LMFDB - Embedded newform 240.2.bb.a.173.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(173,240)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("240.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bb (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			173.8
Character	$\chi$	$=$	240.173
Dual form			240.2.bb.a.197.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23701 + 0.685419i) q^{2} +(0.117548 + 1.72806i) q^{3} +(1.06040 - 1.69575i) q^{4} +(-1.15738 + 1.91324i) q^{5} +(-1.32985 - 2.05706i) q^{6} +(0.912923 + 0.912923i) q^{7} +(-0.149432 + 2.82448i) q^{8} +(-2.97237 + 0.406258i) q^{9} +(0.120323 - 3.15999i) q^{10} +(-1.03554 - 1.03554i) q^{11} +(3.05499 + 1.63310i) q^{12} +2.08132i q^{13} +(-1.75503 - 0.503562i) q^{14} +(-3.44223 - 1.77512i) q^{15} +(-1.75110 - 3.59634i) q^{16} +(1.49126 + 1.49126i) q^{17} +(3.39840 - 2.53986i) q^{18} +(-2.35078 + 2.35078i) q^{19} +(2.01708 + 3.99142i) q^{20} +(-1.47027 + 1.68489i) q^{21} +(1.99075 + 0.571195i) q^{22} +(-4.27105 - 4.27105i) q^{23} +(-4.89842 + 0.0737840i) q^{24} +(-2.32095 - 4.42868i) q^{25} +(-1.42658 - 2.57462i) q^{26} +(-1.05143 - 5.08866i) q^{27} +(2.51615 - 0.580021i) q^{28} +(2.58251 + 2.58251i) q^{29} +(5.47478 - 0.163524i) q^{30} -5.18620 q^{31} +(4.63114 + 3.24847i) q^{32} +(1.66774 - 1.91119i) q^{33} +(-2.86685 - 0.822570i) q^{34} +(-2.80323 + 0.690039i) q^{35} +(-2.46299 + 5.47117i) q^{36} +10.8954i q^{37} +(1.29667 - 4.51922i) q^{38} +(-3.59664 + 0.244654i) q^{39} +(-5.23094 - 3.55489i) q^{40} +9.82802 q^{41} +(0.663884 - 3.09199i) q^{42} +0.814988 q^{43} +(-2.85409 + 0.657923i) q^{44} +(2.66289 - 6.15703i) q^{45} +(8.21081 + 2.35588i) q^{46} +(6.63331 + 6.63331i) q^{47} +(6.00884 - 3.44875i) q^{48} -5.33314i q^{49} +(5.90654 + 3.88751i) q^{50} +(-2.40169 + 2.75228i) q^{51} +(3.52938 + 2.20703i) q^{52} +7.26025i q^{53} +(4.78850 + 5.57407i) q^{54} +(3.17974 - 0.782718i) q^{55} +(-2.71495 + 2.44211i) q^{56} +(-4.33861 - 3.78596i) q^{57} +(-4.96470 - 1.42449i) q^{58} +(6.09835 - 6.09835i) q^{59} +(-6.66029 + 3.95480i) q^{60} +(9.87198 + 9.87198i) q^{61} +(6.41539 - 3.55472i) q^{62} +(-3.08442 - 2.34266i) q^{63} +(-7.95534 - 0.844133i) q^{64} +(-3.98205 - 2.40887i) q^{65} +(-0.753050 + 3.50727i) q^{66} +10.8038 q^{67} +(4.11014 - 0.947466i) q^{68} +(6.87857 - 7.88268i) q^{69} +(2.99467 - 2.77498i) q^{70} -2.57569 q^{71} +(-0.703301 - 8.45608i) q^{72} +(7.40366 - 7.40366i) q^{73} +(-7.46794 - 13.4778i) q^{74} +(7.38019 - 4.53131i) q^{75} +(1.49356 + 6.47909i) q^{76} -1.89073i q^{77} +(4.28139 - 2.76785i) q^{78} +8.54920i q^{79} +(8.90733 + 0.812052i) q^{80} +(8.66991 - 2.41509i) q^{81} +(-12.1574 + 6.73632i) q^{82} -11.5636 q^{83} +(1.29808 + 4.27987i) q^{84} +(-4.57909 + 1.12718i) q^{85} +(-1.00815 + 0.558608i) q^{86} +(-4.15916 + 4.76629i) q^{87} +(3.07959 - 2.77011i) q^{88} +9.67152i q^{89} +(0.926126 + 9.44152i) q^{90} +(-1.90008 + 1.90008i) q^{91} +(-11.7716 + 2.71359i) q^{92} +(-0.609625 - 8.96205i) q^{93} +(-12.7521 - 3.65889i) q^{94} +(-1.77685 - 7.21834i) q^{95} +(-5.06917 + 8.38472i) q^{96} +(-6.58488 + 6.58488i) q^{97} +(3.65544 + 6.59717i) q^{98} +(3.49869 + 2.65730i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{4} - 4 q^{6} - 12 q^{10} + 4 q^{12} - 4 q^{15} - 12 q^{16} + 16 q^{18} - 8 q^{19} - 4 q^{21} - 20 q^{22} - 12 q^{24} - 36 q^{28} - 16 q^{30} - 16 q^{31} - 4 q^{33} + 28 q^{34} - 20 q^{36} + 24 q^{39}+ \cdots - 32 q^{99}+O(q^{100}) $ 88 * q - 4 * q^4 - 4 * q^6 - 12 * q^10 + 4 * q^12 - 4 * q^15 - 12 * q^16 + 16 * q^18 - 8 * q^19 - 4 * q^21 - 20 * q^22 - 12 * q^24 - 36 * q^28 - 16 * q^30 - 16 * q^31 - 4 * q^33 + 28 * q^34 - 20 * q^36 + 24 * q^39 - 4 * q^40 - 20 * q^42 - 40 * q^43 + 8 * q^45 - 36 * q^46 + 16 * q^48 - 4 * q^51 + 24 * q^52 - 24 * q^54 + 12 * q^57 + 44 * q^58 - 56 * q^60 - 24 * q^61 - 32 * q^63 - 28 * q^64 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 28 * q^70 + 64 * q^72 - 24 * q^75 - 36 * q^76 + 20 * q^78 - 8 * q^81 - 48 * q^82 + 48 * q^84 - 24 * q^85 - 12 * q^87 + 60 * q^88 + 76 * q^90 - 8 * q^91 - 20 * q^94 + 48 * q^96 - 8 * q^97 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.23701	+	0.685419i	−0.874700	+	0.484665i
$2$	−1.23701	+	0.685419i	−0.874700	+	0.484665i
$3$	0.117548	+	1.72806i	0.0678662	+	0.997694i
$3$	0.117548	+	1.72806i	0.0678662	+	0.997694i
$4$	1.06040	−	1.69575i	0.530200	−	0.847873i
$5$	−1.15738	+	1.91324i	−0.517596	+	0.855625i
$5$	−1.15738	+	1.91324i	−0.517596	+	0.855625i
$6$	−1.32985	−	2.05706i	−0.542910	−	0.839791i
$7$	0.912923	+	0.912923i	0.345052	+	0.345052i	0.858263	−	0.513210i	$-0.171544\pi$
$7$	0.912923	+	0.912923i	0.345052	+	0.345052i	−0.513210	+	0.858263i	$0.671544\pi$
$8$	−0.149432	+	2.82448i	−0.0528321	+	0.998603i
$9$	−2.97237	+	0.406258i	−0.990788	+	0.135419i
$10$	0.120323	−	3.15999i	0.0380495	−	0.999276i
$11$	−1.03554	−	1.03554i	−0.312226	−	0.312226i	0.533545	−	0.845771i	$-0.320859\pi$
$11$	−1.03554	−	1.03554i	−0.312226	−	0.312226i	−0.845771	+	0.533545i	$0.820859\pi$
