LMFDB - Embedded newform 99.2.m.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(4,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("99.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.m (of order $15$, degree $8$, 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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			4.1
Root			$0.669131 + 0.743145i$ of defining polynomial
Character	$\chi$	$=$	99.4
Dual form			99.2.m.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.273659 - 2.60369i) q^{2} +(-1.28716 + 1.15897i) q^{3} +(-4.74803 - 1.00922i) q^{4} +(-0.338261 - 3.21834i) q^{5} +(2.66535 + 3.66854i) q^{6} +(-0.669131 + 0.743145i) q^{7} +(-2.30902 + 7.10642i) q^{8} +(0.313585 - 2.98357i) q^{9} -8.47214 q^{10} +(3.19003 - 0.907591i) q^{11} +(7.28115 - 4.20378i) q^{12} +(2.25841 - 1.00551i) q^{13} +(1.75181 + 1.94558i) q^{14} +(4.16535 + 3.75050i) q^{15} +(9.00217 + 4.00802i) q^{16} +(1.50000 - 1.08981i) q^{17} +(-7.68247 - 1.63296i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-1.64195 + 15.6222i) q^{20} -1.73205i q^{21} +(-1.49011 - 8.55422i) q^{22} +(-1.19098 + 2.06284i) q^{23} +(-5.26403 - 11.8232i) q^{24} +(-5.35256 + 1.13772i) q^{25} +(-2.00000 - 6.15537i) q^{26} +(3.05422 + 4.20378i) q^{27} +(3.92705 - 2.85317i) q^{28} +(1.24064 - 1.37787i) q^{29} +(10.9050 - 9.81894i) q^{30} +(-1.47815 + 0.658114i) q^{31} +(5.42705 - 9.39993i) q^{32} +(-3.05422 + 4.86536i) q^{33} +(-2.42705 - 4.20378i) q^{34} +(2.61803 + 1.90211i) q^{35} +(-4.50000 + 13.8496i) q^{36} +(1.88197 + 5.79210i) q^{37} +(-2.39169 - 1.06485i) q^{38} +(-1.74159 + 3.91168i) q^{39} +(23.6519 + 5.02738i) q^{40} +(-7.67636 - 8.52546i) q^{41} +(-4.50973 - 0.473991i) q^{42} +(2.42705 + 4.20378i) q^{43} +(-16.0623 + 1.08981i) q^{44} -9.70820 q^{45} +(5.04508 + 3.66547i) q^{46} +(5.81438 - 1.23588i) q^{47} +(-16.2324 + 5.27424i) q^{48} +(0.627171 + 5.96713i) q^{49} +(1.49750 + 14.2478i) q^{50} +(-0.667687 + 3.14122i) q^{51} +(-11.7378 + 2.49494i) q^{52} +(5.73607 + 4.16750i) q^{53} +(11.7812 - 6.80185i) q^{54} +(-4.00000 - 9.95959i) q^{55} +(-3.73607 - 6.47106i) q^{56} +(0.704489 + 1.58231i) q^{57} +(-3.24803 - 3.60730i) q^{58} +(0.604528 + 0.128496i) q^{59} +(-15.9921 - 22.0113i) q^{60} +(3.78747 + 1.68629i) q^{61} +(1.30902 + 4.02874i) q^{62} +(2.00739 + 2.22943i) q^{63} +(-7.04508 - 5.11855i) q^{64} +(-4.00000 - 6.92820i) q^{65} +(11.8321 + 9.28370i) q^{66} +(-3.00000 + 5.19615i) q^{67} +(-8.22191 + 3.66063i) q^{68} +(-0.857778 - 4.03553i) q^{69} +(5.66897 - 6.29602i) q^{70} +(11.3992 - 8.28199i) q^{71} +(20.4784 + 9.11757i) q^{72} +(-2.11803 - 6.51864i) q^{73} +(15.5959 - 3.31500i) q^{74} +(5.57104 - 7.66788i) q^{75} +(-2.42705 + 4.20378i) q^{76} +(-1.46007 + 2.97795i) q^{77} +(9.70820 + 5.60503i) q^{78} +(0.999533 - 9.50992i) q^{79} +(9.85410 - 30.3278i) q^{80} +(-8.80333 - 1.87121i) q^{81} +(-24.2984 + 17.6538i) q^{82} +(-13.0053 - 5.79033i) q^{83} +(-1.74803 + 8.22383i) q^{84} +(-4.01478 - 4.45887i) q^{85} +(11.6095 - 5.16889i) q^{86} +3.21140i q^{87} +(-0.916102 + 24.7653i) q^{88} -11.2361 q^{89} +(-2.65674 + 25.2772i) q^{90} +(-0.763932 + 2.35114i) q^{91} +(7.73669 - 8.59247i) q^{92} +(1.13989 - 2.56023i) q^{93} +(-1.62670 - 15.4771i) q^{94} +(-3.16535 - 0.672816i) q^{95} +(3.90871 + 18.3890i) q^{96} +(-0.627171 + 5.96713i) q^{97} +15.7082 q^{98} +(-1.70751 - 9.80227i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 3 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} - 14 q^{8} - 3 q^{9} - 32 q^{10} + q^{11} + 18 q^{12} + 8 q^{13} - q^{14} + 12 q^{15} + 14 q^{16} + 12 q^{17} - 3 q^{18} - 2 q^{19} + 24 q^{20} + 11 q^{22}+ \cdots - 3 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 + 3 * q^3 - 6 * q^4 + 6 * q^5 - q^7 - 14 * q^8 - 3 * q^9 - 32 * q^10 + q^11 + 18 * q^12 + 8 * q^13 - q^14 + 12 * q^15 + 14 * q^16 + 12 * q^17 - 3 * q^18 - 2 * q^19 + 24 * q^20 + 11 * q^22 - 14 * q^23 - 39 * q^24 - 9 * q^25 - 16 * q^26 + 18 * q^28 - 9 * q^29 + 18 * q^30 - 3 * q^31 + 30 * q^32 - 6 * q^34 + 12 * q^35 - 36 * q^36 + 24 * q^37 - 4 * q^38 - 24 * q^39 + 12 * q^40 + 3 * q^41 - 12 * q^42 + 6 * q^43 - 48 * q^44 - 24 * q^45 + 18 * q^46 + 23 * q^47 - 6 * q^49 - 24 * q^50 + 27 * q^51 + 12 * q^52 + 28 * q^53 + 54 * q^54 - 32 * q^55 - 12 * q^56 + 3 * q^57 + 6 * q^58 + 3 * q^59 + 6 * q^62 + 3 * q^63 - 34 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 9 * q^68 - 18 * q^69 - 6 * q^70 + 42 * q^71 + 39 * q^72 - 8 * q^73 + 13 * q^74 - 6 * q^76 - 11 * q^77 + 24 * q^78 - 22 * q^79 + 52 * q^80 + 9 * q^81 - 96 * q^82 - 17 * q^83 + 18 * q^84 - 6 * q^85 + 21 * q^86 + 37 * q^88 - 72 * q^89 + 42 * q^90 - 24 * q^91 - 21 * q^92 + 9 * q^93 + 28 * q^94 - 4 * q^95 + 6 * q^97 + 72 * q^98 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.273659	−	2.60369i	0.193506	−	1.84109i	−0.279641	−	0.960105i	$-0.590215\pi$
$2$	0.273659	−	2.60369i	0.193506	−	1.84109i	0.473147	−	0.880984i	$-0.343118\pi$
$3$	−1.28716	+	1.15897i	−0.743145	+	0.669131i
$3$	−1.28716	+	1.15897i	−0.743145	+	0.669131i
$4$	−4.74803	−	1.00922i	−2.37401	−	0.504612i
$5$	−0.338261	−	3.21834i	−0.151275	−	1.43929i	−0.762069	−	0.647496i	$-0.775816\pi$
$5$	−0.338261	−	3.21834i	−0.151275	−	1.43929i	0.610794	−	0.791790i	$-0.290850\pi$
$6$	2.66535	+	3.66854i	1.08813	+	1.49768i
$7$	−0.669131	+	0.743145i	−0.252908	+	0.280882i	−0.856208	−	0.516632i	$-0.827186\pi$
$7$	−0.669131	+	0.743145i	−0.252908	+	0.280882i	0.603300	+	0.797514i	$0.293852\pi$
$8$	−2.30902	+	7.10642i	−0.816361	+	2.51250i
$9$	0.313585	−	2.98357i	0.104528	−	0.994522i
$10$	−8.47214			−2.67912
$11$	3.19003	−	0.907591i	0.961830	−	0.273649i
$11$	3.19003	−	0.907591i	0.961830	−	0.273649i
$12$	7.28115	−	4.20378i	2.10189	−	1.21353i
$13$	2.25841	−	1.00551i	0.626370	−	0.278878i	−0.0689034	−	0.997623i	$-0.521950\pi$
$13$	2.25841	−	1.00551i	0.626370	−	0.278878i	0.695273	+	0.718746i	$0.255283\pi$
$14$	1.75181	+	1.94558i	0.468190	+	0.519978i
$15$	4.16535	+	3.75050i	1.07549	+	0.968375i
$16$	9.00217	+	4.00802i	2.25054	+	1.00201i
$17$	1.50000	−	1.08981i	0.363803	−	0.264319i	−0.390833	−	0.920461i	$-0.627813\pi$
$17$	1.50000	−	1.08981i	0.363803	−	0.264319i	0.754637	+	0.656143i	$0.227813\pi$
$18$	−7.68247	−	1.63296i	−1.81078	−	0.384892i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i	−0.909332	−	0.416071i	$-0.863407\pi$
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i	0.980226	+	0.197884i	$0.0634068\pi$
$20$	−1.64195	+	15.6222i	−0.367152	+	3.49322i
$21$		−	1.73205i		−	0.377964i
$22$	−1.49011	−	8.55422i	−0.317692	−	1.82377i
$23$	−1.19098	+	2.06284i	−0.248337	+	0.430133i	−0.963065	−	0.269271i	$-0.913217\pi$
$23$	−1.19098	+	2.06284i	−0.248337	+	0.430133i	0.714727	+	0.699403i	$0.246551\pi$
$24$	−5.26403	−	11.8232i	−1.07452	−	2.41340i
$25$	−5.35256	+	1.13772i	−1.07051	+	0.227544i
$26$	−2.00000	−	6.15537i	−0.392232	−	1.20717i
$27$	3.05422	+	4.20378i	0.587785	+	0.809017i
$28$	3.92705	−	2.85317i	0.742143	−	0.539198i
$29$	1.24064	−	1.37787i	0.230380	−	0.255863i	−0.616860	−	0.787073i	$-0.711596\pi$
$29$	1.24064	−	1.37787i	0.230380	−	0.255863i	0.847241	+	0.531209i	$0.178262\pi$
$30$	10.9050	−	9.81894i	1.99098	−	1.79268i
$31$	−1.47815	+	0.658114i	−0.265483	+	0.118201i	−0.535162	−	0.844750i	$-0.679749\pi$
$31$	−1.47815	+	0.658114i	−0.265483	+	0.118201i	0.269678	+	0.962950i	$0.413083\pi$
$32$	5.42705	−	9.39993i	0.959376	−	1.66169i
$33$	−3.05422	+	4.86536i	−0.531672	+	0.846950i
$34$	−2.42705	−	4.20378i	−0.416236	−	0.720942i
$35$	2.61803	+	1.90211i	0.442529	+	0.321516i
$36$	−4.50000	+	13.8496i	−0.750000	+	2.30826i
$37$	1.88197	+	5.79210i	0.309393	+	0.952215i	0.978001	+	0.208599i	$0.0668905\pi$
$37$	1.88197	+	5.79210i	0.309393	+	0.952215i	−0.668608	+	0.743615i	$0.733109\pi$
$38$	−2.39169	−	1.06485i	−0.387984	−	0.172742i
$39$	−1.74159	+	3.91168i	−0.278878	+	0.626370i
$40$	23.6519	+	5.02738i	3.73970	+	0.794898i
$41$	−7.67636	−	8.52546i	−1.19885	−	1.33145i	−0.929684	−	0.368358i	$-0.879920\pi$
$41$	−7.67636	−	8.52546i	−1.19885	−	1.33145i	−0.269162	−	0.963095i	$-0.586747\pi$
$42$	−4.50973	−	0.473991i	−0.695866	−	0.0731385i
$43$	2.42705	+	4.20378i	0.370122	+	0.641070i	0.989584	−	0.143957i	$-0.0459826\pi$
$43$	2.42705	+	4.20378i	0.370122	+	0.641070i	−0.619462	+	0.785027i	$0.712649\pi$
$44$	−16.0623	+	1.08981i	−2.42148	+	0.164296i
$45$	−9.70820			−1.44721
$46$	5.04508	+	3.66547i	0.743857	+	0.540444i
$47$	5.81438	−	1.23588i	0.848114	−	0.180272i	0.236700	−	0.971583i	$-0.423934\pi$
$47$	5.81438	−	1.23588i	0.848114	−	0.180272i	0.611414	+	0.791311i	$0.290601\pi$
$48$	−16.2324	+	5.27424i	−2.34295	+	0.761271i
$49$	0.627171	+	5.96713i	0.0895958	+	0.852447i
$50$	1.49750	+	14.2478i	0.211778	+	2.01494i
$51$	−0.667687	+	3.14122i	−0.0934949	+	0.439859i
$52$	−11.7378	+	2.49494i	−1.62774	+	0.345986i
$53$	5.73607	+	4.16750i	0.787910	+	0.572450i	0.907342	−	0.420393i	$-0.138108\pi$
$53$	5.73607	+	4.16750i	0.787910	+	0.572450i	−0.119433	+	0.992842i	$0.538108\pi$
$54$	11.7812	−	6.80185i	1.60321	−	0.925615i
$55$	−4.00000	−	9.95959i	−0.539360	−	1.34295i
$56$	−3.73607	−	6.47106i	−0.499253	−	0.864732i
$57$	0.704489	+	1.58231i	0.0933118	+	0.209582i
$58$	−3.24803	−	3.60730i	−0.426487	−	0.473662i
$59$	0.604528	+	0.128496i	0.0787029	+	0.0167288i	0.247095	−	0.968991i	$-0.420524\pi$
$59$	0.604528	+	0.128496i	0.0787029	+	0.0167288i	−0.168392	+	0.985720i	$0.553857\pi$
$60$	−15.9921	−	22.0113i	−2.06457	−	2.84164i
$61$	3.78747	+	1.68629i	0.484935	+	0.215907i	0.634617	−	0.772827i	$-0.281158\pi$
$61$	3.78747	+	1.68629i	0.484935	+	0.215907i	−0.149681	+	0.988734i	$0.547825\pi$
$62$	1.30902	+	4.02874i	0.166245	+	0.511650i
$63$	2.00739	+	2.22943i	0.252908	+	0.280882i
