LMFDB - Embedded newform 975.2.bn.d.218.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(218,975)] 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("975.218"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,2,0,0,-12,12,0,0,0,0,12,24,0,0,16,0,0,0,0,0,-20,0,0,0,0, 32,36,0,0,0,0,-30,0,0,-4,84,0,0,0,0,48,-8,0,0,0,0,28,0,0,-16,-28,0,0,0, 0,0,-84,0,0,-32,0,-90,0,0,0,-36,0,0,0,0,-90,0,0,0,72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(76)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			218.9
Character	$\chi$	$=$	975.218
Dual form			975.2.bn.d.407.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.01047 - 0.270756i) q^{2} +(0.981641 + 1.42702i) q^{3} +(-0.784302 - 0.452817i) q^{4} +(-0.605549 - 1.70775i) q^{6} +(-0.396013 + 0.106111i) q^{7} +(2.14935 + 2.14935i) q^{8} +(-1.07276 + 2.80164i) q^{9} +(-0.440197 - 0.762444i) q^{11} +(-0.123725 - 1.56372i) q^{12} +(-0.187578 + 3.60067i) q^{13} +0.428892 q^{14} +(-0.684279 - 1.18521i) q^{16} +(-2.55774 + 0.685345i) q^{17} +(1.84256 - 2.54053i) q^{18} +(1.91991 - 3.32538i) q^{19} +(-0.540166 - 0.460955i) q^{21} +(0.238372 + 0.889616i) q^{22} +(-3.37426 - 0.904132i) q^{23} +(-0.957273 + 5.17705i) q^{24} +(1.16444 - 3.58759i) q^{26} +(-5.05106 + 1.21935i) q^{27} +(0.358643 + 0.0960982i) q^{28} +(-2.13030 - 3.68979i) q^{29} +7.83820i q^{31} +(-1.20289 - 4.48924i) q^{32} +(0.655906 - 1.37662i) q^{33} +2.77009 q^{34} +(2.11000 - 1.71157i) q^{36} +(-1.79187 + 6.68733i) q^{37} +(-2.84038 + 2.84038i) q^{38} +(-5.32235 + 3.26689i) q^{39} +(-2.14922 - 3.72255i) q^{41} +(0.421017 + 0.612036i) q^{42} +(9.78689 - 2.62239i) q^{43} +0.797316i q^{44} +(3.16481 + 1.82720i) q^{46} +(-8.73570 + 8.73570i) q^{47} +(1.01960 - 2.13993i) q^{48} +(-5.91661 + 3.41596i) q^{49} +(-3.48878 - 2.97718i) q^{51} +(1.77756 - 2.73907i) q^{52} +(-4.55030 + 4.55030i) q^{53} +(5.43411 + 0.135481i) q^{54} +(-1.07924 - 0.623101i) q^{56} +(6.63004 - 0.524583i) q^{57} +(1.15358 + 4.30522i) q^{58} +(-3.44655 - 1.98987i) q^{59} +(-1.37989 + 2.39004i) q^{61} +(2.12224 - 7.92030i) q^{62} +(0.127543 - 1.22332i) q^{63} +7.59907i q^{64} +(-1.03550 + 1.21344i) q^{66} +(1.47705 - 5.51244i) q^{67} +(2.31638 + 0.620672i) q^{68} +(-2.02210 - 5.70267i) q^{69} +(-1.91546 + 3.31767i) q^{71} +(-8.32745 + 3.71596i) q^{72} +(-11.1297 + 11.1297i) q^{73} +(3.62127 - 6.27222i) q^{74} +(-3.01158 + 1.73874i) q^{76} +(0.255228 + 0.255228i) q^{77} +(6.26263 - 1.86004i) q^{78} -1.92220i q^{79} +(-6.69836 - 6.01099i) q^{81} +(1.16382 + 4.34345i) q^{82} +(-9.67699 - 9.67699i) q^{83} +(0.214925 + 0.606124i) q^{84} -10.5994 q^{86} +(3.17421 - 6.66202i) q^{87} +(0.692621 - 2.58490i) q^{88} +(1.54079 - 0.889574i) q^{89} +(-0.307789 - 1.44582i) q^{91} +(2.23704 + 2.23704i) q^{92} +(-11.1853 + 7.69430i) q^{93} +(11.1924 - 6.46196i) q^{94} +(5.22543 - 6.12337i) q^{96} +(-3.99780 + 1.07121i) q^{97} +(6.90347 - 1.84978i) q^{98} +(2.60832 - 0.415352i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) $ 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.01047	−	0.270756i	−0.714513	−	0.191453i	−0.116791	−	0.993157i	$-0.537261\pi$
$2$	−1.01047	−	0.270756i	−0.714513	−	0.191453i	−0.597722	+	0.801703i	$0.703927\pi$
$3$	0.981641	+	1.42702i	0.566751	+	0.823889i
$3$	0.981641	+	1.42702i	0.566751	+	0.823889i
$4$	−0.784302	−	0.452817i	−0.392151	−	0.226409i
$5$		0			0
$5$		0			0
$6$	−0.605549	−	1.70775i	−0.247214	−	0.697186i
$7$	−0.396013	+	0.106111i	−0.149679	+	0.0401064i	−0.332881	−	0.942969i	$-0.608021\pi$
$7$	−0.396013	+	0.106111i	−0.149679	+	0.0401064i	0.183202	+	0.983075i	$0.441354\pi$
$8$	2.14935	+	2.14935i	0.759910	+	0.759910i
$9$	−1.07276	+	2.80164i	−0.357588	+	0.933880i
$10$		0			0
$11$	−0.440197	−	0.762444i	−0.132725	−	0.229886i	0.792001	−	0.610519i	$-0.209039\pi$
$11$	−0.440197	−	0.762444i	−0.132725	−	0.229886i	−0.924726	+	0.380634i	$0.875706\pi$
$12$	−0.123725	−	1.56372i	−0.0357162	−	0.451406i
$13$	−0.187578	+	3.60067i	−0.0520249	+	0.998646i
$13$	−0.187578	+	3.60067i	−0.0520249	+	0.998646i
$14$	0.428892			0.114626
$15$		0			0
$16$	−0.684279	−	1.18521i	−0.171070	−	0.296302i
$17$	−2.55774	+	0.685345i	−0.620344	+	0.166221i	−0.555284	−	0.831661i	$-0.687390\pi$
$17$	−2.55774	+	0.685345i	−0.620344	+	0.166221i	−0.0650597	+	0.997881i	$0.520724\pi$
$18$	1.84256	−	2.54053i	0.434295	−	0.598808i
$19$	1.91991	−	3.32538i	0.440458	−	0.762895i	−0.557266	−	0.830334i	$-0.688150\pi$
$19$	1.91991	−	3.32538i	0.440458	−	0.762895i	0.997723	+	0.0674392i	$0.0214829\pi$
$20$		0			0
$21$	−0.540166	−	0.460955i	−0.117874	−	0.100589i
$22$	0.238372	+	0.889616i	0.0508211	+	0.189667i
$23$	−3.37426	−	0.904132i	−0.703583	−	0.188524i	−0.110748	−	0.993849i	$-0.535325\pi$
$23$	−3.37426	−	0.904132i	−0.703583	−	0.188524i	−0.592835	+	0.805324i	$0.701991\pi$
$24$	−0.957273	+	5.17705i	−0.195402	+	1.05676i
$25$		0			0
$26$	1.16444	−	3.58759i	0.228366	−	0.703585i
$27$	−5.05106	+	1.21935i	−0.972077	+	0.234664i
$28$	0.358643	+	0.0960982i	0.0677772	+	0.0181609i
$29$	−2.13030	−	3.68979i	−0.395587	−	0.685176i	0.597589	−	0.801802i	$-0.296125\pi$
$29$	−2.13030	−	3.68979i	−0.395587	−	0.685176i	−0.993176	+	0.116626i	$0.962792\pi$
$30$		0			0
$31$			7.83820i			1.40778i	0.710308	+	0.703891i	$0.248556\pi$
$31$			7.83820i			1.40778i	−0.710308	+	0.703891i	$0.751444\pi$
$32$	−1.20289	−	4.48924i	−0.212643	−	0.793593i
$33$	0.655906	−	1.37662i	0.114179	−	0.239638i
$34$	2.77009			0.475067
$35$		0			0
$36$	2.11000	−	1.71157i	0.351667	−	0.285261i
$37$	−1.79187	+	6.68733i	−0.294581	+	1.09939i	0.646969	+	0.762517i	$0.276036\pi$
$37$	−1.79187	+	6.68733i	−0.294581	+	1.09939i	−0.941550	+	0.336874i	$0.890630\pi$
$38$	−2.84038	+	2.84038i	−0.460771	+	0.460771i
$39$	−5.32235	+	3.26689i	−0.852259	+	0.523120i
$40$		0			0
$41$	−2.14922	−	3.72255i	−0.335651	−	0.581365i	0.647958	−	0.761676i	$-0.275623\pi$
$41$	−2.14922	−	3.72255i	−0.335651	−	0.581365i	−0.983610	+	0.180311i	$0.942290\pi$
$42$	0.421017	+	0.612036i	0.0649644	+	0.0944392i
$43$	9.78689	−	2.62239i	1.49249	−	0.399911i	0.581911	−	0.813253i	$-0.302305\pi$
$43$	9.78689	−	2.62239i	1.49249	−	0.399911i	0.910576	+	0.413342i	$0.135639\pi$
$44$			0.797316i			0.120200i
$45$		0			0
$46$	3.16481	+	1.82720i	0.466625	+	0.269406i
$47$	−8.73570	+	8.73570i	−1.27423	+	1.27423i	−0.330388	+	0.943845i	$0.607180\pi$
$47$	−8.73570	+	8.73570i	−1.27423	+	1.27423i	−0.943845	+	0.330388i	$0.892820\pi$
$48$	1.01960	−	2.13993i	0.147166	−	0.308872i
$49$	−5.91661	+	3.41596i	−0.845230	+	0.487994i
$50$		0			0
$51$	−3.48878	−	2.97718i	−0.488527	−	0.416889i
$52$	1.77756	−	2.73907i	0.246504	−	0.379841i
$53$	−4.55030	+	4.55030i	−0.625032	+	0.625032i	−0.946814	−	0.321782i	$-0.895718\pi$
$53$	−4.55030	+	4.55030i	−0.625032	+	0.625032i	0.321782	+	0.946814i	$0.395718\pi$
$54$	5.43411	+	0.135481i	0.739488	+	0.0184367i
$55$		0			0
$56$	−1.07924	−	0.623101i	−0.144220	−	0.0832654i
$57$	6.63004	−	0.524583i	0.878171	−	0.0694827i
$58$	1.15358	+	4.30522i	0.151473	+	0.565304i
$59$	−3.44655	−	1.98987i	−0.448703	−	0.259059i	0.258579	−	0.965990i	$-0.416746\pi$
$59$	−3.44655	−	1.98987i	−0.448703	−	0.259059i	−0.707282	+	0.706931i	$0.750079\pi$
$60$		0			0
$61$	−1.37989	+	2.39004i	−0.176677	+	0.306014i	−0.940740	−	0.339128i	$-0.889868\pi$
$61$	−1.37989	+	2.39004i	−0.176677	+	0.306014i	0.764063	+	0.645141i	$0.223202\pi$
$62$	2.12224	−	7.92030i	0.269524	−	1.00588i
$63$	0.127543	−	1.22332i	0.0160689	−	0.154124i
$64$			7.59907i			0.949883i
$65$		0			0
$66$	−1.03550	+	1.21344i	−0.127462	+	0.149365i
$67$	1.47705	−	5.51244i	0.180451	−	0.673452i	−0.815108	−	0.579309i	$-0.803322\pi$
$67$	1.47705	−	5.51244i	0.180451	−	0.673452i	0.995559	−	0.0941427i	$-0.0300110\pi$
$68$	2.31638	+	0.620672i	0.280902	+	0.0752675i
$69$	−2.02210	−	5.70267i	−0.243433	−	0.686521i
$70$		0			0
$71$	−1.91546	+	3.31767i	−0.227323	+	0.393734i	−0.957014	−	0.290042i	$-0.906331\pi$
$71$	−1.91546	+	3.31767i	−0.227323	+	0.393734i	0.729691	+	0.683777i	$0.239664\pi$
$72$	−8.32745	+	3.71596i	−0.981399	+	0.437930i
$73$	−11.1297	+	11.1297i	−1.30264	+	1.30264i	−0.376028	+	0.926608i	$0.622710\pi$
$73$	−11.1297	+	11.1297i	−1.30264	+	1.30264i	−0.926608	+	0.376028i	$0.877290\pi$
$74$	3.62127	−	6.27222i	0.420964	−	0.729131i
$75$		0			0
$76$	−3.01158	+	1.73874i	−0.345452	+	0.199447i
