LMFDB - Embedded newform 245.4.l.b.117.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(68,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 10]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("245.68");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.l (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:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			117.3
Character	$\chi$	$=$	245.117
Dual form			245.4.l.b.178.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80016 + 0.482353i) q^{2} +(-2.44552 + 9.12679i) q^{3} +(-3.92027 + 2.26337i) q^{4} +(-5.02060 + 9.98967i) q^{5} -17.6093i q^{6} +(16.5079 - 16.5079i) q^{8} +(-53.9351 - 31.1395i) q^{9} +O(q^{10})$	\(q+(-1.80016 + 0.482353i) q^{2} +(-2.44552 + 9.12679i) q^{3} +(-3.92027 + 2.26337i) q^{4} +(-5.02060 + 9.98967i) q^{5} -17.6093i q^{6} +(16.5079 - 16.5079i) q^{8} +(-53.9351 - 31.1395i) q^{9} +(4.21937 - 20.4048i) q^{10} +(-12.4959 - 21.6436i) q^{11} +(-11.0702 - 41.3147i) q^{12} +(8.80162 + 8.80162i) q^{13} +(-78.8957 - 70.2519i) q^{15} +(-3.64732 + 6.31735i) q^{16} +(-9.90033 - 2.65279i) q^{17} +(112.112 + 30.0404i) q^{18} +(-42.5490 + 73.6970i) q^{19} +(-2.92819 - 50.5258i) q^{20} +(32.9346 + 32.9346i) q^{22} +(6.92268 + 25.8358i) q^{23} +(110.294 + 191.034i) q^{24} +(-74.5871 - 100.308i) q^{25} +(-20.0899 - 11.5989i) q^{26} +(235.708 - 235.708i) q^{27} +162.511i q^{29} +(175.911 + 88.4095i) q^{30} +(-23.0483 + 13.3070i) q^{31} +(-44.8199 + 167.270i) q^{32} +(228.096 - 61.1181i) q^{33} +19.1018 q^{34} +281.921 q^{36} +(73.9723 - 19.8208i) q^{37} +(41.0472 - 153.190i) q^{38} +(-101.855 + 58.8061i) q^{39} +(82.0288 + 247.788i) q^{40} -137.076i q^{41} +(-221.858 + 221.858i) q^{43} +(97.9751 + 56.5659i) q^{44} +(581.860 - 382.455i) q^{45} +(-24.9239 - 43.1695i) q^{46} +(-84.1770 - 314.153i) q^{47} +(-48.7375 - 48.7375i) q^{48} +(182.653 + 144.594i) q^{50} +(48.4229 - 83.8709i) q^{51} +(-54.4261 - 14.5834i) q^{52} +(-210.603 - 56.4309i) q^{53} +(-310.619 + 538.008i) q^{54} +(278.950 - 16.1664i) q^{55} +(-568.563 - 568.563i) q^{57} +(-78.3878 - 292.547i) q^{58} +(342.874 + 593.875i) q^{59} +(468.299 + 96.8366i) q^{60} +(-20.5175 - 11.8458i) q^{61} +(35.0721 - 35.0721i) q^{62} -381.090i q^{64} +(-132.115 + 43.7359i) q^{65} +(-381.130 + 220.045i) q^{66} +(220.609 - 823.325i) q^{67} +(44.8163 - 12.0085i) q^{68} -252.727 q^{69} +265.331 q^{71} +(-1404.40 + 376.308i) q^{72} +(222.936 - 832.009i) q^{73} +(-123.602 + 71.3614i) q^{74} +(1097.90 - 435.435i) q^{75} -385.216i q^{76} +(154.991 - 154.991i) q^{78} +(125.680 + 72.5612i) q^{79} +(-44.7965 - 68.1525i) q^{80} +(734.067 + 1271.44i) q^{81} +(66.1190 + 246.760i) q^{82} +(454.928 + 454.928i) q^{83} +(76.2061 - 85.5825i) q^{85} +(292.367 - 506.395i) q^{86} +(-1483.21 - 397.425i) q^{87} +(-563.572 - 151.009i) q^{88} +(104.617 - 181.203i) q^{89} +(-862.965 + 969.144i) q^{90} +(-85.6148 - 85.6148i) q^{92} +(-65.0848 - 242.900i) q^{93} +(303.065 + 524.924i) q^{94} +(-522.587 - 795.053i) q^{95} +(-1417.03 - 818.123i) q^{96} +(-1012.24 + 1012.24i) q^{97} +1556.47i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} + 352 q^{8}+O(q^{10}) $ 32 * q - 4 * q^2 + 352 * q^8	$ 32 q - 4 q^{2} + 352 q^{8} + 152 q^{11} - 960 q^{15} + 504 q^{16} - 288 q^{18} + 696 q^{22} + 72 q^{23} + 160 q^{25} - 1780 q^{30} - 432 q^{32} + 688 q^{36} + 256 q^{37} - 624 q^{43} + 1856 q^{46} - 40 q^{50} - 696 q^{51} - 1768 q^{53} - 7840 q^{57} + 4764 q^{58} + 2000 q^{60} + 1000 q^{65} - 4504 q^{67} + 12736 q^{71} - 7848 q^{72} + 10680 q^{78} + 3088 q^{81} - 4560 q^{85} + 9336 q^{86} + 2048 q^{88} - 12656 q^{92} + 3960 q^{93} - 1240 q^{95}+O(q^{100}) $ 32 * q - 4 * q^2 + 352 * q^8 + 152 * q^11 - 960 * q^15 + 504 * q^16 - 288 * q^18 + 696 * q^22 + 72 * q^23 + 160 * q^25 - 1780 * q^30 - 432 * q^32 + 688 * q^36 + 256 * q^37 - 624 * q^43 + 1856 * q^46 - 40 * q^50 - 696 * q^51 - 1768 * q^53 - 7840 * q^57 + 4764 * q^58 + 2000 * q^60 + 1000 * q^65 - 4504 * q^67 + 12736 * q^71 - 7848 * q^72 + 10680 * q^78 + 3088 * q^81 - 4560 * q^85 + 9336 * q^86 + 2048 * q^88 - 12656 * q^92 + 3960 * q^93 - 1240 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.80016	+	0.482353i	−0.636454	+	0.170537i	−0.562597	−	0.826731i	$-0.690198\pi$
$2$	−1.80016	+	0.482353i	−0.636454	+	0.170537i	−0.0738575	+	0.997269i	$0.523531\pi$
$3$	−2.44552	+	9.12679i	−0.470640	+	1.75645i	0.166839	+	0.985984i	$0.446644\pi$
$3$	−2.44552	+	9.12679i	−0.470640	+	1.75645i	−0.637479	+	0.770468i	$0.720023\pi$
$4$	−3.92027	+	2.26337i	−0.490034	+	0.282921i
$5$	−5.02060	+	9.98967i	−0.449057	+	0.893503i
$5$	−5.02060	+	9.98967i	−0.449057	+	0.893503i
$6$		−	17.6093i		−	1.19816i
$7$		0			0
$7$		0			0
$8$	16.5079	−	16.5079i	0.729553	−	0.729553i
$9$	−53.9351	−	31.1395i	−1.99760	−	1.15331i
$10$	4.21937	−	20.4048i	0.133428	−	0.645255i
$11$	−12.4959	−	21.6436i	−0.342515	−	0.593254i	0.642384	−	0.766383i	$-0.277946\pi$
$11$	−12.4959	−	21.6436i	−0.342515	−	0.593254i	−0.984899	+	0.173129i	$0.944612\pi$
$12$	−11.0702	−	41.3147i	−0.266308	−	0.993876i
$13$	8.80162	+	8.80162i	0.187779	+	0.187779i	0.794735	−	0.606956i	$-0.207610\pi$
$13$	8.80162	+	8.80162i	0.187779	+	0.187779i	−0.606956	+	0.794735i	$0.707610\pi$
$14$		0			0
$15$	−78.8957	−	70.2519i	−1.35805	−	1.20926i
$16$	−3.64732	+	6.31735i	−0.0569894	+	0.0987086i
$17$	−9.90033	−	2.65279i	−0.141246	−	0.0378468i	0.187503	−	0.982264i	$-0.439960\pi$
$17$	−9.90033	−	2.65279i	−0.141246	−	0.0378468i	−0.328749	+	0.944417i	$0.606627\pi$
$18$	112.112	+	30.0404i	1.46806	+	0.393366i
$19$	−42.5490	+	73.6970i	−0.513758	+	0.889855i	0.486115	+	0.873895i	$0.338414\pi$
$19$	−42.5490	+	73.6970i	−0.513758	+	0.889855i	−0.999873	+	0.0159598i	$0.994920\pi$
$20$	−2.92819	−	50.5258i	−0.0327382	−	0.564895i
$21$		0			0
$22$	32.9346	+	32.9346i	0.319167	+	0.319167i
$23$	6.92268	+	25.8358i	0.0627599	+	0.234223i	0.990180	−	0.139798i	$-0.0446454\pi$
$23$	6.92268	+	25.8358i	0.0627599	+	0.234223i	−0.927420	+	0.374021i	$0.877979\pi$
$24$	110.294	+	191.034i	0.938068	+	1.62478i
$25$	−74.5871	−	100.308i	−0.596696	−	0.802467i
$26$	−20.0899	−	11.5989i	−0.151536	−	0.0874896i
$27$	235.708	−	235.708i	1.68008	−	1.68008i
$28$		0			0
$29$			162.511i			1.04061i	0.853981	+	0.520304i	$0.174181\pi$
$29$			162.511i			1.04061i	−0.853981	+	0.520304i	$0.825819\pi$
$30$	175.911	+	88.4095i	1.07056	+	0.538043i
$31$	−23.0483	+	13.3070i	−0.133536	+	0.0770968i	−0.565280	−	0.824899i	$-0.691232\pi$
$31$	−23.0483	+	13.3070i	−0.133536	+	0.0770968i	0.431744	+	0.901996i	$0.357898\pi$
$32$	−44.8199	+	167.270i	−0.247597	+	0.924045i
$33$	228.096	−	61.1181i	1.20322	−	0.322403i
$34$	19.1018			0.0963510
$35$		0			0
$36$	281.921			1.30519
$37$	73.9723	−	19.8208i	0.328675	−	0.0880681i	−0.0907083	−	0.995878i	$-0.528913\pi$
$37$	73.9723	−	19.8208i	0.328675	−	0.0880681i	0.419383	+	0.907809i	$0.362246\pi$
$38$	41.0472	−	153.190i	0.175230	−	0.653967i
$39$	−101.855	+	58.8061i	−0.418202	+	0.241449i
$40$	82.0288	+	247.788i	0.324247	+	0.979468i
$41$		−	137.076i		−	0.522139i	−0.965320	−	0.261069i	$-0.915925\pi$
$41$		−	137.076i		−	0.522139i	0.965320	−	0.261069i	$-0.0840752\pi$
$42$		0			0
$43$	−221.858	+	221.858i	−0.786815	+	0.786815i	−0.980971	−	0.194155i	$-0.937803\pi$
$43$	−221.858	+	221.858i	−0.786815	+	0.786815i	0.194155	+	0.980971i	$0.437803\pi$
$44$	97.9751	+	56.5659i	0.335689	+	0.193810i
$45$	581.860	−	382.455i	1.92752	−	1.26696i
$46$	−24.9239	−	43.1695i	−0.0798876	−	0.138369i
$47$	−84.1770	−	314.153i	−0.261244	−	0.974977i	−0.964509	−	0.264049i	$-0.914942\pi$
$47$	−84.1770	−	314.153i	−0.261244	−	0.974977i	0.703265	−	0.710928i	$-0.251725\pi$
$48$	−48.7375	−	48.7375i	−0.146555	−	0.146555i
$49$		0			0
$50$	182.653	+	144.594i	0.516621	+	0.408974i
$51$	48.4229	−	83.8709i	0.132952	−	0.230280i
$52$	−54.4261	−	14.5834i	−0.145145	−	0.0388915i
$53$	−210.603	−	56.4309i	−0.545821	−	0.146252i	−0.0246368	−	0.999696i	$-0.507843\pi$
$53$	−210.603	−	56.4309i	−0.545821	−	0.146252i	−0.521184	+	0.853444i	$0.674510\pi$
$54$	−310.619	+	538.008i	−0.782776	+	1.35581i
$55$	278.950	−	16.1664i	0.683883	−	0.0396340i
$56$		0			0
$57$	−568.563	−	568.563i	−1.32119	−	1.32119i
$58$	−78.3878	−	292.547i	−0.177463	−	0.662299i
$59$	342.874	+	593.875i	0.756583	+	1.31044i	0.944584	+	0.328271i	$0.106466\pi$
$59$	342.874	+	593.875i	0.756583	+	1.31044i	−0.188001	+	0.982169i	$0.560201\pi$
$60$	468.299	+	96.8366i	1.00762	+	0.208359i
$61$	−20.5175	−	11.8458i	−0.0430655	−	0.0248639i	0.478313	−	0.878190i	$-0.341249\pi$
$61$	−20.5175	−	11.8458i	−0.0430655	−	0.0248639i	−0.521378	+	0.853326i	$0.674582\pi$
$62$	35.0721	−	35.0721i	0.0718414	−	0.0718414i
$63$		0			0
$64$		−	381.090i		−	0.744316i
$65$	−132.115	+	43.7359i	−0.252105	+	0.0834579i
