LMFDB - Embedded newform 273.2.by.c.97.6

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			97.6
Character	$\chi$	$=$	273.97
Dual form			273.2.by.c.76.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0578232 + 0.215799i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.68883 - 0.975044i) q^{4} +(-1.08760 - 1.08760i) q^{5} +(-0.0578232 + 0.215799i) q^{6} +(-0.643420 + 2.56632i) q^{7} +(0.624019 + 0.624019i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.0578232 + 0.215799i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.68883 - 0.975044i) q^{4} +(-1.08760 - 1.08760i) q^{5} +(-0.0578232 + 0.215799i) q^{6} +(-0.643420 + 2.56632i) q^{7} +(0.624019 + 0.624019i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.171815 - 0.297592i) q^{10} +(4.17464 - 1.11859i) q^{11} +1.95009 q^{12} +(3.01096 + 1.98346i) q^{13} +(-0.591015 + 0.00954346i) q^{14} +(-0.398089 - 1.48569i) q^{15} +(1.85151 - 3.20690i) q^{16} +(-3.78401 - 6.55410i) q^{17} +(-0.157976 + 0.157976i) q^{18} +(-1.31714 + 4.91565i) q^{19} +(-2.89722 - 0.776309i) q^{20} +(-1.84038 + 1.90079i) q^{21} +(0.482783 + 0.836204i) q^{22} +(-1.85976 - 1.07373i) q^{23} +(0.228407 + 0.852426i) q^{24} -2.63425i q^{25} +(-0.253926 + 0.764453i) q^{26} +1.00000i q^{27} +(1.41565 + 4.96143i) q^{28} +(-2.66646 + 4.61844i) q^{29} +(0.297592 - 0.171815i) q^{30} +(-1.09410 - 1.09410i) q^{31} +(2.50396 + 0.670934i) q^{32} +(4.17464 + 1.11859i) q^{33} +(1.19557 - 1.19557i) q^{34} +(3.49092 - 2.09135i) q^{35} +(1.68883 + 0.975044i) q^{36} +(-2.82556 + 0.757106i) q^{37} -1.13695 q^{38} +(1.61584 + 3.22321i) q^{39} -1.35737i q^{40} +(-1.37894 + 0.369486i) q^{41} +(-0.516606 - 0.287243i) q^{42} +(-6.58558 + 3.80219i) q^{43} +(5.95956 - 5.95956i) q^{44} +(0.398089 - 1.48569i) q^{45} +(0.124173 - 0.463422i) q^{46} +(-5.26364 + 5.26364i) q^{47} +(3.20690 - 1.85151i) q^{48} +(-6.17202 - 3.30245i) q^{49} +(0.568470 - 0.152321i) q^{50} -7.56802i q^{51} +(7.01895 + 0.413900i) q^{52} -13.1808 q^{53} +(-0.215799 + 0.0578232i) q^{54} +(-5.75692 - 3.32376i) q^{55} +(-2.00294 + 1.19993i) q^{56} +(-3.59850 + 3.59850i) q^{57} +(-1.15084 - 0.308366i) q^{58} +(8.73809 + 2.34136i) q^{59} +(-2.12091 - 2.12091i) q^{60} +(10.1891 - 5.88266i) q^{61} +(0.172842 - 0.299371i) q^{62} +(-2.54421 + 0.725943i) q^{63} -6.82688i q^{64} +(-1.11751 - 5.43193i) q^{65} +0.965565i q^{66} +(-1.28138 - 4.78216i) q^{67} +(-12.7811 - 7.37915i) q^{68} +(-1.07373 - 1.85976i) q^{69} +(0.653167 + 0.632408i) q^{70} +(-5.25942 - 1.40926i) q^{71} +(-0.228407 + 0.852426i) q^{72} +(-8.04396 + 8.04396i) q^{73} +(-0.326766 - 0.565975i) q^{74} +(1.31713 - 2.28133i) q^{75} +(2.56854 + 9.58594i) q^{76} +(0.184619 + 11.4332i) q^{77} +(-0.602133 + 0.535073i) q^{78} +9.06635 q^{79} +(-5.50153 + 1.47413i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.159469 - 0.276209i) q^{82} +(-1.13072 - 1.13072i) q^{83} +(-1.25473 + 5.00455i) q^{84} +(-3.01275 + 11.2437i) q^{85} +(-1.20131 - 1.20131i) q^{86} +(-4.61844 + 2.66646i) q^{87} +(3.30308 + 1.90703i) q^{88} +(0.217351 + 0.811166i) q^{89} +0.343629 q^{90} +(-7.02751 + 6.45090i) q^{91} -4.18775 q^{92} +(-0.400469 - 1.49457i) q^{93} +(-1.44025 - 0.831529i) q^{94} +(6.77878 - 3.91373i) q^{95} +(1.83303 + 1.83303i) q^{96} +(4.35890 - 16.2676i) q^{97} +(0.355779 - 1.52288i) q^{98} +(3.05605 + 3.05605i) 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} + 2 q^{21} - 4 q^{22} - 18 q^{23} - 4 q^{24} + 28 q^{26} - 18 q^{28} - 18 q^{29} + 14 q^{31} - 8 q^{32} - 4 q^{33} + 66 q^{34} - 20 q^{35} + 6 q^{36} - 24 q^{37} - 24 q^{38} + 8 q^{39} + 16 q^{42} - 6 q^{43} - 20 q^{44} - 4 q^{45} - 58 q^{46} + 28 q^{47} + 60 q^{48} + 10 q^{49} + 70 q^{50} - 28 q^{52} - 80 q^{53} + 4 q^{54} - 60 q^{55} - 120 q^{56} + 16 q^{57} - 4 q^{58} + 42 q^{59} - 58 q^{60} - 36 q^{61} - 52 q^{62} + 2 q^{63} + 14 q^{65} + 26 q^{67} + 72 q^{68} - 2 q^{69} + 68 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} + 32 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} + 54 q^{89} - 4 q^{90} - 54 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} - 22 q^{96} + 40 q^{97} + 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 + 2 * q^21 - 4 * q^22 - 18 * q^23 - 4 * q^24 + 28 * q^26 - 18 * q^28 - 18 * q^29 + 14 * q^31 - 8 * q^32 - 4 * q^33 + 66 * q^34 - 20 * q^35 + 6 * q^36 - 24 * q^37 - 24 * q^38 + 8 * q^39 + 16 * q^42 - 6 * q^43 - 20 * q^44 - 4 * q^45 - 58 * q^46 + 28 * q^47 + 60 * q^48 + 10 * q^49 + 70 * q^50 - 28 * q^52 - 80 * q^53 + 4 * q^54 - 60 * q^55 - 120 * q^56 + 16 * q^57 - 4 * q^58 + 42 * q^59 - 58 * q^60 - 36 * q^61 - 52 * q^62 + 2 * q^63 + 14 * q^65 + 26 * q^67 + 72 * q^68 - 2 * q^69 + 68 * 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 + 32 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 + 54 * q^89 - 4 * q^90 - 54 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 - 22 * q^96 + 40 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$-1$

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 $

$2$	0.0578232	+	0.215799i	0.0408872	+	0.152593i	0.983351	−	0.181714i	$-0.0581645\pi$
$2$	0.0578232	+	0.215799i	0.0408872	+	0.152593i	−0.942464	+	0.334307i	$0.891498\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	1.68883	−	0.975044i	0.844413	−	0.487522i
$5$	−1.08760	−	1.08760i	−0.486390	−	0.486390i	0.420775	−	0.907165i	$-0.361758\pi$
$5$	−1.08760	−	1.08760i	−0.486390	−	0.486390i	−0.907165	+	0.420775i	$0.861758\pi$
$6$	−0.0578232	+	0.215799i	−0.0236062	+	0.0880997i
$7$	−0.643420	+	2.56632i	−0.243190	+	0.969979i
$7$	−0.643420	+	2.56632i	−0.243190	+	0.969979i
$8$	0.624019	+	0.624019i	0.220624	+	0.220624i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.171815	−	0.297592i	0.0543326	−	0.0941068i
$11$	4.17464	−	1.11859i	1.25870	−	0.337268i	0.433010	−	0.901389i	$-0.357452\pi$
$11$	4.17464	−	1.11859i	1.25870	−	0.337268i	0.825692	+	0.564121i	$0.190785\pi$
$12$	1.95009			0.562942
$13$	3.01096	+	1.98346i	0.835090	+	0.550113i
$13$	3.01096	+	1.98346i	0.835090	+	0.550113i
$14$	−0.591015	+	0.00954346i	−0.157955	+	0.00255060i
$15$	−0.398089	−	1.48569i	−0.102786	−	0.383603i
$16$	1.85151	−	3.20690i	0.462877	−	0.801726i
$17$	−3.78401	−	6.55410i	−0.917757	−	1.58960i	−0.802813	−	0.596231i	$-0.796664\pi$
$17$	−3.78401	−	6.55410i	−0.917757	−	1.58960i	−0.114944	−	0.993372i	$-0.536669\pi$
$18$	−0.157976	+	0.157976i	−0.0372353	+	0.0372353i
$19$	−1.31714	+	4.91565i	−0.302173	+	1.12773i	0.633178	+	0.774006i	$0.281750\pi$
$19$	−1.31714	+	4.91565i	−0.302173	+	1.12773i	−0.935351	+	0.353720i	$0.884916\pi$
$20$	−2.89722	−	0.776309i	−0.647839	−	0.173588i
$21$	−1.84038	+	1.90079i	−0.401604	+	0.414786i
$22$	0.482783	+	0.836204i	0.102930	+	0.178279i
$23$	−1.85976	−	1.07373i	−0.387787	−	0.223889i	0.293414	−	0.955985i	$-0.405209\pi$
$23$	−1.85976	−	1.07373i	−0.387787	−	0.223889i	−0.681201	+	0.732097i	$0.738542\pi$
$24$	0.228407	+	0.852426i	0.0466233	+	0.174001i
$25$		−	2.63425i		−	0.526850i
$26$	−0.253926	+	0.764453i	−0.0497989	+	0.149922i
$27$			1.00000i			0.192450i
$28$	1.41565	+	4.96143i	0.267533	+	0.937623i
$29$	−2.66646	+	4.61844i	−0.495148	+	0.857622i	−0.999984	−	0.00559304i	$-0.998220\pi$
$29$	−2.66646	+	4.61844i	−0.495148	+	0.857622i	0.504836	+	0.863215i	$0.331553\pi$
$30$	0.297592	−	0.171815i	0.0543326	−	0.0313689i
$31$	−1.09410	−	1.09410i	−0.196507	−	0.196507i	0.601994	−	0.798501i	$-0.294373\pi$
$31$	−1.09410	−	1.09410i	−0.196507	−	0.196507i	−0.798501	+	0.601994i	$0.794373\pi$
$32$	2.50396	+	0.670934i	0.442642	+	0.118605i
$33$	4.17464	+	1.11859i	0.726712	+	0.194722i
$34$	1.19557	−	1.19557i	0.205038	−	0.205038i
$35$	3.49092	−	2.09135i	0.590073	−	0.353502i
$36$	1.68883	+	0.975044i	0.281471	+	0.162507i
$37$	−2.82556	+	0.757106i	−0.464519	+	0.124467i	−0.483485	−	0.875353i	$-0.660629\pi$
$37$	−2.82556	+	0.757106i	−0.464519	+	0.124467i	0.0189661	+	0.999820i	$0.493963\pi$
$38$	−1.13695			−0.184438
$39$	1.61584	+	3.22321i	0.258741	+	0.516126i
$40$		−	1.35737i		−	0.214618i
$41$	−1.37894	+	0.369486i	−0.215354	+	0.0577039i	−0.364883	−	0.931053i	$-0.618891\pi$
$41$	−1.37894	+	0.369486i	−0.215354	+	0.0577039i	0.149529	+	0.988757i	$0.452224\pi$
$42$	−0.516606	−	0.287243i	−0.0797140	−	0.0443225i
$43$	−6.58558	+	3.80219i	−1.00429	+	0.579828i	−0.909515	−	0.415671i	$-0.863547\pi$
$43$	−6.58558	+	3.80219i	−1.00429	+	0.579828i	−0.0947764	+	0.995499i	$0.530214\pi$
$44$	5.95956	−	5.95956i	0.898438	−	0.898438i
$45$	0.398089	−	1.48569i	0.0593436	−	0.221473i
$46$	0.124173	−	0.463422i	0.0183084	−	0.0683278i
$47$	−5.26364	+	5.26364i	−0.767781	+	0.767781i	−0.977716	−	0.209934i	$-0.932675\pi$
$47$	−5.26364	+	5.26364i	−0.767781	+	0.767781i	0.209934	+	0.977716i	$0.432675\pi$
$48$	3.20690	−	1.85151i	0.462877	−	0.267242i
$49$	−6.17202	−	3.30245i	−0.881717	−	0.471778i
$50$	0.568470	−	0.152321i	0.0803937	−	0.0215414i
$51$		−	7.56802i		−	1.05974i
$52$	7.01895	+	0.413900i	0.973353	+	0.0573976i
$53$	−13.1808			−1.81053			−0.905263	−	0.424851i	$-0.860327\pi$
$53$	−13.1808			−1.81053			−0.905263	+	0.424851i	$0.860327\pi$
$54$	−0.215799	+	0.0578232i	−0.0293666	+	0.00786874i
$55$	−5.75692	−	3.32376i	−0.776263	−	0.448176i
$56$	−2.00294	+	1.19993i	−0.267654	+	0.160347i
$57$	−3.59850	+	3.59850i	−0.476633	+	0.476633i
$58$	−1.15084	−	0.308366i	−0.151112	−	0.0404905i
$59$	8.73809	+	2.34136i	1.13760	+	0.304820i	0.777987	−	0.628281i	$-0.216241\pi$
$59$	8.73809	+	2.34136i	1.13760	+	0.304820i	0.359616	+	0.933101i	$0.382908\pi$
$60$	−2.12091	−	2.12091i	−0.273809	−	0.273809i
$61$	10.1891	−	5.88266i	1.30458	−	0.753197i	0.323391	−	0.946266i	$-0.395177\pi$
