LMFDB - Embedded newform 418.2.u.b.251.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(5,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([36, 80]))

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

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

chi := DirichletCharacter("418.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.u (of order $45$, degree $24$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$11$ over $\Q(\zeta_{45})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label			251.6
Character	$\chi$	$=$	418.251
Dual form			418.2.u.b.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.615661 + 0.788011i) q^{2} +(-0.149553 - 0.144422i) q^{3} +(-0.241922 - 0.970296i) q^{4} +(-0.227007 - 0.141850i) q^{5} +(0.205880 - 0.0289345i) q^{6} +(-4.29887 + 1.91398i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-0.103190 - 2.95498i) q^{9} +O(q^{10})$	\(q+(-0.615661 + 0.788011i) q^{2} +(-0.149553 - 0.144422i) q^{3} +(-0.241922 - 0.970296i) q^{4} +(-0.227007 - 0.141850i) q^{5} +(0.205880 - 0.0289345i) q^{6} +(-4.29887 + 1.91398i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-0.103190 - 2.95498i) q^{9} +(0.251538 - 0.0915525i) q^{10} +(2.16343 - 2.51387i) q^{11} +(-0.103952 + 0.180049i) q^{12} +(4.86764 + 2.58817i) q^{13} +(1.13841 - 4.56592i) q^{14} +(0.0134634 + 0.0539988i) q^{15} +(-0.882948 + 0.469472i) q^{16} +(0.215789 - 6.17939i) q^{17} +(2.39208 + 1.73795i) q^{18} +(0.374857 - 4.34275i) q^{19} +(-0.0827182 + 0.254580i) q^{20} +(0.919329 + 0.334608i) q^{21} +(0.649018 + 3.25250i) q^{22} +(-1.00149 - 0.840349i) q^{23} +(-0.0778819 - 0.192764i) q^{24} +(-2.16044 - 4.42957i) q^{25} +(-5.03632 + 2.24232i) q^{26} +(-0.828673 + 0.920335i) q^{27} +(2.89712 + 3.70814i) q^{28} +(4.26673 + 1.22346i) q^{29} +(-0.0508405 - 0.0226356i) q^{30} +(-6.66050 - 7.39723i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-0.686606 + 0.0635110i) q^{33} +(4.73657 + 3.97446i) q^{34} +(1.24737 + 0.175306i) q^{35} +(-2.84224 + 0.814998i) q^{36} +(-0.869982 - 0.632079i) q^{37} +(3.19135 + 2.96906i) q^{38} +(-0.354182 - 1.09006i) q^{39} +(-0.149686 - 0.221918i) q^{40} +(3.21188 + 3.10168i) q^{41} +(-0.829670 + 0.518436i) q^{42} +(5.77707 - 4.84754i) q^{43} +(-2.96258 - 1.49101i) q^{44} +(-0.395737 + 0.685437i) q^{45} +(1.27878 - 0.271814i) q^{46} +(-6.14322 + 9.10769i) q^{47} +(0.199849 + 0.0573059i) q^{48} +(10.1330 - 11.2539i) q^{49} +(4.82065 + 1.02466i) q^{50} +(-0.924710 + 0.892982i) q^{51} +(1.33370 - 5.34919i) q^{52} +(-2.15937 + 1.34933i) q^{53} +(-0.215052 - 1.21962i) q^{54} +(-0.847706 + 0.263785i) q^{55} -4.70570 q^{56} +(-0.683248 + 0.595334i) q^{57} +(-3.59096 + 2.60899i) q^{58} +(4.88616 + 7.24403i) q^{59} +(0.0491377 - 0.0261270i) q^{60} +(2.09577 - 5.18722i) q^{61} +(9.92971 - 0.694353i) q^{62} +(6.09936 + 12.5055i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-0.737857 - 1.27801i) q^{65} +(0.372669 - 0.580154i) q^{66} +(3.64234 - 1.32570i) q^{67} +(-6.04804 + 1.28555i) q^{68} +(0.0284111 + 0.270313i) q^{69} +(-0.906101 + 0.875012i) q^{70} +(-3.57839 - 2.23603i) q^{71} +(1.10763 - 2.74148i) q^{72} +(-4.97321 + 10.1966i) q^{73} +(1.03370 - 0.296408i) q^{74} +(-0.316625 + 0.974471i) q^{75} +(-4.30444 + 0.686885i) q^{76} +(-4.48881 + 14.9476i) q^{77} +(1.07704 + 0.392009i) q^{78} +(-6.41707 - 0.901861i) q^{79} +(0.267030 + 0.0186725i) q^{80} +(-8.59187 + 0.600802i) q^{81} +(-4.42159 + 0.621414i) q^{82} +(-0.0872925 - 0.0185546i) q^{83} +(0.102263 - 0.972970i) q^{84} +(-0.925530 + 1.37215i) q^{85} +(0.263192 + 7.53684i) q^{86} +(-0.461407 - 0.799181i) q^{87} +(2.99888 - 1.41659i) q^{88} +(0.840705 - 4.76787i) q^{89} +(-0.296492 - 0.733842i) q^{90} +(-25.8791 - 1.80964i) q^{91} +(-0.573105 + 1.17504i) q^{92} +(-0.0722231 + 2.06820i) q^{93} +(-3.39482 - 10.4482i) q^{94} +(-0.701113 + 0.932661i) q^{95} +(-0.168197 + 0.122202i) q^{96} +(4.47115 - 5.72281i) q^{97} +(2.62966 + 14.9135i) q^{98} +(-7.65168 - 6.13348i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.615661	+	0.788011i	−0.435338	+	0.557208i
$2$	−0.615661	+	0.788011i	−0.435338	+	0.557208i
$3$	−0.149553	−	0.144422i	−0.0863445	−	0.0833819i	0.650234	−	0.759734i	$-0.274671\pi$
$3$	−0.149553	−	0.144422i	−0.0863445	−	0.0833819i	−0.736578	+	0.676352i	$0.763560\pi$
$4$	−0.241922	−	0.970296i	−0.120961	−	0.485148i
$5$	−0.227007	−	0.141850i	−0.101521	−	0.0634371i	0.478209	−	0.878246i	$-0.341286\pi$
$5$	−0.227007	−	0.141850i	−0.101521	−	0.0634371i	−0.579729	+	0.814809i	$0.696842\pi$
$6$	0.205880	−	0.0289345i	0.0840501	−	0.0118125i
$7$	−4.29887	+	1.91398i	−1.62482	+	0.723416i	−0.998426	−	0.0560904i	$-0.982136\pi$
$7$	−4.29887	+	1.91398i	−1.62482	+	0.723416i	−0.626394	+	0.779507i	$0.715470\pi$
$8$	0.913545	+	0.406737i	0.322987	+	0.143803i
$9$	−0.103190	−	2.95498i	−0.0343967	−	0.984992i
$10$	0.251538	−	0.0915525i	0.0795434	−	0.0289514i
$11$	2.16343	−	2.51387i	0.652299	−	0.757962i
$11$	2.16343	−	2.51387i	0.652299	−	0.757962i
$12$	−0.103952	+	0.180049i	−0.0300082	+	0.0519758i
$13$	4.86764	+	2.58817i	1.35004	+	0.717829i	0.977648	−	0.210246i	$-0.0674266\pi$
$13$	4.86764	+	2.58817i	1.35004	+	0.717829i	0.372392	+	0.928076i	$0.378538\pi$
$14$	1.13841	−	4.56592i	0.304253	−	1.22029i
$15$	0.0134634	+	0.0539988i	0.00347624	+	0.0139424i
$16$	−0.882948	+	0.469472i	−0.220737	+	0.117368i
$17$	0.215789	−	6.17939i	0.0523365	−	1.49872i	−0.635073	−	0.772452i	$-0.719030\pi$
$17$	0.215789	−	6.17939i	0.0523365	−	1.49872i	0.687409	−	0.726270i	$-0.258748\pi$
$18$	2.39208	+	1.73795i	0.563819	+	0.409639i
$19$	0.374857	−	4.34275i	0.0859980	−	0.996295i
$19$	0.374857	−	4.34275i	0.0859980	−	0.996295i
$20$	−0.0827182	+	0.254580i	−0.0184963	+	0.0569259i
$21$	0.919329	+	0.334608i	0.200614	+	0.0730175i
$22$	0.649018	+	3.25250i	0.138371	+	0.693436i
$23$	−1.00149	−	0.840349i	−0.208825	−	0.175225i	0.532376	−	0.846508i	$-0.321299\pi$
$23$	−1.00149	−	0.840349i	−0.208825	−	0.175225i	−0.741201	+	0.671283i	$0.765744\pi$
$24$	−0.0778819	−	0.192764i	−0.0158976	−	0.0393479i
$25$	−2.16044	−	4.42957i	−0.432089	−	0.885914i
$26$	−5.03632	+	2.24232i	−0.987705	+	0.439754i
$27$	−0.828673	+	0.920335i	−0.159478	+	0.177119i
$28$	2.89712	+	3.70814i	0.547504	+	0.700773i
$29$	4.26673	+	1.22346i	0.792311	+	0.227192i	0.647297	−	0.762238i	$-0.275899\pi$
$29$	4.26673	+	1.22346i	0.792311	+	0.227192i	0.145014	+	0.989430i	$0.453677\pi$
$30$	−0.0508405	−	0.0226356i	−0.00928216	−	0.00413269i
$31$	−6.66050	−	7.39723i	−1.19626	−	1.32858i	−0.931269	−	0.364331i	$-0.881298\pi$
$31$	−6.66050	−	7.39723i	−1.19626	−	1.32858i	−0.264991	−	0.964251i	$-0.585369\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	−0.686606	+	0.0635110i	−0.119523	+	0.0110558i
$34$	4.73657	+	3.97446i	0.812316	+	0.681614i
$35$	1.24737	+	0.175306i	0.210844	+	0.0296322i
$36$	−2.84224	+	0.814998i	−0.473706	+	0.135833i
$37$	−0.869982	−	0.632079i	−0.143024	−	0.103913i	0.513972	−	0.857807i	$-0.328173\pi$
$37$	−0.869982	−	0.632079i	−0.143024	−	0.103913i	−0.656997	+	0.753894i	$0.728173\pi$
$38$	3.19135	+	2.96906i	0.517705	+	0.481644i
$39$	−0.354182	−	1.09006i	−0.0567146	−	0.174550i
$40$	−0.149686	−	0.221918i	−0.0236674	−	0.0350883i
$41$	3.21188	+	3.10168i	0.501612	+	0.484401i	0.901874	−	0.432000i	$-0.142192\pi$
$41$	3.21188	+	3.10168i	0.501612	+	0.484401i	−0.400262	+	0.916401i	$0.631081\pi$
$42$	−0.829670	+	0.518436i	−0.128021	+	0.0799964i
$43$	5.77707	−	4.84754i	0.880995	−	0.739243i	−0.0853884	−	0.996348i	$-0.527213\pi$
$43$	5.77707	−	4.84754i	0.880995	−	0.739243i	0.966383	+	0.257105i	$0.0827687\pi$
$44$	−2.96258	−	1.49101i	−0.446626	−	0.224778i
$45$	−0.395737	+	0.685437i	−0.0589930	+	0.102179i
$46$	1.27878	−	0.271814i	0.188546	−	0.0400767i
$47$	−6.14322	+	9.10769i	−0.896080	+	1.32849i	0.0480241	+	0.998846i	$0.484708\pi$
$47$	−6.14322	+	9.10769i	−0.896080	+	1.32849i	−0.944104	+	0.329647i	$0.893070\pi$
$48$	0.199849	+	0.0573059i	0.0288458	+	0.00827139i
$49$	10.1330	−	11.2539i	1.44758	−	1.60770i
$50$	4.82065	+	1.02466i	0.681743	+	0.144909i
$51$	−0.924710	+	0.892982i	−0.129485	+	0.125043i
$52$	1.33370	−	5.34919i	0.184951	−	0.741799i
$53$	−2.15937	+	1.34933i	−0.296613	+	0.185344i	−0.670059	−	0.742307i	$-0.733731\pi$
$53$	−2.15937	+	1.34933i	−0.296613	+	0.185344i	0.373447	+	0.927652i	$0.378176\pi$
$54$	−0.215052	−	1.21962i	−0.0292648	−	0.165969i
$55$	−0.847706	+	0.263785i	−0.114305	+	0.0355687i
$56$	−4.70570			−0.628825
$57$	−0.683248	+	0.595334i	−0.0904984	+	0.0788539i
$58$	−3.59096	+	2.60899i	−0.471516	+	0.342577i
$59$	4.88616	+	7.24403i	0.636124	+	0.943093i	0.999932	+	0.0116188i	$0.00369846\pi$
$59$	4.88616	+	7.24403i	0.636124	+	0.943093i	−0.363809	+	0.931474i	$0.618524\pi$
$60$	0.0491377	−	0.0261270i	0.00634365	−	0.00337298i
$61$	2.09577	−	5.18722i	0.268336	−	0.664155i	−0.731508	−	0.681833i	$-0.761183\pi$
$61$	2.09577	−	5.18722i	0.268336	−	0.664155i	0.999844	+	0.0176780i	$0.00562739\pi$
$62$	9.92971	−	0.694353i	1.26107	−	0.0881829i
$63$	6.09936	+	12.5055i	0.768447	+	1.57555i
$64$	0.669131	+	0.743145i	0.0836413	+	0.0928931i
$65$	−0.737857	−	1.27801i	−0.0915199	−	0.158517i
$66$	0.372669	−	0.580154i	0.0458724	−	0.0714120i
$67$	3.64234	−	1.32570i	0.444982	−	0.161960i	−0.109804	−	0.993953i	$-0.535022\pi$
$67$	3.64234	−	1.32570i	0.444982	−	0.161960i	0.554786	+	0.831993i	$0.312800\pi$
$68$	−6.04804	+	1.28555i	−0.733433	+	0.155896i
$69$	0.0284111	+	0.270313i	0.00342029	+	0.0325419i
$70$	−0.906101	+	0.875012i	−0.108300	+	0.104584i
$71$	−3.57839	−	2.23603i	−0.424677	−	0.265367i	0.300701	−	0.953718i	$-0.402779\pi$
$71$	−3.57839	−	2.23603i	−0.424677	−	0.265367i	−0.725378	+	0.688351i	$0.758335\pi$
