LMFDB - Embedded newform 980.2.s.g.619.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(19,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("980.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.s (of order $6$, degree $2$, not 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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			619.8
Character	$\chi$	$=$	980.619
Dual form			980.2.s.g.19.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21565 - 0.722628i) q^{2} +(1.80140 + 1.04004i) q^{3} +(0.955617 + 1.75693i) q^{4} +(-0.656871 + 2.13741i) q^{5} +(-1.43832 - 2.56607i) q^{6} +(0.107908 - 2.82637i) q^{8} +(0.663371 + 1.14899i) q^{9} +O(q^{10})$	\(q+(-1.21565 - 0.722628i) q^{2} +(1.80140 + 1.04004i) q^{3} +(0.955617 + 1.75693i) q^{4} +(-0.656871 + 2.13741i) q^{5} +(-1.43832 - 2.56607i) q^{6} +(0.107908 - 2.82637i) q^{8} +(0.663371 + 1.14899i) q^{9} +(2.34308 - 2.12367i) q^{10} +(-0.671209 - 0.387523i) q^{11} +(-0.105824 + 4.15882i) q^{12} -4.18932 q^{13} +(-3.40628 + 3.16717i) q^{15} +(-2.17359 + 3.35790i) q^{16} +(-2.09014 + 3.62023i) q^{17} +(0.0238661 - 1.87615i) q^{18} +(2.44239 + 4.23034i) q^{19} +(-4.38299 + 0.888471i) q^{20} +(0.535922 + 0.956127i) q^{22} +(0.948617 + 1.64305i) q^{23} +(3.13392 - 4.97920i) q^{24} +(-4.13704 - 2.80801i) q^{25} +(5.09276 + 3.02732i) q^{26} -3.48051i q^{27} +9.98465 q^{29} +(6.42954 - 1.38869i) q^{30} +(-5.17418 + 8.96194i) q^{31} +(5.06884 - 2.51134i) q^{32} +(-0.806079 - 1.39617i) q^{33} +(5.15697 - 2.89055i) q^{34} +(-1.38477 + 2.26349i) q^{36} +(-2.95987 + 1.70888i) q^{37} +(0.0878697 - 6.90756i) q^{38} +(-7.54666 - 4.35707i) q^{39} +(5.97023 + 2.08720i) q^{40} +3.02483i q^{41} -9.19046 q^{43} +(0.0394304 - 1.54959i) q^{44} +(-2.89162 + 0.663156i) q^{45} +(0.0341284 - 2.68288i) q^{46} +(-7.16411 + 4.13620i) q^{47} +(-7.40787 + 3.78831i) q^{48} +(3.00006 + 6.40310i) q^{50} +(-7.53038 + 4.34767i) q^{51} +(-4.00339 - 7.36034i) q^{52} +(-2.24383 - 1.29548i) q^{53} +(-2.51512 + 4.23109i) q^{54} +(1.26919 - 1.18010i) q^{55} +10.1607i q^{57} +(-12.1379 - 7.21519i) q^{58} +(2.30377 - 3.99024i) q^{59} +(-8.81959 - 2.95800i) q^{60} +(2.82504 - 1.63104i) q^{61} +(12.7662 - 7.15559i) q^{62} +(-7.97671 - 0.609973i) q^{64} +(2.75185 - 8.95430i) q^{65} +(-0.0290003 + 2.27975i) q^{66} +(-1.13535 + 1.96648i) q^{67} +(-8.35786 - 0.212672i) q^{68} +3.94640i q^{69} -4.41264i q^{71} +(3.31906 - 1.75095i) q^{72} +(1.37461 - 2.38090i) q^{73} +(4.83305 + 0.0614803i) q^{74} +(-4.53204 - 9.36105i) q^{75} +(-5.09842 + 8.33369i) q^{76} +(6.02557 + 10.7501i) q^{78} +(-12.3093 + 7.10679i) q^{79} +(-5.74944 - 6.85156i) q^{80} +(5.60999 - 9.71679i) q^{81} +(2.18583 - 3.67714i) q^{82} -2.36160i q^{83} +(-6.36497 - 6.84552i) q^{85} +(11.1724 + 6.64128i) q^{86} +(17.9864 + 10.3845i) q^{87} +(-1.16771 + 1.85527i) q^{88} +(12.4312 - 7.17714i) q^{89} +(3.99442 + 1.28340i) q^{90} +(-1.98021 + 3.23678i) q^{92} +(-18.6416 + 10.7627i) q^{93} +(11.6980 + 0.148808i) q^{94} +(-10.6463 + 2.44160i) q^{95} +(11.7429 + 0.747866i) q^{96} +14.4115 q^{97} -1.02829i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 16 q^{4} + 64 q^{9}+O(q^{10}) $ 96 * q - 16 * q^4 + 64 * q^9	$ 96 q - 16 q^{4} + 64 q^{9} - 16 q^{16} + 16 q^{25} - 96 q^{29} + 8 q^{30} + 352 q^{36} + 48 q^{44} + 32 q^{46} + 64 q^{50} - 24 q^{60} - 160 q^{64} + 16 q^{65} + 112 q^{74} + 48 q^{81} - 128 q^{85} + 112 q^{86}+O(q^{100}) $ 96 * q - 16 * q^4 + 64 * q^9 - 16 * q^16 + 16 * q^25 - 96 * q^29 + 8 * q^30 + 352 * q^36 + 48 * q^44 + 32 * q^46 + 64 * q^50 - 24 * q^60 - 160 * q^64 + 16 * q^65 + 112 * q^74 + 48 * q^81 - 128 * q^85 + 112 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	−1.21565	−	0.722628i	−0.859595	−	0.510975i
$2$	−1.21565	−	0.722628i	−0.859595	−	0.510975i
$3$	1.80140	+	1.04004i	1.04004	+	0.600468i	0.919845	−	0.392282i	$-0.128314\pi$
$3$	1.80140	+	1.04004i	1.04004	+	0.600468i	0.120196	+	0.992750i	$0.461648\pi$
$4$	0.955617	+	1.75693i	0.477809	+	0.878464i
$5$	−0.656871	+	2.13741i	−0.293762	+	0.955879i
$5$	−0.656871	+	2.13741i	−0.293762	+	0.955879i
$6$	−1.43832	−	2.56607i	−0.587190	−	1.04759i
$7$		0			0
$7$		0			0
$8$	0.107908	−	2.82637i	0.0381511	−	0.999272i
$9$	0.663371	+	1.14899i	0.221124	+	0.382998i
$10$	2.34308	−	2.12367i	0.740947	−	0.671564i
$11$	−0.671209	−	0.387523i	−0.202377	−	0.116843i	0.395387	−	0.918515i	$-0.370611\pi$
$11$	−0.671209	−	0.387523i	−0.202377	−	0.116843i	−0.597764	+	0.801672i	$0.703944\pi$
$12$	−0.105824	+	4.15882i	−0.0305488	+	1.20055i
$13$	−4.18932			−1.16191			−0.580955	−	0.813936i	$-0.697321\pi$
$13$	−4.18932			−1.16191			−0.580955	+	0.813936i	$0.697321\pi$
$14$		0			0
$15$	−3.40628	+	3.16717i	−0.879499	+	0.817759i
$16$	−2.17359	+	3.35790i	−0.543398	+	0.839475i
$17$	−2.09014	+	3.62023i	−0.506934	+	0.878035i	0.493034	+	0.870010i	$0.335888\pi$
$17$	−2.09014	+	3.62023i	−0.506934	+	0.878035i	−0.999968	+	0.00802529i	$0.997445\pi$
$18$	0.0238661	−	1.87615i	0.00562529	−	0.442212i
$19$	2.44239	+	4.23034i	0.560322	+	0.970507i	0.997468	+	0.0711161i	$0.0226561\pi$
$19$	2.44239	+	4.23034i	0.560322	+	0.970507i	−0.437146	+	0.899391i	$0.644011\pi$
$20$	−4.38299	+	0.888471i	−0.980067	+	0.198668i
$21$		0			0
$22$	0.535922	+	0.956127i	0.114259	+	0.203847i
$23$	0.948617	+	1.64305i	0.197800	+	0.342600i	0.947815	−	0.318821i	$-0.103287\pi$
$23$	0.948617	+	1.64305i	0.197800	+	0.342600i	−0.750015	+	0.661421i	$0.769954\pi$
$24$	3.13392	−	4.97920i	0.639710	−	1.01638i
$25$	−4.13704	−	2.80801i	−0.827408	−	0.561601i
$26$	5.09276	+	3.02732i	0.998772	+	0.593707i
$27$		−	3.48051i		−	0.669825i
$28$		0			0
$29$	9.98465			1.85410			0.927052	−	0.374933i	$-0.122334\pi$
$29$	9.98465			1.85410			0.927052	+	0.374933i	$0.122334\pi$
$30$	6.42954	−	1.38869i	1.17387	−	0.253540i
$31$	−5.17418	+	8.96194i	−0.929310	+	1.60961i	−0.144832	+	0.989456i	$0.546264\pi$
$31$	−5.17418	+	8.96194i	−0.929310	+	1.60961i	−0.784479	+	0.620156i	$0.787069\pi$
$32$	5.06884	−	2.51134i	0.896053	−	0.443946i
$33$	−0.806079	−	1.39617i	−0.140320	−	0.243042i
$34$	5.15697	−	2.89055i	0.884413	−	0.495725i
$35$		0			0
$36$	−1.38477	+	2.26349i	−0.230795	+	0.377249i
$37$	−2.95987	+	1.70888i	−0.486599	+	0.280938i	−0.723163	−	0.690678i	$-0.757312\pi$
$37$	−2.95987	+	1.70888i	−0.486599	+	0.280938i	0.236563	+	0.971616i	$0.423979\pi$
$38$	0.0878697	−	6.90756i	0.0142543	−	1.12055i
$39$	−7.54666	−	4.35707i	−1.20843	−	0.697689i
$40$	5.97023	+	2.08720i	0.943975	+	0.330016i
$41$			3.02483i			0.472399i	0.971705	+	0.236199i	$0.0759019\pi$
$41$			3.02483i			0.472399i	−0.971705	+	0.236199i	$0.924098\pi$
$42$		0			0
$43$	−9.19046			−1.40153			−0.700766	−	0.713392i	$-0.747158\pi$
$43$	−9.19046			−1.40153			−0.700766	+	0.713392i	$0.747158\pi$
$44$	0.0394304	−	1.54959i	0.00594436	−	0.233609i
$45$	−2.89162	+	0.663156i	−0.431057	+	0.0988575i
$46$	0.0341284	−	2.68288i	0.00503195	−	0.395569i
$47$	−7.16411	+	4.13620i	−1.04499	+	0.603327i	−0.921244	−	0.388986i	$-0.872825\pi$
$47$	−7.16411	+	4.13620i	−1.04499	+	0.603327i	−0.123750	+	0.992313i	$0.539492\pi$
$48$	−7.40787	+	3.78831i	−1.06923	+	0.546796i
$49$		0			0
$50$	3.00006	+	6.40310i	0.424272	+	0.905535i
$51$	−7.53038	+	4.34767i	−1.05446	+	0.608795i
$52$	−4.00339	−	7.36034i	−0.555170	−	1.02070i
$53$	−2.24383	−	1.29548i	−0.308214	−	0.177947i	0.337913	−	0.941177i	$-0.390279\pi$
$53$	−2.24383	−	1.29548i	−0.308214	−	0.177947i	−0.646127	+	0.763230i	$0.723612\pi$
$54$	−2.51512	+	4.23109i	−0.342264	+	0.575779i
$55$	1.26919	−	1.18010i	0.171138	−	0.159124i
$56$		0			0
$57$			10.1607i			1.34582i
$58$	−12.1379	−	7.21519i	−1.59378	−	0.947401i
$59$	2.30377	−	3.99024i	0.299925	−	0.519485i	−0.676194	−	0.736724i	$-0.736372\pi$
$59$	2.30377	−	3.99024i	0.299925	−	0.519485i	0.976118	+	0.217239i	$0.0697051\pi$
$60$	−8.81959	−	2.95800i	−1.13860	−	0.381876i
$61$	2.82504	−	1.63104i	0.361709	−	0.208833i	−0.308121	−	0.951347i	$-0.599700\pi$
$61$	2.82504	−	1.63104i	0.361709	−	0.208833i	0.669830	+	0.742514i	$0.266367\pi$
$62$	12.7662	−	7.15559i	1.62130	−	0.908761i
$63$		0			0
$64$	−7.97671	−	0.609973i	−0.997089	−	0.0762466i
$65$	2.75185	−	8.95430i	0.341324	−	1.11064i
$66$	−0.0290003	+	2.27975i	−0.00356969	+	0.280618i
$67$	−1.13535	+	1.96648i	−0.138705	+	0.240243i	−0.927006	−	0.375045i	$-0.877627\pi$
$67$	−1.13535	+	1.96648i	−0.138705	+	0.240243i	0.788302	+	0.615289i	$0.210960\pi$
$68$	−8.35786	−	0.212672i	−1.01354	−	0.0257903i
$69$			3.94640i			0.475091i
$70$		0			0
$71$		−	4.41264i		−	0.523684i	−0.965111	−	0.261842i	$-0.915670\pi$
$71$		−	4.41264i		−	0.523684i	0.965111	−	0.261842i	$-0.0843300\pi$
$72$	3.31906	−	1.75095i	0.391155	−	0.206351i
