LMFDB - Embedded newform 700.2.be.e.207.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			207.14
Character	$\chi$	$=$	700.207
Dual form			700.2.be.e.443.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.05431 - 0.942570i) q^{2} +(1.20413 - 0.322645i) q^{3} +(0.223125 - 1.98751i) q^{4} +(0.965404 - 1.47514i) q^{6} +(0.451584 - 2.60693i) q^{7} +(-1.63813 - 2.30576i) q^{8} +(-1.25225 + 0.722989i) q^{9} +(0.824629 + 0.476100i) q^{11} +(-0.372591 - 2.46521i) q^{12} +(3.15680 - 3.15680i) q^{13} +(-1.98110 - 3.17415i) q^{14} +(-3.90043 - 0.886929i) q^{16} +(-2.56885 + 0.688322i) q^{17} +(-0.638792 + 1.94259i) q^{18} +(1.99048 + 3.44760i) q^{19} +(-0.297348 - 3.28477i) q^{21} +(1.31817 - 0.275315i) q^{22} +(0.141582 - 0.528392i) q^{23} +(-2.71646 - 2.24790i) q^{24} +(0.352732 - 6.30375i) q^{26} +(-3.91905 + 3.91905i) q^{27} +(-5.08055 - 1.47920i) q^{28} -7.23080i q^{29} +(3.41863 + 1.97375i) q^{31} +(-4.94824 + 2.74133i) q^{32} +(1.14657 + 0.307222i) q^{33} +(-2.05957 + 3.14702i) q^{34} +(1.15754 + 2.65019i) q^{36} +(-0.269180 + 1.00460i) q^{37} +(5.34818 + 1.75867i) q^{38} +(2.78267 - 4.81972i) q^{39} +3.71449 q^{41} +(-3.40962 - 3.18289i) q^{42} +(8.73324 + 8.73324i) q^{43} +(1.13025 - 1.53273i) q^{44} +(-0.348775 - 0.690538i) q^{46} +(-3.09794 - 0.830089i) q^{47} +(-4.98278 + 0.190479i) q^{48} +(-6.59214 - 2.35449i) q^{49} +(-2.87114 + 1.65765i) q^{51} +(-5.56983 - 6.97856i) q^{52} +(0.760768 + 2.83923i) q^{53} +(-0.437903 + 7.82586i) q^{54} +(-6.75070 + 3.22924i) q^{56} +(3.50914 + 3.50914i) q^{57} +(-6.81553 - 7.62348i) q^{58} +(6.30084 - 10.9134i) q^{59} +(3.01183 + 5.21665i) q^{61} +(5.46468 - 1.14136i) q^{62} +(1.31928 + 3.59102i) q^{63} +(-2.63307 + 7.55427i) q^{64} +(1.49841 - 0.756815i) q^{66} +(3.85605 + 14.3910i) q^{67} +(0.794874 + 5.25921i) q^{68} -0.681932i q^{69} +7.60710i q^{71} +(3.71839 + 1.70305i) q^{72} +(-3.80964 - 14.2178i) q^{73} +(0.663102 + 1.31287i) q^{74} +(7.29629 - 3.18685i) q^{76} +(1.61355 - 1.93475i) q^{77} +(-1.60914 - 7.70432i) q^{78} +(5.34864 + 9.26412i) q^{79} +(-1.28561 + 2.22674i) q^{81} +(3.91621 - 3.50117i) q^{82} +(-5.72446 - 5.72446i) q^{83} +(-6.59488 - 0.141933i) q^{84} +(17.4392 + 0.975826i) q^{86} +(-2.33298 - 8.70680i) q^{87} +(-0.253076 - 2.68131i) q^{88} +(-1.83403 + 1.05888i) q^{89} +(-6.80400 - 9.65512i) q^{91} +(-1.01860 - 0.399294i) q^{92} +(4.75329 + 1.27364i) q^{93} +(-4.04859 + 2.04485i) q^{94} +(-5.07384 + 4.89744i) q^{96} +(3.08588 + 3.08588i) q^{97} +(-9.16941 + 3.73120i) q^{98} -1.37686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42}+ \cdots + 90 q^{98}+O(q^{100}) $ 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Character values

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

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

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 $

$2$	1.05431	−	0.942570i	0.745507	−	0.666497i
$2$	1.05431	−	0.942570i	0.745507	−	0.666497i
$3$	1.20413	−	0.322645i	0.695203	−	0.186279i	0.106122	−	0.994353i	$-0.466157\pi$
$3$	1.20413	−	0.322645i	0.695203	−	0.186279i	0.589081	+	0.808074i	$0.299490\pi$
$4$	0.223125	−	1.98751i	0.111563	−	0.993757i
$5$		0			0
$5$		0			0
$6$	0.965404	−	1.47514i	0.394125	−	0.602224i
$7$	0.451584	−	2.60693i	0.170683	−	0.985326i
$7$	0.451584	−	2.60693i	0.170683	−	0.985326i
$8$	−1.63813	−	2.30576i	−0.579166	−	0.815210i
$9$	−1.25225	+	0.722989i	−0.417418	+	0.240996i
$10$		0			0
$11$	0.824629	+	0.476100i	0.248635	+	0.143549i	0.619139	−	0.785281i	$-0.287482\pi$
$11$	0.824629	+	0.476100i	0.248635	+	0.143549i	−0.370504	+	0.928831i	$0.620815\pi$
$12$	−0.372591	−	2.46521i	−0.107558	−	0.711645i
$13$	3.15680	−	3.15680i	0.875540	−	0.875540i	−0.117529	−	0.993069i	$-0.537497\pi$
$13$	3.15680	−	3.15680i	0.875540	−	0.875540i	0.993069	+	0.117529i	$0.0374974\pi$
$14$	−1.98110	−	3.17415i	−0.529472	−	0.848327i
$15$		0			0
$16$	−3.90043	−	0.886929i	−0.975108	−	0.221732i
$17$	−2.56885	+	0.688322i	−0.623038	+	0.166943i	−0.556508	−	0.830842i	$-0.687859\pi$
$17$	−2.56885	+	0.688322i	−0.623038	+	0.166943i	−0.0665295	+	0.997784i	$0.521193\pi$
$18$	−0.638792	+	1.94259i	−0.150565	+	0.457872i
$19$	1.99048	+	3.44760i	0.456646	+	0.790935i	0.998781	−	0.0493567i	$-0.0157171\pi$
$19$	1.99048	+	3.44760i	0.456646	+	0.790935i	−0.542135	+	0.840292i	$0.682384\pi$
$20$		0			0
$21$	−0.297348	−	3.28477i	−0.0648866	−	0.716797i
$22$	1.31817	−	0.275315i	0.281034	−	0.0586973i
$23$	0.141582	−	0.528392i	0.0295219	−	0.110177i	−0.949593	−	0.313486i	$-0.898503\pi$
$23$	0.141582	−	0.528392i	0.0295219	−	0.110177i	0.979115	+	0.203309i	$0.0651696\pi$
$24$	−2.71646	−	2.24790i	−0.554495	−	0.458850i
$25$		0			0
$26$	0.352732	−	6.30375i	0.0691765	−	1.23627i
$27$	−3.91905	+	3.91905i	−0.754222	+	0.754222i
$28$	−5.08055	−	1.47920i	−0.960133	−	0.279543i
$29$		−	7.23080i		−	1.34273i	−0.741129	−	0.671363i	$-0.765709\pi$
$29$		−	7.23080i		−	1.34273i	0.741129	−	0.671363i	$-0.234291\pi$
$30$		0			0
$31$	3.41863	+	1.97375i	0.614004	+	0.354495i	0.774531	−	0.632536i	$-0.217986\pi$
$31$	3.41863	+	1.97375i	0.614004	+	0.354495i	−0.160527	+	0.987031i	$0.551319\pi$
$32$	−4.94824	+	2.74133i	−0.874734	+	0.484604i
$33$	1.14657	+	0.307222i	0.199592	+	0.0534805i
$34$	−2.05957	+	3.14702i	−0.353213	+	0.539710i
$35$		0			0
$36$	1.15754	+	2.65019i	0.192924	+	0.441698i
$37$	−0.269180	+	1.00460i	−0.0442530	+	0.165154i	−0.984516	−	0.175294i	$-0.943912\pi$
$37$	−0.269180	+	1.00460i	−0.0442530	+	0.165154i	0.940263	+	0.340449i	$0.110579\pi$
$38$	5.34818	+	1.75867i	0.867589	+	0.285294i
$39$	2.78267	−	4.81972i	0.445584	−	0.771773i
$40$		0			0
$41$	3.71449			0.580106			0.290053	−	0.957011i	$-0.406327\pi$
$41$	3.71449			0.580106			0.290053	+	0.957011i	$0.406327\pi$
$42$	−3.40962	−	3.18289i	−0.526116	−	0.491130i
$43$	8.73324	+	8.73324i	1.33181	+	1.33181i	0.903754	+	0.428052i	$0.140800\pi$
$43$	8.73324	+	8.73324i	1.33181	+	1.33181i	0.428052	+	0.903754i	$0.359200\pi$
$44$	1.13025	−	1.53273i	0.170392	−	0.231068i
$45$		0			0
$46$	−0.348775	−	0.690538i	−0.0514241	−	0.101814i
$47$	−3.09794	−	0.830089i	−0.451880	−	0.121081i	0.0256988	−	0.999670i	$-0.491819\pi$
$47$	−3.09794	−	0.830089i	−0.451880	−	0.121081i	−0.477579	+	0.878589i	$0.658486\pi$
$48$	−4.98278	+	0.190479i	−0.719202	+	0.0274933i
$49$	−6.59214	−	2.35449i	−0.941735	−	0.336356i
$50$		0			0
$51$	−2.87114	+	1.65765i	−0.402040	+	0.232118i
$52$	−5.56983	−	6.97856i	−0.772397	−	0.967752i
$53$	0.760768	+	2.83923i	0.104500	+	0.389998i	0.998288	−	0.0584914i	$-0.0186290\pi$
$53$	0.760768	+	2.83923i	0.104500	+	0.389998i	−0.893788	+	0.448489i	$0.851962\pi$
$54$	−0.437903	+	7.82586i	−0.0595911	+	1.06496i
$55$		0			0
$56$	−6.75070	+	3.22924i	−0.902101	+	0.431525i
$57$	3.50914	+	3.50914i	0.464797	+	0.464797i
$58$	−6.81553	−	7.62348i	−0.894923	−	1.00101i
$59$	6.30084	−	10.9134i	0.820300	−	1.42080i	−0.0851594	−	0.996367i	$-0.527140\pi$
$59$	6.30084	−	10.9134i	0.820300	−	1.42080i	0.905459	−	0.424433i	$-0.139527\pi$
$60$		0			0
$61$	3.01183	+	5.21665i	0.385626	+	0.667923i	0.991856	−	0.127366i	$-0.0406523\pi$
$61$	3.01183	+	5.21665i	0.385626	+	0.667923i	−0.606230	+	0.795289i	$0.707319\pi$
$62$	5.46468	−	1.14136i	0.694015	−	0.144953i
$63$	1.31928	+	3.59102i	0.166214	+	0.452426i
$64$	−2.63307	+	7.55427i	−0.329134	+	0.944283i
$65$		0			0
$66$	1.49841	−	0.756815i	0.184442	−	0.0931574i
$67$	3.85605	+	14.3910i	0.471092	+	1.75814i	0.635858	+	0.771806i	$0.280647\pi$
$67$	3.85605	+	14.3910i	0.471092	+	1.75814i	−0.164766	+	0.986333i	$0.552687\pi$
$68$	0.794874	+	5.25921i	0.0963927	+	0.637773i
$69$		−	0.681932i		−	0.0820949i
$70$		0			0
$71$			7.60710i			0.902797i	0.892322	+	0.451399i	$0.149075\pi$
$71$			7.60710i			0.902797i	−0.892322	+	0.451399i	$0.850925\pi$
$72$	3.71839	+	1.70305i	0.438216	+	0.200706i
$73$	−3.80964	−	14.2178i	−0.445885	−	1.66406i	−0.713590	−	0.700564i	$-0.752932\pi$
$73$	−3.80964	−	14.2178i	−0.445885	−	1.66406i	0.267705	−	0.963501i	$-0.413735\pi$
$74$	0.663102	+	1.31287i	0.0770841	+	0.152618i
$75$		0			0
$76$	7.29629	−	3.18685i	0.836942	−	0.365557i
$77$	1.61355	−	1.93475i	0.183881	−	0.220485i
$78$	−1.60914	−	7.70432i	−0.182199	−	0.872343i
$79$	5.34864	+	9.26412i	0.601769	+	1.04230i	0.992553	+	0.121813i	$0.0388707\pi$
$79$	5.34864	+	9.26412i	0.601769	+	1.04230i	−0.390784	+	0.920483i	$0.627796\pi$
$80$		0			0
$81$	−1.28561	+	2.22674i	−0.142846	+	0.247416i
$82$	3.91621	−	3.50117i	0.432473	−	0.386639i
$83$	−5.72446	−	5.72446i	−0.628341	−	0.628341i	0.319309	−	0.947651i	$-0.396549\pi$
