LMFDB - Embedded newform 224.2.x.b.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(27,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4]))

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

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

chi := DirichletCharacter("224.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.x (of order $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			27.1
Character	$\chi$	$=$	224.27
Dual form			224.2.x.b.83.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40726 - 0.140045i) q^{2} +(-0.311327 - 0.751610i) q^{3} +(1.96078 + 0.394159i) q^{4} +(-1.37157 + 3.31126i) q^{5} +(0.332860 + 1.10131i) q^{6} +(-2.28614 - 1.33176i) q^{7} +(-2.70413 - 0.829281i) q^{8} +(1.65333 - 1.65333i) q^{9} +O(q^{10})$	\(q+(-1.40726 - 0.140045i) q^{2} +(-0.311327 - 0.751610i) q^{3} +(1.96078 + 0.394159i) q^{4} +(-1.37157 + 3.31126i) q^{5} +(0.332860 + 1.10131i) q^{6} +(-2.28614 - 1.33176i) q^{7} +(-2.70413 - 0.829281i) q^{8} +(1.65333 - 1.65333i) q^{9} +(2.39388 - 4.46773i) q^{10} +(-5.28229 - 2.18800i) q^{11} +(-0.314188 - 1.59645i) q^{12} +(0.105369 + 0.254384i) q^{13} +(3.03069 + 2.19429i) q^{14} +2.91578 q^{15} +(3.68928 + 1.54571i) q^{16} -5.29348 q^{17} +(-2.55821 + 2.09513i) q^{18} +(-3.74605 + 1.55167i) q^{19} +(-3.99450 + 5.95202i) q^{20} +(-0.289226 + 2.13289i) q^{21} +(7.12715 + 3.81884i) q^{22} +(0.968314 + 0.968314i) q^{23} +(0.218571 + 2.29062i) q^{24} +(-5.54771 - 5.54771i) q^{25} +(-0.112657 - 0.372741i) q^{26} +(-4.01221 - 1.66191i) q^{27} +(-3.95768 - 3.51238i) q^{28} +(1.68537 + 4.06885i) q^{29} +(-4.10327 - 0.408339i) q^{30} +1.43114 q^{31} +(-4.97531 - 2.69189i) q^{32} +4.65140i q^{33} +(7.44932 + 0.741324i) q^{34} +(7.54539 - 5.74340i) q^{35} +(3.89348 - 2.59013i) q^{36} +(-5.41648 - 2.24358i) q^{37} +(5.48898 - 1.65899i) q^{38} +(0.158393 - 0.158393i) q^{39} +(6.45486 - 7.81665i) q^{40} +(0.427071 + 0.427071i) q^{41} +(0.705717 - 2.96104i) q^{42} +(2.09991 + 0.869810i) q^{43} +(-9.49497 - 6.37223i) q^{44} +(3.20695 + 7.74225i) q^{45} +(-1.22707 - 1.49828i) q^{46} -5.50376i q^{47} +(0.0132023 - 3.25412i) q^{48} +(3.45284 + 6.08916i) q^{49} +(7.03015 + 8.58401i) q^{50} +(1.64800 + 3.97863i) q^{51} +(0.106338 + 0.540322i) q^{52} +(-2.37839 + 5.74193i) q^{53} +(5.41349 + 2.90064i) q^{54} +(14.4901 - 14.4901i) q^{55} +(5.07760 + 5.49709i) q^{56} +(2.33249 + 2.33249i) q^{57} +(-1.80194 - 5.96196i) q^{58} +(9.62996 + 3.98886i) q^{59} +(5.71719 + 1.14928i) q^{60} +(7.27600 - 3.01382i) q^{61} +(-2.01399 - 0.200423i) q^{62} +(-5.98157 + 1.57790i) q^{63} +(6.62459 + 4.48496i) q^{64} -0.986852 q^{65} +(0.651404 - 6.54575i) q^{66} +(2.12190 - 0.878921i) q^{67} +(-10.3793 - 2.08647i) q^{68} +(0.426332 - 1.02926i) q^{69} +(-11.4227 + 7.02578i) q^{70} +(-2.53724 + 2.53724i) q^{71} +(-5.84188 + 3.09973i) q^{72} +(-11.0124 - 11.0124i) q^{73} +(7.30820 + 3.91585i) q^{74} +(-2.44256 + 5.89686i) q^{75} +(-7.95677 + 1.56593i) q^{76} +(9.16216 + 12.0368i) q^{77} +(-0.245083 + 0.200718i) q^{78} -7.98231 q^{79} +(-10.1784 + 10.0961i) q^{80} -3.48146i q^{81} +(-0.541192 - 0.660810i) q^{82} +(-5.90559 + 2.44618i) q^{83} +(-1.40781 + 4.06813i) q^{84} +(7.26038 - 17.5281i) q^{85} +(-2.83331 - 1.51813i) q^{86} +(2.53348 - 2.53348i) q^{87} +(12.4695 + 10.2971i) q^{88} +(10.4668 - 10.4668i) q^{89} +(-3.42875 - 11.3445i) q^{90} +(0.0978891 - 0.721882i) q^{91} +(1.51698 + 2.28032i) q^{92} +(-0.445552 - 1.07566i) q^{93} +(-0.770772 + 7.74523i) q^{94} -14.5324i q^{95} +(-0.474301 + 4.57755i) q^{96} +7.99833i q^{97} +(-4.00630 - 9.05260i) q^{98} +(-12.3508 + 5.11588i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9	$ 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{11} - 20 q^{14} - 16 q^{15} + 16 q^{16} - 16 q^{18} - 4 q^{21} + 32 q^{22} - 48 q^{23} - 8 q^{25} - 24 q^{28} - 8 q^{29} + 16 q^{30} - 8 q^{32} + 20 q^{35} + 32 q^{36} - 8 q^{37} - 8 q^{39} + 16 q^{42} + 32 q^{43} - 144 q^{44} - 8 q^{46} + 16 q^{50} - 32 q^{51} - 32 q^{53} + 64 q^{56} - 8 q^{57} - 72 q^{58} - 88 q^{60} + 112 q^{64} - 16 q^{65} - 64 q^{67} - 40 q^{70} + 56 q^{71} - 8 q^{72} - 168 q^{74} + 52 q^{77} + 192 q^{78} - 16 q^{79} - 24 q^{84} - 48 q^{85} - 8 q^{86} - 96 q^{88} - 52 q^{91} - 8 q^{92} - 32 q^{93} + 88 q^{98} + 16 q^{99}+O(q^{100}) $ 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^11 - 20 * q^14 - 16 * q^15 + 16 * q^16 - 16 * q^18 - 4 * q^21 + 32 * q^22 - 48 * q^23 - 8 * q^25 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 8 * q^32 + 20 * q^35 + 32 * q^36 - 8 * q^37 - 8 * q^39 + 16 * q^42 + 32 * q^43 - 144 * q^44 - 8 * q^46 + 16 * q^50 - 32 * q^51 - 32 * q^53 + 64 * q^56 - 8 * q^57 - 72 * q^58 - 88 * q^60 + 112 * q^64 - 16 * q^65 - 64 * q^67 - 40 * q^70 + 56 * q^71 - 8 * q^72 - 168 * q^74 + 52 * q^77 + 192 * q^78 - 16 * q^79 - 24 * q^84 - 48 * q^85 - 8 * q^86 - 96 * q^88 - 52 * q^91 - 8 * q^92 - 32 * q^93 + 88 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$

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 $

$2$	−1.40726	−	0.140045i	−0.995085	−	0.0990265i
$2$	−1.40726	−	0.140045i	−0.995085	−	0.0990265i
$3$	−0.311327	−	0.751610i	−0.179745	−	0.433942i	0.808168	−	0.588952i	$-0.200459\pi$
$3$	−0.311327	−	0.751610i	−0.179745	−	0.433942i	−0.987913	+	0.155010i	$0.950459\pi$
$4$	1.96078	+	0.394159i	0.980388	+	0.197079i
$5$	−1.37157	+	3.31126i	−0.613384	+	1.48084i	0.245876	+	0.969301i	$0.420924\pi$
$5$	−1.37157	+	3.31126i	−0.613384	+	1.48084i	−0.859260	+	0.511539i	$0.829076\pi$
$6$	0.332860	+	1.10131i	0.135889	+	0.449609i
$7$	−2.28614	−	1.33176i	−0.864079	−	0.503357i
$7$	−2.28614	−	1.33176i	−0.864079	−	0.503357i
$8$	−2.70413	−	0.829281i	−0.956053	−	0.293195i
$9$	1.65333	−	1.65333i	0.551109	−	0.551109i
$10$	2.39388	−	4.46773i	0.757012	−	1.41282i
$11$	−5.28229	−	2.18800i	−1.59267	−	0.659706i	−0.602316	−	0.798258i	$-0.705755\pi$
$11$	−5.28229	−	2.18800i	−1.59267	−	0.659706i	−0.990355	+	0.138552i	$0.955755\pi$
$12$	−0.314188	−	1.59645i	−0.0906984	−	0.460855i
$13$	0.105369	+	0.254384i	0.0292242	+	0.0705534i	0.937818	−	0.347128i	$-0.112843\pi$
$13$	0.105369	+	0.254384i	0.0292242	+	0.0705534i	−0.908594	+	0.417681i	$0.862843\pi$
$14$	3.03069	+	2.19429i	0.809986	+	0.586450i
$15$	2.91578			0.752851
$16$	3.68928	+	1.54571i	0.922319	+	0.386429i
$17$	−5.29348			−1.28386			−0.641929	−	0.766764i	$-0.721866\pi$
$17$	−5.29348			−1.28386			−0.641929	+	0.766764i	$0.721866\pi$
$18$	−2.55821	+	2.09513i	−0.602975	+	0.493826i
$19$	−3.74605	+	1.55167i	−0.859403	+	0.355977i	−0.768474	−	0.639881i	$-0.778984\pi$
$19$	−3.74605	+	1.55167i	−0.859403	+	0.355977i	−0.0909292	+	0.995857i	$0.528984\pi$
$20$	−3.99450	+	5.95202i	−0.893197	+	1.33091i
$21$	−0.289226	+	2.13289i	−0.0631143	+	0.465436i
$22$	7.12715	+	3.81884i	1.51951	+	0.814180i
$23$	0.968314	+	0.968314i	0.201907	+	0.201907i	0.800817	−	0.598909i	$-0.204399\pi$
$23$	0.968314	+	0.968314i	0.201907	+	0.201907i	−0.598909	+	0.800817i	$0.704399\pi$
$24$	0.218571	+	2.29062i	0.0446157	+	0.467572i
$25$	−5.54771	−	5.54771i	−1.10954	−	1.10954i
$26$	−0.112657	−	0.372741i	−0.0220939	−	0.0731006i
$27$	−4.01221	−	1.66191i	−0.772150	−	0.319835i
$28$	−3.95768	−	3.51238i	−0.747930	−	0.663777i
$29$	1.68537	+	4.06885i	0.312966	+	0.755566i	0.999592	+	0.0285554i	$0.00909070\pi$
$29$	1.68537	+	4.06885i	0.312966	+	0.755566i	−0.686627	+	0.727010i	$0.740909\pi$
$30$	−4.10327	−	0.408339i	−0.749151	−	0.0745522i
$31$	1.43114			0.257040			0.128520	−	0.991707i	$-0.458977\pi$
$31$	1.43114			0.257040			0.128520	+	0.991707i	$0.458977\pi$
$32$	−4.97531	−	2.69189i	−0.879519	−	0.475863i
$33$			4.65140i			0.809706i
$34$	7.44932	+	0.741324i	1.27755	+	0.127136i
$35$	7.54539	−	5.74340i	1.27540	−	0.970811i
$36$	3.89348	−	2.59013i	0.648913	−	0.431688i
$37$	−5.41648	−	2.24358i	−0.890463	−	0.368842i	−0.109918	−	0.993941i	$-0.535059\pi$
$37$	−5.41648	−	2.24358i	−0.890463	−	0.368842i	−0.780546	+	0.625099i	$0.785059\pi$
$38$	5.48898	−	1.65899i	0.890430	−	0.269123i
$39$	0.158393	−	0.158393i	0.0253632	−	0.0253632i
$40$	6.45486	−	7.81665i	1.02060	−	1.23592i
$41$	0.427071	+	0.427071i	0.0666973	+	0.0666973i	0.739669	−	0.672971i	$-0.234982\pi$
$41$	0.427071	+	0.427071i	0.0666973	+	0.0666973i	−0.672971	+	0.739669i	$0.734982\pi$
$42$	0.705717	−	2.96104i	0.108895	−	0.456898i
$43$	2.09991	+	0.869810i	0.320233	+	0.132645i	0.537009	−	0.843577i	$-0.319554\pi$
$43$	2.09991	+	0.869810i	0.320233	+	0.132645i	−0.216776	+	0.976221i	$0.569554\pi$
$44$	−9.49497	−	6.37223i	−1.43142	−	0.960650i
$45$	3.20695	+	7.74225i	0.478063	+	1.15415i
$46$	−1.22707	−	1.49828i	−0.180921	−	0.220909i
$47$		−	5.50376i		−	0.802806i	−0.915902	−	0.401403i	$-0.868523\pi$
$47$		−	5.50376i		−	0.802806i	0.915902	−	0.401403i	$-0.131477\pi$
$48$	0.0132023	−	3.25412i	0.00190559	−	0.469692i
$49$	3.45284	+	6.08916i	0.493263	+	0.869880i
$50$	7.03015	+	8.58401i	0.994214	+	1.21396i
$51$	1.64800	+	3.97863i	0.230767	+	0.557120i
$52$	0.106338	+	0.540322i	0.0147464	+	0.0749291i
$53$	−2.37839	+	5.74193i	−0.326696	+	0.788715i	0.672137	+	0.740427i	$0.265377\pi$
$53$	−2.37839	+	5.74193i	−0.326696	+	0.788715i	−0.998833	+	0.0482882i	$0.984623\pi$
$54$	5.41349	+	2.90064i	0.736683	+	0.394726i
$55$	14.4901	−	14.4901i	1.95384	−	1.95384i
$56$	5.07760	+	5.49709i	0.678523	+	0.734579i
$57$	2.33249	+	2.33249i	0.308946	+	0.308946i
$58$	−1.80194	−	5.96196i	−0.236606	−	0.782844i
$59$	9.62996	+	3.98886i	1.25371	+	0.519306i	0.907975	−	0.419025i	$-0.137628\pi$
