LMFDB - Embedded newform 273.2.by.d.76.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(76,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("273.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.by (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			76.3
Character	$\chi$	$=$	273.76
Dual form			273.2.by.d.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.281068 + 1.04896i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.710736 + 0.410344i) q^{4} +(-1.02734 + 1.02734i) q^{5} +(-0.281068 - 1.04896i) q^{6} +(2.23270 + 1.41953i) q^{7} +(-2.16598 + 2.16598i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.281068 + 1.04896i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.710736 + 0.410344i) q^{4} +(-1.02734 + 1.02734i) q^{5} +(-0.281068 - 1.04896i) q^{6} +(2.23270 + 1.41953i) q^{7} +(-2.16598 + 2.16598i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.788887 - 1.36639i) q^{10} +(0.972198 + 0.260500i) q^{11} -0.820687 q^{12} +(-3.05530 - 1.91446i) q^{13} +(-2.11656 + 1.94303i) q^{14} +(0.376033 - 1.40338i) q^{15} +(-0.842549 - 1.45934i) q^{16} +(-2.37035 + 4.10557i) q^{17} +(0.767891 + 0.767891i) q^{18} +(0.391878 + 1.46251i) q^{19} +(-1.15173 + 0.308606i) q^{20} +(-2.64334 - 0.112997i) q^{21} +(-0.546507 + 0.946578i) q^{22} +(-0.337046 + 0.194594i) q^{23} +(0.792804 - 2.95878i) q^{24} +2.88914i q^{25} +(2.86693 - 2.66679i) q^{26} +1.00000i q^{27} +(1.00437 + 1.92508i) q^{28} +(-4.30065 - 7.44895i) q^{29} +(1.36639 + 0.788887i) q^{30} +(2.92542 - 2.92542i) q^{31} +(-4.14997 + 1.11198i) q^{32} +(-0.972198 + 0.260500i) q^{33} +(-3.64034 - 3.64034i) q^{34} +(-3.75209 + 0.835406i) q^{35} +(0.710736 - 0.410344i) q^{36} +(9.77690 + 2.61971i) q^{37} -1.64425 q^{38} +(3.60320 + 0.130321i) q^{39} -4.45041i q^{40} +(8.64616 + 2.31673i) q^{41} +(0.861486 - 2.74099i) q^{42} +(-8.28885 - 4.78557i) q^{43} +(0.584082 + 0.584082i) q^{44} +(0.376033 + 1.40338i) q^{45} +(-0.109388 - 0.408241i) q^{46} +(4.78928 + 4.78928i) q^{47} +(1.45934 + 0.842549i) q^{48} +(2.96989 + 6.33875i) q^{49} +(-3.03058 - 0.812042i) q^{50} -4.74070i q^{51} +(-1.38592 - 2.61440i) q^{52} +12.7329 q^{53} +(-1.04896 - 0.281068i) q^{54} +(-1.26640 + 0.731158i) q^{55} +(-7.91065 + 1.76131i) q^{56} +(-1.07063 - 1.07063i) q^{57} +(9.02241 - 2.41755i) q^{58} +(0.889636 - 0.238377i) q^{59} +(0.843127 - 0.843127i) q^{60} +(8.36449 + 4.82924i) q^{61} +(2.24640 + 3.89088i) q^{62} +(2.34570 - 1.22381i) q^{63} -8.03588i q^{64} +(5.10564 - 1.17203i) q^{65} -1.09301i q^{66} +(1.71328 - 6.39405i) q^{67} +(-3.36939 + 1.94532i) q^{68} +(0.194594 - 0.337046i) q^{69} +(0.178284 - 4.17059i) q^{70} +(-2.56663 + 0.687727i) q^{71} +(0.792804 + 2.95878i) q^{72} +(-2.46596 - 2.46596i) q^{73} +(-5.49594 + 9.51925i) q^{74} +(-1.44457 - 2.50206i) q^{75} +(-0.321609 + 1.20026i) q^{76} +(1.80084 + 1.96168i) q^{77} +(-1.14944 + 3.74297i) q^{78} +7.06532 q^{79} +(2.36483 + 0.633653i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.86031 + 8.41830i) q^{82} +(2.43414 - 2.43414i) q^{83} +(-1.83235 - 1.16499i) q^{84} +(-1.78266 - 6.65299i) q^{85} +(7.34959 - 7.34959i) q^{86} +(7.44895 + 4.30065i) q^{87} +(-2.67000 + 1.54152i) q^{88} +(2.79345 - 10.4253i) q^{89} -1.57777 q^{90} +(-4.10393 - 8.61149i) q^{91} -0.319401 q^{92} +(-1.07078 + 3.99619i) q^{93} +(-6.36986 + 3.67764i) q^{94} +(-1.90509 - 1.09990i) q^{95} +(3.03799 - 3.03799i) q^{96} +(3.55710 + 13.2753i) q^{97} +(-7.48383 + 1.33367i) q^{98} +(0.711699 - 0.711699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q - 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 16 * q^9	$ 32 q - 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 16 q^{9} + 2 q^{10} - 4 q^{11} + 32 q^{12} + 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} - 8 q^{17} + 2 q^{18} + 2 q^{19} + 44 q^{20} - 4 q^{21} - 4 q^{22} - 18 q^{23} + 4 q^{24} - 28 q^{26} - 32 q^{28} - 18 q^{29} - 14 q^{31} - 8 q^{32} + 4 q^{33} - 66 q^{34} + 22 q^{35} + 6 q^{36} - 24 q^{37} + 24 q^{38} + 8 q^{39} - 26 q^{42} - 6 q^{43} - 20 q^{44} + 4 q^{45} - 58 q^{46} - 28 q^{47} - 60 q^{48} + 8 q^{49} + 70 q^{50} + 28 q^{52} - 80 q^{53} - 4 q^{54} + 60 q^{55} - 54 q^{56} + 16 q^{57} - 4 q^{58} - 42 q^{59} - 58 q^{60} + 36 q^{61} + 52 q^{62} + 4 q^{63} + 14 q^{65} + 26 q^{67} - 72 q^{68} + 2 q^{69} - 116 q^{70} - 4 q^{71} + 4 q^{72} + 12 q^{73} - 18 q^{74} + 16 q^{75} - 48 q^{76} + 28 q^{77} - 14 q^{78} - 4 q^{79} - 98 q^{80} - 16 q^{81} + 20 q^{82} - 36 q^{83} - 18 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} - 54 q^{89} + 4 q^{90} + 148 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} + 22 q^{96} - 40 q^{97} + 36 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 16 * q^9 + 2 * q^10 - 4 * q^11 + 32 * q^12 + 6 * q^13 + 34 * q^14 + 4 * q^15 + 14 * q^16 - 8 * q^17 + 2 * q^18 + 2 * q^19 + 44 * q^20 - 4 * q^21 - 4 * q^22 - 18 * q^23 + 4 * q^24 - 28 * q^26 - 32 * q^28 - 18 * q^29 - 14 * q^31 - 8 * q^32 + 4 * q^33 - 66 * q^34 + 22 * q^35 + 6 * q^36 - 24 * q^37 + 24 * q^38 + 8 * q^39 - 26 * q^42 - 6 * q^43 - 20 * q^44 + 4 * q^45 - 58 * q^46 - 28 * q^47 - 60 * q^48 + 8 * q^49 + 70 * q^50 + 28 * q^52 - 80 * q^53 - 4 * q^54 + 60 * q^55 - 54 * q^56 + 16 * q^57 - 4 * q^58 - 42 * q^59 - 58 * q^60 + 36 * q^61 + 52 * q^62 + 4 * q^63 + 14 * q^65 + 26 * q^67 - 72 * q^68 + 2 * q^69 - 116 * q^70 - 4 * q^71 + 4 * q^72 + 12 * q^73 - 18 * q^74 + 16 * q^75 - 48 * q^76 + 28 * q^77 - 14 * q^78 - 4 * q^79 - 98 * q^80 - 16 * q^81 + 20 * q^82 - 36 * q^83 - 18 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 - 54 * q^89 + 4 * q^90 + 148 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 + 22 * q^96 - 40 * q^97 + 36 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$-1$

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 $

$2$	−0.281068	+	1.04896i	−0.198745	+	0.741726i	0.792521	+	0.609845i	$0.208768\pi$
$2$	−0.281068	+	1.04896i	−0.198745	+	0.741726i	−0.991266	+	0.131881i	$0.957898\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.710736	+	0.410344i	0.355368	+	0.205172i
$5$	−1.02734	+	1.02734i	−0.459441	+	0.459441i	−0.898472	−	0.439031i	$-0.855322\pi$
$5$	−1.02734	+	1.02734i	−0.459441	+	0.459441i	0.439031	+	0.898472i	$0.355322\pi$
$6$	−0.281068	−	1.04896i	−0.114745	−	0.428235i
$7$	2.23270	+	1.41953i	0.843881	+	0.536531i
$7$	2.23270	+	1.41953i	0.843881	+	0.536531i
$8$	−2.16598	+	2.16598i	−0.765790	+	0.765790i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.788887	−	1.36639i	−0.249468	−	0.432091i
$11$	0.972198	+	0.260500i	0.293129	+	0.0785436i	0.402387	−	0.915470i	$-0.368181\pi$
$11$	0.972198	+	0.260500i	0.293129	+	0.0785436i	−0.109258	+	0.994013i	$0.534847\pi$
$12$	−0.820687			−0.236912
$13$	−3.05530	−	1.91446i	−0.847387	−	0.530975i
$13$	−3.05530	−	1.91446i	−0.847387	−	0.530975i
$14$	−2.11656	+	1.94303i	−0.565676	+	0.519295i
$15$	0.376033	−	1.40338i	0.0970914	−	0.362350i
$16$	−0.842549	−	1.45934i	−0.210637	−	0.364834i
$17$	−2.37035	+	4.10557i	−0.574895	+	0.995747i	0.421159	+	0.906987i	$0.361624\pi$
$17$	−2.37035	+	4.10557i	−0.574895	+	0.995747i	−0.996053	+	0.0887595i	$0.971710\pi$
$18$	0.767891	+	0.767891i	0.180994	+	0.180994i
$19$	0.391878	+	1.46251i	0.0899030	+	0.335522i	0.996197	−	0.0871243i	$-0.0277677\pi$
$19$	0.391878	+	1.46251i	0.0899030	+	0.335522i	−0.906294	+	0.422647i	$0.861101\pi$
$20$	−1.15173	+	0.308606i	−0.257535	+	0.0690064i
$21$	−2.64334	−	0.112997i	−0.576823	−	0.0246580i
$22$	−0.546507	+	0.946578i	−0.116516	+	0.201811i
$23$	−0.337046	+	0.194594i	−0.0702790	+	0.0405756i	−0.534728	−	0.845024i	$-0.679586\pi$
$23$	−0.337046	+	0.194594i	−0.0702790	+	0.0405756i	0.464449	+	0.885600i	$0.346252\pi$
$24$	0.792804	−	2.95878i	0.161830	−	0.603959i
$25$			2.88914i			0.577827i
$26$	2.86693	−	2.66679i	0.562252	−	0.523000i
$27$			1.00000i			0.192450i
$28$	1.00437	+	1.92508i	0.189807	+	0.363806i
$29$	−4.30065	−	7.44895i	−0.798611	−	1.38324i	−0.920521	−	0.390694i	$-0.872235\pi$
$29$	−4.30065	−	7.44895i	−0.798611	−	1.38324i	0.121909	−	0.992541i	$-0.461098\pi$
$30$	1.36639	+	0.788887i	0.249468	+	0.144030i
$31$	2.92542	−	2.92542i	0.525420	−	0.525420i	−0.393783	−	0.919203i	$-0.628834\pi$
$31$	2.92542	−	2.92542i	0.525420	−	0.525420i	0.919203	+	0.393783i	$0.128834\pi$
$32$	−4.14997	+	1.11198i	−0.733618	+	0.196572i
$33$	−0.972198	+	0.260500i	−0.169238	+	0.0453472i
$34$	−3.64034	−	3.64034i	−0.624313	−	0.624313i
$35$	−3.75209	+	0.835406i	−0.634218	+	0.141209i
$36$	0.710736	−	0.410344i	0.118456	−	0.0683906i
$37$	9.77690	+	2.61971i	1.60731	+	0.430678i	0.947240	−	0.320524i	$-0.103859\pi$
$37$	9.77690	+	2.61971i	1.60731	+	0.430678i	0.660072	+	0.751202i	$0.270526\pi$
$38$	−1.64425			−0.266733
$39$	3.60320	+	0.130321i	0.576973	+	0.0208681i
$40$		−	4.45041i		−	0.703671i
$41$	8.64616	+	2.31673i	1.35030	+	0.361813i	0.860247	−	0.509878i	$-0.170310\pi$
$41$	8.64616	+	2.31673i	1.35030	+	0.361813i	0.490056	+	0.871691i	$0.336976\pi$
$42$	0.861486	−	2.74099i	0.132930	−	0.422944i
$43$	−8.28885	−	4.78557i	−1.26404	−	0.729792i	−0.290184	−	0.956971i	$-0.593717\pi$
$43$	−8.28885	−	4.78557i	−1.26404	−	0.729792i	−0.973853	+	0.227179i	$0.927050\pi$
$44$	0.584082	+	0.584082i	0.0880537	+	0.0880537i
$45$	0.376033	+	1.40338i	0.0560558	+	0.209203i
$46$	−0.109388	−	0.408241i	−0.0161284	−	0.0601919i
$47$	4.78928	+	4.78928i	0.698588	+	0.698588i	0.964106	−	0.265518i	$-0.0855430\pi$
$47$	4.78928	+	4.78928i	0.698588	+	0.698588i	−0.265518	+	0.964106i	$0.585543\pi$
$48$	1.45934	+	0.842549i	0.210637	+	0.121611i
$49$	2.96989	+	6.33875i	0.424269	+	0.905536i
$50$	−3.03058	−	0.812042i	−0.428589	−	0.114840i
$51$		−	4.74070i		−	0.663831i
$52$	−1.38592	−	2.61440i	−0.192193	−	0.362552i