$77$	0.255228	+	0.255228i	0.0290860	+	0.0290860i
$78$	6.26263	−	1.86004i	0.709103	−	0.210609i
$79$		−	1.92220i		−	0.216264i	−0.994137	−	0.108132i	$-0.965513\pi$
$79$		−	1.92220i		−	0.216264i	0.994137	−	0.108132i	$-0.0344870\pi$
$80$		0			0
$81$	−6.69836	−	6.01099i	−0.744262	−	0.667888i
$82$	1.16382	+	4.34345i	0.128523	+	0.479654i
$83$	−9.67699	−	9.67699i	−1.06219	−	1.06219i	−0.997934	−	0.0642539i	$-0.979533\pi$
$83$	−9.67699	−	9.67699i	−1.06219	−	1.06219i	−0.0642539	−	0.997934i	$-0.520467\pi$
$84$	0.214925	+	0.606124i	0.0234502	+	0.0661336i
$85$		0			0
$86$	−10.5994			−1.14296
$87$	3.17421	−	6.66202i	0.340311	−	0.714244i
$88$	0.692621	−	2.58490i	0.0738337	−	0.275551i
$89$	1.54079	−	0.889574i	0.163323	−	0.0942947i	−0.416111	−	0.909314i	$-0.636607\pi$
$89$	1.54079	−	0.889574i	0.163323	−	0.0942947i	0.579434	+	0.815019i	$0.303274\pi$
$90$		0			0
$91$	−0.307789	−	1.44582i	−0.0322650	−	0.151563i
$92$	2.23704	+	2.23704i	0.233227	+	0.233227i
$93$	−11.1853	+	7.69430i	−1.15986	+	0.797861i
$94$	11.1924	−	6.46196i	1.15441	−	0.666500i
$95$		0			0
$96$	5.22543	−	6.12337i	0.533318	−	0.624963i
$97$	−3.99780	+	1.07121i	−0.405916	+	0.108765i	−0.455999	−	0.889980i	$-0.650718\pi$
$97$	−3.99780	+	1.07121i	−0.405916	+	0.108765i	0.0500834	+	0.998745i	$0.484051\pi$
$98$	6.90347	−	1.84978i	0.697356	−	0.186856i
$99$	2.60832	−	0.415352i	0.262146	−	0.0417445i
$100$		0			0
$101$	0.815875	−	0.471046i	0.0811826	−	0.0468708i	−0.458859	−	0.888509i	$-0.651742\pi$
$101$	0.815875	−	0.471046i	0.0811826	−	0.0468708i	0.540042	+	0.841638i	$0.318408\pi$
$102$	2.71924	+	3.95297i	0.269244	+	0.391403i
$103$	−4.29455	−	4.29455i	−0.423154	−	0.423154i	0.463134	−	0.886288i	$-0.346725\pi$
$103$	−4.29455	−	4.29455i	−0.423154	−	0.423154i	−0.886288	+	0.463134i	$0.846725\pi$
$104$	−8.14227	+	7.33593i	−0.798415	+	0.719347i
$105$		0			0
$106$	5.82998	−	3.36594i	0.566258	−	0.326929i
$107$	0.548581	−	2.04733i	0.0530334	−	0.197923i	−0.934326	−	0.356419i	$-0.883998\pi$
$107$	0.548581	−	2.04733i	0.0530334	−	0.197923i	0.987360	+	0.158495i	$0.0506643\pi$
$108$	4.51370	+	1.33087i	0.434331	+	0.128063i
$109$	8.75477			0.838555			0.419277	−	0.907858i	$-0.362283\pi$
$109$	8.75477			0.838555			0.419277	+	0.907858i	$0.362283\pi$
$110$		0			0
$111$	−11.3019	+	4.00753i	−1.07273	+	0.380378i
$112$	0.396748	+	0.396748i	0.0374891	+	0.0374891i
$113$	−0.382672	−	1.42815i	−0.0359988	−	0.134349i	0.945588	−	0.325367i	$-0.105488\pi$
$113$	−0.382672	−	1.42815i	−0.0359988	−	0.134349i	−0.981587	+	0.191018i	$0.938821\pi$
$114$	−6.84152	−	1.26504i	−0.640767	−	0.118482i
$115$		0			0
$116$			3.85854i			0.358257i
$117$	−9.88655	−	4.38819i	−0.914011	−	0.405688i
$118$	2.94388	+	2.94388i	0.271006	+	0.271006i
$119$	0.940178	−	0.542812i	0.0861859	−	0.0497595i
$120$		0			0
$121$	5.11245	−	8.85503i	0.464768	−	0.805002i
$122$	2.04146	−	2.04146i	0.184825	−	0.184825i
$123$	3.20239	−	6.72118i	0.288750	−	0.606028i
$124$	3.54927	−	6.14752i	0.318734	−	0.552063i
$125$		0			0
$126$	−0.460099	+	1.20160i	−0.0409889	+	0.107047i
$127$	12.3168	+	3.30028i	1.09294	+	0.292852i	0.759887	−	0.650055i	$-0.225254\pi$
$127$	12.3168	+	3.30028i	1.09294	+	0.292852i	0.333054	+	0.942908i	$0.391921\pi$
$128$	−0.348287	+	1.29983i	−0.0307845	+	0.114889i
$129$	13.3494	+	11.3918i	1.17535	+	1.00299i
$130$		0			0
$131$			14.4459i			1.26214i	0.775725	+	0.631071i	$0.217384\pi$
$131$			14.4459i			1.26214i	−0.775725	+	0.631071i	$0.782616\pi$
$132$	−1.13778	+	0.782678i	−0.0990314	+	0.0681233i
$133$	−0.407449	+	1.52062i	−0.0353303	+	0.131855i
$134$	−2.98505	+	5.17026i	−0.257869	+	0.446642i
$135$		0			0
$136$	−6.97053	−	4.02444i	−0.597718	−	0.345093i
$137$	4.47333	+	16.6947i	0.382183	+	1.42633i	0.842560	+	0.538602i	$0.181047\pi$
$137$	4.47333	+	16.6947i	0.382183	+	1.42633i	−0.460378	+	0.887723i	$0.652286\pi$
$138$	0.499252	+	6.30989i	0.0424992	+	0.537134i
$139$	−7.96426	−	4.59817i	−0.675520	−	0.390012i	0.122645	−	0.992451i	$-0.460862\pi$
$139$	−7.96426	−	4.59817i	−0.675520	−	0.390012i	−0.798165	+	0.602439i	$0.794196\pi$
$140$		0			0
$141$	−21.0413	−	3.89069i	−1.77200	−	0.327655i
$142$	2.83379	−	2.83379i	0.237807	−	0.237807i
$143$	2.82788	−	1.44199i	0.236479	−	0.120585i
$144$	4.05459	−	0.645658i	0.337883	−	0.0538048i
$145$		0			0
$146$	14.2597	−	8.23286i	1.18014	−	0.681357i
$147$	−10.6826	−	5.08987i	−0.881088	−	0.419805i
$148$	4.43350	−	4.43350i	0.364432	−	0.364432i
$149$	1.47738	+	0.852967i	0.121032	+	0.0698778i	0.559294	−	0.828970i	$-0.311072\pi$
$149$	1.47738	+	0.852967i	0.121032	+	0.0698778i	−0.438262	+	0.898847i	$0.644406\pi$
$150$		0			0
$151$			17.4866i			1.42304i	0.702666	+	0.711520i	$0.251993\pi$
$151$			17.4866i			1.42304i	−0.702666	+	0.711520i	$0.748007\pi$
$152$	11.2740	−	3.02085i	0.914440	−	0.245023i
$153$	0.823763	−	7.90108i	0.0665973	−	0.638765i
$154$	−0.188797	−	0.327006i	−0.0152137	−	0.0263509i
$155$		0			0
$156$	5.65364	−	0.152172i	0.452653	−	0.0121835i
$157$	3.64849	−	3.64849i	0.291181	−	0.291181i	−0.546365	−	0.837547i	$-0.683989\pi$
$157$	3.64849	−	3.64849i	0.291181	−	0.291181i	0.837547	+	0.546365i	$0.183989\pi$
$158$	−0.520447	+	1.94233i	−0.0414045	+	0.154524i
$159$	−10.9601	−	2.02660i	−0.869194	−	0.160720i
$160$		0			0
$161$	1.43219			0.112873
$162$	5.14101	+	7.88757i	0.403916	+	0.619706i
$163$	1.33210	+	4.97146i	0.104338	+	0.389395i	0.998269	−	0.0588093i	$-0.0187304\pi$
$163$	1.33210	+	4.97146i	0.104338	+	0.389395i	−0.893931	+	0.448204i	$0.852064\pi$
$164$			3.89281i			0.303977i
$165$		0			0
$166$	7.15824	+	12.3984i	0.555588	+	0.962306i
$167$	−8.36399	−	2.24112i	−0.647225	−	0.173423i	−0.0797510	−	0.996815i	$-0.525413\pi$
$167$	−8.36399	−	2.24112i	−0.647225	−	0.173423i	−0.567474	+	0.823391i	$0.692079\pi$
$168$	−0.170252	−	2.15176i	−0.0131352	−	0.166012i
$169$	−12.9296	−	1.35081i	−0.994587	−	0.103909i
$170$		0			0
$171$	7.25691	+	8.94624i	0.554950	+	0.684136i
$172$	−8.86334	−	2.37492i	−0.675823	−	0.181086i
$173$	−3.68187	−	13.7409i	−0.279927	−	1.04470i	−0.952467	−	0.304642i	$-0.901463\pi$
$173$	−3.68187	−	13.7409i	−0.279927	−	1.04470i	0.672540	−	0.740061i	$-0.265203\pi$
$174$	−5.01123	+	5.87237i	−0.379901	+	0.445183i
$175$		0			0
$176$	−0.602436	+	1.04345i	−0.0454103	+	0.0786530i
$177$	−0.543698	−	6.87163i	−0.0408668	−	0.516503i
$178$	−1.79778	+	0.481714i	−0.134750	+	0.0361060i
$179$	9.67835	+	16.7634i	0.723394	+	1.25295i	0.959632	+	0.281259i	$0.0907521\pi$
$179$	9.67835	+	16.7634i	0.723394	+	1.25295i	−0.236238	+	0.971695i	$0.575915\pi$
$180$		0			0
$181$	24.4852			1.81997			0.909984	−	0.414644i	$-0.136094\pi$
$181$	24.4852			1.81997			0.909984	+	0.414644i	$0.136094\pi$
$182$	−0.0804508	+	1.54430i	−0.00596341	+	0.114471i
$183$	−4.76519	+	0.377032i	−0.352253	+	0.0278710i
$184$	−5.30918	−	9.19577i	−0.391398	−	0.677921i
$185$		0			0
$186$	13.3857	−	4.74641i	0.981486	−	0.348024i
$187$	1.64845	+	1.64845i	0.120547	+	0.120547i
$188$	10.8071	−	2.89576i	0.788189	−	0.211195i
$189$	1.87090	−	1.01885i	0.136088	−	0.0741107i
$190$		0			0
$191$	20.3420	+	11.7444i	1.47189	+	0.849798i	0.999501	−	0.0315908i	$-0.0100573\pi$
$191$	20.3420	+	11.7444i	1.47189	+	0.849798i	0.472392	+	0.881389i	$0.343391\pi$
$192$	−10.8440	+	7.45955i	−0.782599	+	0.538347i
$193$	−5.43240	−	1.45561i	−0.391032	−	0.104777i	0.0579453	−	0.998320i	$-0.481545\pi$
$193$	−5.43240	−	1.45561i	−0.391032	−	0.104777i	−0.448978	+	0.893543i	$0.648212\pi$
$194$	4.32971			0.310855
$195$		0			0
$196$	6.18721			0.441944
$197$	12.2140	+	3.27274i	0.870213	+	0.233173i	0.666180	−	0.745791i	$-0.267928\pi$
$197$	12.2140	+	3.27274i	0.870213	+	0.233173i	0.204033	+	0.978964i	$0.434595\pi$
$198$	−2.74810	−	0.286515i	−0.195299	−	0.0203618i
$199$	10.2770	+	5.93343i	0.728518	+	0.420610i	0.817880	−	0.575389i	$-0.195149\pi$
$199$	10.2770	+	5.93343i	0.728518	+	0.420610i	−0.0893620	+	0.995999i	$0.528483\pi$
$200$		0			0
$201$	9.31629	−	3.30345i	0.657121	−	0.233008i
$202$	−0.951959	+	0.255077i	−0.0669796	+	0.0179471i
$203$	1.23516	+	1.23516i	0.0866910	+	0.0866910i
$204$	1.38814	+	3.91479i	0.0971894	+	0.274090i
$205$		0			0
$206$	3.17676	+	5.50230i	0.221335	+	0.383364i
$207$	6.15284	−	8.48355i	0.427652	−	0.589648i
$208$	4.39589	−	2.24154i	0.304800	−	0.155423i
$209$	−3.38056			−0.233838
$210$		0			0
$211$	3.11693	+	5.39868i	0.214578	+	0.371661i	0.953142	−	0.302523i	$-0.0978289\pi$
