LMFDB - Embedded newform 189.2.ba.a.131.19

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			131.19
Character	$\chi$	$=$	189.131
Dual form			189.2.ba.a.101.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34473 + 1.60259i) q^{2} +(0.0648568 + 1.73084i) q^{3} +(-0.412694 + 2.34051i) q^{4} +(0.275976 + 0.231571i) q^{5} +(-2.68661 + 2.43145i) q^{6} +(2.18789 - 1.48767i) q^{7} +(-0.682329 + 0.393943i) q^{8} +(-2.99159 + 0.224513i) q^{9} +O(q^{10})$	\(q+(1.34473 + 1.60259i) q^{2} +(0.0648568 + 1.73084i) q^{3} +(-0.412694 + 2.34051i) q^{4} +(0.275976 + 0.231571i) q^{5} +(-2.68661 + 2.43145i) q^{6} +(2.18789 - 1.48767i) q^{7} +(-0.682329 + 0.393943i) q^{8} +(-2.99159 + 0.224513i) q^{9} +0.753678i q^{10} +(-4.02242 - 4.79373i) q^{11} +(-4.07780 - 0.562508i) q^{12} +(-0.429890 - 1.18111i) q^{13} +(5.32625 + 1.50578i) q^{14} +(-0.382913 + 0.492688i) q^{15} +(2.91769 + 1.06195i) q^{16} -0.937219 q^{17} +(-4.38269 - 4.49238i) q^{18} +7.64344i q^{19} +(-0.655887 + 0.550354i) q^{20} +(2.71680 + 3.69039i) q^{21} +(2.27331 - 12.8926i) q^{22} +(-0.584919 - 1.60705i) q^{23} +(-0.726104 - 1.15545i) q^{24} +(-0.845703 - 4.79622i) q^{25} +(1.31476 - 2.27722i) q^{26} +(-0.582620 - 5.16339i) q^{27} +(2.57896 + 5.73471i) q^{28} +(-0.731568 + 2.00997i) q^{29} +(-1.30449 + 0.0488812i) q^{30} +(5.71494 + 1.00770i) q^{31} +(2.76059 + 7.58465i) q^{32} +(8.03628 - 7.27305i) q^{33} +(-1.26031 - 1.50198i) q^{34} +(0.948304 + 0.0960919i) q^{35} +(0.709137 - 7.09448i) q^{36} +(1.66757 + 2.88831i) q^{37} +(-12.2493 + 10.2784i) q^{38} +(2.01643 - 0.820673i) q^{39} +(-0.279532 - 0.0492890i) q^{40} +(-8.66669 + 3.15442i) q^{41} +(-2.26081 + 9.31652i) q^{42} +(-0.688669 - 3.90564i) q^{43} +(12.8798 - 7.43615i) q^{44} +(-0.877596 - 0.630805i) q^{45} +(1.78889 - 3.09844i) q^{46} +(0.876005 + 4.96807i) q^{47} +(-1.64883 + 5.11892i) q^{48} +(2.57370 - 6.50969i) q^{49} +(6.54914 - 7.80496i) q^{50} +(-0.0607850 - 1.62217i) q^{51} +(2.94182 - 0.518722i) q^{52} +(-3.01037 + 1.73804i) q^{53} +(7.49133 - 7.87709i) q^{54} -2.25443i q^{55} +(-0.906803 + 1.87698i) q^{56} +(-13.2295 + 0.495729i) q^{57} +(-4.20492 + 1.53047i) q^{58} +(6.00562 - 2.18587i) q^{59} +(-0.995112 - 1.09954i) q^{60} +(-10.3015 + 1.81644i) q^{61} +(6.07015 + 10.5138i) q^{62} +(-6.21126 + 4.94169i) q^{63} +(-5.33790 + 9.24552i) q^{64} +(0.154873 - 0.425509i) q^{65} +(22.4624 + 3.09856i) q^{66} +(-0.222678 - 0.186849i) q^{67} +(0.386785 - 2.19357i) q^{68} +(2.74361 - 1.11663i) q^{69} +(1.12122 + 1.64896i) q^{70} +(-4.18316 - 2.41515i) q^{71} +(1.95280 - 1.33171i) q^{72} +(-3.19638 - 1.84543i) q^{73} +(-2.38635 + 6.55643i) q^{74} +(8.24663 - 1.77484i) q^{75} +(-17.8895 - 3.15440i) q^{76} +(-15.9321 - 4.50413i) q^{77} +(4.02677 + 2.12793i) q^{78} +(7.90824 - 6.63581i) q^{79} +(0.559294 + 0.968725i) q^{80} +(8.89919 - 1.34330i) q^{81} +(-16.7096 - 9.64732i) q^{82} +(6.06917 + 2.20900i) q^{83} +(-9.75859 + 4.83569i) q^{84} +(-0.258650 - 0.217033i) q^{85} +(5.33306 - 6.35570i) q^{86} +(-3.52637 - 1.13586i) q^{87} +(4.63307 + 1.68630i) q^{88} +5.12391 q^{89} +(-0.169211 - 2.25469i) q^{90} +(-2.69765 - 1.94461i) q^{91} +(4.00271 - 0.705785i) q^{92} +(-1.37351 + 9.95699i) q^{93} +(-6.78379 + 8.08461i) q^{94} +(-1.77000 + 2.10940i) q^{95} +(-12.9487 + 5.27004i) q^{96} +(-7.91567 + 1.39575i) q^{97} +(13.8933 - 4.62921i) q^{98} +(13.1097 + 13.4378i) 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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.34473	+	1.60259i	0.950871	+	1.13320i	0.990980	+	0.134008i	$0.0427849\pi$
$2$	1.34473	+	1.60259i	0.950871	+	1.13320i	−0.0401094	+	0.999195i	$0.512771\pi$
$3$	0.0648568	+	1.73084i	0.0374451	+	0.999299i
$3$	0.0648568	+	1.73084i	0.0374451	+	0.999299i
$4$	−0.412694	+	2.34051i	−0.206347	+	1.17025i
$5$	0.275976	+	0.231571i	0.123420	+	0.103562i	0.702409	−	0.711774i	$-0.252108\pi$
$5$	0.275976	+	0.231571i	0.123420	+	0.103562i	−0.578989	+	0.815336i	$0.696552\pi$
$6$	−2.68661	+	2.43145i	−1.09680	+	0.992637i
$7$	2.18789	−	1.48767i	0.826944	−	0.562285i
$7$	2.18789	−	1.48767i	0.826944	−	0.562285i
$8$	−0.682329	+	0.393943i	−0.241240	+	0.139280i
$9$	−2.99159	+	0.224513i	−0.997196	+	0.0748377i
$10$			0.753678i			0.238334i
$11$	−4.02242	−	4.79373i	−1.21281	−	1.44536i	−0.860478	−	0.509488i	$-0.829835\pi$
$11$	−4.02242	−	4.79373i	−1.21281	−	1.44536i	−0.352327	−	0.935877i	$-0.614610\pi$
$12$	−4.07780	−	0.562508i	−1.17716	−	0.162382i
$13$	−0.429890	−	1.18111i	−0.119230	−	0.327582i	0.865693	−	0.500576i	$-0.166878\pi$
$13$	−0.429890	−	1.18111i	−0.119230	−	0.327582i	−0.984923	+	0.172994i	$0.944656\pi$
$14$	5.32625	+	1.50578i	1.42350	+	0.402435i
$15$	−0.382913	+	0.492688i	−0.0988676	+	0.127211i
$16$	2.91769	+	1.06195i	0.729422	+	0.265488i
$17$	−0.937219			−0.227309			−0.113654	−	0.993520i	$-0.536256\pi$
$17$	−0.937219			−0.227309			−0.113654	+	0.993520i	$0.536256\pi$
$18$	−4.38269	−	4.49238i	−1.03301	−	1.05886i
$19$			7.64344i			1.75352i	0.480924	+	0.876762i	$0.340301\pi$
$19$			7.64344i			1.75352i	−0.480924	+	0.876762i	$0.659699\pi$
$20$	−0.655887	+	0.550354i	−0.146661	+	0.123063i
$21$	2.71680	+	3.69039i	0.592855	+	0.805309i
$22$	2.27331	−	12.8926i	0.484672	−	2.74871i
$23$	−0.584919	−	1.60705i	−0.121964	−	0.335093i	0.863653	−	0.504086i	$-0.168171\pi$
$23$	−0.584919	−	1.60705i	−0.121964	−	0.335093i	−0.985617	+	0.168993i	$0.945948\pi$
$24$	−0.726104	−	1.15545i	−0.148215	−	0.235855i
$25$	−0.845703	−	4.79622i	−0.169141	−	0.959245i
$26$	1.31476	−	2.27722i	0.257845	−	0.446600i
$27$	−0.582620	−	5.16339i	−0.112125	−	0.993694i
$28$	2.57896	+	5.73471i	0.487378	+	1.08376i
$29$	−0.731568	+	2.00997i	−0.135849	+	0.373241i	−0.988899	−	0.148587i	$-0.952528\pi$
$29$	−0.731568	+	2.00997i	−0.135849	+	0.373241i	0.853051	+	0.521828i	$0.174750\pi$
$30$	−1.30449	+	0.0488812i	−0.238167	+	0.00892444i
$31$	5.71494	+	1.00770i	1.02643	+	0.180988i	0.661421	−	0.750014i	$-0.269953\pi$
$31$	5.71494	+	1.00770i	1.02643	+	0.180988i	0.365013	+	0.931002i	$0.381065\pi$
$32$	2.76059	+	7.58465i	0.488007	+	1.34079i
$33$	8.03628	−	7.27305i	1.39894	−	1.26608i
$34$	−1.26031	−	1.50198i	−0.216141	−	0.257587i
$35$	0.948304	+	0.0960919i	0.160293	+	0.0162425i
$36$	0.709137	−	7.09448i	0.118189	−	1.18241i
$37$	1.66757	+	2.88831i	0.274146	+	0.474835i	0.969919	−	0.243427i	$-0.0782715\pi$
$37$	1.66757	+	2.88831i	0.274146	+	0.474835i	−0.695773	+	0.718261i	$0.744938\pi$
$38$	−12.2493	+	10.2784i	−1.98710	+	1.66738i
$39$	2.01643	−	0.820673i	0.322888	−	0.131413i
$40$	−0.279532	−	0.0492890i	−0.0441978	−	0.00779327i
$41$	−8.66669	+	3.15442i	−1.35351	+	0.492637i	−0.914041	−	0.405621i	$-0.867055\pi$
$41$	−8.66669	+	3.15442i	−1.35351	+	0.492637i	−0.439468	+	0.898258i	$0.644833\pi$
$42$	−2.26081	+	9.31652i	−0.348850	+	1.43757i
$43$	−0.688669	−	3.90564i	−0.105021	−	0.595604i	−0.991212	−	0.132284i	$-0.957769\pi$
$43$	−0.688669	−	3.90564i	−0.105021	−	0.595604i	0.886191	−	0.463320i	$-0.153342\pi$
$44$	12.8798	−	7.43615i	1.94170	−	1.12104i
$45$	−0.877596	−	0.630805i	−0.130824	−	0.0940348i
$46$	1.78889	−	3.09844i	0.263757	−	0.456841i
$47$	0.876005	+	4.96807i	0.127778	+	0.724667i	0.979619	+	0.200866i	$0.0643755\pi$
$47$	0.876005	+	4.96807i	0.127778	+	0.724667i	−0.851840	+	0.523802i	$0.824513\pi$
$48$	−1.64883	+	5.11892i	−0.237989	+	0.738852i
$49$	2.57370	−	6.50969i	0.367672	−	0.929956i
$50$	6.54914	−	7.80496i	0.926189	−	1.10379i
$51$	−0.0607850	−	1.62217i	−0.00851161	−	0.227150i
$52$	2.94182	−	0.518722i	0.407957	−	0.0719338i
$53$	−3.01037	+	1.73804i	−0.413506	+	0.238738i	−0.692295	−	0.721614i	$-0.743400\pi$
$53$	−3.01037	+	1.73804i	−0.413506	+	0.238738i	0.278789	+	0.960352i	$0.410067\pi$
$54$	7.49133	−	7.87709i	1.01944	−	1.07194i
$55$		−	2.25443i		−	0.303987i
$56$	−0.906803	+	1.87698i	−0.121177	+	0.250822i
$57$	−13.2295	+	0.495729i	−1.75229	+	0.0656609i
$58$	−4.20492	+	1.53047i	−0.552133	+	0.200960i
$59$	6.00562	−	2.18587i	0.781866	−	0.284576i	0.0799153	−	0.996802i	$-0.474535\pi$
$59$	6.00562	−	2.18587i	0.781866	−	0.284576i	0.701950	+	0.712226i	$0.252313\pi$
$60$	−0.995112	−	1.09954i	−0.128468	−	0.141950i
$61$	−10.3015	+	1.81644i	−1.31898	+	0.232571i	−0.788451	−	0.615098i	$-0.789116\pi$
$61$	−10.3015	+	1.81644i	−1.31898	+	0.232571i	−0.530525	+	0.847669i	$0.678005\pi$
$62$	6.07015	+	10.5138i	0.770910	+	1.33526i
$63$	−6.21126	+	4.94169i	−0.782545	+	0.622595i
$64$	−5.33790	+	9.24552i	−0.667238	+	1.15569i
$65$	0.154873	−	0.425509i	0.0192096	−	0.0527779i
$66$	22.4624	+	3.09856i	2.76493	+	0.381406i
$67$	−0.222678	−	0.186849i	−0.0272045	−	0.0228273i	0.629084	−	0.777337i	$-0.283430\pi$
$67$	−0.222678	−	0.186849i	−0.0272045	−	0.0228273i	−0.656289	+	0.754510i	$0.727875\pi$
$68$	0.386785	−	2.19357i	0.0469046	−	0.266009i
$69$	2.74361	−	1.11663i	0.330291	−	0.134426i
$70$	1.12122	+	1.64896i	0.134011	+	0.197089i
$71$	−4.18316	−	2.41515i	−0.496450	−	0.286625i	0.230797	−	0.973002i	$-0.425867\pi$
$71$	−4.18316	−	2.41515i	−0.496450	−	0.286625i	−0.727246	+	0.686377i	$0.759200\pi$
$72$	1.95280	−	1.33171i	0.230140	−	0.156943i
$73$	−3.19638	−	1.84543i	−0.374108	−	0.215992i	0.301143	−	0.953579i	$-0.402632\pi$
$73$	−3.19638	−	1.84543i	−0.374108	−	0.215992i	−0.675252	+	0.737587i	$0.735965\pi$
$74$	−2.38635	+	6.55643i	−0.277407	+	0.762170i
$75$	8.24663	−	1.77484i	0.952238	−	0.204941i
