LMFDB - Embedded newform 115.2.g.a.96.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			96.1
Root			$0.959493 + 0.281733i$ of defining polynomial
Character	$\chi$	$=$	115.96
Dual form			115.2.g.a.6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.925839 + 2.02730i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-1.94306 + 2.24241i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(1.45949 + 1.68434i) q^{6} +(-0.0125459 - 0.0872586i) q^{7} +(-2.06815 - 0.607265i) q^{8} +(-1.68251 + 1.08128i) q^{9} +O(q^{10})$	\(q+(0.925839 + 2.02730i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-1.94306 + 2.24241i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(1.45949 + 1.68434i) q^{6} +(-0.0125459 - 0.0872586i) q^{7} +(-2.06815 - 0.607265i) q^{8} +(-1.68251 + 1.08128i) q^{9} +(0.317178 - 2.20602i) q^{10} +(1.01365 - 2.21959i) q^{11} +(-1.23259 + 2.69900i) q^{12} +(0.512546 - 3.56484i) q^{13} +(0.165284 - 0.106222i) q^{14} +(-0.959493 - 0.281733i) q^{15} +(0.160869 + 1.11887i) q^{16} +(-2.21537 - 2.55667i) q^{17} +(-3.74982 - 2.40986i) q^{18} +(1.87358 - 2.16222i) q^{19} +(2.84695 - 0.835939i) q^{20} +(-0.0366213 - 0.0801894i) q^{21} +5.43826 q^{22} +(-4.28287 + 2.15802i) q^{23} -2.15546 q^{24} +(0.415415 + 0.909632i) q^{25} +(7.70154 - 2.26138i) q^{26} +(-3.27430 + 3.77875i) q^{27} +(0.220047 + 0.141416i) q^{28} +(4.87604 + 5.62725i) q^{29} +(-0.317178 - 2.20602i) q^{30} +(1.65370 + 0.485571i) q^{31} +(-5.74593 + 3.69269i) q^{32} +(0.347262 - 2.41526i) q^{33} +(3.13208 - 6.85830i) q^{34} +(-0.0366213 + 0.0801894i) q^{35} +(0.844535 - 5.87387i) q^{36} +(0.595421 - 0.382654i) q^{37} +(6.11811 + 1.79644i) q^{38} +(-0.512546 - 3.56484i) q^{39} +(1.41153 + 1.62899i) q^{40} +(-4.66991 - 3.00117i) q^{41} +(0.128663 - 0.148485i) q^{42} +(2.30014 - 0.675383i) q^{43} +(3.00764 + 6.58582i) q^{44} +2.00000 q^{45} +(-8.34021 - 6.68469i) q^{46} -11.6146 q^{47} +(0.469574 + 1.02822i) q^{48} +(6.70899 - 1.96994i) q^{49} +(-1.45949 + 1.68434i) q^{50} +(-2.84593 - 1.82897i) q^{51} +(6.99792 + 8.07603i) q^{52} +(1.47653 + 10.2695i) q^{53} +(-10.6921 - 3.13950i) q^{54} +(-2.05274 + 1.31921i) q^{55} +(-0.0270422 + 0.188083i) q^{56} +(1.18852 - 2.60249i) q^{57} +(-6.89372 + 15.0951i) q^{58} +(-1.64421 + 11.4357i) q^{59} +(2.49611 - 1.60416i) q^{60} +(-3.89722 - 1.14433i) q^{61} +(0.546662 + 3.80211i) q^{62} +(0.115460 + 0.133248i) q^{63} +(-10.9041 - 7.00766i) q^{64} +(-2.35848 + 2.72183i) q^{65} +(5.21797 - 1.53213i) q^{66} +(-5.07177 - 11.1056i) q^{67} +10.0377 q^{68} +(-3.50140 + 3.27723i) q^{69} -0.196474 q^{70} +(0.787956 + 1.72538i) q^{71} +(4.13631 - 1.21453i) q^{72} +(3.61246 - 4.16900i) q^{73} +(1.32702 + 0.852823i) q^{74} +(0.654861 + 0.755750i) q^{75} +(1.20812 + 8.40266i) q^{76} +(-0.206395 - 0.0606031i) q^{77} +(6.75247 - 4.33955i) q^{78} +(-0.997420 + 6.93721i) q^{79} +(0.469574 - 1.02822i) q^{80} +(0.415415 - 0.909632i) q^{81} +(1.76070 - 12.2459i) q^{82} +(3.51021 - 2.25587i) q^{83} +(0.250975 + 0.0736930i) q^{84} +(0.481446 + 3.34853i) q^{85} +(3.49877 + 4.03779i) q^{86} +(6.26391 + 4.02557i) q^{87} +(-3.44426 + 3.97489i) q^{88} +(15.3009 - 4.49275i) q^{89} +(1.85168 + 4.05461i) q^{90} -0.317493 q^{91} +(3.48270 - 13.7971i) q^{92} +1.72352 q^{93} +(-10.7532 - 23.5463i) q^{94} +(-2.74514 + 0.806046i) q^{95} +(-4.47283 + 5.16192i) q^{96} +(12.0969 + 7.77424i) q^{97} +(10.2051 + 11.7773i) q^{98} +(0.694523 + 4.83052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9	\( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9} - 5 q^{10} + 8 q^{11} + q^{12} - 3 q^{14} - q^{15} + 5 q^{16} - 23 q^{17} - 10 q^{18} - 13 q^{19} + q^{20} + 6 q^{21} + 4 q^{22} - 21 q^{23} - 6 q^{24} - q^{25} + 11 q^{26} - 5 q^{27} - 6 q^{28} + 2 q^{29} + 5 q^{30} - 20 q^{31} - 15 q^{32} + 3 q^{33} + 16 q^{34} + 6 q^{35} + 24 q^{36} + 13 q^{37} + 21 q^{38} - 6 q^{40} - 5 q^{41} + 3 q^{42} + 15 q^{43} + 19 q^{44} + 20 q^{45} - 16 q^{46} - 52 q^{47} + 6 q^{48} + 4 q^{49} - 6 q^{50} - 10 q^{51} + 22 q^{52} + 6 q^{53} - 30 q^{54} + 3 q^{55} + 3 q^{56} + 2 q^{57} + 45 q^{58} + 5 q^{59} + 10 q^{60} - 3 q^{61} - 54 q^{62} - 10 q^{63} - 34 q^{64} - 4 q^{66} + 20 q^{67} + 32 q^{68} - q^{69} - 8 q^{70} - 22 q^{71} + 32 q^{72} + 43 q^{73} + q^{74} + q^{75} - 2 q^{76} + 4 q^{77} + 11 q^{78} + 51 q^{79} + 6 q^{80} - q^{81} + 58 q^{82} - 17 q^{83} + 6 q^{84} + q^{85} - 9 q^{86} - 2 q^{87} + 7 q^{88} + 57 q^{89} + 10 q^{90} - 22 q^{91} - 43 q^{92} + 20 q^{93} - 81 q^{94} - 9 q^{95} - 7 q^{96} + 52 q^{97} + 24 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9 - 5 * q^10 + 8 * q^11 + q^12 - 3 * q^14 - q^15 + 5 * q^16 - 23 * q^17 - 10 * q^18 - 13 * q^19 + q^20 + 6 * q^21 + 4 * q^22 - 21 * q^23 - 6 * q^24 - q^25 + 11 * q^26 - 5 * q^27 - 6 * q^28 + 2 * q^29 + 5 * q^30 - 20 * q^31 - 15 * q^32 + 3 * q^33 + 16 * q^34 + 6 * q^35 + 24 * q^36 + 13 * q^37 + 21 * q^38 - 6 * q^40 - 5 * q^41 + 3 * q^42 + 15 * q^43 + 19 * q^44 + 20 * q^45 - 16 * q^46 - 52 * q^47 + 6 * q^48 + 4 * q^49 - 6 * q^50 - 10 * q^51 + 22 * q^52 + 6 * q^53 - 30 * q^54 + 3 * q^55 + 3 * q^56 + 2 * q^57 + 45 * q^58 + 5 * q^59 + 10 * q^60 - 3 * q^61 - 54 * q^62 - 10 * q^63 - 34 * q^64 - 4 * q^66 + 20 * q^67 + 32 * q^68 - q^69 - 8 * q^70 - 22 * q^71 + 32 * q^72 + 43 * q^73 + q^74 + q^75 - 2 * q^76 + 4 * q^77 + 11 * q^78 + 51 * q^79 + 6 * q^80 - q^81 + 58 * q^82 - 17 * q^83 + 6 * q^84 + q^85 - 9 * q^86 - 2 * q^87 + 7 * q^88 + 57 * q^89 + 10 * q^90 - 22 * q^91 - 43 * q^92 + 20 * q^93 - 81 * q^94 - 9 * q^95 - 7 * q^96 + 52 * q^97 + 24 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.925839	+	2.02730i	0.654667	+	1.43352i	0.887410	+	0.460982i	$0.152503\pi$
$2$	0.925839	+	2.02730i	0.654667	+	1.43352i	−0.232743	+	0.972538i	$0.574770\pi$
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i	0.00724338	−	0.999974i	$-0.497694\pi$
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i	0.546720	+	0.837315i	$0.315876\pi$
$4$	−1.94306	+	2.24241i	−0.971531	+	1.12121i
$5$	−0.841254	−	0.540641i	−0.376220	−	0.241782i
$5$	−0.841254	−	0.540641i	−0.376220	−	0.241782i
$6$	1.45949	+	1.68434i	0.595836	+	0.687631i
$7$	−0.0125459	−	0.0872586i	−0.00474190	−	0.0329807i	0.987313	−	0.158785i	$-0.0507578\pi$
$7$	−0.0125459	−	0.0872586i	−0.00474190	−	0.0329807i	−0.992055	+	0.125805i	$0.959849\pi$
$8$	−2.06815	−	0.607265i	−0.731203	−	0.214700i
$9$	−1.68251	+	1.08128i	−0.560836	+	0.360427i
$10$	0.317178	−	2.20602i	0.100301	−	0.697606i
$11$	1.01365	−	2.21959i	0.305628	−	0.669231i	−0.693037	−	0.720902i	$-0.743728\pi$
$11$	1.01365	−	2.21959i	0.305628	−	0.669231i	0.998664	+	0.0516714i	$0.0164549\pi$
$12$	−1.23259	+	2.69900i	−0.355819	+	0.779135i
$13$	0.512546	−	3.56484i	0.142155	−	0.988707i	−0.786455	−	0.617648i	$-0.788086\pi$
$13$	0.512546	−	3.56484i	0.142155	−	0.988707i	0.928609	−	0.371059i	$-0.121005\pi$
$14$	0.165284	−	0.106222i	0.0441741	−	0.0283890i
$15$	−0.959493	−	0.281733i	−0.247740	−	0.0727430i
$16$	0.160869	+	1.11887i	0.0402172	+	0.279717i
$17$	−2.21537	−	2.55667i	−0.537306	−	0.620084i	0.420572	−	0.907259i	$-0.361829\pi$
$17$	−2.21537	−	2.55667i	−0.537306	−	0.620084i	−0.957878	+	0.287175i	$0.907284\pi$
$18$	−3.74982	−	2.40986i	−0.883840	−	0.568010i
$19$	1.87358	−	2.16222i	0.429828	−	0.496048i	−0.498978	−	0.866615i	$-0.666291\pi$
$19$	1.87358	−	2.16222i	0.429828	−	0.496048i	0.928806	+	0.370567i	$0.120837\pi$
$20$	2.84695	−	0.835939i	0.636597	−	0.186922i
$21$	−0.0366213	−	0.0801894i	−0.00799142	−	0.0174988i
$22$	5.43826			1.15944
$23$	−4.28287	+	2.15802i	−0.893039	+	0.449979i
$23$	−4.28287	+	2.15802i	−0.893039	+	0.449979i
$24$	−2.15546			−0.439982
$25$	0.415415	+	0.909632i	0.0830830	+	0.181926i
$26$	7.70154	−	2.26138i	1.51040	−	0.443492i
$27$	−3.27430	+	3.77875i	−0.630140	+	0.727220i
$28$	0.220047	+	0.141416i	0.0415850	+	0.0267251i
$29$	4.87604	+	5.62725i	0.905458	+	1.04495i	0.998783	+	0.0493188i	$0.0157050\pi$
$29$	4.87604	+	5.62725i	0.905458	+	1.04495i	−0.0933249	+	0.995636i	$0.529750\pi$
$30$	−0.317178	−	2.20602i	−0.0579085	−	0.402763i
$31$	1.65370	+	0.485571i	0.297014	+	0.0872110i	0.426844	−	0.904325i	$-0.359625\pi$
$31$	1.65370	+	0.485571i	0.297014	+	0.0872110i	−0.129831	+	0.991536i	$0.541443\pi$
$32$	−5.74593	+	3.69269i	−1.01575	+	0.652781i
$33$	0.347262	−	2.41526i	0.0604505	−	0.420442i
$34$	3.13208	−	6.85830i	0.537147	−	1.17619i
$35$	−0.0366213	+	0.0801894i	−0.00619013	+	0.0135545i
$36$	0.844535	−	5.87387i	0.140756	−	0.978979i
$37$	0.595421	−	0.382654i	0.0978866	−	0.0629079i	−0.490782	−	0.871283i	$-0.663289\pi$
$37$	0.595421	−	0.382654i	0.0978866	−	0.0629079i	0.588668	+	0.808375i	$0.299652\pi$
$38$	6.11811	+	1.79644i	0.992489	+	0.291421i
$39$	−0.512546	−	3.56484i	−0.0820730	−	0.570830i
$40$	1.41153	+	1.62899i	0.223182	+	0.257566i
$41$	−4.66991	−	3.00117i	−0.729317	−	0.468704i	0.122550	−	0.992462i	$-0.460893\pi$
$41$	−4.66991	−	3.00117i	−0.729317	−	0.468704i	−0.851867	+	0.523759i	$0.824529\pi$
$42$	0.128663	−	0.148485i	0.0198531	−	0.0229117i
$43$	2.30014	−	0.675383i	0.350768	−	0.102995i	−0.101602	−	0.994825i	$-0.532397\pi$
$43$	2.30014	−	0.675383i	0.350768	−	0.102995i	0.452370	+	0.891830i	$0.350579\pi$
$44$	3.00764	+	6.58582i	0.453419	+	0.992850i
$45$	2.00000			0.298142
$46$	−8.34021	−	6.68469i	−1.22970	−	0.985604i
$47$	−11.6146			−1.69416			−0.847079	−	0.531466i	$-0.821641\pi$
$47$	−11.6146			−1.69416			−0.847079	+	0.531466i	$0.821641\pi$
$48$	0.469574	+	1.02822i	0.0677772	+	0.148411i
$49$	6.70899	−	1.96994i	0.958428	−	0.281420i
$50$	−1.45949	+	1.68434i	−0.206403	+	0.238202i
$51$	−2.84593	−	1.82897i	−0.398510	−	0.256107i
$52$	6.99792	+	8.07603i	0.970437	+	1.11994i
$53$	1.47653	+	10.2695i	0.202817	+	1.41062i	0.795874	+	0.605462i	$0.207012\pi$
$53$	1.47653	+	10.2695i	0.202817	+	1.41062i	−0.593058	+	0.805160i	$0.702079\pi$
$54$	−10.6921	−	3.13950i	−1.45502	−	0.427231i