$61$	10.1891	−	5.88266i	1.30458	−	0.753197i	0.981185	+	0.193068i	$0.0618439\pi$
$62$	0.172842	−	0.299371i	0.0219510	−	0.0380202i
$63$	−2.54421	+	0.725943i	−0.320540	+	0.0914602i
$64$		−	6.82688i		−	0.853360i
$65$	−1.11751	−	5.43193i	−0.138610	−	0.673748i
$66$			0.965565i			0.118853i
$67$	−1.28138	−	4.78216i	−0.156545	−	0.584234i	−0.998968	−	0.0454175i	$-0.985538\pi$
$67$	−1.28138	−	4.78216i	−0.156545	−	0.584234i	0.842423	−	0.538817i	$-0.181128\pi$
$68$	−12.7811	−	7.37915i	−1.54993	−	0.894854i
$69$	−1.07373	−	1.85976i	−0.129262	−	0.223889i
$70$	0.653167	+	0.632408i	0.0780684	+	0.0755873i
$71$	−5.25942	−	1.40926i	−0.624179	−	0.167248i	−0.0671520	−	0.997743i	$-0.521391\pi$
$71$	−5.25942	−	1.40926i	−0.624179	−	0.167248i	−0.557027	+	0.830495i	$0.688058\pi$
$72$	−0.228407	+	0.852426i	−0.0269180	+	0.100459i
$73$	−8.04396	+	8.04396i	−0.941474	+	0.941474i	−0.998380	−	0.0569055i	$-0.981877\pi$
$73$	−8.04396	+	8.04396i	−0.941474	+	0.941474i	0.0569055	+	0.998380i	$0.481877\pi$
$74$	−0.326766	−	0.565975i	−0.0379857	−	0.0657932i
$75$	1.31713	−	2.28133i	0.152089	−	0.263425i
$76$	2.56854	+	9.58594i	0.294632	+	1.09958i
$77$	0.184619	+	11.4332i	0.0210392	+	1.30293i
$78$	−0.602133	+	0.535073i	−0.0681781	+	0.0605851i
$79$	9.06635			1.02004			0.510022	−	0.860161i	$-0.329637\pi$
$79$	9.06635			1.02004			0.510022	+	0.860161i	$0.329637\pi$
$80$	−5.50153	+	1.47413i	−0.615090	+	0.164813i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.159469	−	0.276209i	−0.0176104	−	0.0305022i
$83$	−1.13072	−	1.13072i	−0.124113	−	0.124113i	0.642322	−	0.766435i	$-0.277971\pi$
$83$	−1.13072	−	1.13072i	−0.124113	−	0.124113i	−0.766435	+	0.642322i	$0.777971\pi$
$84$	−1.25473	+	5.00455i	−0.136902	+	0.546041i
$85$	−3.01275	+	11.2437i	−0.326778	+	1.21955i
$86$	−1.20131	−	1.20131i	−0.129540	−	0.129540i
$87$	−4.61844	+	2.66646i	−0.495148	+	0.285874i
$88$	3.30308	+	1.90703i	0.352109	+	0.203290i
$89$	0.217351	+	0.811166i	0.0230392	+	0.0859834i	0.976488	−	0.215571i	$-0.0691612\pi$
$89$	0.217351	+	0.811166i	0.0230392	+	0.0859834i	−0.953449	+	0.301554i	$0.902495\pi$
$90$	0.343629			0.0362217
$91$	−7.02751	+	6.45090i	−0.736683	+	0.676238i
$92$	−4.18775			−0.436603
$93$	−0.400469	−	1.49457i	−0.0415267	−	0.154980i
$94$	−1.44025	−	0.831529i	−0.148551	−	0.0857657i
$95$	6.77878	−	3.91373i	0.695488	−	0.401540i
$96$	1.83303	+	1.83303i	0.187082	+	0.187082i
$97$	4.35890	−	16.2676i	0.442579	−	1.65173i	−0.279672	−	0.960096i	$-0.590226\pi$
$97$	4.35890	−	16.2676i	0.442579	−	1.65173i	0.722251	−	0.691631i	$-0.243108\pi$
$98$	0.355779	−	1.52288i	0.0359391	−	0.153834i
$99$	3.05605	+	3.05605i	0.307145	+	0.307145i
$100$	−2.56851	−	4.44879i	−0.256851	−	0.444879i
$101$	5.48585	−	9.50177i	0.545863	−	0.945462i	−0.452690	−	0.891668i	$-0.649535\pi$
$101$	5.48585	−	9.50177i	0.545863	−	0.945462i	0.998552	−	0.0537934i	$-0.0171313\pi$
$102$	1.63317	−	0.437607i	0.161708	−	0.0433296i
$103$	4.70231			0.463332			0.231666	−	0.972795i	$-0.425582\pi$
$103$	4.70231			0.463332			0.231666	+	0.972795i	$0.425582\pi$
$104$	0.641180	+	3.11661i	0.0628728	+	0.305609i
$105$	4.06890	−	0.0657028i	0.397084	−	0.00641194i
$106$	−0.762158	−	2.84441i	−0.0740274	−	0.276274i
$107$	6.55307	−	11.3502i	0.633509	−	1.09727i	−0.353320	−	0.935503i	$-0.614947\pi$
$107$	6.55307	−	11.3502i	0.633509	−	1.09727i	0.986829	−	0.161767i	$-0.0517194\pi$
$108$	0.975044	+	1.68883i	0.0938236	+	0.162507i
$109$	−0.872057	+	0.872057i	−0.0835279	+	0.0835279i	−0.747636	−	0.664108i	$-0.768811\pi$
$109$	−0.872057	+	0.872057i	−0.0835279	+	0.0835279i	0.664108	+	0.747636i	$0.268811\pi$
$110$	0.384381	−	1.43453i	0.0366493	−	0.136777i
$111$	−2.82556	−	0.757106i	−0.268190	−	0.0718613i
$112$	7.03865	+	6.81495i	0.665090	+	0.643952i
$113$	6.21370	+	10.7625i	0.584536	+	1.01245i	0.994933	+	0.100539i	$0.0320568\pi$
$113$	6.21370	+	10.7625i	0.584536	+	1.01245i	−0.410397	+	0.911907i	$0.634610\pi$
$114$	−0.984631	−	0.568477i	−0.0922192	−	0.0532428i
$115$	0.854883	+	3.19047i	0.0797183	+	0.297513i
$116$			10.3996i			0.965583i
$117$	−0.212247	+	3.59930i	−0.0196222	+	0.332755i
$118$			2.02106i			0.186053i
$119$	19.2546	−	5.49395i	1.76507	−	0.503630i
$120$	0.678683	−	1.17551i	0.0619550	−	0.107309i
$121$	6.65011	−	3.83944i	0.604556	−	0.349040i
$122$	1.85864	+	1.85864i	0.168273	+	0.168273i
$123$	−1.37894	−	0.369486i	−0.124335	−	0.0333154i
$124$	−2.91455	−	0.780950i	−0.261734	−	0.0701314i
$125$	−8.30301	+	8.30301i	−0.742644	+	0.742644i
$126$	−0.303772	−	0.507062i	−0.0270622	−	0.0451727i
$127$	5.51334	+	3.18313i	0.489230	+	0.282457i	0.724255	−	0.689532i	$-0.242184\pi$
$127$	5.51334	+	3.18313i	0.489230	+	0.282457i	−0.235025	+	0.971989i	$0.575517\pi$
$128$	6.48115	−	1.73662i	0.572858	−	0.153497i
$129$	−7.60437			−0.669528
$130$	1.10759	−	0.555250i	0.0971420	−	0.0486986i
$131$			3.73498i			0.326327i	0.986599	+	0.163163i	$0.0521698\pi$
$131$			3.73498i			0.326327i	−0.986599	+	0.163163i	$0.947830\pi$
$132$	8.14092	−	2.18135i	0.708576	−	0.189862i
$133$	−11.7677	−	6.54304i	−1.02039	−	0.567354i
$134$	0.957894	−	0.553040i	0.0827494	−	0.0477754i
$135$	1.08760	−	1.08760i	0.0936057	−	0.0936057i
$136$	1.72859	−	6.45118i	0.148225	−	0.553184i
$137$	0.00793713	−	0.0296218i	0.000678115	−	0.00253076i	−0.965586	−	0.260084i	$-0.916250\pi$
$137$	0.00793713	−	0.0296218i	0.000678115	−	0.00253076i	0.966264	+	0.257553i	$0.0829163\pi$
$138$	0.339248	−	0.339248i	0.0288787	−	0.0288787i
$139$	−2.85559	+	1.64867i	−0.242208	+	0.139839i	−0.616191	−	0.787597i	$-0.711325\pi$
$139$	−2.85559	+	1.64867i	−0.242208	+	0.139839i	0.373983	+	0.927435i	$0.377992\pi$
$140$	3.85639	−	6.93572i	0.325924	−	0.586175i
$141$	−7.19027	+	1.92663i	−0.605530	+	0.162251i
$142$		−	1.21647i		−	0.102084i
$143$	14.7884	+	4.91220i	1.23667	+	0.410779i
$144$	3.70301			0.308585
$145$	7.92305	−	2.12297i	0.657974	−	0.176303i
$146$	−2.20101	−	1.27075i	−0.182157	−	0.105168i
$147$	−3.69390	−	5.94601i	−0.304668	−	0.490419i
$148$	−4.03366	+	4.03366i	−0.331565	+	0.331565i
$149$	4.52646	+	1.21286i	0.370822	+	0.0993615i	0.439417	−	0.898283i	$-0.355185\pi$
$149$	4.52646	+	1.21286i	0.370822	+	0.0993615i	−0.0685950	+	0.997645i	$0.521852\pi$
$150$	0.568470	+	0.152321i	0.0464153	+	0.0124370i
$151$	−4.74970	−	4.74970i	−0.386525	−	0.386525i	0.486921	−	0.873446i	$-0.338120\pi$
$151$	−4.74970	−	4.74970i	−0.386525	−	0.386525i	−0.873446	+	0.486921i	$0.838120\pi$
$152$	−3.88938	+	2.24553i	−0.315470	+	0.182137i
$153$	3.78401	−	6.55410i	0.305919	−	0.529868i
$154$	−2.45660	+	0.700945i	−0.197959	+	0.0564838i
$155$			2.37989i			0.191158i
$156$	5.87164	+	3.86792i	0.470107	+	0.309682i
$157$			17.1115i			1.36565i	0.730584	+	0.682823i	$0.239248\pi$
$157$			17.1115i			1.36565i	−0.730584	+	0.682823i	$0.760752\pi$
$158$	0.524246	+	1.95651i	0.0417068	+	0.155652i
$159$	−11.4149	−	6.59042i	−0.905263	−	0.522654i
$160$	−1.99360	−	3.45301i	−0.157608	−	0.272985i
$161$	3.95215	−	4.08188i	0.311473	−	0.321697i
$162$	−0.215799	−	0.0578232i	−0.0169548	−	0.00454302i
$163$	5.05271	−	18.8570i	0.395759	−	1.47699i	−0.424726	−	0.905322i	$-0.639630\pi$
$163$	5.05271	−	18.8570i	0.395759	−	1.47699i	0.820484	−	0.571669i	$-0.193704\pi$
$164$	−1.96852	+	1.96852i	−0.153716	+	0.153716i
$165$	−3.32376	−	5.75692i	−0.258754	−	0.448176i
$166$	0.178627	−	0.309390i	0.0138641	−	0.0240134i
$167$	3.66374	+	13.6733i	0.283508	+	1.05807i	0.949922	+	0.312486i	$0.101162\pi$
$167$	3.66374	+	13.6733i	0.283508	+	1.05807i	−0.666414	+	0.745582i	$0.732172\pi$
$168$	−2.33456	+	0.0376975i	−0.180115	+	0.00290843i
$169$	5.13177	+	11.9442i	0.394751	+	0.918788i
$170$	−2.60060			−0.199457
$171$	−4.91565	+	1.31714i	−0.375909	+	0.100724i
$172$	−7.41460	+	12.8425i	−0.565358	+	0.979228i
$173$	9.66072	+	16.7329i	0.734491	+	1.27218i	0.954946	+	0.296778i	$0.0959122\pi$
$173$	9.66072	+	16.7329i	0.734491	+	1.27218i	−0.220456	+	0.975397i	$0.570754\pi$
$174$	−0.842472	−	0.842472i	−0.0638676	−	0.0638676i
$175$	6.76034	+	1.69493i	0.511034	+	0.128125i
$176$	4.14216	−	15.4588i	0.312227	−	1.16525i
$177$	6.39672	+	6.39672i	0.480807	+	0.480807i
$178$	−0.162481	+	0.0938085i	−0.0121785	+	0.00703124i
$179$	3.56116	+	2.05604i	0.266173	+	0.153675i	0.627147	−	0.778901i	$-0.284222\pi$
$179$	3.56116	+	2.05604i	0.266173	+	0.153675i	−0.360974	+	0.932576i	$0.617556\pi$
$180$	−0.776309	−	2.89722i	−0.0578626	−	0.215946i
$181$	−2.09652			−0.155833			−0.0779165	−	0.996960i	$-0.524827\pi$
$181$	−2.09652			−0.155833			−0.0779165	+	0.996960i	$0.524827\pi$
$182$	−1.79845	−	1.14352i	−0.133310	−	0.0847633i
$183$	11.7653			0.869717
$184$	−0.490496	−	1.83056i	−0.0361598	−	0.134950i
$185$	3.89650	+	2.24965i	0.286477	+	0.165397i
$186$	0.299371	−	0.172842i	0.0219510	−	0.0126734i
$187$	−23.1283	−	23.1283i	−1.69131	−	1.69131i
$188$	−3.75709	+	14.0217i	−0.274014	+	1.02263i
$189$	−2.56632	−	0.643420i	−0.186672	−	0.0468019i
$190$	1.23655	+	1.23655i	0.0897089	+	0.0897089i
$191$	4.22074	+	7.31054i	0.305402	+	0.528972i	0.977351	−	0.211626i	$-0.0678758\pi$
$191$	4.22074	+	7.31054i	0.305402	+	0.528972i	−0.671949	+	0.740598i	$0.734542\pi$
$192$	3.41344	−	5.91225i	0.246344	−	0.426680i
$193$	1.96647	−	0.526915i	0.141550	−	0.0379282i	−0.187348	−	0.982294i	$-0.559989\pi$
$193$	1.96647	−	0.526915i	0.141550	−	0.0379282i	0.328898	+	0.944365i	$0.393323\pi$
$194$	3.76259			0.270138
$195$	1.74818	−	5.26295i	0.125189	−	0.376887i
$196$	−13.6435	+	0.440734i	−0.974535	+	0.0314810i
$197$	3.46988	+	12.9498i	0.247219	+	0.922632i	0.972255	+	0.233922i	$0.0751561\pi$
$197$	3.46988	+	12.9498i	0.247219	+	0.922632i	−0.725037	+	0.688710i	$0.758177\pi$
$198$	−0.482783	+	0.836204i	−0.0343099	+	0.0594264i
