LMFDB - Embedded newform 115.2.j.a.9.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(4,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 4]))

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

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

chi := DirichletCharacter("115.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.j (of order $22$, degree $10$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			9.3
Character	$\chi$	$=$	115.9
Dual form			115.2.j.a.64.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.394732 - 1.34433i) q^{2} +(-1.97191 + 1.70867i) q^{3} +(0.0310904 - 0.0199806i) q^{4} +(2.16612 + 0.554912i) q^{5} +(3.07540 + 1.97644i) q^{6} +(2.68179 + 1.22473i) q^{7} +(-2.15687 - 1.86894i) q^{8} +(0.541936 - 3.76925i) q^{9} +O(q^{10})$	\(q+(-0.394732 - 1.34433i) q^{2} +(-1.97191 + 1.70867i) q^{3} +(0.0310904 - 0.0199806i) q^{4} +(2.16612 + 0.554912i) q^{5} +(3.07540 + 1.97644i) q^{6} +(2.68179 + 1.22473i) q^{7} +(-2.15687 - 1.86894i) q^{8} +(0.541936 - 3.76925i) q^{9} +(-0.109049 - 3.13103i) q^{10} +(1.52091 + 0.446579i) q^{11} +(-0.0271673 + 0.0925233i) q^{12} +(4.24625 - 1.93920i) q^{13} +(0.587861 - 4.08866i) q^{14} +(-5.21956 + 2.60695i) q^{15} +(-1.63039 + 3.57005i) q^{16} +(-0.714176 + 1.11128i) q^{17} +(-5.28104 + 0.759299i) q^{18} +(-4.70724 + 3.02516i) q^{19} +(0.0784330 - 0.0260279i) q^{20} +(-7.38094 + 2.16724i) q^{21} -2.22088i q^{22} +(-4.51845 + 1.60736i) q^{23} +7.44658 q^{24} +(4.38415 + 2.40401i) q^{25} +(-4.28306 - 4.94291i) q^{26} +(1.13981 + 1.77358i) q^{27} +(0.107849 - 0.0155063i) q^{28} +(-4.78017 - 3.07203i) q^{29} +(5.56493 + 5.98778i) q^{30} +(4.02560 - 4.64579i) q^{31} +(-0.206907 - 0.0297487i) q^{32} +(-3.76216 + 1.71812i) q^{33} +(1.77584 + 0.521433i) q^{34} +(5.12947 + 4.14108i) q^{35} +(-0.0584628 - 0.128016i) q^{36} +(-0.226161 - 0.0325170i) q^{37} +(5.92491 + 5.13396i) q^{38} +(-5.05979 + 11.0794i) q^{39} +(-3.63495 - 5.24523i) q^{40} +(-0.944912 - 6.57201i) q^{41} +(5.82698 + 9.06696i) q^{42} +(-4.67889 + 4.05429i) q^{43} +(0.0562086 - 0.0165043i) q^{44} +(3.26550 - 7.86391i) q^{45} +(3.94440 + 5.43983i) q^{46} -9.26629i q^{47} +(-2.88507 - 9.82563i) q^{48} +(1.10802 + 1.27872i) q^{49} +(1.50123 - 6.84269i) q^{50} +(-0.490520 - 3.41164i) q^{51} +(0.0932714 - 0.145133i) q^{52} +(-7.81920 - 3.57091i) q^{53} +(1.93436 - 2.23238i) q^{54} +(3.04666 + 1.81131i) q^{55} +(-3.49533 - 7.65371i) q^{56} +(4.11326 - 14.0085i) q^{57} +(-2.24294 + 7.63876i) q^{58} +(4.84630 + 10.6119i) q^{59} +(-0.110190 + 0.185341i) q^{60} +(-2.17039 + 2.50477i) q^{61} +(-7.83452 - 3.57791i) q^{62} +(6.06969 - 9.44462i) q^{63} +(1.15877 + 8.05944i) q^{64} +(10.2740 - 1.84424i) q^{65} +(3.79477 + 4.37939i) q^{66} +(2.96939 + 10.1128i) q^{67} +0.0488198i q^{68} +(6.16355 - 10.8901i) q^{69} +(3.54223 - 8.53032i) q^{70} +(-7.18012 + 2.10827i) q^{71} +(-8.21339 + 7.11694i) q^{72} +(0.164990 + 0.256729i) q^{73} +(0.0455592 + 0.316871i) q^{74} +(-12.7528 + 2.75057i) q^{75} +(-0.0859054 + 0.188107i) q^{76} +(3.53182 + 3.06034i) q^{77} +(16.8916 + 2.42865i) q^{78} +(-3.42189 - 7.49289i) q^{79} +(-5.51268 + 6.82843i) q^{80} +(5.68318 + 1.66873i) q^{81} +(-8.46197 + 3.86445i) q^{82} +(6.71269 + 0.965140i) q^{83} +(-0.186174 + 0.214856i) q^{84} +(-2.16365 + 2.01086i) q^{85} +(7.29721 + 4.68964i) q^{86} +(14.6752 - 2.10997i) q^{87} +(-2.44578 - 3.80570i) q^{88} +(5.15177 + 5.94546i) q^{89} +(-11.8607 - 1.28578i) q^{90} +13.7626 q^{91} +(-0.108365 + 0.140255i) q^{92} +16.0395i q^{93} +(-12.4570 + 3.65770i) q^{94} +(-11.8751 + 3.94075i) q^{95} +(0.458834 - 0.294875i) q^{96} +(-5.61695 + 0.807595i) q^{97} +(1.28166 - 1.99430i) q^{98} +(2.50750 - 5.49066i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9}+O(q^{10}) $ 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9	$ 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9} - 13 q^{10} - 26 q^{11} - 26 q^{14} - 10 q^{15} - 18 q^{16} - 14 q^{19} + 49 q^{20} - 22 q^{21} - 68 q^{24} + 21 q^{25} - 42 q^{26} - 24 q^{29} + 19 q^{30} - 12 q^{31} + 8 q^{34} - 37 q^{35} - 10 q^{36} + 14 q^{39} - q^{40} + 8 q^{41} + 166 q^{44} - 42 q^{45} - 18 q^{46} + 32 q^{49} - 23 q^{50} - 22 q^{51} + 116 q^{54} + 27 q^{55} - 116 q^{56} + 50 q^{59} + 123 q^{60} - 38 q^{61} + 10 q^{64} + 76 q^{65} - 28 q^{66} + 80 q^{69} + 102 q^{70} - 110 q^{71} + 22 q^{74} + 6 q^{75} + 4 q^{76} + 42 q^{79} + 18 q^{80} + 204 q^{81} + 56 q^{84} - 121 q^{85} + 132 q^{86} - 66 q^{89} - 198 q^{90} + 76 q^{91} - 70 q^{94} - 74 q^{95} + 236 q^{96} - 60 q^{99}+O(q^{100}) $ 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9 - 13 * q^10 - 26 * q^11 - 26 * q^14 - 10 * q^15 - 18 * q^16 - 14 * q^19 + 49 * q^20 - 22 * q^21 - 68 * q^24 + 21 * q^25 - 42 * q^26 - 24 * q^29 + 19 * q^30 - 12 * q^31 + 8 * q^34 - 37 * q^35 - 10 * q^36 + 14 * q^39 - q^40 + 8 * q^41 + 166 * q^44 - 42 * q^45 - 18 * q^46 + 32 * q^49 - 23 * q^50 - 22 * q^51 + 116 * q^54 + 27 * q^55 - 116 * q^56 + 50 * q^59 + 123 * q^60 - 38 * q^61 + 10 * q^64 + 76 * q^65 - 28 * q^66 + 80 * q^69 + 102 * q^70 - 110 * q^71 + 22 * q^74 + 6 * q^75 + 4 * q^76 + 42 * q^79 + 18 * q^80 + 204 * q^81 + 56 * q^84 - 121 * q^85 + 132 * q^86 - 66 * q^89 - 198 * q^90 + 76 * q^91 - 70 * q^94 - 74 * q^95 + 236 * q^96 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{5}{11}\right)$

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 $

$2$	−0.394732	−	1.34433i	−0.279117	−	0.950587i	−0.973059	−	0.230555i	$-0.925946\pi$
$2$	−0.394732	−	1.34433i	−0.279117	−	0.950587i	0.693942	−	0.720031i	$-0.255872\pi$
$3$	−1.97191	+	1.70867i	−1.13848	+	0.986503i	−0.999993	−	0.00386079i	$-0.998771\pi$
$3$	−1.97191	+	1.70867i	−1.13848	+	0.986503i	−0.138492	+	0.990364i	$0.544226\pi$
$4$	0.0310904	−	0.0199806i	0.0155452	−	0.00999030i
$5$	2.16612	+	0.554912i	0.968718	+	0.248164i
$5$	2.16612	+	0.554912i	0.968718	+	0.248164i
$6$	3.07540	+	1.97644i	1.25553	+	0.806878i
$7$	2.68179	+	1.22473i	1.01362	+	0.462906i	0.851774	−	0.523909i	$-0.175527\pi$
$7$	2.68179	+	1.22473i	1.01362	+	0.462906i	0.161849	+	0.986816i	$0.448254\pi$
$8$	−2.15687	−	1.86894i	−0.762570	−	0.660771i
$9$	0.541936	−	3.76925i	0.180645	−	1.25642i
$10$	−0.109049	−	3.13103i	−0.0344844	−	0.990117i
$11$	1.52091	+	0.446579i	0.458571	+	0.134649i	0.502856	−	0.864370i	$-0.332283\pi$
$11$	1.52091	+	0.446579i	0.458571	+	0.134649i	−0.0442848	+	0.999019i	$0.514101\pi$
$12$	−0.0271673	+	0.0925233i	−0.00784252	+	0.0267092i
$13$	4.24625	−	1.93920i	1.17770	−	0.537837i	0.272222	−	0.962234i	$-0.412241\pi$
$13$	4.24625	−	1.93920i	1.17770	−	0.537837i	0.905476	+	0.424398i	$0.139514\pi$
$14$	0.587861	−	4.08866i	0.157113	−	1.09274i
$15$	−5.21956	+	2.60695i	−1.34769	+	0.673112i
$16$	−1.63039	+	3.57005i	−0.407597	+	0.892513i
$17$	−0.714176	+	1.11128i	−0.173213	+	0.269525i	−0.916996	−	0.398897i	$-0.869393\pi$
$17$	−0.714176	+	1.11128i	−0.173213	+	0.269525i	0.743783	+	0.668421i	$0.233030\pi$
$18$	−5.28104	+	0.759299i	−1.24475	+	0.178968i
$19$	−4.70724	+	3.02516i	−1.07991	+	0.694019i	−0.954538	−	0.298091i	$-0.903650\pi$
$19$	−4.70724	+	3.02516i	−1.07991	+	0.694019i	−0.125376	+	0.992109i	$0.540014\pi$
$20$	0.0784330	−	0.0260279i	0.0175382	−	0.00582002i
$21$	−7.38094	+	2.16724i	−1.61065	+	0.472930i
$22$		−	2.22088i		−	0.473494i
$23$	−4.51845	+	1.60736i	−0.942162	+	0.335157i
$23$	−4.51845	+	1.60736i	−0.942162	+	0.335157i
$24$	7.44658			1.52003
$25$	4.38415	+	2.40401i	0.876829	+	0.480802i
$26$	−4.28306	−	4.94291i	−0.839976	−	0.969384i
$27$	1.13981	+	1.77358i	0.219357	+	0.341326i
$28$	0.107849	−	0.0155063i	0.0203815	−	0.00293042i
$29$	−4.78017	−	3.07203i	−0.887655	−	0.570461i	0.0154501	−	0.999881i	$-0.495082\pi$
$29$	−4.78017	−	3.07203i	−0.887655	−	0.570461i	−0.903105	+	0.429419i	$0.858718\pi$
$30$	5.56493	+	5.98778i	1.01601	+	1.09321i
$31$	4.02560	−	4.64579i	0.723020	−	0.834409i	−0.268647	−	0.963239i	$-0.586577\pi$
$31$	4.02560	−	4.64579i	0.723020	−	0.834409i	0.991667	+	0.128829i	$0.0411220\pi$
$32$	−0.206907	−	0.0297487i	−0.0365764	−	0.00525889i
$33$	−3.76216	+	1.71812i	−0.654907	+	0.299086i
$34$	1.77584	+	0.521433i	0.304553	+	0.0894249i
$35$	5.12947	+	4.14108i	0.867038	+	0.699970i
$36$	−0.0584628	−	0.128016i	−0.00974379	−	0.0213359i
$37$	−0.226161	−	0.0325170i	−0.0371806	−	0.00534577i	0.123699	−	0.992320i	$-0.460524\pi$
$37$	−0.226161	−	0.0325170i	−0.0371806	−	0.00534577i	−0.160880	+	0.986974i	$0.551433\pi$
$38$	5.92491	+	5.13396i	0.961147	+	0.832839i
$39$	−5.05979	+	11.0794i	−0.810214	+	1.77412i
$40$	−3.63495	−	5.24523i	−0.574736	−	0.829343i
$41$	−0.944912	−	6.57201i	−0.147570	−	1.02637i	−0.920181	−	0.391494i	$-0.871958\pi$
$41$	−0.944912	−	6.57201i	−0.147570	−	1.02637i	0.772610	−	0.634881i	$-0.218951\pi$
$42$	5.82698	+	9.06696i	0.899122	+	1.39906i
$43$	−4.67889	+	4.05429i	−0.713525	+	0.618273i	−0.934064	−	0.357105i	$-0.883764\pi$
$43$	−4.67889	+	4.05429i	−0.713525	+	0.618273i	0.220539	+	0.975378i	$0.429218\pi$
$44$	0.0562086	−	0.0165043i	0.00847376	−	0.00248812i
$45$	3.26550	−	7.86391i	0.486792	−	1.17228i
$46$	3.94440	+	5.43983i	0.581570	+	0.802059i
$47$		−	9.26629i		−	1.35163i	−0.737073	−	0.675813i	$-0.763792\pi$
$47$		−	9.26629i		−	1.35163i	0.737073	−	0.675813i	$-0.236208\pi$
$48$	−2.88507	−	9.82563i	−0.416423	−	1.41821i
$49$	1.10802	+	1.27872i	0.158289	+	0.182675i
$50$	1.50123	−	6.84269i	0.212306	−	0.967702i
$51$	−0.490520	−	3.41164i	−0.0686865	−	0.477725i
$52$	0.0932714	−	0.145133i	0.0129344	−	0.0201263i
$53$	−7.81920	−	3.57091i	−1.07405	−	0.490502i	−0.201732	−	0.979441i	$-0.564657\pi$
$53$	−7.81920	−	3.57091i	−1.07405	−	0.490502i	−0.872318	+	0.488938i	$0.837384\pi$
$54$	1.93436	−	2.23238i	0.263234	−	0.303788i
$55$	3.04666	+	1.81131i	0.410811	+	0.244237i
$56$	−3.49533	−	7.65371i	−0.467084	−	1.02277i