$72$	1.10763	−	2.74148i	0.130535	−	0.323086i
$73$	−4.97321	+	10.1966i	−0.582070	+	1.19342i	0.381102	+	0.924533i	$0.375545\pi$
$73$	−4.97321	+	10.1966i	−0.582070	+	1.19342i	−0.963172	+	0.268887i	$0.913344\pi$
$74$	1.03370	−	0.296408i	0.120165	−	0.0344568i
$75$	−0.316625	+	0.974471i	−0.0365607	+	0.112522i
$76$	−4.30444	+	0.686885i	−0.493753	+	0.0787911i
$77$	−4.48881	+	14.9476i	−0.511547	+	1.70343i
$78$	1.07704	+	0.392009i	0.121950	+	0.0443863i
$79$	−6.41707	−	0.901861i	−0.721977	−	0.101467i	−0.231392	−	0.972861i	$-0.574328\pi$
$79$	−6.41707	−	0.901861i	−0.721977	−	0.101467i	−0.490585	+	0.871393i	$0.663217\pi$
$80$	0.267030	+	0.0186725i	0.0298548	+	0.00208765i
$81$	−8.59187	+	0.600802i	−0.954653	+	0.0667558i
$82$	−4.42159	+	0.621414i	−0.488283	+	0.0686237i
$83$	−0.0872925	−	0.0185546i	−0.00958160	−	0.00203663i	0.203118	−	0.979154i	$-0.434892\pi$
$83$	−0.0872925	−	0.0185546i	−0.00958160	−	0.00203663i	−0.212700	+	0.977118i	$0.568226\pi$
$84$	0.102263	−	0.972970i	0.0111578	−	0.106160i
$85$	−0.925530	+	1.37215i	−0.100388	+	0.148831i
$86$	0.263192	+	7.53684i	0.0283807	+	0.812718i
$87$	−0.461407	−	0.799181i	−0.0494680	−	0.0856812i
$88$	2.99888	−	1.41659i	0.319681	−	0.151009i
$89$	0.840705	−	4.76787i	0.0891145	−	0.505394i	−0.907278	−	0.420531i	$-0.861844\pi$
$89$	0.840705	−	4.76787i	0.0891145	−	0.505394i	0.996393	−	0.0848625i	$-0.0270451\pi$
$90$	−0.296492	−	0.733842i	−0.0312530	−	0.0773538i
$91$	−25.8791	−	1.80964i	−2.71286	−	0.189702i
$92$	−0.573105	+	1.17504i	−0.0597503	+	0.122506i
$93$	−0.0722231	+	2.06820i	−0.00748919	+	0.214462i
$94$	−3.39482	−	10.4482i	−0.350149	−	1.07765i
$95$	−0.701113	+	0.932661i	−0.0719326	+	0.0956890i
$96$	−0.168197	+	0.122202i	−0.0171666	+	0.0124722i
$97$	4.47115	−	5.72281i	0.453976	−	0.581063i	−0.505509	−	0.862821i	$-0.668695\pi$
$97$	4.47115	−	5.72281i	0.453976	−	0.581063i	0.959486	+	0.281758i	$0.0909175\pi$
$98$	2.62966	+	14.9135i	0.265635	+	1.50649i
$99$	−7.65168	−	6.13348i	−0.769023	−	0.616438i
$100$	−3.77533	+	3.16788i	−0.377533	+	0.316788i
$101$	−7.69884	−	4.09355i	−0.766064	−	0.407323i	0.0399640	−	0.999201i	$-0.487276\pi$
$101$	−7.69884	−	4.09355i	−0.766064	−	0.407323i	−0.806028	+	0.591878i	$0.798387\pi$
$102$	−0.134371	−	1.27846i	−0.0133047	−	0.126586i
$103$	0.527543	−	5.01923i	0.0519803	−	0.494560i	−0.937299	−	0.348526i	$-0.886682\pi$
$103$	0.527543	−	5.01923i	0.0519803	−	0.494560i	0.989280	−	0.146034i	$-0.0466509\pi$
$104$	3.39411	+	4.34426i	0.332820	+	0.425990i
$105$	−0.161230	−	0.206365i	−0.0157344	−	0.0201391i
$106$	0.266159	−	2.53234i	0.0258517	−	0.245962i
$107$	0.684843	+	6.51585i	0.0662063	+	0.629911i	0.976436	+	0.215807i	$0.0692382\pi$
$107$	0.684843	+	6.51585i	0.0662063	+	0.629911i	−0.910230	+	0.414104i	$0.864095\pi$
$108$	1.09347	+	0.581409i	0.105219	+	0.0559461i
$109$	−10.2480	+	8.59910i	−0.981581	+	0.823644i	−0.984327	−	0.176352i	$-0.943570\pi$
$109$	−10.2480	+	8.59910i	−0.981581	+	0.823644i	0.00274609	+	0.999996i	$0.499126\pi$
$110$	0.314035	−	0.830403i	0.0299420	−	0.0791759i
$111$	0.0388225	+	0.220174i	0.00368487	+	0.0208979i
$112$	2.89712	−	3.70814i	0.273752	−	0.350386i
$113$	7.26179	−	5.27600i	0.683132	−	0.496324i	−0.191263	−	0.981539i	$-0.561258\pi$
$113$	7.26179	−	5.27600i	0.683132	−	0.496324i	0.874395	+	0.485215i	$0.161258\pi$
$114$	−0.0484800	−	0.904931i	−0.00454057	−	0.0847546i
$115$	0.108142	+	0.332826i	0.0100843	+	0.0310362i
$116$	0.154907	−	4.43597i	0.0143828	−	0.411869i
$117$	7.14569	−	14.6508i	0.660619	−	1.35447i
$118$	−8.71660	−	0.609524i	−0.802428	−	0.0561112i
$119$	10.8996	+	26.9774i	0.999163	+	2.47301i
$120$	−0.00966384	+	0.0548064i	−0.000882184	+	0.00500311i
$121$	−1.63913	−	10.8772i	−0.149011	−	0.988835i
$122$	2.79730	+	4.84506i	0.253255	+	0.438651i
$123$	−0.0323971	−	0.927731i	−0.00292115	−	0.0836507i
$124$	−5.56618	+	8.25220i	−0.499858	+	0.741070i
$125$	−0.277799	+	2.64308i	−0.0248471	+	0.236404i
$126$	−13.6096	−	2.89282i	−1.21244	−	0.257713i
$127$	1.18652	−	0.166755i	0.105287	−	0.0147971i	−0.0863328	−	0.996266i	$-0.527515\pi$
$127$	1.18652	−	0.166755i	0.105287	−	0.0147971i	0.191620	+	0.981469i	$0.438626\pi$
$128$	−0.997564	+	0.0697565i	−0.0881730	+	0.00616566i
$129$	−1.56407	−	0.109370i	−0.137709	−	0.00962952i
$130$	1.46135	+	0.205380i	0.128169	+	0.0180130i
$131$	13.8396	+	5.03719i	1.20917	+	0.440101i	0.866415	−	0.499324i	$-0.166418\pi$
$131$	13.8396	+	5.03719i	1.20917	+	0.440101i	0.342753	+	0.939425i	$0.388641\pi$
$132$	0.227729	+	0.650846i	0.0198213	+	0.0566489i
$133$	6.70048	+	19.3864i	0.581005	+	1.68101i
$134$	−1.19778	+	3.68639i	−0.103472	+	0.318455i
$135$	0.318664	−	0.0913753i	0.0274262	−	0.00786434i
$136$	2.71052	−	5.55739i	0.232425	−	0.476542i
$137$	1.58142	−	3.91416i	0.135110	−	0.334409i	−0.844428	−	0.535670i	$-0.820059\pi$
$137$	1.58142	−	3.91416i	0.135110	−	0.334409i	0.979538	+	0.201260i	$0.0645037\pi$
$138$	−0.230502	−	0.144033i	−0.0196216	−	0.0122609i
$139$	−7.00481	+	6.76447i	−0.594141	+	0.573755i	−0.929725	−	0.368255i	$-0.879955\pi$
$139$	−7.00481	+	6.76447i	−0.594141	+	0.573755i	0.335584	+	0.942010i	$0.391066\pi$
$140$	−0.131667	−	1.25273i	−0.0111279	−	0.105875i
$141$	2.23408	−	0.474869i	0.188144	−	0.0399912i
$142$	3.96509	−	1.44317i	0.332743	−	0.121108i
$143$	17.0371	−	6.63730i	1.42472	−	0.555039i
$144$	1.47839	+	2.56064i	0.123199	+	0.213387i
$145$	−0.795028	−	0.882968i	−0.0660235	−	0.0733265i
$146$	−4.97321	−	10.1966i	−0.411585	−	0.843875i
$147$	−3.14073	+	0.219621i	−0.259043	+	0.0181141i
$148$	−0.402836	+	0.997053i	−0.0331129	+	0.0819573i
$149$	15.2945	−	8.13222i	1.25297	−	0.666217i	0.295666	−	0.955291i	$-0.404459\pi$
$149$	15.2945	−	8.13222i	1.25297	−	0.666217i	0.957307	+	0.289074i	$0.0933475\pi$
$150$	−0.572960	−	0.849448i	−0.0467820	−	0.0693571i
$151$	3.49639	−	2.54028i	0.284532	−	0.206725i	−0.436360	−	0.899772i	$-0.643732\pi$
$151$	3.49639	−	2.54028i	0.284532	−	0.206725i	0.720892	+	0.693048i	$0.243732\pi$
$152$	2.10880	−	3.81483i	0.171047	−	0.309424i
$153$	−18.2822			−1.47803
$154$	−9.01527	−	12.7399i	−0.726471	−	1.02661i
$155$	0.462684	+	2.62401i	0.0371637	+	0.210766i
$156$	−0.971998	+	0.607371i	−0.0778221	+	0.0486286i
$157$	1.21516	−	4.87376i	0.0969806	−	0.388968i	−0.902115	−	0.431496i	$-0.857986\pi$
$157$	1.21516	−	4.87376i	0.0969806	−	0.388968i	0.999095	+	0.0425284i	$0.0135413\pi$
$158$	4.66142	−	4.50148i	0.370843	−	0.358119i
$159$	0.517813	+	0.110065i	0.0410652	+	0.00872868i
$160$	−0.179114	+	0.198926i	−0.0141602	+	0.0157265i
$161$	5.91368	+	1.69572i	0.466063	+	0.133641i
$162$	4.81625	−	7.14038i	0.378400	−	0.561001i
$163$	−10.2423	+	2.17707i	−0.802238	+	0.170521i	−0.590745	−	0.806859i	$-0.701166\pi$
$163$	−10.2423	+	2.17707i	−0.802238	+	0.170521i	−0.211493	+	0.977379i	$0.567833\pi$
$164$	2.23252	−	3.86684i	0.174331	−	0.301950i
$165$	0.164873	+	0.0829773i	0.0128354	+	0.00645978i
$166$	0.0683639	−	0.0573641i	0.00530607	−	0.00445232i
$167$	−11.5588	+	7.22274i	−0.894446	+	0.558912i	−0.897466	−	0.441083i	$-0.854594\pi$
$167$	−11.5588	+	7.22274i	−0.894446	+	0.558912i	0.00301970	+	0.999995i	$0.499039\pi$
$168$	0.703751	+	0.679605i	0.0542956	+	0.0524326i
$169$	9.72579	+	14.4191i	0.748138	+	1.10916i
$170$	−0.511459	−	1.57411i	−0.0392272	−	0.120729i
$171$	−12.8714	−	0.659563i	−0.984301	−	0.0504381i
$172$	−6.10115	−	4.43274i	−0.465208	−	0.337993i
$173$	5.05136	−	1.44845i	0.384048	−	0.110124i	−0.0780577	−	0.996949i	$-0.524872\pi$
$173$	5.05136	−	1.44845i	0.384048	−	0.110124i	0.462106	+	0.886825i	$0.347094\pi$
$174$	0.913833	+	0.128431i	0.0692775	+	0.00973632i
$175$	17.7656	+	14.9071i	1.34295	+	1.12687i
$176$	−0.730005	+	3.23529i	−0.0550262	+	0.243869i
$177$	0.315455	−	1.78903i	0.0237111	−	0.134472i
$178$	3.23955	+	3.59788i	0.242814	+	0.269673i
$179$	−13.2297	−	5.89024i	−0.988834	−	0.440257i	−0.152396	−	0.988319i	$-0.548699\pi$
$179$	−13.2297	−	5.89024i	−0.988834	−	0.440257i	−0.836438	+	0.548062i	$0.815366\pi$
$180$	0.760814	+	0.218160i	0.0567077	+	0.0162607i
$181$	9.43618	+	12.0778i	0.701386	+	0.897733i	0.998366	−	0.0571509i	$-0.0182016\pi$
$181$	9.43618	+	12.0778i	0.701386	+	0.897733i	−0.296980	+	0.954884i	$0.595979\pi$
$182$	17.3587	−	19.2788i	1.28672	−	1.42904i
$183$	−1.06258	+	0.473089i	−0.0785479	+	0.0349718i
$184$	−0.573105	−	1.17504i	−0.0422499	−	0.0866250i
$185$	0.107832	+	0.266893i	0.00792795	+	0.0196224i
$186$	−1.58530	−	1.33022i	−0.116240	−	0.0975367i
$187$	−15.0674	−	13.9112i	−1.10184	−	1.01728i
$188$	10.3233	+	3.75739i	0.752906	+	0.274036i
$189$	1.80086	−	5.54246i	0.130993	−	0.403155i
$190$	−0.303299	−	1.12669i	−0.0220036	−	0.0817385i
$191$	14.4090	+	10.4688i	1.04260	+	0.757493i	0.970791	−	0.239926i	$-0.0771232\pi$
$191$	14.4090	+	10.4688i	1.04260	+	0.757493i	0.0718078	+	0.997418i	$0.477123\pi$
$192$	0.00725572	−	0.207777i	0.000523636	−	0.0149950i
$193$	11.4982	−	6.11368i	0.827655	−	0.440072i	−0.000886296	−	1.00000i	$-0.500282\pi$
$193$	11.4982	−	6.11368i	0.827655	−	0.440072i	0.828542	+	0.559927i	$0.189171\pi$
$194$	1.75692	+	7.04663i	0.126140	+	0.505918i
$195$	−0.0742230	+	0.297692i	−0.00531522	+	0.0213182i
$196$	−13.3710	−	7.10948i	−0.955071	−	0.507820i
$197$	−4.56906	+	7.91384i	−0.325532	+	0.563838i	−0.981620	−	0.190847i	$-0.938877\pi$
$197$	−4.56906	+	7.91384i	−0.325532	+	0.563838i	0.656088	+	0.754684i	$0.272210\pi$
$198$	9.54409	−	2.25346i	0.678269	−	0.160146i
$199$	−7.48325	+	2.72368i	−0.530473	+	0.193077i	−0.593350	−	0.804945i	$-0.702195\pi$
$199$	−7.48325	+	2.72368i	−0.530473	+	0.193077i	0.0628763	+	0.998021i	$0.479973\pi$
$200$	−0.171997	−	4.92534i	−0.0121620	−	0.348274i
$201$	−0.736183	−	0.327770i	−0.0519263	−	0.0231191i
$202$	7.96564	−	3.54653i	0.560461	−	0.249533i
