LMFDB - Embedded newform 700.2.be.e.543.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(107,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("700.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.be (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			543.8
Character	$\chi$	$=$	700.543
Dual form			700.2.be.e.107.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.429119 - 1.34754i) q^{2} +(0.727420 + 2.71477i) q^{3} +(-1.63171 + 1.15651i) q^{4} +(3.34610 - 2.14518i) q^{6} +(0.496852 + 2.59868i) q^{7} +(2.25864 + 1.70252i) q^{8} +(-4.24276 + 2.44956i) q^{9} +(2.75736 + 1.59196i) q^{11} +(-4.32659 - 3.58846i) q^{12} +(-2.41925 - 2.41925i) q^{13} +(3.28861 - 1.78467i) q^{14} +(1.32498 - 3.77418i) q^{16} +(0.600458 + 2.24094i) q^{17} +(5.12151 + 4.66612i) q^{18} +(1.39787 + 2.42118i) q^{19} +(-6.69340 + 3.23917i) q^{21} +(0.961994 - 4.39878i) q^{22} +(-5.19830 - 1.39288i) q^{23} +(-2.97897 + 7.37012i) q^{24} +(-2.22189 + 4.29818i) q^{26} +(-3.77420 - 3.77420i) q^{27} +(-3.81611 - 3.66569i) q^{28} +1.72334i q^{29} +(-3.01685 - 1.74178i) q^{31} +(-5.65442 - 0.165897i) q^{32} +(-2.31605 + 8.64362i) q^{33} +(2.76208 - 1.77077i) q^{34} +(4.09004 - 8.90375i) q^{36} +(-2.32734 - 0.623610i) q^{37} +(2.66278 - 2.92265i) q^{38} +(4.80790 - 8.32752i) q^{39} +2.72503 q^{41} +(7.23716 + 7.62961i) q^{42} +(3.96477 - 3.96477i) q^{43} +(-6.34034 + 0.591276i) q^{44} +(0.353728 + 7.60261i) q^{46} +(-1.63570 + 6.10452i) q^{47} +(11.2098 + 0.851615i) q^{48} +(-6.50628 + 2.58232i) q^{49} +(-5.64685 + 3.26021i) q^{51} +(6.74541 + 1.14965i) q^{52} +(-12.6093 + 3.37866i) q^{53} +(-3.46629 + 6.70545i) q^{54} +(-3.30209 + 6.71537i) q^{56} +(-5.55610 + 5.55610i) q^{57} +(2.32227 - 0.739519i) q^{58} +(0.951402 - 1.64788i) q^{59} +(5.83980 + 10.1148i) q^{61} +(-1.05253 + 4.81275i) q^{62} +(-8.47363 - 9.80850i) q^{63} +(2.20286 + 7.69073i) q^{64} +(12.6415 - 0.588172i) q^{66} +(5.67039 - 1.51938i) q^{67} +(-3.57144 - 2.96214i) q^{68} -15.1254i q^{69} -0.562181i q^{71} +(-13.7532 - 1.69071i) q^{72} +(3.23402 - 0.866554i) q^{73} +(0.158369 + 3.40378i) q^{74} +(-5.08103 - 2.33403i) q^{76} +(-2.76700 + 7.95646i) q^{77} +(-13.2848 - 2.90533i) q^{78} +(4.13532 + 7.16259i) q^{79} +(0.151981 - 0.263239i) q^{81} +(-1.16936 - 3.67208i) q^{82} +(4.38250 - 4.38250i) q^{83} +(7.17559 - 13.0264i) q^{84} +(-7.04404 - 3.64132i) q^{86} +(-4.67848 + 1.25360i) q^{87} +(3.51752 + 8.29011i) q^{88} +(2.51180 - 1.45019i) q^{89} +(5.08485 - 7.48887i) q^{91} +(10.0930 - 3.73908i) q^{92} +(2.53401 - 9.45706i) q^{93} +(8.92798 - 0.415394i) q^{94} +(-3.66277 - 15.4711i) q^{96} +(10.9216 - 10.9216i) q^{97} +(6.27174 + 7.65933i) q^{98} -15.5984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42}+ \cdots + 90 q^{98}+O(q^{100}) $ 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.429119	−	1.34754i	−0.303433	−	0.952853i
$2$	−0.429119	−	1.34754i	−0.303433	−	0.952853i
$3$	0.727420	+	2.71477i	0.419976	+	1.56737i	0.774655	+	0.632384i	$0.217924\pi$
$3$	0.727420	+	2.71477i	0.419976	+	1.56737i	−0.354678	+	0.934988i	$0.615410\pi$
$4$	−1.63171	+	1.15651i	−0.815857	+	0.578253i
$5$		0			0
$5$		0			0
$6$	3.34610	−	2.14518i	1.36604	−	0.875768i
$7$	0.496852	+	2.59868i	0.187792	+	0.982209i
$7$	0.496852	+	2.59868i	0.187792	+	0.982209i
$8$	2.25864	+	1.70252i	0.798548	+	0.601931i
$9$	−4.24276	+	2.44956i	−1.41425	+	0.816519i
$10$		0			0
$11$	2.75736	+	1.59196i	0.831375	+	0.479994i	0.854323	−	0.519742i	$-0.173972\pi$
$11$	2.75736	+	1.59196i	0.831375	+	0.479994i	−0.0229484	+	0.999737i	$0.507305\pi$
$12$	−4.32659	−	3.58846i	−1.24898	−	1.03590i
$13$	−2.41925	−	2.41925i	−0.670980	−	0.670980i	0.286962	−	0.957942i	$-0.407355\pi$
$13$	−2.41925	−	2.41925i	−0.670980	−	0.670980i	−0.957942	+	0.286962i	$0.907355\pi$
$14$	3.28861	−	1.78467i	0.878918	−	0.476973i
$15$		0			0
$16$	1.32498	−	3.77418i	0.331246	−	0.943544i
$17$	0.600458	+	2.24094i	0.145632	+	0.543508i	0.999726	+	0.0233890i	$0.00744564\pi$
$17$	0.600458	+	2.24094i	0.145632	+	0.543508i	−0.854094	+	0.520119i	$0.825888\pi$
$18$	5.12151	+	4.66612i	1.20715	+	1.09982i
$19$	1.39787	+	2.42118i	0.320693	+	0.555456i	0.980631	−	0.195863i	$-0.0627510\pi$
$19$	1.39787	+	2.42118i	0.320693	+	0.555456i	−0.659938	+	0.751320i	$0.729418\pi$
$20$		0			0
$21$	−6.69340	+	3.23917i	−1.46062	+	0.706845i
$22$	0.961994	−	4.39878i	0.205098	−	0.937824i
$23$	−5.19830	−	1.39288i	−1.08392	−	0.290435i	−0.327719	−	0.944775i	$-0.606280\pi$
$23$	−5.19830	−	1.39288i	−1.08392	−	0.290435i	−0.756201	+	0.654340i	$0.772947\pi$
$24$	−2.97897	+	7.37012i	−0.608079	+	1.50442i
$25$		0			0
$26$	−2.22189	+	4.29818i	−0.435748	+	0.842942i
$27$	−3.77420	−	3.77420i	−0.726345	−	0.726345i
$28$	−3.81611	−	3.66569i	−0.721177	−	0.692751i
$29$			1.72334i			0.320017i	0.987116	+	0.160009i	$0.0511522\pi$
$29$			1.72334i			0.320017i	−0.987116	+	0.160009i	$0.948848\pi$
$30$		0			0
$31$	−3.01685	−	1.74178i	−0.541843	−	0.312833i	0.203983	−	0.978974i	$-0.434611\pi$
$31$	−3.01685	−	1.74178i	−0.541843	−	0.312833i	−0.745825	+	0.666141i	$0.767945\pi$
$32$	−5.65442	−	0.165897i	−0.999570	−	0.0293267i
$33$	−2.31605	+	8.64362i	−0.403173	+	1.50466i
$34$	2.76208	−	1.77077i	0.473693	−	0.303684i
$35$		0			0
$36$	4.09004	−	8.90375i	0.681673	−	1.48396i
$37$	−2.32734	−	0.623610i	−0.382613	−	0.102521i	0.0623856	−	0.998052i	$-0.480129\pi$
$37$	−2.32734	−	0.623610i	−0.382613	−	0.102521i	−0.444999	+	0.895531i	$0.646796\pi$
$38$	2.66278	−	2.92265i	0.431959	−	0.474117i
$39$	4.80790	−	8.32752i	0.769880	−	1.33347i
$40$		0			0
$41$	2.72503			0.425578			0.212789	−	0.977098i	$-0.431745\pi$
$41$	2.72503			0.425578			0.212789	+	0.977098i	$0.431745\pi$
$42$	7.23716	+	7.62961i	1.11672	+	1.17728i
$43$	3.96477	−	3.96477i	0.604622	−	0.604622i	−0.336914	−	0.941536i	$-0.609383\pi$
$43$	3.96477	−	3.96477i	0.604622	−	0.604622i	0.941536	+	0.336914i	$0.109383\pi$
$44$	−6.34034	+	0.591276i	−0.955842	+	0.0891383i
$45$		0			0
$46$	0.353728	+	7.60261i	0.0521544	+	1.12094i
$47$	−1.63570	+	6.10452i	−0.238591	+	0.890435i	0.737905	+	0.674904i	$0.235815\pi$
$47$	−1.63570	+	6.10452i	−0.238591	+	0.890435i	−0.976497	+	0.215531i	$0.930852\pi$
$48$	11.2098	+	0.851615i	1.61800	+	0.122920i
$49$	−6.50628	+	2.58232i	−0.929468	+	0.368903i
$50$		0			0
$51$	−5.64685	+	3.26021i	−0.790717	+	0.456521i
$52$	6.74541	+	1.14965i	0.935420	+	0.159427i
$53$	−12.6093	+	3.37866i	−1.73202	+	0.464094i	−0.980648	−	0.195780i	$-0.937276\pi$
$53$	−12.6093	+	3.37866i	−1.73202	+	0.464094i	−0.751376	+	0.659874i	$0.770610\pi$
$54$	−3.46629	+	6.70545i	−0.471703	+	0.912496i
$55$		0			0
$56$	−3.30209	+	6.71537i	−0.441261	+	0.897379i
$57$	−5.55610	+	5.55610i	−0.735924	+	0.735924i
$58$	2.32227	−	0.739519i	0.304929	−	0.0971036i
$59$	0.951402	−	1.64788i	0.123862	−	0.214535i	−0.797426	−	0.603417i	$-0.793805\pi$
$59$	0.951402	−	1.64788i	0.123862	−	0.214535i	0.921288	+	0.388882i	$0.127139\pi$
$60$		0			0
$61$	5.83980	+	10.1148i	0.747709	+	1.29507i	0.948918	+	0.315522i	$0.102180\pi$
$61$	5.83980	+	10.1148i	0.747709	+	1.29507i	−0.201209	+	0.979548i	$0.564487\pi$
$62$	−1.05253	+	4.81275i	−0.133671	+	0.611220i
$63$	−8.47363	−	9.80850i	−1.06758	−	1.23575i
$64$	2.20286	+	7.69073i	0.275358	+	0.961342i
$65$		0			0
$66$	12.6415	−	0.588172i	1.55606	−	0.0723990i
$67$	5.67039	−	1.51938i	0.692748	−	0.185621i	0.104768	−	0.994497i	$-0.466590\pi$
$67$	5.67039	−	1.51938i	0.692748	−	0.185621i	0.587980	+	0.808875i	$0.299923\pi$
$68$	−3.57144	−	2.96214i	−0.433100	−	0.359212i
$69$		−	15.1254i		−	1.82088i
$70$		0			0
$71$		−	0.562181i		−	0.0667186i	−0.999443	−	0.0333593i	$-0.989379\pi$
$71$		−	0.562181i		−	0.0667186i	0.999443	−	0.0333593i	$-0.0106206\pi$
$72$	−13.7532	−	1.69071i	−1.62084	−	0.199253i
$73$	3.23402	−	0.866554i	0.378514	−	0.101423i	−0.0645454	−	0.997915i	$-0.520560\pi$
$73$	3.23402	−	0.866554i	0.378514	−	0.101423i	0.443059	+	0.896492i	$0.353893\pi$
$74$	0.158369	+	3.40378i	0.0184100	+	0.395682i
$75$		0			0
$76$	−5.08103	−	2.33403i	−0.582834	−	0.267731i
$77$	−2.76700	+	7.95646i	−0.315329	+	0.906723i
$78$	−13.2848	−	2.90533i	−1.50421	−	0.328963i
$79$	4.13532	+	7.16259i	0.465260	+	0.805855i	0.999213	−	0.0396596i	$-0.0126274\pi$
$79$	4.13532	+	7.16259i	0.465260	+	0.805855i	−0.533953	+	0.845514i	$0.679294\pi$
$80$		0			0
$81$	0.151981	−	0.263239i	0.0168868	−	0.0292487i
$82$	−1.16936	−	3.67208i	−0.129134	−	0.405513i
$83$	4.38250	−	4.38250i	0.481042	−	0.481042i	−0.424423	−	0.905464i	$-0.639523\pi$
