LMFDB - Embedded newform 171.2.x.a.110.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(14,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([15, 7]))

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

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

chi := DirichletCharacter("171.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.x (of order $18$, degree $6$, 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:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			110.6
Character	$\chi$	$=$	171.110
Dual form			171.2.x.a.14.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.907216 + 0.761244i) q^{2} +(0.509726 - 1.65535i) q^{3} +(-0.103749 + 0.588390i) q^{4} +(-1.20969 + 3.32360i) q^{5} +(0.797694 + 1.88978i) q^{6} +(0.600840 + 1.04068i) q^{7} +(-1.53807 - 2.66402i) q^{8} +(-2.48036 - 1.68755i) q^{9} +O(q^{10})$	\(q+(-0.907216 + 0.761244i) q^{2} +(0.509726 - 1.65535i) q^{3} +(-0.103749 + 0.588390i) q^{4} +(-1.20969 + 3.32360i) q^{5} +(0.797694 + 1.88978i) q^{6} +(0.600840 + 1.04068i) q^{7} +(-1.53807 - 2.66402i) q^{8} +(-2.48036 - 1.68755i) q^{9} +(-1.43262 - 3.93610i) q^{10} +3.37386i q^{11} +(0.921107 + 0.471658i) q^{12} +(1.06414 + 2.92371i) q^{13} +(-1.33731 - 0.486740i) q^{14} +(4.88511 + 3.69659i) q^{15} +(2.30046 + 0.837300i) q^{16} +(-1.91063 + 5.24942i) q^{17} +(3.53486 - 0.357190i) q^{18} +(3.51512 - 2.57759i) q^{19} +(-1.83007 - 1.05659i) q^{20} +(2.02896 - 0.464135i) q^{21} +(-2.56833 - 3.06082i) q^{22} +(2.71688 + 0.479060i) q^{23} +(-5.19387 + 1.18813i) q^{24} +(-5.75276 - 4.82714i) q^{25} +(-3.19107 - 1.84236i) q^{26} +(-4.05778 + 3.24567i) q^{27} +(-0.674665 + 0.245558i) q^{28} +(1.75252 - 9.93902i) q^{29} +(-7.24586 + 0.365160i) q^{30} -0.427425i q^{31} +(3.05685 - 1.11260i) q^{32} +(5.58491 + 1.71974i) q^{33} +(-2.26273 - 6.21681i) q^{34} +(-4.18565 + 0.738044i) q^{35} +(1.25027 - 1.28434i) q^{36} -0.0841209i q^{37} +(-1.22679 + 5.01429i) q^{38} +(5.38219 - 0.271239i) q^{39} +(10.7147 - 1.88930i) q^{40} +(-1.55749 + 1.30689i) q^{41} +(-1.48738 + 1.96561i) q^{42} +(-0.0600559 - 0.340594i) q^{43} +(-1.98514 - 0.350034i) q^{44} +(8.60921 - 6.20232i) q^{45} +(-2.82948 + 1.63360i) q^{46} +(7.15417 + 1.26147i) q^{47} +(2.55863 - 3.38127i) q^{48} +(2.77798 - 4.81161i) q^{49} +8.89363 q^{50} +(7.71572 + 5.83852i) q^{51} +(-1.83069 + 0.322799i) q^{52} +(-4.91060 - 4.12048i) q^{53} +(1.21053 - 6.03349i) q^{54} +(-11.2134 - 4.08133i) q^{55} +(1.84827 - 3.20130i) q^{56} +(-2.47506 - 7.13261i) q^{57} +(5.97611 + 10.3509i) q^{58} +(0.479154 + 2.71742i) q^{59} +(-2.68186 + 2.49083i) q^{60} +(4.68956 - 1.70686i) q^{61} +(0.325375 + 0.387767i) q^{62} +(0.265907 - 3.59522i) q^{63} +(-4.37436 + 7.57662i) q^{64} -11.0045 q^{65} +(-6.37587 + 2.69131i) q^{66} +(-4.40746 + 5.25261i) q^{67} +(-2.89048 - 1.66882i) q^{68} +(2.17788 - 4.25320i) q^{69} +(3.23546 - 3.85587i) q^{70} +(10.6625 - 8.94693i) q^{71} +(-0.680687 + 9.20329i) q^{72} +(2.30724 + 13.0850i) q^{73} +(0.0640366 + 0.0763159i) q^{74} +(-10.9229 + 7.06231i) q^{75} +(1.15194 + 2.33568i) q^{76} +(-3.51112 + 2.02715i) q^{77} +(-4.67633 + 4.34323i) q^{78} +(-5.23326 + 14.3783i) q^{79} +(-5.56570 + 6.63295i) q^{80} +(3.30437 + 8.37145i) q^{81} +(0.418116 - 2.37126i) q^{82} +(9.41085 - 5.43336i) q^{83} +(0.0625900 + 1.24197i) q^{84} +(-15.1357 - 12.7004i) q^{85} +(0.313759 + 0.263275i) q^{86} +(-15.5592 - 7.96720i) q^{87} +(8.98802 - 5.18924i) q^{88} +(-0.172118 + 0.976130i) q^{89} +(-3.08893 + 12.1806i) q^{90} +(-2.40328 + 2.86412i) q^{91} +(-0.563748 + 1.54888i) q^{92} +(-0.707538 - 0.217870i) q^{93} +(-7.45066 + 4.30164i) q^{94} +(4.31467 + 14.8009i) q^{95} +(-0.283590 - 5.62728i) q^{96} +(-2.27491 - 2.71113i) q^{97} +(1.14258 + 6.47989i) q^{98} +(5.69355 - 8.36838i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) $ 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.907216	+	0.761244i	−0.641498	+	0.538281i	−0.904478	−	0.426520i	$-0.859739\pi$
$2$	−0.907216	+	0.761244i	−0.641498	+	0.538281i	0.262980	+	0.964801i	$0.415295\pi$
$3$	0.509726	−	1.65535i	0.294290	−	0.955716i
$3$	0.509726	−	1.65535i	0.294290	−	0.955716i
$4$	−0.103749	+	0.588390i	−0.0518745	+	0.294195i
$5$	−1.20969	+	3.32360i	−0.540991	+	1.48636i	0.304574	+	0.952489i	$0.401486\pi$
$5$	−1.20969	+	3.32360i	−0.540991	+	1.48636i	−0.845565	+	0.533872i	$0.820736\pi$
$6$	0.797694	+	1.88978i	0.325657	+	0.771501i
$7$	0.600840	+	1.04068i	0.227096	+	0.393342i	0.956946	−	0.290265i	$-0.0937435\pi$
$7$	0.600840	+	1.04068i	0.227096	+	0.393342i	−0.729850	+	0.683607i	$0.760410\pi$
$8$	−1.53807	−	2.66402i	−0.543790	−	0.941873i
$9$	−2.48036	−	1.68755i	−0.826786	−	0.562516i
$10$	−1.43262	−	3.93610i	−0.453035	−	1.24470i
$11$			3.37386i			1.01726i	0.860986	+	0.508628i	$0.169847\pi$
$11$			3.37386i			1.01726i	−0.860986	+	0.508628i	$0.830153\pi$
$12$	0.921107	+	0.471658i	0.265901	+	0.136156i
$13$	1.06414	+	2.92371i	0.295141	+	0.810892i	0.995294	+	0.0968998i	$0.0308926\pi$
$13$	1.06414	+	2.92371i	0.295141	+	0.810892i	−0.700154	+	0.713992i	$0.746885\pi$
$14$	−1.33731	−	0.486740i	−0.357410	−	0.130087i
$15$	4.88511	+	3.69659i	1.26133	+	0.954455i
$16$	2.30046	+	0.837300i	0.575116	+	0.209325i
$17$	−1.91063	+	5.24942i	−0.463396	+	1.27317i	0.459519	+	0.888168i	$0.348022\pi$
$17$	−1.91063	+	5.24942i	−0.463396	+	1.27317i	−0.922916	+	0.385003i	$0.874201\pi$
$18$	3.53486	−	0.357190i	0.833174	−	0.0841905i
$19$	3.51512	−	2.57759i	0.806423	−	0.591339i
$19$	3.51512	−	2.57759i	0.806423	−	0.591339i
$20$	−1.83007	−	1.05659i	−0.409216	−	0.236261i
$21$	2.02896	−	0.464135i	0.442755	−	0.101283i
$22$	−2.56833	−	3.06082i	−0.547570	−	0.652569i
$23$	2.71688	+	0.479060i	0.566509	+	0.0998909i	0.449565	−	0.893248i	$-0.351579\pi$
$23$	2.71688	+	0.479060i	0.566509	+	0.0998909i	0.116944	+	0.993138i	$0.462690\pi$
$24$	−5.19387	+	1.18813i	−1.06020	+	0.242525i
$25$	−5.75276	−	4.82714i	−1.15055	−	0.965428i
$26$	−3.19107	−	1.84236i	−0.625820	−	0.361317i
$27$	−4.05778	+	3.24567i	−0.780921	+	0.624630i
$28$	−0.674665	+	0.245558i	−0.127500	+	0.0464061i
$29$	1.75252	−	9.93902i	0.325434	−	1.84563i	−0.181170	−	0.983452i	$-0.557988\pi$
$29$	1.75252	−	9.93902i	0.325434	−	1.84563i	0.506604	−	0.862179i	$-0.330900\pi$
$30$	−7.24586	+	0.365160i	−1.32291	+	0.0666687i
$31$		−	0.427425i		−	0.0767678i	−0.999263	−	0.0383839i	$-0.987779\pi$
$31$		−	0.427425i		−	0.0767678i	0.999263	−	0.0383839i	$-0.0122210\pi$
$32$	3.05685	−	1.11260i	0.540380	−	0.196682i
$33$	5.58491	+	1.71974i	0.972209	+	0.299369i
$34$	−2.26273	−	6.21681i	−0.388056	−	1.06617i
$35$	−4.18565	+	0.738044i	−0.707505	+	0.124752i
$36$	1.25027	−	1.28434i	0.208378	−	0.214056i
$37$		−	0.0841209i		−	0.0138294i	−0.999976	−	0.00691470i	$-0.997799\pi$
$37$		−	0.0841209i		−	0.0138294i	0.999976	−	0.00691470i	$-0.00220103\pi$
$38$	−1.22679	+	5.01429i	−0.199012	+	0.813425i
$39$	5.38219	−	0.271239i	0.861840	−	0.0434330i
$40$	10.7147	−	1.88930i	1.69415	−	0.298724i
$41$	−1.55749	+	1.30689i	−0.243238	+	0.204101i	−0.756254	−	0.654278i	$-0.772973\pi$
$41$	−1.55749	+	1.30689i	−0.243238	+	0.204101i	0.513016	+	0.858379i	$0.328528\pi$
$42$	−1.48738	+	1.96561i	−0.229508	+	0.303299i
$43$	−0.0600559	−	0.340594i	−0.00915844	−	0.0519401i	0.979886	−	0.199558i	$-0.0639506\pi$
$43$	−0.0600559	−	0.340594i	−0.00915844	−	0.0519401i	−0.989044	+	0.147618i	$0.952839\pi$
$44$	−1.98514	−	0.350034i	−0.299272	−	0.0527697i
$45$	8.60921	−	6.20232i	1.28339	−	0.924587i
$46$	−2.82948	+	1.63360i	−0.417184	+	0.240861i
$47$	7.15417	+	1.26147i	1.04354	+	0.184005i	0.669044	−	0.743223i	$-0.266704\pi$
$47$	7.15417	+	1.26147i	1.04354	+	0.184005i	0.374498	+	0.927228i	$0.377815\pi$
$48$	2.55863	−	3.38127i	0.369306	−	0.488045i
$49$	2.77798	−	4.81161i	0.396855	−	0.687373i
$50$	8.89363			1.25775
$51$	7.71572	+	5.83852i	1.08042	+	0.817557i
$52$	−1.83069	+	0.322799i	−0.253870	+	0.0447642i
$53$	−4.91060	−	4.12048i	−0.674523	−	0.565992i	0.239878	−	0.970803i	$-0.422893\pi$
$53$	−4.91060	−	4.12048i	−0.674523	−	0.565992i	−0.914400	+	0.404812i	$0.867337\pi$
$54$	1.21053	−	6.03349i	0.164733	−	0.821054i
$55$	−11.2134	−	4.08133i	−1.51201	−	0.550327i
$56$	1.84827	−	3.20130i	0.246985	−	0.427791i
$57$	−2.47506	−	7.13261i	−0.327830	−	0.944737i
$58$	5.97611	+	10.3509i	0.784702	+	1.35914i
$59$	0.479154	+	2.71742i	0.0623805	+	0.353777i	0.999982	+	0.00606461i	$0.00193044\pi$
$59$	0.479154	+	2.71742i	0.0623805	+	0.353777i	−0.937601	+	0.347713i	$0.886958\pi$
$60$	−2.68186	+	2.49083i	−0.346227	+	0.321565i
$61$	4.68956	−	1.70686i	0.600437	−	0.218541i	−0.0238768	−	0.999715i	$-0.507601\pi$
$61$	4.68956	−	1.70686i	0.600437	−	0.218541i	0.624314	+	0.781174i	$0.285379\pi$
$62$	0.325375	+	0.387767i	0.0413227	+	0.0492464i
$63$	0.265907	−	3.59522i	0.0335011	−	0.452955i
$64$	−4.37436	+	7.57662i	−0.546795	+	0.947077i
$65$	−11.0045			−1.36495
$66$	−6.37587	+	2.69131i	−0.784815	+	0.331277i
$67$	−4.40746	+	5.25261i	−0.538457	+	0.641708i	−0.964841	−	0.262834i	$-0.915343\pi$
$67$	−4.40746	+	5.25261i	−0.538457	+	0.641708i	0.426384	+	0.904542i	$0.359787\pi$
$68$	−2.89048	−	1.66882i	−0.350522	−	0.202374i
$69$	2.17788	−	4.25320i	0.262186	−	0.512025i
$70$	3.23546	−	3.85587i	0.386711	−	0.460865i
$71$	10.6625	−	8.94693i	1.26541	−	1.06181i	0.270327	−	0.962769i	$-0.412868\pi$
$71$	10.6625	−	8.94693i	1.26541	−	1.06181i	0.995084	−	0.0990373i	$-0.0315763\pi$
$72$	−0.680687	+	9.20329i	−0.0802197	+	1.08462i