$203$	−20.6838	+	2.90692i	−1.45172	+	0.204025i
$204$	1.09016	+	0.681210i	0.0763268	+	0.0476943i
$205$	−0.289147	−	1.15971i	−0.0201949	−	0.0809974i
$206$	3.63042	+	3.50586i	0.252943	+	0.244265i
$207$	−2.37987	+	3.04609i	−0.165412	+	0.211718i
$208$	−5.51294			−0.382254
$209$	−10.1062	−	10.3376i	−0.699057	−	0.715066i
$210$	0.261881			0.0180715
$211$	17.0557	−	21.8303i	1.17416	−	1.50286i	0.349771	−	0.936835i	$-0.386259\pi$
$211$	17.0557	−	21.8303i	1.17416	−	1.50286i	0.824390	−	0.566023i	$-0.191519\pi$
$212$	1.83165	+	1.76880i	0.125798	+	0.121482i
$213$	0.212228	+	0.851201i	0.0145416	+	0.0583233i
$214$	−5.55619	−	3.47189i	−0.379813	−	0.237334i
$215$	−1.99906	+	0.280949i	−0.136334	+	0.0191606i
$216$	−1.13136	+	0.503716i	−0.0769796	+	0.0342735i
$217$	42.7908	+	19.0517i	2.90483	+	1.29331i
$218$	−0.466879	−	13.3697i	−0.0316211	−	0.905509i
$219$	2.21637	−	0.806691i	0.149768	−	0.0545111i
$220$	0.461028	+	0.758710i	0.0310825	+	0.0511522i
$221$	17.0437	−	29.5206i	1.14648	−	1.98577i
$222$	−0.197401	−	0.104960i	−0.0132487	−	0.00704444i
$223$	6.65510	−	26.6921i	0.445658	−	1.78744i	−0.154980	−	0.987918i	$-0.549531\pi$
$223$	6.65510	−	26.6921i	0.445658	−	1.78744i	0.600639	−	0.799520i	$-0.294913\pi$
$224$	1.13841	+	4.56592i	0.0760633	+	0.305073i
$225$	−12.8663	+	6.84115i	−0.857755	+	0.456077i
$226$	−0.313260	+	8.97060i	−0.0208378	+	0.596715i
$227$	12.6785	+	9.21148i	0.841503	+	0.611388i	0.922790	−	0.385303i	$-0.125903\pi$
$227$	12.6785	+	9.21148i	0.841503	+	0.611388i	−0.0812872	+	0.996691i	$0.525903\pi$
$228$	0.742943	+	0.518929i	0.0492026	+	0.0343669i
$229$	4.56030	−	14.0351i	0.301353	−	0.927469i	−0.679660	−	0.733527i	$-0.737873\pi$
$229$	4.56030	−	14.0351i	0.301353	−	0.927469i	0.981013	−	0.193942i	$-0.0621272\pi$
$230$	−0.328849	−	0.119691i	−0.0216837	−	0.00789221i
$231$	2.83007	−	1.58717i	0.186205	−	0.104428i
$232$	3.40022	+	2.85312i	0.223235	+	0.187317i
$233$	6.36520	+	15.7544i	0.416998	+	1.03211i	0.978797	+	0.204832i	$0.0656649\pi$
$233$	6.36520	+	15.7544i	0.416998	+	1.03211i	−0.561799	+	0.827274i	$0.689891\pi$
$234$	7.14569	+	14.6508i	0.467128	+	0.957755i
$235$	2.68647	−	1.19610i	0.175246	−	0.0780247i
$236$	5.84678	−	6.49351i	0.380593	−	0.422692i
$237$	0.829444	+	1.06164i	0.0538782	+	0.0689610i
$238$	−27.9689	−	8.01996i	−1.81296	−	0.519857i
$239$	11.1525	+	4.96541i	0.721395	+	0.321186i	0.734388	−	0.678730i	$-0.237469\pi$
$239$	11.1525	+	4.96541i	0.721395	+	0.321186i	−0.0129933	+	0.999916i	$0.504136\pi$
$240$	−0.0372384	−	0.0413574i	−0.00240373	−	0.00266961i
$241$	0.522752	−	2.96467i	0.0336734	−	0.190971i	−0.963331	−	0.268316i	$-0.913533\pi$
$241$	0.522752	−	2.96467i	0.0336734	−	0.190971i	0.997004	+	0.0773443i	$0.0246441\pi$
$242$	9.58049	+	5.40502i	0.615857	+	0.347448i
$243$	4.21779	+	3.53915i	0.270572	+	0.227036i
$244$	−5.54015	−	0.778617i	−0.354672	−	0.0498459i
$245$	−3.89663	+	1.11734i	−0.248946	+	0.0713842i
$246$	0.751008	+	0.545639i	0.0478825	+	0.0347887i
$247$	13.0644	−	20.1688i	0.831271	−	1.28331i
$248$	−3.07594	−	9.46678i	−0.195323	−	0.601141i
$249$	0.0103752	+	0.0153818i	0.000657500	+	0.000974784i
$250$	−1.91174	−	1.84615i	−0.120909	−	0.116761i
$251$	−16.0835	+	10.0501i	−1.01518	+	0.634354i	−0.932105	−	0.362189i	$-0.882029\pi$
$251$	−16.0835	+	10.0501i	−1.01518	+	0.634354i	−0.0830743	+	0.996543i	$0.526474\pi$
$252$	10.6585	−	8.94355i	0.671423	−	0.563391i
$253$	−4.27918	+	0.699579i	−0.269030	+	0.0439822i
$254$	−0.599093	+	1.03766i	−0.0375904	+	0.0651085i
$255$	0.336585	−	0.0715433i	0.0210778	−	0.00448021i
$256$	0.559193	−	0.829038i	0.0349496	−	0.0518148i
$257$	−8.21188	−	2.35472i	−0.512243	−	0.146883i	0.00955178	−	0.999954i	$-0.496960\pi$
$257$	−8.21188	−	2.35472i	−0.512243	−	0.146883i	−0.521795	+	0.853071i	$0.674737\pi$
$258$	1.04912	−	1.16517i	0.0653154	−	0.0725401i
$259$	4.94972	+	1.05210i	0.307561	+	0.0653741i
$260$	−1.06154	+	1.02512i	−0.0658339	+	0.0635750i
$261$	3.17502	−	12.7343i	0.196529	−	0.788235i
$262$	−12.4898	+	7.80452i	−0.771625	+	0.482165i
$263$	−4.44434	−	25.2051i	−0.274050	−	1.55422i	−0.741963	−	0.670441i	$-0.766105\pi$
$263$	−4.44434	−	25.2051i	−0.274050	−	1.55422i	0.467913	−	0.883774i	$-0.345006\pi$
$264$	−0.653078	−	0.221247i	−0.0401942	−	0.0136168i
$265$	0.681594			0.0418700
$266$	−19.4019	−	6.65540i	−1.18961	−	0.408069i
$267$	−0.814314	+	0.591634i	−0.0498352	+	0.0362074i
$268$	−2.16748	−	3.21343i	−0.132400	−	0.196291i
$269$	25.4785	−	13.5471i	1.55345	−	0.825984i	0.553474	−	0.832867i	$-0.313302\pi$
$269$	25.4785	−	13.5471i	1.55345	−	0.825984i	0.999976	+	0.00688237i	$0.00219074\pi$
$270$	−0.124184	+	0.307367i	−0.00755761	+	0.0187057i
$271$	−4.06702	+	0.284394i	−0.247054	+	0.0172757i	−0.192747	−	0.981249i	$-0.561740\pi$
$271$	−4.06702	+	0.284394i	−0.247054	+	0.0172757i	−0.0543073	+	0.998524i	$0.517295\pi$
$272$	2.71052	+	5.55739i	0.164349	+	0.336966i
$273$	3.60894	+	4.00813i	0.218423	+	0.242583i
$274$	2.11078	+	3.65598i	0.127517	+	0.220866i
$275$	−15.8094	−	4.15198i	−0.953340	−	0.250374i
$276$	0.255411	−	0.0929619i	0.0153739	−	0.00559565i
$277$	8.91724	−	1.89542i	0.535785	−	0.113885i	0.0679304	−	0.997690i	$-0.478360\pi$
$277$	8.91724	−	1.89542i	0.535785	−	0.113885i	0.467855	+	0.883805i	$0.345027\pi$
$278$	−1.01788	−	9.68449i	−0.0610485	−	0.580837i
$279$	−21.1713	+	20.4449i	−1.26749	+	1.22401i
$280$	1.06823	+	0.667501i	0.0638387	+	0.0398908i
$281$	−11.0157	+	27.2647i	−0.657139	+	1.62648i	0.116755	+	0.993161i	$0.462751\pi$
$281$	−11.0157	+	27.2647i	−0.657139	+	1.62648i	−0.773894	+	0.633315i	$0.781694\pi$
$282$	−1.00124	+	2.05284i	−0.0596228	+	0.122245i
$283$	−4.35450	+	1.24863i	−0.258848	+	0.0742235i	−0.402552	−	0.915397i	$-0.631877\pi$
$283$	−4.35450	+	1.24863i	−0.258848	+	0.0742235i	0.143704	+	0.989621i	$0.454099\pi$
$284$	−1.30392	+	4.01304i	−0.0773731	+	0.238130i
$285$	0.239550	−	0.0382264i	0.0141897	−	0.00226434i
$286$	−5.25884	+	17.5118i	−0.310962	+	1.03549i
$287$	−19.7440	−	7.18623i	−1.16545	−	0.424190i
$288$	−2.92800	−	0.411504i	−0.172534	−	0.0242481i
$289$	−21.1797	−	1.48103i	−1.24587	−	0.0871195i
$290$	1.18526	−	0.0828812i	0.0696007	−	0.00486695i
$291$	−1.49517	+	0.210133i	−0.0876485	+	0.0123182i
$292$	11.0968	+	2.35870i	0.649393	+	0.138033i
$293$	0.403974	−	3.84356i	0.0236004	−	0.224543i	−0.976364	−	0.216132i	$-0.930656\pi$
$293$	0.403974	−	3.84356i	0.0236004	−	0.224543i	0.999965	−	0.00841133i	$-0.00267744\pi$
$294$	1.76056	−	2.61014i	0.102678	−	0.152227i
$295$	−0.0816289	−	2.33754i	−0.00475262	−	0.136097i
$296$	−0.537678	−	0.931286i	−0.0312519	−	0.0541299i
$297$	0.520828	+	4.07426i	0.0302215	+	0.236413i
$298$	−3.00795	+	17.0589i	−0.174246	+	0.988196i
$299$	−2.69992	−	6.68254i	−0.156140	−	0.386461i
$300$	1.02212	+	0.0714738i	0.0590123	+	0.00412654i
$301$	−15.5568	+	31.8961i	−0.896678	+	1.83846i
$302$	−0.150828	+	4.31915i	−0.00867917	+	0.248539i
$303$	0.560188	+	1.72408i	0.0321820	+	0.0990460i
$304$	1.70782	+	4.01041i	0.0979502	+	0.230013i
$305$	−1.21156	+	0.880250i	−0.0693737	+	0.0504029i
$306$	11.2557	−	14.4066i	0.643443	−	0.823569i
$307$	2.07283	+	11.7556i	0.118303	+	0.670929i	0.985062	+	0.172202i	$0.0550880\pi$
$307$	2.07283	+	11.7556i	0.118303	+	0.670929i	−0.866759	+	0.498727i	$0.833801\pi$
$308$	15.5895	+	0.739322i	0.888295	+	0.0421268i
$309$	−0.803782	+	0.674453i	−0.0457255	+	0.0383683i
$310$	−2.35261	−	1.25090i	−0.133619	−	0.0710465i
$311$	3.09631	+	29.4594i	0.175575	+	1.67049i	0.627641	+	0.778503i	$0.284021\pi$
$311$	3.09631	+	29.4594i	0.175575	+	1.67049i	−0.452065	+	0.891985i	$0.649313\pi$
$312$	0.119806	−	1.13988i	0.00678269	−	0.0645330i
$313$	9.70971	+	12.4279i	0.548825	+	0.702464i	0.979818	−	0.199891i	$-0.0640589\pi$
$313$	9.70971	+	12.4279i	0.548825	+	0.702464i	−0.430993	+	0.902355i	$0.641837\pi$
$314$	3.09244	+	3.95815i	0.174517	+	0.223371i
$315$	0.389310	−	3.70404i	0.0219351	−	0.208699i
$316$	0.677359	+	6.44464i	0.0381044	+	0.362539i
$317$	−11.5456	−	6.13890i	−0.648465	−	0.344795i	0.112440	−	0.993659i	$-0.464133\pi$
$317$	−11.5456	−	6.13890i	−0.648465	−	0.344795i	−0.760905	+	0.648864i	$0.775245\pi$
$318$	−0.405529	+	0.340280i	−0.0227410	+	0.0190819i
$319$	12.3064	−	8.07913i	0.689026	−	0.452345i
$320$	−0.0464824	−	0.263615i	−0.00259845	−	0.0147365i
$321$	0.838609	−	1.07337i	0.0468066	−	0.0599097i
$322$	−4.97707	+	3.61605i	−0.277361	+	0.201515i
$323$	−26.7547	−	3.25350i	−1.48867	−	0.181030i
$324$	2.66152	+	8.19131i	0.147862	+	0.455073i
$325$	0.948209	−	27.1531i	0.0525972	−	1.50619i
$326$	4.59023	−	9.41137i	0.254229	−	0.521247i
$327$	2.77452	+	0.194013i	0.153431	+	0.0107290i
$328$	1.67263	+	4.13992i	0.0923558	+	0.228589i
$329$	8.97694	−	50.9108i	0.494915	−	2.80680i
$330$	−0.166893	+	0.0788359i	−0.00918716	+	0.00433978i
$331$	−3.74999	−	6.49517i	−0.206118	−	0.357007i	0.744370	−	0.667767i	$-0.232750\pi$
$331$	−3.74999	−	6.49517i	−0.206118	−	0.357007i	−0.950488	+	0.310760i	$0.899416\pi$
$332$	0.00311452	+	0.0891883i	0.000170932	+	0.00489485i
$333$	−1.77800	+	2.63600i	−0.0974340	+	0.144452i
$334$	1.42471	−	13.5552i	0.0779567	−	0.741708i
$335$	−1.01489	−	0.215721i	−0.0554492	−	0.0117861i
$336$	−0.968808	+	0.136157i	−0.0528528	+	0.00742798i
$337$	19.6365	−	1.37312i	1.06967	−	0.0747984i	0.475950	−	0.879472i	$-0.342104\pi$
$337$	19.6365	−	1.37312i	1.06967	−	0.0747984i	0.593717	+	0.804674i	$0.297660\pi$
$338$	−17.3502	−	1.21324i	−0.943725	−	0.0659917i
$339$	−1.84799	−	0.259718i	−0.100369	−	0.0141060i
$340$	1.55530	+	0.566084i	0.0843481	+	0.0307002i
$341$	−33.0052	+	0.740245i	−1.78733	+	0.0400865i
$342$	8.44417	−	9.73673i	0.456608	−	0.526502i
$343$	−11.8419	+	36.4457i	−0.639404	+	1.96788i
$344$	7.24929	−	2.07870i	0.390855	−	0.112076i
