LMFDB - Embedded newform 189.2.ba.a.101.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.5
Character	$\chi$	$=$	189.101
Dual form			189.2.ba.a.131.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08992 + 1.29892i) q^{2} +(1.72029 - 0.201542i) q^{3} +(-0.151961 - 0.861812i) q^{4} +(1.13756 - 0.954530i) q^{5} +(-1.61319 + 2.45417i) q^{6} +(2.51978 - 0.806679i) q^{7} +(-1.65184 - 0.953692i) q^{8} +(2.91876 - 0.693419i) q^{9} +O(q^{10})$	\(q+(-1.08992 + 1.29892i) q^{2} +(1.72029 - 0.201542i) q^{3} +(-0.151961 - 0.861812i) q^{4} +(1.13756 - 0.954530i) q^{5} +(-1.61319 + 2.45417i) q^{6} +(2.51978 - 0.806679i) q^{7} +(-1.65184 - 0.953692i) q^{8} +(2.91876 - 0.693419i) q^{9} +2.51796i q^{10} +(-0.0836396 + 0.0996778i) q^{11} +(-0.435107 - 1.45194i) q^{12} +(-0.311287 + 0.855253i) q^{13} +(-1.69855 + 4.15219i) q^{14} +(1.76456 - 1.87133i) q^{15} +(4.68381 - 1.70477i) q^{16} -5.63249 q^{17} +(-2.28052 + 4.54700i) q^{18} +0.0959743i q^{19} +(-0.995491 - 0.835316i) q^{20} +(4.17215 - 1.89556i) q^{21} +(-0.0383126 - 0.217282i) q^{22} +(-2.22151 + 6.10356i) q^{23} +(-3.03385 - 1.30771i) q^{24} +(-0.485315 + 2.75236i) q^{25} +(-0.771624 - 1.33649i) q^{26} +(4.88135 - 1.78113i) q^{27} +(-1.07811 - 2.04899i) q^{28} +(0.238914 + 0.656410i) q^{29} +(0.507475 + 4.33161i) q^{30} +(-8.96076 + 1.58002i) q^{31} +(-1.58590 + 4.35722i) q^{32} +(-0.123795 + 0.188331i) q^{33} +(6.13896 - 7.31613i) q^{34} +(2.09641 - 3.32285i) q^{35} +(-1.04113 - 2.41005i) q^{36} +(1.72508 - 2.98792i) q^{37} +(-0.124663 - 0.104604i) q^{38} +(-0.363133 + 1.53402i) q^{39} +(-2.78941 + 0.491848i) q^{40} +(-2.04536 - 0.744450i) q^{41} +(-2.08514 + 7.48528i) q^{42} +(1.37972 - 7.82480i) q^{43} +(0.0986135 + 0.0569345i) q^{44} +(2.65839 - 3.57486i) q^{45} +(-5.50674 - 9.53795i) q^{46} +(2.18137 - 12.3712i) q^{47} +(7.71390 - 3.87667i) q^{48} +(5.69854 - 4.06530i) q^{49} +(-3.04613 - 3.63023i) q^{50} +(-9.68949 + 1.13518i) q^{51} +(0.784371 + 0.138306i) q^{52} +(1.26661 + 0.731275i) q^{53} +(-3.00674 + 8.28175i) q^{54} +0.193227i q^{55} +(-4.93160 - 1.07058i) q^{56} +(0.0193428 + 0.165103i) q^{57} +(-1.11302 - 0.405105i) q^{58} +(5.96770 + 2.17206i) q^{59} +(-1.88088 - 1.23635i) q^{60} +(-7.69007 - 1.35597i) q^{61} +(7.71419 - 13.3614i) q^{62} +(6.79526 - 4.10176i) q^{63} +(1.05325 + 1.82428i) q^{64} +(0.462256 + 1.27004i) q^{65} +(-0.109700 - 0.366065i) q^{66} +(-11.0280 + 9.25358i) q^{67} +(0.855917 + 4.85415i) q^{68} +(-2.59151 + 10.9476i) q^{69} +(2.03119 + 6.34470i) q^{70} +(2.38823 - 1.37884i) q^{71} +(-5.48265 - 1.63818i) q^{72} +(-6.94774 + 4.01128i) q^{73} +(2.00086 + 5.49732i) q^{74} +(-0.280165 + 4.83265i) q^{75} +(0.0827118 - 0.0145843i) q^{76} +(-0.130345 + 0.318636i) q^{77} +(-1.59677 - 2.14363i) q^{78} +(0.310233 + 0.260316i) q^{79} +(3.70088 - 6.41012i) q^{80} +(8.03834 - 4.04785i) q^{81} +(3.19626 - 1.84536i) q^{82} +(-4.54412 + 1.65393i) q^{83} +(-2.26762 - 3.30756i) q^{84} +(-6.40732 + 5.37638i) q^{85} +(8.65997 + 10.3205i) q^{86} +(0.543293 + 1.08106i) q^{87} +(0.233222 - 0.0848857i) q^{88} +15.9719 q^{89} +(1.74600 + 7.34933i) q^{90} +(-0.0944582 + 2.40615i) q^{91} +(5.59770 + 0.987026i) q^{92} +(-15.0966 + 4.52406i) q^{93} +(13.6916 + 16.3170i) q^{94} +(0.0916104 + 0.109177i) q^{95} +(-1.85003 + 7.81528i) q^{96} +(10.2887 + 1.81418i) q^{97} +(-0.930470 + 11.8328i) q^{98} +(-0.175006 + 0.348933i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.08992	+	1.29892i	−0.770690	+	0.918472i	−0.998473	−	0.0552397i	$-0.982408\pi$
$2$	−1.08992	+	1.29892i	−0.770690	+	0.918472i	0.227784	+	0.973712i	$0.426852\pi$
$3$	1.72029	−	0.201542i	0.993207	−	0.116360i
$3$	1.72029	−	0.201542i	0.993207	−	0.116360i
$4$	−0.151961	−	0.861812i	−0.0759803	−	0.430906i
$5$	1.13756	−	0.954530i	0.508734	−	0.426879i	−0.351949	−	0.936019i	$-0.614481\pi$
$5$	1.13756	−	0.954530i	0.508734	−	0.426879i	0.860684	+	0.509140i	$0.170037\pi$
$6$	−1.61319	+	2.45417i	−0.658581	+	1.00191i
$7$	2.51978	−	0.806679i	0.952386	−	0.304896i
$7$	2.51978	−	0.806679i	0.952386	−	0.304896i
$8$	−1.65184	−	0.953692i	−0.584015	−	0.337181i
$9$	2.91876	−	0.693419i	0.972921	−	0.231140i
$10$			2.51796i			0.796250i
$11$	−0.0836396	+	0.0996778i	−0.0252183	+	0.0300540i	−0.778506	−	0.627637i	$-0.784022\pi$
$11$	−0.0836396	+	0.0996778i	−0.0252183	+	0.0300540i	0.753288	+	0.657691i	$0.228467\pi$
$12$	−0.435107	−	1.45194i	−0.125605	−	0.419138i
$13$	−0.311287	+	0.855253i	−0.0863354	+	0.237205i	−0.975346	−	0.220683i	$-0.929171\pi$
$13$	−0.311287	+	0.855253i	−0.0863354	+	0.237205i	0.889010	+	0.457887i	$0.151394\pi$
$14$	−1.69855	+	4.15219i	−0.453955	+	1.10972i
$15$	1.76456	−	1.87133i	0.455607	−	0.483176i
$16$	4.68381	−	1.70477i	1.17095	−	0.426191i
$17$	−5.63249			−1.36608			−0.683040	−	0.730381i	$-0.739342\pi$
$17$	−5.63249			−1.36608			−0.683040	+	0.730381i	$0.739342\pi$
$18$	−2.28052	+	4.54700i	−0.537525	+	1.07174i
$19$			0.0959743i			0.0220180i	0.999939	+	0.0110090i	$0.00350435\pi$
$19$			0.0959743i			0.0220180i	−0.999939	+	0.0110090i	$0.996496\pi$
$20$	−0.995491	−	0.835316i	−0.222598	−	0.186782i
$21$	4.17215	−	1.89556i	0.910438	−	0.413645i
$22$	−0.0383126	−	0.217282i	−0.00816828	−	0.0463246i
$23$	−2.22151	+	6.10356i	−0.463218	+	1.27268i	0.459835	+	0.888005i	$0.347909\pi$
$23$	−2.22151	+	6.10356i	−0.463218	+	1.27268i	−0.923052	+	0.384675i	$0.874313\pi$
$24$	−3.03385	−	1.30771i	−0.619282	−	0.266935i
$25$	−0.485315	+	2.75236i	−0.0970630	+	0.550472i
$26$	−0.771624	−	1.33649i	−0.151328	−	0.262108i
$27$	4.88135	−	1.78113i	0.939416	−	0.342779i
$28$	−1.07811	−	2.04899i	−0.203744	−	0.387223i
$29$	0.238914	+	0.656410i	0.0443651	+	0.121892i	0.959897	−	0.280354i	$-0.0904518\pi$
$29$	0.238914	+	0.656410i	0.0443651	+	0.121892i	−0.915532	+	0.402246i	$0.868230\pi$
$30$	0.507475	+	4.33161i	0.0926518	+	0.790841i
$31$	−8.96076	+	1.58002i	−1.60940	+	0.283781i	−0.904804	−	0.425828i	$-0.859983\pi$
$31$	−8.96076	+	1.58002i	−1.60940	+	0.283781i	−0.704596	+	0.709609i	$0.748872\pi$
$32$	−1.58590	+	4.35722i	−0.280350	+	0.770254i
$33$	−0.123795	+	0.188331i	−0.0215499	+	0.0327842i
$34$	6.13896	−	7.31613i	1.05282	−	1.25471i
$35$	2.09641	−	3.32285i	0.354358	−	0.561664i
$36$	−1.04113	−	2.41005i	−0.173522	−	0.401675i
$37$	1.72508	−	2.98792i	0.283601	−	0.491211i	−0.688668	−	0.725077i	$-0.741804\pi$
$37$	1.72508	−	2.98792i	0.283601	−	0.491211i	0.972269	+	0.233866i	$0.0751376\pi$
$38$	−0.124663	−	0.104604i	−0.0202229	−	0.0169691i
$39$	−0.363133	+	1.53402i	−0.0581477	+	0.245639i
$40$	−2.78941	+	0.491848i	−0.441044	+	0.0777680i
$41$	−2.04536	−	0.744450i	−0.319432	−	0.116264i	0.177328	−	0.984152i	$-0.443255\pi$
$41$	−2.04536	−	0.744450i	−0.319432	−	0.116264i	−0.496760	+	0.867888i	$0.665477\pi$
$42$	−2.08514	+	7.48528i	−0.321744	+	1.15500i
$43$	1.37972	−	7.82480i	0.210406	−	1.19327i	−0.678297	−	0.734788i	$-0.737282\pi$
$43$	1.37972	−	7.82480i	0.210406	−	1.19327i	0.888703	−	0.458483i	$-0.151607\pi$
$44$	0.0986135	+	0.0569345i	0.0148665	+	0.00858320i
$45$	2.65839	−	3.57486i	0.396290	−	0.532908i
$46$	−5.50674	−	9.53795i	−0.811924	−	1.40629i
$47$	2.18137	−	12.3712i	0.318186	−	1.80452i	−0.235585	−	0.971854i	$-0.575701\pi$
$47$	2.18137	−	12.3712i	0.318186	−	1.80452i	0.553771	−	0.832669i	$-0.313188\pi$
$48$	7.71390	−	3.87667i	1.11341	−	0.559549i
$49$	5.69854	−	4.06530i	0.814077	−	0.580757i
$50$	−3.04613	−	3.63023i	−0.430787	−	0.513392i
$51$	−9.68949	+	1.13518i	−1.35680	+	0.158957i
$52$	0.784371	+	0.138306i	0.108773	+	0.0191795i
$53$	1.26661	+	0.731275i	0.173982	+	0.100448i	0.584462	−	0.811421i	$-0.301306\pi$
$53$	1.26661	+	0.731275i	0.173982	+	0.100448i	−0.410480	+	0.911869i	$0.634639\pi$
$54$	−3.00674	+	8.28175i	−0.409166	+	1.12700i
$55$			0.193227i			0.0260547i
$56$	−4.93160	−	1.07058i	−0.659013	−	0.143063i
$57$	0.0193428	+	0.165103i	0.00256202	+	0.0218685i
$58$	−1.11302	−	0.405105i	−0.146146	−	0.0531929i
$59$	5.96770	+	2.17206i	0.776928	+	0.282779i	0.699891	−	0.714250i	$-0.253232\pi$
$59$	5.96770	+	2.17206i	0.776928	+	0.282779i	0.0770368	+	0.997028i	$0.475454\pi$
$60$	−1.88088	−	1.23635i	−0.242820	−	0.159612i
$61$	−7.69007	−	1.35597i	−0.984613	−	0.173614i	−0.341913	−	0.939732i	$-0.611075\pi$
$61$	−7.69007	−	1.35597i	−0.984613	−	0.173614i	−0.642700	+	0.766118i	$0.722186\pi$
$62$	7.71419	−	13.3614i	0.979703	−	1.69690i
$63$	6.79526	−	4.10176i	0.856122	−	0.516774i
$64$	1.05325	+	1.82428i	0.131656	+	0.228035i
$65$	0.462256	+	1.27004i	0.0573358	+	0.157529i
$66$	−0.109700	−	0.366065i	−0.0135031	−	0.0450595i
$67$	−11.0280	+	9.25358i	−1.34728	+	1.13050i	−0.367592	+	0.929987i	$0.619818\pi$
$67$	−11.0280	+	9.25358i	−1.34728	+	1.13050i	−0.979690	+	0.200517i	$0.935738\pi$
$68$	0.855917	+	4.85415i	0.103795	+	0.588652i
$69$	−2.59151	+	10.9476i	−0.311982	+	1.31793i
$70$	2.03119	+	6.34470i	0.242773	+	0.758337i
$71$	2.38823	−	1.37884i	0.283431	−	0.163639i	−0.351545	−	0.936171i	$-0.614344\pi$
$71$	2.38823	−	1.37884i	0.283431	−	0.163639i	0.634975	+	0.772532i	$0.281010\pi$
$72$	−5.48265	−	1.63818i	−0.646136	−	0.193062i
$73$	−6.94774	+	4.01128i	−0.813171	+	0.469485i	−0.848056	−	0.529907i	$-0.822227\pi$
$73$	−6.94774	+	4.01128i	−0.813171	+	0.469485i	0.0348847	+	0.999391i	$0.488894\pi$
$74$	2.00086	+	5.49732i	0.232595	+	0.639051i
$75$	−0.280165	+	4.83265i	−0.0323507	+	0.558027i
$76$	0.0827118	−	0.0145843i	0.00948770	−	0.00167294i
$77$	−0.130345	+	0.318636i	−0.0148542	+	0.0363119i