$57$	4.11326	−	14.0085i	0.544814	−	1.85547i
$58$	−2.24294	+	7.63876i	−0.294513	+	1.00302i
$59$	4.84630	+	10.6119i	0.630934	+	1.38155i	0.907293	+	0.420499i	$0.138145\pi$
$59$	4.84630	+	10.6119i	0.630934	+	1.38155i	−0.276359	+	0.961055i	$0.589128\pi$
$60$	−0.110190	+	0.185341i	−0.0142255	+	0.0239274i
$61$	−2.17039	+	2.50477i	−0.277891	+	0.320703i	−0.877488	−	0.479599i	$-0.840782\pi$
$61$	−2.17039	+	2.50477i	−0.277891	+	0.320703i	0.599597	+	0.800302i	$0.295328\pi$
$62$	−7.83452	−	3.57791i	−0.994986	−	0.454395i
$63$	6.06969	−	9.44462i	0.764709	−	1.18991i
$64$	1.15877	+	8.05944i	0.144847	+	1.00743i
$65$	10.2740	−	1.84424i	1.27433	−	0.228750i
$66$	3.79477	+	4.37939i	0.467103	+	0.539066i
$67$	2.96939	+	10.1128i	0.362769	+	1.23548i	0.915568	+	0.402163i	$0.131741\pi$
$67$	2.96939	+	10.1128i	0.362769	+	1.23548i	−0.552799	+	0.833315i	$0.686440\pi$
$68$			0.0488198i			0.00592027i
$69$	6.16355	−	10.8901i	0.742004	−	1.31102i
$70$	3.54223	−	8.53032i	0.423377	−	1.01957i
$71$	−7.18012	+	2.10827i	−0.852123	+	0.250206i	−0.678495	−	0.734605i	$-0.737367\pi$
$71$	−7.18012	+	2.10827i	−0.852123	+	0.250206i	−0.173628	+	0.984811i	$0.555549\pi$
$72$	−8.21339	+	7.11694i	−0.967957	+	0.838740i
$73$	0.164990	+	0.256729i	0.0193106	+	0.0300479i	0.850775	−	0.525531i	$-0.176133\pi$
$73$	0.164990	+	0.256729i	0.0193106	+	0.0300479i	−0.831464	+	0.555579i	$0.812497\pi$
$74$	0.0455592	+	0.316871i	0.00529615	+	0.0368355i
$75$	−12.7528	+	2.75057i	−1.47257	+	0.317608i
$76$	−0.0859054	+	0.188107i	−0.00985403	+	0.0215773i
$77$	3.53182	+	3.06034i	0.402488	+	0.348758i
$78$	16.8916	+	2.42865i	1.91260	+	0.274990i
$79$	−3.42189	−	7.49289i	−0.384992	−	0.843016i	−0.998574	−	0.0533846i	$-0.982999\pi$
$79$	−3.42189	−	7.49289i	−0.384992	−	0.843016i	0.613582	−	0.789631i	$-0.289728\pi$
$80$	−5.51268	+	6.82843i	−0.616336	+	0.763442i
$81$	5.68318	+	1.66873i	0.631465	+	0.185415i
$82$	−8.46197	+	3.86445i	−0.934469	+	0.426758i
$83$	6.71269	+	0.965140i	0.736814	+	0.105938i	0.500497	−	0.865738i	$-0.333151\pi$
$83$	6.71269	+	0.965140i	0.736814	+	0.105938i	0.236317	+	0.971676i	$0.424060\pi$
$84$	−0.186174	+	0.214856i	−0.0203132	+	0.0234427i
$85$	−2.16365	+	2.01086i	−0.234681	+	0.218108i
$86$	7.29721	+	4.68964i	0.786879	+	0.505696i
$87$	14.6752	−	2.10997i	1.57334	−	0.226213i
$88$	−2.44578	−	3.80570i	−0.260721	−	0.405689i
$89$	5.15177	+	5.94546i	0.546086	+	0.630217i	0.959967	−	0.280114i	$-0.0903723\pi$
$89$	5.15177	+	5.94546i	0.546086	+	0.630217i	−0.413881	+	0.910331i	$0.635827\pi$
$90$	−11.8607	−	1.28578i	−1.25023	−	0.135533i
$91$	13.7626			1.44271
$92$	−0.108365	+	0.140255i	−0.0112978	+	0.0146226i
$93$			16.0395i			1.66322i
$94$	−12.4570	+	3.65770i	−1.28484	+	0.377263i
$95$	−11.8751	+	3.94075i	−1.21836	+	0.404312i
$96$	0.458834	−	0.294875i	0.0468295	−	0.0300955i
$97$	−5.61695	+	0.807595i	−0.570315	+	0.0819989i	−0.421438	−	0.906857i	$-0.638475\pi$
$97$	−5.61695	+	0.807595i	−0.570315	+	0.0819989i	−0.148876	+	0.988856i	$0.547566\pi$
$98$	1.28166	−	1.99430i	0.129467	−	0.201455i
$99$	2.50750	−	5.49066i	0.252013	−	0.551832i
$100$	0.184338	−	0.0128561i	0.0184338	−	0.00128561i
$101$	0.745671	−	5.18625i	0.0741970	−	0.516052i	−0.918500	−	0.395420i	$-0.870599\pi$
$101$	0.745671	−	5.18625i	0.0741970	−	0.516052i	0.992697	−	0.120631i	$-0.0384919\pi$
$102$	−4.39275	+	2.00610i	−0.434947	+	0.198634i
$103$	5.25232	−	17.8877i	0.517526	−	1.76253i	−0.120706	−	0.992688i	$-0.538516\pi$
$103$	5.25232	−	17.8877i	0.517526	−	1.76253i	0.638232	−	0.769844i	$-0.279666\pi$
$104$	−12.7829	−	3.75339i	−1.25346	−	0.368050i
$105$	−17.1906	+	0.598726i	−1.67763	+	0.0584297i
$106$	−1.71400	+	11.9212i	−0.166479	+	1.15789i
$107$	−5.85951	−	5.07730i	−0.566460	−	0.490841i	0.323904	−	0.946090i	$-0.395005\pi$
$107$	−5.85951	−	5.07730i	−0.566460	−	0.490841i	−0.890364	+	0.455249i	$0.849550\pi$
$108$	0.0708745	+	0.0323673i	0.00681990	+	0.00311454i
$109$	4.92636	+	3.16598i	0.471860	+	0.303246i	0.754874	−	0.655870i	$-0.227698\pi$
$109$	4.92636	+	3.16598i	0.471860	+	0.303246i	−0.283014	+	0.959116i	$0.591334\pi$
$110$	1.23240	−	4.81070i	0.117504	−	0.458682i
$111$	0.501531	−	0.322314i	0.0476032	−	0.0305927i
$112$	−8.74473	+	7.57735i	−0.826299	+	0.715992i
$113$	2.56064	+	8.72074i	0.240885	+	0.820378i	0.987836	+	0.155499i	$0.0496987\pi$
$113$	2.56064	+	8.72074i	0.240885	+	0.820378i	−0.746951	+	0.664879i	$0.768483\pi$
$114$	−20.4557			−1.91585
$115$	−10.6794	+	0.974385i	−0.995864	+	0.0908619i
$116$	−0.209998			−0.0194979
$117$	−5.00812	−	17.0561i	−0.463001	−	1.57684i
$118$	12.3530	−	10.7039i	1.13718	−	0.985374i
$119$	−3.27629	+	2.10555i	−0.300337	+	0.193015i
$120$	16.1302	+	4.13220i	1.47248	+	0.377216i
$121$	−7.14006	−	4.58864i	−0.649096	−	0.417149i
$122$	4.22397	+	1.92902i	0.382420	+	0.174645i
$123$	13.0927	+	11.3449i	1.18053	+	1.02293i
$124$	0.0323319	−	0.224874i	0.00290349	−	0.0201942i
$125$	8.16257	+	7.64019i	0.730082	+	0.683359i
$126$	−15.0926	−	4.43159i	−1.34456	−	0.394797i
$127$	1.78354	−	6.07417i	0.158263	−	0.538996i	−0.841736	−	0.539889i	$-0.818466\pi$
$127$	1.78354	−	6.07417i	0.158263	−	0.538996i	1.00000		0.000893287i	$0.000284342\pi$
$128$	9.99687	−	4.56542i	0.883607	−	0.403530i
$129$	2.29893	−	15.9894i	0.202409	−	1.40779i
$130$	−6.53473	−	13.0837i	−0.573134	−	1.14751i
$131$	−1.99588	+	4.37037i	−0.174381	+	0.381841i	−0.976561	−	0.215241i	$-0.930946\pi$
$131$	−1.99588	+	4.37037i	−0.174381	+	0.381841i	0.802180	+	0.597082i	$0.203673\pi$
$132$	−0.0826379	+	0.128587i	−0.00719271	+	0.0111921i
$133$	−16.3289	+	2.34773i	−1.41589	+	0.203574i
$134$	12.4229	−	7.98370i	1.07317	−	0.689687i
$135$	1.48479	+	4.47429i	0.127790	+	0.385085i
$136$	3.61730	−	1.06214i	0.310181	−	0.0910774i
$137$			4.56852i			0.390315i	0.980772	+	0.195158i	$0.0625218\pi$
$137$			4.56852i			0.390315i	−0.980772	+	0.195158i	$0.937478\pi$
$138$	−17.0729	−	3.98718i	−1.45334	−	0.339411i
$139$	−15.2156			−1.29057			−0.645284	−	0.763943i	$-0.723261\pi$
$139$	−15.2156			−1.29057			−0.645284	+	0.763943i	$0.723261\pi$
$140$	0.242218	+	0.0262581i	0.0204712	+	0.00221922i
$141$	15.8331	+	18.2723i	1.33338	+	1.53881i
$142$	5.66844	+	8.82026i	0.475685	+	0.740180i
$143$	7.32416	−	1.05306i	0.612477	−	0.0880609i
$144$	12.5728	+	8.08007i	1.04774	+	0.673339i
$145$	−8.64971	−	9.30695i	−0.718319	−	0.772900i
$146$	0.280003	−	0.323141i	0.0231732	−	0.0267433i
$147$	−4.36984	−	0.628289i	−0.360419	−	0.0518204i
$148$	−0.00768115	+	0.00350786i	−0.000631386	+	0.000288345i
$149$	9.48896	+	2.78621i	0.777366	+	0.228255i	0.646264	−	0.763114i	$-0.276330\pi$
$149$	9.48896	+	2.78621i	0.777366	+	0.228255i	0.131101	+	0.991369i	$0.458149\pi$
$150$	8.73162	+	16.0583i	0.712934	+	1.31115i
$151$	−7.52665	−	16.4811i	−0.612510	−	1.34121i	−0.920844	−	0.389932i	$-0.872499\pi$
$151$	−7.52665	−	16.4811i	−0.612510	−	1.34121i	0.308333	−	0.951278i	$-0.400229\pi$
$152$	15.8068	+	2.27267i	1.28210	+	0.184338i
$153$	3.80165	+	3.29415i	0.307345	+	0.266316i
$154$	2.71999	−	5.95596i	0.219183	−	0.479945i
$155$	11.2979	−	7.82949i	0.907473	−	0.628880i
$156$	0.0640619	+	0.445560i	0.00512905	+	0.0356734i
$157$	12.2151	+	19.0071i	0.974873	+	1.51693i	0.851355	+	0.524590i	$0.175781\pi$
$157$	12.2151	+	19.0071i	0.974873	+	1.51693i	0.123518	+	0.992342i	$0.460582\pi$
$158$	−8.72221	+	7.55784i	−0.693902	+	0.601269i
$159$	21.5203	−	6.31893i	1.70667	−	0.501124i
$160$	−0.431678	−	0.179255i	−0.0341271	−	0.0141713i
$161$	−14.0861	−	1.22330i	−1.11014	−	0.0964095i
$162$		−	8.29879i		−	0.652014i
$163$	−1.81699	−	6.18810i	−0.142318	−	0.484689i	0.857225	−	0.514943i	$-0.172187\pi$
$163$	−1.81699	−	6.18810i	−0.142318	−	0.484689i	−0.999542	+	0.0302534i	$0.990369\pi$
$164$	−0.160690	−	0.185446i	−0.0125478	−	0.0144809i
$165$	−9.10268	+	1.63398i	−0.708643	+	0.127206i
$166$	−1.35224	−	9.40506i	−0.104954	−	0.729974i
$167$	−5.28392	+	8.22194i	−0.408882	+	0.636233i	−0.983228	−	0.182380i	$-0.941620\pi$
$167$	−5.28392	+	8.22194i	−0.408882	+	0.636233i	0.574346	+	0.818613i	$0.305256\pi$
$168$	19.9702	+	9.12008i	1.54073	+	0.703630i
$169$	5.75697	−	6.64390i	0.442844	−	0.511069i
$170$	3.55732	+	2.11492i	0.272834	+	0.162207i
$171$	8.85154	+	19.3822i	0.676894	+	1.48219i
$172$	−0.0644617	+	0.219536i	−0.00491516	+	0.0167395i
$173$	−2.53455	+	8.63190i	−0.192699	+	0.656271i	0.805290	+	0.592881i	$0.202009\pi$
$173$	−2.53455	+	8.63190i	−0.192699	+	0.656271i	−0.997989	+	0.0633903i	$0.979809\pi$
$174$	−8.62926	−	18.8954i	−0.654182	−	1.43246i
$175$	8.81310	+	11.8165i	0.666208	+	0.893242i
$176$	−4.07398	+	4.70162i	−0.307088	+	0.354398i
$177$	−27.6888	−	12.6450i	−2.08122	−	0.950459i
$178$	5.95910	−	9.27255i	0.446654	−	0.695007i
$179$	1.93200	+	13.4374i	0.144405	+	1.00436i	0.925175	+	0.379540i	$0.123918\pi$
$179$	1.93200	+	13.4374i	0.144405	+	1.00436i	−0.780771	+	0.624818i	$0.785173\pi$
$180$	−0.0555999	−	0.309739i	−0.00414417	−	0.0230866i
$181$	−2.05334	−	2.36968i	−0.152623	−	0.176137i	0.674289	−	0.738468i	$-0.264450\pi$
$181$	−2.05334	−	2.36968i	−0.152623	−	0.176137i	−0.826912	+	0.562331i	$0.809905\pi$
$182$	−5.43252	−	18.5015i	−0.402685	−	1.37142i
$183$		−	8.64768i		−	0.639255i
$184$	12.7498	+	4.97785i	0.939927	+	0.366972i
$185$	−0.471848	−	0.195935i	−0.0346909	−	0.0144054i
$186$	21.5625	−	6.33131i	1.58104	−	0.464235i
$187$	−1.58247	+	1.37122i	−0.115722	+	0.100273i
$188$	−0.185146	−	0.288093i	−0.0135032	−	0.0210113i
$189$	0.884575	+	6.15235i	0.0643433	+	0.447518i
$190$	9.98516	+	14.4086i	0.724400	+	1.04531i
$191$	0.574624	−	1.25825i	0.0415783	−	0.0910439i	−0.887703	−	0.460416i	$-0.847700\pi$
$191$	0.574624	−	1.25825i	0.0415783	−	0.0910439i	0.929281	+	0.369373i	$0.120427\pi$
$192$	−16.0559	−	13.9126i	−1.15874	−	1.00405i
$193$	2.60238	+	0.374166i	0.187324	+	0.0269331i	0.235338	−	0.971914i	$-0.424380\pi$
$193$	2.60238	+	0.374166i	0.187324	+	0.0269331i	−0.0480145	+	0.998847i	$0.515289\pi$