$345$	0.0318944	−	0.0653931i	0.00171713	−	0.00352065i
$346$	−1.96853	+	4.87229i	−0.105829	+	0.261936i
$347$	5.91051	+	3.69330i	0.317293	+	0.198267i	0.679211	−	0.733943i	$-0.262322\pi$
$347$	5.91051	+	3.69330i	0.317293	+	0.198267i	−0.361918	+	0.932210i	$0.617878\pi$
$348$	−0.663817	+	0.641041i	−0.0355843	+	0.0343634i
$349$	0.194549	+	1.85101i	0.0104140	+	0.0990825i	0.998494	−	0.0548574i	$-0.0174704\pi$
$349$	0.194549	+	1.85101i	0.0104140	+	0.0990825i	−0.988080	+	0.153940i	$0.950804\pi$
$350$	−22.6845	+	4.82174i	−1.21254	+	0.257733i
$351$	−6.41567	+	2.33511i	−0.342443	+	0.124639i
$352$	−2.10001	−	2.56709i	−0.111931	−	0.136827i
$353$	15.2301	+	26.3793i	0.810616	+	1.40403i	0.912434	+	0.409225i	$0.134201\pi$
$353$	15.2301	+	26.3793i	0.810616	+	1.40403i	−0.101818	+	0.994803i	$0.532466\pi$
$354$	1.21556	+	1.35002i	0.0646065	+	0.0717528i
$355$	0.495139	+	1.01519i	0.0262793	+	0.0538805i
$356$	−4.82963	+	0.337721i	−0.255970	+	0.0178992i
$357$	2.26606	−	5.60869i	0.119932	−	0.296843i
$358$	12.7866	−	6.79875i	0.675792	−	0.359325i
$359$	3.43708	+	5.09568i	0.181402	+	0.268939i	0.908760	−	0.417318i	$-0.137030\pi$
$359$	3.43708	+	5.09568i	0.181402	+	0.268939i	−0.727358	+	0.686258i	$0.759252\pi$
$360$	−0.640316	+	0.465217i	−0.0337476	+	0.0245191i
$361$	−18.7190	−	3.25582i	−0.985209	−	0.171359i
$362$	−15.3269			−0.805564
$363$	−1.32577	+	1.86344i	−0.0695847	+	0.0978053i
$364$	4.50482	+	25.5481i	0.236117	+	1.33909i
$365$	2.57533	−	1.60925i	0.134799	−	0.0842318i
$366$	0.281388	−	1.12858i	0.0147084	−	0.0589920i
$367$	−3.69055	+	3.56392i	−0.192645	+	0.186035i	−0.784725	−	0.619844i	$-0.787196\pi$
$367$	−3.69055	+	3.56392i	−0.192645	+	0.186035i	0.592080	+	0.805879i	$0.298307\pi$
$368$	1.27878	+	0.271814i	0.0666611	+	0.0141693i
$369$	8.83395	−	9.81110i	0.459877	−	0.510745i
$370$	−0.276702	−	0.0793431i	−0.0143851	−	0.00412485i
$371$	6.70028	−	9.93357i	0.347861	−	0.515725i
$372$	2.02424	−	0.430265i	0.104952	−	0.0223082i
$373$	−12.5699	+	21.7717i	−0.650846	+	1.12730i	0.332072	+	0.943254i	$0.392252\pi$
$373$	−12.5699	+	21.7717i	−0.650846	+	1.12730i	−0.982918	+	0.184044i	$0.941081\pi$
$374$	20.2385	−	3.30868i	1.04651	−	0.171088i
$375$	0.423263	−	0.355160i	0.0218572	−	0.0183404i
$376$	−9.31654	+	5.82162i	−0.480464	+	0.300227i
$377$	17.6024	+	16.9984i	0.906567	+	0.875462i
$378$	3.25880	+	4.83137i	0.167615	+	0.248499i
$379$	2.55483	+	7.86295i	0.131233	+	0.403893i	0.994985	−	0.100024i	$-0.0318919\pi$
$379$	2.55483	+	7.86295i	0.131233	+	0.403893i	−0.863752	+	0.503917i	$0.831892\pi$
$380$	1.07457	+	0.454655i	0.0551244	+	0.0233233i
$381$	−0.201531	−	0.146421i	−0.0103248	−	0.00750138i
$382$	−17.1206	+	4.90924i	−0.875964	+	0.251179i
$383$	34.9970	+	4.91850i	1.78826	+	0.251324i	0.953949	−	0.299969i	$-0.0969763\pi$
$383$	34.9970	+	4.91850i	1.78826	+	0.251324i	0.834312	+	0.551293i	$0.185865\pi$
$384$	0.159263	+	0.133638i	0.00812736	+	0.00681966i
$385$	3.13930	−	2.75647i	0.159993	−	0.140483i
$386$	−2.26133	+	12.8246i	−0.115099	+	0.652756i
$387$	−14.9205	−	16.5709i	−0.758451	−	0.842345i
$388$	−6.63449	−	2.95386i	−0.336815	−	0.149960i
$389$	8.20405	+	2.35247i	0.415962	+	0.119275i	0.477089	−	0.878855i	$-0.341692\pi$
$389$	8.20405	+	2.35247i	0.415962	+	0.119275i	−0.0611274	+	0.998130i	$0.519470\pi$
$390$	−0.188888	−	0.241766i	−0.00956473	−	0.0122423i
$391$	−5.40896	+	6.00725i	−0.273543	+	0.303800i
$392$	13.8344	−	6.15945i	0.698740	−	0.311099i
$393$	−1.34227	−	2.75206i	−0.0677085	−	0.138823i
$394$	−3.42320	−	8.47271i	−0.172458	−	0.426849i
$395$	1.32879	+	1.11499i	0.0668587	+	0.0561011i
$396$	−4.10018	+	8.90822i	−0.206042	+	0.447655i
$397$	−20.5137	−	7.46639i	−1.02956	−	0.374727i	−0.228644	−	0.973510i	$-0.573429\pi$
$397$	−20.5137	−	7.46639i	−1.02956	−	0.374727i	−0.800912	+	0.598783i	$0.795651\pi$
$398$	2.46086	−	7.57375i	0.123352	−	0.379638i
$399$	1.79774	−	3.86699i	0.0899994	−	0.193591i
$400$	3.98712	+	2.89681i	0.199356	+	0.144840i
$401$	−0.408420	+	11.6956i	−0.0203955	+	0.584051i	0.945576	+	0.325402i	$0.105500\pi$
$401$	−0.408420	+	11.6956i	−0.0203955	+	0.584051i	−0.965971	+	0.258649i	$0.916723\pi$
$402$	0.711525	−	0.378325i	0.0354877	−	0.0188691i
$403$	−13.2756	−	53.2456i	−0.661305	−	2.65235i
$404$	−2.10943	+	8.46048i	−0.104948	+	0.420924i
$405$	2.03564	+	1.08237i	0.101152	+	0.0537833i
$406$	10.4435	−	18.0887i	0.518303	−	0.897728i
$407$	−3.47111	+	0.819565i	−0.172057	+	0.0406244i
$408$	−1.20797	+	0.439666i	−0.0598036	+	0.0217667i
$409$	1.02469	+	29.3432i	0.0506674	+	1.45093i	0.712710	+	0.701459i	$0.247468\pi$
$409$	1.02469	+	29.3432i	0.0506674	+	1.45093i	−0.662042	+	0.749466i	$0.730310\pi$
$410$	1.09188	+	0.486136i	0.0539240	+	0.0240085i
$411$	−0.801796	+	0.356983i	−0.0395497	+	0.0176087i
$412$	−4.99776	+	0.702390i	−0.246222	+	0.0346043i
$413$	−34.8699	−	21.7891i	−1.71584	−	1.07217i
$414$	−0.935160	−	3.75072i	−0.0459606	−	0.184338i
$415$	0.0171840	+	0.0165944i	0.000843531	+	0.000814589i
$416$	3.39411	−	4.34426i	0.166410	−	0.212995i
$417$	2.02453			0.0991415
$418$	14.3681	−	1.59930i	0.702767	−	0.0782244i
$419$	20.0973			0.981817			0.490908	−	0.871211i	$-0.336665\pi$
$419$	20.0973			0.981817			0.490908	+	0.871211i	$0.336665\pi$
$420$	−0.161230	+	0.206365i	−0.00786721	+	0.0100696i
$421$	−23.7326	−	22.9183i	−1.15665	−	1.11697i	−0.991420	−	0.130714i	$-0.958273\pi$
$421$	−23.7326	−	22.9183i	−1.15665	−	1.11697i	−0.165234	−	0.986254i	$-0.552838\pi$
$422$	6.70196	+	26.8801i	0.326247	+	1.30850i
$423$	27.5469	+	17.2132i	1.33938	+	0.836936i
$424$	−2.52151	+	0.354375i	−0.122455	+	0.0172100i
$425$	−27.8382	+	12.3944i	−1.35035	+	0.601216i
$426$	−0.801416	−	0.356814i	−0.0388288	−	0.0172877i
$427$	0.918781	+	26.3104i	0.0444629	+	1.27325i
$428$	6.15662	−	2.24083i	0.297591	−	0.108314i
$429$	−3.50653	−	1.46790i	−0.169297	−	0.0708711i
$430$	1.00935	−	1.74825i	0.0486752	−	0.0843080i
$431$	−0.244753	−	0.130137i	−0.0117893	−	0.00626850i	0.463566	−	0.886062i	$-0.346570\pi$
$431$	−0.244753	−	0.130137i	−0.0117893	−	0.00626850i	−0.475356	+	0.879794i	$0.657681\pi$
$432$	0.299604	−	1.20165i	0.0144147	−	0.0578142i
$433$	−0.335577	−	1.34593i	−0.0161268	−	0.0646811i	0.961693	−	0.274128i	$-0.0883892\pi$
$433$	−0.335577	−	1.34593i	−0.0161268	−	0.0646811i	−0.977820	+	0.209447i	$0.932834\pi$
$434$	−41.3575	+	21.9902i	−1.98523	+	1.05556i
$435$	−0.00862089	+	0.246870i	−0.000413340	+	0.0118365i
$436$	10.8229	+	7.86329i	0.518322	+	0.376583i
$437$	−4.02484	+	4.03421i	−0.192534	+	0.192982i
$438$	−0.728850	+	2.24317i	−0.0348258	+	0.107183i
$439$	24.9662	+	9.08696i	1.19157	+	0.433697i	0.860275	−	0.509830i	$-0.170292\pi$
$439$	24.9662	+	9.08696i	1.19157	+	0.433697i	0.331297	+	0.943527i	$0.392514\pi$
$440$	−0.881709	−	0.103814i	−0.0420338	−	0.00494913i
$441$	−34.3006	−	28.7816i	−1.63336	−	1.37055i
$442$	12.7694	+	31.6053i	0.607377	+	1.50331i
$443$	−1.28369	−	2.63196i	−0.0609902	−	0.125048i	0.866122	−	0.499833i	$-0.166605\pi$
$443$	−1.28369	−	2.63196i	−0.0609902	−	0.125048i	−0.927112	+	0.374785i	$0.877717\pi$
$444$	0.204241	−	0.0909341i	0.00969287	−	0.00431554i
$445$	−0.867167	+	0.963086i	−0.0411077	+	0.0456547i
$446$	16.9364	+	21.6776i	0.801962	+	1.02646i
$447$	−3.46180	−	0.992656i	−0.163738	−	0.0469510i
$448$	−4.29887	−	1.91398i	−0.203102	−	0.0904270i
$449$	−9.86940	−	10.9611i	−0.465766	−	0.517285i	0.463801	−	0.885939i	$-0.346485\pi$
$449$	−9.86940	−	10.9611i	−0.465766	−	0.517285i	−0.929567	+	0.368654i	$0.879819\pi$
$450$	2.53040	−	14.3506i	0.119284	−	0.676495i
$451$	14.7459	−	1.36400i	0.694358	−	0.0642281i
$452$	−6.87606	−	5.76970i	−0.323423	−	0.271384i
$453$	−0.889767	−	0.125049i	−0.0418049	−	0.00587530i
$454$	−15.0644	+	4.31965i	−0.707008	+	0.202731i
$455$	5.61803	+	4.08173i	0.263377	+	0.191355i
$456$	−0.866323	+	0.265963i	−0.0405693	+	0.0124548i
$457$	5.26316	+	16.1983i	0.246200	+	0.757726i	0.995437	+	0.0954237i	$0.0304206\pi$
$457$	5.26316	+	16.1983i	0.246200	+	0.757726i	−0.749237	+	0.662302i	$0.769579\pi$
$458$	8.25225	+	12.2345i	0.385602	+	0.571679i
$459$	5.50829	+	5.31929i	0.257105	+	0.248283i
$460$	0.296778	−	0.185447i	0.0138373	−	0.00864652i
$461$	−2.61953	+	2.19805i	−0.122004	+	0.102373i	−0.701748	−	0.712425i	$-0.747597\pi$
$461$	−2.61953	+	2.19805i	−0.122004	+	0.102373i	0.579745	+	0.814798i	$0.303152\pi$
$462$	−0.491654	+	3.20729i	−0.0228738	+	0.149217i
$463$	2.91194	−	5.04362i	0.135329	−	0.234397i	−0.790394	−	0.612599i	$-0.790124\pi$
$463$	2.91194	−	5.04362i	0.135329	−	0.234397i	0.925723	+	0.378202i	$0.123457\pi$
$464$	−4.34168	+	0.922852i	−0.201557	+	0.0428423i
$465$	0.309768	−	0.459250i	0.0143652	−	0.0212972i
$466$	−16.3335	−	4.68354i	−0.756633	−	0.216961i
$467$	24.6177	−	27.3407i	1.13917	−	1.26518i	0.179589	−	0.983742i	$-0.442523\pi$
$467$	24.6177	−	27.3407i	1.13917	−	1.26518i	0.959581	−	0.281434i	$-0.0908100\pi$
$468$	−15.9443	−	3.38907i	−0.737027	−	0.156660i
$469$	−13.1206	+	12.6704i	−0.605851	+	0.585064i
$470$	−0.711423	+	2.85336i	−0.0328155	+	0.131616i
$471$	−0.885607	+	0.553389i	−0.0408066	+	0.0254988i
$472$	1.51732	+	8.60513i	0.0698402	+	0.396083i
$473$	0.312199	−	25.0101i	0.0143549	−	1.14997i
$474$	−1.34724			−0.0618808
$475$	−20.0464	+	7.72182i	−0.919790	+	0.354301i
$476$	23.5392	−	17.1022i	1.07892	−	0.783880i
$477$	4.21005	+	6.24166i	0.192765	+	0.285786i
$478$	−10.7790	+	5.73127i	−0.493018	+	0.262142i
$479$	−1.12183	+	2.77663i	−0.0512578	+	0.126867i	−0.950640	−	0.310295i	$-0.899572\pi$
$479$	−1.12183	+	2.77663i	−0.0512578	+	0.126867i	0.899382	+	0.437163i	$0.144017\pi$
$480$	0.0555163	−	0.00388208i	0.00253396	−	0.000177192i
$481$	−2.59883	−	5.32839i	−0.118497	−	0.242954i
$482$	2.01436	+	2.23717i	0.0917515	+	0.101900i