$78$	−1.59677	−	2.14363i	−0.180799	−	0.242719i
$79$	0.310233	+	0.260316i	0.0349039	+	0.0292879i	0.660073	−	0.751202i	$-0.270525\pi$
$79$	0.310233	+	0.260316i	0.0349039	+	0.0292879i	−0.625169	+	0.780490i	$0.714970\pi$
$80$	3.70088	−	6.41012i	0.413771	−	0.716673i
$81$	8.03834	−	4.04785i	0.893149	−	0.449761i
$82$	3.19626	−	1.84536i	0.352968	−	0.203786i
$83$	−4.54412	+	1.65393i	−0.498782	+	0.181542i	−0.579146	−	0.815224i	$-0.696614\pi$
$83$	−4.54412	+	1.65393i	−0.498782	+	0.181542i	0.0803638	+	0.996766i	$0.474392\pi$
$84$	−2.26762	−	3.30756i	−0.247417	−	0.360885i
$85$	−6.40732	+	5.37638i	−0.694972	+	0.583150i
$86$	8.65997	+	10.3205i	0.933828	+	1.11289i
$87$	0.543293	+	1.08106i	0.0582472	+	0.115902i
$88$	0.233222	−	0.0848857i	0.0248615	−	0.00904884i
$89$	15.9719			1.69302			0.846508	−	0.532376i	$-0.178701\pi$
$89$	15.9719			1.69302			0.846508	+	0.532376i	$0.178701\pi$
$90$	1.74600	+	7.34933i	0.184045	+	0.774688i
$91$	−0.0944582	+	2.40615i	−0.00990191	+	0.252233i
$92$	5.59770	+	0.987026i	0.583601	+	0.102905i
$93$	−15.0966	+	4.52406i	−1.56545	+	0.469123i
$94$	13.6916	+	16.3170i	1.41218	+	1.68297i
$95$	0.0916104	+	0.109177i	0.00939903	+	0.0112013i
$96$	−1.85003	+	7.81528i	−0.188818	+	0.797643i
$97$	10.2887	+	1.81418i	1.04466	+	0.184202i	0.669541	−	0.742775i	$-0.266491\pi$
$97$	10.2887	+	1.81418i	1.04466	+	0.184202i	0.375118	+	0.926977i	$0.377602\pi$
$98$	−0.930470	+	11.8328i	−0.0939916	+	1.19529i
$99$	−0.175006	+	0.348933i	−0.0175887	+	0.0350691i
$100$	2.44576			0.244576
$101$	4.01032	−	1.45964i	0.399042	−	0.145239i	−0.134701	−	0.990886i	$-0.543007\pi$
$101$	4.01032	−	1.45964i	0.399042	−	0.145239i	0.533743	+	0.845647i	$0.320785\pi$
$102$	9.08626	−	13.8231i	0.899673	−	1.36869i
$103$	−2.60642	−	3.10621i	−0.256818	−	0.306064i	0.622194	−	0.782863i	$-0.286241\pi$
$103$	−2.60642	−	3.10621i	−0.256818	−	0.306064i	−0.879012	+	0.476799i	$0.841797\pi$
$104$	1.32985	−	1.11587i	0.130402	−	0.109420i
$105$	2.93673	−	6.13877i	0.286595	−	0.599082i
$106$	−2.33036	+	0.848183i	−0.226345	+	0.0823828i
$107$	−8.99730	+	5.19460i	−0.869802	+	0.502181i	−0.867283	−	0.497816i	$-0.834135\pi$
$107$	−8.99730	+	5.19460i	−0.869802	+	0.502181i	−0.00251969	+	0.999997i	$0.500802\pi$
$108$	−2.27677	−	3.93614i	−0.219083	−	0.378756i
$109$	2.59277	−	4.49081i	0.248342	−	0.430142i	−0.714724	−	0.699407i	$-0.753447\pi$
$109$	2.59277	−	4.49081i	0.248342	−	0.430142i	0.963066	+	0.269265i	$0.0867808\pi$
$110$	−0.250985	−	0.210601i	−0.0239305	−	0.0200801i
$111$	2.36543	−	5.48775i	0.224517	−	0.520874i
$112$	10.4269	−	8.07395i	0.985253	−	0.762917i
$113$	−15.1938	+	2.67908i	−1.42931	+	0.252026i	−0.834132	−	0.551565i	$-0.814031\pi$
$113$	−15.1938	+	2.67908i	−1.42931	+	0.252026i	−0.595181	+	0.803592i	$0.702920\pi$
$114$	−0.235537	−	0.154825i	−0.0220601	−	0.0145006i
$115$	3.29892	+	9.06369i	0.307625	+	0.845194i
$116$	0.529396	−	0.305647i	0.0491532	−	0.0283786i
$117$	−0.315523	+	2.71213i	−0.0291701	+	0.250737i
$118$	−9.32564	+	5.38416i	−0.858494	+	0.495652i
$119$	−14.1926	+	4.54361i	−1.30103	+	0.416512i
$120$	−4.69945	+	1.40830i	−0.428999	+	0.128560i
$121$	1.90719	+	10.8162i	0.173381	+	0.983292i
$122$	10.1428	−	8.51086i	0.918290	−	0.770537i
$123$	−3.66864	−	0.868441i	−0.330790	−	0.0783047i
$124$	2.72337	+	7.48239i	0.244565	+	0.671938i
$125$	5.78760	+	10.0244i	0.517658	+	0.896611i
$126$	−2.07844	+	13.2971i	−0.185162	+	1.18460i
$127$	−0.565054	+	0.978702i	−0.0501404	+	0.0868458i	−0.890006	−	0.455948i	$-0.849300\pi$
$127$	−0.565054	+	0.978702i	−0.0501404	+	0.0868458i	0.839866	+	0.542794i	$0.182634\pi$
$128$	−12.6503	−	2.23060i	−1.11814	−	0.197159i
$129$	0.796493	−	13.7390i	0.0701273	−	1.20965i
$130$	−2.15349	−	0.783808i	−0.188874	−	0.0687445i
$131$	6.15002	+	2.23842i	0.537330	+	0.195572i	0.596408	−	0.802681i	$-0.296594\pi$
$131$	6.15002	+	2.23842i	0.537330	+	0.195572i	−0.0590784	+	0.998253i	$0.518816\pi$
$132$	0.181118	+	0.0780688i	0.0157643	+	0.00679502i
$133$	0.0774204	+	0.241834i	0.00671320	+	0.0209696i
$134$		−	24.4101i		−	2.10871i
$135$	3.85271	−	6.68555i	0.331588	−	0.575400i
$136$	9.30399	+	5.37166i	0.797811	+	0.460616i
$137$	4.57928	+	0.807451i	0.391234	+	0.0689852i	0.365805	−	0.930691i	$-0.380794\pi$
$137$	4.57928	+	0.807451i	0.391234	+	0.0689852i	0.0254292	+	0.999677i	$0.491905\pi$
$138$	−11.3955	−	15.2981i	−0.970045	−	1.30226i
$139$	−8.26472	−	9.84951i	−0.701005	−	0.835425i	0.291635	−	0.956530i	$-0.405801\pi$
$139$	−8.26472	−	9.84951i	−0.701005	−	0.835425i	−0.992640	+	0.121105i	$0.961356\pi$
$140$	−3.18224	−	1.30177i	−0.268949	−	0.110019i
$141$	1.25927	−	21.7216i	0.106050	−	1.82929i
$142$	−0.811975	+	4.60494i	−0.0681394	+	0.386438i
$143$	−0.0592139	−	0.102561i	−0.00495171	−	0.00857662i
$144$	12.4888	−	8.22364i	1.04073	−	0.685304i
$145$	0.898343	+	0.518658i	0.0746033	+	0.0430722i
$146$	2.36216	−	13.3965i	0.195494	−	1.10870i
$147$	8.98378	−	8.14197i	0.740970	−	0.671538i
$148$	−2.83717	−	1.03265i	−0.233214	−	0.0848829i
$149$	20.1468	−	3.55243i	1.65049	−	0.291027i	0.730486	−	0.682927i	$-0.239293\pi$
$149$	20.1468	−	3.55243i	1.65049	−	0.291027i	0.920007	+	0.391901i	$0.128182\pi$
$150$	−5.97185	−	5.63111i	−0.487600	−	0.459779i
$151$	−10.4393	−	8.75958i	−0.849535	−	0.712845i	0.110152	−	0.993915i	$-0.464866\pi$
$151$	−10.4393	−	8.75958i	−0.849535	−	0.712845i	−0.959687	+	0.281070i	$0.909311\pi$
$152$	0.0915300	−	0.158535i	0.00742406	−	0.0128589i
$153$	−16.4399	+	3.90567i	−1.32909	+	0.315755i
$154$	−0.271816	−	0.516595i	−0.0219035	−	0.0416284i
$155$	−8.68526	+	10.3507i	−0.697617	+	0.831388i
$156$	1.37722	+	0.0798418i	0.110265	+	0.00639246i
$157$	1.36266	−	3.74388i	0.108752	−	0.298794i	−0.873365	−	0.487067i	$-0.838067\pi$
$157$	1.36266	−	3.74388i	0.108752	−	0.298794i	0.982117	+	0.188273i	$0.0602889\pi$
$158$	−0.676258	+	0.119242i	−0.0538002	+	0.00948642i
$159$	2.32631	+	1.00273i	0.184488	+	0.0795215i
$160$	2.35503	+	6.47040i	0.186182	+	0.511530i
$161$	−0.674106	+	17.1716i	−0.0531270	+	1.35332i
$162$	−3.50333	+	14.8530i	−0.275248	+	1.16696i
$163$	−12.3022	−	21.3081i	−0.963584	−	1.66898i	−0.713372	−	0.700785i	$-0.752833\pi$
$163$	−12.3022	−	21.3081i	−0.963584	−	1.66898i	−0.250212	−	0.968191i	$-0.580500\pi$
$164$	−0.330762	+	1.87584i	−0.0258282	+	0.146479i
$165$	0.0389432	+	0.332405i	0.00303173	+	0.0258777i
$166$	2.80442	−	7.70508i	0.217665	−	0.598030i
$167$	−3.18840	−	18.0823i	−0.246726	−	1.39925i	−0.816450	−	0.577417i	$-0.804061\pi$
$167$	−3.18840	−	18.0823i	−0.246726	−	1.39925i	0.569724	−	0.821836i	$-0.307050\pi$
$168$	−8.69952	−	0.847786i	−0.671183	−	0.0654081i
$169$	9.32402	+	7.82378i	0.717232	+	0.601829i
$170$		−	14.1824i		−	1.08774i
$171$	0.0665504	+	0.280126i	0.00508924	+	0.0214218i
$172$	−6.95317			−0.530174
$173$	−3.04671	+	1.10891i	−0.231637	+	0.0843090i	−0.455231	−	0.890373i	$-0.650443\pi$
$173$	−3.04671	+	1.10891i	−0.231637	+	0.0843090i	0.223594	+	0.974682i	$0.428221\pi$
$174$	−1.99635	−	0.472577i	−0.151343	−	0.0358260i
$175$	0.997384	+	7.32682i	0.0753951	+	0.553855i
$176$	−0.221824	+	0.609457i	−0.0167206	+	0.0459396i
$177$	10.7039	+	2.53383i	0.804554	+	0.190454i
$178$	−17.4081	+	20.7461i	−1.30479	+	1.55499i
$179$			19.6751i			1.47058i	0.677750	+	0.735292i	$0.262955\pi$
$179$			19.6751i			1.47058i	−0.677750	+	0.735292i	$0.737045\pi$
$180$	−3.48482	−	1.74780i	−0.259743	−	0.130273i
$181$	14.9844	+	8.65126i	1.11378	+	0.643043i	0.939806	−	0.341707i	$-0.111005\pi$
$181$	14.9844	+	8.65126i	1.11378	+	0.643043i	0.173976	+	0.984750i	$0.444338\pi$
$182$	−3.02244	−	2.74521i	−0.224038	−	0.203488i
$183$	−13.5024	−	0.782779i	−0.998126	−	0.0578647i
$184$	9.49051	−	7.96348i	0.699650	−	0.587076i
$185$	−0.889674	−	5.04559i	−0.0654101	−	0.370959i
$186$	10.5777	−	24.5401i	0.775597	−	1.79937i
$187$	0.471099	−	0.561434i	0.0344502	−	0.0410561i
$188$	−10.9931			−0.801755
$189$	10.8631	−	8.42573i	0.790175	−	0.612882i
$190$	−0.241660			−0.0175318
$191$	3.40180	−	4.05411i	0.246146	−	0.293345i	−0.628799	−	0.777568i	$-0.716453\pi$
$191$	3.40180	−	4.05411i	0.246146	−	0.293345i	0.874945	+	0.484223i	$0.160898\pi$
$192$	2.17955	+	2.92600i	0.157296	+	0.211166i
$193$	3.06808	+	17.3999i	0.220845	+	1.25248i	0.870470	+	0.492221i	$0.163815\pi$
$193$	3.06808	+	17.3999i	0.220845	+	1.25248i	−0.649625	+	0.760255i	$0.725074\pi$
$194$	−13.5703	+	11.3868i	−0.974292	+	0.817528i
$195$	1.05118	+	2.09166i	0.0752764	+	0.149787i
$196$	−4.36948	−	4.29330i	−0.312105	−	0.306665i
$197$	17.9168	+	10.3443i	1.27652	+	0.736997i	0.976206	−	0.216844i	$-0.0695763\pi$
$197$	17.9168	+	10.3443i	1.27652	+	0.736997i	0.300311	+	0.953841i	$0.402910\pi$
$198$	−0.262493	−	0.607627i	−0.0186545	−	0.0431821i
$199$		−	12.7755i		−	0.905634i	−0.891604	−	0.452817i	$-0.850419\pi$
$199$		−	12.7755i		−	0.905634i	0.891604	−	0.452817i	$-0.149581\pi$
$200$	3.42657	−	4.08362i	0.242295	−	0.288756i
$201$	−17.1063	+	18.1414i	−1.20658	+	1.27960i
$202$	−2.47498	+	6.79996i	−0.174139	+	0.478443i
$203$	1.13152	+	1.46128i	0.0794172	+	0.102562i
$204$	2.45073	+	8.17801i	0.171586	+	0.572575i
$205$	−3.03733	+	1.10550i	−0.212136	+	0.0772113i
$206$	6.87550			0.479039
$207$	−2.25175	+	19.3553i	−0.156507	+	1.34528i
$208$			4.53651i			0.314550i
$209$	−0.00956651	−	0.00802726i	−0.000661729	−	0.000555257i
$210$	4.77294	+	10.5053i	0.329364	+	0.724936i
$211$	3.56749	+	20.2322i	0.245596	+	1.39284i	0.819104	+	0.573645i	$0.194471\pi$