$211$	3.11693	+	5.39868i	0.214578	+	0.371661i	−0.738564	+	0.674184i	$0.764496\pi$
$212$	5.62927	−	1.50836i	0.386620	−	0.103594i
$213$	−6.61466	+	0.523366i	−0.453229	+	0.0358604i
$214$	−1.10865	+	1.92025i	−0.0757861	+	0.131265i
$215$		0			0
$216$	−13.4773	−	8.23568i	−0.917014	−	0.560367i
$217$	−0.831723	−	3.10403i	−0.0564610	−	0.210715i
$218$	−8.84647	−	2.37040i	−0.599158	−	0.160544i
$219$	−26.8077	−	4.95693i	−1.81150	−	0.334959i
$220$		0			0
$221$	−1.98792	−	9.33814i	−0.133722	−	0.628151i
$222$	12.5054	−	0.989450i	0.839304	−	0.0664075i
$223$	−2.19220	−	0.587397i	−0.146800	−	0.0393350i	0.184671	−	0.982800i	$-0.440878\pi$
$223$	−2.19220	−	0.587397i	−0.146800	−	0.0393350i	−0.331471	+	0.943465i	$0.607545\pi$
$224$	0.952720	+	1.65016i	0.0636563	+	0.110256i
$225$		0			0
$226$			1.54672i			0.102886i
$227$	2.38781	+	8.91142i	0.158484	+	0.591472i	0.998782	+	0.0493459i	$0.0157137\pi$
$227$	2.38781	+	8.91142i	0.158484	+	0.591472i	−0.840297	+	0.542126i	$0.817620\pi$
$228$	−5.43750	−	2.59077i	−0.360107	−	0.171578i
$229$	17.3079			1.14374			0.571869	−	0.820345i	$-0.306218\pi$
$229$	17.3079			1.14374			0.571869	+	0.820345i	$0.306218\pi$
$230$		0			0
$231$	−0.113673	+	0.614758i	−0.00747913	+	0.0404481i
$232$	3.35189	−	12.5094i	0.220062	−	0.821283i
$233$	14.0715	−	14.0715i	0.921854	−	0.921854i	−0.0753068	−	0.997160i	$-0.523994\pi$
$233$	14.0715	−	14.0715i	0.921854	−	0.921854i	0.997160	+	0.0753068i	$0.0239936\pi$
$234$	8.80197	+	7.11099i	0.575403	+	0.464860i
$235$		0			0
$236$	1.80209	+	3.12132i	0.117306	+	0.203180i
$237$	2.74302	−	1.88691i	0.178178	−	0.122568i
$238$	−1.09699	+	0.293939i	−0.0711076	+	0.0190532i
$239$		−	13.6042i		−	0.879984i	−0.898002	−	0.439992i	$-0.854981\pi$
$239$		−	13.6042i		−	0.879984i	0.898002	−	0.439992i	$-0.145019\pi$
$240$		0			0
$241$	−16.3605	−	9.44575i	−1.05387	−	0.608454i	−0.130142	−	0.991495i	$-0.541543\pi$
$241$	−16.3605	−	9.44575i	−1.05387	−	0.608454i	−0.923731	+	0.383041i	$0.874877\pi$
$242$	−7.56355	+	7.56355i	−0.486203	+	0.486203i
$243$	2.00241	−	15.4593i	0.128455	−	0.991715i
$244$	2.16451	−	1.24968i	0.138568	−	0.0800024i
$245$		0			0
$246$	−5.05573	+	5.92451i	−0.322342	+	0.377733i
$247$	11.6135	+	7.53673i	0.738947	+	0.479551i
$248$	−16.8470	+	16.8470i	−1.06979	+	1.06979i
$249$	4.30992	−	23.3086i	0.273130	−	1.47712i
$250$		0			0
$251$	−13.2104	−	7.62703i	−0.833833	−	0.481414i	0.0213304	−	0.999772i	$-0.493210\pi$
$251$	−13.2104	−	7.62703i	−0.833833	−	0.481414i	−0.855163	+	0.518359i	$0.826543\pi$
$252$	−0.653972	+	0.901698i	−0.0411963	+	0.0568017i
$253$	0.795993	+	2.97069i	0.0500436	+	0.186765i
$254$	−11.5522	−	6.66969i	−0.724852	−	0.418494i
$255$		0			0
$256$	8.30294	−	14.3811i	0.518934	−	0.898819i
$257$	7.53822	−	28.1330i	0.470221	−	1.75489i	−0.168751	−	0.985659i	$-0.553973\pi$
$257$	7.53822	−	28.1330i	0.470221	−	1.75489i	0.638972	−	0.769230i	$-0.279360\pi$
$258$	−10.4048	−	15.1256i	−0.647776	−	0.941677i
$259$		−	2.83841i		−	0.176370i
$260$		0			0
$261$	12.6228	−	2.01006i	0.781329	−	0.124420i
$262$	3.91130	−	14.5972i	0.241641	−	0.901816i
$263$	18.9951	+	5.08972i	1.17129	+	0.313845i	0.791465	−	0.611214i	$-0.209319\pi$
$263$	18.9951	+	5.08972i	1.17129	+	0.313845i	0.379822	+	0.925060i	$0.375985\pi$
$264$	4.36860	−	1.54906i	0.268869	−	0.0953379i
$265$		0			0
$266$	0.823433	−	1.42623i	0.0504879	−	0.0874477i
$267$	2.78194	+	1.32549i	0.170252	+	0.0811187i
$268$	−3.65458	+	3.65458i	−0.223239	+	0.223239i
$269$	15.6000	−	27.0200i	0.951148	−	1.64744i	0.208201	−	0.978086i	$-0.433239\pi$
$269$	15.6000	−	27.0200i	0.951148	−	1.64744i	0.742947	−	0.669350i	$-0.233427\pi$
$270$		0			0
$271$	12.3700	−	7.14185i	0.751427	−	0.433836i	−0.0747824	−	0.997200i	$-0.523826\pi$
$271$	12.3700	−	7.14185i	0.751427	−	0.433836i	0.826209	+	0.563363i	$0.190493\pi$
$272$	2.56249	+	2.56249i	0.155374	+	0.155374i
$273$	1.76107	−	1.85849i	0.106585	−	0.112481i
$274$		−	18.0807i		−	1.09230i
$275$		0			0
$276$	−0.996326	+	5.38826i	−0.0599718	+	0.324335i
$277$	−4.19871	−	15.6698i	−0.252276	−	0.941507i	−0.969586	−	0.244752i	$-0.921293\pi$
$277$	−4.19871	−	15.6698i	−0.252276	−	0.941507i	0.717310	−	0.696755i	$-0.245373\pi$
$278$	6.80270	+	6.80270i	0.407999	+	0.407999i
$279$	−21.9598	−	8.40853i	−1.31470	−	0.503406i
$280$		0			0
$281$	−6.00560			−0.358264			−0.179132	−	0.983825i	$-0.557329\pi$
$281$	−6.00560			−0.358264			−0.179132	+	0.983825i	$0.557329\pi$
$282$	20.2083	+	9.62850i	1.20339	+	0.573369i
$283$	−8.01173	+	29.9002i	−0.476248	+	1.77738i	0.140348	+	0.990102i	$0.455178\pi$
$283$	−8.01173	+	29.9002i	−0.476248	+	1.77738i	−0.616596	+	0.787280i	$0.711489\pi$
$284$	3.00459	−	1.73470i	0.178290	−	0.102936i
$285$		0			0
$286$	−3.24793	+	0.691426i	−0.192054	+	0.0408848i
$287$	1.24612	+	1.24612i	0.0735564	+	0.0735564i
$288$	13.8676	+	1.44583i	0.817159	+	0.0851965i
$289$	−8.65008	+	4.99413i	−0.508828	+	0.293772i
$290$		0			0
$291$	−5.45304	−	4.65340i	−0.319663	−	0.272787i
$292$	13.7688	−	3.68934i	0.805758	−	0.215902i
$293$	13.8318	−	3.70623i	0.808064	−	0.216520i	0.168943	−	0.985626i	$-0.445965\pi$
$293$	13.8318	−	3.70623i	0.808064	−	0.216520i	0.639121	+	0.769106i	$0.279298\pi$
$294$	9.41640	+	8.03556i	0.549175	+	0.468643i
$295$		0			0
$296$	−18.2248	+	10.5221i	−1.05929	+	0.611583i
$297$	3.15315	+	3.31440i	0.182964	+	0.192321i
$298$	−1.26191	−	1.26191i	−0.0731005	−	0.0731005i
$299$	3.88842	−	11.9800i	0.224873	−	0.692822i
$300$		0			0
$301$	−3.59747	+	2.07700i	−0.207355	+	0.119716i
$302$	4.73460	−	17.6698i	0.272445	−	1.01678i
$303$	1.47309	+	0.701871i	0.0846266	+	0.0403214i
$304$	−5.25502			−0.301396
$305$		0			0
$306$	−2.97165	+	7.76080i	−0.169878	+	0.443655i
$307$	12.4805	+	12.4805i	0.712300	+	0.712300i	0.967016	−	0.254716i	$-0.0819821\pi$
$307$	12.4805	+	12.4805i	0.712300	+	0.712300i	−0.254716	+	0.967016i	$0.581982\pi$
$308$	−0.0846044	−	0.315748i	−0.00482078	−	0.0179914i
$309$	1.91270	−	10.3441i	0.108809	−	0.588455i
$310$		0			0
$311$		−	13.6423i		−	0.773585i	−0.922167	−	0.386792i	$-0.873583\pi$
$311$		−	13.6423i		−	0.773585i	0.922167	−	0.386792i	$-0.126417\pi$
$312$	−18.4613	−	4.41792i	−1.04516	−	0.250116i
$313$	−2.73940	−	2.73940i	−0.154840	−	0.154840i	0.625436	−	0.780276i	$-0.284921\pi$
$313$	−2.73940	−	2.73940i	−0.154840	−	0.154840i	−0.780276	+	0.625436i	$0.784921\pi$
$314$	−4.67456	+	2.69886i	−0.263801	+	0.152305i
$315$		0			0
$316$	−0.870405	+	1.50759i	−0.0489641	+	0.0848084i
$317$	−5.58971	+	5.58971i	−0.313949	+	0.313949i	−0.846437	−	0.532488i	$-0.821257\pi$
$317$	−5.58971	+	5.58971i	−0.313949	+	0.313949i	0.532488	+	0.846437i	$0.321257\pi$
$318$	10.5262	+	5.01534i	0.590280	+	0.281247i
$319$	−1.87551	+	3.24847i	−0.105008	+	0.181879i
$320$		0			0
$321$	3.46009	−	1.22691i	0.193124	−	0.0684795i
$322$	−1.44719	−	0.387774i	−0.0806489	−	0.0216098i
$323$	−2.63160	+	9.82127i	−0.146426	+	0.546470i
$324$	2.53166	+	7.74756i	0.140648	+	0.430420i
$325$		0			0
$326$		−	5.38421i		−	0.298204i
$327$	8.59404	+	12.4932i	0.475251	+	0.690877i
$328$	3.38165	−	12.6205i	0.186720	−	0.696850i
$329$	2.53250	−	4.38641i	0.139621	−	0.241831i
$330$		0			0
$331$	5.92414	+	3.42030i	0.325620	+	0.187997i	0.653895	−	0.756585i	$-0.273134\pi$
$331$	5.92414	+	3.42030i	0.325620	+	0.187997i	−0.328275	+	0.944582i	$0.606467\pi$
$332$	3.20778	+	11.9716i	0.176050	+	0.657026i
$333$	−16.8132	−	12.1941i	−0.921360	−	0.668232i
$334$	7.84479	+	4.52919i	0.429248	+	0.247826i
$335$		0			0
$336$	−0.176703	+	0.955630i	−0.00963992	+	0.0521339i
$337$	−15.6466	+	15.6466i	−0.852323	+	0.852323i	−0.990419	−	0.138096i	$-0.955902\pi$
$337$	−15.6466	+	15.6466i	−0.852323	+	0.852323i	0.138096	+	0.990419i	$0.455902\pi$
$338$	12.6993	+	4.86573i	0.690751	+	0.264661i
$339$	1.66235	−	1.94801i	0.0902866	−	0.105802i
$340$		0			0
$341$	5.97619	−	3.45036i	0.323629	−	0.186847i
$342$	−4.91067	−	11.0048i	−0.265539	−	0.595071i
$343$	4.00990	−	4.00990i	0.216514	−	0.216514i
$344$	26.6719	+	15.3990i	1.43805	+	0.830260i
$345$		0			0
$346$			14.8817i			0.800046i
$347$	−6.13932	+	1.64503i	−0.329576	+	0.0883097i	−0.419813	−	0.907611i	$-0.637904\pi$
$347$	−6.13932	+	1.64503i	−0.329576	+	0.0883097i	0.0902367	+	0.995920i	$0.471238\pi$
$348$	−5.50621	+	3.78770i	−0.295164	+	0.203042i
$349$	2.24199	+	3.88324i	0.120011	+	0.207865i	0.919772	−	0.392454i	$-0.128374\pi$
