LMFDB - Embedded newform 875.2.bb.c.493.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] 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("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			493.14
Character	$\chi$	$=$	875.493
Dual form			875.2.bb.c.607.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.863911 - 1.33031i) q^{2} +(0.702377 - 1.82975i) q^{3} +(-0.209899 - 0.471441i) q^{4} +(-1.82734 - 2.51512i) q^{6} +(2.08368 + 1.63042i) q^{7} +(2.32486 + 0.368222i) q^{8} +(-0.625235 - 0.562964i) q^{9} +(1.39398 + 1.54818i) q^{11} +(-1.01005 + 0.0529345i) q^{12} +(-1.94768 - 0.992394i) q^{13} +(3.96908 - 1.36339i) q^{14} +(3.18894 - 3.54168i) q^{16} +(3.18817 - 3.93706i) q^{17} +(-1.28906 + 0.345403i) q^{18} +(-6.86927 - 3.05840i) q^{19} +(4.44680 - 2.66745i) q^{21} +(3.26382 - 0.516939i) q^{22} +(1.68435 + 1.09383i) q^{23} +(2.30669 - 3.99530i) q^{24} +(-3.00281 + 1.73368i) q^{26} +(3.76970 - 1.92076i) q^{27} +(0.331286 - 1.32456i) q^{28} +(-4.12547 + 5.67823i) q^{29} +(6.31745 - 0.663990i) q^{31} +(-0.738117 - 2.75469i) q^{32} +(3.81188 - 1.46324i) q^{33} +(-2.48320 - 7.64252i) q^{34} +(-0.134168 + 0.412927i) q^{36} +(-0.138578 - 2.64422i) q^{37} +(-10.0030 + 6.49605i) q^{38} +(-3.18385 + 2.86675i) q^{39} +(-8.47974 + 2.75523i) q^{41} +(0.293115 - 8.22005i) q^{42} +(-0.986332 - 0.986332i) q^{43} +(0.437278 - 0.982142i) q^{44} +(2.91025 - 1.29573i) q^{46} +(-2.04177 + 1.65339i) q^{47} +(-4.24056 - 8.32258i) q^{48} +(1.68344 + 6.79456i) q^{49} +(-4.96456 - 8.59887i) q^{51} +(-0.0590385 + 1.12652i) q^{52} +(-8.62323 - 3.31015i) q^{53} +(0.701489 - 6.67422i) q^{54} +(4.24391 + 4.55777i) q^{56} +(-10.4209 + 10.4209i) q^{57} +(3.98974 + 10.3936i) q^{58} +(-10.2924 - 2.18773i) q^{59} +(1.78346 + 8.39053i) q^{61} +(4.57440 - 8.97777i) q^{62} +(-0.384920 - 2.19243i) q^{63} +(4.76284 + 1.54754i) q^{64} +(1.34656 - 6.33508i) q^{66} +(2.55191 + 2.06649i) q^{67} +(-2.52529 - 0.676649i) q^{68} +(3.18448 - 2.31366i) q^{69} +(5.41526 + 3.93442i) q^{71} +(-1.24629 - 1.53904i) q^{72} +(-8.26979 - 0.433401i) q^{73} +(-3.63734 - 2.10002i) q^{74} +3.88041i q^{76} +(0.380434 + 5.49868i) q^{77} +(1.06309 + 6.71211i) q^{78} +(-2.65691 - 0.279252i) q^{79} +(-1.13060 - 10.7569i) q^{81} +(-3.66043 + 13.6609i) q^{82} +(0.456772 - 2.88395i) q^{83} +(-2.19093 - 1.53651i) q^{84} +(-2.16423 + 0.460021i) q^{86} +(7.49212 + 11.5369i) q^{87} +(2.67075 + 4.11259i) q^{88} +(12.3861 - 2.63274i) q^{89} +(-2.44033 - 5.24338i) q^{91} +(0.162132 - 1.02366i) q^{92} +(3.22229 - 12.0258i) q^{93} +(0.435611 + 4.14456i) q^{94} +(-5.55884 - 0.584258i) q^{96} +(0.527619 + 3.33125i) q^{97} +(10.4932 + 3.63040i) q^{98} -1.75274i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) $ 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.863911	−	1.33031i	0.610877	−	0.940669i	−0.388934	−	0.921265i	$-0.627157\pi$
$2$	0.863911	−	1.33031i	0.610877	−	0.940669i	0.999812	−	0.0194031i	$-0.00617659\pi$
$3$	0.702377	−	1.82975i	0.405518	−	1.05641i	−0.567028	−	0.823698i	$-0.691907\pi$
$3$	0.702377	−	1.82975i	0.405518	−	1.05641i	0.972546	−	0.232711i	$-0.0747597\pi$
$4$	−0.209899	−	0.471441i	−0.104950	−	0.235721i
$5$		0			0
$5$		0			0
$6$	−1.82734	−	2.51512i	−0.746010	−	1.02679i
$7$	2.08368	+	1.63042i	0.787557	+	0.616242i
$7$	2.08368	+	1.63042i	0.787557	+	0.616242i
$8$	2.32486	+	0.368222i	0.821963	+	0.130186i
$9$	−0.625235	−	0.562964i	−0.208412	−	0.187655i
$10$		0			0
$11$	1.39398	+	1.54818i	0.420302	+	0.466792i	0.915694	−	0.401877i	$-0.131642\pi$
$11$	1.39398	+	1.54818i	0.420302	+	0.466792i	−0.495392	+	0.868670i	$0.664975\pi$
$12$	−1.01005	+	0.0529345i	−0.291576	+	0.0152809i
$13$	−1.94768	−	0.992394i	−0.540190	−	0.275241i	0.162534	−	0.986703i	$-0.448033\pi$
$13$	−1.94768	−	0.992394i	−0.540190	−	0.275241i	−0.702724	+	0.711462i	$0.748033\pi$
$14$	3.96908	−	1.36339i	1.06078	−	0.364382i
$15$		0			0
$16$	3.18894	−	3.54168i	0.797235	−	0.885420i
$17$	3.18817	−	3.93706i	0.773245	−	0.954878i	−0.226572	−	0.973994i	$-0.572752\pi$
$17$	3.18817	−	3.93706i	0.773245	−	0.954878i	0.999817	+	0.0191163i	$0.00608526\pi$
$18$	−1.28906	+	0.345403i	−0.303835	+	0.0814123i
$19$	−6.86927	−	3.05840i	−1.57592	−	0.701644i	−0.582148	−	0.813083i	$-0.697788\pi$
$19$	−6.86927	−	3.05840i	−1.57592	−	0.701644i	−0.993771	+	0.111438i	$0.964454\pi$
$20$		0			0
$21$	4.44680	−	2.66745i	0.970372	−	0.582086i
$22$	3.26382	−	0.516939i	0.695850	−	0.110212i
$23$	1.68435	+	1.09383i	0.351210	+	0.228079i	0.708171	−	0.706041i	$-0.249520\pi$
$23$	1.68435	+	1.09383i	0.351210	+	0.228079i	−0.356961	+	0.934119i	$0.616187\pi$
$24$	2.30669	−	3.99530i	0.470851	−	0.815537i
$25$		0			0
$26$	−3.00281	+	1.73368i	−0.588900	+	0.340002i
$27$	3.76970	−	1.92076i	0.725479	−	0.369650i
$28$	0.331286	−	1.32456i	0.0626072	−	0.250318i
$29$	−4.12547	+	5.67823i	−0.766081	+	1.05442i	0.230603	+	0.973048i	$0.425930\pi$
$29$	−4.12547	+	5.67823i	−0.766081	+	1.05442i	−0.996684	+	0.0813721i	$0.974070\pi$
$30$		0			0
$31$	6.31745	−	0.663990i	1.13465	−	0.119256i	0.481471	−	0.876462i	$-0.340103\pi$
$31$	6.31745	−	0.663990i	1.13465	−	0.119256i	0.653176	+	0.757206i	$0.273436\pi$
$32$	−0.738117	−	2.75469i	−0.130482	−	0.486965i
$33$	3.81188	−	1.46324i	0.663564	−	0.254718i
$34$	−2.48320	−	7.64252i	−0.425866	−	1.31068i
$35$		0			0
$36$	−0.134168	+	0.412927i	−0.0223614	+	0.0688212i
$37$	−0.138578	−	2.64422i	−0.0227820	−	0.434707i	−0.986080	−	0.166272i	$-0.946827\pi$
$37$	−0.138578	−	2.64422i	−0.0227820	−	0.434707i	0.963298	−	0.268435i	$-0.0865063\pi$
$38$	−10.0030	+	6.49605i	−1.62271	+	1.05380i
$39$	−3.18385	+	2.86675i	−0.509823	+	0.459047i
$40$		0			0
$41$	−8.47974	+	2.75523i	−1.32431	+	0.430295i	−0.883974	−	0.467536i	$-0.845142\pi$
$41$	−8.47974	+	2.75523i	−1.32431	+	0.430295i	−0.440339	+	0.897832i	$0.645142\pi$
$42$	0.293115	−	8.22005i	0.0452287	−	1.26838i
$43$	−0.986332	−	0.986332i	−0.150414	−	0.150414i	0.627889	−	0.778303i	$-0.283919\pi$
$43$	−0.986332	−	0.986332i	−0.150414	−	0.150414i	−0.778303	+	0.627889i	$0.783919\pi$
$44$	0.437278	−	0.982142i	0.0659221	−	0.148063i
$45$		0			0
$46$	2.91025	−	1.29573i	0.429093	−	0.191044i
$47$	−2.04177	+	1.65339i	−0.297822	+	0.241172i	−0.766571	−	0.642160i	$-0.778038\pi$
$47$	−2.04177	+	1.65339i	−0.297822	+	0.241172i	0.468748	+	0.883332i	$0.344705\pi$
$48$	−4.24056	−	8.32258i	−0.612073	−	1.20126i
$49$	1.68344	+	6.79456i	0.240492	+	0.970651i
$50$		0			0
$51$	−4.96456	−	8.59887i	−0.695178	−	1.20408i
$52$	−0.0590385	+	1.12652i	−0.00818716	+	0.156220i
$53$	−8.62323	−	3.31015i	−1.18449	−	0.454684i	−0.315220	−	0.949019i	$-0.602078\pi$
$53$	−8.62323	−	3.31015i	−1.18449	−	0.454684i	−0.869271	+	0.494335i	$0.835412\pi$
$54$	0.701489	−	6.67422i	0.0954606	−	0.908247i
$55$		0			0
$56$	4.24391	+	4.55777i	0.567117	+	0.609057i
$57$	−10.4209	+	10.4209i	−1.38029	+	1.38029i
$58$	3.98974	+	10.3936i	0.523878	+	1.36475i
$59$	−10.2924	−	2.18773i	−1.33996	−	0.284818i	−0.518498	−	0.855079i	$-0.673509\pi$
$59$	−10.2924	−	2.18773i	−1.33996	−	0.284818i	−0.821464	+	0.570261i	$0.806842\pi$
$60$		0			0
$61$	1.78346	+	8.39053i	0.228349	+	1.07430i	0.931637	+	0.363391i	$0.118381\pi$
$61$	1.78346	+	8.39053i	0.228349	+	1.07430i	−0.703288	+	0.710905i	$0.748285\pi$
$62$	4.57440	−	8.97777i	0.580949	−	1.14018i
$63$	−0.384920	−	2.19243i	−0.0484953	−	0.276221i
$64$	4.76284	+	1.54754i	0.595355	+	0.193443i
$65$		0			0
$66$	1.34656	−	6.33508i	0.165751	−	0.779795i
$67$	2.55191	+	2.06649i	0.311765	+	0.252462i	0.772413	−	0.635121i	$-0.219050\pi$
$67$	2.55191	+	2.06649i	0.311765	+	0.252462i	−0.460648	+	0.887583i	$0.652383\pi$
$68$	−2.52529	−	0.676649i	−0.306236	−	0.0820558i
$69$	3.18448	−	2.31366i	0.383366	−	0.278532i
$70$		0			0
$71$	5.41526	+	3.93442i	0.642673	+	0.466930i	0.860768	−	0.508998i	$-0.169984\pi$
$71$	5.41526	+	3.93442i	0.642673	+	0.466930i	−0.218094	+	0.975928i	$0.569984\pi$
$72$	−1.24629	−	1.53904i	−0.146877	−	0.181378i
$73$	−8.26979	−	0.433401i	−0.967906	−	0.0507258i	−0.438173	−	0.898891i	$-0.644374\pi$
$73$	−8.26979	−	0.433401i	−0.967906	−	0.0507258i	−0.529733	+	0.848165i	$0.677708\pi$
$74$	−3.63734	−	2.10002i	−0.422832	−	0.244122i
$75$		0			0
$76$			3.88041i			0.445114i
$77$	0.380434	+	5.49868i	0.0433545	+	0.626633i
$78$	1.06309	+	6.71211i	0.120372	+	0.759996i
$79$	−2.65691	−	0.279252i	−0.298926	−	0.0314184i	−0.0461216	−	0.998936i	$-0.514686\pi$
$79$	−2.65691	−	0.279252i	−0.298926	−	0.0314184i	−0.252804	+	0.967517i	$0.581353\pi$
$80$		0			0