$66$	−381.130	+	220.045i	−0.710815	+	0.410389i
$67$	220.609	−	823.325i	0.402265	−	1.50127i	−0.406781	−	0.913526i	$-0.633349\pi$
$67$	220.609	−	823.325i	0.402265	−	1.50127i	0.809045	−	0.587746i	$-0.199985\pi$
$68$	44.8163	−	12.0085i	0.0799231	−	0.0214153i
$69$	−252.727			−0.440939
$70$		0			0
$71$	265.331			0.443506			0.221753	−	0.975103i	$-0.428822\pi$
$71$	265.331			0.443506			0.221753	+	0.975103i	$0.428822\pi$
$72$	−1404.40	+	376.308i	−2.29876	+	0.615950i
$73$	222.936	−	832.009i	0.357434	−	1.33396i	−0.519959	−	0.854191i	$-0.674053\pi$
$73$	222.936	−	832.009i	0.357434	−	1.33396i	0.877393	−	0.479772i	$-0.159280\pi$
$74$	−123.602	+	71.3614i	−0.194168	+	0.112103i
$75$	1097.90	−	435.435i	1.69032	−	0.670396i
$76$		−	385.216i		−	0.581413i
$77$		0			0
$78$	154.991	−	154.991i	0.224990	−	0.224990i
$79$	125.680	+	72.5612i	0.178988	+	0.103339i	0.586817	−	0.809719i	$-0.300381\pi$
$79$	125.680	+	72.5612i	0.178988	+	0.103339i	−0.407829	+	0.913058i	$0.633714\pi$
$80$	−44.7965	−	68.1525i	−0.0626050	−	0.0952460i
$81$	734.067	+	1271.44i	1.00695	+	1.74409i
$82$	66.1190	+	246.760i	0.0890442	+	0.332318i
$83$	454.928	+	454.928i	0.601625	+	0.601625i	0.940744	−	0.339119i	$-0.110129\pi$
$83$	454.928	+	454.928i	0.601625	+	0.601625i	−0.339119	+	0.940744i	$0.610129\pi$
$84$		0			0
$85$	76.2061	−	85.5825i	0.0972437	−	0.109208i
$86$	292.367	−	506.395i	0.366591	−	0.634953i
$87$	−1483.21	−	397.425i	−1.82778	−	0.489752i
$88$	−563.572	−	151.009i	−0.682693	−	0.182927i
$89$	104.617	−	181.203i	0.124600	−	0.215814i	−0.796976	−	0.604011i	$-0.793568\pi$
$89$	104.617	−	181.203i	0.124600	−	0.215814i	0.921577	+	0.388196i	$0.126902\pi$
$90$	−862.965	+	969.144i	−1.01072	+	1.13508i
$91$		0			0
$92$	−85.6148	−	85.6148i	−0.0970213	−	0.0970213i
$93$	−65.0848	−	242.900i	−0.0725697	−	0.270834i
$94$	303.065	+	524.924i	0.332540	+	0.575976i
$95$	−522.587	−	795.053i	−0.564382	−	0.858639i
$96$	−1417.03	−	818.123i	−1.50651	−	0.869785i
$97$	−1012.24	+	1012.24i	−1.05956	+	1.05956i	−0.0614533	+	0.998110i	$0.519574\pi$
$97$	−1012.24	+	1012.24i	−1.05956	+	1.05956i	−0.998110	+	0.0614533i	$0.980426\pi$
$98$		0			0
$99$			1556.47i			1.58011i
$100$	519.437	+	224.418i	0.519437	+	0.224418i
$101$	−789.846	+	456.018i	−0.778145	+	0.449262i	−0.835772	−	0.549076i	$-0.814980\pi$
$101$	−789.846	+	456.018i	−0.778145	+	0.449262i	0.0576276	+	0.998338i	$0.481646\pi$
$102$	−46.7138	+	174.338i	−0.0453466	+	0.169236i
$103$	−812.131	+	217.610i	−0.776909	+	0.208172i	−0.625421	−	0.780287i	$-0.715073\pi$
$103$	−812.131	+	217.610i	−0.776909	+	0.208172i	−0.151487	+	0.988459i	$0.548406\pi$
$104$	290.593			0.273990
$105$		0			0
$106$	406.339			0.372332
$107$	594.957	−	159.418i	0.537539	−	0.144033i	0.0201715	−	0.999797i	$-0.493579\pi$
$107$	594.957	−	159.418i	0.537539	−	0.144033i	0.517367	+	0.855763i	$0.326912\pi$
$108$	−390.546	+	1457.54i	−0.347966	+	1.29863i
$109$	−886.155	+	511.622i	−0.778699	+	0.449582i	−0.835969	−	0.548776i	$-0.815094\pi$
$109$	−886.155	+	511.622i	−0.778699	+	0.449582i	0.0572698	+	0.998359i	$0.481760\pi$
$110$	−494.358	+	163.654i	−0.428501	+	0.141853i
$111$			723.602i			0.618750i
$112$		0			0
$113$	678.584	−	678.584i	0.564919	−	0.564919i	−0.365782	−	0.930701i	$-0.619198\pi$
$113$	678.584	−	678.584i	0.564919	−	0.564919i	0.930701	+	0.365782i	$0.119198\pi$
$114$	1297.75	+	749.259i	1.06619	+	0.615566i
$115$	−292.847	−	60.5560i	−0.237462	−	0.0491032i
$116$	−367.824	−	637.090i	−0.294410	−	0.509934i
$117$	−200.639	−	748.795i	−0.158539	−	0.591676i
$118$	−903.687	−	903.687i	−0.705009	−	0.705009i
$119$		0			0
$120$	−2462.11	+	142.690i	−1.87299	+	0.108548i
$121$	353.203	−	611.765i	0.265366	−	0.459628i
$122$	42.6487	+	11.4277i	0.0316495	+	0.00848045i
$123$	1251.07	+	335.222i	0.917112	+	0.245739i
$124$	60.2372	−	104.334i	0.0436247	−	0.0755602i
$125$	1376.52	−	241.491i	0.984957	−	0.172797i
$126$		0			0
$127$	−2.16418	−	2.16418i	−0.00151212	−	0.00151212i	0.706350	−	0.707862i	$-0.250340\pi$
$127$	−2.16418	−	2.16418i	−0.00151212	−	0.00151212i	−0.707862	+	0.706350i	$0.750340\pi$
$128$	−174.739	−	652.136i	−0.120663	−	0.450322i
$129$	−1482.30	−	2567.41i	−1.01170	−	1.75231i
$130$	216.732	−	142.458i	0.146221	−	0.0961105i
$131$	1729.20	+	998.353i	1.15329	+	0.665851i	0.949686	−	0.313203i	$-0.101402\pi$
$131$	1729.20	+	998.353i	1.15329	+	0.665851i	0.203602	+	0.979054i	$0.434735\pi$
$132$	−755.866	+	755.866i	−0.498406	+	0.498406i
$133$		0			0
$134$			1588.53i			1.02409i
$135$	1171.25	+	3538.05i	0.746705	+	2.25560i
$136$	−207.226	+	119.642i	−0.130658	+	0.0754352i
$137$	0.498474	−	1.86033i	0.000310857	−	0.00116014i	−0.965770	−	0.259399i	$-0.916476\pi$
$137$	0.498474	−	1.86033i	0.000310857	−	0.00116014i	0.966081	+	0.258239i	$0.0831422\pi$
$138$	454.951	−	121.904i	0.280638	−	0.0751966i
$139$	−2121.99			−1.29486			−0.647428	−	0.762126i	$-0.724156\pi$
$139$	−2121.99			−1.29486			−0.647428	+	0.762126i	$0.724156\pi$
$140$		0			0
$141$	3073.06			1.83545
$142$	−477.639	+	127.983i	−0.282271	+	0.0756344i
$143$	80.5143	−	300.484i	0.0470835	−	0.175718i
$144$	393.438	−	227.151i	0.227684	−	0.131453i
$145$	−1623.44	−	815.906i	−0.929787	−	0.467292i
$146$			1605.29i			0.909962i
$147$		0			0
$148$	−245.130	+	245.130i	−0.136146	+	0.136146i
$149$	−1741.71	−	1005.58i	−0.957627	−	0.552886i	−0.0621854	−	0.998065i	$-0.519807\pi$
$149$	−1741.71	−	1005.58i	−0.957627	−	0.552886i	−0.895442	+	0.445178i	$0.853140\pi$
$150$	−1766.36	+	1313.43i	−0.961487	+	0.714940i
$151$	150.331	+	260.382i	0.0810185	+	0.140328i	0.903688	−	0.428192i	$-0.140849\pi$
$151$	150.331	+	260.382i	0.0810185	+	0.140328i	−0.822669	+	0.568520i	$0.807516\pi$
$152$	514.188	+	1918.97i	0.274382	+	1.02401i
$153$	451.369	+	451.369i	0.238504	+	0.238504i
$154$		0			0
$155$	−17.2156	−	297.054i	−0.00892123	−	0.153935i
$156$	266.200	−	461.072i	0.136622	−	0.236637i
$157$	2284.66	+	612.172i	1.16137	+	0.311189i	0.787514	−	0.616297i	$-0.211368\pi$
$157$	2284.66	+	612.172i	1.16137	+	0.311189i	0.373859	+	0.927486i	$0.378034\pi$
$158$	−261.244	−	70.0002i	−0.131541	−	0.0352463i
$159$	1030.07	−	1784.13i	0.513771	−	0.889877i
$160$	−1445.95	−	1287.53i	−0.714452	−	0.636177i
$161$		0			0
$162$	−1934.72	−	1934.72i	−0.938310	−	0.938310i
$163$	−900.205	−	3359.61i	−0.432574	−	1.61439i	−0.746807	−	0.665041i	$-0.768414\pi$
$163$	−900.205	−	3359.61i	−0.432574	−	1.61439i	0.314233	−	0.949346i	$-0.398253\pi$
$164$	310.254	+	537.376i	0.147724	+	0.255866i
$165$	−534.629	+	2585.45i	−0.252248	+	1.21986i
$166$	−1038.38	−	599.510i	−0.485506	−	0.280307i
$167$	2190.81	−	2190.81i	1.01515	−	1.01515i	0.0152650	−	0.999883i	$-0.495141\pi$
$167$	2190.81	−	2190.81i	1.01515	−	1.01515i	0.999883	−	0.0152650i	$-0.00485918\pi$
$168$		0			0
$169$		−	2042.06i		−	0.929478i
$170$	−95.9026	+	190.821i	−0.0432670	+	0.0860899i
$171$	4589.77	−	2649.90i	2.05256	−	1.18505i
$172$	367.598	−	1371.89i	0.162960	−	0.608173i
$173$	742.283	−	198.894i	0.326213	−	0.0874084i	−0.0919961	−	0.995759i	$-0.529325\pi$
$173$	742.283	−	198.894i	0.326213	−	0.0874084i	0.418209	+	0.908351i	$0.362658\pi$
$174$	2861.72			1.24682
$175$		0			0
$176$	182.307			0.0780790
$177$	−6258.68	+	1677.01i	−2.65780	+	0.712156i
$178$	−100.925	+	376.657i	−0.0424980	+	0.158605i
$179$	2786.71	−	1608.91i	1.16362	−	0.671817i	0.211452	−	0.977388i	$-0.432181\pi$
$179$	2786.71	−	1608.91i	1.16362	−	0.671817i	0.952169	+	0.305571i	$0.0988473\pi$
$180$	−1415.41	+	2816.30i	−0.586103	+	1.16619i
$181$			1653.80i			0.679148i	0.940579	+	0.339574i	$0.110283\pi$
$181$			1653.80i			0.679148i	−0.940579	+	0.339574i	$0.889717\pi$
$182$		0			0
$183$	158.290	−	158.290i	0.0639406	−	0.0639406i
$184$	540.773	+	312.215i	0.216665	+	0.125091i
$185$	−173.382	+	838.471i	−0.0689044	+	0.333219i
$186$	234.327	+	405.866i	0.0923746	+	0.159997i
$187$	66.2981	+	247.428i	0.0259262	+	0.0967579i
$188$	1041.04	+	1041.04i	0.403860	+	0.403860i
$189$		0			0
$190$	1324.24	+	1179.16i	0.505633	+	0.450237i
$191$	1126.40	−	1950.99i	0.426721	−	0.739103i	−0.569858	−	0.821743i	$-0.693002\pi$
$191$	1126.40	−	1950.99i	0.426721	−	0.739103i	0.996579	+	0.0826402i	$0.0263352\pi$
$192$	3478.13	+	931.961i	1.30736	+	0.350305i
$193$	−3007.55	−	805.870i	−1.12170	−	0.300558i	−0.350128	−	0.936702i	$-0.613862\pi$
$193$	−3007.55	−	805.870i	−1.12170	−	0.300558i	−0.771571	+	0.636143i	$0.780529\pi$
$194$	1333.95	−	2310.46i	0.493668	−	0.855059i
$195$	−76.0791	−	1312.74i	−0.0279392	−	0.482089i
$196$		0			0
$197$	−3634.93	−	3634.93i	−1.31461	−	1.31461i	−0.917978	−	0.396630i	$-0.870179\pi$
$197$	−3634.93	−	3634.93i	−1.31461	−	1.31461i	−0.396630	−	0.917978i	$-0.629821\pi$
$198$	−750.767	−	2801.90i	−0.269468	−	1.00567i
$199$	−2475.73	−	4288.09i	−0.881908	−	1.52751i	−0.849217	−	0.528045i	$-0.822925\pi$
