LMFDB - Embedded newform 980.2.x.n.667.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(67,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("980.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, 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:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			667.18
Character	$\chi$	$=$	980.667
Dual form			980.2.x.n.263.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.604271 - 1.27862i) q^{2} +(0.844627 - 3.15219i) q^{3} +(-1.26971 - 1.54526i) q^{4} +(-1.79332 + 1.33567i) q^{5} +(-3.52006 - 2.98473i) q^{6} +(-2.74304 + 0.689718i) q^{8} +(-6.62484 - 3.82485i) q^{9} +O(q^{10})$	\(q+(0.604271 - 1.27862i) q^{2} +(0.844627 - 3.15219i) q^{3} +(-1.26971 - 1.54526i) q^{4} +(-1.79332 + 1.33567i) q^{5} +(-3.52006 - 2.98473i) q^{6} +(-2.74304 + 0.689718i) q^{8} +(-6.62484 - 3.82485i) q^{9} +(0.624159 + 3.10007i) q^{10} +(-1.96875 + 1.13666i) q^{11} +(-5.94339 + 2.69721i) q^{12} +(1.38240 - 1.38240i) q^{13} +(2.69561 + 6.78102i) q^{15} +(-0.775657 + 3.92407i) q^{16} +(0.0499069 - 0.186255i) q^{17} +(-8.89371 + 6.15937i) q^{18} +(3.45645 - 5.98675i) q^{19} +(4.34096 + 1.07522i) q^{20} +(0.263690 + 3.20413i) q^{22} +(-3.23487 + 0.866782i) q^{23} +(-0.142725 + 9.22915i) q^{24} +(1.43197 - 4.79056i) q^{25} +(-0.932215 - 2.60291i) q^{26} +(-10.7295 + 10.7295i) q^{27} +7.33156i q^{29} +(10.2992 + 0.650933i) q^{30} +(0.430790 - 0.248717i) q^{31} +(4.54867 + 3.36297i) q^{32} +(1.92011 + 7.16594i) q^{33} +(-0.207991 - 0.176360i) q^{34} +(2.50125 + 15.0936i) q^{36} +(-3.37605 + 0.904610i) q^{37} +(-5.56612 - 8.03710i) q^{38} +(-3.18998 - 5.52522i) q^{39} +(3.99791 - 4.90069i) q^{40} +3.22939 q^{41} +(-2.91165 - 2.91165i) q^{43} +(4.25618 + 1.59900i) q^{44} +(16.9892 - 1.98943i) q^{45} +(-0.846460 + 4.65993i) q^{46} +(0.645725 + 2.40988i) q^{47} +(11.7143 + 5.75940i) q^{48} +(-5.25998 - 4.72573i) q^{50} +(-0.544959 - 0.314632i) q^{51} +(-3.89143 - 0.380917i) q^{52} +(-6.98469 - 1.87154i) q^{53} +(7.23537 + 20.2024i) q^{54} +(2.01239 - 4.66799i) q^{55} +(-15.9520 - 15.9520i) q^{57} +(9.37424 + 4.43025i) q^{58} +(-2.61146 - 4.52318i) q^{59} +(7.05580 - 12.7754i) q^{60} +(5.00922 - 8.67623i) q^{61} +(-0.0576991 - 0.701107i) q^{62} +(7.04858 - 3.78386i) q^{64} +(-0.632652 + 4.32552i) q^{65} +(10.3227 + 1.87509i) q^{66} +(-12.0126 - 3.21877i) q^{67} +(-0.351180 + 0.159371i) q^{68} +10.9290i q^{69} -3.60061i q^{71} +(20.8103 + 5.92247i) q^{72} +(-12.6457 - 3.38841i) q^{73} +(-0.883401 + 4.86330i) q^{74} +(-13.8913 - 8.56008i) q^{75} +(-13.6398 + 2.26034i) q^{76} +(-8.99224 + 0.740035i) q^{78} +(5.66954 - 9.81994i) q^{79} +(-3.85027 - 8.07313i) q^{80} +(13.2844 + 23.0093i) q^{81} +(1.95143 - 4.12915i) q^{82} +(-0.591847 - 0.591847i) q^{83} +(0.159277 + 0.400674i) q^{85} +(-5.48231 + 1.96345i) q^{86} +(23.1105 + 6.19243i) q^{87} +(4.61640 - 4.47579i) q^{88} +(-3.45672 - 1.99574i) q^{89} +(7.72235 - 22.9248i) q^{90} +(5.44676 + 3.89816i) q^{92} +(-0.420146 - 1.56801i) q^{93} +(3.47150 + 0.630586i) q^{94} +(1.79781 + 15.3528i) q^{95} +(14.4427 - 11.4978i) q^{96} +(-1.09368 - 1.09368i) q^{97} +17.3902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 4 q^{2} - 32 q^{8}+O(q^{10}) $ 112 * q + 4 * q^2 - 32 * q^8	$ 112 q + 4 q^{2} - 32 q^{8} - 32 q^{16} + 40 q^{22} - 32 q^{25} + 28 q^{30} + 64 q^{32} + 32 q^{36} + 8 q^{37} + 184 q^{46} - 24 q^{50} - 96 q^{53} - 16 q^{57} - 124 q^{58} - 8 q^{60} + 120 q^{65} + 80 q^{72} - 72 q^{78} + 72 q^{81} + 192 q^{85} - 104 q^{86} - 48 q^{88} - 304 q^{92} + 176 q^{93}+O(q^{100}) $ 112 * q + 4 * q^2 - 32 * q^8 - 32 * q^16 + 40 * q^22 - 32 * q^25 + 28 * q^30 + 64 * q^32 + 32 * q^36 + 8 * q^37 + 184 * q^46 - 24 * q^50 - 96 * q^53 - 16 * q^57 - 124 * q^58 - 8 * q^60 + 120 * q^65 + 80 * q^72 - 72 * q^78 + 72 * q^81 + 192 * q^85 - 104 * q^86 - 48 * q^88 - 304 * q^92 + 176 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.604271	−	1.27862i	0.427284	−	0.904117i
$2$	0.604271	−	1.27862i	0.427284	−	0.904117i
$3$	0.844627	−	3.15219i	0.487646	−	1.81992i	−0.0801936	−	0.996779i	$-0.525554\pi$
$3$	0.844627	−	3.15219i	0.487646	−	1.81992i	0.567839	−	0.823139i	$-0.307779\pi$
$4$	−1.26971	−	1.54526i	−0.634857	−	0.772630i
$5$	−1.79332	+	1.33567i	−0.801996	+	0.597330i
$5$	−1.79332	+	1.33567i	−0.801996	+	0.597330i
$6$	−3.52006	−	2.98473i	−1.43706	−	1.21851i
$7$		0			0
$7$		0			0
$8$	−2.74304	+	0.689718i	−0.969812	+	0.243852i
$9$	−6.62484	−	3.82485i	−2.20828	−	1.27495i
$10$	0.624159	+	3.10007i	0.197376	+	0.980328i
$11$	−1.96875	+	1.13666i	−0.593601	+	0.342716i	−0.766520	−	0.642220i	$-0.778013\pi$
$11$	−1.96875	+	1.13666i	−0.593601	+	0.342716i	0.172919	+	0.984936i	$0.444680\pi$
$12$	−5.94339	+	2.69721i	−1.71571	+	0.778618i
$13$	1.38240	−	1.38240i	0.383410	−	0.383410i	−0.488919	−	0.872329i	$-0.662609\pi$
$13$	1.38240	−	1.38240i	0.383410	−	0.383410i	0.872329	+	0.488919i	$0.162609\pi$
$14$		0			0
$15$	2.69561	+	6.78102i	0.696002	+	1.75085i
$16$	−0.775657	+	3.92407i	−0.193914	+	0.981018i
$17$	0.0499069	−	0.186255i	0.0121042	−	0.0451735i	−0.959610	−	0.281335i	$-0.909223\pi$
$17$	0.0499069	−	0.186255i	0.0121042	−	0.0451735i	0.971714	+	0.236162i	$0.0758894\pi$
$18$	−8.89371	+	6.15937i	−2.09627	+	1.45178i
$19$	3.45645	−	5.98675i	0.792965	−	1.37346i	−0.131158	−	0.991361i	$-0.541870\pi$
$19$	3.45645	−	5.98675i	0.792965	−	1.37346i	0.924123	−	0.382094i	$-0.124797\pi$
$20$	4.34096	+	1.07522i	0.970667	+	0.240427i
$21$		0			0
$22$	0.263690	+	3.20413i	0.0562189	+	0.683122i
$23$	−3.23487	+	0.866782i	−0.674518	+	0.180736i	−0.579789	−	0.814767i	$-0.696865\pi$
$23$	−3.23487	+	0.866782i	−0.674518	+	0.180736i	−0.0947286	+	0.995503i	$0.530198\pi$
$24$	−0.142725	+	9.22915i	−0.0291336	+	1.88389i
$25$	1.43197	−	4.79056i	0.286394	−	0.958112i
$26$	−0.932215	−	2.60291i	−0.182822	−	0.510472i
$27$	−10.7295	+	10.7295i	−2.06489	+	2.06489i
$28$		0			0
$29$			7.33156i			1.36144i	0.732546	+	0.680718i	$0.238332\pi$
$29$			7.33156i			1.36144i	−0.732546	+	0.680718i	$0.761668\pi$
$30$	10.2992	+	0.650933i	1.88037	+	0.118844i
$31$	0.430790	−	0.248717i	0.0773722	−	0.0446709i	−0.460815	−	0.887496i	$-0.652443\pi$
$31$	0.430790	−	0.248717i	0.0773722	−	0.0446709i	0.538187	+	0.842825i	$0.319109\pi$
$32$	4.54867	+	3.36297i	0.804099	+	0.594495i
$33$	1.92011	+	7.16594i	0.334248	+	1.24743i
$34$	−0.207991	−	0.176360i	−0.0356702	−	0.0302455i
$35$		0			0
$36$	2.50125	+	15.0936i	0.416876	+	2.51559i
$37$	−3.37605	+	0.904610i	−0.555019	+	0.148717i	−0.525417	−	0.850845i	$-0.676091\pi$
$37$	−3.37605	+	0.904610i	−0.555019	+	0.148717i	−0.0296020	+	0.999562i	$0.509424\pi$
$38$	−5.56612	−	8.03710i	−0.902944	−	1.30379i
$39$	−3.18998	−	5.52522i	−0.510806	−	0.884743i
$40$	3.99791	−	4.90069i	0.632125	−	0.774866i
$41$	3.22939			0.504346			0.252173	−	0.967682i	$-0.418855\pi$
$41$	3.22939			0.504346			0.252173	+	0.967682i	$0.418855\pi$
$42$		0			0
$43$	−2.91165	−	2.91165i	−0.444022	−	0.444022i	0.449339	−	0.893361i	$-0.351660\pi$
$43$	−2.91165	−	2.91165i	−0.444022	−	0.444022i	−0.893361	+	0.449339i	$0.851660\pi$
$44$	4.25618	+	1.59900i	0.641644	+	0.241059i
$45$	16.9892	−	1.98943i	2.53260	−	0.296567i
$46$	−0.846460	+	4.65993i	−0.124804	+	0.687069i
$47$	0.645725	+	2.40988i	0.0941887	+	0.351517i	0.996895	−	0.0787399i	$-0.0250897\pi$
$47$	0.645725	+	2.40988i	0.0941887	+	0.351517i	−0.902707	+	0.430257i	$0.858423\pi$
$48$	11.7143	+	5.75940i	1.69081	+	0.831298i
$49$		0			0
$50$	−5.25998	−	4.72573i	−0.743874	−	0.668320i
$51$	−0.544959	−	0.314632i	−0.0763095	−	0.0440573i
$52$	−3.89143	−	0.380917i	−0.539644	−	0.0528237i
$53$	−6.98469	−	1.87154i	−0.959421	−	0.257076i	−0.255066	−	0.966924i	$-0.582097\pi$
$53$	−6.98469	−	1.87154i	−0.959421	−	0.257076i	−0.704355	+	0.709847i	$0.748764\pi$
$54$	7.23537	+	20.2024i	0.984610	+	2.74920i
$55$	2.01239	−	4.66799i	0.271351	−	0.629432i
$56$		0			0
$57$	−15.9520	−	15.9520i	−2.11289	−	2.11289i
$58$	9.37424	+	4.43025i	1.23090	+	0.581720i
$59$	−2.61146	−	4.52318i	−0.339983	−	0.588868i	0.644446	−	0.764650i	$-0.277088\pi$
$59$	−2.61146	−	4.52318i	−0.339983	−	0.588868i	−0.984429	+	0.175782i	$0.943755\pi$
$60$	7.05580	−	12.7754i	0.910899	−	1.64929i
$61$	5.00922	−	8.67623i	0.641365	−	1.11088i	−0.343763	−	0.939056i	$-0.611702\pi$
$61$	5.00922	−	8.67623i	0.641365	−	1.11088i	0.985128	−	0.171821i	$-0.0549649\pi$
$62$	−0.0576991	−	0.701107i	−0.00732779	−	0.0890407i
$63$		0			0
$64$	7.04858	−	3.78386i	0.881072	−	0.472982i
$65$	−0.632652	+	4.32552i	−0.0784708	+	0.536515i
$66$	10.3227	+	1.87509i	1.27064	+	0.230808i
$67$	−12.0126	−	3.21877i	−1.46757	−	0.393235i	−0.565474	−	0.824766i	$-0.691307\pi$
$67$	−12.0126	−	3.21877i	−1.46757	−	0.393235i	−0.902098	+	0.431531i	$0.857974\pi$
$68$	−0.351180	+	0.159371i	−0.0425868	+	0.0193266i
$69$			10.9290i			1.31570i
$70$		0			0
$71$		−	3.60061i		−	0.427314i	−0.976909	−	0.213657i	$-0.931462\pi$