$73$	1.37461	−	2.38090i	0.160886	−	0.278663i	−0.774301	−	0.632818i	$-0.781898\pi$
$73$	1.37461	−	2.38090i	0.160886	−	0.278663i	0.935187	+	0.354155i	$0.115231\pi$
$74$	4.83305	+	0.0614803i	0.561831	+	0.00714694i
$75$	−4.53204	−	9.36105i	−0.523315	−	1.08092i
$76$	−5.09842	+	8.33369i	−0.584828	+	0.955940i
$77$		0			0
$78$	6.02557	+	10.7501i	0.682262	+	1.21721i
$79$	−12.3093	+	7.10679i	−1.38491	+	0.799576i	−0.992736	−	0.120316i	$-0.961609\pi$
$79$	−12.3093	+	7.10679i	−1.38491	+	0.799576i	−0.392171	+	0.919892i	$0.628276\pi$
$80$	−5.74944	−	6.85156i	−0.642807	−	0.766028i
$81$	5.60999	−	9.71679i	0.623332	−	1.07964i
$82$	2.18583	−	3.67714i	0.241384	−	0.406072i
$83$		−	2.36160i		−	0.259220i	−0.991565	−	0.129610i	$-0.958628\pi$
$83$		−	2.36160i		−	0.259220i	0.991565	−	0.129610i	$-0.0413725\pi$
$84$		0			0
$85$	−6.36497	−	6.84552i	−0.690378	−	0.742501i
$86$	11.1724	+	6.64128i	1.20475	+	0.716148i
$87$	17.9864	+	10.3845i	1.92834	+	1.11333i
$88$	−1.16771	+	1.85527i	−0.124478	+	0.197772i
$89$	12.4312	−	7.17714i	1.31770	−	0.760775i	0.334343	−	0.942452i	$-0.391486\pi$
$89$	12.4312	−	7.17714i	1.31770	−	0.760775i	0.983358	+	0.181677i	$0.0581524\pi$
$90$	3.99442	+	1.28340i	0.421048	+	0.135282i
$91$		0			0
$92$	−1.98021	+	3.23678i	−0.206451	+	0.337458i
$93$	−18.6416	+	10.7627i	−1.93304	+	1.11604i
$94$	11.6980	+	0.148808i	1.20656	+	0.0153484i
$95$	−10.6463	+	2.44160i	−1.09229	+	0.250502i
$96$	11.7429	+	0.747866i	1.19851	+	0.0763287i
$97$	14.4115			1.46327			0.731633	−	0.681699i	$-0.238759\pi$
$97$	14.4115			1.46327			0.731633	+	0.681699i	$0.238759\pi$
$98$		0			0
$99$		−	1.02829i		−	0.103347i
$100$	0.980035	−	9.95186i	0.0980035	−	0.995186i
$101$	1.46513	+	0.845894i	0.145786	+	0.0841696i	0.571119	−	0.820867i	$-0.306510\pi$
$101$	1.46513	+	0.845894i	0.145786	+	0.0841696i	−0.425333	+	0.905037i	$0.639843\pi$
$102$	12.2961	+	0.156416i	1.21749	+	0.0154875i
$103$	−0.479386	+	0.276774i	−0.0472353	+	0.0272713i	−0.523432	−	0.852068i	$-0.675348\pi$
$103$	−0.479386	+	0.276774i	−0.0472353	+	0.0272713i	0.476196	+	0.879339i	$0.342015\pi$
$104$	−0.452060	+	11.8406i	−0.0443281	+	1.16106i
$105$		0			0
$106$	1.79157	+	3.19630i	0.174013	+	0.310452i
$107$	4.04571	+	7.00738i	0.391114	+	0.677429i	0.992597	−	0.121457i	$-0.0387566\pi$
$107$	4.04571	+	7.00738i	0.391114	+	0.677429i	−0.601483	+	0.798886i	$0.705423\pi$
$108$	6.11501	−	3.32604i	0.588417	−	0.320048i
$109$	−6.90132	+	11.9534i	−0.661026	+	1.14493i	0.319320	+	0.947647i	$0.396546\pi$
$109$	−6.90132	+	11.9534i	−0.661026	+	1.14493i	−0.980346	+	0.197284i	$0.936788\pi$
$110$	−2.39567	+	0.517432i	−0.228418	+	0.0493352i
$111$	−7.10923			−0.674778
$112$		0			0
$113$		−	13.0010i		−	1.22303i	−0.791232	−	0.611516i	$-0.790560\pi$
$113$		−	13.0010i		−	1.22303i	0.791232	−	0.611516i	$-0.209440\pi$
$114$	7.34244	−	12.3519i	0.687682	−	1.15686i
$115$	−4.13500	+	0.948310i	−0.385591	+	0.0884303i
$116$	9.54151	+	17.5423i	0.885907	+	1.62876i
$117$	−2.77908	−	4.81350i	−0.256926	−	0.445008i
$118$	−5.68403	+	3.18597i	−0.523258	+	0.293293i
$119$		0			0
$120$	8.58401	+	9.96917i	0.783610	+	0.910057i
$121$	−5.19965	−	9.00606i	−0.472696	−	0.818733i
$122$	−4.61289	−	0.0586797i	−0.417632	−	0.00531261i
$123$	−3.14595	+	5.44894i	−0.283660	+	0.491314i
$124$	−20.6900	−	0.526472i	−1.85802	−	0.0472786i
$125$	8.71936	−	6.99805i	0.779883	−	0.625925i
$126$		0			0
$127$	15.3261			1.35997			0.679987	−	0.733224i	$-0.261985\pi$
$127$	15.3261			1.35997			0.679987	+	0.733224i	$0.261985\pi$
$128$	9.25612	+	6.50571i	0.818133	+	0.575029i
$129$	−16.5557	−	9.55845i	−1.45765	−	0.841575i
$130$	−9.81591	+	8.89675i	−0.860913	+	0.780296i
$131$	6.99388	+	12.1138i	0.611058	+	1.05838i	0.991062	+	0.133399i	$0.0425891\pi$
$131$	6.99388	+	12.1138i	0.611058	+	1.05838i	−0.380004	+	0.924985i	$0.624078\pi$
$132$	1.68267	−	2.75043i	0.146457	−	0.239394i
$133$		0			0
$134$	2.80122	−	1.57012i	0.241988	−	0.135637i
$135$	7.43928	+	2.28625i	0.640271	+	0.196769i
$136$	10.0066	+	6.29816i	0.858056	+	0.540063i
$137$	3.02510	+	1.74654i	0.258452	+	0.149217i	0.623628	−	0.781721i	$-0.285658\pi$
$137$	3.02510	+	1.74654i	0.258452	+	0.149217i	−0.365176	+	0.930938i	$0.618991\pi$
$138$	2.85178	−	4.79745i	0.242760	−	0.408386i
$139$	13.1731			1.11733			0.558664	−	0.829394i	$-0.311314\pi$
$139$	13.1731			1.11733			0.558664	+	0.829394i	$0.311314\pi$
$140$		0			0
$141$	−17.2073			−1.44911
$142$	−3.18870	+	5.36423i	−0.267590	+	0.450156i
$143$	2.81191	+	1.62346i	0.235144	+	0.135760i
$144$	−5.30010	−	0.269905i	−0.441675	−	0.0224921i
$145$	−6.55863	+	21.3413i	−0.544665	+	1.77230i
$146$	−3.39155	+	1.90101i	−0.280687	+	0.157329i
$147$		0			0
$148$	−5.83088	−	3.56724i	−0.479296	−	0.293225i
$149$	5.02398	+	8.70180i	0.411581	+	0.712879i	0.995063	−	0.0992472i	$-0.0316434\pi$
$149$	5.02398	+	8.70180i	0.411581	+	0.712879i	−0.583482	+	0.812126i	$0.698310\pi$
$150$	−1.25517	+	14.6547i	−0.102484	+	1.19656i
$151$	17.2276	+	9.94636i	1.40196	+	0.809423i	0.994594	−	0.103841i	$-0.0331133\pi$
$151$	17.2276	+	9.94636i	1.40196	+	0.809423i	0.407368	+	0.913264i	$0.366447\pi$
$152$	12.2201	−	6.44660i	0.991177	−	0.522889i
$153$	−5.54616			−0.448381
$154$		0			0
$155$	−15.7566	−	16.9462i	−1.26560	−	1.36115i
$156$	0.443331	−	17.4226i	0.0354949	−	1.39493i
$157$	−6.91712	+	11.9808i	−0.552046	+	0.956172i	0.446081	+	0.894993i	$0.352819\pi$
$157$	−6.91712	+	11.9808i	−0.552046	+	0.956172i	−0.998127	+	0.0611792i	$0.980514\pi$
$158$	20.0994	+	0.255681i	1.59902	+	0.0203409i
$159$	−2.69470	−	4.66735i	−0.213703	−	0.370145i
$160$	2.03819	+	12.4838i	0.161133	+	0.986933i
$161$		0			0
$162$	−13.8414	+	7.75829i	−1.08748	+	0.609549i
$163$	4.03480	+	6.98847i	0.316030	+	0.547379i	0.979656	−	0.200685i	$-0.0643168\pi$
$163$	4.03480	+	6.98847i	0.316030	+	0.547379i	−0.663626	+	0.748064i	$0.730983\pi$
$164$	−5.31441	+	2.89058i	−0.414985	+	0.225716i
$165$	3.51368	−	0.805818i	0.273539	−	0.0627328i
$166$	−1.70656	+	2.87089i	−0.132455	+	0.222824i
$167$			18.9334i			1.46511i	0.680707	+	0.732555i	$0.261673\pi$
$167$			18.9334i			1.46511i	−0.680707	+	0.732555i	$0.738327\pi$
$168$		0			0
$169$	4.55043			0.350033
$170$	2.79082	+	12.9213i	0.214046	+	0.991016i
$171$	−3.24042	+	5.61257i	−0.247801	+	0.429204i
$172$	−8.78256	−	16.1470i	−0.669664	−	1.23119i
$173$	−4.40688	−	7.63294i	−0.335049	−	0.580322i	0.648445	−	0.761261i	$-0.275419\pi$
$173$	−4.40688	−	7.63294i	−0.335049	−	0.580322i	−0.983494	+	0.180940i	$0.942086\pi$
$174$	−14.3611	−	25.6213i	−1.08871	−	1.94235i
$175$		0			0
$176$	2.76020	−	1.41154i	0.208058	−	0.106399i
$177$	8.30003	−	4.79202i	0.623868	−	0.360190i
$178$	−20.2984	−	0.258211i	−1.52143	−	0.0193538i
$179$	−5.01117	−	2.89320i	−0.374553	−	0.216248i	0.300893	−	0.953658i	$-0.402715\pi$
$179$	−5.01117	−	2.89320i	−0.374553	−	0.216248i	−0.675446	+	0.737410i	$0.736049\pi$
$180$	−3.92840	−	4.44664i	−0.292805	−	0.331433i
$181$		−	1.23162i		−	0.0915458i	−0.998952	−	0.0457729i	$-0.985425\pi$
$181$		−	1.23162i		−	0.0915458i	0.998952	−	0.0457729i	$-0.0145751\pi$
$182$		0			0
$183$	6.78538			0.501590
$184$	4.74624	−	2.50384i	0.349897	−	0.184586i
$185$	−1.70833	−	7.44897i	−0.125599	−	0.547659i
$186$	30.4391	+	0.387210i	2.23190	+	0.0283916i
$187$	2.80585	−	1.61996i	0.205184	−	0.118463i
$188$	−14.1132	−	8.63420i	−1.02931	−	0.629714i
$189$		0			0
$190$	14.7066	+	4.72519i	1.06693	+	0.342801i
$191$	15.1066	−	8.72177i	1.09307	−	0.631085i	0.158679	−	0.987330i	$-0.449276\pi$
$191$	15.1066	−	8.72177i	1.09307	−	0.631085i	0.934393	+	0.356245i	$0.115943\pi$
$192$	−13.7349	−	9.39492i	−0.991230	−	0.678020i
$193$	8.25255	+	4.76461i	0.594032	+	0.342964i	0.766690	−	0.642017i	$-0.221902\pi$
$193$	8.25255	+	4.76461i	0.594032	+	0.342964i	−0.172658	+	0.984982i	$0.555236\pi$
$194$	−17.5194	−	10.4141i	−1.25782	−	0.747692i
$195$	14.2700	−	13.2683i	1.02190	−	0.950161i
$196$		0			0
$197$		−	5.88709i		−	0.419438i	−0.977762	−	0.209719i	$-0.932745\pi$
$197$		−	5.88709i		−	0.419438i	0.977762	−	0.209719i	$-0.0672548\pi$
$198$	−0.743068	+	1.25004i	−0.0528076	+	0.0888363i
$199$	−6.99130	+	12.1093i	−0.495600	+	0.858405i	−0.999987	−	0.00507288i	$-0.998385\pi$
$199$	−6.99130	+	12.1093i	−0.495600	+	0.858405i	0.504387	+	0.863478i	$0.331719\pi$
$200$	−8.38287	+	11.3898i	−0.592759	+	0.805380i
$201$	−4.09043	+	2.36161i	−0.288517	+	0.166575i
$202$	−1.16982	−	2.08706i	−0.0823084	−	0.146845i
$203$		0			0
$204$	−14.8347	−	9.07563i	−1.03864	−	0.635421i
$205$	−6.46530	−	1.98692i	−0.451556	−	0.138773i
$206$	0.782771	+	0.00995747i	0.0545382	+	0.000693770i
$207$	−1.25857	+	2.17991i	−0.0874767	+	0.151514i
$208$	9.10587	−	14.0673i	0.631379	−	0.975394i
$209$		−	3.78592i		−	0.261878i