$483$	−0.639510	−	1.10766i	−0.0290987	−	0.0504004i
$484$	−10.1576	+	4.22187i	−0.461707	+	0.191903i
$485$	−1.82676	+	0.664886i	−0.0829489	+	0.0301909i
$486$	−5.38562	+	1.14475i	−0.244297	+	0.0519269i
$487$	1.29098	+	12.2829i	0.0585000	+	0.556591i	0.984041	+	0.177943i	$0.0569442\pi$
$487$	1.29098	+	12.2829i	0.0585000	+	0.556591i	−0.925541	+	0.378648i	$0.876389\pi$
$488$	4.02442	−	3.88633i	0.182177	−	0.175926i
$489$	1.84618	+	1.15362i	0.0834872	+	0.0521686i
$490$	1.51853	−	3.75849i	0.0686001	−	0.169791i
$491$	0.802430	−	1.64522i	0.0362131	−	0.0742480i	−0.879920	−	0.475121i	$-0.842404\pi$
$491$	0.802430	−	1.64522i	0.0362131	−	0.0742480i	0.916134	+	0.400873i	$0.131293\pi$
$492$	−0.892336	+	0.255873i	−0.0402296	+	0.0115357i
$493$	8.48098	−	26.1018i	0.381964	−	1.17556i
$494$	7.84992	+	22.7120i	0.353185	+	1.02186i
$495$	0.866952	+	2.47773i	0.0389666	+	0.111366i
$496$	9.35366	+	3.40445i	0.419992	+	0.152864i
$497$	19.6627	+	2.76342i	0.881994	+	0.123956i
$498$	−0.0185086	−	0.00129425i	−0.000829392	−	5.79967e-5i
$499$	33.3014	−	2.32866i	1.49078	−	0.104245i	0.699029	−	0.715093i	$-0.253616\pi$
$499$	33.3014	−	2.32866i	1.49078	−	0.104245i	0.791748	+	0.610848i	$0.209171\pi$
$500$	2.63177	−	0.369871i	0.117696	−	0.0165412i
$501$	2.77177	+	0.589159i	0.123834	+	0.0263217i
$502$	1.98241	−	18.8614i	0.0884793	−	0.841824i
$503$	3.19910	−	4.74286i	0.142641	−	0.211473i	−0.750947	−	0.660363i	$-0.770402\pi$
$503$	3.19910	−	4.74286i	0.142641	−	0.211473i	0.893587	+	0.448889i	$0.148180\pi$
$504$	0.485581	+	13.9052i	0.0216295	+	0.619388i
$505$	1.16702	+	2.02134i	0.0519318	+	0.0899485i
$506$	2.08325	−	3.80275i	0.0926119	−	0.169053i
$507$	0.627906	−	3.56103i	0.0278863	−	0.158151i
$508$	−0.448848	−	1.11094i	−0.0199144	−	0.0492899i
$509$	16.4222	+	1.14835i	0.727902	+	0.0508999i	0.428899	−	0.903352i	$-0.358901\pi$
$509$	16.4222	+	1.14835i	0.727902	+	0.0508999i	0.299003	+	0.954252i	$0.403346\pi$
$510$	−0.150845	+	0.309279i	−0.00667954	+	0.0136951i
$511$	1.86311	−	53.3524i	0.0824190	−	2.36017i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	3.68615	+	3.94371i	0.162748	+	0.174119i
$514$	6.91128	−	5.02134i	0.304844	−	0.221482i
$515$	−0.831732	+	1.06457i	−0.0366505	+	0.0469105i
$516$	0.272261	+	1.54407i	0.0119856	+	0.0679738i
$517$	9.60516	+	35.1471i	0.422435	+	1.54577i
$518$	−3.87642	+	3.25270i	−0.170320	+	0.142915i
$519$	−0.964635	−	0.512905i	−0.0423428	−	0.0225141i
$520$	−0.154254	−	1.46763i	−0.00676449	−	0.0643598i
$521$	−0.986652	+	9.38737i	−0.0432260	+	0.411268i	0.951418	+	0.307904i	$0.0996275\pi$
$521$	−0.986652	+	9.38737i	−0.0432260	+	0.411268i	−0.994644	+	0.103364i	$0.967039\pi$
$522$	8.08004	+	10.3420i	0.353654	+	0.452656i
$523$	9.95168	+	12.7376i	0.435157	+	0.556975i	0.954739	−	0.297445i	$-0.0961346\pi$
$523$	9.95168	+	12.7376i	0.435157	+	0.556975i	−0.519582	+	0.854420i	$0.673912\pi$
$524$	1.53947	−	14.6471i	0.0672521	−	0.639861i
$525$	−0.503989	−	4.79513i	−0.0219959	−	0.209277i
$526$	22.5981	+	12.0156i	0.985325	+	0.523907i
$527$	−47.1477	+	39.5616i	−2.05378	+	1.72333i
$528$	0.576420	−	0.378419i	0.0250855	−	0.0164686i
$529$	−3.69711	−	20.9674i	−0.160744	−	0.911625i
$530$	−0.419631	+	0.537103i	−0.0182276	+	0.0233303i
$531$	20.9017	−	15.1860i	0.907058	−	0.659016i
$532$	17.1895	−	11.1914i	0.745261	−	0.485210i
$533$	7.60662	+	23.4108i	0.329479	+	1.01403i
$534$	0.0351280	−	1.00593i	0.00152014	−	0.0435310i
$535$	0.768806	−	1.57629i	0.0332384	−	0.0681488i
$536$	3.86665	+	0.270383i	0.167014	+	0.0116788i
$537$	1.12786	+	2.79156i	0.0486709	+	0.120465i
$538$	−5.01082	+	28.4178i	−0.216032	+	1.22518i
$539$	−6.36870	−	49.8202i	−0.274319	−	2.14591i
$540$	−0.165753	−	0.287092i	−0.00713287	−	0.0123545i
$541$	−0.663693	−	19.0057i	−0.0285344	−	0.817118i	−0.926332	−	0.376709i	$-0.877056\pi$
$541$	−0.663693	−	19.0057i	−0.0285344	−	0.817118i	0.897797	−	0.440409i	$-0.145167\pi$
$542$	2.27980	−	3.37995i	0.0979259	−	0.145181i
$543$	0.333081	−	3.16905i	0.0142939	−	0.135997i
$544$	−6.04804	−	1.28555i	−0.259308	−	0.0551175i
$545$	3.54615	−	0.498378i	0.151900	−	0.0213482i
$546$	−5.38034	+	0.376230i	−0.230257	+	0.0161011i
$547$	0.406741	+	0.0284421i	0.0173910	+	0.00121610i	0.0784493	−	0.996918i	$-0.475003\pi$
$547$	0.406741	+	0.0284421i	0.0173910	+	0.00121610i	−0.0610583	+	0.998134i	$0.519448\pi$
$548$	−4.18047	−	0.587527i	−0.178581	−	0.0250979i
$549$	−15.5444	−	5.65769i	−0.663417	−	0.241464i
$550$	13.0050	−	9.90172i	0.554536	−	0.422211i
$551$	6.91261	−	18.0707i	0.294487	−	0.769838i
$552$	−0.0839916	+	0.258499i	−0.00357492	+	0.0110025i
$553$	29.3123	−	8.40516i	1.24649	−	0.357424i
$554$	−3.99639	+	8.19382i	−0.169790	+	0.348122i
$555$	0.0224186	−	0.0554879i	0.000951615	−	0.00235533i
$556$	8.25815	+	5.16027i	0.350224	+	0.218844i
$557$	7.53140	−	7.27299i	0.319116	−	0.308166i	−0.517796	−	0.855504i	$-0.673248\pi$
$557$	7.53140	−	7.27299i	0.319116	−	0.308166i	0.836912	+	0.547338i	$0.184359\pi$
$558$	−3.07644	−	29.2704i	−0.130236	−	1.23911i
$559$	40.6670	−	8.64403i	1.72003	−	0.365603i
$560$	−1.18366	+	0.430818i	−0.0500189	+	0.0182054i
$561$	0.244297	+	4.25651i	0.0103142	+	0.179710i
$562$	−14.7030	−	25.4663i	−0.620207	−	1.07423i
$563$	1.43588	+	1.59470i	0.0605150	+	0.0672087i	0.772642	−	0.634842i	$-0.218935\pi$
$563$	1.43588	+	1.59470i	0.0605150	+	0.0672087i	−0.712127	+	0.702051i	$0.752268\pi$
$564$	−1.00124	−	2.05284i	−0.0421597	−	0.0864402i
$565$	−2.39687	+	0.167606i	−0.100837	+	0.00705123i
$566$	1.69696	−	4.20013i	0.0713286	−	0.176544i
$567$	35.7854	−	19.0274i	1.50285	−	0.799077i
$568$	−2.35955	−	3.49817i	−0.0990044	−	0.146780i
$569$	−17.5876	+	12.7782i	−0.737311	+	0.535688i	−0.891868	−	0.452296i	$-0.850605\pi$
$569$	−17.5876	+	12.7782i	−0.737311	+	0.535688i	0.154557	+	0.987984i	$0.450605\pi$
$570$	−0.117359	+	0.212302i	−0.00491562	+	0.00889237i
$571$	−39.0258			−1.63318			−0.816589	−	0.577219i	$-0.804138\pi$
$571$	−39.0258			−1.63318			−0.816589	+	0.577219i	$0.804138\pi$
$572$	−10.5618	−	14.9254i	−0.441611	−	0.624061i
$573$	−0.642995	−	3.64661i	−0.0268615	−	0.152339i
$574$	17.8185	−	11.1342i	0.743728	−	0.464733i
$575$	−1.55872	+	6.25169i	−0.0650032	+	0.260714i
$576$	2.12693	−	2.05395i	0.0886220	−	0.0855812i
$577$	−37.6911	−	8.01150i	−1.56910	−	0.333523i	−0.660382	−	0.750930i	$-0.729606\pi$
$577$	−37.6911	−	8.01150i	−1.56910	−	0.333523i	−0.908720	+	0.417407i	$0.862939\pi$
$578$	14.2066	−	15.7780i	0.590917	−	0.656280i
$579$	−2.60253	−	0.746264i	−0.108158	−	0.0310137i
$580$	−0.664406	+	0.985022i	−0.0275879	+	0.0409008i
$581$	0.410772	−	0.0873123i	0.0170417	−	0.00362233i
$582$	0.754933	−	1.30758i	0.0312930	−	0.0542010i
$583$	−1.27962	+	8.34757i	−0.0529965	+	0.345721i
$584$	−8.69057	+	7.29226i	−0.359618	+	0.301756i
$585$	−3.70033	+	2.31223i	−0.152990	+	0.0955988i
$586$	2.78006	+	2.68467i	0.114843	+	0.110903i
$587$	10.3058	+	15.2789i	0.425365	+	0.630630i	0.979416	−	0.201853i	$-0.0646964\pi$
$587$	10.3058	+	15.2789i	0.425365	+	0.630630i	−0.554051	+	0.832483i	$0.686919\pi$
$588$	0.972909	+	2.99431i	0.0401221	+	0.123483i
$589$	−34.6211	+	26.1520i	−1.42654	+	1.07757i
$590$	1.89227	+	1.37481i	0.0779034	+	0.0566001i
$591$	1.82625	−	0.523668i	0.0751218	−	0.0215408i
$592$	1.06489	+	0.149661i	0.0437668	+	0.00615102i
$593$	14.2563	+	11.9625i	0.585436	+	0.491239i	0.886727	−	0.462293i	$-0.152973\pi$
$593$	14.2563	+	11.9625i	0.585436	+	0.491239i	−0.301291	+	0.953532i	$0.597418\pi$
$594$	−3.53122	−	2.09795i	−0.144888	−	0.0860799i
$595$	1.35246	−	7.67016i	0.0554453	−	0.314446i
$596$	−11.5907	−	12.8728i	−0.474775	−	0.527291i
$597$	1.51250	+	0.673409i	0.0619025	+	0.0275608i
$598$	6.92815	+	1.98662i	0.283313	+	0.0812387i
$599$	−19.7587	−	25.2899i	−0.807317	−	1.03332i	−0.998658	−	0.0517951i	$-0.983506\pi$
$599$	−19.7587	−	25.2899i	−0.807317	−	1.03332i	0.191341	−	0.981524i	$-0.438716\pi$
$600$	−0.685604	+	0.761440i	−0.0279897	+	0.0310857i
$601$	−15.2793	+	6.80277i	−0.623254	+	0.277491i	−0.693968	−	0.720006i	$-0.744139\pi$
$601$	−15.2793	+	6.80277i	−0.623254	+	0.277491i	0.0707137	+	0.997497i	$0.477472\pi$
$602$	−15.5568	−	31.8961i	−0.634047	−	1.29999i
$603$	−4.29327	−	10.6262i	−0.174836	−	0.432733i
$604$	−3.31067	−	2.77799i	−0.134709	−	0.113035i
$605$	−1.17083	+	2.70171i	−0.0476011	+	0.109840i
$606$	−1.70348	−	0.620017i	−0.0691992	−	0.0251865i
$607$	4.34467	−	13.3715i	0.176345	−	0.542733i	−0.823348	−	0.567537i	$-0.807896\pi$
$607$	4.34467	−	13.3715i	0.176345	−	0.542733i	0.999692	+	0.0248042i	$0.00789624\pi$
$608$	−4.21168	−	1.12327i	−0.170806	−	0.0455547i
$609$	3.51314	+	2.55245i	0.142360	+	0.103430i
$610$	0.0522644	−	1.49666i	0.00211613	−	0.0605979i
$611$	−53.4752	+	28.4333i	−2.16338	+	1.15029i
$612$	4.42287	+	17.7392i	0.178784	+	0.717063i
$613$	−3.00592	+	12.0561i	−0.121408	+	0.486941i	0.878549	+	0.477653i	$0.158512\pi$
$613$	−3.00592	+	12.0561i	−0.121408	+	0.486941i	−0.999957	+	0.00928871i	$0.997043\pi$
$614$	−10.5397	−	5.60407i	−0.425349	−	0.226162i
$615$	−0.124244	+	0.215197i	−0.00501000	+	0.00867757i
$616$	−10.1805	+	11.8295i	−0.410182	+	0.476625i
$617$	−44.3005	+	16.1241i	−1.78347	+	0.649131i	−0.783870	+	0.620925i	$0.786757\pi$
$617$	−44.3005	+	16.1241i	−1.78347	+	0.649131i	−0.999602	+	0.0282060i	$0.991021\pi$
$618$	−0.0366187	−	1.04862i	−0.00147302	−	0.0421818i
$619$	17.5739	+	7.82442i	0.706356	+	0.314490i	0.728290	−	0.685270i	$-0.240316\pi$
$619$	17.5739	+	7.82442i	0.706356	+	0.314490i	−0.0219337	+	0.999759i	$0.506982\pi$
$620$	2.43413	−	1.08375i	0.0977572	−	0.0435243i
$621$	1.60331	−	0.225330i	0.0643386	−	0.00904220i
$622$	−25.1206	−	15.6971i	−1.00724	−	0.629396i
$623$	5.51153	+	22.1056i	0.220815	+	0.885640i
$624$	0.824477	+	0.796189i	0.0330055	+	0.0318731i