$83$	−5.72446	−	5.72446i	−0.628341	−	0.628341i	−0.947651	+	0.319309i	$0.896549\pi$
$84$	−6.59488	−	0.141933i	−0.719561	−	0.0154861i
$85$		0			0
$86$	17.4392	+	0.975826i	1.88052	+	0.105226i
$87$	−2.33298	−	8.70680i	−0.250122	−	0.933467i
$88$	−0.253076	−	2.68131i	−0.0269780	−	0.285828i
$89$	−1.83403	+	1.05888i	−0.194407	+	0.112241i	−0.594044	−	0.804433i	$-0.702469\pi$
$89$	−1.83403	+	1.05888i	−0.194407	+	0.112241i	0.399637	+	0.916673i	$0.369136\pi$
$90$		0			0
$91$	−6.80400	−	9.65512i	−0.713253	−	1.01213i
$92$	−1.01860	−	0.399294i	−0.106196	−	0.0416293i
$93$	4.75329	+	1.27364i	0.492893	+	0.132070i
$94$	−4.04859	+	2.04485i	−0.417580	+	0.210910i
$95$		0			0
$96$	−5.07384	+	4.89744i	−0.517846	+	0.499843i
$97$	3.08588	+	3.08588i	0.313324	+	0.313324i	0.846196	−	0.532872i	$-0.178887\pi$
$97$	3.08588	+	3.08588i	0.313324	+	0.313324i	−0.532872	+	0.846196i	$0.678887\pi$
$98$	−9.16941	+	3.73120i	−0.926251	+	0.376908i
$99$	−1.37686			−0.138379
$100$		0			0
$101$	0.715074	−	1.23854i	0.0711525	−	0.123240i	−0.828254	−	0.560353i	$-0.810666\pi$
$101$	0.715074	−	1.23854i	0.0711525	−	0.123240i	0.899407	+	0.437113i	$0.143999\pi$
$102$	−1.46461	+	4.45393i	−0.145018	+	0.441004i
$103$	−2.63366	+	9.82894i	−0.259502	+	0.968474i	0.706028	+	0.708183i	$0.250485\pi$
$103$	−2.63366	+	9.82894i	−0.259502	+	0.968474i	−0.965530	+	0.260291i	$0.916182\pi$
$104$	−12.4501	−	2.10758i	−1.22083	−	0.206666i
$105$		0			0
$106$	3.47825	+	2.27634i	0.337838	+	0.221097i
$107$	0.0388547	+	0.0104111i	0.00375622	+	0.00100648i	0.260697	−	0.965421i	$-0.416048\pi$
$107$	0.0388547	+	0.0104111i	0.00375622	+	0.00100648i	−0.256940	+	0.966427i	$0.582714\pi$
$108$	6.91473	+	8.66361i	0.665371	+	0.833656i
$109$	5.44983	+	3.14646i	0.521999	+	0.301376i	0.737752	−	0.675072i	$-0.235887\pi$
$109$	5.44983	+	3.14646i	0.521999	+	0.301376i	−0.215753	+	0.976448i	$0.569221\pi$
$110$		0			0
$111$			1.29651i			0.123059i
$112$	−4.07353	+	9.76762i	−0.384912	+	0.922953i
$113$	−10.8513	+	10.8513i	−1.02081	+	1.02081i	−0.0210265	+	0.999779i	$0.506693\pi$
$113$	−10.8513	+	10.8513i	−1.02081	+	1.02081i	−0.999779	+	0.0210265i	$0.993307\pi$
$114$	7.00732	+	0.392101i	0.656295	+	0.0367236i
$115$		0			0
$116$	−14.3713	−	1.61337i	−1.33434	−	0.149798i
$117$	−1.67078	+	6.23545i	−0.154464	+	0.576468i
$118$	−3.64360	−	17.4450i	−0.335420	−	1.60595i
$119$	0.634353	+	7.00765i	0.0581511	+	0.642390i
$120$		0			0
$121$	−5.04666	−	8.74107i	−0.458787	−	0.794643i
$122$	8.09245	+	2.66108i	0.732656	+	0.240923i
$123$	4.47272	−	1.19846i	0.403292	−	0.108062i
$124$	4.68563	−	6.35419i	0.420782	−	0.570623i
$125$		0			0
$126$	4.77572	+	2.54252i	0.425455	+	0.226506i
$127$	1.22418	−	1.22418i	0.108629	−	0.108629i	−0.650703	−	0.759332i	$-0.725526\pi$
$127$	1.22418	−	1.22418i	0.108629	−	0.108629i	0.759332	+	0.650703i	$0.225526\pi$
$128$	4.34436	+	10.4464i	0.383991	+	0.923337i
$129$	13.3337	+	7.69820i	1.17396	+	0.677788i
$130$		0			0
$131$	−1.12982	+	0.652300i	−0.0987126	+	0.0569918i	−0.548544	−	0.836122i	$-0.684818\pi$
$131$	−1.12982	+	0.652300i	−0.0987126	+	0.0569918i	0.449831	+	0.893114i	$0.351484\pi$
$132$	0.866437	−	2.21027i	0.0754137	−	0.192380i
$133$	9.88652	−	3.63214i	0.857270	−	0.314947i
$134$	17.6300	+	11.5379i	1.52300	+	0.996724i
$135$		0			0
$136$	5.79522	+	4.79560i	0.496936	+	0.411219i
$137$	1.12037	−	0.300203i	0.0957198	−	0.0256480i	−0.210641	−	0.977563i	$-0.567555\pi$
$137$	1.12037	−	0.300203i	0.0957198	−	0.0256480i	0.306361	+	0.951915i	$0.400889\pi$
$138$	−0.642768	−	0.718965i	−0.0547161	−	0.0612024i
$139$	−17.4513			−1.48020			−0.740099	−	0.672498i	$-0.765221\pi$
$139$	−17.4513			−1.48020			−0.740099	+	0.672498i	$0.765221\pi$
$140$		0			0
$141$	−3.99813			−0.336704
$142$	7.17023	+	8.02022i	0.601712	+	0.673042i
$143$	4.10614	−	1.10024i	0.343373	−	0.0920065i
$144$	5.52556	−	1.70931i	0.460464	−	0.142442i
$145$		0			0
$146$	−17.4178	−	11.3990i	−1.44151	−	0.943392i
$147$	−8.69745	−	0.708187i	−0.717353	−	0.0584103i
$148$	1.93659	+	0.759151i	0.159186	+	0.0624018i
$149$	9.70894	−	5.60546i	0.795387	−	0.459217i	−0.0464684	−	0.998920i	$-0.514797\pi$
$149$	9.70894	−	5.60546i	0.795387	−	0.459217i	0.841856	+	0.539703i	$0.181463\pi$
$150$		0			0
$151$	13.0081	+	7.51022i	1.05858	+	0.611173i	0.925040	−	0.379870i	$-0.124031\pi$
$151$	13.0081	+	7.51022i	1.05858	+	0.611173i	0.133543	+	0.991043i	$0.457365\pi$
$152$	4.68870	−	10.2372i	0.380304	−	0.830345i
$153$	2.71920	−	2.71920i	0.219835	−	0.219835i
$154$	−0.122463	−	3.56070i	−0.00986832	−	0.286929i
$155$		0			0
$156$	−8.95839	−	6.60600i	−0.717245	−	0.528903i
$157$	7.27171	−	1.94845i	0.580345	−	0.155503i	0.0433084	−	0.999062i	$-0.486210\pi$
$157$	7.27171	−	1.94845i	0.580345	−	0.155503i	0.537037	+	0.843559i	$0.319544\pi$
$158$	14.3712	+	4.72576i	1.14331	+	0.375961i
$159$	1.83212	+	3.17333i	0.145297	+	0.251662i
$160$		0			0
$161$	−1.31354	−	0.607707i	−0.103522	−	0.0478941i
$162$	0.743432	+	3.55944i	0.0584095	+	0.279656i
$163$	1.72089	−	6.42243i	0.134790	−	0.503044i	−0.865208	−	0.501412i	$-0.832814\pi$
$163$	1.72089	−	6.42243i	0.134790	−	0.503044i	0.999999	−	0.00163153i	$-0.000519334\pi$
$164$	0.828796	−	7.38261i	0.0647181	−	0.576485i
$165$		0			0
$166$	−11.4310	−	0.639635i	−0.887221	−	0.0496453i
$167$	5.93258	−	5.93258i	0.459077	−	0.459077i	−0.439276	−	0.898352i	$-0.644765\pi$
$167$	5.93258	−	5.93258i	0.459077	−	0.459077i	0.898352	+	0.439276i	$0.144765\pi$
$168$	−7.08681	+	6.06650i	−0.546759	+	0.468040i
$169$		−	6.93083i		−	0.533141i
$170$		0			0
$171$	−4.98516	−	2.87818i	−0.381225	−	0.220100i
$172$	19.3060	−	15.4088i	1.47207	−	1.17491i
$173$	−2.13818	−	0.572923i	−0.162563	−	0.0435585i	0.176620	−	0.984279i	$-0.443484\pi$
$173$	−2.13818	−	0.572923i	−0.162563	−	0.0435585i	−0.339182	+	0.940721i	$0.610150\pi$
$174$	−10.6664	−	6.98064i	−0.808621	−	0.529201i
$175$		0			0
$176$	−2.79414	−	2.58838i	−0.210616	−	0.195106i
$177$	4.06587	−	15.1740i	0.305610	−	1.14055i
$178$	−0.935563	+	2.84508i	−0.0701234	+	0.213248i
$179$	−8.23493	+	14.2633i	−0.615507	+	1.06609i	0.374788	+	0.927111i	$0.377716\pi$
$179$	−8.23493	+	14.2633i	−0.615507	+	1.06609i	−0.990295	+	0.138980i	$0.955618\pi$
$180$		0			0
$181$	−5.97636			−0.444219			−0.222110	−	0.975022i	$-0.571294\pi$
$181$	−5.97636			−0.444219			−0.222110	+	0.975022i	$0.571294\pi$
$182$	−16.2741	−	3.76622i	−1.20632	−	0.279171i
$183$	5.30976	+	5.30976i	0.392508	+	0.392508i
$184$	−1.45027	+	0.539119i	−0.106916	+	0.0397444i
$185$		0			0
$186$	6.21192	−	3.13750i	0.455480	−	0.230052i
$187$	−2.44606	−	0.655419i	−0.178873	−	0.0479290i
$188$	−2.34104	+	5.97198i	−0.170738	+	0.435551i
$189$	8.44690	+	11.9865i	0.614422	+	0.871887i
$190$		0			0
$191$	−6.96830	+	4.02315i	−0.504209	+	0.291105i	−0.730450	−	0.682966i	$-0.760690\pi$
$191$	−6.96830	+	4.02315i	−0.504209	+	0.291105i	0.226241	+	0.974071i	$0.427356\pi$
$192$	−0.733203	+	9.94585i	−0.0529144	+	0.717780i
$193$	3.76831	+	14.0635i	0.271249	+	1.01231i	0.958314	+	0.285718i	$0.0922321\pi$
$193$	3.76831	+	14.0635i	0.271249	+	1.01231i	−0.687065	+	0.726596i	$0.741101\pi$
$194$	6.16213	+	0.344807i	0.442415	+	0.0247557i
$195$		0			0
$196$	−6.15046	+	12.5766i	−0.439319	+	0.898331i
$197$	−16.4919	−	16.4919i	−1.17500	−	1.17500i	−0.981001	−	0.194001i	$-0.937854\pi$
$197$	−16.4919	−	16.4919i	−1.17500	−	1.17500i	−0.194001	−	0.981001i	$-0.562146\pi$
$198$	−1.45163	+	1.29778i	−0.103163	+	0.0922295i
$199$	4.82793	−	8.36222i	0.342243	−	0.592782i	−0.642606	−	0.766197i	$-0.722147\pi$
$199$	4.82793	−	8.36222i	0.342243	−	0.592782i	0.984849	+	0.173415i	$0.0554801\pi$
$200$		0			0
$201$	9.28636	+	16.0844i	0.655009	+	1.13451i
$202$	−0.413507	−	1.97981i	−0.0290943	−	0.139299i
$203$	−18.8502	−	3.26531i	−1.32302	−	0.229180i
$204$	2.65399	+	6.07630i	0.185816	+	0.425426i
$205$		0			0
$206$	6.48778	+	12.8451i	0.452025	+	0.894962i
$207$	0.204725	+	0.764042i	0.0142293	+	0.0531046i
$208$	−15.1128	+	9.51304i	−1.04788	+	0.659610i
$209$			3.79066i			0.262205i
$210$		0			0
$211$		−	10.4344i		−	0.718333i	−0.933274	−	0.359166i	$-0.883061\pi$
$211$		−	10.4344i		−	0.718333i	0.933274	−	0.359166i	$-0.116939\pi$
$212$	5.81275	−	0.878535i	0.399221	−	0.0603381i
$213$	2.45439	+	9.15992i	0.168172	+	0.627628i
$214$	0.0507779	−	0.0256468i	0.00347111	−	0.00175318i
$215$		0			0
$216$	15.4563	+	2.61649i	1.05167	+	0.178029i
$217$	6.68921	−	8.02081i	0.454093	−	0.544488i
$218$	8.71155	−	1.81951i	0.590020	−	0.123233i
$219$	−9.17459	−	15.8909i	−0.619961	−	1.07380i