$210$		0			0
$211$		−	20.4896i		−	1.41056i	−0.708927	−	0.705282i	$-0.750820\pi$
$211$		−	20.4896i		−	1.41056i	0.708927	−	0.705282i	$-0.249180\pi$
$212$	0.131815	−	5.18023i	0.00905307	−	0.355780i
$213$	4.58933	−	7.94895i	0.314456	−	0.544653i
$214$	0.145552	−	11.4421i	0.00994975	−	0.782164i
$215$	6.03694	−	19.6438i	0.411716	−	1.33969i
$216$	−9.83721	−	0.375574i	−0.669337	−	0.0255546i
$217$		0			0
$218$	17.0275	−	9.54412i	1.15325	−	0.646410i
$219$	4.95246	−	2.85931i	0.334656	−	0.193214i
$220$	3.28621	+	1.10216i	0.221556	+	0.0743076i
$221$	8.75628	−	15.1663i	0.589011	−	1.02020i
$222$	8.64234	+	5.13733i	0.580036	+	0.344795i
$223$		−	4.98483i		−	0.333809i	−0.985973	−	0.166904i	$-0.946623\pi$
$223$		−	4.98483i		−	0.333809i	0.985973	−	0.166904i	$-0.0533771\pi$
$224$		0			0
$225$	0.481984	−	6.61618i	0.0321323	−	0.441079i
$226$	−9.39490	+	15.8047i	−0.624939	+	1.05131i
$227$	3.61060	+	2.08458i	0.239644	+	0.138358i	0.615013	−	0.788517i	$-0.289151\pi$
$227$	3.61060	+	2.08458i	0.239644	+	0.138358i	−0.375369	+	0.926875i	$0.622484\pi$
$228$	−17.8517	+	9.70978i	−1.18226	+	0.643046i
$229$	0.877281	−	0.506498i	0.0579723	−	0.0334703i	−0.470734	−	0.882275i	$-0.656011\pi$
$229$	0.877281	−	0.506498i	0.0579723	−	0.0334703i	0.528706	+	0.848805i	$0.322677\pi$
$230$	5.71199	+	1.83525i	0.376638	+	0.121013i
$231$		0			0
$232$	1.07742	−	28.2203i	0.0707361	−	1.85275i
$233$	17.0821	−	9.86235i	1.11908	−	0.646104i	0.177918	−	0.984045i	$-0.443064\pi$
$233$	17.0821	−	9.86235i	1.11908	−	0.646104i	0.941167	+	0.337942i	$0.109731\pi$
$234$	−0.0999827	+	7.85978i	−0.00653607	+	0.513810i
$235$	−4.13486	−	18.0296i	−0.269729	−	1.17612i
$236$	9.21208	+	0.234408i	0.599655	+	0.0152587i
$237$	−29.5654			−1.92048
$238$		0			0
$239$			21.5726i			1.39541i	0.716383	+	0.697707i	$0.245796\pi$
$239$			21.5726i			1.39541i	−0.716383	+	0.697707i	$0.754204\pi$
$240$	−3.23116	−	18.3221i	−0.208571	−	1.18269i
$241$	9.00949	+	5.20163i	0.580353	+	0.335067i	0.761273	−	0.648431i	$-0.224574\pi$
$241$	9.00949	+	5.20163i	0.580353	+	0.335067i	−0.180921	+	0.983498i	$0.557908\pi$
$242$	−0.187068	+	14.7056i	−0.0120252	+	0.945315i
$243$	11.1691	−	6.44847i	0.716497	−	0.413670i
$244$	5.56527	+	3.40474i	0.356280	+	0.217966i
$245$		0			0
$246$	7.76193	−	4.35066i	0.494883	−	0.277388i
$247$	−10.2320	−	17.7223i	−0.651044	−	1.12764i
$248$	24.7714	+	15.5912i	1.57299	+	0.990042i
$249$	2.45616	−	4.25420i	0.155653	−	0.269599i
$250$	−15.6567	+	2.20634i	−0.990216	+	0.139541i
$251$	−6.03246			−0.380766			−0.190383	−	0.981710i	$-0.560973\pi$
$251$	−6.03246			−0.380766			−0.190383	+	0.981710i	$0.560973\pi$
$252$		0			0
$253$		−	1.47044i		−	0.0924460i
$254$	−18.6312	−	11.0751i	−1.16903	−	0.694913i
$255$	−4.34626	−	18.9514i	−0.272173	−	1.18678i
$256$	−6.55101	−	14.5974i	−0.409438	−	0.912338i
$257$	0.809807	+	1.40263i	0.0505144	+	0.0874935i	0.890177	−	0.455615i	$-0.150581\pi$
$257$	0.809807	+	1.40263i	0.0505144	+	0.0874935i	−0.839663	+	0.543108i	$0.817247\pi$
$258$	13.2188	+	23.5834i	0.822966	+	1.46824i
$259$		0			0
$260$	18.3618	−	3.72209i	1.13875	−	0.230834i
$261$	6.62353	+	11.4723i	0.409986	+	0.710117i
$262$	0.251618	−	19.7801i	0.0155450	−	1.22202i
$263$	−2.51554	+	4.35704i	−0.155115	+	0.268667i	−0.933101	−	0.359615i	$-0.882908\pi$
$263$	−2.51554	+	4.35704i	−0.155115	+	0.268667i	0.777986	+	0.628282i	$0.216241\pi$
$264$	−4.03307	+	2.12762i	−0.248218	+	0.130946i
$265$	4.24287	−	3.94502i	0.260637	−	0.242341i
$266$		0			0
$267$	29.8581			1.82728
$268$	−4.53991	−	0.115521i	−0.277319	−	0.00705659i
$269$	10.8402	+	6.25857i	0.660937	+	0.381592i	0.792634	−	0.609698i	$-0.208709\pi$
$269$	10.8402	+	6.25857i	0.660937	+	0.381592i	−0.131697	+	0.991290i	$0.542043\pi$
$270$	−7.39147	−	8.15512i	−0.449830	−	0.496305i
$271$	−1.83085	−	3.17112i	−0.111216	−	0.192632i	0.805045	−	0.593214i	$-0.202141\pi$
$271$	−1.83085	−	3.17112i	−0.111216	−	0.192632i	−0.916261	+	0.400582i	$0.868808\pi$
$272$	−7.61327	−	14.8874i	−0.461622	−	0.902681i
$273$		0			0
$274$	−2.41537	−	4.30921i	−0.145918	−	0.260329i
$275$	1.68865	+	3.48796i	0.101830	+	0.210332i
$276$	−6.93355	+	3.77125i	−0.417351	+	0.227003i
$277$	−22.4228	−	12.9458i	−1.34726	−	0.777839i	−0.359396	−	0.933185i	$-0.617017\pi$
$277$	−22.4228	−	12.9458i	−1.34726	−	0.777839i	−0.987860	+	0.155346i	$0.950351\pi$
$278$	−16.0139	−	9.51926i	−0.960450	−	0.570927i
$279$	−13.7296			−0.821970
$280$		0			0
$281$	14.7079			0.877397			0.438698	−	0.898634i	$-0.355440\pi$
$281$	14.7079			0.877397			0.438698	+	0.898634i	$0.355440\pi$
$282$	20.9181	+	12.4345i	1.24565	+	0.740462i
$283$	−26.1700	−	15.1093i	−1.55565	−	0.898153i	−0.997665	−	0.0682999i	$-0.978243\pi$
$283$	−26.1700	−	15.1093i	−1.55565	−	0.898153i	−0.557982	−	0.829853i	$-0.688424\pi$
$284$	7.75269	−	4.21680i	0.460038	−	0.250221i
$285$	−21.7177	−	6.67430i	−1.28644	−	0.395351i
$286$	−2.24515	−	4.00553i	−0.132758	−	0.236852i
$287$		0			0
$288$	6.24804	+	4.15811i	0.368169	+	0.245019i
$289$	−0.237391	−	0.411173i	−0.0139642	−	0.0241866i
$290$	23.3948	−	21.2041i	1.37379	−	1.24515i
$291$	25.9609	+	14.9885i	1.52186	+	0.878644i
$292$	5.49667	+	0.139867i	0.321668	+	0.00818508i
$293$	13.9578			0.815421			0.407710	−	0.913111i	$-0.366327\pi$
$293$	13.9578			0.815421			0.407710	+	0.913111i	$0.366327\pi$
$294$		0			0
$295$	7.01550	+	7.54516i	0.408458	+	0.439296i
$296$	4.51053	+	8.55008i	0.262169	+	0.496963i
$297$	−1.34878	+	2.33615i	−0.0782640	+	0.135557i
$298$	0.180748	−	14.2088i	0.0104704	−	0.823095i
$299$	−3.97406	−	6.88328i	−0.229826	−	0.398071i
$300$	12.1158	−	16.9080i	0.699505	−	0.976187i
$301$		0			0
$302$	−13.7552	−	24.5405i	−0.791525	−	1.41214i
$303$	1.75953	+	3.04759i	0.101082	+	0.175080i
$304$	−19.5138	−	0.993730i	−1.11919	−	0.0569943i
$305$	1.63051	+	7.10964i	0.0933626	+	0.407097i
$306$	6.74220	+	4.00781i	0.385426	+	0.229111i
$307$			23.2065i			1.32446i	0.749300	+	0.662231i	$0.230390\pi$
$307$			23.2065i			1.32446i	−0.749300	+	0.662231i	$0.769610\pi$
$308$		0			0
$309$	−1.15142			−0.0655022
$310$	6.90872	+	31.9868i	0.392389	+	1.81673i
$311$	−2.38233	+	4.12632i	−0.135090	+	0.233982i	−0.925632	−	0.378426i	$-0.876466\pi$
$311$	−2.38233	+	4.12632i	−0.135090	+	0.233982i	0.790542	+	0.612408i	$0.209799\pi$
$312$	−13.1290	+	20.8595i	−0.743284	+	1.18094i
$313$	0.0497672	+	0.0861993i	0.00281301	+	0.00487227i	0.867428	−	0.497562i	$-0.165771\pi$
$313$	0.0497672	+	0.0861993i	0.00281301	+	0.00487227i	−0.864615	+	0.502434i	$0.832438\pi$
$314$	17.0665	−	9.56597i	0.963116	−	0.539839i
$315$		0			0
$316$	−24.2491	−	14.8352i	−1.36412	−	0.834546i
$317$	15.3161	−	8.84275i	0.860237	−	0.496658i	−0.00385460	−	0.999993i	$-0.501227\pi$
$317$	15.3161	−	8.84275i	0.860237	−	0.496658i	0.864092	+	0.503334i	$0.167894\pi$
$318$	−0.0969470	+	7.62114i	−0.00543652	+	0.427372i
$319$	−6.70179	−	3.86928i	−0.375228	−	0.216638i
$320$	6.54343	−	16.6488i	0.365789	−	0.930698i
$321$			16.8308i			0.939405i
$322$		0			0
$323$	−20.4198			−1.13619
$324$	22.4327	+	0.570816i	1.24626	+	0.0317120i
$325$	17.3314	+	11.7636i	0.961373	+	0.652529i
$326$	0.145160	−	11.4112i	0.00803965	−	0.632008i
$327$	−24.8641	+	14.3553i	−1.37499	+	0.793851i
$328$	8.54928	+	0.326402i	0.472055	+	0.0180225i
$329$		0			0
$330$	−4.85371	−	1.55949i	−0.267188	−	0.0858470i
$331$	−3.58702	+	2.07097i	−0.197160	+	0.113831i	−0.595330	−	0.803481i	$-0.702979\pi$
$331$	−3.58702	+	2.07097i	−0.197160	+	0.113831i	0.398170	+	0.917312i	$0.369645\pi$
$332$	4.14917	−	2.25679i	0.227715	−	0.123857i
$333$	−3.92698	−	2.26725i	−0.215197	−	0.124244i
$334$	13.6818	−	23.0164i	0.748635	−	1.25940i
$335$	−3.45739	−	3.71842i	−0.188897	−	0.203159i
$336$		0			0
$337$			28.4342i			1.54891i	0.632630	+	0.774454i	$0.281975\pi$
$337$			28.4342i			1.54891i	−0.632630	+	0.774454i	$0.718025\pi$
$338$	−5.53174	−	3.28827i	−0.300887	−	0.178858i
$339$	13.5216	−	23.4201i	0.734392	−	1.27200i
$340$	5.94461	−	17.7245i	0.322392	−	0.961245i
$341$	6.94591	−	4.01022i	0.376142	−	0.217166i
$342$	7.99503	−	4.48132i	0.432322	−	0.242322i
$343$		0			0
$344$	−0.991720	+	25.9756i	−0.0534699	+	1.40051i
$345$	−8.43508	−	2.59228i	−0.454130	−	0.139564i
$346$	−0.158546	+	12.4635i	−0.00852349	+	0.670043i
$347$	−10.7361	+	18.5954i	−0.576342	+	0.998254i	0.419552	+	0.907731i	$0.362187\pi$
$347$	−10.7361	+	18.5954i	−0.576342	+	0.998254i	−0.995894	+	0.0905227i	$0.971146\pi$
$348$	−1.05662	+	41.5244i	−0.0566406	+	2.22594i
$349$		−	13.8800i		−	0.742981i	−0.928437	−	0.371490i	$-0.878847\pi$
$349$		−	13.8800i		−	0.742981i	0.928437	−	0.371490i	$-0.121153\pi$
$350$		0			0
$351$			14.5810i			0.778276i
$352$	−4.37546	−	0.278657i	−0.233213	−	0.0148525i
