LMFDB - Embedded newform 189.2.bd.a.47.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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([7, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (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			47.7
Character	$\chi$	$=$	189.47
Dual form			189.2.bd.a.185.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38665 - 0.244504i) q^{2} +(-0.458387 + 1.67029i) q^{3} +(-0.0163608 - 0.00595485i) q^{4} +(1.98299 + 0.721749i) q^{5} +(1.04402 - 2.20404i) q^{6} +(-2.18605 + 1.49037i) q^{7} +(2.46004 + 1.42030i) q^{8} +(-2.57976 - 1.53128i) q^{9} +O(q^{10})$	\(q+(-1.38665 - 0.244504i) q^{2} +(-0.458387 + 1.67029i) q^{3} +(-0.0163608 - 0.00595485i) q^{4} +(1.98299 + 0.721749i) q^{5} +(1.04402 - 2.20404i) q^{6} +(-2.18605 + 1.49037i) q^{7} +(2.46004 + 1.42030i) q^{8} +(-2.57976 - 1.53128i) q^{9} +(-2.57325 - 1.48566i) q^{10} +(-1.26664 - 3.48007i) q^{11} +(0.0174459 - 0.0245978i) q^{12} +(-2.27684 + 6.25557i) q^{13} +(3.39569 - 1.53213i) q^{14} +(-2.11451 + 2.98133i) q^{15} +(-3.03727 - 2.54857i) q^{16} +(-1.61887 + 2.80397i) q^{17} +(3.20283 + 2.75412i) q^{18} +(-4.61385 + 2.66381i) q^{19} +(-0.0281454 - 0.0236168i) q^{20} +(-1.48730 - 4.33451i) q^{21} +(0.905502 + 5.13536i) q^{22} +(0.689782 - 0.121627i) q^{23} +(-3.49997 + 3.45793i) q^{24} +(-0.418902 - 0.351501i) q^{25} +(4.68670 - 8.11761i) q^{26} +(3.74022 - 3.60704i) q^{27} +(0.0446405 - 0.0113661i) q^{28} +(1.50083 + 4.12351i) q^{29} +(3.66104 - 3.61707i) q^{30} +(-0.513951 + 1.41207i) q^{31} +(-0.0633067 - 0.0754460i) q^{32} +(6.39336 - 0.520445i) q^{33} +(2.93040 - 3.49232i) q^{34} +(-5.41058 + 1.37761i) q^{35} +(0.0330885 + 0.0404152i) q^{36} +6.49662 q^{37} +(7.04913 - 2.56567i) q^{38} +(-9.40496 - 6.67047i) q^{39} +(3.85312 + 4.59197i) q^{40} +(10.4849 + 3.81619i) q^{41} +(1.00256 + 6.37411i) q^{42} +(1.29121 - 7.32280i) q^{43} +0.0644796i q^{44} +(-4.01044 - 4.89845i) q^{45} -0.986227 q^{46} +(-5.63412 + 2.05065i) q^{47} +(5.64911 - 3.90490i) q^{48} +(2.55760 - 6.51603i) q^{49} +(0.494929 + 0.589833i) q^{50} +(-3.94139 - 3.98930i) q^{51} +(0.0745020 - 0.0887880i) q^{52} +(0.766350 - 0.442452i) q^{53} +(-6.06833 + 4.08721i) q^{54} -7.81514i q^{55} +(-7.49453 + 0.561517i) q^{56} +(-2.33441 - 8.92755i) q^{57} +(-1.07292 - 6.08484i) q^{58} +(4.77604 - 4.00757i) q^{59} +(0.0523485 - 0.0361855i) q^{60} +(2.54368 + 6.98869i) q^{61} +(1.05793 - 1.83239i) q^{62} +(7.92166 - 0.497345i) q^{63} +(4.03421 + 6.98746i) q^{64} +(-9.02990 + 10.7614i) q^{65} +(-8.99262 - 0.841528i) q^{66} +(1.82662 + 10.3593i) q^{67} +(0.0431834 - 0.0362352i) q^{68} +(-0.113034 + 1.20789i) q^{69} +(7.83942 - 0.587358i) q^{70} +(-3.83248 + 2.21268i) q^{71} +(-4.17142 - 7.43105i) q^{72} +3.06138i q^{73} +(-9.00855 - 1.58845i) q^{74} +(0.779129 - 0.538566i) q^{75} +(0.0913491 - 0.0161073i) q^{76} +(7.95554 + 5.71984i) q^{77} +(11.4105 + 11.5492i) q^{78} +(-1.65307 + 9.37505i) q^{79} +(-4.18344 - 7.24593i) q^{80} +(4.31035 + 7.90069i) q^{81} +(-13.6058 - 7.85533i) q^{82} +(11.4377 - 4.16299i) q^{83} +(-0.00147789 + 0.0797727i) q^{84} +(-5.23397 + 4.39182i) q^{85} +(-3.58091 + 9.83847i) q^{86} +(-7.57543 + 0.616671i) q^{87} +(1.82677 - 10.3601i) q^{88} +(-2.17916 - 3.77442i) q^{89} +(4.36339 + 7.77303i) q^{90} +(-4.34583 - 17.0683i) q^{91} +(-0.0120097 - 0.00211763i) q^{92} +(-2.12298 - 1.50572i) q^{93} +(8.31397 - 1.46598i) q^{94} +(-11.0718 + 1.95226i) q^{95} +(0.155036 - 0.0711573i) q^{96} +(-6.85869 - 1.20937i) q^{97} +(-5.13970 + 8.41014i) q^{98} +(-2.06134 + 10.9174i) 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} - 15 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 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.38665	−	0.244504i	−0.980512	−	0.172891i	−0.339654	−	0.940550i	$-0.610310\pi$
$2$	−1.38665	−	0.244504i	−0.980512	−	0.172891i	−0.640858	+	0.767660i	$0.721421\pi$
$3$	−0.458387	+	1.67029i	−0.264650	+	0.964345i
$3$	−0.458387	+	1.67029i	−0.264650	+	0.964345i
$4$	−0.0163608	−	0.00595485i	−0.00818041	−	0.00297743i
$5$	1.98299	+	0.721749i	0.886819	+	0.322776i	0.744958	−	0.667111i	$-0.232469\pi$
$5$	1.98299	+	0.721749i	0.886819	+	0.322776i	0.141861	+	0.989887i	$0.454691\pi$
$6$	1.04402	−	2.20404i	0.426219	−	0.899796i
$7$	−2.18605	+	1.49037i	−0.826248	+	0.563307i
$7$	−2.18605	+	1.49037i	−0.826248	+	0.563307i
$8$	2.46004	+	1.42030i	0.869754	+	0.502153i
$9$	−2.57976	−	1.53128i	−0.859921	−	0.510428i
$10$	−2.57325	−	1.48566i	−0.813732	−	0.469808i
$11$	−1.26664	−	3.48007i	−0.381907	−	1.04928i	−0.970552	−	0.240890i	$-0.922561\pi$
$11$	−1.26664	−	3.48007i	−0.381907	−	1.04928i	0.588645	−	0.808392i	$-0.299662\pi$
$12$	0.0174459	−	0.0245978i	0.00503621	−	0.00710076i
$13$	−2.27684	+	6.25557i	−0.631482	+	1.73498i	0.0454806	+	0.998965i	$0.485518\pi$
$13$	−2.27684	+	6.25557i	−0.631482	+	1.73498i	−0.676963	+	0.736017i	$0.736704\pi$
$14$	3.39569	−	1.53213i	0.907536	−	0.409478i
$15$	−2.11451	+	2.98133i	−0.545964	+	0.769777i
$16$	−3.03727	−	2.54857i	−0.759318	−	0.637143i
$17$	−1.61887	+	2.80397i	−0.392635	+	0.680063i	−0.992796	−	0.119816i	$-0.961770\pi$
$17$	−1.61887	+	2.80397i	−0.392635	+	0.680063i	0.600161	+	0.799879i	$0.295103\pi$
$18$	3.20283	+	2.75412i	0.754914	+	0.649153i
$19$	−4.61385	+	2.66381i	−1.05849	+	0.611120i	−0.925014	−	0.379932i	$-0.875947\pi$
$19$	−4.61385	+	2.66381i	−1.05849	+	0.611120i	−0.133476	+	0.991052i	$0.542614\pi$
$20$	−0.0281454	−	0.0236168i	−0.00629351	−	0.00528088i
$21$	−1.48730	−	4.33451i	−0.324555	−	0.945867i
$22$	0.905502	+	5.13536i	0.193054	+	1.09486i
$23$	0.689782	−	0.121627i	0.143829	−	0.0253610i	−0.101270	−	0.994859i	$-0.532291\pi$
$23$	0.689782	−	0.121627i	0.143829	−	0.0253610i	0.245099	+	0.969498i	$0.421179\pi$
$24$	−3.49997	+	3.45793i	−0.714428	+	0.705848i
$25$	−0.418902	−	0.351501i	−0.0837805	−	0.0703002i
$26$	4.68670	−	8.11761i	0.919138	−	1.59199i
$27$	3.74022	−	3.60704i	0.719806	−	0.694175i
$28$	0.0446405	−	0.0113661i	0.00843625	−	0.00214799i
$29$	1.50083	+	4.12351i	0.278698	+	0.765716i	0.997511	+	0.0705128i	$0.0224636\pi$
$29$	1.50083	+	4.12351i	0.278698	+	0.765716i	−0.718813	+	0.695204i	$0.755314\pi$
$30$	3.66104	−	3.61707i	0.668411	−	0.660383i
$31$	−0.513951	+	1.41207i	−0.0923084	+	0.253615i	−0.977251	−	0.212084i	$-0.931975\pi$
$31$	−0.513951	+	1.41207i	−0.0923084	+	0.253615i	0.884943	+	0.465699i	$0.154197\pi$
$32$	−0.0633067	−	0.0754460i	−0.0111911	−	0.0133371i
$33$	6.39336	−	0.520445i	1.11294	−	0.0905978i
$34$	2.93040	−	3.49232i	0.502560	−	0.598927i
$35$	−5.41058	+	1.37761i	−0.914554	+	0.232859i
$36$	0.0330885	+	0.0404152i	0.00551475	+	0.00673586i
$37$	6.49662			1.06804			0.534019	−	0.845473i	$-0.320681\pi$
$37$	6.49662			1.06804			0.534019	+	0.845473i	$0.320681\pi$
$38$	7.04913	−	2.56567i	1.14352	−	0.416207i
$39$	−9.40496	−	6.67047i	−1.50600	−	1.06813i
$40$	3.85312	+	4.59197i	0.609232	+	0.726054i
$41$	10.4849	+	3.81619i	1.63746	+	0.595988i	0.986593	−	0.163200i	$-0.0521817\pi$
$41$	10.4849	+	3.81619i	1.63746	+	0.595988i	0.650871	+	0.759188i	$0.274404\pi$
$42$	1.00256	+	6.37411i	0.154699	+	0.983546i
$43$	1.29121	−	7.32280i	0.196907	−	1.11672i	−0.712769	−	0.701399i	$-0.752559\pi$
$43$	1.29121	−	7.32280i	0.196907	−	1.11672i	0.909676	−	0.415318i	$-0.136330\pi$
$44$			0.0644796i			0.00972066i
$45$	−4.01044	−	4.89845i	−0.597841	−	0.730219i
$46$	−0.986227			−0.145411
$47$	−5.63412	+	2.05065i	−0.821821	+	0.299119i	−0.718498	−	0.695529i	$-0.755170\pi$
$47$	−5.63412	+	2.05065i	−0.821821	+	0.299119i	−0.103324	+	0.994648i	$0.532948\pi$
$48$	5.64911	−	3.90490i	0.815379	−	0.563624i
$49$	2.55760	−	6.51603i	0.365371	−	0.930862i
$50$	0.494929	+	0.589833i	0.0699935	+	0.0834150i
$51$	−3.94139	−	3.98930i	−0.551905	−	0.558614i
$52$	0.0745020	−	0.0887880i	0.0103316	−	0.0123127i
$53$	0.766350	−	0.442452i	0.105266	−	0.0607755i	−0.446443	−	0.894812i	$-0.647309\pi$
$53$	0.766350	−	0.442452i	0.105266	−	0.0607755i	0.551709	+	0.834037i	$0.313976\pi$
$54$	−6.06833	+	4.08721i	−0.825795	+	0.556199i
$55$		−	7.81514i		−	1.05379i
$56$	−7.49453	+	0.561517i	−1.00150	+	0.0750358i
$57$	−2.33441	−	8.92755i	−0.309201	−	1.18248i
$58$	−1.07292	−	6.08484i	−0.140881	−	0.798978i
$59$	4.77604	−	4.00757i	0.621787	−	0.521742i	−0.276577	−	0.960992i	$-0.589200\pi$
$59$	4.77604	−	4.00757i	0.621787	−	0.521742i	0.898365	+	0.439250i	$0.144756\pi$
$60$	0.0523485	−	0.0361855i	0.00675816	−	0.00467152i
$61$	2.54368	+	6.98869i	0.325684	+	0.894811i	0.989190	+	0.146639i	$0.0468456\pi$
$61$	2.54368	+	6.98869i	0.325684	+	0.894811i	−0.663506	+	0.748171i	$0.730932\pi$
$62$	1.05793	−	1.83239i	0.134357	−	0.232713i
$63$	7.92166	−	0.497345i	0.998035	−	0.0626596i
$64$	4.03421	+	6.98746i	0.504277	+	0.873433i
$65$	−9.02990	+	10.7614i	−1.12002	+	1.33479i
$66$	−8.99262	−	0.841528i	−1.10692	−	0.103585i
$67$	1.82662	+	10.3593i	0.223157	+	1.26559i	0.866177	+	0.499738i	$0.166570\pi$
$67$	1.82662	+	10.3593i	0.223157	+	1.26559i	−0.643019	+	0.765850i	$0.722319\pi$
$68$	0.0431834	−	0.0362352i	0.00523675	−	0.00439416i
$69$	−0.113034	+	1.20789i	−0.0136077	+	0.145413i
$70$	7.83942	−	0.587358i	0.936990	−	0.0702027i
$71$	−3.83248	+	2.21268i	−0.454832	+	0.262597i	−0.709869	−	0.704334i	$-0.751246\pi$
$71$	−3.83248	+	2.21268i	−0.454832	+	0.262597i	0.255037	+	0.966931i	$0.417912\pi$
$72$	−4.17142	−	7.43105i	−0.491607	−	0.875758i
$73$			3.06138i			0.358307i	0.983821	+	0.179154i	$0.0573359\pi$
$73$			3.06138i			0.358307i	−0.983821	+	0.179154i	$0.942664\pi$