$625$	−14.7330	+	18.8574i	−0.589319	+	0.754294i
$626$	−15.7712			−0.630343
$627$	0.0184339	+	3.00556i	0.000736179	+	0.120031i
$628$	−5.02296			−0.200438
$629$	−4.09360	+	5.23956i	−0.163222	+	0.208915i
$630$	2.67914	+	2.58721i	0.106739	+	0.103077i
$631$	−4.55821	−	18.2820i	−0.181460	−	0.727795i	−0.990203	−	0.139633i	$-0.955408\pi$
$631$	−4.55821	−	18.2820i	−0.181460	−	0.727795i	0.808744	−	0.588161i	$-0.200148\pi$
$632$	−5.49547	−	3.43395i	−0.218598	−	0.136595i
$633$	−5.70349	+	0.801574i	−0.226693	+	0.0318597i
$634$	11.9457	−	5.31856i	0.474424	−	0.211227i
$635$	−0.293003	−	0.130453i	−0.0116275	−	0.00517689i
$636$	−0.0184751	−	0.529059i	−0.000732587	−	0.0209785i
$637$	78.4509	−	28.5538i	3.10834	−	1.13134i
$638$	−1.21014	+	14.6716i	−0.0479098	+	0.580854i
$639$	−6.23814	+	10.8048i	−0.246777	+	0.427431i
$640$	0.236349	+	0.125669i	0.00934251	+	0.00496750i
$641$	4.94594	−	19.8371i	0.195353	−	0.783517i	−0.790017	−	0.613085i	$-0.789928\pi$
$641$	4.94594	−	19.8371i	0.195353	−	0.783517i	0.985369	−	0.170432i	$-0.0545163\pi$
$642$	0.329528	+	1.32167i	0.0130054	+	0.0521620i
$643$	−16.0824	+	8.55118i	−0.634229	+	0.337226i	−0.755262	−	0.655423i	$-0.772490\pi$
$643$	−16.0824	+	8.55118i	−0.634229	+	0.337226i	0.121033	+	0.992648i	$0.461379\pi$
$644$	0.214702	−	6.14825i	0.00846043	−	0.242275i
$645$	0.339540	+	0.246690i	0.0133694	+	0.00971342i
$646$	19.0356	−	19.0799i	0.748946	−	0.750689i
$647$	12.6529	−	38.9418i	0.497439	−	1.53096i	−0.315683	−	0.948865i	$-0.602234\pi$
$647$	12.6529	−	38.9418i	0.497439	−	1.53096i	0.813122	−	0.582094i	$-0.197766\pi$
$648$	−8.09344	−	2.94577i	−0.317940	−	0.115721i
$649$	28.7815	+	3.38877i	1.12977	+	0.133021i
$650$	20.8132	+	17.4643i	0.816361	+	0.685008i
$651$	−3.64801	−	9.02915i	−0.142977	−	0.353880i
$652$	4.59023	+	9.41137i	0.179767	+	0.368578i
$653$	3.68479	−	1.64057i	0.144197	−	0.0642006i	−0.333369	−	0.942796i	$-0.608186\pi$
$653$	3.68479	−	1.64057i	0.144197	−	0.0642006i	0.477566	+	0.878596i	$0.341519\pi$
$654$	−1.86105	+	2.06690i	−0.0727727	+	0.0808223i
$655$	−2.42715	−	3.10661i	−0.0948367	−	0.121385i
$656$	−4.29207	−	1.23073i	−0.167577	−	0.0480520i
$657$	30.6438	+	13.6435i	1.19553	+	0.532284i
$658$	34.5915	+	38.4177i	1.34852	+	1.49768i
$659$	5.16446	−	29.2891i	0.201179	−	1.14094i	−0.702162	−	0.712017i	$-0.747782\pi$
$659$	5.16446	−	29.2891i	0.201179	−	1.14094i	0.903341	−	0.428924i	$-0.141107\pi$
$660$	0.0406261	−	0.180050i	0.00158137	−	0.00700843i
$661$	8.22983	+	6.90565i	0.320103	+	0.268599i	0.788653	−	0.614839i	$-0.210779\pi$
$661$	8.22983	+	6.90565i	0.320103	+	0.268599i	−0.468550	+	0.883437i	$0.655223\pi$
$662$	7.42699	+	1.04379i	0.288658	+	0.0405682i
$663$	−6.81235	+	1.95341i	−0.264570	+	0.0758641i
$664$	−0.0721989	−	0.0524555i	−0.00280186	−	0.00203567i
$665$	1.22890	−	5.35130i	0.0476546	−	0.207515i
$666$	−0.982547	−	3.02397i	−0.0380729	−	0.117176i
$667$	−3.24494	−	4.81082i	−0.125645	−	0.186276i
$668$	9.80452	+	9.46811i	0.379348	+	0.366332i
$669$	−4.85021	+	3.03075i	−0.187520	+	0.117176i
$670$	0.794817	−	0.666930i	0.0307064	−	0.0257658i
$671$	−8.50595	−	16.4907i	−0.328369	−	0.636616i
$672$	0.489165	−	0.847258i	0.0188699	−	0.0326837i
$673$	−24.4524	+	5.19752i	−0.942570	+	0.200349i	−0.653473	−	0.756950i	$-0.726689\pi$
$673$	−24.4524	+	5.19752i	−0.942570	+	0.200349i	−0.289098	+	0.957300i	$0.593355\pi$
$674$	−11.0074	+	16.3191i	−0.423989	+	0.628589i
$675$	5.86699	+	1.68233i	0.225821	+	0.0647530i
$676$	11.6379	−	12.9252i	0.447611	−	0.497122i
$677$	−16.7257	−	3.55516i	−0.642821	−	0.136636i	−0.125044	−	0.992151i	$-0.539907\pi$
$677$	−16.7257	−	3.55516i	−0.642821	−	0.136636i	−0.517777	+	0.855515i	$0.673240\pi$
$678$	1.34240	−	1.29634i	0.0515545	−	0.0497856i
$679$	−8.26754	+	33.1593i	−0.317279	+	1.27254i
$680$	−1.40362	+	0.877079i	−0.0538263	+	0.0336344i
$681$	−0.565773	−	3.20866i	−0.0216805	−	0.122956i
$682$	19.7367	−	26.4642i	0.755759	−	1.01337i
$683$	10.4332			0.399215			0.199607	−	0.979876i	$-0.436033\pi$
$683$	10.4332			0.399215			0.199607	+	0.979876i	$0.436033\pi$
$684$	2.47390	+	12.6486i	0.0945920	+	0.483632i
$685$	−0.914216	+	0.664217i	−0.0349304	+	0.0253784i
$686$	−21.4290	−	31.7698i	−0.818162	−	1.21298i
$687$	−2.70899	+	1.44039i	−0.103354	+	0.0549544i
$688$	−2.82507	+	6.99229i	−0.107705	+	0.266579i
$689$	−14.0033	+	0.979209i	−0.533485	+	0.0373049i
$690$	0.0318944	+	0.0653931i	0.00121420	+	0.00248947i
$691$	2.42424	+	2.69240i	0.0922226	+	0.102424i	0.787489	−	0.616328i	$-0.211380\pi$
$691$	2.42424	+	2.69240i	0.0922226	+	0.102424i	−0.695267	+	0.718752i	$0.744714\pi$
$692$	−2.62746	−	4.55090i	−0.0998812	−	0.172999i
$693$	44.6329	+	11.7219i	1.69546	+	0.445277i
$694$	−6.54923	+	2.38373i	−0.248606	+	0.0904850i
$695$	2.54968	−	0.541951i	0.0967148	−	0.0205574i
$696$	−0.0964604	−	0.917759i	−0.00365632	−	0.0347876i
$697$	19.8596	−	19.1782i	0.752235	−	0.726425i
$698$	−1.57840	−	0.986291i	−0.0597431	−	0.0373317i
$699$	1.32334	−	3.27539i	0.0500535	−	0.123887i
$700$	10.1664	−	20.8442i	0.384254	−	0.787837i
$701$	−11.0023	+	3.15486i	−0.415551	+	0.119157i	−0.476897	−	0.878959i	$-0.658238\pi$
$701$	−11.0023	+	3.15486i	−0.415551	+	0.119157i	0.0613460	+	0.998117i	$0.480461\pi$
$702$	2.10979	−	6.49325i	0.0796287	−	0.245072i
$703$	−3.07108	+	3.54118i	−0.115828	+	0.133558i
$704$	3.31579	−	0.0743669i	0.124969	−	0.00280281i
$705$	−0.574513	−	0.209105i	−0.0216374	−	0.00787537i
$706$	−30.1637	−	4.23924i	−1.13523	−	0.159546i
$707$	40.9313	+	2.86219i	1.53938	+	0.107644i
$708$	−1.81221	+	0.126722i	−0.0681069	+	0.00476250i
$709$	34.2948	−	4.81982i	1.28797	−	0.181012i	0.538260	−	0.842779i	$-0.319082\pi$
$709$	34.2948	−	4.81982i	1.28797	−	0.181012i	0.749710	+	0.661767i	$0.230193\pi$
$710$	−1.10482	−	0.234836i	−0.0414630	−	0.00881323i
$711$	−2.00280	+	19.0554i	−0.0751108	+	0.714632i
$712$	2.70729	−	4.01372i	0.101460	−	0.150421i
$713$	0.454158	+	13.0054i	0.0170084	+	0.487056i
$714$	3.02458	+	5.23873i	0.113192	+	0.196055i
$715$	−4.80905	−	0.909999i	−0.179848	−	0.0340320i
$716$	−2.51472	+	14.2617i	−0.0939796	+	0.532985i
$717$	−0.950776	−	2.35325i	−0.0355074	−	0.0878839i
$718$	−6.13152	−	0.428758i	−0.228826	−	0.0160011i
$719$	12.3918	−	25.4070i	0.462137	−	0.947522i	−0.532725	−	0.846288i	$-0.678832\pi$
$719$	12.3918	−	25.4070i	0.462137	−	0.947522i	0.994863	−	0.101234i	$-0.0322790\pi$
$720$	0.0276221	−	0.790992i	0.00102941	−	0.0294785i
$721$	7.33887	+	22.5867i	0.273314	+	0.841174i
$722$	14.0902	−	12.7463i	0.524382	−	0.474367i
$723$	−0.506342	+	0.367879i	−0.0188311	+	0.0136816i
$724$	9.43618	−	12.0778i	0.350693	−	0.448866i
$725$	−3.79861	−	21.5430i	−0.141077	−	0.800086i
$726$	−0.652189	−	2.19197i	−0.0242050	−	0.0813515i
$727$	7.77160	−	6.52115i	0.288233	−	0.241856i	−0.487194	−	0.873294i	$-0.661979\pi$
$727$	7.77160	−	6.52115i	0.288233	−	0.241856i	0.775426	+	0.631438i	$0.217535\pi$
$728$	−22.9056	−	12.1791i	−0.848940	−	0.451389i
$729$	2.58121	+	24.5586i	0.0956004	+	0.909577i
$730$	−0.317430	+	3.02014i	−0.0117486	+	0.111780i
$731$	−28.7082	−	36.7448i	−1.06181	−	1.35906i
$732$	0.716097	+	0.916562i	0.0264677	+	0.0338771i
$733$	1.82484	−	17.3622i	0.0674022	−	0.641289i	−0.907713	−	0.419591i	$-0.862174\pi$
$733$	1.82484	−	17.3622i	0.0674022	−	0.641289i	0.975115	−	0.221698i	$-0.0711598\pi$
$734$	−0.536280	−	5.10236i	−0.0197944	−	0.188332i
$735$	0.744121	+	0.395656i	0.0274473	+	0.0145940i
$736$	−1.00149	+	0.840349i	−0.0369154	+	0.0309757i
$737$	4.54730	−	12.0244i	0.167502	−	0.442926i
$738$	2.29253	+	13.0016i	0.0843891	+	0.478594i
$739$	19.4316	−	24.8713i	0.714802	−	0.914905i	−0.284236	−	0.958754i	$-0.591740\pi$
$739$	19.4316	−	24.8713i	0.714802	−	0.914905i	0.999038	+	0.0438494i	$0.0139622\pi$
$740$	0.232878	−	0.169196i	0.00856077	−	0.00621976i
$741$	−4.86663	+	1.12951i	−0.178780	+	0.0414936i
$742$	3.70266	+	11.3956i	0.135929	+	0.418346i
$743$	0.851207	−	24.3754i	0.0312278	−	0.894246i	−0.878178	−	0.478335i	$-0.841241\pi$
$743$	0.851207	−	24.3754i	0.0312278	−	0.894246i	0.909405	−	0.415911i	$-0.136537\pi$
$744$	−0.907191	+	1.86002i	−0.0332592	+	0.0681916i
$745$	−4.62550	−	0.323447i	−0.169465	−	0.0118502i
$746$	−9.41755	−	23.3093i	−0.344801	−	0.853413i
$747$	−0.0458207	+	0.259862i	−0.00167649	+	0.00950785i
$748$	−9.85281	+	17.9852i	−0.360254	+	0.657605i
$749$	−15.4152	−	26.7000i	−0.563261	−	0.975596i
$750$	0.0192831	+	0.552194i	0.000704117	+	0.0201633i
$751$	−21.4064	+	31.7363i	−0.781131	+	1.15807i	0.202746	+	0.979231i	$0.435013\pi$
$751$	−21.4064	+	31.7363i	−0.781131	+	1.15807i	−0.983878	+	0.178843i	$0.942764\pi$
$752$	1.14834	−	10.9257i	0.0418755	−	0.398419i
$753$	3.85678	+	0.819783i	0.140549	+	0.0298746i
$754$	−24.2320	+	3.40559i	−0.882478	+	0.124024i
$755$	−1.15404	+	0.0806985i	−0.0419999	+	0.00293692i
$756$	−5.81349	−	0.406519i	−0.211435	−	0.0147850i
$757$	−22.1135	−	3.10785i	−0.803729	−	0.112957i	−0.274666	−	0.961540i	$-0.588567\pi$
$757$	−22.1135	−	3.10785i	−0.803729	−	0.112957i	−0.529062	+	0.848583i	$0.677456\pi$
$758$	−7.76900	−	2.82769i	−0.282183	−	0.102706i
$759$	0.740999	+	0.513383i	0.0268966	+	0.0186346i
$760$	−1.01985	+	0.566860i	−0.0369937	+	0.0205622i
$761$	4.34575	−	13.3748i	0.157533	−	0.484837i	−0.840876	−	0.541229i	$-0.817959\pi$
$761$	4.34575	−	13.3748i	0.157533	−	0.484837i	0.998409	+	0.0563912i	$0.0179594\pi$
$762$	0.239457	−	0.0686631i	0.00867459	−	0.00248740i
$763$	27.5963	−	56.5809i	0.999054	−	2.04837i
$764$	6.67193	−	16.5136i	0.241382	−	0.597442i
$765$	4.15019	+	2.59333i	0.150050	+	0.0937619i
$766$	−25.4221	+	24.5498i	−0.918538	+	0.887022i
$767$	5.03529	+	47.9076i	0.181814	+	1.72984i
$768$	−0.203360	+	0.0432255i	−0.00733812	+	0.00155977i