$53$	12.7329			1.74900			0.874498	−	0.485029i	$-0.161191\pi$
$53$	12.7329			1.74900			0.874498	+	0.485029i	$0.161191\pi$
$54$	−1.04896	−	0.281068i	−0.142745	−	0.0382484i
$55$	−1.26640	+	0.731158i	−0.170762	+	0.0985893i
$56$	−7.91065	+	1.76131i	−1.05710	+	0.235365i
$57$	−1.07063	−	1.07063i	−0.141808	−	0.141808i
$58$	9.02241	−	2.41755i	1.18470	−	0.317440i
$59$	0.889636	−	0.238377i	0.115821	−	0.0310341i	−0.200443	−	0.979705i	$-0.564238\pi$
$59$	0.889636	−	0.238377i	0.115821	−	0.0310341i	0.316264	+	0.948671i	$0.397572\pi$
$60$	0.843127	−	0.843127i	0.108847	−	0.108847i
$61$	8.36449	+	4.82924i	1.07096	+	0.618321i	0.928445	−	0.371471i	$-0.121146\pi$
$61$	8.36449	+	4.82924i	1.07096	+	0.618321i	0.142519	+	0.989792i	$0.454480\pi$
$62$	2.24640	+	3.89088i	0.285293	+	0.494142i
$63$	2.34570	−	1.22381i	0.295530	−	0.154186i
$64$		−	8.03588i		−	1.00449i
$65$	5.10564	−	1.17203i	0.633277	−	0.145373i
$66$		−	1.09301i		−	0.134541i
$67$	1.71328	−	6.39405i	0.209311	−	0.781158i	−0.778782	−	0.627295i	$-0.784162\pi$
$67$	1.71328	−	6.39405i	0.209311	−	0.781158i	0.988092	−	0.153863i	$-0.0491713\pi$
$68$	−3.36939	+	1.94532i	−0.408598	+	0.235904i
$69$	0.194594	−	0.337046i	0.0234263	−	0.0405756i
$70$	0.178284	−	4.17059i	0.0213090	−	0.498481i
$71$	−2.56663	+	0.687727i	−0.304603	+	0.0816182i	−0.407883	−	0.913034i	$-0.633733\pi$
$71$	−2.56663	+	0.687727i	−0.304603	+	0.0816182i	0.103280	+	0.994652i	$0.467066\pi$
$72$	0.792804	+	2.95878i	0.0934328	+	0.348696i
$73$	−2.46596	−	2.46596i	−0.288619	−	0.288619i	0.547915	−	0.836534i	$-0.315422\pi$
$73$	−2.46596	−	2.46596i	−0.288619	−	0.288619i	−0.836534	+	0.547915i	$0.815422\pi$
$74$	−5.49594	+	9.51925i	−0.638890	+	1.10659i
$75$	−1.44457	−	2.50206i	−0.166804	−	0.288914i
$76$	−0.321609	+	1.20026i	−0.0368911	+	0.137680i
$77$	1.80084	+	1.96168i	0.205225	+	0.223554i
$78$	−1.14944	+	3.74297i	−0.130149	+	0.423808i
$79$	7.06532			0.794911			0.397455	−	0.917622i	$-0.369893\pi$
$79$	7.06532			0.794911			0.397455	+	0.917622i	$0.369893\pi$
$80$	2.36483	+	0.633653i	0.264396	+	0.0708446i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.86031	+	8.41830i	−0.536731	+	0.929646i
$83$	2.43414	−	2.43414i	0.267181	−	0.267181i	−0.560782	−	0.827963i	$-0.689499\pi$
$83$	2.43414	−	2.43414i	0.267181	−	0.267181i	0.827963	+	0.560782i	$0.189499\pi$
$84$	−1.83235	−	1.16499i	−0.199925	−	0.127111i
$85$	−1.78266	−	6.65299i	−0.193357	−	0.721618i
$86$	7.34959	−	7.34959i	0.792526	−	0.792526i
$87$	7.44895	+	4.30065i	0.798611	+	0.461078i
$88$	−2.67000	+	1.54152i	−0.284623	+	0.164327i
$89$	2.79345	−	10.4253i	0.296105	−	1.10508i	−0.644231	−	0.764831i	$-0.722822\pi$
$89$	2.79345	−	10.4253i	0.296105	−	1.10508i	0.940336	−	0.340248i	$-0.110511\pi$
$90$	−1.57777			−0.166312
$91$	−4.10393	−	8.61149i	−0.430209	−	0.902729i
$92$	−0.319401			−0.0332999
$93$	−1.07078	+	3.99619i	−0.111034	+	0.414386i
$94$	−6.36986	+	3.67764i	−0.657001	+	0.379320i
$95$	−1.90509	−	1.09990i	−0.195458	−	0.112848i
$96$	3.03799	−	3.03799i	0.310063	−	0.310063i
$97$	3.55710	+	13.2753i	0.361169	+	1.34790i	0.872541	+	0.488541i	$0.162471\pi$
$97$	3.55710	+	13.2753i	0.361169	+	1.34790i	−0.511372	+	0.859359i	$0.670863\pi$
$98$	−7.48383	+	1.33367i	−0.755981	+	0.134721i
$99$	0.711699	−	0.711699i	0.0715284	−	0.0715284i
$100$	−1.18554	+	2.05341i	−0.118554	+	0.205341i
$101$	1.97748	+	3.42510i	0.196767	+	0.340810i	0.947478	−	0.319820i	$-0.103622\pi$
$101$	1.97748	+	3.42510i	0.196767	+	0.340810i	−0.750711	+	0.660630i	$0.770289\pi$
$102$	4.97280	+	1.33246i	0.492380	+	0.131933i
$103$	−12.7709			−1.25835			−0.629176	−	0.777263i	$-0.716607\pi$
$103$	−12.7709			−1.25835			−0.629176	+	0.777263i	$0.716607\pi$
$104$	10.7644	−	2.47103i	1.05554	−	0.242305i
$105$	2.83170	−	2.59953i	0.276346	−	0.253688i
$106$	−3.57880	+	13.3563i	−0.347604	+	1.29728i
$107$	1.79997	+	3.11764i	0.174010	+	0.301394i	0.939818	−	0.341675i	$-0.110994\pi$
$107$	1.79997	+	3.11764i	0.174010	+	0.301394i	−0.765808	+	0.643069i	$0.777661\pi$
$108$	−0.410344	+	0.710736i	−0.0394853	+	0.0683906i
$109$	−0.0623175	−	0.0623175i	−0.00596893	−	0.00596893i	0.704116	−	0.710085i	$-0.251343\pi$
$109$	−0.0623175	−	0.0623175i	−0.00596893	−	0.00596893i	−0.710085	+	0.704116i	$0.751343\pi$
$110$	−0.411010	−	1.53391i	−0.0391882	−	0.146252i
$111$	−9.77690	+	2.61971i	−0.927983	+	0.248652i
$112$	0.190411	−	4.45428i	0.0179922	−	0.420890i
$113$	−1.09268	+	1.89259i	−0.102791	+	0.178039i	−0.912834	−	0.408332i	$-0.866111\pi$
$113$	−1.09268	+	1.89259i	−0.102791	+	0.178039i	0.810042	+	0.586371i	$0.199444\pi$
$114$	1.42397	−	0.822127i	0.133367	−	0.0769993i
$115$	0.146347	−	0.546176i	0.0136470	−	0.0509312i
$116$		−	7.05898i		−	0.655410i
$117$	−3.18562	+	1.68874i	−0.294511	+	0.156124i
$118$			1.00019i			0.0920751i
$119$	−11.1202	+	5.80172i	−1.01939	+	0.531843i
$120$	2.22520	+	3.85416i	0.203132	+	0.351835i
$121$	−8.64897	−	4.99349i	−0.786270	−	0.453953i
$122$	−7.41666	+	7.41666i	−0.671473	+	0.671473i
$123$	−8.64616	+	2.31673i	−0.779598	+	0.208893i
$124$	3.27962	−	0.878773i	0.294519	−	0.0789161i
$125$	−8.10484	−	8.10484i	−0.724919	−	0.724919i
$126$	0.624427	+	2.80451i	0.0556284	+	0.249846i
$127$	−12.3666	+	7.13987i	−1.09736	+	0.633561i	−0.935526	−	0.353257i	$-0.885074\pi$
$127$	−12.3666	+	7.13987i	−1.09736	+	0.633561i	−0.161834	+	0.986818i	$0.551741\pi$
$128$	0.129367	+	0.0346639i	0.0114346	+	0.00306389i
$129$	9.57113			0.842691
$130$	−0.205617	+	5.68503i	−0.0180338	+	0.498610i
$131$		−	17.8888i		−	1.56295i	−0.623934	−	0.781477i	$-0.714467\pi$
$131$		−	17.8888i		−	1.56295i	0.623934	−	0.781477i	$-0.285533\pi$
$132$	−0.797871	−	0.213789i	−0.0694457	−	0.0186079i
$133$	−1.20112	+	3.82162i	−0.104151	+	0.331377i
$134$	6.22555	+	3.59432i	0.537805	+	0.310502i
$135$	−1.02734	−	1.02734i	−0.0884196	−	0.0884196i
$136$	−3.75845	−	14.0267i	−0.322284	−	1.20278i
$137$	−0.654988	−	2.44445i	−0.0559594	−	0.208843i	0.932285	−	0.361724i	$-0.117812\pi$
$137$	−0.654988	−	2.44445i	−0.0559594	−	0.208843i	−0.988245	+	0.152881i	$0.951145\pi$
$138$	0.298853	+	0.298853i	0.0254401	+	0.0254401i
$139$	−8.86338	−	5.11727i	−0.751782	−	0.434041i	0.0745556	−	0.997217i	$-0.476246\pi$
$139$	−8.86338	−	5.11727i	−0.751782	−	0.434041i	−0.826337	+	0.563176i	$0.809579\pi$
$140$	−3.00955	−	0.945892i	−0.254353	−	0.0799424i
$141$	−6.54227	−	1.75300i	−0.550959	−	0.147629i
$142$		−	2.88559i		−	0.242153i
$143$	−2.47164	−	2.65714i	−0.206689	−	0.222201i
$144$	−1.68510			−0.140425
$145$	12.0709	+	3.23438i	1.00243	+	0.268601i
$146$	3.27979	−	1.89359i	0.271437	−	0.156714i
$147$	−5.74137	−	4.00458i	−0.473540	−	0.330292i
$148$	5.87381	+	5.87381i	0.482825	+	0.482825i
$149$	8.14575	−	2.18265i	0.667326	−	0.178809i	0.0907761	−	0.995871i	$-0.471065\pi$
$149$	8.14575	−	2.18265i	0.667326	−	0.178809i	0.576550	+	0.817062i	$0.304399\pi$
$150$	3.03058	−	0.812042i	0.247446	−	0.0663030i
$151$	−0.453678	+	0.453678i	−0.0369198	+	0.0369198i	−0.725326	−	0.688406i	$-0.758311\pi$
$151$	−0.453678	+	0.453678i	−0.0369198	+	0.0369198i	0.688406	+	0.725326i	$0.258311\pi$
$152$	−4.01656	−	2.31896i	−0.325786	−	0.188093i
$153$	2.37035	+	4.10557i	0.191632	+	0.331916i
$154$	−2.56388	+	1.33764i	−0.206603	+	0.107790i
$155$			6.01081i			0.482800i
$156$	2.50744	+	1.57117i	0.200756	+	0.125794i
$157$		−	8.10530i		−	0.646874i	−0.946250	−	0.323437i	$-0.895162\pi$
$157$		−	8.10530i		−	0.646874i	0.946250	−	0.323437i	$-0.104838\pi$
$158$	−1.98583	+	7.41123i	−0.157984	+	0.589606i
$159$	−11.0270	+	6.36644i	−0.874498	+	0.504892i
$160$	3.12105	−	5.40583i	0.246741	−	0.427368i
$161$	−1.02875	−	0.0439771i	−0.0810771	−	0.00346588i
$162$	1.04896	−	0.281068i	0.0824140	−	0.0220828i
$163$	3.55525	+	13.2684i	0.278469	+	1.03926i	0.953481	+	0.301453i	$0.0974717\pi$
$163$	3.55525	+	13.2684i	0.278469	+	1.03926i	−0.675012	+	0.737807i	$0.735862\pi$
$164$	5.19448	+	5.19448i	0.405621	+	0.405621i
$165$	0.731158	−	1.26640i	0.0569206	−	0.0985893i
$166$	1.86915	+	3.23746i	0.145074	+	0.251276i
$167$	5.75214	−	21.4673i	0.445114	−	1.66119i	−0.270523	−	0.962714i	$-0.587196\pi$
$167$	5.75214	−	21.4673i	0.445114	−	1.66119i	0.715636	−	0.698473i	$-0.246137\pi$
$168$	5.97016	−	5.48067i	0.460608	−	0.422843i
$169$	5.66969	+	11.6985i	0.436130	+	0.899884i
$170$	7.47975			0.573671
$171$	1.46251	+	0.391878i	0.111841	+	0.0299677i
$172$	−3.92745	−	6.80255i	−0.299466	−	0.518690i
$173$	−6.33728	+	10.9765i	−0.481815	+	0.834527i	−0.999782	−	0.0208728i	$-0.993355\pi$
$173$	−6.33728	+	10.9765i	−0.481815	+	0.834527i	0.517967	+	0.855400i	$0.326689\pi$
$174$	−6.60487	+	6.60487i	−0.500714	+	0.500714i
$175$	−4.10121	+	6.45057i	−0.310022	+	0.487617i
$176$	−0.438968	−	1.63825i	−0.0330884	−	0.123488i
$177$	−0.651259	+	0.651259i	−0.0489516	+	0.0489516i
$178$	10.1505	+	5.86042i	0.760816	+	0.439257i
$179$	9.48849	−	5.47818i	0.709203	−	0.409459i	−0.101563	−	0.994829i	$-0.532384\pi$
$179$	9.48849	−	5.47818i	0.709203	−	0.409459i	0.810766	+	0.585370i	$0.199051\pi$
$180$	−0.308606	+	1.15173i	−0.0230021	+	0.0858451i
$181$	−4.38394			−0.325856			−0.162928	−	0.986638i	$-0.552094\pi$
$181$	−4.38394			−0.325856			−0.162928	+	0.986638i	$0.552094\pi$
$182$	10.1866	−	1.88445i	0.755079	−	0.139684i
$183$	−9.65848			−0.713976
$184$	0.308549	−	1.15152i	0.0227466	−	0.0848913i
$185$	−12.7356	+	7.35288i	−0.936338	+	0.540595i
$186$	−3.89088	−	2.24640i	−0.285293	−	0.164714i
$187$	−3.37395	+	3.37395i	−0.246728	+	0.246728i
$188$	1.43866	+	5.36916i	0.104925	+	0.391586i
$189$	−1.41953	+	2.23270i	−0.103255	+	0.162405i
$190$	1.68921	−	1.68921i	0.122548	−	0.122548i
$191$	−4.92507	+	8.53047i	−0.356366	+	0.617243i	−0.987351	−	0.158552i	$-0.949318\pi$
$191$	−4.92507	+	8.53047i	−0.356366	+	0.617243i	0.630985	+	0.775795i	$0.282651\pi$
$192$	4.01794	+	6.95928i	0.289970	+	0.502243i