$64$	−7.04508	−	5.11855i	−0.880636	−	0.639819i
$65$	−4.00000	−	6.92820i	−0.496139	−	0.859338i
$66$	11.8321	+	9.28370i	1.45643	+	1.14274i
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	−0.989017	−	0.147802i	$-0.952780\pi$
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	0.622509	+	0.782613i	$0.286114\pi$
$68$	−8.22191	+	3.66063i	−0.997053	+	0.443917i
$69$	−0.857778	−	4.03553i	−0.103264	−	0.485821i
$70$	5.66897	−	6.29602i	0.677571	−	0.752519i
$71$	11.3992	−	8.28199i	1.35283	−	0.982892i	0.353970	−	0.935257i	$-0.384832\pi$
$71$	11.3992	−	8.28199i	1.35283	−	0.982892i	0.998865	−	0.0476350i	$-0.0151684\pi$
$72$	20.4784	+	9.11757i	2.41340	+	1.07452i
$73$	−2.11803	−	6.51864i	−0.247897	−	0.762949i	−0.995146	−	0.0984051i	$-0.968626\pi$
$73$	−2.11803	−	6.51864i	−0.247897	−	0.762949i	0.747249	−	0.664544i	$-0.231374\pi$
$74$	15.5959	−	3.31500i	1.81298	−	0.385361i
$75$	5.57104	−	7.66788i	0.643288	−	0.885410i
$76$	−2.42705	+	4.20378i	−0.278402	+	0.482206i
$77$	−1.46007	+	2.97795i	−0.166391	+	0.339369i
$78$	9.70820	+	5.60503i	1.09924	+	0.634645i
$79$	0.999533	−	9.50992i	0.112456	−	1.06995i	−0.782149	−	0.623092i	$-0.785876\pi$
$79$	0.999533	−	9.50992i	0.112456	−	1.06995i	0.894605	−	0.446858i	$-0.147457\pi$
$80$	9.85410	−	30.3278i	1.10172	−	3.39075i
$81$	−8.80333	−	1.87121i	−0.978148	−	0.207912i
$82$	−24.2984	+	17.6538i	−2.68331	+	1.94954i
$83$	−13.0053	−	5.79033i	−1.42752	−	0.635571i	−0.459894	−	0.887974i	$-0.652113\pi$
$83$	−13.0053	−	5.79033i	−1.42752	−	0.635571i	−0.967622	+	0.252402i	$0.918779\pi$
$84$	−1.74803	+	8.22383i	−0.190726	+	0.897293i
$85$	−4.01478	−	4.45887i	−0.435464	−	0.483632i
$86$	11.6095	−	5.16889i	1.25189	−	0.557376i
$87$			3.21140i			0.344298i
$88$	−0.916102	+	24.7653i	−0.0976568	+	2.63999i
$89$	−11.2361			−1.19102			−0.595510	−	0.803348i	$-0.703050\pi$
$89$	−11.2361			−1.19102			−0.595510	+	0.803348i	$0.703050\pi$
$90$	−2.65674	+	25.2772i	−0.280045	+	2.66445i
$91$	−0.763932	+	2.35114i	−0.0800818	+	0.246467i
$92$	7.73669	−	8.59247i	0.806606	−	0.895827i
$93$	1.13989	−	2.56023i	0.118201	−	0.265483i
$94$	−1.62670	−	15.4771i	−0.167782	−	1.59634i
$95$	−3.16535	−	0.672816i	−0.324758	−	0.0690295i
$96$	3.90871	+	18.3890i	0.398931	+	1.87682i
$97$	−0.627171	+	5.96713i	−0.0636795	+	0.605870i	0.915422	+	0.402496i	$0.131857\pi$
$97$	−0.627171	+	5.96713i	−0.0636795	+	0.605870i	−0.979101	+	0.203374i	$0.934809\pi$
$98$	15.7082			1.58677
$99$	−1.70751	−	9.80227i	−0.171611	−	0.985165i
$100$	26.5623			2.65623
$101$	−0.0493516	+	0.469550i	−0.00491067	+	0.0467219i	−0.996703	−	0.0811387i	$-0.974144\pi$
$101$	−0.0493516	+	0.469550i	−0.00491067	+	0.0467219i	0.991792	+	0.127861i	$0.0408110\pi$
$102$	7.99606	+	2.59808i	0.791728	+	0.257248i
$103$	5.63798	+	1.19839i	0.555526	+	0.118081i	0.477116	−	0.878840i	$-0.341682\pi$
$103$	5.63798	+	1.19839i	0.555526	+	0.118081i	0.0784104	+	0.996921i	$0.475016\pi$
$104$	1.93086	+	18.3709i	0.189337	+	1.80142i
$105$	−5.57433	+	0.585886i	−0.543999	+	0.0571766i
$106$	12.4206	−	13.7945i	1.20640	−	1.33984i
$107$	−4.64590	+	14.2986i	−0.449136	+	1.38230i	0.428748	+	0.903424i	$0.358955\pi$
$107$	−4.64590	+	14.2986i	−0.449136	+	1.38230i	−0.877884	+	0.478874i	$0.841045\pi$
$108$	−10.2590	−	23.0420i	−0.987171	−	2.21722i
$109$	13.8541			1.32698			0.663491	−	0.748184i	$-0.269074\pi$
$109$	13.8541			1.32698			0.663491	+	0.748184i	$0.269074\pi$
$110$	−27.0264	+	7.68924i	−2.57686	+	0.733140i
$111$	−9.13525	−	5.27424i	−0.867080	−	0.500609i
$112$	−9.00217	+	4.00802i	−0.850625	+	0.378723i
$113$	8.54074	+	9.48545i	0.803445	+	0.892316i	0.996035	−	0.0889633i	$-0.0283554\pi$
$113$	8.54074	+	9.48545i	0.803445	+	0.892316i	−0.192590	+	0.981279i	$0.561689\pi$
$114$	4.31263	−	1.40126i	0.403915	−	0.131240i
$115$	7.04179	+	3.13521i	0.656651	+	0.292360i
$116$	−7.28115	+	5.29007i	−0.676038	+	0.491170i
$117$	−2.29180	−	7.05342i	−0.211877	−	0.652089i
$118$	0.500000	−	1.53884i	0.0460287	−	0.141662i
$119$	−0.193806	+	1.84395i	−0.0177662	+	0.169034i
$120$	−36.2705	+	20.9408i	−3.31103	+	1.91162i
$121$	9.35256	−	5.79048i	0.850232	−	0.526407i
$122$	5.42705	−	9.39993i	0.491342	−	0.851029i
$123$	19.7615	+	2.07701i	1.78183	+	0.187278i
$124$	7.68247	−	1.63296i	0.689906	−	0.146644i
$125$	0.472136	+	1.45309i	0.0422291	+	0.129968i
$126$	6.35410	−	4.61653i	0.566068	−	0.411273i
$127$	−7.73607	+	5.62058i	−0.686465	+	0.498746i	−0.875496	−	0.483225i	$-0.839465\pi$
$127$	−7.73607	+	5.62058i	−0.686465	+	0.498746i	0.189031	+	0.981971i	$0.439465\pi$
$128$	−0.729466	+	0.810154i	−0.0644763	+	0.0716082i
$129$	−7.99606	−	2.59808i	−0.704014	−	0.228748i
$130$	−19.1335	+	8.51880i	−1.67812	+	0.747148i
$131$	−8.38197	+	14.5180i	−0.732336	+	1.26844i	0.223547	+	0.974693i	$0.428236\pi$
$131$	−8.38197	+	14.5180i	−0.732336	+	1.26844i	−0.955882	+	0.293750i	$0.905097\pi$
$132$	19.4118	−	20.0185i	1.68958	−	1.74238i
$133$	0.500000	+	0.866025i	0.0433555	+	0.0750939i
$134$	12.7082	+	9.23305i	1.09782	+	0.797614i
$135$	12.4961	−	11.2515i	1.07549	−	0.968375i
$136$	4.28115	+	13.1760i	0.367106	+	1.12984i
$137$	−5.83022	−	2.59578i	−0.498109	−	0.221772i	0.142275	−	0.989827i	$-0.454558\pi$
$137$	−5.83022	−	2.59578i	−0.498109	−	0.221772i	−0.640384	+	0.768055i	$0.721225\pi$
$138$	−10.7420	+	1.12903i	−0.914421	+	0.0961095i
$139$	3.62717	+	0.770979i	0.307653	+	0.0653936i	0.359151	−	0.933280i	$-0.383066\pi$
$139$	3.62717	+	0.770979i	0.307653	+	0.0653936i	−0.0514983	+	0.998673i	$0.516400\pi$
$140$	−10.5108	−	11.6735i	−0.888328	−	0.986588i
$141$	−6.05171	+	8.32946i	−0.509646	+	0.701467i
$142$	−18.4443	−	31.9464i	−1.54781	−	2.68088i
$143$	6.29180	−	5.25731i	0.526146	−	0.439638i
$144$	14.7812	−	25.6017i	1.23176	−	2.13348i
$145$	−4.85410	−	3.52671i	−0.403111	−	0.292877i
$146$	−17.5521	+	3.73082i	−1.45263	+	0.308765i
$147$	−7.72299	−	6.95381i	−0.636981	−	0.573541i
$148$	−3.09010	−	29.4004i	−0.254005	−	2.41669i
$149$	−0.750550	−	7.14101i	−0.0614874	−	0.585014i	−0.981277	−	0.192602i	$-0.938307\pi$
$149$	−0.750550	−	7.14101i	−0.0614874	−	0.585014i	0.919790	−	0.392412i	$-0.128359\pi$
$150$	−18.4402	−	16.6037i	−1.50564	−	1.35568i
$151$	11.0787	−	2.35486i	0.901574	−	0.191636i	0.266271	−	0.963898i	$-0.414208\pi$
$151$	11.0787	−	2.35486i	0.901574	−	0.191636i	0.635303	+	0.772263i	$0.280875\pi$
$152$	6.04508	+	4.39201i	0.490321	+	0.356239i
$153$	−2.78115	−	4.81710i	−0.224843	−	0.389439i
$154$	7.35410	+	4.61653i	0.592610	+	0.372010i
$155$	2.61803	+	4.53457i	0.210286	+	0.364225i
$156$	12.2169	−	16.8151i	0.978134	−	1.34629i
$157$	9.27020	+	10.2956i	0.739843	+	0.821679i	0.989175	−	0.146739i	$-0.0468778\pi$
$157$	9.27020	+	10.2956i	0.739843	+	0.821679i	−0.249332	+	0.968418i	$0.580211\pi$
$158$	−24.4874	−	5.20495i	−1.94811	−	0.414084i
$159$	−12.2133	+	1.28367i	−0.968575	+	0.101801i
$160$	−32.0879	−	14.2865i	−2.53677	−	1.12944i
$161$	−0.736068	−	2.26538i	−0.0580103	−	0.178537i
$162$	−7.28115	+	22.4091i	−0.572061	+	1.76062i
$163$	−5.89919	−	4.28601i	−0.462060	−	0.335706i	0.332279	−	0.943181i	$-0.392182\pi$
$163$	−5.89919	−	4.28601i	−0.462060	−	0.335706i	−0.794339	+	0.607475i	$0.792182\pi$
$164$	27.8435	+	48.2263i	2.17421	+	3.76584i
$165$	16.6915	+	8.18376i	1.29943	+	0.637105i
$166$	−18.6353	+	32.2772i	−1.44638	+	2.50520i
$167$	−9.35111	+	4.16338i	−0.723611	+	0.322172i	−0.735284	−	0.677760i	$-0.762951\pi$
$167$	−9.35111	+	4.16338i	−0.723611	+	0.322172i	0.0116727	+	0.999932i	$0.496284\pi$
$168$	12.3087	+	3.99933i	0.949636	+	0.308555i
$169$	−4.60934	+	5.11919i	−0.354564	+	0.393784i
$170$	−12.7082	+	9.23305i	−0.974675	+	0.708143i
$171$	−2.74064	−	1.22021i	−0.209582	−	0.0933118i
$172$	−7.28115	−	22.4091i	−0.555183	−	1.70868i
$173$	11.6496	−	2.47619i	0.885701	−	0.188261i	0.257468	−	0.966287i	$-0.417112\pi$
$173$	11.6496	−	2.47619i	0.885701	−	0.188261i	0.628233	+	0.778025i	$0.283779\pi$
$174$	8.36149	+	0.878828i	0.633883	+	0.0666238i
$175$	2.73607	−	4.73901i	0.206827	−	0.358235i
$176$	32.3548	+	4.61542i	2.43884	+	0.347900i
$177$	−0.927051	+	0.535233i	−0.0696814	+	0.0402306i
$178$	−3.07485	+	29.2553i	−0.230470	+	2.19277i
$179$	−7.09017	+	21.8213i	−0.529944	+	1.63100i	0.224382	+	0.974501i	$0.427964\pi$
$179$	−7.09017	+	21.8213i	−0.529944	+	1.63100i	−0.754327	+	0.656499i	$0.772036\pi$
$180$	46.0948	+	9.79776i	3.43571	+	0.730282i
$181$	17.0623	−	12.3965i	1.26823	−	0.921424i	0.269101	−	0.963112i	$-0.413274\pi$
$181$	17.0623	−	12.3965i	1.26823	−	0.921424i	0.999131	+	0.0416882i	$0.0132736\pi$
$182$	5.91259	+	2.63245i	0.438270	+	0.195131i
$183$	−6.82945	+	2.21902i	−0.504847	+	0.164035i
$184$	−11.9094	−	13.2268i	−0.877975	−	0.975090i
$185$	18.0043	−	8.01605i	1.32371	−	0.589352i
$186$	−6.35410	−	3.66854i	−0.465905	−	0.268991i
$187$	3.79594	−	4.83792i	0.277586	−	0.353784i
$188$	−28.8541			−2.10440
$189$	−5.16769	−	0.543146i	−0.375894	−	0.0395080i
$190$	−2.61803	+	8.05748i	−0.189932	+	0.584551i
$191$	−7.99228	+	8.87632i	−0.578301	+	0.642268i	−0.959327	−	0.282296i	$-0.908904\pi$
$191$	−7.99228	+	8.87632i	−0.578301	+	0.642268i	0.381026	+	0.924564i	$0.375571\pi$
$192$	15.0004	−	1.57661i	1.08256	−	0.113782i
$193$	1.14981	+	10.9397i	0.0827654	+	0.787460i	0.954646	+	0.297742i	$0.0962335\pi$
$193$	1.14981	+	10.9397i	0.0827654	+	0.787460i	−0.871881	+	0.489718i	$0.837100\pi$
$194$	15.3649	+	3.26592i	1.10314	+	0.234479i
$195$	13.1782	+	4.28187i	0.943712	+	0.306631i
$196$	3.04435	−	28.9651i	0.217454	−	2.06893i
$197$	3.76393			0.268169			0.134085	−	0.990970i	$-0.457191\pi$
$197$	3.76393			0.268169			0.134085	+	0.990970i	$0.457191\pi$
$198$	−25.9894	+	1.76336i	−1.84698	+	0.125316i
$199$	−13.8541			−0.982091			−0.491046	−	0.871134i	$-0.663385\pi$