$199$	−2475.73	−	4288.09i	−0.881908	−	1.52751i	−0.0326916	−	0.999465i	$-0.510408\pi$
$200$	−2887.15	−	424.605i	−1.02076	−	0.150120i
$201$	6974.82	+	4026.91i	2.44759	+	1.41312i
$202$	1201.89	−	1201.89i	0.418638	−	0.418638i
$203$		0			0
$204$			438.396i			0.150460i
$205$	1369.35	+	688.205i	0.466533	+	0.234470i
$206$	1357.00	−	783.467i	0.458966	−	0.264984i
$207$	431.137	−	1609.02i	0.144764	−	0.540265i
$208$	−87.7053	+	23.5006i	−0.0292369	+	0.00783399i
$209$	2126.76			0.703880
$210$		0			0
$211$	148.487			0.0484469			0.0242234	−	0.999707i	$-0.492289\pi$
$211$	148.487			0.0484469			0.0242234	+	0.999707i	$0.492289\pi$
$212$	953.345	−	255.448i	0.308849	−	0.0827559i
$213$	−648.870	+	2421.62i	−0.208732	+	0.778998i
$214$	−994.125	+	573.958i	−0.317556	+	0.183341i
$215$	−1102.43	−	3330.15i	−0.349698	−	1.05635i
$216$		−	7782.09i		−	2.45141i
$217$		0			0
$218$	1348.44	−	1348.44i	0.418936	−	0.418936i
$219$	7048.38	+	4069.38i	2.17482	+	1.25563i
$220$	−1056.97	+	694.744i	−0.323913	+	0.212907i
$221$	−63.7902	−	110.488i	−0.0194163	−	0.0336299i
$222$	−349.031	−	1302.60i	−0.105520	−	0.393806i
$223$	−3171.97	−	3171.97i	−0.952515	−	0.952515i	0.0464080	−	0.998923i	$-0.485223\pi$
$223$	−3171.97	−	3171.97i	−0.952515	−	0.952515i	−0.998923	+	0.0464080i	$0.985223\pi$
$224$		0			0
$225$	899.314	+	7732.75i	0.266463	+	2.29118i
$226$	−894.246	+	1548.88i	−0.263205	+	0.455885i
$227$	4036.62	+	1081.61i	1.18026	+	0.316251i	0.795031	−	0.606569i	$-0.207455\pi$
$227$	4036.62	+	1081.61i	1.18026	+	0.316251i	0.385232	+	0.922820i	$0.374121\pi$
$228$	3515.79	+	942.053i	1.02122	+	0.273636i
$229$	−2892.95	+	5010.73i	−0.834809	+	1.44593i	0.0593765	+	0.998236i	$0.481089\pi$
$229$	−2892.95	+	5010.73i	−0.834809	+	1.44593i	−0.894186	+	0.447696i	$0.852245\pi$
$230$	556.382	−	32.2448i	0.159508	−	0.00924417i
$231$		0			0
$232$	2682.72	+	2682.72i	0.759178	+	0.759178i
$233$	1132.09	+	4225.03i	0.318309	+	1.18794i	0.920869	+	0.389871i	$0.127480\pi$
$233$	1132.09	+	4225.03i	0.318309	+	1.18794i	−0.602561	+	0.798073i	$0.705853\pi$
$234$	722.366	+	1251.17i	0.201806	+	0.349538i
$235$	3560.90	+	736.337i	0.988458	+	0.204397i
$236$	−2688.32	−	1552.10i	−0.741503	−	0.428107i
$237$	−969.603	+	969.603i	−0.265749	+	0.265749i
$238$		0			0
$239$			1703.12i			0.460946i	0.973079	+	0.230473i	$0.0740273\pi$
$239$			1703.12i			0.460946i	−0.973079	+	0.230473i	$0.925973\pi$
$240$	731.564	−	242.180i	0.196759	−	0.0651361i
$241$	−1747.63	+	1008.99i	−0.467115	+	0.269689i	−0.715031	−	0.699092i	$-0.753588\pi$
$241$	−1747.63	+	1008.99i	−0.467115	+	0.269689i	0.247916	+	0.968781i	$0.420254\pi$
$242$	−340.736	+	1271.65i	−0.0905098	+	0.337787i
$243$	−4705.80	+	1260.91i	−1.24229	+	0.332871i
$244$	107.246			0.0281381
$245$		0			0
$246$	−2413.82			−0.625608
$247$	−1023.15	+	274.153i	−0.263569	+	0.0706232i
$248$	−160.810	+	600.149i	−0.0411751	+	0.153667i
$249$	−5264.57	+	3039.50i	−1.33987	+	0.773576i
$250$	−2361.48	+	1098.69i	−0.597412	+	0.277950i
$251$			841.491i			0.211611i	0.994387	+	0.105806i	$0.0337422\pi$
$251$			841.491i			0.211611i	−0.994387	+	0.105806i	$0.966258\pi$
$252$		0			0
$253$	472.674	−	472.674i	0.117458	−	0.117458i
$254$	4.93977	+	2.85198i	0.00122027	+	0.000704523i
$255$	594.730	+	904.811i	0.146053	+	0.222202i
$256$	2153.48	+	3729.93i	0.525751	+	0.910628i
$257$	886.472	+	3308.36i	0.215162	+	0.802995i	0.986109	+	0.166097i	$0.0531164\pi$
$257$	886.472	+	3308.36i	0.215162	+	0.802995i	−0.770948	+	0.636899i	$0.780217\pi$
$258$	3906.78	+	3906.78i	0.942733	+	0.942733i
$259$		0			0
$260$	418.936	−	470.482i	0.0999281	−	0.112223i
$261$	5060.52	−	8765.08i	1.20015	−	2.07872i
$262$	−3594.40	−	963.116i	−0.847567	−	0.227105i
$263$	4744.01	+	1271.15i	1.11228	+	0.298033i	0.767754	−	0.640745i	$-0.221374\pi$
$263$	4744.01	+	1271.15i	1.11228	+	0.298033i	0.344522	+	0.938778i	$0.388041\pi$
$264$	2756.45	−	4774.31i	0.642605	−	1.11303i
$265$	1621.08	−	1820.54i	0.375782	−	0.422017i
$266$		0			0
$267$	1397.96	+	1397.96i	0.320425	+	0.320425i
$268$	998.642	+	3726.98i	0.227619	+	0.849484i
$269$	1583.07	+	2741.96i	0.358816	+	0.621487i	0.987763	−	0.155961i	$-0.0498473\pi$
$269$	1583.07	+	2741.96i	0.358816	+	0.621487i	−0.628948	+	0.777448i	$0.716514\pi$
$270$	−3815.03	−	5804.11i	−0.859908	−	1.30825i
$271$	−5034.71	−	2906.79i	−1.12855	−	0.651568i	−0.184980	−	0.982742i	$-0.559222\pi$
$271$	−5034.71	−	2906.79i	−1.12855	−	0.651568i	−0.943570	+	0.331174i	$0.892555\pi$
$272$	52.8683	−	52.8683i	0.0117853	−	0.0117853i
$273$		0			0
$274$			3.58934i			0.000791386i
$275$	−1239.00	+	2867.78i	−0.271689	+	0.628850i
$276$	990.761	−	572.016i	0.216075	−	0.124751i
$277$	−309.110	+	1153.61i	−0.0670491	+	0.250231i	−0.991313	−	0.131523i	$-0.958013\pi$
$277$	−309.110	+	1153.61i	−0.0670491	+	0.250231i	0.924264	+	0.381754i	$0.124680\pi$
$278$	3819.94	−	1023.55i	0.824117	−	0.220822i
$279$	1657.49			0.355667
$280$		0			0
$281$	−4548.77			−0.965683			−0.482842	−	0.875708i	$-0.660395\pi$
$281$	−4548.77			−0.965683			−0.482842	+	0.875708i	$0.660395\pi$
$282$	−5532.02	+	1482.30i	−1.16818	+	0.313013i
$283$	1586.52	−	5920.96i	0.333246	−	1.24369i	−0.572512	−	0.819896i	$-0.694031\pi$
$283$	1586.52	−	5920.96i	0.333246	−	1.24369i	0.905758	−	0.423795i	$-0.139302\pi$
$284$	−1040.17	+	600.542i	−0.217333	+	0.125477i
$285$	8534.28	−	2825.23i	1.77378	−	0.587200i
$286$			579.756i			0.119866i
$287$		0			0
$288$	7626.06	−	7626.06i	1.56031	−	1.56031i
$289$	−4163.80	−	2403.97i	−0.847507	−	0.489309i
$290$	3316.01	+	685.696i	0.671457	+	0.138846i
$291$	−6763.07	−	11714.0i	−1.36240	−	2.35975i
$292$	1009.17	+	3766.29i	0.202252	+	0.754813i
$293$	−3204.15	−	3204.15i	−0.638869	−	0.638869i	0.311408	−	0.950276i	$-0.399199\pi$
$293$	−3204.15	−	3204.15i	−0.638869	−	0.638869i	−0.950276	+	0.311408i	$0.899199\pi$
$294$		0			0
$295$	−7654.05	+	443.586i	−1.51063	+	0.0875477i
$296$	893.926	−	1548.33i	0.175535	−	0.304036i
$297$	−8046.98	−	2156.18i	−1.57216	−	0.421260i
$298$	3620.41	+	970.086i	0.703774	+	0.188576i
$299$	−166.466	+	288.328i	−0.0321973	+	0.0557673i
$300$	−3318.51	+	4191.98i	−0.638648	+	0.806746i
$301$		0			0
$302$	−396.217	−	396.217i	−0.0754958	−	0.0754958i
$303$	−2230.40	−	8323.96i	−0.422881	−	1.57821i
$304$	−310.380	−	537.593i	−0.0585575	−	0.101425i
$305$	221.346	−	145.490i	0.0415548	−	0.0273139i
$306$	−1030.26	−	594.820i	−0.192470	−	0.111123i
$307$	189.516	−	189.516i	0.0352321	−	0.0352321i	−0.689271	−	0.724503i	$-0.742069\pi$
$307$	189.516	−	189.516i	0.0352321	−	0.0352321i	0.724503	+	0.689271i	$0.242069\pi$
$308$		0			0
$309$		−	7944.32i		−	1.46258i
$310$	174.276	+	526.443i	0.0319297	+	0.0964514i
$311$	−8553.67	+	4938.47i	−1.55960	+	0.900433i	−0.562301	+	0.826933i	$0.690084\pi$
$311$	−8553.67	+	4938.47i	−1.55960	+	0.900433i	−0.997295	+	0.0735006i	$0.976583\pi$
$312$	−710.649	+	2652.18i	−0.128951	+	0.481250i
$313$	−5088.47	+	1363.45i	−0.918906	+	0.246220i	−0.687118	−	0.726546i	$-0.741124\pi$
$313$	−5088.47	+	1363.45i	−0.918906	+	0.246220i	−0.231788	+	0.972766i	$0.574458\pi$
$314$	−4408.04			−0.792230
$315$		0			0
$316$	−656.932			−0.116947
$317$	−4171.83	+	1117.84i	−0.739158	+	0.198057i	−0.608704	−	0.793397i	$-0.708310\pi$
$317$	−4171.83	+	1117.84i	−0.739158	+	0.198057i	−0.130454	+	0.991454i	$0.541644\pi$
$318$	−993.710	+	3708.58i	−0.175234	+	0.653983i
$319$	3517.34	−	2030.73i	0.617345	−	0.356424i
$320$	3806.96	+	1913.30i	0.665049	+	0.334240i
$321$			5819.91i			1.01195i
$322$		0			0
$323$	616.751	−	616.751i	0.106244	−	0.106244i
$324$	−5755.49	−	3322.93i	−0.986881	−	0.569776i
$325$	226.389	−	1539.36i	0.0386395	−	0.262734i
$326$	3241.03	+	5613.64i	0.550627	+	0.953713i
$327$	−2502.36	−	9338.93i	−0.423183	−	1.57934i
$328$	−2262.84	−	2262.84i	−0.380928	−	0.380928i
$329$		0			0
$330$	−284.679	−	4912.12i	−0.0474881	−	0.819404i
$331$	−3441.74	+	5961.27i	−0.571526	+	0.989912i	0.424883	+	0.905248i	$0.360315\pi$
$331$	−3441.74	+	5961.27i	−0.571526	+	0.989912i	−0.996410	+	0.0846643i	$0.973018\pi$
$332$	−2813.11	−	753.772i	−0.465029	−	0.124604i
$333$	−4606.91	−	1234.42i	−0.758130	−	0.203140i
$334$	−2887.07	+	5000.56i	−0.472975	+	0.819216i
$335$	7117.16	+	6337.41i	1.16075	+	1.03358i
$336$		0			0
$337$	−506.829	−	506.829i	−0.0819251	−	0.0819251i	0.664957	−	0.746882i	$-0.268450\pi$
$337$	−506.829	−	506.829i	−0.0819251	−	0.0819251i	−0.746882	+	0.664957i	$0.768450\pi$
$338$	984.994	+	3676.05i	0.158511	+	0.591570i
$339$	4533.81	+	7852.78i	0.726379	+	1.25813i
$340$	−105.044	+	507.990i	−0.0167553	+	0.0810282i
$341$	576.022	+	332.566i	0.0914760	+	0.0528137i
$342$	−6984.15	+	6984.15i	−1.10427	+	1.10427i
$343$		0			0
$344$			7324.82i			1.14805i
$345$	1268.84	−	2524.66i	0.198007	−	0.393981i
$346$	−1240.30	+	716.085i	−0.192713	+	0.111263i