$71$		−	3.60061i		−	0.427314i	0.976909	−	0.213657i	$-0.0685375\pi$
$72$	20.8103	+	5.92247i	2.45252	+	0.697969i
$73$	−12.6457	−	3.38841i	−1.48007	−	0.396584i	−0.573700	−	0.819066i	$-0.694492\pi$
$73$	−12.6457	−	3.38841i	−1.48007	−	0.396584i	−0.906371	+	0.422482i	$0.861159\pi$
$74$	−0.883401	+	4.86330i	−0.102693	+	0.565347i
$75$	−13.8913	−	8.56008i	−1.60403	−	0.988433i
$76$	−13.6398	+	2.26034i	−1.56459	+	0.259279i
$77$		0			0
$78$	−8.99224	+	0.740035i	−1.01817	+	0.0837925i
$79$	5.66954	−	9.81994i	0.637874	−	1.10483i	−0.348025	−	0.937485i	$-0.613148\pi$
$79$	5.66954	−	9.81994i	0.637874	−	1.10483i	0.985899	−	0.167344i	$-0.0535191\pi$
$80$	−3.85027	−	8.07313i	−0.430473	−	0.902603i
$81$	13.2844	+	23.0093i	1.47605	+	2.55659i
$82$	1.95143	−	4.12915i	0.215499	−	0.455988i
$83$	−0.591847	−	0.591847i	−0.0649636	−	0.0649636i	0.673879	−	0.738842i	$-0.264627\pi$
$83$	−0.591847	−	0.591847i	−0.0649636	−	0.0649636i	−0.738842	+	0.673879i	$0.764627\pi$
$84$		0			0
$85$	0.159277	+	0.400674i	0.0172760	+	0.0434592i
$86$	−5.48231	+	1.96345i	−0.591172	+	0.211725i
$87$	23.1105	+	6.19243i	2.47770	+	0.663898i
$88$	4.61640	−	4.47579i	0.492110	−	0.477121i
$89$	−3.45672	−	1.99574i	−0.366412	−	0.211548i	0.305478	−	0.952199i	$-0.401184\pi$
$89$	−3.45672	−	1.99574i	−0.366412	−	0.211548i	−0.671890	+	0.740651i	$0.734517\pi$
$90$	7.72235	−	22.9248i	0.814008	−	2.41648i
$91$		0			0
$92$	5.44676	+	3.89816i	0.567864	+	0.406411i
$93$	−0.420146	−	1.56801i	−0.0435671	−	0.162595i
$94$	3.47150	+	0.630586i	0.358058	+	0.0650400i
$95$	1.79781	+	15.3528i	0.184452	+	1.57517i
$96$	14.4427	−	11.4978i	1.47405	−	1.17349i
$97$	−1.09368	−	1.09368i	−0.111047	−	0.111047i	0.649400	−	0.760447i	$-0.275020\pi$
$97$	−1.09368	−	1.09368i	−0.111047	−	0.111047i	−0.760447	+	0.649400i	$0.775020\pi$
$98$		0			0
$99$	17.3902			1.74778
$100$	−9.22085	+	3.86987i	−0.922085	+	0.386987i
$101$	−2.49645	−	4.32397i	−0.248406	−	0.430251i	0.714678	−	0.699454i	$-0.246573\pi$
$101$	−2.49645	−	4.32397i	−0.248406	−	0.430251i	−0.963084	+	0.269202i	$0.913240\pi$
$102$	−0.731597	+	0.506670i	−0.0724389	+	0.0501678i
$103$	10.0333	−	2.68842i	0.988612	−	0.264898i	0.271945	−	0.962313i	$-0.412333\pi$
$103$	10.0333	−	2.68842i	0.988612	−	0.264898i	0.716667	+	0.697415i	$0.245667\pi$
$104$	−2.83852	+	4.74546i	−0.278340	+	0.465331i
$105$		0			0
$106$	−6.61363	+	7.79981i	−0.642373	+	0.757585i
$107$	0.553575	+	2.06597i	0.0535161	+	0.199725i	0.987508	−	0.157570i	$-0.0503659\pi$
$107$	0.553575	+	2.06597i	0.0535161	+	0.199725i	−0.933992	+	0.357295i	$0.883699\pi$
$108$	30.2033	+	2.95648i	2.90631	+	0.284488i
$109$	−8.19415	+	4.73090i	−0.784857	+	0.453138i	−0.838149	−	0.545441i	$-0.816362\pi$
$109$	−8.19415	+	4.73090i	−0.784857	+	0.453138i	0.0532916	+	0.998579i	$0.483029\pi$
$110$	−4.75254	−	5.39381i	−0.453137	−	0.514280i
$111$			11.4060i			1.08261i
$112$		0			0
$113$	12.1490	−	12.1490i	1.14289	−	1.14289i	0.154967	−	0.987920i	$-0.450473\pi$
$113$	12.1490	−	12.1490i	1.14289	−	1.14289i	0.987920	−	0.154967i	$-0.0495270\pi$
$114$	−30.0358	+	10.7571i	−2.81311	+	1.00750i
$115$	4.64342	−	5.87514i	0.433001	−	0.547859i
$116$	11.3292	−	9.30897i	1.05189	−	0.864316i
$117$	−14.4457	+	3.87071i	−1.33550	+	0.357847i
$118$	−7.36144	+	0.605825i	−0.677676	+	0.0557707i
$119$		0			0
$120$	−12.0712	−	16.7414i	−1.10194	−	1.52828i
$121$	−2.91601	+	5.05068i	−0.265092	+	0.459153i
$122$	−8.06663	−	11.6477i	−0.730318	−	1.05453i
$123$	2.72763	−	10.1797i	0.245942	−	0.917869i
$124$	−0.931312	−	0.349884i	−0.0836343	−	0.0314205i
$125$	3.83064	+	10.5036i	0.342622	+	0.939473i
$126$		0			0
$127$	−2.01009	+	2.01009i	−0.178367	+	0.178367i	−0.790643	−	0.612277i	$-0.790254\pi$
$127$	−2.01009	+	2.01009i	−0.178367	+	0.178367i	0.612277	+	0.790643i	$0.290254\pi$
$128$	−0.578844	−	11.2989i	−0.0511630	−	0.998690i
$129$	−11.6373	+	6.71882i	−1.02461	+	0.591559i
$130$	5.14838	+	3.42271i	0.451543	+	0.300191i
$131$	−5.65370	−	3.26417i	−0.493966	−	0.285191i	0.232252	−	0.972656i	$-0.425391\pi$
$131$	−5.65370	−	3.26417i	−0.493966	−	0.285191i	−0.726218	+	0.687464i	$0.758724\pi$
$132$	8.63525	−	12.0657i	0.751602	−	1.05019i
$133$		0			0
$134$	−11.3744	+	13.4145i	−0.982601	+	1.15883i
$135$	4.91031	−	33.5725i	0.422613	−	2.88946i
$136$	−0.00843325	+	0.545328i	−0.000723145	+	0.0467615i
$137$	1.52380	−	5.68690i	0.130187	−	0.485865i	−0.869784	−	0.493432i	$-0.835742\pi$
$137$	1.52380	−	5.68690i	0.130187	−	0.485865i	0.999971	+	0.00756731i	$0.00240877\pi$
$138$	13.9740	+	6.60411i	1.18955	+	0.562179i
$139$	−6.55194			−0.555729			−0.277864	−	0.960620i	$-0.589627\pi$
$139$	−6.55194			−0.555729			−0.277864	+	0.960620i	$0.589627\pi$
$140$		0			0
$141$	8.14180			0.685663
$142$	−4.60380	−	2.17575i	−0.386342	−	0.182585i
$143$	−1.15029	+	4.29293i	−0.0961919	+	0.358993i
$144$	20.1476	−	23.0296i	1.67897	−	1.91913i
$145$	−9.79254	−	13.1478i	−0.813226	−	1.09187i
$146$	−11.9739	+	14.1215i	−0.990969	+	1.16870i
$147$		0			0
$148$	5.68447	+	4.06828i	0.467261	+	0.334410i
$149$	12.4603	+	7.19395i	1.02079	+	0.589352i	0.914332	−	0.404966i	$-0.132717\pi$
$149$	12.4603	+	7.19395i	1.02079	+	0.589352i	0.106455	+	0.994318i	$0.466050\pi$
$150$	−19.3391	+	12.5890i	−1.57903	+	1.02789i
$151$	6.33365	−	3.65673i	0.515425	−	0.297581i	−0.219636	−	0.975582i	$-0.570487\pi$
$151$	6.33365	−	3.65673i	0.515425	−	0.297581i	0.735061	+	0.678001i	$0.237154\pi$
$152$	−5.35203	+	18.8059i	−0.434107	+	1.52536i
$153$	−1.04302	+	1.04302i	−0.0843235	+	0.0843235i
$154$		0			0
$155$	−0.440339	+	1.02142i	−0.0353689	+	0.0820426i
$156$	−4.48753	+	11.9448i	−0.359290	+	0.956349i
$157$	−5.19817	+	19.3998i	−0.414859	+	1.54828i	0.370258	+	0.928929i	$0.379269\pi$
$157$	−5.19817	+	19.3998i	−0.414859	+	1.54828i	−0.785117	+	0.619347i	$0.787397\pi$
$158$	−9.12998	−	13.1831i	−0.726342	−	1.04879i
$159$	−11.7989	+	20.4363i	−0.935715	+	1.62071i
$160$	−12.6490	+	0.0446550i	−0.999994	+	0.00353029i
$161$		0			0
$162$	37.4475	−	3.08182i	2.94215	−	0.242131i
$163$	12.8941	−	3.45495i	1.00994	−	0.270613i	0.284336	−	0.958725i	$-0.408227\pi$
$163$	12.8941	−	3.45495i	1.00994	−	0.270613i	0.725604	+	0.688112i	$0.241560\pi$
$164$	−4.10040	−	4.99025i	−0.320187	−	0.389673i
$165$	−13.0147	−	10.2862i	−1.01319	−	0.800777i
$166$	−1.11438	+	0.399108i	−0.0864927	+	0.0309768i
$167$	4.21040	−	4.21040i	0.325811	−	0.325811i	−0.525180	−	0.850991i	$-0.676002\pi$
$167$	4.21040	−	4.21040i	0.325811	−	0.325811i	0.850991	+	0.525180i	$0.176002\pi$
$168$		0			0
$169$			9.17792i			0.705994i
$170$	0.608553	+	0.0384620i	0.0466739	+	0.00294990i
$171$	−45.7969	+	26.4409i	−3.50218	+	2.02198i
$172$	−0.802296	+	8.19622i	−0.0611745	+	0.624956i
$173$	−5.25823	−	19.6240i	−0.399776	−	1.49198i	−0.813491	−	0.581578i	$-0.802436\pi$
$173$	−5.25823	−	19.6240i	−0.399776	−	1.49198i	0.413715	−	0.910406i	$-0.364231\pi$
$174$	21.8827	−	25.8075i	1.65892	−	1.95646i
$175$		0			0
$176$	−2.93326	−	8.60719i	−0.221103	−	0.648791i
$177$	−16.4637	+	4.41142i	−1.23748	+	0.331583i
$178$	−4.64058	+	3.21385i	−0.347826	+	0.240888i
$179$	1.59053	+	2.75487i	0.118881	+	0.205909i	0.919325	−	0.393500i	$-0.128736\pi$
$179$	1.59053	+	2.75487i	0.118881	+	0.205909i	−0.800443	+	0.599409i	$0.795402\pi$
$180$	−24.6456	−	23.7267i	−1.83697	−	1.76848i
$181$	9.22913			0.685996			0.342998	−	0.939336i	$-0.388558\pi$
$181$	9.22913			0.685996			0.342998	+	0.939336i	$0.388558\pi$
$182$		0			0
$183$	−23.1182	−	23.1182i	−1.70895	−	1.70895i
$184$	8.27556	−	4.60877i	0.610083	−	0.339763i
$185$	4.84606	−	6.13154i	0.356290	−	0.450800i
$186$	−2.25876	−	0.410296i	−0.165620	−	0.0300843i
$187$	0.113454	+	0.423417i	0.00829660	+	0.0309633i
$188$	2.90400	−	4.05767i	0.211796	−	0.295936i
$189$		0			0
$190$	20.7167	+	6.97856i	1.50295	+	0.506278i
$191$	−12.7944	−	7.38687i	−0.925773	−	0.534495i	−0.0403006	−	0.999188i	$-0.512832\pi$
$191$	−12.7944	−	7.38687i	−0.925773	−	0.534495i	−0.885472	+	0.464692i	$0.846165\pi$
$192$	−5.97402	−	25.4144i	−0.431138	−	1.83413i
$193$	−2.95127	−	0.790790i	−0.212437	−	0.0569223i	0.151031	−	0.988529i	$-0.451741\pi$
$193$	−2.95127	−	0.790790i	−0.212437	−	0.0569223i	−0.363468	+	0.931607i	$0.618407\pi$
$194$	−2.05928	+	0.737520i	−0.147848	+	0.0529508i
$195$	13.1005	+	5.64769i	0.938148	+	0.404440i
$196$		0			0
$197$	6.45634	+	6.45634i	0.459995	+	0.459995i	0.898654	−	0.438658i	$-0.144546\pi$
$197$	6.45634	+	6.45634i	0.459995	+	0.459995i	−0.438658	+	0.898654i	$0.644546\pi$
$198$	10.5084	−	22.2354i	0.746800	−	1.58020i
$199$	7.48432	+	12.9632i	0.530549	+	0.918939i	0.999365	+	0.0356423i	$0.0113477\pi$
$199$	7.48432	+	12.9632i	0.530549	+	0.918939i	−0.468815	+	0.883296i	$0.655319\pi$
$200$	−0.623816	+	14.1284i	−0.0441105	+	0.999027i
$201$	−20.2923	+	35.1474i	−1.43131	+	2.47910i
$202$	−7.03722	+	0.579143i	−0.495137	+	0.0407484i
$203$		0			0
$204$	0.205753	+	1.24160i	0.0144056	+	0.0869291i
$205$	−5.79132	+	4.31340i	−0.404483	+	0.301261i
$206$	2.62539	−	14.4533i	0.182920	−	1.00701i
