LMFDB - Embedded newform 418.2.u.b.5.6

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			5.6
Character	$\chi$	$=$	418.5
Dual form			418.2.u.b.251.6

$q$-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 $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{5}\right)$

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	−0.736578	−	0.676352i	$-0.763560\pi$
$3$	−0.149553	+	0.144422i	−0.0863445	+	0.0833819i	0.650234	+	0.759734i	$0.274671\pi$
$4$	−0.241922	+	0.970296i	−0.120961	+	0.485148i
$5$	−0.227007	+	0.141850i	−0.101521	+	0.0634371i	−0.579729	−	0.814809i	$-0.696842\pi$
$5$	−0.227007	+	0.141850i	−0.101521	+	0.0634371i	0.478209	+	0.878246i	$0.341286\pi$
$6$	0.205880	+	0.0289345i	0.0840501	+	0.0118125i
$7$	−4.29887	−	1.91398i	−1.62482	−	0.723416i	−0.626394	−	0.779507i	$-0.715470\pi$
$7$	−4.29887	−	1.91398i	−1.62482	−	0.723416i	−0.998426	+	0.0560904i	$0.982136\pi$
$8$	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	0.372392	−	0.928076i	$-0.378538\pi$
$13$	4.86764	−	2.58817i	1.35004	−	0.717829i	0.977648	+	0.210246i	$0.0674266\pi$
$14$	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	0.687409	+	0.726270i	$0.258748\pi$
$17$	0.215789	+	6.17939i	0.0523365	+	1.49872i	−0.635073	+	0.772452i	$0.719030\pi$
$18$	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	−0.741201	−	0.671283i	$-0.765744\pi$
$23$	−1.00149	+	0.840349i	−0.208825	+	0.175225i	0.532376	+	0.846508i	$0.321299\pi$
$24$	−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	0.145014	−	0.989430i	$-0.453677\pi$
$29$	4.26673	−	1.22346i	0.792311	−	0.227192i	0.647297	+	0.762238i	$0.275899\pi$
$30$	−0.0508405	+	0.0226356i	−0.00928216	+	0.00413269i
$31$	−6.66050	+	7.39723i	−1.19626	+	1.32858i	−0.264991	+	0.964251i	$0.585369\pi$
$31$	−6.66050	+	7.39723i	−1.19626	+	1.32858i	−0.931269	+	0.364331i	$0.881298\pi$
$32$	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	−0.656997	−	0.753894i	$-0.728173\pi$
$37$	−0.869982	+	0.632079i	−0.143024	+	0.103913i	0.513972	+	0.857807i	$0.328173\pi$
$38$	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	−0.400262	−	0.916401i	$-0.631081\pi$
$41$	3.21188	−	3.10168i	0.501612	−	0.484401i	0.901874	+	0.432000i	$0.142192\pi$
$42$	−0.829670	−	0.518436i	−0.128021	−	0.0799964i
$43$	5.77707	+	4.84754i	0.880995	+	0.739243i	0.966383	−	0.257105i	$-0.0827687\pi$
$43$	5.77707	+	4.84754i	0.880995	+	0.739243i	−0.0853884	+	0.996348i	$0.527213\pi$
$44$	−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	−0.944104	−	0.329647i	$-0.893070\pi$
$47$	−6.14322	−	9.10769i	−0.896080	−	1.32849i	0.0480241	−	0.998846i	$-0.484708\pi$
$48$	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	0.373447	−	0.927652i	$-0.378176\pi$
$53$	−2.15937	−	1.34933i	−0.296613	−	0.185344i	−0.670059	+	0.742307i	$0.733731\pi$
$54$	−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	−0.363809	−	0.931474i	$-0.618524\pi$
$59$	4.88616	−	7.24403i	0.636124	−	0.943093i	0.999932	−	0.0116188i	$-0.00369846\pi$
$60$	0.0491377	+	0.0261270i	0.00634365	+	0.00337298i
$61$	2.09577	+	5.18722i	0.268336	+	0.664155i	0.999844	−	0.0176780i	$-0.00562739\pi$
$61$	2.09577	+	5.18722i	0.268336	+	0.664155i	−0.731508	+	0.681833i	$0.761183\pi$
$62$	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	0.554786	−	0.831993i	$-0.312800\pi$
$67$	3.64234	+	1.32570i	0.444982	+	0.161960i	−0.109804	+	0.993953i	$0.535022\pi$
$68$	−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	−0.725378	−	0.688351i	$-0.758335\pi$
$71$	−3.57839	+	2.23603i	−0.424677	+	0.265367i	0.300701	+	0.953718i	$0.402779\pi$
$72$	1.10763	+	2.74148i	0.130535	+	0.323086i
$73$	−4.97321	−	10.1966i	−0.582070	−	1.19342i	−0.963172	−	0.268887i	$-0.913344\pi$
$73$	−4.97321	−	10.1966i	−0.582070	−	1.19342i	0.381102	−	0.924533i	$-0.375545\pi$
$74$	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	−0.490585	−	0.871393i	$-0.663217\pi$
$79$	−6.41707	+	0.901861i	−0.721977	+	0.101467i	−0.231392	+	0.972861i	$0.574328\pi$
