LMFDB - Embedded newform 700.2.be.e.543.5

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)

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")

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);

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			543.5
Character	$\chi$	$=$	700.543
Dual form			700.2.be.e.107.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.942570 - 1.05431i) q^{2} +(0.322645 + 1.20413i) q^{3} +(-0.223125 + 1.98751i) q^{4} +(0.965404 - 1.47514i) q^{6} +(-2.60693 - 0.451584i) q^{7} +(2.30576 - 1.63813i) q^{8} +(1.25225 - 0.722989i) q^{9} +(0.824629 + 0.476100i) q^{11} +(-2.46521 + 0.372591i) q^{12} +(3.15680 + 3.15680i) q^{13} +(1.98110 + 3.17415i) q^{14} +(-3.90043 - 0.886929i) q^{16} +(0.688322 + 2.56885i) q^{17} +(-1.94259 - 0.638792i) q^{18} +(-1.99048 - 3.44760i) q^{19} +(-0.297348 - 3.28477i) q^{21} +(-0.275315 - 1.31817i) q^{22} +(0.528392 + 0.141582i) q^{23} +(2.71646 + 2.24790i) q^{24} +(0.352732 - 6.30375i) q^{26} +(3.91905 + 3.91905i) q^{27} +(1.47920 - 5.08055i) q^{28} +7.23080i q^{29} +(3.41863 + 1.97375i) q^{31} +(2.74133 + 4.94824i) q^{32} +(-0.307222 + 1.14657i) q^{33} +(2.05957 - 3.14702i) q^{34} +(1.15754 + 2.65019i) q^{36} +(1.00460 + 0.269180i) q^{37} +(-1.75867 + 5.34818i) q^{38} +(-2.78267 + 4.81972i) q^{39} +3.71449 q^{41} +(-3.18289 + 3.40962i) q^{42} +(-8.73324 + 8.73324i) q^{43} +(-1.13025 + 1.53273i) q^{44} +(-0.348775 - 0.690538i) q^{46} +(-0.830089 + 3.09794i) q^{47} +(-0.190479 - 4.98278i) q^{48} +(6.59214 + 2.35449i) q^{49} +(-2.87114 + 1.65765i) q^{51} +(-6.97856 + 5.56983i) q^{52} +(-2.83923 + 0.760768i) q^{53} +(0.437903 - 7.82586i) q^{54} +(-6.75070 + 3.22924i) q^{56} +(3.50914 - 3.50914i) q^{57} +(7.62348 - 6.81553i) q^{58} +(-6.30084 + 10.9134i) q^{59} +(3.01183 + 5.21665i) q^{61} +(-1.14136 - 5.46468i) q^{62} +(-3.59102 + 1.31928i) q^{63} +(2.63307 - 7.55427i) q^{64} +(1.49841 - 0.756815i) q^{66} +(14.3910 - 3.85605i) q^{67} +(-5.25921 + 0.794874i) q^{68} +0.681932i q^{69} +7.60710i q^{71} +(1.70305 - 3.71839i) q^{72} +(14.2178 - 3.80964i) q^{73} +(-0.663102 - 1.31287i) q^{74} +(7.29629 - 3.18685i) q^{76} +(-1.93475 - 1.61355i) q^{77} +(7.70432 - 1.60914i) q^{78} +(-5.34864 - 9.26412i) q^{79} +(-1.28561 + 2.22674i) q^{81} +(-3.50117 - 3.91621i) q^{82} +(5.72446 - 5.72446i) q^{83} +(6.59488 + 0.141933i) q^{84} +(17.4392 + 0.975826i) q^{86} +(-8.70680 + 2.33298i) q^{87} +(2.68131 - 0.253076i) q^{88} +(1.83403 - 1.05888i) q^{89} +(-6.80400 - 9.65512i) q^{91} +(-0.399294 + 1.01860i) q^{92} +(-1.27364 + 4.75329i) q^{93} +(4.04859 - 2.04485i) q^{94} +(-5.07384 + 4.89744i) q^{96} +(3.08588 - 3.08588i) q^{97} +(-3.73120 - 9.16941i) 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 $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.942570	−	1.05431i	−0.666497	−	0.745507i
$2$	−0.942570	−	1.05431i	−0.666497	−	0.745507i
$3$	0.322645	+	1.20413i	0.186279	+	0.695203i	0.994353	+	0.106122i	$0.0338435\pi$
$3$	0.322645	+	1.20413i	0.186279	+	0.695203i	−0.808074	+	0.589081i	$0.799490\pi$
$4$	−0.223125	+	1.98751i	−0.111563	+	0.993757i
$5$		0			0
$5$		0			0
$6$	0.965404	−	1.47514i	0.394125	−	0.602224i
$7$	−2.60693	−	0.451584i	−0.985326	−	0.170683i
$7$	−2.60693	−	0.451584i	−0.985326	−	0.170683i
$8$	2.30576	−	1.63813i	0.815210	−	0.579166i
$9$	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	$0.620815\pi$
$12$	−2.46521	+	0.372591i	−0.711645	+	0.107558i
$13$	3.15680	+	3.15680i	0.875540	+	0.875540i	0.993069	−	0.117529i	$-0.0374974\pi$
$13$	3.15680	+	3.15680i	0.875540	+	0.875540i	−0.117529	+	0.993069i	$0.537497\pi$
$14$	1.98110	+	3.17415i	0.529472	+	0.848327i
$15$		0			0
$16$	−3.90043	−	0.886929i	−0.975108	−	0.221732i
$17$	0.688322	+	2.56885i	0.166943	+	0.623038i	0.997784	+	0.0665295i	$0.0211927\pi$
$17$	0.688322	+	2.56885i	0.166943	+	0.623038i	−0.830842	+	0.556508i	$0.812141\pi$
$18$	−1.94259	−	0.638792i	−0.457872	−	0.150565i
$19$	−1.99048	−	3.44760i	−0.456646	−	0.790935i	0.542135	−	0.840292i	$-0.317616\pi$
$19$	−1.99048	−	3.44760i	−0.456646	−	0.790935i	−0.998781	+	0.0493567i	$0.984283\pi$
$20$		0			0
$21$	−0.297348	−	3.28477i	−0.0648866	−	0.716797i
$22$	−0.275315	−	1.31817i	−0.0586973	−	0.281034i
$23$	0.528392	+	0.141582i	0.110177	+	0.0295219i	0.313486	−	0.949593i	$-0.398503\pi$
$23$	0.528392	+	0.141582i	0.110177	+	0.0295219i	−0.203309	+	0.979115i	$0.565170\pi$
$24$	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
$28$	1.47920	−	5.08055i	0.279543	−	0.960133i
$29$			7.23080i			1.34273i	0.741129	+	0.671363i	$0.234291\pi$
$29$			7.23080i			1.34273i	−0.741129	+	0.671363i	$0.765709\pi$
$30$		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	$0.551319\pi$
$32$	2.74133	+	4.94824i	0.484604	+	0.874734i
$33$	−0.307222	+	1.14657i	−0.0534805	+	0.199592i
$34$	2.05957	−	3.14702i	0.353213	−	0.539710i
$35$		0			0
$36$	1.15754	+	2.65019i	0.192924	+	0.441698i
$37$	1.00460	+	0.269180i	0.165154	+	0.0442530i	0.340449	−	0.940263i	$-0.389421\pi$
$37$	1.00460	+	0.269180i	0.165154	+	0.0442530i	−0.175294	+	0.984516i	$0.556088\pi$
$38$	−1.75867	+	5.34818i	−0.285294	+	0.867589i
$39$	−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	$0.406327\pi$
$42$	−3.18289	+	3.40962i	−0.491130	+	0.526116i
$43$	−8.73324	+	8.73324i	−1.33181	+	1.33181i	−0.428052	+	0.903754i	$0.640800\pi$
$43$	−8.73324	+	8.73324i	−1.33181	+	1.33181i	−0.903754	+	0.428052i	$0.859200\pi$
$44$	−1.13025	+	1.53273i	−0.170392	+	0.231068i
$45$		0			0
$46$	−0.348775	−	0.690538i	−0.0514241	−	0.101814i
$47$	−0.830089	+	3.09794i	−0.121081	+	0.451880i	−0.999670	−	0.0256988i	$-0.991819\pi$
$47$	−0.830089	+	3.09794i	−0.121081	+	0.451880i	0.878589	+	0.477579i	$0.158486\pi$
$48$	−0.190479	−	4.98278i	−0.0274933	−	0.719202i
$49$	6.59214	+	2.35449i	0.941735	+	0.336356i
$50$		0			0
$51$	−2.87114	+	1.65765i	−0.402040	+	0.232118i
$52$	−6.97856	+	5.56983i	−0.967752	+	0.772397i
$53$	−2.83923	+	0.760768i	−0.389998	+	0.104500i	−0.448489	−	0.893788i	$-0.648038\pi$
$53$	−2.83923	+	0.760768i	−0.389998	+	0.104500i	0.0584914	+	0.998288i	$0.481371\pi$
$54$	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
$58$	7.62348	−	6.81553i	1.00101	−	0.894923i
$59$	−6.30084	+	10.9134i	−0.820300	+	1.42080i	0.0851594	+	0.996367i	$0.472860\pi$
$59$	−6.30084	+	10.9134i	−0.820300	+	1.42080i	−0.905459	+	0.424433i	$0.860473\pi$
$60$		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	$0.707319\pi$
$62$	−1.14136	−	5.46468i	−0.144953	−	0.694015i
$63$	−3.59102	+	1.31928i	−0.452426	+	0.166214i
$64$	2.63307	−	7.55427i	0.329134	−	0.944283i
$65$		0			0
$66$	1.49841	−	0.756815i	0.184442	−	0.0931574i
$67$	14.3910	−	3.85605i	1.75814	−	0.471092i	0.771806	−	0.635858i	$-0.219353\pi$
$67$	14.3910	−	3.85605i	1.75814	−	0.471092i	0.986333	+	0.164766i	$0.0526868\pi$
$68$	−5.25921	+	0.794874i	−0.637773	+	0.0963927i
$69$			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	$0.850925\pi$
$72$	1.70305	−	3.71839i	0.200706	−	0.438216i
$73$	14.2178	−	3.80964i	1.66406	−	0.445885i	0.700564	−	0.713590i	$-0.252932\pi$
