LMFDB - Embedded newform 243.2.i.a.103.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(4,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(162))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("243.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.i (of order $81$, degree $54$, 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			103.26
Character	$\chi$	$=$	243.103
Dual form			243.2.i.a.151.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.57987 + 0.718157i) q^{2} +(1.51424 - 0.840877i) q^{3} +(4.42767 + 2.67211i) q^{4} +(-3.51654 + 0.136458i) q^{5} +(4.51043 - 1.08189i) q^{6} +(-3.43073 - 0.536556i) q^{7} +(5.82837 + 6.17771i) q^{8} +(1.58585 - 2.54658i) q^{9} +O(q^{10})$	\(q+(2.57987 + 0.718157i) q^{2} +(1.51424 - 0.840877i) q^{3} +(4.42767 + 2.67211i) q^{4} +(-3.51654 + 0.136458i) q^{5} +(4.51043 - 1.08189i) q^{6} +(-3.43073 - 0.536556i) q^{7} +(5.82837 + 6.17771i) q^{8} +(1.58585 - 2.54658i) q^{9} +(-9.17022 - 2.17338i) q^{10} +(-0.305175 - 2.23427i) q^{11} +(8.95148 + 0.323098i) q^{12} +(-1.63172 + 2.37910i) q^{13} +(-8.46551 - 3.84805i) q^{14} +(-5.21014 + 3.16360i) q^{15} +(5.77961 + 10.9723i) q^{16} +(1.77656 - 0.892221i) q^{17} +(5.92015 - 5.43097i) q^{18} +(0.153093 + 2.62850i) q^{19} +(-15.9347 - 8.79239i) q^{20} +(-5.64612 + 2.07234i) q^{21} +(0.817247 - 5.98331i) q^{22} +(1.99084 - 5.15640i) q^{23} +(14.0203 + 4.45360i) q^{24} +(7.36244 - 0.572254i) q^{25} +(-5.91820 + 4.96596i) q^{26} +(0.260003 - 5.18964i) q^{27} +(-13.7564 - 11.5430i) q^{28} +(3.05917 + 2.18657i) q^{29} +(-15.7135 + 4.42000i) q^{30} +(-5.26689 + 6.03518i) q^{31} +(3.43474 + 15.8565i) q^{32} +(-2.34086 - 3.12661i) q^{33} +(5.22405 - 1.02597i) q^{34} +(12.1375 + 1.41867i) q^{35} +(13.8264 - 7.03784i) q^{36} +(0.347087 + 0.466219i) q^{37} +(-1.49272 + 6.89116i) q^{38} +(-0.470282 + 4.97461i) q^{39} +(-21.3387 - 20.9288i) q^{40} +(0.455952 - 1.77012i) q^{41} +(-16.0546 + 1.29158i) q^{42} +(0.802684 + 0.728397i) q^{43} +(4.61902 - 10.7081i) q^{44} +(-5.22921 + 9.17155i) q^{45} +(8.83921 - 11.8731i) q^{46} +(7.33012 + 8.39939i) q^{47} +(17.9781 + 11.7548i) q^{48} +(4.81625 + 1.54427i) q^{49} +(19.4052 + 3.81105i) q^{50} +(1.93989 - 2.84491i) q^{51} +(-13.5819 + 6.17375i) q^{52} +(0.570971 - 3.23814i) q^{53} +(4.39775 - 13.2019i) q^{54} +(1.37804 + 7.81526i) q^{55} +(-16.6809 - 24.3213i) q^{56} +(2.44207 + 3.85146i) q^{57} +(6.32199 + 7.83804i) q^{58} +(-10.5222 + 4.29880i) q^{59} +(-31.5223 + 0.0853119i) q^{60} +(2.86548 - 1.72933i) q^{61} +(-17.9221 + 11.7876i) q^{62} +(-6.80701 + 7.88572i) q^{63} +(-1.08412 + 18.6136i) q^{64} +(5.41335 - 8.58886i) q^{65} +(-3.79371 - 9.74737i) q^{66} +(-5.67055 + 4.05307i) q^{67} +(10.2501 + 0.796703i) q^{68} +(-1.32129 - 9.48207i) q^{69} +(30.2944 + 12.3766i) q^{70} +(-3.36638 - 11.2445i) q^{71} +(24.9750 - 5.04547i) q^{72} +(5.59498 - 1.32604i) q^{73} +(0.560623 + 1.45205i) q^{74} +(10.6673 - 7.05744i) q^{75} +(-6.34581 + 12.0472i) q^{76} +(-0.151842 + 7.82892i) q^{77} +(-4.78582 + 12.4961i) q^{78} +(-1.57898 + 1.54866i) q^{79} +(-21.8215 - 37.7959i) q^{80} +(-3.97014 - 8.07700i) q^{81} +(2.44752 - 4.23923i) q^{82} +(-3.97987 - 15.4508i) q^{83} +(-30.5367 - 5.91142i) q^{84} +(-6.12558 + 3.37995i) q^{85} +(1.54772 + 2.45562i) q^{86} +(6.47096 + 0.738600i) q^{87} +(12.0240 - 14.9074i) q^{88} +(2.46600 - 8.23703i) q^{89} +(-20.0773 + 19.9060i) q^{90} +(6.87450 - 7.28654i) q^{91} +(22.5932 - 17.5111i) q^{92} +(-2.90049 + 13.5675i) q^{93} +(12.8787 + 26.9335i) q^{94} +(-0.897036 - 9.22234i) q^{95} +(18.5344 + 21.1224i) q^{96} +(4.01124 + 0.155654i) q^{97} +(11.3163 + 7.44284i) q^{98} +(-6.17372 - 2.76608i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9}+O(q^{10}) $ 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18} - 54 q^{19} - 54 q^{20} - 54 q^{21} - 54 q^{22} - 54 q^{23} - 54 q^{24} - 54 q^{25} - 54 q^{26} - 54 q^{27} - 54 q^{28} - 54 q^{29} - 54 q^{30} - 54 q^{31} - 54 q^{32} - 54 q^{33} - 54 q^{34} - 54 q^{35} - 54 q^{36} - 54 q^{37} - 54 q^{38} - 54 q^{39} - 54 q^{40} - 54 q^{41} - 54 q^{42} - 54 q^{43} - 54 q^{44} - 54 q^{45} - 54 q^{46} - 54 q^{47} - 54 q^{48} - 54 q^{49} - 54 q^{50} - 54 q^{51} - 54 q^{52} - 54 q^{53} - 54 q^{54} - 54 q^{55} - 54 q^{56} - 54 q^{57} - 54 q^{58} - 54 q^{59} - 54 q^{60} - 54 q^{61} - 54 q^{62} - 54 q^{63} - 54 q^{64} + 54 q^{66} - 54 q^{67} + 135 q^{68} + 54 q^{69} - 54 q^{70} + 54 q^{71} + 270 q^{72} - 54 q^{73} + 162 q^{74} + 81 q^{75} - 54 q^{76} + 162 q^{77} + 162 q^{78} - 54 q^{79} + 351 q^{80} + 54 q^{81} - 27 q^{82} + 54 q^{83} + 324 q^{84} - 54 q^{85} + 162 q^{86} + 162 q^{87} - 54 q^{88} + 81 q^{89} + 162 q^{90} - 54 q^{91} + 270 q^{92} + 54 q^{93} - 54 q^{94} + 54 q^{95} + 135 q^{96} - 54 q^{97} + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{81}\right)$

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 $

$2$	2.57987	+	0.718157i	1.82425	+	0.507814i	0.998424	−	0.0561163i	$-0.0178718\pi$
$2$	2.57987	+	0.718157i	1.82425	+	0.507814i	0.825823	+	0.563930i	$0.190711\pi$
$3$	1.51424	−	0.840877i	0.874248	−	0.485480i
$3$	1.51424	−	0.840877i	0.874248	−	0.485480i
$4$	4.42767	+	2.67211i	2.21383	+	1.33606i
$5$	−3.51654	+	0.136458i	−1.57264	+	0.0610257i	−0.810248	−	0.586087i	$-0.800668\pi$
$5$	−3.51654	+	0.136458i	−1.57264	+	0.0610257i	−0.762395	+	0.647112i	$0.775976\pi$
$6$	4.51043	−	1.08189i	1.84138	−	0.441681i
$7$	−3.43073	−	0.536556i	−1.29669	−	0.202799i	−0.531752	−	0.846900i	$-0.678466\pi$
$7$	−3.43073	−	0.536556i	−1.29669	−	0.202799i	−0.764940	+	0.644101i	$0.777232\pi$
$8$	5.82837	+	6.17771i	2.06064	+	2.18415i
$9$	1.58585	−	2.54658i	0.528618	−	0.848860i
$10$	−9.17022	−	2.17338i	−2.89988	−	0.687284i
$11$	−0.305175	−	2.23427i	−0.0920136	−	0.673659i	−0.977796	−	0.209558i	$-0.932797\pi$
$11$	−0.305175	−	2.23427i	−0.0920136	−	0.673659i	0.885783	−	0.464100i	$-0.153622\pi$
$12$	8.95148	+	0.323098i	2.58407	+	0.0932703i
$13$	−1.63172	+	2.37910i	−0.452557	+	0.659844i	−0.982083	−	0.188449i	$-0.939654\pi$
$13$	−1.63172	+	2.37910i	−0.452557	+	0.659844i	0.529526	+	0.848294i	$0.322370\pi$
$14$	−8.46551	−	3.84805i	−2.26250	−	1.02843i
$15$	−5.21014	+	3.16360i	−1.34525	+	0.816839i
$16$	5.77961	+	10.9723i	1.44490	+	2.74308i
$17$	1.77656	−	0.892221i	0.430879	−	0.216395i	−0.220122	−	0.975472i	$-0.570646\pi$
$17$	1.77656	−	0.892221i	0.430879	−	0.216395i	0.651001	+	0.759077i	$0.274349\pi$
$18$	5.92015	−	5.43097i	1.39539	−	1.28009i
$19$	0.153093	+	2.62850i	0.0351219	+	0.603020i	0.969249	+	0.246081i	$0.0791428\pi$
$19$	0.153093	+	2.62850i	0.0351219	+	0.603020i	−0.934127	+	0.356940i	$0.883820\pi$
$20$	−15.9347	−	8.79239i	−3.56310	−	1.96604i
$21$	−5.64612	+	2.07234i	−1.23209	+	0.452222i
$22$	0.817247	−	5.98331i	0.174238	−	1.27565i
$23$	1.99084	−	5.15640i	0.415118	−	1.07518i	−0.554850	−	0.831950i	$-0.687224\pi$
$23$	1.99084	−	5.15640i	0.415118	−	1.07518i	0.969968	−	0.243232i	$-0.0782077\pi$
$24$	14.0203	+	4.45360i	2.86187	+	0.909088i
$25$	7.36244	−	0.572254i	1.47249	−	0.114451i
$26$	−5.91820	+	4.96596i	−1.16065	+	0.973904i
$27$	0.260003	−	5.18964i	0.0500376	−	0.998747i
$28$	−13.7564	−	11.5430i	−2.59971	−	2.18142i
$29$	3.05917	+	2.18657i	0.568074	+	0.406035i	0.828938	−	0.559340i	$-0.188946\pi$
$29$	3.05917	+	2.18657i	0.568074	+	0.406035i	−0.260864	+	0.965376i	$0.584007\pi$
$30$	−15.7135	+	4.42000i	−2.86887	+	0.806978i
$31$	−5.26689	+	6.03518i	−0.945961	+	1.08395i	0.0504009	+	0.998729i	$0.483950\pi$
$31$	−5.26689	+	6.03518i	−0.945961	+	1.08395i	−0.996362	+	0.0852220i	$0.972840\pi$
$32$	3.43474	+	15.8565i	0.607182	+	2.80306i
$33$	−2.34086	−	3.12661i	−0.407491	−	0.544274i
$34$	5.22405	−	1.02597i	0.895918	−	0.175953i
$35$	12.1375	+	1.41867i	2.05161	+	0.239799i
$36$	13.8264	−	7.03784i	2.30440	−	1.17297i
$37$	0.347087	+	0.466219i	0.0570608	+	0.0766459i	0.829738	−	0.558154i	$-0.188490\pi$
$37$	0.347087	+	0.466219i	0.0570608	+	0.0766459i	−0.772677	+	0.634800i	$0.781083\pi$
$38$	−1.49272	+	6.89116i	−0.242151	+	1.11789i
$39$	−0.470282	+	4.97461i	−0.0753054	+	0.796575i
$40$	−21.3387	−	20.9288i	−3.37394	−	3.30914i
$41$	0.455952	−	1.77012i	0.0712078	−	0.276446i	−0.922871	−	0.385110i	$-0.874164\pi$
$41$	0.455952	−	1.77012i	0.0712078	−	0.276446i	0.994078	+	0.108664i	$0.0346574\pi$
$42$	−16.0546	+	1.29158i	−2.47727	+	0.199295i
$43$	0.802684	+	0.728397i	0.122408	+	0.111079i	0.730913	−	0.682471i	$-0.239095\pi$
$43$	0.802684	+	0.728397i	0.122408	+	0.111079i	−0.608505	+	0.793550i	$0.708230\pi$
$44$	4.61902	−	10.7081i	0.696343	−	1.61430i
$45$	−5.22921	+	9.17155i	−0.779524	+	1.36721i
$46$	8.83921	−	11.8731i	1.30327	−	1.75060i
$47$	7.33012	+	8.39939i	1.06921	+	1.22518i	0.973240	+	0.229792i	$0.0738046\pi$
$47$	7.33012	+	8.39939i	1.06921	+	1.22518i	0.0959682	+	0.995384i	$0.469405\pi$
$48$	17.9781	+	11.7548i	2.59491	+	1.69666i
$49$	4.81625	+	1.54427i	0.688036	+	0.220610i
$50$	19.4052	+	3.81105i	2.74430	+	0.538964i
$51$	1.93989	−	2.84491i	0.271639	−	0.398366i
$52$	−13.5819	+	6.17375i	−1.88348	+	0.856145i
$53$	0.570971	−	3.23814i	0.0784290	−	0.444793i	−0.920153	−	0.391559i	$-0.871936\pi$
$53$	0.570971	−	3.23814i	0.0784290	−	0.444793i	0.998582	−	0.0532340i	$-0.0169529\pi$
$54$	4.39775	−	13.2019i	0.598459	−	1.79655i
$55$	1.37804	+	7.81526i	0.185815	+	1.05381i
$56$	−16.6809	−	24.3213i	−2.22907	−	3.25007i
$57$	2.44207	+	3.85146i	0.323460	+	0.510138i
$58$	6.32199	+	7.83804i	0.830118	+	1.02918i
$59$	−10.5222	+	4.29880i	−1.36988	+	0.559656i	−0.939362	−	0.342928i	$-0.888581\pi$
$59$	−10.5222	+	4.29880i	−1.36988	+	0.559656i	−0.430515	+	0.902584i	$0.641668\pi$
$60$	−31.5223	+	0.0853119i	−4.06951	+	0.0110137i
$61$	2.86548	−	1.72933i	0.366887	−	0.221418i	−0.321256	−	0.946992i	$-0.604105\pi$