$349$	2.24199	+	3.88324i	0.120011	+	0.207865i	−0.799761	+	0.600319i	$0.795040\pi$
$350$		0			0
$351$	−3.44301	−	18.4159i	−0.183774	−	0.982969i
$352$	−2.89329	+	2.89329i	−0.154213	+	0.154213i
$353$	−5.09337	+	19.0087i	−0.271093	+	1.01173i	0.687322	+	0.726353i	$0.258786\pi$
$353$	−5.09337	+	19.0087i	−0.271093	+	1.01173i	−0.958415	+	0.285379i	$0.907880\pi$
$354$	−1.31114	+	7.09081i	−0.0696863	+	0.376872i
$355$		0			0
$356$	−1.61126			−0.0853965
$357$	1.69752	+	0.808805i	0.0898422	+	0.0428065i
$358$	−5.24093	−	19.5594i	−0.276992	−	1.03375i
$359$			28.4889i			1.50359i	0.659399	+	0.751793i	$0.270811\pi$
$359$			28.4889i			1.50359i	−0.659399	+	0.751793i	$0.729189\pi$
$360$		0			0
$361$	2.12789	+	3.68561i	0.111994	+	0.193980i
$362$	−24.7416	−	6.62950i	−1.30039	−	0.348439i
$363$	17.6549	−	1.39689i	0.926641	−	0.0733178i
$364$	−0.413291	+	1.27333i	−0.0216624	+	0.0667406i
$365$		0			0
$366$	4.91719	+	0.909222i	0.257026	+	0.0475258i
$367$	6.74878	+	1.80833i	0.352284	+	0.0943941i	0.430621	−	0.902533i	$-0.358295\pi$
$367$	6.74878	+	1.80833i	0.352284	+	0.0943941i	−0.0783376	+	0.996927i	$0.524961\pi$
$368$	1.23736	+	4.61788i	0.0645017	+	0.240724i
$369$	12.7348	−	2.02791i	0.662950	−	0.105569i
$370$		0			0
$371$	1.31914	−	2.28482i	0.0684864	−	0.118622i
$372$	12.2567	−	0.969778i	0.635482	−	0.0502807i
$373$	12.7108	−	3.40584i	0.658139	−	0.176348i	0.0857330	−	0.996318i	$-0.472677\pi$
$373$	12.7108	−	3.40584i	0.658139	−	0.176348i	0.572406	+	0.819970i	$0.306010\pi$
$374$	−1.21939	−	2.11204i	−0.0630530	−	0.109211i
$375$		0			0
$376$	−37.5522			−1.93661
$377$	13.6853	−	6.97838i	0.704829	−	0.359405i
$378$	−2.16636	+	0.522969i	−0.111425	+	0.0268986i
$379$	3.61705	+	6.26491i	0.185795	+	0.321807i	0.943844	−	0.330391i	$-0.107181\pi$
$379$	3.61705	+	6.26491i	0.185795	+	0.321807i	−0.758049	+	0.652198i	$0.773847\pi$
$380$		0			0
$381$	7.38112	+	20.8160i	0.378146	+	1.06644i
$382$	−17.3751	−	17.3751i	−0.888990	−	0.888990i
$383$	−7.54590	+	2.02192i	−0.385578	+	0.103315i	−0.446400	−	0.894833i	$-0.647294\pi$
$383$	−7.54590	+	2.02192i	−0.385578	+	0.103315i	0.0608227	+	0.998149i	$0.480628\pi$
$384$	−2.19677	+	0.778949i	−0.112103	+	0.0397506i
$385$		0			0
$386$	5.09518	+	2.94170i	0.259338	+	0.149729i
$387$	−3.15203	+	30.2325i	−0.160227	+	1.53681i
$388$	3.62055	+	0.970123i	0.183805	+	0.0492505i
$389$	−28.6894			−1.45461			−0.727306	−	0.686314i	$-0.759228\pi$
$389$	−28.6894			−1.45461			−0.727306	+	0.686314i	$0.759228\pi$
$390$		0			0
$391$	9.25014			0.467800
$392$	−20.0590	−	5.37478i	−1.01313	−	0.271467i
$393$	−20.6145	+	14.1807i	−1.03987	+	0.715319i
$394$	−11.4558	−	6.61403i	−0.577136	−	0.333210i
$395$		0			0
$396$	−2.23379	−	0.855331i	−0.112252	−	0.0429820i
$397$	−24.4939	+	6.56311i	−1.22931	+	0.329393i	−0.814312	−	0.580428i	$-0.802885\pi$
$397$	−24.4939	+	6.56311i	−1.22931	+	0.329393i	−0.415001	+	0.909821i	$0.636219\pi$
$398$	−8.77813	−	8.77813i	−0.440008	−	0.440008i
$399$	−2.56992	+	0.911266i	−0.128657	+	0.0456203i
$400$		0			0
$401$	−10.3734	−	17.9672i	−0.518023	−	0.897241i	−0.999781	−	0.0209373i	$-0.993335\pi$
$401$	−10.3734	−	17.9672i	−0.518023	−	0.897241i	0.481758	−	0.876304i	$-0.339998\pi$
$402$	−10.3083	+	0.815614i	−0.514131	+	0.0406792i
$403$	−28.2228	−	1.47028i	−1.40588	−	0.0732397i
$404$	−0.853190			−0.0424478
$405$		0			0
$406$	−0.913668	−	1.58252i	−0.0453446	−	0.0785391i
$407$	5.88750	−	1.57755i	0.291832	−	0.0781962i
$408$	−1.09961	−	13.8976i	−0.0544388	−	0.688035i
$409$	−13.5268	+	23.4291i	−0.668856	+	1.15849i	0.309368	+	0.950942i	$0.399882\pi$
$409$	−13.5268	+	23.4291i	−0.668856	+	1.15849i	−0.978224	+	0.207550i	$0.933451\pi$
$410$		0			0
$411$	−19.4324	+	22.7717i	−0.958532	+	1.12325i
$412$	1.42358	+	5.31287i	0.0701347	+	0.261746i
$413$	1.57603	+	0.422296i	0.0775513	+	0.0207798i
$414$	−8.51425	+	6.90649i	−0.418453	+	0.339436i
$415$		0			0
$416$	16.3899	−	3.48912i	0.803581	−	0.171068i
$417$	−1.25637	−	15.8789i	−0.0615248	−	0.777593i
$418$	3.41597	+	0.915305i	0.167080	+	0.0447690i
$419$	6.46519	+	11.1980i	0.315845	+	0.547060i	0.979617	−	0.200876i	$-0.0643787\pi$
$419$	6.46519	+	11.1980i	0.315845	+	0.547060i	−0.663772	+	0.747935i	$0.731045\pi$
$420$		0			0
$421$		−	16.5986i		−	0.808966i	−0.914545	−	0.404483i	$-0.867451\pi$
$421$		−	16.5986i		−	0.808966i	0.914545	−	0.404483i	$-0.132549\pi$
$422$	−1.68785	−	6.29915i	−0.0821634	−	0.306638i
$423$	−15.1029	−	33.8456i	−0.734330	−	1.64563i
$424$	−19.5604			−0.949936
$425$		0			0
$426$	6.82564	+	1.26211i	0.330704	+	0.0611494i
$427$	0.292845	−	1.09291i	0.0141718	−	0.0528897i
$428$	−1.35732	+	1.35732i	−0.0656086	+	0.0656086i
$429$	4.83371	+	2.61993i	0.233373	+	0.126491i
$430$		0			0
$431$	10.4373	+	18.0779i	0.502745	+	0.870781i	0.999995	+	0.00317304i	$0.00101001\pi$
$431$	10.4373	+	18.0779i	0.502745	+	0.870781i	−0.497250	+	0.867608i	$0.665657\pi$
$432$	4.90152	+	5.15217i	0.235824	+	0.247884i
$433$	39.1549	−	10.4915i	1.88166	−	0.504191i	0.882221	−	0.470835i	$-0.156047\pi$
$433$	39.1549	−	10.4915i	1.88166	−	0.504191i	0.999444	−	0.0333555i	$-0.0106194\pi$
$434$			3.36174i			0.161369i
$435$		0			0
$436$	−6.86639	−	3.96431i	−0.328840	−	0.189856i
$437$	−9.48487	+	9.48487i	−0.453723	+	0.453723i
$438$	25.7464	+	12.2672i	1.23021	+	0.586149i
$439$	19.3023	−	11.1442i	0.921248	−	0.531883i	0.0372151	−	0.999307i	$-0.488151\pi$
$439$	19.3023	−	11.1442i	0.921248	−	0.531883i	0.884033	+	0.467424i	$0.154818\pi$
$440$		0			0
$441$	−3.22316	−	20.2407i	−0.153484	−	0.963844i
$442$	−0.519609	+	9.97419i	−0.0247153	+	0.474424i
$443$	−1.29342	+	1.29342i	−0.0614522	+	0.0614522i	−0.737165	−	0.675713i	$-0.763836\pi$
$443$	−1.29342	+	1.29342i	−0.0614522	+	0.0614522i	0.675713	+	0.737165i	$0.263836\pi$
$444$	10.6788	+	1.97458i	0.506793	+	0.0937096i
$445$		0			0
$446$	2.05612	+	1.18710i	0.0973599	+	0.0562108i
$447$	0.233059	+	2.94556i	0.0110233	+	0.139320i
$448$	−0.806348	−	3.00933i	−0.0380964	−	0.142178i
$449$	5.11305	+	2.95202i	0.241300	+	0.139314i	0.615774	−	0.787923i	$-0.288843\pi$
$449$	5.11305	+	2.95202i	0.241300	+	0.139314i	−0.374474	+	0.927237i	$0.622177\pi$
$450$		0			0
$451$	−1.89216	+	3.27732i	−0.0890983	+	0.154323i
$452$	−0.346561	+	1.29338i	−0.0163009	+	0.0608356i
$453$	−24.9537	+	17.1656i	−1.17243	+	0.806508i
$454$		−	9.65127i		−	0.452956i
$455$		0			0
$456$	15.3778	+	13.1228i	0.720131	+	0.614530i
$457$	−6.48293	+	24.1946i	−0.303259	+	1.13178i	0.631175	+	0.775640i	$0.282573\pi$
$457$	−6.48293	+	24.1946i	−0.303259	+	1.13178i	−0.934434	+	0.356137i	$0.884094\pi$
$458$	−17.4892	−	4.68621i	−0.817216	−	0.218972i
$459$	12.0836	−	6.58050i	0.564016	−	0.307151i
$460$		0			0
$461$	6.00551	−	10.4018i	0.279704	−	0.484462i	−0.691607	−	0.722274i	$-0.743097\pi$
$461$	6.00551	−	10.4018i	0.279704	−	0.484462i	0.971311	+	0.237812i	$0.0764302\pi$
$462$	0.281313	−	0.590419i	0.0130879	−	0.0274688i
$463$	3.70703	−	3.70703i	0.172280	−	0.172280i	−0.615700	−	0.787980i	$-0.711127\pi$
$463$	3.70703	−	3.70703i	0.172280	−	0.172280i	0.787980	+	0.615700i	$0.211127\pi$
$464$	−2.91544	+	5.04969i	−0.135346	+	0.234426i
$465$		0			0
$466$	−18.0288	+	10.4089i	−0.835168	+	0.482185i
$467$	−4.97371	−	4.97371i	−0.230156	−	0.230156i	0.582602	−	0.812758i	$-0.302035\pi$
$467$	−4.97371	−	4.97371i	−0.230156	−	0.230156i	−0.812758	+	0.582602i	$0.802035\pi$
$468$	5.76699	+	7.91846i	0.266579	+	0.366031i
$469$			2.33973i			0.108039i
$470$		0			0
$471$	8.78798	+	1.62496i	0.404929	+	0.0748741i
$472$	−3.13093	−	11.6848i	−0.144113	−	0.537835i
$473$	−6.30759	−	6.30759i	−0.290023	−	0.290023i
$474$	−3.28264	+	1.16399i	−0.150777	+	0.0534637i
$475$		0			0
$476$	−0.983178			−0.0450639
$477$	−7.86690	−	17.6297i	−0.360201	−	0.807208i
$478$	−3.68342	+	13.7467i	−0.168476	+	0.628760i
$479$	0.897191	−	0.517993i	0.0409937	−	0.0236677i	−0.479363	−	0.877617i	$-0.659132\pi$
$479$	0.897191	−	0.517993i	0.0409937	−	0.0236677i	0.520357	+	0.853949i	$0.325799\pi$
$480$		0			0
$481$	−23.7428	−	7.70631i	−1.08258	−	0.351378i
$482$	13.9744	+	13.9744i	0.636515	+	0.636515i
$483$	1.40590	+	2.04377i	0.0639706	+	0.0929946i
$484$	−8.01941	+	4.63001i	−0.364519	+	0.210455i
$485$		0			0
$486$	−6.20908	+	15.0791i	−0.281650	+	0.684000i
$487$	−35.9674	+	9.63744i	−1.62984	+	0.436714i	−0.953871	−	0.300217i	$-0.902941\pi$
$487$	−35.9674	+	9.63744i	−1.62984	+	0.436714i	−0.675968	+	0.736931i	$0.736274\pi$