$83$	4.38250	−	4.38250i	0.481042	−	0.481042i	0.905464	+	0.424423i	$0.139523\pi$
$84$	7.17559	−	13.0264i	0.782921	−	1.42129i
$85$		0			0
$86$	−7.04404	−	3.64132i	−0.759578	−	0.392654i
$87$	−4.67848	+	1.25360i	−0.501586	+	0.134400i
$88$	3.51752	+	8.29011i	0.374969	+	0.883729i
$89$	2.51180	−	1.45019i	0.266250	−	0.153720i	−0.360932	−	0.932592i	$-0.617541\pi$
$89$	2.51180	−	1.45019i	0.266250	−	0.153720i	0.627182	+	0.778872i	$0.284208\pi$
$90$		0			0
$91$	5.08485	−	7.48887i	0.533037	−	0.785047i
$92$	10.0930	−	3.73908i	1.05227	−	0.389826i
$93$	2.53401	−	9.45706i	0.262765	−	0.980652i
$94$	8.92798	−	0.415394i	0.920850	−	0.0428446i
$95$		0			0
$96$	−3.66277	−	15.4711i	−0.373830	−	1.57902i
$97$	10.9216	−	10.9216i	1.10892	−	1.10892i	0.115629	−	0.993292i	$-0.463111\pi$
$97$	10.9216	−	10.9216i	1.10892	−	1.10892i	0.993292	−	0.115629i	$-0.0368885\pi$
$98$	6.27174	+	7.65933i	0.633541	+	0.773709i
$99$	−15.5984			−1.56770
$100$		0			0
$101$	5.73271	−	9.92934i	0.570426	−	0.988007i	−0.426096	−	0.904678i	$-0.640111\pi$
$101$	5.73271	−	9.92934i	0.570426	−	0.988007i	0.996522	−	0.0833288i	$-0.0265552\pi$
$102$	6.81642	+	6.21032i	0.674926	+	0.614914i
$103$	12.6556	+	3.39107i	1.24700	+	0.334132i	0.821176	−	0.570676i	$-0.193319\pi$
$103$	12.6556	+	3.39107i	1.24700	+	0.334132i	0.425821	+	0.904807i	$0.359985\pi$
$104$	−1.34539	−	9.58302i	−0.131926	−	0.939693i
$105$		0			0
$106$	9.96376	+	15.5417i	0.967766	+	1.50954i
$107$	0.106381	−	0.397018i	0.0102842	−	0.0383812i	−0.960593	−	0.277959i	$-0.910342\pi$
$107$	0.106381	−	0.397018i	0.0102842	−	0.0383812i	0.970877	+	0.239577i	$0.0770089\pi$
$108$	10.5233	+	1.79353i	1.01260	+	0.172582i
$109$	−6.32499	−	3.65173i	−0.605824	−	0.349773i	0.165505	−	0.986209i	$-0.447074\pi$
$109$	−6.32499	−	3.65173i	−0.605824	−	0.349773i	−0.771329	+	0.636436i	$0.780408\pi$
$110$		0			0
$111$		−	6.77183i		−	0.642753i
$112$	10.4662	+	1.56800i	0.988963	+	0.148162i
$113$	11.6304	+	11.6304i	1.09410	+	1.09410i	0.995086	+	0.0990127i	$0.0315684\pi$
$113$	11.6304	+	11.6304i	1.09410	+	1.09410i	0.0990127	+	0.995086i	$0.468432\pi$
$114$	9.87128	+	5.10283i	0.924530	+	0.477924i
$115$		0			0
$116$	−1.99306	−	2.81201i	−0.185051	−	0.261088i
$117$	16.1904	+	4.33820i	1.49680	+	0.401067i
$118$	−2.62884	−	0.574915i	−0.242004	−	0.0529252i
$119$	−5.52515	+	2.67381i	−0.506489	+	0.245108i
$120$		0			0
$121$	−0.431317	−	0.747063i	−0.0392106	−	0.0679148i
$122$	11.1241	−	12.2098i	1.00713	−	1.10542i
$123$	1.98224	+	7.39783i	0.178733	+	0.667040i
$124$	6.93702	−	0.646921i	0.622963	−	0.0580952i
$125$		0			0
$126$	−9.58112	+	15.6275i	−0.853554	+	1.39221i
$127$	1.32146	+	1.32146i	0.117261	+	0.117261i	0.763302	−	0.646042i	$-0.223577\pi$
$127$	1.32146	+	1.32146i	0.117261	+	0.117261i	−0.646042	+	0.763302i	$0.723577\pi$
$128$	9.41826	−	6.26868i	0.832465	−	0.554078i
$129$	13.6475	+	7.87939i	1.20159	+	0.693741i
$130$		0			0
$131$	−3.52422	+	2.03471i	−0.307912	+	0.177773i	−0.645992	−	0.763344i	$-0.723556\pi$
$131$	−3.52422	+	2.03471i	−0.307912	+	0.177773i	0.338080	+	0.941118i	$0.390223\pi$
$132$	−6.21727	−	16.7824i	−0.541144	−	1.46072i
$133$	−5.59733	+	4.83558i	−0.485350	+	0.419298i
$134$	−4.48068	−	6.98907i	−0.387072	−	0.603764i
$135$		0			0
$136$	−2.45903	+	6.08376i	−0.210860	+	0.521678i
$137$	−4.17132	−	15.5676i	−0.356380	−	1.33003i	−0.878739	−	0.477303i	$-0.841615\pi$
$137$	−4.17132	−	15.5676i	−0.356380	−	1.33003i	0.522359	−	0.852726i	$-0.325052\pi$
$138$	−20.3820	+	6.49058i	−1.73503	+	0.552515i
$139$	17.0814			1.44882			0.724411	−	0.689369i	$-0.242112\pi$
$139$	17.0814			1.44882			0.724411	+	0.689369i	$0.242112\pi$
$140$		0			0
$141$	−17.7622			−1.49585
$142$	−0.757560	+	0.241242i	−0.0635730	+	0.0202446i
$143$	−2.81939	−	10.5221i	−0.235769	−	0.879902i
$144$	3.62347	+	19.2585i	0.301956	+	1.60488i
$145$		0			0
$146$	−2.55549	−	3.98611i	−0.211494	−	0.329893i
$147$	−11.7432	−	15.7846i	−0.968562	−	1.30189i
$148$	4.51877	−	1.67403i	0.371441	−	0.137605i
$149$	−7.75810	+	4.47914i	−0.635569	+	0.366946i	−0.782905	−	0.622141i	$-0.786263\pi$
$149$	−7.75810	+	4.47914i	−0.635569	+	0.366946i	0.147337	+	0.989086i	$0.452930\pi$
$150$		0			0
$151$	5.83274	+	3.36754i	0.474662	+	0.274046i	0.718189	−	0.695848i	$-0.244971\pi$
$151$	5.83274	+	3.36754i	0.474662	+	0.274046i	−0.243527	+	0.969894i	$0.578305\pi$
$152$	−0.964826	+	7.84845i	−0.0782577	+	0.636593i
$153$	−8.03690	−	8.03690i	−0.649745	−	0.649745i
$154$	11.9090	+	0.314371i	0.959655	+	0.0253327i
$155$		0			0
$156$	1.78572	+	19.1485i	0.142972	+	1.53311i
$157$	2.94647	+	10.9964i	0.235154	+	0.877606i	0.978080	+	0.208232i	$0.0667708\pi$
$157$	2.94647	+	10.9964i	0.235154	+	0.877606i	−0.742926	+	0.669374i	$0.766563\pi$
$158$	7.87732	−	8.64611i	0.626686	−	0.687847i
$159$	−18.3446	−	31.7737i	−1.45482	−	2.51982i
$160$		0			0
$161$	1.03686	−	14.2008i	0.0817163	−	1.11918i
$162$	−0.419942	−	0.0918394i	−0.0329937	−	0.00721558i
$163$	0.00273302		0.000732309i	0.000214066		5.73589e-5i	0.258926	−	0.965897i	$-0.416631\pi$
$163$	0.00273302		0.000732309i	0.000214066		5.73589e-5i	−0.258712	+	0.965954i	$0.583298\pi$
$164$	−4.44647	+	3.15152i	−0.347211	+	0.246092i
$165$		0			0
$166$	−7.78619	−	4.02497i	−0.604326	−	0.312398i
$167$	2.32482	+	2.32482i	0.179900	+	0.179900i	0.791312	−	0.611412i	$-0.209398\pi$
$167$	2.32482	+	2.32482i	0.179900	+	0.179900i	−0.611412	+	0.791312i	$0.709398\pi$
$168$	−20.6327	−	4.07952i	−1.59185	−	0.314742i
$169$		−	1.29445i		−	0.0995729i
$170$		0			0
$171$	−11.8616	−	6.84831i	−0.907081	−	0.523703i
$172$	−1.88409	+	11.0547i	−0.143661	+	0.842910i
$173$	4.15945	−	15.5233i	0.316237	−	1.18021i	−0.606596	−	0.795010i	$-0.707465\pi$
$173$	4.15945	−	15.5233i	0.316237	−	1.18021i	0.922833	−	0.385201i	$-0.125868\pi$
$174$	3.69689	+	5.76649i	0.280261	+	0.437157i
$175$		0			0
$176$	9.66180	−	8.29743i	0.728286	−	0.625443i
$177$	5.16567	+	1.38414i	0.388276	+	0.104038i
$178$	−3.03204	−	2.76244i	−0.227261	−	0.207054i
$179$	−9.08714	+	15.7394i	−0.679205	+	1.17642i	0.296016	+	0.955183i	$0.404342\pi$
$179$	−9.08714	+	15.7394i	−0.679205	+	1.17642i	−0.975221	+	0.221235i	$0.928991\pi$
$180$		0			0
$181$	−4.28458			−0.318471			−0.159235	−	0.987241i	$-0.550903\pi$
$181$	−4.28458			−0.318471			−0.159235	+	0.987241i	$0.550903\pi$
$182$	−12.2735	−	3.63841i	−0.909775	−	0.269697i
$183$	−23.2114	+	23.2114i	−1.71584	+	1.71584i
$184$	−9.36965	−	11.9962i	−0.690740	−	0.884371i
$185$		0			0
$186$	−13.8311	+	0.643525i	−1.01415	+	0.0471855i
$187$	−1.91181	+	7.13498i	−0.139806	+	0.521761i
$188$	−4.39092	−	11.8525i	−0.320241	−	0.864434i
$189$	7.93272	−	11.6832i	0.577020	−	0.849824i
$190$		0			0
$191$	10.0103	−	5.77946i	0.724321	−	0.418187i	−0.0920200	−	0.995757i	$-0.529332\pi$
$191$	10.0103	−	5.77946i	0.724321	−	0.418187i	0.816341	+	0.577570i	$0.195999\pi$
$192$	−19.2762	+	11.5747i	−1.39114	+	0.835329i
$193$	4.46599	−	1.19666i	0.321469	−	0.0861374i	−0.0944758	−	0.995527i	$-0.530118\pi$
$193$	4.46599	−	1.19666i	0.321469	−	0.0861374i	0.415945	+	0.909390i	$0.363451\pi$
$194$	−19.4040	−	10.0306i	−1.39312	−	0.720156i
$195$		0			0
$196$	7.62992	−	11.7382i	0.544994	−	0.838440i
$197$	−6.77330	+	6.77330i	−0.482578	+	0.482578i	−0.905954	−	0.423376i	$-0.860845\pi$
$197$	−6.77330	+	6.77330i	−0.482578	+	0.482578i	0.423376	+	0.905954i	$0.360845\pi$
$198$	6.69356	+	21.0194i	0.475691	+	1.49379i
$199$	−0.869824	+	1.50658i	−0.0616602	+	0.106799i	−0.895208	−	0.445649i	$-0.852973\pi$
$199$	−0.869824	+	1.50658i	−0.0616602	+	0.106799i	0.833547	+	0.552448i	$0.186306\pi$
$200$		0			0
$201$	8.24951	+	14.2886i	0.581876	+	1.00784i
$202$	−15.8402	−	3.46418i	−1.11451	−	0.243739i
$203$	−4.47842	+	0.856247i	−0.314324	+	0.0600968i
$204$	5.44359	−	11.8504i	0.381128	−	0.829691i
$205$		0			0
$206$	−0.861178	−	18.5091i	−0.0600011	−	1.28959i
$207$	25.4670	−	6.82387i	1.77008	−	0.474292i
$208$	−12.3362	+	5.92521i	−0.855358	+	0.410840i
$209$			8.90141i			0.615723i
$210$		0			0
$211$			23.7584i			1.63560i	0.575506	+	0.817798i	$0.304805\pi$
$211$			23.7584i			1.63560i	−0.575506	+	0.817798i	$0.695195\pi$
$212$	16.6674	−	20.0958i	1.14472	−	1.38018i
$213$	1.52619	−	0.408942i	0.104573	−	0.0280202i
$214$	−0.580647	+	0.0270159i	−0.0396922	+	0.00184677i
$215$		0			0
$216$	−2.09890	−	14.9502i	−0.142812	−	1.01723i
$217$	3.02740	−	8.70524i	0.205513	−	0.590950i
$218$	−2.20668	+	10.0902i	−0.149455	+	0.683393i
$219$	4.70499	+	8.14928i	0.317934	+	0.550677i
$220$		0			0