$55$	−2.05274	+	1.31921i	−0.276791	+	0.177883i
$56$	−0.0270422	+	0.188083i	−0.00361367	+	0.0251336i
$57$	1.18852	−	2.60249i	0.157423	−	0.344708i
$58$	−6.89372	+	15.0951i	−0.905190	+	1.98209i
$59$	−1.64421	+	11.4357i	−0.214058	+	1.48881i	0.545359	+	0.838203i	$0.316393\pi$
$59$	−1.64421	+	11.4357i	−0.214058	+	1.48881i	−0.759417	+	0.650604i	$0.774516\pi$
$60$	2.49611	−	1.60416i	0.322247	−	0.207096i
$61$	−3.89722	−	1.14433i	−0.498988	−	0.146516i	0.0225474	−	0.999746i	$-0.492822\pi$
$61$	−3.89722	−	1.14433i	−0.498988	−	0.146516i	−0.521535	+	0.853230i	$0.674641\pi$
$62$	0.546662	+	3.80211i	0.0694261	+	0.482869i
$63$	0.115460	+	0.133248i	0.0145466	+	0.0167876i
$64$	−10.9041	−	7.00766i	−1.36302	−	0.875958i
$65$	−2.35848	+	2.72183i	−0.292533	+	0.337601i
$66$	5.21797	−	1.53213i	0.642288	−	0.188593i
$67$	−5.07177	−	11.1056i	−0.619615	−	1.35677i	−0.915799	−	0.401637i	$-0.868441\pi$
$67$	−5.07177	−	11.1056i	−0.619615	−	1.35677i	0.296184	−	0.955131i	$-0.404286\pi$
$68$	10.0377			1.21725
$69$	−3.50140	+	3.27723i	−0.421518	+	0.394532i
$70$	−0.196474			−0.0234831
$71$	0.787956	+	1.72538i	0.0935131	+	0.204765i	0.950608	−	0.310393i	$-0.100461\pi$
$71$	0.787956	+	1.72538i	0.0935131	+	0.204765i	−0.857095	+	0.515158i	$0.827733\pi$
$72$	4.13631	−	1.21453i	0.487468	−	0.143134i
$73$	3.61246	−	4.16900i	0.422806	−	0.487944i	−0.503884	−	0.863772i	$-0.668096\pi$
$73$	3.61246	−	4.16900i	0.422806	−	0.487944i	0.926690	+	0.375827i	$0.122641\pi$
$74$	1.32702	+	0.852823i	0.154263	+	0.0991387i
$75$	0.654861	+	0.755750i	0.0756168	+	0.0872664i
$76$	1.20812	+	8.40266i	0.138581	+	0.963852i
$77$	−0.206395	−	0.0606031i	−0.0235209	−	0.00690637i
$78$	6.75247	−	4.33955i	0.764566	−	0.491357i
$79$	−0.997420	+	6.93721i	−0.112219	+	0.780497i	0.853535	+	0.521036i	$0.174454\pi$
$79$	−0.997420	+	6.93721i	−0.112219	+	0.780497i	−0.965753	+	0.259461i	$0.916455\pi$
$80$	0.469574	−	1.02822i	0.0525000	−	0.114959i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	1.76070	−	12.2459i	0.194436	−	1.35234i
$83$	3.51021	−	2.25587i	0.385295	−	0.247614i	−0.333626	−	0.942705i	$-0.608272\pi$
$83$	3.51021	−	2.25587i	0.385295	−	0.247614i	0.718922	+	0.695091i	$0.244636\pi$
$84$	0.250975	+	0.0736930i	0.0273836	+	0.00804056i
$85$	0.481446	+	3.34853i	0.0522201	+	0.363199i
$86$	3.49877	+	4.03779i	0.377282	+	0.435406i
$87$	6.26391	+	4.02557i	0.671561	+	0.431586i
$88$	−3.44426	+	3.97489i	−0.367160	+	0.423725i
$89$	15.3009	−	4.49275i	1.62189	−	0.476231i	0.660367	−	0.750943i	$-0.270401\pi$
$89$	15.3009	−	4.49275i	1.62189	−	0.476231i	0.961526	+	0.274713i	$0.0885827\pi$
$90$	1.85168	+	4.05461i	0.195184	+	0.427393i
$91$	−0.317493			−0.0332823
$92$	3.48270	−	13.7971i	0.363096	−	1.43845i
$93$	1.72352			0.178720
$94$	−10.7532	−	23.5463i	−1.10911	−	2.42861i
$95$	−2.74514	+	0.806046i	−0.281645	+	0.0826985i
$96$	−4.47283	+	5.16192i	−0.456506	+	0.526836i
$97$	12.0969	+	7.77424i	1.22826	+	0.789354i	0.983619	−	0.180260i	$-0.0576938\pi$
$97$	12.0969	+	7.77424i	1.22826	+	0.789354i	0.244640	+	0.969614i	$0.421330\pi$
$98$	10.2051	+	11.7773i	1.03087	+	1.18969i
$99$	0.694523	+	4.83052i	0.0698022	+	0.485485i
$100$	−2.84695	−	0.835939i	−0.284695	−	0.0835939i
$101$	14.6237	−	9.39808i	1.45511	−	0.935144i	0.456137	−	0.889910i	$-0.349233\pi$
$101$	14.6237	−	9.39808i	1.45511	−	0.935144i	0.998976	−	0.0452346i	$-0.0144035\pi$
$102$	1.07300	−	7.46289i	0.106243	−	0.738937i
$103$	0.483270	−	1.05821i	0.0476180	−	0.104269i	−0.884328	−	0.466867i	$-0.845383\pi$
$103$	0.483270	−	1.05821i	0.0476180	−	0.104269i	0.931946	+	0.362598i	$0.118110\pi$
$104$	−3.22482	+	7.06137i	−0.316220	+	0.692425i
$105$	−0.0125459	+	0.0872586i	−0.00122435	+	0.00851557i
$106$	−19.4523	+	12.5013i	−1.88938	+	1.21423i
$107$	−16.4556	−	4.83181i	−1.59083	−	0.467108i	−0.637851	−	0.770160i	$-0.720176\pi$
$107$	−16.4556	−	4.83181i	−1.59083	−	0.467108i	−0.952974	+	0.303051i	$0.901995\pi$
$108$	−2.11134	−	14.6847i	−0.203164	−	1.41303i
$109$	−1.71227	−	1.97606i	−0.164006	−	0.189273i	0.667798	−	0.744343i	$-0.267237\pi$
$109$	−1.71227	−	1.97606i	−0.164006	−	0.189273i	−0.831804	+	0.555070i	$0.812692\pi$
$110$	−4.57495	−	2.94014i	−0.436205	−	0.280332i
$111$	0.463496	−	0.534903i	0.0439931	−	0.0507707i
$112$	0.0956126	−	0.0280744i	0.00903454	−	0.00265278i
$113$	−7.44256	−	16.2969i	−0.700137	−	1.53309i	−0.839805	−	0.542888i	$-0.817331\pi$
$113$	−7.44256	−	16.2969i	−0.700137	−	1.53309i	0.139668	−	0.990198i	$-0.455396\pi$
$114$	6.37640			0.597205
$115$	4.76969	+	0.500049i	0.444776	+	0.0466298i
$116$	−22.0931			−2.05129
$117$	2.99223	+	6.55207i	0.276632	+	0.605739i
$118$	−24.7060	+	7.25434i	−2.27437	+	0.667816i
$119$	−0.195298	+	0.225386i	−0.0179029	+	0.0206611i
$120$	1.81329	+	1.16533i	0.165530	+	0.106380i
$121$	3.30439	+	3.81347i	0.300399	+	0.346679i
$122$	−1.28830	−	8.96031i	−0.116637	−	0.811228i
$123$	−5.32627	−	1.56393i	−0.480254	−	0.141015i
$124$	−4.30209	+	2.76479i	−0.386339	+	0.248285i
$125$	0.142315	−	0.989821i	0.0127290	−	0.0885323i
$126$	−0.163236	+	0.357438i	−0.0145422	+	0.0318431i
$127$	1.24283	−	2.72142i	0.110283	−	0.241487i	−0.846441	−	0.532482i	$-0.821259\pi$
$127$	1.24283	−	2.72142i	0.110283	−	0.241487i	0.956724	+	0.290996i	$0.0939865\pi$
$128$	2.16711	−	15.0726i	0.191548	−	1.33224i
$129$	2.01669	−	1.29605i	0.177560	−	0.114111i
$130$	−7.70154	−	2.26138i	−0.675470	−	0.198336i
$131$	1.91036	+	13.2869i	0.166909	+	1.16088i	0.885226	+	0.465162i	$0.154004\pi$
$131$	1.91036	+	13.2869i	0.166909	+	1.16088i	−0.718316	+	0.695716i	$0.755087\pi$
$132$	4.74125	+	5.47170i	0.412673	+	0.476250i
$133$	−0.212178	−	0.136359i	−0.0183982	−	0.0118238i
$134$	17.8188	−	20.5640i	1.53931	−	1.77646i
$135$	4.79746	−	1.40866i	0.412900	−	0.121238i
$136$	3.02915	+	6.63291i	0.259747	+	0.568767i
$137$	19.2932			1.64833			0.824165	−	0.566350i	$-0.191645\pi$
$137$	19.2932			1.64833			0.824165	+	0.566350i	$0.191645\pi$
$138$	−9.88567	−	4.06421i	−0.841524	−	0.345968i
$139$	15.4962			1.31437			0.657185	−	0.753729i	$-0.271747\pi$
$139$	15.4962			1.31437			0.657185	+	0.753729i	$0.271747\pi$
$140$	−0.108660	−	0.237933i	−0.00918348	−	0.0201090i
$141$	−11.1441	+	3.27220i	−0.938502	+	0.275569i
$142$	−2.76835	+	3.19485i	−0.232315	+	0.268106i
$143$	−7.39292	−	4.75114i	−0.618227	−	0.397310i
$144$	−1.48047	−	1.70856i	−0.123373	−	0.142380i
$145$	−1.05967	−	7.37013i	−0.0880004	−	0.612056i
$146$	11.7964	+	3.46373i	0.976275	+	0.286660i
$147$	5.88224	−	3.78028i	0.485159	−	0.311793i
$148$	−0.298872	+	2.07870i	−0.0245671	+	0.170868i
$149$	−6.62691	+	14.5109i	−0.542898	+	1.18878i	0.417122	+	0.908850i	$0.363039\pi$
$149$	−6.62691	+	14.5109i	−0.542898	+	1.18878i	−0.960020	+	0.279930i	$0.909689\pi$
$150$	−0.925839	+	2.02730i	−0.0755944	+	0.165529i
$151$	−0.0629411	+	0.437765i	−0.00512208	+	0.0356248i	−0.992222	−	0.124479i	$-0.960274\pi$
$151$	−0.0629411	+	0.437765i	−0.00512208	+	0.0356248i	0.987100	+	0.160104i	$0.0511830\pi$
$152$	−5.18789	+	3.33405i	−0.420793	+	0.270427i
$153$	6.49186	+	1.90618i	0.524836	+	0.154106i
$154$	−0.0682278	−	0.474535i	−0.00549795	−	0.0382391i
$155$	−1.12866	−	1.30255i	−0.0906564	−	0.104623i
$156$	8.98974	+	5.77735i	0.719755	+	0.462559i
$157$	−4.66176	+	5.37996i	−0.372049	+	0.429367i	−0.910640	−	0.413200i	$-0.864411\pi$
$157$	−4.66176	+	5.37996i	−0.372049	+	0.429367i	0.538592	+	0.842567i	$0.318957\pi$
$158$	−14.9873	+	4.40066i	−1.19232	+	0.350098i
$159$	4.30997	+	9.43751i	0.341803	+	0.748443i
$160$	6.83020			0.539975
$161$	0.242038	+	0.346643i	0.0190753	+	0.0273193i
$162$	2.22871			0.175104
$163$	−2.96870	−	6.50054i	−0.232526	−	0.509162i	0.757017	−	0.653395i	$-0.226656\pi$
$163$	−2.96870	−	6.50054i	−0.232526	−	0.509162i	−0.989544	+	0.144233i	$0.953929\pi$
$164$	15.8038	−	4.64041i	1.23407	−	0.362355i
$165$	−1.59792	+	1.84410i	−0.124398	+	0.143563i
$166$	7.82322	+	5.02768i	0.607200	+	0.390224i
$167$	−0.872694	−	1.00714i	−0.0675311	−	0.0779351i	0.720979	−	0.692957i	$-0.243693\pi$
$167$	−0.872694	−	1.00714i	−0.0675311	−	0.0779351i	−0.788510	+	0.615022i	$0.789147\pi$
$168$	0.0270422	+	0.188083i	0.00208635	+	0.0145109i
$169$	0.0280633	+	0.00824014i	0.00215872	+	0.000633857i
$170$	−6.34275	+	4.07624i	−0.486466	+	0.312633i
$171$	−0.814334	+	5.66382i	−0.0622737	+	0.433123i
$172$	−2.95483	+	6.47018i	−0.225304	+	0.493346i
$173$	1.12194	−	2.45670i	0.0852992	−	0.186779i	−0.862176	−	0.506609i	$-0.830899\pi$
$173$	1.12194	−	2.45670i	0.0852992	−	0.186779i	0.947475	+	0.319830i	$0.103626\pi$
$174$	−2.36168	+	16.4259i	−0.179039	+	1.24524i
$175$	0.0741615	−	0.0476607i	0.00560608	−	0.00360281i
$176$	2.64649	+	0.777080i	0.199487	+	0.0585746i
$177$	1.64421	+	11.4357i	0.123587	+	0.859563i
$178$	23.2743	+	26.8600i	1.74449	+	2.01324i
$179$	−16.6467	−	10.6982i	−1.24423	−	0.799620i	−0.258188	−	0.966095i	$-0.583125\pi$
$179$	−16.6467	−	10.6982i	−1.24423	−	0.799620i	−0.986046	+	0.166474i	$0.946762\pi$
$180$	−3.88612	+	4.48482i	−0.289654	+	0.334279i
$181$	−3.82402	+	1.12283i	−0.284237	+	0.0834596i	−0.420744	−	0.907180i	$-0.638231\pi$
$181$	−3.82402	+	1.12283i	−0.284237	+	0.0834596i	0.136506	+	0.990639i	$0.456413\pi$
$182$	−0.293947	−	0.643655i	−0.0217888	−	0.0477109i
$183$	−4.06175			−0.300253
$184$	10.1681	−	1.86229i	0.749603	−	0.137290i
$185$	−0.707778			−0.0520369
$186$	1.59570	+	3.49409i	0.117002	+	0.256199i
$187$	−7.92038	+	2.32563i	−0.579195	+	0.170067i
$188$	22.5678	−	26.0447i	1.64593	−	1.89950i
$189$	0.370807	+	0.238303i	0.0269723	+	0.0173340i
$190$	−4.17565	−	4.81896i	−0.302934	−	0.349604i
$191$	0.850935	+	5.91838i	0.0615715	+	0.428239i	0.997170	+	0.0751744i	$0.0239513\pi$
$191$	0.850935	+	5.91838i	0.0615715	+	0.428239i	−0.935599	+	0.353065i	$0.885140\pi$
$192$	−12.4367	−	3.65175i	−0.897544	−	0.263543i
$193$	8.48523	−	5.45312i	0.610780	−	0.392524i	−0.198370	−	0.980127i	$-0.563565\pi$
