LMFDB - Embedded newform 495.2.bc.c.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(23,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 0]))

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

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

chi := DirichletCharacter("495.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$29$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.4
Character	$\chi$	$=$	495.23
Dual form			495.2.bc.c.452.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.629065 + 2.34770i) q^{2} +(-1.69619 - 0.350640i) q^{3} +(-3.38393 - 1.95371i) q^{4} +(0.435925 - 2.19316i) q^{5} +(1.89021 - 3.76157i) q^{6} +(1.65959 + 0.444685i) q^{7} +(3.27818 - 3.27818i) q^{8} +(2.75410 + 1.18950i) q^{9} +O(q^{10})$	\(q+(-0.629065 + 2.34770i) q^{2} +(-1.69619 - 0.350640i) q^{3} +(-3.38393 - 1.95371i) q^{4} +(0.435925 - 2.19316i) q^{5} +(1.89021 - 3.76157i) q^{6} +(1.65959 + 0.444685i) q^{7} +(3.27818 - 3.27818i) q^{8} +(2.75410 + 1.18950i) q^{9} +(4.87467 + 2.40306i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(5.05473 + 4.50041i) q^{12} +(-5.97853 + 1.60194i) q^{13} +(-2.08798 + 3.61648i) q^{14} +(-1.50842 + 3.56717i) q^{15} +(1.72657 + 2.99051i) q^{16} +(4.36974 + 4.36974i) q^{17} +(-4.52511 + 5.71754i) q^{18} +0.121312i q^{19} +(-5.75996 + 6.56985i) q^{20} +(-2.65905 - 1.33619i) q^{21} +(-0.629065 - 2.34770i) q^{22} +(1.73646 + 6.48055i) q^{23} +(-6.70987 + 4.41095i) q^{24} +(-4.61994 - 1.91211i) q^{25} -15.0435i q^{26} +(-4.25439 - 2.98332i) q^{27} +(-4.74715 - 4.74715i) q^{28} +(0.446884 + 0.774026i) q^{29} +(-7.42575 - 5.78530i) q^{30} +(-0.845872 + 1.46509i) q^{31} +(0.849191 - 0.227540i) q^{32} +(1.64426 - 0.544431i) q^{33} +(-13.0077 + 7.51000i) q^{34} +(1.69872 - 3.44590i) q^{35} +(-6.99576 - 9.40593i) q^{36} +(-5.50427 + 5.50427i) q^{37} +(-0.284805 - 0.0763132i) q^{38} +(10.7024 - 0.620883i) q^{39} +(-5.76055 - 8.61863i) q^{40} +(2.63164 + 1.51938i) q^{41} +(4.80968 - 5.40210i) q^{42} +(-0.840639 + 3.13731i) q^{43} +3.90743 q^{44} +(3.80935 - 5.52167i) q^{45} -16.3068 q^{46} +(-2.33916 + 8.72985i) q^{47} +(-1.88000 - 5.67788i) q^{48} +(-3.50569 - 2.02401i) q^{49} +(7.39530 - 9.64340i) q^{50} +(-5.87969 - 8.94411i) q^{51} +(23.3607 + 6.25947i) q^{52} +(6.96722 - 6.96722i) q^{53} +(9.68023 - 8.11134i) q^{54} +(0.719060 + 2.11730i) q^{55} +(6.89819 - 3.98267i) q^{56} +(0.0425368 - 0.205768i) q^{57} +(-2.09830 + 0.562238i) q^{58} +(-3.56502 + 6.17479i) q^{59} +(12.0736 - 9.12403i) q^{60} +(-4.93392 - 8.54580i) q^{61} +(-2.90749 - 2.90749i) q^{62} +(4.04172 + 3.19879i) q^{63} +9.04308i q^{64} +(0.907134 + 13.8102i) q^{65} +(0.243814 + 4.20272i) q^{66} +(3.39507 + 12.6706i) q^{67} +(-6.24968 - 23.3241i) q^{68} +(-0.673020 - 11.6011i) q^{69} +(7.02134 + 6.15579i) q^{70} +11.2337i q^{71} +(12.9278 - 5.12905i) q^{72} +(2.61564 + 2.61564i) q^{73} +(-9.45985 - 16.3849i) q^{74} +(7.16582 + 4.86323i) q^{75} +(0.237009 - 0.410512i) q^{76} +(-1.65959 + 0.444685i) q^{77} +(-5.27486 + 25.5166i) q^{78} +(5.13437 - 2.96433i) q^{79} +(7.31134 - 2.48302i) q^{80} +(6.17017 + 6.55202i) q^{81} +(-5.22252 + 5.22252i) q^{82} +(-6.05000 - 1.62109i) q^{83} +(6.38751 + 9.71659i) q^{84} +(11.4884 - 7.67868i) q^{85} +(-6.83665 - 3.94714i) q^{86} +(-0.486595 - 1.46959i) q^{87} +(-1.19990 + 4.47808i) q^{88} -13.2222 q^{89} +(10.5669 + 12.4167i) q^{90} -10.6342 q^{91} +(6.78509 - 25.3223i) q^{92} +(1.94848 - 2.18848i) q^{93} +(-19.0236 - 10.9833i) q^{94} +(0.266057 + 0.0528829i) q^{95} +(-1.52017 + 0.0881904i) q^{96} +(-5.75725 - 1.54265i) q^{97} +(6.95709 - 6.95709i) q^{98} +(-2.97987 + 0.346913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 4 q^{2} + 8 q^{3} - 6 q^{4} + 2 q^{5} - 2 q^{6} + 8 q^{7} - 2 q^{8} - 16 q^{9}+O(q^{10}) $ 116 * q - 4 * q^2 + 8 * q^3 - 6 * q^4 + 2 * q^5 - 2 * q^6 + 8 * q^7 - 2 * q^8 - 16 * q^9	\( 116 q - 4 q^{2} + 8 q^{3} - 6 q^{4} + 2 q^{5} - 2 q^{6} + 8 q^{7} - 2 q^{8} - 16 q^{9} + 6 q^{10} + 6 q^{12} - 12 q^{13} + 10 q^{14} - 18 q^{15} + 62 q^{16} + 8 q^{17} - 12 q^{18} - 18 q^{20} - 10 q^{21} - 4 q^{22} - 40 q^{23} + 62 q^{24} - 6 q^{25} - 58 q^{27} + 18 q^{28} + 2 q^{29} - 70 q^{30} - 2 q^{31} - 66 q^{32} + 24 q^{34} - 2 q^{35} + 24 q^{36} - 14 q^{37} - 6 q^{38} - 4 q^{39} - 100 q^{40} + 6 q^{41} - 30 q^{42} - 22 q^{43} + 120 q^{44} + 94 q^{45} - 44 q^{46} + 32 q^{47} + 108 q^{48} + 18 q^{49} - 22 q^{50} - 8 q^{51} - 126 q^{52} + 44 q^{53} - 28 q^{54} + 2 q^{55} + 42 q^{56} + 20 q^{57} + 2 q^{58} - 22 q^{59} - 68 q^{60} - 10 q^{61} + 16 q^{62} - 8 q^{63} - 60 q^{65} + 6 q^{66} + 36 q^{67} - 48 q^{68} + 76 q^{69} + 154 q^{70} - 228 q^{72} + 12 q^{73} + 8 q^{74} - 72 q^{75} - 6 q^{76} - 8 q^{77} - 110 q^{78} + 6 q^{79} - 4 q^{80} + 44 q^{81} - 50 q^{82} + 30 q^{83} - 222 q^{84} - 126 q^{85} + 90 q^{86} + 112 q^{87} + 2 q^{88} - 8 q^{89} + 72 q^{90} + 72 q^{91} - 132 q^{92} + 112 q^{93} - 42 q^{94} + 78 q^{95} + 68 q^{96} - 72 q^{97} - 16 q^{98} + 4 q^{99}+O(q^{100}) \) 116 * q - 4 * q^2 + 8 * q^3 - 6 * q^4 + 2 * q^5 - 2 * q^6 + 8 * q^7 - 2 * q^8 - 16 * q^9 + 6 * q^10 + 6 * q^12 - 12 * q^13 + 10 * q^14 - 18 * q^15 + 62 * q^16 + 8 * q^17 - 12 * q^18 - 18 * q^20 - 10 * q^21 - 4 * q^22 - 40 * q^23 + 62 * q^24 - 6 * q^25 - 58 * q^27 + 18 * q^28 + 2 * q^29 - 70 * q^30 - 2 * q^31 - 66 * q^32 + 24 * q^34 - 2 * q^35 + 24 * q^36 - 14 * q^37 - 6 * q^38 - 4 * q^39 - 100 * q^40 + 6 * q^41 - 30 * q^42 - 22 * q^43 + 120 * q^44 + 94 * q^45 - 44 * q^46 + 32 * q^47 + 108 * q^48 + 18 * q^49 - 22 * q^50 - 8 * q^51 - 126 * q^52 + 44 * q^53 - 28 * q^54 + 2 * q^55 + 42 * q^56 + 20 * q^57 + 2 * q^58 - 22 * q^59 - 68 * q^60 - 10 * q^61 + 16 * q^62 - 8 * q^63 - 60 * q^65 + 6 * q^66 + 36 * q^67 - 48 * q^68 + 76 * q^69 + 154 * q^70 - 228 * q^72 + 12 * q^73 + 8 * q^74 - 72 * q^75 - 6 * q^76 - 8 * q^77 - 110 * q^78 + 6 * q^79 - 4 * q^80 + 44 * q^81 - 50 * q^82 + 30 * q^83 - 222 * q^84 - 126 * q^85 + 90 * q^86 + 112 * q^87 + 2 * q^88 - 8 * q^89 + 72 * q^90 + 72 * q^91 - 132 * q^92 + 112 * q^93 - 42 * q^94 + 78 * q^95 + 68 * q^96 - 72 * q^97 - 16 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.629065	+	2.34770i	−0.444816	+	1.66008i	0.271605	+	0.962409i	$0.412445\pi$
$2$	−0.629065	+	2.34770i	−0.444816	+	1.66008i	−0.716422	+	0.697668i	$0.754221\pi$
$3$	−1.69619	−	0.350640i	−0.979294	−	0.202442i
$3$	−1.69619	−	0.350640i	−0.979294	−	0.202442i
$4$	−3.38393	−	1.95371i	−1.69197	−	0.976857i
$5$	0.435925	−	2.19316i	0.194951	−	0.980813i
$5$	0.435925	−	2.19316i	0.194951	−	0.980813i
$6$	1.89021	−	3.76157i	0.771675	−	1.53565i
$7$	1.65959	+	0.444685i	0.627265	+	0.168075i	0.558428	−	0.829553i	$-0.311405\pi$
$7$	1.65959	+	0.444685i	0.627265	+	0.168075i	0.0688368	+	0.997628i	$0.478071\pi$
$8$	3.27818	−	3.27818i	1.15901	−	1.15901i
$9$	2.75410	+	1.18950i	0.918034	+	0.396501i
$10$	4.87467	+	2.40306i	1.54151	+	0.759916i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	5.05473	+	4.50041i	1.45918	+	1.29916i
$13$	−5.97853	+	1.60194i	−1.65814	+	0.444299i	−0.961877	−	0.273483i	$-0.911824\pi$
$13$	−5.97853	+	1.60194i	−1.65814	+	0.444299i	−0.696268	+	0.717782i	$0.745158\pi$
$14$	−2.08798	+	3.61648i	−0.558035	+	0.966546i
$15$	−1.50842	+	3.56717i	−0.389473	+	0.921038i
$16$	1.72657	+	2.99051i	0.431643	+	0.747628i
$17$	4.36974	+	4.36974i	1.05982	+	1.05982i	0.998093	+	0.0617247i	$0.0196601\pi$
$17$	4.36974	+	4.36974i	1.05982	+	1.05982i	0.0617247	+	0.998093i	$0.480340\pi$
$18$	−4.52511	+	5.71754i	−1.06658	+	1.34764i
$19$			0.121312i			0.0278309i	0.999903	+	0.0139154i	$0.00442957\pi$
$19$			0.121312i			0.0278309i	−0.999903	+	0.0139154i	$0.995570\pi$
$20$	−5.75996	+	6.56985i	−1.28797	+	1.46906i
$21$	−2.65905	−	1.33619i	−0.580252	−	0.291580i
$22$	−0.629065	−	2.34770i	−0.134117	−	0.500532i
$23$	1.73646	+	6.48055i	0.362077	+	1.35129i	0.871341	+	0.490679i	$0.163251\pi$
$23$	1.73646	+	6.48055i	0.362077	+	1.35129i	−0.509264	+	0.860610i	$0.670082\pi$
$24$	−6.70987	+	4.41095i	−1.36965	+	0.900381i
$25$	−4.61994	−	1.91211i	−0.923988	−	0.382422i
$26$		−	15.0435i		−	2.95028i
$27$	−4.25439	−	2.98332i	−0.818757	−	0.574140i
$28$	−4.74715	−	4.74715i	−0.897126	−	0.897126i
$29$	0.446884	+	0.774026i	0.0829843	+	0.143733i	0.904530	−	0.426409i	$-0.140222\pi$
$29$	0.446884	+	0.774026i	0.0829843	+	0.143733i	−0.821546	+	0.570142i	$0.806888\pi$
$30$	−7.42575	−	5.78530i	−1.35575	−	1.05625i
$31$	−0.845872	+	1.46509i	−0.151923	+	0.263139i	−0.931934	−	0.362627i	$-0.881880\pi$
$31$	−0.845872	+	1.46509i	−0.151923	+	0.263139i	0.780011	+	0.625765i	$0.215213\pi$
$32$	0.849191	−	0.227540i	0.150117	−	0.0402238i
$33$	1.64426	−	0.544431i	0.286229	−	0.0947732i
$34$	−13.0077	+	7.51000i	−2.23080	+	1.28795i
$35$	1.69872	−	3.44590i	0.287137	−	0.582463i
$36$	−6.99576	−	9.40593i	−1.16596	−	1.56765i
$37$	−5.50427	+	5.50427i	−0.904897	+	0.904897i	−0.995855	−	0.0909578i	$-0.971007\pi$
$37$	−5.50427	+	5.50427i	−0.904897	+	0.904897i	0.0909578	+	0.995855i	$0.471007\pi$
$38$	−0.284805	−	0.0763132i	−0.0462014	−	0.0123796i
$39$	10.7024	−	0.620883i	1.71376	−	0.0994209i
$40$	−5.76055	−	8.61863i	−0.910823	−	1.36272i
$41$	2.63164	+	1.51938i	0.410993	+	0.237287i	0.691216	−	0.722648i	$-0.257075\pi$
$41$	2.63164	+	1.51938i	0.410993	+	0.237287i	−0.280223	+	0.959935i	$0.590409\pi$
$42$	4.80968	−	5.40210i	0.742150	−	0.833563i
$43$	−0.840639	+	3.13731i	−0.128196	+	0.478435i	−0.999933	−	0.0115388i	$-0.996327\pi$
$43$	−0.840639	+	3.13731i	−0.128196	+	0.478435i	0.871737	+	0.489974i	$0.162994\pi$
$44$	3.90743			0.589067
$45$	3.80935	−	5.52167i	0.567865	−	0.823122i
$46$	−16.3068			−2.40430
$47$	−2.33916	+	8.72985i	−0.341201	+	1.27338i	0.555787	+	0.831325i	$0.312417\pi$
$47$	−2.33916	+	8.72985i	−0.341201	+	1.27338i	−0.896988	+	0.442055i	$0.854250\pi$
