LMFDB - Embedded newform 875.2.bb.c.607.14

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			607.14
Character	$\chi$	$=$	875.607
Dual form			875.2.bb.c.493.14

$q$-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 $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{5}{6}\right)$

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	0.999812	+	0.0194031i	$0.00617659\pi$
$2$	0.863911	+	1.33031i	0.610877	+	0.940669i	−0.388934	+	0.921265i	$0.627157\pi$
$3$	0.702377	+	1.82975i	0.405518	+	1.05641i	0.972546	+	0.232711i	$0.0747597\pi$
$3$	0.702377	+	1.82975i	0.405518	+	1.05641i	−0.567028	+	0.823698i	$0.691907\pi$
$4$	−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	−0.495392	−	0.868670i	$-0.664975\pi$
$11$	1.39398	−	1.54818i	0.420302	−	0.466792i	0.915694	+	0.401877i	$0.131642\pi$
$12$	−1.01005	−	0.0529345i	−0.291576	−	0.0152809i
$13$	−1.94768	+	0.992394i	−0.540190	+	0.275241i	−0.702724	−	0.711462i	$-0.748033\pi$
$13$	−1.94768	+	0.992394i	−0.540190	+	0.275241i	0.162534	+	0.986703i	$0.448033\pi$
$14$	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	0.999817	−	0.0191163i	$-0.00608526\pi$
$17$	3.18817	+	3.93706i	0.773245	+	0.954878i	−0.226572	+	0.973994i	$0.572752\pi$
$18$	−1.28906	−	0.345403i	−0.303835	−	0.0814123i
$19$	−6.86927	+	3.05840i	−1.57592	+	0.701644i	−0.993771	−	0.111438i	$-0.964454\pi$
$19$	−6.86927	+	3.05840i	−1.57592	+	0.701644i	−0.582148	+	0.813083i	$0.697788\pi$
$20$		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	−0.356961	−	0.934119i	$-0.616187\pi$
$23$	1.68435	−	1.09383i	0.351210	−	0.228079i	0.708171	+	0.706041i	$0.249520\pi$
$24$	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	−0.996684	−	0.0813721i	$-0.974070\pi$
$29$	−4.12547	−	5.67823i	−0.766081	−	1.05442i	0.230603	−	0.973048i	$-0.425930\pi$
$30$		0			0
$31$	6.31745	+	0.663990i	1.13465	+	0.119256i	0.653176	−	0.757206i	$-0.273436\pi$
$31$	6.31745	+	0.663990i	1.13465	+	0.119256i	0.481471	+	0.876462i	$0.340103\pi$
$32$	−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	0.963298	+	0.268435i	$0.0865063\pi$
$37$	−0.138578	+	2.64422i	−0.0227820	+	0.434707i	−0.986080	+	0.166272i	$0.946827\pi$
$38$	−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	−0.440339	−	0.897832i	$-0.645142\pi$
$41$	−8.47974	−	2.75523i	−1.32431	−	0.430295i	−0.883974	+	0.467536i	$0.845142\pi$
$42$	0.293115	+	8.22005i	0.0452287	+	1.26838i
$43$	−0.986332	+	0.986332i	−0.150414	+	0.150414i	−0.778303	−	0.627889i	$-0.783919\pi$
$43$	−0.986332	+	0.986332i	−0.150414	+	0.150414i	0.627889	+	0.778303i	$0.283919\pi$
$44$	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	0.468748	−	0.883332i	$-0.344705\pi$
$47$	−2.04177	−	1.65339i	−0.297822	−	0.241172i	−0.766571	+	0.642160i	$0.778038\pi$
$48$	−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	−0.869271	−	0.494335i	$-0.835412\pi$
$53$	−8.62323	+	3.31015i	−1.18449	+	0.454684i	−0.315220	+	0.949019i	$0.602078\pi$
$54$	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	−0.821464	−	0.570261i	$-0.806842\pi$
$59$	−10.2924	+	2.18773i	−1.33996	+	0.284818i	−0.518498	+	0.855079i	$0.673509\pi$
$60$		0			0
$61$	1.78346	−	8.39053i	0.228349	−	1.07430i	−0.703288	−	0.710905i	$-0.748285\pi$
$61$	1.78346	−	8.39053i	0.228349	−	1.07430i	0.931637	−	0.363391i	$-0.118381\pi$
$62$	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	−0.460648	−	0.887583i	$-0.652383\pi$
$67$	2.55191	−	2.06649i	0.311765	−	0.252462i	0.772413	+	0.635121i	$0.219050\pi$
$68$	−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	−0.218094	−	0.975928i	$-0.569984\pi$
$71$	5.41526	−	3.93442i	0.642673	−	0.466930i	0.860768	+	0.508998i	$0.169984\pi$
$72$	−1.24629	+	1.53904i	−0.146877	+	0.181378i
$73$	−8.26979	+	0.433401i	−0.967906	+	0.0507258i	−0.529733	−	0.848165i	$-0.677708\pi$
$73$	−8.26979	+	0.433401i	−0.967906	+	0.0507258i	−0.438173	+	0.898891i	$0.644374\pi$
$74$	−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	−0.252804	−	0.967517i	$-0.581353\pi$
$79$	−2.65691	+	0.279252i	−0.298926	+	0.0314184i	−0.0461216	+	0.998936i	$0.514686\pi$