$211$	3.56749	+	20.2322i	0.245596	+	1.39284i	−0.573508	+	0.819200i	$0.694418\pi$
$212$	0.437747	−	1.20270i	0.0300646	−	0.0826018i
$213$	3.83054	−	2.85333i	0.262464	−	0.195507i
$214$	3.05900	−	17.3484i	0.209109	−	1.18591i
$215$	−5.89948	−	10.2182i	−0.402341	−	0.696876i
$216$	−9.76188	−	1.71316i	−0.664212	−	0.116566i
$217$	−21.3045	+	11.2098i	−1.44625	+	0.760968i
$218$	3.00727	+	8.26242i	0.203678	+	0.559601i
$219$	−11.1436	+	8.30080i	−0.753018	+	0.560916i
$220$	0.166525	−	0.0293628i	0.0112271	−	0.00197964i
$221$	1.75332	−	4.81720i	0.117941	−	0.324040i
$222$	4.54999	+	9.05370i	0.305376	+	0.607645i
$223$	12.6494	−	15.0750i	0.847070	−	1.00950i	−0.152705	−	0.988272i	$-0.548798\pi$
$223$	12.6494	−	15.0750i	0.847070	−	1.00950i	0.999775	−	0.0212263i	$-0.00675706\pi$
$224$	−0.481231	+	12.2585i	−0.0321536	+	0.819056i
$225$	0.492018	+	8.37001i	0.0328012	+	0.558000i
$226$	13.0801	−	22.6554i	0.870077	−	1.50702i
$227$	−0.244120	−	0.204841i	−0.0162028	−	0.0135958i	0.634650	−	0.772799i	$-0.281144\pi$
$227$	−0.244120	−	0.204841i	−0.0162028	−	0.0135958i	−0.650853	+	0.759204i	$0.725589\pi$
$228$	0.139349	−	0.0417591i	0.00922858	−	0.00276556i
$229$	8.52907	−	1.50391i	0.563617	−	0.0993809i	0.115422	−	0.993317i	$-0.463178\pi$
$229$	8.52907	−	1.50391i	0.563617	−	0.0993809i	0.448195	+	0.893936i	$0.352067\pi$
$230$	−15.3685	−	5.59369i	−1.01337	−	0.368837i
$231$	−0.160012	+	0.574415i	−0.0105280	+	0.0377937i
$232$	0.231365	−	1.31214i	0.0151899	−	0.0861460i
$233$	−6.35900	−	3.67137i	−0.416592	−	0.240520i	0.277026	−	0.960862i	$-0.410651\pi$
$233$	−6.35900	−	3.67137i	−0.416592	−	0.240520i	−0.693618	+	0.720343i	$0.743984\pi$
$234$	−3.17894	−	3.36584i	−0.207814	−	0.220032i
$235$	−9.32722	−	16.1552i	−0.608440	−	1.05385i
$236$	0.965055	−	5.47310i	0.0628197	−	0.356268i
$237$	0.586153	+	0.385293i	0.0380748	+	0.0250275i
$238$	9.56704	−	23.3872i	0.620139	−	1.51596i
$239$	−3.02456	−	3.60453i	−0.195642	−	0.233157i	0.659301	−	0.751879i	$-0.270852\pi$
$239$	−3.02456	−	3.60453i	−0.195642	−	0.233157i	−0.854943	+	0.518722i	$0.826408\pi$
$240$	5.07467	−	11.7731i	0.327568	−	0.759951i
$241$	−6.53071	−	1.15154i	−0.420680	−	0.0741773i	−0.0406989	−	0.999171i	$-0.512958\pi$
$241$	−6.53071	−	1.15154i	−0.420680	−	0.0741773i	−0.379981	+	0.924994i	$0.624070\pi$
$242$	−16.1280	−	9.31152i	−1.03675	−	0.598567i
$243$	13.0124	−	8.58351i	0.834748	−	0.550633i
$244$			6.83345i			0.437467i
$245$	2.60201	−	10.0640i	0.166236	−	0.642963i
$246$	5.12656	−	3.81872i	0.326857	−	0.243473i
$247$	−0.0820823	−	0.0298755i	−0.00522277	−	0.00190093i
$248$	16.3086	+	5.93585i	1.03560	+	0.376927i
$249$	−7.48385	+	3.76106i	−0.474270	+	0.238347i
$250$	−19.3289	−	3.40820i	−1.22247	−	0.215554i
$251$	−7.34905	+	12.7289i	−0.463868	+	0.803443i	−0.999150	−	0.0412308i	$-0.986872\pi$
$251$	−7.34905	+	12.7289i	−0.463868	+	0.803443i	0.535282	+	0.844674i	$0.320205\pi$
$252$	−4.56756	−	5.23293i	−0.287729	−	0.329644i
$253$	−0.422583	−	0.731935i	−0.0265675	−	0.0460163i
$254$	−0.655388	−	1.80066i	−0.0411227	−	0.112984i
$255$	−9.93885	+	10.5403i	−0.622395	+	0.660056i
$256$	13.4579	−	11.2925i	0.841118	−	0.705782i
$257$	−2.45224	−	13.9074i	−0.152967	−	0.867517i	−0.960621	−	0.277861i	$-0.910375\pi$
$257$	−2.45224	−	13.9074i	−0.152967	−	0.867517i	0.807655	−	0.589656i	$-0.200737\pi$
$258$	16.9776	+	16.0089i	1.05698	+	0.996673i
$259$	1.93651	−	8.92047i	0.120329	−	0.554291i
$260$	1.02429	−	0.591374i	0.0635237	−	0.0366754i
$261$	1.15250	+	1.75024i	0.0713379	+	0.108337i
$262$	−9.61055	+	5.54865i	−0.593742	+	0.342797i
$263$	5.34900	+	14.6963i	0.329834	+	0.906211i	0.988153	+	0.153472i	$0.0490454\pi$
$263$	5.34900	+	14.6963i	0.329834	+	0.906211i	−0.658319	+	0.752739i	$0.728732\pi$
$264$	0.384099	−	0.193031i	0.0236397	−	0.0118803i
$265$	2.13887	−	0.377141i	0.131390	−	0.0231676i
$266$	−0.398504	−	0.163017i	−0.0244338	−	0.00999520i
$267$	27.4762	−	3.21900i	1.68152	−	0.197000i
$268$	9.65066	+	8.09787i	0.589508	+	0.494656i
$269$	−2.15558	+	3.73358i	−0.131428	+	0.227640i	−0.924227	−	0.381843i	$-0.875290\pi$
$269$	−2.15558	+	3.73358i	−0.131428	+	0.227640i	0.792799	+	0.609483i	$0.208623\pi$
$270$	4.48482	+	12.2911i	0.272937	+	0.748010i
$271$	16.1867	−	9.34540i	0.983272	−	0.567692i	0.0800157	−	0.996794i	$-0.474503\pi$
$271$	16.1867	−	9.34540i	0.983272	−	0.567692i	0.903256	+	0.429101i	$0.141170\pi$
$272$	−26.3815	+	9.60207i	−1.59961	+	0.582211i
$273$	0.322446	+	4.15831i	0.0195153	+	0.251672i
$274$	−6.03986	+	5.06804i	−0.364881	+	0.306172i
$275$	−0.233757	−	0.278581i	−0.0140961	−	0.0167991i
$276$	9.82857	+	0.569795i	0.591610	+	0.0342976i
$277$	−8.83184	+	3.21453i	−0.530654	+	0.193142i	−0.593430	−	0.804885i	$-0.702227\pi$
$277$	−8.83184	+	3.21453i	−0.530654	+	0.193142i	0.0627763	+	0.998028i	$0.480005\pi$
$278$	21.8016			1.30757
$279$	−25.0587	+	10.8253i	−1.50023	+	0.648092i
$280$	−6.63192	+	3.48950i	−0.396333	+	0.208538i
$281$	27.0442	+	4.76862i	1.61332	+	0.284472i	0.906272	−	0.422694i	$-0.138916\pi$
$281$	27.0442	+	4.76862i	1.61332	+	0.284472i	0.707048	+	0.707166i	$0.250027\pi$
$282$	26.8420	+	25.3105i	1.59842	+	1.50722i
$283$	−13.9408	−	16.6140i	−0.828694	−	0.987599i	−0.999997	−	0.00238075i	$-0.999242\pi$
$283$	−13.9408	−	16.6140i	−0.828694	−	0.987599i	0.171303	−	0.985218i	$-0.445202\pi$
$284$	−1.55122	−	1.84867i	−0.0920481	−	0.109699i
$285$	0.179600	+	0.169352i	0.0106386	+	0.0100316i
$286$	0.197757	+	0.0348699i	0.0116936	+	0.00206190i
$287$	−5.75438	−	0.225899i	−0.339670	−	0.0133344i
$288$	−1.60748	+	13.8174i	−0.0947217	+	0.814196i
$289$	14.7249			0.866172
$290$	−1.65281	+	0.601575i	−0.0970566	+	0.0353257i
$291$	18.0651	+	1.04730i	1.05900	+	0.0613936i
$292$	4.51275	+	5.37809i	0.264089	+	0.314729i
$293$	7.22978	−	6.06651i	0.422368	−	0.354409i	−0.406695	−	0.913564i	$-0.633319\pi$
$293$	7.22978	−	6.06651i	0.422368	−	0.354409i	0.829063	+	0.559155i	$0.188874\pi$
$294$	0.784125	+	20.5433i	0.0457311	+	1.19811i
$295$	8.86194	−	3.22548i	0.515962	−	0.187795i
$296$	−5.69911	+	3.29038i	−0.331254	+	0.191250i
$297$	−0.230735	+	0.635535i	−0.0133886	+	0.0368775i
$298$	−17.3441	+	30.0409i	−1.00472	+	1.74022i
$299$	−4.52856	−	3.79991i	−0.261893	−	0.219755i
$300$	4.20741	−	0.492924i	0.242915	−	0.0284590i
$301$	−2.83551	−	20.8297i	−0.163436	−	1.20061i
$302$	22.7559	−	4.01248i	1.30946	−	0.230892i
$303$	6.60472	−	3.31924i	0.379431	−	0.190685i
$304$	0.163614	+	0.449525i	0.00938389	+	0.0257820i
$305$	−10.0423	+	5.79790i	−0.575018	+	0.331987i
$306$	12.8450	−	25.6109i	0.734301	−	1.46408i
$307$	−4.86656	+	2.80971i	−0.277749	+	0.160358i	−0.632404	−	0.774639i	$-0.717932\pi$
$307$	−4.86656	+	2.80971i	−0.277749	+	0.160358i	0.354655	+	0.934997i	$0.384598\pi$
$308$	0.294412	+	0.0639128i	0.0167757	+	0.00364177i
$309$	−5.10982	−	4.81827i	−0.290687	−	0.274102i
$310$	−3.97844	−	22.5628i	−0.225960	−	1.28148i
$311$	−13.3712	+	11.2198i	−0.758213	+	0.636216i	−0.937661	−	0.347551i	$-0.887013\pi$
$311$	−13.3712	+	11.2198i	−0.758213	+	0.636216i	0.179448	+	0.983767i	$0.442569\pi$
$312$	2.06282	−	2.18764i	0.116784	−	0.123851i
$313$	0.170801	+	0.469272i	0.00965424	+	0.0265248i	0.944426	−	0.328724i	$-0.106618\pi$
$313$	0.170801	+	0.469272i	0.00965424	+	0.0265248i	−0.934772	+	0.355248i	$0.884396\pi$
$314$	3.37779	+	5.85051i	0.190620	+	0.330163i
$315$	3.81479	−	11.1523i	0.214939	−	0.628361i
$316$	0.177200	−	0.306920i	0.00996830	−	0.0172656i
$317$	7.69250	+	1.35640i	0.432054	+	0.0761828i	0.385446	−	0.922730i	$-0.374048\pi$
$317$	7.69250	+	1.35640i	0.432054	+	0.0761828i	0.0466081	+	0.998913i	$0.485159\pi$
$318$	−3.83794	+	1.92878i	−0.215221	+	0.108161i
$319$	−0.0854121	−	0.0310875i	−0.00478216	−	0.00174056i
$320$	2.93946	+	1.06988i	0.164321	+	0.0598079i
$321$	−14.4310	+	10.7495i	−0.805460	+	0.599980i
$322$	−21.5698	−	19.5913i	−1.20204	−	1.09178i
$323$		−	0.540574i		−	0.0300784i
$324$	−4.71000	−	6.31242i	−0.261666	−	0.350690i
$325$	−2.20289	−	1.27184i	−0.122194	−	0.0705490i
$326$	41.0858	+	7.24454i	2.27553	+	0.401238i
$327$	3.55522	−	8.24803i	0.196604	−	0.456117i
$328$	2.66864	+	3.18036i	0.147351	+	0.175606i
$329$	−4.48300	−	32.9323i	−0.247156	−	1.81562i
$330$	−0.474211	−	0.311710i	−0.0261044	−	0.0171591i
$331$	−5.48925	+	31.1311i	−0.301716	+	1.71112i	0.336855	+	0.941556i	$0.390637\pi$
$331$	−5.48925	+	31.1311i	−0.301716	+	1.71112i	−0.638572	+	0.769562i	$0.720474\pi$
$332$	2.11590	+	3.66485i	0.116125	+	0.201135i
$333$	2.96321	−	9.91723i	0.162383	−	0.543461i
$334$	26.9625	+	15.5668i	1.47532	+	0.851779i
$335$	−3.71223	+	21.0531i	−0.202821	+	1.15025i
$336$	16.3101	−	15.9910i	0.889787	−	0.872379i
$337$	−6.59007	−	2.39859i	−0.358984	−	0.130659i	0.156231	−	0.987721i	$-0.450066\pi$
$337$	−6.59007	−	2.39859i	−0.358984	−	0.130659i	−0.515215	+	0.857061i	$0.672288\pi$
$338$	−20.3249	+	3.58382i	−1.10553	+	0.194934i
$339$	−25.5977	+	7.67096i	−1.39028	+	0.416629i
$340$	5.60709	+	4.70491i	0.304087	+	0.255159i
$341$	0.591981	−	1.02534i	0.0320576	−	0.0555253i
$342$	−0.436395	−	0.218872i	−0.0235975	−	0.0118352i
$343$	11.0797	−	14.8405i	0.598245	−	0.801313i
$344$	−9.74154	+	11.6095i	−0.525229	+	0.625943i
$345$	7.50179	+	14.9273i	0.403883	+	0.803657i
$346$	1.88029	−	5.16605i	0.101085	−	0.277728i
$347$	−10.4676	+	1.84572i	−0.561929	+	0.0990832i	−0.447396	−	0.894336i	$-0.647648\pi$
$347$	−10.4676	+	1.84572i	−0.561929	+	0.0990832i	−0.114533	+	0.993419i	$0.536537\pi$
$348$	0.849112	−	0.632496i	0.0455172	−	0.0339053i
