812 + 7.06396i) q^{78} +(1.00589 + 0.844043i) q^{79} +(9.31009 - 16.1256i) q^{80} +(6.25512 - 6.47097i) q^{81} +(-1.22900 + 0.709566i) q^{82} +(-12.7610 + 4.64462i) q^{83} +(1.51538 - 3.44629i) q^{84} +(11.1062 - 9.31918i) q^{85} +(0.0850005 + 0.101300i) q^{86} +(6.07120 + 9.91005i) q^{87} +(-8.89304 + 3.23680i) q^{88} +8.72878 q^{89} +(7.37529 + 17.3870i) q^{90} +(7.78701 - 3.59337i) q^{91} +(-0.294633 - 0.0519517i) q^{92} +(1.13267 - 0.446007i) q^{93} +(3.83912 + 4.57528i) q^{94} +(3.66499 + 4.36777i) q^{95} +(1.12385 - 7.51349i) q^{96} +(-4.18960 - 0.738740i) q^{97} +(-8.94667 - 7.62970i) q^{98} +(4.19674 - 13.7148i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

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