$74$	−9.00855	−	1.58845i	−1.04722	−	0.184654i
$75$	0.779129	−	0.538566i	0.0899661	−	0.0621883i
$76$	0.0913491	−	0.0161073i	0.0104785	−	0.00184763i
$77$	7.95554	+	5.71984i	0.906618	+	0.651836i
$78$	11.4105	+	11.5492i	1.29198	+	1.30769i
$79$	−1.65307	+	9.37505i	−0.185985	+	1.05478i	0.738697	+	0.674037i	$0.235441\pi$
$79$	−1.65307	+	9.37505i	−0.185985	+	1.05478i	−0.924683	+	0.380739i	$0.875670\pi$
$80$	−4.18344	−	7.24593i	−0.467723	−	0.810120i
$81$	4.31035	+	7.90069i	0.478927	+	0.877855i
$82$	−13.6058	−	7.85533i	−1.50251	−	0.867476i
$83$	11.4377	−	4.16299i	1.25545	−	0.456947i	0.373212	−	0.927746i	$-0.378256\pi$
$83$	11.4377	−	4.16299i	1.25545	−	0.456947i	0.882241	+	0.470799i	$0.156034\pi$
$84$	−0.00147789	+	0.0797727i	−0.000161251	+	0.00870392i
$85$	−5.23397	+	4.39182i	−0.567704	+	0.476360i
$86$	−3.58091	+	9.83847i	−0.386140	+	1.06091i
$87$	−7.57543	+	0.616671i	−0.812172	+	0.0661140i
$88$	1.82677	−	10.3601i	0.194734	−	1.10439i
$89$	−2.17916	−	3.77442i	−0.230991	−	0.400088i	0.727109	−	0.686522i	$-0.240863\pi$
$89$	−2.17916	−	3.77442i	−0.230991	−	0.400088i	−0.958100	+	0.286434i	$0.907530\pi$
$90$	4.36339	+	7.77303i	0.459942	+	0.819349i
$91$	−4.34583	−	17.0683i	−0.455567	−	1.78924i
$92$	−0.0120097	−	0.00211763i	−0.00125210	−	0.000220778i
$93$	−2.12298	−	1.50572i	−0.220143	−	0.156136i
$94$	8.31397	−	1.46598i	0.857520	−	0.151204i
$95$	−11.0718	+	1.95226i	−1.13594	+	0.200298i
$96$	0.155036	−	0.0711573i	0.0158233	−	0.00726246i
$97$	−6.85869	−	1.20937i	−0.696394	−	0.122793i	−0.185765	−	0.982594i	$-0.559476\pi$
$97$	−6.85869	−	1.20937i	−0.696394	−	0.122793i	−0.510629	+	0.859801i	$0.670587\pi$
$98$	−5.13970	+	8.41014i	−0.519188	+	0.849552i
$99$	−2.06134	+	10.9174i	−0.207172	+	1.09724i
$100$	0.00476045	+	0.00824535i	0.000476045	+	0.000824535i
$101$	0.645643	−	3.66163i	0.0642439	−	0.364345i	−0.935690	−	0.352824i	$-0.885221\pi$
$101$	0.645643	−	3.66163i	0.0642439	−	0.364345i	0.999934	−	0.0115214i	$-0.00366744\pi$
$102$	4.48994	+	6.49546i	0.444570	+	0.643147i
$103$	−2.12266	+	5.83195i	−0.209152	+	0.574639i	−0.999265	−	0.0383208i	$-0.987799\pi$
$103$	−2.12266	+	5.83195i	−0.209152	+	0.574639i	0.790114	+	0.612960i	$0.210021\pi$
$104$	−14.4859	+	12.1551i	−1.42046	+	1.19191i
$105$	0.179126	−	9.66873i	0.0174809	−	0.943571i
$106$	−1.17084	+	0.426152i	−0.113722	+	0.0413915i
$107$	2.47461	+	1.42872i	0.239230	+	0.138119i	0.614823	−	0.788665i	$-0.289228\pi$
$107$	2.47461	+	1.42872i	0.239230	+	0.138119i	−0.375593	+	0.926785i	$0.622561\pi$
$108$	−0.0826725	+	0.0367417i	−0.00795517	+	0.00353547i
$109$	2.81692	+	4.87905i	0.269812	+	0.467328i	0.968813	−	0.247792i	$-0.0797051\pi$
$109$	2.81692	+	4.87905i	0.269812	+	0.467328i	−0.699001	+	0.715121i	$0.746372\pi$
$110$	−1.91084	+	10.8369i	−0.182191	+	1.03326i
$111$	−2.97797	+	10.8513i	−0.282656	+	1.02996i
$112$	10.4379	+	1.04464i	0.986292	+	0.0987093i
$113$	9.04367	−	1.59464i	0.850757	−	0.150011i	0.268765	−	0.963206i	$-0.413385\pi$
$113$	9.04367	−	1.59464i	0.850757	−	0.150011i	0.581992	+	0.813194i	$0.302273\pi$
$114$	1.05420	+	12.9502i	0.0987346	+	1.21290i
$115$	1.45561	+	0.256664i	0.135737	+	0.0239340i
$116$		−	0.0764013i		−	0.00709368i
$117$	15.4528	−	12.6514i	1.42861	−	1.16962i
$118$	−7.60258	+	4.38935i	−0.699874	+	0.404073i
$119$	−0.640023	−	8.54234i	−0.0586708	−	0.783075i
$120$	−9.43616	+	4.33094i	−0.861399	+	0.395359i
$121$	−2.08004	+	1.74536i	−0.189095	+	0.158669i
$122$	−1.81843	−	10.3128i	−0.164633	−	0.933680i
$123$	−11.1803	+	15.7635i	−1.00809	+	1.42135i
$124$	0.0168173	−	0.0200421i	0.00151024	−	0.00179984i
$125$	−5.85261	−	10.1370i	−0.523474	−	0.906683i
$126$	−11.1062	−	1.24723i	−0.989418	−	0.111112i
$127$	−0.958294	+	1.65981i	−0.0850349	+	0.147285i	−0.905406	−	0.424547i	$-0.860433\pi$
$127$	−0.958294	+	1.65981i	−0.0850349	+	0.147285i	0.820371	+	0.571831i	$0.193767\pi$
$128$	−3.81822	−	10.4905i	−0.337486	−	0.927235i
$129$	11.6393	+	5.51337i	1.02479	+	0.485425i
$130$	15.1525	−	12.7145i	1.32897	−	1.11513i
$131$	−1.51205	−	8.57526i	−0.132108	−	0.749224i	−0.976830	−	0.214018i	$-0.931345\pi$
$131$	−1.51205	−	8.57526i	−0.132108	−	0.749224i	0.844721	−	0.535206i	$-0.179766\pi$
$132$	−0.107700	−	0.0295566i	−0.00937407	−	0.00257257i
$133$	6.11604	−	12.6996i	0.530328	−	1.10119i
$134$		−	14.8114i		−	1.27951i
$135$	10.0202	−	4.45322i	0.862401	−	0.383272i
$136$	−7.96498	+	4.59858i	−0.682991	+	0.394325i
$137$	−4.48477	+	5.34474i	−0.383160	+	0.456632i	−0.922809	−	0.385258i	$-0.874112\pi$
$137$	−4.48477	+	5.34474i	−0.383160	+	0.456632i	0.539649	+	0.841890i	$0.318557\pi$
$138$	0.452074	−	1.64729i	0.0384831	−	0.140226i
$139$	−6.76177	−	8.05836i	−0.573526	−	0.683501i	0.398825	−	0.917027i	$-0.369418\pi$
$139$	−6.76177	−	8.05836i	−0.573526	−	0.683501i	−0.972351	+	0.233526i	$0.924974\pi$
$140$	0.0967249	+	0.00968035i	0.00817475	+	0.000818139i
$141$	−0.842583	−	10.3506i	−0.0709583	−	0.871681i
$142$	5.85533	−	2.13117i	0.491368	−	0.178843i
$143$	24.6538			2.06165
$144$	3.93285	+	11.2256i	0.327738	+	0.935469i
$145$			9.26009i			0.769009i
$146$	0.748521	−	4.24507i	0.0619480	−	0.351325i
$147$	9.71132	+	7.25880i	0.800976	+	0.598696i
$148$	−0.106290	−	0.0386864i	−0.00873699	−	0.00318000i
$149$	−7.15261	−	8.52415i	−0.585965	−	0.698326i	0.388860	−	0.921297i	$-0.372869\pi$
$149$	−7.15261	−	8.52415i	−0.585965	−	0.698326i	−0.974825	+	0.222971i	$0.928424\pi$
$150$	−1.21206	+	0.556304i	−0.0989646	+	0.0454221i
$151$	18.9758	−	6.90663i	1.54423	−	0.562054i	0.577175	−	0.816621i	$-0.304155\pi$
$151$	18.9758	−	6.90663i	1.54423	−	0.562054i	0.967055	+	0.254567i	$0.0819330\pi$
$152$	−15.1337			−1.22750
$153$	8.46999	−	4.75463i	0.684758	−	0.384389i
$154$	−9.63305	−	9.87659i	−0.776253	−	0.795878i
$155$	−2.03832	+	2.42917i	−0.163722	+	0.195116i
$156$	0.114151	+	0.165140i	0.00913942	+	0.0132217i
$157$	−3.14481	−	3.74783i	−0.250983	−	0.299110i	0.625812	−	0.779974i	$-0.284768\pi$
$157$	−3.14481	−	3.74783i	−0.250983	−	0.299110i	−0.876795	+	0.480864i	$0.840323\pi$
$158$	4.58448	−	12.5958i	0.364722	−	1.00207i
$159$	0.387740	+	1.48284i	0.0307498	+	0.117597i
$160$	−0.0710834	−	0.195300i	−0.00561963	−	0.0154398i
$161$	−1.32663	+	1.29391i	−0.104553	+	0.101975i
$162$	−4.04520	−	12.0094i	−0.317821	−	0.943549i
$163$	−4.68621	+	8.11676i	−0.367053	+	0.635754i	−0.989103	−	0.147223i	$-0.952966\pi$
$163$	−4.68621	+	8.11676i	−0.367053	+	0.635754i	0.622051	+	0.782977i	$0.286300\pi$
$164$	−0.148817	−	0.124872i	−0.0116206	−	0.00975086i
$165$	13.0536	+	3.58236i	1.01622	+	0.278886i
$166$	−16.8780	+	2.97605i	−1.30999	+	0.230986i
$167$	1.49566	+	8.48231i	0.115738	+	0.656381i	0.986382	+	0.164468i	$0.0525908\pi$
$167$	1.49566	+	8.48231i	0.115738	+	0.656381i	−0.870645	+	0.491912i	$0.836298\pi$
$168$	2.49750	−	12.7755i	0.192686	−	0.985648i
$169$	−23.9896	−	20.1296i	−1.84535	−	1.54843i
$170$	8.33152	−	4.81021i	0.638999	−	0.368926i
$171$	15.9817	+	0.193119i	1.22215	+	0.0147682i
$172$	−0.0647314	+	0.112118i	−0.00493572	+	0.00854892i
$173$	6.49113	+	5.44671i	0.493512	+	0.414106i	0.855283	−	0.518161i	$-0.173383\pi$
$173$	6.49113	+	5.44671i	0.493512	+	0.414106i	−0.361771	+	0.932267i	$0.617828\pi$
$174$	10.6553	+	0.997119i	0.807775	+	0.0755914i
$175$	1.43961	+	0.144078i	0.108824	+	0.0108912i
$176$	−5.02208	+	13.7981i	−0.378554	+	1.04007i
$177$	4.50455	+	9.81441i	0.338583	+	0.737696i
$178$	2.09888	+	5.76663i	0.157318	+	0.432227i
$179$	−4.18791	−	2.41789i	−0.313019	−	0.180722i	0.335258	−	0.942126i	$-0.391177\pi$
$179$	−4.18791	−	2.41789i	−0.313019	−	0.180722i	−0.648277	+	0.761405i	$0.724510\pi$
$180$	0.0364445	+	0.104024i	0.00271641	+	0.00775352i
$181$	3.95269	+	2.28209i	0.293801	+	0.169626i	0.639655	−	0.768662i	$-0.279077\pi$
$181$	3.95269	+	2.28209i	0.293801	+	0.169626i	−0.345854	+	0.938288i	$0.612411\pi$
$182$	1.85289	+	24.7304i	0.137345	+	1.83314i
$183$	−12.8392	+	1.04516i	−0.949098	+	0.0772604i
$184$	1.86964	+	0.680492i	0.137831	+	0.0501665i
$185$	12.8827	+	4.68892i	0.947156	+	0.344737i
$186$	2.57568	+	2.60700i	0.188858	+	0.191154i
$187$	11.8086	+	2.08217i	0.863528	+	0.152263i
$188$	0.104390			0.00761344
$189$	−2.80047	+	13.4595i	−0.203704	+	0.979032i
$190$	15.8301			1.14844
$191$	−10.1847	−	1.79584i	−0.736940	−	0.129942i	−0.207434	−	0.978249i	$-0.566511\pi$
$191$	−10.1847	−	1.79584i	−0.736940	−	0.129942i	−0.529505	+	0.848307i	$0.677622\pi$
$192$	−13.5203	+	3.53536i	−0.975747	+	0.255142i
$193$	−9.77771	−	3.55879i	−0.703815	−	0.256168i	−0.0347759	−	0.999395i	$-0.511072\pi$
$193$	−9.77771	−	3.55879i	−0.703815	−	0.256168i	−0.669039	+	0.743228i	$0.733294\pi$
$194$	9.21492	+	3.35396i	0.661593	+	0.240800i
$195$	−13.8355	−	20.0155i	−0.990783	−	1.43334i
$196$	−0.0806464	+	0.0913776i	−0.00576046	+	0.00652697i
$197$	12.2795	+	7.08959i	0.874880	+	0.505112i	0.868967	−	0.494870i	$-0.164784\pi$
$197$	12.2795	+	7.08959i	0.874880	+	0.505112i	0.00591309	+	0.999983i	$0.498118\pi$
$198$	5.52770	−	14.6346i	0.392837	−	1.04003i
$199$	17.4224	+	10.0588i	1.23504	+	0.713050i	0.968076	−	0.250657i	$-0.0806466\pi$
$199$	17.4224	+	10.0588i	1.23504	+	0.713050i	0.266963	+	0.963707i	$0.413980\pi$
$200$	−0.531277	−	1.45967i	−0.0375670	−	0.103214i
$201$	−18.1403	−	1.69757i	−1.27952	−	0.119737i
$202$	−1.79057	+	4.91954i	−0.125984	+	0.346138i
$203$	−9.42645	−	6.77738i	−0.661607	−	0.475679i
$204$	0.0407286	+	0.0887387i	0.00285158	+	0.00621295i
$205$	18.0371	+	15.1349i	1.25976	+	1.05707i
$206$	4.36933	−	7.56790i	0.304425	−	0.527280i
