LMFDB - Embedded newform 99.2.m.a.70.1

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			70.1
Root			$-0.978148 + 0.207912i$ of defining polynomial
Character	$\chi$	$=$	99.70
Dual form			99.2.m.a.58.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.39169 + 1.06485i) q^{2} +(0.360114 + 1.69420i) q^{3} +(3.24803 - 3.60730i) q^{4} +(2.95630 + 1.31623i) q^{5} +(-2.66535 - 3.66854i) q^{6} +(0.978148 + 0.207912i) q^{7} +(-2.30902 + 7.10642i) q^{8} +(-2.74064 + 1.22021i) q^{9} -8.47214 q^{10} +(-2.38101 - 2.30885i) q^{11} +(7.28115 + 4.20378i) q^{12} +(-0.258409 + 2.45859i) q^{13} +(-2.56082 + 0.544320i) q^{14} +(-1.16535 + 5.48255i) q^{15} +(-1.03003 - 9.80012i) q^{16} +(1.50000 - 1.08981i) q^{17} +(5.25542 - 5.83674i) q^{18} +(0.309017 - 0.951057i) q^{19} +(14.3502 - 6.38910i) q^{20} +1.73205i q^{21} +(8.15323 + 2.98664i) q^{22} +(-1.19098 - 2.06284i) q^{23} +(-12.8712 - 1.35282i) q^{24} +(3.66157 + 4.06659i) q^{25} +(-2.00000 - 6.15537i) q^{26} +(-3.05422 - 4.20378i) q^{27} +(3.92705 - 2.85317i) q^{28} +(-1.81359 - 0.385489i) q^{29} +(-3.05093 - 14.3535i) q^{30} +(0.169131 - 1.60917i) 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} +(0.273659 + 2.60369i) q^{38} +(-4.25841 + 0.447577i) q^{39} +(-16.1798 + 17.9695i) q^{40} +(11.2214 - 2.38519i) q^{41} +(-1.84437 - 4.14253i) q^{42} +(2.42705 - 4.20378i) q^{43} +(-16.0623 + 1.08981i) q^{44} -9.70820 q^{45} +(5.04508 + 3.66547i) q^{46} +(-3.97749 - 4.41745i) q^{47} +(16.2324 - 5.27424i) q^{48} +(-5.48127 - 2.44042i) q^{49} +(-13.0877 - 5.82701i) q^{50} +(2.38653 + 2.14885i) q^{51} +(8.02957 + 8.91774i) 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} +(1.72256 + 0.181049i) q^{57} +(4.74803 - 1.00922i) q^{58} +(-0.413545 + 0.459289i) q^{59} +(15.9921 + 22.0113i) q^{60} +(-0.433364 - 4.12319i) q^{61} +(1.30902 + 4.02874i) q^{62} +(-2.93444 + 0.623735i) q^{63} +(-7.04508 - 5.11855i) q^{64} +(-4.00000 + 6.92820i) q^{65} +(-2.12388 + 14.8887i) q^{66} +(-3.00000 - 5.19615i) q^{67} +(0.940756 - 8.95070i) q^{68} +(3.06598 - 2.76062i) q^{69} +(-8.28700 - 1.76146i) q^{70} +(11.3992 - 8.28199i) q^{71} +(-2.34315 - 22.2936i) q^{72} +(-2.11803 - 6.51864i) q^{73} +(-10.6688 - 11.8489i) q^{74} +(-5.57104 + 7.66788i) q^{75} +(-2.42705 - 4.20378i) q^{76} +(-1.84894 - 2.75344i) q^{77} +(9.70820 - 5.60503i) q^{78} +(-8.73560 + 3.88934i) q^{79} +(9.85410 - 30.3278i) q^{80} +(6.02218 - 6.68830i) q^{81} +(-24.2984 + 17.6538i) q^{82} +(1.48807 + 14.1581i) q^{83} +(6.24803 + 5.62575i) q^{84} +(5.86889 - 1.24747i) q^{85} +(-1.32837 + 12.6386i) q^{86} -3.21140i q^{87} +(21.9055 - 11.5893i) q^{88} -11.2361 q^{89} +(23.2190 - 10.3378i) q^{90} +(-0.763932 + 2.35114i) q^{91} +(-11.3096 - 2.40394i) q^{92} +(2.78716 - 0.292943i) q^{93} +(14.2169 + 6.32976i) q^{94} +(2.16535 - 2.40487i) q^{95} +(-13.9710 + 12.5796i) q^{96} +(5.48127 - 2.44042i) q^{97} +15.7082 q^{98} +(9.34277 + 3.42238i) 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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.39169	+	1.06485i	−1.69118	+	0.752963i	−0.691655	+	0.722228i	$0.743118\pi$
$2$	−2.39169	+	1.06485i	−1.69118	+	0.752963i	−0.999528	+	0.0307347i	$0.990215\pi$
$3$	0.360114	+	1.69420i	0.207912	+	0.978148i
$3$	0.360114	+	1.69420i	0.207912	+	0.978148i
$4$	3.24803	−	3.60730i	1.62401	−	1.80365i
$5$	2.95630	+	1.31623i	1.32210	+	0.588635i	0.941782	−	0.336223i	$-0.109150\pi$
$5$	2.95630	+	1.31623i	1.32210	+	0.588635i	0.380313	+	0.924858i	$0.375816\pi$
$6$	−2.66535	−	3.66854i	−1.08813	−	1.49768i
$7$	0.978148	+	0.207912i	0.369705	+	0.0785832i	0.389018	−	0.921230i	$-0.372814\pi$
$7$	0.978148	+	0.207912i	0.369705	+	0.0785832i	−0.0193127	+	0.999813i	$0.506148\pi$
$8$	−2.30902	+	7.10642i	−0.816361	+	2.51250i
$9$	−2.74064	+	1.22021i	−0.913545	+	0.406737i
$10$	−8.47214			−2.67912
$11$	−2.38101	−	2.30885i	−0.717902	−	0.696144i
$11$	−2.38101	−	2.30885i	−0.717902	−	0.696144i
$12$	7.28115	+	4.20378i	2.10189	+	1.21353i
$13$	−0.258409	+	2.45859i	−0.0716696	+	0.681891i	0.898419	+	0.439140i	$0.144717\pi$
$13$	−0.258409	+	2.45859i	−0.0716696	+	0.681891i	−0.970088	+	0.242752i	$0.921950\pi$
$14$	−2.56082	+	0.544320i	−0.684409	+	0.145476i
$15$	−1.16535	+	5.48255i	−0.300893	+	1.41559i
$16$	−1.03003	−	9.80012i	−0.257509	−	2.45003i
$17$	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	$0.227813\pi$
$18$	5.25542	−	5.83674i	1.23871	−	1.37573i
$19$	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	$0.0634068\pi$
$20$	14.3502	−	6.38910i	3.20879	−	1.42865i
$21$			1.73205i			0.377964i
$22$	8.15323	+	2.98664i	1.73827	+	0.636754i
$23$	−1.19098	−	2.06284i	−0.248337	−	0.430133i	0.714727	−	0.699403i	$-0.246551\pi$
$23$	−1.19098	−	2.06284i	−0.248337	−	0.430133i	−0.963065	+	0.269271i	$0.913217\pi$
$24$	−12.8712	−	1.35282i	−2.62733	−	0.276143i
$25$	3.66157	+	4.06659i	0.732315	+	0.813318i
$26$	−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
$29$	−1.81359	−	0.385489i	−0.336774	−	0.0715836i	0.0364206	−	0.999337i	$-0.488404\pi$
$29$	−1.81359	−	0.385489i	−0.336774	−	0.0715836i	−0.373195	+	0.927753i	$0.621738\pi$
$30$	−3.05093	−	14.3535i	−0.557021	−	2.62058i
$31$	0.169131	−	1.60917i	0.0303768	−	0.289016i	−0.968779	−	0.247927i	$-0.920251\pi$
$31$	0.169131	−	1.60917i	0.0303768	−	0.289016i	0.999156	−	0.0410886i	$-0.0130826\pi$
$32$	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	$0.733109\pi$
$38$	0.273659	+	2.60369i	0.0443934	+	0.422375i
$39$	−4.25841	+	0.447577i	−0.681891	+	0.0716696i
$40$	−16.1798	+	17.9695i	−2.55825	+	2.84123i
$41$	11.2214	−	2.38519i	1.75249	−	0.372504i	0.783849	−	0.620951i	$-0.213253\pi$
$41$	11.2214	−	2.38519i	1.75249	−	0.372504i	0.968646	+	0.248447i	$0.0799201\pi$
$42$	−1.84437	−	4.14253i	−0.284593	−	0.639207i
$43$	2.42705	−	4.20378i	0.370122	−	0.641070i	−0.619462	−	0.785027i	$-0.712649\pi$
$43$	2.42705	−	4.20378i	0.370122	−	0.641070i	0.989584	+	0.143957i	$0.0459826\pi$
$44$	−16.0623	+	1.08981i	−2.42148	+	0.164296i
$45$	−9.70820			−1.44721
$46$	5.04508	+	3.66547i	0.743857	+	0.540444i
$47$	−3.97749	−	4.41745i	−0.580177	−	0.644352i	0.379588	−	0.925156i	$-0.376066\pi$
$47$	−3.97749	−	4.41745i	−0.580177	−	0.644352i	−0.959765	+	0.280804i	$0.909399\pi$
$48$	16.2324	−	5.27424i	2.34295	−	0.761271i
$49$	−5.48127	−	2.44042i	−0.783039	−	0.348631i
$50$	−13.0877	−	5.82701i	−1.85088	−	0.824063i
$51$	2.38653	+	2.14885i	0.334182	+	0.300899i
$52$	8.02957	+	8.91774i	1.11350	+	1.23667i
$53$	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
$57$	1.72256	+	0.181049i	0.228159	+	0.0239805i
$58$	4.74803	−	1.00922i	0.623447	−	0.132518i
$59$	−0.413545	+	0.459289i	−0.0538390	+	0.0597943i	−0.769463	−	0.638692i	$-0.779476\pi$
$59$	−0.413545	+	0.459289i	−0.0538390	+	0.0597943i	0.715624	+	0.698486i	$0.246143\pi$
$60$	15.9921	+	22.0113i	2.06457	+	2.84164i
$61$	−0.433364	−	4.12319i	−0.0554866	−	0.527920i	−0.986596	−	0.163180i	$-0.947825\pi$
$61$	−0.433364	−	4.12319i	−0.0554866	−	0.527920i	0.931110	−	0.364739i	$-0.118842\pi$
$62$	1.30902	+	4.02874i	0.166245	+	0.511650i
$63$	−2.93444	+	0.623735i	−0.369705	+	0.0785832i
$64$	−7.04508	−	5.11855i	−0.880636	−	0.639819i
$65$	−4.00000	+	6.92820i	−0.496139	+	0.859338i
$66$	−2.12388	+	14.8887i	−0.261432	+	1.83268i
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	0.622509	−	0.782613i	$-0.286114\pi$
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	−0.989017	+	0.147802i	$0.952780\pi$
$68$	0.940756	−	8.95070i	0.114083	−	1.08543i
$69$	3.06598	−	2.76062i	0.369101	−	0.332340i
$70$	−8.28700	−	1.76146i	−0.990486	−	0.210534i
$71$	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	$-0.0151684\pi$
$72$	−2.34315	−	22.2936i	−0.276143	−	2.62733i
$73$	−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	$-0.231374\pi$
$74$	−10.6688	−	11.8489i	−1.24022	−	1.37741i
$75$	−5.57104	+	7.66788i	−0.643288	+	0.885410i
$76$	−2.42705	−	4.20378i	−0.278402	−	0.482206i
