LMFDB - Embedded newform 324.2.p.a.191.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			191.17
Character	$\chi$	$=$	324.191
Dual form			324.2.p.a.95.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.827495 + 1.14684i) q^{2} +(-1.73159 + 0.0397552i) q^{3} +(-0.630505 - 1.89802i) q^{4} +(-0.871413 + 0.822136i) q^{5} +(1.38729 - 2.01877i) q^{6} +(-0.486686 - 4.16387i) q^{7} +(2.69847 + 0.847508i) q^{8} +(2.99684 - 0.137680i) q^{9} +O(q^{10})$	\(q+(-0.827495 + 1.14684i) q^{2} +(-1.73159 + 0.0397552i) q^{3} +(-0.630505 - 1.89802i) q^{4} +(-0.871413 + 0.822136i) q^{5} +(1.38729 - 2.01877i) q^{6} +(-0.486686 - 4.16387i) q^{7} +(2.69847 + 0.847508i) q^{8} +(2.99684 - 0.137680i) q^{9} +(-0.221772 - 1.67969i) q^{10} +(1.23281 + 4.11786i) q^{11} +(1.16723 + 3.26153i) q^{12} +(0.314209 + 5.39476i) q^{13} +(5.17804 + 2.88743i) q^{14} +(1.47625 - 1.45825i) q^{15} +(-3.20493 + 2.39342i) q^{16} +(0.718194 - 1.97322i) q^{17} +(-2.32197 + 3.55084i) q^{18} +(-0.831015 - 2.28320i) q^{19} +(2.10986 + 1.13560i) q^{20} +(1.00828 + 7.19078i) q^{21} +(-5.74268 - 1.99367i) q^{22} +(-0.264063 - 0.0308645i) q^{23} +(-4.70635 - 1.36026i) q^{24} +(-0.207271 + 3.55870i) q^{25} +(-6.44696 - 4.10379i) q^{26} +(-5.18384 + 0.357546i) q^{27} +(-7.59623 + 3.54908i) q^{28} +(3.36063 + 6.69156i) q^{29} +(0.450796 + 2.89972i) q^{30} +(7.02089 + 5.22686i) q^{31} +(-0.0928137 - 5.65609i) q^{32} +(-2.29843 - 7.08145i) q^{33} +(1.66868 + 2.45649i) q^{34} +(3.84737 + 3.22833i) q^{35} +(-2.15084 - 5.60124i) q^{36} +(6.14830 - 5.15904i) q^{37} +(3.30613 + 0.936287i) q^{38} +(-0.758552 - 9.32904i) q^{39} +(-3.04825 + 1.47998i) q^{40} +(1.37980 + 2.09788i) q^{41} +(-9.08105 - 4.79400i) q^{42} +(-1.18633 + 5.00551i) q^{43} +(7.03847 - 4.93621i) q^{44} +(-2.49829 + 2.58378i) q^{45} +(0.253907 - 0.277299i) q^{46} +(4.90669 + 6.59083i) q^{47} +(5.45448 - 4.27184i) q^{48} +(-10.2896 + 2.43868i) q^{49} +(-3.90976 - 3.18251i) q^{50} +(-1.16517 + 3.44537i) q^{51} +(10.0412 - 3.99779i) q^{52} +(1.82674 - 1.05467i) q^{53} +(3.87955 - 6.24092i) q^{54} +(-4.45972 - 2.57482i) q^{55} +(2.21560 - 11.6485i) q^{56} +(1.52975 + 3.92053i) q^{57} +(-10.4551 - 1.68311i) q^{58} +(-1.22969 + 4.10744i) q^{59} +(-3.69856 - 1.88251i) q^{60} +(2.85672 - 6.62262i) q^{61} +(-11.8042 + 3.72667i) q^{62} +(-2.03180 - 12.4114i) q^{63} +(6.56346 + 4.57394i) q^{64} +(-4.70903 - 4.44274i) q^{65} +(10.0233 + 3.22392i) q^{66} +(0.625206 - 1.24489i) q^{67} +(-4.19803 - 0.119018i) q^{68} +(0.458476 + 0.0429469i) q^{69} +(-6.88606 + 1.74091i) q^{70} +(1.46821 + 8.32664i) q^{71} +(8.20356 + 2.16832i) q^{72} +(2.71694 - 15.4085i) q^{73} +(0.828926 + 11.3202i) q^{74} +(0.217432 - 6.17047i) q^{75} +(-3.80958 + 3.01684i) q^{76} +(16.5462 - 7.13734i) q^{77} +(11.3267 + 6.84979i) q^{78} +(-2.18206 + 3.31767i) q^{79} +(0.825104 - 4.72054i) q^{80} +(8.96209 - 0.825209i) q^{81} +(-3.54772 - 0.153572i) q^{82} +(-3.77521 - 2.48300i) q^{83} +(13.0125 - 6.44755i) q^{84} +(0.996412 + 2.30994i) q^{85} +(-4.75887 - 5.50257i) q^{86} +(-6.08527 - 11.4535i) q^{87} +(-0.163229 + 12.1567i) q^{88} +(-5.72896 - 1.01017i) q^{89} +(-0.895874 - 5.00322i) q^{90} +(22.3101 - 3.93388i) q^{91} +(0.107911 + 0.520655i) q^{92} +(-12.3651 - 8.77169i) q^{93} +(-11.6189 + 0.173334i) q^{94} +(2.60125 + 1.30640i) q^{95} +(0.385575 + 9.79037i) q^{96} +(1.75301 - 1.85808i) q^{97} +(5.71781 - 13.8186i) q^{98} +(4.26146 + 12.1708i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{37}{54}\right)$

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 $

$2$	−0.827495	+	1.14684i	−0.585127	+	0.810942i
$2$	−0.827495	+	1.14684i	−0.585127	+	0.810942i
$3$	−1.73159	+	0.0397552i	−0.999737	+	0.0229527i
$3$	−1.73159	+	0.0397552i	−0.999737	+	0.0229527i
$4$	−0.630505	−	1.89802i	−0.315252	−	0.949008i
$5$	−0.871413	+	0.822136i	−0.389708	+	0.367670i	−0.856014	−	0.516953i	$-0.827066\pi$
$5$	−0.871413	+	0.822136i	−0.389708	+	0.367670i	0.466306	+	0.884624i	$0.345585\pi$
$6$	1.38729	−	2.01877i	0.566360	−	0.824158i
$7$	−0.486686	−	4.16387i	−0.183950	−	1.57379i	−0.698041	−	0.716058i	$-0.745945\pi$
$7$	−0.486686	−	4.16387i	−0.183950	−	1.57379i	0.514091	−	0.857736i	$-0.328129\pi$
$8$	2.69847	+	0.847508i	0.954053	+	0.299639i
$9$	2.99684	−	0.137680i	0.998946	−	0.0458933i
$10$	−0.221772	−	1.67969i	−0.0701305	−	0.531164i
$11$	1.23281	+	4.11786i	0.371705	+	1.24158i	0.915485	+	0.402353i	$0.131807\pi$
$11$	1.23281	+	4.11786i	0.371705	+	1.24158i	−0.543780	+	0.839228i	$0.683007\pi$
$12$	1.16723	+	3.26153i	0.336952	+	0.941522i
$13$	0.314209	+	5.39476i	0.0871459	+	1.49624i	0.704586	+	0.709619i	$0.251133\pi$
$13$	0.314209	+	5.39476i	0.0871459	+	1.49624i	−0.617440	+	0.786618i	$0.711830\pi$
$14$	5.17804	+	2.88743i	1.38389	+	0.771697i
$15$	1.47625	−	1.45825i	0.381166	−	0.376518i
$16$	−3.20493	+	2.39342i	−0.801232	+	0.598354i
$17$	0.718194	−	1.97322i	0.174188	−	0.478576i	−0.821621	−	0.570033i	$-0.806930\pi$
$17$	0.718194	−	1.97322i	0.174188	−	0.478576i	0.995809	+	0.0914572i	$0.0291525\pi$
$18$	−2.32197	+	3.55084i	−0.547294	+	0.836940i
$19$	−0.831015	−	2.28320i	−0.190648	−	0.523801i	0.807134	−	0.590368i	$-0.201017\pi$
$19$	−0.831015	−	2.28320i	−0.190648	−	0.523801i	−0.997782	+	0.0665674i	$0.978795\pi$
$20$	2.10986	+	1.13560i	0.471778	+	0.253927i
$21$	1.00828	+	7.19078i	0.220024	+	1.56916i
$22$	−5.74268	−	1.99367i	−1.22434	−	0.425052i
$23$	−0.264063	−	0.0308645i	−0.0550609	−	0.00643569i	0.0885179	−	0.996075i	$-0.471787\pi$
$23$	−0.264063	−	0.0308645i	−0.0550609	−	0.00643569i	−0.143579	+	0.989639i	$0.545861\pi$
$24$	−4.70635	−	1.36026i	−0.960679	−	0.277662i
$25$	−0.207271	+	3.55870i	−0.0414542	+	0.711740i
$26$	−6.44696	−	4.10379i	−1.26435	−	0.804819i
$27$	−5.18384	+	0.357546i	−0.997630	+	0.0688097i
$28$	−7.59623	+	3.54908i	−1.43555	+	0.670712i
$29$	3.36063	+	6.69156i	0.624053	+	1.24259i	0.954343	+	0.298712i	$0.0965570\pi$
$29$	3.36063	+	6.69156i	0.624053	+	1.24259i	−0.330290	+	0.943879i	$0.607147\pi$
$30$	0.450796	+	2.89972i	0.0823037	+	0.529414i
$31$	7.02089	+	5.22686i	1.26099	+	0.938772i	0.999649	−	0.0264745i	$-0.00842808\pi$
$31$	7.02089	+	5.22686i	1.26099	+	0.938772i	0.261340	+	0.965247i	$0.415835\pi$
$32$	−0.0928137	−	5.65609i	−0.0164073	−	0.999865i
$33$	−2.29843	−	7.08145i	−0.400104	−	1.23272i
$34$	1.66868	+	2.45649i	0.286176	+	0.421284i
$35$	3.84737	+	3.22833i	0.650324	+	0.545687i
$36$	−2.15084	−	5.60124i	−0.358473	−	0.933540i
$37$	6.14830	−	5.15904i	1.01077	−	0.848140i	0.0223339	−	0.999751i	$-0.492890\pi$
$37$	6.14830	−	5.15904i	1.01077	−	0.848140i	0.988440	+	0.151610i	$0.0484459\pi$
$38$	3.30613	+	0.936287i	0.536325	+	0.151886i
$39$	−0.758552	−	9.32904i	−0.121466	−	1.49384i
$40$	−3.04825	+	1.47998i	−0.481970	+	0.234005i
$41$	1.37980	+	2.09788i	0.215489	+	0.327634i	0.927015	−	0.375025i	$-0.122366\pi$
$41$	1.37980	+	2.09788i	0.215489	+	0.327634i	−0.711526	+	0.702660i	$0.751996\pi$
$42$	−9.08105	−	4.79400i	−1.40124	−	0.739730i
$43$	−1.18633	+	5.00551i	−0.180913	+	0.763334i	0.804611	+	0.593802i	$0.202374\pi$
$43$	−1.18633	+	5.00551i	−0.180913	+	0.763334i	−0.985525	+	0.169532i	$0.945774\pi$
$44$	7.03847	−	4.93621i	1.06109	−	0.744162i
$45$	−2.49829	+	2.58378i	−0.372423	+	0.385168i
$46$	0.253907	−	0.277299i	0.0374366	−	0.0408854i
$47$	4.90669	+	6.59083i	0.715714	+	0.961371i	0.999997	+	0.00263014i	$0.000837201\pi$
$47$	4.90669	+	6.59083i	0.715714	+	0.961371i	−0.284283	+	0.958741i	$0.591755\pi$
$48$	5.45448	−	4.27184i	0.787287	−	0.616587i
$49$	−10.2896	+	2.43868i	−1.46994	+	0.348383i
$50$	−3.90976	−	3.18251i	−0.552924	−	0.450076i
$51$	−1.16517	+	3.44537i	−0.163157	+	0.482448i
$52$	10.0412	−	3.99779i	1.39247	−	0.554394i
$53$	1.82674	−	1.05467i	0.250922	−	0.144870i	−0.369264	−	0.929324i	$-0.620390\pi$
$53$	1.82674	−	1.05467i	0.250922	−	0.144870i	0.620186	+	0.784454i	$0.287057\pi$
$54$	3.87955	−	6.24092i	0.527940	−	0.849282i
$55$	−4.45972	−	2.57482i	−0.601348	−	0.347189i
$56$	2.21560	−	11.6485i	0.296072	−	1.55660i
$57$	1.52975	+	3.92053i	0.202620	+	0.519287i
$58$	−10.4551	−	1.68311i	−1.37282	−	0.221004i
$59$	−1.22969	+	4.10744i	−0.160092	+	0.534743i	−0.999968	−	0.00803483i	$-0.997442\pi$
$59$	−1.22969	+	4.10744i	−0.160092	+	0.534743i	0.839876	+	0.542778i	$0.182628\pi$
$60$	−3.69856	−	1.88251i	−0.477482	−	0.243031i
$61$	2.85672	−	6.62262i	0.365765	−	0.847939i	−0.631593	−	0.775300i	$-0.717599\pi$
$61$	2.85672	−	6.62262i	0.365765	−	0.847939i	0.997358	−	0.0726390i	$-0.0231421\pi$
$62$	−11.8042	+	3.72667i	−1.49913	+	0.473288i
$63$	−2.03180	−	12.4114i	−0.255983	−	1.56369i
$64$	6.56346	+	4.57394i	0.820433	+	0.571743i
$65$	−4.70903	−	4.44274i	−0.584083	−	0.551054i
$66$	10.0233	+	3.22392i	1.23378	+	0.396838i
$67$	0.625206	−	1.24489i	0.0763811	−	0.152087i	−0.852201	−	0.523215i	$-0.824732\pi$
$67$	0.625206	−	1.24489i	0.0763811	−	0.152087i	0.928582	+	0.371128i	$0.121029\pi$
$68$	−4.19803	−	0.119018i	−0.509086	−	0.0144331i
$69$	0.458476	+	0.0429469i	0.0551941	+	0.00517020i
$70$	−6.88606	+	1.74091i	−0.823042	+	0.208079i
$71$	1.46821	+	8.32664i	0.174245	+	0.988190i	0.939012	+	0.343884i	$0.111743\pi$
$71$	1.46821	+	8.32664i	0.174245	+	0.988190i	−0.764768	+	0.644306i	$0.777146\pi$
$72$	8.20356	+	2.16832i	0.966799	+	0.255539i
$73$	2.71694	−	15.4085i	0.317993	−	1.80343i	−0.236929	−	0.971527i	$-0.576141\pi$
$73$	2.71694	−	15.4085i	0.317993	−	1.80343i	0.554922	−	0.831902i	$-0.312748\pi$
$74$	0.828926	+	11.3202i	0.0963607	+	1.31595i
$75$	0.217432	−	6.17047i	0.0251069	−	0.712504i