$81$	−1.13060	−	10.7569i	−0.125622	−	1.19521i
$82$	−3.66043	+	13.6609i	−0.404227	+	1.50860i
$83$	0.456772	−	2.88395i	0.0501373	−	0.316554i	−0.949855	−	0.312690i	$-0.898770\pi$
$83$	0.456772	−	2.88395i	0.0501373	−	0.316554i	0.999993	−	0.00386431i	$-0.00123005\pi$
$84$	−2.19093	−	1.53651i	−0.239050	−	0.167647i
$85$		0			0
$86$	−2.16423	+	0.460021i	−0.233375	+	0.0496053i
$87$	7.49212	+	11.5369i	0.803240	+	1.23688i
$88$	2.67075	+	4.11259i	0.284703	+	0.438404i
$89$	12.3861	−	2.63274i	1.31292	−	0.279070i	0.502327	−	0.864678i	$-0.332477\pi$
$89$	12.3861	−	2.63274i	1.31292	−	0.279070i	0.810595	+	0.585608i	$0.199144\pi$
$90$		0			0
$91$	−2.44033	−	5.24338i	−0.255816	−	0.549656i
$92$	0.162132	−	1.02366i	0.0169035	−	0.106724i
$93$	3.22229	−	12.0258i	0.334136	−	1.24701i
$94$	0.435611	+	4.14456i	0.0449298	+	0.427479i
$95$		0			0
$96$	−5.55884	−	0.584258i	−0.567347	−	0.0596306i
$97$	0.527619	+	3.33125i	0.0535716	+	0.338237i	0.999888	+	0.0149946i	$0.00477310\pi$
$97$	0.527619	+	3.33125i	0.0535716	+	0.338237i	−0.946316	+	0.323243i	$0.895227\pi$
$98$	10.4932	+	3.63040i	1.05997	+	0.366726i
$99$		−	1.75274i		−	0.176157i
$100$		0			0
$101$	−2.45915	−	1.41979i	−0.244695	−	0.141275i	0.372638	−	0.927977i	$-0.378453\pi$
$101$	−2.45915	−	1.41979i	−0.244695	−	0.141275i	−0.617333	+	0.786702i	$0.711787\pi$
$102$	−15.7281	−	0.824274i	−1.55731	−	0.0816152i
$103$	4.59308	+	5.67198i	0.452570	+	0.558877i	0.951454	−	0.307792i	$-0.0995900\pi$
$103$	4.59308	+	5.67198i	0.452570	+	0.558877i	−0.498884	+	0.866669i	$0.666257\pi$
$104$	−4.16268	−	3.02436i	−0.408184	−	0.296563i
$105$		0			0
$106$	−11.8532	+	8.61186i	−1.15129	+	0.836458i
$107$	−11.2003	−	3.00110i	−1.08277	−	0.290127i	−0.327040	−	0.945011i	$-0.606051\pi$
$107$	−11.2003	−	3.00110i	−1.08277	−	0.290127i	−0.755730	+	0.654883i	$0.772718\pi$
$108$	−1.69678	−	1.37403i	−0.163273	−	0.132216i
$109$	−2.03244	+	9.56186i	−0.194672	+	0.915860i	0.766998	+	0.641650i	$0.221750\pi$
$109$	−2.03244	+	9.56186i	−0.194672	+	0.915860i	−0.961670	+	0.274210i	$0.911584\pi$
$110$		0			0
$111$	−4.93560	−	1.60367i	−0.468467	−	0.152214i
$112$	12.4192	−	2.18040i	1.17350	−	0.206028i
$113$	−4.16132	+	8.16704i	−0.391464	+	0.768291i	−0.999675	−	0.0254843i	$-0.991887\pi$
$113$	−4.16132	+	8.16704i	−0.391464	+	0.768291i	0.608212	+	0.793775i	$0.291887\pi$
$114$	4.86028	+	22.8658i	0.455207	+	2.14158i
$115$		0			0
$116$	3.54288	+	0.753063i	0.328949	+	0.0699202i
$117$	0.659077	+	1.71696i	0.0609317	+	0.158733i
$118$	−11.8021	+	11.8021i	−1.08647	+	1.08647i
$119$	13.0622	−	3.00551i	1.19741	−	0.275515i
$120$		0			0
$121$	0.696156	−	6.62348i	0.0632869	−	0.602135i
$122$	12.7027	+	4.87612i	1.15005	+	0.441463i
$123$	−0.914571	+	17.4511i	−0.0824641	+	1.57351i
$124$	−1.63906	−	2.83893i	−0.147192	−	0.254944i
$125$		0			0
$126$	−3.24914	−	1.38201i	−0.289457	−	0.123119i
$127$	−1.11576	−	2.18980i	−0.0990074	−	0.194313i	0.836190	−	0.548440i	$-0.184778\pi$
$127$	−1.11576	−	2.18980i	−0.0990074	−	0.194313i	−0.935197	+	0.354127i	$0.884778\pi$
$128$	10.6060	−	8.58857i	0.937447	−	0.759130i
$129$	−2.49752	+	1.11197i	−0.219895	+	0.0979034i
$130$		0			0
$131$	2.26610	−	5.08975i	0.197990	−	0.444693i	−0.787079	−	0.616852i	$-0.788408\pi$
$131$	2.26610	−	5.08975i	0.197990	−	0.444693i	0.985069	+	0.172159i	$0.0550742\pi$
$132$	−1.48995	−	1.48995i	−0.129683	−	0.129683i
$133$	−9.32688	−	17.5725i	−0.808743	−	1.52373i
$134$	4.95369	−	1.60955i	0.427934	−	0.139044i
$135$		0			0
$136$	8.86178	−	7.97918i	0.759891	−	0.684209i
$137$	7.61653	−	4.94623i	0.650724	−	0.422585i	−0.176621	−	0.984279i	$-0.556517\pi$
$137$	7.61653	−	4.94623i	0.650724	−	0.422585i	0.827345	+	0.561694i	$0.189850\pi$
$138$	−0.326769	−	6.23513i	−0.0278165	−	0.530770i
$139$	−5.50579	+	16.9451i	−0.466995	+	1.43726i	0.389461	+	0.921043i	$0.372661\pi$
$139$	−5.50579	+	16.9451i	−0.466995	+	1.43726i	−0.856456	+	0.516220i	$0.827339\pi$
$140$		0			0
$141$	1.59121	+	4.89724i	0.134004	+	0.412422i
$142$	9.91229	−	3.80497i	0.831821	−	0.319306i
$143$	−1.17864	−	4.39874i	−0.0985627	−	0.367841i
$144$	−3.98768	+	0.419122i	−0.332306	+	0.0349268i
$145$		0			0
$146$	−7.72092	+	10.6269i	−0.638988	+	0.879491i
$147$	13.6148	+	1.69206i	1.12293	+	0.139559i
$148$	−1.21751	+	0.620350i	−0.100078	+	0.0509925i
$149$	12.6781	−	7.31970i	1.03863	−	0.599653i	0.119185	−	0.992872i	$-0.461972\pi$
$149$	12.6781	−	7.31970i	1.03863	−	0.599653i	0.919445	+	0.393219i	$0.128638\pi$
$150$		0			0
$151$	−8.05257	+	13.9475i	−0.655309	+	1.13503i	0.326508	+	0.945195i	$0.394128\pi$
$151$	−8.05257	+	13.9475i	−0.655309	+	1.13503i	−0.981816	+	0.189833i	$0.939205\pi$
$152$	−14.8440	−	9.63977i	−1.20400	−	0.781889i
$153$	−4.20978	+	0.666764i	−0.340341	+	0.0539047i
$154$	7.64359	+	4.24428i	0.615938	+	0.342014i
$155$		0			0
$156$	2.01979	+	0.899269i	0.161713	+	0.0719991i
$157$	4.14906	−	1.11174i	0.331131	−	0.0887263i	−0.0894230	−	0.995994i	$-0.528502\pi$
$157$	4.14906	−	1.11174i	0.331131	−	0.0887263i	0.420554	+	0.907267i	$0.361836\pi$
$158$	−2.66682	+	3.29325i	−0.212161	+	0.261997i
$159$	−12.1135	+	13.4534i	−0.960664	+	1.06693i
$160$		0			0
$161$	1.72624	+	5.02538i	0.136046	+	0.396055i
$162$	−15.2867	−	7.78897i	−1.20104	−	0.611959i
$163$	15.2329	−	0.798321i	1.19313	−	0.0625294i	0.554595	−	0.832121i	$-0.312873\pi$
$163$	15.2329	−	0.798321i	1.19313	−	0.0625294i	0.638537	+	0.769591i	$0.279540\pi$
$164$	3.07882	+	3.41938i	0.240416	+	0.267009i
$165$		0			0
$166$	−3.44192	−	3.09912i	−0.267145	−	0.240538i
$167$	−16.7023	−	2.64539i	−1.29246	−	0.204706i	−0.527929	−	0.849289i	$-0.677031\pi$
$167$	−16.7023	−	2.64539i	−1.29246	−	0.204706i	−0.764535	+	0.644583i	$0.777031\pi$
$168$	11.3204	−	4.56405i	0.873390	−	0.352124i
$169$	−4.83258	−	6.65148i	−0.371737	−	0.511652i
$170$		0			0
$171$	2.57314	+	5.77937i	0.196773	+	0.441959i
$172$	−0.257967	+	0.672028i	−0.0196698	+	0.0512417i
$173$	10.2096	−	15.7214i	0.776219	−	1.19527i	−0.200277	−	0.979739i	$-0.564184\pi$
$173$	10.2096	−	15.7214i	0.776219	−	1.19527i	0.976496	−	0.215533i	$-0.0691490\pi$
$174$	21.8201			1.65418
$175$		0			0
$176$	9.92847			0.748387
$177$	−11.2322	+	17.2960i	−0.844262	+	1.30005i
$178$	7.19811	−	18.7517i	0.539521	−	1.40550i
$179$	−3.98974	−	8.96111i	−0.298207	−	0.669785i	0.700845	−	0.713314i	$-0.252807\pi$
$179$	−3.98974	−	8.96111i	−0.298207	−	0.669785i	−0.999052	+	0.0435289i	$0.986140\pi$
$180$		0			0
$181$	−0.493376	−	0.679074i	−0.0366723	−	0.0504751i	0.790287	−	0.612737i	$-0.209931\pi$
$181$	−0.493376	−	0.679074i	−0.0366723	−	0.0504751i	−0.826959	+	0.562262i	$0.809931\pi$
$182$	−9.08353	−	1.28343i	−0.673316	−	0.0951344i
$183$	16.6053	+	2.63002i	1.22750	+	0.194416i
$184$	3.51310	+	3.16321i	0.258989	+	0.233195i
$185$		0			0
$186$	−13.2142	−	14.6758i	−0.968909	−	1.07608i
$187$	10.5395	−	0.552353i	0.770726	−	0.0403920i
$188$	1.20804	+	0.615528i	0.0881055	+	0.0448920i
$189$	10.9865	+	2.14396i	0.799150	+	0.155950i
$190$		0			0
$191$	−1.82056	+	2.02194i	−0.131731	+	0.146302i	−0.805401	−	0.592730i	$-0.798050\pi$
$191$	−1.82056	+	2.02194i	−0.131731	+	0.146302i	0.673670	+	0.739032i	$0.264717\pi$
$192$	6.17693	−	7.62788i	0.445782	−	0.550494i
$193$	6.77095	−	1.81427i	0.487384	−	0.130594i	−0.00675479	−	0.999977i	$-0.502150\pi$
$193$	6.77095	−	1.81427i	0.487384	−	0.130594i	0.494139	+	0.869383i	$0.335483\pi$
$194$	4.88740	+	2.17601i	0.350895	+	0.156229i
$195$		0			0
$196$	2.84988	−	2.21982i	0.203563	−	0.158558i
$197$	−14.6392	+	2.31863i	−1.04300	+	0.165195i	−0.654352	−	0.756190i	$-0.727058\pi$
$197$	−14.6392	+	2.31863i	−1.04300	+	0.165195i	−0.388650	+	0.921385i	$0.627058\pi$
$198$	−2.33167	−	1.51421i	−0.165705	−	0.107610i
$199$	10.5072	−	18.1990i	0.744835	−	1.29009i	−0.205437	−	0.978670i	$-0.565862\pi$
$199$	10.5072	−	18.1990i	0.744835	−	1.29009i	0.950272	−	0.311422i	$-0.100805\pi$
$200$		0			0
$201$	5.57358	−	3.21791i	0.393130	−	0.226974i
$202$	−4.01325	+	2.04485i	−0.282371	+	0.143875i
$203$	−17.8541	+	5.10534i	−1.25311	+	0.358324i
$204$	−3.01181	+	4.14540i	−0.210869	+	0.290236i
$205$		0			0
$206$	11.5135	−	1.21012i	0.802183	−	0.0843128i
$207$	−0.437326	−	1.63212i	−0.0303963	−	0.113440i
$208$	−9.72579	+	3.73338i	−0.674362	+	0.258863i
$209$	−4.84072	−	14.8982i	−0.334839	−	1.03053i
$210$		0			0
$211$	−7.71478	+	23.7437i	−0.531108	+	1.63458i	0.220805	+	0.975318i	$0.429132\pi$
$211$	−7.71478	+	23.7437i	−0.531108	+	1.63458i	−0.751912	+	0.659263i	$0.770868\pi$
$212$	0.249468	+	4.76014i	0.0171336	+	0.326928i