$48$	−1.88000	−	5.67788i	−0.271355	−	0.819531i
$49$	−3.50569	−	2.02401i	−0.500813	−	0.289145i
$50$	7.39530	−	9.64340i	1.04585	−	1.36378i
$51$	−5.87969	−	8.94411i	−0.823322	−	1.25243i
$52$	23.3607	+	6.25947i	3.23954	+	0.868033i
$53$	6.96722	−	6.96722i	0.957022	−	0.957022i	−0.0420919	−	0.999114i	$-0.513402\pi$
$53$	6.96722	−	6.96722i	0.957022	−	0.957022i	0.999114	+	0.0420919i	$0.0134022\pi$
$54$	9.68023	−	8.11134i	1.31731	−	1.10381i
$55$	0.719060	+	2.11730i	0.0969581	+	0.285496i
$56$	6.89819	−	3.98267i	0.921809	−	0.532207i
$57$	0.0425368	−	0.205768i	0.00563414	−	0.0272546i
$58$	−2.09830	+	0.562238i	−0.275520	+	0.0738255i
$59$	−3.56502	+	6.17479i	−0.464126	+	0.803889i	−0.999162	−	0.0409402i	$-0.986965\pi$
$59$	−3.56502	+	6.17479i	−0.464126	+	0.803889i	0.535036	+	0.844829i	$0.320298\pi$
$60$	12.0736	−	9.12403i	1.55870	−	1.17791i
$61$	−4.93392	−	8.54580i	−0.631723	−	1.09418i	−0.987199	−	0.159492i	$-0.949015\pi$
$61$	−4.93392	−	8.54580i	−0.631723	−	1.09418i	0.355476	−	0.934685i	$-0.384319\pi$
$62$	−2.90749	−	2.90749i	−0.369252	−	0.369252i
$63$	4.04172	+	3.19879i	0.509209	+	0.403010i
$64$			9.04308i			1.13039i
$65$	0.907134	+	13.8102i	0.112516	+	1.71295i
$66$	0.243814	+	4.20272i	0.0300114	+	0.517319i
$67$	3.39507	+	12.6706i	0.414774	+	1.54796i	0.785287	+	0.619132i	$0.212515\pi$
$67$	3.39507	+	12.6706i	0.414774	+	1.54796i	−0.370513	+	0.928827i	$0.620818\pi$
$68$	−6.24968	−	23.3241i	−0.757886	−	2.82847i
$69$	−0.673020	−	11.6011i	−0.0810221	−	1.39661i
$70$	7.02134	+	6.15579i	0.839211	+	0.735758i
$71$			11.2337i			1.33319i	0.745418	+	0.666597i	$0.232250\pi$
$71$			11.2337i			1.33319i	−0.745418	+	0.666597i	$0.767750\pi$
$72$	12.9278	−	5.12905i	1.52356	−	0.604464i
$73$	2.61564	+	2.61564i	0.306138	+	0.306138i	0.843409	−	0.537271i	$-0.180545\pi$
$73$	2.61564	+	2.61564i	0.306138	+	0.306138i	−0.537271	+	0.843409i	$0.680545\pi$
$74$	−9.45985	−	16.3849i	−1.09969	−	1.90471i
$75$	7.16582	+	4.86323i	0.827438	+	0.561557i
$76$	0.237009	−	0.410512i	0.0271868	−	0.0470889i
$77$	−1.65959	+	0.444685i	−0.189128	+	0.0506766i
$78$	−5.27486	+	25.5166i	−0.597260	+	2.88919i
$79$	5.13437	−	2.96433i	0.577662	−	0.333513i	−0.182542	−	0.983198i	$-0.558432\pi$
$79$	5.13437	−	2.96433i	0.577662	−	0.333513i	0.760204	+	0.649685i	$0.225099\pi$
$80$	7.31134	−	2.48302i	0.817433	−	0.277610i
$81$	6.17017	+	6.55202i	0.685575	+	0.728002i
$82$	−5.22252	+	5.22252i	−0.576730	+	0.576730i
$83$	−6.05000	−	1.62109i	−0.664074	−	0.177938i	−0.0889902	−	0.996033i	$-0.528364\pi$
$83$	−6.05000	−	1.62109i	−0.664074	−	0.177938i	−0.575084	+	0.818094i	$0.695031\pi$
$84$	6.38751	+	9.71659i	0.696935	+	1.06017i
$85$	11.4884	−	7.67868i	1.24610	−	0.832870i
$86$	−6.83665	−	3.94714i	−0.737215	−	0.425631i
$87$	−0.486595	−	1.46959i	−0.0521684	−	0.157556i
$88$	−1.19990	+	4.47808i	−0.127909	+	0.477365i
$89$	−13.2222			−1.40155			−0.700773	−	0.713385i	$-0.747161\pi$
$89$	−13.2222			−1.40155			−0.700773	+	0.713385i	$0.747161\pi$
$90$	10.5669	+	12.4167i	1.11385	+	1.30884i
$91$	−10.6342			−1.11477
$92$	6.78509	−	25.3223i	0.707395	−	2.64003i
$93$	1.94848	−	2.18848i	0.202048	−	0.226934i
$94$	−19.0236	−	10.9833i	−1.96214	−	1.13284i
$95$	0.266057	+	0.0528829i	0.0272969	+	0.00542567i
$96$	−1.52017	+	0.0881904i	−0.155152	+	0.00900089i
$97$	−5.75725	−	1.54265i	−0.584560	−	0.156632i	−0.0455942	−	0.998960i	$-0.514518\pi$
$97$	−5.75725	−	1.54265i	−0.584560	−	0.156632i	−0.538966	+	0.842328i	$0.681185\pi$
$98$	6.95709	−	6.95709i	0.702772	−	0.702772i
$99$	−2.97987	+	0.346913i	−0.299489	+	0.0348661i
$100$	11.8979	+	15.4965i	1.18979	+	1.54965i
$101$	6.90626	−	3.98733i	0.687198	−	0.396754i	−0.115363	−	0.993323i	$-0.536803\pi$
$101$	6.90626	−	3.98733i	0.687198	−	0.396754i	0.802562	+	0.596569i	$0.203470\pi$
$102$	24.6968	−	8.17735i	2.44535	−	0.809678i
$103$	1.22934	−	0.329400i	0.121130	−	0.0324567i	−0.197745	−	0.980254i	$-0.563362\pi$
$103$	1.22934	−	0.329400i	0.121130	−	0.0324567i	0.318875	+	0.947797i	$0.396695\pi$
$104$	−14.3472	+	24.8501i	−1.40686	+	2.43676i
$105$	−4.08962	+	5.24925i	−0.399106	+	0.512274i
$106$	11.9741	+	20.7398i	1.16303	+	2.01443i
$107$	−2.36301	−	2.36301i	−0.228441	−	0.228441i	0.583600	−	0.812041i	$-0.301644\pi$
$107$	−2.36301	−	2.36301i	−0.228441	−	0.228441i	−0.812041	+	0.583600i	$0.801644\pi$
$108$	8.56802	+	18.4072i	0.824458	+	1.77123i
$109$			2.52041i			0.241411i	0.992688	+	0.120706i	$0.0385157\pi$
$109$			2.52041i			0.241411i	−0.992688	+	0.120706i	$0.961484\pi$
$110$	−5.42312	+	0.356222i	−0.517074	+	0.0339644i
$111$	11.2663	−	7.40626i	1.06935	−	0.702971i
$112$	1.53556	+	5.73080i	0.145097	+	0.541510i
$113$	1.15253	+	4.30130i	0.108421	+	0.404632i	0.998711	−	0.0507621i	$-0.0161650\pi$
$113$	1.15253	+	4.30130i	0.108421	+	0.404632i	−0.890290	+	0.455394i	$0.849498\pi$
$114$	0.456323	+	0.229305i	0.0427386	+	0.0214764i
$115$	14.9699	−	0.983308i	1.39595	−	0.0916939i
$116$		−	3.49233i		−	0.324255i
$117$	−18.3710	−	2.69956i	−1.69840	−	0.249574i
$118$	−12.2539	−	12.2539i	−1.12807	−	1.12807i
$119$	5.30881	+	9.19513i	0.486658	+	0.842916i
$120$	6.74894	+	16.6387i	0.616091	+	1.51890i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	23.1667	−	6.20751i	2.09742	−	0.562001i
$123$	−3.93100	−	3.49990i	−0.354446	−	0.315576i
$124$	5.72475	−	3.30519i	0.514098	−	0.296814i
$125$	−6.20751	+	9.29875i	−0.555217	+	0.831706i
$126$	−10.0523	+	7.47651i	−0.895532	+	0.666061i
$127$	3.15532	−	3.15532i	0.279990	−	0.279990i	−0.553115	−	0.833105i	$-0.686561\pi$
$127$	3.15532	−	3.15532i	0.279990	−	0.279990i	0.833105	+	0.553115i	$0.186561\pi$
$128$	−19.5321	−	5.23361i	−1.72641	−	0.462590i
$129$	2.52595	−	5.02670i	0.222397	−	0.442576i
$130$	−32.9929	−	6.55784i	−2.89367	−	0.575161i
$131$	5.20303	+	3.00397i	0.454591	+	0.262458i	0.709767	−	0.704437i	$-0.248800\pi$
$131$	5.20303	+	3.00397i	0.454591	+	0.262458i	−0.255176	+	0.966895i	$0.582134\pi$
$132$	−6.62773	−	1.37010i	−0.576870	−	0.119252i
$133$	−0.0539457	+	0.201328i	−0.00467768	+	0.0174573i
$134$	−31.8825			−2.75423
$135$	−8.39750	+	8.03007i	−0.722741	+	0.691119i
$136$	28.6496			2.45668
$137$	2.37301	−	8.85620i	0.202740	−	0.756636i	−0.787386	−	0.616460i	$-0.788566\pi$
$137$	2.37301	−	8.85620i	0.202740	−	0.756636i	0.990127	−	0.140177i	$-0.0447670\pi$
$138$	27.6593	+	5.71780i	2.35452	+	0.486731i
$139$	17.7032	+	10.2209i	1.50156	+	0.866928i	0.999998	+	0.00180897i	$0.000575812\pi$
$139$	17.7032	+	10.2209i	1.50156	+	0.866928i	0.501566	+	0.865120i	$0.332758\pi$
$140$	−12.4807	+	8.34187i	−1.05481	+	0.705017i
$141$	7.02868	−	13.9873i	0.591922	−	1.17794i
$142$	−26.3734	−	7.06672i	−2.21320	−	0.593026i
$143$	4.37659	−	4.37659i	0.365988	−	0.365988i
$144$	1.19794	+	10.2899i	0.0998285	+	0.857496i
$145$	1.89237	−	0.642673i	0.157153	−	0.0533711i
$146$	−7.78617	+	4.49534i	−0.644388	+	0.372037i
$147$	5.23661	+	4.66234i	0.431908	+	0.384543i
$148$	29.3799	−	7.87231i	2.41501	−	0.647100i
$149$	8.24870	−	14.2872i	0.675760	−	1.17045i	−0.300486	−	0.953786i	$-0.597149\pi$
$149$	8.24870	−	14.2872i	0.675760	−	1.17045i	0.976246	−	0.216665i	$-0.0695178\pi$
$150$	−15.9252	+	13.7639i	−1.30029	+	1.12382i
$151$	7.00584	+	12.1345i	0.570127	+	0.987489i	0.996552	+	0.0829660i	$0.0264393\pi$
$151$	7.00584	+	12.1345i	0.570127	+	0.987489i	−0.426426	+	0.904523i	$0.640227\pi$
$152$	0.397683	+	0.397683i	0.0322563	+	0.0322563i
$153$	6.83690	+	17.2325i	0.552731	+	1.39317i
$154$		−	4.17595i		−	0.336508i
$155$	2.84445	+	2.49381i	0.228472	+	0.200307i
$156$	−37.4293	−	18.8084i	−2.99674	−	1.50588i
$157$	−0.786990	−	2.93709i	−0.0628086	−	0.234405i	0.927385	−	0.374109i	$-0.122051\pi$
$157$	−0.786990	−	2.93709i	−0.0628086	−	0.234405i	−0.990193	+	0.139704i	$0.955385\pi$
$158$	3.72952	+	13.9187i	0.296704	+	1.10732i
$159$	−14.2607	+	9.37473i	−1.13095	+	0.743465i
$160$	−0.128850	−	1.96161i	−0.0101865	−	0.155079i
$161$			11.5272i			0.908473i
$162$	−19.2636	+	10.3641i	−1.51349	+	0.814279i
$163$	−7.20550	−	7.20550i	−0.564378	−	0.564378i	0.366170	−	0.930548i	$-0.380669\pi$
$163$	−7.20550	−	7.20550i	−0.564378	−	0.564378i	−0.930548	+	0.366170i	$0.880669\pi$
$164$	−5.93686	−	10.2829i	−0.463591	−	0.802963i
$165$	−0.477252	−	3.84347i	−0.0371540	−	0.299213i
$166$	7.61169	−	13.1838i	0.590782	−	1.02326i
$167$	−0.327115	+	0.0876503i	−0.0253130	+	0.00678259i	−0.271453	−	0.962452i	$-0.587504\pi$
$167$	−0.327115	+	0.0876503i	−0.0253130	+	0.00678259i	0.246140	+	0.969234i	$0.420838\pi$
$168$	−13.0971	+	4.33657i	−1.01046	+	0.334574i
$169$	21.9182	−	12.6545i	1.68602	−	0.973423i
$170$	10.8003	+	31.8018i	0.828344	+	2.43909i
$171$	−0.144301	+	0.334106i	−0.0110350	+	0.0255497i
$172$	8.97407	−	8.97407i	0.684267	−	0.684267i
$173$	−1.90335	−	0.510000i	−0.144709	−	0.0387746i	0.185738	−	0.982599i	$-0.440533\pi$
$173$	−1.90335	−	0.510000i	−0.144709	−	0.0387746i	−0.330446	+	0.943825i	$0.607199\pi$
$174$	3.75625	−	0.217913i	0.284761	−	0.0165200i
$175$	−6.81691	−	5.22773i	−0.515310	−	0.395179i
$176$	−2.99051	−	1.72657i	−0.225418	−	0.130145i
$177$	8.21206	−	9.22356i	0.617256	−	0.693285i
$178$	8.31759	−	31.0417i	0.623430	−	2.32667i
$179$	19.9146			1.48848			0.744242	−	0.667910i	$-0.232811\pi$
$179$	19.9146			1.48848			0.744242	+	0.667910i	$0.232811\pi$
$180$	−23.6784	+	11.2426i	−1.76488	+	0.837971i
$181$	−0.0289021			−0.00214828			−0.00107414	−	0.999999i	$-0.500342\pi$
$181$	−0.0289021			−0.00214828			−0.00107414	+	0.999999i	$0.500342\pi$
$182$	6.68963	−	24.9661i	0.495869	−	1.85061i
$183$	5.37235	+	16.2253i	0.397136	+	1.19941i
$184$	26.9369	+	15.5520i	1.98581	+	1.14651i
$185$	9.67233	+	14.4712i	0.711124	+	1.06395i
$186$	3.91217	+	5.95114i	0.286854	+	0.436359i
$187$	−5.96918	−	1.59944i	−0.436509	−	0.116962i
$188$	24.9712	−	24.9712i	1.82121	−	1.82121i
$189$	−5.73389	−	6.84294i	−0.417079	−	0.497751i
$190$	−0.291521	+	0.591356i	−0.0211491	+	0.0429015i