$61$	2.86548	−	1.72933i	0.366887	−	0.221418i	0.688143	+	0.725575i	$0.258426\pi$
$62$	−17.9221	+	11.7876i	−2.27611	+	1.49702i
$63$	−6.80701	+	7.88572i	−0.857602	+	0.993507i
$64$	−1.08412	+	18.6136i	−0.135515	+	2.32670i
$65$	5.41335	−	8.58886i	0.671443	−	1.06532i
$66$	−3.79371	−	9.74737i	−0.466974	−	1.19982i
$67$	−5.67055	+	4.05307i	−0.692768	+	0.495161i	−0.872537	−	0.488548i	$-0.837527\pi$
$67$	−5.67055	+	4.05307i	−0.692768	+	0.495161i	0.179769	+	0.983709i	$0.442465\pi$
$68$	10.2501	+	0.796703i	1.24301	+	0.0966144i
$69$	−1.32129	−	9.48207i	−0.159064	−	1.14151i
$70$	30.2944	+	12.3766i	3.62087	+	1.47929i
$71$	−3.36638	−	11.2445i	−0.399515	−	1.33447i	−0.887172	−	0.461439i	$-0.847333\pi$
$71$	−3.36638	−	11.2445i	−0.399515	−	1.33447i	0.487657	−	0.873035i	$-0.337852\pi$
$72$	24.9750	−	5.04547i	2.94333	−	0.594615i
$73$	5.59498	−	1.32604i	0.654843	−	0.155201i	0.110254	−	0.993903i	$-0.464834\pi$
$73$	5.59498	−	1.32604i	0.654843	−	0.155201i	0.544589	+	0.838703i	$0.316685\pi$
$74$	0.560623	+	1.45205i	0.0651711	+	0.168797i
$75$	10.6673	−	7.05744i	1.23176	−	0.814923i
$76$	−6.34581	+	12.0472i	−0.727915	+	1.38191i
$77$	−0.151842	+	7.82892i	−0.0173040	+	0.892188i
$78$	−4.78582	+	12.4961i	−0.541887	+	1.41491i
$79$	−1.57898	+	1.54866i	−0.177650	+	0.174238i	−0.783602	−	0.621264i	$-0.786620\pi$
$79$	−1.57898	+	1.54866i	−0.177650	+	0.174238i	0.605952	+	0.795501i	$0.292792\pi$
$80$	−21.8215	−	37.7959i	−2.43971	−	4.22571i
$81$	−3.97014	−	8.07700i	−0.441127	−	0.897445i
$82$	2.44752	−	4.23923i	0.270283	−	0.468145i
$83$	−3.97987	−	15.4508i	−0.436848	−	1.69595i	−0.686100	−	0.727508i	$-0.740679\pi$
$83$	−3.97987	−	15.4508i	−0.436848	−	1.69595i	0.249252	−	0.968439i	$-0.419815\pi$
$84$	−30.5367	−	5.91142i	−3.33183	−	0.644989i
$85$	−6.12558	+	3.37995i	−0.664413	+	0.366608i
$86$	1.54772	+	2.45562i	0.166895	+	0.264797i
$87$	6.47096	+	0.738600i	0.693760	+	0.0791863i
$88$	12.0240	−	14.9074i	1.28177	−	1.58914i
$89$	2.46600	−	8.23703i	0.261396	−	0.873123i	−0.722038	−	0.691854i	$-0.756794\pi$
$89$	2.46600	−	8.23703i	0.261396	−	0.873123i	0.983433	−	0.181269i	$-0.0580206\pi$
$90$	−20.0773	+	19.9060i	−2.11633	+	2.09828i
$91$	6.87450	−	7.28654i	0.720643	−	0.763837i
$92$	22.5932	−	17.5111i	2.35551	−	1.82566i
$93$	−2.90049	+	13.5675i	−0.300767	+	1.40689i
$94$	12.8787	+	26.9335i	1.32834	+	2.77798i
$95$	−0.897036	−	9.22234i	−0.0920340	−	0.946192i
$96$	18.5344	+	21.1224i	1.89166	+	2.15580i
$97$	4.01124	+	0.155654i	0.407279	+	0.0158043i	0.241601	−	0.970376i	$-0.422327\pi$
$97$	4.01124	+	0.155654i	0.407279	+	0.0158043i	0.165678	+	0.986180i	$0.447019\pi$
$98$	11.3163	+	7.44284i	1.14312	+	0.751841i
$99$	−6.17372	−	2.76608i	−0.620482	−	0.278001i
$100$	34.1276	+	17.1395i	3.41276	+	1.71395i
$101$	0.0135561	+	0.698949i	0.00134888	+	0.0695480i	0.999881	+	0.0153944i	$0.00490038\pi$
$101$	0.0135561	+	0.698949i	0.00134888	+	0.0695480i	−0.998533	+	0.0541536i	$0.982754\pi$
$102$	7.04776	−	5.94635i	0.697833	−	0.588777i
$103$	−4.73288	−	3.66826i	−0.466344	−	0.361444i	0.352165	−	0.935938i	$-0.385446\pi$
$103$	−4.73288	−	3.66826i	−0.466344	−	0.361444i	−0.818509	+	0.574494i	$0.805199\pi$
$104$	−24.2077	+	3.78601i	−2.37376	+	0.371249i
$105$	19.5720	−	8.05793i	1.91003	−	0.786373i
$106$	3.79853	−	7.94395i	0.368946	−	0.771584i
$107$	14.7855	+	5.38148i	1.42937	+	0.520247i	0.936750	−	0.349999i	$-0.113818\pi$
$107$	14.7855	+	5.38148i	1.42937	+	0.520247i	0.492617	+	0.870246i	$0.336040\pi$
$108$	15.0185	−	22.2833i	1.44516	−	2.14421i
$109$	−7.14750	+	2.60148i	−0.684606	+	0.249176i	−0.660824	−	0.750541i	$-0.729793\pi$
$109$	−7.14750	+	2.60148i	−0.684606	+	0.249176i	−0.0237821	+	0.999717i	$0.507571\pi$
$110$	−2.05741	+	21.1520i	−0.196166	+	2.01677i
$111$	0.917606	+	0.414110i	0.0870953	+	0.0393056i
$112$	−13.9410	−	40.7441i	−1.31730	−	3.84995i
$113$	−13.2652	+	12.0375i	−1.24788	+	1.13239i	−0.261979	+	0.965074i	$0.584375\pi$
$113$	−13.2652	+	12.0375i	−1.24788	+	1.13239i	−0.985903	+	0.167319i	$0.946489\pi$
$114$	3.53428	+	11.6901i	0.331015	+	1.09487i
$115$	−6.29722	+	18.4043i	−0.587219	+	1.71621i
$116$	7.70226	+	17.8558i	0.715137	+	1.65787i
$117$	3.47091	+	7.92821i	0.320886	+	0.732963i
$118$	−30.2332	+	3.53376i	−2.78319	+	0.325309i
$119$	−6.57361	+	2.10774i	−0.602602	+	0.193217i
$120$	−49.9105	−	13.7481i	−4.55618	−	1.25502i
$121$	5.69824	−	1.58621i	0.518021	−	0.144201i
$122$	8.63451	−	2.40358i	0.781732	−	0.217610i
$123$	−0.798027	−	3.06378i	−0.0719557	−	0.276252i
$124$	−39.4467	+	12.6481i	−3.54242	+	1.13583i
$125$	−8.33528	+	0.974254i	−0.745530	+	0.0871400i
$126$	−23.2244	+	15.4557i	−2.06899	+	1.37690i
$127$	−0.563057	−	1.30531i	−0.0499632	−	0.115828i	0.891406	−	0.453205i	$-0.149719\pi$
$127$	−0.563057	−	1.30531i	−0.0499632	−	0.115828i	−0.941370	+	0.337377i	$0.890460\pi$
$128$	−5.65970	+	16.5411i	−0.500252	+	1.46204i
$129$	1.82795	+	0.428010i	0.160942	+	0.0376842i
$130$	20.1339	−	18.2706i	1.76586	−	1.60243i
$131$	−2.22093	−	6.49092i	−0.194044	−	0.567114i	0.805636	−	0.592411i	$-0.201824\pi$
$131$	−2.22093	−	6.49092i	−0.194044	−	0.567114i	−0.999680	+	0.0252962i	$0.991947\pi$
$132$	−2.00987	−	20.0986i	−0.174937	−	1.74936i
$133$	0.885119	−	9.09982i	0.0767496	−	0.789054i
$134$	−17.5400	+	6.38406i	−1.51523	+	0.551498i
$135$	−0.206143	+	18.2851i	−0.0177420	+	1.57373i
$136$	15.8663	+	5.77487i	1.36053	+	0.495191i
$137$	−4.48316	+	9.37572i	−0.383022	+	0.801022i	0.616881	+	0.787057i	$0.288396\pi$
$137$	−4.48316	+	9.37572i	−0.383022	+	0.801022i	−0.999902	+	0.0139655i	$0.995554\pi$
$138$	3.40086	−	25.4115i	0.289501	−	2.16317i
$139$	−12.4487	+	1.94695i	−1.05589	+	0.165138i	−0.658552	−	0.752535i	$-0.728831\pi$
$139$	−12.4487	+	1.94695i	−1.05589	+	0.165138i	−0.397336	+	0.917673i	$0.630065\pi$
$140$	49.9499	+	38.7141i	4.22154	+	3.27194i
$141$	18.1624	+	6.55497i	1.52955	+	0.552028i
$142$	−0.609525	−	31.4269i	−0.0511502	−	2.63729i
$143$	5.81352	+	2.91966i	0.486151	+	0.244154i
$144$	37.1075	+	2.68224i	3.09229	+	0.223520i
$145$	−11.0561	−	7.27169i	−0.918157	−	0.603881i
$146$	15.3867	+	0.597072i	1.27341	+	0.0494141i
$147$	8.59150	−	1.71148i	0.708615	−	0.141160i
$148$	0.290998	+	2.99172i	0.0239199	+	0.245918i
$149$	−0.0524588	−	0.109708i	−0.00429759	−	0.00898765i	0.900007	−	0.435875i	$-0.143561\pi$
$149$	−0.0524588	−	0.109708i	−0.00429759	−	0.00898765i	−0.904305	+	0.426887i	$0.859610\pi$
$150$	32.5887	−	10.5465i	2.66086	−	0.861118i
$151$	2.39813	−	1.85869i	0.195157	−	0.151258i	−0.510336	−	0.859975i	$-0.670479\pi$
$151$	2.39813	−	1.85869i	0.195157	−	0.151258i	0.705493	+	0.708717i	$0.250726\pi$
$152$	−15.3459	+	16.2657i	−1.24471	+	1.31932i
$153$	0.545247	−	5.93908i	0.0440806	−	0.480146i
$154$	−6.01413	+	20.0886i	−0.484632	+	1.61878i
$155$	17.6977	−	21.9417i	1.42151	−	1.76240i
$156$	−15.3750	+	20.7693i	−1.23098	+	1.66287i
$157$	10.3424	+	16.4094i	0.825417	+	1.30961i	0.948359	+	0.317200i	$0.102743\pi$
$157$	10.3424	+	16.4094i	0.825417	+	1.30961i	−0.122941	+	0.992414i	$0.539233\pi$
$158$	−5.18576	+	2.86138i	−0.412557	+	0.227639i
$159$	−1.85829	−	5.38344i	−0.147372	−	0.426935i
$160$	−14.2421	−	55.2913i	−1.12594	−	4.37116i
$161$	−9.59671	+	16.6220i	−0.756326	+	1.31000i
$162$	−4.44192	−	23.6888i	−0.348990	−	1.86117i
$163$	11.6564	+	20.1895i	0.913001	+	1.58136i	0.809802	+	0.586703i	$0.199575\pi$
$163$	11.6564	+	20.1895i	0.913001	+	1.58136i	0.103199	+	0.994661i	$0.467092\pi$
$164$	6.74875	−	6.61913i	0.526989	−	0.516867i
$165$	8.65836	+	10.6754i	0.674052	+	0.831081i
$166$	0.828540	−	42.7193i	0.0643072	−	3.31566i
$167$	9.40517	−	17.8553i	0.727794	−	1.38168i	−0.188861	−	0.982004i	$-0.560480\pi$
$167$	9.40517	−	17.8553i	0.727794	−	1.38168i	0.916655	−	0.399679i	$-0.130878\pi$
$168$	−45.7100	−	22.8017i	−3.52661	−	1.75919i
$169$	1.68468	+	4.36344i	0.129591	+	0.335649i
$170$	−18.2306	+	4.32073i	−1.39822	+	0.331385i
$171$	6.93648	+	3.77856i	0.530446	+	0.288953i
$172$	1.60766	+	5.36996i	0.122583	+	0.409456i
$173$	−6.03559	−	2.46581i	−0.458877	−	0.187472i	0.136961	−	0.990576i	$-0.456266\pi$
$173$	−6.03559	−	2.46581i	−0.458877	−	0.187472i	−0.595838	+	0.803105i	$0.703180\pi$
$174$	16.1638	+	6.55266i	1.22538	+	0.496756i
$175$	−25.5656	−	1.98711i	−1.93258	−	0.150212i
$176$	22.7513	−	16.2617i	1.71495	−	1.22577i
$177$	−12.3184	+	15.3573i	−0.925909	+	1.15433i
$178$	12.2775	−	19.4795i	0.920235	−	1.46005i
$179$	0.101316	−	1.73952i	0.00757268	−	0.130018i	−0.992403	−	0.123030i	$-0.960739\pi$
$179$	0.101316	−	1.73952i	0.00757268	−	0.130018i	0.999976	−	0.00698754i	$-0.00222422\pi$
$180$	−47.6606	+	26.6355i	−3.55241	+	1.98530i
$181$	−9.71472	+	6.38947i	−0.722090	+	0.474926i	−0.856597	−	0.515987i	$-0.827425\pi$
$181$	−9.71472	+	6.38947i	−0.722090	+	0.474926i	0.134507	+	0.990913i	$0.457055\pi$
$182$	22.9682	−	13.8614i	1.70252	−	1.02747i
$183$	2.88488	−	5.02813i	0.213256	−	0.371690i
$184$	43.4581	−	17.7546i	3.20377	−	1.30888i
$185$	−1.28416	−	1.59211i	−0.0944136	−	0.117054i
$186$	−17.2265	+	32.9195i	−1.26311	+	2.41378i
$187$	−2.53563	−	3.69703i	−0.185423	−	0.270354i
$188$	10.0112	+	56.7766i	0.730145	+	4.14086i
$189$	−3.67653	+	17.6647i	−0.267428	+	1.28492i
$190$	4.30885	−	24.4367i	0.312597	−	1.77282i
$191$	−2.81476	+	1.27946i	−0.203669	+	0.0925787i	−0.513048	−	0.858360i	$-0.671484\pi$
$191$	−2.81476	+	1.27946i	−0.203669	+	0.0925787i	0.309379	+	0.950939i	$0.399879\pi$
$192$	14.0101	+	29.0971i	1.01109	+	2.09990i
$193$	9.00633	+	1.76879i	0.648290	+	0.127320i	0.506039	−	0.862511i	$-0.331109\pi$
$193$	9.00633	+	1.76879i	0.648290	+	0.127320i	0.142251	+	0.989831i	$0.454566\pi$
$194$	10.2367	+	3.28227i	0.734952	+	0.235653i
$195$	0.974940	−	17.5576i	0.0698169	−	1.25732i
$196$	17.1983	+	19.7071i	1.22845	+	1.40765i
$197$	−2.39351	+	3.21504i	−0.170530	+	0.229062i	−0.879170	−	0.476509i	$-0.841902\pi$