$73$	14.2178	−	3.80964i	1.66406	−	0.445885i	0.963501	+	0.267705i	$0.0862652\pi$
$74$	−0.663102	−	1.31287i	−0.0770841	−	0.152618i
$75$		0			0
$76$	7.29629	−	3.18685i	0.836942	−	0.365557i
$77$	−1.93475	−	1.61355i	−0.220485	−	0.183881i
$78$	7.70432	−	1.60914i	0.872343	−	0.182199i
$79$	−5.34864	−	9.26412i	−0.601769	−	1.04230i	−0.992553	−	0.121813i	$-0.961129\pi$
$79$	−5.34864	−	9.26412i	−0.601769	−	1.04230i	0.390784	−	0.920483i	$-0.372204\pi$
$80$		0			0
$81$	−1.28561	+	2.22674i	−0.142846	+	0.247416i
$82$	−3.50117	−	3.91621i	−0.386639	−	0.432473i
$83$	5.72446	−	5.72446i	0.628341	−	0.628341i	−0.319309	−	0.947651i	$-0.603451\pi$
$83$	5.72446	−	5.72446i	0.628341	−	0.628341i	0.947651	+	0.319309i	$0.103451\pi$
$84$	6.59488	+	0.141933i	0.719561	+	0.0154861i
$85$		0			0
$86$	17.4392	+	0.975826i	1.88052	+	0.105226i
$87$	−8.70680	+	2.33298i	−0.933467	+	0.250122i
$88$	2.68131	−	0.253076i	0.285828	−	0.0269780i
$89$	1.83403	−	1.05888i	0.194407	−	0.112241i	−0.399637	−	0.916673i	$-0.630864\pi$
$89$	1.83403	−	1.05888i	0.194407	−	0.112241i	0.594044	+	0.804433i	$0.297531\pi$
$90$		0			0
$91$	−6.80400	−	9.65512i	−0.713253	−	1.01213i
$92$	−0.399294	+	1.01860i	−0.0416293	+	0.106196i
$93$	−1.27364	+	4.75329i	−0.132070	+	0.492893i
$94$	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	−0.532872	−	0.846196i	$-0.678887\pi$
$97$	3.08588	−	3.08588i	0.313324	−	0.313324i	0.846196	+	0.532872i	$0.178887\pi$
$98$	−3.73120	−	9.16941i	−0.376908	−	0.926251i
$99$	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	$0.143999\pi$
$102$	4.45393	+	1.46461i	0.441004	+	0.145018i
$103$	−9.82894	−	2.63366i	−0.968474	−	0.259502i	−0.260291	−	0.965530i	$-0.583818\pi$
$103$	−9.82894	−	2.63366i	−0.968474	−	0.259502i	−0.708183	+	0.706028i	$0.750485\pi$
$104$	12.4501	+	2.10758i	1.22083	+	0.206666i
$105$		0			0
$106$	3.47825	+	2.27634i	0.337838	+	0.221097i
$107$	0.0104111	−	0.0388547i	0.00100648	−	0.00375622i	−0.965421	−	0.260697i	$-0.916048\pi$
$107$	0.0104111	−	0.0388547i	0.00100648	−	0.00375622i	0.966427	+	0.256940i	$0.0827144\pi$
$108$	−8.66361	+	6.91473i	−0.833656	+	0.665371i
$109$	−5.44983	−	3.14646i	−0.521999	−	0.301376i	0.215753	−	0.976448i	$-0.430779\pi$
$109$	−5.44983	−	3.14646i	−0.521999	−	0.301376i	−0.737752	+	0.675072i	$0.764113\pi$
$110$		0			0
$111$			1.29651i			0.123059i
$112$	9.76762	+	4.07353i	0.922953	+	0.384912i
$113$	−10.8513	−	10.8513i	−1.02081	−	1.02081i	−0.999779	−	0.0210265i	$-0.993307\pi$
$113$	−10.8513	−	10.8513i	−1.02081	−	1.02081i	−0.0210265	−	0.999779i	$-0.506693\pi$
$114$	−7.00732	−	0.392101i	−0.656295	−	0.0367236i
$115$		0			0
$116$	−14.3713	−	1.61337i	−1.33434	−	0.149798i
$117$	6.23545	+	1.67078i	0.576468	+	0.154464i
$118$	17.4450	−	3.64360i	1.60595	−	0.335420i
$119$	−0.634353	−	7.00765i	−0.0581511	−	0.642390i
$120$		0			0
$121$	−5.04666	−	8.74107i	−0.458787	−	0.794643i
$122$	2.66108	−	8.09245i	0.240923	−	0.732656i
$123$	1.19846	+	4.47272i	0.108062	+	0.403292i
$124$	−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	$-0.274474\pi$
$127$	−1.22418	−	1.22418i	−0.108629	−	0.108629i	−0.759332	+	0.650703i	$0.774474\pi$
$128$	−10.4464	+	4.34436i	−0.923337	+	0.383991i
$129$	−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	$0.351484\pi$
$132$	−2.21027	−	0.866437i	−0.192380	−	0.0754137i
$133$	3.63214	+	9.88652i	0.314947	+	0.857270i
$134$	−17.6300	−	11.5379i	−1.52300	−	0.996724i
$135$		0			0
$136$	5.79522	+	4.79560i	0.496936	+	0.411219i
$137$	−0.300203	−	1.12037i	−0.0256480	−	0.0957198i	0.951915	−	0.306361i	$-0.0991115\pi$
$137$	−0.300203	−	1.12037i	−0.0256480	−	0.0957198i	−0.977563	+	0.210641i	$0.932445\pi$
$138$	0.718965	−	0.642768i	0.0612024	−	0.0547161i
$139$	17.4513			1.48020			0.740099	−	0.672498i	$-0.234779\pi$
$139$	17.4513			1.48020			0.740099	+	0.672498i	$0.234779\pi$
$140$		0			0
$141$	−3.99813			−0.336704
$142$	8.02022	−	7.17023i	0.673042	−	0.601712i
$143$	1.10024	+	4.10614i	0.0920065	+	0.343373i
$144$	−5.52556	+	1.70931i	−0.460464	+	0.142442i
$145$		0			0
$146$	−17.4178	−	11.3990i	−1.44151	−	0.943392i
$147$	−0.708187	+	8.69745i	−0.0584103	+	0.717353i
$148$	−0.759151	+	1.93659i	−0.0624018	+	0.159186i
$149$	−9.70894	+	5.60546i	−0.795387	+	0.459217i	−0.841856	−	0.539703i	$-0.818537\pi$
$149$	−9.70894	+	5.60546i	−0.795387	+	0.459217i	0.0464684	+	0.998920i	$0.485203\pi$
$150$		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	$0.457365\pi$
$152$	−10.2372	−	4.68870i	−0.830345	−	0.380304i
$153$	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
$157$	−1.94845	−	7.27171i	−0.155503	−	0.580345i	−0.999062	−	0.0433084i	$-0.986210\pi$
$157$	−1.94845	−	7.27171i	−0.155503	−	0.580345i	0.843559	−	0.537037i	$-0.180456\pi$
$158$	−4.72576	+	14.3712i	−0.375961	+	1.14331i
$159$	−1.83212	−	3.17333i	−0.145297	−	0.251662i
$160$		0			0
$161$	−1.31354	−	0.607707i	−0.103522	−	0.0478941i
$162$	3.55944	−	0.743432i	0.279656	−	0.0584095i
$163$	6.42243	+	1.72089i	0.503044	+	0.134790i	0.501412	−	0.865208i	$-0.332814\pi$
$163$	6.42243	+	1.72089i	0.503044	+	0.134790i	0.00163153	+	0.999999i	$0.499481\pi$
$164$	−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	$-0.355235\pi$
$167$	−5.93258	−	5.93258i	−0.459077	−	0.459077i	−0.898352	+	0.439276i	$0.855235\pi$
$168$	−6.06650	−	7.08681i	−0.468040	−	0.546759i
$169$			6.93083i			0.533141i
$170$		0			0
$171$	−4.98516	−	2.87818i	−0.381225	−	0.220100i
$172$	−15.4088	−	19.3060i	−1.17491	−	1.47207i
$173$	0.572923	−	2.13818i	0.0435585	−	0.162563i	−0.940721	−	0.339182i	$-0.889850\pi$
$173$	0.572923	−	2.13818i	0.0435585	−	0.162563i	0.984279	+	0.176620i	$0.0565163\pi$
$174$	10.6664	+	6.98064i	0.808621	+	0.529201i
$175$		0			0
$176$	−2.79414	−	2.58838i	−0.210616	−	0.195106i
$177$	−15.1740	−	4.06587i	−1.14055	−	0.305610i
$178$	−2.84508	−	0.935563i	−0.213248	−	0.0701234i
$179$	8.23493	−	14.2633i	0.615507	−	1.06609i	−0.374788	−	0.927111i	$-0.622284\pi$
$179$	8.23493	−	14.2633i	0.615507	−	1.06609i	0.990295	−	0.138980i	$-0.0443822\pi$
$180$		0			0
$181$	−5.97636			−0.444219			−0.222110	−	0.975022i	$-0.571294\pi$
$181$	−5.97636			−0.444219			−0.222110	+	0.975022i	$0.571294\pi$
$182$	−3.76622	+	16.2741i	−0.279171	+	1.20632i
$183$	−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
$187$	−0.655419	+	2.44606i	−0.0479290	+	0.178873i
$188$	−5.97198	−	2.34104i	−0.435551	−	0.170738i
$189$	−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	$0.427356\pi$
$192$	9.94585	+	0.733203i	0.717780	+	0.0529144i
$193$	−14.0635	+	3.76831i	−1.01231	+	0.271249i	−0.726596	−	0.687065i	$-0.758899\pi$
$193$	−14.0635	+	3.76831i	−1.01231	+	0.271249i	−0.285718	+	0.958314i	$0.592232\pi$
$194$	−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	−0.194001	+	0.981001i	$0.562146\pi$
$197$	−16.4919	+	16.4919i	−1.17500	+	1.17500i	−0.981001	+	0.194001i	$0.937854\pi$
$198$	−1.29778	−	1.45163i	−0.0922295	−	0.103163i
$199$	−4.82793	+	8.36222i	−0.342243	+	0.592782i	−0.984849	−	0.173415i	$-0.944520\pi$
$199$	−4.82793	+	8.36222i	−0.342243	+	0.592782i	0.642606	+	0.766197i	$0.277853\pi$
$200$		0			0