$488$	−8.10291	+	2.17117i	−0.366802	+	0.0982842i
$489$	−5.78673	+	6.78112i	−0.261685	+	0.306653i
$490$		0			0
$491$	−19.2248	+	11.0994i	−0.867603	+	0.500911i	−0.866551	−	0.499089i	$-0.833668\pi$
$491$	−19.2248	+	11.0994i	−0.867603	+	0.500911i	−0.00105176	+	0.999999i	$0.500335\pi$
$492$	−5.55511	+	3.82134i	−0.250444	+	0.172279i
$493$	7.97754	+	7.97754i	0.359290	+	0.359290i
$494$	−9.69449	−	10.7601i	−0.436176	−	0.484119i
$495$		0			0
$496$	9.28989	−	5.36352i	0.417128	−	0.240829i
$497$	0.406504	−	1.51709i	0.0182342	−	0.0680509i
$498$	−10.6660	+	22.3858i	−0.477954	+	1.00313i
$499$	−2.69061			−0.120448			−0.0602240	−	0.998185i	$-0.519182\pi$
$499$	−2.69061			−0.120448			−0.0602240	+	0.998185i	$0.519182\pi$
$500$		0			0
$501$	−5.01231	−	14.1355i	−0.223933	−	0.631530i
$502$	11.2837	+	11.2837i	0.503616	+	0.503616i
$503$	4.29176	+	16.0171i	0.191360	+	0.714166i	0.993179	+	0.116599i	$0.0371992\pi$
$503$	4.29176	+	16.0171i	0.191360	+	0.714166i	−0.801819	+	0.597567i	$0.796134\pi$
$504$	2.90348	−	2.35521i	0.129331	−	0.104909i
$505$		0			0
$506$		−	3.21732i		−	0.143027i
$507$	−10.7646	−	19.7768i	−0.478073	−	0.878320i
$508$	−8.16568	−	8.16568i	−0.362293	−	0.362293i
$509$	−29.8804	+	17.2515i	−1.32443	+	0.764658i	−0.984431	−	0.175770i	$-0.943759\pi$
$509$	−29.8804	+	17.2515i	−1.32443	+	0.764658i	−0.339995	+	0.940427i	$0.610425\pi$
$510$		0			0
$511$	3.22653	−	5.58852i	0.142733	−	0.247221i
$512$	−10.3806	+	10.3806i	−0.458762	+	0.458762i
$513$	−5.64277	+	19.1377i	−0.249135	+	0.844952i
$514$	−15.2343	+	26.3866i	−0.671958	+	1.16387i
$515$		0			0
$516$	−5.31155	−	14.9795i	−0.233828	−	0.659435i
$517$	10.5059	+	2.81505i	0.462050	+	0.123806i
$518$	−0.768516	+	2.86814i	−0.0337667	+	0.126019i
$519$	15.9943	−	18.7427i	0.702070	−	0.822715i
$520$		0			0
$521$			42.5919i			1.86598i	0.359898	+	0.932992i	$0.382812\pi$
$521$			42.5919i			1.86598i	−0.359898	+	0.932992i	$0.617188\pi$
$522$	−13.2992	−	1.38657i	−0.582090	−	0.0606884i
$523$	8.56640	−	31.9703i	0.374583	−	1.39796i	−0.479371	−	0.877612i	$-0.659135\pi$
$523$	8.56640	−	31.9703i	0.374583	−	1.39796i	0.853954	−	0.520349i	$-0.174198\pi$
$524$	6.54134	−	11.3299i	0.285760	−	0.494950i
$525$		0			0
$526$	−17.8160	−	10.2861i	−0.776813	−	0.448493i
$527$	−5.37187	−	20.0481i	−0.234002	−	0.873309i
$528$	−2.08040	+	0.164605i	−0.0905377	+	0.00716353i
$529$	−9.35037	−	5.39844i	−0.406538	−	0.234715i
$530$		0			0
$531$	9.27223	−	7.52134i	0.402380	−	0.326398i
$532$	1.00813	−	1.00813i	0.0437078	−	0.0437078i
$533$	13.8068	−	7.04035i	0.598040	−	0.304951i
$534$	−2.45219	−	2.09260i	−0.106117	−	0.0905556i
$535$		0			0
$536$	15.0229	−	8.67346i	0.648889	−	0.374636i
$537$	−14.4210	+	30.2668i	−0.622312	+	1.30611i
$538$	−23.0792	+	23.0792i	−0.995014	+	0.995014i
$539$	5.20895	+	3.00739i	0.224366	+	0.129538i
$540$		0			0
$541$			4.59490i			0.197550i	0.995110	+	0.0987752i	$0.0314925\pi$
$541$			4.59490i			0.197550i	−0.995110	+	0.0987752i	$0.968508\pi$
$542$	−14.4333	+	3.86739i	−0.619963	+	0.166119i
$543$	24.0356	+	34.9408i	1.03147	+	1.49945i
$544$	6.15336	+	10.6579i	0.263823	+	0.456955i
$545$		0			0
$546$	−2.28271	+	1.40114i	−0.0976911	+	0.0599632i
$547$	−10.5892	+	10.5892i	−0.452763	+	0.452763i	−0.896271	−	0.443507i	$-0.853734\pi$
$547$	−10.5892	+	10.5892i	−0.452763	+	0.452763i	0.443507	+	0.896271i	$0.353734\pi$
$548$	4.05120	−	15.1193i	0.173059	−	0.645864i
$549$	−5.21574	−	6.42991i	−0.222602	−	0.274422i
$550$		0			0
$551$	−16.3599			−0.696957
$552$	7.91083	−	16.6032i	0.336707	−	0.706681i
$553$	0.203968	+	0.761217i	0.00867358	+	0.0323703i
$554$			16.9707i			0.721018i
$555$		0			0
$556$	4.16426	+	7.21271i	0.176604	+	0.305887i
$557$	−0.0735142	−	0.0196981i	−0.00311490	−	0.000834634i	0.257261	−	0.966342i	$-0.417180\pi$
$557$	−0.0735142	−	0.0196981i	−0.00311490	−	0.000834634i	−0.260376	+	0.965507i	$0.583847\pi$
$558$	19.9132	+	14.4423i	0.842991	+	0.611393i
$559$	7.60655	+	35.7312i	0.321723	+	1.51127i
$560$		0			0
$561$	−0.734183	+	3.97055i	−0.0309972	+	0.167637i
$562$	6.06850	+	1.62605i	0.255984	+	0.0685908i
$563$	1.99623	+	7.45003i	0.0841311	+	0.313981i	0.995148	−	0.0983870i	$-0.0313683\pi$
$563$	1.99623	+	7.45003i	0.0841311	+	0.313981i	−0.911017	+	0.412368i	$0.864702\pi$
$564$	14.7410	+	12.5793i	0.620708	+	0.529686i
$565$		0			0
$566$	16.1913	−	28.0441i	0.680571	−	1.17878i
$567$	3.29048	+	1.66966i	0.138187	+	0.0701191i
$568$	−11.2478	+	3.01384i	−0.471948	+	0.126458i
$569$	12.0281	+	20.8333i	0.504244	+	0.873377i	0.999988	+	0.00490805i	$0.00156229\pi$
$569$	12.0281	+	20.8333i	0.504244	+	0.873377i	−0.495743	+	0.868469i	$0.665104\pi$
$570$		0			0
$571$	−24.0278			−1.00553			−0.502767	−	0.864422i	$-0.667685\pi$
$571$	−24.0278			−1.00553			−0.502767	+	0.864422i	$0.667685\pi$
$572$	−2.87087	−	0.149559i	−0.120037	−	0.00625338i
$573$	3.20897	+	40.5572i	0.134057	+	1.69430i
$574$	−0.921781	−	1.59657i	−0.0384744	−	0.0666396i
$575$		0			0
$576$	−21.2898	−	8.15200i	−0.887077	−	0.339667i
$577$	6.28126	+	6.28126i	0.261492	+	0.261492i	0.825660	−	0.564168i	$-0.190803\pi$
$577$	6.28126	+	6.28126i	0.261492	+	0.261492i	−0.564168	+	0.825660i	$0.690803\pi$
$578$	10.0929	−	2.70438i	0.419808	−	0.112487i
$579$	−3.25548	−	9.18101i	−0.135293	−	0.381550i
$580$		0			0
$581$	4.85906	+	2.80538i	0.201588	+	0.116387i
$582$	4.25022	+	6.17858i	0.176177	+	0.256110i
$583$	5.47238	+	1.46632i	0.226643	+	0.0607288i
$584$	−47.8434			−1.97977
$585$		0			0
$586$	−14.9802			−0.618826
$587$	41.6351	+	11.1561i	1.71847	+	0.460462i	0.977475	−	0.211053i	$-0.0676891\pi$
$587$	41.6351	+	11.1561i	1.71847	+	0.460462i	0.740992	+	0.671514i	$0.234356\pi$
$588$	6.07362	+	8.82927i	0.250472	+	0.364113i
$589$	26.0650	+	15.0486i	1.07399	+	0.620068i
$590$		0			0
$591$	7.31952	+	20.6423i	0.301085	+	0.849110i
$592$	9.15201	−	2.45227i	0.376145	−	0.100788i
$593$	−18.7850	−	18.7850i	−0.771409	−	0.771409i	0.206944	−	0.978353i	$-0.433648\pi$
$593$	−18.7850	−	18.7850i	−0.771409	−	0.771409i	−0.978353	+	0.206944i	$0.933648\pi$
$594$	−2.28878	−	4.20284i	−0.0939099	−	0.172445i
$595$		0			0
$596$	−0.772476	−	1.33797i	−0.0316418	−	0.0548053i
$597$	1.62121	+	20.4900i	0.0663517	+	0.838599i
$598$	−7.17280	+	11.0527i	−0.293318	+	0.451978i
$599$	17.2478			0.704727			0.352363	−	0.935863i	$-0.385378\pi$
$599$	17.2478			0.704727			0.352363	+	0.935863i	$0.385378\pi$
$600$		0			0
$601$	−17.2038	−	29.7979i	−0.701758	−	1.21548i	−0.967849	−	0.251533i	$-0.919065\pi$
$601$	−17.2038	−	29.7979i	−0.701758	−	1.21548i	0.266091	−	0.963948i	$-0.414268\pi$
$602$	4.19751	−	1.12472i	0.171078	−	0.0458402i
$603$	13.8593	+	10.0517i	0.564396	+	0.409338i
$604$	7.91823	−	13.7148i	0.322188	−	0.558046i
$605$		0			0
$606$	−1.29848	−	1.10807i	−0.0527472	−	0.0450122i
$607$	−6.69769	−	24.9961i	−0.271851	−	1.01456i	−0.957922	−	0.287027i	$-0.907333\pi$
$607$	−6.69769	−	24.9961i	−0.271851	−	1.01456i	0.686072	−	0.727534i	$-0.259334\pi$
$608$	−17.2379	−	4.61888i	−0.699088	−	0.187320i
$609$	−0.550111	+	2.97507i	−0.0222916	+	0.120556i
$610$		0			0
$611$	−29.8157	−	33.0930i	−1.20622	−	1.33880i
$612$	−4.22382	+	5.82382i	−0.170738	+	0.235414i
$613$	27.0052	+	7.23603i	1.09073	+	0.292260i	0.758985	−	0.651108i	$-0.225696\pi$
$613$	27.0052	+	7.23603i	1.09073	+	0.292260i	0.331746	+	0.943369i	$0.392362\pi$
$614$	−9.23205	−	15.9904i	−0.372575	−	0.645319i
$615$		0			0
$616$			1.09715i			0.0442054i
$617$	−7.95090	−	29.6732i	−0.320091	−	1.19460i	−0.919155	−	0.393895i	$-0.871127\pi$
$617$	−7.95090	−	29.6732i	−0.320091	−	1.19460i	0.599064	−	0.800701i	$-0.295539\pi$
$618$	−4.73345	+	9.93457i	−0.190407	+	0.399627i
$619$	−13.4208			−0.539429			−0.269714	−	0.962940i	$-0.586929\pi$
$619$	−13.4208			−0.539429			−0.269714	+	0.962940i	$0.586929\pi$
$620$		0			0
$621$	18.1461	+	0.452412i	0.728176	+	0.0181546i
$622$	−3.69373	+	13.7852i	−0.148105	+	0.552736i
$623$	−0.515779	+	0.515779i	−0.0206642	+	0.0206642i
$624$	7.51391	+	4.07263i	0.300797	+	0.163036i
$625$		0			0
$626$	2.02638	+	3.50979i	0.0809905	+	0.140280i
$627$	−3.31849	−	4.82412i	−0.132528	−	0.192657i
$628$	−4.51362	+	1.20942i	−0.180113	+	0.0482612i
$629$		−	18.3325i		−	0.730966i
$630$		0			0
$631$	−1.20146	−	0.693665i	−0.0478295	−	0.0276144i	0.475895	−	0.879502i	$-0.342124\pi$
$631$	−1.20146	−	0.693665i	−0.0478295	−	0.0276144i	−0.523724	+	0.851888i	$0.675458\pi$