$194$	3.30286	+	7.23226i	0.237132	+	0.519246i
$195$	−17.1082	+	21.1915i	−1.22514	+	1.51756i
$196$	0.0599985	+	0.0176172i	0.00428561	+	0.00125837i
$197$	12.7168	−	5.80756i	0.906033	−	0.413771i	0.0927834	−	0.995686i	$-0.470424\pi$
$197$	12.7168	−	5.80756i	0.906033	−	0.413771i	0.813250	+	0.581915i	$0.197696\pi$
$198$	−8.37106	−	1.20358i	−0.594905	−	0.0855345i
$199$	8.88720	−	10.2564i	0.629997	−	0.727055i	−0.347576	−	0.937652i	$-0.612995\pi$
$199$	8.88720	−	10.2564i	0.629997	−	0.727055i	0.977573	+	0.210597i	$0.0675407\pi$
$200$	−4.96309	−	13.3789i	−0.350943	−	0.946028i
$201$	−23.1349	−	14.8679i	−1.63181	−	1.04870i
$202$	−7.26639	+	1.04475i	−0.511261	+	0.0735083i
$203$	−9.05701	−	14.0930i	−0.635678	−	0.989134i
$204$	−0.0834170	−	0.0962684i	−0.00584036	−	0.00674013i
$205$	1.60009	−	14.7601i	0.111755	−	1.03089i
$206$	−26.1203			−1.81989
$207$	3.60982	+	17.9022i	0.250900	+	1.24429i
$208$			18.3210i			1.27033i
$209$	−8.51024	+	2.49883i	−0.588666	+	0.172848i
$210$	7.59057	+	22.8736i	0.523799	+	1.57843i
$211$	5.33889	−	3.43110i	0.367545	−	0.236207i	−0.343811	−	0.939039i	$-0.611718\pi$
$211$	5.33889	−	3.43110i	0.367545	−	0.236207i	0.711356	+	0.702832i	$0.248082\pi$
$212$	−0.314451	+	0.0452113i	−0.0215966	+	0.00310512i
$213$	10.5562	−	16.4258i	0.723300	−	1.12548i
$214$	−4.51264	+	9.88130i	−0.308478	+	0.675472i
$215$	−12.3848	+	6.18569i	−0.844637	+	0.421861i
$216$	0.856291	−	5.95564i	0.0582632	−	0.405230i
$217$	16.4857	−	7.52877i	1.11912	−	0.511086i
$218$	2.31154	−	7.87238i	0.156557	−	0.533185i
$219$	−0.764012	−	0.224334i	−0.0516272	−	0.0151591i
$220$	0.130913	−	0.00455952i	0.00882614	−	0.000307403i
$221$	−0.877579	+	6.10370i	−0.0590324	+	0.410579i
$222$	−0.631268	−	0.546997i	−0.0423679	−	0.0367120i
$223$	8.76703	+	4.00377i	0.587084	+	0.268112i	0.686732	−	0.726911i	$-0.259045\pi$
$223$	8.76703	+	4.00377i	0.587084	+	0.268112i	−0.0996485	+	0.995023i	$0.531772\pi$
$224$	−0.518448	−	0.333186i	−0.0346403	−	0.0222619i
$225$	11.4372	−	15.2221i	0.762482	−	1.01481i
$226$	10.7128	−	6.88471i	0.712606	−	0.457964i
$227$	14.1856	−	12.2919i	0.941530	−	0.815841i	−0.0415273	−	0.999137i	$-0.513222\pi$
$227$	14.1856	−	12.2919i	0.941530	−	0.815841i	0.983058	+	0.183297i	$0.0586769\pi$
$228$	−0.152015	−	0.517714i	−0.0100674	−	0.0342865i
$229$	−16.6093			−1.09757			−0.548786	−	0.835963i	$-0.684910\pi$
$229$	−16.6093			−1.09757			−0.548786	+	0.835963i	$0.684910\pi$
$230$	5.52541	+	13.9721i	0.364335	+	0.921293i
$231$	−12.1936			−0.802278
$232$	4.56878	+	15.5598i	0.299955	+	1.02155i
$233$	10.2086	−	8.84581i	0.668789	−	0.579509i	−0.252875	−	0.967499i	$-0.581376\pi$
$233$	10.2086	−	8.84581i	0.668789	−	0.579509i	0.921663	+	0.387990i	$0.126831\pi$
$234$	−20.9522	+	13.4652i	−1.36969	+	0.880245i
$235$	5.14198	−	20.0719i	0.335425	−	1.30935i
$236$	0.362706	+	0.233097i	0.0236101	+	0.0151733i
$237$	19.5506	+	8.92844i	1.26995	+	0.579965i
$238$	4.12381	+	3.57330i	0.267307	+	0.231623i
$239$	−0.556606	+	3.87128i	−0.0360038	+	0.250412i	−0.999873	−	0.0159656i	$-0.994918\pi$
$239$	−0.556606	+	3.87128i	−0.0360038	+	0.250412i	0.963869	+	0.266378i	$0.0858269\pi$
$240$	−0.797034	−	22.8844i	−0.0514483	−	1.47718i
$241$	9.35355	+	2.74645i	0.602515	+	0.176914i	0.568743	−	0.822515i	$-0.307430\pi$
$241$	9.35355	+	2.74645i	0.602515	+	0.176914i	0.0337718	+	0.999430i	$0.489248\pi$
$242$	−3.35025	+	11.4099i	−0.215362	+	0.733456i
$243$	−19.8113	+	9.04751i	−1.27089	+	0.580398i
$244$	−0.0174317	+	0.121240i	−0.00111595	+	0.00776160i
$245$	1.69053	+	3.38472i	0.108004	+	0.216242i
$246$	10.0832	−	22.0791i	0.642881	−	1.40771i
$247$	−14.1217	+	21.9738i	−0.898544	+	1.39816i
$248$	−17.3654	+	2.49677i	−1.10271	+	0.158545i
$249$	−14.8860	+	9.56662i	−0.943359	+	0.606260i
$250$	7.04893	−	13.9890i	0.445814	−	0.884744i
$251$	16.5033	−	4.84581i	1.04168	−	0.305865i	0.284228	−	0.958757i	$-0.408263\pi$
$251$	16.5033	−	4.84581i	1.04168	−	0.305865i	0.757451	+	0.652892i	$0.226444\pi$
$252$		−	0.414913i		−	0.0261371i
$253$	−7.58996	+	0.426798i	−0.477177	+	0.0268326i
$254$	−8.86973			−0.556536
$255$	0.830636	−	7.66221i	0.0520164	−	0.479826i
$256$	0.580645	+	0.670100i	0.0362903	+	0.0418812i
$257$	4.80672	+	7.47940i	0.299835	+	0.466552i	0.958181	−	0.286163i	$-0.0923800\pi$
$257$	4.80672	+	7.47940i	0.299835	+	0.466552i	−0.658346	+	0.752715i	$0.728744\pi$
$258$	−22.4025	+	3.22100i	−1.39472	+	0.200531i
$259$	−0.566693	−	0.364191i	−0.0352126	−	0.0226297i
$260$	0.282573	−	0.262618i	0.0175244	−	0.0162869i
$261$	−14.1698	+	16.3528i	−0.877087	+	1.01221i
$262$	6.66307	+	0.958004i	0.411646	+	0.0591857i
$263$	−2.35945	+	1.07753i	−0.145490	+	0.0664431i	−0.486830	−	0.873497i	$-0.661847\pi$
$263$	−2.35945	+	1.07753i	−0.145490	+	0.0664431i	0.341339	+	0.939940i	$0.389119\pi$
$264$	11.3256	+	3.32548i	0.697040	+	0.204669i
$265$	−14.9558	−	12.0740i	−0.918727	−	0.741699i
$266$	9.60165	+	21.0247i	0.588715	+	1.28911i
$267$	−20.3177	−	2.92124i	−1.24342	−	0.178777i
$268$	0.294380	+	0.255081i	0.0179821	+	0.0155816i
$269$	−1.13907	+	2.49422i	−0.0694504	+	0.152075i	−0.941174	−	0.337924i	$-0.890275\pi$
$269$	−1.13907	+	2.49422i	−0.0694504	+	0.152075i	0.871723	+	0.489999i	$0.163003\pi$
$270$	5.42884	−	3.76219i	0.330389	−	0.228960i
$271$	1.97254	+	13.7193i	0.119823	+	0.833390i	0.957749	+	0.287606i	$0.0928593\pi$
$271$	1.97254	+	13.7193i	0.119823	+	0.833390i	−0.837925	+	0.545785i	$0.816232\pi$
$272$	−2.80294	−	4.36146i	−0.169953	−	0.264452i
$273$	−27.1386	+	23.5157i	−1.64250	+	1.42324i
$274$	6.14161	−	1.80334i	0.371028	−	0.108944i
$275$	5.59430	+	5.61415i	0.337349	+	0.338546i
$276$	−0.0259640	−	0.461730i	−0.00156285	−	0.0277929i
$277$		−	2.92978i		−	0.176033i	−0.996119	−	0.0880167i	$-0.971947\pi$
$277$		−	2.92978i		−	0.176033i	0.996119	−	0.0880167i	$-0.0280529\pi$
$278$	6.00607	+	20.4548i	0.360220	+	1.22680i
$279$	−15.3295	−	17.6912i	−0.917754	−	1.05915i
$280$	−3.32417	−	18.5185i	−0.198657	−	1.10669i
$281$	3.47962	+	24.2013i	0.207577	+	1.44373i	0.781032	+	0.624491i	$0.214694\pi$
$281$	3.47962	+	24.2013i	0.207577	+	1.44373i	−0.573455	+	0.819237i	$0.694397\pi$
$282$	18.3143	−	28.4975i	1.09060	−	1.69700i
$283$	−18.1109	−	8.27096i	−1.07658	−	0.491657i	−0.203420	−	0.979092i	$-0.565206\pi$
$283$	−18.1109	−	8.27096i	−1.07658	−	0.491657i	−0.873160	+	0.487434i	$0.837933\pi$
$284$	−0.181108	+	0.209010i	−0.0107468	+	0.0124025i
$285$	16.6833	−	28.0615i	0.988232	−	1.66222i
$286$	−4.30673	−	9.43043i	−0.254663	−	0.557633i
$287$	5.51490	−	18.7820i	0.325534	−	1.10867i
$288$	−0.224261	+	0.763762i	−0.0132147	+	0.0450051i
$289$	6.33716	+	13.8764i	0.372774	+	0.816262i
$290$	−9.09732	+	15.3018i	−0.534213	+	0.898555i
$291$	9.69622	−	11.1900i	0.568402	−	0.655971i
$292$	0.0102592	+	0.00468522i	0.000600375	+	0.000274182i
$293$	−6.06437	+	9.43634i	−0.354284	+	0.551277i	−0.971957	−	0.235158i	$-0.924439\pi$
$293$	−6.06437	+	9.43634i	−0.354284	+	0.551277i	0.617673	+	0.786435i	$0.288076\pi$
$294$	0.880287	+	6.12253i	0.0513394	+	0.357073i
$295$	4.60898	+	25.6759i	0.268345	+	1.49491i
$296$	0.427028	+	0.492817i	0.0248205	+	0.0286444i
$297$	0.941505	+	3.20647i	0.0546317	+	0.186058i
$298$		−	13.8561i		−	0.802663i
$299$	−16.0695	+	15.5874i	−0.929323	+	0.901443i
$300$	−0.341533	+	0.340325i	−0.0197184	+	0.0196487i
$301$	−17.5133	+	5.14236i	−1.00945	+	0.296400i
$302$	−19.1850	+	16.6239i	−1.10397	+	0.956599i
$303$	7.39121	+	11.5010i	0.424614	+	0.660713i
$304$	−3.12534	−	21.7372i	−0.179251	−	1.24672i
$305$	−6.09126	+	4.22125i	−0.348785	+	0.241708i
$306$	2.92780	−	6.41098i	0.167371	−	0.366491i
$307$	−5.74551	−	4.97852i	−0.327914	−	0.284139i	0.475307	−	0.879820i	$-0.342337\pi$
$307$	−5.74551	−	4.97852i	−0.327914	−	0.284139i	−0.803221	+	0.595681i	$0.796882\pi$
$308$	0.170953	+	0.0245794i	0.00974096	+	0.00140054i
$309$	20.2072	+	44.2476i	1.14955	+	2.51716i
$310$	−14.9851	−	12.0976i	−0.851096	−	0.687100i
$311$	16.5580	+	4.86186i	0.938916	+	0.275691i	0.715165	−	0.698956i	$-0.246351\pi$
$311$	16.5580	+	4.86186i	0.938916	+	0.275691i	0.223751	+	0.974646i	$0.428170\pi$
$312$	31.6200	−	14.4404i	1.79013	−	0.817526i
$313$	2.68453	+	0.385977i	0.151738	+	0.0218167i	0.217765	−	0.976001i	$-0.430123\pi$
$313$	2.68453	+	0.385977i	0.151738	+	0.0218167i	−0.0660270	+	0.997818i	$0.521032\pi$
$314$	20.7302	−	23.9239i	1.16987	−	1.35010i
$315$	18.3886	−	17.0900i	1.03608	−	0.962914i
$316$	−0.256100	−	0.164586i	−0.0144068	−	0.00925867i
$317$	2.90177	−	0.417211i	0.162980	−	0.0234329i	−0.0603419	−	0.998178i	$-0.519219\pi$
$317$	2.90177	−	0.417211i	0.162980	−	0.0234329i	0.223322	+	0.974745i	$0.428310\pi$
$318$	−16.9895	−	26.4362i	−0.952724	−	1.48247i
$319$	−5.89829	−	6.80699i	−0.330241	−	0.381118i
$320$	−1.96224	+	18.1007i	−0.109693	+	1.01186i
$321$	20.2299			1.12912
$322$	3.91572	+	19.4193i	0.218215	+	1.08220i
$323$		−	7.39154i		−	0.411277i
$324$	0.210035	−	0.0616717i	0.0116686	−	0.00342621i
$325$	23.2780	+	1.70631i	1.29123	+	0.0946492i
$326$	−7.60164	+	4.88528i	−0.421016	+	0.270570i
$327$	−15.1240	+	2.17450i	−0.836358	+	0.120250i
$328$	−10.2446	+	15.9410i	−0.565666	+	0.880193i
$329$	11.3487	−	24.8503i	0.625676	−	1.37004i
$330$	5.78974	+	11.5920i	0.318714	+	0.638121i
$331$	−1.19997	+	8.34600i	−0.0659565	+	0.458738i	0.929901	+	0.367810i	$0.119892\pi$
$331$	−1.19997	+	8.34600i	−0.0659565	+	0.458738i	−0.995857	+	0.0909277i	$0.971017\pi$
$332$	0.227984	−	0.104117i	0.0125123	−	0.00571416i
$333$	−0.245129	+	0.834834i	−0.0134330	+	0.0457486i
$334$	13.1388	+	3.85789i	0.718921	+	0.211094i
$335$	0.820330	+	23.5533i	0.0448194	+	1.28686i
$336$	4.29664	−	29.8838i	0.234401	−	1.63029i
$337$	2.58459	+	2.23956i	0.140792	+	0.121997i	0.722410	−	0.691465i	$-0.243035\pi$
$337$	2.58459	+	2.23956i	0.140792	+	0.121997i	−0.581618	+	0.813462i	$0.697580\pi$
$338$	−11.2041	−	5.11672i	−0.609421	−	0.278313i