$349$	−2.52401	−	6.93467i	−0.135107	−	0.371204i	0.853627	−	0.520885i	$-0.174398\pi$
$349$	−2.52401	−	6.93467i	−0.135107	−	0.371204i	−0.988734	+	0.149680i	$0.952176\pi$
$350$	−10.6040	−	6.69013i	−0.566807	−	0.357602i
$351$	0.00381826	+	4.72923i	0.000203804	+	0.252428i
$352$	−0.301674	−	0.522514i	−0.0160793	−	0.0278501i
$353$	2.89186	−	16.4006i	0.153918	−	0.872915i	−0.805850	−	0.592120i	$-0.798291\pi$
$353$	2.89186	−	16.4006i	0.153918	−	0.872915i	0.959768	−	0.280794i	$-0.0905979\pi$
$354$	−14.9576	+	11.1418i	−0.794989	+	0.592180i
$355$	1.40062	−	3.84816i	0.0743370	−	0.204239i
$356$	−2.42710	−	13.7648i	−0.128636	−	0.729531i
$357$	−23.4996	+	10.6767i	−1.24373	+	0.565071i
$358$	−25.5563	−	21.4443i	−1.35069	−	1.13336i
$359$		−	17.3398i		−	0.915160i	−0.889169	−	0.457580i	$-0.848716\pi$
$359$		−	17.3398i		−	0.915160i	0.889169	−	0.457580i	$-0.151284\pi$
$360$	−7.80056	+	3.36981i	−0.411126	+	0.177605i
$361$	18.9908			0.999515
$362$	−27.5691	+	10.0343i	−1.44900	+	0.527392i
$363$	5.46083	+	18.2226i	0.286619	+	0.956438i
$364$	2.08801	−	0.284236i	0.109441	−	0.0148980i
$365$	−4.07462	+	11.1949i	−0.213275	+	0.585969i
$366$	15.7333	−	16.6853i	0.822392	−	0.872155i
$367$	17.1783	−	20.4723i	0.896698	−	1.06864i	−0.100581	−	0.994929i	$-0.532070\pi$
$367$	17.1783	−	20.4723i	0.896698	−	1.06864i	0.997279	−	0.0737143i	$-0.0234853\pi$
$368$			32.3750i			1.68767i
$369$	−6.48614	−	0.754582i	−0.337655	−	0.0392820i
$370$	7.52347	+	4.34368i	0.391127	+	0.225817i
$371$	3.78147	+	0.820906i	0.196324	+	0.0426193i
$372$	6.19298	+	12.3230i	0.321091	+	0.638916i
$373$	−14.1817	+	11.8999i	−0.734300	+	0.616151i	−0.931300	−	0.364253i	$-0.881325\pi$
$373$	−14.1817	+	11.8999i	−0.734300	+	0.616151i	0.197000	+	0.980403i	$0.436880\pi$
$374$	0.215795	+	1.22384i	0.0111585	+	0.0632831i
$375$	11.9767	+	16.0784i	0.618472	+	0.830285i
$376$	−15.4016	+	18.3549i	−0.794276	+	0.946582i
$377$	−0.635767			−0.0327437
$378$	−0.895601	+	23.2936i	−0.0460647	+	1.19809i
$379$	35.2309			1.80969			0.904846	−	0.425739i	$-0.139986\pi$
$379$	35.2309			1.80969			0.904846	+	0.425739i	$0.139986\pi$
$380$	0.0801689	−	0.0955416i	0.00411258	−	0.00490118i
$381$	−0.774805	+	1.79753i	−0.0396945	+	0.0920902i
$382$	1.55825	+	8.83730i	0.0797272	+	0.452156i
$383$	−12.7995	+	10.7400i	−0.654022	+	0.548790i	−0.908288	−	0.418345i	$-0.862610\pi$
$383$	−12.7995	+	10.7400i	−0.654022	+	0.548790i	0.254266	+	0.967134i	$0.418166\pi$
$384$	−22.2118	−	1.28769i	−1.13349	−	0.0657122i
$385$	0.155872	+	0.486887i	0.00794396	+	0.0248141i
$386$	−25.9450	−	14.9794i	−1.32057	−	0.762429i
$387$	−1.39878	−	23.7955i	−0.0711039	−	1.20959i
$388$		−	9.14261i		−	0.464146i
$389$	6.09977	−	7.26943i	0.309271	−	0.368575i	−0.588912	−	0.808197i	$-0.700443\pi$
$389$	6.09977	−	7.26943i	0.309271	−	0.368575i	0.898183	+	0.439623i	$0.144888\pi$
$390$	−3.86260	−	0.914354i	−0.195590	−	0.0463001i
$391$	12.5126	−	34.3782i	0.632792	−	1.73858i
$392$	−13.2901	+	1.28058i	−0.671253	+	0.0646793i
$393$	11.0309	+	2.61124i	0.556436	+	0.131720i
$394$	−32.9642	+	11.9980i	−1.66071	+	0.604449i
$395$	0.601390			0.0302592
$396$	0.327309	+	0.0977978i	0.0164479	+	0.00491453i
$397$			38.0530i			1.90983i	0.296886	+	0.954913i	$0.404052\pi$
$397$			38.0530i			1.90983i	−0.296886	+	0.954913i	$0.595948\pi$
$398$	16.5943	+	13.9243i	0.831799	+	0.697962i
$399$	0.181925	+	0.400420i	0.00910763	+	0.0200461i
$400$	2.41901	+	13.7189i	0.120950	+	0.685943i
$401$	−1.92376	+	5.28549i	−0.0960680	+	0.263945i	−0.978413	−	0.206658i	$-0.933741\pi$
$401$	−1.92376	+	5.28549i	−0.0960680	+	0.263945i	0.882345	+	0.470603i	$0.155963\pi$
$402$	−4.91965	−	41.9923i	−0.245370	−	2.09439i
$403$	1.43804	−	8.15556i	0.0716341	−	0.406257i
$404$	−1.86734	−	3.23434i	−0.0929039	−	0.160914i
$405$	5.28034	−	12.2775i	0.262382	−	0.610075i
$406$	−3.13134	−	0.122927i	−0.155406	−	0.00610076i
$407$	0.153545	+	0.421860i	0.00761092	+	0.0209108i
$408$	17.0881	+	7.36565i	0.845989	+	0.364654i
$409$	−2.17218	+	0.383014i	−0.107407	+	0.0189388i	−0.227093	−	0.973873i	$-0.572922\pi$
$409$	−2.17218	+	0.383014i	−0.107407	+	0.0189388i	0.119686	+	0.992812i	$0.461811\pi$
$410$	1.87450	−	5.15014i	0.0925749	−	0.254347i
$411$	8.04040	+	0.466129i	0.396604	+	0.0229924i
$412$	−2.28090	+	2.71827i	−0.112372	+	0.133919i
$413$	16.7894	+	0.659100i	0.826153	+	0.0324322i
$414$	−22.6866	−	24.0205i	−1.11499	−	1.18054i
$415$	−3.59051	+	6.21895i	−0.176251	+	0.305276i
$416$	−3.23285	−	2.71269i	−0.158504	−	0.133000i
$417$	−16.2028	−	15.2783i	−0.793453	−	0.748181i
$418$	0.0208535	−	0.00367703i	0.00101998	−	0.000179849i
$419$	−11.5894	−	4.21819i	−0.566178	−	0.206072i	0.0430419	−	0.999073i	$-0.486295\pi$
$419$	−11.5894	−	4.21819i	−0.566178	−	0.206072i	−0.609220	+	0.793001i	$0.708517\pi$
$420$	−5.73673	−	1.59806i	−0.279924	−	0.0779772i
$421$	3.05146	−	17.3057i	0.148719	−	0.843427i	−0.815587	−	0.578635i	$-0.803586\pi$
$421$	3.05146	−	17.3057i	0.148719	−	0.843427i	0.964306	−	0.264792i	$-0.0853034\pi$
$422$	−30.1683	−	17.4176i	−1.46857	−	0.847878i
$423$	−2.21150	−	37.6211i	−0.107527	−	1.82920i
$424$	−1.39482	−	2.41590i	−0.0677386	−	0.117327i
$425$	2.73353	−	15.5026i	0.132596	−	0.751988i
$426$	−0.468741	+	8.08545i	−0.0227106	+	0.391742i
$427$	−20.4711	+	2.78668i	−0.990665	+	0.134857i
$428$	5.84400	+	6.96461i	0.282480	+	0.336647i
$429$	−0.122535	−	0.164501i	−0.00591605	−	0.00794217i
$430$	19.7026	+	3.47409i	0.950141	+	0.167536i
$431$	−30.8867	−	17.8324i	−1.48776	−	0.858957i	−0.487856	−	0.872924i	$-0.662221\pi$
$431$	−30.8867	−	17.8324i	−1.48776	−	0.858957i	−0.999902	+	0.0139669i	$0.995554\pi$
$432$	19.8269	−	16.6640i	0.953921	−	0.801748i
$433$			7.92231i			0.380722i	0.981714	+	0.190361i	$0.0609659\pi$
$433$			7.92231i			0.380722i	−0.981714	+	0.190361i	$0.939034\pi$
$434$	8.65970	−	39.8905i	0.415679	−	1.91481i
$435$	1.64994	+	0.711187i	0.0791084	+	0.0340988i
$436$	−4.26424	−	1.55205i	−0.204220	−	0.0743299i
$437$	−0.585785	−	0.213208i	−0.0280219	−	0.0101991i
$438$	1.36364	−	23.5219i	0.0651573	−	1.12392i
$439$	16.5370	+	2.91592i	0.789269	+	0.139169i	0.553731	−	0.832696i	$-0.313204\pi$
$439$	16.5370	+	2.91592i	0.789269	+	0.139169i	0.235538	+	0.971865i	$0.424315\pi$
$440$	0.184279	−	0.319180i	0.00878514	−	0.0152163i
$441$	13.8137	−	15.8171i	0.657796	−	0.753196i
$442$	4.34616	+	7.52778i	0.206726	+	0.358060i
$443$	−5.93568	−	16.3082i	−0.282013	−	0.774824i	−0.997122	−	0.0758113i	$-0.975845\pi$
$443$	−5.93568	−	16.3082i	−0.282013	−	0.774824i	0.715109	−	0.699013i	$-0.246377\pi$
$444$	−5.08886	−	1.20464i	−0.241507	−	0.0571695i
$445$	18.1690	−	15.2456i	0.861295	−	0.722713i
$446$	5.79430	+	32.8611i	0.274368	+	1.55602i
$447$	33.9424	−	10.1716i	1.60542	−	0.481101i
$448$	4.12555	+	3.74714i	0.194914	+	0.177036i
$449$	−6.63080	+	3.82829i	−0.312927	+	0.180668i	−0.648235	−	0.761440i	$-0.724493\pi$
$449$	−6.63080	+	3.82829i	−0.312927	+	0.180668i	0.335309	+	0.942108i	$0.391159\pi$
$450$	−11.4082	−	8.48354i	−0.537787	−	0.399918i
$451$	0.245278	−	0.141612i	0.0115497	−	0.00666823i
$452$	4.61772	+	12.6871i	0.217199	+	0.596750i
$453$	−19.7239	−	12.9650i	−0.926711	−	0.609150i
$454$	0.532142	−	0.0938310i	0.0249747	−	0.00440371i
$455$	2.18929	+	2.82732i	0.102636	+	0.132547i
$456$	0.125506	−	0.291172i	0.00587737	−	0.0136354i
$457$	22.7892	+	19.1224i	1.06603	+	0.894507i	0.994687	−	0.102945i	$-0.0328265\pi$
$457$	22.7892	+	19.1224i	1.06603	+	0.894507i	0.0713449	+	0.997452i	$0.477271\pi$
$458$	−7.34256	+	12.7177i	−0.343095	+	0.594258i
$459$	−27.4941	+	10.0322i	−1.28332	+	0.468263i
$460$	7.30989	−	4.22037i	0.340826	−	0.196776i
$461$	0.444066	−	0.161627i	0.0206822	−	0.00752772i	−0.331658	−	0.943400i	$-0.607608\pi$
$461$	0.444066	−	0.161627i	0.0206822	−	0.00752772i	0.352341	+	0.935872i	$0.385386\pi$
$462$	−0.571716	−	0.833908i	−0.0265986	−	0.0387969i
$463$	1.97532	−	1.65749i	0.0918008	−	0.0770300i	−0.595732	−	0.803183i	$-0.703138\pi$
$463$	1.97532	−	1.65749i	0.0918008	−	0.0770300i	0.687533	+	0.726153i	$0.258694\pi$
$464$	2.23805	+	2.66720i	0.103899	+	0.123822i
$465$	−12.8550	+	19.5566i	−0.596138	+	0.906915i
$466$	11.6996	−	4.25831i	0.541974	−	0.197262i
$467$	−5.31125			−0.245775			−0.122888	−	0.992421i	$-0.539216\pi$
$467$	−5.31125			−0.245775			−0.122888	+	0.992421i	$0.539216\pi$
$468$	2.38529	−	0.140216i	0.110260	−	0.00648148i
$469$	−20.3234	+	32.2130i	−0.938447	+	1.48746i
$470$	31.1502	+	5.49262i	1.43685	+	0.253355i
$471$	1.58962	−	6.71518i	0.0732457	−	0.309419i
$472$	−7.78622	−	9.27925i	−0.358390	−	0.427112i
$473$	0.664559	+	0.791991i	0.0305565	+	0.0364158i
$474$	−1.13932	+	0.341425i	−0.0523309	+	0.0156822i
$475$	−0.264156	−	0.0465778i	−0.0121203	−	0.00213714i
$476$	6.07245	+	11.5409i	0.278330	+	0.528977i
$477$	4.20400	+	1.25613i	0.192488	+	0.0575142i
$478$	7.97850			0.364928
$479$	30.9511	−	11.2653i	1.41419	−	0.514723i	0.481834	−	0.876262i	$-0.339971\pi$
$479$	30.9511	−	11.2653i	1.41419	−	0.514723i	0.932357	+	0.361539i	$0.117749\pi$
$480$	5.35539	+	10.6563i	0.244439	+	0.486391i
$481$	2.01843	+	2.40548i	0.0920327	+	0.109680i
$482$	8.61371	−	7.22776i	0.392344	−	0.329215i
$483$	2.30115	+	29.6760i	0.104706	+	1.35030i
$484$	9.03172	−	3.28728i	0.410533	−	0.149422i
$485$	13.4357	−	7.75713i	0.610086	−	0.352233i
$486$	−3.03324	+	26.2574i	−0.137591	+	1.19106i
$487$	−12.1204	+	20.9931i	−0.549226	+	0.951288i	0.449101	+	0.893481i	$0.351744\pi$
$487$	−12.1204	+	20.9931i	−0.549226	+	0.951288i	−0.998328	+	0.0578073i	$0.981589\pi$
