LMFDB - Embedded newform 680.2.ba.b.21.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(21,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.21"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.ba (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [140] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$70$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.12
Character	$\chi$	$=$	680.21
Dual form			680.2.ba.b.421.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21931 - 0.716444i) q^{2} +(1.45367 + 1.45367i) q^{3} +(0.973417 + 1.74713i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.730995 - 2.81394i) q^{6} +(2.29587 + 2.29587i) q^{7} +(0.0648259 - 2.82768i) q^{8} +1.22630i q^{9} +(0.355578 + 1.36878i) q^{10} +(-1.09460 + 1.09460i) q^{11} +(-1.12472 + 3.95477i) q^{12} +4.71671i q^{13} +(-1.15451 - 4.44422i) q^{14} -2.05580i q^{15} +(-2.10492 + 3.40137i) q^{16} +(3.97639 + 1.09009i) q^{17} +(0.878574 - 1.49523i) q^{18} -0.745881 q^{19} +(0.547097 - 1.92372i) q^{20} +6.67485i q^{21} +(2.11887 - 0.550434i) q^{22} +(-4.07696 - 4.07696i) q^{23} +(4.20475 - 4.01628i) q^{24} +1.00000i q^{25} +(3.37925 - 5.75111i) q^{26} +(2.57837 - 2.57837i) q^{27} +(-1.77634 + 6.24601i) q^{28} +(1.12764 + 1.12764i) q^{29} +(-1.47286 + 2.50665i) q^{30} +(-2.80824 + 2.80824i) q^{31} +(5.00343 - 2.63926i) q^{32} -3.18237 q^{33} +(-4.06746 - 4.17801i) q^{34} -3.24684i q^{35} +(-2.14250 + 1.19370i) q^{36} +(1.26731 + 1.26731i) q^{37} +(0.909458 + 0.534382i) q^{38} +(-6.85652 + 6.85652i) q^{39} +(-2.04531 + 1.95364i) q^{40} +(7.84093 + 7.84093i) q^{41} +(4.78215 - 8.13869i) q^{42} -0.369903 q^{43} +(-2.97791 - 0.846905i) q^{44} +(0.867124 - 0.867124i) q^{45} +(2.05015 + 7.89198i) q^{46} -4.80980 q^{47} +(-8.00431 + 1.88461i) q^{48} +3.54199i q^{49} +(0.716444 - 1.21931i) q^{50} +(4.19573 + 7.36498i) q^{51} +(-8.24069 + 4.59132i) q^{52} -4.20348 q^{53} +(-4.99108 + 1.29657i) q^{54} +1.54800 q^{55} +(6.64081 - 6.34315i) q^{56} +(-1.08426 - 1.08426i) q^{57} +(-0.567048 - 2.18283i) q^{58} +1.36323 q^{59} +(3.59174 - 2.00115i) q^{60} +(-6.16035 + 6.16035i) q^{61} +(5.43606 - 1.41216i) q^{62} +(-2.81542 + 2.81542i) q^{63} +(-7.99160 - 0.366615i) q^{64} +(3.33522 - 3.33522i) q^{65} +(3.88028 + 2.27999i) q^{66} -2.67648i q^{67} +(1.96617 + 8.00838i) q^{68} -11.8531i q^{69} +(-2.32618 + 3.95890i) q^{70} +(-5.28414 + 5.28414i) q^{71} +(3.46758 + 0.0794959i) q^{72} +(3.29661 - 3.29661i) q^{73} +(-0.637284 - 2.45320i) q^{74} +(-1.45367 + 1.45367i) q^{75} +(-0.726053 - 1.30315i) q^{76} -5.02611 q^{77} +(13.2725 - 3.44789i) q^{78} +(7.71039 + 7.71039i) q^{79} +(3.89353 - 0.916729i) q^{80} +11.1751 q^{81} +(-3.94291 - 15.1781i) q^{82} +11.2746 q^{83} +(-11.6618 + 6.49741i) q^{84} +(-2.04093 - 3.58254i) q^{85} +(0.451026 + 0.265015i) q^{86} +3.27843i q^{87} +(3.02422 + 3.16614i) q^{88} +4.31221 q^{89} +(-1.67854 + 0.436044i) q^{90} +(-10.8289 + 10.8289i) q^{91} +(3.15440 - 11.0916i) q^{92} -8.16450 q^{93} +(5.86462 + 3.44595i) q^{94} +(0.527418 + 0.527418i) q^{95} +(11.1099 + 3.43672i) q^{96} +(11.3656 - 11.3656i) q^{97} +(2.53764 - 4.31877i) q^{98} +(-1.34231 - 1.34231i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 8 q^{4} - 4 q^{6} - 12 q^{7} + 20 q^{12} + 28 q^{14} - 24 q^{16} - 16 q^{17} - 8 q^{20} + 40 q^{22} + 4 q^{23} + 48 q^{24} - 20 q^{28} + 28 q^{31} - 8 q^{34} - 56 q^{38} + 24 q^{40} + 44 q^{41}+ \cdots + 176 q^{98}+O(q^{100}) $ 140 * q - 8 * q^4 - 4 * q^6 - 12 * q^7 + 20 * q^12 + 28 * q^14 - 24 * q^16 - 16 * q^17 - 8 * q^20 + 40 * q^22 + 4 * q^23 + 48 * q^24 - 20 * q^28 + 28 * q^31 - 8 * q^34 - 56 * q^38 + 24 * q^40 + 44 * q^41 + 28 * q^44 - 40 * q^46 - 120 * q^47 + 32 * q^48 - 48 * q^52 - 4 * q^54 + 16 * q^55 + 16 * q^56 - 16 * q^57 - 52 * q^58 - 72 * q^62 + 44 * q^63 - 104 * q^64 + 8 * q^68 + 12 * q^71 - 104 * q^72 + 36 * q^73 + 20 * q^74 + 28 * q^78 - 44 * q^79 - 76 * q^81 - 44 * q^82 + 48 * q^84 + 120 * q^86 + 28 * q^88 + 24 * q^89 + 28 * q^90 - 72 * q^92 + 8 * q^95 - 116 * q^96 + 12 * q^97 + 176 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.21931	−	0.716444i	−0.862180	−	0.506602i
$2$	−1.21931	−	0.716444i	−0.862180	−	0.506602i
$3$	1.45367	+	1.45367i	0.839275	+	0.839275i	0.988764	−	0.149488i	$-0.0477626\pi$
$3$	1.45367	+	1.45367i	0.839275	+	0.839275i	−0.149488	+	0.988764i	$0.547763\pi$
$4$	0.973417	+	1.74713i	0.486708	+	0.873564i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	−0.730995	−	2.81394i	−0.298428	−	1.14879i
$7$	2.29587	+	2.29587i	0.867755	+	0.867755i	0.992224	−	0.124468i	$-0.0397225\pi$
$7$	2.29587	+	2.29587i	0.867755	+	0.867755i	−0.124468	+	0.992224i	$0.539722\pi$
$8$	0.0648259	−	2.82768i	0.0229194	−	0.999737i
$9$			1.22630i			0.408766i
$10$	0.355578	+	1.36878i	0.112444	+	0.432847i
$11$	−1.09460	+	1.09460i	−0.330034	+	0.330034i	−0.852599	−	0.522565i	$-0.824975\pi$
$11$	−1.09460	+	1.09460i	−0.330034	+	0.330034i	0.522565	+	0.852599i	$0.324975\pi$
$12$	−1.12472	+	3.95477i	−0.324679	+	1.14164i
$13$			4.71671i			1.30818i	0.756417	+	0.654090i	$0.226948\pi$
$13$			4.71671i			1.30818i	−0.756417	+	0.654090i	$0.773052\pi$
$14$	−1.15451	−	4.44422i	−0.308555	−	1.18777i
$15$		−	2.05580i		−	0.530804i
$16$	−2.10492	+	3.40137i	−0.526230	+	0.850342i
$17$	3.97639	+	1.09009i	0.964417	+	0.264384i
$17$	3.97639	+	1.09009i	0.964417	+	0.264384i
$18$	0.878574	−	1.49523i	0.207082	−	0.352430i
$19$	−0.745881			−0.171117			−0.0855585	−	0.996333i	$-0.527267\pi$
$19$	−0.745881			−0.171117			−0.0855585	+	0.996333i	$0.527267\pi$
$20$	0.547097	−	1.92372i	0.122335	−	0.430156i
$21$			6.67485i			1.45657i
$22$	2.11887	−	0.550434i	0.451745	−	0.117353i
$23$	−4.07696	−	4.07696i	−0.850106	−	0.850106i	0.140040	−	0.990146i	$-0.455277\pi$
$23$	−4.07696	−	4.07696i	−0.850106	−	0.850106i	−0.990146	+	0.140040i	$0.955277\pi$
$24$	4.20475	−	4.01628i	0.858291	−	0.819819i
$25$			1.00000i			0.200000i
$26$	3.37925	−	5.75111i	0.662726	−	1.12789i
$27$	2.57837	−	2.57837i	0.496208	−	0.496208i
$28$	−1.77634	+	6.24601i	−0.335696	+	1.18038i
$29$	1.12764	+	1.12764i	0.209397	+	0.209397i	0.804011	−	0.594614i	$-0.202695\pi$
$29$	1.12764	+	1.12764i	0.209397	+	0.209397i	−0.594614	+	0.804011i	$0.702695\pi$
$30$	−1.47286	+	2.50665i	−0.268907	+	0.457649i
$31$	−2.80824	+	2.80824i	−0.504375	+	0.504375i	−0.912795	−	0.408419i	$-0.866080\pi$
$31$	−2.80824	+	2.80824i	−0.504375	+	0.504375i	0.408419	+	0.912795i	$0.366080\pi$
$32$	5.00343	−	2.63926i	0.884490	−	0.466559i
$33$	−3.18237			−0.553979
$34$	−4.06746	−	4.17801i	−0.697564	−	0.716523i
$35$		−	3.24684i		−	0.548817i
$36$	−2.14250	+	1.19370i	−0.357084	+	0.198950i
$37$	1.26731	+	1.26731i	0.208345	+	0.208345i	0.803564	−	0.595219i	$-0.202935\pi$
$37$	1.26731	+	1.26731i	0.208345	+	0.208345i	−0.595219	+	0.803564i	$0.702935\pi$
$38$	0.909458	+	0.534382i	0.147534	+	0.0866882i
$39$	−6.85652	+	6.85652i	−1.09792	+	1.09792i
$40$	−2.04531	+	1.95364i	−0.323392	+	0.308897i
$41$	7.84093	+	7.84093i	1.22455	+	1.22455i	0.965998	+	0.258549i	$0.0832445\pi$
$41$	7.84093	+	7.84093i	1.22455	+	1.22455i	0.258549	+	0.965998i	$0.416756\pi$
$42$	4.78215	−	8.13869i	0.737902	−	1.25583i
$43$	−0.369903			−0.0564097			−0.0282049	−	0.999602i	$-0.508979\pi$
$43$	−0.369903			−0.0564097			−0.0282049	+	0.999602i	$0.508979\pi$
$44$	−2.97791	−	0.846905i	−0.448937	−	0.127676i
$45$	0.867124	−	0.867124i	0.129263	−	0.129263i
$46$	2.05015	+	7.89198i	0.302279	+	1.16361i
$47$	−4.80980			−0.701581			−0.350790	−	0.936454i	$-0.614087\pi$
$47$	−4.80980			−0.701581			−0.350790	+	0.936454i	$0.614087\pi$
$48$	−8.00431	+	1.88461i	−1.15532	+	0.272020i
$49$			3.54199i			0.505999i
$50$	0.716444	−	1.21931i	0.101320	−	0.172436i
$51$	4.19573	+	7.36498i	0.587520	+	1.03130i
$52$	−8.24069	+	4.59132i	−1.14278	+	0.636702i
$53$	−4.20348			−0.577392			−0.288696	−	0.957421i	$-0.593222\pi$
$53$	−4.20348			−0.577392			−0.288696	+	0.957421i	$0.593222\pi$
$54$	−4.99108	+	1.29657i	−0.679201	+	0.176441i
$55$	1.54800			0.208732
$56$	6.64081	−	6.34315i	0.887416	−	0.847639i
$57$	−1.08426	−	1.08426i	−0.143614	−	0.143614i
$58$	−0.567048	−	2.18283i	−0.0744571	−	0.286620i
$59$	1.36323			0.177477			0.0887387	−	0.996055i	$-0.471716\pi$
$59$	1.36323			0.177477			0.0887387	+	0.996055i	$0.471716\pi$
$60$	3.59174	−	2.00115i	0.463692	−	0.258347i
$61$	−6.16035	+	6.16035i	−0.788752	+	0.788752i	−0.981290	−	0.192538i	$-0.938328\pi$
$61$	−6.16035	+	6.16035i	−0.788752	+	0.788752i	0.192538	+	0.981290i	$0.438328\pi$
$62$	5.43606	−	1.41216i	0.690380	−	0.179345i
$63$	−2.81542	+	2.81542i	−0.354709	+	0.354709i
$64$	−7.99160	−	0.366615i	−0.998949	−	0.0458268i
$65$	3.33522	−	3.33522i	0.413683	−	0.413683i
$66$	3.88028	+	2.27999i	0.477630	+	0.280647i
$67$		−	2.67648i		−	0.326984i	−0.986545	−	0.163492i	$-0.947724\pi$
$67$		−	2.67648i		−	0.326984i	0.986545	−	0.163492i	$-0.0522758\pi$
