LMFDB - Embedded newform 55.2.g.a.36.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,2,Mod(16,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("55.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	55.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.439177211117$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			36.2
Root			$0.453245 + 1.39494i$ of defining polynomial
Character	$\chi$	$=$	55.36
Dual form			55.2.g.a.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0756511 + 0.0549637i) q^{2} +(0.453245 + 1.39494i) q^{3} +(-0.615332 + 1.89380i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.110960 - 0.0806171i) q^{6} +(1.39815 - 4.30308i) q^{7} +(-0.115332 - 0.354955i) q^{8} +(0.686611 - 0.498852i) q^{9} +O(q^{10})$	\(q+(-0.0756511 + 0.0549637i) q^{2} +(0.453245 + 1.39494i) q^{3} +(-0.615332 + 1.89380i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.110960 - 0.0806171i) q^{6} +(1.39815 - 4.30308i) q^{7} +(-0.115332 - 0.354955i) q^{8} +(0.686611 - 0.498852i) q^{9} +0.0935099 q^{10} +(-2.39815 + 2.29104i) q^{11} -2.92064 q^{12} +(0.924349 - 0.671579i) q^{13} +(0.130741 + 0.402380i) q^{14} +(0.453245 - 1.39494i) q^{15} +(-3.19369 - 2.32035i) q^{16} +(-2.72899 - 1.98273i) q^{17} +(-0.0245241 + 0.0754774i) q^{18} +(1.88030 + 5.78696i) q^{19} +(1.61096 - 1.17043i) q^{20} +6.63626 q^{21} +(0.0554990 - 0.305131i) q^{22} -5.45258 q^{23} +(0.442869 - 0.321763i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.0330155 + 0.101611i) q^{26} +(4.56691 + 3.31805i) q^{27} +(7.28883 + 5.29564i) q^{28} +(1.02619 - 3.15830i) q^{29} +(0.0423829 + 0.130441i) q^{30} +(-1.44887 + 1.05267i) q^{31} +1.11558 q^{32} +(-4.28282 - 2.30689i) q^{33} +0.315430 q^{34} +(-3.66042 + 2.65945i) q^{35} +(0.522231 + 1.60726i) q^{36} +(0.460067 - 1.41594i) q^{37} +(-0.460319 - 0.334441i) q^{38} +(1.35577 + 0.985026i) q^{39} +(-0.115332 + 0.354955i) q^{40} +(-0.539933 - 1.66174i) q^{41} +(-0.502041 + 0.364754i) q^{42} -0.263041 q^{43} +(-2.86310 - 5.95137i) q^{44} -0.848698 q^{45} +(0.412494 - 0.299694i) q^{46} +(2.13986 + 6.58580i) q^{47} +(1.78924 - 5.50670i) q^{48} +(-10.8985 - 7.91824i) q^{49} +(-0.0756511 - 0.0549637i) q^{50} +(1.52890 - 4.70546i) q^{51} +(0.703052 + 2.16377i) q^{52} +(1.16479 - 0.846269i) q^{53} -0.527864 q^{54} +(3.28679 - 0.443888i) q^{55} -1.68865 q^{56} +(-7.22025 + 5.24582i) q^{57} +(0.0959593 + 0.295332i) q^{58} +(-2.18416 + 6.72216i) q^{59} +(2.36285 + 1.71671i) q^{60} +(-2.02452 - 1.47090i) q^{61} +(0.0517503 - 0.159271i) q^{62} +(-1.18661 - 3.65201i) q^{63} +(6.30297 - 4.57938i) q^{64} -1.14256 q^{65} +(0.450796 - 0.0608810i) q^{66} -0.516598 q^{67} +(5.43413 - 3.94812i) q^{68} +(-2.47136 - 7.60605i) q^{69} +(0.130741 - 0.402380i) q^{70} +(8.68098 + 6.30710i) q^{71} +(-0.256258 - 0.186183i) q^{72} +(-1.75560 + 5.40317i) q^{73} +(0.0430208 + 0.132404i) q^{74} +(-1.18661 + 0.862123i) q^{75} -12.1163 q^{76} +(6.50552 + 13.5227i) q^{77} -0.156706 q^{78} +(9.14460 - 6.64394i) q^{79} +(1.21988 + 3.75440i) q^{80} +(-1.77179 + 5.45300i) q^{81} +(0.132182 + 0.0960360i) q^{82} +(-3.62511 - 2.63380i) q^{83} +(-4.08350 + 12.5677i) q^{84} +(1.04238 + 3.20812i) q^{85} +(0.0198994 - 0.0144577i) q^{86} +4.87077 q^{87} +(1.08980 + 0.587008i) q^{88} +13.2676 q^{89} +(0.0642049 - 0.0466476i) q^{90} +(-1.59747 - 4.91652i) q^{91} +(3.35515 - 10.3261i) q^{92} +(-2.12511 - 1.54398i) q^{93} +(-0.523863 - 0.380608i) q^{94} +(1.88030 - 5.78696i) q^{95} +(0.505633 + 1.55618i) q^{96} +(2.71551 - 1.97293i) q^{97} +1.25970 q^{98} +(-0.503711 + 2.76938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} + 13 q^{6} - 3 q^{7} - 2 q^{8} - 5 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 + 13 * q^6 - 3 * q^7 - 2 * q^8 - 5 * q^9	\( 8 q - 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} + 13 q^{6} - 3 q^{7} - 2 q^{8} - 5 q^{9} + 6 q^{10} - 5 q^{11} - 28 q^{12} + 4 q^{13} + 16 q^{14} + q^{15} - 20 q^{16} + q^{17} + 14 q^{18} - q^{19} - q^{20} - 12 q^{21} + 33 q^{22} - 18 q^{23} + 25 q^{24} - 2 q^{25} - 14 q^{26} + 10 q^{27} + 4 q^{28} + 19 q^{29} - 12 q^{30} + 6 q^{31} + 12 q^{32} - 19 q^{33} - 20 q^{34} - 8 q^{35} + 21 q^{36} + 4 q^{37} - 6 q^{38} + 9 q^{39} - 2 q^{40} - 4 q^{41} + 29 q^{42} + 42 q^{43} - 28 q^{44} - 41 q^{46} + 4 q^{47} - 19 q^{48} - 15 q^{49} - 4 q^{50} + 13 q^{51} - 26 q^{52} + 3 q^{53} - 40 q^{54} + 5 q^{55} + 30 q^{56} - 5 q^{57} - 6 q^{58} - 19 q^{59} + 22 q^{60} - 2 q^{61} - 38 q^{62} + q^{63} + 6 q^{64} + 14 q^{65} + 13 q^{66} - 2 q^{67} + 35 q^{68} - 21 q^{69} + 16 q^{70} + 40 q^{71} - 34 q^{72} - 23 q^{73} + 48 q^{74} + q^{75} + 16 q^{76} - 28 q^{77} + 12 q^{78} + 17 q^{79} + 15 q^{80} + 2 q^{82} - 25 q^{83} - 4 q^{84} - 4 q^{85} - 31 q^{86} + 30 q^{87} + 22 q^{88} - 16 q^{90} - 12 q^{91} + 81 q^{92} - 13 q^{93} + 33 q^{94} - q^{95} + 23 q^{96} + 12 q^{97} - 84 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 + 13 * q^6 - 3 * q^7 - 2 * q^8 - 5 * q^9 + 6 * q^10 - 5 * q^11 - 28 * q^12 + 4 * q^13 + 16 * q^14 + q^15 - 20 * q^16 + q^17 + 14 * q^18 - q^19 - q^20 - 12 * q^21 + 33 * q^22 - 18 * q^23 + 25 * q^24 - 2 * q^25 - 14 * q^26 + 10 * q^27 + 4 * q^28 + 19 * q^29 - 12 * q^30 + 6 * q^31 + 12 * q^32 - 19 * q^33 - 20 * q^34 - 8 * q^35 + 21 * q^36 + 4 * q^37 - 6 * q^38 + 9 * q^39 - 2 * q^40 - 4 * q^41 + 29 * q^42 + 42 * q^43 - 28 * q^44 - 41 * q^46 + 4 * q^47 - 19 * q^48 - 15 * q^49 - 4 * q^50 + 13 * q^51 - 26 * q^52 + 3 * q^53 - 40 * q^54 + 5 * q^55 + 30 * q^56 - 5 * q^57 - 6 * q^58 - 19 * q^59 + 22 * q^60 - 2 * q^61 - 38 * q^62 + q^63 + 6 * q^64 + 14 * q^65 + 13 * q^66 - 2 * q^67 + 35 * q^68 - 21 * q^69 + 16 * q^70 + 40 * q^71 - 34 * q^72 - 23 * q^73 + 48 * q^74 + q^75 + 16 * q^76 - 28 * q^77 + 12 * q^78 + 17 * q^79 + 15 * q^80 + 2 * q^82 - 25 * q^83 - 4 * q^84 - 4 * q^85 - 31 * q^86 + 30 * q^87 + 22 * q^88 - 16 * q^90 - 12 * q^91 + 81 * q^92 - 13 * q^93 + 33 * q^94 - q^95 + 23 * q^96 + 12 * q^97 - 84 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.0756511	+	0.0549637i	−0.0534934	+	0.0388652i	−0.614211	−	0.789142i	$-0.710525\pi$
$2$	−0.0756511	+	0.0549637i	−0.0534934	+	0.0388652i	0.560717	+	0.828007i	$0.310525\pi$
$3$	0.453245	+	1.39494i	0.261681	+	0.805372i	0.992439	+	0.122735i	$0.0391667\pi$
$3$	0.453245	+	1.39494i	0.261681	+	0.805372i	−0.730758	+	0.682636i	$0.760833\pi$
$4$	−0.615332	+	1.89380i	−0.307666	+	0.946898i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	−0.110960	−	0.0806171i	−0.0452992	−	0.0329118i
$7$	1.39815	−	4.30308i	0.528453	−	1.62641i	−0.228932	−	0.973442i	$-0.573523\pi$
$7$	1.39815	−	4.30308i	0.528453	−	1.62641i	0.757385	−	0.652968i	$-0.226477\pi$
$8$	−0.115332	−	0.354955i	−0.0407760	−	0.125496i
$9$	0.686611	−	0.498852i	0.228870	−	0.166284i
$10$	0.0935099			0.0295704
$11$	−2.39815	+	2.29104i	−0.723071	+	0.690774i
$11$	−2.39815	+	2.29104i	−0.723071	+	0.690774i
$12$	−2.92064			−0.843116
$13$	0.924349	−	0.671579i	0.256368	−	0.186262i	−0.452176	−	0.891929i	$-0.649352\pi$
$13$	0.924349	−	0.671579i	0.256368	−	0.186262i	0.708544	+	0.705666i	$0.249352\pi$
$14$	0.130741	+	0.402380i	0.0349421	+	0.107541i
$15$	0.453245	−	1.39494i	0.117027	−	0.360173i
$16$	−3.19369	−	2.32035i	−0.798421	−	0.580087i
$17$	−2.72899	−	1.98273i	−0.661878	−	0.480883i	0.205418	−	0.978674i	$-0.434144\pi$
$17$	−2.72899	−	1.98273i	−0.661878	−	0.480883i	−0.867297	+	0.497792i	$0.834144\pi$
$18$	−0.0245241	+	0.0754774i	−0.00578038	+	0.0177902i
$19$	1.88030	+	5.78696i	0.431369	+	1.32762i	0.896762	+	0.442514i	$0.145913\pi$
$19$	1.88030	+	5.78696i	0.431369	+	1.32762i	−0.465392	+	0.885105i	$0.654087\pi$
$20$	1.61096	−	1.17043i	0.360222	−	0.261716i
$21$	6.63626			1.44815
$22$	0.0554990	−	0.305131i	0.0118324	−	0.0650542i
$23$	−5.45258			−1.13694			−0.568471	−	0.822703i	$-0.692465\pi$
$23$	−5.45258			−1.13694			−0.568471	+	0.822703i	$0.692465\pi$
$24$	0.442869	−	0.321763i	0.0904003	−	0.0656797i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−0.0330155	+	0.101611i	−0.00647488	+	0.0199276i
$27$	4.56691	+	3.31805i	0.878902	+	0.638559i
$28$	7.28883	+	5.29564i	1.37746	+	1.00078i
$29$	1.02619	−	3.15830i	0.190559	−	0.586482i	−0.809440	−	0.587202i	$-0.800229\pi$
$29$	1.02619	−	3.15830i	0.190559	−	0.586482i	1.00000		0.000720503i	$0.000229343\pi$
$30$	0.0423829	+	0.130441i	0.00773802	+	0.0238152i
$31$	−1.44887	+	1.05267i	−0.260225	+	0.189065i	−0.710246	−	0.703953i	$-0.751416\pi$
$31$	−1.44887	+	1.05267i	−0.260225	+	0.189065i	0.450021	+	0.893018i	$0.351416\pi$
$32$	1.11558			0.197209
$33$	−4.28282	−	2.30689i	−0.745544	−	0.401578i
$34$	0.315430			0.0540957
$35$	−3.66042	+	2.65945i	−0.618723	+	0.449529i
$36$	0.522231	+	1.60726i	0.0870385	+	0.267877i
$37$	0.460067	−	1.41594i	0.0756345	−	0.232779i	−0.906091	−	0.423084i	$-0.860948\pi$
$37$	0.460067	−	1.41594i	0.0756345	−	0.232779i	0.981725	+	0.190305i	$0.0609476\pi$
$38$	−0.460319	−	0.334441i	−0.0746736	−	0.0542536i
$39$	1.35577	+	0.985026i	0.217097	+	0.157730i
$40$	−0.115332	+	0.354955i	−0.0182356	+	0.0561233i
$41$	−0.539933	−	1.66174i	−0.0843234	−	0.259521i	0.900001	−	0.435888i	$-0.143566\pi$
$41$	−0.539933	−	1.66174i	−0.0843234	−	0.259521i	−0.984325	+	0.176367i	$0.943566\pi$
$42$	−0.502041	+	0.364754i	−0.0774665	+	0.0562827i
$43$	−0.263041			−0.0401134			−0.0200567	−	0.999799i	$-0.506385\pi$
$43$	−0.263041			−0.0401134			−0.0200567	+	0.999799i	$0.506385\pi$
$44$	−2.86310	−	5.95137i	−0.431628	−	0.897202i
$45$	−0.848698			−0.126516
$46$	0.412494	−	0.299694i	0.0608189	−	0.0441875i
$47$	2.13986	+	6.58580i	0.312130	+	0.960638i	0.976920	+	0.213607i	$0.0685212\pi$
$47$	2.13986	+	6.58580i	0.312130	+	0.960638i	−0.664790	+	0.747031i	$0.731479\pi$
$48$	1.78924	−	5.50670i	0.258254	−	0.794824i
$49$	−10.8985	−	7.91824i	−1.55693	−	1.13118i
$50$	−0.0756511	−	0.0549637i	−0.0106987	−	0.00777305i