$191$	−0.987101	+	0.569903i	−0.0714241	+	0.0412367i	−0.535287	−	0.844670i	$-0.679796\pi$
$191$	−0.987101	+	0.569903i	−0.0714241	+	0.0412367i	0.463863	+	0.885907i	$0.346463\pi$
$192$	3.17087	−	15.3388i	0.228837	−	1.10698i
$193$	−9.39666	+	2.51783i	−0.676386	+	0.181237i	−0.580630	−	0.814168i	$-0.697194\pi$
$193$	−9.39666	+	2.51783i	−0.676386	+	0.181237i	−0.0957565	+	0.995405i	$0.530527\pi$
$194$	7.24337	−	12.5459i	0.520043	−	0.900742i
$195$	3.30374	−	23.7428i	0.236586	−	1.70026i
$196$	7.90868	+	13.6982i	0.564906	+	0.978446i
$197$	11.8760	+	11.8760i	0.846133	+	0.846133i	0.989648	−	0.143515i	$-0.0458405\pi$
$197$	11.8760	+	11.8760i	0.846133	+	0.846133i	−0.143515	+	0.989648i	$0.545840\pi$
$198$	1.06009	−	7.21409i	0.0753371	−	0.512683i
$199$		−	25.7543i		−	1.82568i	−0.408322	−	0.912838i	$-0.633886\pi$
$199$		−	25.7543i		−	1.82568i	0.408322	−	0.912838i	$-0.366114\pi$
$200$	−21.4132	+	8.87676i	−1.51414	+	0.627682i
$201$	−1.31587	−	22.6821i	−0.0928142	−	1.59987i
$202$	5.01658	+	18.7221i	0.352965	+	1.31728i
$203$	0.397445	+	1.48329i	0.0278952	+	0.104106i
$204$	2.42226	+	41.7535i	0.169592	+	2.92333i
$205$	4.47944	−	5.10928i	0.312858	−	0.356848i
$206$			3.09333i			0.215523i
$207$	−2.92624	+	19.9136i	−0.203388	+	1.38409i
$208$	−15.1130	−	15.1130i	−1.04790	−	1.04790i
$209$	−0.0606560	−	0.105059i	−0.00419566	−	0.00726710i
$210$	−9.75104	−	12.9033i	−0.672886	−	0.890415i
$211$	−7.61926	+	13.1969i	−0.524531	+	0.908515i	0.475061	+	0.879953i	$0.342426\pi$
$211$	−7.61926	+	13.1969i	−0.524531	+	0.908515i	−0.999592	+	0.0285620i	$0.990907\pi$
$212$	−37.1886	+	9.96465i	−2.55412	+	0.684375i
$213$	3.93898	−	19.0544i	0.269895	−	1.30559i
$214$	7.03414	−	4.06116i	0.480844	−	0.277615i
$215$	6.51418	+	3.21129i	0.444263	+	0.219008i
$216$	−23.7265	+	4.16680i	−1.61438	+	0.283515i
$217$	−2.05530	+	2.05530i	−0.139523	+	0.139523i
$218$	−5.91716	−	1.58550i	−0.400761	−	0.107384i
$219$	−3.51947	−	5.35377i	−0.237824	−	0.361774i
$220$	1.70334	−	8.56964i	0.114839	−	0.577765i
$221$	−33.1247	−	19.1245i	−2.22821	−	1.28646i
$222$	10.3005	+	31.1089i	0.691322	+	2.08789i
$223$	2.84238	−	10.6079i	0.190340	−	0.710357i	−0.803085	−	0.595865i	$-0.796809\pi$
$223$	2.84238	−	10.6079i	0.190340	−	0.710357i	0.993424	−	0.114492i	$-0.0365240\pi$
$224$	1.51049			0.100924
$225$	−10.4493	−	10.7616i	−0.696622	−	0.717438i
$226$	−10.8232			−0.719947
$227$	3.67608	−	13.7193i	0.243990	−	0.910584i	−0.729898	−	0.683556i	$-0.760432\pi$
$227$	3.67608	−	13.7193i	0.243990	−	0.910584i	0.973888	−	0.227028i	$-0.0729009\pi$
$228$	−0.545954	+	0.613200i	−0.0361567	+	0.0406102i
$229$	−11.2306	−	6.48401i	−0.742141	−	0.428475i	0.0807064	−	0.996738i	$-0.474282\pi$
$229$	−11.2306	−	6.48401i	−0.742141	−	0.428475i	−0.822847	+	0.568263i	$0.807616\pi$
$230$	−7.10852	+	35.7634i	−0.468722	+	2.35817i
$231$	2.97090	−	0.172352i	0.195471	−	0.0113399i
$232$	4.00236	+	1.07243i	0.262768	+	0.0704084i
$233$	12.4730	−	12.4730i	0.817131	−	0.817131i	−0.168560	−	0.985691i	$-0.553912\pi$
$233$	12.4730	−	12.4730i	0.817131	−	0.817131i	0.985691	+	0.168560i	$0.0539118\pi$
$234$	17.8943	−	41.4314i	1.16979	−	2.70846i
$235$	18.1263	+	8.93571i	1.18243	+	0.582901i
$236$	24.1276	−	13.9300i	1.57057	−	0.906769i
$237$	−9.74827	+	3.22775i	−0.633218	+	0.209665i
$238$	−24.9270	+	6.67917i	−1.61578	+	0.432946i
$239$	−1.86592	+	3.23186i	−0.120696	+	0.209052i	−0.920042	−	0.391819i	$-0.871846\pi$
$239$	−1.86592	+	3.23186i	−0.120696	+	0.209052i	0.799346	+	0.600871i	$0.205179\pi$
$240$	−13.2721	+	1.64802i	−0.856708	+	0.106379i
$241$	−4.66679	−	8.08311i	−0.300614	−	0.520679i	0.675661	−	0.737212i	$-0.263858\pi$
$241$	−4.66679	−	8.08311i	−0.300614	−	0.520679i	−0.976275	+	0.216533i	$0.930525\pi$
$242$	1.71864	+	1.71864i	0.110478	+	0.110478i
$243$	−8.16837	−	13.2770i	−0.524001	−	0.851718i
$244$			38.5579i			2.46841i
$245$	−5.96721	+	6.80624i	−0.381231	+	0.434835i
$246$	10.6896	−	7.02714i	0.681543	−	0.448034i
$247$	−0.194335	−	0.725267i	−0.0123652	−	0.0461477i
$248$	2.02992	+	7.57576i	0.128900	+	0.481061i
$249$	9.69352	+	4.87105i	0.614302	+	0.308690i
$250$	−17.9258	−	20.4229i	−1.13373	−	1.29166i
$251$			11.1472i			0.703608i	0.936074	+	0.351804i	$0.114432\pi$
$251$			11.1472i			0.703608i	−0.936074	+	0.351804i	$0.885568\pi$
$252$	−7.42739	−	18.7209i	−0.467882	−	1.17930i
$253$	−4.74410	−	4.74410i	−0.298259	−	0.298259i
$254$	5.42285	+	9.39266i	0.340260	+	0.589348i
$255$	−22.1790	+	8.99618i	−1.38890	+	0.563363i
$256$	15.5308	−	26.9002i	0.970676	−	1.68126i
$257$	−4.40386	+	1.18001i	−0.274705	+	0.0736071i	−0.393542	−	0.919307i	$-0.628750\pi$
$257$	−4.40386	+	1.18001i	−0.274705	+	0.0736071i	0.118836	+	0.992914i	$0.462084\pi$
$258$	10.2122	+	9.09229i	0.635785	+	0.566061i
$259$	−11.5825	+	6.68716i	−0.719701	+	0.415520i
$260$	23.9115	−	48.5051i	1.48293	−	3.00816i
$261$	0.310060	+	2.66332i	0.0191922	+	0.164855i
$262$	−10.3255	+	10.3255i	−0.637909	+	0.637909i
$263$	−20.5007	−	5.49314i	−1.26413	−	0.338722i	−0.436348	−	0.899778i	$-0.643728\pi$
$263$	−20.5007	−	5.49314i	−1.26413	−	0.338722i	−0.827778	+	0.561056i	$0.810395\pi$
$264$	3.60544	−	7.17493i	0.221900	−	0.441586i
$265$	−12.2431	−	18.3175i	−0.752087	−	1.12523i
$266$	−0.438723	−	0.253297i	−0.0268998	−	0.0155306i
$267$	22.4273	+	4.63621i	1.37253	+	0.283732i
$268$	13.2660	−	49.5094i	0.810351	−	3.02427i
$269$	−26.0526			−1.58845			−0.794227	−	0.607621i	$-0.792124\pi$
$269$	−26.0526			−1.58845			−0.794227	+	0.607621i	$0.792124\pi$
$270$	−13.5697	−	24.7663i	−0.825823	−	1.50723i
$271$	10.9457			0.664903			0.332452	−	0.943120i	$-0.392124\pi$
$271$	10.9457			0.664903			0.332452	+	0.943120i	$0.392124\pi$
$272$	−5.52309	+	20.6125i	−0.334887	+	1.24981i
$273$	18.0377	+	3.72879i	1.09169	+	0.225677i
$274$	19.2989	+	11.1423i	1.16589	+	0.673128i
$275$	4.95704	−	0.654035i	0.298921	−	0.0394398i
$276$	−20.3878	+	40.5723i	−1.22720	+	2.44216i
$277$	−29.5820	−	7.92648i	−1.77741	−	0.476256i	−0.787304	−	0.616566i	$-0.788524\pi$
$277$	−29.5820	−	7.92648i	−1.77741	−	0.476256i	−0.990108	+	0.140310i	$0.955190\pi$
$278$	−35.1322	+	35.1322i	−2.10709	+	2.10709i
$279$	−4.07235	+	3.02885i	−0.243805	+	0.181333i
$280$	−5.72756	−	16.8650i	−0.342287	−	1.00788i
$281$	7.48909	−	4.32383i	0.446762	−	0.257938i	−0.259700	−	0.965689i	$-0.583624\pi$
$281$	7.48909	−	4.32383i	0.446762	−	0.257938i	0.706462	+	0.707751i	$0.250290\pi$
$282$	28.4164	+	25.3001i	1.69217	+	1.50660i
$283$	−5.83012	+	1.56218i	−0.346565	+	0.0928617i	−0.427903	−	0.903825i	$-0.640747\pi$
$283$	−5.83012	+	1.56218i	−0.346565	+	0.0928617i	0.0813379	+	0.996687i	$0.474081\pi$
$284$	21.9474	−	38.0141i	1.30234	−	2.25572i
$285$	−0.432740	−	0.182990i	−0.0256333	−	0.0108394i
$286$	7.52176	+	13.0281i	0.444771	+	0.770366i
$287$	3.69179	+	3.69179i	0.217919	+	0.217919i
$288$	2.60942	+	0.383446i	0.153762	+	0.0225948i
$289$			21.1893i			1.24643i
$290$	0.318379	+	4.84701i	0.0186959	+	0.284626i
$291$	9.22446	+	4.63534i	0.540747	+	0.271729i
$292$	−3.74094	−	13.9614i	−0.218922	−	0.817029i
$293$	−2.35338	−	8.78295i	−0.137486	−	0.513105i	−0.999975	−	0.00702978i	$-0.997762\pi$
$293$	−2.35338	−	8.78295i	−0.137486	−	0.513105i	0.862489	−	0.506076i	$-0.168904\pi$
$294$	−14.2400	+	9.36109i	−0.830491	+	0.545950i
$295$	11.9882	+	10.5104i	0.697983	+	0.611940i
$296$			36.0880i			2.09757i
$297$	5.17607	+	0.456433i	0.300346	+	0.0264850i
$298$	28.3531	+	28.3531i	1.64245	+	1.64245i
$299$	−20.7629	−	35.9625i	−1.20075	−	2.07976i
$300$	−14.7473	−	30.4568i	−0.851436	−	1.75843i
$301$	−2.79023	+	4.83282i	−0.160826	+	0.278559i
$302$	−32.8952	+	8.81425i	−1.89291	+	0.507203i
$303$	−13.1124	+	4.34165i	−0.753289	+	0.249421i
$304$	−0.362785	+	0.209454i	−0.0208072	+	0.0120130i
$305$	−20.8931	+	7.09557i	−1.19634	+	0.406291i
$306$	−44.7577	+	5.21063i	−2.55863	+	0.297872i
$307$	−6.19549	+	6.19549i	−0.353595	+	0.353595i	−0.861445	−	0.507850i	$-0.830440\pi$
$307$	−6.19549	+	6.19549i	−0.353595	+	0.353595i	0.507850	+	0.861445i	$0.330440\pi$
$308$	6.48472	+	1.73758i	0.369501	+	0.0990076i
$309$	−2.20069	+	0.127669i	−0.125193	+	0.00726286i
$310$	−7.64406	+	5.10916i	−0.434154	+	0.290181i
$311$	7.96574	+	4.59902i	0.451696	+	0.260787i	0.708546	−	0.705664i	$-0.249351\pi$
$311$	7.96574	+	4.59902i	0.451696	+	0.260787i	−0.256850	+	0.966451i	$0.582685\pi$
$312$	33.0491	−	37.1198i	1.87103	−	2.10149i
$313$	−0.852982	+	3.18337i	−0.0482134	+	0.179935i	−0.985834	−	0.167727i	$-0.946357\pi$
$313$	−0.852982	+	3.18337i	−0.0482134	+	0.179935i	0.937620	+	0.347661i	$0.113024\pi$
$314$	7.39047			0.417068
$315$	8.77736	−	7.46973i	0.494548	−	0.420872i
$316$	−23.1658			−1.30318
$317$	−7.85324	+	29.3087i	−0.441082	+	1.64614i	0.284997	+	0.958529i	$0.408008\pi$
$317$	−7.85324	+	29.3087i	−0.441082	+	1.64614i	−0.726079	+	0.687612i	$0.758659\pi$
$318$	−13.0382	−	39.3772i	−0.731144	−	2.20816i
$319$	−0.774026	−	0.446884i	−0.0433371	−	0.0250207i
$320$	19.8330	+	3.94210i	1.10870	+	0.220370i
$321$	3.17955	+	4.83668i	0.177465	+	0.269957i
$322$	−27.0625	−	7.25137i	−1.50813	−	0.404103i
$323$	−0.530102	+	0.530102i	−0.0294957	+	0.0294957i
$324$	−8.07866	−	34.2264i	−0.448815	−	1.90146i
$325$	30.6835	+	4.03072i	1.70202	+	0.223584i
$326$	21.4491	−	12.3836i	1.18796	−	0.685867i
$327$	0.883755	−	4.27508i	0.0488717	−	0.236412i
$328$	13.6078	−	3.64619i	0.751364	−	0.201327i
$329$	−7.76407	+	13.4478i	−0.428047	+	0.741399i
$330$	9.32354	+	1.29734i	0.513244	+	0.0714164i
$331$	0.123305	+	0.213570i	0.00677744	+	0.0117389i	0.869394	−	0.494119i	$-0.164509\pi$
$331$	0.123305	+	0.213570i	0.00677744	+	0.0117389i	−0.862617	+	0.505858i	$0.831176\pi$
$332$	17.3057	+	17.3057i	0.949771	+	0.949771i
$333$	−21.7067	+	8.61199i	−1.18952	+	0.471934i
$334$		−	0.823108i		−	0.0450384i
$335$	29.2687	−	1.92253i	1.59912	−	0.105039i
$336$	−0.595156	−	10.2589i	−0.0324684	−	0.559671i