$769$	37.2891	−	13.5721i	1.34468	−	0.489423i	0.433395	−	0.901204i	$-0.357316\pi$
$769$	37.2891	−	13.5721i	1.34468	−	0.489423i	0.911283	+	0.411781i	$0.135093\pi$
$770$	0.239381	+	4.17085i	0.00862670	+	0.150307i
$771$	0.888039	+	1.53813i	0.0319819	+	0.0553944i
$772$	−8.71373	−	9.67758i	−0.313614	−	0.348304i
$773$	6.87715	+	14.1002i	0.247354	+	0.507150i	0.985959	−	0.166988i	$-0.0534041\pi$
$773$	6.87715	+	14.1002i	0.247354	+	0.507150i	−0.738605	+	0.674138i	$0.764515\pi$
$774$	22.2440	−	1.55545i	0.799544	−	0.0559096i
$775$	−18.3769	+	45.4844i	−0.660118	+	1.63385i
$776$	6.41227	−	3.40947i	0.230187	−	0.122393i
$777$	−0.588301	−	0.872192i	−0.0211052	−	0.0312897i
$778$	−6.90469	+	5.01655i	−0.247545	+	0.179852i
$779$	14.6738	−	12.7857i	0.525744	−	0.458096i
$780$	0.306806			0.0109854
$781$	−13.3627	+	4.15813i	−0.478154	+	0.148790i
$782$	−1.40370	−	7.96075i	−0.0501960	−	0.284676i
$783$	−4.66172	+	2.91297i	−0.166596	+	0.104101i
$784$	−3.66357	+	14.6938i	−0.130842	+	0.524777i
$785$	−0.967191	+	0.934006i	−0.0345205	+	0.0333361i
$786$	2.99504	+	0.636615i	0.106829	+	0.0227073i
$787$	−34.7156	+	38.5556i	−1.23748	+	1.37436i	−0.335809	+	0.941930i	$0.609010\pi$
$787$	−34.7156	+	38.5556i	−1.23748	+	1.37436i	−0.901669	+	0.432428i	$0.857657\pi$
$788$	8.78412	+	2.51881i	0.312921	+	0.0897288i
$789$	−2.97550	+	4.41136i	−0.105931	+	0.157049i
$790$	−1.69671	+	0.360646i	−0.0603662	+	0.0128312i
$791$	−21.1193	+	36.5797i	−0.750917	+	1.30063i
$792$	−4.49545	−	8.71543i	−0.159739	−	0.309689i
$793$	23.6269	−	19.8253i	0.839015	−	0.704017i
$794$	18.5131	−	11.5683i	0.657006	−	0.410543i
$795$	−0.101934	−	0.0984370i	−0.00361524	−	0.00349120i
$796$	4.45314	+	6.60205i	0.157837	+	0.234003i
$797$	14.4894	+	44.5938i	0.513241	+	1.57959i	0.786460	+	0.617641i	$0.211912\pi$
$797$	14.4894	+	44.5938i	0.513241	+	1.57959i	−0.273219	+	0.961952i	$0.588088\pi$
$798$	1.94043	+	3.79739i	0.0686905	+	0.134426i
$799$	54.9544	+	39.9267i	1.94415	+	1.41250i
$800$	−4.73743	+	1.35844i	−0.167493	+	0.0480280i
$801$	−14.1757	−	1.99226i	−0.500874	−	0.0703932i
$802$	−8.96482	−	7.52238i	−0.316559	−	0.265624i
$803$	14.8737	+	34.5616i	0.524883	+	1.21965i
$804$	−0.139935	+	0.793610i	−0.00493512	+	0.0279885i
$805$	−1.10191	−	1.22379i	−0.0388372	−	0.0431331i
$806$	50.1314	+	22.3199i	1.76580	+	0.786186i
$807$	−5.76689	−	1.65363i	−0.203004	−	0.0582105i
$808$	−5.36825	−	6.87104i	−0.188854	−	0.241723i
$809$	−9.33345	+	10.3658i	−0.328147	+	0.364444i	−0.884531	−	0.466481i	$-0.845522\pi$
$809$	−9.33345	+	10.3658i	−0.328147	+	0.364444i	0.556384	+	0.830925i	$0.312188\pi$
$810$	−2.10618	+	0.937732i	−0.0740037	+	0.0329486i
$811$	11.9026	+	24.4039i	0.417956	+	0.856937i	0.999070	+	0.0431151i	$0.0137282\pi$
$811$	11.9026	+	24.4039i	0.417956	+	0.856937i	−0.581114	+	0.813822i	$0.697383\pi$
$812$	7.82443	+	19.3661i	0.274584	+	0.679618i
$813$	0.649308	+	0.544834i	0.0227722	+	0.0191082i
$814$	1.49120	−	3.23985i	0.0522667	−	0.113557i
$815$	2.63389	+	0.958656i	0.0922610	+	0.0335803i
$816$	0.397241	−	1.22258i	0.0139062	−	0.0427989i
$817$	−18.8861	−	26.9055i	−0.660740	−	0.941305i
$818$	−23.7536	−	17.2580i	−0.830524	−	0.603411i
$819$	−2.67698	+	76.6587i	−0.0935413	+	2.67867i
$820$	−1.05531	+	0.561117i	−0.0368529	+	0.0195951i
$821$	3.52093	+	14.1217i	0.122881	+	0.492850i	0.999923	+	0.0124349i	$0.00395826\pi$
$821$	3.52093	+	14.1217i	0.122881	+	0.492850i	−0.877041	+	0.480415i	$0.840486\pi$
$822$	0.212329	−	0.851605i	0.00740582	−	0.0297031i
$823$	7.38342	+	3.92583i	0.257370	+	0.136846i	0.593144	−	0.805097i	$-0.297887\pi$
$823$	7.38342	+	3.92583i	0.257370	+	0.136846i	−0.335774	+	0.941943i	$0.608998\pi$
$824$	2.52344	−	4.37073i	0.0879082	−	0.152261i
$825$	1.76470	+	2.90416i	0.0614390	+	0.101110i
$826$	38.6381	−	14.0631i	1.34439	−	0.489319i
$827$	0.924910	+	26.4859i	0.0321623	+	0.921007i	0.903053	+	0.429530i	$0.141321\pi$
$827$	0.924910	+	26.4859i	0.0321623	+	0.921007i	−0.870891	+	0.491477i	$0.836457\pi$
$828$	3.53135	+	1.57226i	0.122723	+	0.0546398i
$829$	−24.9963	+	11.1291i	−0.868159	+	0.386529i	−0.791967	−	0.610564i	$-0.790943\pi$
$829$	−24.9963	+	11.1291i	−0.868159	+	0.386529i	−0.0761917	+	0.997093i	$0.524276\pi$
$830$	−0.0236561	+	0.00332465i	−0.000821117	+	0.000115400i
$831$	−1.60734	−	1.00438i	−0.0557580	−	0.0348415i
$832$	1.33370	+	5.34919i	0.0462378	+	0.185450i
$833$	−67.3555	−	65.0445i	−2.33373	−	2.25366i
$834$	−1.24642	+	1.59535i	−0.0431601	+	0.0552424i
$835$	3.64847			0.126260
$836$	−7.58562	+	12.3068i	−0.262354	+	0.425641i
$837$	12.3273			0.426094
$838$	−12.3731	+	15.8369i	−0.427423	+	0.547076i
$839$	12.0307	+	11.6179i	0.415345	+	0.401094i	0.872752	−	0.488163i	$-0.162333\pi$
$839$	12.0307	+	11.6179i	0.415345	+	0.401094i	−0.457407	+	0.889257i	$0.651222\pi$
$840$	−0.0633547	−	0.254102i	−0.00218594	−	0.00876735i
$841$	−7.88531	−	4.92729i	−0.271907	−	0.169906i
$842$	32.6711	−	4.59162i	1.12592	−	0.158238i
$843$	5.58504	−	2.48662i	0.192359	−	0.0856437i
$844$	−25.3080	−	11.2678i	−0.871136	−	0.387855i
$845$	−0.162480	−	4.65283i	−0.00558949	−	0.160062i
$846$	−30.5238	+	11.1097i	−1.04943	+	0.381961i
$847$	27.8651	+	43.6224i	0.957456	+	1.49888i
$848$	1.27314	−	2.20515i	0.0437199	−	0.0757251i
$849$	0.831558	+	0.442147i	0.0285390	+	0.0151745i
$850$	7.37202	−	29.5676i	0.252858	−	1.01416i
$851$	0.340110	+	1.36411i	0.0116588	+	0.0467610i
$852$	0.774574	−	0.411848i	0.0265365	−	0.0141097i
$853$	−1.70907	+	48.9414i	−0.0585175	+	1.67572i	0.515509	+	0.856884i	$0.327603\pi$
$853$	−1.70907	+	48.9414i	−0.0585175	+	1.67572i	−0.574026	+	0.818837i	$0.694619\pi$
$854$	−21.2986	−	15.4743i	−0.728822	−	0.529520i
$855$	2.82834	+	1.97553i	0.0967271	+	0.0675617i
$856$	−2.02460	+	6.23107i	−0.0691993	+	0.212974i
$857$	−24.8223	−	9.03457i	−0.847913	−	0.308615i	−0.118724	−	0.992927i	$-0.537880\pi$
$857$	−24.8223	−	9.03457i	−0.847913	−	0.308615i	−0.729189	+	0.684312i	$0.760103\pi$
$858$	3.31556	−	1.85945i	0.113191	−	0.0634805i
$859$	−14.5108	−	12.1760i	−0.495104	−	0.415441i	0.360747	−	0.932664i	$-0.382522\pi$
$859$	−14.5108	−	12.1760i	−0.495104	−	0.415441i	−0.855851	+	0.517222i	$0.826966\pi$
$860$	0.756219	+	1.87171i	0.0257869	+	0.0638247i
$861$	1.91493	+	3.92619i	0.0652606	+	0.133804i
$862$	0.253235	−	0.112747i	0.00862521	−	0.00384019i
$863$	15.5398	−	17.2587i	0.528982	−	0.587495i	−0.418134	−	0.908385i	$-0.637316\pi$
$863$	15.5398	−	17.2587i	0.528982	−	0.587495i	0.947116	+	0.320891i	$0.103982\pi$
$864$	0.762455	+	0.975898i	0.0259393	+	0.0332007i
$865$	−1.35216	−	0.387725i	−0.0459747	−	0.0131830i
$866$	1.26721	+	0.564197i	0.0430615	+	0.0191722i
$867$	2.95360	+	3.28030i	0.100309	+	0.111405i
$868$	8.13373	−	46.1287i	0.276077	−	1.56571i
$869$	−16.1501	+	14.1806i	−0.547853	+	0.481044i
$870$	−0.189229	−	0.158782i	−0.00641545	−	0.00538320i
$871$	21.1607	+	2.97395i	0.717004	+	0.100768i
$872$	−12.8596	+	3.68743i	−0.435481	+	0.124872i
$873$	−17.3721	−	12.6216i	−0.587958	−	0.427176i
$874$	−0.701059	−	5.65532i	−0.0237137	−	0.191294i
$875$	−3.86458	−	11.8939i	−0.130646	−	0.402089i
$876$	−1.31892	−	1.95537i	−0.0445621	−	0.0660660i
$877$	−18.0771	−	17.4569i	−0.610422	−	0.589477i	0.323820	−	0.946119i	$-0.395033\pi$
$877$	−18.0771	−	17.4569i	−0.610422	−	0.589477i	−0.934241	+	0.356641i	$0.883922\pi$
$878$	−22.5313	+	14.0791i	−0.760396	+	0.475148i
$879$	−0.615509	+	0.516473i	−0.0207606	+	0.0174202i
$880$	0.624641	−	0.630882i	0.0210566	−	0.0212670i
$881$	0.763150	−	1.32181i	0.0257112	−	0.0445331i	−0.852884	−	0.522101i	$-0.825148\pi$
$881$	0.763150	−	1.32181i	0.0257112	−	0.0445331i	0.878595	+	0.477568i	$0.158482\pi$
$882$	43.7977	−	9.30950i	1.47475	−	0.313467i
$883$	13.3295	−	19.7618i	0.448573	−	0.665036i	−0.535144	−	0.844761i	$-0.679743\pi$
$883$	13.3295	−	19.7618i	0.448573	−	0.665036i	0.983717	+	0.179724i	$0.0575206\pi$
$884$	−32.7669	−	9.39576i	−1.10207	−	0.316014i
$885$	−0.325384	+	0.361376i	−0.0109377	+	0.0121475i
$886$	2.86434	+	0.608834i	0.0962293	+	0.0204542i
$887$	8.35738	−	8.07063i	0.280613	−	0.270985i	−0.541010	−	0.841016i	$-0.681958\pi$
$887$	8.35738	−	8.07063i	0.280613	−	0.270985i	0.821623	+	0.570031i	$0.193069\pi$
$888$	−0.0540865	+	0.216929i	−0.00181502	+	0.00727966i
$889$	−4.78155	+	2.98784i	−0.160368	+	0.100209i
$890$	−0.225041	−	1.27627i	−0.00754340	−	0.0427807i
$891$	−17.0776	+	22.8987i	−0.572121	+	0.767135i
$892$	−27.5093			−0.921079
$893$	37.2496	+	30.0925i	1.24651	+	1.00701i
$894$	2.91352	−	2.11680i	0.0974428	−	0.0707963i
$895$	2.16770	+	3.21375i	0.0724583	+	0.107424i
$896$	4.15488	−	2.20919i	0.138805	−	0.0738039i
$897$	−0.561322	+	1.38932i	−0.0187420	+	0.0463881i
$898$	14.7137	−	1.02888i	0.491001	−	0.0343341i
$899$	−19.3683	−	39.7108i	−0.645968	−	1.32443i
$900$	9.75058	+	10.8291i	0.325019	+	0.360971i
$901$	7.87205	+	13.6348i	0.262256	+	0.454241i
$902$	−8.00365	+	12.4597i	−0.266492	+	0.414863i
$903$	6.93306	−	2.52343i	0.230718	−	0.0839743i
$904$	8.77992	−	1.86623i	0.292016	−	0.0620698i
$905$	−0.428852	−	4.08025i	−0.0142555	−	0.135632i
$906$	0.646335	−	0.624159i	0.0214730	−	0.0207363i
$907$	−11.0833	−	6.92560i	−0.368014	−	0.229961i	0.333288	−	0.942825i	$-0.391842\pi$
$907$	−11.0833	−	6.92560i	−0.368014	−	0.229961i	−0.701302	+	0.712864i	$0.747397\pi$
$908$	5.87065	−	14.5304i	0.194824	−	0.482207i
$909$	−11.3019	+	23.1723i	−0.374860	+	0.768577i
$910$	−6.67525	+	1.91410i	−0.221282	+	0.0634517i
$911$	8.53399	−	26.2649i	0.282744	−	0.870195i	−0.704322	−	0.709880i	$-0.748749\pi$
$911$	8.53399	−	26.2649i	0.282744	−	0.870195i	0.987066	−	0.160315i	$-0.0512510\pi$
$912$	0.323780	−	0.846414i	0.0107214	−	0.0280276i
$913$	−0.235495	+	0.179301i	−0.00779376	+	0.00593399i
$914$	−16.0048	−	5.82527i	−0.529391	−	0.192683i