$193$	12.2874	+	3.29240i	0.884465	+	0.236992i	0.672333	−	0.740249i	$-0.265292\pi$
$193$	12.2874	+	3.29240i	0.884465	+	0.236992i	0.212133	+	0.977241i	$0.431959\pi$
$194$	−14.9250			−1.07155
$195$	−3.83560	+	3.56783i	−0.274673	+	0.255498i
$196$	−0.490261	+	5.72385i	−0.0350187	+	0.408847i
$197$	−0.404048	+	1.50793i	−0.0287873	+	0.107436i	−0.978825	−	0.204701i	$-0.934378\pi$
$197$	−0.404048	+	1.50793i	−0.0287873	+	0.107436i	0.950037	+	0.312136i	$0.101045\pi$
$198$	0.546507	+	0.946578i	0.0388385	+	0.0672703i
$199$	−5.84499	+	10.1238i	−0.414340	+	0.717659i	−0.995359	−	0.0962317i	$-0.969321\pi$
$199$	−5.84499	+	10.1238i	−0.414340	+	0.717659i	0.581019	+	0.813890i	$0.302654\pi$
$200$	−6.25781	−	6.25781i	−0.442494	−	0.442494i
$201$	1.71328	+	6.39405i	0.120846	+	0.451002i
$202$	−4.14860	+	1.11161i	−0.291894	+	0.0782128i
$203$	0.971923	−	22.7362i	0.0682156	−	1.59577i
$204$	1.94532	−	3.36939i	0.136199	−	0.235904i
$205$	−11.2626	+	6.50249i	−0.786617	+	0.454153i
$206$	3.58948	−	13.3961i	0.250091	−	0.933351i
$207$			0.389187i			0.0270504i
$208$	−0.219604	+	6.07174i	−0.0152268	+	0.420999i
$209$			1.52393i			0.105413i
$210$	1.93090	+	3.70098i	0.133244	+	0.255392i
$211$	−11.0809	−	19.1926i	−0.762838	−	1.32127i	−0.941382	−	0.337343i	$-0.890472\pi$
$211$	−11.0809	−	19.1926i	−0.762838	−	1.32127i	0.178544	−	0.983932i	$-0.442861\pi$
$212$	9.04972	+	5.22486i	0.621537	+	0.358845i
$213$	1.87891	−	1.87891i	0.128740	−	0.128740i
$214$	−3.77619	+	1.01183i	−0.258135	+	0.0691670i
$215$	13.4319	−	3.59907i	0.916048	−	0.245454i
$216$	−2.16598	−	2.16598i	−0.147376	−	0.147376i
$217$	10.6843	−	2.37887i	0.725296	−	0.161488i
$218$	0.0828838	−	0.0478530i	0.00561360	−	0.00324101i
$219$	3.36856	+	0.902603i	0.227626	+	0.0609923i
$220$	−1.20010			−0.0809110
$221$	15.1021	−	8.00580i	1.01588	−	0.538528i
$222$		−	10.9919i		−	0.737727i
$223$	13.2842	+	3.55949i	0.889575	+	0.238361i	0.674534	−	0.738244i	$-0.264345\pi$
$223$	13.2842	+	3.55949i	0.889575	+	0.238361i	0.215041	+	0.976605i	$0.431011\pi$
$224$	−10.8441	−	3.40828i	−0.724553	−	0.227725i
$225$	2.50206	+	1.44457i	0.166804	+	0.0963045i
$226$	−1.67813	−	1.67813i	−0.111627	−	0.111627i
$227$	1.04021	+	3.88213i	0.0690413	+	0.257666i	0.991816	−	0.127674i	$-0.0407510\pi$
$227$	1.04021	+	3.88213i	0.0690413	+	0.257666i	−0.922775	+	0.385339i	$0.874084\pi$
$228$	−0.321609	−	1.20026i	−0.0212991	−	0.0794893i
$229$	−1.36272	−	1.36272i	−0.0900509	−	0.0900509i	0.660646	−	0.750697i	$-0.270282\pi$
$229$	−1.36272	−	1.36272i	−0.0900509	−	0.0900509i	−0.750697	+	0.660646i	$0.770282\pi$
$230$	0.531783	+	0.307025i	0.0350647	+	0.0202446i
$231$	−2.54041	−	0.798444i	−0.167147	−	0.0525338i
$232$	25.4494	+	6.81915i	1.67084	+	0.447699i
$233$		−	1.13013i		−	0.0740376i	−0.999315	−	0.0370188i	$-0.988214\pi$
$233$		−	1.13013i		−	0.0740376i	0.999315	−	0.0370188i	$-0.0117861\pi$
$234$	−0.876040	−	3.81623i	−0.0572685	−	0.249475i
$235$	−9.84046			−0.641921
$236$	0.730113	+	0.195633i	0.0475263	+	0.0127346i
$237$	−6.11875	+	3.53266i	−0.397455	+	0.229471i
$238$	−2.96022	−	13.2953i	−0.191883	−	0.861809i
$239$	3.62833	+	3.62833i	0.234697	+	0.234697i	0.814650	−	0.579953i	$-0.196929\pi$
$239$	3.62833	+	3.62833i	0.234697	+	0.234697i	−0.579953	+	0.814650i	$0.696929\pi$
$240$	−2.36483	+	0.633653i	−0.152649	+	0.0409021i
$241$	9.46780	−	2.53689i	0.609875	−	0.163415i	0.0593540	−	0.998237i	$-0.481096\pi$
$241$	9.46780	−	2.53689i	0.609875	−	0.163415i	0.550521	+	0.834822i	$0.314429\pi$
$242$	7.66890	−	7.66890i	0.492976	−	0.492976i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	3.96330	+	6.86463i	0.253724	+	0.439463i
$245$	−9.56316	−	3.46098i	−0.610968	−	0.221114i
$246$		−	9.72062i		−	0.619764i
$247$	1.60261	−	5.21863i	0.101972	−	0.332054i
$248$			12.6728i			0.804723i
$249$	−0.890956	+	3.32509i	−0.0564620	+	0.210719i
$250$	10.7797	−	6.22363i	0.681765	−	0.393617i
$251$	14.1820	−	24.5639i	0.895158	−	1.55046i	0.0615480	−	0.998104i	$-0.480396\pi$
$251$	14.1820	−	24.5639i	0.895158	−	1.55046i	0.833610	−	0.552354i	$-0.186270\pi$
$252$	2.16935	+	0.0927353i	0.136656	+	0.00584178i
$253$	−0.378367	+	0.101383i	−0.0237878	+	0.00637391i
$254$	−4.01357	−	14.9789i	−0.251834	−	0.939857i
$255$	4.87032	+	4.87032i	0.304992	+	0.304992i
$256$	7.96316	−	13.7926i	0.497698	−	0.862037i
$257$	3.32083	+	5.75185i	0.207148	+	0.358790i	0.950815	−	0.309760i	$-0.100249\pi$
$257$	3.32083	+	5.75185i	0.207148	+	0.358790i	−0.743667	+	0.668550i	$0.766915\pi$
$258$	−2.69014	+	10.0397i	−0.167481	+	0.625046i
$259$	18.1101	+	19.7276i	1.12531	+	1.22581i
$260$	4.10970	+	1.26206i	0.254873	+	0.0782698i
$261$	−8.60131			−0.532408
$262$	18.7646	+	5.02797i	1.15928	+	0.310629i
$263$	−6.24723	−	10.8205i	−0.385221	−	0.667222i	0.606579	−	0.795023i	$-0.292541\pi$
$263$	−6.24723	−	10.8205i	−0.385221	−	0.667222i	−0.991800	+	0.127801i	$0.959208\pi$
$264$	1.54152	−	2.67000i	0.0948743	−	0.164327i
$265$	−13.0810	+	13.0810i	−0.803561	+	0.803561i
$266$	−3.67113	−	2.33406i	−0.225091	−	0.143111i
$267$	2.79345	+	10.4253i	0.170956	+	0.638017i
$268$	3.84145	−	3.84145i	0.234654	−	0.234654i
$269$	−7.27737	−	4.20159i	−0.443709	−	0.256176i	0.261460	−	0.965214i	$-0.415796\pi$
$269$	−7.27737	−	4.20159i	−0.443709	−	0.256176i	−0.705170	+	0.709038i	$0.749129\pi$
$270$	1.36639	−	0.788887i	0.0831560	−	0.0480101i
$271$	−0.0939748	+	0.350719i	−0.00570857	+	0.0213047i	−0.968721	−	0.248151i	$-0.920177\pi$
$271$	−0.0939748	+	0.350719i	−0.00570857	+	0.0213047i	0.963013	+	0.269456i	$0.0868438\pi$
$272$	7.98855			0.484377
$273$	7.85986	+	5.40580i	0.475700	+	0.327174i
$274$	2.74822			0.166026
$275$	−0.752619	+	2.80881i	−0.0453846	+	0.169378i
$276$	0.276610	−	0.159701i	0.0166499	−	0.00961285i
$277$	13.5251	+	7.80875i	0.812647	+	0.469182i	0.847874	−	0.530197i	$-0.177882\pi$
$277$	13.5251	+	7.80875i	0.812647	+	0.469182i	−0.0352270	+	0.999379i	$0.511215\pi$
$278$	7.85901	−	7.85901i	0.471352	−	0.471352i
$279$	−1.07078	−	3.99619i	−0.0641057	−	0.239246i
$280$	6.31747	−	9.93642i	0.377541	−	0.593814i
$281$	−0.848694	+	0.848694i	−0.0506289	+	0.0506289i	−0.731968	−	0.681339i	$-0.761398\pi$
$281$	−0.848694	+	0.848694i	−0.0506289	+	0.0506289i	0.681339	+	0.731968i	$0.261398\pi$
$282$	3.67764	−	6.36986i	0.219000	−	0.379320i
$283$	−11.9723	−	20.7366i	−0.711678	−	1.23266i	−0.964227	−	0.265078i	$-0.914602\pi$
$283$	−11.9723	−	20.7366i	−0.711678	−	1.23266i	0.252549	−	0.967584i	$-0.418731\pi$
$284$	−2.10640	−	0.564409i	−0.124992	−	0.0334915i
$285$	2.19981			0.130305
$286$	3.48193	−	1.84581i	0.205891	−	0.109145i
$287$	16.0156	+	17.4460i	0.945371	+	1.02981i
$288$	−1.11198	+	4.14997i	−0.0655241	+	0.244539i
$289$	−2.73713	−	4.74084i	−0.161007	−	0.278873i
$290$	−6.78546	+	11.7528i	−0.398456	+	0.690146i
$291$	−9.71818	−	9.71818i	−0.569690	−	0.569690i
$292$	−0.740755	−	2.76454i	−0.0433494	−	0.161782i
$293$	18.6502	−	4.99730i	1.08956	−	0.291946i	0.331051	−	0.943613i	$-0.392597\pi$
$293$	18.6502	−	4.99730i	1.08956	−	0.291946i	0.758505	+	0.651667i	$0.225930\pi$
$294$	5.81435	−	4.89690i	0.339100	−	0.285593i
$295$	−0.669066	+	1.15886i	−0.0389545	+	0.0674712i
$296$	−26.8508	+	15.5023i	−1.56067	+	0.901055i
$297$	−0.260500	+	0.972198i	−0.0151157	+	0.0564127i
$298$			9.15803i			0.530510i
$299$	1.40232	+	0.0507193i	0.0810982	+	0.00293317i
$300$		−	2.37108i		−	0.136894i
$301$	−11.7133	−	22.4510i	−0.675141	−	1.29405i
$302$	−0.348375	−	0.603403i	−0.0200467	−	0.0347220i
$303$	−3.42510	−	1.97748i	−0.196767	−	0.113603i
$304$	1.80412	−	1.80412i	0.103473	−	0.103473i
$305$	−13.5545	+	3.63191i	−0.776127	+	0.207963i
$306$	−4.97280	+	1.33246i	−0.284276	+	0.0761715i
$307$	−17.1942	−	17.1942i	−0.981322	−	0.981322i	0.0185063	−	0.999829i	$-0.494109\pi$
$307$	−17.1942	−	17.1942i	−0.981322	−	0.981322i	−0.999829	+	0.0185063i	$0.994109\pi$
$308$	0.474959	+	2.13320i	0.0270633	+	0.121550i
$309$	11.0599	−	6.38543i	0.629176	−	0.363255i
$310$	−6.30509	−	1.68944i	−0.358105	−	0.0959539i
$311$	−14.0638			−0.797487			−0.398744	−	0.917062i	$-0.630554\pi$
$311$	−14.0638			−0.797487			−0.398744	+	0.917062i	$0.630554\pi$
$312$	−8.08672	+	7.52218i	−0.457820	+	0.425859i
$313$		−	18.8063i		−	1.06300i	−0.847060	−	0.531498i	$-0.821629\pi$
$313$		−	18.8063i		−	1.06300i	0.847060	−	0.531498i	$-0.178371\pi$
$314$	8.50213	+	2.27814i	0.479803	+	0.128563i
$315$	−1.15256	+	3.66710i	−0.0649394	+	0.206618i
$316$	5.02158	+	2.89921i	0.282486	+	0.163093i
$317$	−1.67207	−	1.67207i	−0.0939128	−	0.0939128i	0.658590	−	0.752502i	$-0.271153\pi$
$317$	−1.67207	−	1.67207i	−0.0939128	−	0.0939128i	−0.752502	+	0.658590i	$0.771153\pi$
$318$	−3.57880	−	13.3563i	−0.200689	−	0.748982i
$319$	−2.24064	−	8.36218i	−0.125452	−	0.468192i
$320$	8.25560	+	8.25560i	0.461502	+	0.461502i
$321$	−3.11764	−	1.79997i	−0.174010	−	0.100465i
$322$	0.335279	−	1.06676i	0.0186844	−	0.0594482i
$323$	−6.93332	−	1.85778i	−0.385780	−	0.103369i
$324$		−	0.820687i		−	0.0455937i
$325$	5.53113	−	8.82717i	0.306812	−	0.489643i
$326$	−14.9172			−0.826190
$327$	0.0851272	+	0.0228098i	0.00470755	+	0.00126138i
$328$	−23.7454	+	13.7094i	−1.31112	+	0.756976i
$329$	3.89450	+	17.4915i	0.214711	+	0.964339i
$330$	1.12290	+	1.12290i	0.0618136	+	0.0618136i
$331$	−33.2290	+	8.90368i	−1.82643	+	0.489391i	−0.997545	−	0.0700274i	$-0.977691\pi$
$331$	−33.2290	+	8.90368i	−1.82643	+	0.489391i	−0.828886	+	0.559418i	$0.811025\pi$
$332$	2.72886	−	0.731196i	0.149766	−	0.0401296i
$333$	7.15719	−	7.15719i	0.392212	−	0.392212i
$334$	20.9015	+	12.0675i	1.14368	+	0.660304i
$335$	4.80875	+	8.32901i	0.262730	+	0.455062i
$336$	2.06224	+	3.95273i	0.112504	+	0.215639i
$337$			3.43766i			0.187261i	0.995607	+	0.0936305i	$0.0298472\pi$
$337$			3.43766i			0.187261i	−0.995607	+	0.0936305i	$0.970153\pi$
$338$	−13.8648	+	2.65921i	−0.754145	+	0.144642i