$213$	11.0026	−	7.14516i	0.753884	−	0.489578i
$214$	−13.6684	+	12.3071i	−0.934353	+	0.841295i
$215$		0			0
$216$	9.47131	−	3.07741i	0.644441	−	0.209392i
$217$	14.2461	+	8.91657i	0.967090	+	0.605296i
$218$	10.9644	+	10.9644i	0.742600	+	0.742600i
$219$	−6.60153	+	14.8273i	−0.446090	+	1.00193i
$220$		0			0
$221$	−10.1167	+	4.50423i	−0.680521	+	0.302987i
$222$	−6.39730	+	5.18043i	−0.429359	+	0.347688i
$223$	5.91390	+	11.6067i	0.396024	+	0.777241i	0.999802	−	0.0199118i	$-0.00633854\pi$
$223$	5.91390	+	11.6067i	0.396024	+	0.777241i	−0.603778	+	0.797153i	$0.706339\pi$
$224$	2.95331	−	6.94333i	0.197326	−	0.463921i
$225$		0			0
$226$	7.26966	+	12.5914i	0.483571	+	0.837569i
$227$	−0.162101	+	3.09307i	−0.0107590	+	0.205294i	0.987961	+	0.154706i	$0.0494430\pi$
$227$	−0.162101	+	3.09307i	−0.0107590	+	0.205294i	−0.998720	+	0.0505884i	$0.983890\pi$
$228$	7.10021	+	2.72551i	0.470223	+	0.180502i
$229$	0.0558012	−	0.530913i	0.00368745	−	0.0350837i	−0.992523	−	0.122054i	$-0.961052\pi$
$229$	0.0558012	−	0.530913i	0.00368745	−	0.0350837i	0.996211	+	0.0869703i	$0.0277185\pi$
$230$		0			0
$231$	10.3285	+	3.16605i	0.679562	+	0.208311i
$232$	−11.6820	+	11.6820i	−0.766961	+	0.766961i
$233$	8.89443	+	23.1708i	0.582694	+	1.51797i	0.834960	+	0.550311i	$0.185491\pi$
$233$	8.89443	+	23.1708i	0.582694	+	1.51797i	−0.252266	+	0.967658i	$0.581176\pi$
$234$	2.85346	+	0.606522i	0.186537	+	0.0396496i
$235$		0			0
$236$	1.12899	+	5.31148i	0.0734910	+	0.345748i
$237$	−2.37712	+	4.66535i	−0.154410	+	0.303047i
$238$	7.28633	−	19.9732i	0.472303	−	1.29467i
$239$	−25.9462	−	8.43043i	−1.67832	−	0.545320i	−0.693736	−	0.720229i	$-0.744037\pi$
$239$	−25.9462	−	8.43043i	−1.67832	−	0.545320i	−0.984585	+	0.174910i	$0.944037\pi$
$240$		0			0
$241$	−3.97979	+	18.7235i	−0.256361	+	1.20608i	0.641958	+	0.766740i	$0.278122\pi$
$241$	−3.97979	+	18.7235i	−0.256361	+	1.20608i	−0.898319	+	0.439344i	$0.855211\pi$
$242$	−8.20984	−	6.64820i	−0.527749	−	0.427362i
$243$	−8.21660	−	2.20163i	−0.527095	−	0.141235i
$244$	3.58129	−	2.60196i	0.229269	−	0.166574i
$245$		0			0
$246$	22.4251	+	16.2928i	1.42977	+	1.03879i
$247$	10.3440	+	12.7738i	0.658175	+	0.812779i
$248$	14.9317	+	0.782537i	0.948164	+	0.0496912i
$249$	−4.95609	−	2.86140i	−0.314079	−	0.181334i
$250$		0			0
$251$			7.49714i			0.473215i	0.971605	+	0.236608i	$0.0760356\pi$
$251$			7.49714i			0.473215i	−0.971605	+	0.236608i	$0.923964\pi$
$252$	−0.952810	+	0.641657i	−0.0600214	+	0.0404206i
$253$	0.654514	+	4.13244i	0.0411489	+	0.259804i
$254$	−3.87701	−	0.407490i	−0.243265	−	0.0255682i
$255$		0			0
$256$	−1.21584	−	11.5680i	−0.0759901	−	0.722998i
$257$	3.54307	−	13.2229i	0.221011	−	0.824824i	−0.762953	−	0.646454i	$-0.776251\pi$
$257$	3.54307	−	13.2229i	0.221011	−	0.824824i	0.983964	−	0.178369i	$-0.0570822\pi$
$258$	−0.678378	+	4.28311i	−0.0422340	+	0.266655i
$259$	4.02244	−	5.73564i	0.249942	−	0.356395i
$260$		0			0
$261$	5.77603	−	1.22773i	0.357527	−	0.0759947i
$262$	−4.81321	−	7.41170i	−0.297361	−	0.457896i
$263$	10.6570	+	16.4103i	0.657137	+	1.01190i	0.997435	+	0.0715841i	$0.0228054\pi$
$263$	10.6570	+	16.4103i	0.657137	+	1.01190i	−0.340298	+	0.940318i	$0.610528\pi$
$264$	9.40091	−	1.99822i	0.578586	−	0.122982i
$265$		0			0
$266$	−31.4345	−	2.77350i	−1.92737	−	0.170054i
$267$	3.88242	−	24.5127i	0.237600	−	1.50015i
$268$	0.438587	−	1.63683i	0.0267910	−	0.0999853i
$269$	0.965195	+	9.18322i	0.0588490	+	0.559911i	0.983730	+	0.179654i	$0.0574978\pi$
$269$	0.965195	+	9.18322i	0.0588490	+	0.559911i	−0.924881	+	0.380257i	$0.875836\pi$
$270$		0			0
$271$	1.10014	+	0.115630i	0.0668289	+	0.00702400i	0.137884	−	0.990448i	$-0.455970\pi$
$271$	1.10014	+	0.115630i	0.0668289	+	0.00702400i	−0.0710550	+	0.997472i	$0.522637\pi$
$272$	−3.77692	−	23.8465i	−0.229010	−	1.44591i
$273$	−11.3081	+	0.782368i	−0.684399	+	0.0473511i
$274$		−	14.4054i		−	0.870263i
$275$		0			0
$276$	−1.75918	−	1.01566i	−0.105890	−	0.0611356i
$277$	19.4143	+	1.01746i	1.16649	+	0.0611331i	0.625727	−	0.780042i	$-0.284802\pi$
$277$	19.4143	+	1.01746i	1.16649	+	0.0611331i	0.540763	+	0.841175i	$0.318136\pi$
$278$	17.7856	+	21.9634i	1.06671	+	1.31728i
$279$	−4.32369	−	3.14135i	−0.258853	−	0.188067i
$280$		0			0
$281$	−1.38801	+	1.00845i	−0.0828017	+	0.0601589i	−0.628416	−	0.777878i	$-0.716296\pi$
$281$	−1.38801	+	1.00845i	−0.0828017	+	0.0601589i	0.545614	+	0.838036i	$0.316296\pi$
$282$	7.88949	+	2.11398i	0.469812	+	0.125886i
$283$	−20.5156	−	16.6132i	−1.21953	−	0.987553i	−0.999928	−	0.0119625i	$-0.996192\pi$
$283$	−20.5156	−	16.6132i	−1.21953	−	0.987553i	−0.219598	−	0.975590i	$-0.570475\pi$
$284$	0.718188	−	3.37881i	0.0426166	−	0.200495i
$285$		0			0
$286$	−6.86990	−	2.23217i	−0.406226	−	0.131991i
$287$	−22.1613	−	8.08454i	−1.30814	−	0.477215i
$288$	−1.08929	+	2.13786i	−0.0641873	+	0.125975i
$289$	−1.80153	−	8.47555i	−0.105973	−	0.498562i
$290$		0			0
$291$	6.46596	+	1.37438i	0.379041	+	0.0805678i
$292$	1.53150	+	3.98969i	0.0896242	+	0.233479i
$293$	4.33790	−	4.33790i	0.253423	−	0.253423i	−0.568950	−	0.822372i	$-0.692650\pi$
$293$	4.33790	−	4.33790i	0.253423	−	0.253423i	0.822372	+	0.568950i	$0.192650\pi$
$294$	14.0129	−	16.6500i	0.817250	−	0.971051i
$295$		0			0
$296$	0.651485	−	6.19847i	0.0378668	−	0.360279i
$297$	8.22857	+	3.15865i	0.477470	+	0.183284i
$298$	1.21530	−	23.1893i	0.0704005	−	1.34332i
$299$	−2.19506	−	3.80196i	−0.126944	−	0.219873i
$300$		0			0
$301$	−0.447061	−	3.66334i	−0.0257682	−	0.211151i
$302$	11.5977	+	22.7617i	0.667372	+	1.30979i
$303$	−4.32512	+	3.50242i	−0.248472	+	0.201209i
$304$	−32.7376	+	14.5757i	−1.87763	+	0.835974i
$305$		0			0
$306$	−2.74988	+	6.17632i	−0.157200	+	0.353077i
$307$	−12.5574	−	12.5574i	−0.716687	−	0.716687i	0.251239	−	0.967925i	$-0.419162\pi$
$307$	−12.5574	−	12.5574i	−0.716687	−	0.716687i	−0.967925	+	0.251239i	$0.919162\pi$
$308$	2.51245	−	1.33352i	0.143160	−	0.0759844i
$309$	13.6044	−	4.42034i	0.773928	−	0.251464i
$310$		0			0
$311$	4.72615	−	4.25544i	0.267995	−	0.241304i	−0.524166	−	0.851616i	$-0.675623\pi$
$311$	4.72615	−	4.25544i	0.267995	−	0.241304i	0.792161	+	0.610312i	$0.208956\pi$
$312$	−8.45761	+	5.49244i	−0.478818	+	0.310948i
$313$	−0.399757	−	7.62782i	−0.0225956	−	0.431150i	−0.986382	−	0.164473i	$-0.947408\pi$
$313$	−0.399757	−	7.62782i	−0.0225956	−	0.431150i	0.963786	−	0.266677i	$-0.0859257\pi$
$314$	2.10547	−	6.47997i	0.118818	−	0.365686i
$315$		0			0
$316$	0.426032	+	1.31119i	0.0239662	+	0.0737603i
$317$	−13.1753	+	5.05753i	−0.740000	+	0.284059i	−0.699021	−	0.715101i	$-0.746381\pi$
$317$	−13.1753	+	5.05753i	−0.740000	+	0.284059i	−0.0409785	+	0.999160i	$0.513048\pi$
$318$	7.43217	+	27.7372i	0.416775	+	1.55543i
$319$	−14.5417	+	1.52840i	−0.814181	+	0.0855738i
$320$		0			0
$321$	−13.3581	+	18.3858i	−0.745575	+	1.02620i
$322$	8.17661	+	2.04506i	0.455665	+	0.113967i
$323$	−33.9415	+	17.2941i	−1.88856	+	0.962268i
$324$	−4.83394	+	2.79088i	−0.268552	+	0.155049i
$325$		0			0
$326$	12.0978	−	20.9541i	0.670037	−	1.16054i
$327$	16.0683	+	10.4349i	0.888580	+	0.577051i
$328$	−20.7288	+	3.28311i	−1.14455	+	0.181280i
$329$	−6.95011	+	0.116192i	−0.383172	+	0.00640585i
$330$		0			0
$331$	−9.40598	−	4.18781i	−0.516999	−	0.230183i	0.131614	−	0.991301i	$-0.457984\pi$
$331$	−9.40598	−	4.18781i	−0.516999	−	0.230183i	−0.648613	+	0.761118i	$0.724651\pi$
$332$	−1.45549	+	0.389997i	−0.0798802	+	0.0214038i
$333$	−1.40196	+	1.73127i	−0.0768267	+	0.0948730i
$334$	−17.9485	+	19.9338i	−0.982097	+	1.09073i
$335$		0			0
$336$	4.73334	−	24.2555i	0.258225	−	1.32325i
$337$	−22.9028	−	11.6695i	−1.24759	−	0.635681i	−0.299629	−	0.954056i	$-0.596863\pi$
$337$	−22.9028	−	11.6695i	−1.24759	−	0.635681i	−0.947965	+	0.318375i	$0.896863\pi$
$338$	−13.0234	+	0.682529i	−0.708381	+	0.0371247i
$339$	12.0209	+	13.3505i	0.652884	+	0.725101i
$340$		0			0
$341$	9.83439	+	8.85492i	0.532562	+	0.479521i
$342$	9.91130	+	1.56980i	0.535942	+	0.0848848i
$343$	−7.57025	+	16.9024i	−0.408755	+	0.912644i
$344$	−1.92990	−	2.65628i	−0.104053	−	0.143217i
$345$		0			0
$346$	−12.0941	−	27.1637i	−0.650181	−	1.46033i
$347$	−1.63539	+	4.26035i	−0.0877926	+	0.228707i	−0.970447	−	0.241316i	$-0.922421\pi$
$347$	−1.63539	+	4.26035i	−0.0877926	+	0.228707i	0.882654	+	0.470023i	$0.155754\pi$
$348$	3.86636	−	5.95367i	0.207259	−	0.319150i
$349$	35.4204			1.89601			0.948005	−	0.318256i	$-0.103097\pi$
$349$	35.4204			1.89601			0.948005	+	0.318256i	$0.103097\pi$
$350$		0			0
$351$	−9.24834			−0.493640