$201$	9.28636	+	16.0844i	0.655009	+	1.13451i
$202$	−1.97981	+	0.413507i	−0.139299	+	0.0290943i
$203$	3.26531	−	18.8502i	0.229180	−	1.32302i
$204$	−2.65399	−	6.07630i	−0.185816	−	0.425426i
$205$		0			0
$206$	6.48778	+	12.8451i	0.452025	+	0.894962i
$207$	0.764042	−	0.204725i	0.0531046	−	0.0142293i
$208$	−9.51304	−	15.1128i	−0.659610	−	1.04788i
$209$		−	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	$-0.116939\pi$
$212$	−0.878535	−	5.81275i	−0.0603381	−	0.399221i
$213$	−9.15992	+	2.45439i	−0.627628	+	0.168172i
$214$	−0.0507779	+	0.0256468i	−0.00347111	+	0.00175318i
$215$		0			0
$216$	15.4563	+	2.61649i	1.05167	+	0.178029i
$217$	−8.02081	−	6.68921i	−0.544488	−	0.454093i
$218$	1.81951	+	8.71155i	0.123233	+	0.590020i
$219$	9.17459	+	15.8909i	0.619961	+	1.07380i
$220$		0			0
$221$	−5.93647	+	10.2823i	−0.399330	+	0.691660i
$222$	1.36692	−	1.22205i	0.0917416	−	0.0820187i
$223$	10.7262	−	10.7262i	0.718279	−	0.718279i	−0.249973	−	0.968253i	$-0.580422\pi$
$223$	10.7262	−	10.7262i	0.718279	−	0.718279i	0.968253	+	0.249973i	$0.0804218\pi$
$224$	−4.91191	−	14.1377i	−0.328191	−	0.944611i
$225$		0			0
$226$	−1.21249	+	21.6687i	−0.0806539	+	1.44138i
$227$	9.68083	−	2.59397i	0.642539	−	0.172168i	0.0771860	−	0.997017i	$-0.475406\pi$
$227$	9.68083	−	2.59397i	0.642539	−	0.172168i	0.565353	+	0.824849i	$0.308740\pi$
$228$	6.19149	+	7.75744i	0.410041	+	0.513749i
$229$	14.7989	−	8.54416i	0.977940	−	0.564614i	0.0762921	−	0.997086i	$-0.475692\pi$
$229$	14.7989	−	8.54416i	0.977940	−	0.564614i	0.901647	+	0.432472i	$0.142359\pi$
$230$		0			0
$231$	1.31868	−	2.85029i	0.0867627	−	0.187535i
$232$	11.8450	+	16.6725i	0.777661	+	1.09460i
$233$	0.485407	−	1.81156i	0.0318001	−	0.118680i	−0.948201	−	0.317670i	$-0.897100\pi$
$233$	0.485407	−	1.81156i	0.0318001	−	0.118680i	0.980001	+	0.198990i	$0.0637663\pi$
$234$	−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
$238$	−6.79029	+	7.27400i	−0.440149	+	0.471503i
$239$	−15.2182			−0.984385			−0.492193	−	0.870486i	$-0.663804\pi$
$239$	−15.2182			−0.984385			−0.492193	+	0.870486i	$0.663804\pi$
$240$		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	$0.0271667\pi$
$242$	−4.45894	+	13.5598i	−0.286632	+	0.871656i
$243$	12.9645	+	3.47383i	0.831673	+	0.222846i
$244$	−11.0402	+	4.82210i	−0.706775	+	0.308703i
$245$		0			0
$246$	3.58599	−	5.47940i	0.228634	−	0.349354i
$247$	4.59987	−	17.1670i	0.292683	−	1.09231i
$248$	11.1158	−	1.04917i	0.705854	−	0.0666222i
$249$	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	$-0.153615\pi$
$252$	−1.82084	−	7.43158i	−0.114702	−	0.468145i
$253$	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
$257$	12.7677	+	3.42109i	0.796426	+	0.213402i	0.634014	−	0.773321i	$-0.281406\pi$
$257$	12.7677	+	3.42109i	0.796426	+	0.213402i	0.162412	+	0.986723i	$0.448073\pi$
$258$	4.45165	+	21.3139i	0.277148	+	1.32694i
$259$	−2.49735	−	1.15539i	−0.155178	−	0.0717926i
$260$		0			0
$261$	5.22778	+	9.05478i	0.323592	+	0.560477i
$262$	1.75266	+	0.576336i	0.108279	+	0.0356061i
$263$	2.73529	+	10.2083i	0.168665	+	0.629468i	0.997544	+	0.0700398i	$0.0223126\pi$
$263$	2.73529	+	10.2083i	0.168665	+	0.629468i	−0.828879	+	0.559428i	$0.811021\pi$
$264$	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
$268$	4.45297	+	29.4627i	0.272009	+	1.79972i
$269$	10.5625	+	6.09826i	0.644007	+	0.371818i	0.786156	−	0.618027i	$-0.212068\pi$
$269$	10.5625	+	6.09826i	0.644007	+	0.371818i	−0.142149	+	0.989845i	$0.545401\pi$
$270$		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	$0.269268\pi$
$272$	−0.406362	−	10.6301i	−0.0246393	−	0.644546i
$273$	9.43072	−	11.3081i	0.570773	−	0.684395i
$274$	−0.898253	+	1.37253i	−0.0542655	+	0.0829178i
$275$		0			0
$276$	−1.35535	−	0.152156i	−0.0815824	−	0.00915872i
$277$	1.06292	+	3.96687i	0.0638646	+	0.238346i	0.990478	−	0.137669i	$-0.0439609\pi$
$277$	1.06292	+	3.96687i	0.0638646	+	0.238346i	−0.926614	+	0.376015i	$0.877294\pi$
$278$	−16.4490	−	18.3990i	−0.986548	−	1.10350i
$279$	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	$0.912849\pi$
$282$	3.76852	+	4.21526i	0.224412	+	0.251015i
$283$	−5.05423	−	18.8626i	−0.300443	−	1.12127i	−0.936798	−	0.349872i	$-0.886225\pi$
$283$	−5.05423	−	18.8626i	−0.300443	−	1.12127i	0.636355	−	0.771396i	$-0.280441\pi$
$284$	−15.1192	−	1.69734i	−0.897161	−	0.100718i
$285$		0			0
$286$	3.29208	−	5.03032i	0.194665	−	0.297449i
$287$	−9.68341	−	1.67740i	−0.571594	−	0.0990140i
$288$	7.01036	+	4.21450i	0.413090	+	0.248342i
$289$	8.59722	−	4.96361i	0.505719	−	0.291977i
$290$		0			0
$291$	4.71144	+	2.72015i	0.276190	+	0.159458i
$292$	4.39938	+	29.1081i	0.257454	+	1.70342i
$293$	−12.6859	−	12.6859i	−0.741121	−	0.741121i	0.231673	−	0.972794i	$-0.425580\pi$
$293$	−12.6859	−	12.6859i	−0.741121	−	0.741121i	−0.972794	+	0.231673i	$0.925580\pi$
$294$	9.83729	−	7.45130i	0.573723	−	0.434569i
$295$		0			0
$296$	2.75731	−	1.02499i	0.160265	−	0.0595764i
$297$	1.36590	+	5.09762i	0.0792577	+	0.295794i
$298$	15.0612	+	4.95266i	0.872473	+	0.286900i
$299$	1.22108	+	2.11498i	0.0706170	+	0.122312i
$300$		0			0
$301$	26.7107	−	18.8231i	1.53958	−	1.08495i
$302$	−4.34295	−	20.7934i	−0.249909	−	1.19653i
$303$	1.72208	+	0.461430i	0.0989309	+	0.0265085i
$304$	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	$-0.381962\pi$
$307$	−9.98091	−	9.98091i	−0.569640	−	0.569640i	−0.932028	+	0.362387i	$0.881962\pi$
$308$	3.63864	−	3.48532i	0.207331	−	0.198594i
$309$		−	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	$0.795988\pi$
$312$	1.47916	+	15.6715i	0.0837409	+	0.887224i
$313$	−1.27037	+	4.74109i	−0.0718056	+	0.267982i	−0.992490	−	0.122326i	$-0.960965\pi$
$313$	−1.27037	+	4.74109i	−0.0718056	+	0.267982i	0.920684	+	0.390308i	$0.127631\pi$
$314$	−5.83006	+	8.90835i	−0.329009	+	0.502727i
$315$		0			0
$316$	19.6060	−	8.56345i	1.10292	−	0.481732i
$317$	33.2307	+	8.90414i	1.86642	+	0.500106i	1.00000		0.000794747i	$0.000252976\pi$
$317$	33.2307	+	8.90414i	1.86642	+	0.500106i	0.866423	+	0.499312i	$0.166414\pi$
$318$	−1.61876	+	4.92271i	−0.0907756	+	0.276052i
$319$	−3.44258	+	5.96272i	−0.192747	+	0.333848i
$320$		0			0
$321$	0.0501451			0.00279883
$322$	0.597395	+	1.95768i	0.0332915	+	0.109097i
$323$	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
$327$	2.03038	−	7.57748i	0.112280	−	0.419035i
$328$	8.56473	−	6.08482i	0.472908	−	0.335978i
$329$	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	$0.217454\pi$
$332$	10.1002	+	12.6547i	0.554320	+	0.694518i
$333$	1.45262	−	0.389229i	0.0796032	−	0.0213296i
$334$	−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	−0.879912	−	0.475136i	$-0.842399\pi$
$337$	−7.43071	+	7.43071i	−0.404776	+	0.404776i	0.475136	+	0.879912i	$0.342399\pi$
$338$	7.30722	−	6.53279i	0.397461	−	0.355337i
$339$	9.56524	−	16.5675i	0.519513	−	0.899822i
$340$		0			0
$341$	1.87940	+	3.25522i	0.101775	+	0.176280i
$342$	1.66437	+	7.96877i	0.0899989	+	0.430902i
$343$	−16.1220	−	9.11490i	−0.870506	−	0.492158i
$344$	−5.83059	+	34.4429i	−0.314364	+	1.85704i
$345$		0			0
$346$	−2.79431	+	1.41134i	−0.150223	+	0.0758743i
