LMFDB - Embedded newform 65.2.o.a.63.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(2,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("65.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.o (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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			63.4
Root			$1.02262i$ of defining polynomial
Character	$\chi$	$=$	65.63
Dual form			65.2.o.a.32.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.511309 + 0.885613i) q^{2} +(-0.721300 + 2.69193i) q^{3} +(0.477126 - 0.826407i) q^{4} +(-1.69584 - 1.45744i) q^{5} +(-2.75281 + 0.737614i) q^{6} +(0.834479 + 0.481787i) q^{7} +3.02107 q^{8} +(-4.12812 - 2.38337i) q^{9} +O(q^{10})$	\(q+(0.511309 + 0.885613i) q^{2} +(-0.721300 + 2.69193i) q^{3} +(0.477126 - 0.826407i) q^{4} +(-1.69584 - 1.45744i) q^{5} +(-2.75281 + 0.737614i) q^{6} +(0.834479 + 0.481787i) q^{7} +3.02107 q^{8} +(-4.12812 - 2.38337i) q^{9} +(0.423625 - 2.24706i) q^{10} +(1.60661 + 0.430490i) q^{11} +(1.88048 + 1.88048i) q^{12} +(1.82127 - 3.11175i) q^{13} +0.985368i q^{14} +(5.14652 - 3.51384i) q^{15} +(0.590448 + 1.02269i) q^{16} +(-7.00342 + 1.87656i) q^{17} -4.87456i q^{18} +(-0.707496 - 2.64041i) q^{19} +(-2.01357 + 0.706075i) q^{20} +(-1.89884 + 1.89884i) q^{21} +(0.440226 + 1.64295i) q^{22} +(-3.72214 - 0.997344i) q^{23} +(-2.17910 + 8.13250i) q^{24} +(0.751762 + 4.94316i) q^{25} +(3.68704 + 0.0218799i) q^{26} +(3.48159 - 3.48159i) q^{27} +(0.796304 - 0.459747i) q^{28} +(0.253107 - 0.146132i) q^{29} +(5.74336 + 2.76117i) q^{30} +(-0.125649 - 0.125649i) q^{31} +(2.41727 - 4.18683i) q^{32} +(-2.31769 + 4.01436i) q^{33} +(-5.24282 - 5.24282i) q^{34} +(-0.712972 - 2.03323i) q^{35} +(-3.93927 + 2.27434i) q^{36} +(3.53443 - 2.04061i) q^{37} +(1.97663 - 1.97663i) q^{38} +(7.06291 + 7.14724i) q^{39} +(-5.12326 - 4.40302i) q^{40} +(-1.79277 + 6.69071i) q^{41} +(-2.65254 - 0.710745i) q^{42} +(2.05706 + 7.67707i) q^{43} +(1.12232 - 1.12232i) q^{44} +(3.52703 + 10.0583i) q^{45} +(-1.01990 - 3.80633i) q^{46} +7.84582i q^{47} +(-3.17888 + 0.851780i) q^{48} +(-3.03576 - 5.25810i) q^{49} +(-3.99335 + 3.19325i) q^{50} -20.2063i q^{51} +(-1.70259 - 2.98981i) q^{52} +(-1.99855 - 1.99855i) q^{53} +(4.86351 + 1.30317i) q^{54} +(-2.09714 - 3.07157i) q^{55} +(2.52102 + 1.45551i) q^{56} +7.61811 q^{57} +(0.258832 + 0.149437i) q^{58} +(4.87924 - 1.30739i) q^{59} +(-0.448318 - 5.92967i) q^{60} +(-1.04169 + 1.80425i) q^{61} +(0.0470311 - 0.175522i) q^{62} +(-2.29655 - 3.97775i) q^{63} +7.30568 q^{64} +(-7.62376 + 2.62264i) q^{65} -4.74023 q^{66} +(-3.64915 - 6.32050i) q^{67} +(-1.79071 + 6.68304i) q^{68} +(5.36956 - 9.30034i) q^{69} +(1.43611 - 1.67103i) q^{70} +(12.6082 - 3.37837i) q^{71} +(-12.4713 - 7.20034i) q^{72} +3.22747 q^{73} +(3.61437 + 2.08676i) q^{74} +(-13.8489 - 1.54181i) q^{75} +(-2.51962 - 0.675130i) q^{76} +(1.13328 + 1.13328i) q^{77} +(-2.71836 + 9.90945i) q^{78} +13.5845i q^{79} +(0.489192 - 2.59485i) q^{80} +(-0.289196 - 0.500902i) q^{81} +(-6.84204 + 1.83332i) q^{82} -8.56854i q^{83} +(0.663230 + 2.47521i) q^{84} +(14.6117 + 7.02469i) q^{85} +(-5.74712 + 5.74712i) q^{86} +(0.210809 + 0.786751i) q^{87} +(4.85368 + 1.30054i) q^{88} +(0.134207 - 0.500868i) q^{89} +(-7.10435 + 8.26648i) q^{90} +(3.01901 - 1.71922i) q^{91} +(-2.60014 + 2.60014i) q^{92} +(0.428870 - 0.247608i) q^{93} +(-6.94836 + 4.01164i) q^{94} +(-2.64843 + 5.50885i) q^{95} +(9.52707 + 9.52707i) q^{96} +(-3.75660 + 6.50662i) q^{97} +(3.10442 - 5.37702i) q^{98} +(-5.60626 - 5.60626i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21} + 16 q^{22} - 2 q^{23} - 32 q^{24} - 18 q^{25} - 24 q^{26} + 4 q^{27} + 6 q^{28} + 14 q^{30} - 6 q^{32} - 18 q^{33} - 2 q^{34} - 20 q^{35} + 36 q^{36} + 42 q^{37} + 8 q^{38} - 4 q^{39} - 16 q^{40} + 10 q^{41} - 56 q^{42} - 22 q^{43} + 36 q^{44} + 52 q^{45} + 4 q^{46} + 28 q^{48} - 18 q^{49} + 44 q^{50} + 46 q^{52} - 10 q^{53} + 48 q^{54} + 26 q^{55} - 12 q^{57} - 90 q^{58} + 16 q^{59} - 92 q^{60} - 16 q^{61} - 40 q^{62} - 32 q^{63} - 20 q^{64} + 8 q^{65} - 32 q^{66} - 58 q^{67} + 28 q^{68} + 16 q^{69} + 32 q^{70} - 16 q^{71} - 66 q^{72} + 72 q^{73} - 18 q^{74} - 34 q^{75} - 64 q^{76} + 28 q^{77} + 32 q^{78} - 34 q^{80} - 14 q^{81} + 22 q^{82} + 40 q^{84} - 6 q^{85} + 60 q^{86} + 62 q^{87} + 50 q^{88} + 6 q^{89} - 46 q^{90} + 8 q^{91} - 8 q^{92} + 48 q^{93} + 48 q^{94} + 14 q^{95} + 56 q^{96} - 22 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9 - 10 * q^10 - 16 * q^11 + 24 * q^12 + 2 * q^13 + 12 * q^15 - 2 * q^16 - 10 * q^17 + 20 * q^19 + 14 * q^20 + 4 * q^21 + 16 * q^22 - 2 * q^23 - 32 * q^24 - 18 * q^25 - 24 * q^26 + 4 * q^27 + 6 * q^28 + 14 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 - 20 * q^35 + 36 * q^36 + 42 * q^37 + 8 * q^38 - 4 * q^39 - 16 * q^40 + 10 * q^41 - 56 * q^42 - 22 * q^43 + 36 * q^44 + 52 * q^45 + 4 * q^46 + 28 * q^48 - 18 * q^49 + 44 * q^50 + 46 * q^52 - 10 * q^53 + 48 * q^54 + 26 * q^55 - 12 * q^57 - 90 * q^58 + 16 * q^59 - 92 * q^60 - 16 * q^61 - 40 * q^62 - 32 * q^63 - 20 * q^64 + 8 * q^65 - 32 * q^66 - 58 * q^67 + 28 * q^68 + 16 * q^69 + 32 * q^70 - 16 * q^71 - 66 * q^72 + 72 * q^73 - 18 * q^74 - 34 * q^75 - 64 * q^76 + 28 * q^77 + 32 * q^78 - 34 * q^80 - 14 * q^81 + 22 * q^82 + 40 * q^84 - 6 * q^85 + 60 * q^86 + 62 * q^87 + 50 * q^88 + 6 * q^89 - 46 * q^90 + 8 * q^91 - 8 * q^92 + 48 * q^93 + 48 * q^94 + 14 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.511309	+	0.885613i	0.361550	+	0.626223i	0.988216	−	0.153065i	$-0.0489144\pi$
$2$	0.511309	+	0.885613i	0.361550	+	0.626223i	−0.626666	+	0.779288i	$0.715581\pi$
$3$	−0.721300	+	2.69193i	−0.416443	+	1.55418i	0.365486	+	0.930817i	$0.380903\pi$
$3$	−0.721300	+	2.69193i	−0.416443	+	1.55418i	−0.781929	+	0.623368i	$0.785764\pi$
$4$	0.477126	−	0.826407i	0.238563	−	0.413204i
$5$	−1.69584	−	1.45744i	−0.758404	−	0.651785i
$5$	−1.69584	−	1.45744i	−0.758404	−	0.651785i
$6$	−2.75281	+	0.737614i	−1.12383	+	0.301130i
$7$	0.834479	+	0.481787i	0.315404	+	0.182098i	0.649342	−	0.760497i	$-0.275044\pi$
$7$	0.834479	+	0.481787i	0.315404	+	0.182098i	−0.333938	+	0.942595i	$0.608378\pi$
$8$	3.02107			1.06811
$9$	−4.12812	−	2.38337i	−1.37604	−	0.794457i
$10$	0.423625	−	2.24706i	0.133962	−	0.710583i
$11$	1.60661	+	0.430490i	0.484411	+	0.129797i	0.492756	−	0.870168i	$-0.335990\pi$
$11$	1.60661	+	0.430490i	0.484411	+	0.129797i	−0.00834492	+	0.999965i	$0.502656\pi$
$12$	1.88048	+	1.88048i	0.542847	+	0.542847i
$13$	1.82127	−	3.11175i	0.505130	−	0.863043i
$13$	1.82127	−	3.11175i	0.505130	−	0.863043i
$14$			0.985368i			0.263351i
$15$	5.14652	−	3.51384i	1.32883	−	0.907268i
$16$	0.590448	+	1.02269i	0.147612	+	0.255671i
$17$	−7.00342	+	1.87656i	−1.69858	+	0.455133i	−0.972581	−	0.232564i	$-0.925289\pi$
$17$	−7.00342	+	1.87656i	−1.69858	+	0.455133i	−0.725998	+	0.687697i	$0.758622\pi$
$18$		−	4.87456i		−	1.14894i
$19$	−0.707496	−	2.64041i	−0.162311	−	0.605752i	−0.998368	−	0.0571095i	$-0.981812\pi$
$19$	−0.707496	−	2.64041i	−0.162311	−	0.605752i	0.836057	−	0.548642i	$-0.184855\pi$
$20$	−2.01357	+	0.706075i	−0.450247	+	0.157883i
$21$	−1.89884	+	1.89884i	−0.414362	+	0.414362i
$22$	0.440226	+	1.64295i	0.0938565	+	0.350277i
$23$	−3.72214	−	0.997344i	−0.776120	−	0.207961i	−0.151046	−	0.988527i	$-0.548264\pi$
$23$	−3.72214	−	0.997344i	−0.776120	−	0.207961i	−0.625073	+	0.780566i	$0.714931\pi$
$24$	−2.17910	+	8.13250i	−0.444806	+	1.66004i
$25$	0.751762	+	4.94316i	0.150352	+	0.988632i
$26$	3.68704	+	0.0218799i	0.723087	+	0.00429099i
$27$	3.48159	−	3.48159i	0.670033	−	0.670033i
$28$	0.796304	−	0.459747i	0.150487	−	0.0868839i
$29$	0.253107	−	0.146132i	0.0470008	−	0.0271360i	−0.476315	−	0.879274i	$-0.658028\pi$
$29$	0.253107	−	0.146132i	0.0470008	−	0.0271360i	0.523316	+	0.852139i	$0.324695\pi$
$30$	5.74336	+	2.76117i	1.04859	+	0.504118i
$31$	−0.125649	−	0.125649i	−0.0225673	−	0.0225673i	0.695733	−	0.718300i	$-0.255080\pi$
$31$	−0.125649	−	0.125649i	−0.0225673	−	0.0225673i	−0.718300	+	0.695733i	$0.755080\pi$
$32$	2.41727	−	4.18683i	0.427317	−	0.740134i
$33$	−2.31769	+	4.01436i	−0.403458	+	0.698811i
$34$	−5.24282	−	5.24282i	−0.899136	−	0.899136i
$35$	−0.712972	−	2.03323i	−0.120514	−	0.343679i
$36$	−3.93927	+	2.27434i	−0.656545	+	0.379057i
$37$	3.53443	−	2.04061i	0.581057	−	0.335474i	−0.180496	−	0.983576i	$-0.557770\pi$
$37$	3.53443	−	2.04061i	0.581057	−	0.335474i	0.761553	+	0.648102i	$0.224437\pi$
$38$	1.97663	−	1.97663i	0.320652	−	0.320652i
$39$	7.06291	+	7.14724i	1.13097	+	1.14447i
$40$	−5.12326	−	4.40302i	−0.810059	−	0.696178i
$41$	−1.79277	+	6.69071i	−0.279984	+	1.04491i	0.672444	+	0.740148i	$0.265245\pi$
$41$	−1.79277	+	6.69071i	−0.279984	+	1.04491i	−0.952427	+	0.304765i	$0.901422\pi$
$42$	−2.65254	−	0.710745i	−0.409295	−	0.109670i
$43$	2.05706	+	7.67707i	0.313699	+	1.17074i	0.925194	+	0.379494i	$0.123902\pi$
$43$	2.05706	+	7.67707i	0.313699	+	1.17074i	−0.611495	+	0.791248i	$0.709432\pi$
$44$	1.12232	−	1.12232i	0.169195	−	0.169195i
$45$	3.52703	+	10.0583i	0.525779	+	1.49940i
$46$	−1.01990	−	3.80633i	−0.150376	−	0.561212i
$47$			7.84582i			1.14443i	0.820103	+	0.572215i	$0.193916\pi$
$47$			7.84582i			1.14443i	−0.820103	+	0.572215i	$0.806084\pi$
$48$	−3.17888	+	0.851780i	−0.458832	+	0.122944i
$49$	−3.03576	−	5.25810i	−0.433680	−	0.751156i
$50$	−3.99335	+	3.19325i	−0.564744	+	0.451594i
$51$		−	20.2063i		−	2.82944i
$52$	−1.70259	−	2.98981i	−0.236107	−	0.414612i
$53$	−1.99855	−	1.99855i	−0.274522	−	0.274522i	0.556395	−	0.830918i	$-0.312184\pi$
$53$	−1.99855	−	1.99855i	−0.274522	−	0.274522i	−0.830918	+	0.556395i	$0.812184\pi$
$54$	4.86351	+	1.30317i	0.661840	+	0.177339i
$55$	−2.09714	−	3.07157i	−0.282779	−	0.414171i
$56$	2.52102	+	1.45551i	0.336886	+	0.194501i
$57$	7.61811			1.00904
$58$	0.258832	+	0.149437i	0.0339863	+	0.0196220i