$353$	5.48320	−	9.49718i	0.291841	−	0.505484i	−0.682404	−	0.730975i	$-0.739065\pi$
$353$	5.48320	−	9.49718i	0.291841	−	0.505484i	0.974245	+	0.225492i	$0.0723988\pi$
$354$	−13.5528	−	0.172402i	−0.720323	−	0.00916308i
$355$	9.43162	+	2.89854i	0.500578	+	0.153838i
$356$	24.4892	+	14.9821i	1.29792	+	0.794048i
$357$		0			0
$358$	4.00113	+	7.13834i	0.211466	+	0.377273i
$359$	22.6532	−	13.0788i	1.19559	−	0.690275i	0.236022	−	0.971748i	$-0.424156\pi$
$359$	22.6532	−	13.0788i	1.19559	−	0.690275i	0.959569	+	0.281473i	$0.0908230\pi$
$360$	1.56230	+	8.24434i	0.0823402	+	0.434515i
$361$	−2.43052	+	4.20979i	−0.127922	+	0.221568i
$362$	−0.890005	+	1.49722i	−0.0467776	+	0.0786923i
$363$		−	21.6314i		−	1.13535i
$364$		0			0
$365$	4.18601	+	4.50205i	0.219106	+	0.235648i
$366$	−8.24866	−	4.90331i	−0.431164	−	0.256300i
$367$	5.66399	+	3.27010i	0.295658	+	0.170698i	0.640491	−	0.767966i	$-0.278731\pi$
$367$	5.66399	+	3.27010i	0.295658	+	0.170698i	−0.344833	+	0.938664i	$0.612064\pi$
$368$	−7.57912	−	0.385962i	−0.395089	−	0.0201197i
$369$	−3.47551	+	2.00658i	−0.180928	+	0.104459i
$370$	−3.30610	+	10.2898i	−0.171876	+	0.534943i
$371$		0			0
$372$	−36.7235	−	22.4669i	−1.90403	−	1.16485i
$373$	−2.40702	+	1.38969i	−0.124631	+	0.0719555i	−0.561019	−	0.827803i	$-0.689591\pi$
$373$	−2.40702	+	1.38969i	−0.124631	+	0.0719555i	0.436389	+	0.899758i	$0.356257\pi$
$374$	−4.58156	−	0.0582811i	−0.236907	−	0.00301364i
$375$	22.9854	−	3.53783i	1.18696	−	0.182693i
$376$	10.9174	+	20.6947i	0.563020	+	1.06725i
$377$	−41.8289			−2.15430
$378$		0			0
$379$			7.04001i			0.361621i	0.983518	+	0.180811i	$0.0578721\pi$
$379$			7.04001i			0.361621i	−0.983518	+	0.180811i	$0.942128\pi$
$380$	−14.4635	−	16.3716i	−0.741962	−	0.839843i
$381$	27.6086	+	15.9398i	1.41443	+	0.816621i
$382$	−24.6669	−	0.313783i	−1.26207	−	0.0160545i
$383$	4.89111	−	2.82389i	0.249924	−	0.144294i	−0.369805	−	0.929109i	$-0.620576\pi$
$383$	4.89111	−	2.82389i	0.249924	−	0.144294i	0.619730	+	0.784815i	$0.287242\pi$
$384$	9.90780	+	21.3462i	0.505606	+	1.08932i
$385$		0			0
$386$	−6.58918	−	11.7556i	−0.335381	−	0.598346i
$387$	−6.09668	−	10.5598i	−0.309912	−	0.536783i
$388$	13.7719	+	25.3199i	0.699161	+	1.28543i
$389$	−9.59281	+	16.6152i	−0.486375	+	0.842426i	−0.999877	−	0.0156622i	$-0.995014\pi$
$389$	−9.59281	+	16.6152i	−0.486375	+	0.842426i	0.513503	+	0.858088i	$0.328348\pi$
$390$	−26.9354	+	5.81769i	−1.36393	+	0.294590i
$391$	−7.93098			−0.401087
$392$		0			0
$393$			29.0957i			1.46768i
$394$	−4.25417	+	7.15665i	−0.214322	+	0.360547i
$395$	−7.10448	−	30.9783i	−0.357465	−	1.55869i
$396$	1.80662	−	0.982648i	0.0907863	−	0.0493799i
$397$	−7.67920	−	13.3008i	−0.385408	−	0.667546i	0.606418	−	0.795146i	$-0.292606\pi$
$397$	−7.67920	−	13.3008i	−0.385408	−	0.667546i	−0.991826	+	0.127600i	$0.959273\pi$
$398$	17.2495	−	9.66857i	0.864639	−	0.484642i
$399$		0			0
$400$	18.4212	−	7.78832i	0.921062	−	0.389416i
$401$	−4.47566	−	7.75206i	−0.223504	−	0.387120i	0.732366	−	0.680911i	$-0.238416\pi$
$401$	−4.47566	−	7.75206i	−0.223504	−	0.387120i	−0.955869	+	0.293792i	$0.905083\pi$
$402$	6.67911	+	0.0849636i	0.333124	+	0.00423760i
$403$	21.6763	−	37.5445i	1.07977	−	1.87022i
$404$	−0.0860696	+	3.38248i	−0.00428212	+	0.168285i
$405$	17.0837	+	18.3735i	0.848897	+	0.912988i
$406$		0			0
$407$	2.64892			0.131302
$408$	11.4755	+	21.7528i	0.568123	+	1.07692i
$409$	3.90450	+	2.25427i	0.193065	+	0.111466i	0.593417	−	0.804895i	$-0.297779\pi$
$409$	3.90450	+	2.25427i	0.193065	+	0.111466i	−0.400351	+	0.916362i	$0.631112\pi$
$410$	6.42374	+	7.08741i	0.317246	+	0.350022i
$411$	3.63295	+	6.29246i	0.179200	+	0.310384i
$412$	−0.944381	−	0.577757i	−0.0465263	−	0.0284640i
$413$		0			0
$414$	3.10525	−	1.74053i	0.152615	−	0.0855424i
$415$	5.04771	+	1.55127i	0.247783	+	0.0761488i
$416$	−21.2350	+	10.5208i	−1.04113	+	0.515826i
$417$	23.7301	+	13.7006i	1.16207	+	0.670920i
$418$	−2.73582	+	4.60237i	−0.133813	+	0.225109i
$419$	−29.0565			−1.41950			−0.709751	−	0.704453i	$-0.751192\pi$
$419$	−29.0565			−1.41950			−0.709751	+	0.704453i	$0.751192\pi$
$420$		0			0
$421$	−11.9368			−0.581763			−0.290882	−	0.956759i	$-0.593949\pi$
$421$	−11.9368			−0.581763			−0.290882	+	0.956759i	$0.593949\pi$
$422$	−14.8064	+	24.9083i	−0.720764	+	1.21252i
$423$	−9.50493	−	5.48768i	−0.462146	−	0.266820i
$424$	−3.90362	+	6.20210i	−0.189576	+	0.301201i
$425$	18.8126	−	9.10792i	0.912547	−	0.441799i
$426$	−11.3232	+	6.34678i	−0.548609	+	0.307502i
$427$		0			0
$428$	−8.44530	+	13.8044i	−0.408219	+	0.667261i
$429$	3.37693	+	5.84901i	0.163040	+	0.282393i
$430$	−21.5340	+	19.5175i	−1.03846	+	0.941218i
$431$	−11.2507	−	6.49560i	−0.541927	−	0.312882i	0.203932	−	0.978985i	$-0.434628\pi$
$431$	−11.2507	−	6.49560i	−0.541927	−	0.312882i	−0.745860	+	0.666103i	$0.767961\pi$
$432$	11.6872	+	7.56521i	0.562302	+	0.363981i
$433$	15.4967			0.744724			0.372362	−	0.928088i	$-0.378548\pi$
$433$	15.4967			0.744724			0.372362	+	0.928088i	$0.378548\pi$
$434$		0			0
$435$	−34.0106	+	31.6231i	−1.63068	+	1.51621i
$436$	−27.5963	−	0.702209i	−1.32163	−	0.0336297i
$437$	−4.63378	+	8.02595i	−0.221664	+	0.383933i
$438$	−8.08668	−	0.102869i	−0.386397	−	0.00491527i
$439$	1.27117	+	2.20174i	0.0606698	+	0.105083i	0.894765	−	0.446537i	$-0.147343\pi$
$439$	1.27117	+	2.20174i	0.0606698	+	0.105083i	−0.834095	+	0.551621i	$0.814010\pi$
$440$	−3.19843	−	3.71455i	−0.152479	−	0.177084i
$441$		0			0
$442$	−21.6042	+	12.1094i	−1.02761	+	0.575987i
$443$	−15.0485	−	26.0648i	−0.714977	−	1.23838i	−0.962968	−	0.269614i	$-0.913104\pi$
$443$	−15.0485	−	26.0648i	−0.714977	−	1.23838i	0.247991	−	0.968762i	$-0.420230\pi$
$444$	−6.79370	−	12.4904i	−0.322415	−	0.592768i
$445$	7.17481	+	31.2850i	0.340119	+	1.48305i
$446$	−3.60218	+	6.05981i	−0.170568	+	0.286940i
$447$			20.9006i			0.988565i
$448$		0			0
$449$	6.40778			0.302402			0.151201	−	0.988503i	$-0.451686\pi$
$449$	6.40778			0.302402			0.151201	+	0.988503i	$0.451686\pi$
$450$	−5.36696	+	7.69468i	−0.253001	+	0.362730i
$451$	1.17219	−	2.03029i	0.0551963	−	0.0956028i
$452$	22.8418	−	12.4240i	1.07439	−	0.584376i
$453$	20.6892	+	35.8348i	0.972065	+	1.68367i
$454$	−2.88285	−	5.14324i	−0.135299	−	0.241384i
$455$		0			0
$456$	28.7180	+	1.09642i	1.34484	+	0.0513446i
$457$	2.73341	−	1.57813i	0.127863	−	0.0738220i	−0.434704	−	0.900573i	$-0.643147\pi$
$457$	2.73341	−	1.57813i	0.127863	−	0.0738220i	0.562567	+	0.826751i	$0.309814\pi$
$458$	−1.43248	−	0.0182223i	−0.0669353	−	0.000851470i
$459$	12.6003	+	7.27477i	0.588130	+	0.339557i
$460$	−5.61759	−	6.35867i	−0.261921	−	0.296475i
$461$		−	9.88170i		−	0.460237i	−0.973163	−	0.230118i	$-0.926089\pi$
$461$		−	9.88170i		−	0.460237i	0.973163	−	0.230118i	$-0.0739114\pi$
$462$		0			0
$463$	9.55216			0.443926			0.221963	−	0.975055i	$-0.428754\pi$
$463$	9.55216			0.443926			0.221963	+	0.975055i	$0.428754\pi$
$464$	−21.7026	+	33.5275i	−1.00752	+	1.55647i
$465$	−10.7592	−	46.9144i	−0.498947	−	2.17560i
$466$	−27.8927	−	0.354817i	−1.29210	−	0.0164366i
$467$	11.6614	−	6.73269i	0.539624	−	0.311552i	−0.205303	−	0.978699i	$-0.565818\pi$
$467$	11.6614	−	6.73269i	0.539624	−	0.311552i	0.744926	+	0.667147i	$0.232485\pi$
$468$	5.80124	−	9.48250i	0.268163	−	0.438329i
$469$		0			0
$470$	−8.00214	+	24.9057i	−0.369111	+	1.14881i
$471$	−24.9211	+	14.3882i	−1.14830	+	0.662972i
$472$	−11.0293	−	6.94187i	−0.507664	−	0.319525i
$473$	6.16872	+	3.56151i	0.283638	+	0.163758i
$474$	35.9412	+	21.3648i	1.65084	+	0.981318i
$475$	1.77456	−	24.3593i	0.0814224	−	1.11768i
$476$		0			0
$477$		−	3.43753i		−	0.157394i
$478$	15.5890	−	26.2248i	0.713022	−	1.19949i
$479$	7.01200	−	12.1451i	0.320387	−	0.554926i	−0.660181	−	0.751106i	$-0.729521\pi$
$479$	7.01200	−	12.1451i	0.320387	−	0.554926i	0.980568	+	0.196181i	$0.0628539\pi$
$480$	−9.31209	+	24.6082i	−0.425037	+	1.12321i
$481$	12.3998	−	7.15906i	0.565384	−	0.326425i
$482$	−7.19356	−	12.8339i	−0.327658	−	0.584568i
$483$		0			0
$484$	10.8541	−	17.7418i	0.493369	−	0.806444i
$485$	−9.46649	+	30.8033i	−0.429851	+	1.39870i
$486$	−18.2376	−	0.231996i	−0.827273	−	0.0105236i
$487$	15.1689	−	26.2733i	0.687368	−	1.19056i	−0.285318	−	0.958433i	$-0.592099\pi$
$487$	15.1689	−	26.2733i	0.687368	−	1.19056i	0.972686	−	0.232124i	$-0.0745675\pi$
$488$	−4.30507	−	8.16060i	−0.194881	−	0.369413i
$489$			16.7854i			0.759063i
$490$		0			0
$491$			8.93052i			0.403029i	0.979486	+	0.201514i	$0.0645862\pi$
$491$			8.93052i			0.403029i	−0.979486	+	0.201514i	$0.935414\pi$
$492$	−12.5797	−	0.320100i	−0.567137	−	0.0144312i
$493$	−20.8693	+	36.1468i	−0.939908	+	1.62797i
$494$	−0.368115	+	28.9380i	−0.0165623	+	1.30198i
$495$	2.19787	+	0.675451i	0.0987868	+	0.0303593i