$197$	−2.39351	+	3.21504i	−0.170530	+	0.229062i	0.708639	+	0.705571i	$0.249309\pi$
$198$	−13.9409	−	11.5698i	−0.990739	−	0.822232i
$199$	6.53734	−	15.1553i	0.463420	−	1.07433i	−0.512989	−	0.858395i	$-0.671462\pi$
$199$	6.53734	−	15.1553i	0.463420	−	1.07433i	0.976408	−	0.215932i	$-0.0692791\pi$
$200$	46.4463	+	42.1477i	3.28425	+	2.98030i
$201$	−5.17845	+	10.9056i	−0.365260	+	0.769219i
$202$	−0.466982	+	1.81294i	−0.0328567	+	0.127558i
$203$	−9.32197	−	9.14293i	−0.654274	−	0.641708i
$204$	16.1911	−	7.41270i	1.13360	−	0.518993i
$205$	−1.36183	+	6.28689i	−0.0951141	+	0.439096i
$206$	−9.57584	−	12.8626i	−0.667181	−	0.896179i
$207$	−9.97400	−	13.2471i	−0.693241	−	0.920738i
$208$	−35.5349	−	4.15344i	−2.46391	−	0.287989i
$209$	5.82608	−	1.14420i	0.402998	−	0.0791462i
$210$	56.2802	−	6.73266i	3.88370	−	0.464597i
$211$	−5.29295	−	24.4350i	−0.364382	−	1.68217i	−0.679941	−	0.733267i	$-0.737994\pi$
$211$	−5.29295	−	24.4350i	−0.364382	−	1.68217i	0.315559	−	0.948906i	$-0.397808\pi$
$212$	11.1807	−	12.8117i	0.767897	−	0.879912i
$213$	−14.5527	−	14.1961i	−0.997136	−	0.972704i
$214$	34.2799	+	24.5018i	2.34333	+	1.67491i
$215$	−2.92206	−	2.45190i	−0.199283	−	0.167218i
$216$	33.5755	−	28.6409i	2.28452	−	1.94877i
$217$	21.3075	−	17.8791i	1.44644	−	1.21371i
$218$	−20.3079	+	1.57846i	−1.37543	+	0.106907i
$219$	7.35712	−	6.71263i	0.497148	−	0.453597i
$220$	−14.7817	+	38.2857i	−0.996584	+	2.58122i
$221$	−0.776156	+	5.68247i	−0.0522099	+	0.382244i
$222$	2.06991	+	1.72734i	0.138923	+	0.115931i
$223$	−8.91346	−	4.91824i	−0.596889	−	0.329350i	0.155736	−	0.987799i	$-0.450225\pi$
$223$	−8.91346	−	4.91824i	−0.596889	−	0.329350i	−0.752625	+	0.658449i	$0.771213\pi$
$224$	−3.27574	−	56.2423i	−0.218870	−	3.75785i
$225$	10.2185	−	19.6566i	0.681231	−	1.31044i
$226$	−42.8673	+	21.5288i	−2.85149	+	1.43207i
$227$	3.74958	+	7.11840i	0.248868	+	0.472465i	0.977076	−	0.212892i	$-0.0682883\pi$
$227$	3.74958	+	7.11840i	0.248868	+	0.472465i	−0.728208	+	0.685357i	$0.759646\pi$
$228$	0.521144	+	23.5785i	0.0345136	+	1.56152i
$229$	11.9353	+	5.42525i	0.788706	+	0.358511i	0.767323	−	0.641261i	$-0.221588\pi$
$229$	11.9353	+	5.42525i	0.788706	+	0.358511i	0.0213826	+	0.999771i	$0.493193\pi$
$230$	−29.4632	+	42.9584i	−1.94275	+	2.83260i
$231$	6.35323	+	11.9826i	0.418012	+	0.788394i
$232$	4.32202	+	31.6428i	0.283755	+	2.07745i
$233$	−12.6130	−	2.98934i	−0.826306	−	0.195838i	−0.204358	−	0.978896i	$-0.565511\pi$
$233$	−12.6130	−	2.98934i	−0.826306	−	0.195838i	−0.621948	+	0.783058i	$0.713659\pi$
$234$	3.26082	+	22.9464i	0.213167	+	1.50006i
$235$	−26.9228	−	28.5365i	−1.75625	−	1.86152i
$236$	−58.0758	−	9.08289i	−3.78041	−	0.591246i
$237$	−1.08873	+	3.67277i	−0.0707209	+	0.238572i
$238$	−18.4728	+	0.716828i	−1.19741	+	0.0464651i
$239$	−12.2967	−	7.42110i	−0.795408	−	0.480031i	0.0598666	−	0.998206i	$-0.480932\pi$
$239$	−12.2967	−	7.42110i	−0.795408	−	0.480031i	−0.855274	+	0.518175i	$0.826611\pi$
$240$	−64.8246	−	38.8829i	−4.18441	−	2.50988i
$241$	−0.547763	−	0.152480i	−0.0352845	−	0.00982212i	0.250485	−	0.968120i	$-0.419410\pi$
$241$	−0.547763	−	0.152480i	−0.0352845	−	0.00982212i	−0.285770	+	0.958298i	$0.592249\pi$
$242$	15.8399			1.01823
$243$	−12.8035	−	8.89213i	−0.821346	−	0.570430i
$244$	17.3084			1.10805
$245$	−17.1472	−	4.77326i	−1.09550	−	0.304953i
$246$	0.141466	−	8.47728i	0.00901956	−	0.540492i
$247$	−6.50329	−	3.92475i	−0.413794	−	0.249726i
$248$	−67.9810	+	2.63797i	−4.31680	+	0.167511i
$249$	−19.0187	−	20.0497i	−1.20526	−	1.27060i
$250$	−22.2036	−	3.47259i	−1.40428	−	0.219626i
$251$	10.3643	+	10.9855i	0.654189	+	0.693399i	0.966525	−	0.256572i	$-0.0825931\pi$
$251$	10.3643	+	10.9855i	0.654189	+	0.693399i	−0.312337	+	0.949972i	$0.601112\pi$
$252$	−51.2107	+	16.7263i	−3.22597	+	1.05366i
$253$	−12.1283	−	2.87447i	−0.762503	−	0.180716i
$254$	−0.515196	−	3.77190i	−0.0323263	−	0.236670i
$255$	−6.43349	+	10.2689i	−0.402881	+	0.643065i
$256$	−5.38877	+	7.85702i	−0.336798	+	0.491064i
$257$	17.8094	+	8.09537i	1.11092	+	0.504975i	0.883316	−	0.468778i	$-0.155306\pi$
$257$	17.8094	+	8.09537i	1.11092	+	0.504975i	0.227605	+	0.973754i	$0.426911\pi$
$258$	4.40850	+	2.41697i	0.274461	+	0.150474i
$259$	−0.940608	−	1.78570i	−0.0584465	−	0.110958i
$260$	46.9189	−	23.5636i	2.90979	−	1.46135i
$261$	10.4197	−	4.32286i	0.644961	−	0.267578i
$262$	−1.06823	−	18.3407i	−0.0659952	−	1.13309i
$263$	−8.12111	−	4.48104i	−0.500769	−	0.276313i	0.212552	−	0.977150i	$-0.431822\pi$
$263$	−8.12111	−	4.48104i	−0.500769	−	0.276313i	−0.713321	+	0.700837i	$0.752810\pi$
$264$	5.67194	−	32.6842i	0.349084	−	2.01157i
$265$	−1.56597	+	11.4650i	−0.0961970	+	0.704286i
$266$	8.81860	−	22.8407i	0.540703	−	1.40046i
$267$	−3.19220	−	14.5465i	−0.195359	−	0.890228i
$268$	−35.9376	+	2.79329i	−2.19524	+	0.170627i
$269$	−4.50400	+	3.77930i	−0.274614	+	0.230428i	−0.769685	−	0.638424i	$-0.779587\pi$
$269$	−4.50400	+	3.77930i	−0.274614	+	0.230428i	0.495071	+	0.868853i	$0.335142\pi$
$270$	−13.6634	+	47.0251i	−0.831526	+	2.86186i
$271$	−13.8736	−	11.6414i	−0.842764	−	0.707163i	0.115420	−	0.993317i	$-0.463179\pi$
$271$	−13.8736	−	11.6414i	−0.842764	−	0.707163i	−0.958184	+	0.286154i	$0.907623\pi$
$272$	20.0575	+	14.3363i	1.21617	+	0.869264i
$273$	4.28256	−	16.8142i	0.259193	−	1.01764i
$274$	−18.2992	+	20.9686i	−1.10550	+	1.26676i
$275$	−3.52540	−	16.2751i	−0.212590	−	0.981424i
$276$	19.4869	−	45.5141i	1.17298	−	2.73963i
$277$	−6.91358	+	1.35778i	−0.415397	+	0.0815813i	−0.396044	−	0.918231i	$-0.629617\pi$
$277$	−6.91358	+	1.35778i	−0.415397	+	0.0815813i	−0.0193527	+	0.999813i	$0.506161\pi$
$278$	−33.5144	−	3.91727i	−2.01006	−	0.234942i
$279$	7.01657	+	22.9835i	0.420071	+	1.37598i
$280$	61.9777	+	83.2504i	3.70387	+	4.97516i
$281$	−5.69383	+	26.2856i	−0.339665	+	1.56807i	0.413666	+	0.910429i	$0.364248\pi$
$281$	−5.69383	+	26.2856i	−0.339665	+	1.56807i	−0.753331	+	0.657641i	$0.771554\pi$
$282$	42.1493	+	29.9545i	2.50995	+	1.78376i
$283$	8.50564	+	8.34227i	0.505608	+	0.495897i	0.907652	−	0.419724i	$-0.137873\pi$
$283$	8.50564	+	8.34227i	0.505608	+	0.495897i	−0.402044	+	0.915620i	$0.631700\pi$
$284$	15.1413	−	58.7822i	0.898471	−	3.48808i
$285$	−9.11318	−	13.2106i	−0.539818	−	0.782526i
$286$	12.9014	+	11.7074i	0.762875	+	0.692272i
$287$	−2.51401	+	5.82814i	−0.148397	+	0.344024i
$288$	45.8269	+	16.3993i	2.70037	+	0.966336i
$289$	−7.79159	+	10.4659i	−0.458329	+	0.615643i
$290$	−23.3011	−	26.7001i	−1.36829	−	1.56788i
$291$	6.20486	−	3.13726i	0.363736	−	0.183909i
$292$	28.3160	+	9.07917i	1.65707	+	0.531318i
$293$	13.9083	+	2.73150i	0.812530	+	0.159576i	0.581684	−	0.813415i	$-0.302394\pi$
$293$	13.9083	+	2.73150i	0.812530	+	0.159576i	0.230846	+	0.972990i	$0.425851\pi$
$294$	23.3941	+	1.75465i	1.36437	+	0.102333i
$295$	36.4152	−	16.5527i	2.12017	−	0.963737i
$296$	−0.857214	+	4.86150i	−0.0498245	+	0.282569i
$297$	−11.6744	+	1.00283i	−0.677419	+	0.0581901i
$298$	−0.0565493	−	0.320707i	−0.00327581	−	0.0185781i
$299$	9.01911	+	13.1502i	0.521589	+	0.760495i
$300$	66.0896	−	2.74373i	3.81569	−	0.158409i
$301$	−2.36296	−	2.92961i	−0.136199	−	0.168860i
$302$	7.52172	−	3.07296i	0.432826	−	0.176829i
$303$	0.608257	+	1.04698i	0.0349435	+	0.0601473i
$304$	−27.9560	+	16.8715i	−1.60338	+	0.967647i
$305$	−9.84059	+	6.47226i	−0.563471	+	0.370600i
$306$	5.67186	−	14.9305i	0.324239	−	0.853521i
$307$	0.808201	−	13.8763i	0.0461264	−	0.791960i	−0.893353	−	0.449355i	$-0.851654\pi$
$307$	0.808201	−	13.8763i	0.0461264	−	0.791960i	0.939480	−	0.342605i	$-0.111309\pi$
$308$	−21.5921	+	34.2581i	−1.23032	+	1.95204i
$309$	−10.2513	−	1.57486i	−0.583174	−	0.0895906i
$310$	61.4153	−	43.8970i	3.48815	−	2.49318i
$311$	−2.68794	−	0.208923i	−0.152419	−	0.0118470i	0.00105605	−	0.999999i	$-0.499664\pi$
$311$	−2.68794	−	0.208923i	−0.152419	−	0.0118470i	−0.153475	+	0.988152i	$0.549047\pi$
$312$	−33.4727	+	26.0886i	−1.89502	+	1.47698i
$313$	−11.9006	−	4.86193i	−0.672661	−	0.274812i	0.0160253	−	0.999872i	$-0.494899\pi$
$313$	−11.9006	−	4.86193i	−0.672661	−	0.274812i	−0.688686	+	0.725059i	$0.741812\pi$
$314$	14.8977	+	49.7617i	0.840725	+	2.80822i
$315$	22.8610	−	28.6593i	1.28807	−	1.61477i
$316$	−11.1294	+	2.63772i	−0.626078	+	0.148383i
$317$	8.91302	+	23.0853i	0.500605	+	1.29660i	0.921107	+	0.389309i	$0.127286\pi$
$317$	8.91302	+	23.0853i	0.500605	+	1.29660i	−0.420502	+	0.907292i	$0.638146\pi$
$318$	−0.927993	−	15.2231i	−0.0520393	−	0.853672i
$319$	3.95180	−	7.50232i	0.221259	−	0.420049i
$320$	1.27238	−	65.6034i	0.0711280	−	3.66734i
$321$	26.9139	−	4.28392i	1.50219	−	0.239105i
$322$	−36.6955	+	35.9907i	−2.04496	+	2.00568i
$323$	2.61719	+	4.53310i	0.145624	+	0.252228i
$324$	4.00417	−	46.3710i	0.222454	−	2.57616i
$325$	−10.6520	+	18.4498i	−0.590866	+	1.02341i
$326$	15.5729	+	60.4575i	0.862501	+	3.34843i
$327$	−8.63551	+	9.94943i	−0.477545	+	0.550205i
$328$	13.5927	−	7.50014i	0.750532	−	0.414126i
$329$	−20.6409	−	32.7490i	−1.13797	−	1.80551i
$330$	14.6708	+	33.7593i	0.807603	+	1.85839i
$331$	−2.68057	+	3.32339i	−0.147338	+	0.182670i	−0.846656	−	0.532140i	$-0.821388\pi$
$331$	−2.68057	+	3.32339i	−0.147338	+	0.182670i	0.699319	+	0.714810i	$0.253487\pi$
$332$	23.6647	−	79.0457i	1.29877	−	4.33820i
$333$	1.73769	−	0.144531i	0.0952250	−	0.00792024i
$334$	37.0871	−	39.3100i	2.02931	−	2.15095i
$335$	19.3876	−	15.0265i	1.05926	−	0.820988i
$336$	−55.3708	−	49.9737i	−3.02072	−	2.72629i
$337$	−4.76025	−	9.95522i	−0.259307	−	0.542295i	0.730803	−	0.682589i	$-0.239146\pi$
$337$	−4.76025	−	9.95522i	−0.259307	−	0.542295i	−0.990110	+	0.140294i	$0.955195\pi$
$338$	1.21264	+	12.4670i	0.0659587	+	0.678115i
$339$	−9.96461	+	29.3820i	−0.541203	+	1.59581i
$340$	−36.1537	−	1.40293i	−1.96071	−	0.0760844i