$207$	−1.96572	−	0.742482i	−0.136627	−	0.0516061i
$208$	22.8582	−	13.1972i	1.58493	−	0.915058i
$209$	15.1144	+	12.6825i	1.04548	+	0.877264i
$210$	−2.61243	+	13.3634i	−0.180275	+	0.922161i
$211$	0.582787	+	3.30515i	0.0401207	+	0.227536i	0.998275	−	0.0587176i	$-0.0187011\pi$
$211$	0.582787	+	3.30515i	0.0401207	+	0.227536i	−0.958154	+	0.286254i	$0.907590\pi$
$212$	−0.0151729	+	0.00267538i	−0.00104208	+	0.000183746i
$213$	−1.93907	−	7.41563i	−0.132863	−	0.508111i
$214$	−3.08210	−	2.58619i	−0.210688	−	0.176788i
$215$	7.84567	−	13.5891i	0.535070	−	0.926768i
$216$	14.3242	−	3.56120i	0.974636	−	0.242309i
$217$	−0.980985	−	3.85283i	−0.0665936	−	0.261547i
$218$	−2.71314	−	7.45430i	−0.183757	−	0.504869i
$219$	−5.11340	−	1.40330i	−0.345532	−	0.0948260i
$220$	−0.0465380	+	0.127862i	−0.00313759	+	0.00862047i
$221$	−13.8545	−	16.5112i	−0.931956	−	1.11066i
$222$	6.78259	−	14.3188i	0.455217	−	0.961015i
$223$	−6.45098	+	7.68798i	−0.431990	+	0.514825i	−0.937495	−	0.347998i	$-0.886862\pi$
$223$	−6.45098	+	7.68798i	−0.431990	+	0.514825i	0.505506	+	0.862823i	$0.331306\pi$
$224$	0.250834	+	0.0705780i	0.0167595	+	0.00471569i
$225$	0.542421	+	1.54825i	0.0361614	+	0.103216i
$226$	−12.9303			−0.860113
$227$	−16.6785	+	6.07047i	−1.10699	+	0.402911i	−0.829889	−	0.557929i	$-0.811596\pi$
$227$	−16.6785	+	6.07047i	−1.10699	+	0.402911i	−0.277102	+	0.960841i	$0.589374\pi$
$228$	−0.0149693	+	0.159963i	−0.000991367	+	0.0105938i
$229$	−8.39720	−	10.0074i	−0.554903	−	0.661307i	0.413557	−	0.910478i	$-0.364286\pi$
$229$	−8.39720	−	10.0074i	−0.554903	−	0.661307i	−0.968459	+	0.249171i	$0.919842\pi$
$230$	−1.95568	−	0.711808i	−0.128953	−	0.0469352i
$231$	−13.2005	+	10.6662i	−0.868531	+	0.701784i
$232$	−2.16452	+	12.2756i	−0.142108	+	0.805934i
$233$			18.9719i			1.24289i	0.783457	+	0.621446i	$0.213455\pi$
$233$			18.9719i			1.24289i	−0.783457	+	0.621446i	$0.786545\pi$
$234$	−24.5209	+	13.7648i	−1.60298	+	0.899835i
$235$	−12.6525			−0.825355
$236$	−0.102004	+	0.0371266i	−0.00663992	+	0.00241674i
$237$	−14.9013	−	7.05853i	−0.967946	−	0.458501i
$238$	−1.20115	+	12.0017i	−0.0778589	+	0.777958i
$239$	−13.6545	−	16.2728i	−0.883236	−	1.05260i	−0.998244	−	0.0592349i	$-0.981134\pi$
$239$	−13.6545	−	16.2728i	−0.883236	−	1.05260i	0.115008	−	0.993365i	$-0.463311\pi$
$240$	14.0205	−	3.66613i	0.905018	−	0.236648i
$241$	−7.57437	+	9.02679i	−0.487908	+	0.581466i	−0.952684	−	0.303962i	$-0.901690\pi$
$241$	−7.57437	+	9.02679i	−0.487908	+	0.581466i	0.464776	+	0.885428i	$0.346135\pi$
$242$	3.31104	−	1.91163i	0.212842	−	0.122884i
$243$	−15.1723	+	3.57797i	−0.973302	+	0.229527i
$244$		−	0.129488i		−	0.00828962i
$245$	9.77462	−	11.0753i	0.624477	−	0.707573i
$246$	19.3574	−	19.1249i	1.23419	−	1.21936i
$247$	−6.15863	−	34.9274i	−0.391865	−	2.22237i
$248$	−3.26990	+	2.74377i	−0.207639	+	0.174230i
$249$	1.71051	+	21.0126i	0.108399	+	1.33162i
$250$	5.63700	+	15.4875i	0.356515	+	0.979517i
$251$	−13.6923	+	23.7157i	−0.864248	+	1.49692i	0.00354445	+	0.999994i	$0.498872\pi$
$251$	−13.6923	+	23.7157i	−0.864248	+	1.49692i	−0.867792	+	0.496927i	$0.834462\pi$
$252$	−0.132566	−	0.0390353i	−0.00835090	−	0.00245899i
$253$	−1.29698	−	2.24643i	−0.0815404	−	0.141232i
$254$	1.73465	−	2.06728i	0.108842	−	0.129713i
$255$	−4.93645	−	10.7554i	−0.309132	−	0.673531i
$256$	−0.0725551	−	0.411480i	−0.00453469	−	0.0257175i
$257$	12.2349	−	10.2663i	0.763190	−	0.640392i	−0.175765	−	0.984432i	$-0.556240\pi$
$257$	12.2349	−	10.2663i	0.763190	−	0.640392i	0.938955	+	0.344040i	$0.111796\pi$
$258$	−14.7917	−	10.4910i	−0.920891	−	0.653141i
$259$	−14.2019	+	9.68236i	−0.882463	+	0.601633i
$260$	0.211819	−	0.122294i	0.0131365	−	0.00758434i
$261$	2.44246	−	12.9359i	0.151185	−	0.800711i
$262$			12.2606i			0.757463i
$263$	28.4125	+	5.00989i	1.75199	+	0.308923i	0.955338	−	0.295514i	$-0.0954910\pi$
$263$	28.4125	+	5.00989i	1.75199	+	0.308923i	0.796653	+	0.604437i	$0.206602\pi$
$264$	16.4671	+	7.80019i	1.01348	+	0.480068i
$265$	1.83900	−	0.324266i	0.112969	−	0.0199195i
$266$	−11.5859	+	16.1145i	−0.710378	+	0.988043i
$267$	7.30329	−	1.90970i	0.446954	−	0.116871i
$268$	0.0318030	−	0.180364i	0.00194268	−	0.0110175i
$269$	−4.08105	−	7.06859i	−0.248826	−	0.430979i	0.714374	−	0.699764i	$-0.246711\pi$
$269$	−4.08105	−	7.06859i	−0.248826	−	0.430979i	−0.963200	+	0.268784i	$0.913378\pi$
$270$	−14.9834	+	3.72509i	−0.911858	+	0.226702i
$271$	10.1461	+	5.85783i	0.616329	+	0.355838i	0.775438	−	0.631423i	$-0.217529\pi$
$271$	10.1461	+	5.85783i	0.616329	+	0.355838i	−0.159109	+	0.987261i	$0.550862\pi$
$272$	12.0631	−	4.39061i	0.731432	−	0.266220i
$273$	30.5011	+	0.565073i	1.84601	+	0.0341998i
$274$	7.52564	−	6.31476i	0.454640	−	0.381488i
$275$	−0.692649	+	1.90304i	−0.0417683	+	0.114757i
$276$	0.00904214	−	0.0190890i	0.000544273	−	0.00114902i
$277$	−1.65265	+	9.37262i	−0.0992979	+	0.563146i	0.894047	+	0.447972i	$0.147854\pi$
$277$	−1.65265	+	9.37262i	−0.0992979	+	0.563146i	−0.993345	+	0.115174i	$0.963257\pi$
$278$	7.40592	+	12.8274i	0.444178	+	0.769339i
$279$	3.48815	−	2.85580i	0.208830	−	0.170972i
$280$	−15.2668	−	4.29568i	−0.912367	−	0.256716i
$281$	20.5328	+	3.62048i	1.22488	+	0.215980i	0.748426	−	0.663218i	$-0.230810\pi$
$281$	20.5328	+	3.62048i	1.22488	+	0.215980i	0.476457	+	0.879198i	$0.341921\pi$
$282$	−1.36241	+	14.5588i	−0.0811301	+	0.866961i
$283$	1.45014	−	0.255698i	0.0862017	−	0.0151997i	−0.130381	−	0.991464i	$-0.541620\pi$
$283$	1.45014	−	0.255698i	0.0862017	−	0.0151997i	0.216583	+	0.976264i	$0.430509\pi$
$284$	0.0758787	−	0.0133795i	0.00450258	−	0.000793925i
$285$	1.81433	−	19.3881i	0.107472	−	1.14845i
$286$	−34.1863	−	6.02796i	−2.02148	−	0.356441i
$287$	−28.6080	+	7.28400i	−1.68868	+	0.429961i
$288$	0.0477871	+	0.291573i	0.00281588	+	0.0171811i
$289$	3.25849	+	5.64387i	0.191676	+	0.331992i
$290$	2.26413	−	12.8405i	0.132954	−	0.754022i
$291$	5.16394	−	10.9017i	0.302716	−	0.639067i
$292$	0.0182301	−	0.0500867i	0.00106683	−	0.00293110i
$293$	4.11874	−	3.45603i	0.240619	−	0.201904i	−0.514501	−	0.857490i	$-0.672023\pi$
$293$	4.11874	−	3.45603i	0.240619	−	0.201904i	0.755120	+	0.655586i	$0.227578\pi$
$294$	−11.6914	−	12.4399i	−0.681858	−	0.725510i
$295$	12.3633	−	4.49987i	0.719818	−	0.261992i
$296$	15.9819	+	9.22716i	0.928930	+	0.536318i
$297$	−17.2903	−	8.44742i	−1.00328	−	0.490169i
$298$	7.83400	+	13.5689i	0.453811	+	0.786024i
$299$	−0.809676	+	4.59190i	−0.0468248	+	0.265557i
$300$	−0.0159543	+	0.00417179i	−0.000921121	+	0.000240859i
$301$	8.09104	+	17.9323i	0.466360	+	1.03360i
$302$	−28.0016	+	4.93743i	−1.61131	+	0.284117i
$303$	5.82003	+	2.75686i	0.334352	+	0.158377i
$304$	20.8024	+	3.66803i	1.19310	+	0.210376i
$305$			15.6944i			0.898658i
$306$	−12.9075	+	4.52207i	−0.737870	+	0.258510i
$307$	−6.76941	+	3.90832i	−0.386351	+	0.223060i	−0.680578	−	0.732676i	$-0.738271\pi$
$307$	−6.76941	+	3.90832i	−0.386351	+	0.223060i	0.294227	+	0.955736i	$0.404938\pi$
$308$	−0.0960984	−	0.140955i	−0.00547571	−	0.00803167i
$309$	−8.76807	−	6.21875i	−0.498798	−	0.353772i
$310$	3.42038	−	2.87004i	0.194265	−	0.163007i
$311$	2.15372	+	12.2144i	0.122126	+	0.692612i	0.982973	+	0.183749i	$0.0588232\pi$
$311$	2.15372	+	12.2144i	0.122126	+	0.692612i	−0.860847	+	0.508864i	$0.830066\pi$
$312$	−13.6625	−	29.7675i	−0.773485	−	1.68525i
$313$	−4.55606	+	5.42970i	−0.257524	+	0.306905i	−0.879279	−	0.476307i	$-0.841975\pi$
$313$	−4.55606	+	5.42970i	−0.257524	+	0.306905i	0.621756	+	0.783211i	$0.286420\pi$
$314$	3.44439	+	5.96587i	0.194378	+	0.336673i
$315$	16.0675	+	4.73121i	0.905302	+	0.266574i
$316$	0.0828727	−	0.143540i	0.00466196	−	0.00807475i
$317$	−5.78906	−	15.9053i	−0.325146	−	0.893332i	−0.989321	−	0.145754i	$-0.953439\pi$
$317$	−5.78906	−	15.9053i	−0.325146	−	0.893332i	0.664175	−	0.747578i	$-0.268783\pi$
$318$	−0.175100	−	2.15099i	−0.00981909	−	0.120622i
$319$	12.4491	−	10.4460i	0.697015	−	0.584865i
$320$	2.95660	+	16.7677i	0.165279	+	0.937345i
$321$	−3.52071	+	3.47842i	−0.196507	+	0.194147i
$322$	2.15594	−	1.46984i	0.120146	−	0.0819111i
$323$		−	17.2495i		−	0.959788i
$324$	−0.0234734	−	0.154929i	−0.00130408	−	0.00860718i
$325$	3.15261	−	1.82016i	0.174875	−	0.100964i
$326$	8.48274	−	10.1093i	0.469815	−	0.559904i
$327$	−9.44069	+	2.46859i	−0.522071	+	0.136513i
$328$	20.3730	+	24.2797i	1.12491	+	1.34062i
$329$	9.26022	−	12.8798i	0.510533	−	0.710084i
$330$	−17.2249	−	8.15915i	−0.948199	−	0.449146i
$331$	−13.5894	+	4.94613i	−0.746940	+	0.271864i	−0.687318	−	0.726357i	$-0.741212\pi$
$331$	−13.5894	+	4.94613i	−0.746940	+	0.271864i	−0.0596225	+	0.998221i	$0.518990\pi$
$332$	−0.211921			−0.0116306
$333$	−16.7597	−	9.94816i	−0.918427	−	0.545156i
$334$		−	12.1277i		−	0.663599i
$335$	−3.85463	+	21.8607i	−0.210601	+	1.19438i
$336$	−6.52947	+	16.9556i	−0.356212	+	0.925002i
$337$	−14.9144	−	5.42839i	−0.812438	−	0.295703i	−0.0978073	−	0.995205i	$-0.531183\pi$
$337$	−14.9144	−	5.42839i	−0.812438	−	0.295703i	−0.714630	+	0.699502i	$0.753405\pi$
$338$	28.3434	+	33.7784i	1.54168	+	1.83730i
$339$	−1.48198	+	15.8366i	−0.0804902	+	0.860123i
$340$	0.111785	−	0.0406863i	0.00606238	−	0.00220653i
$341$	5.56510			0.301367
$342$	−22.1138	−	4.17538i	−1.19578	−	0.225779i
$343$	4.12028	+	18.0561i	0.222474	+	0.974939i
$344$	13.5770	−	16.1804i	0.732023	−	0.872391i
$345$	−1.09594	+	2.31365i	−0.0590034	+	0.124563i
$346$	−7.66921	−	9.13981i	−0.412299	−	0.491359i
$347$	1.75821	−	4.83065i	0.0943858	−	0.259323i	−0.883511	−	0.468410i	$-0.844827\pi$