$207$	24.7458	+	6.63062i	1.71995	+	0.460860i
$208$	4.35238	+	6.49692i	0.301783	+	0.450481i
$209$			15.7152i			1.08705i
$210$		0			0
$211$		−	16.6114i		−	1.14358i	−0.820401	−	0.571789i	$-0.806250\pi$
$211$		−	16.6114i		−	1.14358i	0.820401	−	0.571789i	$-0.193750\pi$
$212$	5.97654	+	13.1695i	0.410470	+	0.904484i
$213$	−11.3498	−	3.04118i	−0.777677	−	0.208378i
$214$	2.97609	+	0.540596i	0.203441	+	0.0369544i
$215$	9.11052	+	1.33251i	0.621332	+	0.0908761i
$216$	22.0312	−	36.8318i	1.49903	−	2.50609i
$217$		0			0
$218$	1.09751	+	13.3359i	0.0743325	+	0.903222i
$219$	−21.3619	+	36.9998i	−1.44350	+	2.50022i
$220$	−9.76843	+	2.81734i	−0.658587	+	0.189945i
$221$	−0.188488	−	0.326471i	−0.0126791	−	0.0219608i
$222$	14.5839	+	6.89232i	0.978807	+	0.462582i
$223$	−10.5774	−	10.5774i	−0.708318	−	0.708318i	0.257863	−	0.966181i	$-0.416982\pi$
$223$	−10.5774	−	10.5774i	−0.708318	−	0.708318i	−0.966181	+	0.257863i	$0.916982\pi$
$224$		0			0
$225$	−27.8098	+	26.2596i	−1.85398	+	1.75064i
$226$	−8.19264	−	22.8753i	−0.544966	−	1.52164i
$227$	−8.10649	−	2.17213i	−0.538047	−	0.144169i	−0.0204453	−	0.999791i	$-0.506508\pi$
$227$	−8.10649	−	2.17213i	−0.538047	−	0.144169i	−0.517602	+	0.855622i	$0.673175\pi$
$228$	−4.39552	+	44.9044i	−0.291100	+	2.97387i
$229$	8.28192	+	4.78157i	0.547285	+	0.315975i	0.748026	−	0.663669i	$-0.231002\pi$
$229$	8.28192	+	4.78157i	0.547285	+	0.315975i	−0.200741	+	0.979644i	$0.564335\pi$
$230$	−4.70616	−	9.48732i	−0.310315	−	0.625575i
$231$		0			0
$232$	−5.05671	−	20.1108i	−0.331989	−	1.32034i
$233$	2.57959	+	9.62717i	0.168995	+	0.630697i	0.997497	+	0.0707108i	$0.0225268\pi$
$233$	2.57959	+	9.62717i	0.168995	+	0.630697i	−0.828502	+	0.559986i	$0.810807\pi$
$234$	−3.77996	+	20.8094i	−0.247104	+	1.36036i
$235$	−4.37679	−	3.45920i	−0.285511	−	0.225653i
$236$	−3.67369	+	9.77853i	−0.239137	+	0.636528i
$237$	−26.1657	−	26.1657i	−1.69964	−	1.69964i
$238$		0			0
$239$	19.5170			1.26245			0.631225	−	0.775600i	$-0.282552\pi$
$239$	19.5170			1.26245			0.631225	+	0.775600i	$0.282552\pi$
$240$	−28.7001	+	5.31800i	−1.85258	+	0.343276i
$241$	4.81231	+	8.33517i	0.309988	+	0.536915i	0.978359	−	0.206913i	$-0.0663416\pi$
$241$	4.81231	+	8.33517i	0.309988	+	0.536915i	−0.668371	+	0.743828i	$0.733008\pi$
$242$	4.69581	+	6.78043i	0.301858	+	0.435863i
$243$	39.7800	−	10.6590i	2.55189	−	0.683776i
$244$	−19.7673	+	3.27577i	−1.26547	+	0.209710i
$245$		0			0
$246$	−11.3676	−	9.63886i	−0.724774	−	0.614551i
$247$	−3.49790	−	13.0543i	−0.222566	−	0.830627i
$248$	−1.01013	+	0.979365i	−0.0641434	+	0.0621897i
$249$	−2.36550	+	1.36572i	−0.149908	+	0.0865493i
$250$	15.7448	+	1.44913i	0.995791	+	0.0916511i
$251$		−	27.2830i		−	1.72209i	−0.508532	−	0.861043i	$-0.669812\pi$
$251$		−	27.2830i		−	1.72209i	0.508532	−	0.861043i	$-0.330188\pi$
$252$		0			0
$253$	5.38343	−	5.38343i	0.338453	−	0.338453i
$254$	1.35549	+	3.78477i	0.0850511	+	0.237477i
$255$	1.39753	−	0.163650i	0.0875167	−	0.0102482i
$256$	−14.7967	−	6.08747i	−0.924794	−	0.380467i
$257$	27.8738	−	7.46875i	1.73872	−	0.465888i	0.756556	−	0.653929i	$-0.226880\pi$
$257$	27.8738	−	7.46875i	1.73872	−	0.465888i	0.982161	+	0.188041i	$0.0602136\pi$
$258$	1.55868	+	18.9397i	0.0970391	+	1.17913i
$259$		0			0
$260$	7.48734	−	4.51456i	0.464345	−	0.279981i
$261$	28.0421	−	48.5704i	1.73576	−	3.00643i
$262$	−7.58998	+	5.25647i	−0.468910	+	0.324746i
$263$	−1.35037	+	5.03964i	−0.0832672	+	0.310757i	−0.994980	−	0.100070i	$-0.968093\pi$
$263$	−1.35037	+	5.03964i	−0.0832672	+	0.310757i	0.911713	+	0.410827i	$0.134760\pi$
$264$	−10.2094	−	18.3321i	−0.628346	−	1.12827i
$265$	15.0255	−	5.97298i	0.923011	−	0.366917i
$266$		0			0
$267$	−9.21059	+	9.21059i	−0.563679	+	0.563679i
$268$	10.2787	+	22.6495i	0.627873	+	1.38354i
$269$	11.0061	−	6.35438i	0.671054	−	0.387433i	−0.125422	−	0.992104i	$-0.540028\pi$
$269$	11.0061	−	6.35438i	0.671054	−	0.387433i	0.796476	+	0.604670i	$0.206695\pi$
$270$	−39.9591	−	26.5653i	−2.43183	−	1.61671i
$271$	−25.0351	−	14.4540i	−1.52078	−	0.878021i	−0.999700	−	0.0245112i	$-0.992197\pi$
$271$	−25.0351	−	14.4540i	−1.52078	−	0.878021i	−0.521077	−	0.853510i	$-0.674470\pi$
$272$	0.692168	+	0.340309i	0.0419689	+	0.0206342i
$273$		0			0
$274$	−6.35057	−	5.38479i	−0.383652	−	0.325307i
$275$	2.62604	+	11.0591i	0.158356	+	0.666888i
$276$	16.8882	−	13.8768i	1.01655	−	0.835282i
$277$	5.66377	−	21.1375i	0.340303	−	1.27003i	−0.557701	−	0.830042i	$-0.688316\pi$
$277$	5.66377	−	21.1375i	0.340303	−	1.27003i	0.898004	−	0.439987i	$-0.145017\pi$
$278$	−3.95915	+	8.37741i	−0.237454	+	0.502444i
$279$	−3.80522			−0.227813
$280$		0			0
$281$	6.96882			0.415725			0.207862	−	0.978158i	$-0.433349\pi$
$281$	6.96882			0.415725			0.207862	+	0.978158i	$0.433349\pi$
$282$	4.91985	−	10.4102i	0.292973	−	0.619920i
$283$	6.97386	−	26.0268i	0.414553	−	1.54713i	−0.371176	−	0.928562i	$-0.621046\pi$
$283$	6.97386	−	26.0268i	0.414553	−	1.54713i	0.785729	−	0.618570i	$-0.212288\pi$
$284$	−5.56389	+	4.57175i	−0.330156	+	0.271283i
$285$	49.9135	+	7.30036i	2.95662	+	0.432436i
$286$	4.79392	+	4.06487i	0.283471	+	0.240361i
$287$		0			0
$288$	−17.2714	−	39.6772i	−1.01772	−	2.33800i
$289$	14.6902	+	8.48141i	0.864131	+	0.498906i
$290$	−22.7283	+	4.57606i	−1.33465	+	0.268715i
$291$	−4.37126	+	2.52375i	−0.256248	+	0.147945i
$292$	10.8205	+	23.8433i	0.633220	+	1.39532i
$293$	9.60083	−	9.60083i	0.560886	−	0.560886i	−0.368673	−	0.929559i	$-0.620188\pi$
$293$	9.60083	−	9.60083i	0.560886	−	0.560886i	0.929559	+	0.368673i	$0.120188\pi$
$294$		0			0
$295$	10.7247	+	4.62345i	0.624414	+	0.269188i
$296$	8.63672	−	4.80991i	0.501999	−	0.279570i
$297$	8.92794	−	33.3195i	0.518051	−	1.93339i
$298$	16.7277	−	11.5848i	0.969009	−	0.671091i
$299$	−3.27366	+	5.67014i	−0.189320	+	0.327913i
$300$	4.41040	+	32.3345i	0.254634	+	1.86683i
$301$		0			0
$302$	−0.848314	−	10.3080i	−0.0488150	−	0.593156i
$303$	−15.7386	+	4.21713i	−0.904156	+	0.242268i
$304$	20.8114	+	18.2071i	1.19362	+	1.04425i
$305$	2.60546	+	22.2499i	0.149188	+	1.27402i
$306$	0.703357	+	1.96390i	0.0402082	+	0.112268i
$307$	−9.95915	+	9.95915i	−0.568399	+	0.568399i	−0.931680	−	0.363281i	$-0.881657\pi$
$307$	−9.95915	+	9.95915i	−0.568399	+	0.568399i	0.363281	+	0.931680i	$0.381657\pi$
$308$		0			0
$309$		−	33.8977i		−	1.92837i
$310$	1.03992	+	1.18024i	0.0590635	+	0.0670331i
$311$	7.83321	−	4.52251i	0.444181	−	0.256448i	−0.261189	−	0.965288i	$-0.584114\pi$
$311$	7.83321	−	4.52251i	0.444181	−	0.256448i	0.705369	+	0.708840i	$0.250781\pi$
$312$	12.5611	+	12.9557i	0.711133	+	0.733473i
$313$	4.12250	+	15.3854i	0.233018	+	0.869634i	0.979032	+	0.203704i	$0.0652981\pi$
$313$	4.12250	+	15.3854i	0.233018	+	0.869634i	−0.746015	+	0.665929i	$0.768035\pi$
$314$	21.6638	+	18.3692i	1.22256	+	1.03664i
$315$		0			0
$316$	−22.3731	+	3.70758i	−1.25858	+	0.208568i
$317$	−11.8007	+	3.16198i	−0.662792	+	0.177595i	−0.574506	−	0.818500i	$-0.694806\pi$
$317$	−11.8007	+	3.16198i	−0.662792	+	0.177595i	−0.0882865	+	0.996095i	$0.528139\pi$
$318$	19.0005	+	27.4354i	1.06549	+	1.53850i
$319$	−8.33348	−	14.4340i	−0.466585	−	0.808150i
$320$	−7.58635	+	16.2002i	−0.424090	+	0.905620i
$321$	6.97990			0.389580
$322$		0			0
$323$	−0.942563	−	0.942563i	−0.0524456	−	0.0524456i
$324$	18.6880	−	49.7432i	1.03822	−	2.76351i
$325$	−4.64293	−	8.60204i	−0.257543	−	0.477156i
$326$	3.37395	−	18.5743i	0.186866	−	1.02873i
$327$	7.99169	+	29.8254i	0.441941	+	1.64935i
$328$	−8.85836	+	2.22737i	−0.489121	+	0.122986i
$329$		0			0
$330$	−21.0164	+	10.4251i	−1.15692	+	0.573886i
$331$	25.1183	+	14.5020i	1.38062	+	0.797104i	0.992233	−	0.124390i	$-0.0396975\pi$
$331$	25.1183	+	14.5020i	1.38062	+	0.797104i	0.388392	+	0.921494i	$0.373031\pi$
$332$	−0.163082	+	1.66603i	−0.00895027	+	0.0914355i
$333$	25.8258	+	6.92000i	1.41524	+	0.379214i
$334$	−2.83926	−	7.92771i	−0.155357	−	0.433785i
$335$	25.8416	−	10.2726i	1.41188	−	0.561252i
$336$		0			0
$337$	0.436142	+	0.436142i	0.0237582	+	0.0237582i	0.718886	−	0.695128i	$-0.244652\pi$
$337$	0.436142	+	0.436142i	0.0237582	+	0.0237582i	−0.695128	+	0.718886i	$0.744652\pi$
$338$	11.7350	+	5.54595i	0.638301	+	0.301660i
$339$	−28.0347	−	48.5575i	−1.52264	−	2.63728i
$340$	0.416909	−	0.754864i	0.0226101	−	0.0409383i
$341$	−0.565413	+	0.979324i	−0.0306188	+	0.0530333i
$342$	6.13394	+	74.5341i	0.331685	+	4.03034i
$343$		0			0
$344$	9.99500	+	5.97856i	0.538894	+	0.322343i
$345$	−14.5976	−	19.5992i	−0.785909	−	1.05519i
$346$	−28.2689	−	5.13495i	−1.51975	−	0.276057i
$347$	−20.0808	−	5.38063i	−1.07799	−	0.288847i	−0.324219	−	0.945982i	$-0.605102\pi$
$347$	−20.0808	−	5.38063i	−1.07799	−	0.288847i	−0.753773	+	0.657135i	$0.771768\pi$
$348$	−19.7747	−	43.5743i	−1.06004	−	2.33583i
$349$		−	11.4922i		−	0.615164i	−0.951522	−	0.307582i	$-0.900480\pi$
$349$		−	11.4922i		−	0.615164i	0.951522	−	0.307582i	$-0.0995198\pi$
$350$		0			0
$351$			29.6650i			1.58340i
$352$	−12.7778	−	1.45056i	−0.681057	−	0.0773154i