$193$	8.48523	−	5.45312i	0.610780	−	0.392524i	0.809149	+	0.587603i	$0.199928\pi$
$194$	−4.56092	+	31.7219i	−0.327455	+	2.27750i
$195$	−1.49611	+	3.27603i	−0.107139	+	0.234602i
$196$	−8.61857	+	18.8720i	−0.615612	+	1.34800i
$197$	0.728029	−	5.06355i	0.0518699	−	0.360763i	−0.947312	−	0.320313i	$-0.896212\pi$
$197$	0.728029	−	5.06355i	0.0518699	−	0.360763i	0.999182	−	0.0404498i	$-0.0128791\pi$
$198$	−9.14991	+	5.88029i	−0.650255	+	0.417894i
$199$	−25.5033	−	7.48844i	−1.80788	−	0.530842i	−0.809468	−	0.587164i	$-0.800244\pi$
$199$	−25.5033	−	7.48844i	−1.80788	−	0.530842i	−0.998413	+	0.0563229i	$0.982062\pi$
$200$	−0.306755	−	2.13353i	−0.0216908	−	0.150863i
$201$	−7.99514	−	9.22689i	−0.563934	−	0.650814i
$202$	32.5920	+	20.9456i	2.29316	+	1.47373i
$203$	0.429852	−	0.496076i	0.0301697	−	0.0348177i
$204$	9.63112	−	2.82795i	0.674313	−	0.197996i
$205$	2.30602	+	5.04949i	0.161060	+	0.352671i
$206$	2.59275			0.180646
$207$	4.87252	−	8.26187i	0.338664	−	0.574240i
$208$	4.07103			0.282275
$209$	−2.90009	−	6.35031i	−0.200603	−	0.439260i
$210$	−0.188515	+	0.0553531i	−0.0130088	+	0.00381972i
$211$	9.65433	−	11.1417i	0.664631	−	0.767026i	−0.318895	−	0.947790i	$-0.603312\pi$
$211$	9.65433	−	11.1417i	0.664631	−	0.767026i	0.983526	+	0.180765i	$0.0578572\pi$
$212$	−25.8974	−	16.6432i	−1.77864	−	1.14306i
$213$	1.24213	+	1.43350i	0.0851096	+	0.0982217i
$214$	−5.43971	−	37.8340i	−0.371851	−	2.58628i
$215$	−2.30014	−	0.675383i	−0.156868	−	0.0460607i
$216$	9.06646	−	5.82666i	0.616895	−	0.396454i
$217$	0.0216231	−	0.150392i	0.00146787	−	0.0102092i
$218$	2.42080	−	5.30081i	0.163957	−	0.359016i
$219$	2.29158	−	5.01787i	0.154851	−	0.339076i
$220$	1.03037	−	7.16640i	0.0694677	−	0.483159i
$221$	−10.2496	+	6.58702i	−0.689463	+	0.443091i
$222$	1.51353	+	0.444413i	0.101582	+	0.0298271i
$223$	0.144012	+	1.00163i	0.00964378	+	0.0670740i	0.994075	−	0.108696i	$-0.0346676\pi$
$223$	0.144012	+	1.00163i	0.00964378	+	0.0670740i	−0.984431	+	0.175770i	$0.943758\pi$
$224$	0.394306	+	0.455054i	0.0263457	+	0.0304046i
$225$	−1.68251	−	1.08128i	−0.112167	−	0.0720854i
$226$	26.1482	−	30.1767i	1.73935	−	2.00732i
$227$	−4.83803	+	1.42057i	−0.321111	+	0.0942867i	−0.438316	−	0.898821i	$-0.644425\pi$
$227$	−4.83803	+	1.42057i	−0.321111	+	0.0942867i	0.117205	+	0.993108i	$0.462607\pi$
$228$	3.52649	+	7.72193i	0.233547	+	0.511397i
$229$	−22.9504			−1.51661			−0.758304	−	0.651901i	$-0.773972\pi$
$229$	−22.9504			−1.51661			−0.758304	+	0.651901i	$0.773972\pi$
$230$	3.40221	+	10.1326i	0.224335	+	0.668122i
$231$	−0.215109			−0.0141531
$232$	−6.66717	−	14.5991i	−0.437721	−	0.958476i
$233$	−20.6511	+	6.06370i	−1.35290	+	0.397246i	−0.876254	−	0.481850i	$-0.839965\pi$
$233$	−20.6511	+	6.06370i	−1.35290	+	0.397246i	−0.476644	+	0.879097i	$0.658147\pi$
$234$	−10.5127	+	12.1323i	−0.687237	+	0.793114i
$235$	9.77080	+	6.27931i	0.637377	+	0.409617i
$236$	−22.4489	−	25.9074i	−1.46130	−	1.68643i
$237$	0.997420	+	6.93721i	0.0647894	+	0.450620i
$238$	−0.637740	−	0.187257i	−0.0413386	−	0.0121381i
$239$	−7.37760	+	4.74129i	−0.477217	+	0.306689i	−0.757047	−	0.653361i	$-0.773358\pi$
$239$	−7.37760	+	4.74129i	−0.477217	+	0.306689i	0.279830	+	0.960050i	$0.409722\pi$
$240$	0.160869	−	1.11887i	0.0103840	−	0.0722226i
$241$	3.66317	−	8.02123i	0.235966	−	0.516693i	−0.754191	−	0.656655i	$-0.771971\pi$
$241$	3.66317	−	8.02123i	0.235966	−	0.516693i	0.990157	+	0.139962i	$0.0446980\pi$
$242$	−4.67172	+	10.2296i	−0.300310	+	0.657587i
$243$	2.27704	−	15.8371i	0.146072	−	1.01595i
$244$	10.1386	−	6.51568i	0.649057	−	0.417123i
$245$	−6.70899	−	1.96994i	−0.428622	−	0.125855i
$246$	−1.76070	−	12.2459i	−0.112258	−	0.780771i
$247$	−6.74767	−	7.78723i	−0.429344	−	0.495490i
$248$	−3.12524	−	2.00847i	−0.198453	−	0.127538i
$249$	2.73247	−	3.15343i	0.173163	−	0.199841i
$250$	2.13843	−	0.627899i	0.135246	−	0.0397118i
$251$	−2.44763	−	5.35957i	−0.154493	−	0.338293i	0.816521	−	0.577316i	$-0.195900\pi$
$251$	−2.44763	−	5.35957i	−0.154493	−	0.338293i	−0.971014	+	0.239023i	$0.923173\pi$
$252$	−0.523141			−0.0329548
$253$	0.448583	+	11.6937i	0.0282022	+	0.735175i
$254$	6.66780			0.418375
$255$	1.40533	+	3.07725i	0.0880054	+	0.192705i
$256$	7.68968	−	2.25789i	0.480605	−	0.141118i
$257$	5.05121	−	5.82941i	0.315086	−	0.363628i	−0.576011	−	0.817442i	$-0.695391\pi$
$257$	5.05121	−	5.82941i	0.315086	−	0.363628i	0.891097	+	0.453814i	$0.149937\pi$
$258$	4.49462	+	2.88852i	0.279823	+	0.179831i
$259$	−0.0408599	−	0.0471549i	−0.00253891	−	0.00293006i
$260$	−1.52079	−	10.5774i	−0.0943156	−	0.655980i
$261$	−14.2886	−	4.19552i	−0.884443	−	0.259696i
$262$	−25.1678	+	16.1744i	−1.55487	+	0.999256i
$263$	−3.18652	+	22.1627i	−0.196489	+	1.36661i	0.617883	+	0.786270i	$0.287991\pi$
$263$	−3.18652	+	22.1627i	−0.196489	+	1.36661i	−0.814372	+	0.580343i	$0.802919\pi$
$264$	−2.18489	+	4.78424i	−0.134471	+	0.294450i
$265$	4.30997	−	9.43751i	0.264759	−	0.579742i
$266$	0.0799977	−	0.556396i	0.00490497	−	0.0341148i
$267$	13.4154	−	8.62153i	0.821007	−	0.527629i
$268$	34.7581	+	10.2059i	2.12319	+	0.623425i
$269$	−1.31816	−	9.16802i	−0.0803698	−	0.558984i	−0.989727	−	0.142968i	$-0.954335\pi$
$269$	−1.31816	−	9.16802i	−0.0803698	−	0.558984i	0.909357	−	0.416016i	$-0.136574\pi$
$270$	7.29746	+	8.42172i	0.444110	+	0.512530i
$271$	18.4727	+	11.8717i	1.12214	+	0.721154i	0.963905	−	0.266247i	$-0.0857838\pi$
$271$	18.4727	+	11.8717i	1.12214	+	0.721154i	0.158233	+	0.987402i	$0.449420\pi$
$272$	2.50419	−	2.88999i	0.151839	−	0.175232i
$273$	−0.304632	+	0.0894481i	−0.0184372	+	0.00541365i
$274$	17.8624	+	39.1132i	1.07911	+	2.36291i
$275$	2.44009			0.147143
$276$	−0.545473	−	14.2194i	−0.0328336	−	0.855909i
$277$	12.5089			0.751589			0.375795	−	0.926703i	$-0.377370\pi$
$277$	12.5089			0.751589			0.375795	+	0.926703i	$0.377370\pi$
$278$	14.3470	+	31.4155i	0.860474	+	1.88418i
$279$	−3.30740	+	0.971141i	−0.198009	+	0.0581407i
$280$	0.124435	−	0.143605i	0.00743639	−	0.00858206i
$281$	−20.6303	−	13.2583i	−1.23070	−	0.790922i	−0.246699	−	0.969092i	$-0.579346\pi$
$281$	−20.6303	−	13.2583i	−1.23070	−	0.790922i	−0.984000	+	0.178171i	$0.942982\pi$
$282$	−16.9514	−	19.5629i	−1.00944	−	1.16496i
$283$	2.51410	+	17.4860i	0.149448	+	1.03943i	0.917126	+	0.398597i	$0.130503\pi$
$283$	2.51410	+	17.4860i	0.149448	+	1.03943i	−0.767678	+	0.640836i	$0.778588\pi$
$284$	−5.40006	−	1.58560i	−0.320435	−	0.0940882i
$285$	−2.40685	+	1.54679i	−0.142570	+	0.0916239i
$286$	2.78736	−	19.3865i	0.164820	−	1.14635i
$287$	−0.203290	+	0.445142i	−0.0119998	+	0.0262759i
$288$	5.67474	−	12.4259i	0.334387	−	0.732205i
$289$	0.790638	−	5.49901i	0.0465081	−	0.323471i
$290$	13.9604	−	8.97182i	0.819784	−	0.526843i
$291$	13.7972	+	4.05122i	0.808806	+	0.237487i
$292$	2.32939	+	16.2012i	0.136317	+	0.948106i
$293$	−5.55996	−	6.41653i	−0.324816	−	0.374858i	0.569731	−	0.821831i	$-0.307047\pi$
$293$	−5.55996	−	6.41653i	−0.324816	−	0.374858i	−0.894547	+	0.446973i	$0.852502\pi$
$294$	13.1098	+	8.42515i	0.764578	+	0.491365i
$295$	7.56583	−	8.73143i	0.440500	−	0.508364i
$296$	−1.46379	+	0.429809i	−0.0850813	+	0.0249821i
$297$	5.06826	+	11.0979i	0.294090	+	0.643968i
$298$	−35.5535			−2.05956
$299$	5.49782	+	16.3738i	0.317947	+	0.946921i
$300$	−2.96714			−0.171308
$301$	−0.0877903	−	0.192234i	−0.00506015	−	0.0110802i
$302$	−0.945756	+	0.277699i	−0.0544222	+	0.0159798i
$303$	11.3836	−	13.1374i	0.653970	−	0.754722i
$304$	2.72064	+	1.74845i	0.156039	+	0.100280i
$305$	2.65988	+	3.06967i	0.152304	+	0.175769i
$306$	2.14600	+	14.9258i	0.122679	+	0.853251i
$307$	14.0850	+	4.13574i	0.803875	+	0.236039i	0.657759	−	0.753228i	$-0.271504\pi$
$307$	14.0850	+	4.13574i	0.803875	+	0.236039i	0.146116	+	0.989267i	$0.453323\pi$
$308$	0.536936	−	0.345068i	0.0305948	−	0.0196621i
$309$	0.165561	−	1.15150i	0.00941843	−	0.0655066i
$310$	1.59570	−	3.49409i	0.0906295	−	0.198451i
$311$	12.5355	−	27.4490i	0.710826	−	1.55649i	−0.115506	−	0.993307i	$-0.536849\pi$
$311$	12.5355	−	27.4490i	0.710826	−	1.55649i	0.826332	−	0.563184i	$-0.190424\pi$
$312$	−1.10477	+	7.68388i	−0.0625455	+	0.435014i
$313$	−4.68243	+	3.00922i	−0.264667	+	0.170091i	−0.666243	−	0.745734i	$-0.732099\pi$
$313$	−4.68243	+	3.00922i	−0.264667	+	0.170091i	0.401576	+	0.915826i	$0.368462\pi$
$314$	−15.2228	−	4.46983i	−0.859074	−	0.252247i
$315$	−0.0250918	−	0.174517i	−0.00141376	−	0.00983293i
$316$	−13.6180	−	15.7160i	−0.766074	−	0.884097i
$317$	2.36484	+	1.51979i	0.132823	+	0.0853600i	0.605365	−	0.795948i	$-0.293027\pi$
$317$	2.36484	+	1.51979i	0.132823	+	0.0853600i	−0.472542	+	0.881308i	$0.656664\pi$
$318$	−15.1424	+	17.4752i	−0.849142	+	0.979962i
$319$	17.4328	−	5.11873i	0.976049	−	0.286594i
$320$	5.38451	+	11.7904i	0.301004	+	0.659106i
$321$	−17.1503			−0.957238
$322$	−0.478662	+	0.811620i	−0.0266748	+	0.0452298i
$323$	−9.67876			−0.538541
$324$	1.23259	+	2.69900i	0.0684774	+	0.149945i
$325$	3.45561	−	1.01466i	0.191683	−	0.0562831i
$326$	10.4300	−	12.0369i	0.577667	−	0.666663i
$327$	−2.19963	−	1.41362i	−0.121640	−	0.0781732i
$328$	7.83558	+	9.04274i	0.432648	+	0.499302i
$329$	0.145715	+	1.01347i	0.00803354	+	0.0558745i
$330$	−5.21797	−	1.53213i	−0.287240	−	0.0843412i
$331$	−11.6540	+	7.48954i	−0.640560	+	0.411663i	−0.820206	−	0.572069i	$-0.806141\pi$
$331$	−11.6540	+	7.48954i	−0.640560	+	0.411663i	0.179646	+	0.983731i	$0.442505\pi$
$332$	−1.76195	+	12.2546i	−0.0966995	+	0.672560i
$333$	−0.588043	+	1.28764i	−0.0322246	+	0.0705620i
$334$	1.23381	−	2.70167i	0.0675111	−	0.147829i
$335$	−1.73751	+	12.0847i	−0.0949303	+	0.660255i
$336$	0.0838301	−	0.0538744i	0.00457331	−	0.00293909i
$337$	−20.7059	−	6.07980i	−1.12792	−	0.331188i	−0.336031	−	0.941851i	$-0.609085\pi$
$337$	−20.7059	−	6.07980i	−1.12792	−	0.331188i	−0.791890	+	0.610663i	$0.790903\pi$
$338$	0.00927685	+	0.0645219i	0.000504594	+	0.00350953i
$339$	−11.7325	−	13.5400i	−0.637220	−	0.735391i