$347$	1.75821	−	4.83065i	0.0943858	−	0.259323i	0.977897	+	0.209087i	$0.0670492\pi$
$348$	0.127613	+	0.0350214i	0.00684075	+	0.00187734i
$349$	−3.81124	−	10.4713i	−0.204011	−	0.560516i	0.794921	−	0.606713i	$-0.207512\pi$
$349$	−3.81124	−	10.4713i	−0.204011	−	0.560516i	−0.998932	+	0.0461967i	$0.985290\pi$
$350$	−1.96101	−	0.551775i	−0.104820	−	0.0294936i
$351$	14.0482	+	31.6099i	0.749837	+	1.68721i
$352$	−0.182371	+	0.315875i	−0.00972038	+	0.0168362i
$353$	2.35970	+	1.98003i	0.125594	+	0.105386i	0.703421	−	0.710773i	$-0.251655\pi$
$353$	2.35970	+	1.98003i	0.125594	+	0.105386i	−0.577827	+	0.816159i	$0.696099\pi$
$354$	−3.84658	−	14.7106i	−0.204443	−	0.781858i
$355$	−9.19676	+	1.62164i	−0.488113	+	0.0860676i
$356$	0.0131768	+	0.0747292i	0.000698368	+	0.00396064i
$357$	14.5616	+	2.84667i	0.770681	+	0.150662i
$358$	5.21599	+	4.37674i	0.275674	+	0.231318i
$359$	18.9719	−	10.9534i	1.00130	−	0.578099i	0.0926653	−	0.995697i	$-0.470461\pi$
$359$	18.9719	−	10.9534i	1.00130	−	0.578099i	0.908632	+	0.417598i	$0.137128\pi$
$360$	−2.90853	−	17.7464i	−0.153293	−	0.935318i
$361$	4.69176	−	8.12637i	0.246935	−	0.427704i
$362$	−4.92303	−	4.13091i	−0.258749	−	0.217116i
$363$	−1.96180	−	4.27433i	−0.102968	−	0.224344i
$364$	−0.0305378	+	0.305130i	−0.00160062	+	0.0159932i
$365$	−2.20955	+	6.07068i	−0.115653	+	0.317754i
$366$	18.0590	+	1.68996i	0.943959	+	0.0883355i
$367$	2.26195	+	6.21467i	0.118073	+	0.324403i	0.984624	−	0.174685i	$-0.0558907\pi$
$367$	2.26195	+	6.21467i	0.118073	+	0.324403i	−0.866551	+	0.499088i	$0.833668\pi$
$368$	−2.40503	−	1.38854i	−0.125371	−	0.0723829i
$369$	−21.2048	−	25.9002i	−1.10388	−	1.34831i
$370$	−16.7174	−	9.65179i	−0.869096	−	0.501773i
$371$	−1.01586	+	2.10937i	−0.0527408	+	0.109513i
$372$	0.0257674	+	0.0372769i	0.00133598	+	0.00193272i
$373$	−23.1460	−	8.42445i	−1.19845	−	0.436201i	−0.335769	−	0.941944i	$-0.608996\pi$
$373$	−23.1460	−	8.42445i	−1.19845	−	0.436201i	−0.862684	+	0.505743i	$0.831218\pi$
$374$	−15.8653	−	5.77449i	−0.820375	−	0.298592i
$375$	19.6146	−	5.12890i	1.01289	−	0.264855i
$376$	−16.7727	−	2.95748i	−0.864986	−	0.152520i
$377$	−29.2121			−1.50450
$378$	7.17418	−	17.9789i	0.369000	−	0.924734i
$379$	2.06704			0.106176			0.0530882	−	0.998590i	$-0.483094\pi$
$379$	2.06704			0.106176			0.0530882	+	0.998590i	$0.483094\pi$
$380$	0.192769	+	0.0339905i	0.00988887	+	0.00174367i
$381$	−2.33311	−	2.36147i	−0.119529	−	0.120982i
$382$	13.6836	+	4.98041i	0.700112	+	0.254820i
$383$	6.49822	+	2.36516i	0.332044	+	0.120854i	0.502662	−	0.864483i	$-0.332354\pi$
$383$	6.49822	+	2.36516i	0.332044	+	0.120854i	−0.170618	+	0.985337i	$0.554576\pi$
$384$	19.2724	−	1.56885i	0.983490	−	0.0800600i
$385$	11.6475	+	17.0843i	0.593609	+	0.870695i
$386$	12.6881	+	7.32550i	0.645810	+	0.372858i
$387$	−14.5443	+	16.9139i	−0.739327	+	0.859781i
$388$	0.105012	+	0.0606288i	0.00533118	+	0.00307796i
$389$	−4.62127	−	12.6968i	−0.234308	−	0.643755i	−1.00000		0.000547677i	$-0.999826\pi$
$389$	−4.62127	−	12.6968i	−0.234308	−	0.643755i	0.765692	−	0.643207i	$-0.222397\pi$
$390$	14.2912	+	31.1374i	0.723663	+	1.57670i
$391$	−0.775631	+	2.13103i	−0.0392254	+	0.107771i
$392$	15.5465	−	12.3971i	0.785217	−	0.626149i
$393$	15.0163	+	1.40522i	0.757473	+	0.0708841i
$394$	−15.2940	−	12.8332i	−0.770501	−	0.646527i
$395$	−10.0445	+	17.3975i	−0.505392	+	0.875364i
$396$	0.0987364	−	0.166342i	0.00496169	−	0.00835900i
$397$	18.6484	−	10.7666i	0.935934	−	0.540362i	0.0472507	−	0.998883i	$-0.484954\pi$
$397$	18.6484	−	10.7666i	0.935934	−	0.540362i	0.888683	+	0.458521i	$0.151621\pi$
$398$	−21.6994	−	18.2079i	−1.08769	−	0.912681i
$399$	18.4085	+	16.0369i	0.921577	+	0.802849i
$400$	0.376494	+	2.13521i	0.0188247	+	0.106760i
$401$	26.0547	−	4.59414i	1.30111	−	0.229420i	0.520188	−	0.854052i	$-0.325862\pi$
$401$	26.0547	−	4.59414i	1.30111	−	0.229420i	0.780920	+	0.624631i	$0.214751\pi$
$402$	24.7393	+	6.78933i	1.23388	+	0.338621i
$403$	−7.66311	−	6.43011i	−0.381727	−	0.320307i
$404$	−0.0323677	+	0.0560625i	−0.00161035	+	0.00278921i
$405$	2.84505	+	18.7780i	0.141372	+	0.933084i
$406$	11.4141	+	11.7027i	0.566473	+	0.580794i
$407$	−8.22890	−	22.6087i	−0.407891	−	1.12067i
$408$	−4.02994	−	15.4118i	−0.199512	−	0.762997i
$409$	−8.57817	+	23.5683i	−0.424163	+	1.16538i	0.525140	+	0.851016i	$0.324013\pi$
$409$	−8.57817	+	23.5683i	−0.424163	+	1.16538i	−0.949303	+	0.314362i	$0.898209\pi$
$410$	−21.3106	−	25.3970i	−1.05246	−	1.25427i
$411$	−6.87153	−	9.94085i	−0.338947	−	0.490346i
$412$	0.0694568	−	0.0827754i	0.00342189	−	0.00407805i
$413$	−4.46788	+	15.8788i	−0.219850	+	0.781345i
$414$	2.54423	+	1.51019i	0.125042	+	0.0742219i
$415$	25.6855			1.26085
$416$	0.616097	−	0.224241i	0.0302066	−	0.0109943i
$417$	16.5593	−	7.60029i	0.810914	−	0.372188i
$418$	−17.8575	−	21.2817i	−0.873437	−	1.04092i
$419$	−22.3814	−	8.14616i	−1.09340	−	0.397966i	−0.268522	−	0.963273i	$-0.586535\pi$
$419$	−22.3814	−	8.14616i	−1.09340	−	0.397966i	−0.824880	+	0.565307i	$0.808758\pi$
$420$	−0.0605065	+	0.157122i	−0.00295242	+	0.00766676i
$421$	−1.34235	+	7.61285i	−0.0654222	+	0.371027i	0.934466	+	0.356053i	$0.115878\pi$
$421$	−1.34235	+	7.61285i	−0.0654222	+	0.371027i	−0.999888	+	0.0149744i	$0.995233\pi$
$422$		−	4.72559i		−	0.230038i
$423$	17.6748	+	3.33724i	0.859380	+	0.162262i
$424$	2.51366			0.122074
$425$	1.66375	−	0.605555i	0.0807037	−	0.0293737i
$426$	0.875664	+	10.7570i	0.0424261	+	0.521179i
$427$	−15.9763	−	11.4866i	−0.773149	−	0.555875i
$428$	−0.0319789	−	0.0381110i	−0.00154576	−	0.00184216i
$429$	−11.3010	+	41.1791i	−0.545617	+	1.98814i
$430$	−14.2018	+	16.9251i	−0.684872	+	0.816199i
$431$	−4.73254	+	2.73233i	−0.227959	+	0.131612i	−0.609630	−	0.792686i	$-0.708682\pi$
$431$	−4.73254	+	2.73233i	−0.227959	+	0.131612i	0.381671	+	0.924298i	$0.375349\pi$
$432$	−20.5529	+	1.42333i	−0.988850	+	0.0684800i
$433$		−	35.5423i		−	1.70805i	−0.520229	−	0.854027i	$-0.674154\pi$
$433$		−	35.5423i		−	1.70805i	0.520229	−	0.854027i	$-0.325846\pi$
$434$	0.418253	+	5.58239i	0.0200768	+	0.267963i
$435$	−15.4671	−	4.24471i	−0.741589	−	0.203518i
$436$	−0.0170331	−	0.0965996i	−0.000815738	−	0.00462628i
$437$	−2.85856	+	2.39862i	−0.136744	+	0.114741i
$438$	6.74740	+	3.19614i	0.322403	+	0.152717i
$439$	−1.38811	−	3.81379i	−0.0662506	−	0.182022i	0.902150	−	0.431423i	$-0.141988\pi$
$439$	−1.38811	−	3.81379i	−0.0662506	−	0.182022i	−0.968400	+	0.249401i	$0.919766\pi$
$440$	11.0999	−	19.2255i	0.529165	−	0.916541i
$441$	−16.5759	+	12.8934i	−0.789328	+	0.613972i
$442$	15.1744	+	26.2828i	0.721771	+	1.25014i
$443$	5.32766	−	6.34926i	0.253125	−	0.301662i	−0.624486	−	0.781036i	$-0.714692\pi$
$443$	5.32766	−	6.34926i	0.253125	−	0.301662i	0.877611	+	0.479373i	$0.159136\pi$
$444$	0.113340	−	0.159802i	0.00537886	−	0.00758388i
$445$	−1.59707	−	9.05744i	−0.0757084	−	0.429364i
$446$	10.8250	−	9.08327i	0.512579	−	0.430105i
$447$	17.5165	−	8.03960i	0.828502	−	0.380260i
$448$	−19.2329	−	9.26244i	−0.908668	−	0.437609i
$449$	25.1276	−	14.5074i	1.18585	−	0.684648i	0.228486	−	0.973547i	$-0.426623\pi$
$449$	25.1276	−	14.5074i	1.18585	−	0.684648i	0.957359	+	0.288899i	$0.0932893\pi$
$450$	−0.373597	−	2.27951i	−0.0176115	−	0.107457i
$451$		−	41.3219i		−	1.94577i
$452$	−0.157458	−	0.0277641i	−0.00740619	−	0.00130591i
$453$	2.83783	+	34.8611i	0.133333	+	1.63792i
$454$	24.6115	−	4.33968i	1.15508	−	0.203671i
$455$	3.70129	−	36.9828i	0.173519	−	1.73378i
$456$	6.93708	−	25.2777i	0.324858	−	1.18373i
$457$	−1.13908	+	6.46004i	−0.0532839	+	0.302188i	−0.999790	−	0.0204982i	$-0.993475\pi$
$457$	−1.13908	+	6.46004i	−0.0532839	+	0.302188i	0.946506	+	0.322686i	$0.104586\pi$
$458$	9.19715	+	15.9299i	0.429755	+	0.744357i
$459$	4.05909	+	16.3268i	0.189462	+	0.762071i
$460$	−0.0222866	−	0.0128672i	−0.00103912	−	0.000599936i
$461$	20.7893	−	7.56669i	0.968255	−	0.352416i	0.190992	−	0.981592i	$-0.438830\pi$
$461$	20.7893	−	7.56669i	0.968255	−	0.352416i	0.777263	+	0.629176i	$0.216607\pi$
$462$	20.9125	−	11.5627i	0.972936	−	0.537946i
$463$	12.6417	−	10.6077i	0.587511	−	0.492980i	−0.299893	−	0.953973i	$-0.596951\pi$
$463$	12.6417	−	10.6077i	0.587511	−	0.492980i	0.887404	+	0.460993i	$0.152507\pi$
$464$	5.95062	−	16.3492i	0.276251	−	0.758992i
$465$	−3.12309	−	4.51809i	−0.144830	−	0.209521i
$466$	4.63872	−	26.3075i	0.214884	−	1.21867i
$467$	0.713130	+	1.23518i	0.0329997	+	0.0571572i	0.882054	−	0.471149i	$-0.156161\pi$
$467$	0.713130	+	1.23518i	0.0329997	+	0.0571572i	−0.849054	+	0.528306i	$0.822827\pi$
$468$	−0.328157	+	0.114968i	−0.0151691	+	0.00531441i
$469$	−19.4322	−	19.9235i	−0.897298	−	0.919983i
$470$	17.5446	+	3.09358i	0.809271	+	0.142696i
$471$	7.70152	−	3.53479i	0.354867	−	0.162875i
$472$	17.4412	−	3.07535i	0.802796	−	0.141555i
$473$	−27.1194	+	4.78188i	−1.24695	+	0.219871i
$474$	18.9372	+	13.4312i	0.869812	+	0.616914i
$475$	2.86909	+	0.505897i	0.131643	+	0.0232122i
$476$	−0.0403971	+	0.143571i	−0.00185160	+	0.00658056i
$477$	−2.65452	−	0.0320766i	−0.121542	−	0.00146868i
$478$	14.9553	+	25.9033i	0.684038	+	1.18479i
$479$	4.17371	−	23.6703i	0.190702	−	1.08152i	−0.727706	−	0.685889i	$-0.759414\pi$
$479$	4.17371	−	23.6703i	0.190702	−	1.08152i	0.918408	−	0.395635i	$-0.129475\pi$
$480$	0.358792	−	0.0292071i	0.0163765	−	0.00133312i
$481$	−14.7918	+	40.6400i	−0.674446	+	1.85303i
$482$	12.7101	−	10.6651i	0.578930	−	0.485780i
$483$	−1.55311	−	2.80897i	−0.0706688	−	0.127812i
$484$	0.0444246	−	0.0161692i	0.00201930	−	0.000734965i