$339$		−	2.18537i		−	0.118693i
$340$	1.46301	−	5.46002i	0.0793428	−	0.296111i
$341$	3.60616	−	2.08201i	0.195284	−	0.112747i
$342$	−0.822127	+	1.42397i	−0.0444556	+	0.0769993i
$343$	−2.36717	+	18.3684i	−0.127815	+	0.991798i
$344$	28.3189	−	7.58803i	1.52685	−	0.409119i
$345$	0.146347	+	0.546176i	0.00787908	+	0.0294051i
$346$	−9.73268	−	9.73268i	−0.523232	−	0.523232i
$347$	−9.46705	+	16.3974i	−0.508218	+	0.880259i	0.491737	+	0.870744i	$0.336362\pi$
$347$	−9.46705	+	16.3974i	−0.508218	+	0.880259i	−0.999955	+	0.00951518i	$0.996971\pi$
$348$	3.52949	+	6.11326i	0.189201	+	0.327705i
$349$	−8.44404	+	31.5136i	−0.451999	+	1.68688i	0.244765	+	0.969582i	$0.421289\pi$
$349$	−8.44404	+	31.5136i	−0.451999	+	1.68688i	−0.696764	+	0.717300i	$0.745377\pi$
$350$	−5.61366	−	6.11504i	−0.300063	−	0.326863i
$351$	1.91446	−	3.05530i	0.102186	−	0.163080i
$352$	−4.32426			−0.230484
$353$	−31.7685	−	8.51233i	−1.69086	−	0.453066i	−0.720251	−	0.693713i	$-0.755974\pi$
$353$	−31.7685	−	8.51233i	−1.69086	−	0.453066i	−0.970613	+	0.240647i	$0.922640\pi$
$354$	−0.500096	−	0.866191i	−0.0265798	−	0.0460375i
$355$	1.93028	−	3.34334i	0.102449	−	0.177446i
$356$	6.26336	−	6.26336i	0.331957	−	0.331957i
$357$	6.72955	−	10.5846i	0.356166	−	0.560194i
$358$	3.07948	+	11.4928i	0.162756	+	0.607412i
$359$	−1.45164	+	1.45164i	−0.0766146	+	0.0766146i	−0.744376	−	0.667761i	$-0.767253\pi$
$359$	−1.45164	+	1.45164i	−0.0766146	+	0.0766146i	0.667761	+	0.744376i	$0.267253\pi$
$360$	−3.85416	−	2.22520i	−0.203132	−	0.117278i
$361$	14.4691	−	8.35375i	0.761533	−	0.439671i
$362$	1.23218	−	4.59857i	0.0647622	−	0.241696i
$363$	9.98697			0.524180
$364$	0.616856	−	7.80452i	0.0323320	−	0.409068i
$365$	5.06677			0.265207
$366$	2.71469	−	10.1313i	0.141899	−	0.529574i
$367$	−0.400843	+	0.231427i	−0.0209238	+	0.0120804i	−0.510425	−	0.859922i	$-0.670512\pi$
$367$	−0.400843	+	0.231427i	−0.0209238	+	0.0120804i	0.489502	+	0.872002i	$0.337179\pi$
$368$	0.567956	+	0.327909i	0.0296067	+	0.0170935i
$369$	6.32943	−	6.32943i	0.329497	−	0.329497i
$370$	−4.13331	−	15.4257i	−0.214881	−	0.801946i
$371$	28.4287	+	18.0747i	1.47594	+	0.938390i
$372$	−2.40085	+	2.40085i	−0.124478	+	0.124478i
$373$	5.17460	−	8.96266i	0.267930	−	0.464069i	−0.700397	−	0.713754i	$-0.746994\pi$
$373$	5.17460	−	8.96266i	0.267930	−	0.464069i	0.968327	+	0.249685i	$0.0803269\pi$
$374$	−2.59083	−	4.48744i	−0.133968	−	0.232040i
$375$	11.0714	+	2.96658i	0.571726	+	0.153193i
$376$	−20.7470			−1.06994
$377$	−1.12093	+	30.9922i	−0.0577309	+	1.59618i
$378$	−1.94303	−	2.11656i	−0.0999384	−	0.108864i
$379$	3.99214	−	14.8989i	0.205062	−	0.765303i	−0.784368	−	0.620295i	$-0.787013\pi$
$379$	3.99214	−	14.8989i	0.205062	−	0.765303i	0.989431	−	0.145007i	$-0.0463206\pi$
$380$	−0.902677	−	1.56348i	−0.0463064	−	0.0802050i
$381$	7.13987	−	12.3666i	0.365787	−	0.633561i
$382$	−7.56383	−	7.56383i	−0.386999	−	0.386999i
$383$	8.40301	+	31.3605i	0.429374	+	1.60245i	0.754182	+	0.656665i	$0.228034\pi$
$383$	8.40301	+	31.3605i	0.429374	+	1.60245i	−0.324808	+	0.945780i	$0.605300\pi$
$384$	−0.129367	+	0.0346639i	−0.00660176	+	0.00176894i
$385$	−3.86539	−	0.165238i	−0.196999	−	0.00842128i
$386$	−6.90717	+	11.9636i	−0.351566	+	0.608930i
$387$	−8.28885	+	4.78557i	−0.421346	+	0.243264i
$388$	−2.91927	+	10.8948i	−0.148203	+	0.553102i
$389$			37.3829i			1.89539i	0.319179	+	0.947694i	$0.396593\pi$
$389$			37.3829i			1.89539i	−0.319179	+	0.947694i	$0.603407\pi$
$390$	−2.66444	−	5.02619i	−0.134919	−	0.254511i
$391$		−	1.84502i		−	0.0933068i
$392$	−20.1623	−	7.29690i	−1.01835	−	0.368549i
$393$	8.94441	+	15.4922i	0.451186	+	0.781477i
$394$	−1.46819	−	0.847660i	−0.0739664	−	0.0427045i
$395$	−7.25850	+	7.25850i	−0.365215	+	0.365215i
$396$	0.797871	−	0.213789i	0.0400945	−	0.0107433i
$397$	−34.9889	+	9.37524i	−1.75604	+	0.470530i	−0.985899	−	0.167343i	$-0.946481\pi$
$397$	−34.9889	+	9.37524i	−1.75604	+	0.470530i	−0.770142	+	0.637873i	$0.779815\pi$
$398$	−8.97663	−	8.97663i	−0.449958	−	0.449958i
$399$	−0.870606	−	3.91018i	−0.0435848	−	0.195754i
$400$	4.21622	−	2.43424i	0.210811	−	0.121712i
$401$	−33.6403	−	9.01390i	−1.67992	−	0.450133i	−0.712161	−	0.702016i	$-0.752284\pi$
$401$	−33.6403	−	9.01390i	−1.67992	−	0.450133i	−0.967758	+	0.251883i	$0.918950\pi$
$402$	−7.18864			−0.358537
$403$	−14.5386	+	3.33743i	−0.724220	+	0.166249i
$404$			3.24579i			0.161484i
$405$	1.40338	+	0.376033i	0.0697343	+	0.0186853i
$406$	23.5761	+	7.40990i	1.17006	+	0.367747i
$407$	8.82265	+	5.09376i	0.437323	+	0.252488i
$408$	10.2683	+	10.2683i	0.508355	+	0.508355i
$409$	2.97572	+	11.1055i	0.147140	+	0.549134i	0.999651	+	0.0264241i	$0.00841204\pi$
$409$	2.97572	+	11.1055i	0.147140	+	0.549134i	−0.852511	+	0.522709i	$0.824921\pi$
$410$	−3.65528	−	13.6417i	−0.180521	−	0.673715i
$411$	1.78946	+	1.78946i	0.0882676	+	0.0882676i
$412$	−9.07672	−	5.24044i	−0.447178	−	0.258178i
$413$	2.32467	+	0.730638i	0.114390	+	0.0359523i
$414$	−0.408241	−	0.109388i	−0.0200640	−	0.00537613i
$415$			5.00138i			0.245508i
$416$	14.8082	+	4.54751i	0.726034	+	0.222960i
$417$	10.2345			0.501188
$418$	−1.59854	−	0.428328i	−0.0781872	−	0.0209502i
$419$	25.3323	−	14.6256i	1.23756	−	0.714507i	0.268967	−	0.963149i	$-0.413318\pi$
$419$	25.3323	−	14.6256i	1.23756	−	0.714507i	0.968595	+	0.248642i	$0.0799844\pi$
$420$	3.07929	−	0.685607i	0.150254	−	0.0334542i
$421$	−8.84750	−	8.84750i	−0.431201	−	0.431201i	0.457836	−	0.889037i	$-0.348625\pi$
$421$	−8.84750	−	8.84750i	−0.431201	−	0.431201i	−0.889037	+	0.457836i	$0.848625\pi$
$422$	23.2467	−	6.22894i	1.13163	−	0.303220i
$423$	6.54227	−	1.75300i	0.318096	−	0.0852336i
$424$	−27.5792	+	27.5792i	−1.33936	+	1.33936i
$425$	−11.8615	−	6.84826i	−0.575369	−	0.332190i
$426$	1.44279	+	2.49899i	0.0699036	+	0.121077i
$427$	11.8202	+	22.6559i	0.572017	+	1.09639i
$428$			2.95443i			0.142808i
$429$	3.46907	+	1.06533i	0.167488	+	0.0514346i
$430$			15.1011i			0.728239i
$431$	−3.91058	+	14.5945i	−0.188366	+	0.702992i	0.805519	+	0.592570i	$0.201887\pi$
$431$	−3.91058	+	14.5945i	−0.188366	+	0.702992i	−0.993885	+	0.110422i	$0.964780\pi$
$432$	1.45934	−	0.842549i	0.0702124	−	0.0405372i
$433$	16.6099	−	28.7692i	0.798222	−	1.38256i	−0.122550	−	0.992462i	$-0.539107\pi$
$433$	16.6099	−	28.7692i	0.798222	−	1.38256i	0.920773	−	0.390100i	$-0.127559\pi$
$434$	−0.507674	+	11.8760i	−0.0243691	+	0.570066i
$435$	−12.0709	+	3.23438i	−0.578754	+	0.155077i
$436$	−0.0187197	−	0.0698628i	−0.000896511	−	0.00334582i
$437$	−0.416676	−	0.416676i	−0.0199323	−	0.0199323i
$438$	−1.89359	+	3.27979i	−0.0904791	+	0.156714i
$439$	−3.12262	−	5.40854i	−0.149035	−	0.258135i	0.781836	−	0.623484i	$-0.214283\pi$
$439$	−3.12262	−	5.40854i	−0.149035	−	0.258135i	−0.930871	+	0.365348i	$0.880950\pi$
$440$	1.15933	−	4.32668i	0.0552689	−	0.206266i
$441$	6.97446	+	0.597379i	0.332117	+	0.0284466i
$442$	4.15304	+	18.0916i	0.197540	+	0.860530i
$443$	−17.0915			−0.812043			−0.406022	−	0.913863i	$-0.633084\pi$
$443$	−17.0915			−0.812043			−0.406022	+	0.913863i	$0.633084\pi$
$444$	−8.02378	−	2.14997i	−0.380792	−	0.102033i
$445$	7.84051	+	13.5802i	0.371676	+	0.643762i
$446$	−7.46751	+	12.9341i	−0.353597	+	0.612448i
$447$	−5.96311	+	5.96311i	−0.282045	+	0.282045i
$448$	11.4072	−	17.9417i	0.538937	−	0.847666i
$449$	−9.60577	−	35.8492i	−0.453324	−	1.69183i	−0.692968	−	0.720968i	$-0.743697\pi$
$449$	−9.60577	−	35.8492i	−0.453324	−	1.69183i	0.239644	−	0.970861i	$-0.422969\pi$
$450$	−2.21854	+	2.21854i	−0.104583	+	0.104583i
$451$	7.80227	+	4.50464i	0.367395	+	0.212115i
$452$	−1.55322	+	0.896753i	−0.0730574	+	0.0421797i
$453$	0.166058	−	0.619735i	0.00780207	−	0.0291177i
$454$	−4.36456			−0.204839
$455$	13.0631	+	4.63080i	0.612407	+	0.217095i
$456$	4.63793			0.217191
$457$	2.07001	−	7.72540i	0.0968312	−	0.361379i	−0.900460	−	0.434940i	$-0.856770\pi$
$457$	2.07001	−	7.72540i	0.0968312	−	0.361379i	0.997291	+	0.0735609i	$0.0234363\pi$
$458$	1.81245	−	1.04642i	0.0846902	−	0.0488959i
$459$	−4.10557	−	2.37035i	−0.191632	−	0.110639i
$460$	0.328134	−	0.328134i	0.0152993	−	0.0152993i
$461$	2.87961	+	10.7469i	0.134117	+	0.500531i	1.00000		0.000284720i	$9.06291e-5\pi$
$461$	2.87961	+	10.7469i	0.134117	+	0.500531i	−0.865883	+	0.500247i	$0.833243\pi$
$462$	1.55156	−	2.44037i	0.0721852	−	0.113536i
$463$	24.2312	−	24.2312i	1.12612	−	1.12612i	0.135316	−	0.990803i	$-0.456795\pi$
$463$	24.2312	−	24.2312i	1.12612	−	1.12612i	0.990803	−	0.135316i	$-0.0432049\pi$
$464$	−7.24702	+	12.5522i	−0.336435	+	0.582722i
$465$	−3.00540	−	5.20551i	−0.139372	−	0.241400i
$466$	1.18546	+	0.317644i	0.0549156	+	0.0147146i
$467$	10.5574			0.488538			0.244269	−	0.969707i	$-0.421452\pi$
$467$	10.5574			0.488538			0.244269	+	0.969707i	$0.421452\pi$
$468$	−2.95710	−	0.106953i	−0.136692	−	0.00494389i
$469$	12.9018	−	11.8439i	0.595748	−	0.546902i
$470$	2.76583	−	10.3222i	0.127578	−	0.476129i
$471$	4.05265	+	7.01940i	0.186736	+	0.323437i
$472$	−1.41061	+	2.44325i	−0.0649287	+	0.112460i
$473$	−6.81176	−	6.81176i	−0.313205	−	0.313205i
$474$	−1.98583	−	7.41123i	−0.0912123	−	0.340409i
$475$	−4.22539	+	1.13219i	−0.193874	+	0.0519484i
$476$	−10.2843	−	0.439630i	−0.471378	−	0.0201504i
$477$	6.36644	−	11.0270i	0.291499	−	0.504892i
$478$	−4.82578	+	2.78616i	−0.220726	+	0.127436i
$479$	2.28082	−	8.51215i	0.104214	−	0.388930i	−0.894041	−	0.447985i	$-0.852142\pi$
$479$	2.28082	−	8.51215i	0.104214	−	0.388930i	0.998255	+	0.0590545i	$0.0188086\pi$
$480$			6.24211i			0.284912i
$481$	−24.8560	−	26.7215i	−1.13334	−	1.21839i
$482$			10.6444i			0.484838i
$483$	0.912915	−	0.476292i	0.0415391	−	0.0216720i
$484$	−4.09809	−	7.09810i	−0.186277	−	0.322641i
$485$	−17.2926	−	9.98389i	−0.785217	−	0.453345i
$486$	−0.767891	+	0.767891i	−0.0348322	+	0.0348322i