$341$	15.0916	+	9.92588i	0.817254	+	0.537517i
$342$	15.1817	+	14.7297i	0.820930	+	0.796490i
$343$	6.02689	+	3.02682i	0.325422	+	0.163433i
$344$	0.178514	+	9.20411i	0.00962481	+	0.496253i
$345$	5.94025	+	33.1638i	0.319813	+	1.78548i
$346$	−13.8002	−	10.6960i	−0.741904	−	0.575019i
$347$	−20.3801	+	3.18739i	−1.09406	+	0.171108i	−0.675703	−	0.737174i	$-0.736160\pi$
$347$	−20.3801	+	3.18739i	−1.09406	+	0.171108i	−0.418358	+	0.908282i	$0.637394\pi$
$348$	26.6777	+	20.5614i	1.43007	+	1.10221i
$349$	13.2299	−	27.6680i	0.708182	−	1.48104i	−0.161214	−	0.986919i	$-0.551541\pi$
$349$	13.2299	−	27.6680i	0.708182	−	1.48104i	0.869396	−	0.494117i	$-0.164508\pi$
$350$	−64.5289	−	23.4866i	−3.44922	−	1.25541i
$351$	11.9224	+	9.08661i	0.636373	+	0.485007i
$352$	34.3796	−	12.5131i	1.83244	−	0.666953i
$353$	1.56304	−	16.0694i	0.0831921	−	0.855289i	−0.857152	−	0.515064i	$-0.827768\pi$
$353$	1.56304	−	16.0694i	0.0831921	−	0.855289i	0.940344	−	0.340225i	$-0.110503\pi$
$354$	−42.8089	+	30.7734i	−2.27527	+	1.63559i
$355$	13.3724	+	39.0823i	0.709732	+	2.07427i
$356$	32.9289	−	29.8814i	1.74523	−	1.58371i
$357$	−8.18168	+	8.71923i	−0.433021	+	0.461471i
$358$	1.51063	−	4.41499i	0.0798393	−	0.233339i
$359$	−5.07277	−	11.7600i	−0.267730	−	0.620669i	0.730318	−	0.683107i	$-0.239372\pi$
$359$	−5.07277	−	11.7600i	−0.267730	−	0.620669i	−0.998049	+	0.0624379i	$0.980112\pi$
$360$	−87.1369	+	21.1506i	−4.59252	+	1.11474i
$361$	11.9859	−	1.40095i	0.630838	−	0.0737344i
$362$	−29.6514	+	9.50734i	−1.55844	+	0.499695i
$363$	7.29469	−	7.19342i	0.382872	−	0.377557i
$364$	49.9085	−	13.8930i	2.61591	−	0.728189i
$365$	−19.4940	+	5.42653i	−1.02036	+	0.284038i
$366$	11.0536	−	10.9002i	0.577782	−	0.569760i
$367$	30.2454	−	9.69781i	1.57880	−	0.506221i	0.618640	−	0.785675i	$-0.287684\pi$
$367$	30.2454	−	9.69781i	1.57880	−	0.506221i	0.960159	+	0.279454i	$0.0901533\pi$
$368$	68.0838	−	7.95786i	3.54911	−	0.414832i
$369$	−3.78467	−	3.96826i	−0.197022	−	0.206579i
$370$	−2.16959	−	5.02968i	−0.112792	−	0.261481i
$371$	−3.69629	+	10.8028i	−0.191902	+	0.560854i
$372$	−49.0964	+	52.3221i	−2.54553	+	2.71277i
$373$	−19.7351	+	17.9087i	−1.02185	+	0.927277i	−0.997374	−	0.0724237i	$-0.976927\pi$
$373$	−19.7351	+	17.9087i	−1.02185	+	0.927277i	−0.0244731	+	0.999700i	$0.507791\pi$
$374$	−3.88655	−	11.3589i	−0.200969	−	0.587353i
$375$	−11.8024	+	8.48420i	−0.609473	+	0.438122i
$376$	−9.16633	+	94.2381i	−0.472717	+	4.85996i
$377$	−10.1938	+	3.71023i	−0.525006	+	0.191087i
$378$	−22.1710	+	42.9325i	−1.14036	+	2.20821i
$379$	−16.8995	−	6.15091i	−0.868068	−	0.315951i	−0.130684	−	0.991424i	$-0.541717\pi$
$379$	−16.8995	−	6.15091i	−0.868068	−	0.315951i	−0.737385	+	0.675473i	$0.763939\pi$
$380$	20.6713	−	43.2305i	1.06042	−	2.21768i
$381$	−1.95021	−	1.50310i	−0.0999123	−	0.0770059i
$382$	−8.18057	+	1.27942i	−0.418555	+	0.0654607i
$383$	−12.3584	−	9.57846i	−0.631483	−	0.489436i	0.245856	−	0.969306i	$-0.420931\pi$
$383$	−12.3584	−	9.57846i	−0.631483	−	0.489436i	−0.877340	+	0.479870i	$0.840684\pi$
$384$	5.33887	+	29.8063i	0.272448	+	1.52105i
$385$	−0.534359	−	27.5514i	−0.0272335	−	1.40415i
$386$	21.9649	+	11.0312i	1.11799	+	0.561474i
$387$	3.12786	−	0.888969i	0.158998	−	0.0451888i
$388$	17.3445	+	11.4077i	0.880534	+	0.579136i
$389$	29.9502	+	1.16220i	1.51854	+	0.0589261i	0.784476	−	0.620159i	$-0.212932\pi$
$389$	29.9502	+	1.16220i	1.51854	+	0.0589261i	0.734060	+	0.679085i	$0.237623\pi$
$390$	15.1243	−	44.5962i	0.765850	−	2.25821i
$391$	−1.06381	−	10.9369i	−0.0537991	−	0.553103i
$392$	18.5308	+	38.7540i	0.935949	+	1.95737i
$393$	−8.82109	−	7.96129i	−0.444965	−	0.401594i
$394$	−8.48385	+	6.57548i	−0.427410	+	0.331268i
$395$	5.34123	−	5.66138i	0.268747	−	0.284855i
$396$	−19.9439	−	28.7441i	−1.00222	−	1.44445i
$397$	−5.23059	+	17.4714i	−0.262516	+	0.876864i	0.720518	+	0.693437i	$0.243904\pi$
$397$	−5.23059	+	17.4714i	−0.262516	+	0.876864i	−0.983033	+	0.183427i	$0.941281\pi$
$398$	27.7494	−	34.4038i	1.39095	−	1.72451i
$399$	−6.31154	−	14.5236i	−0.315972	−	0.727089i
$400$	48.8310	+	77.4756i	2.44155	+	3.87378i
$401$	2.07598	−	1.14548i	0.103670	−	0.0572024i	−0.430430	−	0.902624i	$-0.641638\pi$
$401$	2.07598	−	1.14548i	0.103670	−	0.0572024i	0.534100	+	0.845421i	$0.320651\pi$
$402$	−21.1917	+	24.4160i	−1.05694	+	1.21776i
$403$	−5.76425	−	22.3782i	−0.287138	−	1.11474i
$404$	−1.80765	+	3.13094i	−0.0899338	+	0.155770i
$405$	15.0633	+	27.8613i	0.748503	+	1.38444i
$406$	−17.4835	−	30.2822i	−0.867690	−	1.50288i
$407$	0.935738	−	0.917765i	0.0463828	−	0.0454919i
$408$	28.8814	−	4.59708i	1.42984	−	0.227589i
$409$	−0.117638	+	6.06536i	−0.00581680	+	0.299913i	0.985594	+	0.169128i	$0.0540952\pi$
$409$	−0.117638	+	6.06536i	−0.00581680	+	0.299913i	−0.991411	+	0.130784i	$0.958250\pi$
$410$	−8.02832	+	15.2414i	−0.396490	+	0.752719i
$411$	1.09525	+	17.9669i	0.0540247	+	0.886241i
$412$	−11.1536	−	28.8886i	−0.549499	−	1.42324i
$413$	38.4054	−	9.10225i	1.88981	−	0.447892i
$414$	−16.2182	−	41.3388i	−0.797080	−	2.03169i
$415$	16.1037	+	53.7902i	0.790501	+	2.64046i
$416$	−43.3288	−	17.7018i	−2.12437	−	0.867900i
$417$	−17.2133	+	13.4160i	−0.842937	+	0.656985i
$418$	15.8523	+	1.23214i	0.775360	+	0.0602657i
$419$	−24.5351	+	17.5366i	−1.19862	+	0.856720i	−0.992552	−	0.121819i	$-0.961127\pi$
$419$	−24.5351	+	17.5366i	−1.19862	+	0.856720i	−0.206064	+	0.978538i	$0.566066\pi$
$420$	108.190	+	16.6208i	5.27913	+	0.811011i
$421$	−8.52740	+	13.5296i	−0.415600	+	0.659395i	−0.986897	−	0.161349i	$-0.948416\pi$
$421$	−8.52740	+	13.5296i	−0.415600	+	0.659395i	0.571297	+	0.820743i	$0.306440\pi$
$422$	3.89301	−	66.8403i	0.189509	−	3.25374i
$423$	33.0142	−	5.34655i	1.60521	−	0.259958i
$424$	23.3321	−	15.3458i	1.13311	−	0.745257i
$425$	12.5692	−	7.58557i	0.609698	−	0.367954i
$426$	−27.3491	−	47.0754i	−1.32507	−	2.28081i
$427$	−10.7586	+	4.39536i	−0.520643	+	0.212706i
$428$	51.0853	+	63.3359i	2.46930	+	3.06145i
$429$	11.2582	−	0.467386i	0.543549	−	0.0225656i
$430$	−5.77770	−	8.42410i	−0.278626	−	0.406246i
$431$	1.91990	+	10.8883i	0.0924782	+	0.524470i	0.995491	+	0.0948563i	$0.0302392\pi$
$431$	1.91990	+	10.8883i	0.0924782	+	0.524470i	−0.903013	+	0.429614i	$0.858650\pi$
$432$	58.4451	−	27.1413i	2.81194	−	1.30583i
$433$	5.97542	−	33.8883i	0.287160	−	1.62857i	−0.410306	−	0.911948i	$-0.634578\pi$
$433$	5.97542	−	33.8883i	0.287160	−	1.62857i	0.697466	−	0.716618i	$-0.254311\pi$
$434$	67.8106	−	30.8237i	3.25501	−	1.47958i
$435$	−22.8562	−	1.71430i	−1.09587	−	0.0821945i
$436$	−38.5982	−	7.58044i	−1.84852	−	0.363037i
$437$	13.8584	+	4.44351i	0.662937	+	0.212562i
$438$	23.8012	−	12.0342i	1.13726	−	0.575015i
$439$	−13.2555	−	15.1891i	−0.632650	−	0.724937i	0.344192	−	0.938899i	$-0.388153\pi$
$439$	−13.2555	−	15.1891i	−0.632650	−	0.724937i	−0.976842	+	0.213963i	$0.931363\pi$
$440$	−40.2487	+	54.0634i	−1.91878	+	2.57737i
$441$	11.5705	−	9.81599i	0.550975	−	0.467428i
$442$	−6.08329	+	14.1027i	−0.289353	+	0.670795i
$443$	11.7676	+	10.6785i	0.559094	+	0.507351i	0.901836	−	0.432079i	$-0.142220\pi$
$443$	11.7676	+	10.6785i	0.559094	+	0.507351i	−0.342742	+	0.939430i	$0.611356\pi$
$444$	2.95631	+	4.28549i	0.140300	+	0.203380i
$445$	−7.54779	+	29.3023i	−0.357799	+	1.38906i
$446$	−19.4635	−	19.0897i	−0.921625	−	0.903924i
$447$	−0.171686	−	0.122013i	−0.00812049	−	0.00577103i
$448$	13.7066	−	63.2765i	0.647574	−	2.98953i
$449$	9.07259	+	12.1866i	0.428162	+	0.575122i	0.962887	−	0.269905i	$-0.0869922\pi$
$449$	9.07259	+	12.1866i	0.428162	+	0.575122i	−0.534725	+	0.845026i	$0.679585\pi$
$450$	40.4788	−	43.3730i	1.90819	−	2.04462i
$451$	−4.09407	−	0.478528i	−0.192782	−	0.0225330i
$452$	−90.8993	+	17.8520i	−4.27554	+	0.839689i
$453$	2.06842	−	4.83104i	0.0971828	−	0.226982i
$454$	4.56131	+	21.0574i	0.214073	+	0.988271i
$455$	−23.1801	+	26.5615i	−1.08670	+	1.24522i
$456$	−9.55992	+	37.5341i	−0.447684	+	1.75770i
$457$	23.9805	+	17.1402i	1.12176	+	0.801786i	0.982090	−	0.188412i	$-0.0603341\pi$
$457$	23.9805	+	17.1402i	1.12176	+	0.801786i	0.139670	+	0.990198i	$0.455396\pi$
$458$	26.8953	+	22.5679i	1.25674	+	1.05453i
$459$	−4.16840	−	9.45169i	−0.194564	−	0.441167i
$460$	−77.0604	+	64.6614i	−3.59296	+	3.01485i
$461$	−28.8210	+	2.24014i	−1.34233	+	0.104334i	−0.728467	−	0.685081i	$-0.759767\pi$
$461$	−28.8210	+	2.24014i	−1.34233	+	0.104334i	−0.613860	+	0.789415i	$0.710384\pi$
$462$	7.78518	+	35.4761i	0.362200	+	1.65050i
$463$	3.84725	−	9.96462i	0.178797	−	0.463095i	−0.814293	−	0.580454i	$-0.802875\pi$
$463$	3.84725	−	9.96462i	0.178797	−	0.463095i	0.993090	+	0.117359i	$0.0374429\pi$
$464$	−6.31087	+	46.2037i	−0.292975	+	2.14495i
$465$	8.34830	−	48.1065i	0.387143	−	2.23089i
$466$	−30.3932	−	16.7702i	−1.40794	−	0.776867i
$467$	0.270504	+	4.64438i	0.0125174	+	0.214916i	0.998767	+	0.0496511i	$0.0158109\pi$
$467$	0.270504	+	4.64438i	0.0125174	+	0.214916i	−0.986249	+	0.165265i	$0.947152\pi$
$468$	−5.81700	+	44.3781i	−0.268891	+	2.05138i
$469$	21.6288	−	10.8624i	0.998725	−	0.501579i
$470$	−48.9637	−	92.9554i	−2.25853	−	4.28771i
$471$	29.4593	+	16.1511i	1.35741	+	0.744203i
$472$	−87.8841	−	39.9482i	−4.04520	−	1.83877i
$473$	1.38248	−	2.01570i	0.0635664	−	0.0926821i
$474$	−5.44642	+	8.69341i	−0.250163	+	0.399302i
$475$	2.63131	+	19.2646i	0.120733	+	0.883921i
$476$	−34.7379	−	8.23304i	−1.59221	−	0.377361i
$477$	−7.34071	−	6.58924i	−0.336108	−	0.301700i
$478$	−26.3944	−	27.9765i	−1.20725	−	1.27961i
$479$	−9.57753	−	1.49790i	−0.437609	−	0.0684407i	−0.0681224	−	0.997677i	$-0.521701\pi$
$479$	−9.57753	−	1.49790i	−0.437609	−	0.0684407i	−0.369486	+	0.929236i	$0.620466\pi$
$480$	−68.0592	−	71.7485i	−3.10646	−	3.27486i
$481$	−1.67553	+	0.0650182i	−0.0763976	+	0.00296458i
$482$	−1.30366	−	0.786760i	−0.0593799	−	0.0358359i