$73$	2.30724	+	13.0850i	0.270042	+	1.53148i	0.754283	+	0.656549i	$0.227985\pi$
$73$	2.30724	+	13.0850i	0.270042	+	1.53148i	−0.484241	+	0.874934i	$0.660904\pi$
$74$	0.0640366	+	0.0763159i	0.00744410	+	0.00887154i
$75$	−10.9229	+	7.06231i	−1.26127	+	0.815485i
$76$	1.15194	+	2.33568i	0.132136	+	0.267921i
$77$	−3.51112	+	2.02715i	−0.400130	+	0.231015i
$78$	−4.67633	+	4.34323i	−0.529490	+	0.491774i
$79$	−5.23326	+	14.3783i	−0.588788	+	1.61768i	0.183935	+	0.982938i	$0.441117\pi$
$79$	−5.23326	+	14.3783i	−0.588788	+	1.61768i	−0.772723	+	0.634744i	$0.781106\pi$
$80$	−5.56570	+	6.63295i	−0.622265	+	0.741586i
$81$	3.30437	+	8.37145i	0.367152	+	0.930161i
$82$	0.418116	−	2.37126i	0.0461732	−	0.261861i
$83$	9.41085	−	5.43336i	1.03298	−	0.596389i	0.115140	−	0.993349i	$-0.463268\pi$
$83$	9.41085	−	5.43336i	1.03298	−	0.596389i	0.917836	+	0.396961i	$0.129935\pi$
$84$	0.0625900	+	1.24197i	0.00682913	+	0.135510i
$85$	−15.1357	−	12.7004i	−1.64170	−	1.37755i
$86$	0.313759	+	0.263275i	0.0338335	+	0.0283897i
$87$	−15.5592	−	7.96720i	−1.66813	−	0.854174i
$88$	8.98802	−	5.18924i	0.958126	−	0.553174i
$89$	−0.172118	+	0.976130i	−0.0182445	+	0.103470i	−0.992570	−	0.121674i	$-0.961174\pi$
$89$	−0.172118	+	0.976130i	−0.0182445	+	0.103470i	0.974326	+	0.225143i	$0.0722850\pi$
$90$	−3.08893	+	12.1806i	−0.325602	+	1.28394i
$91$	−2.40328	+	2.86412i	−0.251933	+	0.300242i
$92$	−0.563748	+	1.54888i	−0.0587748	+	0.161482i
$93$	−0.707538	−	0.217870i	−0.0733682	−	0.0225920i
$94$	−7.45066	+	4.30164i	−0.768477	+	0.443680i
$95$	4.31467	+	14.8009i	0.442676	+	1.51854i
$96$	−0.283590	−	5.62728i	−0.0289438	−	0.574332i
$97$	−2.27491	−	2.71113i	−0.230982	−	0.275274i	0.638087	−	0.769964i	$-0.279726\pi$
$97$	−2.27491	−	2.71113i	−0.230982	−	0.275274i	−0.869069	+	0.494690i	$0.835281\pi$
$98$	1.14258	+	6.47989i	0.115418	+	0.654568i
$99$	5.69355	−	8.36838i	0.572223	−	0.841054i
$100$	3.43708	−	2.88405i	0.343708	−	0.288405i
$101$	12.3020	−	14.6609i	1.22409	−	1.45882i	0.377979	−	0.925814i	$-0.376619\pi$
$101$	12.3020	−	14.6609i	1.22409	−	1.45882i	0.846114	−	0.533002i	$-0.178936\pi$
$102$	−11.4444	+	0.576746i	−1.13316	+	0.0571064i
$103$	−2.33357	−	1.34729i	−0.229934	−	0.132752i	0.380608	−	0.924737i	$-0.375715\pi$
$103$	−2.33357	−	1.34729i	−0.229934	−	0.132752i	−0.610542	+	0.791984i	$0.709048\pi$
$104$	6.15209	−	7.33178i	0.603262	−	0.718940i
$105$	−0.911816	+	7.30492i	−0.0889841	+	0.712887i
$106$	7.59167			0.737368
$107$	−4.21568	+	7.30177i	−0.407545	+	0.705888i	−0.994614	−	0.103648i	$-0.966948\pi$
$107$	−4.21568	+	7.30177i	−0.407545	+	0.705888i	0.587069	+	0.809537i	$0.300282\pi$
$108$	−1.48873	−	2.72429i	−0.143253	−	0.262145i
$109$	5.35264	+	6.37903i	0.512690	+	0.611000i	0.958836	−	0.283960i	$-0.0916483\pi$
$109$	5.35264	+	6.37903i	0.512690	+	0.611000i	−0.446146	+	0.894960i	$0.647204\pi$
$110$	13.2798	−	4.83346i	1.26618	−	0.460853i
$111$	−0.139250	−	0.0428786i	−0.0132170	−	0.00406986i
$112$	0.510844	+	2.89714i	0.0482702	+	0.273754i
$113$	3.10179	+	5.37245i	0.291791	+	0.505398i	0.974233	−	0.225542i	$-0.0724154\pi$
$113$	3.10179	+	5.37245i	0.291791	+	0.505398i	−0.682442	+	0.730940i	$0.739082\pi$
$114$	7.67507	+	4.58668i	0.718836	+	0.429582i
$115$	−4.87880	+	8.45033i	−0.454950	+	0.787997i
$116$	5.66620	+	2.06233i	0.526093	+	0.191482i
$117$	2.29444	−	9.04765i	0.212121	−	0.836456i
$118$	−2.50331	−	2.10053i	−0.230449	−	0.193369i
$119$	−6.61097	+	1.16569i	−0.606027	+	0.106859i
$120$	2.33413	−	18.6996i	0.213076	−	1.70704i
$121$	−0.382923			−0.0348112
$122$	−2.95511	+	5.11839i	−0.267543	+	0.463398i
$123$	1.36946	+	3.24434i	0.123480	+	0.292532i
$124$	0.251492	+	0.0443449i	0.0225847	+	0.00398229i
$125$	7.68732	−	4.43828i	0.687575	−	0.396971i
$126$	2.49560	+	3.46406i	0.222326	+	0.308603i
$127$	−4.02385	−	0.709513i	−0.357059	−	0.0629591i	−0.00775837	−	0.999970i	$-0.502470\pi$
$127$	−4.02385	−	0.709513i	−0.357059	−	0.0629591i	−0.349300	+	0.937011i	$0.613581\pi$
$128$	−0.669401	−	3.79636i	−0.0591672	−	0.335554i
$129$	−0.594414	−	0.0741961i	−0.0523352	−	0.00653260i
$130$	9.98350	−	8.37715i	0.875611	−	0.734725i
$131$	−13.7346	+	2.42178i	−1.20000	+	0.211592i	−0.737697	−	0.675132i	$-0.764087\pi$
$131$	−13.7346	+	2.42178i	−1.20000	+	0.211592i	−0.462300	+	0.886724i	$0.652976\pi$
$132$	−1.59131	+	3.10768i	−0.138506	+	0.270489i
$133$	4.79448	+	2.10941i	0.415734	+	0.182909i
$134$		−	8.12040i		−	0.701496i
$135$	−5.87866	−	17.4127i	−0.505955	−	1.49865i
$136$	16.9232	−	2.98402i	1.45115	−	0.255878i
$137$	0.492495	+	1.35312i	0.0420767	+	0.115605i	0.958952	−	0.283570i	$-0.0915189\pi$
$137$	0.492495	+	1.35312i	0.0420767	+	0.115605i	−0.916875	+	0.399175i	$0.869297\pi$
$138$	1.26192	+	5.51647i	0.107422	+	0.469593i
$139$	−5.31290	+	1.93374i	−0.450634	+	0.164018i	−0.557360	−	0.830271i	$-0.688186\pi$
$139$	−5.31290	+	1.93374i	−0.450634	+	0.164018i	0.106725	+	0.994289i	$0.465963\pi$
$140$		−	2.53937i		−	0.214616i
$141$	5.73484	−	11.1996i	0.482961	−	0.943180i
$142$	−2.86242	+	16.2336i	−0.240209	+	1.36229i
$143$	−9.86419	+	3.59027i	−0.824885	+	0.300234i
$144$	−4.29299	−	5.95894i	−0.357749	−	0.496579i
$145$	30.9134	+	17.8478i	2.56722	+	1.48218i
$146$	−12.0540	−	10.1145i	−0.997600	−	0.837086i
$147$	−6.54888	−	7.05113i	−0.540143	−	0.581568i
$148$	0.0494959	+	0.00872746i	0.00406854	+	0.000717393i
$149$	3.17185	+	3.78007i	0.259848	+	0.309675i	0.880157	−	0.474682i	$-0.157437\pi$
$149$	3.17185	+	3.78007i	0.259848	+	0.309675i	−0.620309	+	0.784358i	$0.712993\pi$
$150$	4.53331	−	14.7221i	0.370143	−	1.20205i
$151$	2.49334	+	1.43953i	0.202905	+	0.117147i	0.598010	−	0.801489i	$-0.295958\pi$
$151$	2.49334	+	1.43953i	0.202905	+	0.117147i	−0.395105	+	0.918636i	$0.629292\pi$
$152$	−12.2732	−	5.39982i	−0.995491	−	0.437983i
$153$	13.5977	−	9.79616i	1.09931	−	0.791972i
$154$	1.64219	−	4.51188i	0.132332	−	0.363578i
$155$	1.42059	+	0.517053i	0.114105	+	0.0415307i
$156$	−0.398802	+	3.19496i	−0.0319297	+	0.255802i
$157$	4.30069	+	1.56532i	0.343232	+	0.124926i	0.507884	−	0.861425i	$-0.330428\pi$
$157$	4.30069	+	1.56532i	0.343232	+	0.124926i	−0.164652	+	0.986352i	$0.552650\pi$
$158$	−6.19768	−	17.0280i	−0.493061	−	1.35467i
$159$	−9.32389	+	6.02844i	−0.739433	+	0.478086i
$160$			11.5057i			0.909603i
$161$	1.13386	+	3.11526i	0.0893608	+	0.245517i
$162$	−9.37049	−	5.07928i	−0.736215	−	0.399066i
$163$	−7.45014	−	12.9040i	−0.583540	−	1.01072i	−0.995056	−	0.0993184i	$-0.968334\pi$
$163$	−7.45014	−	12.9040i	−0.583540	−	1.01072i	0.411516	−	0.911403i	$-0.365000\pi$
$164$	−0.607371	−	1.05200i	−0.0474277	−	0.0821471i
$165$	−12.4718	+	16.4817i	−0.970926	+	1.28310i
$166$	−4.40156	+	12.0932i	−0.341627	+	0.938614i
$167$	1.69841	−	9.63214i	0.131427	−	0.745357i	−0.845855	−	0.533413i	$-0.820909\pi$
$167$	1.69841	−	9.63214i	0.131427	−	0.745357i	0.977282	−	0.211944i	$-0.0679796\pi$
$168$	−4.35715	−	4.69131i	−0.336161	−	0.361943i
$169$	2.54288	−	2.13373i	0.195606	−	0.164133i
$170$	23.3994			1.79465
$171$	−13.0686	+	0.461421i	−0.999377	+	0.0352858i
$172$	0.206633			0.0157556
$173$	−10.3368	+	8.67358i	−0.785890	+	0.659440i	−0.944724	−	0.327865i	$-0.893671\pi$
$173$	−10.3368	+	8.67358i	−0.785890	+	0.659440i	0.158835	+	0.987305i	$0.449226\pi$
$174$	20.1806	−	4.61642i	1.52989	−	0.349970i
$175$	1.56704	−	8.88715i	0.118457	−	0.671805i
$176$	−2.82493	+	7.76144i	−0.212937	+	0.585040i
$177$	4.74251	+	0.591970i	0.356469	+	0.0444952i
$178$	−0.586925	−	1.01658i	−0.0439919	−	0.0761962i
$179$	5.61287	+	9.72177i	0.419525	+	0.726639i	0.995892	−	0.0905521i	$-0.0288632\pi$
$179$	5.61287	+	9.72177i	0.419525	+	0.726639i	−0.576366	+	0.817191i	$0.695530\pi$
$180$	2.75618	+	5.70905i	0.205434	+	0.425528i
$181$	−8.71982	−	23.9575i	−0.648139	−	1.78075i	−0.624497	−	0.781027i	$-0.714696\pi$
$181$	−8.71982	−	23.9575i	−0.648139	−	1.78075i	−0.0236417	−	0.999720i	$-0.507526\pi$
$182$		−	4.42786i		−	0.328215i
$183$	−0.435060	−	8.63289i	−0.0321606	−	0.638162i
$184$	−2.90254	−	7.97466i	−0.213978	−	0.587899i
$185$	0.279585	+	0.101760i	0.0205555	+	0.00748158i
$186$	0.807741	−	0.340954i	0.0592265	−	0.0250000i
$187$	−17.7108	−	6.44620i	−1.29514	−	0.471393i
$188$	−1.48447	+	4.07856i	−0.108266	+	0.297460i
$189$	−5.81580	−	2.27274i	−0.423037	−	0.165318i
$190$	−15.1815	−	10.1431i	−1.10138	−	0.735860i
$191$	7.17902	+	4.14481i	0.519456	+	0.299908i	0.736712	−	0.676207i	$-0.236377\pi$
$191$	7.17902	+	4.14481i	0.519456	+	0.299908i	−0.217256	+	0.976115i	$0.569711\pi$
$192$	10.3122	+	11.1031i	0.744221	+	0.801297i
$193$	−9.42655	−	11.2341i	−0.678538	−	0.808650i	0.311381	−	0.950285i	$-0.399209\pi$
$193$	−9.42655	−	11.2341i	−0.678538	−	0.808650i	−0.989919	+	0.141635i	$0.954764\pi$
$194$	4.12767	+	0.727820i	0.296349	+	0.0522544i
$195$	−5.60930	+	18.2164i	−0.401690	+	1.30450i
$196$	2.54289	+	2.13374i	0.181635	+	0.152410i
$197$	−4.15947	−	2.40147i	−0.296350	−	0.171098i	0.344452	−	0.938804i	$-0.388065\pi$
$197$	−4.15947	−	2.40147i	−0.296350	−	0.171098i	−0.640802	+	0.767706i	$0.721398\pi$
$198$	1.20511	+	11.9261i	0.0856434	+	0.847552i
$199$	7.95338	−	2.89479i	0.563800	−	0.205206i	−0.0443673	−	0.999015i	$-0.514127\pi$
$199$	7.95338	−	2.89479i	0.563800	−	0.205206i	0.608167	+	0.793809i	$0.291905\pi$
$200$	−4.01143	+	22.7499i	−0.283651	+	1.60866i
$201$	6.44830	+	9.97327i	0.454828	+	0.703460i
$202$			22.6654i			1.59473i
$203$	11.3964	−	4.14794i	0.799869	−	0.291128i
$204$	−4.23582	+	3.93411i	−0.296567	+	0.275443i