$80$	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	−0.212700	−	0.977118i	$-0.568226\pi$
$83$	−0.0872925	+	0.0185546i	−0.00958160	+	0.00203663i	0.203118	+	0.979154i	$0.434892\pi$
$84$	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	0.996393	+	0.0848625i	$0.0270451\pi$
$89$	0.840705	+	4.76787i	0.0891145	+	0.505394i	−0.907278	+	0.420531i	$0.861844\pi$
$90$	−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	0.959486	−	0.281758i	$-0.0909175\pi$
$97$	4.47115	+	5.72281i	0.453976	+	0.581063i	−0.505509	+	0.862821i	$0.668695\pi$
$98$	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	−0.806028	−	0.591878i	$-0.798387\pi$
$101$	−7.69884	+	4.09355i	−0.766064	+	0.407323i	0.0399640	+	0.999201i	$0.487276\pi$
$102$	−0.134371	+	1.27846i	−0.0133047	+	0.126586i
$103$	0.527543	+	5.01923i	0.0519803	+	0.494560i	0.989280	+	0.146034i	$0.0466509\pi$
$103$	0.527543	+	5.01923i	0.0519803	+	0.494560i	−0.937299	+	0.348526i	$0.886682\pi$
$104$	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	−0.910230	−	0.414104i	$-0.864095\pi$
$107$	0.684843	−	6.51585i	0.0662063	−	0.629911i	0.976436	−	0.215807i	$-0.0692382\pi$
$108$	1.09347	−	0.581409i	0.105219	−	0.0559461i
$109$	−10.2480	−	8.59910i	−0.981581	−	0.823644i	0.00274609	−	0.999996i	$-0.499126\pi$
$109$	−10.2480	−	8.59910i	−0.981581	−	0.823644i	−0.984327	+	0.176352i	$0.943570\pi$
$110$	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	0.874395	−	0.485215i	$-0.161258\pi$
$113$	7.26179	+	5.27600i	0.683132	+	0.496324i	−0.191263	+	0.981539i	$0.561258\pi$
$114$	−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	0.191620	−	0.981469i	$-0.438626\pi$
$127$	1.18652	+	0.166755i	0.105287	+	0.0147971i	−0.0863328	+	0.996266i	$0.527515\pi$
$128$	−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	0.342753	−	0.939425i	$-0.388641\pi$
$131$	13.8396	−	5.03719i	1.20917	−	0.440101i	0.866415	+	0.499324i	$0.166418\pi$
$132$	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	0.979538	−	0.201260i	$-0.0645037\pi$
$137$	1.58142	+	3.91416i	0.135110	+	0.334409i	−0.844428	+	0.535670i	$0.820059\pi$
$138$	−0.230502	+	0.144033i	−0.0196216	+	0.0122609i
$139$	−7.00481	−	6.76447i	−0.594141	−	0.573755i	0.335584	−	0.942010i	$-0.391066\pi$
$139$	−7.00481	−	6.76447i	−0.594141	−	0.573755i	−0.929725	+	0.368255i	$0.879955\pi$
$140$	−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	0.957307	−	0.289074i	$-0.0933475\pi$
$149$	15.2945	+	8.13222i	1.25297	+	0.666217i	0.295666	+	0.955291i	$0.404459\pi$
$150$	−0.572960	+	0.849448i	−0.0467820	+	0.0693571i
$151$	3.49639	+	2.54028i	0.284532	+	0.206725i	0.720892	−	0.693048i	$-0.243732\pi$
$151$	3.49639	+	2.54028i	0.284532	+	0.206725i	−0.436360	+	0.899772i	$0.643732\pi$
$152$	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	0.999095	−	0.0425284i	$-0.0135413\pi$
$157$	1.21516	+	4.87376i	0.0969806	+	0.388968i	−0.902115	+	0.431496i	$0.857986\pi$
$158$	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	−0.211493	−	0.977379i	$-0.567833\pi$
$163$	−10.2423	−	2.17707i	−0.802238	−	0.170521i	−0.590745	+	0.806859i	$0.701166\pi$
$164$	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	0.00301970	−	0.999995i	$-0.499039\pi$
$167$	−11.5588	−	7.22274i	−0.894446	−	0.558912i	−0.897466	+	0.441083i	$0.854594\pi$
$168$	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	0.462106	−	0.886825i	$-0.347094\pi$
$173$	5.05136	+	1.44845i	0.384048	+	0.110124i	−0.0780577	+	0.996949i	$0.524872\pi$
$174$	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	−0.836438	−	0.548062i	$-0.815366\pi$
$179$	−13.2297	+	5.89024i	−0.988834	+	0.440257i	−0.152396	+	0.988319i	$0.548699\pi$
$180$	0.760814	−	0.218160i	0.0567077	−	0.0162607i
$181$	9.43618	−	12.0778i	0.701386	−	0.897733i	−0.296980	−	0.954884i	$-0.595979\pi$
$181$	9.43618	−	12.0778i	0.701386	−	0.897733i	0.998366	+	0.0571509i	$0.0182016\pi$
$182$	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	0.0718078	−	0.997418i	$-0.477123\pi$
