LMFDB - Embedded newform 162.2.g.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	162.13
Dual form			162.2.g.a.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.893633 - 0.448799i) q^{2} +(-1.41362 - 1.00084i) q^{3} +(0.597159 + 0.802123i) q^{4} +(0.308002 + 1.02880i) q^{5} +(0.814085 + 1.52881i) q^{6} +(-2.06499 - 4.78718i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(0.996657 + 2.82961i) q^{9} +O(q^{10})$	\(q+(-0.893633 - 0.448799i) q^{2} +(-1.41362 - 1.00084i) q^{3} +(0.597159 + 0.802123i) q^{4} +(0.308002 + 1.02880i) q^{5} +(0.814085 + 1.52881i) q^{6} +(-2.06499 - 4.78718i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(0.996657 + 2.82961i) q^{9} +(0.186483 - 1.05760i) q^{10} +(-5.51869 + 1.30795i) q^{11} +(-0.0413635 - 1.73156i) q^{12} +(-2.75916 - 1.81473i) q^{13} +(-0.303142 + 5.20475i) q^{14} +(0.594259 - 1.76259i) q^{15} +(-0.286803 + 0.957990i) q^{16} +(-1.32917 + 0.483778i) q^{17} +(0.379280 - 2.97593i) q^{18} +(-0.526489 - 0.191626i) q^{19} +(-0.641296 + 0.861410i) q^{20} +(-1.87207 + 8.83399i) q^{21} +(5.51869 + 1.30795i) q^{22} +(0.185413 - 0.429835i) q^{23} +(-0.740157 + 1.56594i) q^{24} +(3.21388 - 2.11380i) q^{25} +(1.65123 + 2.86001i) q^{26} +(1.42307 - 4.99749i) q^{27} +(2.60678 - 4.51508i) q^{28} +(-0.413128 - 7.09314i) q^{29} +(-1.32210 + 1.30840i) q^{30} +(2.69492 - 0.314991i) q^{31} +(0.686242 - 0.727374i) q^{32} +(9.11038 + 3.67435i) q^{33} +(1.40491 + 0.164210i) q^{34} +(4.28902 - 3.59892i) q^{35} +(-1.67453 + 2.48917i) q^{36} +(-3.28779 - 2.75878i) q^{37} +(0.384486 + 0.407532i) q^{38} +(2.08417 + 5.32681i) q^{39} +(0.959683 - 0.481971i) q^{40} +(5.78531 - 2.90549i) q^{41} +(5.63763 - 7.05416i) q^{42} +(6.69559 + 7.09691i) q^{43} +(-4.34467 - 3.64561i) q^{44} +(-2.60412 + 1.89688i) q^{45} +(-0.358600 + 0.300901i) q^{46} +(1.37768 + 0.161028i) q^{47} +(1.36422 - 1.06719i) q^{48} +(-13.8493 + 14.6794i) q^{49} +(-3.82070 + 0.446576i) q^{50} +(2.36312 + 0.646400i) q^{51} +(-0.192021 - 3.29687i) q^{52} +(-3.96592 + 6.86918i) q^{53} +(-3.51457 + 3.82724i) q^{54} +(-3.04538 - 5.27476i) q^{55} +(-4.35587 + 2.86490i) q^{56} +(0.552471 + 0.797817i) q^{57} +(-2.81421 + 6.52407i) q^{58} +(-1.06624 - 0.252703i) q^{59} +(1.76868 - 0.575877i) q^{60} +(5.03022 - 6.75675i) q^{61} +(-2.54964 - 0.927991i) q^{62} +(11.4878 - 10.6143i) q^{63} +(-0.939693 + 0.342020i) q^{64} +(1.01716 - 3.39756i) q^{65} +(-6.49229 - 7.37225i) q^{66} +(-0.100933 + 1.73295i) q^{67} +(-1.18177 - 0.777265i) q^{68} +(-0.692297 + 0.422057i) q^{69} +(-5.44800 + 1.29120i) q^{70} +(1.32440 - 7.51103i) q^{71} +(2.61355 - 1.47287i) q^{72} +(-1.86793 - 10.5936i) q^{73} +(1.69994 + 3.94090i) q^{74} +(-6.65878 - 0.228447i) q^{75} +(-0.160690 - 0.536741i) q^{76} +(17.6574 + 23.7181i) q^{77} +(0.528187 - 5.69558i) q^{78} +(-1.99908 - 1.00398i) q^{79} -1.07391 q^{80} +(-7.01335 + 5.64029i) q^{81} -6.47392 q^{82} +(-10.3349 - 5.19037i) q^{83} +(-8.20387 + 3.77366i) q^{84} +(-0.907095 - 1.21844i) q^{85} +(-2.79831 - 9.34701i) q^{86} +(-6.51505 + 10.4405i) q^{87} +(2.24639 + 5.20772i) q^{88} +(-0.973720 - 5.52224i) q^{89} +(3.17844 - 0.526388i) q^{90} +(-2.98980 + 16.9560i) q^{91} +(0.455501 - 0.107956i) q^{92} +(-4.12485 - 2.25189i) q^{93} +(-1.15887 - 0.762203i) q^{94} +(0.0349852 - 0.600672i) q^{95} +(-1.69807 + 0.341417i) q^{96} +(-0.471322 + 1.57433i) q^{97} +(18.9642 - 6.90241i) q^{98} +(-9.20123 - 14.3121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

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 $

$2$	−0.893633	−	0.448799i	−0.631894	−	0.317349i
$2$	−0.893633	−	0.448799i	−0.631894	−	0.317349i
$3$	−1.41362	−	1.00084i	−0.816155	−	0.577833i
$3$	−1.41362	−	1.00084i	−0.816155	−	0.577833i
$4$	0.597159	+	0.802123i	0.298579	+	0.401062i
$5$	0.308002	+	1.02880i	0.137743	+	0.460092i	0.998830	−	0.0483653i	$-0.0154012\pi$
$5$	0.308002	+	1.02880i	0.137743	+	0.460092i	−0.861087	+	0.508457i	$0.830216\pi$
$6$	0.814085	+	1.52881i	0.332349	+	0.624135i
$7$	−2.06499	−	4.78718i	−0.780493	−	1.80939i	−0.547256	−	0.836966i	$-0.684327\pi$
$7$	−2.06499	−	4.78718i	−0.780493	−	1.80939i	−0.233237	−	0.972420i	$-0.574932\pi$
$8$	−0.173648	−	0.984808i	−0.0613939	−	0.348182i
$9$	0.996657	+	2.82961i	0.332219	+	0.943202i
$10$	0.186483	−	1.05760i	0.0589711	−	0.334442i
$11$	−5.51869	+	1.30795i	−1.66395	+	0.394363i	−0.951569	−	0.307434i	$-0.900530\pi$
$11$	−5.51869	+	1.30795i	−1.66395	+	0.394363i	−0.712377	+	0.701797i	$0.752381\pi$
$12$	−0.0413635	−	1.73156i	−0.0119406	−	0.499857i
$13$	−2.75916	−	1.81473i	−0.765253	−	0.503315i	0.105870	−	0.994380i	$-0.466237\pi$
$13$	−2.75916	−	1.81473i	−0.765253	−	0.503315i	−0.871123	+	0.491065i	$0.836608\pi$
$14$	−0.303142	+	5.20475i	−0.0810181	+	1.39103i
$15$	0.594259	−	1.76259i	0.153437	−	0.455099i
$16$	−0.286803	+	0.957990i	−0.0717008	+	0.239497i
$17$	−1.32917	+	0.483778i	−0.322371	+	0.117333i	−0.498136	−	0.867099i	$-0.665982\pi$
$17$	−1.32917	+	0.483778i	−0.322371	+	0.117333i	0.175766	+	0.984432i	$0.443760\pi$
$18$	0.379280	−	2.97593i	0.0893971	−	0.701433i
$19$	−0.526489	−	0.191626i	−0.120785	−	0.0439621i	0.280921	−	0.959731i	$-0.409360\pi$
$19$	−0.526489	−	0.191626i	−0.120785	−	0.0439621i	−0.401706	+	0.915769i	$0.631582\pi$
$20$	−0.641296	+	0.861410i	−0.143398	+	0.192617i
$21$	−1.87207	+	8.83399i	−0.408519	+	1.92773i
$22$	5.51869	+	1.30795i	1.17659	+	0.278856i
$23$	0.185413	−	0.429835i	0.0386612	−	0.0896268i	−0.897791	−	0.440421i	$-0.854829\pi$
$23$	0.185413	−	0.429835i	0.0386612	−	0.0896268i	0.936453	+	0.350794i	$0.114088\pi$
$24$	−0.740157	+	1.56594i	−0.151084	+	0.319646i
$25$	3.21388	−	2.11380i	0.642776	−	0.422761i
$26$	1.65123	+	2.86001i	0.323832	+	0.560894i
$27$	1.42307	−	4.99749i	0.273871	−	0.961767i
$28$	2.60678	−	4.51508i	0.492636	−	0.853271i
$29$	−0.413128	−	7.09314i	−0.0767160	−	1.31716i	−0.788618	−	0.614883i	$-0.789203\pi$
$29$	−0.413128	−	7.09314i	−0.0767160	−	1.31716i	0.711902	−	0.702279i	$-0.247834\pi$
$30$	−1.32210	+	1.30840i	−0.241381	+	0.238881i
$31$	2.69492	−	0.314991i	0.484022	−	0.0565740i	0.129417	−	0.991590i	$-0.458689\pi$
$31$	2.69492	−	0.314991i	0.484022	−	0.0565740i	0.354605	+	0.935016i	$0.384615\pi$
$32$	0.686242	−	0.727374i	0.121312	−	0.128583i
$33$	9.11038	+	3.67435i	1.58591	+	0.639621i
$34$	1.40491	+	0.164210i	0.240940	+	0.0281618i
$35$	4.28902	−	3.59892i	0.724977	−	0.608328i
$36$	−1.67453	+	2.48917i	−0.279088	+	0.414861i
$37$	−3.28779	−	2.75878i	−0.540510	−	0.453541i	0.331203	−	0.943560i	$-0.392546\pi$
$37$	−3.28779	−	2.75878i	−0.540510	−	0.453541i	−0.871712	+	0.490018i	$0.836990\pi$
$38$	0.384486	+	0.407532i	0.0623719	+	0.0661104i
$39$	2.08417	+	5.32681i	0.333734	+	0.852972i
$40$	0.959683	−	0.481971i	0.151739	−	0.0762063i
$41$	5.78531	−	2.90549i	0.903513	−	0.453761i	0.0645280	−	0.997916i	$-0.479446\pi$
$41$	5.78531	−	2.90549i	0.903513	−	0.453761i	0.838985	+	0.544155i	$0.183150\pi$
$42$	5.63763	−	7.05416i	0.869905	−	1.08848i
$43$	6.69559	+	7.09691i	1.02107	+	1.08227i	0.996585	+	0.0825691i	$0.0263125\pi$
$43$	6.69559	+	7.09691i	1.02107	+	1.08227i	0.0244831	+	0.999700i	$0.492206\pi$
$44$	−4.34467	−	3.64561i	−0.654984	−	0.549597i
$45$	−2.60412	+	1.89688i	−0.388199	+	0.282770i
$46$	−0.358600	+	0.300901i	−0.0528727	+	0.0443655i
$47$	1.37768	+	0.161028i	0.200956	+	0.0234883i	0.215975	−	0.976399i	$-0.430707\pi$
$47$	1.37768	+	0.161028i	0.200956	+	0.0234883i	−0.0150195	+	0.999887i	$0.504781\pi$
$48$	1.36422	−	1.06719i	0.196908	−	0.154036i
$49$	−13.8493	+	14.6794i	−1.97847	+	2.09705i
$50$	−3.82070	+	0.446576i	−0.540329	+	0.0631554i
$51$	2.36312	+	0.646400i	0.330904	+	0.0905141i
$52$	−0.192021	−	3.29687i	−0.0266285	−	0.457193i
$53$	−3.96592	+	6.86918i	−0.544761	+	0.943554i	0.453861	+	0.891073i	$0.350046\pi$
$53$	−3.96592	+	6.86918i	−0.544761	+	0.943554i	−0.998622	+	0.0524814i	$0.983287\pi$
$54$	−3.51457	+	3.82724i	−0.478273	+	0.520822i
$55$	−3.04538	−	5.27476i	−0.410639	−	0.711248i
$56$	−4.35587	+	2.86490i	−0.582078	+	0.382839i
$57$	0.552471	+	0.797817i	0.0731765	+	0.105673i
$58$	−2.81421	+	6.52407i	−0.369524	+	0.856652i
$59$	−1.06624	−	0.252703i	−0.138812	−	0.0328991i	0.160622	−	0.987016i	$-0.448650\pi$
$59$	−1.06624	−	0.252703i	−0.138812	−	0.0328991i	−0.299435	+	0.954117i	$0.596798\pi$
$60$	1.76868	−	0.575877i	0.228336	−	0.0743454i
$61$	5.03022	−	6.75675i	0.644053	−	0.865114i	−0.353470	−	0.935446i	$-0.614999\pi$
$61$	5.03022	−	6.75675i	0.644053	−	0.865114i	0.997524	+	0.0703322i	$0.0224059\pi$
$62$	−2.54964	−	0.927991i	−0.323804	−	0.117855i
$63$	11.4878	−	10.6143i	1.44732	−	1.33727i
$64$	−0.939693	+	0.342020i	−0.117462	+	0.0427525i
$65$	1.01716	−	3.39756i	0.126163	−	0.421415i
$66$	−6.49229	−	7.37225i	−0.799146	−	0.907461i
$67$	−0.100933	+	1.73295i	−0.0123309	+	0.211714i	0.986514	+	0.163674i	$0.0523345\pi$
$67$	−0.100933	+	1.73295i	−0.0123309	+	0.211714i	−0.998845	+	0.0480399i	$0.984703\pi$
$68$	−1.18177	−	0.777265i	−0.143311	−	0.0942572i
$69$	−0.692297	+	0.422057i	−0.0833428	+	0.0508096i
$70$	−5.44800	+	1.29120i	−0.651160	+	0.154328i
$71$	1.32440	−	7.51103i	0.157177	−	0.891395i	−0.799591	−	0.600544i	$-0.794951\pi$
$71$	1.32440	−	7.51103i	0.157177	−	0.891395i	0.956768	−	0.290851i	$-0.0939384\pi$
$72$	2.61355	−	1.47287i	0.308010	−	0.173580i
$73$	−1.86793	−	10.5936i	−0.218625	−	1.23988i	−0.874504	−	0.485018i	$-0.838813\pi$
$73$	−1.86793	−	10.5936i	−0.218625	−	1.23988i	0.655879	−	0.754866i	$-0.272298\pi$
$74$	1.69994	+	3.94090i	0.197614	+	0.458120i