$205$	−2.45949	−	6.75740i	−0.171778	−	0.471957i
$206$	3.14267	−	0.554138i	0.218960	−	0.0386086i
$207$	−5.93041	−	5.77311i	−0.412192	−	0.401259i
$208$			7.61690i			0.528137i
$209$	8.69642	+	11.8595i	0.601544	+	0.820339i
$210$	−4.73362	−	7.32125i	−0.326650	−	0.505214i
$211$	−9.03433	+	1.59300i	−0.621949	+	0.109666i	−0.475738	−	0.879587i	$-0.657819\pi$
$211$	−9.03433	+	1.59300i	−0.621949	+	0.109666i	−0.146211	+	0.989253i	$0.546708\pi$
$212$	2.93392	−	2.46185i	0.201502	−	0.169081i
$213$	−9.37533	−	22.2107i	−0.642387	−	1.52185i
$214$	−1.73390	−	9.83344i	−0.118527	−	0.672200i
$215$	1.20465	+	0.212412i	0.0821564	+	0.0144864i
$216$	14.8877	+	5.81793i	1.01298	+	0.395860i
$217$	0.444815	−	0.256814i	0.0301960	−	0.0174337i
$218$	−9.71200	−	1.71249i	−0.657779	−	0.115984i
$219$	22.8363	+	2.85048i	1.54313	+	0.192617i
$220$	3.56479	−	6.17440i	0.240338	−	0.416278i
$221$	−17.3810			−1.16917
$222$	0.158970	−	0.0671028i	0.0106694	−	0.00450364i
$223$	26.8017	−	4.72586i	1.79477	−	0.316467i	0.825862	−	0.563873i	$-0.190689\pi$
$223$	26.8017	−	4.72586i	1.79477	−	0.316467i	0.968912	+	0.247406i	$0.0795781\pi$
$224$	2.99455	+	2.51272i	0.200082	+	0.167888i
$225$	6.12289	+	21.6811i	0.408192	+	1.44541i
$226$	−6.90374	−	2.51275i	−0.459230	−	0.167146i
$227$	6.43268	−	11.1417i	0.426952	−	0.739502i	−0.569649	−	0.821888i	$-0.692921\pi$
$227$	6.43268	−	11.1417i	0.426952	−	0.739502i	0.996600	+	0.0823860i	$0.0262541\pi$
$228$	4.45354	−	0.716301i	0.294943	−	0.0474382i
$229$	−8.07409	−	13.9847i	−0.533551	−	0.924138i	−0.999232	−	0.0391849i	$-0.987524\pi$
$229$	−8.07409	−	13.9847i	−0.533551	−	0.924138i	0.465681	−	0.884953i	$-0.345809\pi$
$230$	−2.00664	−	11.3802i	−0.132314	−	0.750390i
$231$	1.56593	+	6.84542i	0.103030	+	0.450396i
$232$	−29.1732	+	10.6182i	−1.91532	+	0.697118i
$233$	−16.8874	−	20.1256i	−1.10633	−	1.31847i	−0.943335	−	0.331843i	$-0.892330\pi$
$233$	−16.8874	−	20.1256i	−1.10633	−	1.31847i	−0.162993	−	0.986627i	$-0.552115\pi$
$234$	4.80592	+	9.95481i	0.314173	+	0.650766i
$235$	−12.8470	+	22.2516i	−0.838044	+	1.45154i
$236$	−1.64861			−0.107315
$237$	21.1335	+	15.9919i	1.37277	+	1.03878i
$238$	5.11020	−	6.09010i	0.331245	−	0.394762i
$239$	−1.15583	−	0.667321i	−0.0747646	−	0.0431654i	0.462152	−	0.886801i	$-0.347078\pi$
$239$	−1.15583	−	0.667321i	−0.0747646	−	0.0431654i	−0.536916	+	0.843636i	$0.680411\pi$
$240$	8.14286	+	12.5942i	0.525619	+	0.812950i
$241$	12.7591	−	15.2057i	0.821885	−	0.979484i	−0.178105	−	0.984011i	$-0.556997\pi$
$241$	12.7591	−	15.2057i	0.821885	−	0.979484i	0.999990	+	0.00452763i	$0.00144119\pi$
$242$	0.347394	−	0.291498i	0.0223313	−	0.0187382i
$243$	15.5420	−	1.20274i	0.997019	−	0.0771556i
$244$	0.517762	+	2.93637i	0.0331463	+	0.187982i
$245$	12.6314	+	15.0535i	0.806989	+	0.961732i
$246$	−3.71213	−	1.90082i	−0.236677	−	0.121192i
$247$	11.2767	+	7.53426i	0.717520	+	0.479394i
$248$	−1.13867	+	0.657410i	−0.0723055	+	0.0417456i
$249$	−4.19715	−	18.3478i	−0.265984	−	1.16274i
$250$	−3.59544	+	9.87840i	−0.227396	+	0.624765i
$251$	0.253817	−	0.302487i	0.0160208	−	0.0190928i	−0.757975	−	0.652284i	$-0.773811\pi$
$251$	0.253817	−	0.302487i	0.0160208	−	0.0190928i	0.773995	+	0.633191i	$0.218255\pi$
$252$	2.08780	+	0.529457i	0.131519	+	0.0333527i
$253$	−1.61628	+	9.16638i	−0.101615	+	0.576286i
$254$	4.19061	−	2.41945i	0.262942	−	0.151810i
$255$	−28.7386	+	18.5812i	−1.79968	+	1.16360i
$256$	−9.90658	−	8.31261i	−0.619161	−	0.519538i
$257$	8.20729	+	6.88674i	0.511957	+	0.429583i	0.861817	−	0.507219i	$-0.169327\pi$
$257$	8.20729	+	6.88674i	0.511957	+	0.429583i	−0.349860	+	0.936802i	$0.613771\pi$
$258$	0.595743	−	0.385183i	0.0370894	−	0.0239804i
$259$	0.0875434	−	0.0505432i	0.00543968	−	0.00314060i
$260$	1.14171	−	6.47496i	0.0708059	−	0.401560i
$261$	−21.1195	+	21.6949i	−1.30726	+	1.34288i
$262$	10.6167	−	12.6525i	0.655900	−	0.781671i
$263$	−6.16418	+	16.9359i	−0.380100	+	1.04431i	0.591214	+	0.806514i	$0.298649\pi$
$263$	−6.16418	+	16.9359i	−0.380100	+	1.04431i	−0.971314	+	0.237801i	$0.923574\pi$
$264$	−4.00857	−	17.5234i	−0.246711	−	1.07849i
$265$	19.6352	−	11.3364i	1.20618	−	0.696387i
$266$	−5.95540	+	1.73608i	−0.365149	+	0.106446i
$267$	1.52810	+	0.782474i	0.0935184	+	0.0478866i
$268$	−2.63331	−	3.13826i	−0.160855	−	0.191699i
$269$	−3.20257	−	18.1627i	−0.195264	−	1.10740i	−0.912042	−	0.410097i	$-0.865495\pi$
$269$	−3.20257	−	18.1627i	−0.195264	−	1.10740i	0.716778	−	0.697302i	$-0.245616\pi$
$270$	18.5886	+	11.3220i	1.13126	+	0.689035i
$271$	15.3895	−	12.9133i	0.934845	−	0.784428i	−0.0418362	−	0.999124i	$-0.513321\pi$
$271$	15.3895	−	12.9133i	0.934845	−	0.784428i	0.976681	+	0.214697i	$0.0688763\pi$
$272$	−8.79067	+	10.4763i	−0.533013	+	0.635220i
$273$	3.51611	+	5.43819i	0.212804	+	0.329134i
$274$	−1.47685	−	0.852662i	−0.0892200	−	0.0515112i
$275$	16.2861	−	19.4090i	0.982088	−	1.17041i
$276$	2.27659	+	1.72271i	0.137034	+	0.103695i
$277$	−14.4634			−0.869021			−0.434511	−	0.900667i	$-0.643079\pi$
$277$	−14.4634			−0.869021			−0.434511	+	0.900667i	$0.643079\pi$
$278$	3.34790	−	5.79873i	0.200794	−	0.347785i
$279$	−0.721300	+	1.06017i	−0.0431831	+	0.0634706i
$280$	8.40400	+	10.0155i	0.502235	+	0.598540i
$281$	−22.0627	+	8.03017i	−1.31615	+	0.479040i	−0.902223	−	0.431270i	$-0.858066\pi$
$281$	−22.0627	+	8.03017i	−1.31615	+	0.479040i	−0.413928	+	0.910310i	$0.635844\pi$
$282$	3.32292	+	14.5261i	0.197877	+	0.865017i
$283$	2.74950	+	15.5932i	0.163441	+	0.926918i	0.950658	+	0.310242i	$0.100410\pi$
$283$	2.74950	+	15.5932i	0.163441	+	0.926918i	−0.787217	+	0.616676i	$0.788479\pi$
$284$	4.15806	+	7.20196i	0.246735	+	0.427358i
$285$	26.7000	+	0.402132i	1.58157	+	0.0238202i
$286$	6.21588	−	10.7662i	0.367553	−	0.636620i
$287$	−2.29586	−	0.835623i	−0.135520	−	0.0493253i
$288$	−9.45967	−	2.39893i	−0.557416	−	0.141358i
$289$	−10.8831	−	9.13200i	−0.640182	−	0.537177i
$290$	−41.6317	+	7.34078i	−2.44470	+	0.431066i
$291$	−5.64745	+	2.38384i	−0.331059	+	0.139743i
$292$	−7.93845			−0.464563
$293$	−5.23556	+	9.06825i	−0.305865	+	0.529773i	−0.977453	−	0.211151i	$-0.932279\pi$
$293$	−5.23556	+	9.06825i	−0.305865	+	0.529773i	0.671589	+	0.740924i	$0.265612\pi$
$294$	11.3089	+	1.41160i	0.659547	+	0.0823261i
$295$	−9.61124	−	1.69472i	−0.559588	−	0.0986705i
$296$	−0.224100	+	0.129384i	−0.0130255	+	0.00752030i
$297$	−10.9504	−	13.6904i	−0.635409	−	0.794397i
$298$	−5.75511	−	1.01478i	−0.333385	−	0.0587847i
$299$	1.49052	+	8.45318i	0.0861992	+	0.488860i
$300$	−3.02215	−	7.15964i	−0.174484	−	0.413362i
$301$	0.318367	−	0.267142i	0.0183504	−	0.0153978i
$302$	−3.35783	+	0.592075i	−0.193221	+	0.0340701i
$303$	−17.9983	−	27.8371i	−1.03398	−	1.59920i
$304$	10.2446	−	2.98644i	0.587568	−	0.171284i
$305$			17.6510i			1.01069i
$306$	−4.87877	+	19.2384i	−0.278901	+	1.09979i
$307$	−32.0322	+	5.64814i	−1.82817	+	0.322357i	−0.978704	−	0.205279i	$-0.934190\pi$
$307$	−32.0322	+	5.64814i	−1.82817	+	0.322357i	−0.849471	+	0.527635i	$0.823079\pi$
$308$	−0.828477	−	2.27622i	−0.0472069	−	0.129700i
$309$	−3.41972	+	3.17613i	−0.194541	+	0.180684i
$310$	−1.68239	+	0.612339i	−0.0955531	+	0.0347785i
$311$			4.22301i			0.239465i	0.992806	+	0.119733i	$0.0382037\pi$
$311$			4.22301i			0.239465i	−0.992806	+	0.119733i	$0.961796\pi$
$312$	−9.00077	−	13.9211i	−0.509568	−	0.788125i
$313$	−4.93706	+	27.9995i	−0.279059	+	1.58262i	0.446706	+	0.894681i	$0.352597\pi$
$313$	−4.93706	+	27.9995i	−0.279059	+	1.58262i	−0.725765	+	0.687942i	$0.758514\pi$
$314$	−5.09325	+	1.85379i	−0.287429	+	0.104615i
$315$	11.6274	+	5.23288i	0.655130	+	0.294839i
$316$	−7.91708	−	4.57093i	−0.445371	−	0.257135i
$317$	2.33530	+	1.95955i	0.131164	+	0.110059i	0.706010	−	0.708202i	$-0.250494\pi$
$317$	2.33530	+	1.95955i	0.131164	+	0.110059i	−0.574846	+	0.818262i	$0.694938\pi$
$318$	3.86967	−	12.5669i	0.217000	−	0.704714i
$319$	33.5329	+	5.91275i	1.87748	+	0.331050i
$320$	−19.8900	−	23.7040i	−1.11189	−	1.32510i
$321$	9.93813	+	10.7003i	0.554692	+	0.597233i
$322$	−3.40013	−	1.96307i	−0.189482	−	0.109397i
$323$	6.81474	+	23.3771i	0.379182	+	1.30074i
$324$	−5.26850	+	1.07573i	−0.292694	+	0.0597625i
$325$	7.99140	−	21.9562i	0.443283	−	1.21791i
$326$	16.5820	+	6.03536i	0.918392	+	0.334267i
$327$	13.2879	−	5.60893i	0.734822	−	0.310175i
$328$	5.87709	+	2.13909i	0.324508	+	0.118111i
$329$	2.98571	+	8.20318i	0.164608	+	0.452256i
$330$	−1.23200	−	24.4465i	−0.0678192	−	1.34574i
$331$		−	15.7759i		−	0.867122i	−0.901124	−	0.433561i	$-0.857257\pi$
$331$		−	15.7759i		−	0.867122i	0.901124	−	0.433561i	$-0.142743\pi$
$332$	2.22057	+	6.10095i	0.121869	+	0.334833i
$333$	−0.141958	+	0.208650i	−0.00777926	+	0.0114340i
$334$	5.79159	+	10.0313i	0.316902	+	0.548890i
$335$	−12.1259	−	21.0027i	−0.662509	−	1.14750i
$336$	5.05617	+	0.631122i	0.275836	+	0.0344305i
$337$	2.31078	−	6.34880i	0.125876	−	0.345841i	−0.860707	−	0.509100i	$-0.829978\pi$
$337$	2.31078	−	6.34880i	0.125876	−	0.345841i	0.986583	+	0.163259i	$0.0522005\pi$
$338$	−0.682652	+	3.87151i	−0.0371314	+	0.210583i
$339$	10.4743	−	2.39606i	0.568888	−	0.130136i
$340$	9.04307	−	7.58804i	0.490429	−	0.411519i
$341$	1.44207			0.0780926
$342$	11.5047	−	10.3670i	0.622105	−	0.560582i
$343$	15.0882			0.814689
$344$	−0.814979	+	0.683848i	−0.0439407	+	0.0368706i
$345$	11.5014	+	12.3835i	0.619214	+	0.666703i
$346$	2.77497	−	15.7376i	0.149183	−	0.846059i
$347$	−0.0305956	+	0.0840608i	−0.00164246	+	0.00451262i	−0.940511	−	0.339763i	$-0.889653\pi$