$220$		0			0
$221$	−5.93647	+	10.2823i	−0.399330	+	0.691660i
$222$	1.22205	+	1.36692i	0.0820187	+	0.0917416i
$223$	−10.7262	−	10.7262i	−0.718279	−	0.718279i	0.249973	−	0.968253i	$-0.419578\pi$
$223$	−10.7262	−	10.7262i	−0.718279	−	0.718279i	−0.968253	+	0.249973i	$0.919578\pi$
$224$	4.91191	+	14.1377i	0.328191	+	0.944611i
$225$		0			0
$226$	−1.21249	+	21.6687i	−0.0806539	+	1.44138i
$227$	2.59397	+	9.68083i	0.172168	+	0.642539i	0.997017	+	0.0771860i	$0.0245935\pi$
$227$	2.59397	+	9.68083i	0.172168	+	0.642539i	−0.824849	+	0.565353i	$0.808740\pi$
$228$	7.75744	−	6.19149i	0.513749	−	0.410041i
$229$	−14.7989	+	8.54416i	−0.977940	+	0.564614i	−0.901647	−	0.432472i	$-0.857641\pi$
$229$	−14.7989	+	8.54416i	−0.977940	+	0.564614i	−0.0762921	+	0.997086i	$0.524308\pi$
$230$		0			0
$231$	1.31868	−	2.85029i	0.0867627	−	0.187535i
$232$	−16.6725	+	11.8450i	−1.09460	+	0.777661i
$233$	−1.81156	−	0.485407i	−0.118680	−	0.0318001i	0.198990	−	0.980001i	$-0.436234\pi$
$233$	−1.81156	−	0.485407i	−0.118680	−	0.0318001i	−0.317670	+	0.948201i	$0.602900\pi$
$234$	4.11583	+	8.14891i	0.269060	+	0.532711i
$235$		0			0
$236$	−20.2846	−	14.9581i	−1.32042	−	0.973687i
$237$	9.42947	+	9.42947i	0.612510	+	0.612510i
$238$	7.27400	+	6.79029i	0.471503	+	0.440149i
$239$	15.2182			0.984385			0.492193	−	0.870486i	$-0.336196\pi$
$239$	15.2182			0.984385			0.492193	+	0.870486i	$0.336196\pi$
$240$		0			0
$241$	6.58780	−	11.4104i	0.424357	−	0.735008i	−0.572003	−	0.820252i	$-0.693833\pi$
$241$	6.58780	−	11.4104i	0.424357	−	0.735008i	0.996360	+	0.0852432i	$0.0271667\pi$
$242$	−13.5598	−	4.45894i	−0.871656	−	0.286632i
$243$	3.47383	−	12.9645i	0.222846	−	0.831673i
$244$	11.0402	−	4.82210i	0.706775	−	0.308703i
$245$		0			0
$246$	3.58599	−	5.47940i	0.228634	−	0.349354i
$247$	17.1670	+	4.59987i	1.09231	+	0.292683i
$248$	−1.04917	−	11.1158i	−0.0666222	−	0.705854i
$249$	−8.73995	−	5.04601i	−0.553872	−	0.319778i
$250$		0			0
$251$		−	14.7048i		−	0.928161i	−0.885793	−	0.464080i	$-0.846385\pi$
$251$		−	14.7048i		−	0.928161i	0.885793	−	0.464080i	$-0.153615\pi$
$252$	7.43158	−	1.82084i	0.468145	−	0.114702i
$253$	0.368320	−	0.368320i	0.0231561	−	0.0231561i
$254$	0.136786	−	2.44454i	0.00858275	−	0.153384i
$255$		0			0
$256$	14.4267	+	6.91881i	0.901670	+	0.432426i
$257$	−3.42109	+	12.7677i	−0.213402	+	0.796426i	0.773321	+	0.634014i	$0.218594\pi$
$257$	−3.42109	+	12.7677i	−0.213402	+	0.796426i	−0.986723	+	0.162412i	$0.948073\pi$
$258$	21.3139	−	4.45165i	1.32694	−	0.277148i
$259$	2.49735	+	1.15539i	0.155178	+	0.0717926i
$260$		0			0
$261$	5.22778	+	9.05478i	0.323592	+	0.560477i
$262$	−0.576336	+	1.75266i	−0.0356061	+	0.108279i
$263$	10.2083	−	2.73529i	0.629468	−	0.168665i	0.0700398	−	0.997544i	$-0.477687\pi$
$263$	10.2083	−	2.73529i	0.629468	−	0.168665i	0.559428	+	0.828879i	$0.311021\pi$
$264$	−1.16985	−	3.14698i	−0.0719991	−	0.193683i
$265$		0			0
$266$	6.99988	−	13.1481i	0.429190	−	0.806164i
$267$	−1.86676	+	1.86676i	−0.114244	+	0.114244i
$268$	29.4627	−	4.45297i	1.79972	−	0.272009i
$269$	−10.5625	−	6.09826i	−0.644007	−	0.371818i	0.142149	−	0.989845i	$-0.454599\pi$
$269$	−10.5625	−	6.09826i	−0.644007	−	0.371818i	−0.786156	+	0.618027i	$0.787932\pi$
$270$		0			0
$271$	5.70012	−	3.29096i	0.346257	−	0.199912i	−0.316778	−	0.948500i	$-0.602601\pi$
$271$	5.70012	−	3.29096i	0.346257	−	0.199912i	0.663036	+	0.748588i	$0.269268\pi$
$272$	10.6301	−	0.406362i	0.644546	−	0.0246393i
$273$	−11.3081	−	9.43072i	−0.684395	−	0.570773i
$274$	0.898253	−	1.37253i	0.0542655	−	0.0829178i
$275$		0			0
$276$	−1.35535	−	0.152156i	−0.0815824	−	0.00915872i
$277$	−3.96687	+	1.06292i	−0.238346	+	0.0638646i	−0.376015	−	0.926614i	$-0.622706\pi$
$277$	−3.96687	+	1.06292i	−0.238346	+	0.0638646i	0.137669	+	0.990478i	$0.456039\pi$
$278$	−18.3990	+	16.4490i	−1.10350	+	0.986548i
$279$	−5.70799			−0.341728
$280$		0			0
$281$	−32.2773			−1.92550			−0.962752	−	0.270386i	$-0.912849\pi$
$281$	−32.2773			−1.92550			−0.962752	+	0.270386i	$0.912849\pi$
$282$	−4.21526	+	3.76852i	−0.251015	+	0.224412i
$283$	−18.8626	+	5.05423i	−1.12127	+	0.300443i	−0.771396	−	0.636355i	$-0.780441\pi$
$283$	−18.8626	+	5.05423i	−1.12127	+	0.300443i	−0.349872	+	0.936798i	$0.613775\pi$
$284$	15.1192	+	1.69734i	0.897161	+	0.100718i
$285$		0			0
$286$	3.29208	−	5.03032i	0.194665	−	0.297449i
$287$	1.67740	−	9.68341i	0.0990140	−	0.571594i
$288$	4.21450	−	7.01036i	0.248342	−	0.413090i
$289$	−8.59722	+	4.96361i	−0.505719	+	0.291977i
$290$		0			0
$291$	4.71144	+	2.72015i	0.276190	+	0.159458i
$292$	−29.1081	+	4.39938i	−1.70342	+	0.257454i
$293$	−12.6859	+	12.6859i	−0.741121	+	0.741121i	−0.972794	−	0.231673i	$-0.925580\pi$
$293$	−12.6859	+	12.6859i	−0.741121	+	0.741121i	0.231673	+	0.972794i	$0.425580\pi$
$294$	−9.83729	+	7.45130i	−0.573723	+	0.434569i
$295$		0			0
$296$	2.75731	−	1.02499i	0.160265	−	0.0595764i
$297$	−5.09762	+	1.36590i	−0.295794	+	0.0792577i
$298$	4.95266	−	15.0612i	0.286900	−	0.872473i
$299$	−1.22108	−	2.11498i	−0.0706170	−	0.122312i
$300$		0			0
$301$	26.7107	−	18.8231i	1.53958	−	1.08495i
$302$	20.7934	−	4.34295i	1.19653	−	0.249909i
$303$	0.461430	−	1.72208i	0.0265085	−	0.0989309i
$304$	−4.70593	−	15.2126i	−0.269904	−	0.872500i
$305$		0			0
$306$	0.303836	−	5.42991i	0.0173691	−	0.310407i
$307$	9.98091	−	9.98091i	0.569640	−	0.569640i	−0.362387	−	0.932028i	$-0.618038\pi$
$307$	9.98091	−	9.98091i	0.569640	−	0.569640i	0.932028	+	0.362387i	$0.118038\pi$
$308$	−3.48532	−	3.63864i	−0.198594	−	0.207331i
$309$			12.6850i			0.721626i
$310$		0			0
$311$	−12.0711	−	6.96926i	−0.684490	−	0.395190i	0.117055	−	0.993125i	$-0.462655\pi$
$311$	−12.0711	−	6.96926i	−0.684490	−	0.395190i	−0.801544	+	0.597935i	$0.795988\pi$
$312$	−15.6715	+	1.47916i	−0.887224	+	0.0837409i
$313$	4.74109	+	1.27037i	0.267982	+	0.0718056i	0.390308	−	0.920684i	$-0.372369\pi$
$313$	4.74109	+	1.27037i	0.267982	+	0.0718056i	−0.122326	+	0.992490i	$0.539035\pi$
$314$	5.83006	−	8.90835i	0.329009	−	0.502727i
$315$		0			0
$316$	19.6060	−	8.56345i	1.10292	−	0.481732i
$317$	−8.90414	+	33.2307i	−0.500106	+	1.86642i	−0.000794747		1.00000i	$0.500253\pi$
$317$	−8.90414	+	33.2307i	−0.500106	+	1.86642i	−0.499312	+	0.866423i	$0.666414\pi$
$318$	4.92271	+	1.61876i	0.276052	+	0.0907756i
$319$	3.44258	−	5.96272i	0.192747	−	0.333848i
$320$		0			0
$321$	0.0501451			0.00279883
$322$	−1.95768	+	0.597395i	−0.109097	+	0.0332915i
$323$	−7.48630	−	7.48630i	−0.416549	−	0.416549i
$324$	4.13883	+	3.05201i	0.229935	+	0.169556i
$325$		0			0
$326$	−4.23925	−	8.39327i	−0.234790	−	0.464860i
$327$	7.57748	+	2.03038i	0.419035	+	0.112280i
$328$	−6.08482	−	8.56473i	−0.335978	−	0.472908i
$329$	−3.56296	+	7.70124i	−0.196432	+	0.424583i
$330$		0			0
$331$	11.2201	−	6.47792i	0.616712	−	0.356059i	−0.158876	−	0.987299i	$-0.550787\pi$
$331$	11.2201	−	6.47792i	0.616712	−	0.356059i	0.775588	+	0.631240i	$0.217454\pi$
$332$	−12.6547	+	10.1002i	−0.694518	+	0.554320i
$333$	−0.389229	−	1.45262i	−0.0213296	−	0.0796032i
$334$	0.662889	−	11.8466i	0.0362717	−	0.648219i
$335$		0			0
$336$	−1.75358	+	13.0758i	−0.0956655	+	0.713341i
$337$	−7.43071	−	7.43071i	−0.404776	−	0.404776i	0.475136	−	0.879912i	$-0.342399\pi$
$337$	−7.43071	−	7.43071i	−0.404776	−	0.404776i	−0.879912	+	0.475136i	$0.842399\pi$
$338$	−6.53279	−	7.30722i	−0.355337	−	0.397461i
$339$	−9.56524	+	16.5675i	−0.519513	+	0.899822i
$340$		0			0
$341$	1.87940	+	3.25522i	0.101775	+	0.176280i
$342$	−7.96877	+	1.66437i	−0.430902	+	0.0899989i
$343$	−9.11490	+	16.1220i	−0.492158	+	0.870506i
$344$	5.83059	−	34.4429i	0.314364	−	1.85704i
$345$		0			0
$346$	−2.79431	+	1.41134i	−0.150223	+	0.0758743i
$347$	−2.37153	−	8.85066i	−0.127310	−	0.475128i	0.872601	−	0.488433i	$-0.162431\pi$
$347$	−2.37153	−	8.85066i	−0.127310	−	0.475128i	−0.999911	+	0.0133050i	$0.995765\pi$
$348$	−17.8254	+	2.69413i	−0.955544	+	0.144420i
$349$		−	19.9513i		−	1.06797i	−0.845495	−	0.533984i	$-0.820694\pi$
$349$		−	19.9513i		−	1.06797i	0.845495	−	0.533984i	$-0.179306\pi$
$350$		0			0
$351$			24.7434i			1.32070i
$352$	−5.38561	−	0.0952748i	−0.287054	−	0.00507817i
$353$	−0.641552	−	2.39430i	−0.0341464	−	0.127436i	0.946749	−	0.321973i	$-0.104346\pi$
$353$	−0.641552	−	2.39430i	−0.0341464	−	0.127436i	−0.980895	+	0.194537i	$0.937679\pi$
$354$	−10.0159	−	19.8305i	−0.532340	−	1.05398i
$355$		0			0
$356$	1.69532	+	3.88142i	0.0898516	+	0.205715i
$357$	3.02482	+	8.23343i	0.160091	+	0.435759i
$358$	4.76203	+	22.7999i	0.251681	+	1.20501i