$199$	−13.8541			−0.982091			−0.491046	+	0.871134i	$0.663385\pi$
$200$	4.27402	−	40.6646i	0.302219	−	2.87542i
$201$	−2.16068	−	10.1652i	−0.152403	−	0.716998i
$202$	1.20906	+	0.256993i	0.0850689	+	0.0180820i
$203$	0.193806	+	1.84395i	0.0136025	+	0.129420i
$204$	6.34040	−	14.2408i	0.443917	−	0.997053i
$205$	−24.8412	+	27.5890i	−1.73499	+	1.92690i
$206$	4.66312	−	14.3516i	0.324895	−	0.999924i
$207$	5.78115	+	4.20025i	0.401818	+	0.291938i
$208$	24.3607			1.68911
$209$	0.122602	−	3.31436i	0.00848058	−	0.229259i
$210$			14.6742i			1.01261i
$211$	10.5312	−	4.68880i	0.725000	−	0.322791i	−0.0108449	−	0.999941i	$-0.503452\pi$
$211$	10.5312	−	4.68880i	0.725000	−	0.322791i	0.735844	+	0.677151i	$0.236785\pi$
$212$	−23.0291	−	25.5764i	−1.58164	−	1.75659i
$213$	−5.07406	+	23.8716i	−0.347669	+	1.63565i
$214$	35.9578	+	16.0094i	2.45802	+	1.09438i
$215$	12.7082	−	9.23305i	0.866692	−	0.629689i
$216$	−36.9261	+	11.9980i	−2.51250	+	0.816361i
$217$	0.500000	−	1.53884i	0.0339422	−	0.104463i
$218$	3.79130	−	36.0718i	0.256779	−	2.44309i
$219$	10.2812	+	5.93583i	0.694736	+	0.401106i
$220$	8.94065	+	51.3253i	0.602778	+	3.46035i
$221$	2.29180	−	3.96951i	0.154163	−	0.267018i
$222$	−16.2324	+	22.3420i	−1.08945	+	1.49950i
$223$	−22.0148	+	4.67938i	−1.47422	+	0.313355i	−0.873782	−	0.486319i	$-0.838339\pi$
$223$	−22.0148	+	4.67938i	−1.47422	+	0.313355i	−0.600436	+	0.799673i	$0.705006\pi$
$224$	3.35410	+	10.3229i	0.224105	+	0.689725i
$225$	1.71598	+	16.3265i	0.114399	+	1.08843i
$226$	27.0344	−	19.6417i	1.79830	−	1.30654i
$227$	−9.62341	+	10.6879i	−0.638728	+	0.709380i	−0.972403	−	0.233309i	$-0.925045\pi$
$227$	−9.62341	+	10.6879i	−0.638728	+	0.709380i	0.333674	+	0.942688i	$0.391711\pi$
$228$	−1.74803	−	8.22383i	−0.115766	−	0.544636i
$229$	−11.1273	+	4.95419i	−0.735312	+	0.327382i	−0.740000	−	0.672607i	$-0.765175\pi$
$229$	−11.1273	+	4.95419i	−0.735312	+	0.327382i	0.00468769	+	0.999989i	$0.498508\pi$
$230$	10.0902	−	17.4767i	0.665326	−	1.15238i
$231$	−1.57199	−	5.52529i	−0.103430	−	0.363537i
$232$	6.92705	+	11.9980i	0.454783	+	0.787708i
$233$	−23.5623	−	17.1190i	−1.54362	−	1.12150i	−0.948015	−	0.318225i	$-0.896913\pi$
$233$	−23.5623	−	17.1190i	−1.54362	−	1.12150i	−0.595603	−	0.803279i	$-0.703087\pi$
$234$	−18.9921	+	4.03690i	−1.24155	+	0.263900i
$235$	−5.94427	−	18.2946i	−0.387762	−	1.19341i
$236$	−2.74064	−	1.22021i	−0.178400	−	0.0794289i
$237$	9.73513	+	13.3993i	0.632365	+	0.870376i
$238$	4.74803	+	1.00922i	0.307769	+	0.0654183i
$239$	1.02234	+	1.13542i	0.0661297	+	0.0734445i	0.775302	−	0.631591i	$-0.217598\pi$
$239$	1.02234	+	1.13542i	0.0661297	+	0.0734445i	−0.709172	+	0.705035i	$0.750931\pi$
$240$	22.4651	+	50.4575i	1.45012	+	3.25702i
$241$	−13.4164	−	23.2379i	−0.864227	−	1.49688i	−0.867813	−	0.496891i	$-0.834475\pi$
$241$	−13.4164	−	23.2379i	−0.864227	−	1.49688i	0.00358606	−	0.999994i	$-0.498859\pi$
$242$	−12.5172	−	25.9358i	−0.804637	−	1.66722i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	−16.2812	−	11.8290i	−1.04229	−	0.757271i
$245$	18.9921	−	4.03690i	1.21336	−	0.257908i
$246$	10.8158	−	50.8844i	0.689591	−	3.24427i
$247$	−0.258409	−	2.45859i	−0.0164421	−	0.156437i
$248$	−1.26377	−	12.0239i	−0.0802493	−	0.763521i
$249$	23.4508	−	7.61962i	1.48613	−	0.482873i
$250$	3.91259	−	0.831647i	0.247454	−	0.0525980i
$251$	−0.354102	−	0.257270i	−0.0223507	−	0.0162387i	0.576554	−	0.817059i	$-0.304397\pi$
$251$	−0.354102	−	0.257270i	−0.0223507	−	0.0162387i	−0.598905	+	0.800820i	$0.704397\pi$
$252$	−7.28115	−	12.6113i	−0.458670	−	0.794439i
$253$	−1.92705	+	7.66145i	−0.121153	+	0.481671i
$254$	12.5172	+	21.6805i	0.785400	+	1.36035i
$255$	10.3354	+	1.08629i	0.647226	+	0.0680262i
$256$	−9.74408	−	10.8219i	−0.609005	−	0.676369i
$257$	25.5200	+	5.42445i	1.59190	+	0.338368i	0.916795	−	0.399357i	$-0.130767\pi$
$257$	25.5200	+	5.42445i	1.59190	+	0.338368i	0.675101	+	0.737725i	$0.264100\pi$
$258$	−8.95278	+	20.1083i	−0.557376	+	1.25189i
$259$	−5.56365	−	2.47710i	−0.345708	−	0.153919i
$260$	12.0000	+	36.9322i	0.744208	+	2.29044i
$261$	−3.72191	−	4.13360i	−0.230380	−	0.255863i
$262$	35.5066	+	25.7970i	2.19360	+	1.59375i
$263$	−0.354102	−	0.613323i	−0.0218349	−	0.0378191i	0.854902	−	0.518790i	$-0.173617\pi$
$263$	−0.354102	−	0.613323i	−0.0218349	−	0.0378191i	−0.876736	+	0.480971i	$0.840284\pi$
$264$	−27.5231	−	32.9388i	−1.69393	−	2.02724i
$265$	11.4721	−	19.8703i	0.704728	−	1.22062i
$266$	2.39169	−	1.06485i	0.146644	−	0.0652902i
$267$	14.4627	−	13.0222i	0.885101	−	0.796948i
$268$	19.4882	−	21.6438i	1.19043	−	1.32211i
$269$	−9.92705	+	7.21242i	−0.605263	+	0.439749i	−0.847743	−	0.530407i	$-0.822039\pi$
$269$	−9.92705	+	7.21242i	−0.605263	+	0.439749i	0.242480	+	0.970156i	$0.422039\pi$
$270$	−25.8758	−	35.6150i	−1.57475	−	2.16746i
$271$	4.70820	+	14.4904i	0.286003	+	0.880227i	0.986096	+	0.166175i	$0.0531418\pi$
$271$	4.70820	+	14.4904i	0.286003	+	0.880227i	−0.700093	+	0.714051i	$0.746858\pi$
$272$	17.8713	−	3.79865i	1.08360	−	0.230327i
$273$	−1.74159	−	3.91168i	−0.105406	−	0.236746i
$274$	−8.35410	+	14.4697i	−0.504690	+	0.874148i
$275$	−16.0422	+	8.48729i	−0.967382	+	0.511803i
$276$			20.0265i			1.20545i
$277$	1.54325	−	14.6831i	0.0927250	−	0.882219i	−0.844983	−	0.534794i	$-0.820389\pi$
$277$	1.54325	−	14.6831i	0.0927250	−	0.882219i	0.937708	−	0.347425i	$-0.112944\pi$
$278$	3.00000	−	9.23305i	0.179928	−	0.553762i
$279$	1.50000	+	4.61653i	0.0898027	+	0.276384i
$280$	−19.5623	+	14.2128i	−1.16907	+	0.849380i
$281$	5.77931	+	2.57311i	0.344764	+	0.153499i	0.571812	−	0.820385i	$-0.306241\pi$
$281$	5.77931	+	2.57311i	0.344764	+	0.153499i	−0.227048	+	0.973884i	$0.572907\pi$
$282$	20.0312	+	18.0362i	1.19284	+	1.07404i
$283$	−11.3752	−	12.6335i	−0.676187	−	0.750981i	0.303211	−	0.952924i	$-0.401941\pi$
$283$	−11.3752	−	12.6335i	−0.676187	−	0.750981i	−0.979397	+	0.201942i	$0.935275\pi$
$284$	−62.4821	+	27.8188i	−3.70763	+	1.65074i
$285$	4.85410	−	2.80252i	0.287532	−	0.166007i
$286$	−11.9666	−	17.8206i	−0.707601	−	1.05375i
$287$	11.4721			0.677179
$288$	−26.3435	−	19.1396i	−1.55230	−	1.12781i
$289$	−4.19098	+	12.8985i	−0.246528	+	0.758736i
$290$	−10.5108	+	11.6735i	−0.617218	+	0.685490i
$291$	−6.10844	−	8.40755i	−0.358083	−	0.492859i
$292$	3.47772	+	33.0883i	0.203518	+	1.93634i
$293$	6.67063	+	1.41789i	0.389703	+	0.0828338i	0.398596	−	0.917127i	$-0.369498\pi$
$293$	6.67063	+	1.41789i	0.389703	+	0.0828338i	−0.00889341	+	0.999960i	$0.502831\pi$
$294$	−20.2190	+	18.2053i	−1.17920	+	1.06176i
$295$	0.209057	−	1.98904i	0.0121718	−	0.115807i
$296$	−45.5066			−2.64502
$297$	13.5584	+	10.6382i	0.786736	+	0.617290i
$298$	−18.7984			−1.08896
$299$	−0.615520	+	5.85629i	−0.0355965	+	0.338678i
$300$	−34.1901	+	30.7849i	−1.97396	+	1.77737i
$301$	−4.74803	−	1.00922i	−0.273672	−	0.0581707i
$302$	−3.09953	−	29.4900i	−0.178358	−	1.69696i
$303$	−0.480669	−	0.661585i	−0.0276137	−	0.0380070i
$304$	6.59368	−	7.32302i	0.378174	−	0.420004i
$305$	4.14590	−	12.7598i	0.237393	−	0.730622i
$306$	−13.3033	+	5.92302i	−0.760501	+	0.338597i
$307$	1.14590			0.0653999			0.0326999	−	0.999465i	$-0.489589\pi$
$307$	1.14590			0.0653999			0.0326999	+	0.999465i	$0.489589\pi$
$308$	9.93789	−	12.6658i	0.566264	−	0.721704i
$309$	−8.64590	+	4.99171i	−0.491848	+	0.283969i
$310$	12.5231	−	5.57563i	0.711262	−	0.316674i
$311$	−4.80459	−	5.33603i	−0.272443	−	0.302579i	0.591361	−	0.806407i	$-0.298591\pi$
$311$	−4.80459	−	5.33603i	−0.272443	−	0.302579i	−0.863804	+	0.503829i	$0.831924\pi$
$312$	−23.7767	−	21.4086i	−1.34609	−	1.21202i
$313$	−4.99904	−	2.22572i	−0.282563	−	0.125805i	0.260562	−	0.965457i	$-0.416092\pi$
$313$	−4.99904	−	2.22572i	−0.282563	−	0.125805i	−0.543125	+	0.839652i	$0.682759\pi$
$314$	29.3435	−	21.3193i	1.65595	−	1.20312i
$315$	6.49606	−	7.21460i	0.366011	−	0.406497i
$316$	−14.3435	+	44.1446i	−0.806883	+	2.48333i
$317$	−0.319411	+	3.03899i	−0.0179399	+	0.170687i	−0.999823	−	0.0187996i	$-0.994016\pi$
$317$	−0.319411	+	3.03899i	−0.0179399	+	0.170687i	0.981883	+	0.189486i	$0.0606822\pi$
$318$			32.1509i			1.80293i
$319$	2.70713	−	5.52142i	0.151570	−	0.309140i
$320$	−14.0902	+	24.4049i	−0.787664	+	1.36427i
$321$	−10.5916	−	23.7891i	−0.591165	−	1.32778i
$322$	−6.09979	+	1.29655i	−0.339928	+	0.0722540i
$323$	−0.572949	−	1.76336i	−0.0318797	−	0.0981157i
$324$	39.9100	+	17.7691i	2.21722	+	0.987171i
$325$	−10.9443	+	7.95148i	−0.607079	+	0.441069i
$326$	−12.7738	+	14.1868i	−0.707476	+	0.785732i
$327$	−17.8325	+	16.0565i	−0.986140	+	0.887924i
$328$	78.3104	−	34.8660i	4.32397	−	1.92515i
$329$	−2.97214	+	5.14789i	−0.163859	+	0.283812i
$330$	25.8758	−	41.2200i	1.42441	−	2.26909i
$331$	6.20820	+	10.7529i	0.341234	+	0.591034i	0.984662	−	0.174472i	$-0.0558219\pi$
$331$	6.20820	+	10.7529i	0.341234	+	0.591034i	−0.643428	+	0.765506i	$0.722489\pi$
$332$	55.9058	+	40.6179i	3.06823	+	2.22920i
$333$	17.8713	−	3.79865i	0.979339	−	0.208165i
$334$	8.28115	+	25.4868i	0.453125	+	1.39457i
$335$	17.7378	+	7.89736i	0.969118	+	0.431479i
$336$	6.94210	−	15.5922i	0.378723	−	0.850625i
$337$	2.47262	+	0.525572i	0.134692	+	0.0286298i	0.274765	−	0.961512i	$-0.411400\pi$
$337$	2.47262	+	0.525572i	0.134692	+	0.0286298i	−0.140072	+	0.990141i	$0.544733\pi$
$338$	12.0674	+	13.4022i	0.656380	+	0.728984i
$339$	−21.9867	−	2.31089i	−1.19415	−	0.125510i
$340$	14.5623	+	25.2227i	0.789752	+	1.36789i
$341$	−4.11803	+	3.44095i	−0.223004	+	0.186338i
$342$	−3.92705	+	6.80185i	−0.212351	+	0.367802i
$343$	−10.5172	−	7.64121i	−0.567877	−	0.412586i
$344$	−35.4779	+	7.54106i	−1.91284	+	0.406587i
$345$	−12.6976	+	4.12569i	−0.683613	+	0.222119i
$346$	−3.25923	−	31.0095i	−0.175217	−	1.66708i