$487$	19.8298	−	5.31338i	0.898574	−	0.240772i	0.220170	−	0.975461i	$-0.429339\pi$
$487$	19.8298	−	5.31338i	0.898574	−	0.240772i	0.678404	+	0.734689i	$0.262672\pi$
$488$	−28.5774	+	7.65728i	−1.29364	+	0.346629i
$489$	−9.71313	−	9.71313i	−0.439243	−	0.439243i
$490$	6.31832	−	9.05859i	0.285432	−	0.409225i
$491$	−2.72329	+	1.57229i	−0.122900	+	0.0709565i	−0.560190	−	0.828364i	$-0.689272\pi$
$491$	−2.72329	+	1.57229i	−0.122900	+	0.0709565i	0.437290	+	0.899321i	$0.355938\pi$
$492$	−7.09579	−	1.90131i	−0.319903	−	0.0857177i
$493$	40.7762			1.83647
$494$	5.02369	+	3.14786i	0.226026	+	0.141629i
$495$			1.46232i			0.0657262i
$496$	−6.73398	−	1.80436i	−0.302364	−	0.0810183i
$497$	−6.70676	−	2.10792i	−0.300840	−	0.0945530i
$498$	−3.23746	−	1.86915i	−0.145074	−	0.0837587i
$499$	−10.7019	−	10.7019i	−0.479082	−	0.479082i	0.425756	−	0.904838i	$-0.360008\pi$
$499$	−10.7019	−	10.7019i	−0.479082	−	0.479082i	−0.904838	+	0.425756i	$0.860008\pi$
$500$	−2.43463	−	9.08617i	−0.108880	−	0.406346i
$501$	5.75214	+	21.4673i	0.256986	+	0.959087i
$502$	21.7804	+	21.7804i	0.972107	+	0.972107i
$503$	−22.4889	−	12.9840i	−1.00273	−	0.578926i	−0.0936745	−	0.995603i	$-0.529861\pi$
$503$	−22.4889	−	12.9840i	−1.00273	−	0.578926i	−0.909055	+	0.416677i	$0.863195\pi$
$504$	−2.42998	+	7.73148i	−0.108240	+	0.344387i
$505$	−5.55031	−	1.48720i	−0.246985	−	0.0661795i
$506$		−	0.425387i		−	0.0189108i
$507$	−10.7593	−	7.29634i	−0.477839	−	0.324042i
$508$	−11.7192			−0.519955
$509$	31.8249	+	8.52745i	1.41061	+	0.377973i	0.882144	−	0.470980i	$-0.156100\pi$
$509$	31.8249	+	8.52745i	1.41061	+	0.377973i	0.528469	+	0.848952i	$0.322766\pi$
$510$	−6.47766	+	3.73988i	−0.286835	+	0.165605i
$511$	−2.00525	−	9.00624i	−0.0887069	−	0.398412i
$512$	12.4191	+	12.4191i	0.548851	+	0.548851i
$513$	−1.46251	+	0.391878i	−0.0645713	+	0.0173018i
$514$	−6.96683	+	1.86676i	−0.307294	+	0.0823391i
$515$	13.1201	−	13.1201i	0.578139	−	0.578139i
$516$	6.80255	+	3.92745i	0.299466	+	0.172897i
$517$	3.40852	+	5.90373i	0.149907	+	0.259646i
$518$	−25.7836	+	13.4520i	−1.13287	+	0.591046i
$519$		−	12.6746i		−	0.556352i
$520$	−8.52012	+	13.5973i	−0.373632	+	0.596282i
$521$			26.4544i			1.15899i	0.814976	+	0.579495i	$0.196750\pi$
$521$			26.4544i			1.15899i	−0.814976	+	0.579495i	$0.803250\pi$
$522$	2.41755	−	9.02241i	0.105813	−	0.394900i
$523$	9.23888	−	5.33407i	0.403988	−	0.233243i	−0.284215	−	0.958761i	$-0.591733\pi$
$523$	9.23888	−	5.33407i	0.403988	−	0.233243i	0.688203	+	0.725518i	$0.258400\pi$
$524$	7.34057	−	12.7142i	0.320674	−	0.555424i
$525$	0.326464	−	7.63696i	0.0142481	−	0.333304i
$526$	13.1062	−	3.51179i	0.571456	−	0.153121i
$527$	5.07623	+	18.9448i	0.221124	+	0.825247i
$528$	1.19928	+	1.19928i	0.0521920	+	0.0521920i
$529$	−11.4243	+	19.7874i	−0.496707	+	0.860322i
$530$	−10.0448	−	17.3981i	−0.436318	−	0.755726i
$531$	0.238377	−	0.889636i	0.0103447	−	0.0386069i
$532$	−2.42186	+	2.22329i	−0.105001	+	0.0963919i
$533$	−21.9813	−	23.6310i	−0.952116	−	1.02357i
$534$	−11.7208			−0.507210
$535$	−5.05207	−	1.35370i	−0.218420	−	0.0585255i
$536$	10.1385	+	17.5603i	0.437915	+	0.758490i
$537$	−5.47818	+	9.48849i	−0.236401	+	0.409459i
$538$	6.45273	−	6.45273i	0.278197	−	0.278197i
$539$	1.23608	+	6.93618i	0.0532415	+	0.298762i
$540$	−0.308606	−	1.15173i	−0.0132803	−	0.0495627i
$541$	3.42225	−	3.42225i	0.147134	−	0.147134i	−0.629702	−	0.776836i	$-0.716823\pi$
$541$	3.42225	−	3.42225i	0.147134	−	0.147134i	0.776836	+	0.629702i	$0.216823\pi$
$542$	−0.341476	−	0.197151i	−0.0146677	−	0.00846838i
$543$	3.79661	−	2.19197i	0.162928	−	0.0940665i
$544$	5.27157	−	19.6738i	0.226017	−	0.843506i
$545$	0.128043			0.00548475
$546$	−7.87961	+	6.72527i	−0.337216	+	0.287815i
$547$	−19.6406			−0.839770			−0.419885	−	0.907577i	$-0.637930\pi$
$547$	−19.6406			−0.839770			−0.419885	+	0.907577i	$0.637930\pi$
$548$	0.537540	−	2.00613i	0.0229626	−	0.0856975i
$549$	8.36449	−	4.82924i	0.356988	−	0.206107i
$550$	−2.73479	−	1.57893i	−0.116612	−	0.0673259i
$551$	9.20882	−	9.20882i	0.392309	−	0.392309i
$552$	0.308549	+	1.15152i	0.0131327	+	0.0490120i
$553$	15.7747	+	10.0294i	0.670810	+	0.426494i
$554$	−11.9925	+	11.9925i	−0.509514	+	0.509514i
$555$	7.35288	−	12.7356i	0.312113	−	0.540595i
$556$	−4.19968	−	7.27406i	−0.178106	−	0.308489i
$557$	−34.1973	−	9.16315i	−1.44899	−	0.388255i	−0.553316	−	0.832971i	$-0.686638\pi$
$557$	−34.1973	−	9.16315i	−1.44899	−	0.388255i	−0.895672	+	0.444716i	$0.853305\pi$
$558$	4.49280			0.190195
$559$	16.1631	+	30.4900i	0.683627	+	1.28959i
$560$	4.38045	+	4.77169i	0.185108	+	0.201641i
$561$	1.23495	−	4.60890i	0.0521397	−	0.194588i
$562$	−0.651705	−	1.12879i	−0.0274905	−	0.0476149i
$563$	−15.9428	+	27.6137i	−0.671908	+	1.16378i	0.305455	+	0.952207i	$0.401192\pi$
$563$	−15.9428	+	27.6137i	−0.671908	+	1.16378i	−0.977362	+	0.211572i	$0.932142\pi$
$564$	−3.93050	−	3.93050i	−0.165504	−	0.165504i
$565$	−0.821772	−	3.06689i	−0.0345722	−	0.129025i
$566$	25.1168	−	6.73003i	1.05574	−	0.282884i
$567$	0.112997	−	2.64334i	0.00474543	−	0.111010i
$568$	4.06967	−	7.04888i	0.170760	−	0.295764i
$569$	23.6253	−	13.6401i	0.990426	−	0.571823i	0.0850245	−	0.996379i	$-0.472903\pi$
$569$	23.6253	−	13.6401i	0.990426	−	0.571823i	0.905402	+	0.424556i	$0.139570\pi$
$570$	−0.618295	+	2.30751i	−0.0258975	+	0.0966509i
$571$		−	33.0144i		−	1.38161i	−0.723042	−	0.690804i	$-0.757257\pi$
$571$		−	33.0144i		−	1.38161i	0.723042	−	0.690804i	$-0.242743\pi$
$572$	−0.666344	−	2.90275i	−0.0278612	−	0.121370i
$573$		−	9.85014i		−	0.411496i
$574$	−22.8016	+	11.8962i	−0.951721	+	0.496537i
$575$	−0.562208	−	0.973772i	−0.0234457	−	0.0406091i
$576$	−6.95928	−	4.01794i	−0.289970	−	0.167414i
$577$	18.3031	−	18.3031i	0.761967	−	0.761967i	−0.214711	−	0.976678i	$-0.568881\pi$
$577$	18.3031	−	18.3031i	0.761967	−	0.761967i	0.976678	+	0.214711i	$0.0688808\pi$
$578$	5.74226	−	1.53863i	0.238847	−	0.0639988i
$579$	−12.2874	+	3.29240i	−0.510646	+	0.136827i
$580$	7.25199	+	7.25199i	0.301123	+	0.301123i
$581$	8.89002	−	1.97937i	0.368820	−	0.0821181i
$582$	12.9254	−	7.46250i	0.535776	−	0.309331i
$583$	12.3789	+	3.31691i	0.512681	+	0.137373i
$584$	10.6824			0.442042
$585$	1.53781	−	5.00763i	0.0635807	−	0.207040i
$586$			20.9678i			0.866174i
$587$	−30.3048	−	8.12014i	−1.25081	−	0.335154i	−0.428162	−	0.903702i	$-0.640839\pi$
$587$	−30.3048	−	8.12014i	−1.25081	−	0.335154i	−0.822650	+	0.568548i	$0.807505\pi$
$588$	−2.43735	−	5.20213i	−0.100515	−	0.214532i
$589$	5.42485	+	3.13204i	0.223527	+	0.129053i
$590$	−1.02754	−	1.02754i	−0.0423031	−	0.0423031i
$591$	−0.404048	−	1.50793i	−0.0166203	−	0.0620279i
$592$	−4.41447	−	16.4750i	−0.181434	−	0.677120i
$593$	14.5568	+	14.5568i	0.597777	+	0.597777i	0.939721	−	0.341943i	$-0.111085\pi$
$593$	14.5568	+	14.5568i	0.597777	+	0.597777i	−0.341943	+	0.939721i	$0.611085\pi$
$594$	−0.946578	−	0.546507i	−0.0388385	−	0.0224234i
$595$	5.46395	−	17.3846i	0.224000	−	0.712701i
$596$	6.68512	+	1.79127i	0.273833	+	0.0733733i
$597$		−	11.6900i		−	0.478439i
$598$	−0.447349	+	1.45672i	−0.0182934	+	0.0595696i
$599$	17.9695			0.734214			0.367107	−	0.930179i	$-0.380348\pi$
$599$	17.9695			0.734214			0.367107	+	0.930179i	$0.380348\pi$
$600$	8.54833	+	2.29052i	0.348984	+	0.0935100i
$601$	15.4598	−	8.92570i	0.630617	−	0.364087i	−0.150374	−	0.988629i	$-0.548048\pi$
$601$	15.4598	−	8.92570i	0.630617	−	0.364087i	0.780991	+	0.624542i	$0.214714\pi$
$602$	26.8423	−	5.97648i	1.09401	−	0.243583i
$603$	−4.68077	−	4.68077i	−0.190616	−	0.190616i
$604$	−0.508609	+	0.136281i	−0.0206950	+	0.00554521i
$605$	14.0155	−	3.75543i	0.569810	−	0.152680i
$606$	3.03698	−	3.03698i	0.123369	−	0.123369i
$607$	−22.2125	−	12.8244i	−0.901578	−	0.520526i	−0.0238664	−	0.999715i	$-0.507598\pi$
$607$	−22.2125	−	12.8244i	−0.901578	−	0.520526i	−0.877712	+	0.479189i	$0.840931\pi$
$608$	−3.25256	−	5.63361i	−0.131909	−	0.228473i
$609$	10.5264	+	20.1760i	0.426550	+	0.817575i
$610$		−	15.2389i		−	0.617005i
$611$	−5.46380	−	23.8015i	−0.221042	−	0.962907i
$612$			3.89063i			0.157270i
$613$	0.916231	−	3.41942i	0.0370062	−	0.138109i	−0.944951	−	0.327211i	$-0.893891\pi$
$613$	0.916231	−	3.41942i	0.0370062	−	0.138109i	0.981957	+	0.189102i	$0.0605578\pi$
$614$	22.8687	−	13.2032i	0.922905	−	0.532839i
$615$	6.50249	−	11.2626i	0.262206	−	0.454153i
$616$	−8.14954	−	0.348376i	−0.328354	−	0.0140365i
$617$	−5.87829	+	1.57508i	−0.236651	+	0.0634105i	−0.375195	−	0.926946i	$-0.622424\pi$
$617$	−5.87829	+	1.57508i	−0.236651	+	0.0634105i	0.138544	+	0.990356i	$0.455758\pi$
$618$	3.58948	+	13.3961i	0.144390	+	0.538871i
$619$	34.1674	+	34.1674i	1.37331	+	1.37331i	0.855496	+	0.517810i	$0.173253\pi$
$619$	34.1674	+	34.1674i	1.37331	+	1.37331i	0.517810	+	0.855496i	$0.326747\pi$
$620$	−2.46650	+	4.27210i	−0.0990569	+	0.171572i
$621$	−0.194594	−	0.337046i	−0.00780878	−	0.0135252i
$622$	3.95289	−	14.7524i	0.158496	−	0.591517i
$623$	21.0359	−	19.3112i	0.842786	−	0.773685i
$624$	−2.84569	−	5.36808i	−0.113919	−	0.214895i
$625$	2.20722			0.0882889
$626$	19.7270	+	5.28584i	0.788451	+	0.211265i
$627$	−0.761966	−	1.31976i	−0.0304300	−	0.0527063i
$628$	3.32596	−	5.76073i	0.132720	−	0.229878i
$629$	−33.9301	+	33.9301i	−1.35288	+	1.35288i
$630$	−3.52269	−	2.23969i	−0.140347	−	0.0892315i
$631$	2.80135	+	10.4548i	0.111520	+	0.416199i	0.999003	−	0.0446417i	$-0.0142146\pi$
$631$	2.80135	+	10.4548i	0.111520	+	0.416199i	−0.887483	+	0.460841i	$0.847548\pi$
$632$	−15.3033	+	15.3033i	−0.608734	+	0.608734i
$633$	19.1926	+	11.0809i	0.762838	+	0.440425i
$634$	2.22390	−	1.28397i	0.0883222	−	0.0509928i
$635$	5.36966	−	20.0398i	0.213088	−	0.795257i
$636$	−10.4497			−0.414358
$637$	3.06139	−	25.0525i	0.121297	−	0.992616i
$638$	9.40135			0.372203
$639$	−0.687727	+	2.56663i	−0.0272061	+	0.101534i