$75$	−6.65878	−	0.228447i	−0.768890	−	0.0263788i
$76$	−0.160690	−	0.536741i	−0.0184324	−	0.0615684i
$77$	17.6574	+	23.7181i	2.01225	+	2.70292i
$78$	0.528187	−	5.69558i	0.0598054	−	0.644898i
$79$	−1.99908	−	1.00398i	−0.224914	−	0.112956i	0.332774	−	0.943007i	$-0.392015\pi$
$79$	−1.99908	−	1.00398i	−0.224914	−	0.112956i	−0.557689	+	0.830050i	$0.688312\pi$
$80$	−1.07391			−0.120067
$81$	−7.01335	+	5.64029i	−0.779261	+	0.626699i
$82$	−6.47392			−0.714925
$83$	−10.3349	−	5.19037i	−1.13440	−	0.569717i	−0.220391	−	0.975412i	$-0.570733\pi$
$83$	−10.3349	−	5.19037i	−1.13440	−	0.569717i	−0.914009	+	0.405694i	$0.867030\pi$
$84$	−8.20387	+	3.77366i	−0.895115	+	0.411740i
$85$	−0.907095	−	1.21844i	−0.0983883	−	0.132158i
$86$	−2.79831	−	9.34701i	−0.301750	−	1.00791i
$87$	−6.51505	+	10.4405i	−0.698487	+	1.11934i
$88$	2.24639	+	5.20772i	0.239466	+	0.555145i
$89$	−0.973720	−	5.52224i	−0.103214	−	0.585356i	−0.991919	−	0.126876i	$-0.959505\pi$
$89$	−0.973720	−	5.52224i	−0.103214	−	0.585356i	0.888704	−	0.458480i	$-0.151606\pi$
$90$	3.17844	−	0.526388i	0.335037	−	0.0554862i
$91$	−2.98980	+	16.9560i	−0.313416	+	1.77747i
$92$	0.455501	−	0.107956i	0.0474893	−	0.0112552i
$93$	−4.12485	−	2.25189i	−0.427727	−	0.233510i
$94$	−1.15887	−	0.762203i	−0.119529	−	0.0786152i
$95$	0.0349852	−	0.600672i	0.00358940	−	0.0616276i
$96$	−1.69807	+	0.341417i	−0.173308	+	0.0348457i
$97$	−0.471322	+	1.57433i	−0.0478555	+	0.159848i	−0.978577	−	0.205879i	$-0.933995\pi$
$97$	−0.471322	+	1.57433i	−0.0478555	+	0.159848i	0.930722	+	0.365728i	$0.119180\pi$
$98$	18.9642	−	6.90241i	1.91568	−	0.697249i
$99$	−9.20123	−	14.3121i	−0.924758	−	1.43842i
$100$	3.61473	+	1.31565i	0.361473	+	0.131565i
$101$	4.20558	−	5.64907i	0.418471	−	0.562104i	−0.542038	−	0.840354i	$-0.682347\pi$
$101$	4.20558	−	5.64907i	0.418471	−	0.562104i	0.960509	+	0.278250i	$0.0897545\pi$
$102$	−1.82166	−	1.63821i	−0.180371	−	0.162207i
$103$	2.74489	+	0.650550i	0.270462	+	0.0641006i	0.363609	−	0.931552i	$-0.381545\pi$
$103$	2.74489	+	0.650550i	0.270462	+	0.0641006i	−0.0931471	+	0.995652i	$0.529693\pi$
$104$	−1.30804	+	3.03237i	−0.128263	+	0.297348i
$105$	−9.66498	+	0.794904i	−0.943205	+	0.0775747i
$106$	6.62696	−	4.35862i	0.643667	−	0.423346i
$107$	−4.20659	−	7.28602i	−0.406666	−	0.704366i	0.587848	−	0.808972i	$-0.299975\pi$
$107$	−4.20659	−	7.28602i	−0.406666	−	0.704366i	−0.994514	+	0.104605i	$0.966642\pi$
$108$	4.85840	−	1.84281i	0.467500	−	0.177325i
$109$	−8.42332	+	14.5896i	−0.806808	+	1.39743i	0.108256	+	0.994123i	$0.465473\pi$
$109$	−8.42332	+	14.5896i	−0.806808	+	1.39743i	−0.915064	+	0.403309i	$0.867860\pi$
$110$	0.354146	+	6.08046i	0.0337665	+	0.579749i
$111$	1.88661	+	7.19042i	0.179069	+	0.682484i
$112$	5.17832	−	0.605259i	0.489305	−	0.0571916i
$113$	4.68823	−	4.96923i	0.441032	−	0.467466i	−0.468281	−	0.883580i	$-0.655127\pi$
$113$	4.68823	−	4.96923i	0.441032	−	0.467466i	0.909313	+	0.416113i	$0.136608\pi$
$114$	−0.135646	−	0.960903i	−0.0127044	−	0.0899968i
$115$	0.499320	+	0.0583622i	0.0465618	+	0.00544230i
$116$	5.44287	−	4.56711i	0.505357	−	0.424045i
$117$	2.38503	−	9.61600i	0.220496	−	0.889000i
$118$	0.839412	+	0.704350i	0.0772741	+	0.0648407i
$119$	5.06065	+	5.36398i	0.463909	+	0.491715i
$120$	−1.83900	−	0.279160i	−0.167877	−	0.0254837i
$121$	18.9152	−	9.49957i	1.71956	−	0.863597i
$122$	−7.52759	+	3.78050i	−0.681516	+	0.342270i
$123$	−11.0862	−	1.68287i	−0.999605	−	0.151740i
$124$	1.86196	+	1.97356i	0.167209	+	0.177231i
$125$	7.27788	+	6.10687i	0.650953	+	0.546215i
$126$	−15.0295	+	4.32958i	−1.33894	+	0.385709i
$127$	−0.965931	+	0.810512i	−0.0857125	+	0.0719213i	−0.684637	−	0.728884i	$-0.740039\pi$
$127$	−0.965931	+	0.810512i	−0.0857125	+	0.0719213i	0.598925	+	0.800805i	$0.295595\pi$
$128$	0.993238	+	0.116093i	0.0877907	+	0.0102613i
$129$	−2.36220	−	16.7335i	−0.207980	−	1.47331i
$130$	−2.43379	+	2.57967i	−0.213457	+	0.226252i
$131$	2.66534	−	0.311534i	0.232872	−	0.0272188i	0.00114347	−	0.999999i	$-0.499636\pi$
$131$	2.66534	−	0.311534i	0.232872	−	0.0272188i	0.231728	+	0.972781i	$0.425562\pi$
$132$	2.49307	+	9.50182i	0.216994	+	0.827027i
$133$	0.169844	+	2.91611i	0.0147273	+	0.252859i
$134$	0.867945	−	1.50332i	0.0749790	−	0.129867i
$135$	5.57971	−	0.0751794i	0.480225	−	0.00647041i
$136$	0.707236	+	1.22497i	0.0606450	+	0.105040i
$137$	−15.9362	+	10.4814i	−1.36152	+	0.895485i	−0.999329	−	0.0366189i	$-0.988341\pi$
$137$	−15.9362	+	10.4814i	−1.36152	+	0.895485i	−0.362190	+	0.932104i	$0.617971\pi$
$138$	0.808078	−	0.0664611i	0.0687882	−	0.00565754i
$139$	−5.10799	+	11.8416i	−0.433254	+	1.00440i	0.552085	+	0.833788i	$0.313832\pi$
$139$	−5.10799	+	11.8416i	−0.433254	+	1.00440i	−0.985339	+	0.170607i	$0.945427\pi$
$140$	5.44800	+	1.29120i	0.460440	+	0.109126i
$141$	−1.78636	−	1.60647i	−0.150439	−	0.135289i
$142$	−4.55447	+	6.11771i	−0.382203	+	0.513387i
$143$	17.6005	+	6.40607i	1.47183	+	0.535702i
$144$	−2.99658	+	0.143247i	−0.249715	+	0.0119372i
$145$	7.17015	−	2.60972i	0.595449	−	0.216726i
$146$	−3.08514	+	10.3051i	−0.255328	+	0.852855i
$147$	34.2692	−	6.89024i	2.82648	−	0.568297i
$148$	0.249552	−	4.28465i	0.0205131	−	0.352196i
$149$	−4.12368	−	2.71219i	−0.337825	−	0.222191i	0.369249	−	0.929330i	$-0.379615\pi$
$149$	−4.12368	−	2.71219i	−0.337825	−	0.222191i	−0.707074	+	0.707139i	$0.749985\pi$
$150$	5.84798	+	3.19260i	0.477485	+	0.260675i
$151$	7.91920	−	1.87689i	0.644456	−	0.152739i	0.104624	−	0.994512i	$-0.466636\pi$
$151$	7.91920	−	1.87689i	0.644456	−	0.152739i	0.539832	+	0.841773i	$0.318488\pi$
$152$	−0.0972913	+	0.551766i	−0.00789137	+	0.0447542i
$153$	−2.69363	−	3.27886i	−0.217767	−	0.265080i
$154$	−5.13462	−	29.1199i	−0.413759	−	2.34655i
$155$	1.15410	+	2.67551i	0.0926996	+	0.214902i
$156$	−3.02818	+	4.85271i	−0.242448	+	0.388528i
$157$	−2.05866	−	6.87641i	−0.164299	−	0.548797i	0.835701	−	0.549185i	$-0.185062\pi$
$157$	−2.05866	−	6.87641i	−0.164299	−	0.548797i	−1.00000		0.000387867i	$0.999877\pi$
$158$	1.33586	+	1.79437i	0.106275	+	0.142753i
$159$	12.4812	−	5.74119i	0.989826	−	0.455306i
$160$	0.959683	+	0.481971i	0.0758696	+	0.0381032i
$161$	−2.44057			−0.192344
$162$	8.79872	−	1.89277i	0.691293	−	0.148710i
$163$	−2.16637			−0.169684			−0.0848418	−	0.996394i	$-0.527038\pi$
$163$	−2.16637			−0.169684			−0.0848418	+	0.996394i	$0.527038\pi$
$164$	5.78531	+	2.90549i	0.451756	+	0.226881i
$165$	−0.974143	+	10.5044i	−0.0758369	+	0.817770i
$166$	6.90615	+	9.27657i	0.536021	+	0.720001i
$167$	−3.79628	−	12.6805i	−0.293765	−	0.981243i	−0.969703	−	0.244285i	$-0.921447\pi$
$167$	−3.79628	−	12.6805i	−0.293765	−	0.981243i	0.675939	−	0.736958i	$-0.263738\pi$
$168$	9.02486	+	0.309621i	0.696283	+	0.0238878i
$169$	−0.829309	−	1.92255i	−0.0637930	−	0.147889i
$170$	0.263775	+	1.49594i	0.0202306	+	0.114733i
$171$	0.0174982	−	1.68074i	0.00133812	−	0.128530i
$172$	−1.69427	+	9.60867i	−0.129187	+	0.732655i
$173$	11.9681	−	2.83648i	0.909915	−	0.215654i	0.251102	−	0.967961i	$-0.419207\pi$
$173$	11.9681	−	2.83648i	0.909915	−	0.215654i	0.658813	+	0.752307i	$0.271059\pi$
$174$	10.5077	−	6.40601i	0.796590	−	0.485638i
$175$	−16.7558	−	11.0205i	−1.26662	−	0.833068i
$176$	0.329772	−	5.66197i	0.0248575	−	0.426787i
$177$	1.25434	+	1.42435i	0.0942822	+	0.107061i
$178$	−1.60823	+	5.37186i	−0.120542	+	0.402638i
$179$	−20.3238	+	7.39727i	−1.51907	+	0.552898i	−0.960917	−	0.276838i	$-0.910714\pi$
$179$	−20.3238	+	7.39727i	−1.51907	+	0.552898i	−0.558157	+	0.829735i	$0.688491\pi$
$180$	−3.07660	−	0.956085i	−0.229317	−	0.0712624i
$181$	9.01352	+	3.28065i	0.669970	+	0.243849i	0.654535	−	0.756032i	$-0.272865\pi$
$181$	9.01352	+	3.28065i	0.669970	+	0.243849i	0.0154348	+	0.999881i	$0.495087\pi$
$182$	10.2816	−	13.8106i	0.762125	−	1.02371i
$183$	−13.8732	+	4.51708i	−1.02554	+	0.333912i
$184$	−0.455501	−	0.107956i	−0.0335800	−	0.00795861i
$185$	1.82558	−	4.23218i	0.134220	−	0.311156i
$186$	2.67545	+	3.86359i	0.196174	+	0.283292i
$187$	6.70251	−	4.40831i	0.490136	−	0.322367i
$188$	0.693531	+	1.20123i	0.0505809	+	0.0876087i
$189$	−26.8625	+	3.50724i	−1.95396	+	0.255114i
$190$	−0.300845	+	0.521079i	−0.0218256	+	0.0378030i
$191$	−0.223393	−	3.83552i	−0.0161642	−	0.277528i	−0.996699	−	0.0811837i	$-0.974130\pi$
$191$	−0.223393	−	3.83552i	−0.0161642	−	0.277528i	0.980535	−	0.196345i	$-0.0629071\pi$
$192$	1.67068	+	0.456990i	0.120571	+	0.0329804i
$193$	−6.64292	+	0.776446i	−0.478168	+	0.0558898i	−0.351763	−	0.936089i	$-0.614418\pi$
$193$	−6.64292	+	0.776446i	−0.478168	+	0.0558898i	−0.126405	+	0.991979i	$0.540344\pi$
$194$	1.12774	−	1.19534i	0.0809673	−	0.0858204i
$195$	−4.83828	+	3.78485i	−0.346476	+	0.271039i
$196$	−20.0449	−	2.34291i	−1.43178	−	0.167351i
$197$	−4.92101	+	4.12922i	−0.350607	+	0.294194i	−0.801034	−	0.598619i	$-0.795716\pi$
$197$	−4.92101	+	4.12922i	−0.350607	+	0.294194i	0.450427	+	0.892813i	$0.351272\pi$
$198$	1.79925	+	16.9193i	0.127867	+	1.20240i
$199$	15.5119	+	13.0161i	1.09961	+	0.922685i	0.997399	−	0.0720778i	$-0.0229630\pi$
$199$	15.5119	+	13.0161i	1.09961	+	0.922685i	0.102214	+	0.994762i	$0.467407\pi$
$200$	−2.63977	−	2.79800i	−0.186660	−	0.197848i
$201$	1.87708	−	2.34872i	0.132399	−	0.165666i
$202$	−6.29354	+	3.16074i	−0.442812	+	0.222389i
$203$	−33.1030	+	16.6250i	−2.32338	+	1.16684i
$204$	0.892668	+	2.28152i	0.0624992	+	0.159738i
$205$	4.77104	+	5.05701i	0.333224	+	0.353197i
$206$	−2.16095	−	1.81326i	−0.150561	−	0.126335i
$207$	1.40106	+	0.0962470i	0.0973801	+	0.00668963i