$347$	−2.81062	−	26.7412i	−0.150882	−	1.43555i	−0.763828	−	0.645420i	$-0.776682\pi$
$347$	−2.81062	−	26.7412i	−0.150882	−	1.43555i	0.612946	−	0.790125i	$-0.289984\pi$
$348$	3.24102	−	15.2478i	0.173737	−	0.817369i
$349$	10.6169	−	2.25669i	0.568310	−	0.120798i	0.0852099	−	0.996363i	$-0.472844\pi$
$349$	10.6169	−	2.25669i	0.568310	−	0.120798i	0.483100	+	0.875565i	$0.339511\pi$
$350$	−11.5902	−	8.42075i	−0.619521	−	0.450108i
$351$	11.1246	+	6.42280i	0.593788	+	0.342824i
$352$	8.78115	−	34.9116i	0.468037	−	1.86079i
$353$	−5.20820	−	9.02087i	−0.277205	−	0.480133i	0.693484	−	0.720472i	$-0.256075\pi$
$353$	−5.20820	−	9.02087i	−0.277205	−	0.480133i	−0.970689	+	0.240339i	$0.922741\pi$
$354$	1.13989	+	2.56023i	0.0605843	+	0.136075i
$355$	−30.5102	−	33.8850i	−1.61931	−	1.79843i
$356$	53.3492	+	11.3397i	2.82750	+	0.601004i
$357$	−1.88761	−	2.59808i	−0.0999031	−	0.137505i
$358$	54.8757	+	24.4322i	2.90027	+	1.29128i
$359$	−4.98936	−	15.3557i	−0.263328	−	0.810441i	−0.992074	−	0.125656i	$-0.959896\pi$
$359$	−4.98936	−	15.3557i	−0.263328	−	0.810441i	0.728746	−	0.684784i	$-0.240104\pi$
$360$	22.4164	−	68.9906i	1.18145	−	3.63612i
$361$	14.5623	+	10.5801i	0.766437	+	0.556849i
$362$	−27.6074	−	47.8174i	−1.45101	−	2.51323i
$363$	−5.32730	+	18.2926i	−0.279610	+	0.960114i
$364$	6.00000	−	10.3923i	0.314485	−	0.544705i
$365$	−20.2627	+	9.02156i	−1.06060	+	0.472210i
$366$	3.90871	+	18.3890i	0.204312	+	0.961210i
$367$	0.473881	−	0.526298i	0.0247364	−	0.0274725i	−0.730650	−	0.682753i	$-0.760783\pi$
$367$	0.473881	−	0.526298i	0.0247364	−	0.0274725i	0.755386	+	0.655280i	$0.227449\pi$
$368$	−18.9894	+	13.7966i	−0.989889	+	0.719196i
$369$	−27.8435	+	20.2295i	−1.44947	+	1.05310i
$370$	−15.9443	−	49.0714i	−0.828903	−	2.55110i
$371$	−6.93523	+	1.47413i	−0.360059	+	0.0765330i
$372$	−7.99606	+	11.0056i	−0.414576	+	0.570615i
$373$	−12.8262	+	22.2157i	−0.664117	+	1.15029i	0.315406	+	0.948957i	$0.397859\pi$
$373$	−12.8262	+	22.2157i	−0.664117	+	1.15029i	−0.979524	+	0.201328i	$0.935474\pi$
$374$	−11.5577	−	11.2074i	−0.597633	−	0.579520i
$375$	−2.29180	−	1.32317i	−0.118348	−	0.0683282i
$376$	−4.64278	+	44.1731i	−0.239433	+	2.27805i
$377$	1.41641	−	4.35926i	0.0729487	−	0.224513i
$378$	−2.82837	+	13.3064i	−0.145476	+	0.684409i
$379$	7.11803	−	5.17155i	0.365629	−	0.265645i	−0.389767	−	0.920913i	$-0.627445\pi$
$379$	7.11803	−	5.17155i	0.365629	−	0.265645i	0.755396	+	0.655269i	$0.227445\pi$
$380$	14.3502	+	6.38910i	0.736148	+	0.327754i
$381$	3.44352	−	16.2005i	0.176417	−	0.829975i
$382$	20.9241	+	23.2385i	1.07057	+	1.18899i
$383$	12.0094	−	5.34692i	0.613650	−	0.273215i	−0.0762846	−	0.997086i	$-0.524306\pi$
$383$	12.0094	−	5.34692i	0.613650	−	0.273215i	0.689935	+	0.723871i	$0.257639\pi$
$384$		−	1.88823i		−	0.0963583i
$385$	10.0779	+	3.69169i	0.513620	+	0.188146i
$386$	28.7984			1.46580
$387$	13.3033	−	5.92302i	0.676246	−	0.301084i
$388$	9.00000	−	27.6992i	0.456906	−	1.40621i
$389$	5.78964	−	6.43004i	0.293546	−	0.326016i	−0.578274	−	0.815843i	$-0.696273\pi$
$389$	5.78964	−	6.43004i	0.293546	−	0.326016i	0.871820	+	0.489827i	$0.162940\pi$
$390$	14.7550	−	33.1403i	0.747148	−	1.67812i
$391$	0.461640	+	4.39221i	0.0233462	+	0.222124i
$392$	−43.8531	−	9.32127i	−2.21492	−	0.470795i
$393$	−6.03692	−	28.4015i	−0.304522	−	1.43266i
$394$	1.03003	−	9.80012i	0.0518924	−	0.493723i
$395$	−30.9443			−1.55698
$396$	−1.78537	+	48.2647i	−0.0897184	+	2.42539i
$397$	38.1246			1.91342			0.956710	−	0.291044i	$-0.0940026\pi$
$397$	38.1246			1.91342			0.956710	+	0.291044i	$0.0940026\pi$
$398$	−3.79130	+	36.0718i	−0.190041	+	1.80812i
$399$	−1.64728	−	0.535233i	−0.0824671	−	0.0267952i
$400$	−52.7446	−	11.2112i	−2.63723	−	0.560561i
$401$	0.581419	+	5.53184i	0.0290347	+	0.276247i	0.999401	+	0.0346079i	$0.0110182\pi$
$401$	0.581419	+	5.53184i	0.0290347	+	0.276247i	−0.970366	+	0.241639i	$0.922315\pi$
$402$	−27.0584	+	2.84395i	−1.34955	+	0.141843i
$403$	−2.67652	+	2.97258i	−0.133327	+	0.148075i
$404$	0.708204	−	2.17963i	0.0352345	−	0.108441i
$405$	−3.04435	+	28.9651i	−0.151275	+	1.43929i
$406$	4.85410			0.240905
$407$	11.2604	+	16.7689i	0.558156	+	0.831203i
$408$	−20.7812	−	11.9980i	−1.02882	−	0.593990i
$409$	7.98680	−	3.55595i	0.394922	−	0.175831i	−0.199661	−	0.979865i	$-0.563984\pi$
$409$	7.98680	−	3.55595i	0.394922	−	0.175831i	0.594583	+	0.804034i	$0.297317\pi$
$410$	65.0351	+	72.2288i	3.21186	+	3.56713i
$411$	10.5129	−	3.41584i	0.518562	−	0.168491i
$412$	−25.5598	−	11.3800i	−1.25924	−	0.560651i
$413$	−0.500000	+	0.363271i	−0.0246034	+	0.0178754i
$414$	12.5182	−	13.9029i	0.615238	−	0.683291i
$415$	−14.2361	+	43.8141i	−0.698821	+	2.15075i
$416$	2.80479	−	26.6858i	0.137516	−	1.30838i
$417$	−5.56231	+	3.21140i	−0.272387	+	0.157263i
$418$	−8.59602	−	1.22622i	−0.420445	−	0.0599765i
$419$	1.54508	−	2.67617i	0.0754823	−	0.130739i	−0.825814	−	0.563943i	$-0.809284\pi$
$419$	1.54508	−	2.67617i	0.0754823	−	0.130739i	0.901296	+	0.433204i	$0.142617\pi$
$420$	27.0584	+	2.84395i	1.32031	+	0.138770i
$421$	−5.63798	+	1.19839i	−0.274778	+	0.0584059i	−0.343240	−	0.939248i	$-0.611524\pi$
$421$	−5.63798	+	1.19839i	−0.274778	+	0.0584059i	0.0684615	+	0.997654i	$0.478191\pi$
$422$	−9.32624	−	28.7032i	−0.453994	−	1.39725i
$423$	−1.86404	−	17.7351i	−0.0906326	−	0.862311i
$424$	−42.8607	+	31.1401i	−2.08150	+	1.51230i
$425$	−6.78893	+	7.53987i	−0.329312	+	0.365737i
$426$	60.7657	+	19.7440i	2.94411	+	0.956599i
$427$	−3.78747	+	1.68629i	−0.183288	+	0.0816052i
$428$	36.4894	−	63.2014i	1.76378	−	3.05496i
$429$	−2.00552	+	14.0590i	−0.0968275	+	0.678776i
$430$	−20.5623	−	35.6150i	−0.991602	−	1.71751i
$431$	−19.4721	−	14.1473i	−0.937940	−	0.681453i	0.00998408	−	0.999950i	$-0.496822\pi$
$431$	−19.4721	−	14.1473i	−0.937940	−	0.681453i	−0.947924	+	0.318497i	$0.896822\pi$
$432$	10.6458	+	50.0845i	0.512196	+	2.40969i
$433$	−8.57295	−	26.3848i	−0.411990	−	1.26797i	−0.914916	−	0.403644i	$-0.867743\pi$
$433$	−8.57295	−	26.3848i	−0.411990	−	1.26797i	0.502926	−	0.864329i	$-0.332257\pi$
$434$	−3.86984	−	1.72296i	−0.185758	−	0.0827049i
$435$	10.3354	−	1.08629i	0.495543	−	0.0520837i
$436$	−65.7797	−	13.9819i	−3.15027	−	0.669612i
$437$	1.59385	+	1.77015i	0.0762440	+	0.0846776i
$438$	18.2686	−	25.1446i	0.872907	−	1.20145i
$439$	−6.35410	−	11.0056i	−0.303265	−	0.525270i	0.673609	−	0.739088i	$-0.264743\pi$
$439$	−6.35410	−	11.0056i	−0.303265	−	0.525270i	−0.976873	+	0.213818i	$0.931410\pi$
$440$	80.0132	−	5.42882i	3.81448	−	0.258809i
$441$	18.0000			0.857143
$442$	−9.70820	−	7.05342i	−0.461772	−	0.335497i
$443$	−3.16535	+	0.672816i	−0.150390	+	0.0319665i	−0.282492	−	0.959270i	$-0.591161\pi$
$443$	−3.16535	+	0.672816i	−0.150390	+	0.0319665i	0.132101	+	0.991236i	$0.457828\pi$
$444$	38.0516	+	34.2618i	1.80585	+	1.62599i
$445$	3.80073	+	36.1615i	0.180172	+	1.71422i
$446$	6.15913	+	58.6002i	0.291643	+	2.77480i
$447$	9.24228	+	8.32179i	0.437145	+	0.393607i
$448$	8.51791	−	1.81054i	0.402433	−	0.0855399i
$449$	1.19098	+	0.865300i	0.0562060	+	0.0408360i	0.615533	−	0.788111i	$-0.288941\pi$
$449$	1.19098	+	0.865300i	0.0562060	+	0.0408360i	−0.559328	+	0.828947i	$0.688941\pi$
$450$	42.9787			2.02604
$451$	−32.2254	−	20.2295i	−1.51744	−	0.952568i
$452$	−30.9787	−	53.6567i	−1.45712	−	2.52380i
$453$	−11.5309	+	15.8710i	−0.541771	+	0.745684i
$454$	25.1944	+	27.9812i	1.18243	+	1.31322i
$455$	7.82518	+	1.66329i	0.366850	+	0.0779764i
$456$	−12.8712	+	1.35282i	−0.602750	+	0.0633516i
$457$	−0.913545	−	0.406737i	−0.0427339	−	0.0190263i	0.385258	−	0.922809i	$-0.374112\pi$
$457$	−0.913545	−	0.406737i	−0.0427339	−	0.0190263i	−0.427992	+	0.903782i	$0.640779\pi$
$458$	9.85410	+	30.3278i	0.460452	+	1.41713i
$459$	9.16267	+	2.97713i	0.427677	+	0.138961i
$460$	−30.2705	−	21.9928i	−1.41137	−	1.02542i
$461$	11.4271	+	19.7922i	0.532211	+	0.921816i	0.999293	+	0.0376022i	$0.0119720\pi$
$461$	11.4271	+	19.7922i	0.532211	+	0.921816i	−0.467082	+	0.884214i	$0.654695\pi$
$462$	−14.8163	+	2.58094i	−0.689319	+	0.120076i
$463$	−8.50000	+	14.7224i	−0.395029	+	0.684209i	−0.993105	−	0.117230i	$-0.962599\pi$
$463$	−8.50000	+	14.7224i	−0.395029	+	0.684209i	0.598076	+	0.801439i	$0.295932\pi$
$464$	16.6909	−	7.43129i	0.774857	−	0.344989i
$465$	−8.62526	−	2.80252i	−0.399987	−	0.129964i
$466$	−51.0207	+	56.6642i	−2.36349	+	2.62492i
$467$	4.23607	−	3.07768i	0.196022	−	0.142418i	−0.485445	−	0.874267i	$-0.661342\pi$
$467$	4.23607	−	3.07768i	0.196022	−	0.142418i	0.681467	+	0.731849i	$0.261342\pi$
$468$	3.76302	+	35.8028i	0.173946	+	1.65498i
$469$	−1.85410	−	5.70634i	−0.0856145	−	0.263494i
$470$	−49.2602	+	10.4706i	−2.27220	+	0.482972i
$471$	−23.8646	−	2.50827i	−1.09962	−	0.115575i
$472$	−2.30902	+	3.99933i	−0.106281	+	0.184084i
$473$	11.5577	+	11.2074i	0.531422	+	0.515316i
$474$	37.5517	−	21.6805i	1.72480	−	0.995817i
$475$	−0.571994	+	5.44216i	−0.0262449	+	0.249703i
$476$	2.78115	−	8.55951i	0.127474	−	0.392324i
$477$	14.2327	−	15.8071i	0.651673	−	0.723756i
$478$	3.23607	−	2.35114i	0.148014	−	0.107539i
$479$	−14.8324	−	6.60380i	−0.677709	−	0.301735i	0.0388671	−	0.999244i	$-0.487625\pi$
$479$	−14.8324	−	6.60380i	−0.677709	−	0.301735i	−0.716576	+	0.697509i	$0.754292\pi$
$480$	57.8600	−	18.7999i	2.64094	−	0.858092i
$481$	10.0742	+	11.1886i	0.459346	+	0.510156i
$482$	−64.1759	+	28.5729i	−2.92313	+	1.30146i
$483$	3.57295	+	2.06284i	0.162575	+	0.0938626i
$484$	−50.2501	+	18.0545i	−2.28410	+	0.820661i
$485$	19.4164			0.881654
$486$	−16.5994	−	37.2828i	−0.752963	−	1.69118i
$487$	10.5000	−	32.3157i	0.475800	−	1.46436i	−0.369075	−	0.929400i	$-0.620325\pi$
$487$	10.5000	−	32.3157i	0.475800	−	1.46436i	0.844875	−	0.534963i	$-0.179675\pi$
$488$	−20.7288	+	23.0217i	−0.938349	+	1.04214i