$359$	−7.94645	−	13.7637i	−0.419398	−	0.726418i	0.576481	−	0.817110i	$-0.304425\pi$
$359$	−7.94645	−	13.7637i	−0.419398	−	0.726418i	−0.995879	+	0.0906921i	$0.971092\pi$
$360$		0			0
$361$	1.57601	−	2.72973i	0.0829481	−	0.143670i
$362$	−6.30091	+	5.63313i	−0.331169	+	0.296071i
$363$	−8.89708	−	8.89708i	−0.466976	−	0.466976i
$364$	−20.7078	+	11.3688i	−1.08539	+	0.595884i
$365$		0			0
$366$	10.6029	+	0.593297i	0.554224	+	0.0310121i
$367$	−2.78634	−	10.3988i	−0.145446	−	0.542812i	−0.999735	−	0.0230136i	$-0.992674\pi$
$367$	−2.78634	−	10.3988i	−0.145446	−	0.542812i	0.854289	−	0.519798i	$-0.173993\pi$
$368$	−1.02088	+	1.93538i	−0.0532169	+	0.100889i
$369$	−4.65148	+	2.68553i	−0.242147	+	0.139803i
$370$		0			0
$371$	7.74521	−	0.701119i	0.402111	−	0.0364003i
$372$	3.59195	−	9.16305i	0.186234	−	0.475082i
$373$	−14.2618	−	3.82144i	−0.738448	−	0.197867i	−0.130060	−	0.991506i	$-0.541517\pi$
$373$	−14.2618	−	3.82144i	−0.738448	−	0.197867i	−0.608388	+	0.793640i	$0.708184\pi$
$374$	−3.19667	+	1.61457i	−0.165296	+	0.0834873i
$375$		0			0
$376$	3.16083	+	8.50289i	0.163007	+	0.438503i
$377$	−22.8262	−	22.8262i	−1.17561	−	1.17561i
$378$	20.2037	+	4.67561i	1.03917	+	0.240488i
$379$	−26.4563			−1.35897			−0.679483	−	0.733691i	$-0.737796\pi$
$379$	−26.4563			−1.35897			−0.679483	+	0.733691i	$0.737796\pi$
$380$		0			0
$381$	1.07909	−	1.86905i	0.0552837	−	0.0957542i
$382$	−3.55463	+	10.8097i	−0.181871	+	0.553075i
$383$	7.60437	−	28.3799i	0.388565	−	1.45015i	−0.443904	−	0.896074i	$-0.646407\pi$
$383$	7.60437	−	28.3799i	0.388565	−	1.45015i	0.832470	−	0.554071i	$-0.186926\pi$
$384$	8.60163	+	11.1771i	0.438950	+	0.570377i
$385$		0			0
$386$	17.2288	+	11.2754i	0.876922	+	0.573901i
$387$	−17.2503	−	4.62219i	−0.876880	−	0.234959i
$388$	6.82177	−	5.44470i	0.346323	−	0.276413i
$389$	−8.09963	−	4.67632i	−0.410667	−	0.237099i	0.280409	−	0.959881i	$-0.409530\pi$
$389$	−8.09963	−	4.67632i	−0.410667	−	0.237099i	−0.691076	+	0.722782i	$0.742863\pi$
$390$		0			0
$391$			1.45481i			0.0735731i
$392$	5.36988	+	19.0569i	0.271220	+	0.962517i
$393$	−1.14998	+	1.14998i	−0.0580090	+	0.0580090i
$394$	−32.9324	−	1.84276i	−1.65911	−	0.0928370i
$395$		0			0
$396$	−0.307212	+	2.73653i	−0.0154380	+	0.137516i
$397$	4.59912	−	17.1641i	0.230823	−	0.861443i	−0.749164	−	0.662384i	$-0.769545\pi$
$397$	4.59912	−	17.1641i	0.230823	−	0.861443i	0.979987	−	0.199059i	$-0.0637886\pi$
$398$	−2.79186	−	13.3670i	−0.139943	−	0.670028i
$399$	10.7327	−	7.56340i	0.537309	−	0.378644i
$400$		0			0
$401$	−3.07671	−	5.32902i	−0.153644	−	0.266118i	0.778921	−	0.627122i	$-0.215767\pi$
$401$	−3.07671	−	5.32902i	−0.153644	−	0.266118i	−0.932564	+	0.361004i	$0.882434\pi$
$402$	24.9514	+	8.20490i	1.24446	+	0.409223i
$403$	17.0227	−	4.56121i	0.847960	−	0.227210i
$404$	−2.30207	−	1.69757i	−0.114532	−	0.0844573i
$405$		0			0
$406$	−22.9516	+	14.3250i	−1.13907	+	0.710935i
$407$	−0.700261	+	0.700261i	−0.0347107	+	0.0347107i
$408$	8.52545	+	3.90471i	0.422073	+	0.193312i
$409$	5.66917	+	3.27310i	0.280322	+	0.161844i	0.633569	−	0.773686i	$-0.281589\pi$
$409$	5.66917	+	3.27310i	0.280322	+	0.161844i	−0.353247	+	0.935530i	$0.614922\pi$
$410$		0			0
$411$	1.25221	−	0.722965i	0.0617670	−	0.0356612i
$412$	18.9475	+	7.42751i	0.933478	+	0.365927i
$413$	−25.6050	−	21.3541i	−1.25994	−	1.05077i
$414$	0.936005	+	0.612568i	0.0460022	+	0.0301061i
$415$		0			0
$416$	−6.96678	+	24.2745i	−0.341575	+	1.19015i
$417$	−21.0136	+	5.63057i	−1.02904	+	0.275730i
$418$	3.57296	+	3.99652i	0.174759	+	0.195476i
$419$	−17.7908			−0.869139			−0.434569	−	0.900638i	$-0.643099\pi$
$419$	−17.7908			−0.869139			−0.434569	+	0.900638i	$0.643099\pi$
$420$		0			0
$421$	−16.4678			−0.802591			−0.401295	−	0.915949i	$-0.631440\pi$
$421$	−16.4678			−0.802591			−0.401295	+	0.915949i	$0.631440\pi$
$422$	−9.83513	−	11.0010i	−0.478767	−	0.535522i
$423$	4.47954	−	1.20029i	0.217803	−	0.0583601i
$424$	5.30034	−	6.40517i	0.257407	−	0.311062i
$425$		0			0
$426$	11.2215	+	7.34393i	0.543686	+	0.355815i
$427$	14.9595	−	5.49588i	0.723942	−	0.265964i
$428$	0.0293616	−	0.0749013i	0.00141925	−	0.00362049i
$429$	4.58934	−	2.64965i	0.221575	−	0.127926i
$430$		0			0
$431$	−13.1055	−	7.56644i	−0.631268	−	0.364463i	0.149975	−	0.988690i	$-0.452081\pi$
$431$	−13.1055	−	7.56644i	−0.631268	−	0.364463i	−0.781243	+	0.624227i	$0.785414\pi$
$432$	18.7619	−	11.8101i	0.902683	−	0.568212i
$433$	5.45382	−	5.45382i	0.262094	−	0.262094i	−0.563811	−	0.825904i	$-0.690665\pi$
$433$	5.45382	−	5.45382i	0.262094	−	0.262094i	0.825904	+	0.563811i	$0.190665\pi$
$434$	−0.507689	−	14.7614i	−0.0243698	−	0.708572i
$435$		0			0
$436$	7.46963	−	10.1296i	0.357730	−	0.485118i
$437$	2.10350	−	0.563632i	0.100624	−	0.0269622i
$438$	−24.6511	−	8.10614i	−1.17787	−	0.387327i
$439$	12.8732	+	22.2970i	0.614402	+	1.06418i	0.990489	+	0.137592i	$0.0439362\pi$
$439$	12.8732	+	22.2970i	0.614402	+	1.06418i	−0.376087	+	0.926585i	$0.622730\pi$
$440$		0			0
$441$	9.95730	−	1.81762i	0.474157	−	0.0865536i
$442$	3.43289	+	16.4362i	0.163286	+	0.781790i
$443$	−4.47481	+	16.7002i	−0.212605	+	0.793452i	0.774391	+	0.632707i	$0.218056\pi$
$443$	−4.47481	+	16.7002i	−0.212605	+	0.793452i	−0.986996	+	0.160745i	$0.948610\pi$
$444$	2.57683	+	0.289284i	0.122291	+	0.0137288i
$445$		0			0
$446$	−21.4189	−	1.19851i	−1.01421	−	0.0567513i
$447$	9.88223	−	9.88223i	0.467413	−	0.467413i
$448$	18.5044	+	10.2756i	0.874250	+	0.485477i
$449$		−	11.0999i		−	0.523839i	−0.965090	−	0.261919i	$-0.915645\pi$
$449$		−	11.0999i		−	0.523839i	0.965090	−	0.261919i	$-0.0843555\pi$
$450$		0			0
$451$	3.06308	+	1.76847i	0.144235	+	0.0832739i
$452$	19.1459	+	23.9883i	0.900549	+	1.12832i
$453$	18.0865	+	4.84627i	0.849779	+	0.227698i
$454$	11.8597	+	7.76157i	0.556603	+	0.364268i
$455$		0			0
$456$	2.34281	−	13.8397i	0.109712	−	0.648101i
$457$	5.49672	−	20.5140i	0.257126	−	0.959606i	−0.709770	−	0.704434i	$-0.751201\pi$
$457$	5.49672	−	20.5140i	0.257126	−	0.959606i	0.966896	−	0.255172i	$-0.0821322\pi$
$458$	−7.54913	+	22.9572i	−0.352748	+	1.07272i
$459$	7.36989	−	12.7650i	0.343997	−	0.595821i
$460$		0			0
$461$	−8.61652			−0.401311			−0.200656	−	0.979662i	$-0.564307\pi$
$461$	−8.61652			−0.401311			−0.200656	+	0.979662i	$0.564307\pi$
$462$	−1.29630	−	4.24802i	−0.0603094	−	0.197636i
$463$	1.63340	+	1.63340i	0.0759103	+	0.0759103i	0.744043	−	0.668132i	$-0.232906\pi$
$463$	1.63340	+	1.63340i	0.0759103	+	0.0759103i	−0.668132	+	0.744043i	$0.732906\pi$
$464$	−6.41320	+	28.2032i	−0.297725	+	1.30930i
$465$		0			0
$466$	−2.36747	+	1.19576i	−0.109671	+	0.0553924i
$467$	−24.6125	−	6.59489i	−1.13893	−	0.305175i	−0.360409	−	0.932794i	$-0.617363\pi$
$467$	−24.6125	−	6.59489i	−1.13893	−	0.305175i	−0.778521	+	0.627619i	$0.784030\pi$
$468$	12.0203	+	4.71199i	0.555637	+	0.217812i
$469$	39.2576	−	3.55372i	1.81275	−	0.164095i
$470$		0			0
$471$	8.12741	−	4.69236i	0.374491	−	0.216213i
$472$	−35.4852	+	3.34928i	−1.63334	+	0.154163i
$473$	3.04379	+	11.3596i	0.139953	+	0.522313i
$474$	18.8295	+	1.05362i	0.864867	+	0.0483944i
$475$		0			0
$476$	14.0693	+	0.302795i	0.644867	+	0.0138786i
$477$	−3.00540	−	3.00540i	−0.137608	−	0.137608i
$478$	16.0447	−	14.3442i	0.733867	−	0.656090i
$479$	−4.63924	+	8.03541i	−0.211972	+	0.367147i	−0.952332	−	0.305064i	$-0.901322\pi$
$479$	−4.63924	+	8.03541i	−0.211972	+	0.367147i	0.740359	+	0.672211i	$0.234655\pi$
$480$		0			0
$481$	2.32156	+	4.02106i	0.105854	+	0.183345i
$482$	−3.80954	−	18.2395i	−0.173520	−	0.830787i
$483$	−1.77775	−	0.307949i	−0.0808903	−	0.0140122i
$484$	−18.4990	+	8.07996i	−0.840865	+	0.367271i
$485$		0			0
$486$	−8.55746	−	16.9429i	−0.388174	−	0.768544i
$487$	4.60932	+	17.2022i	0.208868	+	0.779506i	0.988236	+	0.152939i	$0.0488738\pi$
$487$	4.60932	+	17.2022i	0.208868	+	0.779506i	−0.779368	+	0.626567i	$0.784459\pi$
$488$	7.09457	−	15.4901i	0.321156	−	0.701204i
$489$		−	8.28866i		−	0.374826i
$490$		0			0
$491$		−	2.49970i		−	0.112810i	−0.998408	−	0.0564049i	$-0.982036\pi$
$491$		−	2.49970i		−	0.112810i	0.998408	−	0.0564049i	$-0.0179638\pi$
$492$	−1.38398	−	9.15701i	−0.0623949	−	0.412830i
$493$	4.97711	+	18.5748i	0.224158	+	0.836569i
$494$	22.4349	−	11.3314i	1.00940	−	0.509823i
$495$		0			0
$496$	−11.5836	−	10.7305i	−0.520117	−	0.481816i
$497$	19.8312	+	3.43524i	0.889550	+	0.154092i
$498$	−13.9708	+	2.91797i	−0.626047	+	0.130757i
$499$	−3.26199	−	5.64993i	−0.146027	−	0.252926i	0.783729	−	0.621103i	$-0.213315\pi$
$499$	−3.26199	−	5.64993i	−0.146027	−	0.252926i	−0.929756	+	0.368178i	$0.879982\pi$