$199$	−3.76822	−	6.52675i	−0.267122	−	0.462669i	0.700995	−	0.713166i	$-0.252739\pi$
$199$	−3.76822	−	6.52675i	−0.267122	−	0.462669i	−0.968117	+	0.250497i	$0.919406\pi$
$200$	1.64382	−	1.64382i	0.116236	−	0.116236i
$201$	1.28138	−	4.78216i	0.0903814	−	0.337308i
$202$	2.36768	+	0.634419i	0.166590	+	0.0446376i
$203$	−10.1367	−	9.81458i	−0.711460	−	0.688849i
$204$	−7.37915	−	12.7811i	−0.516644	−	0.894854i
$205$	1.90159	+	1.09788i	0.132813	+	0.0766794i
$206$	0.271903	+	1.01475i	0.0189444	+	0.0707013i
$207$		−	2.14747i		−	0.149259i
$208$	11.9356	−	5.98347i	0.827584	−	0.414879i
$209$			21.9944i			1.52139i
$210$	0.249455	+	0.874266i	0.0172141	+	0.0603301i
$211$	8.48310	−	14.6932i	0.584001	−	1.01152i	−0.410998	−	0.911636i	$-0.634820\pi$
$211$	8.48310	−	14.6932i	0.584001	−	1.01152i	0.994999	−	0.0998830i	$-0.0318469\pi$
$212$	−22.2601	+	12.8519i	−1.52883	+	0.882671i
$213$	−3.85017	−	3.85017i	−0.263809	−	0.263809i
$214$	2.82829	+	0.757839i	0.193338	+	0.0518048i
$215$	11.2977	+	3.02722i	0.770499	+	0.206455i
$216$	−0.624019	+	0.624019i	−0.0424591	+	0.0424591i
$217$	3.51179	−	2.10385i	0.238396	−	0.142819i
$218$	−0.238614	−	0.137764i	−0.0161610	−	0.00933056i
$219$	−10.9883	+	2.94429i	−0.742517	+	0.198957i
$220$	−12.9632			−0.873982
$221$	1.60629	−	27.2396i	0.108051	−	1.83233i
$222$		−	0.653531i		−	0.0438622i
$223$	12.1895	−	3.26617i	0.816269	−	0.218719i	0.173555	−	0.984824i	$-0.444475\pi$
$223$	12.1895	−	3.26617i	0.816269	−	0.218719i	0.642715	+	0.766106i	$0.277808\pi$
$224$	−3.33293	+	5.99427i	−0.222691	+	0.400509i
$225$	2.28133	−	1.31713i	0.152089	−	0.0878084i
$226$	−1.96323	+	1.96323i	−0.130592	+	0.130592i
$227$	5.09212	−	19.0040i	0.337976	−	1.26134i	−0.562631	−	0.826708i	$-0.690211\pi$
$227$	5.09212	−	19.0040i	0.337976	−	1.26134i	0.900607	−	0.434635i	$-0.143122\pi$
$228$	−2.56854	+	9.58594i	−0.170106	+	0.634844i
$229$	−19.8246	+	19.8246i	−1.31004	+	1.31004i	−0.388666	+	0.921379i	$0.627064\pi$
$229$	−19.8246	+	19.8246i	−1.31004	+	1.31004i	−0.921379	+	0.388666i	$0.872936\pi$
$230$	−0.639068	+	0.368966i	−0.0421389	+	0.0243289i
$231$	−5.55672	+	9.99375i	−0.365605	+	0.657541i
$232$	−4.54591	+	1.21807i	−0.298454	+	0.0799704i
$233$			10.8900i			0.713427i	0.934214	+	0.356714i	$0.116103\pi$
$233$			10.8900i			0.713427i	−0.934214	+	0.356714i	$0.883897\pi$
$234$	−0.788999	+	0.162320i	−0.0515785	+	0.0106112i
$235$	11.4495			0.746882
$236$	17.0400	−	4.56586i	1.10921	−	0.297212i
$237$	7.85169	+	4.53318i	0.510022	+	0.294461i
$238$	2.29896	+	3.83746i	0.149019	+	0.248745i
$239$	−10.0403	+	10.0403i	−0.649451	+	0.649451i	−0.952860	−	0.303409i	$-0.901875\pi$
$239$	−10.0403	+	10.0403i	−0.649451	+	0.649451i	0.303409	+	0.952860i	$0.401875\pi$
$240$	−5.50153	−	1.47413i	−0.355122	−	0.0951547i
$241$	−15.1305	−	4.05421i	−0.974642	−	0.261155i	−0.263856	−	0.964562i	$-0.584994\pi$
$241$	−15.1305	−	4.05421i	−0.974642	−	0.261155i	−0.710787	+	0.703408i	$0.751661\pi$
$242$	1.21308	+	1.21308i	0.0779797	+	0.0779797i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	11.4717	−	19.8696i	0.734400	−	1.27202i
$245$	3.12095	+	10.3044i	0.199390	+	0.658326i
$246$		−	0.318939i		−	0.0203348i
$247$	−13.7159	+	12.1883i	−0.872719	+	0.775524i
$248$		−	1.36548i		−	0.0867082i
$249$	−0.413872	−	1.54459i	−0.0262281	−	0.0978846i
$250$	−2.27189	−	1.31168i	−0.143687	−	0.0829577i
$251$	−10.7847	−	18.6797i	−0.680727	−	1.17905i	−0.974759	−	0.223258i	$-0.928331\pi$
$251$	−10.7847	−	18.6797i	−0.680727	−	1.17905i	0.294033	−	0.955795i	$-0.405003\pi$
$252$	−3.58890	+	3.70671i	−0.226079	+	0.233501i
$253$	−8.96490	−	2.40214i	−0.563619	−	0.151021i
$254$	−0.368118	+	1.37383i	−0.0230977	+	0.0862020i
$255$	−8.23098	+	8.23098i	−0.515444	+	0.515444i
$256$	−6.07736	−	10.5263i	−0.379835	−	0.657893i
$257$	1.05953	−	1.83517i	0.0660920	−	0.114475i	−0.831086	−	0.556144i	$-0.812280\pi$
$257$	1.05953	−	1.83517i	0.0660920	−	0.114475i	0.897178	+	0.441669i	$0.145614\pi$
$258$	−0.439709	−	1.64102i	−0.0273751	−	0.102165i
$259$	−0.124957	−	7.73843i	−0.00776444	−	0.480843i
$260$	−7.18365	−	8.08396i	−0.445511	−	0.501346i
$261$	−5.33291			−0.330099
$262$	−0.806006	+	0.215969i	−0.0497952	+	0.0133426i
$263$	5.53188	−	9.58150i	0.341111	−	0.590821i	−0.643529	−	0.765422i	$-0.722530\pi$
$263$	5.53188	−	9.58150i	0.341111	−	0.590821i	0.984639	+	0.174601i	$0.0558636\pi$
$264$	1.90703	+	3.30308i	0.117370	+	0.203290i
$265$	14.3355	+	14.3355i	0.880621	+	0.880621i
$266$	0.731539	−	2.91779i	0.0448536	−	0.178901i
$267$	−0.217351	+	0.811166i	−0.0133017	+	0.0496425i
$268$	−6.82684	−	6.82684i	−0.417016	−	0.417016i
$269$	23.8459	−	13.7675i	1.45391	−	0.839416i	0.455211	−	0.890383i	$-0.349564\pi$
$269$	23.8459	−	13.7675i	1.45391	−	0.839416i	0.998700	+	0.0509670i	$0.0162303\pi$
$270$	0.297592	+	0.171815i	0.0181109	+	0.0104563i
$271$	3.80218	+	14.1899i	0.230966	+	0.861978i	0.979926	+	0.199362i	$0.0638870\pi$
$271$	3.80218	+	14.1899i	0.230966	+	0.861978i	−0.748960	+	0.662616i	$0.769446\pi$
$272$	−28.0245			−1.69923
$273$	−9.31145	+	2.07288i	−0.563555	+	0.125457i
$274$	0.00685131			0.000413903
$275$	−2.94665	−	10.9971i	−0.177690	−	0.663148i
$276$	−3.62669	−	2.09387i	−0.218301	−	0.126036i
$277$	4.50623	−	2.60167i	0.270753	−	0.156319i	−0.358477	−	0.933539i	$-0.616704\pi$
$277$	4.50623	−	2.60167i	0.270753	−	0.156319i	0.629230	+	0.777219i	$0.283370\pi$
$278$	−0.520902	−	0.520902i	−0.0312416	−	0.0312416i
$279$	0.400469	−	1.49457i	0.0239755	−	0.0894777i
$280$	3.48344	+	0.873357i	0.208175	+	0.0521931i
$281$	−10.7634	−	10.7634i	−0.642088	−	0.642088i	0.308980	−	0.951068i	$-0.400012\pi$
$281$	−10.7634	−	10.7634i	−0.642088	−	0.642088i	−0.951068	+	0.308980i	$0.900012\pi$
$282$	−0.831529	−	1.44025i	−0.0495168	−	0.0857657i
$283$	−2.03356	+	3.52223i	−0.120882	+	0.209375i	−0.920116	−	0.391646i	$-0.871906\pi$
$283$	−2.03356	+	3.52223i	−0.120882	+	0.209375i	0.799233	+	0.601021i	$0.205239\pi$
$284$	−10.2563	+	2.74818i	−0.608601	+	0.163074i
$285$	7.82746			0.463659
$286$	−0.204938	+	3.47536i	−0.0121183	+	0.205502i
$287$	−0.0609819	−	3.77654i	−0.00359965	−	0.222922i
$288$	0.670934	+	2.50396i	0.0395352	+	0.147547i
$289$	−20.1375	+	34.8791i	−1.18456	+	2.05171i
$290$	0.916273	+	1.58703i	0.0538054	+	0.0931937i
$291$	11.9087	−	11.9087i	0.698102	−	0.698102i
$292$	−5.74163	+	21.4280i	−0.336003	+	1.25398i
$293$	−21.3183	−	5.71221i	−1.24543	−	0.333711i	−0.424858	−	0.905260i	$-0.639676\pi$
$293$	−21.3183	−	5.71221i	−1.24543	−	0.333711i	−0.820568	+	0.571549i	$0.806343\pi$
$294$	1.06955	−	1.14096i	0.0623775	−	0.0665421i
$295$	−6.95708	−	12.0500i	−0.405057	−	0.701579i
$296$	−2.23565	−	1.29075i	−0.129944	−	0.0750235i
$297$	1.11859	+	4.17464i	0.0649073	+	0.242237i
$298$			1.04694i			0.0606475i
$299$	−3.46996	−	6.92173i	−0.200673	−	0.400294i
$300$		−	5.13702i		−	0.296586i
$301$	−5.52034	−	19.3471i	−0.318187	−	1.11515i
$302$	0.750339	−	1.29962i	0.0431771	−	0.0747850i
$303$	9.50177	−	5.48585i	0.545863	−	0.315154i
$304$	13.3253	+	13.3253i	0.764259	+	0.764259i
$305$	−17.4796	−	4.68365i	−1.00088	−	0.268185i
$306$	1.63317	+	0.437607i	0.0933623	+	0.0250164i
$307$	9.60326	−	9.60326i	0.548087	−	0.548087i	−0.377800	−	0.925887i	$-0.623319\pi$
$307$	9.60326	−	9.60326i	0.548087	−	0.548087i	0.925887	+	0.377800i	$0.123319\pi$
$308$	11.4597	+	19.1287i	0.652975	+	1.08996i
$309$	4.07232	+	2.35115i	0.231666	+	0.133753i
$310$	−0.513579	+	0.137613i	−0.0291693	+	0.00781590i
$311$	16.2194			0.919715			0.459858	−	0.887993i	$-0.347900\pi$
$311$	16.2194			0.919715			0.459858	+	0.887993i	$0.347900\pi$
$312$	−1.00303	+	3.01966i	−0.0567853	+	0.170954i
$313$		−	24.2234i		−	1.36919i	−0.728926	−	0.684593i	$-0.759980\pi$
$313$		−	24.2234i		−	1.36919i	0.728926	−	0.684593i	$-0.240020\pi$
$314$	−3.69265	+	0.989442i	−0.208388	+	0.0558375i
$315$	3.55662	+	1.97755i	0.200393	+	0.111422i
$316$	15.3115	−	8.84009i	0.861338	−	0.497294i
$317$	−18.9182	+	18.9182i	−1.06255	+	1.06255i	−0.0646418	+	0.997909i	$0.520590\pi$
$317$	−18.9182	+	18.9182i	−1.06255	+	1.06255i	−0.997909	+	0.0646418i	$0.979410\pi$
$318$	0.762158	−	2.84441i	0.0427397	−	0.159507i
$319$	−5.96535	+	22.2630i	−0.333996	+	1.24649i
$320$	−7.42492	+	7.42492i	−0.415065	+	0.415065i
$321$	11.3502	−	6.55307i	0.633509	−	0.365757i
$322$	1.10939	+	0.616844i	0.0618241	+	0.0343754i
$323$	37.2017	−	9.96817i	2.06996	−	0.554644i
$324$			1.95009i			0.108338i
$325$	5.22494	−	7.93163i	0.289827	−	0.439968i
$326$	4.36148			0.241560
$327$	−1.19125	+	0.319195i	−0.0658764	+	0.0176515i
$328$	−1.09105	−	0.629918i	−0.0602432	−	0.0347814i
$329$	−10.1215	−	16.8949i	−0.558015	−	0.931448i
$330$	1.05015	−	1.05015i	0.0578088	−	0.0578088i
$331$	13.9589	+	3.74029i	0.767253	+	0.205585i	0.621157	−	0.783686i	$-0.286663\pi$
$331$	13.9589	+	3.74029i	0.767253	+	0.205585i	0.146095	+	0.989271i	$0.453329\pi$
$332$	−3.01209	−	0.807087i	−0.165310	−	0.0442947i
$333$	−2.06845	−	2.06845i	−0.113350	−	0.113350i
$334$	−2.73883	+	1.58126i	−0.149862	+	0.0865229i
$335$	−3.80746	+	6.59471i	−0.208024	+	0.360307i
$336$	2.68818	+	9.42125i	0.146652	+	0.513971i
$337$		−	5.15524i		−	0.280824i	−0.990093	−	0.140412i	$-0.955157\pi$
$337$		−	5.15524i		−	0.280824i	0.990093	−	0.140412i	$-0.0448426\pi$
$338$	−2.28082	+	1.79809i	−0.124060	+	0.0978030i
$339$			12.4274i			0.674964i
$340$	5.87512	+	21.9263i	0.318623	+	1.18912i
$341$	−5.79134	−	3.34363i	−0.313619	−	0.181068i
$342$	−0.568477	−	0.984631i	−0.0307397	−	0.0532428i
$343$	12.4463	−	13.7145i	0.672040	−	0.740515i
$344$	−6.48216	−	1.73689i	−0.349495	−	0.0936469i
$345$	−0.854883	+	3.19047i	−0.0460254	+	0.171769i
$346$	−3.05232	+	3.05232i	−0.164094	+	0.164094i
$347$	11.9012	+	20.6134i	0.638888	+	1.10659i	0.985677	+	0.168643i	$0.0539385\pi$