$347$	−533.761	+	1992.02i	−0.0825758	+	0.308177i	−0.994844	−	0.101416i	$-0.967663\pi$
$347$	−533.761	+	1992.02i	−0.0825758	+	0.308177i	0.912268	+	0.409593i	$0.134329\pi$
$348$	6714.11	−	1799.04i	1.03424	−	0.277123i
$349$	−10334.5			−1.58508			−0.792542	−	0.609817i	$-0.791243\pi$
$349$	−10334.5			−1.58508			−0.792542	+	0.609817i	$0.791243\pi$
$350$		0			0
$351$	4149.23			0.630967
$352$	4180.40	−	1120.13i	0.632999	−	0.169612i
$353$	2025.74	−	7560.18i	0.305438	−	1.13991i	−0.627130	−	0.778914i	$-0.715771\pi$
$353$	2025.74	−	7560.18i	0.305438	−	1.13991i	0.932568	−	0.360994i	$-0.117563\pi$
$354$	10457.7	−	6037.78i	1.57012	−	0.906510i
$355$	−1332.12	+	2650.56i	−0.199159	+	0.396274i
$356$			947.153i			0.141008i
$357$		0			0
$358$	−4240.47	+	4240.47i	−0.626022	+	0.626022i
$359$	−25.0513	−	14.4634i	−0.00368289	−	0.00212632i	0.498157	−	0.867087i	$-0.334010\pi$
$359$	−25.0513	−	14.4634i	−0.00368289	−	0.00212632i	−0.501840	+	0.864960i	$0.667343\pi$
$360$	3291.75	−	15918.8i	0.481918	−	2.33054i
$361$	−191.327	−	331.388i	−0.0278943	−	0.0483144i
$362$	−797.714	−	2977.11i	−0.115820	−	0.432247i
$363$	4719.69	+	4719.69i	0.682423	+	0.682423i
$364$		0			0
$365$	7192.22	+	6404.25i	1.03139	+	0.918393i
$366$	−208.596	+	361.300i	−0.0297910	+	0.0515996i
$367$	960.461	+	257.355i	0.136609	+	0.0366044i	0.326476	−	0.945206i	$-0.394139\pi$
$367$	960.461	+	257.355i	0.136609	+	0.0366044i	−0.189866	+	0.981810i	$0.560805\pi$
$368$	−188.463	−	50.4985i	−0.0266965	−	0.00715330i
$369$	−4268.48	+	7393.22i	−0.602190	+	1.04302i
$370$	−92.3223	−	1593.02i	−0.0129719	−	0.223830i
$371$		0			0
$372$	804.923	+	804.923i	0.112186	+	0.112186i
$373$	905.081	+	3377.81i	0.125639	+	0.468891i	0.999862	−	0.0166344i	$-0.00529513\pi$
$373$	905.081	+	3377.81i	0.125639	+	0.468891i	−0.874223	+	0.485525i	$0.838628\pi$
$374$	−238.695	−	413.432i	−0.0330017	−	0.0571606i
$375$	−1162.26	+	13153.8i	−0.160050	+	1.81136i
$376$	−6575.59	−	3796.42i	−0.901888	−	0.520705i
$377$	−1430.37	+	1430.37i	−0.195405	+	0.195405i
$378$		0			0
$379$		−	4711.22i		−	0.638521i	−0.947667	−	0.319260i	$-0.896566\pi$
$379$		−	4711.22i		−	0.638521i	0.947667	−	0.319260i	$-0.103434\pi$
$380$	3848.19	+	1934.02i	0.519494	+	0.261087i
$381$	25.0445	−	14.4595i	0.00336764	−	0.00194431i
$382$	−1086.65	+	4055.43i	−0.145544	+	0.543177i
$383$	9487.63	−	2542.20i	1.26578	−	0.339166i	0.437370	−	0.899282i	$-0.355910\pi$
$383$	9487.63	−	2542.20i	1.26578	−	0.339166i	0.828414	+	0.560116i	$0.189243\pi$
$384$	6379.24			0.847758
$385$		0			0
$386$	5802.79			0.765167
$387$	18874.5	−	5057.41i	2.47918	−	0.664296i
$388$	1677.19	−	6259.35i	0.219449	−	0.818996i
$389$	−3044.63	+	1757.82i	−0.396835	+	0.229113i	−0.685117	−	0.728433i	$-0.740249\pi$
$389$	−3044.63	+	1757.82i	−0.396835	+	0.229113i	0.288282	+	0.957545i	$0.406916\pi$
$390$	770.159	+	2326.45i	0.0999962	+	0.302063i
$391$		−	274.147i		−	0.0354584i
$392$		0			0
$393$	−13340.5	+	13340.5i	−1.71232	+	1.71232i
$394$	8296.79	+	4790.15i	1.06088	+	0.612498i
$395$	−1355.85	+	891.198i	−0.172709	+	0.113522i
$396$	−3522.87	−	6101.78i	−0.447047	−	0.774308i
$397$	−1097.34	−	4095.34i	−0.138726	−	0.517731i	−0.999955	−	0.00951408i	$-0.996972\pi$
$397$	−1097.34	−	4095.34i	−0.138726	−	0.517731i	0.861229	−	0.508217i	$-0.169695\pi$
$398$	6525.09	+	6525.09i	0.821792	+	0.821792i
$399$		0			0
$400$	905.726	−	105.335i	0.113216	−	0.0131669i
$401$	−4518.60	+	7826.45i	−0.562714	+	0.974649i	0.434544	+	0.900650i	$0.356909\pi$
$401$	−4518.60	+	7826.45i	−0.562714	+	0.974649i	−0.997258	+	0.0739988i	$0.976424\pi$
$402$	−14498.2	−	3884.78i	−1.79877	−	0.481979i
$403$	−319.986	−	85.7399i	−0.0395524	−	0.0105980i
$404$	2064.28	−	3575.43i	0.254212	−	0.440308i
$405$	−16386.7	+	949.683i	−2.01053	+	0.116519i
$406$		0			0
$407$	−1353.35	−	1353.35i	−0.164823	−	0.164823i
$408$	−585.172	−	2183.89i	−0.0710057	−	0.264997i
$409$	5487.37	+	9504.41i	0.663406	+	1.14905i	0.979715	+	0.200397i	$0.0642232\pi$
$409$	5487.37	+	9504.41i	0.663406	+	1.14905i	−0.316309	+	0.948656i	$0.602443\pi$
$410$	−2797.00	−	578.375i	−0.336913	−	0.0696680i
$411$	15.7598	+	9.09893i	0.00189142	+	0.00109201i
$412$	2691.24	−	2691.24i	0.321816	−	0.321816i
$413$		0			0
$414$			3104.47i			0.368542i
$415$	−6828.60	+	2260.57i	−0.807717	+	0.267390i
$416$	−1866.74	+	1077.76i	−0.220010	+	0.127023i
$417$	5189.37	−	19367.0i	0.609411	−	2.27435i
$418$	−3828.51	+	1025.85i	−0.447987	+	0.120038i
$419$	−6134.21			−0.715216			−0.357608	−	0.933872i	$-0.616408\pi$
$419$	−6134.21			−0.715216			−0.357608	+	0.933872i	$0.616408\pi$
$420$		0			0
$421$	2593.11			0.300192			0.150096	−	0.988671i	$-0.452042\pi$
$421$	2593.11			0.300192			0.150096	+	0.988671i	$0.452042\pi$
$422$	−267.302	+	71.6232i	−0.0308342	+	0.00826200i
$423$	−5242.45	+	19565.1i	−0.602593	+	2.24891i
$424$	−4408.16	+	2545.05i	−0.504904	+	0.291507i
$425$	472.340	+	1190.95i	0.0539102	+	0.135928i
$426$		−	4672.29i		−	0.531393i
$427$		0			0
$428$	−1971.57	+	1971.57i	−0.222662	+	0.222662i
$429$	2545.55	+	1469.68i	0.286481	+	0.165400i
$430$	3590.86	+	5463.06i	0.402713	+	0.612680i
$431$	5204.87	+	9015.10i	0.581693	+	1.00752i	0.995279	+	0.0970570i	$0.0309429\pi$
$431$	5204.87	+	9015.10i	0.581693	+	1.00752i	−0.413586	+	0.910465i	$0.635724\pi$
$432$	629.347	+	2348.76i	0.0700914	+	0.261585i
$433$	−5550.33	−	5550.33i	−0.616009	−	0.616009i	0.328496	−	0.944505i	$-0.393458\pi$
$433$	−5550.33	−	5550.33i	−0.616009	−	0.616009i	−0.944505	+	0.328496i	$0.893458\pi$
$434$		0			0
$435$	11416.7	−	12821.5i	1.25837	−	1.41320i
$436$	2315.98	−	4011.39i	0.254393	−	0.440622i
$437$	−2198.57	−	589.105i	−0.240668	−	0.0644868i
$438$	−14651.1	−	3925.76i	−1.59831	−	0.428265i
$439$	−2627.69	+	4551.28i	−0.285678	+	0.494809i	−0.972773	−	0.231759i	$-0.925552\pi$
$439$	−2627.69	+	4551.28i	−0.285678	+	0.494809i	0.687095	+	0.726567i	$0.258885\pi$
$440$	4338.00	−	4871.75i	0.470014	−	0.527844i
$441$		0			0
$442$	168.127	+	168.127i	0.0180927	+	0.0180927i
$443$	−1115.93	−	4164.70i	−0.119682	−	0.446661i	0.879912	−	0.475137i	$-0.157601\pi$
$443$	−1115.93	−	4164.70i	−0.119682	−	0.446661i	−0.999594	+	0.0284756i	$0.990935\pi$
$444$	−1637.78	−	2836.72i	−0.175058	−	0.303209i
$445$	1284.91	+	1954.84i	0.136878	+	0.208244i
$446$	7240.07	+	4180.06i	0.768671	+	0.443793i
$447$	13437.1	−	13437.1i	1.42182	−	1.42182i
$448$		0			0
$449$		−	6234.57i		−	0.655295i	−0.944800	−	0.327648i	$-0.893744\pi$
$449$		−	6234.57i		−	0.655295i	0.944800	−	0.327648i	$-0.106256\pi$
$450$	−5348.82	−	13486.4i	−0.560324	−	1.41279i
$451$	−2966.82	+	1712.90i	−0.309761	+	0.178841i
$452$	−1124.35	+	4196.12i	−0.117002	+	0.436657i
$453$	−2744.09	+	735.276i	−0.284610	+	0.0762611i
$454$	−7788.29			−0.805116
$455$		0			0
$456$	−18771.5			−1.92776
$457$	4013.82	−	1075.50i	0.410850	−	0.110087i	−0.0474731	−	0.998873i	$-0.515117\pi$
$457$	4013.82	−	1075.50i	0.410850	−	0.110087i	0.458323	+	0.888786i	$0.348450\pi$
$458$	2790.84	−	10415.6i	0.284732	−	1.06264i
$459$	−2958.87	+	1708.31i	−0.300890	+	0.173719i
$460$	1285.10	−	425.425i	0.130257	−	0.0431208i
$461$			11965.0i			1.20882i	0.796672	+	0.604411i	$0.206592\pi$
$461$			11965.0i			1.20882i	−0.796672	+	0.604411i	$0.793408\pi$
$462$		0			0
$463$	4892.04	−	4892.04i	0.491042	−	0.491042i	−0.417592	−	0.908634i	$-0.637126\pi$
$463$	4892.04	−	4892.04i	0.491042	−	0.491042i	0.908634	+	0.417592i	$0.137126\pi$
$464$	−1026.64	−	592.732i	−0.102717	−	0.0593036i
$465$	2753.25	+	569.328i	0.274579	+	0.0567784i
$466$	−4075.91	−	7059.68i	−0.405178	−	0.701789i
$467$	−2489.42	−	9290.63i	−0.246673	−	0.920598i	−0.972535	−	0.232757i	$-0.925225\pi$
$467$	−2489.42	−	9290.63i	−0.246673	−	0.920598i	0.725862	−	0.687841i	$-0.241441\pi$
$468$	2481.36	+	2481.36i	0.245087	+	0.245087i
$469$		0			0
$470$	−6765.38	+	392.084i	−0.663966	+	0.0384797i
$471$	−11174.3	+	19354.5i	−1.09318	+	1.89344i
$472$	15463.7	+	4143.50i	1.50800	+	0.404068i
$473$	7574.14	+	2029.49i	0.736278	+	0.197285i
$474$	1277.75	−	2213.14i	0.123817	−	0.214457i
$475$	10566.0	−	1228.82i	1.02064	−	0.118699i
$476$		0			0
$477$	9601.66	+	9601.66i	0.921656	+	0.921656i
$478$	−821.507	−	3065.90i	−0.0786085	−	0.293371i
$479$	−3705.78	−	6418.60i	−0.353489	−	0.612261i	0.633369	−	0.773850i	$-0.281672\pi$
$479$	−3705.78	−	6418.60i	−0.353489	−	0.612261i	−0.986858	+	0.161589i	$0.948338\pi$
$480$	15287.1	−	10048.2i	1.45367	−	0.955491i
$481$	825.531	+	476.621i	0.0782557	+	0.0451809i
$482$	2659.33	−	2659.33i	0.251305	−	0.251305i
$483$		0			0
$484$			3197.72i			0.300311i
$485$	−5029.90	−	15194.0i	−0.470920	−	1.42253i
$486$	7863.01	−	4539.71i	0.733896	−	0.423715i
$487$	−919.203	+	3430.51i	−0.0855299	+	0.319202i	−0.995414	−	0.0956605i	$-0.969504\pi$
$487$	−919.203	+	3430.51i	−0.0855299	+	0.319202i	0.909884	+	0.414863i	$0.136170\pi$
$488$	−534.250	+	143.152i	−0.0495581	+	0.0132791i