$489$	12.5606	−	1.32017i	0.568009	−	0.0597001i
$490$	−5.31348	−	50.5543i	−0.240038	−	2.28381i
$491$	8.14429	+	1.73112i	0.367547	+	0.0781245i	0.387983	−	0.921667i	$-0.373172\pi$
$491$	8.14429	+	1.73112i	0.367547	+	0.0781245i	−0.0204359	+	0.999791i	$0.506505\pi$
$492$	−91.7318	−	29.8055i	−4.13559	−	1.34373i
$493$	0.359337	−	3.41886i	0.0161837	−	0.153978i
$494$	−6.47214			−0.291195
$495$	−30.9694	+	8.81108i	−1.39197	+	0.396029i
$496$	−15.9443			−0.715919
$497$	−1.47282	+	14.0130i	−0.0660652	+	0.628568i
$498$	−13.4216	−	63.1437i	−0.601437	−	2.82954i
$499$	−11.3305	−	2.40836i	−0.507221	−	0.107813i	−0.0528088	−	0.998605i	$-0.516817\pi$
$499$	−11.3305	−	2.40836i	−0.507221	−	0.107813i	−0.454412	+	0.890791i	$0.650151\pi$
$500$	−0.775226	−	7.37578i	−0.0346691	−	0.329855i
$501$	7.21119	−	16.1966i	0.322172	−	0.723611i
$502$	−0.766755	+	0.851568i	−0.0342220	+	0.0380073i
$503$	−5.70820	+	17.5680i	−0.254516	+	0.783320i	0.739408	+	0.673257i	$0.235105\pi$
$503$	−5.70820	+	17.5680i	−0.254516	+	0.783320i	−0.993925	+	0.110063i	$0.964895\pi$
$504$	−20.4784	+	9.11757i	−0.912181	+	0.406129i
$505$	1.52786			0.0679891
$506$	19.4207	+	7.11407i	0.863356	+	0.316259i
$507$		−	11.9313i		−	0.529888i
$508$	42.4035	−	18.8793i	1.88135	−	0.837631i
$509$	−3.22498	−	3.58171i	−0.142945	−	0.158756i	0.667421	−	0.744681i	$-0.267398\pi$
$509$	−3.22498	−	3.58171i	−0.142945	−	0.158756i	−0.810366	+	0.585924i	$0.800732\pi$
$510$	5.65674	−	26.6129i	0.250485	−	1.17844i
$511$	6.26153	+	2.78781i	0.276994	+	0.123326i
$512$	−32.6074	+	23.6907i	−1.44106	+	1.04699i
$513$	4.94183	−	1.60570i	0.218187	−	0.0708934i
$514$	21.1074	−	64.9619i	0.931007	−	2.86535i
$515$	1.94971	−	18.5503i	0.0859147	−	0.817424i
$516$	35.3435	+	20.4056i	1.55591	+	0.898304i
$517$	17.4263	−	9.21958i	0.766410	−	0.405477i
$518$	−7.97214	+	13.8081i	−0.350276	+	0.606695i
$519$	−12.1251	+	16.6888i	−0.532232	+	0.732555i
$520$	58.4708	−	12.4284i	2.56411	−	0.545019i
$521$	1.34752	+	4.14725i	0.0590361	+	0.181694i	0.976226	−	0.216757i	$-0.0695478\pi$
$521$	1.34752	+	4.14725i	0.0590361	+	0.181694i	−0.917190	+	0.398451i	$0.869548\pi$
$522$	−11.7812	+	8.55951i	−0.515647	+	0.374640i
$523$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$523$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$524$	54.4497	−	60.4725i	2.37865	−	2.64176i
$525$	1.97059	+	9.27090i	0.0860036	+	0.404615i
$526$	−1.69381	+	0.754131i	−0.0738535	+	0.0328817i
$527$	−1.50000	+	2.59808i	−0.0653410	+	0.113174i
$528$	−46.9951	+	31.5574i	−2.04520	+	1.37336i
$529$	8.66312	+	15.0050i	0.376657	+	0.652390i
$530$	−48.5967	−	35.3076i	−2.11091	−	1.53366i
$531$	0.572949	−	1.76336i	0.0248639	−	0.0765231i
$532$	−1.50000	−	4.61653i	−0.0650332	−	0.200152i
$533$	−25.9088	−	11.5353i	−1.12223	−	0.499651i
$534$	−29.9481	−	41.2200i	−1.29598	−	1.78376i
$535$	47.5893	+	10.1154i	2.05746	+	0.437328i
$536$	−29.9990	−	33.3173i	−1.29576	−	1.43909i
$537$	−16.1640	−	36.3049i	−0.697527	−	1.56667i
$538$	16.0623	+	27.8207i	0.692495	+	1.19944i
$539$	7.41641	+	18.4661i	0.319447	+	0.795391i
$540$	−70.6869	+	40.8111i	−3.04188	+	1.75623i
$541$	18.6803	+	13.5721i	0.803131	+	0.583508i	0.911831	−	0.410566i	$-0.134669\pi$
$541$	18.6803	+	13.5721i	0.803131	+	0.583508i	−0.108700	+	0.994075i	$0.534669\pi$
$542$	39.0169	−	8.29329i	1.67592	−	0.356228i
$543$	−7.59486	+	35.7310i	−0.325927	+	1.53336i
$544$	−2.10359	−	20.0144i	−0.0901909	−	0.858109i
$545$	−4.68631	−	44.5872i	−0.200739	−	1.90991i
$546$	−10.6614	+	3.46410i	−0.456266	+	0.148250i
$547$	16.3094	−	3.46667i	0.697340	−	0.148224i	0.154416	−	0.988006i	$-0.450651\pi$
$547$	16.3094	−	3.46667i	0.697340	−	0.148224i	0.542924	+	0.839782i	$0.317317\pi$
$548$	25.0623	+	18.2088i	1.07061	+	0.777843i
$549$	6.21885	−	10.7714i	0.265414	−	0.459710i
$550$	17.7082	+	44.0916i	0.755080	+	1.88007i
$551$	−0.927051	−	1.60570i	−0.0394937	−	0.0684051i
$552$	30.6588	+	3.22237i	1.30493	+	0.137153i
$553$	6.39843	+	7.10618i	0.272089	+	0.302185i
$554$	−37.8078	−	8.03630i	−1.60630	−	0.341430i
$555$	−13.8842	+	31.1844i	−0.589352	+	1.32371i
$556$	−16.4438	−	7.32126i	−0.697373	−	0.310491i
$557$	9.47214	+	29.1522i	0.401347	+	1.23522i	0.923907	+	0.382617i	$0.124977\pi$
$557$	9.47214	+	29.1522i	0.401347	+	1.23522i	−0.522560	+	0.852603i	$0.675023\pi$
$558$	12.4305	−	2.64218i	0.526225	−	0.111853i
$559$	9.70820	+	7.05342i	0.410613	+	0.298328i
$560$	15.9443	+	27.6163i	0.673768	+	1.16700i
$561$	0.721004	+	10.6266i	0.0304408	+	0.448654i
$562$	8.28115	−	14.3434i	0.349319	−	0.605039i
$563$	38.6475	−	17.2070i	1.62880	−	0.725187i	0.630115	−	0.776502i	$-0.283008\pi$
$563$	38.6475	−	17.2070i	1.62880	−	0.725187i	0.998683	+	0.0513142i	$0.0163410\pi$
$564$	37.1400	−	33.4410i	1.56388	−	1.40812i
$565$	27.6384	−	30.6956i	1.16276	−	1.29137i
$566$	−36.0066	+	26.1603i	−1.51347	+	1.09960i
$567$	7.28115	−	5.29007i	0.305780	−	0.222162i
$568$	32.5344	+	100.131i	1.36511	+	4.20139i
$569$	−13.8913	+	2.95268i	−0.582353	+	0.123783i	−0.489663	−	0.871912i	$-0.662880\pi$
$569$	−13.8913	+	2.95268i	−0.582353	+	0.123783i	−0.0926905	+	0.995695i	$0.529547\pi$
$570$	−5.96852	−	13.4055i	−0.249994	−	0.561495i
$571$	13.7361	−	23.7916i	0.574837	−	0.995646i	−0.421223	−	0.906957i	$-0.638399\pi$
$571$	13.7361	−	23.7916i	0.574837	−	0.995646i	0.996059	−	0.0886889i	$-0.0282677\pi$
$572$	−35.1794	+	18.6120i	−1.47093	+	0.778208i
$573$		−	20.6881i		−	0.864257i
$574$	3.13945	−	29.8699i	0.131038	−	1.24675i
$575$	4.02786	−	12.3965i	0.167974	−	0.516969i
$576$	−17.4808	+	19.4144i	−0.728366	+	0.808932i
$577$	−6.94427	+	5.04531i	−0.289094	+	0.210039i	−0.722874	−	0.690980i	$-0.757179\pi$
$577$	−6.94427	+	5.04531i	−0.289094	+	0.210039i	0.433780	+	0.901019i	$0.357179\pi$
$578$	32.4369	+	14.4418i	1.34920	+	0.600701i
$579$	−14.1588	−	12.7487i	−0.588420	−	0.529816i
$580$	19.4882	+	21.6438i	0.809202	+	0.898710i
$581$	13.0053	−	5.79033i	0.539551	−	0.240223i
$582$	−23.5623	+	13.6037i	−0.976689	+	0.563892i
$583$	22.0806	+	8.08843i	0.914485	+	0.334988i
$584$	51.2148			2.11928
$585$	−21.9251	+	9.76168i	−0.906491	+	0.403596i
$586$	5.51722	−	16.9803i	0.227914	−	0.701448i
$587$	−8.97733	+	9.97033i	−0.370534	+	0.411520i	−0.899359	−	0.437211i	$-0.855966\pi$
$587$	−8.97733	+	9.97033i	−0.370534	+	0.411520i	0.528825	+	0.848731i	$0.322633\pi$
$588$	29.6510	+	40.8111i	1.22279	+	1.68302i
$589$	0.169131	+	1.60917i	0.00696891	+	0.0663047i
$590$	−5.12165	−	1.08864i	−0.210855	−	0.0448186i
$591$	−4.84480	+	4.36228i	−0.199288	+	0.179440i
$592$	−6.27308	+	59.6844i	−0.257822	+	2.45301i
$593$	6.94427			0.285167			0.142584	−	0.989783i	$-0.454459\pi$
$593$	6.94427			0.285167			0.142584	+	0.989783i	$0.454459\pi$
$594$	31.4089	−	32.3906i	1.28872	−	1.32900i
$595$	6.00000			0.245976
$596$	−3.64325	+	34.6632i	−0.149233	+	1.41986i
$597$	17.8325	−	16.0565i	0.729836	−	0.657147i
$598$	15.0795	+	3.20525i	0.616648	+	0.131072i
$599$	−3.27808	−	31.1889i	−0.133939	−	1.27434i	−0.830570	−	0.556914i	$-0.811985\pi$
$599$	−3.27808	−	31.1889i	−0.133939	−	1.27434i	0.696631	−	0.717429i	$-0.254681\pi$
$600$	41.6276	+	57.2954i	1.69944	+	2.33908i
$601$	−5.70625	+	6.33744i	−0.232763	+	0.258509i	−0.848199	−	0.529677i	$-0.822313\pi$
$601$	−5.70625	+	6.33744i	−0.232763	+	0.258509i	0.615436	+	0.788187i	$0.288980\pi$
$602$	−3.92705	+	12.0862i	−0.160055	+	0.492598i
$603$	14.5623	+	10.5801i	0.593023	+	0.430856i
$604$	−54.9787			−2.23705
$605$	−21.7994	−	28.1410i	−0.886270	−	1.14409i
$606$	−1.85410	+	1.07047i	−0.0753177	+	0.0434847i
$607$	−27.7868	+	12.3715i	−1.12783	+	0.502142i	−0.883912	−	0.467653i	$-0.845100\pi$
$607$	−27.7868	+	12.3715i	−1.12783	+	0.502142i	−0.243918	+	0.969796i	$0.578433\pi$
$608$	−7.26281	−	8.06617i	−0.294546	−	0.327126i
$609$	−2.38653	−	2.14885i	−0.0967073	−	0.0870756i
$610$	−32.0879	−	14.2865i	−1.29920	−	0.578442i
$611$	11.8885	−	8.63753i	0.480959	−	0.349437i
$612$	8.34346	+	25.6785i	0.337264	+	1.03799i
$613$	4.06231	−	12.5025i	0.164075	−	0.504971i	−0.834892	−	0.550414i	$-0.814470\pi$
$613$	4.06231	−	12.5025i	0.164075	−	0.504971i	0.998967	+	0.0454430i	$0.0144699\pi$
$614$	0.313585	−	2.98357i	0.0126553	−	0.120407i
$615$		−	64.3017i		−	2.59290i
$616$	−17.7912	−	17.2520i	−0.716829	−	0.695104i
$617$	−21.0795	+	36.5108i	−0.848630	+	1.46987i	0.0338015	+	0.999429i	$0.489239\pi$
$617$	−21.0795	+	36.5108i	−0.848630	+	1.46987i	−0.882431	+	0.470441i	$0.844095\pi$
$618$	10.6309	+	23.8773i	0.427636	+	0.960485i
$619$	−7.27516	+	1.54638i	−0.292413	+	0.0621544i	−0.351783	−	0.936082i	$-0.614424\pi$
$619$	−7.27516	+	1.54638i	−0.292413	+	0.0621544i	0.0593692	+	0.998236i	$0.481091\pi$
$620$	−7.85410	−	24.1724i	−0.315428	−	0.970789i
$621$	−12.3093	+	1.29375i	−0.493953	+	0.0519166i
$622$	−15.2082	+	11.0494i	−0.609793	+	0.443041i
$623$	7.51840	−	8.35003i	0.301218	−	0.334537i
$624$	−31.3562	+	28.2333i	−1.25525	+	1.13023i
$625$	−20.4784	+	9.11757i	−0.819136	+	0.364703i
$626$	−7.16312	+	12.4069i	−0.286296	+	0.495879i
$627$	3.68343	+	4.40822i	0.147102	+	0.176047i
$628$	−33.6246	−	58.2395i	−1.34177	−	2.32401i
$629$	9.13525	+	6.63715i	0.364246	+	0.264641i
$630$	−17.0069	−	18.8881i	−0.677571	−	0.752519i
$631$	7.69098	+	23.6704i	0.306173	+	0.942304i	0.979237	+	0.202720i	$0.0649780\pi$
$631$	7.69098	+	23.6704i	0.306173	+	0.942304i	−0.673064	+	0.739585i	$0.735022\pi$
$632$	65.2736	+	29.0617i	2.59644	+	1.15601i
$633$	−8.12125	+	18.2406i	−0.322791	+	0.725000i
$634$	7.82518	+	1.66329i	0.310778	+	0.0660578i
$635$	20.7058	+	22.9961i	0.821683	+	0.912571i
$636$	59.2844	+	6.23104i	2.35078	+	0.247077i
$637$	7.41641	+	12.8456i	0.293849	+	0.508961i
$638$	−13.6353	−	8.55951i	−0.539825	−	0.338874i
$639$	−21.1353	−	36.6073i	−0.836098	−	1.44816i
$640$	2.85410	+	2.07363i	0.112818	+	0.0819673i