$76$	−17.8895	−	3.15440i	−2.05207	−	0.361835i
$77$	−15.9321	−	4.50413i	−1.81563	−	0.513293i
$78$	4.02677	+	2.12793i	0.455942	+	0.240941i
$79$	7.90824	−	6.63581i	0.889747	−	0.746586i	−0.0784124	−	0.996921i	$-0.524985\pi$
$79$	7.90824	−	6.63581i	0.889747	−	0.746586i	0.968159	+	0.250335i	$0.0805406\pi$
$80$	0.559294	+	0.968725i	0.0625309	+	0.108307i
$81$	8.89919	−	1.34330i	0.988799	−	0.149256i
$82$	−16.7096	−	9.64732i	−1.84527	−	1.06537i
$83$	6.06917	+	2.20900i	0.666178	+	0.242469i	0.652901	−	0.757443i	$-0.273552\pi$
$83$	6.06917	+	2.20900i	0.666178	+	0.242469i	0.0132766	+	0.999912i	$0.495774\pi$
$84$	−9.75859	+	4.83569i	−1.06475	+	0.527618i
$85$	−0.258650	−	0.217033i	−0.0280545	−	0.0235405i
$86$	5.33306	−	6.35570i	0.575079	−	0.685353i
$87$	−3.52637	−	1.13586i	−0.378066	−	0.121777i
$88$	4.63307	+	1.68630i	0.493887	+	0.179760i
$89$	5.12391			0.543133			0.271566	−	0.962420i	$-0.412458\pi$
$89$	5.12391			0.543133			0.271566	+	0.962420i	$0.412458\pi$
$90$	−0.169211	−	2.25469i	−0.0178364	−	0.237666i
$91$	−2.69765	−	1.94461i	−0.282791	−	0.203851i
$92$	4.00271	−	0.705785i	0.417311	−	0.0735832i
$93$	−1.37351	+	9.95699i	−0.142426	+	1.03249i
$94$	−6.78379	+	8.08461i	−0.699695	+	0.833864i
$95$	−1.77000	+	2.10940i	−0.181598	+	0.216420i
$96$	−12.9487	+	5.27004i	−1.32158	+	0.537871i
$97$	−7.91567	+	1.39575i	−0.803714	+	0.141717i	−0.560390	−	0.828229i	$-0.689349\pi$
$97$	−7.91567	+	1.39575i	−0.803714	+	0.141717i	−0.243324	+	0.969945i	$0.578238\pi$
$98$	13.8933	−	4.62921i	1.40344	−	0.467621i
$99$	13.1097	+	13.4378i	1.31757	+	1.35055i
$100$	11.5746			1.15746
$101$	−13.3809	−	4.87023i	−1.33145	−	0.484606i	−0.424337	−	0.905504i	$-0.639493\pi$
$101$	−13.3809	−	4.87023i	−1.33145	−	0.484606i	−0.907108	+	0.420898i	$0.861715\pi$
$102$	2.51794	−	2.27880i	0.249313	−	0.225635i
$103$	4.11263	−	4.90124i	0.405230	−	0.482934i	−0.524377	−	0.851486i	$-0.675702\pi$
$103$	4.11263	−	4.90124i	0.405230	−	0.482934i	0.929607	+	0.368552i	$0.120146\pi$
$104$	0.758617	+	0.636556i	0.0743886	+	0.0624194i
$105$	−0.104815	+	1.64759i	−0.0102289	+	0.160788i
$106$	−6.83352	−	2.48720i	−0.663730	−	0.241578i
$107$	−2.81413	−	1.62474i	−0.272053	−	0.157070i	0.357767	−	0.933811i	$-0.383538\pi$
$107$	−2.81413	−	1.62474i	−0.272053	−	0.157070i	−0.629820	+	0.776741i	$0.716871\pi$
$108$	12.3254	+	0.767274i	1.18601	+	0.0738310i
$109$	6.30335	+	10.9177i	0.603751	+	1.04573i	0.992247	+	0.124278i	$0.0396613\pi$
$109$	6.30335	+	10.9177i	0.603751	+	1.04573i	−0.388496	+	0.921450i	$0.627005\pi$
$110$	3.61293	−	3.03161i	0.344479	−	0.289052i
$111$	−4.89103	+	3.07361i	−0.464236	+	0.291734i
$112$	7.96340	−	2.01711i	0.752471	−	0.190599i
$113$	−14.5530	−	2.56609i	−1.36903	−	0.241397i	−0.559674	−	0.828713i	$-0.689074\pi$
$113$	−14.5530	−	2.56609i	−1.36903	−	0.241397i	−0.809358	+	0.587315i	$0.800185\pi$
$114$	−18.5847	−	20.5349i	−1.74061	−	1.92327i
$115$	0.210723	−	0.578957i	0.0196500	−	0.0539880i
$116$	−4.40242	−	2.54174i	−0.408755	−	0.235995i
$117$	1.55123	+	3.43689i	0.143411	+	0.317740i
$118$	11.5790	+	6.68515i	1.06594	+	0.615418i
$119$	−2.05053	+	1.39427i	−0.187972	+	0.127812i
$120$	0.0671816	−	0.487020i	0.00613281	−	0.0444587i
$121$	−4.88989	+	27.7319i	−0.444535	+	2.52108i
$122$	−16.7638	−	14.0665i	−1.51773	−	1.27352i
$123$	−6.02187	−	14.7960i	−0.542974	−	1.33411i
$124$	−4.71705	+	12.9600i	−0.423604	+	1.16384i
$125$	1.77792	−	3.07945i	0.159022	−	0.275435i
$126$	−16.2720	−	3.30885i	−1.44963	−	0.294775i
$127$	7.01123	+	12.1438i	0.622146	+	1.07759i	0.989085	+	0.147344i	$0.0470724\pi$
$127$	7.01123	+	12.1438i	0.622146	+	1.07759i	−0.366939	+	0.930245i	$0.619594\pi$
$128$	−6.09727	+	1.07511i	−0.538928	+	0.0950275i
$129$	6.71535	−	1.44528i	0.591254	−	0.127250i
$130$	0.890179	−	0.323999i	0.0780739	−	0.0284166i
$131$	2.46411	−	0.896863i	0.215290	−	0.0783593i	−0.232123	−	0.972686i	$-0.574567\pi$
$131$	2.46411	−	0.896863i	0.215290	−	0.0783593i	0.447414	+	0.894327i	$0.352345\pi$
$132$	13.7061	+	21.8105i	1.19296	+	1.89836i
$133$	11.3709	+	16.7230i	0.985980	+	1.45007i
$134$		−	0.608125i		−	0.0525340i
$135$	1.03490	−	1.55989i	0.0890701	−	0.134254i
$136$	0.639491	−	0.369210i	0.0548359	−	0.0316595i
$137$	9.59321	−	1.69154i	0.819603	−	0.144518i	0.251902	−	0.967753i	$-0.418944\pi$
$137$	9.59321	−	1.69154i	0.819603	−	0.144518i	0.567701	+	0.823235i	$0.307833\pi$
$138$	5.47892	+	2.89532i	0.466397	+	0.246466i
$139$	0.0836111	−	0.0996438i	0.00709180	−	0.00845168i	−0.762487	−	0.647004i	$-0.776022\pi$
$139$	0.0836111	−	0.0996438i	0.00709180	−	0.00845168i	0.769579	+	0.638552i	$0.220466\pi$
$140$	−0.616263	+	2.17985i	−0.0520837	+	0.184231i
$141$	−8.54210	+	1.83843i	−0.719374	+	0.154824i
$142$	−1.75474	−	9.95163i	−0.147255	−	0.835122i
$143$	−3.93274	+	6.81171i	−0.328873	+	0.569624i
$144$	−8.96694	−	2.52186i	−0.747245	−	0.210155i
$145$	−0.667345	+	0.385292i	−0.0554199	+	0.0319967i
$146$	−1.34081	−	7.60411i	−0.110966	−	0.629321i
$147$	11.4341	+	4.03246i	0.943071	+	0.332592i
$148$	−7.44829	+	2.71096i	−0.612246	+	0.222839i
$149$	14.1676	+	2.49814i	1.16066	+	0.204655i	0.720624	−	0.693326i	$-0.243855\pi$
$149$	14.1676	+	2.49814i	1.16066	+	0.204655i	0.440034	+	0.897981i	$0.354966\pi$
$150$	13.9339	+	10.8293i	1.13770	+	0.884208i
$151$	15.5163	−	13.0197i	1.26269	−	1.05953i	0.267305	−	0.963612i	$-0.413867\pi$
$151$	15.5163	−	13.0197i	1.26269	−	1.05953i	0.995390	−	0.0959147i	$-0.0305776\pi$
$152$	−3.01107	−	5.21533i	−0.244230	−	0.423019i
$153$	2.80377	−	0.210418i	0.226672	−	0.0170113i
$154$	−14.2061	−	31.5895i	−1.14476	−	2.54555i
$155$	1.34383	+	1.60152i	0.107939	+	0.128637i
$156$	1.08862	+	5.05816i	0.0871593	+	0.404977i
$157$	−1.35670	−	3.72752i	−0.108277	−	0.297488i	0.873707	−	0.486452i	$-0.161709\pi$
$157$	−1.35670	−	3.72752i	−0.108277	−	0.297488i	−0.981984	+	0.188964i	$0.939487\pi$
$158$	21.2690	+	3.75029i	1.69207	+	0.298357i
$159$	−3.20350	−	5.09773i	−0.254054	−	0.404277i
$160$	−0.994530	+	2.73245i	−0.0786245	+	0.216019i
$161$	−3.67049	−	2.64588i	−0.289275	−	0.208525i
$162$	14.1198	+	12.4554i	1.10936	+	0.978587i
$163$	−8.65872	+	14.9973i	−0.678203	+	1.17468i	0.297318	+	0.954778i	$0.403908\pi$
$163$	−8.65872	+	14.9973i	−0.678203	+	1.17468i	−0.975522	+	0.219904i	$0.929426\pi$
$164$	−3.80624	−	21.5863i	−0.297217	−	1.68560i
$165$	3.90205	−	0.146215i	0.303774	−	0.0113828i
$166$	4.62130	+	12.6969i	0.358682	+	0.985472i
$167$	2.13178	−	12.0899i	0.164962	−	0.935548i	−0.784141	−	0.620583i	$-0.786896\pi$
$167$	2.13178	−	12.0899i	0.164962	−	0.935548i	0.949103	−	0.314965i	$-0.101993\pi$
$168$	−3.30755	−	1.44779i	−0.255183	−	0.111700i
$169$	8.74835	−	7.34074i	0.672950	−	0.564672i
$170$		−	0.706361i		−	0.0541754i
$171$	−1.71605	−	22.8660i	−0.131230	−	1.74861i
$172$	9.42537			0.718678
$173$	19.8439	+	7.22261i	1.50871	+	0.549125i	0.958298	−	0.285771i	$-0.0922495\pi$
$173$	19.8439	+	7.22261i	1.50871	+	0.549125i	0.550409	+	0.834895i	$0.314472\pi$
$174$	−2.92170	−	7.17876i	−0.221494	−	0.544221i
$175$	−8.98548	−	9.23547i	−0.679238	−	0.698136i
$176$	−6.64546	−	18.2582i	−0.500920	−	1.37627i
$177$	4.17289	+	10.2530i	0.313653	+	0.770661i
$178$	6.89029	+	8.21153i	0.516449	+	0.615480i
$179$			9.39393i			0.702135i	0.936350	+	0.351068i	$0.114181\pi$
$179$			9.39393i			0.702135i	−0.936350	+	0.351068i	$0.885819\pi$
$180$	1.83858	−	1.79369i	0.137040	−	0.133694i
$181$	−8.05463	+	4.65035i	−0.598696	+	0.345657i	−0.768529	−	0.639816i	$-0.779011\pi$
$181$	−8.05463	+	4.65035i	−0.598696	+	0.345657i	0.169832	+	0.985473i	$0.445677\pi$
$182$	−0.511210	−	6.93822i	−0.0378934	−	0.514295i
$183$	−3.81208	−	17.7125i	−0.281797	−	1.30934i
$184$	1.03219	+	0.866113i	0.0760943	+	0.0638507i
$185$	−0.208641	+	1.18326i	−0.0153396	+	0.0869952i
$186$	−17.8040	+	11.1883i	−1.30545	+	0.820368i
$187$	3.76989	+	4.49278i	0.275681	+	0.328544i
$188$	−11.9893			−0.874411
$189$	−8.95610	−	10.4302i	−0.651460	−	0.758683i
$190$	−5.76069			−0.417924
$191$	−5.86657	−	6.99151i	−0.424490	−	0.505888i	0.510834	−	0.859679i	$-0.329337\pi$
$191$	−5.86657	−	6.99151i	−0.424490	−	0.505888i	−0.935324	+	0.353791i	$0.884892\pi$
$192$	−16.3487	−	8.63940i	−1.17986	−	0.623495i
$193$	−0.608638	+	3.45176i	−0.0438107	+	0.248463i	−0.998846	−	0.0480295i	$-0.984706\pi$
$193$	−0.608638	+	3.45176i	−0.0438107	+	0.248463i	0.955035	+	0.296492i	$0.0958169\pi$
$194$	−12.8813	−	10.8087i	−0.924822	−	0.776018i
$195$	0.746530	+	0.240462i	0.0534602	+	0.0172198i
$196$	14.1738	+	8.71028i	1.01242	+	0.622163i
$197$	−17.0883	+	9.86593i	−1.21749	+	0.702918i	−0.964380	−	0.264519i	$-0.914787\pi$
$197$	−17.0883	+	9.86593i	−1.21749	+	0.702918i	−0.253110	+	0.967438i	$0.581453\pi$
$198$	−3.90626	+	39.0797i	−0.277605	+	2.77727i
$199$		−	11.1409i		−	0.789757i	−0.918733	−	0.394878i	$-0.870787\pi$
$199$		−	11.1409i		−	0.789757i	0.918733	−	0.394878i	$-0.129213\pi$
$200$	2.46648	+	2.93944i	0.174407	+	0.207850i
$201$	0.308963	−	0.397538i	0.0217926	−	0.0280402i
$202$	−10.1887	−	27.9932i	−0.716875	−	1.96960i
$203$	1.38957	+	5.48591i	0.0975286	+	0.385035i
$204$	3.82179	+	0.527194i	0.267579	+	0.0369109i
$205$	−3.12227	−	1.13641i	−0.218069	−	0.0793705i
$206$	13.3851			0.932584
$207$	2.11064	+	4.67631i	0.146700	+	0.325026i
$208$		−	3.90265i		−	0.270600i
$209$	36.6406	−	30.7451i	2.53448	−	2.12668i
$210$	−2.78136	+	2.04760i	−0.191932	+	0.141298i
$211$	−1.40219	+	7.95221i	−0.0965307	+	0.547453i	0.897737	+	0.440532i	$0.145210\pi$