$59$	9.62996	+	3.98886i	1.25371	+	0.519306i	0.345740	+	0.938330i	$0.387628\pi$
$60$	5.71719	+	1.14928i	0.738086	+	0.148372i
$61$	7.27600	−	3.01382i	0.931596	−	0.385880i	0.135312	−	0.990803i	$-0.456796\pi$
$61$	7.27600	−	3.01382i	0.931596	−	0.385880i	0.796284	+	0.604923i	$0.206796\pi$
$62$	−2.01399	−	0.200423i	−0.255777	−	0.0254538i
$63$	−5.98157	+	1.57790i	−0.753606	+	0.198797i
$64$	6.62459	+	4.48496i	0.828073	+	0.560620i
$65$	−0.986852			−0.122404
$66$	0.651404	−	6.54575i	0.0801823	−	0.805726i
$67$	2.12190	−	0.878921i	0.259232	−	0.107377i	−0.249283	−	0.968431i	$-0.580195\pi$
$67$	2.12190	−	0.878921i	0.259232	−	0.107377i	0.508514	+	0.861053i	$0.330195\pi$
$68$	−10.3793	−	2.08647i	−1.25868	−	0.253022i
$69$	0.426332	−	1.02926i	0.0513244	−	0.123908i
$70$	−11.4227	+	7.02578i	−1.36527	+	0.839741i
$71$	−2.53724	+	2.53724i	−0.301115	+	0.301115i	−0.841450	−	0.540335i	$-0.818297\pi$
$71$	−2.53724	+	2.53724i	−0.301115	+	0.301115i	0.540335	+	0.841450i	$0.318297\pi$
$72$	−5.84188	+	3.09973i	−0.688472	+	0.365307i
$73$	−11.0124	−	11.0124i	−1.28890	−	1.28890i	−0.935455	−	0.353447i	$-0.885010\pi$
$73$	−11.0124	−	11.0124i	−1.28890	−	1.28890i	−0.353447	−	0.935455i	$-0.614990\pi$
$74$	7.30820	+	3.91585i	0.849561	+	0.455208i
$75$	−2.44256	+	5.89686i	−0.282043	+	0.680911i
$76$	−7.95677	+	1.56593i	−0.912704	+	0.179624i
$77$	9.16216	+	12.0368i	1.04413	+	1.37172i
$78$	−0.245083	+	0.200718i	−0.0277501	+	0.0227269i
$79$	−7.98231			−0.898080			−0.449040	−	0.893512i	$-0.648234\pi$
$79$	−7.98231			−0.898080			−0.449040	+	0.893512i	$0.648234\pi$
$80$	−10.1784	+	10.0961i	−1.13798	+	1.12878i
$81$		−	3.48146i		−	0.386829i
$82$	−0.541192	−	0.660810i	−0.0597647	−	0.0729743i
$83$	−5.90559	+	2.44618i	−0.648223	+	0.268503i	−0.682473	−	0.730910i	$-0.739096\pi$
$83$	−5.90559	+	2.44618i	−0.648223	+	0.268503i	0.0342502	+	0.999413i	$0.489096\pi$
$84$	−1.40781	+	4.06813i	−0.153604	+	0.443869i
$85$	7.26038	−	17.5281i	0.787499	−	1.90119i
$86$	−2.83331	−	1.51813i	−0.305524	−	0.163704i
$87$	2.53348	−	2.53348i	0.271618	−	0.271618i
$88$	12.4695	+	10.2971i	1.32925	+	1.09768i
$89$	10.4668	−	10.4668i	1.10948	−	1.10948i	0.116264	−	0.993218i	$-0.462908\pi$
$89$	10.4668	−	10.4668i	1.10948	−	1.10948i	0.993218	−	0.116264i	$-0.0370919\pi$
$90$	−3.42875	−	11.3445i	−0.361422	−	1.19581i
$91$	0.0978891	−	0.721882i	0.0102616	−	0.0756738i
$92$	1.51698	+	2.28032i	0.158156	+	0.237739i
$93$	−0.445552	−	1.07566i	−0.0462016	−	0.111540i
$94$	−0.770772	+	7.74523i	−0.0794990	+	0.798860i
$95$		−	14.5324i		−	1.49099i
$96$	−0.474301	+	4.57755i	−0.0484081	+	0.467194i
$97$			7.99833i			0.812107i	0.913849	+	0.406054i	$0.133095\pi$
$97$			7.99833i			0.812107i	−0.913849	+	0.406054i	$0.866905\pi$
$98$	−4.00630	−	9.05260i	−0.404698	−	0.914451i
$99$	−12.3508	+	5.11588i	−1.24131	+	0.514166i
$100$	−8.69113	−	13.0645i	−0.869113	−	1.30645i
$101$	−2.23582	+	5.39774i	−0.222472	+	0.537095i	−0.995224	−	0.0976125i	$-0.968879\pi$
$101$	−2.23582	+	5.39774i	−0.222472	+	0.537095i	0.772752	+	0.634707i	$0.218879\pi$
$102$	−1.76199	−	5.82978i	−0.174463	−	0.577234i
$103$	5.02917	+	5.02917i	0.495539	+	0.495539i	0.910046	−	0.414507i	$-0.136046\pi$
$103$	5.02917	+	5.02917i	0.495539	+	0.495539i	−0.414507	+	0.910046i	$0.636046\pi$
$104$	−0.0739759	−	0.775266i	−0.00725393	−	0.0760211i
$105$	−6.66588	−	3.88311i	−0.650523	−	0.378953i
$106$	4.15114	−	7.74732i	0.403194	−	0.752487i
$107$	−0.274004	−	0.113496i	−0.0264890	−	0.0109721i	0.369400	−	0.929271i	$-0.379563\pi$
$107$	−0.274004	−	0.113496i	−0.0264890	−	0.0109721i	−0.395889	+	0.918299i	$0.629563\pi$
$108$	−7.21199	−	4.84009i	−0.693974	−	0.465737i
$109$	−8.69436	+	3.60132i	−0.832769	+	0.344944i	−0.757998	−	0.652257i	$-0.773822\pi$
$109$	−8.69436	+	3.60132i	−0.832769	+	0.344944i	−0.0747706	+	0.997201i	$0.523822\pi$
$110$	−22.4206	+	18.3621i	−2.13772	+	1.75075i
$111$			4.76956i			0.452707i
$112$	−6.37568	−	8.44694i	−0.602445	−	0.798161i
$113$		−	9.76376i		−	0.918497i	−0.888308	−	0.459249i	$-0.848119\pi$
$113$		−	9.76376i		−	0.918497i	0.888308	−	0.459249i	$-0.151881\pi$
$114$	−2.95578	−	3.60908i	−0.276834	−	0.338022i
$115$	−4.53445	+	1.87823i	−0.422840	+	0.175146i
$116$	1.70086	+	8.64239i	0.157921	+	0.802426i
$117$	0.594790	+	0.246370i	0.0549883	+	0.0227769i
$118$	−12.9933	−	6.96200i	−1.19613	−	0.640904i
$119$	12.1016	+	7.04964i	1.10935	+	0.646239i
$120$	−7.88464	−	2.41800i	−0.719766	−	0.220732i
$121$	15.3371	+	15.3371i	1.39428	+	1.39428i
$122$	−10.6613	+	3.22227i	−0.965230	+	0.291730i
$123$	0.188032	−	0.453950i	0.0169543	−	0.0409313i
$124$	2.80614	+	0.564096i	0.251999	+	0.0506573i
$125$	9.42267	−	3.90300i	0.842789	−	0.349095i
$126$	8.63861	−	1.38284i	0.769588	−	0.123193i
$127$			19.5490i			1.73469i	0.497705	+	0.867346i	$0.334176\pi$
$127$			19.5490i			1.73469i	−0.497705	+	0.867346i	$0.665824\pi$
$128$	−8.69444	−	7.23925i	−0.768487	−	0.639866i
$129$		−	1.84911i		−	0.162805i
$130$	1.38876	+	0.138203i	0.121802	+	0.0121212i
$131$	−6.95520	−	16.7913i	−0.607679	−	1.46707i	−0.865517	−	0.500879i	$-0.833010\pi$
$131$	−6.95520	−	16.7913i	−0.607679	−	1.46707i	0.257839	−	0.966188i	$-0.416990\pi$
$132$	−1.83339	+	9.12036i	−0.159576	+	0.793825i
$133$	10.6304	+	1.44151i	0.921775	+	0.124995i
$134$	−3.10916	+	0.939711i	−0.268591	+	0.0811787i
$135$	11.0060	−	11.0060i	0.947250	−	0.947250i
$136$	14.3142	+	4.38979i	1.22744	+	0.376421i
$137$	−9.87319	+	9.87319i	−0.843524	+	0.843524i	−0.989315	−	0.145791i	$-0.953427\pi$
$137$	−9.87319	+	9.87319i	−0.843524	+	0.843524i	0.145791	+	0.989315i	$0.453427\pi$
$138$	−0.744103	+	1.38873i	−0.0633422	+	0.118216i
$139$	−7.57631	+	18.2908i	−0.642614	+	1.55141i	0.180527	+	0.983570i	$0.442220\pi$
$139$	−7.57631	+	18.2908i	−0.642614	+	1.55141i	−0.823141	+	0.567837i	$0.807780\pi$
$140$	17.0586	−	8.28743i	1.44172	−	0.700415i
$141$	−4.13668	+	1.71347i	−0.348371	+	0.144300i
$142$	3.92588	−	3.21523i	0.329453	−	0.269816i
$143$		−	1.57428i		−	0.131648i
$144$	8.65516	−	3.54401i	0.721263	−	0.295334i
$145$	−15.7846			−1.31084
$146$	13.9551	+	17.0395i	1.15493	+	1.41020i
$147$	3.50171	−	4.49091i	0.288816	−	0.370404i
$148$	−9.73617	−	6.53410i	−0.800308	−	0.537100i
$149$	−2.06244	+	4.97918i	−0.168962	+	0.407910i	−0.985567	−	0.169287i	$-0.945854\pi$
$149$	−2.06244	+	4.97918i	−0.168962	+	0.407910i	0.816605	+	0.577197i	$0.195854\pi$
$150$	4.26315	−	7.95636i	0.348084	−	0.649634i
$151$	−1.82839	−	1.82839i	−0.148792	−	0.148792i	0.628786	−	0.777578i	$-0.283552\pi$
$151$	−1.82839	−	1.82839i	−0.148792	−	0.148792i	−0.777578	+	0.628786i	$0.783552\pi$
$152$	11.4166	−	1.08937i	0.926005	−	0.0883594i
$153$	−8.75186	+	8.75186i	−0.707546	+	0.707546i
$154$	−11.2079	−	18.2220i	−0.903156	−	1.46837i
$155$	−1.96290	+	4.73887i	−0.157664	+	0.380635i
$156$	0.373005	−	0.248141i	0.0298643	−	0.0198672i
$157$	9.99837	−	4.14146i	0.797957	−	0.330525i	0.0538192	−	0.998551i	$-0.482861\pi$
$157$	9.99837	−	4.14146i	0.797957	−	0.330525i	0.744138	+	0.668026i	$0.232861\pi$
$158$	11.2332	+	1.11788i	0.893666	+	0.0889337i
$159$	5.05615			0.400979
$160$	15.7375	−	12.7824i	1.24416	−	1.01054i
$161$	−0.924139	−	3.50326i	−0.0728324	−	0.276095i
$162$	−0.487560	+	4.89933i	−0.0383063	+	0.384928i
$163$	−5.89470	+	2.44167i	−0.461709	+	0.191246i	−0.601398	−	0.798949i	$-0.705390\pi$
$163$	−5.89470	+	2.44167i	−0.461709	+	0.191246i	0.139690	+	0.990195i	$0.455390\pi$
$164$	0.669057	+	1.00572i	0.0522446	+	0.0785339i
$165$	−15.4020	−	6.37972i	−1.19904	−	0.496661i
$166$	8.65329	−	2.61537i	0.671626	−	0.202992i
$167$	5.00406	+	5.00406i	0.387226	+	0.387226i	0.873697	−	0.486471i	$-0.161716\pi$
$167$	5.00406	+	5.00406i	0.387226	+	0.387226i	−0.486471	+	0.873697i	$0.661716\pi$
$168$	2.55087	−	5.52776i	0.196804	−	0.426476i
$169$	9.13878	−	9.13878i	0.702983	−	0.702983i
$170$	−12.6720	+	23.6499i	−0.971896	+	1.81386i
$171$	−3.62804	+	8.75886i	−0.277443	+	0.669807i
$172$	3.77460	+	2.53320i	0.287811	+	0.193155i
$173$	−8.89691	−	21.4790i	−0.676419	−	1.63302i	−0.770487	−	0.637455i	$-0.779987\pi$
$173$	−8.89691	−	21.4790i	−0.676419	−	1.63302i	0.0940681	−	0.995566i	$-0.470013\pi$
$174$	−3.92007	+	3.21047i	−0.297180	+	0.243385i
$175$	5.29462	+	20.0710i	0.400235	+	1.51723i
$176$	−16.1058	−	16.2370i	−1.21402	−	1.22391i
$177$		−	8.47981i		−	0.637382i
$178$	−16.1954	+	13.2638i	−1.21390	+	0.994161i
$179$	−7.86244	−	18.9816i	−0.587666	−	1.41875i	−0.885728	−	0.464205i	$-0.846340\pi$
$179$	−7.86244	−	18.9816i	−0.587666	−	1.41875i	0.298061	−	0.954547i	$-0.403660\pi$
$180$	3.23642	+	16.4449i	0.241229	+	1.22573i
$181$	−18.8806	−	7.82061i	−1.40339	−	0.581301i	−0.452758	−	0.891634i	$-0.649560\pi$
$181$	−18.8806	−	7.82061i	−1.40339	−	0.581301i	−0.950628	+	0.310332i	$0.899560\pi$
$182$	−0.238851	+	1.00217i	−0.0177048	+	0.0742857i
$183$	−4.53043	−	4.53043i	−0.334899	−	0.334899i
$184$	−1.81544	−	3.42145i	−0.133836	−	0.252232i
$185$	14.8581	−	14.8581i	1.09239	−	1.09239i
$186$	0.476368	+	1.57613i	0.0349290	+	0.115567i
$187$	27.9617	+	11.5821i	2.04476	+	0.846969i
$188$	2.16936	−	10.7916i	0.158217	−	0.787061i
$189$	6.95920	+	9.14265i	0.506207	+	0.665030i
$190$	−2.03518	+	20.4509i	−0.147647	+	1.48366i
$191$		−	1.01843i		−	0.0736910i	−0.999321	−	0.0368455i	$-0.988269\pi$
$191$		−	1.01843i		−	0.0736910i	0.999321	−	0.0368455i	$-0.0117309\pi$
$192$	1.30853	−	6.37539i	0.0944348	−	0.460104i
$193$	3.70779			0.266893			0.133446	−	0.991056i	$-0.457396\pi$
$193$	3.70779			0.266893			0.133446	+	0.991056i	$0.457396\pi$
$194$	1.12012	−	11.2557i	0.0804201	−	0.808115i
$195$	0.307234	+	0.741728i	0.0220015	+	0.0531162i