$339$	−19.9503	−	12.8213i	−1.08355	−	0.696355i
$340$	−0.0270907	+	0.105749i	−0.00146920	+	0.00573507i
$341$	8.19728	−	5.26808i	0.443908	−	0.285282i
$342$	22.5621	−	19.5502i	1.22002	−	1.05715i
$343$	−4.40888	−	15.0153i	−0.238057	−	0.810748i
$344$	17.6690			0.952649
$345$	19.3940	−	20.1691i	1.04414	−	1.08587i
$346$	12.6046			0.677628
$347$	−2.04586	−	6.96754i	−0.109827	−	0.374037i	0.886177	−	0.463348i	$-0.153352\pi$
$347$	−2.04586	−	6.96754i	−0.109827	−	0.374037i	−0.996004	+	0.0893103i	$0.971534\pi$
$348$	0.414099	−	0.358818i	0.0221980	−	0.0192347i
$349$	29.2341	−	18.7876i	1.56487	−	1.00568i	0.583825	−	0.811879i	$-0.301555\pi$
$349$	29.2341	−	18.7876i	1.56487	−	1.00568i	0.981041	−	0.193799i	$-0.0620810\pi$
$350$	12.4065	−	16.5121i	0.663153	−	0.882607i
$351$	8.27926	+	5.32076i	0.441914	+	0.284001i
$352$	−0.301401	−	0.137645i	−0.0160648	−	0.00733653i
$353$	18.0897	+	15.6748i	0.962815	+	0.834284i	0.986220	−	0.165442i	$-0.0529050\pi$
$353$	18.0897	+	15.6748i	0.962815	+	0.834284i	−0.0234042	+	0.999726i	$0.507450\pi$
$354$	−6.06950	+	42.2143i	−0.322590	+	2.24367i
$355$	−16.7229	+	0.582436i	−0.887559	+	0.0309125i
$356$	0.278964	+	0.0819113i	0.0147851	+	0.00434129i
$357$	2.86288	−	9.75007i	0.151520	−	0.516028i
$358$	17.3017	−	7.90142i	0.914423	−	0.417603i
$359$	1.74258	−	12.1199i	0.0919697	−	0.639663i	−0.890740	−	0.454512i	$-0.849814\pi$
$359$	1.74258	−	12.1199i	0.0919697	−	0.639663i	0.982710	−	0.185151i	$-0.0592773\pi$
$360$	−21.7405	+	10.8584i	−1.14582	+	0.572290i
$361$	5.11361	−	11.1972i	0.269137	−	0.589328i
$362$	−2.37512	+	3.69575i	−0.124833	+	0.194244i
$363$	21.9201	−	3.15163i	1.15051	−	0.165418i
$364$	0.427884	−	0.274984i	0.0224272	−	0.0144131i
$365$	0.214926	+	0.647661i	0.0112497	+	0.0339001i
$366$	−11.6254	+	3.41351i	−0.607667	+	0.178427i
$367$			0.210443i			0.0109850i	0.999985	+	0.00549251i	$0.00174833\pi$
$367$			0.210443i			0.0109850i	−0.999985	+	0.00549251i	$0.998252\pi$
$368$	1.62848	−	18.7517i	0.0848903	−	0.977501i
$369$	−25.2836			−1.31621
$370$	−0.0771490	+	0.711662i	−0.00401078	+	0.0369975i
$371$	−16.5961	−	19.1529i	−0.861626	−	0.994369i
$372$	0.320480	+	0.498676i	0.0166161	+	0.0258551i
$373$	−11.2723	+	1.62071i	−0.583655	+	0.0839170i	−0.427817	−	0.903866i	$-0.640717\pi$
$373$	−11.2723	+	1.62071i	−0.583655	+	0.0839170i	−0.155839	+	0.987783i	$0.549808\pi$
$374$	2.46802	+	1.58610i	0.127618	+	0.0820154i
$375$	−29.1505	−	1.11864i	−1.50532	−	0.0577664i
$376$	−17.3182	+	19.9862i	−0.893115	+	1.03071i
$377$	−26.2551	−	3.77491i	−1.35220	−	0.194418i
$378$	7.92164	−	3.61769i	0.407445	−	0.186074i
$379$	8.35975	+	2.45465i	0.429412	+	0.126087i	0.489294	−	0.872119i	$-0.337254\pi$
$379$	8.35975	+	2.45465i	0.429412	+	0.126087i	−0.0598825	+	0.998205i	$0.519073\pi$
$380$	−0.290464	+	0.359792i	−0.0149005	+	0.0184569i
$381$	6.86179	+	15.0252i	0.351540	+	0.769766i
$382$	−1.91833	−	0.275814i	−0.0981503	−	0.0141119i
$383$	6.13203	+	5.31344i	0.313332	+	0.271504i	0.797302	−	0.603581i	$-0.206260\pi$
$383$	6.13203	+	5.31344i	0.313332	+	0.271504i	−0.483969	+	0.875085i	$0.660805\pi$
$384$	−11.9122	+	26.0840i	−0.607890	+	1.33109i
$385$	5.95213	+	8.58891i	0.303348	+	0.437732i
$386$	−0.524239	−	3.64616i	−0.0266831	−	0.185585i
$387$	12.7459	+	19.8331i	0.647912	+	1.00817i
$388$	−0.158497	+	0.137338i	−0.00804646	+	0.00697230i
$389$	−29.3900	+	8.62967i	−1.49013	+	0.437542i	−0.922583	−	0.385799i	$-0.873926\pi$
$389$	−29.3900	+	8.62967i	−1.49013	+	0.437542i	−0.567548	+	0.823341i	$0.692108\pi$
$390$	35.2416	+	14.6341i	1.78453	+	0.741027i
$391$	1.44074	−	6.16920i	0.0728616	−	0.311990i
$392$		−	4.82887i		−	0.243895i
$393$	−3.53183	−	12.0283i	−0.178157	−	0.606747i
$394$	−12.8270	−	14.8032i	−0.646215	−	0.745772i
$395$	−3.25432	−	18.1293i	−0.163743	−	0.912186i
$396$	−0.0317474	−	0.220808i	−0.00159537	−	0.0110960i
$397$	−14.0670	+	21.8887i	−0.706004	+	1.09856i	0.284177	+	0.958772i	$0.408280\pi$
$397$	−14.0670	+	21.8887i	−0.706004	+	1.09856i	−0.990181	+	0.139792i	$0.955357\pi$
$398$	−17.2960	−	7.89883i	−0.866972	−	0.395933i
$399$	28.1876	−	32.5302i	1.41114	−	1.62855i
$400$	−15.7303	+	11.7321i	−0.786515	+	0.586607i
$401$	−13.4921	−	29.5435i	−0.673762	−	1.47533i	−0.869120	−	0.494601i	$-0.835314\pi$
$401$	−13.4921	−	29.5435i	−0.673762	−	1.47533i	0.195358	−	0.980732i	$-0.437413\pi$
$402$	−10.8553	+	36.9698i	−0.541414	+	1.84389i
$403$	8.08461	−	27.5336i	0.402723	−	1.37155i
$404$	−0.0804412	−	0.176142i	−0.00400210	−	0.00876338i
$405$	11.3844	+	6.76834i	0.565698	+	0.336321i
$406$	−15.3706	+	17.7386i	−0.762828	+	0.880351i
$407$	−0.329449	−	0.150454i	−0.0163302	−	0.00745774i
$408$	−5.31816	+	8.27523i	−0.263288	+	0.409685i
$409$	−2.99322	−	20.8183i	−0.148005	−	1.02940i	−0.919479	−	0.393138i	$-0.871389\pi$
$409$	−2.99322	−	20.8183i	−0.148005	−	1.02940i	0.771474	−	0.636261i	$-0.219520\pi$
$410$	−20.4741	+	3.67522i	−1.01114	+	0.181506i
$411$	−7.80611	−	9.00873i	−0.385047	−	0.444368i
$412$	−0.194111	−	0.661082i	−0.00956317	−	0.0325692i
$413$			34.3944i			1.69244i
$414$	22.6417	−	11.9194i	1.11278	−	0.585805i
$415$	14.0049	+	5.81556i	0.687475	+	0.285475i
$416$	−0.936268	+	0.274913i	−0.0459043	+	0.0134787i
$417$	30.0038	−	25.9984i	1.46929	−	1.27315i
$418$	6.71852	+	10.4542i	0.328614	+	0.511333i
$419$	1.82939	+	12.7237i	0.0893716	+	0.621593i	0.984447	+	0.175679i	$0.0562122\pi$
$419$	1.82939	+	12.7237i	0.0893716	+	0.621593i	−0.895076	+	0.445914i	$0.852879\pi$
$420$	−0.522500	+	0.362093i	−0.0254954	+	0.0176683i
$421$	−10.5373	+	23.0735i	−0.513558	+	1.12453i	0.458264	+	0.888816i	$0.348471\pi$
$421$	−10.5373	+	23.0735i	−0.513558	+	1.12453i	−0.971821	+	0.235718i	$0.924256\pi$
$422$	−6.71997	−	5.82288i	−0.327123	−	0.283454i
$423$	−34.9269	−	5.02173i	−1.69820	−	0.244165i
$424$	10.1912	+	22.3156i	0.494929	+	1.08374i
$425$	−5.80258	+	3.15512i	−0.281466	+	0.153046i
$426$	−26.2486	−	7.70729i	−1.27175	−	0.373419i
$427$	−8.88823	+	4.05912i	−0.430132	+	0.196435i
$428$	−0.283622	−	0.0407787i	−0.0137094	−	0.00197111i
$429$	−12.6433	+	14.5911i	−0.610424	+	0.704466i
$430$	13.2043	+	14.2076i	0.636768	+	0.685152i
$431$	16.3004	+	10.4756i	0.785163	+	0.504594i	0.870743	−	0.491738i	$-0.163638\pi$
$431$	16.3004	+	10.4756i	0.785163	+	0.504594i	−0.0855803	+	0.996331i	$0.527274\pi$
$432$	−8.19012	+	1.17756i	−0.394047	+	0.0566554i
$433$	4.18197	+	6.50727i	0.200973	+	0.312720i	0.927081	−	0.374860i	$-0.122309\pi$
$433$	4.18197	+	6.50727i	0.200973	+	0.312720i	−0.726109	+	0.687580i	$0.758673\pi$
$434$	−16.6286	−	19.1904i	−0.798198	−	0.921170i
$435$	32.9590	+	3.57298i	1.58026	+	0.171311i
$436$	0.216421			0.0103647
$437$	16.4069	−	21.2352i	0.784849	−	1.01582i
$438$			1.11564i			0.0533073i
$439$	23.5703	−	6.92087i	1.12495	−	0.330315i	0.334229	−	0.942492i	$-0.391524\pi$
$439$	23.5703	−	6.92087i	1.12495	−	0.330315i	0.790721	+	0.612177i	$0.209706\pi$
$440$	−3.18601	−	9.60080i	−0.151887	−	0.457700i
$441$	5.42030	−	3.48342i	0.258110	−	0.165877i
$442$	8.55181	−	1.22956i	0.406768	−	0.0584844i
$443$	14.9111	−	23.2021i	0.708446	−	1.10236i	−0.281313	−	0.959616i	$-0.590770\pi$
$443$	14.9111	−	23.2021i	0.708446	−	1.10236i	0.989759	−	0.142748i	$-0.0455937\pi$
$444$	0.00915277	−	0.0200418i	0.000434371	−	0.000951140i
$445$	7.86014	+	15.7373i	0.372606	+	0.746022i
$446$	1.92177	−	13.3662i	0.0909985	−	0.632909i
$447$	−23.4721	+	10.7194i	−1.11019	+	0.507008i
$448$	−6.76308	+	23.0329i	−0.319526	+	1.08820i
$449$	−29.4956	−	8.66069i	−1.39198	−	0.408723i	−0.502059	−	0.864833i	$-0.667424\pi$
$449$	−29.4956	−	8.66069i	−1.39198	−	0.408723i	−0.889923	+	0.456110i	$0.849242\pi$
$450$	−24.9782	−	9.36680i	−1.17748	−	0.441555i
$451$	1.49780	−	10.4174i	0.0705284	−	0.490536i
$452$	0.253857	+	0.219968i	0.0119404	+	0.0103464i
$453$	43.0027	+	19.6387i	2.02044	+	0.922705i
$454$	−22.1239	−	14.2181i	−1.03832	−	0.667291i
$455$	29.8114	+	7.63702i	1.39758	+	0.358029i
$456$	−35.0528	+	22.5271i	−1.64150	+	1.05493i
$457$	−6.82146	+	5.91082i	−0.319094	+	0.276497i	−0.799649	−	0.600468i	$-0.794981\pi$
$457$	−6.82146	+	5.91082i	−0.319094	+	0.276497i	0.480554	+	0.876965i	$0.340435\pi$
$458$	6.55621	+	22.3284i	0.306352	+	1.04334i
$459$	−2.78497			−0.129991
$460$	−0.312560	+	0.243676i	−0.0145732	+	0.0113614i
$461$	30.1893			1.40606			0.703028	−	0.711162i	$-0.251831\pi$
$461$	30.1893			1.40606			0.703028	+	0.711162i	$0.251831\pi$
$462$	4.81319	+	16.3922i	0.223930	+	0.762635i
$463$	−21.9850	+	19.0501i	−1.02173	+	0.885332i	−0.993450	−	0.114268i	$-0.963548\pi$
$463$	−21.9850	+	19.0501i	−1.02173	+	0.885332i	−0.0282782	+	0.999600i	$0.509002\pi$
$464$	18.7608	−	12.0568i	0.870949	−	0.559725i
$465$	−8.90054	+	34.7436i	−0.412753	+	1.61119i
$466$	−15.9214	−	10.2320i	−0.737544	−	0.473990i
$467$	19.4254	+	8.87127i	0.898899	+	0.410513i	0.810613	−	0.585582i	$-0.199134\pi$
$467$	19.4254	+	8.87127i	0.898899	+	0.410513i	0.0882857	+	0.996095i	$0.471861\pi$
$468$	−0.496495	−	0.430215i	−0.0229505	−	0.0198867i
$469$	−4.42222	+	30.7572i	−0.204199	+	1.42024i
$470$	−29.0130	+	1.01048i	−1.33827	+	0.0466101i
$471$	−56.5641	−	16.6087i	−2.60634	−	0.765289i
$472$	9.38020	−	31.9460i	0.431758	−	1.47043i
$473$	−8.92673	+	4.07670i	−0.410451	+	0.187447i
$474$	4.28557	−	29.8068i	0.196843	−	1.36907i
$475$	−27.9097	+	1.94648i	−1.28059	+	0.0893105i
$476$	−0.0597912	+	0.130925i	−0.00274053	+	0.00600092i
$477$	−17.6971	+	27.5373i	−0.810297	+	1.26085i
$478$	5.42400	−	0.779853i	0.248088	−	0.0356696i
$479$	21.8930	−	14.0698i	1.00032	−	0.642865i	0.0654482	−	0.997856i	$-0.479152\pi$
$479$	21.8930	−	14.0698i	1.00032	−	0.642865i	0.934870	+	0.354991i	$0.115516\pi$
$480$	1.15752	−	0.384121i	0.0528332	−	0.0175326i
$481$	−1.02339	+	0.300495i	−0.0466627	+	0.0137014i
$482$		−	13.6584i		−	0.622123i
$483$	29.8669	−	21.6564i	1.35899	−	0.985399i
$484$	−0.313671			−0.0142578