$347$	−8.85066	+	2.37153i	−0.475128	+	0.127310i	−0.488433	−	0.872601i	$-0.662431\pi$
$347$	−8.85066	+	2.37153i	−0.475128	+	0.127310i	0.0133050	+	0.999911i	$0.495765\pi$
$348$	−2.69413	−	17.8254i	−0.144420	−	0.955544i
$349$			19.9513i			1.06797i	0.845495	+	0.533984i	$0.179306\pi$
$349$			19.9513i			1.06797i	−0.845495	+	0.533984i	$0.820694\pi$
$350$		0			0
$351$			24.7434i			1.32070i
$352$	−0.0952748	+	5.38561i	−0.00507817	+	0.287054i
$353$	2.39430	−	0.641552i	0.127436	−	0.0341464i	−0.194537	−	0.980895i	$-0.562321\pi$
$353$	2.39430	−	0.641552i	0.127436	−	0.0341464i	0.321973	+	0.946749i	$0.395654\pi$
$354$	10.0159	+	19.8305i	0.532340	+	1.05398i
$355$		0			0
$356$	1.69532	+	3.88142i	0.0898516	+	0.205715i
$357$	8.23343	−	3.02482i	0.435759	−	0.160091i
$358$	−22.7999	+	4.76203i	−1.20501	+	0.251681i
$359$	7.94645	+	13.7637i	0.419398	+	0.726418i	0.995879	−	0.0906921i	$-0.0289079\pi$
$359$	7.94645	+	13.7637i	0.419398	+	0.726418i	−0.576481	+	0.817110i	$0.695575\pi$
$360$		0			0
$361$	1.57601	−	2.72973i	0.0829481	−	0.143670i
$362$	5.63313	+	6.30091i	0.296071	+	0.331169i
$363$	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
$367$	−10.3988	+	2.78634i	−0.542812	+	0.145446i	−0.519798	−	0.854289i	$-0.673993\pi$
$367$	−10.3988	+	2.78634i	−0.542812	+	0.145446i	−0.0230136	+	0.999735i	$0.507326\pi$
$368$	−1.93538	−	1.02088i	−0.100889	−	0.0532169i
$369$	4.65148	−	2.68553i	0.242147	−	0.139803i
$370$		0			0
$371$	7.74521	−	0.701119i	0.402111	−	0.0364003i
$372$	−9.16305	−	3.59195i	−0.475082	−	0.186234i
$373$	3.82144	−	14.2618i	0.197867	−	0.738448i	−0.793640	−	0.608388i	$-0.791816\pi$
$373$	3.82144	−	14.2618i	0.197867	−	0.738448i	0.991506	−	0.130060i	$-0.0415169\pi$
$374$	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
$378$	−4.67561	+	20.2037i	−0.240488	+	1.03917i
$379$	26.4563			1.35897			0.679483	−	0.733691i	$-0.262204\pi$
$379$	26.4563			1.35897			0.679483	+	0.733691i	$0.262204\pi$
$380$		0			0
$381$	1.07909	−	1.86905i	0.0552837	−	0.0957542i
$382$	10.8097	+	3.55463i	0.553075	+	0.181871i
$383$	28.3799	+	7.60437i	1.45015	+	0.388565i	0.896074	−	0.443904i	$-0.146407\pi$
$383$	28.3799	+	7.60437i	1.45015	+	0.388565i	0.554071	+	0.832470i	$0.313074\pi$
$384$	−8.60163	−	11.1771i	−0.438950	−	0.570377i
$385$		0			0
$386$	17.2288	+	11.2754i	0.876922	+	0.573901i
$387$	−4.62219	+	17.2503i	−0.234959	+	0.876880i
$388$	5.44470	+	6.82177i	0.276413	+	0.346323i
$389$	8.09963	+	4.67632i	0.410667	+	0.237099i	0.691076	−	0.722782i	$-0.257137\pi$
$389$	8.09963	+	4.67632i	0.410667	+	0.237099i	−0.280409	+	0.959881i	$0.590470\pi$
$390$		0			0
$391$			1.45481i			0.0735731i
$392$	19.0569	−	5.36988i	0.962517	−	0.271220i
$393$	−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
$397$	−17.1641	−	4.59912i	−0.861443	−	0.230823i	−0.199059	−	0.979987i	$-0.563789\pi$
$397$	−17.1641	−	4.59912i	−0.861443	−	0.230823i	−0.662384	+	0.749164i	$0.730455\pi$
$398$	13.3670	−	2.79186i	0.670028	−	0.139943i
$399$	−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	$0.882434\pi$
$402$	8.20490	−	24.9514i	0.409223	−	1.24446i
$403$	4.56121	+	17.0227i	0.227210	+	0.847960i
$404$	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
$408$	−3.90471	+	8.52545i	−0.193312	+	0.422073i
$409$	−5.66917	−	3.27310i	−0.280322	−	0.161844i	0.353247	−	0.935530i	$-0.385078\pi$
$409$	−5.66917	−	3.27310i	−0.280322	−	0.161844i	−0.633569	+	0.773686i	$0.718411\pi$
$410$		0			0
$411$	1.25221	−	0.722965i	0.0617670	−	0.0356612i
$412$	7.42751	−	18.9475i	0.365927	−	0.933478i
$413$	21.3541	−	25.6050i	1.05077	−	1.25994i
$414$	−0.936005	−	0.612568i	−0.0460022	−	0.0301061i
$415$		0			0
$416$	−6.96678	+	24.2745i	−0.341575	+	1.19015i
$417$	5.63057	+	21.0136i	0.275730	+	1.02904i
$418$	−3.99652	+	3.57296i	−0.195476	+	0.174759i
$419$	17.7908			0.869139			0.434569	−	0.900638i	$-0.356901\pi$
$419$	17.7908			0.869139			0.434569	+	0.900638i	$0.356901\pi$
$420$		0			0
$421$	−16.4678			−0.802591			−0.401295	−	0.915949i	$-0.631440\pi$
$421$	−16.4678			−0.802591			−0.401295	+	0.915949i	$0.631440\pi$
$422$	−11.0010	+	9.83513i	−0.535522	+	0.478767i
$423$	1.20029	+	4.47954i	0.0583601	+	0.217803i
$424$	−5.30034	+	6.40517i	−0.257407	+	0.311062i
$425$		0			0
$426$	11.2215	+	7.34393i	0.543686	+	0.355815i
$427$	−5.49588	−	14.9595i	−0.265964	−	0.723942i
$428$	0.0749013	+	0.0293616i	0.00362049	+	0.00141925i
$429$	−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	$0.785414\pi$
$432$	−11.8101	−	18.7619i	−0.568212	−	0.902683i
$433$	5.45382	+	5.45382i	0.262094	+	0.262094i	0.825904	−	0.563811i	$-0.190665\pi$
$433$	5.45382	+	5.45382i	0.262094	+	0.262094i	−0.563811	+	0.825904i	$0.690665\pi$
$434$	0.507689	+	14.7614i	0.0243698	+	0.708572i
$435$		0			0
$436$	7.46963	−	10.1296i	0.357730	−	0.485118i
$437$	−0.563632	−	2.10350i	−0.0269622	−	0.100624i
$438$	8.10614	−	24.6511i	0.387327	−	1.17787i
$439$	−12.8732	−	22.2970i	−0.614402	−	1.06418i	−0.990489	−	0.137592i	$-0.956064\pi$
$439$	−12.8732	−	22.2970i	−0.614402	−	1.06418i	0.376087	−	0.926585i	$-0.377270\pi$
$440$		0			0
$441$	9.95730	−	1.81762i	0.474157	−	0.0865536i
$442$	16.4362	−	3.43289i	0.781790	−	0.163286i
$443$	−16.7002	−	4.47481i	−0.793452	−	0.212605i	−0.160745	−	0.986996i	$-0.551390\pi$
$443$	−16.7002	−	4.47481i	−0.793452	−	0.212605i	−0.632707	+	0.774391i	$0.718056\pi$
$444$	−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
$448$	−10.2756	+	18.5044i	−0.485477	+	0.874250i
$449$			11.0999i			0.523839i	0.965090	+	0.261919i	$0.0843555\pi$
$449$			11.0999i			0.523839i	−0.965090	+	0.261919i	$0.915645\pi$
$450$		0			0
$451$	3.06308	+	1.76847i	0.144235	+	0.0832739i
$452$	23.9883	−	19.1459i	1.12832	−	0.900549i
$453$	−4.84627	+	18.0865i	−0.227698	+	0.849779i
$454$	−11.8597	−	7.76157i	−0.556603	−	0.364268i
$455$		0			0
$456$	2.34281	−	13.8397i	0.109712	−	0.648101i
$457$	−20.5140	−	5.49672i	−0.959606	−	0.257126i	−0.255172	−	0.966896i	$-0.582132\pi$
$457$	−20.5140	−	5.49672i	−0.959606	−	0.257126i	−0.704434	+	0.709770i	$0.748799\pi$
$458$	−22.9572	−	7.54913i	−1.07272	−	0.352748i
$459$	−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	$0.564307\pi$
$462$	−4.24802	+	1.29630i	−0.197636	+	0.0603094i
$463$	−1.63340	+	1.63340i	−0.0759103	+	0.0759103i	−0.744043	−	0.668132i	$-0.767094\pi$
$463$	−1.63340	+	1.63340i	−0.0759103	+	0.0759103i	0.668132	+	0.744043i	$0.267094\pi$
$464$	6.41320	−	28.2032i	0.297725	−	1.30930i
$465$		0			0
$466$	−2.36747	+	1.19576i	−0.109671	+	0.0553924i
$467$	−6.59489	+	24.6125i	−0.305175	+	1.13893i	0.627619	+	0.778521i	$0.284030\pi$
$467$	−6.59489	+	24.6125i	−0.305175	+	1.13893i	−0.932794	+	0.360409i	$0.882637\pi$
$468$	−4.71199	+	12.0203i	−0.217812	+	0.555637i
$469$	−39.2576	+	3.55372i	−1.81275	+	0.164095i
$470$		0			0
$471$	8.12741	−	4.69236i	0.374491	−	0.216213i
$472$	3.34928	+	35.4852i	0.154163	+	1.63334i
$473$	−11.3596	+	3.04379i	−0.522313	+	0.139953i
$474$	−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
$478$	14.3442	+	16.0447i	0.656090	+	0.733867i