$347$	11.9012	+	20.6134i	0.638888	+	1.10659i	−0.346789	+	0.937943i	$0.612728\pi$
$348$	−5.19982	+	9.00636i	−0.278740	+	0.482791i
$349$	−3.16538	−	11.8134i	−0.169439	−	0.632355i	−0.997432	−	0.0716166i	$-0.977184\pi$
$349$	−3.16538	−	11.8134i	−0.169439	−	0.632355i	0.827993	−	0.560738i	$-0.189482\pi$
$350$	0.0251399	+	1.55688i	0.00134378	+	0.0832189i
$351$	−1.98346	+	3.01096i	−0.105869	+	0.160713i
$352$	11.2036			0.597156
$353$	−16.5186	+	4.42614i	−0.879196	+	0.235580i	−0.670060	−	0.742307i	$-0.733732\pi$
$353$	−16.5186	+	4.42614i	−0.879196	+	0.235580i	−0.209136	+	0.977887i	$0.567065\pi$
$354$	−1.01053	+	1.75029i	−0.0537090	+	0.0930267i
$355$	4.18744	+	7.25286i	0.222246	+	0.384942i
$356$	1.15799	+	1.15799i	0.0613734	+	0.0613734i
$357$	19.4220	+	4.86942i	1.02792	+	0.257717i
$358$	−0.237773	+	0.887382i	−0.0125667	+	0.0468996i
$359$	14.6210	+	14.6210i	0.771665	+	0.771665i	0.978397	−	0.206733i	$-0.0662831\pi$
$359$	14.6210	+	14.6210i	0.771665	+	0.771665i	−0.206733	+	0.978397i	$0.566283\pi$
$360$	1.17551	−	0.678683i	0.0619550	−	0.0357697i
$361$	−5.97423	−	3.44922i	−0.314433	−	0.181538i
$362$	−0.121228	−	0.452427i	−0.00637158	−	0.0237790i
$363$	7.67889			0.403037
$364$	−5.57833	+	17.7466i	−0.292384	+	0.930173i
$365$	17.4972			0.915846
$366$	0.680309	+	2.53895i	0.0355603	+	0.132713i
$367$	0.401157	+	0.231608i	0.0209402	+	0.0120898i	0.510434	−	0.859917i	$-0.329485\pi$
$367$	0.401157	+	0.231608i	0.0209402	+	0.0120898i	−0.489493	+	0.872007i	$0.662818\pi$
$368$	−6.88672	+	3.97605i	−0.358995	+	0.207266i
$369$	−1.00945	−	1.00945i	−0.0525500	−	0.0525500i
$370$	−0.260164	+	0.970945i	−0.0135253	+	0.0504770i
$371$	8.48081	−	33.8263i	0.440302	−	1.75617i
$372$	−2.13360	−	2.13360i	−0.110622	−	0.110622i
$373$	−0.348917	−	0.604342i	−0.0180662	−	0.0312916i	0.856851	−	0.515564i	$-0.172418\pi$
$373$	−0.348917	−	0.604342i	−0.0180662	−	0.0312916i	−0.874917	+	0.484273i	$0.839084\pi$
$374$	3.65371	−	6.32841i	0.188929	−	0.327234i
$375$	−11.3421	+	3.03911i	−0.585705	+	0.156939i
$376$	−6.56923			−0.338782
$377$	−17.1891	+	8.61712i	−0.885283	+	0.443804i
$378$	−0.00954346	−	0.591015i	−0.000490863	−	0.0303985i
$379$	1.85118	+	6.90871i	0.0950889	+	0.354877i	0.997033	−	0.0769763i	$-0.0245266\pi$
$379$	1.85118	+	6.90871i	0.0950889	+	0.354877i	−0.901944	+	0.431853i	$0.857860\pi$
$380$	7.63212	−	13.2192i	0.391519	−	0.678132i
$381$	3.18313	+	5.51334i	0.163077	+	0.282457i
$382$	−1.33355	+	1.33355i	−0.0682305	+	0.0682305i
$383$	0.496583	−	1.85327i	0.0253742	−	0.0946979i	−0.952078	−	0.305857i	$-0.901057\pi$
$383$	0.496583	−	1.85327i	0.0253742	−	0.0946979i	0.977452	+	0.211159i	$0.0677238\pi$
$384$	6.48115	+	1.73662i	0.330740	+	0.0886215i
$385$	12.2340	−	12.6355i	0.623500	−	0.643967i
$386$	0.227416	+	0.393895i	0.0115751	+	0.0200487i
$387$	−6.58558	−	3.80219i	−0.334764	−	0.193276i
$388$	−8.50023	−	31.7233i	−0.431534	−	1.61051i
$389$			6.17075i			0.312870i	0.987688	+	0.156435i	$0.0500001\pi$
$389$			6.17075i			0.312870i	−0.987688	+	0.156435i	$0.950000\pi$
$390$	1.23682	+	0.0729343i	0.0626291	+	0.00369317i
$391$			16.2521i			0.821903i
$392$	−1.79067	−	5.91225i	−0.0904424	−	0.298614i
$393$	−1.86749	+	3.23459i	−0.0942025	+	0.163163i
$394$	−2.59391	+	1.49759i	−0.130679	+	0.0754477i
$395$	−9.86057	−	9.86057i	−0.496139	−	0.496139i
$396$	8.14092	+	2.18135i	0.409096	+	0.109617i
$397$	30.1243	+	8.07177i	1.51189	+	0.405111i	0.917063	−	0.398741i	$-0.130553\pi$
$397$	30.1243	+	8.07177i	1.51189	+	0.405111i	0.594830	+	0.803852i	$0.297220\pi$
$398$	1.19058	−	1.19058i	0.0596782	−	0.0596782i
$399$	−6.91957	−	11.5503i	−0.346412	−	0.578237i
$400$	−8.44780	−	4.87734i	−0.422390	−	0.243867i
$401$	24.2526	−	6.49846i	1.21112	−	0.324517i	0.403916	−	0.914796i	$-0.367649\pi$
$401$	24.2526	−	6.49846i	1.21112	−	0.324517i	0.807199	+	0.590279i	$0.200982\pi$
$402$	1.10608			0.0551663
$403$	−1.12419	−	5.46441i	−0.0559999	−	0.272202i
$404$		−	21.3958i		−	1.06448i
$405$	1.48569	−	0.398089i	0.0738245	−	0.0197812i
$406$	1.53184	−	2.75501i	0.0760239	−	0.136729i
$407$	−10.9488	+	6.32129i	−0.542712	+	0.313335i
$408$	4.72259	−	4.72259i	0.233803	−	0.233803i
$409$	−3.92450	+	14.6464i	−0.194054	+	0.724219i	0.798456	+	0.602053i	$0.205651\pi$
$409$	−3.92450	+	14.6464i	−0.194054	+	0.724219i	−0.992510	+	0.122165i	$0.961016\pi$
$410$	−0.126966	+	0.473844i	−0.00627041	+	0.0234015i
$411$	0.0216847	−	0.0216847i	0.00106963	−	0.00106963i
$412$	7.94138	−	4.58496i	0.391244	−	0.225885i
$413$	−11.6310	+	20.9183i	−0.572322	+	1.02932i
$414$	0.463422	−	0.124173i	0.0227759	−	0.00610279i
$415$			2.45954i			0.120734i
$416$	6.20855	+	6.98666i	0.304399	+	0.342549i
$417$	−3.29735			−0.161472
$418$	−4.74638	+	1.27179i	−0.232153	+	0.0622052i
$419$	−3.99149	−	2.30449i	−0.194997	−	0.112582i	0.399323	−	0.916810i	$-0.369245\pi$
$419$	−3.99149	−	2.30449i	−0.194997	−	0.112582i	−0.594320	+	0.804229i	$0.702579\pi$
$420$	6.80759	−	4.07831i	0.332176	−	0.199001i
$421$	12.6437	−	12.6437i	0.616216	−	0.616216i	−0.328342	−	0.944559i	$-0.606490\pi$
$421$	12.6437	−	12.6437i	0.616216	−	0.616216i	0.944559	+	0.328342i	$0.106490\pi$
$422$	3.66129	+	0.981041i	0.178229	+	0.0477563i
$423$	−7.19027	−	1.92663i	−0.349603	−	0.0936758i
$424$	−8.22509	−	8.22509i	−0.399446	−	0.399446i
$425$	−17.2652	+	9.96804i	−0.837483	+	0.483521i
$426$	0.608234	−	1.05349i	0.0294690	−	0.0510418i
$427$	8.54095	+	29.9334i	0.413325	+	1.44858i
$428$		−	25.5581i		−	1.23540i
$429$	10.3510	+	11.6483i	0.499751	+	0.562384i
$430$			2.61309i			0.126014i
$431$	2.12448	+	7.92867i	0.102333	+	0.381911i	0.998029	−	0.0627557i	$-0.0199889\pi$
$431$	2.12448	+	7.92867i	0.102333	+	0.381911i	−0.895696	+	0.444666i	$0.853322\pi$
$432$	3.20690	+	1.85151i	0.154292	+	0.0890807i
$433$	−8.67779	−	15.0304i	−0.417028	−	0.722314i	0.578611	−	0.815604i	$-0.303595\pi$
$433$	−8.67779	−	15.0304i	−0.417028	−	0.722314i	−0.995639	+	0.0932901i	$0.970262\pi$
$434$	0.657073	+	0.636190i	0.0315405	+	0.0305381i
$435$	7.92305	+	2.12297i	0.379881	+	0.101789i
$436$	−0.622458	+	2.32305i	−0.0298103	+	0.111254i
$437$	7.72766	−	7.72766i	0.369664	−	0.369664i
$438$	−1.27075	−	2.20101i	−0.0607189	−	0.105168i
$439$	7.78946	−	13.4917i	0.371771	−	0.643926i	−0.618067	−	0.786125i	$-0.712084\pi$
$439$	7.78946	−	13.4917i	0.371771	−	0.643926i	0.989838	+	0.142199i	$0.0454174\pi$
$440$	−1.51834	−	5.66652i	−0.0723840	−	0.270141i
$441$	−0.226007	−	6.99635i	−0.0107622	−	0.333160i
$442$	5.97116	−	1.22844i	0.284019	−	0.0584311i
$443$	−30.0278			−1.42667			−0.713333	−	0.700825i	$-0.752815\pi$
$443$	−30.0278			−1.42667			−0.713333	+	0.700825i	$0.752815\pi$
$444$	−5.51008	+	1.47642i	−0.261497	+	0.0700679i
$445$	0.645833	−	1.11862i	0.0306154	−	0.0530274i
$446$	1.40967	+	2.44162i	0.0667499	+	0.115614i
$447$	3.31360	+	3.31360i	0.156728	+	0.156728i
$448$	17.5200	+	4.39255i	0.827741	+	0.207529i
$449$	1.79908	−	6.71427i	0.0849040	−	0.316866i	−0.910392	−	0.413747i	$-0.864220\pi$
$449$	1.79908	−	6.71427i	0.0849040	−	0.316866i	0.995296	+	0.0968807i	$0.0308865\pi$
$450$	0.416149	+	0.416149i	0.0196174	+	0.0196174i
$451$	−5.34327	+	3.08494i	−0.251605	+	0.145264i
$452$	20.9877	+	12.1173i	0.987179	+	0.569948i
$453$	−1.73851	−	6.48821i	−0.0816824	−	0.304843i
$454$	4.39550			0.206291
$455$	14.6591	+	0.627126i	0.687230	+	0.0294001i
$456$	−4.49107			−0.210314
$457$	5.76514	+	21.5158i	0.269682	+	1.00647i	0.959322	+	0.282314i	$0.0911020\pi$
$457$	5.76514	+	21.5158i	0.269682	+	1.00647i	−0.689640	+	0.724152i	$0.742231\pi$
$458$	−5.42445	−	3.13181i	−0.253468	−	0.146340i
$459$	6.55410	−	3.78401i	0.305919	−	0.176623i
$460$	4.55459	+	4.55459i	0.212359	+	0.212359i
$461$	3.01705	−	11.2598i	0.140518	−	0.524420i	−0.859396	−	0.511311i	$-0.829160\pi$
$461$	3.01705	−	11.2598i	0.140518	−	0.524420i	0.999914	−	0.0131099i	$-0.00417312\pi$
$462$	−2.47795	−	0.621264i	−0.115285	−	0.0289038i
$463$	16.6774	+	16.6774i	0.775063	+	0.775063i	0.978987	−	0.203924i	$-0.0653694\pi$
$463$	16.6774	+	16.6774i	0.775063	+	0.775063i	−0.203924	+	0.978987i	$0.565369\pi$
$464$	9.87392	+	17.1021i	0.458385	+	0.793947i
$465$	−1.18995	+	2.06105i	−0.0551824	+	0.0955788i
$466$	−2.35005	+	0.629695i	−0.108864	+	0.0291700i
$467$	17.0336			0.788223			0.394111	−	0.919063i	$-0.371052\pi$
$467$	17.0336			0.788223			0.394111	+	0.919063i	$0.371052\pi$
$468$	3.15103	+	6.28554i	0.145656	+	0.290549i
$469$	13.0970	−	0.211485i	0.604765	−	0.00976549i
$470$	0.662046	+	2.47079i	0.0305379	+	0.113969i
$471$	−8.55575	+	14.8190i	−0.394228	+	0.682823i
$472$	3.99168	+	6.91379i	0.183732	+	0.318233i
$473$	−23.2393	+	23.2393i	−1.06855	+	1.06855i
$474$	−0.524246	+	1.95651i	−0.0240794	+	0.0898656i
$475$	12.9491	+	3.46969i	0.594143	+	0.159200i
$476$	27.1609	−	28.0524i	1.24492	−	1.28578i
$477$	−6.59042	−	11.4149i	−0.301754	−	0.522654i
$478$	−2.74724	−	1.58612i	−0.125656	−	0.0725475i
$479$	−8.69175	−	32.4380i	−0.397136	−	1.48213i	−0.818111	−	0.575060i	$-0.804979\pi$
$479$	−8.69175	−	32.4380i	−0.397136	−	1.48213i	0.420976	−	0.907072i	$-0.361688\pi$
$480$		−	3.98720i		−	0.181990i
$481$	−10.0093	−	3.32477i	−0.456386	−	0.151596i
$482$		−	3.49958i		−	0.159402i
$483$	5.46361	−	1.55894i	0.248603	−	0.0709341i
$484$	7.48725	−	12.9683i	0.340330	−	0.589468i
$485$	−22.4334	+	12.9519i	−1.01865	+	0.588117i
$486$	−0.157976	−	0.157976i	−0.00716594	−	0.00716594i
$487$	−3.78357	−	1.01381i	−0.171450	−	0.0459399i	0.172073	−	0.985084i	$-0.444954\pi$
$487$	−3.78357	−	1.01381i	−0.171450	−	0.0459399i	−0.343523	+	0.939144i	$0.611620\pi$
$488$	10.0291	+	2.68728i	0.453994	+	0.121647i
$489$	13.8043	−	13.8043i	0.624250	−	0.624250i
$490$	−2.04323	+	1.26933i	−0.0923035	+	0.0573427i