$211$	−1.40219	+	7.95221i	−0.0965307	+	0.547453i	−0.994268	+	0.106921i	$0.965901\pi$
$212$	−2.82553	−	7.76307i	−0.194058	−	0.533170i
$213$	3.90892	−	7.39700i	0.267835	−	0.506834i
$214$	−1.18047	−	6.69475i	−0.0806950	−	0.457644i
$215$	0.714376	−	1.23734i	0.0487201	−	0.0843856i
$216$	2.43162	+	3.29361i	0.165450	+	0.224102i
$217$	14.0028	−	6.29720i	0.950570	−	0.427481i
$218$	−9.02032	+	24.7831i	−0.610933	+	1.67853i
$219$	2.98683	−	5.65210i	0.201832	−	0.381934i
$220$	5.27650	+	0.930390i	0.355742	+	0.0627269i
$221$	0.402901	+	1.10696i	0.0271021	+	0.0744623i
$222$	−11.5029	−	3.70514i	−0.772023	−	0.248673i
$223$	4.16647	+	4.96540i	0.279007	+	0.332508i	0.887290	−	0.461213i	$-0.152586\pi$
$223$	4.16647	+	4.96540i	0.279007	+	0.332508i	−0.608282	+	0.793721i	$0.708141\pi$
$224$	17.3233	+	12.4875i	1.15746	+	0.834358i
$225$	3.60681	+	14.1584i	0.240454	+	0.943896i
$226$	−15.4575	−	26.7733i	−1.02822	−	1.78093i
$227$	5.31375	−	4.45877i	0.352686	−	0.295939i	−0.449181	−	0.893441i	$-0.648284\pi$
$227$	5.31375	−	4.45877i	0.352686	−	0.295939i	0.801868	+	0.597502i	$0.203840\pi$
$228$	4.29950	−	31.1684i	0.284741	−	2.06418i
$229$	−18.1760	−	3.20491i	−1.20110	−	0.211787i	−0.462927	−	0.886396i	$-0.653201\pi$
$229$	−18.1760	−	3.20491i	−1.20110	−	0.211787i	−0.738175	+	0.674610i	$0.764312\pi$
$230$	1.21120	−	0.440840i	0.0798641	−	0.0290682i
$231$	6.76261	−	27.8679i	0.444947	−	1.83358i
$232$	−0.292641	−	1.65965i	−0.0192129	−	0.108962i
$233$	20.8367	−	12.0300i	1.36505	−	0.788115i	0.374763	−	0.927121i	$-0.377724\pi$
$233$	20.8367	−	12.0300i	1.36505	−	0.788115i	0.990292	+	0.139006i	$0.0443908\pi$
$234$	−3.42194	+	7.10769i	−0.223699	+	0.464644i
$235$	−0.908705	+	1.57392i	−0.0592774	+	0.102671i
$236$	2.63755	+	14.9583i	0.171690	+	0.973702i
$237$	11.9984	+	13.2575i	0.779379	+	0.861167i
$238$	−4.99186	−	1.41124i	−0.323574	−	0.0914772i
$239$	−3.56306	+	4.24628i	−0.230475	+	0.274669i	−0.868871	−	0.495039i	$-0.835154\pi$
$239$	−3.56306	+	4.24628i	−0.230475	+	0.274669i	0.638396	+	0.769708i	$0.279598\pi$
$240$	−1.64043	+	1.03087i	−0.105889	+	0.0665426i
$241$	−10.0391	+	1.77016i	−0.646673	+	0.114026i	−0.487358	−	0.873202i	$-0.662039\pi$
$241$	−10.0391	+	1.77016i	−0.646673	+	0.114026i	−0.159314	+	0.987228i	$0.550928\pi$
$242$	−51.0185	+	29.4556i	−3.27960	+	1.89348i
$243$	2.90221	+	15.3159i	0.186177	+	0.982516i
$244$		−	24.8604i		−	1.59153i
$245$	2.21773	−	1.20052i	0.141686	−	0.0766985i
$246$	15.6142	−	29.5473i	0.995524	−	1.88387i
$247$	9.02777	−	3.28584i	0.574423	−	0.209073i
$248$	−4.29645	+	1.56378i	−0.272825	+	0.0993000i
$249$	−3.42979	+	10.6480i	−0.217354	+	0.674790i
$250$	7.32595	−	1.29176i	0.463333	−	0.0816982i
$251$	10.3890	+	17.9942i	0.655746	+	1.13579i	0.981706	+	0.190402i	$0.0609792\pi$
$251$	10.3890	+	17.9942i	0.655746	+	1.13579i	−0.325960	+	0.945384i	$0.605688\pi$
$252$	−9.00271	−	16.5769i	−0.567117	−	1.04425i
$253$	−5.35099	+	9.26818i	−0.336414	+	0.582685i
$254$	−10.0333	+	27.5663i	−0.629547	+	1.72967i
$255$	0.358873	−	0.461756i	0.0224735	−	0.0289163i
$256$	6.43410	+	5.39885i	0.402132	+	0.337428i
$257$	−4.40206	+	24.9653i	−0.274593	+	1.55729i	0.465658	+	0.884965i	$0.345818\pi$
$257$	−4.40206	+	24.9653i	−0.274593	+	1.55729i	−0.740251	+	0.672330i	$0.765294\pi$
$258$	11.3466	+	8.81845i	0.706406	+	0.549013i
$259$	7.94528	+	3.83851i	0.493696	+	0.238514i
$260$	0.931991	+	0.538085i	0.0577996	+	0.0333706i
$261$	1.73728	−	6.17723i	0.107535	−	0.382361i
$262$	4.75088	+	2.74292i	0.293510	+	0.169458i
$263$	−1.35880	+	3.73327i	−0.0837872	+	0.230203i	−0.974510	−	0.224343i	$-0.927976\pi$
$263$	−1.35880	+	3.73327i	−0.0837872	+	0.230203i	0.890723	+	0.454546i	$0.150199\pi$
$264$	−2.61822	+	8.12845i	−0.161140	+	0.500271i
$265$	−1.23327	−	0.217458i	−0.0757591	−	0.0133584i
$266$	−11.5093	+	40.7108i	−0.705680	+	2.49614i
$267$	0.332320	+	8.86864i	0.0203377	+	0.542752i
$268$	0.529220	−	0.444068i	0.0323272	−	0.0271258i
$269$	−2.35052	−	4.07121i	−0.143313	−	0.248226i	0.785429	−	0.618952i	$-0.212442\pi$
$269$	−2.35052	−	4.07121i	−0.143313	−	0.248226i	−0.928742	+	0.370726i	$0.879109\pi$
$270$	3.89153	−	0.439108i	0.236831	−	0.0267233i
$271$	−7.44995	−	4.30123i	−0.452552	−	0.261281i	0.256355	−	0.966583i	$-0.417478\pi$
$271$	−7.44995	−	4.30123i	−0.452552	−	0.261281i	−0.708907	+	0.705302i	$0.750812\pi$
$272$	−2.73451	−	0.995282i	−0.165804	−	0.0603478i
$273$	3.19084	−	4.79532i	0.193119	−	0.290226i
$274$	15.6112	+	13.0993i	0.943105	+	0.791359i
$275$	−19.5900	+	23.3465i	−1.18132	+	1.40785i
$276$	1.48120	+	6.88225i	0.0891578	+	0.414263i
$277$	−14.9283	−	5.43344i	−0.896952	−	0.326464i	−0.147921	−	0.988999i	$-0.547258\pi$
$277$	−14.9283	−	5.43344i	−0.896952	−	0.326464i	−0.749031	+	0.662535i	$0.769480\pi$
$278$	0.272123			0.0163209
$279$	−17.3230	−	1.73154i	−1.03710	−	0.103665i
$280$	−0.684909	+	0.308011i	−0.0409312	+	0.0184072i
$281$	21.2686	−	3.75023i	1.26878	−	0.223720i	0.501569	−	0.865118i	$-0.332756\pi$
$281$	21.2686	−	3.75023i	1.26878	−	0.223720i	0.767208	+	0.641398i	$0.221645\pi$
$282$	−14.4331	−	11.2173i	−0.859479	−	0.667980i
$283$	−2.92239	+	3.48277i	−0.173718	+	0.207029i	−0.845877	−	0.533377i	$-0.820923\pi$
$283$	−2.92239	+	3.48277i	−0.173718	+	0.207029i	0.672159	+	0.740407i	$0.265367\pi$
$284$	7.37903	−	8.79399i	0.437865	−	0.521827i
$285$	−3.76583	−	2.92677i	−0.223068	−	0.173367i
$286$	−16.2049	+	2.85736i	−0.958216	+	0.168959i
$287$	−14.2690	+	19.7946i	−0.842274	+	1.16844i
$288$	−9.96139	−	22.0703i	−0.586980	−	1.30051i
$289$	−16.1216			−0.948331
$290$	−1.51487	−	0.551366i	−0.0889560	−	0.0323773i
$291$	−2.92919	−	13.6102i	−0.171712	−	0.797844i
$292$	5.63837	−	6.71955i	0.329961	−	0.393232i
$293$	−6.06074	−	5.08556i	−0.354072	−	0.297102i	0.448351	−	0.893858i	$-0.352012\pi$
$293$	−6.06074	−	5.08556i	−0.354072	−	0.297102i	−0.802423	+	0.596756i	$0.796456\pi$
$294$	8.91348	+	23.7468i	0.519845	+	1.38494i
$295$	2.16359	+	0.787482i	0.125969	+	0.0458490i
$296$	−2.27565	−	1.31385i	−0.132270	−	0.0763660i
$297$	−22.4083	+	23.5622i	−1.30026	+	1.36722i
$298$	15.0482	+	26.0643i	0.871720	+	1.50986i
$299$	−1.64666	+	1.38171i	−0.0952288	+	0.0799064i
$300$	0.750692	+	20.0337i	0.0433412	+	1.15665i
$301$	−7.31701	−	7.52058i	−0.421746	−	0.433479i
$302$	41.7305	+	7.35821i	2.40132	+	0.423417i
$303$	7.56174	−	23.4759i	0.434410	−	1.34866i
$304$	−8.11696	+	22.3012i	−0.465540	+	1.27906i
$305$	−3.26361	−	1.88424i	−0.186873	−	0.107891i
$306$	4.10754	+	4.21035i	0.234813	+	0.240690i
$307$	16.6860	+	9.63367i	0.952321	+	0.549823i	0.893801	−	0.448464i	$-0.148029\pi$
$307$	16.6860	+	9.63367i	0.952321	+	0.549823i	0.0585197	+	0.998286i	$0.481362\pi$
$308$	17.1170	−	35.4303i	0.975333	−	2.01883i
$309$	8.74998	+	6.80041i	0.497769	+	0.386862i
$310$	−0.759480	+	4.30723i	−0.0431356	+	0.244634i
$311$	10.1814	+	8.54323i	0.577336	+	0.484442i	0.884071	−	0.467353i	$-0.154792\pi$
$311$	10.1814	+	8.54323i	0.577336	+	0.484442i	−0.306735	+	0.951795i	$0.599237\pi$
$312$	−1.05257	+	1.35433i	−0.0595901	+	0.0766737i
$313$	5.11582	−	14.0556i	0.289163	−	0.794470i	−0.707021	−	0.707193i	$-0.749961\pi$
$313$	5.11582	−	14.0556i	0.289163	−	0.794470i	0.996184	−	0.0872770i	$-0.0278165\pi$
$314$	4.14928	−	7.18676i	0.234157	−	0.405573i
$315$	−2.85851	−	0.0745606i	−0.161059	−	0.00420102i
$316$	12.2675	+	21.2479i	0.690098	+	1.19528i
$317$	−16.3443	+	2.88195i	−0.917990	+	0.161866i	−0.612629	−	0.790370i	$-0.709888\pi$
$317$	−16.3443	+	2.88195i	−0.917990	+	0.161866i	−0.305361	+	0.952237i	$0.598777\pi$
$318$	3.86173	−	11.9890i	0.216555	−	0.672310i
$319$	12.5779	−	4.57798i	0.704228	−	0.256318i
$320$	−3.61412	+	1.31543i	−0.202036	+	0.0735350i
$321$	2.62964	−	4.97618i	0.146772	−	0.277743i
$322$	−0.695564	−	9.44031i	−0.0387623	−	0.526088i
$323$		−	7.16357i		−	0.398592i
$324$	−0.528641	+	21.3830i	−0.0293689	+	1.18794i
$325$	−5.30133	+	3.06072i	−0.294065	+	0.169778i
$326$	−35.6783	+	6.29105i	−1.97604	+	0.348429i
$327$	−18.4880	+	11.6182i	−1.02239	+	0.642485i
$328$	4.67087	−	5.56653i	0.257906	−	0.307360i
$329$	9.30743	+	9.56637i	0.513135	+	0.527411i
$330$	5.48154	+	6.05677i	0.301749	+	0.333414i
$331$	−3.98781	−	22.6160i	−0.219190	−	1.24309i	−0.873486	−	0.486848i	$-0.838146\pi$
$331$	−3.98781	−	22.6160i	−0.219190	−	1.24309i	0.654297	−	0.756238i	$-0.272965\pi$
$332$	−7.67488	+	13.2933i	−0.421214	+	0.729564i
$333$	−5.63713	−	8.26623i	−0.308913	−	0.452987i
$334$	22.2419	−	12.8414i	1.21702	−	0.702649i
$335$	−0.0181849	−	0.103132i	−0.000993547	−	0.00563469i
$336$	4.00778	+	13.6525i	0.218642	+	0.744806i
$337$	25.8190	−	9.39733i	1.40645	−	0.511905i	0.476363	−	0.879249i	$-0.341955\pi$
$337$	25.8190	−	9.39733i	1.40645	−	0.511905i	0.930085	+	0.367344i	$0.119733\pi$
$338$	23.5284	+	4.14870i	1.27978	+	0.225659i
$339$	3.49762	−	25.3553i	0.189965	−	1.37711i
$340$	0.614710	−	0.515803i	0.0333373	−	0.0279733i
$341$	−18.1573	−	31.4493i	−0.983271	−	1.70308i
$342$	34.3372	−	33.4988i	1.85675	−	1.81141i
$343$	−4.05327	−	18.0713i	−0.218856	−	0.975757i
$344$	2.00849	+	2.39363i	0.108291	+	0.129056i
$345$	1.01575	+	0.327178i	0.0546860	+	0.0176147i
$346$	15.1099	+	41.5142i	0.812316	+	2.23182i
$347$	9.82099	+	1.73171i	0.527218	+	0.0929628i	0.430921	−	0.902390i	$-0.358189\pi$
$347$	9.82099	+	1.73171i	0.527218	+	0.0929628i	0.0962976	+	0.995353i	$0.469300\pi$
$348$	4.11381	−	7.78472i	0.220523	−	0.417305i