$352$	3.23582	−	4.98272i	0.172470	−	0.265580i
$353$	3.83210	−	9.98297i	0.203962	−	0.531340i	−0.793000	−	0.609221i	$-0.791482\pi$
$353$	3.83210	−	9.98297i	0.203962	−	0.531340i	0.996963	+	0.0778814i	$0.0248155\pi$
$354$	13.3054	+	29.8845i	0.707175	+	1.58834i
$355$		0			0
$356$	−3.84101	−	5.28670i	−0.203573	−	0.280194i
$357$	3.67525	−	26.0116i	0.194515	−	1.37668i
$358$	−15.3678	−	2.43402i	−0.812214	−	0.128642i
$359$	−2.83659	−	2.55408i	−0.149710	−	0.134799i	0.590873	−	0.806765i	$-0.298784\pi$
$359$	−2.83659	−	2.55408i	−0.149710	−	0.134799i	−0.740582	+	0.671966i	$0.765450\pi$
$360$		0			0
$361$	25.1196	+	27.8982i	1.32209	+	1.46833i
$362$	−1.32961	+	0.0696818i	−0.0698827	+	0.00366240i
$363$	−11.6304	−	5.92598i	−0.610437	−	0.311033i
$364$	−1.95972	+	2.25105i	−0.102717	+	0.117987i
$365$		0			0
$366$	17.8442	−	19.8180i	0.932731	−	1.03590i
$367$	−5.24006	+	6.47094i	−0.273529	+	0.337780i	−0.895337	−	0.445390i	$-0.853065\pi$
$367$	−5.24006	+	6.47094i	−0.273529	+	0.337780i	0.621808	+	0.783170i	$0.286399\pi$
$368$	9.24526	−	2.47726i	0.481943	−	0.129136i
$369$	6.85293	+	3.05112i	0.356749	+	0.158835i
$370$		0			0
$371$	−12.5711	−	20.9568i	−0.652659	−	1.08802i
$372$	−6.34579	+	1.00507i	−0.329014	+	0.0521107i
$373$	14.6190	+	9.49367i	0.756941	+	0.491563i	0.864498	−	0.502635i	$-0.167636\pi$
$373$	14.6190	+	9.49367i	0.756941	+	0.491563i	−0.107557	+	0.994199i	$0.534303\pi$
$374$	8.37041	−	14.4980i	0.432824	−	0.749672i
$375$		0			0
$376$	−5.35564	+	3.09208i	−0.276196	+	0.159462i
$377$	13.6702	−	6.96529i	0.704049	−	0.358731i
$378$	12.3435	−	12.7632i	0.634880	−	0.656469i
$379$	−6.41691	+	8.83212i	−0.329614	+	0.453675i	−0.941372	−	0.337370i	$-0.890463\pi$
$379$	−6.41691	+	8.83212i	−0.329614	+	0.453675i	0.611758	+	0.791045i	$0.290463\pi$
$380$		0			0
$381$	−4.79047	+	0.503499i	−0.245423	+	0.0257950i
$382$	1.11699	+	4.16868i	0.0571504	+	0.213288i
$383$	−15.4910	+	5.94645i	−0.791555	+	0.303849i	−0.720349	−	0.693612i	$-0.756018\pi$
$383$	−15.4910	+	5.94645i	−0.791555	+	0.303849i	−0.0712062	+	0.997462i	$0.522685\pi$
$384$	−8.26557	−	25.4388i	−0.421800	−	1.29817i
$385$		0			0
$386$	3.43596	−	10.5748i	0.174886	−	0.538244i
$387$	0.0614198	+	1.17196i	0.00312214	+	0.0595740i
$388$	1.45974	−	0.947969i	0.0741072	−	0.0481258i
$389$	14.2859	−	12.8631i	0.724323	−	0.652183i	−0.222133	−	0.975016i	$-0.571302\pi$
$389$	14.2859	−	12.8631i	0.724323	−	0.652183i	0.946456	+	0.322833i	$0.104635\pi$
$390$		0			0
$391$	9.67645	−	3.14407i	0.489359	−	0.159002i
$392$	1.41186	+	16.4163i	0.0713099	+	0.829148i
$393$	−7.72133	−	7.72133i	−0.389490	−	0.389490i
$394$	−9.56251	+	21.4777i	−0.481752	+	1.08203i
$395$		0			0
$396$	−0.826312	+	0.367898i	−0.0415237	+	0.0184876i
$397$	−0.945508	+	0.765657i	−0.0474537	+	0.0384272i	−0.652754	−	0.757570i	$-0.726386\pi$
$397$	−0.945508	+	0.765657i	−0.0474537	+	0.0384272i	0.605300	+	0.795997i	$0.293053\pi$
$398$	−15.1329	−	29.7001i	−0.758546	−	1.48873i
$399$	−38.7044	+	4.72336i	−1.93765	+	0.236464i
$400$		0			0
$401$	2.37174	+	4.10797i	0.118439	+	0.205142i	0.919149	−	0.393910i	$-0.128878\pi$
$401$	2.37174	+	4.10797i	0.118439	+	0.205142i	−0.800710	+	0.599052i	$0.795544\pi$
$402$	0.534274	−	10.1945i	0.0266471	−	0.508458i
$403$	−12.9633	−	4.97615i	−0.645749	−	0.247880i
$404$	−0.153175	+	1.45736i	−0.00762072	+	0.0725063i
$405$		0			0
$406$	−8.63267	+	28.1619i	−0.428432	+	1.39765i
$407$	3.90054	−	3.90054i	0.193342	−	0.193342i
$408$	−8.37563	−	21.8193i	−0.414656	−	1.08021i
$409$	24.2503	+	5.15456i	1.19910	+	0.254877i	0.763827	−	0.645421i	$-0.223318\pi$
$409$	24.2503	+	5.15456i	1.19910	+	0.254877i	0.435274	+	0.900298i	$0.356651\pi$
$410$		0			0
$411$	−3.70072	−	17.4105i	−0.182543	−	0.858797i
$412$	1.70992	−	3.35591i	0.0842419	−	0.165334i
$413$	−17.8792	−	21.3396i	−0.879779	−	1.05005i
$414$	−2.54904	−	0.828232i	−0.125278	−	0.0407054i
$415$		0			0
$416$	−1.29612	+	6.09776i	−0.0635475	+	0.298968i
$417$	27.1382	+	21.9761i	1.32896	+	1.07617i
$418$	−24.0011	−	6.43108i	−1.17393	−	0.314554i
$419$	−19.6973	+	14.3109i	−0.962276	+	0.699135i	−0.953678	−	0.300828i	$-0.902737\pi$
$419$	−19.6973	+	14.3109i	−0.962276	+	0.699135i	−0.00859807	+	0.999963i	$0.502737\pi$
$420$		0			0
$421$	−6.00083	−	4.35986i	−0.292463	−	0.212486i	0.431872	−	0.901935i	$-0.357853\pi$
$421$	−6.00083	−	4.35986i	−0.292463	−	0.212486i	−0.724335	+	0.689448i	$0.757853\pi$
$422$	24.9215	+	30.7754i	1.21316	+	1.49812i
$423$	2.20738	+	0.115684i	0.107327	+	0.00562475i
$424$	−18.8290	−	10.8709i	−0.914415	−	0.527938i
$425$		0			0
$426$		−	20.8096i		−	1.00823i
$427$	−9.96394	+	20.3910i	−0.482189	+	0.986788i
$428$	0.936083	+	5.91019i	0.0452473	+	0.285680i
$429$	−8.87646	−	0.932953i	−0.428559	−	0.0450434i
$430$		0			0
$431$	−1.88691	−	17.9528i	−0.0908895	−	0.864756i	−0.941058	−	0.338245i	$-0.890167\pi$
$431$	−1.88691	−	17.9528i	−0.0908895	−	0.864756i	0.850169	−	0.526511i	$-0.176500\pi$
$432$	5.21865	−	19.4763i	0.251082	−	0.937052i
$433$	3.94891	−	24.9324i	0.189773	−	1.19818i	−0.690366	−	0.723460i	$-0.742551\pi$
$433$	3.94891	−	24.9324i	0.189773	−	1.19818i	0.880139	−	0.474717i	$-0.157449\pi$
$434$	24.1691	−	11.2486i	1.16016	−	0.539949i
$435$		0			0
$436$	4.93446	−	1.04885i	0.236318	−	0.0502309i
$437$	−8.22487	−	12.6652i	−0.393449	−	0.605858i
$438$	14.0217	+	21.5915i	0.669982	+	1.03168i
$439$	27.2854	−	5.79968i	1.30226	−	0.276804i	0.495977	−	0.868335i	$-0.334810\pi$
$439$	27.2854	−	5.79968i	1.30226	−	0.276804i	0.806282	+	0.591532i	$0.201477\pi$
$440$		0			0
$441$	2.77255	−	5.19591i	0.132026	−	0.247424i
$442$	−2.74789	+	17.3495i	−0.130704	+	0.825232i
$443$	7.92554	−	29.5785i	0.376554	−	1.40532i	−0.474507	−	0.880252i	$-0.657374\pi$
$443$	7.92554	−	29.5785i	0.376554	−	1.40532i	0.851061	−	0.525066i	$-0.175960\pi$
$444$	0.279941	+	2.66346i	0.0132854	+	0.126402i
$445$		0			0
$446$	20.5495	+	2.15984i	0.973048	+	0.102271i
$447$	−4.48846	−	28.3390i	−0.212297	−	1.34039i
$448$	7.40109	+	10.9900i	0.349669	+	0.519230i
$449$			30.4224i			1.43572i	0.696187	+	0.717861i	$0.254879\pi$
$449$			30.4224i			1.43572i	−0.696187	+	0.717861i	$0.745121\pi$
$450$		0			0
$451$	−16.0862	−	9.28737i	−0.757469	−	0.437325i
$452$	4.72374	+	0.247561i	0.222186	+	0.0116443i
$453$	19.8645	+	24.5306i	0.933315	+	1.15255i
$454$	3.97469	+	2.88778i	0.186541	+	0.135530i
$455$		0			0
$456$	−28.0645	+	20.3900i	−1.31424	+	0.954851i
$457$	38.9922	+	10.4479i	1.82398	+	0.488733i	0.997266	−	0.0738955i	$-0.0235431\pi$
$457$	38.9922	+	10.4479i	1.82398	+	0.488733i	0.826710	+	0.562628i	$0.190210\pi$
$458$	−0.658070	−	0.532894i	−0.0307496	−	0.0249005i
$459$	4.45630	−	20.9653i	0.208002	−	0.978575i
$460$		0			0
$461$	−16.9923	−	5.52114i	−0.791411	−	0.257145i	−0.114706	−	0.993399i	$-0.536593\pi$
$461$	−16.9923	−	5.52114i	−0.791411	−	0.257145i	−0.676705	+	0.736255i	$0.736593\pi$
$462$	13.1347	−	11.0048i	0.611080	−	0.511990i
$463$	15.5311	−	30.4814i	0.721790	−	1.41659i	−0.179668	−	0.983727i	$-0.557502\pi$
$463$	15.5311	−	30.4814i	0.721790	−	1.41659i	0.901458	−	0.432866i	$-0.142498\pi$
$464$	6.95456	+	32.7186i	0.322857	+	1.51892i
$465$		0			0
$466$	38.5083	+	8.18518i	1.78386	+	0.379171i
$467$	−2.39302	−	6.23404i	−0.110736	−	0.288477i	0.867003	−	0.498303i	$-0.166043\pi$
$467$	−2.39302	−	6.23404i	−0.110736	−	0.288477i	−0.977739	+	0.209826i	$0.932710\pi$
$468$	0.671104	−	0.671104i	0.0310218	−	0.0310218i
$469$	1.94810	+	8.46660i	0.0899548	+	0.390951i
$470$		0			0
$471$	0.879999	−	8.37263i	0.0405482	−	0.385790i
$472$	−23.1230	−	8.87607i	−1.06432	−	0.408554i
$473$	0.152085	−	2.90195i	0.00699285	−	0.133432i
$474$	4.15273	+	7.19274i	0.190741	+	0.330374i
$475$		0			0
$476$	−4.15867	−	5.52721i	−0.190612	−	0.253339i
$477$	3.52805	+	6.92419i	0.161538	+	0.317037i
$478$	−33.6303	+	27.2333i	−1.53821	+	1.24562i
$479$	4.62700	−	2.06007i	0.211413	−	0.0941271i	−0.298298	−	0.954473i	$-0.596419\pi$
$479$	4.62700	−	2.06007i	0.211413	−	0.0941271i	0.509711	+	0.860346i	$0.329752\pi$
$480$		0			0
$481$	−2.35420	+	5.28762i	−0.107342	+	0.241095i
$482$	21.4697	+	21.4697i	0.977920	+	0.977920i
$483$	10.4077	+	0.371123i	0.473566	+	0.0168867i
$484$	−3.26870	+	1.06207i	−0.148577	+	0.0482758i
$485$		0			0
$486$	−10.0272	+	9.02858i	−0.454845	+	0.409544i
$487$	−15.7690	+	10.2405i	−0.714563	+	0.464043i	−0.850027	−	0.526740i	$-0.823414\pi$
$487$	−15.7690	+	10.2405i	−0.714563	+	0.464043i	0.135464	+	0.990782i	$0.456748\pi$
$488$	1.05673	+	20.1635i	0.0478357	+	0.912760i
$489$	9.23849	−	28.4332i	0.417779	−	1.28579i