$496$	−18.8468	−	36.8540i	−0.846245	−	1.65479i
$497$		0			0
$498$	−6.06005	+	3.39673i	−0.271557	+	0.152211i
$499$	−4.78683	+	2.76368i	−0.214288	+	0.123719i	−0.603303	−	0.797512i	$-0.706149\pi$
$499$	−4.78683	+	2.76368i	−0.214288	+	0.123719i	0.389015	+	0.921232i	$0.372816\pi$
$500$	20.6274	+	8.63183i	0.922487	+	0.386027i
$501$	−19.6915	+	34.1067i	−0.879752	+	1.52378i
$502$	7.33337	+	4.35923i	0.327305	+	0.194562i
$503$			20.6496i			0.920720i	0.887732	+	0.460360i	$0.152280\pi$
$503$			20.6496i			0.920720i	−0.887732	+	0.460360i	$0.847720\pi$
$504$		0			0
$505$	−2.77042	+	2.57594i	−0.123282	+	0.114628i
$506$	−1.06258	+	1.78755i	−0.0472376	+	0.0794661i
$507$	8.19716	+	4.73263i	0.364049	+	0.210184i
$508$	14.6459	+	26.9269i	0.649808	+	1.19469i
$509$	−25.8094	+	14.9010i	−1.14398	+	0.660477i	−0.947413	−	0.320013i	$-0.896313\pi$
$509$	−25.8094	+	14.9010i	−1.14398	+	0.660477i	−0.196567	+	0.980490i	$0.562979\pi$
$510$	−8.41126	+	26.1790i	−0.372457	+	1.15923i
$511$		0			0
$512$	−2.58476	+	22.4793i	−0.114231	+	0.993454i
$513$	14.7238	−	8.50077i	0.650070	−	0.375318i
$514$	0.0291344	−	2.29030i	0.00128506	−	0.101021i
$515$	−0.276684	−	1.20645i	−0.0121921	−	0.0531625i
$516$	0.972572	−	38.2214i	0.0428151	−	1.68260i
$517$	6.41149			0.281977
$518$		0			0
$519$		−	18.3333i		−	0.804745i
$520$	−25.0112	−	8.74396i	−1.09681	−	0.383448i
$521$	−30.3848	−	17.5426i	−1.33118	−	0.768557i	−0.345700	−	0.938345i	$-0.612358\pi$
$521$	−30.3848	−	17.5426i	−1.33118	−	0.768557i	−0.985481	+	0.169788i	$0.945692\pi$
$522$	0.238294	−	18.7327i	0.0104299	−	0.819906i
$523$	−18.9563	+	10.9444i	−0.828903	+	0.478567i	−0.853477	−	0.521131i	$-0.825510\pi$
$523$	−18.9563	+	10.9444i	−0.828903	+	0.478567i	0.0245740	+	0.999698i	$0.492177\pi$
$524$	−14.5995	+	23.8639i	−0.637783	+	1.04250i
$525$		0			0
$526$	6.20654	−	3.47884i	0.270618	−	0.151685i
$527$	−21.6295	−	37.4635i	−0.942198	−	1.63193i
$528$	6.44029	+	0.327968i	0.280278	+	0.0142730i
$529$	9.70025	−	16.8013i	0.421750	−	0.730492i
$530$	−8.00864	+	1.72976i	−0.347873	+	0.0751359i
$531$	6.11301			0.265282
$532$		0			0
$533$		−	12.6720i		−	0.548885i
$534$	−36.2970	−	21.5763i	−1.57073	−	0.933697i
$535$	−17.6351	+	4.04440i	−0.762434	+	0.174855i
$536$	5.43547	+	3.42110i	0.234777	+	0.147769i
$537$	−6.01810	−	10.4237i	−0.259700	−	0.449814i
$538$	−8.65524	−	15.4416i	−0.373154	−	0.665737i
$539$		0			0
$540$	3.09233	+	15.2551i	0.133073	+	0.656473i
$541$	12.7190	+	22.0300i	0.546834	+	0.947145i	0.998489	+	0.0549521i	$0.0175006\pi$
$541$	12.7190	+	22.0300i	0.546834	+	0.947145i	−0.451655	+	0.892193i	$0.649166\pi$
$542$	−0.0658684	+	5.17801i	−0.00282929	+	0.222414i
$543$	1.28094	−	2.21865i	0.0549703	−	0.0952114i
$544$	−1.50297	+	23.5995i	−0.0644391	+	1.01182i
$545$	−21.0161	−	22.6028i	−0.900231	−	0.968198i
$546$		0			0
$547$	43.6348			1.86569			0.932845	−	0.360278i	$-0.117318\pi$
$547$	43.6348			1.86569			0.932845	+	0.360278i	$0.117318\pi$
$548$	−0.177711	+	6.98391i	−0.00759142	+	0.298338i
$549$	3.74810	+	2.16397i	0.159965	+	0.0923558i
$550$	0.467681	−	5.46041i	0.0199420	−	0.232833i
$551$	24.3864	+	42.2385i	1.03890	+	1.79942i
$552$	11.1540	+	0.425847i	0.474745	+	0.0181252i
$553$		0			0
$554$	17.9033	+	31.9410i	0.760639	+	1.35704i
$555$	4.66985	−	15.1953i	0.198224	−	0.645006i
$556$	12.5884	+	23.1442i	0.533869	+	0.981533i
$557$	−15.6367	−	9.02785i	−0.662548	−	0.382522i	0.130699	−	0.991422i	$-0.458278\pi$
$557$	−15.6367	−	9.02785i	−0.662548	−	0.382522i	−0.793247	+	0.608900i	$0.791611\pi$
$558$	16.6904	+	9.92140i	0.706562	+	0.420006i
$559$	38.5018			1.62845
$560$		0			0
$561$	6.73928			0.284533
$562$	−17.8796	−	10.6283i	−0.754206	−	0.448328i
$563$	4.48428	+	2.58900i	0.188990	+	0.109113i	0.591510	−	0.806298i	$-0.298532\pi$
$563$	4.48428	+	2.58900i	0.188990	+	0.109113i	−0.402520	+	0.915411i	$0.631865\pi$
$564$	−16.4436	−	30.2320i	−0.692400	−	1.27300i
$565$	27.7885	+	8.53999i	1.16907	+	0.359280i
$566$	20.8953	+	37.2788i	0.878293	+	1.56695i
$567$		0			0
$568$	−12.4717	−	0.476157i	−0.523303	−	0.0199791i
$569$	−10.8957	−	18.8719i	−0.456772	−	0.791153i	0.542016	−	0.840368i	$-0.317661\pi$
$569$	−10.8957	−	18.8719i	−0.456772	−	0.791153i	−0.998788	+	0.0492155i	$0.984328\pi$
$570$	21.5781	+	23.8074i	0.903806	+	0.997183i
$571$	−14.0484	−	8.11085i	−0.587908	−	0.339429i	0.176362	−	0.984325i	$-0.443567\pi$
$571$	−14.0484	−	8.11085i	−0.587908	−	0.339429i	−0.764270	+	0.644897i	$0.776900\pi$
$572$	−0.165187	+	6.49173i	−0.00690681	+	0.271433i
$573$	36.2840			1.51579
$574$		0			0
$575$	0.689234	−	9.46110i	0.0287431	−	0.394555i
$576$	−4.59067	−	9.56982i	−0.191278	−	0.398743i
$577$	21.6559	−	37.5091i	0.901547	−	1.56153i	0.0760616	−	0.997103i	$-0.475765\pi$
$577$	21.6559	−	37.5091i	0.901547	−	1.56153i	0.825486	−	0.564423i	$-0.190901\pi$
$578$	−0.00854060	+	0.671388i	−0.000355242	+	0.0279261i
$579$	9.91079	+	17.1660i	0.411878	+	0.713394i
$580$	−43.7627	+	8.87107i	−1.81715	+	0.368351i
$581$		0			0
$582$	−20.7283	−	36.9809i	−0.859215	−	1.53291i
$583$	1.00405	+	1.73907i	0.0415836	+	0.0720250i
$584$	−6.58096	−	4.14208i	−0.272322	−	0.171400i
$585$	12.1139	−	2.77818i	0.500849	−	0.114863i
$586$	−16.9678	−	10.0863i	−0.700932	−	0.416660i
$587$			30.4825i			1.25815i	0.777345	+	0.629074i	$0.216566\pi$
$587$			30.4825i			1.25815i	−0.777345	+	0.629074i	$0.783434\pi$
$588$		0			0
$589$	−50.5494			−2.08285
$590$	−3.07605	−	14.2419i	−0.126639	−	0.586329i
$591$	6.12281	−	10.6050i	0.251859	−	0.436232i
$592$	0.695289	−	13.6534i	0.0285762	−	0.561149i
$593$	8.11692	+	14.0589i	0.333322	+	0.577331i	0.983161	−	0.182741i	$-0.0584970\pi$
$593$	8.11692	+	14.0589i	0.333322	+	0.577331i	−0.649839	+	0.760072i	$0.725164\pi$
$594$	3.32781	−	1.86528i	0.136542	−	0.0765335i
$595$		0			0
$596$	−10.4874	+	17.1424i	−0.429582	+	0.702179i
$597$	−25.1883	+	14.5425i	−1.03089	+	0.595184i
$598$	−0.142975	+	11.2394i	−0.00584667	+	0.459615i
$599$	18.5297	+	10.6981i	0.757103	+	0.437114i	0.828255	−	0.560352i	$-0.189334\pi$
$599$	18.5297	+	10.6981i	0.757103	+	0.437114i	−0.0711514	+	0.997466i	$0.522667\pi$
$600$	−26.9468	+	11.7991i	−1.10010	+	0.481696i
$601$			6.40965i			0.261455i	0.991418	+	0.130728i	$0.0417313\pi$
$601$			6.40965i			0.261455i	−0.991418	+	0.130728i	$0.958269\pi$
$602$		0			0
$603$	−3.01262			−0.122683
$604$	−1.01204	+	39.7726i	−0.0411794	+	1.61832i
$605$	22.6651	−	5.19797i	0.921469	−	0.211327i
$606$	0.0633025	−	4.97629i	0.00257149	−	0.202148i
$607$	−39.5383	+	22.8274i	−1.60481	+	0.926537i	−0.614302	+	0.789071i	$0.710562\pi$
$607$	−39.5383	+	22.8274i	−1.60481	+	0.926537i	−0.990507	+	0.137466i	$0.956104\pi$
$608$	23.0039	+	15.3093i	0.932932	+	0.620873i
$609$		0			0
$610$	3.15550	−	9.82110i	0.127762	−	0.397645i
$611$	30.0128	−	17.3279i	1.21419	−	0.701011i
$612$	−5.30001	−	9.74421i	−0.214240	−	0.393886i
$613$	1.47202	+	0.849869i	0.0594541	+	0.0343259i	0.529432	−	0.848352i	$-0.322405\pi$
$613$	1.47202	+	0.849869i	0.0594541	+	0.0343259i	−0.469978	+	0.882678i	$0.655738\pi$
$614$	16.7696	−	28.2110i	0.676767	−	1.13850i
$615$	−9.58014	−	10.3034i	−0.386308	−	0.415474i
$616$		0			0
$617$			21.5543i			0.867744i	0.900975	+	0.433872i	$0.142853\pi$
$617$			21.5543i			0.867744i	−0.900975	+	0.433872i	$0.857147\pi$
$618$	1.39973	+	0.832051i	0.0563054	+	0.0334700i
$619$	−0.105260	+	0.182315i	−0.00423074	+	0.00732786i	−0.868133	−	0.496332i	$-0.834680\pi$
$619$	−0.105260	+	0.182315i	−0.00423074	+	0.00732786i	0.863902	+	0.503659i	$0.168013\pi$
$620$	14.7160	−	43.8772i	0.591007	−	1.76215i
$621$	5.71867	−	3.30168i	0.229482	−	0.132492i
$622$	5.87788	−	3.29463i	0.235681	−	0.132102i
$623$		0			0
$624$	31.0340	−	15.8705i	1.24235	−	0.635327i
$625$	9.23021	+	23.2337i	0.369208	+	0.929347i
$626$	0.00179047	−	0.140752i	7.15617e−5	−	0.00562556i
$627$	3.93752	−	6.81998i	0.157249	−	0.272364i
$628$	−27.6595	−	0.703816i	−1.10373	−	0.0280853i
$629$		−	14.2872i		−	0.569669i
$630$		0			0
$631$			30.0918i			1.19793i	0.800774	+	0.598967i	$0.204422\pi$
$631$			30.0918i			1.19793i	−0.800774	+	0.598967i	$0.795578\pi$
$632$	18.7581	+	35.5575i	0.746158	+	1.41440i
$633$	21.3101	−	36.9101i	0.846999	−	1.46705i
$634$	−25.0090	−	0.318135i	−0.993236	−	0.0126348i
$635$	−10.0673	+	32.7582i	−0.399508	+	1.29997i
$636$	5.62510	−	9.19459i	0.223050	−	0.364589i
$637$		0			0
$638$	5.35099	+	9.54660i	0.211848	+	0.377953i
$639$	5.07009	−	2.92722i	0.200570	−	0.115799i
$640$	−19.9854	+	15.5107i	−0.789994	+	0.613114i
$641$	14.0965	−	24.4159i	0.556780	−	0.964371i	−0.440983	−	0.897516i	$-0.645370\pi$
$641$	14.0965	−	24.4159i	0.556780	−	0.964371i	0.997763	−	0.0668557i	$-0.0212967\pi$
$642$	12.1624	−	20.4604i	0.480013	−	0.807508i