$349$	−9.55483	+	26.2517i	−0.511458	+	1.40522i	0.368259	+	0.929723i	$0.379954\pi$
$349$	−9.55483	+	26.2517i	−0.511458	+	1.40522i	−0.879717	+	0.475497i	$0.842268\pi$
$350$	2.71761	−	26.8193i	0.145262	−	1.43355i
$351$	−5.84808	+	2.90783i	−0.312148	+	0.155208i
$352$	25.2545	−	43.7421i	1.34607	−	2.33146i
$353$	4.10320	+	23.2704i	0.218392	+	1.23856i	0.874923	+	0.484262i	$0.160912\pi$
$353$	4.10320	+	23.2704i	0.218392	+	1.23856i	−0.656532	+	0.754298i	$0.727977\pi$
$354$	−10.8199	+	20.4750i	−0.575073	+	1.08823i
$355$	−0.595172	−	1.63522i	−0.0315884	−	0.0867885i
$356$	−2.11461	+	11.9925i	−0.112074	+	0.635603i
$357$	−2.54624	−	3.45870i	−0.134761	−	0.183054i
$358$	−15.0546	+	12.6323i	−0.795662	+	0.667640i
$359$		−	0.0297974i		−	0.00157265i	−1.00000		0.000786324i	$-0.999750\pi$
$359$		−	0.0297974i		−	0.00157265i	1.00000		0.000786324i	$-0.000250295\pi$
$360$	0.847309	+	0.0846938i	0.0446571	+	0.00446375i
$361$	−39.4221			−2.07485
$362$	−18.2839	−	6.65481i	−0.960983	−	0.349769i
$363$	−48.3165	−	6.66499i	−2.53596	−	0.349821i
$364$	5.66468	−	5.51134i	0.296910	−	0.288873i
$365$	−0.454775	−	1.24948i	−0.0238040	−	0.0654010i
$366$	23.2596	−	29.9278i	1.21580	−	1.56435i
$367$	−10.0778	−	12.0103i	−0.526059	−	0.626933i	0.435943	−	0.899974i	$-0.356415\pi$
$367$	−10.0778	−	12.0103i	−0.526059	−	0.626933i	−0.962002	+	0.273041i	$0.911970\pi$
$368$		−	5.31003i		−	0.276805i
$369$	25.2190	−	11.3825i	1.31285	−	0.592549i
$370$	−2.17685	+	1.25681i	−0.113169	+	0.0653383i
$371$	−4.00073	+	8.28106i	−0.207708	+	0.429931i
$372$	−22.7375	−	7.32390i	−1.17889	−	0.379726i
$373$	11.7396	+	9.85066i	0.607852	+	0.510048i	0.893959	−	0.448150i	$-0.147917\pi$
$373$	11.7396	+	9.85066i	0.607852	+	0.510048i	−0.286107	+	0.958198i	$0.592361\pi$
$374$	−2.13059	+	12.0832i	−0.110170	+	0.624807i
$375$	5.44534	+	2.87757i	0.281196	+	0.148597i
$376$	−2.55486	−	3.04476i	−0.131757	−	0.157021i
$377$	2.68849			0.138464
$378$	4.67172	−	28.3788i	0.240287	−	1.45965i
$379$	17.9559			0.922330			0.461165	−	0.887314i	$-0.347432\pi$
$379$	17.9559			0.922330			0.461165	+	0.887314i	$0.347432\pi$
$380$	−4.20660	−	5.01323i	−0.215794	−	0.257173i
$381$	−20.5642	+	12.9229i	−1.05354	+	0.662060i
$382$	3.31556	−	18.8034i	0.169639	−	0.962068i
$383$	−26.4748	−	22.2150i	−1.35280	−	1.13513i	−0.978135	−	0.207973i	$-0.933313\pi$
$383$	−26.4748	−	22.2150i	−1.35280	−	1.13513i	−0.374665	−	0.927160i	$-0.622242\pi$
$384$	−2.25629	−	10.4836i	−0.115141	−	0.534991i
$385$	−3.35384	−	4.93244i	−0.170927	−	0.251380i
$386$	−6.35021	+	3.66630i	−0.323217	+	0.186610i
$387$	2.93708	+	11.5294i	0.149300	+	0.586074i
$388$		−	19.1027i		−	0.969792i
$389$	0.222028	+	0.264602i	0.0112573	+	0.0134159i	0.771644	−	0.636055i	$-0.219435\pi$
$389$	0.222028	+	0.264602i	0.0112573	+	0.0134159i	−0.760386	+	0.649471i	$0.774990\pi$
$390$	0.618523	+	1.51974i	0.0313201	+	0.0769551i
$391$	0.548197	+	1.50616i	0.0277235	+	0.0761697i
$392$	0.808334	+	5.45564i	0.0408270	+	0.275551i
$393$	1.71214	+	4.20681i	0.0863659	+	0.212205i
$394$	−38.7903	−	14.1185i	−1.95423	−	0.711280i
$395$	3.71914			0.187130
$396$	−36.8615	+	25.1376i	−1.85236	+	1.26321i
$397$			2.62188i			0.131589i	0.997833	+	0.0657943i	$0.0209581\pi$
$397$			2.62188i			0.131589i	−0.997833	+	0.0657943i	$0.979042\pi$
$398$	17.8543	−	14.9815i	0.894955	−	0.750956i
$399$	−28.2073	+	20.7657i	−1.41213	+	1.03959i
$400$	2.62586	−	14.8920i	0.131293	−	0.744599i
$401$	−5.90492	−	16.2236i	−0.294878	−	0.810169i	−0.995335	−	0.0964756i	$-0.969243\pi$
$401$	−5.90492	−	16.2236i	−0.294878	−	0.810169i	0.700458	−	0.713694i	$-0.252979\pi$
$402$	1.05256	−	0.0394411i	0.0524972	−	0.00196714i
$403$	−1.26659	−	7.18320i	−0.0630934	−	0.357821i
$404$	16.9210	−	29.3081i	0.841852	−	1.45813i
$405$	2.76703	+	1.69008i	0.137495	+	0.0839805i
$406$	−6.92307	+	9.60400i	−0.343586	+	0.476638i
$407$	7.13813	−	19.6118i	0.353824	−	0.972123i
$408$	0.680518	+	1.08291i	0.0336907	+	0.0536120i
$409$	−22.7379	−	4.00930i	−1.12432	−	0.198247i	−0.419581	−	0.907718i	$-0.637823\pi$
$409$	−22.7379	−	4.00930i	−1.12432	−	0.198247i	−0.704735	+	0.709471i	$0.748934\pi$
$410$	−2.37741	−	6.53189i	−0.117412	−	0.322587i
$411$	3.54997	+	16.4946i	0.175107	+	0.813617i
$412$	9.77413	+	11.6484i	0.481537	+	0.573873i
$413$	9.88779	−	13.7168i	0.486546	−	0.674959i
$414$	−4.65597	+	9.67089i	−0.228828	+	0.475298i
$415$	1.16340	+	2.01507i	0.0571092	+	0.0989161i
$416$	7.77158	−	6.52113i	0.381033	−	0.319725i
$417$	0.177890	+	0.138254i	0.00871130	+	0.00677035i
$418$	98.5437	+	17.3759i	4.81993	+	0.849884i
$419$	21.7961	−	7.93314i	1.06481	−	0.387559i	0.250577	−	0.968097i	$-0.419380\pi$
$419$	21.7961	−	7.93314i	1.06481	−	0.387559i	0.814234	+	0.580537i	$0.197157\pi$
$420$	−3.81294	−	0.925272i	−0.186052	−	0.0451487i
$421$	−3.28202	−	18.6133i	−0.159956	−	0.907156i	−0.954114	−	0.299444i	$-0.903199\pi$
$421$	−3.28202	−	18.6133i	−0.159956	−	0.907156i	0.794158	−	0.607712i	$-0.207912\pi$
$422$	−14.6297	+	8.44647i	−0.712163	+	0.411168i
$423$	−3.73604	−	14.6657i	−0.181653	−	0.713073i
$424$	1.36937	−	2.37183i	0.0665027	−	0.115186i
$425$	0.792609	+	4.49511i	0.0384472	+	0.218045i
$426$	17.1108	−	3.68260i	0.829023	−	0.178423i
$427$	−19.8363	+	19.2994i	−0.959947	+	0.933963i
$428$	4.96409	−	5.91598i	0.239949	−	0.285959i
$429$	−12.0450	−	6.36515i	−0.581539	−	0.307312i
$430$	2.94359	−	0.519035i	0.141953	−	0.0250301i
$431$	35.0297	−	20.2244i	1.68732	−	0.974175i	0.730764	−	0.682630i	$-0.239164\pi$
$431$	35.0297	−	20.2244i	1.68732	−	0.974175i	0.956557	−	0.291545i	$-0.0941692\pi$
$432$	3.78336	−	15.6839i	0.182027	−	0.754591i
$433$		−	5.57490i		−	0.267912i	−0.990987	−	0.133956i	$-0.957232\pi$
$433$		−	5.57490i		−	0.267912i	0.990987	−	0.133956i	$-0.0427681\pi$
$434$	28.9218	+	13.9727i	1.38829	+	0.670710i
$435$	−0.710158	−	1.13008i	−0.0340495	−	0.0541830i
$436$	−28.1543	+	10.2473i	−1.34835	+	0.490759i
$437$	12.2834	−	4.47079i	0.587594	−	0.213867i
$438$	13.0745	−	2.81390i	0.624724	−	0.134453i
$439$	−33.6601	+	5.93518i	−1.60651	+	0.283271i	−0.903718	−	0.428127i	$-0.859174\pi$
$439$	−33.6601	+	5.93518i	−1.60651	+	0.283271i	−0.702789	+	0.711398i	$0.748062\pi$
$440$	0.888115	+	1.53826i	0.0423392	+	0.0733337i
$441$	−6.23794	+	20.0521i	−0.297045	+	0.954864i
$442$	−1.23221	+	2.13426i	−0.0586104	+	0.101516i
$443$	−4.54519	+	12.4878i	−0.215949	+	0.593314i	−0.999611	−	0.0278724i	$-0.991127\pi$
$443$	−4.54519	+	12.4878i	−0.215949	+	0.593314i	0.783663	+	0.621186i	$0.213349\pi$
$444$	−5.17530	−	12.7160i	−0.245609	−	0.603472i
$445$	1.41407	+	1.18655i	0.0670335	+	0.0562478i
$446$	−2.35472	+	13.3543i	−0.111499	+	0.632344i
$447$	−3.40500	+	24.6839i	−0.161051	+	1.16751i
$448$	2.07551	+	28.1692i	0.0980587	+	1.33087i
$449$	−10.5259	−	6.07712i	−0.496747	−	0.286797i	0.230622	−	0.973043i	$-0.425924\pi$
$449$	−10.5259	−	6.07712i	−0.496747	−	0.286797i	−0.727369	+	0.686247i	$0.759257\pi$
$450$	−17.8400	+	24.8196i	−0.840986	+	1.17001i
$451$	49.9825	+	28.8574i	2.35358	+	1.35884i
$452$	12.0119	−	33.0024i	0.564992	−	1.55230i
$453$	23.5413	+	26.0117i	1.10607	+	1.22214i
$454$	14.2912	+	2.51992i	0.670718	+	0.118266i
$455$	−0.294171	−	1.16136i	−0.0137910	−	0.0544456i
$456$	8.83160	−	5.54993i	0.413578	−	0.259899i
$457$	−10.9634	+	9.19939i	−0.512846	+	0.430329i	−0.862129	−	0.506688i	$-0.830870\pi$
$457$	−10.9634	+	9.19939i	−0.512846	+	0.430329i	0.349283	+	0.937017i	$0.386425\pi$
$458$	−19.3057	−	33.4384i	−0.902095	−	1.56248i
$459$	0.546043	+	4.83922i	0.0254871	+	0.225876i
$460$	1.26809	+	0.732131i	0.0591249	+	0.0341358i
$461$	−23.2811	−	8.47362i	−1.08431	−	0.394656i	−0.262798	−	0.964851i	$-0.584645\pi$
$461$	−23.2811	−	8.47362i	−1.08431	−	0.394656i	−0.821509	+	0.570195i	$0.806868\pi$
$462$	53.7548	−	26.6373i	2.50090	−	1.23928i
$463$	−13.5051	−	11.3321i	−0.627634	−	0.526647i	0.272559	−	0.962139i	$-0.412130\pi$
$463$	−13.5051	−	11.3321i	−0.627634	−	0.526647i	−0.900193	+	0.435492i	$0.856574\pi$
$464$	−4.26897	+	5.08756i	−0.198182	+	0.236184i
$465$	−2.68480	+	2.42982i	−0.124505	+	0.112680i
$466$	47.2990	+	17.2154i	2.19108	+	0.797490i
$467$	3.57088			0.165240			0.0826202	−	0.996581i	$-0.473671\pi$
$467$	3.57088			0.165240			0.0826202	+	0.996581i	$0.473671\pi$
$468$	−8.68424	+	2.21228i	−0.401429	+	0.102263i
$469$	−0.765164	−	0.0775343i	−0.0353320	−	0.00358020i
$470$	−3.74432	+	0.660225i	−0.172713	+	0.0304539i
$471$	6.36373	−	2.58999i	0.293225	−	0.119340i
$472$	−3.23670	+	3.85735i	−0.148981	+	0.177549i
$473$	−15.9525	+	19.0114i	−0.733495	+	0.874145i
$474$	−5.11171	+	37.0563i	−0.234788	+	1.70205i
$475$	36.6596	−	6.46408i	1.68206	−	0.296592i
$476$	−2.41705	−	5.37468i	−0.110785	−	0.246348i
$477$	8.61557	−	5.87536i	0.394480	−	0.269014i
$478$	−11.5964			−0.530408
$479$	6.03889	+	2.19798i	0.275924	+	0.100428i	0.476276	−	0.879296i	$-0.341986\pi$
$479$	6.03889	+	2.19798i	0.275924	+	0.100428i	−0.200352	+	0.979724i	$0.564209\pi$
$480$	−4.79392	−	1.54415i	−0.218812	−	0.0704805i
$481$	2.69455	−	3.21124i	0.122861	−	0.146420i
$482$	−16.3367	−	13.7081i	−0.744117	−	0.624388i
$483$	4.34153	−	6.52462i	0.197547	−	0.296881i
$484$	−62.8887	−	22.8896i	−2.85858	−	1.04044i
$485$	−2.50775	−	1.44785i	−0.113871	−	0.0657434i
$486$	−20.6425	+	25.2469i	−0.936361	+	1.14522i
$487$	8.85684	+	15.3405i	0.401342	+	0.695144i	0.993888	−	0.110392i	$-0.0352107\pi$
$487$	8.85684	+	15.3405i	0.401342	+	0.695144i	−0.592546	+	0.805536i	$0.701877\pi$