$196$	4.37015	+	13.3004i	0.312154	+	0.950032i
$197$	15.3126	+	6.34270i	1.09098	+	0.451899i	0.854348	−	0.519701i	$-0.173956\pi$
$197$	15.3126	+	6.34270i	1.09098	+	0.451899i	0.236632	+	0.971599i	$0.423956\pi$
$198$	18.0973	−	5.46972i	1.28612	−	0.388716i
$199$	−3.61849	−	3.61849i	−0.256508	−	0.256508i	0.567124	−	0.823632i	$-0.308056\pi$
$199$	−3.61849	−	3.61849i	−0.256508	−	0.256508i	−0.823632	+	0.567124i	$0.808056\pi$
$200$	10.4011	+	19.6023i	0.735468	+	1.38609i
$201$	−1.32121	−	1.32121i	−0.0931910	−	0.0931910i
$202$	3.90230	−	7.28292i	0.274565	−	0.512424i
$203$	1.56573	−	11.5464i	0.109892	−	0.810401i
$204$	1.66315	+	8.45078i	0.116444	+	0.591673i
$205$	−1.99990	+	0.828386i	−0.139679	+	0.0578570i
$206$	−6.37306	−	7.78168i	−0.444032	−	0.542175i
$207$	3.20188			0.222546
$208$	−0.00446834	+	1.10136i	−0.000309824	+	0.0763658i
$209$	23.1828			1.60359
$210$	8.83683	+	6.39808i	0.609799	+	0.441509i
$211$	−6.81295	−	16.4479i	−0.469023	−	1.13232i	−0.964591	−	0.263752i	$-0.915040\pi$
$211$	−6.81295	−	16.4479i	−0.469023	−	1.13232i	0.495568	−	0.868569i	$-0.334960\pi$
$212$	−6.92671	+	10.3212i	−0.475729	+	0.708861i
$213$	2.69692	+	1.11710i	0.184790	+	0.0765425i
$214$	0.369701	+	0.198092i	0.0252722	+	0.0135413i
$215$	−5.76034	+	5.76034i	−0.392852	+	0.392852i
$216$	9.47133	+	7.82127i	0.644442	+	0.532170i
$217$	−3.27178	−	1.90593i	−0.222103	−	0.129383i
$218$	12.7396	−	3.85041i	0.862834	−	0.260782i
$219$	−4.84856	+	11.7055i	−0.327635	+	0.790982i
$220$	34.1231	−	22.7004i	2.30058	−	1.53046i
$221$	−0.557770	−	1.34658i	−0.0375197	−	0.0905806i
$222$	0.667951	−	6.71203i	0.0448300	−	0.450482i
$223$	−17.3122			−1.15931			−0.579655	−	0.814862i	$-0.696813\pi$
$223$	−17.3122			−1.15931			−0.579655	+	0.814862i	$0.696813\pi$
$224$	7.78930	+	12.7799i	0.520445	+	0.853895i
$225$	−18.3444			−1.22296
$226$	−1.36736	+	13.7402i	−0.0909555	+	0.913983i
$227$	−1.97300	−	4.76324i	−0.130952	−	0.316147i	0.844780	−	0.535114i	$-0.179731\pi$
$227$	−1.97300	−	4.76324i	−0.130952	−	0.316147i	−0.975732	+	0.218967i	$0.929731\pi$
$228$	3.65412	+	5.49287i	0.242000	+	0.363774i
$229$	−5.23276	+	12.6330i	−0.345790	+	0.834812i	0.651317	+	0.758806i	$0.274217\pi$
$229$	−5.23276	+	12.6330i	−0.345790	+	0.834812i	−0.997107	+	0.0760061i	$0.975783\pi$
$230$	6.64420	−	2.00814i	0.438105	−	0.132413i
$231$	6.19454	−	10.6337i	0.407571	−	0.699649i
$232$	−1.18324	−	12.4003i	−0.0776834	−	0.814120i
$233$	18.4547	−	18.4547i	1.20901	−	1.20901i	0.237658	−	0.971349i	$-0.423620\pi$
$233$	18.4547	−	18.4547i	1.20901	−	1.20901i	0.971349	−	0.237658i	$-0.0763798\pi$
$234$	−0.802522	−	0.430004i	−0.0524625	−	0.0281103i
$235$	18.2244	+	7.54878i	1.18883	+	0.492428i
$236$	17.3099	+	11.6170i	1.12678	+	0.756202i
$237$	2.48511	+	5.99958i	0.161425	+	0.389715i
$238$	−16.0429	−	11.6155i	−1.03991	−	0.752918i
$239$	−14.1947			−0.918177			−0.459088	−	0.888391i	$-0.651824\pi$
$239$	−14.1947			−0.918177			−0.459088	+	0.888391i	$0.651824\pi$
$240$	10.7571	+	4.50696i	0.694370	+	0.290923i
$241$	−9.94215			−0.640430			−0.320215	−	0.947345i	$-0.603755\pi$
$241$	−9.94215			−0.640430			−0.320215	+	0.947345i	$0.603755\pi$
$242$	−19.4354	−	23.7312i	−1.24936	−	1.52550i
$243$	−14.6533	+	6.06961i	−0.940012	+	0.389366i
$244$	15.4545	−	3.04152i	0.989374	−	0.194713i
$245$	−24.8986	+	3.08156i	−1.59071	+	0.196874i
$246$	−0.328184	+	0.612493i	−0.0209242	+	0.0390512i
$247$	−0.789437	−	0.789437i	−0.0502307	−	0.0502307i
$248$	−3.86998	−	1.18682i	−0.245744	−	0.0753628i
$249$	3.67714	+	3.67714i	0.233029	+	0.233029i
$250$	−13.8068	+	4.17295i	−0.873216	+	0.263920i
$251$	−11.4857	−	4.75754i	−0.724972	−	0.300293i	−0.0104881	−	0.999945i	$-0.503339\pi$
$251$	−11.4857	−	4.75754i	−0.724972	−	0.300293i	−0.714484	+	0.699652i	$0.753339\pi$
$252$	−12.3504	+	0.736223i	−0.778005	+	0.0463777i
$253$	−2.99625	−	7.23359i	−0.188373	−	0.454772i
$254$	2.73773	−	27.5106i	0.171781	−	1.72617i
$255$	−15.4346			−0.966555
$256$	11.2215	+	11.4051i	0.701346	+	0.712821i
$257$			10.7998i			0.673671i	0.941563	+	0.336836i	$0.109357\pi$
$257$			10.7998i			0.673671i	−0.941563	+	0.336836i	$0.890643\pi$
$258$	−0.258957	+	2.60218i	−0.0161220	+	0.162005i
$259$	9.39490	+	12.3426i	0.583771	+	0.766929i
$260$	−1.93499	−	0.388977i	−0.120003	−	0.0241233i
$261$	9.51360	+	3.94066i	0.588877	+	0.243921i
$262$	7.43626	+	24.6039i	0.459414	+	1.52003i
$263$	−10.9514	+	10.9514i	−0.675292	+	0.675292i	−0.958931	−	0.283639i	$-0.908458\pi$
$263$	−10.9514	+	10.9514i	−0.675292	+	0.675292i	0.283639	+	0.958931i	$0.408458\pi$
$264$	3.85732	−	12.5780i	0.237402	−	0.774121i
$265$	−15.7509	−	15.7509i	−0.967571	−	0.967571i
$266$	−14.7579	−	3.51732i	−0.904867	−	0.215661i
$267$	−11.1256	−	4.60837i	−0.680875	−	0.282027i
$268$	4.50701	−	0.886999i	0.275309	−	0.0541821i
$269$	0.661310	+	1.59654i	0.0403208	+	0.0973430i	0.942757	−	0.333481i	$-0.108223\pi$
$269$	0.661310	+	1.59654i	0.0403208	+	0.0973430i	−0.902436	+	0.430824i	$0.858223\pi$
$270$	−17.0297	+	13.9471i	−1.03640	+	0.848791i
$271$			10.3316i			0.627603i	0.949489	+	0.313801i	$0.101603\pi$
$271$			10.3316i			0.627603i	−0.949489	+	0.313801i	$0.898397\pi$
$272$	−19.5291	−	8.18221i	−1.18413	−	0.496120i
$273$	−0.573049	+	0.151167i	−0.0346825	+	0.00914905i
$274$	15.2769	−	12.5115i	0.922909	−	0.755847i
$275$	17.1662	+	41.4430i	1.03516	+	2.49911i
$276$	1.24163	−	1.85010i	0.0747375	−	0.111363i
$277$	8.07181	−	19.4871i	0.484988	−	1.17086i	−0.472225	−	0.881478i	$-0.656549\pi$
$277$	8.07181	−	19.4871i	0.484988	−	1.17086i	0.957212	−	0.289386i	$-0.0934511\pi$
$278$	13.2234	−	24.6790i	0.793086	−	1.48015i
$279$	2.36614	−	2.36614i	0.141657	−	0.141657i
$280$	−25.1666	+	9.27361i	−1.50399	+	0.554204i
$281$	−16.9858	−	16.9858i	−1.01329	−	1.01329i	−0.999911	−	0.0133765i	$-0.995742\pi$
$281$	−16.9858	−	16.9858i	−1.01329	−	1.01329i	−0.0133765	−	0.999911i	$-0.504258\pi$
$282$	6.06135	−	1.83198i	0.360948	−	0.109093i
$283$	−0.542456	−	0.224693i	−0.0322457	−	0.0133566i	0.366502	−	0.930417i	$-0.380555\pi$
$283$	−0.542456	−	0.224693i	−0.0322457	−	0.0133566i	−0.398748	+	0.917061i	$0.630555\pi$
$284$	−5.97502	+	3.97488i	−0.354552	+	0.235865i
$285$	−10.9227	+	4.52432i	−0.647003	+	0.267997i
$286$	−0.220469	+	2.21542i	−0.0130366	+	0.131001i
$287$	−0.407588	−	1.54510i	−0.0240592	−	0.0912043i
$288$	−12.6764	+	3.77525i	−0.746964	+	0.222459i
$289$	11.0210			0.648293
$290$	22.2131	+	2.21055i	1.30440	+	0.129808i
$291$	6.01162	−	2.49009i	0.352407	−	0.145972i
$292$	−17.2522	−	25.9334i	−1.00961	−	1.51764i
$293$	5.67524	−	13.7012i	0.331551	−	0.800435i	−0.666918	−	0.745131i	$-0.732387\pi$
$293$	5.67524	−	13.7012i	0.331551	−	0.800435i	0.998470	−	0.0553044i	$-0.0176129\pi$
$294$	−5.55675	+	5.82949i	−0.324076	+	0.339983i
$295$	−26.4163	+	26.4163i	−1.53802	+	1.53802i
$296$	12.7863	+	10.5587i	0.743187	+	0.613712i
$297$	17.5574	+	17.5574i	1.01878	+	1.01878i
$298$	3.59971	−	6.71818i	0.208525	−	0.389173i
$299$	−0.144293	+	0.348354i	−0.00834468	+	0.0201458i
$300$	−7.11361	+	10.5997i	−0.410705	+	0.611972i
$301$	−3.64230	−	4.78507i	−0.209939	−	0.275807i
$302$	2.31697	+	2.82908i	0.133326	+	0.162795i
$303$	4.75306			0.273056
$304$	−16.2187	−	0.0658008i	−0.930204	−	0.00377393i
$305$			28.2264i			1.61624i
$306$	13.5418	−	11.0905i	0.774134	−	0.634003i
$307$	21.2769	−	8.81316i	1.21433	−	0.502994i	0.318730	−	0.947846i	$-0.396744\pi$
$307$	21.2769	−	8.81316i	1.21433	−	0.502994i	0.895604	+	0.444852i	$0.146744\pi$
$308$	13.2205	+	27.2128i	0.753309	+	1.55059i
$309$	2.21426	−	5.34569i	0.125965	−	0.304106i
$310$	3.42597	−	6.39394i	0.194582	−	0.363151i
$311$	−2.17216	+	2.17216i	−0.123172	+	0.123172i	−0.766006	−	0.642834i	$-0.777759\pi$
$311$	−2.17216	+	2.17216i	−0.123172	+	0.123172i	0.642834	+	0.766006i	$0.277759\pi$
$312$	−0.559667	+	0.296962i	−0.0316849	+	0.0168122i
$313$	5.31954	−	5.31954i	0.300678	−	0.300678i	−0.540601	−	0.841279i	$-0.681803\pi$
$313$	5.31954	−	5.31954i	0.300678	−	0.300678i	0.841279	+	0.540601i	$0.181803\pi$
$314$	−14.6503	+	4.42791i	−0.826766	+	0.249881i
$315$	2.97928	−	21.9707i	0.167864	−	1.23791i
$316$	−15.6515	−	3.14630i	−0.880466	−	0.176993i
$317$	−5.64194	−	13.6209i	−0.316883	−	0.765023i	−0.999416	−	0.0341685i	$-0.989122\pi$
$317$	−5.64194	−	13.6209i	−0.316883	−	0.765023i	0.682533	−	0.730855i	$-0.260878\pi$
$318$	−7.11533	−	0.708086i	−0.399008	−	0.0397075i
$319$		−	25.1804i		−	1.40983i
$320$	−23.9369	+	15.7843i	−1.33812	+	0.882369i
$321$			0.241278i			0.0134669i
$322$	0.809894	+	5.05943i	0.0451336	+	0.281951i
$323$	19.8297	−	8.21372i	1.10335	−	0.457024i
$324$	1.37225	−	6.82636i	0.0762360	−	0.379242i
$325$	0.826689	−	1.99580i	0.0458565	−	0.110707i
$326$	8.63734	−	2.61054i	0.478378	−	0.144585i
$327$	5.41358	+	5.41358i	0.299372	+	0.299372i
$328$	−0.800692	−	1.50902i	−0.0442108	−	0.0833215i
$329$	−7.32967	+	12.5823i	−0.404098	+	0.693687i
$330$	20.7812	+	11.1349i	1.14397	+	0.612957i
$331$	1.66979	+	0.691648i	0.0917797	+	0.0380164i	0.428101	−	0.903731i	$-0.359183\pi$
$331$	1.66979	+	0.691648i	0.0917797	+	0.0380164i	−0.336321	+	0.941747i	$0.609183\pi$
$332$	−12.5437	+	2.46866i	−0.688426	+	0.135485i
$333$	−12.6646	+	5.24584i	−0.694015	+	0.287470i
$334$	−6.34123	−	7.74282i	−0.346977	−	0.423668i
$335$			8.23167i			0.449744i
$336$	−4.36388	+	7.42178i	−0.238069	+	0.404891i
$337$			6.59711i			0.359367i	0.983724	+	0.179684i	$0.0575074\pi$
$337$			6.59711i			0.359367i	−0.983724	+	0.179684i	$0.942493\pi$
$338$	−14.1405	+	11.5808i	−0.769142	+	0.629914i
$339$	−7.33854	+	3.03972i	−0.398575	+	0.165095i
$340$	21.1448	−	31.5069i	1.14674	−	1.70870i