$347$	−0.0305956	+	0.0840608i	−0.00164246	+	0.00451262i	0.938869	+	0.344275i	$0.111875\pi$
$348$	6.30208	−	8.32831i	0.337827	−	0.446444i
$349$	−6.30204	−	10.9154i	−0.337340	−	0.584290i	0.646591	−	0.762837i	$-0.276194\pi$
$349$	−6.30204	−	10.9154i	−0.337340	−	0.584290i	−0.983932	+	0.178546i	$0.942861\pi$
$350$	5.34364	+	9.25546i	0.285630	+	0.494725i
$351$	−13.8075	−	8.40993i	−0.736989	−	0.448889i
$352$	3.75377	+	10.3134i	0.200076	+	0.549706i
$353$		−	22.2462i		−	1.18405i	−0.805920	−	0.592024i	$-0.798329\pi$
$353$		−	22.2462i		−	1.18405i	0.805920	−	0.592024i	$-0.201671\pi$
$354$	−4.75311	+	3.07316i	−0.252625	+	0.163337i
$355$	16.8377	+	46.2611i	0.893650	+	2.45528i
$356$	−0.556488	−	0.202545i	−0.0294938	−	0.0107349i
$357$	−1.44015	+	11.5376i	−0.0762210	+	0.610637i
$358$	−12.4927	−	4.54698i	−0.660261	−	0.240315i
$359$	0.731181	−	2.00890i	0.0385902	−	0.106026i	−0.918901	−	0.394488i	$-0.870922\pi$
$359$	0.731181	−	2.00890i	0.0385902	−	0.106026i	0.957491	+	0.288463i	$0.0931441\pi$
$360$	−29.7647	−	13.3955i	−1.56874	−	0.706004i
$361$	5.71208	−	18.1210i	0.300636	−	0.953739i
$362$	26.1483	+	15.0967i	1.37432	+	0.793466i
$363$	−0.195186	+	0.633871i	−0.0102446	+	0.0332696i
$364$	−1.43588	−	1.71122i	−0.0752606	−	0.0896921i
$365$	−46.2804	−	8.16048i	−2.42243	−	0.427139i
$366$	6.96643	+	7.50071i	0.364141	+	0.392068i
$367$	19.8141	+	16.6260i	1.03429	+	0.867872i	0.991355	−	0.131206i	$-0.0418850\pi$
$367$	19.8141	+	16.6260i	1.03429	+	0.867872i	0.0429341	+	0.999078i	$0.486329\pi$
$368$	5.84897	+	3.37691i	0.304899	+	0.176033i
$369$	6.06856	−	0.613215i	0.315917	−	0.0319227i
$370$	−0.331108	+	0.120514i	−0.0172135	+	0.00626520i
$371$	1.33764	−	7.58613i	0.0694468	−	0.393852i
$372$	0.201598	−	0.393704i	0.0104524	−	0.0204126i
$373$			4.92510i			0.255012i	0.991838	+	0.127506i	$0.0406972\pi$
$373$			4.92510i			0.255012i	−0.991838	+	0.127506i	$0.959303\pi$
$374$	20.9746	−	7.63414i	1.08457	−	0.394752i
$375$	−3.42847	−	14.9875i	−0.177045	−	0.773951i
$376$	−7.64304	−	20.9991i	−0.394159	−	1.08294i
$377$	30.9238	−	5.45270i	1.59266	−	0.280828i
$378$	7.00630	−	2.36538i	0.360365	−	0.121662i
$379$		−	4.36686i		−	0.224311i	−0.993691	−	0.112155i	$-0.964225\pi$
$379$		−	4.36686i		−	0.224311i	0.993691	−	0.112155i	$-0.0357754\pi$
$380$	−9.15636	+	1.00313i	−0.469711	+	0.0514593i
$381$	−3.22555	+	6.29921i	−0.165250	+	0.322718i
$382$	−9.66813	+	1.70475i	−0.494665	+	0.0872227i
$383$	21.8328	−	18.3199i	1.11560	−	0.936101i	0.117227	−	0.993105i	$-0.462599\pi$
$383$	21.8328	−	18.3199i	1.11560	−	0.936101i	0.998374	+	0.0570044i	$0.0181549\pi$
$384$	−6.62551	−	0.827010i	−0.338107	−	0.0422032i
$385$	−2.49006	−	14.1218i	−0.126905	−	0.719714i
$386$	17.1038	+	3.01587i	0.870562	+	0.153504i
$387$	−0.425809	+	0.946143i	−0.0216451	+	0.0480952i
$388$	1.83122	−	1.05726i	0.0929662	−	0.0536741i
$389$	0.266820	+	0.0470475i	0.0135283	+	0.00238540i	0.180408	−	0.983592i	$-0.442258\pi$
$389$	0.266820	+	0.0470475i	0.0135283	+	0.00238540i	−0.166880	+	0.985977i	$0.553369\pi$
$390$	−8.77826	−	20.7962i	−0.444505	−	1.05306i
$391$	−7.70575	+	13.3467i	−0.389696	+	0.674974i
$392$	−17.0910			−0.863223
$393$	−2.99198	+	23.9700i	−0.150926	+	1.20913i
$394$	5.60165	−	0.987722i	0.282207	−	0.0497607i
$395$	−41.4570	−	34.7866i	−2.08593	−	1.75030i
$396$	4.33317	+	4.21823i	0.217750	+	0.211974i
$397$	−17.4513	−	6.35175i	−0.875855	−	0.318785i	−0.135319	−	0.990802i	$-0.543206\pi$
$397$	−17.4513	−	6.35175i	−0.875855	−	0.318785i	−0.740536	+	0.672017i	$0.765428\pi$
$398$	−5.01179	+	8.68067i	−0.251218	+	0.435123i
$399$	5.93568	−	6.86131i	0.297156	−	0.343495i
$400$	−9.19225	−	15.9214i	−0.459612	−	0.796072i
$401$	0.520392	+	2.95129i	0.0259871	+	0.147380i	0.995040	−	0.0994712i	$-0.0317151\pi$
$401$	0.520392	+	2.95129i	0.0259871	+	0.147380i	−0.969053	+	0.246852i	$0.920604\pi$
$402$	−13.4421	−	4.13918i	−0.670431	−	0.206443i
$403$	1.24967	−	0.454842i	0.0622504	−	0.0226573i
$404$	7.35002	+	8.75941i	0.365677	+	0.435797i
$405$	−31.8206	+	0.855522i	−1.58118	+	0.0425112i
$406$	−7.18137	+	12.4385i	−0.356406	+	0.617313i
$407$	0.283812			0.0140680
$408$	3.68661	−	29.5349i	0.182514	−	1.46219i
$409$	5.56405	−	6.63097i	0.275124	−	0.327881i	−0.610734	−	0.791836i	$-0.709126\pi$
$409$	5.56405	−	6.63097i	0.275124	−	0.327881i	0.885859	+	0.463955i	$0.153570\pi$
$410$	7.37532	+	4.25814i	0.364241	+	0.210295i
$411$	2.49092	−	0.125532i	0.122868	−	0.00619202i
$412$	1.03484	−	1.23327i	0.0509828	−	0.0607589i
$413$	−2.54008	+	2.13138i	−0.124989	+	0.104878i
$414$	9.77491	+	0.722965i	0.480411	+	0.0355318i
$415$	6.67409	+	37.8506i	0.327618	+	1.85801i
$416$	6.50587	+	7.75339i	0.318976	+	0.380141i
$417$	0.492889	+	9.78038i	0.0241369	+	0.478947i
$418$	−16.9175	−	4.13903i	−0.827462	−	0.202446i
$419$	7.45530	−	4.30432i	0.364215	−	0.210280i	−0.306713	−	0.951802i	$-0.599229\pi$
$419$	7.45530	−	4.30432i	0.364215	−	0.210280i	0.670928	+	0.741522i	$0.265896\pi$
$420$	−4.20354	−	1.29438i	−0.205112	−	0.0631593i
$421$	5.95550	−	16.3626i	0.290253	−	0.797465i	−0.705776	−	0.708435i	$-0.749401\pi$
$421$	5.95550	−	16.3626i	0.290253	−	0.797465i	0.996029	−	0.0890293i	$-0.0283765\pi$
$422$	6.98343	−	8.32252i	0.339948	−	0.405134i
$423$	−15.6161	−	15.2019i	−0.759281	−	0.739142i
$424$	−3.42419	+	19.4195i	−0.166293	+	0.943095i
$425$	36.3311	−	20.9757i	1.76232	−	1.01747i
$426$	25.4132	+	13.0130i	1.23127	+	0.630481i
$427$	4.59398	+	3.85481i	0.222318	+	0.186547i
$428$	−3.85891	−	3.23801i	−0.186528	−	0.156515i
$429$	0.915121	+	18.1587i	0.0441825	+	0.876712i
$430$	−1.25457	+	0.724329i	−0.0605009	+	0.0349302i
$431$	−0.502283	+	2.84859i	−0.0241941	+	0.137212i	−0.994512	−	0.104620i	$-0.966637\pi$
$431$	−0.502283	+	2.84859i	−0.0241941	+	0.137212i	0.970318	+	0.241832i	$0.0777483\pi$
$432$	−12.0524	+	4.06897i	−0.579870	+	0.195768i
$433$	1.11574	−	1.32969i	0.0536191	−	0.0639008i	−0.738568	−	0.674179i	$-0.764498\pi$
$433$	1.11574	−	1.32969i	0.0536191	−	0.0639008i	0.792187	+	0.610278i	$0.208942\pi$
$434$	−0.208045	+	0.571598i	−0.00998647	+	0.0274376i
$435$	45.3017	−	42.0749i	2.17205	−	2.01734i
$436$	−4.30868	+	2.48762i	−0.206349	+	0.119135i
$437$	10.7850	−	5.31906i	0.515916	−	0.254445i
$438$	−22.8874	+	14.7980i	−1.09360	+	0.707076i
$439$	16.8651	+	20.0990i	0.804927	+	0.959275i	0.999768	−	0.0215601i	$-0.00686333\pi$
$439$	16.8651	+	20.0990i	0.804927	+	0.959275i	−0.194840	+	0.980835i	$0.562419\pi$
$440$	6.37422	+	36.1500i	0.303879	+	1.72338i
$441$	−15.0102	+	7.24654i	−0.714772	+	0.345073i
$442$	15.7683	−	13.2312i	0.750021	−	0.629342i
$443$	−9.01043	+	10.7382i	−0.428098	+	0.510188i	−0.936373	−	0.351008i	$-0.885839\pi$
$443$	−9.01043	+	10.7382i	−0.428098	+	0.510188i	0.508274	+	0.861195i	$0.330284\pi$
$444$	0.0396763	−	0.0774844i	0.00188295	−	0.00367724i
$445$	−3.03606	−	1.75287i	−0.143923	−	0.0830940i
$446$	−20.7174	+	24.6900i	−0.980996	+	1.16911i
$447$	7.87411	−	3.32373i	0.372433	−	0.157207i
$448$	−10.5132			−0.496700
$449$	2.51755	−	4.36052i	0.118810	−	0.205786i	−0.800486	−	0.599351i	$-0.795425\pi$
$449$	2.51755	−	4.36052i	0.118810	−	0.205786i	0.919296	+	0.393566i	$0.128759\pi$
$450$	−22.0594	−	15.0084i	−1.03989	−	0.707504i
$451$	−4.40925	−	5.25474i	−0.207623	−	0.247436i
$452$	−3.48290	+	1.26767i	−0.163822	+	0.0596263i
$453$	3.65384	−	3.39358i	0.171672	−	0.159444i
$454$	2.64575	+	15.0048i	0.124171	+	0.704210i
$455$	−6.61197	−	11.4523i	−0.309974	−	0.536891i
$456$	−15.1946	+	17.5641i	−0.711551	+	0.822513i
$457$	−5.41934	+	9.38658i	−0.253506	+	0.439085i	−0.964489	−	0.264124i	$-0.914917\pi$
$457$	−5.41934	+	9.38658i	−0.253506	+	0.439085i	0.710983	+	0.703210i	$0.248250\pi$
$458$	17.9707	+	6.54082i	0.839718	+	0.305632i
$459$	−9.28496	−	27.5023i	−0.433385	−	1.28370i
$460$	−4.46591	−	3.74735i	−0.208224	−	0.174721i
$461$	−11.0137	+	1.94201i	−0.512958	+	0.0904483i	−0.424135	−	0.905599i	$-0.639422\pi$
$461$	−11.0137	+	1.94201i	−0.512958	+	0.0904483i	−0.0888231	+	0.996047i	$0.528311\pi$
$462$	−6.63167	−	5.01822i	−0.308533	−	0.233469i
$463$	−0.379160			−0.0176211			−0.00881053	−	0.999961i	$-0.502805\pi$
$463$	−0.379160			−0.0176211			−0.00881053	+	0.999961i	$0.502805\pi$
$464$	12.3535	−	21.3970i	0.573499	−	0.993329i
$465$	1.58001	−	2.08802i	0.0732714	−	0.0968296i
$466$	30.6410	+	5.40283i	1.41942	+	0.250281i
$467$	27.8806	−	16.0968i	1.29016	−	0.744873i	0.311476	−	0.950254i	$-0.399177\pi$
$467$	27.8806	−	16.0968i	1.29016	−	0.744873i	0.978682	+	0.205381i	$0.0658433\pi$
$468$	5.08550	+	2.28871i	0.235077	+	0.105796i
$469$	−8.11448	−	1.43080i	−0.374692	−	0.0660683i
$470$	−5.28394	−	29.9667i	−0.243730	−	1.38226i
$471$	4.78333	−	6.32126i	0.220404	−	0.291268i
$472$	6.50227	−	5.45605i	0.299291	−	0.251135i
$473$	1.14912	−	0.202620i	0.0528364	−	0.00931649i
$474$	−31.3464	+	1.57972i	−1.43979	+	0.0725590i
$475$	−32.6640	−	2.13970i	−1.49873	−	0.0981763i
$476$		−	4.01077i		−	0.183833i
$477$	5.22654	+	18.5071i	0.239307	+	0.847384i
$478$	1.55658	−	0.274468i	0.0711965	−	0.0125539i
$479$	11.5934	+	31.8527i	0.529718	+	1.45539i	0.859404	+	0.511297i	$0.170835\pi$
$479$	11.5934	+	31.8527i	0.529718	+	1.45539i	−0.329686	+	0.944091i	$0.606943\pi$
$480$	19.0459	+	5.86474i	0.869323	+	0.267687i
$481$	0.245946	−	0.0895168i	0.0112141	−	0.00408162i
$482$			23.5076i			1.07074i
$483$	5.73480	−	0.289009i	0.260942	−	0.0131504i
$484$	0.0397279	−	0.225308i	0.00180581	−	0.0102413i