$221$	3.96874	−	6.87406i	0.266966	−	0.462399i
$222$	−9.12529	+	2.90592i	−0.612449	+	0.195032i
$223$	13.2313	−	13.2313i	0.886031	−	0.886031i	−0.108108	−	0.994139i	$-0.534479\pi$
$223$	13.2313	−	13.2313i	0.886031	−	0.886031i	0.994139	+	0.108108i	$0.0344793\pi$
$224$	−2.37830	−	14.7765i	−0.158907	−	0.987294i
$225$		0			0
$226$	10.6816	−	20.6633i	0.710530	−	1.37450i
$227$	−20.0810	+	5.38070i	−1.33283	+	0.357130i	−0.853768	−	0.520654i	$-0.825688\pi$
$227$	−20.0810	+	5.38070i	−1.33283	+	0.357130i	−0.479058	+	0.877783i	$0.659022\pi$
$228$	2.64030	−	15.4916i	0.174858	−	1.02596i
$229$	15.4800	−	8.93740i	1.02295	−	0.590600i	0.107992	−	0.994152i	$-0.465558\pi$
$229$	15.4800	−	8.93740i	1.02295	−	0.590600i	0.914957	+	0.403552i	$0.132224\pi$
$230$		0			0
$231$	−23.6127	−	1.72408i	−1.55360	−	0.113436i
$232$	−2.93403	+	3.89241i	−0.192628	+	0.255549i
$233$	0.0913229	−	0.340822i	0.00598276	−	0.0223280i	−0.962870	−	0.269966i	$-0.912988\pi$
$233$	0.0913229	−	0.340822i	0.00598276	−	0.0223280i	0.968853	+	0.247638i	$0.0796543\pi$
$234$	−1.10171	−	23.6787i	−0.0720208	−	1.54793i
$235$		0			0
$236$	0.353364	+	3.78917i	0.0230020	+	0.246654i
$237$	−16.4367	+	16.4367i	−1.06768	+	1.06768i
$238$	5.97401	+	6.29796i	0.387237	+	0.408236i
$239$	24.1080			1.55941			0.779707	−	0.626145i	$-0.215368\pi$
$239$	24.1080			1.55941			0.779707	+	0.626145i	$0.215368\pi$
$240$		0			0
$241$	−2.17712	+	3.77087i	−0.140240	+	0.242903i	−0.927587	−	0.373607i	$-0.878121\pi$
$241$	−2.17712	+	3.77087i	−0.140240	+	0.242903i	0.787347	+	0.616510i	$0.211454\pi$
$242$	−0.821609	+	0.901794i	−0.0528150	+	0.0579695i
$243$	−14.6418	−	3.92325i	−0.939270	−	0.251677i
$244$	−21.2267	−	9.75074i	−1.35890	−	0.624227i
$245$		0			0
$246$	9.11823	−	5.84569i	0.581357	−	0.372708i
$247$	2.47564	−	9.23923i	0.157521	−	0.587878i
$248$	−3.84856	−	9.07029i	−0.244384	−	0.575964i
$249$	15.0854	+	8.70955i	0.955998	+	0.551945i
$250$		0			0
$251$			13.3373i			0.841841i	0.907098	+	0.420920i	$0.138293\pi$
$251$			13.3373i			0.841841i	−0.907098	+	0.420920i	$0.861707\pi$
$252$	25.1701	+	6.20485i	1.58557	+	0.390869i
$253$	−12.1162	−	12.1162i	−0.761736	−	0.761736i
$254$	1.21365	−	2.34778i	0.0761514	−	0.147313i
$255$		0			0
$256$	−12.4888	−	10.0015i	−0.780552	−	0.625091i
$257$	9.71554	+	2.60327i	0.606039	+	0.162388i	0.548773	−	0.835971i	$-0.315095\pi$
$257$	9.71554	+	2.60327i	0.606039	+	0.162388i	0.0572656	+	0.998359i	$0.481762\pi$
$258$	4.76137	−	21.7717i	0.296430	−	1.35545i
$259$	0.464217	−	6.35786i	0.0288450	−	0.395058i
$260$		0			0
$261$	−4.22143	−	7.31173i	−0.261300	−	0.452585i
$262$	4.25415	+	3.87589i	0.262822	+	0.239453i
$263$	2.78295	+	10.3861i	0.171604	+	0.640435i	0.997105	+	0.0760347i	$0.0242260\pi$
$263$	2.78295	+	10.3861i	0.171604	+	0.640435i	−0.825501	+	0.564401i	$0.809107\pi$
$264$	−19.9470	+	15.5797i	−1.22765	+	0.958862i
$265$		0			0
$266$	8.91804	+	5.46758i	0.546800	+	0.335239i
$267$	5.76406	+	5.76406i	0.352755	+	0.352755i
$268$	−7.49529	+	9.03703i	−0.457848	+	0.552024i
$269$	−8.18828	−	4.72750i	−0.499248	−	0.288241i	0.229155	−	0.973390i	$-0.426404\pi$
$269$	−8.18828	−	4.72750i	−0.499248	−	0.288241i	−0.728403	+	0.685149i	$0.759737\pi$
$270$		0			0
$271$	12.4949	−	7.21392i	0.759010	−	0.438214i	−0.0699304	−	0.997552i	$-0.522278\pi$
$271$	12.4949	−	7.21392i	0.759010	−	0.438214i	0.828940	+	0.559337i	$0.188944\pi$
$272$	9.25330	+	0.702976i	0.561064	+	0.0426242i
$273$	24.0294	+	8.35664i	1.45432	+	0.505767i
$274$	−19.1879	+	12.3013i	−1.15918	+	0.743152i
$275$		0			0
$276$	17.4926	+	24.6803i	1.05293	+	1.48558i
$277$	−8.56419	−	31.9620i	−0.514572	−	1.92041i	−0.362259	−	0.932078i	$-0.617994\pi$
$277$	−8.56419	−	31.9620i	−0.514572	−	1.92041i	−0.152314	−	0.988332i	$-0.548672\pi$
$278$	−7.32993	−	23.0178i	−0.439620	−	1.38051i
$279$	17.0664			1.02174
$280$		0			0
$281$	−10.1670			−0.606514			−0.303257	−	0.952909i	$-0.598074\pi$
$281$	−10.1670			−0.606514			−0.303257	+	0.952909i	$0.598074\pi$
$282$	7.62209	+	23.9352i	0.453889	+	1.42532i
$283$	7.16893	+	26.7548i	0.426148	+	1.59041i	0.761402	+	0.648280i	$0.224511\pi$
$283$	7.16893	+	26.7548i	0.426148	+	1.59041i	−0.335254	+	0.942128i	$0.608822\pi$
$284$	0.650166	+	0.917319i	0.0385803	+	0.0544329i
$285$		0			0
$286$	−12.9691	+	8.31446i	−0.766877	+	0.491644i
$287$	1.35394	+	7.08148i	0.0799204	+	0.418007i
$288$	24.3967	−	13.1470i	1.43759	−	0.774692i
$289$	10.0612	−	5.80882i	0.591834	−	0.341695i
$290$		0			0
$291$	37.5943	+	21.7051i	2.20381	+	1.27237i
$292$	−4.27483	+	5.15414i	−0.250165	+	0.301623i
$293$	3.07964	+	3.07964i	0.179914	+	0.179914i	0.791318	−	0.611404i	$-0.209395\pi$
$293$	3.07964	+	3.07964i	0.179914	+	0.179914i	−0.611404	+	0.791318i	$0.709395\pi$
$294$	−16.2311	+	22.5979i	−0.946619	+	1.31793i
$295$		0			0
$296$	−4.19491	−	5.37085i	−0.243824	−	0.312174i
$297$	−4.39844	−	16.4152i	−0.255223	−	0.952506i
$298$	9.36496	+	8.53225i	0.542498	+	0.494260i
$299$	9.20626	+	15.9457i	0.532412	+	0.922164i
$300$		0			0
$301$	12.2731	+	8.33327i	0.707408	+	0.480322i
$302$	2.03494	−	9.30491i	0.117098	−	0.535437i
$303$	31.1260	+	8.34018i	1.78814	+	0.479131i
$304$	10.9901	−	2.06778i	0.630326	−	0.118595i
$305$		0			0
$306$	−7.38124	+	14.2788i	−0.421958	+	0.816265i
$307$	13.3345	+	13.3345i	0.761042	+	0.761042i	0.976511	−	0.215469i	$-0.0691280\pi$
$307$	13.3345	+	13.3345i	0.761042	+	0.761042i	−0.215469	+	0.976511i	$0.569128\pi$
$308$	−4.68675	−	16.1827i	−0.267052	−	0.922096i
$309$			36.8239i			2.09484i
$310$		0			0
$311$	1.35454	+	0.782046i	0.0768091	+	0.0443457i	0.537913	−	0.843001i	$-0.319213\pi$
$311$	1.35454	+	0.782046i	0.0768091	+	0.0443457i	−0.461104	+	0.887346i	$0.652546\pi$
$312$	25.0370	−	10.6233i	1.41744	−	0.601426i
$313$	−3.15193	+	11.7632i	−0.178157	+	0.664893i	0.817835	+	0.575453i	$0.195174\pi$
$313$	−3.15193	+	11.7632i	−0.178157	+	0.664893i	−0.995992	+	0.0894395i	$0.971492\pi$
$314$	13.5536	−	8.68922i	0.764876	−	0.490361i
$315$		0			0
$316$	−15.0313	−	6.90478i	−0.845574	−	0.388424i
$317$	−26.4565	−	7.08901i	−1.48595	−	0.398158i	−0.577581	−	0.816334i	$-0.696003\pi$
$317$	−26.4565	−	7.08901i	−1.48595	−	0.398158i	−0.908366	+	0.418175i	$0.862670\pi$
$318$	−34.9443	+	38.3547i	−1.95958	+	2.15082i
$319$	−2.74350	+	4.75188i	−0.153606	+	0.266054i
$320$		0			0
$321$	1.15520			0.0644768
$322$	−19.5810	+	4.69660i	−1.09121	+	0.261731i
$323$	−4.58635	+	4.58635i	−0.255191	+	0.255191i
$324$	0.0564478	+	0.605297i	0.00313599	+	0.0336276i
$325$		0			0
$326$	−0.000185973	−	0.00399709i	−1.03001e−5	−	0.000221378i
$327$	5.31269	−	19.8272i	0.293792	−	1.09645i
$328$	6.15485	+	4.63941i	0.339845	+	0.256169i
$329$	−16.6764	−	1.21762i	−0.919399	−	0.0671296i
$330$		0			0
$331$	−3.38809	+	1.95612i	−0.186226	+	0.107518i	−0.590215	−	0.807246i	$-0.700957\pi$
$331$	−3.38809	+	1.95612i	−0.186226	+	0.107518i	0.403988	+	0.914764i	$0.367624\pi$
$332$	−2.08260	+	12.2194i	−0.114297	+	0.670625i
$333$	11.4019	−	3.05513i	0.624821	−	0.167420i
$334$	2.13515	−	4.13040i	0.116830	−	0.226005i
$335$		0			0
$336$	3.35656	+	29.5539i	0.183115	+	1.61230i
$337$	−12.6447	+	12.6447i	−0.688801	+	0.688801i	−0.961967	−	0.273166i	$-0.911929\pi$
$337$	−12.6447	+	12.6447i	−0.688801	+	0.688801i	0.273166	+	0.961967i	$0.411929\pi$
$338$	−1.74432	+	0.555471i	−0.0948783	+	0.0302137i
$339$	−23.1137	+	40.0341i	−1.25537	+	2.17436i
$340$		0			0
$341$	−5.54569	−	9.60542i	−0.300316	−	0.520163i
$342$	−4.13831	+	18.9227i	−0.223774	+	1.02322i
$343$	−9.94328	−	15.6247i	−0.536886	−	0.843655i
$344$	15.7051	−	2.20488i	0.846761	−	0.118879i
$345$		0			0
$346$	−22.7031	+	1.05631i	−1.22052	+	0.0567876i
$347$	5.79511	−	1.55280i	0.311098	−	0.0833585i	−0.0998921	−	0.994998i	$-0.531850\pi$
$347$	5.79511	−	1.55280i	0.311098	−	0.0833585i	0.410990	+	0.911640i	$0.365183\pi$
$348$	6.18416	−	7.45621i	0.331506	−	0.399695i
$349$			15.1860i			0.812888i	0.913676	+	0.406444i	$0.133231\pi$
$349$			15.1860i			0.812888i	−0.913676	+	0.406444i	$0.866769\pi$
$350$		0			0
$351$			18.2615i			0.974725i
$352$	−15.3272	−	9.45906i	−0.816941	−	0.504169i
$353$	33.2384	−	8.90620i	1.76910	−	0.474029i	0.780573	−	0.625065i	$-0.214927\pi$
$353$	33.2384	−	8.90620i	1.76910	−	0.474029i	0.988528	+	0.151035i	$0.0482607\pi$
$354$	−0.351508	−	7.55490i	−0.0186825	−	0.401538i
$355$		0			0
$356$	−2.42139	+	5.27121i	−0.128333	+	0.279373i
$357$	−11.2779	−	13.0545i	−0.596889	−	0.690918i
$358$	25.1089	+	5.49120i	1.32705	+	0.290219i