$51$	1.52890	−	4.70546i	0.214088	−	0.658896i
$52$	0.703052	+	2.16377i	0.0974958	+	0.300061i
$53$	1.16479	−	0.846269i	0.159996	−	0.116244i	−0.504907	−	0.863174i	$-0.668473\pi$
$53$	1.16479	−	0.846269i	0.159996	−	0.116244i	0.664903	+	0.746930i	$0.268473\pi$
$54$	−0.527864			−0.0718332
$55$	3.28679	−	0.443888i	0.443190	−	0.0598539i
$56$	−1.68865			−0.225656
$57$	−7.22025	+	5.24582i	−0.956345	+	0.694826i
$58$	0.0959593	+	0.295332i	0.0126001	+	0.0387790i
$59$	−2.18416	+	6.72216i	−0.284354	+	0.875150i	0.702238	+	0.711942i	$0.252184\pi$
$59$	−2.18416	+	6.72216i	−0.284354	+	0.875150i	−0.986592	+	0.163208i	$0.947816\pi$
$60$	2.36285	+	1.71671i	0.305042	+	0.221626i
$61$	−2.02452	−	1.47090i	−0.259214	−	0.188330i	0.450587	−	0.892733i	$-0.351215\pi$
$61$	−2.02452	−	1.47090i	−0.259214	−	0.188330i	−0.709800	+	0.704403i	$0.751215\pi$
$62$	0.0517503	−	0.159271i	0.00657229	−	0.0202274i
$63$	−1.18661	−	3.65201i	−0.149499	−	0.460110i
$64$	6.30297	−	4.57938i	0.787872	−	0.572422i
$65$	−1.14256			−0.141717
$66$	0.450796	−	0.0608810i	0.0554891	−	0.00749394i
$67$	−0.516598			−0.0631124			−0.0315562	−	0.999502i	$-0.510046\pi$
$67$	−0.516598			−0.0631124			−0.0315562	+	0.999502i	$0.510046\pi$
$68$	5.43413	−	3.94812i	0.658984	−	0.478780i
$69$	−2.47136	−	7.60605i	−0.297516	−	0.915661i
$70$	0.130741	−	0.402380i	0.0156266	−	0.0480937i
$71$	8.68098	+	6.30710i	1.03024	+	0.748515i	0.968357	−	0.249568i	$-0.0802887\pi$
$71$	8.68098	+	6.30710i	1.03024	+	0.748515i	0.0618853	+	0.998083i	$0.480289\pi$
$72$	−0.256258	−	0.186183i	−0.0302003	−	0.0219418i
$73$	−1.75560	+	5.40317i	−0.205477	+	0.632393i	0.794216	+	0.607635i	$0.207882\pi$
$73$	−1.75560	+	5.40317i	−0.205477	+	0.632393i	−0.999693	+	0.0247584i	$0.992118\pi$
$74$	0.0430208	+	0.132404i	0.00500106	+	0.0153917i
$75$	−1.18661	+	0.862123i	−0.137018	+	0.0995494i
$76$	−12.1163			−1.38984
$77$	6.50552	+	13.5227i	0.741373	+	1.54105i
$78$	−0.156706			−0.0177435
$79$	9.14460	−	6.64394i	1.02885	−	0.747502i	0.0607700	−	0.998152i	$-0.480644\pi$
$79$	9.14460	−	6.64394i	1.02885	−	0.747502i	0.968078	+	0.250650i	$0.0806444\pi$
$80$	1.21988	+	3.75440i	0.136387	+	0.419755i
$81$	−1.77179	+	5.45300i	−0.196865	+	0.605888i
$82$	0.132182	+	0.0960360i	0.0145971	+	0.0106054i
$83$	−3.62511	−	2.63380i	−0.397907	−	0.289097i	0.370781	−	0.928720i	$-0.379090\pi$
$83$	−3.62511	−	2.63380i	−0.397907	−	0.289097i	−0.768688	+	0.639624i	$0.779090\pi$
$84$	−4.08350	+	12.5677i	−0.445547	+	1.37125i
$85$	1.04238	+	3.20812i	0.113062	+	0.347970i
$86$	0.0198994	−	0.0144577i	0.00214580	−	0.00155902i
$87$	4.87077			0.522202
$88$	1.08980	+	0.587008i	0.116173	+	0.0625752i
$89$	13.2676			1.40637			0.703183	−	0.711009i	$-0.251762\pi$
$89$	13.2676			1.40637			0.703183	+	0.711009i	$0.251762\pi$
$90$	0.0642049	−	0.0466476i	0.00676779	−	0.00491709i
$91$	−1.59747	−	4.91652i	−0.167461	−	0.515391i
$92$	3.35515	−	10.3261i	0.349798	−	1.07657i
$93$	−2.12511	−	1.54398i	−0.220363	−	0.160103i
$94$	−0.523863	−	0.380608i	−0.0540323	−	0.0392568i
$95$	1.88030	−	5.78696i	0.192914	−	0.593729i
$96$	0.505633	+	1.55618i	0.0516060	+	0.158827i
$97$	2.71551	−	1.97293i	0.275718	−	0.200321i	−0.441330	−	0.897345i	$-0.645493\pi$
$97$	2.71551	−	1.97293i	0.275718	−	0.200321i	0.717048	+	0.697024i	$0.245493\pi$
$98$	1.25970			0.127249
$99$	−0.503711	+	2.76938i	−0.0506248	+	0.278333i
$100$	−1.99126			−0.199126
$101$	7.55216	−	5.48696i	0.751468	−	0.545973i	−0.144814	−	0.989459i	$-0.546258\pi$
$101$	7.55216	−	5.48696i	0.751468	−	0.545973i	0.896282	+	0.443486i	$0.146258\pi$
$102$	0.142967	+	0.440007i	0.0141558	+	0.0435672i
$103$	−4.30027	+	13.2349i	−0.423718	+	1.30407i	0.480498	+	0.876996i	$0.340456\pi$
$103$	−4.30027	+	13.2349i	−0.423718	+	1.30407i	−0.904216	+	0.427075i	$0.859544\pi$
$104$	−0.344987	−	0.250648i	−0.0338288	−	0.0245781i
$105$	−5.36885	−	3.90070i	−0.523946	−	0.380669i
$106$	−0.0416035	+	0.128042i	−0.00404089	+	0.0124366i
$107$	−5.18787	−	15.9666i	−0.501531	−	1.54355i	−0.806526	−	0.591198i	$-0.798655\pi$
$107$	−5.18787	−	15.9666i	−0.501531	−	1.54355i	0.304996	−	0.952354i	$-0.401345\pi$
$108$	−9.09388	+	6.60709i	−0.875059	+	0.635768i
$109$	−3.65293			−0.349888			−0.174944	−	0.984578i	$-0.555974\pi$
$109$	−3.65293			−0.349888			−0.174944	+	0.984578i	$0.555974\pi$
$110$	−0.224251	+	0.214235i	−0.0213815	+	0.0204265i
$111$	2.18368			0.207266
$112$	−14.4499	+	10.4985i	−1.36539	+	0.992012i
$113$	−3.67802	−	11.3198i	−0.345999	−	1.06488i	−0.961047	−	0.276386i	$-0.910863\pi$
$113$	−3.67802	−	11.3198i	−0.345999	−	1.06488i	0.615047	−	0.788490i	$-0.289137\pi$
$114$	0.257890	−	0.793704i	0.0241536	−	0.0743372i
$115$	4.41123	+	3.20495i	0.411350	+	0.298863i
$116$	5.34973	+	3.88681i	0.496710	+	0.360881i
$117$	0.299650	−	0.922227i	0.0277026	−	0.0852599i
$118$	−0.204241	−	0.628588i	−0.0188019	−	0.0578662i
$119$	−12.3474	+	8.97091i	−1.13188	+	0.822362i
$120$	−0.547416			−0.0499721
$121$	0.502293	−	10.9885i	0.0456630	−	0.998957i
$122$	0.234004			0.0211857
$123$	2.07332	−	1.50635i	0.186945	−	0.135823i
$124$	−1.10200	−	3.39161i	−0.0989626	−	0.304576i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	0.290497	+	0.211058i	0.0258795	+	0.0188026i
$127$	−15.9883	−	11.6162i	−1.41873	−	1.03077i	−0.991979	−	0.126404i	$-0.959656\pi$
$127$	−15.9883	−	11.6162i	−1.41873	−	1.03077i	−0.426756	−	0.904367i	$-0.640344\pi$
$128$	−0.914596	+	2.81484i	−0.0808397	+	0.248799i
$129$	−0.119222	−	0.366928i	−0.0104969	−	0.0323062i
$130$	0.0864358	−	0.0627993i	0.00758092	−	0.00550786i
$131$	−1.93479			−0.169043			−0.0845215	−	0.996422i	$-0.526936\pi$
$131$	−1.93479			−0.169043			−0.0845215	+	0.996422i	$0.526936\pi$
$132$	7.00414	−	6.69129i	0.609632	−	0.582402i
$133$	27.5307			2.38721
$134$	0.0390812	−	0.0283941i	0.00337610	−	0.00245288i
$135$	−1.74440	−	5.36872i	−0.150134	−	0.462066i
$136$	−0.389040	+	1.19734i	−0.0333599	+	0.102671i
$137$	10.1413	+	7.36808i	0.866429	+	0.629498i	0.929626	−	0.368503i	$-0.120130\pi$
$137$	10.1413	+	7.36808i	0.866429	+	0.629498i	−0.0631970	+	0.998001i	$0.520130\pi$
$138$	0.605018	+	0.439571i	0.0515025	+	0.0374188i
$139$	−3.47491	+	10.6947i	−0.294738	+	0.907111i	0.688571	+	0.725169i	$0.258238\pi$
$139$	−3.47491	+	10.6947i	−0.294738	+	0.907111i	−0.983309	+	0.181942i	$0.941762\pi$
$140$	−2.78408	−	8.56853i	−0.235298	−	0.724173i
$141$	−8.21695	+	5.96996i	−0.691992	+	0.502762i
$142$	−1.00339			−0.0842024
$143$	−0.678120	+	3.72827i	−0.0567072	+	0.311773i
$144$	−3.35033			−0.279194
$145$	−2.68661	+	1.95194i	−0.223111	+	0.162100i
$146$	−0.164166	−	0.505250i	−0.0135864	−	0.0418148i
$147$	6.10581	−	18.7917i	0.503599	−	1.54992i
$148$	2.39841	+	1.74255i	0.197148	+	0.143236i
$149$	14.0232	+	10.1885i	1.14883	+	0.834672i	0.988325	−	0.152363i	$-0.0486884\pi$
$149$	14.0232	+	10.1885i	1.14883	+	0.834672i	0.160503	+	0.987035i	$0.448688\pi$
$150$	0.0423829	−	0.130441i	0.00346055	−	0.0106505i
$151$	−0.00166997	−	0.00513965i	−0.000135901	−	0.000418259i	0.950989	−	0.309226i	$-0.100070\pi$
$151$	−0.00166997	−	0.00513965i	−0.000135901	−	0.000418259i	−0.951124	+	0.308808i	$0.900070\pi$
$152$	1.83725	−	1.33484i	0.149021	−	0.108270i
$153$	−2.86285			−0.231447
$154$	−1.23541	−	0.665437i	−0.0995519	−	0.0536225i
$155$	1.79091			0.143849
$156$	−2.69969	+	1.96144i	−0.216148	+	0.157041i
$157$	0.171454	+	0.527682i	0.0136835	+	0.0421136i	0.957665	−	0.287884i	$-0.0929519\pi$
$157$	0.171454	+	0.527682i	0.0136835	+	0.0421136i	−0.943982	+	0.329998i	$0.892952\pi$
$158$	−0.326623	+	1.00524i	−0.0259847	+	0.0799728i
$159$	1.70843	+	1.24125i	0.135488	+	0.0984375i
$160$	−0.902527	−	0.655724i	−0.0713510	−	0.0518395i
$161$	−7.62356	+	23.4629i	−0.600820	+	1.84914i
$162$	−0.165679	−	0.509909i	−0.0130170	−	0.0400622i
$163$	6.44324	−	4.68129i	0.504673	−	0.366667i	−0.306126	−	0.951991i	$-0.599033\pi$
$163$	6.44324	−	4.68129i	0.504673	−	0.366667i	0.810799	+	0.585324i	$0.199033\pi$
$164$	3.47924			0.271683
$165$	2.10892	+	4.38370i	0.164179	+	0.341270i
$166$	0.419007			0.0325212
$167$	−2.77204	+	2.01400i	−0.214507	+	0.155848i	−0.689850	−	0.723952i	$-0.742324\pi$
$167$	−2.77204	+	2.01400i	−0.214507	+	0.155848i	0.475344	+	0.879800i	$0.342324\pi$
$168$	−0.765373	−	2.35558i	−0.0590498	−	0.181737i
$169$	−3.61382	+	11.1222i	−0.277986	+	0.855553i
$170$	−0.255188	−	0.185405i	−0.0195720	−	0.0142199i
$171$	4.17787	+	3.03540i	0.319489	+	0.232123i
$172$	0.161858	−	0.498147i	0.0123415	−	0.0379834i
$173$	6.35552	+	19.5603i	0.483201	+	1.48714i	0.834569	+	0.550903i	$0.185717\pi$
$173$	6.35552	+	19.5603i	0.483201	+	1.48714i	−0.351368	+	0.936237i	$0.614283\pi$
$174$	−0.368479	+	0.267716i	−0.0279343	+	0.0202955i
$175$	4.52452			0.342022
$176$	12.9750	−	1.75230i	0.978024	−	0.132084i
$177$	−10.3670			−0.779231
$178$	−1.00371	+	0.729238i	−0.0752313	+	0.0546587i
$179$	−0.792419	−	2.43882i	−0.0592282	−	0.182286i	0.917065	−	0.398738i	$-0.130552\pi$
$179$	−0.792419	−	2.43882i	−0.0592282	−	0.182286i	−0.976293	+	0.216452i	$0.930552\pi$
$180$	0.522231	−	1.60726i	0.0389248	−	0.119798i
$181$	−10.8545	−	7.88624i	−0.806807	−	0.586179i	0.106096	−	0.994356i	$-0.466165\pi$
$181$	−10.8545	−	7.88624i	−0.806807	−	0.586179i	−0.912903	+	0.408177i	$0.866165\pi$
$182$	0.391081	+	0.284137i	0.0289888	+	0.0210616i
$183$	1.13422	−	3.49078i	0.0838442	−	0.258046i
$184$	0.628857	+	1.93542i	0.0463599	+	0.142681i
$185$	−1.20447	+	0.875099i	−0.0885544	+	0.0643385i
$186$	0.245630			0.0180104
$187$	11.0871	−	1.49733i	0.810766	−	0.109496i
$188$	−13.7889			−1.00566
$189$	20.6631	−	15.0126i	1.50302	−	1.09201i
$190$	0.175826	+	0.541138i	0.0127558	+	0.0392583i
$191$	5.62097	−	17.2996i	0.406719	−	1.25175i	−0.512733	−	0.858548i	$-0.671367\pi$
$191$	5.62097	−	17.2996i	0.406719	−	1.25175i	0.919452	−	0.393203i	$-0.128633\pi$
$192$	9.24477	+	6.71672i	0.667184	+	0.484738i