$479$	4.63924	−	8.03541i	0.211972	−	0.367147i	−0.740359	−	0.672211i	$-0.765345\pi$
$479$	4.63924	−	8.03541i	0.211972	−	0.367147i	0.952332	+	0.305064i	$0.0986780\pi$
$480$		0			0
$481$	2.32156	+	4.02106i	0.105854	+	0.183345i
$482$	−18.2395	+	3.80954i	−0.830787	+	0.173520i
$483$	0.307949	−	1.77775i	0.0140122	−	0.0808903i
$484$	18.4990	−	8.07996i	0.840865	−	0.367271i
$485$		0			0
$486$	−8.55746	−	16.9429i	−0.388174	−	0.768544i
$487$	17.2022	−	4.60932i	0.779506	−	0.208868i	0.152939	−	0.988236i	$-0.451126\pi$
$487$	17.2022	−	4.60932i	0.779506	−	0.208868i	0.626567	+	0.779368i	$0.284459\pi$
$488$	15.4901	+	7.09457i	0.701204	+	0.321156i
$489$			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	$-0.0179638\pi$
$492$	−9.15701	+	1.38398i	−0.412830	+	0.0623949i
$493$	−18.5748	+	4.97711i	−0.836569	+	0.224158i
$494$	−22.4349	+	11.3314i	−1.00940	+	0.509823i
$495$		0			0
$496$	−11.5836	−	10.7305i	−0.520117	−	0.481816i
$497$	3.43524	−	19.8312i	0.154092	−	0.889550i
$498$	−2.91797	−	13.9708i	−0.130757	−	0.626047i
$499$	3.26199	+	5.64993i	0.146027	+	0.252926i	0.929756	−	0.368178i	$-0.120018\pi$
$499$	3.26199	+	5.64993i	0.146027	+	0.252926i	−0.783729	+	0.621103i	$0.786685\pi$
$500$		0			0
$501$	5.22947	−	9.05770i	0.233635	−	0.404668i
$502$	−15.5034	+	13.8603i	−0.691951	+	0.618617i
$503$	−14.6078	+	14.6078i	−0.651327	+	0.651327i	−0.953313	−	0.301985i	$-0.902351\pi$
$503$	−14.6078	+	14.6078i	−0.651327	+	0.651327i	0.301985	+	0.953313i	$0.402351\pi$
$504$	−6.11889	+	8.92451i	−0.272557	+	0.397529i
$505$		0			0
$506$	0.0411550	−	0.735489i	0.00182956	−	0.0326965i
$507$	−8.34561	+	2.23620i	−0.370641	+	0.0993131i
$508$	2.70623	−	2.15993i	0.120069	−	0.0958316i
$509$	29.8459	−	17.2316i	1.32290	−	0.763775i	0.338708	−	0.940892i	$-0.390010\pi$
$509$	29.8459	−	17.2316i	1.32290	−	0.763775i	0.984190	+	0.177116i	$0.0566769\pi$
$510$		0			0
$511$	−38.7851	+	3.51094i	−1.71575	+	0.155315i
$512$	−6.30364	−	21.7316i	−0.278584	−	0.960412i
$513$	5.71056	−	21.3121i	0.252128	−	0.940953i
$514$	−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
$518$	1.13579	+	3.72201i	0.0499036	+	0.163536i
$519$	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	$-0.0997908\pi$
$522$	4.61897	−	14.0465i	0.202167	−	0.614796i
$523$	−17.8250	−	4.77618i	−0.779431	−	0.208848i	−0.152897	−	0.988242i	$-0.548860\pi$
$523$	−17.8250	−	4.77618i	−0.779431	−	0.208848i	−0.626534	+	0.779394i	$0.715527\pi$
$524$	−1.04437	−	2.39107i	−0.0456233	−	0.104455i
$525$		0			0
$526$	8.18443	−	12.5058i	0.356858	−	0.545280i
$527$	−2.71715	+	10.1405i	−0.118361	+	0.441728i
$528$	2.21522	−	4.19963i	0.0964053	−	0.182765i
$529$	−19.6594	−	11.3504i	−0.854758	−	0.493495i
$530$		0			0
$531$			18.2217i			0.790756i
$532$	−20.4600	+	5.01301i	−0.887055	+	0.217341i
$533$	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
$537$	19.8318	+	5.31392i	0.855806	+	0.229312i
$538$	−3.52645	−	16.8842i	−0.152036	−	0.727928i
$539$	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	$0.855130\pi$
$542$	−8.84244	−	2.90771i	−0.379815	−	0.124897i
$543$	−1.92824	−	7.19630i	−0.0827488	−	0.308823i
$544$	−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	$-0.0927960\pi$
$547$	15.6791	+	15.6791i	0.670391	+	0.670391i	−0.287415	+	0.957806i	$0.592796\pi$
$548$	2.29374	−	0.346674i	0.0979836	−	0.0148092i
$549$	7.54315	+	4.35504i	0.321934	+	0.185869i
$550$		0			0
$551$	24.9289	−	14.3927i	1.06201	−	0.613151i
$552$	1.11709	+	1.57237i	0.0475466	+	0.0669246i
$553$	9.76000	+	26.5663i	0.415037	+	1.12971i
$554$	3.18042	−	4.85969i	0.135123	−	0.206469i
$555$		0			0
$556$	−3.89382	+	34.6847i	−0.165135	+	1.47096i
$557$	−5.52434	−	20.6171i	−0.234074	−	0.873575i	−0.978564	−	0.205942i	$-0.933974\pi$
$557$	−5.52434	−	20.6171i	−0.234074	−	0.873575i	0.744491	−	0.667633i	$-0.232692\pi$
$558$	−5.38017	−	6.01797i	−0.227761	−	0.254761i
$559$	−55.1382			−2.33210
$560$		0			0
$561$	−3.15683			−0.133282
$562$	30.4236	+	34.0302i	1.28334	+	1.43548i
$563$	3.52319	+	13.1487i	0.148485	+	0.554153i	0.999576	+	0.0291340i	$0.00927495\pi$
$563$	3.52319	+	13.1487i	0.148485	+	0.554153i	−0.851091	+	0.525019i	$0.824058\pi$
$564$	0.892084	−	7.94635i	0.0375635	−	0.334602i
$565$		0			0
$566$	−15.1231	+	23.1081i	−0.635669	+	0.971305i
$567$	4.35705	−	5.22439i	0.182979	−	0.219404i
$568$	12.4614	+	17.5402i	0.522869	+	0.735969i
$569$	−20.3421	+	11.7445i	−0.852787	+	0.492357i	−0.861590	−	0.507605i	$-0.830531\pi$
$569$	−20.3421	+	11.7445i	−0.852787	+	0.492357i	0.00880335	+	0.999961i	$0.497198\pi$
$570$		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	$0.474623\pi$
$572$	−8.40651	+	1.27056i	−0.351494	+	0.0531246i
$573$	−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
$577$	−7.22183	−	26.9522i	−0.300649	−	1.12204i	−0.936627	−	0.350329i	$-0.886070\pi$
$577$	−7.22183	−	26.9522i	−0.300649	−	1.12204i	0.635978	−	0.771707i	$-0.280597\pi$
$578$	−13.3366	−	4.38556i	−0.554731	−	0.182415i
$579$	−9.07505	−	15.7184i	−0.377146	−	0.653236i
$580$		0			0
$581$	−17.5083	+	12.3382i	−0.726368	+	0.511874i
$582$	−1.57299	−	7.53124i	−0.0652024	−	0.312180i
$583$	−2.70351	−	0.724403i	−0.111968	−	0.0300017i
$584$	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	$-0.0178802\pi$
$587$	22.8296	+	22.8296i	0.942280	+	0.942280i	−0.0561427	+	0.998423i	$0.517880\pi$
$588$	−17.1283	−	3.34815i	−0.706359	−	0.138075i
$589$		−	15.7148i		−	0.647516i
$590$		0			0
$591$	−25.1794	−	14.5374i	−1.03574	−	0.597987i
$592$	−3.67961	−	1.94092i	−0.151231	−	0.0797715i
$593$	−9.88391	+	36.8872i	−0.405883	+	1.51478i	0.396537	+	0.918019i	$0.370212\pi$
$593$	−9.88391	+	36.8872i	−0.405883	+	1.51478i	−0.802421	+	0.596759i	$0.796455\pi$
$594$	4.08700	−	6.24494i	0.167691	−	0.256233i
$595$		0			0
$596$	−8.97462	−	20.5474i	−0.367615	−	0.841653i
$597$	−11.6269	−	3.11542i	−0.475857	−	0.127506i
$598$	1.07888	−	3.28091i	0.0441186	−	0.134166i
$599$	−14.4801	+	25.0802i	−0.591640	+	1.02475i	0.402372	+	0.915476i	$0.368186\pi$
$599$	−14.4801	+	25.0802i	−0.591640	+	1.02475i	−0.994012	+	0.109274i	$0.965147\pi$
$600$		0			0
$601$	−8.88262			−0.362330			−0.181165	−	0.983453i	$-0.557987\pi$
$601$	−8.88262			−0.362330			−0.181165	+	0.983453i	$0.557987\pi$
$602$	−45.0220	−	10.4192i	−1.83496	−	0.424653i
$603$	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
$607$	11.8891	−	44.3709i	0.482565	−	1.80096i	−0.108218	−	0.994127i	$-0.534515\pi$
$607$	11.8891	−	44.3709i	0.482565	−	1.80096i	0.590783	−	0.806830i	$-0.298819\pi$
$608$	11.6030	−	19.3004i	0.470565	−	0.782734i
$609$	23.7515	−	2.15006i	0.962461	−	0.0871249i
$610$		0			0
$611$	−12.4000	+	7.15915i	−0.501651	+	0.289628i
$612$	−6.01118	+	4.79773i	−0.242988	+	0.193937i
$613$	0.223941	−	0.0600047i	0.00904487	−	0.00242357i	−0.254294	−	0.967127i	$-0.581843\pi$
$613$	0.223941	−	0.0600047i	0.00904487	−	0.00242357i	0.263339	+	0.964703i	$0.415176\pi$
$614$	−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	0.0957517	−	0.995405i	$-0.469475\pi$
$617$	27.1038	−	27.1038i	1.09116	−	1.09116i	0.995405	−	0.0957517i	$-0.0305255\pi$
$618$	−13.3739	+	11.9565i	−0.537978	+	0.480962i