$488$	11.4096	+	9.57381i	0.516489	+	0.433386i
$489$	−25.4578	−	34.1765i	−1.15124	−	1.54552i
$490$	10.2363	+	14.3487i	0.462427	+	0.648208i
$491$	−11.3569	+	2.00253i	−0.512529	+	0.0903727i	−0.423931	−	0.905695i	$-0.639350\pi$
$491$	−11.3569	+	2.00253i	−0.512529	+	0.0903727i	−0.0885987	+	0.996067i	$0.528239\pi$
$492$	−0.190944	+	3.29365i	−0.00860841	+	0.148489i
$493$	−1.34568	−	3.69722i	−0.0606063	−	0.166514i
$494$	0.128269	−	0.0740561i	0.00577109	−	0.00333194i
$495$	0.133987	+	0.563982i	0.00602226	+	0.0253491i
$496$	−39.2769	+	22.6765i	−1.76358	+	1.01821i
$497$	4.90552	−	5.40091i	0.220043	−	0.242264i
$498$	3.27151	−	13.8201i	0.146600	−	0.619295i
$499$	0.886056	+	5.02507i	0.0396653	+	0.224953i	0.998196	−	0.0600353i	$-0.0191213\pi$
$499$	0.886056	+	5.02507i	0.0396653	+	0.224953i	−0.958531	+	0.284988i	$0.908010\pi$
$500$	7.75967	−	6.51114i	0.347023	−	0.291187i
$501$	−9.12931	−	30.4642i	−0.407867	−	1.36104i
$502$	−8.52393	−	23.4193i	−0.380442	−	1.04525i
$503$	12.9688	+	22.4626i	0.578251	+	1.00156i	0.995680	+	0.0928501i	$0.0295977\pi$
$503$	12.9688	+	22.4626i	0.578251	+	1.00156i	−0.417429	+	0.908709i	$0.637069\pi$
$504$	−15.1365	+	0.294884i	−0.674234	+	0.0131352i
$505$	3.16873	−	5.48841i	0.141007	−	0.244231i
$506$	1.41130	+	0.248851i	0.0627401	+	0.0110628i
$507$	17.6168	+	11.5800i	0.782389	+	0.514284i
$508$	0.929323	+	0.338246i	0.0412321	+	0.0150072i
$509$	−25.9098	−	9.43040i	−1.14843	−	0.417995i	−0.303480	−	0.952838i	$-0.598149\pi$
$509$	−25.9098	−	9.43040i	−1.14843	−	0.417995i	−0.844952	+	0.534843i	$0.820371\pi$
$510$	−2.85835	−	24.3978i	−0.126570	−	1.08035i
$511$	−14.2709	+	15.7121i	−0.631309	+	0.695063i
$512$			4.09759i			0.181090i
$513$	0.170943	+	0.468484i	0.00754731	+	0.0206841i
$514$	20.7372	+	11.9726i	0.914680	+	0.528091i
$515$	−5.92995	−	1.04561i	−0.261305	−	0.0460751i
$516$	−11.9614	+	1.40135i	−0.526573	+	0.0616912i
$517$	1.05068	+	1.25216i	0.0462090	+	0.0550697i
$518$	9.47629	+	12.2380i	0.416364	+	0.537705i
$519$	−5.01772	+	2.52168i	−0.220253	+	0.110690i
$520$	0.447651	−	2.53875i	0.0196308	−	0.111332i
$521$	−6.28697	−	10.8894i	−0.275437	−	0.477071i	0.694808	−	0.719195i	$-0.255489\pi$
$521$	−6.28697	−	10.8894i	−0.275437	−	0.477071i	−0.970245	+	0.242124i	$0.922156\pi$
$522$	−3.52954	−	0.410618i	−0.154484	−	0.0179723i
$523$	2.96092	+	1.70949i	0.129472	+	0.0747507i	0.563337	−	0.826227i	$-0.309517\pi$
$523$	2.96092	+	1.70949i	0.129472	+	0.0747507i	−0.433865	+	0.900978i	$0.642851\pi$
$524$	0.994539	−	5.64031i	0.0434467	−	0.246398i
$525$	3.19244	+	12.4032i	0.139330	+	0.541320i
$526$	−24.9192	−	9.06984i	−1.08653	−	0.395464i
$527$	50.4714	−	8.89946i	2.19857	−	0.387667i
$528$	−0.258770	+	1.09315i	−0.0112615	+	0.0475731i
$529$	−14.6993	−	12.3342i	−0.639099	−	0.536268i
$530$	−1.84132	+	3.18927i	−0.0799820	+	0.138533i
$531$	18.9244	+	2.20162i	0.821250	+	0.0955423i
$532$	0.196650	−	0.103471i	0.00852588	−	0.00448604i
$533$	1.27339	−	1.51756i	0.0551565	−	0.0657330i
$534$	−25.7656	+	39.1977i	−1.11499	+	1.69625i
$535$	−5.27662	+	14.4974i	−0.228128	+	0.626777i
$536$	27.0416	−	4.76816i	1.16802	−	0.205953i
$537$	3.96535	+	33.8467i	0.171118	+	1.46059i
$538$	−2.50019	−	6.86922i	−0.107791	−	0.296153i
$539$	−0.0714035	+	0.908038i	−0.00307557	+	0.0391120i
$540$	−6.34714	−	2.30437i	−0.273138	−	0.0991643i
$541$	−1.35102	−	2.34004i	−0.0580850	−	0.100606i	0.835521	−	0.549459i	$-0.185166\pi$
$541$	−1.35102	−	2.34004i	−0.0580850	−	0.100606i	−0.893606	+	0.448853i	$0.851833\pi$
$542$	−5.50332	+	31.2109i	−0.236388	+	1.34062i
$543$	27.5211	+	11.8626i	1.18104	+	0.509075i
$544$	8.93255	−	24.5420i	0.382980	−	1.05223i
$545$	−1.33717	−	7.58347i	−0.0572781	−	0.324840i
$546$	−5.75273	−	4.11339i	−0.246194	−	0.176037i
$547$	23.8134	+	19.9818i	1.01819	+	0.854362i	0.989399	−	0.145224i	$-0.0463903\pi$
$547$	23.8134	+	19.9818i	1.01819	+	0.854362i	0.0287897	+	0.999585i	$0.490835\pi$
$548$		−	4.06918i		−	0.173827i
$549$	−23.3857	+	1.37469i	−0.998079	+	0.0586705i
$550$	0.616631			0.0262932
$551$	−0.0629985	+	0.0229296i	−0.00268383	+	0.000976833i
$552$	14.7214	−	15.6122i	0.626585	−	0.664499i
$553$	0.991708	+	0.405680i	0.0421717	+	0.0172513i
$554$	5.45060	−	14.9754i	0.231574	−	0.636244i
$555$	−2.54739	−	8.50055i	−0.108131	−	0.360828i
$556$	−7.23252	+	8.61938i	−0.306727	+	0.365543i
$557$		−	31.1769i		−	1.32101i	−0.750822	−	0.660504i	$-0.770343\pi$
$557$		−	31.1769i		−	1.32101i	0.750822	−	0.660504i	$-0.229657\pi$
$558$	13.2509	−	44.3478i	0.560954	−	1.87739i
$559$	6.26269	+	3.61577i	0.264884	+	0.152931i
$560$	4.15449	−	19.1375i	0.175559	−	0.808706i
$561$	0.697272	−	1.06077i	0.0294389	−	0.0447859i
$562$	−35.6700	+	29.9307i	−1.50465	+	1.26255i
$563$	4.71848	+	26.7598i	0.198860	+	1.12779i	0.906813	+	0.421533i	$0.138508\pi$
$563$	4.71848	+	26.7598i	0.198860	+	1.12779i	−0.707953	+	0.706260i	$0.750381\pi$
$564$	−18.9113	+	2.21557i	−0.796309	+	0.0932924i
$565$	−14.7267	+	17.5506i	−0.619556	+	0.738358i
$566$	36.7745			1.54575
$567$	16.9895	−	16.6840i	0.713492	−	0.700663i
$568$	−5.25997			−0.220704
$569$	−10.4176	+	12.4152i	−0.436729	+	0.520473i	−0.938851	−	0.344324i	$-0.888108\pi$
$569$	−10.4176	+	12.4152i	−0.436729	+	0.520473i	0.502122	+	0.864797i	$0.332553\pi$
$570$	−0.415724	+	0.0487045i	−0.0174127	+	0.00204001i
$571$	6.42712	+	36.4500i	0.268967	+	1.52539i	0.757497	+	0.652839i	$0.226422\pi$
$571$	6.42712	+	36.4500i	0.268967	+	1.52539i	−0.488530	+	0.872547i	$0.662467\pi$
$572$	−0.0793905	+	0.0666165i	−0.00331948	+	0.00278538i
$573$	5.03499	−	7.65982i	0.210340	−	0.319994i
$574$	6.56524	−	7.22825i	0.274028	−	0.301701i
$575$	−15.7210	−	9.07655i	−0.655613	−	0.378518i
$576$	4.33916	+	4.59429i	0.180798	+	0.191429i
$577$		−	43.3528i		−	1.80480i	−0.430899	−	0.902400i	$-0.641804\pi$
$577$		−	43.3528i		−	1.80480i	0.430899	−	0.902400i	$-0.358196\pi$
$578$	−16.0490	+	19.1264i	−0.667550	+	0.795555i
$579$	8.78479	+	29.3145i	0.365083	+	1.21827i
$580$	0.310473	−	0.853018i	0.0128917	−	0.0354196i
$581$	−10.1160	+	7.83317i	−0.419682	+	0.324975i
$582$	−21.0499	+	22.3236i	−0.872546	+	0.925343i
$583$	−0.178830	+	0.0650889i	−0.00740639	+	0.00269571i
$584$	15.3021			0.633205
$585$	2.22988	+	3.38640i	0.0921944	+	0.140011i
$586$			16.0029i			0.661073i
$587$	26.0768	+	21.8811i	1.07631	+	0.903128i	0.995609	−	0.0936106i	$-0.0298409\pi$
$587$	26.0768	+	21.8811i	1.07631	+	0.903128i	0.0806972	+	0.996739i	$0.474285\pi$
$588$	−8.38203	−	6.50507i	−0.345669	−	0.268265i
$589$	−0.151642	−	0.860003i	−0.00624829	−	0.0354358i
$590$	−5.46917	+	15.0264i	−0.225162	+	0.618628i
$591$	32.9068	+	14.1841i	1.35360	+	0.583455i
$592$	2.98622	−	16.9357i	0.122733	−	0.696053i
$593$	1.09399	+	1.89484i	0.0449246	+	0.0778118i	0.887613	−	0.460589i	$-0.152362\pi$
$593$	1.09399	+	1.89484i	0.0449246	+	0.0778118i	−0.842689	+	0.538401i	$0.819029\pi$
$594$	−0.574024	−	0.992388i	−0.0235525	−	0.0407182i
$595$	−11.8080	+	18.7159i	−0.484081	+	0.767278i
$596$	−6.12306	−	16.8230i	−0.250810	−	0.689095i
$597$	−2.57480	−	21.9776i	−0.105380	−	0.899482i
$598$	9.87153	−	1.74062i	0.403677	−	0.0711791i
$599$	0.819728	−	2.25218i	0.0334932	−	0.0920217i	−0.921819	−	0.387621i	$-0.873297\pi$
$599$	0.819728	−	2.25218i	0.0334932	−	0.0920217i	0.955312	+	0.295599i	$0.0955192\pi$
$600$	5.07165	−	7.71560i	0.207049	−	0.314988i
$601$	−9.51673	+	11.3416i	−0.388196	+	0.462634i	−0.924383	−	0.381465i	$-0.875420\pi$
$601$	−9.51673	+	11.3416i	−0.388196	+	0.462634i	0.536187	+	0.844099i	$0.319864\pi$
$602$	30.1465	+	19.0197i	1.22868	+	0.775183i
$603$	−25.7715	+	34.6560i	−1.04949	+	1.41130i
$604$	−5.96276	+	10.3278i	−0.242621	+	0.420232i
$605$	12.4940	+	10.4837i	0.507951	+	0.426222i
$606$	−2.88720	+	12.1967i	−0.117284	+	0.495456i
$607$	1.02359	−	0.180486i	0.0415461	−	0.00732570i	−0.152836	−	0.988251i	$-0.548841\pi$
$607$	1.02359	−	0.180486i	0.0415461	−	0.00732570i	0.194383	+	0.980926i	$0.437730\pi$
$608$	−0.418181	−	0.152205i	−0.0169595	−	0.00617274i
$609$	2.24105	+	2.28577i	0.0908118	+	0.0926240i
$610$	3.41427	−	19.3633i	0.138240	−	0.783997i
$611$	9.90146	+	5.71661i	0.400570	+	0.231269i
$612$	5.86417	+	13.5746i	0.237045	+	0.548720i
$613$	−12.0184	−	20.8164i	−0.485417	−	0.840768i	0.514442	−	0.857525i	$-0.327999\pi$
$613$	−12.0184	−	20.8164i	−0.485417	−	0.840768i	−0.999860	+	0.0167574i	$0.994666\pi$
$614$	1.65458	−	9.38360i	0.0667735	−	0.378691i
$615$	−5.00227	+	2.51392i	−0.201711	+	0.101371i
$616$	0.519190	−	0.402028i	0.0209188	−	0.0161982i
$617$	−10.4252	−	12.4243i	−0.419702	−	0.500182i	0.514220	−	0.857659i	$-0.328082\pi$
$617$	−10.4252	−	12.4243i	−0.419702	−	0.500182i	−0.933922	+	0.357477i	$0.883637\pi$
$618$	11.8278	−	1.38570i	0.475785	−	0.0557410i
$619$	2.85812	+	0.503964i	0.114878	+	0.0202560i	0.230791	−	0.973003i	$-0.425869\pi$
$619$	2.85812	+	0.503964i	0.114878	+	0.0202560i	−0.115914	+	0.993259i	$0.536980\pi$
$620$	10.2402	+	5.91216i	0.411255	+	0.237438i
$621$	0.0272492	+	33.7504i	0.00109347	+	1.35436i
$622$		−	29.5968i		−	1.18672i
$623$	40.2455	−	12.8842i	1.61240	−	0.516193i
$624$	0.914296	+	7.80409i	0.0366011	+	0.312414i
$625$	3.02102	+	1.09956i	0.120841	+	0.0439825i
$626$	−0.795704	−	0.289612i	−0.0318027	−	0.0115752i
$627$	−0.0180750	−	0.0118811i	−0.000721844	−	0.000474486i
$628$	−3.43359	−	0.605435i	−0.137015	−	0.0241595i
$629$	−9.71647	+	16.8294i	−0.387421	+	0.671033i
$630$	10.3281	+	17.1102i	0.411481	+	0.681687i