$489$	32863.9			3.03918
$490$		0			0
$491$	3326.90			0.305786			0.152893	−	0.988243i	$-0.451141\pi$
$491$	3326.90			0.305786			0.152893	+	0.988243i	$0.451141\pi$
$492$	−5663.25	+	1517.46i	−0.518941	+	0.139050i
$493$	431.108	−	1608.92i	0.0393836	−	0.146982i
$494$	1709.61	−	987.041i	0.155706	−	0.0898969i
$495$	−15548.6	−	7814.41i	−1.41183	−	0.709559i
$496$		−	194.139i		−	0.0175748i
$497$		0			0
$498$	8010.98	−	8010.98i	0.720845	−	0.720845i
$499$	−16510.1	−	9532.13i	−1.48115	−	0.855144i	−0.481381	−	0.876511i	$-0.659865\pi$
$499$	−16510.1	−	9532.13i	−1.48115	−	0.855144i	−0.999772	+	0.0213673i	$0.993198\pi$
$500$	−4849.75	+	4062.29i	−0.433775	+	0.363342i
$501$	14637.4	+	25352.7i	1.30529	+	2.26083i
$502$	−405.896	−	1514.82i	−0.0360877	−	0.134681i
$503$	−8758.73	−	8758.73i	−0.776407	−	0.776407i	0.202811	−	0.979218i	$-0.434992\pi$
$503$	−8758.73	−	8758.73i	−0.776407	−	0.776407i	−0.979218	+	0.202811i	$0.934992\pi$
$504$		0			0
$505$	−589.963	−	10179.8i	−0.0519862	−	0.897019i
$506$	−622.896	+	1078.89i	−0.0547255	+	0.0947873i
$507$	18637.5	+	4993.90i	1.63258	+	0.437449i
$508$	13.3825	+	3.58583i	0.00116880	+	0.000313180i
$509$	263.598	−	456.565i	0.0229543	−	0.0397581i	−0.854320	−	0.519747i	$-0.826026\pi$
$509$	263.598	−	456.565i	0.0229543	−	0.0397581i	0.877274	+	0.479989i	$0.159359\pi$
$510$	−1507.05	−	1341.94i	−0.130850	−	0.116514i
$511$		0			0
$512$	−1856.58	−	1856.58i	−0.160254	−	0.160254i
$513$	7341.84	+	27400.1i	0.631872	+	2.35818i
$514$	−3191.59	−	5528.00i	−0.273881	−	0.474377i
$515$	1903.54	−	9205.45i	0.162874	−	0.787652i
$516$	11622.0	+	6709.97i	0.991532	+	0.572462i
$517$	−5747.53	+	5747.53i	−0.488929	+	0.488929i
$518$		0			0
$519$			7261.07i			0.614115i
$520$	−1458.95	+	2902.92i	−0.123037	+	0.244811i
$521$	−8083.62	+	4667.08i	−0.679750	+	0.392454i	−0.799761	−	0.600319i	$-0.795040\pi$
$521$	−8083.62	+	4667.08i	−0.679750	+	0.392454i	0.120011	+	0.992773i	$0.461707\pi$
$522$	−4881.91	+	18219.5i	−0.409340	+	1.52768i
$523$	−2772.44	+	742.873i	−0.231798	+	0.0621101i	−0.372848	−	0.927892i	$-0.621619\pi$
$523$	−2772.44	+	742.873i	−0.231798	+	0.0621101i	0.141050	+	0.990002i	$0.454952\pi$
$524$	−9038.57			−0.753534
$525$		0			0
$526$	−9153.15			−0.758738
$527$	263.487	−	70.6010i	0.0217792	−	0.00583573i
$528$	−445.835	+	1663.88i	−0.0367471	+	0.137142i
$529$	9917.37	−	5725.79i	0.815104	−	0.470600i
$530$	−2040.07	+	4059.20i	−0.167198	+	0.332680i
$531$		−	42707.6i		−	3.49031i
$532$		0			0
$533$	1206.49	−	1206.49i	0.0980469	−	0.0980469i
$534$	−3190.86	−	1842.24i	−0.258581	−	0.149292i
$535$	−1394.51	+	6743.80i	−0.112691	+	0.544972i
$536$	−9949.57	−	17233.2i	−0.801784	−	1.38873i
$537$	7869.21	+	29368.3i	0.632368	+	2.36003i
$538$	−4172.37	−	4172.37i	−0.334357	−	0.334357i
$539$		0			0
$540$	−12599.5	−	11219.1i	−1.00407	−	0.894065i
$541$	12085.5	−	20932.7i	0.960439	−	1.66353i	0.239039	−	0.971010i	$-0.423168\pi$
$541$	12085.5	−	20932.7i	0.960439	−	1.66353i	0.721400	−	0.692519i	$-0.243499\pi$
$542$	10465.4	+	2804.20i	0.829387	+	0.222234i
$543$	−15093.9	−	4044.39i	−1.19289	−	0.319634i
$544$	887.463	−	1537.13i	0.0699442	−	0.121147i
$545$	−661.900	−	11421.0i	−0.0520232	−	0.897658i
$546$		0			0
$547$	5768.43	+	5768.43i	0.450896	+	0.450896i	0.895652	−	0.444756i	$-0.146710\pi$
$547$	5768.43	+	5768.43i	0.450896	+	0.450896i	−0.444756	+	0.895652i	$0.646710\pi$
$548$	2.25646	+	8.42123i	0.000175896	+	0.000656455i
$549$	737.743	+	1277.81i	0.0573517	+	0.0993361i
$550$	847.122	−	5760.11i	0.0656753	−	0.446567i
$551$	−11976.6	−	6914.69i	−0.925990	−	0.534620i
$552$	−4172.00	+	4172.00i	−0.321688	+	0.321688i
$553$		0			0
$554$		−	2225.79i		−	0.170695i
$555$	−7228.54	−	3632.92i	−0.552855	−	0.277854i
$556$	8318.80	−	4802.86i	0.634524	−	0.366343i
$557$	3970.26	−	14817.2i	0.302020	−	1.12716i	−0.633460	−	0.773776i	$-0.718366\pi$
$557$	3970.26	−	14817.2i	0.302020	−	1.12716i	0.935480	−	0.353380i	$-0.114968\pi$
$558$	−2983.75	+	799.493i	−0.226366	+	0.0606546i
$559$	−3905.43			−0.295495
$560$		0			0
$561$	−2420.36			−0.182153
$562$	8188.54	−	2194.11i	0.614613	−	0.164685i
$563$	−1969.07	+	7348.66i	−0.147400	+	0.550105i	0.852237	+	0.523156i	$0.175246\pi$
$563$	−1969.07	+	7348.66i	−0.147400	+	0.550105i	−0.999637	+	0.0269484i	$0.991421\pi$
$564$	−12047.3	+	6955.49i	−0.899434	+	0.519289i
$565$	3371.93	+	10185.7i	0.251076	+	0.758437i
$566$			11424.0i			0.848383i
$567$		0			0
$568$	4380.05	−	4380.05i	0.323561	−	0.323561i
$569$	2570.41	+	1484.03i	0.189380	+	0.109339i	0.591692	−	0.806164i	$-0.298460\pi$
$569$	2570.41	+	1484.03i	0.189380	+	0.109339i	−0.402312	+	0.915503i	$0.631793\pi$
$570$	−14000.4	+	9202.41i	−1.02879	+	0.676222i
$571$	−3509.31	−	6078.30i	−0.257198	−	0.445480i	0.708292	−	0.705919i	$-0.249466\pi$
$571$	−3509.31	−	6078.30i	−0.257198	−	0.445480i	−0.965490	+	0.260440i	$0.916133\pi$
$572$	364.468	+	1360.21i	0.0266419	+	0.0994289i
$573$	15051.6	+	15051.6i	1.09737	+	1.09737i
$574$		0			0
$575$	2075.20	−	2621.42i	0.150508	−	0.190123i
$576$	−11866.9	+	20554.1i	−0.858430	+	1.48684i
$577$	−236.305	−	63.3177i	−0.0170494	−	0.00456837i	0.250284	−	0.968172i	$-0.419476\pi$
$577$	−236.305	−	63.3177i	−0.0170494	−	0.00456837i	−0.267334	+	0.963604i	$0.586143\pi$
$578$	8655.09	+	2319.13i	0.622845	+	0.166891i
$579$	14710.0	−	25478.5i	1.05583	−	1.82876i
$580$	8211.01	−	475.864i	0.587834	−	0.0340676i
$581$		0			0
$582$	17824.9	+	17824.9i	1.26953	+	1.26953i
$583$	1410.31	+	5263.36i	0.100187	+	0.373904i
$584$	−10054.5	−	17414.9i	−0.712429	−	1.23396i
$585$	8487.54	+	1755.08i	0.599857	+	0.124041i
$586$	7313.53	+	4222.47i	0.515562	+	0.297660i
$587$	1167.08	−	1167.08i	0.0820620	−	0.0820620i	−0.664884	−	0.746946i	$-0.731519\pi$
$587$	1167.08	−	1167.08i	0.0820620	−	0.0820620i	0.746946	+	0.664884i	$0.231519\pi$
$588$		0			0
$589$		−	2264.79i		−	0.158436i
$590$	13564.6	−	4490.48i	0.946517	−	0.313339i
$591$	42064.5	−	24286.0i	2.92776	−	1.69034i
$592$	−144.586	+	539.601i	−0.0100379	+	0.0374620i
$593$	−9993.22	+	2677.67i	−0.692027	+	0.185428i	−0.587657	−	0.809110i	$-0.699949\pi$
$593$	−9993.22	+	2677.67i	−0.692027	+	0.185428i	−0.104371	+	0.994538i	$0.533283\pi$
$594$	15525.9			1.07245
$595$		0			0
$596$	9103.98			0.625694
$597$	45190.9	−	12108.9i	3.09806	−	0.830123i
$598$	160.591	−	599.332i	0.0109817	−	0.0409842i
$599$	−23501.3	+	13568.5i	−1.60307	+	0.925533i	−0.612201	+	0.790702i	$0.709716\pi$
$599$	−23501.3	+	13568.5i	−1.60307	+	0.925533i	−0.990869	+	0.134830i	$0.956951\pi$
$600$	10935.9	−	25312.1i	0.744091	−	1.72227i
$601$			14268.6i			0.968436i	0.874947	+	0.484218i	$0.160896\pi$
$601$			14268.6i			0.968436i	−0.874947	+	0.484218i	$0.839104\pi$
$602$		0			0
$603$	−37536.5	+	37536.5i	−2.53500	+	2.53500i
$604$	−1178.68	−	680.512i	−0.0794037	−	0.0458437i
$605$	4338.04	+	6599.81i	0.291515	+	0.443505i
$606$	8030.17	+	13908.7i	0.538289	+	0.932345i
$607$	6079.64	+	22689.5i	0.406532	+	1.51720i	0.801212	+	0.598380i	$0.204189\pi$
$607$	6079.64	+	22689.5i	0.406532	+	1.51720i	−0.394680	+	0.918819i	$0.629145\pi$
$608$	−10420.3	−	10420.3i	−0.695061	−	0.695061i
$609$		0			0
$610$	−328.281	+	368.673i	−0.0217897	+	0.0244707i
$611$	2024.16	−	3505.95i	0.134024	−	0.232137i
$612$	−2791.11	−	747.875i	−0.184353	−	0.0493972i
$613$	−14603.2	−	3912.91i	−0.962181	−	0.257816i	−0.256658	−	0.966502i	$-0.582621\pi$
$613$	−14603.2	−	3912.91i	−0.962181	−	0.257816i	−0.705523	+	0.708687i	$0.749288\pi$
$614$	−249.747	+	432.574i	−0.0164152	+	0.0284320i
$615$	−9629.86	+	10814.7i	−0.631404	+	0.709092i
$616$		0			0
$617$	−7458.41	−	7458.41i	−0.486652	−	0.486652i	0.420596	−	0.907248i	$-0.361821\pi$
$617$	−7458.41	−	7458.41i	−0.486652	−	0.486652i	−0.907248	+	0.420596i	$0.861821\pi$
$618$	3831.96	+	14301.1i	0.249424	+	0.930864i
$619$	−11038.7	−	19119.6i	−0.716772	−	1.24149i	−0.962272	−	0.272089i	$-0.912285\pi$
$619$	−11038.7	−	19119.6i	−0.716772	−	1.24149i	0.245500	−	0.969397i	$-0.421048\pi$
$620$	739.834	+	1125.57i	0.0479233	+	0.0729096i
$621$	7721.44	+	4457.97i	0.498954	+	0.288071i
$622$	13015.9	−	13015.9i	0.839054	−	0.839054i
$623$		0			0
$624$		−	857.939i		−	0.0550402i
$625$	−4498.54	+	14963.4i	−0.287907	+	0.957658i
$626$	8502.42	−	4908.88i	0.542852	−	0.313416i
$627$	−5201.02	+	19410.5i	−0.331274	+	1.23633i
$628$	−10342.1	+	2771.15i	−0.657155	+	0.176084i
$629$	−784.930			−0.0497571
$630$		0			0
$631$	17501.0			1.10413			0.552064	−	0.833802i	$-0.313840\pi$
$631$	17501.0			1.10413			0.552064	+	0.833802i	$0.313840\pi$
$632$	3272.54	−	876.874i	0.205972	−	0.0551902i
$633$	−363.128	+	1355.21i	−0.0228010	+	0.0850946i
$634$	6970.78	−	4024.58i	0.436664	−	0.252108i
$635$	32.4849	−	10.7539i	0.00203012	−	0.000672058i
$636$			9325.69i			0.581427i
$637$		0			0
$638$	−5352.25	+	5352.25i	−0.332128	+	0.332128i