$208$	2.52983	−	2.12278i	0.175412	−	0.147188i
$209$	3.15617	+	0.368903i	0.218317	+	0.0255176i
$210$	8.99369	+	3.62728i	0.620624	+	0.250306i
$211$	4.98594	−	5.28479i	0.343247	−	0.363820i	−0.532636	−	0.846344i	$-0.678799\pi$
$211$	4.98594	−	5.28479i	0.343247	−	0.363820i	0.875883	+	0.482524i	$0.160280\pi$
$212$	−7.87821	+	0.920831i	−0.541078	+	0.0632429i
$213$	−9.38950	+	9.29226i	−0.643358	+	0.636695i
$214$	0.489183	+	8.39894i	0.0334398	+	0.574140i
$215$	−5.23903	+	9.07427i	−0.357299	+	0.618860i
$216$	−5.16868	−	0.533650i	−0.351684	−	0.0363103i
$217$	−7.07290	−	12.2506i	−0.480140	−	0.831626i
$218$	14.0752	−	9.25738i	0.953290	−	0.626989i
$219$	−7.96187	+	16.8448i	−0.538013	+	1.13827i
$220$	2.41243	−	5.59264i	0.162646	−	0.377056i
$221$	4.54531	+	1.07726i	0.305751	+	0.0724643i
$222$	1.54112	−	7.27230i	0.103433	−	0.488085i
$223$	10.1697	−	13.6602i	0.681012	−	0.914758i	−0.318437	−	0.947944i	$-0.603158\pi$
$223$	10.1697	−	13.6602i	0.681012	−	0.914758i	0.999449	+	0.0331861i	$0.0105654\pi$
$224$	−4.89915	−	1.78315i	−0.327338	−	0.119141i
$225$	9.18437	+	6.98728i	0.612291	+	0.465819i
$226$	−6.41974	+	2.33660i	−0.427035	+	0.155428i
$227$	−0.986451	+	3.29498i	−0.0654731	+	0.218695i	−0.984465	−	0.175581i	$-0.943820\pi$
$227$	−0.986451	+	3.29498i	−0.0654731	+	0.218695i	0.918992	+	0.394276i	$0.129005\pi$
$228$	−0.310035	+	0.919572i	−0.0205325	+	0.0609002i
$229$	1.38456	−	23.7720i	0.0914944	−	1.57090i	−0.570442	−	0.821338i	$-0.693228\pi$
$229$	1.38456	−	23.7720i	0.0914944	−	1.57090i	0.661936	−	0.749560i	$-0.269735\pi$
$230$	−0.420016	−	0.276249i	−0.0276950	−	0.0182153i
$231$	−1.22308	−	51.2006i	−0.0804729	−	3.36875i
$232$	−6.91364	+	1.63856i	−0.453902	+	0.107577i
$233$	2.27078	−	12.8782i	0.148764	−	0.843681i	−0.815504	−	0.578751i	$-0.803540\pi$
$233$	2.27078	−	12.8782i	0.148764	−	0.843681i	0.964268	−	0.264929i	$-0.0853487\pi$
$234$	−6.44700	+	7.52277i	−0.421453	+	0.491779i
$235$	0.258663	+	1.46695i	0.0168733	+	0.0956934i
$236$	−0.434014	−	1.00616i	−0.0282519	−	0.0654953i
$237$	1.82113	+	3.42000i	0.118295	+	0.222153i
$238$	−2.11502	−	7.06464i	−0.137096	−	0.457933i
$239$	−8.89870	−	11.9530i	−0.575609	−	0.773177i	0.415012	−	0.909816i	$-0.363777\pi$
$239$	−8.89870	−	11.9530i	−0.575609	−	0.773177i	−0.990621	+	0.136639i	$0.956370\pi$
$240$	1.51811	+	1.07481i	0.0979934	+	0.0693787i
$241$	3.45496	+	1.73515i	0.222554	+	0.111771i	0.556583	−	0.830792i	$-0.312112\pi$
$241$	3.45496	+	1.73515i	0.222554	+	0.111771i	−0.334029	+	0.942563i	$0.608408\pi$
$242$	−21.1666			−1.36064
$243$	15.5592	−	0.954039i	0.998125	−	0.0612016i
$244$	8.42358			0.539265
$245$	−19.3677	−	9.72681i	−1.23736	−	0.621423i
$246$	9.15168	+	6.47933i	0.583490	+	0.413107i
$247$	1.10492	+	1.48416i	0.0703043	+	0.0944350i
$248$	−0.778173	−	2.59928i	−0.0494140	−	0.165054i
$249$	9.41491	+	17.6807i	0.596646	+	1.12047i
$250$	−3.76299	−	8.72360i	−0.237993	−	0.551729i
$251$	4.35201	+	24.6815i	0.274696	+	1.55788i	0.739924	+	0.672690i	$0.234861\pi$
$251$	4.35201	+	24.6815i	0.274696	+	1.55788i	−0.465228	+	0.885191i	$0.654028\pi$
$252$	15.3740	+	2.87619i	0.968470	+	0.181183i
$253$	−0.461031	+	2.61463i	−0.0289847	+	0.164381i
$254$	1.22694	−	0.290791i	0.0769854	−	0.0182459i
$255$	0.0628320	+	2.63027i	0.00393469	+	0.164714i
$256$	−0.835488	−	0.549509i	−0.0522180	−	0.0343443i
$257$	1.24192	−	21.3229i	0.0774689	−	1.33009i	−0.705802	−	0.708409i	$-0.749413\pi$
$257$	1.24192	−	21.3229i	0.0774689	−	1.33009i	0.783271	−	0.621680i	$-0.213550\pi$
$258$	−5.39906	+	16.0138i	−0.336131	+	0.996975i
$259$	−6.41755	+	21.4361i	−0.398767	+	1.33198i
$260$	3.33266	−	1.21299i	0.206683	−	0.0752265i
$261$	19.6590	−	8.23841i	1.21686	−	0.509945i
$262$	−2.52165	−	0.917806i	−0.155788	−	0.0567022i
$263$	−1.09986	+	1.47736i	−0.0678200	+	0.0910981i	−0.834739	−	0.550646i	$-0.814381\pi$
$263$	−1.09986	+	1.47736i	−0.0678200	+	0.0910981i	0.766919	+	0.641744i	$0.221789\pi$
$264$	2.03652	−	9.61002i	0.125339	−	0.591456i
$265$	−8.28850	−	1.96441i	−0.509158	−	0.120673i
$266$	1.15697	−	2.68215i	0.0709383	−	0.164453i
$267$	−4.15038	+	8.78090i	−0.253999	+	0.537382i
$268$	−1.45031	+	0.953887i	−0.0885921	+	0.0582679i
$269$	6.45590	+	11.1819i	0.393623	+	0.681775i	0.992924	−	0.118749i	$-0.0378882\pi$
$269$	6.45590	+	11.1819i	0.393623	+	0.681775i	−0.599301	+	0.800523i	$0.704555\pi$
$270$	−5.01995	−	2.43699i	−0.305504	−	0.148310i
$271$	−3.07287	+	5.32237i	−0.186664	+	0.323311i	−0.944136	−	0.329557i	$-0.893101\pi$
$271$	−3.07287	+	5.32237i	−0.186664	+	0.323311i	0.757472	+	0.652867i	$0.226434\pi$
$272$	−0.0822442	−	1.41208i	−0.00498679	−	0.0856198i
$273$	21.1966	−	20.9771i	1.28288	−	1.26959i
$274$	18.9451	−	2.21437i	1.14452	−	0.133775i
$275$	−14.9716	+	15.8690i	−0.902824	+	0.956938i
$276$	−0.751953	−	0.303273i	−0.0452622	−	0.0182549i
$277$	−10.6331	−	1.24283i	−0.638879	−	0.0746743i	−0.209515	−	0.977806i	$-0.567188\pi$
$277$	−10.6331	−	1.24283i	−0.638879	−	0.0746743i	−0.429365	+	0.903131i	$0.641262\pi$
$278$	9.87918	−	8.28962i	0.592514	−	0.497178i
$279$	3.57721	+	7.31162i	0.214162	+	0.437735i
$280$	−4.28902	−	3.59892i	−0.256318	−	0.215076i
$281$	9.37188	+	9.93361i	0.559080	+	0.592590i	0.943830	−	0.330431i	$-0.107194\pi$
$281$	9.37188	+	9.93361i	0.559080	+	0.592590i	−0.384751	+	0.923021i	$0.625713\pi$
$282$	0.875369	+	2.23731i	0.0521275	+	0.133230i
$283$	−12.6807	+	6.36849i	−0.753790	+	0.378568i	−0.783825	−	0.620981i	$-0.786734\pi$
$283$	−12.6807	+	6.36849i	−0.753790	+	0.378568i	0.0300353	+	0.999549i	$0.490438\pi$
$284$	6.81565	−	3.42295i	0.404434	−	0.203115i
$285$	−0.650629	+	0.814109i	−0.0385400	+	0.0482237i
$286$	−12.8534	−	13.6238i	−0.760035	−	0.805590i
$287$	−25.8557	−	21.6955i	−1.52621	−	1.28065i
$288$	2.74213	+	1.21685i	0.161581	+	0.0717037i
$289$	−11.4901	+	9.64135i	−0.675889	+	0.567138i
$290$	−7.57872	−	0.885826i	−0.445038	−	0.0520175i
$291$	2.24191	−	1.75379i	0.131423	−	0.102809i
$292$	7.38190	−	7.82435i	0.431993	−	0.457886i
$293$	4.91970	−	0.575030i	0.287412	−	0.0335936i	0.0288345	−	0.999584i	$-0.490820\pi$
$293$	4.91970	−	0.575030i	0.287412	−	0.0335936i	0.258577	+	0.965991i	$0.416746\pi$
$294$	−33.7164	−	9.22266i	−1.96638	−	0.537877i
$295$	−0.0684228	−	1.17477i	−0.00398373	−	0.0683980i
$296$	−2.14595	+	3.71690i	−0.124731	+	0.216040i
$297$	−1.31702	+	29.4409i	−0.0764215	+	1.70833i
$298$	2.46783	+	4.27440i	0.142957	+	0.247610i
$299$	−1.29162	+	0.849510i	−0.0746961	+	0.0491284i
$300$	−3.79311	−	5.47758i	−0.218995	−	0.316248i
$301$	20.1479	−	46.7081i	1.16131	−	2.69221i
$302$	−7.91920	−	1.87689i	−0.455699	−	0.108003i
$303$	−11.5989	+	3.77656i	−0.666339	+	0.216958i
$304$	0.334575	−	0.449412i	0.0191892	−	0.0257756i
$305$	8.50064	+	3.09398i	0.486745	+	0.177161i
$306$	0.935561	+	4.13900i	0.0534824	+	0.236611i
$307$	29.8416	−	10.8615i	1.70315	−	0.619896i	0.706973	−	0.707241i	$-0.250060\pi$
$307$	29.8416	−	10.8615i	1.70315	−	0.619896i	0.996178	+	0.0873444i	$0.0278381\pi$
$308$	−8.48051	+	28.3269i	−0.483222	+	1.61407i
$309$	−3.22914	−	3.66681i	−0.183699	−	0.208598i
$310$	0.169423	−	2.90888i	0.00962258	−	0.165213i
$311$	14.2314	+	9.36016i	0.806991	+	0.530766i	0.884673	−	0.466212i	$-0.154382\pi$
$311$	14.2314	+	9.36016i	0.806991	+	0.530766i	−0.0776823	+	0.996978i	$0.524752\pi$
$312$	4.88397	−	2.97749i	0.276500	−	0.168567i
$313$	−24.5742	+	5.82419i	−1.38902	+	0.329203i	−0.856032	−	0.516923i	$-0.827078\pi$
$313$	−24.5742	+	5.82419i	−1.38902	+	0.329203i	−0.532984	+	0.846125i	$0.678929\pi$
$314$	−1.24644	+	7.06891i	−0.0703406	+	0.398922i
$315$	14.4582	+	8.54936i	0.814627	+	0.481702i
$316$	−0.388456	−	2.20304i	−0.0218524	−	0.123931i
$317$	6.46401	+	14.9853i	0.363055	+	0.841656i	0.997631	+	0.0687955i	$0.0219156\pi$
$317$	6.46401	+	14.9853i	0.363055	+	0.841656i	−0.634576	+	0.772861i	$0.718825\pi$
$318$	−13.7303	−	0.471053i	−0.769956	−	0.0264153i
$319$	11.5574	+	38.6044i	0.647091	+	2.16143i
$320$	−0.641296	−	0.861410i	−0.0358495	−	0.0481543i
$321$	−1.34558	+	14.5098i	−0.0751031	+	0.809857i
$322$	2.18098	+	1.09533i	0.121541	+	0.0610402i
$323$	0.792498			0.0440957
$324$	−8.71229	−	2.25742i	−0.484016	−	0.125412i
$325$	−12.7036			−0.704668
$326$	1.93594	+	0.972267i	0.107222	+	0.0538489i
$327$	26.5092	−	12.1939i	1.46596	−	0.674322i
$328$	−3.86596	−	5.19288i	−0.213462	−	0.286729i
$329$	−2.07403	−	6.92774i	−0.114345	−	0.381939i
$330$	5.58491	−	8.94992i	0.307439	−	0.492677i
$331$	−9.09083	−	21.0749i	−0.499677	−	1.15838i	−0.962340	−	0.271848i	$-0.912365\pi$
$331$	−9.09083	−	21.0749i	−0.499677	−	1.15838i	0.462663	−	0.886534i	$-0.346894\pi$
$332$	−2.00824	−	11.3893i	−0.110217	−	0.625070i
$333$	4.52947	−	12.0527i	0.248214	−	0.660485i
$334$	−2.29850	+	13.0354i	−0.125768	+	0.713267i
$335$	−1.81394	+	0.429913i	−0.0991064	+	0.0234886i
$336$	−7.92595	−	4.32704i	−0.432396	−	0.236059i
$337$	22.7711	+	14.9768i	1.24042	+	0.815838i	0.988398	−	0.151883i	$-0.0485338\pi$
$337$	22.7711	+	14.9768i	1.24042	+	0.815838i	0.252023	+	0.967721i	$0.418904\pi$
$338$	−0.121743	+	2.09025i	−0.00662196	+	0.113695i
$339$	−11.6008	+	2.33247i	−0.630067	+	0.126683i
$340$	0.435660	−	1.45520i	0.0236270	−	0.0789195i
$341$	−14.4604	+	5.26316i	−0.783076	+	0.285016i
$342$	−0.769953	+	1.49411i	−0.0416343	+	0.0807924i
$343$	64.5773	+	23.5042i	3.48684	+	1.26911i
$344$	5.82642	−	7.82624i	0.314139	−	0.421963i
$345$	−0.647439	−	0.582239i	−0.0348570	−	0.0313467i
$346$	−11.9681	−	2.83648i	−0.643407	−	0.152490i
$347$	4.50877	−	10.4525i	0.242044	−	0.561120i	−0.753282	−	0.657698i	$-0.771530\pi$