$12$	3.05499	+	1.63310i	0.881900	+	0.471436i
$13$			2.08132i			0.577254i	0.957442	+	0.288627i	$0.0931987\pi$
$13$			2.08132i			0.577254i	−0.957442	+	0.288627i	$0.906801\pi$
$14$	−1.75503	−	0.503562i	−0.469052	−	0.134583i
$15$	−3.44223	−	1.77512i	−0.888780	−	0.458334i
$16$	−1.75110	−	3.59634i	−0.437776	−	0.899084i
$17$	1.49126	+	1.49126i	0.361684	+	0.361684i	0.864433	−	0.502749i	$-0.167678\pi$
$17$	1.49126	+	1.49126i	0.361684	+	0.361684i	−0.502749	+	0.864433i	$0.667678\pi$
$18$	3.39840	−	2.53986i	0.801010	−	0.598652i
$19$	−2.35078	+	2.35078i	−0.539306	+	0.539306i	−0.923325	−	0.384019i	$-0.874540\pi$
$19$	−2.35078	+	2.35078i	−0.539306	+	0.539306i	0.384019	+	0.923325i	$0.374540\pi$
$20$	2.01708	+	3.99142i	0.451032	+	0.892508i
$21$	−1.47027	+	1.68489i	−0.320839	+	0.367674i
$22$	1.99075	+	0.571195i	0.424429	+	0.121779i
$23$	−4.27105	−	4.27105i	−0.890576	−	0.890576i	0.104001	−	0.994577i	$-0.466835\pi$
$23$	−4.27105	−	4.27105i	−0.890576	−	0.890576i	−0.994577	+	0.104001i	$0.966835\pi$
$24$	−4.89842	+	0.0737840i	−0.999887	+	0.0150611i
$25$	−2.32095	−	4.42868i	−0.464189	−	0.885736i
$26$	−1.42658	−	2.57462i	−0.279775	−	0.504924i
$27$	−1.05143	−	5.08866i	−0.202348	−	0.979314i
$28$	2.51615	−	0.580021i	0.475507	−	0.109614i
$29$	2.58251	+	2.58251i	0.479560	+	0.479560i	0.904991	−	0.425431i	$-0.139878\pi$
$29$	2.58251	+	2.58251i	0.479560	+	0.479560i	−0.425431	+	0.904991i	$0.639878\pi$
$30$	5.47478	−	0.163524i	0.999554	−	0.0298552i
$31$	−5.18620			−0.931469			−0.465734	−	0.884925i	$-0.654210\pi$
$31$	−5.18620			−0.931469			−0.465734	+	0.884925i	$0.654210\pi$
$32$	4.63114	+	3.24847i	0.818677	+	0.574255i
$33$	1.66774	−	1.91119i	0.290317	−	0.332696i
$34$	−2.86685	−	0.822570i	−0.491661	−	0.141070i
$35$	−2.80323	+	0.690039i	−0.473833	+	0.116638i
$36$	−2.46299	+	5.47117i	−0.410498	+	0.911862i
$37$			10.8954i			1.79120i	0.444863	+	0.895599i	$0.353253\pi$
$37$			10.8954i			1.79120i	−0.444863	+	0.895599i	$0.646747\pi$
$38$	1.29667	−	4.51922i	0.210348	−	0.733114i
$39$	−3.59664	+	0.244654i	−0.575923	+	0.0391760i
$40$	−5.23094	−	3.55489i	−0.827085	−	0.562077i
$41$	9.82802			1.53488			0.767439	−	0.641122i	$-0.221531\pi$
$41$	9.82802			1.53488			0.767439	+	0.641122i	$0.221531\pi$
$42$	0.663884	−	3.09199i	0.102440	−	0.477104i
$43$	0.814988			0.124284			0.0621422	−	0.998067i	$-0.480207\pi$
$43$	0.814988			0.124284			0.0621422	+	0.998067i	$0.480207\pi$
$44$	−2.85409	+	0.657923i	−0.430270	+	0.0991856i
$45$	2.66289	−	6.15703i	0.396960	−	0.917836i