$500$		0			0
$501$	5.22947	−	9.05770i	0.233635	−	0.404668i
$502$	−13.8603	−	15.5034i	−0.618617	−	0.691951i
$503$	14.6078	+	14.6078i	0.651327	+	0.651327i	0.953313	−	0.301985i	$-0.0976493\pi$
$503$	14.6078	+	14.6078i	0.651327	+	0.651327i	−0.301985	+	0.953313i	$0.597649\pi$
$504$	6.11889	−	8.92451i	0.272557	−	0.397529i
$505$		0			0
$506$	0.0411550	−	0.735489i	0.00182956	−	0.0326965i
$507$	−2.23620	−	8.34561i	−0.0993131	−	0.370641i
$508$	−2.15993	−	2.70623i	−0.0958316	−	0.120069i
$509$	−29.8459	+	17.2316i	−1.32290	+	0.763775i	−0.984190	−	0.177116i	$-0.943323\pi$
$509$	−29.8459	+	17.2316i	−1.32290	+	0.763775i	−0.338708	+	0.940892i	$0.609990\pi$
$510$		0			0
$511$	−38.7851	+	3.51094i	−1.71575	+	0.155315i
$512$	21.7316	−	6.30364i	0.960412	−	0.278584i
$513$	−21.3121	−	5.71056i	−0.940953	−	0.252128i
$514$	8.42755	+	16.6857i	0.371723	+	0.735973i
$515$		0			0
$516$	18.2754	−	24.7832i	0.804528	−	1.09102i
$517$	−2.15944	−	2.15944i	−0.0949721	−	0.0949721i
$518$	3.72201	−	1.13579i	0.163536	−	0.0499036i
$519$	−2.75949			−0.121128
$520$		0			0
$521$	16.9526	−	29.3627i	0.742705	−	1.28640i	−0.208555	−	0.978011i	$-0.566876\pi$
$521$	16.9526	−	29.3627i	0.742705	−	1.28640i	0.951259	−	0.308392i	$-0.0997908\pi$
$522$	14.0465	+	4.61897i	0.614796	+	0.202167i
$523$	−4.77618	+	17.8250i	−0.208848	+	0.779431i	0.779394	+	0.626534i	$0.215527\pi$
$523$	−4.77618	+	17.8250i	−0.208848	+	0.779431i	−0.988242	+	0.152897i	$0.951140\pi$
$524$	1.04437	+	2.39107i	0.0456233	+	0.104455i
$525$		0			0
$526$	8.18443	−	12.5058i	0.356858	−	0.545280i
$527$	−10.1405	−	2.71715i	−0.441728	−	0.118361i
$528$	−4.19963	−	2.21522i	−0.182765	−	0.0964053i
$529$	19.6594	+	11.3504i	0.854758	+	0.493495i
$530$		0			0
$531$			18.2217i			0.790756i
$532$	−5.01301	−	20.4600i	−0.217341	−	0.887055i
$533$	11.7259	−	11.7259i	0.507906	−	0.507906i
$534$	−0.208587	+	3.72769i	−0.00902643	+	0.161313i
$535$		0			0
$536$	26.8655	−	32.4654i	1.16041	−	1.40229i
$537$	−5.31392	+	19.8318i	−0.229312	+	0.855806i
$538$	−16.8842	+	3.52645i	−0.727928	+	0.152036i
$539$	−4.31510	−	5.08010i	−0.185864	−	0.218815i
$540$		0			0
$541$	−1.59149	−	2.75655i	−0.0684236	−	0.118513i	0.829784	−	0.558085i	$-0.188464\pi$
$541$	−1.59149	−	2.75655i	−0.0684236	−	0.118513i	−0.898208	+	0.439572i	$0.855130\pi$
$542$	2.90771	−	8.84244i	0.124897	−	0.379815i
$543$	−7.19630	+	1.92824i	−0.308823	+	0.0827488i
$544$	10.8244	−	10.4481i	0.464092	−	0.447957i
$545$		0			0
$546$	−20.8113	+	0.715760i	−0.890640	+	0.0306317i
$547$	−15.6791	+	15.6791i	−0.670391	+	0.670391i	−0.957806	−	0.287415i	$-0.907204\pi$
$547$	−15.6791	+	15.6791i	−0.670391	+	0.670391i	0.287415	+	0.957806i	$0.407204\pi$
$548$	−0.346674	−	2.29374i	−0.0148092	−	0.0979836i
$549$	−7.54315	−	4.35504i	−0.321934	−	0.185869i
$550$		0			0
$551$	24.9289	−	14.3927i	1.06201	−	0.613151i
$552$	−1.57237	+	1.11709i	−0.0669246	+	0.0475466i
$553$	26.5663	−	9.76000i	1.12971	−	0.415037i
$554$	−3.18042	+	4.85969i	−0.135123	+	0.206469i
$555$		0			0
$556$	−3.89382	+	34.6847i	−0.165135	+	1.47096i
$557$	20.6171	−	5.52434i	0.873575	−	0.234074i	0.205942	−	0.978564i	$-0.433974\pi$
$557$	20.6171	−	5.52434i	0.873575	−	0.234074i	0.667633	+	0.744491i	$0.267308\pi$
$558$	−6.01797	+	5.38017i	−0.254761	+	0.227761i
$559$	55.1382			2.33210
$560$		0			0
$561$	−3.15683			−0.133282
$562$	−34.0302	+	30.4236i	−1.43548	+	1.28334i
$563$	13.1487	−	3.52319i	0.554153	−	0.148485i	0.0291340	−	0.999576i	$-0.490725\pi$
$563$	13.1487	−	3.52319i	0.554153	−	0.148485i	0.525019	+	0.851091i	$0.324058\pi$
$564$	−0.892084	+	7.94635i	−0.0375635	+	0.334602i
$565$		0			0
$566$	−15.1231	+	23.1081i	−0.635669	+	0.971305i
$567$	5.22439	+	4.35705i	0.219404	+	0.182979i
$568$	17.5402	−	12.4614i	0.735969	−	0.522869i
$569$	20.3421	−	11.7445i	0.852787	−	0.492357i	−0.00880335	−	0.999961i	$-0.502802\pi$
$569$	20.3421	−	11.7445i	0.852787	−	0.492357i	0.861590	+	0.507605i	$0.169469\pi$
$570$		0			0
$571$	23.4830	+	13.5579i	0.982734	+	0.567382i	0.903094	−	0.429442i	$-0.141290\pi$
$571$	23.4830	+	13.5579i	0.982734	+	0.567382i	0.0796395	+	0.996824i	$0.474623\pi$
$572$	−1.27056	−	8.40651i	−0.0531246	−	0.351494i
$573$	−7.09267	+	7.09267i	−0.296301	+	0.296301i
$574$	−7.35879	−	11.7904i	−0.307150	−	0.492120i
$575$		0			0
$576$	−2.16438	−	11.3635i	−0.0901826	−	0.473480i
$577$	26.9522	−	7.22183i	1.12204	−	0.300649i	0.350329	−	0.936627i	$-0.386070\pi$
$577$	26.9522	−	7.22183i	1.12204	−	0.300649i	0.771707	+	0.635978i	$0.219403\pi$
$578$	−4.38556	+	13.3366i	−0.182415	+	0.554731i
$579$	9.07505	+	15.7184i	0.377146	+	0.653236i
$580$		0			0
$581$	−17.5083	+	12.3382i	−0.726368	+	0.511874i
$582$	7.53124	−	1.57299i	0.312180	−	0.0652024i
$583$	−0.724403	+	2.70351i	−0.0300017	+	0.111968i
$584$	−26.5421	+	32.0747i	−1.09832	+	1.32726i
$585$		0			0
$586$	−1.41749	+	25.3323i	−0.0585560	+	1.04647i
$587$	−22.8296	+	22.8296i	−0.942280	+	0.942280i	−0.998423	−	0.0561427i	$-0.982120\pi$
$587$	−22.8296	+	22.8296i	−0.942280	+	0.942280i	0.0561427	+	0.998423i	$0.482120\pi$
$588$	−3.34815	+	17.1283i	−0.138075	+	0.706359i
$589$			15.7148i			0.647516i
$590$		0			0
$591$	−25.1794	−	14.5374i	−1.03574	−	0.597987i
$592$	1.94092	−	3.67961i	0.0797715	−	0.151231i
$593$	36.8872	+	9.88391i	1.51478	+	0.405883i	0.918019	−	0.396537i	$-0.129788\pi$
$593$	36.8872	+	9.88391i	1.51478	+	0.405883i	0.596759	+	0.802421i	$0.296455\pi$
$594$	−4.08700	+	6.24494i	−0.167691	+	0.256233i
$595$		0			0
$596$	−8.97462	−	20.5474i	−0.367615	−	0.841653i
$597$	3.11542	−	11.6269i	0.127506	−	0.475857i
$598$	−3.28091	−	1.07888i	−0.134166	−	0.0441186i
$599$	14.4801	−	25.0802i	0.591640	−	1.02475i	−0.402372	−	0.915476i	$-0.631814\pi$
$599$	14.4801	−	25.0802i	0.591640	−	1.02475i	0.994012	−	0.109274i	$-0.0348526\pi$
$600$		0			0
$601$	−8.88262			−0.362330			−0.181165	−	0.983453i	$-0.557987\pi$
$601$	−8.88262			−0.362330			−0.181165	+	0.983453i	$0.557987\pi$
$602$	10.4192	−	45.0220i	0.424653	−	1.83496i
$603$	−15.2333	−	15.2333i	−0.620347	−	0.620347i
$604$	17.8291	−	24.1780i	0.725456	−	0.983791i
$605$		0			0
$606$	−1.13669	−	2.25053i	−0.0461749	−	0.0914215i
$607$	44.3709	+	11.8891i	1.80096	+	0.482565i	0.994127	−	0.108218i	$-0.0345145\pi$
$607$	44.3709	+	11.8891i	1.80096	+	0.482565i	0.806830	+	0.590783i	$0.201181\pi$
$608$	−19.3004	−	11.6030i	−0.782734	−	0.470565i
$609$	−23.7515	+	2.15006i	−0.962461	+	0.0871249i
$610$		0			0
$611$	−12.4000	+	7.15915i	−0.501651	+	0.289628i
$612$	−4.79773	−	6.01118i	−0.193937	−	0.242988i
$613$	−0.0600047	−	0.223941i	−0.00242357	−	0.00904487i	0.964703	−	0.263339i	$-0.0848237\pi$
$613$	−0.0600047	−	0.223941i	−0.00242357	−	0.00904487i	−0.967127	+	0.254294i	$0.918157\pi$
$614$	1.11524	−	19.9306i	0.0450073	−	0.804335i
$615$		0			0
$616$	−7.10426	−	0.551085i	−0.286239	−	0.0222038i
$617$	27.1038	+	27.1038i	1.09116	+	1.09116i	0.995405	+	0.0957517i	$0.0305255\pi$
$617$	27.1038	+	27.1038i	1.09116	+	1.09116i	0.0957517	+	0.995405i	$0.469475\pi$
$618$	11.9565	+	13.3739i	0.480962	+	0.537978i
$619$	−7.14970	+	12.3836i	−0.287371	+	0.497741i	−0.973181	−	0.230039i	$-0.926115\pi$
$619$	−7.14970	+	12.3836i	−0.287371	+	0.497741i	0.685811	+	0.727780i	$0.259448\pi$
$620$		0			0
$621$	1.51593	+	2.62566i	0.0608320	+	0.105364i
$622$	−19.2957	+	4.03012i	−0.773685	+	0.161593i
$623$	1.93220	+	5.25935i	0.0774119	+	0.210711i
$624$	−15.1284	+	16.3310i	−0.605619	+	0.653762i
$625$		0			0
$626$	6.19597	−	3.12944i	0.247641	−	0.125078i
$627$	1.22304	+	4.56444i	0.0488434	+	0.182286i
$628$	−2.25007	−	14.8874i	−0.0897875	−	0.594071i
$629$		−	2.76594i		−	0.110285i
$630$		0			0
$631$			30.7128i			1.22266i	0.791377	+	0.611328i	$0.209364\pi$
$631$			30.7128i			1.22266i	−0.791377	+	0.611328i	$0.790636\pi$
$632$	12.5991	−	27.5085i	0.501165	−	1.09423i
$633$	−3.36660	−	12.5643i	−0.133810	−	0.499387i
$634$	21.9346	+	43.4281i	0.871132	+	1.72475i
$635$		0			0
$636$	6.71584	−	2.93332i	0.266300	−	0.116314i
$637$	−28.2428	+	13.3774i	−1.11902	+	0.530033i
$638$	−1.99075	−	9.53141i	−0.0788144	−	0.377352i
$639$	−5.49985	−	9.52602i	−0.217571	−	0.376843i
$640$		0			0
$641$	−20.7752	+	35.9837i	−0.820572	+	1.42127i	0.0846851	+	0.996408i	$0.473012\pi$
$641$	−20.7752	+	35.9837i	−0.820572	+	1.42127i	−0.905257	+	0.424864i	$0.860322\pi$
$642$	0.0528683	−	0.0472652i	0.00208655	−	0.00186541i
$643$	12.5692	+	12.5692i	0.495681	+	0.495681i	0.910090	−	0.414410i	$-0.136012\pi$
$643$	12.5692	+	12.5692i	0.495681	+	0.495681i	−0.414410	+	0.910090i	$0.636012\pi$