$639$	−14310.6	−	8262.25i	−0.885947	−	0.511502i
$640$	7391.92	+	1528.53i	0.456549	+	0.0944069i
$641$	−9065.53	−	15702.0i	−0.558607	−	0.967535i	−0.997613	−	0.0690513i	$-0.978003\pi$
$641$	−9065.53	−	15702.0i	−0.558607	−	0.967535i	0.439006	−	0.898484i	$-0.355331\pi$
$642$	−2807.25	−	10476.8i	−0.172575	−	0.644059i
$643$	4575.87	+	4575.87i	0.280645	+	0.280645i	0.833366	−	0.552721i	$-0.186411\pi$
$643$	4575.87	+	4575.87i	0.280645	+	0.280645i	−0.552721	+	0.833366i	$0.686411\pi$
$644$		0			0
$645$	33089.6	−	1917.69i	2.02000	−	0.117068i
$646$	−812.762	+	1407.74i	−0.0495011	+	0.0857384i
$647$	501.532	+	134.385i	0.0304749	+	0.00816572i	0.274024	−	0.961723i	$-0.411645\pi$
$647$	501.532	+	134.385i	0.0304749	+	0.00816572i	−0.243549	+	0.969888i	$0.578312\pi$
$648$	33106.7	+	8870.92i	2.00703	+	0.537782i
$649$	8569.07	−	14842.1i	0.518282	−	0.897692i
$650$	334.978	+	2880.31i	0.0202137	+	0.173808i
$651$		0			0
$652$	11133.1	+	11133.1i	0.668721	+	0.668721i
$653$	−2326.81	−	8683.76i	−0.139441	−	0.520401i	−0.999940	−	0.0109488i	$-0.996515\pi$
$653$	−2326.81	−	8683.76i	−0.139441	−	0.520401i	0.860499	−	0.509452i	$-0.170152\pi$
$654$	9009.32	+	15604.6i	0.538673	+	0.933009i
$655$	−18654.8	+	12261.8i	−1.11283	+	0.731462i
$656$	865.958	+	499.961i	0.0515396	+	0.0297564i
$657$	−37932.4	+	37932.4i	−2.25249	+	2.25249i
$658$		0			0
$659$		−	14558.0i		−	0.860546i	−0.902699	−	0.430273i	$-0.858417\pi$
$659$		−	14558.0i		−	0.860546i	0.902699	−	0.430273i	$-0.141583\pi$
$660$	−3755.95	−	11345.7i	−0.221515	−	0.669140i
$661$	−19817.7	+	11441.8i	−1.16614	+	0.673273i	−0.952768	−	0.303698i	$-0.901779\pi$
$661$	−19817.7	+	11441.8i	−1.16614	+	0.673273i	−0.213374	+	0.976971i	$0.568445\pi$
$662$	3320.27	−	12391.4i	0.194933	−	0.727501i
$663$	1164.40	−	312.000i	0.0682074	−	0.0182761i
$664$	15019.8			0.877834
$665$		0			0
$666$	8888.63			0.517158
$667$	−4198.61	+	1125.01i	−0.243734	+	0.0653084i
$668$	−3629.96	+	13547.2i	−0.210250	+	0.784665i
$669$	36707.0	−	21192.8i	2.12134	−	1.22476i
$670$	−15868.9	−	7975.40i	−0.915030	−	0.459875i
$671$			592.097i			0.0340651i
$672$		0			0
$673$	−19499.1	+	19499.1i	−1.11684	+	1.11684i	−0.124641	+	0.992202i	$0.539778\pi$
$673$	−19499.1	+	19499.1i	−1.11684	+	1.11684i	−0.992202	+	0.124641i	$0.960222\pi$
$674$	1156.85	+	667.906i	0.0661129	+	0.0381703i
$675$	−41224.3	−	6062.73i	−2.35070	−	0.345710i
$676$	4621.95	+	8005.45i	0.262969	+	0.455476i
$677$	965.893	+	3604.76i	0.0548335	+	0.204641i	0.987908	−	0.155042i	$-0.0495513\pi$
$677$	965.893	+	3604.76i	0.0548335	+	0.204641i	−0.933074	+	0.359684i	$0.882885\pi$
$678$	−11949.4	−	11949.4i	−0.676865	−	0.676865i
$679$		0			0
$680$	−154.784	−	2670.79i	−0.00872896	−	0.150618i
$681$	−19743.2	+	34196.3i	−1.11096	+	1.92424i
$682$	−1197.35	−	320.828i	−0.0672270	−	0.0180134i
$683$	−15689.3	−	4203.93i	−0.878965	−	0.235518i	−0.209005	−	0.977915i	$-0.567022\pi$
$683$	−15689.3	−	4203.93i	−0.878965	−	0.235518i	−0.669961	+	0.742397i	$0.733689\pi$
$684$	−11995.4	+	20776.7i	−0.670551	+	1.16143i
$685$	16.0814	+	14.3196i	0.000896993	+	0.000798719i
$686$		0			0
$687$	−38657.2	−	38657.2i	−2.14682	−	2.14682i
$688$	−592.367	−	2210.74i	−0.0328253	−	0.122506i
$689$	−1356.96	−	2350.33i	−0.0750308	−	0.129957i
$690$	−1066.35	+	5156.84i	−0.0588337	+	0.284518i
$691$	−11381.8	−	6571.27i	−0.626604	−	0.361770i	0.152832	−	0.988252i	$-0.451161\pi$
$691$	−11381.8	−	6571.27i	−0.626604	−	0.361770i	−0.779436	+	0.626482i	$0.784494\pi$
$692$	−2459.78	+	2459.78i	−0.135126	+	0.135126i
$693$		0			0
$694$		−	3843.43i		−	0.210223i
$695$	10653.7	−	21198.0i	0.581464	−	1.15696i
$696$	−31045.3	+	17924.0i	−1.69076	+	0.976161i
$697$	−363.634	+	1357.10i	−0.0197613	+	0.0737501i
$698$	18603.8	−	4984.88i	1.00883	−	0.270316i
$699$	−41329.6			−2.23638
$700$		0			0
$701$	−13075.3			−0.704488			−0.352244	−	0.935908i	$-0.614581\pi$
$701$	−13075.3			−0.704488			−0.352244	+	0.935908i	$0.614581\pi$
$702$	−7469.30	+	2001.39i	−0.401582	+	0.107604i
$703$	−1686.71	+	6294.88i	−0.0904914	+	0.337718i
$704$	−8248.16	+	4762.08i	−0.441568	+	0.254940i
$705$	−15428.6	+	30698.9i	−0.824222	+	1.63998i
$706$			14586.7i			0.777588i
$707$		0			0
$708$	20740.0	−	20740.0i	1.10093	−	1.10093i
$709$	−5900.52	−	3406.66i	−0.312551	−	0.180451i	0.335517	−	0.942034i	$-0.391089\pi$
$709$	−5900.52	−	3406.66i	−0.312551	−	0.180451i	−0.648067	+	0.761583i	$0.724422\pi$
$710$	1119.53	−	5414.00i	0.0591762	−	0.286175i
$711$	−4519.03	−	7827.20i	−0.238364	−	0.412859i
$712$	−1264.26	−	4718.29i	−0.0665453	−	0.248350i
$713$	−503.352	−	503.352i	−0.0264385	−	0.0264385i
$714$		0			0
$715$	2597.50	+	2312.92i	0.135862	+	0.120977i
$716$	−7283.11	+	12614.7i	−0.380143	+	0.658427i
$717$	−15544.1	−	4165.02i	−0.809629	−	0.216939i
$718$	52.0729	+	13.9529i	0.00270661	+	0.000725233i
$719$	5890.49	−	10202.6i	0.305533	−	0.529199i	−0.671847	−	0.740690i	$-0.734499\pi$
$719$	5890.49	−	10202.6i	0.305533	−	0.529199i	0.977380	+	0.211491i	$0.0678321\pi$
$720$	293.872	+	5070.75i	0.0152111	+	0.262466i
$721$		0			0
$722$	504.266	+	504.266i	0.0259929	+	0.0259929i
$723$	−4935.03	−	18417.8i	−0.253853	−	0.947392i
$724$	−3743.16	−	6483.34i	−0.192146	−	0.332806i
$725$	16301.3	−	12121.3i	0.835053	−	0.620927i
$726$	−10772.8	−	6219.66i	−0.550709	−	0.317952i
$727$	11932.2	−	11932.2i	0.608722	−	0.608722i	−0.333890	−	0.942612i	$-0.608361\pi$
$727$	11932.2	−	11932.2i	0.608722	−	0.608722i	0.942612	+	0.333890i	$0.108361\pi$
$728$		0			0
$729$		−	6392.84i		−	0.324790i
$730$	−16036.3	−	8059.51i	−0.813054	−	0.408624i
$731$	2785.01	−	1607.93i	0.140913	−	0.0813562i
$732$	−262.271	+	978.810i	−0.0132429	+	0.0494233i
$733$	32374.0	−	8674.60i	1.63133	−	0.437113i	0.677025	−	0.735960i	$-0.263269\pi$
$733$	32374.0	−	8674.60i	1.63133	−	0.437113i	0.954301	+	0.298847i	$0.0966020\pi$
$734$	−1853.12			−0.0931881
$735$		0			0
$736$	−4631.83			−0.231972
$737$	−20576.5	+	5513.45i	−1.02842	+	0.275564i
$738$	4117.82	−	15367.9i	0.205392	−	0.766533i
$739$	22011.8	−	12708.5i	1.09569	−	0.632599i	0.160608	−	0.987018i	$-0.448655\pi$
$739$	22011.8	−	12708.5i	1.09569	−	0.632599i	0.935087	+	0.354419i	$0.115321\pi$
$740$	−1218.07	−	3679.46i	−0.0605094	−	0.182784i
$741$		−	10008.6i		−	0.496185i
$742$		0			0
$743$	6699.21	−	6699.21i	0.330781	−	0.330781i	−0.522102	−	0.852883i	$-0.674852\pi$
$743$	6699.21	−	6699.21i	0.330781	−	0.330781i	0.852883	+	0.522102i	$0.174852\pi$
$744$	−5084.18	−	2935.35i	−0.250531	−	0.144644i
$745$	18789.8	−	12350.5i	0.924035	−	0.607366i
$746$	−3258.59	−	5644.04i	−0.159927	−	0.277001i
$747$	−10370.4	−	38702.8i	−0.507942	−	1.89567i
$748$	−819.929	−	819.929i	−0.0400796	−	0.0400796i
$749$		0			0
$750$	−4252.50	−	24239.6i	−0.207039	−	1.18014i
$751$	6683.80	−	11576.7i	0.324761	−	0.562502i	−0.656703	−	0.754149i	$-0.728050\pi$
$751$	6683.80	−	11576.7i	0.324761	−	0.562502i	0.981464	+	0.191647i	$0.0613829\pi$
$752$	2291.63	+	614.041i	0.111127	+	0.0297763i
$753$	−7680.12	−	2057.88i	−0.371685	−	0.0995928i
$754$	1884.95	−	3264.83i	0.0910423	−	0.157690i
$755$	−3355.88	+	194.488i	−0.161766	+	0.00937503i
$756$		0			0
$757$	6207.76	+	6207.76i	0.298051	+	0.298051i	0.840250	−	0.542199i	$-0.182408\pi$
$757$	6207.76	+	6207.76i	0.298051	+	0.298051i	−0.542199	+	0.840250i	$0.682408\pi$
$758$	2272.47	+	8480.98i	0.108892	+	0.406389i
$759$	3158.07	+	5469.93i	0.151028	+	0.261589i
$760$	−21751.5	−	4497.85i	−1.03817	−	0.214676i
$761$	−8248.29	−	4762.15i	−0.392905	−	0.226844i	0.290513	−	0.956871i	$-0.406174\pi$
$761$	−8248.29	−	4762.15i	−0.392905	−	0.226844i	−0.683418	+	0.730027i	$0.739507\pi$
$762$	−38.1097	+	38.1097i	−0.00181177	+	0.00181177i
$763$		0			0
$764$			10197.9i			0.482914i
$765$	−6775.18	+	2242.88i	−0.320205	+	0.106002i
$766$	−15853.1	+	9152.77i	−0.747773	+	0.431727i
$767$	−2209.22	+	8244.91i	−0.104003	+	0.388144i
$768$	−39308.7	+	10532.7i	−1.84691	+	0.494879i
$769$	−4045.49			−0.189706			−0.0948532	−	0.995491i	$-0.530238\pi$
$769$	−4045.49			−0.189706			−0.0948532	+	0.995491i	$0.530238\pi$
$770$		0			0
$771$	−32362.6			−1.51169
$772$	13614.4	−	3647.97i	0.634706	−	0.170069i
$773$	1263.64	−	4715.96i	0.0587968	−	0.219433i	−0.930276	−	0.366860i	$-0.880433\pi$
$773$	1263.64	−	4715.96i	0.0587968	−	0.219433i	0.989073	+	0.147428i	$0.0470994\pi$
$774$	−31537.7	+	18208.3i	−1.46460	+	0.845588i
$775$	3053.91	+	1319.41i	0.141548	+	0.0611545i
$776$			33420.0i			1.54601i
$777$		0			0
$778$	4632.95	−	4632.95i	0.213495	−	0.213495i
$779$	10102.1	+	5832.45i	0.464628	+	0.268253i
$780$	3269.47	+	4974.11i	0.150085	+	0.228336i
$781$	−3315.56	−	5742.71i	−0.151908	−	0.263112i
$782$	132.236	+	493.510i	0.00604698	+	0.0225676i
$783$	38305.3	+	38305.3i	1.74830	+	1.74830i
$784$		0			0
$785$	−17585.8	+	19749.5i	−0.799570	+	0.897949i