$640$	−0.168516	+	0.0972930i	−0.00666120	+	0.00384584i
$641$	26.3470	+	15.2114i	1.04064	+	0.600815i	0.920015	−	0.391883i	$-0.128176\pi$
$641$	26.3470	+	15.2114i	1.04064	+	0.600815i	0.120627	+	0.992698i	$0.461510\pi$
$642$	2.76436	−	2.76436i	0.109101	−	0.109101i
$643$	5.55469	+	20.7304i	0.219056	+	0.817527i	0.984699	+	0.174262i	$0.0557539\pi$
$643$	5.55469	+	20.7304i	0.219056	+	0.817527i	−0.765644	+	0.643265i	$0.777579\pi$
$644$	−0.713127	−	0.453399i	−0.0281011	−	0.0178664i
$645$	−9.83283	+	9.83283i	−0.387167	+	0.387167i
$646$	3.89746	−	6.75060i	0.153344	−	0.265599i
$647$	−3.76958	−	6.52911i	−0.148198	−	0.256686i	0.782364	−	0.622822i	$-0.214014\pi$
$647$	−3.76958	−	6.52911i	−0.148198	−	0.256686i	−0.930561	+	0.366136i	$0.880681\pi$
$648$	2.95878	+	0.792804i	0.116232	+	0.0311443i
$649$	0.927000			0.0363879
$650$	7.70471	+	8.28296i	0.302204	+	0.324884i
$651$	−8.06343	+	7.40230i	−0.316031	+	0.290119i
$652$	−2.91775	+	10.8892i	−0.114268	+	0.426454i
$653$	−11.4217	−	19.7830i	−0.446966	−	0.774167i	0.551221	−	0.834359i	$-0.314162\pi$
$653$	−11.4217	−	19.7830i	−0.446966	−	0.774167i	−0.998187	+	0.0601918i	$0.980829\pi$
$654$	−0.0478530	+	0.0828838i	−0.00187120	+	0.00324101i
$655$	18.3779	+	18.3779i	0.718086	+	0.718086i
$656$	−3.90392	−	14.5696i	−0.152422	−	0.568848i
$657$	−3.36856	+	0.902603i	−0.131420	+	0.0352139i
$658$	−19.4425	−	0.831126i	−0.757947	−	0.0324007i
$659$	13.0916	−	22.6753i	0.509975	−	0.883303i	−0.489958	−	0.871746i	$-0.662988\pi$
$659$	13.0916	−	22.6753i	0.509975	−	0.883303i	0.999933	−	0.0115568i	$-0.00367874\pi$
$660$	1.03932	−	0.600052i	0.0404555	−	0.0233570i
$661$	−4.50623	+	16.8175i	−0.175272	+	0.654124i	0.821233	+	0.570593i	$0.193287\pi$
$661$	−4.50623	+	16.8175i	−0.175272	+	0.654124i	−0.996505	+	0.0835312i	$0.973380\pi$
$662$		−	37.3584i		−	1.45197i
$663$	−9.07588	+	14.4843i	−0.352478	+	0.562522i
$664$			10.5446i			0.409209i
$665$	−2.69215	−	5.16008i	−0.104397	−	0.200099i
$666$	5.49594	+	9.51925i	0.212963	+	0.368863i
$667$	2.89904	+	1.67376i	0.112251	+	0.0648083i
$668$	12.8972	−	12.8972i	0.499008	−	0.499008i
$669$	−13.2842	+	3.55949i	−0.513597	+	0.137618i
$670$	−10.0884	+	2.70317i	−0.389748	+	0.104433i
$671$	6.87393	+	6.87393i	0.265365	+	0.265365i
$672$	11.0954	−	2.47041i	0.428015	−	0.0952980i
$673$	13.2813	−	7.66796i	0.511957	−	0.295578i	−0.221681	−	0.975119i	$-0.571154\pi$
$673$	13.2813	−	7.66796i	0.511957	−	0.295578i	0.733638	+	0.679541i	$0.237821\pi$
$674$	−3.60596	−	0.966213i	−0.138896	−	0.0372172i
$675$	−2.88914			−0.111203
$676$	−0.770743	+	10.6411i	−0.0296440	+	0.409271i
$677$		−	4.31369i		−	0.165789i	−0.996558	−	0.0828943i	$-0.973584\pi$
$677$		−	4.31369i		−	0.165789i	0.996558	−	0.0828943i	$-0.0264164\pi$
$678$	2.29236	+	0.614237i	0.0880376	+	0.0235896i
$679$	−10.9027	+	34.6891i	−0.418406	+	1.33124i
$680$	18.2714	+	10.5490i	0.700678	+	0.404537i
$681$	−2.84191	−	2.84191i	−0.108902	−	0.108902i
$682$	1.17037	+	4.36789i	0.0448159	+	0.167255i
$683$	−2.11067	−	7.87714i	−0.0807627	−	0.301410i	0.913715	−	0.406355i	$-0.133200\pi$
$683$	−2.11067	−	7.87714i	−0.0807627	−	0.301410i	−0.994478	+	0.104944i	$0.966534\pi$
$684$	0.878653	+	0.878653i	0.0335961	+	0.0335961i
$685$	3.18418	+	1.83839i	0.121661	+	0.0702412i
$686$	−18.6023	−	7.64581i	−0.710239	−	0.291918i
$687$	1.86151	+	0.498789i	0.0710209	+	0.0190300i
$688$			16.1283i			0.614886i
$689$	−38.9028	−	24.3766i	−1.48208	−	0.928674i
$690$	−0.614050			−0.0233765
$691$	−8.79665	−	2.35706i	−0.334640	−	0.0896666i	0.0875862	−	0.996157i	$-0.472085\pi$
$691$	−8.79665	−	2.35706i	−0.334640	−	0.0896666i	−0.422227	+	0.906490i	$0.638751\pi$
$692$	−9.00827	+	5.20093i	−0.342443	+	0.197710i
$693$	2.59928	−	0.578733i	0.0987386	−	0.0219843i
$694$	−14.5393	−	14.5393i	−0.551905	−	0.551905i
$695$	14.3629	−	3.84853i	0.544816	−	0.145983i
$696$	−25.4494	+	6.81915i	−0.964657	+	0.258479i
$697$	−30.0059	+	30.0059i	−1.13656	+	1.13656i
$698$	−30.6831	−	17.7149i	−1.16137	−	0.670518i
$699$	0.565067	+	0.978726i	0.0213728	+	0.0370188i
$700$	−5.56182	+	2.90175i	−0.210217	+	0.109676i
$701$			42.0549i			1.58839i	0.607663	+	0.794195i	$0.292107\pi$
$701$			42.0549i			1.58839i	−0.607663	+	0.794195i	$0.707893\pi$
$702$	2.66679	+	2.86693i	0.100651	+	0.108205i
$703$			15.3254i			0.578009i
$704$	2.09335	−	7.81247i	0.0788959	−	0.294444i
$705$	8.52208	−	4.92023i	0.320960	−	0.185306i
$706$	17.8582	−	30.9312i	0.672101	−	1.16411i
$707$	−0.446900	+	10.4543i	−0.0168074	+	0.393175i
$708$	−0.730113	+	0.195633i	−0.0274393	+	0.00735235i
$709$	4.70279	+	17.5510i	0.176617	+	0.659143i	0.996271	+	0.0862837i	$0.0274991\pi$
$709$	4.70279	+	17.5510i	0.176617	+	0.659143i	−0.819654	+	0.572859i	$0.805834\pi$
$710$	2.96449	+	2.96449i	0.111255	+	0.111255i
$711$	3.53266	−	6.11875i	0.132485	−	0.229471i
$712$	16.5304	+	28.6315i	0.619504	+	1.07301i
$713$	−0.416733	+	1.55527i	−0.0156068	+	0.0582453i
$714$	9.21130	+	10.0340i	0.344724	+	0.375513i
$715$	5.26901	+	0.190570i	0.197050	+	0.00712693i
$716$	8.99175			0.336038
$717$	−4.95639	−	1.32806i	−0.185100	−	0.0495974i
$718$	−1.11470	−	1.93072i	−0.0416003	−	0.0720538i
$719$	−22.3307	+	38.6778i	−0.832793	+	1.44244i	0.0630222	+	0.998012i	$0.479926\pi$
$719$	−22.3307	+	38.6778i	−0.832793	+	1.44244i	−0.895815	+	0.444427i	$0.853407\pi$
$720$	1.73117	−	1.73117i	0.0645170	−	0.0645170i
$721$	−28.5135	−	18.1286i	−1.06190	−	0.675144i
$722$	4.69594	+	17.5255i	0.174765	+	0.652231i
$723$	−6.93091	+	6.93091i	−0.257763	+	0.257763i
$724$	−3.11583	−	1.79892i	−0.115799	−	0.0668565i
$725$	21.5210	−	12.4252i	0.799271	−	0.461459i
$726$	−2.80701	+	10.4759i	−0.104178	+	0.388798i
$727$	21.6855			0.804272			0.402136	−	0.915580i	$-0.368268\pi$
$727$	21.6855			0.804272			0.402136	+	0.915580i	$0.368268\pi$
$728$	27.5413	+	9.76327i	1.02075	+	0.361851i
$729$	−1.00000			−0.0370370
$730$	−1.42410	+	5.31483i	−0.0527085	+	0.196711i
$731$	39.2949	−	22.6869i	1.45338	−	0.839107i
$732$	−6.86463	−	3.96330i	−0.253724	−	0.146488i
$733$	36.4440	−	36.4440i	1.34609	−	1.34609i	0.456223	−	0.889865i	$-0.349202\pi$
$733$	36.4440	−	36.4440i	1.34609	−	1.34609i	0.889865	−	0.456223i	$-0.150798\pi$
$734$	−0.130093	−	0.485514i	−0.00480183	−	0.0179207i
$735$	10.0124	−	1.78428i	0.369314	−	0.0658143i
$736$	1.18235	−	1.18235i	0.0435819	−	0.0435819i
$737$	3.33130	−	5.76998i	0.122710	−	0.212540i
$738$	4.86031	+	8.41830i	0.178910	+	0.309882i
$739$	−6.28312	−	1.68356i	−0.231128	−	0.0619307i	0.141396	−	0.989953i	$-0.454841\pi$
$739$	−6.28312	−	1.68356i	−0.231128	−	0.0619307i	−0.372524	+	0.928022i	$0.621508\pi$
$740$	−12.0688			−0.443659
$741$	1.22142	+	5.32077i	0.0448699	+	0.195464i
$742$	−26.9500	+	24.7403i	−0.989364	+	0.908246i
$743$	6.75798	−	25.2211i	0.247926	−	0.925273i	−0.723964	−	0.689838i	$-0.757682\pi$
$743$	6.75798	−	25.2211i	0.247926	−	0.925273i	0.971890	−	0.235435i	$-0.0756515\pi$
$744$	−6.33639	−	10.9750i	−0.232303	−	0.402361i
$745$	−6.12615	+	10.6108i	−0.224445	+	0.388750i
$746$	7.94705	+	7.94705i	0.290962	+	0.290962i
$747$	−0.890956	−	3.32509i	−0.0325984	−	0.121659i
$748$	−3.78247	+	1.01351i	−0.138301	+	0.0370576i
$749$	−0.406783	+	9.51586i	−0.0148635	+	0.347702i
$750$	−6.22363	+	10.7797i	−0.227255	+	0.393617i
$751$	31.8018	−	18.3608i	1.16046	−	0.669993i	0.209048	−	0.977905i	$-0.432964\pi$
$751$	31.8018	−	18.3608i	1.16046	−	0.669993i	0.951415	+	0.307912i	$0.0996303\pi$
$752$	2.95397	−	11.0244i	0.107720	−	0.402017i
$753$			28.3639i			1.03364i
$754$	−32.1945	−	9.88671i	−1.17245	−	0.360053i
$755$		−	0.932165i		−	0.0339250i
$756$	−1.92508	+	1.00437i	−0.0700146	+	0.0365284i
$757$	25.3385	+	43.8875i	0.920943	+	1.59512i	0.797959	+	0.602711i	$0.205913\pi$
$757$	25.3385	+	43.8875i	0.920943	+	1.59512i	0.122984	+	0.992409i	$0.460754\pi$
$758$	14.5062	+	8.37517i	0.526890	+	0.304200i
$759$	0.276984	−	0.276984i	0.0100539	−	0.0100539i
$760$	6.50876	−	1.74402i	0.236097	−	0.0632621i
$761$	−25.8358	+	6.92269i	−0.936548	+	0.250947i	−0.694645	−	0.719353i	$-0.744438\pi$
$761$	−25.8358	+	6.92269i	−0.936548	+	0.250947i	−0.241903	+	0.970300i	$0.577772\pi$
$762$	10.9653	+	10.9653i	0.397230	+	0.397230i
$763$	−0.0506748	−	0.227597i	−0.00183455	−	0.00823958i
$764$	−7.00085	+	4.04194i	−0.253282	+	0.146232i
$765$	−6.65299	−	1.78266i	−0.240539	−	0.0644523i
$766$	−35.2576			−1.27391
$767$	−3.17447	−	0.974858i	−0.114623	−	0.0352001i
$768$			15.9263i			0.574692i
$769$	22.6180	+	6.06047i	0.815626	+	0.218546i	0.642433	−	0.766342i	$-0.277925\pi$
$769$	22.6180	+	6.06047i	0.815626	+	0.218546i	0.173193	+	0.984888i	$0.444592\pi$
$770$	1.25976	−	4.00820i	0.0453988	−	0.144445i
$771$	−5.75185	−	3.32083i	−0.207148	−	0.119597i
$772$	7.38208	+	7.38208i	0.265687	+	0.265687i
$773$	−3.07578	−	11.4790i	−0.110628	−	0.412869i	0.888295	−	0.459274i	$-0.151890\pi$
$773$	−3.07578	−	11.4790i	−0.110628	−	0.412869i	−0.998923	+	0.0464045i	$0.985224\pi$
$774$	−2.69014	−	10.0397i	−0.0966949	−	0.360870i
$775$	8.45192	+	8.45192i	0.303602	+	0.303602i
$776$	−36.4586	−	21.0494i	−1.30879	−	0.755628i
$777$	−25.5476	−	8.02955i	−0.916516	−	0.288058i
$778$	−39.2131	−	10.5071i	−1.40586	−	0.376699i
$779$			13.5530i			0.485585i
$780$	−4.19014	+	0.961872i	−0.150031	+	0.0344405i
$781$	−2.67443			−0.0956986
$782$	1.93535	+	0.518576i	0.0692080	+	0.0185442i
$783$	7.44895	−	4.30065i	0.266204	−	0.153693i
$784$	6.74810	−	9.67477i	0.241004	−	0.345528i
$785$	8.32692	+	8.32692i	0.297201	+	0.297201i
$786$	−18.7646	+	5.02797i	−0.669312	+	0.179342i
$787$	−1.37868	+	0.369415i	−0.0491445	+	0.0131682i	−0.283308	−	0.959029i	$-0.591432\pi$
$787$	−1.37868	+	0.369415i	−0.0491445	+	0.0131682i	0.234163	+	0.972197i	$0.424765\pi$
$788$	−0.905941	+	0.905941i	−0.0322728	+	0.0322728i
$789$	10.8205	+	6.24723i	0.385221	+	0.222407i