$491$	−6.15458	−	3.55335i	−0.277752	−	0.160360i	0.354653	−	0.934998i	$-0.384599\pi$
$491$	−6.15458	−	3.55335i	−0.277752	−	0.160360i	−0.632405	+	0.774638i	$0.717932\pi$
$492$	−2.68905	+	0.720529i	−0.121232	+	0.0324840i
$493$	40.3596			1.81770
$494$	−3.42332	−	2.25510i	−0.154023	−	0.101462i
$495$		−	6.64752i		−	0.298784i
$496$	−5.53442	+	1.48294i	−0.248503	+	0.0665861i
$497$	7.00063	−	12.5906i	0.314021	−	0.564767i
$498$	0.309390	−	0.178627i	0.0138641	−	0.00800445i
$499$	5.42530	−	5.42530i	0.242870	−	0.242870i	−0.575167	−	0.818036i	$-0.695063\pi$
$499$	5.42530	−	5.42530i	0.242870	−	0.242870i	0.818036	+	0.575167i	$0.195063\pi$
$500$	−5.92654	+	22.1181i	−0.265043	+	0.989153i
$501$	−3.66374	+	13.6733i	−0.163684	+	0.610876i
$502$	3.40746	−	3.40746i	0.152082	−	0.152082i
$503$	−11.4527	+	6.61222i	−0.510651	+	0.294824i	−0.733101	−	0.680120i	$-0.761928\pi$
$503$	−11.4527	+	6.61222i	−0.510651	+	0.294824i	0.222450	+	0.974944i	$0.428594\pi$
$504$	−2.04064	−	1.13463i	−0.0908972	−	0.0505406i
$505$	−16.3005	+	4.36772i	−0.725364	+	0.194361i
$506$		−	2.07352i		−	0.0921792i
$507$	−1.52788	+	12.9099i	−0.0678555	+	0.573349i
$508$	12.4148			0.550816
$509$	−38.3913	+	10.2869i	−1.70167	+	0.455960i	−0.973358	−	0.229290i	$-0.926360\pi$
$509$	−38.3913	+	10.2869i	−1.70167	+	0.455960i	−0.728308	+	0.685250i	$0.759693\pi$
$510$	−2.25218	−	1.30030i	−0.0997283	−	0.0575781i
$511$	−15.4677	−	25.8190i	−0.684253	−	1.14217i
$512$	11.4092	−	11.4092i	0.504221	−	0.504221i
$513$	−4.91565	−	1.31714i	−0.217031	−	0.0581533i
$514$	0.457294	+	0.122531i	0.0201704	+	0.00540463i
$515$	−5.11423	−	5.11423i	−0.225360	−	0.225360i
$516$	−12.8425	+	7.41460i	−0.565358	+	0.326409i
$517$	−16.0860	+	27.8617i	−0.707460	+	1.22536i
$518$	1.66272	−	0.474426i	0.0730558	−	0.0208451i
$519$			19.3214i			0.848117i
$520$	2.69228	−	4.08698i	0.118064	−	0.179226i
$521$			9.34550i			0.409434i	0.978821	+	0.204717i	$0.0656274\pi$
$521$			9.34550i			0.409434i	−0.978821	+	0.204717i	$0.934373\pi$
$522$	−0.308366	−	1.15084i	−0.0134968	−	0.0503708i
$523$	16.9149	+	9.76580i	0.739635	+	0.427028i	0.821937	−	0.569579i	$-0.192894\pi$
$523$	16.9149	+	9.76580i	0.739635	+	0.427028i	−0.0823016	+	0.996607i	$0.526227\pi$
$524$	3.64177	+	6.30773i	0.159091	+	0.275554i
$525$	5.00716	+	4.84802i	0.218530	+	0.211585i
$526$	2.38755	+	0.639743i	0.104102	+	0.0278941i
$527$	−3.03076	+	11.3110i	−0.132022	+	0.492713i
$528$	11.3166	−	11.3166i	0.492492	−	0.492492i
$529$	−9.19419	−	15.9248i	−0.399748	−	0.692383i
$530$	−2.26466	+	3.92251i	−0.0983706	+	0.170383i
$531$	2.34136	+	8.73809i	0.101607	+	0.379201i
$532$	−26.2533	+	0.423927i	−1.13822	+	0.0183796i
$533$	−4.88479	−	1.62256i	−0.211584	−	0.0702811i
$534$	−0.187617			−0.00811898
$535$	−19.4716	+	5.21741i	−0.841833	+	0.225568i
$536$	2.18456	−	3.78376i	0.0943585	−	0.163434i
$537$	2.05604	+	3.56116i	0.0887245	+	0.153675i
$538$	4.34985	+	4.34985i	0.187536	+	0.187536i
$539$	−29.4601	−	6.88256i	−1.26894	−	0.296453i
$540$	0.776309	−	2.89722i	0.0334070	−	0.124677i
$541$	−0.184083	−	0.184083i	−0.00791436	−	0.00791436i	0.703139	−	0.711053i	$-0.251781\pi$
$541$	−0.184083	−	0.184083i	−0.00791436	−	0.00791436i	−0.711053	+	0.703139i	$0.751781\pi$
$542$	−2.84232	+	1.64102i	−0.122088	+	0.0704877i
$543$	−1.81564	−	1.04826i	−0.0779165	−	0.0449851i
$544$	−5.07764	−	18.9500i	−0.217702	−	0.812475i
$545$	1.89690			0.0812542
$546$	−0.985745	−	1.88954i	−0.0421860	−	0.0808650i
$547$	−26.9425			−1.15198			−0.575990	−	0.817457i	$-0.695383\pi$
$547$	−26.9425			−1.15198			−0.575990	+	0.817457i	$0.695383\pi$
$548$	−0.0154781	−	0.0577651i	−0.000661192	−	0.00246760i
$549$	10.1891	+	5.88266i	0.434859	+	0.251066i
$550$	2.20277	−	1.27177i	0.0939265	−	0.0542285i
$551$	−19.1905	−	19.1905i	−0.817543	−	0.817543i
$552$	0.490496	−	1.83056i	0.0208769	−	0.0779136i
$553$	−5.83347	+	23.2672i	−0.248065	+	0.989421i
$554$	0.822003	+	0.822003i	0.0349236	+	0.0349236i
$555$	2.24965	+	3.89650i	0.0954922	+	0.165397i
$556$	−3.21506	+	5.56864i	−0.136349	+	0.236163i
$557$	29.5799	−	7.92591i	1.25334	−	0.335832i	0.429715	−	0.902965i	$-0.358614\pi$
$557$	29.5799	−	7.92591i	1.25334	−	0.335832i	0.823626	+	0.567133i	$0.191948\pi$
$558$	0.345684			0.0146340
$559$	−27.3704	−	1.61400i	−1.15765	−	0.0682651i
$560$	−0.243299	−	15.0672i	−0.0102812	−	0.636705i
$561$	−8.46553	−	31.5938i	−0.357415	−	1.33389i
$562$	1.70035	−	2.94510i	0.0717250	−	0.124231i
$563$	7.49329	+	12.9788i	0.315804	+	0.546989i	0.979608	−	0.200917i	$-0.0643923\pi$
$563$	7.49329	+	12.9788i	0.315804	+	0.546989i	−0.663804	+	0.747907i	$0.731059\pi$
$564$	−10.2646	+	10.2646i	−0.432216	+	0.432216i
$565$	4.94722	−	18.4633i	0.208131	−	0.776756i
$566$	−0.877680	−	0.235174i	−0.0368917	−	0.00988509i
$567$	−1.90079	−	1.84038i	−0.0798257	−	0.0772887i
$568$	−2.40258	−	4.16138i	−0.100810	−	0.174608i
$569$	6.07156	+	3.50542i	0.254533	+	0.146955i	0.621838	−	0.783146i	$-0.286386\pi$
$569$	6.07156	+	3.50542i	0.254533	+	0.146955i	−0.367305	+	0.930101i	$0.619720\pi$
$570$	0.452609	+	1.68916i	0.0189577	+	0.0707512i
$571$		−	0.237494i		−	0.00993882i	−0.999988	−	0.00496941i	$-0.998418\pi$
$571$		−	0.237494i		−	0.00993882i	0.999988	−	0.00496941i	$-0.00158182\pi$
$572$	29.7646	−	6.12345i	1.24452	−	0.256034i
$573$			8.44149i			0.352648i
$574$	0.811447	−	0.231531i	0.0338692	−	0.00966393i
$575$	−2.82848	+	4.89908i	−0.117956	+	0.204306i
$576$	5.91225	−	3.41344i	0.246344	−	0.142227i
$577$	3.41695	+	3.41695i	0.142250	+	0.142250i	0.774645	−	0.632396i	$-0.217928\pi$
$577$	3.41695	+	3.41695i	0.142250	+	0.142250i	−0.632396	+	0.774645i	$0.717928\pi$
$578$	−8.69131	−	2.32883i	−0.361511	−	0.0968665i
$579$	1.96647	+	0.526915i	0.0817238	+	0.0218978i
$580$	11.3107	−	11.3107i	0.469649	−	0.469649i
$581$	3.62932	−	2.17426i	0.150570	−	0.0902037i
$582$	3.25850	+	1.88129i	0.135069	+	0.0779821i
$583$	−55.0253	+	14.7440i	−2.27891	+	0.610633i
$584$	−10.0392			−0.415424
$585$	4.14544	−	3.68376i	0.171393	−	0.152305i
$586$		−	4.93076i		−	0.203688i
$587$	7.16064	−	1.91869i	0.295551	−	0.0791927i	−0.107997	−	0.994151i	$-0.534444\pi$
$587$	7.16064	−	1.91869i	0.295551	−	0.0791927i	0.403548	+	0.914959i	$0.367777\pi$
$588$	−12.0360	−	6.44006i	−0.496355	−	0.265584i
$589$	6.81931	−	3.93713i	0.280985	−	0.162227i
$590$	2.19810	−	2.19810i	0.0904945	−	0.0904945i
$591$	−3.46988	+	12.9498i	−0.142732	+	0.532682i
$592$	−2.80357	+	10.4631i	−0.115226	+	0.430030i
$593$	−20.9219	+	20.9219i	−0.859161	+	0.859161i	−0.991239	−	0.132078i	$-0.957835\pi$
$593$	−20.9219	+	20.9219i	−0.859161	+	0.859161i	0.132078	+	0.991239i	$0.457835\pi$
$594$	−0.836204	+	0.482783i	−0.0343099	+	0.0198088i
$595$	−26.9166	−	14.9661i	−1.10347	−	0.613551i
$596$	8.82700	−	2.36519i	0.361568	−	0.0968818i
$597$		−	7.53644i		−	0.308446i
$598$	1.29306	−	1.14905i	0.0528771	−	0.0469882i
$599$	−35.0083			−1.43040			−0.715199	−	0.698920i	$-0.753664\pi$
$599$	−35.0083			−1.43040			−0.715199	+	0.698920i	$0.753664\pi$
$600$	2.24550	−	0.601681i	0.0916723	−	0.0245635i
$601$	25.0031	+	14.4355i	1.01990	+	0.588838i	0.914074	−	0.405547i	$-0.132919\pi$
$601$	25.0031	+	14.4355i	1.01990	+	0.588838i	0.105823	+	0.994385i	$0.466252\pi$
$602$	3.85589	−	2.31000i	0.157154	−	0.0941485i
$603$	3.50079	−	3.50079i	0.142563	−	0.142563i
$604$	−12.6526	−	3.39025i	−0.514826	−	0.137947i
$605$	−11.4084	−	3.05688i	−0.463819	−	0.124280i
$606$	1.73327	+	1.73327i	0.0704091	+	0.0704091i
$607$	−22.1458	+	12.7859i	−0.898871	+	0.518964i	−0.876834	−	0.480793i	$-0.840349\pi$
$607$	−22.1458	+	12.7859i	−0.898871	+	0.518964i	−0.0220376	+	0.999757i	$0.507015\pi$
$608$	−6.59615	+	11.4249i	−0.267509	+	0.463339i
$609$	−3.87139	−	13.5681i	−0.156877	−	0.549805i
$610$		−	4.04291i		−	0.163693i
$611$	−26.2889	+	5.40839i	−1.06353	+	0.218800i
$612$		−	14.7583i		−	0.596569i
$613$	−6.84627	−	25.5506i	−0.276518	−	1.03198i	−0.954817	−	0.297194i	$-0.903949\pi$
$613$	−6.84627	−	25.5506i	−0.276518	−	1.03198i	0.678299	−	0.734786i	$-0.262718\pi$
$614$	2.62767	+	1.51708i	0.106044	+	0.0612245i
$615$	1.09788	+	1.90159i	0.0442708	+	0.0766794i
$616$	−7.01933	+	7.24974i	−0.282817	+	0.292100i
$617$	−41.2766	−	11.0600i	−1.66173	−	0.445260i	−0.698870	−	0.715249i	$-0.746313\pi$
$617$	−41.2766	−	11.0600i	−1.66173	−	0.445260i	−0.962864	+	0.269988i	$0.912980\pi$
$618$	−0.271903	+	1.01475i	−0.0109375	+	0.0408194i
$619$	−7.36404	+	7.36404i	−0.295986	+	0.295986i	−0.839439	−	0.543453i	$-0.817116\pi$
$619$	−7.36404	+	7.36404i	−0.295986	+	0.295986i	0.543453	+	0.839439i	$0.317116\pi$
$620$	2.32050	+	4.01922i	0.0931935	+	0.161416i
$621$	1.07373	−	1.85976i	0.0430874	−	0.0746296i
$622$	0.937855	+	3.50012i	0.0376046	+	0.140342i
$623$	−2.22156	+	0.0358728i	−0.0890050	+	0.00143722i
$624$	13.3283	+	0.785953i	0.533557	+	0.0314633i
$625$	4.88945			0.195578
$626$	5.22738	−	1.40067i	0.208928	−	0.0559822i
$627$	−10.9972	+	19.0477i	−0.439186	+	0.760693i
$628$	16.6845	+	28.8983i	0.665782	+	1.15317i
$629$	15.6541	+	15.6541i	0.624169	+	0.624169i
$630$	−0.221098	+	0.881864i	−0.00880876	+	0.0351343i
$631$	−3.47681	+	12.9756i	−0.138410	+	0.516552i	0.861551	+	0.507671i	$0.169494\pi$
$631$	−3.47681	+	12.9756i	−0.138410	+	0.516552i	−0.999961	+	0.00888079i	$0.997173\pi$
$632$	5.65758	+	5.65758i	0.225046	+	0.225046i
$633$	14.6932	−	8.48310i	0.584001	−	0.337173i
$634$	−5.17644	−	2.98862i	−0.205583	−	0.118693i
$635$	−2.53434	−	9.45828i	−0.100572	−	0.375340i
$636$	−25.7038			−1.01922
$637$	−12.0334	−	22.1855i	−0.476782	−	0.879021i
$638$	−5.14927			−0.203862
$639$	−1.40926	−	5.25942i	−0.0557494	−	0.208060i
$640$	−8.93765	−	5.16016i	−0.353292	−	0.203973i