$77$	−1.84894	−	2.75344i	−0.210707	−	0.313783i
$78$	9.70820	−	5.60503i	1.09924	−	0.634645i
$79$	−8.73560	+	3.88934i	−0.982832	+	0.437585i	−0.834293	−	0.551322i	$-0.814124\pi$
$79$	−8.73560	+	3.88934i	−0.982832	+	0.437585i	−0.148539	+	0.988907i	$0.547457\pi$
$80$	9.85410	−	30.3278i	1.10172	−	3.39075i
$81$	6.02218	−	6.68830i	0.669131	−	0.743145i
$82$	−24.2984	+	17.6538i	−2.68331	+	1.94954i
$83$	1.48807	+	14.1581i	0.163337	+	1.55405i	0.702398	+	0.711784i	$0.252113\pi$
$83$	1.48807	+	14.1581i	0.163337	+	1.55405i	−0.539061	+	0.842267i	$0.681221\pi$
$84$	6.24803	+	5.62575i	0.681716	+	0.613820i
$85$	5.86889	−	1.24747i	0.636570	−	0.135307i
$86$	−1.32837	+	12.6386i	−0.143242	+	1.36285i
$87$		−	3.21140i		−	0.344298i
$88$	21.9055	−	11.5893i	2.33513	−	1.23542i
$89$	−11.2361			−1.19102			−0.595510	−	0.803348i	$-0.703050\pi$
$89$	−11.2361			−1.19102			−0.595510	+	0.803348i	$0.703050\pi$
$90$	23.2190	−	10.3378i	2.44750	−	1.08970i
$91$	−0.763932	+	2.35114i	−0.0800818	+	0.246467i
$92$	−11.3096	−	2.40394i	−1.17911	−	0.250628i
$93$	2.78716	−	0.292943i	0.289016	−	0.0303768i
$94$	14.2169	+	6.32976i	1.46636	+	0.652865i
$95$	2.16535	−	2.40487i	0.222160	−	0.246734i
$96$	−13.9710	+	12.5796i	−1.42591	+	1.28390i
$97$	5.48127	−	2.44042i	0.556539	−	0.247787i	−0.109139	−	0.994027i	$-0.534809\pi$
$97$	5.48127	−	2.44042i	0.556539	−	0.247787i	0.665678	+	0.746239i	$0.268143\pi$
$98$	15.7082			1.58677
$99$	9.34277	+	3.42238i	0.938983	+	0.343963i
$100$	26.5623			2.65623
$101$	0.431318	−	0.192035i	0.0429177	−	0.0191082i	−0.385166	−	0.922847i	$-0.625856\pi$
$101$	0.431318	−	0.192035i	0.0429177	−	0.0191082i	0.428083	+	0.903739i	$0.359189\pi$
$102$	−7.99606	−	2.59808i	−0.791728	−	0.257248i
$103$	−3.85682	+	4.28344i	−0.380024	+	0.422060i	−0.902564	−	0.430555i	$-0.858318\pi$
$103$	−3.85682	+	4.28344i	−0.380024	+	0.422060i	0.522540	+	0.852615i	$0.324984\pi$
$104$	−16.8751	−	7.51329i	−1.65474	−	0.736739i
$105$	−2.27977	+	5.12045i	−0.222483	+	0.499705i
$106$	−18.1567	−	3.85932i	−1.76353	−	0.374850i
$107$	−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	$0.841045\pi$
$108$	−25.0845	−	2.63649i	−2.41376	−	0.253696i
$109$	13.8541			1.32698			0.663491	−	0.748184i	$-0.269074\pi$
$109$	13.8541			1.32698			0.663491	+	0.748184i	$0.269074\pi$
$110$	20.1722	+	19.5609i	1.92335	+	1.86506i
$111$	−9.13525	+	5.27424i	−0.867080	+	0.500609i
$112$	1.03003	−	9.80012i	0.0973291	−	0.926024i
$113$	−12.4850	+	2.65377i	−1.17449	+	0.249646i	−0.753518	−	0.657427i	$-0.771645\pi$
$113$	−12.4850	+	2.65377i	−1.17449	+	0.249646i	−0.420973	+	0.907073i	$0.638311\pi$
$114$	−4.31263	+	1.40126i	−0.403915	+	0.131240i
$115$	−0.805727	−	7.66598i	−0.0751344	−	0.714856i
$116$	−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
$119$	1.69381	−	0.754131i	0.155271	−	0.0691311i
$120$	−36.2705	−	20.9408i	−3.31103	−	1.91162i
$121$	0.338426	+	10.9948i	0.0307660	+	0.999527i
$122$	5.42705	+	9.39993i	0.491342	+	0.851029i
$123$	8.08199	+	18.1524i	0.728728	+	1.63675i
$124$	−5.25542	−	5.83674i	−0.471951	−	0.524154i
$125$	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	$0.439465\pi$
$128$	1.06635	+	0.226659i	0.0942527	+	0.0200340i
$129$	7.99606	+	2.59808i	0.704014	+	0.228748i
$130$	2.18927	−	20.8295i	0.192012	−	1.82687i
$131$	−8.38197	−	14.5180i	−0.732336	−	1.26844i	−0.955882	−	0.293750i	$-0.905097\pi$
$131$	−8.38197	−	14.5180i	−0.732336	−	1.26844i	0.223547	−	0.974693i	$-0.428236\pi$
$132$	−7.63062	−	26.8203i	−0.664160	−	2.33441i
$133$	0.500000	−	0.866025i	0.0433555	−	0.0750939i
$134$	12.7082	+	9.23305i	1.09782	+	0.797614i
$135$	−3.49606	−	16.4477i	−0.300893	−	1.41559i
$136$	4.28115	+	13.1760i	0.367106	+	1.12984i
$137$	0.667097	+	6.34700i	0.0569940	+	0.542261i	0.985347	+	0.170562i	$0.0545582\pi$
$137$	0.667097	+	6.34700i	0.0569940	+	0.542261i	−0.928353	+	0.371700i	$0.878775\pi$
$138$	−4.39324	+	9.86737i	−0.373977	+	0.839967i
$139$	−2.48127	+	2.75573i	−0.210459	+	0.233738i	−0.839127	−	0.543935i	$-0.816934\pi$
$139$	−2.48127	+	2.75573i	−0.210459	+	0.233738i	0.628668	+	0.777674i	$0.283600\pi$
$140$	15.3649	−	3.26592i	1.29857	−	0.276021i
$141$	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
$146$	12.0071	+	13.3352i	0.993711	+	1.10363i
$147$	2.16068	−	10.1652i	0.178210	−	0.838412i
$148$	27.0065	+	12.0241i	2.21992	+	0.988373i
$149$	6.55957	+	2.92051i	0.537381	+	0.239257i	0.657437	−	0.753510i	$-0.271641\pi$
$149$	6.55957	+	2.92051i	0.537381	+	0.239257i	−0.120056	+	0.992767i	$0.538307\pi$
$150$	5.15907	−	24.2715i	0.421237	−	1.98176i
$151$	−7.57873	−	8.41704i	−0.616748	−	0.684969i	0.351147	−	0.936320i	$-0.385792\pi$
$151$	−7.57873	−	8.41704i	−0.616748	−	0.684969i	−0.967896	+	0.251352i	$0.919125\pi$
$152$	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
$157$	−13.5514	+	2.88043i	−1.08152	+	0.229883i	−0.714008	−	0.700137i	$-0.753122\pi$
$157$	−13.5514	+	2.88043i	−1.08152	+	0.229883i	−0.367508	+	0.930021i	$0.619789\pi$
$158$	16.7513	−	18.6042i	1.33266	−	1.48007i
$159$	−4.99494	+	11.2188i	−0.396125	+	0.889711i
$160$	3.67152	+	34.9322i	0.290259	+	2.76163i
$161$	−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
$165$	15.4331	−	10.3634i	1.20147	−	0.806789i
$166$	−18.6353	−	32.2772i	−1.44638	−	2.50520i
$167$	1.06996	−	10.1800i	0.0827960	−	0.787752i	−0.871803	−	0.489857i	$-0.837049\pi$
$167$	1.06996	−	10.1800i	0.0827960	−	0.787752i	0.954599	−	0.297895i	$-0.0962844\pi$
$168$	−12.3087	−	3.99933i	−0.949636	−	0.308555i
$169$	6.73801	+	1.43221i	0.518309	+	0.110170i
$170$	−12.7082	+	9.23305i	−0.974675	+	0.708143i
$171$	0.313585	+	2.98357i	0.0239805	+	0.228159i
$172$	−7.28115	−	22.4091i	−0.555183	−	1.70868i
$173$	−7.96923	−	8.85073i	−0.605889	−	0.672908i	0.359673	−	0.933078i	$-0.382888\pi$
$173$	−7.96923	−	8.85073i	−0.605889	−	0.672908i	−0.965563	+	0.260170i	$0.916221\pi$
$174$	3.41966	+	7.68068i	0.259244	+	0.582271i
$175$	2.73607	+	4.73901i	0.206827	+	0.358235i
$176$	−20.1745	+	25.7124i	−1.52071	+	1.93814i
$177$	−0.927051	−	0.535233i	−0.0696814	−	0.0402306i
$178$	26.8732	−	11.9647i	2.01423	−	0.896795i
$179$	−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	$0.772036\pi$
$180$	−31.5325	+	35.0204i	−2.35030	+	2.61027i
$181$	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	$0.0132736\pi$
$182$	−0.676522	−	6.43668i	−0.0501472	−	0.477119i
$183$	6.82945	−	2.21902i	0.504847	−	0.164035i
$184$	17.4094	−	3.70049i	1.28344	−	0.272804i
$185$	−2.06007	+	19.6002i	−0.151459	+	1.44104i
$186$	−6.35410	+	3.66854i	−0.465905	+	0.268991i
$187$	−6.08773	−	0.868416i	−0.445179	−	0.0635049i
$188$	−28.8541			−2.10440
$189$	−2.11347	−	4.74692i	−0.153732	−	0.345288i
$190$	−2.61803	+	8.05748i	−0.189932	+	0.584551i
$191$	11.6833	+	2.48335i	0.845371	+	0.179689i	0.610183	−	0.792261i	$-0.291096\pi$
$191$	11.6833	+	2.48335i	0.845371	+	0.179689i	0.235188	+	0.971950i	$0.424429\pi$
$192$	6.13483	−	13.7791i	0.442743	−	0.994418i
$193$	−10.0490	−	4.47410i	−0.723343	−	0.322053i	0.0118325	−	0.999930i	$-0.496234\pi$
$193$	−10.0490	−	4.47410i	−0.723343	−	0.322053i	−0.735175	+	0.677877i	$0.762900\pi$
$194$	−10.5108	+	11.6735i	−0.754634	+	0.838106i
$195$	−13.1782	−	4.28187i	−0.943712	−	0.306631i
$196$	−26.6067	+	11.8460i	−1.90048	+	0.846146i
$197$	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	$0.663385\pi$
$200$	−37.3535	+	16.6309i	−2.64129	+	1.17598i
$201$	7.72299	−	6.95381i	0.544738	−	0.490484i
$202$	−0.827091	+	0.918578i	−0.0581939	+	0.0646309i
$203$	−1.69381	−	0.754131i	−0.118882	−	0.0529296i
$204$	15.5031	−	1.62944i	1.08543	−	0.114083i
$205$	36.3133	+	7.71864i	2.53623	+	0.539093i
$206$	4.66312	−	14.3516i	0.324895	−	0.999924i
$207$	5.78115	+	4.20025i	0.401818	+	0.291938i
$208$	24.3607			1.68911
$209$	−2.93162	+	1.55100i	−0.202784	+	0.107285i
$210$		−	14.6742i		−	1.01261i
$211$	−1.20499	+	11.4647i	−0.0829549	+	0.789263i	0.871397	+	0.490579i	$0.163215\pi$
$211$	−1.20499	+	11.4647i	−0.0829549	+	0.789263i	−0.954352	+	0.298685i	$0.903452\pi$