$359$	−4.20241	−	7.27878i	−0.221795	−	0.384159i	0.733558	−	0.679626i	$-0.237858\pi$
$359$	−4.20241	−	7.27878i	−0.221795	−	0.384159i	−0.955353	+	0.295467i	$0.904525\pi$
$360$		0			0
$361$	5.59193	−	9.68551i	0.294312	−	0.509764i
$362$	1.83859	+	5.77364i	0.0966344	+	0.303456i
$363$	1.71435	−	1.71435i	0.0899803	−	0.0899803i
$364$	0.363904	+	18.1004i	0.0190737	+	0.948717i
$365$		0			0
$366$	41.2387	+	21.3178i	2.15558	+	1.11430i
$367$	29.7056	−	7.95960i	1.55062	−	0.415488i	0.620941	−	0.783857i	$-0.286751\pi$
$367$	29.7056	−	7.95960i	1.55062	−	0.415488i	0.929679	+	0.368369i	$0.120084\pi$
$368$	−12.1446	+	17.7737i	−0.633083	+	0.926521i
$369$	−11.5616	+	6.67511i	−0.601875	+	0.347493i
$370$		0			0
$371$	−15.0450	−	31.0889i	−0.781099	−	1.61406i
$372$	6.80237	+	18.3618i	0.352687	+	0.952017i
$373$	−3.89204	+	14.5253i	−0.201522	+	0.752091i	0.788959	+	0.614446i	$0.210620\pi$
$373$	−3.89204	+	14.5253i	−0.201522	+	0.752091i	−0.990482	+	0.137646i	$0.956046\pi$
$374$	10.4350	−	0.485514i	0.539583	−	0.0251053i
$375$		0			0
$376$	−14.0875	+	11.0031i	−0.726507	+	0.567440i
$377$	4.16920	−	4.16920i	0.214725	−	0.214725i
$378$	−19.1476	−	5.67617i	−0.984844	−	0.291951i
$379$	1.92262			0.0987586			0.0493793	−	0.998780i	$-0.484276\pi$
$379$	1.92262			0.0987586			0.0493793	+	0.998780i	$0.484276\pi$
$380$		0			0
$381$	−2.62620	+	4.54871i	−0.134544	+	0.233038i
$382$	−12.0836	−	11.0092i	−0.618253	−	0.563280i
$383$	15.4407	+	4.13733i	0.788984	+	0.211408i	0.630742	−	0.775993i	$-0.282751\pi$
$383$	15.4407	+	4.13733i	0.788984	+	0.211408i	0.158242	+	0.987400i	$0.449417\pi$
$384$	23.8691	+	21.0084i	1.21806	+	1.07208i
$385$		0			0
$386$	−3.52898	−	5.50459i	−0.179621	−	0.280176i
$387$	−7.10963	+	26.5335i	−0.361403	+	1.34877i
$388$	−5.19004	+	30.4519i	−0.263484	+	1.54596i
$389$	−9.81327	−	5.66569i	−0.497552	−	0.287262i	0.230150	−	0.973155i	$-0.426078\pi$
$389$	−9.81327	−	5.66569i	−0.497552	−	0.287262i	−0.727702	+	0.685893i	$0.759412\pi$
$390$		0			0
$391$		−	12.4854i		−	0.631415i
$392$	−19.0917	−	5.24454i	−0.964279	−	0.264889i
$393$	−8.08735	−	8.08735i	−0.407953	−	0.407953i
$394$	12.0338	+	6.22073i	0.606255	+	0.313396i
$395$		0			0
$396$	25.4521	−	18.0396i	1.27902	−	0.906526i
$397$	11.2650	+	3.01844i	0.565372	+	0.151491i	0.530173	−	0.847889i	$-0.322127\pi$
$397$	11.2650	+	3.01844i	0.565372	+	0.151491i	0.0351987	+	0.999380i	$0.488794\pi$
$398$	2.40343	+	0.525620i	0.120473	+	0.0263469i
$399$	−17.1991	−	11.6780i	−0.861031	−	0.584630i
$400$		0			0
$401$	13.8361	+	23.9649i	0.690943	+	1.19675i	0.971529	+	0.236919i	$0.0761376\pi$
$401$	13.8361	+	23.9649i	0.690943	+	1.19675i	−0.280587	+	0.959829i	$0.590529\pi$
$402$	15.7144	−	17.2480i	0.783761	−	0.860253i
$403$	3.08472	+	11.5123i	0.153661	+	0.573470i
$404$	2.12921	+	22.8318i	0.105932	+	1.13592i
$405$		0			0
$406$	3.07560	+	5.66741i	0.152639	+	0.281269i
$407$	−5.42456	−	5.42456i	−0.268885	−	0.268885i
$408$	−18.3047	−	2.25024i	−0.906220	−	0.111403i
$409$	−11.9780	−	6.91550i	−0.592274	−	0.341950i	0.173722	−	0.984795i	$-0.444421\pi$
$409$	−11.9780	−	6.91550i	−0.592274	−	0.341950i	−0.765996	+	0.642845i	$0.777754\pi$
$410$		0			0
$411$	39.2281	−	22.6483i	1.93498	−	1.11716i
$412$	−24.5722	+	9.10307i	−1.21058	+	0.448476i
$413$	4.75501	+	1.65364i	0.233979	+	0.0813702i
$414$	−20.1238	−	31.3895i	−0.989031	−	1.54271i
$415$		0			0
$416$	13.2781	+	14.0808i	0.651013	+	0.690369i
$417$	12.4253	+	46.3719i	0.608471	+	2.27084i
$418$	11.9950	−	3.81976i	0.586694	−	0.186830i
$419$	−20.6976			−1.01114			−0.505572	−	0.862784i	$-0.668719\pi$
$419$	−20.6976			−1.01114			−0.505572	+	0.862784i	$0.668719\pi$
$420$		0			0
$421$	26.7517			1.30380			0.651898	−	0.758306i	$-0.273973\pi$
$421$	26.7517			1.30380			0.651898	+	0.758306i	$0.273973\pi$
$422$	32.0153	−	10.1952i	1.55848	−	0.496293i
$423$	−8.01348	−	29.9067i	−0.389629	−	1.45411i
$424$	−34.2321	−	13.8364i	−1.66246	−	0.671957i
$425$		0			0
$426$	−1.20598	−	1.88112i	−0.0584300	−	0.0911404i
$427$	−23.3837	+	20.2013i	−1.13162	+	0.977611i
$428$	0.285571	+	0.770850i	0.0138036	+	0.0372605i
$429$	26.5142	−	15.3080i	1.28012	−	0.739076i
$430$		0			0
$431$	−34.9346	−	20.1695i	−1.68274	−	0.971531i	−0.959827	−	0.280594i	$-0.909469\pi$
$431$	−34.9346	−	20.1695i	−1.68274	−	0.971531i	−0.722914	−	0.690937i	$-0.757198\pi$
$432$	−19.2452	+	9.24374i	−0.925937	+	0.444740i
$433$	−16.5835	−	16.5835i	−0.796954	−	0.796954i	0.185660	−	0.982614i	$-0.440558\pi$
$433$	−16.5835	−	16.5835i	−0.796954	−	0.796954i	−0.982614	+	0.185660i	$0.940558\pi$
$434$	−13.0298	−	0.343956i	−0.625448	−	0.0165104i
$435$		0			0
$436$	14.5438	−	1.35630i	0.696523	−	0.0649552i
$437$	−3.89412	−	14.5331i	−0.186281	−	0.695210i
$438$	8.96246	−	9.83716i	0.428243	−	0.470038i
$439$	−2.87067	−	4.97215i	−0.137010	−	0.237308i	0.789354	−	0.613939i	$-0.210416\pi$
$439$	−2.87067	−	4.97215i	−0.137010	−	0.237308i	−0.926363	+	0.376631i	$0.877082\pi$
$440$		0			0
$441$	21.2790	−	26.8936i	1.01329	−	1.28065i
$442$	−10.9661	−	2.39824i	−0.521604	−	0.114073i
$443$	−0.826713	−	0.221517i	−0.0392783	−	0.0105246i	0.239126	−	0.970988i	$-0.423139\pi$
$443$	−0.826713	−	0.221517i	−0.0392783	−	0.0105246i	−0.278405	+	0.960464i	$0.589806\pi$
$444$	7.83166	+	11.0497i	0.371674	+	0.524395i
$445$		0			0
$446$	−23.5074	−	12.1518i	−1.11311	−	0.575407i
$447$	−17.8032	−	17.8032i	−0.842064	−	0.842064i
$448$	−18.8913	+	9.54570i	−0.892528	+	0.450992i
$449$		−	4.66158i		−	0.219993i	−0.993932	−	0.109997i	$-0.964916\pi$
$449$		−	4.66158i		−	0.219993i	0.993932	−	0.109997i	$-0.0350840\pi$
$450$		0			0
$451$	7.51388	+	4.33814i	0.353815	+	0.204275i
$452$	−32.4282	−	5.52687i	−1.52529	−	0.259962i
$453$	−4.89923	+	18.2842i	−0.230186	+	0.859065i
$454$	15.8678	+	24.7510i	0.744715	+	1.16162i
$455$		0			0
$456$	−22.0086	+	3.08984i	−1.03065	+	0.144695i
$457$	30.7250	+	8.23274i	1.43726	+	0.385111i	0.891572	−	0.452880i	$-0.149603\pi$
$457$	30.7250	+	8.23274i	1.43726	+	0.385111i	0.545684	+	0.837991i	$0.316270\pi$
$458$	−18.6863	−	17.0247i	−0.873151	−	0.795513i
$459$	6.19150	−	10.7240i	0.288995	−	0.500553i
$460$		0			0
$461$	−23.4445			−1.09192			−0.545959	−	0.837812i	$-0.683835\pi$
$461$	−23.4445			−1.09192			−0.545959	+	0.837812i	$0.683835\pi$
$462$	7.80940	+	32.5589i	0.363326	+	1.51478i
$463$	1.84160	−	1.84160i	0.0855866	−	0.0855866i	−0.663017	−	0.748604i	$-0.730724\pi$
$463$	1.84160	−	1.84160i	0.0855866	−	0.0855866i	0.748604	+	0.663017i	$0.230724\pi$
$464$	6.50421	+	2.28341i	0.301950	+	0.106004i
$465$		0			0
$466$	−0.498458	+	0.0231919i	−0.0230906	+	0.00107434i
$467$	2.14751	−	8.01462i	0.0993749	−	0.370872i	−0.898271	−	0.439441i	$-0.855177\pi$
$467$	2.14751	−	8.01462i	0.0993749	−	0.370872i	0.997646	+	0.0685687i	$0.0218432\pi$
$468$	−31.4352	+	11.6456i	−1.45309	+	0.538317i
$469$	6.76572	+	13.9806i	0.312412	+	0.645565i
$470$		0			0
$471$	−27.7093	+	15.9980i	−1.27678	+	0.737147i
$472$	4.95441	−	2.10217i	0.228045	−	0.0967603i
$473$	17.2441	−	4.62053i	0.792883	−	0.212452i
$474$	29.2023	+	15.0957i	1.34131	+	0.693371i
$475$		0			0
$476$	5.92318	−	10.7528i	0.271488	−	0.492852i
$477$	45.2221	−	45.2221i	2.07058	−	2.07058i
$478$	−10.3452	−	32.4864i	−0.473177	−	1.48589i
$479$	6.99926	−	12.1231i	0.319805	−	0.553918i	−0.660643	−	0.750701i	$-0.729716\pi$
$479$	6.99926	−	12.1231i	0.319805	−	0.553918i	0.980447	+	0.196783i	$0.0630494\pi$
$480$		0			0
$481$	4.12176	+	7.13910i	0.187936	+	0.325515i
$482$	6.01563	+	1.31559i	0.274005	+	0.0599236i
$483$	39.3060	−	7.51507i	1.78849	−	0.341948i
$484$	1.56777	+	0.720172i	0.0712622	+	0.0327351i
$485$		0			0
$486$	0.996328	+	21.4139i	0.0451943	+	0.971353i
$487$	−25.6423	+	6.87083i	−1.16196	+	0.311347i	−0.787750	−	0.615995i	$-0.788754\pi$
$487$	−25.6423	+	6.87083i	−1.16196	+	0.311347i	−0.374214	+	0.927342i	$0.622087\pi$
$488$	−4.03070	+	32.7881i	−0.182461	+	1.48425i
$489$			0.00795220i			0.000359611i
$490$		0			0
$491$		−	35.5868i		−	1.60601i	−0.595973	−	0.803004i	$-0.703234\pi$
$491$		−	35.5868i		−	1.60601i	0.595973	−	0.803004i	$-0.296766\pi$
$492$	−11.7901	−	9.77867i	−0.531538	−	0.440856i
$493$	−3.86191	+	1.03480i	−0.173932	+	0.0466049i
$494$	−13.5126	+	0.628702i	−0.607959	+	0.0282866i
$495$		0			0
$496$	−10.5711	+	9.07830i	−0.474655	+	0.407628i
$497$	1.46093	−	0.279321i	0.0655316	−	0.0125293i
$498$	5.26303	−	24.0656i	0.235842	−	1.07840i
$499$	−4.94115	−	8.55833i	−0.221196	−	0.383123i	0.733975	−	0.679176i	$-0.237663\pi$
$499$	−4.94115	−	8.55833i	−0.221196	−	0.383123i	−0.955172	+	0.296053i	$0.904330\pi$