$631$	−23.7928	−	41.2104i	−0.947177	−	1.64056i	−0.751333	−	0.659923i	$-0.770589\pi$
$631$	−23.7928	−	41.2104i	−0.947177	−	1.64056i	−0.195844	−	0.980635i	$-0.562745\pi$
$632$	−0.264194	−	0.725868i	−0.0105091	−	0.0288735i
$633$	10.2147	+	34.0862i	0.406000	+	1.35481i
$634$	−10.1461	+	8.51355i	−0.402951	+	0.338116i
$635$	0.291415	+	1.65270i	0.0115645	+	0.0655854i
$636$	0.510656	−	2.15721i	0.0202488	−	0.0855391i
$637$	1.70298	+	6.13917i	0.0674745	+	0.243243i
$638$	0.133472	−	0.0770603i	0.00528422	−	0.00305085i
$639$	6.01456	−	5.68056i	0.237932	−	0.224720i
$640$	−16.5198	+	9.53769i	−0.653001	+	0.377010i
$641$	−13.3093	−	36.5671i	−0.525687	−	1.44431i	−0.864103	−	0.503315i	$-0.832113\pi$
$641$	−13.3093	−	36.5671i	−0.525687	−	1.44431i	0.338416	−	0.940997i	$-0.390109\pi$
$642$	1.76591	−	30.4608i	0.0696950	−	1.20219i
$643$	−11.9667	+	2.11005i	−0.471919	+	0.0832121i	−0.404550	−	0.914516i	$-0.632572\pi$
$643$	−11.9667	+	2.11005i	−0.471919	+	0.0832121i	−0.0673696	+	0.997728i	$0.521461\pi$
$644$	14.9012	−	2.02846i	0.587188	−	0.0799326i
$645$	−12.2082	−	16.3892i	−0.480697	−	0.645326i
$646$	0.702160	+	0.589183i	0.0276261	+	0.0231811i
$647$	1.58605	−	2.74713i	0.0623542	−	0.108001i	−0.833163	−	0.553027i	$-0.813472\pi$
$647$	1.58605	−	2.74713i	0.0623542	−	0.108001i	0.895517	+	0.445027i	$0.146806\pi$
$648$	−17.1385	−	0.979692i	−0.673263	−	0.0384859i
$649$	−0.715642	+	0.413176i	−0.0280914	+	0.0162186i
$650$	4.05299	−	1.47517i	0.158971	−	0.0578608i
$651$	−34.3906	+	23.5777i	−1.34788	+	0.924084i
$652$	−16.4941	+	13.8402i	−0.645958	+	0.542023i
$653$	−0.976148	−	1.16333i	−0.0381996	−	0.0455246i	0.746606	−	0.665266i	$-0.231682\pi$
$653$	−0.976148	−	1.16333i	−0.0381996	−	0.0455246i	−0.784806	+	0.619742i	$0.787237\pi$
$654$	6.83859	+	13.6076i	0.267410	+	0.532100i
$655$	9.13269	−	3.32403i	0.356844	−	0.129881i
$656$	−10.8492			−0.423590
$657$	−17.4973	+	16.5257i	−0.682635	+	0.644727i
$658$	47.6624	+	30.0705i	1.85807	+	1.17227i
$659$	−37.4050	−	6.59551i	−1.45709	−	0.256925i	−0.611708	−	0.791083i	$-0.709517\pi$
$659$	−37.4050	−	6.59551i	−1.45709	−	0.256925i	−0.845384	+	0.534159i	$0.820628\pi$
$660$	0.280552	−	0.0840742i	0.0109205	−	0.00327258i
$661$	16.6985	+	19.9005i	0.649495	+	0.774038i	0.985838	−	0.167701i	$-0.0536344\pi$
$661$	16.6985	+	19.9005i	0.649495	+	0.774038i	−0.336342	+	0.941740i	$0.609190\pi$
$662$	−34.4538	−	41.0604i	−1.33909	−	1.59586i
$663$	2.04534	−	8.64033i	0.0794344	−	0.335563i
$664$	9.08352	+	1.60167i	0.352509	+	0.0621568i
$665$	0.318908	+	0.201201i	0.0123667	+	0.00780226i
$666$	9.65198	+	14.6579i	0.374007	+	0.567984i
$667$	−4.53718			−0.175680
$668$	−15.0991	+	5.49561i	−0.584200	+	0.212631i
$669$	18.7224	−	28.4827i	0.723850	−	1.10121i
$670$	−23.3002	−	27.7680i	−0.900164	−	1.07277i
$671$	0.778354	−	0.653117i	0.0300480	−	0.0252133i
$672$	1.64275	+	21.1851i	0.0633704	+	0.817234i
$673$	−27.9585	+	10.1760i	−1.07772	+	0.392258i	−0.819058	−	0.573710i	$-0.805503\pi$
$673$	−27.9585	+	10.1760i	−1.07772	+	0.392258i	−0.258661	+	0.965968i	$0.583281\pi$
$674$	10.2982	−	5.94568i	0.396672	−	0.229019i
$675$	2.53332	+	14.2996i	0.0975074	+	0.550393i
$676$	5.32574	−	9.22446i	0.204836	−	0.354787i
$677$	−13.8303	−	11.6050i	−0.531543	−	0.446018i	0.337091	−	0.941472i	$-0.390557\pi$
$677$	−13.8303	−	11.6050i	−0.531543	−	0.446018i	−0.868634	+	0.495455i	$0.835002\pi$
$678$	17.9355	−	41.6100i	0.688810	−	1.59802i
$679$	27.3887	−	3.72836i	1.05108	−	0.143081i
$680$	15.7113	−	2.77033i	0.602501	−	0.106237i
$681$	−0.461240	−	0.303184i	−0.0176748	−	0.0116181i
$682$	0.686620	+	1.88647i	0.0262920	+	0.0722368i
$683$	5.53793	−	3.19733i	0.211903	−	0.122342i	−0.390292	−	0.920691i	$-0.627626\pi$
$683$	5.53793	−	3.19733i	0.211903	−	0.122342i	0.602195	+	0.798349i	$0.294293\pi$
$684$	0.231303	−	0.0999221i	0.00884409	−	0.00382062i
$685$	5.97996	−	3.45253i	0.228483	−	0.131915i
$686$	7.20067	+	30.5665i	0.274923	+	1.16704i
$687$	14.3693	−	4.30611i	0.548224	−	0.164288i
$688$	−6.87710	−	39.0019i	−0.262187	−	1.48694i
$689$	−1.01970	+	0.855632i	−0.0388476	+	0.0325970i
$690$	−27.5656	−	6.52533i	−1.04940	−	0.248415i
$691$	8.16206	+	22.4251i	0.310500	+	0.853091i	0.992556	+	0.121791i	$0.0388637\pi$
$691$	8.16206	+	22.4251i	0.310500	+	0.853091i	−0.682056	+	0.731300i	$0.738914\pi$
$692$	1.41865	+	2.45718i	0.0539291	+	0.0934080i
$693$	−0.159498	+	1.02041i	−0.00605883	+	0.0387620i
$694$	9.01139	−	15.6082i	0.342068	−	0.592478i
$695$	−18.8033	−	3.31553i	−0.713251	−	0.125765i
$696$	0.133563	−	2.30388i	0.00506271	−	0.0873283i
$697$	11.5205	+	4.19311i	0.436369	+	0.158825i
$698$	11.7585	+	4.27975i	0.445066	+	0.161991i
$699$	−11.6792	−	5.03420i	−0.441749	−	0.190411i
$700$	6.16278	−	1.97295i	0.232931	−	0.0745703i
$701$		−	7.66638i		−	0.289555i	−0.989464	−	0.144778i	$-0.953753\pi$
$701$		−	7.66638i		−	0.289555i	0.989464	−	0.144778i	$-0.0462467\pi$
$702$	−6.14703	−	5.14952i	−0.232005	−	0.194356i
$703$	0.286764	+	0.165563i	0.0108155	+	0.00624433i
$704$	−0.269933	−	0.0475965i	−0.0101735	−	0.00179386i
$705$	−19.3014	−	25.9117i	−0.726934	−	0.975893i
$706$	18.1511	+	21.6316i	0.683124	+	0.814116i
$707$	8.92765	−	6.91300i	0.335759	−	0.259990i
$708$	0.557112	−	9.60979i	0.0209375	−	0.361158i
$709$	−2.85710	+	16.2034i	−0.107301	+	0.608533i	0.882976	+	0.469419i	$0.155537\pi$
$709$	−2.85710	+	16.2034i	−0.107301	+	0.608533i	−0.990276	+	0.139114i	$0.955575\pi$
$710$	3.47188	+	6.01347i	0.130297	+	0.225682i
$711$	1.08600	+	0.544680i	0.0407283	+	0.0204271i
$712$	−26.3830	−	15.2323i	−0.988746	−	0.570853i
$713$	10.2627	−	58.2025i	0.384340	−	2.17970i
$714$	11.7445	−	42.1608i	0.439528	−	1.57783i
$715$	−0.165258	−	0.0601488i	−0.00618028	−	0.00224944i
$716$	16.9562	−	2.98984i	0.633684	−	0.111736i
$717$	−5.92956	−	5.59124i	−0.221444	−	0.208809i
$718$	22.5229	+	18.8990i	0.840549	+	0.705304i
$719$	23.3674	−	40.4735i	0.871457	−	1.50941i	0.0109676	−	0.999940i	$-0.496509\pi$
$719$	23.3674	−	40.4735i	0.871457	−	1.50941i	0.860490	−	0.509468i	$-0.170158\pi$
$720$	6.35710	−	21.2759i	0.236915	−	0.792905i
$721$	−9.07331	−	5.72441i	−0.337908	−	0.213188i
$722$	−20.6984	+	24.6674i	−0.770316	+	0.918027i
$723$	−11.4668	−	0.664767i	−0.426454	−	0.0247230i
$724$	5.17871	−	14.2284i	0.192465	−	0.528794i
$725$	−1.92262	+	0.339010i	−0.0714044	+	0.0125905i
$726$	−29.6215	−	12.7680i	−1.09936	−	0.473865i
$727$	−2.15305	−	5.91545i	−0.0798522	−	0.219392i	0.893342	−	0.449378i	$-0.148354\pi$
$727$	−2.15305	−	5.91545i	−0.0798522	−	0.219392i	−0.973194	+	0.229986i	$0.926132\pi$
$728$	2.45076	−	3.88451i	0.0908312	−	0.143969i
$729$	20.6551	−	17.3886i	0.765006	−	0.644024i
$730$	−10.1002	−	17.4941i	−0.373827	−	0.647487i
$731$	−7.77128	+	44.0731i	−0.287431	+	1.63010i
$732$	1.37723	+	11.7555i	0.0509037	+	0.434495i
$733$	4.65518	−	12.7900i	0.171943	−	0.472409i	−0.823550	−	0.567243i	$-0.808010\pi$
$733$	4.65518	−	12.7900i	0.171943	−	0.472409i	0.995493	+	0.0948343i	$0.0302321\pi$
$734$	7.86881	+	44.6262i	0.290443	+	1.64718i
$735$	2.44788	−	17.8373i	0.0902916	−	0.657939i
$736$	−23.0714	−	19.3592i	−0.850424	−	0.713590i
$737$		−	1.87321i		−	0.0690006i
$738$	8.04951	−	7.60251i	0.296306	−	0.279852i
$739$	25.3280			0.931705			0.465852	−	0.884863i	$-0.345748\pi$
$739$	25.3280			0.931705			0.465852	+	0.884863i	$0.345748\pi$
$740$	−4.21316	+	1.53346i	−0.154879	+	0.0563712i
$741$	−0.147226	−	0.0348514i	−0.00540849	−	0.00128030i
$742$	−5.18778	+	4.01708i	−0.190449	+	0.147472i
$743$	7.84457	−	21.5528i	0.287789	−	0.790695i	−0.708586	−	0.705625i	$-0.750666\pi$
$743$	7.84457	−	21.5528i	0.287789	−	0.790695i	0.996375	−	0.0850699i	$-0.0271114\pi$
$744$	29.2518	+	6.92449i	1.07242	+	0.253864i
$745$	19.5274	−	23.2719i	0.715430	−	0.852616i
$746$		−	31.3907i		−	1.14930i
$747$	−12.1164	+	7.97840i	−0.443314	+	0.291914i
$748$	−0.555439	−	0.320683i	−0.0203089	−	0.0117253i
$749$	−18.4808	+	20.3471i	−0.675274	+	0.743469i
$750$	−33.9381	−	1.96750i	−1.23924	−	0.0718431i
$751$	0.154318	−	0.129489i	0.00563116	−	0.00472510i	−0.639968	−	0.768402i	$-0.721052\pi$
$751$	0.154318	−	0.129489i	0.00563116	−	0.00472510i	0.645599	+	0.763677i	$0.276608\pi$
$752$	−10.8728	−	61.6629i	−0.396492	−	2.24862i
$753$	−10.0770	+	23.3785i	−0.367228	+	0.851961i
$754$	0.692935	−	0.825808i	0.0252352	−	0.0300741i
$755$	−20.2366			−0.736486
$756$	−8.91216	−	8.08157i	−0.324132	−	0.293924i
$757$	−32.2011			−1.17037			−0.585184	−	0.810901i	$-0.698978\pi$
$757$	−32.2011			−1.17037			−0.585184	+	0.810901i	$0.698978\pi$
$758$	−38.3989	+	45.7620i	−1.39471	+	1.66215i
$759$	−0.874478	−	1.17397i	−0.0317415	−	0.0426124i
$760$	−0.0472048	−	0.267712i	−0.00171230	−	0.00971092i
$761$	−40.6980	+	34.1497i	−1.47530	+	1.23792i	−0.564269	+	0.825591i	$0.690842\pi$
$761$	−40.6980	+	34.1497i	−1.47530	+	1.23792i	−0.911033	+	0.412334i	$0.864714\pi$
$762$	−1.49036	−	2.96557i	−0.0539902	−	0.107431i
$763$	2.91056	−	13.4074i	0.105369	−	0.485380i
$764$	−4.01082	−	2.31565i	−0.145106	−	0.0837772i
$765$	−14.9734	+	20.1353i	−0.541363	+	0.727994i
$766$		−	28.3312i		−	1.02365i
$767$	−3.71533	+	4.42776i	−0.134153	+	0.159877i
$768$	20.8755	−	22.1387i	0.753280	−	0.798860i
$769$	2.05952	−	5.65850i	0.0742683	−	0.204051i	−0.897003	−	0.442024i	$-0.854261\pi$
$769$	2.05952	−	5.65850i	0.0742683	−	0.204051i	0.971272	+	0.237973i	$0.0764830\pi$
$770$	−0.802313	−	0.328204i	−0.0289134	−	0.0118277i
$771$	−7.02147	−	23.4304i	−0.252872	−	0.843825i