$212$	33.6643	−	7.15557i	2.31208	−	0.491447i
$213$	18.1364	+	16.3301i	1.24268	+	1.11892i
$214$	−4.11431	−	39.1451i	−0.281249	−	2.67590i
$215$	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
$218$	−33.1348	+	14.7525i	−2.24417	+	0.999168i
$219$	10.2812	−	5.93583i	0.694736	−	0.401106i
$220$	−48.9194	−	17.9198i	−3.29814	−	1.20816i
$221$	2.29180	+	3.96951i	0.154163	+	0.267018i
$222$	16.2324	−	22.3420i	1.08945	−	1.49950i
$223$	15.0598	+	16.7256i	1.00848	+	1.12003i	0.992755	+	0.120156i	$0.0383394\pi$
$223$	15.0598	+	16.7256i	1.00848	+	1.12003i	0.0157264	+	0.999876i	$0.494994\pi$
$224$	3.35410	+	10.3229i	0.224105	+	0.689725i
$225$	−14.9971	−	6.67715i	−0.999809	−	0.445144i
$226$	27.0344	−	19.6417i	1.79830	−	1.30654i
$227$	14.0677	+	2.99018i	0.933705	+	0.198465i	0.649555	−	0.760315i	$-0.274955\pi$
$227$	14.0677	+	2.99018i	0.933705	+	0.198465i	0.284150	+	0.958780i	$0.408289\pi$
$228$	6.24803	−	5.62575i	0.413786	−	0.372574i
$229$	1.27319	−	12.1136i	0.0841349	−	0.800490i	−0.868360	−	0.495935i	$-0.834825\pi$
$229$	1.27319	−	12.1136i	0.0841349	−	0.800490i	0.952495	−	0.304555i	$-0.0985079\pi$
$230$	10.0902	+	17.4767i	0.665326	+	1.15238i
$231$	3.99904	−	4.12403i	0.263118	−	0.271341i
$232$	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	$-0.703087\pi$
$234$	12.9921	+	14.4292i	0.849321	+	0.943267i
$235$	−5.94427	−	18.2946i	−0.387762	−	1.19341i
$236$	0.313585	+	2.98357i	0.0204127	+	0.194214i
$237$	−9.73513	−	13.3993i	−0.632365	−	0.870376i
$238$	−3.24803	+	3.60730i	−0.210538	+	0.233827i
$239$	−1.49448	+	0.317661i	−0.0966697	+	0.0205478i	−0.255993	−	0.966679i	$-0.582402\pi$
$239$	−1.49448	+	0.317661i	−0.0966697	+	0.0205478i	0.159323	+	0.987227i	$0.449069\pi$
$240$	54.9300	+	5.77338i	3.54572	+	0.372670i
$241$	−13.4164	+	23.2379i	−0.864227	+	1.49688i	0.00358606	+	0.999994i	$0.498859\pi$
$241$	−13.4164	+	23.2379i	−0.864227	+	1.49688i	−0.867813	+	0.496891i	$0.834475\pi$
$242$	−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
$245$	−12.9921	−	14.4292i	−0.830036	−	0.921848i
$246$	−38.6593	−	34.8090i	−2.46483	−	2.21934i
$247$	2.25841	+	1.00551i	0.143699	+	0.0639790i
$248$	11.0449	+	4.91752i	0.701353	+	0.312263i
$249$	−23.4508	+	7.61962i	−1.48613	+	0.482873i
$250$	−2.67652	−	2.97258i	−0.169278	−	0.188002i
$251$	−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
$255$	4.22693	+	9.49384i	0.264701	+	0.594528i
$256$	14.2441	−	3.02767i	0.890255	−	0.189230i
$257$	−17.4577	+	19.3888i	−1.08898	+	1.20944i	−0.112544	+	0.993647i	$0.535900\pi$
$257$	−17.4577	+	19.3888i	−1.08898	+	1.20944i	−0.976439	+	0.215792i	$0.930767\pi$
$258$	−21.8907	+	2.30080i	−1.36285	+	0.143242i
$259$	0.636596	+	6.05681i	0.0395562	+	0.376352i
$260$	12.0000	+	36.9322i	0.744208	+	2.29044i
$261$	5.44076	−	1.15647i	0.336774	−	0.0715836i
$262$	35.5066	+	25.7970i	2.19360	+	1.59375i
$263$	−0.354102	+	0.613323i	−0.0218349	+	0.0378191i	−0.876736	−	0.480971i	$-0.840284\pi$
$263$	−0.354102	+	0.613323i	−0.0218349	+	0.0378191i	0.854902	+	0.518790i	$0.173617\pi$
$264$	27.5231	+	32.9388i	1.69393	+	2.02724i
$265$	11.4721	+	19.8703i	0.704728	+	1.22062i
$266$	−0.273659	+	2.60369i	−0.0167791	+	0.159643i
$267$	−4.04626	−	19.0362i	−0.247627	−	1.16499i
$268$	−28.4882	−	6.05535i	−1.74019	−	0.369889i
$269$	−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	$0.746858\pi$
$272$	−12.2254	−	13.5776i	−0.741271	−	0.823265i
$273$	−4.25841	−	0.447577i	−0.257731	−	0.0270886i
$274$	−8.35410	−	14.4697i	−0.504690	−	0.874148i
$275$	0.670897	−	18.1366i	0.0404566	−	1.09368i
$276$		−	20.0265i		−	1.20545i
$277$	−13.4875	+	6.00503i	−0.810387	+	0.360807i	−0.769733	−	0.638366i	$-0.779611\pi$
$277$	−13.4875	+	6.00503i	−0.810387	+	0.360807i	−0.0406537	+	0.999173i	$0.512944\pi$
$278$	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
$281$	−0.661272	−	6.29158i	−0.0394482	−	0.375324i	−0.996380	−	0.0850115i	$-0.972907\pi$
$281$	−0.661272	−	6.29158i	−0.0394482	−	0.375324i	0.956932	−	0.290313i	$-0.0937594\pi$
$282$	−5.60420	+	26.3657i	−0.333725	+	1.57005i
$283$	16.6285	−	3.53450i	0.988462	−	0.210104i	0.314812	−	0.949154i	$-0.398059\pi$
$283$	16.6285	−	3.53450i	0.988462	−	0.210104i	0.673651	+	0.739050i	$0.264725\pi$
$284$	7.14924	−	68.0204i	0.424229	−	4.03627i
$285$	4.85410	+	2.80252i	0.287532	+	0.166007i
$286$	−9.44980	+	19.2737i	−0.558778	+	1.13968i
$287$	11.4721			0.677179
$288$	−26.3435	−	19.1396i	−1.55230	−	1.12781i
$289$	−4.19098	+	12.8985i	−0.246528	+	0.758736i
$290$	15.3649	+	3.26592i	0.902260	+	0.191781i
$291$	6.10844	+	8.40755i	0.358083	+	0.492859i
$292$	−30.3941	−	13.5323i	−1.77868	−	0.791920i
$293$	−4.56324	+	5.06800i	−0.266588	+	0.296075i	−0.861544	−	0.507682i	$-0.830502\pi$
$293$	−4.56324	+	5.06800i	−0.266588	+	0.296075i	0.594957	+	0.803758i	$0.297169\pi$
$294$	5.65674	+	26.6129i	0.329908	+	1.55209i
$295$	−1.82709	+	0.813473i	−0.106377	+	0.0473622i
$296$	−45.5066			−2.64502
$297$	−2.43375	+	17.0610i	−0.141221	+	0.989978i
$298$	−18.7984			−1.08896
$299$	5.37945	−	2.39509i	0.311102	−	0.138511i
$300$	9.56545	+	45.0019i	0.552261	+	2.59819i
$301$	3.24803	−	3.60730i	0.187213	−	0.207921i
$302$	27.0889	+	12.0607i	1.55879	+	0.694018i
$303$	0.480669	+	0.661585i	0.0276137	+	0.0380070i
$304$	−9.63877	−	2.04878i	−0.552821	−	0.117506i
$305$	4.14590	−	12.7598i	0.237393	−	0.730622i
$306$	1.52218	−	14.4825i	0.0870170	−	0.827911i
$307$	1.14590			0.0653999			0.0326999	−	0.999465i	$-0.489589\pi$
$307$	1.14590			0.0653999			0.0326999	+	0.999465i	$0.489589\pi$
$308$	−15.9379	−	2.27354i	−0.908146	−	0.129547i
$309$	−8.64590	−	4.99171i	−0.491848	−	0.283969i
$310$	−1.43290	+	13.6331i	−0.0813831	+	0.774309i
$311$	7.02343	−	1.49288i	0.398262	−	0.0846533i	−0.00442652	−	0.999990i	$-0.501409\pi$
$311$	7.02343	−	1.49288i	0.398262	−	0.0846533i	0.402689	+	0.915337i	$0.368076\pi$
$312$	6.65207	−	31.2955i	0.376599	−	1.77176i
$313$	0.571994	+	5.44216i	0.0323310	+	0.307609i	0.998722	+	0.0505336i	$0.0160922\pi$
$313$	0.571994	+	5.44216i	0.0323310	+	0.307609i	−0.966391	+	0.257075i	$0.917241\pi$
$314$	29.3435	−	21.3193i	1.65595	−	1.20312i
$315$	−9.49606	−	2.01845i	−0.535042	−	0.113727i
$316$	−14.3435	+	44.1446i	−0.806883	+	2.48333i
$317$	2.79155	−	1.24288i	0.156789	−	0.0698069i	−0.326842	−	0.945079i	$-0.605984\pi$
$317$	2.79155	−	1.24288i	0.156789	−	0.0698069i	0.483631	+	0.875272i	$0.339318\pi$
$318$		−	32.1509i		−	1.80293i
$319$	3.42813	+	5.10515i	0.191938	+	0.285834i
$320$	−14.0902	−	24.4049i	−0.787664	−	1.36427i
$321$	−25.8978	−	2.72196i	−1.44547	−	0.151925i
$322$	4.17274	+	4.63430i	0.232538	+	0.258260i
$323$	−0.572949	−	1.76336i	−0.0318797	−	0.0981157i
$324$	−4.56653	−	43.4476i	−0.253696	−	2.41376i
$325$	−10.9443	+	7.95148i	−0.607079	+	0.441069i
$326$	18.6730	+	3.96907i	1.03420	+	0.219826i
$327$	4.98905	+	23.4716i	0.275895	+	1.29798i
$328$	−8.96032	+	85.2518i	−0.494751	+	4.70724i
$329$	−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	−0.643428	−	0.765506i	$-0.722489\pi$
$331$	6.20820	−	10.7529i	0.341234	−	0.591034i	0.984662	+	0.174472i	$0.0558219\pi$
$332$	55.9058	+	40.6179i	3.06823	+	2.22920i
$333$	−12.2254	−	13.5776i	−0.669945	−	0.744050i
$334$	8.28115	+	25.4868i	0.453125	+	1.39457i
$335$	−2.02957	−	19.3100i	−0.110887	−	1.05502i
$336$	16.9743	−	1.78407i	0.926024	−	0.0973291i
$337$	−1.69147	+	1.87857i	−0.0921403	+	0.102332i	−0.787451	−	0.616377i	$-0.788600\pi$
$337$	−1.69147	+	1.87857i	−0.0921403	+	0.102332i	0.695311	+	0.718709i	$0.255267\pi$
$338$	−17.6403	+	3.74957i	−0.959508	+	0.203950i
$339$	−8.99204	−	20.1965i	−0.488381	−	1.09692i
$340$	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
$344$	24.2697	+	26.9542i	1.30853	+	1.45328i
$345$	12.6976	−	4.12569i	0.683613	−	0.222119i
$346$	28.4847	+	12.6822i	1.53134	+	0.681799i
$347$	24.5639	+	10.9366i	1.31866	+	0.587105i	0.940864	−	0.338784i	$-0.110016\pi$
$347$	24.5639	+	10.9366i	1.31866	+	0.587105i	0.377795	+	0.925889i	$0.376682\pi$