$500$		0			0
$501$	−4.62022	+	8.00245i	−0.206416	+	0.357523i
$502$	17.9725	−	5.72327i	0.802151	−	0.255442i
$503$	−16.5308	+	16.5308i	−0.737071	+	0.737071i	−0.972010	−	0.234939i	$-0.924511\pi$
$503$	−16.5308	+	16.5308i	−0.737071	+	0.737071i	0.234939	+	0.972010i	$0.424511\pi$
$504$	−2.43970	−	36.5803i	−0.108673	−	1.62942i
$505$		0			0
$506$	−11.1277	+	21.5262i	−0.494687	+	0.956958i
$507$	3.51413	−	0.941607i	0.156068	−	0.0418182i
$508$	−3.68452	−	0.627968i	−0.163474	−	0.0278616i
$509$	0.789343	−	0.455727i	0.0349870	−	0.0201998i	−0.482404	−	0.875949i	$-0.660236\pi$
$509$	0.789343	−	0.455727i	0.0349870	−	0.0201998i	0.517391	+	0.855749i	$0.326903\pi$
$510$		0			0
$511$	3.85873	+	7.97365i	0.170700	+	0.352733i
$512$	−8.11815	+	21.1210i	−0.358775	+	0.933424i
$513$	3.86218	−	14.4138i	0.170519	−	0.636386i
$514$	−0.661113	−	14.2092i	−0.0291604	−	0.626739i
$515$		0			0
$516$	−31.3814	+	2.92651i	−1.38149	+	0.128833i
$517$	−14.2284	+	14.2284i	−0.625763	+	0.625763i
$518$	−8.76666	+	2.10273i	−0.385185	+	0.0923885i
$519$	45.1677			1.98264
$520$		0			0
$521$	3.24107	−	5.61370i	0.141994	−	0.245941i	−0.786254	−	0.617904i	$-0.787982\pi$
$521$	3.24107	−	5.61370i	0.141994	−	0.245941i	0.928247	+	0.371963i	$0.121315\pi$
$522$	−8.04134	+	8.82613i	−0.351960	+	0.386309i
$523$	−4.55591	−	1.22075i	−0.199216	−	0.0533798i	0.157831	−	0.987466i	$-0.449550\pi$
$523$	−4.55591	−	1.22075i	−0.199216	−	0.0533798i	−0.357047	+	0.934086i	$0.616217\pi$
$524$	3.39736	−	7.39585i	0.148415	−	0.323089i
$525$		0			0
$526$	12.8015	−	8.20701i	0.558170	−	0.357842i
$527$	2.09173	−	7.80645i	0.0911173	−	0.340054i
$528$	29.5538	+	20.1938i	1.28616	+	0.878824i
$529$	5.16358	+	2.98119i	0.224503	+	0.129617i
$530$		0			0
$531$			9.32205i			0.404542i
$532$	3.54087	−	14.3636i	0.153516	−	0.622743i
$533$	−6.59253	−	6.59253i	−0.285554	−	0.285554i
$534$	5.29382	−	10.2408i	0.229086	−	0.443161i
$535$		0			0
$536$	15.3941	+	6.22222i	0.664924	+	0.268759i
$537$	−49.3390	−	13.2203i	−2.12913	−	0.570500i
$538$	−2.85675	+	13.0627i	−0.123163	+	0.563172i
$539$	−22.0511	−	3.23736i	−0.949808	−	0.139443i
$540$		0			0
$541$	−9.43554	−	16.3428i	−0.405666	−	0.702633i	0.588733	−	0.808328i	$-0.299627\pi$
$541$	−9.43554	−	16.3428i	−0.405666	−	0.702633i	−0.994399	+	0.105694i	$0.966294\pi$
$542$	−15.0828	−	13.7417i	−0.647862	−	0.590256i
$543$	−3.11669	−	11.6317i	−0.133750	−	0.499162i
$544$	−3.02348	−	12.7708i	−0.129631	−	0.547545i
$545$		0			0
$546$	0.949434	−	35.9665i	0.0406320	−	1.53922i
$547$	9.42028	+	9.42028i	0.402782	+	0.402782i	0.879212	−	0.476430i	$-0.158069\pi$
$547$	9.42028	+	9.42028i	0.402782	+	0.402782i	−0.476430	+	0.879212i	$0.658069\pi$
$548$	24.8104	+	20.5777i	1.05985	+	0.879035i
$549$	−49.5537	−	28.6098i	−2.11490	−	1.22104i
$550$		0			0
$551$	−4.17252	+	2.40901i	−0.177756	+	0.102627i
$552$	25.7512	−	34.1627i	1.09605	−	1.45406i
$553$	−16.5586	+	14.3051i	−0.704145	+	0.608316i
$554$	−39.3949	+	25.2560i	−1.67373	+	1.07303i
$555$		0			0
$556$	−27.8719	+	19.7547i	−1.18203	+	0.837786i
$557$	9.82230	+	36.6573i	0.416184	+	1.55322i	0.782452	+	0.622711i	$0.213969\pi$
$557$	9.82230	+	36.6573i	0.416184	+	1.55322i	−0.366268	+	0.930509i	$0.619365\pi$
$558$	−7.32349	−	22.9976i	−0.310028	−	0.973564i
$559$	−19.1836			−0.811378
$560$		0			0
$561$	−20.7605			−0.876510
$562$	4.36286	+	13.7005i	0.184036	+	0.577919i
$563$	−9.81479	−	36.6293i	−0.413644	−	1.54374i	−0.787536	−	0.616269i	$-0.788643\pi$
$563$	−9.81479	−	36.6293i	−0.413644	−	1.54374i	0.373892	−	0.927472i	$-0.378023\pi$
$564$	28.9828	−	20.5421i	1.22040	−	0.864978i
$565$		0			0
$566$	32.9768	−	21.1414i	1.38612	−	0.888638i
$567$	0.759585	+	0.264159i	0.0318996	+	0.0110936i
$568$	0.957124	−	1.26976i	0.0401600	−	0.0532780i
$569$	7.96777	−	4.60019i	0.334026	−	0.192850i	−0.323601	−	0.946194i	$-0.604894\pi$
$569$	7.96777	−	4.60019i	0.334026	−	0.192850i	0.657627	+	0.753344i	$0.271560\pi$
$570$		0			0
$571$	14.8692	+	8.58473i	0.622256	+	0.359260i	0.777747	−	0.628578i	$-0.216363\pi$
$571$	14.8692	+	8.58473i	0.622256	+	0.359260i	−0.155491	+	0.987837i	$0.549696\pi$
$572$	16.7693	+	13.9084i	0.701160	+	0.581540i
$573$	22.9716	+	22.9716i	0.959652	+	0.959652i
$574$	8.96156	−	4.86328i	0.374048	−	0.202989i
$575$		0			0
$576$	−28.1851	−	27.2339i	−1.17438	−	1.13474i
$577$	−7.92529	−	29.5776i	−0.329934	−	1.23133i	−0.909258	−	0.416233i	$-0.863350\pi$
$577$	−7.92529	−	29.5776i	−0.329934	−	1.23133i	0.579324	−	0.815097i	$-0.303317\pi$
$578$	−12.1450	−	11.0651i	−0.505167	−	0.460249i
$579$	6.49731	+	11.2537i	0.270019	+	0.467687i
$580$		0			0
$581$	13.5662	+	9.21126i	0.562819	+	0.382147i
$582$	13.1160	−	59.9737i	0.543675	−	2.48599i
$583$	−40.1471	−	10.7574i	−1.66272	−	0.445525i
$584$	8.77981	+	3.54876i	0.363311	+	0.146849i
$585$		0			0
$586$	2.82840	−	5.47146i	0.116840	−	0.226024i
$587$	−31.4917	−	31.4917i	−1.29980	−	1.29980i	−0.928520	−	0.371283i	$-0.878918\pi$
$587$	−31.4917	−	31.4917i	−1.29980	−	1.29980i	−0.371283	−	0.928520i	$-0.621082\pi$
$588$	37.4165	+	12.1749i	1.54303	+	0.502084i
$589$		−	9.73911i		−	0.401293i
$590$		0			0
$591$	−23.3150	−	13.4609i	−0.959050	−	0.553708i
$592$	−5.43731	+	7.95753i	−0.223472	+	0.327053i
$593$	−1.97132	+	7.35708i	−0.0809525	+	0.302119i	−0.994517	−	0.104575i	$-0.966652\pi$
$593$	−1.97132	+	7.35708i	−0.0809525	+	0.302119i	0.913564	+	0.406694i	$0.133318\pi$
$594$	−20.2326	+	12.9711i	−0.830155	+	0.532212i
$595$		0			0
$596$	7.47885	−	16.2810i	0.306346	−	0.666895i
$597$	−4.72275	−	1.26546i	−0.193289	−	0.0517917i
$598$	17.5369	−	19.2484i	0.717136	−	0.787125i
$599$	0.0710719	−	0.123100i	0.00290392	−	0.00502974i	−0.864570	−	0.502513i	$-0.832409\pi$
$599$	0.0710719	−	0.123100i	0.00290392	−	0.00502974i	0.867474	+	0.497483i	$0.165742\pi$
$600$		0			0
$601$	−13.9872			−0.570550			−0.285275	−	0.958446i	$-0.592085\pi$
$601$	−13.9872			−0.570550			−0.285275	+	0.958446i	$0.592085\pi$
$602$	5.96279	−	20.1144i	0.243025	−	0.819801i
$603$	−20.3363	+	20.3363i	−0.828157	+	0.828157i
$604$	−13.4119	+	1.25075i	−0.545724	+	0.0508923i
$605$		0			0
$606$	−2.11803	−	45.5223i	−0.0860390	−	1.84922i
$607$	8.48876	−	31.6805i	0.344548	−	1.28587i	−0.548591	−	0.836091i	$-0.684835\pi$
$607$	8.48876	−	31.6805i	0.344548	−	1.28587i	0.893139	−	0.449781i	$-0.148498\pi$
$608$	−7.50247	−	13.9223i	−0.304265	−	0.564622i
$609$	−5.58221	−	11.5350i	−0.226203	−	0.467423i
$610$		0			0
$611$	18.7255	−	10.8112i	0.757554	−	0.437374i
$612$	22.4087	+	3.81920i	0.905817	+	0.154382i
$613$	5.00032	−	1.33983i	0.201961	−	0.0541153i	−0.156420	−	0.987691i	$-0.549995\pi$
$613$	5.00032	−	1.33983i	0.201961	−	0.0541153i	0.358381	+	0.933575i	$0.383329\pi$
$614$	12.2467	−	23.6909i	0.494236	−	0.956086i
$615$		0			0
$616$	−19.7957	+	13.2599i	−0.797590	+	0.534256i
$617$	−18.4714	+	18.4714i	−0.743630	+	0.743630i	−0.973275	−	0.229644i	$-0.926244\pi$
$617$	−18.4714	+	18.4714i	−0.743630	+	0.743630i	0.229644	+	0.973275i	$0.426244\pi$
$618$	49.6215	−	15.8018i	1.99607	−	0.635642i
$619$	−4.38197	+	7.58980i	−0.176126	+	0.305060i	−0.940551	−	0.339654i	$-0.889690\pi$
$619$	−4.38197	+	7.58980i	−0.176126	+	0.305060i	0.764424	+	0.644714i	$0.223023\pi$
$620$		0			0
$621$	14.3624	+	24.8764i	0.576343	+	0.998255i
$622$	0.472576	−	2.16089i	0.0189486	−	0.0866437i
$623$	5.01657	+	5.80684i	0.200985	+	0.232646i
$624$	−25.0592	−	29.1797i	−1.00317	−	1.16812i
$625$		0			0
$626$	17.2038	−	0.800447i	0.687604	−	0.0319923i
$627$	−24.1653	+	6.47506i	−0.965068	+	0.258589i
$628$	−17.5252	−	14.5353i	−0.699330	−	0.580022i
$629$		−	5.58989i		−	0.222883i
$630$		0			0
$631$			31.2397i			1.24363i	0.783164	+	0.621816i	$0.213605\pi$
$631$			31.2397i			1.24363i	−0.783164	+	0.621816i	$0.786395\pi$
$632$	−2.85425	+	23.2181i	−0.113536	+	0.923568i
$633$	−64.4986	+	17.2823i	−2.56359	+	0.686911i
$634$	1.80029	+	38.6932i	0.0714985	+	1.53670i
$635$		0			0
$636$	66.6796	+	30.6300i	2.64402	+	1.21456i
$637$	21.9876	+	9.49304i	0.871180	+	0.376128i
$638$	7.58062	+	1.65785i	0.300120	+	0.0656348i
$639$	1.37709	+	2.38520i	0.0544770	+	0.0943569i
$640$		0			0
$641$	−24.9696	+	43.2485i	−0.986238	+	1.70821i	−0.349939	+	0.936772i	$0.613798\pi$
$641$	−24.9696	+	43.2485i	−0.986238	+	1.70821i	−0.636299	+	0.771443i	$0.719535\pi$
$642$	−0.495716	−	1.55667i	−0.0195644	−	0.0614369i
$643$	−16.3136	+	16.3136i	−0.643345	+	0.643345i	−0.951376	−	0.308031i	$-0.900330\pi$
$643$	−16.3136	+	16.3136i	−0.643345	+	0.643345i	0.308031	+	0.951376i	$0.400330\pi$