$641$	−34.6762	+	7.37065i	−1.36963	+	0.291123i	−0.833269	−	0.552868i	$-0.813533\pi$
$641$	−34.6762	+	7.37065i	−1.36963	+	0.291123i	−0.536357	+	0.843991i	$0.680200\pi$
$642$	−64.8380	+	21.0671i	−2.55895	+	0.831454i
$643$	0.0152505	+	0.145099i	0.000601421	+	0.00572214i	0.994818	−	0.101667i	$-0.0324176\pi$
$643$	0.0152505	+	0.145099i	0.000601421	+	0.00572214i	−0.994217	+	0.107389i	$0.965751\pi$
$644$	1.20859	+	11.4990i	0.0476251	+	0.453123i
$645$	−5.65674	+	26.6129i	−0.222734	+	1.04788i
$646$	−4.74803	+	1.00922i	−0.186809	+	0.0397074i
$647$	−14.7082	−	10.6861i	−0.578239	−	0.420115i	0.259850	−	0.965649i	$-0.416327\pi$
$647$	−14.7082	−	10.6861i	−0.578239	−	0.420115i	−0.838089	+	0.545534i	$0.816327\pi$
$648$	33.6246	−	58.2395i	1.32090	−	2.28787i
$649$	2.04508	−	0.138757i	0.0802766	−	0.00544670i
$650$	17.7082	+	30.6715i	0.694573	+	1.20304i
$651$	1.13989	+	2.56023i	0.0446757	+	0.100343i
$652$	23.6840	+	26.3037i	0.927535	+	1.03013i
$653$	−42.4131	−	9.01519i	−1.65975	−	0.352792i	−0.719824	−	0.694157i	$-0.755777\pi$
$653$	−42.4131	−	9.01519i	−1.65975	−	0.352792i	−0.939931	+	0.341365i	$0.889111\pi$
$654$	36.9261	+	50.8244i	1.44392	+	1.98739i
$655$	49.5591	+	22.0651i	1.93644	+	0.862157i
$656$	−34.9336	−	107.515i	−1.36393	−	4.19774i
$657$	−20.1130	+	4.27514i	−0.784682	+	0.166789i
$658$	12.5902	+	9.14729i	0.490816	+	0.356599i
$659$	18.4894	+	32.0245i	0.720243	+	1.24750i	0.960902	+	0.276888i	$0.0893031\pi$
$659$	18.4894	+	32.0245i	0.720243	+	1.24750i	−0.240659	+	0.970610i	$0.577364\pi$
$660$	−70.9925	−	55.7022i	−2.76338	−	2.16821i
$661$	8.85410	−	15.3358i	0.344385	−	0.596492i	−0.640857	−	0.767660i	$-0.721421\pi$
$661$	8.85410	−	15.3358i	0.344385	−	0.596492i	0.985242	+	0.171168i	$0.0547542\pi$
$662$	29.6962	−	13.2216i	1.15418	−	0.513873i
$663$	1.65061	+	7.76553i	0.0641045	+	0.301588i
$664$	71.1780	−	79.0512i	2.76224	−	3.06778i
$665$	2.61803	−	1.90211i	0.101523	−	0.0737608i
$666$	−4.99989	−	47.5708i	−0.193742	−	1.84333i
$667$	1.36475	+	4.20025i	0.0528431	+	0.162634i
$668$	48.6011	−	10.3305i	1.88043	−	0.399699i
$669$	22.9134	−	31.5375i	0.885882	−	1.21931i
$670$	25.4164	−	44.0225i	0.981922	−	1.70074i
$671$	13.6126	+	1.94184i	0.525508	+	0.0749638i
$672$	−16.2812	−	9.39993i	−0.628059	−	0.362610i
$673$	0.986508	−	9.38599i	0.0380271	−	0.361803i	−0.958917	−	0.283686i	$-0.908443\pi$
$673$	0.986508	−	9.38599i	0.0380271	−	0.361803i	0.996944	−	0.0781171i	$-0.0248908\pi$
$674$	2.04508	−	6.29412i	0.0787737	−	0.242441i
$675$	−21.1306	−	19.0261i	−0.813318	−	0.732315i
$676$	27.0517	−	19.6542i	1.04045	−	0.755930i
$677$	21.8742	+	9.73901i	0.840693	+	0.374301i	0.781469	−	0.623944i	$-0.214471\pi$
$677$	21.8742	+	9.73901i	0.840693	+	0.374301i	0.0592240	+	0.998245i	$0.481137\pi$
$678$	−12.0337	+	56.6141i	−0.462152	+	2.17425i
$679$	−4.01478	−	4.45887i	−0.154073	−	0.171116i
$680$	40.9568	−	18.2351i	1.57062	−	0.699286i
$681$		−	24.9103i		−	0.954565i
$682$	7.83225	+	11.6637i	0.299912	+	0.446628i
$683$	−14.4721			−0.553761			−0.276880	−	0.960904i	$-0.589301\pi$
$683$	−14.4721			−0.553761			−0.276880	+	0.960904i	$0.589301\pi$
$684$	11.7812	+	8.55951i	0.450464	+	0.327281i
$685$	−6.38197	+	19.6417i	−0.243842	+	0.750470i
$686$	−22.7735	+	25.2925i	−0.869496	+	0.965673i
$687$	8.58091	−	19.2730i	0.327382	−	0.735312i
$688$	4.99989	+	47.5708i	0.190619	+	1.81362i
$689$	17.1448	+	3.64425i	0.653166	+	0.138835i
$690$	7.26722	+	34.1896i	0.276658	+	1.30157i
$691$	3.61634	−	34.4072i	0.137572	−	1.30891i	−0.680054	−	0.733162i	$-0.738043\pi$
$691$	3.61634	−	34.4072i	0.137572	−	1.30891i	0.817626	−	0.575750i	$-0.195290\pi$
$692$	−57.8115			−2.19766
$693$	8.42705	+	5.29007i	0.320117	+	0.200953i
$694$	−70.3951			−2.67216
$695$	1.25434	−	11.9343i	0.0475799	−	0.452692i
$696$	−22.8216	−	7.41517i	−0.865049	−	0.281071i
$697$	−20.8057	−	4.42239i	−0.788072	−	0.167510i
$698$	−2.97032	−	28.2607i	−0.112428	−	1.06968i
$699$	50.1690	−	5.27297i	1.89756	−	0.199442i
$700$	−17.7737	+	19.7396i	−0.671781	+	0.746088i
$701$	12.8926	−	39.6794i	0.486947	−	1.49867i	−0.342194	−	0.939629i	$-0.611170\pi$
$701$	12.8926	−	39.6794i	0.486947	−	1.49867i	0.829141	−	0.559040i	$-0.188830\pi$
$702$	19.7673	−	27.2074i	0.746070	−	1.02688i
$703$	6.09017			0.229695
$704$	−27.1196	−	9.93427i	−1.02211	−	0.374412i
$705$	28.8541	+	16.6589i	1.08671	+	0.627411i
$706$	−24.9129	+	11.0919i	−0.937607	+	0.417450i
$707$	−0.315921	−	0.350865i	−0.0118814	−	0.0131957i
$708$	4.94183	−	1.60570i	0.185726	−	0.0603459i
$709$	−27.6220	−	12.2981i	−1.03737	−	0.461865i	−0.183863	−	0.982952i	$-0.558860\pi$
$709$	−27.6220	−	12.2981i	−1.03737	−	0.461865i	−0.853504	+	0.521086i	$0.825527\pi$
$710$	−96.5755	+	70.1662i	−3.62441	+	2.63329i
$711$	−28.0600	−	5.96435i	−1.05233	−	0.223680i
$712$	25.9443	−	79.8483i	0.972303	−	2.99244i
$713$	0.402863	−	3.83299i	0.0150874	−	0.143547i
$714$	−7.28115	+	4.20378i	−0.272490	+	0.157322i
$715$	−19.0481	−	18.4708i	−0.712358	−	0.690769i
$716$	55.6869	−	96.4526i	2.08112	−	3.60460i
$717$	−2.63184	−	0.276618i	−0.0982879	−	0.0103305i
$718$	−41.3468	+	8.78853i	−1.54305	+	0.327985i
$719$	9.14590	+	28.1482i	0.341084	+	1.04975i	0.963647	+	0.267180i	$0.0860917\pi$
$719$	9.14590	+	28.1482i	0.341084	+	1.04975i	−0.622562	+	0.782570i	$0.713908\pi$
$720$	−87.3949	−	38.9107i	−3.25702	−	1.45012i
$721$	−4.66312	+	3.38795i	−0.173664	+	0.126174i
$722$	31.5325	−	35.0204i	1.17352	−	1.30332i
$723$	44.2011	+	14.3618i	1.64386	+	0.534122i
$724$	−93.5232	+	41.6392i	−3.47576	+	1.54751i
$725$	−5.07295	+	8.78661i	−0.188405	+	0.326326i
$726$	46.1705	+	18.8766i	1.71355	+	0.700575i
$727$	17.4164	+	30.1661i	0.645939	+	1.11880i	0.984084	+	0.177705i	$0.0568672\pi$
$727$	17.4164	+	30.1661i	0.645939	+	1.11880i	−0.338145	+	0.941094i	$0.609799\pi$
$728$	−14.9443	−	10.8576i	−0.553872	−	0.402411i
$729$	−8.34346	+	25.6785i	−0.309017	+	0.951057i
$730$	17.9443	+	55.2268i	0.664147	+	2.04404i
$731$	8.22191	+	3.66063i	0.304098	+	0.135393i
$732$	34.6659	−	3.64353i	1.28129	−	0.134669i
$733$	−38.6641	−	8.21831i	−1.42809	−	0.303550i	−0.571948	−	0.820290i	$-0.693812\pi$
$733$	−38.6641	−	8.21831i	−1.42809	−	0.303550i	−0.856142	+	0.516740i	$0.827145\pi$
$734$	−1.24064	−	1.37787i	−0.0457927	−	0.0508580i
$735$	−19.7673	+	27.2074i	−0.729129	+	1.00356i
$736$	12.9271	+	22.3903i	0.476497	+	0.825318i
$737$	−4.85410	+	19.2986i	−0.178803	+	0.710875i
$738$	45.0517	+	78.0318i	1.65837	+	2.87239i
$739$	19.8541	+	14.4248i	0.730345	+	0.530627i	0.889673	−	0.456599i	$-0.150933\pi$
$739$	19.8541	+	14.4248i	0.730345	+	0.530627i	−0.159328	+	0.987226i	$0.550933\pi$
$740$	−93.5751	+	19.8900i	−3.43989	+	0.731171i
$741$	3.18205	+	2.86513i	0.116895	+	0.105253i
$742$	1.94029	+	18.4606i	0.0712303	+	0.677711i
$743$	−0.246758	−	2.34775i	−0.00905268	−	0.0861305i	0.989063	−	0.147496i	$-0.0471212\pi$
$743$	−0.246758	−	2.34775i	−0.00905268	−	0.0861305i	−0.998115	+	0.0613652i	$0.980455\pi$
$744$	15.5620	+	14.0121i	0.570532	+	0.513709i
$745$	−22.7283	+	4.83105i	−0.832701	+	0.176996i
$746$	54.3328	+	39.4751i	1.98927	+	1.44529i
$747$	−21.3541	+	36.9864i	−0.781306	+	1.35326i
$748$	−22.9058	+	19.1396i	−0.837518	+	0.699815i
$749$	−7.51722	−	13.0202i	−0.274673	−	0.475748i
$750$	−4.07230	+	5.60503i	−0.148699	+	0.204667i
$751$	32.9542	+	36.5993i	1.20251	+	1.33553i	0.927379	+	0.374122i	$0.122056\pi$
$751$	32.9542	+	36.5993i	1.20251	+	1.33553i	0.275135	+	0.961406i	$0.411277\pi$
$752$	57.2954	+	12.1785i	2.08935	+	0.444105i
$753$	0.753955	−	0.0792439i	0.0274757	−	0.00288781i
$754$	−10.9625	−	4.88084i	−0.399232	−	0.177750i
$755$	−11.3262	−	34.8586i	−0.412204	−	1.26863i
$756$	23.9882	+	7.79423i	0.872441	+	0.283473i
$757$	−8.89919	−	6.46564i	−0.323446	−	0.234998i	0.414198	−	0.910187i	$-0.364062\pi$
$757$	−8.89919	−	6.46564i	−0.323446	−	0.234998i	−0.737645	+	0.675189i	$0.764062\pi$
$758$	−11.5172	−	19.9484i	−0.418324	−	0.724559i
$759$	−6.39895	−	12.0949i	−0.232267	−	0.439019i
$760$	12.0902	−	20.9408i	0.438557	−	0.759602i
$761$	−36.5224	+	16.2608i	−1.32393	+	0.589454i	−0.942272	−	0.334848i	$-0.891315\pi$
$761$	−36.5224	+	16.2608i	−1.32393	+	0.589454i	−0.381663	+	0.924302i	$0.624648\pi$
$762$	−41.2387	−	13.3993i	−1.49392	−	0.485404i
$763$	−9.27020	+	10.2956i	−0.335604	+	0.372726i
$764$	46.9058	−	34.0790i	1.69699	−	1.23294i
$765$	−14.5623	+	10.5801i	−0.526501	+	0.382526i
$766$	−10.6353	−	32.7319i	−0.384267	−	1.18265i
$767$	1.49448	−	0.317661i	0.0539624	−	0.0114701i
$768$	25.0845	+	2.63649i	0.905158	+	0.0951360i
$769$	−4.39919	+	7.61962i	−0.158639	+	0.274770i	−0.934378	−	0.356283i	$-0.884044\pi$
$769$	−4.39919	+	7.61962i	−0.158639	+	0.274770i	0.775739	+	0.631054i	$0.217377\pi$
$770$	12.3699	−	25.2296i	0.445782	−	0.909212i
$771$	−39.1353	+	22.5947i	−1.40942	+	0.813730i
$772$	5.58131	−	53.1026i	0.200876	−	1.91121i
$773$	−2.36475	+	7.27794i	−0.0850540	+	0.261769i	−0.984534	−	0.175192i	$-0.943945\pi$
$773$	−2.36475	+	7.27794i	−0.0850540	+	0.261769i	0.899480	+	0.436961i	$0.143945\pi$
$774$	−11.7812	−	36.2587i	−0.423465	−	1.30329i
$775$	7.16312	−	5.20431i	0.257307	−	0.186944i
$776$	−40.9568	−	18.2351i	−1.47026	−	0.654604i
$777$	10.0322	−	3.25966i	0.359903	−	0.116940i
$778$	−15.1575	−	16.8341i	−0.543421	−	0.603531i
$779$	−10.4803	+	4.66614i	−0.375496	+	0.167182i
$780$	−58.2492	−	33.6302i	−2.08566	−	1.20415i
$781$	28.8471	−	36.7656i	1.03223	−	1.31558i
$782$	11.5623			0.413467
$783$	9.58142	+	1.00705i	0.342412	+	0.0359890i
$784$	−18.2705	+	56.2308i	−0.652518	+	2.00824i
$785$	29.9990	−	33.3173i	1.07071	−	1.18914i
$786$	−75.6008	+	7.94596i	−2.69659	+	0.283423i
$787$	−3.76302	−	35.8028i	−0.134137	−	1.27623i	−0.829881	−	0.557941i	$-0.811592\pi$