$68$	1.96617	+	8.00838i	0.238433	+	0.971159i
$69$		−	11.8531i		−	1.42695i
$70$	−2.32618	+	3.95890i	−0.278032	+	0.473179i
$71$	−5.28414	+	5.28414i	−0.627112	+	0.627112i	−0.947340	−	0.320228i	$-0.896240\pi$
$71$	−5.28414	+	5.28414i	−0.627112	+	0.627112i	0.320228	+	0.947340i	$0.396240\pi$
$72$	3.46758	+	0.0794959i	0.408659	+	0.00936869i
$73$	3.29661	−	3.29661i	0.385839	−	0.385839i	−0.487362	−	0.873200i	$-0.662041\pi$
$73$	3.29661	−	3.29661i	0.385839	−	0.385839i	0.873200	+	0.487362i	$0.162041\pi$
$74$	−0.637284	−	2.45320i	−0.0740827	−	0.285178i
$75$	−1.45367	+	1.45367i	−0.167855	+	0.167855i
$76$	−0.726053	−	1.30315i	−0.0832840	−	0.149482i
$77$	−5.02611			−0.572778
$78$	13.2725	−	3.44789i	1.50282	−	0.390397i
$79$	7.71039	+	7.71039i	0.867487	+	0.867487i	0.992194	−	0.124707i	$-0.0397989\pi$
$79$	7.71039	+	7.71039i	0.867487	+	0.867487i	−0.124707	+	0.992194i	$0.539799\pi$
$80$	3.89353	−	0.916729i	0.435310	−	0.102493i
$81$	11.1751			1.24168
$82$	−3.94291	−	15.1781i	−0.435422	−	1.67614i
$83$	11.2746			1.23755			0.618775	−	0.785568i	$-0.287629\pi$
$83$	11.2746			1.23755			0.618775	+	0.785568i	$0.287629\pi$
$84$	−11.6618	+	6.49741i	−1.27241	+	0.708926i
$85$	−2.04093	−	3.58254i	−0.221370	−	0.388581i
$86$	0.451026	+	0.265015i	0.0486353	+	0.0285773i
$87$			3.27843i			0.351484i
$88$	3.02422	+	3.16614i	0.322383	+	0.337512i
$89$	4.31221			0.457093			0.228547	−	0.973533i	$-0.426603\pi$
$89$	4.31221			0.457093			0.228547	+	0.973533i	$0.426603\pi$
$90$	−1.67854	+	0.436044i	−0.176933	+	0.0459631i
$91$	−10.8289	+	10.8289i	−1.13518	+	1.13518i
$92$	3.15440	−	11.0916i	0.328868	−	1.15638i
$93$	−8.16450			−0.846620
$94$	5.86462	+	3.44595i	0.604889	+	0.355422i
$95$	0.527418	+	0.527418i	0.0541119	+	0.0541119i
$96$	11.1099	+	3.43672i	1.13390	+	0.350759i
$97$	11.3656	−	11.3656i	1.15400	−	1.15400i	0.168259	−	0.985743i	$-0.446186\pi$
$97$	11.3656	−	11.3656i	1.15400	−	1.15400i	0.985743	−	0.168259i	$-0.0538145\pi$
$98$	2.53764	−	4.31877i	0.256340	−	0.436262i
$99$	−1.34231	−	1.34231i	−0.134907	−	0.134907i
$100$	−1.74713	+	0.973417i	−0.174713	+	0.0973417i
$101$		−	9.80713i		−	0.975846i	−0.872887	−	0.487923i	$-0.837755\pi$
$101$		−	9.80713i		−	0.975846i	0.872887	−	0.487923i	$-0.162245\pi$
$102$	0.160705	−	11.9862i	0.0159121	−	1.18681i
$103$	3.32933			0.328048			0.164024	−	0.986456i	$-0.447553\pi$
$103$	3.32933			0.328048			0.164024	+	0.986456i	$0.447553\pi$
$104$	13.3374	+	0.305765i	1.30784	+	0.0299827i
$105$	4.71983	−	4.71983i	0.460608	−	0.460608i
$106$	5.12532	+	3.01155i	0.497816	+	0.292508i
$107$	−6.90166	−	6.90166i	−0.667208	−	0.667208i	0.289860	−	0.957069i	$-0.406391\pi$
$107$	−6.90166	−	6.90166i	−0.667208	−	0.667208i	−0.957069	+	0.289860i	$0.906391\pi$
$108$	7.01458	+	1.99492i	0.674978	+	0.191961i
$109$	5.76662	−	5.76662i	0.552342	−	0.552342i	−0.374774	−	0.927116i	$-0.622280\pi$
$109$	5.76662	−	5.76662i	0.552342	−	0.552342i	0.927116	+	0.374774i	$0.122280\pi$
$110$	−1.88748	−	1.10905i	−0.179965	−	0.105744i
$111$			3.68450i			0.349717i
$112$	−12.6417	+	2.97648i	−1.19453	+	0.281250i
$113$	5.00131	+	5.00131i	0.470484	+	0.470484i	0.902071	−	0.431587i	$-0.142046\pi$
$113$	5.00131	+	5.00131i	0.470484	+	0.470484i	−0.431587	+	0.902071i	$0.642046\pi$
$114$	0.545236	+	2.09886i	0.0510660	+	0.196577i
$115$			5.76570i			0.537654i
$116$	−0.872469	+	3.06780i	−0.0810067	+	0.284838i
$117$	−5.78409			−0.534739
$118$	−1.66219	−	0.976677i	−0.153017	−	0.0899104i
$119$	6.62658	+	11.6320i	0.607457	+	1.06630i
$120$	−5.81314	−	0.133269i	−0.530665	−	0.0121657i
$121$			8.60370i			0.782155i
$122$	11.9249	−	3.09781i	1.07963	−	0.280463i
$123$			22.7962i			2.05546i
$124$	−7.63995	−	2.17277i	−0.686088	−	0.195121i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	5.44994	−	1.41577i	0.485519	−	0.126127i
$127$		−	16.6460i		−	1.47709i	−0.674203	−	0.738546i	$-0.735513\pi$
$127$		−	16.6460i		−	1.47709i	0.674203	−	0.738546i	$-0.264487\pi$
$128$	9.48155	+	6.17254i	0.838058	+	0.545581i
$129$	−0.537716	−	0.537716i	−0.0473433	−	0.0473433i
$130$	−6.45614	+	1.67716i	−0.566241	+	0.147096i
$131$	−6.35709	−	6.35709i	−0.555422	−	0.555422i	0.372579	−	0.928001i	$-0.378474\pi$
$131$	−6.35709	−	6.35709i	−0.555422	−	0.555422i	−0.928001	+	0.372579i	$0.878474\pi$
$132$	−3.09777	−	5.56001i	−0.269626	−	0.483937i
$133$	−1.71244	−	1.71244i	−0.148488	−	0.148488i
$134$	−1.91755	+	3.26345i	−0.165651	+	0.281919i
$135$	−3.64637			−0.313829
$136$	3.34019	−	11.1733i	0.286419	−	0.958104i
$137$	−16.2109			−1.38499			−0.692497	−	0.721420i	$-0.743490\pi$
$137$	−16.2109			−1.38499			−0.692497	+	0.721420i	$0.743490\pi$
$138$	−8.49208	+	14.4526i	−0.722894	+	1.23028i
$139$	−14.9852	−	14.9852i	−1.27103	−	1.27103i	−0.945548	−	0.325482i	$-0.894473\pi$
$139$	−14.9852	−	14.9852i	−1.27103	−	1.27103i	−0.325482	−	0.945548i	$-0.605527\pi$
$140$	5.67265	−	3.16053i	0.479427	−	0.267114i
$141$	−6.99184	−	6.99184i	−0.588819	−	0.588819i
$142$	10.2288	−	2.65720i	0.858380	−	0.222987i
$143$	−5.16291	−	5.16291i	−0.431744	−	0.431744i
$144$	−4.17109	−	2.58126i	−0.347591	−	0.215105i
$145$		−	1.59472i		−	0.132435i
$146$	−6.38141	+	1.65774i	−0.528129	+	0.137196i
$147$	−5.14888	+	5.14888i	−0.424672	+	0.424672i
$148$	−0.980534	+	3.44778i	−0.0805994	+	0.283406i
$149$		−	11.0213i		−	0.902899i	−0.892297	−	0.451450i	$-0.850907\pi$
$149$		−	11.0213i		−	0.902899i	0.892297	−	0.451450i	$-0.149093\pi$
$150$	2.81394	−	0.730995i	0.229757	−	0.0596855i
$151$			18.6138i			1.51477i	0.652969	+	0.757384i	$0.273523\pi$
$151$			18.6138i			1.51477i	−0.652969	+	0.757384i	$0.726477\pi$
$152$	−0.0483525	+	2.10912i	−0.00392190	+	0.171072i
$153$	−1.33677	+	4.87625i	−0.108071	+	0.394221i
$154$	6.12836	+	3.60092i	0.493838	+	0.290171i
$155$	3.97146			0.318995
$156$	−18.6535	−	5.30497i	−1.49347	−	0.424738i
$157$			2.74930i			0.219418i	0.993964	+	0.109709i	$0.0349919\pi$
$157$			2.74930i			0.219418i	−0.993964	+	0.109709i	$0.965008\pi$
$158$	−3.87727	−	14.9254i	−0.308459	−	1.18740i
$159$	−6.11046	−	6.11046i	−0.484591	−	0.484591i
$160$	−5.40420	−	1.67172i	−0.427239	−	0.132161i
$161$		−	18.7203i		−	1.47537i
$162$	−13.6259	−	8.00632i	−1.07055	−	0.629036i
$163$	15.0382	−	15.0382i	1.17788	−	1.17788i	0.197601	−	0.980283i	$-0.436685\pi$
$163$	15.0382	−	15.0382i	1.17788	−	1.17788i	0.980283	−	0.197601i	$-0.0633150\pi$
$164$	−6.06662	+	21.3316i	−0.473724	+	1.66572i
$165$	2.25027	+	2.25027i	0.175184	+	0.175184i
$166$	−13.7472	−	8.07763i	−1.06699	−	0.626946i
$167$	13.3612	−	13.3612i	1.03392	−	1.03392i	0.0345138	−	0.999404i	$-0.489012\pi$
$167$	13.3612	−	13.3612i	1.03392	−	1.03392i	0.999404	−	0.0345138i	$-0.0109883\pi$
$168$	18.8744	+	0.432703i	1.45619	+	0.0333838i
$169$	−9.24732			−0.711332
$170$	−0.0781715	+	5.83043i	−0.00599548	+	0.447173i
$171$		−	0.914673i		−	0.0699468i
$172$	−0.360070	−	0.646269i	−0.0274551	−	0.0492775i
$173$	−6.76590	−	6.76590i	−0.514402	−	0.514402i	0.401470	−	0.915872i	$-0.368499\pi$
$173$	−6.76590	−	6.76590i	−0.514402	−	0.514402i	−0.915872	+	0.401470i	$0.868499\pi$
$174$	2.34881	−	3.99741i	0.178063	−	0.303043i
$175$	−2.29587	+	2.29587i	−0.173551	+	0.173551i
$176$	−1.41909	−	6.02718i	−0.106968	−	0.454316i
$177$	1.98168	+	1.98168i	0.148952	+	0.148952i
$178$	−5.25790	−	3.08945i	−0.394097	−	0.231564i
$179$	1.55713			0.116386			0.0581928	−	0.998305i	$-0.481466\pi$
$179$	1.55713			0.116386			0.0581928	+	0.998305i	$0.481466\pi$
$180$	2.35905	+	0.670904i	0.175833	+	0.0500063i
$181$	15.0091	−	15.0091i	1.11562	−	1.11562i	0.123240	−	0.992377i	$-0.460672\pi$
$181$	15.0091	−	15.0091i	1.11562	−	1.11562i	0.992377	−	0.123240i	$-0.0393285\pi$
$182$	20.9621	−	5.44546i	1.55381	−	0.403645i
$183$	−17.9102			−1.32396
$184$	−11.7927	+	11.2641i	−0.869366	+	0.830398i
$185$		−	1.79225i		−	0.131769i
$186$	9.95503	+	5.84941i	0.729938	+	0.428899i
$187$	−5.54577	+	3.15935i	−0.405547	+	0.231035i
$188$	−4.68194	−	8.40333i	−0.341465	−	0.612876i
$189$	11.8392			0.861174
$190$	−0.265219	−	1.02095i	−0.0192410	−	0.0740674i
$191$	−24.8007			−1.79451			−0.897256	−	0.441510i	$-0.854443\pi$
$191$	−24.8007			−1.79451			−0.897256	+	0.441510i	$0.854443\pi$
$192$	−11.0842	−	12.1501i	−0.799932	−	0.876855i
$193$	−12.5943	−	12.5943i	−0.906554	−	0.906554i	0.0894383	−	0.995992i	$-0.471493\pi$
$193$	−12.5943	−	12.5943i	−0.906554	−	0.906554i	−0.995992	+	0.0894383i	$0.971493\pi$
$194$	−22.0010	+	5.71534i	−1.57958	+	0.410337i
$195$	9.69659			0.694387
$196$	−6.18832	+	3.44784i	−0.442023	+	0.246274i
$197$	15.9411	−	15.9411i	1.13576	−	1.13576i	0.146557	−	0.989202i	$-0.453181\pi$
$197$	15.9411	−	15.9411i	1.13576	−	1.13576i	0.989202	−	0.146557i	$-0.0468191\pi$
$198$	0.674996	+	2.59837i	0.0479699	+	0.184658i
$199$	−2.56094	+	2.56094i	−0.181540	+	0.181540i	−0.792027	−	0.610486i	$-0.790974\pi$
$199$	−2.56094	+	2.56094i	−0.181540	+	0.181540i	0.610486	+	0.792027i	$0.290974\pi$