$348$	−11.5845	−	10.4307i	−0.620993	−	0.559145i
$349$	−7.26281	−	8.06617i	−0.388769	−	0.431772i	0.516711	−	0.856160i	$-0.327156\pi$
$349$	−7.26281	−	8.06617i	−0.388769	−	0.431772i	−0.905481	+	0.424388i	$0.860489\pi$
$350$	−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	−0.970689	−	0.240339i	$-0.922741\pi$
$353$	−5.20820	+	9.02087i	−0.277205	+	0.480133i	0.693484	+	0.720472i	$0.256075\pi$
$354$	2.78716	+	0.292943i	0.148136	+	0.0155697i
$355$	44.6003	−	9.48010i	2.36714	−	0.503151i
$356$	−36.4951	+	40.5319i	−1.93423	+	2.14819i
$357$	1.88761	+	2.59808i	0.0999031	+	0.137505i
$358$	−6.27891	−	59.7398i	−0.331851	−	3.15735i
$359$	−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
$363$	−18.5055	+	4.53274i	−0.971288	+	0.237907i
$364$	6.00000	+	10.3923i	0.314485	+	0.544705i
$365$	2.31848	−	22.0588i	0.121355	−	1.15461i
$366$	−13.9710	+	12.5796i	−0.730277	+	0.657544i
$367$	−0.692728	−	0.147244i	−0.0361601	−	0.00768607i	0.189796	−	0.981824i	$-0.439217\pi$
$367$	−0.692728	−	0.147244i	−0.0361601	−	0.00768607i	−0.225956	+	0.974137i	$0.572551\pi$
$368$	−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
$371$	4.74425	+	5.26902i	0.246309	+	0.273554i
$372$	7.99606	−	11.0056i	0.414576	−	0.570615i
$373$	−12.8262	−	22.2157i	−0.664117	−	1.15029i	−0.979524	−	0.201328i	$-0.935474\pi$
$373$	−12.8262	−	22.2157i	−0.664117	−	1.15029i	0.315406	−	0.948957i	$-0.397859\pi$
$374$	15.4847	−	4.40554i	0.800696	−	0.227805i
$375$	−2.29180	+	1.32317i	−0.118348	+	0.0683282i
$376$	40.5764	−	18.0658i	2.09257	−	0.931671i
$377$	1.41641	−	4.35926i	0.0729487	−	0.224513i
$378$	10.1095	+	9.10265i	0.519978	+	0.468190i
$379$	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	$0.227445\pi$
$380$	−1.64195	−	15.6222i	−0.0842305	−	0.801400i
$381$	−12.3083	−	11.0824i	−0.630571	−	0.567769i
$382$	−30.5872	+	6.50150i	−1.56498	+	0.332646i
$383$	−1.37412	+	13.0739i	−0.0702143	+	0.668044i	0.901644	+	0.432479i	$0.142361\pi$
$383$	−1.37412	+	13.0739i	−0.0702143	+	0.668044i	−0.971858	+	0.235566i	$0.924306\pi$
$384$			1.88823i			0.0963583i
$385$	−1.84187	−	10.5736i	−0.0938706	−	0.538880i
$386$	28.7984			1.46580
$387$	−1.52218	+	14.4825i	−0.0773765	+	0.736188i
$388$	9.00000	−	27.6992i	0.456906	−	1.40621i
$389$	−8.46340	−	1.79895i	−0.429111	−	0.0912104i	−0.0117074	−	0.999931i	$-0.503727\pi$
$389$	−8.46340	−	1.79895i	−0.429111	−	0.0912104i	−0.417404	+	0.908721i	$0.637060\pi$
$390$	36.0778	−	3.79193i	1.82687	−	0.192012i
$391$	−4.03459	−	1.79631i	−0.204038	−	0.0908435i
$392$	29.9990	−	33.3173i	1.51518	−	1.68278i
$393$	21.5779	−	19.4289i	1.08846	−	0.980057i
$394$	−9.00217	+	4.00802i	−0.453523	+	0.201921i
$395$	−30.9443			−1.55698
$396$	42.6911	−	22.5862i	2.14531	−	1.13500i
$397$	38.1246			1.91342			0.956710	−	0.291044i	$-0.0940026\pi$
$397$	38.1246			1.91342			0.956710	+	0.291044i	$0.0940026\pi$
$398$	33.1348	−	14.7525i	1.66090	−	0.739478i
$399$	1.64728	+	0.535233i	0.0824671	+	0.0267952i
$400$	36.0815	−	40.0726i	1.80408	−	2.00363i
$401$	−5.08142	−	2.26239i	−0.253754	−	0.112979i	0.275918	−	0.961181i	$-0.411018\pi$
$401$	−5.08142	−	2.26239i	−0.253754	−	0.112979i	−0.529672	+	0.848203i	$0.677685\pi$
$402$	−11.0662	+	24.8552i	−0.551934	+	1.23966i
$403$	3.91259	+	0.831647i	0.194900	+	0.0414273i
$404$	0.708204	−	2.17963i	0.0352345	−	0.108441i
$405$	26.6067	−	11.8460i	1.32210	−	0.588635i
$406$	4.85410			0.240905
$407$	8.89210	−	18.1362i	0.440765	−	0.898979i
$408$	−20.7812	+	11.9980i	−1.02882	+	0.593990i
$409$	−0.913855	+	8.69475i	−0.0451872	+	0.429928i	0.948418	+	0.317021i	$0.102683\pi$
$409$	−0.913855	+	8.69475i	−0.0451872	+	0.429928i	−0.993606	+	0.112906i	$0.963984\pi$
$410$	−95.0696	+	20.2077i	−4.69515	+	0.997985i
$411$	−10.5129	+	3.41584i	−0.518562	+	0.168491i
$412$	2.92457	+	27.8254i	0.144083	+	1.37086i
$413$	−0.500000	+	0.363271i	−0.0246034	+	0.0178754i
$414$	−18.2994	−	3.88965i	−0.899366	−	0.191166i
$415$	−14.2361	+	43.8141i	−0.698821	+	2.15075i
$416$	−24.5130	+	10.9139i	−1.20185	+	0.535097i
$417$	−5.56231	−	3.21140i	−0.272387	−	0.157263i
$418$	5.35995	−	6.83126i	0.262164	−	0.334128i
$419$	1.54508	+	2.67617i	0.0754823	+	0.130739i	0.901296	−	0.433204i	$-0.142617\pi$
$419$	1.54508	+	2.67617i	0.0754823	+	0.130739i	−0.825814	+	0.563943i	$0.809284\pi$
$420$	11.0662	+	24.8552i	0.539978	+	1.21281i
$421$	3.85682	+	4.28344i	0.187970	+	0.208762i	0.829763	−	0.558116i	$-0.188476\pi$
$421$	3.85682	+	4.28344i	0.187970	+	0.208762i	−0.641793	+	0.766878i	$0.721809\pi$
$422$	−9.32624	−	28.7032i	−0.453994	−	1.39725i
$423$	16.2911	+	7.25326i	0.792100	+	0.352666i
$424$	−42.8607	+	31.1401i	−2.08150	+	1.51230i
$425$	9.92419	+	2.10945i	0.481394	+	0.102323i
$426$	−60.7657	−	19.7440i	−2.94411	−	0.956599i
$427$	0.433364	−	4.12319i	0.0209720	−	0.199535i
$428$	36.4894	+	63.2014i	1.76378	+	3.05496i
$429$	11.1727	+	8.76634i	0.539423	+	0.423243i
$430$	−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	$0.896822\pi$
$432$	−38.0516	+	34.2618i	−1.83076	+	1.64842i
$433$	−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	$-0.332257\pi$
$434$	0.442790	+	4.21286i	0.0212546	+	0.202224i
$435$	4.22693	−	9.49384i	0.202666	−	0.455195i
$436$	44.9985	−	49.9759i	2.15504	−	2.39341i
$437$	−2.32991	+	0.495239i	−0.111455	+	0.0236905i
$438$	−18.2686	+	25.1446i	−0.872907	+	1.20145i
$439$	−6.35410	+	11.0056i	−0.303265	+	0.525270i	−0.976873	−	0.213818i	$-0.931410\pi$
$439$	−6.35410	+	11.0056i	−0.303265	+	0.525270i	0.673609	+	0.739088i	$0.264743\pi$
$440$	80.0132	−	5.42882i	3.81448	−	0.258809i
$441$	18.0000			0.857143
$442$	−9.70820	−	7.05342i	−0.461772	−	0.335497i
$443$	2.16535	+	2.40487i	0.102879	+	0.114259i	0.792385	−	0.610021i	$-0.208839\pi$
$443$	2.16535	+	2.40487i	0.102879	+	0.114259i	−0.689506	+	0.724280i	$0.742172\pi$
$444$	−10.6458	+	50.0845i	−0.505227	+	2.37691i
$445$	−33.2171	−	14.7892i	−1.57464	−	0.701076i
$446$	−53.8288	−	23.9661i	−2.54887	−	1.13483i
$447$	−2.58574	+	12.1649i	−0.122301	+	0.575382i
$448$	−5.82693	−	6.47146i	−0.275296	−	0.305748i
$449$	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
$454$	−36.8297	+	7.82839i	−1.72850	+	0.367405i
$455$	−5.35304	+	5.94516i	−0.250955	+	0.278713i
$456$	−5.26403	+	11.8232i	−0.246511	+	0.553673i
$457$	0.104528	+	0.994522i	0.00488964	+	0.0465218i	0.996695	−	0.0812390i	$-0.0258877\pi$
$457$	0.104528	+	0.994522i	0.00488964	+	0.0465218i	−0.991805	+	0.127761i	$0.959221\pi$
$458$	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	−0.467082	−	0.884214i	$-0.654695\pi$
$461$	11.4271	−	19.7922i	0.532211	−	0.921816i	0.999293	−	0.0376022i	$-0.0119720\pi$
$462$	−5.17301	+	14.1218i	−0.240670	+	0.657006i
$463$	−8.50000	−	14.7224i	−0.395029	−	0.684209i	0.598076	−	0.801439i	$-0.295932\pi$
$463$	−8.50000	−	14.7224i	−0.395029	−	0.684209i	−0.993105	+	0.117230i	$0.962599\pi$
$464$	−1.90979	+	18.1704i	−0.0886597	+	0.843541i
$465$	8.62526	+	2.80252i	0.399987	+	0.129964i
$466$	74.5830	+	15.8531i	3.45499	+	0.734381i
$467$	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	$0.261342\pi$
$468$	−32.8876	−	14.6425i	−1.52023	−	0.676851i
$469$	−1.85410	−	5.70634i	−0.0856145	−	0.263494i
$470$	33.6979	+	37.4253i	1.55437	+	1.72630i
$471$	−9.76006	−	21.9214i	−0.449720	−	1.01009i
$472$	−2.30902	−	3.99933i	−0.106281	−	0.184084i
$473$	−15.4847	+	4.40554i	−0.711988	+	0.202567i
$474$	37.5517	+	21.6805i	1.72480	+	0.995817i
$475$	4.99904	−	2.22572i	0.229372	−	0.102123i
$476$	2.78115	−	8.55951i	0.127474	−	0.392324i
$477$	−20.8057	−	4.42239i	−0.952627	−	0.202487i
$478$	3.23607	−	2.35114i	0.148014	−	0.107539i
$479$	1.69713	+	16.1471i	0.0775439	+	0.737781i	0.962348	+	0.271819i	$0.0876251\pi$
$479$	1.69713	+	16.1471i	0.0775439	+	0.737781i	−0.884805	+	0.465962i	$0.845708\pi$
$480$	−57.8600	+	18.7999i	−2.64094	+	0.858092i
$481$	−14.7267	+	3.13026i	−0.671481	+	0.142728i
$482$	7.34304	−	69.8644i	0.334466	−	3.18224i
$483$	3.57295	−	2.06284i	0.162575	−	0.0938626i