$787$	−3.76302	−	35.8028i	−0.134137	−	1.27623i	0.695743	−	0.718291i	$-0.255075\pi$
$788$	−17.8713	−	3.79865i	−0.636637	−	0.135321i
$789$	1.16661	+	0.379054i	0.0415324	+	0.0134947i
$790$	−8.46818	+	80.5694i	−0.301284	+	2.86653i
$791$	−12.7639			−0.453833
$792$	73.6017	+	10.4993i	2.61532	+	0.373076i
$793$	10.2492			0.363961
$794$	10.4331	−	99.2648i	0.370258	−	3.52277i
$795$	8.26254	+	38.8722i	0.293042	+	1.37866i
$796$	65.7797	+	13.9819i	2.33150	+	0.495575i
$797$	0.969032	+	9.21973i	0.0343249	+	0.326579i	0.998188	+	0.0601798i	$0.0191674\pi$
$797$	0.969032	+	9.21973i	0.0343249	+	0.326579i	−0.963863	+	0.266400i	$0.914166\pi$
$798$	−1.84437	+	4.14253i	−0.0652902	+	0.146644i
$799$	7.37468	−	8.19041i	0.260897	−	0.289756i
$800$	−18.3541	+	56.4881i	−0.648915	+	1.99716i
$801$	−3.52347	+	33.5235i	−0.124496	+	1.18450i
$802$	14.5623			0.514213
$803$	−12.6728	−	18.8723i	−0.447215	−	0.665990i
$804$			50.4453i			1.77907i
$805$	−7.04179	+	3.13521i	−0.248191	+	0.110502i
$806$	7.00723	+	7.78231i	0.246819	+	0.274120i
$807$	4.41878	−	20.7887i	0.155548	−	0.731797i
$808$	−3.22286	−	1.43491i	−0.113380	−	0.0504800i
$809$	5.59017	−	4.06150i	0.196540	−	0.142795i	−0.485163	−	0.874424i	$-0.661240\pi$
$809$	5.59017	−	4.06150i	0.196540	−	0.142795i	0.681703	+	0.731629i	$0.261240\pi$
$810$	74.5830	+	15.8531i	2.62058	+	0.557021i
$811$	−15.9721	+	49.1572i	−0.560858	+	1.72614i	0.119092	+	0.992883i	$0.462002\pi$
$811$	−15.9721	+	49.1572i	−0.560858	+	1.72614i	−0.679950	+	0.733259i	$0.737998\pi$
$812$	0.940756	−	8.95070i	0.0330141	−	0.314108i
$813$	−22.8541	−	13.1948i	−0.801528	−	0.462763i
$814$	46.7425	−	24.7296i	1.63833	−	0.866772i
$815$	−11.7984	+	20.4354i	−0.413279	+	0.715820i
$816$	−18.6007	+	25.6017i	−0.651156	+	0.896239i
$817$	4.74803	−	1.00922i	0.166112	−	0.0353083i
$818$	−7.07295	−	21.7683i	−0.247300	−	0.761111i
$819$	6.77523	+	3.01652i	0.236746	+	0.105406i
$820$	145.790	−	105.923i	5.09122	−	3.69899i
$821$	−8.84241	+	9.82050i	−0.308602	+	0.342738i	−0.877417	−	0.479728i	$-0.840735\pi$
$821$	−8.84241	+	9.82050i	−0.308602	+	0.342738i	0.568815	+	0.822466i	$0.307402\pi$
$822$	−6.01685	−	28.3071i	−0.209862	−	0.987322i
$823$	−50.8920	+	22.6586i	−1.77398	+	0.789828i	−0.789638	+	0.613573i	$0.789732\pi$
$823$	−50.8920	+	22.6586i	−1.77398	+	0.789828i	−0.984344	+	0.176255i	$0.943602\pi$
$824$	−21.5344	+	37.2987i	−0.750188	+	1.29936i
$825$	10.8125	−	29.5170i	0.376442	−	1.02765i
$826$	0.809017	+	1.40126i	0.0281493	+	0.0487560i
$827$	22.6246	+	16.4377i	0.786735	+	0.571596i	0.906993	−	0.421146i	$-0.138372\pi$
$827$	22.6246	+	16.4377i	0.786735	+	0.571596i	−0.120258	+	0.992743i	$0.538372\pi$
$828$	−23.2101	−	25.7774i	−0.806606	−	0.895827i
$829$	−7.27458	−	22.3888i	−0.252656	−	0.777597i	−0.994282	−	0.106783i	$-0.965945\pi$
$829$	−7.27458	−	22.3888i	−0.252656	−	0.777597i	0.741626	−	0.670814i	$-0.234055\pi$
$830$	110.183	+	49.0565i	3.82449	+	1.70277i
$831$	15.0308	+	20.6881i	0.521412	+	0.717662i
$832$	−21.0574	−	4.47589i	−0.730035	−	0.155174i
$833$	7.44382	+	8.26720i	0.257913	+	0.286441i
$834$	6.83932	+	15.3614i	0.236826	+	0.531920i
$835$	16.5623	+	28.6868i	0.573162	+	0.992746i
$836$	−3.92705	+	15.6129i	−0.135820	+	0.539985i
$837$	−7.28115	−	4.20378i	−0.251673	−	0.145304i
$838$	−6.54508	−	4.75528i	−0.226096	−	0.164269i
$839$	30.0372	−	6.38459i	1.03700	−	0.220421i	0.342201	−	0.939627i	$-0.388828\pi$
$839$	30.0372	−	6.38459i	1.03700	−	0.220421i	0.694797	+	0.719206i	$0.255494\pi$
$840$	8.70767	−	40.9664i	0.300443	−	1.41347i
$841$	2.67199	+	25.4223i	0.0921375	+	0.876630i
$842$	1.57735	+	15.0075i	0.0543591	+	0.517193i
$843$	−10.4211	+	3.38601i	−0.358921	+	0.116620i
$844$	−54.7346	+	11.6342i	−1.88404	+	0.400466i
$845$	18.0344	+	13.1028i	0.620404	+	0.450750i
$846$	−46.6869			−1.60513
$847$	−1.95492	+	10.8249i	−0.0671717	+	0.371948i
$848$	34.9336	+	60.5068i	1.19963	+	2.07781i
$849$	29.2836	+	3.07783i	1.00501	+	0.105631i
$850$	17.7737	+	19.7396i	0.609631	+	0.677064i
$851$	−14.1896	−	3.01609i	−0.486412	−	0.103390i
$852$	48.1836	−	108.222i	1.65074	−	3.70763i
$853$	−50.7587	−	22.5992i	−1.73794	−	0.773783i	−0.994470	−	0.105018i	$-0.966510\pi$
$853$	−50.7587	−	22.5992i	−1.73794	−	0.773783i	−0.743474	−	0.668765i	$-0.766823\pi$
$854$	3.35410	+	10.3229i	0.114775	+	0.353241i
$855$	−3.00000	+	9.23305i	−0.102598	+	0.315764i
$856$	−90.8845	−	66.0314i	−3.10637	−	2.25691i
$857$	9.68034	+	16.7668i	0.330674	+	0.572744i	0.982644	−	0.185500i	$-0.0593906\pi$
$857$	9.68034	+	16.7668i	0.330674	+	0.572744i	−0.651970	+	0.758245i	$0.726057\pi$
$858$	36.0565	+	9.06914i	1.23095	+	0.309615i
$859$	6.21885	−	10.7714i	0.212184	−	0.367514i	−0.740214	−	0.672372i	$-0.765276\pi$
$859$	6.21885	−	10.7714i	0.212184	−	0.367514i	0.952398	+	0.304858i	$0.0986089\pi$
$860$	−69.6571	+	31.0134i	−2.37529	+	1.05755i
$861$	−14.7665	+	13.2958i	−0.503242	+	0.453121i
$862$	−42.1640	+	46.8279i	−1.43611	+	1.59496i
$863$	33.5344	−	24.3642i	1.14153	−	0.829367i	0.154195	−	0.988041i	$-0.450722\pi$
$863$	33.5344	−	24.3642i	1.14153	−	0.829367i	0.987331	+	0.158674i	$0.0507217\pi$
$864$	56.0906	−	5.89536i	1.90824	−	0.200564i
$865$	−11.9098	−	36.6547i	−0.404946	−	1.24630i
$866$	−71.0440	+	15.1009i	−2.41417	+	0.513149i
$867$	−9.55449	−	21.4597i	−0.324487	−	0.728811i
$868$	−3.92705	+	6.80185i	−0.133293	+	0.230870i
$869$	−5.44258	−	31.2441i	−0.184627	−	1.05988i
$870$		−	27.2074i		−	0.922417i
$871$	−1.55045	+	14.7516i	−0.0525350	+	0.499838i
$872$	−31.9894	+	98.4531i	−1.08330	+	3.33404i
$873$	17.6067	+	3.74241i	0.595895	+	0.126661i
$874$	5.04508	−	3.66547i	0.170653	−	0.123986i
$875$	−1.39577	−	0.621438i	−0.0471857	−	0.0210084i
$876$	−42.8246	−	38.5595i	−1.44691	−	1.30280i
$877$	−25.1571	−	27.9398i	−0.849496	−	0.943461i	0.149477	−	0.988765i	$-0.452241\pi$
$877$	−25.1571	−	27.9398i	−0.849496	−	0.943461i	−0.998973	+	0.0453042i	$0.985574\pi$
$878$	−30.3941	+	13.5323i	−1.02575	+	0.456694i
$879$	−10.2295	+	5.90600i	−0.345032	+	0.199204i
$880$	3.90961	−	105.690i	0.131793	−	3.56281i
$881$	24.1803			0.814656			0.407328	−	0.913282i	$-0.366461\pi$
$881$	24.1803			0.814656			0.407328	+	0.913282i	$0.366461\pi$
$882$	4.92586	−	46.8665i	0.165862	−	1.57808i
$883$	−1.34346	+	4.13474i	−0.0452110	+	0.139145i	−0.971114	−	0.238616i	$-0.923306\pi$
$883$	−1.34346	+	4.13474i	−0.0452110	+	0.139145i	0.925903	+	0.377762i	$0.123306\pi$
$884$	−14.8876	+	16.5344i	−0.500725	+	0.556112i
$885$	2.03615	+	2.80252i	0.0684444	+	0.0942056i
$886$	0.885579	+	8.42572i	0.0297516	+	0.283068i
$887$	−24.4874	−	5.20495i	−0.822206	−	0.174765i	−0.222446	−	0.974945i	$-0.571404\pi$
$887$	−24.4874	−	5.20495i	−0.822206	−	0.174765i	−0.599760	+	0.800180i	$0.704737\pi$
$888$	58.5745	−	52.7407i	1.96563	−	1.76986i
$889$	0.999533	−	9.50992i	0.0335233	−	0.318953i
$890$	95.1935			3.19089
$891$	−29.7812	+	2.02063i	−0.997706	+	0.0676935i
$892$	109.249			3.65793
$893$	0.621346	−	5.91171i	0.0207925	−	0.197828i
$894$	24.1966	−	21.7867i	0.809255	−	0.728657i
$895$	72.6267	+	15.4373i	2.42764	+	0.516011i
$896$	−0.113954	−	1.08420i	−0.00380693	−	0.0362205i
$897$	−5.99497	−	8.25137i	−0.200166	−	0.275505i
$898$	2.57890	−	2.86416i	0.0860589	−	0.0955781i
$899$	−0.927051	+	2.85317i	−0.0309189	+	0.0951585i
$900$	8.32955	−	79.2504i	0.277652	−	2.64168i
$901$	13.1459			0.437953
$902$	−61.4901	+	78.3691i	−2.04739	+	2.60941i
$903$	7.28115	−	4.20378i	0.242302	−	0.139893i
$904$	−87.1283	+	38.7920i	−2.89785	+	1.29020i
$905$	−45.6676	−	50.7191i	−1.51804	−	1.68596i
$906$	38.1676	+	34.3663i	1.26803	+	1.14174i
$907$	−37.8358	−	16.8456i	−1.25632	−	0.559348i	−0.332833	−	0.942986i	$-0.608004\pi$
$907$	−37.8358	−	16.8456i	−1.25632	−	0.559348i	−0.923484	+	0.383638i	$0.874671\pi$
$908$	56.4787	−	41.0342i	1.87431	−	1.36177i
$909$	1.38546	+	0.294488i	0.0459527	+	0.00976754i
$910$	6.47214	−	19.9192i	0.214549	−	0.660315i
$911$	−0.332436	+	3.16292i	−0.0110141	+	0.104792i	−0.998648	−	0.0519872i	$-0.983444\pi$
$911$	−0.332436	+	3.16292i	−0.0110141	+	0.104792i	0.987634	+	0.156779i	$0.0501112\pi$
$912$			17.0678i			0.565172i
$913$	−46.7425	−	6.66783i	−1.54695	−	0.220673i
$914$	−1.30902	+	2.26728i	−0.0432984	+	0.0749951i
$915$	9.45171	+	21.2289i	0.312464	+	0.701805i
$916$	57.8326	−	12.2927i	1.91084	−	0.406162i
$917$	−5.18034	−	15.9434i	−0.171070	−	0.526499i
$918$	10.2590	−	23.0420i	0.338597	−	0.760501i
$919$	−45.1976	+	32.8380i	−1.49093	+	1.08322i	−0.517106	+	0.855922i	$0.672991\pi$
$919$	−45.1976	+	32.8380i	−1.49093	+	1.08322i	−0.973824	+	0.227303i	$0.927009\pi$
$920$	−38.5397	+	42.8027i	−1.27062	+	1.41116i
$921$	−1.47496	+	1.32806i	−0.0486016	+	0.0437610i
$922$	54.6600	−	24.3362i	1.80013	−	0.801470i
$923$	17.4164	−	30.1661i	0.573268	−	0.992929i
$924$	1.88761	+	27.8207i	0.0620979	+	0.915235i
$925$	−16.6631	−	28.8614i	−0.547880	−	0.948956i
$926$	36.0066	+	26.1603i	1.18325	+	0.859681i
$927$	5.34346	−	16.4455i	0.175502	−	0.540140i
$928$	−6.21885	−	19.1396i	−0.204144	−	0.628290i
$929$	−13.4561	−	5.99102i	−0.441479	−	0.196559i	0.173945	−	0.984755i	$-0.444349\pi$
$929$	−13.4561	−	5.99102i	−0.441479	−	0.196559i	−0.615424	+	0.788196i	$0.711015\pi$
$930$	−9.65727	+	21.6906i	−0.316674	+	0.711262i
$931$	5.86889	+	1.24747i	0.192345	+	0.0408842i
$932$	94.5976	+	105.061i	3.09865	+	3.44140i
$933$	12.3686	+	1.29999i	0.404929	+	0.0425598i
$934$	−6.85410	−	11.8717i	−0.224273	−	0.388452i
$935$	−16.8541	−	10.5801i	−0.551188	−	0.346007i
$936$	55.4164			1.81134
$937$	−4.88197	−	3.54696i	−0.159487	−	0.115874i	0.505179	−	0.863014i	$-0.331426\pi$
$937$	−4.88197	−	3.54696i	−0.159487	−	0.115874i	−0.664666	+	0.747140i	$0.731426\pi$
$938$	−15.3649	+	3.26592i	−0.501683	+	0.106636i
$939$	9.01413	−	2.92887i	0.294165	−	0.0955800i