$191$	14.4090	−	10.4688i	1.04260	−	0.757493i	0.970791	+	0.239926i	$0.0771232\pi$
$192$	0.00725572	+	0.207777i	0.000523636	+	0.0149950i
$193$	11.4982	+	6.11368i	0.827655	+	0.440072i	0.828542	−	0.559927i	$-0.189171\pi$
$193$	11.4982	+	6.11368i	0.827655	+	0.440072i	−0.000886296		1.00000i	$0.500282\pi$
$194$	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	0.656088	−	0.754684i	$-0.272210\pi$
$197$	−4.56906	−	7.91384i	−0.325532	−	0.563838i	−0.981620	+	0.190847i	$0.938877\pi$
$198$	9.54409	+	2.25346i	0.678269	+	0.160146i
$199$	−7.48325	−	2.72368i	−0.530473	−	0.193077i	0.0628763	−	0.998021i	$-0.479973\pi$
$199$	−7.48325	−	2.72368i	−0.530473	−	0.193077i	−0.593350	+	0.804945i	$0.702195\pi$
$200$	−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	0.824390	+	0.566023i	$0.191519\pi$
$211$	17.0557	+	21.8303i	1.17416	+	1.50286i	0.349771	+	0.936835i	$0.386259\pi$
$212$	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	0.600639	+	0.799520i	$0.294913\pi$
$223$	6.65510	+	26.6921i	0.445658	+	1.78744i	−0.154980	+	0.987918i	$0.549531\pi$
$224$	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	−0.0812872	−	0.996691i	$-0.525903\pi$
$227$	12.6785	−	9.21148i	0.841503	−	0.611388i	0.922790	+	0.385303i	$0.125903\pi$
$228$	0.742943	−	0.518929i	0.0492026	−	0.0343669i
$229$	4.56030	+	14.0351i	0.301353	+	0.927469i	0.981013	+	0.193942i	$0.0621272\pi$
$229$	4.56030	+	14.0351i	0.301353	+	0.927469i	−0.679660	+	0.733527i	$0.737873\pi$
$230$	−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	−0.561799	−	0.827274i	$-0.689891\pi$
$233$	6.36520	−	15.7544i	0.416998	−	1.03211i	0.978797	−	0.204832i	$-0.0656649\pi$
$234$	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	−0.0129933	−	0.999916i	$-0.504136\pi$
$239$	11.1525	−	4.96541i	0.721395	−	0.321186i	0.734388	+	0.678730i	$0.237469\pi$
$240$	−0.0372384	+	0.0413574i	−0.00240373	+	0.00266961i
$241$	0.522752	+	2.96467i	0.0336734	+	0.190971i	0.997004	−	0.0773443i	$-0.0246441\pi$
$241$	0.522752	+	2.96467i	0.0336734	+	0.190971i	−0.963331	+	0.268316i	$0.913533\pi$
$242$	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	−0.0830743	−	0.996543i	$-0.526474\pi$
$251$	−16.0835	−	10.0501i	−1.01518	−	0.634354i	−0.932105	+	0.362189i	$0.882029\pi$
$252$	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	−0.521795	−	0.853071i	$-0.674737\pi$
$257$	−8.21188	+	2.35472i	−0.512243	+	0.146883i	0.00955178	+	0.999954i	$0.496960\pi$
$258$	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	0.467913	+	0.883774i	$0.345006\pi$
$263$	−4.44434	+	25.2051i	−0.274050	+	1.55422i	−0.741963	+	0.670441i	$0.766105\pi$
$264$	−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	0.999976	−	0.00688237i	$-0.00219074\pi$
$269$	25.4785	+	13.5471i	1.55345	+	0.825984i	0.553474	+	0.832867i	$0.313302\pi$
$270$	−0.124184	−	0.307367i	−0.00755761	−	0.0187057i
$271$	−4.06702	−	0.284394i	−0.247054	−	0.0172757i	−0.0543073	−	0.998524i	$-0.517295\pi$
$271$	−4.06702	−	0.284394i	−0.247054	−	0.0172757i	−0.192747	+	0.981249i	$0.561740\pi$
$272$	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	0.467855	−	0.883805i	$-0.345027\pi$
$277$	8.91724	+	1.89542i	0.535785	+	0.113885i	0.0679304	+	0.997690i	$0.478360\pi$
$278$	−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	−0.773894	−	0.633315i	$-0.781694\pi$
$281$	−11.0157	−	27.2647i	−0.657139	−	1.62648i	0.116755	−	0.993161i	$-0.462751\pi$
$282$	−1.00124	−	2.05284i	−0.0596228	−	0.122245i
$283$	−4.35450	−	1.24863i	−0.258848	−	0.0742235i	0.143704	−	0.989621i	$-0.454099\pi$
$283$	−4.35450	−	1.24863i	−0.258848	−	0.0742235i	−0.402552	+	0.915397i	$0.631877\pi$
$284$	−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	0.999965	+	0.00841133i	$0.00267744\pi$
$293$	0.403974	+	3.84356i	0.0236004	+	0.224543i	−0.976364	+	0.216132i	$0.930656\pi$
$294$	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	−0.866759	−	0.498727i	$-0.833801\pi$
$307$	2.07283	−	11.7556i	0.118303	−	0.670929i	0.985062	−	0.172202i	$-0.0550880\pi$