$193$	−12.6924	−	9.22156i	−0.913618	−	0.663782i	0.0283094	−	0.999599i	$-0.490988\pi$
$193$	−12.6924	−	9.22156i	−0.913618	−	0.663782i	−0.941927	+	0.335817i	$0.890988\pi$
$194$	−0.0969914	+	0.298509i	−0.00696358	+	0.0214317i
$195$	−0.517859	−	1.59381i	−0.0370846	−	0.114135i
$196$	21.7018	−	15.7672i	1.55013	−	1.12623i
$197$	−21.8486			−1.55665			−0.778325	−	0.627862i	$-0.783930\pi$
$197$	−21.8486			−1.55665			−0.778325	+	0.627862i	$0.783930\pi$
$198$	−0.114109	−	0.237192i	−0.00810937	−	0.0168565i
$199$	−4.55200			−0.322683			−0.161341	−	0.986899i	$-0.551582\pi$
$199$	−4.55200			−0.322683			−0.161341	+	0.986899i	$0.551582\pi$
$200$	0.301943	−	0.219374i	0.0213506	−	0.0155121i
$201$	−0.234145	−	0.720625i	−0.0165153	−	0.0508290i
$202$	−0.269745	+	0.830190i	−0.0189792	+	0.0584119i
$203$	−12.1556	−	8.83159i	−0.853158	−	0.619856i
$204$	7.97040	+	5.79084i	0.558040	+	0.405440i
$205$	−0.539933	+	1.66174i	−0.0377106	+	0.116061i
$206$	−0.402118	−	1.23759i	−0.0280169	−	0.0862271i
$207$	−3.74380	+	2.72003i	−0.260212	+	0.189055i
$208$	−4.51038			−0.312738
$209$	−17.7674	−	9.57019i	−1.22900	−	0.661984i
$210$	0.620556			0.0428225
$211$	−15.3393	+	11.1447i	−1.05600	+	0.767230i	−0.973345	−	0.229348i	$-0.926341\pi$
$211$	−15.3393	+	11.1447i	−1.05600	+	0.767230i	−0.0826575	+	0.996578i	$0.526341\pi$
$212$	0.885929	+	2.72661i	0.0608459	+	0.187264i
$213$	−4.86345	+	14.9681i	−0.333238	+	1.02560i
$214$	1.27005	+	0.922748i	0.0868191	+	0.0630778i
$215$	0.212805	+	0.154612i	0.0145132	+	0.0105444i
$216$	0.651050	−	2.00372i	0.0442983	−	0.136336i
$217$	2.50396	+	7.70641i	0.169980	+	0.523145i
$218$	0.276348	−	0.200779i	0.0187167	−	0.0135985i
$219$	−8.33284			−0.563081
$220$	−1.18183	+	6.49764i	−0.0796790	+	0.438071i
$221$	−3.85410			−0.259255
$222$	−0.165198	+	0.120023i	−0.0110873	+	0.00805543i
$223$	1.50785	+	4.64070i	0.100973	+	0.310764i	0.988764	−	0.149483i	$-0.0477609\pi$
$223$	1.50785	+	4.64070i	0.100973	+	0.310764i	−0.887791	+	0.460247i	$0.847761\pi$
$224$	1.55976	−	4.80045i	0.104216	−	0.320743i
$225$	0.686611	+	0.498852i	0.0457741	+	0.0332568i
$226$	0.900424	+	0.654197i	0.0598953	+	0.0435165i
$227$	5.04404	−	15.5240i	0.334785	−	1.03036i	−0.632043	−	0.774933i	$-0.717784\pi$
$227$	5.04404	−	15.5240i	0.334785	−	1.03036i	0.966828	−	0.255428i	$-0.0822164\pi$
$228$	−5.49166	−	16.9016i	−0.363694	−	1.11934i
$229$	3.90890	−	2.83998i	0.258307	−	0.187671i	−0.451093	−	0.892477i	$-0.648966\pi$
$229$	3.90890	−	2.83998i	0.258307	−	0.187671i	0.709401	+	0.704806i	$0.248966\pi$
$230$	−0.509871			−0.0336199
$231$	−15.9148	+	15.2039i	−1.04712	+	1.00035i
$232$	−1.23941			−0.0813711
$233$	6.81172	−	4.94900i	0.446251	−	0.324220i	−0.341863	−	0.939750i	$-0.611058\pi$
$233$	6.81172	−	4.94900i	0.446251	−	0.324220i	0.788114	+	0.615530i	$0.211058\pi$
$234$	0.0280202	+	0.0862373i	0.00183174	+	0.00563751i
$235$	2.13986	−	6.58580i	0.139589	−	0.429610i
$236$	−11.3864	−	8.27272i	−0.741193	−	0.538508i
$237$	13.4127	+	9.74488i	0.871247	+	0.632998i
$238$	0.441019	−	1.35732i	0.0285870	−	0.0879819i
$239$	−7.01245	−	21.5821i	−0.453598	−	1.39603i	−0.872773	−	0.488126i	$-0.837681\pi$
$239$	−7.01245	−	21.5821i	−0.453598	−	1.39603i	0.419175	−	0.907905i	$-0.362319\pi$
$240$	−4.68428	+	3.40333i	−0.302369	+	0.219684i
$241$	11.6065			0.747638			0.373819	−	0.927502i	$-0.378048\pi$
$241$	11.6065			0.747638			0.373819	+	0.927502i	$0.378048\pi$
$242$	0.565971	+	0.858902i	0.0363820	+	0.0552123i
$243$	8.52534			0.546901
$244$	4.03135	−	2.92894i	0.258080	−	0.187506i
$245$	4.16287	+	12.8120i	0.265956	+	0.818528i
$246$	−0.0740540	+	0.227915i	−0.00472151	+	0.0145313i
$247$	5.62445	+	4.08640i	0.357875	+	0.260011i
$248$	0.540751	+	0.392879i	0.0343377	+	0.0249478i
$249$	2.03094	−	6.25058i	0.128705	−	0.396114i
$250$	0.0288961	+	0.0889332i	0.00182755	+	0.00562463i
$251$	−2.68032	+	1.94736i	−0.169180	+	0.122917i	−0.669153	−	0.743124i	$-0.733343\pi$
$251$	−2.68032	+	1.94736i	−0.169180	+	0.122917i	0.499973	+	0.866041i	$0.333343\pi$
$252$	7.64633			0.481674
$253$	13.0761	−	12.4921i	0.822090	−	0.785370i
$254$	1.84800			0.115954
$255$	−4.00270	+	2.90813i	−0.250659	+	0.182114i
$256$	4.72952	+	14.5560i	0.295595	+	0.909748i
$257$	−8.29606	+	25.5326i	−0.517494	+	1.59268i	0.261204	+	0.965284i	$0.415880\pi$
$257$	−8.29606	+	25.5326i	−0.517494	+	1.59268i	−0.778698	+	0.627399i	$0.784120\pi$
$258$	0.0291870	+	0.0212056i	0.00181711	+	0.00132020i
$259$	−5.44965	−	3.95940i	−0.338625	−	0.246025i
$260$	0.703052	−	2.16377i	0.0436015	−	0.134192i
$261$	−0.870929	−	2.68044i	−0.0539091	−	0.165915i
$262$	0.146369	−	0.106343i	0.00904269	−	0.00656990i
$263$	12.1682			0.750324			0.375162	−	0.926959i	$-0.377587\pi$
$263$	12.1682			0.750324			0.375162	+	0.926959i	$0.377587\pi$
$264$	−0.324897	+	1.78627i	−0.0199960	+	0.109937i
$265$	−1.43976			−0.0884436
$266$	−2.08273	+	1.51319i	−0.127700	+	0.0927795i
$267$	6.01349	+	18.5076i	0.368019	+	1.13265i
$268$	0.317879	−	0.978331i	0.0194176	−	0.0597611i
$269$	1.69369	+	1.23053i	0.103266	+	0.0750270i	0.638220	−	0.769854i	$-0.279671\pi$
$269$	1.69369	+	1.23053i	0.103266	+	0.0750270i	−0.534954	+	0.844881i	$0.679671\pi$
$270$	0.427051	+	0.310271i	0.0259895	+	0.0188825i
$271$	4.67938	−	14.4017i	0.284252	−	0.874838i	−0.702370	−	0.711812i	$-0.747875\pi$
$271$	4.67938	−	14.4017i	0.284252	−	0.874838i	0.986622	−	0.163026i	$-0.0521254\pi$
$272$	4.11492	+	12.6644i	0.249504	+	0.767894i
$273$	6.13422	−	4.45677i	0.371260	−	0.269736i
$274$	−1.17218			−0.0708138
$275$	−2.91998	−	1.57281i	−0.176081	−	0.0948441i
$276$	15.9250			0.958574
$277$	−6.69110	+	4.86137i	−0.402029	+	0.292091i	−0.770367	−	0.637601i	$-0.779927\pi$
$277$	−6.69110	+	4.86137i	−0.402029	+	0.292091i	0.368338	+	0.929692i	$0.379927\pi$
$278$	−0.324939	−	1.00006i	−0.0194885	−	0.0599795i
$279$	−0.469687	+	1.44555i	−0.0281194	+	0.0865426i
$280$	1.36615	+	0.992564i	0.0816429	+	0.0593171i
$281$	−1.97985	−	1.43844i	−0.118108	−	0.0858104i	0.527163	−	0.849764i	$-0.323256\pi$
$281$	−1.97985	−	1.43844i	−0.118108	−	0.0858104i	−0.645271	+	0.763954i	$0.723256\pi$
$282$	0.293490	−	0.903268i	0.0174771	−	0.0537888i
$283$	8.06372	+	24.8176i	0.479339	+	1.47525i	0.840016	+	0.542562i	$0.182546\pi$
$283$	8.06372	+	24.8176i	0.479339	+	1.47525i	−0.360677	+	0.932691i	$0.617454\pi$
$284$	−17.2860	+	12.5590i	−1.02574	+	0.745242i
$285$	8.92472			0.528655
$286$	−0.153619	−	0.319320i	−0.00908369	−	0.0188818i
$287$	−7.90553			−0.466648
$288$	0.765973	−	0.556512i	0.0451354	−	0.0327928i
$289$	−1.73710	−	5.34624i	−0.102182	−	0.314485i
$290$	0.0959593	−	0.295332i	0.00563492	−	0.0173425i
$291$	3.98292	+	2.89376i	0.233483	+	0.169635i
$292$	−9.15223	−	6.64949i	−0.535594	−	0.389132i
$293$	4.15719	−	12.7945i	0.242866	−	0.747463i	−0.753115	−	0.657889i	$-0.771449\pi$
$293$	4.15719	−	12.7945i	0.242866	−	0.747463i	0.995980	−	0.0895739i	$-0.0285505\pi$
$294$	0.570953	+	1.75721i	0.0332987	+	0.102483i
$295$	5.71821	−	4.15452i	0.332927	−	0.241886i
$296$	−0.555655			−0.0322968
$297$	−18.5539	+	2.50575i	−1.07661	+	0.145399i
$298$	−1.62087			−0.0938944
$299$	−5.04009	+	3.66184i	−0.291476	+	0.211770i
$300$	−0.902527	−	2.77769i	−0.0521074	−	0.160370i
$301$	−0.367773	+	1.13189i	−0.0211981	+	0.0652409i
$302$	0.000408830	0	0.000297032i	2.35255e−5	0	1.70923e-5i
$303$	11.0770	+	8.04791i	0.636357	+	0.462340i
$304$	7.42268	−	22.8447i	0.425720	−	1.31023i
$305$	0.773299	+	2.37997i	0.0442790	+	0.136277i
$306$	0.216577	−	0.157353i	0.0123809	−	0.00899526i
$307$	27.1844			1.55150			0.775748	−	0.631042i	$-0.217373\pi$
$307$	27.1844			1.55150			0.775748	+	0.631042i	$0.217373\pi$
$308$	−29.6123	+	3.99921i	−1.68731	+	0.227876i
$309$	−20.4110			−1.16114
$310$	−0.135484	+	0.0984349i	−0.00769497	+	0.00559072i
$311$	−4.07872	−	12.5530i	−0.231283	−	0.711817i	−0.997593	−	0.0693450i	$-0.977909\pi$
$311$	−4.07872	−	12.5530i	−0.231283	−	0.711817i	0.766310	−	0.642472i	$-0.222091\pi$
$312$	0.193276	−	0.594843i	0.0109421	−	0.0336764i
$313$	−13.0833	−	9.50561i	−0.739515	−	0.537289i	0.153044	−	0.988219i	$-0.451092\pi$
$313$	−13.0833	−	9.50561i	−0.739515	−	0.537289i	−0.892559	+	0.450931i	$0.851092\pi$
$314$	−0.0419741	−	0.0304959i	−0.00236873	−	0.00172099i
$315$	−1.18661	+	3.65201i	−0.0668580	+	0.205768i
$316$	6.95531	+	21.4062i	0.391267	+	1.20420i
$317$	4.35344	−	3.16296i	0.244514	−	0.177650i	−0.458778	−	0.888551i	$-0.651713\pi$
$317$	4.35344	−	3.16296i	0.244514	−	0.177650i	0.703292	+	0.710901i	$0.251713\pi$
$318$	−0.197469			−0.0110735
$319$	4.77481	+	9.92514i	0.267338	+	0.555701i
$320$	−7.79091			−0.435525
$321$	19.9212	−	14.4736i	1.11189	−	0.807837i
$322$	−0.712878	−	2.19401i	−0.0397271	−	0.122268i
$323$	6.34266	−	19.5207i	0.352915	−	1.08616i
$324$	−9.23663	−	6.71080i	−0.513146	−	0.372822i
$325$	0.924349	+	0.671579i	0.0512737	+	0.0372525i
$326$	−0.230137	+	0.708289i	−0.0127461	+	0.0392285i
$327$	−1.65567	−	5.09564i	−0.0915590	−	0.281790i
$328$	−0.527573	+	0.383304i	−0.0291304	+	0.0211644i
$329$	31.3311			1.72734
$330$	−0.400486	−	0.215717i	−0.0220460	−	0.0118748i
$331$	−18.5702			−1.02071			−0.510356	−	0.859963i	$-0.670486\pi$
$331$	−18.5702			−1.02071			−0.510356	+	0.859963i	$0.670486\pi$
$332$	7.21852	−	5.24456i	0.396168	−	0.287833i
$333$	−0.390457	−	1.20170i	−0.0213969	−	0.0658530i
$334$	0.0990106	−	0.304723i	0.00541762	−	0.0166737i
$335$	0.417936	+	0.303648i	0.0228343	+	0.0165901i
$336$	−21.1941	−	15.3984i	−1.15623	−	0.840054i
$337$	2.78305	−	8.56535i	0.151603	−	0.466585i	−0.846198	−	0.532868i	$-0.821114\pi$
$337$	2.78305	−	8.56535i	0.151603	−	0.466585i	0.997801	+	0.0662836i	$0.0211142\pi$
$338$	−0.337928	−	1.04003i	−0.0183808	−	0.0565704i
$339$	14.1234	−	10.2613i	0.767080	−	0.557316i
$340$	−6.71695			−0.364278
$341$	1.06292	−	5.84388i	0.0575604	−	0.316464i
$342$	−0.482897			−0.0261121
$343$	−23.6877	+	17.2101i	−1.27902	+	0.929260i
$344$	0.0303371	+	0.0933679i	0.00163567	+	0.00503406i