$772$	14.5292	−	5.28821i	0.522919	−	0.190327i
$773$	−30.0117			−1.07944			−0.539722	−	0.841843i	$-0.681471\pi$
$773$	−30.0117			−1.07944			−0.539722	+	0.841843i	$0.681471\pi$
$774$	32.4328	+	24.1182i	1.16577	+	0.866912i
$775$		−	25.4300i		−	0.913474i
$776$	−15.2652	−	12.8090i	−0.547987	−	0.459816i
$777$	1.53351	−	15.7360i	0.0550143	−	0.564527i
$778$	2.79411	+	15.8462i	0.100174	+	0.568113i
$779$	0.0714481	−	0.196302i	0.00255989	−	0.00703325i
$780$	1.64288	−	1.22377i	0.0588247	−	0.0438179i
$781$	−0.0623103	+	0.353379i	−0.00222964	+	0.0126449i
$782$	31.0166	+	53.7224i	1.10915	+	1.92111i
$783$	2.33537	+	2.77863i	0.0834594	+	0.0993001i
$784$	19.7605	−	28.7557i	0.705731	−	1.02699i
$785$	−2.02353	−	5.55961i	−0.0722230	−	0.198431i
$786$	−15.4146	+	11.4822i	−0.549821	+	0.409556i
$787$	21.3412	−	3.76304i	0.760733	−	0.134138i	0.220193	−	0.975456i	$-0.429331\pi$
$787$	21.3412	−	3.76304i	0.760733	−	0.134138i	0.540540	+	0.841319i	$0.318220\pi$
$788$	6.19215	−	17.0128i	0.220586	−	0.606056i
$789$	12.1637	+	24.2037i	0.433040	+	0.861675i
$790$	−0.655466	+	0.781154i	−0.0233204	+	0.0277922i
$791$	−36.1238	+	19.0072i	−1.28442	+	0.675818i
$792$	0.621857	−	0.409481i	0.0220967	−	0.0145503i
$793$	3.55351	−	6.15486i	0.126189	−	0.218566i
$794$	−49.4277	−	41.4747i	−1.75412	−	1.47188i
$795$	3.60346	−	1.07986i	0.127801	−	0.0382987i
$796$	−11.0101	+	1.94138i	−0.390243	+	0.0688103i
$797$	24.4999	+	8.91724i	0.867832	+	0.315865i	0.737289	−	0.675578i	$-0.236106\pi$
$797$	24.4999	+	8.91724i	0.867832	+	0.315865i	0.130543	+	0.991443i	$0.458328\pi$
$798$	−0.718395	−	0.200120i	−0.0254309	−	0.00708418i
$799$	−12.2866	+	69.6805i	−0.434667	+	2.46512i
$800$	−11.2230	−	6.47958i	−0.396792	−	0.229088i
$801$	46.6181	−	11.0752i	1.64717	−	0.391323i
$802$	−4.76866	−	8.25956i	−0.168387	−	0.291655i
$803$	0.181271	−	1.02804i	0.00639690	−	0.0362786i
$804$	18.2340	+	11.9856i	0.643062	+	0.422701i
$805$	15.6240	+	20.1773i	0.550674	+	0.711157i
$806$	9.02603	+	10.7568i	0.317928	+	0.378892i
$807$	−2.95575	+	6.85726i	−0.104047	+	0.241387i
$808$	−8.01647	−	1.41352i	−0.282018	−	0.0497275i
$809$	27.9055	+	16.1113i	0.981106	+	0.566442i	0.902604	−	0.430472i	$-0.141653\pi$
$809$	27.9055	+	16.1113i	0.981106	+	0.566442i	0.0785018	+	0.996914i	$0.474986\pi$
$810$	10.1923	+	20.2402i	0.358122	+	0.711169i
$811$		−	40.6903i		−	1.42883i	−0.699722	−	0.714415i	$-0.746693\pi$
$811$		−	40.6903i		−	1.42883i	0.699722	−	0.714415i	$-0.253307\pi$
$812$	1.08740	−	1.19721i	0.0381603	−	0.0420140i
$813$	25.9623	−	19.3390i	0.910536	−	0.678250i
$814$	−0.715312	−	0.260352i	−0.0250717	−	0.00912535i
$815$	−34.3338	−	12.4965i	−1.20266	−	0.437732i
$816$	−43.4485	+	21.8353i	−1.52100	+	0.764388i
$817$	0.750980	+	0.132418i	0.0262735	+	0.00463272i
$818$	1.87000	−	3.23893i	0.0653829	−	0.113247i
$819$	1.39277	+	7.08849i	0.0486674	+	0.247692i
$820$	1.41429	+	2.44962i	0.0493890	+	0.0855443i
$821$	5.34412	+	14.6829i	0.186511	+	0.512435i	0.997343	−	0.0728435i	$-0.0232074\pi$
$821$	5.34412	+	14.6829i	0.186511	+	0.512435i	−0.810832	+	0.585279i	$0.800985\pi$
$822$	−9.36886	+	9.93576i	−0.326776	+	0.346549i
$823$	−17.5657	+	14.7394i	−0.612301	+	0.513782i	−0.895373	−	0.445317i	$-0.853091\pi$
$823$	−17.5657	+	14.7394i	−0.612301	+	0.513782i	0.283072	+	0.959099i	$0.408647\pi$
$824$	1.34303	+	7.61670i	0.0467867	+	0.265340i
$825$	−0.458275	−	0.432127i	−0.0159551	−	0.0150447i
$826$	−19.1552	+	21.0897i	−0.666496	+	0.733803i
$827$	−10.7093	+	6.18300i	−0.372398	+	0.215004i	−0.674506	−	0.738270i	$-0.735643\pi$
$827$	−10.7093	+	6.18300i	−0.372398	+	0.215004i	0.302108	+	0.953274i	$0.402310\pi$
$828$	17.0228	−	1.00066i	0.591582	−	0.0347753i
$829$	−44.8345	+	25.8852i	−1.55717	+	0.899030i	−0.559640	+	0.828736i	$0.689061\pi$
$829$	−44.8345	+	25.8852i	−1.55717	+	0.899030i	−0.997526	+	0.0702945i	$0.977606\pi$
$830$	−4.16452	−	11.4419i	−0.144553	−	0.397155i
$831$	−14.5454	+	7.30989i	−0.504575	+	0.253577i
$832$	−1.88808	+	0.332919i	−0.0654574	+	0.0115419i
$833$	−32.0970	+	22.8977i	−1.11209	+	0.793360i
$834$	37.5049	−	4.39393i	1.29869	−	0.152149i
$835$	−20.8871	−	17.5264i	−0.722830	−	0.606526i
$836$	−0.00546425	+	0.00946436i	−0.000188985	+	0.000327332i
$837$	−40.9264	+	23.6729i	−1.41462	+	0.818256i
$838$	18.1106	−	10.4561i	0.625619	−	0.361201i
$839$	−21.8923	+	7.96815i	−0.755806	+	0.275091i	−0.691047	−	0.722810i	$-0.742850\pi$
$839$	−21.8923	+	7.96815i	−0.755806	+	0.275091i	−0.0647595	+	0.997901i	$0.520628\pi$
$840$	−10.7055	+	7.33955i	−0.369375	+	0.253238i
$841$	21.8415	−	18.3272i	0.753155	−	0.631972i
$842$	19.1528	+	22.8254i	0.660048	+	0.786615i
$843$	47.4848	+	2.75285i	1.63546	+	0.0948132i
$844$	16.8943	−	6.14901i	0.581525	−	0.211658i
$845$	18.0747			0.621789
$846$	51.2771	+	38.1315i	1.76294	+	1.31099i
$847$	13.5309	+	25.7159i	0.464927	+	0.883610i
$848$	7.17919	+	1.26588i	0.246534	+	0.0434706i
$849$	−27.3306	−	25.7711i	−0.937982	−	0.884463i
$850$	17.1573	+	20.4472i	0.588490	+	0.701335i
$851$	14.4047	+	17.1668i	0.493785	+	0.588471i
$852$	−3.04113	−	2.86761i	−0.104187	−	0.0982427i
$853$	−33.4290	−	5.89444i	−1.14459	−	0.201822i	−0.430976	−	0.902363i	$-0.641831\pi$
$853$	−33.4290	−	5.89444i	−1.14459	−	0.201822i	−0.713612	+	0.700541i	$0.752942\pi$
$854$	18.6922	−	29.6275i	0.639633	−	1.01383i
$855$	0.343094	+	0.255137i	0.0117336	+	0.00872551i
$856$	19.8162			0.677303
$857$	−28.5626	+	10.3959i	−0.975680	+	0.355119i	−0.780159	−	0.625581i	$-0.784862\pi$
$857$	−28.5626	+	10.3959i	−0.975680	+	0.355119i	−0.195521	+	0.980699i	$0.562640\pi$
$858$	0.347226	+	0.0201299i	0.0118541	+	0.000687222i
$859$	−22.8877	−	27.2765i	−0.780919	−	0.930663i	0.218056	−	0.975936i	$-0.430029\pi$
$859$	−22.8877	−	27.2765i	−0.780919	−	0.930663i	−0.998975	+	0.0452734i	$0.985584\pi$
$860$	−7.90968	+	6.63701i	−0.269718	+	0.226320i
$861$	−9.94471	+	0.771138i	−0.338915	+	0.0262803i
$862$	56.8268	−	20.6833i	1.93553	−	0.704475i
$863$	0.566188	−	0.326889i	0.0192733	−	0.0111274i	−0.490332	−	0.871535i	$-0.663125\pi$
$863$	0.566188	−	0.326889i	0.0192733	−	0.0111274i	0.509606	+	0.860408i	$0.329791\pi$
$864$	0.0194527	+	24.0938i	0.000661795	+	0.819687i
$865$	−2.40734	+	4.16964i	−0.0818521	+	0.141772i
$866$	−10.2904	−	8.63468i	−0.349683	−	0.293419i
$867$	25.3311	−	2.96769i	0.860288	−	0.100788i
$868$	12.8982	+	16.6571i	0.437792	+	0.565377i
$869$	−0.0518955	+	0.00915058i	−0.00176043	+	0.000310412i
$870$	−2.72207	+	1.36799i	−0.0922868	+	0.0463793i
$871$	−4.48129	−	12.3122i	−0.151843	−	0.417184i
$872$	−8.56571	+	4.94541i	−0.290071	+	0.167473i
$873$	31.2882	−	1.83923i	1.05895	−	0.0622485i
$874$	0.915398	−	0.528505i	0.0309638	−	0.0178770i
$875$	22.6699	+	20.5905i	0.766383	+	0.696087i
$876$	8.84713	+	8.34233i	0.298917	+	0.281861i
$877$	6.18570	+	35.0809i	0.208876	+	1.18460i	0.891222	+	0.453567i	$0.149849\pi$
$877$	6.18570	+	35.0809i	0.208876	+	1.18460i	−0.682346	+	0.731030i	$0.739040\pi$
$878$	−21.8116	+	18.3021i	−0.736104	+	0.617665i
$879$	11.2146	−	11.8932i	0.378260	−	0.401148i
$880$	0.329406	+	0.905035i	0.0111043	+	0.0305087i
$881$	−23.1789	−	40.1470i	−0.780916	−	1.35259i	−0.931409	−	0.363975i	$-0.881419\pi$
$881$	−23.1789	−	40.1470i	−0.780916	−	1.35259i	0.150492	−	0.988611i	$-0.451914\pi$
$882$	5.48925	+	35.1822i	0.184832	+	1.18465i
$883$	7.99748	−	13.8520i	0.269137	−	0.466158i	−0.699503	−	0.714630i	$-0.746595\pi$
$883$	7.99748	−	13.8520i	0.269137	−	0.466158i	0.968639	+	0.248472i	$0.0799284\pi$
$884$	−4.41796	−	0.779005i	−0.148592	−	0.0262008i
$885$	14.5950	−	7.33480i	0.490605	−	0.246557i
$886$	27.6523	+	10.0646i	0.928999	+	0.338128i
$887$	20.8828	+	7.60073i	0.701177	+	0.255207i	0.667913	−	0.744239i	$-0.267188\pi$
$887$	20.8828	+	7.60073i	0.701177	+	0.255207i	0.0332635	+	0.999447i	$0.489410\pi$
$888$	−9.14095	+	6.80901i	−0.306750	+	0.228495i
$889$	−0.634311	+	2.92193i	−0.0212741	+	0.0979983i
$890$			40.2166i			1.34806i
$891$	−0.268843	+	1.13980i	−0.00900658	+	0.0381849i
$892$	−14.9141	−	8.61063i	−0.499359	−	0.288305i
$893$	1.18732	+	0.209356i	0.0397320	+	0.00700583i
$894$	−23.7824	+	55.1745i	−0.795401	+	1.84531i
$895$	18.7805	+	22.3817i	0.627762	+	0.748137i
$896$	−33.6754	+	4.58416i	−1.12502	+	0.153146i
$897$	−8.55625	−	5.62424i	−0.285685	−	0.187788i
$898$	2.25441	−	12.7854i	0.0752305	−	0.426653i
$899$	−3.17799	−	5.50444i	−0.105992	−	0.183583i
$900$	7.13860	−	1.69594i	0.237953	−	0.0565313i
$901$	−7.13414	−	4.11890i	−0.237673	−	0.137220i
$902$	−0.0833923	+	0.472941i	−0.00277666	+	0.0157472i
$903$	−9.07594	−	35.2616i	−0.302028	−	1.17343i
$904$	27.6528	+	10.0648i	0.919718	+	0.334750i
$905$	25.3036	−	4.46171i	0.841121	−	0.148312i
$906$	38.3380	−	11.4889i	1.27369	−	0.381693i
$907$	17.5317	+	14.7108i	0.582130	+	0.488465i	0.885646	−	0.464361i	$-0.153716\pi$
$907$	17.5317	+	14.7108i	0.582130	+	0.488465i	−0.303516	+	0.952826i	$0.598160\pi$
$908$	−0.139438	+	0.241513i	−0.00462740	+	0.00801490i
$909$	10.6930	−	7.04117i	0.354666	−	0.233541i
$910$	−6.05861	−	0.237842i	−0.200841	−	0.00788439i
$911$	−18.2077	+	21.6991i	−0.603248	+	0.718923i	−0.978094	−	0.208164i	$-0.933251\pi$
$911$	−18.2077	+	21.6991i	−0.603248	+	0.718923i	0.374846	+	0.927087i	$0.377696\pi$
$912$	0.372060	+	0.740336i	0.0123202	+	0.0245150i
$913$	0.215209	−	0.591282i	0.00712238	−	0.0195686i
$914$	−49.6767	+	8.75934i	−1.64316	+	0.289733i
$915$	−16.1070	+	11.9980i	−0.532482	+	0.396641i
$916$	−2.59217	−	7.12192i	−0.0856476	−	0.235315i