$632$	4.13148	−	4.13148i	0.164342	−	0.164342i
$633$	−4.64431	+	9.74748i	−0.184595	+	0.387428i
$634$	7.16170	−	4.13481i	0.284427	−	0.164214i
$635$		0			0
$636$	7.67837	+	6.55240i	0.304467	+	0.259820i
$637$	−11.1899	−	21.9445i	−0.443360	−	0.869473i
$638$	2.77469	−	2.77469i	0.109851	−	0.109851i
$639$	−7.24007	−	8.92548i	−0.286413	−	0.353087i
$640$		0			0
$641$	7.29569	+	4.21217i	0.288162	+	0.166371i	0.637113	−	0.770771i	$-0.280129\pi$
$641$	7.29569	+	4.21217i	0.288162	+	0.166371i	−0.348950	+	0.937141i	$0.613462\pi$
$642$	−3.82853	+	0.302921i	−0.151100	+	0.0119553i
$643$	−9.38439	−	35.0230i	−0.370084	−	1.38117i	−0.860396	−	0.509626i	$-0.829784\pi$
$643$	−9.38439	−	35.0230i	−0.370084	−	1.38117i	0.490312	−	0.871547i	$-0.336883\pi$
$644$	−1.12327	−	0.648521i	−0.0442631	−	0.0255553i
$645$		0			0
$646$	5.31833	−	9.21162i	0.209247	−	0.362426i
$647$	−5.74546	+	21.4424i	−0.225877	+	0.842986i	0.756174	+	0.654371i	$0.227066\pi$
$647$	−5.74546	+	21.4424i	−0.225877	+	0.842986i	−0.982051	+	0.188615i	$0.939600\pi$
$648$	−1.47740	−	27.3168i	−0.0580377	−	1.07311i
$649$			3.50374i			0.137534i
$650$		0			0
$651$	3.61306	−	4.23393i	0.141607	−	0.165941i
$652$	1.20639	−	4.50233i	0.0472461	−	0.176325i
$653$	5.12398	+	1.37297i	0.200517	+	0.0537283i	0.357679	−	0.933844i	$-0.383568\pi$
$653$	5.12398	+	1.37297i	0.200517	+	0.0537283i	−0.157163	+	0.987573i	$0.550235\pi$
$654$	−5.30144	−	14.9510i	−0.207303	−	0.584629i
$655$		0			0
$656$	−2.94133	+	5.09453i	−0.114840	+	0.198908i
$657$	−19.2419	−	43.1210i	−0.750699	−	1.68231i
$658$	−3.74667	+	3.74667i	−0.146060	+	0.146060i
$659$	−5.11174	+	8.85379i	−0.199125	+	0.344895i	−0.948245	−	0.317540i	$-0.897143\pi$
$659$	−5.11174	+	8.85379i	−0.199125	+	0.344895i	0.749120	+	0.662434i	$0.230477\pi$
$660$		0			0
$661$	0.0211888	−	0.0122334i	0.000824148	−	0.000475822i	−0.499588	−	0.866263i	$-0.666515\pi$
$661$	0.0211888	−	0.0122334i	0.000824148	−	0.000475822i	0.500412	+	0.865787i	$0.333182\pi$
$662$	−5.06012	−	5.06012i	−0.196667	−	0.196667i
$663$	11.3743	−	12.0035i	0.441740	−	0.466177i
$664$		−	41.5985i		−	1.61433i
$665$		0			0
$666$	13.6877	+	16.8741i	0.530389	+	0.653858i
$667$	3.85214	+	14.3764i	0.149156	+	0.556656i
$668$	5.54507	+	5.54507i	0.214545	+	0.214545i
$669$	−1.31372	−	3.70492i	−0.0507914	−	0.143240i
$670$		0			0
$671$	2.42970			0.0937975
$672$	−1.41958	+	2.97941i	−0.0547615	+	0.114933i
$673$	6.47686	−	24.1720i	0.249665	−	0.931761i	−0.721317	−	0.692605i	$-0.756463\pi$
$673$	6.47686	−	24.1720i	0.249665	−	0.931761i	0.970981	−	0.239155i	$-0.0768706\pi$
$674$	20.0468	−	11.5741i	0.772176	−	0.445816i
$675$		0			0
$676$	9.52906	+	6.91420i	0.366502	+	0.265931i
$677$	−6.93371	−	6.93371i	−0.266484	−	0.266484i	0.561198	−	0.827682i	$-0.310341\pi$
$677$	−6.93371	−	6.93371i	−0.266484	−	0.266484i	−0.827682	+	0.561198i	$0.810341\pi$
$678$	−2.20720	+	1.51832i	−0.0847670	+	0.0583109i
$679$	1.46952	−	0.848426i	0.0563949	−	0.0325596i
$680$		0			0
$681$	−10.3728	+	12.1553i	−0.397486	+	0.465790i
$682$	−6.97299	+	1.86841i	−0.267010	+	0.0715450i
$683$	−5.21434	+	1.39718i	−0.199521	+	0.0534615i	−0.357196	−	0.934030i	$-0.616267\pi$
$683$	−5.21434	+	1.39718i	−0.199521	+	0.0534615i	0.157674	+	0.987491i	$0.449600\pi$
$684$	−1.64060	−	10.3026i	−0.0627299	−	0.393930i
$685$		0			0
$686$	−5.13760	+	2.96620i	−0.196155	+	0.113250i
$687$	16.9901	+	24.6987i	0.648214	+	0.942314i
$688$	−9.80504	−	9.80504i	−0.373814	−	0.373814i
$689$	−15.5306	−	17.2377i	−0.591668	−	0.656703i
$690$		0			0
$691$	15.9273	−	9.19562i	0.605902	−	0.349818i	−0.165458	−	0.986217i	$-0.552910\pi$
$691$	15.9273	−	9.19562i	0.605902	−	0.349818i	0.771360	+	0.636399i	$0.219577\pi$
$692$	−3.33442	+	12.4442i	−0.126756	+	0.473059i
$693$	−0.988857	+	0.441258i	−0.0375636	+	0.0167620i
$694$	6.64903			0.252394
$695$		0			0
$696$	21.1415	−	7.49654i	0.801366	−	0.284156i
$697$	8.04838	+	8.04838i	0.304854	+	0.304854i
$698$	−1.21406	−	4.53095i	−0.0459530	−	0.171499i
$699$	33.8934	+	6.26713i	1.28197	+	0.237044i
$700$		0			0
$701$			14.5957i			0.551274i	0.961262	+	0.275637i	$0.0888887\pi$
$701$			14.5957i			0.551274i	−0.961262	+	0.275637i	$0.911111\pi$
$702$	−1.50714	+	19.5410i	−0.0568835	+	0.737528i
$703$	18.7977	+	18.7977i	0.708969	+	0.708969i
$704$	5.79387	−	3.34509i	0.218365	−	0.126073i
$705$		0			0
$706$	10.2934	−	17.8288i	0.387399	−	0.670994i
$707$	−0.273114	+	0.273114i	−0.0102715	+	0.0102715i
$708$	−2.68517	+	5.63563i	−0.100915	+	0.211800i
$709$	−8.47600	+	14.6809i	−0.318323	+	0.551352i	−0.980138	−	0.198315i	$-0.936453\pi$
$709$	−8.47600	+	14.6809i	−0.318323	+	0.551352i	0.661815	+	0.749667i	$0.269786\pi$
$710$		0			0
$711$	5.38531	+	2.06207i	0.201965	+	0.0773335i
$712$	5.22370	+	1.39969i	0.195766	+	0.0524555i
$713$	7.08676	−	26.4482i	0.265401	−	0.990492i
$714$	−1.49631	−	1.27689i	−0.0559980	−	0.0477864i
$715$		0			0
$716$		−	17.5301i		−	0.655130i
$717$	19.4135	−	13.3545i	0.725009	−	0.498731i
$718$	7.71353	−	28.7873i	0.287866	−	1.07433i
$719$	16.1158	−	27.9135i	0.601020	−	1.04100i	−0.391647	−	0.920115i	$-0.628095\pi$
$719$	16.1158	−	27.9135i	0.601020	−	1.04100i	0.992667	−	0.120881i	$-0.0385720\pi$
$720$		0			0
$721$	2.15640	+	1.24500i	0.0803085	+	0.0463661i
$722$	−1.15228	−	4.30035i	−0.0428833	−	0.160043i
$723$	−2.58089	−	32.6191i	−0.0959844	−	1.21312i
$724$	−19.2038	−	11.0873i	−0.713702	−	0.412056i
$725$		0			0
$726$	−18.2180	−	3.36864i	−0.676134	−	0.125022i
$727$	16.7058	−	16.7058i	0.619582	−	0.619582i	−0.325842	−	0.945424i	$-0.605648\pi$
$727$	16.7058	−	16.7058i	0.619582	−	0.619582i	0.945424	+	0.325842i	$0.105648\pi$
$728$	2.44602	−	3.76911i	0.0906556	−	0.139693i
$729$	24.0264	−	12.3180i	0.889866	−	0.456223i
$730$		0			0
$731$	−23.2351	+	13.4148i	−0.859381	+	0.496164i
$732$	3.90808	+	1.86205i	0.144447	+	0.0688235i
$733$	6.44344	−	6.44344i	0.237994	−	0.237994i	−0.578025	−	0.816019i	$-0.696176\pi$
$733$	6.44344	−	6.44344i	0.237994	−	0.237994i	0.816019	+	0.578025i	$0.196176\pi$
$734$	−6.32985	−	3.65454i	−0.233639	−	0.134892i
$735$		0			0
$736$			16.2355i			0.598447i
$737$	−4.85313	+	1.30039i	−0.178767	+	0.0479005i
$738$	−13.4173	−	1.39888i	−0.493898	−	0.0514935i
$739$	25.1561	+	43.5716i	0.925382	+	1.60281i	0.790946	+	0.611886i	$0.209589\pi$
$739$	25.1561	+	43.5716i	0.925382	+	1.60281i	0.134436	+	0.990922i	$0.457078\pi$
$740$		0			0
$741$	0.645197	+	23.9710i	0.0237019	+	0.880596i
$742$	−1.95159	+	1.95159i	−0.0716450	+	0.0716450i
$743$	−6.98181	+	26.0565i	−0.256138	+	0.955920i	0.711316	+	0.702872i	$0.248099\pi$
$743$	−6.98181	+	26.0565i	−0.256138	+	0.955920i	−0.967454	+	0.253047i	$0.918567\pi$
$744$	−40.5788	−	7.50330i	−1.48769	−	0.275084i
$745$		0			0
$746$	−13.7661			−0.504011
$747$	37.4925	−	16.7303i	1.37178	−	0.612130i
$748$	−0.546436	−	2.03933i	−0.0199797	−	0.0745652i
$749$			0.868983i			0.0317519i
$750$		0			0
$751$	1.46634	+	2.53977i	0.0535073	+	0.0926774i	0.891538	−	0.452945i	$-0.149627\pi$
$751$	1.46634	+	2.53977i	0.0535073	+	0.0926774i	−0.838031	+	0.545622i	$0.816293\pi$
$752$	16.3313	+	4.37595i	0.595540	+	0.159575i
$753$	−2.08396	−	26.3385i	−0.0759436	−	0.959827i
$754$	−15.7181	+	3.34610i	−0.572418	+	0.121858i
$755$		0			0
$756$	−1.92871	−	0.0480858i	−0.0701463	−	0.00174887i
$757$	−29.6744	−	7.95123i	−1.07853	−	0.288993i	−0.324539	−	0.945872i	$-0.605209\pi$
$757$	−29.6744	−	7.95123i	−1.07853	−	0.288993i	−0.753995	+	0.656880i	$0.771876\pi$
$758$	−1.95867	−	7.30986i	−0.0711422	−	0.265506i
$759$	−3.45784	+	4.05204i	−0.125512	+	0.147080i
$760$		0			0
$761$	15.7186	−	27.2253i	0.569797	−	0.986918i	−0.426788	−	0.904352i	$-0.640355\pi$
$761$	15.7186	−	27.2253i	0.569797	−	0.986918i	0.996586	−	0.0825663i	$-0.0263116\pi$
$762$	−1.82238	−	23.0325i	−0.0660179	−	0.834380i
$763$	−3.46701	+	0.928982i	−0.125514	+	0.0336314i
$764$	−10.6362	−	18.4224i	−0.384803	−	0.666498i
$765$		0			0
$766$	8.17238			0.295280
$767$	7.81135	−	12.0366i	0.282052	−	0.434618i
$768$	28.6726	−	2.26864i	1.03463	−	0.0818624i
$769$	−16.7826	−	29.0682i	−0.605194	−	1.04823i	−0.992021	−	0.126075i	$-0.959762\pi$
$769$	−16.7826	−	29.0682i	−0.605194	−	1.04823i	0.386826	−	0.922153i	$-0.373571\pi$
$770$		0			0
$771$	47.5461	−	16.8593i	1.71233	−	0.607174i
$772$	3.60152	+	3.60152i	0.129621	+	0.129621i
$773$	−41.8728	+	11.2198i	−1.50606	+	0.403547i	−0.915124	−	0.403172i	$-0.867907\pi$