$337$	4.83680	+	18.0512i	0.263477	+	0.983311i	0.963176	+	0.268873i	$0.0866511\pi$
$337$	4.83680	+	18.0512i	0.263477	+	0.983311i	−0.699698	+	0.714439i	$0.746682\pi$
$338$	15.9210	+	59.4180i	0.865989	+	3.23191i
$339$	−0.446699	−	7.69993i	−0.0242614	−	0.418203i
$340$	−53.8781	+	3.53902i	−2.92195	+	0.191930i
$341$		−	1.69174i		−	0.0916131i
$342$	−0.693607	−	0.548950i	−0.0375059	−	0.0296838i
$343$	−13.4223	−	13.4223i	−0.724735	−	0.724735i
$344$	7.52889	+	13.0404i	0.405931	+	0.703093i
$345$	−25.7365	−	3.58117i	−1.38561	−	0.192803i
$346$	2.39466	−	4.14767i	0.128738	−	0.222980i
$347$	−10.8490	+	2.90698i	−0.582405	+	0.156055i	−0.537980	−	0.842958i	$-0.680812\pi$
$347$	−10.8490	+	2.90698i	−0.582405	+	0.156055i	−0.0444253	+	0.999013i	$0.514146\pi$
$348$	−1.22455	+	5.92365i	−0.0656429	+	0.317541i
$349$	23.6576	−	13.6587i	1.26636	−	0.731134i	0.292064	−	0.956399i	$-0.405658\pi$
$349$	23.6576	−	13.6587i	1.26636	−	0.731134i	0.974298	+	0.225265i	$0.0723248\pi$
$350$	16.5614	−	12.7155i	0.885246	−	0.679672i
$351$	30.2141	+	11.0206i	1.61271	+	0.588234i
$352$	−0.621651	+	0.621651i	−0.0331341	+	0.0331341i
$353$	0.705656	+	0.189080i	0.0375583	+	0.0100637i	0.277549	−	0.960711i	$-0.410478\pi$
$353$	0.705656	+	0.189080i	0.0375583	+	0.0100637i	−0.239991	+	0.970775i	$0.577144\pi$
$354$	16.4883	+	25.0817i	0.876341	+	1.33308i
$355$	24.6373	+	4.89704i	1.30761	+	0.259908i
$356$	44.7429	+	25.8323i	2.37137	+	1.36911i
$357$	−5.78056	−	17.4581i	−0.305940	−	0.923983i
$358$	−12.5275	+	46.7534i	−0.662101	+	2.47100i
$359$	17.1171			0.903403			0.451702	−	0.892169i	$-0.350817\pi$
$359$	17.1171			0.903403			0.451702	+	0.892169i	$0.350817\pi$
$360$	−5.61327	−	30.5888i	−0.295845	−	1.61217i
$361$	18.9853			0.999225
$362$	0.0181813	−	0.0678536i	0.000955589	−	0.00356631i
$363$	−1.15176	+	1.29362i	−0.0604516	+	0.0678975i
$364$	35.9856	+	20.7763i	1.88616	+	1.08897i
$365$	6.87676	−	4.59631i	0.359946	−	0.240582i
$366$	−41.4717	+	2.40592i	−2.16776	+	0.125759i
$367$	−24.7909	−	6.64270i	−1.29407	−	0.346746i	−0.454868	−	0.890559i	$-0.650314\pi$
$367$	−24.7909	−	6.64270i	−1.29407	−	0.346746i	−0.839207	+	0.543813i	$0.816980\pi$
$368$	−16.3821	+	16.3821i	−0.853974	+	0.853974i
$369$	5.44050	+	7.31486i	0.283221	+	0.380796i
$370$	−40.0587	+	13.6044i	−2.08255	+	0.707259i
$371$	14.6609	−	8.46450i	0.761158	−	0.439455i
$372$	−10.8692	+	3.59889i	−0.563541	+	0.186594i
$373$	−11.4807	+	3.07626i	−0.594451	+	0.159283i	−0.543486	−	0.839418i	$-0.682896\pi$
$373$	−11.4807	+	3.07626i	−0.594451	+	0.159283i	−0.0509641	+	0.998700i	$0.516229\pi$
$374$	7.51000	−	13.0077i	0.388333	−	0.672612i
$375$	13.7896	−	13.5958i	0.712093	−	0.702085i
$376$	20.9498	+	36.2862i	1.08041	+	1.87132i
$377$	−3.91165	−	3.91165i	−0.201460	−	0.201460i
$378$	19.6722	−	9.15682i	1.01183	−	0.470976i
$379$			9.40499i			0.483102i	0.970388	+	0.241551i	$0.0776561\pi$
$379$			9.40499i			0.483102i	−0.970388	+	0.241551i	$0.922344\pi$
$380$	−0.797002	−	0.698752i	−0.0408853	−	0.0358452i
$381$	−6.45840	+	4.24564i	−0.330874	+	0.217510i
$382$	−0.717012	−	2.67592i	−0.0366855	−	0.136912i
$383$	−7.59477	−	28.3441i	−0.388075	−	1.44831i	−0.833263	−	0.552877i	$-0.813530\pi$
$383$	−7.59477	−	28.3441i	−0.388075	−	1.44831i	0.445188	−	0.895437i	$-0.353137\pi$
$384$	31.2950	+	15.7259i	1.59701	+	0.802509i
$385$	0.251813	+	3.83360i	0.0128336	+	0.195378i
$386$		−	23.6444i		−	1.20347i
$387$	−6.04704	+	7.64053i	−0.307388	+	0.388390i
$388$	16.4682	+	16.4682i	0.836049	+	0.836049i
$389$	15.2157	+	26.3544i	0.771466	+	1.33622i	0.936759	+	0.349974i	$0.113810\pi$
$389$	15.2157	+	26.3544i	0.771466	+	1.33622i	−0.165293	+	0.986245i	$0.552857\pi$
$390$	53.6627	+	22.6920i	2.71732	+	1.14905i
$391$	−20.7305	+	35.9062i	−1.04838	+	1.81586i
$392$	−18.1274	+	4.85721i	−0.915570	+	0.245326i
$393$	−7.77200	−	6.91968i	−0.392045	−	0.349052i
$394$	−35.3522	+	20.4106i	−1.78102	+	1.02827i
$395$	−4.26307	−	12.5528i	−0.214498	−	0.631597i
$396$	10.7615	+	4.64789i	0.540784	+	0.233566i
$397$	27.1249	−	27.1249i	1.36136	−	1.36136i	0.489177	−	0.872184i	$-0.337297\pi$
$397$	27.1249	−	27.1249i	1.36136	−	1.36136i	0.872184	−	0.489177i	$-0.162703\pi$
$398$	60.4635	+	16.2011i	3.03076	+	0.812090i
$399$	0.162096	−	0.322574i	0.00811493	−	0.0161489i
$400$	−2.25848	−	17.1174i	−0.112924	−	0.855869i
$401$	−33.6309	−	19.4168i	−1.67945	−	0.969629i	−0.962014	−	0.273000i	$-0.911984\pi$
$401$	−33.6309	−	19.4168i	−1.67945	−	0.969629i	−0.717432	−	0.696629i	$-0.754683\pi$
$402$	54.0787	+	11.1793i	2.69720	+	0.557571i
$403$	2.71007	−	10.1141i	0.134998	−	0.503821i
$404$	−31.1604			−1.55029
$405$	17.0594	−	10.6760i	0.847688	−	0.530495i
$406$	−3.73233			−0.185233
$407$	2.01470	−	7.51898i	0.0998652	−	0.372702i
$408$	−48.5951	−	10.0457i	−2.40582	−	0.497336i
$409$	11.3312	+	6.54207i	0.560292	+	0.323485i	0.753263	−	0.657720i	$-0.228479\pi$
$409$	11.3312	+	6.54207i	0.560292	+	0.323485i	−0.192971	+	0.981205i	$0.561812\pi$
$410$	9.17721	+	13.7305i	0.453230	+	0.678099i
$411$	−7.13041	+	14.1897i	−0.351717	+	0.699926i
$412$	−4.80355	−	1.28711i	−0.236654	−	0.0634112i
$413$	−8.66229	+	8.66229i	−0.426244	+	0.426244i
$414$	−44.9105	−	19.3969i	−2.20723	−	0.953307i
$415$	−6.19267	+	12.5620i	−0.303986	+	0.616643i
$416$	−4.71241	+	2.72071i	−0.231045	+	0.133394i
$417$	−26.4440	−	23.5441i	−1.29497	−	1.15296i
$418$	0.284805	−	0.0763132i	0.0139302	−	0.00373260i
$419$	1.56943	−	2.71834i	0.0766718	−	0.132799i	−0.825140	−	0.564928i	$-0.808904\pi$
$419$	1.56943	−	2.71834i	0.0766718	−	0.132799i	0.901812	+	0.432128i	$0.142237\pi$
$420$	24.0945	−	9.77316i	1.17569	−	0.476881i
$421$	−1.44133	−	2.49646i	−0.0702462	−	0.121670i	0.828763	−	0.559600i	$-0.189045\pi$
$421$	−1.44133	−	2.49646i	−0.0702462	−	0.121670i	−0.899009	+	0.437930i	$0.855712\pi$
$422$	−26.1895	−	26.1895i	−1.27488	−	1.27488i
$423$	−16.8264	+	21.2605i	−0.818130	+	1.03372i
$424$		−	45.6796i		−	2.21840i
$425$	−11.8325	−	28.5434i	−0.573962	−	1.38456i
$426$	42.2563	+	21.2340i	2.04732	+	1.02879i
$427$	−4.38808	−	16.3765i	−0.212354	−	0.792516i
$428$	3.37962	+	12.6129i	0.163360	+	0.609669i
$429$	−8.95811	+	5.88890i	−0.432502	+	0.284319i
$430$	−11.6370	+	13.2732i	−0.561186	+	0.640092i
$431$			21.7347i			1.04692i	0.852050	+	0.523461i	$0.175359\pi$
$431$			21.7347i			1.04692i	−0.852050	+	0.523461i	$0.824641\pi$
$432$	1.57613	−	17.8737i	0.0758317	−	0.859950i
$433$	7.27828	+	7.27828i	0.349772	+	0.349772i	0.860025	−	0.510253i	$-0.170448\pi$
$433$	7.27828	+	7.27828i	0.349772	+	0.349772i	−0.510253	+	0.860025i	$0.670448\pi$
$434$	−3.53232	−	6.11816i	−0.169557	−	0.293681i
$435$	−3.43517	+	0.426552i	−0.164704	+	0.0204516i
$436$	4.92415	−	8.52888i	0.235824	−	0.408459i
$437$	−0.786169	+	0.210653i	−0.0376076	+	0.0100769i
$438$	14.7830	−	4.89481i	0.706361	−	0.233883i
$439$	20.4371	−	11.7993i	0.975408	−	0.563152i	0.0745275	−	0.997219i	$-0.476255\pi$
$439$	20.4371	−	11.7993i	0.975408	−	0.563152i	0.900881	+	0.434067i	$0.142922\pi$
$440$	9.29810	+	4.58368i	0.443269	+	0.218518i
$441$	−7.24747	−	9.74436i	−0.345118	−	0.464017i
$442$	65.7363	−	65.7363i	3.12676	−	3.12676i
$443$	37.4447	+	10.0333i	1.77905	+	0.476695i	0.990410	−	0.138158i	$-0.0441183\pi$
$443$	37.4447	+	10.0333i	1.77905	+	0.476695i	0.788641	+	0.614854i	$0.210785\pi$
$444$	−52.5941	+	3.05116i	−2.49601	+	0.144802i
$445$	−5.76386	+	28.9984i	−0.273233	+	1.37465i
$446$	23.1161	+	13.3461i	1.09458	+	0.631956i
$447$	−19.0010	+	21.3414i	−0.898716	+	1.00941i
$448$	−4.02132	+	15.0078i	−0.189990	+	0.709051i
$449$	−9.22532			−0.435370			−0.217685	−	0.976019i	$-0.569850\pi$
$449$	−9.22532			−0.435370			−0.217685	+	0.976019i	$0.569850\pi$
$450$	31.8383	−	17.7622i	1.50087	−	0.837318i
$451$	−3.03875			−0.143089
$452$	4.50343	−	16.8070i	0.211823	−	0.790536i
$453$	−7.62838	−	23.0388i	−0.358413	−	1.08246i
$454$	29.8964	+	17.2607i	1.40311	+	0.810085i
$455$	−4.63573	+	23.3227i	−0.217326	+	1.09338i
$456$	−0.535101	−	0.813988i	−0.0250584	−	0.0381185i
$457$	−12.4488	−	3.33565i	−0.582331	−	0.156035i	−0.0443852	−	0.999014i	$-0.514133\pi$
$457$	−12.4488	−	3.33565i	−0.582331	−	0.156035i	−0.537946	+	0.842979i	$0.680800\pi$
$458$	22.2873	−	22.2873i	1.04142	−	1.04142i
$459$	−5.55426	−	31.6269i	−0.259251	−	1.47622i
$460$	−52.5782	−	25.9194i	−2.45147	−	1.20850i
$461$	−12.9542	+	7.47911i	−0.603338	+	0.348337i	−0.770353	−	0.637617i	$-0.779920\pi$
$461$	−12.9542	+	7.47911i	−0.603338	+	0.348337i	0.167016	+	0.985954i	$0.446587\pi$
$462$	−1.46426	+	7.08320i	−0.0681233	+	0.329540i
$463$	−14.1915	+	3.80260i	−0.659534	+	0.176722i	−0.573036	−	0.819530i	$-0.694234\pi$
$463$	−14.1915	+	3.80260i	−0.659534	+	0.176722i	−0.0864983	+	0.996252i	$0.527568\pi$
$464$	−1.54316	+	2.67282i	−0.0716392	+	0.124083i
$465$	−3.95030	−	5.22734i	−0.183191	−	0.242412i
$466$	21.4365	+	37.1291i	0.993027	+	1.71997i
$467$	3.99190	+	3.99190i	0.184723	+	0.184723i	0.793410	−	0.608687i	$-0.208304\pi$
$467$	3.99190	+	3.99190i	0.184723	+	0.184723i	−0.608687	+	0.793410i	$0.708304\pi$
$468$	56.8921	+	45.0268i	2.62984	+	2.08136i
$469$			22.5377i			1.04069i
$470$	−32.3810	+	36.9340i	−1.49362	+	1.70364i
$471$	0.305023	+	5.25780i	0.0140547	+	0.242267i
$472$	8.55531	+	31.9288i	0.393790	+	1.46964i
$473$	−0.840639	−	3.13731i	−0.0386526	−	0.144254i
$474$	−1.44549	−	24.9165i	−0.0663936	−	1.14445i
$475$	0.231962	−	0.560454i	0.0106431	−	0.0257154i
$476$		−	41.4876i		−	1.90158i
$477$	27.4760	−	10.9009i	1.25804	−	0.499119i
$478$	−6.41366	−	6.41366i	−0.293354	−	0.293354i
$479$	13.9054	+	24.0848i	0.635354	+	1.10046i	0.986440	+	0.164122i	$0.0524790\pi$
$479$	13.9054	+	24.0848i	0.635354	+	1.10046i	−0.351087	+	0.936343i	$0.614188\pi$
$480$	−0.469265	+	3.37243i	−0.0214189	+	0.153930i
$481$	24.0899	−	41.7250i	1.09841	−	1.90249i
$482$	21.9125	−	5.87142i	0.998085	−	0.267436i
$483$	4.04191	−	19.5523i	0.183913	−	0.889662i