$490$		0			0
$491$	−8.10726	−	24.9516i	−0.365876	−	1.12605i	−0.949431	−	0.313976i	$-0.898339\pi$
$491$	−8.10726	−	24.9516i	−0.365876	−	1.12605i	0.583555	−	0.812073i	$-0.301661\pi$
$492$	8.41912	−	3.23180i	0.379563	−	0.145701i
$493$	9.20282	+	34.3454i	0.414474	+	1.54684i
$494$	25.9294	−	2.72529i	1.16662	−	0.122617i
$495$		0			0
$496$	17.7943	−	24.4918i	0.798989	−	1.09971i
$497$	4.86891	+	17.0272i	0.218400	+	0.763776i
$498$	−8.08815	+	4.12112i	−0.362439	+	0.184672i
$499$	2.61768	−	1.51132i	0.117183	−	0.0676558i	−0.440263	−	0.897869i	$-0.645115\pi$
$499$	2.61768	−	1.51132i	0.117183	−	0.0676558i	0.557446	+	0.830213i	$0.311781\pi$
$500$		0			0
$501$	−16.5717	+	28.7031i	−0.740370	+	1.28236i
$502$	9.97349	+	6.47686i	0.445139	+	0.289076i
$503$	−13.8594	+	2.19511i	−0.617958	+	0.0978750i	−0.457562	−	0.889178i	$-0.651277\pi$
$503$	−13.8594	+	2.19511i	−0.617958	+	0.0978750i	−0.160396	+	0.987053i	$0.551277\pi$
$504$	−0.0875827	−	5.23885i	−0.00390124	−	0.233357i
$505$		0			0
$506$	6.06285	+	2.69935i	0.269527	+	0.120001i
$507$	−15.5649	+	4.17060i	−0.691260	+	0.185223i
$508$	−0.798164	+	0.985650i	−0.0354128	+	0.0437311i
$509$	−15.1783	+	16.8573i	−0.672768	+	0.747185i	−0.978796	−	0.204838i	$-0.934333\pi$
$509$	−15.1783	+	16.8573i	−0.672768	+	0.747185i	0.306028	+	0.952023i	$0.401000\pi$
$510$		0			0
$511$	−16.5250	−	14.3863i	−0.731022	−	0.636414i
$512$	7.88049	+	4.01531i	0.348272	+	0.177453i
$513$	−31.7696	+	1.66497i	−1.40266	+	0.0735103i
$514$	−14.5296	−	16.1368i	−0.640875	−	0.711764i
$515$		0			0
$516$	1.04846	+	0.944034i	0.0461557	+	0.0415588i
$517$	−5.40593	−	0.856215i	−0.237752	−	0.0376563i
$518$	−4.15513	−	10.3062i	−0.182566	−	0.452827i
$519$	−21.5953	−	29.7233i	−0.947927	−	1.30471i
$520$		0			0
$521$	−17.0862	−	38.3763i	−0.748562	−	1.68130i	−0.731877	−	0.681437i	$-0.761355\pi$
$521$	−17.0862	−	38.3763i	−0.748562	−	1.68130i	−0.0166856	−	0.999861i	$-0.505311\pi$
$522$	3.35671	−	8.74454i	0.146919	−	0.382738i
$523$	−14.3920	+	22.1618i	−0.629320	+	0.969068i	0.369880	+	0.929079i	$0.379399\pi$
$523$	−14.3920	+	22.1618i	−0.629320	+	0.969068i	−0.999200	+	0.0399883i	$0.987268\pi$
$524$	−2.87517			−0.125602
$525$		0			0
$526$	31.0374			1.35329
$527$	17.5269	−	26.9891i	0.763485	−	1.17566i
$528$	6.97353	−	18.1667i	0.303484	−	0.790603i
$529$	−7.71438	−	17.3268i	−0.335408	−	0.753338i
$530$		0			0
$531$	5.20358	+	7.16212i	0.225816	+	0.310809i
$532$	−6.32672	+	8.08554i	−0.274298	+	0.350553i
$533$	19.2501	+	3.04892i	0.833815	+	0.132063i
$534$	−29.2553	−	26.3416i	−1.26600	−	1.13991i
$535$		0			0
$536$	5.17191	+	5.74398i	0.223392	+	0.248102i
$537$	−19.1989	+	1.00617i	−0.828496	+	0.0434196i
$538$	13.0503	+	6.64948i	0.562640	+	0.286679i
$539$	−8.17248	+	12.0778i	−0.352014	+	0.520226i
$540$		0			0
$541$	−3.31932	+	3.68648i	−0.142709	+	0.158494i	−0.810262	−	0.586068i	$-0.800675\pi$
$541$	−3.31932	+	3.68648i	−0.142709	+	0.158494i	0.667553	+	0.744562i	$0.267342\pi$
$542$	1.10425	−	1.36363i	0.0474315	−	0.0585731i
$543$	−1.58907	+	0.425791i	−0.0681937	+	0.0182724i
$544$	−13.1986	−	5.87641i	−0.565886	−	0.251949i
$545$		0			0
$546$	−8.72843	+	15.7192i	−0.373542	+	0.672718i
$547$	17.1842	−	2.72171i	0.734743	−	0.116372i	0.222161	−	0.975010i	$-0.428689\pi$
$547$	17.1842	−	2.72171i	0.734743	−	0.116372i	0.512582	+	0.858638i	$0.328689\pi$
$548$	−3.93056	−	2.55254i	−0.167905	−	0.109039i
$549$	3.60848	−	6.25007i	0.154006	−	0.266747i
$550$		0			0
$551$	45.7053	−	26.3880i	1.94711	−	1.12416i
$552$	8.25542	−	4.20635i	0.351374	−	0.179034i
$553$	−5.08085	−	4.91376i	−0.216060	−	0.208954i
$554$	18.1257	−	24.9479i	0.770088	−	1.05994i
$555$		0			0
$556$	9.14427	−	0.961102i	0.387804	−	0.0407598i
$557$	−2.83348	−	10.5747i	−0.120058	−	0.448064i	0.879557	−	0.475793i	$-0.157839\pi$
$557$	−2.83348	−	10.5747i	−0.120058	−	0.448064i	−0.999615	+	0.0277296i	$0.991172\pi$
$558$	−7.91423	+	3.03799i	−0.335036	+	0.128608i
$559$	0.942233	+	2.89989i	0.0398522	+	0.122652i
$560$		0			0
$561$	6.39205	−	19.6727i	0.269872	−	0.830582i
$562$	0.142428	+	2.71769i	0.00600796	+	0.114639i
$563$	1.67086	−	1.08507i	0.0704183	−	0.0457302i	−0.508950	−	0.860796i	$-0.669966\pi$
$563$	1.67086	−	1.08507i	0.0704183	−	0.0457302i	0.579368	+	0.815066i	$0.303299\pi$
$564$	1.97477	−	1.77809i	0.0831527	−	0.0748710i
$565$		0			0
$566$	−39.8243	+	12.9397i	−1.67394	+	0.543896i
$567$	15.1825	−	24.2573i	0.637606	−	1.01871i
$568$	11.1410	+	11.1410i	0.467466	+	0.467466i
$569$	12.9886	−	29.1729i	0.544511	−	1.22299i	−0.406447	−	0.913674i	$-0.633232\pi$
$569$	12.9886	−	29.1729i	0.544511	−	1.22299i	0.950959	−	0.309318i	$-0.100101\pi$
$570$		0			0
$571$	−13.4872	+	6.00488i	−0.564421	+	0.251297i	−0.669053	−	0.743214i	$-0.733300\pi$
$571$	−13.4872	+	6.00488i	−0.564421	+	0.251297i	0.104632	+	0.994511i	$0.466634\pi$
$572$	−1.82635	+	1.47895i	−0.0763636	+	0.0618380i
$573$	2.42093	+	4.75134i	0.101136	+	0.198490i
$574$	−29.9003	+	22.4969i	−1.24801	+	0.939004i
$575$		0			0
$576$	−2.10668	−	3.64889i	−0.0877785	−	0.152037i
$577$	−0.424978	+	8.10906i	−0.0176921	+	0.337585i	0.975415	+	0.220375i	$0.0707282\pi$
$577$	−0.424978	+	8.10906i	−0.0176921	+	0.337585i	−0.993107	+	0.117209i	$0.962605\pi$
$578$	−12.8314	−	4.92553i	−0.533718	−	0.204875i
$579$	1.43609	−	13.6635i	0.0596819	−	0.567835i
$580$		0			0
$581$	5.65382	−	5.26449i	0.234560	−	0.218408i
$582$	7.41437	−	7.41437i	0.307335	−	0.307335i
$583$	−6.89595	−	17.9646i	−0.285601	−	0.744016i
$584$	−19.0665	−	4.05272i	−0.788979	−	0.167703i
$585$		0			0
$586$	−2.02318	−	9.51830i	−0.0835767	−	0.393197i
$587$	−3.16940	+	6.22031i	−0.130815	+	0.256739i	−0.947118	−	0.320884i	$-0.896020\pi$
$587$	−3.16940	+	6.22031i	−0.130815	+	0.256739i	0.816303	+	0.577624i	$0.196020\pi$
$588$	−2.06003	−	6.77373i	−0.0849541	−	0.279344i
$589$	−45.4270	−	14.7601i	−1.87179	−	0.608181i
$590$		0			0
$591$	−6.03974	+	28.4148i	−0.248442	+	1.16883i
$592$	−9.80688	−	7.94146i	−0.403060	−	0.326392i
$593$	−8.18799	−	2.19397i	−0.336240	−	0.0900954i	0.0867484	−	0.996230i	$-0.472352\pi$
$593$	−8.18799	−	2.19397i	−0.336240	−	0.0900954i	−0.422989	+	0.906135i	$0.639019\pi$
$594$	11.3107	−	8.21773i	0.464085	−	0.337177i
$595$		0			0
$596$	−6.11193	−	4.44058i	−0.250355	−	0.181893i
$597$	−25.9197	−	32.0081i	−1.06082	−	1.31001i
$598$	−6.95412	−	0.364450i	−0.284375	−	0.0149035i
$599$	20.6751	+	11.9368i	0.844762	+	0.487723i	0.858880	−	0.512177i	$-0.171161\pi$
$599$	20.6751	+	11.9368i	0.844762	+	0.487723i	−0.0141183	+	0.999900i	$0.504494\pi$
$600$		0			0
$601$			9.32470i			0.380362i	0.981749	+	0.190181i	$0.0609075\pi$
$601$			9.32470i			0.380362i	−0.981749	+	0.190181i	$0.939092\pi$
$602$	−5.25958	−	2.57007i	−0.214365	−	0.104748i
$603$	−0.432180	−	2.72868i	−0.0175997	−	0.111120i
$604$	8.26564	+	0.868753i	0.336324	+	0.0353491i
$605$		0			0
$606$	0.922764	+	8.77952i	0.0374847	+	0.356643i
$607$	5.76957	−	21.5323i	0.234180	−	0.873971i	−0.744337	−	0.667804i	$-0.767234\pi$
$607$	5.76957	−	21.5323i	0.234180	−	0.873971i	0.978517	−	0.206167i	$-0.0660989\pi$
$608$	−3.35461	+	21.1802i	−0.136047	+	0.858969i
$609$	−3.19878	+	36.2545i	−0.129621	+	1.46910i
$610$		0			0
$611$	5.61753	−	1.19404i	0.227261	−	0.0483058i
$612$	1.19797	+	1.84471i	0.0484250	+	0.0745680i
$613$	−11.2408	−	17.3094i	−0.454013	−	0.699118i	0.535343	−	0.844635i	$-0.320182\pi$
$613$	−11.2408	−	17.3094i	−0.454013	−	0.699118i	−0.989356	+	0.145516i	$0.953516\pi$
$614$	−27.5536	+	5.85669i	−1.11197	+	0.236357i
$615$		0			0
$616$	−1.14028	+	12.9238i	−0.0459432	+	0.520714i
$617$	1.89563	−	11.9685i	0.0763151	−	0.481835i	−0.919698	−	0.392627i	$-0.871566\pi$
$617$	1.89563	−	11.9685i	0.0763151	−	0.481835i	0.996013	−	0.0892079i	$-0.0284335\pi$
$618$	5.87259	−	21.9168i	0.236230	−	0.881624i
$619$	1.68698	+	16.0505i	0.0678054	+	0.645125i	0.974662	+	0.223685i	$0.0718086\pi$
$619$	1.68698	+	16.0505i	0.0678054	+	0.645125i	−0.906856	+	0.421440i	$0.861525\pi$
$620$		0			0
$621$	8.45046	+	0.888179i	0.339105	+	0.0356414i
$622$	−1.57807	−	9.96354i	−0.0632749	−	0.399502i
$623$	30.1011	+	14.7088i	1.20597	+	0.589294i
$624$			20.4181i			0.817376i
$625$		0			0
$626$	−10.4927	−	6.05796i	−0.419372	−	0.242125i
$627$	−30.6600	−	1.60683i	−1.22444	−	0.0641704i
$628$	−1.39500	−	1.72269i	−0.0556667	−	0.0687427i
$629$	−10.8523	−	7.88463i	−0.432708	−	0.314381i
$630$		0			0
$631$	32.3943	−	23.5358i	1.28960	−	0.936947i	0.289799	−	0.957087i	$-0.406411\pi$
$631$	32.3943	−	23.5358i	1.28960	−	0.936947i	0.999797	+	0.0201409i	$0.00641148\pi$