$340$	−8.44426	−	5.42680i	−0.457955	−	0.294310i
$341$	2.75404	−	3.17834i	0.149140	−	0.172117i
$342$	−12.2362	+	3.59288i	−0.661659	+	0.194281i
$343$	−0.512414	−	1.12203i	−0.0276677	−	0.0605839i
$344$	−5.16718			−0.278596
$345$	4.71737	−	0.863983i	0.253974	−	0.0465153i
$346$	6.01920			0.323594
$347$	7.85449	+	17.1989i	0.421651	+	0.923288i	0.994608	+	0.103702i	$0.0330689\pi$
$347$	7.85449	+	17.1989i	0.421651	+	0.923288i	−0.572957	+	0.819585i	$0.694204\pi$
$348$	−21.1981	+	6.22434i	−1.13634	+	0.333659i
$349$	−13.7056	+	15.8171i	−0.733643	+	0.846669i	−0.992877	−	0.119146i	$-0.961984\pi$
$349$	−13.7056	+	15.8171i	−0.733643	+	0.846669i	0.259234	+	0.965815i	$0.416530\pi$
$350$	0.165284	+	0.106222i	0.00883481	+	0.00567779i
$351$	11.7924	+	13.6091i	0.629431	+	0.726402i
$352$	2.37187	+	16.4967i	0.126421	+	0.879277i
$353$	−1.54672	−	0.454159i	−0.0823238	−	0.0241724i	0.240311	−	0.970696i	$-0.422750\pi$
$353$	−1.54672	−	0.454159i	−0.0823238	−	0.0241724i	−0.322635	+	0.946523i	$0.604569\pi$
$354$	−21.6615	+	13.9210i	−1.15129	+	0.739891i
$355$	0.269942	−	1.87748i	0.0143270	−	0.0996465i
$356$	−19.6560	+	43.0406i	−1.04177	+	2.28115i
$357$	−0.123889	+	0.271278i	−0.00655688	+	0.0143576i
$358$	6.27632	−	43.6527i	0.331714	−	2.30712i
$359$	29.2892	−	18.8230i	1.54583	−	0.993442i	0.559464	−	0.828854i	$-0.311007\pi$
$359$	29.2892	−	18.8230i	1.54583	−	0.993442i	0.986362	−	0.164588i	$-0.0526294\pi$
$360$	−4.13631	−	1.21453i	−0.218003	−	0.0640113i
$361$	1.53906	+	10.7044i	0.0810034	+	0.563391i
$362$	−5.81675	−	6.71289i	−0.305722	−	0.352822i
$363$	4.24491	+	2.72804i	0.222800	+	0.143185i
$364$	0.616908	−	0.711950i	0.0323348	−	0.0373163i
$365$	−5.29292	+	1.55414i	−0.277044	+	0.0813475i
$366$	−3.76052	−	8.23440i	−0.196566	−	0.430419i
$367$	−22.6244			−1.18098			−0.590491	−	0.807044i	$-0.701066\pi$
$367$	−22.6244			−1.18098			−0.590491	+	0.807044i	$0.701066\pi$
$368$	−3.10352	−	4.44480i	−0.161782	−	0.231701i
$369$	11.1023			0.577961
$370$	−0.655288	−	1.43488i	−0.0340668	−	0.0745959i
$371$	0.877577	−	0.257680i	0.0455615	−	0.0133781i
$372$	−3.34890	+	3.86483i	−0.173632	+	0.200382i
$373$	9.08151	+	5.83633i	0.470223	+	0.302194i	0.754209	−	0.656635i	$-0.228021\pi$
$373$	9.08151	+	5.83633i	0.470223	+	0.302194i	−0.283986	+	0.958828i	$0.591657\pi$
$374$	−12.0478	−	13.9038i	−0.622974	−	0.718951i
$375$	−0.142315	−	0.989821i	−0.00734911	−	0.0511142i
$376$	24.0207	+	7.05312i	1.23877	+	0.363737i
$377$	22.5594	−	14.4981i	1.16187	−	0.746688i
$378$	−0.139806	+	0.972370i	−0.00719083	+	0.0500133i
$379$	−1.53173	+	3.35401i	−0.0786795	+	0.172284i	−0.944884	−	0.327406i	$-0.893826\pi$
$379$	−1.53173	+	3.35401i	−0.0786795	+	0.172284i	0.866204	+	0.499690i	$0.166553\pi$
$380$	3.52649	−	7.72193i	0.180905	−	0.396127i
$381$	0.425774	−	2.96133i	0.0218131	−	0.151713i
$382$	−11.2105	+	7.20457i	−0.573580	+	0.368618i
$383$	5.70202	+	1.67426i	0.291360	+	0.0855509i	0.424146	−	0.905594i	$-0.360574\pi$
$383$	5.70202	+	1.67426i	0.291360	+	0.0855509i	−0.132787	+	0.991145i	$0.542392\pi$
$384$	−2.16711	−	15.0726i	−0.110590	−	0.769171i
$385$	0.140866	+	0.162568i	0.00717921	+	0.00828525i
$386$	18.9111	+	12.1534i	0.962549	+	0.618593i
$387$	−3.13973	+	3.62344i	−0.159601	+	0.184190i
$388$	−40.9382	+	12.0205i	−2.07832	+	0.610250i
$389$	2.75929	+	6.04199i	0.139901	+	0.306341i	0.966594	−	0.256313i	$-0.0825077\pi$
$389$	2.75929	+	6.04199i	0.139901	+	0.306341i	−0.826693	+	0.562654i	$0.809780\pi$
$390$	−8.02667			−0.406446
$391$	15.0055	+	6.16908i	0.758860	+	0.311984i
$392$	−15.0715			−0.761226
$393$	5.57632	+	12.2104i	0.281288	+	0.615935i
$394$	10.9394	−	3.21210i	0.551119	−	0.161823i
$395$	4.58962	−	5.29670i	0.230929	−	0.266506i
$396$	−12.1815	−	7.82858i	−0.612144	−	0.393401i
$397$	2.98449	+	3.44429i	0.149787	+	0.172864i	0.825685	−	0.564132i	$-0.190789\pi$
$397$	2.98449	+	3.44429i	0.149787	+	0.172864i	−0.675897	+	0.736996i	$0.736244\pi$
$398$	−8.43058	−	58.6360i	−0.422587	−	2.93916i
$399$	−0.242000	−	0.0710577i	−0.0121152	−	0.00355733i
$400$	−0.950930	+	0.611126i	−0.0475465	+	0.0305563i
$401$	3.97219	−	27.6272i	0.198362	−	1.37964i	−0.610676	−	0.791880i	$-0.709102\pi$
$401$	3.97219	−	27.6272i	0.198362	−	1.37964i	0.809038	−	0.587756i	$-0.199989\pi$
$402$	11.3035	−	24.7512i	0.563767	−	1.23448i
$403$	2.57858	−	5.64630i	0.128448	−	0.281262i
$404$	−7.34038	+	51.0534i	−0.365197	+	2.54000i
$405$	−0.841254	+	0.540641i	−0.0418022	+	0.0268647i
$406$	1.40367	+	0.412155i	0.0696629	+	0.0204549i
$407$	−0.245784	−	1.70947i	−0.0121831	−	0.0847351i
$408$	4.77515	+	5.51082i	0.236405	+	0.272826i
$409$	6.83017	+	4.38949i	0.337730	+	0.217046i	0.698502	−	0.715608i	$-0.253850\pi$
$409$	6.83017	+	4.38949i	0.337730	+	0.217046i	−0.360772	+	0.932654i	$0.617487\pi$
$410$	−8.10184	+	9.35002i	−0.400121	+	0.461764i
$411$	18.5117	−	5.43552i	0.913115	−	0.268115i
$412$	1.43393	+	3.13987i	0.0706446	+	0.154690i
$413$	1.01850			0.0501169
$414$	21.2605	+	2.22893i	1.04490	+	0.109546i
$415$	−4.17259			−0.204824
$416$	10.2188	+	22.3760i	0.501016	+	1.09707i
$417$	14.8685	−	4.36578i	0.728113	−	0.213793i
$418$	10.1890	−	11.7587i	0.498360	−	0.575138i
$419$	−23.3315	−	14.9942i	−1.13982	−	0.732517i	−0.172232	−	0.985056i	$-0.555098\pi$
$419$	−23.3315	−	14.9942i	−1.13982	−	0.732517i	−0.967587	+	0.252539i	$0.918734\pi$
$420$	−0.171292	−	0.197682i	−0.00835821	−	0.00964589i
$421$	4.97445	+	34.5981i	0.242440	+	1.68621i	0.639799	+	0.768543i	$0.279018\pi$
$421$	4.97445	+	34.5981i	0.242440	+	1.68621i	−0.397359	+	0.917663i	$0.630073\pi$
$422$	31.5259	+	9.25685i	1.53466	+	0.450616i
$423$	19.5416	−	12.5586i	0.950145	−	0.610621i
$424$	3.18261	−	22.1355i	0.154561	−	1.07500i
$425$	1.40533	−	3.07725i	0.0681687	−	0.149269i
$426$	−1.75612	+	3.84537i	−0.0850844	+	0.186309i
$427$	−0.0509583	+	0.354423i	−0.00246604	+	0.0171517i
$428$	42.8092	−	27.5118i	2.06926	−	1.32983i
$429$	−8.43201	−	2.47586i	−0.407101	−	0.119536i
$430$	−0.760355	−	5.28838i	−0.0366676	−	0.255028i
$431$	6.06858	+	7.00351i	0.292313	+	0.337347i	0.882843	−	0.469669i	$-0.155627\pi$
$431$	6.06858	+	7.00351i	0.292313	+	0.337347i	−0.590530	+	0.807016i	$0.701081\pi$
$432$	−4.75465	−	3.05563i	−0.228758	−	0.147014i
$433$	−14.8185	+	17.1014i	−0.712129	+	0.821841i	−0.990337	−	0.138680i	$-0.955714\pi$
$433$	−14.8185	+	17.1014i	−0.712129	+	0.821841i	0.278208	+	0.960521i	$0.410260\pi$
$434$	0.324909	−	0.0954019i	0.0155961	−	0.00457944i
$435$	−3.09315	−	6.77305i	−0.148305	−	0.324743i
$436$	7.75820			0.371550
$437$	−3.35816	+	13.3037i	−0.160642	+	0.636404i
$438$	12.2944			0.587448
$439$	−7.68428	−	16.8262i	−0.366751	−	0.803072i	−0.999586	−	0.0287853i	$-0.990836\pi$
$439$	−7.68428	−	16.8262i	−0.366751	−	0.803072i	0.632835	−	0.774287i	$-0.281891\pi$
$440$	5.04649	−	1.48178i	0.240582	−	0.0706412i
$441$	−9.15787	+	10.5687i	−0.436089	+	0.503274i
$442$	−22.8434	−	14.6805i	−1.08655	−	0.698282i
$443$	14.6551	+	16.9129i	0.696284	+	0.803554i	0.988245	−	0.152876i	$-0.0488534\pi$
$443$	14.6551	+	16.9129i	0.696284	+	0.803554i	−0.291962	+	0.956430i	$0.594308\pi$
$444$	0.298872	+	2.07870i	0.0141838	+	0.0986507i
$445$	−15.3009	−	4.49275i	−0.725333	−	0.212977i
$446$	−1.89727	+	1.21930i	−0.0898384	+	0.0577356i
$447$	−2.27028	+	15.7901i	−0.107381	+	0.746848i
$448$	−0.474677	+	1.03940i	−0.0224264	+	0.0491069i
$449$	2.04143	−	4.47012i	0.0963412	−	0.210958i	−0.855325	−	0.518092i	$-0.826643\pi$
$449$	2.04143	−	4.47012i	0.0963412	−	0.210958i	0.951666	+	0.307134i	$0.0993699\pi$
$450$	0.634356	−	4.41204i	0.0299038	−	0.207986i
$451$	−11.3950	+	7.32313i	−0.536570	+	0.344833i
$452$	51.0058	+	14.9767i	2.39911	+	0.704442i
$453$	0.0629411	+	0.437765i	0.00295723	+	0.0205680i
$454$	−7.35916	−	8.49293i	−0.345383	−	0.398593i
$455$	0.267092	+	0.171650i	0.0125215	+	0.00804706i
$456$	−4.03843	+	4.66060i	−0.189117	+	0.218252i
$457$	−11.1134	+	3.26318i	−0.519861	+	0.152645i	−0.531128	−	0.847291i	$-0.678232\pi$
$457$	−11.1134	+	3.26318i	−0.519861	+	0.152645i	0.0112669	+	0.999937i	$0.496414\pi$
$458$	−21.2484	−	46.5275i	−0.992873	−	2.17409i
$459$	16.9148			0.789516
$460$	−10.3891	+	9.72399i	−0.484395	+	0.453383i
$461$	−15.5495			−0.724210			−0.362105	−	0.932137i	$-0.617942\pi$
$461$	−15.5495			−0.724210			−0.362105	+	0.932137i	$0.617942\pi$
$462$	−0.199156	−	0.436091i	−0.00926558	−	0.0202888i
$463$	−9.71687	+	2.85313i	−0.451581	+	0.132596i	−0.499611	−	0.866250i	$-0.666524\pi$
$463$	−9.71687	+	2.85313i	−0.451581	+	0.132596i	0.0480300	+	0.998846i	$0.484706\pi$
$464$	−5.51175	+	6.36089i	−0.255876	+	0.295297i
$465$	−1.44991	−	0.931803i	−0.0672381	−	0.0432113i
$466$	−31.4125	−	36.2520i	−1.45516	−	1.67934i
$467$	−0.0227489	−	0.158222i	−0.00105269	−	0.00732164i	0.989288	−	0.145975i	$-0.0466318\pi$
$467$	−0.0227489	−	0.158222i	−0.00105269	−	0.00732164i	−0.990341	+	0.138653i	$0.955723\pi$
$468$	−20.5065	−	6.02126i	−0.947914	−	0.278333i
$469$	−0.905432	+	0.581886i	−0.0418089	+	0.0268690i
$470$	−3.68389	+	25.6220i	−0.169925	+	1.18185i
$471$	−2.95722	+	6.47540i	−0.136261	+	0.298371i
$472$	10.3450	−	22.6524i	0.476168	−	1.04266i
$473$	0.832472	−	5.78997i	0.0382771	−	0.266223i
$474$	−13.1404	+	8.44481i	−0.603558	+	0.387883i
$475$	2.74514	+	0.806046i	0.125956	+	0.0369839i
$476$	−0.125932	−	0.875877i	−0.00577209	−	0.0401458i
$477$	−13.5885	−	15.6819i	−0.622173	−	0.718026i
$478$	−16.4425	−	10.5670i	−0.752063	−	0.483321i
$479$	−3.84712	+	4.43982i	−0.175779	+	0.202860i	−0.836802	−	0.547506i	$-0.815577\pi$
$479$	−3.84712	+	4.43982i	−0.175779	+	0.202860i	0.661022	+	0.750366i	$0.270123\pi$
$480$	6.55353	−	1.92429i	0.299126	−	0.0878314i
$481$	−1.05892	−	2.31870i	−0.0482825	−	0.105724i
$482$	19.6530			0.895169
$483$	0.329895	+	0.264411i	0.0150107	+	0.0120311i
$484$	−14.9720			−0.680545
$485$	−5.97353	−	13.0802i	−0.271244	−	0.593942i
$486$	34.2149	−	10.0464i	1.55202	−	0.455714i
$487$	4.54083	−	5.24040i	0.205765	−	0.237465i	−0.643482	−	0.765461i	$-0.722511\pi$