$485$	−12.6151	−	1.36756i	−0.572823	−	0.0620979i
$486$	19.9830	+	23.0616i	0.906447	+	1.04610i
$487$	−8.74048	−	13.6005i	−0.396069	−	0.616295i	0.584751	−	0.811213i	$-0.301192\pi$
$487$	−8.74048	−	13.6005i	−0.396069	−	0.616295i	−0.980820	+	0.194918i	$0.937556\pi$
$488$	9.36254	−	1.34613i	0.423822	−	0.0609364i
$489$	14.1564	+	9.09775i	0.640174	+	0.411415i
$490$	3.88289	−	3.60869i	0.175411	−	0.163024i
$491$	−11.1213	+	12.8347i	−0.501899	+	0.579223i	−0.949006	−	0.315258i	$-0.897909\pi$
$491$	−11.1213	+	12.8347i	−0.501899	+	0.579223i	0.447107	+	0.894481i	$0.352454\pi$
$492$	0.633735	+	0.0911173i	0.0285710	+	0.00410788i
$493$	6.82776	−	3.11813i	0.307507	−	0.140434i
$494$	35.1144	+	10.3105i	1.57987	+	0.463893i
$495$	8.47838	−	10.5020i	0.381075	−	0.472029i
$496$	10.0224	+	21.9461i	0.450020	+	0.985407i
$497$	−21.8377	−	3.13978i	−0.979553	−	0.140839i
$498$	18.7367	+	16.2354i	0.839611	+	0.727527i
$499$	−8.55147	+	18.7251i	−0.382816	+	0.838251i	0.615911	+	0.787816i	$0.288788\pi$
$499$	−8.55147	+	18.7251i	−0.382816	+	0.838251i	−0.998727	+	0.0504351i	$0.983939\pi$
$500$	0.406433	+	0.0744438i	0.0181762	+	0.00332923i
$501$	−3.62917	−	25.2415i	−0.162139	−	1.12770i
$502$	−13.0288	−	20.2731i	−0.581502	−	0.904834i
$503$	4.26993	−	3.69991i	0.190387	−	0.164971i	−0.554452	−	0.832216i	$-0.687072\pi$
$503$	4.26993	−	3.69991i	0.190387	−	0.164971i	0.744838	+	0.667245i	$0.232527\pi$
$504$	−30.7430	+	9.02695i	−1.36940	+	0.402092i
$505$	4.49313	−	10.8203i	0.199942	−	0.481495i
$506$	3.56976	+	10.0350i	0.158695	+	0.446108i
$507$			22.9380i			1.01871i
$508$	−0.0659147	−	0.224485i	−0.00292449	−	0.00995990i
$509$	−23.0053	−	26.5496i	−1.01969	−	1.17679i	−0.984135	−	0.177421i	$-0.943225\pi$
$509$	−23.0053	−	26.5496i	−1.01969	−	1.17679i	−0.0355580	−	0.999368i	$-0.511321\pi$
$510$	−10.6284	+	1.90787i	−0.470635	+	0.0844817i
$511$	0.128044	+	0.890564i	0.00566432	+	0.0393962i
$512$	12.5549	−	19.5359i	0.554855	−	0.863372i
$513$	−10.7307	−	4.90056i	−0.473773	−	0.216365i
$514$	8.15743	−	9.41418i	0.359809	−	0.415242i
$515$	21.3033	−	35.8324i	0.938734	−	1.57897i
$516$	−0.248003	−	0.543051i	−0.0109177	−	0.0239065i
$517$	4.13813	−	14.0932i	0.181995	−	0.619817i
$518$	−0.265903	+	0.905581i	−0.0116831	+	0.0397889i
$519$	−9.75117	−	21.3521i	−0.428029	−	0.937252i
$520$	−25.6064	−	15.2237i	−1.12292	−	0.667602i
$521$	6.79035	−	7.83648i	0.297491	−	0.343323i	−0.587250	−	0.809405i	$-0.699790\pi$
$521$	6.79035	−	7.83648i	0.297491	−	0.343323i	0.884741	+	0.466083i	$0.154335\pi$
$522$	27.5768	+	12.5939i	1.20701	+	0.551221i
$523$	21.3504	−	33.2219i	0.933589	−	1.45269i	0.0423796	−	0.999102i	$-0.486506\pi$
$523$	21.3504	−	33.2219i	0.933589	−	1.45269i	0.891210	−	0.453592i	$-0.149858\pi$
$524$	0.0252698	+	0.175755i	0.00110392	+	0.00767791i
$525$	−37.5692	−	8.24237i	−1.63965	−	0.359727i
$526$	2.37990	+	2.74655i	0.103769	+	0.119755i
$527$	2.28779	+	7.79148i	0.0996575	+	0.339402i
$528$		−	16.2323i		−	0.706420i
$529$	17.8328	−	14.5255i	0.775339	−	0.631545i
$530$	−10.3279	+	24.8715i	−0.448617	+	1.08035i
$531$	42.6253	−	12.5159i	1.84978	−	0.543145i
$532$	−0.460761	+	0.399252i	−0.0199765	+	0.0173098i
$533$	−16.7568	−	26.0740i	−0.725816	−	1.12939i
$534$	4.09291	+	28.4668i	0.177118	+	1.23188i
$535$	−9.87495	−	14.2495i	−0.426931	−	0.616062i
$536$	12.4957	−	27.3617i	0.539731	−	1.18185i
$537$	−26.7698	−	23.1962i	−1.15520	−	1.00099i
$538$	3.80269	+	0.546744i	0.163945	+	0.0235718i
$539$	1.11415	+	2.43964i	0.0479897	+	0.105083i
$540$	0.135562	+	0.109440i	0.00583364	+	0.00470957i
$541$	4.70539	+	1.38163i	0.202300	+	0.0594007i	0.381313	−	0.924446i	$-0.375472\pi$
$541$	4.70539	+	1.38163i	0.202300	+	0.0594007i	−0.179013	+	0.983847i	$0.557290\pi$
$542$	17.6647	−	8.06721i	0.758765	−	0.346516i
$543$	8.09800	+	1.16432i	0.347519	+	0.0499656i
$544$	0.180827	−	0.208686i	0.00775290	−	0.00894732i
$545$	8.91425	+	9.59159i	0.381844	+	0.410859i
$546$	42.3254	+	27.2009i	1.81136	+	1.16409i
$547$	−19.3788	+	2.78626i	−0.828579	+	0.119132i	−0.543539	−	0.839384i	$-0.682916\pi$
$547$	−19.3788	+	2.78626i	−0.828579	+	0.119132i	−0.285040	+	0.958516i	$0.592007\pi$
$548$	0.0912818	+	0.142037i	0.00389936	+	0.00606753i
$549$	8.26488	+	9.53818i	0.352736	+	0.407079i
$550$	5.33903	−	9.73668i	0.227657	−	0.415173i
$551$	31.7947			1.35450
$552$	−33.6470	+	11.9693i	−1.43211	+	0.509448i
$553$		−	24.2853i		−	1.03272i
$554$	−3.93860	+	1.15648i	−0.167335	+	0.0491340i
$555$	1.26523	−	0.419866i	0.0537061	−	0.0178223i
$556$	−0.473058	+	0.304016i	−0.0200621	+	0.0128932i
$557$	−20.7623	+	2.98516i	−0.879725	+	0.126485i	−0.567353	−	0.823474i	$-0.692033\pi$
$557$	−20.7623	+	2.98516i	−0.879725	+	0.126485i	−0.312372	+	0.949960i	$0.601124\pi$
$558$	−17.7318	+	27.5913i	−0.750648	+	1.16803i
$559$	−12.0057	+	26.2888i	−0.507787	+	1.11190i
$560$	−23.1469	+	11.5609i	−0.978134	+	0.488537i
$561$	0.777531	−	5.40784i	0.0328274	−	0.228319i
$562$	31.1611	−	14.2308i	1.31445	−	0.600289i
$563$	−0.692647	+	2.35894i	−0.0291916	+	0.0994174i	−0.972800	−	0.231645i	$-0.925589\pi$
$563$	−0.692647	+	2.35894i	−0.0291916	+	0.0994174i	0.943609	+	0.331063i	$0.107407\pi$
$564$	0.857348	+	0.251740i	0.0361009	+	0.0106002i
$565$	0.707408	+	20.3111i	0.0297609	+	0.854494i
$566$	−3.96998	+	27.6118i	−0.166871	+	1.16061i
$567$	13.1974	+	11.4356i	0.554237	+	0.480249i
$568$	19.4268	+	8.87194i	0.815132	+	0.372258i
$569$	−4.13174	−	2.65531i	−0.173212	−	0.111316i	0.451162	−	0.892442i	$-0.351010\pi$
$569$	−4.13174	−	2.65531i	−0.173212	−	0.111316i	−0.624374	+	0.781126i	$0.714646\pi$
$570$	−44.3094	−	11.3511i	−1.85592	−	0.475445i
$571$	−6.45163	+	4.14621i	−0.269992	+	0.173514i	−0.668631	−	0.743595i	$-0.733119\pi$
$571$	−6.45163	+	4.14621i	−0.269992	+	0.173514i	0.398638	+	0.917108i	$0.369483\pi$
$572$	0.206670	−	0.179081i	0.00864133	−	0.00748775i
$573$	1.01683	+	3.46301i	0.0424787	+	0.144669i
$574$	−27.4262			−1.14475
$575$	−23.6737	−	3.81552i	−0.987260	−	0.159118i
$576$	31.0060			1.29192
$577$	9.77699	+	33.2974i	0.407021	+	1.38619i	0.867022	+	0.498269i	$0.166031\pi$
$577$	9.77699	+	33.2974i	0.407021	+	1.38619i	−0.460001	+	0.887918i	$0.652151\pi$
$578$	16.1531	−	13.9967i	0.671880	−	0.582187i
$579$	−5.77100	+	3.70880i	−0.239835	+	0.154132i
$580$	−0.454881	−	0.116531i	−0.0188879	−	0.00483867i
$581$	16.8200	+	10.8096i	0.697812	+	0.448457i
$582$	−18.8705	−	8.61788i	−0.782209	−	0.357223i
$583$	−10.2976	−	8.92292i	−0.426483	−	0.369550i
$584$	0.123950	−	0.862089i	0.00512908	−	0.0356735i
$585$	−1.38355	−	39.7246i	−0.0572029	−	1.64241i
$586$	15.0794	+	4.42770i	0.622923	+	0.182907i
$587$	−6.36972	+	21.6933i	−0.262906	+	0.895377i	0.717194	+	0.696874i	$0.245426\pi$
$587$	−6.36972	+	21.6933i	−0.262906	+	0.895377i	−0.980100	+	0.198503i	$0.936392\pi$
$588$	−0.148414	+	0.0677783i	−0.00612048	+	0.00279513i
$589$	−4.89521	+	34.0469i	−0.201704	+	1.40288i
$590$	32.6977	−	16.3311i	1.34614	−	0.672341i
$591$	−15.1532	+	33.1808i	−0.623318	+	1.36488i
$592$	0.484818	−	0.754391i	0.0199259	−	0.0310053i
$593$	13.3866	−	1.92471i	0.549723	−	0.0790383i	0.138144	−	0.990412i	$-0.455886\pi$
$593$	13.3866	−	1.92471i	0.549723	−	0.0790383i	0.411579	+	0.911374i	$0.364977\pi$
$594$	3.93892	−	2.53139i	0.161616	−	0.103864i
$595$	−8.26524	+	2.74281i	−0.338842	+	0.112444i
$596$	0.350686	−	0.102971i	0.0143646	−	0.00421784i
$597$			35.4100i			1.44923i
$598$	27.2978	+	15.4499i	1.11629	+	0.631793i
$599$	24.1718			0.987634			0.493817	−	0.869566i	$-0.335601\pi$
$599$	24.1718			0.987634			0.493817	+	0.869566i	$0.335601\pi$
$600$	32.6469	+	17.9017i	1.33280	+	0.730832i
$601$	3.63800	+	4.19847i	0.148397	+	0.171259i	0.825081	−	0.565014i	$-0.191129\pi$
$601$	3.63800	+	4.19847i	0.148397	+	0.171259i	−0.676684	+	0.736273i	$0.736584\pi$
$602$	13.8261	+	21.5138i	0.563509	+	0.876836i
$603$	39.7269	−	5.71187i	1.61781	−	0.232605i
$604$	−0.563308	−	0.362016i	−0.0229207	−	0.0147302i
$605$	−12.9199	−	13.9016i	−0.525270	−	0.565182i
$606$	12.5436	−	14.4760i	0.509547	−	0.588049i
$607$	−13.6988	−	1.96959i	−0.556016	−	0.0799431i	−0.141422	−	0.989949i	$-0.545167\pi$
$607$	−13.6988	−	1.96959i	−0.556016	−	0.0799431i	−0.414594	+	0.910006i	$0.636077\pi$
$608$	1.06396	−	0.485892i	0.0431491	−	0.0197055i
$609$	41.9399	+	12.3147i	1.69949	+	0.499016i
$610$	8.07918	+	6.52242i	0.327116	+	0.264085i
$611$	−17.9692	−	39.3470i	−0.726955	−	1.59181i
$612$	0.184014	+	0.0264572i	0.00743831	+	0.00106947i
$613$	2.55345	+	2.21258i	0.103133	+	0.0893651i	0.704901	−	0.709306i	$-0.250991\pi$
$613$	2.55345	+	2.21258i	0.103133	+	0.0893651i	−0.601768	+	0.798671i	$0.705537\pi$
$614$	−4.42484	+	9.68906i	−0.178572	+	0.391019i
$615$	22.0649	+	31.8397i	0.889743	+	1.28390i
$616$	−1.89809	−	13.2015i	−0.0764764	−	0.531905i
$617$	−20.9757	−	32.6389i	−0.844451	−	1.31399i	−0.947643	−	0.319331i	$-0.896542\pi$
$617$	−20.9757	−	32.6389i	−0.844451	−	1.31399i	0.103192	−	0.994661i	$-0.467094\pi$
$618$	51.5070	−	44.6311i	2.07192	−	1.79533i
$619$	2.59883	−	0.763087i	0.104456	−	0.0306710i	−0.229087	−	0.973406i	$-0.573574\pi$
$619$	2.59883	−	0.763087i	0.104456	−	0.0306710i	0.333543	+	0.942735i	$0.391756\pi$
$620$	0.194820	−	0.469162i	0.00782416	−	0.0188420i
$621$	−8.00097	−	6.18176i	−0.321068	−	0.248066i
$622$		−	24.1785i		−	0.969471i
$623$	6.53437	+	22.2540i	0.261794	+	0.891589i
$624$	−31.3046	−	36.1274i	−1.25319	−	1.44625i
$625$	13.4415	+	21.0791i	0.537658	+	0.843163i
$626$	−0.540786	−	3.76125i	−0.0216142	−	0.150330i
$627$	12.5118	−	19.4687i	0.499672	−	0.777505i
$628$	0.759546	+	0.346873i	0.0303092	+	0.0138418i
$629$	0.197654	−	0.228105i	0.00788099	−	0.00909515i
$630$	−30.2332	−	17.9744i	−1.20452	−	0.716118i
$631$	−16.5157	−	36.1643i	−0.657480	−	1.43968i	−0.884852	−	0.465872i	$-0.845741\pi$
$631$	−16.5157	−	36.1643i	−0.657480	−	1.43968i	0.227373	−	0.973808i	$-0.426986\pi$