$59$	4.87924	−	1.30739i	0.635223	−	0.170207i	0.0731843	−	0.997318i	$-0.476684\pi$
$59$	4.87924	−	1.30739i	0.635223	−	0.170207i	0.562039	+	0.827111i	$0.310017\pi$
$60$	−0.448318	−	5.92967i	−0.0578776	−	0.765517i
$61$	−1.04169	+	1.80425i	−0.133374	+	0.231011i	−0.924975	−	0.380027i	$-0.875915\pi$
$61$	−1.04169	+	1.80425i	−0.133374	+	0.231011i	0.791601	+	0.611038i	$0.209248\pi$
$62$	0.0470311	−	0.175522i	0.00597296	−	0.0222914i
$63$	−2.29655	−	3.97775i	−0.289339	−	0.501149i
$64$	7.30568			0.913209
$65$	−7.62376	+	2.62264i	−0.945611	+	0.325299i
$66$	−4.74023			−0.583482
$67$	−3.64915	−	6.32050i	−0.445814	−	0.772173i	0.552294	−	0.833649i	$-0.313752\pi$
$67$	−3.64915	−	6.32050i	−0.445814	−	0.772173i	−0.998109	+	0.0614765i	$0.980419\pi$
$68$	−1.79071	+	6.68304i	−0.217156	+	0.810437i
$69$	5.36956	−	9.30034i	0.646419	−	1.11963i
$70$	1.43611	−	1.67103i	0.171648	−	0.199726i
$71$	12.6082	−	3.37837i	1.49632	−	0.400939i	0.584457	−	0.811425i	$-0.301308\pi$
$71$	12.6082	−	3.37837i	1.49632	−	0.400939i	0.911867	+	0.410486i	$0.134641\pi$
$72$	−12.4713	−	7.20034i	−1.46976	−	0.848568i
$73$	3.22747			0.377746			0.188873	−	0.982001i	$-0.439517\pi$
$73$	3.22747			0.377746			0.188873	+	0.982001i	$0.439517\pi$
$74$	3.61437	+	2.08676i	0.420163	+	0.242581i
$75$	−13.8489	−	1.54181i	−1.59913	−	0.178033i
$76$	−2.51962	−	0.675130i	−0.289020	−	0.0774427i
$77$	1.13328	+	1.13328i	0.129149	+	0.129149i
$78$	−2.71836	+	9.90945i	−0.307793	+	1.12202i
$79$			13.5845i			1.52838i	0.644992	+	0.764190i	$0.276861\pi$
$79$			13.5845i			1.52838i	−0.644992	+	0.764190i	$0.723139\pi$
$80$	0.489192	−	2.59485i	0.0546934	−	0.290113i
$81$	−0.289196	−	0.500902i	−0.0321329	−	0.0556558i
$82$	−6.84204	+	1.83332i	−0.755577	+	0.202456i
$83$		−	8.56854i		−	0.940519i	−0.882528	−	0.470260i	$-0.844160\pi$
$83$		−	8.56854i		−	0.940519i	0.882528	−	0.470260i	$-0.155840\pi$
$84$	0.663230	+	2.47521i	0.0723643	+	0.270067i
$85$	14.6117	+	7.02469i	1.58486	+	0.761934i
$86$	−5.74712	+	5.74712i	−0.619728	+	0.619728i
$87$	0.210809	+	0.786751i	0.0226011	+	0.0843486i
$88$	4.85368	+	1.30054i	0.517404	+	0.138638i
$89$	0.134207	−	0.500868i	0.0142259	−	0.0530919i	−0.958448	−	0.285267i	$-0.907918\pi$
$89$	0.134207	−	0.500868i	0.0142259	−	0.0530919i	0.972674	+	0.232175i	$0.0745843\pi$
$90$	−7.10435	+	8.26648i	−0.748864	+	0.871363i
$91$	3.01901	−	1.71922i	0.316479	−	0.180223i
$92$	−2.60014	+	2.60014i	−0.271084	+	0.271084i
$93$	0.428870	−	0.247608i	0.0444718	−	0.0256758i
$94$	−6.94836	+	4.01164i	−0.716669	+	0.413769i
$95$	−2.64843	+	5.50885i	−0.271723	+	0.565196i
$96$	9.52707	+	9.52707i	0.972353	+	0.972353i
$97$	−3.75660	+	6.50662i	−0.381425	+	0.660648i	−0.991266	−	0.131876i	$-0.957900\pi$
$97$	−3.75660	+	6.50662i	−0.381425	+	0.660648i	0.609841	+	0.792524i	$0.291233\pi$
$98$	3.10442	−	5.37702i	0.313594	−	0.543161i
$99$	−5.60626	−	5.60626i	−0.563450	−	0.563450i
$100$	4.44375	+	1.73725i	0.444375	+	0.173725i
$101$	8.44685	−	4.87679i	0.840493	−	0.485259i	−0.0169388	−	0.999857i	$-0.505392\pi$
$101$	8.44685	−	4.87679i	0.840493	−	0.485259i	0.857432	+	0.514598i	$0.172059\pi$
$102$	17.8949	−	10.3316i	1.77186	−	1.02298i
$103$	−2.52321	+	2.52321i	−0.248619	+	0.248619i	−0.820404	−	0.571784i	$-0.806251\pi$
$103$	−2.52321	+	2.52321i	−0.248619	+	0.248619i	0.571784	+	0.820404i	$0.306251\pi$
$104$	5.50220	−	9.40081i	0.539535	−	0.921825i
$105$	5.98759	−	0.452697i	0.584329	−	0.0441787i
$106$	0.748066	−	2.79182i	0.0726586	−	0.271166i
$107$	0.429359	+	0.115046i	0.0415077	+	0.0111220i	0.279513	−	0.960142i	$-0.409827\pi$
$107$	0.429359	+	0.115046i	0.0415077	+	0.0111220i	−0.238005	+	0.971264i	$0.576494\pi$
$108$	−1.21605	−	4.53837i	−0.117015	−	0.436705i
$109$	−6.42134	+	6.42134i	−0.615053	+	0.615053i	−0.944258	−	0.329206i	$-0.893219\pi$
$109$	−6.42134	+	6.42134i	−0.615053	+	0.615053i	0.329206	+	0.944258i	$0.393219\pi$
$110$	1.64793	−	3.42778i	0.157124	−	0.326826i
$111$	2.94378	+	10.9863i	0.279411	+	1.04278i
$112$			1.13788i			0.107520i
$113$	−1.86865	+	0.500704i	−0.175788	+	0.0471023i	−0.345639	−	0.938367i	$-0.612338\pi$
$113$	−1.86865	+	0.500704i	−0.175788	+	0.0471023i	0.169851	+	0.985470i	$0.445671\pi$
$114$	3.89521	+	6.74670i	0.364820	+	0.631886i
$115$	4.85860	+	7.11612i	0.453066	+	0.663581i
$116$		−	0.278893i		−	0.0258946i
$117$	−14.9349	+	8.50489i	−1.38073	+	0.786277i
$118$	3.65264	+	3.65264i	0.336253	+	0.336253i
$119$	−6.74831	−	1.80821i	−0.618617	−	0.165758i
$120$	15.5480	−	10.6155i	1.41933	−	0.969062i
$121$	−7.13041	−	4.11674i	−0.648219	−	0.374249i
$122$	−2.13050			−0.192886
$123$	−16.7178	−	9.65202i	−1.50739	−	0.870293i
$124$	−0.163788	+	0.0438869i	−0.0147086	+	0.00394116i
$125$	5.92947	−	9.47847i	0.530348	−	0.847780i
$126$	2.34850	−	4.06772i	0.209221	−	0.362381i
$127$	−0.562967	+	2.10102i	−0.0499553	+	0.186436i	−0.986395	−	0.164393i	$-0.947433\pi$
$127$	−0.562967	+	2.10102i	−0.0499553	+	0.186436i	0.936440	+	0.350829i	$0.114100\pi$
$128$	−1.09908	−	1.90366i	−0.0971460	−	0.168262i
$129$	−22.1499			−1.95019
$130$	−6.22074	−	5.41072i	−0.545595	−	0.474552i
$131$	−0.0622493			−0.00543874			−0.00271937	−	0.999996i	$-0.500866\pi$
$131$	−0.0622493			−0.00543874			−0.00271937	+	0.999996i	$0.500866\pi$
$132$	2.21166	+	3.83072i	0.192501	+	0.333421i
$133$	0.681725	−	2.54423i	0.0591130	−	0.220613i
$134$	3.73168	−	6.46346i	0.322368	−	0.558358i
$135$	−10.9784	+	0.830034i	−0.944872	+	0.0714380i
$136$	−21.1578	+	5.66923i	−1.81427	+	0.486132i
$137$	−3.82564	−	2.20873i	−0.326846	−	0.188705i	0.327594	−	0.944819i	$-0.393762\pi$
$137$	−3.82564	−	2.20873i	−0.326846	−	0.188705i	−0.654440	+	0.756114i	$0.727096\pi$
$138$	10.9820			0.934850
$139$	11.9066	+	6.87430i	1.00991	+	0.583070i	0.911165	−	0.412043i	$-0.135184\pi$
$139$	11.9066	+	6.87430i	1.00991	+	0.583070i	0.0987430	+	0.995113i	$0.468518\pi$
$140$	−2.02046	−	0.380905i	−0.170760	−	0.0321923i
$141$	−21.1204	−	5.65919i	−1.77866	−	0.476590i
$142$	9.43864	+	9.43864i	0.792073	+	0.792073i
$143$	4.26565	−	4.21532i	0.356711	−	0.352503i
$144$		−	5.62903i		−	0.469085i
$145$	−0.642207	−	0.121072i	−0.0533324	−	0.0100544i
$146$	1.65023	+	2.85829i	0.136574	+	0.236553i
$147$	16.3441	−	4.37939i	1.34804	−	0.361206i
$148$		−	3.89451i		−	0.320127i
$149$	−1.12129	−	4.18471i	−0.0918596	−	0.342825i	0.904665	−	0.426124i	$-0.140121\pi$
$149$	−1.12129	−	4.18471i	−0.0918596	−	0.342825i	−0.996525	+	0.0832987i	$0.973454\pi$
$150$	−5.71560	−	13.0531i	−0.466677	−	1.06578i
$151$	4.74990	−	4.74990i	0.386542	−	0.386542i	−0.486910	−	0.873452i	$-0.661876\pi$
$151$	4.74990	−	4.74990i	0.386542	−	0.386542i	0.873452	+	0.486910i	$0.161876\pi$
$152$	−2.13740	−	7.97687i	−0.173366	−	0.647010i
$153$	33.3835	+	8.94508i	2.69890	+	0.723167i
$154$	−0.424190	+	1.58310i	−0.0341822	+	0.127570i
$155$	0.0299556	+	0.396208i	0.00240610	+	0.0318242i
$156$	9.27643	−	2.42670i	0.742709	−	0.194292i
$157$	14.4488	−	14.4488i	1.15314	−	1.15314i	0.167218	−	0.985920i	$-0.446522\pi$
$157$	14.4488	−	14.4488i	1.15314	−	1.15314i	0.985920	−	0.167218i	$-0.0534784\pi$
$158$	−12.0306	+	6.94589i	−0.957106	+	0.552586i
$159$	6.82151	−	3.93840i	0.540981	−	0.312336i
$160$	−10.2013	+	3.57719i	−0.806487	+	0.282802i
$161$	−2.62554	−	2.62554i	−0.206922	−	0.206922i
$162$	0.295737	−	0.512231i	0.0232353	−	0.0402447i
$163$	−10.6926	+	18.5201i	−0.837508	+	1.45061i	0.0544633	+	0.998516i	$0.482655\pi$
$163$	−10.6926	+	18.5201i	−0.837508	+	1.45061i	−0.891972	+	0.452091i	$0.850678\pi$
$164$	4.67387	+	4.67387i	0.364968	+	0.364968i
$165$	9.78111	−	3.42984i	0.761459	−	0.267012i
$166$	7.58841	−	4.38117i	0.588975	−	0.340045i
$167$	1.48475	−	0.857220i	0.114893	−	0.0663337i	−0.441452	−	0.897285i	$-0.645536\pi$
$167$	1.48475	−	0.857220i	0.114893	−	0.0663337i	0.556345	+	0.830951i	$0.312203\pi$
$168$	−5.73655	+	5.73655i	−0.442584	+	0.442584i
$169$	−6.36593	−	11.3347i	−0.489687	−	0.871898i
$170$	1.24992	+	16.5321i	0.0958646	+	1.26795i
$171$	−3.37245	+	12.5862i	−0.257898	+	0.962488i
$172$	7.32587	+	1.96296i	0.558592	+	0.149674i
$173$	−3.92804	−	14.6596i	−0.298643	−	1.11455i	−0.938281	−	0.345875i	$-0.887582\pi$
$173$	−3.92804	−	14.6596i	−0.298643	−	1.11455i	0.639638	−	0.768677i	$-0.279084\pi$
$174$	−0.588968	+	0.588968i	−0.0446496	+	0.0446496i
$175$	−1.75422	+	4.48716i	−0.132607	+	0.339197i
$176$	0.508363	+	1.89724i	0.0383193	+	0.143010i
$177$			14.0776i			1.05814i
$178$	0.512196	−	0.137243i	0.0383907	−	0.0102868i
$179$	1.37961	+	2.38956i	0.103117	+	0.178604i	0.912967	−	0.408033i	$-0.133785\pi$
$179$	1.37961	+	2.38956i	0.103117	+	0.178604i	−0.809850	+	0.586637i	$0.800452\pi$
$180$	9.99508	+	1.88431i	0.744990	+	0.140448i
$181$			10.3568i			0.769818i	0.922954	+	0.384909i	$0.125767\pi$
$181$			10.3568i			0.769818i	−0.922954	+	0.384909i	$0.874233\pi$
$182$	3.06621	+	1.79462i	0.227283	+	0.133026i
$183$	−4.10555	−	4.10555i	−0.303491	−	0.303491i
$184$	−11.2449	−	3.01305i	−0.828981	−	0.222125i
$185$	−8.96789	−	1.69066i	−0.659333	−	0.124300i
$186$	0.438570	+	0.253209i	0.0321575	+	0.0185662i
$187$	−12.0596			−0.881885
$188$	6.48384	+	3.74345i	0.472883	+	0.273019i
$189$	4.58270	−	1.22793i	0.333342	−	0.0893188i
$190$	−6.23287	+	0.471242i	−0.452180	+	0.0341875i
$191$	−9.28983	+	16.0905i	−0.672189	+	1.16427i	0.305093	+	0.952322i	$0.401312\pi$
$191$	−9.28983	+	16.0905i	−0.672189	+	1.16427i	−0.977282	+	0.211943i	$0.932021\pi$
$192$	−5.26958	+	19.6663i	−0.380299	+	1.41930i
$193$	−6.28576	−	10.8872i	−0.452459	−	0.783681i	0.546079	−	0.837733i	$-0.316120\pi$
$193$	−6.28576	−	10.8872i	−0.452459	−	0.783681i	−0.998538	+	0.0540520i	$0.982786\pi$
$194$	−7.68313			−0.551617
$195$	−1.56094	−	22.4143i	−0.111781	−	1.60512i
$196$	−5.79377			−0.413841
$197$	−7.14308	−	12.3722i	−0.508924	−	0.881481i	−0.999947	−	0.0103349i	$-0.996710\pi$
$197$	−7.14308	−	12.3722i	−0.508924	−	0.881481i	0.491023	−	0.871147i	$-0.336623\pi$
$198$	2.09845	−	7.83150i	0.149130	−	0.556561i