$76$	−3.80958	+	3.01684i	−0.436989	+	0.346056i
$77$	16.5462	−	7.13734i	1.88562	−	0.813375i
$78$	11.3267	+	6.84979i	1.28249	+	0.775586i
$79$	−2.18206	+	3.31767i	−0.245501	+	0.373267i	−0.937126	−	0.348990i	$-0.886525\pi$
$79$	−2.18206	+	3.31767i	−0.245501	+	0.373267i	0.691625	+	0.722257i	$0.256895\pi$
$80$	0.825104	−	4.72054i	0.0922494	−	0.527772i
$81$	8.96209	−	0.825209i	0.995788	−	0.0916898i
$82$	−3.54772	−	0.153572i	−0.391780	−	0.0169592i
$83$	−3.77521	−	2.48300i	−0.414384	−	0.272544i	0.325152	−	0.945662i	$-0.394585\pi$
$83$	−3.77521	−	2.48300i	−0.414384	−	0.272544i	−0.739536	+	0.673117i	$0.764955\pi$
$84$	13.0125	−	6.44755i	1.41978	−	0.703485i
$85$	0.996412	+	2.30994i	0.108076	+	0.250548i
$86$	−4.75887	−	5.50257i	−0.513162	−	0.593358i
$87$	−6.08527	−	11.4535i	−0.652409	−	1.22794i
$88$	−0.163229	+	12.1567i	−0.0174002	+	1.29591i
$89$	−5.72896	−	1.01017i	−0.607268	−	0.107078i	−0.138445	−	0.990370i	$-0.544211\pi$
$89$	−5.72896	−	1.01017i	−0.607268	−	0.107078i	−0.468823	+	0.883292i	$0.655322\pi$
$90$	−0.895874	−	5.00322i	−0.0944335	−	0.527386i
$91$	22.3101	−	3.93388i	2.33874	−	0.412383i
$92$	0.107911	+	0.520655i	0.0112505	+	0.0542821i
$93$	−12.3651	−	8.77169i	−1.28221	−	0.909582i
$94$	−11.6189	+	0.173334i	−1.19840	+	0.0178780i
$95$	2.60125	+	1.30640i	0.266883	+	0.134034i
$96$	0.385575	+	9.79037i	0.0393526	+	0.999225i
$97$	1.75301	−	1.85808i	0.177991	−	0.188659i	−0.632236	−	0.774776i	$-0.717863\pi$
$97$	1.75301	−	1.85808i	0.177991	−	0.188659i	0.810226	+	0.586117i	$0.199344\pi$
$98$	5.71781	−	13.8186i	0.577586	−	1.39589i
$99$	4.26146	+	12.1708i	0.428293	+	1.22321i
$100$	6.88516	−	1.85037i	0.688516	−	0.185037i
$101$	−9.56834	−	4.12738i	−0.952085	−	0.410689i	−0.137350	−	0.990523i	$-0.543858\pi$
$101$	−9.56834	−	4.12738i	−0.952085	−	0.410689i	−0.814735	+	0.579833i	$0.803118\pi$
$102$	−2.98713	−	4.18730i	−0.295770	−	0.414604i
$103$	−11.4702	−	3.43397i	−1.13020	−	0.338359i	−0.333508	−	0.942747i	$-0.608232\pi$
$103$	−11.4702	−	3.43397i	−1.13020	−	0.338359i	−0.796690	+	0.604389i	$0.793417\pi$
$104$	−3.72422	+	14.8239i	−0.365189	+	1.45360i
$105$	−6.79042	−	5.43720i	−0.662678	−	0.530616i
$106$	−0.302077	+	2.96772i	−0.0293403	+	0.288251i
$107$	5.31323	−	9.20279i	0.513649	−	0.889667i	−0.486225	−	0.873834i	$-0.661627\pi$
$107$	5.31323	−	9.20279i	0.513649	−	0.889667i	0.999875	−	0.0158334i	$-0.00504012\pi$
$108$	3.94706	+	9.61357i	0.379806	+	0.925066i
$109$	7.41990	+	12.8517i	0.710698	+	1.23096i	0.964596	+	0.263734i	$0.0849540\pi$
$109$	7.41990	+	12.8517i	0.710698	+	1.23096i	−0.253898	+	0.967231i	$0.581713\pi$
$110$	6.64331	−	2.98395i	0.633415	−	0.284509i
$111$	−10.4413	+	9.17779i	−0.991041	+	0.871117i
$112$	11.5257	+	12.1801i	1.08907	+	1.15091i
$113$	2.43991	+	10.2948i	0.229527	+	0.968451i	0.958767	+	0.284193i	$0.0917257\pi$
$113$	2.43991	+	10.2948i	0.229527	+	0.968451i	−0.729240	+	0.684258i	$0.760126\pi$
$114$	−5.76210	−	1.48983i	−0.539670	−	0.139536i
$115$	0.255482	−	0.190200i	0.0238239	−	0.0177362i
$116$	10.5818	−	10.5976i	0.982495	−	0.983961i
$117$	1.68438	+	16.1240i	0.155721	+	1.49066i
$118$	−3.69304	−	4.80915i	−0.339972	−	0.442718i
$119$	−8.56576	−	2.03012i	−0.785222	−	0.186101i
$120$	5.21949	−	2.68391i	0.476472	−	0.245006i
$121$	−6.24657	+	4.10843i	−0.567870	+	0.373494i
$122$	5.23119	+	8.75639i	0.473610	+	0.792766i
$123$	−2.47266	−	3.57783i	−0.222952	−	0.322602i
$124$	5.49396	−	16.6213i	0.493372	−	1.49264i
$125$	−6.59550	−	7.86021i	−0.589919	−	0.703039i
$126$	15.9153	+	7.94024i	1.41785	+	0.707372i
$127$	−7.09447	+	8.45487i	−0.629533	+	0.750248i	−0.982678	−	0.185321i	$-0.940668\pi$
$127$	−7.09447	+	8.45487i	−0.629533	+	0.750248i	0.353145	+	0.935568i	$0.385112\pi$
$128$	−10.6768	+	3.74235i	−0.943708	+	0.330781i
$129$	1.85524	−	8.71468i	0.163345	−	0.767285i
$130$	8.99183	−	1.72418i	0.788636	−	0.151221i
$131$	−8.96379	+	12.0405i	−0.783170	+	1.05198i	0.214003	+	0.976833i	$0.431350\pi$
$131$	−8.96379	+	12.0405i	−0.783170	+	1.05198i	−0.997173	+	0.0751466i	$0.976058\pi$
$132$	−11.9915	+	8.82733i	−1.04373	+	0.768321i
$133$	−9.10248	+	4.57144i	−0.789285	+	0.396394i
$134$	0.910338	+	1.74715i	0.0786412	+	0.150931i
$135$	4.22331	−	4.57339i	0.363485	−	0.393614i
$136$	3.61034	−	4.71600i	0.309584	−	0.404394i
$137$	−13.8098	−	0.804327i	−1.17985	−	0.0687183i	−0.543017	−	0.839722i	$-0.682718\pi$
$137$	−13.8098	−	0.804327i	−1.17985	−	0.0687183i	−0.636831	+	0.771003i	$0.719755\pi$
$138$	−0.428640	+	0.490263i	−0.0364883	+	0.0417339i
$139$	0.721848	−	6.17581i	0.0612264	−	0.523825i	−0.927470	−	0.373896i	$-0.878022\pi$
$139$	0.721848	−	6.17581i	0.0612264	−	0.523825i	0.988697	−	0.149929i	$-0.0479044\pi$
$140$	3.70163	−	9.33784i	0.312845	−	0.789191i
$141$	−8.75841	−	11.2176i	−0.737591	−	0.944690i
$142$	−10.7643	−	5.20644i	−0.903319	−	0.436915i
$143$	−21.8275	+	7.94455i	−1.82531	+	0.664357i
$144$	−9.27513	+	7.61393i	−0.772927	+	0.634495i
$145$	−8.42986	−	3.06822i	−0.700062	−	0.254802i
$146$	15.4229	+	15.8664i	1.27641	+	1.31311i
$147$	17.7205	−	4.63187i	1.46156	−	0.382031i
$148$	−13.6685	−	8.41677i	−1.12354	−	0.691855i
$149$	2.18605	−	0.127323i	0.179088	−	0.0104307i	0.0316336	−	0.999500i	$-0.489929\pi$
$149$	2.18605	−	0.127323i	0.179088	−	0.0104307i	0.147454	+	0.989069i	$0.452892\pi$
$150$	6.89664	+	5.35539i	0.563109	+	0.437266i
$151$	20.0666	−	6.00756i	1.63300	−	0.488888i	0.666489	−	0.745515i	$-0.267796\pi$
$151$	20.0666	−	6.00756i	1.63300	−	0.488888i	0.966511	+	0.256627i	$0.0826111\pi$
$152$	−0.307443	−	6.86542i	−0.0249369	−	0.556859i
$153$	1.88064	−	6.01231i	0.152041	−	0.486066i
$154$	−5.50649	+	24.8820i	−0.443725	+	2.00505i
$155$	−10.4153	+	1.21737i	−0.836576	+	0.0977817i
$156$	−17.2284	+	7.32175i	−1.37938	+	0.586209i
$157$	4.00508	+	4.24514i	0.319640	+	0.338799i	0.867193	−	0.497972i	$-0.165922\pi$
$157$	4.00508	+	4.24514i	0.319640	+	0.338799i	−0.547553	+	0.836771i	$0.684440\pi$
$158$	−1.99920	−	5.24784i	−0.159048	−	0.417496i
$159$	−3.12125	+	1.89888i	−0.247531	+	0.150591i
$160$	4.73095	+	4.85249i	0.374015	+	0.383623i
$161$			1.11454i			0.0878383i
$162$	−6.46970	+	10.9610i	−0.508307	+	0.861176i
$163$			1.17594i			0.0921066i	0.998939	+	0.0460533i	$0.0146644\pi$
$163$			1.17594i			0.0921066i	−0.998939	+	0.0460533i	$0.985336\pi$
$164$	3.11185	−	3.94161i	0.242994	−	0.307788i
$165$	7.82479	+	4.28125i	0.609159	+	0.333295i
$166$	5.97158	−	2.27492i	0.463485	−	0.176568i
$167$	−2.52839	−	2.67993i	−0.195652	−	0.207379i	0.622119	−	0.782923i	$-0.286272\pi$
$167$	−2.52839	−	2.67993i	−0.195652	−	0.207379i	−0.817771	+	0.575543i	$0.804791\pi$
$168$	−3.37343	+	20.2586i	−0.260266	+	1.56299i
$169$	−16.0926	+	1.88095i	−1.23789	+	0.144689i
$170$	−3.47367	−	0.768736i	−0.266418	−	0.0589594i
$171$	−2.80477	−	6.72795i	−0.214486	−	0.514500i
$172$	10.2485	−	0.904329i	0.781443	−	0.0689544i
$173$	−8.06047	+	2.41315i	−0.612826	+	0.183468i	−0.578150	−	0.815931i	$-0.696225\pi$
$173$	−8.06047	+	2.41315i	−0.612826	+	0.183468i	−0.0346761	+	0.999399i	$0.511040\pi$
$174$	18.1709	+	2.49883i	1.37753	+	0.189436i
$175$	14.9188	−	0.868923i	1.12776	−	0.0656844i
$176$	−13.8068	−	10.2468i	−1.04073	−	0.772383i
$177$	1.96603	−	7.16131i	0.147776	−	0.538277i
$178$	5.89919	−	5.73431i	0.442163	−	0.429805i
$179$	−4.33094	−	1.57633i	−0.323710	−	0.117821i	0.175054	−	0.984559i	$-0.443990\pi$
$179$	−4.33094	−	1.57633i	−0.323710	−	0.117821i	−0.498763	+	0.866738i	$0.666212\pi$
$180$	6.47925	+	3.11271i	0.482935	+	0.232008i
$181$	6.71677	−	2.44470i	0.499253	−	0.181713i	−0.0801047	−	0.996786i	$-0.525525\pi$
$181$	6.71677	−	2.44470i	0.499253	−	0.181713i	0.579358	+	0.815073i	$0.303303\pi$
$182$	−13.9500	+	28.8415i	−1.03404	+	2.13788i
$183$	−4.68339	+	11.5813i	−0.346206	+	0.856111i
$184$	−0.686407	−	0.307082i	−0.0506026	−	0.0226384i
$185$	−1.11628	+	9.55039i	−0.0820705	+	0.702158i
$186$	20.2919	−	6.92236i	1.48787	−	0.507572i
$187$	9.01083	+	0.524821i	0.658937	+	0.0383787i
$188$	9.41580	−	13.4685i	0.686718	−	0.982292i
$189$	4.01167	+	21.4108i	0.291806	+	1.55741i
$190$	−3.65076	+	1.90220i	−0.264854	+	0.138000i
$191$	23.1317	−	11.6172i	1.67375	−	0.840591i	0.679485	−	0.733690i	$-0.262203\pi$
$191$	23.1317	−	11.6172i	1.67375	−	0.840591i	0.994270	−	0.106901i	$-0.0340929\pi$
$192$	−11.5471	−	7.65929i	−0.833340	−	0.552761i
$193$	−4.13885	+	5.55944i	−0.297921	+	0.400177i	−0.925727	−	0.378193i	$-0.876546\pi$
$193$	−4.13885	+	5.55944i	−0.297921	+	0.400177i	0.627806	+	0.778370i	$0.283953\pi$
$194$	0.680322	+	3.54797i	0.0488443	+	0.254730i
$195$	8.33075	+	7.50582i	0.596578	+	0.537503i
$196$	11.1163	+	17.9922i	0.794022	+	1.28516i
$197$	−9.13758	+	10.8897i	−0.651026	+	0.775862i	−0.986068	−	0.166341i	$-0.946805\pi$
$197$	−9.13758	+	10.8897i	−0.651026	+	0.775862i	0.335043	+	0.942203i	$0.391249\pi$
$198$	−17.4844	−	5.18405i	−1.24256	−	0.368415i
$199$	2.76771	+	3.29843i	0.196198	+	0.233819i	0.855170	−	0.518348i	$-0.173453\pi$
$199$	2.76771	+	3.29843i	0.196198	+	0.233819i	−0.658972	+	0.752167i	$0.729008\pi$
$200$	−3.57534	+	9.42738i	−0.252815	+	0.666616i
$201$	−1.03311	+	2.18050i	−0.0728701	+	0.153800i
$202$	12.6512	−	7.55801i	0.890136	−	0.531780i
$203$	26.2272	−	17.2499i	1.84079	−	1.21071i
$204$	7.27401	+	0.0391976i	0.509283	+	0.00274438i
$205$	−2.92712	−	0.693740i	−0.204439	−	0.0484529i
$206$	13.4298	−	10.3130i	0.935698	−	0.718541i
$207$	−0.795602	−	0.0561398i	−0.0552982	−	0.00390199i
$208$	−13.9189	−	16.5378i	−0.965103	−	1.14669i
$209$	8.37739	−	6.23674i	0.579476	−	0.431404i
$210$	11.8547	−	3.28831i	0.818049	−	0.226915i