$347$	4.50877	−	10.4525i	0.242044	−	0.561120i	0.995325	+	0.0965778i	$0.0307896\pi$
$348$	−12.2651	+	1.00875i	−0.657477	+	0.0540748i
$349$	12.3021	−	8.09124i	0.658518	−	0.433114i	−0.175779	−	0.984430i	$-0.556244\pi$
$349$	12.3021	−	8.09124i	0.658518	−	0.433114i	0.834297	+	0.551315i	$0.185874\pi$
$350$	10.0275	+	17.3682i	0.535995	+	0.928371i
$351$	−12.9956	+	11.2064i	−0.693652	+	0.598152i
$352$	−2.83578	+	4.91172i	−0.151148	+	0.261795i
$353$	−1.12945	−	19.3920i	−0.0601148	−	1.03213i	−0.884631	−	0.466293i	$-0.845589\pi$
$353$	−1.12945	−	19.3920i	−0.0601148	−	1.03213i	0.824516	−	0.565839i	$-0.191448\pi$
$354$	−0.481673	−	1.83580i	−0.0256006	−	0.0975716i
$355$	8.13524	−	0.950874i	0.431774	−	0.0504671i
$356$	3.84805	−	4.07870i	0.203946	−	0.216171i
$357$	−1.78539	−	12.6475i	−0.0944930	−	0.669378i
$358$	21.4819	+	2.51088i	1.13535	+	0.132704i
$359$	−12.8043	+	10.7441i	−0.675784	+	0.567050i	−0.914771	−	0.403972i	$-0.867629\pi$
$359$	−12.8043	+	10.7441i	−0.675784	+	0.567050i	0.238987	+	0.971023i	$0.423185\pi$
$360$	2.32026	+	2.23517i	0.122289	+	0.117804i
$361$	−14.3144	−	12.0112i	−0.753388	−	0.632168i
$362$	−6.58242	−	6.97696i	−0.345964	−	0.366701i
$363$	−36.2465	−	5.50220i	−1.90245	−	0.288790i
$364$	−15.3862	+	7.72723i	−0.806455	+	0.405017i
$365$	10.3233	−	5.18456i	0.540347	−	0.271372i
$366$	14.4248	+	2.18968i	0.753998	+	0.114457i
$367$	−4.81051	−	5.09884i	−0.251107	−	0.266157i	0.589543	−	0.807737i	$-0.299308\pi$
$367$	−4.81051	−	5.09884i	−0.251107	−	0.266157i	−0.840649	+	0.541580i	$0.817826\pi$
$368$	0.358600	+	0.300901i	0.0186933	+	0.0156856i
$369$	13.9874	+	13.4744i	0.728153	+	0.701447i
$370$	−3.53080	+	2.96269i	−0.183558	+	0.154023i
$371$	41.0736	+	4.80082i	2.13243	+	0.249246i
$372$	−0.656896	−	4.65338i	−0.0340585	−	0.241266i
$373$	4.31982	−	4.57874i	0.223672	−	0.237078i	−0.605814	−	0.795607i	$-0.707152\pi$
$373$	4.31982	−	4.57874i	0.223672	−	0.237078i	0.829485	+	0.558528i	$0.188634\pi$
$374$	−7.96802	+	0.931328i	−0.412017	+	0.0481578i
$375$	−4.17621	−	15.9168i	−0.215658	−	0.821938i
$376$	−0.0806504	−	1.38471i	−0.00415923	−	0.0714112i
$377$	−11.7322	+	20.3208i	−0.604240	+	1.04658i
$378$	25.5793	+	8.92169i	1.31566	+	0.458882i
$379$	−4.24620	−	7.35464i	−0.218113	−	0.377782i	0.736118	−	0.676853i	$-0.236657\pi$
$379$	−4.24620	−	7.35464i	−0.218113	−	0.377782i	−0.954231	+	0.299071i	$0.903323\pi$
$380$	0.502705	−	0.330634i	0.0257882	−	0.0169612i
$381$	2.17665	−	0.179021i	0.111513	−	0.00917150i
$382$	−1.52175	+	3.52780i	−0.0778593	+	0.180498i
$383$	26.2193	+	6.21409i	1.33974	+	0.317525i	0.837138	−	0.546991i	$-0.184227\pi$
$383$	26.2193	+	6.21409i	1.33974	+	0.317525i	0.502605	+	0.864516i	$0.332375\pi$
$384$	−1.28787	−	1.15818i	−0.0657216	−	0.0591031i
$385$	−18.9625	+	25.4711i	−0.966421	+	1.29813i
$386$	6.28480	+	2.28748i	0.319888	+	0.116430i
$387$	−13.4083	+	26.0191i	−0.681581	+	1.32262i
$388$	−1.54426	+	0.562063i	−0.0783978	+	0.0285344i
$389$	8.78641	−	29.3487i	0.445489	−	1.48804i	−0.380730	−	0.924686i	$-0.624327\pi$
$389$	8.78641	−	29.3487i	0.445489	−	1.48804i	0.826218	−	0.563350i	$-0.190488\pi$
$390$	6.02228	−	1.21085i	0.304950	−	0.0613138i
$391$	−0.0385001	+	0.661021i	−0.00194703	+	0.0334293i
$392$	16.8612	+	11.0898i	0.851621	+	0.560120i
$393$	−4.07958	−	2.22718i	−0.205788	−	0.112346i
$394$	6.25076	−	1.48146i	0.314909	−	0.0746348i
$395$	0.417168	−	2.36588i	0.0209900	−	0.119040i
$396$	5.98550	−	15.9271i	0.300783	−	0.800369i
$397$	−3.88827	−	22.0515i	−0.195147	−	1.10673i	−0.912210	−	0.409724i	$-0.865625\pi$
$397$	−3.88827	−	22.0515i	−0.195147	−	1.10673i	0.717063	−	0.697008i	$-0.245486\pi$
$398$	−8.02038	−	18.5933i	−0.402025	−	0.932000i
$399$	2.67845	−	4.29226i	0.134090	−	0.214882i
$400$	1.10325	+	3.68511i	0.0551625	+	0.184255i
$401$	13.9066	+	18.6798i	0.694461	+	0.932823i	0.999811	−	0.0194168i	$-0.00618095\pi$
$401$	13.9066	+	18.6798i	0.694461	+	0.932823i	−0.305350	+	0.952240i	$0.598774\pi$
$402$	−2.73153	+	1.25646i	−0.136236	+	0.0626667i
$403$	−8.00734	−	4.02144i	−0.398874	−	0.200322i
$404$	7.04265			0.350385
$405$	−7.96284	−	5.47809i	−0.395677	−	0.272209i
$406$	37.0432			1.83842
$407$	21.7526	+	10.9246i	1.07824	+	0.541512i
$408$	0.226227	−	2.43947i	0.0111999	−	0.120772i
$409$	3.63030	+	4.87634i	0.179507	+	0.241120i	0.882765	−	0.469815i	$-0.155679\pi$
$409$	3.63030	+	4.87634i	0.179507	+	0.241120i	−0.703258	+	0.710935i	$0.748272\pi$
$410$	−1.99398	−	6.66035i	−0.0984755	−	0.328931i
$411$	33.0179	+	1.13276i	1.62865	+	0.0558751i
$412$	1.11731	+	2.59022i	0.0550460	+	0.127611i
$413$	0.992034	+	5.62610i	0.0488148	+	0.276842i
$414$	−1.20883	−	0.714802i	−0.0594110	−	0.0351306i
$415$	2.15668	−	12.2311i	0.105867	−	0.600403i
$416$	−3.21344	+	0.761598i	−0.157552	+	0.0373404i
$417$	19.0723	−	11.6274i	0.933975	−	0.569394i
$418$	−2.65489	−	1.74615i	−0.129855	−	0.0854070i
$419$	0.839499	−	14.4136i	0.0410122	−	0.704152i	−0.913658	−	0.406485i	$-0.866754\pi$
$419$	0.839499	−	14.4136i	0.0410122	−	0.704152i	0.954670	−	0.297667i	$-0.0962086\pi$
$420$	−6.40914	−	7.27782i	−0.312734	−	0.355121i
$421$	−1.71397	+	5.72504i	−0.0835336	+	0.279022i	−0.989543	−	0.144235i	$-0.953928\pi$
$421$	−1.71397	+	5.72504i	−0.0835336	+	0.279022i	0.906010	+	0.423257i	$0.139113\pi$
$422$	−6.82741	+	2.48498i	−0.332353	+	0.120967i
$423$	0.917431	+	4.05879i	0.0446070	+	0.197345i
$424$	7.45349	+	2.71285i	0.361974	+	0.131748i
$425$	−3.24918	+	4.36440i	−0.157608	+	0.211705i
$426$	12.5611	−	4.08986i	0.608588	−	0.198155i
$427$	−42.7332	−	10.1279i	−2.06800	−	0.490126i
$428$	3.33229	−	7.72511i	0.161072	−	0.373407i
$429$	−18.4691	−	26.6710i	−0.891695	−	1.28769i
$430$	8.75429	−	5.75779i	0.422170	−	0.277665i
$431$	−4.17774	−	7.23605i	−0.201234	−	0.348548i	0.747692	−	0.664046i	$-0.231162\pi$
$431$	−4.17774	−	7.23605i	−0.201234	−	0.348548i	−0.948926	+	0.315497i	$0.897829\pi$
$432$	4.37940	+	2.79658i	0.210704	+	0.134551i
$433$	0.106189	−	0.183924i	0.00510310	−	0.00883883i	−0.863463	−	0.504413i	$-0.831709\pi$
$433$	0.106189	−	0.183924i	0.00510310	−	0.00883883i	0.868566	+	0.495574i	$0.165042\pi$
$434$	0.822505	+	14.1219i	0.0394815	+	0.677871i
$435$	−12.7478	−	3.48698i	−0.611210	−	0.167188i
$436$	−16.7327	+	1.95578i	−0.801352	+	0.0936647i
$437$	−0.179985	+	0.190773i	−0.00860987	+	0.00912593i
$438$	14.6749	−	11.4798i	0.701195	−	0.548525i
$439$	−22.5058	−	2.63055i	−1.07414	−	0.125549i	−0.439415	−	0.898284i	$-0.644814\pi$
$439$	−22.5058	−	2.63055i	−1.07414	−	0.125549i	−0.634729	+	0.772735i	$0.718888\pi$
$440$	−4.66580	+	3.91507i	−0.222433	+	0.186644i
$441$	−55.3398	−	24.5577i	−2.63523	−	1.16941i
$442$	−3.57837	−	3.00261i	−0.170206	−	0.142819i
$443$	12.5701	+	13.3236i	0.597225	+	0.633021i	0.953512	−	0.301355i	$-0.0974390\pi$
$443$	12.5701	+	13.3236i	0.597225	+	0.633021i	−0.356287	+	0.934377i	$0.615958\pi$
$444$	−4.64100	+	5.80711i	−0.220252	+	0.275593i
$445$	5.38136	−	2.70262i	0.255101	−	0.128116i
$446$	−15.2187	+	7.64310i	−0.720625	+	0.361911i
$447$	3.11487	+	7.96113i	0.147329	+	0.376549i
$448$	3.57777	+	3.79221i	0.169034	+	0.179165i
$449$	12.9119	+	10.8344i	0.609352	+	0.511307i	0.894436	−	0.447196i	$-0.147577\pi$
$449$	12.9119	+	10.8344i	0.609352	+	0.511307i	−0.285084	+	0.958502i	$0.592022\pi$
$450$	−5.07156	−	10.3660i	−0.239076	−	0.488658i
$451$	−28.1270	+	23.6014i	−1.32445	+	1.11135i
$452$	6.78555	+	0.793118i	0.319166	+	0.0373051i
$453$	−13.0732	−	5.27261i	−0.614233	−	0.247729i
$454$	2.36031	−	2.50178i	0.110775	−	0.117414i
$455$	−18.3652	+	2.14658i	−0.860972	+	0.100633i
$456$	0.689760	−	0.682617i	0.0323010	−	0.0319665i
$457$	0.722429	+	12.4036i	0.0337938	+	0.580217i	0.972123	+	0.234473i	$0.0753364\pi$
$457$	0.722429	+	12.4036i	0.0337938	+	0.580217i	−0.938329	+	0.345744i	$0.887627\pi$
$458$	−11.9061	+	20.6220i	−0.556338	+	0.963605i
$459$	0.526167	+	7.33095i	0.0245594	+	0.342180i
$460$	0.251360	+	0.435368i	0.0117197	+	0.0202991i
$461$	24.6019	−	16.1809i	1.14583	−	0.753621i	0.172945	−	0.984931i	$-0.444672\pi$
$461$	24.6019	−	16.1809i	1.14583	−	0.753621i	0.972880	+	0.231310i	$0.0743013\pi$
$462$	−21.8858	+	46.3034i	−1.01822	+	2.15423i
$463$	−10.7936	+	25.0223i	−0.501620	+	1.16289i	0.459855	+	0.887994i	$0.347901\pi$
$463$	−10.7936	+	25.0223i	−0.501620	+	1.16289i	−0.961475	+	0.274892i	$0.911358\pi$
$464$	6.91364	+	1.63856i	0.320957	+	0.0760683i
$465$	1.04628	−	4.93722i	0.0485200	−	0.228958i
$466$	−7.80898	+	10.4893i	−0.361744	+	0.485907i
$467$	1.56709	+	0.570374i	0.0725163	+	0.0263938i	0.378024	−	0.925796i	$-0.376604\pi$
$467$	1.56709	+	0.570374i	0.0725163	+	0.0263938i	−0.305507	+	0.952190i	$0.598826\pi$
$468$	9.13746	−	3.82919i	0.422379	−	0.177004i
$469$	8.50439	−	3.09534i	0.392696	−	0.142930i
$470$	0.427217	−	1.42700i	0.0197061	−	0.0658228i
$471$	−3.97198	+	11.7810i	−0.183019	+	0.542841i
$472$	−0.0637136	+	1.09392i	−0.00293266	+	0.0503518i
$473$	−46.2333	−	30.4081i	−2.12581	−	1.39817i
$474$	−0.0925315	−	3.87355i	−0.00425011	−	0.177918i
$475$	−2.09713	+	0.497030i	−0.0962231	+	0.0228053i
$476$	−1.28056	+	7.26241i	−0.0586943	+	0.332872i
$477$	−23.3897	−	4.37578i	−1.07094	−	0.200353i
$478$	2.58766	+	14.6754i	0.118357	+	0.671235i
$479$	−13.2595	−	30.7391i	−0.605844	−	1.40450i	−0.894499	−	0.447071i	$-0.852467\pi$
$479$	−13.2595	−	30.7391i	−0.605844	−	1.40450i	0.288655	−	0.957433i	$-0.406792\pi$
$480$	−0.874256	−	1.64181i	−0.0399042	−	0.0749380i
$481$	4.06510	+	13.5784i	0.185353	+	0.619121i
$482$	−2.30874	−	3.10117i	−0.105160	−	0.141254i
$483$	3.45005	+	2.44261i	0.156983	+	0.111143i