$632$	−6.62319	+	22.5565i	−0.263456	+	0.897250i
$633$	−4.66521	+	15.8883i	−0.185426	+	0.631501i
$634$	−1.70629	−	3.73626i	−0.0677655	−	0.148386i
$635$	7.23399	−	12.1677i	0.287072	−	0.482860i
$636$	0.542819	−	0.626447i	0.0215242	−	0.0248402i
$637$	7.18464	+	3.28111i	0.284666	+	0.130002i
$638$	−6.82262	+	10.6162i	−0.270110	+	0.420299i
$639$	4.05544	+	28.2062i	0.160431	+	1.11582i
$640$	24.1878	−	4.34185i	0.956108	−	0.171627i
$641$	−6.33688	−	7.31315i	−0.250292	−	0.288852i	0.616675	−	0.787218i	$-0.288479\pi$
$641$	−6.33688	−	7.31315i	−0.250292	−	0.288852i	−0.866967	+	0.498366i	$0.833934\pi$
$642$	−7.98538	−	27.1957i	−0.315158	−	1.07333i
$643$			32.3558i			1.27599i	0.770041	+	0.637994i	$0.220235\pi$
$643$			32.3558i			1.27599i	−0.770041	+	0.637994i	$0.779765\pi$
$644$	−0.462386	+	0.243417i	−0.0182206	+	0.00959196i
$645$	13.8525	−	33.3592i	0.545440	−	1.31352i
$646$	−9.93669	+	2.91768i	−0.390954	+	0.114794i
$647$	−16.6254	+	14.4060i	−0.653611	+	0.566357i	−0.917274	−	0.398258i	$-0.869615\pi$
$647$	−16.6254	+	14.4060i	−0.653611	+	0.566357i	0.263662	+	0.964615i	$0.415070\pi$
$648$	−9.13914	−	14.2208i	−0.359019	−	0.558645i
$649$	2.63172	+	18.3040i	0.103304	+	0.718495i
$650$	−6.89473	−	31.9670i	−0.270433	−	1.25385i
$651$	−19.6442	+	43.0148i	−0.769916	+	1.68588i
$652$	−0.180133	−	0.156086i	−0.00705454	−	0.00611280i
$653$	−2.06514	−	0.296923i	−0.0808152	−	0.0116195i	0.101789	−	0.994806i	$-0.467543\pi$
$653$	−2.06514	−	0.296923i	−0.0808152	−	0.0116195i	−0.182604	+	0.983187i	$0.558453\pi$
$654$	8.89317	+	19.4733i	0.347750	+	0.761467i
$655$	−6.74849	+	8.35920i	−0.263685	+	0.326621i
$656$	25.0030	+	7.34153i	0.976202	+	0.286639i
$657$	1.05709	−	0.482757i	0.0412410	−	0.0188341i
$658$	−37.8867	−	5.44729i	−1.47698	−	0.212358i
$659$	2.87363	−	3.31634i	0.111941	−	0.129186i	−0.697014	−	0.717058i	$-0.745488\pi$
$659$	2.87363	−	3.31634i	0.111941	−	0.129186i	0.808954	+	0.587871i	$0.200034\pi$
$660$	−0.250358	+	0.232678i	−0.00974518	+	0.00905699i
$661$	−18.4504	−	11.8574i	−0.717639	−	0.461199i	0.130176	−	0.991491i	$-0.458446\pi$
$661$	−18.4504	−	11.8574i	−0.717639	−	0.461199i	−0.847815	+	0.530292i	$0.822082\pi$
$662$	11.6935	−	1.68127i	0.454480	−	0.0653443i
$663$	−8.69871	−	13.5355i	−0.337830	−	0.525674i
$664$	−12.6746	−	14.6273i	−0.491871	−	0.567650i
$665$	−36.6730	−	3.97560i	−1.42212	−	0.154167i
$666$	1.21906			0.0472374
$667$	26.5368	+	6.19737i	1.02751	+	0.239963i
$668$			0.361199i			0.0139752i
$669$	−24.1290	+	7.08490i	−0.932879	+	0.273918i
$670$	31.3397	−	10.4000i	1.21076	−	0.401789i
$671$	−4.41955	+	2.84027i	−0.170615	+	0.109647i
$672$	1.59164	−	0.228843i	0.0613989	−	0.00882783i
$673$	−17.8662	+	27.8003i	−0.688690	+	1.07162i	0.304202	+	0.952608i	$0.401610\pi$
$673$	−17.8662	+	27.8003i	−0.688690	+	1.07162i	−0.992892	+	0.119016i	$0.962026\pi$
$674$	1.99050	−	4.35858i	0.0766711	−	0.167886i
$675$	0.733390	+	10.5158i	0.0282282	+	0.404752i
$676$	0.0462375	−	0.321589i	0.00177837	−	0.0123688i
$677$	−28.8393	+	13.1705i	−1.10838	+	0.506182i	−0.883608	−	0.468228i	$-0.844893\pi$
$677$	−28.8393	+	13.1705i	−1.10838	+	0.506182i	−0.224777	+	0.974410i	$0.572165\pi$
$678$	−9.36103	+	31.8807i	−0.359508	+	1.22437i
$679$	−16.0526	−	4.71346i	−0.616042	−	0.180886i
$680$	8.42490	−	0.293428i	0.323080	−	0.0112524i
$681$	−6.96995	+	48.4770i	−0.267089	+	1.85764i
$682$	−10.3178	−	8.94040i	−0.395088	−	0.342346i
$683$	−14.1586	−	6.46599i	−0.541762	−	0.247414i	0.125687	−	0.992070i	$-0.459886\pi$
$683$	−14.1586	−	6.46599i	−0.541762	−	0.247414i	−0.667449	+	0.744656i	$0.732614\pi$
$684$	0.662465	+	0.425741i	0.0253300	+	0.0162786i
$685$	−2.53513	+	9.89596i	−0.0968623	+	0.378105i
$686$	−18.4452	+	11.8540i	−0.704240	+	0.452588i
$687$	32.7521	−	28.3798i	1.24957	−	1.08276i
$688$	−6.84559	−	23.3139i	−0.260986	−	0.888836i
$689$	−40.1270			−1.52872
$690$	−34.7694	−	18.1107i	−1.32365	−	0.689461i
$691$	−42.2733			−1.60815			−0.804076	−	0.594527i	$-0.797339\pi$
$691$	−42.2733			−1.60815			−0.804076	+	0.594527i	$0.797339\pi$
$692$	0.0936701	+	0.319011i	0.00356080	+	0.0121270i
$693$	13.4492	−	11.6538i	0.510893	−	0.442691i
$694$	−8.55913	+	5.50062i	−0.324900	+	0.208801i
$695$	−32.9587	−	8.44330i	−1.25020	−	0.320273i
$696$	−35.5959	−	22.8761i	−1.34926	−	0.867116i
$697$	7.97817	+	3.64351i	0.302195	+	0.138008i
$698$	−36.7964	−	31.8843i	−1.39277	−	1.20684i
$699$	−5.01590	+	34.8864i	−0.189719	+	1.31952i
$700$	0.510103	+	0.191288i	0.0192801	+	0.00723001i
$701$	41.6290	+	12.2234i	1.57231	+	0.461671i	0.947672	−	0.319246i	$-0.103430\pi$
$701$	41.6290	+	12.2234i	1.57231	+	0.461671i	0.624635	+	0.780917i	$0.285248\pi$
$702$	3.88478	−	13.2303i	0.146622	−	0.499347i
$703$	1.16296	−	0.531107i	0.0438620	−	0.0200311i
$704$	−1.83679	+	12.7751i	−0.0692266	+	0.481481i
$705$	24.1568	+	48.3660i	0.909796	+	1.82157i
$706$	13.9316	−	30.5058i	0.524321	−	1.14810i
$707$	8.35152	−	12.9952i	0.314091	−	0.488736i
$708$	−1.11351	+	0.160099i	−0.0418483	+	0.00601688i
$709$	30.2132	−	19.4168i	1.13468	−	0.729215i	0.168148	−	0.985762i	$-0.446221\pi$
$709$	30.2132	−	19.4168i	1.13468	−	0.729215i	0.966532	+	0.256547i	$0.0825849\pi$
$710$	7.38404	+	22.2512i	0.277118	+	0.835074i
$711$	−30.0970	+	8.83727i	−1.12873	+	0.331424i
$712$		−	22.4519i		−	0.841422i
$713$	−10.7220	+	27.4624i	−0.401544	+	1.02847i
$714$	−14.2374			−0.532821
$715$	16.4494	+	1.78322i	0.615171	+	0.0666887i
$716$	0.328554	+	0.379171i	0.0122786	+	0.0141703i
$717$	−5.51717	−	8.58489i	−0.206043	−	0.320608i
$718$	−16.9810	+	2.44150i	−0.633725	+	0.0911160i
$719$	0.284312	+	0.182716i	0.0106030	+	0.00681416i	0.545932	−	0.837830i	$-0.316176\pi$
$719$	0.284312	+	0.182716i	0.0106030	+	0.00681416i	−0.535329	+	0.844644i	$0.679812\pi$
$720$	22.7505	+	24.4792i	0.847862	+	0.912286i
$721$	35.9934	−	41.5386i	1.34046	−	1.54698i
$722$	−17.0713	−	2.45448i	−0.635329	−	0.0913465i
$723$	−23.1372	+	10.5664i	−0.860481	+	0.392968i
$724$	−0.111187	−	0.0326473i	−0.00413222	−	0.00121333i
$725$	−13.5718	−	24.9598i	−0.504043	−	0.926984i
$726$	−12.8894	−	28.2238i	−0.478370	−	1.04748i
$727$	3.30099	+	0.474610i	0.122427	+	0.0176023i	0.203256	−	0.979126i	$-0.434848\pi$
$727$	3.30099	+	0.474610i	0.122427	+	0.0176023i	−0.0808290	+	0.996728i	$0.525757\pi$
$728$	−29.6841	−	25.7214i	−1.10017	−	0.953300i
$729$	16.2253	−	35.5284i	0.600936	−	1.31587i
$730$	0.785834	−	0.544584i	0.0290850	−	0.0201560i
$731$	−1.16389	−	8.09503i	−0.0430480	−	0.299405i
$732$	−0.172786	−	0.268860i	−0.00638635	−	0.00993735i
$733$	28.7160	−	24.8826i	1.06065	−	0.919060i	0.0637693	−	0.997965i	$-0.479688\pi$
$733$	28.7160	−	24.8826i	1.06065	−	0.919060i	0.996882	+	0.0789050i	$0.0251424\pi$
$734$	0.282905	−	0.0830684i	0.0104422	−	0.00306611i
$735$	−9.11696	−	3.78583i	−0.336284	−	0.139642i
$736$	0.982716	−	0.198155i	0.0362234	−	0.00730411i
$737$			16.7067i			0.615400i
$738$	9.98023	+	33.9896i	0.367377	+	1.25117i
$739$	10.3211	+	11.9112i	0.379668	+	0.438161i	0.913133	−	0.407662i	$-0.133656\pi$
$739$	10.3211	+	11.9112i	0.379668	+	0.438161i	−0.533465	+	0.845822i	$0.679110\pi$
$740$	−0.0185848	+	0.00333609i	−0.000683192	+	0.000122637i
$741$	−9.69927	−	67.4599i	−0.356312	−	2.47820i
$742$	−19.1969	+	29.8709i	−0.704739	+	1.09660i
$743$	23.4293	+	10.6998i	0.859538	+	0.392538i	0.795895	−	0.605435i	$-0.207001\pi$
$743$	23.4293	+	10.6998i	0.859538	+	0.392538i	0.0636434	+	0.997973i	$0.479728\pi$
$744$	29.9770	−	34.5953i	1.09901	−	1.26832i
$745$	19.0081	+	11.3008i	0.696403	+	0.414029i
$746$	6.62828	+	14.5139i	0.242679	+	0.531392i
$747$	7.27570	−	24.7787i	0.266204	−	0.906607i
$748$	−0.0218019	+	0.0742504i	−0.000797155	+	0.00271486i
$749$	−9.49567	−	20.7926i	−0.346964	−	0.759746i
$750$	10.0028	+	39.6295i	0.365250	+	1.44706i
$751$	−26.6918	+	30.8040i	−0.973998	+	1.12405i	0.0182565	+	0.999833i	$0.494188\pi$
$751$	−26.6918	+	30.8040i	−0.973998	+	1.12405i	−0.992255	+	0.124220i	$0.960357\pi$
$752$	33.0811	+	15.1076i	1.20634	+	0.550919i
$753$	−24.2632	+	37.7543i	−0.884200	+	1.37584i
$754$	5.28897	+	36.7856i	0.192613	+	1.33965i
$755$	−7.15808	−	39.8766i	−0.260509	−	1.45126i
$756$	0.150429	+	0.173605i	0.00547107	+	0.00631395i
$757$	9.34741	+	31.8344i	0.339737	+	1.15704i	0.935337	+	0.353758i	$0.115096\pi$
$757$	9.34741	+	31.8344i	0.339737	+	1.15704i	−0.595600	+	0.803281i	$0.703085\pi$
$758$		−	12.2072i		−	0.443386i
$759$	14.2375	−	13.8104i	0.516788	−	0.501285i
$760$	32.9782	+	13.6942i	1.19624	+	0.496742i
$761$	−27.2664	+	8.00614i	−0.988407	+	0.290222i	−0.735690	−	0.677318i	$-0.763142\pi$
$761$	−27.2664	+	8.00614i	−0.988407	+	0.290222i	−0.252716	+	0.967540i	$0.581324\pi$
$762$	17.4903	−	15.1555i	0.633608	−	0.549025i
$763$	9.33400	+	14.5240i	0.337914	+	0.525804i
$764$	−0.00727531	−	0.0506009i	−0.000263211	−	0.00183068i
$765$	6.40686	+	9.24509i	0.231640	+	0.334257i
$766$	4.72252	−	10.3409i	0.170632	−	0.373631i
$767$	41.1572	+	35.6629i	1.48610	+	1.28771i
$768$	−2.28996	−	0.329247i	−0.0826319	−	0.0118807i
$769$	−4.94521	−	10.8285i	−0.178329	−	0.390486i	0.799267	−	0.600976i	$-0.205221\pi$
$769$	−4.94521	−	10.8285i	−0.178329	−	0.390486i	−0.977596	+	0.210490i	$0.932494\pi$
$770$	9.19686	−	11.3920i	0.331432	−	0.410537i
$771$	−22.2583	−	6.53562i	−0.801612	−	0.235375i
$772$	0.0883852	−	0.0403642i	0.00318105	−	0.00145274i
$773$	23.9836	+	3.44832i	0.862629	+	0.124027i	0.559408	−	0.828893i	$-0.311029\pi$
$773$	23.9836	+	3.44832i	0.862629	+	0.124027i	0.303222	+	0.952920i	$0.401938\pi$
$774$	21.6310	−	24.9635i	0.777511	−	0.897295i
$775$	28.8174	−	10.6902i	1.03515	−	0.384005i
$776$	13.6244	+	8.75587i	0.489087	+	0.314317i
$777$	1.73975	−	0.250139i	0.0624133	−	0.00897367i
$778$	23.2023	+	36.1035i	0.831843	+	1.29437i
$779$	24.3293	+	28.0775i	0.871687	+	1.00598i
$780$	−0.108481	+	1.00068i	−0.00388424	+	0.0358303i
$781$	−11.8618			−0.424449
$782$	−8.86216	+	0.498336i	−0.316910	+	0.0178205i