$644$	−1.50091	+	2.47509i	−0.0591442	+	0.0975322i
$645$		0			0
$646$	−14.9492	−	0.836497i	−0.588169	−	0.0329115i
$647$	9.22084	+	34.4127i	0.362509	+	1.35290i	0.870767	+	0.491696i	$0.163623\pi$
$647$	9.22084	+	34.4127i	0.362509	+	1.35290i	−0.508258	+	0.861205i	$0.669710\pi$
$648$	7.24033	−	0.683380i	0.284427	−	0.0268457i
$649$	10.3917	−	5.99966i	0.407910	−	0.235507i
$650$		0			0
$651$	5.46679	−	11.8163i	0.214261	−	0.463118i
$652$	−12.3807	−	4.85329i	−0.484866	−	0.190070i
$653$	12.7132	+	3.40648i	0.497505	+	0.133306i	0.498842	−	0.866693i	$-0.333759\pi$
$653$	12.7132	+	3.40648i	0.497505	+	0.133306i	−0.00133684	+	0.999999i	$0.500426\pi$
$654$	9.90276	−	5.00166i	0.387229	−	0.195580i
$655$		0			0
$656$	−14.4881	−	3.29449i	−0.565666	−	0.128628i
$657$	15.0499	+	15.0499i	0.587153	+	0.587153i
$658$	3.50250	+	11.4778i	0.136542	+	0.447451i
$659$	−10.3786			−0.404294			−0.202147	−	0.979355i	$-0.564792\pi$
$659$	−10.3786			−0.404294			−0.202147	+	0.979355i	$0.564792\pi$
$660$		0			0
$661$	−11.5282	+	19.9675i	−0.448397	+	0.776646i	−0.998282	−	0.0585946i	$-0.981338\pi$
$661$	−11.5282	+	19.9675i	−0.448397	+	0.776646i	0.549885	+	0.835240i	$0.314671\pi$
$662$	5.72352	−	17.4054i	0.222451	−	0.676481i
$663$	−3.83074	+	14.2965i	−0.148774	+	0.555231i
$664$	−3.82184	+	22.5767i	−0.148316	+	0.876144i
$665$		0			0
$666$	−1.77956	−	1.16463i	−0.0689567	−	0.0451286i
$667$	−3.82069	−	1.02375i	−0.147938	−	0.0396398i
$668$	−10.4674	−	13.1148i	−0.404995	−	0.507427i
$669$	−16.3765	−	9.45496i	−0.633151	−	0.365550i
$670$		0			0
$671$			5.73573i			0.221425i
$672$	10.4760	+	15.4387i	0.404121	+	0.595562i
$673$	−27.9624	+	27.9624i	−1.07787	+	1.07787i	−0.0811716	+	0.996700i	$0.525866\pi$
$673$	−27.9624	+	27.9624i	−1.07787	+	1.07787i	−0.996700	+	0.0811716i	$0.974134\pi$
$674$	−14.8382	−	0.830285i	−0.571546	−	0.0319814i
$675$		0			0
$676$	−13.7751	−	1.54644i	−0.529813	−	0.0594786i
$677$	8.86132	−	33.0709i	0.340568	−	1.27102i	−0.557137	−	0.830421i	$-0.688100\pi$
$677$	8.86132	−	33.0709i	0.340568	−	1.27102i	0.897705	−	0.440597i	$-0.145233\pi$
$678$	5.53131	+	26.4831i	0.212429	+	1.01708i
$679$	9.43821	−	6.65114i	0.362205	−	0.255247i
$680$		0			0
$681$	6.24694	+	10.8200i	0.239383	+	0.414624i
$682$	5.04973	+	1.66053i	0.193364	+	0.0635850i
$683$	−1.86138	+	0.498756i	−0.0712239	+	0.0190844i	−0.294255	−	0.955727i	$-0.595072\pi$
$683$	−1.86138	+	0.498756i	−0.0712239	+	0.0190844i	0.223031	+	0.974811i	$0.428405\pi$
$684$	−6.83274	+	9.26588i	−0.261256	+	0.354290i
$685$		0			0
$686$	5.58620	+	25.5889i	0.213282	+	0.976991i
$687$	−15.0630	+	15.0630i	−0.574691	+	0.574691i
$688$	−26.3176	−	41.8091i	−1.00335	−	1.59396i
$689$	11.3645	+	6.56128i	0.432952	+	0.249965i
$690$		0			0
$691$	30.8812	−	17.8293i	1.17478	−	0.678257i	0.219976	−	0.975505i	$-0.429402\pi$
$691$	30.8812	−	17.8293i	1.17478	−	0.678257i	0.954800	+	0.297248i	$0.0960688\pi$
$692$	−1.61577	+	4.12182i	−0.0614225	+	0.156688i
$693$	−0.621767	+	3.58937i	−0.0236190	+	0.136349i
$694$	−10.8427	−	7.09598i	−0.411582	−	0.269360i
$695$		0			0
$696$	−16.2541	+	19.6422i	−0.616109	+	0.744534i
$697$	−9.54198	+	2.55677i	−0.361428	+	0.0968444i
$698$	−18.8055	−	21.0348i	−0.711797	−	0.796177i
$699$	−2.33797			−0.0884301
$700$		0			0
$701$	33.6504			1.27096			0.635479	−	0.772119i	$-0.280803\pi$
$701$	33.6504			1.27096			0.635479	+	0.772119i	$0.280803\pi$
$702$	23.3223	+	26.0871i	0.880245	+	0.984594i
$703$	−3.99924	+	1.07159i	−0.150834	+	0.0404159i
$704$	−5.76789	+	4.97586i	−0.217385	+	0.187535i
$705$		0			0
$706$	−2.93319	−	1.91962i	−0.110392	−	0.0722460i
$707$	−2.90588	−	2.42345i	−0.109287	−	0.0911433i
$708$	−29.2514	−	11.4667i	−1.09934	−	0.430944i
$709$	7.92917	−	4.57791i	0.297786	−	0.171927i	−0.343662	−	0.939093i	$-0.611667\pi$
$709$	7.92917	−	4.57791i	0.297786	−	0.171927i	0.641448	+	0.767167i	$0.278334\pi$
$710$		0			0
$711$	−13.3957	−	7.73401i	−0.502378	−	0.290048i
$712$	5.44589	+	2.49425i	0.204093	+	0.0934762i
$713$	1.52693	−	1.52693i	0.0571839	−	0.0571839i
$714$	10.9497	+	5.82945i	0.409781	+	0.218162i
$715$		0			0
$716$	26.5111	+	19.5495i	0.990767	+	0.730601i
$717$	18.3247	−	4.91009i	0.684348	−	0.183370i
$718$	−21.3512	−	7.02104i	−0.796820	−	0.262023i
$719$	6.67322	+	11.5584i	0.248869	+	0.431054i	0.963212	−	0.268742i	$-0.0866078\pi$
$719$	6.67322	+	11.5584i	0.248869	+	0.431054i	−0.714343	+	0.699796i	$0.753274\pi$
$720$		0			0
$721$	24.4340	+	11.3043i	0.909970	+	0.420996i
$722$	−0.911364	−	4.36348i	−0.0339175	−	0.162392i
$723$	4.25104	−	15.8651i	0.158098	−	0.590029i
$724$	−1.33348	+	11.8781i	−0.0495582	+	0.441446i
$725$		0			0
$726$	−17.7664	−	0.994134i	−0.659372	−	0.0368958i
$727$	6.15934	−	6.15934i	0.228437	−	0.228437i	−0.583602	−	0.812040i	$-0.698357\pi$
$727$	6.15934	−	6.15934i	0.228437	−	0.228437i	0.812040	+	0.583602i	$0.198357\pi$
$728$	−11.1166	+	31.5047i	−0.412008	+	1.16764i
$729$		−	24.4454i		−	0.905384i
$730$		0			0
$731$	−28.4457	−	16.4231i	−1.05210	−	0.607431i
$732$	11.7380	−	9.36848i	0.433847	−	0.346269i
$733$	9.92223	+	2.65865i	0.366486	+	0.0981996i	0.437362	−	0.899286i	$-0.355913\pi$
$733$	9.92223	+	2.65865i	0.366486	+	0.0981996i	−0.0708761	+	0.997485i	$0.522580\pi$
$734$	−12.7392	−	8.33717i	−0.470213	−	0.307731i
$735$		0			0
$736$	0.747914	+	3.00273i	0.0275685	+	0.110682i
$737$	−3.67173	+	13.7031i	−0.135250	+	0.504760i
$738$	−2.37279	+	7.21572i	−0.0873435	+	0.265614i
$739$	−21.8583	+	37.8597i	−0.804070	+	1.39269i	0.112847	+	0.993612i	$0.464003\pi$
$739$	−21.8583	+	37.8597i	−0.804070	+	1.39269i	−0.916917	+	0.399078i	$0.869330\pi$
$740$		0			0
$741$	22.1553			0.813897
$742$	7.50497	−	8.03959i	0.275516	−	0.295143i
$743$	26.0186	+	26.0186i	0.954529	+	0.954529i	0.999010	−	0.0444813i	$-0.0141635\pi$
$743$	26.0186	+	26.0186i	0.954529	+	0.954529i	−0.0444813	+	0.999010i	$0.514164\pi$
$744$	−4.84979	−	13.0463i	−0.177802	−	0.478302i
$745$		0			0
$746$	−18.6383	+	9.41377i	−0.682396	+	0.344663i
$747$	11.3072	+	3.02975i	0.413709	+	0.110853i
$748$	−1.84843	+	4.71534i	−0.0675854	+	0.172410i
$749$	0.0446871	−	0.0965899i	0.00163283	−	0.00352932i
$750$		0			0
$751$	−7.30460	+	4.21731i	−0.266548	+	0.153892i	−0.627318	−	0.778763i	$-0.715847\pi$
$751$	−7.30460	+	4.21731i	−0.266548	+	0.153892i	0.360770	+	0.932655i	$0.382514\pi$
$752$	11.3471	+	5.98535i	0.413784	+	0.218263i
$753$	−4.74444	−	17.7065i	−0.172897	−	0.645260i
$754$	−45.5811	−	2.55053i	−1.65997	−	0.0928850i
$755$		0			0
$756$	25.7080	−	14.1139i	0.934991	−	0.513316i
$757$	−3.33081	−	3.33081i	−0.121060	−	0.121060i	0.643981	−	0.765041i	$-0.277282\pi$
$757$	−3.33081	−	3.33081i	−0.121060	−	0.121060i	−0.765041	+	0.643981i	$0.777282\pi$
$758$	−27.8930	+	24.9369i	−1.01312	+	0.905748i
$759$	0.324667	−	0.562340i	0.0117847	−	0.0204117i
$760$		0			0
$761$	17.2317	+	29.8462i	0.624649	+	1.08192i	0.988609	+	0.150509i	$0.0480913\pi$
$761$	17.2317	+	29.8462i	0.624649	+	1.08192i	−0.363959	+	0.931415i	$0.618575\pi$
$762$	−0.624010	−	2.98767i	−0.0226055	−	0.108232i
$763$	10.6636	−	12.7864i	0.386050	−	0.462899i
$764$	6.44127	+	14.7473i	0.233037	+	0.533537i
$765$		0			0
$766$	−18.7327	−	37.0888i	−0.676840	−	1.34007i
$767$	−14.5609	−	54.3419i	−0.525763	−	1.96217i
$768$	19.6039	+	3.67642i	0.707396	+	0.132661i
$769$			18.7498i			0.676135i	0.941122	+	0.338067i	$0.109773\pi$
$769$			18.7498i			0.676135i	−0.941122	+	0.338067i	$0.890227\pi$
$770$		0			0
$771$			16.4777i			0.593431i
$772$	28.7922	−	4.35164i	1.03626	−	0.156619i
$773$	−11.5075	−	42.9466i	−0.413896	−	1.54468i	−0.787036	−	0.616907i	$-0.788386\pi$
$773$	−11.5075	−	42.9466i	−0.413896	−	1.54468i	0.373140	−	0.927775i	$-0.378281\pi$
$774$	−22.5438	+	11.3864i	−0.810320	+	0.409274i
$775$		0			0
$776$	2.06023	−	12.1704i	0.0739581	−	0.436891i
$777$	3.37991	+	0.585483i	0.121254	+	0.0210041i
$778$	−12.9472	+	2.70418i	−0.464181	+	0.0969497i
$779$	7.39361	+	12.8061i	0.264903	+	0.458826i
$780$		0			0
$781$	−3.62174	+	6.27304i	−0.129596	+	0.224467i
$782$	1.37126	+	1.53382i	0.0490363	+	0.0548493i
$783$	28.3379	+	28.3379i	1.01271	+	1.01271i
$784$	23.6239	+	15.0303i	0.843712	+	0.536796i
$785$		0			0
$786$	−0.128496	+	2.29637i	−0.00458329	+	0.0819089i
$787$	−0.279451	−	1.04293i	−0.00996136	−	0.0371763i	0.960766	−	0.277359i	$-0.0894592\pi$
$787$	−0.279451	−	1.04293i	−0.00996136	−	0.0371763i	−0.970728	+	0.240183i	$0.922793\pi$
$788$	−36.4577	+	29.0982i	−1.29875	+	1.03658i
$789$	11.4095	−	6.58729i	0.406189	−	0.234514i
$790$		0			0
$791$	23.3883	+	33.1889i	0.831592	+	1.18006i