$484$	−3.38393	+	1.95371i	−0.153815	+	0.0888052i
$485$	−5.89301	+	11.9541i	−0.267588	+	0.542808i
$486$	36.3088	−	10.8248i	1.64700	−	0.491024i
$487$	8.61733	−	8.61733i	0.390488	−	0.390488i	−0.484373	−	0.874862i	$-0.660952\pi$
$487$	8.61733	−	8.61733i	0.390488	−	0.390488i	0.874862	+	0.484373i	$0.160952\pi$
$488$	−44.1889	−	11.8404i	−2.00034	−	0.535989i
$489$	9.69534	+	14.7484i	0.438439	+	0.666946i
$490$	−12.2253	−	18.2908i	−0.552281	−	0.826294i
$491$	−28.2955	−	16.3364i	−1.27696	−	0.737251i	−0.300668	−	0.953729i	$-0.597210\pi$
$491$	−28.2955	−	16.3364i	−1.27696	−	0.737251i	−0.976288	+	0.216478i	$0.930543\pi$
$492$	6.46441	+	19.5235i	0.291438	+	0.880187i
$493$	−1.42952	+	5.33506i	−0.0643825	+	0.240279i
$494$	1.82496			0.0821089
$495$	−0.538164	+	6.68658i	−0.0241887	+	0.300540i
$496$	−5.84184			−0.262306
$497$	−4.99546	+	18.6433i	−0.224077	+	0.836266i
$498$	−17.5336	+	19.6933i	−0.785701	+	0.882478i
$499$	−26.6913	−	15.4102i	−1.19486	−	0.689856i	−0.235459	−	0.971884i	$-0.575659\pi$
$499$	−26.6913	−	15.4102i	−1.19486	−	0.689856i	−0.959406	+	0.282029i	$0.908993\pi$
$500$	39.1729	−	19.3386i	1.75187	−	0.864850i
$501$	0.585583	−	0.0339717i	0.0261619	−	0.00151774i
$502$	−26.1704	−	7.01234i	−1.16804	−	0.312976i
$503$	3.08953	−	3.08953i	0.137755	−	0.137755i	−0.634866	−	0.772622i	$-0.718945\pi$
$503$	3.08953	−	3.08953i	0.137755	−	0.137755i	0.772622	+	0.634866i	$0.218945\pi$
$504$	23.7357	−	2.76328i	1.05727	−	0.123086i
$505$	−5.73426	−	16.8847i	−0.255171	−	0.751361i
$506$	14.1221	−	8.15338i	0.627803	−	0.362462i
$507$	−41.6146	+	13.7790i	−1.84817	+	0.611947i
$508$	−16.8420	+	4.51280i	−0.747243	+	0.200223i
$509$	−2.23757	+	3.87559i	−0.0991787	+	0.171783i	−0.911345	−	0.411644i	$-0.864955\pi$
$509$	−2.23757	+	3.87559i	−0.0991787	+	0.171783i	0.812166	+	0.583426i	$0.198288\pi$
$510$	−7.16833	−	57.7289i	−0.317419	−	2.55628i
$511$	3.17775	+	5.50403i	0.140576	+	0.243484i
$512$	24.7867	+	24.7867i	1.09543	+	1.09543i
$513$	0.361912	−	0.516109i	0.0159788	−	0.0227867i
$514$		−	11.0813i		−	0.488774i
$515$	−0.186530	−	2.83973i	−0.00821949	−	0.125134i
$516$	−18.3684	+	12.0750i	−0.808623	+	0.531574i
$517$	−2.33916	−	8.72985i	−0.102876	−	0.383938i
$518$	−8.41331	−	31.3989i	−0.369660	−	1.37959i
$519$	3.04961	+	1.53244i	0.133863	+	0.0672669i
$520$	48.2461	+	42.2986i	2.11573	+	1.85492i
$521$			10.6602i			0.467030i	0.972353	+	0.233515i	$0.0750228\pi$
$521$			10.6602i			0.467030i	−0.972353	+	0.233515i	$0.924977\pi$
$522$	−6.44772	−	0.947471i	−0.282209	−	0.0414697i
$523$	−11.7724	−	11.7724i	−0.514773	−	0.514773i	0.401212	−	0.915985i	$-0.368589\pi$
$523$	−11.7724	−	11.7724i	−0.514773	−	0.514773i	−0.915985	+	0.401212i	$0.868589\pi$
$524$	−11.7378	−	20.3305i	−0.512768	−	0.888140i
$525$	9.72970	+	11.2575i	0.424639	+	0.491317i
$526$	25.7925	−	44.6740i	1.12461	−	1.94788i
$527$	−10.0983	+	2.70584i	−0.439890	+	0.117868i
$528$	4.46707	+	3.97719i	0.194404	+	0.173085i
$529$	−19.0637	+	11.0064i	−0.828857	+	0.478541i
$530$	50.7056	−	17.2203i	2.20251	−	0.748000i
$531$	−17.1633	+	12.7654i	−0.744826	+	0.553972i
$532$	0.575886	−	0.575886i	0.0249678	−	0.0249678i
$533$	−18.1673	−	4.86790i	−0.786912	−	0.210852i
$534$	−24.9927	+	49.7360i	−1.08154	+	2.15229i
$535$	−6.21257	+	4.15238i	−0.268593	+	0.179523i
$536$	52.6661	+	30.4068i	2.27483	+	1.31337i
$537$	−33.7788	−	6.98284i	−1.45766	−	0.301332i
$538$	16.3888	−	61.1637i	0.706570	−	2.63695i
$539$	4.04802			0.174361
$540$	44.1050	−	10.7669i	1.89798	−	0.463334i
$541$	23.3263			1.00288			0.501438	−	0.865194i	$-0.332805\pi$
$541$	23.3263			1.00288			0.501438	+	0.865194i	$0.332805\pi$
$542$	−6.88555	+	25.6972i	−0.295760	+	1.10379i
$543$	0.0490235	+	0.0101342i	0.00210380	+	0.000434902i
$544$	4.70504	+	2.71646i	0.201727	+	0.116467i
$545$	5.52766	+	1.09871i	0.236779	+	0.0470634i
$546$	−20.1010	+	40.0015i	−0.860242	+	1.71190i
$547$	26.3721	+	7.06639i	1.12759	+	0.302137i	0.773952	−	0.633245i	$-0.218277\pi$
$547$	26.3721	+	7.06639i	1.12759	+	0.302137i	0.353640	+	0.935382i	$0.384944\pi$
$548$	−25.3326	+	25.3326i	−1.08216	+	1.08216i
$549$	−3.42328	−	29.4049i	−0.146102	−	1.25497i
$550$	−1.58282	+	12.0491i	−0.0674917	+	0.513775i
$551$	−0.0938986	+	0.0542124i	−0.00400022	+	0.00230953i
$552$	−40.2368	−	35.8242i	−1.71259	−	1.52478i
$553$	9.83914	−	2.63639i	0.418403	−	0.112111i
$554$	37.2180	−	64.4635i	1.58124	−	2.73879i
$555$	−11.3319	−	27.9374i	−0.481012	−	1.18588i
$556$	−39.9376	−	69.1739i	−1.69373	−	2.93363i
$557$	31.4507	+	31.4507i	1.33261	+	1.33261i	0.903031	+	0.429576i	$0.141337\pi$
$557$	31.4507	+	31.4507i	1.33261	+	1.33261i	0.429576	+	0.903031i	$0.358663\pi$
$558$	−4.54907	−	11.4660i	−0.192578	−	0.485395i
$559$		−	20.1031i		−	0.850272i
$560$	13.2380	−	0.869546i	0.559407	−	0.0367450i
$561$	9.56402	+	4.80598i	0.403793	+	0.202908i
$562$	5.43994	+	20.3021i	0.229470	+	0.856393i
$563$	11.0498	+	41.2386i	0.465695	+	1.73800i	0.654573	+	0.755999i	$0.272848\pi$
$563$	11.0498	+	41.2386i	0.465695	+	1.73800i	−0.188878	+	0.982001i	$0.560485\pi$
$564$	−51.1117	+	33.5999i	−2.15219	+	1.41481i
$565$	9.93587	−	0.652645i	0.418005	−	0.0274570i
$566$		−	14.6701i		−	0.616630i
$567$	7.32635	+	13.6174i	0.307678	+	0.571879i
$568$	36.8261	+	36.8261i	1.54519	+	1.54519i
$569$	10.4709	+	18.1362i	0.438965	+	0.760310i	0.997610	−	0.0690973i	$-0.0220119\pi$
$569$	10.4709	+	18.1362i	0.438965	+	0.760310i	−0.558645	+	0.829407i	$0.688679\pi$
$570$	0.701827	−	0.900833i	0.0293963	−	0.0377317i
$571$	−12.1458	+	21.0372i	−0.508287	+	0.880379i	0.491667	+	0.870783i	$0.336388\pi$
$571$	−12.1458	+	21.0372i	−0.508287	+	0.880379i	−0.999954	+	0.00959542i	$0.996946\pi$
$572$	−23.3607	+	6.25947i	−0.976759	+	0.261722i
$573$	1.87414	−	0.620545i	0.0782933	−	0.0259236i
$574$	−10.9896	+	6.34485i	−0.458697	+	0.264829i
$575$	4.36919	−	33.2601i	0.182208	−	1.38704i
$576$	−10.7568	+	24.9056i	−0.448198	+	1.03773i
$577$	15.6364	−	15.6364i	0.650952	−	0.650952i	−0.302271	−	0.953222i	$-0.597745\pi$
$577$	15.6364	−	15.6364i	0.650952	−	0.650952i	0.953222	+	0.302271i	$0.0977446\pi$
$578$	−49.7461	−	13.3294i	−2.06917	−	0.554431i
$579$	16.8213	−	0.975864i	0.699071	−	0.0405555i
$580$	−7.65926	−	1.52239i	−0.318034	−	0.0632140i
$581$	−9.31964	−	5.38069i	−0.386644	−	0.223229i
$582$	−16.6852	+	18.7403i	−0.691624	+	0.776812i
$583$	−2.55018	+	9.51741i	−0.105618	+	0.394171i
$584$	17.1491			0.709635
$585$	−13.9289	+	39.1138i	−0.575891	+	1.61716i
$586$	22.1002			0.912950
$587$	−9.32215	+	34.7908i	−0.384767	+	1.43597i	0.453768	+	0.891120i	$0.350079\pi$
$587$	−9.32215	+	34.7908i	−0.384767	+	1.43597i	−0.838535	+	0.544848i	$0.816587\pi$
$588$	−8.61146	−	26.0079i	−0.355131	−	1.07255i
$589$	−0.177733	−	0.102614i	−0.00732338	−	0.00422815i
$590$	−32.2167	+	21.5331i	−1.32634	+	0.886504i
$591$	−15.9798	−	24.3082i	−0.657321	−	0.999907i
$592$	−25.9641	−	6.95707i	−1.06712	−	0.285934i
$593$	17.1023	−	17.1023i	0.702308	−	0.702308i	−0.262597	−	0.964906i	$-0.584579\pi$
$593$	17.1023	−	17.1023i	0.702308	−	0.702308i	0.964906	+	0.262597i	$0.0845791\pi$
$594$	−4.32765	+	11.8647i	−0.177566	+	0.486816i
$595$	22.4807	−	7.63471i	0.921617	−	0.312993i
$596$	−55.8261	+	32.2312i	−2.28673	+	1.32024i
$597$	−9.03049	+	43.6842i	−0.369594	+	1.78787i
$598$	97.4904	−	26.1225i	3.98668	−	1.06823i
$599$	−6.23915	+	10.8065i	−0.254925	+	0.441543i	−0.964875	−	0.262709i	$-0.915384\pi$
$599$	−6.23915	+	10.8065i	−0.254925	+	0.441543i	0.709950	+	0.704252i	$0.248717\pi$
$600$	39.4334	−	7.54831i	1.60986	−	0.308159i
$601$	−1.53918	−	2.66594i	−0.0627846	−	0.108746i	0.832925	−	0.553387i	$-0.186665\pi$
$601$	−1.53918	−	2.66594i	−0.0627846	−	0.108746i	−0.895709	+	0.444641i	$0.853331\pi$
$602$	−9.59078	−	9.59078i	−0.390891	−	0.390891i
$603$	−5.72130	+	38.9346i	−0.232989	+	1.58554i
$604$		−	54.7496i		−	2.22773i
$605$	−1.68137	−	1.47410i	−0.0683576	−	0.0599308i
$606$	−1.94433	−	33.5153i	−0.0789832	−	1.36146i
$607$	−11.7638	−	43.9030i	−0.477477	−	1.78197i	−0.611782	−	0.791027i	$-0.709547\pi$
$607$	−11.7638	−	43.9030i	−0.477477	−	1.78197i	0.134305	−	0.990940i	$-0.457120\pi$
$608$	0.0276034	+	0.103017i	0.00111946	+	0.00417790i
$609$	−0.154042	−	2.65529i	−0.00624212	−	0.107598i
$610$	−3.51514	−	53.5145i	−0.142324	−	2.16674i
$611$		−	55.9388i		−	2.26304i
$612$	10.5318	−	71.6711i	0.425724	−	2.89713i
$613$	9.65198	+	9.65198i	0.389840	+	0.389840i	0.874630	−	0.484790i	$-0.161104\pi$
$613$	9.65198	+	9.65198i	0.389840	+	0.389840i	−0.484790	+	0.874630i	$0.661104\pi$
$614$	−10.6478	−	18.4425i	−0.429710	−	0.744280i
$615$	−9.38948	+	7.09563i	−0.378621	+	0.286123i
$616$	−3.98267	+	6.89819i	−0.160466	+	0.277936i
$617$	20.2519	−	5.42647i	0.815310	−	0.218462i	0.173015	−	0.984919i	$-0.444649\pi$
$617$	20.2519	−	5.42647i	0.815310	−	0.218462i	0.642295	+	0.766458i	$0.277982\pi$
$618$	1.08465	−	5.24687i	0.0436308	−	0.211060i
$619$	24.6352	−	14.2231i	0.990173	−	0.571677i	0.0848469	−	0.996394i	$-0.472960\pi$
$619$	24.6352	−	14.2231i	0.990173	−	0.571677i	0.905326	+	0.424717i	$0.139627\pi$
$620$	−4.75326	−	13.9961i	−0.190895	−	0.562098i
$621$	11.9460	−	32.7512i	0.479375	−	1.31426i
$622$	−15.8081	+	15.8081i	−0.633848	+	0.633848i
$623$	−21.9433	−	5.87970i	−0.879141	−	0.235565i
$624$	20.3353	+	30.9337i	0.814062	+	1.23834i
$625$	17.6877	+	17.6677i	0.707507	+	0.706706i
$626$	−6.93703	−	4.00509i	−0.277259	−	0.160076i
$627$	0.0660460	+	0.199469i	0.00263762	+	0.00796601i
$628$	−3.07511	+	11.4765i	−0.122710	+	0.457960i
$629$	−48.1045			−1.91805
$630$	12.0152	+	25.3056i	0.478696	+	1.00820i
$631$	−15.1092			−0.601488			−0.300744	−	0.953705i	$-0.597235\pi$
$631$	−15.1092			−0.601488			−0.300744	+	0.953705i	$0.597235\pi$
$632$	7.11379	−	26.5490i	0.282971	−	1.05606i
$633$	17.5511	−	19.7129i	0.697592	−	0.783516i
$634$	−63.8679	−	36.8741i	−2.53652	−	1.46446i