$917$	17.3024	+	0.679237i	0.571374	+	0.0224304i
$918$	16.9354	−	46.6469i	0.558953	−	1.53958i
$919$	0.486170	+	0.842071i	0.0160373	+	0.0277774i	0.873933	−	0.486047i	$-0.161562\pi$
$919$	0.486170	+	0.842071i	0.0160373	+	0.0277774i	−0.857895	+	0.513824i	$0.828228\pi$
$920$	3.19468	−	18.1180i	0.105326	−	0.597331i
$921$	−7.80559	+	5.81431i	−0.257203	+	0.191588i
$922$	−0.274057	+	0.752965i	−0.00902558	+	0.0247976i
$923$	0.435837	+	2.47176i	0.0143458	+	0.0813588i
$924$	0.519353	+	0.0506120i	0.0170855	+	0.00166501i
$925$	7.38662	+	6.19811i	0.242871	+	0.203793i
$926$			4.37230i			0.143683i
$927$	−9.76143	−	7.25895i	−0.320607	−	0.238415i
$928$	−3.23901			−0.106326
$929$	−2.35873	+	0.858508i	−0.0773875	+	0.0281667i	−0.380424	−	0.924812i	$-0.624222\pi$
$929$	−2.35873	+	0.858508i	−0.0773875	+	0.0281667i	0.303036	+	0.952979i	$0.402000\pi$
$930$	−11.3914	−	38.0127i	−0.373539	−	1.24649i
$931$	0.390164	+	0.546913i	0.0127871	+	0.0179244i
$932$	−2.19771	+	6.03817i	−0.0719885	+	0.197787i
$933$	−20.7411	+	21.9961i	−0.679032	+	0.720120i
$934$	5.78884	−	6.89887i	0.189417	−	0.225738i
$935$		−	1.08835i		−	0.0355927i
$936$	3.10773	−	4.17911i	0.101579	−	0.136598i
$937$	6.98943	+	4.03535i	0.228335	+	0.131829i	0.609804	−	0.792553i	$-0.291248\pi$
$937$	6.98943	+	4.03535i	0.228335	+	0.131829i	−0.381469	+	0.924382i	$0.624582\pi$
$938$	−19.6911	−	61.5079i	−0.642937	−	2.00830i
$939$	0.388404	+	0.772857i	0.0126751	+	0.0252212i
$940$	−12.5054	+	10.4933i	−0.407881	+	0.342252i
$941$	8.17252	+	46.3487i	0.266417	+	1.51092i	0.764971	+	0.644065i	$0.222753\pi$
$941$	8.17252	+	46.3487i	0.266417	+	1.51092i	−0.498554	+	0.866858i	$0.666136\pi$
$942$	6.98989	+	9.38378i	0.227743	+	0.305740i
$943$	9.08759	−	10.8302i	0.295933	−	0.352679i
$944$	31.6544			1.03026
$945$	4.31487	−	19.9540i	0.140363	−	0.649103i
$946$	−1.75305			−0.0569964
$947$	−23.2570	+	27.7166i	−0.755749	+	0.900667i	−0.997571	−	0.0696536i	$-0.977811\pi$
$947$	−23.2570	+	27.7166i	−0.755749	+	0.900667i	0.241822	+	0.970321i	$0.422255\pi$
$948$	0.242978	−	0.563703i	0.00789156	−	0.0183082i
$949$	−1.26792	−	7.19073i	−0.0411584	−	0.233421i
$950$	0.348409	−	0.292350i	0.0113039	−	0.00948509i
$951$	13.5067	+	0.783026i	0.437984	+	0.0253914i
$952$	27.7772	+	6.03005i	0.900263	+	0.195435i
$953$	41.0448	+	23.6972i	1.32957	+	0.767629i	0.985233	−	0.171216i	$-0.0547697\pi$
$953$	41.0448	+	23.6972i	1.32957	+	0.767629i	0.344339	+	0.938845i	$0.388103\pi$
$954$	−6.21363	+	4.09156i	−0.201174	+	0.132469i
$955$		−	7.85893i		−	0.254309i
$956$	−2.64681	+	3.15435i	−0.0856039	+	0.102019i
$957$	−0.153199	−	0.0362652i	−0.00495221	−	0.00117229i
$958$	−19.1016	+	52.4811i	−0.617143	+	1.69559i
$959$	12.1901	−	1.65941i	0.393639	−	0.0535852i
$960$	5.27234	+	1.24807i	0.170164	+	0.0402812i
$961$	48.6682	−	17.7138i	1.56994	−	0.571413i
$962$	−5.32444			−0.171667
$963$	−22.6590	+	21.4007i	−0.730175	+	0.689627i
$964$			5.80324i			0.186910i
$965$	20.0989	+	16.8650i	0.647007	+	0.542903i
$966$	−41.0547	−	29.3554i	−1.32091	−	0.944496i
$967$	−9.82570	−	55.7243i	−0.315973	−	1.79197i	−0.566710	−	0.823918i	$-0.691784\pi$
$967$	−9.82570	−	55.7243i	−0.315973	−	1.79197i	0.250736	−	0.968055i	$-0.419327\pi$
$968$	7.16496	−	19.6856i	0.230290	−	0.632718i
$969$	−0.108948	−	0.929942i	−0.00349992	−	0.0298740i
$970$	−4.56802	+	25.9066i	−0.146670	+	0.831809i
$971$	3.04373	+	5.27190i	0.0976780	+	0.169183i	0.910723	−	0.413017i	$-0.135525\pi$
$971$	3.04373	+	5.27190i	0.0976780	+	0.169183i	−0.813045	+	0.582201i	$0.802192\pi$
$972$	−9.37475	−	9.90991i	−0.300695	−	0.317860i
$973$	−28.7706	−	18.1516i	−0.922344	−	0.581913i
$974$	−14.0580	−	38.6241i	−0.450448	−	1.23760i
$975$	−4.04593	−	1.74395i	−0.129573	−	0.0558512i
$976$	−38.3304	+	6.75868i	−1.22693	+	0.216340i
$977$	5.88779	−	16.1766i	0.188367	−	0.517535i	−0.809178	−	0.587564i	$-0.800087\pi$
$977$	5.88779	−	16.1766i	0.188367	−	0.517535i	0.997545	+	0.0700293i	$0.0223093\pi$
$978$	72.1394	+	4.18216i	2.30676	+	0.133731i
$979$	−1.33588	+	1.59204i	−0.0426950	+	0.0508819i
$980$	−9.06865	−	0.713113i	−0.289687	−	0.0227796i
$981$	4.45367	−	14.9055i	0.142195	−	0.475896i
$982$	9.77699	−	16.9342i	0.311996	−	0.540393i
$983$	−8.63928	−	7.24922i	−0.275550	−	0.231214i	0.494531	−	0.869160i	$-0.335340\pi$
$983$	−8.63928	−	7.24922i	−0.275550	−	0.231214i	−0.770081	+	0.637946i	$0.779784\pi$
$984$	5.23180	+	4.93328i	0.166784	+	0.157267i
$985$	30.2554	−	5.33484i	0.964017	−	0.169982i
$986$	6.26906	+	2.28175i	0.199647	+	0.0726657i
$987$	−14.3493	−	55.7494i	−0.456742	−	1.77452i
$988$	−0.0132738	+	0.0752794i	−0.000422296	+	0.00239496i
$989$	44.6940	+	25.8041i	1.42119	+	0.820523i
$990$	−0.878600	−	0.440658i	−0.0279237	−	0.0140050i
$991$	−17.6534	−	30.5766i	−0.560780	−	0.971299i	−0.997429	−	0.0716671i	$-0.977168\pi$
$991$	−17.6534	−	30.5766i	−0.560780	−	0.971299i	0.436649	−	0.899632i	$-0.356165\pi$
$992$	7.32633	−	41.5497i	0.232611	−	1.31920i
$993$	−3.16886	+	54.6606i	−0.100561	+	1.73460i
$994$	1.66871	+	12.2584i	0.0529283	+	0.388813i
$995$	−12.1946	−	14.5330i	−0.386596	−	0.460727i
$996$	4.37857	+	5.87814i	0.138740	+	0.186256i
$997$	1.60718	+	0.283390i	0.0509001	+	0.00897505i	0.199040	−	0.979991i	$-0.436218\pi$
$997$	1.60718	+	0.283390i	0.0509001	+	0.00897505i	−0.148140	+	0.988966i	$0.547329\pi$
$998$	−7.49288	−	4.32601i	−0.237183	−	0.136938i
$999$	3.09883	−	17.6577i	0.0980425	−	0.558664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.101.5	✓	132
3.2	odd	2		567.2.ba.a.143.18		132
7.5	odd	6		189.2.bd.a.47.18	yes	132
21.5	even	6		567.2.bd.a.467.5		132
27.4	even	9		567.2.bd.a.17.5		132
27.23	odd	18		189.2.bd.a.185.18	yes	132
189.131	even	18	inner	189.2.ba.a.131.5	yes	132
189.166	odd	18		567.2.ba.a.341.18		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.5	✓	132	1.1	even	1	trivial
189.2.ba.a.131.5	yes	132	189.131	even	18	inner
189.2.bd.a.47.18	yes	132	7.5	odd	6
189.2.bd.a.185.18	yes	132	27.23	odd	18
567.2.ba.a.143.18		132	3.2	odd	2
567.2.ba.a.341.18		132	189.166	odd	18
567.2.bd.a.17.5		132	27.4	even	9
567.2.bd.a.467.5		132	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.08992 + 1.29892i) q^{2} +(1.72029 - 0.201542i) q^{3} +(-0.151961 - 0.861812i) q^{4} +(1.13756 - 0.954530i) q^{5} +(-1.61319 + 2.45417i) q^{6} +(2.51978 - 0.806679i) q^{7} +(-1.65184 - 0.953692i) q^{8} +(2.91876 - 0.693419i) q^{9} +O(q^{10})\)	\(q+(-1.08992 + 1.29892i) q^{2} +(1.72029 - 0.201542i) q^{3} +(-0.151961 - 0.861812i) q^{4} +(1.13756 - 0.954530i) q^{5} +(-1.61319 + 2.45417i) q^{6} +(2.51978 - 0.806679i) q^{7} +(-1.65184 - 0.953692i) q^{8} +(2.91876 - 0.693419i) q^{9} +2.51796i q^{10} +(-0.0836396 + 0.0996778i) q^{11} +(-0.435107 - 1.45194i) q^{12} +(-0.311287 + 0.855253i) q^{13} +(-1.69855 + 4.15219i) q^{14} +(1.76456 - 1.87133i) q^{15} +(4.68381 - 1.70477i) q^{16} -5.63249 q^{17} +(-2.28052 + 4.54700i) q^{18} +0.0959743i q^{19} +(-0.995491 - 0.835316i) q^{20} +(4.17215 - 1.89556i) q^{21} +(-0.0383126 - 0.217282i) q^{22} +(-2.22151 + 6.10356i) q^{23} +(-3.03385 - 1.30771i) q^{24} +(-0.485315 + 2.75236i) q^{25} +(-0.771624 - 1.33649i) q^{26} +(4.88135 - 1.78113i) q^{27} +(-1.07811 - 2.04899i) q^{28} +(0.238914 + 0.656410i) q^{29} +(0.507475 + 4.33161i) q^{30} +(-8.96076 + 1.58002i) q^{31} +(-1.58590 + 4.35722i) q^{32} +(-0.123795 + 0.188331i) q^{33} +(6.13896 - 7.31613i) q^{34} +(2.09641 - 3.32285i) q^{35} +(-1.04113 - 2.41005i) q^{36} +(1.72508 - 2.98792i) q^{37} +(-0.124663 - 0.104604i) q^{38} +(-0.363133 + 1.53402i) q^{39} +(-2.78941 + 0.491848i) q^{40} +(-2.04536 - 0.744450i) q^{41} +(-2.08514 + 7.48528i) q^{42} +(1.37972 - 7.82480i) q^{43} +(0.0986135 + 0.0569345i) q^{44} +(2.65839 - 3.57486i) q^{45} +(-5.50674 - 9.53795i) q^{46} +(2.18137 - 12.3712i) q^{47} +(7.71390 - 3.87667i) q^{48} +(5.69854 - 4.06530i) q^{49} +(-3.04613 - 3.63023i) q^{50} +(-9.68949 + 1.13518i) q^{51} +(0.784371 + 0.138306i) q^{52} +(1.26661 + 0.731275i) q^{53} +(-3.00674 + 8.28175i) q^{54} +0.193227i q^{55} +(-4.93160 - 1.07058i) q^{56} +(0.0193428 + 0.165103i) q^{57} +(-1.11302 - 0.405105i) q^{58} +(5.96770 + 2.17206i) q^{59} +(-1.88088 - 1.23635i) q^{60} +(-7.69007 - 1.35597i) q^{61} +(7.71419 - 13.3614i) q^{62} +(6.79526 - 4.10176i) q^{63} +(1.05325 + 1.82428i) q^{64} +(0.462256 + 1.27004i) q^{65} +(-0.109700 - 0.366065i) q^{66} +(-11.0280 + 9.25358i) q^{67} +(0.855917 + 4.85415i) q^{68} +(-2.59151 + 10.9476i) q^{69} +(2.03119 + 6.34470i) q^{70} +(2.38823 - 1.37884i) q^{71} +(-5.48265 - 1.63818i) q^{72} +(-6.94774 + 4.01128i) q^{73} +(2.00086 + 5.49732i) q^{74} +(-0.280165 + 4.83265i) q^{75} +(0.0827118 - 0.0145843i) q^{76} +(-0.130345 + 0.318636i) q^{77} +(-1.59677 - 2.14363i) q^{78} +(0.310233 + 0.260316i) q^{79} +(3.70088 - 6.41012i) q^{80} +(8.03834 - 4.04785i) q^{81} +(3.19626 - 1.84536i) q^{82} +(-4.54412 + 1.65393i) q^{83} +(-2.26762 - 3.30756i) q^{84} +(-6.40732 + 5.37638i) q^{85} +(8.65997 + 10.3205i) q^{86} +(0.543293 + 1.08106i) q^{87} +(0.233222 - 0.0848857i) q^{88} +15.9719 q^{89} +(1.74600 + 7.34933i) q^{90} +(-0.0944582 + 2.40615i) q^{91} +(5.59770 + 0.987026i) q^{92} +(-15.0966 + 4.52406i) q^{93} +(13.6916 + 16.3170i) q^{94} +(0.0916104 + 0.109177i) q^{95} +(-1.85003 + 7.81528i) q^{96} +(10.2887 + 1.81418i) q^{97} +(-0.930470 + 11.8328i) q^{98} +(-0.175006 + 0.348933i) 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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