$200$	2.82768	+	0.0648259i	0.199947	+	0.00458389i
$201$	3.89071	−	3.89071i	0.274429	−	0.274429i
$202$	−7.02626	+	11.9579i	−0.494366	+	0.841355i
$203$			5.17782i			0.363412i
$204$	−8.78337	+	14.4997i	−0.614959	+	1.01518i
$205$		−	11.0887i		−	0.774472i
$206$	−4.05947	−	2.38527i	−0.282837	−	0.166190i
$207$	4.99957	−	4.99957i	0.347494	−	0.347494i
$208$	−16.0433	−	9.92829i	−1.11240	−	0.688403i
$209$	0.816442	−	0.816442i	0.0564744	−	0.0564744i
$210$	−9.13641	+	2.37343i	−0.630472	+	0.163782i
$211$	−17.0697	+	17.0697i	−1.17512	+	1.17512i	−0.194153	+	0.980971i	$0.562196\pi$
$211$	−17.0697	+	17.0697i	−1.17512	+	1.17512i	−0.980971	+	0.194153i	$0.937804\pi$
$212$	−4.09173	−	7.34401i	−0.281021	−	0.504389i
$213$	−15.3628			−1.05264
$214$	3.47059	+	13.3599i	0.237244	+	0.913263i
$215$	0.261561	+	0.261561i	0.0178383	+	0.0178383i
$216$	−7.12368	−	7.45797i	−0.484705	−	0.507450i
$217$	−12.8947			−0.875349
$218$	−11.1627	+	2.89982i	−0.756036	+	0.196401i
$219$	9.58434			0.647650
$220$	1.50685	+	2.70455i	0.101592	+	0.182341i
$221$	−5.14161	+	18.7555i	−0.345862	+	1.26163i
$222$	2.63973	−	4.49253i	0.177167	−	0.301519i
$223$		−	13.3751i		−	0.895661i	−0.894118	−	0.447831i	$-0.852197\pi$
$223$		−	13.3751i		−	0.895661i	0.894118	−	0.447831i	$-0.147803\pi$
$224$	17.5466	+	5.42783i	1.17238	+	0.362662i
$225$	−1.22630			−0.0817532
$226$	−2.51497	−	9.68129i	−0.167294	−	0.643990i
$227$	−2.89482	+	2.89482i	−0.192136	+	0.192136i	−0.796618	−	0.604483i	$-0.793380\pi$
$227$	−2.89482	+	2.89482i	−0.192136	+	0.192136i	0.604483	+	0.796618i	$0.293380\pi$
$228$	0.838908	−	2.94979i	0.0555580	−	0.195355i
$229$	9.50826			0.628324			0.314162	−	0.949369i	$-0.398277\pi$
$229$	9.50826			0.628324			0.314162	+	0.949369i	$0.398277\pi$
$230$	4.13080	−	7.03015i	0.272377	−	0.463554i
$231$	−7.30629	−	7.30629i	−0.480718	−	0.480718i
$232$	3.26171	−	3.11551i	0.214142	−	0.204543i
$233$	−11.1670	+	11.1670i	−0.731575	+	0.731575i	−0.970932	−	0.239357i	$-0.923063\pi$
$233$	−11.1670	+	11.1670i	−0.731575	+	0.731575i	0.239357	+	0.970932i	$0.423063\pi$
$234$	7.05258	+	4.14397i	0.461042	+	0.270900i
$235$	3.40104	+	3.40104i	0.221859	+	0.221859i
$236$	1.32699	+	2.38174i	0.0863797	+	0.155038i
$237$			22.4167i			1.45612i
$238$	0.253811	−	18.9305i	0.0164521	−	1.22708i
$239$	22.0892			1.42883			0.714415	−	0.699722i	$-0.246693\pi$
$239$	22.0892			1.42883			0.714415	+	0.699722i	$0.246693\pi$
$240$	6.99252	+	4.32729i	0.451365	+	0.279325i
$241$	17.7308	−	17.7308i	1.14214	−	1.14214i	0.154086	−	0.988057i	$-0.450757\pi$
$241$	17.7308	−	17.7308i	1.14214	−	1.14214i	0.988057	−	0.154086i	$-0.0492432\pi$
$242$	6.16407	−	10.4906i	0.396241	−	0.674358i
$243$	8.50974	+	8.50974i	0.545900	+	0.545900i
$244$	−16.7595	−	4.76634i	−1.07292	−	0.305134i
$245$	2.50457	−	2.50457i	0.160011	−	0.160011i
$246$	16.3322	−	27.7956i	1.04130	−	1.77218i
$247$		−	3.51810i		−	0.223852i
$248$	7.75878	+	8.12287i	0.492683	+	0.515803i
$249$	16.3895	+	16.3895i	1.03865	+	1.03865i
$250$	−1.36878	+	0.355578i	−0.0865694	+	0.0224887i
$251$		−	5.10364i		−	0.322139i	−0.986943	−	0.161069i	$-0.948506\pi$
$251$		−	5.10364i		−	0.322139i	0.986943	−	0.161069i	$-0.0514943\pi$
$252$	−7.65947	−	2.17832i	−0.482501	−	0.137221i
$253$	8.92529			0.561128
$254$	−11.9259	+	20.2966i	−0.748298	+	1.27352i
$255$	2.24099	−	8.17466i	0.140336	−	0.511917i
$256$	−7.13863	−	14.3192i	−0.446164	−	0.894951i
$257$			0.476282i			0.0297097i	0.999890	+	0.0148548i	$0.00472861\pi$
$257$			0.476282i			0.0297097i	−0.999890	+	0.0148548i	$0.995271\pi$
$258$	0.270398	+	1.04088i	0.0168342	+	0.0648027i
$259$			5.81915i			0.361584i
$260$	9.07361	+	2.58050i	0.562721	+	0.160036i
$261$	−1.38282	+	1.38282i	−0.0855946	+	0.0855946i
$262$	3.19675	+	12.3057i	0.197496	+	0.760252i
$263$		−	4.83867i		−	0.298365i	−0.988810	−	0.149183i	$-0.952336\pi$
$263$		−	4.83867i		−	0.298365i	0.988810	−	0.149183i	$-0.0476642\pi$
$264$	−0.206300	+	8.99873i	−0.0126969	+	0.553834i
$265$	2.97231	+	2.97231i	0.182587	+	0.182587i
$266$	0.861124	+	3.31486i	0.0527989	+	0.203247i
$267$	6.26852	+	6.26852i	0.383627	+	0.383627i
$268$	4.67615	−	2.60533i	0.285641	−	0.159146i
$269$	10.1755	+	10.1755i	0.620410	+	0.620410i	0.945636	−	0.325226i	$-0.105440\pi$
$269$	10.1755	+	10.1755i	0.620410	+	0.620410i	−0.325226	+	0.945636i	$0.605440\pi$
$270$	4.44604	+	2.61242i	0.270577	+	0.158987i
$271$	−0.529438			−0.0321611			−0.0160805	−	0.999871i	$-0.505119\pi$
$271$	−0.529438			−0.0321611			−0.0160805	+	0.999871i	$0.505119\pi$
$272$	−12.0778	+	11.2306i	−0.732322	+	0.680958i
$273$	−31.4833			−1.90546
$274$	19.7661	+	11.6142i	1.19411	+	0.701641i
$275$	−1.09460	−	1.09460i	−0.0660068	−	0.0660068i
$276$	20.7089	−	11.5380i	1.24653	−	0.694506i
$277$	15.9430	+	15.9430i	0.957923	+	0.957923i	0.999150	−	0.0412266i	$-0.0131266\pi$
$277$	15.9430	+	15.9430i	0.957923	+	0.957923i	−0.0412266	+	0.999150i	$0.513127\pi$
$278$	7.53552	+	29.0077i	0.451950	+	1.73976i
$279$	−3.44374	−	3.44374i	−0.206172	−	0.206172i
$280$	−9.18105	−	0.210480i	−0.548673	−	0.0125786i
$281$		−	16.9884i		−	1.01344i	−0.862110	−	0.506722i	$-0.830857\pi$
$281$		−	16.9884i		−	1.01344i	0.862110	−	0.506722i	$-0.169143\pi$
$282$	3.51594	+	13.5345i	0.209371	+	0.805966i
$283$	−9.22385	+	9.22385i	−0.548301	+	0.548301i	−0.925949	−	0.377648i	$-0.876733\pi$
$283$	−9.22385	+	9.22385i	−0.548301	+	0.548301i	0.377648	+	0.925949i	$0.376733\pi$
$284$	−14.3757	−	4.08840i	−0.853044	−	0.242602i
$285$			1.53338i			0.0908296i
$286$	2.59623	+	9.99410i	0.153519	+	0.590963i
$287$			36.0034i			2.12522i
$288$	3.23652	+	6.13570i	0.190714	+	0.361550i
$289$	14.6234	+	8.66922i	0.860202	+	0.509954i
$290$	−1.14253	+	1.94446i	−0.0670917	+	0.114182i
$291$	33.0436			1.93705
$292$	8.96857	+	2.55063i	0.524846	+	0.149264i
$293$		−	14.4830i		−	0.846106i	−0.906105	−	0.423053i	$-0.860958\pi$
$293$		−	14.4830i		−	0.846106i	0.906105	−	0.423053i	$-0.139042\pi$
$294$	9.96694	−	2.58918i	0.581284	−	0.151004i
$295$	−0.963949	−	0.963949i	−0.0561233	−	0.0561233i
$296$	3.66571	−	3.50140i	0.213065	−	0.203515i
$297$			5.64457i			0.327531i
$298$	−7.89614	+	13.4383i	−0.457411	+	0.778462i
$299$	19.2298	−	19.2298i	1.11209	−	1.11209i
$300$	−3.95477	−	1.12472i	−0.228329	−	0.0649357i
$301$	−0.849248	−	0.849248i	−0.0489498	−	0.0489498i
$302$	13.3357	−	22.6959i	0.767385	−	1.30600i
$303$	14.2563	−	14.2563i	0.819004	−	0.819004i
$304$	1.57002	−	2.53702i	0.0900468	−	0.145508i
$305$	8.71205			0.498851
$306$	5.12349	−	4.98792i	0.292890	−	0.285140i
$307$		−	8.35650i		−	0.476931i	−0.971151	−	0.238465i	$-0.923356\pi$
$307$		−	8.35650i		−	0.476931i	0.971151	−	0.238465i	$-0.0766444\pi$
$308$	−4.89250	−	8.78126i	−0.278776	−	0.500359i
$309$	4.83973	+	4.83973i	0.275323	+	0.275323i
$310$	−4.84242	−	2.84532i	−0.275031	−	0.161604i
$311$	−16.7309	+	16.7309i	−0.948721	+	0.948721i	−0.998748	−	0.0500270i	$-0.984069\pi$
$311$	−16.7309	+	16.7309i	−0.948721	+	0.948721i	0.0500270	+	0.998748i	$0.484069\pi$
$312$	18.9436	+	19.8326i	1.07247	+	1.12280i
$313$	20.3932	+	20.3932i	1.15269	+	1.15269i	0.986010	+	0.166684i	$0.0533060\pi$
$313$	20.3932	+	20.3932i	1.15269	+	1.15269i	0.166684	+	0.986010i	$0.446694\pi$
$314$	1.96972	−	3.35224i	0.111158	−	0.189178i
$315$	3.98160			0.224338
$316$	−5.96563	+	20.9765i	−0.335593	+	1.18002i
$317$	21.8638	−	21.8638i	1.22799	−	1.22799i	0.263269	−	0.964722i	$-0.415199\pi$
$317$	21.8638	−	21.8638i	1.22799	−	1.22799i	0.964722	−	0.263269i	$-0.0848006\pi$
$318$	3.07272	+	11.8283i	0.172310	+	0.663299i
$319$	−2.46863			−0.138217
$320$	5.39168	+	5.91015i	0.301404	+	0.330387i
$321$		−	20.0654i		−	1.11994i
$322$	−13.4121	+	22.8258i	−0.747424	+	1.27203i
$323$	−2.96592	−	0.813074i	−0.165028	−	0.0452407i
$324$	10.8780	+	19.5243i	0.604334	+	1.08468i
$325$	−4.71671			−0.261636
$326$	−29.1102	+	7.56216i	−1.61227	+	0.418829i
$327$	16.7655			0.927134
$328$	22.6800	−	21.6634i	1.25229	−	1.19616i
$329$	−11.0426	−	11.0426i	−0.608801	−	0.608801i
$330$	−1.13158	−	4.35597i	−0.0622914	−	0.239788i
$331$	17.4746			0.960489			0.480244	−	0.877135i	$-0.340548\pi$
$331$	17.4746			0.960489			0.480244	+	0.877135i	$0.340548\pi$
$332$	10.9749	+	19.6982i	0.602326	+	1.08108i
$333$	−1.55410	+	1.55410i	−0.0851642	+	0.0851642i
$334$	−25.8639	+	6.71883i	−1.41521	+	0.367638i
$335$	−1.89256	+	1.89256i	−0.103401	+	0.103401i
$336$	−22.7036	−	14.0500i	−1.23858	−	0.766491i
$337$	7.64846	−	7.64846i	0.416638	−	0.416638i	−0.467405	−	0.884043i	$-0.654811\pi$
$337$	7.64846	−	7.64846i	0.416638	−	0.416638i	0.884043	+	0.467405i	$0.154811\pi$
$338$	11.2753	+	6.62518i	0.613296	+	0.360363i
$339$			14.5405i			0.789731i
$340$	4.27249	−	7.05307i	0.231708	−	0.382507i
$341$		−	6.14780i		−	0.332922i
$342$	−0.655312	+	1.11527i	−0.0354352	+	0.0603067i
$343$	7.93912	−	7.93912i	0.428672	−	0.428672i
$344$	−0.0239793	+	1.04597i	−0.00129288	+	0.0563949i