$80$		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	0.999993	+	0.00386431i	$0.00123005\pi$
$83$	0.456772	+	2.88395i	0.0501373	+	0.316554i	−0.949855	+	0.312690i	$0.898770\pi$
$84$	−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	0.810595	−	0.585608i	$-0.199144\pi$
$89$	12.3861	+	2.63274i	1.31292	+	0.279070i	0.502327	+	0.864678i	$0.332477\pi$
$90$		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	−0.946316	−	0.323243i	$-0.895227\pi$
$97$	0.527619	−	3.33125i	0.0535716	−	0.338237i	0.999888	−	0.0149946i	$-0.00477310\pi$
$98$	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	−0.617333	−	0.786702i	$-0.711787\pi$
$101$	−2.45915	+	1.41979i	−0.244695	+	0.141275i	0.372638	+	0.927977i	$0.378453\pi$
$102$	−15.7281	+	0.824274i	−1.55731	+	0.0816152i
$103$	4.59308	−	5.67198i	0.452570	−	0.558877i	−0.498884	−	0.866669i	$-0.666257\pi$
$103$	4.59308	−	5.67198i	0.452570	−	0.558877i	0.951454	+	0.307792i	$0.0995900\pi$
$104$	−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	−0.755730	−	0.654883i	$-0.772718\pi$
$107$	−11.2003	+	3.00110i	−1.08277	+	0.290127i	−0.327040	+	0.945011i	$0.606051\pi$
$108$	−1.69678	+	1.37403i	−0.163273	+	0.132216i
$109$	−2.03244	−	9.56186i	−0.194672	−	0.915860i	−0.961670	−	0.274210i	$-0.911584\pi$
$109$	−2.03244	−	9.56186i	−0.194672	−	0.915860i	0.766998	−	0.641650i	$-0.221750\pi$
$110$		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	0.608212	−	0.793775i	$-0.291887\pi$
$113$	−4.16132	−	8.16704i	−0.391464	−	0.768291i	−0.999675	+	0.0254843i	$0.991887\pi$
$114$	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	−0.935197	−	0.354127i	$-0.884778\pi$
$127$	−1.11576	+	2.18980i	−0.0990074	+	0.194313i	0.836190	+	0.548440i	$0.184778\pi$
$128$	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	0.985069	−	0.172159i	$-0.0550742\pi$
$131$	2.26610	+	5.08975i	0.197990	+	0.444693i	−0.787079	+	0.616852i	$0.788408\pi$
$132$	−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	0.827345	−	0.561694i	$-0.189850\pi$
$137$	7.61653	+	4.94623i	0.650724	+	0.422585i	−0.176621	+	0.984279i	$0.556517\pi$
$138$	−0.326769	+	6.23513i	−0.0278165	+	0.530770i
$139$	−5.50579	−	16.9451i	−0.466995	−	1.43726i	−0.856456	−	0.516220i	$-0.827339\pi$
$139$	−5.50579	−	16.9451i	−0.466995	−	1.43726i	0.389461	−	0.921043i	$-0.372661\pi$
$140$		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	0.919445	−	0.393219i	$-0.128638\pi$
$149$	12.6781	+	7.31970i	1.03863	+	0.599653i	0.119185	+	0.992872i	$0.461972\pi$
$150$		0			0
$151$	−8.05257	−	13.9475i	−0.655309	−	1.13503i	−0.981816	−	0.189833i	$-0.939205\pi$
$151$	−8.05257	−	13.9475i	−0.655309	−	1.13503i	0.326508	−	0.945195i	$-0.394128\pi$
$152$	−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	0.420554	−	0.907267i	$-0.361836\pi$
$157$	4.14906	+	1.11174i	0.331131	+	0.0887263i	−0.0894230	+	0.995994i	$0.528502\pi$
$158$	−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	0.638537	−	0.769591i	$-0.279540\pi$
$163$	15.2329	+	0.798321i	1.19313	+	0.0625294i	0.554595	+	0.832121i	$0.312873\pi$
$164$	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	−0.764535	−	0.644583i	$-0.777031\pi$
$167$	−16.7023	+	2.64539i	−1.29246	+	0.204706i	−0.527929	+	0.849289i	$0.677031\pi$
$168$	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	0.976496	+	0.215533i	$0.0691490\pi$
$173$	10.2096	+	15.7214i	0.776219	+	1.19527i	−0.200277	+	0.979739i	$0.564184\pi$
$174$	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	−0.999052	−	0.0435289i	$-0.986140\pi$
$179$	−3.98974	+	8.96111i	−0.298207	+	0.669785i	0.700845	+	0.713314i	$0.252807\pi$
$180$		0			0
$181$	−0.493376	+	0.679074i	−0.0366723	+	0.0504751i	−0.826959	−	0.562262i	$-0.809931\pi$
$181$	−0.493376	+	0.679074i	−0.0366723	+	0.0504751i	0.790287	+	0.612737i	$0.209931\pi$
$182$	−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	0.673670	−	0.739032i	$-0.264717\pi$
$191$	−1.82056	−	2.02194i	−0.131731	−	0.146302i	−0.805401	+	0.592730i	$0.798050\pi$
$192$	6.17693	+	7.62788i	0.445782	+	0.550494i