$211$	−2.39428	−	10.1023i	−0.164829	−	0.695468i	−0.991203	−	0.132347i	$-0.957749\pi$
$211$	−2.39428	−	10.1023i	−0.164829	−	0.695468i	0.826374	−	0.563121i	$-0.190400\pi$
$212$	−3.15355	−	2.80221i	−0.216587	−	0.192457i
$213$	−2.87337	−	14.3600i	−0.196880	−	0.983930i
$214$	6.15749	+	13.7087i	0.420918	+	0.937108i
$215$	−3.08143	−	5.33719i	−0.210152	−	0.363994i
$216$	−14.2914	−	3.42852i	−0.972409	−	0.233281i
$217$	18.3470	−	31.7779i	1.24547	−	2.15723i
$218$	−20.8788	−	2.12520i	−1.41409	−	0.143937i
$219$	−4.09206	+	26.7893i	−0.276516	+	1.81025i
$220$	−2.07518	+	10.0881i	−0.139908	+	0.680136i
$221$	10.8707	+	3.25448i	0.731243	+	0.218920i
$222$	−1.88540	−	19.5691i	−0.126540	−	1.31339i
$223$	12.6162	+	5.44210i	0.844843	+	0.364430i	0.774099	−	0.633065i	$-0.218203\pi$
$223$	12.6162	+	5.44210i	0.844843	+	0.364430i	0.0707444	+	0.997494i	$0.477463\pi$
$224$	−23.5060	+	3.13921i	−1.57056	+	0.209747i
$225$	−0.131196	+	10.6934i	−0.00874638	+	0.712893i
$226$	−13.8255	−	5.72068i	−0.919660	−	0.380534i
$227$	−15.0330	+	15.9341i	−0.997776	+	1.05758i	0.000564321		1.00000i	$0.499820\pi$
$227$	−15.0330	+	15.9341i	−0.997776	+	1.05758i	−0.998341	+	0.0575815i	$0.981661\pi$
$228$	6.47672	−	5.37540i	0.428931	−	0.355995i
$229$	3.48071	+	1.74808i	0.230011	+	0.115516i	0.560073	−	0.828443i	$-0.310773\pi$
$229$	3.48071	+	1.74808i	0.230011	+	0.115516i	−0.330061	+	0.943959i	$0.607069\pi$
$230$	0.00671899	+	0.450388i	0.000443037	+	0.0296977i
$231$	−28.3676	+	13.0168i	−1.86645	+	0.856441i
$232$	3.39740	+	20.9051i	0.223050	+	1.37249i
$233$	−2.01716	+	0.355679i	−0.132148	+	0.0233013i	−0.239331	−	0.970938i	$-0.576928\pi$
$233$	−2.01716	+	0.355679i	−0.132148	+	0.0233013i	0.107183	+	0.994239i	$0.465817\pi$
$234$	−19.8855	−	11.4108i	−1.29996	−	0.745945i
$235$	−9.69430	−	1.70937i	−0.632387	−	0.111507i
$236$	8.57131	−	0.255795i	0.557945	−	0.0166508i
$237$	3.64655	−	5.83160i	0.236869	−	0.378803i
$238$	9.41636	−	8.14368i	0.610372	−	0.527876i
$239$	5.73402	+	13.2930i	0.370903	+	0.859850i	0.996799	+	0.0799435i	$0.0254740\pi$
$239$	5.73402	+	13.2930i	0.370903	+	0.859850i	−0.625896	+	0.779906i	$0.715267\pi$
$240$	−1.24108	+	8.20686i	−0.0801113	+	0.529751i
$241$	−6.31151	−	4.15115i	−0.406560	−	0.267399i	0.329716	−	0.944080i	$-0.393047\pi$
$241$	−6.31151	−	4.15115i	−0.406560	−	0.267399i	−0.736276	+	0.676681i	$0.763417\pi$
$242$	0.457270	−	10.5635i	0.0293944	−	0.679050i
$243$	−15.4859	+	1.78522i	−0.993421	+	0.114522i
$244$	−14.3710	−	1.24651i	−0.920009	−	0.0797993i
$245$	6.96157	−	10.5846i	0.444758	−	0.676222i
$246$	6.14932	+	0.124884i	0.392067	+	0.00796232i
$247$	12.0562	−	5.20053i	0.767116	−	0.330902i
$248$	14.5159	+	20.0548i	0.921758	+	1.27348i
$249$	6.63585	+	4.14946i	0.420530	+	0.262961i
$250$	14.4722	−	1.05973i	0.915301	−	0.0670231i
$251$	−0.520787	+	2.95353i	−0.0328718	+	0.186425i	−0.996822	−	0.0796561i	$-0.974618\pi$
$251$	−0.520787	+	2.95353i	−0.0328718	+	0.186425i	0.963951	+	0.266081i	$0.0857289\pi$
$252$	−22.2760	+	11.6819i	−1.40326	+	0.735888i
$253$	−0.198442	−	1.12542i	−0.0124760	−	0.0707547i
$254$	−3.82577	−	15.1326i	−0.240050	−	0.949505i
$255$	−1.81721	−	3.96027i	−0.113798	−	0.248002i
$256$	4.54313	−	15.3414i	0.283945	−	0.958840i
$257$	12.7070	−	25.3017i	0.792641	−	1.57828i	−0.0230103	−	0.999735i	$-0.507325\pi$
$257$	12.7070	−	25.3017i	0.792641	−	1.57828i	0.815652	−	0.578543i	$-0.196379\pi$
$258$	8.45918	+	9.33903i	0.526646	+	0.581423i
$259$	−24.4738	−	23.0899i	−1.52073	−	1.43473i
$260$	−5.46333	+	11.7390i	−0.338821	+	0.728021i
$261$	10.9926	+	19.5908i	0.680422	+	1.21264i
$262$	−6.39104	−	20.2435i	−0.394840	−	1.25065i
$263$	8.25930	−	19.1472i	0.509290	−	1.18067i	−0.448652	−	0.893706i	$-0.648096\pi$
$263$	8.25930	−	19.1472i	0.509290	−	1.18067i	0.957942	−	0.286961i	$-0.0926449\pi$
$264$	−0.200647	−	21.0570i	−0.0123490	−	1.29597i
$265$	−0.724765	+	2.42088i	−0.0445219	+	0.148714i
$266$	2.28953	−	14.2220i	0.140380	−	0.872005i
$267$	9.96039	+	1.52145i	0.609566	+	0.0931111i
$268$	−2.75701	−	0.401744i	−0.168411	−	0.0245404i
$269$	9.08666	+	5.24618i	0.554023	+	0.319865i	0.750743	−	0.660594i	$-0.229696\pi$
$269$	9.08666	+	5.24618i	0.554023	+	0.319865i	−0.196720	+	0.980460i	$0.563029\pi$
$270$	1.75020	+	8.62793i	0.106513	+	0.525079i
$271$	−19.6522	+	11.3462i	−1.19379	+	0.689233i	−0.959163	−	0.282854i	$-0.908719\pi$
$271$	−19.6522	+	11.3462i	−1.19379	+	0.689233i	−0.234623	+	0.972086i	$0.575385\pi$
$272$	2.42098	+	8.04297i	0.146793	+	0.487676i
$273$	−38.4757	+	7.69883i	−2.32866	+	0.465954i
$274$	12.3500	−	15.1721i	0.746088	−	0.916579i
$275$	−14.9097	+	3.53367i	−0.899092	+	0.213089i
$276$	−0.207558	−	0.897274i	−0.0124935	−	0.0540095i
$277$	1.94673	+	2.61491i	0.116968	+	0.157115i	0.856751	−	0.515730i	$-0.172479\pi$
$277$	1.94673	+	2.61491i	0.116968	+	0.157115i	−0.739783	+	0.672845i	$0.765072\pi$
$278$	6.48536	+	5.93830i	0.388966	+	0.356155i
$279$	21.7601	+	14.6974i	1.30274	+	0.879912i
$280$	7.64597	+	11.9722i	0.456934	+	0.715476i
$281$	−1.75681	+	7.41256i	−0.104802	+	0.442196i	−0.999994	−	0.00348557i	$-0.998891\pi$
$281$	−1.75681	+	7.41256i	−0.104802	+	0.442196i	0.895192	+	0.445682i	$0.147039\pi$
$282$	20.1124	−	0.762056i	1.19767	−	0.0453798i
$283$	7.64780	+	11.6279i	0.454614	+	0.691208i	0.987963	−	0.154688i	$-0.0494371\pi$
$283$	7.64780	+	11.6279i	0.454614	+	0.691208i	−0.533349	+	0.845895i	$0.679067\pi$
$284$	14.8784	−	8.03667i	0.882869	−	0.476889i
$285$	−4.55625	−	2.15874i	−0.269889	−	0.127873i
$286$	8.95096	−	31.6068i	0.529281	−	1.86895i
$287$	8.06378	−	6.76631i	0.475990	−	0.399403i
$288$	−1.05688	−	16.9376i	−0.0622771	−	0.998059i
$289$	9.64496	+	8.09308i	0.567350	+	0.476064i
$290$	10.4944	−	7.12881i	0.616255	−	0.418618i
$291$	−2.96163	+	3.28713i	−0.173614	+	0.192695i
$292$	−30.9586	+	4.55835i	−1.81172	+	0.266757i
$293$	7.53307	+	5.60816i	0.440087	+	0.327632i	0.794293	−	0.607535i	$-0.207842\pi$
$293$	7.53307	+	5.60816i	0.440087	+	0.327632i	−0.354206	+	0.935167i	$0.615249\pi$
$294$	−9.35157	+	24.1555i	−0.545395	+	1.40878i
$295$	−2.30531	−	4.59025i	−0.134220	−	0.267255i
$296$	20.9633	−	8.71076i	1.21847	−	0.506303i
$297$	−7.86298	−	20.9055i	−0.456257	−	1.21306i
$298$	−1.66292	+	2.61242i	−0.0963306	+	0.151333i
$299$	0.0835357	−	1.43425i	0.00483099	−	0.0829449i
$300$	−11.8487	+	3.47782i	−0.684087	+	0.200792i
$301$	21.4197	+	2.50360i	1.23461	+	0.144305i
$302$	−9.71531	+	27.9845i	−0.559053	+	1.61033i
$303$	16.7326	+	6.76655i	0.961261	+	0.388728i
$304$	8.12798	+	5.32851i	0.466172	+	0.305611i
$305$	2.95531	+	8.11964i	0.169220	+	0.464929i
$306$	5.33896	+	7.13195i	0.305208	+	0.407706i
$307$	11.0938	−	30.4800i	0.633156	−	1.73958i	−0.0390692	−	0.999237i	$-0.512439\pi$
$307$	11.0938	−	30.4800i	0.633156	−	1.73958i	0.672226	−	0.740346i	$-0.265339\pi$
$308$	−23.9793	−	26.9049i	−1.36634	−	1.53305i
$309$	19.9983	+	5.49024i	1.13767	+	0.312329i
$310$	7.22246	−	12.9521i	0.410208	−	0.735629i
$311$	−1.94542	−	33.4015i	−0.110315	−	1.89403i	−0.371044	−	0.928615i	$-0.621000\pi$
$311$	−1.94542	−	33.4015i	−0.110315	−	1.89403i	0.260729	−	0.965412i	$-0.416037\pi$
$312$	5.85951	−	25.8170i	0.331729	−	1.46160i
$313$	2.23944	+	7.48024i	0.126580	+	0.422808i	0.997663	−	0.0683287i	$-0.0217667\pi$
$313$	2.23944	+	7.48024i	0.126580	+	0.422808i	−0.871082	+	0.491137i	$0.836581\pi$
$314$	−8.18270	+	1.08038i	−0.461776	+	0.0609691i
$315$	11.9744	+	9.14507i	0.674682	+	0.515266i
$316$	7.67278	+	2.04979i	0.431628	+	0.115310i
$317$	−1.03609	−	8.86431i	−0.0581926	−	0.497869i	−0.990634	−	0.136547i	$-0.956400\pi$
$317$	−1.03609	−	8.86431i	−0.0581926	−	0.497869i	0.932441	−	0.361322i	$-0.117675\pi$
$318$	0.405093	−	5.15090i	0.0227165	−	0.288848i
$319$	−23.4119	+	22.0880i	−1.31081	+	1.23669i
$320$	−9.47989	+	1.41026i	−0.529942	+	0.0788360i
$321$	−8.83450	+	16.1467i	−0.493094	+	0.901222i
$322$	−1.27821	−	0.922278i	−0.0712317	−	0.0513966i
$323$	−5.10208			−0.283887
$324$	−7.21690	−	16.4899i	−0.400939	−	0.916105i
$325$	−19.2635			−1.06854
$326$	−1.34862	−	0.973083i	−0.0746931	−	0.0538941i
$327$	−13.3592	−	21.9589i	−0.738765	−	1.21433i
$328$	1.94537	+	6.83046i	0.107415	+	0.377149i
$329$	25.0553	−	23.6385i	1.38134	−	1.30323i
$330$	−11.3849	+	5.43110i	−0.626718	+	0.298972i
$331$	−1.07499	−	9.19713i	−0.0590868	−	0.505520i	−0.990082	−	0.140489i	$-0.955132\pi$
$331$	−1.07499	−	9.19713i	−0.0590868	−	0.505520i	0.930995	−	0.365031i	$-0.118942\pi$
$332$	−2.33248	+	8.73096i	−0.128011	+	0.479174i
$333$	17.7152	−	16.3073i	0.970785	−	0.893634i
$334$	5.16569	−	0.682035i	0.282654	−	0.0373193i
$335$	0.478654	+	1.59882i	0.0261517	+	0.0873526i
$336$	−20.4420	−	20.6327i	−1.11520	−	1.12561i
$337$	0.157179	+	2.69865i	0.00856207	+	0.147005i	0.999880	+	0.0155155i	$0.00493894\pi$
$337$	0.157179	+	2.69865i	0.00856207	+	0.147005i	−0.991318	+	0.131490i	$0.958024\pi$
$338$	11.1594	−	20.0122i	0.606990	−	1.08852i
$339$	−4.63420	−	17.7294i	−0.251695	−	0.962928i
$340$	3.75606	−	3.34763i	0.203701	−	0.181551i
$341$	−12.8681	+	35.3547i	−0.696845	+	1.91457i
$342$	10.0368	+	2.35071i	0.542731	+	0.127112i
$343$	5.12541	+	14.0820i	0.276746	+	0.760354i
$344$	−7.44348	+	12.5018i	−0.401326	+	0.674052i
$345$	−0.434830	+	0.339505i	−0.0234105	+	0.0182783i
$346$	3.90249	−	11.2410i	0.209799	−	0.604318i
$347$	−22.7738	−	2.66188i	−1.22256	−	0.142897i	−0.519779	−	0.854301i	$-0.673986\pi$
$347$	−22.7738	−	2.66188i	−1.22256	−	0.142897i	−0.702783	+	0.711404i	$0.748060\pi$
$348$	−17.9021	+	18.7714i	−0.959652	+	1.00625i