$345$	−8.38141	+	8.38141i	−0.451240	+	0.451240i
$346$	3.40232	+	13.0971i	0.182910	+	0.704104i
$347$	−3.16691	+	3.16691i	−0.170009	+	0.170009i	−0.786983	−	0.616974i	$-0.788358\pi$
$347$	−3.16691	+	3.16691i	−0.170009	+	0.170009i	0.616974	+	0.786983i	$0.288358\pi$
$348$	−5.72783	+	3.19128i	−0.307044	+	0.171070i
$349$	−35.9768			−1.92580			−0.962898	−	0.269866i	$-0.913021\pi$
$349$	−35.9768			−1.92580			−0.962898	+	0.269866i	$0.913021\pi$
$350$	4.44422	−	1.15451i	0.237554	−	0.0617109i
$351$	12.1614	+	12.1614i	0.649129	+	0.649129i
$352$	−2.58783	+	8.36568i	−0.137932	+	0.445892i
$353$	8.29838			0.441678			0.220839	−	0.975310i	$-0.429120\pi$
$353$	8.29838			0.441678			0.220839	+	0.975310i	$0.429120\pi$
$354$	−0.996514	−	3.83604i	−0.0529641	−	0.203883i
$355$	7.47290			0.396621
$356$	4.19758	+	7.53398i	0.222471	+	0.399300i
$357$	−7.27615	+	26.5418i	−0.385095	+	1.40474i
$358$	−1.89862	−	1.11560i	−0.100345	−	0.0589612i
$359$		−	13.1867i		−	0.695969i	−0.937500	−	0.347985i	$-0.886866\pi$
$359$		−	13.1867i		−	0.695969i	0.937500	−	0.347985i	$-0.113134\pi$
$360$	−2.39574	−	2.50816i	−0.126267	−	0.132192i
$361$	−18.4437			−0.970719
$362$	−29.0538	+	7.54751i	−1.52704	+	0.396689i
$363$	−12.5069	+	12.5069i	−0.656443	+	0.656443i
$364$	−29.4606	−	8.37847i	−1.54415	−	0.439151i
$365$	−4.66211			−0.244026
$366$	21.8380	+	12.8317i	1.14149	+	0.670721i
$367$	−8.69113	−	8.69113i	−0.453673	−	0.453673i	0.442899	−	0.896572i	$-0.353950\pi$
$367$	−8.69113	−	8.69113i	−0.453673	−	0.453673i	−0.896572	+	0.442899i	$0.853950\pi$
$368$	22.4489	−	5.28558i	1.17023	−	0.275530i
$369$	−9.61532	+	9.61532i	−0.500554	+	0.500554i
$370$	−1.28404	+	2.18530i	−0.0667543	+	0.113608i
$371$	−9.65061	−	9.65061i	−0.501035	−	0.501035i
$372$	−7.94747	−	14.2644i	−0.412057	−	0.739577i
$373$			18.4960i			0.957687i	0.877900	+	0.478844i	$0.158944\pi$
$373$			18.4960i			0.957687i	−0.877900	+	0.478844i	$0.841056\pi$
$374$	9.02549	+	0.121009i	0.466697	+	0.00625724i
$375$	2.05580			0.106161
$376$	−0.311799	+	13.6006i	−0.0160798	+	0.701396i
$377$	−5.31875	+	5.31875i	−0.273929	+	0.273929i
$378$	−14.4356	−	8.48211i	−0.742487	−	0.436273i
$379$	−8.03416	−	8.03416i	−0.412687	−	0.412687i	0.469987	−	0.882674i	$-0.344259\pi$
$379$	−8.03416	−	8.03416i	−0.412687	−	0.412687i	−0.882674	+	0.469987i	$0.844259\pi$
$380$	−0.408069	+	1.43486i	−0.0209335	+	0.0736070i
$381$	24.1977	−	24.1977i	1.23969	−	1.23969i
$382$	30.2396	+	17.7683i	1.54719	+	0.909104i
$383$			26.0044i			1.32876i	0.747394	+	0.664381i	$0.231305\pi$
$383$			26.0044i			1.32876i	−0.747394	+	0.664381i	$0.768695\pi$
$384$	4.81019	+	22.7558i	0.245469	+	1.16125i
$385$	3.55399	+	3.55399i	0.181128	+	0.181128i
$386$	6.33318	+	24.3793i	0.322350	+	1.24087i
$387$		−	0.453612i		−	0.0230584i
$388$	30.9206	+	8.79370i	1.56976	+	0.446433i
$389$	−7.32758			−0.371523			−0.185762	−	0.982595i	$-0.559475\pi$
$389$	−7.32758			−0.371523			−0.185762	+	0.982595i	$0.559475\pi$
$390$	−11.8231	−	6.94706i	−0.598687	−	0.351778i
$391$	−11.7674	−	20.6559i	−0.595102	−	1.04461i
$392$	10.0156	+	0.229613i	0.505866	+	0.0115972i
$393$		−	18.4822i		−	0.932304i
$394$	−30.8581	+	8.01621i	−1.55461	+	0.403851i
$395$		−	10.9041i		−	0.548647i
$396$	1.03856	−	3.65180i	0.0521895	−	0.183510i
$397$	−15.1009	+	15.1009i	−0.757894	+	0.757894i	−0.975939	−	0.218044i	$-0.930032\pi$
$397$	−15.1009	+	15.1009i	−0.757894	+	0.757894i	0.218044	+	0.975939i	$0.430032\pi$
$398$	4.95734	−	1.28780i	0.248489	−	0.0645517i
$399$		−	4.97865i		−	0.249244i
$400$	−3.40137	−	2.10492i	−0.170068	−	0.105246i
$401$	2.53948	+	2.53948i	0.126816	+	0.126816i	0.767666	−	0.640850i	$-0.221418\pi$
$401$	2.53948	+	2.53948i	0.126816	+	0.126816i	−0.640850	+	0.767666i	$0.721418\pi$
$402$	−7.53144	+	1.95649i	−0.375634	+	0.0975810i
$403$	−13.2457	−	13.2457i	−0.659813	−	0.659813i
$404$	17.1343	−	9.54643i	0.852465	−	0.474953i
$405$	−7.90198	−	7.90198i	−0.392653	−	0.392653i
$406$	3.70961	−	6.31335i	0.184105	−	0.313326i
$407$	−2.77440			−0.137522
$408$	21.0978	−	11.3868i	1.04450	−	0.563729i
$409$	−0.200830			−0.00993041			−0.00496521	−	0.999988i	$-0.501580\pi$
$409$	−0.200830			−0.00993041			−0.00496521	+	0.999988i	$0.501580\pi$
$410$	−7.94446	+	13.5206i	−0.392349	+	0.667734i
$411$	−23.5653	−	23.5653i	−1.16239	−	1.16239i
$412$	3.24082	+	5.81676i	0.159664	+	0.286571i
$413$	3.12979	+	3.12979i	0.154007	+	0.154007i
$414$	−9.67793	+	2.51410i	−0.475644	+	0.123561i
$415$	−7.97236	−	7.97236i	−0.391348	−	0.391348i
$416$	12.4486	+	23.5997i	0.610343	+	1.15707i
$417$		−	43.5671i		−	2.13349i
$418$	−1.58043	+	0.410558i	−0.0773012	+	0.0200811i
$419$	24.2109	−	24.2109i	1.18278	−	1.18278i	0.203757	−	0.979021i	$-0.434685\pi$
$419$	24.2109	−	24.2109i	1.18278	−	1.18278i	0.979021	−	0.203757i	$-0.0653154\pi$
$420$	12.8405	+	3.65179i	0.626553	+	0.178189i
$421$			37.0799i			1.80716i	0.428414	+	0.903582i	$0.359072\pi$
$421$			37.0799i			1.80716i	−0.428414	+	0.903582i	$0.640928\pi$
$422$	33.0426	−	8.58370i	1.60849	−	0.417848i
$423$		−	5.89824i		−	0.286782i
$424$	−0.272494	+	11.8861i	−0.0132335	+	0.577240i
$425$	−1.09009	+	3.97639i	−0.0528769	+	0.192883i
$426$	18.7319	+	11.0066i	0.907565	+	0.533270i
$427$	−28.2867			−1.36889
$428$	5.33990	−	18.7763i	0.258114	−	0.907586i
$429$		−	15.0103i		−	0.724704i
$430$	−0.131529	−	0.506317i	−0.00634291	−	0.0244168i
$431$	−16.9004	−	16.9004i	−0.814064	−	0.814064i	0.171177	−	0.985240i	$-0.445243\pi$
$431$	−16.9004	−	16.9004i	−0.814064	−	0.814064i	−0.985240	+	0.171177i	$0.945243\pi$
$432$	3.34273	+	14.1973i	0.160827	+	0.683066i
$433$			10.8366i			0.520775i	0.965504	+	0.260388i	$0.0838504\pi$
$433$			10.8366i			0.520775i	−0.965504	+	0.260388i	$0.916150\pi$
$434$	15.7226	+	9.23832i	0.754708	+	0.443454i
$435$	2.31820	−	2.31820i	0.111149	−	0.111149i
$436$	15.6884	+	4.46171i	0.751336	+	0.213677i
$437$	3.04093	+	3.04093i	0.145467	+	0.145467i
$438$	−11.6863	−	6.86664i	−0.558391	−	0.328101i
$439$	6.56207	−	6.56207i	0.313191	−	0.313191i	−0.532954	−	0.846144i	$-0.678918\pi$
$439$	6.56207	−	6.56207i	0.313191	−	0.313191i	0.846144	+	0.532954i	$0.178918\pi$
$440$	0.100350	−	4.37725i	0.00478402	−	0.208677i
$441$	−4.34354			−0.206835
$442$	19.7065	−	19.1850i	0.937340	−	0.912538i
$443$			37.2794i			1.77120i	0.464452	+	0.885598i	$0.346251\pi$
$443$			37.2794i			1.77120i	−0.464452	+	0.885598i	$0.653749\pi$
$444$	−6.43729	+	3.58655i	−0.305500	+	0.170210i
$445$	−3.04919	−	3.04919i	−0.144546	−	0.144546i
$446$	−9.58249	+	16.3083i	−0.453744	+	0.772221i
$447$	16.0213	−	16.0213i	0.757781	−	0.757781i
$448$	−17.5059	−	19.1893i	−0.827077	−	0.906610i
$449$	−25.9359	−	25.9359i	−1.22399	−	1.22399i	−0.966201	−	0.257789i	$-0.917006\pi$
$449$	−25.9359	−	25.9359i	−1.22399	−	1.22399i	−0.257789	−	0.966201i	$-0.582994\pi$
$450$	1.49523	+	0.878574i	0.0704860	+	0.0414164i
$451$	−17.1654			−0.808285
$452$	−3.86958	+	13.6063i	−0.182010	+	0.639987i
$453$	−27.0583	+	27.0583i	−1.27131	+	1.27131i
$454$	5.60365	−	1.45570i	0.262992	−	0.0683192i
$455$	15.3144			0.717951
$456$	−3.13624	+	2.99567i	−0.146868	+	0.140285i
$457$			5.43380i			0.254183i	0.991891	+	0.127091i	$0.0405641\pi$
$457$			5.43380i			0.254183i	−0.991891	+	0.127091i	$0.959436\pi$
$458$	−11.5935	−	6.81214i	−0.541728	−	0.318310i
$459$	13.0633	−	7.44198i	0.609741	−	0.347362i
$460$	−10.0734	+	5.61243i	−0.469675	+	0.261681i
$461$	21.0735			0.981491			0.490745	−	0.871303i	$-0.336725\pi$
$461$	21.0735			0.981491			0.490745	+	0.871303i	$0.336725\pi$
$462$	3.67406	+	14.1431i	0.170933	+	0.657999i
$463$	1.28819			0.0598675			0.0299337	−	0.999552i	$-0.490470\pi$
$463$	1.28819			0.0598675			0.0299337	+	0.999552i	$0.490470\pi$
$464$	−6.20911	+	1.46193i	−0.288251	+	0.0678684i
$465$	5.77318	+	5.77318i	0.267725	+	0.267725i
$466$	21.6165	−	5.61547i	1.00137	−	0.260132i
$467$	25.8427			1.19586			0.597928	−	0.801550i	$-0.295991\pi$
$467$	25.8427			1.19586			0.597928	+	0.801550i	$0.295991\pi$
$468$	−5.63033	−	10.1056i	−0.260262	−	0.467129i
$469$	6.14483	−	6.14483i	0.283742	−	0.283742i
$470$	−1.71026	−	6.58356i	−0.0788882	−	0.303677i
$471$	−3.99657	+	3.99657i	−0.184152	+	0.184152i
$472$	0.0883726	−	3.85478i	0.00406768	−	0.177431i
$473$	0.404896	−	0.404896i	0.0186171	−	0.0186171i
$474$	16.0603	−	27.3328i	0.737674	−	1.25544i
$475$		−	0.745881i		−	0.0342234i
$476$	−13.8721	+	22.9002i	−0.635827	+	1.04963i
$477$		−	5.15472i		−	0.236018i
$478$	−26.9335	−	15.8257i	−1.23191	−	0.723849i
$479$	−10.8081	+	10.8081i	−0.493833	+	0.493833i	−0.909512	−	0.415679i	$-0.863544\pi$
$479$	−10.8081	+	10.8081i	−0.493833	+	0.493833i	0.415679	+	0.909512i	$0.363544\pi$
$480$	−5.42577	−	10.2860i	−0.247652	−	0.469491i
$481$	−5.97753	+	5.97753i	−0.272552	+	0.272552i
$482$	−34.3225	+	8.91618i	−1.56335	+	0.406121i
$483$	27.2131	−	27.2131i	1.23824	−	1.23824i
$484$	−15.0318	+	8.37499i	−0.683263	+	0.380681i
$485$	−16.0734			−0.729855