$193$	6.77095	+	1.81427i	0.487384	+	0.130594i	0.494139	−	0.869383i	$-0.335483\pi$
$193$	6.77095	+	1.81427i	0.487384	+	0.130594i	−0.00675479	+	0.999977i	$0.502150\pi$
$194$	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	−0.388650	−	0.921385i	$-0.627058\pi$
$197$	−14.6392	−	2.31863i	−1.04300	−	0.165195i	−0.654352	+	0.756190i	$0.727058\pi$
$198$	−2.33167	+	1.51421i	−0.165705	+	0.107610i
$199$	10.5072	+	18.1990i	0.744835	+	1.29009i	0.950272	+	0.311422i	$0.100805\pi$
$199$	10.5072	+	18.1990i	0.744835	+	1.29009i	−0.205437	+	0.978670i	$0.565862\pi$
$200$		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	−0.751912	−	0.659263i	$-0.770868\pi$
$211$	−7.71478	−	23.7437i	−0.531108	−	1.63458i	0.220805	−	0.975318i	$-0.429132\pi$
$212$	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	−0.603778	−	0.797153i	$-0.706339\pi$
$223$	5.91390	−	11.6067i	0.396024	−	0.777241i	0.999802	+	0.0199118i	$0.00633854\pi$
$224$	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	−0.998720	−	0.0505884i	$-0.983890\pi$
$227$	−0.162101	−	3.09307i	−0.0107590	−	0.205294i	0.987961	−	0.154706i	$-0.0494430\pi$
$228$	7.10021	−	2.72551i	0.470223	−	0.180502i
$229$	0.0558012	+	0.530913i	0.00368745	+	0.0350837i	0.996211	−	0.0869703i	$-0.0277185\pi$
$229$	0.0558012	+	0.530913i	0.00368745	+	0.0350837i	−0.992523	+	0.122054i	$0.961052\pi$
$230$		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	−0.252266	−	0.967658i	$-0.581176\pi$
$233$	8.89443	−	23.1708i	0.582694	−	1.51797i	0.834960	−	0.550311i	$-0.185491\pi$
$234$	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	−0.984585	−	0.174910i	$-0.944037\pi$
$239$	−25.9462	+	8.43043i	−1.67832	+	0.545320i	−0.693736	+	0.720229i	$0.744037\pi$
$240$		0			0
$241$	−3.97979	−	18.7235i	−0.256361	−	1.20608i	−0.898319	−	0.439344i	$-0.855211\pi$
$241$	−3.97979	−	18.7235i	−0.256361	−	1.20608i	0.641958	−	0.766740i	$-0.278122\pi$
$242$	−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	$-0.923964\pi$
$251$		−	7.49714i		−	0.473215i	0.971605	−	0.236608i	$-0.0760356\pi$
$252$	−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	0.983964	+	0.178369i	$0.0570822\pi$
$257$	3.54307	+	13.2229i	0.221011	+	0.824824i	−0.762953	+	0.646454i	$0.776251\pi$
$258$	−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	−0.340298	−	0.940318i	$-0.610528\pi$
$263$	10.6570	−	16.4103i	0.657137	−	1.01190i	0.997435	−	0.0715841i	$-0.0228054\pi$
$264$	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	−0.924881	−	0.380257i	$-0.875836\pi$
$269$	0.965195	−	9.18322i	0.0588490	−	0.559911i	0.983730	−	0.179654i	$-0.0574978\pi$
$270$		0			0
$271$	1.10014	−	0.115630i	0.0668289	−	0.00702400i	−0.0710550	−	0.997472i	$-0.522637\pi$
$271$	1.10014	−	0.115630i	0.0668289	−	0.00702400i	0.137884	+	0.990448i	$0.455970\pi$
$272$	−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	0.540763	−	0.841175i	$-0.318136\pi$
$277$	19.4143	−	1.01746i	1.16649	−	0.0611331i	0.625727	+	0.780042i	$0.284802\pi$
$278$	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	0.545614	−	0.838036i	$-0.316296\pi$
$281$	−1.38801	−	1.00845i	−0.0828017	−	0.0601589i	−0.628416	+	0.777878i	$0.716296\pi$
$282$	7.88949	−	2.11398i	0.469812	−	0.125886i
$283$	−20.5156	+	16.6132i	−1.21953	+	0.987553i	−0.219598	+	0.975590i	$0.570475\pi$
$283$	−20.5156	+	16.6132i	−1.21953	+	0.987553i	−0.999928	+	0.0119625i	$0.996192\pi$
$284$	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	0.822372	−	0.568950i	$-0.192650\pi$
$293$	4.33790	+	4.33790i	0.253423	+	0.253423i	−0.568950	+	0.822372i	$0.692650\pi$
$294$	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	−0.967925	−	0.251239i	$-0.919162\pi$
$307$	−12.5574	+	12.5574i	−0.716687	+	0.716687i	0.251239	+	0.967925i	$0.419162\pi$
$308$	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	0.792161	−	0.610312i	$-0.208956\pi$
$311$	4.72615	+	4.25544i	0.267995	+	0.241304i	−0.524166	+	0.851616i	$0.675623\pi$
$312$	−8.45761	−	5.49244i	−0.478818	−	0.310948i
$313$	−0.399757	+	7.62782i	−0.0225956	+	0.431150i	0.963786	+	0.266677i	$0.0859257\pi$