$641$	−9.03607	+	5.21698i	−0.356903	+	0.206058i	−0.667722	−	0.744411i	$-0.732730\pi$
$641$	−9.03607	+	5.21698i	−0.356903	+	0.206058i	0.310818	+	0.950469i	$0.399397\pi$
$642$	2.07045	+	2.07045i	0.0817143	+	0.0817143i
$643$	2.33827	−	8.72656i	0.0922125	−	0.344142i	−0.904370	−	0.426750i	$-0.859658\pi$
$643$	2.33827	−	8.72656i	0.0922125	−	0.344142i	0.996582	+	0.0826083i	$0.0263251\pi$
$644$	2.69448	−	10.7471i	0.106177	−	0.423495i
$645$	8.27052	+	8.27052i	0.325651	+	0.325651i
$646$	4.30225	+	7.45171i	0.169270	+	0.293184i
$647$	4.86550	−	8.42729i	0.191283	−	0.331311i	−0.754393	−	0.656423i	$-0.772069\pi$
$647$	4.86550	−	8.42729i	0.191283	−	0.331311i	0.945676	+	0.325112i	$0.105402\pi$
$648$	−0.852426	+	0.228407i	−0.0334864	+	0.00897267i
$649$	39.0974			1.53471
$650$	2.01376	+	0.668905i	0.0789863	+	0.0262366i
$651$	4.09322	−	0.0660957i	0.160426	−	0.00259049i
$652$	−9.85322	−	36.7727i	−0.385882	−	1.44013i
$653$	19.3917	−	33.5874i	0.758855	−	1.31437i	−0.184580	−	0.982817i	$-0.559093\pi$
$653$	19.3917	−	33.5874i	0.758855	−	1.31437i	0.943435	−	0.331557i	$-0.107574\pi$
$654$	−0.137764	−	0.238614i	−0.00538700	−	0.00933056i
$655$	4.06217	−	4.06217i	0.158722	−	0.158722i
$656$	−1.36821	+	5.10623i	−0.0534196	+	0.199365i
$657$	−10.9883	−	2.94429i	−0.428692	−	0.114868i
$658$	3.06066	−	3.16113i	0.119317	−	0.123233i
$659$	16.5452	+	28.6571i	0.644509	+	1.11632i	0.984415	+	0.175863i	$0.0562717\pi$
$659$	16.5452	+	28.6571i	0.644509	+	1.11632i	−0.339905	+	0.940460i	$0.610395\pi$
$660$	−11.2265	−	6.48162i	−0.436991	−	0.252297i
$661$	−3.34087	−	12.4683i	−0.129945	−	0.484960i	0.870023	−	0.493011i	$-0.164104\pi$
$661$	−3.34087	−	12.4683i	−0.129945	−	0.484960i	−0.999968	+	0.00805129i	$0.997437\pi$
$662$			3.22860i			0.125483i
$663$	15.0109	−	22.7870i	0.582974	−	0.884974i
$664$		−	1.41118i		−	0.0547645i
$665$	5.68229	+	19.9147i	0.220350	+	0.772260i
$666$	0.326766	−	0.565975i	0.0126619	−	0.0219311i
$667$	9.91794	−	5.72612i	0.384024	−	0.221716i
$668$	19.5194	+	19.5194i	0.755229	+	0.755229i
$669$	12.1895	+	3.26617i	0.471273	+	0.126277i
$670$	−1.64329	−	0.440319i	−0.0634859	−	0.0170110i
$671$	35.9554	−	35.9554i	1.38804	−	1.38804i
$672$	−5.88354	+	3.52473i	−0.226962	+	0.135969i
$673$	22.5255	+	13.0051i	0.868295	+	0.501310i	0.866781	−	0.498689i	$-0.166185\pi$
$673$	22.5255	+	13.0051i	0.868295	+	0.501310i	0.00151340	+	0.999999i	$0.499518\pi$
$674$	1.11250	−	0.298092i	0.0428517	−	0.0114821i
$675$	2.63425			0.101392
$676$	20.3128	+	15.1680i	0.781262	+	0.583386i
$677$		−	41.0161i		−	1.57638i	−0.615434	−	0.788188i	$-0.711019\pi$
$677$		−	41.0161i		−	1.57638i	0.615434	−	0.788188i	$-0.288981\pi$
$678$	−2.68183	+	0.718593i	−0.102995	+	0.0275974i
$679$	38.9434	+	21.6533i	1.49451	+	0.830976i
$680$	−8.89631	+	5.13629i	−0.341158	+	0.196968i
$681$	13.9119	−	13.9119i	0.533106	−	0.533106i
$682$	0.386679	−	1.44311i	0.0148067	−	0.0552594i
$683$	8.69145	−	32.4369i	0.332569	−	1.24116i	−0.573912	−	0.818917i	$-0.694575\pi$
$683$	8.69145	−	32.4369i	0.332569	−	1.24116i	0.906481	−	0.422247i	$-0.138759\pi$
$684$	−7.01739	+	7.01739i	−0.268317	+	0.268317i
$685$	−0.0408491	+	0.0235842i	−0.00156076	+	0.000901107i
$686$	3.67927	+	1.89289i	0.140475	+	0.0722710i
$687$	−27.0809	+	7.25630i	−1.03320	+	0.276845i
$688$			28.1591i			1.07356i
$689$	−39.6870	−	26.1437i	−1.51195	−	0.995994i
$690$	−0.737933			−0.0280926
$691$	−33.3878	+	8.94624i	−1.27013	+	0.340331i	−0.830082	−	0.557642i	$-0.811706\pi$
$691$	−33.3878	+	8.94624i	−1.27013	+	0.340331i	−0.440051	+	0.897973i	$0.645040\pi$
$692$	32.6305	+	18.8392i	1.24043	+	0.716160i
$693$	−9.80913	+	5.87649i	−0.372618	+	0.223229i
$694$	−3.76020	+	3.76020i	−0.142735	+	0.142735i
$695$	4.89884	+	1.31264i	0.185823	+	0.0497912i
$696$	−4.54591	−	1.21807i	−0.172312	−	0.0461710i
$697$	7.63956	+	7.63956i	0.289369	+	0.289369i
$698$	2.36628	−	1.36617i	0.0895651	−	0.0517104i
$699$	−5.44500	+	9.43101i	−0.205949	+	0.356714i
$700$	13.0697	−	3.72918i	0.493987	−	0.140950i
$701$			4.79362i			0.181053i	0.995894	+	0.0905263i	$0.0288549\pi$
$701$			4.79362i			0.181053i	−0.995894	+	0.0905263i	$0.971145\pi$
$702$	−0.764453	−	0.253926i	−0.0288524	−	0.00958381i
$703$		−	14.8867i		−	0.561461i
$704$	−7.63649	−	28.4998i	−0.287811	−	1.07413i
$705$	9.91554	+	5.72474i	0.373441	+	0.215606i
$706$	−1.91032	−	3.30876i	−0.0718957	−	0.124527i
$707$	20.8549	+	20.1921i	0.784329	+	0.759402i
$708$	17.0400	+	4.56586i	0.640404	+	0.171596i
$709$	2.76549	−	10.3209i	0.103860	−	0.387611i	−0.894353	−	0.447361i	$-0.852364\pi$
$709$	2.76549	−	10.3209i	0.103860	−	0.387611i	0.998213	+	0.0597505i	$0.0190305\pi$
$710$	−1.32303	+	1.32303i	−0.0496524	+	0.0496524i
$711$	4.53318	+	7.85169i	0.170007	+	0.294461i
$712$	−0.370552	+	0.641814i	−0.0138870	+	0.0240530i
$713$	0.859994	+	3.20954i	0.0322070	+	0.120198i
$714$	0.0722252	+	4.47281i	0.00270296	+	0.167391i
$715$	−10.7413	−	21.4263i	−0.401703	−	0.801300i
$716$	8.01890			0.299680
$717$	−13.7153	+	3.67499i	−0.512206	+	0.137245i
$718$	−2.30976	+	4.00062i	−0.0861995	+	0.149302i
$719$	14.9272	+	25.8547i	0.556690	+	0.964216i	0.997770	+	0.0667479i	$0.0212623\pi$
$719$	14.9272	+	25.8547i	0.556690	+	0.964216i	−0.441080	+	0.897468i	$0.645404\pi$
$720$	−4.02740	−	4.02740i	−0.150092	−	0.150092i
$721$	−3.02556	+	12.0676i	−0.112678	+	0.449423i
$722$	0.398890	−	1.48868i	0.0148452	−	0.0554029i
$723$	−11.0763	−	11.0763i	−0.411932	−	0.411932i
$724$	−3.54065	+	2.04420i	−0.131587	+	0.0759720i
$725$	12.1661	+	7.02412i	0.451839	+	0.260869i
$726$	0.444018	+	1.65710i	0.0164791	+	0.0615007i
$727$	−41.2241			−1.52892			−0.764459	−	0.644672i	$-0.776994\pi$
$727$	−41.2241			−1.52892			−0.764459	+	0.644672i	$0.776994\pi$
$728$	−8.41078	−	0.359819i	−0.311724	−	0.0133358i
$729$	−1.00000			−0.0370370
$730$	1.01175	+	3.77589i	0.0374464	+	0.139752i
$731$	49.8398	+	28.7750i	1.84339	+	1.06428i
$732$	19.8696	−	11.4717i	0.734400	−	0.424006i
$733$	−14.3345	−	14.3345i	−0.529456	−	0.529456i	0.390954	−	0.920410i	$-0.372145\pi$
$733$	−14.3345	−	14.3345i	−0.529456	−	0.529456i	−0.920410	+	0.390954i	$0.872145\pi$
$734$	−0.0267847	+	0.0999617i	−0.000988640	+	0.00368965i
$735$	−2.44940	+	10.4844i	−0.0903473	+	0.386722i
$736$	−3.93636	−	3.93636i	−0.145096	−	0.145096i
$737$	−10.6986	−	18.5305i	−0.394087	−	0.682579i
$738$	0.159469	−	0.276209i	0.00587015	−	0.0101674i
$739$	24.4381	−	6.54818i	0.898972	−	0.240879i	0.220397	−	0.975410i	$-0.429265\pi$
$739$	24.4381	−	6.54818i	0.898972	−	0.240879i	0.678575	+	0.734532i	$0.262598\pi$
$740$	8.77402			0.322539
$741$	−17.9724	+	3.69746i	−0.660234	+	0.135830i
$742$	7.79007	−	0.125791i	0.285982	−	0.00461793i
$743$	10.9162	+	40.7397i	0.400476	+	1.49460i	0.812250	+	0.583310i	$0.198243\pi$
$743$	10.9162	+	40.7397i	0.400476	+	1.49460i	−0.411774	+	0.911286i	$0.635091\pi$
$744$	0.682741	−	1.18254i	0.0250305	−	0.0433541i
$745$	−3.60387	−	6.24209i	−0.132036	−	0.228693i
$746$	0.110241	−	0.110241i	0.00403621	−	0.00403621i
$747$	0.413872	−	1.54459i	0.0151428	−	0.0565137i
$748$	−61.6106	−	16.5085i	−2.25271	−	0.603611i
$749$	24.9120	+	24.1203i	0.910265	+	0.881335i
$750$	−1.31168	−	2.27189i	−0.0478957	−	0.0829577i
$751$	−6.23654	−	3.60067i	−0.227574	−	0.131390i	0.381878	−	0.924213i	$-0.375277\pi$
$751$	−6.23654	−	3.60067i	−0.227574	−	0.131390i	−0.609453	+	0.792823i	$0.708611\pi$
$752$	7.13433	+	26.6257i	0.260162	+	0.970938i
$753$		−	21.5695i		−	0.786035i
$754$	−2.85350	−	3.21112i	−0.103918	−	0.116942i
$755$			10.3315i			0.376004i
$756$	−4.96143	+	1.41565i	−0.180446	+	0.0514868i
$757$	−11.5449	+	19.9964i	−0.419607	+	0.726780i	−0.995900	−	0.0904628i	$-0.971165\pi$
$757$	−11.5449	+	19.9964i	−0.419607	+	0.726780i	0.576293	+	0.817243i	$0.304499\pi$
$758$	−1.38385	+	0.798968i	−0.0502638	+	0.0290198i
$759$	−6.56277	−	6.56277i	−0.238213	−	0.238213i
$760$	6.67233	+	1.78785i	0.242031	+	0.0648520i
$761$	−5.76843	−	1.54565i	−0.209105	−	0.0560296i	0.152746	−	0.988266i	$-0.451188\pi$
$761$	−5.76843	−	1.54565i	−0.209105	−	0.0560296i	−0.361851	+	0.932236i	$0.617855\pi$
$762$	−1.00572	+	1.00572i	−0.0364332	+	0.0364332i
$763$	−1.67688	−	2.79908i	−0.0607071	−	0.101333i
$764$	14.2562	+	8.23082i	0.515771	+	0.297780i
$765$	−11.2437	+	3.01275i	−0.406518	+	0.108926i
$766$	0.428649			0.0154877
$767$	21.6660	+	24.3814i	0.782315	+	0.880362i
$768$		−	12.1547i		−	0.438596i
$769$	32.9326	−	8.82426i	1.18758	−	0.318211i	0.389650	−	0.920963i	$-0.372596\pi$
$769$	32.9326	−	8.82426i	1.18758	−	0.318211i	0.797929	+	0.602752i	$0.205929\pi$
$770$	3.43415	+	1.90945i	0.123758	+	0.0688119i
$771$	1.83517	−	1.05953i	0.0660920	−	0.0381582i
$772$	2.80726	−	2.80726i	0.101036	−	0.101036i
$773$	0.0200118	−	0.0746850i	0.000719774	−	0.00268623i	−0.965565	−	0.260162i	$-0.916224\pi$
$773$	0.0200118	−	0.0746850i	0.000719774	−	0.00268623i	0.966285	+	0.257476i	$0.0828907\pi$
$774$	0.439709	−	1.64102i	0.0158050	−	0.0589852i
$775$	−2.88214	+	2.88214i	−0.103530	+	0.103530i
$776$	12.8713	−	7.43127i	0.462054	−	0.266767i
$777$	3.76100	−	6.76415i	0.134925	−	0.242663i
$778$	−1.33164	+	0.356813i	−0.0477417	+	0.0127924i
$779$		−	7.26504i		−	0.260297i
$780$	−2.17924	−	10.5927i	−0.0780293	−	0.379281i
$781$	−23.5326			−0.842063
$782$	−3.50718	+	0.939747i	−0.125417	+	0.0336053i
$783$	−4.61844	−	2.66646i	−0.165049	−	0.0952914i
$784$	−22.0182	+	13.6786i	−0.786363	+	0.488521i
$785$	18.6105	−	18.6105i	0.664236	−	0.664236i
$786$	−0.806006	−	0.215969i	−0.0287493	−	0.00770335i
$787$	13.7109	+	3.67383i	0.488742	+	0.130958i	0.494770	−	0.869024i	$-0.335252\pi$
$787$	13.7109	+	3.67383i	0.488742	+	0.130958i	−0.00602847	+	0.999982i	$0.501919\pi$
$788$	18.4866	+	18.4866i	0.658558	+	0.658558i