$644$	14.7314	+	24.3707i	0.580499	+	0.960341i
$645$		0			0
$646$	8.14837	+	4.21219i	0.320593	+	0.165727i
$647$	15.5722	−	4.17257i	0.612208	−	0.164041i	0.0606248	−	0.998161i	$-0.480691\pi$
$647$	15.5722	−	4.17257i	0.612208	−	0.164041i	0.551583	+	0.834120i	$0.314024\pi$
$648$	0.791438	−	0.335810i	0.0310906	−	0.0131919i
$649$	5.24671	−	3.02919i	0.205951	−	0.118906i
$650$		0			0
$651$	25.8349	+	1.88633i	1.01255	+	0.0739310i
$652$	−0.00530642	+	0.00196583i	−0.000207816	+	7.69879e-5i
$653$	−5.86041	+	21.8713i	−0.229335	+	0.855891i	0.751286	+	0.659977i	$0.229434\pi$
$653$	−5.86041	+	21.8713i	−0.229335	+	0.855891i	−0.980621	+	0.195914i	$0.937233\pi$
$654$	−28.9977	+	1.34918i	−1.13390	+	0.0527572i
$655$		0			0
$656$	3.61062	−	10.2847i	0.140971	−	0.401552i
$657$	−11.5985	+	11.5985i	−0.452501	+	0.452501i
$658$	5.51536	+	22.9946i	0.215011	+	0.896421i
$659$	0.119381			0.00465044			0.00232522	−	0.999997i	$-0.499260\pi$
$659$	0.119381			0.00465044			0.00232522	+	0.999997i	$0.499260\pi$
$660$		0			0
$661$	10.3433	−	17.9151i	0.402307	−	0.696816i	−0.591697	−	0.806161i	$-0.701542\pi$
$661$	10.3433	−	17.9151i	0.402307	−	0.696816i	0.994004	+	0.109344i	$0.0348751\pi$
$662$	4.08983	+	3.72618i	0.158956	+	0.144822i
$663$	21.5484	+	5.77388i	0.836871	+	0.224239i
$664$	17.3597	−	2.43718i	0.673689	−	0.0945810i
$665$		0			0
$666$	−9.00968	−	14.0535i	−0.349118	−	0.544562i
$667$	2.40041	−	8.95846i	0.0929443	−	0.346873i
$668$	−6.48210	−	1.10477i	−0.250800	−	0.0427449i
$669$	45.5445	+	26.2951i	1.76085	+	1.01663i
$670$		0			0
$671$			37.1869i			1.43559i
$672$	38.3847	−	17.2052i	1.48072	−	0.663706i
$673$	−34.9098	−	34.9098i	−1.34568	−	1.34568i	−0.890299	−	0.455376i	$-0.849505\pi$
$673$	−34.9098	−	34.9098i	−1.34568	−	1.34568i	−0.455376	−	0.890299i	$-0.650495\pi$
$674$	22.4653	+	11.6131i	0.865330	+	0.447321i
$675$		0			0
$676$	1.49704	+	2.11217i	0.0575784	+	0.0812373i
$677$	−4.94915	−	1.32612i	−0.190211	−	0.0509669i	0.162456	−	0.986716i	$-0.448059\pi$
$677$	−4.94915	−	1.32612i	−0.190211	−	0.0509669i	−0.352667	+	0.935749i	$0.614725\pi$
$678$	63.8660	+	13.9672i	2.45276	+	0.536408i
$679$	33.8082	+	22.9554i	1.29744	+	0.880946i
$680$		0			0
$681$	−29.2147	−	50.6014i	−1.11951	−	1.93905i
$682$	−10.5639	+	11.5949i	−0.404513	+	0.443992i
$683$	10.8385	+	40.4498i	0.414724	+	1.54777i	0.785389	+	0.619003i	$0.212463\pi$
$683$	10.8385	+	40.4498i	0.414724	+	1.54777i	−0.370665	+	0.928767i	$0.620870\pi$
$684$	27.2749	−	2.54356i	1.04288	−	0.0972553i
$685$		0			0
$686$	−16.7880	+	20.1038i	−0.640970	+	0.767566i
$687$	35.5235	+	35.5235i	1.35530	+	1.35530i
$688$	−9.71049	−	20.2170i	−0.370209	−	0.770766i
$689$	38.6789	+	22.3313i	1.47355	+	0.850755i
$690$		0			0
$691$	−29.5825	+	17.0795i	−1.12537	+	0.649734i	−0.942767	−	0.333452i	$-0.891787\pi$
$691$	−29.5825	+	17.0795i	−1.12537	+	0.649734i	−0.182606	+	0.983186i	$0.558453\pi$
$692$	11.1657	+	30.1400i	0.424457	+	1.14575i
$693$	−7.75009	−	40.5352i	−0.294402	−	1.53981i
$694$	−4.57924	−	7.14280i	−0.173826	−	0.271137i
$695$		0			0
$696$	−12.7013	−	5.13379i	−0.481440	−	0.194596i
$697$	1.63627	+	6.10663i	0.0619780	+	0.231305i
$698$	20.4637	−	6.51659i	0.774562	−	0.246657i
$699$	0.991682			0.0375089
$700$		0			0
$701$	−28.1444			−1.06300			−0.531499	−	0.847059i	$-0.678371\pi$
$701$	−28.1444			−1.06300			−0.531499	+	0.847059i	$0.678371\pi$
$702$	24.6080	−	7.83633i	0.928770	−	0.295763i
$703$	−1.74345	−	6.50664i	−0.0657554	−	0.245402i
$704$	−6.16927	+	24.7130i	−0.232513	+	0.931406i
$705$		0			0
$706$	−26.2647	−	40.9682i	−0.988483	−	1.54186i
$707$	28.6515	+	9.96406i	1.07755	+	0.374737i
$708$	−10.0297	+	3.71562i	−0.376938	+	0.139641i
$709$	−3.23053	+	1.86515i	−0.121325	+	0.0700471i	−0.559434	−	0.828875i	$-0.688982\pi$
$709$	−3.23053	+	1.86515i	−0.121325	+	0.0700471i	0.438109	+	0.898922i	$0.355648\pi$
$710$		0			0
$711$	−35.0903	−	20.2594i	−1.31599	−	0.759788i
$712$	8.14221	+	1.00094i	0.305142	+	0.0375118i
$713$	13.2564	+	13.2564i	0.496456	+	0.496456i
$714$	−12.7519	+	20.7993i	−0.477228	+	0.778395i
$715$		0			0
$716$	−3.37509	−	36.1915i	−0.126133	−	1.35254i
$717$	17.5366	+	65.4475i	0.654917	+	2.44418i
$718$	−8.00510	+	8.78636i	−0.298748	+	0.327904i
$719$	−14.3205	−	24.8039i	−0.534066	−	0.925029i	−0.999208	−	0.0397933i	$-0.987330\pi$
$719$	−14.3205	−	24.8039i	−0.534066	−	0.925029i	0.465142	−	0.885236i	$-0.346003\pi$
$720$		0			0
$721$	−2.52432	+	34.5728i	−0.0940106	+	1.28756i
$722$	−15.4512	−	3.37911i	−0.575034	−	0.125757i
$723$	−11.8207	−	3.16736i	−0.439618	−	0.117795i
$724$	6.99122	−	4.95515i	0.259827	−	0.184157i
$725$		0			0
$726$	−3.04582	−	1.57450i	−0.113041	−	0.0584350i
$727$	35.3576	+	35.3576i	1.31134	+	1.31134i	0.920429	+	0.390911i	$0.127840\pi$
$727$	35.3576	+	35.3576i	1.31134	+	1.31134i	0.390911	+	0.920429i	$0.372160\pi$
$728$	24.2348	−	8.25757i	0.898200	−	0.306046i
$729$		−	43.5147i		−	1.61166i
$730$		0			0
$731$	11.2655	+	6.50414i	0.416669	+	0.240564i
$732$	11.0303	−	64.7186i	0.407690	−	2.39207i
$733$	5.31453	−	19.8341i	0.196297	−	0.732589i	−0.795631	−	0.605782i	$-0.792860\pi$
$733$	5.31453	−	19.8341i	0.196297	−	0.732589i	0.991927	−	0.126807i	$-0.0404730\pi$
$734$	−23.4731	−	36.6138i	−0.866407	−	1.35144i
$735$		0			0
$736$	29.1623	+	8.73831i	1.07494	+	0.322098i
$737$	18.0541	+	4.83758i	0.665031	+	0.178194i
$738$	13.9563	+	12.7153i	0.513738	+	0.468058i
$739$	24.2010	−	41.9174i	0.890249	−	1.54196i	0.0506730	−	0.998715i	$-0.483863\pi$
$739$	24.2010	−	41.9174i	0.890249	−	1.54196i	0.839576	−	0.543242i	$-0.182803\pi$
$740$		0			0
$741$	26.8832			0.987579
$742$	−35.4374	+	33.6146i	−1.30095	+	1.23403i
$743$	3.78255	−	3.78255i	0.138768	−	0.138768i	−0.634310	−	0.773078i	$-0.718716\pi$
$743$	3.78255	−	3.78255i	0.138768	−	0.138768i	0.773078	+	0.634310i	$0.218716\pi$
$744$	21.8242	−	17.0459i	0.800115	−	0.624931i
$745$		0			0
$746$	21.2435	−	0.988403i	0.777781	−	0.0361880i
$747$	−7.85869	+	29.3290i	−0.287535	+	1.07309i
$748$	−5.13212	−	13.8533i	−0.187649	−	0.506526i
$749$	1.08458	+	0.0791901i	0.0396296	+	0.00289354i
$750$		0			0
$751$	−15.5554	+	8.98090i	−0.567623	+	0.327718i	−0.756200	−	0.654341i	$-0.772946\pi$
$751$	−15.5554	+	8.98090i	−0.567623	+	0.327718i	0.188576	+	0.982059i	$0.439613\pi$
$752$	20.8723	+	14.2618i	0.761133	+	0.520075i
$753$	−36.2076	+	9.70180i	−1.31948	+	0.353553i
$754$	−7.40724	−	3.82908i	−0.269756	−	0.139447i
$755$		0			0
$756$	0.567715	+	28.2378i	0.0206476	+	1.02700i
$757$	35.0017	−	35.0017i	1.27216	−	1.27216i	0.327204	−	0.944954i	$-0.393894\pi$
$757$	35.0017	−	35.0017i	1.27216	−	1.27216i	0.944954	−	0.327204i	$-0.106106\pi$
$758$	−0.825034	−	2.59081i	−0.0299666	−	0.0941024i
$759$	24.0790	−	41.7061i	0.874013	−	1.51384i
$760$		0			0
$761$	−18.0493	−	31.2622i	−0.654285	−	1.13325i	−0.982073	−	0.188503i	$-0.939636\pi$
$761$	−18.0493	−	31.2622i	−0.654285	−	1.13325i	0.327788	−	0.944751i	$-0.393697\pi$
$762$	7.25651	+	1.58697i	0.262876	+	0.0574897i
$763$	6.34710	−	18.2510i	0.229781	−	0.660730i
$764$	−9.64999	+	21.0074i	−0.349125	+	0.760022i
$765$		0			0
$766$	−1.05069	−	22.5824i	−0.0379631	−	0.815934i
$767$	−6.28831	+	1.68495i	−0.227058	+	0.0608399i
$768$	18.0670	−	41.1796i	0.651937	−	1.48594i
$769$		−	22.5137i		−	0.811865i	−0.913903	−	0.405933i	$-0.866947\pi$
$769$		−	22.5137i		−	0.811865i	0.913903	−	0.405933i	$-0.133053\pi$
$770$		0			0
$771$			28.2691i			1.01809i
$772$	−5.90328	+	7.11756i	−0.212464	+	0.256167i
$773$	22.3506	−	5.98883i	0.803896	−	0.215403i	0.166602	−	0.986024i	$-0.446720\pi$
$773$	22.3506	−	5.98883i	0.803896	−	0.215403i	0.637294	+	0.770621i	$0.280054\pi$
$774$	38.8057	−	1.80552i	1.39484	−	0.0648982i
$775$		0			0
$776$	43.2622	−	6.07370i	1.55302	−	0.218033i
$777$	17.5978	−	3.36460i	0.631318	−	0.120704i
$778$	−3.42368	+	15.6550i	−0.122745	+	0.561259i
$779$	3.80923	+	6.59778i	0.136480	+	0.236390i
$780$		0			0
$781$	0.894971	−	1.55014i	0.0320246	−	0.0554682i
$782$	−16.8246	+	5.35773i	−0.601646	+	0.191592i
$783$	6.50425	−	6.50425i	0.232443	−	0.232443i
$784$	1.12541	+	27.9774i	0.0401933	+	0.999192i
$785$		0			0
$786$	−7.42758	+	14.3684i	−0.264933	+	0.512505i
$787$	−35.5681	+	9.53044i	−1.26787	+	0.339724i	−0.829213	−	0.558933i	$-0.811211\pi$
$787$	−35.5681	+	9.53044i	−1.26787	+	0.339724i	−0.438653	+	0.898657i	$0.644544\pi$
$788$	3.21873	−	18.8855i	0.114662	−	0.672767i
$789$	−26.1715	+	15.1101i	−0.931731	+	0.537935i
$790$		0			0
$791$	−24.4452	+	36.0024i	−0.869170	+	1.28010i