$313$	−0.399757	+	7.62782i	−0.0225956	+	0.431150i	−0.986382	+	0.164473i	$0.947408\pi$
$314$	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	−0.0409785	−	0.999160i	$-0.513048\pi$
$317$	−13.1753	−	5.05753i	−0.740000	−	0.284059i	−0.699021	+	0.715101i	$0.746381\pi$
$318$	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	−0.648613	−	0.761118i	$-0.724651\pi$
$331$	−9.40598	+	4.18781i	−0.516999	+	0.230183i	0.131614	+	0.991301i	$0.457984\pi$
$332$	−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	−0.947965	−	0.318375i	$-0.896863\pi$
$337$	−22.9028	+	11.6695i	−1.24759	+	0.635681i	−0.299629	+	0.954056i	$0.596863\pi$
$338$	−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	0.882654	−	0.470023i	$-0.155754\pi$
$347$	−1.63539	−	4.26035i	−0.0877926	−	0.228707i	−0.970447	+	0.241316i	$0.922421\pi$
$348$	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	0.996963	−	0.0778814i	$-0.0248155\pi$
$353$	3.83210	+	9.98297i	0.203962	+	0.531340i	−0.793000	+	0.609221i	$0.791482\pi$
$354$	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	−0.740582	−	0.671966i	$-0.765450\pi$
$359$	−2.83659	+	2.55408i	−0.149710	+	0.134799i	0.590873	+	0.806765i	$0.298784\pi$
$360$		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	0.621808	−	0.783170i	$-0.286399\pi$
$367$	−5.24006	−	6.47094i	−0.273529	−	0.337780i	−0.895337	+	0.445390i	$0.853065\pi$
$368$	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	−0.107557	−	0.994199i	$-0.534303\pi$
$373$	14.6190	−	9.49367i	0.756941	−	0.491563i	0.864498	+	0.502635i	$0.167636\pi$
$374$	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	0.611758	−	0.791045i	$-0.290463\pi$
$379$	−6.41691	−	8.83212i	−0.329614	−	0.453675i	−0.941372	+	0.337370i	$0.890463\pi$
$380$		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	−0.0712062	−	0.997462i	$-0.522685\pi$
$383$	−15.4910	−	5.94645i	−0.791555	−	0.303849i	−0.720349	+	0.693612i	$0.756018\pi$
$384$	−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	0.946456	−	0.322833i	$-0.104635\pi$
$389$	14.2859	+	12.8631i	0.724323	+	0.652183i	−0.222133	+	0.975016i	$0.571302\pi$
$390$		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	0.605300	−	0.795997i	$-0.293053\pi$
$397$	−0.945508	−	0.765657i	−0.0474537	−	0.0384272i	−0.652754	+	0.757570i	$0.726386\pi$
$398$	−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	−0.800710	−	0.599052i	$-0.795544\pi$
$401$	2.37174	−	4.10797i	0.118439	−	0.205142i	0.919149	+	0.393910i	$0.128878\pi$
$402$	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	0.435274	−	0.900298i	$-0.356651\pi$
$409$	24.2503	−	5.15456i	1.19910	−	0.254877i	0.763827	+	0.645421i	$0.223318\pi$
$410$		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	−0.00859807	−	0.999963i	$-0.502737\pi$
$419$	−19.6973	−	14.3109i	−0.962276	−	0.699135i	−0.953678	+	0.300828i	$0.902737\pi$
$420$		0			0
$421$	−6.00083	+	4.35986i	−0.292463	+	0.212486i	−0.724335	−	0.689448i	$-0.757853\pi$
$421$	−6.00083	+	4.35986i	−0.292463	+	0.212486i	0.431872	+	0.901935i	$0.357853\pi$
$422$	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	0.850169	+	0.526511i	$0.176500\pi$
$431$	−1.88691	+	17.9528i	−0.0908895	+	0.864756i	−0.941058	+	0.338245i	$0.890167\pi$
$432$	5.21865	+	19.4763i	0.251082	+	0.937052i
$433$	3.94891	+	24.9324i	0.189773	+	1.19818i	0.880139	+	0.474717i	$0.157449\pi$
$433$	3.94891	+	24.9324i	0.189773	+	1.19818i	−0.690366	+	0.723460i	$0.742551\pi$
$434$	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	0.806282	−	0.591532i	$-0.201477\pi$
$439$	27.2854	+	5.79968i	1.30226	+	0.276804i	0.495977	+	0.868335i	$0.334810\pi$
$440$		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	0.851061	+	0.525066i	$0.175960\pi$
$443$	7.92554	+	29.5785i	0.376554	+	1.40532i	−0.474507	+	0.880252i	$0.657374\pi$
$444$	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	$-0.745121\pi$
$449$		−	30.4224i		−	1.43572i	0.696187	−	0.717861i	$-0.254879\pi$
$450$		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	0.826710	−	0.562628i	$-0.190210\pi$