$485$	11.7627	−	4.28126i	0.534115	−	0.194402i
$486$	−13.1844	+	12.9224i	−0.598055	+	0.586172i
$487$	−8.91799	−	5.14880i	−0.404113	−	0.233315i	0.284144	−	0.958782i	$-0.408291\pi$
$487$	−8.91799	−	5.14880i	−0.404113	−	0.233315i	−0.688257	+	0.725467i	$0.741624\pi$
$488$	−11.7600	−	9.86781i	−0.532350	−	0.446695i
$489$	−25.1582	+	5.75507i	−1.13769	+	0.260253i
$490$	−22.9188	−	4.04120i	−1.03536	−	0.182563i
$491$	−22.6124	−	26.9484i	−1.02048	−	1.21616i	−0.976139	−	0.217148i	$-0.930325\pi$
$491$	−22.6124	−	26.9484i	−1.02048	−	1.21616i	−0.0443440	−	0.999016i	$-0.514120\pi$
$492$	−2.05101	+	0.469180i	−0.0924668	+	0.0211523i
$493$	48.8256	+	28.1895i	2.19900	+	1.26959i
$494$	−15.9658	+	1.74914i	−0.718337	+	0.0786974i
$495$	20.9257	+	29.0463i	0.940542	+	1.30553i
$496$	0.357883	−	0.983275i	0.0160694	−	0.0441504i
$497$	15.7174	+	5.72067i	0.705023	+	0.256607i
$498$	17.7749	+	13.4503i	0.796510	+	0.602724i
$499$	23.5317	+	8.56484i	1.05342	+	0.383415i	0.809954	−	0.586494i	$-0.199492\pi$
$499$	23.5317	+	8.56484i	1.05342	+	0.383415i	0.243470	+	0.969908i	$0.421714\pi$
$500$	1.81388	+	4.98361i	0.0811194	+	0.222874i
$501$	−15.0788	−	7.72120i	−0.673672	−	0.344958i
$502$			0.467638i			0.0208717i
$503$	2.28846	+	6.28749i	0.102037	+	0.280345i	0.980198	−	0.198021i	$-0.0634514\pi$
$503$	2.28846	+	6.28749i	0.102037	+	0.280345i	−0.878160	+	0.478366i	$0.841229\pi$
$504$	−9.98671	+	4.82132i	−0.444843	+	0.214759i
$505$	33.8455	+	58.6221i	1.50610	+	2.60865i
$506$	−5.51154	−	9.54627i	−0.245018	−	0.424384i
$507$	−2.23590	−	5.29698i	−0.0992998	−	0.235247i
$508$	0.834940	−	2.29398i	0.0370445	−	0.101779i
$509$	−6.81147	+	38.6297i	−0.301913	+	1.71223i	0.335778	+	0.941941i	$0.391001\pi$
$509$	−6.81147	+	38.6297i	−0.301913	+	1.71223i	−0.637691	+	0.770292i	$0.720110\pi$
$510$	11.9273	−	38.7342i	0.528149	−	1.71518i
$511$	−12.2311	+	10.2631i	−0.541071	+	0.454013i
$512$	23.0252			1.01758
$513$	−5.89756	+	21.8682i	−0.260384	+	0.965505i
$514$	−12.6883			−0.559656
$515$	7.30076	−	6.12607i	0.321710	−	0.269947i
$516$	0.105326	−	0.342049i	0.00463672	−	0.0150579i
$517$	−4.25603	+	24.1371i	−0.187180	+	1.06155i
$518$	−0.0409450	+	0.112496i	−0.00179902	+	0.00494277i
$519$	9.08888	+	21.5321i	0.398958	+	0.945154i
$520$	16.9258	+	29.3163i	0.742245	+	1.28561i
$521$	−18.7475	−	32.4716i	−0.821343	−	1.42261i	−0.904682	−	0.426087i	$-0.859892\pi$
$521$	−18.7475	−	32.4716i	−0.821343	−	1.42261i	0.0833394	−	0.996521i	$-0.473441\pi$
$522$	2.64478	−	35.7590i	0.115759	−	1.56513i
$523$	−1.75650	−	4.82594i	−0.0768063	−	0.211024i	0.895347	−	0.445369i	$-0.146928\pi$
$523$	−1.75650	−	4.82594i	−0.0768063	−	0.211024i	−0.972153	+	0.234345i	$0.924705\pi$
$524$		−	8.33255i		−	0.364009i
$525$	−13.9126	−	7.12401i	−0.607194	−	0.310917i
$526$	−7.30015	−	20.0570i	−0.318302	−	0.874527i
$527$	2.24373	+	0.816652i	0.0977385	+	0.0355739i
$528$	11.4079	+	8.63245i	0.496467	+	0.375679i
$529$	−14.4610	−	5.26336i	−0.628738	−	0.228842i
$530$	−9.18358	+	25.2317i	−0.398909	+	1.09599i
$531$	3.39729	−	7.54876i	0.147430	−	0.327588i
$532$	−1.73858	+	2.60217i	−0.0753769	+	0.112818i
$533$	−5.47835	−	3.16293i	−0.237294	−	0.137002i
$534$	−1.98197	+	0.453387i	−0.0857683	+	0.0196200i
$535$	−19.1685	−	22.8441i	−0.828727	−	0.987638i
$536$	20.7720	+	3.66267i	0.897215	+	0.158203i
$537$	18.9539	−	4.33582i	0.817923	−	0.187104i
$538$	16.7317	+	14.0395i	0.721354	+	0.605288i
$539$	16.2337	+	9.37252i	0.699234	+	0.403703i
$540$	10.8554	−	1.65239i	0.467141	−	0.0711076i
$541$	−24.1017	+	8.77231i	−1.03621	+	0.377151i	−0.803444	−	0.595381i	$-0.797001\pi$
$541$	−24.1017	+	8.77231i	−1.03621	+	0.377151i	−0.232770	+	0.972532i	$0.574779\pi$
$542$	−4.13140	+	23.4303i	−0.177459	+	1.00642i
$543$	−44.1027	+	2.22259i	−1.89263	+	0.0953803i
$544$			18.1725i			0.779138i
$545$	−27.6764	+	10.0734i	−1.18553	+	0.431496i
$546$	−7.32966	−	2.25700i	−0.313680	−	0.0965905i
$547$	5.07749	+	13.9503i	0.217098	+	0.596471i	0.999659	−	0.0261023i	$-0.00830955\pi$
$547$	5.07749	+	13.9503i	0.217098	+	0.596471i	−0.782562	+	0.622573i	$0.786087\pi$
$548$	−0.847257	+	0.149394i	−0.0361930	+	0.00638181i
$549$	−14.5122	−	3.68023i	−0.619366	−	0.157068i
$550$			30.0058i			1.27945i
$551$	−19.4584	−	39.4541i	−0.828956	−	1.68080i
$552$	−14.6803	+	0.739825i	−0.624837	+	0.0314890i
$553$	−18.1076	+	3.19286i	−0.770014	+	0.135774i
$554$	13.1214	−	11.0102i	0.557476	−	0.467778i
$555$	0.310961	−	0.410940i	0.0131995	−	0.0174434i
$556$	−0.586583	−	3.32668i	−0.0248767	−	0.141083i
$557$	−19.5097	−	3.44009i	−0.826653	−	0.145761i	−0.255713	−	0.966753i	$-0.582310\pi$
$557$	−19.5097	−	3.44009i	−0.826653	−	0.145761i	−0.570940	+	0.820991i	$0.693421\pi$
$558$	−0.152672	−	1.51089i	−0.00646312	−	0.0639609i
$559$	0.931891	−	0.538028i	0.0394148	−	0.0227561i
$560$	−10.2469	−	1.80681i	−0.433011	−	0.0763515i
$561$	−19.6984	+	26.0317i	−0.831665	+	1.09906i
$562$	13.9027	−	24.0802i	0.586451	−	1.01576i
$563$	25.3883			1.06999			0.534995	−	0.844855i	$-0.320314\pi$
$563$	25.3883			1.06999			0.534995	+	0.844855i	$0.320314\pi$
$564$	5.99477	+	4.53627i	0.252425	+	0.191011i
$565$	−21.6081	+	3.81009i	−0.909060	+	0.160292i
$566$	−14.3646	−	12.0533i	−0.603789	−	0.506639i
$567$	−6.72665	+	8.46870i	−0.282493	+	0.355652i
$568$	−40.2346	−	14.6442i	−1.68820	−	0.614456i
$569$	−8.40455	+	14.5571i	−0.352337	+	0.610266i	−0.986659	−	0.162804i	$-0.947946\pi$
$569$	−8.40455	+	14.5571i	−0.352337	+	0.610266i	0.634321	+	0.773070i	$0.281280\pi$
$570$	−24.5288	+	19.9604i	−1.02740	+	0.836050i
$571$	−16.4890	−	28.5599i	−0.690045	−	1.19519i	−0.971823	−	0.235713i	$-0.924257\pi$
$571$	−16.4890	−	28.5599i	−0.690045	−	1.19519i	0.281778	−	0.959480i	$-0.409076\pi$
$572$	−1.08908	−	6.17648i	−0.0455367	−	0.258251i
$573$	10.5204	−	9.77107i	0.439498	−	0.408192i
$574$	2.71895	−	0.989617i	0.113487	−	0.0413058i
$575$	−13.3171	−	15.8707i	−0.555361	−	0.661854i
$576$	23.6359	−	11.4108i	0.984829	−	0.475450i
$577$	5.61500	−	9.72547i	0.233756	−	0.404877i	−0.725155	−	0.688586i	$-0.758232\pi$
$577$	5.61500	−	9.72547i	0.233756	−	0.404877i	0.958910	+	0.283709i	$0.0915651\pi$
$578$	16.8250			0.699828
$579$	−23.4014	+	9.87791i	−0.972527	+	0.410512i
$580$	−13.7087	+	16.3374i	−0.569223	+	0.678374i
$581$	11.3088	+	6.52916i	0.469169	+	0.270875i
$582$	3.30877	−	6.46174i	0.137153	−	0.267848i
$583$	13.9019	−	16.5677i	0.575759	−	0.686163i
$584$	31.3100	−	26.2722i	1.29562	−	1.08715i
$585$	27.2952	+	18.5707i	1.12852	+	0.767804i
$586$	−2.15338	−	12.2124i	−0.0889551	−	0.504490i
$587$	20.7748	+	24.7585i	0.857468	+	1.02189i	0.999487	+	0.0320272i	$0.0101963\pi$
$587$	20.7748	+	24.7585i	0.857468	+	1.02189i	−0.142019	+	0.989864i	$0.545359\pi$
$588$	4.82825	−	3.12175i	0.199114	−	0.128739i
$589$	−1.10173	−	1.50245i	−0.0453958	−	0.0619073i
$590$	10.0096	−	5.77902i	0.412087	−	0.237919i
$591$	−6.09547	+	5.66129i	−0.250734	+	0.232874i
$592$	0.0704345	−	0.193517i	0.00289484	−	0.00795350i
$593$	−7.58328	+	9.03740i	−0.311408	+	0.371121i	−0.898934	−	0.438084i	$-0.855657\pi$
$593$	−7.58328	+	9.03740i	−0.311408	+	0.371121i	0.587526	+	0.809205i	$0.300102\pi$
$594$	20.3561	+	4.08417i	0.835223	+	0.167575i
$595$	4.12294	−	23.3824i	0.169024	−	0.958584i
$596$	−2.55323	+	1.47411i	−0.104584	+	0.0603818i
$597$	−0.737851	−	14.6412i	−0.0301982	−	0.599223i
$598$	−7.78716	−	6.53420i	−0.318441	−	0.267203i
$599$	2.67689	+	2.24618i	0.109375	+	0.0917763i	0.695835	−	0.718202i	$-0.255035\pi$
$599$	2.67689	+	2.24618i	0.109375	+	0.0917763i	−0.586460	+	0.809978i	$0.699479\pi$
$600$	35.6144	+	18.2365i	1.45395	+	0.744504i
$601$	7.81604	−	4.51259i	0.318823	−	0.184072i	−0.332045	−	0.943264i	$-0.607739\pi$
$601$	7.81604	−	4.51259i	0.318823	−	0.184072i	0.650868	+	0.759191i	$0.274405\pi$
$602$	−0.0854675	+	0.484710i	−0.00348340	+	0.0197553i
$603$	19.7961	−	5.59055i	0.806160	−	0.227665i
$604$	−1.10568	+	1.31770i	−0.0449897	+	0.0536166i
$605$	0.463219	−	1.27268i	0.0188325	−	0.0517420i
$606$	37.5192	+	11.5532i	1.52411	+	0.469315i
$607$	−20.8371	+	12.0303i	−0.845753	+	0.488296i	−0.859216	−	0.511613i	$-0.829048\pi$
$607$	−20.8371	+	12.0303i	−0.845753	+	0.488296i	0.0134624	+	0.999909i	$0.495715\pi$
$608$	7.87736	−	11.7902i	0.319469	−	0.478157i
$609$	−1.05726	−	20.9793i	−0.0428425	−	0.850124i
$610$	−13.4367	−	16.0133i	−0.544038	−	0.648359i
$611$	3.92488	+	22.2591i	0.158784	+	0.900508i
$612$	4.35321	+	9.01708i	0.175968	+	0.364494i
$613$	22.1292	−	18.5686i	0.893788	−	0.749977i	−0.0751781	−	0.997170i	$-0.523953\pi$
$613$	22.1292	−	18.5686i	0.893788	−	0.749977i	0.968966	+	0.247193i	$0.0795081\pi$
$614$	24.7605	−	29.5084i	0.999253	−	1.19086i
$615$	−12.4395	+	0.626897i	−0.501610	+	0.0252789i
$616$	10.8007	+	6.23580i	0.435173	+	0.251247i
$617$	9.34181	−	11.1331i	0.376087	−	0.448203i	−0.544488	−	0.838769i	$-0.683276\pi$
$617$	9.34181	−	11.1331i	0.376087	−	0.448203i	0.920575	+	0.390565i	$0.127720\pi$
$618$	0.684609	−	5.48468i	0.0275390	−	0.220626i
$619$	−29.4065			−1.18195			−0.590973	−	0.806691i	$-0.701256\pi$
$619$	−29.4065			−1.18195			−0.590973	+	0.806691i	$0.701256\pi$
$620$	−0.451613	+	0.782217i	−0.0181372	+	0.0314146i
$621$	−12.5794	+	6.87420i	−0.504794	+	0.275852i
$622$	−3.21474	−	3.83118i	−0.128900	−	0.153616i
$623$	−1.11926	+	0.407377i	−0.0448422	+	0.0163212i
$624$	12.6086	+	3.88253i	0.504749	+	0.155426i
$625$	−1.06845	−	6.05948i	−0.0427380	−	0.242379i
$626$	−16.8355	−	29.1599i	−0.672880	−	1.16546i
$627$	24.0644	−	8.35051i	0.961040	−	0.333487i