$789$	9.58150	−	5.53188i	0.341111	−	0.196940i
$790$	1.55773	−	2.69807i	0.0554216	−	0.0959931i
$791$	−31.6179	+	9.02159i	−1.12420	+	0.320771i
$792$			3.81407i			0.135527i
$793$	42.3469	+	2.49715i	1.50378	+	0.0886765i
$794$			6.96753i			0.247268i
$795$	5.24715	+	19.5826i	0.186097	+	0.694524i
$796$	−12.7277	−	7.34835i	−0.451122	−	0.260455i
$797$	4.85453	+	8.40830i	0.171956	+	0.297837i	0.939104	−	0.343634i	$-0.111658\pi$
$797$	4.85453	+	8.40830i	0.171956	+	0.297837i	−0.767147	+	0.641471i	$0.778324\pi$
$798$	2.09243	−	2.16111i	0.0740711	−	0.0765025i
$799$	54.4161	+	14.5808i	1.92510	+	0.515830i
$800$	1.76741	−	6.59606i	0.0624873	−	0.233206i
$801$	−0.593815	+	0.593815i	−0.0209814	+	0.0209814i
$802$	2.80472	+	4.85792i	0.0990382	+	0.171539i
$803$	−24.5827	+	42.5786i	−0.867506	+	1.50256i
$804$	−2.49880	−	9.32564i	−0.0881258	−	0.328890i
$805$	−8.73782	+	0.141095i	−0.307968	+	0.00497293i
$806$	1.11421	−	0.558569i	0.0392464	−	0.0196748i
$807$	27.5349			0.969274
$808$	9.35256	−	2.50601i	0.329022	−	0.0881612i
$809$	22.8046	−	39.4988i	0.801768	−	1.38870i	−0.116683	−	0.993169i	$-0.537226\pi$
$809$	22.8046	−	39.4988i	0.801768	−	1.38870i	0.918451	−	0.395534i	$-0.129441\pi$
$810$	0.171815	+	0.297592i	0.00603695	+	0.0104563i
$811$	−6.90491	−	6.90491i	−0.242464	−	0.242464i	0.575405	−	0.817869i	$-0.304845\pi$
$811$	−6.90491	−	6.90491i	−0.242464	−	0.242464i	−0.817869	+	0.575405i	$0.804845\pi$
$812$	−26.6888	−	6.69134i	−0.936595	−	0.234820i
$813$	−3.80218	+	14.1899i	−0.133348	+	0.497663i
$814$	−1.99722	−	1.99722i	−0.0700027	−	0.0700027i
$815$	−26.0042	+	15.0135i	−0.910886	+	0.525900i
$816$	−24.2699	−	14.0122i	−0.849617	−	0.490527i
$817$	−10.0161	−	37.3804i	−0.350417	−	1.30778i
$818$	−3.38761			−0.118445
$819$	−9.10040	−	2.86056i	−0.317994	−	0.0999559i
$820$	4.28193			0.149531
$821$	4.30181	+	16.0546i	0.150134	+	0.560308i	0.999473	+	0.0324603i	$0.0103342\pi$
$821$	4.30181	+	16.0546i	0.150134	+	0.560308i	−0.849339	+	0.527848i	$0.822999\pi$
$822$	0.00593341	+	0.00342565i	0.000206951	+	0.000119483i
$823$	8.40900	−	4.85494i	0.293119	−	0.169233i	−0.346228	−	0.938150i	$-0.612538\pi$
$823$	8.40900	−	4.85494i	0.293119	−	0.169233i	0.639348	+	0.768918i	$0.279204\pi$
$824$	2.93433	+	2.93433i	0.102222	+	0.102222i
$825$	2.94665	−	10.9971i	0.102589	−	0.382869i
$826$	−5.18669	−	1.30039i	−0.180468	−	0.0452463i
$827$	−23.2961	−	23.2961i	−0.810086	−	0.810086i	0.174560	−	0.984647i	$-0.444150\pi$
$827$	−23.2961	−	23.2961i	−0.810086	−	0.810086i	−0.984647	+	0.174560i	$0.944150\pi$
$828$	−2.09387	−	3.62669i	−0.0727671	−	0.126036i
$829$	−14.7204	+	25.4965i	−0.511261	+	0.885531i	0.488653	+	0.872478i	$0.337488\pi$
$829$	−14.7204	+	25.4965i	−0.511261	+	0.885531i	−0.999915	+	0.0130527i	$0.995845\pi$
$830$	−0.530767	+	0.142219i	−0.0184232	+	0.00493648i
$831$	5.20334			0.180502
$832$	13.5408	−	20.5555i	0.469444	−	0.712633i
$833$	1.71043	+	52.9485i	0.0592628	+	1.83456i
$834$	−0.190663	−	0.711565i	−0.00660213	−	0.0246395i
$835$	10.8863	−	18.8557i	0.376738	−	0.652529i
$836$	21.4455	+	37.1447i	0.741708	+	1.28468i
$837$	1.09410	−	1.09410i	0.0378177	−	0.0378177i
$838$	0.266506	−	0.994613i	0.00920629	−	0.0343583i
$839$	18.5876	+	4.98054i	0.641716	+	0.171947i	0.564981	−	0.825104i	$-0.308884\pi$
$839$	18.5876	+	4.98054i	0.641716	+	0.171947i	0.0767354	+	0.997051i	$0.475550\pi$
$840$	2.58007	+	2.49807i	0.0890208	+	0.0861916i
$841$	0.280024	+	0.485016i	0.00965600	+	0.0167247i
$842$	3.45960	+	1.99740i	0.119226	+	0.0688350i
$843$	−3.93966	−	14.7030i	−0.135689	−	0.506399i
$844$		−	33.0856i		−	1.13885i
$845$	7.40925	−	18.5719i	0.254886	−	0.638892i
$846$		−	1.66306i		−	0.0571771i
$847$	5.57443	+	19.5367i	0.191540	+	0.671289i
$848$	−24.4044	+	42.2697i	−0.838051	+	1.45155i
$849$	−3.52223	+	2.03356i	−0.120882	+	0.0697915i
$850$	−3.14942	−	3.14942i	−0.108024	−	0.108024i
$851$	6.06779	+	1.62586i	0.208001	+	0.0557337i
$852$	−10.2563	−	2.74818i	−0.351376	−	0.0941510i
$853$	14.9327	−	14.9327i	0.511287	−	0.511287i	−0.403634	−	0.914921i	$-0.632253\pi$
$853$	14.9327	−	14.9327i	0.511287	−	0.511287i	0.914921	+	0.403634i	$0.132253\pi$
$854$	−5.96575	+	3.57398i	−0.204144	+	0.122299i
$855$	6.77878	+	3.91373i	0.231829	+	0.133847i
$856$	11.1720	−	2.99353i	0.381851	−	0.102317i
$857$	−5.36310			−0.183200			−0.0916001	−	0.995796i	$-0.529198\pi$
$857$	−5.36310			−0.183200			−0.0916001	+	0.995796i	$0.529198\pi$
$858$	−1.91516	+	2.90728i	−0.0653825	+	0.0992529i
$859$		−	21.1000i		−	0.719923i	−0.932967	−	0.359962i	$-0.882790\pi$
$859$		−	21.1000i		−	0.719923i	0.932967	−	0.359962i	$-0.117210\pi$
$860$	22.0316	−	5.90334i	0.751270	−	0.201302i
$861$	1.83546	−	3.30107i	0.0625522	−	0.112500i
$862$	−1.58816	+	0.916923i	−0.0540929	+	0.0312305i
$863$	0.437792	−	0.437792i	0.0149026	−	0.0149026i	−0.699616	−	0.714519i	$-0.746646\pi$
$863$	0.437792	−	0.437792i	0.0149026	−	0.0149026i	0.714519	+	0.699616i	$0.246646\pi$
$864$	−0.670934	+	2.50396i	−0.0228256	+	0.0851864i
$865$	7.69166	−	28.7056i	0.261524	−	0.976021i
$866$	2.74176	−	2.74176i	0.0931690	−	0.0931690i
$867$	−34.8791	+	20.1375i	−1.18456	+	0.683905i
$868$	3.87945	−	6.97718i	0.131677	−	0.236821i
$869$	37.8488	−	10.1416i	1.28393	−	0.344029i
$870$			1.83255i			0.0621291i
$871$	5.62706	−	16.9405i	0.190666	−	0.574006i
$872$	−1.08836			−0.0368565
$873$	16.2676	−	4.35890i	0.550576	−	0.147526i
$874$	2.11446	+	1.22079i	0.0715228	+	0.0412937i
$875$	−15.9659	−	26.6505i	−0.539745	−	0.900953i
$876$	−15.6864	+	15.6864i	−0.529995	+	0.529995i
$877$	−0.601435	−	0.161154i	−0.0203090	−	0.00544178i	0.248650	−	0.968593i	$-0.420013\pi$
$877$	−0.601435	−	0.161154i	−0.0203090	−	0.00544178i	−0.268959	+	0.963152i	$0.586680\pi$
$878$	3.36192	+	0.900824i	0.113459	+	0.0304013i
$879$	−15.6061	−	15.6061i	−0.526379	−	0.526379i
$880$	−21.3180	+	12.3079i	−0.718628	+	0.414900i
$881$	9.21121	−	15.9543i	0.310333	−	0.537513i	−0.668101	−	0.744070i	$-0.732893\pi$
$881$	9.21121	−	15.9543i	0.310333	−	0.537513i	0.978435	+	0.206557i	$0.0662260\pi$
$882$	1.49674	−	0.453324i	0.0503978	−	0.0152642i
$883$			15.8935i			0.534859i	0.963577	+	0.267429i	$0.0861742\pi$
$883$			15.8935i			0.534859i	−0.963577	+	0.267429i	$0.913826\pi$
$884$	−23.8470	−	47.5691i	−0.802062	−	1.59992i
$885$		−	13.9142i		−	0.467719i
$886$	−1.73631	−	6.47998i	−0.0583324	−	0.217699i
$887$	29.3404	+	16.9397i	0.985154	+	0.568779i	0.903822	−	0.427908i	$-0.140749\pi$
$887$	29.3404	+	16.9397i	0.985154	+	0.568779i	0.0813318	+	0.996687i	$0.474083\pi$
$888$	−1.29075	−	2.23565i	−0.0433148	−	0.0750235i
$889$	−11.7163	+	12.1009i	−0.392953	+	0.405852i
$890$	0.278740	+	0.0746883i	0.00934340	+	0.00250356i
$891$	−1.11859	+	4.17464i	−0.0374742	+	0.139856i
$892$	17.4013	−	17.4013i	0.582638	−	0.582638i
$893$	−18.9412	−	32.8072i	−0.633844	−	1.09785i
$894$	−0.523469	+	0.906676i	−0.0175074	+	0.0303238i
$895$	−1.63697	−	6.10926i	−0.0547179	−	0.204210i
$896$	0.286621	+	17.7501i	0.00957535	+	0.592989i
$897$	0.455793	−	7.72937i	0.0152185	−	0.258076i
$898$	1.55296			0.0518231
$899$	7.97042	−	2.13567i	0.265828	−	0.0712285i
$900$	2.56851	−	4.44879i	0.0856170	−	0.148293i
$901$	49.8764	+	86.3885i	1.66162	+	2.87802i
$902$	−0.974693	−	0.974693i	−0.0324537	−	0.0324537i
$903$	4.89281	−	19.5153i	0.162822	−	0.649428i
$904$	−2.83850	+	10.5934i	−0.0944073	+	0.352333i
$905$	2.28017	+	2.28017i	0.0757956	+	0.0757956i
$906$	1.29962	−	0.750339i	0.0431771	−	0.0249283i
$907$	37.0978	+	21.4184i	1.23181	+	0.711187i	0.967407	−	0.253225i	$-0.0814914\pi$
$907$	37.0978	+	21.4184i	1.23181	+	0.711187i	0.264404	+	0.964412i	$0.414825\pi$
$908$	−9.93007	−	37.0595i	−0.329541	−	1.22986i
$909$	10.9717			0.363908
$910$	0.712304	+	3.19969i	0.0236127	+	0.106069i
$911$	−9.59124			−0.317772			−0.158886	−	0.987297i	$-0.550790\pi$
$911$	−9.59124			−0.317772			−0.158886	+	0.987297i	$0.550790\pi$
$912$	4.87740	+	18.2027i	0.161507	+	0.602752i
$913$	−5.98517	−	3.45554i	−0.198080	−	0.114362i
$914$	−4.30973	+	2.48822i	−0.142553	+	0.0823032i
$915$	−12.7960	−	12.7960i	−0.423021	−	0.423021i
$916$	−14.1504	+	52.8101i	−0.467543	+	1.74489i
$917$	−9.58517	−	2.40316i	−0.316530	−	0.0793594i
$918$	1.19557	+	1.19557i	0.0394596	+	0.0394596i
$919$	−3.74479	−	6.48617i	−0.123529	−	0.213959i	0.797628	−	0.603150i	$-0.206088\pi$
$919$	−3.74479	−	6.48617i	−0.123529	−	0.213959i	−0.921157	+	0.389191i	$0.872755\pi$
$920$	−1.45745	+	2.52438i	−0.0480507	+	0.0832262i
$921$	13.1183	−	3.51504i	0.432263	−	0.115824i
$922$	2.60431			0.0857683
$923$	−13.0407	−	14.6751i	−0.429240	−	0.483036i
$924$	0.360022	+	22.2957i	0.0118439	+	0.733476i
$925$	1.99441	+	7.44323i	0.0655757	+	0.244732i
$926$	−2.63462	+	4.56330i	−0.0865791	+	0.149959i
$927$	2.35115	+	4.07232i	0.0772221	+	0.133753i
$928$	−9.77536	+	9.77536i	−0.320892	+	0.320892i
$929$	−9.80192	+	36.5812i	−0.321590	+	1.20019i	0.596105	+	0.802907i	$0.296714\pi$
$929$	−9.80192	+	36.5812i	−0.321590	+	1.20019i	−0.917695	+	0.397285i	$0.869952\pi$
$930$	−0.513579	−	0.137613i	−0.0168409	−	0.00451251i
$931$	24.3631	−	25.9897i	0.798468	−	0.851777i
$932$	10.6182	+	18.3913i	0.347811	+	0.602427i
$933$	14.0464	+	8.10968i	0.459858	+	0.265499i
$934$	0.984940	+	3.67585i	0.0322282	+	0.120277i
$935$			50.3086i			1.64527i
$936$	−2.37848	+	2.11358i	−0.0777429	+	0.0690847i
$937$			9.27559i			0.303020i	0.988456	+	0.151510i	$0.0484136\pi$
$937$			9.27559i			0.303020i	−0.988456	+	0.151510i	$0.951586\pi$
$938$	0.802951	+	2.81410i	0.0262173	+	0.0918837i
$939$	12.1117	−	20.9780i	0.395250	−	0.684593i
$940$	19.3362	−	11.1637i	0.630676	−	0.364121i
$941$	−38.7691	−	38.7691i	−1.26384	−	1.26384i	−0.949219	−	0.314617i	$-0.898124\pi$