$457$	38.9922	−	10.4479i	1.82398	−	0.488733i	0.997266	+	0.0738955i	$0.0235431\pi$
$458$	−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	−0.676705	−	0.736255i	$-0.736593\pi$
$461$	−16.9923	+	5.52114i	−0.791411	+	0.257145i	−0.114706	+	0.993399i	$0.536593\pi$
$462$	13.1347	+	11.0048i	0.611080	+	0.511990i
$463$	15.5311	+	30.4814i	0.721790	+	1.41659i	0.901458	+	0.432866i	$0.142498\pi$
$463$	15.5311	+	30.4814i	0.721790	+	1.41659i	−0.179668	+	0.983727i	$0.557502\pi$
$464$	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	−0.977739	−	0.209826i	$-0.932710\pi$
$467$	−2.39302	+	6.23404i	−0.110736	+	0.288477i	0.867003	+	0.498303i	$0.166043\pi$
$468$	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	0.509711	−	0.860346i	$-0.329752\pi$
$479$	4.62700	+	2.06007i	0.211413	+	0.0941271i	−0.298298	+	0.954473i	$0.596419\pi$
$480$		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	0.135464	−	0.990782i	$-0.456748\pi$
$487$	−15.7690	−	10.2405i	−0.714563	−	0.464043i	−0.850027	+	0.526740i	$0.823414\pi$
$488$	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	0.583555	+	0.812073i	$0.301661\pi$
$491$	−8.10726	+	24.9516i	−0.365876	+	1.12605i	−0.949431	+	0.313976i	$0.898339\pi$
$492$	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	0.557446	−	0.830213i	$-0.311781\pi$
$499$	2.61768	+	1.51132i	0.117183	+	0.0676558i	−0.440263	+	0.897869i	$0.645115\pi$
$500$		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	−0.160396	−	0.987053i	$-0.551277\pi$
$503$	−13.8594	−	2.19511i	−0.617958	−	0.0978750i	−0.457562	+	0.889178i	$0.651277\pi$
$504$	−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	0.306028	−	0.952023i	$-0.401000\pi$
$509$	−15.1783	−	16.8573i	−0.672768	−	0.747185i	−0.978796	+	0.204838i	$0.934333\pi$
$510$		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	−0.0166856	+	0.999861i	$0.505311\pi$
$521$	−17.0862	+	38.3763i	−0.748562	+	1.68130i	−0.731877	+	0.681437i	$0.761355\pi$
$522$	3.35671	+	8.74454i	0.146919	+	0.382738i
$523$	−14.3920	−	22.1618i	−0.629320	−	0.969068i	−0.999200	−	0.0399883i	$-0.987268\pi$
$523$	−14.3920	−	22.1618i	−0.629320	−	0.969068i	0.369880	−	0.929079i	$-0.379399\pi$
$524$	−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	0.667553	−	0.744562i	$-0.267342\pi$
$541$	−3.31932	−	3.68648i	−0.142709	−	0.158494i	−0.810262	+	0.586068i	$0.800675\pi$
$542$	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	0.512582	−	0.858638i	$-0.328689\pi$
$547$	17.1842	+	2.72171i	0.734743	+	0.116372i	0.222161	+	0.975010i	$0.428689\pi$
$548$	−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	−0.999615	−	0.0277296i	$-0.991172\pi$
$557$	−2.83348	+	10.5747i	−0.120058	+	0.448064i	0.879557	+	0.475793i	$0.157839\pi$
$558$	−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	0.579368	−	0.815066i	$-0.303299\pi$
$563$	1.67086	+	1.08507i	0.0704183	+	0.0457302i	−0.508950	+	0.860796i	$0.669966\pi$
$564$	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	0.950959	+	0.309318i	$0.100101\pi$
$569$	12.9886	+	29.1729i	0.544511	+	1.22299i	−0.406447	+	0.913674i	$0.633232\pi$
$570$		0			0
$571$	−13.4872	−	6.00488i	−0.564421	−	0.251297i	0.104632	−	0.994511i	$-0.466634\pi$
$571$	−13.4872	−	6.00488i	−0.564421	−	0.251297i	−0.669053	+	0.743214i	$0.733300\pi$
$572$	−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	−0.993107	−	0.117209i	$-0.962605\pi$
$577$	−0.424978	−	8.10906i	−0.0176921	−	0.337585i	0.975415	−	0.220375i	$-0.0707282\pi$
$578$	−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	0.816303	−	0.577624i	$-0.196020\pi$
$587$	−3.16940	−	6.22031i	−0.130815	−	0.256739i	−0.947118	+	0.320884i	$0.896020\pi$
$588$	−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	−0.422989	−	0.906135i	$-0.639019\pi$
$593$	−8.18799	+	2.19397i	−0.336240	+	0.0900954i	0.0867484	+	0.996230i	$0.472352\pi$
$594$	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	−0.0141183	−	0.999900i	$-0.504494\pi$
$599$	20.6751	−	11.9368i	0.844762	−	0.487723i	0.858880	+	0.512177i	$0.171161\pi$
$600$		0			0
$601$		−	9.32470i		−	0.380362i	−0.981749	−	0.190181i	$-0.939092\pi$