$341$	−7.55969	−	3.13132i	−0.409380	−	0.169571i
$342$	6.33224	−	11.8179i	0.342408	−	0.639041i
$343$	0.215612	−	18.5190i	0.0116419	−	0.999932i
$344$	−4.95710	−	4.09349i	−0.267269	−	0.220706i
$345$	2.82339	+	2.82339i	0.152006	+	0.152006i
$346$	9.51226	+	31.4726i	0.511382	+	1.69198i
$347$	−2.33276	+	5.63178i	−0.125229	+	0.302330i	−0.974043	−	0.226361i	$-0.927317\pi$
$347$	−2.33276	+	5.63178i	−0.125229	+	0.302330i	0.848814	+	0.528691i	$0.177317\pi$
$348$	5.96618	−	3.96899i	0.319821	−	0.212760i
$349$	−9.19809	+	3.80997i	−0.492362	+	0.203943i	−0.615029	−	0.788505i	$-0.710856\pi$
$349$	−9.19809	+	3.80997i	−0.492362	+	0.203943i	0.122666	+	0.992448i	$0.460856\pi$
$350$	−4.64008	−	28.9867i	−0.248023	−	1.54940i
$351$		−	1.19576i		−	0.0638247i
$352$	20.3912	+	25.1053i	1.08686	+	1.33812i
$353$			22.4549i			1.19515i	0.801812	+	0.597577i	$0.203870\pi$
$353$			22.4549i			1.19515i	−0.801812	+	0.597577i	$0.796130\pi$
$354$	−1.18755	+	11.9333i	−0.0631177	+	0.634249i
$355$	−4.92145	−	11.8814i	−0.261204	−	0.630602i
$356$	24.6487	−	16.3975i	1.30638	−	0.869066i
$357$	1.53101	−	11.2904i	0.0810298	−	0.597554i
$358$	8.40624	+	27.8132i	0.444284	+	1.46997i
$359$	3.52551	−	3.52551i	0.186069	−	0.186069i	−0.607925	−	0.793994i	$-0.707998\pi$
$359$	3.52551	−	3.52551i	0.186069	−	0.186069i	0.793994	+	0.607925i	$0.207998\pi$
$360$	−2.25148	−	23.5955i	−0.118663	−	1.24359i
$361$	−1.80979	+	1.80979i	−0.0952520	+	0.0952520i
$362$	25.4748	+	13.6498i	1.33892	+	0.717417i
$363$	6.75266	−	16.3024i	0.354423	−	0.855652i
$364$	0.476475	−	1.37687i	0.0249741	−	0.0721673i
$365$	51.5691	−	21.3606i	2.69925	−	1.11807i
$366$	5.74104	+	7.00996i	0.300089	+	0.366417i
$367$			10.3253i			0.538978i	0.963003	+	0.269489i	$0.0868548\pi$
$367$			10.3253i			0.538978i	−0.963003	+	0.269489i	$0.913145\pi$
$368$	2.07564	+	5.06912i	0.108200	+	0.264246i
$369$	1.41218			0.0735150
$370$	−22.9901	+	18.8285i	−1.19520	+	0.978847i
$371$	13.0842	−	9.95941i	0.679297	−	0.517067i
$372$	−0.449647	−	2.28474i	−0.0233131	−	0.118458i
$373$	−9.91074	+	23.9266i	−0.513159	+	1.23887i	0.428877	+	0.903363i	$0.358909\pi$
$373$	−9.91074	+	23.9266i	−0.513159	+	1.23887i	−0.942036	+	0.335512i	$0.891091\pi$
$374$	−37.7275	−	20.2150i	−1.95084	−	1.04529i
$375$	−5.86706	−	5.86706i	−0.302974	−	0.302974i
$376$	−4.56416	+	14.8829i	−0.235379	+	0.767525i
$377$	−0.857462	+	0.857462i	−0.0441615	+	0.0441615i
$378$	−8.51304	−	13.8407i	−0.437864	−	0.711889i
$379$	−1.01518	+	2.45085i	−0.0521461	+	0.125892i	−0.947806	−	0.318848i	$-0.896704\pi$
$379$	−1.01518	+	2.45085i	−0.0521461	+	0.125892i	0.895660	+	0.444740i	$0.146704\pi$
$380$	5.72806	−	28.4947i	0.293843	−	1.46175i
$381$	14.6932	−	6.08613i	0.752756	−	0.311802i
$382$	−0.142626	+	1.43320i	−0.00729736	+	0.0733288i
$383$	−11.8843			−0.607260			−0.303630	−	0.952790i	$-0.598199\pi$
$383$	−11.8843			−0.607260			−0.303630	+	0.952790i	$0.598199\pi$
$384$	−2.73428	+	8.78860i	−0.139533	+	0.448491i
$385$	−52.4235	+	13.8290i	−2.67175	+	0.704791i
$386$	−5.21783	−	0.519256i	−0.265581	−	0.0264294i
$387$	4.90992	−	2.03375i	0.249585	−	0.103382i
$388$	−3.15261	+	15.6829i	−0.160050	+	0.796180i
$389$	−13.6989	−	5.67426i	−0.694560	−	0.287696i	0.00733858	−	0.999973i	$-0.497664\pi$
$389$	−13.6989	−	5.67426i	−0.694560	−	0.287696i	−0.701899	+	0.712277i	$0.747664\pi$
$390$	−0.328483	−	1.08683i	−0.0166334	−	0.0550339i
$391$	−5.12576	−	5.12576i	−0.259221	−	0.259221i
$392$	−4.28730	−	19.3292i	−0.216541	−	0.976273i
$393$	−10.4552	+	10.4552i	−0.527395	+	0.527395i
$394$	−20.6606	−	11.0703i	−1.04087	−	0.557714i
$395$	10.9483	−	26.4315i	0.550868	−	1.32991i
$396$	−26.2337	+	5.16290i	−1.31829	+	0.259446i
$397$	1.97409	+	4.76586i	0.0990765	+	0.239192i	0.965644	−	0.259868i	$-0.0836789\pi$
$397$	1.97409	+	4.76586i	0.0990765	+	0.239192i	−0.866568	+	0.499059i	$0.833679\pi$
$398$	4.58542	+	5.59892i	0.229846	+	0.280648i
$399$	−2.22608	−	8.43872i	−0.111444	−	0.422464i
$400$	−11.8919	−	29.0422i	−0.594593	−	1.45211i
$401$			10.6645i			0.532558i	0.963896	+	0.266279i	$0.0857942\pi$
$401$			10.6645i			0.532558i	−0.963896	+	0.266279i	$0.914206\pi$
$402$	1.67426	+	2.04432i	0.0835046	+	0.101961i
$403$	0.150798	+	0.364058i	0.00751178	+	0.0181350i
$404$	−6.51150	+	9.70248i	−0.323959	+	0.482717i
$405$	11.5280	+	4.77506i	0.572832	+	0.237275i
$406$	−3.82041	+	16.0296i	−0.189604	+	0.795536i
$407$	23.7025	+	23.7025i	1.17489	+	1.17489i
$408$	−1.15700	−	12.1254i	−0.0572802	−	0.600296i
$409$	−8.02235	+	8.02235i	−0.396680	+	0.396680i	−0.877060	−	0.480380i	$-0.840499\pi$
$409$	−8.02235	+	8.02235i	−0.396680	+	0.396680i	0.480380	+	0.877060i	$0.340499\pi$
$410$	2.93040	−	0.885682i	0.144722	−	0.0437407i
$411$	10.4946	+	4.34700i	0.517659	+	0.214422i
$412$	7.87879	+	11.8434i	0.388160	+	0.583481i
$413$	−16.7032	−	21.9439i	−0.821912	−	1.07979i
$414$	−4.50589	−	0.448406i	−0.221452	−	0.0220380i
$415$		−	22.9101i		−	1.12461i
$416$	0.160528	−	1.54928i	0.00787054	−	0.0759598i
$417$	16.1063			0.788727
$418$	−32.6243	−	3.24662i	−1.59570	−	0.158798i
$419$	−7.42712	−	17.9307i	−0.362839	−	0.875970i	−0.994883	−	0.101038i	$-0.967784\pi$
$419$	−7.42712	−	17.9307i	−0.362839	−	0.875970i	0.632044	−	0.774933i	$-0.282216\pi$
$420$	−11.5397	−	10.2413i	−0.563081	−	0.499726i
$421$	−4.68956	−	1.94248i	−0.228555	−	0.0946706i	0.265467	−	0.964120i	$-0.414474\pi$
$421$	−4.68956	−	1.94248i	−0.228555	−	0.0946706i	−0.494022	+	0.869449i	$0.664474\pi$
$422$	7.28416	+	24.1006i	0.354587	+	1.17320i
$423$	−9.09952	−	9.09952i	−0.442434	−	0.442434i
$424$	11.1931	−	13.5546i	0.543586	−	0.658267i
$425$	29.3667	+	29.3667i	1.42449	+	1.42449i
$426$	−3.63883	−	1.94974i	−0.176302	−	0.0944654i
$427$	−20.6476	−	2.79987i	−0.999208	−	0.135495i
$428$	−0.492525	−	0.330542i	−0.0238071	−	0.0159773i
$429$	−1.18324	+	0.490115i	−0.0571275	+	0.0236630i
$430$	8.91301	−	7.29960i	0.429823	−	0.352018i
$431$	18.9939			0.914904			0.457452	−	0.889234i	$-0.348762\pi$
$431$	18.9939			0.914904			0.457452	+	0.889234i	$0.348762\pi$
$432$	−12.2333	−	12.3330i	−0.588576	−	0.593371i
$433$	13.8910			0.667560			0.333780	−	0.942651i	$-0.391676\pi$
$433$	13.8910			0.667560			0.333780	+	0.942651i	$0.391676\pi$
$434$	4.33733	+	3.14034i	0.208199	+	0.150741i
$435$	4.91417	+	11.8639i	0.235617	+	0.568829i
$436$	−18.4672	+	3.63442i	−0.884417	+	0.174057i
$437$	−5.12986	−	2.12486i	−0.245394	−	0.101646i
$438$	8.46248	−	15.7936i	0.404353	−	0.754649i
$439$	−13.4642	+	13.4642i	−0.642611	+	0.642611i	−0.951197	−	0.308586i	$-0.900144\pi$
$439$	−13.4642	+	13.4642i	−0.642611	+	0.642611i	0.308586	+	0.951197i	$0.400144\pi$
$440$	−51.1992	+	27.1666i	−2.44083	+	1.29512i
$441$	15.7761	+	4.35869i	0.751241	+	0.207557i
$442$	0.596348	+	1.97310i	0.0283654	+	0.0938508i
$443$	−4.89175	+	11.8097i	−0.232414	+	0.561097i	−0.996460	−	0.0840644i	$-0.973210\pi$
$443$	−4.89175	+	11.8097i	−0.232414	+	0.561097i	0.764046	+	0.645161i	$0.223210\pi$
$444$	−1.87997	+	9.35204i	−0.0892192	+	0.443828i
$445$	20.3024	+	49.0144i	0.962427	+	2.32351i
$446$	24.3628	+	2.42448i	1.15361	+	0.114802i
$447$	4.38449			0.207379
$448$	−9.17183	−	19.0756i	−0.433328	−	0.901236i
$449$	36.0648			1.70200			0.851001	−	0.525163i	$-0.175996\pi$
$449$	36.0648			1.70200			0.851001	+	0.525163i	$0.175996\pi$
$450$	25.8153	+	2.56903i	1.21695	+	0.121105i
$451$	−1.32148	−	3.19035i	−0.0622263	−	0.150228i
$452$	3.84847	−	19.1445i	0.181017	−	0.900483i
$453$	−0.805008	+	1.94346i	−0.0378226	+	0.0913118i
$454$	2.10946	+	6.97944i	0.0990019	+	0.327561i
$455$	2.25608	+	1.31425i	0.105767	+	0.0616129i
$456$	−4.37306	−	8.24165i	−0.204787	−	0.385951i
$457$	5.72823	−	5.72823i	0.267955	−	0.267955i	−0.560320	−	0.828276i	$-0.689322\pi$
$457$	5.72823	−	5.72823i	0.267955	−	0.267955i	0.828276	+	0.560320i	$0.189322\pi$
$458$	9.13305	−	17.0451i	0.426759	−	0.796466i
$459$	21.2386	+	8.79731i	0.991332	+	0.410623i
$460$	−9.63136	+	1.89549i	−0.449064	+	0.0883778i
$461$	5.94446	+	14.3512i	0.276861	+	0.668402i	0.999745	−	0.0225670i	$-0.00718391\pi$
$461$	5.94446	+	14.3512i	0.276861	+	0.668402i	−0.722884	+	0.690969i	$0.757184\pi$
$462$	−10.2065	+	14.0970i	−0.474851	+	0.655850i
$463$	−6.42418			−0.298557			−0.149279	−	0.988795i	$-0.547695\pi$
$463$	−6.42418			−0.298557			−0.149279	+	0.988795i	$0.547695\pi$
$464$	−0.0714707	+	17.6162i	−0.00331795	+	0.817812i
$465$	4.17288			0.193513
$466$	−28.5551	+	23.3861i	−1.32279	+	1.08334i
$467$	31.5563	−	13.0711i	1.46025	−	0.604857i	0.495640	−	0.868528i	$-0.334933\pi$
$467$	31.5563	−	13.0711i	1.46025	−	0.604857i	0.964613	+	0.263671i	$0.0849334\pi$
$468$	1.06914	+	0.717518i	0.0494210	+	0.0331673i
$469$	−6.02147	−	0.816527i	−0.278046	−	0.0377037i
$470$	−24.5893	−	13.1753i	−1.13422	−	0.607733i
$471$	−6.22553	−	6.22553i	−0.286857	−	0.286857i
$472$	−22.7327	−	18.7723i	−1.04636	−	0.864066i
$473$	−9.18918	−	9.18918i	−0.422519	−	0.422519i
$474$	−2.65699	−	8.79101i	−0.122040	−	0.403784i
$475$	29.3902	+	12.1738i	1.34851	+	0.558573i
$476$	20.9499	+	18.5927i	0.960237	+	0.852196i
$477$	5.56104	+	13.4255i	0.254623	+	0.614714i
$478$	19.9756	+	1.98789i	0.913664	+	0.0909238i
$479$	30.0577			1.37337			0.686686	−	0.726954i	$-0.259065\pi$
$479$	30.0577			1.37337			0.686686	+	0.726954i	$0.259065\pi$
$480$	−14.5069	−	7.84896i	−0.662147	−	0.358254i
$481$		−	1.61427i		−	0.0736043i
$482$	13.9912	+	1.39234i	0.637282	+	0.0634195i
$483$	−2.34537	+	1.78525i	−0.106718	+	0.0812317i
$484$	24.0274	+	36.1179i	1.09215	+	1.64172i
$485$	−26.4845	−	10.9703i	−1.20260	−	0.498134i
$486$	21.4711	−	6.48941i	0.973949	−	0.294366i