$308$	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	−0.452065	−	0.891985i	$-0.649313\pi$
$311$	3.09631	−	29.4594i	0.175575	−	1.67049i	0.627641	−	0.778503i	$-0.284021\pi$
$312$	0.119806	+	1.13988i	0.00678269	+	0.0645330i
$313$	9.70971	−	12.4279i	0.548825	−	0.702464i	−0.430993	−	0.902355i	$-0.641837\pi$
$313$	9.70971	−	12.4279i	0.548825	−	0.702464i	0.979818	+	0.199891i	$0.0640589\pi$
$314$	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	−0.760905	−	0.648864i	$-0.775245\pi$
$317$	−11.5456	+	6.13890i	−0.648465	+	0.344795i	0.112440	+	0.993659i	$0.464133\pi$
$318$	−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	−0.950488	−	0.310760i	$-0.899416\pi$
$331$	−3.74999	+	6.49517i	−0.206118	+	0.357007i	0.744370	+	0.667767i	$0.232750\pi$
$332$	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	0.593717	−	0.804674i	$-0.297660\pi$
$337$	19.6365	+	1.37312i	1.06967	+	0.0747984i	0.475950	+	0.879472i	$0.342104\pi$
$338$	−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	−0.361918	−	0.932210i	$-0.617878\pi$
$347$	5.91051	−	3.69330i	0.317293	−	0.198267i	0.679211	+	0.733943i	$0.262322\pi$
$348$	−0.663817	−	0.641041i	−0.0355843	−	0.0343634i
$349$	0.194549	−	1.85101i	0.0104140	−	0.0990825i	−0.988080	−	0.153940i	$-0.950804\pi$
$349$	0.194549	−	1.85101i	0.0104140	−	0.0990825i	0.998494	+	0.0548574i	$0.0174704\pi$
$350$	−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	−0.101818	−	0.994803i	$-0.532466\pi$
$353$	15.2301	−	26.3793i	0.810616	−	1.40403i	0.912434	−	0.409225i	$-0.134201\pi$
$354$	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	−0.727358	−	0.686258i	$-0.759252\pi$
$359$	3.43708	−	5.09568i	0.181402	−	0.268939i	0.908760	+	0.417318i	$0.137030\pi$
$360$	−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	0.592080	−	0.805879i	$-0.298307\pi$
$367$	−3.69055	−	3.56392i	−0.192645	−	0.186035i	−0.784725	+	0.619844i	$0.787196\pi$
$368$	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	−0.982918	−	0.184044i	$-0.941081\pi$
$373$	−12.5699	−	21.7717i	−0.650846	−	1.12730i	0.332072	−	0.943254i	$-0.392252\pi$
$374$	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	−0.863752	−	0.503917i	$-0.831892\pi$
$379$	2.55483	−	7.86295i	0.131233	−	0.403893i	0.994985	+	0.100024i	$0.0318919\pi$
$380$	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	0.834312	−	0.551293i	$-0.185865\pi$
$383$	34.9970	−	4.91850i	1.78826	−	0.251324i	0.953949	+	0.299969i	$0.0969763\pi$
$384$	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	−0.0611274	−	0.998130i	$-0.519470\pi$
$389$	8.20405	−	2.35247i	0.415962	−	0.119275i	0.477089	+	0.878855i	$0.341692\pi$
$390$	−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	−0.800912	−	0.598783i	$-0.795651\pi$
$397$	−20.5137	+	7.46639i	−1.02956	+	0.374727i	−0.228644	+	0.973510i	$0.573429\pi$
$398$	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	−0.965971	−	0.258649i	$-0.916723\pi$
$401$	−0.408420	−	11.6956i	−0.0203955	−	0.584051i	0.945576	−	0.325402i	$-0.105500\pi$
$402$	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	−0.662042	−	0.749466i	$-0.730310\pi$
$409$	1.02469	−	29.3432i	0.0506674	−	1.45093i	0.712710	−	0.701459i	$-0.247468\pi$
$410$	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	−0.165234	+	0.986254i	$0.552838\pi$
$421$	−23.7326	+	22.9183i	−1.15665	+	1.11697i	−0.991420	+	0.130714i	$0.958273\pi$
$422$	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	−0.475356	−	0.879794i	$-0.657681\pi$
$431$	−0.244753	+	0.130137i	−0.0117893	+	0.00626850i	0.463566	+	0.886062i	$0.346570\pi$
$432$	0.299604	+	1.20165i	0.0144147	+	0.0578142i
$433$	−0.335577	+	1.34593i	−0.0161268	+	0.0646811i	−0.977820	−	0.209447i	$-0.932834\pi$
$433$	−0.335577	+	1.34593i	−0.0161268	+	0.0646811i	0.961693	+	0.274128i	$0.0883892\pi$
$434$	−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	0.331297	−	0.943527i	$-0.392514\pi$
$439$	24.9662	−	9.08696i	1.19157	−	0.433697i	0.860275	+	0.509830i	$0.170292\pi$