$484$	40.7607	+	34.4906i	1.85276	+	1.56775i
$485$	19.4164			0.881654
$486$	−40.5875	−	4.26592i	−1.84109	−	0.193506i
$487$	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	$-0.179675\pi$
$488$	30.3018	+	6.44084i	1.37170	+	0.291563i
$489$	5.13699	−	11.5379i	0.232303	−	0.521760i
$490$	46.4381	+	20.6756i	2.09786	+	0.934027i
$491$	−5.57134	+	6.18760i	−0.251431	+	0.279243i	−0.855627	−	0.517594i	$-0.826828\pi$
$491$	−5.57134	+	6.18760i	−0.251431	+	0.279243i	0.604196	+	0.796836i	$0.293495\pi$
$492$	91.7318	+	29.8055i	4.13559	+	1.34373i
$493$	−3.14049	+	1.39824i	−0.141441	+	0.0629734i
$494$	−6.47214			−0.291195
$495$	23.1153	+	22.4148i	1.03896	+	1.00747i
$496$	−15.9443			−0.715919
$497$	12.8720	−	5.73099i	0.577389	−	0.257070i
$498$	47.9733	−	43.1953i	2.14973	−	1.93563i
$499$	7.75094	−	8.60829i	0.346980	−	0.385360i	−0.544242	−	0.838928i	$-0.683183\pi$
$499$	7.75094	−	8.60829i	0.346980	−	0.385360i	0.891221	+	0.453569i	$0.149849\pi$
$500$	6.77523	+	3.01652i	0.302997	+	0.134903i
$501$	17.6323	−	1.85323i	0.787752	−	0.0827960i
$502$	1.12086	+	0.238246i	0.0500263	+	0.0106334i
$503$	−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	$0.964895\pi$
$504$	2.34315	−	22.2936i	0.104372	−	0.993036i
$505$	1.52786			0.0679891
$506$	−3.54939	−	20.3759i	−0.157789	−	0.905818i
$507$			11.9313i			0.529888i
$508$	−4.85184	+	46.1621i	−0.215265	+	2.04811i
$509$	4.71434	−	1.00206i	0.208959	−	0.0444157i	−0.102243	−	0.994760i	$-0.532602\pi$
$509$	4.71434	−	1.00206i	0.208959	−	0.0444157i	0.311202	+	0.950344i	$0.399268\pi$
$510$	−20.2190	−	18.2053i	−0.895314	−	0.806145i
$511$	−0.716449	−	6.81655i	−0.0316938	−	0.301547i
$512$	−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
$515$	−17.0399	+	7.58665i	−0.750867	+	0.334308i
$516$	35.3435	−	20.4056i	1.55591	−	0.898304i
$517$	−0.728782	+	19.7014i	−0.0320518	+	0.866469i
$518$	−7.97214	−	13.8081i	−0.350276	−	0.606695i
$519$	12.1251	−	16.6888i	0.532232	−	0.732555i
$520$	−39.9987	−	44.4230i	−1.75406	−	1.94808i
$521$	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	$0.300000\pi$
$524$	−79.5956	−	16.9186i	−3.47715	−	0.739091i
$525$	−7.04354	+	6.34203i	−0.307405	+	0.276789i
$526$	0.193806	−	1.84395i	0.00845036	−	0.0803998i
$527$	−1.50000	−	2.59808i	−0.0653410	−	0.113174i
$528$	−50.8271	−	24.9203i	−2.21196	−	1.08451i
$529$	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
$533$	2.96450	+	28.2053i	0.128407	+	1.22171i
$534$	29.9481	+	41.2200i	1.29598	+	1.78376i
$535$	−32.5549	+	36.1558i	−1.40747	+	1.56315i
$536$	43.8531	−	9.32127i	1.89417	−	0.402617i
$537$	−39.5229	−	4.15403i	−1.70554	−	0.179260i
$538$	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	$0.534669\pi$
$542$	−26.6906	−	29.6430i	−1.14646	−	1.27327i
$543$	27.1465	+	24.4428i	1.16497	+	1.04894i
$544$	18.3847	+	8.18542i	0.788240	+	0.350947i
$545$	40.9568	+	18.2351i	1.75440	+	0.781108i
$546$	10.6614	−	3.46410i	0.456266	−	0.148250i
$547$	−11.1569	−	12.3910i	−0.477036	−	0.529802i	0.455810	−	0.890077i	$-0.349349\pi$
$547$	−11.1569	−	12.3910i	−0.477036	−	0.529802i	−0.932846	+	0.360275i	$0.882683\pi$
$548$	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
$552$	12.5388	+	28.1625i	0.533685	+	1.19868i
$553$	−9.35335	+	1.98812i	−0.397745	+	0.0845433i
$554$	25.8636	−	28.7244i	1.09884	−	1.22038i
$555$	−33.9486	+	3.56814i	−1.44104	+	0.151459i
$556$	1.88151	+	17.9014i	0.0797939	+	0.759188i
$557$	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	$0.675023\pi$
$558$	−8.50345	−	9.44404i	−0.359980	−	0.399798i
$559$	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
$563$	−4.42207	+	42.0732i	−0.186368	+	1.77317i	0.357413	+	0.933947i	$0.383659\pi$
$563$	−4.42207	+	42.0732i	−0.186368	+	1.77317i	−0.543781	+	0.839227i	$0.683008\pi$
$564$	−10.3908	−	48.8847i	−0.437530	−	2.05842i
$565$	−40.4023	−	8.58778i	−1.69974	−	0.361291i
$566$	−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
$569$	9.50274	+	10.5539i	0.398376	+	0.442441i	0.908642	−	0.417575i	$-0.137120\pi$
$569$	9.50274	+	10.5539i	0.398376	+	0.442441i	−0.510267	+	0.860016i	$0.670453\pi$
$570$	−14.5938	−	1.53387i	−0.611266	−	0.0642467i
$571$	13.7361	+	23.7916i	0.574837	+	0.995646i	0.996059	+	0.0886889i	$0.0282677\pi$
$571$	13.7361	+	23.7916i	0.574837	+	0.995646i	−0.421223	+	0.906957i	$0.638399\pi$
$572$	1.47123	−	39.7723i	0.0615152	−	1.66296i
$573$			20.6881i			0.864257i
$574$	−27.4378	+	12.2161i	−1.14523	+	0.509890i
$575$	4.02786	−	12.3965i	0.167974	−	0.516969i
$576$	25.5537	+	5.43161i	1.06474	+	0.226317i
$577$	−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	$0.357179\pi$
$578$	−3.71145	−	35.3121i	−0.154376	−	1.46879i
$579$	3.96125	−	18.6362i	0.164624	−	0.774495i
$580$	−28.4882	+	6.05535i	−1.18291	+	0.251435i
$581$	−1.48807	+	14.1581i	−0.0617357	+	0.587376i
$582$	−23.5623	−	13.6037i	−0.976689	−	0.563892i
$583$	−4.03552	−	23.1666i	−0.167134	−	0.959462i
$584$	51.2148			2.11928
$585$	2.50868	−	23.8685i	0.103721	−	0.986842i
$586$	5.51722	−	16.9803i	0.227914	−	0.701448i
$587$	13.1232	+	2.78943i	0.541654	+	0.115132i	0.470610	−	0.882341i	$-0.344034\pi$
$587$	13.1232	+	2.78943i	0.541654	+	0.115132i	0.0710433	+	0.997473i	$0.477367\pi$
$588$	−29.6510	−	40.8111i	−1.22279	−	1.68302i
$589$	−1.47815	−	0.658114i	−0.0609060	−	0.0271171i
$590$	3.50361	−	3.89116i	0.144241	−	0.160196i
$591$	1.35544	+	6.37686i	0.0557555	+	0.262309i
$592$	54.8247	−	24.4095i	2.25328	−	1.00323i
$593$	6.94427			0.285167			0.142584	−	0.989783i	$-0.454459\pi$
$593$	6.94427			0.285167			0.142584	+	0.989783i	$0.454459\pi$
$594$	−12.3466	−	43.3962i	−0.506587	−	1.78057i
$595$	6.00000			0.245976
$596$	31.8408	−	14.1764i	1.30425	−	0.580690i
$597$	−4.98905	−	23.4716i	−0.204188	−	0.960630i
$598$	−10.3156	+	11.4566i	−0.421836	+	0.468496i
$599$	28.6494	+	12.7555i	1.17058	+	0.521177i	0.897587	−	0.440838i	$-0.145319\pi$
$599$	28.6494	+	12.7555i	1.17058	+	0.521177i	0.272996	+	0.962015i	$0.411985\pi$
$600$	−41.6276	−	57.2954i	−1.69944	−	2.33908i
$601$	8.34151	+	1.77304i	0.340257	+	0.0723239i	0.374871	−	0.927077i	$-0.377687\pi$
$601$	8.34151	+	1.77304i	0.340257	+	0.0723239i	−0.0346141	+	0.999401i	$0.511020\pi$
$602$	−3.92705	+	12.0862i	−0.160055	+	0.492598i
$603$	14.5623	+	10.5801i	0.593023	+	0.430856i
$604$	−54.9787			−2.23705
$605$	−13.4712	+	32.9493i	−0.547681	+	1.33958i
$606$	−1.85410	−	1.07047i	−0.0753177	−	0.0434847i
$607$	3.17938	−	30.2498i	0.129047	−	1.22780i	−0.717909	−	0.696137i	$-0.754900\pi$
$607$	3.17938	−	30.2498i	0.129047	−	1.22780i	0.846956	−	0.531663i	$-0.178433\pi$
$608$	10.6169	−	2.25669i	0.430573	−	0.0915211i
$609$	0.667687	−	3.14122i	0.0270561	−	0.127289i
$610$	3.67152	+	34.9322i	0.148656	+	1.41436i
$611$	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	$0.0144699\pi$
$614$	−2.74064	+	1.22021i	−0.110603	+	0.0492437i
$615$			64.3017i			2.59290i
$616$	23.8363	−	6.78164i	0.960393	−	0.273240i
$617$	−21.0795	−	36.5108i	−0.848630	−	1.46987i	−0.882431	−	0.470441i	$-0.844095\pi$
$617$	−21.0795	−	36.5108i	−0.848630	−	1.46987i	0.0338015	−	0.999429i	$-0.489239\pi$
$618$	25.9938	+	2.73205i	1.04562	+	0.109899i
$619$	4.97679	+	5.52728i	0.200034	+	0.222160i	0.834813	−	0.550533i	$-0.185576\pi$
$619$	4.97679	+	5.52728i	0.200034	+	0.222160i	−0.634779	+	0.772694i	$0.718909\pi$
$620$	−7.85410	−	24.1724i	−0.315428	−	0.970789i
$621$	−5.03420	+	11.3070i	−0.202016	+	0.453735i
$622$	−15.2082	+	11.0494i	−0.609793	+	0.443041i
$623$	−10.9905	−	2.33611i	−0.440326	−	0.0935943i
$624$	8.77261	+	41.2719i	0.351186	+	1.65220i
$625$	2.34315	−	22.2936i	0.0937261	−	0.891744i
$626$	−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
$630$	24.8610	−	5.28437i	0.990486	−	0.210534i
$631$	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	$0.735022\pi$
$632$	−7.46865	−	71.0594i	−0.297087	−	2.82659i
$633$	−19.8575	+	2.08710i	−0.789263	+	0.0829549i
$634$	−5.35304	+	5.94516i	−0.212597	+	0.236112i