$487$	4.54083	−	5.24040i	0.205765	−	0.237465i	0.849247	+	0.527996i	$0.177056\pi$
$488$	7.36514	+	4.73329i	0.333404	+	0.214266i
$489$	−4.67986	−	5.40085i	−0.211631	−	0.244235i
$490$	−2.21778	−	15.4250i	−0.100189	−	0.696831i
$491$	21.0671	+	6.18586i	0.950745	+	0.279164i	0.720097	−	0.693873i	$-0.244097\pi$
$491$	21.0671	+	6.18586i	0.950745	+	0.279164i	0.230648	+	0.973037i	$0.425915\pi$
$492$	13.8563	−	8.90487i	0.624688	−	0.401463i
$493$	3.58481	−	24.9329i	0.161452	−	1.12292i
$494$	9.53982	−	20.8893i	0.429217	−	0.939854i
$495$	2.02730	−	4.43918i	0.0911205	−	0.199526i
$496$	−0.277260	+	1.92839i	−0.0124493	+	0.0865871i
$497$	0.140669	−	0.0904024i	0.00630986	−	0.00405510i
$498$	8.92279	+	2.61997i	0.399840	+	0.117404i
$499$	4.04910	+	28.1621i	0.181263	+	1.26071i	0.853783	+	0.520630i	$0.174303\pi$
$499$	4.04910	+	28.1621i	0.181263	+	1.26071i	−0.672520	+	0.740079i	$0.734788\pi$
$500$	1.94306	+	2.24241i	0.0868963	+	0.100284i
$501$	−1.12109	−	0.720480i	−0.0500866	−	0.0321887i
$502$	8.59936	−	9.92419i	0.383808	−	0.442938i
$503$	−32.9609	+	9.67821i	−1.46966	+	0.431530i	−0.915987	−	0.401207i	$-0.868591\pi$
$503$	−32.9609	+	9.67821i	−1.46966	+	0.431530i	−0.553668	+	0.832737i	$0.686773\pi$
$504$	−0.157872	−	0.345691i	−0.00703217	−	0.0153983i
$505$	−17.3832			−0.773544
$506$	−23.2913	+	11.7359i	−1.03543	+	0.521723i
$507$	0.0292481			0.00129895
$508$	3.68765	+	8.07482i	0.163613	+	0.358262i
$509$	6.60273	−	1.93874i	0.292661	−	0.0859329i	−0.132107	−	0.991236i	$-0.542174\pi$
$509$	6.60273	−	1.93874i	0.292661	−	0.0859329i	0.424767	+	0.905303i	$0.360356\pi$
$510$	−4.93741	+	5.69808i	−0.218632	+	0.252315i
$511$	−0.409102	−	0.262914i	−0.0180976	−	0.0116306i
$512$	−8.24708	−	9.51763i	−0.364473	−	0.420624i
$513$	2.03584	+	14.1595i	0.0898843	+	0.625159i
$514$	16.4946	+	4.84325i	0.727545	+	0.213626i
$515$	−0.978666	+	0.628951i	−0.0431252	+	0.0277149i
$516$	−1.01228	+	7.04056i	−0.0445631	+	0.309943i
$517$	−11.7731	+	25.7796i	−0.517782	+	1.13378i
$518$	0.0577675	−	0.126493i	0.00253816	−	0.00555779i
$519$	0.384358	−	2.67327i	0.0168714	−	0.117343i
$520$	6.53056	−	4.19694i	0.286384	−	0.184048i
$521$	5.29187	+	1.55383i	0.231841	+	0.0680747i	0.395589	−	0.918427i	$-0.370540\pi$
$521$	5.29187	+	1.55383i	0.231841	+	0.0680747i	−0.163748	+	0.986502i	$0.552358\pi$
$522$	−4.72337	−	32.8517i	−0.206736	−	1.43788i
$523$	3.11663	+	3.59678i	0.136281	+	0.157276i	0.819787	−	0.572668i	$-0.194092\pi$
$523$	3.11663	+	3.59678i	0.136281	+	0.157276i	−0.683507	+	0.729944i	$0.739546\pi$
$524$	−33.5066	−	21.5334i	−1.46374	−	0.940689i
$525$	0.0577299	−	0.0666238i	0.00251954	−	0.00290770i
$526$	−47.8808	+	14.0591i	−2.08770	+	0.613005i
$527$	−2.42212	−	5.30369i	−0.105509	−	0.231033i
$528$	2.75822			0.120036
$529$	13.6859	−	18.4850i	0.595039	−	0.803697i
$530$	23.1230			1.00440
$531$	−9.59886	−	21.0186i	−0.416555	−	0.912129i
$532$	0.718048	−	0.210838i	0.0311313	−	0.00914098i
$533$	−13.0922	+	15.1092i	−0.567087	+	0.654453i
$534$	29.8989	+	19.2149i	1.29385	+	0.831508i
$535$	11.2311	+	12.9614i	0.485562	+	0.560368i
$536$	3.74514	+	26.0480i	0.161766	+	1.12510i
$537$	−18.9864	−	5.57492i	−0.819325	−	0.240576i
$538$	17.3660	−	11.1604i	0.748700	−	0.481160i
$539$	2.42813	−	16.8880i	0.104587	−	0.727419i
$540$	−6.16297	+	13.4950i	−0.265212	+	0.580733i
$541$	−7.02447	+	15.3814i	−0.302006	+	0.661300i	−0.998411	−	0.0563484i	$-0.982054\pi$
$541$	−7.02447	+	15.3814i	−0.302006	+	0.661300i	0.696406	+	0.717648i	$0.254782\pi$
$542$	−6.96478	+	48.4411i	−0.299163	+	2.08072i
$543$	−3.35278	+	2.15470i	−0.143882	+	0.0924671i
$544$	22.1704	+	6.50980i	0.950546	+	0.279106i
$545$	0.372112	+	2.58809i	0.0159395	+	0.110862i
$546$	−0.463379	−	0.534768i	−0.0198308	−	0.0228859i
$547$	−32.4460	−	20.8518i	−1.38729	−	0.891557i	−0.387746	−	0.921766i	$-0.626746\pi$
$547$	−32.4460	−	20.8518i	−1.38729	−	0.891557i	−0.999544	+	0.0302093i	$0.990383\pi$
$548$	−37.4879	+	43.2633i	−1.60140	+	1.84812i
$549$	7.79444	−	2.28865i	0.332659	−	0.0976774i
$550$	2.25913	+	4.94681i	0.0963298	+	0.210933i
$551$	21.3030			0.907539
$552$	9.23157	−	4.65154i	0.392922	−	0.197983i
$553$	0.617845			0.0262734
$554$	11.5813	+	25.3594i	0.492040	+	1.07742i
$555$	−0.679108	+	0.199404i	−0.0288265	+	0.00846423i
$556$	−30.1100	+	34.7488i	−1.27695	+	1.47368i
$557$	35.4471	+	22.7805i	1.50194	+	0.965239i	0.994632	+	0.103475i	$0.0329961\pi$
$557$	35.4471	+	22.7805i	1.50194	+	0.965239i	0.507309	+	0.861764i	$0.330640\pi$
$558$	−5.03092	−	5.80599i	−0.212976	−	0.245787i
$559$	−1.22870	−	8.54579i	−0.0519685	−	0.361449i
$560$	−0.0956126	−	0.0280744i	−0.00404037	−	0.00118636i
$561$	−6.94434	+	4.46286i	−0.293190	+	0.188422i
$562$	7.77824	−	54.0988i	0.328105	−	2.28202i
$563$	−2.50064	+	5.47564i	−0.105389	+	0.230771i	−0.954979	−	0.296674i	$-0.904123\pi$
$563$	−2.50064	+	5.47564i	−0.105389	+	0.230771i	0.849589	+	0.527445i	$0.176850\pi$
$564$	14.3160	−	31.3477i	0.602814	−	1.31998i
$565$	−2.54971	+	17.7336i	−0.107267	+	0.746058i
$566$	−33.1217	+	21.2860i	−1.39221	+	0.894719i
$567$	−0.0845850	−	0.0248364i	−0.00355224	−	0.00104303i
$568$	−0.581849	−	4.04685i	−0.0244139	−	0.169802i
$569$	11.4512	+	13.2154i	0.480061	+	0.554020i	0.943183	−	0.332275i	$-0.107816\pi$
$569$	11.4512	+	13.2154i	0.480061	+	0.554020i	−0.463121	+	0.886295i	$0.653271\pi$
$570$	−5.36417	−	3.44734i	−0.224680	−	0.144393i
$571$	−8.64327	+	9.97487i	−0.361710	+	0.417435i	−0.907212	−	0.420674i	$-0.861794\pi$
$571$	−8.64327	+	9.97487i	−0.361710	+	0.417435i	0.545502	+	0.838109i	$0.316339\pi$
$572$	25.0189	−	7.34622i	1.04609	−	0.307161i
$573$	2.48387	+	5.43891i	0.103765	+	0.227214i
$574$	−1.09065			−0.0455229
$575$	−3.74217	−	2.99936i	−0.156059	−	0.125082i
$576$	25.9235			1.08015
$577$	−13.4953	−	29.5506i	−0.561818	−	1.23021i	−0.951041	−	0.309065i	$-0.899984\pi$
$577$	−13.4953	−	29.5506i	−0.561818	−	1.23021i	0.389223	−	0.921143i	$-0.372743\pi$
$578$	11.8802	−	3.48833i	0.494149	−	0.145095i
$579$	6.60519	−	7.62280i	0.274502	−	0.316793i
$580$	18.5859	+	11.9444i	0.771736	+	0.495965i
$581$	−0.240883	−	0.277994i	−0.00999351	−	0.0115331i
$582$	4.56092	+	31.7219i	0.189056	+	1.31491i
$583$	24.2907	+	7.13240i	1.00602	+	0.295394i
$584$	−10.0028	+	6.42841i	−0.413919	+	0.266009i
$585$	1.02509	−	7.12967i	0.0423823	−	0.294776i
$586$	7.86064	−	17.2124i	0.324720	−	0.711037i
$587$	−5.47162	+	11.9812i	−0.225838	+	0.494516i	−0.988301	−	0.152515i	$-0.951263\pi$
$587$	−5.47162	+	11.9812i	−0.225838	+	0.494516i	0.762463	+	0.647032i	$0.223990\pi$
$588$	−2.95259	+	20.5357i	−0.121763	+	0.846879i
$589$	4.14825	−	2.66592i	0.170926	−	0.109847i
$590$	24.7060	+	7.25434i	1.01713	+	0.298656i
$591$	−0.728029	−	5.06355i	−0.0299471	−	0.208287i
$592$	0.523923	+	0.604640i	0.0215331	+	0.0248505i
$593$	26.5698	+	17.0754i	1.09109	+	0.701202i	0.957094	−	0.289779i	$-0.0935818\pi$
$593$	26.5698	+	17.0754i	1.09109	+	0.701202i	0.133999	+	0.990982i	$0.457218\pi$
$594$	−17.8065	+	20.5498i	−0.730610	+	0.843169i
$595$	0.286148	−	0.0840206i	0.0117309	−	0.00344451i
$596$	−19.6630	−	43.0559i	−0.805426	−	1.76364i
$597$	−26.5800			−1.08785
$598$	−28.1046	+	26.3053i	−1.14928	+	1.07570i
$599$	−5.38162			−0.219887			−0.109943	−	0.993938i	$-0.535067\pi$
$599$	−5.38162			−0.219887			−0.109943	+	0.993938i	$0.535067\pi$
$600$	−0.895412	−	1.96068i	−0.0365551	−	0.0800444i
$601$	−32.4793	+	9.53678i	−1.32486	+	0.389013i	−0.866243	−	0.499622i	$-0.833472\pi$
$601$	−32.4793	+	9.53678i	−1.32486	+	0.389013i	−0.458614	+	0.888636i	$0.651654\pi$
$602$	0.308437	−	0.355955i	0.0125710	−	0.0145077i
$603$	20.5416	+	13.2013i	0.836518	+	0.537598i
$604$	−0.859352	−	0.991745i	−0.0349665	−	0.0403535i
$605$	−0.718112	−	4.99458i	−0.0291954	−	0.203058i
$606$	37.1728	+	10.9149i	1.51004	+	0.443388i
$607$	18.3320	−	11.7812i	0.744072	−	0.478186i	−0.112863	−	0.993611i	$-0.536002\pi$
$607$	18.3320	−	11.7812i	0.744072	−	0.478186i	0.856935	+	0.515424i	$0.172366\pi$
$608$	−2.78103	+	19.3425i	−0.112786	+	0.784442i
$609$	0.272679	−	0.597084i	0.0110495	−	0.0241951i
$610$	−3.76052	+	8.23440i	−0.152259	+	0.333401i
$611$	−5.95300	+	41.4040i	−0.240833	+	1.67503i
$612$	−16.8885	+	10.8536i	−0.682678	+	0.438731i
$613$	6.50705	+	1.91064i	0.262817	+	0.0771701i	0.410486	−	0.911867i	$-0.365359\pi$
$613$	6.50705	+	1.91064i	0.262817	+	0.0771701i	−0.147669	+	0.989037i	$0.547177\pi$
$614$	4.65607	+	32.3837i	0.187904	+	1.30690i
$615$	3.63522	+	4.19526i	0.146586	+	0.169169i
$616$	0.390055	+	0.250673i	0.0157158	+	0.0100999i
$617$	21.1308	−	24.3863i	0.850695	−	0.981755i	−0.149280	−	0.988795i	$-0.547696\pi$
$617$	21.1308	−	24.3863i	0.850695	−	0.981755i	0.999975	+	0.00704038i	$0.00224104\pi$
$618$	2.48773	−	0.730462i	0.100071	−	0.0293835i
$619$	−14.5801	−	31.9260i	−0.586024	−	1.28321i	−0.937815	−	0.347134i	$-0.887155\pi$
$619$	−14.5801	−	31.9260i	−0.586024	−	1.28321i	0.351792	−	0.936078i	$-0.385573\pi$
$620$	5.11391			0.205379
$621$	5.86879	−	23.2499i	0.235506	−	0.932986i
$622$	67.2534			2.69661
$623$	−0.583995	−	1.27877i	−0.0233973	−	0.0512329i
$624$	3.90613	−	1.14694i	0.156370	−	0.0459144i
$625$	−0.654861	+	0.755750i	−0.0261944	+	0.0302300i
$626$	−10.4358	−	6.70667i	−0.417098	−	0.268052i
$627$	−4.57170	−	5.27603i	−0.182576	−	0.210704i
$628$	−3.00600	−	20.9072i	−0.119952	−	0.834287i
$629$	−2.29740	−	0.674577i	−0.0916033	−	0.0268971i
$630$	0.330568	−	0.212443i	0.0131702	−	0.00846395i
$631$	1.85675	−	12.9139i	0.0739159	−	0.514096i	−0.918904	−	0.394480i	$-0.870925\pi$
$631$	1.85675	−	12.9139i	0.0739159	−	0.514096i	0.992820	−	0.119616i	$-0.0381663\pi$
$632$	6.27554	−	13.7415i	0.249628	−	0.546608i
$633$	6.12428	−	13.4103i	0.243418	−	0.533012i
$634$	−0.891617	+	6.20133i	−0.0354106	+	0.246286i
$635$	−2.51684	+	1.61748i	−0.0998779	+	0.0641876i
$636$	−29.5373	−	8.67294i	−1.17123	−	0.343904i
$637$	−3.58384	−	24.9261i	−0.141997	−	0.987610i