$440$	−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	−0.927112	−	0.374785i	$-0.877717\pi$
$443$	−1.28369	+	2.63196i	−0.0609902	+	0.125048i	0.866122	+	0.499833i	$0.166605\pi$
$444$	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	−0.929567	−	0.368654i	$-0.879819\pi$
$449$	−9.86940	+	10.9611i	−0.465766	+	0.517285i	0.463801	+	0.885939i	$0.346485\pi$
$450$	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	−0.749237	−	0.662302i	$-0.769579\pi$
$457$	5.26316	−	16.1983i	0.246200	−	0.757726i	0.995437	−	0.0954237i	$-0.0304206\pi$
$458$	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	0.579745	−	0.814798i	$-0.303152\pi$
$461$	−2.61953	−	2.19805i	−0.122004	−	0.102373i	−0.701748	+	0.712425i	$0.747597\pi$
$462$	−0.491654	−	3.20729i	−0.0228738	−	0.149217i
$463$	2.91194	+	5.04362i	0.135329	+	0.234397i	0.925723	−	0.378202i	$-0.123457\pi$
$463$	2.91194	+	5.04362i	0.135329	+	0.234397i	−0.790394	+	0.612599i	$0.790124\pi$
$464$	−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	0.959581	+	0.281434i	$0.0908100\pi$
$467$	24.6177	+	27.3407i	1.13917	+	1.26518i	0.179589	+	0.983742i	$0.442523\pi$
$468$	−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	0.899382	−	0.437163i	$-0.144017\pi$
$479$	−1.12183	−	2.77663i	−0.0512578	−	0.126867i	−0.950640	+	0.310295i	$0.899572\pi$
$480$	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	−0.925541	−	0.378648i	$-0.876389\pi$
$487$	1.29098	−	12.2829i	0.0585000	−	0.556591i	0.984041	−	0.177943i	$-0.0569442\pi$
$488$	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	0.916134	−	0.400873i	$-0.131293\pi$
$491$	0.802430	+	1.64522i	0.0362131	+	0.0742480i	−0.879920	+	0.475121i	$0.842404\pi$
$492$	−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	0.791748	−	0.610848i	$-0.209171\pi$
$499$	33.3014	+	2.32866i	1.49078	+	0.104245i	0.699029	+	0.715093i	$0.253616\pi$
$500$	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	0.893587	−	0.448889i	$-0.148180\pi$
$503$	3.19910	+	4.74286i	0.142641	+	0.211473i	−0.750947	+	0.660363i	$0.770402\pi$
$504$	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	0.299003	−	0.954252i	$-0.403346\pi$
$509$	16.4222	−	1.14835i	0.727902	−	0.0508999i	0.428899	+	0.903352i	$0.358901\pi$
$510$	−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	−0.994644	−	0.103364i	$-0.967039\pi$
$521$	−0.986652	−	9.38737i	−0.0432260	−	0.411268i	0.951418	−	0.307904i	$-0.0996275\pi$
$522$	8.08004	−	10.3420i	0.353654	−	0.452656i
$523$	9.95168	−	12.7376i	0.435157	−	0.556975i	−0.519582	−	0.854420i	$-0.673912\pi$
$523$	9.95168	−	12.7376i	0.435157	−	0.556975i	0.954739	+	0.297445i	$0.0961346\pi$
$524$	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	0.897797	+	0.440409i	$0.145167\pi$
$541$	−0.663693	+	19.0057i	−0.0285344	+	0.817118i	−0.926332	+	0.376709i	$0.877056\pi$
$542$	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	−0.0610583	−	0.998134i	$-0.519448\pi$
$547$	0.406741	−	0.0284421i	0.0173910	−	0.00121610i	0.0784493	+	0.996918i	$0.475003\pi$
$548$	−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	0.836912	−	0.547338i	$-0.184359\pi$
$557$	7.53140	+	7.27299i	0.319116	+	0.308166i	−0.517796	+	0.855504i	$0.673248\pi$
$558$	−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	−0.712127	−	0.702051i	$-0.752268\pi$
$563$	1.43588	−	1.59470i	0.0605150	−	0.0672087i	0.772642	+	0.634842i	$0.218935\pi$
$564$	−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	0.154557	−	0.987984i	$-0.450605\pi$
$569$	−17.5876	−	12.7782i	−0.737311	−	0.535688i	−0.891868	+	0.452296i	$0.850605\pi$
$570$	−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	−0.908720	−	0.417407i	$-0.862939\pi$
$577$	−37.6911	+	8.01150i	−1.56910	+	0.333523i	−0.660382	+	0.750930i	$0.729606\pi$
$578$	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	−0.554051	−	0.832483i	$-0.686919\pi$
$587$	10.3058	−	15.2789i	0.425365	−	0.630630i	0.979416	+	0.201853i	$0.0646964\pi$