$635$	−30.2681	+	6.43368i	−1.20115	+	0.255313i
$636$	24.2460	+	54.4573i	0.961415	+	2.15937i
$637$	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
$641$	23.7212	+	26.3451i	0.936933	+	1.04057i	0.999096	+	0.0425035i	$0.0135334\pi$
$641$	23.7212	+	26.3451i	0.936933	+	1.04057i	−0.0621633	+	0.998066i	$0.519800\pi$
$642$	64.8380	−	21.0671i	2.55895	−	0.831454i
$643$	−0.133284	−	0.0593421i	−0.00525623	−	0.00234022i	0.404107	−	0.914712i	$-0.367582\pi$
$643$	−0.133284	−	0.0593421i	−0.00525623	−	0.00234022i	−0.409363	+	0.912372i	$0.634249\pi$
$644$	−10.5627	−	4.70281i	−0.416228	−	0.185317i
$645$	20.2190	+	18.2053i	0.796124	+	0.716833i
$646$	3.24803	+	3.60730i	0.127792	+	0.141927i
$647$	−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
$651$	2.78716	+	0.292943i	0.109238	+	0.0114813i
$652$	−34.6217	+	7.35906i	−1.35589	+	0.288203i
$653$	29.0140	−	32.2233i	1.13540	−	1.26099i	0.174335	−	0.984686i	$-0.444223\pi$
$653$	29.0140	−	32.2233i	1.13540	−	1.26099i	0.961069	−	0.276307i	$-0.0891108\pi$
$654$	−36.9261	−	50.8244i	−1.44392	−	1.98739i
$655$	−5.67059	−	53.9520i	−0.221568	−	2.10808i
$656$	−34.9336	−	107.515i	−1.36393	−	4.19774i
$657$	13.7589	+	15.2808i	0.536785	+	0.596160i
$658$	12.5902	+	9.14729i	0.490816	+	0.356599i
$659$	18.4894	−	32.0245i	0.720243	−	1.24750i	−0.240659	−	0.970610i	$-0.577364\pi$
$659$	18.4894	−	32.0245i	0.720243	−	1.24750i	0.960902	−	0.276888i	$-0.0893031\pi$
$660$	12.7433	−	89.3324i	0.496032	−	3.47726i
$661$	8.85410	+	15.3358i	0.344385	+	0.596492i	0.985242	−	0.171168i	$-0.0547542\pi$
$661$	8.85410	+	15.3358i	0.344385	+	0.596492i	−0.640857	+	0.767660i	$0.721421\pi$
$662$	−3.39786	+	32.3285i	−0.132062	+	1.25648i
$663$	−5.89984	+	5.31224i	−0.229131	+	0.206310i
$664$	−104.049	−	22.1164i	−4.03790	−	0.858281i
$665$	2.61803	−	1.90211i	0.101523	−	0.0737608i
$666$	43.6975	+	19.4554i	1.69324	+	0.753880i
$667$	1.36475	+	4.20025i	0.0528431	+	0.162634i
$668$	−33.2470	−	36.9246i	−1.28637	−	1.42865i
$669$	−22.9134	+	31.5375i	−0.885882	+	1.21931i
$670$	25.4164	+	44.0225i	0.981922	+	1.70074i
$671$	−8.48797	+	10.8179i	−0.327675	+	0.417621i
$672$	−16.2812	+	9.39993i	−0.628059	+	0.362610i
$673$	−8.62176	+	3.83866i	−0.332345	+	0.147969i	−0.566123	−	0.824320i	$-0.691557\pi$
$673$	−8.62176	+	3.83866i	−0.332345	+	0.147969i	0.233779	+	0.972290i	$0.424891\pi$
$674$	2.04508	−	6.29412i	0.0787737	−	0.242441i
$675$	5.91177	−	27.8127i	0.227544	−	1.07051i
$676$	27.0517	−	19.6542i	1.04045	−	0.755930i
$677$	−2.50286	−	23.8131i	−0.0961926	−	0.915212i	−0.931086	−	0.364800i	$-0.881137\pi$
$677$	−2.50286	−	23.8131i	−0.0961926	−	0.915212i	0.834893	−	0.550412i	$-0.185529\pi$
$678$	43.0124	+	38.7286i	1.65188	+	1.48736i
$679$	5.86889	−	1.24747i	0.225227	−	0.0478735i
$680$	−4.68631	+	44.5872i	−0.179712	+	1.70984i
$681$			24.9103i			0.954565i
$682$	6.18497	−	12.6148i	0.236835	−	0.483046i
$683$	−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
$686$	33.2907	+	7.07616i	1.27105	+	0.270169i
$687$	20.9814	−	2.20523i	0.800490	−	0.0841349i
$688$	−43.6975	−	19.4554i	−1.66595	−	0.741729i
$689$	−11.7284	+	13.0257i	−0.446818	+	0.496241i
$690$	−25.9754	+	23.3884i	−0.988867	+	0.890380i
$691$	−31.6057	+	14.0718i	−1.20234	+	0.535315i	−0.907427	−	0.420210i	$-0.861957\pi$
$691$	−31.6057	+	14.0718i	−1.20234	+	0.535315i	−0.294911	+	0.955525i	$0.595290\pi$
$692$	−57.8115			−2.19766
$693$	8.42705	+	5.29007i	0.320117	+	0.200953i
$694$	−70.3951			−2.67216
$695$	−10.9625	+	4.88084i	−0.415833	+	0.185141i
$696$	22.8216	+	7.41517i	0.865049	+	0.281071i
$697$	14.2327	−	15.8071i	0.539104	−	0.598735i
$698$	25.9597	+	11.5580i	0.982588	+	0.437477i
$699$	20.5180	−	46.0841i	0.776060	−	1.74306i
$700$	25.9819	+	5.52261i	0.982022	+	0.208735i
$701$	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
$704$	4.95645	+	28.4534i	0.186803	+	1.07238i
$705$	28.8541	−	16.6589i	1.08671	−	0.627411i
$706$	2.85054	−	27.1211i	0.107282	−	1.02072i
$707$	0.461819	−	0.0981626i	0.0173685	−	0.00369178i
$708$	−4.94183	+	1.60570i	−0.185726	+	0.0603459i
$709$	3.16053	+	30.0704i	0.118696	+	1.12932i	0.878026	+	0.478613i	$0.158860\pi$
$709$	3.16053	+	30.0704i	0.118696	+	1.12932i	−0.759330	+	0.650706i	$0.774473\pi$
$710$	−96.5755	+	70.1662i	−3.62441	+	2.63329i
$711$	19.1953	−	21.3185i	0.719880	−	0.799508i
$712$	25.9443	−	79.8483i	0.972303	−	2.99244i
$713$	−3.52090	+	1.56760i	−0.131859	+	0.0587072i
$714$	−7.28115	−	4.20378i	−0.272490	−	0.157322i
$715$	25.5202	−	7.26073i	0.954402	−	0.271536i
$716$	55.6869	+	96.4526i	2.08112	+	3.60460i
$717$	−1.07636	−	2.41755i	−0.0401975	−	0.0902851i
$718$	28.2845	+	31.4131i	1.05557	+	1.17233i
$719$	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	$0.713908\pi$
$720$	9.99978	+	95.1416i	0.372670	+	3.54572i
$721$	−4.66312	+	3.38795i	−0.173664	+	0.126174i
$722$	−46.0948	−	9.79776i	−1.71547	−	0.364635i
$723$	−44.2011	−	14.3618i	−1.64386	−	0.534122i
$724$	10.7010	−	101.813i	0.397699	−	3.78385i
$725$	−5.07295	−	8.78661i	−0.188405	−	0.326326i
$726$	39.4328	−	30.5465i	1.46349	−	1.13369i
$727$	17.4164	−	30.1661i	0.645939	−	1.11880i	−0.338145	−	0.941094i	$-0.609799\pi$
$727$	17.4164	−	30.1661i	0.645939	−	1.11880i	0.984084	−	0.177705i	$-0.0568672\pi$
$728$	−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
$731$	−0.940756	−	8.95070i	−0.0347951	−	0.331053i
$732$	14.1776	−	31.8433i	0.524018	−	1.17696i
$733$	26.4493	−	29.3749i	0.976927	−	1.08499i	−0.0194385	−	0.999811i	$-0.506188\pi$
$733$	26.4493	−	29.3749i	0.976927	−	1.08499i	0.996366	−	0.0851767i	$-0.0271455\pi$
$734$	1.81359	−	0.385489i	0.0669407	−	0.0142287i
$735$	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	$0.550933\pi$
$740$	64.0128	+	71.0934i	2.35316	+	2.61345i
$741$	−0.890250	+	4.18830i	−0.0327041	+	0.153861i
$742$	−16.9575	−	7.54997i	−0.622530	−	0.277168i
$743$	2.15659	+	0.960175i	0.0791176	+	0.0352254i	0.445914	−	0.895076i	$-0.352879\pi$
$743$	2.15659	+	0.960175i	0.0791176	+	0.0352254i	−0.366796	+	0.930301i	$0.619545\pi$
$744$	−4.35383	+	20.4832i	−0.159619	+	0.750950i
$745$	15.5480	+	17.2678i	0.569633	+	0.632642i
$746$	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
$751$	−48.1730	+	10.2395i	−1.75786	+	0.373644i	−0.970169	−	0.242429i	$-0.922056\pi$
$751$	−48.1730	+	10.2395i	−1.75786	+	0.373644i	−0.787689	+	0.616073i	$0.788723\pi$
$752$	−39.1946	+	43.5301i	−1.42928	+	1.58738i
$753$	0.308350	−	0.692567i	0.0112369	−	0.0252385i
$754$	1.25434	+	11.9343i	0.0456804	+	0.434620i
$755$	−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
$759$	−13.6740	−	0.505819i	−0.496335	−	0.0183601i
$760$	12.0902	+	20.9408i	0.438557	+	0.759602i
$761$	4.17891	−	39.7597i	0.151485	−	1.44129i	−0.609637	−	0.792680i	$-0.708685\pi$
$761$	4.17891	−	39.7597i	0.151485	−	1.44129i	0.761123	−	0.648608i	$-0.224648\pi$
$762$	41.2387	+	13.3993i	1.49392	+	0.485404i
$763$	13.5514	+	2.88043i	0.490592	+	0.104279i
$764$	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
$767$	−1.02234	−	1.13542i	−0.0369146	−	0.0409978i
$768$	10.2590	+	23.0420i	0.370189	+	0.831458i
$769$	−4.39919	−	7.61962i	−0.158639	−	0.274770i	0.775739	−	0.631054i	$-0.217377\pi$
$769$	−4.39919	−	7.61962i	−0.158639	−	0.274770i	−0.934378	+	0.356283i	$0.884044\pi$
$770$	15.6645	+	23.3275i	0.564509	+	0.840664i
$771$	−39.1353	−	22.5947i	−1.40942	−	0.813730i
$772$	−48.7789	+	21.7178i	−1.75559	+	0.781639i
$773$	−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
$776$	4.68631	+	44.5872i	0.168229	+	1.60059i
$777$	−10.0322	+	3.25966i	−0.359903	+	0.116940i
$778$	22.1575	−	4.70971i	0.794384	−	0.168851i
$779$	1.19916	−	11.4093i	0.0429645	−	0.408780i
$780$	−58.2492	+	33.6302i	−2.08566	+	1.20415i
$781$	−46.2635	−	6.59949i	−1.65544	−	0.236148i
$782$	11.5623			0.413467
$783$	3.91858	+	8.80128i	0.140039	+	0.314532i
$784$	−18.2705	+	56.2308i	−0.652518	+	2.00824i
$785$	−43.8531	−	9.32127i	−1.56518	−	0.332690i
$786$	−30.9190	+	69.4452i	−1.10284	+	2.47703i