$786$	17580.3	−	30450.0i	0.797798	−	1.38183i
$787$	−34101.5	−	9137.48i	−1.54459	−	0.413870i	−0.616841	−	0.787087i	$-0.711588\pi$
$787$	−34101.5	−	9137.48i	−1.54459	−	0.413870i	−0.927744	+	0.373217i	$0.878255\pi$
$788$	22477.1	+	6022.72i	1.01613	+	0.272272i
$789$	−23203.1	+	40189.0i	−1.04696	+	1.81339i
$790$	2010.88	−	2258.30i	0.0905620	−	0.101705i
$791$		0			0
$792$	25694.0	+	25694.0i	1.15277	+	1.15277i
$793$	−76.3252	−	284.850i	−0.00341789	−	0.0127557i
$794$	3950.80	+	6842.98i	0.176585	+	0.305854i
$795$	12651.3	+	19247.4i	0.564396	+	0.858661i
$796$	19411.1	+	11207.0i	0.864331	+	0.499022i
$797$	3736.59	−	3736.59i	0.166069	−	0.166069i	−0.619180	−	0.785249i	$-0.712535\pi$
$797$	3736.59	−	3736.59i	0.166069	−	0.166069i	0.785249	+	0.619180i	$0.212535\pi$
$798$		0			0
$799$			3333.52i			0.147599i
$800$	20121.6	−	7980.37i	0.889256	−	0.352686i
$801$	−11285.1	+	6515.46i	−0.497803	+	0.287406i
$802$	4359.12	−	16268.5i	0.191928	−	0.716283i
$803$	−20793.5	+	5571.60i	−0.913806	+	0.244853i
$804$	−36457.6			−1.59920
$805$		0			0
$806$	617.384			0.0269807
$807$	−28896.7	+	7742.84i	−1.26049	+	0.337746i
$808$	−5510.80	+	20566.6i	−0.239937	+	0.895458i
$809$	−25645.0	+	14806.1i	−1.11450	+	0.643455i	−0.939991	−	0.341200i	$-0.889167\pi$
$809$	−25645.0	+	14806.1i	−1.11450	+	0.643455i	−0.174507	+	0.984656i	$0.555833\pi$
$810$	29040.7	−	9613.77i	1.25974	−	0.417029i
$811$			13678.2i			0.592241i	0.955151	+	0.296121i	$0.0956931\pi$
$811$			13678.2i			0.592241i	−0.955151	+	0.296121i	$0.904307\pi$
$812$		0			0
$813$	38842.2	−	38842.2i	1.67559	−	1.67559i
$814$	3089.04	+	1783.46i	0.133011	+	0.0767938i
$815$	38081.0	+	7874.53i	1.63671	+	0.338445i
$816$	353.228	+	611.808i	0.0151537	+	0.0262470i
$817$	−6910.44	−	25790.1i	−0.295919	−	1.10438i
$818$	−14462.7	−	14462.7i	−0.618184	−	0.618184i
$819$		0			0
$820$	−6925.87	+	401.385i	−0.294954	+	0.0170939i
$821$	3587.21	−	6213.22i	0.152490	−	0.264121i	−0.779652	−	0.626213i	$-0.784604\pi$
$821$	3587.21	−	6213.22i	0.152490	−	0.264121i	0.932142	+	0.362092i	$0.117937\pi$
$822$	−32.7591	−	8.77779i	−0.00139003	−	0.000372458i
$823$	−3549.61	−	951.115i	−0.150342	−	0.0402841i	0.182863	−	0.983138i	$-0.441464\pi$
$823$	−3549.61	−	951.115i	−0.150342	−	0.0402841i	−0.333205	+	0.942854i	$0.608130\pi$
$824$	−9814.29	+	16998.8i	−0.414923	+	0.718668i
$825$	−23143.7	−	18321.3i	−0.976677	−	0.773171i
$826$		0			0
$827$	25938.0	+	25938.0i	1.09063	+	1.09063i	0.995461	+	0.0951702i	$0.0303395\pi$
$827$	25938.0	+	25938.0i	1.09063	+	1.09063i	0.0951702	+	0.995461i	$0.469660\pi$
$828$	1951.65	+	7283.64i	0.0819135	+	0.305705i
$829$	9131.95	+	15817.0i	0.382588	+	0.662662i	0.991431	−	0.130628i	$-0.0416995\pi$
$829$	9131.95	+	15817.0i	0.382588	+	0.662662i	−0.608843	+	0.793291i	$0.708366\pi$
$830$	11202.2	−	7363.19i	0.468475	−	0.307928i
$831$	−9772.85	−	5642.36i	−0.407962	−	0.235537i
$832$	3354.21	−	3354.21i	0.139767	−	0.139767i
$833$		0			0
$834$			37366.9i			1.55145i
$835$	10886.3	+	32884.6i	0.451180	+	1.36290i
$836$	−8337.48	+	4813.64i	−0.344925	+	0.199143i
$837$	−2296.12	+	8569.24i	−0.0948215	+	0.353879i
$838$	11042.6	−	2958.85i	0.455202	−	0.121971i
$839$	24855.3			1.02277			0.511383	−	0.859353i	$-0.329134\pi$
$839$	24855.3			1.02277			0.511383	+	0.859353i	$0.329134\pi$
$840$		0			0
$841$	−2020.98			−0.0828645
$842$	−4668.03	+	1250.80i	−0.191058	+	0.0511939i
$843$	11124.1	−	41515.7i	0.454489	−	1.69618i
$844$	−582.111	+	336.082i	−0.0237406	+	0.0137067i
$845$	20399.5	+	10252.4i	0.830492	+	0.417388i
$846$		−	37749.1i		−	1.53409i
$847$		0			0
$848$	1124.63	−	1124.63i	0.0455424	−	0.0455424i
$849$	50159.5	+	28959.6i	2.02764	+	1.17066i
$850$	−1424.75	−	1916.07i	−0.0574923	−	0.0773185i
$851$	1024.17	+	1773.92i	0.0412552	+	0.0714561i
$852$	−2937.27	−	10962.0i	−0.118109	−	0.440790i
$853$	−10701.3	−	10701.3i	−0.429551	−	0.429551i	0.458924	−	0.888475i	$-0.348235\pi$
$853$	−10701.3	−	10701.3i	−0.429551	−	0.429551i	−0.888475	+	0.458924i	$0.848235\pi$
$854$		0			0
$855$	3428.26	+	59154.4i	0.137127	+	2.36613i
$856$	7189.83	−	12453.1i	0.287083	−	0.497243i
$857$	−22822.2	−	6115.18i	−0.909673	−	0.243746i	−0.226507	−	0.974009i	$-0.572731\pi$
$857$	−22822.2	−	6115.18i	−0.909673	−	0.243746i	−0.683166	+	0.730263i	$0.739397\pi$
$858$	−5291.32	−	1417.80i	−0.210539	−	0.0564138i
$859$	13331.4	−	23090.7i	0.529524	−	0.917163i	−0.469883	−	0.882729i	$-0.655704\pi$
$859$	13331.4	−	23090.7i	0.529524	−	0.917163i	0.999407	−	0.0344343i	$-0.0109629\pi$
$860$	11859.2	+	10559.9i	0.470227	+	0.418709i
$861$		0			0
$862$	−13718.1	−	13718.1i	−0.542041	−	0.542041i
$863$	9694.97	+	36182.1i	0.382411	+	1.42718i	0.842208	+	0.539153i	$0.181255\pi$
$863$	9694.97	+	36182.1i	0.382411	+	1.42718i	−0.459797	+	0.888024i	$0.652078\pi$
$864$	28862.5	+	49991.3i	1.13648	+	1.96845i
$865$	−1739.82	+	8413.74i	−0.0683882	+	0.330723i
$866$	12668.7	+	7314.29i	0.497114	+	0.287009i
$867$	32123.2	−	32123.2i	1.25832	−	1.25832i
$868$		0			0
$869$		−	3626.88i		−	0.141581i
$870$	−14367.6	+	28587.6i	−0.559892	+	1.11404i
$871$	9188.32	−	5304.88i	0.357445	−	0.206371i
$872$	−6182.75	+	23074.3i	−0.240108	+	0.896096i
$873$	86116.1	−	23074.7i	3.33859	−	0.894572i
$874$	4241.95			0.164172
$875$		0			0
$876$	−36842.1			−1.42098
$877$	29063.5	−	7787.53i	1.11905	−	0.299848i	0.348549	−	0.937291i	$-0.386675\pi$
$877$	29063.5	−	7787.53i	1.11905	−	0.299848i	0.770497	+	0.637443i	$0.220008\pi$
$878$	2534.94	−	9460.53i	0.0974375	−	0.363642i
$879$	37079.4	−	21407.8i	1.42282	−	0.821465i
$880$	−915.291	+	1821.19i	−0.0350619	+	0.0697639i
$881$		−	30534.2i		−	1.16768i	−0.811870	−	0.583839i	$-0.801550\pi$
$881$		−	30534.2i		−	1.16768i	0.811870	−	0.583839i	$-0.198450\pi$
$882$		0			0
$883$	5071.07	−	5071.07i	0.193268	−	0.193268i	−0.603839	−	0.797106i	$-0.706363\pi$
$883$	5071.07	−	5071.07i	0.193268	−	0.193268i	0.797106	+	0.603839i	$0.206363\pi$
$884$	500.150	+	288.762i	0.0190293	+	0.0109865i
$885$	14669.6	−	70941.7i	0.557190	−	2.69455i
$886$	4017.71	+	6958.87i	0.152345	+	0.263869i
$887$	8323.07	+	31062.1i	0.315064	+	1.17583i	0.923930	+	0.382561i	$0.124958\pi$
$887$	8323.07	+	31062.1i	0.315064	+	1.17583i	−0.608867	+	0.793273i	$0.708376\pi$
$888$	11945.1	+	11945.1i	0.451411	+	0.451411i
$889$		0			0
$890$	−3255.98	−	2899.26i	−0.122630	−	0.109195i
$891$	18345.7	−	31775.7i	0.689792	−	1.19475i
$892$	19614.3	+	5255.65i	0.736252	+	0.197278i
$893$	26733.7	+	7163.29i	1.00180	+	0.268433i
$894$	−17707.5	+	30670.4i	−0.662448	+	1.14739i
$895$	2081.49	+	35916.0i	0.0777391	+	1.34138i
$896$		0			0
$897$	−2224.41	−	2224.41i	−0.0827993	−	0.0827993i
$898$	3007.26	+	11223.3i	0.111752	+	0.417065i
$899$	−2162.53	−	3745.62i	−0.0802275	−	0.138958i
$900$	−21027.6	−	28279.0i	−0.778801	−	1.04737i
$901$	1935.34	+	1117.37i	0.0715599	+	0.0413151i
$902$	4514.55	−	4514.55i	0.166650	−	0.166650i
$903$		0			0
$904$		−	22404.0i		−	0.824276i
$905$	−16520.9	−	8303.07i	−0.606821	−	0.304976i
$906$	4585.15	−	2647.24i	0.168136	−	0.0970734i
$907$	2463.55	−	9194.08i	0.0901883	−	0.336587i	−0.906058	−	0.423154i	$-0.860923\pi$
$907$	2463.55	−	9194.08i	0.0901883	−	0.336587i	0.996246	+	0.0865668i	$0.0275896\pi$
$908$	−18272.7	+	4896.16i	−0.667844	+	0.178948i
$909$	56800.6			2.07256
$910$		0			0
$911$	22469.7			0.817185			0.408593	−	0.912717i	$-0.366020\pi$
$911$	22469.7			0.817185			0.408593	+	0.912717i	$0.366020\pi$
$912$	5665.54	−	1518.08i	0.205707	−	0.0551190i
$913$	4161.53	−	15531.0i	0.150851	−	0.562982i
$914$	−6706.76	+	3872.15i	−0.242713	+	0.140131i
$915$	786.554	+	2375.98i	0.0284182	+	0.0858441i
$916$		−	26191.3i		−	0.944742i
$917$		0			0
$918$	4502.45	−	4502.45i	0.161877	−	0.161877i
$919$	−5070.27	−	2927.32i	−0.181994	−	0.105074i	0.406235	−	0.913769i	$-0.366841\pi$
$919$	−5070.27	−	2927.32i	−0.181994	−	0.105074i	−0.588229	+	0.808694i	$0.700175\pi$
$920$	−5833.94	+	3834.63i	−0.209064	+	0.137418i
$921$	1266.21	+	2193.14i	0.0453019	+	0.0784651i
$922$	−5771.37	−	21539.0i	−0.206149	−	0.769360i
$923$	2335.34	+	2335.34i	0.0832813	+	0.0832813i
$924$		0			0
$925$	−7505.57	−	5941.66i	−0.266791	−	0.211201i
$926$	−6446.79	+	11166.2i	−0.228785	+	0.396267i
$927$	50578.6	+	13552.5i	1.79204	+	0.480175i
$928$	−27183.3	−	7283.74i	−0.961569	−	0.257652i
$929$	−15405.4	+	26683.0i	−0.544064	+	0.942346i	0.454601	+	0.890695i	$0.349782\pi$
$929$	−15405.4	+	26683.0i	−0.544064	+	0.942346i	−0.998665	+	0.0516513i	$0.983552\pi$
$930$	−5230.93	+	303.155i	−0.184440	+	0.0106891i
$931$		0			0
$932$	−14000.9	−	14000.9i	−0.492077	−	0.492077i
$933$	−24154.2	−	90144.7i	−0.847560	−	3.16314i
$934$	8962.72	+	15523.9i	0.313993	+	0.543851i
$935$	−2804.58	−	579.942i	−0.0980959	−	0.0202846i
$936$	−15673.1	−	9048.90i	−0.547321	−	0.315996i
$937$	−35445.3	+	35445.3i	−1.23580	+	1.23580i	−0.274101	+	0.961701i	$0.588380\pi$