$638$	26.5172	+	30.6024i	1.04982	+	1.21156i
$639$	−3.19136	−	2.05097i	−0.126248	−	0.0811349i
$640$	−9.97196	+	11.5083i	−0.394176	+	0.454904i
$641$	34.6688	−	10.1797i	1.36934	−	0.402073i	0.487291	−	0.873239i	$-0.337985\pi$
$641$	34.6688	−	10.1797i	1.36934	−	0.402073i	0.882044	+	0.471166i	$0.156167\pi$
$642$	−15.8784	−	34.7689i	−0.626672	−	1.37222i
$643$	31.5510			1.24425			0.622126	−	0.782917i	$-0.286269\pi$
$643$	31.5510			1.24425			0.622126	+	0.782917i	$0.286269\pi$
$644$	−1.24761	−	0.130798i	−0.0491628	−	0.00515417i
$645$	−2.39725			−0.0943915
$646$	−8.96097	−	19.6218i	−0.352565	−	0.772009i
$647$	13.3013	−	3.90562i	0.522929	−	0.153546i	−0.00960580	−	0.999954i	$-0.503058\pi$
$647$	13.3013	−	3.90562i	0.522929	−	0.153546i	0.532535	+	0.846408i	$0.321239\pi$
$648$	−1.41153	+	1.62899i	−0.0554501	+	0.0639928i
$649$	23.7160	+	15.2413i	0.930934	+	0.598275i
$650$	5.25635	+	6.06616i	0.206171	+	0.237934i
$651$	−0.0216231	−	0.150392i	−0.000847474	−	0.00589431i
$652$	20.3453	+	5.97391i	0.796782	+	0.233956i
$653$	−4.75724	+	3.05729i	−0.186165	+	0.119641i	−0.630404	−	0.776267i	$-0.717111\pi$
$653$	−4.75724	+	3.05729i	−0.186165	+	0.119641i	0.444239	+	0.895909i	$0.353474\pi$
$654$	0.829328	−	5.76810i	0.0324293	−	0.225551i
$655$	5.57632	−	12.2104i	0.217885	−	0.477101i
$656$	2.60667	−	5.70780i	0.101773	−	0.222852i
$657$	−1.57012	+	10.9204i	−0.0612564	+	0.426047i
$658$	−1.91971	+	1.23372i	−0.0748379	+	0.0480954i
$659$	−28.0838	−	8.24614i	−1.09399	−	0.321224i	−0.315527	−	0.948917i	$-0.602181\pi$
$659$	−28.0838	−	8.24614i	−1.09399	−	0.321224i	−0.778461	+	0.627692i	$0.784000\pi$
$660$	−1.03037	−	7.16640i	−0.0401072	−	0.278952i
$661$	−10.5207	−	12.1415i	−0.409207	−	0.472250i	0.513312	−	0.858202i	$-0.328418\pi$
$661$	−10.5207	−	12.1415i	−0.409207	−	0.472250i	−0.922519	+	0.385952i	$0.873873\pi$
$662$	−25.9733	−	16.6920i	−1.00948	−	0.648753i
$663$	−7.97864	+	9.20784i	−0.309865	+	0.357603i
$664$	−8.62956	+	2.53387i	−0.334892	+	0.0983331i
$665$	0.104775	+	0.229424i	0.00406299	+	0.00889670i
$666$	−3.15486			−0.122248
$667$	−33.0272	−	13.5782i	−1.27882	−	0.525749i
$668$	3.95413			0.152990
$669$	0.420370	+	0.920482i	0.0162524	+	0.0355879i
$670$	−26.1079	+	7.66597i	−1.00864	+	0.296162i
$671$	−6.49036	+	7.49027i	−0.250558	+	0.289159i
$672$	0.506538	+	0.325532i	0.0195401	+	0.0125577i
$673$	−2.50376	−	2.88949i	−0.0965128	−	0.111382i	0.705438	−	0.708771i	$-0.250750\pi$
$673$	−2.50376	−	2.88949i	−0.0965128	−	0.111382i	−0.801951	+	0.597389i	$0.796205\pi$
$674$	−6.84471	−	47.6060i	−0.263649	−	1.83372i
$675$	−4.79746	−	1.40866i	−0.184655	−	0.0542195i
$676$	−0.0730065	+	0.0469185i	−0.00280794	+	0.00180456i
$677$	−2.33764	+	16.2586i	−0.0898428	+	0.624870i	0.894297	+	0.447474i	$0.147676\pi$
$677$	−2.33764	+	16.2586i	−0.0898428	+	0.624870i	−0.984140	+	0.177396i	$0.943233\pi$
$678$	16.5873	−	36.3211i	0.637031	−	1.39490i
$679$	0.526602	−	1.15310i	0.0202091	−	0.0442518i
$680$	1.03774	−	7.21764i	0.0397955	−	0.276784i
$681$	−4.24183	+	2.72606i	−0.162547	+	0.104463i
$682$	8.99325	+	2.64066i	0.344369	+	0.101116i
$683$	−1.04764	−	7.28651i	−0.0400869	−	0.278811i	0.959912	−	0.280302i	$-0.0904345\pi$
$683$	−1.04764	−	7.28651i	−0.0400869	−	0.278811i	−0.999999	+	0.00149105i	$0.999525\pi$
$684$	−11.1183	−	12.8312i	−0.425119	−	0.490614i
$685$	−16.2305	−	10.4307i	−0.620135	−	0.398536i
$686$	1.80028	−	2.07764i	0.0687351	−	0.0793245i
$687$	−22.0208	+	6.46589i	−0.840145	+	0.246689i
$688$	1.12569	+	2.46491i	0.0429163	+	0.0939737i
$689$	37.3658			1.42352
$690$	6.11907	+	8.76362i	0.232949	+	0.333625i
$691$	−9.67502			−0.368055			−0.184028	−	0.982921i	$-0.558914\pi$
$691$	−9.67502			−0.368055			−0.184028	+	0.982921i	$0.558914\pi$
$692$	3.32894	+	7.28935i	0.126547	+	0.277100i
$693$	0.412791	−	0.121206i	0.0156806	−	0.00460425i
$694$	−27.5955	+	31.8469i	−1.04751	+	1.20889i
$695$	−13.0362	−	8.37787i	−0.494492	−	0.317791i
$696$	−10.5101	−	12.1293i	−0.398386	−	0.459762i
$697$	2.67257	+	18.5881i	0.101231	+	0.704076i
$698$	−44.7552	−	13.1413i	−1.69401	−	0.497406i
$699$	−18.1062	+	11.6362i	−0.684840	+	0.440120i
$700$	−0.0372254	+	0.258908i	−0.00140699	+	0.00978581i
$701$	17.6838	−	38.7221i	0.667908	−	1.46252i	−0.207057	−	0.978329i	$-0.566388\pi$
$701$	17.6838	−	38.7221i	0.667908	−	1.46252i	0.874965	−	0.484186i	$-0.160884\pi$
$702$	−16.6720	+	36.5066i	−0.629244	+	1.37785i
$703$	0.288184	−	2.00436i	0.0108691	−	0.0755960i
$704$	−26.6071	+	17.0994i	−1.00279	+	0.644456i
$705$	11.1441	+	3.27220i	0.419711	+	0.123238i
$706$	−0.511298	−	3.55616i	−0.0192430	−	0.133838i
$707$	−1.00353	−	1.15814i	−0.0377417	−	0.0435562i
$708$	−28.8385	−	18.5334i	−1.08382	−	0.696526i
$709$	−22.9666	+	26.5049i	−0.862529	+	0.995411i	0.137459	+	0.990507i	$0.456106\pi$
$709$	−22.9666	+	26.5049i	−0.862529	+	0.995411i	−0.999988	+	0.00490358i	$0.998439\pi$
$710$	4.05615	−	1.19099i	0.152225	−	0.0446972i
$711$	−5.82291	−	12.7504i	−0.218376	−	0.478177i
$712$	−34.3729			−1.28818
$713$	−8.13045	+	1.48909i	−0.304488	+	0.0557668i
$714$	−0.664664			−0.0248744
$715$	3.65066	+	7.99383i	0.136527	+	0.298952i
$716$	56.3353	−	16.5415i	2.10535	−	0.618187i
$717$	−5.74298	+	6.62775i	−0.214475	+	0.247518i
$718$	65.2771	+	41.9511i	2.43612	+	1.56560i
$719$	−14.5394	−	16.7793i	−0.542226	−	0.625763i	0.416828	−	0.908986i	$-0.363142\pi$
$719$	−14.5394	−	16.7793i	−0.542226	−	0.625763i	−0.959054	+	0.283223i	$0.908596\pi$
$720$	0.321738	+	2.23773i	0.0119905	+	0.0833955i
$721$	−0.0984013	−	0.0288932i	−0.00366466	−	0.00107604i
$722$	−20.2762	+	13.0307i	−0.754602	+	0.484953i
$723$	1.25495	−	8.72835i	0.0466720	−	0.324611i
$724$	4.91245	−	10.7568i	0.182570	−	0.399772i
$725$	−3.09315	+	6.77305i	−0.114877	+	0.251545i
$726$	−1.60046	+	11.1315i	−0.0593987	+	0.413127i
$727$	0.587772	−	0.377738i	0.0217993	−	0.0140095i	−0.529696	−	0.848188i	$-0.677694\pi$
$727$	0.587772	−	0.377738i	0.0217993	−	0.0140095i	0.551495	+	0.834178i	$0.314058\pi$
$728$	0.656624	+	0.192802i	0.0243361	+	0.00714573i
$729$	−1.85009	−	12.8677i	−0.0685220	−	0.476581i
$730$	−8.05111	−	9.29147i	−0.297985	−	0.343893i
$731$	−6.82240	−	4.38449i	−0.252336	−	0.162166i
$732$	7.89223	−	9.10812i	0.291705	−	0.336646i
$733$	35.7918	−	10.5094i	1.32200	−	0.388174i	0.456785	−	0.889577i	$-0.349001\pi$
$733$	35.7918	−	10.5094i	1.32200	−	0.388174i	0.865214	+	0.501403i	$0.167183\pi$
$734$	−20.9465	−	45.8664i	−0.773149	−	1.69296i
$735$	−6.99223			−0.257912
$736$	16.6402	−	28.2151i	0.613364	−	1.04002i
$737$	−29.7909			−1.09736
$738$	10.2789	+	22.5077i	0.378372	+	0.828518i
$739$	23.5752	−	6.92231i	0.867229	−	0.254641i	0.182293	−	0.983244i	$-0.441648\pi$
$739$	23.5752	−	6.92231i	0.867229	−	0.254641i	0.684936	+	0.728603i	$0.259830\pi$
$740$	1.37526	−	1.58713i	0.0505554	−	0.0583441i
$741$	−8.66826	−	5.57075i	−0.318437	−	0.204647i
$742$	1.33489	+	1.54054i	0.0490053	+	0.0565552i
$743$	−5.88612	−	40.9388i	−0.215941	−	1.50190i	−0.752811	−	0.658236i	$-0.771303\pi$
$743$	−5.88612	−	40.9388i	−0.215941	−	1.50190i	0.536871	−	0.843665i	$-0.319606\pi$
$744$	−3.56450	−	1.04663i	−0.130681	−	0.0383713i
$745$	13.4201	−	8.62458i	0.491675	−	0.315980i
$746$	−3.42400	+	23.8145i	−0.125362	+	0.871910i
$747$	−3.46671	+	7.59104i	−0.126840	+	0.277742i
$748$	10.1748	−	22.2796i	0.372026	−	0.814623i
$749$	−0.215166	+	1.49651i	−0.00786201	+	0.0546815i
$750$	1.87491	−	1.20493i	0.0684620	−	0.0439978i
$751$	39.3106	+	11.5426i	1.43446	+	0.421197i	0.904372	−	0.426744i	$-0.140339\pi$
$751$	39.3106	+	11.5426i	1.43446	+	0.421197i	0.530091	+	0.847941i	$0.322158\pi$
$752$	−1.86842	−	12.9952i	−0.0681344	−	0.473885i
$753$	−3.85845	−	4.45289i	−0.140610	−	0.162272i
$754$	50.2783	+	32.3119i	1.83103	+	1.17673i
$755$	0.289623	−	0.334243i	0.0105405	−	0.0121643i
$756$	−1.25488	+	0.368465i	−0.0456394	+	0.0134009i
$757$	4.14940	+	9.08592i	0.150812	+	0.330233i	0.969927	−	0.243397i	$-0.0782618\pi$
$757$	4.14940	+	9.08592i	0.150812	+	0.330233i	−0.819114	+	0.573630i	$0.805535\pi$
$758$	−8.21774			−0.298482
$759$	3.72490	+	11.0936i	0.135205	+	0.402673i
$760$	6.16685			0.223695
$761$	−7.00401	−	15.3366i	−0.253895	−	0.555953i	0.739170	−	0.673519i	$-0.235218\pi$
$761$	−7.00401	−	15.3366i	−0.253895	−	0.555953i	−0.993065	+	0.117566i	$0.962491\pi$
$762$	6.39771	−	1.87854i	0.231764	−	0.0680522i
$763$	−0.150947	+	0.174202i	−0.00546464	+	0.00630653i
$764$	−14.9249	−	9.59163i	−0.539963	−	0.347013i
$765$	−4.43074	−	5.11335i	−0.160194	−	0.184873i
$766$	1.88491	+	13.1098i	0.0681045	+	0.473677i
$767$	39.9238	+	11.7227i	1.44157	+	0.423282i
$768$	6.74207	−	4.33287i	0.243283	−	0.156349i
$769$	6.22901	−	43.3237i	0.224624	−	1.56229i	−0.495599	−	0.868551i	$-0.665051\pi$
$769$	6.22901	−	43.3237i	0.224624	−	1.56229i	0.720223	−	0.693743i	$-0.244039\pi$
$770$	−0.199156	+	0.436091i	−0.00717708	+	0.0157156i
$771$	3.20427	−	7.01636i	0.115399	−	0.252688i
$772$	−4.25916	+	29.6231i	−0.153291	+	1.06616i
$773$	28.2907	−	18.1814i	1.01755	−	0.653938i	0.0782114	−	0.996937i	$-0.475079\pi$
$773$	28.2907	−	18.1814i	1.01755	−	0.653938i	0.939336	+	0.342999i	$0.111443\pi$
$774$	−10.2527	−	3.01046i	−0.368525	−	0.108209i
$775$	0.245282	+	1.70597i	0.00881079	+	0.0612804i
$776$	−20.2973	−	23.4244i	−0.728632	−	0.840886i
$777$	−0.0524899	−	0.0337332i	−0.00188306	−	0.00121017i
$778$	−9.69430	+	11.1878i	−0.347558	+	0.401103i
$779$	−15.2386	+	4.47446i	−0.545980	+	0.160314i
$780$	−4.43918	−	9.72044i	−0.158948	−	0.348048i
$781$	4.62835			0.165615
$782$	1.38607	+	36.1323i	0.0495659	+	1.29209i
$783$	−37.2296			−1.33048
$784$	3.28337	+	7.18957i	0.117263	+	0.256770i
$785$	6.83034	−	2.00557i	0.243785	−	0.0715819i
$786$	−19.5915	+	22.6098i	−0.698805	+	0.806464i
$787$	1.05221	+	0.676215i	0.0375073	+	0.0241045i	0.559260	−	0.828992i	$-0.311085\pi$
$787$	1.05221	+	0.676215i	0.0375073	+	0.0241045i	−0.521753	+	0.853097i	$0.674722\pi$
$788$	9.93997	+	11.4713i	0.354097	+	0.408649i