$349$	0.219766	−	3.77324i	0.0117638	−	0.201977i	−0.987305	−	0.158835i	$-0.949226\pi$
$349$	0.219766	−	3.77324i	0.0117638	−	0.201977i	0.999069	−	0.0431418i	$-0.0137367\pi$
$350$	−11.3487	+	17.8286i	−0.606616	+	0.952980i
$351$	−3.55768	−	27.8532i	−0.189895	−	1.48669i
$352$	23.1766	−	7.35505i	1.23531	−	0.392026i
$353$	−9.57266	−	19.0607i	−0.509501	−	1.01450i	−0.990466	−	0.137761i	$-0.956010\pi$
$353$	−9.57266	−	19.0607i	−0.509501	−	1.01450i	0.480964	−	0.876740i	$-0.340287\pi$
$354$	6.58603	+	8.18068i	0.350044	+	0.434798i
$355$	−8.12504	−	6.04887i	−0.431232	−	0.321041i
$356$	1.69482	+	11.5106i	0.0898250	+	0.610059i
$357$	14.9131	+	3.17482i	0.789287	+	0.168029i
$358$	5.39164	−	3.66251i	0.284957	−	0.193569i
$359$	16.8609	+	14.1480i	0.889886	+	0.746703i	0.968187	−	0.250227i	$-0.0805053\pi$
$359$	16.8609	+	14.1480i	0.889886	+	0.746703i	−0.0783016	+	0.996930i	$0.524950\pi$
$360$	−8.93134	+	4.85494i	−0.470723	+	0.255878i
$361$	10.0324	−	8.41823i	0.528024	−	0.443064i
$362$	−2.75440	+	9.72607i	−0.144768	+	0.511191i
$363$	10.6532	−	7.36247i	0.559147	−	0.386429i
$364$	−21.5332	−	39.8647i	−1.12865	−	2.08948i
$365$	10.3003	+	15.6609i	0.539143	+	0.819727i
$366$	−9.40641	−	14.9546i	−0.491681	−	0.781687i
$367$	−4.89437	+	20.6510i	−0.255484	+	1.07797i	0.682388	+	0.730990i	$0.260942\pi$
$367$	−4.89437	+	20.6510i	−0.255484	+	1.07797i	−0.937872	+	0.346982i	$0.887207\pi$
$368$	0.920173	−	0.533093i	0.0479673	−	0.0277894i
$369$	4.42387	+	6.09705i	0.230298	+	0.317400i
$370$	−10.0291	−	9.18310i	−0.521388	−	0.477406i
$371$	−5.28055	−	7.09302i	−0.274153	−	0.368251i
$372$	−8.85253	+	28.9998i	−0.458982	+	1.50357i
$373$	0.436266	−	0.103397i	0.0225890	−	0.00535368i	−0.219306	−	0.975656i	$-0.570379\pi$
$373$	0.436266	−	0.103397i	0.0225890	−	0.00535368i	0.241895	+	0.970302i	$0.422231\pi$
$374$	−8.05830	+	9.89974i	−0.416685	+	0.511903i
$375$	11.7332	+	13.3485i	0.605901	+	0.689313i
$376$	7.65477	+	21.9436i	0.394764	+	1.13165i
$377$	−35.0434	+	20.2323i	−1.80483	+	1.04202i
$378$	−27.8745	−	13.1166i	−1.43371	−	0.674643i
$379$	−10.3858	−	5.99627i	−0.533485	−	0.308008i	0.208949	−	0.977926i	$-0.432996\pi$
$379$	−10.3858	−	5.99627i	−0.533485	−	0.308008i	−0.742434	+	0.669919i	$0.766329\pi$
$380$	0.839463	−	5.76091i	0.0430635	−	0.295528i
$381$	11.9486	−	14.9224i	0.612147	−	0.764500i
$382$	−5.81828	+	36.1417i	−0.297689	+	1.84917i
$383$	4.31051	−	14.3981i	0.220257	−	0.735709i	−0.774421	−	0.632671i	$-0.781959\pi$
$383$	4.31051	−	14.3981i	0.220257	−	0.735709i	0.994677	−	0.103038i	$-0.0328562\pi$
$384$	18.3392	−	6.90470i	0.935867	−	0.352354i
$385$	−8.55072	+	19.8228i	−0.435785	+	1.01026i
$386$	−2.95093	−	9.34702i	−0.150199	−	0.475751i
$387$	−2.86608	+	15.1641i	−0.145691	+	0.770832i
$388$	−4.63194	−	2.15571i	−0.235151	−	0.109439i
$389$	−11.3558	−	10.7136i	−0.575761	−	0.543203i	0.342326	−	0.939581i	$-0.388785\pi$
$389$	−11.3558	−	10.7136i	−0.575761	−	0.543203i	−0.918087	+	0.396379i	$0.870267\pi$
$390$	−15.5017	+	3.34305i	−0.784957	+	0.169282i
$391$	−0.250550	+	0.498887i	−0.0126709	+	0.0252298i
$392$	−29.8330	−	2.13982i	−1.50679	−	0.108077i
$393$	15.0430	−	21.2055i	0.758818	−	1.06968i
$394$	−4.92754	−	19.4906i	−0.248246	−	0.981922i
$395$	−0.826094	−	4.68501i	−0.0415653	−	0.235728i
$396$	20.4135	−	15.7621i	1.02582	−	0.792075i
$397$	−3.54905	+	20.1277i	−0.178122	+	1.01018i	0.756357	+	0.654159i	$0.226977\pi$
$397$	−3.54905	+	20.1277i	−0.178122	+	1.01018i	−0.934479	+	0.356019i	$0.884134\pi$
$398$	−6.07305	+	0.444700i	−0.304414	+	0.0222908i
$399$	15.5801	−	8.27774i	0.779979	−	0.414406i
$400$	−7.85316	−	11.9015i	−0.392658	−	0.595073i
$401$	−9.34829	+	4.03246i	−0.466831	+	0.201371i	−0.616484	−	0.787367i	$-0.711444\pi$
$401$	−9.34829	+	4.03246i	−0.466831	+	0.201371i	0.149653	+	0.988739i	$0.452184\pi$
$402$	−1.64579	−	2.98917i	−0.0820847	−	0.149086i
$403$	−25.9916	+	39.5184i	−1.29474	+	1.96855i
$404$	−1.80095	+	20.7632i	−0.0896005	+	1.03301i
$405$	−7.13125	+	8.08715i	−0.354354	+	0.401854i
$406$	−1.91992	+	44.3527i	−0.0952840	+	2.20119i
$407$	28.8238	+	18.9577i	1.42874	+	0.939700i
$408$	−6.06416	+	8.30973i	−0.300221	+	0.411393i
$409$	−8.52501	−	19.7632i	−0.421535	−	0.977227i	−0.988185	−	0.153268i	$-0.951020\pi$
$409$	−8.52501	−	19.7632i	−0.421535	−	0.977227i	0.566650	−	0.823959i	$-0.308239\pi$
$410$	3.21779	−	2.78288i	0.158915	−	0.137437i
$411$	23.9449	+	0.843759i	1.18111	+	0.0416195i
$412$	0.714320	+	23.9358i	0.0351920	+	1.17923i
$413$	17.7013	+	3.12122i	0.871025	+	0.153585i
$414$	0.722741	−	0.865977i	0.0355208	−	0.0425604i
$415$	5.33113	−	0.940022i	0.261695	−	0.0461439i
$416$	30.4841	−	2.27790i	1.49461	−	0.111683i
$417$	−1.00443	+	10.7227i	−0.0491870	+	0.525092i
$418$	0.220319	+	14.7684i	0.0107762	+	0.722348i
$419$	7.77151	+	3.90300i	0.379663	+	0.190674i	0.628388	−	0.777900i	$-0.283715\pi$
$419$	7.77151	+	3.90300i	0.379663	+	0.190674i	−0.248725	+	0.968574i	$0.580011\pi$
$420$	−6.03849	+	16.3165i	−0.294648	+	0.796164i
$421$	−12.6920	+	13.4527i	−0.618570	+	0.655646i	−0.958596	−	0.284770i	$-0.908083\pi$
$421$	−12.6920	+	13.4527i	−0.618570	+	0.655646i	0.340026	+	0.940416i	$0.389564\pi$
$422$	13.5670	+	5.61370i	0.660430	+	0.273271i
$423$	15.6120	+	19.0761i	0.759080	+	0.927511i
$424$	5.82324	−	1.29782i	0.282802	−	0.0630275i
$425$	6.87324	+	2.96483i	0.333401	+	0.143815i
$426$	18.8464	+	8.58750i	0.913110	+	0.416066i
$427$	−28.9660	−	8.67186i	−1.40176	−	0.419661i
$428$	−20.8170	−	4.28220i	−1.00623	−	0.206988i
$429$	37.4805	−	14.6245i	1.80958	−	0.706078i
$430$	8.67080	+	0.882579i	0.418143	+	0.0425617i
$431$	11.2192	−	19.4322i	0.540409	−	0.936016i	−0.458471	−	0.888709i	$-0.651603\pi$
$431$	11.2192	−	19.4322i	0.540409	−	0.936016i	0.998880	−	0.0473067i	$-0.0150638\pi$
$432$	15.7581	−	13.5530i	0.758160	−	0.652068i
$433$	−2.97416	−	5.15140i	−0.142929	−	0.247560i	0.785669	−	0.618647i	$-0.212319\pi$
$433$	−2.97416	−	5.15140i	−0.142929	−	0.247560i	−0.928598	+	0.371086i	$0.878985\pi$
$434$	21.2623	+	47.3372i	1.02062	+	2.27226i
$435$	14.7191	+	4.97778i	0.705726	+	0.238666i
$436$	19.7144	−	22.1861i	0.944146	−	1.06252i
$437$	0.148970	+	0.628555i	0.00712622	+	0.0300679i
$438$	−27.3370	−	26.8610i	−1.30621	−	1.28347i
$439$	−3.91868	+	2.91735i	−0.187028	+	0.139237i	−0.686601	−	0.727035i	$-0.740898\pi$
$439$	−3.91868	+	2.91735i	−0.187028	+	0.139237i	0.499572	+	0.866272i	$0.333490\pi$
$440$	−9.85223	−	10.7277i	−0.469687	−	0.511424i
$441$	−30.5005	+	8.72501i	−1.45241	+	0.415477i
$442$	−12.7278	+	9.77395i	−0.605402	+	0.464900i
$443$	−29.4245	−	6.97373i	−1.39800	−	0.331332i	−0.538567	−	0.842583i	$-0.681034\pi$
$443$	−29.4245	−	6.97373i	−1.39800	−	0.331332i	−0.859432	+	0.511251i	$0.829182\pi$
$444$	24.0028	+	14.0310i	1.13912	+	0.665884i
$445$	5.82278	−	3.82970i	0.276026	−	0.181545i
$446$	−16.6811	+	9.96551i	−0.789872	+	0.471881i
$447$	−3.78029	+	0.307378i	−0.178801	+	0.0145385i
$448$	15.8510	−	29.5555i	0.748887	−	1.39636i
$449$	5.94581	+	7.08595i	0.280600	+	0.334406i	0.887874	−	0.460086i	$-0.152181\pi$
$449$	5.94581	+	7.08595i	0.280600	+	0.334406i	−0.607274	+	0.794492i	$0.707737\pi$
$450$	−12.1551	−	8.99919i	−0.572997	−	0.424226i
$451$	−6.93776	+	8.26810i	−0.326686	+	0.389330i
$452$	18.0013	−	11.1219i	0.846709	−	0.523130i
$453$	−34.5084	+	11.2004i	−1.62135	+	0.526241i
$454$	−5.83415	−	30.4259i	−0.273810	−	1.42796i
$455$	−16.2072	+	21.7700i	−0.759803	+	1.02059i
$456$	0.805302	+	11.8759i	0.0377117	+	0.556140i
$457$	25.4519	−	12.7824i	1.19059	−	0.597937i	0.260573	−	0.965454i	$-0.416088\pi$
$457$	25.4519	−	12.7824i	1.19059	−	0.597937i	0.930017	+	0.367517i	$0.119792\pi$
$458$	−4.88504	+	2.54530i	−0.228263	+	0.118934i
$459$	−3.01748	+	10.4856i	−0.140844	+	0.489428i
$460$	−0.522085	−	0.364988i	−0.0243423	−	0.0170176i
$461$	−21.2749	−	1.23912i	−0.990872	−	0.0577117i	−0.444956	−	0.895552i	$-0.646781\pi$
$461$	−21.2749	−	1.23912i	−0.990872	−	0.0577117i	−0.545915	+	0.837841i	$0.683818\pi$
$462$	8.54581	−	43.3045i	0.397587	−	2.01471i
$463$	−2.34936	+	20.1001i	−0.109184	+	0.934129i	0.821977	+	0.569521i	$0.192871\pi$
$463$	−2.34936	+	20.1001i	−0.109184	+	0.934129i	−0.931161	+	0.364608i	$0.881203\pi$
$464$	−26.7863	−	13.4026i	−1.24352	−	0.622200i
$465$	17.9867	−	2.52206i	0.834111	−	0.116958i
$466$	1.26128	−	2.60769i	0.0584276	−	0.120799i
$467$	37.7820	−	13.7515i	1.74834	−	0.636344i	0.748695	−	0.662915i	$-0.230681\pi$
$467$	37.7820	−	13.7515i	1.74834	−	0.636344i	0.999647	+	0.0265705i	$0.00845866\pi$
$468$	29.5415	−	13.3632i	1.36556	−	0.617715i
$469$	−5.48782	−	1.99740i	−0.253404	−	0.0922316i
$470$	9.98236	−	9.70337i	0.460452	−	0.447583i
$471$	−7.10394	−	7.19164i	−0.327332	−	0.331373i
$472$	−6.79936	+	10.0416i	−0.312966	+	0.462204i
$473$	−22.0745	+	1.28569i	−1.01499	+	0.0591162i
$474$	3.67043	+	9.00765i	0.168589	+	0.413735i
$475$	8.29746	−	2.48410i	0.380713	−	0.113978i
$476$	1.54755	+	17.5380i	0.0709317	+	0.803851i
$477$	5.32924	−	3.41218i	0.244009	−	0.156233i
$478$	−19.9898	−	4.42382i	−0.914313	−	0.202341i
$479$	−9.39870	+	1.09855i	−0.429438	+	0.0501941i	−0.328066	−	0.944655i	$-0.606397\pi$
$479$	−9.39870	+	1.09855i	−0.429438	+	0.0501941i	−0.101371	+	0.994849i	$0.532323\pi$
$480$	−8.38501	−	8.21446i	−0.382721	−	0.374937i
$481$	29.7636	+	31.5476i	1.35710	+	1.43845i
$482$	9.98346	−	3.80327i	0.454734	−	0.173234i
$483$	−0.0443089	−	1.92994i	−0.00201612	−	0.0878151i
$484$	11.7364	+	9.26570i	0.533471	+	0.421168i
$485$			3.06036i			0.138964i
$486$	10.7671	−	19.2372i	0.488407	−	0.872616i
$487$			4.49318i			0.203606i	0.994805	+	0.101803i	$0.0324611\pi$