$483$	−0.554688	+	33.2393i	−0.0252392	+	1.51244i
$484$	29.4684	+	8.20310i	1.33947	+	0.372868i
$485$	−14.1269			−0.641469
$486$	−26.6455	−	32.1355i	−1.20867	−	1.45770i
$487$	30.6732			1.38994			0.694969	−	0.719040i	$-0.255418\pi$
$487$	30.6732			1.38994			0.694969	+	0.719040i	$0.255418\pi$
$488$	27.3844	+	7.62296i	1.23963	+	0.345075i
$489$	34.6275	+	20.7702i	1.56591	+	0.939260i
$490$	−40.8098	−	24.6288i	−1.84360	−	1.11262i
$491$	35.0800	−	1.36126i	1.58314	−	0.0614330i	0.767905	−	0.640564i	$-0.221299\pi$
$491$	35.0800	−	1.36126i	1.58314	−	0.0614330i	0.815235	+	0.579131i	$0.196608\pi$
$492$	4.65337	−	15.6978i	0.209790	−	0.707713i
$493$	7.38571	+	1.15510i	0.332635	+	0.0520232i
$494$	−13.9591	−	14.7958i	−0.628048	−	0.665692i
$495$	22.0876	+	8.88456i	0.992762	+	0.399331i
$496$	−96.6605	−	22.9089i	−4.34018	−	1.02864i
$497$	5.51582	+	40.3830i	0.247418	+	1.81142i
$498$	−34.6671	−	65.3840i	−1.55347	−	2.92993i
$499$	−15.2857	+	22.2871i	−0.684283	+	0.997709i	0.314542	+	0.949244i	$0.398149\pi$
$499$	−15.2857	+	22.2871i	−0.684283	+	0.997709i	−0.998825	+	0.0484651i	$0.984567\pi$
$500$	−39.5092	−	17.9591i	−1.76690	−	0.803156i
$501$	−0.772391	−	34.9458i	−0.0345079	−	1.56126i
$502$	18.8493	+	35.7844i	0.841284	+	1.59714i
$503$	−15.9307	+	8.00071i	−0.710316	+	0.356734i	−0.766990	−	0.641659i	$-0.778247\pi$
$503$	−15.9307	+	8.00071i	−0.710316	+	0.356734i	0.0566747	+	0.998393i	$0.481950\pi$
$504$	−88.3895	+	3.90917i	−3.93718	+	0.174128i
$505$	−0.143047	−	2.45603i	−0.00636553	−	0.109292i
$506$	−29.2253	−	16.1258i	−1.29922	−	0.716881i
$507$	6.22013	+	5.19069i	0.276246	+	0.230526i
$508$	0.994911	−	7.28404i	0.0441421	−	0.323177i
$509$	12.4098	−	32.1422i	0.550055	−	1.42468i	−0.327339	−	0.944907i	$-0.606152\pi$
$509$	12.4098	−	32.1422i	0.550055	−	1.42468i	0.877394	−	0.479771i	$-0.159280\pi$
$510$	−23.9723	+	21.8723i	−1.06151	+	0.968521i
$511$	−19.9063	+	1.54724i	−0.880605	+	0.0684460i
$512$	7.23991	−	6.07501i	0.319962	−	0.268480i
$513$	13.6808	−	0.111079i	0.604022	−	0.00490427i
$514$	40.1323	+	33.6750i	1.77016	+	1.48534i
$515$	17.1439	+	12.2537i	0.755450	+	0.539963i
$516$	6.94986	+	6.77957i	0.305951	+	0.298454i
$517$	16.5296	−	18.9408i	0.726969	−	0.833014i
$518$	−1.14424	−	5.28239i	−0.0502749	−	0.232095i
$519$	−11.2128	+	1.34136i	−0.492186	+	0.0588790i
$520$	84.6105	−	16.6170i	3.71042	−	0.728702i
$521$	1.59725	+	0.186692i	0.0699768	+	0.00817912i	0.151009	−	0.988532i	$-0.451748\pi$
$521$	1.59725	+	0.186692i	0.0699768	+	0.00817912i	−0.0810325	+	0.996711i	$0.525822\pi$
$522$	29.9859	−	3.66948i	1.31245	−	0.160609i
$523$	25.3488	+	34.0494i	1.10843	+	1.48888i	0.852900	+	0.522074i	$0.174842\pi$
$523$	25.3488	+	34.0494i	1.10843	+	1.48888i	0.255527	+	0.966802i	$0.417751\pi$
$524$	7.51091	−	34.6742i	0.328116	−	1.51475i
$525$	−40.3834	+	18.4885i	−1.76247	+	0.806905i
$526$	−17.7334	−	17.3927i	−0.773211	−	0.758360i
$527$	−3.97222	+	15.4211i	−0.173032	+	0.671753i
$528$	20.7770	−	43.7552i	0.904201	−	1.90420i
$529$	−5.59247	−	5.07490i	−0.243151	−	0.220648i
$530$	−12.2737	+	28.4535i	−0.533133	+	1.23594i
$531$	−5.73945	+	33.6129i	−0.249071	+	1.45868i
$532$	28.2348	−	37.9259i	1.22413	−	1.64429i
$533$	3.46730	+	3.97309i	0.150185	+	0.172093i
$534$	2.21116	−	39.8205i	0.0956863	−	1.72320i
$535$	−52.7280	−	16.9066i	−2.27963	−	0.730935i
$536$	−58.0887	−	11.4083i	−2.50905	−	0.492762i
$537$	−1.30931	−	2.71925i	−0.0565008	−	0.117344i
$538$	−14.3339	+	6.51555i	−0.617978	+	0.280905i
$539$	1.98052	−	11.2321i	0.0853070	−	0.483800i
$540$	−49.7724	+	80.4093i	−2.14186	+	3.46027i
$541$	2.24013	+	12.7044i	0.0963107	+	0.546205i	0.994338	+	0.106265i	$0.0338892\pi$
$541$	2.24013	+	12.7044i	0.0963107	+	0.546205i	−0.898027	+	0.439940i	$0.855000\pi$
$542$	−27.4319	−	39.9967i	−1.17830	−	1.71801i
$543$	−9.33767	+	17.8441i	−0.400718	+	0.765763i
$544$	20.2495	+	25.1055i	0.868192	+	1.07639i
$545$	24.7794	−	10.1235i	1.06143	−	0.433644i
$546$	23.1237	−	40.3029i	0.989603	−	1.72481i
$547$	5.98649	−	3.61286i	0.255964	−	0.154475i	−0.382912	−	0.923785i	$-0.625079\pi$
$547$	5.98649	−	3.61286i	0.255964	−	0.154475i	0.638876	+	0.769310i	$0.279400\pi$
$548$	−44.9029	+	29.5331i	−1.91816	+	1.26159i
$549$	0.140361	−	10.0396i	0.00599046	−	0.428481i
$550$	2.59296	−	44.5194i	0.110564	−	1.89832i
$551$	−5.27906	+	8.37580i	−0.224896	+	0.356821i
$552$	50.8766	−	63.4276i	2.16545	−	2.69966i
$553$	6.24800	−	4.46581i	0.265692	−	0.189905i
$554$	−18.8113	−	1.46213i	−0.799215	−	0.0621199i
$555$	−3.28330	−	1.33102i	−0.139368	−	0.0564986i
$556$	−60.3214	−	24.6440i	−2.55820	−	1.04514i
$557$	−9.55467	−	31.9148i	−0.404844	−	1.35227i	−0.881084	−	0.472959i	$-0.843186\pi$
$557$	−9.55467	−	31.9148i	−0.404844	−	1.35227i	0.476240	−	0.879315i	$-0.341999\pi$
$558$	1.59614	+	64.3335i	0.0675700	+	2.72345i
$559$	−3.04268	+	0.721129i	−0.128692	+	0.0305005i
$560$	54.5838	+	141.376i	2.30659	+	5.97421i
$561$	−6.94830	−	3.46605i	−0.293357	−	0.146337i
$562$	−33.5666	+	63.7246i	−1.41592	+	2.68806i
$563$	−0.796122	+	41.0478i	−0.0335525	+	1.72996i	0.484656	+	0.874705i	$0.338945\pi$
$563$	−0.796122	+	41.0478i	−0.0335525	+	1.72996i	−0.518208	+	0.855255i	$0.673401\pi$
$564$	62.9016	+	77.5552i	2.64863	+	3.26566i
$565$	45.0048	−	44.1404i	1.89337	−	1.85700i
$566$	15.9524	+	27.6304i	0.670530	+	1.16139i
$567$	9.28671	+	29.8402i	0.390005	+	1.25317i
$568$	49.8447	−	86.3335i	2.09144	−	3.62247i
$569$	−7.25036	−	28.1476i	−0.303951	−	1.18001i	−0.919877	−	0.392206i	$-0.871712\pi$
$569$	−7.25036	−	28.1476i	−0.303951	−	1.18001i	0.615927	−	0.787803i	$-0.288782\pi$
$570$	−14.0236	−	40.6263i	−0.587385	−	1.70165i
$571$	17.1842	−	9.48182i	0.719135	−	0.396802i	−0.0809266	−	0.996720i	$-0.525788\pi$
$571$	17.1842	−	9.48182i	0.719135	−	0.396802i	0.800061	+	0.599918i	$0.204800\pi$
$572$	17.9387	+	28.4617i	0.750055	+	1.19004i
$573$	−3.18635	+	4.30428i	−0.133112	+	0.179814i
$574$	−10.6714	+	13.2304i	−0.445414	+	0.552226i
$575$	11.7067	−	39.1029i	0.488201	−	1.63071i
$576$	45.6818	+	32.2792i	1.90341	+	1.34497i
$577$	−1.52241	+	1.61366i	−0.0633786	+	0.0671774i	−0.758287	−	0.651921i	$-0.773963\pi$
$577$	−1.52241	+	1.61366i	−0.0633786	+	0.0671774i	0.694908	+	0.719098i	$0.255445\pi$
$578$	−27.6175	+	21.4052i	−1.14874	+	0.890338i
$579$	15.1251	−	4.89485i	0.628577	−	0.203423i
$580$	−29.5219	−	61.7397i	−1.22583	−	2.56360i
$581$	5.36363	+	55.1429i	0.222521	+	2.28771i
$582$	18.2608	−	3.63766i	0.756935	−	0.150786i
$583$	−7.40913	−	0.287508i	−0.306855	−	0.0119074i
$584$	40.8015	+	26.8356i	1.68838	+	1.11046i
$585$	−13.2875	−	27.4062i	−0.549369	−	1.13311i
$586$	33.9200	+	17.0352i	1.40122	+	0.703719i
$587$	0.00727026	+	0.374853i	0.000300076	+	0.0154718i	0.999932	−	0.0116548i	$-0.00370994\pi$
$587$	0.00727026	+	0.374853i	0.000300076	+	0.0154718i	−0.999632	+	0.0271267i	$0.991364\pi$
$588$	42.6136	+	15.3796i	1.75735	+	0.634244i
$589$	−16.6698	−	12.9201i	−0.686868	−	0.532363i
$590$	105.834	−	16.5521i	4.35712	−	0.681441i
$591$	−0.920896	+	6.88099i	−0.0378806	+	0.283046i
$592$	−3.10947	+	6.50291i	−0.127798	+	0.267268i
$593$	−2.72790	−	0.992874i	−0.112021	−	0.0407724i	0.285401	−	0.958408i	$-0.407873\pi$
$593$	−2.72790	−	0.992874i	−0.112021	−	0.0407724i	−0.397423	+	0.917636i	$0.630095\pi$
$594$	−30.8387	−	5.79690i	−1.26533	−	0.237850i
$595$	22.8287	−	8.30898i	0.935887	−	0.340635i
$596$	0.0608826	−	0.625927i	0.00249385	−	0.0256390i
$597$	−2.84460	−	28.4458i	−0.116422	−	1.16421i
$598$	13.8243	+	40.4030i	0.565317	+	1.65220i
$599$	−5.40057	+	4.90076i	−0.220661	+	0.200240i	−0.774838	−	0.632159i	$-0.782169\pi$
$599$	−5.40057	+	4.90076i	−0.220661	+	0.200240i	0.554177	+	0.832399i	$0.313033\pi$
$600$	105.772	+	24.7663i	4.31812	+	1.01108i
$601$	−5.11858	+	14.9596i	−0.208791	+	0.610215i	−0.999999	−	0.00133218i	$-0.999576\pi$
$601$	−5.11858	+	14.9596i	−0.208791	+	0.610215i	0.791208	+	0.611547i	$0.209452\pi$
$602$	−3.99222	−	9.25501i	−0.162711	−	0.377206i
$603$	1.32880	+	20.8681i	0.0541130	+	0.849814i
$604$	15.5848	−	1.82160i	0.634136	−	0.0741198i
$605$	−19.8216	+	6.35554i	−0.805863	+	0.258390i
$606$	0.817332	+	3.13790i	0.0332018	+	0.127468i
$607$	42.1352	−	11.7291i	1.71021	−	0.476071i	0.731593	−	0.681741i	$-0.238777\pi$
$607$	42.1352	−	11.7291i	1.71021	−	0.476071i	0.978621	+	0.205670i	$0.0659375\pi$
$608$	−41.1531	+	11.4557i	−1.66898	+	0.464592i
$609$	−21.8038	−	6.00597i	−0.883534	−	0.243374i
$610$	−30.0356	+	9.63052i	−1.21611	+	0.389928i
$611$	−31.9437	+	3.73368i	−1.29230	+	0.151049i
$612$	18.2841	−	24.8393i	0.739089	−	1.00407i
$613$	−6.48640	−	15.0372i	−0.261983	−	0.607346i	0.735555	−	0.677465i	$-0.236921\pi$
$613$	−6.48640	−	15.0372i	−0.261983	−	0.607346i	−0.997539	+	0.0701190i	$0.977662\pi$
$614$	12.0504	−	35.2186i	0.486314	−	1.42131i
$615$	3.22437	+	10.6650i	0.130019	+	0.430054i
$616$	−49.2498	+	44.6918i	−1.98433	+	1.80068i
$617$	2.28849	+	6.68838i	0.0921313	+	0.269264i	0.982586	−	0.185808i	$-0.0594902\pi$
$617$	2.28849	+	6.68838i	0.0921313	+	0.269264i	−0.890455	+	0.455072i	$0.849614\pi$
$618$	−25.3160	−	11.4250i	−1.01836	−	0.459579i
$619$	0.587886	−	6.04400i	0.0236291	−	0.242929i	−0.976049	−	0.217552i	$-0.930193\pi$
$619$	0.587886	−	6.04400i	0.0236291	−	0.242929i	0.999678	−	0.0253771i	$-0.00807866\pi$
$620$	136.990	−	49.8603i	5.50165	−	2.00244i
$621$	−26.2422	−	11.6724i	−1.05306	−	0.468398i
$622$	−6.78452	−	2.46936i	−0.272034	−	0.0990124i
$623$	−12.8798	+	26.9358i	−0.516019	+	1.07916i
$624$	−57.3010	+	23.5912i	−2.29388	+	0.944404i
$625$	−7.30143	+	1.14192i	−0.292057	+	0.0456769i
$626$	−27.2104	−	21.0897i	−1.08755	−	0.842912i
$627$	7.85995	−	6.63161i	0.313896	−	0.264841i
$628$	1.94515	+	100.292i	0.0776201	+	4.00207i
$629$	1.03259	+	0.518587i	0.0411721	+	0.0206774i
$630$	79.5604	−	57.5196i	3.16976	−	2.29163i