$789$	3.18652	+	22.1627i	0.113443	+	0.789014i
$790$	14.9873	+	4.40066i	0.533223	+	0.156569i
$791$	−1.32867	+	0.853887i	−0.0472422	+	0.0303607i
$792$	1.49702	−	10.4120i	0.0531943	−	0.369975i
$793$	−6.07684	+	13.3064i	−0.215795	+	0.472525i
$794$	−4.21946	+	9.23933i	−0.149743	+	0.327892i
$795$	1.47653	−	10.2695i	0.0523671	−	0.364221i
$796$	66.3466	−	42.6384i	2.35159	−	1.51128i
$797$	11.7261	+	3.44308i	0.415358	+	0.121960i	0.482733	−	0.875768i	$-0.339644\pi$
$797$	11.7261	+	3.44308i	0.415358	+	0.121960i	−0.0673749	+	0.997728i	$0.521462\pi$
$798$	−0.0799977	−	0.556396i	−0.00283189	−	0.0196962i
$799$	25.7306	+	29.6947i	0.910282	+	1.05052i
$800$	−5.74593	−	3.69269i	−0.203149	−	0.130556i
$801$	−20.8860	+	24.1037i	−0.737969	+	0.851662i
$802$	59.6863	−	17.5255i	2.10760	−	0.618846i
$803$	−5.59168	−	12.2441i	−0.197326	−	0.432084i
$804$	36.2255			1.27758
$805$	−0.0162064	−	0.422470i	−0.000571202	−	0.0148901i
$806$	13.8341			0.487285
$807$	−3.84770	−	8.42528i	−0.135445	−	0.296584i
$808$	−35.9512	+	10.5562i	−1.26476	+	0.371367i
$809$	17.5520	−	20.2561i	0.617097	−	0.712167i	−0.358056	−	0.933700i	$-0.616560\pi$
$809$	17.5520	−	20.2561i	0.617097	−	0.712167i	0.975153	+	0.221533i	$0.0711059\pi$
$810$	−1.87491	−	1.20493i	−0.0658776	−	0.0423369i
$811$	25.9259	+	29.9201i	0.910381	+	1.05064i	0.998512	+	0.0545266i	$0.0173650\pi$
$811$	25.9259	+	29.9201i	0.910381	+	1.05064i	−0.0881316	+	0.996109i	$0.528090\pi$
$812$	0.277177	+	1.92781i	0.00972702	+	0.0676529i
$813$	21.0691	+	6.18644i	0.738925	+	0.216968i
$814$	3.23805	−	2.08097i	0.113494	−	0.0729379i
$815$	−1.01703	+	7.07361i	−0.0356250	+	0.247778i
$816$	1.58855	−	3.47844i	0.0556104	−	0.121770i
$817$	2.84917	−	6.23880i	0.0996797	−	0.218268i
$818$	−2.57518	+	17.9108i	−0.0900392	+	0.626236i
$819$	0.534184	−	0.343299i	0.0186659	−	0.0119958i
$820$	−15.8038	−	4.64041i	−0.551892	−	0.162050i
$821$	4.50608	+	31.3404i	0.157263	+	1.09379i	0.903648	+	0.428275i	$0.140879\pi$
$821$	4.50608	+	31.3404i	0.157263	+	1.09379i	−0.746385	+	0.665514i	$0.768212\pi$
$822$	28.1583	+	32.4964i	0.982134	+	1.13344i
$823$	−39.4672	−	25.3640i	−1.37574	−	0.884134i	−0.376632	−	0.926363i	$-0.622918\pi$
$823$	−39.4672	−	25.3640i	−1.37574	−	0.884134i	−0.999108	+	0.0422285i	$0.986554\pi$
$824$	−1.64209	+	1.89508i	−0.0572050	+	0.0660181i
$825$	2.34125	−	0.687454i	0.0815120	−	0.0239341i
$826$	0.942962	+	2.06480i	0.0328099	+	0.0718436i
$827$	−24.2676			−0.843869			−0.421934	−	0.906626i	$-0.638649\pi$
$827$	−24.2676			−0.843869			−0.421934	+	0.906626i	$0.638649\pi$
$828$	9.05891	+	26.9795i	0.314819	+	0.937603i
$829$	−21.8597			−0.759220			−0.379610	−	0.925147i	$-0.623942\pi$
$829$	−21.8597			−0.759220			−0.379610	+	0.925147i	$0.623942\pi$
$830$	−3.86314	−	8.45911i	−0.134092	−	0.293620i
$831$	12.0022	−	3.52417i	0.416353	−	0.122252i
$832$	−30.5700	+	35.2797i	−1.05983	+	1.22310i
$833$	−19.8994	−	12.7886i	−0.689473	−	0.443098i
$834$	22.6166	+	26.1009i	0.783148	+	0.903801i
$835$	0.189655	+	1.31908i	0.00656327	+	0.0456485i
$836$	19.8751	+	5.83585i	0.687393	+	0.201837i
$837$	−7.24957	+	4.65902i	−0.250582	+	0.161039i
$838$	8.79669	−	61.1823i	0.303876	−	2.11351i
$839$	−11.3411	+	24.8335i	−0.391538	+	0.857348i	0.606521	+	0.795068i	$0.292565\pi$
$839$	−11.3411	+	24.8335i	−0.391538	+	0.857348i	−0.998059	+	0.0622806i	$0.980163\pi$
$840$	0.0789359	−	0.172846i	0.00272355	−	0.00596374i
$841$	−3.76305	+	26.1726i	−0.129760	+	0.902504i
$842$	−65.5352	+	42.1169i	−2.25849	+	1.45145i
$843$	−23.5299	−	6.90899i	−0.810412	−	0.237958i
$844$	6.22531	+	43.2980i	0.214284	+	1.49038i
$845$	−0.0191534	−	0.0221042i	−0.000658898	−	0.000760408i
$846$	43.5525	+	27.9895i	1.49737	+	0.962298i
$847$	0.291301	−	0.336180i	0.0100092	−	0.0115513i
$848$	−11.2527	+	3.30408i	−0.386418	+	0.113463i
$849$	7.33863	+	16.0694i	0.251861	+	0.551499i
$850$	7.53964			0.258607
$851$	−1.72433	+	2.92379i	−0.0591094	+	0.100226i
$852$	−5.62804			−0.192813
$853$	−11.7016	−	25.6230i	−0.400657	−	0.877316i	−0.997203	−	0.0747372i	$-0.976188\pi$
$853$	−11.7016	−	25.6230i	−0.400657	−	0.877316i	0.596547	−	0.802578i	$-0.296539\pi$
$854$	−0.765701	+	0.224830i	−0.0262018	+	0.00769353i
$855$	3.74715	−	4.32445i	0.128150	−	0.147893i
$856$	31.0986	+	19.9858i	1.06293	+	0.683102i
$857$	7.35982	+	8.49369i	0.251407	+	0.290139i	0.867399	−	0.497613i	$-0.165790\pi$
$857$	7.35982	+	8.49369i	0.251407	+	0.290139i	−0.615992	+	0.787752i	$0.711245\pi$
$858$	−2.78736	−	19.3865i	−0.0951588	−	0.661844i
$859$	8.44772	+	2.48047i	0.288233	+	0.0846327i	0.422653	−	0.906292i	$-0.361099\pi$
$859$	8.44772	+	2.48047i	0.288233	+	0.0846327i	−0.134420	+	0.990924i	$0.542917\pi$
$860$	5.98380	−	3.84556i	0.204046	−	0.131132i
$861$	−0.0696439	+	0.484384i	−0.00237346	+	0.0165078i
$862$	−8.57972	+	18.7870i	−0.292226	+	0.639887i
$863$	−19.8827	+	43.5371i	−0.676816	+	1.48202i	0.189166	+	0.981945i	$0.439421\pi$
$863$	−19.8827	+	43.5371i	−0.676816	+	1.48202i	−0.865982	+	0.500075i	$0.833306\pi$
$864$	4.86019	−	33.8034i	0.165347	−	1.15001i
$865$	−2.27202	+	1.46014i	−0.0772511	+	0.0496463i
$866$	−48.3892	−	14.2084i	−1.64433	−	0.482820i
$867$	−0.790638	−	5.49901i	−0.0268515	−	0.186756i
$868$	0.295225	+	0.340708i	0.0100206	+	0.0115644i
$869$	14.3867	+	9.24578i	0.488036	+	0.313641i
$870$	10.8673	−	12.5415i	0.368435	−	0.425197i
$871$	−42.1892	+	12.3879i	−1.42953	+	0.419747i
$872$	2.34124	+	5.12661i	0.0792845	+	0.173609i
$873$	−28.7593			−0.973356
$874$	−30.0798	+	5.50910i	−1.01746	+	0.186348i
$875$	−0.0881559			−0.00298021
$876$	6.79944	+	14.8887i	0.229732	+	0.503043i
$877$	45.2435	−	13.2847i	1.52776	−	0.448592i	0.593398	−	0.804909i	$-0.297786\pi$
$877$	45.2435	−	13.2847i	1.52776	−	0.448592i	0.934365	+	0.356317i	$0.115968\pi$
$878$	26.9975	−	31.1567i	0.911121	−	1.05149i
$879$	−7.14248	−	4.59020i	−0.240910	−	0.154823i
$880$	−1.80625	−	2.08452i	−0.0608886	−	0.0702692i
$881$	−5.26169	−	36.5959i	−0.177271	−	1.23295i	−0.863043	−	0.505130i	$-0.831445\pi$
$881$	−5.26169	−	36.5959i	−0.177271	−	1.23295i	0.685773	−	0.727816i	$-0.259464\pi$
$882$	−29.9048	−	8.78083i	−1.00695	−	0.295666i
$883$	−45.8990	+	29.4975i	−1.54462	+	0.992670i	−0.557967	+	0.829863i	$0.688418\pi$
$883$	−45.8990	+	29.4975i	−1.54462	+	0.992670i	−0.986658	+	0.162807i	$0.947945\pi$
$884$	5.14479	−	35.7828i	0.173038	−	1.20351i
$885$	4.79943	−	10.5093i	0.161331	−	0.353266i
$886$	−20.7193	+	45.3689i	−0.696077	+	1.52420i
$887$	2.01788	−	14.0346i	0.0677537	−	0.471237i	−0.927492	−	0.373843i	$-0.878040\pi$
$887$	2.01788	−	14.0346i	0.0677537	−	0.471237i	0.995246	−	0.0973946i	$-0.0310509\pi$
$888$	−1.28341	+	0.824797i	−0.0430684	+	0.0276784i
$889$	−0.253060	−	0.0743050i	−0.00848734	−	0.00249211i
$890$	−5.05800	−	35.1791i	−0.169544	−	1.17921i
$891$	−1.59792	−	1.84410i	−0.0535324	−	0.0617797i
$892$	−2.52589	−	1.62329i	−0.0845730	−	0.0543517i
$893$	−21.7608	+	25.1133i	−0.728197	+	0.840384i
$894$	−34.1133	+	10.0166i	−1.14092	+	0.335004i
$895$	8.22023	+	17.9998i	0.274772	+	0.601666i
$896$	−1.34240			−0.0448465
$897$	9.88816	+	14.1616i	0.330156	+	0.472843i
$898$	10.9523			0.365484
$899$	5.33109	+	11.6735i	0.177802	+	0.389332i
$900$	5.69389	−	1.67188i	0.189796	−	0.0557293i
$901$	22.9847	−	26.5257i	0.765730	−	0.883699i
$902$	−25.3962	−	16.3211i	−0.845600	−	0.543434i
$903$	−0.138393	−	0.159714i	−0.00460542	−	0.00531494i
$904$	5.49580	+	38.2242i	0.182788	+	1.27132i
$905$	3.82402	+	1.12283i	0.127115	+	0.0373243i
$906$	−0.829210	+	0.532901i	−0.0275486	+	0.0177044i
$907$	−7.08860	+	49.3023i	−0.235373	+	1.63706i	0.438873	+	0.898549i	$0.355378\pi$
$907$	−7.08860	+	49.3023i	−0.235373	+	1.63706i	−0.674246	+	0.738506i	$0.735531\pi$
$908$	6.21507	−	13.6091i	0.206254	−	0.451634i
$909$	−14.4425	+	31.6247i	−0.479028	+	1.04892i
$910$	−0.100702	+	0.700397i	−0.00333823	+	0.0232179i
$911$	−17.7763	+	11.4241i	−0.588955	+	0.378498i	−0.800913	−	0.598781i	$-0.795652\pi$
$911$	−17.7763	+	11.4241i	−0.588955	+	0.378498i	0.211959	+	0.977279i	$0.432016\pi$
$912$	3.10303	+	0.911132i	0.102752	+	0.0301706i
$913$	−1.44898	−	10.0779i	−0.0479543	−	0.333529i
$914$	−16.9046	−	19.5090i	−0.559156	−	0.645300i
$915$	3.41696	+	2.19595i	0.112961	+	0.0725958i
$916$	44.5941	−	51.4644i	1.47343	−	1.70043i
$917$	1.13543	−	0.333391i	0.0374951	−	0.0110095i
$918$	15.6604	+	34.2915i	0.516870	+	1.13179i
$919$	−1.66022			−0.0547657			−0.0273829	−	0.999625i	$-0.508717\pi$
$919$	−1.66022			−0.0547657			−0.0273829	+	0.999625i	$0.508717\pi$
$920$	−9.56079	−	3.93064i	−0.315210	−	0.129589i
$921$	14.6797			0.483711
$922$	−14.3963	−	31.5235i	−0.474116	−	1.03817i
$923$	6.55457	−	1.92459i	0.215746	−	0.0633488i
$924$	0.417970	−	0.482363i	0.0137502	−	0.0158686i
$925$	0.595421	+	0.382654i	0.0195773	+	0.0125816i
$926$	−14.7804	−	17.0575i	−0.485715	−	0.560545i
$927$	0.331122	+	2.30300i	0.0108755	+	0.0756406i
$928$	−48.7971	−	14.3281i	−1.60184	−	0.470343i
$929$	24.5455	−	15.7744i	0.805311	−	0.517542i	−0.0720340	−	0.997402i	$-0.522949\pi$
$929$	24.5455	−	15.7744i	0.805311	−	0.517542i	0.877345	+	0.479860i	$0.159313\pi$
$930$	0.546662	−	3.80211i	0.0179257	−	0.124676i
$931$	8.31037	−	18.1972i	0.272361	−	0.596388i
$932$	26.5290	−	58.0904i	0.868986	−	1.90281i
$933$	4.29449	−	29.8688i	0.140595	−	0.977861i
$934$	0.299702	−	0.192607i	0.00980656	−	0.00630229i
$935$	7.92038	+	2.32563i	0.259024	+	0.0760563i
$936$	−2.20955	−	15.3678i	−0.0722214	−	0.502311i
$937$	−12.0573	−	13.9149i	−0.393895	−	0.454580i	0.523813	−	0.851833i	$-0.324509\pi$
$937$	−12.0573	−	13.9149i	−0.393895	−	0.454580i	−0.917709	+	0.397253i	$0.869963\pi$
$938$	−2.01794	−	1.29685i	−0.0658881	−	0.0423437i
$939$	−3.64497	+	4.20652i	−0.118949	+	0.137275i
$940$	−33.0661	+	9.70907i	−1.07850	+	0.316675i
$941$	17.9910	+	39.3947i	0.586489	+	1.28423i	0.937541	+	0.347876i	$0.113097\pi$
$941$	17.9910	+	39.3947i	0.586489	+	1.28423i	−0.351052	+	0.936356i	$0.614176\pi$