$487$	18.5311	−	18.5311i	0.839726	−	0.839726i	−0.149097	−	0.988823i	$-0.547637\pi$
$487$	18.5311	−	18.5311i	0.839726	−	0.839726i	0.988823	+	0.149097i	$0.0476367\pi$
$488$	−22.1745	+	2.11589i	−1.00379	+	0.0957819i
$489$	3.67036	+	3.67036i	0.165979	+	0.165979i
$490$	35.4704	−	0.849650i	1.60239	−	0.0383833i
$491$	−4.29893	−	1.78068i	−0.194008	−	0.0803608i	0.283564	−	0.958953i	$-0.408483\pi$
$491$	−4.29893	−	1.78068i	−0.194008	−	0.0803608i	−0.477572	+	0.878592i	$0.658483\pi$
$492$	0.547617	−	0.815979i	0.0246885	−	0.0367872i
$493$	−8.92148	−	21.5384i	−0.401803	−	0.970039i
$494$	1.00039	+	1.22150i	0.0450096	+	0.0549580i
$495$		−	47.9136i		−	2.15356i
$496$	5.27986	+	2.21213i	0.237073	+	0.0993276i
$497$	9.17945	−	2.42149i	0.411755	−	0.108618i
$498$	−4.65974	−	5.68967i	−0.208808	−	0.254960i
$499$	−0.103405	−	0.249641i	−0.00462903	−	0.0111755i	0.921548	−	0.388264i	$-0.126925\pi$
$499$	−0.103405	−	0.249641i	−0.00462903	−	0.0111755i	−0.926177	+	0.377089i	$0.876925\pi$
$500$	20.0141	−	3.93887i	0.895059	−	0.176152i
$501$	2.20320	−	5.31900i	0.0984318	−	0.237635i
$502$	15.4972	+	8.30362i	0.691672	+	0.370609i
$503$	−30.2868	+	30.2868i	−1.35042	+	1.35042i	−0.465235	+	0.885187i	$0.654030\pi$
$503$	−30.2868	+	30.2868i	−1.35042	+	1.35042i	−0.885187	+	0.465235i	$0.845970\pi$
$504$	17.4834	+	0.693554i	0.778774	+	0.0308934i
$505$	−14.8067	−	14.8067i	−0.658891	−	0.658891i
$506$	3.20349	+	10.5992i	0.142412	+	0.471190i
$507$	−9.71394	−	4.02365i	−0.431411	−	0.178696i
$508$	−7.70541	+	38.3312i	−0.341872	+	1.70067i
$509$	3.22636	−	1.33640i	0.143006	−	0.0592350i	−0.310033	−	0.950726i	$-0.600340\pi$
$509$	3.22636	−	1.33640i	0.143006	−	0.0592350i	0.453039	+	0.891491i	$0.350340\pi$
$510$	21.7206	+	2.16154i	0.961804	+	0.0957145i
$511$	10.5100	+	39.8416i	0.464934	+	1.76249i
$512$	−14.1944	−	17.6215i	−0.627311	−	0.778769i
$513$	17.6087			0.777443
$514$	1.51245	−	15.1981i	0.0667113	−	0.670360i
$515$	−23.5508	+	9.75505i	−1.03777	+	0.429859i
$516$	0.728842	−	3.62568i	0.0320855	−	0.159612i
$517$	−12.0422	+	29.0725i	−0.529616	+	1.27861i
$518$	−11.4926	−	18.6849i	−0.504955	−	0.820969i
$519$	−13.3740	+	13.3740i	−0.587054	+	0.587054i
$520$	2.66857	+	0.818378i	0.117025	+	0.0358882i
$521$	14.0142	+	14.0142i	0.613975	+	0.613975i	0.943979	−	0.330005i	$-0.107050\pi$
$521$	14.0142	+	14.0142i	0.613975	+	0.613975i	−0.330005	+	0.943979i	$0.607050\pi$
$522$	−12.8363	−	6.87788i	−0.561828	−	0.301037i
$523$	10.7118	−	25.8607i	0.468396	−	1.13081i	−0.496467	−	0.868056i	$-0.665370\pi$
$523$	10.7118	−	25.8607i	0.468396	−	1.13081i	0.964863	−	0.262753i	$-0.0846304\pi$
$524$	−7.01913	−	35.6655i	−0.306632	−	1.55805i
$525$	13.4372	−	10.2281i	0.586448	−	0.446392i
$526$	16.9452	−	13.8778i	0.738845	−	0.605101i
$527$	−7.57571			−0.330003
$528$	−7.18974	+	17.1603i	−0.312893	+	0.746807i
$529$		−	21.1247i		−	0.918467i
$530$	19.9598	+	24.3715i	0.867000	+	1.05863i
$531$	22.5164	−	9.32659i	0.977128	−	0.404740i
$532$	20.2757	+	7.01656i	0.879063	+	0.304207i
$533$	−0.0636398	+	0.153640i	−0.00275655	+	0.00665489i
$534$	15.0112	+	8.04326i	0.649600	+	0.348066i
$535$	0.751631	−	0.751631i	0.0324958	−	0.0324958i
$536$	−6.46676	+	0.617059i	−0.279322	+	0.0266529i
$537$	−11.8190	+	11.8190i	−0.510026	+	0.510026i
$538$	−0.707050	−	2.33937i	−0.0304831	−	0.100857i
$539$	−4.91586	−	39.7195i	−0.211741	−	1.71084i
$540$	25.9185	−	17.2423i	1.11536	−	0.741988i
$541$	−10.6310	−	25.6655i	−0.457063	−	1.10345i	−0.969581	−	0.244770i	$-0.921287\pi$
$541$	−10.6310	−	25.6655i	−0.457063	−	1.10345i	0.512518	−	0.858676i	$-0.328713\pi$
$542$	1.44689	−	14.5393i	0.0621493	−	0.624518i
$543$			16.6256i			0.713474i
$544$	26.3367	+	14.2495i	1.12918	+	0.610941i
$545$		−	33.7288i		−	1.44478i
$546$	0.827601	−	0.132479i	0.0354180	−	0.00566959i
$547$	−17.4319	+	7.22052i	−0.745334	+	0.308727i	−0.722836	−	0.691020i	$-0.757162\pi$
$547$	−17.4319	+	7.22052i	−0.745334	+	0.308727i	−0.0224976	+	0.999747i	$0.507162\pi$
$548$	−23.2507	+	15.4675i	−0.993221	+	0.660739i
$549$	7.04678	−	17.0124i	0.300749	−	0.726073i
$550$	−18.3535	−	60.7252i	−0.782598	−	2.58933i
$551$	−12.6270	−	12.6270i	−0.537927	−	0.537927i
$552$	−2.00640	+	2.42969i	−0.0853980	+	0.103414i
$553$	18.2487	+	10.6305i	0.776012	+	0.452055i
$554$	−14.0882	+	26.2930i	−0.598551	+	1.11708i
$555$	−15.7933	−	6.54178i	−0.670387	−	0.277683i
$556$	−22.0649	+	32.8779i	−0.935761	+	1.39433i
$557$	−34.0169	+	14.0903i	−1.44134	+	0.597023i	−0.960123	−	0.279578i	$-0.909806\pi$
$557$	−34.0169	+	14.0903i	−1.44134	+	0.597023i	−0.481218	+	0.876601i	$0.659806\pi$
$558$	−3.66114	+	2.99841i	−0.154989	+	0.126933i
$559$			0.625834i			0.0264699i
$560$	36.7147	−	9.52597i	1.55148	−	0.402546i
$561$		−	24.6221i		−	1.03955i
$562$	21.5247	+	26.2822i	0.907964	+	1.10865i
$563$	−5.78346	+	2.39559i	−0.243744	+	0.100962i	−0.501211	−	0.865325i	$-0.667112\pi$
$563$	−5.78346	+	2.39559i	−0.243744	+	0.100962i	0.257467	+	0.966287i	$0.417112\pi$
$564$	−8.78648	+	1.72922i	−0.369977	+	0.0728132i
$565$	32.3303	+	13.3917i	1.36015	+	0.563392i
$566$	0.731911	+	0.392170i	0.0307645	+	0.0164841i
$567$	−4.63646	+	7.95909i	−0.194713	+	0.334251i
$568$	8.96509	−	4.75692i	0.376167	−	0.199596i
$569$	13.9970	+	13.9970i	0.586786	+	0.586786i	0.936760	−	0.349974i	$-0.113809\pi$
$569$	13.9970	+	13.9970i	0.586786	+	0.586786i	−0.349974	+	0.936760i	$0.613809\pi$
$570$	16.0047	−	4.83724i	0.670362	−	0.202610i
$571$	−4.72056	+	11.3964i	−0.197549	+	0.476926i	−0.991349	−	0.131253i	$-0.958100\pi$
$571$	−4.72056	+	11.3964i	−0.197549	+	0.476926i	0.793800	+	0.608179i	$0.208100\pi$
$572$	0.620515	−	3.08680i	0.0259451	−	0.129066i
$573$	−0.765461	+	0.317064i	−0.0319776	+	0.0132456i
$574$	0.357201	+	2.23144i	0.0149093	+	0.0931385i
$575$		−	10.7438i		−	0.448049i
$576$	18.3677	−	3.53750i	0.765322	−	0.147396i
$577$		−	3.86125i		−	0.160746i	−0.996765	−	0.0803729i	$-0.974389\pi$
$577$		−	3.86125i		−	0.160746i	0.996765	−	0.0803729i	$-0.0256111\pi$
$578$	−15.5094	−	1.54343i	−0.645106	−	0.0641982i
$579$	−1.15434	−	2.78681i	−0.0479725	−	0.115816i
$580$	−30.9501	−	6.22164i	−1.28513	−	0.258340i
$581$	16.7587	+	2.27252i	0.695268	+	0.0942802i
$582$	−8.80865	+	2.66232i	−0.365130	+	0.110357i
$583$	25.1267	−	25.1267i	1.04064	−	1.04064i
$584$	20.6465	+	38.9112i	0.854358	+	1.61016i
$585$	−1.63159	+	1.63159i	−0.0674579	+	0.0674579i
$586$	−9.90534	+	18.4865i	−0.409186	+	0.763669i
$587$	2.92601	−	7.06401i	0.120769	−	0.291563i	−0.851921	−	0.523671i	$-0.824562\pi$
$587$	2.92601	−	7.06401i	0.120769	−	0.291563i	0.972690	+	0.232108i	$0.0745622\pi$
$588$	8.63620	−	7.42543i	0.356151	−	0.306220i
$589$	−5.36112	+	2.22065i	−0.220901	+	0.0915002i
$590$	40.8741	−	33.4752i	1.68276	−	1.37815i
$591$		−	13.4838i		−	0.554649i
$592$	−16.5150	−	16.6495i	−0.678760	−	0.684290i
$593$	24.1361			0.991150			0.495575	−	0.868565i	$-0.334957\pi$
$593$	24.1361			0.991150			0.495575	+	0.868565i	$0.334957\pi$
$594$	−22.2491	−	27.1667i	−0.912890	−	1.11466i
$595$	−39.9414	+	30.4026i	−1.63744	+	1.24638i
$596$	−6.00657	+	8.95012i	−0.246039	+	0.366611i
$597$	−1.59316	+	3.84623i	−0.0652037	+	0.157416i
$598$	0.251843	−	0.470018i	0.0102986	−	0.0192205i
$599$	−5.85464	−	5.85464i	−0.239214	−	0.239214i	0.577310	−	0.816525i	$-0.304102\pi$
$599$	−5.85464	−	5.85464i	−0.239214	−	0.239214i	−0.816525	+	0.577310i	$0.804102\pi$
$600$	11.4951	−	13.9203i	0.469287	−	0.568293i
$601$	−13.4335	+	13.4335i	−0.547964	+	0.547964i	−0.925852	−	0.377887i	$-0.876651\pi$
$601$	−13.4335	+	13.4335i	−0.547964	+	0.547964i	0.377887	+	0.925852i	$0.376651\pi$
$602$	4.45555	+	7.24394i	0.181595	+	0.295241i
$603$	2.05506	−	4.96135i	0.0836884	−	0.202042i
$604$	−2.86438	−	4.30574i	−0.116550	−	0.175198i
$605$	−71.8210	+	29.7492i	−2.91994	+	1.20948i
$606$	−6.68880	−	0.665641i	−0.271714	−	0.0270398i
$607$	9.43873			0.383106			0.191553	−	0.981482i	$-0.438648\pi$
$607$	9.43873			0.383106			0.191553	+	0.981482i	$0.438648\pi$
$608$	22.8147	+	2.36393i	0.925258	+	0.0958702i
$609$	−9.16587	+	2.41790i	−0.371420	+	0.0979784i
$610$	3.95295	−	39.7219i	0.160050	−	1.60829i
$611$	1.40007	−	0.579927i	0.0566407	−	0.0234613i
$612$	−20.6101	+	13.7108i	−0.833112	+	0.554227i
$613$	33.9466	+	14.0611i	1.37109	+	0.567923i	0.942083	−	0.335379i	$-0.108864\pi$
$613$	33.9466	+	14.0611i	1.37109	+	0.567923i	0.429005	+	0.903302i	$0.358864\pi$
$614$	−31.1764	+	9.42272i	−1.25818	+	0.380270i
$615$	1.24525	+	1.24525i	0.0502132	+	0.0502132i
$616$	−14.7937	−	40.1470i	−0.596057	−	1.61757i
$617$	−23.1176	+	23.1176i	−0.930680	+	0.930680i	−0.997748	−	0.0670682i	$-0.978635\pi$
$617$	−23.1176	+	23.1176i	−0.930680	+	0.930680i	0.0670682	+	0.997748i	$0.478635\pi$
$618$	−3.86468	+	7.21270i	−0.155460	+	0.290137i
$619$	−4.99740	+	12.0648i	−0.200862	+	0.484924i	−0.991927	−	0.126808i	$-0.959527\pi$
$619$	−4.99740	+	12.0648i	−0.200862	+	0.484924i	0.791065	+	0.611732i	$0.209527\pi$
$620$	−5.71668	+	8.51816i	−0.229587	+	0.342098i
$621$	−2.27583	−	5.49434i	−0.0913258	−	0.220480i
$622$	3.36099	−	2.75259i	0.134763	−	0.110369i
$623$	−37.8679	+	9.98933i	−1.51715	+	0.400214i
$624$	0.829186	−	0.339526i	0.0331940	−	0.0135919i
$625$		−	2.67410i		−	0.106964i
$626$	−8.23096	+	6.74102i	−0.328975	+	0.269425i
$627$	−7.21742	−	17.4244i	−0.288236	−	0.695864i
$628$	21.2370	−	4.17953i	0.847447	−	0.166781i
$629$	28.6720	+	11.8763i	1.14323	+	0.473541i
$630$	−7.26952	+	30.5013i	−0.289624	+	1.21520i
$631$	19.9610	+	19.9610i	0.794634	+	0.794634i	0.982244	−	0.187610i	$-0.0600741\pi$
$631$	19.9610	+	19.9610i	0.794634	+	0.794634i	−0.187610	+	0.982244i	$0.560074\pi$