$588$	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	−0.301291	−	0.953532i	$-0.597418\pi$
$593$	14.2563	−	11.9625i	0.585436	−	0.491239i	0.886727	+	0.462293i	$0.152973\pi$
$594$	−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	0.191341	+	0.981524i	$0.438716\pi$
$599$	−19.7587	+	25.2899i	−0.807317	+	1.03332i	−0.998658	+	0.0517951i	$0.983506\pi$
$600$	−0.685604	−	0.761440i	−0.0279897	−	0.0310857i
$601$	−15.2793	−	6.80277i	−0.623254	−	0.277491i	0.0707137	−	0.997497i	$-0.477472\pi$
$601$	−15.2793	−	6.80277i	−0.623254	−	0.277491i	−0.693968	+	0.720006i	$0.744139\pi$
$602$	−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	0.999692	−	0.0248042i	$-0.00789624\pi$
$607$	4.34467	+	13.3715i	0.176345	+	0.542733i	−0.823348	+	0.567537i	$0.807896\pi$
$608$	−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	−0.999957	−	0.00928871i	$-0.997043\pi$
$613$	−3.00592	−	12.0561i	−0.121408	−	0.486941i	0.878549	−	0.477653i	$-0.158512\pi$
$614$	−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	−0.999602	−	0.0282060i	$-0.991021\pi$
$617$	−44.3005	−	16.1241i	−1.78347	−	0.649131i	−0.783870	−	0.620925i	$-0.786757\pi$
$618$	−0.0366187	+	1.04862i	−0.00147302	+	0.0421818i
$619$	17.5739	−	7.82442i	0.706356	−	0.314490i	−0.0219337	−	0.999759i	$-0.506982\pi$
$619$	17.5739	−	7.82442i	0.706356	−	0.314490i	0.728290	+	0.685270i	$0.240316\pi$
$620$	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	0.808744	+	0.588161i	$0.200148\pi$
$631$	−4.55821	+	18.2820i	−0.181460	+	0.727795i	−0.990203	+	0.139633i	$0.955408\pi$
$632$	−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	0.985369	+	0.170432i	$0.0545163\pi$
$641$	4.94594	+	19.8371i	0.195353	+	0.783517i	−0.790017	+	0.613085i	$0.789928\pi$
$642$	0.329528	−	1.32167i	0.0130054	−	0.0521620i
$643$	−16.0824	−	8.55118i	−0.634229	−	0.337226i	0.121033	−	0.992648i	$-0.461379\pi$
$643$	−16.0824	−	8.55118i	−0.634229	−	0.337226i	−0.755262	+	0.655423i	$0.772490\pi$
$644$	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	0.813122	+	0.582094i	$0.197766\pi$
$647$	12.6529	+	38.9418i	0.497439	+	1.53096i	−0.315683	+	0.948865i	$0.602234\pi$
$648$	−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	0.477566	−	0.878596i	$-0.341519\pi$
$653$	3.68479	+	1.64057i	0.144197	+	0.0642006i	−0.333369	+	0.942796i	$0.608186\pi$
$654$	−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	0.903341	+	0.428924i	$0.141107\pi$
$659$	5.16446	+	29.2891i	0.201179	+	1.14094i	−0.702162	+	0.712017i	$0.747782\pi$
$660$	0.0406261	+	0.180050i	0.00158137	+	0.00700843i
$661$	8.22983	−	6.90565i	0.320103	−	0.268599i	−0.468550	−	0.883437i	$-0.655223\pi$
$661$	8.22983	−	6.90565i	0.320103	−	0.268599i	0.788653	+	0.614839i	$0.210779\pi$
$662$	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	−0.289098	−	0.957300i	$-0.593355\pi$
$673$	−24.4524	−	5.19752i	−0.942570	−	0.200349i	−0.653473	+	0.756950i	$0.726689\pi$
$674$	−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	−0.517777	−	0.855515i	$-0.673240\pi$
$677$	−16.7257	+	3.55516i	−0.642821	+	0.136636i	−0.125044	+	0.992151i	$0.539907\pi$
$678$	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	−0.695267	−	0.718752i	$-0.744714\pi$
$691$	2.42424	−	2.69240i	0.0922226	−	0.102424i	0.787489	+	0.616328i	$0.211380\pi$
$692$	−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	0.0613460	−	0.998117i	$-0.480461\pi$
$701$	−11.0023	−	3.15486i	−0.415551	−	0.119157i	−0.476897	+	0.878959i	$0.658238\pi$
$702$	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	0.749710	−	0.661767i	$-0.230193\pi$
$709$	34.2948	+	4.81982i	1.28797	+	0.181012i	0.538260	+	0.842779i	$0.319082\pi$
$710$	−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	0.994863	+	0.101234i	$0.0322790\pi$
$719$	12.3918	+	25.4070i	0.462137	+	0.947522i	−0.532725	+	0.846288i	$0.678832\pi$
$720$	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	0.775426	−	0.631438i	$-0.217535\pi$