$601$		−	9.32470i		−	0.380362i	0.981749	−	0.190181i	$-0.0609075\pi$
$602$	−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	0.978517	+	0.206167i	$0.0660989\pi$
$607$	5.76957	+	21.5323i	0.234180	+	0.873971i	−0.744337	+	0.667804i	$0.767234\pi$
$608$	−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	−0.989356	−	0.145516i	$-0.953516\pi$
$613$	−11.2408	+	17.3094i	−0.454013	+	0.699118i	0.535343	+	0.844635i	$0.320182\pi$
$614$	−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	0.996013	+	0.0892079i	$0.0284335\pi$
$617$	1.89563	+	11.9685i	0.0763151	+	0.481835i	−0.919698	+	0.392627i	$0.871566\pi$
$618$	5.87259	+	21.9168i	0.236230	+	0.881624i
$619$	1.68698	−	16.0505i	0.0678054	−	0.645125i	−0.906856	−	0.421440i	$-0.861525\pi$
$619$	1.68698	−	16.0505i	0.0678054	−	0.645125i	0.974662	−	0.223685i	$-0.0718086\pi$
$620$		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	0.999797	−	0.0201409i	$-0.00641148\pi$
$631$	32.3943	+	23.5358i	1.28960	+	0.936947i	0.289799	+	0.957087i	$0.406411\pi$
$632$	−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	0.570406	−	0.821363i	$-0.306786\pi$
$641$	36.0927	−	7.67174i	1.42558	−	0.303015i	0.855170	+	0.518348i	$0.173453\pi$
$642$	12.9186	−	33.6541i	0.509856	−	1.32822i
$643$	−15.3835	−	15.3835i	−0.606667	−	0.606667i	0.335406	−	0.942074i	$-0.391126\pi$
$643$	−15.3835	−	15.3835i	−0.606667	−	0.606667i	−0.942074	+	0.335406i	$0.891126\pi$
$644$	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	−0.904747	−	0.425949i	$-0.859940\pi$
$647$	−32.8659	+	12.6160i	−1.29209	+	0.495987i	−0.387343	+	0.921936i	$0.626607\pi$
$648$	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	0.971723	−	0.236122i	$-0.0758765\pi$
$653$	24.0920	+	19.5093i	0.942794	+	0.763459i	−0.0289295	+	0.999581i	$0.509210\pi$
$654$	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	0.437613	−	0.899163i	$-0.355824\pi$
$659$	6.75492	+	2.19481i	0.263134	+	0.0854976i	−0.174479	+	0.984661i	$0.555824\pi$
$660$		0			0
$661$	3.56987	+	3.21432i	0.138852	+	0.125023i	0.735630	−	0.677383i	$-0.236886\pi$
$661$	3.56987	+	3.21432i	0.138852	+	0.125023i	−0.596778	+	0.802406i	$0.703553\pi$
$662$	−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	0.665231	−	0.746638i	$-0.268333\pi$
$673$	11.7311	+	5.97729i	0.452201	+	0.230408i	−0.213030	+	0.977046i	$0.568333\pi$
$674$	−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	−0.541134	+	0.840937i	$0.682005\pi$
$677$	−39.7955	+	25.8435i	−1.52947	+	0.993247i	−0.988333	+	0.152311i	$0.951329\pi$
$678$	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	0.945355	−	0.326043i	$-0.105716\pi$
$683$	11.2348	+	13.8738i	0.429886	+	0.530865i	−0.515469	+	0.856908i	$0.672382\pi$
$684$	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	−0.772819	−	0.634626i	$-0.781154\pi$
$691$	−5.84754	+	5.26515i	−0.222451	+	0.200296i	0.550368	+	0.834922i	$0.314487\pi$
$692$	−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	−0.628104	−	0.778129i	$-0.716169\pi$
$709$	2.13303	−	1.92059i	0.0801077	−	0.0721293i	0.708212	+	0.706000i	$0.249502\pi$
$710$		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	−0.307696	−	0.951485i	$-0.599558\pi$
$719$	5.18872	−	2.31017i	0.193507	−	0.0861547i	0.501202	+	0.865330i	$0.332891\pi$
$720$		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	0.976988	−	0.213294i	$-0.0684191\pi$
$727$	37.1735	+	18.9408i	1.37869	+	0.702477i	0.401701	+	0.915771i	$0.368419\pi$
$728$	−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	0.871996	−	0.489513i	$-0.162825\pi$
$733$	32.2848	+	12.3930i	1.19247	+	0.457745i	0.320471	+	0.947258i	$0.396159\pi$
$734$	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	0.774919	−	0.632061i	$-0.217791\pi$
$739$	6.17964	+	5.56417i	0.227322	+	0.204681i	−0.547597	+	0.836742i	$0.684457\pi$
$740$		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	−0.866855	−	0.498560i	$-0.833862\pi$
$743$	−10.0390	+	10.0390i	−0.368295	+	0.368295i	0.498560	+	0.866855i	$0.333862\pi$