$46$	8.21081	+	2.35588i	1.21062	+	0.347356i
$47$	6.63331	+	6.63331i	0.967568	+	0.967568i	0.999490	−	0.0319224i	$-0.0101629\pi$
$47$	6.63331	+	6.63331i	0.967568	+	0.967568i	−0.0319224	+	0.999490i	$0.510163\pi$
$48$	6.00884	−	3.44875i	0.867301	−	0.497784i
$49$		−	5.33314i		−	0.761878i
$50$	5.90654	+	3.88751i	0.835311	+	0.549777i
$51$	−2.40169	+	2.75228i	−0.336304	+	0.385396i
$52$	3.52938	+	2.20703i	0.489438	+	0.306060i
$53$			7.26025i			0.997273i	0.866811	+	0.498636i	$0.166166\pi$
$53$			7.26025i			0.997273i	−0.866811	+	0.498636i	$0.833834\pi$
$54$	4.78850	+	5.57407i	0.651633	+	0.758535i
$55$	3.17974	−	0.782718i	0.428756	−	0.105542i
$56$	−2.71495	+	2.44211i	−0.362800	+	0.326341i
$57$	−4.33861	−	3.78596i	−0.574663	−	0.501462i
$58$	−4.96470	−	1.42449i	−0.651897	−	0.187045i
$59$	6.09835	−	6.09835i	0.793938	−	0.793938i	−0.188194	−	0.982132i	$-0.560263\pi$
$59$	6.09835	−	6.09835i	0.793938	−	0.793938i	0.982132	+	0.188194i	$0.0602633\pi$
$60$	−6.66029	+	3.95480i	−0.859840	+	0.510563i
$61$	9.87198	+	9.87198i	1.26398	+	1.26398i	0.949148	+	0.314829i	$0.101947\pi$
$61$	9.87198	+	9.87198i	1.26398	+	1.26398i	0.314829	+	0.949148i	$0.398053\pi$
$62$	6.41539	−	3.55472i	0.814756	−	0.451450i
$63$	−3.08442	−	2.34266i	−0.388601	−	0.295147i
$64$	−7.95534	−	0.844133i	−0.994418	−	0.105517i
$65$	−3.98205	−	2.40887i	−0.493913	−	0.298784i
$66$	−0.753050	+	3.50727i	−0.0926940	+	0.431715i
$67$	10.8038			1.31990			0.659949	−	0.751310i	$-0.270578\pi$
$67$	10.8038			1.31990			0.659949	+	0.751310i	$0.270578\pi$
$68$	4.11014	−	0.947466i	0.498427	−	0.114897i
$69$	6.87857	−	7.88268i	0.828083	−	0.948963i
$70$	2.99467	−	2.77498i	0.357932	−	0.331673i
$71$	−2.57569			−0.305678			−0.152839	−	0.988251i	$-0.548842\pi$
$71$	−2.57569			−0.305678			−0.152839	+	0.988251i	$0.548842\pi$
$72$	−0.703301	−	8.45608i	−0.0828848	−	0.996559i
$73$	7.40366	−	7.40366i	0.866533	−	0.866533i	−0.125554	−	0.992087i	$-0.540071\pi$
$73$	7.40366	−	7.40366i	0.866533	−	0.866533i	0.992087	+	0.125554i	$0.0400708\pi$
$74$	−7.46794	−	13.4778i	−0.868130	−	1.56676i
$75$	7.38019	−	4.53131i	0.852191	−	0.523231i
$76$	1.49356	+	6.47909i	0.171323	+	0.743203i
$77$		−	1.89073i		−	0.215469i
$78$	4.28139	−	2.76785i	0.484773	−	0.313397i
$79$			8.54920i			0.961861i	0.876759	+	0.480930i	$0.159701\pi$
$79$			8.54920i			0.961861i	−0.876759	+	0.480930i	$0.840299\pi$
$80$	8.90733	+	0.812052i	0.995870	+	0.0907902i
$81$	8.66991	−	2.41509i	0.963323	−	0.268344i
$82$	−12.1574	+	6.73632i	−1.34256	+	0.743902i