$632$	21.5852	+	6.61958i	0.858612	+	0.263313i
$633$	−10.2414	+	10.2414i	−0.407057	+	0.407057i
$634$	6.03217	+	19.9582i	0.239568	+	0.792643i
$635$	−64.7318	−	26.8128i	−2.56880	−	1.06403i
$636$	9.91397	+	1.99293i	0.393114	+	0.0790246i
$637$	−1.18516	+	1.51996i	−0.0469578	+	0.0602229i
$638$	−3.52638	+	35.4354i	−0.139611	+	1.40290i
$639$			8.38977i			0.331894i
$640$	35.8961	−	18.8604i	1.41892	−	0.745523i
$641$	14.6955			0.580437			0.290219	−	0.956960i	$-0.406272\pi$
$641$	14.6955			0.580437			0.290219	+	0.956960i	$0.406272\pi$
$642$	0.0337897	−	0.339542i	0.00133357	−	0.0134007i
$643$	16.0999	+	38.8686i	0.634919	+	1.53283i	0.833368	+	0.552718i	$0.186409\pi$
$643$	16.0999	+	38.8686i	0.634919	+	1.53283i	−0.198450	+	0.980111i	$0.563591\pi$
$644$	−0.431188	−	7.23336i	−0.0169912	−	0.285034i
$645$	6.12287	+	2.53618i	0.241088	+	0.0998619i
$646$	−29.0558	+	8.78182i	−1.14319	+	0.345516i
$647$	20.2079	+	20.2079i	0.794456	+	0.794456i	0.982215	−	0.187759i	$-0.0601224\pi$
$647$	20.2079	+	20.2079i	0.794456	+	0.794456i	−0.187759	+	0.982215i	$0.560122\pi$
$648$	−2.88711	+	9.41430i	−0.113416	+	0.369829i
$649$	−42.1407	−	42.1407i	−1.65417	−	1.65417i
$650$	−1.44287	+	2.69285i	−0.0565940	+	0.105622i
$651$	−0.413922	+	3.05247i	−0.0162229	+	0.119636i
$652$	−12.5206	+	2.46411i	−0.490344	+	0.0965019i
$653$	−32.4008	+	13.4209i	−1.26794	+	0.525199i	−0.912338	−	0.409437i	$-0.865725\pi$
$653$	−32.4008	+	13.4209i	−1.26794	+	0.525199i	−0.355605	+	0.934636i	$0.615725\pi$
$654$	−6.86018	−	8.37647i	−0.268254	−	0.327546i
$655$	65.1401			2.54523
$656$	0.915454	+	2.23571i	0.0357425	+	0.0872900i
$657$	−36.4141			−1.42065
$658$	12.0769	−	16.6802i	0.470805	−	0.650261i
$659$	−9.51545	−	22.9723i	−0.370669	−	0.894875i	−0.993637	−	0.112627i	$-0.964073\pi$
$659$	−9.51545	−	22.9723i	−0.370669	−	0.894875i	0.622968	−	0.782247i	$-0.285927\pi$
$660$	−27.6852	−	18.5800i	−1.07765	−	0.723227i
$661$	−28.1486	−	11.6596i	−1.09486	−	0.453504i	−0.239158	−	0.970981i	$-0.576871\pi$
$661$	−28.1486	−	11.6596i	−1.09486	−	0.453504i	−0.855697	+	0.517477i	$0.826871\pi$
$662$	−2.25296	−	1.20717i	−0.0875640	−	0.0469182i
$663$	−0.838451	+	0.838451i	−0.0325627	+	0.0325627i
$664$	17.9980	−	1.71737i	0.698459	−	0.0666470i
$665$	−19.3536	+	33.2230i	−0.750500	+	1.28833i
$666$	18.5570	−	5.60867i	0.719071	−	0.217331i
$667$	−2.30795	+	5.57189i	−0.0893643	+	0.215744i
$668$	7.83944	+	11.7842i	0.303317	+	0.455946i
$669$	5.38975	+	13.0120i	0.208380	+	0.503074i
$670$	1.15280	−	11.5841i	0.0445366	−	0.447534i
$671$	−45.0282			−1.73829
$672$	7.18050	−	9.83325i	0.276994	−	0.379326i
$673$	−14.2449			−0.549101			−0.274550	−	0.961573i	$-0.588529\pi$
$673$	−14.2449			−0.549101			−0.274550	+	0.961573i	$0.588529\pi$
$674$	0.923889	−	9.28386i	0.0355869	−	0.357601i
$675$	13.0388	+	31.4784i	0.501863	+	1.21160i
$676$	21.5212	−	14.3170i	0.827739	−	0.550652i
$677$	1.35098	−	3.26156i	0.0519225	−	0.125352i	−0.895790	−	0.444478i	$-0.853389\pi$
$677$	1.35098	−	3.26156i	0.0519225	−	0.125352i	0.947712	+	0.319126i	$0.103389\pi$
$678$	10.7529	−	3.24996i	0.412964	−	0.124814i
$679$	10.6518	−	18.2853i	0.408780	−	0.701724i
$680$	−34.1687	+	41.3773i	−1.31031	+	1.58675i
$681$	−2.96585	+	2.96585i	−0.113652	+	0.113652i
$682$	10.1999	+	5.46529i	0.390576	+	0.209277i
$683$	38.0612	+	15.7655i	1.45637	+	0.603249i	0.963705	−	0.266968i	$-0.0860220\pi$
$683$	38.0612	+	15.7655i	1.45637	+	0.603249i	0.492667	+	0.870218i	$0.336022\pi$
$684$	−10.5662	+	15.7441i	−0.404007	+	0.601992i
$685$	−19.1509	−	46.2345i	−0.731720	−	1.76653i
$686$	−2.89691	+	26.0309i	−0.110604	+	0.993865i
$687$	11.1242			0.424414
$688$	6.40266	+	6.45483i	0.244099	+	0.246088i
$689$	−1.71126			−0.0651939
$690$	−3.57785	−	4.36866i	−0.136207	−	0.166312i
$691$	−17.9922	+	7.45260i	−0.684454	+	0.283510i	−0.697687	−	0.716402i	$-0.745788\pi$
$691$	−17.9922	+	7.45260i	−0.684454	+	0.283510i	0.0132334	+	0.999912i	$0.495788\pi$
$692$	−8.97868	−	45.6224i	−0.341318	−	1.73430i
$693$	35.0488	+	4.75271i	1.33139	+	0.180540i
$694$	4.07151	−	7.59870i	0.154552	−	0.288443i
$695$	−50.1742	−	50.1742i	−1.90322	−	1.90322i
$696$	−8.95182	+	4.74988i	−0.339318	+	0.180044i
$697$	−2.26070	−	2.26070i	−0.0856299	−	0.0856299i
$698$	13.4777	−	4.07349i	0.510138	−	0.154184i
$699$	−19.6162	−	8.12528i	−0.741952	−	0.307326i
$700$	2.47038	+	41.4417i	0.0933716	+	1.56635i
$701$	−7.55914	−	18.2494i	−0.285505	−	0.689270i	0.714441	−	0.699696i	$-0.246681\pi$
$701$	−7.55914	−	18.2494i	−0.285505	−	0.689270i	−0.999946	+	0.0104263i	$0.996681\pi$
$702$	−0.167459	+	1.68274i	−0.00632034	+	0.0635110i
$703$	23.7717			0.896566
$704$	−25.1799	−	38.1854i	−0.949004	−	1.43917i
$705$		−	16.0478i		−	0.604394i
$706$	3.14469	−	31.5999i	0.118352	−	1.18928i
$707$	12.2999	−	9.36240i	0.462584	−	0.352109i
$708$	3.34239	−	16.6270i	0.125615	−	0.624881i
$709$	−24.8971	−	10.3127i	−0.935031	−	0.387303i	−0.137446	−	0.990509i	$-0.543889\pi$
$709$	−24.8971	−	10.3127i	−0.935031	−	0.387303i	−0.797585	+	0.603207i	$0.793889\pi$
$710$	5.26185	+	17.4095i	0.197474	+	0.653368i
$711$	−13.1974	+	13.1974i	−0.494940	+	0.494940i
$712$	−36.9836	+	19.6237i	−1.38602	+	0.735429i
$713$	1.38579	+	1.38579i	0.0518983	+	0.0518983i
$714$	−3.73570	+	15.6742i	−0.139805	+	0.586593i
$715$	5.21284	+	2.15923i	0.194949	+	0.0807506i
$716$	−7.93470	−	40.3177i	−0.296534	−	1.50674i
$717$	4.41918	+	10.6688i	0.165037	+	0.398435i
$718$	−5.45504	+	4.46758i	−0.203580	+	0.166729i
$719$			43.9669i			1.63969i	0.572586	+	0.819845i	$0.305940\pi$
$719$			43.9669i			1.63969i	−0.572586	+	0.819845i	$0.694060\pi$
$720$	−0.135995	+	33.5203i	−0.00506825	+	1.24923i
$721$	−4.79974	−	18.1950i	−0.178752	−	0.677618i
$722$	2.80030	−	2.29340i	0.104216	−	0.0853513i
$723$	3.09526	+	7.47261i	0.115114	+	0.277910i
$724$	−33.9381	−	22.7764i	−1.26130	−	0.846479i
$725$	13.2228	−	31.9227i	0.491083	−	1.18558i
$726$	−11.7858	+	21.9960i	−0.437413	+	0.816349i
$727$	11.8881	−	11.8881i	0.440907	−	0.440907i	−0.451410	−	0.892317i	$-0.649079\pi$
$727$	11.8881	−	11.8881i	0.440907	−	0.440907i	0.892317	+	0.451410i	$0.149079\pi$
$728$	−0.863348	+	1.87088i	−0.0319978	+	0.0693395i
$729$	1.73866	+	1.73866i	0.0643949	+	0.0643949i
$730$	−75.5627	+	22.8380i	−2.79670	+	0.845273i
$731$	−11.1158	−	4.60433i	−0.411134	−	0.170297i
$732$	−7.09744	−	10.6689i	−0.262329	−	0.394332i
$733$	11.4956	−	4.76163i	0.424599	−	0.175875i	−0.160143	−	0.987094i	$-0.551196\pi$
$733$	11.4956	−	4.76163i	0.424599	−	0.175875i	0.584742	+	0.811219i	$0.301196\pi$
$734$	1.44601	−	14.5305i	0.0533731	−	0.536329i
$735$	10.0677	+	17.7547i	0.371354	+	0.654890i
$736$	−2.21107	−	7.42426i	−0.0815012	−	0.273662i
$737$	−13.1316			−0.483708
$738$	−1.98730	−	0.197768i	−0.0731537	−	0.00727993i
$739$	−0.622209	+	0.257727i	−0.0228883	+	0.00948066i	−0.394098	−	0.919068i	$-0.628943\pi$
$739$	−0.622209	+	0.257727i	−0.0228883	+	0.00948066i	0.371210	+	0.928549i	$0.378943\pi$
$740$	34.9899	−	23.2770i	1.28626	−	0.855680i
$741$	−0.347576	+	0.839122i	−0.0127685	+	0.0308259i
$742$	−19.8076	+	12.1831i	−0.727161	+	0.447257i
$743$	24.5070	−	24.5070i	0.899074	−	0.899074i	−0.0962798	−	0.995354i	$-0.530694\pi$
$743$	24.5070	−	24.5070i	0.899074	−	0.899074i	0.995354	+	0.0962798i	$0.0306944\pi$
$744$	0.312806	+	3.27820i	0.0114680	+	0.120185i
$745$	−13.6586	−	13.6586i	−0.500411	−	0.500411i
$746$	17.2978	−	32.2831i	0.633318	−	1.18197i
$747$	−5.71955	+	13.8082i	−0.209267	+	0.505216i
$748$	50.2615	+	33.7313i	1.83774	+	1.23334i
$749$	0.475261	+	0.624375i	0.0173657	+	0.0228142i
$750$	7.43484	+	9.07814i	0.271482	+	0.331487i
$751$	−52.2891			−1.90806			−0.954028	−	0.299719i	$-0.903107\pi$
$751$	−52.2891			−1.90806			−0.954028	+	0.299719i	$0.903107\pi$
$752$	8.50724	−	20.3049i	0.310227	−	0.740443i
$753$			10.1139i			0.368572i
$754$	1.32676	−	1.08659i	0.0483176	−	0.0395713i
$755$	8.56203	−	3.54651i	0.311604	−	0.129071i
$756$	10.0418	+	20.6697i	0.365216	+	0.751750i
$757$	−1.07264	+	2.58959i	−0.0389859	+	0.0941204i	−0.942173	−	0.335126i	$-0.891221\pi$
$757$	−1.07264	+	2.58959i	−0.0389859	+	0.0941204i	0.903187	+	0.429247i	$0.141221\pi$
$758$	1.77185	−	3.30682i	0.0643564	−	0.120109i
$759$	−4.50402	+	4.50402i	−0.163486	+	0.163486i
$760$	−12.0514	+	39.2973i	−0.437151	+	1.42546i
$761$	−1.72551	+	1.72551i	−0.0625496	+	0.0625496i	−0.737690	−	0.675140i	$-0.764083\pi$
$761$	−1.72551	+	1.72551i	−0.0625496	+	0.0625496i	0.675140	+	0.737690i	$0.264083\pi$
$762$	−21.5295	+	6.50708i	−0.779933	+	0.235726i
$763$	24.6726	+	3.34567i	0.893208	+	0.121121i
$764$	0.401423	−	1.99691i	0.0145230	−	0.0722457i
$765$	−16.9759	−	40.9835i	−0.613765	−	1.48176i
$766$	16.7243	+	1.66433i	0.604275	+	0.0601348i
$767$			2.87001i			0.103630i
$768$	5.07864	−	11.9849i	0.183260	−	0.432469i
$769$		−	19.9305i		−	0.718714i	−0.933200	−	0.359357i	$-0.882996\pi$
$769$		−	19.9305i		−	0.718714i	0.933200	−	0.359357i	$-0.117004\pi$
$770$	75.7103	−	12.1194i	2.72841	−	0.436753i
$771$	8.11721	−	3.36226i	0.292334	−	0.121089i
$772$	7.27014	+	1.46146i	0.261658	+	0.0525991i
$773$	5.53504	−	13.3628i	0.199082	−	0.480626i	−0.792537	−	0.609824i	$-0.791240\pi$
$773$	5.53504	−	13.3628i	0.199082	−	0.480626i	0.991619	+	0.129198i	$0.0412403\pi$
$774$	−7.19436	+	2.17442i	−0.258596	+	0.0781579i
$775$	−7.93953	−	7.93953i	−0.285196	−	0.285196i
$776$	6.63286	−	21.6285i	0.238106	−	0.776417i
$777$	6.35190	−	10.9039i	0.227873	−	0.391174i
$778$	18.4832	+	9.90362i	0.662657	+	0.355062i
$779$	−2.26250	−	0.937159i	−0.0810626	−	0.0335772i
$780$	0.310057	+	1.57546i	0.0111018	+	0.0564105i