$790$	−5.57374	−	9.65400i	−0.198305	−	0.343474i
$791$	−5.12621	+	2.67448i	−0.182267	+	0.0950935i
$792$			3.08305i			0.109551i
$793$	−16.3106	−	30.7683i	−0.579208	−	1.09261i
$794$		−	39.3369i		−	1.39602i
$795$	4.78799	−	17.8690i	0.169813	−	0.633749i
$796$	−8.30849	+	4.79691i	−0.294487	+	0.170022i
$797$	15.8960	−	27.5327i	0.563065	−	0.975258i	−0.434161	−	0.900835i	$-0.642955\pi$
$797$	15.8960	−	27.5327i	0.563065	−	0.975258i	0.997227	−	0.0744227i	$-0.0237114\pi$
$798$	4.34632	+	0.185796i	0.153858	+	0.00657711i
$799$	−31.0150	+	8.31044i	−1.09723	+	0.294002i
$800$	−3.21266	−	11.9898i	−0.113585	−	0.423904i
$801$	−7.63184	−	7.63184i	−0.269658	−	0.269658i
$802$	18.9104	−	32.7538i	0.667750	−	1.15658i
$803$	−1.75502	−	3.03978i	−0.0619333	−	0.107272i
$804$	−1.40607	+	5.24752i	−0.0495882	+	0.185066i
$805$	1.10206	−	1.01170i	0.0388426	−	0.0356578i
$806$	0.585506	−	16.1884i	0.0206236	−	0.570213i
$807$	8.40319			0.295806
$808$	−11.7019	−	3.13551i	−0.411671	−	0.110307i
$809$	7.21908	+	12.5038i	0.253809	+	0.439611i	0.964571	−	0.263822i	$-0.0849831\pi$
$809$	7.21908	+	12.5038i	0.253809	+	0.439611i	−0.710762	+	0.703432i	$0.751650\pi$
$810$	−0.788887	+	1.36639i	−0.0277187	+	0.0480101i
$811$	−16.5212	+	16.5212i	−0.580138	+	0.580138i	−0.934941	−	0.354803i	$-0.884548\pi$
$811$	−16.5212	+	16.5212i	−0.580138	+	0.580138i	0.354803	+	0.934941i	$0.384548\pi$
$812$	10.0204	−	15.7606i	0.351648	−	0.553088i
$813$	−0.0939748	−	0.350719i	−0.00329584	−	0.0123002i
$814$	−7.82291	+	7.82291i	−0.274193	+	0.274193i
$815$	−17.2836	−	9.97871i	−0.605419	−	0.349539i
$816$	−6.91828	+	3.99427i	−0.242188	+	0.139828i
$817$	3.75072	−	13.9979i	0.131221	−	0.489723i
$818$	−12.4856			−0.436550
$819$	−9.50973	−	0.751633i	−0.332297	−	0.0262642i
$820$	−10.6730			−0.372718
$821$	−7.38477	+	27.5603i	−0.257730	+	0.961862i	0.708821	+	0.705388i	$0.249227\pi$
$821$	−7.38477	+	27.5603i	−0.257730	+	0.961862i	−0.966551	+	0.256474i	$0.917439\pi$
$822$	−2.38003	+	1.37411i	−0.0830130	+	0.0479276i
$823$	0.0527072	+	0.0304305i	0.00183726	+	0.00106074i	0.500918	−	0.865495i	$-0.332996\pi$
$823$	0.0527072	+	0.0304305i	0.00183726	+	0.00106074i	−0.499081	+	0.866555i	$0.666329\pi$
$824$	27.6614	−	27.6614i	0.963632	−	0.963632i
$825$	−0.752619	−	2.80881i	−0.0262028	−	0.0977903i
$826$	−1.41980	+	2.23313i	−0.0494011	+	0.0777004i
$827$	−37.2665	+	37.2665i	−1.29588	+	1.29588i	−0.364798	+	0.931087i	$0.618862\pi$
$827$	−37.2665	+	37.2665i	−1.29588	+	1.29588i	−0.931087	+	0.364798i	$0.881138\pi$
$828$	−0.159701	+	0.276610i	−0.00554998	+	0.00961285i
$829$	−2.17299	−	3.76373i	−0.0754711	−	0.130720i	0.825820	−	0.563934i	$-0.190713\pi$
$829$	−2.17299	−	3.76373i	−0.0754711	−	0.130720i	−0.901291	+	0.433214i	$0.857379\pi$
$830$	−5.24624	−	1.40573i	−0.182100	−	0.0487935i
$831$	−15.6175			−0.541765
$832$	−15.3844	+	24.5520i	−0.533357	+	0.851188i
$833$	−33.0638	−	2.83200i	−1.14559	−	0.0981228i
$834$	−2.87660	+	10.7356i	−0.0996085	+	0.371744i
$835$	16.1448	+	27.9636i	0.558714	+	0.967722i
$836$	−0.625336	+	1.08311i	−0.0216277	+	0.0374603i
$837$	2.92542	+	2.92542i	0.101117	+	0.101117i
$838$	8.22156	+	30.6833i	0.284009	+	1.05994i
$839$	−46.4621	+	12.4495i	−1.60405	+	0.429804i	−0.946263	−	0.323399i	$-0.895174\pi$
$839$	−46.4621	+	12.4495i	−1.60405	+	0.429804i	−0.657788	+	0.753203i	$0.728508\pi$
$840$	−0.502883	+	11.7639i	−0.0173511	+	0.405894i
$841$	−22.4912	+	38.9560i	−0.775560	+	1.34331i
$842$	11.7674	−	6.79392i	0.405532	−	0.234134i
$843$	0.310644	−	1.15934i	0.0106991	−	0.0399297i
$844$		−	18.1879i		−	0.626052i
$845$	−17.8431	−	6.19363i	−0.613820	−	0.213067i
$846$			7.35528i			0.252880i
$847$	−12.2222	−	23.4264i	−0.419958	−	0.804940i
$848$	−10.7281	−	18.5816i	−0.368404	−	0.638094i
$849$	20.7366	+	11.9723i	0.711678	+	0.410887i
$850$	10.5174	−	10.5174i	0.360745	−	0.360745i
$851$	−3.80505	+	1.01956i	−0.130435	+	0.0349500i
$852$	2.10640	−	0.564409i	0.0721642	−	0.0193363i
$853$	−3.74166	−	3.74166i	−0.128112	−	0.128112i	0.640143	−	0.768255i	$-0.278875\pi$
$853$	−3.74166	−	3.74166i	−0.128112	−	0.128112i	−0.768255	+	0.640143i	$0.778875\pi$
$854$	−27.0873	+	6.03102i	−0.926909	+	0.206377i
$855$	−1.90509	+	1.09990i	−0.0651527	+	0.0376159i
$856$	−10.6514	−	2.85405i	−0.364059	−	0.0975493i
$857$	−10.1411			−0.346413			−0.173207	−	0.984885i	$-0.555413\pi$
$857$	−10.1411			−0.346413			−0.173207	+	0.984885i	$0.555413\pi$
$858$	−2.09253	+	3.33948i	−0.0714378	+	0.114008i
$859$		−	32.3015i		−	1.10211i	−0.834468	−	0.551056i	$-0.814225\pi$
$859$		−	32.3015i		−	1.10211i	0.834468	−	0.551056i	$-0.185775\pi$
$860$	11.0234	+	2.95371i	0.375894	+	0.100721i
$861$	−22.5929	−	7.10089i	−0.769965	−	0.241998i
$862$	−14.2099	−	8.20407i	−0.483990	−	0.279432i
$863$	30.9883	+	30.9883i	1.05486	+	1.05486i	0.998405	+	0.0564495i	$0.0179780\pi$
$863$	30.9883	+	30.9883i	1.05486	+	1.05486i	0.0564495	+	0.998405i	$0.482022\pi$
$864$	−1.11198	−	4.14997i	−0.0378304	−	0.141185i
$865$	−4.76606	−	17.7872i	−0.162051	−	0.604782i
$866$	25.5092	+	25.5092i	0.866839	+	0.866839i
$867$	4.74084	+	2.73713i	0.161007	+	0.0929577i
$868$	8.56986	+	2.69348i	0.290880	+	0.0914227i
$869$	6.86889	+	1.84051i	0.233011	+	0.0624352i
$870$		−	13.5709i		−	0.460097i
$871$	−17.4757	+	16.2557i	−0.592143	+	0.550804i
$872$	0.269957			0.00914189
$873$	13.2753	+	3.55710i	0.449300	+	0.120390i
$874$	0.554190	−	0.319962i	0.0187458	−	0.0108229i
$875$	−6.59063	−	29.6007i	−0.222804	−	1.00069i
$876$	2.02378	+	2.02378i	0.0683772	+	0.0683772i
$877$	−17.0303	+	4.56327i	−0.575074	+	0.154091i	−0.534623	−	0.845091i	$-0.679546\pi$
$877$	−17.0303	+	4.56327i	−0.575074	+	0.154091i	−0.0404512	+	0.999182i	$0.512880\pi$
$878$	6.55100	−	1.75533i	0.221086	−	0.0592397i
$879$	−13.6529	+	13.6529i	−0.460500	+	0.460500i
$880$	2.13401	+	1.23207i	0.0719376	+	0.0415332i
$881$	−2.42023	−	4.19196i	−0.0815396	−	0.141231i	0.822372	−	0.568950i	$-0.192650\pi$
$881$	−2.42023	−	4.19196i	−0.0815396	−	0.141231i	−0.903911	+	0.427720i	$0.859317\pi$
$882$	−2.58692	+	7.14802i	−0.0871062	+	0.240686i
$883$		−	23.3796i		−	0.786785i	−0.919371	−	0.393393i	$-0.871301\pi$
$883$		−	23.3796i		−	0.786785i	0.919371	−	0.393393i	$-0.128699\pi$
$884$	14.0187	+	0.507031i	0.471500	+	0.0170533i
$885$		−	1.33813i		−	0.0449808i
$886$	4.80387	−	17.9283i	0.161389	−	0.602313i
$887$	43.5357	−	25.1353i	1.46178	−	0.843962i	0.462690	−	0.886520i	$-0.346884\pi$
$887$	43.5357	−	25.1353i	1.46178	−	0.843962i	0.999094	+	0.0425584i	$0.0135509\pi$
$888$	15.5023	−	26.8508i	0.520224	−	0.901055i
$889$	−37.7462	−	1.61357i	−1.26597	−	0.0541174i
$890$	−16.4487	+	4.40743i	−0.551363	+	0.147737i
$891$	−0.260500	−	0.972198i	−0.00872707	−	0.0325699i
$892$	7.98094	+	7.98094i	0.267222	+	0.267222i
$893$	−5.12755	+	8.88117i	−0.171587	+	0.297197i
$894$	−4.57901	−	7.93108i	−0.153145	−	0.265255i
$895$	−4.11996	+	15.3759i	−0.137715	+	0.513960i
$896$	0.239632	+	0.261035i	0.00800555	+	0.00872056i
$897$	−1.23980	+	0.657235i	−0.0413958	+	0.0219444i
$898$	40.3042			1.34497
$899$	−34.3725	−	9.21008i	−1.14639	−	0.307173i
$900$	1.18554	+	2.05341i	0.0395179	+	0.0684471i
$901$	−30.1814	+	52.2757i	−1.00549	+	1.74156i
$902$	−6.91815	+	6.91815i	−0.230349	+	0.230349i
$903$	21.3695	+	13.5865i	0.711131	+	0.452130i
$904$	−1.73257	−	6.46604i	−0.0576244	−	0.215057i
$905$	4.50381	−	4.50381i	0.149712	−	0.149712i
$906$	0.603403	+	0.348375i	0.0200467	+	0.0115740i
$907$	−31.7089	+	18.3071i	−1.05288	+	0.607878i	−0.923453	−	0.383712i	$-0.874646\pi$
$907$	−31.7089	+	18.3071i	−1.05288	+	0.607878i	−0.129422	+	0.991590i	$0.541312\pi$
$908$	−0.853689	+	3.18601i	−0.0283307	+	0.105732i
$909$	3.95497			0.131178
$910$	−8.52913	+	12.4011i	−0.282738	+	0.411092i
$911$	40.8424			1.35317			0.676585	−	0.736365i	$-0.263459\pi$
$911$	40.8424			1.35317			0.676585	+	0.736365i	$0.263459\pi$
$912$	−0.660353	+	2.46447i	−0.0218665	+	0.0816068i
$913$	3.00056	−	1.73237i	0.0993039	−	0.0573331i
$914$	7.52181	+	4.34272i	0.248799	+	0.143644i
$915$	9.92257	−	9.92257i	0.328030	−	0.328030i
$916$	−0.409350	−	1.52772i	−0.0135253	−	0.0504771i
$917$	25.3937	−	39.9404i	0.838573	−	1.31895i
$918$	3.64034	−	3.64034i	0.120149	−	0.120149i
$919$	12.1413	−	21.0293i	0.400504	−	0.693693i	−0.593283	−	0.804994i	$-0.702168\pi$
$919$	12.1413	−	21.0293i	0.400504	−	0.693693i	0.993787	+	0.111301i	$0.0355018\pi$
$920$	0.866021	+	1.49999i	0.0285519	+	0.0494533i
$921$	23.4877	+	6.29350i	0.773945	+	0.207378i
$922$	−12.0824			−0.397912
$923$	9.15845	+	2.81250i	0.301454	+	0.0925746i
$924$	−1.47793	−	1.60993i	−0.0486202	−	0.0529627i
$925$	−7.56871	+	28.2468i	−0.248858	+	0.928749i
$926$	18.6069	+	32.2281i	0.611461	+	1.05908i
$927$	−6.38543	+	11.0599i	−0.209725	+	0.363255i
$928$	26.1307	+	26.1307i	0.857781	+	0.857781i
$929$	−0.812091	−	3.03077i	−0.0266438	−	0.0994362i	0.951324	−	0.308194i	$-0.0997246\pi$
$929$	−0.812091	−	3.03077i	−0.0266438	−	0.0994362i	−0.977967	+	0.208758i	$0.933058\pi$
$930$	6.30509	−	1.68944i	0.206752	−	0.0553990i
$931$	−8.10665	+	6.82750i	−0.265685	+	0.223762i
$932$	0.463744	−	0.803228i	0.0151904	−	0.0263106i
$933$	12.1796	−	7.03192i	0.398744	−	0.230215i
$934$	−2.96734	+	11.0743i	−0.0970944	+	0.362361i
$935$		−	6.93241i		−	0.226714i
$936$	3.24222	−	10.5578i	0.105975	−	0.345091i
$937$		−	39.6319i		−	1.29472i	−0.762185	−	0.647359i	$-0.775874\pi$
$937$		−	39.6319i		−	1.29472i	0.762185	−	0.647359i	$-0.224126\pi$
$938$	8.79753	+	16.8624i	0.287250	+	0.550576i
$939$	9.40316	+	16.2867i	0.306860	+	0.531498i
$940$	−6.99397	−	4.03797i	−0.228118	−	0.131704i
$941$	−9.63423	+	9.63423i	−0.314067	+	0.314067i	−0.846483	−	0.532416i	$-0.821284\pi$
$941$	−9.63423	+	9.63423i	−0.314067	+	0.314067i	0.532416	+	0.846483i	$0.321284\pi$
$942$	−8.50213	+	2.27814i	−0.277014	+	0.0742258i
$943$	−3.36498	+	0.901643i	−0.109579	+	0.0293615i