$619$	7.14970	−	12.3836i	0.287371	−	0.497741i	−0.685811	−	0.727780i	$-0.740552\pi$
$619$	7.14970	−	12.3836i	0.287371	−	0.497741i	0.973181	+	0.230039i	$0.0738855\pi$
$620$		0			0
$621$	1.51593	+	2.62566i	0.0608320	+	0.105364i
$622$	4.03012	+	19.2957i	0.161593	+	0.773685i
$623$	−5.25935	+	1.93220i	−0.210711	+	0.0774119i
$624$	15.1284	−	16.3310i	0.605619	−	0.653762i
$625$		0			0
$626$	6.19597	−	3.12944i	0.247641	−	0.125078i
$627$	4.56444	−	1.22304i	0.182286	−	0.0488434i
$628$	14.8874	−	2.25007i	0.594071	−	0.0897875i
$629$			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	$0.790636\pi$
$632$	−27.5085	−	12.5991i	−1.09423	−	0.501165i
$633$	12.5643	−	3.36660i	0.499387	−	0.133810i
$634$	−21.9346	−	43.4281i	−0.871132	−	1.72475i
$635$		0			0
$636$	6.71584	−	2.93332i	0.266300	−	0.116314i
$637$	13.3774	+	28.2428i	0.530033	+	1.11902i
$638$	9.53141	−	1.99075i	0.377352	−	0.0788144i
$639$	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	$0.860322\pi$
$642$	−0.0472652	−	0.0528683i	−0.00186541	−	0.00208655i
$643$	−12.5692	+	12.5692i	−0.495681	+	0.495681i	−0.910090	−	0.414410i	$-0.863988\pi$
$643$	−12.5692	+	12.5692i	−0.495681	+	0.495681i	0.414410	+	0.910090i	$0.363988\pi$
$644$	1.50091	−	2.47509i	0.0591442	−	0.0975322i
$645$		0			0
$646$	−14.9492	−	0.836497i	−0.588169	−	0.0329115i
$647$	34.4127	−	9.22084i	1.35290	−	0.362509i	0.491696	−	0.870767i	$-0.336377\pi$
$647$	34.4127	−	9.22084i	1.35290	−	0.362509i	0.861205	+	0.508258i	$0.169710\pi$
$648$	0.683380	+	7.24033i	0.0268457	+	0.284427i
$649$	−10.3917	+	5.99966i	−0.407910	+	0.235507i
$650$		0			0
$651$	5.46679	−	11.8163i	0.214261	−	0.463118i
$652$	−4.85329	+	12.3807i	−0.190070	+	0.484866i
$653$	−3.40648	+	12.7132i	−0.133306	+	0.497505i	−0.999999	−	0.00133684i	$-0.999574\pi$
$653$	−3.40648	+	12.7132i	−0.133306	+	0.497505i	0.866693	+	0.498842i	$0.166241\pi$
$654$	−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
$658$	−11.4778	+	3.50250i	−0.447451	+	0.136542i
$659$	10.3786			0.404294			0.202147	−	0.979355i	$-0.435208\pi$
$659$	10.3786			0.404294			0.202147	+	0.979355i	$0.435208\pi$
$660$		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	$0.314671\pi$
$662$	−17.4054	−	5.72352i	−0.676481	−	0.222451i
$663$	−14.2965	−	3.83074i	−0.555231	−	0.148774i
$664$	3.82184	−	22.5767i	0.148316	−	0.876144i
$665$		0			0
$666$	−1.77956	−	1.16463i	−0.0689567	−	0.0451286i
$667$	−1.02375	+	3.82069i	−0.0396398	+	0.147938i
$668$	13.1148	−	10.4674i	0.507427	−	0.404995i
$669$	16.3765	+	9.45496i	0.633151	+	0.365550i
$670$		0			0
$671$			5.73573i			0.221425i
$672$	15.4387	−	10.4760i	0.595562	−	0.404121i
$673$	−27.9624	−	27.9624i	−1.07787	−	1.07787i	−0.996700	−	0.0811716i	$-0.974134\pi$
$673$	−27.9624	−	27.9624i	−1.07787	−	1.07787i	−0.0811716	−	0.996700i	$-0.525866\pi$
$674$	14.8382	+	0.830285i	0.571546	+	0.0319814i
$675$		0			0
$676$	−13.7751	−	1.54644i	−0.529813	−	0.0594786i
$677$	−33.0709	−	8.86132i	−1.27102	−	0.340568i	−0.440597	−	0.897705i	$-0.645233\pi$
$677$	−33.0709	−	8.86132i	−1.27102	−	0.340568i	−0.830421	+	0.557137i	$0.811900\pi$
$678$	−26.4831	+	5.53131i	−1.01708	+	0.212429i
$679$	−9.43821	+	6.65114i	−0.362205	+	0.255247i
$680$		0			0
$681$	6.24694	+	10.8200i	0.239383	+	0.414624i
$682$	1.66053	−	5.04973i	0.0635850	−	0.193364i
$683$	−0.498756	−	1.86138i	−0.0190844	−	0.0712239i	0.955727	−	0.294255i	$-0.0950715\pi$
$683$	−0.498756	−	1.86138i	−0.0190844	−	0.0712239i	−0.974811	+	0.223031i	$0.928405\pi$
$684$	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
$688$	41.8091	−	26.3176i	1.59396	−	1.00335i
$689$	−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	$0.0960688\pi$
$692$	4.12182	+	1.61577i	0.156688	+	0.0614225i
$693$	−3.58937	−	0.621767i	−0.136349	−	0.0236190i
$694$	10.8427	+	7.09598i	0.411582	+	0.269360i
$695$		0			0
$696$	−16.2541	+	19.6422i	−0.616109	+	0.744534i
$697$	2.55677	+	9.54198i	0.0968444	+	0.361428i
$698$	21.0348	−	18.8055i	0.796177	−	0.711797i
$699$	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	$0.280803\pi$
$702$	26.0871	−	23.3223i	0.984594	−	0.880245i
$703$	−1.07159	−	3.99924i	−0.0404159	−	0.150834i
$704$	5.76789	−	4.97586i	0.217385	−	0.187535i
$705$		0			0
$706$	−2.93319	−	1.91962i	−0.110392	−	0.0722460i
$707$	−2.42345	+	2.90588i	−0.0911433	+	0.109287i
$708$	11.4667	−	29.2514i	0.430944	−	1.09934i
$709$	−7.92917	+	4.57791i	−0.297786	+	0.171927i	−0.641448	−	0.767167i	$-0.721666\pi$
$709$	−7.92917	+	4.57791i	−0.297786	+	0.171927i	0.343662	+	0.939093i	$0.388333\pi$
$710$		0			0
$711$	−13.3957	−	7.73401i	−0.502378	−	0.290048i
$712$	2.49425	−	5.44589i	0.0934762	−	0.204093i
$713$	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
$717$	−4.91009	−	18.3247i	−0.183370	−	0.684348i
$718$	7.02104	−	21.3512i	0.262023	−	0.796820i
$719$	−6.67322	−	11.5584i	−0.248869	−	0.431054i	0.714343	−	0.699796i	$-0.246726\pi$
$719$	−6.67322	−	11.5584i	−0.248869	−	0.431054i	−0.963212	+	0.268742i	$0.913392\pi$
$720$		0			0
$721$	24.4340	+	11.3043i	0.909970	+	0.420996i
$722$	−4.36348	+	0.911364i	−0.162392	+	0.0339175i
$723$	15.8651	+	4.25104i	0.590029	+	0.158098i
$724$	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	$-0.301643\pi$
$727$	−6.15934	−	6.15934i	−0.228437	−	0.228437i	−0.812040	+	0.583602i	$0.801643\pi$
$728$	−31.5047	−	11.1166i	−1.16764	−	0.412008i
$729$			24.4454i			0.905384i
$730$		0			0
$731$	−28.4457	−	16.4231i	−1.05210	−	0.607431i
$732$	−9.36848	−	11.7380i	−0.346269	−	0.433847i
$733$	−2.65865	+	9.92223i	−0.0981996	+	0.366486i	−0.997485	−	0.0708761i	$-0.977420\pi$
$733$	−2.65865	+	9.92223i	−0.0981996	+	0.366486i	0.899286	+	0.437362i	$0.144087\pi$
$734$	12.7392	+	8.33717i	0.470213	+	0.307731i
$735$		0			0
$736$	0.747914	+	3.00273i	0.0275685	+	0.110682i
$737$	13.7031	+	3.67173i	0.504760	+	0.135250i
$738$	−7.21572	−	2.37279i	−0.265614	−	0.0873435i
$739$	21.8583	−	37.8597i	0.804070	−	1.39269i	−0.112847	−	0.993612i	$-0.535997\pi$
$739$	21.8583	−	37.8597i	0.804070	−	1.39269i	0.916917	−	0.399078i	$-0.130670\pi$
$740$		0			0
$741$	22.1553			0.813897
$742$	−8.03959	−	7.50497i	−0.295143	−	0.275516i
$743$	−26.0186	+	26.0186i	−0.954529	+	0.954529i	−0.999010	−	0.0444813i	$-0.985836\pi$
$743$	−26.0186	+	26.0186i	−0.954529	+	0.954529i	0.0444813	+	0.999010i	$0.485836\pi$
$744$	4.84979	+	13.0463i	0.177802	+	0.478302i
$745$		0			0
$746$	−18.6383	+	9.41377i	−0.682396	+	0.344663i
$747$	3.02975	−	11.3072i	0.110853	−	0.413709i
$748$	−4.71534	−	1.84843i	−0.172410	−	0.0675854i
$749$	−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	$0.382514\pi$
$752$	5.98535	−	11.3471i	0.218263	−	0.413784i
$753$	17.7065	−	4.74444i	0.645260	−	0.172897i
$754$	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	−0.765041	−	0.643981i	$-0.777282\pi$
$757$	−3.33081	+	3.33081i	−0.121060	+	0.121060i	0.643981	+	0.765041i	$0.277282\pi$
$758$	−24.9369	−	27.8930i	−0.905748	−	1.01312i
$759$	−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	$0.618575\pi$
$762$	−2.98767	+	0.624010i	−0.108232	+	0.0226055i
$763$	12.7864	+	10.6636i	0.462899	+	0.386050i