$783$		−	11.9796i		−	0.428115i
$784$	−6.37162	+	1.87088i	−0.227558	+	0.0668170i
$785$	15.9121	+	47.9500i	0.567929	+	1.71141i
$786$	−14.7759	+	9.49590i	−0.527039	+	0.338708i
$787$	−21.9769	+	3.15980i	−0.783391	+	0.112635i	−0.522393	−	0.852705i	$-0.674961\pi$
$787$	−21.9769	+	3.15980i	−0.783391	+	0.112635i	−0.260998	+	0.965339i	$0.584052\pi$
$788$	0.279331	−	0.434648i	0.00995077	−	0.0154837i
$789$	2.81150	−	6.15632i	0.100092	−	0.219171i
$790$	−23.0873	+	11.5311i	−0.821408	+	0.410259i
$791$	−3.81348	+	26.5233i	−0.135592	+	0.943061i
$792$	−15.6701	+	7.15629i	−0.556812	+	0.254288i
$793$	−4.35880	+	14.8447i	−0.154785	+	0.527151i
$794$	34.9784	+	10.2706i	1.24134	+	0.364490i
$795$	50.1220	−	1.74568i	1.77764	−	0.0619130i
$796$	0.0713782	−	0.496446i	0.00252993	−	0.0175961i
$797$	6.59484	+	5.71446i	0.233601	+	0.202417i	0.763793	−	0.645461i	$-0.223335\pi$
$797$	6.59484	+	5.71446i	0.233601	+	0.202417i	−0.530192	+	0.847878i	$0.677880\pi$
$798$	−54.8579	−	25.0528i	−1.94195	−	0.886859i
$799$	10.2974	+	6.61776i	0.364297	+	0.234119i
$800$	−0.835594	−	0.627830i	−0.0295427	−	0.0221971i
$801$	25.2018	−	16.1962i	0.890462	−	0.572265i
$802$	−34.3906	+	29.7996i	−1.21437	+	1.05226i
$803$	0.136285	+	0.464143i	0.00480938	+	0.0163792i
$804$	−1.01634			−0.0358436
$805$	−29.8334	−	10.4664i	−1.05149	−	0.368892i
$806$	−40.2056			−1.41618
$807$	−2.01565	−	6.86468i	−0.0709543	−	0.241648i
$808$	−11.3011	+	9.79248i	−0.397572	+	0.344498i
$809$	−42.8271	+	27.5233i	−1.50572	+	0.967669i	−0.511621	+	0.859211i	$0.670955\pi$
$809$	−42.8271	+	27.5233i	−1.50572	+	0.967669i	−0.994101	+	0.108457i	$0.965409\pi$
$810$	4.60510	−	17.9762i	0.161807	−	0.631618i
$811$	0.148167	+	0.0952212i	0.00520285	+	0.00334367i	0.543240	−	0.839578i	$-0.317198\pi$
$811$	0.148167	+	0.0952212i	0.00520285	+	0.00334367i	−0.538037	+	0.842921i	$0.680834\pi$
$812$	−0.563172	−	0.257192i	−0.0197635	−	0.00902568i
$813$	−27.3315	−	23.6829i	−0.958559	−	0.830596i
$814$	−0.0722166	+	0.502277i	−0.00253119	+	0.0176048i
$815$	−0.501965	−	14.4124i	−0.0175831	−	0.504845i
$816$	12.9795	+	3.81111i	0.454372	+	0.133416i
$817$	9.75981	−	33.2389i	0.341453	−	1.16288i
$818$	−26.8052	+	12.2415i	−0.937222	+	0.428015i
$819$	7.45843	−	51.8745i	0.260619	−	1.81264i
$820$	−0.245168	−	0.490868i	−0.00856163	−	0.0171419i
$821$	12.4719	−	27.3097i	0.435273	−	0.953115i	−0.557169	−	0.830399i	$-0.688112\pi$
$821$	12.4719	−	27.3097i	0.435273	−	0.953115i	0.992442	−	0.122716i	$-0.0391603\pi$
$822$	−9.02941	+	14.0500i	−0.314937	+	0.490051i
$823$	2.06963	−	0.297567i	0.0721426	−	0.0103725i	−0.106149	−	0.994350i	$-0.533852\pi$
$823$	2.06963	−	0.297567i	0.0721426	−	0.0103725i	0.178292	+	0.983978i	$0.442943\pi$
$824$	−44.7597	+	28.7653i	−1.55928	+	1.00209i
$825$	−20.6242	−	1.51178i	−0.718043	−	0.0526335i
$826$	46.2375	−	13.5766i	1.60881	−	0.472389i
$827$		−	3.18639i		−	0.110802i	−0.998464	−	0.0554008i	$-0.982356\pi$
$827$		−	3.18639i		−	0.110802i	0.998464	−	0.0554008i	$-0.0176436\pi$
$828$	0.469928	+	0.484462i	0.0163311	+	0.0168362i
$829$	31.5021			1.09411			0.547057	−	0.837095i	$-0.315748\pi$
$829$	31.5021			1.09411			0.547057	+	0.837095i	$0.315748\pi$
$830$	2.28986	−	21.1229i	0.0794823	−	0.733185i
$831$	5.00603	+	5.77727i	0.173657	+	0.200411i
$832$	20.5493	+	31.9753i	0.712418	+	1.10854i
$833$	−2.21234	+	0.318087i	−0.0766531	+	0.0110211i
$834$	−46.7940	−	30.0727i	−1.62034	−	1.04133i
$835$	−16.0081	+	14.8776i	−0.553982	+	0.514860i
$836$	−0.214659	+	0.247729i	−0.00742413	+	0.00856790i
$837$	12.8281	+	1.84441i	0.443405	+	0.0637520i
$838$	16.3828	−	7.48176i	0.565933	−	0.258453i
$839$	11.4981	+	3.37616i	0.396960	+	0.116558i	0.474119	−	0.880461i	$-0.342767\pi$
$839$	11.4981	+	3.37616i	0.396960	+	0.116558i	−0.0771588	+	0.997019i	$0.524585\pi$
$840$	38.1970	+	30.8369i	1.31792	+	1.06397i
$841$	1.36562	+	2.99030i	0.0470904	+	0.103114i
$842$	35.1779	+	5.05782i	1.21231	+	0.174304i
$843$	−48.2136	−	41.7773i	−1.66057	−	1.43889i
$844$	0.0974330	−	0.213348i	0.00335378	−	0.00734376i
$845$	16.1571	−	11.1969i	0.555820	−	0.385184i
$846$	7.03588	+	48.9356i	0.241899	+	1.68244i
$847$	−13.5283	−	21.0505i	−0.464838	−	0.723302i
$848$	25.4967	−	22.0930i	0.875559	−	0.758676i
$849$	49.8454	−	14.6359i	1.71069	−	0.502304i
$850$	6.53199	+	6.55517i	0.224046	+	0.224840i
$851$	1.07416	−	0.216595i	0.0368219	−	0.00742478i
$852$		−	0.721604i		−	0.0247218i
$853$	−14.4664	−	49.2681i	−0.495321	−	1.68691i	−0.705057	−	0.709150i	$-0.749079\pi$
$853$	−14.4664	−	49.2681i	−0.495321	−	1.68691i	0.209736	−	0.977758i	$-0.432739\pi$
$854$	8.96527	+	10.3465i	0.306785	+	0.354049i
$855$	8.41809	+	46.8959i	0.287893	+	1.60381i
$856$	3.14906	+	21.9022i	0.107633	+	0.748601i
$857$	−0.418936	+	0.651877i	−0.0143106	+	0.0222677i	−0.848335	−	0.529460i	$-0.822395\pi$
$857$	−0.418936	+	0.651877i	−0.0143106	+	0.0222677i	0.834025	+	0.551727i	$0.186031\pi$
$858$	24.6060	+	11.2372i	0.840036	+	0.383632i
$859$	12.2578	−	14.1463i	0.418231	−	0.482664i	−0.507066	−	0.861907i	$-0.669270\pi$
$859$	12.2578	−	14.1463i	0.418231	−	0.482664i	0.925297	+	0.379243i	$0.123816\pi$
$860$	−0.261455	+	0.439772i	−0.00891555	+	0.0149961i
$861$	21.2174	+	46.4597i	0.723088	+	1.58334i
$862$	7.64845	−	26.0482i	0.260507	−	0.887207i
$863$	10.0402	−	34.1937i	0.341772	−	1.16397i	−0.591952	−	0.805973i	$-0.701643\pi$
$863$	10.0402	−	34.1937i	0.341772	−	1.16397i	0.933724	−	0.357994i	$-0.116539\pi$
$864$	−0.183073	−	0.400875i	−0.00622828	−	0.0136380i
$865$	−10.2801	+	17.2913i	−0.349534	+	0.587921i
$866$	7.09718	−	8.19059i	0.241172	−	0.278327i
$867$	−36.2066	−	16.5350i	−1.22964	−	0.561559i
$868$	0.362118	−	0.563467i	0.0122911	−	0.0191253i
$869$	−1.85821	−	12.9241i	−0.0630355	−	0.438421i
$870$	−8.20669	−	45.7182i	−0.278233	−	1.54999i
$871$	32.2195	+	37.1833i	1.09172	+	1.25991i
$872$	−4.70851	−	16.0357i	−0.159450	−	0.543037i
$873$			21.6093i			0.731365i
$874$	−35.0235	−	13.6741i	−1.18469	−	0.462534i
$875$	12.5331	+	30.4864i	0.423697	+	1.03063i
$876$	−0.0282358	+	0.00829078i	−0.000953999	+	0.000280119i
$877$	30.5321	−	26.4562i	1.03099	−	0.893362i	0.0366249	−	0.999329i	$-0.488339\pi$
$877$	30.5321	−	26.4562i	1.03099	−	0.893362i	0.994370	+	0.105967i	$0.0337939\pi$
$878$	−18.6079	−	28.9544i	−0.627986	−	0.977165i
$879$	−4.16521	−	28.9697i	−0.140489	−	0.977122i
$880$	−11.4337	+	7.92357i	−0.385430	+	0.267104i
$881$	5.52226	−	12.0921i	0.186050	−	0.407392i	−0.793507	−	0.608561i	$-0.791747\pi$
$881$	5.52226	−	12.0921i	0.186050	−	0.407392i	0.979556	+	0.201169i	$0.0644742\pi$
$882$	−6.82244	−	5.91168i	−0.229723	−	0.199056i
$883$	−29.6115	−	4.25750i	−0.996508	−	0.143276i	−0.375284	−	0.926910i	$-0.622455\pi$
$883$	−29.6115	−	4.25750i	−0.996508	−	0.143276i	−0.621223	+	0.783633i	$0.713364\pi$
$884$	0.0946712	+	0.207301i	0.00318414	+	0.00697229i
$885$	−52.9603	−	42.7555i	−1.78024	−	1.43721i
$886$	−37.0772	−	10.8868i	−1.24563	−	0.365750i
$887$	−30.5833	+	13.9669i	−1.02689	+	0.468964i	−0.856355	−	0.516388i	$-0.827276\pi$
$887$	−30.5833	+	13.9669i	−1.02689	+	0.468964i	−0.170533	+	0.985352i	$0.554549\pi$
$888$	−1.68413	−	0.242141i	−0.0565156	−	0.00812571i
$889$	12.2223	−	14.1053i	0.409924	−	0.473077i
$890$	18.0536	−	16.7787i	0.605157	−	0.562422i
$891$	7.89837	+	5.07598i	0.264605	+	0.170052i
$892$	0.352568	−	0.0506916i	0.0118049	−	0.00169728i
$893$	28.0320	+	43.6186i	0.938054	+	1.45964i
$894$	23.6756	+	27.3231i	0.791830	+	0.913820i
$895$	−3.27162	+	30.1791i	−0.109358	+	1.00878i
$896$	32.4010			1.08244
$897$	5.05386	−	58.1945i	0.168743	−	1.94306i
$898$			43.0705i			1.43728i
$899$	−33.5151	+	9.84091i	−1.11779	+	0.328213i
$900$	0.0514417	−	0.701784i	0.00171472	−	0.0233928i
$901$	9.55256	−	6.13906i	0.318242	−	0.204522i
$902$	−14.5957	+	2.09854i	−0.485983	+	0.0698737i
$903$	25.7480	−	40.0647i	0.856841	−	1.33327i
$904$	10.7756	−	23.5952i	0.358390	−	0.784766i
$905$	−3.13281	−	6.27242i	−0.104138	−	0.208502i
$906$	9.42637	−	65.5619i	0.313170	−	2.17815i
$907$	33.0858	−	15.1098i	1.09860	−	0.501712i	0.218177	−	0.975909i	$-0.429989\pi$
$907$	33.0858	−	15.1098i	1.09860	−	0.501712i	0.880419	+	0.474197i	$0.157262\pi$
$908$	0.195437	−	0.665596i	0.00648579	−	0.0220886i
$909$	−19.1442	−	5.62123i	−0.634972	−	0.186445i
$910$	−1.50080	−	43.0910i	−0.0497510	−	1.42845i
$911$	−4.37201	+	30.4080i	−0.144851	+	1.00746i	0.779632	+	0.626238i	$0.215406\pi$
$911$	−4.37201	+	30.4080i	−0.144851	+	1.00746i	−0.924483	+	0.381223i	$0.875503\pi$
$912$	43.3048	+	37.5238i	1.43396	+	1.24254i
$913$	9.77838	+	4.46564i	0.323617	+	0.147791i
$914$	10.6388	+	6.83711i	0.351899	+	0.226152i
$915$	4.79870	−	18.7319i	0.158640	−	0.619258i
$916$	−0.516390	+	0.331863i	−0.0170620	+	0.0109651i
$917$	−10.7051	+	9.27601i	−0.353513	+	0.306321i
$918$	1.09932	+	3.74393i	0.0362828	+	0.123568i
$919$	−19.6529			−0.648290			−0.324145	−	0.946007i	$-0.605077\pi$
$919$	−19.6529			−0.648290			−0.324145	+	0.946007i	$0.605077\pi$
$920$	24.8553	+	17.8576i	0.819454	+	0.588749i
$921$	19.8363			0.653629
$922$	−11.9167	−	40.5845i	−0.392455	−	1.33658i
$923$	−26.4002	+	22.8759i	−0.868974	+	0.752970i
$924$	−0.379103	+	0.243635i	−0.0124716	+	0.00801499i
$925$	−0.913351	−	0.686253i	−0.0300308	−	0.0225639i
$926$	34.2878	+	22.0354i	1.12677	+	0.724129i
$927$	−64.5769	−	29.4913i	−2.12098	−	0.968621i
$928$	0.897662	+	0.777828i	0.0294672	+	0.0255335i
$929$	1.48994	−	10.3628i	0.0488834	−	0.339991i	−0.950673	−	0.310196i	$-0.899605\pi$
$929$	1.48994	−	10.3628i	0.0488834	−	0.339991i	0.999556	−	0.0297953i	$-0.00948555\pi$
$930$	50.2202	−	1.74910i	1.64679	−	0.0573553i
$931$	−9.08406	−	2.66732i	−0.297718	−	0.0874179i
$932$	0.140645	−	0.478994i	0.00460699	−	0.0156900i
$933$	−40.9582	+	18.7050i	−1.34091	+	0.612374i
$934$	4.25813	−	29.6159i	0.139330	−	0.969063i
$935$	−4.18872	+	2.09209i	−0.136986	+	0.0684186i