$631$	−22.1240	−	14.5512i	−0.880743	−	0.579274i	0.0266090	−	0.999646i	$-0.491529\pi$
$631$	−22.1240	−	14.5512i	−0.880743	−	0.579274i	−0.907352	+	0.420372i	$0.861899\pi$
$632$	−18.7701	−	0.728364i	−0.746633	−	0.0289728i
$633$	−28.5616	−	32.5497i	−1.13522	−	1.29374i
$634$	6.41560	+	65.9582i	0.254796	+	2.61953i
$635$	2.15813	+	4.51334i	0.0856427	+	0.179107i
$636$	6.15727	−	28.8016i	0.244152	−	1.14206i
$637$	−11.5327	+	8.93854i	−0.456944	+	0.354158i
$638$	15.5830	−	16.5170i	0.616937	−	0.653915i
$639$	−33.9735	−	9.25934i	−1.34397	−	0.366294i
$640$	17.6454	−	58.9397i	0.697495	−	2.32980i
$641$	−18.0665	+	22.3989i	−0.713584	+	0.884705i	−0.997242	−	0.0742202i	$-0.976353\pi$
$641$	−18.0665	+	22.3989i	−0.713584	+	0.884705i	0.283658	+	0.958926i	$0.408452\pi$
$642$	72.5111	+	8.27647i	2.86179	+	0.326646i
$643$	−18.0533	−	28.6435i	−0.711952	−	1.12959i	−0.985818	−	0.167821i	$-0.946327\pi$
$643$	−18.0533	−	28.6435i	−0.711952	−	1.12959i	0.273865	−	0.961768i	$-0.411698\pi$
$644$	−86.9068	+	47.9532i	−3.42461	+	1.88962i
$645$	−6.48645	−	1.25568i	−0.255404	−	0.0494422i
$646$	3.49653	+	13.5744i	0.137569	+	0.534077i
$647$	7.77654	−	13.4694i	0.305727	−	0.529535i	−0.671696	−	0.740827i	$-0.734434\pi$
$647$	7.77654	−	13.4694i	0.305727	−	0.529535i	0.977423	+	0.211292i	$0.0677671\pi$
$648$	26.7579	−	71.6022i	1.05115	−	2.81280i
$649$	12.8158	+	22.1976i	0.503064	+	0.871333i
$650$	−40.7306	+	39.9483i	−1.59759	+	1.56690i
$651$	17.2305	−	44.9902i	0.675318	−	1.76330i
$652$	−2.33786	+	120.540i	−0.0915578	+	4.72070i
$653$	−4.79220	+	9.09776i	−0.187533	+	0.356023i	−0.960436	−	0.278502i	$-0.910162\pi$
$653$	−4.79220	+	9.09776i	−0.187533	+	0.356023i	0.772903	+	0.634525i	$0.218804\pi$
$654$	−29.4238	+	19.4666i	−1.15056	+	0.761205i
$655$	8.69573	+	22.5225i	0.339770	+	0.880027i
$656$	22.0575	−	5.22772i	0.861200	−	0.204108i
$657$	5.49596	−	16.3510i	0.214418	−	0.637912i
$658$	−29.7320	−	99.3117i	−1.15907	−	3.87157i
$659$	−12.4153	−	5.07221i	−0.483631	−	0.197585i	0.123253	−	0.992375i	$-0.460667\pi$
$659$	−12.4153	−	5.07221i	−0.483631	−	0.197585i	−0.606884	+	0.794790i	$0.707581\pi$
$660$	9.81041	+	70.4033i	0.381870	+	2.74045i
$661$	15.2379	+	1.18438i	0.592685	+	0.0460671i	0.370333	−	0.928899i	$-0.379244\pi$
$661$	15.2379	+	1.18438i	0.592685	+	0.0460671i	0.222352	+	0.974966i	$0.428626\pi$
$662$	−9.30225	+	6.64885i	−0.361542	+	0.258415i
$663$	3.60297	+	9.25728i	0.139928	+	0.359523i
$664$	72.2545	−	114.639i	2.80402	−	4.44888i
$665$	−1.87081	+	32.1206i	−0.0725470	+	1.24558i
$666$	4.58682	+	0.875065i	0.177736	+	0.0339081i
$667$	17.3651	−	11.4212i	0.672380	−	0.442231i
$668$	89.3543	−	53.9256i	3.45722	−	2.08644i
$669$	−17.6328	+	0.0477213i	−0.681722	+	0.00184501i
$670$	60.8091	−	24.8432i	2.34926	−	0.959778i
$671$	−4.73826	−	5.87452i	−0.182918	−	0.226783i
$672$	−52.2531	−	82.4099i	−2.01571	−	3.17903i
$673$	11.5361	+	16.8201i	0.444685	+	0.648366i	0.980626	−	0.195889i	$-0.0627593\pi$
$673$	11.5361	+	16.8201i	0.444685	+	0.648366i	−0.535941	+	0.844255i	$0.680043\pi$
$674$	−5.13144	−	29.1018i	−0.197656	−	1.12096i
$675$	−1.05554	−	38.3572i	−0.0406278	−	1.47637i
$676$	−4.20038	+	23.8215i	−0.161553	+	0.916212i
$677$	13.4120	−	6.09652i	0.515466	−	0.234308i	−0.139147	−	0.990272i	$-0.544436\pi$
$677$	13.4120	−	6.09652i	0.515466	−	0.234308i	0.654614	+	0.755963i	$0.272831\pi$
$678$	−46.8084	+	68.6458i	−1.79766	+	2.63633i
$679$	−13.6779	−	2.68626i	−0.524911	−	0.103089i
$680$	−56.5826	−	18.1425i	−2.16984	−	0.695732i
$681$	11.6635	+	7.62604i	0.446945	+	0.292230i
$682$	31.8060	+	36.4456i	1.21792	+	1.39558i
$683$	23.8037	−	31.9739i	0.910822	−	1.22345i	−0.0634310	−	0.997986i	$-0.520204\pi$
$683$	23.8037	−	31.9739i	0.910822	−	1.22345i	0.974253	−	0.225459i	$-0.0723883\pi$
$684$	20.6157	+	35.2653i	0.788261	+	1.34840i
$685$	14.4858	−	33.5818i	0.553474	−	1.28310i
$686$	13.3749	+	12.1371i	0.510656	+	0.463395i
$687$	22.6349	−	1.82096i	0.863574	−	0.0694741i
$688$	−3.35300	+	13.0171i	−0.127832	+	0.496274i
$689$	6.77220	+	6.64213i	0.258000	+	0.253045i
$690$	−8.49168	+	89.8244i	−0.323273	+	3.41956i
$691$	−0.264884	+	1.22284i	−0.0100766	+	0.0465190i	−0.982095	−	0.188384i	$-0.939675\pi$
$691$	−0.264884	+	1.22284i	−0.0100766	+	0.0465190i	0.972019	+	0.234903i	$0.0754774\pi$
$692$	−20.1347	−	27.0455i	−0.765405	−	1.02812i
$693$	19.6962	+	12.8022i	0.748196	+	0.486315i
$694$	−54.8671	−	6.41305i	−2.08273	−	0.243436i
$695$	43.5108	−	8.54524i	1.65046	−	0.324139i
$696$	33.1523	+	44.2806i	1.25663	+	1.67845i
$697$	−0.769309	−	3.55152i	−0.0291396	−	0.134524i
$698$	54.0015	−	61.8789i	2.04399	−	2.34215i
$699$	−21.6128	+	6.07941i	−0.817472	+	0.229944i
$700$	−107.886	−	77.1124i	−4.07771	−	2.91457i
$701$	−2.95564	−	2.48008i	−0.111633	−	0.0936713i	0.585262	−	0.810844i	$-0.300991\pi$
$701$	−2.95564	−	2.48008i	−0.111633	−	0.0936713i	−0.696896	+	0.717173i	$0.745436\pi$
$702$	24.2328	+	32.0045i	0.914608	+	1.20793i
$703$	−1.17232	+	0.983695i	−0.0442149	+	0.0371007i
$704$	41.9187	−	3.25818i	1.57987	−	0.122797i
$705$	−64.7633	−	20.5724i	−2.43913	−	0.774801i
$706$	15.5728	−	40.3346i	0.586091	−	1.51801i
$707$	0.328518	−	2.40518i	0.0123552	−	0.0904559i
$708$	−95.5783	+	35.0809i	−3.59205	+	1.31842i
$709$	7.26991	+	4.01136i	0.273027	+	0.150650i	0.613718	−	0.789525i	$-0.289673\pi$
$709$	7.26991	+	4.01136i	0.273027	+	0.150650i	−0.340691	+	0.940175i	$0.610661\pi$
$710$	6.43186	+	110.431i	0.241383	+	4.14439i
$711$	1.43974	+	6.47695i	0.0539946	+	0.242905i
$712$	65.2588	−	32.7742i	2.44568	−	1.22826i
$713$	20.6343	+	39.1732i	0.772760	+	1.46705i
$714$	−27.3695	+	16.6188i	−1.02428	+	0.621943i
$715$	−20.8419	−	9.47380i	−0.779442	−	0.354300i
$716$	5.09679	−	7.43130i	0.190476	−	0.277721i
$717$	−24.8604	−	0.897321i	−0.928429	−	0.0335111i
$718$	−4.64158	−	33.9824i	−0.173222	−	1.26821i
$719$	16.2321	+	3.84707i	0.605354	+	0.143472i	0.521852	−	0.853036i	$-0.325241\pi$
$719$	16.2321	+	3.84707i	0.605354	+	0.143472i	0.0835020	+	0.996508i	$0.473390\pi$
$720$	−130.856	−	4.36858i	−4.87671	−	0.162807i
$721$	14.2690	+	15.1242i	0.531404	+	0.563256i
$722$	31.9283	+	4.99350i	1.18825	+	0.185839i
$723$	−0.957662	+	0.229709i	−0.0356158	+	0.00854298i
$724$	−60.0870	+	2.33165i	−2.23311	+	0.0866550i
$725$	23.7743	+	14.3478i	0.882954	+	0.532866i
$726$	23.9854	−	13.3194i	0.890182	−	0.494329i
$727$	−51.5142	−	14.3400i	−1.91056	−	0.531840i	−0.989965	−	0.141315i	$-0.954867\pi$
$727$	−51.5142	−	14.3400i	−1.91056	−	0.531840i	−0.920592	−	0.390525i	$-0.872294\pi$
$728$	85.0813			3.15332
$729$	−26.8648	−	2.69864i	−0.994992	−	0.0999498i
$730$	−54.1892			−2.00563
$731$	2.07591	+	0.577868i	0.0767802	+	0.0213732i
$732$	26.2090	−	14.5542i	0.968713	−	0.537939i
$733$	20.3675	+	12.2919i	0.752292	+	0.454010i	0.840308	−	0.542109i	$-0.182374\pi$
$733$	20.3675	+	12.2919i	0.752292	+	0.454010i	−0.0880168	+	0.996119i	$0.528053\pi$
$734$	84.9940	−	3.29815i	3.13718	−	0.121737i
$735$	−29.9788	+	7.19085i	−1.10578	+	0.265239i
$736$	88.6005	+	13.8569i	3.26586	+	0.510771i
$737$	10.7862	+	11.4327i	0.397313	+	0.421128i
$738$	−6.91413	−	12.9556i	−0.254513	−	0.476902i
$739$	−12.6011	−	2.98652i	−0.463540	−	0.109861i	−0.00779154	−	0.999970i	$-0.502480\pi$
$739$	−12.6011	−	2.98652i	−0.463540	−	0.109861i	−0.455748	+	0.890109i	$0.650628\pi$
$740$	−1.43155	−	10.4808i	−0.0526247	−	0.385281i
$741$	−13.1478	−	0.474561i	−0.482996	−	0.0174334i
$742$	−17.2941	+	25.2154i	−0.634886	+	0.925686i
$743$	2.51318	+	1.14238i	0.0921997	+	0.0419099i	0.459380	−	0.888240i	$-0.348072\pi$
$743$	2.51318	+	1.14238i	0.0921997	+	0.0419099i	−0.367180	+	0.930150i	$0.619677\pi$
$744$	−100.721	+	61.1582i	−3.69263	+	2.24217i
$745$	0.199444	+	0.378635i	0.00730705	+	0.0138721i
$746$	−63.7754	+	32.0292i	−2.33499	+	1.17267i
$747$	−45.6582	−	14.3676i	−1.67055	−	0.525684i
$748$	−1.34803	−	23.1447i	−0.0492887	−	0.846255i
$749$	−47.8375	−	26.3956i	−1.74794	−	0.964474i
$750$	−36.5417	+	13.4122i	−1.33431	+	0.489744i
$751$	2.87073	−	21.0175i	0.104755	−	0.766939i	−0.861207	−	0.508254i	$-0.830291\pi$
$751$	2.87073	−	21.0175i	0.104755	−	0.766939i	0.965962	−	0.258685i	$-0.0832891\pi$
$752$	−49.7955	+	128.974i	−1.81585	+	4.70318i
$753$	24.9315	+	7.91962i	0.908555	+	0.288607i
$754$	−28.9632	+	2.25120i	−1.05478	+	0.0819838i
$755$	−8.17949	+	6.86341i	−0.297682	+	0.249785i
$756$	−63.4806	+	68.3895i	−2.30877	+	2.48730i
$757$	33.2104	+	27.8669i	1.20705	+	1.01284i	0.999400	+	0.0346355i	$0.0110270\pi$
$757$	33.2104	+	27.8669i	1.20705	+	1.01284i	0.207653	+	0.978202i	$0.433417\pi$
$758$	−39.1812	−	28.0051i	−1.42313	−	1.01719i
$759$	−20.7823	+	5.84580i	−0.754350	+	0.212189i
$760$	51.7447	−	59.2929i	1.87698	−	2.15078i
$761$	−7.89806	−	36.4615i	−0.286304	−	1.32173i	−0.863180	−	0.504896i	$-0.831531\pi$
$761$	−7.89806	−	36.4615i	−0.286304	−	1.32173i	0.576876	−	0.816832i	$-0.304272\pi$
$762$	−3.95184	−	5.27836i	−0.143160	−	0.191215i
$763$	25.9169	−	5.08992i	0.938256	−	0.184268i
$764$	−15.8817	−	1.85630i	−0.574579	−	0.0671586i
$765$	−1.10695	+	20.9594i	−0.0400218	+	0.757789i
$766$	−25.0042	−	33.5865i	−0.903439	−	1.21353i
$767$	6.94201	−	32.0479i	0.250661	−	1.15718i
$768$	−1.55311	+	16.4287i	−0.0560431	+	0.592820i
$769$	32.7917	+	32.1619i	1.18250	+	1.15979i	0.983713	+	0.179745i	$0.0575273\pi$
$769$	32.7917	+	32.1619i	1.18250	+	1.15979i	0.198787	+	0.980043i	$0.436300\pi$
$770$	18.4077	−	71.4629i	0.663366	−	2.57534i
$771$	33.7750	−	2.71718i	1.21638	−	0.0978568i
$772$	35.1507	+	31.8975i	1.26510	+	1.14802i
$773$	7.22941	−	16.7596i	0.260024	−	0.602803i	−0.737328	−	0.675535i	$-0.763913\pi$
$773$	7.22941	−	16.7596i	0.260024	−	0.602803i	0.997351	+	0.0727325i	$0.0231719\pi$
$774$	8.70790	−	0.0471345i	0.312999	−	0.00169421i
$775$	−35.3235	+	47.4477i	−1.26886	+	1.70437i