$635$	−5.54466	−	8.29562i	−0.220033	−	0.329202i
$636$	66.5728	−	3.86212i	2.63978	−	0.153143i
$637$	24.2012	+	6.48470i	0.958887	+	0.256933i
$638$	1.53606	−	1.53606i	0.0608133	−	0.0608133i
$639$	−13.3625	+	30.9388i	−0.528612	+	1.22392i
$640$	−19.9927	+	40.5556i	−0.790280	+	1.60310i
$641$	36.3252	−	20.9723i	1.43476	−	0.828358i	0.437279	−	0.899326i	$-0.355942\pi$
$641$	36.3252	−	20.9723i	1.43476	−	0.828358i	0.997479	+	0.0709678i	$0.0226088\pi$
$642$	−13.3552	+	4.42204i	−0.527089	+	0.174524i
$643$	7.33113	−	1.96437i	0.289112	−	0.0774672i	−0.111348	−	0.993781i	$-0.535517\pi$
$643$	7.33113	−	1.96437i	0.289112	−	0.0774672i	0.400460	+	0.916314i	$0.368850\pi$
$644$	22.5209	−	39.0074i	0.887448	−	1.53711i
$645$	−9.92326	−	7.73108i	−0.390728	−	0.304411i
$646$	−0.911054	−	1.57799i	−0.0358449	−	0.0620852i
$647$	8.86824	+	8.86824i	0.348646	+	0.348646i	0.859605	−	0.510959i	$-0.170710\pi$
$647$	8.86824	+	8.86824i	0.348646	+	0.348646i	−0.510959	+	0.859605i	$0.670710\pi$
$648$	41.7056	+	1.25178i	1.63835	+	0.0491744i
$649$		−	7.13003i		−	0.279878i
$650$	−28.7649	+	69.5002i	−1.12825	+	2.72602i
$651$	4.20685	−	2.76551i	0.164880	−	0.108389i
$652$	10.3054	+	38.4604i	0.403592	+	1.50623i
$653$	−5.24000	−	19.5560i	−0.205057	−	0.765284i	−0.989432	−	0.144997i	$-0.953683\pi$
$653$	−5.24000	−	19.5560i	−0.205057	−	0.765284i	0.784375	−	0.620287i	$-0.212984\pi$
$654$	9.48068	+	4.76410i	0.370724	+	0.186291i
$655$	8.85632	−	10.1016i	0.346045	−	0.394702i
$656$			10.4933i			0.409693i
$657$	4.09244	+	10.3151i	0.159661	+	0.402429i
$658$	−26.6872	−	26.6872i	−1.04038	−	1.04038i
$659$	−15.2483	−	26.4108i	−0.593989	−	1.02882i	−0.993689	−	0.112172i	$-0.964219\pi$
$659$	−15.2483	−	26.4108i	−0.593989	−	1.02882i	0.399700	−	0.916646i	$-0.369114\pi$
$660$	−5.89405	+	13.9384i	−0.229425	+	0.542553i
$661$	−8.35070	+	14.4638i	−0.324805	+	0.562578i	−0.981473	−	0.191602i	$-0.938632\pi$
$661$	−8.35070	+	14.4638i	−0.324805	+	0.562578i	0.656668	+	0.754180i	$0.271965\pi$
$662$	−0.578966	+	0.155133i	−0.0225021	+	0.00602943i
$663$	49.4798	+	44.0536i	1.92164	+	1.71090i
$664$	−25.1472	+	14.5188i	−0.975902	+	0.563437i
$665$	0.418029	+	0.206076i	0.0162105	+	0.00799127i
$666$	−6.56349	−	56.3783i	−0.254330	−	2.18462i
$667$	−4.24012	+	4.24012i	−0.164178	+	0.164178i
$668$	1.27818	+	0.342487i	0.0494543	+	0.0132512i
$669$	−8.54075	+	16.9963i	−0.330204	+	0.657116i
$670$	−13.8984	+	69.9236i	−0.536941	+	2.70138i
$671$	8.54580	+	4.93392i	0.329907	+	0.190472i
$672$	−2.56208	−	0.529638i	−0.0988342	−	0.0204312i
$673$	−9.42616	+	35.1789i	−0.363352	+	1.35605i	0.506290	+	0.862364i	$0.331017\pi$
$673$	−9.42616	+	35.1789i	−0.363352	+	1.35605i	−0.869641	+	0.493684i	$0.835650\pi$
$674$	−45.4215			−1.74957
$675$	13.9506	+	21.9176i	0.536959	+	0.843609i
$676$	−98.8931			−3.80358
$677$	4.37757	−	16.3373i	0.168244	−	0.627894i	−0.829361	−	0.558714i	$-0.811295\pi$
$677$	4.37757	−	16.3373i	0.168244	−	0.627894i	0.997604	−	0.0691799i	$-0.0220382\pi$
$678$	18.3581	+	3.79504i	0.705040	+	0.145748i
$679$	−8.86866	−	5.12033i	−0.340348	−	0.196500i
$680$	12.4891	−	62.8333i	0.478934	−	2.40955i
$681$	−11.0459	+	21.9816i	−0.423279	+	0.842336i
$682$	3.97171	+	1.06422i	0.152085	+	0.0407510i
$683$	−1.27738	+	1.27738i	−0.0488775	+	0.0488775i	−0.731123	−	0.682246i	$-0.761003\pi$
$683$	−1.27738	+	1.27738i	−0.0488775	+	0.0488775i	0.682246	+	0.731123i	$0.261003\pi$
$684$	1.14105	−	0.848669i	0.0436292	−	0.0324497i
$685$	−18.3886	−	9.06504i	−0.702594	−	0.346357i
$686$	39.9550	−	23.0680i	1.52549	−	0.880741i
$687$	16.7757	+	14.9360i	0.640033	+	0.569844i
$688$	−10.8336	+	2.90285i	−0.413027	+	0.110670i
$689$	−30.4927	+	52.8148i	−1.16168	+	2.01208i
$690$	24.5975	−	58.1689i	0.936409	−	2.21445i
$691$	17.1455	+	29.6969i	0.652245	+	1.12972i	0.982577	+	0.185857i	$0.0595060\pi$
$691$	17.1455	+	29.6969i	0.652245	+	1.12972i	−0.330332	+	0.943865i	$0.607161\pi$
$692$	5.44440	+	5.44440i	0.206965	+	0.206965i
$693$	−5.09963	−	0.749374i	−0.193719	−	0.0284663i
$694$		−	27.2989i		−	1.03625i
$695$	30.1334	−	34.3704i	1.14303	−	1.30374i
$696$	−6.41272	−	3.22243i	−0.243073	−	0.122146i
$697$	4.86029	+	18.1389i	0.184097	+	0.687058i
$698$	17.1844	+	64.1332i	0.650440	+	2.42748i
$699$	−25.5300	+	16.7830i	−0.965633	+	0.634790i
$700$	12.8545	+	31.0086i	0.485853	+	1.17201i
$701$		−	5.72568i		−	0.216256i	−0.994137	−	0.108128i	$-0.965514\pi$
$701$		−	5.72568i		−	0.216256i	0.994137	−	0.108128i	$-0.0344856\pi$
$702$	−44.8796	+	64.0010i	−1.69387	+	2.41556i
$703$	−0.667735	−	0.667735i	−0.0251841	−	0.0251841i
$704$	−4.52154	−	7.83154i	−0.170412	−	0.295162i
$705$	−27.6124	−	21.5124i	−1.03994	−	0.810205i
$706$	−0.887807	+	1.53773i	−0.0334130	+	0.0578731i
$707$	13.2346	−	3.54621i	0.497740	−	0.133369i
$708$	−45.8093	+	15.1679i	−1.72162	+	0.570044i
$709$	11.4688	−	6.62149i	0.430718	−	0.248675i	−0.268934	−	0.963159i	$-0.586671\pi$
$709$	11.4688	−	6.62149i	0.430718	−	0.248675i	0.699653	+	0.714483i	$0.253338\pi$
$710$	−26.9953	+	54.7606i	−1.01311	+	2.05513i
$711$	17.6667	−	2.05673i	0.662552	−	0.0771334i
$712$	−43.3446	+	43.3446i	−1.62441	+	1.62441i
$713$	−10.9634	−	2.93764i	−0.410584	−	0.110016i
$714$	44.6229	−	2.58872i	1.66997	−	0.0968806i
$715$	−7.69071	−	11.5064i	−0.287616	−	0.430316i
$716$	−67.3895	−	38.9074i	−2.51846	−	1.45404i
$717$	4.29816	−	4.82758i	0.160518	−	0.180289i
$718$	−10.7677	+	40.1857i	−0.401848	+	1.49972i
$719$	−21.1710			−0.789545			−0.394772	−	0.918779i	$-0.629177\pi$
$719$	−21.1710			−0.789545			−0.394772	+	0.918779i	$0.629177\pi$
$720$	23.0898	+	1.85836i	0.860504	+	0.0692569i
$721$	2.18667			0.0814359
$722$	−11.9430	+	44.5718i	−0.444472	+	1.65879i
$723$	5.08148	+	15.3468i	0.188982	+	0.570755i
$724$	0.0978029	+	0.0564665i	0.00363482	+	0.00209856i
$725$	−0.584556	−	4.43044i	−0.0217098	−	0.164542i
$726$	−2.31251	−	3.51775i	−0.0858252	−	0.130556i
$727$	−10.3089	−	2.76227i	−0.382337	−	0.102447i	0.0625310	−	0.998043i	$-0.480083\pi$
$727$	−10.3089	−	2.76227i	−0.382337	−	0.102447i	−0.444868	+	0.895596i	$0.646749\pi$
$728$	−34.8610	+	34.8610i	−1.29203	+	1.29203i
$729$	9.19965	+	25.3844i	0.340728	+	0.940162i
$730$	6.46485	+	19.0360i	0.239275	+	0.704553i
$731$	−17.3826	+	10.0358i	−0.642919	+	0.371189i
$732$	13.5199	−	65.4014i	0.499711	−	2.41730i
$733$	−4.21061	+	1.12823i	−0.155522	+	0.0416721i	−0.335740	−	0.941955i	$-0.608986\pi$
$733$	−4.21061	+	1.12823i	−0.155522	+	0.0416721i	0.180218	+	0.983627i	$0.442320\pi$
$734$	31.1902	−	54.0230i	1.15125	−	1.99402i
$735$	12.5080	−	9.45232i	0.461366	−	0.348654i
$736$	2.94917	+	5.10812i	0.108708	+	0.188288i
$737$	−9.27551	−	9.27551i	−0.341668	−	0.341668i
$738$	−20.5955	+	8.17116i	−0.758132	+	0.300784i
$739$			25.1168i			0.923936i	0.886897	+	0.461968i	$0.152857\pi$
$739$			25.1168i			0.923936i	−0.886897	+	0.461968i	$0.847143\pi$
$740$	−4.45787	−	67.8666i	−0.163874	−	2.49483i
$741$	0.0753206	+	1.29833i	0.00276697	+	0.0476954i
$742$	10.6494	+	39.7442i	0.390953	+	1.45906i
$743$	−0.829514	−	3.09579i	−0.0304319	−	0.113573i	0.949039	−	0.315158i	$-0.102058\pi$
$743$	−0.829514	−	3.09579i	−0.0304319	−	0.113573i	−0.979471	+	0.201585i	$0.935391\pi$
$744$	−0.786759	−	13.5617i	−0.0288440	−	0.497195i
$745$	−27.7383	−	24.3189i	−1.01625	−	0.890975i
$746$		−	28.8885i		−	1.05768i
$747$	−14.7340	−	11.6612i	−0.539090	−	0.426659i
$748$	17.0745	+	17.0745i	0.624304	+	0.624304i
$749$	−2.87083	−	4.97242i	−0.104898	−	0.181688i
$750$	23.2444	+	40.9266i	0.848765	+	1.49443i
$751$	−24.6082	+	42.6226i	−0.897965	+	1.55532i	−0.0678736	+	0.997694i	$0.521621\pi$
$751$	−24.6082	+	42.6226i	−0.897965	+	1.55532i	−0.830092	+	0.557627i	$0.811712\pi$
$752$	−30.1455	+	8.07745i	−1.09929	+	0.294554i
$753$	3.90867	−	18.9078i	0.142440	−	0.689039i
$754$	11.6441	−	6.72271i	0.424052	−	0.244827i
$755$	29.6669	−	10.0752i	1.07969	−	0.366675i
$756$	6.03397	+	34.3584i	0.219453	+	1.24960i
$757$	−37.1191	+	37.1191i	−1.34912	+	1.34912i	−0.462493	+	0.886623i	$0.653045\pi$
$757$	−37.1191	+	37.1191i	−1.34912	+	1.34912i	−0.886623	+	0.462493i	$0.846955\pi$
$758$	−22.0801	−	5.91635i	−0.801986	−	0.214892i
$759$	6.38341	+	9.71034i	0.231703	+	0.352463i
$760$	1.04554	−	0.698824i	0.0379258	−	0.0253490i
$761$	8.56115	+	4.94278i	0.310341	+	0.179176i	0.647079	−	0.762423i	$-0.275990\pi$
$761$	8.56115	+	4.94278i	0.310341	+	0.179176i	−0.336738	+	0.941598i	$0.609324\pi$
$762$	−5.90474	−	17.8332i	−0.213906	−	0.646028i
$763$	−1.12079	+	4.18283i	−0.0405752	+	0.151429i
$764$	4.45371			0.161130
$765$	40.7742	−	7.48237i	1.47419	−	0.270526i
$766$	71.3211			2.57693
$767$	11.4219	−	42.6271i	0.412421	−	1.53917i
$768$	−35.7754	+	40.1820i	−1.29094	+	1.44994i
$769$	30.5590	+	17.6432i	1.10198	+	0.636231i	0.936742	−	0.350022i	$-0.113826\pi$
$769$	30.5590	+	17.6432i	1.10198	+	0.636231i	0.165243	+	0.986253i	$0.447159\pi$
$770$	−9.15855	−	1.82040i	−0.330051	−	0.0656027i
$771$	7.88354	−	0.457351i	0.283919	−	0.0164711i
$772$	36.7168	+	9.83824i	1.32147	+	0.354086i
$773$	−18.7375	+	18.7375i	−0.673941	+	0.673941i	−0.958622	−	0.284681i	$-0.908112\pi$
$773$	−18.7375	+	18.7375i	−0.673941	+	0.673941i	0.284681	+	0.958622i	$0.408112\pi$
$774$	−14.1337	−	19.0030i	−0.508026	−	0.683050i
$775$	6.70929	−	5.15124i	0.241005	−	0.185038i
$776$	−23.9304	+	13.8162i	−0.859051	+	0.495973i
$777$	21.9909	−	7.28138i	0.788918	−	0.261218i
$778$	−71.4439	+	19.1433i	−2.56139	+	0.686321i
$779$	−0.184319	+	0.319249i	−0.00660390	+	0.0114383i
$780$	−57.5663	+	73.8895i	−2.06120	+	2.64567i
$781$	−5.61685	−	9.72866i	−0.200987	−	0.348119i
$782$	−71.2563	−	71.2563i	−2.54812	−	2.54812i
$783$	0.407946	−	4.62620i	0.0145788	−	0.165327i
$784$		−	13.9784i		−	0.499229i
$785$	−6.78458	+	0.445650i	−0.242152	+	0.0159059i
$786$	21.1344	−	13.8934i	0.753841	−	0.495561i
$787$	−1.84911	−	6.90099i	−0.0659138	−	0.245994i	0.925106	−	0.379709i	$-0.123976\pi$