$199$	−7.36781	+	12.7614i	−0.522291	+	0.904634i	0.477373	+	0.878701i	$0.341589\pi$
$199$	−7.36781	+	12.7614i	−0.522291	+	0.904634i	−0.999664	+	0.0259331i	$0.991744\pi$
$200$	2.27113	+	14.9336i	0.160593	+	1.05597i
$201$	19.6465	−	5.26425i	1.38575	−	0.371312i
$202$	8.63790	+	4.98709i	0.607760	+	0.350891i
$203$	0.281617			0.0197656
$204$	−16.6986	−	9.64094i	−1.16914	−	0.675001i
$205$	12.7915	−	8.73354i	0.893400	−	0.609977i
$206$	−3.52473	−	0.944449i	−0.245580	−	0.0658029i
$207$	12.9884	+	12.9884i	0.902756	+	0.902756i
$208$	4.25770	+	0.0252664i	0.295219	+	0.00175191i
$209$		−	4.54668i		−	0.314500i
$210$	3.46242	+	5.07122i	0.238930	+	0.349947i
$211$	4.26604	+	7.38900i	0.293686	+	0.508680i	0.974678	−	0.223611i	$-0.0717845\pi$
$211$	4.26604	+	7.38900i	0.293686	+	0.508680i	−0.680992	+	0.732291i	$0.738451\pi$
$212$	−2.60518	+	0.698056i	−0.178925	+	0.0479427i
$213$			36.3773i			2.49253i
$214$	0.117649	+	0.439070i	0.00804229	+	0.0300142i
$215$	7.70038	−	16.0171i	0.525161	−	1.09236i
$216$	10.5181	−	10.5181i	0.715669	−	0.715669i
$217$	−0.0443156	−	0.165388i	−0.00300834	−	0.0112273i
$218$	−8.97011	−	2.40353i	−0.607532	−	0.162788i
$219$	−2.32797	+	8.68810i	−0.157310	+	0.587087i
$220$	−3.53897	+	0.267567i	−0.238597	+	0.0180394i
$221$	−6.91576	+	25.2106i	−0.465205	+	1.69585i
$222$	−8.22445	+	8.22445i	−0.551989	+	0.551989i
$223$	6.11483	−	3.53040i	0.409479	−	0.236413i	−0.281087	−	0.959682i	$-0.590695\pi$
$223$	6.11483	−	3.53040i	0.409479	−	0.236413i	0.690566	+	0.723269i	$0.257362\pi$
$224$	4.03432	−	2.32922i	0.269555	−	0.155627i
$225$	8.67803	−	22.1977i	0.578535	−	1.47985i
$226$	−1.39889	−	1.39889i	−0.0930527	−	0.0930527i
$227$	8.58775	−	14.8744i	0.569989	−	0.987249i	−0.426578	−	0.904451i	$-0.640281\pi$
$227$	8.58775	−	14.8744i	0.569989	−	0.987249i	0.996566	−	0.0827985i	$-0.0263858\pi$
$228$	3.63480	−	6.29566i	0.240721	−	0.416940i
$229$	8.90647	+	8.90647i	0.588556	+	0.588556i	0.937240	−	0.348684i	$-0.113371\pi$
$229$	8.90647	+	8.90647i	0.588556	+	0.588556i	−0.348684	+	0.937240i	$0.613371\pi$
$230$	−3.81788	+	7.94137i	−0.251744	+	0.523638i
$231$	−3.86813	+	2.23327i	−0.254504	+	0.146938i
$232$	0.764655	−	0.441474i	0.0502021	−	0.0289842i
$233$	17.5822	−	17.5822i	1.15185	−	1.15185i	0.165666	−	0.986182i	$-0.447023\pi$
$233$	17.5822	−	17.5822i	1.15185	−	1.15185i	0.986182	−	0.165666i	$-0.0529773\pi$
$234$	−15.1684	−	8.87790i	−0.991588	−	0.580366i
$235$	11.4348	−	13.3053i	0.745923	−	0.867940i
$236$	1.24758	−	4.65603i	0.0812105	−	0.303082i
$237$	−36.5686	−	9.79852i	−2.37538	−	0.636482i
$238$	−1.84910	−	6.90095i	−0.119860	−	0.447322i
$239$	2.23488	−	2.23488i	0.144562	−	0.144562i	−0.631122	−	0.775684i	$-0.717405\pi$
$239$	2.23488	−	2.23488i	0.144562	−	0.144562i	0.775684	+	0.631122i	$0.217405\pi$
$240$	6.63230	+	3.18854i	0.428113	+	0.205819i
$241$	−4.66361	−	17.4048i	−0.300409	−	1.12114i	−0.936825	−	0.349797i	$-0.886250\pi$
$241$	−4.66361	−	17.4048i	−0.300409	−	1.12114i	0.636416	−	0.771346i	$-0.280416\pi$
$242$		−	8.41971i		−	0.541239i
$243$	15.8248	−	4.24025i	1.01516	−	0.272012i
$244$	0.994033	+	1.72172i	0.0636364	+	0.110222i
$245$	−2.51516	+	13.3413i	−0.160688	+	0.852346i
$246$		−	19.7406i		−	1.25862i
$247$	−9.50483	−	2.60736i	−0.604778	−	0.165902i
$248$	−0.379596	−	0.379596i	−0.0241044	−	0.0241044i
$249$	23.0659	+	6.18048i	1.46174	+	0.391672i
$250$	11.4260	+	0.404792i	0.722647	+	0.0256013i
$251$	12.1009	+	6.98644i	0.763800	+	0.440980i	0.830658	−	0.556782i	$-0.187964\pi$
$251$	12.1009	+	6.98644i	0.763800	+	0.440980i	−0.0668586	+	0.997762i	$0.521298\pi$
$252$	−4.38299			−0.276102
$253$	−5.55068	−	3.20468i	−0.348968	−	0.201477i
$254$	−2.14854	+	0.575700i	−0.134812	+	0.0361227i
$255$	−29.4493	+	34.2666i	−1.84419	+	2.14586i
$256$	8.42962	−	14.6005i	0.526851	−	0.912533i
$257$	−5.99887	+	22.3881i	−0.374199	+	1.39653i	0.480312	+	0.877098i	$0.340524\pi$
$257$	−5.99887	+	22.3881i	−0.374199	+	1.39653i	−0.854511	+	0.519433i	$0.826143\pi$
$258$	−11.3254	−	19.6162i	−0.705090	−	1.22125i
$259$	3.93255			0.244357
$260$	−1.47013	+	7.55166i	−0.0911735	+	0.468334i
$261$	−1.39314			−0.0862334
$262$	−0.0318286	−	0.0551288i	−0.00196638	−	0.00340587i
$263$	0.336737	−	1.25672i	0.0207641	−	0.0774926i	−0.954766	−	0.297357i	$-0.903895\pi$
$263$	0.336737	−	1.25672i	0.0207641	−	0.0774926i	0.975530	+	0.219864i	$0.0705615\pi$
$264$	−7.00191	+	12.1277i	−0.430938	+	0.746407i
$265$	0.476468	+	6.30199i	0.0292692	+	0.387128i
$266$	2.60178	−	0.697144i	0.159525	−	0.0427446i
$267$	1.25150	+	0.722551i	0.0765903	+	0.0442194i
$268$	−6.96441			−0.425419
$269$	6.87429	+	3.96887i	0.419133	+	0.241986i	0.694706	−	0.719294i	$-0.255534\pi$
$269$	6.87429	+	3.96887i	0.419133	+	0.241986i	−0.275574	+	0.961280i	$0.588868\pi$
$270$	−6.34846	−	9.29823i	−0.386355	−	0.565872i
$271$	−0.865041	−	0.231787i	−0.0525475	−	0.0140801i	0.232450	−	0.972608i	$-0.425326\pi$
$271$	−0.865041	−	0.231787i	−0.0525475	−	0.0140801i	−0.284997	+	0.958528i	$0.591993\pi$
$272$	−6.05429	−	6.05429i	−0.367095	−	0.367095i
$273$	2.45041	+	9.36704i	0.148305	+	0.566919i
$274$		−	4.51738i		−	0.272905i
$275$	−0.920192	+	8.26535i	−0.0554897	+	0.498420i
$276$	−5.12391	−	8.87488i	−0.308423	−	0.534205i
$277$	9.22930	−	2.47298i	0.554535	−	0.148587i	0.0293404	−	0.999569i	$-0.490659\pi$
$277$	9.22930	−	2.47298i	0.554535	−	0.148587i	0.525194	+	0.850982i	$0.323993\pi$
$278$			14.0596i			0.843236i
$279$	0.219227	+	0.818165i	0.0131248	+	0.0489823i
$280$	−2.15394	−	6.14255i	−0.128723	−	0.367087i
$281$	5.58408	−	5.58408i	0.333118	−	0.333118i	−0.520651	−	0.853769i	$-0.674311\pi$
$281$	5.58408	−	5.58408i	0.333118	−	0.333118i	0.853769	+	0.520651i	$0.174311\pi$
$282$	−5.78719	−	21.5981i	−0.344622	−	1.28615i
$283$	−20.3851	−	5.46218i	−1.21177	−	0.324693i	−0.404314	−	0.914620i	$-0.632490\pi$
$283$	−20.3851	−	5.46218i	−1.21177	−	0.324693i	−0.807457	+	0.589927i	$0.799157\pi$
$284$	3.22382	−	12.0315i	0.191298	−	0.713936i
$285$	−12.9191	−	11.1029i	−0.765262	−	0.657679i
$286$	5.91420	+	1.62238i	0.349714	+	0.0959335i
$287$	−4.71953	+	4.71953i	−0.278585	+	0.278585i
$288$	−19.9576	+	11.5225i	−1.17601	+	0.678970i
$289$	30.8040	−	17.7847i	1.81200	−	1.04616i
$290$	−0.221144	−	0.630652i	−0.0129860	−	0.0370332i
$291$	−14.8057	−	14.8057i	−0.867927	−	0.867927i
$292$	1.53991	−	2.66720i	0.0901164	−	0.156086i
$293$	−2.01079	+	3.48280i	−0.117472	+	0.203467i	−0.918765	−	0.394805i	$-0.870812\pi$
$293$	−2.01079	+	3.48280i	−0.117472	+	0.203467i	0.801293	+	0.598272i	$0.204146\pi$
$294$	12.2353	+	12.2353i	0.713579	+	0.713579i
$295$	−10.1799	−	4.89405i	−0.592694	−	0.284943i
$296$	10.6778	−	6.16482i	0.620633	−	0.358323i
$297$	7.09234	−	4.09477i	0.411539	−	0.237602i
$298$	3.13271	−	3.13271i	0.181473	−	0.181473i
$299$	−9.88252	+	9.76592i	−0.571521	+	0.564778i
$300$	−7.88183	+	10.7092i	−0.455058	+	0.618294i
$301$	−1.98213	+	7.39742i	−0.114248	+	0.426380i
$302$	6.63524	+	1.77791i	0.381815	+	0.102307i
$303$	7.03525	+	26.2559i	0.404165	+	1.50836i
$304$	2.28257	−	2.28257i	0.130914	−	0.130914i
$305$	4.39612	−	1.54154i	0.251721	−	0.0882683i
$306$	9.14740	+	34.1386i	0.522922	+	1.95157i
$307$		−	24.2191i		−	1.38226i	−0.722732	−	0.691128i	$-0.757114\pi$
$307$		−	24.2191i		−	1.38226i	0.722732	−	0.691128i	$-0.242886\pi$
$308$	1.47727	−	0.395832i	0.0841750	−	0.0225546i
$309$	−4.97231	−	8.61229i	−0.282865	−	0.489936i
$310$	−0.335570	+	0.229114i	−0.0190591	+	0.0130128i
$311$		−	7.87243i		−	0.446405i	−0.974772	−	0.223202i	$-0.928349\pi$
$311$		−	7.87243i		−	0.446405i	0.974772	−	0.223202i	$-0.0716511\pi$
$312$	21.3376	+	21.5923i	1.20800	+	1.22242i
$313$	3.39121	+	3.39121i	0.191683	+	0.191683i	0.796423	−	0.604740i	$-0.206723\pi$
$313$	3.39121	+	3.39121i	0.191683	+	0.191683i	−0.604740	+	0.796423i	$0.706723\pi$
$314$	20.1838	+	5.40824i	1.13904	+	0.305204i
$315$	−1.90272	+	10.0927i	−0.107206	+	0.568660i
$316$	11.2264	+	6.48154i	0.631532	+	0.364615i
$317$	22.9255			1.28762			0.643812	−	0.765184i	$-0.277352\pi$
$317$	22.9255			1.28762			0.643812	+	0.765184i	$0.277352\pi$
$318$	6.97580	+	4.02748i	0.391183	+	0.225850i
$319$	0.469553	−	0.125816i	0.0262899	−	0.00704436i
$320$	−12.3893	−	10.6476i	−0.692581	−	0.595216i
$321$	−0.619393	+	1.07282i	−0.0345712	+	0.0598790i
$322$	0.982751	−	3.66768i	0.0547666	−	0.204392i
$323$	9.90979	+	17.1643i	0.551395	+	0.955044i
$324$	−0.551932			−0.0306629
$325$	16.7510	+	6.66356i	0.929180	+	0.369628i
$326$	−21.8689			−1.21120
$327$	−12.6541	−	21.9175i	−0.699771	−	1.21204i
$328$	−5.41609	+	20.2131i	−0.299053	+	1.11608i
$329$	−3.78001	+	6.54718i	−0.208399	+	0.360958i
$330$	8.03868	+	6.90858i	0.442515	+	0.380305i
$331$	−32.4118	+	8.68470i	−1.78151	+	0.477354i	−0.990858	−	0.134910i	$-0.956925\pi$
$331$	−32.4118	+	8.68470i	−1.78151	+	0.477354i	−0.790653	+	0.612264i	$0.790259\pi$
$332$	−7.08110	−	4.08828i	−0.388626	−	0.224373i
$333$	−19.4541			−1.06608
$334$	1.51833	+	0.876609i	0.0830794	+	0.0479659i
$335$	−3.02336	+	16.0370i	−0.165184	+	0.876194i
$336$	−3.06309	−	0.820752i	−0.167105	−	0.0447757i
$337$	14.5544	+	14.5544i	0.792826	+	0.792826i	0.981953	−	0.189126i	$-0.0605656\pi$
$337$	14.5544	+	14.5544i	0.792826	+	0.792826i	−0.189126	+	0.981953i	$0.560566\pi$
$338$	6.78318	−	11.4333i	0.368957	−	0.621888i
$339$		−	5.39143i		−	0.292822i
$340$	12.7769	−	8.72352i	0.692923	−	0.473099i
$341$	−0.147779	−	0.255960i	−0.00800267	−	0.0138610i
$342$	−12.8708	+	3.44873i	−0.695975	+	0.186486i
$343$		−	12.5954i		−	0.680087i
$344$	6.21454	+	23.1930i	0.335065	+	1.25048i
$345$	−22.6606	+	7.94613i	−1.22000	+	0.427805i
$346$	10.9743	−	10.9743i	0.589983	−	0.589983i
$347$	5.90442	+	22.0356i	0.316966	+	1.18293i	0.922145	+	0.386844i	$0.126435\pi$
$347$	5.90442	+	22.0356i	0.316966	+	1.18293i	−0.605179	+	0.796089i	$0.706899\pi$
$348$	0.750759	+	0.201165i	0.0402449	+	0.0107836i
$349$	2.68798	−	10.0317i	0.143884	−	0.536983i	−0.855918	−	0.517111i	$-0.827008\pi$