$764$	−6.44127	−	14.7473i	−0.233037	−	0.533537i
$765$		0			0
$766$	−18.7327	−	37.0888i	−0.676840	−	1.34007i
$767$	−54.3419	+	14.5609i	−1.96217	+	0.525763i
$768$	−3.67642	+	19.6039i	−0.132661	+	0.707396i
$769$		−	18.7498i		−	0.676135i	−0.941122	−	0.338067i	$-0.890227\pi$
$769$		−	18.7498i		−	0.676135i	0.941122	−	0.338067i	$-0.109773\pi$
$770$		0			0
$771$			16.4777i			0.593431i
$772$	−4.35164	−	28.7922i	−0.156619	−	1.03626i
$773$	42.9466	−	11.5075i	1.54468	−	0.413896i	0.616907	−	0.787036i	$-0.288386\pi$
$773$	42.9466	−	11.5075i	1.54468	−	0.413896i	0.927775	+	0.373140i	$0.121719\pi$
$774$	22.5438	−	11.3864i	0.810320	−	0.409274i
$775$		0			0
$776$	2.06023	−	12.1704i	0.0739581	−	0.436891i
$777$	0.585483	−	3.37991i	0.0210041	−	0.121254i
$778$	−2.70418	−	12.9472i	−0.0969497	−	0.464181i
$779$	−7.39361	−	12.8061i	−0.264903	−	0.458826i
$780$		0			0
$781$	−3.62174	+	6.27304i	−0.129596	+	0.224467i
$782$	1.53382	−	1.37126i	0.0548493	−	0.0490363i
$783$	−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
$787$	−1.04293	+	0.279451i	−0.0371763	+	0.00996136i	−0.277359	−	0.960766i	$-0.589459\pi$
$787$	−1.04293	+	0.279451i	−0.0371763	+	0.00996136i	0.240183	+	0.970728i	$0.422793\pi$
$788$	−29.0982	−	36.4577i	−1.03658	−	1.29875i
$789$	−11.4095	+	6.58729i	−0.406189	+	0.234514i
$790$		0			0
$791$	23.3883	+	33.1889i	0.831592	+	1.18006i
$792$	3.17471	−	2.25547i	0.112808	−	0.0801447i
$793$	−6.96017	+	25.9757i	−0.247163	+	0.922424i
$794$	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	−0.415681	−	0.909510i	$-0.636457\pi$
$797$	13.9414	−	13.9414i	0.493829	−	0.493829i	0.909510	+	0.415681i	$0.136457\pi$
$798$	18.0905	+	4.18657i	0.640397	+	0.148203i
$799$	−8.52950			−0.301752
$800$		0			0
$801$	1.53111	−	2.65196i	0.0540992	−	0.0937025i
$802$	−2.71841	+	8.26676i	−0.0959902	+	0.291910i
$803$	13.5382	+	3.62754i	0.477751	+	0.128013i
$804$	−34.0401	+	14.8679i	−1.20050	+	0.524352i
$805$		0			0
$806$	13.6479	−	20.8540i	0.480726	−	0.734550i
$807$	−3.93515	+	14.6862i	−0.138524	+	0.516978i
$808$	−0.380106	−	4.02717i	−0.0133721	−	0.141675i
$809$	4.37439	+	2.52555i	0.153795	+	0.0887937i	0.574923	−	0.818208i	$-0.305032\pi$
$809$	4.37439	+	2.52555i	0.153795	+	0.0887937i	−0.421127	+	0.907001i	$0.638365\pi$
$810$		0			0
$811$		−	21.1629i		−	0.743131i	−0.928407	−	0.371565i	$-0.878821\pi$
$811$		−	21.1629i		−	0.743131i	0.928407	−	0.371565i	$-0.121179\pi$
$812$	36.7364	+	10.6958i	1.28919	+	0.375349i
$813$	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
$817$	47.4920	+	12.7255i	1.66154	+	0.445207i
$818$	1.89274	+	9.06216i	0.0661781	+	0.316851i
$819$	−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	$-0.434475\pi$
$822$	−1.94252	−	0.638770i	−0.0677533	−	0.0222797i
$823$	1.23565	+	4.61152i	0.0430722	+	0.160748i	0.984112	−	0.177548i	$-0.0568164\pi$
$823$	1.23565	+	4.61152i	0.0430722	+	0.160748i	−0.941040	+	0.338295i	$0.890150\pi$
$824$	−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	$-0.201135\pi$
$827$	6.21884	+	6.21884i	0.216250	+	0.216250i	−0.590666	+	0.806916i	$0.701135\pi$
$828$	0.236416	+	1.56422i	0.00821602	+	0.0543606i
$829$	−33.7077	−	19.4612i	−1.17072	−	0.675915i	−0.216869	−	0.976201i	$-0.569585\pi$
$829$	−33.7077	−	19.4612i	−1.17072	−	0.675915i	−0.953849	+	0.300286i	$0.902918\pi$
$830$		0			0
$831$	−4.43367	+	2.55978i	−0.153802	+	0.0887978i
$832$	32.1594	−	15.5353i	1.11493	−	0.538588i
$833$	−1.51083	+	18.5549i	−0.0523470	+	0.642889i
$834$	16.8475	−	25.7431i	0.583383	−	0.891410i
$835$		0			0
$836$	7.53399	+	0.845791i	0.260568	+	0.0292523i
$837$	5.66257	+	21.1330i	0.195727	+	0.730464i
$838$	−16.7691	−	18.7570i	−0.579279	−	0.647949i
$839$	−15.0742			−0.520418			−0.260209	−	0.965552i	$-0.583791\pi$
$839$	−15.0742			−0.520418			−0.260209	+	0.965552i	$0.583791\pi$
$840$		0			0
$841$	−23.2844			−0.802910
$842$	15.5220	+	17.3621i	0.534925	+	0.598337i
$843$	−10.4141	−	38.8660i	−0.358681	−	1.33862i
$844$	20.7385	+	2.32817i	0.713848	+	0.0801390i
$845$		0			0
$846$	3.59146	−	5.48776i	0.123477	−	0.188673i
$847$	9.20895	+	25.0663i	0.316423	+	0.861289i
$848$	11.7489	−	0.449132i	0.403461	−	0.0154233i
$849$	21.0823	−	12.1719i	0.723543	−	0.417738i
$850$		0			0
$851$	0.492709	+	0.284465i	0.0168898	+	0.00975135i
$852$	−2.83434	−	18.7531i	−0.0971028	−	0.642471i
$853$	14.0097	+	14.0097i	0.479684	+	0.479684i	0.905031	−	0.425346i	$-0.139848\pi$
$853$	14.0097	+	14.0097i	0.479684	+	0.479684i	−0.425346	+	0.905031i	$0.639848\pi$
$854$	−10.5917	+	19.8947i	−0.362440	+	0.680784i
$855$		0			0
$856$	−0.0396435	−	0.106644i	−0.00135499	−	0.00364503i
$857$	9.22615	+	34.4324i	0.315159	+	1.17619i	0.923841	+	0.382776i	$0.125032\pi$
$857$	9.22615	+	34.4324i	0.315159	+	1.17619i	−0.608682	+	0.793414i	$0.708302\pi$
$858$	7.11932	+	2.34108i	0.243049	+	0.0799233i
$859$	26.2004	+	45.3805i	0.893947	+	1.54836i	0.835103	+	0.550094i	$0.185408\pi$
$859$	26.2004	+	45.3805i	0.893947	+	1.54836i	0.0588442	+	0.998267i	$0.481258\pi$
$860$		0			0
$861$	−1.10450	−	12.2013i	−0.0376411	−	0.415818i
$862$	4.37546	+	20.9491i	0.149029	+	0.713528i
$863$	−5.09743	−	1.36585i	−0.173518	−	0.0464941i	0.171014	−	0.985269i	$-0.445296\pi$
$863$	−5.09743	−	1.36585i	−0.173518	−	0.0464941i	−0.344532	+	0.938775i	$0.611962\pi$
$864$	−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
$868$	15.0846	−	14.4489i	0.512003	−	0.490429i
$869$		−	10.1859i		−	0.345535i
$870$		0			0
$871$	57.6023	+	33.2567i	1.95178	+	1.12686i
$872$	−17.7203	+	1.67254i	−0.600085	+	0.0566392i
$873$	1.63325	−	6.09536i	0.0552771	−	0.206297i
$874$	−1.68647	+	2.57694i	−0.0570458	+	0.0871662i
$875$		0			0
$876$	−33.6304	+	14.6890i	−1.13627	+	0.496295i
$877$	−10.7858	−	2.89005i	−0.364211	−	0.0975901i	0.0720722	−	0.997399i	$-0.477039\pi$
$877$	−10.7858	−	2.89005i	−0.364211	−	0.0975901i	−0.436283	+	0.899809i	$0.643705\pi$
$878$	−11.3740	+	34.5887i	−0.383854	+	1.16731i
$879$	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	$0.378747\pi$
$882$	−11.3018	−	8.78481i	−0.380551	−	0.295800i
$883$	−5.32169	+	5.32169i	−0.179089	+	0.179089i	−0.790959	−	0.611869i	$-0.790418\pi$
$883$	−5.32169	+	5.32169i	−0.179089	+	0.179089i	0.611869	+	0.790959i	$0.290418\pi$
$884$	−19.1116	−	14.0930i	−0.642792	−	0.474000i
$885$		0			0
$886$	11.0233	+	21.8250i	0.370335	+	0.733225i
$887$	−1.31079	+	4.89193i	−0.0440120	+	0.164255i	−0.984434	−	0.175754i	$-0.943764\pi$
$887$	−1.31079	+	4.89193i	−0.0440120	+	0.164255i	0.940422	+	0.340009i	$0.110430\pi$
$888$	2.12385	+	2.98944i	0.0712718	+	0.100319i
$889$	2.63853	+	3.74417i	0.0884936	+	0.125576i
$890$		0			0
$891$	−2.12030	+	1.22416i	−0.0710327	+	0.0410108i
$892$	18.9252	+	23.7118i	0.633662	+	0.793929i
$893$	12.3327	−	3.30454i	0.412699	−	0.110582i
$894$	−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
$898$	11.7028	−	10.4625i	0.390526	−	0.349137i
$899$	−14.2718	+	24.7194i	−0.475990	+	0.824439i
$900$		0			0
$901$	−3.90860	−	6.76989i	−0.130214	−	0.225538i
$902$	−1.02265	−	4.89633i	−0.0340507	−	0.163030i
$903$	31.2835	+	26.0899i	1.04105	+	0.868218i
$904$	−42.7964	−	7.24469i	−1.42339	−	0.240955i