$643$		−	0.884403i		−	0.0348774i	−0.999848	−	0.0174387i	$-0.994449\pi$
$643$		−	0.884403i		−	0.0348774i	0.999848	−	0.0174387i	$-0.00555120\pi$
$644$		0			0
$645$	31.3053	−	29.1077i	1.23265	−	1.14611i
$646$	24.8233	+	14.7559i	0.976660	+	0.580563i
$647$	27.5619	+	15.9129i	1.08357	+	0.625599i	0.931857	−	0.362826i	$-0.118188\pi$
$647$	27.5619	+	15.9129i	1.08357	+	0.625599i	0.151712	+	0.988425i	$0.451521\pi$
$648$	−26.8579	−	16.9044i	−1.05508	−	0.664068i
$649$	−3.09262	+	1.78552i	−0.121396	+	0.0700879i
$650$	−12.5682	−	26.8246i	−0.492966	−	1.05215i
$651$		0			0
$652$	−8.42252	+	13.7671i	−0.329851	+	0.539163i
$653$	27.4461	−	15.8460i	1.07405	−	0.620101i	0.144763	−	0.989466i	$-0.453758\pi$
$653$	27.4461	−	15.8460i	1.07405	−	0.620101i	0.929284	+	0.369365i	$0.120425\pi$
$654$	40.5997	+	0.516460i	1.58757	+	0.0201952i
$655$	−30.4861	+	6.99161i	−1.19119	+	0.273185i
$656$	−10.1571	−	6.57474i	−0.396567	−	0.256700i
$657$	3.64751			0.142303
$658$		0			0
$659$		−	21.5313i		−	0.838739i	−0.907816	−	0.419370i	$-0.862251\pi$
$659$		−	21.5313i		−	0.838739i	0.907816	−	0.419370i	$-0.137749\pi$
$660$	4.77350	+	5.40323i	0.185808	+	0.210320i
$661$	−18.3387	−	10.5879i	−0.713295	−	0.411821i	0.0989851	−	0.995089i	$-0.468440\pi$
$661$	−18.3387	−	10.5879i	−0.713295	−	0.411821i	−0.812280	+	0.583268i	$0.801774\pi$
$662$	5.85710	+	0.0745070i	0.227643	+	0.00289580i
$663$	31.5472	−	18.2138i	1.22519	−	0.707365i
$664$	−6.67476	−	0.254835i	−0.259031	−	0.00988951i
$665$		0			0
$666$	3.13547	+	5.59393i	0.121497	+	0.216760i
$667$	9.47162	+	16.4053i	0.366742	+	0.635217i
$668$	−33.2646	+	18.0931i	−1.28705	+	0.700043i
$669$	5.18443	−	8.97969i	0.200442	−	0.347175i
$670$	1.51595	+	7.01871i	0.0585661	+	0.271156i
$671$	−2.52825			−0.0976022
$672$		0			0
$673$		−	33.5756i		−	1.29424i	−0.762387	−	0.647121i	$-0.775973\pi$
$673$		−	33.5756i		−	1.29424i	0.762387	−	0.647121i	$-0.224027\pi$
$674$	20.5473	−	34.5660i	0.791454	−	1.33143i
$675$	−9.77330	+	14.3990i	−0.376174	+	0.554219i
$676$	4.34847	+	7.99478i	0.167249	+	0.307491i
$677$	10.3498	+	17.9264i	0.397775	+	0.688966i	0.993451	−	0.114259i	$-0.0364493\pi$
$677$	10.3498	+	17.9264i	0.397775	+	0.688966i	−0.595676	+	0.803225i	$0.703116\pi$
$678$	−33.3615	+	18.6996i	−1.28124	+	0.718153i
$679$		0			0
$680$	−20.0348	+	17.2511i	−0.768299	+	0.661548i
$681$	4.33610	+	7.51034i	0.166160	+	0.287797i
$682$	−11.3417	−	0.144276i	−0.434297	−	0.00552460i
$683$	−14.0608	+	24.3540i	−0.538021	+	0.931880i	0.460989	+	0.887406i	$0.347495\pi$
$683$	−14.0608	+	24.3540i	−0.538021	+	0.931880i	−0.999011	+	0.0444746i	$0.985839\pi$
$684$	−12.9575	−	0.329713i	−0.495442	−	0.0126069i
$685$	−5.72018	+	5.31863i	−0.218557	+	0.203214i
$686$		0			0
$687$	2.10712			0.0803915
$688$	19.9763	−	30.8606i	0.761589	−	1.17655i
$689$	9.40013	+	5.42717i	0.358117	+	0.206759i
$690$	8.38087	+	9.24674i	0.319054	+	0.352017i
$691$	−19.6729	−	34.0745i	−0.748393	−	1.29626i	−0.948593	−	0.316500i	$-0.897492\pi$
$691$	−19.6729	−	34.0745i	−0.748393	−	1.29626i	0.200199	−	0.979755i	$-0.435841\pi$
$692$	9.19923	−	15.0367i	0.349702	−	0.571611i
$693$		0			0
$694$	26.4889	−	14.8474i	1.00550	−	0.563598i
$695$	−8.65303	+	28.1563i	−0.328228	+	1.06803i
$696$	31.2911	−	49.7156i	1.18609	−	1.88447i
$697$	−10.9506	−	6.32232i	−0.414783	−	0.239475i
$698$	−10.0301	+	16.8733i	−0.379645	+	0.638663i
$699$	41.0290			1.55186
$700$		0			0
$701$	−14.6649			−0.553887			−0.276944	−	0.960886i	$-0.589322\pi$
$701$	−14.6649			−0.553887			−0.276944	+	0.960886i	$0.589322\pi$
$702$	10.5366	−	17.7254i	0.397680	−	0.669002i
$703$	−14.4583	−	8.34750i	−0.545305	−	0.314832i
$704$	5.11766	+	3.50058i	0.192879	+	0.131933i
$705$	11.3030	−	36.7790i	0.425694	−	1.38518i
$706$	−13.5286	+	7.58295i	−0.509155	+	0.285388i
$707$		0			0
$708$	16.3509	+	10.0032i	0.614504	+	0.375943i
$709$	0.829336	+	1.43645i	0.0311464	+	0.0539471i	0.881178	−	0.472784i	$-0.156751\pi$
$709$	0.829336	+	1.43645i	0.0311464	+	0.0539471i	−0.850032	+	0.526731i	$0.823418\pi$
$710$	−9.37100	−	10.3392i	−0.351687	−	0.388022i
$711$	−16.3313	−	9.42888i	−0.612472	−	0.353611i
$712$	−18.9438	−	35.9095i	−0.709949	−	1.34577i
$713$	−19.6333			−0.735272
$714$		0			0
$715$	−5.31706	+	4.94381i	−0.198847	+	0.184888i
$716$	0.294383	−	11.5691i	0.0110016	−	0.432356i
$717$	−22.4364	+	38.8610i	−0.837902	+	1.45129i
$718$	−36.9896	−	0.470537i	−1.38044	−	0.0175603i
$719$	−11.0891	−	19.2068i	−0.413552	−	0.716294i	0.581723	−	0.813387i	$-0.302379\pi$
$719$	−11.0891	−	19.2068i	−0.413552	−	0.716294i	−0.995275	+	0.0970934i	$0.969045\pi$
$720$	4.05838	−	11.1512i	0.151247	−	0.415581i
$721$		0			0
$722$	5.99679	−	3.36128i	0.223177	−	0.125094i
$723$	10.8198	+	18.7405i	0.402394	+	0.696966i
$724$	2.16387	−	1.17696i	0.0804197	−	0.0437414i
$725$	−41.3069	−	28.0370i	−1.53410	−	1.04127i
$726$	−15.6315	+	26.2963i	−0.580138	+	0.975946i
$727$		−	31.0654i		−	1.15215i	−0.817396	−	0.576076i	$-0.804583\pi$
$727$		−	31.0654i		−	1.15215i	0.817396	−	0.576076i	$-0.195417\pi$
$728$		0			0
$729$	−6.83323			−0.253083
$730$	−1.83542	−	8.49785i	−0.0679320	−	0.314520i
$731$	19.2094	−	33.2716i	0.710484	−	1.23059i
$732$	6.48423	+	11.9214i	0.239664	+	0.440628i
$733$	−7.90070	−	13.6844i	−0.291819	−	0.505445i	0.682421	−	0.730959i	$-0.260927\pi$
$733$	−7.90070	−	13.6844i	−0.291819	−	0.505445i	−0.974240	+	0.225514i	$0.927594\pi$
$734$	−4.52237	−	8.06826i	−0.166924	−	0.297805i
$735$		0			0
$736$	8.93466	+	5.94608i	0.329336	+	0.219175i
$737$	1.52411	−	0.879944i	0.0561413	−	0.0324132i
$738$	5.67502	+	0.0721908i	0.208900	+	0.00265738i
$739$	6.77920	+	3.91397i	0.249377	+	0.143978i	0.619479	−	0.785013i	$-0.287344\pi$
$739$	6.77920	+	3.91397i	0.249377	+	0.143978i	−0.370102	+	0.928991i	$0.620677\pi$
$740$	11.4548	−	10.1198i	0.421086	−	0.372010i
$741$		−	42.5666i		−	1.56372i
$742$		0			0
$743$	−37.7406			−1.38457			−0.692284	−	0.721625i	$-0.743395\pi$
$743$	−37.7406			−1.38457			−0.692284	+	0.721625i	$0.743395\pi$
$744$	28.4078	+	53.8493i	1.04148	+	1.97421i
$745$	−21.8994	+	5.02235i	−0.802332	+	0.184005i
$746$	3.93032	+	0.0499969i	0.143899	+	0.00183052i
$747$	2.71347	−	1.56662i	0.0992805	−	0.0573196i
$748$	5.52746	+	3.38161i	0.202104	+	0.123644i
$749$		0			0
$750$	−30.4987	−	12.3091i	−1.11366	−	0.449465i
$751$	2.38279	−	1.37570i	0.0869491	−	0.0502001i	−0.455895	−	0.890034i	$-0.650681\pi$
$751$	2.38279	−	1.37570i	0.0869491	−	0.0502001i	0.542844	+	0.839833i	$0.317347\pi$
$752$	1.68289	−	33.0468i	0.0613686	−	1.20509i
$753$	−10.8669	−	6.27401i	−0.396012	−	0.228638i
$754$	50.8494	+	30.2268i	1.85183	+	1.10079i
$755$	−32.5758	+	30.2890i	−1.18555	+	1.10233i
$756$		0			0
$757$			19.3492i			0.703257i	0.936140	+	0.351628i	$0.114372\pi$
$757$			19.3492i			0.703257i	−0.936140	+	0.351628i	$0.885628\pi$
$758$	5.08731	−	8.55820i	0.184779	−	0.310848i
$759$	1.52932	−	2.64886i	0.0555109	−	0.0961476i
$760$	5.75203	+	30.3538i	0.208648	+	1.10105i
$761$	−13.2370	+	7.64240i	−0.479842	+	0.277037i	−0.720351	−	0.693610i	$-0.756019\pi$
$761$	−13.2370	+	7.64240i	−0.479842	+	0.277037i	0.240509	+	0.970647i	$0.422686\pi$
$762$	−22.0438	−	39.3280i	−0.798564	−	1.42470i
$763$		0			0
$764$	29.7596	+	18.2064i	1.07666	+	0.658686i
$765$	3.64311	−	11.8544i	0.131717	−	0.428598i
$766$	−7.98651	−	0.101595i	−0.288564	−	0.00367077i
$767$	−9.65122	+	16.7164i	−0.348485	+	0.603594i
$768$	3.38090	−	33.1091i	0.121998	−	1.19472i
$769$			8.96913i			0.323435i	0.986837	+	0.161718i	$0.0517033\pi$
$769$			8.96913i			0.323435i	−0.986837	+	0.161718i	$0.948297\pi$
$770$		0			0
$771$			3.36893i			0.121329i
$772$	−0.484799	+	19.0523i	−0.0174483	+	0.685707i
$773$	−3.34226	+	5.78897i	−0.120213	+	0.208215i	−0.919852	−	0.392267i	$-0.871691\pi$
$773$	−3.34226	+	5.78897i	−0.120213	+	0.208215i	0.799639	+	0.600481i	$0.205024\pi$
$774$	−0.219340	+	17.2426i	−0.00788402	+	0.619774i
$775$	46.5710	−	22.5468i	1.67288	−	0.809905i
$776$	1.55511	−	40.7322i	0.0558251	−	1.46220i
$777$		0			0
$778$	23.6682	−	13.2663i	0.848544	−	0.475620i
$779$	−12.7961	+	7.38781i	−0.458466	+	0.264696i
$780$	36.9481	+	12.3920i	1.32295	+	0.443705i
$781$	−1.71000	+	2.96180i	−0.0611886	+	0.105982i
$782$	9.64131	+	5.73115i	0.344773	+	0.204946i
$783$		−	34.7517i		−	1.24193i
$784$		0			0
$785$	−21.0642	−	22.6546i	−0.751814	−	0.808576i
$786$	21.0254	−	35.3702i	0.749950	−	1.26161i
$787$	12.6092	+	7.27993i	0.449470	+	0.259502i	0.707606	−	0.706607i	$-0.249775\pi$
$787$	12.6092	+	7.27993i	0.449470	+	0.259502i	−0.258136	+	0.966109i	$0.583108\pi$
$788$	10.3432	−	5.62580i	0.368461	−	0.200411i
$789$	−9.06300	+	5.23253i	−0.322651	+	0.186283i
$790$	−13.7492	+	42.7927i	−0.489175	+	1.52250i
$791$		0			0
$792$	−2.90631	−	0.110960i	−0.103271	−	0.00394279i