$349$	2.68798	−	10.0317i	0.143884	−	0.536983i	0.999803	−	0.0198718i	$-0.00632581\pi$
$350$	−4.87083	+	0.740762i	−0.260357	+	0.0395954i
$351$	−4.49290	−	17.1748i	−0.239813	−	0.916721i
$352$	5.68599	−	5.68599i	0.303064	−	0.303064i
$353$	3.72420	−	2.15017i	0.198219	−	0.114442i	−0.397605	−	0.917556i	$-0.630159\pi$
$353$	3.72420	−	2.15017i	0.198219	−	0.114442i	0.595825	+	0.803115i	$0.296825\pi$
$354$	−12.4673	+	7.19799i	−0.662629	+	0.382569i
$355$	−26.3054	−	12.6465i	−1.39614	−	0.671208i
$356$	−0.349887	−	0.349887i	−0.0185440	−	0.0185440i
$357$	9.73511	−	16.8617i	0.515237	−	0.892416i
$358$	−1.41082	+	2.44361i	−0.0745640	+	0.129149i
$359$	10.4273	+	10.4273i	0.550333	+	0.550333i	0.926537	−	0.376204i	$-0.122771\pi$
$359$	10.4273	+	10.4273i	0.550333	+	0.550333i	−0.376204	+	0.926537i	$0.622771\pi$
$360$	10.6554	+	30.3868i	0.561589	+	1.60153i
$361$	9.98326	−	5.76384i	0.525435	−	0.303360i
$362$	−9.17216	+	5.29555i	−0.482078	+	0.278328i
$363$	16.2251	−	16.2251i	0.851599	−	0.851599i
$364$	0.0196734	−	3.31522i	0.00103117	−	0.173765i
$365$	−5.47327	−	4.70382i	−0.286484	−	0.246209i
$366$	1.53673	−	5.73514i	0.0803259	−	0.299780i
$367$	−11.0341	−	2.95657i	−0.575973	−	0.154331i	−0.0409383	−	0.999162i	$-0.513035\pi$
$367$	−11.0341	−	2.95657i	−0.575973	−	0.154331i	−0.535034	+	0.844830i	$0.679701\pi$
$368$	−1.17776	−	4.39546i	−0.0613950	−	0.229129i
$369$	23.3472	−	23.3472i	1.21541	−	1.21541i
$370$	−3.08809	−	8.80653i	−0.160542	−	0.457830i
$371$	−0.704874	−	2.63063i	−0.0365953	−	0.136575i
$372$		−	0.472562i		−	0.0245012i
$373$	−27.1975	+	7.28755i	−1.40823	+	0.377335i	−0.881294	−	0.472568i	$-0.843327\pi$
$373$	−27.1975	+	7.28755i	−1.40823	+	0.377335i	−0.526939	+	0.849903i	$0.676661\pi$
$374$	−6.16618	−	10.6801i	−0.318846	−	0.552257i
$375$	21.2384	+	22.7985i	1.09675	+	1.17731i
$376$			23.7028i			1.22238i
$377$	0.00625324	−	1.05375i	0.000322058	−	0.0542709i
$378$	3.43065	+	3.43065i	0.176453	+	0.176453i
$379$	−16.3551	−	4.38232i	−0.840103	−	0.225105i	−0.186987	−	0.982362i	$-0.559872\pi$
$379$	−16.3551	−	4.38232i	−0.840103	−	0.225105i	−0.653116	+	0.757258i	$0.726539\pi$
$380$	3.28892	+	4.81710i	0.168718	+	0.247112i
$381$	−5.24973	−	3.03093i	−0.268952	−	0.155279i
$382$	−18.9999			−0.972119
$383$	−5.71918	−	3.30197i	−0.292236	−	0.168723i	0.346714	−	0.937971i	$-0.387298\pi$
$383$	−5.71918	−	3.30197i	−0.292236	−	0.168723i	−0.638950	+	0.769248i	$0.720631\pi$
$384$	5.91729	−	1.58553i	0.301966	−	0.0809114i
$385$	−0.270181	−	3.57354i	−0.0137697	−	0.182124i
$386$	6.42793	−	11.1335i	0.327173	−	0.566680i
$387$	9.80550	−	36.5946i	0.498441	−	1.86021i
$388$	3.58475	+	6.20897i	0.181988	+	0.315212i
$389$	−33.6949			−1.70840			−0.854199	−	0.519946i	$-0.825952\pi$
$389$	−33.6949			−1.70840			−0.854199	+	0.519946i	$0.825952\pi$
$390$	19.0523	−	12.8430i	0.964750	−	0.650332i
$391$	27.9393			1.41295
$392$	−9.17126	−	15.8851i	−0.463218	−	0.802318i
$393$	0.0449004	−	0.167570i	0.00226492	−	0.00845281i
$394$	7.30464	−	12.6520i	0.368003	−	0.637399i
$395$	19.7986	−	23.0372i	0.996175	−	1.15913i
$396$	−7.30795	+	1.95816i	−0.367238	+	0.0984012i
$397$	5.04104	+	2.91045i	0.253002	+	0.146071i	0.621138	−	0.783701i	$-0.286671\pi$
$397$	5.04104	+	2.91045i	0.253002	+	0.146071i	−0.368136	+	0.929772i	$0.620004\pi$
$398$	−15.0689			−0.755337
$399$	6.35716	+	3.67031i	0.318256	+	0.183745i
$400$	−4.61142	+	3.68750i	−0.230571	+	0.184375i
$401$	0.255004	+	0.0683280i	0.0127343	+	0.00341214i	0.265181	−	0.964199i	$-0.414568\pi$
$401$	0.255004	+	0.0683280i	0.0127343	+	0.00341214i	−0.252446	+	0.967611i	$0.581235\pi$
$402$	14.7075	+	14.7075i	0.733544	+	0.733544i
$403$	−0.619831	+	0.162147i	−0.0308760	+	0.00807713i
$404$		−	9.30738i		−	0.463060i
$405$	−0.239602	+	1.27094i	−0.0119059	+	0.0631533i
$406$	0.143993	+	0.249404i	0.00714627	+	0.0123777i
$407$	6.55691	−	1.75692i	0.325014	−	0.0870872i
$408$		−	61.0446i		−	3.02216i
$409$	9.61872	+	35.8975i	0.475615	+	1.77502i	0.619042	+	0.785358i	$0.287521\pi$
$409$	9.61872	+	35.8975i	0.475615	+	1.77502i	−0.143427	+	0.989661i	$0.545812\pi$
$410$	14.2750	+	6.86281i	0.704990	+	0.338930i
$411$	8.70518	−	8.70518i	0.429395	−	0.429395i
$412$	0.881310	+	3.28909i	0.0434190	+	0.162042i
$413$	4.70151	+	1.25977i	0.231346	+	0.0619890i
$414$	−4.86161	+	18.1438i	−0.238935	+	0.891718i
$415$	−12.4881	+	14.5309i	−0.613016	+	0.713293i
$416$	−8.62585	−	15.1473i	−0.422917	−	0.742657i
$417$	−27.0934	+	27.0934i	−1.32677	+	1.32677i
$418$	4.02660	−	2.32476i	0.196947	−	0.113708i
$419$	−29.3721	+	16.9580i	−1.43492	+	0.828451i	−0.997490	−	0.0708027i	$-0.977444\pi$
$419$	−29.3721	+	16.9580i	−1.43492	+	0.828451i	−0.437428	+	0.899253i	$0.644111\pi$
$420$	2.48272	−	5.16418i	0.121145	−	0.251986i
$421$	−21.5599	−	21.5599i	−1.05076	−	1.05076i	−0.998641	−	0.0521230i	$-0.983401\pi$
$421$	−21.5599	−	21.5599i	−1.05076	−	1.05076i	−0.0521230	−	0.998641i	$-0.516599\pi$
$422$	−4.36253	+	7.55613i	−0.212365	+	0.367826i
$423$	18.6995	−	32.3885i	0.909201	−	1.57478i
$424$	−6.03777	−	6.03777i	−0.293220	−	0.293220i
$425$	−14.5411	−	33.2083i	−0.705345	−	1.61084i
$426$	−32.2162	+	18.6000i	−1.56088	+	0.901175i
$427$	−1.73853	+	1.00374i	−0.0841335	+	0.0485745i
$428$	0.299934	−	0.299934i	0.0144979	−	0.0144979i
$429$	8.27052	+	14.5233i	0.399305	+	0.701192i
$430$	18.1223	−	1.37015i	0.873933	−	0.0660745i
$431$	1.19014	−	4.44167i	0.0573271	−	0.213948i	−0.931320	−	0.364201i	$-0.881342\pi$
$431$	1.19014	−	4.44167i	0.0573271	−	0.213948i	0.988648	+	0.150253i	$0.0480089\pi$
$432$	5.61627	+	1.50488i	0.270213	+	0.0724033i
$433$	−1.03596	−	3.86627i	−0.0497853	−	0.185801i	0.936555	−	0.350520i	$-0.113995\pi$
$433$	−1.03596	−	3.86627i	−0.0497853	−	0.185801i	−0.986341	+	0.164719i	$0.947328\pi$
$434$	0.123811	−	0.123811i	0.00594311	−	0.00594311i
$435$	0.789140	−	1.64145i	0.0378364	−	0.0787013i
$436$	2.24285	+	8.37043i	0.107413	+	0.400871i
$437$			10.5336i			0.503890i
$438$	−8.88461	+	2.38062i	−0.424523	+	0.113751i
$439$	−11.3618	−	19.6793i	−0.542271	−	0.939242i	−0.998773	−	0.0495192i	$-0.984231\pi$
$439$	−11.3618	−	19.6793i	−0.542271	−	0.939242i	0.456502	−	0.889723i	$-0.349102\pi$
$440$	−6.33562	−	9.27944i	−0.302039	−	0.442380i
$441$			28.9414i			1.37816i
$442$	−25.8629	+	6.76571i	−1.23017	+	0.321812i
$443$	1.84874	+	1.84874i	0.0878361	+	0.0878361i	0.749660	−	0.661824i	$-0.230217\pi$
$443$	1.84874	+	1.84874i	0.0878361	+	0.0878361i	−0.661824	+	0.749660i	$0.730217\pi$
$444$	10.4837	+	2.80911i	0.497536	+	0.133314i
$445$	−0.957576	+	0.653794i	−0.0453935	+	0.0309928i
$446$	6.25313	+	3.61025i	0.296094	+	0.170950i
$447$	12.0737			0.571067
$448$	6.09644	+	3.51978i	0.288030	+	0.166294i
$449$	−31.0770	+	8.32705i	−1.46661	+	0.392978i	−0.901769	−	0.432219i	$-0.857731\pi$
$449$	−31.0770	+	8.32705i	−1.46661	+	0.392978i	−0.564845	+	0.825197i	$0.691064\pi$
$450$	24.0957	−	3.66451i	1.13588	−	0.172746i
$451$	−5.76056	+	9.97759i	−0.271254	+	0.469826i
$452$	−0.477798	+	1.78317i	−0.0224737	+	0.0838731i
$453$	9.36029	+	16.2125i	0.439785	+	0.761729i
$454$	17.5640			0.824318
$455$	−7.62543	−	1.48449i	−0.357486	−	0.0695939i
$456$	23.0149			1.07777
$457$	14.1837	+	24.5669i	0.663486	+	1.14919i	0.979693	+	0.200501i	$0.0642571\pi$
$457$	14.1837	+	24.5669i	0.663486	+	1.14919i	−0.316208	+	0.948690i	$0.602410\pi$
$458$	−3.33373	+	12.4416i	−0.155775	+	0.581360i
$459$	−17.8496	+	30.9165i	−0.833149	+	1.44306i
$460$	8.19898	−	0.619891i	0.382279	−	0.0289026i
$461$	−11.1174	+	2.97890i	−0.517790	+	0.138741i	−0.508244	−	0.861213i	$-0.669705\pi$
$461$	−11.1174	+	2.97890i	−0.517790	+	0.138741i	−0.00954570	+	0.999954i	$0.503039\pi$
$462$	−3.95562	−	2.28378i	−0.184032	−	0.106251i
$463$	29.9456			1.39169			0.695845	−	0.718192i	$-0.255030\pi$
$463$	29.9456			1.39169			0.695845	+	0.718192i	$0.255030\pi$
$464$	0.298893	+	0.172566i	0.0138758	+	0.00801118i
$465$	−1.08817	−	0.205146i	−0.0504626	−	0.00951342i
$466$	24.5609	+	6.58109i	1.13776	+	0.304863i
$467$	−16.1332	−	16.1332i	−0.746557	−	0.746557i	0.227274	−	0.973831i	$-0.427019\pi$
$467$	−16.1332	−	16.1332i	−0.746557	−	0.746557i	−0.973831	+	0.227274i	$0.927019\pi$
$468$	−0.0973232	+	16.4002i	−0.00449877	+	0.758100i
$469$		−	7.03244i		−	0.324728i
$470$	17.6300	+	3.32368i	0.813213	+	0.153310i
$471$	28.4732	+	49.3170i	1.31197	+	2.27241i
$472$	14.7405	−	3.94971i	0.678488	−	0.181800i
$473$			13.2196i			0.607837i
$474$	−10.0201	−	37.3957i	−0.460240	−	1.71764i
$475$	12.5201	−	5.48223i	0.574462	−	0.251542i
$476$	−4.71411	+	4.71411i	−0.216071	+	0.216071i
$477$	3.48697	+	13.0136i	0.159657	+	0.595850i
$478$	3.12195	+	0.836524i	0.142795	+	0.0382617i
$479$	10.0493	−	37.5043i	0.459162	−	1.71362i	−0.216393	−	0.976306i	$-0.569429\pi$
$479$	10.0493	−	37.5043i	0.459162	−	1.71362i	0.675555	−	0.737309i	$-0.263904\pi$
$480$	−2.27132	−	30.0415i	−0.103671	−	1.37120i
$481$	0.0873213	−	14.7148i	0.00398151	−	0.670935i
$482$	13.0294	−	13.0294i	0.593473	−	0.593473i
$483$	8.96157	−	5.17396i	0.407765	−	0.235424i
$484$	−6.80421	+	3.92841i	−0.309282	+	0.178564i
$485$	15.8536	−	5.55920i	0.719874	−	0.252430i
$486$	11.8466	+	11.8466i	0.537372	+	0.537372i
$487$	−14.4718	+	25.0660i	−0.655782	+	1.13585i	0.325916	+	0.945399i	$0.394327\pi$
$487$	−14.4718	+	25.0660i	−0.655782	+	1.13585i	−0.981697	+	0.190448i	$0.939006\pi$
$488$	−3.14701	+	5.45078i	−0.142458	+	0.246745i
$489$	−42.1422	−	42.1422i	−1.90574	−	1.90574i
$490$	−13.1013	+	4.59408i	−0.591855	+	0.207539i
$491$	6.30003	−	3.63733i	0.284317	−	0.164150i	−0.351059	−	0.936353i	$-0.614178\pi$
$491$	6.30003	−	3.63733i	0.284317	−	0.164150i	0.635376	+	0.772203i	$0.280845\pi$
$492$	−15.9530	+	9.21046i	−0.719216	+	0.415240i
$493$	−1.49839	+	1.49839i	−0.0674842	+	0.0674842i
$494$	−2.55079	−	9.75077i	−0.114766	−	0.438708i
$495$	1.33657	+	17.6781i	0.0600743	+	0.794571i
$496$	0.0543104	−	0.202689i	0.00243861	−	0.00910102i