$484$	18.9152	+	9.49957i	0.859782	+	0.431799i
$485$	−1.76483			−0.0801368
$486$	−14.3324	−	6.13041i	−0.650131	−	0.278081i
$487$	−17.7293			−0.803393			−0.401696	−	0.915773i	$-0.631579\pi$
$487$	−17.7293			−0.803393			−0.401696	+	0.915773i	$0.631579\pi$
$488$	−7.52759	−	3.78050i	−0.340758	−	0.171135i
$489$	3.06244	+	2.16818i	0.138488	+	0.0980487i
$490$	12.9422	+	17.3844i	0.584669	+	0.785347i
$491$	−4.58939	−	15.3296i	−0.207116	−	0.691817i	−0.996918	−	0.0784541i	$-0.975002\pi$
$491$	−4.58939	−	15.3296i	−0.207116	−	0.691817i	0.789801	−	0.613363i	$-0.210184\pi$
$492$	−5.27032	−	9.89740i	−0.237604	−	0.446209i
$493$	3.98062	+	9.22811i	0.179278	+	0.415613i
$494$	−0.321300	−	1.82218i	−0.0144560	−	0.0819839i
$495$	11.8903	−	13.8744i	0.534429	−	0.623606i
$496$	−0.471154	+	2.67204i	−0.0211554	+	0.119978i
$497$	−38.6916	+	9.17007i	−1.73555	+	0.411334i
$498$	−0.478370	−	20.0255i	−0.0214363	−	0.897363i
$499$	6.16978	+	4.05793i	0.276197	+	0.181658i	0.680049	−	0.733167i	$-0.261958\pi$
$499$	6.16978	+	4.05793i	0.276197	+	0.181658i	−0.403852	+	0.914824i	$0.632329\pi$
$500$	−0.552411	+	9.48452i	−0.0247045	+	0.424161i
$501$	−7.32454	+	21.7248i	−0.327236	+	0.970593i
$502$	7.18793	−	24.0094i	0.320813	−	1.07159i
$503$	25.1227	−	9.14393i	1.12017	−	0.407708i	0.285454	−	0.958392i	$-0.407856\pi$
$503$	25.1227	−	9.14393i	1.12017	−	0.407708i	0.834713	+	0.550685i	$0.185633\pi$
$504$	−12.4479	−	9.47008i	−0.554472	−	0.421831i
$505$	7.10708	+	2.58676i	0.316261	+	0.115109i
$506$	1.58544	−	2.12961i	0.0704813	−	0.0946728i
$507$	−0.751831	+	3.54777i	−0.0333900	+	0.157562i
$508$	−1.22694	−	0.290791i	−0.0544369	−	0.0129018i
$509$	15.6362	−	36.2487i	0.693061	−	1.60670i	−0.0981636	−	0.995170i	$-0.531297\pi$
$509$	15.6362	−	36.2487i	0.693061	−	1.60670i	0.791225	−	0.611526i	$-0.209444\pi$
$510$	1.12431	−	2.37869i	0.0497854	−	0.105330i
$511$	−46.8561	+	30.8177i	−2.07279	+	1.36330i
$512$	0.500000	+	0.866025i	0.0220971	+	0.0382733i
$513$	−1.70688	+	2.35842i	−0.0753607	+	0.104127i
$514$	−10.6795	+	18.4975i	−0.471054	+	0.815890i
$515$	0.176145	+	3.02430i	0.00776190	+	0.133267i
$516$	12.0118	−	11.8874i	0.528788	−	0.523312i
$517$	−7.81361	+	0.913281i	−0.343642	+	0.0401660i
$518$	15.3554	−	16.2758i	0.674680	−	0.715119i
$519$	−19.7572	−	7.96834i	−0.867244	−	0.349772i
$520$	−3.52257	−	0.411729i	−0.154475	−	0.0180555i
$521$	12.7620	−	10.7086i	0.559113	−	0.469152i	−0.318900	−	0.947788i	$-0.603313\pi$
$521$	12.7620	−	10.7086i	0.559113	−	0.469152i	0.878013	+	0.478637i	$0.158869\pi$
$522$	−21.2654	−	1.46084i	−0.930759	−	0.0639394i
$523$	−7.28396	−	6.11197i	−0.318505	−	0.267258i	0.469491	−	0.882937i	$-0.344437\pi$
$523$	−7.28396	−	6.11197i	−0.318505	−	0.267258i	−0.787997	+	0.615679i	$0.788882\pi$
$524$	1.84152	+	1.95190i	0.0804471	+	0.0852690i
$525$	12.6567	+	32.3486i	0.552384	+	1.41181i
$526$	1.64591	−	0.826605i	0.0717649	−	0.0360417i
$527$	−3.42962	+	1.72242i	−0.149396	+	0.0750297i
$528$	−6.13287	+	7.67384i	−0.266899	+	0.333961i
$529$	15.6332	+	16.5702i	0.679703	+	0.720443i
$530$	6.52525	+	5.47533i	0.283439	+	0.237833i
$531$	−0.347623	−	3.26889i	−0.0150856	−	0.141858i
$532$	−2.23765	+	1.87761i	−0.0970146	+	0.0814049i
$533$	−21.2353	−	2.48205i	−0.919801	−	0.107509i
$534$	7.64978	−	5.98421i	0.331038	−	0.258962i
$535$	6.20020	−	6.57183i	0.268058	−	0.284125i
$536$	1.72415	−	0.201524i	0.0744720	−	0.00870453i
$537$	36.1337	+	9.88386i	1.55928	+	0.426520i
$538$	−0.750754	−	12.8899i	−0.0323673	−	0.555725i
$539$	57.2298	−	99.1249i	2.46506	−	4.26961i
$540$	3.39227	+	4.43072i	0.145980	+	0.190668i
$541$	−6.49225	−	11.2449i	−0.279124	−	0.483456i	0.692044	−	0.721856i	$-0.256711\pi$
$541$	−6.49225	−	11.2449i	−0.279124	−	0.483456i	−0.971167	+	0.238399i	$0.923377\pi$
$542$	5.13469	−	3.37714i	0.220554	−	0.145061i
$543$	−9.45832	−	13.6587i	−0.405895	−	0.586149i
$544$	−0.560244	+	1.29879i	−0.0240202	+	0.0556852i
$545$	−17.6042	−	4.17226i	−0.754079	−	0.178720i
$546$	−28.3565	+	9.23279i	−1.21355	+	0.395127i
$547$	5.30799	−	7.12987i	0.226953	−	0.304851i	−0.674031	−	0.738703i	$-0.735439\pi$
$547$	5.30799	−	7.12987i	0.226953	−	0.304851i	0.900984	+	0.433852i	$0.142846\pi$
$548$	−17.9238	−	6.52373i	−0.765666	−	0.278680i
$549$	24.1324	+	7.49937i	1.02994	+	0.320065i
$550$	20.5012	−	7.46181i	0.874172	−	0.318173i
$551$	−1.14172	+	3.81363i	−0.0486391	+	0.162466i
$552$	0.535861	+	0.608490i	0.0228078	+	0.0258991i
$553$	−0.678138	+	11.6432i	−0.0288374	+	0.495118i
$554$	8.94428	+	5.88274i	0.380006	+	0.249934i
$555$	−6.81640	+	4.15560i	−0.289340	+	0.176395i
$556$	−12.5487	+	2.97410i	−0.532185	+	0.126130i
$557$	−4.15726	+	23.5770i	−0.176149	+	0.998989i	0.760661	+	0.649149i	$0.224875\pi$
$557$	−4.15726	+	23.5770i	−0.176149	+	0.998989i	−0.936810	+	0.349839i	$0.886236\pi$
$558$	0.0847388	−	8.13935i	0.00358728	−	0.344566i
$559$	−5.59525	−	31.7322i	−0.236654	−	1.34213i
$560$	2.21762	+	5.14102i	0.0937115	+	0.217248i
$561$	−13.8868	−	0.476423i	−0.586301	−	0.0201146i
$562$	−3.91682	−	13.0831i	−0.165221	−	0.551877i
$563$	15.4509	+	20.7541i	0.651177	+	0.874683i	0.997998	−	0.0632486i	$-0.0201461\pi$
$563$	15.4509	+	20.7541i	0.651177	+	0.874683i	−0.346820	+	0.937932i	$0.612739\pi$
$564$	0.221843	−	2.39220i	0.00934129	−	0.100730i
$565$	6.55632	+	3.29271i	0.275826	+	0.138525i
$566$	14.1901			0.596453
$567$	41.4836	+	21.9270i	1.74215	+	0.920849i
$568$	−7.62690			−0.320018
$569$	22.1765	+	11.1375i	0.929688	+	0.466907i	0.848146	−	0.529763i	$-0.177719\pi$
$569$	22.1765	+	11.1375i	0.929688	+	0.466907i	0.0815422	+	0.996670i	$0.474015\pi$
$570$	0.946795	−	0.435512i	0.0396569	−	0.0182416i
$571$	−6.40856	−	8.60819i	−0.268190	−	0.360242i	0.647543	−	0.762029i	$-0.275797\pi$
$571$	−6.40856	−	8.60819i	−0.268190	−	0.360242i	−0.915733	+	0.401787i	$0.868389\pi$
$572$	5.37185	+	17.9432i	0.224608	+	0.750244i
$573$	−3.52293	+	5.64555i	−0.147172	+	0.235846i
$574$	13.3686	+	30.9918i	0.557994	+	1.29357i
$575$	−0.312692	−	1.77336i	−0.0130402	−	0.0739544i
$576$	−1.90433	−	2.31808i	−0.0793472	−	0.0965868i
$577$	−4.65875	+	26.4211i	−0.193946	+	1.09992i	0.719965	+	0.694010i	$0.244158\pi$
$577$	−4.65875	+	26.4211i	−0.193946	+	1.09992i	−0.913912	+	0.405913i	$0.866953\pi$
$578$	14.5950	−	3.45907i	0.607070	−	0.143878i
$579$	10.1677	+	5.55087i	0.422554	+	0.230686i
$580$	6.37504	+	4.19293i	0.264709	+	0.174102i
$581$	−3.50584	+	60.1930i	−0.145447	+	2.49723i
$582$	−2.79054	+	0.561072i	−0.115672	+	0.0232572i
$583$	12.9021	−	43.0961i	0.534351	−	1.78486i
$584$	−10.1083	+	3.67911i	−0.418283	+	0.152243i
$585$	10.6275	−	0.508031i	0.439393	−	0.0210045i
$586$	−4.65447	−	1.69409i	−0.192275	−	0.0699822i
$587$	−27.2567	+	36.6120i	−1.12500	+	1.51114i	−0.293215	+	0.956047i	$0.594725\pi$
$587$	−27.2567	+	36.6120i	−1.12500	+	1.51114i	−0.831788	+	0.555094i	$0.812682\pi$
$588$	25.9910	+	23.3736i	1.07185	+	0.963910i
$589$	−1.47921	−	0.350578i	−0.0609496	−	0.0144453i
$590$	−0.466093	+	1.08053i	−0.0191888	+	0.0444845i
$591$	11.0891	−	0.912034i	0.456145	−	0.0375160i
$592$	3.58584	−	2.35844i	0.147377	−	0.0969313i
$593$	−11.1174	−	19.2559i	−0.456537	−	0.790745i	0.542238	−	0.840225i	$-0.317577\pi$
$593$	−11.1174	−	19.2559i	−0.456537	−	0.790745i	−0.998775	+	0.0494800i	$0.984244\pi$
$594$	14.3900	−	25.7182i	0.590428	−	1.05523i
$595$	−3.95976	+	6.85850i	−0.162334	+	0.281171i
$596$	−0.286983	−	4.92731i	−0.0117553	−	0.201830i
$597$	−8.90109	−	33.9247i	−0.364298	−	1.38845i
$598$	1.53549	−	0.179473i	0.0627909	−	0.00733920i
$599$	4.24691	−	4.50146i	0.173524	−	0.183925i	−0.634775	−	0.772697i	$-0.718907\pi$
$599$	4.24691	−	4.50146i	0.173524	−	0.183925i	0.808299	+	0.588773i	$0.200389\pi$
$600$	0.931309	+	6.59729i	0.0380205	+	0.269333i
$601$	−5.78820	−	0.676543i	−0.236106	−	0.0275968i	−0.00278278	−	0.999996i	$-0.500886\pi$
$601$	−5.78820	−	0.676543i	−0.236106	−	0.0275968i	−0.233323	+	0.972399i	$0.574960\pi$
$602$	−38.9674	+	32.6975i	−1.58819	+	1.33265i
$603$	−5.00417	+	1.44156i	−0.203786	+	0.0587048i
$604$	6.23451	+	5.23138i	0.253679	+	0.212862i
$605$	15.5990	+	16.5340i	0.634191	+	0.672203i
$606$	12.0601	+	1.83071i	0.489907	+	0.0743676i
$607$	7.03531	−	3.53326i	0.285554	−	0.143411i	−0.300257	−	0.953858i	$-0.597072\pi$
$607$	7.03531	−	3.53326i	0.285554	−	0.143411i	0.585811	+	0.810448i	$0.300776\pi$
$608$	−0.500683	+	0.251452i	−0.0203054	+	0.0101977i
$609$	63.4341	+	9.62926i	2.57048	+	0.390197i
$610$	−6.20788	−	6.57996i	−0.251350	−	0.266415i
$611$	−3.50903	−	2.94442i	−0.141960	−	0.119119i
$612$	1.02153	−	4.11862i	0.0412929	−	0.166485i
$613$	−34.1027	+	28.6156i	−1.37740	+	1.15577i	−0.407233	+	0.913324i	$0.633506\pi$
$613$	−34.1027	+	28.6156i	−1.37740	+	1.15577i	−0.970164	+	0.242449i	$0.922049\pi$
$614$	−31.5421	−	3.68674i	−1.27293	−	0.148785i
$615$	−1.68322	−	11.9237i	−0.0678739	−	0.480811i
$616$	20.2915	−	21.5078i	0.817570	−	0.866573i
$617$	9.49110	−	1.10935i	0.382097	−	0.0446608i	0.0771236	−	0.997022i	$-0.475426\pi$
$617$	9.49110	−	1.10935i	0.382097	−	0.0446608i	0.304974	+	0.952361i	$0.401352\pi$
$618$	1.24000	+	4.72602i	0.0498802	+	0.190108i
$619$	−2.09189	−	35.9163i	−0.0840800	−	1.44360i	−0.731696	−	0.681631i	$-0.761271\pi$
$619$	−2.09189	−	35.9163i	−0.0840800	−	1.44360i	0.647616	−	0.761967i	$-0.275766\pi$
$620$	−1.45690	+	2.52343i	−0.0585107	+	0.101344i
$621$	−1.88424	−	1.53828i	−0.0756118	−	0.0617292i
$622$	−8.51684	−	14.7516i	−0.341494	−	0.591485i
$623$	−24.4253	+	16.0647i	−0.978577	+	0.643620i
$624$	−5.70077	+	0.468865i	−0.228213	+	0.0187696i