$792$	−35.2311	−	26.5565i	−1.25188	−	0.943646i
$793$	10.3424	−	38.5982i	0.367268	−	1.37066i
$794$	−0.766546	−	16.4752i	−0.0272037	−	0.584684i
$795$		0			0
$796$	−0.323065	−	3.46427i	−0.0114507	−	0.122788i
$797$	8.30328	−	8.30328i	0.294117	−	0.294117i	−0.544587	−	0.838704i	$-0.683314\pi$
$797$	8.30328	−	8.30328i	0.294117	−	0.294117i	0.838704	+	0.544587i	$0.183314\pi$
$798$	−8.35605	+	28.1877i	−0.295801	+	0.997832i
$799$	−14.6620			−0.518705
$800$		0			0
$801$	−7.10464	+	12.3056i	−0.251030	+	0.434797i
$802$	26.3562	−	28.9284i	0.930670	−	1.02150i
$803$	10.2969	+	2.75904i	0.363369	+	0.0973645i
$804$	−29.9857	−	13.7743i	−1.05751	−	0.485781i
$805$		0			0
$806$	14.1896	−	9.09693i	0.499807	−	0.320426i
$807$	6.87776	−	25.6682i	0.242109	−	0.903562i
$808$	29.8530	−	12.6667i	1.05022	−	0.445614i
$809$	−27.1489	−	15.6744i	−0.954504	−	0.551083i	−0.0600265	−	0.998197i	$-0.519119\pi$
$809$	−27.1489	−	15.6744i	−0.954504	−	0.551083i	−0.894477	+	0.447114i	$0.852452\pi$
$810$		0			0
$811$		−	9.76550i		−	0.342913i	−0.985192	−	0.171456i	$-0.945153\pi$
$811$		−	9.76550i		−	0.342913i	0.985192	−	0.171456i	$-0.0548473\pi$
$812$	6.31725	−	6.57648i	0.221692	−	0.230789i
$813$	28.6732	+	28.6732i	1.00561	+	1.00561i
$814$	−4.98202	+	9.63757i	−0.174620	+	0.337797i
$815$		0			0
$816$	4.82262	+	25.6319i	0.168826	+	0.897297i
$817$	15.1416	+	4.05719i	0.529739	+	0.141943i
$818$	−4.17892	+	19.1084i	−0.146112	+	0.668109i
$819$	−3.22937	+	44.2291i	−0.112843	+	1.54549i
$820$		0			0
$821$	3.83240	+	6.63791i	0.133752	+	0.231665i	0.925120	−	0.379675i	$-0.123964\pi$
$821$	3.83240	+	6.63791i	0.133752	+	0.231665i	−0.791368	+	0.611340i	$0.790631\pi$
$822$	−47.3530	−	43.1425i	−1.65163	−	1.50477i
$823$	−14.1720	−	52.8907i	−0.494006	−	1.84365i	−0.535530	−	0.844517i	$-0.679888\pi$
$823$	−14.1720	−	52.8907i	−0.494006	−	1.84365i	0.0415239	−	0.999138i	$-0.486779\pi$
$824$	22.8111	+	29.2056i	0.794663	+	1.01743i
$825$		0			0
$826$	0.187877	−	7.11716i	0.00653708	−	0.247638i
$827$	−35.5553	−	35.5553i	−1.23638	−	1.23638i	−0.961470	−	0.274910i	$-0.911352\pi$
$827$	−35.5553	−	35.5553i	−1.23638	−	1.23638i	−0.274910	−	0.961470i	$-0.588648\pi$
$828$	−33.6631	+	40.5874i	−1.16987	+	1.41051i
$829$	−23.4882	−	13.5609i	−0.815780	−	0.470991i	0.0331794	−	0.999449i	$-0.489437\pi$
$829$	−23.4882	−	13.5609i	−0.815780	−	0.470991i	−0.848959	+	0.528459i	$0.822770\pi$
$830$		0			0
$831$	80.5397	−	46.4996i	2.79389	−	1.61305i
$832$	13.2765	−	23.9351i	0.460281	−	0.829800i
$833$	−9.69357	−	13.0296i	−0.335862	−	0.451449i
$834$	57.1560	−	36.6426i	1.97915	−	1.26883i
$835$		0			0
$836$	−10.2945	−	14.5246i	−0.356044	−	0.502342i
$837$	4.81237	+	17.9600i	0.166340	+	0.620789i
$838$	8.88173	+	27.8908i	0.306814	+	0.963472i
$839$	3.82948			0.132208			0.0661042	−	0.997813i	$-0.478943\pi$
$839$	3.82948			0.132208			0.0661042	+	0.997813i	$0.478943\pi$
$840$		0			0
$841$	26.0301			0.897589
$842$	−11.4796	−	36.0489i	−0.395614	−	1.24233i
$843$	−7.39570	−	27.6011i	−0.254722	−	0.950634i
$844$	−27.4767	−	38.7669i	−0.945788	−	1.33441i
$845$		0			0
$846$	−36.8617	+	23.6320i	−1.26733	+	0.812485i
$847$	1.72708	−	1.49203i	0.0593431	−	0.0512669i
$848$	−3.95551	+	52.0665i	−0.135833	+	1.78797i
$849$	−67.4183	+	38.9240i	−2.31379	+	1.33587i
$850$		0			0
$851$	11.2296	+	6.48342i	0.384946	+	0.222249i
$852$	−2.01737	+	2.43233i	−0.0691138	+	0.0833302i
$853$	1.20013	+	1.20013i	0.0410916	+	0.0410916i	0.727354	−	0.686262i	$-0.240750\pi$
$853$	1.20013	+	1.20013i	0.0410916	+	0.0410916i	−0.686262	+	0.727354i	$0.740750\pi$
$854$	37.2564	+	22.8416i	1.27489	+	0.781624i
$855$		0			0
$856$	0.916206	−	0.715604i	0.0313153	−	0.0244588i
$857$	−6.85466	−	25.5819i	−0.234151	−	0.873862i	−0.978530	−	0.206105i	$-0.933921\pi$
$857$	−6.85466	−	25.5819i	−0.234151	−	0.873862i	0.744379	−	0.667757i	$-0.232746\pi$
$858$	−32.0058	−	29.1599i	−1.09266	−	0.995503i
$859$	−19.8151	−	34.3208i	−0.676083	−	1.17101i	−0.976151	−	0.217093i	$-0.930343\pi$
$859$	−19.8151	−	34.3208i	−0.676083	−	1.17101i	0.300068	−	0.953918i	$-0.402991\pi$
$860$		0			0
$861$	−18.2397	+	8.82684i	−0.621608	+	0.300818i
$862$	−12.1881	+	55.7308i	−0.415128	+	1.89820i
$863$	−9.62351	−	2.57861i	−0.327588	−	0.0877769i	0.0912768	−	0.995826i	$-0.470905\pi$
$863$	−9.62351	−	2.57861i	−0.327588	−	0.0877769i	−0.418865	+	0.908049i	$0.637572\pi$
$864$	20.7148	+	21.9670i	0.704731	+	0.747334i
$865$		0			0
$866$	−15.2306	+	29.4632i	−0.517558	+	1.00120i
$867$	23.0883	+	23.0883i	0.784120	+	0.784120i
$868$	5.12781	+	17.7057i	0.174049	+	0.600970i
$869$			26.3331i			0.893290i
$870$		0			0
$871$	−17.3938	−	10.0423i	−0.589368	−	0.340272i
$872$	−8.06870	−	19.0163i	−0.273241	−	0.643974i
$873$	−19.5846	+	73.0908i	−0.662839	+	2.47375i
$874$	−17.9128	+	11.4839i	−0.605909	+	0.388448i
$875$		0			0
$876$	−17.1019	−	7.85595i	−0.577820	−	0.265428i
$877$	2.47836	+	0.664074i	0.0836882	+	0.0224242i	0.300420	−	0.953807i	$-0.402873\pi$
$877$	2.47836	+	0.664074i	0.0836882	+	0.0224242i	−0.216732	+	0.976231i	$0.569540\pi$
$878$	−5.46830	+	6.00198i	−0.184546	+	0.202557i
$879$	−6.12031	+	10.6007i	−0.206433	+	0.357553i
$880$		0			0
$881$	20.5639			0.692816			0.346408	−	0.938084i	$-0.387401\pi$
$881$	20.5639			0.692816			0.346408	+	0.938084i	$0.387401\pi$
$882$	−45.3714	−	17.1337i	−1.52773	−	0.576922i
$883$	26.6080	−	26.6080i	0.895429	−	0.895429i	−0.0995985	−	0.995028i	$-0.531756\pi$
$883$	26.6080	−	26.6080i	0.895429	−	0.895429i	0.995028	+	0.0995985i	$0.0317558\pi$
$884$	1.47404	+	15.8064i	0.0495775	+	0.531626i
$885$		0			0
$886$	0.0562553	+	1.20908i	0.00188993	+	0.0406199i
$887$	1.90478	−	7.10873i	0.0639562	−	0.238688i	−0.926547	−	0.376180i	$-0.877238\pi$
$887$	1.90478	−	7.10873i	0.0639562	−	0.238688i	0.990503	+	0.137492i	$0.0439042\pi$
$888$	11.5292	−	15.2951i	0.386893	−	0.513269i
$889$	−2.77748	+	4.09062i	−0.0931537	+	0.137195i
$890$		0			0
$891$	0.838132	−	0.483895i	0.0280785	−	0.0162111i
$892$	−6.28760	+	36.8917i	−0.210524	+	1.23523i
$893$	−17.0666	+	4.57299i	−0.571112	+	0.153029i
$894$	−16.3508	+	31.6302i	−0.546854	+	1.05787i
$895$		0			0
$896$	20.9698	+	21.3604i	0.700551	+	0.713602i
$897$	−36.5921	+	36.5921i	−1.22177	+	1.22177i
$898$	−6.28165	+	2.00037i	−0.209621	+	0.0667532i
$899$	3.00169	−	5.19908i	0.100112	−	0.173399i
$900$		0			0
$901$	−15.1427	−	26.2280i	−0.504478	−	0.873781i
$902$	2.62146	−	11.9868i	0.0872852	−	0.399117i
$903$	−13.6952	+	39.3804i	−0.455748	+	1.31050i
$904$	6.46788	+	46.0699i	0.215119	+	1.53226i
$905$		0			0
$906$	26.7409	−	1.24418i	0.888408	−	0.0413352i
$907$	13.4573	−	3.60588i	0.446843	−	0.119731i	−0.0283786	−	0.999597i	$-0.509034\pi$
$907$	13.4573	−	3.60588i	0.446843	−	0.119731i	0.475222	+	0.879866i	$0.342368\pi$
$908$	26.5437	−	32.0036i	0.880884	−	1.06208i
$909$			56.1704i			1.86305i
$910$		0			0
$911$			9.10653i			0.301713i	0.988556	+	0.150856i	$0.0482031\pi$
$911$			9.10653i			0.301713i	−0.988556	+	0.150856i	$0.951797\pi$
$912$	13.6080	+	28.3315i	0.450605	+	0.938148i
$913$	19.0609	−	5.10735i	0.630823	−	0.169029i
$914$	−2.09074	−	44.9359i	−0.0691557	−	1.48635i
$915$		0			0
$916$	−14.9228	+	32.4860i	−0.493064	+	1.07337i
$917$	−7.03857	−	8.14737i	−0.232434	−	0.269050i
$918$	−17.1079	−	3.74142i	−0.564644	−	0.123485i
$919$	−17.5872	−	30.4620i	−0.580149	−	1.00485i	−0.995461	−	0.0951683i	$-0.969661\pi$
$919$	−17.5872	−	30.4620i	−0.580149	−	1.00485i	0.415312	−	0.909679i	$-0.363672\pi$
$920$		0			0
$921$	−26.5004	+	45.9000i	−0.873217	+	1.51246i
$922$	10.0605	+	31.5923i	0.331324	+	1.04044i
$923$	−1.36006	+	1.36006i	−0.0447668	+	0.0447668i
$924$	40.5231	−	24.4951i	1.33311	−	0.805829i
$925$		0			0
$926$	−3.27190	−	1.69136i	−0.107521	−	0.0555817i
$927$	−62.0014	+	16.6132i	−2.03639	+	0.545650i
$928$	0.285898	−	9.74452i	0.00938505	−	0.319879i
$929$	32.5064	−	18.7676i	1.06650	−	0.615745i	0.139278	−	0.990253i	$-0.455522\pi$
$929$	32.5064	−	18.7676i	1.06650	−	0.615745i	0.927223	+	0.374509i	$0.122189\pi$
$930$		0			0
$931$	−15.3472	−	12.1431i	−0.502983	−	0.397974i
$932$	0.245150	+	0.661739i	0.00803015	+	0.0216760i
$933$	−1.13775	+	4.24615i	−0.0372483	+	0.139013i
$934$	−11.7215	+	0.545370i	−0.383540	+	0.0178451i
$935$		0			0
$936$	29.1823	+	37.3628i	0.953853	+	1.22124i
$937$	14.9371	−	14.9371i	0.487973	−	0.487973i	−0.419693	−	0.907666i	$-0.637862\pi$
$937$	14.9371	−	14.9371i	0.487973	−	0.487973i	0.907666	+	0.419693i	$0.137862\pi$
$938$	15.9361	−	15.1164i	0.520333	−	0.493568i
$939$	−34.2270			−1.11696
$940$		0			0