$497$	12.1490	+	3.25531i	0.544956	+	0.146021i
$498$	6.32027	+	23.5876i	0.283218	+	1.05698i
$499$	−4.24201	+	4.24201i	−0.189899	+	0.189899i	−0.795652	−	0.605754i	$-0.792872\pi$
$499$	−4.24201	+	4.24201i	−0.189899	+	0.189899i	0.605754	+	0.795652i	$0.292872\pi$
$500$	−5.00397	−	9.42259i	−0.223784	−	0.421391i
$501$	1.23663	+	4.61515i	0.0552483	+	0.206190i
$502$			14.2889i			0.637745i
$503$	−3.50677	+	0.939636i	−0.156359	+	0.0418963i	−0.336149	−	0.941809i	$-0.609125\pi$
$503$	−3.50677	+	0.939636i	−0.156359	+	0.0418963i	0.179790	+	0.983705i	$0.442458\pi$
$504$	−6.93805	−	12.0171i	−0.309046	−	0.535283i
$505$	−21.4321	−	4.04047i	−0.953717	−	0.179799i
$506$		−	6.55433i		−	0.291376i
$507$	35.1039	−	8.96091i	1.55902	−	0.397968i
$508$	1.46769	+	1.46769i	0.0651184	+	0.0651184i
$509$	22.5037	+	6.02986i	0.997460	+	0.267269i	0.720381	−	0.693578i	$-0.243967\pi$
$509$	22.5037	+	6.02986i	0.997460	+	0.267269i	0.277079	+	0.960847i	$0.410634\pi$
$510$	−45.4047	−	8.55987i	−2.01055	−	0.379038i
$511$	2.69325	+	1.55495i	0.119143	+	0.0687870i
$512$	12.8442			0.567640
$513$	−11.6560	−	6.72962i	−0.514627	−	0.297120i
$514$	−22.8945	+	6.13455i	−1.00983	+	0.270584i
$515$	7.95639	−	0.601550i	0.350600	−	0.0265075i
$516$	−10.5683	+	18.3048i	−0.465243	+	0.805824i
$517$	−3.37754	+	12.6052i	−0.148544	+	0.554375i
$518$	2.01075	+	3.48272i	0.0883472	+	0.153022i
$519$	42.2960			1.85659
$520$	−23.0319	+	7.92319i	−1.01002	+	0.347455i
$521$	−13.0530			−0.571862			−0.285931	−	0.958250i	$-0.592303\pi$
$521$	−13.0530			−0.571862			−0.285931	+	0.958250i	$0.592303\pi$
$522$	−0.712327	−	1.23379i	−0.0311777	−	0.0540013i
$523$	4.40520	−	16.4404i	0.192626	−	0.718890i	−0.800243	−	0.599677i	$-0.795296\pi$
$523$	4.40520	−	16.4404i	0.192626	−	0.718890i	0.992869	−	0.119214i	$-0.0380374\pi$
$524$	−0.0297008	+	0.0514432i	−0.00129748	+	0.00224731i
$525$	−10.8138	−	7.95882i	−0.471952	−	0.347351i
$526$	1.28514	−	0.344353i	0.0560349	−	0.0150145i
$527$	1.11577	+	0.644187i	0.0486035	+	0.0280612i
$528$	−5.47391			−0.238221
$529$	−7.05896	−	4.07549i	−0.306911	−	0.177195i
$530$	−5.33750	+	3.64423i	−0.231846	+	0.158295i
$531$	−23.2581	−	6.23198i	−1.00931	−	0.270445i
$532$	−1.77730	−	1.77730i	−0.0770558	−	0.0770558i
$533$	17.5547	+	17.7643i	0.760377	+	0.769456i
$534$			1.47779i			0.0639501i
$535$	−0.560453	−	0.820864i	−0.0242305	−	0.0354891i
$536$	−11.0243	−	19.0947i	−0.476178	−	0.824765i
$537$	−7.42764	+	1.99023i	−0.320526	+	0.0858847i
$538$			8.11728i			0.349961i
$539$	−2.61373	−	9.75457i	−0.112581	−	0.420159i
$540$	−4.55215	+	9.46868i	−0.195893	+	0.407467i
$541$	−10.9728	+	10.9728i	−0.471756	+	0.471756i	−0.902483	−	0.430727i	$-0.858257\pi$
$541$	−10.9728	+	10.9728i	−0.471756	+	0.471756i	0.430727	+	0.902483i	$0.358257\pi$
$542$	−0.237029	−	0.884606i	−0.0101813	−	0.0379971i
$543$	−27.8799	−	7.47039i	−1.19644	−	0.320585i
$544$	−9.07231	+	33.8583i	−0.388972	+	1.45166i
$545$	20.2483	−	1.53089i	0.867340	−	0.0655761i
$546$	−7.04266	+	6.95956i	−0.301398	+	0.297842i
$547$	−20.4450	+	20.4450i	−0.874167	+	0.874167i	−0.992923	−	0.118756i	$-0.962109\pi$
$547$	−20.4450	+	20.4450i	−0.874167	+	0.874167i	0.118756	+	0.992923i	$0.462109\pi$
$548$	−3.65063	+	2.10769i	−0.155947	+	0.0900361i
$549$	8.60042	−	4.96545i	0.367057	−	0.211920i
$550$	−7.79041	+	3.41121i	−0.332184	+	0.145455i
$551$	−0.564920	−	0.564920i	−0.0240664	−	0.0240664i
$552$	16.2218	−	28.0970i	0.690446	−	1.19589i
$553$	−6.54485	+	11.3360i	−0.278315	+	0.482056i
$554$	6.90913	+	6.90913i	0.293541	+	0.293541i
$555$	11.0197	−	22.9214i	0.467759	−	0.972961i
$556$	11.3619	−	6.55982i	0.481854	−	0.278198i
$557$	11.7609	−	6.79015i	0.498324	−	0.287708i	−0.229697	−	0.973262i	$-0.573774\pi$
$557$	11.7609	−	6.79015i	0.498324	−	0.287708i	0.728021	+	0.685555i	$0.240440\pi$
$558$	−0.612485	+	0.612485i	−0.0259286	+	0.0259286i
$559$	27.6356	+	7.58098i	1.16886	+	0.320641i
$560$	1.65839	−	1.92967i	0.0700797	−	0.0815432i
$561$	8.69858	−	32.4636i	0.367254	−	1.37061i
$562$	7.80052	+	2.09014i	0.329045	+	0.0881673i
$563$	1.25538	+	4.68514i	0.0529080	+	0.197455i	0.987321	−	0.158736i	$-0.0507418\pi$
$563$	1.25538	+	4.68514i	0.0529080	+	0.197455i	−0.934413	+	0.356191i	$0.884075\pi$
$564$	−14.7539	+	14.7539i	−0.621251	+	0.621251i
$565$	3.89868	+	1.87433i	0.164019	+	0.0788535i
$566$	−5.58573	−	20.8462i	−0.234786	−	0.876232i
$567$		−	0.557323i		−	0.0234054i
$568$	38.0904	−	10.2063i	1.59824	−	0.428247i
$569$	−0.124396	−	0.215461i	−0.00521497	−	0.00903259i	0.863406	−	0.504509i	$-0.168327\pi$
$569$	−0.124396	−	0.215461i	−0.00521497	−	0.00903259i	−0.868621	+	0.495477i	$0.834993\pi$
$570$	3.22722	−	17.1183i	0.135173	−	0.717009i
$571$		−	7.72842i		−	0.323424i	−0.986838	−	0.161712i	$-0.948298\pi$
$571$		−	7.72842i		−	0.323424i	0.986838	−	0.161712i	$-0.0517016\pi$
$572$	−1.44832	−	5.53640i	−0.0605572	−	0.231489i
$573$	−36.6136	−	36.6136i	−1.52955	−	1.52955i
$574$	−6.59281	−	1.76654i	−0.275179	−	0.0737339i
$575$	2.13187	−	19.1489i	0.0889052	−	0.798565i
$576$	−30.1587	−	17.4121i	−1.25661	−	0.725506i
$577$	−12.1339			−0.505141			−0.252570	−	0.967578i	$-0.581276\pi$
$577$	−12.1339			−0.505141			−0.252570	+	0.967578i	$0.581276\pi$
$578$	31.5007	+	18.1869i	1.31026	+	0.756477i
$579$	33.8416	−	9.06783i	1.40641	−	0.376846i
$580$	−0.406469	+	0.472958i	−0.0168777	+	0.0196385i
$581$	4.12821	−	7.15027i	0.171267	−	0.296643i
$582$	5.54184	−	20.6824i	0.229717	−	0.857315i
$583$	−2.35054	−	4.07125i	−0.0973492	−	0.168614i
$584$	9.75040			0.403475
$585$	37.7225	+	7.34368i	1.55963	+	0.303624i
$586$	−4.11255			−0.169888
$587$	18.2647	+	31.6354i	0.753865	+	1.30573i	0.945937	+	0.324351i	$0.105146\pi$
$587$	18.2647	+	31.6354i	0.753865	+	1.30573i	−0.192072	+	0.981381i	$0.561521\pi$
$588$	4.17904	−	15.5964i	0.172341	−	0.643185i
$589$	−0.242870	+	0.420663i	−0.0100073	+	0.0173331i
$590$	−0.870813	−	11.5178i	−0.0358508	−	0.474180i
$591$	38.4573	−	10.3046i	1.58192	−	0.423875i
$592$	4.17380	+	2.40974i	0.171542	+	0.0990398i
$593$	−16.6936			−0.685525			−0.342762	−	0.939422i	$-0.611363\pi$
$593$	−16.6936			−0.685525			−0.342762	+	0.939422i	$0.611363\pi$
$594$	7.25276	+	4.18738i	0.297584	+	0.171810i
$595$	8.80873	+	12.9017i	0.361123	+	0.528917i
$596$	−3.99327	−	1.06999i	−0.163571	−	0.0438287i
$597$	−29.0384	−	29.0384i	−1.18846	−	1.18846i
$598$	−13.7018	−	3.75868i	−0.560310	−	0.153704i
$599$			13.2549i			0.541579i	0.962639	+	0.270789i	$0.0872847\pi$
$599$			13.2549i			0.541579i	−0.962639	+	0.270789i	$0.912715\pi$
$600$	−41.8384	−	4.65793i	−1.70805	−	0.190159i
$601$	−0.546605	−	0.946748i	−0.0222965	−	0.0386187i	0.854662	−	0.519185i	$-0.173764\pi$
$601$	−0.546605	−	0.946748i	−0.0222965	−	0.0386187i	−0.876958	+	0.480566i	$0.840431\pi$
$602$	−7.56474	+	2.02696i	−0.308316	+	0.0826129i
$603$			34.7891i			1.41672i
$604$	−1.65905	−	6.19166i	−0.0675058	−	0.251935i
$605$	6.09216	+	17.3735i	0.247682	+	0.706332i
$606$	−19.6554	+	19.6554i	−0.798446	+	0.798446i
$607$	−10.8348	−	40.4361i	−0.439771	−	1.64125i	−0.729384	−	0.684105i	$-0.760193\pi$
$607$	−10.8348	−	40.4361i	−0.439771	−	1.64125i	0.289612	−	0.957144i	$-0.406474\pi$
$608$	−12.7652	−	3.42042i	−0.517696	−	0.138716i
$609$	−0.203130	+	0.758093i	−0.00823126	+	0.0307195i
$610$	3.61298	+	3.10506i	0.146285	+	0.125720i
$611$	24.4142	+	14.2894i	0.987693	+	0.578087i
$612$	23.3204	−	23.3204i	0.942673	−	0.942673i
$613$	24.1705	−	13.9548i	0.976235	−	0.563630i	0.0751039	−	0.997176i	$-0.476071\pi$
$613$	24.1705	−	13.9548i	0.976235	−	0.563630i	0.901131	+	0.433546i	$0.142738\pi$
$614$	21.4487	−	12.3834i	0.865601	−	0.499755i
$615$	14.2835	+	40.7334i	0.575967	+	1.64253i
$616$	3.42371	+	3.42371i	0.137945	+	0.137945i
$617$	−2.19132	+	3.79548i	−0.0882193	+	0.152800i	−0.906758	−	0.421650i	$-0.861451\pi$
$617$	−2.19132	+	3.79548i	−0.0882193	+	0.152800i	0.818539	+	0.574451i	$0.194784\pi$
$618$	5.08477	−	8.80708i	0.204540	−	0.354273i
$619$	−8.67268	−	8.67268i	−0.348584	−	0.348584i	0.510998	−	0.859582i	$-0.329276\pi$
$619$	−8.67268	−	8.67268i	−0.348584	−	0.348584i	−0.859582	+	0.510998i	$0.829276\pi$
$620$	0.341722	+	0.164286i	0.0137239	+	0.00659787i
$621$	−16.4313	+	9.48662i	−0.659366	+	0.380685i
$622$	6.97193	−	4.02525i	0.279549	−	0.161398i
$623$	0.353304	−	0.353304i	0.0141548	−	0.0141548i
$624$	−3.13910	+	11.4432i	−0.125664	+	0.458095i
$625$	−23.8697	+	7.43216i	−0.954788	+	0.297287i
$626$	−1.26934	+	4.73726i	−0.0507332	+	0.189339i
$627$	12.2393	+	3.27952i	0.488791	+	0.130971i
$628$	−5.04668	−	18.8345i	−0.201385	−	0.751577i
$629$	−20.9238	+	20.9238i	−0.834287	+	0.834287i
$630$	−9.91112	+	3.47542i	−0.394868	+	0.138464i
$631$	−6.55800	−	24.4748i	−0.261070	−	0.974326i	−0.964612	−	0.263673i	$-0.915066\pi$
$631$	−6.55800	−	24.4748i	−0.261070	−	0.974326i	0.703542	−	0.710653i	$-0.251601\pi$
$632$			41.0398i			1.63248i
$633$	−22.9677	+	6.15419i	−0.912886	+	0.244607i
$634$	11.7220	+	20.3031i	0.465540	+	0.806340i
$635$	4.01681	−	2.74251i	0.159402	−	0.108833i
$636$		−	7.51646i		−	0.298047i
$637$	−21.8908	−	0.129906i	−0.867345	−	0.00514706i
$638$	0.351511	+	0.351511i	0.0139164	+	0.0139164i
$639$	−60.1003	−	16.1038i	−2.37753	−	0.637057i
$640$	−0.910600	+	4.83016i	−0.0359946	+	0.190929i
$641$	−1.41675	−	0.817961i	−0.0559582	−	0.0323075i	0.471760	−	0.881727i	$-0.343619\pi$
$641$	−1.41675	−	0.817961i	−0.0559582	−	0.0323075i	−0.527718	+	0.849420i	$0.676952\pi$
$642$	−1.26681			−0.0499968
$643$	34.3541	+	19.8344i	1.35479	+	0.782191i	0.988917	−	0.148472i	$-0.0474354\pi$
$643$	34.3541	+	19.8344i	1.35479	+	0.782191i	0.365878	+	0.930663i	$0.380769\pi$
$644$	−3.42248	+	0.917051i	−0.134865	+	0.0361369i
$645$	37.5627	+	32.2820i	1.47903	+	1.27110i
$646$	−10.1339	+	17.5525i	−0.398714	+	0.690593i
$647$	−3.84742	+	14.3588i	−0.151258	+	0.564501i	0.848139	+	0.529773i	$0.177723\pi$
$647$	−3.84742	+	14.3588i	−0.151258	+	0.564501i	−0.999397	+	0.0347277i	$0.988944\pi$