$632$	−6.07412	−	1.62756i	−0.241616	−	0.0647407i
$633$	38.0264	+	30.7932i	1.51141	+	1.22392i
$634$	−4.65424	+	21.8965i	−0.184843	+	0.869620i
$635$		0			0
$636$	8.88511	+	2.88695i	0.352318	+	0.114475i
$637$	3.46407	−	14.9043i	0.137251	−	0.590529i
$638$	−10.5295	+	20.6654i	−0.416868	+	0.818149i
$639$	−1.17088	−	5.50853i	−0.0463191	−	0.217914i
$640$		0			0
$641$	36.0927	+	7.67174i	1.42558	+	0.303015i	0.855170	−	0.518348i	$-0.173453\pi$
$641$	36.0927	+	7.67174i	1.42558	+	0.303015i	0.570406	+	0.821363i	$0.306786\pi$
$642$	12.9186	+	33.6541i	0.509856	+	1.32822i
$643$	−15.3835	+	15.3835i	−0.606667	+	0.606667i	−0.942074	−	0.335406i	$-0.891126\pi$
$643$	−15.3835	+	15.3835i	−0.606667	+	0.606667i	0.335406	+	0.942074i	$0.391126\pi$
$644$	2.00684	−	1.86864i	0.0790804	−	0.0736348i
$645$		0			0
$646$	−6.31604	+	60.0932i	−0.248501	+	2.36433i
$647$	−32.8659	−	12.6160i	−1.29209	−	0.495987i	−0.387343	−	0.921936i	$-0.626607\pi$
$647$	−32.8659	−	12.6160i	−1.29209	−	0.495987i	−0.904747	+	0.425949i	$0.859940\pi$
$648$	1.33245	−	25.4247i	0.0523436	−	0.998775i
$649$	−10.9605	−	18.9842i	−0.430238	−	0.745193i
$650$		0			0
$651$	26.3213	−	19.8041i	1.03161	−	0.776184i
$652$	−3.57373	−	7.01384i	−0.139958	−	0.274683i
$653$	24.0920	−	19.5093i	0.942794	−	0.763459i	−0.0289295	−	0.999581i	$-0.509210\pi$
$653$	24.0920	−	19.5093i	0.942794	−	0.763459i	0.971723	+	0.236122i	$0.0758765\pi$
$654$	27.7632	−	12.3610i	1.08563	−	0.483352i
$655$		0			0
$656$	−17.2832	+	38.8188i	−0.674797	+	1.51562i
$657$	4.92657	+	4.92657i	0.192204	+	0.192204i
$658$	−5.84971	+	9.34616i	−0.228045	+	0.364351i
$659$	6.75492	−	2.19481i	0.263134	−	0.0854976i	−0.174479	−	0.984661i	$-0.555824\pi$
$659$	6.75492	−	2.19481i	0.263134	−	0.0854976i	0.437613	+	0.899163i	$0.355824\pi$
$660$		0			0
$661$	3.56987	−	3.21432i	0.138852	−	0.125023i	−0.596778	−	0.802406i	$-0.703553\pi$
$661$	3.56987	−	3.21432i	0.138852	−	0.125023i	0.735630	+	0.677383i	$0.236886\pi$
$662$	−13.6970	+	8.89494i	−0.532349	+	0.345712i
$663$	1.13592	+	21.6747i	0.0441156	+	0.841775i
$664$	2.12387	−	6.53659i	0.0824220	−	0.253669i
$665$		0			0
$666$	1.09196	+	3.36069i	0.0423124	+	0.130224i
$667$	−13.1597	+	5.05154i	−0.509546	+	0.195596i
$668$	2.25866	+	8.42942i	0.0873901	+	0.326144i
$669$	25.3912	−	2.66872i	0.981679	−	0.103179i
$670$		0			0
$671$	−10.5039	+	14.4574i	−0.405498	+	0.558120i
$672$	−10.6303	−	10.2807i	−0.410071	−	0.396585i
$673$	11.7311	−	5.97729i	0.452201	−	0.230408i	−0.213030	−	0.977046i	$-0.568333\pi$
$673$	11.7311	−	5.97729i	0.452201	−	0.230408i	0.665231	+	0.746638i	$0.268333\pi$
$674$	−35.3100	+	20.3863i	−1.36009	+	0.785249i
$675$		0			0
$676$	−2.12143	+	3.67442i	−0.0815934	+	0.141324i
$677$	−39.7955	−	25.8435i	−1.52947	−	0.993247i	−0.988333	−	0.152311i	$-0.951329\pi$
$677$	−39.7955	−	25.8435i	−1.52947	−	0.993247i	−0.541134	−	0.840937i	$-0.682005\pi$
$678$	28.1453	−	4.45777i	1.08091	−	0.171200i
$679$	−4.33196	+	7.80151i	−0.166245	+	0.299394i
$680$		0			0
$681$	5.54570	+	2.46911i	0.212512	+	0.0946164i
$682$	20.2758	−	5.43288i	0.776400	−	0.208036i
$683$	11.2348	−	13.8738i	0.429886	−	0.530865i	−0.515469	−	0.856908i	$-0.672382\pi$
$683$	11.2348	−	13.8738i	0.429886	−	0.530865i	0.945355	+	0.326043i	$0.105716\pi$
$684$	2.18453	−	2.42617i	0.0835277	−	0.0927669i
$685$		0			0
$686$	15.9453	+	24.6729i	0.608796	+	0.942017i
$687$	−0.932248	−	0.475004i	−0.0355675	−	0.0181225i
$688$	−6.63863	+	0.347916i	−0.253095	+	0.0132642i
$689$	13.5103	+	15.0048i	0.514703	+	0.571636i
$690$		0			0
$691$	−5.84754	−	5.26515i	−0.222451	−	0.200296i	0.550368	−	0.834922i	$-0.314487\pi$
$691$	−5.84754	−	5.26515i	−0.222451	−	0.200296i	−0.772819	+	0.634626i	$0.781154\pi$
$692$	−9.55468	−	1.51331i	−0.363214	−	0.0575275i
$693$	2.85770	−	3.65214i	0.108555	−	0.138733i
$694$	4.25473	+	5.85614i	0.161507	+	0.222296i
$695$		0			0
$696$	13.1700	+	29.5804i	0.499209	+	1.12124i
$697$	−16.1873	+	42.1694i	−0.613139	+	1.59728i
$698$	30.6001	−	47.1199i	1.15823	−	1.78352i
$699$	48.6441			1.83989
$700$		0			0
$701$	21.0860			0.796406			0.398203	−	0.917297i	$-0.369634\pi$
$701$	21.0860			0.796406			0.398203	+	0.917297i	$0.369634\pi$
$702$	−7.98974	+	12.3031i	−0.301553	+	0.464351i
$703$	−7.13514	+	18.5877i	−0.269107	+	0.701047i
$704$	4.24346	+	9.53096i	0.159931	+	0.359212i
$705$		0			0
$706$	−9.96981	−	13.7223i	−0.375219	−	0.516444i
$707$	−2.80922	−	6.96785i	−0.105652	−	0.262053i
$708$	10.5117	+	1.66489i	0.395054	+	0.0625703i
$709$	2.13303	+	1.92059i	0.0801077	+	0.0721293i	0.708212	−	0.706000i	$-0.249502\pi$
$709$	2.13303	+	1.92059i	0.0801077	+	0.0721293i	−0.628104	+	0.778129i	$0.716169\pi$
$710$		0			0
$711$	1.50398	+	1.67034i	0.0564038	+	0.0626427i
$712$	29.7654	−	1.55994i	1.11550	−	0.0584611i
$713$	11.3671	+	5.79180i	0.425699	+	0.216905i
$714$	−31.4284	−	27.3609i	−1.17618	−	1.02396i
$715$		0			0
$716$	−3.38719	+	3.76186i	−0.126585	+	0.140587i
$717$	−33.6497	+	41.5539i	−1.25667	+	1.55186i
$718$	−5.84827	+	1.56704i	−0.218256	+	0.0584814i
$719$	5.18872	+	2.31017i	0.193507	+	0.0861547i	0.501202	−	0.865330i	$-0.332891\pi$
$719$	5.18872	+	2.31017i	0.193507	+	0.0861547i	−0.307696	+	0.951485i	$0.599558\pi$
$720$		0			0
$721$	0.322778	+	19.3073i	0.0120209	+	0.719040i
$722$	58.8143	−	9.31526i	2.18884	−	0.346678i
$723$	31.4640	+	20.4330i	1.17016	+	0.759911i
$724$	−0.216584	+	0.375135i	−0.00804929	+	0.0139418i
$725$		0			0
$726$	−17.9310	+	10.3525i	−0.665481	+	0.384216i
$727$	37.1735	−	18.9408i	1.37869	−	0.702477i	0.401701	−	0.915771i	$-0.368419\pi$
$727$	37.1735	−	18.9408i	1.37869	−	0.702477i	0.976988	+	0.213294i	$0.0684191\pi$
$728$	−3.74270	−	13.0887i	−0.138714	−	0.485100i
$729$	9.27315	−	12.7634i	0.343450	−	0.472718i
$730$		0			0
$731$	−7.02785	+	0.738657i	−0.259934	+	0.0273202i
$732$	−2.24553	−	8.38045i	−0.0829973	−	0.309750i
$733$	32.2848	−	12.3930i	1.19247	−	0.457745i	0.320471	−	0.947258i	$-0.396159\pi$
$733$	32.2848	−	12.3930i	1.19247	−	0.457745i	0.871996	+	0.489513i	$0.162825\pi$
$734$	4.08138	+	12.5612i	0.150647	+	0.463642i
$735$		0			0
$736$	1.76991	−	5.44722i	0.0652397	−	0.200787i
$737$	0.358021	+	6.83146i	0.0131879	+	0.251640i
$738$	9.97924	−	6.48059i	0.367341	−	0.238554i
$739$	6.17964	−	5.56417i	0.227322	−	0.204681i	−0.547597	−	0.836742i	$-0.684457\pi$
$739$	6.17964	−	5.56417i	0.227322	−	0.204681i	0.774919	+	0.632061i	$0.217791\pi$
$740$		0			0
$741$	30.6384	−	9.95501i	1.12553	−	0.365706i
$742$	−38.7393	−	1.38139i	−1.42216	−	0.0507123i
$743$	−10.0390	−	10.0390i	−0.368295	−	0.368295i	0.498560	−	0.866855i	$-0.333862\pi$
$743$	−10.0390	−	10.0390i	−0.368295	−	0.368295i	−0.866855	+	0.498560i	$0.833862\pi$
$744$	11.9195	−	26.7717i	0.436991	−	0.981498i
$745$		0			0
$746$	25.2590	−	11.2460i	0.924797	−	0.411746i
$747$	−1.90915	+	1.54600i	−0.0698521	+	0.0565651i
$748$	−2.47264	−	4.85283i	−0.0904086	−	0.177437i
$749$	−18.4447	−	24.5145i	−0.673954	−	0.895740i
$750$		0			0
$751$	19.9959	+	34.6339i	0.729661	+	1.26381i	0.957026	+	0.290000i	$0.0936555\pi$
$751$	19.9959	+	34.6339i	0.729661	+	1.26381i	−0.227365	+	0.973810i	$0.573011\pi$
$752$	−0.655299	+	12.5039i	−0.0238963	+	0.455968i
$753$	13.7179	+	5.26582i	0.499909	+	0.191897i
$754$	2.54383	−	24.2029i	0.0926407	−	0.881417i
$755$		0			0
$756$	−1.29531	−	5.62951i	−0.0471098	−	0.204743i
$757$	−12.1964	+	12.1964i	−0.443287	+	0.443287i	−0.893115	−	0.449828i	$-0.851485\pi$
$757$	−12.1964	+	12.1964i	−0.443287	+	0.443287i	0.449828	+	0.893115i	$0.351485\pi$
$758$	6.20578	+	16.1666i	0.225404	+	0.587198i
$759$	8.02106	+	1.70493i	0.291146	+	0.0618850i
$760$		0			0
$761$	−2.08132	−	9.79185i	−0.0754479	−	0.354954i	0.924188	−	0.381938i	$-0.124743\pi$
$761$	−2.08132	−	9.79185i	−0.0754479	−	0.354954i	−0.999636	+	0.0269835i	$0.991410\pi$
$762$	−3.46873	+	6.80777i	−0.125659	+	0.246619i
$763$	−19.8248	+	16.6101i	−0.717707	+	0.601327i
$764$	1.33536	+	0.433884i	0.0483116	+	0.0156974i
$765$		0			0
$766$	−5.47227	+	25.7450i	−0.197721	+	0.930205i
$767$	17.8753	+	14.4752i	0.645441	+	0.522668i
$768$	−22.0205	−	5.90038i	−0.794597	−	0.212912i
$769$	−33.7752	+	24.5391i	−1.21796	+	0.884902i	−0.995929	−	0.0901368i	$-0.971270\pi$
$769$	−33.7752	+	24.5391i	−1.21796	+	0.884902i	−0.222034	+	0.975039i	$0.571270\pi$
$770$		0			0
$771$	−21.7061	−	15.7704i	−0.781728	−	0.567959i
$772$	−2.27654	−	2.81129i	−0.0819345	−	0.101181i
$773$	−28.5404	−	1.49574i	−1.02653	−	0.0537980i	−0.468370	−	0.883533i	$-0.655158\pi$
$773$	−28.5404	−	1.49574i	−1.02653	−	0.0537980i	−0.558158	+	0.829735i	$0.688492\pi$