$727$	7.77160	+	6.52115i	0.288233	+	0.241856i	−0.487194	+	0.873294i	$0.661979\pi$
$728$	−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	0.975115	+	0.221698i	$0.0711598\pi$
$733$	1.82484	+	17.3622i	0.0674022	+	0.641289i	−0.907713	+	0.419591i	$0.862174\pi$
$734$	−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	0.999038	−	0.0438494i	$-0.0139622\pi$
$739$	19.4316	+	24.8713i	0.714802	+	0.914905i	−0.284236	+	0.958754i	$0.591740\pi$
$740$	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	0.909405	+	0.415911i	$0.136537\pi$
$743$	0.851207	+	24.3754i	0.0312278	+	0.894246i	−0.878178	+	0.478335i	$0.841241\pi$
$744$	−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	−0.983878	−	0.178843i	$-0.942764\pi$
$751$	−21.4064	−	31.7363i	−0.781131	−	1.15807i	0.202746	−	0.979231i	$-0.435013\pi$
$752$	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	−0.529062	−	0.848583i	$-0.677456\pi$
$757$	−22.1135	+	3.10785i	−0.803729	+	0.112957i	−0.274666	+	0.961540i	$0.588567\pi$
$758$	−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	0.998409	−	0.0563912i	$-0.0179594\pi$
$761$	4.34575	+	13.3748i	0.157533	+	0.484837i	−0.840876	+	0.541229i	$0.817959\pi$
$762$	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	0.911283	−	0.411781i	$-0.135093\pi$
$769$	37.2891	+	13.5721i	1.34468	+	0.489423i	0.433395	+	0.901204i	$0.357316\pi$
$770$	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	−0.738605	−	0.674138i	$-0.764515\pi$
$773$	6.87715	−	14.1002i	0.247354	−	0.507150i	0.985959	+	0.166988i	$0.0534041\pi$
$774$	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	−0.901669	−	0.432428i	$-0.857657\pi$
$787$	−34.7156	−	38.5556i	−1.23748	−	1.37436i	−0.335809	−	0.941930i	$-0.609010\pi$
$788$	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	−0.273219	−	0.961952i	$-0.588088\pi$
$797$	14.4894	−	44.5938i	0.513241	−	1.57959i	0.786460	−	0.617641i	$-0.211912\pi$
$798$	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	0.556384	−	0.830925i	$-0.312188\pi$
$809$	−9.33345	−	10.3658i	−0.328147	−	0.364444i	−0.884531	+	0.466481i	$0.845522\pi$
$810$	−2.10618	−	0.937732i	−0.0740037	−	0.0329486i
$811$	11.9026	−	24.4039i	0.417956	−	0.856937i	−0.581114	−	0.813822i	$-0.697383\pi$
$811$	11.9026	−	24.4039i	0.417956	−	0.856937i	0.999070	−	0.0431151i	$-0.0137282\pi$
$812$	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	−0.877041	−	0.480415i	$-0.840486\pi$
$821$	3.52093	−	14.1217i	0.122881	−	0.492850i	0.999923	−	0.0124349i	$-0.00395826\pi$
$822$	0.212329	+	0.851605i	0.00740582	+	0.0297031i
$823$	7.38342	−	3.92583i	0.257370	−	0.136846i	−0.335774	−	0.941943i	$-0.608998\pi$
$823$	7.38342	−	3.92583i	0.257370	−	0.136846i	0.593144	+	0.805097i	$0.297887\pi$
$824$	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	−0.870891	−	0.491477i	$-0.836457\pi$
$827$	0.924910	−	26.4859i	0.0321623	−	0.921007i	0.903053	−	0.429530i	$-0.141321\pi$
$828$	3.53135	−	1.57226i	0.122723	−	0.0546398i
$829$	−24.9963	−	11.1291i	−0.868159	−	0.386529i	−0.0761917	−	0.997093i	$-0.524276\pi$
$829$	−24.9963	−	11.1291i	−0.868159	−	0.386529i	−0.791967	+	0.610564i	$0.790943\pi$
$830$	−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	−0.457407	−	0.889257i	$-0.651222\pi$
$839$	12.0307	−	11.6179i	0.415345	−	0.401094i	0.872752	+	0.488163i	$0.162333\pi$
$840$	−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	−0.574026	−	0.818837i	$-0.694619\pi$
$853$	−1.70907	−	48.9414i	−0.0585175	−	1.67572i	0.515509	−	0.856884i	$-0.327603\pi$
$854$	−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	−0.729189	−	0.684312i	$-0.760103\pi$
$857$	−24.8223	+	9.03457i	−0.847913	+	0.308615i	−0.118724	+	0.992927i	$0.537880\pi$
$858$	3.31556	+	1.85945i	0.113191	+	0.0634805i
$859$	−14.5108	+	12.1760i	−0.495104	+	0.415441i	−0.855851	−	0.517222i	$-0.826966\pi$
$859$	−14.5108	+	12.1760i	−0.495104	+	0.415441i	0.360747	+	0.932664i	$0.382522\pi$
$860$	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	0.947116	−	0.320891i	$-0.103982\pi$