$648$	−0.873682	−	1.51326i	−0.0343215	−	0.0594465i
$649$	8.40185			0.329801
$650$	2.66362	+	18.2421i	0.104476	+	0.715513i
$651$	0.477178			0.0187021
$652$	10.2034	+	17.6729i	0.399597	+	0.692123i
$653$	3.32718	−	12.4172i	0.130203	−	0.485922i	−0.869769	−	0.493459i	$-0.835732\pi$
$653$	3.32718	−	12.4172i	0.130203	−	0.485922i	0.999972	+	0.00753655i	$0.00239898\pi$
$654$	12.9403	−	22.4132i	0.506005	−	0.876426i
$655$	0.105565	+	0.0907243i	0.00412476	+	0.00354489i
$656$	−7.90103	+	2.11708i	−0.308483	+	0.0826579i
$657$	−13.3234	−	7.69225i	−0.519794	−	0.300103i
$658$	−7.73102			−0.301387
$659$	−20.8742	−	12.0517i	−0.813144	−	0.469469i	0.0349025	−	0.999391i	$-0.488888\pi$
$659$	−20.8742	−	12.0517i	−0.813144	−	0.469469i	−0.848047	+	0.529922i	$0.822221\pi$
$660$	1.83239	−	9.71965i	0.0713256	−	0.378337i
$661$	37.8150	+	10.1325i	1.47083	+	0.394108i	0.903217	−	0.429185i	$-0.141199\pi$
$661$	37.8150	+	10.1325i	1.47083	+	0.394108i	0.567616	+	0.823293i	$0.307866\pi$
$662$	−24.2637	−	24.2637i	−0.943036	−	0.943036i
$663$	−62.8768	−	36.8011i	−2.44193	−	1.42924i
$664$		−	25.8862i		−	1.00458i
$665$	−4.86415	+	3.32104i	−0.188624	+	0.128785i
$666$	−9.94705	−	17.2288i	−0.385440	−	0.667602i
$667$	−1.08784	+	0.291487i	−0.0421215	+	0.0112864i
$668$		−	1.63601i		−	0.0632991i
$669$	5.09295	+	19.0071i	0.196905	+	0.734858i
$670$	−15.7484	+	5.52232i	−0.608415	+	0.213346i
$671$	−2.45030	+	2.45030i	−0.0945926	+	0.0945926i
$672$	3.36013	+	12.5402i	0.129620	+	0.483747i
$673$	−9.87723	−	2.64660i	−0.380739	−	0.102019i	0.0633730	−	0.997990i	$-0.479814\pi$
$673$	−9.87723	−	2.64660i	−0.380739	−	0.102019i	−0.444112	+	0.895971i	$0.646481\pi$
$674$	−5.44776	+	20.3313i	−0.209840	+	0.783132i
$675$	19.8274	+	14.5927i	0.763157	+	0.561675i
$676$	−12.4044	−	0.147227i	−0.477093	−	0.00566259i
$677$	29.8933	−	29.8933i	1.14889	−	1.14889i	0.162121	−	0.986771i	$-0.448167\pi$
$677$	29.8933	−	29.8933i	1.14889	−	1.14889i	0.986771	−	0.162121i	$-0.0518333\pi$
$678$	4.77472	−	2.75669i	0.183372	−	0.105870i
$679$	−6.26961	+	3.61976i	−0.240606	+	0.138914i
$680$	44.1429	+	21.2221i	1.69280	+	0.813829i
$681$	33.8465	+	33.8465i	1.29700	+	1.29700i
$682$	0.151121	−	0.261750i	0.00578673	−	0.0100229i
$683$	−10.0103	+	17.3384i	−0.383035	+	0.663436i	−0.991494	−	0.130149i	$-0.958455\pi$
$683$	−10.0103	+	17.3384i	−0.383035	+	0.663436i	0.608459	+	0.793585i	$0.291788\pi$
$684$	8.79221	+	8.79221i	0.336178	+	0.336178i
$685$	3.26859	+	9.32129i	0.124886	+	0.356148i
$686$	11.1546	−	6.44013i	0.425886	−	0.245885i
$687$	−30.3998	+	17.5513i	−1.15983	+	0.669625i
$688$	−6.63664	+	6.63664i	−0.253019	+	0.253019i
$689$	−9.85890	+	2.57908i	−0.375594	+	0.0982550i
$690$	−18.6238	−	16.0056i	−0.708994	−	0.609322i
$691$	−9.15886	+	34.1813i	−0.348420	+	1.30032i	0.540147	+	0.841571i	$0.318369\pi$
$691$	−9.15886	+	34.1813i	−0.348420	+	1.30032i	−0.888566	+	0.458749i	$0.848298\pi$
$692$	−13.9890	−	3.74834i	−0.531782	−	0.142491i
$693$	−1.97729	−	7.37933i	−0.0751109	−	0.280318i
$694$	−16.4960	+	16.4960i	−0.626181	+	0.626181i
$695$	−10.1729	−	29.0109i	−0.385881	−	1.10045i
$696$	0.636870	+	2.37683i	0.0241405	+	0.0900935i
$697$		−	50.2221i		−	1.90230i
$698$	10.2586	−	2.74877i	0.388292	−	0.104043i
$699$	34.6479	+	60.0120i	1.31051	+	2.26986i
$700$	2.87123	+	3.59064i	0.108522	+	0.135714i
$701$			37.1781i			1.40420i	0.712080	+	0.702098i	$0.247753\pi$
$701$			37.1781i			1.40420i	−0.712080	+	0.702098i	$0.752247\pi$
$702$	12.9129	−	12.7606i	0.487367	−	0.481617i
$703$	−7.88864	−	7.88864i	−0.297526	−	0.297526i
$704$	11.7374	+	3.14502i	0.442368	+	0.118532i
$705$	27.5689	+	40.3787i	1.03831	+	1.52075i
$706$	3.80843	+	2.19880i	0.143332	+	0.0827529i
$707$	9.39830			0.353459
$708$	11.6338	+	6.71678i	0.437225	+	0.252432i
$709$	46.5506	−	12.4732i	1.74824	−	0.468440i	0.763994	−	0.645224i	$-0.223236\pi$
$709$	46.5506	−	12.4732i	1.74824	−	0.468440i	0.984250	+	0.176783i	$0.0565692\pi$
$710$	−2.25023	−	29.7626i	−0.0844497	−	1.11697i
$711$	32.3770	−	56.0786i	1.21423	−	2.10311i
$712$	0.405449	−	1.51316i	0.0151948	−	0.0567079i
$713$	0.342369	+	0.593001i	0.0128218	+	0.0222080i
$714$	19.9106			0.745135
$715$	−13.3774	+	0.931609i	−0.500287	+	0.0348402i
$716$	2.63300			0.0983998
$717$	4.40411	+	7.62814i	0.164474	+	0.284878i
$718$	−3.90299	+	14.5662i	−0.145658	+	0.543604i
$719$	16.6992	−	28.9239i	0.622777	−	1.07868i	−0.366190	−	0.930540i	$-0.619338\pi$
$719$	16.6992	−	28.9239i	0.622777	−	1.07868i	0.988966	−	0.148141i	$-0.0473288\pi$
$720$	−8.20394	+	9.54594i	−0.305743	+	0.355756i
$721$	−3.32122	+	0.889918i	−0.123689	+	0.0331423i
$722$	10.2091	+	5.89421i	0.379942	+	0.219360i
$723$	50.2164			1.86757
$724$	8.55897	+	4.94153i	0.318092	+	0.183650i
$725$	0.912629	+	1.14129i	0.0338942	+	0.0423866i
$726$	22.6652	+	6.07313i	0.841186	+	0.225395i
$727$	−23.6487	−	23.6487i	−0.877083	−	0.877083i	0.116149	−	0.993232i	$-0.462945\pi$
$727$	−23.6487	−	23.6487i	−0.877083	−	0.877083i	−0.993232	+	0.116149i	$0.962945\pi$
$728$	9.12066	−	5.19389i	0.338034	−	0.192499i
$729$			43.9226i			1.62676i
$730$	1.36723	−	7.25231i	0.0506036	−	0.268420i
$731$	−28.8130	−	49.9055i	−1.06569	−	1.84582i
$732$	−5.35173	+	1.43399i	−0.197806	+	0.0530018i
$733$		−	14.7049i		−	0.543138i	−0.962419	−	0.271569i	$-0.912458\pi$
$733$		−	14.7049i		−	0.543138i	0.962419	−	0.271569i	$-0.0875424\pi$
$734$	−3.02344	−	11.2836i	−0.111597	−	0.416486i
$735$	−34.0997	−	16.3937i	−1.25779	−	0.604692i
$736$	−13.1731	+	13.1731i	−0.485568	+	0.485568i
$737$	−3.14184	−	11.7255i	−0.115731	−	0.431914i
$738$	32.6142	+	8.73896i	1.20055	+	0.321686i
$739$	5.32432	−	19.8706i	0.195858	−	0.730953i	−0.796185	−	0.605054i	$-0.793152\pi$
$739$	5.32432	−	19.8706i	0.195858	−	0.730953i	0.992043	−	0.125900i	$-0.0401817\pi$
$740$	−5.67600	+	6.60447i	−0.208654	+	0.242785i
$741$	13.8747	−	23.7056i	0.509698	−	0.870848i
$742$	1.96931	−	1.96931i	0.0722956	−	0.0722956i
$743$	−38.6601	+	22.3204i	−1.41830	+	0.818856i	−0.996150	−	0.0876692i	$-0.972058\pi$
$743$	−38.6601	+	22.3204i	−1.41830	+	0.818856i	−0.422151	+	0.906526i	$0.638725\pi$
$744$	1.29565	−	0.748042i	0.0475007	−	0.0274246i
$745$	−4.19742	+	8.73082i	−0.153781	+	0.319872i
$746$	−20.3603	−	20.3603i	−0.745443	−	0.745443i
$747$	−20.4220	+	35.3720i	−0.747202	+	1.29419i
$748$	−5.75395	+	9.96614i	−0.210385	+	0.364398i
$749$	0.302864	+	0.302864i	0.0110664	+	0.0110664i
$750$	−9.33127	+	30.4661i	−0.340730	+	1.11246i
$751$	15.2247	−	8.78996i	0.555555	−	0.320750i	−0.195804	−	0.980643i	$-0.562732\pi$
$751$	15.2247	−	8.78996i	0.555555	−	0.320750i	0.751360	+	0.659893i	$0.229398\pi$
$752$	−8.02381	+	4.63255i	−0.292598	+	0.168932i
$753$	−27.5353	+	27.5353i	−1.00344	+	1.00344i
$754$	0.936413	−	0.533254i	0.0341022	−	0.0194200i
$755$	−14.9778	+	1.13241i	−0.545097	+	0.0412125i
$756$	1.17176	−	4.37306i	0.0426164	−	0.159047i
$757$	33.9933	+	9.10848i	1.23551	+	0.331053i	0.816722	−	0.577032i	$-0.195789\pi$
$757$	33.9933	+	9.10848i	1.23551	+	0.331053i	0.418786	+	0.908085i	$0.362456\pi$
$758$	−4.48144	−	16.7250i	−0.162773	−	0.607478i
$759$	12.6305	−	12.6305i	0.458457	−	0.458457i
$760$	−8.00109	+	16.6426i	−0.290230	+	0.603692i
$761$	−3.03122	−	11.3127i	−0.109882	−	0.410084i	0.888972	−	0.457962i	$-0.151421\pi$
$761$	−3.03122	−	11.3127i	−0.109882	−	0.410084i	−0.998853	+	0.0478787i	$0.984754\pi$
$762$		−	6.19897i		−	0.224565i
$763$	−8.45219	+	2.26476i	−0.305990	+	0.0819897i
$764$	8.86485	+	15.3544i	0.320719	+	0.555502i
$765$	−43.5763	−	63.8238i	−1.57550	−	2.30755i
$766$		−	6.75331i		−	0.244007i
$767$	4.81817	−	17.5641i	0.173974	−	0.634202i
$768$	33.2233	+	33.2233i	1.19884	+	1.19884i
$769$	−18.3227	−	4.90954i	−0.660732	−	0.177043i	−0.0871555	−	0.996195i	$-0.527778\pi$
$769$	−18.3227	−	4.90954i	−0.660732	−	0.177043i	−0.573576	+	0.819152i	$0.694444\pi$
$770$	3.02663	−	2.06646i	0.109072	−	0.0744700i
$771$	−55.9401	−	32.2971i	−2.01463	−	1.16315i
$772$	−11.9964			−0.431760
$773$	−14.2114	−	8.20497i	−0.511149	−	0.295112i	0.222157	−	0.975011i	$-0.428690\pi$
$773$	−14.2114	−	8.20497i	−0.511149	−	0.295112i	−0.733306	+	0.679899i	$0.762024\pi$
$774$	37.4223	−	10.0273i	1.34512	−	0.360423i
$775$	0.526647	−	0.715564i	0.0189177	−	0.0257038i
$776$	−11.3490	+	19.6570i	−0.407404	+	0.705644i
$777$	−2.83655	+	10.5861i	−0.101761	+	0.379775i
$778$	−17.2285	−	29.8406i	−0.617671	−	1.06984i
$779$	18.9346			0.678403
$780$	−19.2681	−	9.40449i	−0.689909	−	0.336735i
$781$	21.7109			0.776876
$782$	14.2856	+	24.7434i	0.510852	+	0.884822i
$783$	0.372446	−	1.38999i	0.0133101	−	0.0496741i
$784$	3.58492	−	6.20926i	0.128033	−	0.221759i
$785$	−45.5610	+	3.44468i	−1.62614	+	0.122946i
$786$	0.171361	−	0.0459159i	0.00611223	−	0.00163777i
$787$	−11.7781	−	6.80008i	−0.419844	−	0.242397i	0.275167	−	0.961396i	$-0.411267\pi$
$787$	−11.7781	−	6.80008i	−0.419844	−	0.242397i	−0.695010	+	0.719000i	$0.744600\pi$
$788$	−13.6326			−0.485642
$789$	3.14011	+	1.81294i	0.111791	+	0.0645424i
$790$	30.5253	+	5.75474i	1.08604	+	0.204745i
$791$	−1.80058	−	0.482465i	−0.0640214	−	0.0171545i
$792$	−16.9369	−	16.9369i	−0.601827	−	0.601827i
$793$	3.71719	+	6.52751i	0.132001	+	0.231799i
$794$			5.95255i			0.211248i
$795$	−17.3082	−	3.26301i	−0.613858	−	0.115727i
$796$	7.03076	+	12.1776i	0.249199	+	0.431625i
$797$	−28.9148	+	7.74769i	−1.02421	+	0.274437i	−0.731557	−	0.681780i	$-0.761206\pi$
$797$	−28.9148	+	7.74769i	−1.02421	+	0.274437i	−0.292657	+	0.956218i	$0.594539\pi$
$798$			7.50664i			0.265732i
$799$	−14.7232	−	54.9476i	−0.520868	−	1.94391i
$800$	22.5134	+	8.80145i	0.795969	+	0.311178i
$801$	−1.74778	+	1.74778i	−0.0617546	+	0.0617546i
$802$	0.0698734	+	0.260771i	0.00246732	+	0.00920815i
$803$	5.18527	+	1.38939i	0.182984	+	0.0490305i
$804$	5.02343	−	18.7477i	0.177163	−	0.661180i
$805$	0.625946	+	8.27906i	0.0220617	+	0.291799i
$806$	−0.460525	−	0.466023i	−0.0162213	−	0.0164150i