$486$	−4.27923	−	16.4727i	−0.194110	−	0.747219i
$487$	−18.1248	−	18.1248i	−0.821314	−	0.821314i	0.164983	−	0.986296i	$-0.447243\pi$
$487$	−18.1248	−	18.1248i	−0.821314	−	0.821314i	−0.986296	+	0.164983i	$0.947243\pi$
$488$	17.0202	+	17.8189i	0.770467	+	0.806623i
$489$	43.7211			1.97714
$490$	−4.84822	+	1.25945i	−0.219020	+	0.0568963i
$491$	−29.0364			−1.31039			−0.655197	−	0.755458i	$-0.727414\pi$
$491$	−29.0364			−1.31039			−0.655197	+	0.755458i	$0.727414\pi$
$492$	−39.8279	+	22.1902i	−1.79558	+	1.00041i
$493$	3.25472	+	5.71316i	0.146585	+	0.257308i
$494$	−2.52052	+	4.28965i	−0.113404	+	0.193000i
$495$			1.89831i			0.0853226i
$496$	−3.64075	−	15.4630i	−0.163474	−	0.694309i
$497$	−24.2634			−1.08836
$498$	−8.24170	−	31.7261i	−0.369319	−	1.42168i
$499$	17.7681	−	17.7681i	0.795408	−	0.795408i	−0.186960	−	0.982368i	$-0.559863\pi$
$499$	17.7681	−	17.7681i	0.795408	−	0.795408i	0.982368	+	0.186960i	$0.0598634\pi$
$500$	1.92372	+	0.547097i	0.0860312	+	0.0244669i
$501$	38.8454			1.73548
$502$	−3.65647	+	6.22290i	−0.163196	+	0.277742i
$503$	−5.98816	−	5.98816i	−0.266999	−	0.266999i	0.560891	−	0.827890i	$-0.310459\pi$
$503$	−5.98816	−	5.98816i	−0.266999	−	0.266999i	−0.827890	+	0.560891i	$0.810459\pi$
$504$	7.77859	+	8.14362i	0.346486	+	0.362746i
$505$	−6.93469	+	6.93469i	−0.308590	+	0.308590i
$506$	−10.8827	−	6.39446i	−0.483793	−	0.284269i
$507$	−13.4425	−	13.4425i	−0.597004	−	0.597004i
$508$	29.0827	−	16.2035i	1.29034	−	0.718913i
$509$			43.9081i			1.94619i	0.230402	+	0.973095i	$0.425996\pi$
$509$			43.9081i			1.94619i	−0.230402	+	0.973095i	$0.574004\pi$
$510$	−8.58914	+	8.36187i	−0.380333	+	0.370270i
$511$	15.1371			0.669627
$512$	−1.55473	+	22.5739i	−0.0687101	+	0.997637i
$513$	−1.92316	+	1.92316i	−0.0849096	+	0.0849096i
$514$	0.341229	−	0.580734i	0.0150510	−	0.0256151i
$515$	−2.35419	−	2.35419i	−0.103738	−	0.103738i
$516$	0.416038	−	1.46288i	0.0183150	−	0.0643998i
$517$	5.26480	−	5.26480i	0.231546	−	0.231546i
$518$	4.16909	−	7.09533i	0.183179	−	0.311751i
$519$		−	19.6707i		−	0.863449i
$520$	−9.21473	−	9.64714i	−0.404092	−	0.423055i
$521$	−15.9434	−	15.9434i	−0.698494	−	0.698494i	0.265591	−	0.964086i	$-0.414433\pi$
$521$	−15.9434	−	15.9434i	−0.698494	−	0.698494i	−0.964086	+	0.265591i	$0.914433\pi$
$522$	2.67680	−	0.695370i	0.117160	−	0.0304355i
$523$			28.5301i			1.24753i	0.781610	+	0.623767i	$0.214399\pi$
$523$			28.5301i			1.24753i	−0.781610	+	0.623767i	$0.785601\pi$
$524$	4.91856	−	17.2948i	0.214868	−	0.755525i
$525$	−6.67485			−0.291314
$526$	−3.46663	+	5.89982i	−0.151152	+	0.257244i
$527$	−14.2279	+	8.10546i	−0.619777	+	0.353079i
$528$	6.69863	−	10.8244i	0.291520	−	0.471072i
$529$			10.2433i			0.445359i
$530$	−1.49466	−	5.75364i	−0.0649240	−	0.249922i
$531$			1.67173i			0.0725467i
$532$	1.32494	−	4.65878i	0.0574433	−	0.201984i
$533$	−36.9834	+	36.9834i	−1.60193	+	1.60193i
$534$	−3.15220	−	12.1343i	−0.136409	−	0.525102i
$535$			9.76042i			0.421980i
$536$	−7.56823	−	0.173505i	−0.326898	−	0.00749428i
$537$	2.26356	+	2.26356i	0.0976796	+	0.0976796i
$538$	−5.11687	−	19.6972i	−0.220604	−	0.849207i
$539$	−3.87706	−	3.87706i	−0.166997	−	0.166997i
$540$	−3.54944	−	6.37068i	−0.152743	−	0.274150i
$541$	6.43629	+	6.43629i	0.276718	+	0.276718i	0.831797	−	0.555080i	$-0.187312\pi$
$541$	6.43629	+	6.43629i	0.276718	+	0.276718i	−0.555080	+	0.831797i	$0.687312\pi$
$542$	0.645548	+	0.379313i	0.0277286	+	0.0162929i
$543$	43.6365			1.87262
$544$	22.7726	−	5.04056i	0.976369	−	0.216112i
$545$	−8.15524			−0.349332
$546$	38.3878	+	22.5560i	1.64285	+	0.965308i
$547$	−9.71044	−	9.71044i	−0.415188	−	0.415188i	0.468353	−	0.883541i	$-0.344848\pi$
$547$	−9.71044	−	9.71044i	−0.415188	−	0.415188i	−0.883541	+	0.468353i	$0.844848\pi$
$548$	−15.7800	−	28.3226i	−0.674089	−	1.20988i
$549$	−7.55443	−	7.55443i	−0.322415	−	0.322415i
$550$	0.550434	+	2.11887i	0.0234706	+	0.0903490i
$551$	−0.841086	−	0.841086i	−0.0358314	−	0.0358314i
$552$	−33.5168	−	0.768388i	−1.42657	−	0.0327048i
$553$			35.4040i			1.50553i
$554$	−8.01715	−	30.8617i	−0.340616	−	1.31119i
$555$	2.60533	−	2.60533i	0.110590	−	0.110590i
$556$	11.5943	−	40.7680i	0.491706	−	1.72895i
$557$		−	22.2667i		−	0.943472i	−0.881740	−	0.471736i	$-0.843628\pi$
$557$		−	22.2667i		−	0.943472i	0.881740	−	0.471736i	$-0.156372\pi$
$558$	1.73173	+	6.66623i	0.0733100	+	0.282204i
$559$		−	1.74473i		−	0.0737940i
$560$	11.0437	+	6.83434i	0.466682	+	0.288804i
$561$	−12.6544	−	3.46905i	−0.534267	−	0.146463i
$562$	−12.1712	+	20.7141i	−0.513413	+	0.873770i
$563$	−21.5087			−0.906484			−0.453242	−	0.891388i	$-0.649733\pi$
$563$	−21.5087			−0.906484			−0.453242	+	0.891388i	$0.649733\pi$
$564$	5.40967	−	19.0216i	0.227788	−	0.800955i
$565$		−	7.07293i		−	0.297560i
$566$	17.8551	−	4.63833i	0.750504	−	0.194964i
$567$	25.6565	+	25.6565i	1.07747	+	1.07747i
$568$	14.5993	+	15.2844i	0.612574	+	0.641321i
$569$			23.2435i			0.974418i	0.873285	+	0.487209i	$0.161985\pi$
$569$			23.2435i			0.974418i	−0.873285	+	0.487209i	$0.838015\pi$
$570$	1.09858	−	1.86966i	0.0460145	−	0.0783115i
$571$	−9.13550	+	9.13550i	−0.382309	+	0.382309i	−0.871933	−	0.489625i	$-0.837134\pi$
$571$	−9.13550	+	9.13550i	−0.382309	+	0.382309i	0.489625	+	0.871933i	$0.337134\pi$
$572$	3.99460	−	14.0459i	0.167023	−	0.587289i
$573$	−36.0519	−	36.0519i	−1.50609	−	1.50609i
$574$	25.7944	−	43.8992i	1.07664	−	1.83232i
$575$	4.07696	−	4.07696i	0.170021	−	0.170021i
$576$	0.449579	−	9.80008i	0.0187325	−	0.408337i
$577$	33.1617			1.38054			0.690270	−	0.723552i	$-0.257492\pi$
$577$	33.1617			1.38054			0.690270	+	0.723552i	$0.257492\pi$
$578$	−11.6194	−	21.0473i	−0.483305	−	0.875452i
$579$		−	36.6157i		−	1.52170i
$580$	2.78619	−	1.55233i	0.115690	−	0.0644570i
$581$	25.8850	+	25.8850i	1.07389	+	1.07389i
$582$	−40.2903	−	23.6739i	−1.67009	−	0.981314i
$583$	4.60112	−	4.60112i	0.190559	−	0.190559i
$584$	−9.10806	−	9.53547i	−0.376894	−	0.394581i
$585$	4.08997	+	4.08997i	0.169099	+	0.169099i
$586$	−10.3763	+	17.6592i	−0.428639	+	0.729496i
$587$	−0.350712			−0.0144754			−0.00723771	−	0.999974i	$-0.502304\pi$
$587$	−0.350712			−0.0144754			−0.00723771	+	0.999974i	$0.502304\pi$
$588$	−14.0078	−	3.98375i	−0.577670	−	0.164287i
$589$	2.09462	−	2.09462i	0.0863072	−	0.0863072i
$590$	0.484734	+	1.86596i	0.0199562	+	0.0768205i
$591$	46.3462			1.90643
$592$	−6.97818	+	1.64301i	−0.286801	+	0.0675271i
$593$			14.8418i			0.609481i	0.952435	+	0.304740i	$0.0985697\pi$
$593$			14.8418i			0.609481i	−0.952435	+	0.304740i	$0.901430\pi$
$594$	4.04402	−	6.88246i	0.165928	−	0.282391i
$595$	3.53934	−	12.9107i	0.145099	−	0.529288i
$596$	19.2556	−	10.7283i	0.788741	−	0.439449i
$597$	−7.44551			−0.304724
$598$	−37.2242	+	9.66997i	−1.52221	+	0.395435i
$599$	28.9695			1.18366			0.591831	−	0.806062i	$-0.298405\pi$
$599$	28.9695			1.18366			0.591831	+	0.806062i	$0.298405\pi$
$600$	4.01628	+	4.20475i	0.163964	+	0.171658i
$601$	12.4976	+	12.4976i	0.509790	+	0.509790i	0.914462	−	0.404672i	$-0.132614\pi$
$601$	12.4976	+	12.4976i	0.509790	+	0.509790i	−0.404672	+	0.914462i	$0.632614\pi$
$602$	0.427055	+	1.64393i	0.0174055	+	0.0670017i
$603$	3.28216			0.133660
$604$	−32.5207	+	18.1190i	−1.32325	+	0.737251i
$605$	6.08374	−	6.08374i	0.247339	−	0.247339i
$606$	−27.5967	+	7.16897i	−1.12104	+	0.291219i
$607$	−17.8876	+	17.8876i	−0.726034	+	0.726034i	−0.969827	−	0.243793i	$-0.921608\pi$
$607$	−17.8876	+	17.8876i	−0.726034	+	0.726034i	0.243793	+	0.969827i	$0.421608\pi$
$608$	−3.73197	+	1.96857i	−0.151351	+	0.0798361i
$609$	−7.52683	+	7.52683i	−0.305002	+	0.305002i
$610$	−10.6227	−	6.24169i	−0.430099	−	0.252719i
$611$		−	22.6864i		−	0.917793i
$612$	−9.82067	+	2.41111i	−0.396977	+	0.0974634i
$613$		−	5.70962i		−	0.230609i	−0.993330	−	0.115305i	$-0.963216\pi$
$613$		−	5.70962i		−	0.230609i	0.993330	−	0.115305i	$-0.0367844\pi$
$614$	−5.98696	+	10.1891i	−0.241614	+	0.411200i
$615$	16.1194	−	16.1194i	0.649995	−	0.649995i
$616$	−0.325822	+	14.2122i	−0.0131277	+	0.572628i
$617$	−32.8853	+	32.8853i	−1.32391	+	1.32391i	−0.413332	+	0.910580i	$0.635635\pi$
$617$	−32.8853	+	32.8853i	−1.32391	+	1.32391i	−0.910580	+	0.413332i	$0.864365\pi$
$618$	−2.43372	−	9.36851i	−0.0978986	−	0.376857i
$619$	−27.9044	+	27.9044i	−1.12157	+	1.12157i	−0.130066	+	0.991505i	$0.541519\pi$
$619$	−27.9044	+	27.9044i	−1.12157	+	1.12157i	−0.991505	+	0.130066i	$0.958481\pi$
$620$	3.86588	+	6.93865i	0.155258	+	0.278663i
$621$	−21.0239			−0.843658
$622$	32.3868	−	8.41334i	1.29859	−	0.337344i
$623$	9.90025	+	9.90025i	0.396645	+	0.396645i
$624$	−8.88914	−	37.7540i	−0.355851	−	1.51137i
$625$	−1.00000			−0.0400000
$626$	−10.2550	−	39.4762i	−0.409873	−	1.57779i
$627$	2.37367			0.0947952
$628$	−4.80338	+	2.67622i	−0.191676	+	0.106793i
$629$	3.65785	+	6.42080i	0.145848	+	0.256014i
$630$	−4.85479	−	2.85259i	−0.193419	−	0.113650i