$628$	−1.36721	+	2.36808i	−0.0545577	+	0.0944967i
$629$	0.441586	+	0.160724i	0.0176072	+	0.00640849i
$630$	−14.5321	+	4.10395i	−0.578972	+	0.163505i
$631$	30.8381	+	25.8763i	1.22765	+	1.03012i	0.998388	+	0.0567516i	$0.0180743\pi$
$631$	30.8381	+	25.8763i	1.22765	+	1.03012i	0.229258	+	0.973366i	$0.426370\pi$
$632$	46.3531	−	8.17331i	1.84383	−	0.325117i
$633$	−1.96807	+	15.7670i	−0.0782236	+	0.626680i
$634$	−3.61032			−0.143384
$635$	7.22576	−	12.5154i	0.286745	−	0.496658i
$636$	−2.57973	−	6.11153i	−0.102293	−	0.242338i
$637$	17.0239	+	3.00178i	0.674513	+	0.118935i
$638$	−34.9226	+	20.1626i	−1.38260	+	0.798244i
$639$	−41.5453	+	4.19807i	−1.64351	+	0.166073i
$640$	13.4274	+	2.36761i	0.530763	+	0.0935879i
$641$	−1.79328	−	10.1702i	−0.0708305	−	0.401700i	−0.999524	−	0.0308514i	$-0.990178\pi$
$641$	−1.79328	−	10.1702i	−0.0708305	−	0.401700i	0.928694	−	0.370848i	$-0.120933\pi$
$642$	−17.1616	−	2.14215i	−0.677314	−	0.0845438i
$643$	9.40792	−	7.89418i	0.371012	−	0.311316i	−0.438150	−	0.898902i	$-0.644366\pi$
$643$	9.40792	−	7.89418i	0.371012	−	0.311316i	0.809162	+	0.587586i	$0.199922\pi$
$644$	−1.95062	+	0.343947i	−0.0768653	+	0.0135534i
$645$	0.965657	−	1.88584i	0.0380227	−	0.0742550i
$646$	−23.9781	−	16.0204i	−0.943408	−	0.630315i
$647$		−	1.83354i		−	0.0720840i	−0.999350	−	0.0360420i	$-0.988525\pi$
$647$		−	1.83354i		−	0.0720840i	0.999350	−	0.0360420i	$-0.0114750\pi$
$648$	17.2193	−	21.6788i	0.676440	−	0.851623i
$649$	−9.16818	+	1.61660i	−0.359882	+	0.0634570i
$650$	9.46410	+	26.0024i	0.371213	+	1.01990i
$651$	−0.198383	−	0.867228i	−0.00777525	−	0.0339894i
$652$	8.36554	−	3.04481i	0.327620	−	0.119244i
$653$		−	25.4356i		−	0.995370i	−0.867358	−	0.497685i	$-0.834184\pi$
$653$		−	25.4356i		−	0.995370i	0.867358	−	0.497685i	$-0.165816\pi$
$654$	−7.78522	+	15.2038i	−0.304426	+	0.594517i
$655$	8.56560	−	48.5779i	0.334686	−	1.89810i
$656$	−4.67719	+	1.70236i	−0.182614	+	0.0664660i
$657$	16.3588	−	36.3491i	0.638217	−	1.41811i
$658$	−8.95331	−	5.16919i	−0.349036	−	0.201516i
$659$	−0.378559	−	0.317648i	−0.0147465	−	0.0123738i	0.635385	−	0.772196i	$-0.280842\pi$
$659$	−0.378559	−	0.317648i	−0.0147465	−	0.0123738i	−0.650131	+	0.759822i	$0.725286\pi$
$660$	−8.40371	−	9.04822i	−0.327114	−	0.352201i
$661$	36.6397	+	6.46056i	1.42512	+	0.251287i	0.832423	−	0.554140i	$-0.186953\pi$
$661$	36.6397	+	6.46056i	1.42512	+	0.251287i	0.592695	+	0.805427i	$0.298064\pi$
$662$	12.0093	+	14.3121i	0.466755	+	0.556257i
$663$	−8.85953	+	28.7716i	−0.344076	+	1.11740i
$664$	−28.9491	−	16.7138i	−1.12344	−	0.648621i
$665$	−12.8107	+	13.3832i	−0.496777	+	0.518978i
$666$	−0.0300472	−	0.297356i	−0.00116430	−	0.0115223i
$667$	9.52278	−	26.1636i	0.368723	−	1.01306i
$668$	5.49124	+	1.99865i	0.212463	+	0.0773300i
$669$	5.83856	−	46.7750i	0.225732	−	1.80843i
$670$	26.9890	+	9.82319i	1.04268	+	0.379503i
$671$	5.75871	+	15.8219i	0.222312	+	0.610798i
$672$	5.68583	−	3.67622i	0.219336	−	0.141813i
$673$			8.50387i			0.327800i	0.986477	+	0.163900i	$0.0524075\pi$
$673$			8.50387i			0.327800i	−0.986477	+	0.163900i	$0.947593\pi$
$674$	2.73662	+	7.51880i	0.105411	+	0.289613i
$675$	39.0108	+	0.915898i	1.50153	+	0.0352529i
$676$	0.991645	+	1.71758i	0.0381402	+	0.0660607i
$677$	−17.6944	−	30.6476i	−0.680051	−	1.17788i	−0.974965	−	0.222359i	$-0.928624\pi$
$677$	−17.6944	−	30.6476i	−0.680051	−	1.17788i	0.294914	−	0.955524i	$-0.404709\pi$
$678$	−7.67850	+	10.1473i	−0.294891	+	0.389704i
$679$	1.45458	−	3.99642i	0.0558216	−	0.153369i
$680$	−10.5542	+	59.8558i	−0.404735	+	2.29537i
$681$	−15.1645	−	16.3275i	−0.581106	−	0.625673i
$682$	−1.30827	+	1.09777i	−0.0500963	+	0.0420358i
$683$	11.3436			0.434052			0.217026	−	0.976166i	$-0.430364\pi$
$683$	11.3436			0.434052			0.217026	+	0.976166i	$0.430364\pi$
$684$	1.08435	−	7.73727i	0.0414613	−	0.295842i
$685$	−5.09300			−0.194594
$686$	−13.6883	+	11.4858i	−0.522622	+	0.438532i
$687$	−27.2652	+	6.23706i	−1.04023	+	0.237959i
$688$	0.147023	−	0.833809i	0.00560520	−	0.0317887i
$689$	6.82152	−	18.7420i	0.259879	−	0.714012i
$690$	−19.8611	−	2.47910i	−0.756099	−	0.0943779i
$691$	7.08458	+	12.2709i	0.269510	+	0.466805i	0.968735	−	0.248096i	$-0.0798049\pi$
$691$	7.08458	+	12.2709i	0.269510	+	0.466805i	−0.699225	+	0.714901i	$0.746472\pi$
$692$	−4.03101	−	6.98192i	−0.153236	−	0.265413i
$693$	12.1298	+	0.897132i	0.460771	+	0.0340792i
$694$	−0.0362340	−	0.0995521i	−0.00137542	−	0.00377895i
$695$		−	19.9972i		−	0.758537i
$696$	2.70646	+	53.7043i	0.102588	+	2.03565i
$697$	−3.88461	−	10.6729i	−0.147140	−	0.404264i
$698$	14.0266	+	5.10527i	0.530916	+	0.193238i
$699$	−41.9228	+	17.6960i	−1.58566	+	0.669322i
$700$	5.06653	+	1.84406i	0.191497	+	0.0696991i
$701$	3.74272	−	10.2830i	0.141360	−	0.388385i	−0.848728	−	0.528830i	$-0.822631\pi$
$701$	3.74272	−	10.2830i	0.141360	−	0.388385i	0.990088	+	0.140445i	$0.0448533\pi$
$702$	18.9284	−	2.88125i	0.714406	−	0.108746i
$703$	−0.216829	−	0.295695i	−0.00817787	−	0.0111523i
$704$	−25.5624	−	14.7585i	−0.963421	−	0.556231i
$705$	30.2858	+	32.6084i	1.14063	+	1.22811i
$706$	16.9348	+	20.1821i	0.637350	+	0.759565i
$707$	22.6489	+	3.99362i	0.851800	+	0.150195i
$708$	−0.840339	+	2.72903i	−0.0315819	+	0.102563i
$709$	−29.5033	−	24.7562i	−1.10802	−	0.929739i	−0.110081	−	0.993923i	$-0.535111\pi$
$709$	−29.5033	−	24.7562i	−1.10802	−	0.929739i	−0.997938	+	0.0641840i	$0.979556\pi$
$710$	−50.4914	−	29.1512i	−1.89491	−	1.09403i
$711$	37.2444	−	26.8319i	1.39677	−	1.00628i
$712$	2.86516	−	1.04283i	0.107376	−	0.0390818i
$713$	0.204762	−	1.16126i	0.00766841	−	0.0434897i
$714$	−7.47644	−	11.5634i	−0.279799	−	0.432751i
$715$		−	37.1278i		−	1.38850i
$716$	−6.30252	+	2.29393i	−0.235536	+	0.0857282i
$717$	−1.69381	+	1.57316i	−0.0632564	+	0.0587506i
$718$	0.865927	+	2.37911i	0.0323161	+	0.0887878i
$719$	−10.1389	+	1.78776i	−0.378116	+	0.0666721i	−0.359476	−	0.933154i	$-0.617045\pi$
$719$	−10.1389	+	1.78776i	−0.378116	+	0.0666721i	−0.0186399	+	0.999826i	$0.505934\pi$
$720$	24.9984	−	7.05971i	0.931634	−	0.263100i
$721$		−	3.23802i		−	0.120590i
$722$	8.61246	+	20.7880i	0.320522	+	0.773649i
$723$	−18.6671	−	28.8715i	−0.694236	−	1.07374i
$724$	15.0010	−	2.64508i	0.557509	−	0.0983038i
$725$	−58.0589	+	48.7172i	−2.15625	+	1.80931i
$726$	−0.305455	−	0.723642i	−0.0113365	−	0.0268569i
$727$	−2.59990	−	14.7447i	−0.0964248	−	0.546852i	−0.994301	−	0.106605i	$-0.966002\pi$
$727$	−2.59990	−	14.7447i	−0.0964248	−	0.546852i	0.897877	−	0.440247i	$-0.145109\pi$
$728$	11.3265	+	1.99717i	0.419788	+	0.0740199i
$729$	5.93120	−	26.3405i	0.219674	−	0.975573i
$730$	48.1984	−	27.8274i	1.78390	−	1.02994i
$731$	1.90266	+	0.335491i	0.0703726	+	0.0124086i
$732$	5.12464	+	0.639669i	0.189412	+	0.0236428i
$733$	−20.9068	+	36.2116i	−0.772209	+	1.33750i	0.164141	+	0.986437i	$0.447515\pi$
$733$	−20.9068	+	36.2116i	−0.772209	+	1.33750i	−0.936350	+	0.351068i	$0.885819\pi$
$734$	−30.6322			−1.13065
$735$	31.3573	−	13.2362i	1.15663	−	0.488224i
$736$	8.83812	−	1.55840i	0.325777	−	0.0574433i
$737$	−17.7215	−	14.8701i	−0.652782	−	0.547749i
$738$	−5.03868	+	5.17597i	−0.185477	+	0.190530i
$739$	−23.5043	−	8.55486i	−0.864619	−	0.314696i	−0.128633	−	0.991692i	$-0.541059\pi$
$739$	−23.5043	−	8.55486i	−0.864619	−	0.314696i	−0.735986	+	0.676997i	$0.763281\pi$
$740$	−0.0888814	+	0.153947i	−0.00326735	+	0.00565921i
$741$	18.2199	−	14.8265i	0.669323	−	0.544665i
$742$	4.56137	+	7.90053i	0.167453	+	0.290038i
$743$	1.54801	+	8.77919i	0.0567909	+	0.322077i	0.999947	−	0.0102723i	$-0.00326982\pi$
$743$	1.54801	+	8.77919i	0.0567909	+	0.322077i	−0.943156	+	0.332349i	$0.892159\pi$
$744$	0.507835	+	2.21999i	0.0186181	+	0.0813889i
$745$	−16.4004	+	5.96926i	−0.600865	+	0.218697i
$746$	−3.74921	−	4.46813i	−0.137268	−	0.163590i
$747$	−32.5114	−	2.40458i	−1.18953	−	0.0879790i
$748$	5.63035	−	9.75206i	0.205866	−	0.356570i
$749$	−10.1318			−0.370207
$750$	14.5195	+	10.9870i	0.530178	+	0.401188i
$751$	2.01949	−	2.40673i	0.0736922	−	0.0878229i	−0.727939	−	0.685642i	$-0.759522\pi$
$751$	2.01949	−	2.40673i	0.0736922	−	0.0878229i	0.801631	+	0.597819i	$0.203966\pi$
$752$	15.4017	+	8.89215i	0.561641	+	0.324263i
$753$	−0.371345	−	0.574341i	−0.0135326	−	0.0209301i
$754$	−23.9037	+	28.4873i	−0.870522	+	1.03745i
$755$	−7.80059	+	6.54547i	−0.283893	+	0.238214i
$756$	1.94064	−	3.18616i	0.0705805	−	0.115880i
$757$	−4.64050	−	26.3176i	−0.168662	−	0.956528i	−0.945208	−	0.326468i	$-0.894141\pi$
$757$	−4.64050	−	26.3176i	−0.168662	−	0.956528i	0.776546	−	0.630060i	$-0.216970\pi$
$758$	3.32425	+	3.96169i	0.120742	+	0.143895i
$759$	14.3497	+	7.34785i	0.520861	+	0.266710i
$760$	32.7937	−	34.2593i	1.18955	−	1.24271i
$761$	−42.5583	+	24.5710i	−1.54274	+	0.890699i	−0.544071	+	0.839039i	$0.683118\pi$
$761$	−42.5583	+	24.5710i	−1.54274	+	0.890699i	−0.998665	+	0.0516602i	$0.983549\pi$
$762$	−1.86897	−	8.17018i	−0.0677057	−	0.295974i
$763$	−3.42248	+	9.40318i	−0.123902	+	0.340418i
$764$	−3.18358	+	3.79404i	−0.115178	+	0.137264i
$765$	16.1095	+	57.0437i	0.582441	+	2.06242i
$766$	−5.86113	+	33.2401i	−0.211771	+	1.20101i
$767$	−7.43505	+	4.29263i	−0.268464	+	0.154998i
$768$	−18.8099	+	12.1617i	−0.678744	+	0.438847i
$769$	34.0697	+	28.5878i	1.22858	+	1.03090i	0.998330	+	0.0577729i	$0.0183999\pi$
$769$	34.0697	+	28.5878i	1.22858	+	1.03090i	0.230253	+	0.973131i	$0.426045\pi$
$770$	13.0092	+	10.9160i	0.468818	+	0.393385i