$353$	17.5453	+	4.70125i	0.933843	+	0.250222i	0.693493	−	0.720464i	$-0.256071\pi$
$353$	17.5453	+	4.70125i	0.933843	+	0.250222i	0.240350	+	0.970686i	$0.422738\pi$
$354$	−4.30800	+	23.7164i	−0.228967	+	1.26051i
$355$	4.80923	+	6.45704i	0.255248	+	0.342704i
$356$	1.30511	+	7.87555i	0.0691706	+	0.417403i
$357$		0			0
$358$	4.48353	−	0.368981i	0.236962	−	0.0195013i
$359$	−11.2339	+	19.4577i	−0.592902	+	1.02694i	0.400938	+	0.916105i	$0.368684\pi$
$359$	−11.2339	+	19.4577i	−0.592902	+	1.02694i	−0.993839	+	0.110831i	$0.964649\pi$
$360$	−45.2299	+	17.1748i	−2.38383	+	0.905194i
$361$	−14.3942	−	24.9314i	−0.757587	−	1.31218i
$362$	5.57689	−	11.8005i	0.293115	−	0.620221i
$363$	13.4578	+	13.4578i	0.706349	+	0.706349i
$364$		0			0
$365$	27.2036	−	10.8140i	1.42390	−	0.566032i
$366$	−43.5289	+	15.5896i	−2.27529	+	0.814883i
$367$	10.3023	+	2.76049i	0.537776	+	0.144097i	0.517476	−	0.855697i	$-0.326872\pi$
$367$	10.3023	+	2.76049i	0.537776	+	0.144097i	0.0202990	+	0.999794i	$0.493538\pi$
$368$	−0.892162	−	13.3662i	−0.0465071	−	0.696762i
$369$	−21.3942	−	12.3519i	−1.11374	−	0.643016i
$370$	−4.91154	−	9.90136i	−0.255339	−	0.514747i
$371$		0			0
$372$	−1.88951	+	2.64015i	−0.0979667	+	0.136886i
$373$	−5.01170	−	18.7039i	−0.259496	−	0.968452i	−0.965534	−	0.260278i	$-0.916186\pi$
$373$	−5.01170	−	18.7039i	−0.259496	−	0.968452i	0.706038	−	0.708174i	$-0.250481\pi$
$374$	0.609945	+	0.110794i	0.0315395	+	0.00572904i
$375$	36.3449	−	3.20325i	1.87684	−	0.165415i
$376$	−3.43339	−	6.16503i	−0.177064	−	0.317937i
$377$	10.1352	+	10.1352i	0.521988	+	0.521988i
$378$		0			0
$379$	11.3167			0.581298			0.290649	−	0.956830i	$-0.406129\pi$
$379$	11.3167			0.581298			0.290649	+	0.956830i	$0.406129\pi$
$380$	21.4414	−	22.2718i	1.09992	−	1.14252i
$381$	4.63841	+	8.03396i	0.237633	+	0.411592i
$382$	−17.1763	+	11.8955i	−0.878814	+	0.608626i
$383$	4.31792	−	1.15698i	0.220635	−	0.0591191i	−0.146808	−	0.989165i	$-0.546900\pi$
$383$	4.31792	−	1.15698i	0.220635	−	0.0591191i	0.367443	+	0.930046i	$0.380233\pi$
$384$	−36.1052	−	7.71872i	−1.84248	−	0.393894i
$385$		0			0
$386$	−2.79448	+	3.29568i	−0.142235	+	0.167746i
$387$	8.15258	+	30.4259i	0.414419	+	1.54663i
$388$	−0.301361	+	3.07869i	−0.0152993	+	0.156297i
$389$	23.3678	−	13.4914i	1.18480	−	0.684043i	0.227677	−	0.973737i	$-0.426887\pi$
$389$	23.3678	−	13.4914i	1.18480	−	0.684043i	0.957119	+	0.289694i	$0.0935535\pi$
$390$	15.1375	−	13.3378i	0.766517	−	0.675385i
$391$			0.645770i			0.0326580i
$392$		0			0
$393$	−15.0645	+	15.0645i	−0.759906	+	0.759906i
$394$	12.1566	−	4.35380i	0.612439	−	0.219341i
$395$	2.94891	+	25.1829i	0.148376	+	1.26709i
$396$	−22.0806	−	26.8724i	−1.10959	−	1.35039i
$397$	8.72496	−	2.33785i	0.437893	−	0.117333i	−0.0331358	−	0.999451i	$-0.510549\pi$
$397$	8.72496	−	2.33785i	0.437893	−	0.117333i	0.471029	+	0.882118i	$0.343883\pi$
$398$	21.0975	−	1.73627i	1.05752	−	0.0870311i
$399$		0			0
$400$	17.6878	+	9.33499i	0.884390	+	0.466749i
$401$	−3.01957	+	5.23005i	−0.150790	+	0.261176i	−0.931518	−	0.363695i	$-0.881515\pi$
$401$	−3.01957	+	5.23005i	−0.150790	+	0.261176i	0.780728	+	0.624871i	$0.214848\pi$
$402$	32.6779	+	47.1846i	1.62982	+	2.35335i
$403$	0.251699	−	0.939353i	0.0125380	−	0.0467925i
$404$	−3.51189	+	9.34786i	−0.174723	+	0.465073i
$405$	−54.5561	−	23.5194i	−2.71092	−	1.16869i
$406$		0			0
$407$	5.61837	−	5.61837i	0.278492	−	0.278492i
$408$	1.71185	+	0.487182i	0.0847494	+	0.0241191i
$409$	18.5956	−	10.7362i	0.919493	−	0.530869i	0.0360194	−	0.999351i	$-0.488532\pi$
$409$	18.5956	−	10.7362i	0.919493	−	0.530869i	0.883473	+	0.468482i	$0.155199\pi$
$410$	2.01565	+	10.0113i	0.0995460	+	0.494424i
$411$	−16.6392	−	9.60663i	−0.820749	−	0.473860i
$412$	−16.8937	−	12.0906i	−0.832295	−	0.595659i
$413$		0			0
$414$	23.4312	−	27.6337i	1.15158	−	1.35812i
$415$	1.85188	+	0.270857i	0.0909053	+	0.0132958i
$416$	10.9371	−	1.63912i	0.536235	−	0.0803643i
$417$	−5.53395	+	20.6530i	−0.270999	+	1.01138i
$418$	20.0938	+	9.49627i	0.982817	+	0.464478i
$419$	−12.1274			−0.592464			−0.296232	−	0.955116i	$-0.595730\pi$
$419$	−12.1274			−0.592464			−0.296232	+	0.955116i	$0.595730\pi$
$420$		0			0
$421$	−30.9496			−1.50839			−0.754196	−	0.656649i	$-0.771973\pi$
$421$	−30.9496			−1.50839			−0.754196	+	0.656649i	$0.771973\pi$
$422$	−21.2396	−	10.0378i	−1.03393	−	0.488633i
$423$	4.93961	−	18.4349i	0.240172	−	0.896334i
$424$	20.4502	+	0.316252i	0.993147	+	0.0153586i
$425$	−0.820801	−	0.505794i	−0.0398147	−	0.0245346i
$426$	−10.7469	+	12.6744i	−0.520687	+	0.614075i
$427$		0			0
$428$	2.48958	−	3.47861i	0.120338	−	0.168145i
$429$	12.5606	+	7.25185i	0.606430	+	0.350123i
$430$	7.20898	−	10.8436i	0.347648	−	0.522927i
$431$	−19.5042	+	11.2608i	−0.939486	+	0.542413i	−0.889799	−	0.456352i	$-0.849156\pi$
$431$	−19.5042	+	11.2608i	−0.939486	+	0.542413i	−0.0496870	+	0.998765i	$0.515822\pi$
$432$	−33.7809	−	50.4258i	−1.62529	−	2.42611i
$433$	−14.7279	+	14.7279i	−0.707779	+	0.707779i	−0.966068	−	0.258289i	$-0.916841\pi$
$433$	−14.7279	+	14.7279i	−0.707779	+	0.707779i	0.258289	+	0.966068i	$0.416841\pi$
$434$		0			0
$435$	−49.7154	+	19.7630i	−2.38367	+	0.947562i
$436$	17.7147	+	6.65522i	0.848380	+	0.318727i
$437$	−5.99198	+	22.3624i	−0.286635	+	1.06974i
$438$	34.4002	+	49.6715i	1.64370	+	2.37340i
$439$	16.3149	−	28.2582i	0.778666	−	1.34869i	−0.154045	−	0.988064i	$-0.549230\pi$
$439$	16.3149	−	28.2582i	0.778666	−	1.34869i	0.932711	−	0.360625i	$-0.117437\pi$
$440$	−2.30048	+	14.1925i	−0.109671	+	0.676601i
$441$		0			0
$442$	−0.531329	+	0.0437268i	−0.0252727	+	0.00207987i
$443$	−35.4675	+	9.50348i	−1.68511	+	0.451524i	−0.969120	−	0.246588i	$-0.920691\pi$
$443$	−35.4675	+	9.50348i	−1.68511	+	0.451524i	−0.715989	+	0.698111i	$0.754024\pi$
$444$	17.6253	−	14.4824i	0.836457	−	0.687302i
$445$	8.86465	−	1.03805i	0.420225	−	0.0492082i
$446$	−19.9161	+	7.13284i	−0.943056	+	0.337750i
$447$	33.2010	−	33.2010i	1.57035	−	1.57035i
$448$		0			0
$449$			29.6263i			1.39815i	0.715047	+	0.699077i	$0.246405\pi$
$449$			29.6263i			1.39815i	−0.715047	+	0.699077i	$0.753595\pi$
$450$	16.7713	+	51.4259i	0.790608	+	2.42424i
$451$	−6.35787	+	3.67072i	−0.299380	+	0.172847i
$452$	−34.1992	−	3.34763i	−1.60860	−	0.157459i
$453$	−6.17715	−	23.0534i	−0.290228	−	1.08315i
$454$	−7.67584	+	9.05253i	−0.360245	+	0.424856i
$455$		0			0
$456$	54.7594	+	32.7546i	2.56434	+	1.53387i
$457$	5.76995	−	1.54605i	0.269907	−	0.0723213i	−0.121327	−	0.992613i	$-0.538715\pi$
$457$	5.76995	−	1.54605i	0.269907	−	0.0723213i	0.391234	+	0.920291i	$0.372048\pi$
$458$	11.1183	−	7.70002i	0.519525	−	0.359799i
$459$	1.46295	+	2.53390i	0.0682846	+	0.118272i
$460$	−14.9744	+	0.284453i	−0.698186	+	0.0132627i
$461$	−6.73072			−0.313481			−0.156740	−	0.987640i	$-0.550099\pi$
$461$	−6.73072			−0.313481			−0.156740	+	0.987640i	$0.550099\pi$
$462$		0			0
$463$	−0.122270	−	0.122270i	−0.00568238	−	0.00568238i	0.704260	−	0.709942i	$-0.251279\pi$
$463$	−0.122270	−	0.122270i	−0.00568238	−	0.00568238i	−0.709942	+	0.704260i	$0.751279\pi$
$464$	−28.7696	−	5.68678i	−1.33559	−	0.264002i
$465$	2.84779	+	2.25076i	0.132063	+	0.104376i
$466$	13.8682	+	2.51911i	0.642433	+	0.116696i
$467$	−1.25037	−	4.66643i	−0.0578601	−	0.215937i	0.930943	−	0.365165i	$-0.118988\pi$
$467$	−1.25037	−	4.66643i	−0.0578601	−	0.215937i	−0.988803	+	0.149229i	$0.952321\pi$
$468$	24.3231	+	17.4077i	1.12434	+	0.804669i
$469$		0			0
$470$	−7.06775	+	3.50594i	−0.326011	+	0.161717i
$471$	56.7615	+	32.7713i	2.61543	+	1.51002i
$472$	10.2831	+	10.6061i	0.473317	+	0.488186i
$473$	9.04187	+	2.42276i	0.415746	+	0.111399i
$474$	−49.2670	+	17.6447i	−2.26291	+	0.810447i
$475$	−23.7304	−	25.1312i	−1.08882	−	1.15310i
$476$		0			0
$477$	39.1141	+	39.1141i	1.79091	+	1.79091i
$478$	11.7936	−	24.9547i	0.539425	−	1.14140i
$479$	15.7076	+	27.2063i	0.717697	+	1.24309i	0.961910	+	0.273365i	$0.0881368\pi$
$479$	15.7076	+	27.2063i	0.717697	+	1.24309i	−0.244214	+	0.969721i	$0.578530\pi$
$480$	−10.5430	+	39.9099i	−0.481218	+	1.82163i
$481$	−3.41653	+	5.91760i	−0.155780	+	0.269819i
$482$	13.5654	−	1.11639i	0.617888	−	0.0508503i
$483$		0			0
$484$	11.5071	−	1.90692i	0.523050	−	0.0866781i
$485$	3.42212	+	0.500521i	0.155391	+	0.0227275i
$486$	10.4091	−	57.3042i	0.472167	−	2.59937i
$487$	−5.63804	−	1.51071i	−0.255484	−	0.0684568i	0.128804	−	0.991670i	$-0.458886\pi$
$487$	−5.63804	−	1.51071i	−0.255484	−	0.0684568i	−0.384288	+	0.923213i	$0.625553\pi$
$488$	−7.75636	+	27.2542i	−0.351114	+	1.23374i
$489$		−	43.5627i		−	1.96997i
$490$		0			0
$491$		−	4.53656i		−	0.204732i	−0.994747	−	0.102366i	$-0.967359\pi$
$491$		−	4.53656i		−	0.204732i	0.994747	−	0.102366i	$-0.0326413\pi$
$492$	−19.1935	+	8.71034i	−0.865311	+	0.392693i
$493$	1.36554	+	0.365895i	0.0615008	+	0.0164791i
$494$	−18.8051	−	3.41589i	−0.846083	−	0.153688i
$495$	−31.1862	+	23.2276i	−1.40171	+	1.04400i
$496$	0.641838	+	1.88337i	0.0288194	+	0.0845659i