$787$	32.8876	+	14.6425i	1.17232	+	0.521949i	0.898131	−	0.439727i	$-0.144925\pi$
$787$	32.8876	+	14.6425i	1.17232	+	0.521949i	0.274186	+	0.961677i	$0.411592\pi$
$788$	12.2254	−	13.5776i	0.435510	−	0.483683i
$789$	−1.16661	−	0.379054i	−0.0415324	−	0.0134947i
$790$	74.0092	−	32.9510i	2.63313	−	1.17234i
$791$	−12.7639			−0.453833
$792$	−45.8935	+	58.4913i	−1.63076	+	2.07840i
$793$	10.2492			0.363961
$794$	−91.1824	+	40.5970i	−3.23594	+	1.44073i
$795$	−29.5331	+	26.5917i	−1.04743	+	0.943110i
$796$	−44.9985	+	49.9759i	−1.59493	+	1.77135i
$797$	−8.46903	−	3.77066i	−0.299989	−	0.133563i	0.251223	−	0.967929i	$-0.419167\pi$
$797$	−8.46903	−	3.77066i	−0.299989	−	0.133563i	−0.551211	+	0.834366i	$0.685834\pi$
$798$	−4.50973	+	0.473991i	−0.159643	+	0.0167791i
$799$	−10.7804	−	2.29145i	−0.381385	−	0.0810658i
$800$	−18.3541	+	56.4881i	−0.648915	+	1.99716i
$801$	30.7940	−	13.7104i	1.08805	−	0.484432i
$802$	14.5623			0.514213
$803$	−10.0075	+	20.4112i	−0.353157	+	0.720295i
$804$		−	50.4453i		−	1.77907i
$805$	0.805727	−	7.66598i	0.0283981	−	0.270190i
$806$	−10.2433	+	2.17728i	−0.360805	+	0.0766914i
$807$	−15.7942	−	14.2211i	−0.555981	−	0.500608i
$808$	0.368762	+	3.50854i	0.0129730	+	0.123430i
$809$	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	$0.261240\pi$
$810$	−51.0207	+	56.6642i	−1.79268	+	1.99098i
$811$	−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	$0.737998\pi$
$812$	−8.22191	+	3.66063i	−0.288532	+	0.128463i
$813$	−22.8541	+	13.1948i	−0.801528	+	0.462763i
$814$	−1.95481	+	52.8450i	−0.0685159	+	1.85222i
$815$	−11.7984	−	20.4354i	−0.413279	−	0.715820i
$816$	18.6007	−	25.6017i	0.651156	−	0.896239i
$817$	−3.24803	−	3.60730i	−0.113634	−	0.126203i
$818$	−7.07295	−	21.7683i	−0.247300	−	0.761111i
$819$	−0.775226	−	7.37578i	−0.0270886	−	0.257731i
$820$	145.790	−	105.923i	5.09122	−	3.69899i
$821$	12.9260	+	2.74751i	0.451121	+	0.0958887i	0.427869	−	0.903841i	$-0.359265\pi$
$821$	12.9260	+	2.74751i	0.451121	+	0.0958887i	0.0232522	+	0.999730i	$0.492598\pi$
$822$	21.5062	−	19.3643i	0.750115	−	0.675407i
$823$	5.82309	−	55.4030i	0.202980	−	1.93123i	−0.136550	−	0.990633i	$-0.543602\pi$
$823$	5.82309	−	55.4030i	0.202980	−	1.93123i	0.339531	−	0.940595i	$-0.389732\pi$
$824$	−21.5344	−	37.2987i	−0.750188	−	1.29936i
$825$	30.9687	−	5.39461i	1.07819	−	0.187816i
$826$	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	$0.538372\pi$
$828$	33.9289	−	7.21182i	1.17911	−	0.250628i
$829$	−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	$-0.234055\pi$
$830$	−12.6072	−	119.949i	−0.437601	−	4.16350i
$831$	−15.0308	−	20.6881i	−0.521412	−	0.717662i
$832$	14.4050	−	15.9983i	0.499402	−	0.554642i
$833$	−10.8815	+	2.31294i	−0.377022	+	0.0801385i
$834$	16.7230	+	1.75766i	0.579070	+	0.0608627i
$835$	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
$839$	−20.5478	−	22.8206i	−0.709389	−	0.787856i	0.275452	−	0.961315i	$-0.411172\pi$
$839$	−20.5478	−	22.8206i	−0.709389	−	0.787856i	−0.984841	+	0.173459i	$0.944506\pi$
$840$	−31.1241	−	28.0242i	−1.07388	−	0.966928i
$841$	−23.3523	−	10.3971i	−0.805253	−	0.358522i
$842$	−13.7856	−	6.13773i	−0.475082	−	0.211520i
$843$	10.4211	−	3.38601i	0.358921	−	0.116620i
$844$	37.4428	+	41.5845i	1.28884	+	1.43140i
$845$	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
$849$	11.9763	+	26.8992i	0.411026	+	0.923179i
$850$	−25.9819	+	5.52261i	−0.891170	+	0.189424i
$851$	9.70680	−	10.7805i	0.332745	−	0.369550i
$852$	117.815	−	12.3828i	4.03627	−	0.424229i
$853$	5.80784	+	55.2579i	0.198857	+	1.89200i	0.406287	+	0.913746i	$0.366823\pi$
$853$	5.80784	+	55.2579i	0.198857	+	1.89200i	−0.207430	+	0.978250i	$0.566510\pi$
$854$	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	−0.651970	−	0.758245i	$-0.726057\pi$
$857$	9.68034	−	16.7668i	0.330674	−	0.572744i	0.982644	+	0.185500i	$0.0593906\pi$
$858$	−36.0565	−	9.06914i	−1.23095	−	0.309615i
$859$	6.21885	+	10.7714i	0.212184	+	0.367514i	0.952398	−	0.304858i	$-0.0986089\pi$
$859$	6.21885	+	10.7714i	0.212184	+	0.367514i	−0.740214	+	0.672372i	$0.765276\pi$
$860$	7.97021	−	75.8315i	0.271782	−	2.58583i
$861$	4.13127	+	19.4361i	0.140793	+	0.662381i
$862$	61.6362	+	13.1012i	2.09934	+	0.446228i
$863$	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	$0.0507217\pi$
$864$	22.9398	−	51.5236i	0.780427	−	1.75287i
$865$	−11.9098	−	36.6547i	−0.404946	−	1.24630i
$866$	48.5998	+	53.9755i	1.65149	+	1.83416i
$867$	−23.3619	−	2.45544i	−0.793412	−	0.0833910i
$868$	−3.92705	−	6.80185i	−0.133293	−	0.230870i
$869$	29.7795	+	10.9086i	1.01020	+	0.370050i
$870$			27.2074i			0.922417i
$871$	13.5505	−	6.03305i	0.459140	−	0.204422i
$872$	−31.9894	+	98.4531i	−1.08330	+	3.33404i
$873$	−12.0444	+	13.3766i	−0.407640	+	0.452730i
$874$	5.04508	−	3.66547i	0.170653	−	0.123986i
$875$	0.159705	+	1.51949i	0.00539902	+	0.0513683i
$876$	11.9812	−	56.3669i	0.404806	−	1.90446i
$877$	36.7752	−	7.81680i	1.24181	−	0.263955i	0.460252	−	0.887788i	$-0.347759\pi$
$877$	36.7752	−	7.81680i	1.24181	−	0.263955i	0.781557	+	0.623834i	$0.214426\pi$
$878$	3.47772	−	33.0883i	0.117367	−	1.11667i
$879$	−10.2295	−	5.90600i	−0.345032	−	0.199204i
$880$	−93.4851	+	49.4592i	−3.15138	+	1.66727i
$881$	24.1803			0.814656			0.407328	−	0.913282i	$-0.366461\pi$
$881$	24.1803			0.814656			0.407328	+	0.913282i	$0.366461\pi$
$882$	−43.0505	+	19.1673i	−1.44958	+	0.645397i
$883$	−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	$0.123306\pi$
$884$	21.7630	+	4.62587i	0.731970	+	0.155585i
$885$	−2.03615	−	2.80252i	−0.0684444	−	0.0942056i
$886$	−7.73968	−	3.44593i	−0.260020	−	0.115768i
$887$	16.7513	−	18.6042i	0.562454	−	0.624668i	−0.393096	−	0.919497i	$-0.628596\pi$
$887$	16.7513	−	18.6042i	0.562454	−	0.624668i	0.955550	+	0.294829i	$0.0952627\pi$
$888$	−16.3875	−	77.0973i	−0.549930	−	2.58722i
$889$	−8.73560	+	3.88934i	−0.292983	+	0.130444i
$890$	95.1935			3.19089
$891$	−29.7812	+	2.02063i	−0.997706	+	0.0676935i
$892$	109.249			3.65793
$893$	−5.43036	+	2.41775i	−0.181720	+	0.0809070i
$894$	−6.76955	−	31.8482i	−0.226408	−	1.06516i
$895$	−49.6824	+	55.1779i	−1.66070	+	1.84439i
$896$	0.995920	+	0.443412i	0.0332713	+	0.0148134i
$897$	5.99497	+	8.25137i	0.200166	+	0.275505i
$898$	−3.76988	−	0.801313i	−0.125803	−	0.0267402i
$899$	−0.927051	+	2.85317i	−0.0309189	+	0.0951585i
$900$	−72.7976	+	32.4116i	−2.42659	+	1.08039i
$901$	13.1459			0.437953
$902$	98.6147	+	14.0674i	3.28351	+	0.468393i
$903$	7.28115	+	4.20378i	0.242302	+	0.139893i
$904$	9.96928	−	94.8514i	0.331573	−	3.15471i
$905$	66.7578	−	14.1898i	2.21910	−	0.471685i
$906$	−10.6783	+	50.2373i	−0.354761	+	1.66902i
$907$	4.32919	+	41.1895i	0.143749	+	1.36768i	0.793982	+	0.607941i	$0.208004\pi$
$907$	4.32919	+	41.1895i	0.143749	+	1.36768i	−0.650233	+	0.759734i	$0.725329\pi$
$908$	56.4787	−	41.0342i	1.87431	−	1.36177i
$909$	−0.947762	+	1.05260i	−0.0314353	+	0.0349124i
$910$	6.47214	−	19.9192i	0.214549	−	0.660315i
$911$	2.90539	−	1.29356i	0.0962597	−	0.0428576i	−0.358042	−	0.933706i	$-0.616556\pi$
$911$	2.90539	−	1.29356i	0.0962597	−	0.0428576i	0.454302	+	0.890848i	$0.349889\pi$
$912$		−	17.0678i		−	0.565172i
$913$	29.1458	−	37.1463i	0.964584	−	1.22936i
$914$	−1.30902	−	2.26728i	−0.0432984	−	0.0749951i
$915$	23.1106	+	2.42902i	0.764013	+	0.0803010i
$916$	−39.5621	−	43.9381i	−1.30717	−	1.45176i
$917$	−5.18034	−	15.9434i	−0.171070	−	0.526499i
$918$	25.0845	−	2.63649i	0.827911	−	0.0870170i
$919$	−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	$0.927009\pi$
$920$	56.3381	+	11.9750i	1.85741	+	0.394805i
$921$	0.412653	+	1.94138i	0.0135974	+	0.0639707i
$922$	−6.25423	+	59.5050i	−0.205972	+	1.95969i
$923$	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
$929$	1.53965	+	14.6488i	0.0505143	+	0.480612i	0.990310	+	0.138875i	$0.0443485\pi$
$929$	1.53965	+	14.6488i	0.0505143	+	0.480612i	−0.939796	+	0.341737i	$0.888985\pi$
$930$	−23.6132	+	2.48185i	−0.774309	+	0.0813831i