$905$		0			0
$906$	23.6367	−	11.9384i	0.785277	−	0.396625i
$907$	3.27202	−	0.876735i	0.108646	−	0.0291115i	−0.204087	−	0.978953i	$-0.565422\pi$
$907$	3.27202	−	0.876735i	0.108646	−	0.0291115i	0.312732	+	0.949841i	$0.398756\pi$
$908$	2.99552	+	19.8196i	0.0994098	+	0.657736i
$909$		−	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	$-0.175355\pi$
$912$	−16.7995	+	10.5748i	−0.556287	+	0.350166i
$913$	7.44597	−	1.99514i	0.246426	−	0.0660295i
$914$	13.5407	+	26.8091i	0.447886	+	0.886767i
$915$		0			0
$916$	13.6796	+	31.3195i	0.451988	+	1.03482i
$917$	3.23992	−	1.19029i	0.106992	−	0.0393069i
$918$	20.4049	−	4.26180i	0.673462	−	0.140660i
$919$	−23.1351	−	40.0712i	−0.763157	−	1.32183i	−0.941215	−	0.337807i	$-0.890315\pi$
$919$	−23.1351	−	40.0712i	−0.763157	−	1.32183i	0.178058	−	0.984020i	$-0.443018\pi$
$920$		0			0
$921$	8.79800	−	15.2386i	0.289904	−	0.502128i
$922$	8.12167	+	9.08446i	0.267473	+	0.299181i
$923$	−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
$927$	−14.2124	+	3.80821i	−0.466797	+	0.125078i
$928$	−35.7797	+	19.8220i	−1.17453	+	0.650689i
$929$	−37.0594	+	21.3962i	−1.21588	+	0.701987i	−0.964034	−	0.265780i	$-0.914370\pi$
$929$	−37.0594	+	21.3962i	−1.21588	+	0.701987i	−0.251844	+	0.967768i	$0.581037\pi$
$930$		0			0
$931$	−5.00414	−	27.4137i	−0.164004	−	0.898447i
$932$	3.49220	+	1.36896i	0.114391	+	0.0448418i
$933$	4.49719	−	16.7837i	0.147231	−	0.549475i
$934$	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	−0.945675	−	0.325114i	$-0.894597\pi$
$937$	−18.9957	+	18.9957i	−0.620561	+	0.620561i	0.325114	+	0.945675i	$0.394597\pi$
$938$	40.7497	+	38.0399i	1.33053	+	1.24205i
$939$	−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	$0.0516963\pi$
$942$	−12.6078	−	4.14590i	−0.410785	−	0.135081i
$943$	1.96271	+	0.525906i	0.0639145	+	0.0171258i
$944$	34.2554	−	36.9785i	1.11492	−	1.20355i
$945$		0			0
$946$	13.9163	+	9.10749i	0.452457	+	0.296110i
$947$	3.97536	−	14.8363i	0.129182	−	0.482114i	−0.870772	−	0.491687i	$-0.836381\pi$
$947$	3.97536	−	14.8363i	0.129182	−	0.482114i	0.999954	+	0.00957300i	$0.00304723\pi$
$948$	16.6373	+	20.8452i	0.540353	+	0.677019i
$949$	56.9090	+	32.8564i	1.84735	+	1.06657i
$950$		0			0
$951$			42.8869i			1.39070i
$952$	−12.9421	−	15.1188i	−0.419456	−	0.490003i
$953$	−22.0087	−	22.0087i	−0.712931	−	0.712931i	0.254216	−	0.967147i	$-0.418183\pi$
$953$	−22.0087	−	22.0087i	−0.712931	−	0.712931i	−0.967147	+	0.254216i	$0.918183\pi$
$954$	6.00141	+	0.335815i	0.194303	+	0.0108724i
$955$		0			0
$956$	3.39557	−	30.2465i	0.109821	−	0.978240i
$957$	−8.29061	−	2.22146i	−0.267997	−	0.0718096i
$958$	−12.8446	+	2.68274i	−0.414990	+	0.0866755i
$959$	0.276665	+	3.05629i	0.00893398	+	0.0986929i
$960$		0			0
$961$	−7.70864	−	13.3518i	−0.248666	−	0.430702i
$962$	2.05120	−	6.23777i	0.0661333	−	0.201114i
$963$	−0.0150542	−	0.0561830i	−0.000485114	−	0.00181047i
$964$	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	$-0.375774\pi$
$967$	−16.9281	−	16.9281i	−0.544372	−	0.544372i	−0.924807	+	0.380435i	$0.875774\pi$
$968$	−25.9554	−	11.8877i	−0.834238	−	0.382086i
$969$	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	$0.536228\pi$
$972$	−9.79698	+	24.9920i	−0.314238	+	0.801620i
$973$	−45.4942	−	7.88071i	−1.45848	−	0.252644i
$974$	−21.0739	−	13.7918i	−0.675251	−	0.441918i
$975$		0			0
$976$	−7.12065	−	23.0185i	−0.227926	−	0.736803i
$977$	−6.04928	−	22.5762i	−0.193534	−	0.722277i	−0.992642	−	0.121090i	$-0.961361\pi$
$977$	−6.04928	−	22.5762i	−0.193534	−	0.722277i	0.799108	−	0.601188i	$-0.205306\pi$
$978$	8.73879	−	7.81264i	0.279436	−	0.249821i
$979$	2.01652			0.0644484
$980$		0			0
$981$	−9.09942			−0.290522
$982$	−2.63545	+	2.35614i	−0.0841006	+	0.0751875i
$983$	−5.14648	−	19.2069i	−0.164147	−	0.612606i	−0.998147	−	0.0608417i	$-0.980622\pi$
$983$	−5.14648	−	19.2069i	−0.164147	−	0.612606i	0.834000	−	0.551764i	$-0.186045\pi$
$984$	10.0903	+	8.34979i	0.321666	+	0.266182i
$985$		0			0
$986$	22.7555	+	14.8923i	0.724682	+	0.474268i
$987$	10.4228	+	1.80549i	0.331763	+	0.0574694i
$988$	33.0932	+	12.9727i	1.05284	+	0.412716i
$989$	−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	$0.783309\pi$
$992$	−0.394977	+	22.3269i	−0.0125405	+	0.708880i
$993$	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
$997$	−4.45792	−	16.6372i	−0.141184	−	0.526905i	−0.999896	−	0.0144466i	$-0.995401\pi$
$997$	−4.45792	−	16.6372i	−0.141184	−	0.526905i	0.858712	−	0.512459i	$-0.171265\pi$
$998$	2.88211	−	8.76459i	0.0912315	−	0.277438i
$999$	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.543.5		72
4.3	odd	2	inner	700.2.be.e.543.2		72
5.2	odd	4	inner	700.2.be.e.207.14		72
5.3	odd	4		140.2.w.b.67.5	yes	72
5.4	even	2		140.2.w.b.123.14	yes	72
7.2	even	3	inner	700.2.be.e.443.8		72
20.3	even	4		140.2.w.b.67.11	yes	72
20.7	even	4	inner	700.2.be.e.207.8		72
20.19	odd	2		140.2.w.b.123.17	yes	72
28.23	odd	6	inner	700.2.be.e.443.14		72
35.2	odd	12	inner	700.2.be.e.107.2		72
35.3	even	12		980.2.k.j.687.8		36
35.4	even	6		980.2.k.k.883.1		36
35.9	even	6		140.2.w.b.23.11	yes	72
35.13	even	4		980.2.x.m.67.5		72
35.18	odd	12		980.2.k.k.687.8		36
35.19	odd	6		980.2.x.m.863.11		72
35.23	odd	12		140.2.w.b.107.17	yes	72
35.24	odd	6		980.2.k.j.883.1		36
35.33	even	12		980.2.x.m.667.17		72
35.34	odd	2		980.2.x.m.263.14		72
140.3	odd	12		980.2.k.j.687.1		36
140.19	even	6		980.2.x.m.863.5		72
140.23	even	12		140.2.w.b.107.14	yes	72
140.39	odd	6		980.2.k.k.883.8		36
140.59	even	6		980.2.k.j.883.8		36
140.79	odd	6		140.2.w.b.23.5	✓	72
140.83	odd	4		980.2.x.m.67.11		72
140.103	odd	12		980.2.x.m.667.14		72
140.107	even	12	inner	700.2.be.e.107.5		72
140.123	even	12		980.2.k.k.687.1		36
140.139	even	2		980.2.x.m.263.17		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.5	✓	72	140.79	odd	6
140.2.w.b.23.11	yes	72	35.9	even	6
140.2.w.b.67.5	yes	72	5.3	odd	4
140.2.w.b.67.11	yes	72	20.3	even	4
140.2.w.b.107.14	yes	72	140.23	even	12
140.2.w.b.107.17	yes	72	35.23	odd	12
140.2.w.b.123.14	yes	72	5.4	even	2
140.2.w.b.123.17	yes	72	20.19	odd	2
700.2.be.e.107.2		72	35.2	odd	12	inner
700.2.be.e.107.5		72	140.107	even	12	inner
700.2.be.e.207.8		72	20.7	even	4	inner
700.2.be.e.207.14		72	5.2	odd	4	inner
700.2.be.e.443.8		72	7.2	even	3	inner
700.2.be.e.443.14		72	28.23	odd	6	inner
700.2.be.e.543.2		72	4.3	odd	2	inner
700.2.be.e.543.5		72	1.1	even	1	trivial
980.2.k.j.687.1		36	140.3	odd	12
980.2.k.j.687.8		36	35.3	even	12
980.2.k.j.883.1		36	35.24	odd	6
980.2.k.j.883.8		36	140.59	even	6
980.2.k.k.687.1		36	140.123	even	12
980.2.k.k.687.8		36	35.18	odd	12
980.2.k.k.883.1		36	35.4	even	6
980.2.k.k.883.8		36	140.39	odd	6
980.2.x.m.67.5		72	35.13	even	4
980.2.x.m.67.11		72	140.83	odd	4
980.2.x.m.263.14		72	35.34	odd	2
980.2.x.m.263.17		72	140.139	even	2
980.2.x.m.667.14		72	140.103	odd	12
980.2.x.m.667.17		72	35.33	even	12
980.2.x.m.863.5		72	140.19	even	6
980.2.x.m.863.11		72	35.19	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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