$781$	18.9539	−	7.85096i	0.678223	−	0.280929i
$782$	6.49545	+	7.93112i	0.232277	+	0.283616i
$783$		−	19.1260i		−	0.683508i
$784$	3.32640	+	27.8017i	0.118800	+	0.992918i
$785$			38.7875i			1.38439i
$786$	16.1774	−	13.2490i	0.577029	−	0.472577i
$787$	17.1890	−	7.11992i	0.612722	−	0.253798i	−0.0546698	−	0.998504i	$-0.517411\pi$
$787$	17.1890	−	7.11992i	0.612722	−	0.253798i	0.667392	+	0.744707i	$0.267411\pi$
$788$	27.5246	+	18.4722i	0.980523	+	0.658046i
$789$	11.6406	+	4.82171i	0.414418	+	0.171658i
$790$	−19.1087	+	35.6628i	−0.679857	+	1.26883i
$791$	−13.0030	+	22.3213i	−0.462332	+	0.793654i
$792$	37.6407	−	3.59168i	1.33750	−	0.127625i
$793$	1.53333	+	1.53333i	0.0544502	+	0.0544502i
$794$	−2.11062	−	6.98328i	−0.0749032	−	0.247827i
$795$	−6.93485	+	16.7422i	−0.245954	+	0.593785i
$796$	−5.66879	−	8.52131i	−0.200925	−	0.302030i
$797$	−26.8554	+	11.1239i	−0.951268	+	0.394028i	−0.803707	−	0.595025i	$-0.797142\pi$
$797$	−26.8554	+	11.1239i	−0.951268	+	0.394028i	−0.147561	+	0.989053i	$0.547142\pi$
$798$	1.95089	+	12.1872i	0.0690607	+	0.431424i
$799$			29.1341i			1.03069i
$800$	12.6678	+	42.5354i	0.447873	+	1.50385i
$801$		−	34.6102i		−	1.22289i
$802$	1.49350	−	15.0077i	0.0527373	−	0.529940i
$803$	34.0755	+	82.2656i	1.20250	+	2.90309i
$804$	−2.06983	−	3.11136i	−0.0729973	−	0.109729i
$805$	12.8677	+	1.74490i	0.453528	+	0.0614995i
$806$	−0.161228	−	0.533444i	−0.00567901	−	0.0187898i
$807$	0.994094	−	0.994094i	0.0349938	−	0.0349938i
$808$	10.5222	−	12.7420i	0.370169	−	0.448263i
$809$	−29.6265	+	29.6265i	−1.04161	+	1.04161i	−0.0425179	+	0.999096i	$0.513538\pi$
$809$	−29.6265	+	29.6265i	−1.04161	+	1.04161i	−0.999096	+	0.0425179i	$0.986462\pi$
$810$	−15.5542	−	8.33420i	−0.546520	−	0.292834i
$811$	0.0959660	−	0.231682i	0.00336982	−	0.00813547i	−0.922186	−	0.386747i	$-0.873599\pi$
$811$	0.0959660	−	0.231682i	0.00336982	−	0.00813547i	0.925555	+	0.378612i	$0.123599\pi$
$812$	7.62117	−	22.0228i	0.267451	−	0.772850i
$813$	7.76536	−	3.21652i	0.272343	−	0.112808i
$814$	−30.0362	−	36.6750i	−1.05277	−	1.28546i
$815$		−	22.8678i		−	0.801024i
$816$	−0.0698861	+	17.2256i	−0.00244650	+	0.603018i
$817$	−9.21602			−0.322428
$818$	12.4130	−	10.1661i	0.434012	−	0.355448i
$819$	−1.03167	−	1.35535i	−0.0360493	−	0.0473598i
$820$	−4.24787	+	0.836000i	−0.148342	+	0.0291944i
$821$	4.02552	−	9.71846i	0.140492	−	0.339177i	−0.837936	−	0.545769i	$-0.816238\pi$
$821$	4.02552	−	9.71846i	0.140492	−	0.339177i	0.978427	+	0.206593i	$0.0662375\pi$
$822$	−14.1599	−	7.58707i	−0.493882	−	0.264630i
$823$	3.19440	+	3.19440i	0.111350	+	0.111350i	0.760586	−	0.649237i	$-0.224912\pi$
$823$	3.19440	+	3.19440i	0.111350	+	0.111350i	−0.649237	+	0.760586i	$0.724912\pi$
$824$	−9.42892	−	17.7701i	−0.328472	−	0.619051i
$825$	25.8046	−	25.8046i	0.898402	−	0.898402i
$826$	20.4327	+	33.2200i	0.710944	+	1.15587i
$827$	6.58578	−	15.8995i	0.229010	−	0.552879i	−0.767047	−	0.641591i	$-0.778275\pi$
$827$	6.58578	−	15.8995i	0.229010	−	0.552879i	0.996057	+	0.0887113i	$0.0282748\pi$
$828$	6.27817	+	1.26205i	0.218181	+	0.0438593i
$829$	40.8651	−	16.9269i	1.41930	−	0.587895i	0.464619	−	0.885511i	$-0.346191\pi$
$829$	40.8651	−	16.9269i	1.41930	−	0.587895i	0.954686	+	0.297615i	$0.0961913\pi$
$830$	−3.20843	+	32.2405i	−0.111366	+	1.11908i
$831$	−17.1596			−0.595261
$832$	−0.442874	+	2.15776i	−0.0153539	+	0.0748070i
$833$	−18.2776	−	32.2329i	−0.633280	−	1.11680i
$834$	−22.6657	−	2.25560i	−0.784850	−	0.0781049i
$835$	−23.4332	+	9.70633i	−0.810938	+	0.335901i
$836$	45.4562	+	9.13770i	1.57214	+	0.316034i
$837$	−5.74203	−	2.37843i	−0.198473	−	0.0822104i
$838$	7.94082	+	26.2733i	0.274311	+	0.907595i
$839$	23.5108	+	23.5108i	0.811683	+	0.811683i	0.984886	−	0.173203i	$-0.0554117\pi$
$839$	23.5108	+	23.5108i	0.811683	+	0.811683i	−0.173203	+	0.984886i	$0.555412\pi$
$840$	14.8052	+	16.0283i	0.510827	+	0.553029i
$841$	6.79107	−	6.79107i	0.234175	−	0.234175i
$842$	6.32741	+	3.39032i	0.218057	+	0.116838i
$843$	−7.47855	+	18.0548i	−0.257575	+	0.621841i
$844$	−6.87556	−	34.9360i	−0.236667	−	1.20255i
$845$	17.7264	+	42.7953i	0.609807	+	1.47220i
$846$	11.5311	+	14.0797i	0.396446	+	0.484072i
$847$	−14.6374	−	55.4880i	−0.502947	−	1.90659i
$848$	−17.6499	+	17.5073i	−0.606100	+	0.601202i
$849$			0.477668i			0.0163935i
$850$	−37.2140	−	45.4393i	−1.27643	−	1.55856i
$851$	−3.07236	−	7.41734i	−0.105319	−	0.254263i
$852$	4.84774	+	3.25340i	0.166081	+	0.111460i
$853$	28.1078	+	11.6426i	0.962393	+	0.398636i	0.807875	−	0.589354i	$-0.200618\pi$
$853$	28.1078	+	11.6426i	0.962393	+	0.398636i	0.154518	+	0.987990i	$0.450618\pi$
$854$	28.6645	+	6.83173i	0.980879	+	0.233777i
$855$	−24.0268	−	24.0268i	−0.821698	−	0.821698i
$856$	0.646821	+	0.534134i	0.0221079	+	0.0182563i
$857$	−7.27401	+	7.27401i	−0.248475	+	0.248475i	−0.820345	−	0.571869i	$-0.806218\pi$
$857$	−7.27401	+	7.27401i	−0.248475	+	0.248475i	0.571869	+	0.820345i	$0.306218\pi$
$858$	1.73377	−	0.524014i	0.0591899	−	0.0178895i
$859$	−9.17589	−	3.80078i	−0.313077	−	0.129681i	0.220612	−	0.975362i	$-0.429195\pi$
$859$	−9.17589	−	3.80078i	−0.313077	−	0.129681i	−0.533689	+	0.845681i	$0.679195\pi$
$860$	−13.5652	+	9.02423i	−0.462570	+	0.307724i
$861$	−1.03442	+	0.787378i	−0.0352529	+	0.0268338i
$862$	−26.7294	−	2.65999i	−0.910407	−	0.0905997i
$863$			0.910399i			0.0309904i	0.999880	+	0.0154952i	$0.00493247\pi$
$863$			0.910399i			0.0309904i	−0.999880	+	0.0154952i	$0.995068\pi$
$864$	15.4883	+	19.0690i	0.526923	+	0.648739i
$865$	83.3254			2.83315
$866$	−19.5483	−	1.94536i	−0.664279	−	0.0661061i
$867$	−3.43113	−	8.28347i	−0.116527	−	0.281322i
$868$	−5.66398	−	5.02670i	−0.192248	−	0.170617i
$869$	42.1649	+	17.4653i	1.43035	+	0.592469i
$870$	−5.25406	−	17.3838i	−0.178129	−	0.589365i
$871$	0.447167	+	0.447167i	0.0151517	+	0.0151517i
$872$	26.4971	−	2.52836i	0.897307	−	0.0856210i
$873$	13.2239	+	13.2239i	0.447560	+	0.447560i
$874$	6.92148	+	3.70864i	0.234123	+	0.125447i
$875$	−26.7393	−	3.62592i	−0.903955	−	0.122579i
$876$	−14.1207	+	21.0407i	−0.477096	+	0.710898i
$877$	−8.74522	+	3.62239i	−0.295305	+	0.122319i	−0.525417	−	0.850845i	$-0.676091\pi$
$877$	−8.74522	+	3.62239i	−0.295305	+	0.122319i	0.230112	+	0.973164i	$0.426091\pi$
$878$	20.8332	−	17.0621i	0.703088	−	0.575817i
$879$	−12.0648			−0.406937
$880$	75.8553	−	31.0603i	2.55708	−	1.04704i
$881$	−24.0665			−0.810821			−0.405411	−	0.914135i	$-0.632871\pi$
$881$	−24.0665			−0.810821			−0.405411	+	0.914135i	$0.632871\pi$
$882$	−21.5906	−	8.34318i	−0.726995	−	0.280929i
$883$	−2.25125	−	5.43499i	−0.0757605	−	0.182902i	0.881462	−	0.472255i	$-0.156560\pi$
$883$	−2.25125	−	5.43499i	−0.0757605	−	0.182902i	−0.957222	+	0.289353i	$0.906560\pi$
$884$	−0.562897	−	2.86018i	−0.0189323	−	0.0961984i
$885$	28.0789	+	11.6306i	0.943861	+	0.390960i
$886$	8.53786	−	15.9343i	0.286835	−	0.535324i
$887$	22.9074	−	22.9074i	0.769155	−	0.769155i	−0.208803	−	0.977958i	$-0.566957\pi$
$887$	22.9074	−	22.9074i	0.769155	−	0.769155i	0.977958	+	0.208803i	$0.0669567\pi$
$888$	3.95531	−	12.8975i	0.132731	−	0.432812i
$889$	26.0345	−	44.6917i	0.873170	−	1.49891i
$890$	−21.7066	−	71.8194i	−0.727608	−	2.40739i
$891$	−7.61742	+	18.3901i	−0.255193	+	0.616091i
$892$	−33.9453	−	6.82376i	−1.13657	−	0.228476i
$893$	8.53999	+	20.6174i	0.285780	+	0.689934i
$894$	−6.17013	−	0.614024i	−0.206360	−	0.0205360i
$895$	73.6369			2.46141
$896$	10.2357	+	28.1288i	0.341952	+	0.939717i
$897$	0.306749			0.0102420
$898$	−50.7526	−	5.05068i	−1.69364	−	0.168543i
$899$	2.41200	+	5.82308i	0.0804446	+	0.194211i
$900$	−35.9692	−	7.23059i	−1.19897	−	0.241020i
$901$	12.5899	−	30.3948i	0.419432	−	1.01260i
$902$	1.41288	+	4.67472i	0.0470439	+	0.155651i
$903$	−2.46256	+	4.22731i	−0.0819489	+	0.140676i
$904$	−8.09690	+	26.4024i	−0.269299	+	0.878132i
$905$	51.7921	−	51.7921i	1.72163	−	1.72163i
$906$	1.40503	−	2.62222i	0.0466790	−	0.0871175i
$907$	21.0151	+	8.70472i	0.697793	+	0.289035i	0.703243	−	0.710950i	$-0.251735\pi$
$907$	21.0151	+	8.70472i	0.697793	+	0.289035i	−0.00544953	+	0.999985i	$0.501735\pi$
$908$	−1.99113	−	10.1173i	−0.0660780	−	0.335755i
$909$	5.22769	+	12.6208i	0.173392	+	0.418604i
$910$	−2.99084	−	2.16544i	−0.0991454	−	0.0717837i
$911$	39.2986			1.30202			0.651010	−	0.759070i	$-0.274346\pi$
$911$	39.2986			1.30202			0.651010	+	0.759070i	$0.274346\pi$
$912$	4.99985	+	12.2106i	0.165562	+	0.404333i
$913$	36.5473			1.20954
$914$	−8.86334	+	7.25892i	−0.293173	+	0.240104i
$915$	21.2152	−	8.78763i	0.701354	−	0.290510i
$916$	−15.2397	+	22.7079i	−0.503533	+	0.750291i
$917$	−6.46146	+	47.6500i	−0.213376	+	1.57354i
$918$	−28.6562	−	15.3545i	−0.945797	−	0.506773i
$919$	13.8310	+	13.8310i	0.456241	+	0.456241i	0.897420	−	0.441178i	$-0.145439\pi$
$919$	13.8310	+	13.8310i	0.456241	+	0.456241i	−0.441178	+	0.897420i	$0.645439\pi$
$920$	13.8193	−	1.31864i	0.455609	−	0.0434742i
$921$	−13.2481	−	13.2481i	−0.436540	−	0.436540i
$922$	−6.35561	−	21.0284i	−0.209311	−	0.692534i
$923$	−0.912778	−	0.378085i	−0.0300445	−	0.0124448i
$924$	16.3375	−	18.4087i	0.537464	−	0.605603i
$925$	17.6023	+	42.4957i	0.578760	+	1.39725i
$926$	9.04051	+	0.899672i	0.297090	+	0.0295651i
$927$	16.6297			0.546193
$928$	2.56763	−	24.7806i	0.0842866	−	0.813463i
$929$		−	49.3151i		−	1.61798i	−0.587825	−	0.808988i	$-0.700016\pi$
$929$		−	49.3151i		−	1.61798i	0.587825	−	0.808988i	$-0.299984\pi$
$930$	−5.87234	−	0.584390i	−0.192562	−	0.0191629i
$931$	−22.3829	−	17.4527i	−0.733569	−	0.571988i
$932$	43.4596	−	28.9114i	1.42357	−	0.947025i