$807$	−15.6423	+	15.6423i	−0.550636	+	0.550636i
$808$	25.5185	−	14.7331i	0.897739	−	0.518310i
$809$	2.54661	−	1.47029i	0.0895342	−	0.0516926i	−0.454564	−	0.890714i	$-0.650205\pi$
$809$	2.54661	−	1.47029i	0.0895342	−	0.0516926i	0.544099	+	0.839021i	$0.316872\pi$
$810$	−1.24807	+	0.437646i	−0.0438526	+	0.0153773i
$811$	16.3366	+	16.3366i	0.573657	+	0.573657i	0.933148	−	0.359492i	$-0.117050\pi$
$811$	16.3366	+	16.3366i	0.573657	+	0.573657i	−0.359492	+	0.933148i	$0.617050\pi$
$812$	0.134367	−	0.232730i	0.00471536	−	0.00816724i
$813$	1.24791	−	2.16144i	0.0437660	−	0.0758050i
$814$	4.90856	+	4.90856i	0.172045	+	0.172045i
$815$	45.1248	−	15.8234i	1.58065	−	0.554270i
$816$	20.6647	−	11.9307i	0.723408	−	0.417660i
$817$	18.8153	−	10.8630i	0.658262	−	0.380048i
$818$	−26.8732	+	26.8732i	−0.939599	+	0.939599i
$819$	−16.5604	−	0.0982738i	−0.578667	−	0.00343397i
$820$	−1.11428	−	14.7380i	−0.0389124	−	0.514674i
$821$	11.8735	−	44.3125i	0.414388	−	1.54652i	−0.371672	−	0.928364i	$-0.621215\pi$
$821$	11.8735	−	44.3125i	0.414388	−	1.54652i	0.786059	−	0.618151i	$-0.212118\pi$
$822$	12.1605	+	3.25838i	0.424145	+	0.113649i
$823$	−4.58752	−	17.1209i	−0.159911	−	0.596796i	−0.998635	−	0.0522385i	$-0.983364\pi$
$823$	−4.58752	−	17.1209i	−0.159911	−	0.596796i	0.838724	−	0.544557i	$-0.183302\pi$
$824$	−7.62280	+	7.62280i	−0.265553	+	0.265553i
$825$	−21.5860	−	8.43889i	−0.751528	−	0.293804i
$826$	1.28826	+	4.80785i	0.0448242	+	0.167286i
$827$		−	5.79276i		−	0.201434i	−0.994915	−	0.100717i	$-0.967886\pi$
$827$		−	5.79276i		−	0.201434i	0.994915	−	0.100717i	$-0.0321137\pi$
$828$	16.9308	−	4.53660i	0.588387	−	0.157658i
$829$	−16.8799	−	29.2368i	−0.586262	−	1.01544i	−0.994717	−	0.102657i	$-0.967265\pi$
$829$	−16.8799	−	29.2368i	−0.586262	−	1.01544i	0.408454	−	0.912779i	$-0.366068\pi$
$830$	−19.2540	−	3.62985i	−0.668317	−	0.125994i
$831$			26.6284i			0.923727i
$832$	13.3056	−	22.7334i	0.461290	−	0.788139i
$833$	31.1279	+	31.1279i	1.07852	+	1.07852i
$834$	−37.8473	−	10.1412i	−1.31055	−	0.351160i
$835$	−3.76724	−	0.710216i	−0.130371	−	0.0245780i
$836$	−3.75741	−	2.16934i	−0.129953	−	0.0750282i
$837$	−0.874920			−0.0302417
$838$	−30.0364	−	17.3415i	−1.03759	−	0.599053i
$839$	−37.8626	+	10.1452i	−1.30716	+	0.350253i	−0.844154	−	0.536101i	$-0.819897\pi$
$839$	−37.8626	+	10.1452i	−1.30716	+	0.350253i	−0.463008	+	0.886354i	$0.653230\pi$
$840$	18.0889	−	1.36763i	0.624127	−	0.0471877i
$841$	−14.4573	+	25.0408i	−0.498527	+	0.863475i
$842$	8.06995	−	30.1175i	0.278109	−	1.03792i
$843$	11.0041	+	19.0597i	0.379002	+	0.656451i
$844$	8.14177			0.280251
$845$	−5.72396	+	28.4998i	−0.196910	+	0.980422i
$846$	38.2449			1.31489
$847$	−3.96679	−	6.87068i	−0.136300	−	0.236079i
$848$	0.863850	−	3.22393i	0.0296647	−	0.110710i
$849$	29.4076	−	50.9354i	1.00927	−	1.74810i
$850$	21.9748	−	29.8575i	0.753728	−	1.02410i
$851$	−15.1908	+	4.07037i	−0.520735	+	0.139531i
$852$	30.0625	+	17.3566i	1.02992	+	0.594626i
$853$	40.6417			1.39154			0.695772	−	0.718262i	$-0.255062\pi$
$853$	40.6417			1.39154			0.695772	+	0.718262i	$0.255062\pi$
$854$	−1.77785	−	1.02644i	−0.0608369	−	0.0351242i
$855$	24.0627	−	16.4290i	0.822926	−	0.561860i
$856$	1.29713	+	0.347564i	0.0443348	+	0.0118795i
$857$	27.2327	+	27.2327i	0.930252	+	0.930252i	0.997721	−	0.0674695i	$-0.0214925\pi$
$857$	27.2327	+	27.2327i	0.930252	+	0.930252i	−0.0674695	+	0.997721i	$0.521493\pi$
$858$	−8.63325	+	14.7504i	−0.294734	+	0.503570i
$859$			44.5502i			1.52003i	0.649904	+	0.760016i	$0.274809\pi$
$859$			44.5502i			1.52003i	−0.649904	+	0.760016i	$0.725191\pi$
$860$	−9.56262	−	14.0058i	−0.326083	−	0.477595i
$861$	−9.30043	−	16.1088i	−0.316958	−	0.548987i
$862$	4.54213	−	1.21706i	0.154706	−	0.0414532i
$863$			55.4497i			1.88753i	0.330615	+	0.943766i	$0.392744\pi$
$863$			55.4497i			1.88753i	−0.330615	+	0.943766i	$0.607256\pi$
$864$	−6.16090	−	22.9928i	−0.209598	−	0.782230i
$865$	−14.7041	+	30.5853i	−0.499956	+	1.03993i
$866$	2.89432	−	2.89432i	0.0983531	−	0.0983531i
$867$	25.6562	+	95.7502i	0.871330	+	3.25185i
$868$	−0.157822	−	0.0422883i	−0.00535683	−	0.00143536i
$869$	−5.84800	+	21.8250i	−0.198380	+	0.740363i
$870$	1.85718	−	0.140414i	0.0629643	−	0.00476048i
$871$	−26.3139	−	0.156154i	−0.891612	−	0.00529107i
$872$	−19.3993	+	19.3993i	−0.656944	+	0.656944i
$873$	31.0154	−	17.9068i	1.04971	−	0.606052i
$874$	−9.32869	+	5.38592i	−0.315548	+	0.182181i
$875$	9.51462	−	5.05285i	0.321653	−	0.170817i
$876$	6.06917	+	6.06917i	0.205058	+	0.205058i
$877$	−2.68849	+	4.65661i	−0.0907839	+	0.157242i	−0.907841	−	0.419314i	$-0.862271\pi$
$877$	−2.68849	+	4.65661i	−0.0907839	+	0.157242i	0.817057	+	0.576557i	$0.195604\pi$
$878$	11.6188	−	20.1244i	0.392116	−	0.679166i
$879$	−7.92505	−	7.92505i	−0.267305	−	0.267305i
$880$	1.90300	−	3.95832i	0.0641500	−	0.133435i
$881$	−37.0890	+	21.4133i	−1.24956	+	0.721434i	−0.971022	−	0.238992i	$-0.923183\pi$
$881$	−37.0890	+	21.4133i	−1.24956	+	0.721434i	−0.278538	+	0.960425i	$0.589850\pi$
$882$	−25.6309	+	14.7980i	−0.863037	+	0.498274i
$883$	−32.9568	+	32.9568i	−1.10908	+	1.10908i	−0.115813	+	0.993271i	$0.536947\pi$
$883$	−32.9568	+	32.9568i	−1.10908	+	1.10908i	−0.993271	+	0.115813i	$0.963053\pi$
$884$	17.5345	+	17.7439i	0.589750	+	0.596791i
$885$	20.5172	−	23.8733i	0.689677	−	0.802494i
$886$	−0.691990	+	2.58254i	−0.0232478	+	0.0867622i
$887$	20.4194	+	5.47136i	0.685616	+	0.183710i	0.584779	−	0.811193i	$-0.301181\pi$
$887$	20.4194	+	5.47136i	0.685616	+	0.183710i	0.100837	+	0.994903i	$0.467848\pi$
$888$	8.89336	+	33.1905i	0.298442	+	1.11380i
$889$	−1.48203	+	1.48203i	−0.0497057	+	0.0497057i
$890$	−1.06863	−	0.513751i	−0.0358204	−	0.0172210i
$891$	−0.248992	−	0.929249i	−0.00834153	−	0.0311310i
$892$		−	6.73778i		−	0.225598i
$893$	20.7162	−	5.55089i	0.693241	−	0.185753i
$894$	6.17340	+	10.6926i	0.206469	+	0.357616i
$895$	1.14302	−	6.06302i	0.0382071	−	0.202664i
$896$		−	2.11809i		−	0.0707605i
$897$	−19.1609	−	33.6472i	−0.639763	−	1.12345i
$898$	−23.2645	−	23.2645i	−0.776346	−	0.776346i
$899$	−0.0501642	−	0.0134414i	−0.00167307	−	0.000448297i
$900$	−14.2038	−	17.7627i	−0.473461	−	0.592090i
$901$	17.7471	+	10.2463i	0.591242	+	0.341354i
$902$	−11.7817			−0.392288
$903$	−18.4836	−	10.6715i	−0.615096	−	0.355126i
$904$	−5.64533	+	1.51266i	−0.187761	+	0.0503104i
$905$	15.0944	−	17.5636i	0.501756	−	0.583833i
$906$	−9.57200	+	16.5792i	−0.318008	+	0.550807i
$907$	2.86355	−	10.6869i	0.0950825	−	0.354853i	−0.901949	−	0.431842i	$-0.857864\pi$
$907$	2.86355	−	10.6869i	0.0950825	−	0.354853i	0.997032	+	0.0769889i	$0.0245306\pi$
$908$	−8.19488	−	14.1940i	−0.271957	−	0.471043i
$909$	−46.4928			−1.54207
$910$	−2.58427	−	7.51221i	−0.0856676	−	0.249027i
$911$	−15.0479			−0.498560			−0.249280	−	0.968431i	$-0.580194\pi$
$911$	−15.0479			−0.498560			−0.249280	+	0.968431i	$0.580194\pi$
$912$	4.49810	+	7.79093i	0.148947	+	0.257983i
$913$	3.68867	−	13.7663i	0.122077	−	0.455598i
$914$	−14.5045	+	25.1226i	−0.479767	+	0.830980i
$915$	0.978791	+	12.9459i	0.0323578	+	0.427980i
$916$	11.6099	−	3.11086i	0.383602	−	0.102786i
$917$	−0.0519457	−	0.0299909i	−0.00171540	−	0.000990386i
$918$	−36.5067			−1.20490
$919$	10.8342	+	6.25513i	0.357388	+	0.206338i	0.667934	−	0.744220i	$-0.267179\pi$
$919$	10.8342	+	6.25513i	0.357388	+	0.206338i	−0.310547	+	0.950558i	$0.600512\pi$
$920$	14.6782	+	21.4983i	0.483925	+	0.708778i
$921$	65.1960	+	17.4692i	2.14828	+	0.575630i
$922$	−8.32259	−	8.32259i	−0.274090	−	0.274090i
$923$	12.4504	−	45.3866i	0.409811	−	1.49392i
$924$			4.26220i			0.140216i
$925$	12.7441	+	15.9372i	0.419023	+	0.524013i
$926$	15.3114	+	26.5202i	0.503165	+	0.871508i
$927$	16.4299	−	4.40237i	0.539628	−	0.144593i
$928$		−	1.41296i		−	0.0463826i
$929$	12.6170	+	47.0874i	0.413952	+	1.54489i	0.786926	+	0.617047i	$0.211671\pi$
$929$	12.6170	+	47.0874i	0.413952	+	1.54489i	−0.372975	+	0.927841i	$0.621662\pi$
$930$	−0.374711	−	1.06859i	−0.0122872	−	0.0350404i
$931$	−11.7357	+	11.7357i	−0.384623	+	0.384623i
$932$	−6.14112	−	22.9190i	−0.201159	−	0.750736i
$933$	21.1920	+	5.67838i	0.693795	+	0.185902i
$934$	6.03874	−	22.5369i	0.197594	−	0.737429i
$935$	20.4512	+	17.5761i	0.668825	+	0.574800i
$936$	−45.1193	+	25.6939i	−1.47477	+	0.839831i
$937$	7.38027	−	7.38027i	0.241103	−	0.241103i	−0.576203	−	0.817306i	$-0.695466\pi$
$937$	7.38027	−	7.38027i	0.241103	−	0.241103i	0.817306	+	0.576203i	$0.195466\pi$
$938$	6.22802	−	3.59575i	0.203352	−	0.117405i
$939$	−11.5750	+	6.68281i	−0.377735	+	0.218085i
$940$	−5.53974	−	15.7981i	−0.180686	−	0.515277i
$941$	−1.54410	−	1.54410i	−0.0503363	−	0.0503363i	0.681491	−	0.731827i	$-0.261332\pi$
$941$	−1.54410	−	1.54410i	−0.0503363	−	0.0503363i	−0.731827	+	0.681491i	$0.761332\pi$
$942$	−29.1172	+	50.4324i	−0.948688	+	1.64318i
$943$	13.3459	−	23.1158i	0.434602	−	0.752753i
$944$	4.21798	+	4.21798i	0.137284	+	0.137284i
$945$	−9.56117	−	4.59662i	−0.311025	−	0.149528i
$946$	−11.7074	+	6.75929i	−0.380642	+	0.219764i
$947$	5.81670	−	3.35827i	0.189017	−	0.109129i	−0.402505	−	0.915418i	$-0.631860\pi$
$947$	5.81670	−	3.35827i	0.189017	−	0.109129i	0.591522	+	0.806289i	$0.298527\pi$
$948$	−25.5454	+	25.5454i	−0.829676	+	0.829676i
$949$	5.87810	−	10.0431i	0.190811	−	0.326011i
$950$	11.2568	+	8.28486i	0.365218	+	0.268796i
$951$	−16.5361	+	61.7137i	−0.536221	+	2.00121i
$952$	−20.3871	−	5.46272i	−0.660751	−	0.177048i
$953$	−4.67309	−	17.4402i	−0.151376	−	0.564944i	−0.999388	−	0.0349673i	$-0.988867\pi$
$953$	−4.67309	−	17.4402i	−0.151376	−	0.564944i	0.848012	−	0.529977i	$-0.177799\pi$
$954$	−9.74205	+	9.74205i	−0.315411	+	0.315411i
$955$	39.2049	−	13.7476i	1.26864	−	0.444860i
$956$	−0.780600	−	2.91324i	−0.0252464	−	0.0942208i
$957$			1.35475i			0.0437929i
$958$	38.3526	−	10.2765i	1.23912	−	0.332020i
$959$	−2.12828	−	3.68629i	−0.0687257	−	0.119036i
$960$	37.5988	−	25.6709i	1.21350	−	0.828526i