$787$	−1.84911	−	6.90099i	−0.0659138	−	0.245994i	−0.991020	+	0.133715i	$0.957309\pi$
$788$	−16.9853	−	63.3902i	−0.605078	−	2.25818i
$789$	32.8469	+	16.5058i	1.16938	+	0.587620i
$790$	32.1519	−	2.11192i	1.14391	−	0.0751387i
$791$			7.65089i			0.272034i
$792$	−8.63132	+	10.9058i	−0.306701	+	0.387521i
$793$	43.1874	+	43.1874i	1.53363	+	1.53363i
$794$	46.6179	+	80.7446i	1.65441	+	2.86552i
$795$	14.3437	+	35.3627i	0.508720	+	1.25419i
$796$	−50.3166	+	87.1509i	−1.78343	+	3.08898i
$797$	19.1521	−	5.13178i	0.678400	−	0.181777i	0.0968645	−	0.995298i	$-0.469119\pi$
$797$	19.1521	−	5.13178i	0.678400	−	0.181777i	0.581536	+	0.813521i	$0.302452\pi$
$798$	0.655340	+	0.583472i	0.0231988	+	0.0206547i
$799$	−48.3687	+	27.9257i	−1.71116	+	0.987939i
$800$	−4.35829	−	0.572524i	−0.154089	−	0.0202418i
$801$	−36.4152	−	15.7278i	−1.28667	−	0.555714i
$802$	66.7409	−	66.7409i	2.35670	−	2.35670i
$803$	−3.57304	−	0.957392i	−0.126090	−	0.0337856i
$804$	−39.8616	+	79.3257i	−1.40581	+	2.79760i
$805$	25.2811	+	5.02500i	0.891042	+	0.177108i
$806$	22.0402	+	12.7249i	0.776332	+	0.448215i
$807$	44.1901	+	9.13507i	1.55556	+	0.321570i
$808$	9.56877	−	35.7112i	0.336628	−	1.25631i
$809$	35.7401			1.25655			0.628277	−	0.777990i	$-0.283760\pi$
$809$	35.7401			1.25655			0.628277	+	0.777990i	$0.283760\pi$
$810$	14.3326	+	46.7663i	0.503597	+	1.64320i
$811$	−9.67429			−0.339710			−0.169855	−	0.985469i	$-0.554330\pi$
$811$	−9.67429			−0.339710			−0.169855	+	0.985469i	$0.554330\pi$
$812$	1.55299	−	5.79584i	0.0544992	−	0.203394i
$813$	−18.5659	−	3.83800i	−0.651136	−	0.134604i
$814$	16.3849	+	9.45985i	0.574292	+	0.331568i
$815$	−18.9439	+	12.6618i	−0.663576	+	0.443523i
$816$	16.5957	−	33.0260i	0.580967	−	1.15614i
$817$	−0.380593	−	0.101980i	−0.0133153	−	0.00356782i
$818$	−22.4869	+	22.4869i	−0.786236	+	0.786236i
$819$	−29.2878	−	12.6495i	−1.02340	−	0.442008i
$820$	−25.1402	+	8.53792i	−0.877934	+	0.298157i
$821$	17.0142	−	9.82313i	0.593798	−	0.342830i	−0.172800	−	0.984957i	$-0.555281\pi$
$821$	17.0142	−	9.82313i	0.593798	−	0.342830i	0.766598	+	0.642127i	$0.221948\pi$
$822$	−28.8277	−	25.6663i	−1.00548	−	0.895216i
$823$	3.74933	−	1.00463i	0.130694	−	0.0350192i	−0.192879	−	0.981222i	$-0.561783\pi$
$823$	3.74933	−	1.00463i	0.130694	−	0.0350192i	0.323573	+	0.946203i	$0.395116\pi$
$824$	2.95016	−	5.10982i	0.102774	−	0.178009i
$825$	−8.63740	−	0.628769i	−0.300716	−	0.0218909i
$826$	−14.8873	−	25.7856i	−0.517997	−	0.897197i
$827$	−3.30044	−	3.30044i	−0.114768	−	0.114768i	0.647391	−	0.762158i	$-0.275860\pi$
$827$	−3.30044	−	3.30044i	−0.114768	−	0.114768i	−0.762158	+	0.647391i	$0.775860\pi$
$828$	48.8078	−	61.6694i	1.69619	−	2.14316i
$829$		−	30.5512i		−	1.06109i	−0.847657	−	0.530544i	$-0.821988\pi$
$829$		−	30.5512i		−	1.06109i	0.847657	−	0.530544i	$-0.178012\pi$
$830$	−25.5962	−	22.4408i	−0.888457	−	0.778933i
$831$	47.3973	+	23.8174i	1.64419	+	0.826217i
$832$	−14.4865	−	54.0643i	−0.502229	−	1.87434i
$833$	−6.47456	−	24.1634i	−0.224330	−	0.837211i
$834$	71.9095	−	47.2720i	2.49002	−	1.63690i
$835$	0.0496339	+	0.755627i	0.00171765	+	0.0261495i
$836$			0.474018i			0.0163943i
$837$	7.96950	−	3.70957i	0.275466	−	0.128222i
$838$	5.39457	+	5.39457i	0.186352	+	0.186352i
$839$	−0.173554	−	0.300605i	−0.00599176	−	0.0103780i	0.863014	−	0.505180i	$-0.168574\pi$
$839$	−0.173554	−	0.300605i	−0.00599176	−	0.0103780i	−0.869006	+	0.494802i	$0.835241\pi$
$840$	3.80147	+	30.6145i	0.131163	+	1.05630i
$841$	14.1006	−	24.4229i	0.486227	−	0.842170i
$842$	6.76764	−	1.81338i	0.233228	−	0.0624933i
$843$	−14.2190	+	4.70805i	−0.489729	+	0.162154i
$844$	51.5661	−	29.7717i	1.77498	−	1.02478i
$845$	−18.1987	−	53.5867i	−0.626054	−	1.84344i
$846$	−39.3283	−	52.8777i	−1.35214	−	1.81797i
$847$	1.21490	−	1.21490i	0.0417445	−	0.0417445i
$848$	32.8650	+	8.80615i	1.12859	+	0.302405i
$849$	10.4367	−	0.605471i	0.358188	−	0.0207797i
$850$	74.4547	−	9.82361i	2.55378	−	0.336947i
$851$	−45.2287	−	26.1128i	−1.55042	−	0.895135i
$852$	−50.5562	+	56.7833i	−1.73203	+	1.94537i
$853$	6.50854	−	24.2902i	0.222848	−	0.831681i	−0.760407	−	0.649447i	$-0.775000\pi$
$853$	6.50854	−	24.2902i	0.222848	−	0.831681i	0.983255	−	0.182234i	$-0.0583329\pi$
$854$	41.2076			1.41010
$855$	0.669845	+	0.462121i	0.0229082	+	0.0158042i
$856$	−15.4928			−0.529532
$857$	11.7711	−	43.9302i	0.402091	−	1.50063i	−0.407266	−	0.913310i	$-0.633518\pi$
$857$	11.7711	−	43.9302i	0.402091	−	1.50063i	0.809358	−	0.587316i	$-0.199815\pi$
$858$	−8.19016	−	24.7355i	−0.279607	−	0.844456i
$859$	−0.106483	−	0.0614781i	−0.00363316	−	0.00209761i	0.498182	−	0.867072i	$-0.334001\pi$
$859$	−0.106483	−	0.0614781i	−0.00363316	−	0.00209761i	−0.501815	+	0.864975i	$0.667334\pi$
$860$	−15.7696	−	23.5936i	−0.537739	−	0.804536i
$861$	−4.96748	−	7.55645i	−0.169291	−	0.257523i
$862$	−51.0265	−	13.6725i	−1.73797	−	0.465688i
$863$	−18.4592	+	18.4592i	−0.628357	+	0.628357i	−0.947655	−	0.319297i	$-0.896553\pi$
$863$	−18.4592	+	18.4592i	−0.628357	+	0.628357i	0.319297	+	0.947655i	$0.396553\pi$
$864$	−4.29161	−	1.56536i	−0.146004	−	0.0532547i
$865$	−1.94823	+	3.95203i	−0.0662418	+	0.134373i
$866$	−21.6658	+	12.5087i	−0.736232	+	0.425064i
$867$	7.42981	−	35.9410i	0.252329	−	1.22062i
$868$	10.9705	−	2.93953i	0.372363	−	0.0997743i
$869$	−2.96433	+	5.13437i	−0.100558	+	0.174172i
$870$	1.15952	−	8.33308i	0.0393116	−	0.282518i
$871$	−40.5951	−	70.3127i	−1.37551	−	2.38246i
$872$	8.26234	+	8.26234i	0.279798	+	0.279798i
$873$	−14.0211	−	11.0969i	−0.474541	−	0.375572i
$874$		−	1.97821i		−	0.0669138i
$875$	−14.4369	+	12.6717i	−0.488057	+	0.428382i
$876$	1.44992	+	24.9929i	0.0489883	+	0.844430i
$877$	−8.50904	−	31.7562i	−0.287330	−	1.07233i	−0.947120	−	0.320880i	$-0.896021\pi$
$877$	−8.50904	−	31.7562i	−0.287330	−	1.07233i	0.659790	−	0.751450i	$-0.270645\pi$
$878$	14.8451	+	55.4027i	0.500998	+	1.86975i
$879$	0.912128	+	15.7227i	0.0307653	+	0.530314i
$880$	−5.09030	+	5.80603i	−0.171594	+	0.195721i
$881$			9.61275i			0.323862i	0.986802	+	0.161931i	$0.0517722\pi$
$881$			9.61275i			0.323862i	−0.986802	+	0.161931i	$0.948228\pi$
$882$	27.4360	−	10.8851i	0.923818	−	0.366519i
$883$	19.6344	+	19.6344i	0.660749	+	0.660749i	0.955557	−	0.294807i	$-0.0952555\pi$
$883$	19.6344	+	19.6344i	0.660749	+	0.660749i	−0.294807	+	0.955557i	$0.595256\pi$
$884$	74.7278	+	129.432i	2.51337	+	4.35328i
$885$	−16.6489	−	22.0312i	−0.559648	−	0.740570i
$886$	−47.1103	+	81.5974i	−1.58270	+	2.74132i
$887$	33.6837	−	9.02551i	1.13099	−	0.303047i	0.355665	−	0.934613i	$-0.384254\pi$
$887$	33.6837	−	9.02551i	1.13099	−	0.303047i	0.775322	+	0.631566i	$0.217588\pi$
$888$	12.6539	−	61.2120i	0.424637	−	2.05414i
$889$	6.63966	−	3.83341i	0.222687	−	0.128568i
$890$	−64.4537	−	31.7737i	−2.16049	−	1.06506i
$891$	−8.61954	−	2.58913i	−0.288765	−	0.0867392i
$892$	−30.3432	+	30.3432i	−1.01597	+	1.01597i
$893$	−1.05904	−	0.283768i	−0.0354393	−	0.00949593i
$894$	−38.1504	−	58.0338i	−1.27594	−	1.94094i
$895$	8.68124	−	43.6759i	0.290182	−	1.45992i
$896$	−30.0879	−	17.3713i	−1.00517	−	0.580333i
$897$	22.6080	+	68.2794i	0.754858	+	2.27978i
$898$	5.80332	−	21.6583i	0.193659	−	0.722747i
$899$	−1.51203			−0.0504289
$900$	14.3348	+	56.8315i	0.477827	+	1.89438i
$901$	60.8899			2.02854
$902$	1.91157	−	7.13409i	0.0636484	−	0.237539i
$903$	6.42733	−	7.21900i	0.213888	−	0.240233i
$904$	17.8786	+	10.3222i	0.594634	+	0.343312i
$905$	−0.0125992	+	0.0633871i	−0.000418810	+	0.00210706i
$906$	58.8871	−	3.41624i	1.95639	−	0.113497i
$907$	−1.93740	−	0.519125i	−0.0643304	−	0.0172373i	0.226510	−	0.974009i	$-0.427268\pi$
$907$	−1.93740	−	0.519125i	−0.0643304	−	0.0172373i	−0.290841	+	0.956771i	$0.593935\pi$
$908$	−39.2433	+	39.2433i	−1.30233	+	1.30233i
$909$	23.7635	−	2.76651i	0.788185	−	0.0917594i
$910$	−51.8385	−	25.5548i	−1.71843	−	0.847133i
$911$	4.22355	−	2.43847i	0.139933	−	0.0807901i	−0.428399	−	0.903590i	$-0.640922\pi$
$911$	4.22355	−	2.43847i	0.139933	−	0.0807901i	0.568332	+	0.822799i	$0.307589\pi$
$912$	0.688795	−	0.228067i	0.0228083	−	0.00755204i
$913$	6.05000	−	1.62109i	0.200226	−	0.0536504i
$914$	15.6622	−	27.1278i	0.518060	−	0.897307i
$915$	37.9267	−	4.70944i	1.25382	−	0.155689i
$916$	25.3358	+	43.8829i	0.837118	+	1.44993i
$917$	7.29906	+	7.29906i	0.241036	+	0.241036i
$918$	77.7445	+	6.85563i	2.56595	+	0.226270i
$919$		−	30.5884i		−	1.00902i	−0.863406	−	0.504509i	$-0.831673\pi$
$919$		−	30.5884i		−	1.00902i	0.863406	−	0.504509i	$-0.168327\pi$
$920$	45.8505	−	52.2974i	1.51165	−	1.72420i
$921$	12.6811	−	8.33633i	0.417856	−	0.274691i
$922$	−9.40970	−	35.1175i	−0.309892	−	1.15653i
$923$	−17.9957	−	67.1609i	−0.592336	−	2.21063i
$924$	−10.3900	−	5.22106i	−0.341807	−	0.171760i
$925$	35.9542	−	14.9046i	1.18217	−	0.490062i
$926$		−	35.7095i		−	1.17349i
$927$	3.77754	+	0.555098i	0.124071	+	0.0182318i
$928$	0.555612	+	0.555612i	0.0182389	+	0.0182389i
$929$	10.4511	+	18.1018i	0.342889	+	0.593902i	0.984968	−	0.172737i	$-0.0552611\pi$
$929$	10.4511	+	18.1018i	0.342889	+	0.593902i	−0.642079	+	0.766639i	$0.721928\pi$
$930$	14.7572	−	5.98579i	0.483909	−	0.196282i
$931$	0.245537	−	0.425283i	0.00804715	−	0.0139381i
$932$	−66.5763	+	17.8391i	−2.18078	+	0.584338i
$933$	−11.8988	−	10.5939i	−0.389549	−	0.346829i
$934$	−11.8830	+	6.86063i	−0.388822	+	0.224487i
$935$	−6.10994	+	12.3942i	−0.199816	+	0.405332i
$936$	−69.0731	+	51.3738i	−2.25772	+	1.67921i
$937$	−23.7618	+	23.7618i	−0.776265	+	0.776265i	−0.979194	−	0.202929i	$-0.934954\pi$
$937$	−23.7618	+	23.7618i	−0.776265	+	0.776265i	0.202929	+	0.979194i	$0.434954\pi$
$938$	−52.9118	−	14.1777i	−1.72763	−	0.462917i
$939$	2.56303	−	5.10050i	0.0836414	−	0.166449i
$940$	−43.8804	−	65.6515i	−1.43122	−	2.14131i
$941$	20.3640	+	11.7572i	0.663848	+	0.383273i	0.793742	−	0.608255i	$-0.208130\pi$