$792$	2.25547	+	3.17471i	0.0801447	+	0.112808i
$793$	25.9757	+	6.96017i	0.922424	+	0.247163i
$794$	−11.3295	−	22.4312i	−0.402069	−	0.796055i
$795$		0			0
$796$	−15.5428	−	11.4614i	−0.550900	−	0.406239i
$797$	13.9414	+	13.9414i	0.493829	+	0.493829i	0.909510	−	0.415681i	$-0.136457\pi$
$797$	13.9414	+	13.9414i	0.493829	+	0.493829i	−0.415681	+	0.909510i	$0.636457\pi$
$798$	4.18657	−	18.0905i	0.148203	−	0.640397i
$799$	8.52950			0.301752
$800$		0			0
$801$	1.53111	−	2.65196i	0.0540992	−	0.0937025i
$802$	−8.26676	−	2.71841i	−0.291910	−	0.0959902i
$803$	3.62754	−	13.5382i	0.128013	−	0.477751i
$804$	34.0401	−	14.8679i	1.20050	−	0.524352i
$805$		0			0
$806$	13.6479	−	20.8540i	0.480726	−	0.734550i
$807$	−14.6862	−	3.93515i	−0.516978	−	0.138524i
$808$	−4.02717	+	0.380106i	−0.141675	+	0.0133721i
$809$	−4.37439	−	2.52555i	−0.153795	−	0.0887937i	0.421127	−	0.907001i	$-0.361635\pi$
$809$	−4.37439	−	2.52555i	−0.153795	−	0.0887937i	−0.574923	+	0.818208i	$0.694968\pi$
$810$		0			0
$811$		−	21.1629i		−	0.743131i	−0.928407	−	0.371565i	$-0.878821\pi$
$811$		−	21.1629i		−	0.743131i	0.928407	−	0.371565i	$-0.121179\pi$
$812$	−10.6958	+	36.7364i	−0.375349	+	1.28919i
$813$	5.80185	−	5.80185i	0.203480	−	0.203480i
$814$	−0.0782451	+	1.39833i	−0.00274249	+	0.0490116i
$815$		0			0
$816$	12.6689	−	3.91907i	0.443501	−	0.137195i
$817$	−12.7255	+	47.4920i	−0.445207	+	1.66154i
$818$	9.06216	−	1.89274i	0.316851	−	0.0661781i
$819$	15.5009	+	7.17144i	0.541644	+	0.250590i
$820$		0			0
$821$	−21.3620	−	37.0001i	−0.745540	−	1.29131i	−0.949942	−	0.312426i	$-0.898858\pi$
$821$	−21.3620	−	37.0001i	−0.745540	−	1.29131i	0.204402	−	0.978887i	$-0.434475\pi$
$822$	0.638770	−	1.94252i	0.0222797	−	0.0677533i
$823$	4.61152	−	1.23565i	0.160748	−	0.0430722i	−0.177548	−	0.984112i	$-0.556816\pi$
$823$	4.61152	−	1.23565i	0.160748	−	0.0430722i	0.338295	+	0.941040i	$0.390150\pi$
$824$	26.9775	−	10.0285i	0.939804	−	0.349359i
$825$		0			0
$826$	−47.1233	+	1.62071i	−1.63963	+	0.0563916i
$827$	−6.21884	+	6.21884i	−0.216250	+	0.216250i	−0.806916	−	0.590666i	$-0.798865\pi$
$827$	−6.21884	+	6.21884i	−0.216250	+	0.216250i	0.590666	+	0.806916i	$0.298865\pi$
$828$	1.56422	−	0.236416i	0.0543606	−	0.00821602i
$829$	33.7077	+	19.4612i	1.17072	+	0.675915i	0.953849	−	0.300286i	$-0.0970821\pi$
$829$	33.7077	+	19.4612i	1.17072	+	0.675915i	0.216869	+	0.976201i	$0.430415\pi$
$830$		0			0
$831$	−4.43367	+	2.55978i	−0.153802	+	0.0887978i
$832$	15.5353	+	32.1594i	0.538588	+	1.11493i
$833$	18.5549	+	1.51083i	0.642889	+	0.0523470i
$834$	−16.8475	+	25.7431i	−0.583383	+	0.891410i
$835$		0			0
$836$	7.53399	+	0.845791i	0.260568	+	0.0292523i
$837$	−21.1330	+	5.66257i	−0.730464	+	0.195727i
$838$	−18.7570	+	16.7691i	−0.647949	+	0.579279i
$839$	15.0742			0.520418			0.260209	−	0.965552i	$-0.416209\pi$
$839$	15.0742			0.520418			0.260209	+	0.965552i	$0.416209\pi$
$840$		0			0
$841$	−23.2844			−0.802910
$842$	−17.3621	+	15.5220i	−0.598337	+	0.534925i
$843$	−38.8660	+	10.4141i	−1.33862	+	0.358681i
$844$	−20.7385	−	2.32817i	−0.713848	−	0.0801390i
$845$		0			0
$846$	3.59146	−	5.48776i	0.123477	−	0.188673i
$847$	−25.0663	+	9.20895i	−0.861289	+	0.316423i
$848$	−0.449132	−	11.7489i	−0.0154233	−	0.403461i
$849$	−21.0823	+	12.1719i	−0.723543	+	0.417738i
$850$		0			0
$851$	0.492709	+	0.284465i	0.0168898	+	0.00975135i
$852$	18.7531	−	2.83434i	0.642471	−	0.0971028i
$853$	14.0097	−	14.0097i	0.479684	−	0.479684i	−0.425346	−	0.905031i	$-0.639848\pi$
$853$	14.0097	−	14.0097i	0.479684	−	0.479684i	0.905031	+	0.425346i	$0.139848\pi$
$854$	10.5917	−	19.8947i	0.362440	−	0.680784i
$855$		0			0
$856$	−0.0396435	−	0.106644i	−0.00135499	−	0.00364503i
$857$	−34.4324	+	9.22615i	−1.17619	+	0.315159i	−0.793414	−	0.608682i	$-0.791698\pi$
$857$	−34.4324	+	9.22615i	−1.17619	+	0.315159i	−0.382776	+	0.923841i	$0.625032\pi$
$858$	2.34108	−	7.11932i	0.0799233	−	0.243049i
$859$	−26.2004	−	45.3805i	−0.893947	−	1.54836i	−0.835103	−	0.550094i	$-0.814592\pi$
$859$	−26.2004	−	45.3805i	−0.893947	−	1.54836i	−0.0588442	−	0.998267i	$-0.518742\pi$
$860$		0			0
$861$	−1.10450	−	12.2013i	−0.0376411	−	0.415818i
$862$	−20.9491	+	4.37546i	−0.713528	+	0.149029i
$863$	−1.36585	+	5.09743i	−0.0464941	+	0.173518i	−0.985269	−	0.171014i	$-0.945296\pi$
$863$	−1.36585	+	5.09743i	−0.0464941	+	0.173518i	0.938775	+	0.344532i	$0.111962\pi$
$864$	8.64899	−	30.1358i	0.294245	−	1.02524i
$865$		0			0
$866$	0.609393	−	10.8906i	0.0207080	−	0.370077i
$867$	−8.75067	+	8.75067i	−0.297188	+	0.297188i
$868$	−14.4489	−	15.0846i	−0.490429	−	0.512003i
$869$			10.1859i			0.345535i
$870$		0			0
$871$	57.6023	+	33.2567i	1.95178	+	1.12686i
$872$	−1.67254	−	17.7203i	−0.0566392	−	0.600085i
$873$	−6.09536	−	1.63325i	−0.206297	−	0.0552771i
$874$	1.68647	−	2.57694i	0.0570458	−	0.0871662i
$875$		0			0
$876$	−33.6304	+	14.6890i	−1.13627	+	0.496295i
$877$	2.89005	−	10.7858i	0.0975901	−	0.364211i	−0.899809	−	0.436283i	$-0.856295\pi$
$877$	2.89005	−	10.7858i	0.0975901	−	0.364211i	0.997399	+	0.0720722i	$0.0229612\pi$
$878$	34.5887	+	11.3740i	1.16731	+	0.383854i
$879$	−11.1824	+	19.3685i	−0.377174	+	0.653285i
$880$		0			0
$881$	22.0701			0.743561			0.371781	−	0.928321i	$-0.378747\pi$
$881$	22.0701			0.743561			0.371781	+	0.928321i	$0.378747\pi$
$882$	8.78481	−	11.3018i	0.295800	−	0.380551i
$883$	5.32169	+	5.32169i	0.179089	+	0.179089i	0.790959	−	0.611869i	$-0.209582\pi$
$883$	5.32169	+	5.32169i	0.179089	+	0.179089i	−0.611869	+	0.790959i	$0.709582\pi$
$884$	19.1116	+	14.0930i	0.642792	+	0.474000i
$885$		0			0
$886$	11.0233	+	21.8250i	0.370335	+	0.733225i
$887$	−4.89193	−	1.31079i	−0.164255	−	0.0440120i	0.175754	−	0.984434i	$-0.443764\pi$
$887$	−4.89193	−	1.31079i	−0.164255	−	0.0440120i	−0.340009	+	0.940422i	$0.610430\pi$
$888$	2.98944	−	2.12385i	0.100319	−	0.0712718i
$889$	−2.63853	−	3.74417i	−0.0884936	−	0.125576i
$890$		0			0
$891$	−2.12030	+	1.22416i	−0.0710327	+	0.0410108i
$892$	−23.7118	+	18.9252i	−0.793929	+	0.633662i
$893$	−3.30454	−	12.3327i	−0.110582	−	0.412699i
$894$	1.10421	−	19.7336i	0.0369303	−	0.659990i
$895$		0			0
$896$	29.1948	−	6.60803i	0.975328	−	0.220759i
$897$	−2.15273	−	2.15273i	−0.0718774	−	0.0718774i
$898$	−10.4625	−	11.7028i	−0.349137	−	0.390526i
$899$	14.2718	−	24.7194i	0.475990	−	0.824439i
$900$		0			0
$901$	−3.90860	−	6.76989i	−0.130214	−	0.225538i
$902$	4.89633	−	1.02265i	0.163030	−	0.0340507i
$903$	26.0899	−	31.2835i	0.868218	−	1.04105i
$904$	42.7964	+	7.24469i	1.42339	+	0.240955i
$905$		0			0
$906$	23.6367	−	11.9384i	0.785277	−	0.396625i
$907$	0.876735	+	3.27202i	0.0291115	+	0.108646i	0.978953	−	0.204087i	$-0.0654224\pi$
$907$	0.876735	+	3.27202i	0.0291115	+	0.108646i	−0.949841	+	0.312732i	$0.898756\pi$
$908$	19.8196	−	2.99552i	0.657736	−	0.0994098i
$909$			2.06796i			0.0685899i
$910$		0			0
$911$		−	31.5983i		−	1.04690i	−0.852057	−	0.523449i	$-0.824645\pi$
$911$		−	31.5983i		−	1.04690i	0.852057	−	0.523449i	$-0.175355\pi$
$912$	−10.5748	−	16.7995i	−0.350166	−	0.556287i
$913$	−1.99514	−	7.44597i	−0.0660295	−	0.246426i
$914$	−13.5407	−	26.8091i	−0.447886	−	0.886767i
$915$		0			0
$916$	13.6796	+	31.3195i	0.451988	+	1.03482i
$917$	1.19029	+	3.23992i	0.0393069	+	0.106992i
$918$	−4.26180	−	20.4049i	−0.140660	−	0.673462i
$919$	23.1351	+	40.0712i	0.763157	+	1.32183i	0.941215	+	0.337807i	$0.109685\pi$
$919$	23.1351	+	40.0712i	0.763157	+	1.32183i	−0.178058	+	0.984020i	$0.556982\pi$
$920$		0			0
$921$	8.79800	−	15.2386i	0.289904	−	0.502128i
$922$	−9.08446	+	8.12167i	−0.299181	+	0.267473i
$923$	24.0141	+	24.0141i	0.790435	+	0.790435i
$924$	−5.37076	−	3.25686i	−0.176685	−	0.107143i
$925$		0			0
$926$	3.26169	+	0.182511i	0.107186	+	0.00599768i
$927$	−3.80821	−	14.2124i	−0.125078	−	0.466797i
$928$	19.8220	+	35.7797i	0.650689	+	1.17453i
$929$	37.0594	−	21.3962i	1.21588	−	0.701987i	0.251844	−	0.967768i	$-0.418963\pi$
$929$	37.0594	−	21.3962i	1.21588	−	0.701987i	0.964034	+	0.265780i	$0.0856296\pi$
$930$		0			0
$931$	−5.00414	−	27.4137i	−0.164004	−	0.898447i
$932$	−1.36896	+	3.49220i	−0.0448418	+	0.114391i
$933$	−16.7837	−	4.49719i	−0.549475	−	0.147231i
$934$	−32.1652	+	16.2459i	−1.05248	+	0.531583i
$935$		0			0
$936$	17.1144	−	6.36204i	0.559402	−	0.207950i
$937$	−18.9957	−	18.9957i	−0.620561	−	0.620561i	0.325114	−	0.945675i	$-0.394597\pi$
$937$	−18.9957	−	18.9957i	−0.620561	−	0.620561i	−0.945675	+	0.325114i	$0.894597\pi$
$938$	38.0399	−	40.7497i	1.24205	−	1.33053i
$939$	6.11875			0.199678