$485$	−12.7278	−	7.34842i	−0.577941	−	0.333674i
$486$	21.9135	−	1.25171i	0.994017	−	0.0567788i
$487$	17.7620	+	30.7647i	0.804874	+	1.39408i	0.916376	+	0.400319i	$0.131101\pi$
$487$	17.7620	+	30.7647i	0.804874	+	1.39408i	−0.111501	+	0.993764i	$0.535566\pi$
$488$	−3.66852	+	20.8052i	−0.166066	+	0.941808i
$489$	−11.4093	−	11.5480i	−0.515945	−	0.522217i
$490$	−16.2620	+	12.9676i	−0.734640	+	0.585818i
$491$	−30.5498	+	5.38675i	−1.37869	+	0.243101i	−0.813360	−	0.581761i	$-0.802364\pi$
$491$	−30.5498	+	5.38675i	−1.37869	+	0.243101i	−0.565334	+	0.824862i	$0.691253\pi$
$492$	0.276788	−	0.191328i	0.0124786	−	0.00862572i
$493$	−13.9919	−	2.46714i	−0.630162	−	0.111115i
$494$			49.9379i			2.24681i
$495$	−11.9672	+	20.1612i	−0.537885	+	0.906179i
$496$	5.15977	−	2.97899i	0.231681	−	0.133761i
$497$	5.08026	−	10.5488i	0.227881	−	0.473180i
$498$	2.76579	−	29.5554i	0.123938	−	1.32441i
$499$	27.8976	−	23.4088i	1.24887	−	1.04792i	0.252089	−	0.967704i	$-0.418883\pi$
$499$	27.8976	−	23.4088i	1.24887	−	1.04792i	0.996777	−	0.0802188i	$-0.0255619\pi$
$500$	0.0353891	+	0.200701i	0.00158265	+	0.00897564i
$501$	−14.8535	−	1.38999i	−0.663607	−	0.0621002i
$502$	24.7850	−	29.5376i	1.10621	−	1.31833i
$503$	9.30116	+	16.1101i	0.414718	+	0.718313i	0.995399	−	0.0958185i	$-0.0305468\pi$
$503$	9.30116	+	16.1101i	0.414718	+	0.718313i	−0.580681	+	0.814131i	$0.697213\pi$
$504$	20.1939	+	10.0277i	0.899509	+	0.446667i
$505$	3.92308	−	6.79497i	0.174575	−	0.302372i
$506$	1.24920	+	3.43214i	0.0555336	+	0.152577i
$507$	44.6189	−	30.8424i	1.98159	−	1.36976i
$508$	0.0255624	−	0.0214494i	0.00113415	−	0.000951665i
$509$	0.776316	+	4.40271i	0.0344096	+	0.195147i	0.997167	−	0.0752205i	$-0.0239661\pi$
$509$	0.776316	+	4.40271i	0.0344096	+	0.195147i	−0.962757	+	0.270367i	$0.912855\pi$
$510$	4.21540	+	16.1210i	0.186661	+	0.713851i
$511$	−4.56259	−	6.69232i	−0.201837	−	0.296051i
$512$			22.9158i			1.01274i
$513$	−7.64837	+	26.6056i	−0.337684	+	1.17467i
$514$	−19.4757	+	11.2443i	−0.859034	+	0.495964i
$515$	−8.41841	+	10.0327i	−0.370959	+	0.442092i
$516$	−0.157598	−	0.159514i	−0.00693787	−	0.00702221i
$517$	14.2729	+	17.0097i	0.627719	+	0.748087i
$518$	22.0605	−	9.95365i	0.969283	−	0.437338i
$519$	−12.0731	+	8.34540i	−0.529948	+	0.366322i
$520$	−37.4983	+	13.6483i	−1.64441	+	0.598516i
$521$	−34.6679			−1.51883			−0.759415	−	0.650607i	$-0.774515\pi$
$521$	−34.6679			−1.51883			−0.759415	+	0.650607i	$0.774515\pi$
$522$	−6.54972	+	17.3404i	−0.286674	+	0.758968i
$523$		−	25.7209i		−	1.12470i	−0.826901	−	0.562348i	$-0.809898\pi$
$523$		−	25.7209i		−	1.12470i	0.826901	−	0.562348i	$-0.190102\pi$
$524$	−0.0263260	+	0.149302i	−0.00115006	+	0.00652231i
$525$	−0.900549	+	2.33852i	−0.0393032	+	0.102061i
$526$	−38.1734	−	13.8940i	−1.66444	−	0.605806i
$527$	−3.12738	−	3.72707i	−0.136231	−	0.162354i
$528$	−20.7448	−	14.7132i	−0.902799	−	0.640310i
$529$	−21.1519	+	7.69867i	−0.919649	+	0.334725i
$530$	−2.62934			−0.114211
$531$	−18.4578	+	3.02512i	−0.800999	+	0.131279i
$532$	−0.175687	+	0.171355i	−0.00761702	+	0.00742919i
$533$	−47.7448	+	56.9001i	−2.06806	+	2.46462i
$534$	−10.5941	+	0.862399i	−0.458450	+	0.0373196i
$535$	3.87595	+	4.61918i	0.167572	+	0.199704i
$536$	−10.2198	+	28.0786i	−0.441426	+	1.21281i
$537$	5.95827	−	5.88671i	0.257118	−	0.254030i
$538$	3.93070	+	10.7995i	0.169465	+	0.465600i
$539$	−25.9158	−	0.647128i	−1.11627	−	0.0278738i
$540$	−0.190457	+	0.0131895i	−0.00819596	+	0.000567587i
$541$	13.1658	−	22.8039i	0.566044	−	0.980416i	−0.430908	−	0.902396i	$-0.641807\pi$
$541$	13.1658	−	22.8039i	0.566044	−	0.980416i	0.996952	−	0.0780204i	$-0.0248599\pi$
$542$	−12.6368	−	10.6035i	−0.542797	−	0.455461i
$543$	−5.62361	+	5.55607i	−0.241332	+	0.238434i
$544$	0.314034	−	0.0553727i	0.0134641	−	0.00237408i
$545$	2.06447	+	11.7082i	0.0884323	+	0.501524i
$546$	−42.1563	−	8.24122i	−1.80412	−	0.352692i
$547$	13.7395	+	11.5288i	0.587459	+	0.492937i	0.887387	−	0.461025i	$-0.152518\pi$
$547$	13.7395	+	11.5288i	0.587459	+	0.492937i	−0.299928	+	0.953962i	$0.596963\pi$
$548$	0.105202	−	0.0607383i	0.00449400	−	0.00259461i
$549$	4.13959	−	21.9243i	0.176673	−	0.935704i
$550$	1.42576	−	2.46950i	0.0607948	−	0.105300i
$551$	−17.9089	−	15.0273i	−0.762944	−	0.640186i
$552$	−1.99364	+	2.81091i	−0.0848549	+	0.119640i
$553$	−10.3586	−	22.9580i	−0.440492	−	0.976273i
$554$	4.58329	−	12.5925i	0.194725	−	0.535004i
$555$	−13.7372	+	19.3686i	−0.583110	+	0.822150i
$556$	0.0626418	+	0.172107i	0.00265660	+	0.00729896i
$557$	0.993267	+	0.573463i	0.0420861	+	0.0242984i	0.520895	−	0.853621i	$-0.325598\pi$
$557$	0.993267	+	0.573463i	0.0420861	+	0.0242984i	−0.478809	+	0.877919i	$0.658931\pi$
$558$	−5.53511	+	3.10713i	−0.234320	+	0.131535i
$559$	42.8684	+	24.7501i	1.81314	+	1.04682i
$560$	19.9443	+	9.60507i	0.842801	+	0.405888i
$561$	−8.89073	+	18.7693i	−0.375367	+	0.792442i
$562$	−27.5866	−	10.0407i	−1.16367	−	0.423542i
$563$	−8.48848	−	3.08955i	−0.357747	−	0.130209i	0.156893	−	0.987616i	$-0.449852\pi$
$563$	−8.48848	−	3.08955i	−0.357747	−	0.130209i	−0.514640	+	0.857406i	$0.672074\pi$
$564$	−0.0478512	+	0.174362i	−0.00201490	+	0.00734198i
$565$	19.0844	+	3.36510i	0.802888	+	0.141571i
$566$	−2.07336			−0.0871497
$567$	−21.1976	−	10.8473i	−0.890214	−	0.455542i
$568$	−12.5707			−0.527455
$569$	−42.2332	−	7.44685i	−1.77051	−	0.312188i	−0.809172	−	0.587572i	$-0.800084\pi$
$569$	−42.2332	−	7.44685i	−1.77051	−	0.312188i	−0.961334	+	0.275384i	$0.911195\pi$
$570$	−7.25632	+	26.4409i	−0.303934	+	1.10749i
$571$	31.1144	+	11.3247i	1.30210	+	0.473925i	0.897680	−	0.440648i	$-0.145251\pi$
$571$	31.1144	+	11.3247i	1.30210	+	0.473925i	0.404419	+	0.914574i	$0.367474\pi$
$572$	−0.403356	−	0.146810i	−0.0168652	−	0.00613842i
$573$	7.66812	−	16.1883i	0.320340	−	0.676275i
$574$	41.4503	−	3.10561i	1.73010	−	0.129625i
$575$	−0.331703	−	0.191509i	−0.0138330	−	0.00798648i
$576$	0.292469	−	24.2035i	0.0121862	−	1.00848i
$577$	36.2292	+	20.9170i	1.50824	+	0.870784i	0.999954	+	0.00959765i	$0.00305507\pi$
$577$	36.2292	+	20.9170i	1.50824	+	0.870784i	0.508289	+	0.861187i	$0.330278\pi$
$578$	−3.13844	−	8.62281i	−0.130542	−	0.358661i
$579$	10.4262	−	14.7003i	0.433298	−	0.610925i
$580$	0.0551425	−	0.151503i	0.00228967	−	0.00629081i
$581$	−18.7990	+	26.1469i	−0.779913	+	1.08476i
$582$	−9.82610	+	13.8542i	−0.407305	+	0.574276i
$583$	−2.51046	−	2.10653i	−0.103973	−	0.0872434i
$584$	−4.34808	+	7.53110i	−0.179925	+	0.311639i
$585$	39.7737	−	13.9346i	1.64444	−	0.576123i
$586$	−6.55628	+	3.78527i	−0.270838	+	0.156368i
$587$	−10.1800	−	8.54200i	−0.420172	−	0.352566i	0.408057	−	0.912957i	$-0.366207\pi$
$587$	−10.1800	−	8.54200i	−0.420172	−	0.352566i	−0.828228	+	0.560391i	$0.810651\pi$
$588$	−0.115660	−	0.176590i	−0.00476974	−	0.00728243i
$589$	−1.39019	−	7.88415i	−0.0572817	−	0.324861i
$590$	−18.2438	+	3.21688i	−0.751087	+	0.132437i
$591$	−17.4705	+	17.2606i	−0.718639	+	0.710008i
$592$	−19.7320	−	16.5571i	−0.810980	−	0.680493i
$593$	−6.07625	+	10.5244i	−0.249522	+	0.432184i	−0.963393	−	0.268093i	$-0.913607\pi$
$593$	−6.07625	+	10.5244i	−0.249522	+	0.432184i	0.713872	+	0.700277i	$0.246940\pi$
$594$	21.9102	+	15.9412i	0.898987	+	0.654075i
$595$	4.89626	−	17.4013i	0.200727	−	0.713383i
$596$	0.0662626	+	0.182055i	0.00271422	+	0.00745726i
$597$	−24.7874	+	24.4896i	−1.01448	+	1.00229i
$598$	2.24548	−	6.16941i	0.0918245	−	0.252286i
$599$	19.6946	+	23.4711i	0.804700	+	0.959004i	0.999763	−	0.0217865i	$-0.00693540\pi$
$599$	19.6946	+	23.4711i	0.804700	+	0.959004i	−0.195062	+	0.980791i	$0.562491\pi$
$600$	2.68161	−	0.218294i	0.109476	−	0.00891181i
$601$	−0.739101	+	0.880827i	−0.0301486	+	0.0359297i	−0.780908	−	0.624646i	$-0.785243\pi$
$601$	−0.739101	+	0.880827i	−0.0301486	+	0.0359297i	0.750759	+	0.660576i	$0.229688\pi$
$602$	−6.83493	−	26.8442i	−0.278571	−	1.09409i
$603$	11.1507	−	29.5216i	0.454093	−	1.20221i
$604$	−0.351588			−0.0143059
$605$	−5.38441	+	1.95976i	−0.218907	+	0.0796758i
$606$	−7.39631	−	5.24583i	−0.300454	−	0.213097i
$607$	1.93858	+	2.31031i	0.0786845	+	0.0937725i	0.803950	−	0.594696i	$-0.202728\pi$
$607$	1.93858	+	2.31031i	0.0786845	+	0.0937725i	−0.725266	+	0.688469i	$0.758283\pi$
$608$	0.493061	+	0.179460i	0.0199963	+	0.00727805i
$609$	15.6412	−	12.6383i	0.633813	−	0.512129i
$610$	3.83735	−	21.7627i	0.155370	−	0.881145i
$611$		−	39.9137i		−	1.61473i
$612$	−0.166889	+	0.0273521i	−0.00674609	+	0.00110564i
$613$	−40.0911			−1.61927			−0.809633	−	0.586937i	$-0.800334\pi$
$613$	−40.0911			−1.61927			−0.809633	+	0.586937i	$0.800334\pi$
$614$	10.3424	−	3.76433i	0.417386	−	0.151916i
$615$	−33.5477	+	23.1896i	−1.35277	+	0.935093i
$616$	11.4470	+	25.3703i	0.461213	+	1.02220i
$617$	6.57249	+	7.83278i	0.264598	+	0.315336i	0.881942	−	0.471357i	$-0.156236\pi$
$617$	6.57249	+	7.83278i	0.264598	+	0.315336i	−0.617344	+	0.786693i	$0.711791\pi$
$618$	10.6378	+	10.7671i	0.427914	+	0.433116i
$619$	25.0122	−	29.8084i	1.00533	−	1.19810i	0.0252085	−	0.999682i	$-0.491975\pi$
$619$	25.0122	−	29.8084i	1.00533	−	1.19810i	0.980117	−	0.198419i	$-0.0635805\pi$
$620$	0.0478139	−	0.0276054i	0.00192025	−	0.00110866i
$621$	2.14122	−	2.94298i	0.0859243	−	0.118098i
$622$		−	17.4637i		−	0.700229i
$623$	10.3890	+	5.00330i	0.416228	+	0.200453i
$624$	11.5652	+	44.2292i	0.462980	+	1.77059i
$625$	−3.81449	−	21.6331i	−0.152580	−	0.865322i
$626$	7.64526	−	6.41513i	0.305566	−	0.256400i
$627$	−28.1117	+	19.4319i	−1.12267	+	0.776037i