$345$	−2.47136	+	7.60605i	−0.133053	+	0.409496i
$346$	−1.55591	−	1.13043i	−0.0836461	−	0.0607725i
$347$	−8.30939	−	6.03712i	−0.446071	−	0.324090i	0.341971	−	0.939710i	$-0.388905\pi$
$347$	−8.30939	−	6.03712i	−0.446071	−	0.324090i	−0.788043	+	0.615621i	$0.788905\pi$
$348$	−2.99714	+	9.22425i	−0.160664	+	0.494472i
$349$	5.33402	+	16.4164i	0.285524	+	0.878752i	0.986241	+	0.165313i	$0.0528633\pi$
$349$	5.33402	+	16.4164i	0.285524	+	0.878752i	−0.700718	+	0.713439i	$0.747137\pi$
$350$	−0.342285	+	0.248685i	−0.0182959	+	0.0132928i
$351$	6.44975			0.344262
$352$	−2.67534	+	2.55585i	−0.142596	+	0.136227i
$353$	−22.8096			−1.21403			−0.607017	−	0.794689i	$-0.707634\pi$
$353$	−22.8096			−1.21403			−0.607017	+	0.794689i	$0.707634\pi$
$354$	0.784275	−	0.569809i	0.0416837	−	0.0302850i
$355$	−3.31584	−	10.2051i	−0.175986	−	0.541631i
$356$	−8.16399	+	25.1262i	−0.432691	+	1.33169i
$357$	−18.1103	−	13.1579i	−0.958500	−	0.696391i
$358$	0.193994	+	0.140945i	0.0102529	+	0.00744916i
$359$	−4.96736	+	15.2879i	−0.262167	+	0.806867i	0.730166	+	0.683270i	$0.239443\pi$
$359$	−4.96736	+	15.2879i	−0.262167	+	0.806867i	−0.992333	+	0.123597i	$0.960557\pi$
$360$	0.0978819	+	0.301250i	0.00515883	+	0.0158773i
$361$	−14.5820	+	10.5945i	−0.767475	+	0.557603i
$362$	1.25461			0.0659408
$363$	15.5560	−	4.27982i	0.816481	−	0.224632i
$364$	10.2939			0.539545
$365$	4.59621	−	3.33934i	0.240577	−	0.174789i
$366$	0.106061	+	0.326422i	0.00554390	+	0.0170624i
$367$	6.79759	−	20.9208i	0.354832	−	1.09206i	−0.601276	−	0.799042i	$-0.705341\pi$
$367$	6.79759	−	20.9208i	0.354832	−	1.09206i	0.956107	−	0.293017i	$-0.0946594\pi$
$368$	17.4138	+	12.6519i	0.907759	+	0.659525i
$369$	−1.19969	−	0.871625i	−0.0624533	−	0.0453750i
$370$	0.0430208	−	0.132404i	0.00223654	−	0.00688337i
$371$	−2.01301	−	6.19539i	−0.104510	−	0.321649i
$372$	4.23163	−	3.07446i	0.219400	−	0.159403i
$373$	−20.2604			−1.04905			−0.524523	−	0.851396i	$-0.675756\pi$
$373$	−20.2604			−1.04905			−0.524523	+	0.851396i	$0.675756\pi$
$374$	−0.756449	+	0.722661i	−0.0391151	+	0.0373679i
$375$	1.46673			0.0757417
$376$	2.09087	−	1.51911i	0.107828	−	0.0783419i
$377$	−1.17249	−	3.60854i	−0.0603861	−	0.185849i
$378$	−0.738036	+	2.27144i	−0.0379605	+	0.116830i
$379$	3.01578	+	2.19109i	0.154910	+	0.112549i	0.662540	−	0.749026i	$-0.269478\pi$
$379$	3.01578	+	2.19109i	0.154910	+	0.112549i	−0.507630	+	0.861575i	$0.669478\pi$
$380$	9.80231	+	7.12180i	0.502848	+	0.365341i
$381$	8.95733	−	27.5678i	0.458898	−	1.41234i
$382$	0.525616	+	1.61768i	0.0268928	+	0.0827677i
$383$	8.89708	−	6.46411i	0.454620	−	0.330301i	−0.336797	−	0.941577i	$-0.609344\pi$
$383$	8.89708	−	6.46411i	0.454620	−	0.330301i	0.791417	+	0.611277i	$0.209344\pi$
$384$	−4.34108			−0.221530
$385$	2.68535	−	14.7639i	0.136858	−	0.752439i
$386$	1.46704			0.0746706
$387$	−0.180607	+	0.131219i	−0.00918078	+	0.00667023i
$388$	2.06539	+	6.35663i	0.104854	+	0.322709i
$389$	2.89926	−	8.92300i	0.146998	−	0.452414i	−0.850264	−	0.526356i	$-0.823558\pi$
$389$	2.89926	−	8.92300i	0.146998	−	0.452414i	0.997263	+	0.0739418i	$0.0235579\pi$
$390$	0.126778	+	0.0921097i	0.00641966	+	0.00466415i
$391$	14.8801	+	10.8110i	0.752517	+	0.546736i
$392$	−1.55367	+	4.78171i	−0.0784723	+	0.241513i
$393$	−0.876932	−	2.69892i	−0.0442354	−	0.136143i
$394$	1.65287	−	1.20088i	0.0832705	−	0.0604996i
$395$	−11.3033			−0.568733
$396$	−4.93469	−	2.65801i	−0.247977	−	0.133570i
$397$	22.3136			1.11989			0.559945	−	0.828530i	$-0.310822\pi$
$397$	22.3136			1.11989			0.559945	+	0.828530i	$0.310822\pi$
$398$	0.344364	−	0.250195i	0.0172614	−	0.0125411i
$399$	12.4781	+	38.4038i	0.624688	+	1.92259i
$400$	1.21988	−	3.75440i	0.0609940	−	0.187720i
$401$	19.9683	+	14.5078i	0.997171	+	0.724487i	0.961480	−	0.274876i	$-0.0886368\pi$
$401$	19.9683	+	14.5078i	0.997171	+	0.724487i	0.0356909	+	0.999363i	$0.488637\pi$
$402$	0.0573216	+	0.0416466i	0.00285894	+	0.00207714i
$403$	−0.632315	+	1.94606i	−0.0314978	+	0.0969404i
$404$	5.74411	+	17.6786i	0.285780	+	0.879541i
$405$	4.63859	−	3.37014i	0.230494	−	0.167463i
$406$	1.40500			0.0697292
$407$	2.14066	+	4.44967i	0.106109	+	0.220562i
$408$	−1.84656			−0.0914182
$409$	−23.8705	+	17.3429i	−1.18032	+	0.857553i	−0.992208	−	0.124594i	$-0.960237\pi$
$409$	−23.8705	+	17.3429i	−1.18032	+	0.857553i	−0.188113	+	0.982147i	$0.560237\pi$
$410$	−0.0504891	−	0.155390i	−0.00249348	−	0.00767414i
$411$	−5.68158	+	17.4861i	−0.280252	+	0.862526i
$412$	−22.4181	−	16.2877i	−1.10446	−	0.802437i
$413$	25.8722	+	18.7972i	1.27309	+	0.924951i
$414$	0.133720	−	0.411547i	0.00657196	−	0.0202264i
$415$	1.38467	+	4.26157i	0.0679707	+	0.209192i
$416$	1.03119	−	0.749203i	0.0505582	−	0.0367327i
$417$	−16.4935			−0.807689
$418$	1.87013	−	0.252566i	0.0914713	−	0.0123534i
$419$	9.03564			0.441420			0.220710	−	0.975339i	$-0.429163\pi$
$419$	9.03564			0.441420			0.220710	+	0.975339i	$0.429163\pi$
$420$	10.6908	−	7.76729i	0.521655	−	0.379005i
$421$	4.39426	+	13.5242i	0.214163	+	0.659127i	0.999212	+	0.0396928i	$0.0126379\pi$
$421$	4.39426	+	13.5242i	0.214163	+	0.659127i	−0.785049	+	0.619434i	$0.787362\pi$
$422$	0.547884	−	1.68621i	0.0266706	−	0.0820835i
$423$	4.75459	+	3.45441i	0.231176	+	0.167959i
$424$	−0.434725	−	0.315846i	−0.0211121	−	0.0153388i
$425$	1.04238	−	3.20812i	0.0505630	−	0.155617i
$426$	−0.454780	−	1.39967i	−0.0220342	−	0.0678142i
$427$	−9.16001	+	6.65514i	−0.443284	+	0.322065i
$428$	33.4298			1.61589
$429$	−5.50808	+	0.743880i	−0.265933	+	0.0359149i
$430$	−0.0245970			−0.00118617
$431$	1.40086	−	1.01778i	0.0674769	−	0.0490248i	−0.553535	−	0.832826i	$-0.686722\pi$
$431$	1.40086	−	1.01778i	0.0674769	−	0.0490248i	0.621012	+	0.783801i	$0.286722\pi$
$432$	−6.88623	−	21.1936i	−0.331314	−	1.01968i
$433$	5.70062	−	17.5447i	0.273955	−	0.843145i	−0.715540	−	0.698572i	$-0.753819\pi$
$433$	5.70062	−	17.5447i	0.273955	−	0.843145i	0.989494	−	0.144573i	$-0.0461809\pi$
$434$	−0.613000	−	0.445371i	−0.0294250	−	0.0213785i
$435$	−3.94054	−	2.86297i	−0.188934	−	0.137269i
$436$	2.24777	−	6.91791i	0.107649	−	0.331308i
$437$	−10.2525	−	31.5539i	−0.490442	−	1.50943i
$438$	0.630389	−	0.458004i	0.0301211	−	0.0218843i
$439$	−17.1704			−0.819499			−0.409750	−	0.912198i	$-0.634384\pi$
$439$	−17.1704			−0.819499			−0.409750	+	0.912198i	$0.634384\pi$
$440$	−0.536632	−	1.11547i	−0.0255829	−	0.0531778i
$441$	−11.4331			−0.544432
$442$	0.291567	−	0.211836i	0.0138684	−	0.0100760i
$443$	11.3098	+	34.8079i	0.537344	+	1.65377i	0.738529	+	0.674221i	$0.235521\pi$
$443$	11.3098	+	34.8079i	0.537344	+	1.65377i	−0.201185	+	0.979553i	$0.564479\pi$
$444$	−1.34369	+	4.13545i	−0.0637686	+	0.196260i
$445$	−10.7337	−	7.79852i	−0.508828	−	0.369685i
$446$	−0.369141	−	0.268196i	−0.0174793	−	0.0126995i
$447$	−7.85640	+	24.1795i	−0.371595	+	1.14365i
$448$	−10.8929	−	33.5249i	−0.514641	−	1.58390i
$449$	13.4320	−	9.75895i	0.633897	−	0.460553i	−0.223851	−	0.974623i	$-0.571863\pi$
$449$	13.4320	−	9.75895i	0.633897	−	0.460553i	0.857748	+	0.514070i	$0.171863\pi$
$450$	−0.0793616			−0.00374114
$451$	5.10196	+	2.74811i	0.240242	+	0.129404i
$452$	23.7006			1.11478
$453$	0.00641262	−	0.00465904i	0.000301291	−	0.000218901i
$454$	0.471667	+	1.45164i	0.0221365	+	0.0681290i
$455$	−1.59747	+	4.91652i	−0.0748907	+	0.230490i
$456$	2.69476	+	1.95785i	0.126193	+	0.0916849i
$457$	25.6178	+	18.6124i	1.19835	+	0.870651i	0.994121	−	0.108272i	$-0.0345318\pi$
$457$	25.6178	+	18.6124i	1.19835	+	0.870651i	0.204227	+	0.978923i	$0.434532\pi$
$458$	−0.139617	+	0.429696i	−0.00652385	+	0.0200784i
$459$	−5.88426	−	18.1099i	−0.274654	−	0.845297i
$460$	−8.78389	+	6.38187i	−0.409551	+	0.297556i
$461$	−25.4351			−1.18463			−0.592315	−	0.805706i	$-0.701786\pi$
$461$	−25.4351			−1.18463			−0.592315	+	0.805706i	$0.701786\pi$
$462$	0.368306	−	2.02493i	0.0171352	−	0.0942083i
$463$	−16.3319			−0.759007			−0.379503	−	0.925190i	$-0.623905\pi$
$463$	−16.3319			−0.759007			−0.379503	+	0.925190i	$0.623905\pi$
$464$	−10.6057	+	7.70549i	−0.492357	+	0.357718i
$465$	0.811719	+	2.49821i	0.0376426	+	0.115852i
$466$	−0.243298	+	0.748795i	−0.0112706	+	0.0346873i
$467$	−6.90020	−	5.01329i	−0.319303	−	0.231987i	0.416575	−	0.909101i	$-0.363230\pi$
$467$	−6.90020	−	5.01329i	−0.319303	−	0.231987i	−0.735878	+	0.677114i	$0.763230\pi$
$468$	1.56213	+	1.13495i	0.0722093	+	0.0524631i
$469$	−0.722284	+	2.22296i	−0.0333520	+	0.102647i
$470$	0.200098	+	0.615837i	0.00922982	+	0.0284065i
$471$	−0.658376	+	0.478338i	−0.0303364	+	0.0220407i
$472$	2.63797			0.121422
$473$	0.630814	−	0.602638i	0.0290049	−	0.0277093i
$474$	−1.55030			−0.0712076
$475$	−4.92268	+	3.57654i	−0.225868	+	0.164103i
$476$	−9.39133	−	28.9036i	−0.430451	−	1.32479i
$477$	0.377594	−	1.16211i	0.0172888	−	0.0532096i
$478$	1.71673	+	1.24728i	0.0785216	+	0.0570493i
$479$	−24.2283	−	17.6029i	−1.10702	−	0.804296i	−0.124827	−	0.992178i	$-0.539838\pi$
$479$	−24.2283	−	17.6029i	−1.10702	−	0.804296i	−0.982192	+	0.187882i	$0.939838\pi$
$480$	0.505633	−	1.55618i	0.0230789	−	0.0710295i
$481$	−0.525653	−	1.61779i	−0.0239677	−	0.0737650i
$482$	−0.878041	+	0.637934i	−0.0399937	+	0.0290571i
$483$	−36.1848			−1.64646
$484$	20.5010	+	7.71283i	0.931862	+	0.350583i
$485$	−3.35655			−0.152413
$486$	−0.644951	+	0.468585i	−0.0292556	+	0.0212554i
$487$	−6.05768	−	18.6436i	−0.274500	−	0.844823i	−0.989351	−	0.145547i	$-0.953506\pi$
$487$	−6.05768	−	18.6436i	−0.274500	−	0.844823i	0.714852	−	0.699276i	$-0.246494\pi$
$488$	−0.288612	+	0.888257i	−0.0130649	+	0.0402095i
$489$	9.45050	+	6.86619i	0.427367	+	0.310500i
$490$	−1.01912	−	0.740434i	−0.0460391	−	0.0334494i
$491$	−4.87911	+	15.0163i	−0.220191	+	0.677678i	0.778553	+	0.627579i	$0.215954\pi$
$491$	−4.87911	+	15.0163i	−0.220191	+	0.677678i	−0.998744	+	0.0500997i	$0.984046\pi$
$492$	1.57695	+	4.85335i	0.0710944	+	0.218806i