$487$			4.49318i			0.203606i	−0.994805	+	0.101803i	$0.967539\pi$
$488$	13.3215	−	15.4498i	0.603035	−	0.699381i
$489$	−0.0467497	−	2.03625i	−0.00211409	−	0.0920823i
$490$	6.37817	+	16.7425i	0.288137	+	0.756349i
$491$	−5.33292	−	5.65256i	−0.240671	−	0.255097i	0.595768	−	0.803157i	$-0.296848\pi$
$491$	−5.33292	−	5.65256i	−0.240671	−	0.255097i	−0.836439	+	0.548060i	$0.815366\pi$
$492$	−5.23176	+	6.94898i	−0.235866	+	0.313284i
$493$	15.6175	−	1.82542i	0.703377	−	0.0822130i
$494$	−4.01223	+	18.1300i	−0.180519	+	0.815706i
$495$	−13.7196	−	7.10231i	−0.616648	−	0.319225i
$496$	−35.0115	+	0.0521987i	−1.57206	+	0.00234379i
$497$	33.9564	−	10.1659i	1.52315	−	0.456003i
$498$	−10.2499	+	4.17663i	−0.459310	+	0.187159i
$499$	10.2838	−	0.598961i	0.460364	−	0.0268132i	0.173604	−	0.984816i	$-0.444459\pi$
$499$	10.2838	−	0.598961i	0.460364	−	0.0268132i	0.286760	+	0.958002i	$0.407422\pi$
$500$	−10.7603	+	17.4743i	−0.481216	+	0.781473i
$501$	4.48468	+	4.54004i	0.200361	+	0.202834i
$502$	−2.95629	−	3.04129i	−0.131946	−	0.135739i
$503$	19.9232	+	7.25145i	0.888331	+	0.323326i	0.745567	−	0.666431i	$-0.232179\pi$
$503$	19.9232	+	7.25145i	0.888331	+	0.323326i	0.142764	+	0.989757i	$0.454401\pi$
$504$	5.03603	−	35.2138i	0.224323	−	1.56855i
$505$	11.7312	−	4.26982i	0.522033	−	0.190005i
$506$	1.45489	+	0.703698i	0.0646779	+	0.0312832i
$507$	27.7911	−	3.89682i	1.23425	−	0.173064i
$508$	20.5206	+	8.13459i	0.910453	+	0.360914i
$509$	1.61064	−	13.7799i	0.0713905	−	0.610785i	−0.909428	−	0.415861i	$-0.863480\pi$
$509$	1.61064	−	13.7799i	0.0713905	−	0.610785i	0.980818	−	0.194923i	$-0.0624458\pi$
$510$	6.04555	+	1.19304i	0.267701	+	0.0528288i
$511$	−65.4813	−	3.81385i	−2.89672	−	0.168715i
$512$	13.8348	+	17.9052i	0.611419	+	0.791307i
$513$	5.12419	+	11.5386i	0.226239	+	0.509441i
$514$	18.5022	+	35.5100i	0.816096	+	1.56628i
$515$	12.8185	−	6.43770i	0.564851	−	0.283679i
$516$	−17.7103	+	1.97336i	−0.779655	+	0.0868725i
$517$	−21.0911	+	28.3302i	−0.927585	+	1.24596i
$518$	46.7325	−	8.96093i	2.05331	−	0.393721i
$519$	13.8615	−	4.49904i	0.608453	−	0.197486i
$520$	−8.94191	−	15.9795i	−0.392129	−	0.700749i
$521$	3.30898	−	3.94348i	0.144969	−	0.172767i	−0.688674	−	0.725071i	$-0.741807\pi$
$521$	3.30898	−	3.94348i	0.144969	−	0.172767i	0.833643	+	0.552304i	$0.186251\pi$
$522$	−31.5639	−	3.60457i	−1.38152	−	0.157768i
$523$	9.65685	+	11.5086i	0.422264	+	0.503235i	0.934674	−	0.355506i	$-0.115691\pi$
$523$	9.65685	+	11.5086i	0.422264	+	0.503235i	−0.512410	+	0.858741i	$0.671247\pi$
$524$	28.5047	+	9.42185i	1.24523	+	0.411595i
$525$	−25.7988	+	2.09772i	−1.12595	+	0.0915522i
$526$	15.1243	+	25.3163i	0.659452	+	1.10384i
$527$	15.3561	−	10.0999i	0.668923	−	0.439957i
$528$	24.3151	+	17.1944i	1.05818	+	0.748292i
$529$	−22.3113	−	5.28786i	−0.970055	−	0.229907i
$530$	−2.17664	−	2.83446i	−0.0945470	−	0.123121i
$531$	−3.11966	+	12.4786i	−0.135382	+	0.541527i
$532$	14.4158	+	14.3943i	0.625005	+	0.624074i
$533$	−10.8840	+	8.10286i	−0.471440	+	0.350974i
$534$	−9.98703	+	10.1640i	−0.432181	+	0.439840i
$535$	2.93592	+	12.3876i	0.126931	+	0.535564i
$536$	2.74215	−	2.82942i	0.118443	−	0.122212i
$537$	7.56210	+	2.55739i	0.326329	+	0.110360i
$538$	−13.5357	+	6.07979i	−0.583566	+	0.262118i
$539$	−22.7272	−	39.3647i	−0.978931	−	1.69556i
$540$	−11.3432	−	5.13237i	−0.488133	−	0.220862i
$541$	−5.27086	+	9.12940i	−0.226612	+	0.392504i	−0.956802	−	0.290741i	$-0.906098\pi$
$541$	−5.27086	+	9.12940i	−0.226612	+	0.392504i	0.730190	+	0.683244i	$0.239432\pi$
$542$	3.24976	−	31.9269i	0.139589	−	1.37138i
$543$	−11.5335	+	4.50026i	−0.494951	+	0.193125i
$544$	−11.2274	−	3.87903i	−0.481370	−	0.166312i
$545$	−17.0316	−	5.09893i	−0.729554	−	0.218414i
$546$	23.0091	−	50.4964i	0.984699	−	2.16105i
$547$	37.8325	+	16.3193i	1.61760	+	0.697765i	0.996311	−	0.0858160i	$-0.0273497\pi$
$547$	37.8325	+	16.3193i	1.61760	+	0.697765i	0.621290	+	0.783581i	$0.286609\pi$
$548$	7.18050	+	26.7183i	0.306736	+	1.14135i
$549$	7.64932	−	20.2402i	0.326465	−	0.863832i
$550$	8.28516	−	20.0233i	0.353281	−	0.853795i
$551$	12.4854	−	13.2338i	0.531896	−	0.563777i
$552$	1.20079	+	0.504453i	0.0511088	+	0.0214709i
$553$	14.8763	+	7.47116i	0.632605	+	0.317706i
$554$	−4.60980	+	0.0687702i	−0.195852	+	0.00292176i
$555$	1.55327	−	16.5818i	0.0659325	−	0.703857i
$556$	−12.1769	+	2.52379i	−0.516416	+	0.107033i
$557$	30.7702	−	5.42561i	1.30377	−	0.229890i	0.521728	−	0.853112i	$-0.325288\pi$
$557$	30.7702	−	5.42561i	1.30377	−	0.229890i	0.782045	+	0.623221i	$0.214176\pi$
$558$	−34.8621	+	12.7934i	−1.47583	+	0.541589i
$559$	−27.3763	−	4.82718i	−1.15789	−	0.204168i
$560$	−20.0573	−	1.13820i	−0.847574	−	0.0480977i
$561$	−15.6240	−	0.550550i	−0.659645	−	0.0232442i
$562$	−7.04730	−	8.14864i	−0.297272	−	0.343730i
$563$	5.97816	+	13.8589i	0.251949	+	0.584084i	0.996510	−	0.0834702i	$-0.0266003\pi$
$563$	5.97816	+	13.8589i	0.251949	+	0.584084i	−0.744561	+	0.667555i	$0.767341\pi$
$564$	−15.7689	+	23.6963i	−0.663991	+	0.997796i
$565$	−10.5899	−	6.96507i	−0.445519	−	0.293023i
$566$	−19.6639	−	0.851202i	−0.826536	−	0.0357787i
$567$	−7.79778	−	36.9153i	−0.327476	−	1.55030i
$568$	−3.09497	+	23.7135i	−0.129862	+	0.994996i
$569$	23.7822	−	36.1591i	0.997002	−	1.51587i	0.146967	−	0.989141i	$-0.453049\pi$
$569$	23.7822	−	36.1591i	0.997002	−	1.51587i	0.850035	−	0.526726i	$-0.176581\pi$
$570$	6.24601	−	3.43897i	0.261617	−	0.144042i
$571$	−2.06774	+	0.891938i	−0.0865324	+	0.0373264i	−0.438906	−	0.898533i	$-0.644634\pi$
$571$	−2.06774	+	0.891938i	−0.0865324	+	0.0373264i	0.352374	+	0.935859i	$0.385375\pi$
$572$	28.8412	+	36.4198i	1.20591	+	1.52279i
$573$	−39.5930	+	21.0359i	−1.65402	+	0.878787i
$574$	1.08717	+	14.8470i	0.0453778	+	0.619701i
$575$	0.164570	−	0.933323i	0.00686304	−	0.0389222i
$576$	20.2994	+	12.8037i	0.845807	+	0.533488i
$577$	3.19693	+	18.1307i	0.133090	+	0.754791i	0.976171	+	0.217004i	$0.0696285\pi$
$577$	3.19693	+	18.1307i	0.133090	+	0.754791i	−0.843081	+	0.537787i	$0.819260\pi$
$578$	−17.2627	+	4.36428i	−0.718032	+	0.181530i
$579$	6.94579	−	9.79123i	0.288657	−	0.406910i
$580$	−0.508462	+	17.9345i	−0.0211127	+	0.744691i
$581$	−8.50153	+	16.9279i	−0.352703	+	0.702289i
$582$	−1.31909	−	6.11660i	−0.0546782	−	0.253541i
$583$	6.59500	+	6.22206i	0.273137	+	0.257691i
$584$	20.3904	−	39.2767i	0.843760	−	1.62528i
$585$	−14.7239	−	12.6658i	−0.608757	−	0.523668i
$586$	−12.6653	+	3.99854i	−0.523198	+	0.165178i
$587$	−8.25613	+	19.1399i	−0.340767	+	0.789986i	0.658532	+	0.752552i	$0.271178\pi$
$587$	−8.25613	+	19.1399i	−0.340767	+	0.789986i	−0.999299	+	0.0374338i	$0.988082\pi$
$588$	−19.9642	−	30.7133i	−0.823310	−	1.26660i
$589$	6.09948	−	20.3737i	0.251325	−	0.839483i
$590$	7.17193	+	1.15458i	0.295264	+	0.0475331i
$591$	15.3897	−	19.2199i	0.633046	−	0.790601i
$592$	−7.35714	+	31.2498i	−0.302377	+	1.28436i
$593$	−27.4720	−	15.8610i	−1.12814	−	0.651331i	−0.184673	−	0.982800i	$-0.559123\pi$
$593$	−27.4720	−	15.8610i	−1.12814	−	0.651331i	−0.943466	+	0.331469i	$0.892456\pi$
$594$	30.4819	+	8.28158i	1.25069	+	0.339797i
$595$	9.13335	−	5.27314i	0.374431	−	0.216178i
$596$	−1.61997	−	4.06888i	−0.0663567	−	0.166668i
$597$	−4.92368	−	5.60151i	−0.201513	−	0.229254i
$598$	1.57574	+	1.28264i	0.0644367	+	0.0524510i
$599$	25.0938	−	5.94734i	1.02530	−	0.243002i	0.316639	−	0.948546i	$-0.397446\pi$
$599$	25.0938	−	5.94734i	1.02530	−	0.243002i	0.708666	+	0.705544i	$0.249297\pi$
$600$	5.81625	−	16.4665i	0.237447	−	0.672244i
$601$	−21.5759	−	28.9815i	−0.880100	−	1.18218i	−0.982281	−	0.187414i	$-0.939989\pi$
$601$	−21.5759	−	28.9815i	−0.880100	−	1.18218i	0.102180	−	0.994766i	$-0.467418\pi$
$602$	−20.5959	+	22.4933i	−0.839426	+	0.916759i
$603$	1.70225	−	3.81681i	0.0693208	−	0.155432i
$604$	−24.0545	−	34.2990i	−0.978765	−	1.39561i
$605$	2.06565	−	8.71566i	0.0839806	−	0.354342i
$606$	−21.6063	+	13.5904i	−0.877696	+	0.552071i
$607$	0.0620158	+	0.0942904i	0.00251714	+	0.00382713i	0.836744	−	0.547594i	$-0.184456\pi$
$607$	0.0620158	+	0.0942904i	0.00251714	+	0.00382713i	−0.834227	+	0.551421i	$0.814086\pi$
$608$	−12.8368	+	4.91221i	−0.520602	+	0.199216i
$609$	−44.7291	+	30.9125i	−1.81251	+	1.25264i
$610$	−11.7575	−	3.32968i	−0.476046	−	0.134815i
$611$	−34.0142	+	28.5413i	−1.37607	+	1.15466i
$612$	−12.5972	+	0.221306i	−0.509212	+	0.00894575i
$613$	−28.5768	−	23.9788i	−1.15420	−	0.968493i	−0.154395	−	0.988009i	$-0.549343\pi$
$613$	−28.5768	−	23.9788i	−1.15420	−	0.968493i	−0.999810	+	0.0195166i	$0.993787\pi$
$614$	25.7757	+	37.9449i	1.04022	+	1.53133i
$615$	5.09616	+	1.08491i	0.205497	+	0.0437477i
$616$	50.6984	−	5.23684i	2.04270	−	0.210998i
$617$	−5.30633	−	3.95041i	−0.213625	−	0.159038i	0.485028	−	0.874499i	$-0.338809\pi$
$617$	−5.30633	−	3.95041i	−0.213625	−	0.159038i	−0.698653	+	0.715461i	$0.746217\pi$
$618$	−22.8450	+	18.3918i	−0.918959	+	0.739828i
$619$	−12.5558	−	25.0007i	−0.504661	−	1.00486i	−0.991345	−	0.131285i	$-0.958090\pi$
$619$	−12.5558	−	25.0007i	−0.504661	−	1.00486i	0.486683	−	0.873578i	$-0.338207\pi$
$620$	8.87748	+	19.0008i	0.356528	+	0.763091i
$621$	1.37989	+	0.0655820i	0.0553732	+	0.00263172i
$622$	39.9162	+	25.4085i	1.60049	+	1.01879i
$623$	−1.41801	+	24.3462i	−0.0568113	+	0.975412i
$624$	24.7594	+	28.0834i	0.991168	+	1.12424i
$625$	−5.49358	−	0.642108i	−0.219743	−	0.0256843i
$626$	−10.4318	−	3.62157i	−0.416938	−	0.144747i
$627$	−14.2583	+	11.1325i	−0.569422	+	0.444591i
$628$	5.53212	−	10.2783i	0.220756	−	0.410148i
$629$	−5.76425	−	15.8371i	−0.229836	−	0.631468i