$773$	−41.8728	+	11.2198i	−1.50606	+	0.403547i	−0.590934	+	0.806720i	$0.701241\pi$
$774$	11.3707	−	29.6957i	0.408710	−	1.06739i
$775$		0			0
$776$	−10.8951	−	6.29028i	−0.391111	−	0.225808i
$777$	4.05047	−	2.78630i	0.145310	−	0.0999580i
$778$	28.9899	+	7.76782i	1.03934	+	0.278490i
$779$	−16.5052			−0.591361
$780$		0			0
$781$	3.37271			0.120685
$782$	−9.34703	−	2.50453i	−0.334249	−	0.0895617i
$783$	15.2594	+	16.0397i	0.545327	+	0.573214i
$784$	8.09723	+	4.67494i	0.289187	+	0.166962i
$785$		0			0
$786$	24.6699	−	8.74768i	0.879947	−	0.312019i
$787$	25.5167	−	6.83718i	0.909572	−	0.243719i	0.226450	−	0.974023i	$-0.427288\pi$
$787$	25.5167	−	6.83718i	0.909572	−	0.243719i	0.683123	+	0.730304i	$0.260621\pi$
$788$	−8.09753	−	8.09753i	−0.288463	−	0.288463i
$789$	11.3832	+	32.1026i	0.405254	+	1.14288i
$790$		0			0
$791$	0.303087	+	0.524962i	0.0107765	+	0.0186655i
$792$	6.49893	+	4.71346i	0.230930	+	0.167485i
$793$	−8.34692	−	5.41686i	−0.296408	−	0.192358i
$794$	26.5274			0.941423
$795$		0			0
$796$	−5.37352	−	9.30721i	−0.190459	−	0.329885i
$797$	8.19629	−	2.19619i	0.290328	−	0.0777930i	−0.110716	−	0.993852i	$-0.535314\pi$
$797$	8.19629	−	2.19619i	0.290328	−	0.0777930i	0.401043	+	0.916059i	$0.368648\pi$
$798$	2.84357	−	0.224989i	0.100661	−	0.00796453i
$799$	16.3567	−	28.3307i	0.578659	−	1.00227i
$800$		0			0
$801$	0.839365	+	5.27103i	0.0296575	+	0.186243i
$802$	5.61731	+	20.9641i	0.198354	+	0.740268i
$803$	13.3851	+	3.58652i	0.472349	+	0.126566i
$804$	−8.80265	−	1.62767i	−0.310445	−	0.0574035i
$805$		0			0
$806$	28.1203	+	9.12715i	0.990494	+	0.321490i
$807$	53.8716	−	4.26243i	1.89637	−	0.150045i
$808$	2.76604	+	0.741159i	0.0973091	+	0.0260739i
$809$	19.9584	+	34.5690i	0.701702	+	1.21538i	0.967869	+	0.251456i	$0.0809093\pi$
$809$	19.9584	+	34.5690i	0.701702	+	1.21538i	−0.266167	+	0.963927i	$0.585757\pi$
$810$		0			0
$811$			1.10001i			0.0386266i	0.999813	+	0.0193133i	$0.00614800\pi$
$811$			1.10001i			0.0386266i	−0.999813	+	0.0193133i	$0.993852\pi$
$812$	−0.409436	−	1.52804i	−0.0143684	−	0.0536235i
$813$	22.3345	+	10.6416i	0.783305	+	0.373216i
$814$	−6.37629			−0.223489
$815$		0			0
$816$	−1.14127	+	6.17215i	−0.0399526	+	0.216069i
$817$	10.0695	−	37.5799i	0.352287	−	1.31475i
$818$	20.0120	−	20.0120i	0.699703	−	0.699703i
$819$	4.38084	+	0.688707i	0.153079	+	0.0240654i
$820$		0			0
$821$	11.8403	+	20.5080i	0.413229	+	0.715733i	0.995241	−	0.0974469i	$-0.0310676\pi$
$821$	11.8403	+	20.5080i	0.413229	+	0.715733i	−0.582012	+	0.813180i	$0.697734\pi$
$822$	25.8016	−	17.7488i	0.899933	−	0.619060i
$823$	−27.3251	+	7.32174i	−0.952494	+	0.255220i	−0.701420	−	0.712748i	$-0.747450\pi$
$823$	−27.3251	+	7.32174i	−0.952494	+	0.255220i	−0.251074	+	0.967968i	$0.580784\pi$
$824$		−	18.4610i		−	0.643119i
$825$		0			0
$826$	−1.47820	−	0.853438i	−0.0514331	−	0.0296949i
$827$	−18.2137	+	18.2137i	−0.633351	+	0.633351i	−0.948907	−	0.315556i	$-0.897809\pi$
$827$	−18.2137	+	18.2137i	−0.633351	+	0.633351i	0.315556	+	0.948907i	$0.397809\pi$
$828$	−8.66718	+	3.86756i	−0.301205	+	0.134407i
$829$	−28.3851	+	16.3881i	−0.985855	+	0.569184i	−0.904033	−	0.427463i	$-0.859407\pi$
$829$	−28.3851	+	16.3881i	−0.985855	+	0.569184i	−0.0818224	+	0.996647i	$0.526074\pi$
$830$		0			0
$831$	18.2395	−	21.3737i	0.632720	−	0.741447i
$832$	−27.3617	−	1.42542i	−0.948597	−	0.0494176i
$833$	12.7921	−	12.7921i	0.443219	−	0.443219i
$834$	−3.02977	+	16.3854i	−0.104912	+	0.567379i
$835$		0			0
$836$	2.65138	+	1.53077i	0.0916999	+	0.0529429i
$837$	−9.55751	−	39.5912i	−0.330356	−	1.36847i
$838$	−3.50097	−	13.0658i	−0.120939	−	0.451351i
$839$	15.2005	+	8.77600i	0.524779	+	0.302981i	0.738888	−	0.673829i	$-0.235351\pi$
$839$	15.2005	+	8.77600i	0.524779	+	0.302981i	−0.214109	+	0.976810i	$0.568685\pi$
$840$		0			0
$841$	5.42365	−	9.39403i	0.187022	−	0.323932i
$842$	−4.49416	+	16.7724i	−0.154879	+	0.578017i
$843$	−5.89534	−	8.57010i	−0.203046	−	0.295170i
$844$		−	5.64560i		−	0.194329i
$845$		0			0
$846$	6.09724	+	38.2893i	0.209627	+	1.31641i
$847$	−1.08498	+	4.04920i	−0.0372804	+	0.139132i
$848$	8.50672	+	2.27937i	0.292122	+	0.0782739i
$849$	−50.5328	+	17.9184i	−1.73428	+	0.614956i
$850$		0			0
$851$	12.0925	−	20.9448i	0.414524	−	0.717977i
$852$	5.42488	+	2.58475i	0.185853	+	0.0885522i
$853$	−12.7997	+	12.7997i	−0.438252	+	0.438252i	−0.891423	−	0.453172i	$-0.850292\pi$
$853$	−12.7997	+	12.7997i	−0.438252	+	0.438252i	0.453172	+	0.891423i	$0.350292\pi$
$854$	−0.591824	+	1.02507i	−0.0202518	+	0.0350772i
$855$		0			0
$856$	5.57953	−	3.22134i	0.190704	−	0.110103i
$857$	−8.76415	−	8.76415i	−0.299378	−	0.299378i	0.541392	−	0.840770i	$-0.317897\pi$
$857$	−8.76415	−	8.76415i	−0.299378	−	0.299378i	−0.840770	+	0.541392i	$0.817897\pi$
$858$	−4.17497	−	3.95612i	−0.142531	−	0.135060i
$859$			15.1747i			0.517755i	0.965910	+	0.258878i	$0.0833526\pi$
$859$			15.1747i			0.517755i	−0.965910	+	0.258878i	$0.916647\pi$
$860$		0			0
$861$	−0.554996	+	3.00149i	−0.0189142	+	0.102290i
$862$	−5.65190	−	21.0932i	−0.192504	−	0.718436i
$863$	−12.5980	−	12.5980i	−0.428840	−	0.428840i	0.459393	−	0.888233i	$-0.348067\pi$
$863$	−12.5980	−	12.5980i	−0.428840	−	0.428840i	−0.888233	+	0.459393i	$0.848067\pi$
$864$	11.5498	+	21.2087i	0.392933	+	0.721534i
$865$		0			0
$866$	−42.4056			−1.44100
$867$	−15.6180	−	7.44139i	−0.530415	−	0.252723i
$868$	−0.753237	+	2.81112i	−0.0255665	+	0.0954156i
$869$	−1.46557	+	0.846148i	−0.0497161	+	0.0287036i
$870$		0			0
$871$	19.5714	+	6.35240i	0.663152	+	0.215243i
$872$	18.8171	+	18.8171i	0.637226	+	0.637226i
$873$	1.28756	−	12.3496i	0.0435772	−	0.417969i
$874$	12.1523	−	7.01613i	0.411057	−	0.237324i
$875$		0			0
$876$	18.7808	+	16.0267i	0.634544	+	0.541493i
$877$	−7.38015	+	1.97751i	−0.249210	+	0.0667756i	−0.381261	−	0.924467i	$-0.624510\pi$
$877$	−7.38015	+	1.97751i	−0.249210	+	0.0667756i	0.132051	+	0.991243i	$0.457844\pi$
$878$	−22.5218	+	6.03470i	−0.760074	+	0.203661i
$879$	18.8667	+	16.1001i	0.636359	+	0.543043i
$880$		0			0
$881$	1.60541	−	0.926884i	0.0540877	−	0.0312275i	−0.472712	−	0.881217i	$-0.656725\pi$
$881$	1.60541	−	0.926884i	0.0540877	−	0.0312275i	0.526800	+	0.849989i	$0.323392\pi$
$882$	−2.22337	+	21.3254i	−0.0748649	+	0.718064i
$883$	−18.1052	−	18.1052i	−0.609287	−	0.609287i	0.333472	−	0.942760i	$-0.391780\pi$
$883$	−18.1052	−	18.1052i	−0.609287	−	0.609287i	−0.942760	+	0.333472i	$0.891780\pi$
$884$	−2.66934	+	8.22409i	−0.0897795	+	0.276606i
$885$		0			0
$886$	1.65717	−	0.956765i	0.0556736	−	0.0321431i
$887$	−10.2957	+	38.4242i	−0.345697	+	1.29016i	0.546099	+	0.837721i	$0.316112\pi$
$887$	−10.2957	+	38.4242i	−0.345697	+	1.29016i	−0.891796	+	0.452438i	$0.850554\pi$
$888$	−32.9054	−	15.6782i	−1.10423	−	0.526125i
$889$	−5.22782			−0.175335
$890$		0			0
$891$	−1.63444	+	7.75315i	−0.0547559	+	0.259740i
$892$	1.45336	+	1.45336i	0.0486621	+	0.0486621i
$893$	12.2778	+	45.8213i	0.410860	+	1.53335i
$894$	0.562027	−	3.03951i	0.0187970	−	0.101656i
$895$		0			0
$896$		−	0.551705i		−	0.0184312i
$897$	20.9127	−	6.21123i	0.698256	−	0.207387i
$898$	−4.36733	−	4.36733i	−0.145740	−	0.145740i
$899$	28.9213	−	16.6977i	0.964579	−	0.556900i
$900$		0			0
$901$	8.51997	−	14.7570i	0.283841	−	0.491628i
$902$	2.79933	−	2.79933i	0.0932075	−	0.0932075i
$903$	−6.49535	−	3.09479i	−0.216152	−	0.102988i
$904$	2.24710	−	3.89210i	0.0747375	−	0.129449i
$905$		0			0
$906$	29.8627	−	10.5890i	0.992123	−	0.351796i
$907$	−6.82165	−	1.82785i	−0.226509	−	0.0606929i	0.143779	−	0.989610i	$-0.454074\pi$
$907$	−6.82165	−	1.82785i	−0.226509	−	0.0606929i	−0.370288	+	0.928917i	$0.620741\pi$
$908$	2.16248	−	8.07048i	0.0717644	−	0.267828i
$909$	0.444459	+	2.79111i	0.0147418	+	0.0925752i
$910$		0			0
$911$			42.3736i			1.40390i	0.712225	+	0.701951i	$0.247687\pi$
$911$			42.3736i			1.40390i	−0.712225	+	0.701951i	$0.752313\pi$
$912$	−5.15854	−	7.49901i	−0.170816	−	0.248317i
$913$	−3.11838	+	11.6380i	−0.103203	+	0.385160i
$914$	13.1017	−	22.6928i	0.433365	−	0.750610i
$915$		0			0
$916$	−13.5746	−	7.83732i	−0.448518	−	0.258952i
$917$	−1.53287	−	5.72076i	−0.0506199	−	0.188916i
$918$	−13.9919	+	3.37771i	−0.461801	+	0.111481i
$919$	−3.72098	−	2.14831i	−0.122744	−	0.0708661i	0.437371	−	0.899281i	$-0.355910\pi$
$919$	−3.72098	−	2.14831i	−0.122744	−	0.0708661i	−0.560115	+	0.828415i	$0.689243\pi$
$920$		0			0