$488$	6.31346	−	5.29762i	0.285797	−	0.239812i
$489$	−26.5195	−	14.0141i	−1.19925	−	0.633741i
$490$	4.90621	+	1.93974i	0.221640	+	0.0876286i
$491$	12.0720	+	2.12862i	0.544803	+	0.0960634i	0.439274	−	0.898353i	$-0.355236\pi$
$491$	12.0720	+	2.12862i	0.544803	+	0.0960634i	0.105528	+	0.994416i	$0.466347\pi$
$492$	37.1154	−	7.98799i	1.67329	−	0.360126i
$493$	0.685639	−	1.88378i	0.0308796	−	0.0848411i
$494$	17.4058	+	10.0492i	0.783124	+	0.452137i
$495$	0.506149	+	6.74432i	0.0227497	+	0.303135i
$496$	15.6043	+	9.00915i	0.700654	+	0.404523i
$497$	−12.7452	+	0.939070i	−0.571701	+	0.0421231i
$498$	−21.6766	+	8.82220i	−0.971350	+	0.395332i
$499$	0.866807	−	4.91590i	0.0388036	−	0.220066i	−0.959240	−	0.282594i	$-0.908805\pi$
$499$	0.866807	−	4.91590i	0.0388036	−	0.220066i	0.998043	+	0.0625278i	$0.0199162\pi$
$500$	6.47374	+	5.43212i	0.289515	+	0.242932i
$501$	21.0640	+	2.90565i	0.941069	+	0.129815i
$502$	−14.8670	+	40.8467i	−0.663547	+	1.82308i
$503$	−10.5236	+	18.2273i	−0.469222	+	0.812717i	−0.999381	−	0.0351814i	$-0.988799\pi$
$503$	−10.5236	+	18.2273i	−0.469222	+	0.812717i	0.530158	+	0.847899i	$0.322132\pi$
$504$	2.29137	−	5.81873i	0.102066	−	0.259187i
$505$	−2.56499	−	4.44269i	−0.114140	−	0.197697i
$506$	−22.0488	+	3.88779i	−0.980187	+	0.172833i
$507$	13.2730	+	14.6659i	0.589475	+	0.651334i
$508$	−31.3162	+	11.3981i	−1.38943	+	0.505711i
$509$	25.7085	−	9.35714i	1.13951	−	0.414748i	0.297774	−	0.954636i	$-0.403756\pi$
$509$	25.7085	−	9.35714i	1.13951	−	0.414748i	0.841737	+	0.539888i	$0.181534\pi$
$510$	1.22260	−	0.0458123i	0.0541374	−	0.00202860i
$511$	−9.73871	+	0.717551i	−0.430815	+	0.0317426i
$512$			29.9539i			1.32379i
$513$	39.4660	−	4.45322i	1.74247	−	0.196614i
$514$	−45.9289	+	26.5170i	−2.02583	+	1.16962i
$515$	2.26997	−	0.400257i	0.100027	−	0.0176374i
$516$	0.611300	+	16.3138i	0.0269110	+	0.718174i
$517$	20.2919	−	24.1830i	0.892438	−	1.06357i
$518$	4.53272	+	17.8948i	0.199156	+	0.786253i
$519$	−11.2141	+	34.8151i	−0.492246	+	1.52821i
$520$	0.0619521	+	0.351348i	0.00271678	+	0.0154076i
$521$	18.9952	−	32.9006i	0.832194	−	1.44140i	−0.0641012	−	0.997943i	$-0.520418\pi$
$521$	18.9952	−	32.9006i	0.832194	−	1.44140i	0.896295	−	0.443458i	$-0.146249\pi$
$522$	12.2358	−	5.52258i	0.535545	−	0.241717i
$523$	−0.735757	+	0.424789i	−0.0321724	+	0.0185747i	−0.516000	−	0.856589i	$-0.672580\pi$
$523$	−0.735757	+	0.424789i	−0.0321724	+	0.0185747i	0.483828	+	0.875163i	$0.339246\pi$
$524$	1.08219	+	6.13740i	0.0472756	+	0.268113i
$525$	15.4023	−	16.1514i	0.672212	−	0.704904i
$526$	−7.81014	+	2.84266i	−0.340538	+	0.123946i
$527$	−5.35615	−	0.944435i	−0.233318	−	0.0411402i
$528$	31.1710	−	12.6864i	1.35654	−	0.552103i
$529$	15.3785	−	12.9041i	0.668632	−	0.561049i
$530$	−1.30992	−	2.26885i	−0.0568993	−	0.0985525i
$531$	−17.4756	+	7.88756i	−0.758376	+	0.342291i
$532$	−43.8329	+	19.7121i	−1.90040	+	0.854629i
$533$	7.45145	+	8.88030i	0.322758	+	0.384648i
$534$	−13.7659	+	12.4585i	−0.595710	+	0.539134i
$535$	−0.400389	−	1.10006i	−0.0173103	−	0.0475598i
$536$	0.225548	+	0.0397701i	0.00974217	+	0.00171781i
$537$	−16.2594	+	0.609261i	−0.701643	+	0.0262915i
$538$	3.36367	−	9.24162i	0.145018	−	0.398434i
$539$	−41.5582	+	13.8471i	−1.79004	+	0.596435i
$540$	3.22383	+	3.06595i	0.138731	+	0.131937i
$541$	20.4690	−	35.4533i	0.880031	−	1.52426i	0.0287257	−	0.999587i	$-0.490855\pi$
$541$	20.4690	−	35.4533i	0.880031	−	1.52426i	0.851305	−	0.524671i	$-0.175812\pi$
$542$	−3.12508	−	17.7232i	−0.134234	−	0.761278i
$543$	−8.57138	−	13.6396i	−0.367833	−	0.585333i
$544$	−2.58727	−	7.10848i	−0.110928	−	0.304773i
$545$	−0.788657	+	4.47270i	−0.0337824	+	0.191589i
$546$	11.9758	−	1.33481i	0.512516	−	0.0571247i
$547$	−9.03807	+	7.58384i	−0.386440	+	0.324262i	−0.815224	−	0.579145i	$-0.803386\pi$
$547$	−9.03807	+	7.58384i	−0.386440	+	0.324262i	0.428784	+	0.903407i	$0.358942\pi$
$548$			23.1510i			0.988964i
$549$	30.4101	−	7.74686i	1.29787	−	0.330628i
$550$	−63.7583			−2.71866
$551$	−15.3630	−	5.59169i	−0.654487	−	0.238214i
$552$	−1.43215	+	1.84273i	−0.0609565	+	0.0784318i
$553$	7.43049	−	26.2832i	0.315977	−	1.11768i
$554$	−11.3670	−	31.2304i	−0.482935	−	1.32685i
$555$	−2.06156	−	0.284381i	−0.0875085	−	0.0120713i
$556$	0.198711	+	0.236815i	0.00842723	+	0.0100432i
$557$		−	31.2086i		−	1.32235i	−0.750232	−	0.661175i	$-0.770058\pi$
$557$		−	31.2086i		−	1.32235i	0.750232	−	0.661175i	$-0.229942\pi$
$558$	−20.5199	−	30.0902i	−0.868676	−	1.27382i
$559$	−4.31695	+	2.49239i	−0.182587	+	0.105417i
$560$	2.66481	+	1.28742i	0.112609	+	0.0544034i
$561$	−7.53176	+	6.81644i	−0.317991	+	0.287791i
$562$	34.6107	+	29.0418i	1.45996	+	1.22505i
$563$	−2.88191	+	16.3441i	−0.121458	+	0.688824i	0.861890	+	0.507095i	$0.169281\pi$
$563$	−2.88191	+	16.3441i	−0.121458	+	0.688824i	−0.983349	+	0.181729i	$0.941831\pi$
$564$	−0.777589	−	20.7515i	−0.0327424	−	0.873798i
$565$	−3.42205	−	4.07824i	−0.143967	−	0.171573i
$566$	−9.51130			−0.399790
$567$	17.4720	−	16.1780i	0.733757	−	0.679412i
$568$	3.80572			0.159684
$569$	−8.45351	−	10.0745i	−0.354389	−	0.422345i	0.559168	−	0.829054i	$-0.311121\pi$
$569$	−8.45351	−	10.0745i	−0.354389	−	0.422345i	−0.913558	+	0.406709i	$0.866676\pi$
$570$	−0.373620	−	9.97081i	−0.0156492	−	0.417631i
$571$	2.47480	−	14.0353i	0.103567	−	0.587359i	−0.888216	−	0.459427i	$-0.848055\pi$
$571$	2.47480	−	14.0353i	0.103567	−	0.587359i	0.991783	−	0.127932i	$-0.0408340\pi$
$572$	−14.3198	−	12.0158i	−0.598742	−	0.502404i
$573$	11.7207	−	10.6075i	0.489638	−	0.443136i
$574$	−50.9108	+	3.75112i	−2.12498	+	0.156569i
$575$	−7.21311	+	4.16449i	−0.300807	+	0.173671i
$576$	13.8931	−	28.8572i	0.578877	−	1.20238i
$577$			0.548136i			0.0228192i	0.999935	+	0.0114096i	$0.00363187\pi$
$577$			0.548136i			0.0228192i	−0.999935	+	0.0114096i	$0.996368\pi$
$578$	−21.6793	−	25.8364i	−0.901740	−	1.07465i
$579$	−6.01390	−	0.829582i	−0.249929	−	0.0344763i
$580$	−0.626368	−	1.72093i	−0.0260085	−	0.0714578i
$581$	16.5649	−	4.19586i	0.687228	−	0.174074i
$582$	17.8726	−	22.9964i	0.740844	−	0.953232i
$583$	20.4407	+	7.43979i	0.846566	+	0.308125i
$584$	2.90798			0.120333
$585$	−0.367782	+	1.30772i	−0.0152059	+	0.0540675i
$586$		−	16.5516i		−	0.683741i
$587$	−19.8533	+	16.6589i	−0.819432	+	0.687585i	−0.952839	−	0.303476i	$-0.901853\pi$
$587$	−19.8533	+	16.6589i	−0.819432	+	0.687585i	0.133407	+	0.991061i	$0.457408\pi$
$588$	−14.1568	+	25.0975i	−0.583816	+	1.03500i
$589$	−7.70228	+	43.6818i	−0.317367	+	1.79988i
$590$	1.64744	+	4.52631i	0.0678241	+	0.186345i
$591$	−18.1846	−	28.9372i	−0.748015	−	1.19032i
$592$	1.79819	+	10.1981i	0.0739053	+	0.419138i
$593$	−1.71212	+	2.96547i	−0.0703082	+	0.121777i	−0.899036	−	0.437874i	$-0.855732\pi$
$593$	−1.71212	+	2.96547i	−0.0703082	+	0.121777i	0.828728	+	0.559651i	$0.189065\pi$
$594$	−67.8939	−	4.22650i	−2.78572	−	0.173415i
$595$	−0.888768	−	0.0900591i	−0.0364359	−	0.00369206i
$596$	−11.6938	+	32.1285i	−0.478997	+	1.31603i
$597$	19.2830	−	0.722563i	0.789203	−	0.0295725i
$598$	−4.42864	−	0.780889i	−0.181101	−	0.0319329i
$599$	9.51273	+	26.1360i	0.388680	+	1.06789i	0.967596	+	0.252502i	$0.0812533\pi$
$599$	9.51273	+	26.1360i	0.388680	+	1.06789i	−0.578917	+	0.815387i	$0.696524\pi$
$600$	−4.92772	+	4.45972i	−0.201173	+	0.182067i
$601$	4.26455	+	5.08229i	0.173955	+	0.207311i	0.845976	−	0.533220i	$-0.179018\pi$
$601$	4.26455	+	5.08229i	0.173955	+	0.207311i	−0.672022	+	0.740531i	$0.734574\pi$
$602$	2.21299	−	21.8394i	0.0901947	−	0.890106i
$603$	0.708112	+	0.508982i	0.0288365	+	0.0207273i
$604$	24.0692	+	41.6890i	0.979361	+	1.69630i
$605$	−7.77140	+	6.52098i	−0.315952	+	0.265115i
$606$	47.7909	−	19.4505i	1.94137	−	0.790124i
$607$	−36.0153	−	6.35047i	−1.46182	−	0.257758i	−0.614530	−	0.788894i	$-0.710654\pi$
$607$	−36.0153	−	6.35047i	−1.46182	−	0.257758i	−0.847287	+	0.531136i	$0.821765\pi$
$608$	−57.9728	+	21.1004i	−2.35111	+	0.855733i
$609$	−9.40508	+	2.76091i	−0.381113	+	0.111878i
$610$	−1.36901	−	7.76403i	−0.0554295	−	0.314357i
$611$	5.49127	−	3.17039i	0.222153	−	0.128260i
$612$	−0.664616	+	6.64908i	−0.0268655	+	0.268773i
$613$	7.90264	−	13.6878i	0.319185	−	0.552844i	−0.661134	−	0.750268i	$-0.729924\pi$
$613$	7.90264	−	13.6878i	0.319185	−	0.552844i	0.980318	+	0.197424i	$0.0632577\pi$
$614$	6.99940	+	39.6956i	0.282473	+	1.60198i
$615$	1.76444	−	5.47784i	0.0711492	−	0.220888i
$616$	12.6453	−	3.20302i	0.509493	−	0.129053i
$617$	10.9448	−	13.0434i	0.440619	−	0.525109i	−0.499336	−	0.866409i	$-0.666423\pi$
$617$	10.9448	−	13.0434i	0.440619	−	0.525109i	0.939955	+	0.341299i	$0.110867\pi$
$618$	0.868115	+	23.1674i	0.0349207	+	0.931930i
$619$	23.4106	−	4.12792i	0.940952	−	0.165915i	0.317925	−	0.948116i	$-0.397014\pi$
$619$	23.4106	−	4.12792i	0.940952	−	0.165915i	0.623027	+	0.782200i	$0.285903\pi$
$620$	−4.30295	+	2.48431i	−0.172811	+	0.0997722i
$621$	−7.95704	+	3.95646i	−0.319305	+	0.158767i
$622$			27.8050i			1.11488i
$623$	11.2105	−	7.62266i	0.449140	−	0.305395i
$624$	6.75484	−	0.253113i	0.270410	−	0.0101326i
$625$	−21.6787	+	7.89041i	−0.867149	+	0.315617i
$626$	29.4048	−	10.7025i	1.17525	−	0.427757i
$627$	55.5911	+	61.4248i	2.22010	+	2.45307i
$628$	9.28418	−	1.63705i	0.370479	−	0.0653254i
$629$	−1.56287	−	2.70698i	−0.0623158	−	0.107934i
$630$	−3.72444	−	4.68129i	−0.148385	−	0.186507i