$630$	−20.3967	+	6.16530i	−0.812625	+	0.245631i
$631$	0.469000	−	1.28857i	0.0186706	−	0.0512970i	−0.930007	−	0.367541i	$-0.880200\pi$
$631$	0.469000	−	1.28857i	0.0186706	−	0.0512970i	0.948678	+	0.316244i	$0.102422\pi$
$632$	−8.69998	+	7.10330i	−0.346067	+	0.282554i
$633$	4.54754	+	17.3978i	0.180748	+	0.691502i
$634$	11.0233	+	6.14694i	0.437793	+	0.244126i
$635$	−0.768830	−	13.2003i	−0.0305101	−	0.523838i
$636$	5.57207	+	4.72692i	0.220947	+	0.187435i
$637$	−16.3892	−	54.7437i	−0.649363	−	2.16902i
$638$	−5.95826	−	45.1275i	−0.235890	−	1.78661i
$639$	5.54640	+	24.7514i	0.219412	+	0.979152i
$640$	6.22721	−	12.0389i	0.246152	−	0.475881i
$641$	3.90006	+	33.3672i	0.154043	+	1.31792i	0.820185	+	0.572098i	$0.193870\pi$
$641$	3.90006	+	33.3672i	0.154043	+	1.31792i	−0.666142	+	0.745825i	$0.732055\pi$
$642$	−11.2073	−	23.4931i	−0.442316	−	0.927200i
$643$	0.227483	−	0.214620i	0.00897107	−	0.00846377i	−0.681743	−	0.731592i	$-0.738778\pi$
$643$	0.227483	−	0.214620i	0.00897107	−	0.00846377i	0.690714	+	0.723128i	$0.257296\pi$
$644$	2.11542	−	0.702724i	0.0833592	−	0.0276912i
$645$	5.54797	+	9.11935i	0.218451	+	0.359074i
$646$	4.22194	−	5.85129i	0.166110	−	0.230216i
$647$	−24.6062			−0.967371			−0.483685	−	0.875242i	$-0.660702\pi$
$647$	−24.6062			−0.967371			−0.483685	+	0.875242i	$0.660702\pi$
$648$	24.8833	+	5.36864i	0.977508	+	0.210900i
$649$	−18.4298			−0.723434
$650$	15.9404	−	22.0922i	0.625235	−	0.866527i
$651$	−30.5062	+	55.7558i	−1.19563	+	2.18524i
$652$	2.23195	−	0.741434i	0.0874099	−	0.0290368i
$653$	−25.1995	+	23.7745i	−0.986133	+	0.930369i	−0.997577	−	0.0695658i	$-0.977839\pi$
$653$	−25.1995	+	23.7745i	−0.986133	+	0.930369i	0.0114441	+	0.999935i	$0.496357\pi$
$654$	36.2381	+	2.84994i	1.41702	+	0.111442i
$655$	−2.08773	−	17.8617i	−0.0815743	−	0.697913i
$656$	−9.44326	−	3.42113i	−0.368698	−	0.133573i
$657$	6.02078	−	46.5509i	0.234893	−	1.81612i
$658$	6.37650	+	48.2952i	0.248582	+	1.88274i
$659$	−12.9669	−	43.3125i	−0.505119	−	1.68722i	−0.706509	−	0.707704i	$-0.749731\pi$
$659$	−12.9669	−	43.3125i	−0.505119	−	1.68722i	0.201390	−	0.979511i	$-0.435454\pi$
$660$	3.19231	−	17.5509i	0.124261	−	0.683168i
$661$	−1.61702	−	27.7631i	−0.0628946	−	1.07986i	−0.871147	−	0.491022i	$-0.836623\pi$
$661$	−1.61702	−	27.7631i	−0.0628946	−	1.07986i	0.808252	−	0.588836i	$-0.200414\pi$
$662$	11.4372	+	6.37773i	0.444521	+	0.247878i
$663$	−18.9530	−	5.20327i	−0.736075	−	0.202078i
$664$	−8.08294	−	9.89981i	−0.313679	−	0.384187i
$665$	4.17368	−	11.4671i	0.161848	−	0.444674i
$666$	4.04272	+	33.8108i	0.156652	+	1.31014i
$667$	−0.680884	−	1.87071i	−0.0263640	−	0.0724344i
$668$	−3.49240	+	6.48863i	−0.135125	+	0.251053i
$669$	−22.0625	−	8.92195i	−0.852985	−	0.344942i
$670$	−2.22968	−	0.774070i	−0.0861399	−	0.0299049i
$671$	30.7928	+	3.59916i	1.18874	+	0.138944i
$672$	40.5781	−	6.37032i	1.56534	−	0.245740i
$673$	0.724425	−	12.4379i	0.0279245	−	0.479446i	−0.955136	−	0.296166i	$-0.904292\pi$
$673$	0.724425	−	12.4379i	0.0279245	−	0.479446i	0.983061	−	0.183279i	$-0.0586713\pi$
$674$	−3.22500	−	2.05286i	−0.124222	−	0.0790733i
$675$	−0.197941	−	18.5218i	−0.00761873	−	0.712906i
$676$	13.7165	+	29.3581i	0.527559	+	1.12916i
$677$	18.4918	+	36.8202i	0.710697	+	1.41511i	0.901189	+	0.433426i	$0.142695\pi$
$677$	18.4918	+	36.8202i	0.710697	+	1.41511i	−0.190492	+	0.981689i	$0.561008\pi$
$678$	24.1676	+	9.35626i	0.928152	+	0.359325i
$679$	−8.58995	−	6.39498i	−0.329652	−	0.245417i
$680$	0.731092	+	7.07777i	0.0280361	+	0.271420i
$681$	25.3976	−	28.1890i	0.973239	−	1.08020i
$682$	−29.8981	−	44.0135i	−1.14486	−	1.68537i
$683$	−5.19618	−	4.36011i	−0.198826	−	0.166835i	0.537939	−	0.842984i	$-0.319203\pi$
$683$	−5.19618	−	4.36011i	−0.198826	−	0.166835i	−0.736765	+	0.676149i	$0.763648\pi$
$684$	−11.0013	+	9.56550i	−0.420647	+	0.365746i
$685$	12.6953	−	10.6526i	0.485062	−	0.407015i
$686$	−20.3911	−	5.77469i	−0.778534	−	0.220479i
$687$	−6.09666	−	2.88858i	−0.232602	−	0.110206i
$688$	−8.17818	−	18.8817i	−0.311790	−	0.719858i
$689$	6.26367	+	9.52344i	0.238627	+	0.362814i
$690$	−0.0295398	−	0.779622i	−0.00112456	−	0.0296797i
$691$	−1.55188	+	6.54790i	−0.0590363	+	0.249094i	−0.994559	−	0.104172i	$-0.966781\pi$
$691$	−1.55188	+	6.54790i	−0.0590363	+	0.249094i	0.935523	+	0.353266i	$0.114929\pi$
$692$	9.66235	+	13.7774i	0.367307	+	0.523738i
$693$	48.6037	−	23.6675i	1.84630	−	0.899056i
$694$	21.8980	−	23.9153i	0.831235	−	0.907813i
$695$	4.44832	+	5.97513i	0.168734	+	0.226650i
$696$	−6.71401	−	36.0641i	−0.254494	−	1.36701i
$697$	5.13055	−	1.21596i	0.194333	−	0.0460579i
$698$	4.14546	+	3.37437i	0.156908	+	0.127722i
$699$	3.47876	−	0.696084i	0.131579	−	0.0263283i
$700$	−11.0556	−	27.7683i	−0.417863	−	1.04954i
$701$	30.5401	−	17.6323i	1.15348	−	0.665964i	0.203749	−	0.979023i	$-0.434687\pi$
$701$	30.5401	−	17.6323i	1.15348	−	0.665964i	0.949734	+	0.313059i	$0.101354\pi$
$702$	34.8873	+	18.9683i	1.31673	+	0.715911i
$703$	−16.8884	−	9.75053i	−0.636959	−	0.367748i
$704$	−10.7434	+	32.6662i	−0.404906	+	1.23115i
$705$	16.8546	+	2.57453i	0.634779	+	0.0969625i
$706$	29.7810	+	4.79431i	1.12082	+	0.180436i
$707$	−12.5291	+	41.8500i	−0.471204	+	1.57393i
$708$	−14.8319	+	0.783687i	−0.557416	+	0.0294528i
$709$	10.7872	−	25.0075i	0.405122	−	0.939178i	−0.586494	−	0.809954i	$-0.699492\pi$
$709$	10.7872	−	25.0075i	0.405122	−	0.939178i	0.991615	−	0.129224i	$-0.0412487\pi$
$710$	13.6605	−	4.31275i	0.512671	−	0.161855i
$711$	−6.08252	+	10.2429i	−0.228112	+	0.384140i
$712$	−14.6033	−	7.58124i	−0.547281	−	0.284119i
$713$	−1.69263	−	1.59692i	−0.0633895	−	0.0598049i
$714$	−15.9816	+	14.4759i	−0.598095	+	0.541747i
$715$	12.4892	−	24.8681i	0.467071	−	0.930016i
$716$	−0.261228	+	9.21408i	−0.00976255	+	0.344346i
$717$	−10.4575	−	22.7900i	−0.390541	−	0.851110i
$718$	−30.1779	+	7.62947i	−1.12623	+	0.284729i
$719$	6.43814	+	36.5125i	0.240102	+	1.36169i	0.831598	+	0.555379i	$0.187427\pi$
$719$	6.43814	+	36.5125i	0.240102	+	1.36169i	−0.591495	+	0.806308i	$0.701462\pi$
$720$	1.82278	−	14.2603i	0.0679310	−	0.531450i
$721$	−8.71617	+	49.4319i	−0.324607	+	1.84094i
$722$	1.35259	+	18.4717i	0.0503384	+	0.687445i
$723$	11.0940	+	6.93718i	0.412590	+	0.257997i
$724$	−8.87504	−	11.2071i	−0.329838	−	0.416510i
$725$	−24.5098	+	10.5725i	−0.910272	+	0.392653i
$726$	−0.371849	+	18.3100i	−0.0138006	+	0.679546i
$727$	0.523129	−	0.795379i	0.0194018	−	0.0294990i	−0.825657	−	0.564173i	$-0.809195\pi$
$727$	0.523129	−	0.795379i	0.0194018	−	0.0294990i	0.845058	+	0.534674i	$0.179566\pi$
$728$	63.5372	+	8.29256i	2.35484	+	0.307343i
$729$	26.7443	−	3.70692i	0.990530	−	0.137293i
$730$	−26.4840	−	1.14643i	−0.980218	−	0.0424312i
$731$	9.02497	+	5.93582i	0.333801	+	0.219544i
$732$	24.9343	+	1.58712i	0.921598	+	0.0586616i
$733$	1.80357	+	4.18114i	0.0666162	+	0.154434i	0.948272	−	0.317460i	$-0.102830\pi$
$733$	1.80357	+	4.18114i	0.0666162	+	0.154434i	−0.881655	+	0.471894i	$0.843571\pi$
$734$	−19.6334	−	22.7017i	−0.724682	−	0.837934i
$735$	−11.6338	+	18.6049i	−0.429120	+	0.686253i
$736$	−0.150064	+	1.49643i	−0.00553142	+	0.0551590i
$737$	5.89702	+	1.03980i	0.217220	+	0.0383017i
$738$	−10.6531	+	0.0282190i	−0.392146	+	0.00103876i
$739$	9.16573	−	1.61617i	0.337167	−	0.0594516i	−0.00250148	−	0.999997i	$-0.500796\pi$
$739$	9.16573	−	1.61617i	0.337167	−	0.0594516i	0.339668	+	0.940545i	$0.389685\pi$
$740$	18.8306	−	3.90285i	0.692227	−	0.143471i
$741$	−20.6697	+	9.48450i	−0.759319	+	0.348422i
$742$	12.5042	−	0.186541i	0.459044	−	0.00684813i
$743$	−15.4824	−	7.77557i	−0.567995	−	0.285258i	0.141534	−	0.989933i	$-0.454796\pi$
$743$	−15.4824	−	7.77557i	−0.567995	−	0.285258i	−0.709530	+	0.704675i	$0.751093\pi$
$744$	−25.9329	−	34.1497i	−0.950745	−	1.25199i
$745$	−1.80027	+	1.90818i	−0.0659569	+	0.0699103i
$746$	−0.242427	+	0.585889i	−0.00887590	+	0.0214509i
$747$	−11.6556	−	6.92137i	−0.426455	−	0.253240i
$748$	−4.68525	−	17.4336i	−0.171310	−	0.637436i
$749$	−40.9051	−	17.6447i	−1.49464	−	0.644724i
$750$	−25.0178	+	2.41037i	−0.913522	+	0.0880141i
$751$	12.7915	+	3.82954i	0.466770	+	0.139742i	0.511547	−	0.859255i	$-0.329073\pi$
$751$	12.7915	+	3.82954i	0.466770	+	0.139742i	−0.0447769	+	0.998997i	$0.514258\pi$
$752$	−31.5002	−	9.37938i	−1.14869	−	0.342031i
$753$	0.784373	−	5.13502i	0.0285842	−	0.187130i
$754$	5.79491	−	56.9315i	0.211038	−	2.07332i
$755$	−12.5473	+	21.7326i	−0.456643	+	0.790929i
$756$	38.1086	−	21.1138i	1.38600	−	0.767902i
$757$	22.6854	+	39.2922i	0.824513	+	1.42810i	0.902291	+	0.431128i	$0.141884\pi$
$757$	22.6854	+	39.2922i	0.824513	+	1.42810i	−0.0777776	+	0.996971i	$0.524782\pi$
$758$	15.4710	−	6.94906i	0.561933	−	0.252401i
$759$	0.388363	+	1.94088i	0.0140967	+	0.0704497i
$760$	5.91222	+	5.72986i	0.214459	+	0.207844i
$761$	−11.7636	−	49.6345i	−0.426430	−	1.79925i	−0.584012	−	0.811745i	$-0.698518\pi$
$761$	−11.7636	−	49.6345i	−0.426430	−	1.79925i	0.157582	−	0.987506i	$-0.449630\pi$
$762$	7.22629	+	26.0515i	0.261781	+	0.943745i
$763$	49.9014	−	37.1502i	1.80655	−	1.34493i
$764$	−36.6343	−	36.5797i	−1.32538	−	1.32341i
$765$	3.30412	+	6.78534i	0.119461	+	0.245324i
$766$	12.9455	+	16.8578i	0.467738	+	0.609098i
$767$	−22.5450	−	5.34327i	−0.814054	−	0.192934i
$768$	−7.25695	+	26.7458i	−0.261863	+	0.965105i
$769$	−9.38151	+	6.17032i	−0.338306	+	0.222507i	−0.707282	−	0.706932i	$-0.750079\pi$
$769$	−9.38151	+	6.17032i	−0.338306	+	0.222507i	0.368976	+	0.929439i	$0.379708\pi$
$770$	−15.6580	−	26.2096i	−0.564275	−	0.944529i
$771$	−20.9975	+	44.3175i	−0.756207	+	1.59606i