$631$		−	21.1025i		−	0.840079i	−0.907506	−	0.420040i	$-0.862016\pi$
$631$		−	21.1025i		−	0.840079i	0.907506	−	0.420040i	$-0.137984\pi$
$632$	22.3024	−	21.3027i	0.887142	−	0.847377i
$633$	−49.6272			−1.97251
$634$	−42.3228	+	10.9945i	−1.68085	+	0.436646i
$635$	−11.7705	+	11.7705i	−0.467097	+	0.467097i
$636$	4.72773	−	16.6238i	0.187467	−	0.659176i
$637$	−16.7065			−0.661937
$638$	3.01002	+	1.76863i	0.119168	+	0.0700209i
$639$	−6.47993	−	6.47993i	−0.256342	−	0.256342i
$640$	−2.33982	−	11.0691i	−0.0924894	−	0.437545i
$641$	−33.4414	+	33.4414i	−1.32086	+	1.32086i	−0.407775	+	0.913082i	$0.633695\pi$
$641$	−33.4414	+	33.4414i	−1.32086	+	1.32086i	−0.913082	+	0.407775i	$0.866305\pi$
$642$	−14.3758	+	24.4659i	−0.567366	+	0.965593i
$643$	28.4397	+	28.4397i	1.12155	+	1.12155i	0.991508	+	0.130045i	$0.0415121\pi$
$643$	28.4397	+	28.4397i	1.12155	+	1.12155i	0.130045	+	0.991508i	$0.458488\pi$
$644$	32.7068	−	18.2227i	1.28883	−	0.718074i
$645$			0.760446i			0.0299425i
$646$	3.03384	+	3.11630i	0.119365	+	0.122609i
$647$	−17.3325			−0.681410			−0.340705	−	0.940170i	$-0.610666\pi$
$647$	−17.3325			−0.681410			−0.340705	+	0.940170i	$0.610666\pi$
$648$	0.724436	−	31.5996i	0.0284585	−	1.24135i
$649$	−1.49219	+	1.49219i	−0.0585736	+	0.0585736i
$650$	5.75111	+	3.37925i	0.225577	+	0.132545i
$651$	−18.7446	−	18.7446i	−0.734659	−	0.734659i
$652$	40.9121	+	11.6352i	1.60224	+	0.455671i
$653$	21.4365	−	21.4365i	0.838876	−	0.838876i	−0.149835	−	0.988711i	$-0.547874\pi$
$653$	21.4365	−	21.4365i	0.838876	−	0.838876i	0.988711	+	0.149835i	$0.0478743\pi$
$654$	−20.4423	−	12.0115i	−0.799357	−	0.469688i
$655$			8.99029i			0.351280i
$656$	−43.1744	+	10.1654i	−1.68568	+	0.396891i
$657$	4.04263	+	4.04263i	0.157718	+	0.157718i
$658$	5.55293	+	21.3758i	0.216476	+	0.833315i
$659$			23.9421i			0.932652i	0.884613	+	0.466326i	$0.154423\pi$
$659$			23.9421i			0.932652i	−0.884613	+	0.466326i	$0.845577\pi$
$660$	−1.74106	+	6.12197i	−0.0677708	+	0.238298i
$661$	29.6618			1.15371			0.576855	−	0.816847i	$-0.304280\pi$
$661$	29.6618			1.15371			0.576855	+	0.816847i	$0.304280\pi$
$662$	−21.3068	−	12.5195i	−0.828114	−	0.486586i
$663$	−34.7384	+	19.7900i	−1.34913	+	0.768582i
$664$	0.730888	−	31.8811i	0.0283639	−	1.23723i
$665$			2.42176i			0.0939118i
$666$	3.00835	−	0.781500i	0.116571	−	0.0302825i
$667$		−	9.19469i		−	0.356020i
$668$	36.3497	+	10.3377i	1.40641	+	0.399977i
$669$	19.4429	−	19.4429i	0.751706	−	0.751706i
$670$	3.66351	−	0.951696i	0.141534	−	0.0367672i
$671$		−	13.4862i		−	0.520630i
$672$	17.6166	+	33.3971i	0.679576	+	1.28832i
$673$	1.70642	+	1.70642i	0.0657778	+	0.0657778i	0.739230	−	0.673453i	$-0.235189\pi$
$673$	1.70642	+	1.70642i	0.0657778	+	0.0657778i	−0.673453	+	0.739230i	$0.735189\pi$
$674$	−14.8055	+	3.84613i	−0.570287	+	0.148147i
$675$	2.57837	+	2.57837i	0.0992416	+	0.0992416i
$676$	−9.00150	−	16.1563i	−0.346211	−	0.621395i
$677$	−15.9782	−	15.9782i	−0.614094	−	0.614094i	0.329916	−	0.944010i	$-0.392979\pi$
$677$	−15.9782	−	15.9782i	−0.614094	−	0.614094i	−0.944010	+	0.329916i	$0.892979\pi$
$678$	10.4174	−	17.7293i	0.400080	−	0.680890i
$679$	52.1878			2.00278
$680$	−10.2626	+	5.53886i	−0.393553	+	0.212406i
$681$	−8.41621			−0.322510
$682$	−4.40456	+	7.49606i	−0.168659	+	0.287039i
$683$	−12.4897	−	12.4897i	−0.477906	−	0.477906i	0.426556	−	0.904461i	$-0.359727\pi$
$683$	−12.4897	−	12.4897i	−0.477906	−	0.477906i	−0.904461	+	0.426556i	$0.859727\pi$
$684$	1.59805	−	0.890358i	0.0611030	−	0.0340437i
$685$	11.4629	+	11.4629i	0.437974	+	0.437974i
$686$	−15.3682	+	3.99229i	−0.586759	+	0.152426i
$687$	13.8219	+	13.8219i	0.527337	+	0.527337i
$688$	0.778617	−	1.25818i	0.0296845	−	0.0479676i
$689$		−	19.8266i		−	0.755332i
$690$	16.2243	−	4.21470i	0.617649	−	0.160451i
$691$	−7.18787	+	7.18787i	−0.273439	+	0.273439i	−0.830483	−	0.557044i	$-0.811936\pi$
$691$	−7.18787	+	7.18787i	−0.273439	+	0.273439i	0.557044	+	0.830483i	$0.311936\pi$
$692$	5.23486	−	18.4069i	0.198999	−	0.699727i
$693$		−	6.16351i		−	0.234132i
$694$	6.13035	−	1.59252i	0.232705	−	0.0604513i
$695$			21.1923i			0.803870i
$696$	9.27036	+	0.212527i	0.351392	+	0.00805582i
$697$	22.6314	+	39.7259i	0.857224	+	1.50473i
$698$	43.8668	+	25.7754i	1.66038	+	0.975612i
$699$	−32.4662			−1.22799
$700$	−6.24601	−	1.77634i	−0.236077	−	0.0671393i
$701$			41.4525i			1.56564i	0.622249	+	0.782819i	$0.286219\pi$
$701$			41.4525i			1.56564i	−0.622249	+	0.782819i	$0.713781\pi$
$702$	−6.11553	−	23.5415i	−0.230816	−	0.888516i
$703$	−0.945264	−	0.945264i	−0.0356513	−	0.0356513i
$704$	9.14889	−	8.34630i	0.344812	−	0.314563i
$705$			9.88796i			0.372402i
$706$	−10.1183	−	5.94532i	−0.380806	−	0.223755i
$707$	22.5159	−	22.5159i	0.846796	−	0.846796i
$708$	−1.53325	+	5.39126i	−0.0576231	+	0.202616i
$709$	−5.94828	−	5.94828i	−0.223392	−	0.223392i	0.586533	−	0.809925i	$-0.300492\pi$
$709$	−5.94828	−	5.94828i	−0.223392	−	0.223392i	−0.809925	+	0.586533i	$0.800492\pi$
$710$	−9.11176	−	5.35392i	−0.341958	−	0.200929i
$711$	−9.45524	+	9.45524i	−0.354599	+	0.354599i
$712$	0.279543	−	12.1936i	0.0104763	−	0.456973i
$713$	22.8982			0.857545
$714$	27.8876	−	27.1497i	1.04367	−	1.01605i
$715$			7.30145i			0.273059i
$716$	1.51574	+	2.72051i	0.0566459	+	0.101670i
$717$	32.1103	+	32.1103i	1.19918	+	1.19918i
$718$	−9.44755	+	16.0787i	−0.352580	+	0.600051i
$719$	−31.5259	+	31.5259i	−1.17572	+	1.17572i	−0.194895	+	0.980824i	$0.562436\pi$
$719$	−31.5259	+	31.5259i	−1.17572	+	1.17572i	−0.980824	+	0.194895i	$0.937564\pi$
$720$	1.12418	+	4.77463i	0.0418958	+	0.177940i
$721$	7.64368	+	7.64368i	0.284666	+	0.284666i
$722$	22.4885	+	13.2138i	0.836934	+	0.491768i
$723$	51.5495			1.91715
$724$	40.8329	+	11.6127i	1.51754	+	0.431583i
$725$	−1.12764	+	1.12764i	−0.0418795	+	0.0418795i
$726$	24.2103	−	6.28927i	0.898528	−	0.233417i
$727$	−11.1110			−0.412084			−0.206042	−	0.978543i	$-0.566058\pi$
$727$	−11.1110			−0.412084			−0.206042	+	0.978543i	$0.566058\pi$
$728$	29.9188	+	31.3228i	1.10886	+	1.16090i
$729$		−	8.78458i		−	0.325355i
$730$	5.68454	+	3.34014i	0.210394	+	0.123624i
$731$	−1.47088	−	0.403226i	−0.0544025	−	0.0149139i
$732$	−17.4341	−	31.2914i	−0.644383	−	1.15656i
$733$	30.4267			1.12384			0.561918	−	0.827193i	$-0.310064\pi$
$733$	30.4267			1.12384			0.561918	+	0.827193i	$0.310064\pi$
$734$	4.37044	+	16.8238i	0.161316	+	0.620980i
$735$	7.28161			0.268586
$736$	−31.1590	−	9.63866i	−1.14853	−	0.355286i
$737$	2.92967	+	2.92967i	0.107916	+	0.107916i
$738$	18.6129	−	4.83519i	0.685149	−	0.177986i
$739$	2.07238			0.0762337			0.0381168	−	0.999273i	$-0.487864\pi$
$739$	2.07238			0.0762337			0.0381168	+	0.999273i	$0.487864\pi$
$740$	3.13129	−	1.74460i	0.115108	−	0.0641329i
$741$	5.11415	−	5.11415i	0.187873	−	0.187873i
$742$	4.85293	+	18.6812i	0.178157	+	0.685807i
$743$	24.1445	−	24.1445i	0.885775	−	0.885775i	−0.108339	−	0.994114i	$-0.534553\pi$
$743$	24.1445	−	24.1445i	0.885775	−	0.885775i	0.994114	+	0.108339i	$0.0345532\pi$
$744$	−0.529272	+	23.0866i	−0.0194040	+	0.846397i
$745$	−7.79323	+	7.79323i	−0.285522	+	0.285522i
$746$	13.2514	−	22.5523i	0.485166	−	0.825699i
$747$			13.8260i			0.505869i
$748$	−10.9181	−	6.61380i	−0.399207	−	0.241825i
$749$		−	31.6905i		−	1.15795i
$750$	−2.50665	−	1.47286i	−0.0915298	−	0.0537813i
$751$	28.2120	−	28.2120i	1.02947	−	1.02947i	0.0299198	−	0.999552i	$-0.490475\pi$
$751$	28.2120	−	28.2120i	1.02947	−	1.02947i	0.999552	−	0.0299198i	$-0.00952519\pi$
$752$	10.1242	−	16.3599i	0.369193	−	0.596584i
$753$	7.41899	−	7.41899i	0.270363	−	0.270363i
$754$	10.2958	−	2.67460i	0.374950	−	0.0974032i
$755$	13.1619	−	13.1619i	0.479012	−	0.479012i
$756$	11.5245	+	20.6846i	0.419141	+	0.752291i
$757$	23.8799			0.867929			0.433964	−	0.900930i	$-0.357114\pi$
$757$	23.8799			0.867929			0.433964	+	0.900930i	$0.357114\pi$
$758$	4.04008	+	15.5521i	0.146742	+	0.564878i
$759$	12.9744	+	12.9744i	0.470941	+	0.470941i
$760$	1.52556	−	1.45718i	0.0553379	−	0.0528575i
$761$	14.9676			0.542575			0.271288	−	0.962498i	$-0.412551\pi$
$761$	14.9676			0.542575			0.271288	+	0.962498i	$0.412551\pi$
$762$	−46.8407	+	12.1681i	−1.69686	+	0.440805i
$763$	26.4788			0.958596
$764$	−24.1414	−	43.3299i	−0.873404	−	1.56762i
$765$	4.39327	−	2.50279i	0.158839	−	0.0904885i
$766$	18.6307	−	31.7073i	0.673154	−	1.14563i
$767$			6.42995i			0.232172i
$768$	10.4382	−	31.1926i	0.376656	−	1.12557i
$769$	40.0587			1.44455			0.722277	−	0.691603i	$-0.243095\pi$
$769$	40.0587			1.44455			0.722277	+	0.691603i	$0.243095\pi$
$770$	−1.78717	−	6.87964i	−0.0644052	−	0.247925i
$771$	−0.692356	+	0.692356i	−0.0249346	+	0.0249346i
$772$	9.74432	−	34.2632i	0.350706	−	1.23316i
$773$	−51.5443			−1.85392			−0.926960	−	0.375160i	$-0.877588\pi$
$773$	−51.5443			−1.85392			−0.926960	+	0.375160i	$0.877588\pi$
$774$	−0.324987	+	0.553092i	−0.0116814	+	0.0198805i
$775$	−2.80824	−	2.80824i	−0.100875	−	0.100875i