$493$	−9.06253	+	6.58432i	−0.408156	+	0.296543i
$494$	−0.650099			−0.0292494
$495$	2.03531	−	1.94440i	0.0914803	−	0.0873942i
$496$	7.06980			0.317443
$497$	39.2773	−	28.5366i	1.76183	−	1.28004i
$498$	0.189913	+	0.584491i	0.00851019	+	0.0261917i
$499$	3.46350	−	10.6596i	0.155048	−	0.477188i	−0.843118	−	0.537729i	$-0.819283\pi$
$499$	3.46350	−	10.6596i	0.155048	−	0.477188i	0.998166	+	0.0605408i	$0.0192825\pi$
$500$	1.61096	+	1.17043i	0.0720443	+	0.0523433i
$501$	−4.06584	−	2.95400i	−0.181648	−	0.131975i
$502$	0.0957345	−	0.294640i	0.00427284	−	0.0131504i
$503$	−0.105965	−	0.326125i	−0.00472473	−	0.0145412i	0.948666	−	0.316279i	$-0.102433\pi$
$503$	−0.105965	−	0.326125i	−0.00472473	−	0.0145412i	−0.953391	+	0.301737i	$0.902433\pi$
$504$	−1.15945	+	0.842387i	−0.0516459	+	0.0375229i
$505$	−9.33498			−0.415401
$506$	−0.302613	+	1.66375i	−0.0134528	+	0.0739628i
$507$	−17.1528			−0.761782
$508$	31.8368	−	23.1308i	1.41253	−	1.02626i
$509$	−6.04518	−	18.6052i	−0.267948	−	0.824659i	−0.991000	−	0.133865i	$-0.957261\pi$
$509$	−6.04518	−	18.6052i	−0.267948	−	0.824659i	0.723052	−	0.690794i	$-0.242739\pi$
$510$	0.142967	−	0.440007i	0.00633068	−	0.0194838i
$511$	20.7957	+	15.1089i	0.919946	+	0.668380i
$512$	−5.94673	−	4.32055i	−0.262811	−	0.190943i
$513$	−10.6143	+	32.6674i	−0.468632	+	1.44230i
$514$	−0.775763	−	2.38755i	−0.0342175	−	0.105311i
$515$	11.2583	−	8.17961i	0.496098	−	0.360436i
$516$	0.768249			0.0338203
$517$	−20.2200	−	10.8913i	−0.889275	−	0.478998i
$518$	0.629896			0.0276760
$519$	−24.4049	+	17.7312i	−1.07126	+	0.778313i
$520$	0.131773	+	0.405557i	0.00577865	+	0.0177848i
$521$	12.9869	−	39.9695i	0.568966	−	1.75110i	−0.0868981	−	0.996217i	$-0.527695\pi$
$521$	12.9869	−	39.9695i	0.568966	−	1.75110i	0.655864	−	0.754879i	$-0.272305\pi$
$522$	0.213214	+	0.154909i	0.00933212	+	0.00678018i
$523$	−24.2790	−	17.6398i	−1.06165	−	0.771333i	−0.0872555	−	0.996186i	$-0.527810\pi$
$523$	−24.2790	−	17.6398i	−1.06165	−	0.771333i	−0.974393	+	0.224853i	$0.927810\pi$
$524$	1.19054	−	3.66409i	0.0520088	−	0.160067i
$525$	2.05072	+	6.31146i	0.0895007	+	0.275455i
$526$	−0.920538	+	0.668810i	−0.0401374	+	0.0291615i
$527$	6.04112			0.263155
$528$	8.32519	+	17.3051i	0.362308	+	0.753109i
$529$	6.73067			0.292638
$530$	0.108919	−	0.0791345i	0.00473115	−	0.00343738i
$531$	1.85369	+	5.70508i	0.0804434	+	0.247579i
$532$	−16.9405	+	52.1375i	−0.734464	+	2.26045i
$533$	−1.61508	−	1.17342i	−0.0699568	−	0.0508266i
$534$	−1.47217	−	1.06960i	−0.0637072	−	0.0462860i
$535$	−5.18787	+	15.9666i	−0.224291	+	0.690298i
$536$	0.0595802	+	0.183369i	0.00257347	+	0.00792033i
$537$	3.04285	−	2.21076i	0.131309	−	0.0954014i
$538$	−0.195764			−0.00843998
$539$	44.2773	−	5.97976i	1.90716	−	0.257567i
$540$	11.2407			0.483721
$541$	8.35196	−	6.06806i	0.359079	−	0.260886i	−0.393589	−	0.919287i	$-0.628767\pi$
$541$	8.35196	−	6.06806i	0.359079	−	0.260886i	0.752668	+	0.658400i	$0.228767\pi$
$542$	0.437568	+	1.34670i	0.0187952	+	0.0578456i
$543$	6.08113	−	18.7158i	0.260966	−	0.803171i
$544$	−3.04442	−	2.21190i	−0.130529	−	0.0948346i
$545$	2.95529	+	2.14714i	0.126591	+	0.0919734i
$546$	−0.219100	+	0.674320i	−0.00937660	+	0.0288582i
$547$	12.9221	+	39.7702i	0.552510	+	1.70045i	0.702431	+	0.711752i	$0.252098\pi$
$547$	12.9221	+	39.7702i	0.552510	+	1.70045i	−0.149921	+	0.988698i	$0.547902\pi$
$548$	−20.1939	+	14.6717i	−0.862641	+	0.626746i
$549$	−2.12382			−0.0906426
$550$	0.307347	−	0.0415079i	0.0131053	−	0.00176990i
$551$	20.2065			0.860826
$552$	−2.41478	+	1.75444i	−0.102780	+	0.0746740i
$553$	−15.8038	−	48.6392i	−0.672047	−	2.06835i
$554$	0.238990	−	0.735536i	0.0101537	−	0.0312499i
$555$	−1.76663	−	1.28353i	−0.0749894	−	0.0544830i
$556$	−18.1153	−	13.1616i	−0.768261	−	0.558174i
$557$	−11.8918	+	36.5993i	−0.503874	+	1.55076i	0.298782	+	0.954321i	$0.403420\pi$
$557$	−11.8918	+	36.5993i	−0.503874	+	1.55076i	−0.802656	+	0.596442i	$0.796580\pi$
$558$	−0.0439203	−	0.135173i	−0.00185930	−	0.00572233i
$559$	−0.243142	+	0.176653i	−0.0102838	+	0.00747163i
$560$	17.8611			0.754768
$561$	7.11385	+	14.7872i	0.300347	+	0.624315i
$562$	0.228840			0.00965303
$563$	−24.8258	+	18.0370i	−1.04628	+	0.760170i	−0.971502	−	0.237030i	$-0.923826\pi$
$563$	−24.8258	+	18.0370i	−1.04628	+	0.760170i	−0.0747817	+	0.997200i	$0.523826\pi$
$564$	−6.24975	−	19.2347i	−0.263162	−	0.809929i
$565$	−3.67802	+	11.3198i	−0.154736	+	0.476227i
$566$	−1.97410	−	1.43427i	−0.0829775	−	0.0602867i
$567$	20.9874	+	15.2483i	0.881389	+	0.640367i
$568$	1.23754	−	3.80877i	0.0519262	−	0.159812i
$569$	4.03220	+	12.4098i	0.169039	+	0.520247i	0.999311	−	0.0371104i	$-0.0118153\pi$
$569$	4.03220	+	12.4098i	0.169039	+	0.520247i	−0.830273	+	0.557357i	$0.811815\pi$
$570$	−0.675165	+	0.490536i	−0.0282795	+	0.0205463i
$571$	16.1300			0.675018			0.337509	−	0.941322i	$-0.390416\pi$
$571$	16.1300			0.675018			0.337509	+	0.941322i	$0.390416\pi$
$572$	−6.64331	−	3.57834i	−0.277771	−	0.149618i
$573$	26.6796			1.11456
$574$	0.598062	−	0.434517i	0.0249626	−	0.0181364i
$575$	−1.68494	−	5.18572i	−0.0702669	−	0.216259i
$576$	2.04326	−	6.28850i	0.0851358	−	0.262021i
$577$	11.7885	+	8.56487i	0.490763	+	0.356560i	0.805478	−	0.592626i	$-0.201909\pi$
$577$	11.7885	+	8.56487i	0.490763	+	0.356560i	−0.314715	+	0.949186i	$0.601909\pi$
$578$	0.425263	+	0.308972i	0.0176886	+	0.0128515i
$579$	7.11080	−	21.8848i	0.295515	−	0.909501i
$580$	−2.04341	−	6.28898i	−0.0848482	−	0.261136i
$581$	−16.4019	+	11.9167i	−0.680465	+	0.494387i
$582$	−0.460364			−0.0190827
$583$	−0.854511	+	4.69806i	−0.0353902	+	0.194574i
$584$	2.12036			0.0877411
$585$	−0.784493	+	0.569967i	−0.0324348	+	0.0235653i
$586$	0.388738	+	1.19641i	0.0160586	+	0.0494234i
$587$	−8.61360	+	26.5099i	−0.355521	+	1.09418i	0.600185	+	0.799861i	$0.295094\pi$
$587$	−8.61360	+	26.5099i	−0.355521	+	1.09418i	−0.955707	+	0.294321i	$0.904906\pi$
$588$	31.8307	+	23.1263i	1.31267	+	0.953713i
$589$	−8.81605	−	6.40524i	−0.363259	−	0.263923i
$590$	−0.204241	+	0.628588i	−0.00840846	+	0.0258786i
$591$	−9.90278	−	30.4776i	−0.407346	−	1.25368i
$592$	−4.75478	+	3.45455i	−0.195420	+	0.141981i
$593$	15.1037			0.620236			0.310118	−	0.950698i	$-0.399631\pi$
$593$	15.1037			0.620236			0.310118	+	0.950698i	$0.399631\pi$
$594$	1.26590	−	1.20936i	0.0519405	−	0.0496205i
$595$	15.2622			0.625690
$596$	−27.9238	+	20.2878i	−1.14380	+	0.831023i
$597$	−2.06317	−	6.34979i	−0.0844400	−	0.259880i
$598$	0.180020	−	0.554044i	0.00736156	−	0.0226566i
$599$	20.9339	+	15.2093i	0.855334	+	0.621437i	0.926612	−	0.376020i	$-0.122708\pi$
$599$	20.9339	+	15.2093i	0.855334	+	0.621437i	−0.0712774	+	0.997457i	$0.522708\pi$
$600$	0.442869	+	0.321763i	0.0180801	+	0.0131359i
$601$	−14.5321	+	44.7252i	−0.592776	+	1.82438i	−0.0272781	+	0.999628i	$0.508684\pi$
$601$	−14.5321	+	44.7252i	−0.592776	+	1.82438i	−0.565498	+	0.824750i	$0.691316\pi$
$602$	−0.0343904	−	0.105843i	−0.00140165	−	0.00431383i
$603$	−0.354702	+	0.257706i	−0.0144446	+	0.0104946i
$604$	0.0107610			0.000437861
$605$	−6.86526	+	8.59466i	−0.279112	+	0.349423i
$606$	−1.28033			−0.0520098
$607$	28.4967	−	20.7041i	1.15665	−	0.840353i	0.167297	−	0.985907i	$-0.446496\pi$
$607$	28.4967	−	20.7041i	1.15665	−	0.840353i	0.989350	+	0.145553i	$0.0464963\pi$
$608$	2.09763	+	6.45584i	0.0850701	+	0.261819i
$609$	6.81009	−	20.9593i	0.275959	−	0.849314i
$610$	−0.189313	−	0.137544i	−0.00766506	−	0.00556899i
$611$	6.40086	+	4.65049i	0.258951	+	0.188139i
$612$	1.76160	−	5.42165i	0.0712085	−	0.219157i
$613$	−7.23461	−	22.2658i	−0.292203	−	0.899309i	−0.984147	−	0.177357i	$-0.943245\pi$
$613$	−7.23461	−	22.2658i	−0.292203	−	0.899309i	0.691943	−	0.721952i	$-0.256755\pi$
$614$	−2.05653	+	1.49416i	−0.0829948	+	0.0602993i
$615$	−2.56276			−0.103341
$616$	4.04965	−	3.86876i	0.163165	−	0.155877i
$617$	22.8910			0.921557			0.460778	−	0.887515i	$-0.347570\pi$
$617$	22.8910			0.921557			0.460778	+	0.887515i	$0.347570\pi$
$618$	1.54411	−	1.12187i	0.0621134	−	0.0451280i
$619$	0.657441	+	2.02339i	0.0264248	+	0.0813271i	0.963399	−	0.268071i	$-0.0863861\pi$
$619$	0.657441	+	2.02339i	0.0264248	+	0.0813271i	−0.936974	+	0.349398i	$0.886386\pi$
$620$	−1.10200	+	3.39161i	−0.0442574	+	0.136210i
$621$	−24.9014	−	18.0920i	−0.999260	−	0.726005i
$622$	0.998521	+	0.725468i	0.0400370	+	0.0290886i
$623$	18.5502	−	57.0916i	0.743198	−	2.28733i
$624$	−2.04431	−	6.29173i	−0.0818377	−	0.251871i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	1.51223			0.0604410
$627$	5.29691	−	29.1221i	0.211538	−	1.16303i
$628$	−1.10482			−0.0440873
$629$	−4.06294	+	2.95190i	−0.162000	+	0.117700i
$630$	−0.110960	−	0.341499i	−0.00442075	−	0.0136057i
$631$	4.77702	−	14.7022i	0.190170	−	0.585284i	−0.809829	−	0.586666i	$-0.800440\pi$
$631$	4.77702	−	14.7022i	0.190170	−	0.585284i	0.999999	+	0.00138227i	$0.000439991\pi$
$632$	−3.41296	−	2.47966i	−0.135760	−	0.0986357i
$633$	−22.4987	−	16.3462i	−0.894242	−	0.649705i
$634$	−0.155494	+	0.478563i	−0.00617547	+	0.0190062i
$635$	6.10700	+	18.7954i	0.242349	+	0.745873i
$636$	−3.40193	+	2.47164i	−0.134895	+	0.0980071i
$637$	−15.3918			−0.609844
$638$	−0.906743	−	0.488406i	−0.0358983	−	0.0193362i
$639$	9.10676			0.360258
$640$	2.39444	−	1.73967i	0.0946487	−	0.0687663i
$641$	4.38201	+	13.4864i	0.173079	+	0.532682i	0.999541	−	0.0303108i	$-0.00964970\pi$
$641$	4.38201	+	13.4864i	0.173079	+	0.532682i	−0.826461	+	0.562993i	$0.809650\pi$
$642$	−0.711537	+	2.18989i	−0.0280821	+	0.0864279i
$643$	10.0270	+	7.28504i	0.395426	+	0.287294i	0.767675	−	0.640839i	$-0.221413\pi$
$643$	10.0270	+	7.28504i	0.395426	+	0.287294i	−0.372249	+	0.928133i	$0.621413\pi$
$644$	−39.7429	−	28.8749i	−1.56609	−	1.13783i
$645$	−0.119222	+	0.366928i	−0.00469437	+	0.0144478i
$646$	0.593101	+	1.82538i	0.0233352	+	0.0718185i
$647$	−26.8970	+	19.5418i	−1.05743	+	0.768267i	−0.973611	−	0.228214i	$-0.926711\pi$