$772$	13.1615	+	4.35035i	0.473691	+	0.156572i
$773$	−3.96279	−	4.72267i	−0.142532	−	0.169862i	0.690056	−	0.723756i	$-0.257586\pi$
$773$	−3.96279	−	4.72267i	−0.142532	−	0.169862i	−0.832588	+	0.553894i	$0.813141\pi$
$774$	−15.0191	−	15.8351i	−0.539852	−	0.569182i
$775$	−20.0561	+	23.9019i	−0.720435	+	0.858581i
$776$	6.30516	−	3.52828i	0.226342	−	0.126658i
$777$	43.2967	+	39.0093i	1.55326	+	1.39945i
$778$	21.6837	−	4.15785i	0.777399	−	0.149066i
$779$	3.64324	−	4.89372i	0.130533	−	0.175336i
$780$	8.99358	−	20.5443i	0.322022	−	0.735606i
$781$	−32.4779	+	16.3110i	−1.16215	+	0.583653i
$782$	−0.364817	−	0.700169i	−0.0130458	−	0.0250380i
$783$	−19.8135	−	33.4864i	−0.708076	−	1.19671i
$784$	27.1407	−	32.4431i	0.969310	−	1.15868i
$785$	−6.98016	−	0.406548i	−0.249133	−	0.0145103i
$786$	11.8715	+	34.7994i	0.423442	+	1.24125i
$787$	6.23327	−	53.3290i	0.222192	−	1.90097i	−0.177168	−	0.984181i	$-0.556693\pi$
$787$	6.23327	−	53.3290i	0.222192	−	1.90097i	0.399360	−	0.916794i	$-0.369232\pi$
$788$	26.4302	+	10.4772i	0.941537	+	0.373236i
$789$	−13.5406	+	33.4835i	−0.482056	+	1.19205i
$790$	6.05657	+	2.92942i	0.215483	+	0.104224i
$791$	41.6786	−	15.1698i	1.48192	−	0.539375i
$792$	1.18456	+	36.4542i	0.0420917	+	1.29534i
$793$	36.6250	+	13.3304i	1.30059	+	0.473377i
$794$	−20.1465	−	20.7257i	−0.714971	−	0.735529i
$795$	1.15876	−	4.22080i	0.0410968	−	0.149696i
$796$	4.51541	−	7.33283i	0.160045	−	0.259905i
$797$	11.6510	−	0.678591i	0.412698	−	0.0240369i	0.149460	−	0.988768i	$-0.452247\pi$
$797$	11.6510	−	0.678591i	0.412698	−	0.0240369i	0.263238	+	0.964731i	$0.415210\pi$
$798$	−3.39914	+	24.7177i	−0.120328	+	0.874997i
$799$	16.5291	−	4.94849i	0.584758	−	0.175065i
$800$	20.1476	+	0.842046i	0.712325	+	0.0297708i
$801$	−17.3078	−	2.23855i	−0.611542	−	0.0790954i
$802$	3.11106	−	14.0579i	0.109855	−	0.496401i
$803$	66.7995	−	7.80774i	2.35730	−	0.275529i
$804$	4.79000	+	0.586051i	0.168930	+	0.0206684i
$805$	−0.916305	−	0.971227i	−0.0322955	−	0.0342313i
$806$	−23.8135	−	62.5096i	−0.838794	−	2.20181i
$807$	−15.9430	−	8.72302i	−0.561219	−	0.307065i
$808$	−22.3219	−	19.2468i	−0.785281	−	0.677101i
$809$			1.74154i			0.0612292i	0.999531	+	0.0306146i	$0.00974645\pi$
$809$			1.74154i			0.0612292i	−0.999531	+	0.0306146i	$0.990254\pi$
$810$	−3.37363	−	14.8705i	−0.118537	−	0.522496i
$811$		−	8.69253i		−	0.305236i	−0.988285	−	0.152618i	$-0.951230\pi$
$811$		−	8.69253i		−	0.305236i	0.988285	−	0.152618i	$-0.0487704\pi$
$812$	−49.2769	−	38.9035i	−1.72928	−	1.36524i
$813$	33.5786	−	20.4283i	1.17765	−	0.716452i
$814$	−45.5931	+	17.3690i	−1.59804	+	0.608784i
$815$	−0.966781	−	1.02473i	−0.0338649	−	0.0358947i
$816$	−4.51190	−	13.8309i	−0.157948	−	0.484179i
$817$	12.4144	−	1.45104i	0.434326	−	0.0507654i
$818$	29.7197	+	6.57708i	1.03913	+	0.229962i
$819$	66.3183	−	14.8609i	2.31735	−	0.519280i
$820$	0.528833	+	5.99313i	0.0184676	+	0.209289i
$821$	32.7995	−	9.81952i	1.14471	−	0.342704i	0.342366	−	0.939567i	$-0.388772\pi$
$821$	32.7995	−	9.81952i	1.14471	−	0.342704i	0.802343	+	0.596863i	$0.203586\pi$
$822$	−20.7819	+	26.7629i	−0.724853	+	0.933462i
$823$	−1.58198	+	0.0921400i	−0.0551444	+	0.00321180i	−0.0856949	−	0.996321i	$-0.527311\pi$
$823$	−1.58198	+	0.0921400i	−0.0551444	+	0.00321180i	0.0305504	+	0.999533i	$0.490274\pi$
$824$	−28.0418	−	18.9876i	−0.976882	−	0.661464i
$825$	25.6772	−	6.71163i	0.893964	−	0.233669i
$826$	−18.2273	+	17.7179i	−0.634209	+	0.616483i
$827$	−0.149073	−	0.0542583i	−0.00518379	−	0.00188675i	0.339427	−	0.940632i	$-0.389767\pi$
$827$	−0.149073	−	0.0542583i	−0.00518379	−	0.00188675i	−0.344611	+	0.938746i	$0.611989\pi$
$828$	0.395077	+	1.54546i	0.0137299	+	0.0537085i
$829$	−1.68008	+	0.611498i	−0.0583515	+	0.0212382i	−0.371031	−	0.928620i	$-0.620996\pi$
$829$	−1.68008	+	0.611498i	−0.0583515	+	0.0212382i	0.312680	+	0.949859i	$0.398773\pi$
$830$	−3.33342	+	6.89184i	−0.115705	+	0.239219i
$831$	−3.47490	−	4.45057i	−0.120543	−	0.154389i
$832$	−22.6130	+	36.8455i	−0.783966	+	1.27739i
$833$	−2.57787	+	22.0551i	−0.0893180	+	0.764165i
$834$	−11.4661	−	10.0249i	−0.397038	−	0.347134i
$835$	4.40654	+	0.256652i	0.152495	+	0.00888179i
$836$	−17.1194	−	11.9681i	−0.592087	−	0.413926i
$837$	−38.2640	−	24.5849i	−1.32260	−	0.849779i
$838$	−10.9070	+	5.68301i	−0.376777	+	0.196316i
$839$	−7.52365	+	3.77852i	−0.259745	+	0.130449i	−0.573907	−	0.818921i	$-0.694573\pi$
$839$	−7.52365	+	3.77852i	−0.259745	+	0.130449i	0.314162	+	0.949369i	$0.398277\pi$
$840$	−13.7157	−	20.4270i	−0.473236	−	0.704800i
$841$	−16.1656	+	21.7141i	−0.557433	+	0.748763i
$842$	−4.92563	−	25.6878i	−0.169748	−	0.885260i
$843$	2.74739	−	12.9054i	0.0946252	−	0.444485i
$844$	−17.6646	+	10.9139i	−0.608042	+	0.375672i
$845$	12.4769	−	14.8694i	0.429218	−	0.511522i
$846$	−34.7961	+	2.11914i	−1.19632	+	0.0728576i
$847$	20.1471	+	24.0104i	0.692262	+	0.825005i
$848$	−3.33031	+	7.75229i	−0.114363	+	0.266215i
$849$	−13.7052	−	19.8308i	−0.470360	−	0.680591i
$850$	−9.08777	+	5.42916i	−0.311708	+	0.186219i
$851$	−1.78277	+	1.17254i	−0.0611125	+	0.0401943i
$852$	−25.4438	+	14.5077i	−0.871691	+	0.497027i
$853$	16.8551	+	3.99474i	0.577109	+	0.136777i	0.508797	−	0.860887i	$-0.330090\pi$
$853$	16.8551	+	3.99474i	0.577109	+	0.136777i	0.0683124	+	0.997664i	$0.478239\pi$
$854$	33.9145	−	26.0436i	1.16053	−	0.891194i
$855$	7.97540	+	3.55693i	0.272753	+	0.121644i
$856$	22.1370	−	20.3304i	0.756628	−	0.694879i
$857$	17.0941	−	12.7261i	0.583922	−	0.434714i	−0.264235	−	0.964458i	$-0.585120\pi$
$857$	17.0941	−	12.7261i	0.583922	−	0.434714i	0.848157	+	0.529745i	$0.177712\pi$
$858$	−14.2429	+	55.0860i	−0.486245	+	1.88061i
$859$	3.00939	+	12.6976i	0.102679	+	0.433237i	0.999966	−	0.00821003i	$-0.00261336\pi$
$859$	3.00939	+	12.6976i	0.102679	+	0.433237i	−0.897287	+	0.441447i	$0.854465\pi$
$860$	−8.18722	+	9.21373i	−0.279182	+	0.314185i
$861$	−13.6942	+	12.0371i	−0.466697	+	0.410223i
$862$	13.0019	+	28.9467i	0.442846	+	0.985928i
$863$	−20.9699	−	36.3209i	−0.713823	−	1.23638i	−0.963412	−	0.268026i	$-0.913629\pi$
$863$	−20.9699	−	36.3209i	−0.713823	−	1.23638i	0.249589	−	0.968352i	$-0.419705\pi$
$864$	2.50344	+	29.2871i	0.0851688	+	0.996367i
$865$	5.04006	−	8.72964i	0.171367	−	0.296817i
$866$	8.36896	+	0.851855i	0.284389	+	0.0289472i
$867$	−17.0229	−	13.6305i	−0.578128	−	0.462916i
$868$	−71.8828	−	14.7868i	−2.43986	−	0.501895i
$869$	−16.3517	−	4.89539i	−0.554695	−	0.166065i
$870$	−17.8887	+	12.7614i	−0.606484	+	0.432652i
$871$	6.91231	+	2.98168i	0.234215	+	0.101030i
$872$	9.13050	+	40.9682i	0.309198	+	1.38736i
$873$	4.99765	−	5.80971i	0.169145	−	0.196629i
$874$	−0.844127	−	0.349280i	−0.0285530	−	0.0118146i
$875$	−29.5189	+	31.2882i	−0.997922	+	1.05774i
$876$	53.4266	−	9.12398i	1.80512	−	0.308271i
$877$	−5.88374	−	2.95493i	−0.198680	−	0.0997808i	0.346678	−	0.937984i	$-0.387310\pi$
$877$	−5.88374	−	2.95493i	−0.198680	−	0.0997808i	−0.545357	+	0.838204i	$0.683606\pi$
$878$	−0.103058	−	6.90821i	−0.00347805	−	0.233141i
$879$	−13.2672	−	9.41159i	−0.447491	−	0.317445i
$880$	20.4557	−	2.42185i	0.689561	−	0.0816404i
$881$	−25.5969	+	4.51342i	−0.862380	+	0.152061i	−0.587309	−	0.809363i	$-0.699813\pi$
$881$	−25.5969	+	4.51342i	−0.862380	+	0.152061i	−0.275071	+	0.961424i	$0.588702\pi$
$882$	15.2328	−	42.1993i	0.512916	−	1.42092i
$883$	33.9741	+	5.99056i	1.14332	+	0.201598i	0.713058	−	0.701105i	$-0.247310\pi$
$883$	33.9741	+	5.99056i	1.14332	+	0.201598i	0.430263	+	0.902704i	$0.358421\pi$
$884$	−0.676984	−	22.6847i	−0.0227694	−	0.762971i
$885$	4.17435	+	7.85680i	0.140319	+	0.264103i
$886$	32.3464	−	27.9746i	1.08670	−	0.939824i
$887$	−6.04647	−	14.0173i	−0.203021	−	0.470655i	0.786038	−	0.618178i	$-0.212129\pi$
$887$	−6.04647	−	14.0173i	−0.203021	−	0.470655i	−0.989059	+	0.147524i	$0.952870\pi$
$888$	−35.9537	+	15.9169i	−1.20653	+	0.534137i
$889$	38.6577	+	25.4256i	1.29654	+	0.852747i
$890$	−0.426247	+	9.84689i	−0.0142878	+	0.330068i
$891$	14.4466	+	35.8873i	0.483979	+	1.20227i
$892$	2.37462	−	27.3770i	0.0795080	−	0.916650i
$893$	10.9706	−	16.6800i	0.367117	−	0.558175i
$894$	2.77565	−	4.58976i	0.0928317	−	0.153504i
$895$	5.07000	−	2.18698i	0.169471	−	0.0731028i
$896$	20.7789	+	42.6356i	0.694175	+	1.42435i
$897$	−0.0876309	+	2.48686i	−0.00292591	+	0.0830340i
$898$	−13.0466	+	0.955341i	−0.435371	+	0.0318801i
$899$	−11.3813	+	64.5463i	−0.379586	+	2.15274i
$900$	20.3789	−	6.49322i	0.679298	−	0.216441i
$901$	−0.769142	−	4.36202i	−0.0256238	−	0.145320i
$902$	−3.74126	−	14.7983i	−0.124570	−	0.492731i
$903$	−37.1897	−	3.48368i	−1.23760	−	0.115929i
$904$	−2.14089	+	29.8480i	−0.0712050	+	0.992729i
$905$	−3.84320	+	7.65244i	−0.127752	+	0.254376i
$906$	15.7104	−	48.8441i	0.521944	−	1.62274i
$907$	40.5599	+	38.2663i	1.34677	+	1.27061i	0.932834	+	0.360307i	$0.117328\pi$
$907$	40.5599	+	38.2663i	1.34677	+	1.27061i	0.413937	+	0.910305i	$0.364153\pi$
$908$	39.7215	+	18.4864i	1.31820	+	0.613493i
$909$	−29.2430	−	11.0517i	−0.969930	−	0.366562i
$910$	−11.5555	−	36.6016i	−0.383060	−	1.21333i
$911$	9.61065	−	22.2800i	0.318415	−	0.738169i	−0.681564	−	0.731758i	$-0.738700\pi$
$911$	9.61065	−	22.2800i	0.318415	−	0.738169i	0.999979	−	0.00641106i	$-0.00204072\pi$
$912$	−14.2862	−	8.90369i	−0.473063	−	0.294831i
$913$	5.57052	−	18.6068i	0.184357	−	0.615797i
$914$	−6.40186	+	39.7668i	−0.211755	+	1.31537i
$915$	−5.44019	−	13.9424i	−0.179847	−	0.460923i
$916$	1.12328	−	7.70860i	0.0371141	−	0.254699i
$917$	54.4974	+	31.4641i	1.79966	+	1.03904i