$497$		0			0
$498$	0.316830	+	3.84984i	0.0141975	+	0.172515i
$499$	16.1667	−	28.0016i	0.723722	−	1.25352i	−0.235776	−	0.971808i	$-0.575763\pi$
$499$	16.1667	−	28.0016i	0.723722	−	1.25352i	0.959498	−	0.281716i	$-0.0909036\pi$
$500$	11.3670	−	19.2559i	0.508349	−	0.861151i
$501$	−9.71578	−	16.8282i	−0.434069	−	0.751829i
$502$	−34.8844	−	16.4863i	−1.55697	−	0.735820i
$503$	19.0966	+	19.0966i	0.851475	+	0.851475i	0.990315	−	0.138840i	$-0.0443373\pi$
$503$	19.0966	+	19.0966i	0.851475	+	0.851475i	−0.138840	+	0.990315i	$0.544337\pi$
$504$		0			0
$505$	10.2523	+	4.41982i	0.456222	+	0.196679i
$506$	−3.63028	−	10.1364i	−0.161386	−	0.450617i
$507$	28.9306	+	7.75192i	1.28485	+	0.344275i
$508$	5.65835	+	0.553874i	0.251049	+	0.0245742i
$509$	−25.4928	−	14.7183i	−1.12995	−	0.652377i	−0.186028	−	0.982544i	$-0.559561\pi$
$509$	−25.4928	−	14.7183i	−1.12995	−	0.652377i	−0.943922	+	0.330167i	$0.892895\pi$
$510$	0.635240	−	1.88579i	0.0281289	−	0.0835042i
$511$		0			0
$512$	−16.7248	+	15.2408i	−0.739137	+	0.673555i
$513$	27.1489	+	101.321i	1.19865	+	4.47343i
$514$	7.29365	−	40.1530i	0.321709	−	1.77107i
$515$	−14.4021	+	18.2224i	−0.634631	+	0.802975i
$516$	25.1584	+	9.45174i	1.10754	+	0.416090i
$517$	−4.01048	−	4.01048i	−0.176381	−	0.176381i
$518$		0			0
$519$	−66.2998			−2.91024
$520$	−1.24800	−	12.3014i	−0.0547285	−	0.539454i
$521$	19.2144	+	33.2803i	0.841798	+	1.45804i	0.888373	+	0.459122i	$0.151836\pi$
$521$	19.2144	+	33.2803i	0.841798	+	1.45804i	−0.0465748	+	0.998915i	$0.514831\pi$
$522$	−45.1578	−	65.2048i	−1.97650	−	2.85393i
$523$	−40.8579	+	10.9478i	−1.78659	+	0.478716i	−0.991759	−	0.128115i	$-0.959107\pi$
$523$	−40.8579	+	10.9478i	−1.78659	+	0.478716i	−0.794831	+	0.606830i	$0.792441\pi$
$524$	2.13459	+	12.8810i	0.0932501	+	0.562709i
$525$		0			0
$526$	5.62777	+	4.77191i	0.245382	+	0.208065i
$527$	−0.0248254	−	0.0926496i	−0.00108141	−	0.00403588i
$528$	−29.6090	+	1.97633i	−1.28857	+	0.0860087i
$529$	−10.2055	+	5.89214i	−0.443717	+	0.256180i
$530$	1.44235	−	22.8212i	0.0626518	−	0.991288i
$531$			39.9538i			1.73385i
$532$		0			0
$533$	4.46432	−	4.46432i	0.193371	−	0.193371i
$534$	6.21111	+	17.3425i	0.268781	+	0.750483i
$535$	−3.75219	−	2.96554i	−0.162221	−	0.128212i
$536$	35.1711	+	0.543906i	1.51916	+	0.0234931i
$537$	10.0273	−	2.68680i	0.432709	−	0.115944i
$538$	−1.47413	−	17.9123i	−0.0635544	−	0.772256i
$539$		0			0
$540$	−58.1129	+	35.0397i	−2.50078	+	1.50787i
$541$	12.8616	−	22.2770i	0.552964	−	0.957762i	−0.445095	−	0.895484i	$-0.646830\pi$
$541$	12.8616	−	22.2770i	0.552964	−	0.957762i	0.998059	−	0.0622786i	$-0.0198367\pi$
$542$	−33.6092	+	23.2762i	−1.44364	+	0.999796i
$543$	7.79517	−	29.0920i	0.334523	−	1.24846i
$544$	0.853381	−	0.679378i	0.0365884	−	0.0291281i
$545$	8.37579	−	19.4287i	0.358779	−	0.832233i
$546$		0			0
$547$	14.6703	−	14.6703i	0.627257	−	0.627257i	−0.320120	−	0.947377i	$-0.603723\pi$
$547$	14.6703	−	14.6703i	0.627257	−	0.627257i	0.947377	+	0.320120i	$0.103723\pi$
$548$	−10.7225	+	4.86607i	−0.458044	+	0.207868i
$549$	−66.3706	+	38.3191i	−2.83263	+	1.63542i
$550$	15.7272	+	3.32499i	0.670608	+	0.141778i
$551$	43.8922	+	25.3412i	1.86987	+	1.07957i
$552$	−7.53796	−	29.9788i	−0.320837	−	1.27598i
$553$		0			0
$554$	−23.6043	−	20.0146i	−1.00285	−	0.850337i
$555$	−15.2347	−	20.4546i	−0.646676	−	0.868249i
$556$	8.31909	+	10.1245i	0.352808	+	0.429373i
$557$	0.0844516	−	0.315178i	0.00357833	−	0.0133545i	−0.964114	−	0.265490i	$-0.914466\pi$
$557$	0.0844516	−	0.315178i	0.00357833	−	0.0133545i	0.967692	+	0.252136i	$0.0811329\pi$
$558$	−2.29939	+	4.86541i	−0.0973407	+	0.205969i
$559$	−8.05015			−0.340485
$560$		0			0
$561$	1.43052			0.0603966
$562$	4.21106	−	8.91044i	0.177633	−	0.375864i
$563$	3.98515	−	14.8728i	0.167954	−	0.626812i	−0.829691	−	0.558223i	$-0.811483\pi$
$563$	3.98515	−	14.8728i	0.167954	−	0.626812i	0.997645	−	0.0685896i	$-0.0218499\pi$
$564$	−10.3377	−	12.5812i	−0.435298	−	0.529764i
$565$	−5.55997	+	38.0142i	−0.233910	+	1.59927i
$566$	−29.0642	−	24.6441i	−1.22166	−	1.03587i
$567$		0			0
$568$	2.48341	+	9.87664i	0.104202	+	0.414415i
$569$	−6.11191	−	3.52871i	−0.256224	−	0.147931i	0.366387	−	0.930463i	$-0.380595\pi$
$569$	−6.11191	−	3.52871i	−0.256224	−	0.147931i	−0.622611	+	0.782531i	$0.713928\pi$
$570$	39.4957	−	59.4088i	1.65429	−	2.48836i
$571$	12.6951	−	7.32953i	0.531274	−	0.306731i	−0.210261	−	0.977645i	$-0.567431\pi$
$571$	12.6951	−	7.32953i	0.531274	−	0.306731i	0.741535	+	0.670914i	$0.234098\pi$
$572$	8.09423	−	3.67330i	0.338437	−	0.153588i
$573$	−34.0914	+	34.0914i	−1.42419	+	1.42419i
$574$		0			0
$575$	−0.479869	+	16.7381i	−0.0200119	+	0.698025i
$576$	−61.1684	−	1.89234i	−2.54868	−	0.0788473i
$577$	1.01912	−	3.80340i	0.0424265	−	0.158338i	−0.941463	−	0.337117i	$-0.890548\pi$
$577$	1.01912	−	3.80340i	0.0424265	−	0.158338i	0.983889	+	0.178779i	$0.0572148\pi$
$578$	19.7213	−	13.6581i	0.820300	−	0.568101i
$579$	−4.98544	+	8.63504i	−0.207188	+	0.358860i
$580$	−7.88305	+	31.8260i	−0.327326	+	1.32150i
$581$		0			0
$582$	0.585477	+	7.11418i	0.0242688	+	0.294892i
$583$	15.8784	−	4.25461i	0.657618	−	0.176208i
$584$	37.0248	+	0.572573i	1.53210	+	0.0236932i
$585$	20.7357	−	26.2361i	0.857316	−	1.08473i
$586$	−6.47426	−	18.0773i	−0.267449	−	0.746765i
$587$	10.0254	−	10.0254i	0.413791	−	0.413791i	−0.469266	−	0.883057i	$-0.655481\pi$
$587$	10.0254	−	10.0254i	0.413791	−	0.413791i	0.883057	+	0.469266i	$0.155481\pi$
$588$		0			0
$589$		−	3.43871i		−	0.141690i
$590$	12.3922	−	10.9189i	0.510179	−	0.449524i
$591$	25.8048	−	14.8984i	1.06147	−	0.612839i
$592$	−0.931097	−	13.9495i	−0.0382679	−	0.573322i
$593$	−3.54698	−	13.2375i	−0.145657	−	0.543599i	−0.999725	−	0.0234382i	$-0.992539\pi$
$593$	−3.54698	−	13.2375i	−0.145657	−	0.543599i	0.854068	−	0.520161i	$-0.174128\pi$
$594$	−37.2079	−	31.5494i	−1.52666	−	1.29449i
$595$		0			0
$596$	−4.70447	−	28.3886i	−0.192702	−	1.16284i
$597$	47.1840	−	12.6429i	1.93111	−	0.517440i
$598$	5.27175	+	7.61205i	0.215578	+	0.311280i
$599$	21.0392	+	36.4409i	0.859637	+	1.48893i	0.872276	+	0.489014i	$0.162643\pi$
$599$	21.0392	+	36.4409i	0.859637	+	1.48893i	−0.0126393	+	0.999920i	$0.504023\pi$
$600$	44.0084	+	13.8996i	1.79664	+	0.567449i
$601$	35.4599			1.44644			0.723220	−	0.690618i	$-0.242661\pi$
$601$	35.4599			1.44644			0.723220	+	0.690618i	$0.242661\pi$
$602$		0			0
$603$	67.2702	+	67.2702i	2.73946	+	2.73946i
$604$	−13.6925	−	5.14413i	−0.557141	−	0.209312i
$605$	−1.51671	−	12.9523i	−0.0616631	−	0.526586i
$606$	−4.11826	+	22.6718i	−0.167293	+	0.920981i
$607$	4.60061	+	17.1697i	0.186733	+	0.696898i	0.994253	+	0.107057i	$0.0341428\pi$
$607$	4.60061	+	17.1697i	0.186733	+	0.696898i	−0.807520	+	0.589841i	$0.799191\pi$
$608$	35.8556	−	15.6078i	1.45414	−	0.632981i
$609$		0			0
$610$	30.0234	+	10.1136i	1.21561	+	0.409487i
$611$	4.22408	+	2.43877i	0.170888	+	0.0986622i
$612$	2.93608	+	0.287402i	0.118684	+	0.0116175i
$613$	−34.1959	−	9.16276i	−1.38116	−	0.370080i	−0.509617	−	0.860401i	$-0.670213\pi$
$613$	−34.1959	−	9.16276i	−1.38116	−	0.370080i	−0.871542	+	0.490321i	$0.836880\pi$
$614$	6.71589	+	18.7519i	0.271031	+	0.756767i
$615$	8.70516	+	21.8986i	0.351026	+	0.883035i
$616$		0			0
$617$	−20.4594	−	20.4594i	−0.823663	−	0.823663i	0.162968	−	0.986631i	$-0.447893\pi$
$617$	−20.4594	−	20.4594i	−0.823663	−	0.823663i	−0.986631	+	0.162968i	$0.947893\pi$
$618$	−43.3420	−	20.4834i	−1.74347	−	0.823962i
$619$	−0.816411	−	1.41407i	−0.0328143	−	0.0568361i	0.849152	−	0.528149i	$-0.177114\pi$
$619$	−0.816411	−	1.41407i	−0.0328143	−	0.0568361i	−0.881966	+	0.471313i	$0.843780\pi$
$620$	2.13747	−	0.616473i	0.0858427	−	0.0247582i
$621$	25.4084	−	44.0087i	1.01961	−	1.76601i
$622$	−1.04916	−	12.7485i	−0.0420676	−	0.511168i
$623$		0			0
$624$	24.1557	−	8.23206i	0.967002	−	0.329546i
$625$	−20.8989	−	13.7199i	−0.835957	−	0.548795i
$626$	22.1631	+	4.02585i	0.885816	+	0.160905i
$627$	49.5375	+	13.2735i	1.97834	+	0.530094i
$628$	36.5780	−	16.5997i	1.45962	−	0.662400i
$629$			0.673953i			0.0268723i
$630$		0			0
$631$			41.6810i			1.65929i	0.558289	+	0.829647i	$0.311458\pi$
$631$			41.6810i			1.65929i	−0.558289	+	0.829647i	$0.688542\pi$
$632$	−8.77882	+	30.8469i	−0.349203	+	1.22702i
$633$	−52.3624	−	14.0305i	−2.08122	−	0.557661i
$634$	−3.08785	+	16.9992i	−0.122634	+	0.675126i
$635$	0.919910	−	6.28954i	0.0365055	−	0.249593i
$636$	46.5607	−	7.71588i	1.84625	−	0.305954i
$637$		0			0
$638$	−23.4912	+	1.93326i	−0.930027	+	0.0765385i
$639$	−13.7718	+	23.8535i	−0.544805	+	0.943630i
$640$	16.1296	+	19.4893i	0.637580	+	0.770384i
$641$	9.61057	+	16.6460i	0.379595	+	0.657477i	0.991003	−	0.133838i	$-0.0427301\pi$
$641$	9.61057	+	16.6460i	0.379595	+	0.657477i	−0.611408	+	0.791315i	$0.709397\pi$
$642$	4.21775	−	8.92460i	0.166461	−	0.352226i
$643$	9.73498	+	9.73498i	0.383910	+	0.383910i	0.872509	−	0.488599i	$-0.162492\pi$
$643$	9.73498	+	9.73498i	0.383910	+	0.383910i	−0.488599	+	0.872509i	$0.662492\pi$