$931$	−4.01478	+	4.45887i	−0.131579	+	0.146134i
$932$	−138.284	+	29.3933i	−4.52966	+	0.962809i
$933$	5.05847	+	11.3615i	0.165607	+	0.371959i
$934$	−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	$0.731426\pi$
$938$	10.5108	+	11.6735i	0.343191	+	0.381152i
$939$	−9.01413	+	2.92887i	−0.294165	+	0.0955800i
$940$	−85.3012	−	37.9786i	−2.78222	−	1.23872i
$941$	−38.5142	−	17.1476i	−1.25553	−	0.558997i	−0.332272	−	0.943184i	$-0.607815\pi$
$941$	−38.5142	−	17.1476i	−1.25553	−	0.558997i	−0.923255	+	0.384187i	$0.874482\pi$
$942$	46.6861	+	42.0364i	1.52112	+	1.36962i
$943$	−18.2848	−	20.3074i	−0.595436	−	0.661298i
$944$	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	−0.990836	−	0.135073i	$-0.956873\pi$
$947$	−11.6459	+	20.1713i	−0.378441	+	0.655479i	0.612395	+	0.790552i	$0.290206\pi$
$948$	−79.9552	−	8.40363i	−2.59682	−	0.272937i
$949$	16.5740	−	3.52291i	0.538015	−	0.114359i
$950$	−9.58612	+	10.6465i	−0.311015	+	0.345417i
$951$	3.11096	+	4.28187i	0.100880	+	0.138849i
$952$	1.44815	+	13.7782i	0.0469347	+	0.446554i
$953$	−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	$-0.379467\pi$
$954$	54.4700	−	11.5780i	1.76353	−	0.374850i
$955$	31.2705	+	22.7194i	1.01189	+	0.735181i
$956$	−3.70820	+	6.42280i	−0.119932	+	0.207728i
$957$	−7.41464	+	7.64638i	−0.239681	+	0.247172i
$958$	−21.2533	−	36.8118i	−0.686663	−	1.18933i
$959$	−0.667097	+	6.34700i	−0.0215417	+	0.204955i
$960$	36.2727	−	32.6601i	1.17070	−	1.05410i
$961$	27.7618	+	5.90094i	0.895540	+	0.190353i
$962$	31.8885	−	23.1684i	1.02813	−	0.746979i
$963$	−4.71458	−	44.8562i	−0.151925	−	1.44547i
$964$	40.2492	+	123.874i	1.29634	+	3.98972i
$965$	−23.8189	−	26.4535i	−0.766757	−	0.851570i
$966$	−6.34878	+	8.73834i	−0.204269	+	0.281152i
$967$	16.2426	+	28.1331i	0.522328	+	0.904699i	0.999663	+	0.0259773i	$0.00826976\pi$
$967$	16.2426	+	28.1331i	0.522328	+	0.904699i	−0.477334	+	0.878722i	$0.658397\pi$
$968$	−78.9151	−	22.9822i	−2.53643	−	0.738675i
$969$	2.78115	−	1.60570i	0.0893435	−	0.0515825i
$970$	−46.4381	+	20.6756i	−1.49104	+	0.663853i
$971$	−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
$974$	9.29858	+	88.4701i	0.297946	+	2.83477i
$975$	−17.4126	−	15.6784i	−0.557649	−	0.502110i
$976$	−39.9613	+	8.49405i	−1.27913	+	0.271888i
$977$	−2.11525	+	20.1252i	−0.0676727	+	0.643863i	0.907139	+	0.420832i	$0.138262\pi$
$977$	−2.11525	+	20.1252i	−0.0676727	+	0.643863i	−0.974811	+	0.223031i	$0.928405\pi$
$978$			33.0651i			1.05731i
$979$	26.7532	+	25.9424i	0.855036	+	0.829122i
$980$	−94.2492			−3.01068
$981$	−37.9691	+	16.9049i	−1.21226	+	0.539732i
$982$	6.73607	−	20.7315i	0.214957	−	0.661568i
$983$	−50.6119	−	10.7579i	−1.61427	−	0.343124i	−0.689688	−	0.724106i	$-0.742252\pi$
$983$	−50.6119	−	10.7579i	−1.61427	−	0.343124i	−0.924582	+	0.380983i	$0.875586\pi$
$984$	−147.660	+	15.5197i	−4.70724	+	0.494751i
$985$	11.1273	+	4.95419i	0.354545	+	0.157854i
$986$	6.02218	−	6.68830i	0.191785	−	0.212999i
$987$	7.65126	−	6.88922i	0.243542	−	0.219286i
$988$	10.9625	−	4.88084i	0.348765	−	0.155280i
$989$	−11.5623			−0.367660
$990$	−79.1532	−	28.9949i	−2.51565	−	0.921519i
$991$	−28.5967			−0.908406			−0.454203	−	0.890898i	$-0.650076\pi$
$991$	−28.5967			−0.908406			−0.454203	+	0.890898i	$0.650076\pi$
$992$	16.0440	−	7.14323i	0.509396	−	0.226798i
$993$	20.4533	+	6.64567i	0.649065	+	0.210894i
$994$	−24.6833	+	27.4135i	−0.782905	+	0.869504i
$995$	−40.9568	−	18.2351i	−1.29842	−	0.578093i
$996$	−48.6825	+	109.343i	−1.54256	+	3.46466i
$997$	−9.40786	−	1.99970i	−0.297950	−	0.0633312i	0.0565113	−	0.998402i	$-0.482002\pi$
$997$	−9.40786	−	1.99970i	−0.297950	−	0.0633312i	−0.354461	+	0.935071i	$0.615336\pi$
$998$	−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.70.1	yes	8
3.2	odd	2		297.2.n.a.235.1		8
9.2	odd	6		891.2.f.a.730.1		4
9.4	even	3	inner	99.2.m.a.4.1	✓	8
9.5	odd	6		297.2.n.a.37.1		8
9.7	even	3		891.2.f.b.730.1		4
11.3	even	5	inner	99.2.m.a.25.1	yes	8
11.5	even	5		1089.2.e.g.727.2		4
11.6	odd	10		1089.2.e.d.727.1		4
33.14	odd	10		297.2.n.a.289.1		8
99.14	odd	30		297.2.n.a.91.1		8
99.16	even	15		9801.2.a.n.1.1		2
99.25	even	15		891.2.f.b.487.1		4
99.38	odd	30		9801.2.a.bb.1.2		2
99.47	odd	30		891.2.f.a.487.1		4
99.49	even	15		1089.2.e.g.364.2		4
99.58	even	15	inner	99.2.m.a.58.1	yes	8
99.61	odd	30		9801.2.a.bc.1.2		2
99.83	even	30		9801.2.a.m.1.1		2
99.94	odd	30		1089.2.e.d.364.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.a.4.1	✓	8	9.4	even	3	inner
99.2.m.a.25.1	yes	8	11.3	even	5	inner
99.2.m.a.58.1	yes	8	99.58	even	15	inner
99.2.m.a.70.1	yes	8	1.1	even	1	trivial
297.2.n.a.37.1		8	9.5	odd	6
297.2.n.a.91.1		8	99.14	odd	30
297.2.n.a.235.1		8	3.2	odd	2
297.2.n.a.289.1		8	33.14	odd	10
891.2.f.a.487.1		4	99.47	odd	30
891.2.f.a.730.1		4	9.2	odd	6
891.2.f.b.487.1		4	99.25	even	15
891.2.f.b.730.1		4	9.7	even	3
1089.2.e.d.364.1		4	99.94	odd	30
1089.2.e.d.727.1		4	11.6	odd	10
1089.2.e.g.364.2		4	99.49	even	15
1089.2.e.g.727.2		4	11.5	even	5
9801.2.a.m.1.1		2	99.83	even	30
9801.2.a.n.1.1		2	99.16	even	15
9801.2.a.bb.1.2		2	99.38	odd	30
9801.2.a.bc.1.2		2	99.61	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.39169 + 1.06485i) q^{2} +(0.360114 + 1.69420i) q^{3} +(3.24803 - 3.60730i) q^{4} +(2.95630 + 1.31623i) q^{5} +(-2.66535 - 3.66854i) q^{6} +(0.978148 + 0.207912i) q^{7} +(-2.30902 + 7.10642i) q^{8} +(-2.74064 + 1.22021i) q^{9} -8.47214 q^{10} +(-2.38101 - 2.30885i) q^{11} +(7.28115 + 4.20378i) q^{12} +(-0.258409 + 2.45859i) q^{13} +(-2.56082 + 0.544320i) q^{14} +(-1.16535 + 5.48255i) q^{15} +(-1.03003 - 9.80012i) q^{16} +(1.50000 - 1.08981i) q^{17} +(5.25542 - 5.83674i) q^{18} +(0.309017 - 0.951057i) q^{19} +(14.3502 - 6.38910i) q^{20} +1.73205i q^{21} +(8.15323 + 2.98664i) q^{22} +(-1.19098 - 2.06284i) q^{23} +(-12.8712 - 1.35282i) q^{24} +(3.66157 + 4.06659i) q^{25} +(-2.00000 - 6.15537i) q^{26} +(-3.05422 - 4.20378i) q^{27} +(3.92705 - 2.85317i) q^{28} +(-1.81359 - 0.385489i) q^{29} +(-3.05093 - 14.3535i) q^{30} +(0.169131 - 1.60917i) 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} +(0.273659 + 2.60369i) q^{38} +(-4.25841 + 0.447577i) q^{39} +(-16.1798 + 17.9695i) q^{40} +(11.2214 - 2.38519i) q^{41} +(-1.84437 - 4.14253i) q^{42} +(2.42705 - 4.20378i) q^{43} +(-16.0623 + 1.08981i) q^{44} -9.70820 q^{45} +(5.04508 + 3.66547i) q^{46} +(-3.97749 - 4.41745i) q^{47} +(16.2324 - 5.27424i) q^{48} +(-5.48127 - 2.44042i) q^{49} +(-13.0877 - 5.82701i) q^{50} +(2.38653 + 2.14885i) q^{51} +(8.02957 + 8.91774i) 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} +(1.72256 + 0.181049i) q^{57} +(4.74803 - 1.00922i) q^{58} +(-0.413545 + 0.459289i) q^{59} +(15.9921 + 22.0113i) q^{60} +(-0.433364 - 4.12319i) q^{61} +(1.30902 + 4.02874i) q^{62} +(-2.93444 + 0.623735i) q^{63} +(-7.04508 - 5.11855i) q^{64} +(-4.00000 + 6.92820i) q^{65} +(-2.12388 + 14.8887i) q^{66} +(-3.00000 - 5.19615i) q^{67} +(0.940756 - 8.95070i) q^{68} +(3.06598 - 2.76062i) q^{69} +(-8.28700 - 1.76146i) q^{70} +(11.3992 - 8.28199i) q^{71} +(-2.34315 - 22.2936i) q^{72} +(-2.11803 - 6.51864i) q^{73} +(-10.6688 - 11.8489i) q^{74} +(-5.57104 + 7.66788i) q^{75} +(-2.42705 - 4.20378i) q^{76} +(-1.84894 - 2.75344i) q^{77} +(9.70820 - 5.60503i) q^{78} +(-8.73560 + 3.88934i) q^{79} +(9.85410 - 30.3278i) q^{80} +(6.02218 - 6.68830i) q^{81} +(-24.2984 + 17.6538i) q^{82} +(1.48807 + 14.1581i) q^{83} +(6.24803 + 5.62575i) q^{84} +(5.86889 - 1.24747i) q^{85} +(-1.32837 + 12.6386i) q^{86} -3.21140i q^{87} +(21.9055 - 11.5893i) q^{88} -11.2361 q^{89} +(23.2190 - 10.3378i) q^{90} +(-0.763932 + 2.35114i) q^{91} +(-11.3096 - 2.40394i) q^{92} +(2.78716 - 0.292943i) q^{93} +(14.2169 + 6.32976i) q^{94} +(2.16535 - 2.40487i) q^{95} +(-13.9710 + 12.5796i) q^{96} +(5.48127 - 2.44042i) q^{97} +15.7082 q^{98} +(9.34277 + 3.42238i) 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

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