$631$	21.9990	−	38.1033i	0.875765	−	1.51687i	0.0198191	−	0.999804i	$-0.493691\pi$
$631$	21.9990	−	38.1033i	0.875765	−	1.51687i	0.855946	−	0.517066i	$-0.172976\pi$
$632$	−2.78189	+	7.64319i	−0.110658	+	0.304030i
$633$	−13.8549	−	1.91120i	−0.550683	−	0.0759635i
$634$	−26.5974	−	22.3179i	−1.05632	−	0.886356i
$635$	−0.877226	+	4.97499i	−0.0348116	+	0.197427i
$636$	13.2533	−	5.39401i	0.525529	−	0.213886i
$637$	−8.79509	−	0.241382i	−0.348474	−	0.00956392i
$638$	24.2506	+	14.0011i	0.960090	+	0.554308i
$639$	13.0565	+	6.28595i	0.516508	+	0.248668i
$640$	−1.93166	−	1.11525i	−0.0763557	−	0.0440840i
$641$	−9.08443	+	24.9593i	−0.358813	+	0.985831i	0.620629	+	0.784105i	$0.286877\pi$
$641$	−9.08443	+	24.9593i	−0.358813	+	0.985831i	−0.979442	+	0.201727i	$0.935345\pi$
$642$	11.5110	−	2.47739i	0.454301	−	0.0977749i
$643$	−21.8428	−	3.85147i	−0.861394	−	0.151887i	−0.274536	−	0.961577i	$-0.588524\pi$
$643$	−21.8428	−	3.85147i	−0.861394	−	0.151887i	−0.586858	+	0.809690i	$0.699635\pi$
$644$	7.70750	−	7.49887i	0.303718	−	0.295497i
$645$	2.18796	+	1.15622i	0.0861508	+	0.0455261i
$646$	11.4803	−	9.63310i	0.451686	−	0.379009i
$647$	−6.41692	−	11.1144i	−0.252275	−	0.436954i	0.711877	−	0.702305i	$-0.247846\pi$
$647$	−6.41692	−	11.1144i	−0.252275	−	0.436954i	−0.964152	+	0.265351i	$0.914512\pi$
$648$	−5.54299	+	4.42234i	−0.217749	+	0.173726i
$649$	−34.6356	−	19.9969i	−1.35957	−	0.784946i
$650$	−12.0340	−	4.38000i	−0.472011	−	0.171798i
$651$	11.8076	+	23.8281i	0.462776	+	0.933896i
$652$	−31.5280	−	26.4551i	−1.23473	−	1.03606i
$653$	6.85654	−	8.17131i	0.268317	−	0.319768i	−0.615015	−	0.788515i	$-0.710850\pi$
$653$	6.85654	−	8.17131i	0.268317	−	0.319768i	0.883332	+	0.468747i	$0.155294\pi$
$654$	−43.4806	−	14.0053i	−1.70022	−	0.547652i
$655$	0.887722	+	0.323104i	0.0346862	+	0.0126247i
$656$	−28.6366			−1.11807
$657$	9.97658	+	4.80314i	0.389223	+	0.187388i
$658$	−2.81498	+	27.7802i	−0.109739	+	1.08299i
$659$	12.4568	−	2.19647i	0.485248	−	0.0855623i	0.0743281	−	0.997234i	$-0.476319\pi$
$659$	12.4568	−	2.19647i	0.485248	−	0.0855623i	0.410920	+	0.911672i	$0.365208\pi$
$660$	−1.26814	+	9.19311i	−0.0493621	+	0.357841i
$661$	21.3936	−	25.4959i	0.832115	−	0.991677i	−0.167867	−	0.985810i	$-0.553688\pi$
$661$	21.3936	−	25.4959i	0.832115	−	0.991677i	0.999983	−	0.00586698i	$-0.00186753\pi$
$662$	30.8816	−	36.8033i	1.20025	−	1.43040i
$663$	−1.88984	+	0.769150i	−0.0733953	+	0.0298713i
$664$	−5.01139	+	0.883643i	−0.194479	+	0.0342920i
$665$	−0.734472	+	7.24830i	−0.0284816	+	0.281077i
$666$	5.66696	−	20.1499i	0.219590	−	0.780793i
$667$	3.65803			0.141639
$668$	27.4168	+	9.97890i	1.06079	+	0.386095i
$669$	−8.32407	+	7.53351i	−0.321827	+	0.291262i
$670$	0.140824	−	0.167828i	0.00544051	−	0.00648375i
$671$	50.1446	+	42.0763i	1.93581	+	1.62434i
$672$	−20.4903	+	30.7936i	−0.790432	+	1.18789i
$673$	21.0468	+	7.66040i	0.811294	+	0.295287i	0.714158	−	0.699984i	$-0.246810\pi$
$673$	21.0468	+	7.66040i	0.811294	+	0.295287i	0.0971357	+	0.995271i	$0.469032\pi$
$674$	49.7797	+	28.7403i	1.91744	+	1.10704i
$675$	−24.2720	+	7.16107i	−0.934231	+	0.275630i
$676$	13.5706	+	23.5051i	0.521948	+	0.904040i
$677$	35.4418	−	29.7392i	1.36214	−	1.14297i	0.386821	−	0.922155i	$-0.373573\pi$
$677$	35.4418	−	29.7392i	1.36214	−	1.14297i	0.975316	−	0.220814i	$-0.0708714\pi$
$678$	45.3376	−	28.4909i	1.74118	−	1.09419i
$679$	−15.2422	+	14.8296i	−0.584941	+	0.569108i
$680$	0.261982	+	0.0461946i	0.0100466	+	0.00177148i
$681$	8.06203	+	8.90805i	0.308938	+	0.341357i
$682$	25.9837	−	71.3896i	0.994968	−	2.73365i
$683$	−7.53532	−	4.35052i	−0.288331	−	0.166468i	0.348858	−	0.937176i	$-0.386570\pi$
$683$	−7.53532	−	4.35052i	−0.288331	−	0.166468i	−0.637189	+	0.770708i	$0.719903\pi$
$684$	54.2262	+	5.42024i	2.07339	+	0.207248i
$685$	3.03920	+	1.75468i	0.116122	+	0.0670431i
$686$	23.5103	−	30.7968i	0.897628	−	1.17583i
$687$	4.36835	−	31.6675i	0.166663	−	1.20819i
$688$	2.13828	−	12.1268i	0.0815210	−	0.462329i
$689$	3.34695	+	2.80842i	0.127509	+	0.106992i
$690$	0.841577	+	2.06780i	0.0320383	+	0.0787196i
$691$	3.89200	−	10.6932i	0.148059	−	0.406787i	−0.843387	−	0.537306i	$-0.819442\pi$
$691$	3.89200	−	10.6932i	0.148059	−	0.406787i	0.991446	+	0.130519i	$0.0416642\pi$
$692$	−25.0940	+	43.4641i	−0.953932	+	1.65226i
$693$	48.6734	+	9.89754i	1.84895	+	0.375977i
$694$	10.4314	+	18.0677i	0.395971	+	0.685841i
$695$	0.0461492	−	0.00813736i	0.00175054	−	0.000308667i
$696$	2.85361	−	0.614154i	0.108166	−	0.0232795i
$697$	8.12259	−	2.95638i	0.307665	−	0.111981i
$698$	−54.9194	+	19.9890i	−2.07873	+	0.756596i
$699$	22.1734	+	35.2846i	0.838676	+	1.33459i
$700$	25.3239	−	17.2191i	0.957155	−	0.650822i
$701$			19.8586i			0.750050i	0.927015	+	0.375025i	$0.122366\pi$
$701$			19.8586i			0.750050i	−0.927015	+	0.375025i	$0.877634\pi$
$702$	−12.5242	−	5.46183i	−0.472695	−	0.206144i
$703$	−22.0766	+	12.7459i	−0.832634	+	0.480722i
$704$	65.7918	−	11.6009i	2.47962	−	0.437224i
$705$	−2.78314	−	1.47074i	−0.104819	−	0.0553913i
$706$	−31.7753	+	37.8683i	−1.19588	+	1.42519i
$707$	−36.5211	+	9.25072i	−1.37352	+	0.347909i
$708$	−25.7193	+	5.53532i	−0.966590	+	0.208030i
$709$	3.55338	+	20.1522i	0.133450	+	0.756831i	0.975927	+	0.218099i	$0.0699855\pi$
$709$	3.55338	+	20.1522i	0.133450	+	0.756831i	−0.842477	+	0.538733i	$0.818903\pi$
$710$	1.82024	−	3.15275i	0.0683125	−	0.118321i
$711$	−22.1684	+	21.6271i	−0.831379	+	0.811079i
$712$	−3.49619	+	2.01852i	−0.131025	+	0.0756474i
$713$	−1.72335	−	9.77363i	−0.0645402	−	0.366025i
$714$	2.11887	−	8.73162i	0.0792968	−	0.326773i
$715$	−2.66274	+	0.969157i	−0.0995807	+	0.0362444i
$716$	−21.9866	−	3.87682i	−0.821676	−	0.144884i
$717$	−7.58071	−	5.89166i	−0.283107	−	0.220028i
$718$	0.0477531	−	0.0400696i	0.00178213	−	0.00149538i
$719$	11.1854	+	19.3737i	0.417146	+	0.722518i	0.995651	−	0.0931608i	$-0.0296971\pi$
$719$	11.1854	+	19.3737i	0.417146	+	0.722518i	−0.578505	+	0.815679i	$0.696364\pi$
$720$	−1.89067	−	2.77246i	−0.0704610	−	0.103323i
$721$	1.70656	−	16.8416i	0.0635557	−	0.627214i
$722$	−53.0123	−	63.1776i	−1.97291	−	2.35123i
$723$	−3.71495	−	17.2612i	−0.138161	−	0.641950i
$724$	−7.56006	−	20.7711i	−0.280967	−	0.771951i
$725$	10.2589	+	1.80893i	0.381007	+	0.0671818i
$726$	−54.2917	−	86.3943i	−2.01495	−	3.20639i
$727$	−2.58356	+	7.09828i	−0.0958190	+	0.263261i	−0.978337	−	0.207018i	$-0.933624\pi$
$727$	−2.58356	+	7.09828i	−0.0958190	+	0.263261i	0.882518	+	0.470278i	$0.155846\pi$
$728$	2.60675	+	0.264143i	0.0966126	+	0.00978978i
$729$	−26.3211	+	6.01659i	−0.974856	+	0.222837i
$730$	1.39086	−	2.40904i	0.0514781	−	0.0891627i
$731$	0.645434	+	3.66044i	0.0238722	+	0.135386i
$732$	43.0293	−	1.61237i	1.59041	−	0.0595948i
$733$	5.82499	+	16.0040i	0.215151	+	0.591123i	0.999576	−	0.0291005i	$-0.00926428\pi$
$733$	5.82499	+	16.0040i	0.215151	+	0.591123i	−0.784425	+	0.620223i	$0.787042\pi$
$734$	5.69560	−	32.3013i	0.210228	−	1.19226i
$735$	2.22174	+	3.76067i	0.0819501	+	0.138715i
$736$	10.5742	−	8.87281i	0.389770	−	0.327056i
$737$			1.81905i			0.0670054i
$738$	52.1543	+	25.1093i	1.91983	+	0.924284i
$739$	6.98225			0.256846			0.128423	−	0.991719i	$-0.459008\pi$
$739$	6.98225			0.256846			0.128423	+	0.991719i	$0.459008\pi$
$740$	−2.68333	−	0.976651i	−0.0986411	−	0.0359024i
$741$	6.27276	+	15.4125i	0.230436	+	0.566191i
$742$	−18.6511	+	4.72428i	−0.684703	+	0.173434i
$743$	−0.493042	−	1.35462i	−0.0180880	−	0.0496962i	0.930320	−	0.366749i	$-0.119529\pi$
$743$	−0.493042	−	1.35462i	−0.0180880	−	0.0496962i	−0.948408	+	0.317052i	$0.897307\pi$
$744$	−2.98530	−	7.33502i	−0.109446	−	0.268915i
$745$	3.33143	+	3.97024i	0.122054	+	0.145458i
$746$			32.0603i			1.17381i
$747$	−18.6524	−	5.24580i	−0.682456	−	0.191934i
$748$	−12.0712	+	6.96930i	−0.441366	+	0.254823i
$749$	−8.57408	+	0.631740i	−0.313290	+	0.0230833i
$750$	2.71097	+	12.5962i	0.0989905	+	0.459949i
$751$	−14.3786	−	12.0651i	−0.524683	−	0.440261i	0.341578	−	0.939854i	$-0.389039\pi$
$751$	−14.3786	−	12.0651i	−0.524683	−	0.440261i	−0.866261	+	0.499592i	$0.833483\pi$
$752$	−2.71994	+	15.4256i	−0.0991861	+	0.562512i
$753$	−30.4713	+	19.1487i	−1.11043	+	0.697816i
$754$	3.61531	+	4.30855i	0.131662	+	0.156908i
$755$	7.29709			0.265568
$756$	28.1080	−	16.6573i	1.02228	−	0.605821i
$757$	−6.53601			−0.237555			−0.118778	−	0.992921i	$-0.537898\pi$
$757$	−6.53601			−0.237555			−0.118778	+	0.992921i	$0.537898\pi$
$758$	24.1458	+	28.7759i	0.877017	+	1.04519i
$759$	−16.3887	−	8.66057i	−0.594874	−	0.314359i
$760$	0.376737	−	2.13658i	0.0136657	−	0.0775020i
$761$	−2.71646	−	2.27938i	−0.0984717	−	0.0826276i	0.592223	−	0.805774i	$-0.298251\pi$
$761$	−2.71646	−	2.27938i	−0.0984717	−	0.0826276i	−0.690694	+	0.723147i	$0.742695\pi$
$762$	−48.3636	−	15.5782i	−1.75203	−	0.564338i
$763$	30.0329	+	14.5095i	1.08727	+	0.525278i
$764$	18.7848	−	10.8454i	0.679609	−	0.392373i
$765$	0.822499	+	0.591202i	0.0297375	+	0.0213750i
$766$		−	72.3016i		−	2.61236i
$767$	−5.16352	−	6.15364i	−0.186444	−	0.222195i
$768$	−8.92724	+	11.4865i	−0.322134	+	0.414485i
$769$	3.05429	+	8.39159i	0.110141	+	0.302609i	0.982502	−	0.186253i	$-0.0596345\pi$
$769$	3.05429	+	8.39159i	0.110141	+	0.302609i	−0.872361	+	0.488862i	$0.837412\pi$
$770$	3.39466	−	12.0076i	0.122335	−	0.432726i
$771$	−43.4964	−	6.00008i	−1.56648	−	0.216087i
$772$	−7.82767	−	2.84904i	−0.281724	−	0.102539i