$771$	15.5834	−	10.0756i	0.561223	−	0.362863i
$772$	7.58804	−	4.38096i	0.273100	−	0.157674i
$773$	−0.398806	+	2.26174i	−0.0143440	+	0.0813491i	−0.991139	−	0.132825i	$-0.957595\pi$
$773$	−0.398806	+	2.26174i	−0.0143440	+	0.0813491i	0.976795	+	0.214175i	$0.0687061\pi$
$774$	−0.333946	−	1.18250i	−0.0120034	−	0.0425041i
$775$	−2.06324	+	2.45887i	−0.0741138	+	0.0883254i
$776$	−3.72353	+	10.2303i	−0.133667	+	0.367247i
$777$	−0.0390435	−	0.170678i	−0.00140068	−	0.00612304i
$778$	−0.277878	+	0.160433i	−0.00996240	+	0.00575179i
$779$	−2.10613	+	8.60841i	−0.0754599	+	0.308428i
$780$	−10.1364	−	5.19038i	−0.362940	−	0.185846i
$781$	30.1857	+	35.9739i	1.08013	+	1.28725i
$782$	−3.16936	−	17.9743i	−0.113336	−	0.642761i
$783$	25.1475	+	46.0185i	0.898698	+	1.64457i
$784$	10.4194	−	8.74292i	0.372122	−	0.312247i
$785$	−10.4050	+	12.4002i	−0.371371	+	0.442583i
$786$	−15.5326	−	24.0236i	−0.554031	−	0.856893i
$787$	0.375457	+	0.216770i	0.0133836	+	0.00772701i	0.506677	−	0.862136i	$-0.330874\pi$
$787$	0.375457	+	0.216770i	0.0133836	+	0.00772701i	−0.493293	+	0.869863i	$0.664207\pi$
$788$	1.84454	−	2.19824i	0.0657091	−	0.0783091i
$789$	24.8929	+	18.8366i	0.886209	+	0.670599i
$790$	64.0916			2.28028
$791$	−3.72735	+	6.45596i	−0.132529	+	0.229548i
$792$	−31.0506	−	2.29654i	−1.10334	−	0.0816041i
$793$	9.98074	+	11.8946i	0.354427	+	0.422389i
$794$	20.6673	−	7.52229i	0.733455	−	0.266956i
$795$	−8.75709	−	38.2815i	−0.310582	−	1.35770i
$796$	0.878111	+	4.98002i	0.0311238	+	0.176512i
$797$	−6.89925	−	11.9498i	−0.244384	−	0.423285i	0.717574	−	0.696482i	$-0.245252\pi$
$797$	−6.89925	−	11.9498i	−0.244384	−	0.423285i	−0.961958	+	0.273197i	$0.911919\pi$
$798$	−0.161804	+	10.7432i	−0.00572781	+	0.380305i
$799$	−20.2910	+	35.1450i	−0.717843	+	1.24334i
$800$	−22.9560	−	8.35531i	−0.811618	−	0.295405i
$801$	2.07418	−	2.13070i	0.0732876	−	0.0752844i
$802$	−2.71876	−	2.28131i	−0.0960028	−	0.0805559i
$803$	−44.1470	+	7.78430i	−1.55791	+	0.274702i
$804$	−6.53717	+	2.75940i	−0.230548	+	0.0973164i
$805$	−11.7255			−0.413270
$806$	−0.787473	+	1.36394i	−0.0277375	+	0.0480428i
$807$	−31.6980	−	3.95662i	−1.11582	−	0.139279i
$808$	−57.9783	−	10.2231i	−2.03967	−	0.359649i
$809$	−45.5549	+	26.3011i	−1.60162	+	0.924698i	−0.610462	+	0.792045i	$0.709016\pi$
$809$	−45.5549	+	26.3011i	−1.60162	+	0.924698i	−0.991163	+	0.132653i	$0.957650\pi$
$810$	28.2169	−	24.9994i	0.991442	−	0.878390i
$811$	4.77978	+	0.842805i	0.167841	+	0.0295949i	0.256937	−	0.966428i	$-0.417287\pi$
$811$	4.77978	+	0.842805i	0.167841	+	0.0295949i	−0.0890961	+	0.996023i	$0.528398\pi$
$812$	1.25824	+	7.13585i	0.0441557	+	0.250419i
$813$	−13.5316	−	32.0572i	−0.474575	−	1.12430i
$814$	−0.257479	+	0.216050i	−0.00902463	+	0.00757256i
$815$	51.9002	−	9.15141i	1.81799	−	0.320560i
$816$	12.8611	+	19.8917i	0.450229	+	0.696348i
$817$	−1.08902	−	1.04243i	−0.0380998	−	0.0364700i
$818$			10.2513i			0.358429i
$819$	10.7943	−	3.04840i	0.377185	−	0.106520i
$820$	4.23115	−	0.746066i	0.147758	−	0.0260538i
$821$	12.7189	+	34.9450i	0.443894	+	1.21959i	0.936910	+	0.349569i	$0.113672\pi$
$821$	12.7189	+	34.9450i	0.443894	+	1.21959i	−0.493016	+	0.870020i	$0.664106\pi$
$822$	−2.16424	+	2.01009i	−0.0754867	+	0.0701098i
$823$	−2.08804	+	0.759986i	−0.0727846	+	0.0264914i	−0.378156	−	0.925742i	$-0.623442\pi$
$823$	−2.08804	+	0.759986i	−0.0727846	+	0.0264914i	0.305371	+	0.952233i	$0.401219\pi$
$824$			8.28891i			0.288758i
$825$	−23.8272	−	36.8524i	−0.829558	−	1.28304i
$826$	0.681899	−	3.86724i	0.0237263	−	0.134559i
$827$	−15.9430	+	5.80279i	−0.554393	+	0.201783i	−0.603997	−	0.796986i	$-0.706426\pi$
$827$	−15.9430	+	5.80279i	−0.554393	+	0.201783i	0.0496041	+	0.998769i	$0.484204\pi$
$828$	4.01211	−	2.89044i	0.139431	−	0.100450i
$829$	−12.8100	−	7.39588i	−0.444911	−	0.256870i	0.260767	−	0.965402i	$-0.416024\pi$
$829$	−12.8100	−	7.39588i	−0.444911	−	0.256870i	−0.705679	+	0.708532i	$0.749358\pi$
$830$	−34.8684	−	29.2581i	−1.21030	−	1.01556i
$831$	−7.37237	+	23.9420i	−0.255745	+	0.830538i
$832$	−26.8068	−	4.72676i	−0.929359	−	0.163871i
$833$	19.9504	+	23.7760i	0.691241	+	0.823789i
$834$	−7.89242	−	8.49771i	−0.273292	−	0.294252i
$835$	29.9589	+	17.2968i	1.03677	+	0.598579i
$836$	−7.88025	+	3.88647i	−0.272544	+	0.134416i
$837$	1.38728	+	1.73440i	0.0479515	+	0.0599496i
$838$	−3.48693	+	9.58025i	−0.120454	+	0.330944i
$839$	−21.5044	−	7.82698i	−0.742416	−	0.270217i	−0.0570049	−	0.998374i	$-0.518155\pi$
$839$	−21.5044	−	7.82698i	−0.742416	−	0.270217i	−0.685411	+	0.728157i	$0.740377\pi$
$840$	20.8629	−	8.80640i	0.719838	−	0.303849i
$841$	−68.4618	−	24.9181i	−2.36075	−	0.859243i
$842$	7.05302	+	19.3780i	0.243063	+	0.667810i
$843$	2.04680	+	40.6147i	0.0704956	+	1.39884i
$844$		−	5.48098i		−	0.188663i
$845$	4.01557	+	11.0327i	0.138140	+	0.379536i
$846$	25.7395	+	1.90373i	0.884944	+	0.0654515i
$847$	−0.230075	−	0.398502i	−0.00790548	−	0.0136927i
$848$	−7.84657	−	13.5907i	−0.269452	−	0.466705i
$849$	27.2136	+	3.39686i	0.933969	+	0.116580i
$850$	−16.9924	+	46.6863i	−0.582836	+	1.60133i
$851$	0.0402990	−	0.228547i	0.00138143	−	0.00783448i
$852$	14.0412	−	3.21201i	0.481045	−	0.110042i
$853$	28.9176	−	24.2647i	0.990120	−	0.830809i	0.00453456	−	0.999990i	$-0.498557\pi$
$853$	28.9176	−	24.2647i	0.990120	−	0.830809i	0.985585	+	0.169181i	$0.0541122\pi$
$854$	−7.10218			−0.243032
$855$	14.2754	−	43.9929i	0.488207	−	1.50452i
$856$	25.9361			0.886476
$857$	−5.49747	+	4.61292i	−0.187790	+	0.157574i	−0.731836	−	0.681481i	$-0.761336\pi$
$857$	−5.49747	+	4.61292i	−0.187790	+	0.157574i	0.544046	+	0.839055i	$0.316892\pi$
$858$	−14.6535	−	15.7773i	−0.500261	−	0.538627i
$859$	9.66766	−	54.8281i	0.329856	−	1.87071i	−0.143225	−	0.989690i	$-0.545747\pi$
$859$	9.66766	−	54.8281i	0.329856	−	1.87071i	0.473081	−	0.881019i	$-0.343142\pi$
$860$	−0.249962	+	0.686765i	−0.00852364	+	0.0234185i
$861$	−2.55350	+	3.37450i	−0.0870232	+	0.115003i
$862$	−1.71279	−	2.96664i	−0.0583380	−	0.101044i
$863$	14.3696	+	24.8889i	0.489147	+	0.847228i	0.999922	−	0.0124866i	$-0.00397472\pi$
$863$	14.3696	+	24.8889i	0.489147	+	0.847228i	−0.510775	+	0.859715i	$0.670641\pi$
$864$	−8.79290	+	14.4363i	−0.299140	+	0.491131i
$865$	−16.3232	−	44.8477i	−0.555006	−	1.52487i
$866$			2.05567i			0.0698544i
$867$	−20.6640	+	13.3605i	−0.701788	+	0.453746i
$868$	0.104958	+	0.288369i	0.00356249	+	0.00978787i
$869$	−48.5103	−	17.6563i	−1.64560	−	0.598949i
$870$	−9.06917	+	72.6567i	−0.307474	+	2.46329i
$871$	−20.0473	−	7.29661i	−0.679276	−	0.247236i
$872$	8.76110	−	24.0709i	0.296688	−	0.815145i
$873$	1.06743	+	10.5636i	0.0361270	+	0.357524i
$874$	−5.73520	+	13.0355i	−0.193996	+	0.440934i
$875$	9.23769	+	5.33338i	0.312291	+	0.180301i
$876$	−4.04643	+	13.1409i	−0.136716	+	0.443990i
$877$	19.0573	+	22.7116i	0.643520	+	0.766917i	0.984922	−	0.173000i	$-0.0553462\pi$
$877$	19.0573	+	22.7116i	0.643520	+	0.766917i	−0.341402	+	0.939917i	$0.610902\pi$
$878$	−30.6006	−	5.39571i	−1.03272	−	0.182096i
$879$	12.3424	+	13.2890i	0.416300	+	0.448227i
$880$	−22.3786	−	18.7779i	−0.754384	−	0.633003i
$881$	36.1615	+	20.8779i	1.21831	+	0.703393i	0.964557	−	0.263875i	$-0.0850007\pi$
$881$	36.1615	+	20.8779i	1.21831	+	0.703393i	0.253756	+	0.967268i	$0.418334\pi$
$882$	8.10112	−	18.0006i	0.272779	−	0.606112i
$883$	26.6924	−	9.71525i	0.898272	−	0.326944i	0.148712	−	0.988881i	$-0.452487\pi$
$883$	26.6924	−	9.71525i	0.898272	−	0.326944i	0.749560	+	0.661936i	$0.230265\pi$
$884$	1.80326	−	10.2268i	0.0606501	−	0.343964i
$885$	−7.70445	+	15.0461i	−0.258982	+	0.505769i
$886$		−	16.6010i		−	0.557722i
$887$	27.8967	−	10.1536i	0.936678	−	0.340923i	0.171825	−	0.985128i	$-0.445034\pi$
$887$	27.8967	−	10.1536i	0.936678	−	0.340923i	0.764853	+	0.644205i	$0.222811\pi$
$888$	0.0999463	+	0.436914i	0.00335398	+	0.0146619i
$889$	−1.67931	−	4.61386i	−0.0563222	−	0.154744i
$890$	4.08872	−	0.720952i	0.137054	−	0.0241664i
$891$	−28.2441	+	11.1485i	−0.946213	+	0.373488i
$892$			16.2601i			0.544430i
$893$	28.3993	−	14.0063i	0.950346	−	0.468702i
$894$	−4.61335	+	9.00946i	−0.154293	+	0.301321i
$895$	−39.1012	+	6.89459i	−1.30701	+	0.230461i
$896$	3.54861	−	2.97764i	0.118551	−	0.0994759i
$897$	14.7527	+	1.84147i	0.492579	+	0.0614847i
$898$	1.03546	+	5.87240i	0.0345538	+	0.195964i
$899$	−4.24819	−	0.749070i	−0.141685	−	0.0249829i
$900$	−13.3922	+	1.35325i	−0.446406	+	0.0451084i
$901$	31.0125	−	17.9051i	1.03317	−	0.596504i
$902$	8.00028	+	1.41067i	0.266380	+	0.0469700i
$903$	−0.279933	−	0.663178i	−0.00931558	−	0.0220692i
$904$	9.54154	−	16.5264i	0.317347	−	0.549661i
$905$	90.1735			2.99747
$906$	−0.731479	+	5.86017i	−0.0243018	+	0.194691i
$907$	0.560680	−	0.0988630i	0.0186171	−	0.00328269i	−0.164332	−	0.986405i	$-0.552547\pi$
$907$	0.560680	−	0.0988630i	0.0186171	−	0.00328269i	0.182949	+	0.983122i	$0.441436\pi$
$908$	5.88829	+	4.94086i	0.195410	+	0.163968i
$909$	−55.2543	+	15.6042i	−1.83267	+	0.517558i
$910$	14.7165	+	5.35635i	0.487846	+	0.177561i
$911$	23.2351	−	40.2444i	0.769814	−	1.33336i	−0.167850	−	0.985813i	$-0.553682\pi$
$911$	23.2351	−	40.2444i	0.769814	−	1.33336i	0.937664	−	0.347544i	$-0.112984\pi$
$912$	0.278339	−	18.4807i	0.00921673	−	0.611956i
$913$	18.3314	+	31.7509i	0.606680	+	1.05080i
$914$	−2.22897	−	12.6411i	−0.0737276	−	0.418130i
$915$	29.2186	+	8.99718i	0.965937	+	0.297438i
$916$	9.06615	−	3.29981i	0.299554	−	0.109029i
$917$	−10.7726	−	12.8383i	−0.355742	−	0.423957i