$933$	2.30886	+	0.956363i	0.0755888	+	0.0313099i
$934$	−46.2386	+	13.9751i	−1.51297	+	0.457280i
$935$	−76.7029	+	76.7029i	−2.50845	+	2.50845i
$936$	−1.40408	−	1.15946i	−0.0458937	−	0.0378982i
$937$	21.0513	+	21.0513i	0.687716	+	0.687716i	0.961727	−	0.274011i	$-0.0883504\pi$
$937$	21.0513	+	21.0513i	0.687716	+	0.687716i	−0.274011	+	0.961727i	$0.588350\pi$
$938$	8.35944	+	1.99234i	0.272945	+	0.0650523i
$939$	−5.65434	−	2.34210i	−0.184522	−	0.0764316i
$940$	32.7585	+	21.9848i	1.06846	+	0.717064i
$941$	−13.9886	−	33.7715i	−0.456016	−	1.10092i	−0.969997	−	0.243118i	$-0.921830\pi$
$941$	−13.9886	−	33.7715i	−0.456016	−	1.10092i	0.513981	−	0.857801i	$-0.328170\pi$
$942$	7.88910	+	9.63280i	0.257041	+	0.313854i
$943$			0.827078i			0.0269334i
$944$	29.3620	+	29.6012i	0.955651	+	0.963437i
$945$	−39.8187	+	10.5039i	−1.29530	+	0.341693i
$946$	11.6447	+	14.2185i	0.378602	+	0.462283i
$947$	14.9909	+	36.1912i	0.487139	+	1.17606i	0.956153	+	0.292866i	$0.0946091\pi$
$947$	14.9909	+	36.1912i	0.487139	+	1.17606i	−0.469015	+	0.883190i	$0.655391\pi$
$948$	2.50795	+	12.7434i	0.0814544	+	0.413885i
$949$	1.64100	−	3.96174i	0.0532693	−	0.128603i
$950$	−39.6548	−	21.2477i	−1.28657	−	0.689366i
$951$	−8.48107	+	8.48107i	−0.275018	+	0.275018i
$952$	−26.8782	−	29.0988i	−0.871127	−	0.943096i
$953$	14.8400	+	14.8400i	0.480715	+	0.480715i	0.905360	−	0.424645i	$-0.139601\pi$
$953$	14.8400	+	14.8400i	0.480715	+	0.480715i	−0.424645	+	0.905360i	$0.639601\pi$
$954$	−5.94567	−	19.6721i	−0.192498	−	0.636906i
$955$	3.37228	+	1.39685i	0.109125	+	0.0452009i
$956$	−27.8325	−	5.59495i	−0.900169	−	0.180954i
$957$	−18.9258	+	7.83934i	−0.611786	+	0.253410i
$958$	−42.2991	−	4.20942i	−1.36662	−	0.136000i
$959$	35.7202	−	9.42277i	1.15346	−	0.304277i
$960$	19.3158	+	13.0772i	0.623416	+	0.422064i
$961$	−28.9518			−0.933930
$962$	−0.226069	+	2.27170i	−0.00728877	+	0.0732425i
$963$	−0.640665	+	0.265372i	−0.0206451	+	0.00855149i
$964$	−19.4943	−	3.91879i	−0.627870	−	0.126216i
$965$	−5.08549	+	12.2775i	−0.163708	+	0.395225i
$966$	3.55057	−	2.18386i	0.114238	−	0.0702645i
$967$	−9.66348	+	9.66348i	−0.310757	+	0.310757i	−0.845203	−	0.534446i	$-0.820520\pi$
$967$	−9.66348	+	9.66348i	−0.310757	+	0.310757i	0.534446	+	0.845203i	$0.320520\pi$
$968$	−28.7547	−	54.1922i	−0.924210	−	1.74180i
$969$	−12.3470	−	12.3470i	−0.396643	−	0.396643i
$970$	35.7344	+	19.1470i	1.14736	+	0.614775i
$971$	−17.7776	+	42.9190i	−0.570511	+	1.37734i	0.330610	+	0.943768i	$0.392746\pi$
$971$	−17.7776	+	42.9190i	−0.570511	+	1.37734i	−0.901121	+	0.433568i	$0.857254\pi$
$972$	−31.1243	+	6.12540i	−0.998312	+	0.196472i
$973$	41.6794	−	31.7255i	1.33618	−	1.01707i
$974$	−28.6733	+	23.4830i	−0.918753	+	0.752443i
$975$	−1.75744			−0.0562830
$976$	31.5017	+	0.127806i	1.00834	+	0.00409096i
$977$		−	19.6064i		−	0.627265i	−0.949544	−	0.313633i	$-0.898454\pi$
$977$		−	19.6064i		−	0.627265i	0.949544	−	0.313633i	$-0.101546\pi$
$978$	−4.65115	−	5.67917i	−0.148727	−	0.181600i
$979$	−78.1903	+	32.3875i	−2.49897	+	1.03511i
$980$	−50.0352	−	3.77176i	−1.59832	−	0.120484i
$981$	−8.42046	+	20.3288i	−0.268845	+	0.649048i
$982$	5.80035	+	3.10792i	0.185097	+	0.0991777i
$983$	−24.9997	+	24.9997i	−0.797365	+	0.797365i	−0.982679	−	0.185314i	$-0.940670\pi$
$983$	−24.9997	+	24.9997i	−0.797365	+	0.797365i	0.185314	+	0.982679i	$0.440670\pi$
$984$	−0.884914	+	1.07161i	−0.0282100	+	0.0341615i
$985$	−42.0047	+	42.0047i	−1.33838	+	1.33838i
$986$	9.53854	+	31.5595i	0.303769	+	1.00506i
$987$	11.7389	+	1.59183i	0.373655	+	0.0506685i
$988$	−1.23675	−	1.85907i	−0.0393461	−	0.0591450i
$989$	1.19112	+	2.87562i	0.0378754	+	0.0914394i
$990$	−6.71004	+	67.4270i	−0.213259	+	2.14297i
$991$		−	45.8636i		−	1.45690i	−0.685096	−	0.728452i	$-0.740240\pi$
$991$		−	45.8636i		−	1.45690i	0.685096	−	0.728452i	$-0.259760\pi$
$992$	−7.12036	−	3.85246i	−0.226072	−	0.122316i
$993$		−	1.47036i		−	0.0466603i
$994$	−13.2570	+	2.12213i	−0.420487	+	0.0673100i
$995$	16.9448	−	7.01876i	0.537186	−	0.222510i
$996$	5.76067	+	8.65942i	0.182534	+	0.274384i
$997$	−9.49428	+	22.9212i	−0.300687	+	0.725922i	0.699252	+	0.714875i	$0.253516\pi$
$997$	−9.49428	+	22.9212i	−0.300687	+	0.725922i	−0.999939	+	0.0110472i	$0.996484\pi$
$998$	0.110557	+	0.365792i	0.00349961	+	0.0115789i
$999$	18.0034	+	18.0034i	0.569603	+	0.569603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.x.b.27.1	✓	112
4.3	odd	2		896.2.x.b.783.17		112
7.6	odd	2	inner	224.2.x.b.27.2	yes	112
28.27	even	2		896.2.x.b.783.12		112
32.13	even	8		896.2.x.b.111.12		112
32.19	odd	8	inner	224.2.x.b.83.2	yes	112
224.13	odd	8		896.2.x.b.111.17		112
224.83	even	8	inner	224.2.x.b.83.1	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.x.b.27.1	✓	112	1.1	even	1	trivial
224.2.x.b.27.2	yes	112	7.6	odd	2	inner
224.2.x.b.83.1	yes	112	224.83	even	8	inner
224.2.x.b.83.2	yes	112	32.19	odd	8	inner
896.2.x.b.111.12		112	32.13	even	8
896.2.x.b.111.17		112	224.13	odd	8
896.2.x.b.783.12		112	28.27	even	2
896.2.x.b.783.17		112	4.3	odd	2

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40726 - 0.140045i) q^{2} +(-0.311327 - 0.751610i) q^{3} +(1.96078 + 0.394159i) q^{4} +(-1.37157 + 3.31126i) q^{5} +(0.332860 + 1.10131i) q^{6} +(-2.28614 - 1.33176i) q^{7} +(-2.70413 - 0.829281i) q^{8} +(1.65333 - 1.65333i) q^{9} +O(q^{10})\)	\(q+(-1.40726 - 0.140045i) q^{2} +(-0.311327 - 0.751610i) q^{3} +(1.96078 + 0.394159i) q^{4} +(-1.37157 + 3.31126i) q^{5} +(0.332860 + 1.10131i) q^{6} +(-2.28614 - 1.33176i) q^{7} +(-2.70413 - 0.829281i) q^{8} +(1.65333 - 1.65333i) q^{9} +(2.39388 - 4.46773i) q^{10} +(-5.28229 - 2.18800i) q^{11} +(-0.314188 - 1.59645i) q^{12} +(0.105369 + 0.254384i) q^{13} +(3.03069 + 2.19429i) q^{14} +2.91578 q^{15} +(3.68928 + 1.54571i) q^{16} -5.29348 q^{17} +(-2.55821 + 2.09513i) q^{18} +(-3.74605 + 1.55167i) q^{19} +(-3.99450 + 5.95202i) q^{20} +(-0.289226 + 2.13289i) q^{21} +(7.12715 + 3.81884i) q^{22} +(0.968314 + 0.968314i) q^{23} +(0.218571 + 2.29062i) q^{24} +(-5.54771 - 5.54771i) q^{25} +(-0.112657 - 0.372741i) q^{26} +(-4.01221 - 1.66191i) q^{27} +(-3.95768 - 3.51238i) q^{28} +(1.68537 + 4.06885i) q^{29} +(-4.10327 - 0.408339i) q^{30} +1.43114 q^{31} +(-4.97531 - 2.69189i) q^{32} +4.65140i q^{33} +(7.44932 + 0.741324i) q^{34} +(7.54539 - 5.74340i) q^{35} +(3.89348 - 2.59013i) q^{36} +(-5.41648 - 2.24358i) q^{37} +(5.48898 - 1.65899i) q^{38} +(0.158393 - 0.158393i) q^{39} +(6.45486 - 7.81665i) q^{40} +(0.427071 + 0.427071i) q^{41} +(0.705717 - 2.96104i) q^{42} +(2.09991 + 0.869810i) q^{43} +(-9.49497 - 6.37223i) q^{44} +(3.20695 + 7.74225i) q^{45} +(-1.22707 - 1.49828i) q^{46} -5.50376i q^{47} +(0.0132023 - 3.25412i) q^{48} +(3.45284 + 6.08916i) q^{49} +(7.03015 + 8.58401i) q^{50} +(1.64800 + 3.97863i) q^{51} +(0.106338 + 0.540322i) q^{52} +(-2.37839 + 5.74193i) q^{53} +(5.41349 + 2.90064i) q^{54} +(14.4901 - 14.4901i) q^{55} +(5.07760 + 5.49709i) q^{56} +(2.33249 + 2.33249i) q^{57} +(-1.80194 - 5.96196i) q^{58} +(9.62996 + 3.98886i) q^{59} +(5.71719 + 1.14928i) q^{60} +(7.27600 - 3.01382i) q^{61} +(-2.01399 - 0.200423i) q^{62} +(-5.98157 + 1.57790i) q^{63} +(6.62459 + 4.48496i) q^{64} -0.986852 q^{65} +(0.651404 - 6.54575i) q^{66} +(2.12190 - 0.878921i) q^{67} +(-10.3793 - 2.08647i) q^{68} +(0.426332 - 1.02926i) q^{69} +(-11.4227 + 7.02578i) q^{70} +(-2.53724 + 2.53724i) q^{71} +(-5.84188 + 3.09973i) q^{72} +(-11.0124 - 11.0124i) q^{73} +(7.30820 + 3.91585i) q^{74} +(-2.44256 + 5.89686i) q^{75} +(-7.95677 + 1.56593i) q^{76} +(9.16216 + 12.0368i) q^{77} +(-0.245083 + 0.200718i) q^{78} -7.98231 q^{79} +(-10.1784 + 10.0961i) q^{80} -3.48146i q^{81} +(-0.541192 - 0.660810i) q^{82} +(-5.90559 + 2.44618i) q^{83} +(-1.40781 + 4.06813i) q^{84} +(7.26038 - 17.5281i) q^{85} +(-2.83331 - 1.51813i) q^{86} +(2.53348 - 2.53348i) q^{87} +(12.4695 + 10.2971i) q^{88} +(10.4668 - 10.4668i) q^{89} +(-3.42875 - 11.3445i) q^{90} +(0.0978891 - 0.721882i) q^{91} +(1.51698 + 2.28032i) q^{92} +(-0.445552 - 1.07566i) q^{93} +(-0.770772 + 7.74523i) q^{94} -14.5324i q^{95} +(-0.474301 + 4.57755i) q^{96} +7.99833i q^{97} +(-4.00630 - 9.05260i) q^{98} +(-12.3508 + 5.11588i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9	\( 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{11} - 20 q^{14} - 16 q^{15} + 16 q^{16} - 16 q^{18} - 4 q^{21} + 32 q^{22} - 48 q^{23} - 8 q^{25} - 24 q^{28} - 8 q^{29} + 16 q^{30} - 8 q^{32} + 20 q^{35} + 32 q^{36} - 8 q^{37} - 8 q^{39} + 16 q^{42} + 32 q^{43} - 144 q^{44} - 8 q^{46} + 16 q^{50} - 32 q^{51} - 32 q^{53} + 64 q^{56} - 8 q^{57} - 72 q^{58} - 88 q^{60} + 112 q^{64} - 16 q^{65} - 64 q^{67} - 40 q^{70} + 56 q^{71} - 8 q^{72} - 168 q^{74} + 52 q^{77} + 192 q^{78} - 16 q^{79} - 24 q^{84} - 48 q^{85} - 8 q^{86} - 96 q^{88} - 52 q^{91} - 8 q^{92} - 32 q^{93} + 88 q^{98} + 16 q^{99}+O(q^{100}) \) 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^11 - 20 * q^14 - 16 * q^15 + 16 * q^16 - 16 * q^18 - 4 * q^21 + 32 * q^22 - 48 * q^23 - 8 * q^25 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 8 * q^32 + 20 * q^35 + 32 * q^36 - 8 * q^37 - 8 * q^39 + 16 * q^42 + 32 * q^43 - 144 * q^44 - 8 * q^46 + 16 * q^50 - 32 * q^51 - 32 * q^53 + 64 * q^56 - 8 * q^57 - 72 * q^58 - 88 * q^60 + 112 * q^64 - 16 * q^65 - 64 * q^67 - 40 * q^70 + 56 * q^71 - 8 * q^72 - 168 * q^74 + 52 * q^77 + 192 * q^78 - 16 * q^79 - 24 * q^84 - 48 * q^85 - 8 * q^86 - 96 * q^88 - 52 * q^91 - 8 * q^92 - 32 * q^93 + 88 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more