$944$	−1.09743	−	1.09743i	−0.0357185	−	0.0357185i
$945$	−0.835406	−	3.75209i	−0.0271757	−	0.122055i
$946$	9.05982	−	5.23069i	0.294560	−	0.170064i
$947$	51.2831	+	13.7413i	1.66648	+	0.446531i	0.964157	−	0.265331i	$-0.0854814\pi$
$947$	51.2831	+	13.7413i	1.66648	+	0.446531i	0.702319	+	0.711862i	$0.252148\pi$
$948$	−5.79842			−0.188324
$949$	2.81326	+	12.2552i	0.0913224	+	0.397821i
$950$		−	4.75047i		−	0.154126i
$951$	2.28409	+	0.612020i	0.0740667	+	0.0198461i
$952$	11.5198	−	36.6526i	0.373359	−	1.18792i
$953$	−28.0071	−	16.1699i	−0.907238	−	0.523794i	−0.0276968	−	0.999616i	$-0.508817\pi$
$953$	−28.0071	−	16.1699i	−0.907238	−	0.523794i	−0.879542	+	0.475822i	$0.842151\pi$
$954$	9.77747	+	9.77747i	0.316557	+	0.316557i
$955$	−3.70398	−	13.8234i	−0.119858	−	0.447316i
$956$	1.08992	+	4.06765i	0.0352506	+	0.131557i
$957$	6.12154	+	6.12154i	0.197881	+	0.197881i
$958$	8.28783	+	4.78498i	0.267768	+	0.154596i
$959$	2.00757	−	6.38749i	0.0648278	−	0.206263i
$960$	−11.2774	−	3.02176i	−0.363975	−	0.0975269i
$961$			13.8839i			0.447867i
$962$	35.0159	−	18.5624i	1.12896	−	0.598475i
$963$	3.59994			0.116006
$964$	7.77010	+	2.08199i	0.250258	+	0.0670565i
$965$	−16.0058	+	9.24094i	−0.515244	+	0.297476i
$966$	0.243019	+	1.09148i	0.00781901	+	0.0351178i
$967$	5.38328	+	5.38328i	0.173115	+	0.173115i	0.788346	−	0.615232i	$-0.210938\pi$
$967$	5.38328	+	5.38328i	0.173115	+	0.173115i	−0.615232	+	0.788346i	$0.710938\pi$
$968$	29.5493	−	7.91771i	0.949750	−	0.254485i
$969$	6.93332	−	1.85778i	0.222730	−	0.0596804i
$970$	15.3331	−	15.3331i	0.492316	−	0.492316i
$971$	36.0969	+	20.8405i	1.15840	+	0.668804i	0.950921	−	0.309434i	$-0.100140\pi$
$971$	36.0969	+	20.8405i	1.15840	+	0.668804i	0.207483	+	0.978239i	$0.433473\pi$
$972$	0.410344	+	0.710736i	0.0131618	+	0.0227969i
$973$	−12.5251	−	24.0071i	−0.401538	−	0.769633i
$974$			22.2941i			0.714348i
$975$	−0.376515	+	10.4101i	−0.0120581	+	0.333391i
$976$		−	16.2755i		−	0.520966i
$977$	−2.38909	+	8.91619i	−0.0764336	+	0.285254i	−0.993555	−	0.113355i	$-0.963840\pi$
$977$	−2.38909	+	8.91619i	−0.0764336	+	0.285254i	0.917121	+	0.398609i	$0.130507\pi$
$978$	12.9187	−	7.45862i	0.413095	−	0.238500i
$979$	5.43157	−	9.40776i	0.173594	−	0.300673i
$980$	−5.37669	−	6.38402i	−0.171752	−	0.203930i
$981$	−0.0851272	+	0.0228098i	−0.00271790	+	0.000728260i
$982$	−0.883840	−	3.29853i	−0.0282045	−	0.105260i
$983$	23.8714	+	23.8714i	0.761380	+	0.761380i	0.976572	−	0.215192i	$-0.0690378\pi$
$983$	23.8714	+	23.8714i	0.761380	+	0.761380i	−0.215192	+	0.976572i	$0.569038\pi$
$984$	13.7094	−	23.7454i	0.437040	−	0.756976i
$985$	−1.13406	−	1.96426i	−0.0361343	−	0.0625864i
$986$	−11.4609	+	42.7726i	−0.364989	+	1.36216i
$987$	−12.1185	−	13.2008i	−0.385736	−	0.420188i
$988$	3.28047	−	3.05145i	0.104365	−	0.0970796i
$989$	3.72497			0.118447
$990$	−1.53391	−	0.411010i	−0.0487508	−	0.0130627i
$991$	−2.66281	−	4.61212i	−0.0845869	−	0.146509i	0.820628	−	0.571462i	$-0.193624\pi$
$991$	−2.66281	−	4.61212i	−0.0845869	−	0.146509i	−0.905215	+	0.424954i	$0.860290\pi$
$992$	−8.88738	+	15.3934i	−0.282175	+	0.488741i
$993$	24.3253	−	24.3253i	0.771940	−	0.771940i
$994$	4.09617	−	6.44265i	0.129923	−	0.204348i
$995$	−4.39582	−	16.4054i	−0.139357	−	0.520087i
$996$	−1.99766	+	1.99766i	−0.0632984	+	0.0632984i
$997$	−28.6452	−	16.5383i	−0.907203	−	0.523774i	−0.0276726	−	0.999617i	$-0.508810\pi$
$997$	−28.6452	−	16.5383i	−0.907203	−	0.523774i	−0.879530	+	0.475843i	$0.842143\pi$
$998$	14.2338	−	8.21788i	0.450563	−	0.260132i
$999$	−2.61971	+	9.77690i	−0.0828841	+	0.309328i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.by.d.76.3	yes	32
3.2	odd	2		819.2.fm.e.622.6		32
7.6	odd	2		273.2.by.c.76.3	✓	32
13.6	odd	12		273.2.by.c.97.3	yes	32
21.20	even	2		819.2.fm.f.622.6		32
39.32	even	12		819.2.fm.f.370.6		32
91.6	even	12	inner	273.2.by.d.97.3	yes	32
273.188	odd	12		819.2.fm.e.370.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.76.3	✓	32	7.6	odd	2
273.2.by.c.97.3	yes	32	13.6	odd	12
273.2.by.d.76.3	yes	32	1.1	even	1	trivial
273.2.by.d.97.3	yes	32	91.6	even	12	inner
819.2.fm.e.370.6		32	273.188	odd	12
819.2.fm.e.622.6		32	3.2	odd	2
819.2.fm.f.370.6		32	39.32	even	12
819.2.fm.f.622.6		32	21.20	even	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.281068 + 1.04896i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.710736 + 0.410344i) q^{4} +(-1.02734 + 1.02734i) q^{5} +(-0.281068 - 1.04896i) q^{6} +(2.23270 + 1.41953i) q^{7} +(-2.16598 + 2.16598i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.281068 + 1.04896i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.710736 + 0.410344i) q^{4} +(-1.02734 + 1.02734i) q^{5} +(-0.281068 - 1.04896i) q^{6} +(2.23270 + 1.41953i) q^{7} +(-2.16598 + 2.16598i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.788887 - 1.36639i) q^{10} +(0.972198 + 0.260500i) q^{11} -0.820687 q^{12} +(-3.05530 - 1.91446i) q^{13} +(-2.11656 + 1.94303i) q^{14} +(0.376033 - 1.40338i) q^{15} +(-0.842549 - 1.45934i) q^{16} +(-2.37035 + 4.10557i) q^{17} +(0.767891 + 0.767891i) q^{18} +(0.391878 + 1.46251i) q^{19} +(-1.15173 + 0.308606i) q^{20} +(-2.64334 - 0.112997i) q^{21} +(-0.546507 + 0.946578i) q^{22} +(-0.337046 + 0.194594i) q^{23} +(0.792804 - 2.95878i) q^{24} +2.88914i q^{25} +(2.86693 - 2.66679i) q^{26} +1.00000i q^{27} +(1.00437 + 1.92508i) q^{28} +(-4.30065 - 7.44895i) q^{29} +(1.36639 + 0.788887i) q^{30} +(2.92542 - 2.92542i) q^{31} +(-4.14997 + 1.11198i) q^{32} +(-0.972198 + 0.260500i) q^{33} +(-3.64034 - 3.64034i) q^{34} +(-3.75209 + 0.835406i) q^{35} +(0.710736 - 0.410344i) q^{36} +(9.77690 + 2.61971i) q^{37} -1.64425 q^{38} +(3.60320 + 0.130321i) q^{39} -4.45041i q^{40} +(8.64616 + 2.31673i) q^{41} +(0.861486 - 2.74099i) q^{42} +(-8.28885 - 4.78557i) q^{43} +(0.584082 + 0.584082i) q^{44} +(0.376033 + 1.40338i) q^{45} +(-0.109388 - 0.408241i) q^{46} +(4.78928 + 4.78928i) q^{47} +(1.45934 + 0.842549i) q^{48} +(2.96989 + 6.33875i) q^{49} +(-3.03058 - 0.812042i) q^{50} -4.74070i q^{51} +(-1.38592 - 2.61440i) q^{52} +12.7329 q^{53} +(-1.04896 - 0.281068i) q^{54} +(-1.26640 + 0.731158i) q^{55} +(-7.91065 + 1.76131i) q^{56} +(-1.07063 - 1.07063i) q^{57} +(9.02241 - 2.41755i) q^{58} +(0.889636 - 0.238377i) q^{59} +(0.843127 - 0.843127i) q^{60} +(8.36449 + 4.82924i) q^{61} +(2.24640 + 3.89088i) q^{62} +(2.34570 - 1.22381i) q^{63} -8.03588i q^{64} +(5.10564 - 1.17203i) q^{65} -1.09301i q^{66} +(1.71328 - 6.39405i) q^{67} +(-3.36939 + 1.94532i) q^{68} +(0.194594 - 0.337046i) q^{69} +(0.178284 - 4.17059i) q^{70} +(-2.56663 + 0.687727i) q^{71} +(0.792804 + 2.95878i) q^{72} +(-2.46596 - 2.46596i) q^{73} +(-5.49594 + 9.51925i) q^{74} +(-1.44457 - 2.50206i) q^{75} +(-0.321609 + 1.20026i) q^{76} +(1.80084 + 1.96168i) q^{77} +(-1.14944 + 3.74297i) q^{78} +7.06532 q^{79} +(2.36483 + 0.633653i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.86031 + 8.41830i) q^{82} +(2.43414 - 2.43414i) q^{83} +(-1.83235 - 1.16499i) q^{84} +(-1.78266 - 6.65299i) q^{85} +(7.34959 - 7.34959i) q^{86} +(7.44895 + 4.30065i) q^{87} +(-2.67000 + 1.54152i) q^{88} +(2.79345 - 10.4253i) q^{89} -1.57777 q^{90} +(-4.10393 - 8.61149i) q^{91} -0.319401 q^{92} +(-1.07078 + 3.99619i) q^{93} +(-6.36986 + 3.67764i) q^{94} +(-1.90509 - 1.09990i) q^{95} +(3.03799 - 3.03799i) q^{96} +(3.55710 + 13.2753i) q^{97} +(-7.48383 + 1.33367i) q^{98} +(0.711699 - 0.711699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q - 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 16 * q^9	\( 32 q - 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 16 q^{9} + 2 q^{10} - 4 q^{11} + 32 q^{12} + 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} - 8 q^{17} + 2 q^{18} + 2 q^{19} + 44 q^{20} - 4 q^{21} - 4 q^{22} - 18 q^{23} + 4 q^{24} - 28 q^{26} - 32 q^{28} - 18 q^{29} - 14 q^{31} - 8 q^{32} + 4 q^{33} - 66 q^{34} + 22 q^{35} + 6 q^{36} - 24 q^{37} + 24 q^{38} + 8 q^{39} - 26 q^{42} - 6 q^{43} - 20 q^{44} + 4 q^{45} - 58 q^{46} - 28 q^{47} - 60 q^{48} + 8 q^{49} + 70 q^{50} + 28 q^{52} - 80 q^{53} - 4 q^{54} + 60 q^{55} - 54 q^{56} + 16 q^{57} - 4 q^{58} - 42 q^{59} - 58 q^{60} + 36 q^{61} + 52 q^{62} + 4 q^{63} + 14 q^{65} + 26 q^{67} - 72 q^{68} + 2 q^{69} - 116 q^{70} - 4 q^{71} + 4 q^{72} + 12 q^{73} - 18 q^{74} + 16 q^{75} - 48 q^{76} + 28 q^{77} - 14 q^{78} - 4 q^{79} - 98 q^{80} - 16 q^{81} + 20 q^{82} - 36 q^{83} - 18 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} - 54 q^{89} + 4 q^{90} + 148 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} + 22 q^{96} - 40 q^{97} + 36 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 16 * q^9 + 2 * q^10 - 4 * q^11 + 32 * q^12 + 6 * q^13 + 34 * q^14 + 4 * q^15 + 14 * q^16 - 8 * q^17 + 2 * q^18 + 2 * q^19 + 44 * q^20 - 4 * q^21 - 4 * q^22 - 18 * q^23 + 4 * q^24 - 28 * q^26 - 32 * q^28 - 18 * q^29 - 14 * q^31 - 8 * q^32 + 4 * q^33 - 66 * q^34 + 22 * q^35 + 6 * q^36 - 24 * q^37 + 24 * q^38 + 8 * q^39 - 26 * q^42 - 6 * q^43 - 20 * q^44 + 4 * q^45 - 58 * q^46 - 28 * q^47 - 60 * q^48 + 8 * q^49 + 70 * q^50 + 28 * q^52 - 80 * q^53 - 4 * q^54 + 60 * q^55 - 54 * q^56 + 16 * q^57 - 4 * q^58 - 42 * q^59 - 58 * q^60 + 36 * q^61 + 52 * q^62 + 4 * q^63 + 14 * q^65 + 26 * q^67 - 72 * q^68 + 2 * q^69 - 116 * q^70 - 4 * q^71 + 4 * q^72 + 12 * q^73 - 18 * q^74 + 16 * q^75 - 48 * q^76 + 28 * q^77 - 14 * q^78 - 4 * q^79 - 98 * q^80 - 16 * q^81 + 20 * q^82 - 36 * q^83 - 18 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 - 54 * q^89 + 4 * q^90 + 148 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 + 22 * q^96 - 40 * q^97 + 36 * q^98 + 4 * q^99

Introduction

L-functions

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