$628$	0.0291338	+	0.0800445i	0.00116257	+	0.00319412i
$629$	−10.5172	+	18.2163i	−0.419349	+	0.726333i
$630$	−21.1233	−	10.4891i	−0.841571	−	0.417897i
$631$	5.94429	+	10.2958i	0.236639	+	0.409870i	0.959748	−	0.280864i	$-0.0906210\pi$
$631$	5.94429	+	10.2958i	0.236639	+	0.409870i	−0.723109	+	0.690734i	$0.757288\pi$
$632$	−17.3820	+	20.7151i	−0.691420	+	0.824002i
$633$	−5.78771	−	0.541613i	−0.230041	−	0.0215272i
$634$	4.13850	+	23.4706i	0.164361	+	0.932137i
$635$	−3.09825	+	2.59974i	−0.122950	+	0.103168i
$636$	0.00248637	−	0.0265695i	9.85909e−5	−	0.00105355i
$637$	34.9383	+	30.8352i	1.38430	+	1.22173i
$638$	−19.8167	+	11.4412i	−0.784550	+	0.452960i
$639$	13.2751	+	0.160413i	0.525156	+	0.00634585i
$640$		−	23.5583i		−	0.931222i
$641$	49.2008	+	8.67542i	1.94331	+	0.342659i	0.999940	+	0.0109243i	$0.00347739\pi$
$641$	49.2008	+	8.67542i	1.94331	+	0.342659i	0.943373	+	0.331734i	$0.107634\pi$
$642$	5.73249	−	3.96254i	0.226243	−	0.156389i
$643$	7.32572	−	1.29172i	0.288898	−	0.0509406i	−0.0273209	−	0.999627i	$-0.508698\pi$
$643$	7.32572	−	1.29172i	0.288898	−	0.0509406i	0.316219	+	0.948686i	$0.397586\pi$
$644$	0.0294098	−	0.0132696i	0.00115891	−	0.000522896i
$645$	19.1014	+	19.3336i	0.752118	+	0.761261i
$646$	−4.21758	+	23.9191i	−0.165938	+	0.941083i
$647$	9.06934	+	15.7086i	0.356553	+	0.617567i	0.987382	−	0.158354i	$-0.0506187\pi$
$647$	9.06934	+	15.7086i	0.356553	+	0.617567i	−0.630830	+	0.775921i	$0.717285\pi$
$648$	−0.617762	+	25.5580i	−0.0242680	+	1.00401i
$649$	−19.9962	−	11.5448i	−0.784919	−	0.453173i
$650$	−4.81662	+	1.75310i	−0.188923	+	0.0687624i
$651$	6.88502	+	0.127554i	0.269845	+	0.00499923i
$652$	0.125004	−	0.104891i	0.00489555	−	0.00410786i
$653$	−7.59970	+	20.8800i	−0.297399	+	0.817097i	0.697533	+	0.716552i	$0.254281\pi$
$653$	−7.59970	+	20.8800i	−0.297399	+	0.817097i	−0.994933	+	0.100545i	$0.967941\pi$
$654$	13.6945	−	1.11479i	0.535499	−	0.0435917i
$655$	3.19081	−	18.0960i	0.124675	−	0.707068i
$656$	−22.1196	−	38.3123i	−0.863625	−	1.49584i
$657$	4.68784	−	7.89763i	0.182890	−	0.308116i
$658$	−15.9899	+	15.5956i	−0.623350	+	0.607979i
$659$	21.2896	+	3.75393i	0.829324	+	0.146232i	0.572167	−	0.820137i	$-0.306103\pi$
$659$	21.2896	+	3.75393i	0.829324	+	0.146232i	0.257157	+	0.966370i	$0.417214\pi$
$660$	−0.192235	−	0.136343i	−0.00748274	−	0.00530713i
$661$	4.72263	−	0.832727i	0.183689	−	0.0323893i	−0.0810468	−	0.996710i	$-0.525826\pi$
$661$	4.72263	−	0.832727i	0.183689	−	0.0323893i	0.264736	+	0.964321i	$0.414715\pi$
$662$	20.0531	−	3.53590i	0.779386	−	0.137427i
$663$	33.9293	−	15.5726i	1.31770	−	0.604790i
$664$	34.0499	+	6.00391i	1.32139	+	0.232997i
$665$	21.2939	−	20.7688i	0.825743	−	0.805381i
$666$	20.8076	+	17.8925i	0.806277	+	0.693319i
$667$	1.53678	+	2.66178i	0.0595043	+	0.103065i
$668$	0.0260407	−	0.147684i	0.00100754	−	0.00571407i
$669$	−9.88414	−	14.2991i	−0.382143	−	0.552835i
$670$	10.6901	−	29.3707i	0.412993	−	1.13469i
$671$	21.0992	−	17.7044i	0.814527	−	0.683469i
$672$	−0.232865	+	0.386614i	−0.00898296	+	0.0149140i
$673$	−41.8330	+	15.2260i	−1.61255	+	0.586918i	−0.981941	−	0.189186i	$-0.939415\pi$
$673$	−41.8330	+	15.2260i	−1.61255	+	0.586918i	−0.630604	+	0.776105i	$0.717193\pi$
$674$	19.3538	+	11.1739i	0.745480	+	0.430403i
$675$	−2.83467	+	0.196307i	−0.109106	+	0.00755584i
$676$	0.272620	+	0.472192i	0.0104854	+	0.0181612i
$677$	−6.96679	+	39.5107i	−0.267756	+	1.51852i	0.493316	+	0.869850i	$0.335785\pi$
$677$	−6.96679	+	39.5107i	−0.267756	+	1.51852i	−0.761072	+	0.648668i	$0.775327\pi$
$678$	5.92710	−	21.5975i	0.227629	−	0.829445i
$679$	16.7958	−	7.57824i	0.644564	−	0.290826i
$680$	−19.1135	+	3.37022i	−0.732968	+	0.129242i
$681$	−2.49427	−	30.6406i	−0.0955805	−	1.17415i
$682$	−7.71686	−	1.36069i	−0.295494	−	0.0521035i
$683$		−	33.0102i		−	1.26310i	−0.775335	−	0.631550i	$-0.782419\pi$
$683$		−	33.0102i		−	1.26310i	0.775335	−	0.631550i	$-0.217581\pi$
$684$	−0.260324	−	0.0983282i	−0.00995373	−	0.00375967i
$685$	−12.7508	+	7.36168i	−0.487183	+	0.281275i
$686$	−1.29860	−	26.0450i	−0.0495808	−	0.994402i
$687$	20.5645	−	9.43853i	0.784583	−	0.360102i
$688$	−22.5844	+	18.9506i	−0.861023	+	0.722484i
$689$	1.02293	+	5.80135i	0.0389707	+	0.221014i
$690$	2.08538	−	2.94027i	0.0793892	−	0.111934i
$691$	−1.88171	+	2.24253i	−0.0715836	+	0.0853100i	−0.800648	−	0.599135i	$-0.795511\pi$
$691$	−1.88171	+	2.24253i	−0.0715836	+	0.0853100i	0.729064	+	0.684445i	$0.239956\pi$
$692$	−0.0737660	−	0.127766i	−0.00280416	−	0.00485695i
$693$	−11.7647	−	26.9380i	−0.446904	−	1.02329i
$694$	−3.61915	+	6.26854i	−0.137381	+	0.237951i
$695$	−7.59239	−	20.8599i	−0.287996	−	0.791262i
$696$	−19.5117	−	9.24237i	−0.739589	−	0.350331i
$697$	−27.6742	+	23.2214i	−1.04823	+	0.879574i
$698$	2.72459	+	15.4519i	0.103127	+	0.584864i
$699$	−31.6887	−	8.69649i	−1.19858	−	0.328931i
$700$	−0.0226952	−	0.0109299i	−0.000857797	−	0.000413110i
$701$		−	6.39386i		−	0.241493i	−0.992683	−	0.120746i	$-0.961471\pi$
$701$		−	6.39386i		−	0.241493i	0.992683	−	0.120746i	$-0.0385288\pi$
$702$	−11.7512	−	47.2668i	−0.443521	−	1.78397i
$703$	−29.9744	+	17.3058i	−1.13051	+	0.652699i
$704$	19.2070	−	22.8900i	0.723890	−	0.862699i
$705$	5.79972	−	21.1333i	0.218430	−	0.795927i
$706$	−2.78796	−	3.32257i	−0.104926	−	0.125046i
$707$	4.04577	+	8.96673i	0.152157	+	0.337229i
$708$	−0.0152548	−	0.187396i	−0.000573309	−	0.00704276i
$709$	33.6905	−	12.2623i	1.26527	−	0.460521i	0.379737	−	0.925094i	$-0.376014\pi$
$709$	33.6905	−	12.2623i	1.26527	−	0.460521i	0.885535	+	0.464573i	$0.153792\pi$
$710$	13.1492			0.493481
$711$	18.6204	−	21.6541i	0.698319	−	0.812092i
$712$		−	12.3803i		−	0.463970i
$713$	−0.182768	+	1.03653i	−0.00684472	+	0.0388184i
$714$	−19.4958	−	7.50772i	−0.729614	−	0.280969i
$715$	48.8882	+	17.7938i	1.82831	+	0.665452i
$716$	0.0541195	+	0.0644971i	0.00202254	+	0.00241037i
$717$	33.4394	−	15.3478i	1.24882	−	0.573173i
$718$	−28.9856	+	10.5499i	−1.08173	+	0.393718i
$719$	−35.6795			−1.33062			−0.665311	−	0.746566i	$-0.731701\pi$
$719$	−35.6795			−1.33062			−0.665311	+	0.746566i	$0.731701\pi$
$720$	−0.303288	+	25.0988i	−0.0113029	+	0.935378i
$721$	−4.05154	−	15.9125i	−0.150887	−	0.592611i
$722$	−8.49278	+	10.1213i	−0.316069	+	0.376676i
$723$	−11.6054	−	16.7892i	−0.431609	−	0.624397i
$724$	−0.0510798	−	0.0608745i	−0.00189836	−	0.00226238i
$725$	0.820714	−	2.25489i	0.0304805	−	0.0837446i
$726$	1.67525	+	6.40668i	0.0621742	+	0.237774i
$727$	0.773622	+	2.12551i	0.0286921	+	0.0788308i	0.953212	−	0.302304i	$-0.0977557\pi$
$727$	0.773622	+	2.12551i	0.0286921	+	0.0788308i	−0.924520	+	0.381135i	$0.875533\pi$
$728$	13.5512	−	48.1610i	0.502242	−	1.78497i
$729$	0.978522	−	26.9823i	0.0362415	−	0.999343i
$730$	4.54818	−	7.87768i	0.168336	−	0.291566i
$731$	18.4426	+	15.4752i	0.682125	+	0.572371i
$732$	0.216283	+	0.0593557i	0.00799405	+	0.00219385i
$733$	15.8797	−	2.80002i	0.586530	−	0.103421i	0.127495	−	0.991839i	$-0.459306\pi$
$733$	15.8797	−	2.80002i	0.586530	−	0.103421i	0.459035	+	0.888418i	$0.348195\pi$
$734$	−1.61703	−	9.17065i	−0.0596858	−	0.338495i
$735$	14.0184	+	21.4032i	0.517077	+	0.789471i
$736$	−0.0528441	−	0.0443414i	−0.00194786	−	0.00163445i
$737$	33.7374	−	19.4783i	1.24273	−	0.717492i
$738$	23.0711	+	41.0992i	0.849258	+	1.51288i
$739$	−12.2994	+	21.3033i	−0.452442	+	0.783653i	−0.998537	−	0.0540705i	$-0.982780\pi$
$739$	−12.2994	+	21.3033i	−0.452442	+	0.783653i	0.546095	+	0.837723i	$0.316114\pi$
$740$	−0.182850	−	0.153429i	−0.00672170	−	0.00564018i
$741$	61.1620	+	5.72352i	2.24684	+	0.210259i
$742$	1.92439	−	2.67658i	0.0706467	−	0.0982602i
$743$	8.41237	−	23.1128i	0.308620	−	0.847926i	−0.684307	−	0.729194i	$-0.739895\pi$
$743$	8.41237	−	23.1128i	0.308620	−	0.847926i	0.992926	−	0.118732i	$-0.0378828\pi$
$744$	−3.08403	−	6.71941i	−0.113066	−	0.246346i
$745$	−8.03125	−	22.0657i	−0.294242	−	0.808424i
$746$	30.0356	+	17.3411i	1.09968	+	0.634902i
$747$	−35.8813	−	6.77486i	−1.31283	−	0.247879i
$748$	−0.180799	−	0.104384i	−0.00661066	−	0.00381667i
$749$	−7.53893	+	0.564844i	−0.275467	+	0.0206389i
$750$	−28.4526	+	2.31616i	−1.03894	+	0.0845741i
$751$	34.3971	+	12.5195i	1.25517	+	0.456843i	0.882144	−	0.470979i	$-0.156099\pi$
$751$	34.3971	+	12.5195i	1.25517	+	0.456843i	0.373022	+	0.927822i	$0.378322\pi$
$752$	22.3386	+	8.13059i	0.814605	+	0.296492i
$753$	−33.3358	−	33.7411i	−1.21482	−	1.22959i
$754$	40.5070	+	7.14247i	1.47518	+	0.260114i
$755$	42.6137			1.55087
$756$	0.125967	−	0.203532i	0.00458138	−	0.00740237i
$757$	−38.6682			−1.40542			−0.702709	−	0.711477i	$-0.748027\pi$
$757$	−38.6682			−1.40542			−0.702709	+	0.711477i	$0.748027\pi$
$758$	−2.86626	−	0.505399i	−0.104107	−	0.0183569i
$759$	4.34672	−	1.13660i	0.157776	−	0.0412559i
$760$	−30.0099	−	10.9227i	−1.08857	−	0.396208i
$761$	45.3555	+	16.5080i	1.64413	+	0.598416i	0.987755	−	0.156015i	$-0.0498647\pi$
$761$	45.3555	+	16.5080i	1.64413	+	0.598416i	0.656380	+	0.754431i	$0.272087\pi$
$762$	2.65782	+	3.84499i	0.0962827	+	0.139289i
$763$	−13.4295	−	6.46757i	−0.486181	−	0.234142i
$764$	0.155936	+	0.0900299i	0.00564158	+	0.00325717i
$765$	20.2275	−	3.31517i	0.731328	−	0.119860i
$766$	−8.43249	−	4.86850i	−0.304678	−	0.175906i
$767$	14.1954	+	39.0014i	0.512565	+	1.40826i
$768$	0.720551	+	0.0674290i	0.0260007	+	0.00243314i
$769$	16.2750	−	44.7151i	0.586891	−	1.61247i	−0.189264	−	0.981926i	$-0.560610\pi$
$769$	16.2750	−	44.7151i	0.586891	−	1.61247i	0.776155	−	0.630543i	$-0.217168\pi$
$770$	−11.9738	−	26.5378i	−0.431506	−	0.956356i