$793$	−11.8350	+	6.83294i	−0.420273	+	0.242645i
$794$	−0.276274	+	21.7183i	−0.00980460	+	0.770753i
$795$	11.7461	−	2.69382i	0.416592	−	0.0955401i
$796$	−27.9562	−	0.711365i	−0.990880	−	0.0252137i
$797$	15.2657			0.540739			0.270369	−	0.962757i	$-0.412854\pi$
$797$	15.2657			0.540739			0.270369	+	0.962757i	$0.412854\pi$
$798$		0			0
$799$		−	34.5810i		−	1.22339i
$800$	−28.0219	−	3.84382i	−0.990723	−	0.135900i
$801$	16.4930	+	9.52221i	0.582750	+	0.336451i
$802$	−0.161020	+	12.6580i	−0.00568583	+	0.446971i
$803$	−1.84530	+	1.06539i	−0.0651194	+	0.0375967i
$804$	−8.05807	−	4.92980i	−0.284186	−	0.173861i
$805$		0			0
$806$	−53.4815	+	29.9771i	−1.88381	+	1.05590i
$807$	13.0183	+	22.5484i	0.458267	+	0.793743i
$808$	2.54891	−	4.04972i	0.0896702	−	0.142469i
$809$	21.2493	−	36.8049i	0.747086	−	1.29399i	−0.202128	−	0.979359i	$-0.564786\pi$
$809$	21.2493	−	36.8049i	0.747086	−	1.29399i	0.949214	−	0.314632i	$-0.101881\pi$
$810$	−7.49062	−	34.6810i	−0.263194	−	1.21857i
$811$	−0.418791			−0.0147057			−0.00735287	−	0.999973i	$-0.502341\pi$
$811$	−0.418791			−0.0147057			−0.00735287	+	0.999973i	$0.502341\pi$
$812$		0			0
$813$		−	7.61664i		−	0.267127i
$814$	−3.22017	−	1.91418i	−0.112867	−	0.0670921i
$815$	−17.5876	+	4.03349i	−0.616066	+	0.141287i
$816$	1.76893	−	34.7363i	0.0619248	−	1.21601i
$817$	−22.4467	−	38.8788i	−0.785309	−	1.36020i
$818$	−3.11752	−	5.56191i	−0.109002	−	0.194468i
$819$		0			0
$820$	−2.68747	−	13.2578i	−0.0938506	−	0.462983i
$821$	5.73024	+	9.92506i	0.199987	+	0.346387i	0.948524	−	0.316706i	$-0.102577\pi$
$821$	5.73024	+	9.92506i	0.199987	+	0.346387i	−0.748537	+	0.663093i	$0.769243\pi$
$822$	0.130703	−	10.2747i	0.00455878	−	0.358372i
$823$	−1.29483	+	2.24271i	−0.0451349	+	0.0781760i	−0.887710	−	0.460402i	$-0.847705\pi$
$823$	−1.29483	+	2.24271i	−0.0451349	+	0.0781760i	0.842575	+	0.538578i	$0.181038\pi$
$824$	0.730535	+	1.38479i	0.0254494	+	0.0482413i
$825$	−0.585671	+	8.03949i	−0.0203904	+	0.279899i
$826$		0			0
$827$	31.8310			1.10687			0.553437	−	0.832891i	$-0.313316\pi$
$827$	31.8310			1.10687			0.553437	+	0.832891i	$0.313316\pi$
$828$	−5.03266	−	0.128060i	−0.174897	−	0.00445038i
$829$	27.3366	+	15.7828i	0.949439	+	0.548159i	0.892907	−	0.450242i	$-0.148662\pi$
$829$	27.3366	+	15.7828i	0.949439	+	0.548159i	0.0565326	+	0.998401i	$0.481996\pi$
$830$	−5.01527	−	5.53342i	−0.174083	−	0.192068i
$831$	−26.9284	−	46.6413i	−0.934135	−	1.61797i
$832$	33.4170	+	2.55537i	1.15853	+	0.0885916i
$833$		0			0
$834$	−18.9471	−	33.8031i	−0.656084	−	1.17051i
$835$	−40.4684	−	12.4368i	−1.40047	−	0.430393i
$836$	6.65160	−	3.61790i	0.230050	−	0.125128i
$837$	31.1922	+	18.0088i	1.07816	+	0.622475i
$838$	35.3226	+	20.9970i	1.22020	+	0.725330i
$839$	−38.7072			−1.33632			−0.668160	−	0.744018i	$-0.732918\pi$
$839$	−38.7072			−1.33632			−0.668160	+	0.744018i	$0.732918\pi$
$840$		0			0
$841$	70.6933			2.43770
$842$	14.5110	+	8.62585i	0.500081	+	0.297267i
$843$	26.4948	+	15.2968i	0.912529	+	0.526849i
$844$	35.9988	−	19.5803i	1.23913	−	0.673980i
$845$	−2.98905	+	9.72613i	−0.102826	+	0.334589i
$846$	7.58914	+	13.5396i	0.260920	+	0.465502i
$847$		0			0
$848$	9.22725	−	4.71873i	0.316865	−	0.162042i
$849$	−31.4285	−	54.4358i	−1.07862	−	1.86823i
$850$	−29.4513	−	2.52248i	−1.01017	−	0.0865205i
$851$	−5.61557	−	3.24215i	−0.192499	−	0.111139i
$852$	18.3514	+	0.466964i	0.628708	+	0.0159979i
$853$	−23.0187			−0.788145			−0.394073	−	0.919079i	$-0.628934\pi$
$853$	−23.0187			−0.788145			−0.394073	+	0.919079i	$0.628934\pi$
$854$		0			0
$855$	−9.86783	−	10.6128i	−0.337473	−	0.362952i
$856$	20.2420	−	10.6785i	0.691857	−	0.364984i
$857$	−11.4647	+	19.8574i	−0.391626	+	0.678316i	−0.992664	−	0.120904i	$-0.961421\pi$
$857$	−11.4647	+	19.8574i	−0.391626	+	0.678316i	0.601038	+	0.799220i	$0.294754\pi$
$858$	0.121492	−	9.55062i	0.00414765	−	0.326053i
$859$	−17.6510	−	30.5724i	−0.602243	−	1.04312i	−0.992481	−	0.122401i	$-0.960940\pi$
$859$	−17.6510	−	30.5724i	−0.602243	−	1.04312i	0.390238	−	0.920714i	$-0.372393\pi$
$860$	40.2817	−	8.16545i	1.37359	−	0.278440i
$861$		0			0
$862$	8.98303	+	16.0265i	0.305963	+	0.545863i
$863$	4.14388	+	7.17741i	0.141059	+	0.244322i	0.927896	−	0.372840i	$-0.121616\pi$
$863$	4.14388	+	7.17741i	0.141059	+	0.244322i	−0.786837	+	0.617161i	$0.788283\pi$
$864$	−8.74075	−	17.6422i	−0.297366	−	0.600199i
$865$	19.2095	−	4.40545i	0.653142	−	0.149790i
$866$	−18.8386	−	11.1984i	−0.640162	−	0.380536i
$867$		−	0.987585i		−	0.0335401i
$868$		0			0
$869$	11.0162			0.373698
$870$	64.1967	−	13.8656i	2.17647	−	0.470089i
$871$	4.75633	−	8.23820i	0.161162	−	0.279141i
$872$	33.0401	+	20.7955i	1.11888	+	0.704226i
$873$	9.56017	+	16.5587i	0.323563	+	0.560427i
$874$	11.4328	−	6.40826i	0.386722	−	0.216763i
$875$		0			0
$876$	9.75625	+	5.96872i	0.329633	+	0.201664i
$877$	2.53119	−	1.46138i	0.0854721	−	0.0493473i	−0.456655	−	0.889644i	$-0.650953\pi$
$877$	2.53119	−	1.46138i	0.0854721	−	0.0493473i	0.542127	+	0.840297i	$0.317619\pi$
$878$	0.0457330	−	3.59513i	0.00154341	−	0.121330i
$879$	25.1436	+	14.5166i	0.848071	+	0.489634i
$880$	1.20394	+	6.82687i	0.0405849	+	0.230134i
$881$			9.44070i			0.318065i	0.987273	+	0.159033i	$0.0508375\pi$
$881$			9.44070i			0.318065i	−0.987273	+	0.159033i	$0.949162\pi$
$882$		0			0
$883$	7.11787			0.239535			0.119768	−	0.992802i	$-0.461785\pi$
$883$	7.11787			0.239535			0.119768	+	0.992802i	$0.461785\pi$
$884$	35.0138	+	0.890951i	1.17764	+	0.0299659i
$885$	4.79047	+	20.8883i	0.161030	+	0.702152i
$886$	−0.541400	+	42.5602i	−0.0181887	+	1.42984i
$887$	−7.27170	+	4.19832i	−0.244160	+	0.140966i	−0.617087	−	0.786895i	$-0.711687\pi$
$887$	−7.27170	+	4.19832i	−0.244160	+	0.140966i	0.372927	+	0.927861i	$0.378354\pi$
$888$	−0.767139	+	20.0933i	−0.0257435	+	0.674287i
$889$		0			0
$890$	13.8853	−	43.2163i	0.465437	−	1.44861i
$891$	−7.53095	+	4.34800i	−0.252296	+	0.145663i
$892$	8.75798	−	4.76359i	0.293239	−	0.159497i
$893$	−34.9951	−	20.2044i	−1.17107	−	0.676115i
$894$	15.1034	−	25.4079i	0.505132	−	0.849766i
$895$	9.47565	−	8.81047i	0.316736	−	0.294502i
$896$		0			0
$897$		−	16.5328i		−	0.552013i
$898$	−7.78962	−	4.63044i	−0.259943	−	0.154520i
$899$	−51.6624	+	89.4819i	−1.72304	+	2.98439i
$900$	12.0847	−	5.47573i	0.402825	−	0.182524i
$901$	9.37985	−	5.41546i	0.312488	−	0.180415i
$902$	−2.89212	+	1.62107i	−0.0962971	+	0.0539758i
$903$		0			0
$904$	−36.7456	−	1.40291i	−1.22214	−	0.0466600i
$905$	2.63248	+	0.809017i	0.0875066	+	0.0268926i
$906$	0.744336	−	58.5133i	0.0247289	−	1.94397i
$907$	−17.8094	+	30.8468i	−0.591351	+	1.02425i	0.402700	+	0.915332i	$0.368072\pi$
$907$	−17.8094	+	30.8468i	−0.591351	+	1.02425i	−0.994051	+	0.108918i	$0.965261\pi$
$908$	−0.212106	+	8.33562i	−0.00703898	+	0.276627i
$909$			2.24457i			0.0744476i
$910$		0			0
$911$		−	54.7177i		−	1.81288i	−0.422338	−	0.906438i	$-0.638791\pi$
$911$		−	54.7177i		−	1.81288i	0.422338	−	0.906438i	$-0.361209\pi$
$912$	−34.1188	−	22.0853i	−1.12979	−	0.731317i
$913$	−0.915175	+	1.58513i	−0.0302879	+	0.0524601i
$914$	−4.46327	−	0.0567764i	−0.147632	−	0.00187800i
$915$	−4.45712	+	14.5031i	−0.147348	+	0.479459i
$916$	1.72823	+	1.05730i	0.0571022	+	0.0349342i
$917$		0			0
$918$	−10.0606	−	17.9489i	−0.332049	−	0.592402i
$919$	−7.53500	+	4.35034i	−0.248557	+	0.143504i	−0.619103	−	0.785310i	$-0.712504\pi$
$919$	−7.53500	+	4.35034i	−0.248557	+	0.143504i	0.370546	+	0.928814i	$0.379170\pi$
$920$	2.23407	+	11.7894i	0.0736553	+	0.388684i
$921$	−24.1357	+	41.8042i	−0.795297	+	1.37750i
$922$	−7.14080	+	12.0127i	−0.235170	+	0.395617i
$923$			18.4860i			0.608473i
$924$		0			0
$925$	17.0436	+	1.24162i	0.560392	+	0.0408241i
$926$	−11.6121	−	6.90266i	−0.381597	−	0.226835i
$927$	−0.636022	−	0.367207i	−0.0208897	−	0.0120607i
$928$	50.6106	−	25.0749i	1.66138	−	0.823123i
$929$	−44.3049	+	25.5794i	−1.45360	+	0.839234i	−0.998683	−	0.0513027i	$-0.983663\pi$
$929$	−44.3049	+	25.5794i	−1.45360	+	0.839234i	−0.454912	+	0.890536i	$0.650329\pi$
$930$	−20.8222	+	64.8065i	−0.682787	+	2.12509i
$931$		0			0
$932$	33.6514	+	20.5874i	1.10229	+	0.674361i
$933$	−8.58308	+	4.95545i	−0.280998	+	0.162234i
$934$	−19.0414	−	0.242222i	−0.623053	−	0.00792574i
$935$	1.61943	+	7.06134i	0.0529610	+	0.230931i
$936$	−13.9046	+	7.33528i	−0.454487	+	0.239761i
$937$	3.45977			0.113026			0.0565129	−	0.998402i	$-0.482002\pi$
$937$	3.45977			0.113026			0.0565129	+	0.998402i	$0.482002\pi$
$938$		0			0
$939$			0.207040i			0.00675649i
$940$	27.7254	−	24.4940i	0.904301	−	0.798908i
$941$	−30.6903	−	17.7190i	−1.00047	−	0.577624i	−0.0920852	−	0.995751i	$-0.529353\pi$
$941$	−30.6903	−	17.7190i	−1.00047	−	0.577624i	−0.908388	+	0.418127i	$0.862687\pi$