$644$		0			0
$645$	11.8953	−	27.5926i	0.468377	−	1.08646i
$646$	−1.77474	+	0.635612i	−0.0698261	+	0.0250078i
$647$	−41.9129	−	11.2305i	−1.64777	−	0.441518i	−0.688780	−	0.724970i	$-0.741854\pi$
$647$	−41.9129	−	11.2305i	−1.64777	−	0.441518i	−0.958986	+	0.283452i	$0.908520\pi$
$648$	−52.3098	−	53.9531i	−2.05492	−	2.11948i
$649$	10.2826	+	5.93668i	0.403629	+	0.233035i
$650$	−13.8043	+	0.738550i	−0.541449	+	0.0289683i
$651$		0			0
$652$	−21.7105	−	15.5379i	−0.850251	−	0.608510i
$653$	−9.62651	−	35.9266i	−0.376714	−	1.40592i	−0.850824	−	0.525451i	$-0.823897\pi$
$653$	−9.62651	−	35.9266i	−0.376714	−	1.40592i	0.474109	−	0.880466i	$-0.342770\pi$
$654$	42.9643	+	7.80432i	1.68004	+	0.305173i
$655$	14.4987	−	1.69780i	0.566512	−	0.0663385i
$656$	−2.50490	+	12.6724i	−0.0977999	+	0.494773i
$657$	70.8158	+	70.8158i	2.76279	+	2.76279i
$658$		0			0
$659$	−31.4251			−1.22415			−0.612074	−	0.790800i	$-0.709665\pi$
$659$	−31.4251			−1.22415			−0.612074	+	0.790800i	$0.709665\pi$
$660$	0.630124	+	33.1716i	0.0245275	+	1.29120i
$661$	1.81769	+	3.14833i	0.0707000	+	0.122456i	0.899208	−	0.437521i	$-0.144143\pi$
$661$	1.81769	+	3.14833i	0.0707000	+	0.122456i	−0.828508	+	0.559977i	$0.810810\pi$
$662$	33.7208	−	23.3534i	1.31059	−	0.907657i
$663$	−1.18830	+	0.318405i	−0.0461498	+	0.0123658i
$664$	2.03167	+	1.21525i	0.0788441	+	0.0471610i
$665$		0			0
$666$	24.4538	−	28.8397i	0.947565	−	1.11752i
$667$	−6.35486	−	23.7166i	−0.246061	−	0.918312i
$668$	−11.8522	−	1.16016i	−0.458574	−	0.0448881i
$669$	−42.2761	+	24.4081i	−1.63449	+	0.943673i
$670$	2.48062	−	39.2489i	0.0958348	−	1.51632i
$671$			22.7751i			0.879224i
$672$		0			0
$673$	7.66159	−	7.66159i	0.295333	−	0.295333i	−0.543850	−	0.839183i	$-0.683034\pi$
$673$	7.66159	−	7.66159i	0.295333	−	0.295333i	0.839183	+	0.543850i	$0.183034\pi$
$674$	0.821205	−	0.294110i	0.0316317	−	0.0113287i
$675$	36.0360	+	66.7646i	1.38703	+	2.56977i
$676$	14.1823	−	11.6533i	0.545472	−	0.448205i
$677$	0.273888	−	0.0733880i	0.0105264	−	0.00282053i	−0.253552	−	0.967322i	$-0.581599\pi$
$677$	0.273888	−	0.0733880i	0.0105264	−	0.00282053i	0.264078	+	0.964501i	$0.414932\pi$
$678$	−79.0270	+	6.50369i	−3.03501	+	0.249773i
$679$		0			0
$680$	−0.713255	−	0.989209i	−0.0273521	−	0.0379344i
$681$	−13.6939	+	23.7186i	−0.524753	+	0.908898i
$682$	0.910515	+	1.31472i	0.0348654	+	0.0503433i
$683$	−11.1511	+	41.6163i	−0.426683	+	1.59240i	0.333536	+	0.942737i	$0.391758\pi$
$683$	−11.1511	+	41.6163i	−0.426683	+	1.59240i	−0.760220	+	0.649666i	$0.774909\pi$
$684$	99.0070	+	37.1958i	3.78563	+	1.42222i
$685$	4.86317	+	12.2337i	0.185812	+	0.467426i
$686$		0			0
$687$	22.0676	−	22.0676i	0.841930	−	0.841930i
$688$	13.6840	−	9.16709i	0.521697	−	0.349492i
$689$	−12.2429	+	7.06844i	−0.466417	+	0.269286i
$690$	−33.8808	+	6.82146i	−1.28982	+	0.259689i
$691$	2.91753	+	1.68444i	0.110988	+	0.0640791i	0.554467	−	0.832206i	$-0.312922\pi$
$691$	2.91753	+	1.68444i	0.110988	+	0.0640791i	−0.443478	+	0.896285i	$0.646256\pi$
$692$	−23.6477	+	33.0422i	−0.898951	+	1.25607i
$693$		0			0
$694$	−19.0140	+	22.4242i	−0.721761	+	0.851212i
$695$	11.7497	−	8.75124i	0.445692	−	0.331953i
$696$	−67.6641	−	1.04639i	−2.56480	−	0.0396635i
$697$	0.161169	−	0.601490i	0.00610471	−	0.0227831i
$698$	−14.6941	−	6.94441i	−0.556180	−	0.262850i
$699$	32.5255			1.23023
$700$		0			0
$701$	−20.4918			−0.773966			−0.386983	−	0.922087i	$-0.626483\pi$
$701$	−20.4918			−0.773966			−0.386983	+	0.922087i	$0.626483\pi$
$702$	37.9301	+	17.9257i	1.43158	+	0.676562i
$703$	−6.25348	+	23.3383i	−0.235855	+	0.880221i
$704$	−9.57595	+	15.4613i	−0.360907	+	0.582720i
$705$	−14.6008	+	10.8748i	−0.549899	+	0.409567i
$706$	16.6132	−	19.5929i	0.625247	−	0.737387i
$707$		0			0
$708$	27.7209	+	19.8394i	1.04182	+	0.745610i
$709$	24.0284	+	13.8728i	0.902407	+	0.521005i	0.877980	−	0.478697i	$-0.158891\pi$
$709$	24.0284	+	13.8728i	0.902407	+	0.521005i	0.0244266	+	0.999702i	$0.492224\pi$
$710$	11.1622	−	2.24736i	0.418908	−	0.0843418i
$711$	−75.1197	+	43.3704i	−2.81721	+	1.62652i
$712$	10.8584	+	3.09024i	0.406937	+	0.115811i
$713$	−1.17797	+	1.17797i	−0.0441153	+	0.0441153i
$714$		0			0
$715$	−3.67111	−	9.23499i	−0.137292	−	0.345369i
$716$	2.23748	−	5.95567i	0.0836186	−	0.222574i
$717$	16.4846	−	61.5213i	0.615628	−	2.29756i
$718$	18.0905	+	26.1215i	0.675133	+	0.974846i
$719$	8.96044	−	15.5199i	0.334168	−	0.578796i	−0.649157	−	0.760655i	$-0.724878\pi$
$719$	8.96044	−	15.5199i	0.334168	−	0.578796i	0.983325	+	0.181859i	$0.0582114\pi$
$720$	−5.37111	+	68.2099i	−0.200170	+	2.54203i
$721$		0			0
$722$	−40.5756	+	3.33926i	−1.51007	+	0.124274i
$723$	30.3387	−	8.12922i	1.12831	−	0.302329i
$724$	−11.7183	−	14.2614i	−0.435509	−	0.530021i
$725$	35.1223	+	10.4986i	1.30441	+	0.389907i
$726$	25.3394	−	9.07516i	0.940435	−	0.336811i
$727$	−12.7173	+	12.7173i	−0.471659	+	0.471659i	−0.902451	−	0.430792i	$-0.858234\pi$
$727$	−12.7173	+	12.7173i	−0.471659	+	0.471659i	0.430792	+	0.902451i	$0.358234\pi$
$728$		0			0
$729$		−	54.6902i		−	2.02556i
$730$	2.61137	−	41.3175i	0.0966510	−	1.52923i
$731$	−0.687621	+	0.396998i	−0.0254326	+	0.0146835i
$732$	−6.37015	+	65.0771i	−0.235448	+	2.40532i
$733$	8.28399	+	30.9163i	0.305976	+	1.14192i	0.932102	+	0.362196i	$0.117973\pi$
$733$	8.28399	+	30.9163i	0.305976	+	1.14192i	−0.626126	+	0.779722i	$0.715360\pi$
$734$	9.75499	−	11.5046i	0.360063	−	0.424642i
$735$		0			0
$736$	−17.6293	−	6.93608i	−0.649826	−	0.255667i
$737$	27.3085	−	7.31728i	1.00592	−	0.269536i
$738$	−28.7213	+	19.8910i	−1.05724	+	0.732198i
$739$	−17.8879	−	30.9827i	−0.658016	−	1.13972i	−0.981128	−	0.193357i	$-0.938062\pi$
$739$	−17.8879	−	30.9827i	−0.658016	−	1.13972i	0.323112	−	0.946361i	$-0.395271\pi$
$740$	−15.6279	+	0.296867i	−0.574494	+	0.0109130i
$741$	−44.1041			−1.62021
$742$		0			0
$743$	−1.03957	−	1.03957i	−0.0381381	−	0.0381381i	0.687781	−	0.725919i	$-0.258585\pi$
$743$	−1.03957	−	1.03957i	−0.0381381	−	0.0381381i	−0.725919	+	0.687781i	$0.758585\pi$
$744$	2.23396	+	4.01133i	0.0819010	+	0.147062i
$745$	−31.9540	+	3.74181i	−1.17070	+	0.137089i
$746$	−26.9435	−	4.89420i	−0.986473	−	0.179189i
$747$	1.65716	+	6.18462i	0.0606325	+	0.226283i
$748$	0.510235	−	0.712935i	0.0186561	−	0.0260675i
$749$		0			0
$750$	17.8665	−	48.4068i	0.652391	−	1.76757i
$751$	−2.97538	−	1.71784i	−0.108573	−	0.0626847i	0.444730	−	0.895665i	$-0.353300\pi$
$751$	−2.97538	−	1.71784i	−0.108573	−	0.0626847i	−0.553303	+	0.832980i	$0.686633\pi$
$752$	−9.95740	+	0.664633i	−0.363109	+	0.0242367i
$753$	−86.0012	−	23.0439i	−3.13406	−	0.839768i
$754$	19.0834	−	6.83459i	0.694975	−	0.248901i
$755$	−6.47404	+	15.0173i	−0.235615	+	0.546537i
$756$		0			0
$757$	21.8519	+	21.8519i	0.794220	+	0.794220i	0.982177	−	0.187957i	$-0.0601866\pi$
$757$	21.8519	+	21.8519i	0.794220	+	0.794220i	−0.187957	+	0.982177i	$0.560187\pi$
$758$	6.83833	−	14.4697i	0.248379	−	0.525562i
$759$	−12.4226	−	21.5166i	−0.450912	−	0.781002i
$760$	−15.5206	−	40.8735i	−0.562992	−	1.48264i
$761$	3.32790	−	5.76410i	0.120636	−	0.208948i	−0.799382	−	0.600823i	$-0.794840\pi$
$761$	3.32790	−	5.76410i	0.120636	−	0.208948i	0.920019	+	0.391874i	$0.128173\pi$
$762$	13.0752	−	1.07605i	0.473665	−	0.0389812i
$763$		0			0
$764$	4.83062	+	29.1499i	0.174766	+	1.05461i
$765$	0.477336	−	3.26361i	0.0172581	−	0.117996i
$766$	1.12986	−	6.22009i	0.0408234	−	0.224741i
$767$	−9.86296	−	2.64277i	−0.356131	−	0.0954249i
$768$	−31.6866	+	41.5004i	−1.14339	+	1.49752i
$769$		−	10.3364i		−	0.372740i	−0.982480	−	0.186370i	$-0.940328\pi$
$769$		−	10.3364i		−	0.372740i	0.982480	−	0.186370i	$-0.0596723\pi$
$770$		0			0
$771$		−	94.1718i		−	3.39151i
$772$	2.52529	+	5.56455i	0.0908871	+	0.200273i
$773$	24.1755	+	6.47780i	0.869531	+	0.232990i	0.665885	−	0.746054i	$-0.268054\pi$
$773$	24.1755	+	6.47780i	0.869531	+	0.232990i	0.203646	+	0.979045i	$0.434721\pi$
$774$	43.8293	+	7.96145i	1.57541	+	0.286168i
$775$	−0.574615	−	2.41988i	−0.0206408	−	0.0869247i
$776$	3.75436	+	2.24569i	0.134774	+	0.0806156i
$777$		0			0
$778$	−3.12984	−	38.0310i	−0.112210	−	1.36348i
$779$	11.1622	−	19.3336i	0.399929	−	0.692697i
$780$	−7.90675	−	27.4147i	−0.283107	−	0.981602i
$781$	4.09267	+	7.08872i	0.146447	+	0.253654i
$782$	0.825691	+	0.390220i	0.0295267	+	0.0139542i
$783$	−78.6639	−	78.6639i	−2.81122	−	2.81122i
$784$		0			0
$785$	−16.5898	−	41.7331i	−0.592116	−	1.48952i
$786$	10.1587	+	28.3648i	0.362348	+	1.01174i
$787$	4.13231	+	1.10725i	0.147301	+	0.0394692i	0.331716	−	0.943379i	$-0.392372\pi$
$787$	4.13231	+	1.10725i	0.147301	+	0.0394692i	−0.184415	+	0.982848i	$0.559039\pi$
$788$	1.77903	−	18.1744i	0.0633752	−	0.647437i
$789$	14.7453	+	8.51323i	0.524948	+	0.303079i
$790$	33.9812	+	11.4468i	1.20900	+	0.407258i
$791$		0			0
$792$	−47.7021	+	11.9944i	−1.69502	+	0.426201i
$793$	−5.06928	−	18.9188i	−0.180015	−	0.671827i
$794$	2.28304	−	12.5686i	0.0810219	−	0.446041i