$771$	11.5394	+	25.1417i	0.415580	+	0.905457i
$772$	0.138779	+	0.116450i	0.00499477	+	0.00419111i
$773$	1.79467	−	3.10845i	0.0645496	−	0.111803i	−0.831944	−	0.554859i	$-0.812772\pi$
$773$	1.79467	−	3.10845i	0.0645496	−	0.111803i	0.896494	+	0.443056i	$0.146106\pi$
$774$	24.3034	−	19.8975i	0.873567	−	0.715202i
$775$	0.711639	−	0.410865i	0.0255628	−	0.0147587i
$776$	−15.1549	−	12.7165i	−0.544031	−	0.456496i
$777$	−9.66242	−	28.1596i	−0.346637	−	1.01022i
$778$	3.30367	+	18.7360i	0.118442	+	0.671719i
$779$	−58.5413	+	10.3224i	−2.09746	+	0.369839i
$780$	0.107171	+	0.409858i	0.00383735	+	0.0146753i
$781$	12.5547	+	10.5346i	0.449242	+	0.376959i
$782$	1.59658	−	2.76535i	0.0570935	−	0.0988888i
$783$	20.4871	+	10.0093i	0.732150	+	0.357702i
$784$	−24.3747	+	13.2727i	−0.870525	+	0.474027i
$785$	−3.53112	−	9.70167i	−0.126031	−	0.346267i
$786$	−20.4788	−	5.62011i	−0.730456	−	0.200463i
$787$	10.6009	−	29.1257i	0.377881	−	1.03822i	−0.594352	−	0.804205i	$-0.702591\pi$
$787$	10.6009	−	29.1257i	0.377881	−	1.03822i	0.972233	−	0.234014i	$-0.0751863\pi$
$788$	−0.158686	−	0.189114i	−0.00565294	−	0.00673692i
$789$	−21.3919	+	45.1608i	−0.761573	+	1.60777i
$790$	18.1819	−	21.6684i	0.646885	−	0.770927i
$791$	−17.3933	+	16.9644i	−0.618434	+	0.603184i
$792$	−20.5769	+	23.9294i	−0.731168	+	0.850292i
$793$	−49.5098			−1.75814
$794$	−28.4913	+	10.3700i	−1.01112	+	0.368017i
$795$	−0.301356	+	3.22031i	−0.0106880	+	0.114213i
$796$	−0.225146	−	0.268318i	−0.00798007	−	0.00951028i
$797$	−18.1049	−	6.58966i	−0.641310	−	0.233418i	0.000836476	−	1.00000i	$-0.499734\pi$
$797$	−18.1049	−	6.58966i	−0.641310	−	0.233418i	−0.642147	+	0.766582i	$0.721956\pi$
$798$	−21.6051	−	26.7386i	−0.764812	−	0.946535i
$799$	3.37096	−	19.1177i	0.119256	−	0.676335i
$800$			0.0538568i			0.00190413i
$801$	−0.157983	+	13.0740i	−0.00558206	+	0.461948i
$802$	−37.2521			−1.31542
$803$	10.6538	−	3.87768i	0.375965	−	0.136840i
$804$	0.286682	+	0.135797i	0.0101105	+	0.00478918i
$805$	−3.56456	+	1.60832i	−0.125634	+	0.0566859i
$806$	9.05389	+	10.7900i	0.318910	+	0.380062i
$807$	13.6773	−	3.57640i	0.481464	−	0.125895i
$808$	6.78892	−	8.09072i	0.238833	−	0.284630i
$809$	10.9220	−	6.30585i	0.383999	−	0.221702i	−0.295558	−	0.955325i	$-0.595506\pi$
$809$	10.9220	−	6.30585i	0.383999	−	0.221702i	0.679557	+	0.733623i	$0.262172\pi$
$810$	0.646192	−	26.7341i	0.0227049	−	0.939342i
$811$			43.6085i			1.53130i	0.643256	+	0.765652i	$0.277583\pi$
$811$			43.6085i			1.53130i	−0.643256	+	0.765652i	$0.722417\pi$
$812$	0.113866	+	0.167017i	0.00399592	+	0.00586114i
$813$	−14.4351	+	14.2617i	−0.506262	+	0.500181i
$814$	5.88270	+	33.3624i	0.206188	+	1.16935i
$815$	−15.1510	+	12.7132i	−0.530715	+	0.445323i
$816$	1.80403	+	22.1615i	0.0631538	+	0.775808i
$817$	13.5491	+	37.2258i	0.474023	+	1.30237i
$818$	17.6575	−	30.5837i	0.617380	−	1.06933i
$819$	−14.9252	+	50.6868i	−0.521528	+	1.77114i
$820$	−0.204975	−	0.355028i	−0.00715805	−	0.0123981i
$821$	17.6656	−	21.0530i	0.616532	−	0.734755i	−0.363938	−	0.931423i	$-0.618568\pi$
$821$	17.6656	−	21.0530i	0.616532	−	0.734755i	0.980470	+	0.196669i	$0.0630123\pi$
$822$	7.09785	+	15.4646i	0.247566	+	0.539391i
$823$	−0.890725	−	5.05155i	−0.0310487	−	0.176086i	0.965340	−	0.260996i	$-0.0840509\pi$
$823$	−0.890725	−	5.05155i	−0.0310487	−	0.176086i	−0.996389	+	0.0849098i	$0.972940\pi$
$824$	−13.5049	+	11.3320i	−0.470467	+	0.394769i
$825$	−2.86113	−	2.02926i	−0.0996118	−	0.0706496i
$826$	10.0778	−	20.9260i	0.350653	−	0.728108i
$827$	22.7209	−	13.1179i	0.790082	−	0.456154i	−0.0499094	−	0.998754i	$-0.515893\pi$
$827$	22.7209	−	13.1179i	0.790082	−	0.456154i	0.839991	+	0.542600i	$0.182560\pi$
$828$	0.0277394	+	0.0238532i	0.000964011	+	0.000828956i
$829$		−	15.8622i		−	0.550916i	−0.961313	−	0.275458i	$-0.911171\pi$
$829$		−	15.8622i		−	0.550916i	0.961313	−	0.275458i	$-0.0888295\pi$
$830$	−35.6169	−	6.28021i	−1.23628	−	0.217989i
$831$	−14.8975	−	7.05669i	−0.516788	−	0.244794i
$832$	−52.8958	+	9.32696i	−1.83383	+	0.323354i
$833$	14.1304	+	17.7201i	0.489588	+	0.613964i
$834$	−24.8204	+	6.49013i	−0.859459	+	0.224735i
$835$	−3.15622	+	17.8998i	−0.109225	+	0.619448i
$836$	−0.171761	−	0.297499i	−0.00594049	−	0.0102892i
$837$	3.17110	+	7.13530i	0.109609	+	0.246632i
$838$	29.0435	+	16.7682i	1.00329	+	0.579249i
$839$	43.7933	−	15.9395i	1.51191	−	0.550291i	0.552800	−	0.833314i	$-0.313560\pi$
$839$	43.7933	−	15.9395i	1.51191	−	0.550291i	0.959113	+	0.283023i	$0.0913373\pi$
$840$	14.1732	−	23.5310i	0.489021	−	0.811897i
$841$	7.46447	−	6.26343i	0.257395	−	0.215980i
$842$	3.72275	−	10.2282i	0.128294	−	0.352486i
$843$	−15.4592	+	32.6362i	−0.532445	+	1.12405i
$844$	0.0101468	−	0.0575454i	0.000349268	−	0.00198079i
$845$	−33.0425	−	57.2312i	−1.13670	−	1.96881i
$846$	−23.6929	−	8.94917i	−0.814578	−	0.307679i
$847$	1.94583	−	6.91547i	0.0668596	−	0.237618i
$848$	−3.45523	−	0.609251i	−0.118653	−	0.0209218i
$849$	−0.237633	+	2.53937i	−0.00815555	+	0.0871508i
$850$	−2.45510	+	0.432901i	−0.0842094	+	0.0148484i
$851$	4.48125	−	0.790165i	0.153615	−	0.0270865i
$852$	−0.0124342	+	0.132873i	−0.000425989	+	0.00455215i
$853$	33.3113	+	5.87368i	1.14056	+	0.201111i	0.711850	−	0.702332i	$-0.247858\pi$
$853$	33.3113	+	5.87368i	1.14056	+	0.201111i	0.428708	+	0.903443i	$0.358969\pi$
$854$	19.3451	+	19.8342i	0.661976	+	0.678712i
$855$	31.5521	+	11.9177i	1.07906	+	0.407577i
$856$	4.05842	+	7.02939i	0.138714	+	0.240260i
$857$	−7.64328	+	43.3472i	−0.261089	+	1.48071i	0.518855	+	0.854862i	$0.326359\pi$
$857$	−7.64328	+	43.3472i	−0.261089	+	1.48071i	−0.779944	+	0.625849i	$0.784753\pi$
$858$	25.7390	−	54.3379i	0.878715	−	1.85507i
$859$	−15.9018	+	43.6898i	−0.542562	+	1.49068i	0.300990	+	0.953627i	$0.402683\pi$
$859$	−15.9018	+	43.6898i	−0.542562	+	1.49068i	−0.843551	+	0.537048i	$0.819539\pi$
$860$	−0.209283	+	0.175609i	−0.00713648	+	0.00598822i
$861$	0.947112	−	51.1226i	0.0322775	−	1.74225i
$862$	7.23046	−	2.63167i	0.246271	−	0.0896351i
$863$	6.24515	+	3.60564i	0.212587	+	0.122737i	0.602513	−	0.798109i	$-0.294166\pi$
$863$	6.24515	+	3.60564i	0.212587	+	0.122737i	−0.389926	+	0.920846i	$0.627499\pi$
$864$	−0.508918	−	0.0538349i	−0.0173137	−	0.00183150i
$865$	8.94069	+	15.4857i	0.303992	+	0.526530i
$866$	−8.69024	+	49.2848i	−0.295306	+	1.67477i
$867$	−10.9206	+	2.85556i	−0.370882	+	0.0969798i
$868$	−0.00689330	+	0.0688770i	−0.000233974	+	0.00233784i
$869$	34.7197	−	6.12203i	1.17779	−	0.207676i
$870$	20.4096	+	9.66771i	0.691951	+	0.327766i
$871$	−68.9621	−	12.1599i	−2.33669	−	0.412022i
$872$			16.0035i			0.541947i
$873$	15.8419	+	13.6225i	0.536167	+	0.461051i
$874$	4.55031	−	2.62712i	0.153916	−	0.0888637i
$875$	27.9020	+	13.4374i	0.943259	+	0.454268i
$876$	0.0753031	+	0.0534087i	0.00254425	+	0.00180451i
$877$	−34.5295	+	28.9737i	−1.16598	+	0.978372i	−0.999970	−	0.00775269i	$-0.997532\pi$
$877$	−34.5295	+	28.9737i	−1.16598	+	0.978372i	−0.166008	+	0.986124i	$0.553088\pi$
$878$	0.992333	+	5.62780i	0.0334896	+	0.189929i
$879$	3.88461	+	8.46371i	0.131025	+	0.285474i
$880$	−19.9175	+	23.7367i	−0.671417	+	0.800164i
$881$	−17.2527	−	29.8826i	−0.581259	−	1.00677i	−0.995330	−	0.0965261i	$-0.969227\pi$
$881$	−17.2527	−	29.8826i	−0.581259	−	1.00677i	0.414071	−	0.910245i	$-0.364106\pi$
$882$	26.1375	−	13.8258i	0.880095	−	0.465540i
$883$	−19.2076	+	33.2686i	−0.646388	+	1.11958i	0.337591	+	0.941293i	$0.390388\pi$
$883$	−19.2076	+	33.2686i	−0.646388	+	1.11958i	−0.983979	+	0.178284i	$0.942945\pi$
$884$	0.128350	+	0.352638i	0.00431687	+	0.0118605i
$885$	1.84893	+	22.7130i	0.0621511	+	0.763489i
$886$	−8.94004	+	7.50158i	−0.300346	+	0.252021i
$887$	−4.68652	−	26.5786i	−0.157358	−	0.892422i	−0.956598	−	0.291410i	$-0.905876\pi$
$887$	−4.68652	−	26.5786i	−0.157358	−	0.892422i	0.799240	−	0.601012i	$-0.205236\pi$
$888$	−22.7380	+	22.4649i	−0.763036	+	0.753872i
$889$	−0.378862	−	5.05664i	−0.0127066	−	0.169594i
$890$			12.9500i			0.434085i
$891$	22.0353	−	25.0077i	0.738211	−	0.837789i
$892$	0.151324	−	0.0873671i	0.00506671	−	0.00292527i
$893$	20.5325	−	24.4697i	0.687093	−	0.818846i
$894$	−26.2550	+	6.86527i	−0.878099	+	0.229609i
$895$	−6.55946	−	7.81726i	−0.219259	−	0.261302i
$896$	23.9815	+	17.2421i	0.801165	+	0.576018i
$897$	−7.29868	−	3.45727i	−0.243696	−	0.115435i
$898$	−38.3904	+	13.9730i	−1.28110	+	0.466284i
$899$	−6.59404			−0.219923
$900$	0.000345119	−	0.0285606i	1.15040e−5	−	0.000952021i
$901$			2.86510i			0.0954503i
$902$	−10.1034	+	57.2992i	−0.336406	+	1.90785i
$903$	−33.6611	+	5.29445i	−1.12017	+	0.176188i
$904$	24.5126	+	8.92187i	0.815278	+	0.296737i
$905$	6.19104	+	7.37819i	0.205797	+	0.245259i
$906$	4.58860	−	49.0341i	0.152446	−	1.62905i
$907$	34.2090	−	12.4511i	1.13589	−	0.413431i	0.295464	−	0.955354i	$-0.404526\pi$
$907$	34.2090	−	12.4511i	1.13589	−	0.413431i	0.840428	+	0.541923i	$0.182304\pi$
$908$	0.309023			0.0102553
$909$	−7.27259	+	8.45746i	−0.241217	+	0.280516i
$910$	−14.1749	+	50.3774i	−0.469892	+	1.66999i
$911$	17.9098	−	21.3441i	0.593378	−	0.707160i	−0.382873	−	0.923801i	$-0.625065\pi$
$911$	17.9098	−	21.3441i	0.593378	−	0.707160i	0.976251	+	0.216640i	$0.0695099\pi$
$912$	−15.6623	+	33.0648i	−0.518629	+	1.09488i
$913$	−28.9750	−	34.5311i	−0.958933	−	1.14281i
$914$	3.15902	−	8.67933i	0.104491	−	0.287087i
$915$	−26.2142	−	7.19411i	−0.866616	−	0.237830i
$916$	0.0777926	+	0.213733i	0.00257034	+	0.00706195i
$917$	16.0857	+	16.4924i	0.531197	+	0.544627i
$918$	−1.63657	−	23.6321i	−0.0540150	−	0.779976i