$776$	−31.4015	−	32.8751i	−1.12725	−	1.18015i
$777$	−8.45911	+	8.45911i	−0.303469	+	0.303469i
$778$	8.93457	+	5.24980i	0.320320	+	0.188214i
$779$	−5.84840	−	5.84840i	−0.209541	−	0.209541i
$780$	9.43882	+	16.9412i	0.337964	+	0.606592i
$781$		−	11.5680i		−	0.413937i
$782$	−0.450713	+	33.6165i	−0.0161175	+	1.20212i
$783$	5.81495			0.207809
$784$	−12.0476	−	7.45561i	−0.430272	−	0.266272i
$785$	1.94405	−	1.94405i	0.0693861	−	0.0693861i
$786$	−13.2415	+	22.5355i	−0.472307	+	0.803814i
$787$	−33.7505	−	33.7505i	−1.20308	−	1.20308i	−0.973226	−	0.229849i	$-0.926177\pi$
$787$	−33.7505	−	33.7505i	−1.20308	−	1.20308i	−0.229849	−	0.973226i	$-0.573823\pi$
$788$	43.3686	+	12.3339i	1.54494	+	0.439375i
$789$	7.03381	−	7.03381i	0.250410	−	0.250410i
$790$	−7.81221	+	13.2955i	−0.277946	+	0.473032i
$791$			22.9647i			0.816530i
$792$	−3.88263	+	3.70860i	−0.137963	+	0.131779i
$793$	−29.0566	−	29.0566i	−1.03183	−	1.03183i
$794$	29.2316	−	7.59370i	1.03739	−	0.269490i
$795$			8.64149i			0.306482i
$796$	−6.96715	−	1.98143i	−0.246944	−	0.0702299i
$797$	9.74242			0.345094			0.172547	−	0.985001i	$-0.444800\pi$
$797$	9.74242			0.345094			0.172547	+	0.985001i	$0.444800\pi$
$798$	−3.56692	+	6.07049i	−0.126268	+	0.214893i
$799$	−19.1256	−	5.24309i	−0.676617	−	0.185487i
$800$	2.63926	+	5.00343i	0.0933118	+	0.176898i
$801$			5.28805i			0.186844i
$802$	−1.27701	−	4.91580i	−0.0450928	−	0.173583i
$803$			7.21693i			0.254680i
$804$	10.5849	+	3.01029i	0.373299	+	0.106165i
$805$	−13.2373	+	13.2373i	−0.466552	+	0.466552i
$806$	6.66075	+	25.6403i	0.234615	+	0.903141i
$807$			29.5835i			1.04139i
$808$	−27.7315	−	0.635757i	−0.975590	−	0.0223658i
$809$	−14.9766	−	14.9766i	−0.526549	−	0.526549i	0.392993	−	0.919542i	$-0.371440\pi$
$809$	−14.9766	−	14.9766i	−0.526549	−	0.526549i	−0.919542	+	0.392993i	$0.871440\pi$
$810$	3.97361	+	15.2963i	0.139619	+	0.537456i
$811$	−3.07087	−	3.07087i	−0.107833	−	0.107833i	0.651132	−	0.758965i	$-0.274294\pi$
$811$	−3.07087	−	3.07087i	−0.107833	−	0.107833i	−0.758965	+	0.651132i	$0.774294\pi$
$812$	−9.04632	+	5.04018i	−0.317463	+	0.176875i
$813$	−0.769627	−	0.769627i	−0.0269920	−	0.0269920i
$814$	3.38284	+	1.98770i	0.118568	+	0.0696688i
$815$	−21.2672			−0.744959
$816$	−33.8827	−	1.23144i	−1.18613	−	0.0431089i
$817$	0.275904			0.00965266
$818$	0.244874	+	0.143883i	0.00856180	+	0.00503077i
$819$	−13.2795	−	13.2795i	−0.464023	−	0.464023i
$820$	19.3735	−	10.7940i	0.676551	−	0.376942i
$821$	−16.1141	−	16.1141i	−0.562388	−	0.562388i	0.367597	−	0.929985i	$-0.380180\pi$
$821$	−16.1141	−	16.1141i	−0.562388	−	0.562388i	−0.929985	+	0.367597i	$0.880180\pi$
$822$	11.8501	+	45.6166i	0.413321	+	1.59106i
$823$	6.64179	+	6.64179i	0.231518	+	0.231518i	0.813326	−	0.581808i	$-0.197655\pi$
$823$	6.64179	+	6.64179i	0.231518	+	0.231518i	−0.581808	+	0.813326i	$0.697655\pi$
$824$	0.215827	−	9.41428i	0.00751868	−	0.327962i
$825$		−	3.18237i		−	0.110796i
$826$	−1.57386	−	6.05849i	−0.0547614	−	0.210802i
$827$	−25.9387	+	25.9387i	−0.901978	+	0.901978i	−0.995607	−	0.0936295i	$-0.970153\pi$
$827$	−25.9387	+	25.9387i	−0.901978	+	0.901978i	0.0936295	+	0.995607i	$0.470153\pi$
$828$	13.6016	+	3.86823i	0.472687	+	0.134430i
$829$		−	13.4578i		−	0.467409i	−0.972308	−	0.233705i	$-0.924915\pi$
$829$		−	13.4578i		−	0.467409i	0.972308	−	0.233705i	$-0.0750849\pi$
$830$	4.00900	+	15.4325i	0.139155	+	0.535670i
$831$			46.3517i			1.60792i
$832$	1.72921	−	37.6940i	0.0599497	−	1.30680i
$833$	−3.86107	+	14.0844i	−0.133778	+	0.487994i
$834$	−31.2134	+	53.1216i	−1.08083	+	1.83945i
$835$	−18.8955			−0.653907
$836$	2.22117	+	0.631691i	0.0768207	+	0.0218475i
$837$			14.4814i			0.500550i
$838$	−46.8662	+	12.1748i	−1.61897	+	0.420570i
$839$	8.38909	+	8.38909i	0.289624	+	0.289624i	0.836931	−	0.547308i	$-0.184347\pi$
$839$	8.38909	+	8.38909i	0.289624	+	0.289624i	−0.547308	+	0.836931i	$0.684347\pi$
$840$	−13.0402	−	13.6522i	−0.449930	−	0.471044i
$841$		−	26.4569i		−	0.912305i
$842$	26.5657	−	45.2118i	0.915514	−	1.55810i
$843$	24.6955	−	24.6955i	0.850558	−	0.850558i
$844$	−46.4388	−	13.2070i	−1.59849	−	0.454604i
$845$	6.53884	+	6.53884i	0.224943	+	0.224943i
$846$	−4.22576	+	7.19177i	−0.145285	+	0.247258i
$847$	−19.7529	+	19.7529i	−0.678719	+	0.678719i
$848$	8.84798	−	14.2976i	0.303841	−	0.490981i
$849$	−26.8168			−0.920351
$850$	4.17801	−	4.06746i	0.143305	−	0.139513i
$851$		−	10.3336i		−	0.354230i
$852$	−14.9544	−	26.8407i	−0.512329	−	0.919549i
$853$	1.76807	+	1.76807i	0.0605376	+	0.0605376i	0.736727	−	0.676190i	$-0.236370\pi$
$853$	1.76807	+	1.76807i	0.0605376	+	0.0605376i	−0.676190	+	0.736727i	$0.736370\pi$
$854$	34.4901	+	20.2658i	1.18023	+	0.693482i
$855$	−0.646772	+	0.646772i	−0.0221191	+	0.0221191i
$856$	−19.9631	+	19.0683i	−0.682325	+	0.651741i
$857$	−29.1729	−	29.1729i	−0.996527	−	0.996527i	0.00346734	−	0.999994i	$-0.498896\pi$
$857$	−29.1729	−	29.1729i	−0.996527	−	0.996527i	−0.999994	+	0.00346734i	$0.998896\pi$
$858$	−10.7540	+	18.3022i	−0.367137	+	0.624825i
$859$	−31.1241			−1.06194			−0.530970	−	0.847391i	$-0.678172\pi$
$859$	−31.1241			−1.06194			−0.530970	+	0.847391i	$0.678172\pi$
$860$	−0.202373	+	0.711589i	−0.00690086	+	0.0242650i
$861$	−52.3370	+	52.3370i	−1.78364	+	1.78364i
$862$	8.49858	+	32.7150i	0.289463	+	1.11428i
$863$	4.19277			0.142724			0.0713618	−	0.997450i	$-0.477265\pi$
$863$	4.19277			0.142724			0.0713618	+	0.997450i	$0.477265\pi$
$864$	6.09572	−	19.7057i	0.207381	−	0.670401i
$865$			9.56843i			0.325336i
$866$	7.76384	−	13.2132i	0.263826	−	0.449002i
$867$	8.65545	+	33.8598i	0.293954	+	1.14994i
$868$	−12.5519	−	22.5287i	−0.426040	−	0.764674i
$869$	−16.8796			−0.572601
$870$	−4.48745	+	1.16574i	−0.152139	+	0.0395221i
$871$	12.6242			0.427753
$872$	−15.9324	−	16.6800i	−0.539538	−	0.564857i
$873$	13.9376	+	13.9376i	0.471717	+	0.471717i
$874$	−1.52917	−	5.88648i	−0.0517250	−	0.199113i
$875$	3.24684			0.109763
$876$	9.32956	+	16.7451i	0.315217	+	0.565764i
$877$	−5.23997	+	5.23997i	−0.176941	+	0.176941i	−0.790021	−	0.613080i	$-0.789930\pi$
$877$	−5.23997	+	5.23997i	−0.176941	+	0.176941i	0.613080	+	0.790021i	$0.289930\pi$
$878$	−12.7025	+	3.29982i	−0.428690	+	0.111364i
$879$	21.0535	−	21.0535i	0.710116	−	0.710116i
$880$	−3.25841	+	5.26531i	−0.109841	+	0.177494i
$881$	2.34608	−	2.34608i	0.0790416	−	0.0790416i	−0.666481	−	0.745522i	$-0.732200\pi$
$881$	2.34608	−	2.34608i	0.0790416	−	0.0790416i	0.745522	+	0.666481i	$0.232200\pi$
$882$	5.29611	+	3.11190i	0.178329	+	0.104783i
$883$			31.6578i			1.06537i	0.846313	+	0.532685i	$0.178817\pi$
$883$			31.6578i			1.06537i	−0.846313	+	0.532685i	$0.821183\pi$
$884$	−37.7732	+	9.27385i	−1.27045	+	0.311913i
$885$		−	2.80252i		−	0.0942057i
$886$	26.7086	−	45.4550i	0.897292	−	1.52709i
$887$	−13.2159	+	13.2159i	−0.443746	+	0.443746i	−0.893269	−	0.449523i	$-0.851594\pi$
$887$	−13.2159	+	13.2159i	−0.443746	+	0.443746i	0.449523	+	0.893269i	$0.351594\pi$
$888$	10.4186	+	0.238851i	0.349625	+	0.00801531i
$889$	38.2169	−	38.2169i	1.28175	−	1.28175i
$890$	1.53333	+	5.90247i	0.0513972	+	0.197851i
$891$	−12.2322	+	12.2322i	−0.409796	+	0.409796i
$892$	23.3680	−	13.0195i	0.782418	−	0.435926i
$893$	3.58754			0.120052
$894$	−31.0132	+	8.05651i	−1.03724	+	0.269450i
$895$	−1.10106	−	1.10106i	−0.0368044	−	0.0368044i
$896$	7.59702	+	35.9397i	0.253799	+	1.20066i
$897$	55.9076			1.86670
$898$	13.0422	+	50.2054i	0.435224	+	1.67538i
$899$	−6.33337			−0.211230
$900$	−1.19370	−	2.14250i	−0.0397900	−	0.0714167i
$901$	−16.7147	−	4.58215i	−0.556847	−	0.152653i
$902$	20.9298	+	12.2980i	0.696887	+	0.409479i
$903$		−	2.46905i		−	0.0821648i
$904$	14.4663	−	13.8179i	0.481144	−	0.459577i
$905$	−21.2261			−0.705578
$906$	52.3780	−	13.6066i	1.74014	−	0.452049i
$907$	5.28525	−	5.28525i	0.175494	−	0.175494i	−0.613894	−	0.789388i	$-0.710398\pi$
$907$	5.28525	−	5.28525i	0.175494	−	0.175494i	0.789388	+	0.613894i	$0.210398\pi$
$908$	−7.87549	−	2.23976i	−0.261357	−	0.0743289i
$909$	12.0265			0.398893
$910$	−18.6730	−	10.9719i	−0.619003	−	0.363715i
$911$	−1.21081	−	1.21081i	−0.0401160	−	0.0401160i	0.686764	−	0.726880i	$-0.259030\pi$
$911$	−1.21081	−	1.21081i	−0.0401160	−	0.0401160i	−0.726880	+	0.686764i	$0.759030\pi$
$912$	5.97027	−	1.40569i	0.197695	−	0.0465472i
$913$	−12.3412	+	12.3412i	−0.408434	+	0.408434i
$914$	3.89301	−	6.62547i	0.128769	−	0.219151i
$915$	12.6644	+	12.6644i	0.418673	+	0.418673i
$916$	9.25550	+	16.6122i	0.305810	+	0.548881i
$917$		−	29.1901i		−	0.963941i
$918$	−21.2599	−	0.285042i	−0.701681	−	0.00940779i
$919$	−23.4449			−0.773374			−0.386687	−	0.922211i	$-0.626381\pi$
$919$	−23.4449			−0.773374			−0.386687	+	0.922211i	$0.626381\pi$
$920$	16.3036	+	0.373767i	0.537513	+	0.0123227i
$921$	12.1476	−	12.1476i	0.400276	−	0.400276i
$922$	−25.6951	−	15.0980i	−0.846222	−	0.497225i
$923$	−24.9237	−	24.9237i	−0.820375	−	0.820375i