$942$	40.6926	+	0.517643i	1.32584	+	0.0168657i
$943$	−4.96996	+	2.86941i	−0.161844	+	0.0934407i
$944$	8.39139	+	16.4090i	0.273116	+	0.534066i
$945$		0			0
$946$	−4.92536	−	8.78724i	−0.160137	−	0.285698i
$947$	23.7352	+	41.1105i	0.771289	+	1.33591i	0.936857	+	0.349714i	$0.113721\pi$
$947$	23.7352	+	41.1105i	0.771289	+	1.33591i	−0.165567	+	0.986199i	$0.552945\pi$
$948$	−28.2532	−	51.9443i	−0.917622	−	1.68707i
$949$	−5.75869	+	9.97435i	−0.186935	+	0.323781i
$950$	−19.7600	+	28.3301i	−0.641099	+	0.919150i
$951$	36.7873			1.19291
$952$		0			0
$953$			40.4830i			1.31137i	0.755033	+	0.655687i	$0.227621\pi$
$953$			40.4830i			1.31137i	−0.755033	+	0.655687i	$0.772379\pi$
$954$	−2.48405	+	4.17884i	−0.0804242	+	0.135295i
$955$	8.71894	+	38.0180i	0.282138	+	1.23023i
$956$	−37.9015	+	20.6151i	−1.22582	+	0.666741i
$957$	−8.04842	−	13.9403i	−0.260169	−	0.450625i
$958$	−17.3006	+	9.69719i	−0.558956	+	0.313302i
$959$		0			0
$960$	29.1028	−	23.1858i	0.939290	−	0.748319i
$961$	−38.0443	−	65.8946i	−1.22723	−	2.12563i
$962$	−20.2472	−	0.257561i	−0.652797	−	0.00830410i
$963$	−5.36762	+	9.29699i	−0.172969	+	0.299591i
$964$	−0.529266	+	20.7998i	−0.0170465	+	0.669917i
$965$	−15.6048	+	14.5093i	−0.502336	+	0.467072i
$966$		0			0
$967$	−24.5121			−0.788255			−0.394127	−	0.919056i	$-0.628953\pi$
$967$	−24.5121			−0.788255			−0.394127	+	0.919056i	$0.628953\pi$
$968$	−26.0155	+	13.7243i	−0.836171	+	0.441116i
$969$	−36.7842	−	21.2374i	−1.18168	−	0.682243i
$970$	33.7673	−	30.6053i	1.08420	−	0.982676i
$971$	−13.9269	−	24.1221i	−0.446935	−	0.774114i	0.551250	−	0.834340i	$-0.314151\pi$
$971$	−13.9269	−	24.1221i	−0.446935	−	0.774114i	−0.998185	+	0.0602263i	$0.980818\pi$
$972$	22.0029	+	13.4610i	0.705743	+	0.431762i
$973$		0			0
$974$	−37.4259	+	20.9777i	−1.19920	+	0.672169i
$975$	18.9862	+	39.2164i	0.608045	+	1.25593i
$976$	−0.663617	+	13.0314i	−0.0212418	+	0.417125i
$977$	40.6996	+	23.4979i	1.30209	+	0.751765i	0.980763	−	0.195202i	$-0.0625362\pi$
$977$	40.6996	+	23.4979i	1.30209	+	0.751765i	0.321332	+	0.946967i	$0.395870\pi$
$978$	12.1296	−	20.4052i	0.387862	−	0.652487i
$979$	−11.1252			−0.355563
$980$		0			0
$981$	−18.3125			−0.584675
$982$	6.45344	−	10.8564i	0.205938	−	0.346442i
$983$	−5.72631	−	3.30609i	−0.182641	−	0.105448i	0.405892	−	0.913921i	$-0.366961\pi$
$983$	−5.72631	−	3.30609i	−0.182641	−	0.105448i	−0.588533	+	0.808473i	$0.700294\pi$
$984$	15.0612	+	9.47959i	0.480135	+	0.302198i
$985$	12.5831	+	3.86706i	0.400931	+	0.123215i
$986$	51.4905	−	28.8611i	1.63979	−	0.919125i
$987$		0			0
$988$	21.3589	−	34.9125i	0.679517	−	1.11072i
$989$	−8.71823	−	15.1004i	−0.277223	−	0.480165i
$990$	−2.18374	−	2.40936i	−0.0694039	−	0.0765743i
$991$	−11.1544	−	6.44002i	−0.354333	−	0.204574i	0.312259	−	0.949997i	$-0.398914\pi$
$991$	−11.1544	−	6.44002i	−0.354333	−	0.204574i	−0.666592	+	0.745423i	$0.732248\pi$
$992$	−3.72061	+	58.4208i	−0.118130	+	1.85486i
$993$	−8.61556			−0.273407
$994$		0			0
$995$	−21.2901	−	22.8975i	−0.674943	−	0.725900i
$996$	9.82148	+	0.249915i	0.311205	+	0.00791885i
$997$	−14.7680	+	25.5789i	−0.467706	+	0.810091i	−0.999319	−	0.0368963i	$-0.988253\pi$
$997$	−14.7680	+	25.5789i	−0.467706	+	0.810091i	0.531613	+	0.846988i	$0.321586\pi$
$998$	7.81624	+	0.0994288i	0.247419	+	0.00314736i
$999$	5.94778	+	10.3019i	0.188180	+	0.325936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.s.g.619.8		96
4.3	odd	2	inner	980.2.s.g.619.25		96
5.4	even	2	inner	980.2.s.g.619.41		96
7.2	even	3	inner	980.2.s.g.19.23		96
7.3	odd	6		980.2.c.e.979.38	yes	48
7.4	even	3		980.2.c.e.979.37	yes	48
7.5	odd	6	inner	980.2.s.g.19.24		96
7.6	odd	2	inner	980.2.s.g.619.7		96
20.19	odd	2	inner	980.2.s.g.619.24		96
28.3	even	6		980.2.c.e.979.9	✓	48
28.11	odd	6		980.2.c.e.979.10	yes	48
28.19	even	6	inner	980.2.s.g.19.41		96
28.23	odd	6	inner	980.2.s.g.19.42		96
28.27	even	2	inner	980.2.s.g.619.26		96
35.4	even	6		980.2.c.e.979.12	yes	48
35.9	even	6	inner	980.2.s.g.19.26		96
35.19	odd	6	inner	980.2.s.g.19.25		96
35.24	odd	6		980.2.c.e.979.11	yes	48
35.34	odd	2	inner	980.2.s.g.619.42		96
140.19	even	6	inner	980.2.s.g.19.8		96
140.39	odd	6		980.2.c.e.979.39	yes	48
140.59	even	6		980.2.c.e.979.40	yes	48
140.79	odd	6	inner	980.2.s.g.19.7		96
140.139	even	2	inner	980.2.s.g.619.23		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.c.e.979.9	✓	48	28.3	even	6
980.2.c.e.979.10	yes	48	28.11	odd	6
980.2.c.e.979.11	yes	48	35.24	odd	6
980.2.c.e.979.12	yes	48	35.4	even	6
980.2.c.e.979.37	yes	48	7.4	even	3
980.2.c.e.979.38	yes	48	7.3	odd	6
980.2.c.e.979.39	yes	48	140.39	odd	6
980.2.c.e.979.40	yes	48	140.59	even	6
980.2.s.g.19.7		96	140.79	odd	6	inner
980.2.s.g.19.8		96	140.19	even	6	inner
980.2.s.g.19.23		96	7.2	even	3	inner
980.2.s.g.19.24		96	7.5	odd	6	inner
980.2.s.g.19.25		96	35.19	odd	6	inner
980.2.s.g.19.26		96	35.9	even	6	inner
980.2.s.g.19.41		96	28.19	even	6	inner
980.2.s.g.19.42		96	28.23	odd	6	inner
980.2.s.g.619.7		96	7.6	odd	2	inner
980.2.s.g.619.8		96	1.1	even	1	trivial
980.2.s.g.619.23		96	140.139	even	2	inner
980.2.s.g.619.24		96	20.19	odd	2	inner
980.2.s.g.619.25		96	4.3	odd	2	inner
980.2.s.g.619.26		96	28.27	even	2	inner
980.2.s.g.619.41		96	5.4	even	2	inner
980.2.s.g.619.42		96	35.34	odd	2	inner

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.21565 - 0.722628i) q^{2} +(1.80140 + 1.04004i) q^{3} +(0.955617 + 1.75693i) q^{4} +(-0.656871 + 2.13741i) q^{5} +(-1.43832 - 2.56607i) q^{6} +(0.107908 - 2.82637i) q^{8} +(0.663371 + 1.14899i) q^{9} +O(q^{10})\)	\(q+(-1.21565 - 0.722628i) q^{2} +(1.80140 + 1.04004i) q^{3} +(0.955617 + 1.75693i) q^{4} +(-0.656871 + 2.13741i) q^{5} +(-1.43832 - 2.56607i) q^{6} +(0.107908 - 2.82637i) q^{8} +(0.663371 + 1.14899i) q^{9} +(2.34308 - 2.12367i) q^{10} +(-0.671209 - 0.387523i) q^{11} +(-0.105824 + 4.15882i) q^{12} -4.18932 q^{13} +(-3.40628 + 3.16717i) q^{15} +(-2.17359 + 3.35790i) q^{16} +(-2.09014 + 3.62023i) q^{17} +(0.0238661 - 1.87615i) q^{18} +(2.44239 + 4.23034i) q^{19} +(-4.38299 + 0.888471i) q^{20} +(0.535922 + 0.956127i) q^{22} +(0.948617 + 1.64305i) q^{23} +(3.13392 - 4.97920i) q^{24} +(-4.13704 - 2.80801i) q^{25} +(5.09276 + 3.02732i) q^{26} -3.48051i q^{27} +9.98465 q^{29} +(6.42954 - 1.38869i) q^{30} +(-5.17418 + 8.96194i) q^{31} +(5.06884 - 2.51134i) q^{32} +(-0.806079 - 1.39617i) q^{33} +(5.15697 - 2.89055i) q^{34} +(-1.38477 + 2.26349i) q^{36} +(-2.95987 + 1.70888i) q^{37} +(0.0878697 - 6.90756i) q^{38} +(-7.54666 - 4.35707i) q^{39} +(5.97023 + 2.08720i) q^{40} +3.02483i q^{41} -9.19046 q^{43} +(0.0394304 - 1.54959i) q^{44} +(-2.89162 + 0.663156i) q^{45} +(0.0341284 - 2.68288i) q^{46} +(-7.16411 + 4.13620i) q^{47} +(-7.40787 + 3.78831i) q^{48} +(3.00006 + 6.40310i) q^{50} +(-7.53038 + 4.34767i) q^{51} +(-4.00339 - 7.36034i) q^{52} +(-2.24383 - 1.29548i) q^{53} +(-2.51512 + 4.23109i) q^{54} +(1.26919 - 1.18010i) q^{55} +10.1607i q^{57} +(-12.1379 - 7.21519i) q^{58} +(2.30377 - 3.99024i) q^{59} +(-8.81959 - 2.95800i) q^{60} +(2.82504 - 1.63104i) q^{61} +(12.7662 - 7.15559i) q^{62} +(-7.97671 - 0.609973i) q^{64} +(2.75185 - 8.95430i) q^{65} +(-0.0290003 + 2.27975i) q^{66} +(-1.13535 + 1.96648i) q^{67} +(-8.35786 - 0.212672i) q^{68} +3.94640i q^{69} -4.41264i q^{71} +(3.31906 - 1.75095i) q^{72} +(1.37461 - 2.38090i) q^{73} +(4.83305 + 0.0614803i) q^{74} +(-4.53204 - 9.36105i) q^{75} +(-5.09842 + 8.33369i) q^{76} +(6.02557 + 10.7501i) q^{78} +(-12.3093 + 7.10679i) q^{79} +(-5.74944 - 6.85156i) q^{80} +(5.60999 - 9.71679i) q^{81} +(2.18583 - 3.67714i) q^{82} -2.36160i q^{83} +(-6.36497 - 6.84552i) q^{85} +(11.1724 + 6.64128i) q^{86} +(17.9864 + 10.3845i) q^{87} +(-1.16771 + 1.85527i) q^{88} +(12.4312 - 7.17714i) q^{89} +(3.99442 + 1.28340i) q^{90} +(-1.98021 + 3.23678i) q^{92} +(-18.6416 + 10.7627i) q^{93} +(11.6980 + 0.148808i) q^{94} +(-10.6463 + 2.44160i) q^{95} +(11.7429 + 0.747866i) q^{96} +14.4115 q^{97} -1.02829i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 16 q^{4} + 64 q^{9}+O(q^{10}) \) 96 * q - 16 * q^4 + 64 * q^9	\( 96 q - 16 q^{4} + 64 q^{9} - 16 q^{16} + 16 q^{25} - 96 q^{29} + 8 q^{30} + 352 q^{36} + 48 q^{44} + 32 q^{46} + 64 q^{50} - 24 q^{60} - 160 q^{64} + 16 q^{65} + 112 q^{74} + 48 q^{81} - 128 q^{85} + 112 q^{86}+O(q^{100}) \) 96 * q - 16 * q^4 + 64 * q^9 - 16 * q^16 + 16 * q^25 - 96 * q^29 + 8 * q^30 + 352 * q^36 + 48 * q^44 + 32 * q^46 + 64 * q^50 - 24 * q^60 - 160 * q^64 + 16 * q^65 + 112 * q^74 + 48 * q^81 - 128 * q^85 + 112 * q^86

Introduction

L-functions

Modular forms

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