$625$	3.57690	−	8.29218i	0.143076	−	0.331687i
$626$	24.5742	+	5.82419i	0.982183	+	0.232782i
$627$	−4.09242	−	3.68029i	−0.163435	−	0.146977i
$628$	4.28638	−	5.75761i	0.171045	−	0.229753i
$629$	5.70467	+	2.07633i	0.227460	+	0.0827887i
$630$	−9.08337	−	14.1288i	−0.361890	−	0.562905i
$631$	17.4364	−	6.34633i	0.694133	−	0.252644i	0.0292289	−	0.999573i	$-0.490695\pi$
$631$	17.4364	−	6.34633i	0.694133	−	0.252644i	0.664904	+	0.746929i	$0.268473\pi$
$632$	−0.641588	+	2.14305i	−0.0255210	+	0.0852460i
$633$	−12.3375	+	2.48059i	−0.490370	+	0.0985947i
$634$	0.948922	−	16.2924i	0.0376865	−	0.647052i
$635$	−1.13136	−	0.744108i	−0.0448967	−	0.0295290i
$636$	12.0584	+	6.58308i	0.478147	+	0.261036i
$637$	64.8514	−	15.3701i	2.56950	−	0.608984i
$638$	6.99756	−	39.6851i	0.277036	−	1.57115i
$639$	22.5732	−	3.73840i	0.892983	−	0.147889i
$640$	0.186483	+	1.05760i	0.00737139	+	0.0418052i
$641$	−15.5596	−	36.0713i	−0.614568	−	1.42473i	−0.886643	−	0.462454i	$-0.846969\pi$
$641$	−15.5596	−	36.0713i	−0.614568	−	1.42473i	0.272075	−	0.962276i	$-0.412290\pi$
$642$	7.71444	−	12.3625i	0.304465	−	0.487910i
$643$	−12.2189	−	40.8138i	−0.481865	−	1.60954i	−0.760633	−	0.649182i	$-0.775111\pi$
$643$	−12.2189	−	40.8138i	−0.481865	−	1.60954i	0.278769	−	0.960358i	$-0.410074\pi$
$644$	−1.45741	−	1.95764i	−0.0574300	−	0.0771418i
$645$	16.4879	−	7.58418i	0.649209	−	0.298627i
$646$	−0.708202	−	0.355672i	−0.0278638	−	0.0139937i
$647$	21.4942			0.845023			0.422512	−	0.906357i	$-0.361149\pi$
$647$	21.4942			0.845023			0.422512	+	0.906357i	$0.361149\pi$
$648$	6.77246	+	5.92737i	0.266047	+	0.232849i
$649$	6.21475			0.243950
$650$	11.3523	+	5.70136i	0.445276	+	0.223626i
$651$	−2.26245	+	24.3966i	−0.0886722	+	0.956176i
$652$	−1.29367	−	1.73770i	−0.0506640	−	0.0680535i
$653$	14.3632	+	47.9765i	0.562077	+	1.87747i	0.472149	+	0.881519i	$0.343478\pi$
$653$	14.3632	+	47.9765i	0.562077	+	1.87747i	0.0899279	+	0.995948i	$0.471336\pi$
$654$	−29.1621	−	1.00048i	−1.14033	−	0.0391219i
$655$	1.14143	+	2.64614i	0.0445995	+	0.103393i
$656$	1.12418	+	6.37557i	0.0438920	+	0.248924i
$657$	28.1139	−	15.8437i	1.09683	−	0.618120i
$658$	−1.25574	+	7.12168i	−0.0489540	+	0.277632i
$659$	19.5762	−	4.63965i	0.762582	−	0.180735i	0.169118	−	0.985596i	$-0.445908\pi$
$659$	19.5762	−	4.63965i	0.762582	−	0.180735i	0.593464	+	0.804861i	$0.297760\pi$
$660$	−9.00757	+	5.49144i	−0.350619	+	0.213754i
$661$	35.3424	+	23.2451i	1.37466	+	0.904128i	0.999737	−	0.0229283i	$-0.00729894\pi$
$661$	35.3424	+	23.2451i	1.37466	+	0.904128i	0.374923	+	0.927056i	$0.377669\pi$
$662$	−1.33454	+	22.9132i	−0.0518684	+	0.890546i
$663$	−5.34720	−	6.07195i	−0.207668	−	0.235815i
$664$	−3.31688	+	11.0792i	−0.128720	+	0.429955i
$665$	−2.94777	+	1.07290i	−0.114310	+	0.0416053i
$666$	−9.45694	+	8.73788i	−0.366449	+	0.338586i
$667$	−3.12548	−	1.13758i	−0.121019	−	0.0440473i
$668$	7.90430	−	10.6173i	0.305827	−	0.410797i
$669$	−28.0477	+	9.13226i	−1.08439	+	0.353074i
$670$	1.81394	+	0.429913i	0.0700788	+	0.0166090i
$671$	−18.9227	+	43.8677i	−0.730502	+	1.69349i
$672$	5.14092	+	7.42394i	0.198315	+	0.286385i
$673$	−21.7023	+	14.2738i	−0.836561	+	0.550215i	−0.893965	−	0.448136i	$-0.852088\pi$
$673$	−21.7023	+	14.2738i	−0.836561	+	0.550215i	0.0574045	+	0.998351i	$0.481718\pi$
$674$	−13.6274	−	23.6034i	−0.524909	−	0.909169i
$675$	−5.99011	−	19.0694i	−0.230559	−	0.733982i
$676$	1.04690	−	1.81328i	0.0402653	−	0.0697415i
$677$	1.09343	+	18.7734i	0.0420238	+	0.721522i	0.951856	+	0.306545i	$0.0991731\pi$
$677$	1.09343	+	18.7734i	0.0420238	+	0.721522i	−0.909832	+	0.414976i	$0.863790\pi$
$678$	11.4136	+	3.12204i	0.438338	+	0.119901i
$679$	8.50986	−	0.994660i	0.326578	−	0.0381715i
$680$	−1.04241	+	1.10489i	−0.0399748	+	0.0423708i
$681$	4.69220	−	3.67058i	0.179805	−	0.140657i
$682$	15.2844	+	1.78649i	0.585270	+	0.0684083i
$683$	25.0008	−	20.9782i	0.956630	−	0.802708i	−0.0237714	−	0.999717i	$-0.507567\pi$
$683$	25.0008	−	20.9782i	0.956630	−	0.802708i	0.980402	+	0.197009i	$0.0631229\pi$
$684$	1.35861	−	0.989635i	0.0519478	−	0.0378396i
$685$	−15.6916	−	13.1668i	−0.599545	−	0.503078i
$686$	−47.1597	−	49.9863i	−1.80057	−	1.90849i
$687$	−25.7491	+	32.2189i	−0.982390	+	1.22923i
$688$	−8.71909	+	4.37889i	−0.332412	+	0.166944i
$689$	23.4083	−	11.7561i	0.891785	−	0.447871i
$690$	0.317264	+	0.810878i	0.0120780	+	0.0308696i
$691$	−1.26019	−	1.33573i	−0.0479400	−	0.0508134i	0.702960	−	0.711230i	$-0.251861\pi$
$691$	−1.26019	−	1.33573i	−0.0479400	−	0.0508134i	−0.750900	+	0.660416i	$0.770380\pi$
$692$	9.42204	+	7.90603i	0.358172	+	0.300542i
$693$	−49.5144	+	73.6024i	−1.88090	+	2.79592i
$694$	−8.72026	+	7.31717i	−0.331017	+	0.277756i
$695$	−13.7559	−	1.60784i	−0.521792	−	0.0609887i
$696$	11.4132	+	4.60310i	0.432616	+	0.174480i
$697$	−6.28403	+	6.66069i	−0.238025	+	0.252292i
$698$	−14.6249	+	1.70941i	−0.553562	+	0.0647021i
$699$	−16.0990	+	15.9323i	−0.608920	+	0.602614i
$700$	−1.16610	−	20.0212i	−0.0440744	−	0.756729i
$701$	−3.97145	+	6.87876i	−0.150000	+	0.259807i	−0.931227	−	0.364440i	$-0.881261\pi$
$701$	−3.97145	+	6.87876i	−0.150000	+	0.259807i	0.781227	+	0.624247i	$0.214594\pi$
$702$	16.6427	−	4.18198i	0.628137	−	0.157839i
$703$	1.20233	+	2.08250i	0.0453468	+	0.0785429i
$704$	4.73852	−	3.11658i	0.178590	−	0.117460i
$705$	1.10253	−	2.33260i	0.0415235	−	0.0878507i
$706$	−7.69379	+	17.8362i	−0.289560	+	0.671275i
$707$	−35.7276	−	8.46760i	−1.34368	−	0.318457i
$708$	−0.393466	+	1.85670i	−0.0147874	+	0.0697792i
$709$	−1.43165	+	1.92304i	−0.0537667	+	0.0722213i	−0.828193	−	0.560443i	$-0.810631\pi$
$709$	−1.43165	+	1.92304i	−0.0537667	+	0.0722213i	0.774427	+	0.632664i	$0.218038\pi$
$710$	−7.69667	−	2.80136i	−0.288851	−	0.105133i
$711$	0.848461	−	6.65724i	0.0318198	−	0.249666i
$712$	−5.26926	+	1.91785i	−0.197474	+	0.0718746i
$713$	0.364278	−	1.21677i	0.0136423	−	0.0455685i
$714$	−4.08071	+	12.1035i	−0.152717	+	0.452963i
$715$	−1.16955	+	20.0804i	−0.0437388	+	0.750966i
$716$	−18.0701	−	11.8849i	−0.675310	−	0.444158i
$717$	0.616389	+	25.8032i	0.0230195	+	0.963639i
$718$	16.2643	−	3.85470i	0.606977	−	0.143856i
$719$	−4.31555	+	24.4747i	−0.160943	+	0.912752i	0.792207	+	0.610253i	$0.208932\pi$
$719$	−4.31555	+	24.4747i	−0.160943	+	0.912752i	−0.953150	+	0.302499i	$0.902179\pi$
$720$	−1.07032	−	3.03875i	−0.0398886	−	0.113248i
$721$	−2.55386	−	14.4837i	−0.0951107	−	0.539399i
$722$	7.40118	+	17.1579i	0.275443	+	0.638550i
$723$	−3.14742	−	5.91070i	−0.117054	−	0.219821i
$724$	2.75101	+	9.18902i	0.102241	+	0.341507i
$725$	−16.3212	−	21.9232i	−0.606155	−	0.814208i
$726$	29.9216	+	21.1843i	1.11050	+	0.786224i
$727$	−0.777379	−	0.390415i	−0.0288314	−	0.0144797i	0.434325	−	0.900756i	$-0.356987\pi$
$727$	−0.777379	−	0.390415i	−0.0288314	−	0.0144797i	−0.463156	+	0.886277i	$0.653283\pi$
$728$	17.2176			0.638126
$729$	−22.9497	−	14.2236i	−0.849990	−	0.526799i
$730$	−11.5521			−0.427561
$731$	−12.3329	−	6.19382i	−0.456149	−	0.229087i
$732$	−11.9078	−	8.43062i	−0.440124	−	0.311605i
$733$	2.75679	+	3.70301i	0.101824	+	0.136774i	0.850115	−	0.526597i	$-0.176532\pi$
$733$	2.75679	+	3.70301i	0.101824	+	0.136774i	−0.748290	+	0.663371i	$0.769125\pi$
$734$	2.01047	+	6.71545i	0.0742079	+	0.247872i
$735$	17.6436	+	33.1339i	0.650795	+	1.22216i
$736$	−0.185413	−	0.429835i	−0.00683440	−	0.0158439i
$737$	−1.70960	−	9.69564i	−0.0629740	−	0.357143i
$738$	−6.45228	−	18.3186i	−0.237512	−	0.674319i
$739$	6.07695	−	34.4641i	0.223544	−	1.26778i	−0.641905	−	0.766784i	$-0.721856\pi$
$739$	6.07695	−	34.4641i	0.223544	−	1.26778i	0.865449	−	0.500997i	$-0.167033\pi$
$740$	4.48489	−	1.06294i	0.164868	−	0.0390744i
$741$	−0.0765347	−	3.20389i	−0.00281157	−	0.117698i
$742$	−34.5501	−	22.7240i	−1.26837	−	0.834223i
$743$	2.94575	−	50.5765i	0.108069	−	1.85547i	−0.314646	−	0.949209i	$-0.601886\pi$
$743$	2.94575	−	50.5765i	0.108069	−	1.85547i	0.422715	−	0.906263i	$-0.361077\pi$
$744$	−1.50141	+	4.45322i	−0.0550443	+	0.163263i
$745$	1.52019	−	5.07779i	0.0556955	−	0.186036i
$746$	−5.91527	+	2.15298i	−0.216573	+	0.0788262i
$747$	4.38638	−	34.4167i	0.160489	−	1.25924i
$748$	7.53846	+	2.74378i	0.275634	+	0.100322i
$749$	−26.1930	+	35.1833i	−0.957070	+	1.28557i
$750$	−3.41144	+	16.0980i	−0.124568	+	0.587816i
$751$	41.9116	+	9.93324i	1.52938	+	0.362469i	0.907299	−	0.420486i	$-0.138140\pi$
$751$	41.9116	+	9.93324i	1.52938	+	0.362469i	0.622078	+	0.782955i	$0.286289\pi$
$752$	−0.549387	+	1.27362i	−0.0200341	+	0.0464442i
$753$	18.5500	−	39.2459i	0.676000	−	1.43020i
$754$	19.6043	−	12.8939i	0.713945	−	0.469569i
$755$	4.37006	+	7.56917i	0.159043	+	0.275470i
$756$	−18.8544	−	19.4527i	−0.685729	−	0.707487i
$757$	24.5670	−	42.5512i	0.892902	−	1.54655i	0.0565218	−	0.998401i	$-0.481999\pi$
$757$	24.5670	−	42.5512i	0.892902	−	1.54655i	0.836380	−	0.548150i	$-0.184668\pi$
$758$	0.493789	+	8.47804i	0.0179352	+	0.307936i
$759$	3.26854	−	3.23469i	0.118641	−	0.117412i
$760$	−0.597621	+	0.0698519i	−0.0216780	+	0.00253380i
$761$	−33.9694	+	36.0055i	−1.23139	+	1.30520i	−0.294467	+	0.955662i	$0.595142\pi$
$761$	−33.9694	+	36.0055i	−1.23139	+	1.30520i	−0.936923	+	0.349536i	$0.886339\pi$
$762$	−2.02547	−	0.816901i	−0.0733751	−	0.0295932i
$763$	87.2372	+	10.1966i	3.15820	+	0.369141i
$764$	2.94316	−	2.46960i	0.106480	−	0.0893470i
$765$	2.54364	−	3.78109i	0.0919657	−	0.136706i
$766$	−20.6415	−	17.3203i	−0.745809	−	0.625808i
$767$	2.48333	+	2.63218i	0.0896680	+	0.0950425i
$768$	0.631096	+	1.61298i	0.0227727	+	0.0582035i