$924$	5.65296	−	19.8771i	0.185969	−	0.653908i
$925$	−1.26731	+	1.26731i	−0.0416689	+	0.0416689i
$926$	−1.57070	−	0.922919i	−0.0516165	−	0.0303290i
$927$			4.08275i			0.134095i
$928$	8.61820	+	2.66594i	0.282906	+	0.0875137i
$929$	−30.9108	−	30.9108i	−1.01415	−	1.01415i	−0.999898	−	0.0142505i	$-0.995464\pi$
$929$	−30.9108	−	30.9108i	−1.01415	−	1.01415i	−0.0142505	−	0.999898i	$-0.504536\pi$
$930$	−2.90312	−	11.1754i	−0.0951969	−	0.366457i
$931$		−	2.64191i		−	0.0865850i
$932$	−30.3803	−	8.64004i	−0.995141	−	0.283014i
$933$	−48.6423			−1.59248
$934$	−31.5101	−	18.5148i	−1.03104	−	0.605823i
$935$	6.15545	+	1.68745i	0.201305	+	0.0551855i
$936$	−0.374959	+	16.3556i	−0.0122559	+	0.534599i
$937$		−	25.4269i		−	0.830662i	−0.909670	−	0.415331i	$-0.863666\pi$
$937$		−	25.4269i		−	0.830662i	0.909670	−	0.415331i	$-0.136334\pi$
$938$	−11.8949	+	3.09001i	−0.388381	+	0.100892i
$939$			59.2900i			1.93486i
$940$	−2.63142	+	9.25268i	−0.0858276	+	0.301789i
$941$	−2.01292	+	2.01292i	−0.0656194	+	0.0656194i	−0.739155	−	0.673535i	$-0.764775\pi$
$941$	−2.01292	+	2.01292i	−0.0656194	+	0.0656194i	0.673535	+	0.739155i	$0.264775\pi$
$942$	7.73636	−	2.00973i	0.252064	−	0.0654804i
$943$		−	63.9344i		−	2.08199i
$944$	−2.86949	+	4.63685i	−0.0933939	+	0.150916i
$945$	−8.37157	−	8.37157i	−0.272327	−	0.272327i
$946$	−0.783778	+	0.203607i	−0.0254828	+	0.00661984i
$947$	36.7429	+	36.7429i	1.19398	+	1.19398i	0.975938	+	0.218046i	$0.0699684\pi$
$947$	36.7429	+	36.7429i	1.19398	+	1.19398i	0.218046	+	0.975938i	$0.430032\pi$
$948$	−39.1649	+	21.8208i	−1.27202	+	0.708706i
$949$	15.5491	+	15.5491i	0.504746	+	0.504746i
$950$	−0.534382	+	0.909458i	−0.0173376	+	0.0295067i
$951$	63.5653			2.06125
$952$	33.3211	−	17.9838i	1.07994	−	0.582859i
$953$	8.39956			0.272089			0.136044	−	0.990703i	$-0.456561\pi$
$953$	8.39956			0.272089			0.136044	+	0.990703i	$0.456561\pi$
$954$	−3.69306	+	6.28518i	−0.119567	+	0.203490i
$955$	17.5367	+	17.5367i	0.567475	+	0.567475i
$956$	21.5020	+	38.5927i	0.695424	+	1.24818i
$957$	−3.58857	−	3.58857i	−0.116002	−	0.116002i
$958$	20.9217	−	5.43497i	0.675950	−	0.175596i
$959$	−37.2181	−	37.2181i	−1.20184	−	1.20184i
$960$	−0.753685	+	16.4291i	−0.0243251	+	0.530247i
$961$			15.2275i			0.491211i
$962$	11.5710	−	3.00588i	0.373064	−	0.0969134i
$963$	8.46349	−	8.46349i	0.272732	−	0.272732i
$964$	48.2375	+	13.7186i	1.55363	+	0.441845i
$965$			17.8110i			0.573355i
$966$	−52.6778	+	13.6845i	−1.69488	+	0.440290i
$967$			26.1643i			0.841388i	0.907203	+	0.420694i	$0.138213\pi$
$967$			26.1643i			0.841388i	−0.907203	+	0.420694i	$0.861787\pi$
$968$	24.3286	+	0.557743i	0.781949	+	0.0179265i
$969$	−3.12952	−	5.49340i	−0.100535	−	0.176473i
$970$	19.5984	+	11.5157i	0.629266	+	0.369746i
$971$	−28.8634			−0.926269			−0.463135	−	0.886288i	$-0.653275\pi$
$971$	−28.8634			−0.926269			−0.463135	+	0.886288i	$0.653275\pi$
$972$	−6.58409	+	23.1512i	−0.211185	+	0.742574i
$973$		−	68.8081i		−	2.20589i
$974$	9.11429	+	35.0851i	0.292041	+	1.12420i
$975$	−6.85652	−	6.85652i	−0.219584	−	0.219584i
$976$	−7.98659	−	33.9207i	−0.255645	−	1.08577i
$977$			13.4896i			0.431570i	0.976441	+	0.215785i	$0.0692311\pi$
$977$			13.4896i			0.431570i	−0.976441	+	0.215785i	$0.930769\pi$
$978$	−53.3094	−	31.3237i	−1.70465	−	1.00162i
$979$	−4.72014	+	4.72014i	−0.150856	+	0.150856i
$980$	6.81379	+	1.93781i	0.217658	+	0.0619012i
$981$	7.07160	+	7.07160i	0.225779	+	0.225779i
$982$	35.4043	+	20.8029i	1.12980	+	0.663849i
$983$	0.0620968	−	0.0620968i	0.00198058	−	0.00198058i	−0.706116	−	0.708096i	$-0.749554\pi$
$983$	0.0620968	−	0.0620968i	0.00198058	−	0.00198058i	0.708096	+	0.706116i	$0.249554\pi$
$984$	64.4605	+	1.47779i	2.05492	+	0.0471101i
$985$	−22.5442			−0.718317
$986$	0.124662	−	9.29792i	0.00397004	−	0.296106i
$987$		−	32.1047i		−	1.02190i
$988$	6.14658	−	3.42458i	0.195549	−	0.108950i
$989$	1.50808	+	1.50808i	0.0479542	+	0.0479542i
$990$	1.36003	−	2.31462i	0.0432246	−	0.0735634i
$991$	−4.80337	+	4.80337i	−0.152584	+	0.152584i	−0.779271	−	0.626687i	$-0.784410\pi$
$991$	−4.80337	+	4.80337i	−0.152584	+	0.152584i	0.626687	+	0.779271i	$0.284410\pi$
$992$	−6.63918	+	21.4625i	−0.210794	+	0.681436i
$993$	25.4022	+	25.4022i	0.806115	+	0.806115i
$994$	29.5845	+	17.3833i	0.938362	+	0.551366i
$995$	3.62172			0.114816
$996$	−12.6808	+	44.5885i	−0.401806	+	1.41284i
$997$	27.5942	−	27.5942i	0.873919	−	0.873919i	−0.118978	−	0.992897i	$-0.537962\pi$
$997$	27.5942	−	27.5942i	0.873919	−	0.873919i	0.992897	+	0.118978i	$0.0379619\pi$
$998$	−34.3945	+	8.93490i	−1.08874	+	0.282829i
$999$	6.53520			0.206765

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.ba.b.21.12	✓	140
8.5	even	2	inner	680.2.ba.b.21.59	yes	140
17.13	even	4	inner	680.2.ba.b.421.59	yes	140
136.13	even	4	inner	680.2.ba.b.421.12	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.ba.b.21.12	✓	140	1.1	even	1	trivial
680.2.ba.b.21.59	yes	140	8.5	even	2	inner
680.2.ba.b.421.12	yes	140	136.13	even	4	inner
680.2.ba.b.421.59	yes	140	17.13	even	4	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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.ba (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21931 - 0.716444i) q^{2} +(1.45367 + 1.45367i) q^{3} +(0.973417 + 1.74713i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.730995 - 2.81394i) q^{6} +(2.29587 + 2.29587i) q^{7} +(0.0648259 - 2.82768i) q^{8} +1.22630i q^{9} +(0.355578 + 1.36878i) q^{10} +(-1.09460 + 1.09460i) q^{11} +(-1.12472 + 3.95477i) q^{12} +4.71671i q^{13} +(-1.15451 - 4.44422i) q^{14} -2.05580i q^{15} +(-2.10492 + 3.40137i) q^{16} +(3.97639 + 1.09009i) q^{17} +(0.878574 - 1.49523i) q^{18} -0.745881 q^{19} +(0.547097 - 1.92372i) q^{20} +6.67485i q^{21} +(2.11887 - 0.550434i) q^{22} +(-4.07696 - 4.07696i) q^{23} +(4.20475 - 4.01628i) q^{24} +1.00000i q^{25} +(3.37925 - 5.75111i) q^{26} +(2.57837 - 2.57837i) q^{27} +(-1.77634 + 6.24601i) q^{28} +(1.12764 + 1.12764i) q^{29} +(-1.47286 + 2.50665i) q^{30} +(-2.80824 + 2.80824i) q^{31} +(5.00343 - 2.63926i) q^{32} -3.18237 q^{33} +(-4.06746 - 4.17801i) q^{34} -3.24684i q^{35} +(-2.14250 + 1.19370i) q^{36} +(1.26731 + 1.26731i) q^{37} +(0.909458 + 0.534382i) q^{38} +(-6.85652 + 6.85652i) q^{39} +(-2.04531 + 1.95364i) q^{40} +(7.84093 + 7.84093i) q^{41} +(4.78215 - 8.13869i) q^{42} -0.369903 q^{43} +(-2.97791 - 0.846905i) q^{44} +(0.867124 - 0.867124i) q^{45} +(2.05015 + 7.89198i) q^{46} -4.80980 q^{47} +(-8.00431 + 1.88461i) q^{48} +3.54199i q^{49} +(0.716444 - 1.21931i) q^{50} +(4.19573 + 7.36498i) q^{51} +(-8.24069 + 4.59132i) q^{52} -4.20348 q^{53} +(-4.99108 + 1.29657i) q^{54} +1.54800 q^{55} +(6.64081 - 6.34315i) q^{56} +(-1.08426 - 1.08426i) q^{57} +(-0.567048 - 2.18283i) q^{58} +1.36323 q^{59} +(3.59174 - 2.00115i) q^{60} +(-6.16035 + 6.16035i) q^{61} +(5.43606 - 1.41216i) q^{62} +(-2.81542 + 2.81542i) q^{63} +(-7.99160 - 0.366615i) q^{64} +(3.33522 - 3.33522i) q^{65} +(3.88028 + 2.27999i) q^{66} -2.67648i q^{67} +(1.96617 + 8.00838i) q^{68} -11.8531i q^{69} +(-2.32618 + 3.95890i) q^{70} +(-5.28414 + 5.28414i) q^{71} +(3.46758 + 0.0794959i) q^{72} +(3.29661 - 3.29661i) q^{73} +(-0.637284 - 2.45320i) q^{74} +(-1.45367 + 1.45367i) q^{75} +(-0.726053 - 1.30315i) q^{76} -5.02611 q^{77} +(13.2725 - 3.44789i) q^{78} +(7.71039 + 7.71039i) q^{79} +(3.89353 - 0.916729i) q^{80} +11.1751 q^{81} +(-3.94291 - 15.1781i) q^{82} +11.2746 q^{83} +(-11.6618 + 6.49741i) q^{84} +(-2.04093 - 3.58254i) q^{85} +(0.451026 + 0.265015i) q^{86} +3.27843i q^{87} +(3.02422 + 3.16614i) q^{88} +4.31221 q^{89} +(-1.67854 + 0.436044i) q^{90} +(-10.8289 + 10.8289i) q^{91} +(3.15440 - 11.0916i) q^{92} -8.16450 q^{93} +(5.86462 + 3.44595i) q^{94} +(0.527418 + 0.527418i) q^{95} +(11.1099 + 3.43672i) q^{96} +(11.3656 - 11.3656i) q^{97} +(2.53764 - 4.31877i) q^{98} +(-1.34231 - 1.34231i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 8 q^{4} - 4 q^{6} - 12 q^{7} + 20 q^{12} + 28 q^{14} - 24 q^{16} - 16 q^{17} - 8 q^{20} + 40 q^{22} + 4 q^{23} + 48 q^{24} - 20 q^{28} + 28 q^{31} - 8 q^{34} - 56 q^{38} + 24 q^{40} + 44 q^{41}+ \cdots + 176 q^{98}+O(q^{100}) \) 140 * q - 8 * q^4 - 4 * q^6 - 12 * q^7 + 20 * q^12 + 28 * q^14 - 24 * q^16 - 16 * q^17 - 8 * q^20 + 40 * q^22 + 4 * q^23 + 48 * q^24 - 20 * q^28 + 28 * q^31 - 8 * q^34 - 56 * q^38 + 24 * q^40 + 44 * q^41 + 28 * q^44 - 40 * q^46 - 120 * q^47 + 32 * q^48 - 48 * q^52 - 4 * q^54 + 16 * q^55 + 16 * q^56 - 16 * q^57 - 52 * q^58 - 72 * q^62 + 44 * q^63 - 104 * q^64 + 8 * q^68 + 12 * q^71 - 104 * q^72 + 36 * q^73 + 20 * q^74 + 28 * q^78 - 44 * q^79 - 76 * q^81 - 44 * q^82 + 48 * q^84 + 120 * q^86 + 28 * q^88 + 24 * q^89 + 28 * q^90 - 72 * q^92 + 8 * q^95 - 116 * q^96 + 12 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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