$961$		−	30.9684i		−	0.998981i
$962$	13.0762	−	7.44646i	0.421595	−	0.240083i
$963$	−1.49825	−	1.49825i	−0.0482804	−	0.0482804i
$964$	−16.6086	−	4.45026i	−0.534927	−	0.143333i
$965$	−5.20782	+	27.6241i	−0.167646	+	0.889253i
$966$	9.16426	+	5.29099i	0.294855	+	0.170235i
$967$	60.0570			1.93130			0.965651	−	0.259841i	$-0.0836701\pi$
$967$	60.0570			1.93130			0.965651	+	0.259841i	$0.0836701\pi$
$968$	−21.5415	−	12.4370i	−0.692369	−	0.399740i
$969$	−53.3528	+	14.2958i	−1.71394	+	0.459249i
$970$	13.0294	+	11.1977i	0.418348	+	0.359536i
$971$	20.4589	−	35.4359i	0.656558	−	1.13719i	−0.324942	−	0.945734i	$-0.605345\pi$
$971$	20.4589	−	35.4359i	0.656558	−	1.13719i	0.981501	−	0.191459i	$-0.0613218\pi$
$972$	4.04627	−	15.1009i	0.129784	−	0.484361i
$973$	6.62390	+	11.4729i	0.212352	+	0.367805i
$974$	−29.5983			−0.948391
$975$	−30.0203	+	40.2861i	−0.961420	+	1.29019i
$976$	−2.46025			−0.0787506
$977$	−18.7479	−	32.4724i	−0.599800	−	1.03888i	−0.992850	−	0.119367i	$-0.961913\pi$
$977$	−18.7479	−	32.4724i	−0.599800	−	1.03888i	0.393050	−	0.919517i	$-0.371420\pi$
$978$	15.7740	−	58.8694i	0.504397	−	1.88244i
$979$	0.431236	−	0.746923i	0.0137824	−	0.0238718i
$980$	9.82532	+	8.44405i	0.313858	+	0.269735i
$981$	41.8125	−	11.2036i	1.33497	−	0.357704i
$982$	6.44253	+	3.71959i	0.205589	+	0.118697i
$983$	−46.1176			−1.47092			−0.735461	−	0.677567i	$-0.763034\pi$
$983$	−46.1176			−1.47092			−0.735461	+	0.677567i	$0.763034\pi$
$984$	−50.5056	−	29.1594i	−1.61006	−	0.929569i
$985$	−5.91812	+	31.3919i	−0.188567	+	1.00023i
$986$	−2.09314	−	0.560854i	−0.0666591	−	0.0178612i
$987$	−14.8980	−	14.8980i	−0.474208	−	0.474208i
$988$	−6.68975	+	6.61082i	−0.212829	+	0.210318i
$989$		−	30.6267i		−	0.973873i
$990$	−14.9725	+	10.2226i	−0.475859	+	0.324897i
$991$	−0.401099	−	0.694724i	−0.0127413	−	0.0220686i	0.859584	−	0.510994i	$-0.170722\pi$
$991$	−0.401099	−	0.694724i	−0.0127413	−	0.0220686i	−0.872326	+	0.488925i	$0.837389\pi$
$992$	−0.829802	+	0.222345i	−0.0263462	+	0.00705945i
$993$		−	93.5143i		−	2.96759i
$994$	3.32894	+	12.4238i	0.105587	+	0.394058i
$995$	31.0936	−	10.9033i	0.985734	−	0.345656i
$996$	16.1129	−	16.1129i	0.510558	−	0.510558i
$997$	4.04012	+	15.0779i	0.127952	+	0.477522i	0.999928	−	0.0120264i	$-0.00382820\pi$
$997$	4.04012	+	15.0779i	0.127952	+	0.477522i	−0.871976	+	0.489549i	$0.837162\pi$
$998$	−5.92576	−	1.58780i	−0.187577	−	0.0502610i
$999$	5.20090	−	19.4100i	0.164549	−	0.614106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.o.a.63.4	yes	20
3.2	odd	2		585.2.cf.a.388.2		20
5.2	odd	4		65.2.t.a.37.2	yes	20
5.3	odd	4		325.2.x.b.232.4		20
5.4	even	2		325.2.s.b.193.2		20
13.2	odd	12		845.2.f.e.408.8		20
13.3	even	3		845.2.k.e.268.3		20
13.4	even	6		845.2.o.f.488.2		20
13.5	odd	4		845.2.t.f.418.4		20
13.6	odd	12		65.2.t.a.58.2	yes	20
13.7	odd	12		845.2.t.g.188.4		20
13.8	odd	4		845.2.t.e.418.2		20
13.9	even	3		845.2.o.e.488.4		20
13.10	even	6		845.2.k.d.268.8		20
13.11	odd	12		845.2.f.d.408.3		20
13.12	even	2		845.2.o.g.258.2		20
15.2	even	4		585.2.dp.a.37.4		20
39.32	even	12		585.2.dp.a.253.4		20
65.2	even	12		845.2.k.e.577.3		20
65.7	even	12		845.2.o.g.357.2		20
65.12	odd	4		845.2.t.g.427.4		20
65.17	odd	12		845.2.t.e.657.2		20
65.19	odd	12		325.2.x.b.318.4		20
65.22	odd	12		845.2.t.f.657.4		20
65.32	even	12	inner	65.2.o.a.32.4	✓	20
65.37	even	12		845.2.k.d.577.8		20
65.42	odd	12		845.2.f.e.437.3		20
65.47	even	4		845.2.o.f.587.2		20
65.57	even	4		845.2.o.e.587.4		20
65.58	even	12		325.2.s.b.32.2		20
65.62	odd	12		845.2.f.d.437.8		20
195.32	odd	12		585.2.cf.a.487.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.4	✓	20	65.32	even	12	inner
65.2.o.a.63.4	yes	20	1.1	even	1	trivial
65.2.t.a.37.2	yes	20	5.2	odd	4
65.2.t.a.58.2	yes	20	13.6	odd	12
325.2.s.b.32.2		20	65.58	even	12
325.2.s.b.193.2		20	5.4	even	2
325.2.x.b.232.4		20	5.3	odd	4
325.2.x.b.318.4		20	65.19	odd	12
585.2.cf.a.388.2		20	3.2	odd	2
585.2.cf.a.487.2		20	195.32	odd	12
585.2.dp.a.37.4		20	15.2	even	4
585.2.dp.a.253.4		20	39.32	even	12
845.2.f.d.408.3		20	13.11	odd	12
845.2.f.d.437.8		20	65.62	odd	12
845.2.f.e.408.8		20	13.2	odd	12
845.2.f.e.437.3		20	65.42	odd	12
845.2.k.d.268.8		20	13.10	even	6
845.2.k.d.577.8		20	65.37	even	12
845.2.k.e.268.3		20	13.3	even	3
845.2.k.e.577.3		20	65.2	even	12
845.2.o.e.488.4		20	13.9	even	3
845.2.o.e.587.4		20	65.57	even	4
845.2.o.f.488.2		20	13.4	even	6
845.2.o.f.587.2		20	65.47	even	4
845.2.o.g.258.2		20	13.12	even	2
845.2.o.g.357.2		20	65.7	even	12
845.2.t.e.418.2		20	13.8	odd	4
845.2.t.e.657.2		20	65.17	odd	12
845.2.t.f.418.4		20	13.5	odd	4
845.2.t.f.657.4		20	65.22	odd	12
845.2.t.g.188.4		20	13.7	odd	12
845.2.t.g.427.4		20	65.12	odd	4

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.511309 + 0.885613i) q^{2} +(-0.721300 + 2.69193i) q^{3} +(0.477126 - 0.826407i) q^{4} +(-1.69584 - 1.45744i) q^{5} +(-2.75281 + 0.737614i) q^{6} +(0.834479 + 0.481787i) q^{7} +3.02107 q^{8} +(-4.12812 - 2.38337i) q^{9} +O(q^{10})\)	\(q+(0.511309 + 0.885613i) q^{2} +(-0.721300 + 2.69193i) q^{3} +(0.477126 - 0.826407i) q^{4} +(-1.69584 - 1.45744i) q^{5} +(-2.75281 + 0.737614i) q^{6} +(0.834479 + 0.481787i) q^{7} +3.02107 q^{8} +(-4.12812 - 2.38337i) q^{9} +(0.423625 - 2.24706i) q^{10} +(1.60661 + 0.430490i) q^{11} +(1.88048 + 1.88048i) q^{12} +(1.82127 - 3.11175i) q^{13} +0.985368i q^{14} +(5.14652 - 3.51384i) q^{15} +(0.590448 + 1.02269i) q^{16} +(-7.00342 + 1.87656i) q^{17} -4.87456i q^{18} +(-0.707496 - 2.64041i) q^{19} +(-2.01357 + 0.706075i) q^{20} +(-1.89884 + 1.89884i) q^{21} +(0.440226 + 1.64295i) q^{22} +(-3.72214 - 0.997344i) q^{23} +(-2.17910 + 8.13250i) q^{24} +(0.751762 + 4.94316i) q^{25} +(3.68704 + 0.0218799i) q^{26} +(3.48159 - 3.48159i) q^{27} +(0.796304 - 0.459747i) q^{28} +(0.253107 - 0.146132i) q^{29} +(5.74336 + 2.76117i) q^{30} +(-0.125649 - 0.125649i) q^{31} +(2.41727 - 4.18683i) q^{32} +(-2.31769 + 4.01436i) q^{33} +(-5.24282 - 5.24282i) q^{34} +(-0.712972 - 2.03323i) q^{35} +(-3.93927 + 2.27434i) q^{36} +(3.53443 - 2.04061i) q^{37} +(1.97663 - 1.97663i) q^{38} +(7.06291 + 7.14724i) q^{39} +(-5.12326 - 4.40302i) q^{40} +(-1.79277 + 6.69071i) q^{41} +(-2.65254 - 0.710745i) q^{42} +(2.05706 + 7.67707i) q^{43} +(1.12232 - 1.12232i) q^{44} +(3.52703 + 10.0583i) q^{45} +(-1.01990 - 3.80633i) q^{46} +7.84582i q^{47} +(-3.17888 + 0.851780i) q^{48} +(-3.03576 - 5.25810i) q^{49} +(-3.99335 + 3.19325i) q^{50} -20.2063i q^{51} +(-1.70259 - 2.98981i) q^{52} +(-1.99855 - 1.99855i) q^{53} +(4.86351 + 1.30317i) q^{54} +(-2.09714 - 3.07157i) q^{55} +(2.52102 + 1.45551i) q^{56} +7.61811 q^{57} +(0.258832 + 0.149437i) q^{58} +(4.87924 - 1.30739i) q^{59} +(-0.448318 - 5.92967i) q^{60} +(-1.04169 + 1.80425i) q^{61} +(0.0470311 - 0.175522i) q^{62} +(-2.29655 - 3.97775i) q^{63} +7.30568 q^{64} +(-7.62376 + 2.62264i) q^{65} -4.74023 q^{66} +(-3.64915 - 6.32050i) q^{67} +(-1.79071 + 6.68304i) q^{68} +(5.36956 - 9.30034i) q^{69} +(1.43611 - 1.67103i) q^{70} +(12.6082 - 3.37837i) q^{71} +(-12.4713 - 7.20034i) q^{72} +3.22747 q^{73} +(3.61437 + 2.08676i) q^{74} +(-13.8489 - 1.54181i) q^{75} +(-2.51962 - 0.675130i) q^{76} +(1.13328 + 1.13328i) q^{77} +(-2.71836 + 9.90945i) q^{78} +13.5845i q^{79} +(0.489192 - 2.59485i) q^{80} +(-0.289196 - 0.500902i) q^{81} +(-6.84204 + 1.83332i) q^{82} -8.56854i q^{83} +(0.663230 + 2.47521i) q^{84} +(14.6117 + 7.02469i) q^{85} +(-5.74712 + 5.74712i) q^{86} +(0.210809 + 0.786751i) q^{87} +(4.85368 + 1.30054i) q^{88} +(0.134207 - 0.500868i) q^{89} +(-7.10435 + 8.26648i) q^{90} +(3.01901 - 1.71922i) q^{91} +(-2.60014 + 2.60014i) q^{92} +(0.428870 - 0.247608i) q^{93} +(-6.94836 + 4.01164i) q^{94} +(-2.64843 + 5.50885i) q^{95} +(9.52707 + 9.52707i) q^{96} +(-3.75660 + 6.50662i) q^{97} +(3.10442 - 5.37702i) q^{98} +(-5.60626 - 5.60626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21} + 16 q^{22} - 2 q^{23} - 32 q^{24} - 18 q^{25} - 24 q^{26} + 4 q^{27} + 6 q^{28} + 14 q^{30} - 6 q^{32} - 18 q^{33} - 2 q^{34} - 20 q^{35} + 36 q^{36} + 42 q^{37} + 8 q^{38} - 4 q^{39} - 16 q^{40} + 10 q^{41} - 56 q^{42} - 22 q^{43} + 36 q^{44} + 52 q^{45} + 4 q^{46} + 28 q^{48} - 18 q^{49} + 44 q^{50} + 46 q^{52} - 10 q^{53} + 48 q^{54} + 26 q^{55} - 12 q^{57} - 90 q^{58} + 16 q^{59} - 92 q^{60} - 16 q^{61} - 40 q^{62} - 32 q^{63} - 20 q^{64} + 8 q^{65} - 32 q^{66} - 58 q^{67} + 28 q^{68} + 16 q^{69} + 32 q^{70} - 16 q^{71} - 66 q^{72} + 72 q^{73} - 18 q^{74} - 34 q^{75} - 64 q^{76} + 28 q^{77} + 32 q^{78} - 34 q^{80} - 14 q^{81} + 22 q^{82} + 40 q^{84} - 6 q^{85} + 60 q^{86} + 62 q^{87} + 50 q^{88} + 6 q^{89} - 46 q^{90} + 8 q^{91} - 8 q^{92} + 48 q^{93} + 48 q^{94} + 14 q^{95} + 56 q^{96} - 22 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9 - 10 * q^10 - 16 * q^11 + 24 * q^12 + 2 * q^13 + 12 * q^15 - 2 * q^16 - 10 * q^17 + 20 * q^19 + 14 * q^20 + 4 * q^21 + 16 * q^22 - 2 * q^23 - 32 * q^24 - 18 * q^25 - 24 * q^26 + 4 * q^27 + 6 * q^28 + 14 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 - 20 * q^35 + 36 * q^36 + 42 * q^37 + 8 * q^38 - 4 * q^39 - 16 * q^40 + 10 * q^41 - 56 * q^42 - 22 * q^43 + 36 * q^44 + 52 * q^45 + 4 * q^46 + 28 * q^48 - 18 * q^49 + 44 * q^50 + 46 * q^52 - 10 * q^53 + 48 * q^54 + 26 * q^55 - 12 * q^57 - 90 * q^58 + 16 * q^59 - 92 * q^60 - 16 * q^61 - 40 * q^62 - 32 * q^63 - 20 * q^64 + 8 * q^65 - 32 * q^66 - 58 * q^67 + 28 * q^68 + 16 * q^69 + 32 * q^70 - 16 * q^71 - 66 * q^72 + 72 * q^73 - 18 * q^74 - 34 * q^75 - 64 * q^76 + 28 * q^77 + 32 * q^78 - 34 * q^80 - 14 * q^81 + 22 * q^82 + 40 * q^84 - 6 * q^85 + 60 * q^86 + 62 * q^87 + 50 * q^88 + 6 * q^89 - 46 * q^90 + 8 * q^91 - 8 * q^92 + 48 * q^93 + 48 * q^94 + 14 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Introduction

L-functions

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