$941$	20.3640	+	11.7572i	0.663848	+	0.383273i	−0.129894	+	0.991528i	$0.541464\pi$
$942$	−12.5356	−	2.59139i	−0.408433	−	0.0844322i
$943$	−5.27667	+	19.6928i	−0.171832	+	0.641286i
$944$	−24.6211			−0.801347
$945$	−17.5072	+	9.59237i	−0.569510	+	0.312040i
$946$	7.89428			0.256665
$947$	−2.52516	+	9.42404i	−0.0820568	+	0.306240i	−0.994741	−	0.102426i	$-0.967339\pi$
$947$	−2.52516	+	9.42404i	−0.0820568	+	0.306240i	0.912684	+	0.408666i	$0.134006\pi$
$948$	39.2936	+	8.12287i	1.27620	+	0.263818i
$949$	−19.8278	−	11.4476i	−0.643638	−	0.371605i
$950$	1.16986	+	0.897139i	0.0379553	+	0.0291070i
$951$	23.5974	−	46.9594i	0.765197	−	1.52276i
$952$	47.5465	+	12.7401i	1.54099	+	0.412907i
$953$	0.281673	−	0.281673i	0.00912428	−	0.00912428i	−0.702530	−	0.711654i	$-0.747946\pi$
$953$	0.281673	−	0.281673i	0.00912428	−	0.00912428i	0.711654	+	0.702530i	$0.247946\pi$
$954$	8.30796	+	71.3628i	0.268980	+	2.31046i
$955$	0.819589	+	2.41331i	0.0265213	+	0.0780928i
$956$	12.6283	−	7.29093i	0.408427	−	0.235806i
$957$	1.15620	+	1.02940i	0.0373745	+	0.0332759i
$958$	−65.2914	+	17.4948i	−2.10947	+	0.565231i
$959$	7.87644	−	13.6424i	0.254344	−	0.440536i
$960$	−32.2582	−	13.6408i	−1.04113	−	0.440254i
$961$	14.0690	+	24.3682i	0.453839	+	0.786072i
$962$	82.8037	+	82.8037i	2.66970	+	2.66970i
$963$	−3.69717	−	9.31879i	−0.119140	−	0.300294i
$964$			36.4703i			1.17463i
$965$	1.42577	+	21.7060i	0.0458973	+	0.698741i
$966$	43.3604	+	21.7889i	1.39510	+	0.701046i
$967$	−3.66081	−	13.6623i	−0.117724	−	0.439351i	0.881752	−	0.471712i	$-0.156364\pi$
$967$	−3.66081	−	13.6623i	−0.117724	−	0.439351i	−0.999476	+	0.0323612i	$0.989697\pi$
$968$	−1.19990	−	4.47808i	−0.0385662	−	0.143931i
$969$	1.08503	−	0.713278i	0.0348561	−	0.0229138i
$970$	−24.3576	−	21.3550i	−0.782076	−	0.685666i
$971$			3.55848i			0.114197i	0.998369	+	0.0570986i	$0.0181849\pi$
$971$			3.55848i			0.114197i	−0.998369	+	0.0570986i	$0.981815\pi$
$972$	1.70180	+	60.8870i	0.0545853	+	1.95295i
$973$	24.8349	+	24.8349i	0.796170	+	0.796170i
$974$	14.8101	+	25.6518i	0.474545	+	0.821936i
$975$	−50.6317	−	17.5957i	−1.62151	−	0.563514i
$976$	17.0375	−	29.5099i	0.545359	−	0.944589i
$977$	15.7747	−	4.22681i	0.504676	−	0.135228i	0.00250685	−	0.999997i	$-0.499202\pi$
$977$	15.7747	−	4.22681i	0.504676	−	0.135228i	0.502169	+	0.864769i	$0.332535\pi$
$978$	−40.7239	+	13.4841i	−1.30221	+	0.431173i
$979$	11.4507	−	6.61108i	0.365967	−	0.211291i
$980$	33.4901	−	11.3736i	1.06980	−	0.363318i
$981$	−2.99803	+	6.94146i	−0.0957196	+	0.221624i
$982$	56.1527	−	56.1527i	1.79190	−	1.79190i
$983$	−33.8731	−	9.07626i	−1.08038	−	0.289488i	−0.325631	−	0.945497i	$-0.605577\pi$
$983$	−33.8731	−	9.07626i	−1.08038	−	0.289488i	−0.754753	+	0.656009i	$0.772243\pi$
$984$	−24.3598	+	1.41320i	−0.776563	+	0.0450511i
$985$	31.2232	−	20.8691i	0.994853	−	0.664944i
$986$	−11.6259	−	6.71220i	−0.370243	−	0.213760i
$987$	17.8846	−	20.0875i	0.569274	−	0.639393i
$988$	−0.759349	+	2.83393i	−0.0241581	+	0.0901594i
$989$	−21.7912			−0.692921
$990$	−15.3596	−	5.46974i	−0.488159	−	0.173840i
$991$	−15.6956			−0.498587			−0.249293	−	0.968428i	$-0.580198\pi$
$991$	−15.6956			−0.498587			−0.249293	+	0.968428i	$0.580198\pi$
$992$	−0.384940	+	1.43661i	−0.0122218	+	0.0456126i
$993$	−0.134262	−	0.405490i	−0.00426067	−	0.0128679i
$994$	−40.6265	−	23.4557i	−1.28859	−	0.743969i
$995$	−56.4835	−	11.2269i	−1.79065	−	0.355918i
$996$	−23.2856	−	35.4217i	−0.737832	−	1.12238i
$997$	53.4886	+	14.3322i	1.69400	+	0.453907i	0.971418	−	0.237376i	$-0.0762874\pi$
$997$	53.4886	+	14.3322i	1.69400	+	0.453907i	0.722584	+	0.691283i	$0.242954\pi$
$998$	52.9691	−	52.9691i	1.67671	−	1.67671i
$999$	39.8383	−	6.99633i	1.26043	−	0.221354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bc.c.23.4	✓	116
5.2	odd	4		495.2.bc.d.122.4	yes	116
9.2	odd	6		495.2.bc.d.353.4	yes	116
45.2	even	12	inner	495.2.bc.c.452.4	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.bc.c.23.4	✓	116	1.1	even	1	trivial
495.2.bc.c.452.4	yes	116	45.2	even	12	inner
495.2.bc.d.122.4	yes	116	5.2	odd	4
495.2.bc.d.353.4	yes	116	9.2	odd	6

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.629065 + 2.34770i) q^{2} +(-1.69619 - 0.350640i) q^{3} +(-3.38393 - 1.95371i) q^{4} +(0.435925 - 2.19316i) q^{5} +(1.89021 - 3.76157i) q^{6} +(1.65959 + 0.444685i) q^{7} +(3.27818 - 3.27818i) q^{8} +(2.75410 + 1.18950i) q^{9} +O(q^{10})\)	\(q+(-0.629065 + 2.34770i) q^{2} +(-1.69619 - 0.350640i) q^{3} +(-3.38393 - 1.95371i) q^{4} +(0.435925 - 2.19316i) q^{5} +(1.89021 - 3.76157i) q^{6} +(1.65959 + 0.444685i) q^{7} +(3.27818 - 3.27818i) q^{8} +(2.75410 + 1.18950i) q^{9} +(4.87467 + 2.40306i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(5.05473 + 4.50041i) q^{12} +(-5.97853 + 1.60194i) q^{13} +(-2.08798 + 3.61648i) q^{14} +(-1.50842 + 3.56717i) q^{15} +(1.72657 + 2.99051i) q^{16} +(4.36974 + 4.36974i) q^{17} +(-4.52511 + 5.71754i) q^{18} +0.121312i q^{19} +(-5.75996 + 6.56985i) q^{20} +(-2.65905 - 1.33619i) q^{21} +(-0.629065 - 2.34770i) q^{22} +(1.73646 + 6.48055i) q^{23} +(-6.70987 + 4.41095i) q^{24} +(-4.61994 - 1.91211i) q^{25} -15.0435i q^{26} +(-4.25439 - 2.98332i) q^{27} +(-4.74715 - 4.74715i) q^{28} +(0.446884 + 0.774026i) q^{29} +(-7.42575 - 5.78530i) q^{30} +(-0.845872 + 1.46509i) q^{31} +(0.849191 - 0.227540i) q^{32} +(1.64426 - 0.544431i) q^{33} +(-13.0077 + 7.51000i) q^{34} +(1.69872 - 3.44590i) q^{35} +(-6.99576 - 9.40593i) q^{36} +(-5.50427 + 5.50427i) q^{37} +(-0.284805 - 0.0763132i) q^{38} +(10.7024 - 0.620883i) q^{39} +(-5.76055 - 8.61863i) q^{40} +(2.63164 + 1.51938i) q^{41} +(4.80968 - 5.40210i) q^{42} +(-0.840639 + 3.13731i) q^{43} +3.90743 q^{44} +(3.80935 - 5.52167i) q^{45} -16.3068 q^{46} +(-2.33916 + 8.72985i) q^{47} +(-1.88000 - 5.67788i) q^{48} +(-3.50569 - 2.02401i) q^{49} +(7.39530 - 9.64340i) q^{50} +(-5.87969 - 8.94411i) q^{51} +(23.3607 + 6.25947i) q^{52} +(6.96722 - 6.96722i) q^{53} +(9.68023 - 8.11134i) q^{54} +(0.719060 + 2.11730i) q^{55} +(6.89819 - 3.98267i) q^{56} +(0.0425368 - 0.205768i) q^{57} +(-2.09830 + 0.562238i) q^{58} +(-3.56502 + 6.17479i) q^{59} +(12.0736 - 9.12403i) q^{60} +(-4.93392 - 8.54580i) q^{61} +(-2.90749 - 2.90749i) q^{62} +(4.04172 + 3.19879i) q^{63} +9.04308i q^{64} +(0.907134 + 13.8102i) q^{65} +(0.243814 + 4.20272i) q^{66} +(3.39507 + 12.6706i) q^{67} +(-6.24968 - 23.3241i) q^{68} +(-0.673020 - 11.6011i) q^{69} +(7.02134 + 6.15579i) q^{70} +11.2337i q^{71} +(12.9278 - 5.12905i) q^{72} +(2.61564 + 2.61564i) q^{73} +(-9.45985 - 16.3849i) q^{74} +(7.16582 + 4.86323i) q^{75} +(0.237009 - 0.410512i) q^{76} +(-1.65959 + 0.444685i) q^{77} +(-5.27486 + 25.5166i) q^{78} +(5.13437 - 2.96433i) q^{79} +(7.31134 - 2.48302i) q^{80} +(6.17017 + 6.55202i) q^{81} +(-5.22252 + 5.22252i) q^{82} +(-6.05000 - 1.62109i) q^{83} +(6.38751 + 9.71659i) q^{84} +(11.4884 - 7.67868i) q^{85} +(-6.83665 - 3.94714i) q^{86} +(-0.486595 - 1.46959i) q^{87} +(-1.19990 + 4.47808i) q^{88} -13.2222 q^{89} +(10.5669 + 12.4167i) q^{90} -10.6342 q^{91} +(6.78509 - 25.3223i) q^{92} +(1.94848 - 2.18848i) q^{93} +(-19.0236 - 10.9833i) q^{94} +(0.266057 + 0.0528829i) q^{95} +(-1.52017 + 0.0881904i) q^{96} +(-5.75725 - 1.54265i) q^{97} +(6.95709 - 6.95709i) q^{98} +(-2.97987 + 0.346913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 4 q^{2} + 8 q^{3} - 6 q^{4} + 2 q^{5} - 2 q^{6} + 8 q^{7} - 2 q^{8} - 16 q^{9}+O(q^{10}) \) 116 * q - 4 * q^2 + 8 * q^3 - 6 * q^4 + 2 * q^5 - 2 * q^6 + 8 * q^7 - 2 * q^8 - 16 * q^9	\( 116 q - 4 q^{2} + 8 q^{3} - 6 q^{4} + 2 q^{5} - 2 q^{6} + 8 q^{7} - 2 q^{8} - 16 q^{9} + 6 q^{10} + 6 q^{12} - 12 q^{13} + 10 q^{14} - 18 q^{15} + 62 q^{16} + 8 q^{17} - 12 q^{18} - 18 q^{20} - 10 q^{21} - 4 q^{22} - 40 q^{23} + 62 q^{24} - 6 q^{25} - 58 q^{27} + 18 q^{28} + 2 q^{29} - 70 q^{30} - 2 q^{31} - 66 q^{32} + 24 q^{34} - 2 q^{35} + 24 q^{36} - 14 q^{37} - 6 q^{38} - 4 q^{39} - 100 q^{40} + 6 q^{41} - 30 q^{42} - 22 q^{43} + 120 q^{44} + 94 q^{45} - 44 q^{46} + 32 q^{47} + 108 q^{48} + 18 q^{49} - 22 q^{50} - 8 q^{51} - 126 q^{52} + 44 q^{53} - 28 q^{54} + 2 q^{55} + 42 q^{56} + 20 q^{57} + 2 q^{58} - 22 q^{59} - 68 q^{60} - 10 q^{61} + 16 q^{62} - 8 q^{63} - 60 q^{65} + 6 q^{66} + 36 q^{67} - 48 q^{68} + 76 q^{69} + 154 q^{70} - 228 q^{72} + 12 q^{73} + 8 q^{74} - 72 q^{75} - 6 q^{76} - 8 q^{77} - 110 q^{78} + 6 q^{79} - 4 q^{80} + 44 q^{81} - 50 q^{82} + 30 q^{83} - 222 q^{84} - 126 q^{85} + 90 q^{86} + 112 q^{87} + 2 q^{88} - 8 q^{89} + 72 q^{90} + 72 q^{91} - 132 q^{92} + 112 q^{93} - 42 q^{94} + 78 q^{95} + 68 q^{96} - 72 q^{97} - 16 q^{98} + 4 q^{99}+O(q^{100}) \) 116 * q - 4 * q^2 + 8 * q^3 - 6 * q^4 + 2 * q^5 - 2 * q^6 + 8 * q^7 - 2 * q^8 - 16 * q^9 + 6 * q^10 + 6 * q^12 - 12 * q^13 + 10 * q^14 - 18 * q^15 + 62 * q^16 + 8 * q^17 - 12 * q^18 - 18 * q^20 - 10 * q^21 - 4 * q^22 - 40 * q^23 + 62 * q^24 - 6 * q^25 - 58 * q^27 + 18 * q^28 + 2 * q^29 - 70 * q^30 - 2 * q^31 - 66 * q^32 + 24 * q^34 - 2 * q^35 + 24 * q^36 - 14 * q^37 - 6 * q^38 - 4 * q^39 - 100 * q^40 + 6 * q^41 - 30 * q^42 - 22 * q^43 + 120 * q^44 + 94 * q^45 - 44 * q^46 + 32 * q^47 + 108 * q^48 + 18 * q^49 - 22 * q^50 - 8 * q^51 - 126 * q^52 + 44 * q^53 - 28 * q^54 + 2 * q^55 + 42 * q^56 + 20 * q^57 + 2 * q^58 - 22 * q^59 - 68 * q^60 - 10 * q^61 + 16 * q^62 - 8 * q^63 - 60 * q^65 + 6 * q^66 + 36 * q^67 - 48 * q^68 + 76 * q^69 + 154 * q^70 - 228 * q^72 + 12 * q^73 + 8 * q^74 - 72 * q^75 - 6 * q^76 - 8 * q^77 - 110 * q^78 + 6 * q^79 - 4 * q^80 + 44 * q^81 - 50 * q^82 + 30 * q^83 - 222 * q^84 - 126 * q^85 + 90 * q^86 + 112 * q^87 + 2 * q^88 - 8 * q^89 + 72 * q^90 + 72 * q^91 - 132 * q^92 + 112 * q^93 - 42 * q^94 + 78 * q^95 + 68 * q^96 - 72 * q^97 - 16 * q^98 + 4 * q^99

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