$776$	22.4174	+	25.6875i	0.804737	+	0.922126i
$777$	−2.92586	−	1.91305i	−0.104965	−	0.0686301i
$778$	76.4332	+	24.5073i	2.74026	+	0.878629i
$779$	4.72256	+	0.927480i	0.169203	+	0.0332304i
$780$	51.2325	−	75.1340i	1.83442	−	2.69023i
$781$	−24.0959	+	10.9529i	−0.862219	+	0.391927i
$782$	5.10993	−	28.9798i	0.182731	−	1.03632i
$783$	12.1429	−	15.3075i	0.433952	−	0.547046i
$784$	10.8918	+	61.7707i	0.388994	+	2.20609i
$785$	−38.6088	−	56.2930i	−1.37801	−	2.00918i
$786$	−17.0399	−	26.8741i	−0.607791	−	0.958566i
$787$	16.6408	+	20.6314i	0.593181	+	0.735428i	0.982621	−	0.185623i	$-0.0594304\pi$
$787$	16.6408	+	20.6314i	0.593181	+	0.735428i	−0.389440	+	0.921052i	$0.627332\pi$
$788$	−19.1886	+	7.83940i	−0.683565	+	0.279267i
$789$	−16.0653	+	0.0434792i	−0.571940	+	0.00154790i
$790$	17.8455	−	10.7698i	0.634913	−	0.383172i
$791$	51.9679	−	34.1798i	1.84777	−	1.21530i
$792$	−18.8947	−	54.2612i	−0.671394	−	1.92809i
$793$	−0.561411	+	9.63905i	−0.0199363	+	0.342293i
$794$	−26.0415	+	41.3176i	−0.924177	+	1.46631i
$795$	7.26935	+	18.6775i	0.257817	+	0.662422i
$796$	69.4417	−	49.6340i	2.46130	−	1.75923i
$797$	−6.13685	−	0.476994i	−0.217378	−	0.0168960i	−0.0316586	−	0.999499i	$-0.510079\pi$
$797$	−6.13685	−	0.476994i	−0.217378	−	0.0168960i	−0.185720	+	0.982603i	$0.559462\pi$
$798$	−5.85276	−	42.0017i	−0.207186	−	1.48685i
$799$	20.5165	+	8.38191i	0.725822	+	0.296531i
$800$	34.3620	+	114.777i	1.21488	+	4.05799i
$801$	−17.0655	−	19.3426i	−0.602981	−	0.683437i
$802$	6.17840	−	1.46431i	0.218167	−	0.0517065i
$803$	−4.67017	−	12.0960i	−0.164807	−	0.426860i
$804$	−52.0693	+	34.4488i	−1.83634	+	1.21491i
$805$	31.4790	−	59.7614i	1.10949	−	2.10631i
$806$	1.20002	−	61.8726i	0.0422688	−	2.17937i
$807$	−3.64221	+	9.51009i	−0.128212	+	0.334771i
$808$	−4.23889	+	4.15748i	−0.149124	+	0.146260i
$809$	−7.95582	−	13.7799i	−0.279712	−	0.484475i	0.691601	−	0.722279i	$-0.256906\pi$
$809$	−7.95582	−	13.7799i	−0.279712	−	0.484475i	−0.971313	+	0.237805i	$0.923572\pi$
$810$	18.8527	+	82.6965i	0.662416	+	2.90566i
$811$	−21.1444	+	36.6232i	−0.742481	+	1.28602i	0.208881	+	0.977941i	$0.433018\pi$
$811$	−21.1444	+	36.6232i	−0.742481	+	1.28602i	−0.951362	+	0.308074i	$0.900315\pi$
$812$	−16.8437	−	65.3912i	−0.591098	−	2.29478i
$813$	−30.7970	−	5.96182i	−1.08010	−	0.209090i
$814$	3.07319	−	1.69571i	0.107715	−	0.0594347i
$815$	−43.7452	−	69.4065i	−1.53233	−	2.43120i
$816$	42.4270	+	4.84265i	1.48524	+	0.169527i
$817$	−1.79171	+	2.22137i	−0.0626839	+	0.0777159i
$818$	−4.65937	+	15.5634i	−0.162911	+	0.544161i
$819$	−7.65383	−	29.0618i	−0.267446	−	1.01550i
$820$	−22.8290	+	24.1973i	−0.797223	+	0.845007i
$821$	16.5945	−	12.8617i	0.579153	−	0.448878i	−0.280429	−	0.959875i	$-0.590477\pi$
$821$	16.5945	−	12.8617i	0.579153	−	0.448878i	0.859582	+	0.510997i	$0.170724\pi$
$822$	−10.0774	+	47.1389i	−0.351491	+	1.64416i
$823$	−3.30738	−	6.91680i	−0.115288	−	0.241104i	0.836433	−	0.548070i	$-0.184637\pi$
$823$	−3.30738	−	6.91680i	−0.115288	−	0.241104i	−0.951721	+	0.306965i	$0.900686\pi$
$824$	−4.92353	−	50.6183i	−0.171519	−	1.76337i
$825$	−19.0236	−	21.6800i	−0.662318	−	0.754799i
$826$	105.618	+	4.09846i	3.67492	+	0.142604i
$827$	−22.8657	−	15.0390i	−0.795118	−	0.522957i	0.0857515	−	0.996317i	$-0.472671\pi$
$827$	−22.8657	−	15.0390i	−0.795118	−	0.522957i	−0.880869	+	0.473359i	$0.843041\pi$
$828$	−8.76383	−	85.3055i	−0.304564	−	2.96457i
$829$	−30.3093	−	15.2219i	−1.05269	−	0.528679i	−0.163651	−	0.986518i	$-0.552327\pi$
$829$	−30.3093	−	15.2219i	−1.05269	−	0.528679i	−0.889035	+	0.457840i	$0.848623\pi$
$830$	2.91578	+	150.337i	0.101208	+	5.21828i
$831$	−9.32710	+	7.86948i	−0.323554	+	0.272989i
$832$	−42.5147	−	32.9514i	−1.47393	−	1.14238i
$833$	9.93418	−	1.55368i	0.344199	−	0.0538317i
$834$	−54.0428	+	22.2498i	−1.87135	+	0.770447i
$835$	−30.6371	+	64.0721i	−1.06024	+	2.21731i
$836$	28.8534	+	10.5018i	0.997915	+	0.363211i
$837$	29.9510	+	28.9024i	1.03526	+	0.999014i
$838$	−75.8915	+	27.6222i	−2.62163	+	0.954194i
$839$	1.72537	−	17.7383i	0.0595663	−	0.612395i	−0.917249	−	0.398313i	$-0.869596\pi$
$839$	1.72537	−	17.7383i	0.0595663	−	0.612395i	0.976816	−	0.214082i	$-0.0686759\pi$
$840$	163.852	+	73.9457i	5.65345	+	2.55137i
$841$	−4.81081	−	14.0601i	−0.165890	−	0.484832i
$842$	−31.7160	+	28.7808i	−1.09301	+	0.991851i
$843$	13.4812	+	44.5906i	0.464316	+	1.53578i
$844$	41.8576	−	122.333i	1.44080	−	4.21089i
$845$	−6.51967	−	15.1143i	−0.224284	−	0.519948i
$846$	89.0122	+	9.91595i	3.06030	+	0.340917i
$847$	−20.4002	+	2.38444i	−0.700958	+	0.0819303i
$848$	38.8299	−	12.4503i	1.33342	−	0.427545i
$849$	19.8944	+	5.48002i	0.682775	+	0.188074i
$850$	37.8747	−	10.5431i	1.29909	−	0.361627i
$851$	3.09500	−	0.861553i	0.106095	−	0.0295336i
$852$	−26.5010	−	101.742i	−0.907908	−	3.48564i
$853$	−30.9435	+	9.92164i	−1.05949	+	0.339710i	−0.783462	−	0.621440i	$-0.786548\pi$
$853$	−30.9435	+	9.92164i	−1.05949	+	0.339710i	−0.276024	+	0.961151i	$0.589017\pi$
$854$	−30.9123	+	3.61313i	−1.05780	+	0.123639i
$855$	−24.9080	−	12.3409i	−0.851836	−	0.422050i
$856$	52.9301	+	122.706i	1.80911	+	4.19399i
$857$	−2.78618	+	8.14291i	−0.0951740	+	0.278156i	−0.983457	−	0.181139i	$-0.942022\pi$
$857$	−2.78618	+	8.14291i	−0.0951740	+	0.278156i	0.888283	+	0.459296i	$0.151898\pi$
$858$	29.3803	+	6.87933i	1.00303	+	0.234856i
$859$	33.4315	−	30.3374i	1.14067	−	1.03510i	0.141688	−	0.989911i	$-0.454747\pi$
$859$	33.4315	−	30.3374i	1.14067	−	1.03510i	0.998978	−	0.0451883i	$-0.0143888\pi$
$860$	−6.38617	−	18.6643i	−0.217767	−	0.636447i
$861$	1.09392	+	10.9392i	0.0372808	+	0.372806i
$862$	−2.86640	+	29.4692i	−0.0976300	+	1.00372i
$863$	4.00961	−	1.45938i	0.136489	−	0.0496779i	−0.272873	−	0.962050i	$-0.587974\pi$
$863$	4.00961	−	1.45938i	0.136489	−	0.0496779i	0.409361	+	0.912372i	$0.365752\pi$
$864$	83.1827	−	13.7023i	2.82993	−	0.466163i
$865$	21.5608	+	7.84750i	0.733090	+	0.266823i
$866$	39.7529	−	83.1362i	1.35086	−	2.82508i
$867$	−2.99780	+	22.3997i	−0.101811	+	0.760734i
$868$	142.117	−	22.2267i	4.82377	−	0.754425i
$869$	3.94199	+	3.05527i	0.133723	+	0.103643i
$870$	−57.7349	−	20.8370i	−1.95740	−	0.706440i
$871$	−0.389922	−	20.1043i	−0.0132120	−	0.681208i
$872$	−57.7294	−	28.9928i	−1.95497	−	0.981820i
$873$	6.75761	−	9.96809i	0.228711	−	0.337369i
$874$	32.5618	+	21.4162i	1.10142	+	0.724414i
$875$	29.1188	+	1.12994i	0.984395	+	0.0381990i
$876$	50.5118	−	10.0622i	1.70664	−	0.339972i
$877$	−0.0808266	−	0.830970i	−0.00272932	−	0.0280599i	0.993839	−	0.110831i	$-0.0353513\pi$
$877$	−0.0808266	−	0.830970i	−0.00272932	−	0.0280599i	−0.996569	+	0.0827713i	$0.973623\pi$
$878$	−23.2893	−	48.7055i	−0.785977	−	1.64373i
$879$	23.3573	−	7.55900i	0.787823	−	0.254959i
$880$	−77.7869	+	60.2894i	−2.62220	+	2.03236i
$881$	−0.508425	+	0.538899i	−0.0171293	+	0.0181560i	−0.735882	−	0.677110i	$-0.763232\pi$
$881$	−0.508425	+	0.538899i	−0.0171293	+	0.0181560i	0.718752	+	0.695266i	$0.244714\pi$
$882$	36.8998	−	17.0146i	1.24248	−	0.572911i
$883$	−8.16597	+	27.2763i	−0.274807	+	0.917919i	0.703489	+	0.710706i	$0.251624\pi$
$883$	−8.16597	+	27.2763i	−0.274807	+	0.917919i	−0.978296	+	0.207213i	$0.933561\pi$
$884$	−18.6208	+	23.0861i	−0.626284	+	0.776470i
$885$	41.2225	−	55.6855i	1.38568	−	1.87185i
$886$	22.6900	+	36.0001i	0.762286	+	1.20945i
$887$	24.2564	−	13.3841i	0.814452	−	0.449396i	−0.0204523	−	0.999791i	$-0.506511\pi$
$887$	24.2564	−	13.3841i	0.814452	−	0.449396i	0.834904	+	0.550395i	$0.185523\pi$
$888$	2.78989	+	8.08229i	0.0936227	+	0.271224i
$889$	1.23132	+	4.78028i	0.0412972	+	0.160325i
$890$	−40.5160	+	70.1758i	−1.35810	+	2.35230i
$891$	−16.8346	+	11.3353i	−0.563982	+	0.379746i
$892$	−26.3238	−	45.5941i	−0.881385	−	1.52660i
$893$	−20.9556	+	20.5531i	−0.701254	+	0.687785i
$894$	−0.355304	−	0.438077i	−0.0118832	−	0.0146515i
$895$	−0.118909	+	6.13091i	−0.00397469	+	0.204934i
$896$	28.2921	−	53.7112i	0.945173	−	1.79437i
$897$	24.7148	+	12.3286i	0.825203	+	0.411640i
$898$	14.6543	+	37.9555i	0.489019	+	1.26659i
$899$	−29.3087	+	6.94628i	−0.977499	+	0.231671i
$900$	97.7685	−	59.7279i	3.25895	−	1.99093i
$901$	−1.87477	−	6.26218i	−0.0624578	−	0.208623i
$902$	−10.2185	−	4.17472i	−0.340239	−	0.139003i
$903$	−6.04154	−	2.44918i	−0.201050	−	0.0815036i
$904$	−151.678	−	11.7894i	−5.04475	−	0.392109i
$905$	33.2903	−	23.7945i	1.10661	−	0.790955i
$906$	8.80571	−	10.9780i	0.292550	−	0.364721i
$907$	−21.5902	+	34.2551i	−0.716889	+	1.13742i	0.267862	+	0.963457i	$0.413683\pi$
$907$	−21.5902	+	34.2551i	−0.716889	+	1.13742i	−0.984752	+	0.173965i	$0.944342\pi$
$908$	−2.41927	+	41.5372i	−0.0802862	+	1.37846i
$909$	1.80143	+	1.07391i	0.0597496	+	0.0356193i
$910$	−78.8771	+	51.8783i	−2.61475	+	1.71975i
$911$	−25.1061	+	15.1516i	−0.831803	+	0.501996i	−0.867541	−	0.497366i	$-0.834301\pi$
$911$	−25.1061	+	15.1516i	−0.831803	+	0.501996i	0.0357381	+	0.999361i	$0.488622\pi$
$912$	−28.1452	+	49.0550i	−0.931981	+	1.62437i
$913$	−33.3068	+	13.6073i	−1.10229	+	0.450336i
$914$	49.5573	+	61.4414i	1.63921	+	2.03230i
$915$	−9.45865	+	18.0753i	−0.312693	+	0.597550i
$916$	38.3486	+	55.9136i	1.26707	+	1.84744i
$917$	4.13667	+	23.4602i	0.136605	+	0.774725i
$918$	−3.96615	−	27.3777i	−0.130903	−	0.903600i
$919$	−4.23880	+	24.0395i	−0.139825	+	0.792988i	0.831552	+	0.555447i	$0.187453\pi$
$919$	−4.23880	+	24.0395i	−0.139825	+	0.792988i	−0.971377	+	0.237542i	$0.923658\pi$
$920$	−150.399	+	68.3648i	−4.95851	+	2.25392i
$921$	−10.4444	−	21.6916i	−0.344155	−	0.714763i
$922$	−75.9633	−	14.9187i	−2.50172	−	0.491321i
$923$	32.2448	+	10.3389i	1.06135	+	0.340308i
$924$	−3.88871	+	70.0313i	−0.127929	+	2.30386i
$925$	2.82221	+	3.23389i	0.0927935	+	0.106330i
$926$	17.0816	−	22.9445i	0.561336	−	0.754004i