$915$	0.308320	+	0.0433315i	0.0101927	+	0.00143249i
$916$	−14.7215	−	1.02943i	−0.486411	−	0.0340132i
$917$	−69.1356	+	4.83443i	−2.28306	+	0.159647i
$918$	−7.58290	+	1.06571i	−0.250273	+	0.0351736i
$919$	13.8083	+	2.93504i	0.455493	+	0.0968180i	0.429944	−	0.902856i	$-0.358533\pi$
$919$	13.8083	+	2.93504i	0.455493	+	0.0968180i	0.0255489	+	0.999674i	$0.491867\pi$
$920$	−0.0365801	+	0.348037i	−0.00120601	+	0.0114744i
$921$	1.38777	−	2.05745i	0.0457285	−	0.0677953i
$922$	−0.119341	−	3.41747i	−0.00393027	−	0.112548i
$923$	−11.6311	−	20.1456i	−0.382842	−	0.663102i
$924$	−2.22468	−	2.36203i	−0.0731867	−	0.0777051i
$925$	−0.920289	+	5.21922i	−0.0302589	+	0.171607i
$926$	2.18166	+	5.39980i	0.0716939	+	0.177449i
$927$	−14.8861	−	1.04094i	−0.488925	−	0.0341890i
$928$	1.94579	−	3.98945i	0.0638736	−	0.130960i
$929$	−0.0117774	+	0.337260i	−0.000386403	+	0.0110651i	−0.999569	−	0.0293664i	$-0.990651\pi$
$929$	−0.0117774	+	0.337260i	−0.000386403	+	0.0110651i	0.999182	+	0.0404315i	$0.0128733\pi$
$930$	0.171182	+	0.526844i	0.00561327	+	0.0172759i
$931$	−45.0744	−	48.2238i	−1.47725	−	1.58047i
$932$	13.7466	−	9.98746i	0.450283	−	0.327150i
$933$	3.79151	−	4.85291i	0.124129	−	0.158877i
$934$	6.38861	+	36.2316i	0.209042	+	1.18553i
$935$	1.44710	+	5.29523i	0.0473253	+	0.173173i
$936$	12.4869	−	10.4778i	0.408148	−	0.342477i
$937$	37.4672	+	19.9216i	1.22400	+	0.650812i	0.950399	−	0.311032i	$-0.100675\pi$
$937$	37.4672	+	19.9216i	1.22400	+	0.650812i	0.273599	+	0.961844i	$0.411786\pi$
$938$	−1.90657	−	18.1398i	−0.0622517	−	0.592286i
$939$	0.342736	−	3.26092i	0.0111848	−	0.106416i
$940$	−1.81048	−	2.31731i	−0.0590515	−	0.0755824i
$941$	18.4558	+	23.6223i	0.601640	+	0.770065i	0.988360	−	0.152133i	$-0.0486141\pi$
$941$	18.4558	+	23.6223i	0.601640	+	0.770065i	−0.386720	+	0.922197i	$0.626392\pi$
$942$	0.109158	−	1.03857i	0.00355656	−	0.0338384i
$943$	−0.610172	−	5.80540i	−0.0198699	−	0.189050i
$944$	−7.71509	−	4.10219i	−0.251105	−	0.133515i
$945$	−1.19500	+	1.00273i	−0.0388734	+	0.0326187i
$946$	19.5161	+	15.6438i	0.634522	+	0.508624i
$947$	−1.17586	−	6.66865i	−0.0382104	−	0.216702i	0.959724	−	0.280945i	$-0.0906478\pi$
$947$	−1.17586	−	6.66865i	−0.0382104	−	0.216702i	−0.997934	+	0.0642430i	$0.979537\pi$
$948$	0.829444	−	1.06164i	0.0269391	−	0.0344805i
$949$	−50.5983	+	36.7618i	−1.64249	+	1.19334i
$950$	6.25690	−	20.5508i	0.203001	−	0.666755i
$951$	0.840088	+	2.58552i	0.0272417	+	0.0838414i
$952$	−1.01544	+	29.0783i	−0.0329105	+	0.942435i
$953$	−10.5204	+	21.5701i	−0.340790	+	0.698724i	−0.998512	−	0.0545376i	$-0.982632\pi$
$953$	−10.5204	+	21.5701i	−0.340790	+	0.698724i	0.657721	+	0.753261i	$0.271520\pi$
$954$	−7.51046	−	0.525183i	−0.243160	−	0.0170034i
$955$	−1.78595	−	4.42039i	−0.0577921	−	0.143041i
$956$	2.11988	−	12.0225i	0.0685619	−	0.388834i
$957$	−3.00726	−	0.569053i	−0.0972110	−	0.0183949i
$958$	−1.49735	−	2.59348i	−0.0483771	−	0.0837915i
$959$	0.693292	+	19.8533i	0.0223876	+	0.641096i
$960$	−0.0311201	+	0.0461375i	−0.00100440	+	0.00148908i
$961$	−7.11643	+	67.7083i	−0.229562	+	2.18414i
$962$	5.79883	+	1.23258i	0.186962	+	0.0397400i
$963$	19.1835	−	2.69606i	0.618179	−	0.0868794i
$964$	−3.00308	+	0.209996i	−0.0967226	+	0.00676350i
$965$	−3.47738	−	0.243162i	−0.111941	−	0.00782767i
$966$	1.26657	+	0.178005i	0.0407513	+	0.00572722i
$967$	−16.4574	−	5.99001i	−0.529235	−	0.192626i	0.0635616	−	0.997978i	$-0.479754\pi$
$967$	−16.4574	−	5.99001i	−0.529235	−	0.192626i	−0.592797	+	0.805352i	$0.701976\pi$
$968$	2.92674	−	10.6035i	0.0940689	−	0.340809i
$969$	3.53137	+	4.35053i	0.113444	+	0.139759i
$970$	0.600728	−	1.84885i	0.0192882	−	0.0593630i
$971$	34.1588	−	9.79489i	1.09621	−	0.314333i	0.321666	−	0.946853i	$-0.395757\pi$
$971$	34.1588	−	9.79489i	1.09621	−	0.314333i	0.774544	+	0.632520i	$0.217980\pi$
$972$	2.41364	−	4.94870i	0.0774177	−	0.158730i
$973$	17.1657	−	42.4866i	0.550308	−	1.36206i
$974$	−10.4739	−	6.54479i	−0.335604	−	0.209709i
$975$	−4.06331	+	3.92389i	−0.130130	+	0.125665i
$976$	0.584794	+	5.56395i	0.0187188	+	0.178098i
$977$	3.03043	−	0.644137i	0.0969520	−	0.0206078i	−0.159180	−	0.987250i	$-0.550885\pi$
$977$	3.03043	−	0.644137i	0.0969520	−	0.0206078i	0.256132	+	0.966642i	$0.417552\pi$
$978$	−2.04569	+	0.744570i	−0.0654139	+	0.0238087i
$979$	−10.1670	−	12.4284i	−0.324940	−	0.397213i
$980$	2.02683	+	3.51057i	0.0647447	+	0.112141i
$981$	26.4676	+	29.3953i	0.845046	+	0.938519i
$982$	0.802430	+	1.64522i	0.0256066	+	0.0525012i
$983$	27.5521	−	1.92663i	0.878775	−	0.0614500i	0.376762	−	0.926310i	$-0.377037\pi$
$983$	27.5521	−	1.92663i	0.878775	−	0.0614500i	0.502013	+	0.864860i	$0.332593\pi$
$984$	0.347746	−	0.860702i	0.0110857	−	0.0274382i
$985$	2.15978	−	1.14838i	0.0688164	−	0.0365903i
$986$	15.3471	+	22.7530i	0.488750	+	0.724602i
$987$	−8.69515	+	6.31739i	−0.276770	+	0.201085i
$988$	−22.7302	−	7.79711i	−0.723145	−	0.248059i
$989$	−9.85930			−0.313507
$990$	−2.48623	−	0.842276i	−0.0790175	−	0.0267693i
$991$	−7.06133	−	40.0468i	−0.224311	−	1.27213i	−0.863999	−	0.503494i	$-0.832048\pi$
$991$	−7.06133	−	40.0468i	−0.224311	−	1.27213i	0.639688	−	0.768635i	$-0.279064\pi$
$992$	−8.44143	+	5.27479i	−0.268016	+	0.167475i
$993$	−0.377221	+	1.51295i	−0.0119708	+	0.0480121i
$994$	−14.2832	+	13.7931i	−0.453035	+	0.437491i
$995$	2.08510	+	0.443202i	0.0661022	+	0.0140505i
$996$	0.0124149	−	0.0137882i	0.000393382	−	0.000436896i
$997$	−2.70046	−	0.774344i	−0.0855244	−	0.0245237i	0.232602	−	0.972572i	$-0.425276\pi$
$997$	−2.70046	−	0.774344i	−0.0855244	−	0.0245237i	−0.318127	+	0.948048i	$0.603054\pi$
$998$	−18.6674	+	27.6756i	−0.590906	+	0.876054i
$999$	1.30265	−	0.276888i	0.0412142	−	0.00876034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.u.b.251.6	yes	264
11.5	even	5	inner	418.2.u.b.137.6	yes	264
19.5	even	9	inner	418.2.u.b.119.6	yes	264
209.5	even	45	inner	418.2.u.b.5.6	✓	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.u.b.5.6	✓	264	209.5	even	45	inner
418.2.u.b.119.6	yes	264	19.5	even	9	inner
418.2.u.b.137.6	yes	264	11.5	even	5	inner
418.2.u.b.251.6	yes	264	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.u (of order \(45\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.615661 + 0.788011i) q^{2} +(-0.149553 - 0.144422i) q^{3} +(-0.241922 - 0.970296i) q^{4} +(-0.227007 - 0.141850i) q^{5} +(0.205880 - 0.0289345i) q^{6} +(-4.29887 + 1.91398i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-0.103190 - 2.95498i) q^{9} +O(q^{10})\)	\(q+(-0.615661 + 0.788011i) q^{2} +(-0.149553 - 0.144422i) q^{3} +(-0.241922 - 0.970296i) q^{4} +(-0.227007 - 0.141850i) q^{5} +(0.205880 - 0.0289345i) q^{6} +(-4.29887 + 1.91398i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-0.103190 - 2.95498i) q^{9} +(0.251538 - 0.0915525i) q^{10} +(2.16343 - 2.51387i) q^{11} +(-0.103952 + 0.180049i) q^{12} +(4.86764 + 2.58817i) q^{13} +(1.13841 - 4.56592i) q^{14} +(0.0134634 + 0.0539988i) q^{15} +(-0.882948 + 0.469472i) q^{16} +(0.215789 - 6.17939i) q^{17} +(2.39208 + 1.73795i) q^{18} +(0.374857 - 4.34275i) q^{19} +(-0.0827182 + 0.254580i) q^{20} +(0.919329 + 0.334608i) q^{21} +(0.649018 + 3.25250i) q^{22} +(-1.00149 - 0.840349i) q^{23} +(-0.0778819 - 0.192764i) q^{24} +(-2.16044 - 4.42957i) q^{25} +(-5.03632 + 2.24232i) q^{26} +(-0.828673 + 0.920335i) q^{27} +(2.89712 + 3.70814i) q^{28} +(4.26673 + 1.22346i) q^{29} +(-0.0508405 - 0.0226356i) q^{30} +(-6.66050 - 7.39723i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-0.686606 + 0.0635110i) q^{33} +(4.73657 + 3.97446i) q^{34} +(1.24737 + 0.175306i) q^{35} +(-2.84224 + 0.814998i) q^{36} +(-0.869982 - 0.632079i) q^{37} +(3.19135 + 2.96906i) q^{38} +(-0.354182 - 1.09006i) q^{39} +(-0.149686 - 0.221918i) q^{40} +(3.21188 + 3.10168i) q^{41} +(-0.829670 + 0.518436i) q^{42} +(5.77707 - 4.84754i) q^{43} +(-2.96258 - 1.49101i) q^{44} +(-0.395737 + 0.685437i) q^{45} +(1.27878 - 0.271814i) q^{46} +(-6.14322 + 9.10769i) q^{47} +(0.199849 + 0.0573059i) q^{48} +(10.1330 - 11.2539i) q^{49} +(4.82065 + 1.02466i) q^{50} +(-0.924710 + 0.892982i) q^{51} +(1.33370 - 5.34919i) q^{52} +(-2.15937 + 1.34933i) q^{53} +(-0.215052 - 1.21962i) q^{54} +(-0.847706 + 0.263785i) q^{55} -4.70570 q^{56} +(-0.683248 + 0.595334i) q^{57} +(-3.59096 + 2.60899i) q^{58} +(4.88616 + 7.24403i) q^{59} +(0.0491377 - 0.0261270i) q^{60} +(2.09577 - 5.18722i) q^{61} +(9.92971 - 0.694353i) q^{62} +(6.09936 + 12.5055i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-0.737857 - 1.27801i) q^{65} +(0.372669 - 0.580154i) q^{66} +(3.64234 - 1.32570i) q^{67} +(-6.04804 + 1.28555i) q^{68} +(0.0284111 + 0.270313i) q^{69} +(-0.906101 + 0.875012i) q^{70} +(-3.57839 - 2.23603i) q^{71} +(1.10763 - 2.74148i) q^{72} +(-4.97321 + 10.1966i) q^{73} +(1.03370 - 0.296408i) q^{74} +(-0.316625 + 0.974471i) q^{75} +(-4.30444 + 0.686885i) q^{76} +(-4.48881 + 14.9476i) q^{77} +(1.07704 + 0.392009i) q^{78} +(-6.41707 - 0.901861i) q^{79} +(0.267030 + 0.0186725i) q^{80} +(-8.59187 + 0.600802i) q^{81} +(-4.42159 + 0.621414i) q^{82} +(-0.0872925 - 0.0185546i) q^{83} +(0.102263 - 0.972970i) q^{84} +(-0.925530 + 1.37215i) q^{85} +(0.263192 + 7.53684i) q^{86} +(-0.461407 - 0.799181i) q^{87} +(2.99888 - 1.41659i) q^{88} +(0.840705 - 4.76787i) q^{89} +(-0.296492 - 0.733842i) q^{90} +(-25.8791 - 1.80964i) q^{91} +(-0.573105 + 1.17504i) q^{92} +(-0.0722231 + 2.06820i) q^{93} +(-3.39482 - 10.4482i) q^{94} +(-0.701113 + 0.932661i) q^{95} +(-0.168197 + 0.122202i) q^{96} +(4.47115 - 5.72281i) q^{97} +(2.62966 + 14.9135i) q^{98} +(-7.65168 - 6.13348i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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