$921$	−5.55854	+	30.0613i	−0.183160	+	0.990552i
$922$	−8.88477	+	8.88477i	−0.292604	+	0.292604i
$923$	−11.5865	−	7.51924i	−0.381375	−	0.247499i
$924$	0.367527	−	0.430683i	0.0120907	−	0.0141684i
$925$		0			0
$926$	−4.74955	+	2.74215i	−0.156080	+	0.0901128i
$927$	16.6388	−	7.42474i	0.546490	−	0.243860i
$928$	−14.0018	+	14.0018i	−0.459633	+	0.459633i
$929$	−33.1937	−	19.1644i	−1.08905	−	0.628762i	−0.155726	−	0.987800i	$-0.549772\pi$
$929$	−33.1937	−	19.1644i	−1.08905	−	0.628762i	−0.933323	+	0.359038i	$0.883105\pi$
$930$		0			0
$931$			26.2333i			0.859762i
$932$	−17.4081	+	4.66449i	−0.570221	+	0.152790i
$933$	19.4678	−	13.3919i	0.637348	−	0.438430i
$934$	3.67914	+	6.37246i	0.120385	+	0.208513i
$935$		0			0
$936$	−11.8179	−	30.6814i	−0.386280	−	1.00285i
$937$	−10.0927	+	10.0927i	−0.329713	+	0.329713i	−0.852477	−	0.522764i	$-0.824901\pi$
$937$	−10.0927	+	10.0927i	−0.329713	+	0.329713i	0.522764	+	0.852477i	$0.324901\pi$
$938$	0.633496	−	2.36424i	0.0206844	−	0.0771952i
$939$	1.22007	−	6.59827i	0.0398153	−	0.215326i
$940$		0			0
$941$	4.90362			0.159853			0.0799267	−	0.996801i	$-0.474531\pi$
$941$	4.90362			0.159853			0.0799267	+	0.996801i	$0.474531\pi$
$942$	−8.44005	−	4.02137i	−0.274992	−	0.131023i
$943$	3.88635	+	14.5041i	0.126557	+	0.472317i
$944$			5.44650i			0.177269i
$945$		0			0
$946$	4.66584	+	8.08147i	0.151699	+	0.262751i
$947$	14.9071	+	3.99434i	0.484415	+	0.129799i	0.492758	−	0.870167i	$-0.335989\pi$
$947$	14.9071	+	3.99434i	0.484415	+	0.129799i	−0.00834264	+	0.999965i	$0.502656\pi$
$948$	−3.00578	+	0.237824i	−0.0976232	+	0.00772415i
$949$	−37.9868	−	42.1622i	−1.23310	−	1.36864i
$950$		0			0
$951$	−13.4637	−	2.48953i	−0.436590	−	0.0807286i
$952$	3.18746	+	0.854078i	0.103306	+	0.0276808i
$953$	5.10687	+	19.0591i	0.165428	+	0.617384i	0.997985	+	0.0634459i	$0.0202090\pi$
$953$	5.10687	+	19.0591i	0.165428	+	0.617384i	−0.832558	+	0.553938i	$0.813124\pi$
$954$	3.17596	+	19.9444i	0.102826	+	0.645722i
$955$		0			0
$956$	−6.16022	+	10.6698i	−0.199236	+	0.345087i
$957$	−6.47670	+	0.512450i	−0.209362	+	0.0165652i
$958$	−1.04684	+	0.280499i	−0.0338218	+	0.00906252i
$959$	−3.54300	−	6.13666i	−0.114409	−	0.198163i
$960$		0			0
$961$	−30.4374			−0.981851
$962$	21.9049	+	14.2155i	0.706243	+	0.458327i
$963$	5.14739	+	3.73323i	0.165872	+	0.120302i
$964$	8.55439	+	14.8166i	0.275518	+	0.477212i
$965$		0			0
$966$	−0.867263	−	2.44583i	−0.0279037	−	0.0786932i
$967$	32.8519	+	32.8519i	1.05645	+	1.05645i	0.998309	+	0.0581387i	$0.0185166\pi$
$967$	32.8519	+	32.8519i	1.05645	+	1.05645i	0.0581387	+	0.998309i	$0.481483\pi$
$968$	30.0210	−	8.04410i	0.964912	−	0.258547i
$969$	−16.5984	+	5.88562i	−0.533218	+	0.189073i
$970$		0			0
$971$	−18.2215	−	10.5202i	−0.584757	−	0.337610i	0.178265	−	0.983983i	$-0.442952\pi$
$971$	−18.2215	−	10.5202i	−0.584757	−	0.337610i	−0.763022	+	0.646373i	$0.776285\pi$
$972$	−8.57074	+	11.2180i	−0.274906	+	0.359819i
$973$	3.64187	+	0.975837i	0.116753	+	0.0312839i
$974$	38.9535			1.24815
$975$		0			0
$976$	3.77693			0.120896
$977$	−12.6370	−	3.38607i	−0.404293	−	0.108330i	0.0509414	−	0.998702i	$-0.483778\pi$
$977$	−12.6370	−	3.38607i	−0.404293	−	0.108330i	−0.455234	+	0.890372i	$0.650444\pi$
$978$	7.68336	−	5.28536i	0.245687	−	0.169007i
$979$	−1.35650	−	0.783177i	−0.0433540	−	0.0250304i
$980$		0			0
$981$	−9.39179	+	24.5277i	−0.299857	+	0.783109i
$982$	22.4314	−	6.01047i	0.715814	−	0.191802i
$983$	20.5744	+	20.5744i	0.656223	+	0.656223i	0.954484	−	0.298261i	$-0.0964067\pi$
$983$	20.5744	+	20.5744i	0.656223	+	0.656223i	−0.298261	+	0.954484i	$0.596407\pi$
$984$	21.3292	−	7.56311i	0.679951	−	0.241103i
$985$		0			0
$986$	−5.90113	−	10.2211i	−0.187930	−	0.325505i
$987$	8.74550	−	0.691962i	0.278372	−	0.0220254i
$988$	−5.69571	−	11.1698i	−0.181205	−	0.355360i
$989$	−35.3945			−1.12548
$990$		0			0
$991$	−19.5736	−	33.9024i	−0.621775	−	1.07695i	−0.989155	−	0.146875i	$-0.953079\pi$
$991$	−19.5736	−	33.9024i	−0.621775	−	1.07695i	0.367380	−	0.930071i	$-0.380255\pi$
$992$	35.1876	−	9.42848i	1.11721	−	0.299355i
$993$	0.934540	+	11.8114i	0.0296567	+	0.374822i
$994$	−0.821523	+	1.42292i	−0.0260571	+	0.0451322i
$995$		0			0
$996$	−13.9348	+	16.3294i	−0.441541	+	0.517415i
$997$	−6.24236	−	23.2968i	−0.197697	−	0.737817i	−0.991552	−	0.129709i	$-0.958596\pi$
$997$	−6.24236	−	23.2968i	−0.197697	−	0.737817i	0.793855	−	0.608108i	$-0.208071\pi$
$998$	2.71879	+	0.728497i	0.0860617	+	0.0230602i
$999$	0.896618	−	35.9630i	0.0283677	−	1.13782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bn.d.218.9		96
3.2	odd	2	inner	975.2.bn.d.218.16		96
5.2	odd	4	inner	975.2.bn.d.257.16		96
5.3	odd	4		195.2.bf.a.62.9	yes	96
5.4	even	2		195.2.bf.a.23.16	yes	96
13.4	even	6	inner	975.2.bn.d.368.9		96
15.2	even	4	inner	975.2.bn.d.257.9		96
15.8	even	4		195.2.bf.a.62.16	yes	96
15.14	odd	2		195.2.bf.a.23.9	yes	96
39.17	odd	6	inner	975.2.bn.d.368.16		96
65.4	even	6		195.2.bf.a.173.16	yes	96
65.17	odd	12	inner	975.2.bn.d.407.16		96
65.43	odd	12		195.2.bf.a.17.9	✓	96
195.17	even	12	inner	975.2.bn.d.407.9		96
195.134	odd	6		195.2.bf.a.173.9	yes	96
195.173	even	12		195.2.bf.a.17.16	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.9	✓	96	65.43	odd	12
195.2.bf.a.17.16	yes	96	195.173	even	12
195.2.bf.a.23.9	yes	96	15.14	odd	2
195.2.bf.a.23.16	yes	96	5.4	even	2
195.2.bf.a.62.9	yes	96	5.3	odd	4
195.2.bf.a.62.16	yes	96	15.8	even	4
195.2.bf.a.173.9	yes	96	195.134	odd	6
195.2.bf.a.173.16	yes	96	65.4	even	6
975.2.bn.d.218.9		96	1.1	even	1	trivial
975.2.bn.d.218.16		96	3.2	odd	2	inner
975.2.bn.d.257.9		96	15.2	even	4	inner
975.2.bn.d.257.16		96	5.2	odd	4	inner
975.2.bn.d.368.9		96	13.4	even	6	inner
975.2.bn.d.368.16		96	39.17	odd	6	inner
975.2.bn.d.407.9		96	195.17	even	12	inner
975.2.bn.d.407.16		96	65.17	odd	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01047 - 0.270756i) q^{2} +(0.981641 + 1.42702i) q^{3} +(-0.784302 - 0.452817i) q^{4} +(-0.605549 - 1.70775i) q^{6} +(-0.396013 + 0.106111i) q^{7} +(2.14935 + 2.14935i) q^{8} +(-1.07276 + 2.80164i) q^{9} +(-0.440197 - 0.762444i) q^{11} +(-0.123725 - 1.56372i) q^{12} +(-0.187578 + 3.60067i) q^{13} +0.428892 q^{14} +(-0.684279 - 1.18521i) q^{16} +(-2.55774 + 0.685345i) q^{17} +(1.84256 - 2.54053i) q^{18} +(1.91991 - 3.32538i) q^{19} +(-0.540166 - 0.460955i) q^{21} +(0.238372 + 0.889616i) q^{22} +(-3.37426 - 0.904132i) q^{23} +(-0.957273 + 5.17705i) q^{24} +(1.16444 - 3.58759i) q^{26} +(-5.05106 + 1.21935i) q^{27} +(0.358643 + 0.0960982i) q^{28} +(-2.13030 - 3.68979i) q^{29} +7.83820i q^{31} +(-1.20289 - 4.48924i) q^{32} +(0.655906 - 1.37662i) q^{33} +2.77009 q^{34} +(2.11000 - 1.71157i) q^{36} +(-1.79187 + 6.68733i) q^{37} +(-2.84038 + 2.84038i) q^{38} +(-5.32235 + 3.26689i) q^{39} +(-2.14922 - 3.72255i) q^{41} +(0.421017 + 0.612036i) q^{42} +(9.78689 - 2.62239i) q^{43} +0.797316i q^{44} +(3.16481 + 1.82720i) q^{46} +(-8.73570 + 8.73570i) q^{47} +(1.01960 - 2.13993i) q^{48} +(-5.91661 + 3.41596i) q^{49} +(-3.48878 - 2.97718i) q^{51} +(1.77756 - 2.73907i) q^{52} +(-4.55030 + 4.55030i) q^{53} +(5.43411 + 0.135481i) q^{54} +(-1.07924 - 0.623101i) q^{56} +(6.63004 - 0.524583i) q^{57} +(1.15358 + 4.30522i) q^{58} +(-3.44655 - 1.98987i) q^{59} +(-1.37989 + 2.39004i) q^{61} +(2.12224 - 7.92030i) q^{62} +(0.127543 - 1.22332i) q^{63} +7.59907i q^{64} +(-1.03550 + 1.21344i) q^{66} +(1.47705 - 5.51244i) q^{67} +(2.31638 + 0.620672i) q^{68} +(-2.02210 - 5.70267i) q^{69} +(-1.91546 + 3.31767i) q^{71} +(-8.32745 + 3.71596i) q^{72} +(-11.1297 + 11.1297i) q^{73} +(3.62127 - 6.27222i) q^{74} +(-3.01158 + 1.73874i) q^{76} +(0.255228 + 0.255228i) q^{77} +(6.26263 - 1.86004i) q^{78} -1.92220i q^{79} +(-6.69836 - 6.01099i) q^{81} +(1.16382 + 4.34345i) q^{82} +(-9.67699 - 9.67699i) q^{83} +(0.214925 + 0.606124i) q^{84} -10.5994 q^{86} +(3.17421 - 6.66202i) q^{87} +(0.692621 - 2.58490i) q^{88} +(1.54079 - 0.889574i) q^{89} +(-0.307789 - 1.44582i) q^{91} +(2.23704 + 2.23704i) q^{92} +(-11.1853 + 7.69430i) q^{93} +(11.1924 - 6.46196i) q^{94} +(5.22543 - 6.12337i) q^{96} +(-3.99780 + 1.07121i) q^{97} +(6.90347 - 1.84978i) q^{98} +(2.60832 - 0.415352i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) \) 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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