$769$	−9.59955	+	4.82108i	−0.346169	+	0.173852i	−0.613385	−	0.789784i	$-0.710193\pi$
$769$	−9.59955	+	4.82108i	−0.346169	+	0.173852i	0.267216	+	0.963637i	$0.413896\pi$
$770$	28.3770	−	14.2515i	1.02264	−	0.513587i
$771$	−23.0964	+	28.8996i	−0.831795	+	1.04080i
$772$	−4.58968	−	4.86478i	−0.165186	−	0.175087i
$773$	−19.9593	−	16.7479i	−0.717887	−	0.602379i	0.208913	−	0.977934i	$-0.433008\pi$
$773$	−19.9593	−	16.7479i	−0.717887	−	0.602379i	−0.926800	+	0.375555i	$0.877452\pi$
$774$	23.6594	−	17.2339i	0.850420	−	0.619459i
$775$	7.99532	−	6.70887i	0.287200	−	0.240990i
$776$	1.63225	+	0.190783i	0.0585944	+	0.00684871i
$777$	30.5260	−	23.8797i	1.09512	−	0.856678i
$778$	−21.0235	+	22.2836i	−0.753728	+	0.798905i
$779$	−3.60267	+	0.421092i	−0.129079	+	0.0150872i
$780$	−5.92513	−	1.62074i	−0.212154	−	0.0580317i
$781$	2.51514	+	43.1833i	0.0899988	+	1.54522i
$782$	0.331071	−	0.573431i	0.0118391	−	0.0205059i
$783$	−36.0358	−	8.02945i	−1.28781	−	0.286949i
$784$	−10.0907	−	17.4775i	−0.360381	−	0.624197i
$785$	6.44036	−	4.23589i	0.229866	−	0.151185i
$786$	2.64609	+	3.82119i	0.0943829	+	0.136297i
$787$	3.86262	−	8.95456i	0.137688	−	0.319196i	−0.835396	−	0.549649i	$-0.814762\pi$
$787$	3.86262	−	8.95456i	0.137688	−	0.319196i	0.973083	+	0.230453i	$0.0740208\pi$
$788$	−6.25076	−	1.48146i	−0.222674	−	0.0527748i
$789$	3.03338	−	0.987659i	0.107991	−	0.0351616i
$790$	−1.43460	+	1.92700i	−0.0510407	+	0.0685596i
$791$	−33.4698	−	12.1820i	−1.19005	−	0.433142i
$792$	−12.4969	+	11.5467i	−0.444059	+	0.410295i
$793$	−26.1408	+	9.51449i	−0.928289	+	0.337869i
$794$	−6.42200	+	21.4510i	−0.227908	+	0.761267i
$795$	9.75076	+	11.0724i	0.345824	+	0.392696i
$796$	−1.17740	+	20.2151i	−0.0417318	+	0.716507i
$797$	0.570220	+	0.375040i	0.0201982	+	0.0132846i	0.559568	−	0.828784i	$-0.310967\pi$
$797$	0.570220	+	0.375040i	0.0201982	+	0.0132846i	−0.539370	+	0.842069i	$0.681337\pi$
$798$	−4.31991	+	2.63362i	−0.152923	+	0.0932291i
$799$	−1.90907	+	0.452459i	−0.0675382	+	0.0160068i
$800$	0.667974	−	3.78827i	0.0236165	−	0.133936i
$801$	14.6553	−	8.25902i	0.517820	−	0.291818i
$802$	−4.04390	−	22.9341i	−0.142795	−	0.809832i
$803$	24.1644	+	56.0194i	0.852744	+	1.97688i
$804$	3.00488	+	0.103090i	0.105974	+	0.00363571i
$805$	−0.751701	−	2.51085i	−0.0264940	−	0.0884960i
$806$	5.35080	+	7.18737i	0.188474	+	0.253164i
$807$	2.06508	−	22.2683i	0.0726943	−	0.783882i
$808$	−6.29354	−	3.16074i	−0.221406	−	0.111194i
$809$	−8.33293			−0.292970			−0.146485	−	0.989213i	$-0.546796\pi$
$809$	−8.33293			−0.292970			−0.146485	+	0.989213i	$0.546796\pi$
$810$	4.65729	+	8.46912i	0.163641	+	0.297575i
$811$	31.2123			1.09601			0.548005	−	0.836475i	$-0.315387\pi$
$811$	31.2123			1.09601			0.548005	+	0.836475i	$0.315387\pi$
$812$	−33.1030	−	16.6250i	−1.16169	−	0.583422i
$813$	9.67069	−	4.44838i	0.339166	−	0.156012i
$814$	−14.5359	−	19.5251i	−0.509484	−	0.684356i
$815$	−0.667247	−	2.22876i	−0.0233726	−	0.0780700i
$816$	−1.29700	+	2.07846i	−0.0454039	+	0.0727606i
$817$	−2.16520	−	5.01950i	−0.0757508	−	0.175610i
$818$	−1.05566	−	5.98694i	−0.0369102	−	0.209328i
$819$	−50.9586	+	8.43936i	−1.78064	+	0.294895i
$820$	−1.20728	+	6.84680i	−0.0421599	+	0.239101i
$821$	−17.8882	+	4.23958i	−0.624302	+	0.147962i	−0.530578	−	0.847636i	$-0.678025\pi$
$821$	−17.8882	+	4.23958i	−0.624302	+	0.147962i	−0.0937235	+	0.995598i	$0.529877\pi$
$822$	−28.9975	−	15.8307i	−1.01140	−	0.552158i
$823$	−15.3848	−	10.1187i	−0.536279	−	0.352716i	0.252301	−	0.967649i	$-0.418813\pi$
$823$	−15.3848	−	10.1187i	−0.536279	−	0.352716i	−0.788580	+	0.614933i	$0.789183\pi$
$824$	0.164022	−	2.81615i	0.00571398	−	0.0981053i
$825$	37.0465	−	7.44865i	1.28979	−	0.259329i
$826$	1.63848	−	5.47289i	0.0570099	−	0.190426i
$827$	23.3620	−	8.50308i	0.812377	−	0.295681i	0.0977715	−	0.995209i	$-0.468829\pi$
$827$	23.3620	−	8.50308i	0.812377	−	0.295681i	0.714605	+	0.699528i	$0.246606\pi$
$828$	0.759451	+	1.18129i	0.0263927	+	0.0410528i
$829$	−5.70127	−	2.07509i	−0.198013	−	0.0720710i	0.241110	−	0.970498i	$-0.422489\pi$
$829$	−5.70127	−	2.07509i	−0.198013	−	0.0720710i	−0.439123	+	0.898427i	$0.644711\pi$
$830$	−7.41660	+	9.96222i	−0.257434	+	0.345794i
$831$	13.7873	+	12.3988i	0.478275	+	0.430111i
$832$	3.21344	+	0.761598i	0.111406	+	0.0264037i
$833$	11.3064	−	26.2113i	0.391745	−	0.908168i
$834$	−22.2620	+	1.83096i	−0.770869	+	0.0634008i
$835$	11.8764	−	7.81120i	0.410998	−	0.270318i
$836$	1.58883	+	2.75193i	0.0549507	+	0.0951774i
$837$	2.26091	−	13.9161i	0.0781484	−	0.481010i
$838$	−7.21903	+	12.5037i	−0.249377	+	0.431934i
$839$	2.89076	+	49.6325i	0.0998002	+	1.71350i	0.562341	+	0.826905i	$0.309901\pi$
$839$	2.89076	+	49.6325i	0.0998002	+	1.71350i	−0.462541	+	0.886598i	$0.653062\pi$
$840$	2.46113	+	9.38011i	0.0849172	+	0.323645i
$841$	−21.3380	+	2.49405i	−0.735792	+	0.0860018i
$842$	4.10105	−	4.34686i	0.141332	−	0.149803i
$843$	−3.30639	−	23.4221i	−0.113878	−	0.806700i
$844$	7.21645	+	0.843483i	0.248401	+	0.0290339i
$845$	1.72249	−	1.44534i	0.0592555	−	0.0497212i
$846$	1.00174	−	4.03881i	0.0344404	−	0.138857i
$847$	−84.5359	−	70.9340i	−2.90469	−	2.43732i
$848$	−5.44316	−	5.76941i	−0.186919	−	0.198122i
$849$	24.2996	+	3.68866i	0.833959	+	0.126595i
$850$	4.86231	−	2.44195i	0.166776	−	0.0837580i
$851$	−1.79542	+	0.901694i	−0.0615462	+	0.0309097i
$852$	−13.0606	−	1.98259i	−0.447447	−	0.0679223i
$853$	−28.2098	−	29.9007i	−0.965887	−	1.02378i	−0.999703	−	0.0243519i	$-0.992248\pi$
$853$	−28.2098	−	29.9007i	−0.965887	−	1.02378i	0.0338168	−	0.999428i	$-0.489234\pi$
$854$	33.6423	+	28.2293i	1.15122	+	0.965986i
$855$	1.73453	−	0.499670i	0.0593198	−	0.0170883i
$856$	−6.44486	+	5.40788i	−0.220281	+	0.184838i
$857$	−3.51142	−	0.410426i	−0.119948	−	0.0140199i	0.0559072	−	0.998436i	$-0.482195\pi$
$857$	−3.51142	−	0.410426i	−0.119948	−	0.0140199i	−0.175855	+	0.984416i	$0.556269\pi$
$858$	4.53465	+	32.1230i	0.154810	+	1.09666i
$859$	−20.6126	+	21.8481i	−0.703293	+	0.745447i	−0.976266	−	0.216575i	$-0.930512\pi$
$859$	−20.6126	+	21.8481i	−0.703293	+	0.745447i	0.272973	+	0.962022i	$0.411993\pi$
$860$	−10.4072	+	1.21643i	−0.354883	+	0.0414799i
$861$	14.8366	+	56.5466i	0.505629	+	1.92710i
$862$	0.485828	+	8.34134i	0.0165474	+	0.284107i
$863$	−16.2324	+	28.1154i	−0.552558	+	0.957059i	0.445531	+	0.895267i	$0.353015\pi$
$863$	−16.2324	+	28.1154i	−0.552558	+	0.957059i	−0.998089	+	0.0617926i	$0.980318\pi$
$864$	−2.65847	−	4.46459i	−0.0904429	−	0.151888i
$865$	6.60435	+	11.4391i	0.224555	+	0.388940i
$866$	−0.177439	+	0.116703i	−0.00602961	+	0.00396574i
$867$	25.8921	−	2.12952i	0.879341	−	0.0723221i
$868$	5.60286	−	12.9889i	0.190174	−	0.440872i
$869$	12.3455	+	2.92593i	0.418791	+	0.0992554i
$870$	9.82689	+	8.83728i	0.333163	+	0.299612i
$871$	3.42333	−	4.59833i	0.115995	−	0.155808i
$872$	15.8307	+	5.76189i	0.536094	+	0.195122i
$873$	−4.92447	+	0.235406i	−0.166668	+	0.00796729i
$874$	0.246460	−	0.0897041i	0.00833663	−	0.00303428i
$875$	14.2059	−	47.4512i	0.480249	−	1.60414i
$876$	−18.2661	+	3.67262i	−0.617154	+	0.124086i
$877$	−3.21360	+	55.1754i	−0.108516	+	1.86314i	0.304625	+	0.952472i	$0.401469\pi$
$877$	−3.21360	+	55.1754i	−0.108516	+	1.86314i	−0.413140	+	0.910667i	$0.635568\pi$
$878$	18.9313	+	12.4513i	0.638902	+	0.420212i
$879$	−7.53010	−	4.11093i	−0.253984	−	0.138658i
$880$	5.92659	−	1.40463i	0.199785	−	0.0473500i
$881$	−1.98467	+	11.2557i	−0.0668654	+	0.379212i	0.932950	+	0.360006i	$0.117225\pi$
$881$	−1.98467	+	11.2557i	−0.0668654	+	0.379212i	−0.999816	+	0.0192069i	$0.993886\pi$
$882$	38.4320	+	46.7820i	1.29407	+	1.57523i
$883$	0.553376	+	3.13835i	0.0186226	+	0.105614i	0.992702	−	0.120591i	$-0.0384791\pi$
$883$	0.553376	+	3.13835i	0.0186226	+	0.105614i	−0.974080	+	0.226205i	$0.927368\pi$
$884$	1.85018	+	4.28920i	0.0622283	+	0.144261i
$885$	−1.07903	+	1.72917i	−0.0362713	+	0.0581254i
$886$	−5.25348	−	17.5478i	−0.176494	−	0.589531i
$887$	−26.7110	−	35.8790i	−0.896866	−	1.20470i	−0.978127	−	0.208007i	$-0.933302\pi$
$887$	−26.7110	−	35.8790i	−0.896866	−	1.20470i	0.0812612	−	0.996693i	$-0.474105\pi$
$888$	6.75357	−	3.10655i	0.226635	−	0.104249i
$889$	5.87471	+	2.95039i	0.197031	+	0.0989529i
$890$	−6.02189			−0.201854
$891$	31.3272	−	40.3001i	1.04950	−	1.35011i
$892$	17.0301			0.570210
$893$	−0.694478	−	0.348780i	−0.0232398	−	0.0116715i
$894$	0.789397	−	8.51228i	0.0264014	−	0.284693i
$895$	−13.8701	−	18.6307i	−0.463625	−	0.622756i
$896$	−1.49527	−	4.99455i	−0.0499534	−	0.166856i
$897$	2.67608	+	0.0918098i	0.0893516	+	0.00306544i
$898$	−6.67606	−	15.4768i	−0.222783	−	0.516469i
$899$	−3.34762	−	18.9853i	−0.111649	−	0.633195i
$900$	−0.120138	+	11.5395i	−0.00400459	+	0.384650i
$901$	1.94822	−	11.0489i	0.0649047	−	0.368093i
$902$	35.7275	−	8.46758i	1.18960	−	0.281940i
$903$	−75.2286	+	45.8629i	−2.50345	+	1.52622i
$904$	−5.70784	−	3.75411i	−0.189840	−	0.124860i
$905$	−0.598947	+	10.2835i	−0.0199097	+	0.341836i
$906$	9.31631	+	10.5790i	0.309514	+	0.351465i
$907$	−10.2468	+	34.2267i	−0.340239	+	1.13648i	0.601145	+	0.799140i	$0.294712\pi$
$907$	−10.2468	+	34.2267i	−0.340239	+	1.13648i	−0.941384	+	0.337338i	$0.890474\pi$
$908$	−3.23204	+	1.17637i	−0.107259	+	0.0390391i
$909$	20.1762	+	6.26995i	0.669202	+	0.207961i
$910$	17.3751	+	6.32401i	0.575978	+	0.209639i
$911$	21.2665	−	28.5659i	0.704592	−	0.946431i	−0.295368	−	0.955384i	$-0.595442\pi$
$911$	21.2665	−	28.5659i	0.704592	−	0.946431i	0.999960	+	0.00895235i	$0.00284966\pi$
$912$	−0.922750	+	0.300445i	−0.0305553	+	0.00994872i