$927$	−16.8472	+	6.23534i	−0.553333	+	0.204795i
$928$	−24.1639	+	56.0181i	−0.793218	+	1.83889i
$929$	7.48434	+	6.79168i	0.245553	+	0.222828i	0.785484	−	0.618881i	$-0.212414\pi$
$929$	7.48434	+	6.79168i	0.245553	+	0.222828i	−0.539931	+	0.841709i	$0.681550\pi$
$930$	56.0856	−	118.113i	1.83912	−	3.87309i
$931$	−3.32178	+	12.8960i	−0.108867	+	0.422648i
$932$	−47.8584	−	46.9392i	−1.56765	−	1.53754i
$933$	−4.24587	+	1.94387i	−0.139004	+	0.0636394i
$934$	−2.63753	+	12.1762i	−0.0863025	+	0.398417i
$935$	9.42111	+	12.6548i	0.308103	+	0.413855i
$936$	−28.7484	+	67.6508i	−0.939671	+	2.21124i
$937$	47.0811	+	5.50299i	1.53807	+	0.179775i	0.842505	−	0.538688i	$-0.181080\pi$
$937$	47.0811	+	5.50299i	1.53807	+	0.179775i	0.695566	+	0.718463i	$0.255154\pi$
$938$	63.6005	−	12.4907i	2.07663	−	0.407837i
$939$	−22.1086	+	2.64480i	−0.721488	+	0.0863098i
$940$	−42.9525	−	198.291i	−1.40096	−	6.46754i
$941$	−5.49256	+	6.29378i	−0.179052	+	0.205171i	−0.835946	−	0.548812i	$-0.815080\pi$
$941$	−5.49256	+	6.29378i	−0.179052	+	0.205171i	0.656893	+	0.753984i	$0.271870\pi$
$942$	64.4022	+	62.8241i	2.09834	+	2.04692i
$943$	−8.21969	−	5.87508i	−0.267670	−	0.191319i
$944$	−107.982	−	90.6077i	−3.51452	−	2.94903i
$945$	10.5182	−	62.6204i	0.342156	−	2.03704i
$946$	5.01421	−	4.20742i	0.163026	−	0.136795i
$947$	16.3812	−	1.27325i	0.532317	−	0.0413749i	0.191478	−	0.981497i	$-0.438672\pi$
$947$	16.3812	−	1.27325i	0.532317	−	0.0413749i	0.340838	+	0.940122i	$0.389289\pi$
$948$	−14.6346	+	13.3526i	−0.475310	+	0.433672i
$949$	−5.97466	+	15.4748i	−0.193946	+	0.502332i
$950$	−7.04656	+	51.5900i	−0.228621	+	1.67380i
$951$	32.9084	+	27.4620i	1.06713	+	0.890516i
$952$	−51.3345	−	28.3252i	−1.66376	−	0.918024i
$953$	−1.46761	−	25.1980i	−0.0475407	−	0.816242i	−0.934845	−	0.355057i	$-0.884461\pi$
$953$	−1.46761	−	25.1980i	−0.0475407	−	0.816242i	0.887304	−	0.461185i	$-0.152576\pi$
$954$	−14.2060	−	22.2712i	−0.459936	−	0.721056i
$955$	9.72360	−	4.88338i	0.314648	−	0.158022i
$956$	−34.6157	−	65.7163i	−1.11955	−	2.12542i
$957$	−0.324538	−	14.6833i	−0.0104908	−	0.474644i
$958$	−23.6331	−	10.7426i	−0.763551	−	0.347076i
$959$	20.4111	−	29.7601i	0.659108	−	0.961003i
$960$	−53.2377	−	100.409i	−1.71824	−	3.24069i
$961$	−4.48807	−	32.8585i	−0.144776	−	1.05995i
$962$	−4.36935	−	1.03556i	−0.140874	−	0.0333877i
$963$	37.1520	−	29.1182i	1.19721	−	0.938321i
$964$	−2.01787	−	2.13882i	−0.0649912	−	0.0688866i
$965$	−31.9125	−	4.99102i	−1.02730	−	0.160667i
$966$	−25.3021	+	85.3550i	−0.814081	+	2.74625i
$967$	22.2472	−	0.863292i	0.715421	−	0.0277616i	0.321505	−	0.946908i	$-0.395811\pi$
$967$	22.2472	−	0.863292i	0.715421	−	0.0277616i	0.393916	+	0.919146i	$0.371120\pi$
$968$	43.0106	+	25.9570i	1.38241	+	0.834290i
$969$	7.77483	+	4.66348i	0.249764	+	0.149812i
$970$	−36.4456	−	10.1453i	−1.17020	−	0.325747i
$971$	−50.8291			−1.63118			−0.815592	−	0.578628i	$-0.803588\pi$
$971$	−50.8291			−1.63118			−0.815592	+	0.578628i	$0.803588\pi$
$972$	−32.9290	−	73.5838i	−1.05620	−	2.36020i
$973$	43.7529			1.40265
$974$	79.1331	+	22.0282i	2.53559	+	0.705829i
$975$	−0.615683	+	36.8944i	−0.0197176	+	1.18157i
$976$	35.5361	+	21.4461i	1.13748	+	0.686474i
$977$	49.5580	−	1.92307i	1.58550	−	0.0615246i	0.769145	−	0.639075i	$-0.220683\pi$
$977$	49.5580	−	1.92307i	1.58550	−	0.0615246i	0.816355	+	0.577550i	$0.195991\pi$
$978$	74.4184	+	78.4524i	2.37964	+	2.50863i
$979$	−19.1563	−	2.99599i	−0.612239	−	0.0957524i
$980$	−63.1676	−	66.9538i	−2.01782	−	2.13876i
$981$	−4.71001	+	22.3272i	−0.150379	+	0.712854i
$982$	91.4797	+	21.6811i	2.91923	+	0.691871i
$983$	0.924373	+	6.76761i	0.0294829	+	0.215853i	0.999646	−	0.0265994i	$-0.00846786\pi$
$983$	0.924373	+	6.76761i	0.0294829	+	0.215853i	−0.970163	+	0.242453i	$0.922048\pi$
$984$	14.2760	−	22.7868i	0.455101	−	0.726418i
$985$	7.97814	−	11.6324i	0.254205	−	0.370639i
$986$	18.2246	+	8.28412i	0.580391	+	0.263820i
$987$	−58.7932	−	32.2334i	−1.87141	−	1.02600i
$988$	−18.3070	−	34.7550i	−0.582424	−	1.10570i
$989$	5.35391	−	2.68884i	0.170245	−	0.0855000i
$990$	50.6026	+	38.7834i	1.60826	+	1.23262i
$991$	0.164266	+	2.82033i	0.00521807	+	0.0895907i	0.999912	−	0.0132909i	$-0.00423075\pi$
$991$	0.164266	+	2.82033i	0.00521807	+	0.0895907i	−0.994694	+	0.102882i	$0.967194\pi$
$992$	−113.787	−	62.7852i	−3.61275	−	1.99343i
$993$	−1.26447	+	7.28644i	−0.0401268	+	0.231228i
$994$	−14.7712	+	108.144i	−0.468514	+	3.43013i
$995$	−20.9207	+	54.1861i	−0.663232	+	1.71781i
$996$	−30.6336	−	139.593i	−0.970662	−	4.42319i
$997$	−35.0405	+	2.72356i	−1.10974	+	0.0862562i	−0.619254	−	0.785191i	$-0.712565\pi$
$997$	−35.0405	+	2.72356i	−1.10974	+	0.0862562i	−0.490490	+	0.871447i	$0.663182\pi$
$998$	−55.4409	+	46.5204i	−1.75495	+	1.47258i
$999$	2.50975	−	1.68004i	0.0794051	−	0.0531541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.103.26	✓	1404
3.2	odd	2		729.2.i.a.685.1		1404
243.92	odd	162		729.2.i.a.613.1		1404
243.151	even	81	inner	243.2.i.a.151.26	yes	1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.103.26	✓	1404	1.1	even	1	trivial
243.2.i.a.151.26	yes	1404	243.151	even	81	inner
729.2.i.a.613.1		1404	243.92	odd	162
729.2.i.a.685.1		1404	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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\), degree \(54\), minimal)

\(f(q)\)	\(=\)	\(q+(2.57987 + 0.718157i) q^{2} +(1.51424 - 0.840877i) q^{3} +(4.42767 + 2.67211i) q^{4} +(-3.51654 + 0.136458i) q^{5} +(4.51043 - 1.08189i) q^{6} +(-3.43073 - 0.536556i) q^{7} +(5.82837 + 6.17771i) q^{8} +(1.58585 - 2.54658i) q^{9} +O(q^{10})\)	\(q+(2.57987 + 0.718157i) q^{2} +(1.51424 - 0.840877i) q^{3} +(4.42767 + 2.67211i) q^{4} +(-3.51654 + 0.136458i) q^{5} +(4.51043 - 1.08189i) q^{6} +(-3.43073 - 0.536556i) q^{7} +(5.82837 + 6.17771i) q^{8} +(1.58585 - 2.54658i) q^{9} +(-9.17022 - 2.17338i) q^{10} +(-0.305175 - 2.23427i) q^{11} +(8.95148 + 0.323098i) q^{12} +(-1.63172 + 2.37910i) q^{13} +(-8.46551 - 3.84805i) q^{14} +(-5.21014 + 3.16360i) q^{15} +(5.77961 + 10.9723i) q^{16} +(1.77656 - 0.892221i) q^{17} +(5.92015 - 5.43097i) q^{18} +(0.153093 + 2.62850i) q^{19} +(-15.9347 - 8.79239i) q^{20} +(-5.64612 + 2.07234i) q^{21} +(0.817247 - 5.98331i) q^{22} +(1.99084 - 5.15640i) q^{23} +(14.0203 + 4.45360i) q^{24} +(7.36244 - 0.572254i) q^{25} +(-5.91820 + 4.96596i) q^{26} +(0.260003 - 5.18964i) q^{27} +(-13.7564 - 11.5430i) q^{28} +(3.05917 + 2.18657i) q^{29} +(-15.7135 + 4.42000i) q^{30} +(-5.26689 + 6.03518i) q^{31} +(3.43474 + 15.8565i) q^{32} +(-2.34086 - 3.12661i) q^{33} +(5.22405 - 1.02597i) q^{34} +(12.1375 + 1.41867i) q^{35} +(13.8264 - 7.03784i) q^{36} +(0.347087 + 0.466219i) q^{37} +(-1.49272 + 6.89116i) q^{38} +(-0.470282 + 4.97461i) q^{39} +(-21.3387 - 20.9288i) q^{40} +(0.455952 - 1.77012i) q^{41} +(-16.0546 + 1.29158i) q^{42} +(0.802684 + 0.728397i) q^{43} +(4.61902 - 10.7081i) q^{44} +(-5.22921 + 9.17155i) q^{45} +(8.83921 - 11.8731i) q^{46} +(7.33012 + 8.39939i) q^{47} +(17.9781 + 11.7548i) q^{48} +(4.81625 + 1.54427i) q^{49} +(19.4052 + 3.81105i) q^{50} +(1.93989 - 2.84491i) q^{51} +(-13.5819 + 6.17375i) q^{52} +(0.570971 - 3.23814i) q^{53} +(4.39775 - 13.2019i) q^{54} +(1.37804 + 7.81526i) q^{55} +(-16.6809 - 24.3213i) q^{56} +(2.44207 + 3.85146i) q^{57} +(6.32199 + 7.83804i) q^{58} +(-10.5222 + 4.29880i) q^{59} +(-31.5223 + 0.0853119i) q^{60} +(2.86548 - 1.72933i) q^{61} +(-17.9221 + 11.7876i) q^{62} +(-6.80701 + 7.88572i) q^{63} +(-1.08412 + 18.6136i) q^{64} +(5.41335 - 8.58886i) q^{65} +(-3.79371 - 9.74737i) q^{66} +(-5.67055 + 4.05307i) q^{67} +(10.2501 + 0.796703i) q^{68} +(-1.32129 - 9.48207i) q^{69} +(30.2944 + 12.3766i) q^{70} +(-3.36638 - 11.2445i) q^{71} +(24.9750 - 5.04547i) q^{72} +(5.59498 - 1.32604i) q^{73} +(0.560623 + 1.45205i) q^{74} +(10.6673 - 7.05744i) q^{75} +(-6.34581 + 12.0472i) q^{76} +(-0.151842 + 7.82892i) q^{77} +(-4.78582 + 12.4961i) q^{78} +(-1.57898 + 1.54866i) q^{79} +(-21.8215 - 37.7959i) q^{80} +(-3.97014 - 8.07700i) q^{81} +(2.44752 - 4.23923i) q^{82} +(-3.97987 - 15.4508i) q^{83} +(-30.5367 - 5.91142i) q^{84} +(-6.12558 + 3.37995i) q^{85} +(1.54772 + 2.45562i) q^{86} +(6.47096 + 0.738600i) q^{87} +(12.0240 - 14.9074i) q^{88} +(2.46600 - 8.23703i) q^{89} +(-20.0773 + 19.9060i) q^{90} +(6.87450 - 7.28654i) q^{91} +(22.5932 - 17.5111i) q^{92} +(-2.90049 + 13.5675i) q^{93} +(12.8787 + 26.9335i) q^{94} +(-0.897036 - 9.22234i) q^{95} +(18.5344 + 21.1224i) q^{96} +(4.01124 + 0.155654i) q^{97} +(11.3163 + 7.44284i) q^{98} +(-6.17372 - 2.76608i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9}+O(q^{10}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18} - 54 q^{19} - 54 q^{20} - 54 q^{21} - 54 q^{22} - 54 q^{23} - 54 q^{24} - 54 q^{25} - 54 q^{26} - 54 q^{27} - 54 q^{28} - 54 q^{29} - 54 q^{30} - 54 q^{31} - 54 q^{32} - 54 q^{33} - 54 q^{34} - 54 q^{35} - 54 q^{36} - 54 q^{37} - 54 q^{38} - 54 q^{39} - 54 q^{40} - 54 q^{41} - 54 q^{42} - 54 q^{43} - 54 q^{44} - 54 q^{45} - 54 q^{46} - 54 q^{47} - 54 q^{48} - 54 q^{49} - 54 q^{50} - 54 q^{51} - 54 q^{52} - 54 q^{53} - 54 q^{54} - 54 q^{55} - 54 q^{56} - 54 q^{57} - 54 q^{58} - 54 q^{59} - 54 q^{60} - 54 q^{61} - 54 q^{62} - 54 q^{63} - 54 q^{64} + 54 q^{66} - 54 q^{67} + 135 q^{68} + 54 q^{69} - 54 q^{70} + 54 q^{71} + 270 q^{72} - 54 q^{73} + 162 q^{74} + 81 q^{75} - 54 q^{76} + 162 q^{77} + 162 q^{78} - 54 q^{79} + 351 q^{80} + 54 q^{81} - 27 q^{82} + 54 q^{83} + 324 q^{84} - 54 q^{85} + 162 q^{86} + 162 q^{87} - 54 q^{88} + 81 q^{89} + 162 q^{90} - 54 q^{91} + 270 q^{92} + 54 q^{93} - 54 q^{94} + 54 q^{95} + 135 q^{96} - 54 q^{97} + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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