$773$	1.68056			0.0604455			0.0302227	−	0.999543i	$-0.490378\pi$
$773$	1.68056			0.0604455			0.0302227	+	0.999543i	$0.490378\pi$
$774$	−14.5274	+	20.2110i	−0.522176	+	0.726468i
$775$		−	28.2624i		−	1.01521i
$776$	4.85124	−	4.07068i	0.174149	−	0.146129i
$777$	−6.12853	+	14.0009i	−0.219860	+	0.502281i
$778$	−0.125481	+	0.711640i	−0.00449872	+	0.0255135i
$779$	−24.1106	−	66.2433i	−0.863851	−	2.37341i
$780$	−0.870891	+	1.64802i	−0.0311829	+	0.0590086i
$781$	5.24885	+	29.7677i	0.187818	+	1.06517i
$782$	−1.67658	+	2.90392i	−0.0599543	+	0.103844i
$783$	10.8045	+	2.60632i	0.386120	+	0.0931422i
$784$	14.4222	−	16.2601i	0.515080	−	0.580718i
$785$	0.488767	−	1.34288i	0.0174449	−	0.0479293i
$786$	−4.43942	+	8.40089i	−0.158349	+	0.299650i
$787$	−19.3925	−	3.41942i	−0.691268	−	0.121889i	−0.183032	−	0.983107i	$-0.558591\pi$
$787$	−19.3925	−	3.41942i	−0.691268	−	0.121889i	−0.508236	+	0.861218i	$0.669702\pi$
$788$	−16.0390	−	44.0669i	−0.571367	−	1.56982i
$789$	−6.54981	−	2.10973i	−0.233179	−	0.0751084i
$790$	5.00126	+	5.96027i	0.177937	+	0.212057i
$791$	−35.6578	+	16.0357i	−1.26785	+	0.570164i
$792$	−14.2388	−	4.00452i	−0.505954	−	0.142295i
$793$	6.57395	+	11.3864i	0.233448	+	0.404343i
$794$	−4.20181	+	3.52574i	−0.149117	+	0.125124i
$795$	0.296399	−	2.14869i	0.0105122	−	0.0762061i
$796$	26.0753	+	4.59778i	0.924215	+	0.162964i
$797$	−6.04013	+	2.19843i	−0.213952	+	0.0778723i	−0.446773	−	0.894647i	$-0.647427\pi$
$797$	−6.04013	+	2.19843i	−0.213952	+	0.0778723i	0.232820	+	0.972520i	$0.425205\pi$
$798$	−71.2102	−	17.2803i	−2.52082	−	0.611717i
$799$	−0.821008	−	4.65617i	−0.0290452	−	0.164723i
$800$	34.0430	−	19.6548i	1.20360	−	0.694900i
$801$	−15.3286	+	1.15038i	−0.541610	+	0.0406468i
$802$	18.0593	−	31.2797i	0.637697	−	1.10452i
$803$	4.01068	+	22.7457i	0.141534	+	0.802678i
$804$	0.802933	+	0.887192i	0.0283173	+	0.0312888i
$805$	−0.400256	−	1.58018i	−0.0141072	−	0.0556940i
$806$	9.80851	−	11.6893i	0.345490	−	0.411739i
$807$	6.89415	−	4.33240i	0.242686	−	0.152508i
$808$	11.0487	−	1.94819i	0.388693	−	0.0685371i
$809$	18.3341	−	10.5852i	0.644592	−	0.372155i	−0.141789	−	0.989897i	$-0.545285\pi$
$809$	18.3341	−	10.5852i	0.644592	−	0.372155i	0.786381	+	0.617741i	$0.211952\pi$
$810$	1.01242	+	6.70712i	0.0355727	+	0.235664i
$811$		−	36.0138i		−	1.26461i	−0.774718	−	0.632307i	$-0.782108\pi$
$811$		−	36.0138i		−	1.26461i	0.774718	−	0.632307i	$-0.217892\pi$
$812$	−13.4133	+	0.988292i	−0.470713	+	0.0346823i
$813$	6.96154	−	13.1736i	0.244152	−	0.462018i
$814$	41.0287	−	14.9332i	1.43805	−	0.523409i
$815$	−5.86254	+	2.13379i	−0.205356	+	0.0747435i
$816$	1.54532	−	4.79755i	0.0540969	−	0.167948i
$817$	29.8525	−	5.26380i	1.04441	−	0.184157i
$818$	−24.1511	−	41.8310i	−0.844424	−	1.46259i
$819$	8.50686	+	5.21181i	0.297254	+	0.182116i
$820$	3.94832	−	6.83869i	0.137881	−	0.238818i
$821$	−9.84670	+	27.0536i	−0.343652	+	0.944177i	0.640673	+	0.767814i	$0.278656\pi$
$821$	−9.84670	+	27.0536i	−0.343652	+	0.944177i	−0.984325	+	0.176363i	$0.943567\pi$
$822$	−21.6603	+	27.8700i	−0.755489	+	0.972076i
$823$	−15.0019	−	12.5881i	−0.522933	−	0.438793i	0.342720	−	0.939438i	$-0.388652\pi$
$823$	−15.0019	−	12.5881i	−0.522933	−	0.438793i	−0.865653	+	0.500645i	$0.833096\pi$
$824$	−0.875358	+	4.96440i	−0.0304945	+	0.172943i
$825$	−41.6795	−	32.3930i	−1.45109	−	1.12778i
$826$	35.2789	−	2.59936i	1.22751	−	0.0904432i
$827$	13.9928	+	8.07875i	0.486577	+	0.280925i	0.723153	−	0.690687i	$-0.242692\pi$
$827$	13.9928	+	8.07875i	0.486577	+	0.280925i	−0.236576	+	0.971613i	$0.576025\pi$
$828$	−11.8160	+	3.01008i	−0.410634	+	0.104607i
$829$	27.8116	+	16.0570i	0.965936	+	0.557683i	0.897995	−	0.440006i	$-0.145024\pi$
$829$	27.8116	+	16.0570i	0.965936	+	0.557683i	0.0679412	+	0.997689i	$0.478357\pi$
$830$	−1.66487	+	4.57420i	−0.0577886	+	0.158773i
$831$	8.43620	−	26.1908i	0.292648	−	0.908548i
$832$	13.2147	+	2.33011i	0.458138	+	0.0807821i
$833$	−2.41212	+	6.10100i	−0.0835751	+	0.211387i
$834$	0.0176490	+	0.471000i	0.000611136	+	0.0163094i
$835$	3.38800	−	2.84287i	0.117247	−	0.0983816i
$836$	56.8377	+	98.4458i	1.96577	+	3.40482i
$837$	1.87350	−	30.0956i	0.0647575	−	1.04026i
$838$	42.0236	+	24.2623i	1.45168	+	0.838128i
$839$	−4.91418	−	1.78862i	−0.169656	−	0.0617499i	0.255795	−	0.966731i	$-0.417663\pi$
$839$	−4.91418	−	1.78862i	−0.169656	−	0.0617499i	−0.425452	+	0.904981i	$0.639885\pi$
$840$	−0.577538	−	1.16549i	−0.0199269	−	0.0402132i
$841$	18.7105	+	15.7000i	0.645190	+	0.541379i
$842$	25.4161	−	30.2897i	0.875895	−	1.04385i
$843$	7.87044	+	36.5692i	0.271072	+	1.25951i
$844$	−18.0335	−	6.56366i	−0.620739	−	0.225931i
$845$	4.11423			0.141534
$846$	18.4792	−	25.7089i	0.635328	−	0.883889i
$847$	30.5573	+	67.9488i	1.04996	+	2.33475i
$848$	−10.6290	+	1.87419i	−0.365003	+	0.0643598i
$849$	−6.21764	−	4.83230i	−0.213389	−	0.165844i
$850$	−6.13798	+	7.31496i	−0.210531	+	0.250901i
$851$	3.66627	−	4.36929i	0.125678	−	0.149777i
$852$	15.6995	+	12.2015i	0.537857	+	0.418018i
$853$	−39.1762	+	6.90782i	−1.34137	+	0.236519i	−0.797838	−	0.602871i	$-0.794023\pi$
$853$	−39.1762	+	6.90782i	−1.34137	+	0.236519i	−0.543529	+	0.839391i	$0.682912\pi$
$854$	−57.6037	−	5.83699i	−1.97116	−	0.199738i
$855$	4.82152	−	6.70785i	0.164892	−	0.229404i
$856$	2.56022			0.0875065
$857$	40.7035	+	14.8148i	1.39040	+	0.506066i	0.925315	−	0.379199i	$-0.123800\pi$
$857$	40.7035	+	14.8148i	1.39040	+	0.506066i	0.465088	+	0.885264i	$0.346023\pi$
$858$	−5.99662	−	27.8627i	−0.204721	−	0.951217i
$859$	−8.80914	+	10.4983i	−0.300564	+	0.358198i	−0.895096	−	0.445874i	$-0.852893\pi$
$859$	−8.80914	+	10.4983i	−0.300564	+	0.358198i	0.594532	+	0.804072i	$0.297337\pi$
$860$	2.60117	+	2.18264i	0.0886993	+	0.0744275i
$861$	−35.1867	−	23.4135i	−1.19916	−	0.797931i
$862$	79.5171	+	28.9419i	2.70836	+	0.985764i
$863$	24.1671	+	13.9529i	0.822659	+	0.474962i	0.851333	−	0.524626i	$-0.175795\pi$
$863$	24.1671	+	13.9529i	0.822659	+	0.474962i	−0.0286735	+	0.999589i	$0.509128\pi$
$864$	37.5541	−	18.6729i	1.27762	−	0.635266i
$865$	3.80390	+	6.58855i	0.129336	+	0.224017i
$866$	8.93428	−	7.49675i	0.303599	−	0.254750i
$867$	−1.04560	−	27.9039i	−0.0355103	−	0.947666i
$868$	8.95976	+	35.3724i	0.304114	+	1.20062i
$869$	−63.6205	−	11.2180i	−2.15818	−	0.380545i
$870$	0.856075	−	2.65775i	0.0290237	−	0.0901060i
$871$	−0.124963	+	0.343333i	−0.00423421	+	0.0116334i
$872$	−8.60191	−	4.96631i	−0.291297	−	0.168181i
$873$	23.3670	−	5.95267i	0.790855	−	0.201467i
$874$	23.6828	+	13.6732i	0.801081	+	0.462504i
$875$	−0.691302	−	9.38246i	−0.0233703	−	0.317185i
$876$	11.9961	+	9.32329i	0.405312	+	0.315005i
$877$	−6.39579	+	36.2723i	−0.215970	+	1.22483i	0.663244	+	0.748403i	$0.269179\pi$
$877$	−6.39579	+	36.2723i	−0.215970	+	1.22483i	−0.879215	+	0.476426i	$0.841932\pi$
$878$	−54.7755	−	45.9621i	−1.84858	−	1.55115i
$879$	8.40920	−	10.8200i	0.283635	−	0.364949i
$880$	2.39410	−	6.57772i	0.0807049	−	0.221735i
$881$	23.0421	−	39.9101i	0.776309	−	1.34461i	−0.157747	−	0.987480i	$-0.550423\pi$
$881$	23.0421	−	39.9101i	0.776309	−	1.34461i	0.934056	−	0.357127i	$-0.116244\pi$
$882$	−40.5238	+	16.9679i	−1.36451	+	0.571339i
$883$	−18.9002	−	32.7361i	−0.636043	−	1.10166i	−0.986293	−	0.165002i	$-0.947237\pi$
$883$	−18.9002	−	32.7361i	−0.636043	−	1.10166i	0.350251	−	0.936656i	$-0.386096\pi$
$884$	−2.75713	+	0.486156i	−0.0927322	+	0.0163512i
$885$	−1.22268	+	3.79589i	−0.0410999	+	0.127598i
$886$	−26.1249	+	9.50870i	−0.877685	+	0.319451i
$887$	−1.27960	+	0.465737i	−0.0429648	+	0.0156379i	−0.363413	−	0.931628i	$-0.618389\pi$
$887$	−1.27960	+	0.465737i	−0.0429648	+	0.0156379i	0.320448	+	0.947266i	$0.396166\pi$
$888$	2.12647	−	4.02400i	0.0713595	−	0.135036i
$889$	33.4057	+	16.1389i	1.12039	+	0.541282i
$890$			3.86177i			0.129447i
$891$	−42.2357	−	37.2570i	−1.41495	−	1.24816i
$892$	−13.3410	+	7.70245i	−0.446691	+	0.257897i
$893$	−37.9731	+	6.69569i	−1.27072	+	0.224063i
$894$	−44.1370	+	27.7365i	−1.47616	+	0.927646i
$895$	−2.17536	+	2.59250i	−0.0727143	+	0.0866576i
$896$	−11.7407	+	11.4229i	−0.392230	+	0.381613i
$897$	−2.49831	−	2.76048i	−0.0834163	−	0.0921699i
$898$	−4.41537	−	25.0408i	−0.147343	−	0.835622i
$899$	−6.20631	+	10.7496i	−0.206992	+	0.358521i
$900$	−34.6264	+	2.59865i	−1.15421	+	0.0866217i
$901$	2.82138	−	1.62892i	0.0939937	−	0.0542673i
$902$	20.9665	+	118.907i	0.698109	+	3.95917i
$903$	12.5423	−	13.1523i	0.417383	−	0.437681i
$904$	10.9408	−	3.98214i	0.363887	−	0.132444i
$905$	−3.29977	−	0.581838i	−0.109688	−	0.0193410i
$906$	−10.0293	+	72.7058i	−0.333203	+	2.41549i
$907$	−24.0479	+	20.1786i	−0.798497	+	0.670019i	−0.947833	−	0.318768i	$-0.896731\pi$
$907$	−24.0479	+	20.1786i	−0.798497	+	0.670019i	0.149336	+	0.988787i	$0.452287\pi$
$908$	8.24282	+	14.2770i	0.273548	+	0.473798i
$909$	41.1234	+	11.5656i	1.36398	+	0.383605i
$910$	1.46561	−	2.03316i	0.0485845	−	0.0673987i
$911$	−23.0479	−	27.4674i	−0.763610	−	0.910034i	0.234461	−	0.972126i	$-0.424668\pi$
$911$	−23.0479	−	27.4674i	−0.763610	−	0.910034i	−0.998070	+	0.0620911i	$0.980223\pi$
$912$	−39.1261	−	12.6027i	−1.29559	−	0.417319i
$913$	−13.8234	−	37.9795i	−0.457488	−	1.25694i
$914$	−29.4857	−	5.19913i	−0.975301	−	0.171972i
$915$	3.04965	−	5.77097i	0.100818	−	0.190782i
$916$	15.0022	−	41.2183i	0.495688	−	1.36189i
$917$	4.05697	−	5.62801i	0.133973	−	0.185853i
$918$	−7.02102	+	7.38255i	−0.231728	+	0.243661i