$940$	9.76022	+	92.8623i	0.318343	+	3.02884i
$941$	4.40682	+	41.9281i	0.143658	+	1.36682i	0.794343	+	0.607469i	$0.207815\pi$
$941$	4.40682	+	41.9281i	0.143658	+	1.36682i	−0.650685	+	0.759348i	$0.725518\pi$
$942$	−13.0615	+	61.4495i	−0.425567	+	2.00213i
$943$	26.7291	−	5.68144i	0.870419	−	0.185013i
$944$	4.92705	+	3.57971i	0.160362	+	0.116510i
$945$			16.8151i			0.546995i
$946$	32.3435	−	27.0256i	1.05158	−	0.878678i
$947$	−11.6459	−	20.1713i	−0.378441	−	0.655479i	0.612395	−	0.790552i	$-0.290206\pi$
$947$	−11.6459	−	20.1713i	−0.378441	−	0.655479i	−0.990836	+	0.135073i	$0.956873\pi$
$948$	−32.6998	−	73.4450i	−1.06204	−	2.38538i
$949$	−11.3379	−	12.5920i	−0.368045	−	0.408755i
$950$	14.0132	+	2.97859i	0.454647	+	0.0966383i
$951$	−3.11096	−	4.28187i	−0.100880	−	0.138849i
$952$	−12.6564	−	5.63497i	−0.410195	−	0.182630i
$953$	−14.6803	−	45.1814i	−0.475543	−	1.46357i	−0.845224	−	0.534412i	$-0.820533\pi$
$953$	−14.6803	−	45.1814i	−0.475543	−	1.46357i	0.369681	−	0.929159i	$-0.379467\pi$
$954$	−37.2618	−	41.3834i	−1.20640	−	1.33984i
$955$	31.2705	+	22.7194i	1.01189	+	0.735181i
$956$	−3.70820	−	6.42280i	−0.119932	−	0.207728i
$957$	2.91464	+	10.2445i	0.0942168	+	0.331156i
$958$	−21.2533	+	36.8118i	−0.686663	+	1.18933i
$959$	5.83022	−	2.59578i	0.188267	−	0.0838221i
$960$	−10.1481	−	47.7432i	−0.327529	−	1.54090i
$961$	−18.9912	+	21.0919i	−0.612621	+	0.680384i
$962$	31.8885	−	23.1684i	1.02813	−	0.746979i
$963$	41.2039	+	18.3452i	1.32778	+	0.591165i
$964$	40.2492	+	123.874i	1.29634	+	3.98972i
$965$	34.8189	−	7.40098i	1.12086	−	0.238246i
$966$	6.34878	−	8.73834i	0.204269	−	0.281152i
$967$	16.2426	−	28.1331i	0.522328	−	0.904699i	−0.477334	−	0.878722i	$-0.658397\pi$
$967$	16.2426	−	28.1331i	0.522328	−	0.904699i	0.999663	−	0.0259773i	$-0.00826976\pi$
$968$	19.5544	+	79.8336i	0.628502	+	2.56595i
$969$	2.78115	+	1.60570i	0.0893435	+	0.0515825i
$970$	5.31348	−	50.5543i	0.170605	−	1.62320i
$971$	−7.50000	+	23.0826i	−0.240686	+	0.740757i	0.755630	+	0.654999i	$0.227331\pi$
$971$	−7.50000	+	23.0826i	−0.240686	+	0.740757i	−0.996316	+	0.0857575i	$0.972669\pi$
$972$	−71.9645	+	23.3827i	−2.30826	+	0.750000i
$973$	−3.00000	+	2.17963i	−0.0961756	+	0.0698757i
$974$	−81.2667	−	36.1822i	−2.60395	−	1.15935i
$975$	4.87157	−	22.9189i	0.156015	−	0.733993i
$976$	27.3367	+	30.3605i	0.875027	+	0.971816i
$977$	18.4866	−	8.23075i	0.591438	−	0.263325i	−0.0891184	−	0.996021i	$-0.528405\pi$
$977$	18.4866	−	8.23075i	0.591438	−	0.263325i	0.680556	+	0.732696i	$0.261738\pi$
$978$		−	33.0651i		−	1.05731i
$979$	−35.8434	+	10.1978i	−1.14556	+	0.325922i
$980$	−94.2492			−3.01068
$981$	4.34444	−	41.3346i	0.138707	−	1.31971i
$982$	6.73607	−	20.7315i	0.214957	−	0.661568i
$983$	34.6226	−	38.4523i	1.10429	−	1.22644i	0.132350	−	0.991203i	$-0.457748\pi$
$983$	34.6226	−	38.4523i	1.10429	−	1.22644i	0.971939	−	0.235234i	$-0.0755857\pi$
$984$	−60.3897	+	135.638i	−1.92515	+	4.32397i
$985$	−1.27319	−	12.1136i	−0.0405673	−	0.385972i
$986$	−8.80333	−	1.87121i	−0.280355	−	0.0595913i
$987$	−2.14061	−	10.0708i	−0.0681365	−	0.320557i
$988$	−1.25434	+	11.9343i	−0.0399059	+	0.379679i
$989$	−11.5623			−0.367660
$990$	14.4663	+	83.0461i	0.459768	+	2.63938i
$991$	−28.5967			−0.908406			−0.454203	−	0.890898i	$-0.650076\pi$
$991$	−28.5967			−0.908406			−0.454203	+	0.890898i	$0.650076\pi$
$992$	−1.83576	+	17.4661i	−0.0582855	+	0.554549i
$993$	−20.4533	−	6.64567i	−0.649065	−	0.210894i
$994$	36.0824	+	7.66956i	1.14447	+	0.243264i
$995$	4.68631	+	44.5872i	0.148566	+	1.41351i
$996$	−119.035	+	12.5111i	−3.77176	+	0.396428i
$997$	6.43572	−	7.14759i	0.203821	−	0.226367i	−0.632565	−	0.774508i	$-0.717998\pi$
$997$	6.43572	−	7.14759i	0.203821	−	0.226367i	0.836386	+	0.548141i	$0.184664\pi$
$998$	−9.37132	+	28.8420i	−0.296644	+	0.912976i
$999$	−18.6007	+	25.6017i	−0.588501	+	0.810002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.m.a.4.1	✓	8
3.2	odd	2		297.2.n.a.37.1		8
9.2	odd	6		297.2.n.a.235.1		8
9.4	even	3		891.2.f.b.730.1		4
9.5	odd	6		891.2.f.a.730.1		4
9.7	even	3	inner	99.2.m.a.70.1	yes	8
11.3	even	5	inner	99.2.m.a.58.1	yes	8
11.5	even	5		1089.2.e.g.364.2		4
11.6	odd	10		1089.2.e.d.364.1		4
33.14	odd	10		297.2.n.a.91.1		8
99.5	odd	30		9801.2.a.bb.1.2		2
99.14	odd	30		891.2.f.a.487.1		4
99.16	even	15		1089.2.e.g.727.2		4
99.25	even	15	inner	99.2.m.a.25.1	yes	8
99.47	odd	30		297.2.n.a.289.1		8
99.49	even	15		9801.2.a.n.1.1		2
99.50	even	30		9801.2.a.m.1.1		2
99.58	even	15		891.2.f.b.487.1		4
99.61	odd	30		1089.2.e.d.727.1		4
99.94	odd	30		9801.2.a.bc.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.a.4.1	✓	8	1.1	even	1	trivial
99.2.m.a.25.1	yes	8	99.25	even	15	inner
99.2.m.a.58.1	yes	8	11.3	even	5	inner
99.2.m.a.70.1	yes	8	9.7	even	3	inner
297.2.n.a.37.1		8	3.2	odd	2
297.2.n.a.91.1		8	33.14	odd	10
297.2.n.a.235.1		8	9.2	odd	6
297.2.n.a.289.1		8	99.47	odd	30
891.2.f.a.487.1		4	99.14	odd	30
891.2.f.a.730.1		4	9.5	odd	6
891.2.f.b.487.1		4	99.58	even	15
891.2.f.b.730.1		4	9.4	even	3
1089.2.e.d.364.1		4	11.6	odd	10
1089.2.e.d.727.1		4	99.61	odd	30
1089.2.e.g.364.2		4	11.5	even	5
1089.2.e.g.727.2		4	99.16	even	15
9801.2.a.m.1.1		2	99.50	even	30
9801.2.a.n.1.1		2	99.49	even	15
9801.2.a.bb.1.2		2	99.5	odd	30
9801.2.a.bc.1.2		2	99.94	odd	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.273659 - 2.60369i) q^{2} +(-1.28716 + 1.15897i) q^{3} +(-4.74803 - 1.00922i) q^{4} +(-0.338261 - 3.21834i) q^{5} +(2.66535 + 3.66854i) q^{6} +(-0.669131 + 0.743145i) q^{7} +(-2.30902 + 7.10642i) q^{8} +(0.313585 - 2.98357i) q^{9} -8.47214 q^{10} +(3.19003 - 0.907591i) q^{11} +(7.28115 - 4.20378i) q^{12} +(2.25841 - 1.00551i) q^{13} +(1.75181 + 1.94558i) q^{14} +(4.16535 + 3.75050i) q^{15} +(9.00217 + 4.00802i) q^{16} +(1.50000 - 1.08981i) q^{17} +(-7.68247 - 1.63296i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-1.64195 + 15.6222i) q^{20} -1.73205i q^{21} +(-1.49011 - 8.55422i) q^{22} +(-1.19098 + 2.06284i) q^{23} +(-5.26403 - 11.8232i) q^{24} +(-5.35256 + 1.13772i) q^{25} +(-2.00000 - 6.15537i) q^{26} +(3.05422 + 4.20378i) q^{27} +(3.92705 - 2.85317i) q^{28} +(1.24064 - 1.37787i) q^{29} +(10.9050 - 9.81894i) q^{30} +(-1.47815 + 0.658114i) q^{31} +(5.42705 - 9.39993i) q^{32} +(-3.05422 + 4.86536i) q^{33} +(-2.42705 - 4.20378i) q^{34} +(2.61803 + 1.90211i) q^{35} +(-4.50000 + 13.8496i) q^{36} +(1.88197 + 5.79210i) q^{37} +(-2.39169 - 1.06485i) q^{38} +(-1.74159 + 3.91168i) q^{39} +(23.6519 + 5.02738i) q^{40} +(-7.67636 - 8.52546i) q^{41} +(-4.50973 - 0.473991i) q^{42} +(2.42705 + 4.20378i) q^{43} +(-16.0623 + 1.08981i) q^{44} -9.70820 q^{45} +(5.04508 + 3.66547i) q^{46} +(5.81438 - 1.23588i) q^{47} +(-16.2324 + 5.27424i) q^{48} +(0.627171 + 5.96713i) q^{49} +(1.49750 + 14.2478i) q^{50} +(-0.667687 + 3.14122i) q^{51} +(-11.7378 + 2.49494i) q^{52} +(5.73607 + 4.16750i) q^{53} +(11.7812 - 6.80185i) q^{54} +(-4.00000 - 9.95959i) q^{55} +(-3.73607 - 6.47106i) q^{56} +(0.704489 + 1.58231i) q^{57} +(-3.24803 - 3.60730i) q^{58} +(0.604528 + 0.128496i) q^{59} +(-15.9921 - 22.0113i) q^{60} +(3.78747 + 1.68629i) q^{61} +(1.30902 + 4.02874i) q^{62} +(2.00739 + 2.22943i) q^{63} +(-7.04508 - 5.11855i) q^{64} +(-4.00000 - 6.92820i) q^{65} +(11.8321 + 9.28370i) q^{66} +(-3.00000 + 5.19615i) q^{67} +(-8.22191 + 3.66063i) q^{68} +(-0.857778 - 4.03553i) q^{69} +(5.66897 - 6.29602i) q^{70} +(11.3992 - 8.28199i) q^{71} +(20.4784 + 9.11757i) q^{72} +(-2.11803 - 6.51864i) q^{73} +(15.5959 - 3.31500i) q^{74} +(5.57104 - 7.66788i) q^{75} +(-2.42705 + 4.20378i) q^{76} +(-1.46007 + 2.97795i) q^{77} +(9.70820 + 5.60503i) q^{78} +(0.999533 - 9.50992i) q^{79} +(9.85410 - 30.3278i) q^{80} +(-8.80333 - 1.87121i) q^{81} +(-24.2984 + 17.6538i) q^{82} +(-13.0053 - 5.79033i) q^{83} +(-1.74803 + 8.22383i) q^{84} +(-4.01478 - 4.45887i) q^{85} +(11.6095 - 5.16889i) q^{86} +3.21140i q^{87} +(-0.916102 + 24.7653i) q^{88} -11.2361 q^{89} +(-2.65674 + 25.2772i) q^{90} +(-0.763932 + 2.35114i) q^{91} +(7.73669 - 8.59247i) q^{92} +(1.13989 - 2.56023i) q^{93} +(-1.62670 - 15.4771i) q^{94} +(-3.16535 - 0.672816i) q^{95} +(3.90871 + 18.3890i) q^{96} +(-0.627171 + 5.96713i) q^{97} +15.7082 q^{98} +(-1.70751 - 9.80227i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 3 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} - 14 q^{8} - 3 q^{9} - 32 q^{10} + q^{11} + 18 q^{12} + 8 q^{13} - q^{14} + 12 q^{15} + 14 q^{16} + 12 q^{17} - 3 q^{18} - 2 q^{19} + 24 q^{20} + 11 q^{22}+ \cdots - 3 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 3 * q^3 - 6 * q^4 + 6 * q^5 - q^7 - 14 * q^8 - 3 * q^9 - 32 * q^10 + q^11 + 18 * q^12 + 8 * q^13 - q^14 + 12 * q^15 + 14 * q^16 + 12 * q^17 - 3 * q^18 - 2 * q^19 + 24 * q^20 + 11 * q^22 - 14 * q^23 - 39 * q^24 - 9 * q^25 - 16 * q^26 + 18 * q^28 - 9 * q^29 + 18 * q^30 - 3 * q^31 + 30 * q^32 - 6 * q^34 + 12 * q^35 - 36 * q^36 + 24 * q^37 - 4 * q^38 - 24 * q^39 + 12 * q^40 + 3 * q^41 - 12 * q^42 + 6 * q^43 - 48 * q^44 - 24 * q^45 + 18 * q^46 + 23 * q^47 - 6 * q^49 - 24 * q^50 + 27 * q^51 + 12 * q^52 + 28 * q^53 + 54 * q^54 - 32 * q^55 - 12 * q^56 + 3 * q^57 + 6 * q^58 + 3 * q^59 + 6 * q^62 + 3 * q^63 - 34 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 9 * q^68 - 18 * q^69 - 6 * q^70 + 42 * q^71 + 39 * q^72 - 8 * q^73 + 13 * q^74 - 6 * q^76 - 11 * q^77 + 24 * q^78 - 22 * q^79 + 52 * q^80 + 9 * q^81 - 96 * q^82 - 17 * q^83 + 18 * q^84 - 6 * q^85 + 21 * q^86 + 37 * q^88 - 72 * q^89 + 42 * q^90 - 24 * q^91 - 21 * q^92 + 9 * q^93 + 28 * q^94 - 4 * q^95 + 6 * q^97 + 72 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

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