$940$		0			0
$941$	10.8404	−	18.7762i	0.353388	−	0.612086i	−0.633453	−	0.773781i	$-0.718363\pi$
$941$	10.8404	−	18.7762i	0.353388	−	0.612086i	0.986841	+	0.161696i	$0.0516963\pi$
$942$	4.14590	−	12.6078i	0.135081	−	0.410785i
$943$	0.525906	−	1.96271i	0.0171258	−	0.0639145i
$944$	−34.2554	+	36.9785i	−1.11492	+	1.20355i
$945$		0			0
$946$	13.9163	+	9.10749i	0.452457	+	0.296110i
$947$	14.8363	+	3.97536i	0.482114	+	0.129182i	0.491687	−	0.870772i	$-0.336381\pi$
$947$	14.8363	+	3.97536i	0.482114	+	0.129182i	−0.00957300	+	0.999954i	$0.503047\pi$
$948$	20.8452	−	16.6373i	0.677019	−	0.540353i
$949$	−56.9090	−	32.8564i	−1.84735	−	1.06657i
$950$		0			0
$951$			42.8869i			1.39070i
$952$	15.1188	−	12.9421i	0.490003	−	0.419456i
$953$	−22.0087	+	22.0087i	−0.712931	+	0.712931i	−0.967147	−	0.254216i	$-0.918183\pi$
$953$	−22.0087	+	22.0087i	−0.712931	+	0.712931i	0.254216	+	0.967147i	$0.418183\pi$
$954$	−6.00141	−	0.335815i	−0.194303	−	0.0108724i
$955$		0			0
$956$	3.39557	−	30.2465i	0.109821	−	0.978240i
$957$	2.22146	−	8.29061i	0.0718096	−	0.267997i
$958$	2.68274	+	12.8446i	0.0866755	+	0.414990i
$959$	−0.276665	−	3.05629i	−0.00893398	−	0.0986929i
$960$		0			0
$961$	−7.70864	−	13.3518i	−0.248666	−	0.430702i
$962$	6.23777	+	2.05120i	0.201114	+	0.0661333i
$963$	−0.0561830	+	0.0150542i	−0.00181047	+	0.000485114i
$964$	−21.2084	−	15.6393i	−0.683078	−	0.503708i
$965$		0			0
$966$	−2.16455	+	1.35098i	−0.0696434	+	0.0434670i
$967$	16.9281	−	16.9281i	0.544372	−	0.544372i	−0.380435	−	0.924807i	$-0.624226\pi$
$967$	16.9281	−	16.9281i	0.544372	−	0.544372i	0.924807	+	0.380435i	$0.124226\pi$
$968$	−11.8877	+	25.9554i	−0.382086	+	0.834238i
$969$	−11.4299	−	6.59904i	−0.367180	−	0.211992i
$970$		0			0
$971$	−32.1198	+	18.5444i	−1.03077	+	0.595118i	−0.917206	−	0.398412i	$-0.869561\pi$
$971$	−32.1198	+	18.5444i	−1.03077	+	0.595118i	−0.113568	+	0.993530i	$0.536228\pi$
$972$	−24.9920	−	9.79698i	−0.801620	−	0.314238i
$973$	−7.88071	+	45.4942i	−0.252644	+	1.45848i
$974$	21.0739	+	13.7918i	0.675251	+	0.441918i
$975$		0			0
$976$	−7.12065	−	23.0185i	−0.227926	−	0.736803i
$977$	22.5762	−	6.04928i	0.722277	−	0.193534i	0.121090	−	0.992642i	$-0.461361\pi$
$977$	22.5762	−	6.04928i	0.722277	−	0.193534i	0.601188	+	0.799108i	$0.294694\pi$
$978$	−7.81264	−	8.73879i	−0.249821	−	0.279436i
$979$	−2.01652			−0.0644484
$980$		0			0
$981$	−9.09942			−0.290522
$982$	−2.35614	−	2.63545i	−0.0751875	−	0.0841006i
$983$	−19.2069	+	5.14648i	−0.612606	+	0.164147i	−0.551764	−	0.834000i	$-0.686045\pi$
$983$	−19.2069	+	5.14648i	−0.612606	+	0.164147i	−0.0608417	+	0.998147i	$0.519378\pi$
$984$	−10.0903	−	8.34979i	−0.321666	−	0.266182i
$985$		0			0
$986$	22.7555	+	14.8923i	0.724682	+	0.474268i
$987$	−1.80549	+	10.4228i	−0.0574694	+	0.331763i
$988$	12.9727	−	33.0932i	0.412716	−	1.05284i
$989$	5.85104	−	3.37810i	0.186052	−	0.107417i
$990$		0			0
$991$	−19.5362	−	11.2792i	−0.620586	−	0.358296i	0.156511	−	0.987676i	$-0.449975\pi$
$991$	−19.5362	−	11.2792i	−0.620586	−	0.358296i	−0.777097	+	0.629380i	$0.783309\pi$
$992$	−22.3269	−	0.394977i	−0.708880	−	0.0125405i
$993$	11.4204	−	11.4204i	0.362414	−	0.362414i
$994$	24.1461	−	15.0705i	0.765868	−	0.478006i
$995$		0			0
$996$	−11.9791	+	16.2449i	−0.379573	+	0.514739i
$997$	16.6372	−	4.45792i	0.526905	−	0.141184i	0.0144466	−	0.999896i	$-0.495401\pi$
$997$	16.6372	−	4.45792i	0.526905	−	0.141184i	0.512459	+	0.858712i	$0.328735\pi$
$998$	−8.76459	−	2.88211i	−0.277438	−	0.0912315i
$999$	−2.88213	−	4.99199i	−0.0911865	−	0.157940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.be.e.207.14		72
4.3	odd	2	inner	700.2.be.e.207.8		72
5.2	odd	4		140.2.w.b.123.14	yes	72
5.3	odd	4	inner	700.2.be.e.543.5		72
5.4	even	2		140.2.w.b.67.5	yes	72
7.2	even	3	inner	700.2.be.e.107.2		72
20.3	even	4	inner	700.2.be.e.543.2		72
20.7	even	4		140.2.w.b.123.17	yes	72
20.19	odd	2		140.2.w.b.67.11	yes	72
28.23	odd	6	inner	700.2.be.e.107.5		72
35.2	odd	12		140.2.w.b.23.11	yes	72
35.4	even	6		980.2.k.k.687.8		36
35.9	even	6		140.2.w.b.107.17	yes	72
35.12	even	12		980.2.x.m.863.11		72
35.17	even	12		980.2.k.j.883.1		36
35.19	odd	6		980.2.x.m.667.17		72
35.23	odd	12	inner	700.2.be.e.443.8		72
35.24	odd	6		980.2.k.j.687.8		36
35.27	even	4		980.2.x.m.263.14		72
35.32	odd	12		980.2.k.k.883.1		36
35.34	odd	2		980.2.x.m.67.5		72
140.19	even	6		980.2.x.m.667.14		72
140.23	even	12	inner	700.2.be.e.443.14		72
140.27	odd	4		980.2.x.m.263.17		72
140.39	odd	6		980.2.k.k.687.1		36
140.47	odd	12		980.2.x.m.863.5		72
140.59	even	6		980.2.k.j.687.1		36
140.67	even	12		980.2.k.k.883.8		36
140.79	odd	6		140.2.w.b.107.14	yes	72
140.87	odd	12		980.2.k.j.883.8		36
140.107	even	12		140.2.w.b.23.5	✓	72
140.139	even	2		980.2.x.m.67.11		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.5	✓	72	140.107	even	12
140.2.w.b.23.11	yes	72	35.2	odd	12
140.2.w.b.67.5	yes	72	5.4	even	2
140.2.w.b.67.11	yes	72	20.19	odd	2
140.2.w.b.107.14	yes	72	140.79	odd	6
140.2.w.b.107.17	yes	72	35.9	even	6
140.2.w.b.123.14	yes	72	5.2	odd	4
140.2.w.b.123.17	yes	72	20.7	even	4
700.2.be.e.107.2		72	7.2	even	3	inner
700.2.be.e.107.5		72	28.23	odd	6	inner
700.2.be.e.207.8		72	4.3	odd	2	inner
700.2.be.e.207.14		72	1.1	even	1	trivial
700.2.be.e.443.8		72	35.23	odd	12	inner
700.2.be.e.443.14		72	140.23	even	12	inner
700.2.be.e.543.2		72	20.3	even	4	inner
700.2.be.e.543.5		72	5.3	odd	4	inner
980.2.k.j.687.1		36	140.59	even	6
980.2.k.j.687.8		36	35.24	odd	6
980.2.k.j.883.1		36	35.17	even	12
980.2.k.j.883.8		36	140.87	odd	12
980.2.k.k.687.1		36	140.39	odd	6
980.2.k.k.687.8		36	35.4	even	6
980.2.k.k.883.1		36	35.32	odd	12
980.2.k.k.883.8		36	140.67	even	12
980.2.x.m.67.5		72	35.34	odd	2
980.2.x.m.67.11		72	140.139	even	2
980.2.x.m.263.14		72	35.27	even	4
980.2.x.m.263.17		72	140.27	odd	4
980.2.x.m.667.14		72	140.19	even	6
980.2.x.m.667.17		72	35.19	odd	6
980.2.x.m.863.5		72	140.47	odd	12
980.2.x.m.863.11		72	35.12	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.05431 - 0.942570i) q^{2} +(1.20413 - 0.322645i) q^{3} +(0.223125 - 1.98751i) q^{4} +(0.965404 - 1.47514i) q^{6} +(0.451584 - 2.60693i) q^{7} +(-1.63813 - 2.30576i) q^{8} +(-1.25225 + 0.722989i) q^{9} +(0.824629 + 0.476100i) q^{11} +(-0.372591 - 2.46521i) q^{12} +(3.15680 - 3.15680i) q^{13} +(-1.98110 - 3.17415i) q^{14} +(-3.90043 - 0.886929i) q^{16} +(-2.56885 + 0.688322i) q^{17} +(-0.638792 + 1.94259i) q^{18} +(1.99048 + 3.44760i) q^{19} +(-0.297348 - 3.28477i) q^{21} +(1.31817 - 0.275315i) q^{22} +(0.141582 - 0.528392i) q^{23} +(-2.71646 - 2.24790i) q^{24} +(0.352732 - 6.30375i) q^{26} +(-3.91905 + 3.91905i) q^{27} +(-5.08055 - 1.47920i) q^{28} -7.23080i q^{29} +(3.41863 + 1.97375i) q^{31} +(-4.94824 + 2.74133i) q^{32} +(1.14657 + 0.307222i) q^{33} +(-2.05957 + 3.14702i) q^{34} +(1.15754 + 2.65019i) q^{36} +(-0.269180 + 1.00460i) q^{37} +(5.34818 + 1.75867i) q^{38} +(2.78267 - 4.81972i) q^{39} +3.71449 q^{41} +(-3.40962 - 3.18289i) q^{42} +(8.73324 + 8.73324i) q^{43} +(1.13025 - 1.53273i) q^{44} +(-0.348775 - 0.690538i) q^{46} +(-3.09794 - 0.830089i) q^{47} +(-4.98278 + 0.190479i) q^{48} +(-6.59214 - 2.35449i) q^{49} +(-2.87114 + 1.65765i) q^{51} +(-5.56983 - 6.97856i) q^{52} +(0.760768 + 2.83923i) q^{53} +(-0.437903 + 7.82586i) q^{54} +(-6.75070 + 3.22924i) q^{56} +(3.50914 + 3.50914i) q^{57} +(-6.81553 - 7.62348i) q^{58} +(6.30084 - 10.9134i) q^{59} +(3.01183 + 5.21665i) q^{61} +(5.46468 - 1.14136i) q^{62} +(1.31928 + 3.59102i) q^{63} +(-2.63307 + 7.55427i) q^{64} +(1.49841 - 0.756815i) q^{66} +(3.85605 + 14.3910i) q^{67} +(0.794874 + 5.25921i) q^{68} -0.681932i q^{69} +7.60710i q^{71} +(3.71839 + 1.70305i) q^{72} +(-3.80964 - 14.2178i) q^{73} +(0.663102 + 1.31287i) q^{74} +(7.29629 - 3.18685i) q^{76} +(1.61355 - 1.93475i) q^{77} +(-1.60914 - 7.70432i) q^{78} +(5.34864 + 9.26412i) q^{79} +(-1.28561 + 2.22674i) q^{81} +(3.91621 - 3.50117i) q^{82} +(-5.72446 - 5.72446i) q^{83} +(-6.59488 - 0.141933i) q^{84} +(17.4392 + 0.975826i) q^{86} +(-2.33298 - 8.70680i) q^{87} +(-0.253076 - 2.68131i) q^{88} +(-1.83403 + 1.05888i) q^{89} +(-6.80400 - 9.65512i) q^{91} +(-1.01860 - 0.399294i) q^{92} +(4.75329 + 1.27364i) q^{93} +(-4.04859 + 2.04485i) q^{94} +(-5.07384 + 4.89744i) q^{96} +(3.08588 + 3.08588i) q^{97} +(-9.16941 + 3.73120i) q^{98} -1.37686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42}+ \cdots + 90 q^{98}+O(q^{100}) \) 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more