$941$	−3.05589	+	5.29296i	−0.0996192	+	0.172546i	−0.911527	−	0.411240i	$-0.865096\pi$
$941$	−3.05589	+	5.29296i	−0.0996192	+	0.172546i	0.811908	+	0.583786i	$0.198429\pi$
$942$	33.4484	+	30.4743i	1.08981	+	0.992905i
$943$	−14.1655	−	3.79564i	−0.461293	−	0.123603i
$944$	−4.95878	−	5.77417i	−0.161395	−	0.187933i
$945$		0			0
$946$	−13.6261	−	21.2543i	−0.443022	−	0.691036i
$947$	−11.1603	+	41.6507i	−0.362660	+	1.35347i	0.507905	+	0.861413i	$0.330420\pi$
$947$	−11.1603	+	41.6507i	−0.362660	+	1.35347i	−0.870565	+	0.492053i	$0.836247\pi$
$948$	7.81083	−	45.8291i	0.253684	−	1.48846i
$949$	−9.92033	−	5.72751i	−0.322028	−	0.185923i
$950$		0			0
$951$		−	76.9801i		−	2.49625i
$952$	−17.0315	−	3.36749i	−0.551994	−	0.109141i
$953$	−26.8326	−	26.8326i	−0.869193	−	0.869193i	0.123190	−	0.992383i	$-0.460687\pi$
$953$	−26.8326	−	26.8326i	−0.869193	−	0.869193i	−0.992383	+	0.123190i	$0.960687\pi$
$954$	−80.3441	−	41.5328i	−2.60123	−	1.34467i
$955$		0			0
$956$	−39.3373	+	27.8810i	−1.27226	+	0.901736i
$957$	−14.8959	−	3.99135i	−0.481517	−	0.129022i
$958$	−19.3398	−	4.22953i	−0.624841	−	0.136650i
$959$	38.3826	−	18.5747i	1.23944	−	0.599809i
$960$		0			0
$961$	−9.43240	−	16.3374i	−0.304271	−	0.527013i
$962$	7.85148	−	8.61774i	0.253142	−	0.277847i
$963$	0.521171	+	1.94504i	0.0167945	+	0.0626779i
$964$	−0.808611	−	8.67084i	−0.0260436	−	0.279269i
$965$		0			0
$966$	−26.9938	−	49.7415i	−0.868511	−	1.60041i
$967$	9.65871	+	9.65871i	0.310603	+	0.310603i	0.845143	−	0.534540i	$-0.179515\pi$
$967$	9.65871	+	9.65871i	0.310603	+	0.310603i	−0.534540	+	0.845143i	$0.679515\pi$
$968$	0.297700	−	2.42167i	0.00956845	−	0.0778353i
$969$	−15.7871	−	9.11468i	−0.507155	−	0.292806i
$970$		0			0
$971$	−18.9435	+	10.9371i	−0.607927	+	0.350987i	−0.772154	−	0.635436i	$-0.780821\pi$
$971$	−18.9435	+	10.9371i	−0.607927	+	0.350987i	0.164226	+	0.986423i	$0.447487\pi$
$972$	28.4284	−	10.5317i	0.911843	−	0.337804i
$973$	8.48690	+	44.3890i	0.272078	+	1.42305i
$974$	20.2623	+	31.6056i	0.649246	+	1.01271i
$975$		0			0
$976$	45.9128	−	8.63844i	1.46963	−	0.276510i
$977$	6.74446	+	25.1707i	0.215774	+	0.805281i	0.985893	+	0.167380i	$0.0535306\pi$
$977$	6.74446	+	25.1707i	0.215774	+	0.805281i	−0.770118	+	0.637901i	$0.779803\pi$
$978$	0.0107159	−	0.00341244i	0.000342657	−	0.000109118i
$979$	9.23458			0.295138
$980$		0			0
$981$	35.7805			1.14238
$982$	−47.9545	+	15.2709i	−1.53029	+	0.487315i
$983$	12.5590	+	46.8710i	0.400571	+	1.49495i	0.812080	+	0.583547i	$0.198336\pi$
$983$	12.5590	+	46.8710i	0.400571	+	1.49495i	−0.411508	+	0.911406i	$0.634998\pi$
$984$	−8.11777	+	20.0838i	−0.258785	+	0.640248i
$985$		0			0
$986$	3.05165	+	4.76002i	0.0971842	+	0.151590i
$987$	−8.82518	−	46.1583i	−0.280909	−	1.46923i
$988$	6.64569	+	17.9389i	0.211427	+	0.570712i
$989$	−26.1325	+	15.0876i	−0.830965	+	0.479758i
$990$		0			0
$991$	−3.40592	−	1.96641i	−0.108193	−	0.0624650i	0.444927	−	0.895567i	$-0.353230\pi$
$991$	−3.40592	−	1.96641i	−0.108193	−	0.0624650i	−0.553120	+	0.833102i	$0.686563\pi$
$992$	16.7696	+	10.3492i	0.532435	+	0.328589i
$993$	−7.77497	−	7.77497i	−0.246731	−	0.246731i
$994$	−1.00331	−	1.84879i	−0.0318230	−	0.0586402i
$995$		0			0
$996$	−34.6877	+	3.23485i	−1.09912	+	0.102500i
$997$	−13.2857	−	49.5831i	−0.420764	−	1.57031i	−0.773004	−	0.634402i	$-0.781247\pi$
$997$	−13.2857	−	49.5831i	−0.420764	−	1.57031i	0.352240	−	0.935910i	$-0.385420\pi$
$998$	−9.41233	+	10.3309i	−0.297942	+	0.327020i
$999$	6.43023	+	11.1375i	0.203443	+	0.352374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.be.e.543.8		72
4.3	odd	2	inner	700.2.be.e.543.4		72
5.2	odd	4	inner	700.2.be.e.207.16		72
5.3	odd	4		140.2.w.b.67.3	yes	72
5.4	even	2		140.2.w.b.123.11	yes	72
7.2	even	3	inner	700.2.be.e.443.6		72
20.3	even	4		140.2.w.b.67.13	yes	72
20.7	even	4	inner	700.2.be.e.207.6		72
20.19	odd	2		140.2.w.b.123.15	yes	72
28.23	odd	6	inner	700.2.be.e.443.16		72
35.2	odd	12	inner	700.2.be.e.107.4		72
35.3	even	12		980.2.k.j.687.11		36
35.4	even	6		980.2.k.k.883.2		36
35.9	even	6		140.2.w.b.23.13	yes	72
35.13	even	4		980.2.x.m.67.3		72
35.18	odd	12		980.2.k.k.687.11		36
35.19	odd	6		980.2.x.m.863.13		72
35.23	odd	12		140.2.w.b.107.15	yes	72
35.24	odd	6		980.2.k.j.883.2		36
35.33	even	12		980.2.x.m.667.15		72
35.34	odd	2		980.2.x.m.263.11		72
140.3	odd	12		980.2.k.j.687.2		36
140.19	even	6		980.2.x.m.863.3		72
140.23	even	12		140.2.w.b.107.11	yes	72
140.39	odd	6		980.2.k.k.883.11		36
140.59	even	6		980.2.k.j.883.11		36
140.79	odd	6		140.2.w.b.23.3	✓	72
140.83	odd	4		980.2.x.m.67.13		72
140.103	odd	12		980.2.x.m.667.11		72
140.107	even	12	inner	700.2.be.e.107.8		72
140.123	even	12		980.2.k.k.687.2		36
140.139	even	2		980.2.x.m.263.15		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.3	✓	72	140.79	odd	6
140.2.w.b.23.13	yes	72	35.9	even	6
140.2.w.b.67.3	yes	72	5.3	odd	4
140.2.w.b.67.13	yes	72	20.3	even	4
140.2.w.b.107.11	yes	72	140.23	even	12
140.2.w.b.107.15	yes	72	35.23	odd	12
140.2.w.b.123.11	yes	72	5.4	even	2
140.2.w.b.123.15	yes	72	20.19	odd	2
700.2.be.e.107.4		72	35.2	odd	12	inner
700.2.be.e.107.8		72	140.107	even	12	inner
700.2.be.e.207.6		72	20.7	even	4	inner
700.2.be.e.207.16		72	5.2	odd	4	inner
700.2.be.e.443.6		72	7.2	even	3	inner
700.2.be.e.443.16		72	28.23	odd	6	inner
700.2.be.e.543.4		72	4.3	odd	2	inner
700.2.be.e.543.8		72	1.1	even	1	trivial
980.2.k.j.687.2		36	140.3	odd	12
980.2.k.j.687.11		36	35.3	even	12
980.2.k.j.883.2		36	35.24	odd	6
980.2.k.j.883.11		36	140.59	even	6
980.2.k.k.687.2		36	140.123	even	12
980.2.k.k.687.11		36	35.18	odd	12
980.2.k.k.883.2		36	35.4	even	6
980.2.k.k.883.11		36	140.39	odd	6
980.2.x.m.67.3		72	35.13	even	4
980.2.x.m.67.13		72	140.83	odd	4
980.2.x.m.263.11		72	35.34	odd	2
980.2.x.m.263.15		72	140.139	even	2
980.2.x.m.667.11		72	140.103	odd	12
980.2.x.m.667.15		72	35.33	even	12
980.2.x.m.863.3		72	140.19	even	6
980.2.x.m.863.13		72	35.19	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.429119 - 1.34754i) q^{2} +(0.727420 + 2.71477i) q^{3} +(-1.63171 + 1.15651i) q^{4} +(3.34610 - 2.14518i) q^{6} +(0.496852 + 2.59868i) q^{7} +(2.25864 + 1.70252i) q^{8} +(-4.24276 + 2.44956i) q^{9} +(2.75736 + 1.59196i) q^{11} +(-4.32659 - 3.58846i) q^{12} +(-2.41925 - 2.41925i) q^{13} +(3.28861 - 1.78467i) q^{14} +(1.32498 - 3.77418i) q^{16} +(0.600458 + 2.24094i) q^{17} +(5.12151 + 4.66612i) q^{18} +(1.39787 + 2.42118i) q^{19} +(-6.69340 + 3.23917i) q^{21} +(0.961994 - 4.39878i) q^{22} +(-5.19830 - 1.39288i) q^{23} +(-2.97897 + 7.37012i) q^{24} +(-2.22189 + 4.29818i) q^{26} +(-3.77420 - 3.77420i) q^{27} +(-3.81611 - 3.66569i) q^{28} +1.72334i q^{29} +(-3.01685 - 1.74178i) q^{31} +(-5.65442 - 0.165897i) q^{32} +(-2.31605 + 8.64362i) q^{33} +(2.76208 - 1.77077i) q^{34} +(4.09004 - 8.90375i) q^{36} +(-2.32734 - 0.623610i) q^{37} +(2.66278 - 2.92265i) q^{38} +(4.80790 - 8.32752i) q^{39} +2.72503 q^{41} +(7.23716 + 7.62961i) q^{42} +(3.96477 - 3.96477i) q^{43} +(-6.34034 + 0.591276i) q^{44} +(0.353728 + 7.60261i) q^{46} +(-1.63570 + 6.10452i) q^{47} +(11.2098 + 0.851615i) q^{48} +(-6.50628 + 2.58232i) q^{49} +(-5.64685 + 3.26021i) q^{51} +(6.74541 + 1.14965i) q^{52} +(-12.6093 + 3.37866i) q^{53} +(-3.46629 + 6.70545i) q^{54} +(-3.30209 + 6.71537i) q^{56} +(-5.55610 + 5.55610i) q^{57} +(2.32227 - 0.739519i) q^{58} +(0.951402 - 1.64788i) q^{59} +(5.83980 + 10.1148i) q^{61} +(-1.05253 + 4.81275i) q^{62} +(-8.47363 - 9.80850i) q^{63} +(2.20286 + 7.69073i) q^{64} +(12.6415 - 0.588172i) q^{66} +(5.67039 - 1.51938i) q^{67} +(-3.57144 - 2.96214i) q^{68} -15.1254i q^{69} -0.562181i q^{71} +(-13.7532 - 1.69071i) q^{72} +(3.23402 - 0.866554i) q^{73} +(0.158369 + 3.40378i) q^{74} +(-5.08103 - 2.33403i) q^{76} +(-2.76700 + 7.95646i) q^{77} +(-13.2848 - 2.90533i) q^{78} +(4.13532 + 7.16259i) q^{79} +(0.151981 - 0.263239i) q^{81} +(-1.16936 - 3.67208i) q^{82} +(4.38250 - 4.38250i) q^{83} +(7.17559 - 13.0264i) q^{84} +(-7.04404 - 3.64132i) q^{86} +(-4.67848 + 1.25360i) q^{87} +(3.51752 + 8.29011i) q^{88} +(2.51180 - 1.45019i) q^{89} +(5.08485 - 7.48887i) q^{91} +(10.0930 - 3.73908i) q^{92} +(2.53401 - 9.45706i) q^{93} +(8.92798 - 0.415394i) q^{94} +(-3.66277 - 15.4711i) q^{96} +(10.9216 - 10.9216i) q^{97} +(6.27174 + 7.65933i) q^{98} -15.5984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42}+ \cdots + 90 q^{98}+O(q^{100}) \) 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more