$647$	−26.8970	+	19.5418i	−1.05743	+	0.768267i	−0.0838181	+	0.996481i	$0.526711\pi$
$648$	2.13991			0.0840637
$649$	−10.1628	−	21.1248i	−0.398923	−	0.829220i
$650$	−0.106840			−0.00419063
$651$	−9.61510	+	6.98578i	−0.376846	+	0.273794i
$652$	4.90068	+	15.0827i	0.191925	+	0.590685i
$653$	−10.7558	+	33.1030i	−0.420908	+	1.29542i	0.485951	+	0.873986i	$0.338474\pi$
$653$	−10.7558	+	33.1030i	−0.420908	+	1.29542i	−0.906858	+	0.421435i	$0.861526\pi$
$654$	0.405329	+	0.294489i	0.0158496	+	0.0115154i
$655$	1.56528	+	1.13724i	0.0611604	+	0.0444356i
$656$	−2.13145	+	6.55992i	−0.0832191	+	0.256122i
$657$	1.48997	+	4.58566i	0.0581293	+	0.178904i
$658$	−2.37023	+	1.72207i	−0.0924011	+	0.0671334i
$659$	−34.4953			−1.34375			−0.671873	−	0.740666i	$-0.734510\pi$
$659$	−34.4953			−1.34375			−0.671873	+	0.740666i	$0.734510\pi$
$660$	−9.59951	+	1.29644i	−0.373661	+	0.0504638i
$661$	1.77827			0.0691668			0.0345834	−	0.999402i	$-0.488990\pi$
$661$	1.77827			0.0691668			0.0345834	+	0.999402i	$0.488990\pi$
$662$	1.40486	−	1.02069i	0.0546014	−	0.0396702i
$663$	−1.74685	−	5.37626i	−0.0678421	−	0.208797i
$664$	−0.516788	+	1.59051i	−0.0200553	+	0.0617238i
$665$	−22.2728	−	16.1821i	−0.863701	−	0.627516i
$666$	0.0955887	+	0.0694493i	0.00370399	+	0.00269110i
$667$	−5.59541	+	17.2209i	−0.216655	+	0.666796i
$668$	−2.10839	−	6.48896i	−0.0815761	−	0.251065i
$669$	−5.79009	+	4.20675i	−0.223858	+	0.162642i
$670$	−0.0483070			−0.00186626
$671$	8.22502	−	1.11081i	0.317523	−	0.0428823i
$672$	7.40331			0.285589
$673$	−15.6111	+	11.3422i	−0.601765	+	0.437208i	−0.846505	−	0.532381i	$-0.821297\pi$
$673$	−15.6111	+	11.3422i	−0.601765	+	0.437208i	0.244740	+	0.969589i	$0.421297\pi$
$674$	0.260243	+	0.800945i	0.0100242	+	0.0308513i
$675$	−1.74440	+	5.36872i	−0.0671421	+	0.206642i
$676$	−18.8395	−	13.6877i	−0.724595	−	0.526449i
$677$	13.6805	+	9.93949i	0.525786	+	0.382006i	0.818779	−	0.574109i	$-0.194651\pi$
$677$	13.6805	+	9.93949i	0.525786	+	0.382006i	−0.292993	+	0.956114i	$0.594651\pi$
$678$	−0.504455	+	1.55255i	−0.0193735	+	0.0596255i
$679$	−4.69298	−	14.4435i	−0.180100	−	0.554291i
$680$	1.01852	−	0.739998i	0.0390585	−	0.0283776i
$681$	23.9412			0.917430
$682$	0.240791	+	0.500518i	0.00922035	+	0.0191658i
$683$	4.14018			0.158420			0.0792098	−	0.996858i	$-0.474760\pi$
$683$	4.14018			0.158420			0.0792098	+	0.996858i	$0.474760\pi$
$684$	−8.31920	+	6.04425i	−0.318093	+	0.231108i
$685$	−3.87363	−	11.9218i	−0.148004	−	0.455509i
$686$	0.846069	−	2.60393i	0.0323031	−	0.0994186i
$687$	5.73331	+	4.16549i	0.218739	+	0.158923i
$688$	0.840072	+	0.610348i	0.0320274	+	0.0232693i
$689$	0.508335	−	1.56450i	0.0193660	−	0.0596025i
$690$	−0.231096	−	0.711241i	−0.00879769	−	0.0270765i
$691$	37.4996	−	27.2450i	1.42655	−	1.03645i	0.435904	−	0.899993i	$-0.356429\pi$
$691$	37.4996	−	27.2450i	1.42655	−	1.03645i	0.990646	−	0.136457i	$-0.0435714\pi$
$692$	−40.9539			−1.55684
$693$	11.2126	+	6.03952i	0.425931	+	0.229422i
$694$	0.960437			0.0364577
$695$	9.09743	−	6.60967i	0.345085	−	0.250719i
$696$	−0.561756	−	1.72891i	−0.0212933	−	0.0655340i
$697$	−1.82132	+	5.60543i	−0.0689872	+	0.212321i
$698$	−1.30583	−	0.948743i	−0.0494265	−	0.0359105i
$699$	9.99096	+	7.25886i	0.377893	+	0.274555i
$700$	−2.78408	+	8.56853i	−0.105228	+	0.323860i
$701$	−14.0465	−	43.2306i	−0.530528	−	1.63280i	−0.753119	−	0.657884i	$-0.771452\pi$
$701$	−14.0465	−	43.2306i	−0.530528	−	1.63280i	0.222591	−	0.974912i	$-0.428548\pi$
$702$	−0.487931	+	0.354502i	−0.0184158	+	0.0133798i
$703$	9.05904			0.341668
$704$	−4.62398	+	25.4224i	−0.174273	+	0.958143i
$705$	10.1567			0.382524
$706$	1.72557	−	1.25370i	0.0649428	−	0.0471837i
$707$	−13.0518	−	40.1692i	−0.490862	−	1.51072i
$708$	6.37915	−	19.6330i	0.239743	−	0.737853i
$709$	11.3458	+	8.24318i	0.426099	+	0.309579i	0.780087	−	0.625671i	$-0.215175\pi$
$709$	11.3458	+	8.24318i	0.426099	+	0.309579i	−0.353988	+	0.935250i	$0.615175\pi$
$710$	0.811757	+	0.589776i	0.0304647	+	0.0221339i
$711$	2.96444	−	9.12360i	0.111175	−	0.342162i
$712$	−1.53018	−	4.70941i	−0.0573460	−	0.176493i
$713$	7.90010	−	5.73976i	0.295861	−	0.214956i
$714$	2.09327			0.0783388
$715$	2.74003	−	2.61764i	0.102471	−	0.0978943i
$716$	5.10622			0.190829
$717$	26.9275	−	19.5640i	1.00563	−	0.730630i
$718$	−0.464497	−	1.42957i	−0.0173349	−	0.0533512i
$719$	4.05999	−	12.4954i	0.151412	−	0.465998i	−0.846368	−	0.532599i	$-0.821215\pi$
$719$	4.05999	−	12.4954i	0.151412	−	0.465998i	0.997780	+	0.0666007i	$0.0212154\pi$
$720$	2.71047	+	1.96927i	0.101013	+	0.0733905i
$721$	50.9383	+	37.0088i	1.89704	+	1.37828i
$722$	0.520835	−	1.60297i	0.0193835	−	0.0596562i
$723$	5.26057	+	16.1904i	0.195643	+	0.602126i
$724$	21.6140	−	15.7035i	0.803279	−	0.583616i
$725$	3.32083			0.123333
$726$	−0.941597	+	1.17879i	−0.0349459	+	0.0437491i
$727$	−18.3635			−0.681063			−0.340532	−	0.940233i	$-0.610607\pi$
$727$	−18.3635			−0.681063			−0.340532	+	0.940233i	$0.610607\pi$
$728$	−1.56090	+	1.13406i	−0.0578509	+	0.0420312i
$729$	9.17943	+	28.2514i	0.339979	+	1.04635i
$730$	−0.164166	+	0.505250i	−0.00607604	+	0.0187001i
$731$	0.717839	+	0.521540i	0.0265502	+	0.0192899i
$732$	5.91290	+	4.29598i	0.218547	+	0.158784i
$733$	−11.4329	+	35.1869i	−0.422284	+	1.29966i	0.483287	+	0.875462i	$0.339443\pi$
$733$	−11.4329	+	35.1869i	−0.422284	+	1.29966i	−0.905571	+	0.424195i	$0.860557\pi$
$734$	0.635642	+	1.95631i	0.0234620	+	0.0722086i
$735$	−15.9852	+	11.6139i	−0.589623	+	0.428387i
$736$	−6.08282			−0.224216
$737$	1.23888	−	1.18354i	0.0456348	−	0.0435964i
$738$	0.138666			0.00510435
$739$	−7.96909	+	5.78988i	−0.293148	+	0.212984i	−0.724632	−	0.689136i	$-0.757990\pi$
$739$	−7.96909	+	5.78988i	−0.293148	+	0.212984i	0.431484	+	0.902121i	$0.357990\pi$
$740$	−0.916110	−	2.81950i	−0.0336769	−	0.103647i
$741$	−3.15105	+	9.69793i	−0.115757	+	0.356262i
$742$	0.492808	+	0.358046i	0.0180915	+	0.0131443i
$743$	−22.2052	−	16.1330i	−0.814629	−	0.591862i	0.100540	−	0.994933i	$-0.467943\pi$
$743$	−22.2052	−	16.1330i	−0.814629	−	0.591862i	−0.915169	+	0.403071i	$0.867943\pi$
$744$	−0.302951	+	0.932388i	−0.0111067	+	0.0341830i
$745$	−5.35640	−	16.4853i	−0.196243	−	0.603974i
$746$	1.53272	−	1.11359i	0.0561170	−	0.0407714i
$747$	−3.80291			−0.139141
$748$	−3.98658	+	21.9180i	−0.145764	+	0.801401i
$749$	−75.9591			−2.77549
$750$	−0.110960	+	0.0806171i	−0.00405168	+	0.00294372i
$751$	4.24232	+	13.0565i	0.154804	+	0.476439i	0.998141	−	0.0609469i	$-0.0194120\pi$
$751$	4.24232	+	13.0565i	0.154804	+	0.476439i	−0.843337	+	0.537385i	$0.819412\pi$
$752$	8.44732	−	25.9982i	0.308042	−	0.948056i
$753$	−3.93131	−	2.85626i	−0.143265	−	0.104088i
$754$	0.287039	+	0.208546i	0.0104533	+	0.00759479i
$755$	−0.00166997	+	0.00513965i	−6.07766e−5	+	0.000187051i
$756$	15.7162	+	48.3694i	0.571592	+	1.75918i
$757$	18.5507	−	13.4779i	0.674236	−	0.489861i	−0.197205	−	0.980362i	$-0.563186\pi$
$757$	18.5507	−	13.4779i	0.674236	−	0.489861i	0.871440	+	0.490501i	$0.163186\pi$
$758$	−0.348578			−0.0126609
$759$	23.3524	+	12.5785i	0.847640	+	0.456571i
$760$	−2.27097			−0.0823767
$761$	16.7319	−	12.1565i	0.606533	−	0.440672i	−0.241659	−	0.970361i	$-0.577692\pi$
$761$	16.7319	−	12.1565i	0.606533	−	0.440672i	0.848192	+	0.529689i	$0.177692\pi$
$762$	0.837599	+	2.57786i	0.0303430	+	0.0933861i
$763$	−5.10737	+	15.7189i	−0.184899	+	0.569061i
$764$	29.3031	+	21.2899i	1.06015	+	0.770243i
$765$	2.31609	+	1.68274i	0.0837385	+	0.0608395i
$766$	−0.317783	+	0.978034i	−0.0114819	+	0.0353378i
$767$	2.49553	+	7.68046i	0.0901084	+	0.277325i
$768$	−18.1611	+	13.1948i	−0.655334	+	0.476128i
$769$	38.4306			1.38584			0.692922	−	0.721013i	$-0.256323\pi$
$769$	38.4306			1.38584			0.692922	+	0.721013i	$0.256323\pi$
$770$	0.608331	+	1.26450i	0.0219227	+	0.0455696i
$771$	−39.3768			−1.41812
$772$	25.2738	−	18.3625i	0.909624	−	0.660880i
$773$	15.4325	+	47.4964i	0.555069	+	1.70833i	0.695762	+	0.718272i	$0.255067\pi$
$773$	15.4325	+	47.4964i	0.555069	+	1.70833i	−0.140693	+	0.990053i	$0.544933\pi$
$774$	0.00645085	−	0.0198537i	0.000231871	−	0.000713626i
$775$	−1.44887	−	1.05267i	−0.0520451	−	0.0378129i
$776$	−1.01349	−	0.736341i	−0.0363821	−	0.0264331i
$777$	3.05312	−	9.39654i	0.109530	−	0.337099i
$778$	0.271109	+	0.834389i	0.00971975	+	0.0299143i
$779$	8.60121	−	6.24914i	0.308170	−	0.223899i
$780$	3.33700			0.119484
$781$	−35.2681	+	4.76305i	−1.26199	+	0.170435i
$782$	−1.71991			−0.0615037
$783$	15.1659	−	11.0187i	0.541986	−	0.393776i
$784$	16.4334	+	50.5767i	0.586906	+	1.80631i
$785$	0.171454	−	0.527682i	0.00611946	−	0.0188338i
$786$	0.214684	+	0.155977i	0.00765751	+	0.00556351i
$787$	12.5834	+	9.14241i	0.448551	+	0.325892i	0.789024	−	0.614363i	$-0.210587\pi$
$787$	12.5834	+	9.14241i	0.448551	+	0.325892i	−0.340472	+	0.940255i	$0.610587\pi$
$788$	13.4442	−	41.3769i	0.478928	−	1.47399i
$789$	5.51518	+	16.9740i	0.196346	+	0.604290i
$790$	0.855110	−	0.621274i	0.0304235	−	0.0221039i
$791$	−53.8524			−1.91477
$792$	1.04110	−	0.140603i	0.0369938	−	0.00499610i
$793$	−2.85919			−0.101533
$794$	−1.68805	+	1.22644i	−0.0599067	+	0.0435248i
$795$	−0.652563	−	2.00838i	−0.0231440	−	0.0712300i
$796$	2.80099	−	8.62057i	0.0992786	−	0.305548i
$797$	−37.3012	−	27.1009i	−1.32127	−	0.959962i	−0.999915	−	0.0130049i	$-0.995860\pi$
$797$	−37.3012	−	27.1009i	−1.32127	−	0.959962i	−0.321359	−	0.946957i	$-0.604140\pi$
$798$	−3.05480	−	2.21944i	−0.108139	−	0.0785674i
$799$	7.21821	−	22.2154i	0.255362	−	0.785923i
$800$	0.344735	+	1.06098i	0.0121882	+	0.0375114i
$801$	9.10970	−	6.61858i	0.321875	−	0.233856i
$802$	−2.30803			−0.0814994
$803$	−8.16868	−	16.9798i	−0.288266	−	0.599203i
$804$	1.50879			0.0532111
$805$	19.9587	−	14.5009i	0.703453	−	0.511088i
$806$	−0.0591277	−	0.181976i	−0.00208268	−	0.00640984i
$807$	−0.948873	+	2.92033i	−0.0334019	+	0.102801i