$937$	−35445.3	+	35445.3i	−1.23580	+	1.23580i	−0.961701	+	0.274101i	$0.911620\pi$
$938$		0			0
$939$		−	49775.8i		−	1.72990i
$940$	−15626.3	+	5173.00i	−0.542207	+	0.179494i
$941$	15479.3	−	8936.97i	0.536249	−	0.309604i	−0.207308	−	0.978276i	$-0.566470\pi$
$941$	15479.3	−	8936.97i	0.536249	−	0.309604i	0.743557	+	0.668672i	$0.233137\pi$
$942$	10779.9	−	40231.3i	0.372855	−	1.39151i
$943$	3541.47	−	948.934i	0.122297	−	0.0327694i
$944$	−5002.29			−0.172469
$945$		0			0
$946$	−14613.6			−0.502252
$947$	−45535.3	+	12201.2i	−1.56251	+	0.418674i	−0.933458	−	0.358687i	$-0.883225\pi$
$947$	−45535.3	+	12201.2i	−1.56251	+	0.418674i	−0.629055	+	0.777361i	$0.716558\pi$
$948$	1606.54	−	5995.68i	0.0550400	−	0.205412i
$949$	9285.23	−	5360.83i	0.317609	−	0.183372i
$950$	−18427.9	+	7308.63i	−0.629346	+	0.249603i
$951$		−	40809.1i		−	1.39151i
$952$		0			0
$953$	−9789.22	+	9789.22i	−0.332743	+	0.332743i	−0.853627	−	0.520884i	$-0.825602\pi$
$953$	−9789.22	+	9789.22i	−0.332743	+	0.332743i	0.520884	+	0.853627i	$0.325602\pi$
$954$	−21916.0	−	12653.2i	−0.743769	−	0.429415i
$955$	13834.5	+	21047.6i	0.468769	+	0.713176i
$956$	−3854.80	−	6676.72i	−0.130411	−	0.225879i
$957$	9932.39	+	37068.2i	0.335495	+	1.25208i
$958$	9767.04	+	9767.04i	0.329393	+	0.329393i
$959$		0			0
$960$	−26772.3	+	30066.3i	−0.900075	+	1.01082i
$961$	−14541.3	+	25186.4i	−0.488112	+	0.845435i
$962$	−1715.99	−	459.799i	−0.0575112	−	0.0154101i
$963$	−37053.3	−	9928.40i	−1.23990	−	0.332231i
$964$	4567.46	−	7911.07i	0.152602	−	0.264314i
$965$	23150.1	−	25998.5i	0.772256	−	0.867275i
$966$		0			0
$967$	−15607.2	−	15607.2i	−0.519021	−	0.519021i	0.398254	−	0.917275i	$-0.369616\pi$
$967$	−15607.2	−	15607.2i	−0.519021	−	0.519021i	−0.917275	+	0.398254i	$0.869616\pi$
$968$	−4268.32	−	15929.6i	−0.141724	−	0.528922i
$969$	4120.68	+	7137.23i	0.136610	+	0.236616i
$970$	16383.5	+	24925.6i	0.542313	+	0.825064i
$971$	−22435.1	−	12952.9i	−0.741479	−	0.428093i	0.0811279	−	0.996704i	$-0.474148\pi$
$971$	−22435.1	−	12952.9i	−0.741479	−	0.428093i	−0.822607	+	0.568611i	$0.807481\pi$
$972$	15594.1	−	15594.1i	0.514590	−	0.514590i
$973$		0			0
$974$		−	6618.87i		−	0.217744i
$975$	13495.8	+	5830.75i	0.443294	+	0.191521i
$976$	149.668	−	86.4108i	0.00490856	−	0.00283396i
$977$	−5496.82	+	20514.4i	−0.179999	+	0.671764i	0.815647	+	0.578549i	$0.196381\pi$
$977$	−5496.82	+	20514.4i	−0.179999	+	0.671764i	−0.995646	+	0.0932148i	$0.970286\pi$
$978$	−59160.5	+	15852.0i	−1.93430	+	0.518294i
$979$	−5229.18			−0.170710
$980$		0			0
$981$	63726.5			2.07404
$982$	−5988.97	+	1604.74i	−0.194619	+	0.0521479i
$983$	−4217.24	+	15739.0i	−0.136835	+	0.510676i	0.863148	+	0.504950i	$0.168489\pi$
$983$	−4217.24	+	15739.0i	−0.136835	+	0.510676i	−0.999984	+	0.00572567i	$0.998177\pi$
$984$	26186.3	−	15118.6i	0.848361	−	0.489802i
$985$	54561.3	−	18062.2i	1.76494	−	0.584274i
$986$			3104.26i			0.100264i
$987$		0			0
$988$	3390.53	−	3390.53i	0.109177	−	0.109177i
$989$	−7267.73	−	4196.03i	−0.233671	−	0.134910i
$990$	31759.4	+	6567.32i	1.01957	+	0.210831i
$991$	28721.6	+	49747.3i	0.920658	+	1.59463i	0.798399	+	0.602129i	$0.205681\pi$
$991$	28721.6	+	49747.3i	0.920658	+	1.59463i	0.122259	+	0.992498i	$0.460986\pi$
$992$	−1192.83	−	4451.71i	−0.0381779	−	0.142482i
$993$	−45990.4	−	45990.4i	−1.46975	−	1.46975i
$994$		0			0
$995$	55266.2	−	3202.92i	1.76086	−	0.102050i
$996$	13759.0	−	23831.4i	0.437723	−	0.758158i
$997$	−21758.6	−	5830.20i	−0.691175	−	0.185200i	−0.103901	−	0.994588i	$-0.533132\pi$
$997$	−21758.6	−	5830.20i	−0.691175	−	0.185200i	−0.587274	+	0.809388i	$0.699799\pi$
$998$	34318.8	+	9195.70i	1.08852	+	0.291668i
$999$	12763.9	−	22107.8i	0.404238	−	0.700160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.l.b.117.3		32
5.3	odd	4	inner	245.4.l.b.68.5		32
7.2	even	3		35.4.f.b.27.5	yes	16
7.3	odd	6	inner	245.4.l.b.227.5		32
7.4	even	3	inner	245.4.l.b.227.6		32
7.5	odd	6		35.4.f.b.27.6	yes	16
7.6	odd	2	inner	245.4.l.b.117.4		32
35.2	odd	12		175.4.f.g.118.3		16
35.3	even	12	inner	245.4.l.b.178.3		32
35.9	even	6		175.4.f.g.132.4		16
35.12	even	12		175.4.f.g.118.4		16
35.13	even	4	inner	245.4.l.b.68.6		32
35.18	odd	12	inner	245.4.l.b.178.4		32
35.19	odd	6		175.4.f.g.132.3		16
35.23	odd	12		35.4.f.b.13.6	yes	16
35.33	even	12		35.4.f.b.13.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.f.b.13.5	✓	16	35.33	even	12
35.4.f.b.13.6	yes	16	35.23	odd	12
35.4.f.b.27.5	yes	16	7.2	even	3
35.4.f.b.27.6	yes	16	7.5	odd	6
175.4.f.g.118.3		16	35.2	odd	12
175.4.f.g.118.4		16	35.12	even	12
175.4.f.g.132.3		16	35.19	odd	6
175.4.f.g.132.4		16	35.9	even	6
245.4.l.b.68.5		32	5.3	odd	4	inner
245.4.l.b.68.6		32	35.13	even	4	inner
245.4.l.b.117.3		32	1.1	even	1	trivial
245.4.l.b.117.4		32	7.6	odd	2	inner
245.4.l.b.178.3		32	35.3	even	12	inner
245.4.l.b.178.4		32	35.18	odd	12	inner
245.4.l.b.227.5		32	7.3	odd	6	inner
245.4.l.b.227.6		32	7.4	even	3	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.80016 + 0.482353i) q^{2} +(-2.44552 + 9.12679i) q^{3} +(-3.92027 + 2.26337i) q^{4} +(-5.02060 + 9.98967i) q^{5} -17.6093i q^{6} +(16.5079 - 16.5079i) q^{8} +(-53.9351 - 31.1395i) q^{9} +O(q^{10})\)	\(q+(-1.80016 + 0.482353i) q^{2} +(-2.44552 + 9.12679i) q^{3} +(-3.92027 + 2.26337i) q^{4} +(-5.02060 + 9.98967i) q^{5} -17.6093i q^{6} +(16.5079 - 16.5079i) q^{8} +(-53.9351 - 31.1395i) q^{9} +(4.21937 - 20.4048i) q^{10} +(-12.4959 - 21.6436i) q^{11} +(-11.0702 - 41.3147i) q^{12} +(8.80162 + 8.80162i) q^{13} +(-78.8957 - 70.2519i) q^{15} +(-3.64732 + 6.31735i) q^{16} +(-9.90033 - 2.65279i) q^{17} +(112.112 + 30.0404i) q^{18} +(-42.5490 + 73.6970i) q^{19} +(-2.92819 - 50.5258i) q^{20} +(32.9346 + 32.9346i) q^{22} +(6.92268 + 25.8358i) q^{23} +(110.294 + 191.034i) q^{24} +(-74.5871 - 100.308i) q^{25} +(-20.0899 - 11.5989i) q^{26} +(235.708 - 235.708i) q^{27} +162.511i q^{29} +(175.911 + 88.4095i) q^{30} +(-23.0483 + 13.3070i) q^{31} +(-44.8199 + 167.270i) q^{32} +(228.096 - 61.1181i) q^{33} +19.1018 q^{34} +281.921 q^{36} +(73.9723 - 19.8208i) q^{37} +(41.0472 - 153.190i) q^{38} +(-101.855 + 58.8061i) q^{39} +(82.0288 + 247.788i) q^{40} -137.076i q^{41} +(-221.858 + 221.858i) q^{43} +(97.9751 + 56.5659i) q^{44} +(581.860 - 382.455i) q^{45} +(-24.9239 - 43.1695i) q^{46} +(-84.1770 - 314.153i) q^{47} +(-48.7375 - 48.7375i) q^{48} +(182.653 + 144.594i) q^{50} +(48.4229 - 83.8709i) q^{51} +(-54.4261 - 14.5834i) q^{52} +(-210.603 - 56.4309i) q^{53} +(-310.619 + 538.008i) q^{54} +(278.950 - 16.1664i) q^{55} +(-568.563 - 568.563i) q^{57} +(-78.3878 - 292.547i) q^{58} +(342.874 + 593.875i) q^{59} +(468.299 + 96.8366i) q^{60} +(-20.5175 - 11.8458i) q^{61} +(35.0721 - 35.0721i) q^{62} -381.090i q^{64} +(-132.115 + 43.7359i) q^{65} +(-381.130 + 220.045i) q^{66} +(220.609 - 823.325i) q^{67} +(44.8163 - 12.0085i) q^{68} -252.727 q^{69} +265.331 q^{71} +(-1404.40 + 376.308i) q^{72} +(222.936 - 832.009i) q^{73} +(-123.602 + 71.3614i) q^{74} +(1097.90 - 435.435i) q^{75} -385.216i q^{76} +(154.991 - 154.991i) q^{78} +(125.680 + 72.5612i) q^{79} +(-44.7965 - 68.1525i) q^{80} +(734.067 + 1271.44i) q^{81} +(66.1190 + 246.760i) q^{82} +(454.928 + 454.928i) q^{83} +(76.2061 - 85.5825i) q^{85} +(292.367 - 506.395i) q^{86} +(-1483.21 - 397.425i) q^{87} +(-563.572 - 151.009i) q^{88} +(104.617 - 181.203i) q^{89} +(-862.965 + 969.144i) q^{90} +(-85.6148 - 85.6148i) q^{92} +(-65.0848 - 242.900i) q^{93} +(303.065 + 524.924i) q^{94} +(-522.587 - 795.053i) q^{95} +(-1417.03 - 818.123i) q^{96} +(-1012.24 + 1012.24i) q^{97} +1556.47i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} + 352 q^{8}+O(q^{10}) \) 32 * q - 4 * q^2 + 352 * q^8	\( 32 q - 4 q^{2} + 352 q^{8} + 152 q^{11} - 960 q^{15} + 504 q^{16} - 288 q^{18} + 696 q^{22} + 72 q^{23} + 160 q^{25} - 1780 q^{30} - 432 q^{32} + 688 q^{36} + 256 q^{37} - 624 q^{43} + 1856 q^{46} - 40 q^{50} - 696 q^{51} - 1768 q^{53} - 7840 q^{57} + 4764 q^{58} + 2000 q^{60} + 1000 q^{65} - 4504 q^{67} + 12736 q^{71} - 7848 q^{72} + 10680 q^{78} + 3088 q^{81} - 4560 q^{85} + 9336 q^{86} + 2048 q^{88} - 12656 q^{92} + 3960 q^{93} - 1240 q^{95}+O(q^{100}) \) 32 * q - 4 * q^2 + 352 * q^8 + 152 * q^11 - 960 * q^15 + 504 * q^16 - 288 * q^18 + 696 * q^22 + 72 * q^23 + 160 * q^25 - 1780 * q^30 - 432 * q^32 + 688 * q^36 + 256 * q^37 - 624 * q^43 + 1856 * q^46 - 40 * q^50 - 696 * q^51 - 1768 * q^53 - 7840 * q^57 + 4764 * q^58 + 2000 * q^60 + 1000 * q^65 - 4504 * q^67 + 12736 * q^71 - 7848 * q^72 + 10680 * q^78 + 3088 * q^81 - 4560 * q^85 + 9336 * q^86 + 2048 * q^88 - 12656 * q^92 + 3960 * q^93 - 1240 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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