$918$	29.3594	+	17.8824i	0.969005	+	0.590206i
$919$	15.4047	−	26.6817i	0.508153	−	0.880147i	−0.491803	−	0.870707i	$-0.663662\pi$
$919$	15.4047	−	26.6817i	0.508153	−	0.880147i	0.999955	−	0.00943987i	$-0.00300485\pi$
$920$	30.0158			0.989591
$921$	−6.97799	+	55.9035i	−0.229933	+	1.84208i
$922$	8.51343	−	10.1459i	0.280375	−	0.334138i
$923$	37.5048	+	21.6534i	1.23448	+	0.712730i
$924$	−4.19024	+	0.211170i	−0.137849	+	0.00694698i
$925$	−0.406064	+	0.483928i	−0.0133513	+	0.0159114i
$926$	0.343980	−	0.288633i	0.0113039	−	0.00948508i
$927$	3.51449	+	7.27978i	0.115431	+	0.239099i
$928$	−5.70100	−	32.3320i	−0.187145	−	1.06135i
$929$	7.14085	+	8.51014i	0.234284	+	0.279209i	0.870358	−	0.492419i	$-0.163887\pi$
$929$	7.14085	+	8.51014i	0.234284	+	0.279209i	−0.636074	+	0.771628i	$0.719443\pi$
$930$	0.156078	+	3.09706i	0.00511801	+	0.101557i
$931$	−2.63741	−	24.0739i	−0.0864377	−	0.788989i
$932$	13.5937	−	7.84834i	0.445277	−	0.257081i
$933$	6.99056	+	2.15258i	0.228861	+	0.0704722i
$934$	−13.0400	+	35.8272i	−0.426683	+	1.17230i
$935$	42.8492	−	51.0657i	1.40132	−	1.67003i
$936$	−27.6321	+	7.80350i	−0.903185	+	0.255065i
$937$	−7.90676	+	44.8415i	−0.258303	+	1.46491i	0.529148	+	0.848529i	$0.322512\pi$
$937$	−7.90676	+	44.8415i	−0.258303	+	1.46491i	−0.787451	+	0.616378i	$0.788600\pi$
$938$	8.45078	−	4.87906i	0.275928	−	0.159307i
$939$	43.8323	+	22.4446i	1.43041	+	0.732452i
$940$	−11.7598	−	9.86761i	−0.383561	−	0.321846i
$941$	−16.9379	−	14.2126i	−0.552160	−	0.463317i	0.323512	−	0.946224i	$-0.395137\pi$
$941$	−16.9379	−	14.2126i	−0.552160	−	0.463317i	−0.875672	+	0.482907i	$0.839581\pi$
$942$	0.472511	+	9.37602i	0.0153952	+	0.305487i
$943$	−4.85759	+	2.80453i	−0.158185	+	0.0913280i
$944$	−1.17302	+	6.65251i	−0.0381784	+	0.216521i
$945$	14.5890	−	16.5801i	0.474581	−	0.539350i
$946$	−0.888253	+	1.05858i	−0.0288796	+	0.0344174i
$947$	−9.32403	+	25.6176i	−0.302990	+	0.832459i	0.690986	+	0.722868i	$0.257176\pi$
$947$	−9.32403	+	25.6176i	−0.302990	+	0.832459i	−0.993977	+	0.109591i	$0.965046\pi$
$948$	−11.6020	+	10.7756i	−0.376816	+	0.349976i
$949$	−35.8016	+	20.6700i	−1.16217	+	0.670978i
$950$	31.2621	−	22.9241i	1.01428	−	0.743756i
$951$	4.43410	−	2.86691i	0.143786	−	0.0929658i
$952$	13.2736	+	15.8188i	0.430199	+	0.512691i
$953$	3.35186	+	19.0093i	0.108577	+	0.615773i	0.989731	+	0.142943i	$0.0456564\pi$
$953$	3.35186	+	19.0093i	0.108577	+	0.615773i	−0.881154	+	0.472830i	$0.843232\pi$
$954$	−18.8301	−	12.8113i	−0.609646	−	0.414781i
$955$	−22.4601	+	18.8463i	−0.726792	+	0.609851i
$956$	0.512561	−	0.610847i	0.0165774	−	0.0197562i
$957$	26.8802	−	52.4947i	0.868914	−	1.69691i
$958$	−34.7655	−	20.0719i	−1.12322	−	0.648492i
$959$	−1.11226	+	1.32554i	−0.0359168	+	0.0428039i
$960$	−49.3769	+	20.8424i	−1.59363	+	0.672686i
$961$	30.8173			0.994107
$962$	−0.154981	+	0.268436i	−0.00499680	+	0.00865472i
$963$	22.7785	−	10.9969i	0.734026	−	0.354369i
$964$	7.62312	+	9.08488i	0.245524	+	0.292604i
$965$	48.7410	−	17.7403i	1.56903	−	0.571080i
$966$	−4.98269	+	4.62778i	−0.160315	+	0.148896i
$967$	−2.02688	−	11.4950i	−0.0651802	−	0.369655i	−0.999898	−	0.0142650i	$-0.995459\pi$
$967$	−2.02688	−	11.4950i	−0.0651802	−	0.369655i	0.934718	−	0.355390i	$-0.115652\pi$
$968$	0.588963	+	1.02011i	0.0189300	+	0.0327877i
$969$	42.1709	+	0.635141i	1.35473	+	0.0204037i
$970$	−7.41220	+	12.8383i	−0.237991	+	0.412213i
$971$	−33.0882	−	12.0431i	−1.06185	−	0.386482i	−0.248727	−	0.968574i	$-0.580012\pi$
$971$	−33.0882	−	12.0431i	−1.06185	−	0.386482i	−0.813123	+	0.582092i	$0.802234\pi$
$972$	−0.904788	+	9.26953i	−0.0290211	+	0.297320i
$973$	−5.20461	−	4.36719i	−0.166852	−	0.140006i
$974$	12.0100	−	2.11769i	0.384826	−	0.0678553i
$975$	−32.2717	−	24.4202i	−1.03352	−	0.782072i
$976$	12.2173			0.391067
$977$	4.31674	−	7.47681i	0.138105	−	0.239204i	−0.788675	−	0.614811i	$-0.789232\pi$
$977$	4.31674	−	7.47681i	0.138105	−	0.239204i	0.926779	+	0.375607i	$0.122566\pi$
$978$	18.4429	−	24.3726i	0.589739	−	0.779351i
$979$	−3.29332	−	0.580702i	−0.105255	−	0.0185593i
$980$	−10.1678	+	5.87038i	−0.324799	+	0.187523i
$981$	−2.51156	−	24.8551i	−0.0801879	−	0.793563i
$982$	41.0286	+	7.23445i	1.30928	+	0.230861i
$983$	−3.66977	−	20.8123i	−0.117048	−	0.663810i	−0.985716	−	0.168416i	$-0.946135\pi$
$983$	−3.66977	−	20.8123i	−0.117048	−	0.663810i	0.868668	−	0.495394i	$-0.164976\pi$
$984$	6.53664	−	8.63829i	0.208381	−	0.275379i
$985$	13.0132	−	10.9194i	0.414636	−	0.347921i
$986$	−65.7545	+	11.5943i	−2.09405	+	0.369237i
$987$	15.1010	−	0.761025i	0.480670	−	0.0242237i
$988$	−5.60303	+	5.85343i	−0.178256	+	0.186222i
$989$		−	0.954125i		−	0.0303394i
$990$	−41.0955	−	10.4216i	−1.30610	−	0.331221i
$991$	−28.2694	+	4.98465i	−0.898006	+	0.158343i	−0.603553	−	0.797323i	$-0.706249\pi$
$991$	−28.2694	+	4.98465i	−0.898006	+	0.158343i	−0.294453	+	0.955666i	$0.595138\pi$
$992$	−0.475555	−	1.30658i	−0.0150989	−	0.0414838i
$993$	−26.1146	−	8.04138i	−0.828722	−	0.255186i
$994$	−18.6139	+	6.77491i	−0.590398	+	0.214887i
$995$			29.9357i			0.949025i
$996$	11.2311	−	0.565998i	0.355871	−	0.0179343i
$997$	4.49366	−	25.4848i	0.142316	−	0.807111i	−0.827168	−	0.561955i	$-0.810050\pi$
$997$	4.49366	−	25.4848i	0.142316	−	0.807111i	0.969483	−	0.245157i	$-0.0788394\pi$
$998$	−27.8683	+	10.1432i	−0.882155	+	0.321078i
$999$	0.273029	+	0.341345i	0.00863826	+	0.0107997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.110.6	yes	108
3.2	odd	2		513.2.bo.a.224.13		108
9.4	even	3		513.2.cd.a.395.6		108
9.5	odd	6		171.2.bd.a.167.13	yes	108
19.14	odd	18		171.2.bd.a.128.13	yes	108
57.14	even	18		513.2.cd.a.413.6		108
171.14	even	18	inner	171.2.x.a.14.6	✓	108
171.166	odd	18		513.2.bo.a.71.13		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.6	✓	108	171.14	even	18	inner
171.2.x.a.110.6	yes	108	1.1	even	1	trivial
171.2.bd.a.128.13	yes	108	19.14	odd	18
171.2.bd.a.167.13	yes	108	9.5	odd	6
513.2.bo.a.71.13		108	171.166	odd	18
513.2.bo.a.224.13		108	3.2	odd	2
513.2.cd.a.395.6		108	9.4	even	3
513.2.cd.a.413.6		108	57.14	even	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.907216 + 0.761244i) q^{2} +(0.509726 - 1.65535i) q^{3} +(-0.103749 + 0.588390i) q^{4} +(-1.20969 + 3.32360i) q^{5} +(0.797694 + 1.88978i) q^{6} +(0.600840 + 1.04068i) q^{7} +(-1.53807 - 2.66402i) q^{8} +(-2.48036 - 1.68755i) q^{9} +O(q^{10})\)	\(q+(-0.907216 + 0.761244i) q^{2} +(0.509726 - 1.65535i) q^{3} +(-0.103749 + 0.588390i) q^{4} +(-1.20969 + 3.32360i) q^{5} +(0.797694 + 1.88978i) q^{6} +(0.600840 + 1.04068i) q^{7} +(-1.53807 - 2.66402i) q^{8} +(-2.48036 - 1.68755i) q^{9} +(-1.43262 - 3.93610i) q^{10} +3.37386i q^{11} +(0.921107 + 0.471658i) q^{12} +(1.06414 + 2.92371i) q^{13} +(-1.33731 - 0.486740i) q^{14} +(4.88511 + 3.69659i) q^{15} +(2.30046 + 0.837300i) q^{16} +(-1.91063 + 5.24942i) q^{17} +(3.53486 - 0.357190i) q^{18} +(3.51512 - 2.57759i) q^{19} +(-1.83007 - 1.05659i) q^{20} +(2.02896 - 0.464135i) q^{21} +(-2.56833 - 3.06082i) q^{22} +(2.71688 + 0.479060i) q^{23} +(-5.19387 + 1.18813i) q^{24} +(-5.75276 - 4.82714i) q^{25} +(-3.19107 - 1.84236i) q^{26} +(-4.05778 + 3.24567i) q^{27} +(-0.674665 + 0.245558i) q^{28} +(1.75252 - 9.93902i) q^{29} +(-7.24586 + 0.365160i) q^{30} -0.427425i q^{31} +(3.05685 - 1.11260i) q^{32} +(5.58491 + 1.71974i) q^{33} +(-2.26273 - 6.21681i) q^{34} +(-4.18565 + 0.738044i) q^{35} +(1.25027 - 1.28434i) q^{36} -0.0841209i q^{37} +(-1.22679 + 5.01429i) q^{38} +(5.38219 - 0.271239i) q^{39} +(10.7147 - 1.88930i) q^{40} +(-1.55749 + 1.30689i) q^{41} +(-1.48738 + 1.96561i) q^{42} +(-0.0600559 - 0.340594i) q^{43} +(-1.98514 - 0.350034i) q^{44} +(8.60921 - 6.20232i) q^{45} +(-2.82948 + 1.63360i) q^{46} +(7.15417 + 1.26147i) q^{47} +(2.55863 - 3.38127i) q^{48} +(2.77798 - 4.81161i) q^{49} +8.89363 q^{50} +(7.71572 + 5.83852i) q^{51} +(-1.83069 + 0.322799i) q^{52} +(-4.91060 - 4.12048i) q^{53} +(1.21053 - 6.03349i) q^{54} +(-11.2134 - 4.08133i) q^{55} +(1.84827 - 3.20130i) q^{56} +(-2.47506 - 7.13261i) q^{57} +(5.97611 + 10.3509i) q^{58} +(0.479154 + 2.71742i) q^{59} +(-2.68186 + 2.49083i) q^{60} +(4.68956 - 1.70686i) q^{61} +(0.325375 + 0.387767i) q^{62} +(0.265907 - 3.59522i) q^{63} +(-4.37436 + 7.57662i) q^{64} -11.0045 q^{65} +(-6.37587 + 2.69131i) q^{66} +(-4.40746 + 5.25261i) q^{67} +(-2.89048 - 1.66882i) q^{68} +(2.17788 - 4.25320i) q^{69} +(3.23546 - 3.85587i) q^{70} +(10.6625 - 8.94693i) q^{71} +(-0.680687 + 9.20329i) q^{72} +(2.30724 + 13.0850i) q^{73} +(0.0640366 + 0.0763159i) q^{74} +(-10.9229 + 7.06231i) q^{75} +(1.15194 + 2.33568i) q^{76} +(-3.51112 + 2.02715i) q^{77} +(-4.67633 + 4.34323i) q^{78} +(-5.23326 + 14.3783i) q^{79} +(-5.56570 + 6.63295i) q^{80} +(3.30437 + 8.37145i) q^{81} +(0.418116 - 2.37126i) q^{82} +(9.41085 - 5.43336i) q^{83} +(0.0625900 + 1.24197i) q^{84} +(-15.1357 - 12.7004i) q^{85} +(0.313759 + 0.263275i) q^{86} +(-15.5592 - 7.96720i) q^{87} +(8.98802 - 5.18924i) q^{88} +(-0.172118 + 0.976130i) q^{89} +(-3.08893 + 12.1806i) q^{90} +(-2.40328 + 2.86412i) q^{91} +(-0.563748 + 1.54888i) q^{92} +(-0.707538 - 0.217870i) q^{93} +(-7.45066 + 4.30164i) q^{94} +(4.31467 + 14.8009i) q^{95} +(-0.283590 - 5.62728i) q^{96} +(-2.27491 - 2.71113i) q^{97} +(1.14258 + 6.47989i) q^{98} +(5.69355 - 8.36838i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Introduction

L-functions

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