$808$	−2.81863	−	2.04786i	−0.0991591	−	0.0720433i
$809$	30.3700	+	22.0651i	1.06775	+	0.775767i	0.975507	−	0.219969i	$-0.0705956\pi$
$809$	30.3700	+	22.0651i	1.06775	+	0.775767i	0.0922454	+	0.995736i	$0.470596\pi$
$810$	−0.165679	+	0.509909i	−0.00582138	+	0.0179164i
$811$	2.22661	+	6.85281i	0.0781870	+	0.240635i	0.982509	−	0.186217i	$-0.0596227\pi$
$811$	2.22661	+	6.85281i	0.0781870	+	0.240635i	−0.904322	+	0.426852i	$0.859623\pi$
$812$	24.2050	−	17.5859i	0.849428	−	0.617146i
$813$	22.2104			0.778953
$814$	−0.406514	−	0.218964i	−0.0142483	−	0.00767468i
$815$	−7.96428			−0.278977
$816$	−15.8011	+	11.4802i	−0.553150	+	0.401887i
$817$	−0.494596	−	1.52221i	−0.0173037	−	0.0532554i
$818$	0.852597	−	2.62402i	0.0298104	−	0.0917469i
$819$	−3.54946	−	2.57883i	−0.124028	−	0.0901117i
$820$	−2.81477	−	2.04505i	−0.0982960	−	0.0714162i
$821$	−2.66807	+	8.21147i	−0.0931163	+	0.286582i	−0.986758	−	0.162198i	$-0.948142\pi$
$821$	−2.66807	+	8.21147i	−0.0931163	+	0.286582i	0.893642	+	0.448781i	$0.148142\pi$
$822$	−0.531284	−	1.63512i	−0.0185306	−	0.0570315i
$823$	20.2352	−	14.7017i	0.705354	−	0.512470i	−0.176318	−	0.984333i	$-0.556419\pi$
$823$	20.2352	−	14.7017i	0.705354	−	0.512470i	0.881672	+	0.471864i	$0.156419\pi$
$824$	5.19375			0.180933
$825$	0.870520	−	4.78608i	0.0303076	−	0.166630i
$826$	−2.99042			−0.104050
$827$	−39.5387	+	28.7265i	−1.37489	+	0.998919i	−0.377558	+	0.925986i	$0.623236\pi$
$827$	−39.5387	+	28.7265i	−1.37489	+	0.998919i	−0.997337	+	0.0729332i	$0.976764\pi$
$828$	−2.84751	−	8.76373i	−0.0989577	−	0.304561i
$829$	1.63522	−	5.03270i	0.0567937	−	0.174793i	−0.918636	−	0.395106i	$-0.870708\pi$
$829$	1.63522	−	5.03270i	0.0567937	−	0.174793i	0.975429	+	0.220313i	$0.0707079\pi$
$830$	−0.338983	−	0.246286i	−0.0117663	−	0.00854871i
$831$	−9.81405	−	7.13033i	−0.340446	−	0.247348i
$832$	2.75073	−	8.46589i	0.0953645	−	0.293502i
$833$	14.0423	+	43.2177i	0.486536	+	1.49740i
$834$	1.24775	−	0.906543i	0.0432060	−	0.0313910i
$835$	3.42643			0.118576
$836$	29.0568	−	27.7590i	1.00495	−	0.960064i
$837$	−10.1097			−0.349441
$838$	−0.683556	+	0.496633i	−0.0236131	+	0.0171559i
$839$	−4.09196	−	12.5938i	−0.141270	−	0.434785i	0.855242	−	0.518228i	$-0.173408\pi$
$839$	−4.09196	−	12.5938i	−0.141270	−	0.434785i	−0.996513	+	0.0834435i	$0.973408\pi$
$840$	−0.765373	+	2.35558i	−0.0264079	+	0.0812751i
$841$	14.5397	+	10.5637i	0.501369	+	0.364266i
$842$	−1.07577	−	0.781592i	−0.0370734	−	0.0269354i
$843$	1.10919	−	3.41375i	0.0382026	−	0.117576i
$844$	−11.6670	−	35.9072i	−0.401593	−	1.23598i
$845$	9.46110	−	6.87389i	0.325472	−	0.236469i
$846$	−0.549557			−0.0188942
$847$	−46.5822	−	17.5251i	−1.60058	−	0.602168i
$848$	−5.68361			−0.195176
$849$	−30.9643	+	22.4969i	−1.06269	+	0.772092i
$850$	0.0974731	+	0.299991i	0.00334330	+	0.0102896i
$851$	−2.50855	+	7.72053i	−0.0859920	+	0.264656i
$852$	−25.3540	−	18.4208i	−0.868614	−	0.631085i
$853$	−1.79509	−	1.30421i	−0.0614626	−	0.0446552i	0.556630	−	0.830761i	$-0.312094\pi$
$853$	−1.79509	−	1.30421i	−0.0614626	−	0.0446552i	−0.618092	+	0.786106i	$0.712094\pi$
$854$	0.327174	−	1.00694i	0.0111956	−	0.0344567i
$855$	−1.59580	−	4.91138i	−0.0545753	−	0.167966i
$856$	−5.06911	+	3.68292i	−0.173259	+	0.125880i
$857$	31.4625			1.07474			0.537368	−	0.843348i	$-0.319418\pi$
$857$	31.4625			1.07474			0.537368	+	0.843348i	$0.319418\pi$
$858$	0.375806	−	0.359020i	0.0128298	−	0.0122567i
$859$	9.07676			0.309695			0.154848	−	0.987938i	$-0.450511\pi$
$859$	9.07676			0.309695			0.154848	+	0.987938i	$0.450511\pi$
$860$	−0.423749	+	0.307872i	−0.0144497	+	0.0104983i
$861$	−3.58314	−	11.0278i	−0.122113	−	0.375826i
$862$	−0.0500352	+	0.153993i	−0.00170421	+	0.00524501i
$863$	−34.3704	−	24.9716i	−1.16998	−	0.850042i	−0.178976	−	0.983853i	$-0.557279\pi$
$863$	−34.3704	−	24.9716i	−1.16998	−	0.850042i	−0.991007	+	0.133811i	$0.957279\pi$
$864$	5.09477	+	3.70157i	0.173328	+	0.125930i
$865$	6.35552	−	19.5603i	0.216094	−	0.665069i
$866$	0.533065	+	1.64060i	0.0181143	+	0.0557500i
$867$	6.67038	−	4.84632i	0.226538	−	0.164590i
$868$	−16.1351			−0.547662
$869$	−6.70865	+	36.8838i	−0.227575	+	1.25120i
$870$	0.455465			0.0154417
$871$	−0.477516	+	0.346936i	−0.0161800	+	0.0117555i
$872$	0.421300	+	1.29663i	0.0142670	+	0.0439094i
$873$	0.880296	−	2.70927i	0.0297935	−	0.0916950i
$874$	2.50993	+	1.82357i	0.0848996	+	0.0616832i
$875$	−3.66042	−	2.65945i	−0.123745	−	0.0899058i
$876$	5.12746	−	15.7807i	0.173241	−	0.533181i
$877$	−9.67537	−	29.7777i	−0.326714	−	1.00552i	−0.970661	−	0.240452i	$-0.922704\pi$
$877$	−9.67537	−	29.7777i	−0.326714	−	1.00552i	0.643947	−	0.765070i	$-0.277296\pi$
$878$	1.29896	−	0.943750i	0.0438378	−	0.0318500i
$879$	19.7319			0.665539
$880$	−11.5269	−	6.20885i	−0.388573	−	0.209300i
$881$	21.5189			0.724990			0.362495	−	0.931986i	$-0.381925\pi$
$881$	21.5189			0.724990			0.362495	+	0.931986i	$0.381925\pi$
$882$	0.864925	−	0.628405i	0.0291235	−	0.0211595i
$883$	−0.201650	−	0.620614i	−0.00678605	−	0.0208853i	0.947606	−	0.319441i	$-0.103495\pi$
$883$	−0.201650	−	0.620614i	−0.00678605	−	0.0208853i	−0.954392	+	0.298556i	$0.903495\pi$
$884$	2.37155	−	7.29889i	0.0797639	−	0.245488i
$885$	8.38708	+	6.09357i	0.281929	+	0.204833i
$886$	−2.76877	−	2.01163i	−0.0930187	−	0.0675820i
$887$	−4.52593	+	13.9294i	−0.151966	+	0.467702i	−0.997841	−	0.0656786i	$-0.979079\pi$
$887$	−4.52593	+	13.9294i	−0.151966	+	0.467702i	0.845875	+	0.533381i	$0.179079\pi$
$888$	−0.251848	−	0.775108i	−0.00845146	−	0.0260109i
$889$	−72.3396	+	52.5578i	−2.42619	+	1.76273i
$890$	1.24065			0.0415868
$891$	−8.24400	−	17.1364i	−0.276184	−	0.574089i
$892$	−9.71637			−0.325328
$893$	−34.0882	+	24.7665i	−1.14072	+	0.828780i
$894$	−0.734651	−	2.26102i	−0.0245704	−	0.0756199i
$895$	−0.792419	+	2.43882i	−0.0264877	+	0.0815206i
$896$	10.8337	+	7.87116i	0.361929	+	0.262957i
$897$	−7.39246	−	5.37094i	−0.246827	−	0.179330i
$898$	−0.479760	+	1.47655i	−0.0160098	+	0.0492731i
$899$	1.83782	+	5.65622i	0.0612946	+	0.188645i
$900$	−1.36722	+	0.993342i	−0.0455739	+	0.0331114i
$901$	−4.85662			−0.161798
$902$	−0.537016	+	0.0725252i	−0.0178807	+	0.00241483i
$903$	−1.74561			−0.0580903
$904$	−3.59382	+	2.61107i	−0.119529	+	0.0868428i
$905$	4.14604	+	12.7602i	0.137819	+	0.424163i
$906$	−0.000229044	0	0.000704924i	−7.60946e−6	0	2.34195e-5i
$907$	−23.2552	−	16.8959i	−0.772175	−	0.561018i	0.130445	−	0.991456i	$-0.458359\pi$
$907$	−23.2552	−	16.8959i	−0.772175	−	0.561018i	−0.902620	+	0.430437i	$0.858359\pi$
$908$	26.2955	+	19.1048i	0.872645	+	0.634014i
$909$	2.44821	−	7.53482i	0.0812020	−	0.249914i
$910$	−0.149380	−	0.459743i	−0.00495188	−	0.0152403i
$911$	−13.9813	+	10.1580i	−0.463222	+	0.336550i	−0.794794	−	0.606880i	$-0.792421\pi$
$911$	−13.9813	+	10.1580i	−0.463222	+	0.336550i	0.331572	+	0.943430i	$0.392421\pi$
$912$	35.2313			1.16663
$913$	14.7277	−	1.98901i	0.487416	−	0.0658266i
$914$	−2.96102			−0.0979418
$915$	−2.96943	+	2.15742i	−0.0981665	+	0.0713221i
$916$	2.97308	+	9.15020i	0.0982333	+	0.302331i
$917$	−2.70513	+	8.32554i	−0.0893313	+	0.274933i
$918$	1.44054	+	1.04661i	0.0475448	+	0.0345433i
$919$	1.77859	+	1.29222i	0.0586701	+	0.0426263i	0.616734	−	0.787172i	$-0.288456\pi$
$919$	1.77859	+	1.29222i	0.0586701	+	0.0426263i	−0.558064	+	0.829798i	$0.688456\pi$
$920$	0.628857	−	1.93542i	0.0207328	−	0.0638090i
$921$	12.3212	+	37.9208i	0.405997	+	1.24953i
$922$	1.92419	−	1.39801i	0.0633699	−	0.0460409i
$923$	12.2600			0.403542
$924$	−19.0003	−	39.4948i	−0.625063	−	1.29928i
$925$	1.48881			0.0489517
$926$	1.23552	−	0.897661i	0.0406019	−	0.0294990i
$927$	3.64963	+	11.2324i	0.119870	+	0.368921i
$928$	1.14481	−	3.52335i	0.0375801	−	0.115660i
$929$	−19.5866	−	14.2305i	−0.642616	−	0.466888i	0.218132	−	0.975919i	$-0.430004\pi$
$929$	−19.5866	−	14.2305i	−0.642616	−	0.466888i	−0.860748	+	0.509031i	$0.830004\pi$
$930$	−0.198719	−	0.144378i	−0.00651624	−	0.00473433i
$931$	25.3301	−	77.9579i	0.830159	−	2.55497i
$932$	5.18094	+	15.9453i	0.169707	+	0.522305i
$933$	15.6621	−	11.3792i	0.512754	−	0.372538i
$934$	0.797556			0.0260968
$935$	−9.84973	−	5.30544i	−0.322121	−	0.173506i
$936$	−0.361908			−0.0118293
$937$	16.8459	−	12.2393i	0.550333	−	0.399840i	−0.277575	−	0.960704i	$-0.589531\pi$
$937$	16.8459	−	12.2393i	0.550333	−	0.399840i	0.827908	+	0.560864i	$0.189531\pi$
$938$	−0.0675407	−	0.207869i	−0.00220528	−	0.00678716i
$939$	7.32984	−	22.5589i	0.239200	−	0.736183i
$940$	11.1554	+	8.10491i	0.363851	+	0.264353i
$941$	−27.6787	−	20.1098i	−0.902301	−	0.655560i	0.0367552	−	0.999324i	$-0.488298\pi$
$941$	−27.6787	−	20.1098i	−0.902301	−	0.655560i	−0.939056	+	0.343764i	$0.888298\pi$
$942$	0.0235156	−	0.0723736i	0.000766180	−	0.00235806i
$943$	2.94403	+	9.06080i	0.0958709	+	0.295060i
$944$	22.5733	−	16.4004i	0.734697	−	0.533789i
$945$	−25.5410			−0.830848
$946$	−0.0145986	+	0.0802621i	−0.000474640	+	0.00260955i
$947$	33.8128			1.09877			0.549383	−	0.835570i	$-0.314863\pi$
$947$	33.8128			1.09877			0.549383	+	0.835570i	$0.314863\pi$
$948$	−26.7081	+	19.4045i	−0.867438	+	0.630230i
$949$	2.00587	+	6.17344i	0.0651133	+	0.200398i
$950$	0.175826	−	0.541138i	0.00570456	−	0.0175568i
$951$	6.38533	+	4.63921i	0.207058	+	0.150437i
$952$	4.60832	+	3.34814i	0.149356	+	0.108514i
$953$	7.91027	−	24.3453i	0.256239	−	0.788622i	−0.737344	−	0.675517i	$-0.763920\pi$
$953$	7.91027	−	24.3453i	0.256239	−	0.788622i	0.993583	−	0.113105i	$-0.0360796\pi$
$954$	0.0353088	+	0.108669i	0.00114316	+	0.00351830i
$955$	−14.7159	+	10.6917i	−0.476195	+	0.345976i
$956$	45.1871			1.46146
$957$	−11.6809	+	11.1591i	−0.377589	+	0.360723i
$958$	2.80042			0.0904774
$959$	45.8845	−	33.3371i	1.48169	−	1.07651i
$960$	−3.53119	−	10.8679i	−0.113969	−	0.350759i
$961$	−8.58840	+	26.4324i	−0.277045	+	0.852658i
$962$	0.128686	+	0.0934959i	0.00414901	+	0.00301443i
$963$	−11.5270	−	8.37488i	−0.371454	−	0.269877i