$919$	24.7371	−	42.8459i	0.816001	−	1.41336i	−0.0926055	−	0.995703i	$-0.529520\pi$
$919$	24.7371	−	42.8459i	0.816001	−	1.41336i	0.908607	−	0.417653i	$-0.137147\pi$
$920$	3.21632	+	2.69881i	0.106039	+	0.0889772i
$921$	−3.42503	−	13.0984i	−0.112859	−	0.431608i
$922$	−30.6776	+	5.40930i	−1.01031	+	0.178146i
$923$	−5.11565	−	29.0123i	−0.168384	−	0.954950i
$924$	0.279487	−	0.0959004i	0.00919445	−	0.00315489i
$925$	−2.72145	−	2.28357i	−0.0894807	−	0.0750832i
$926$	−20.1233	+	11.6182i	−0.661293	+	0.381798i
$927$	14.4063	−	11.7947i	0.473166	−	0.387388i
$928$	0.216089	−	0.374278i	0.00709348	−	0.0122863i
$929$	−23.8911	−	20.0470i	−0.783840	−	0.657720i	0.160372	−	0.987057i	$-0.448730\pi$
$929$	−23.8911	−	20.0470i	−0.783840	−	0.657720i	−0.944213	+	0.329337i	$0.893175\pi$
$930$	3.22595	+	7.02864i	0.105783	+	0.230478i
$931$	5.55711	+	36.8770i	0.182127	+	1.20859i
$932$	0.112975	−	0.310396i	0.00370062	−	0.0101674i
$933$	−21.3888	−	2.00156i	−0.700238	−	0.0655281i
$934$	−0.686858	−	1.88713i	−0.0224747	−	0.0617486i
$935$	21.9134	+	12.6517i	0.716646	+	0.413756i
$936$	55.9831	−	9.17530i	1.82987	−	0.299904i
$937$	−15.9634	−	9.21646i	−0.521501	−	0.301089i	0.216048	−	0.976383i	$-0.430683\pi$
$937$	−15.9634	−	9.21646i	−0.521501	−	0.301089i	−0.737548	+	0.675294i	$0.764017\pi$
$938$	22.0744	+	32.3783i	0.720754	+	1.05719i
$939$	−6.98076	−	10.0989i	−0.227808	−	0.329564i
$940$	0.207005	+	0.0753435i	0.00675175	+	0.00245743i
$941$	−21.6113	−	7.86586i	−0.704507	−	0.256420i	−0.0351733	−	0.999381i	$-0.511198\pi$
$941$	−21.6113	−	7.86586i	−0.704507	−	0.256420i	−0.669334	+	0.742961i	$0.733421\pi$
$942$	−11.5436	+	3.01847i	−0.376111	+	0.0983472i
$943$	7.69644	+	1.35709i	0.250630	+	0.0441929i
$944$	−24.7197			−0.804558
$945$	−15.2677	+	24.6687i	−0.496657	+	0.802474i
$946$	38.7744			1.26066
$947$	17.9325	+	3.16199i	0.582728	+	0.102751i	0.457238	−	0.889344i	$-0.348839\pi$
$947$	17.9325	+	3.16199i	0.582728	+	0.102751i	0.125490	+	0.992095i	$0.459950\pi$
$948$	0.201766	+	0.204219i	0.00655305	+	0.00663271i
$949$	−19.1507	−	6.97027i	−0.621657	−	0.226265i
$950$	−3.85473	−	1.40301i	−0.125064	−	0.0455196i
$951$	29.2202	−	2.37864i	0.947530	−	0.0771327i
$952$	10.5582	−	21.9235i	0.342194	−	0.710544i
$953$	−20.4233	−	11.7914i	−0.661576	−	0.381961i	0.131301	−	0.991343i	$-0.458085\pi$
$953$	−20.4233	−	11.7914i	−0.661576	−	0.381961i	−0.792877	+	0.609381i	$0.791418\pi$
$954$	3.67306	+	0.693521i	0.118920	+	0.0224536i
$955$	−18.9000	−	10.9119i	−0.611590	−	0.353102i
$956$	0.126497	+	0.347547i	0.00409120	+	0.0112405i
$957$	11.7414	+	25.5820i	0.379547	+	0.826948i
$958$	−11.5750	+	31.8020i	−0.373971	+	1.02748i
$959$	1.83827	−	18.3678i	0.0593610	−	0.593128i
$960$	−29.3623	−	2.74772i	−0.947665	−	0.0886823i
$961$	22.0176	+	18.4749i	0.710245	+	0.595966i
$962$	30.4477	−	52.7370i	0.981674	−	1.70031i
$963$	−4.19614	−	7.47508i	−0.135219	−	0.240881i
$964$	0.177676	−	0.102581i	0.00572256	−	0.00330392i
$965$	−16.8205	−	14.1141i	−0.541472	−	0.454349i
$966$	1.46681	+	4.27480i	0.0471940	+	0.137540i
$967$	−6.40078	−	36.3006i	−0.205835	−	1.16735i	−0.896120	−	0.443811i	$-0.853626\pi$
$967$	−6.40078	−	36.3006i	−0.205835	−	1.16735i	0.690285	−	0.723537i	$-0.257485\pi$
$968$	−7.59592	+	1.33936i	−0.244142	+	0.0430488i
$969$	28.8117	+	7.90695i	0.925566	+	0.254008i
$970$	15.8524	+	13.3017i	0.508989	+	0.427092i
$971$	6.28287	−	10.8822i	0.201627	−	0.349228i	−0.747426	−	0.664345i	$-0.768711\pi$
$971$	6.28287	−	10.8822i	0.201627	−	0.349228i	0.949053	+	0.315117i	$0.102044\pi$
$972$	0.269537	+	0.0318102i	0.00864541	+	0.00102031i
$973$	26.7915	+	7.53842i	0.858895	+	0.241671i
$974$	−17.1077	−	47.0029i	−0.548165	−	1.50607i
$975$	1.59509	+	6.10013i	0.0510837	+	0.195360i
$976$	10.0854	−	27.7093i	0.322825	−	0.886953i
$977$	10.4107	+	12.4070i	0.333069	+	0.396936i	0.906423	−	0.422372i	$-0.138802\pi$
$977$	10.4107	+	12.4070i	0.333069	+	0.396936i	−0.573354	+	0.819308i	$0.694358\pi$
$978$	12.9972	+	18.8026i	0.415604	+	0.601242i
$979$	−10.3750	+	12.3645i	−0.331588	+	0.395171i
$980$	−0.225872	+	0.122994i	−0.00721523	+	0.00392891i
$981$	0.204219	−	16.9003i	0.00652020	−	0.539585i
$982$	43.6791			1.39385
$983$	−1.13238	+	0.412151i	−0.0361172	+	0.0131456i	−0.360016	−	0.932946i	$-0.617229\pi$
$983$	−1.13238	+	0.412151i	−0.0361172	+	0.0131456i	0.323898	+	0.946092i	$0.395006\pi$
$984$	−49.8929	+	22.8995i	−1.59053	+	0.730009i
$985$	19.2332	+	22.9213i	0.612822	+	0.730333i
$986$	18.7986	+	6.84215i	0.598671	+	0.217898i
$987$	17.2682	+	21.3712i	0.549653	+	0.680253i
$988$	−0.107227	+	0.608114i	−0.00341134	+	0.0193467i
$989$		−	5.20818i		−	0.165610i
$990$	21.5238	−	25.0306i	0.684073	−	0.795524i
$991$	−53.5562			−1.70127			−0.850635	−	0.525757i	$-0.823782\pi$
$991$	−53.5562			−1.70127			−0.850635	+	0.525757i	$0.823782\pi$
$992$	0.139071	−	0.0506179i	0.00441552	−	0.00160712i
$993$	−2.03229	−	24.9655i	−0.0644928	−	0.792256i
$994$	−9.62380	+	13.3854i	−0.305248	+	0.424560i
$995$	27.2884	+	32.5211i	0.865101	+	1.03099i
$996$	0.0971417	−	0.353970i	0.00307805	−	0.0112160i
$997$	−1.75036	+	2.08600i	−0.0554344	+	0.0660641i	−0.793049	−	0.609158i	$-0.791508\pi$
$997$	−1.75036	+	2.08600i	−0.0554344	+	0.0660641i	0.737615	+	0.675222i	$0.235952\pi$
$998$	−44.4078	+	25.6388i	−1.40570	+	0.811584i
$999$	24.2988	−	23.4336i	0.768780	−	0.741405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.47.7	yes	132
3.2	odd	2		567.2.bd.a.467.16		132
7.3	odd	6		189.2.ba.a.101.16	✓	132
21.17	even	6		567.2.ba.a.143.7		132
27.4	even	9		567.2.ba.a.341.7		132
27.23	odd	18		189.2.ba.a.131.16	yes	132
189.31	odd	18		567.2.bd.a.17.16		132
189.185	even	18	inner	189.2.bd.a.185.7	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.16	✓	132	7.3	odd	6
189.2.ba.a.131.16	yes	132	27.23	odd	18
189.2.bd.a.47.7	yes	132	1.1	even	1	trivial
189.2.bd.a.185.7	yes	132	189.185	even	18	inner
567.2.ba.a.143.7		132	21.17	even	6
567.2.ba.a.341.7		132	27.4	even	9
567.2.bd.a.17.16		132	189.31	odd	18
567.2.bd.a.467.16		132	3.2	odd	2

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.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38665 - 0.244504i) q^{2} +(-0.458387 + 1.67029i) q^{3} +(-0.0163608 - 0.00595485i) q^{4} +(1.98299 + 0.721749i) q^{5} +(1.04402 - 2.20404i) q^{6} +(-2.18605 + 1.49037i) q^{7} +(2.46004 + 1.42030i) q^{8} +(-2.57976 - 1.53128i) q^{9} +O(q^{10})\)	\(q+(-1.38665 - 0.244504i) q^{2} +(-0.458387 + 1.67029i) q^{3} +(-0.0163608 - 0.00595485i) q^{4} +(1.98299 + 0.721749i) q^{5} +(1.04402 - 2.20404i) q^{6} +(-2.18605 + 1.49037i) q^{7} +(2.46004 + 1.42030i) q^{8} +(-2.57976 - 1.53128i) q^{9} +(-2.57325 - 1.48566i) q^{10} +(-1.26664 - 3.48007i) q^{11} +(0.0174459 - 0.0245978i) q^{12} +(-2.27684 + 6.25557i) q^{13} +(3.39569 - 1.53213i) q^{14} +(-2.11451 + 2.98133i) q^{15} +(-3.03727 - 2.54857i) q^{16} +(-1.61887 + 2.80397i) q^{17} +(3.20283 + 2.75412i) q^{18} +(-4.61385 + 2.66381i) q^{19} +(-0.0281454 - 0.0236168i) q^{20} +(-1.48730 - 4.33451i) q^{21} +(0.905502 + 5.13536i) q^{22} +(0.689782 - 0.121627i) q^{23} +(-3.49997 + 3.45793i) q^{24} +(-0.418902 - 0.351501i) q^{25} +(4.68670 - 8.11761i) q^{26} +(3.74022 - 3.60704i) q^{27} +(0.0446405 - 0.0113661i) q^{28} +(1.50083 + 4.12351i) q^{29} +(3.66104 - 3.61707i) q^{30} +(-0.513951 + 1.41207i) q^{31} +(-0.0633067 - 0.0754460i) q^{32} +(6.39336 - 0.520445i) q^{33} +(2.93040 - 3.49232i) q^{34} +(-5.41058 + 1.37761i) q^{35} +(0.0330885 + 0.0404152i) q^{36} +6.49662 q^{37} +(7.04913 - 2.56567i) q^{38} +(-9.40496 - 6.67047i) q^{39} +(3.85312 + 4.59197i) q^{40} +(10.4849 + 3.81619i) q^{41} +(1.00256 + 6.37411i) q^{42} +(1.29121 - 7.32280i) q^{43} +0.0644796i q^{44} +(-4.01044 - 4.89845i) q^{45} -0.986227 q^{46} +(-5.63412 + 2.05065i) q^{47} +(5.64911 - 3.90490i) q^{48} +(2.55760 - 6.51603i) q^{49} +(0.494929 + 0.589833i) q^{50} +(-3.94139 - 3.98930i) q^{51} +(0.0745020 - 0.0887880i) q^{52} +(0.766350 - 0.442452i) q^{53} +(-6.06833 + 4.08721i) q^{54} -7.81514i q^{55} +(-7.49453 + 0.561517i) q^{56} +(-2.33441 - 8.92755i) q^{57} +(-1.07292 - 6.08484i) q^{58} +(4.77604 - 4.00757i) q^{59} +(0.0523485 - 0.0361855i) q^{60} +(2.54368 + 6.98869i) q^{61} +(1.05793 - 1.83239i) q^{62} +(7.92166 - 0.497345i) q^{63} +(4.03421 + 6.98746i) q^{64} +(-9.02990 + 10.7614i) q^{65} +(-8.99262 - 0.841528i) q^{66} +(1.82662 + 10.3593i) q^{67} +(0.0431834 - 0.0362352i) q^{68} +(-0.113034 + 1.20789i) q^{69} +(7.83942 - 0.587358i) q^{70} +(-3.83248 + 2.21268i) q^{71} +(-4.17142 - 7.43105i) q^{72} +3.06138i q^{73} +(-9.00855 - 1.58845i) q^{74} +(0.779129 - 0.538566i) q^{75} +(0.0913491 - 0.0161073i) q^{76} +(7.95554 + 5.71984i) q^{77} +(11.4105 + 11.5492i) q^{78} +(-1.65307 + 9.37505i) q^{79} +(-4.18344 - 7.24593i) q^{80} +(4.31035 + 7.90069i) q^{81} +(-13.6058 - 7.85533i) q^{82} +(11.4377 - 4.16299i) q^{83} +(-0.00147789 + 0.0797727i) q^{84} +(-5.23397 + 4.39182i) q^{85} +(-3.58091 + 9.83847i) q^{86} +(-7.57543 + 0.616671i) q^{87} +(1.82677 - 10.3601i) q^{88} +(-2.17916 - 3.77442i) q^{89} +(4.36339 + 7.77303i) q^{90} +(-4.34583 - 17.0683i) q^{91} +(-0.0120097 - 0.00211763i) q^{92} +(-2.12298 - 1.50572i) q^{93} +(8.31397 - 1.46598i) q^{94} +(-11.0718 + 1.95226i) q^{95} +(0.155036 - 0.0711573i) q^{96} +(-6.85869 - 1.20937i) q^{97} +(-5.13970 + 8.41014i) q^{98} +(-2.06134 + 10.9174i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

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