$941$	−38.7691	−	38.7691i	−1.26384	−	1.26384i	−0.314617	−	0.949219i	$-0.601876\pi$
$942$	−3.69265	−	0.989442i	−0.120313	−	0.0322378i
$943$	2.96122	+	0.793458i	0.0964307	+	0.0258385i
$944$	23.6872	−	23.6872i	0.770951	−	0.770951i
$945$	2.09135	+	3.49092i	0.0680316	+	0.113560i
$946$	−6.35881	−	3.67126i	−0.206743	−	0.119363i
$947$	50.1290	−	13.4320i	1.62898	−	0.436483i	0.675354	−	0.737493i	$-0.263991\pi$
$947$	50.1290	−	13.4320i	1.62898	−	0.436483i	0.953621	+	0.301011i	$0.0973240\pi$
$948$	17.6802			0.574226
$949$	−40.1749	+	8.26517i	−1.30413	+	0.268299i
$950$			2.99502i			0.0971714i
$951$	−25.8427	+	6.92453i	−0.838007	+	0.224543i
$952$	15.4436	+	8.58693i	0.500530	+	0.278304i
$953$	12.2620	−	7.07949i	0.397206	−	0.229327i	−0.288072	−	0.957609i	$-0.593014\pi$
$953$	12.2620	−	7.07949i	0.397206	−	0.229327i	0.685278	+	0.728282i	$0.259681\pi$
$954$	2.08226	−	2.08226i	0.0674155	−	0.0674155i
$955$	3.36046	−	12.5414i	0.108742	−	0.405831i
$956$	−7.16655	+	26.7459i	−0.231783	+	0.865026i
$957$	−16.2976	+	16.2976i	−0.526828	+	0.526828i
$958$	6.49752	−	3.75134i	0.209925	−	0.121200i
$959$	0.0709121	+	0.0394285i	0.00228987	+	0.00127321i
$960$	−10.1426	+	2.71771i	−0.327352	+	0.0877136i
$961$		−	28.6059i		−	0.922770i
$962$	0.138710	−	2.35225i	0.00447219	−	0.0758397i
$963$	13.1061			0.422339
$964$	−29.5058	+	7.90606i	−0.950319	+	0.254637i
$965$	−2.71181	−	1.56566i	−0.0872962	−	0.0504005i
$966$	0.652341	+	1.08890i	0.0209887	+	0.0350348i
$967$	−24.4554	+	24.4554i	−0.786433	+	0.786433i	−0.980908	−	0.194474i	$-0.937700\pi$
$967$	−24.4554	+	24.4554i	−0.786433	+	0.786433i	0.194474	+	0.980908i	$0.437700\pi$
$968$	6.54568	+	1.75391i	0.210386	+	0.0563728i
$969$	37.2017	+	9.96817i	1.19509	+	0.320224i
$970$	−4.09219	−	4.09219i	−0.131392	−	0.131392i
$971$	−4.45063	+	2.56957i	−0.142828	+	0.0824615i	−0.569711	−	0.821845i	$-0.692945\pi$
$971$	−4.45063	+	2.56957i	−0.142828	+	0.0824615i	0.426883	+	0.904307i	$0.359611\pi$
$972$	−0.975044	+	1.68883i	−0.0312745	+	0.0541691i
$973$	−2.39369	−	8.38915i	−0.0767381	−	0.268944i
$974$		−	0.875113i		−	0.0280404i
$975$	8.49074	−	4.25653i	0.271921	−	0.136318i
$976$		−	43.5671i		−	1.39455i
$977$	−4.45430	−	16.6237i	−0.142506	−	0.531839i	−0.999854	−	0.0171015i	$-0.994556\pi$
$977$	−4.45430	−	16.6237i	−0.142506	−	0.531839i	0.857348	−	0.514737i	$-0.172111\pi$
$978$	3.77715	+	2.18074i	0.120780	+	0.0697324i
$979$	1.81473	+	3.14320i	0.0579989	+	0.100457i
$980$	15.3180	+	14.3593i	0.489316	+	0.458692i
$981$	−1.19125	−	0.319195i	−0.0380338	−	0.0101911i
$982$	0.410932	−	1.53362i	0.0131134	−	0.0489398i
$983$	−13.7631	+	13.7631i	−0.438975	+	0.438975i	−0.891667	−	0.452692i	$-0.850464\pi$
$983$	−13.7631	+	13.7631i	−0.438975	+	0.438975i	0.452692	+	0.891667i	$0.350464\pi$
$984$	−0.629918	−	1.09105i	−0.0200811	−	0.0347814i
$985$	10.3103	−	17.8580i	0.328514	−	0.569003i
$986$	2.33372	+	8.70957i	0.0743209	+	0.277369i
$987$	−0.317981	−	19.6922i	−0.0101215	−	0.626809i
$988$	−11.2795	+	33.9575i	−0.358850	+	1.08033i
$989$	16.3301			0.519268
$990$	1.43453	−	0.384381i	0.0455924	−	0.0122164i
$991$	−22.9230	+	39.7039i	−0.728174	+	1.26124i	0.229480	+	0.973313i	$0.426298\pi$
$991$	−22.9230	+	39.7039i	−0.728174	+	1.26124i	−0.957654	+	0.287922i	$0.907036\pi$
$992$	−2.00552	−	3.47366i	−0.0636753	−	0.110289i
$993$	10.2187	+	10.2187i	0.324279	+	0.324279i
$994$	3.12185	+	0.782700i	0.0990190	+	0.0248257i
$995$	−3.00017	+	11.1968i	−0.0951119	+	0.354963i
$996$	−2.20500	−	2.20500i	−0.0698682	−	0.0698682i
$997$	−26.8851	+	15.5221i	−0.851461	+	0.491591i	−0.861143	−	0.508362i	$-0.830251\pi$
$997$	−26.8851	+	15.5221i	−0.851461	+	0.491591i	0.00968271	+	0.999953i	$0.496918\pi$
$998$	1.48448	+	0.857066i	0.0469905	+	0.0271300i
$999$	−0.757106	−	2.82556i	−0.0239538	−	0.0893967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.by.c.97.6	yes	32
3.2	odd	2		819.2.fm.f.370.3		32
7.6	odd	2		273.2.by.d.97.6	yes	32
13.11	odd	12		273.2.by.d.76.6	yes	32
21.20	even	2		819.2.fm.e.370.3		32
39.11	even	12		819.2.fm.e.622.3		32
91.76	even	12	inner	273.2.by.c.76.6	✓	32
273.167	odd	12		819.2.fm.f.622.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.76.6	✓	32	91.76	even	12	inner
273.2.by.c.97.6	yes	32	1.1	even	1	trivial
273.2.by.d.76.6	yes	32	13.11	odd	12
273.2.by.d.97.6	yes	32	7.6	odd	2
819.2.fm.e.370.3		32	21.20	even	2
819.2.fm.e.622.3		32	39.11	even	12
819.2.fm.f.370.3		32	3.2	odd	2
819.2.fm.f.622.3		32	273.167	odd	12

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)

\(f(q)\)	\(=\)	\(q+(0.0578232 + 0.215799i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.68883 - 0.975044i) q^{4} +(-1.08760 - 1.08760i) q^{5} +(-0.0578232 + 0.215799i) q^{6} +(-0.643420 + 2.56632i) q^{7} +(0.624019 + 0.624019i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.0578232 + 0.215799i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.68883 - 0.975044i) q^{4} +(-1.08760 - 1.08760i) q^{5} +(-0.0578232 + 0.215799i) q^{6} +(-0.643420 + 2.56632i) q^{7} +(0.624019 + 0.624019i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.171815 - 0.297592i) q^{10} +(4.17464 - 1.11859i) q^{11} +1.95009 q^{12} +(3.01096 + 1.98346i) q^{13} +(-0.591015 + 0.00954346i) q^{14} +(-0.398089 - 1.48569i) q^{15} +(1.85151 - 3.20690i) q^{16} +(-3.78401 - 6.55410i) q^{17} +(-0.157976 + 0.157976i) q^{18} +(-1.31714 + 4.91565i) q^{19} +(-2.89722 - 0.776309i) q^{20} +(-1.84038 + 1.90079i) q^{21} +(0.482783 + 0.836204i) q^{22} +(-1.85976 - 1.07373i) q^{23} +(0.228407 + 0.852426i) q^{24} -2.63425i q^{25} +(-0.253926 + 0.764453i) q^{26} +1.00000i q^{27} +(1.41565 + 4.96143i) q^{28} +(-2.66646 + 4.61844i) q^{29} +(0.297592 - 0.171815i) q^{30} +(-1.09410 - 1.09410i) q^{31} +(2.50396 + 0.670934i) q^{32} +(4.17464 + 1.11859i) q^{33} +(1.19557 - 1.19557i) q^{34} +(3.49092 - 2.09135i) q^{35} +(1.68883 + 0.975044i) q^{36} +(-2.82556 + 0.757106i) q^{37} -1.13695 q^{38} +(1.61584 + 3.22321i) q^{39} -1.35737i q^{40} +(-1.37894 + 0.369486i) q^{41} +(-0.516606 - 0.287243i) q^{42} +(-6.58558 + 3.80219i) q^{43} +(5.95956 - 5.95956i) q^{44} +(0.398089 - 1.48569i) q^{45} +(0.124173 - 0.463422i) q^{46} +(-5.26364 + 5.26364i) q^{47} +(3.20690 - 1.85151i) q^{48} +(-6.17202 - 3.30245i) q^{49} +(0.568470 - 0.152321i) q^{50} -7.56802i q^{51} +(7.01895 + 0.413900i) q^{52} -13.1808 q^{53} +(-0.215799 + 0.0578232i) q^{54} +(-5.75692 - 3.32376i) q^{55} +(-2.00294 + 1.19993i) q^{56} +(-3.59850 + 3.59850i) q^{57} +(-1.15084 - 0.308366i) q^{58} +(8.73809 + 2.34136i) q^{59} +(-2.12091 - 2.12091i) q^{60} +(10.1891 - 5.88266i) q^{61} +(0.172842 - 0.299371i) q^{62} +(-2.54421 + 0.725943i) q^{63} -6.82688i q^{64} +(-1.11751 - 5.43193i) q^{65} +0.965565i q^{66} +(-1.28138 - 4.78216i) q^{67} +(-12.7811 - 7.37915i) q^{68} +(-1.07373 - 1.85976i) q^{69} +(0.653167 + 0.632408i) q^{70} +(-5.25942 - 1.40926i) q^{71} +(-0.228407 + 0.852426i) q^{72} +(-8.04396 + 8.04396i) q^{73} +(-0.326766 - 0.565975i) q^{74} +(1.31713 - 2.28133i) q^{75} +(2.56854 + 9.58594i) q^{76} +(0.184619 + 11.4332i) q^{77} +(-0.602133 + 0.535073i) q^{78} +9.06635 q^{79} +(-5.50153 + 1.47413i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.159469 - 0.276209i) q^{82} +(-1.13072 - 1.13072i) q^{83} +(-1.25473 + 5.00455i) q^{84} +(-3.01275 + 11.2437i) q^{85} +(-1.20131 - 1.20131i) q^{86} +(-4.61844 + 2.66646i) q^{87} +(3.30308 + 1.90703i) q^{88} +(0.217351 + 0.811166i) q^{89} +0.343629 q^{90} +(-7.02751 + 6.45090i) q^{91} -4.18775 q^{92} +(-0.400469 - 1.49457i) q^{93} +(-1.44025 - 0.831529i) q^{94} +(6.77878 - 3.91373i) q^{95} +(1.83303 + 1.83303i) q^{96} +(4.35890 - 16.2676i) q^{97} +(0.355779 - 1.52288i) q^{98} +(3.05605 + 3.05605i) 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	\( 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9} - 2 q^{10} - 4 q^{11} - 32 q^{12} - 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} + 8 q^{17} + 2 q^{18} - 2 q^{19} - 44 q^{20} + 2 q^{21} - 4 q^{22} - 18 q^{23} - 4 q^{24} + 28 q^{26} - 18 q^{28} - 18 q^{29} + 14 q^{31} - 8 q^{32} - 4 q^{33} + 66 q^{34} - 20 q^{35} + 6 q^{36} - 24 q^{37} - 24 q^{38} + 8 q^{39} + 16 q^{42} - 6 q^{43} - 20 q^{44} - 4 q^{45} - 58 q^{46} + 28 q^{47} + 60 q^{48} + 10 q^{49} + 70 q^{50} - 28 q^{52} - 80 q^{53} + 4 q^{54} - 60 q^{55} - 120 q^{56} + 16 q^{57} - 4 q^{58} + 42 q^{59} - 58 q^{60} - 36 q^{61} - 52 q^{62} + 2 q^{63} + 14 q^{65} + 26 q^{67} + 72 q^{68} - 2 q^{69} + 68 q^{70} - 4 q^{71} + 4 q^{72} - 12 q^{73} - 18 q^{74} - 16 q^{75} + 48 q^{76} - 28 q^{77} - 14 q^{78} - 4 q^{79} + 98 q^{80} - 16 q^{81} - 20 q^{82} + 36 q^{83} + 32 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} + 54 q^{89} - 4 q^{90} - 54 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} - 22 q^{96} + 40 q^{97} + 4 q^{99}+O(q^{100}) \) 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 + 2 * q^21 - 4 * q^22 - 18 * q^23 - 4 * q^24 + 28 * q^26 - 18 * q^28 - 18 * q^29 + 14 * q^31 - 8 * q^32 - 4 * q^33 + 66 * q^34 - 20 * q^35 + 6 * q^36 - 24 * q^37 - 24 * q^38 + 8 * q^39 + 16 * q^42 - 6 * q^43 - 20 * q^44 - 4 * q^45 - 58 * q^46 + 28 * q^47 + 60 * q^48 + 10 * q^49 + 70 * q^50 - 28 * q^52 - 80 * q^53 + 4 * q^54 - 60 * q^55 - 120 * q^56 + 16 * q^57 - 4 * q^58 + 42 * q^59 - 58 * q^60 - 36 * q^61 - 52 * q^62 + 2 * q^63 + 14 * q^65 + 26 * q^67 + 72 * q^68 - 2 * q^69 + 68 * 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 + 32 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 + 54 * q^89 - 4 * q^90 - 54 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 - 22 * q^96 + 40 * q^97 + 4 * q^99

Introduction

L-functions

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