$913$	63.8237	+	15.1265i	2.11226	+	0.500614i
$914$	4.92115	−	11.4085i	0.162777	−	0.377360i
$915$	−8.92013	−	12.8815i	−0.294891	−	0.425848i
$916$	19.8949	−	13.0851i	0.657345	−	0.432343i
$917$	−6.99527	−	12.1162i	−0.231004	−	0.400111i
$918$	2.81992	−	6.78732i	0.0930714	−	0.224015i
$919$	−16.3947	+	28.3964i	−0.540811	+	0.936712i	0.458047	+	0.888928i	$0.348549\pi$
$919$	−16.3947	+	28.3964i	−0.540811	+	0.936712i	−0.998858	+	0.0477840i	$0.984784\pi$
$920$	−0.0292305	−	0.501869i	−0.000963702	−	0.0165461i
$921$	−53.0553	−	14.5125i	−1.74823	−	0.478205i
$922$	−29.2471	+	3.41849i	−0.963201	+	0.112582i
$923$	−17.2847	+	18.3207i	−0.568933	+	0.603034i
$924$	40.3388	−	31.5559i	1.32705	−	1.03811i
$925$	−16.3981	−	1.91666i	−0.539166	−	0.0630195i
$926$	20.8755	−	17.5166i	0.686011	−	0.575632i
$927$	0.894909	+	8.41532i	0.0293927	+	0.276395i
$928$	−5.44287	−	4.56711i	−0.178671	−	0.149923i
$929$	−32.7960	−	34.7617i	−1.07600	−	1.14049i	−0.989543	−	0.144239i	$-0.953927\pi$
$929$	−32.7960	−	34.7617i	−1.07600	−	1.14049i	−0.0864580	−	0.996255i	$-0.527555\pi$
$930$	−3.15081	+	3.94249i	−0.103319	+	0.129279i
$931$	10.1044	−	5.07464i	0.331160	−	0.166315i
$932$	11.6859	−	5.86890i	0.382786	−	0.192242i
$933$	−10.7499	−	27.4751i	−0.351936	−	0.899493i
$934$	−1.14442	−	1.21301i	−0.0374466	−	0.0396910i
$935$	6.59964	+	5.53775i	0.215831	+	0.181104i
$936$	−9.88407	−	0.678996i	−0.323071	−	0.0221937i
$937$	−22.4954	+	18.8759i	−0.734893	+	0.616648i	−0.931461	−	0.363842i	$-0.881465\pi$
$937$	−22.4954	+	18.8759i	−0.734893	+	0.616648i	0.196568	+	0.980490i	$0.437020\pi$
$938$	−8.98899	−	1.05066i	−0.293501	−	0.0343053i
$939$	40.5677	+	16.3615i	1.32388	+	0.533938i
$940$	−1.02221	+	1.08348i	−0.0333409	+	0.0353393i
$941$	−6.83017	+	0.798332i	−0.222657	+	0.0260249i	−0.226690	−	0.973967i	$-0.572790\pi$
$941$	−6.83017	+	0.798332i	−0.222657	+	0.0260249i	0.00403283	+	0.999992i	$0.498716\pi$
$942$	8.83681	−	8.74529i	0.287919	−	0.284937i
$943$	−0.176212	−	3.02544i	−0.00573825	−	0.0985219i
$944$	0.547887	−	0.948968i	0.0178322	−	0.0308863i
$945$	−11.8819	−	26.5558i	−0.386519	−	0.863862i
$946$	27.6685	+	47.9232i	0.899579	+	1.55812i
$947$	−19.6969	+	12.9548i	−0.640063	+	0.420976i	−0.827629	−	0.561276i	$-0.810311\pi$
$947$	−19.6969	+	12.9548i	−0.640063	+	0.420976i	0.187566	+	0.982252i	$0.439940\pi$
$948$	−1.65575	+	3.50305i	−0.0537764	+	0.113774i
$949$	−14.0705	+	32.6191i	−0.456749	+	1.05886i
$950$	2.09713	+	0.497030i	0.0680400	+	0.0161258i
$951$	5.86011	−	27.6529i	0.190027	−	0.896707i
$952$	4.40371	−	5.91521i	0.142725	−	0.191713i
$953$	−30.5290	−	11.1116i	−0.988931	−	0.359941i	−0.203625	−	0.979049i	$-0.565272\pi$
$953$	−30.5290	−	11.1116i	−0.988931	−	0.359941i	−0.785306	+	0.619108i	$0.787494\pi$
$954$	18.9380	+	14.4076i	0.613140	+	0.466464i
$955$	3.87716	−	1.41117i	0.125462	−	0.0456645i
$956$	4.27387	−	14.2757i	0.138227	−	0.461710i
$957$	22.2989	−	66.1392i	0.720820	−	2.13798i
$958$	−1.94651	+	33.4203i	−0.0628889	+	1.07976i
$959$	83.0844	+	54.6454i	2.68293	+	1.76459i
$960$	0.0444208	+	1.85954i	0.00143368	+	0.0600164i
$961$	−23.0010	+	5.45134i	−0.741968	+	0.175850i
$962$	2.46126	−	13.9585i	0.0793542	−	0.450040i
$963$	16.4241	−	19.1647i	0.529258	−	0.617572i
$964$	0.671359	+	3.80747i	0.0216230	+	0.122630i
$965$	−2.84484	−	6.59507i	−0.0915785	−	0.212303i
$966$	−1.98683	−	3.73118i	−0.0639253	−	0.120049i
$967$	2.18338	+	7.29298i	0.0702126	+	0.234526i	0.985892	−	0.167383i	$-0.0535317\pi$
$967$	2.18338	+	7.29298i	0.0702126	+	0.234526i	−0.915679	+	0.401910i	$0.868347\pi$
$968$	−12.6398	−	16.9783i	−0.406260	−	0.545702i
$969$	−1.12029	−	0.793160i	−0.0359890	−	0.0254800i
$970$	1.57711	+	0.792054i	0.0506379	+	0.0254313i
$971$	20.7869			0.667084			0.333542	−	0.942735i	$-0.391756\pi$
$971$	20.7869			0.667084			0.333542	+	0.942735i	$0.391756\pi$
$972$	10.0566	+	11.9107i	0.322565	+	0.382036i
$973$	67.2361			2.15549
$974$	15.8435	+	7.95691i	0.507659	+	0.254956i
$975$	17.9581	+	12.7142i	0.575119	+	0.407180i
$976$	5.03022	+	6.75675i	0.161013	+	0.216278i
$977$	15.3996	+	51.4383i	0.492677	+	1.64566i	0.736948	+	0.675950i	$0.236266\pi$
$977$	15.3996	+	51.4383i	0.492677	+	1.64566i	−0.244270	+	0.969707i	$0.578548\pi$
$978$	−1.76361	−	3.31198i	−0.0563941	−	0.105905i
$979$	12.5965	+	29.2019i	0.402585	+	0.933298i
$980$	−3.76347	−	21.3437i	−0.120220	−	0.681800i
$981$	−49.6780	−	9.29384i	−1.58610	−	0.296729i
$982$	−2.77870	+	15.7588i	−0.0886718	+	0.502883i
$983$	−28.8390	+	6.83498i	−0.919823	+	0.218002i	−0.663141	−	0.748494i	$-0.730777\pi$
$983$	−28.8390	+	6.83498i	−0.919823	+	0.218002i	−0.256681	+	0.966496i	$0.582629\pi$
$984$	0.267784	+	11.2100i	0.00853665	+	0.357360i
$985$	−5.76380	−	3.79091i	−0.183650	−	0.120789i
$986$	0.584358	−	10.0330i	0.0186097	−	0.319517i
$987$	−4.00163	+	11.8690i	−0.127373	+	0.377794i
$988$	−0.530670	+	1.77256i	−0.0168829	+	0.0563927i
$989$	4.29195	−	1.56214i	0.136476	−	0.0496732i
$990$	−16.8523	+	7.06223i	−0.535603	+	0.224452i
$991$	24.2992	+	8.84418i	0.771889	+	0.280945i	0.697786	−	0.716306i	$-0.254168\pi$
$991$	24.2992	+	8.84418i	0.771889	+	0.280945i	0.0741029	+	0.997251i	$0.476391\pi$
$992$	1.62025	−	2.17637i	0.0514430	−	0.0690999i
$993$	−8.24152	+	38.8904i	−0.261537	+	1.23415i
$994$	38.6916	+	9.17007i	1.22722	+	0.290857i
$995$	−8.61319	+	19.9676i	−0.273056	+	0.633016i
$996$	−8.55993	+	18.1101i	−0.271232	+	0.573841i
$997$	1.81511	−	1.19381i	0.0574850	−	0.0378085i	−0.520441	−	0.853898i	$-0.674233\pi$
$997$	1.81511	−	1.19381i	0.0574850	−	0.0378085i	0.577926	+	0.816089i	$0.303862\pi$
$998$	−3.69232	−	6.39529i	−0.116878	−	0.202439i
$999$	−18.4658	+	12.5047i	−0.584231	+	0.395632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.a.13.2	✓	72
3.2	odd	2		486.2.g.a.253.1		72
81.25	even	27	inner	162.2.g.a.25.2	yes	72
81.56	odd	54		486.2.g.a.73.1		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.13.2	✓	72	1.1	even	1	trivial
162.2.g.a.25.2	yes	72	81.25	even	27	inner
486.2.g.a.73.1		72	81.56	odd	54
486.2.g.a.253.1		72	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.893633 - 0.448799i) q^{2} +(-1.41362 - 1.00084i) q^{3} +(0.597159 + 0.802123i) q^{4} +(0.308002 + 1.02880i) q^{5} +(0.814085 + 1.52881i) q^{6} +(-2.06499 - 4.78718i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(0.996657 + 2.82961i) q^{9} +O(q^{10})\)	\(q+(-0.893633 - 0.448799i) q^{2} +(-1.41362 - 1.00084i) q^{3} +(0.597159 + 0.802123i) q^{4} +(0.308002 + 1.02880i) q^{5} +(0.814085 + 1.52881i) q^{6} +(-2.06499 - 4.78718i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(0.996657 + 2.82961i) q^{9} +(0.186483 - 1.05760i) q^{10} +(-5.51869 + 1.30795i) q^{11} +(-0.0413635 - 1.73156i) q^{12} +(-2.75916 - 1.81473i) q^{13} +(-0.303142 + 5.20475i) q^{14} +(0.594259 - 1.76259i) q^{15} +(-0.286803 + 0.957990i) q^{16} +(-1.32917 + 0.483778i) q^{17} +(0.379280 - 2.97593i) q^{18} +(-0.526489 - 0.191626i) q^{19} +(-0.641296 + 0.861410i) q^{20} +(-1.87207 + 8.83399i) q^{21} +(5.51869 + 1.30795i) q^{22} +(0.185413 - 0.429835i) q^{23} +(-0.740157 + 1.56594i) q^{24} +(3.21388 - 2.11380i) q^{25} +(1.65123 + 2.86001i) q^{26} +(1.42307 - 4.99749i) q^{27} +(2.60678 - 4.51508i) q^{28} +(-0.413128 - 7.09314i) q^{29} +(-1.32210 + 1.30840i) q^{30} +(2.69492 - 0.314991i) q^{31} +(0.686242 - 0.727374i) q^{32} +(9.11038 + 3.67435i) q^{33} +(1.40491 + 0.164210i) q^{34} +(4.28902 - 3.59892i) q^{35} +(-1.67453 + 2.48917i) q^{36} +(-3.28779 - 2.75878i) q^{37} +(0.384486 + 0.407532i) q^{38} +(2.08417 + 5.32681i) q^{39} +(0.959683 - 0.481971i) q^{40} +(5.78531 - 2.90549i) q^{41} +(5.63763 - 7.05416i) q^{42} +(6.69559 + 7.09691i) q^{43} +(-4.34467 - 3.64561i) q^{44} +(-2.60412 + 1.89688i) q^{45} +(-0.358600 + 0.300901i) q^{46} +(1.37768 + 0.161028i) q^{47} +(1.36422 - 1.06719i) q^{48} +(-13.8493 + 14.6794i) q^{49} +(-3.82070 + 0.446576i) q^{50} +(2.36312 + 0.646400i) q^{51} +(-0.192021 - 3.29687i) q^{52} +(-3.96592 + 6.86918i) q^{53} +(-3.51457 + 3.82724i) q^{54} +(-3.04538 - 5.27476i) q^{55} +(-4.35587 + 2.86490i) q^{56} +(0.552471 + 0.797817i) q^{57} +(-2.81421 + 6.52407i) q^{58} +(-1.06624 - 0.252703i) q^{59} +(1.76868 - 0.575877i) q^{60} +(5.03022 - 6.75675i) q^{61} +(-2.54964 - 0.927991i) q^{62} +(11.4878 - 10.6143i) q^{63} +(-0.939693 + 0.342020i) q^{64} +(1.01716 - 3.39756i) q^{65} +(-6.49229 - 7.37225i) q^{66} +(-0.100933 + 1.73295i) q^{67} +(-1.18177 - 0.777265i) q^{68} +(-0.692297 + 0.422057i) q^{69} +(-5.44800 + 1.29120i) q^{70} +(1.32440 - 7.51103i) q^{71} +(2.61355 - 1.47287i) q^{72} +(-1.86793 - 10.5936i) q^{73} +(1.69994 + 3.94090i) q^{74} +(-6.65878 - 0.228447i) q^{75} +(-0.160690 - 0.536741i) q^{76} +(17.6574 + 23.7181i) q^{77} +(0.528187 - 5.69558i) q^{78} +(-1.99908 - 1.00398i) q^{79} -1.07391 q^{80} +(-7.01335 + 5.64029i) q^{81} -6.47392 q^{82} +(-10.3349 - 5.19037i) q^{83} +(-8.20387 + 3.77366i) q^{84} +(-0.907095 - 1.21844i) q^{85} +(-2.79831 - 9.34701i) q^{86} +(-6.51505 + 10.4405i) q^{87} +(2.24639 + 5.20772i) q^{88} +(-0.973720 - 5.52224i) q^{89} +(3.17844 - 0.526388i) q^{90} +(-2.98980 + 16.9560i) q^{91} +(0.455501 - 0.107956i) q^{92} +(-4.12485 - 2.25189i) q^{93} +(-1.15887 - 0.762203i) q^{94} +(0.0349852 - 0.600672i) q^{95} +(-1.69807 + 0.341417i) q^{96} +(-0.471322 + 1.57433i) q^{97} +(18.9642 - 6.90241i) q^{98} +(-9.20123 - 14.3121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Introduction

L-functions

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