$744$	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	−0.227365	−	0.973810i	$-0.573011\pi$
$751$	19.9959	−	34.6339i	0.729661	−	1.26381i	0.957026	−	0.290000i	$-0.0936555\pi$
$752$	−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	0.449828	−	0.893115i	$-0.351485\pi$
$757$	−12.1964	−	12.1964i	−0.443287	−	0.443287i	−0.893115	+	0.449828i	$0.851485\pi$
$758$	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	−0.999636	−	0.0269835i	$-0.991410\pi$
$761$	−2.08132	+	9.79185i	−0.0754479	+	0.354954i	0.924188	+	0.381938i	$0.124743\pi$
$762$	−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	−0.222034	−	0.975039i	$-0.571270\pi$
$769$	−33.7752	−	24.5391i	−1.21796	−	0.884902i	−0.995929	+	0.0901368i	$0.971270\pi$
$770$		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	−0.558158	−	0.829735i	$-0.688492\pi$
$773$	−28.5404	+	1.49574i	−1.02653	+	0.0537980i	−0.468370	+	0.883533i	$0.655158\pi$
$774$	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	−0.325800	−	0.945439i	$-0.605634\pi$
$787$	18.8075	−	28.9611i	0.670416	−	1.03235i	0.996216	−	0.0869114i	$-0.0276997\pi$
$788$	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	−0.417172	−	0.908828i	$-0.636979\pi$
$797$	7.35212	−	46.4194i	0.260425	−	1.64426i	0.677597	−	0.735433i	$-0.263021\pi$
$798$	−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	−0.922176	−	0.386770i	$-0.873591\pi$
$809$	−6.74211	−	31.7191i	−0.237040	−	1.11519i	0.685136	−	0.728415i	$-0.259743\pi$
$810$		0			0
$811$	8.85993	−	2.87877i	0.311114	−	0.101087i	−0.149298	−	0.988792i	$-0.547701\pi$
$811$	8.85993	−	2.87877i	0.311114	−	0.101087i	0.460413	+	0.887705i	$0.347701\pi$
$812$	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	0.824366	+	0.566058i	$0.191532\pi$
$821$	3.88835	+	36.9952i	0.135704	+	1.29114i	−0.688661	+	0.725083i	$0.741801\pi$
$822$	−26.3584	+	10.1180i	−0.919354	+	0.352907i
$823$	1.56075	+	29.7808i	0.0544042	+	1.03809i	0.880344	+	0.474335i	$0.157312\pi$
$823$	1.56075	+	29.7808i	0.0544042	+	1.03809i	−0.825940	+	0.563758i	$0.809355\pi$
$824$	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	0.541543	+	0.840673i	$0.317840\pi$
$827$	−13.1390	+	25.7867i	−0.456887	+	0.896691i	−0.998430	+	0.0560176i	$0.982160\pi$
$828$	−0.677656	−	0.548755i	−0.0235502	−	0.0190706i
$829$	8.61441	+	3.83538i	0.299191	+	0.133208i	0.550842	−	0.834610i	$-0.314307\pi$
$829$	8.61441	+	3.83538i	0.299191	+	0.133208i	−0.251651	+	0.967818i	$0.580973\pi$
$830$		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	−0.604101	−	0.796907i	$-0.706468\pi$
$839$	−16.9096	−	52.0423i	−0.583784	−	1.79670i	0.0203179	−	0.999794i	$-0.493532\pi$
$840$		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	0.999970	+	0.00773601i	$0.00246247\pi$
$853$	57.0510	+	9.03599i	1.95339	+	0.309386i	0.953419	+	0.301650i	$0.0975375\pi$
$854$	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	0.483674	−	0.875248i	$-0.339302\pi$
$857$	13.6104	+	3.64690i	0.464923	+	0.124576i	−0.0187505	+	0.999824i	$0.505969\pi$
$858$	−8.90958	−	11.0024i	−0.304168	−	0.375616i
$859$	−14.0269	−	15.5785i	−0.478592	−	0.531530i	0.454702	−	0.890644i	$-0.349746\pi$
$859$	−14.0269	−	15.5785i	−0.478592	−	0.531530i	−0.933294	+	0.359113i	$0.883079\pi$
$860$		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	0.310490	−	0.950577i	$-0.399507\pi$
$863$	15.2735	+	0.800451i	0.519916	+	0.0272477i	0.209427	+	0.977824i	$0.432840\pi$
$864$	−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	0.673824	−	0.738892i	$-0.264650\pi$
$877$	−8.15148	−	12.5522i	−0.275256	−	0.423857i	−0.949080	+	0.315035i	$0.897984\pi$
$878$	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	−0.604967	−	0.796250i	$-0.706814\pi$
$881$	10.0697	−	13.8597i	0.339257	−	0.466947i	0.944224	+	0.329303i	$0.106814\pi$
$882$	−4.51692	+	8.17714i	−0.152093	+	0.275339i
$883$	−26.9691	+	4.27148i	−0.907581	+	0.143747i	−0.592736	−	0.805397i	$-0.701952\pi$
$883$	−26.9691	+	4.27148i	−0.907581	+	0.143747i	−0.314845	+	0.949143i	$0.601952\pi$
$884$	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	0.576216	−	0.817298i	$-0.304529\pi$