$795$	−6.13700	−	52.4083i	−0.217657	−	1.85873i
$796$	10.5286	−	28.0248i	0.373177	−	0.993313i
$797$	−27.3364	−	27.3364i	−0.968306	−	0.968306i	0.0312066	−	0.999513i	$-0.490065\pi$
$797$	−27.3364	−	27.3364i	−0.968306	−	0.968306i	−0.999513	+	0.0312066i	$0.990065\pi$
$798$		0			0
$799$	0.481078			0.0170193
$800$	22.6241	−	16.9750i	0.799882	−	0.600158i
$801$	15.2668	+	26.4429i	0.539427	+	0.934314i
$802$	4.86258	+	7.02123i	0.171704	+	0.247928i
$803$	28.7478	−	7.70294i	1.01449	−	0.271831i
$804$	80.0773	−	13.2701i	2.82411	−	0.468001i
$805$		0			0
$806$	−1.04898	−	0.889450i	−0.0369486	−	0.0313295i
$807$	−10.7342	−	40.0604i	−0.377860	−	1.41019i
$808$	9.83018	+	10.1390i	0.345825	+	0.356689i
$809$	12.5601	−	7.25159i	0.441590	−	0.254952i	−0.262682	−	0.964883i	$-0.584607\pi$
$809$	12.5601	−	7.25159i	0.441590	−	0.254952i	0.704272	+	0.709930i	$0.251274\pi$
$810$	−63.0389	+	55.5442i	−2.21496	+	1.95162i
$811$		−	24.8308i		−	0.871927i	−0.899964	−	0.435964i	$-0.856408\pi$
$811$		−	24.8308i		−	0.871927i	0.899964	−	0.435964i	$-0.143592\pi$
$812$		0			0
$813$	−66.7073	+	66.7073i	−2.33953	+	2.33953i
$814$	−3.78871	−	10.5788i	−0.132794	−	0.370785i
$815$	−18.5084	+	23.4180i	−0.648323	+	0.820298i
$816$	1.65734	−	1.89441i	0.0580186	−	0.0663177i
$817$	−27.4953	+	7.36735i	−0.961939	+	0.257751i
$818$	−2.49065	−	30.2642i	−0.0870836	−	1.05816i
$819$		0			0
$820$	14.0186	+	3.47231i	0.489552	+	0.121258i
$821$	−22.4803	+	38.9370i	−0.784567	+	1.35891i	0.144690	+	0.989477i	$0.453782\pi$
$821$	−22.4803	+	38.9370i	−0.784567	+	1.35891i	−0.929257	+	0.369434i	$0.879552\pi$
$822$	−22.3377	+	15.4701i	−0.779118	+	0.539581i
$823$	4.23553	−	15.8072i	0.147641	−	0.551005i	−0.851982	−	0.523571i	$-0.824600\pi$
$823$	4.23553	−	15.8072i	0.147641	−	0.551005i	0.999624	−	0.0274346i	$-0.00873379\pi$
$824$	−25.6676	+	14.2946i	−0.894172	+	0.497977i
$825$	37.0784	+	1.06301i	1.29090	+	0.0370093i
$826$		0			0
$827$	−15.3869	+	15.3869i	−0.535056	+	0.535056i	−0.922073	−	0.387017i	$-0.873506\pi$
$827$	−15.3869	+	15.3869i	−0.535056	+	0.535056i	0.387017	+	0.922073i	$0.373506\pi$
$828$	−21.1741	−	46.6577i	−0.735850	−	1.62147i
$829$	34.9273	−	20.1653i	1.21307	−	0.700369i	0.249647	−	0.968337i	$-0.419685\pi$
$829$	34.9273	−	20.1653i	1.21307	−	0.700369i	0.963428	+	0.267968i	$0.0863521\pi$
$830$	1.46536	−	2.20417i	0.0508634	−	0.0765080i
$831$	−61.8456	−	35.7066i	−2.14540	−	1.23865i
$832$	4.51316	−	14.9748i	0.156466	−	0.519157i
$833$		0			0
$834$	23.0632	+	19.5558i	0.798614	+	0.677162i
$835$	−1.92688	+	13.1743i	−0.0666823	+	0.455915i
$836$	24.2841	−	19.9539i	0.839885	−	0.690118i
$837$	−1.95356	+	7.29077i	−0.0675248	+	0.252006i
$838$	−7.32826	+	15.5063i	−0.253151	+	0.535657i
$839$	−19.9919			−0.690195			−0.345098	−	0.938567i	$-0.612154\pi$
$839$	−19.9919			−0.690195			−0.345098	+	0.938567i	$0.612154\pi$
$840$		0			0
$841$	−24.7517			−0.853507
$842$	−18.7020	+	39.5727i	−0.644512	+	1.36376i
$843$	5.88605	−	21.9671i	0.202726	−	0.756586i
$844$	−25.6690	+	21.0918i	−0.883563	+	0.726008i
$845$	−12.2587	−	16.4589i	−0.421711	−	0.566204i
$846$	−20.5862	−	17.4555i	−0.707769	−	0.600133i
$847$		0			0
$848$	12.7618	−	25.9568i	0.438242	−	0.891359i
$849$	−76.1512	−	43.9659i	−2.61350	−	1.50891i
$850$	−1.14270	+	0.743852i	−0.0391943	+	0.0255139i
$851$	10.1370	−	5.85259i	0.347492	−	0.200624i
$852$	9.71161	+	21.3999i	0.332714	+	0.733147i
$853$	−4.67428	+	4.67428i	−0.160044	+	0.160044i	−0.782586	−	0.622542i	$-0.786100\pi$
$853$	−4.67428	+	4.67428i	−0.160044	+	0.160044i	0.622542	+	0.782586i	$0.286100\pi$
$854$		0			0
$855$	46.8121	−	108.586i	1.60094	−	3.71358i
$856$	−2.94342	−	5.28523i	−0.100604	−	0.180646i
$857$	4.28833	−	16.0043i	0.146487	−	0.546695i	−0.853198	−	0.521587i	$-0.825340\pi$
$857$	4.28833	−	16.0043i	0.146487	−	0.546695i	0.999685	−	0.0251084i	$-0.00799311\pi$
$858$	16.8623	−	11.6781i	0.575670	−	0.398682i
$859$	−2.05099	+	3.55242i	−0.0699788	+	0.121207i	−0.898892	−	0.438171i	$-0.855627\pi$
$859$	−2.05099	+	3.55242i	−0.0699788	+	0.121207i	0.828913	+	0.559378i	$0.188960\pi$
$860$	−9.50867	−	15.7700i	−0.324243	−	0.537753i
$861$		0			0
$862$	2.61235	+	31.7430i	0.0889771	+	1.08117i
$863$	−47.9390	+	12.8452i	−1.63186	+	0.437257i	−0.954456	−	0.298351i	$-0.903563\pi$
$863$	−47.9390	+	12.8452i	−1.63186	+	0.437257i	−0.677408	+	0.735608i	$0.736897\pi$
$864$	−84.8880	+	12.7220i	−2.88795	+	0.432811i
$865$	35.6409	+	28.1688i	1.21183	+	0.957766i
$866$	9.93169	+	27.7310i	0.337493	+	0.942338i
$867$	39.1428	−	39.1428i	1.32936	−	1.32936i
$868$		0			0
$869$			25.7774i			0.874437i
$870$	−4.77235	+	75.5091i	−0.161798	+	2.56000i
$871$	−21.0559	+	12.1566i	−0.713452	+	0.411912i
$872$	19.2139	−	18.6287i	0.650666	−	0.630848i
$873$	3.06230	+	11.4287i	0.103643	+	0.386802i
$874$	24.9721	+	21.1744i	0.844694	+	0.716234i
$875$		0			0
$876$	84.2978	−	13.9695i	2.84816	−	0.471987i
$877$	9.43608	−	2.52839i	0.318634	−	0.0853776i	−0.0959575	−	0.995385i	$-0.530591\pi$
$877$	9.43608	−	2.52839i	0.318634	−	0.0853776i	0.414591	+	0.910008i	$0.363925\pi$
$878$	−26.2727	−	37.9360i	−0.886661	−	1.28028i
$879$	−22.1545	−	38.3728i	−0.747254	−	1.29428i
$880$	16.7566	+	11.5175i	0.564866	+	0.388256i
$881$	−14.9131			−0.502435			−0.251217	−	0.967931i	$-0.580831\pi$
$881$	−14.9131			−0.502435			−0.251217	+	0.967931i	$0.580831\pi$
$882$		0			0
$883$	−19.0557	−	19.0557i	−0.641277	−	0.641277i	0.309592	−	0.950869i	$-0.399807\pi$
$883$	−19.0557	−	19.0557i	−0.641277	−	0.641277i	−0.950869	+	0.309592i	$0.899807\pi$
$884$	−0.265157	+	0.705788i	−0.00891819	+	0.0237382i
$885$	23.6323	−	29.9011i	0.794392	−	1.00511i
$886$	−9.28067	+	51.0919i	−0.311790	+	1.71647i
$887$	−13.8347	−	51.6318i	−0.464524	−	1.73363i	−0.658464	−	0.752612i	$-0.728794\pi$
$887$	−13.8347	−	51.6318i	−0.464524	−	1.73363i	0.193941	−	0.981013i	$-0.437873\pi$
$888$	−7.86694	−	31.2872i	−0.263997	−	1.04993i
$889$		0			0
$890$	4.02938	−	11.9617i	0.135065	−	0.400958i
$891$	−52.3076	−	30.1998i	−1.75237	−	1.01173i
$892$	−2.91458	+	29.7752i	−0.0975874	+	0.996948i
$893$	16.6593	+	4.46384i	0.557481	+	0.149377i
$894$	−22.3889	−	62.5137i	−0.748797	−	2.09077i
$895$	−6.53192	−	2.81594i	−0.218338	−	0.0941265i
$896$		0			0
$897$	15.1083	+	15.1083i	0.504453	+	0.504453i
$898$	37.8807	+	17.9023i	1.26409	+	0.597409i
$899$	1.82348	+	3.15836i	0.0608165	+	0.105337i
$900$	75.8884	+	9.63112i	2.52961	+	0.321037i
$901$	−0.697169	+	1.20753i	−0.0232261	+	0.0402287i
$902$	0.851558	+	10.3474i	0.0283538	+	0.344530i
$903$		0			0
$904$	−24.9459	+	41.7048i	−0.829690	+	1.38708i
$905$	−16.5507	+	12.3271i	−0.550165	+	0.409766i
$906$	−33.2092	−	6.03233i	−1.10330	−	0.200411i
$907$	44.2268	+	11.8505i	1.46853	+	0.393490i	0.902425	−	0.430846i	$-0.141785\pi$
$907$	44.2268	+	11.8505i	1.46853	+	0.393490i	0.566100	+	0.824336i	$0.308451\pi$
$908$	6.93642	+	15.2846i	0.230193	+	0.507238i
$909$			38.1942i			1.26682i
$910$		0			0
$911$			56.0047i			1.85552i	0.373181	+	0.927758i	$0.378267\pi$
$911$			56.0047i			1.85552i	−0.373181	+	0.927758i	$0.621733\pi$
$912$	74.9700	−	50.2235i	2.48251	−	1.66307i
$913$	1.83793	+	0.492471i	0.0608265	+	0.0162984i
$914$	1.50981	−	8.31178i	0.0499399	−	0.274929i
$915$	72.3366	+	10.5800i	2.39137	+	0.349763i
$916$	−3.12689	−	18.8689i	−0.103316	−	0.623447i
$917$		0			0
$918$	4.12390	−	0.339385i	0.136109	−	0.0112014i
$919$	−19.2225	+	33.2943i	−0.634091	+	1.09828i	0.352616	+	0.935768i	$0.385292\pi$
$919$	−19.2225	+	33.2943i	−0.634091	+	1.09828i	−0.986707	+	0.162509i	$0.948041\pi$
$920$	−8.68490	+	19.3184i	−0.286333	+	0.636909i
$921$	22.9814	+	39.8049i	0.757262	+	1.31162i
$922$	−4.06718	+	8.60600i	−0.133945	+	0.283423i
$923$	−4.97750	−	4.97750i	−0.163836	−	0.163836i
$924$		0			0
$925$	−0.500811	+	17.4685i	−0.0164666	+	0.574362i
$926$	−0.230221	+	0.0824521i	−0.00756552	+	0.00270955i
$927$	−76.7519	−	20.5656i	−2.52086	−	0.675464i
$928$	−24.6558	+	33.3488i	−0.809367	+	1.09473i
$929$	26.9022	+	15.5320i	0.882632	+	0.509588i	0.871525	−	0.490351i	$-0.163131\pi$
$929$	26.9022	+	15.5320i	0.882632	+	0.509588i	0.0111066	+	0.999938i	$0.496465\pi$
$930$	4.59869	−	2.28117i	0.150797	−	0.0748024i
$931$		0			0
$932$	11.6011	−	16.2099i	0.380008	−	0.530972i
$933$	−7.63967	−	28.5116i	−0.250111	−	0.933429i
$934$	−6.72213	−	1.22105i	−0.219955	−	0.0399540i
$935$	−0.769005	−	0.607784i	−0.0251492	−	0.0198767i
$936$	36.9555	−	20.5810i	1.20793	−	0.672711i
$937$	−30.6258	−	30.6258i	−1.00050	−	1.00050i	−1.00000		0.000502083i	$-0.999840\pi$
$937$	−30.6258	−	30.6258i	−1.00050	−	1.00050i	−0.000502083	−	1.00000i	$-0.500160\pi$
$938$		0			0
$939$	51.9797			1.69629
$940$	0.211908	+	11.1555i	0.00691169	+	0.363852i
$941$	20.8453	+	36.1052i	0.679539	+	1.17700i	0.975120	+	0.221678i	$0.0711535\pi$
$941$	20.8453	+	36.1052i	0.679539	+	1.17700i	−0.295581	+	0.955318i	$0.595513\pi$
$942$	76.2012	−	52.7734i	2.48277	−	1.71945i
$943$	−10.4467	+	2.79918i	−0.340190	+	0.0911537i