$964$	−7.14182	+	21.9803i	−0.230023	+	0.707937i
$965$	4.84806	+	14.9208i	0.156065	+	0.480317i
$966$	2.73742	−	1.98885i	0.0880750	−	0.0639902i
$967$	43.8942			1.41154			0.705772	−	0.708439i	$-0.250600\pi$
$967$	43.8942			1.41154			0.705772	+	0.708439i	$0.250600\pi$
$968$	−3.95836	+	1.08904i	−0.127227	+	0.0350029i
$969$	30.1051			0.967114
$970$	0.253927	−	0.184489i	0.00815310	−	0.00592357i
$971$	11.2392	+	34.5906i	0.360682	+	1.11006i	0.952641	+	0.304097i	$0.0983547\pi$
$971$	11.2392	+	34.5906i	0.360682	+	1.11006i	−0.591959	+	0.805968i	$0.701645\pi$
$972$	−5.24591	+	16.1453i	−0.168263	+	0.517860i
$973$	41.1616	+	29.9056i	1.31958	+	0.958730i
$974$	1.48299	+	1.07746i	0.0475182	+	0.0345240i
$975$	−0.517859	+	1.59381i	−0.0165848	+	0.0510426i
$976$	3.05269	+	9.39520i	0.0977141	+	0.300733i
$977$	−8.37462	+	6.08452i	−0.267928	+	0.194661i	−0.713635	−	0.700518i	$-0.752952\pi$
$977$	−8.37462	+	6.08452i	−0.267928	+	0.194661i	0.445707	+	0.895179i	$0.352952\pi$
$978$	−1.09233			−0.0349289
$979$	−31.8178	+	30.3966i	−1.01690	+	0.971481i
$980$	−26.8248			−0.856888
$981$	−2.50814	+	1.82227i	−0.0800789	+	0.0581807i
$982$	−0.456245	−	1.40418i	−0.0145594	−	0.0448091i
$983$	−6.83416	+	21.0334i	−0.217976	+	0.670861i	0.780953	+	0.624590i	$0.214734\pi$
$983$	−6.83416	+	21.0334i	−0.217976	+	0.670861i	−0.998929	+	0.0462712i	$0.985266\pi$
$984$	−0.773808	−	0.562205i	−0.0246681	−	0.0179224i
$985$	17.6759	+	12.8423i	0.563201	+	0.409190i
$986$	0.323692	−	0.996222i	0.0103085	−	0.0317262i
$987$	14.2006	+	43.7051i	0.452012	+	1.39115i
$988$	−11.1997	+	8.13707i	−0.356310	+	0.258875i
$989$	1.43426			0.0456067
$990$	−0.0471019	+	0.258964i	−0.00149700	+	0.00823042i
$991$	−55.5911			−1.76591			−0.882955	−	0.469457i	$-0.844450\pi$
$991$	−55.5911			−1.76591			−0.882955	+	0.469457i	$0.844450\pi$
$992$	−1.61634	+	1.17434i	−0.0513189	+	0.0372853i
$993$	−8.41687	−	25.9044i	−0.267101	−	0.822053i
$994$	−1.40289	+	4.31765i	−0.0444970	+	0.136948i
$995$	3.68265	+	2.67560i	0.116748	+	0.0848222i
$996$	10.5876	+	7.69236i	0.335482	+	0.243742i
$997$	3.33465	−	10.2630i	0.105609	−	0.325032i	−0.884264	−	0.466988i	$-0.845339\pi$
$997$	3.33465	−	10.2630i	0.105609	−	0.325032i	0.989873	+	0.141956i	$0.0453391\pi$
$998$	0.323872	+	0.996775i	0.0102520	+	0.0315524i
$999$	6.79924	−	4.93994i	0.215118	−	0.156293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.2.g.a.36.2	yes	8
3.2	odd	2		495.2.n.f.91.1		8
4.3	odd	2		880.2.bo.e.641.1		8
5.2	odd	4		275.2.z.b.124.2		16
5.3	odd	4		275.2.z.b.124.3		16
5.4	even	2		275.2.h.b.201.1		8
11.2	odd	10		605.2.a.i.1.3		4
11.3	even	5		605.2.g.j.511.1		8
11.4	even	5	inner	55.2.g.a.26.2	✓	8
11.5	even	5		605.2.g.j.251.1		8
11.6	odd	10		605.2.g.g.251.2		8
11.7	odd	10		605.2.g.n.81.1		8
11.8	odd	10		605.2.g.g.511.2		8
11.9	even	5		605.2.a.l.1.2		4
11.10	odd	2		605.2.g.n.366.1		8
33.2	even	10		5445.2.a.bu.1.2		4
33.20	odd	10		5445.2.a.bg.1.3		4
33.26	odd	10		495.2.n.f.136.1		8
44.15	odd	10		880.2.bo.e.81.1		8
44.31	odd	10		9680.2.a.cs.1.1		4
44.35	even	10		9680.2.a.cv.1.1		4
55.4	even	10		275.2.h.b.26.1		8
55.9	even	10		3025.2.a.v.1.3		4
55.24	odd	10		3025.2.a.be.1.2		4
55.37	odd	20		275.2.z.b.224.3		16
55.48	odd	20		275.2.z.b.224.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.2	✓	8	11.4	even	5	inner
55.2.g.a.36.2	yes	8	1.1	even	1	trivial
275.2.h.b.26.1		8	55.4	even	10
275.2.h.b.201.1		8	5.4	even	2
275.2.z.b.124.2		16	5.2	odd	4
275.2.z.b.124.3		16	5.3	odd	4
275.2.z.b.224.2		16	55.48	odd	20
275.2.z.b.224.3		16	55.37	odd	20
495.2.n.f.91.1		8	3.2	odd	2
495.2.n.f.136.1		8	33.26	odd	10
605.2.a.i.1.3		4	11.2	odd	10
605.2.a.l.1.2		4	11.9	even	5
605.2.g.g.251.2		8	11.6	odd	10
605.2.g.g.511.2		8	11.8	odd	10
605.2.g.j.251.1		8	11.5	even	5
605.2.g.j.511.1		8	11.3	even	5
605.2.g.n.81.1		8	11.7	odd	10
605.2.g.n.366.1		8	11.10	odd	2
880.2.bo.e.81.1		8	44.15	odd	10
880.2.bo.e.641.1		8	4.3	odd	2
3025.2.a.v.1.3		4	55.9	even	10
3025.2.a.be.1.2		4	55.24	odd	10
5445.2.a.bg.1.3		4	33.20	odd	10
5445.2.a.bu.1.2		4	33.2	even	10
9680.2.a.cs.1.1		4	44.31	odd	10
9680.2.a.cv.1.1		4	44.35	even	10

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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	55.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0756511 + 0.0549637i) q^{2} +(0.453245 + 1.39494i) q^{3} +(-0.615332 + 1.89380i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.110960 - 0.0806171i) q^{6} +(1.39815 - 4.30308i) q^{7} +(-0.115332 - 0.354955i) q^{8} +(0.686611 - 0.498852i) q^{9} +O(q^{10})\)	\(q+(-0.0756511 + 0.0549637i) q^{2} +(0.453245 + 1.39494i) q^{3} +(-0.615332 + 1.89380i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.110960 - 0.0806171i) q^{6} +(1.39815 - 4.30308i) q^{7} +(-0.115332 - 0.354955i) q^{8} +(0.686611 - 0.498852i) q^{9} +0.0935099 q^{10} +(-2.39815 + 2.29104i) q^{11} -2.92064 q^{12} +(0.924349 - 0.671579i) q^{13} +(0.130741 + 0.402380i) q^{14} +(0.453245 - 1.39494i) q^{15} +(-3.19369 - 2.32035i) q^{16} +(-2.72899 - 1.98273i) q^{17} +(-0.0245241 + 0.0754774i) q^{18} +(1.88030 + 5.78696i) q^{19} +(1.61096 - 1.17043i) q^{20} +6.63626 q^{21} +(0.0554990 - 0.305131i) q^{22} -5.45258 q^{23} +(0.442869 - 0.321763i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.0330155 + 0.101611i) q^{26} +(4.56691 + 3.31805i) q^{27} +(7.28883 + 5.29564i) q^{28} +(1.02619 - 3.15830i) q^{29} +(0.0423829 + 0.130441i) q^{30} +(-1.44887 + 1.05267i) q^{31} +1.11558 q^{32} +(-4.28282 - 2.30689i) q^{33} +0.315430 q^{34} +(-3.66042 + 2.65945i) q^{35} +(0.522231 + 1.60726i) q^{36} +(0.460067 - 1.41594i) q^{37} +(-0.460319 - 0.334441i) q^{38} +(1.35577 + 0.985026i) q^{39} +(-0.115332 + 0.354955i) q^{40} +(-0.539933 - 1.66174i) q^{41} +(-0.502041 + 0.364754i) q^{42} -0.263041 q^{43} +(-2.86310 - 5.95137i) q^{44} -0.848698 q^{45} +(0.412494 - 0.299694i) q^{46} +(2.13986 + 6.58580i) q^{47} +(1.78924 - 5.50670i) q^{48} +(-10.8985 - 7.91824i) q^{49} +(-0.0756511 - 0.0549637i) q^{50} +(1.52890 - 4.70546i) q^{51} +(0.703052 + 2.16377i) q^{52} +(1.16479 - 0.846269i) q^{53} -0.527864 q^{54} +(3.28679 - 0.443888i) q^{55} -1.68865 q^{56} +(-7.22025 + 5.24582i) q^{57} +(0.0959593 + 0.295332i) q^{58} +(-2.18416 + 6.72216i) q^{59} +(2.36285 + 1.71671i) q^{60} +(-2.02452 - 1.47090i) q^{61} +(0.0517503 - 0.159271i) q^{62} +(-1.18661 - 3.65201i) q^{63} +(6.30297 - 4.57938i) q^{64} -1.14256 q^{65} +(0.450796 - 0.0608810i) q^{66} -0.516598 q^{67} +(5.43413 - 3.94812i) q^{68} +(-2.47136 - 7.60605i) q^{69} +(0.130741 - 0.402380i) q^{70} +(8.68098 + 6.30710i) q^{71} +(-0.256258 - 0.186183i) q^{72} +(-1.75560 + 5.40317i) q^{73} +(0.0430208 + 0.132404i) q^{74} +(-1.18661 + 0.862123i) q^{75} -12.1163 q^{76} +(6.50552 + 13.5227i) q^{77} -0.156706 q^{78} +(9.14460 - 6.64394i) q^{79} +(1.21988 + 3.75440i) q^{80} +(-1.77179 + 5.45300i) q^{81} +(0.132182 + 0.0960360i) q^{82} +(-3.62511 - 2.63380i) q^{83} +(-4.08350 + 12.5677i) q^{84} +(1.04238 + 3.20812i) q^{85} +(0.0198994 - 0.0144577i) q^{86} +4.87077 q^{87} +(1.08980 + 0.587008i) q^{88} +13.2676 q^{89} +(0.0642049 - 0.0466476i) q^{90} +(-1.59747 - 4.91652i) q^{91} +(3.35515 - 10.3261i) q^{92} +(-2.12511 - 1.54398i) q^{93} +(-0.523863 - 0.380608i) q^{94} +(1.88030 - 5.78696i) q^{95} +(0.505633 + 1.55618i) q^{96} +(2.71551 - 1.97293i) q^{97} +1.25970 q^{98} +(-0.503711 + 2.76938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} + 13 q^{6} - 3 q^{7} - 2 q^{8} - 5 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 + 13 * q^6 - 3 * q^7 - 2 * q^8 - 5 * q^9	\( 8 q - 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} + 13 q^{6} - 3 q^{7} - 2 q^{8} - 5 q^{9} + 6 q^{10} - 5 q^{11} - 28 q^{12} + 4 q^{13} + 16 q^{14} + q^{15} - 20 q^{16} + q^{17} + 14 q^{18} - q^{19} - q^{20} - 12 q^{21} + 33 q^{22} - 18 q^{23} + 25 q^{24} - 2 q^{25} - 14 q^{26} + 10 q^{27} + 4 q^{28} + 19 q^{29} - 12 q^{30} + 6 q^{31} + 12 q^{32} - 19 q^{33} - 20 q^{34} - 8 q^{35} + 21 q^{36} + 4 q^{37} - 6 q^{38} + 9 q^{39} - 2 q^{40} - 4 q^{41} + 29 q^{42} + 42 q^{43} - 28 q^{44} - 41 q^{46} + 4 q^{47} - 19 q^{48} - 15 q^{49} - 4 q^{50} + 13 q^{51} - 26 q^{52} + 3 q^{53} - 40 q^{54} + 5 q^{55} + 30 q^{56} - 5 q^{57} - 6 q^{58} - 19 q^{59} + 22 q^{60} - 2 q^{61} - 38 q^{62} + q^{63} + 6 q^{64} + 14 q^{65} + 13 q^{66} - 2 q^{67} + 35 q^{68} - 21 q^{69} + 16 q^{70} + 40 q^{71} - 34 q^{72} - 23 q^{73} + 48 q^{74} + q^{75} + 16 q^{76} - 28 q^{77} + 12 q^{78} + 17 q^{79} + 15 q^{80} + 2 q^{82} - 25 q^{83} - 4 q^{84} - 4 q^{85} - 31 q^{86} + 30 q^{87} + 22 q^{88} - 16 q^{90} - 12 q^{91} + 81 q^{92} - 13 q^{93} + 33 q^{94} - q^{95} + 23 q^{96} + 12 q^{97} - 84 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 + 13 * q^6 - 3 * q^7 - 2 * q^8 - 5 * q^9 + 6 * q^10 - 5 * q^11 - 28 * q^12 + 4 * q^13 + 16 * q^14 + q^15 - 20 * q^16 + q^17 + 14 * q^18 - q^19 - q^20 - 12 * q^21 + 33 * q^22 - 18 * q^23 + 25 * q^24 - 2 * q^25 - 14 * q^26 + 10 * q^27 + 4 * q^28 + 19 * q^29 - 12 * q^30 + 6 * q^31 + 12 * q^32 - 19 * q^33 - 20 * q^34 - 8 * q^35 + 21 * q^36 + 4 * q^37 - 6 * q^38 + 9 * q^39 - 2 * q^40 - 4 * q^41 + 29 * q^42 + 42 * q^43 - 28 * q^44 - 41 * q^46 + 4 * q^47 - 19 * q^48 - 15 * q^49 - 4 * q^50 + 13 * q^51 - 26 * q^52 + 3 * q^53 - 40 * q^54 + 5 * q^55 + 30 * q^56 - 5 * q^57 - 6 * q^58 - 19 * q^59 + 22 * q^60 - 2 * q^61 - 38 * q^62 + q^63 + 6 * q^64 + 14 * q^65 + 13 * q^66 - 2 * q^67 + 35 * q^68 - 21 * q^69 + 16 * q^70 + 40 * q^71 - 34 * q^72 - 23 * q^73 + 48 * q^74 + q^75 + 16 * q^76 - 28 * q^77 + 12 * q^78 + 17 * q^79 + 15 * q^80 + 2 * q^82 - 25 * q^83 - 4 * q^84 - 4 * q^85 - 31 * q^86 + 30 * q^87 + 22 * q^88 - 16 * q^90 - 12 * q^91 + 81 * q^92 - 13 * q^93 + 33 * q^94 - q^95 + 23 * q^96 + 12 * q^97 - 84 * q^98 + 4 * q^99

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