$919$	−10.7450	+	18.6110i	−0.354446	+	0.613919i	−0.987023	−	0.160579i	$-0.948664\pi$
$919$	−10.7450	+	18.6110i	−0.354446	+	0.613919i	0.632577	+	0.774498i	$0.281997\pi$
$920$	0.0842934	+	0.478052i	0.00277907	+	0.0157609i
$921$	−15.5921	+	29.5056i	−0.513777	+	0.972241i
$922$	−17.7271	−	48.7048i	−0.583811	−	1.60401i
$923$	−1.05427	+	5.97904i	−0.0347016	+	0.196802i
$924$	62.4342	+	27.3289i	2.05393	+	0.899054i
$925$	12.4427	−	10.4407i	0.409113	−	0.343287i
$926$		−	36.8818i		−	1.21201i
$927$	−11.2029	+	15.5858i	−0.367952	+	0.511906i
$928$	−17.2644			−0.566733
$929$	36.9931	+	13.4644i	1.21371	+	0.441753i	0.867988	−	0.496586i	$-0.165413\pi$
$929$	36.9931	+	13.4644i	1.21371	+	0.441753i	0.345718	+	0.938338i	$0.387635\pi$
$930$	−7.50436	−	1.03518i	−0.246078	−	0.0339450i
$931$	49.7564	+	19.6719i	1.63070	+	0.644721i
$932$	19.5572	+	53.7330i	0.640618	+	1.76008i
$933$	−14.1266	+	18.1765i	−0.462484	+	0.595071i
$934$	4.80188	+	5.72266i	0.157122	+	0.187251i
$935$			2.11289i			0.0690990i
$936$	−2.41239	−	1.73399i	−0.0788513	−	0.0566773i
$937$	−42.7796	+	24.6988i	−1.39755	+	0.806875i	−0.994135	−	0.108143i	$-0.965510\pi$
$937$	−42.7796	+	24.6988i	−1.39755	+	0.806875i	−0.403413	+	0.915018i	$0.632176\pi$
$938$	−0.904687	−	1.33051i	−0.0295391	−	0.0434427i
$939$	24.6597	+	7.94305i	0.804740	+	0.259212i
$940$	−3.30876	−	2.77638i	−0.107920	−	0.0905555i
$941$	2.65678	−	15.0673i	0.0866085	−	0.491181i	−0.910389	−	0.413752i	$-0.864218\pi$
$941$	2.65678	−	15.0673i	0.0866085	−	0.491181i	0.996998	−	0.0774286i	$-0.0246710\pi$
$942$	12.7082	+	6.71561i	0.414056	+	0.218806i
$943$	10.1386	+	12.0827i	0.330159	+	0.393468i
$944$	19.8438			0.645862
$945$	−0.0563415	−	4.95244i	−0.00183279	−	0.161103i
$946$	−51.9193			−1.68804
$947$	−5.35115	−	6.37725i	−0.173889	−	0.207233i	0.672060	−	0.740497i	$-0.265410\pi$
$947$	−5.35115	−	6.37725i	−0.173889	−	0.207233i	−0.845949	+	0.533264i	$0.820965\pi$
$948$	−35.9809	+	22.6110i	−1.16861	+	0.734372i
$949$	−0.805572	+	4.56862i	−0.0261500	+	0.148304i
$950$	59.6567	+	50.0579i	1.93552	+	1.62409i
$951$	−6.04823	−	28.1025i	−0.196127	−	0.911285i
$952$	0.849873	−	1.75914i	0.0275445	−	0.0570141i
$953$	−11.5050	+	6.64241i	−0.372683	+	0.215169i	−0.674630	−	0.738156i	$-0.735697\pi$
$953$	−11.5050	+	6.64241i	−0.372683	+	0.215169i	0.301947	+	0.953325i	$0.402363\pi$
$954$	21.0015	+	5.90645i	0.679948	+	0.191228i
$955$		−	3.28801i		−	0.106398i
$956$	−8.46800	−	10.0918i	−0.273875	−	0.326391i
$957$	8.73950	+	21.4734i	0.282508	+	0.694136i
$958$	4.59825	+	12.6336i	0.148563	+	0.408172i
$959$	18.4724	−	17.9724i	0.596505	−	0.580359i
$960$	−2.51120	−	6.17014i	−0.0810487	−	0.199140i
$961$	2.51466	+	0.915263i	0.0811182	+	0.0295246i
$962$	8.76976			0.282748
$963$	8.78350	+	4.22875i	0.283044	+	0.136269i
$964$		−	24.2270i		−	0.780300i
$965$	−0.967296	+	0.811658i	−0.0311384	+	0.0261282i
$966$	16.2945	−	1.81618i	0.524268	−	0.0584345i
$967$	−2.63510	+	14.9444i	−0.0847390	+	0.480579i	0.912674	+	0.408689i	$0.134014\pi$
$967$	−2.63510	+	14.9444i	−0.0847390	+	0.480579i	−0.997413	+	0.0718894i	$0.977097\pi$
$968$	−7.58827	−	20.8486i	−0.243896	−	0.670100i
$969$	12.3990	−	0.464607i	0.398312	−	0.0149253i
$970$	−1.05194	−	5.96586i	−0.0337758	−	0.191552i
$971$	−1.28302	+	2.22225i	−0.0411740	+	0.0713155i	−0.885878	−	0.463918i	$-0.846443\pi$
$971$	−1.28302	+	2.22225i	−0.0411740	+	0.0713155i	0.844704	+	0.535234i	$0.179776\pi$
$972$	−37.0447	+	0.471842i	−1.18821	+	0.0151343i
$973$	0.0346950	−	0.342395i	0.00111227	−	0.0109767i
$974$	−12.6745	+	34.8228i	−0.406116	+	1.11579i
$975$	−5.64143	−	8.97722i	−0.180671	−	0.287501i
$976$	−31.9856	−	5.63993i	−1.02384	−	0.180530i
$977$	−3.81094	−	10.4705i	−0.121923	−	0.334980i	0.863684	−	0.504034i	$-0.168151\pi$
$977$	−3.81094	−	10.4705i	−0.121923	−	0.334980i	−0.985607	+	0.169053i	$0.945929\pi$
$978$	−13.2027	−	61.3453i	−0.422177	−	1.96161i
$979$	−20.6105	−	24.5626i	−0.658714	−	0.785025i
$980$	1.89458	+	5.68607i	0.0605201	+	0.181635i
$981$	−21.3082	−	31.2461i	−0.680318	−	0.997612i
$982$	12.8223	+	22.2090i	0.409177	+	0.708716i
$983$	−36.7166	+	30.8089i	−1.17108	+	0.982651i	−0.999997	−	0.00260591i	$-0.999171\pi$
$983$	−36.7166	+	30.8089i	−1.17108	+	0.982651i	−0.171081	+	0.985257i	$0.554726\pi$
$984$	9.93768	+	7.72349i	0.316802	+	0.246216i
$985$	−7.00062	−	1.23440i	−0.223058	−	0.0393312i
$986$	3.94093	−	1.43438i	0.125505	−	0.0456800i
$987$	−15.9542	+	16.7301i	−0.507827	+	0.532524i
$988$	3.96482	+	22.4856i	0.126138	+	0.715362i
$989$	−5.87374	+	3.39121i	−0.186774	+	0.107834i
$990$	−10.1278	+	9.88047i	−0.321881	+	0.314022i
$991$	−11.3476	+	19.6547i	−0.360470	+	0.624352i	−0.988038	−	0.154209i	$-0.950717\pi$
$991$	−11.3476	+	19.6547i	−0.360470	+	0.624352i	0.627568	+	0.778561i	$0.284050\pi$
$992$	8.13356	+	46.1277i	0.258241	+	1.46456i
$993$	38.8859	−	8.36904i	1.23401	−	0.265583i
$994$	−18.6439	−	19.1626i	−0.591348	−	0.607800i
$995$	2.57991	−	3.07461i	0.0817885	−	0.0974718i
$996$	−23.5063	−	12.4218i	−0.744825	−	0.393600i
$997$	−19.7591	+	3.48405i	−0.625775	+	0.110341i	−0.477539	−	0.878611i	$-0.658471\pi$
$997$	−19.7591	+	3.48405i	−0.625775	+	0.110341i	−0.148237	+	0.988952i	$0.547360\pi$
$998$	9.04381	−	5.22145i	0.286277	−	0.165282i
$999$	13.9419	−	10.2931i	0.441102	−	0.325658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.131.19	yes	132
3.2	odd	2		567.2.ba.a.341.4		132
7.3	odd	6		189.2.bd.a.185.4	yes	132
21.17	even	6		567.2.bd.a.17.19		132
27.7	even	9		567.2.bd.a.467.19		132
27.20	odd	18		189.2.bd.a.47.4	yes	132
189.101	even	18	inner	189.2.ba.a.101.19	✓	132
189.115	odd	18		567.2.ba.a.143.4		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.19	✓	132	189.101	even	18	inner
189.2.ba.a.131.19	yes	132	1.1	even	1	trivial
189.2.bd.a.47.4	yes	132	27.20	odd	18
189.2.bd.a.185.4	yes	132	7.3	odd	6
567.2.ba.a.143.4		132	189.115	odd	18
567.2.ba.a.341.4		132	3.2	odd	2
567.2.bd.a.17.19		132	21.17	even	6
567.2.bd.a.467.19		132	27.7	even	9

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)

\(f(q)\)	\(=\)	\(q+(1.34473 + 1.60259i) q^{2} +(0.0648568 + 1.73084i) q^{3} +(-0.412694 + 2.34051i) q^{4} +(0.275976 + 0.231571i) q^{5} +(-2.68661 + 2.43145i) q^{6} +(2.18789 - 1.48767i) q^{7} +(-0.682329 + 0.393943i) q^{8} +(-2.99159 + 0.224513i) q^{9} +O(q^{10})\)	\(q+(1.34473 + 1.60259i) q^{2} +(0.0648568 + 1.73084i) q^{3} +(-0.412694 + 2.34051i) q^{4} +(0.275976 + 0.231571i) q^{5} +(-2.68661 + 2.43145i) q^{6} +(2.18789 - 1.48767i) q^{7} +(-0.682329 + 0.393943i) q^{8} +(-2.99159 + 0.224513i) q^{9} +0.753678i q^{10} +(-4.02242 - 4.79373i) q^{11} +(-4.07780 - 0.562508i) q^{12} +(-0.429890 - 1.18111i) q^{13} +(5.32625 + 1.50578i) q^{14} +(-0.382913 + 0.492688i) q^{15} +(2.91769 + 1.06195i) q^{16} -0.937219 q^{17} +(-4.38269 - 4.49238i) q^{18} +7.64344i q^{19} +(-0.655887 + 0.550354i) q^{20} +(2.71680 + 3.69039i) q^{21} +(2.27331 - 12.8926i) q^{22} +(-0.584919 - 1.60705i) q^{23} +(-0.726104 - 1.15545i) q^{24} +(-0.845703 - 4.79622i) q^{25} +(1.31476 - 2.27722i) q^{26} +(-0.582620 - 5.16339i) q^{27} +(2.57896 + 5.73471i) q^{28} +(-0.731568 + 2.00997i) q^{29} +(-1.30449 + 0.0488812i) q^{30} +(5.71494 + 1.00770i) q^{31} +(2.76059 + 7.58465i) q^{32} +(8.03628 - 7.27305i) q^{33} +(-1.26031 - 1.50198i) q^{34} +(0.948304 + 0.0960919i) q^{35} +(0.709137 - 7.09448i) q^{36} +(1.66757 + 2.88831i) q^{37} +(-12.2493 + 10.2784i) q^{38} +(2.01643 - 0.820673i) q^{39} +(-0.279532 - 0.0492890i) q^{40} +(-8.66669 + 3.15442i) q^{41} +(-2.26081 + 9.31652i) q^{42} +(-0.688669 - 3.90564i) q^{43} +(12.8798 - 7.43615i) q^{44} +(-0.877596 - 0.630805i) q^{45} +(1.78889 - 3.09844i) q^{46} +(0.876005 + 4.96807i) q^{47} +(-1.64883 + 5.11892i) q^{48} +(2.57370 - 6.50969i) q^{49} +(6.54914 - 7.80496i) q^{50} +(-0.0607850 - 1.62217i) q^{51} +(2.94182 - 0.518722i) q^{52} +(-3.01037 + 1.73804i) q^{53} +(7.49133 - 7.87709i) q^{54} -2.25443i q^{55} +(-0.906803 + 1.87698i) q^{56} +(-13.2295 + 0.495729i) q^{57} +(-4.20492 + 1.53047i) q^{58} +(6.00562 - 2.18587i) q^{59} +(-0.995112 - 1.09954i) q^{60} +(-10.3015 + 1.81644i) q^{61} +(6.07015 + 10.5138i) q^{62} +(-6.21126 + 4.94169i) q^{63} +(-5.33790 + 9.24552i) q^{64} +(0.154873 - 0.425509i) q^{65} +(22.4624 + 3.09856i) q^{66} +(-0.222678 - 0.186849i) q^{67} +(0.386785 - 2.19357i) q^{68} +(2.74361 - 1.11663i) q^{69} +(1.12122 + 1.64896i) q^{70} +(-4.18316 - 2.41515i) q^{71} +(1.95280 - 1.33171i) q^{72} +(-3.19638 - 1.84543i) q^{73} +(-2.38635 + 6.55643i) q^{74} +(8.24663 - 1.77484i) q^{75} +(-17.8895 - 3.15440i) q^{76} +(-15.9321 - 4.50413i) q^{77} +(4.02677 + 2.12793i) q^{78} +(7.90824 - 6.63581i) q^{79} +(0.559294 + 0.968725i) q^{80} +(8.89919 - 1.34330i) q^{81} +(-16.7096 - 9.64732i) q^{82} +(6.06917 + 2.20900i) q^{83} +(-9.75859 + 4.83569i) q^{84} +(-0.258650 - 0.217033i) q^{85} +(5.33306 - 6.35570i) q^{86} +(-3.52637 - 1.13586i) q^{87} +(4.63307 + 1.68630i) q^{88} +5.12391 q^{89} +(-0.169211 - 2.25469i) q^{90} +(-2.69765 - 1.94461i) q^{91} +(4.00271 - 0.705785i) q^{92} +(-1.37351 + 9.95699i) q^{93} +(-6.78379 + 8.08461i) q^{94} +(-1.77000 + 2.10940i) q^{95} +(-12.9487 + 5.27004i) q^{96} +(-7.91567 + 1.39575i) q^{97} +(13.8933 - 4.62921i) q^{98} +(13.1097 + 13.4378i) 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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