$936$	−21.0749	+	46.1477i	−0.688856	+	1.50838i
$937$	29.6657	−	46.1608i	0.969137	−	1.50801i	0.111491	−	0.993765i	$-0.464437\pi$
$937$	29.6657	−	46.1608i	0.969137	−	1.50801i	0.857646	−	0.514241i	$-0.171926\pi$
$938$	43.0935	−	6.19591i	1.40705	−	0.202304i
$939$	−5.95316	+	3.82586i	−0.194274	+	0.124852i
$940$	−0.241182	−	0.726783i	−0.00786649	−	0.0237050i
$941$	−25.1608	+	7.38787i	−0.820218	+	0.240838i	−0.664810	−	0.747013i	$-0.731487\pi$
$941$	−25.1608	+	7.38787i	−0.820218	+	0.240838i	−0.155408	+	0.987850i	$0.549669\pi$
$942$			82.5969i			2.69115i
$943$	14.8331	+	28.1765i	0.483032	+	0.917552i
$944$	−45.7864			−1.49022
$945$	−1.49792	+	13.8176i	−0.0487274	+	0.449486i
$946$	9.00410	+	10.3913i	0.292749	+	0.337850i
$947$	4.95903	+	7.71640i	0.161147	+	0.250749i	0.912432	−	0.409228i	$-0.134202\pi$
$947$	4.95903	+	7.71640i	0.161147	+	0.250749i	−0.751285	+	0.659978i	$0.770566\pi$
$948$	0.786231	−	0.113043i	0.0255356	−	0.00367146i
$949$	1.19844	+	0.770189i	0.0389029	+	0.0250014i
$950$	13.6336	+	36.7516i	0.442331	+	1.19238i
$951$	−5.00916	+	5.78088i	−0.162433	+	0.187458i
$952$	11.0017	+	1.58180i	0.356567	+	0.0512666i
$953$	−37.8730	+	17.2960i	−1.22683	+	0.560273i	−0.920159	−	0.391544i	$-0.871941\pi$
$953$	−37.8730	+	17.2960i	−1.22683	+	0.560273i	−0.306667	+	0.951817i	$0.599214\pi$
$954$	44.0049	+	12.9210i	1.42471	+	0.418333i
$955$	1.94292	−	2.40666i	0.0628715	−	0.0778776i
$956$	0.0600453	+	0.131481i	0.00194201	+	0.00425240i
$957$	23.2618	+	3.34455i	0.751949	+	0.108114i
$958$	−27.5564	−	23.8777i	−0.890305	−	0.771454i
$959$	−5.59523	+	12.2518i	−0.180679	+	0.395632i
$960$	−27.0588	−	39.0459i	−0.873320	−	1.26020i
$961$	−0.966159	−	6.71978i	−0.0311664	−	0.216767i
$962$	0.807931	+	1.25717i	0.0260488	+	0.0405327i
$963$	−22.3131	+	19.3344i	−0.719028	+	0.623042i
$964$	0.345681	−	0.101501i	0.0111336	−	0.00326913i
$965$	5.42944	+	2.25458i	0.174780	+	0.0725776i
$966$	−40.9028	−	31.6026i	−1.31602	−	1.01680i
$967$			13.6682i			0.439540i	0.975552	+	0.219770i	$0.0705308\pi$
$967$			13.6682i			0.439540i	−0.975552	+	0.219770i	$0.929469\pi$
$968$	6.82431	+	23.2415i	0.219342	+	0.747009i
$969$	12.6297	+	14.5755i	0.405725	+	0.468232i
$970$	3.14113	+	17.4987i	0.100855	+	0.561851i
$971$	3.95275	+	27.4920i	0.126850	+	0.882259i	0.949512	+	0.313729i	$0.101578\pi$
$971$	3.95275	+	27.4920i	0.126850	+	0.882259i	−0.822663	+	0.568530i	$0.807512\pi$
$972$	−0.435166	+	0.677132i	−0.0139580	+	0.0217190i
$973$	−40.8050	−	18.6350i	−1.30815	−	0.597412i
$974$	−14.8334	+	17.1186i	−0.475292	+	0.548516i
$975$	−48.8178	+	36.4098i	−1.56342	+	1.16605i
$976$	−5.40357	−	11.8322i	−0.172964	−	0.378738i
$977$	1.34028	−	4.56457i	0.0428793	−	0.146034i	−0.935271	−	0.353932i	$-0.884844\pi$
$977$	1.34028	−	4.56457i	0.0428793	−	0.146034i	0.978150	+	0.207899i	$0.0666625\pi$
$978$	6.64243	−	22.6220i	0.212402	−	0.723373i
$979$	5.18025	+	11.3432i	0.165561	+	0.362529i
$980$	0.120188	+	0.0714547i	0.00383926	+	0.00228254i
$981$	14.6031	−	16.8529i	0.466242	−	0.538072i
$982$	21.6441	+	9.88451i	0.690690	+	0.315428i
$983$	−19.9889	+	31.1033i	−0.637545	+	0.992040i	0.360692	+	0.932685i	$0.382541\pi$
$983$	−19.9889	+	31.1033i	−0.637545	+	0.992040i	−0.998237	+	0.0593548i	$0.981096\pi$
$984$	−7.03636	−	48.9390i	−0.224311	−	1.56012i
$985$	30.7687	−	5.52317i	0.980374	−	0.175983i
$986$	−6.88694	−	7.94795i	−0.219325	−	0.253114i
$987$	20.0823	+	68.3939i	0.639225	+	2.17700i
$988$			0.965336i			0.0307114i
$989$	14.6247	−	25.8397i	0.465037	−	0.821656i
$990$	−17.4648	−	7.25229i	−0.555069	−	0.230493i
$991$	32.7309	−	9.61067i	1.03973	−	0.305293i	0.283070	−	0.959099i	$-0.408647\pi$
$991$	32.7309	−	9.61067i	1.03973	−	0.305293i	0.756662	+	0.653806i	$0.226829\pi$
$992$	−0.971132	+	0.841491i	−0.0308335	+	0.0267174i
$993$	−11.8943	−	18.5080i	−0.377456	−	0.587332i
$994$	4.39911	+	30.5965i	0.139531	+	0.970461i
$995$	24.9421	−	17.2849i	0.790718	−	0.547968i
$996$	−0.271664	+	0.594860i	−0.00860799	+	0.0188489i
$997$	23.7667	+	20.5939i	0.752698	+	0.652217i	0.944236	−	0.329268i	$-0.106802\pi$
$997$	23.7667	+	20.5939i	0.752698	+	0.652217i	−0.191538	+	0.981485i	$0.561348\pi$
$998$	28.5483	+	4.10463i	0.903681	+	0.129930i
$999$	−0.200109	−	0.438179i	−0.00633118	−	0.0138634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.j.a.9.3	✓	100
5.2	odd	4		575.2.k.g.101.8		100
5.3	odd	4		575.2.k.g.101.3		100
5.4	even	2	inner	115.2.j.a.9.8	yes	100
23.18	even	11	inner	115.2.j.a.64.8	yes	100
115.18	odd	44		575.2.k.g.501.3		100
115.64	even	22	inner	115.2.j.a.64.3	yes	100
115.87	odd	44		575.2.k.g.501.8		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.j.a.9.3	✓	100	1.1	even	1	trivial
115.2.j.a.9.8	yes	100	5.4	even	2	inner
115.2.j.a.64.3	yes	100	115.64	even	22	inner
115.2.j.a.64.8	yes	100	23.18	even	11	inner
575.2.k.g.101.3		100	5.3	odd	4
575.2.k.g.101.8		100	5.2	odd	4
575.2.k.g.501.3		100	115.18	odd	44
575.2.k.g.501.8		100	115.87	odd	44

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.394732 - 1.34433i) q^{2} +(-1.97191 + 1.70867i) q^{3} +(0.0310904 - 0.0199806i) q^{4} +(2.16612 + 0.554912i) q^{5} +(3.07540 + 1.97644i) q^{6} +(2.68179 + 1.22473i) q^{7} +(-2.15687 - 1.86894i) q^{8} +(0.541936 - 3.76925i) q^{9} +O(q^{10})\)	\(q+(-0.394732 - 1.34433i) q^{2} +(-1.97191 + 1.70867i) q^{3} +(0.0310904 - 0.0199806i) q^{4} +(2.16612 + 0.554912i) q^{5} +(3.07540 + 1.97644i) q^{6} +(2.68179 + 1.22473i) q^{7} +(-2.15687 - 1.86894i) q^{8} +(0.541936 - 3.76925i) q^{9} +(-0.109049 - 3.13103i) q^{10} +(1.52091 + 0.446579i) q^{11} +(-0.0271673 + 0.0925233i) q^{12} +(4.24625 - 1.93920i) q^{13} +(0.587861 - 4.08866i) q^{14} +(-5.21956 + 2.60695i) q^{15} +(-1.63039 + 3.57005i) q^{16} +(-0.714176 + 1.11128i) q^{17} +(-5.28104 + 0.759299i) q^{18} +(-4.70724 + 3.02516i) q^{19} +(0.0784330 - 0.0260279i) q^{20} +(-7.38094 + 2.16724i) q^{21} -2.22088i q^{22} +(-4.51845 + 1.60736i) q^{23} +7.44658 q^{24} +(4.38415 + 2.40401i) q^{25} +(-4.28306 - 4.94291i) q^{26} +(1.13981 + 1.77358i) q^{27} +(0.107849 - 0.0155063i) q^{28} +(-4.78017 - 3.07203i) q^{29} +(5.56493 + 5.98778i) q^{30} +(4.02560 - 4.64579i) q^{31} +(-0.206907 - 0.0297487i) q^{32} +(-3.76216 + 1.71812i) q^{33} +(1.77584 + 0.521433i) q^{34} +(5.12947 + 4.14108i) q^{35} +(-0.0584628 - 0.128016i) q^{36} +(-0.226161 - 0.0325170i) q^{37} +(5.92491 + 5.13396i) q^{38} +(-5.05979 + 11.0794i) q^{39} +(-3.63495 - 5.24523i) q^{40} +(-0.944912 - 6.57201i) q^{41} +(5.82698 + 9.06696i) q^{42} +(-4.67889 + 4.05429i) q^{43} +(0.0562086 - 0.0165043i) q^{44} +(3.26550 - 7.86391i) q^{45} +(3.94440 + 5.43983i) q^{46} -9.26629i q^{47} +(-2.88507 - 9.82563i) q^{48} +(1.10802 + 1.27872i) q^{49} +(1.50123 - 6.84269i) q^{50} +(-0.490520 - 3.41164i) q^{51} +(0.0932714 - 0.145133i) q^{52} +(-7.81920 - 3.57091i) q^{53} +(1.93436 - 2.23238i) q^{54} +(3.04666 + 1.81131i) q^{55} +(-3.49533 - 7.65371i) q^{56} +(4.11326 - 14.0085i) q^{57} +(-2.24294 + 7.63876i) q^{58} +(4.84630 + 10.6119i) q^{59} +(-0.110190 + 0.185341i) q^{60} +(-2.17039 + 2.50477i) q^{61} +(-7.83452 - 3.57791i) q^{62} +(6.06969 - 9.44462i) q^{63} +(1.15877 + 8.05944i) q^{64} +(10.2740 - 1.84424i) q^{65} +(3.79477 + 4.37939i) q^{66} +(2.96939 + 10.1128i) q^{67} +0.0488198i q^{68} +(6.16355 - 10.8901i) q^{69} +(3.54223 - 8.53032i) q^{70} +(-7.18012 + 2.10827i) q^{71} +(-8.21339 + 7.11694i) q^{72} +(0.164990 + 0.256729i) q^{73} +(0.0455592 + 0.316871i) q^{74} +(-12.7528 + 2.75057i) q^{75} +(-0.0859054 + 0.188107i) q^{76} +(3.53182 + 3.06034i) q^{77} +(16.8916 + 2.42865i) q^{78} +(-3.42189 - 7.49289i) q^{79} +(-5.51268 + 6.82843i) q^{80} +(5.68318 + 1.66873i) q^{81} +(-8.46197 + 3.86445i) q^{82} +(6.71269 + 0.965140i) q^{83} +(-0.186174 + 0.214856i) q^{84} +(-2.16365 + 2.01086i) q^{85} +(7.29721 + 4.68964i) q^{86} +(14.6752 - 2.10997i) q^{87} +(-2.44578 - 3.80570i) q^{88} +(5.15177 + 5.94546i) q^{89} +(-11.8607 - 1.28578i) q^{90} +13.7626 q^{91} +(-0.108365 + 0.140255i) q^{92} +16.0395i q^{93} +(-12.4570 + 3.65770i) q^{94} +(-11.8751 + 3.94075i) q^{95} +(0.458834 - 0.294875i) q^{96} +(-5.61695 + 0.807595i) q^{97} +(1.28166 - 1.99430i) q^{98} +(2.50750 - 5.49066i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9}+O(q^{10}) \) 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9	\( 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9} - 13 q^{10} - 26 q^{11} - 26 q^{14} - 10 q^{15} - 18 q^{16} - 14 q^{19} + 49 q^{20} - 22 q^{21} - 68 q^{24} + 21 q^{25} - 42 q^{26} - 24 q^{29} + 19 q^{30} - 12 q^{31} + 8 q^{34} - 37 q^{35} - 10 q^{36} + 14 q^{39} - q^{40} + 8 q^{41} + 166 q^{44} - 42 q^{45} - 18 q^{46} + 32 q^{49} - 23 q^{50} - 22 q^{51} + 116 q^{54} + 27 q^{55} - 116 q^{56} + 50 q^{59} + 123 q^{60} - 38 q^{61} + 10 q^{64} + 76 q^{65} - 28 q^{66} + 80 q^{69} + 102 q^{70} - 110 q^{71} + 22 q^{74} + 6 q^{75} + 4 q^{76} + 42 q^{79} + 18 q^{80} + 204 q^{81} + 56 q^{84} - 121 q^{85} + 132 q^{86} - 66 q^{89} - 198 q^{90} + 76 q^{91} - 70 q^{94} - 74 q^{95} + 236 q^{96} - 60 q^{99}+O(q^{100}) \) 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9 - 13 * q^10 - 26 * q^11 - 26 * q^14 - 10 * q^15 - 18 * q^16 - 14 * q^19 + 49 * q^20 - 22 * q^21 - 68 * q^24 + 21 * q^25 - 42 * q^26 - 24 * q^29 + 19 * q^30 - 12 * q^31 + 8 * q^34 - 37 * q^35 - 10 * q^36 + 14 * q^39 - q^40 + 8 * q^41 + 166 * q^44 - 42 * q^45 - 18 * q^46 + 32 * q^49 - 23 * q^50 - 22 * q^51 + 116 * q^54 + 27 * q^55 - 116 * q^56 + 50 * q^59 + 123 * q^60 - 38 * q^61 + 10 * q^64 + 76 * q^65 - 28 * q^66 + 80 * q^69 + 102 * q^70 - 110 * q^71 + 22 * q^74 + 6 * q^75 + 4 * q^76 + 42 * q^79 + 18 * q^80 + 204 * q^81 + 56 * q^84 - 121 * q^85 + 132 * q^86 - 66 * q^89 - 198 * q^90 + 76 * q^91 - 70 * q^94 - 74 * q^95 + 236 * q^96 - 60 * q^99

Introduction

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