$774$	1.61213	+	0.930761i	0.0579466	+	0.0334555i
$775$		0			0
$776$			7.93899i			0.284993i
$777$	−7.66955	−	11.3887i	−0.275143	−	0.408566i
$778$	−4.77008	−	30.1171i	−0.171016	−	1.07975i
$779$	66.6762	+	7.00795i	2.38892	+	0.251086i
$780$		0			0
$781$	1.45762	+	13.8683i	0.0521576	+	0.496246i
$782$	4.17702	−	15.5888i	0.149370	−	0.557456i
$783$	−4.64530	+	29.3293i	−0.166009	+	1.04814i
$784$	29.4325	+	15.7052i	1.05116	+	0.560902i
$785$		0			0
$786$	−16.9423	+	3.60119i	−0.604311	+	0.128450i
$787$	18.8075	+	28.9611i	0.670416	+	1.03235i	0.996216	+	0.0869114i	$0.0276997\pi$
$787$	18.8075	+	28.9611i	0.670416	+	1.03235i	−0.325800	+	0.945439i	$0.605634\pi$
$788$	4.16586	+	6.41486i	0.148403	+	0.228520i
$789$	37.5120	−	7.97342i	1.33546	−	0.283861i
$790$		0			0
$791$	−21.9866	+	10.2328i	−0.781753	+	0.363836i
$792$	0.645396	−	4.07487i	0.0229332	−	0.144794i
$793$	4.85309	−	18.1120i	0.172338	−	0.643175i
$794$	0.201724	+	1.91927i	0.00715891	+	0.0681125i
$795$		0			0
$796$	−10.7852	−	1.13357i	−0.382271	−	0.0401783i
$797$	7.35212	+	46.4194i	0.260425	+	1.64426i	0.677597	+	0.735433i	$0.263021\pi$
$797$	7.35212	+	46.4194i	0.260425	+	1.64426i	−0.417172	+	0.908828i	$0.636979\pi$
$798$	−27.1537	+	55.5693i	−0.961230	+	1.96713i
$799$			13.3099i			0.470869i
$800$		0			0
$801$	−9.22634	−	5.32683i	−0.325997	−	0.188214i
$802$	7.51383	+	0.393783i	0.265322	+	0.0139050i
$803$	−10.8570	−	13.4072i	−0.383134	−	0.473131i
$804$	−2.68694	−	1.95218i	−0.0947612	−	0.0688480i
$805$		0			0
$806$	−17.8190	+	12.9462i	−0.627646	+	0.456012i
$807$	17.4810	+	4.68401i	0.615359	+	0.164885i
$808$	−5.19439	−	4.20634i	−0.182738	−	0.147978i
$809$	−6.74211	+	31.7191i	−0.237040	+	1.11519i	0.685136	+	0.728415i	$0.259743\pi$
$809$	−6.74211	+	31.7191i	−0.237040	+	1.11519i	−0.922176	+	0.386770i	$0.873591\pi$
$810$		0			0
$811$	8.85993	+	2.87877i	0.311114	+	0.101087i	0.460413	−	0.887705i	$-0.347701\pi$
$811$	8.85993	+	2.87877i	0.311114	+	0.101087i	−0.149298	+	0.988792i	$0.547701\pi$
$812$	6.15442	+	7.34554i	0.215978	+	0.257778i
$813$	0.984289	−	1.93178i	0.0345205	−	0.0677503i
$814$	−1.81919	−	8.55862i	−0.0637626	−	0.299980i
$815$		0			0
$816$	−46.2862	−	9.83843i	−1.62034	−	0.344414i
$817$	3.75879	+	9.79198i	0.131503	+	0.342578i
$818$	27.8073	−	27.8073i	0.972258	−	0.972258i
$819$	−1.42606	+	4.65216i	−0.0498305	+	0.162560i
$820$		0			0
$821$	3.88835	−	36.9952i	0.135704	−	1.29114i	−0.688661	−	0.725083i	$-0.741801\pi$
$821$	3.88835	−	36.9952i	0.135704	−	1.29114i	0.824366	−	0.566058i	$-0.191532\pi$
$822$	−26.3584	−	10.1180i	−0.919354	−	0.352907i
$823$	1.56075	−	29.7808i	0.0544042	−	1.03809i	−0.825940	−	0.563758i	$-0.809355\pi$
$823$	1.56075	−	29.7808i	0.0544042	−	1.03809i	0.880344	−	0.474335i	$-0.157312\pi$
$824$	8.58974	+	14.8779i	0.299238	+	0.518295i
$825$		0			0
$826$	−43.8342	+	5.34938i	−1.52519	+	0.186129i
$827$	−13.1390	−	25.7867i	−0.456887	−	0.896691i	−0.998430	−	0.0560176i	$-0.982160\pi$
$827$	−13.1390	−	25.7867i	−0.456887	−	0.896691i	0.541543	−	0.840673i	$-0.317840\pi$
$828$	−0.677656	+	0.548755i	−0.0235502	+	0.0190706i
$829$	8.61441	−	3.83538i	0.299191	−	0.133208i	−0.251651	−	0.967818i	$-0.580973\pi$
$829$	8.61441	−	3.83538i	0.299191	−	0.133208i	0.550842	+	0.834610i	$0.314307\pi$
$830$		0			0
$831$	15.4978	−	34.8087i	0.537614	−	1.20750i
$832$	−7.74074	−	7.74074i	−0.268362	−	0.268362i
$833$	32.1177	+	15.0344i	1.11281	+	0.520911i
$834$	52.6799	−	17.1167i	1.82416	−	0.592704i
$835$		0			0
$836$	−6.00756	+	5.40923i	−0.207776	+	0.187082i
$837$	22.5395	−	14.6373i	0.779080	−	0.505940i
$838$	2.02120	+	38.5668i	0.0698212	+	1.33227i
$839$	−16.9096	+	52.0423i	−0.583784	+	1.79670i	0.0203179	+	0.999794i	$0.493532\pi$
$839$	−16.9096	+	52.0423i	−0.583784	+	1.79670i	−0.604101	+	0.796907i	$0.706468\pi$
$840$		0			0
$841$	−6.26123	−	19.2701i	−0.215905	−	0.664486i
$842$	−10.9841	+	4.21641i	−0.378538	+	0.145307i
$843$	0.870306	+	3.24803i	0.0299749	+	0.111868i
$844$	12.8131	−	1.34671i	0.441044	−	0.0463556i
$845$		0			0
$846$	2.06088	−	2.83656i	0.0708544	−	0.0975228i
$847$	12.2496	−	12.6662i	0.420903	−	0.435215i
$848$	−39.2224	+	19.9848i	−1.34690	+	0.686282i
$849$	−44.8078	+	25.8698i	−1.53780	+	0.887849i
$850$		0			0
$851$	2.65890	−	4.60535i	0.0911460	−	0.157870i
$852$	−5.67796	−	3.68731i	−0.194524	−	0.126325i
$853$	57.0510	−	9.03599i	1.95339	−	0.309386i	0.953419	−	0.301650i	$-0.0975375\pi$
$853$	57.0510	−	9.03599i	1.95339	−	0.309386i	0.999970	−	0.00773601i	$-0.00246247\pi$
$854$	18.5183	+	30.8711i	0.633682	+	1.05639i
$855$		0			0
$856$	−24.9340	−	11.1013i	−0.852226	−	0.379436i
$857$	13.6104	−	3.64690i	0.464923	−	0.124576i	−0.0187505	−	0.999824i	$-0.505969\pi$
$857$	13.6104	−	3.64690i	0.464923	−	0.124576i	0.483674	+	0.875248i	$0.339302\pi$
$858$	−8.90958	+	11.0024i	−0.304168	+	0.375616i
$859$	−14.0269	+	15.5785i	−0.478592	+	0.531530i	−0.933294	−	0.359113i	$-0.883079\pi$
$859$	−14.0269	+	15.5785i	−0.478592	+	0.531530i	0.454702	+	0.890644i	$0.349746\pi$
$860$		0			0
$861$	−30.3583	+	34.8713i	−1.03461	+	1.18841i
$862$	−25.5128	−	12.9994i	−0.868971	−	0.442763i
$863$	15.2735	−	0.800451i	0.519916	−	0.0272477i	0.209427	−	0.977824i	$-0.432840\pi$
$863$	15.2735	−	0.800451i	0.519916	−	0.0272477i	0.310490	+	0.950577i	$0.399507\pi$
$864$	−8.07357	−	8.96661i	−0.274669	−	0.305050i
$865$		0			0
$866$	−29.7563	−	26.7927i	−1.01116	−	0.910452i
$867$	−16.7735	−	2.65667i	−0.569659	−	0.0902252i
$868$	1.21339	−	8.58779i	0.0411851	−	0.291489i
$869$	−3.27136	−	4.50263i	−0.110973	−	0.152741i
$870$		0			0
$871$	−2.91953	−	6.55737i	−0.0989245	−	0.222188i
$872$	−8.24602	+	21.4816i	−0.279246	+	0.727460i
$873$	1.54549	−	2.37985i	0.0523069	−	0.0805456i
$874$	−23.9541			−0.810261
$875$		0			0
$876$	8.37585			0.282994
$877$	−8.15148	+	12.5522i	−0.275256	+	0.423857i	−0.949080	−	0.315035i	$-0.897984\pi$
$877$	−8.15148	+	12.5522i	−0.275256	+	0.423857i	0.673824	+	0.738892i	$0.264650\pi$
$878$	15.8568	−	41.3083i	0.535140	−	1.39409i
$879$	−4.89045	−	10.9841i	−0.164951	−	0.370486i
$880$		0			0
$881$	10.0697	+	13.8597i	0.339257	+	0.466947i	0.944224	−	0.329303i	$-0.106814\pi$
$881$	10.0697	+	13.8597i	0.339257	+	0.466947i	−0.604967	+	0.796250i	$0.706814\pi$
$882$	−4.51692	−	8.17714i	−0.152093	−	0.275339i
$883$	−26.9691	−	4.27148i	−0.907581	−	0.143747i	−0.314845	−	0.949143i	$-0.601952\pi$
$883$	−26.9691	−	4.27148i	−0.907581	−	0.143747i	−0.592736	+	0.805397i	$0.701952\pi$
$884$	4.24696	+	3.82398i	0.142841	+	0.128614i
$885$		0			0
$886$	−32.5015	−	36.0966i	−1.09191	−	1.21269i
$887$	31.6840	−	1.66049i	1.06384	−	0.0557537i	0.487628	−	0.873051i	$-0.337862\pi$
$887$	31.6840	−	1.66049i	1.06384	−	0.0557537i	0.576216	+	0.817298i	$0.304529\pi$
$888$	−10.8841	−	5.54572i	−0.365246	−	0.186102i
$889$	1.24541	−	6.38199i	0.0417698	−	0.214045i
$890$		0			0
$891$	15.0775	−	16.7453i	0.505117	−	0.560989i
$892$	4.23055	−	5.22429i	0.141649	−	0.174922i
$893$	19.0822	−	5.11306i	0.638561	−	0.171102i
$894$	−41.5772	−	18.5114i	−1.39055	−	0.619112i
$895$		0			0
$896$	36.1025	−	0.603560i	1.20610	−	0.0201635i
$897$	−8.49842	+	1.34602i	−0.283754	+	0.0449422i
$898$	40.4711	+	26.2822i	1.35054	+	0.877050i
$899$	−22.2922	+	38.6112i	−0.743485	+	1.28775i
$900$		0			0
$901$	−40.5246	+	23.3969i	−1.35007	+	0.779463i
$902$	−26.2521	+	13.3761i	−0.874099	+	0.445376i
$903$	−7.01702	−	1.75503i	−0.233512	−	0.0584038i
$904$	−12.6818	+	17.4550i	−0.421790	+	0.580544i
$905$		0			0
$906$	49.7944	−	5.23360i	1.65431	−	0.173875i
$907$	3.31110	+	12.3572i	0.109943	+	0.410314i	0.998859	−	0.0477567i	$-0.0152072\pi$
$907$	3.31110	+	12.3572i	0.109943	+	0.410314i	−0.888916	+	0.458071i	$0.848541\pi$
$908$	1.49223	−	0.572812i	0.0495212	−	0.0190094i
$909$	0.738256	+	2.27212i	0.0244864	+	0.0753614i
$910$		0			0
$911$	−2.87409	+	8.84554i	−0.0952228	+	0.293066i	−0.987312	−	0.158794i	$-0.949239\pi$
$911$	−2.87409	+	8.84554i	−0.0952228	+	0.293066i	0.892089	+	0.451860i	$0.149239\pi$
$912$	3.67585	+	70.1394i	0.121720	+	2.32255i
$913$	5.10159	−	3.31301i	0.168838	−	0.109645i
$914$	47.5847	−	42.8454i	1.57396	−	1.41720i
$915$		0			0
$916$	−0.262007	+	0.0851313i	−0.00865696	+	0.00281282i
$917$	13.0203	−	6.91070i	0.429967	−	0.228211i
$918$	−24.0404	−	24.0404i	−0.793450	−	0.793450i
$919$	19.7932	−	44.4563i	0.652917	−	1.46648i	−0.218451	−	0.975848i	$-0.570101\pi$
$919$	19.7932	−	44.4563i	0.652917	−	1.46648i	0.871369	−	0.490629i	$-0.163233\pi$
$920$		0			0
$921$	−31.7969	+	14.1569i	−1.04774	+	0.466485i