$918$	−9.52845	−	12.1374i	−0.314486	−	0.400594i
$919$	43.4357	−	25.0776i	1.43281	−	0.827234i	0.435477	−	0.900200i	$-0.356580\pi$
$919$	43.4357	−	25.0776i	1.43281	−	0.827234i	0.997334	+	0.0729659i	$0.0232464\pi$
$920$	0.850607	−	0.296724i	0.0280437	−	0.00978271i
$921$	−17.9982	+	53.2200i	−0.593061	+	1.75366i
$922$	19.0260	−	23.3737i	0.626587	−	0.769770i
$923$	−44.4589	+	10.5369i	−1.46338	+	0.346828i
$924$	42.5919	+	45.6350i	1.40117	+	1.50128i
$925$	17.0851	+	22.9493i	0.561755	+	0.754568i
$926$	−21.1076	−	19.3271i	−0.693638	−	0.635126i
$927$	−34.8473	−	8.71183i	−1.14453	−	0.286134i
$928$	37.5362	−	19.6291i	1.23219	−	0.644356i
$929$	−13.2922	+	56.0841i	−0.436102	+	1.84006i	0.0987496	+	0.995112i	$0.468516\pi$
$929$	−13.2922	+	56.0841i	−0.436102	+	1.84006i	−0.534851	+	0.844946i	$0.679632\pi$
$930$	−11.9915	+	22.7149i	−0.393215	+	0.744851i
$931$	14.1188	+	21.4666i	0.462725	+	0.703540i
$932$	1.94691	+	3.60434i	0.0637732	+	0.118064i
$933$	4.69656	+	57.7606i	0.153758	+	1.89100i
$934$	−15.4935	+	54.7094i	−0.506964	+	1.79015i
$935$	−8.28363	+	6.95079i	−0.270904	+	0.227315i
$936$	−9.11993	+	44.9375i	−0.298094	+	1.46883i
$937$	−26.3855	−	22.1401i	−0.861977	−	0.723285i	0.100416	−	0.994946i	$-0.467983\pi$
$937$	−26.3855	−	22.1401i	−0.861977	−	0.723285i	−0.962393	+	0.271661i	$0.912427\pi$
$938$	6.83186	−	4.64084i	0.223068	−	0.151529i
$939$	−4.17518	−	12.8637i	−0.136252	−	0.419791i
$940$	2.86790	+	19.4777i	0.0935405	+	0.635293i
$941$	−29.1274	−	21.6846i	−0.949527	−	0.706896i	0.00656058	−	0.999978i	$-0.497912\pi$
$941$	−29.1274	−	21.6846i	−0.949527	−	0.706896i	−0.956087	+	0.293082i	$0.905319\pi$
$942$	14.1262	−	2.19608i	0.460255	−	0.0715521i
$943$	−0.299603	−	0.596559i	−0.00975643	−	0.0194266i
$944$	−5.88975	−	16.1072i	−0.191695	−	0.524245i
$945$	−21.0984	−	15.3595i	−0.686331	−	0.499645i
$946$	16.7920	−	26.3799i	0.545956	−	0.857685i
$947$	−0.584458	+	10.0348i	−0.0189923	+	0.326086i	0.975408	+	0.220407i	$0.0707386\pi$
$947$	−0.584458	+	10.0348i	−0.0189923	+	0.326086i	−0.994400	+	0.105679i	$0.966298\pi$
$948$	−13.3676	−	3.24437i	−0.434161	−	0.105372i
$949$	83.9789	+	9.81572i	2.72607	+	0.318632i
$950$	−4.01723	+	11.5715i	−0.130336	+	0.375428i
$951$	2.14649	+	15.3082i	0.0696047	+	0.496402i
$952$	−21.3939	−	12.7378i	−0.693380	−	0.412834i
$953$	6.84290	+	18.8007i	0.221663	+	0.609014i	0.999818	−	0.0190575i	$-0.00606657\pi$
$953$	6.84290	+	18.8007i	0.221663	+	0.609014i	−0.778155	+	0.628072i	$0.783844\pi$
$954$	−0.496681	+	8.93538i	−0.0160806	+	0.289293i
$955$	−10.6064	+	29.1408i	−0.343215	+	0.942974i
$956$	21.6149	−	19.2645i	0.699076	−	0.623059i
$957$	39.6618	−	39.1782i	1.28208	−	1.26645i
$958$	6.51751	−	11.6879i	0.210571	−	0.377619i
$959$	3.37191	+	57.8935i	0.108885	+	1.86948i
$960$	16.3593	−	2.81888i	0.527993	−	0.0909788i
$961$	13.0820	+	43.6968i	0.421999	+	1.40958i
$962$	−60.8094	+	8.02877i	−1.96057	+	0.258858i
$963$	14.6559	−	28.3108i	0.472278	−	0.912303i
$964$	−3.89950	+	14.5967i	−0.125595	+	0.470127i
$965$	−0.963966	−	8.24726i	−0.0310312	−	0.265489i
$966$	2.25000	+	1.54620i	0.0723926	+	0.0497481i
$967$	−25.6793	+	24.2272i	−0.825791	+	0.779094i	−0.977856	−	0.209277i	$-0.932889\pi$
$967$	−25.6793	+	24.2272i	−0.825791	+	0.779094i	0.152066	+	0.988370i	$0.451408\pi$
$968$	−20.3381	+	5.79246i	−0.653691	+	0.186177i
$969$	8.83473	−	0.202834i	0.283812	−	0.00651597i
$970$	−3.50976	−	2.53243i	−0.112692	−	0.0813115i
$971$	−19.4924			−0.625542			−0.312771	−	0.949829i	$-0.601257\pi$
$971$	−19.4924			−0.625542			−0.312771	+	0.949829i	$0.601257\pi$
$972$	13.1523	+	28.2669i	0.421860	+	0.906661i
$973$	−26.0665			−0.835655
$974$	−5.15298	−	3.71809i	−0.165112	−	0.119135i
$975$	33.3565	−	0.765823i	1.06826	−	0.0245260i
$976$	6.69510	+	28.0623i	0.214305	+	0.898253i
$977$	−15.1243	+	14.2690i	−0.483869	+	0.456507i	−0.889104	−	0.457706i	$-0.848671\pi$
$977$	−15.1243	+	14.2690i	−0.483869	+	0.456507i	0.405235	+	0.914213i	$0.367190\pi$
$978$	2.37395	+	1.63137i	0.0759104	+	0.0521655i
$979$	−2.90295	−	24.8364i	−0.0927788	−	0.793774i
$980$	−24.4790	−	6.53956i	−0.781952	−	0.208899i
$981$	24.0057	+	37.4928i	0.766442	+	1.19705i
$982$	10.8956	−	1.43856i	0.347692	−	0.0459063i
$983$	−3.64856	−	12.1870i	−0.116371	−	0.388706i	0.879882	−	0.475192i	$-0.157621\pi$
$983$	−3.64856	−	12.1870i	−0.116371	−	0.388706i	−0.996253	+	0.0864858i	$0.972436\pi$
$984$	−3.64014	−	11.7503i	−0.116044	−	0.374584i
$985$	−0.990242	−	17.0018i	−0.0315517	−	0.541722i
$986$	−10.8299	+	19.4214i	−0.344895	+	0.618503i
$987$	−42.4459	+	41.9283i	−1.35107	+	1.33459i
$988$	−17.4722	−	19.6039i	−0.555863	−	0.623682i
$989$	0.467758	−	1.28515i	0.0148738	−	0.0408655i
$990$	19.4981	−	9.85708i	0.619691	−	0.313279i
$991$	−5.98468	−	16.4428i	−0.190110	−	0.522322i	0.807617	−	0.589707i	$-0.200757\pi$
$991$	−5.98468	−	16.4428i	−0.190110	−	0.522322i	−0.997727	+	0.0673846i	$0.978535\pi$
$992$	28.9120	−	40.1960i	0.917956	−	1.27622i
$993$	2.22708	+	15.8830i	0.0706743	+	0.504031i
$994$	−16.4401	+	47.3550i	−0.521448	+	1.50201i
$995$	−5.12357	−	0.598860i	−0.162428	−	0.0189851i
$996$	3.69181	−	15.2112i	0.116979	−	0.481986i
$997$	0.756684	−	12.9918i	0.0239644	−	0.411453i	−0.964898	−	0.262623i	$-0.915412\pi$
$997$	0.756684	−	12.9918i	0.0239644	−	0.411453i	0.988863	−	0.148830i	$-0.0475506\pi$
$998$	−7.82284	+	12.2895i	−0.247628	+	0.389018i
$999$	−30.0272	+	28.9419i	−0.950018	+	0.915681i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.191.17	yes	936
3.2	odd	2		972.2.p.a.575.36		936
4.3	odd	2	inner	324.2.p.a.191.18	yes	936
12.11	even	2		972.2.p.a.575.35		936
81.14	odd	54	inner	324.2.p.a.95.18	yes	936
81.67	even	27		972.2.p.a.71.35		936
324.67	odd	54		972.2.p.a.71.36		936
324.95	even	54	inner	324.2.p.a.95.17	✓	936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.95.17	✓	936	324.95	even	54	inner
324.2.p.a.95.18	yes	936	81.14	odd	54	inner
324.2.p.a.191.17	yes	936	1.1	even	1	trivial
324.2.p.a.191.18	yes	936	4.3	odd	2	inner
972.2.p.a.71.35		936	81.67	even	27
972.2.p.a.71.36		936	324.67	odd	54
972.2.p.a.575.35		936	12.11	even	2
972.2.p.a.575.36		936	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.827495 + 1.14684i) q^{2} +(-1.73159 + 0.0397552i) q^{3} +(-0.630505 - 1.89802i) q^{4} +(-0.871413 + 0.822136i) q^{5} +(1.38729 - 2.01877i) q^{6} +(-0.486686 - 4.16387i) q^{7} +(2.69847 + 0.847508i) q^{8} +(2.99684 - 0.137680i) q^{9} +O(q^{10})\)	\(q+(-0.827495 + 1.14684i) q^{2} +(-1.73159 + 0.0397552i) q^{3} +(-0.630505 - 1.89802i) q^{4} +(-0.871413 + 0.822136i) q^{5} +(1.38729 - 2.01877i) q^{6} +(-0.486686 - 4.16387i) q^{7} +(2.69847 + 0.847508i) q^{8} +(2.99684 - 0.137680i) q^{9} +(-0.221772 - 1.67969i) q^{10} +(1.23281 + 4.11786i) q^{11} +(1.16723 + 3.26153i) q^{12} +(0.314209 + 5.39476i) q^{13} +(5.17804 + 2.88743i) q^{14} +(1.47625 - 1.45825i) q^{15} +(-3.20493 + 2.39342i) q^{16} +(0.718194 - 1.97322i) q^{17} +(-2.32197 + 3.55084i) q^{18} +(-0.831015 - 2.28320i) q^{19} +(2.10986 + 1.13560i) q^{20} +(1.00828 + 7.19078i) q^{21} +(-5.74268 - 1.99367i) q^{22} +(-0.264063 - 0.0308645i) q^{23} +(-4.70635 - 1.36026i) q^{24} +(-0.207271 + 3.55870i) q^{25} +(-6.44696 - 4.10379i) q^{26} +(-5.18384 + 0.357546i) q^{27} +(-7.59623 + 3.54908i) q^{28} +(3.36063 + 6.69156i) q^{29} +(0.450796 + 2.89972i) q^{30} +(7.02089 + 5.22686i) q^{31} +(-0.0928137 - 5.65609i) q^{32} +(-2.29843 - 7.08145i) q^{33} +(1.66868 + 2.45649i) q^{34} +(3.84737 + 3.22833i) q^{35} +(-2.15084 - 5.60124i) q^{36} +(6.14830 - 5.15904i) q^{37} +(3.30613 + 0.936287i) q^{38} +(-0.758552 - 9.32904i) q^{39} +(-3.04825 + 1.47998i) q^{40} +(1.37980 + 2.09788i) q^{41} +(-9.08105 - 4.79400i) q^{42} +(-1.18633 + 5.00551i) q^{43} +(7.03847 - 4.93621i) q^{44} +(-2.49829 + 2.58378i) q^{45} +(0.253907 - 0.277299i) q^{46} +(4.90669 + 6.59083i) q^{47} +(5.45448 - 4.27184i) q^{48} +(-10.2896 + 2.43868i) q^{49} +(-3.90976 - 3.18251i) q^{50} +(-1.16517 + 3.44537i) q^{51} +(10.0412 - 3.99779i) q^{52} +(1.82674 - 1.05467i) q^{53} +(3.87955 - 6.24092i) q^{54} +(-4.45972 - 2.57482i) q^{55} +(2.21560 - 11.6485i) q^{56} +(1.52975 + 3.92053i) q^{57} +(-10.4551 - 1.68311i) q^{58} +(-1.22969 + 4.10744i) q^{59} +(-3.69856 - 1.88251i) q^{60} +(2.85672 - 6.62262i) q^{61} +(-11.8042 + 3.72667i) q^{62} +(-2.03180 - 12.4114i) q^{63} +(6.56346 + 4.57394i) q^{64} +(-4.70903 - 4.44274i) q^{65} +(10.0233 + 3.22392i) q^{66} +(0.625206 - 1.24489i) q^{67} +(-4.19803 - 0.119018i) q^{68} +(0.458476 + 0.0429469i) q^{69} +(-6.88606 + 1.74091i) q^{70} +(1.46821 + 8.32664i) q^{71} +(8.20356 + 2.16832i) q^{72} +(2.71694 - 15.4085i) q^{73} +(0.828926 + 11.3202i) q^{74} +(0.217432 - 6.17047i) q^{75} +(-3.80958 + 3.01684i) q^{76} +(16.5462 - 7.13734i) q^{77} +(11.3267 + 6.84979i) q^{78} +(-2.18206 + 3.31767i) q^{79} +(0.825104 - 4.72054i) q^{80} +(8.96209 - 0.825209i) q^{81} +(-3.54772 - 0.153572i) q^{82} +(-3.77521 - 2.48300i) q^{83} +(13.0125 - 6.44755i) q^{84} +(0.996412 + 2.30994i) q^{85} +(-4.75887 - 5.50257i) q^{86} +(-6.08527 - 11.4535i) q^{87} +(-0.163229 + 12.1567i) q^{88} +(-5.72896 - 1.01017i) q^{89} +(-0.895874 - 5.00322i) q^{90} +(22.3101 - 3.93388i) q^{91} +(0.107911 + 0.520655i) q^{92} +(-12.3651 - 8.77169i) q^{93} +(-11.6189 + 0.173334i) q^{94} +(2.60125 + 1.30640i) q^{95} +(0.385575 + 9.79037i) q^{96} +(1.75301 - 1.85808i) q^{97} +(5.71781 - 13.8186i) q^{98} +(4.26146 + 12.1708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

L-functions

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