$944$	19.7749	−	6.73913i	0.643618	−	0.219340i
$945$		0			0
$946$	8.56152	−	10.0971i	0.278359	−	0.328284i
$947$	−2.35220	−	8.77852i	−0.0764362	−	0.285264i	0.917119	−	0.398614i	$-0.130509\pi$
$947$	−2.35220	−	8.77852i	−0.0764362	−	0.285264i	−0.993555	+	0.113350i	$0.963842\pi$
$948$	−7.20987	+	73.6557i	−0.234166	+	2.39223i
$949$	−22.1657	+	12.7973i	−0.719528	+	0.415419i
$950$	−46.4727	+	15.1560i	−1.50777	+	0.491724i
$951$			39.8687i			1.29283i
$952$		0			0
$953$	16.5153	−	16.5153i	0.534984	−	0.534984i	−0.387068	−	0.922051i	$-0.626512\pi$
$953$	16.5153	−	16.5153i	0.534984	−	0.534984i	0.922051	+	0.387068i	$0.126512\pi$
$954$	73.6474	−	26.3764i	2.38442	−	0.853966i
$955$	32.8109	−	3.84215i	1.06174	−	0.124329i
$956$	−24.7810	−	30.1588i	−0.801475	−	0.975407i
$957$	−52.5375	+	14.0774i	−1.69830	+	0.455057i
$958$	44.2780	−	3.64395i	1.43056	−	0.117731i
$959$		0			0
$960$	44.6586	+	37.5968i	1.44135	+	1.21343i
$961$	−15.3763	+	26.6325i	−0.496009	+	0.859113i
$962$	5.50182	+	7.94425i	0.177386	+	0.256133i
$963$	4.23469	−	15.8041i	0.136461	−	0.509279i
$964$	6.76975	−	18.0195i	0.218039	−	0.580370i
$965$	6.34879	−	2.52378i	0.204375	−	0.0812435i
$966$		0			0
$967$	28.7327	−	28.7327i	0.923981	−	0.923981i	−0.0733272	−	0.997308i	$-0.523362\pi$
$967$	28.7327	−	28.7327i	0.923981	−	0.923981i	0.997308	+	0.0733272i	$0.0233617\pi$
$968$	4.51520	−	15.8655i	0.145124	−	0.509935i
$969$	−3.76725	+	2.17502i	−0.121022	+	0.0698718i
$970$	2.70786	−	4.07313i	0.0869443	−	0.130780i
$971$	18.8837	+	10.9025i	0.606006	+	0.349878i	0.771401	−	0.636350i	$-0.219556\pi$
$971$	18.8837	+	10.9025i	0.606006	+	0.349878i	−0.165394	+	0.986227i	$0.552890\pi$
$972$	−66.9801	−	47.9365i	−2.14839	−	1.53756i
$973$		0			0
$974$	−5.33852	+	6.29601i	−0.171057	+	0.201737i
$975$	−31.0368	+	7.36988i	−0.993974	+	0.236025i
$976$	30.1607	+	26.3863i	0.965421	+	0.844606i
$977$	5.90126	−	22.0238i	0.188798	−	0.704604i	−0.804987	−	0.593292i	$-0.797828\pi$
$977$	5.90126	−	22.0238i	0.188798	−	0.704604i	0.993785	−	0.111312i	$-0.0355053\pi$
$978$	−55.6999	−	26.3237i	−1.78109	−	0.841738i
$979$	9.07390			0.290003
$980$		0			0
$981$	72.3799			2.31091
$982$	−5.80051	−	2.74131i	−0.185102	−	0.0874787i
$983$	2.51085	−	9.37063i	0.0800838	−	0.298877i	−0.914254	−	0.405141i	$-0.867222\pi$
$983$	2.51085	−	9.37063i	0.0800838	−	0.298877i	0.994338	+	0.106264i	$0.0338890\pi$
$984$	−0.460914	+	29.8045i	−0.0146934	+	0.950134i
$985$	−20.2018	−	2.95472i	−0.643683	−	0.0941452i
$986$	1.29300	−	1.52490i	0.0411774	−	0.0485627i
$987$		0			0
$988$	−15.7310	+	21.9804i	−0.500470	+	0.699290i
$989$	11.9426	+	6.89505i	0.379752	+	0.219250i
$990$	10.8543	+	53.9109i	0.344971	+	1.71340i
$991$	21.7531	−	12.5591i	0.691009	−	0.398954i	−0.112981	−	0.993597i	$-0.536040\pi$
$991$	21.7531	−	12.5591i	0.691009	−	0.398954i	0.803990	+	0.594643i	$0.202707\pi$
$992$	2.79595	+	0.317404i	0.0887715	+	0.0100776i
$993$	66.9288	−	66.9288i	2.12392	−	2.12392i
$994$		0			0
$995$	−30.7364	−	13.2506i	−0.974408	−	0.420072i
$996$	5.11391	+	1.92124i	0.162041	+	0.0608769i
$997$	−1.72506	+	6.43800i	−0.0546331	+	0.203894i	−0.987847	−	0.155427i	$-0.950325\pi$
$997$	−1.72506	+	6.43800i	−0.0546331	+	0.203894i	0.933214	+	0.359320i	$0.116991\pi$
$998$	−26.0342	−	37.5916i	−0.824098	−	1.18994i
$999$	26.5173	−	45.9293i	0.838970	−	1.45314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.n.667.18		112
4.3	odd	2	inner	980.2.x.n.667.23		112
5.3	odd	4	inner	980.2.x.n.863.6		112
7.2	even	3		980.2.k.m.687.2	yes	56
7.3	odd	6	inner	980.2.x.n.67.22		112
7.4	even	3	inner	980.2.x.n.67.21		112
7.5	odd	6		980.2.k.m.687.1	✓	56
7.6	odd	2	inner	980.2.x.n.667.17		112
20.3	even	4	inner	980.2.x.n.863.21		112
28.3	even	6	inner	980.2.x.n.67.5		112
28.11	odd	6	inner	980.2.x.n.67.6		112
28.19	even	6		980.2.k.m.687.18	yes	56
28.23	odd	6		980.2.k.m.687.17	yes	56
28.27	even	2	inner	980.2.x.n.667.24		112
35.3	even	12	inner	980.2.x.n.263.24		112
35.13	even	4	inner	980.2.x.n.863.5		112
35.18	odd	12	inner	980.2.x.n.263.23		112
35.23	odd	12		980.2.k.m.883.17	yes	56
35.33	even	12		980.2.k.m.883.18	yes	56
140.3	odd	12	inner	980.2.x.n.263.17		112
140.23	even	12		980.2.k.m.883.2	yes	56
140.83	odd	4	inner	980.2.x.n.863.22		112
140.103	odd	12		980.2.k.m.883.1	yes	56
140.123	even	12	inner	980.2.x.n.263.18		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.k.m.687.1	✓	56	7.5	odd	6
980.2.k.m.687.2	yes	56	7.2	even	3
980.2.k.m.687.17	yes	56	28.23	odd	6
980.2.k.m.687.18	yes	56	28.19	even	6
980.2.k.m.883.1	yes	56	140.103	odd	12
980.2.k.m.883.2	yes	56	140.23	even	12
980.2.k.m.883.17	yes	56	35.23	odd	12
980.2.k.m.883.18	yes	56	35.33	even	12
980.2.x.n.67.5		112	28.3	even	6	inner
980.2.x.n.67.6		112	28.11	odd	6	inner
980.2.x.n.67.21		112	7.4	even	3	inner
980.2.x.n.67.22		112	7.3	odd	6	inner
980.2.x.n.263.17		112	140.3	odd	12	inner
980.2.x.n.263.18		112	140.123	even	12	inner
980.2.x.n.263.23		112	35.18	odd	12	inner
980.2.x.n.263.24		112	35.3	even	12	inner
980.2.x.n.667.17		112	7.6	odd	2	inner
980.2.x.n.667.18		112	1.1	even	1	trivial
980.2.x.n.667.23		112	4.3	odd	2	inner
980.2.x.n.667.24		112	28.27	even	2	inner
980.2.x.n.863.5		112	35.13	even	4	inner
980.2.x.n.863.6		112	5.3	odd	4	inner
980.2.x.n.863.21		112	20.3	even	4	inner
980.2.x.n.863.22		112	140.83	odd	4	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.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.604271 - 1.27862i) q^{2} +(0.844627 - 3.15219i) q^{3} +(-1.26971 - 1.54526i) q^{4} +(-1.79332 + 1.33567i) q^{5} +(-3.52006 - 2.98473i) q^{6} +(-2.74304 + 0.689718i) q^{8} +(-6.62484 - 3.82485i) q^{9} +O(q^{10})\)	\(q+(0.604271 - 1.27862i) q^{2} +(0.844627 - 3.15219i) q^{3} +(-1.26971 - 1.54526i) q^{4} +(-1.79332 + 1.33567i) q^{5} +(-3.52006 - 2.98473i) q^{6} +(-2.74304 + 0.689718i) q^{8} +(-6.62484 - 3.82485i) q^{9} +(0.624159 + 3.10007i) q^{10} +(-1.96875 + 1.13666i) q^{11} +(-5.94339 + 2.69721i) q^{12} +(1.38240 - 1.38240i) q^{13} +(2.69561 + 6.78102i) q^{15} +(-0.775657 + 3.92407i) q^{16} +(0.0499069 - 0.186255i) q^{17} +(-8.89371 + 6.15937i) q^{18} +(3.45645 - 5.98675i) q^{19} +(4.34096 + 1.07522i) q^{20} +(0.263690 + 3.20413i) q^{22} +(-3.23487 + 0.866782i) q^{23} +(-0.142725 + 9.22915i) q^{24} +(1.43197 - 4.79056i) q^{25} +(-0.932215 - 2.60291i) q^{26} +(-10.7295 + 10.7295i) q^{27} +7.33156i q^{29} +(10.2992 + 0.650933i) q^{30} +(0.430790 - 0.248717i) q^{31} +(4.54867 + 3.36297i) q^{32} +(1.92011 + 7.16594i) q^{33} +(-0.207991 - 0.176360i) q^{34} +(2.50125 + 15.0936i) q^{36} +(-3.37605 + 0.904610i) q^{37} +(-5.56612 - 8.03710i) q^{38} +(-3.18998 - 5.52522i) q^{39} +(3.99791 - 4.90069i) q^{40} +3.22939 q^{41} +(-2.91165 - 2.91165i) q^{43} +(4.25618 + 1.59900i) q^{44} +(16.9892 - 1.98943i) q^{45} +(-0.846460 + 4.65993i) q^{46} +(0.645725 + 2.40988i) q^{47} +(11.7143 + 5.75940i) q^{48} +(-5.25998 - 4.72573i) q^{50} +(-0.544959 - 0.314632i) q^{51} +(-3.89143 - 0.380917i) q^{52} +(-6.98469 - 1.87154i) q^{53} +(7.23537 + 20.2024i) q^{54} +(2.01239 - 4.66799i) q^{55} +(-15.9520 - 15.9520i) q^{57} +(9.37424 + 4.43025i) q^{58} +(-2.61146 - 4.52318i) q^{59} +(7.05580 - 12.7754i) q^{60} +(5.00922 - 8.67623i) q^{61} +(-0.0576991 - 0.701107i) q^{62} +(7.04858 - 3.78386i) q^{64} +(-0.632652 + 4.32552i) q^{65} +(10.3227 + 1.87509i) q^{66} +(-12.0126 - 3.21877i) q^{67} +(-0.351180 + 0.159371i) q^{68} +10.9290i q^{69} -3.60061i q^{71} +(20.8103 + 5.92247i) q^{72} +(-12.6457 - 3.38841i) q^{73} +(-0.883401 + 4.86330i) q^{74} +(-13.8913 - 8.56008i) q^{75} +(-13.6398 + 2.26034i) q^{76} +(-8.99224 + 0.740035i) q^{78} +(5.66954 - 9.81994i) q^{79} +(-3.85027 - 8.07313i) q^{80} +(13.2844 + 23.0093i) q^{81} +(1.95143 - 4.12915i) q^{82} +(-0.591847 - 0.591847i) q^{83} +(0.159277 + 0.400674i) q^{85} +(-5.48231 + 1.96345i) q^{86} +(23.1105 + 6.19243i) q^{87} +(4.61640 - 4.47579i) q^{88} +(-3.45672 - 1.99574i) q^{89} +(7.72235 - 22.9248i) q^{90} +(5.44676 + 3.89816i) q^{92} +(-0.420146 - 1.56801i) q^{93} +(3.47150 + 0.630586i) q^{94} +(1.79781 + 15.3528i) q^{95} +(14.4427 - 11.4978i) q^{96} +(-1.09368 - 1.09368i) q^{97} +17.3902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 4 q^{2} - 32 q^{8}+O(q^{10}) \) 112 * q + 4 * q^2 - 32 * q^8	\( 112 q + 4 q^{2} - 32 q^{8} - 32 q^{16} + 40 q^{22} - 32 q^{25} + 28 q^{30} + 64 q^{32} + 32 q^{36} + 8 q^{37} + 184 q^{46} - 24 q^{50} - 96 q^{53} - 16 q^{57} - 124 q^{58} - 8 q^{60} + 120 q^{65} + 80 q^{72} - 72 q^{78} + 72 q^{81} + 192 q^{85} - 104 q^{86} - 48 q^{88} - 304 q^{92} + 176 q^{93}+O(q^{100}) \) 112 * q + 4 * q^2 - 32 * q^8 - 32 * q^16 + 40 * q^22 - 32 * q^25 + 28 * q^30 + 64 * q^32 + 32 * q^36 + 8 * q^37 + 184 * q^46 - 24 * q^50 - 96 * q^53 - 16 * q^57 - 124 * q^58 - 8 * q^60 + 120 * q^65 + 80 * q^72 - 72 * q^78 + 72 * q^81 + 192 * q^85 - 104 * q^86 - 48 * q^88 - 304 * q^92 + 176 * q^93

Introduction

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