$863$	15.5398	+	17.2587i	0.528982	+	0.587495i	−0.418134	+	0.908385i	$0.637316\pi$
$864$	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	−0.934241	−	0.356641i	$-0.883922\pi$
$877$	−18.0771	+	17.4569i	−0.610422	+	0.589477i	0.323820	+	0.946119i	$0.395033\pi$
$878$	−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	0.878595	−	0.477568i	$-0.158482\pi$
$881$	0.763150	+	1.32181i	0.0257112	+	0.0445331i	−0.852884	+	0.522101i	$0.825148\pi$
$882$	43.7977	+	9.30950i	1.47475	+	0.313467i
$883$	13.3295	+	19.7618i	0.448573	+	0.665036i	0.983717	−	0.179724i	$-0.0575206\pi$
$883$	13.3295	+	19.7618i	0.448573	+	0.665036i	−0.535144	+	0.844761i	$0.679743\pi$
$884$	−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	0.821623	−	0.570031i	$-0.193069\pi$
$887$	8.35738	+	8.07063i	0.280613	+	0.270985i	−0.541010	+	0.841016i	$0.681958\pi$
$888$	−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	−0.701302	−	0.712864i	$-0.747397\pi$
$907$	−11.0833	+	6.92560i	−0.368014	+	0.229961i	0.333288	+	0.942825i	$0.391842\pi$
$908$	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	0.987066	+	0.160315i	$0.0512510\pi$
$911$	8.53399	+	26.2649i	0.282744	+	0.870195i	−0.704322	+	0.709880i	$0.748749\pi$
$912$	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	0.0255489	−	0.999674i	$-0.491867\pi$
$919$	13.8083	−	2.93504i	0.455493	−	0.0968180i	0.429944	+	0.902856i	$0.358533\pi$
$920$	−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	0.999182	−	0.0404315i	$-0.0128733\pi$
$929$	−0.0117774	−	0.337260i	−0.000386403	−	0.0110651i	−0.999569	+	0.0293664i	$0.990651\pi$
$930$	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	0.273599	−	0.961844i	$-0.411786\pi$
$937$	37.4672	−	19.9216i	1.22400	−	0.650812i	0.950399	+	0.311032i	$0.100675\pi$
$938$	−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	−0.386720	−	0.922197i	$-0.626392\pi$
$941$	18.4558	−	23.6223i	0.601640	−	0.770065i	0.988360	+	0.152133i	$0.0486141\pi$
$942$	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	−0.997934	−	0.0642430i	$-0.979537\pi$
$947$	−1.17586	+	6.66865i	−0.0382104	+	0.216702i	0.959724	+	0.280945i	$0.0906478\pi$
$948$	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	0.657721	−	0.753261i	$-0.271520\pi$
$953$	−10.5204	−	21.5701i	−0.340790	−	0.698724i	−0.998512	+	0.0545376i	$0.982632\pi$
$954$	−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	−0.592797	−	0.805352i	$-0.701976\pi$
$967$	−16.4574	+	5.99001i	−0.529235	+	0.192626i	0.0635616	+	0.997978i	$0.479754\pi$
$968$	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	0.774544	−	0.632520i	$-0.217980\pi$
$971$	34.1588	+	9.79489i	1.09621	+	0.314333i	0.321666	+	0.946853i	$0.395757\pi$
$972$	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	0.256132	−	0.966642i	$-0.417552\pi$
$977$	3.03043	+	0.644137i	0.0969520	+	0.0206078i	−0.159180	+	0.987250i	$0.550885\pi$
$978$	−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	0.502013	−	0.864860i	$-0.332593\pi$
$983$	27.5521	+	1.92663i	0.878775	+	0.0614500i	0.376762	+	0.926310i	$0.377037\pi$
$984$	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	0.639688	+	0.768635i	$0.279064\pi$
$991$	−7.06133	+	40.0468i	−0.224311	+	1.27213i	−0.863999	+	0.503494i	$0.832048\pi$
$992$	−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	−0.318127	−	0.948048i	$-0.603054\pi$
$997$	−2.70046	+	0.774344i	−0.0855244	+	0.0245237i	0.232602	+	0.972572i	$0.425276\pi$
$998$	−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.5.6	✓	264
11.9	even	5	inner	418.2.u.b.119.6	yes	264
19.4	even	9	inner	418.2.u.b.137.6	yes	264
209.42	even	45	inner	418.2.u.b.251.6	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.u.b.5.6	✓	264	1.1	even	1	trivial
418.2.u.b.119.6	yes	264	11.9	even	5	inner
418.2.u.b.137.6	yes	264	19.4	even	9	inner
418.2.u.b.251.6	yes	264	209.42	even	45	inner

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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