$887$	31.6840	+	1.66049i	1.06384	+	0.0557537i	0.487628	+	0.873051i	$0.337862\pi$
$888$	−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	−0.888916	−	0.458071i	$-0.848541\pi$
$907$	3.31110	−	12.3572i	0.109943	−	0.410314i	0.998859	+	0.0477567i	$0.0152072\pi$
$908$	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	0.892089	−	0.451860i	$-0.149239\pi$
$911$	−2.87409	−	8.84554i	−0.0952228	−	0.293066i	−0.987312	+	0.158794i	$0.949239\pi$
$912$	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	0.871369	+	0.490629i	$0.163233\pi$
$919$	19.7932	+	44.4563i	0.652917	+	1.46648i	−0.218451	+	0.975848i	$0.570101\pi$
$920$		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	0.993682	−	0.112229i	$-0.0357991\pi$
$929$	−0.0493594	−	0.469623i	−0.00161943	−	0.0154078i	−0.995302	+	0.0968214i	$0.969132\pi$
$930$		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	−0.991514	−	0.130002i	$-0.958502\pi$
$937$	−15.7304	−	30.8727i	−0.513890	−	1.00857i	0.477624	−	0.878565i	$-0.341498\pi$
$938$	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	0.999671	−	0.0256647i	$-0.00817023\pi$
$941$	2.33096	+	10.9663i	0.0759873	+	0.357492i	−0.923683	+	0.383157i	$0.874837\pi$
$942$	−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	−0.303139	+	0.952946i	$0.598035\pi$
$947$	−36.0736	+	44.5472i	−1.17224	+	1.44759i	−0.869096	+	0.494644i	$0.835299\pi$
$948$	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	−0.904357	−	0.426777i	$-0.859649\pi$
$953$	2.70486	−	17.0778i	0.0876189	−	0.553204i	0.991976	−	0.126427i	$-0.0403510\pi$
$954$	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	0.997400	+	0.0720662i	$0.0229593\pi$
$967$	2.21053	+	13.9567i	0.0710859	+	0.448819i	−0.926314	+	0.376753i	$0.877041\pi$
$968$	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	−0.269328	−	0.963048i	$-0.586802\pi$
$971$	−10.3623	+	1.08912i	−0.332542	+	0.0349516i	−0.0632139	+	0.998000i	$0.520135\pi$
$972$	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	0.350025	−	0.936740i	$-0.386173\pi$
$977$	24.8821	−	1.30401i	0.796048	−	0.0417191i	0.446023	+	0.895021i	$0.352840\pi$
$978$	−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	−0.763145	−	0.646227i	$-0.776346\pi$
$983$	−9.08311	+	7.35536i	−0.289706	+	0.234600i	0.473439	+	0.880827i	$0.343013\pi$
$984$	−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	−0.0372721	−	0.999305i	$-0.511867\pi$
$991$	10.5500	−	2.24247i	0.335132	−	0.0712345i	0.372404	+	0.928071i	$0.378533\pi$
$992$	−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	−0.168296	−	0.985737i	$-0.553826\pi$
$997$	11.5636	−	4.43884i	0.366222	−	0.140580i	0.534518	+	0.845157i	$0.320493\pi$
$998$	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.607.14		288
5.2	odd	4		875.2.bb.b.768.5		288
5.3	odd	4		875.2.bb.a.768.14		288
5.4	even	2		175.2.x.a.117.5	yes	288
7.3	odd	6	inner	875.2.bb.c.857.5		288
25.3	odd	20	inner	875.2.bb.c.243.5		288
25.4	even	10		875.2.bb.b.257.5		288
25.21	even	5		875.2.bb.a.257.14		288
25.22	odd	20		175.2.x.a.103.14	yes	288
35.3	even	12		875.2.bb.a.143.14		288
35.17	even	12		875.2.bb.b.143.5		288
35.24	odd	6		175.2.x.a.17.14	yes	288
175.3	even	60	inner	875.2.bb.c.493.14		288
175.122	even	60		175.2.x.a.3.5	✓	288
175.129	odd	30		875.2.bb.b.507.5		288
175.171	odd	30		875.2.bb.a.507.14		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.5	✓	288	175.122	even	60
175.2.x.a.17.14	yes	288	35.24	odd	6
175.2.x.a.103.14	yes	288	25.22	odd	20
175.2.x.a.117.5	yes	288	5.4	even	2
875.2.bb.a.143.14		288	35.3	even	12
875.2.bb.a.257.14		288	25.21	even	5
875.2.bb.a.507.14		288	175.171	odd	30
875.2.bb.a.768.14		288	5.3	odd	4
875.2.bb.b.143.5		288	35.17	even	12
875.2.bb.b.257.5		288	25.4	even	10
875.2.bb.b.507.5		288	175.129	odd	30
875.2.bb.b.768.5		288	5.2	odd	4
875.2.bb.c.243.5		288	25.3	odd	20	inner
875.2.bb.c.493.14		288	175.3	even	60	inner
875.2.bb.c.607.14		288	1.1	even	1	trivial
875.2.bb.c.857.5		288	7.3	odd	6	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

Related objects

Downloads

Learn more