$942$	−15.8655			−0.516926
$943$	26.4772	+	2.77584i	0.862215	+	0.0903937i
$944$	−13.0596			−0.425053
$945$	−0.183106	−	0.400947i	−0.00595645	−	0.0130428i
$946$	12.5088	−	3.67290i	0.406695	−	0.119416i
$947$	13.8033	−	15.9299i	0.448548	−	0.517652i	−0.485773	−	0.874085i	$-0.661462\pi$
$947$	13.8033	−	15.9299i	0.448548	−	0.517652i	0.934321	+	0.356433i	$0.116007\pi$
$948$	−17.4941	−	11.2428i	−0.568183	−	0.365149i
$949$	−13.0102	−	15.0146i	−0.422330	−	0.487395i
$950$	0.907456	+	6.31150i	0.0294418	+	0.204772i
$951$	2.69722	+	0.791977i	0.0874635	+	0.0256816i
$952$	0.540775	−	0.347535i	0.0175266	−	0.0112637i
$953$	−2.09831	+	14.5941i	−0.0679710	+	0.472749i	0.927198	+	0.374572i	$0.122210\pi$
$953$	−2.09831	+	14.5941i	−0.0679710	+	0.472749i	−0.995169	+	0.0981772i	$0.968699\pi$
$954$	19.2113	−	42.0669i	0.621989	−	1.36197i
$955$	2.48387	−	5.43891i	0.0803760	−	0.175999i
$956$	3.70319	−	25.7562i	0.119770	−	0.833016i
$957$	15.2845	−	9.82277i	0.494079	−	0.317525i
$958$	−12.5627	−	3.68873i	−0.405881	−	0.119178i
$959$	−0.242051	−	1.68350i	−0.00781622	−	0.0543630i
$960$	8.48816	+	9.79585i	0.273954	+	0.316160i
$961$	−23.5799	−	15.1539i	−0.760642	−	0.488835i
$962$	3.72033	−	4.29349i	0.119948	−	0.138428i
$963$	32.9113	−	9.66362i	1.06055	−	0.311406i
$964$	10.8691	+	23.8001i	0.350071	+	0.766549i
$965$	−10.0864			−0.324693
$966$	−0.230613	+	0.913599i	−0.00741984	+	0.0293946i
$967$	−25.3720			−0.815909			−0.407955	−	0.913002i	$-0.633758\pi$
$967$	−25.3720			−0.815909			−0.407955	+	0.913002i	$0.633758\pi$
$968$	−4.51820	−	9.89347i	−0.145220	−	0.317988i
$969$	−9.28671	+	2.72682i	−0.298332	+	0.0875982i
$970$	20.9870	−	24.2203i	0.673853	−	0.777668i
$971$	−32.9014	−	21.1444i	−1.05586	−	0.678557i	−0.106997	−	0.994259i	$-0.534124\pi$
$971$	−32.9014	−	21.1444i	−1.05586	−	0.678557i	−0.948858	+	0.315702i	$0.897760\pi$
$972$	31.0890	+	35.8786i	0.997180	+	1.15081i
$973$	−0.194414	−	1.35218i	−0.00623261	−	0.0433488i
$974$	14.8280	+	4.35388i	0.475118	+	0.139507i
$975$	3.02977	−	1.94711i	0.0970303	−	0.0623576i
$976$	0.653409	−	4.54456i	0.0209151	−	0.145468i
$977$	−9.66014	+	21.1528i	−0.309055	+	0.676736i	−0.998884	−	0.0472363i	$-0.984959\pi$
$977$	−9.66014	+	21.1528i	−0.309055	+	0.676736i	0.689829	+	0.723973i	$0.257686\pi$
$978$	6.61636	−	14.4878i	0.211568	−	0.463269i
$979$	5.53774	−	38.5158i	0.176987	−	1.23097i
$980$	17.4534	−	11.2166i	0.557528	−	0.358302i
$981$	5.01759	+	1.47330i	0.160199	+	0.0470387i
$982$	6.96412	+	48.4365i	0.222234	+	1.54567i
$983$	−0.430697	−	0.497051i	−0.0137371	−	0.0158535i	0.748839	−	0.662751i	$-0.230611\pi$
$983$	−0.430697	−	0.497051i	−0.0137371	−	0.0158535i	−0.762577	+	0.646898i	$0.776066\pi$
$984$	10.0658	+	6.46891i	0.320887	+	0.206221i
$985$	−3.35002	+	3.86613i	−0.106741	+	0.123185i
$986$	53.8655	−	15.8163i	1.71543	−	0.503695i
$987$	0.425341	+	0.931366i	0.0135387	+	0.0296457i
$988$	30.5733			0.972667
$989$	−8.39371	+	7.85633i	−0.266905	+	0.249817i
$990$	10.8765			0.345678
$991$	1.31140	+	2.87157i	0.0416581	+	0.0912185i	0.929317	−	0.369283i	$-0.120397\pi$
$991$	1.31140	+	2.87157i	0.0416581	+	0.0912185i	−0.887659	+	0.460502i	$0.847670\pi$
$992$	−11.2951	+	3.31654i	−0.358620	+	0.105300i
$993$	−9.07184	+	10.4695i	−0.287886	+	0.332238i
$994$	0.313510	+	0.201480i	0.00994392	+	0.00639057i
$995$	17.4062	+	20.0878i	0.551813	+	0.636826i
$996$	1.76195	+	12.2546i	0.0558295	+	0.388303i
$997$	8.45136	+	2.48154i	0.267657	+	0.0785913i	0.412807	−	0.910818i	$-0.364548\pi$
$997$	8.45136	+	2.48154i	0.267657	+	0.0785913i	−0.145150	+	0.989410i	$0.546366\pi$
$998$	−53.3443	+	34.2823i	−1.68858	+	1.08519i
$999$	−0.503637	+	3.50287i	−0.0159344	+	0.110826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.a.96.1	yes	10
5.2	odd	4		575.2.p.a.349.1		20
5.3	odd	4		575.2.p.a.349.2		20
5.4	even	2		575.2.k.a.326.1		10
23.6	even	11	inner	115.2.g.a.6.1	✓	10
23.11	odd	22		2645.2.a.o.1.5		5
23.12	even	11		2645.2.a.n.1.5		5
115.29	even	22		575.2.k.a.351.1		10
115.52	odd	44		575.2.p.a.374.2		20
115.98	odd	44		575.2.p.a.374.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.a.6.1	✓	10	23.6	even	11	inner
115.2.g.a.96.1	yes	10	1.1	even	1	trivial
575.2.k.a.326.1		10	5.4	even	2
575.2.k.a.351.1		10	115.29	even	22
575.2.p.a.349.1		20	5.2	odd	4
575.2.p.a.349.2		20	5.3	odd	4
575.2.p.a.374.1		20	115.98	odd	44
575.2.p.a.374.2		20	115.52	odd	44
2645.2.a.n.1.5		5	23.12	even	11
2645.2.a.o.1.5		5	23.11	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.925839 + 2.02730i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-1.94306 + 2.24241i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(1.45949 + 1.68434i) q^{6} +(-0.0125459 - 0.0872586i) q^{7} +(-2.06815 - 0.607265i) q^{8} +(-1.68251 + 1.08128i) q^{9} +O(q^{10})\)	\(q+(0.925839 + 2.02730i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-1.94306 + 2.24241i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(1.45949 + 1.68434i) q^{6} +(-0.0125459 - 0.0872586i) q^{7} +(-2.06815 - 0.607265i) q^{8} +(-1.68251 + 1.08128i) q^{9} +(0.317178 - 2.20602i) q^{10} +(1.01365 - 2.21959i) q^{11} +(-1.23259 + 2.69900i) q^{12} +(0.512546 - 3.56484i) q^{13} +(0.165284 - 0.106222i) q^{14} +(-0.959493 - 0.281733i) q^{15} +(0.160869 + 1.11887i) q^{16} +(-2.21537 - 2.55667i) q^{17} +(-3.74982 - 2.40986i) q^{18} +(1.87358 - 2.16222i) q^{19} +(2.84695 - 0.835939i) q^{20} +(-0.0366213 - 0.0801894i) q^{21} +5.43826 q^{22} +(-4.28287 + 2.15802i) q^{23} -2.15546 q^{24} +(0.415415 + 0.909632i) q^{25} +(7.70154 - 2.26138i) q^{26} +(-3.27430 + 3.77875i) q^{27} +(0.220047 + 0.141416i) q^{28} +(4.87604 + 5.62725i) q^{29} +(-0.317178 - 2.20602i) q^{30} +(1.65370 + 0.485571i) q^{31} +(-5.74593 + 3.69269i) q^{32} +(0.347262 - 2.41526i) q^{33} +(3.13208 - 6.85830i) q^{34} +(-0.0366213 + 0.0801894i) q^{35} +(0.844535 - 5.87387i) q^{36} +(0.595421 - 0.382654i) q^{37} +(6.11811 + 1.79644i) q^{38} +(-0.512546 - 3.56484i) q^{39} +(1.41153 + 1.62899i) q^{40} +(-4.66991 - 3.00117i) q^{41} +(0.128663 - 0.148485i) q^{42} +(2.30014 - 0.675383i) q^{43} +(3.00764 + 6.58582i) q^{44} +2.00000 q^{45} +(-8.34021 - 6.68469i) q^{46} -11.6146 q^{47} +(0.469574 + 1.02822i) q^{48} +(6.70899 - 1.96994i) q^{49} +(-1.45949 + 1.68434i) q^{50} +(-2.84593 - 1.82897i) q^{51} +(6.99792 + 8.07603i) q^{52} +(1.47653 + 10.2695i) q^{53} +(-10.6921 - 3.13950i) q^{54} +(-2.05274 + 1.31921i) q^{55} +(-0.0270422 + 0.188083i) q^{56} +(1.18852 - 2.60249i) q^{57} +(-6.89372 + 15.0951i) q^{58} +(-1.64421 + 11.4357i) q^{59} +(2.49611 - 1.60416i) q^{60} +(-3.89722 - 1.14433i) q^{61} +(0.546662 + 3.80211i) q^{62} +(0.115460 + 0.133248i) q^{63} +(-10.9041 - 7.00766i) q^{64} +(-2.35848 + 2.72183i) q^{65} +(5.21797 - 1.53213i) q^{66} +(-5.07177 - 11.1056i) q^{67} +10.0377 q^{68} +(-3.50140 + 3.27723i) q^{69} -0.196474 q^{70} +(0.787956 + 1.72538i) q^{71} +(4.13631 - 1.21453i) q^{72} +(3.61246 - 4.16900i) q^{73} +(1.32702 + 0.852823i) q^{74} +(0.654861 + 0.755750i) q^{75} +(1.20812 + 8.40266i) q^{76} +(-0.206395 - 0.0606031i) q^{77} +(6.75247 - 4.33955i) q^{78} +(-0.997420 + 6.93721i) q^{79} +(0.469574 - 1.02822i) q^{80} +(0.415415 - 0.909632i) q^{81} +(1.76070 - 12.2459i) q^{82} +(3.51021 - 2.25587i) q^{83} +(0.250975 + 0.0736930i) q^{84} +(0.481446 + 3.34853i) q^{85} +(3.49877 + 4.03779i) q^{86} +(6.26391 + 4.02557i) q^{87} +(-3.44426 + 3.97489i) q^{88} +(15.3009 - 4.49275i) q^{89} +(1.85168 + 4.05461i) q^{90} -0.317493 q^{91} +(3.48270 - 13.7971i) q^{92} +1.72352 q^{93} +(-10.7532 - 23.5463i) q^{94} +(-2.74514 + 0.806046i) q^{95} +(-4.47283 + 5.16192i) q^{96} +(12.0969 + 7.77424i) q^{97} +(10.2051 + 11.7773i) q^{98} +(0.694523 + 4.83052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9	\( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9} - 5 q^{10} + 8 q^{11} + q^{12} - 3 q^{14} - q^{15} + 5 q^{16} - 23 q^{17} - 10 q^{18} - 13 q^{19} + q^{20} + 6 q^{21} + 4 q^{22} - 21 q^{23} - 6 q^{24} - q^{25} + 11 q^{26} - 5 q^{27} - 6 q^{28} + 2 q^{29} + 5 q^{30} - 20 q^{31} - 15 q^{32} + 3 q^{33} + 16 q^{34} + 6 q^{35} + 24 q^{36} + 13 q^{37} + 21 q^{38} - 6 q^{40} - 5 q^{41} + 3 q^{42} + 15 q^{43} + 19 q^{44} + 20 q^{45} - 16 q^{46} - 52 q^{47} + 6 q^{48} + 4 q^{49} - 6 q^{50} - 10 q^{51} + 22 q^{52} + 6 q^{53} - 30 q^{54} + 3 q^{55} + 3 q^{56} + 2 q^{57} + 45 q^{58} + 5 q^{59} + 10 q^{60} - 3 q^{61} - 54 q^{62} - 10 q^{63} - 34 q^{64} - 4 q^{66} + 20 q^{67} + 32 q^{68} - q^{69} - 8 q^{70} - 22 q^{71} + 32 q^{72} + 43 q^{73} + q^{74} + q^{75} - 2 q^{76} + 4 q^{77} + 11 q^{78} + 51 q^{79} + 6 q^{80} - q^{81} + 58 q^{82} - 17 q^{83} + 6 q^{84} + q^{85} - 9 q^{86} - 2 q^{87} + 7 q^{88} + 57 q^{89} + 10 q^{90} - 22 q^{91} - 43 q^{92} + 20 q^{93} - 81 q^{94} - 9 q^{95} - 7 q^{96} + 52 q^{97} + 24 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9 - 5 * q^10 + 8 * q^11 + q^12 - 3 * q^14 - q^15 + 5 * q^16 - 23 * q^17 - 10 * q^18 - 13 * q^19 + q^20 + 6 * q^21 + 4 * q^22 - 21 * q^23 - 6 * q^24 - q^25 + 11 * q^26 - 5 * q^27 - 6 * q^28 + 2 * q^29 + 5 * q^30 - 20 * q^31 - 15 * q^32 + 3 * q^33 + 16 * q^34 + 6 * q^35 + 24 * q^36 + 13 * q^37 + 21 * q^38 - 6 * q^40 - 5 * q^41 + 3 * q^42 + 15 * q^43 + 19 * q^44 + 20 * q^45 - 16 * q^46 - 52 * q^47 + 6 * q^48 + 4 * q^49 - 6 * q^50 - 10 * q^51 + 22 * q^52 + 6 * q^53 - 30 * q^54 + 3 * q^55 + 3 * q^56 + 2 * q^57 + 45 * q^58 + 5 * q^59 + 10 * q^60 - 3 * q^61 - 54 * q^62 - 10 * q^63 - 34 * q^64 - 4 * q^66 + 20 * q^67 + 32 * q^68 - q^69 - 8 * q^70 - 22 * q^71 + 32 * q^72 + 43 * q^73 + q^74 + q^75 - 2 * q^76 + 4 * q^77 + 11 * q^78 + 51 * q^79 + 6 * q^80 - q^81 + 58 * q^82 - 17 * q^83 + 6 * q^84 + q^85 - 9 * q^86 - 2 * q^87 + 7 * q^88 + 57 * q^89 + 10 * q^90 - 22 * q^91 - 43 * q^92 + 20 * q^93 - 81 * q^94 - 9 * q^95 - 7 * q^96 + 52 * q^97 + 24 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more