$922$	−22.0246	+	17.8352i	−0.725343	+	0.587371i
$923$	−6.64272	−	13.0371i	−0.218648	−	0.429121i
$924$	−0.675327	−	5.53381i	−0.0222166	−	0.182049i
$925$		0			0
$926$	−27.1322	−	46.9943i	−0.891619	−	1.54433i
$927$	0.321368	−	6.13206i	0.0105551	−	0.201403i
$928$	18.6868	+	7.17320i	0.613425	+	0.235472i
$929$	−0.0493594	+	0.469623i	−0.00161943	+	0.0154078i	−0.995302	−	0.0968214i	$-0.969132\pi$
$929$	−0.0493594	+	0.469623i	−0.00161943	+	0.0154078i	0.993682	+	0.112229i	$0.0357991\pi$
$930$		0			0
$931$	9.21644	−	51.8223i	0.302057	−	1.69841i
$932$	9.05674	−	9.05674i	0.296663	−	0.296663i
$933$	−4.46688	−	11.6366i	−0.146239	−	0.380966i
$934$	−10.3605	−	2.20220i	−0.339007	−	0.0720582i
$935$		0			0
$936$	0.900044	+	4.23437i	0.0294189	+	0.138405i
$937$	−15.7304	+	30.8727i	−0.513890	+	1.00857i	0.477624	+	0.878565i	$0.341498\pi$
$937$	−15.7304	+	30.8727i	−0.513890	+	1.00857i	−0.991514	+	0.130002i	$0.958502\pi$
$938$	12.9462	+	4.72282i	0.422707	+	0.154206i
$939$	−14.2378	−	4.62615i	−0.464634	−	0.150969i
$940$		0			0
$941$	2.33096	−	10.9663i	0.0759873	−	0.357492i	−0.923683	−	0.383157i	$-0.874837\pi$
$941$	2.33096	−	10.9663i	0.0759873	−	0.357492i	0.999671	+	0.0256647i	$0.00817023\pi$
$942$	−10.3779	−	8.40387i	−0.338131	−	0.273813i
$943$	−17.2966	−	4.63460i	−0.563253	−	0.150923i
$944$	−40.5702	+	29.4760i	−1.32045	+	0.959362i
$945$		0			0
$946$	−3.72909	−	2.70934i	−0.121243	−	0.0880883i
$947$	−36.0736	−	44.5472i	−1.17224	−	1.44759i	−0.869096	−	0.494644i	$-0.835299\pi$
$947$	−36.0736	−	44.5472i	−1.17224	−	1.44759i	−0.303139	−	0.952946i	$-0.598035\pi$
$948$	2.69839	+	0.141417i	0.0876398	+	0.00459301i
$949$	15.6768	+	9.05102i	0.508892	+	0.293809i
$950$		0			0
$951$			27.6599i			0.896934i
$952$	31.4745	−	2.17761i	1.02010	−	0.0705767i
$953$	2.70486	+	17.0778i	0.0876189	+	0.553204i	0.991976	+	0.126427i	$0.0403510\pi$
$953$	2.70486	+	17.0778i	0.0876189	+	0.553204i	−0.904357	+	0.426777i	$0.859649\pi$
$954$	12.2592	+	1.28849i	0.396906	+	0.0417165i
$955$		0			0
$956$	1.47163	+	14.0017i	0.0475960	+	0.452846i
$957$	−7.41718	+	27.6813i	−0.239764	+	0.894810i
$958$	1.25679	−	7.93504i	0.0406050	−	0.256370i
$959$	23.9349	+	2.11180i	0.772897	+	0.0681937i
$960$		0			0
$961$	9.14667	−	1.94419i	0.295054	−	0.0627156i
$962$	5.00034	+	7.69984i	0.161217	+	0.248253i
$963$	5.31328	+	8.18173i	0.171218	+	0.263653i
$964$	9.66237	−	2.05380i	0.311204	−	0.0661484i
$965$		0			0
$966$	9.48502	−	13.5248i	0.305175	−	0.435153i
$967$	2.21053	−	13.9567i	0.0710859	−	0.448819i	−0.926314	−	0.376753i	$-0.877041\pi$
$967$	2.21053	−	13.9567i	0.0710859	−	0.448819i	0.997400	−	0.0720662i	$-0.0229593\pi$
$968$	4.05738	−	15.1423i	0.130409	−	0.486693i
$969$	7.80416	+	74.2516i	0.250706	+	2.38531i
$970$		0			0
$971$	−10.3623	−	1.08912i	−0.332542	−	0.0349516i	−0.0632139	−	0.998000i	$-0.520135\pi$
$971$	−10.3623	−	1.08912i	−0.332542	−	0.0349516i	−0.269328	+	0.963048i	$0.586802\pi$
$972$	0.686717	+	4.33576i	0.0220265	+	0.139070i
$973$	−39.1000	+	26.3314i	−1.25349	+	0.844144i
$974$			29.8245i			0.955640i
$975$		0			0
$976$	35.4039	+	20.4405i	1.13325	+	0.654283i
$977$	24.8821	+	1.30401i	0.796048	+	0.0417191i	0.446023	−	0.895021i	$-0.352840\pi$
$977$	24.8821	+	1.30401i	0.796048	+	0.0417191i	0.350025	+	0.936740i	$0.386173\pi$
$978$	−29.8436	−	36.8537i	−0.954292	−	1.17845i
$979$	21.3419	+	15.5058i	0.682091	+	0.495568i
$980$		0			0
$981$	6.65373	−	4.83422i	0.212437	−	0.154345i
$982$	−40.1972	−	10.7708i	−1.28274	−	0.343710i
$983$	−9.08311	−	7.35536i	−0.289706	−	0.234600i	0.473439	−	0.880827i	$-0.343013\pi$
$983$	−9.08311	−	7.35536i	−0.289706	−	0.234600i	−0.763145	+	0.646227i	$0.776346\pi$
$984$	−8.55212	+	40.2346i	−0.272632	+	1.28263i
$985$		0			0
$986$	53.6403	+	17.4288i	1.70826	+	0.555046i
$987$	−4.66900	+	12.7986i	−0.148616	+	0.407384i
$988$	3.85090	−	7.55782i	0.122513	−	0.240446i
$989$	−0.582448	−	2.74020i	−0.0185208	−	0.0871333i
$990$		0			0
$991$	10.5500	+	2.24247i	0.335132	+	0.0712345i	0.372404	−	0.928071i	$-0.378533\pi$
$991$	10.5500	+	2.24247i	0.335132	+	0.0712345i	−0.0372721	+	0.999305i	$0.511867\pi$
$992$	−6.49210	−	16.9125i	−0.206124	−	0.536972i
$993$	−14.2692	+	14.2692i	−0.452820	+	0.452820i
$994$	26.8577	+	8.23288i	0.851876	+	0.261131i
$995$		0			0
$996$	−0.308703	+	2.93711i	−0.00978162	+	0.0930659i
$997$	11.5636	+	4.43884i	0.366222	+	0.140580i	0.534518	−	0.845157i	$-0.320493\pi$
$997$	11.5636	+	4.43884i	0.366222	+	0.140580i	−0.168296	+	0.985737i	$0.553826\pi$
$998$	0.250926	−	4.78795i	0.00794293	−	0.151560i
$999$	−5.60130	−	9.70173i	−0.177217	−	0.306949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.c.493.14		288
5.2	odd	4		875.2.bb.a.507.14		288
5.3	odd	4		875.2.bb.b.507.5		288
5.4	even	2		175.2.x.a.3.5	✓	288
7.5	odd	6	inner	875.2.bb.c.243.5		288
25.6	even	5		875.2.bb.a.143.14		288
25.8	odd	20		175.2.x.a.17.14	yes	288
25.17	odd	20	inner	875.2.bb.c.857.5		288
25.19	even	10		875.2.bb.b.143.5		288
35.12	even	12		875.2.bb.a.257.14		288
35.19	odd	6		175.2.x.a.103.14	yes	288
35.33	even	12		875.2.bb.b.257.5		288
175.19	odd	30		875.2.bb.b.768.5		288
175.33	even	60		175.2.x.a.117.5	yes	288
175.117	even	60	inner	875.2.bb.c.607.14		288
175.131	odd	30		875.2.bb.a.768.14		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.5	✓	288	5.4	even	2
175.2.x.a.17.14	yes	288	25.8	odd	20
175.2.x.a.103.14	yes	288	35.19	odd	6
175.2.x.a.117.5	yes	288	175.33	even	60
875.2.bb.a.143.14		288	25.6	even	5
875.2.bb.a.257.14		288	35.12	even	12
875.2.bb.a.507.14		288	5.2	odd	4
875.2.bb.a.768.14		288	175.131	odd	30
875.2.bb.b.143.5		288	25.19	even	10
875.2.bb.b.257.5		288	35.33	even	12
875.2.bb.b.507.5		288	5.3	odd	4
875.2.bb.b.768.5		288	175.19	odd	30
875.2.bb.c.243.5		288	7.5	odd	6	inner
875.2.bb.c.493.14		288	1.1	even	1	trivial
875.2.bb.c.607.14		288	175.117	even	60	inner
875.2.bb.c.857.5		288	25.17	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.863911 - 1.33031i) q^{2} +(0.702377 - 1.82975i) q^{3} +(-0.209899 - 0.471441i) q^{4} +(-1.82734 - 2.51512i) q^{6} +(2.08368 + 1.63042i) q^{7} +(2.32486 + 0.368222i) q^{8} +(-0.625235 - 0.562964i) q^{9} +(1.39398 + 1.54818i) q^{11} +(-1.01005 + 0.0529345i) q^{12} +(-1.94768 - 0.992394i) q^{13} +(3.96908 - 1.36339i) q^{14} +(3.18894 - 3.54168i) q^{16} +(3.18817 - 3.93706i) q^{17} +(-1.28906 + 0.345403i) q^{18} +(-6.86927 - 3.05840i) q^{19} +(4.44680 - 2.66745i) q^{21} +(3.26382 - 0.516939i) q^{22} +(1.68435 + 1.09383i) q^{23} +(2.30669 - 3.99530i) q^{24} +(-3.00281 + 1.73368i) q^{26} +(3.76970 - 1.92076i) q^{27} +(0.331286 - 1.32456i) q^{28} +(-4.12547 + 5.67823i) q^{29} +(6.31745 - 0.663990i) q^{31} +(-0.738117 - 2.75469i) q^{32} +(3.81188 - 1.46324i) q^{33} +(-2.48320 - 7.64252i) q^{34} +(-0.134168 + 0.412927i) q^{36} +(-0.138578 - 2.64422i) q^{37} +(-10.0030 + 6.49605i) q^{38} +(-3.18385 + 2.86675i) q^{39} +(-8.47974 + 2.75523i) q^{41} +(0.293115 - 8.22005i) q^{42} +(-0.986332 - 0.986332i) q^{43} +(0.437278 - 0.982142i) q^{44} +(2.91025 - 1.29573i) q^{46} +(-2.04177 + 1.65339i) q^{47} +(-4.24056 - 8.32258i) q^{48} +(1.68344 + 6.79456i) q^{49} +(-4.96456 - 8.59887i) q^{51} +(-0.0590385 + 1.12652i) q^{52} +(-8.62323 - 3.31015i) q^{53} +(0.701489 - 6.67422i) q^{54} +(4.24391 + 4.55777i) q^{56} +(-10.4209 + 10.4209i) q^{57} +(3.98974 + 10.3936i) q^{58} +(-10.2924 - 2.18773i) q^{59} +(1.78346 + 8.39053i) q^{61} +(4.57440 - 8.97777i) q^{62} +(-0.384920 - 2.19243i) q^{63} +(4.76284 + 1.54754i) q^{64} +(1.34656 - 6.33508i) q^{66} +(2.55191 + 2.06649i) q^{67} +(-2.52529 - 0.676649i) q^{68} +(3.18448 - 2.31366i) q^{69} +(5.41526 + 3.93442i) q^{71} +(-1.24629 - 1.53904i) q^{72} +(-8.26979 - 0.433401i) q^{73} +(-3.63734 - 2.10002i) q^{74} +3.88041i q^{76} +(0.380434 + 5.49868i) q^{77} +(1.06309 + 6.71211i) q^{78} +(-2.65691 - 0.279252i) q^{79} +(-1.13060 - 10.7569i) q^{81} +(-3.66043 + 13.6609i) q^{82} +(0.456772 - 2.88395i) q^{83} +(-2.19093 - 1.53651i) q^{84} +(-2.16423 + 0.460021i) q^{86} +(7.49212 + 11.5369i) q^{87} +(2.67075 + 4.11259i) q^{88} +(12.3861 - 2.63274i) q^{89} +(-2.44033 - 5.24338i) q^{91} +(0.162132 - 1.02366i) q^{92} +(3.22229 - 12.0258i) q^{93} +(0.435611 + 4.14456i) q^{94} +(-5.55884 - 0.584258i) q^{96} +(0.527619 + 3.33125i) q^{97} +(10.4932 + 3.63040i) q^{98} -1.75274i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) \) 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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