$83$	−11.5636			−1.26927			−0.634635	−	0.772812i	$-0.718849\pi$
$83$	−11.5636			−1.26927			−0.634635	+	0.772812i	$0.718849\pi$
$84$	1.29808	+	4.27987i	0.141632	+	0.466972i
$85$	−4.57909	+	1.12718i	−0.496672	+	0.122260i
$86$	−1.00815	+	0.558608i	−0.108712	+	0.0602363i
$87$	−4.15916	+	4.76629i	−0.445908	+	0.511000i
$88$	3.07959	−	2.77011i	0.328286	−	0.295295i
$89$			9.67152i			1.02518i	0.858634	+	0.512590i	$0.171314\pi$
$89$			9.67152i			1.02518i	−0.858634	+	0.512590i	$0.828686\pi$
$90$	0.926126	+	9.44152i	0.0976223	+	0.995224i
$91$	−1.90008	+	1.90008i	−0.199183	+	0.199183i
$92$	−11.7716	+	2.71359i	−1.22728	+	0.282911i
$93$	−0.609625	−	8.96205i	−0.0632152	−	0.929321i
$94$	−12.7521	−	3.65889i	−1.31528	−	0.377386i
$95$	−1.77685	−	7.21834i	−0.182301	−	0.740586i
$96$	−5.06917	+	8.38472i	−0.517370	+	0.855762i
$97$	−6.58488	+	6.58488i	−0.668593	+	0.668593i	−0.957390	−	0.288797i	$-0.906745\pi$
$97$	−6.58488	+	6.58488i	−0.668593	+	0.668593i	0.288797	+	0.957390i	$0.406745\pi$
$98$	3.65544	+	6.59717i	0.369255	+	0.666414i
$99$	3.49869	+	2.65730i	0.351632	+	0.267069i
$100$	−9.97104	−	0.760439i	−0.997104	−	0.0760439i
$101$	−4.86989	−	4.86989i	−0.484572	−	0.484572i	0.422016	−	0.906588i	$-0.361322\pi$
$101$	−4.86989	−	4.86989i	−0.484572	−	0.484572i	−0.906588	+	0.422016i	$0.861322\pi$
$102$	1.08446	−	5.05077i	0.107377	−	0.500101i
$103$	4.41364	−	4.41364i	0.434888	−	0.434888i	−0.455399	−	0.890287i	$-0.650503\pi$
$103$	4.41364	−	4.41364i	0.434888	−	0.434888i	0.890287	+	0.455399i	$0.150503\pi$
$104$	−5.87864	−	0.311015i	−0.576448	−	0.0304975i
$105$	−1.52194	−	4.76304i	−0.148526	−	0.464825i
$106$	−4.97632	−	8.98103i	−0.483343	−	0.872314i
$107$	−8.76918			−0.847748			−0.423874	−	0.905721i	$-0.639330\pi$
$107$	−8.76918			−0.847748			−0.423874	+	0.905721i	$0.639330\pi$
$108$	−9.74401	−	3.61306i	−0.937618	−	0.347667i
$109$	5.82689	−	5.82689i	0.558115	−	0.558115i	−0.370656	−	0.928770i	$-0.620867\pi$
$109$	5.82689	−	5.82689i	0.558115	−	0.558115i	0.928770	+	0.370656i	$0.120867\pi$
$110$	−3.39688	+	3.14769i	−0.323880	+	0.300120i
$111$	−18.8279	+	1.28073i	−1.78707	+	0.121562i
$112$	1.68456	−	4.88180i	0.159176	−	0.461287i
$113$	−6.67807	+	6.67807i	−0.628220	+	0.628220i	−0.947620	−	0.319400i	$-0.896519\pi$
$113$	−6.67807	+	6.67807i	−0.628220	+	0.628220i	0.319400	+	0.947620i	$0.396519\pi$
$114$	7.96189	+	1.70950i	0.745699	+	0.160110i
$115$	13.1148	−	3.22831i	1.22296	−	0.301041i
$116$	7.11777	−	1.64078i	0.660868	−	0.152343i
$117$	−0.845552	−	6.18644i	−0.0781713	−	0.571936i
$118$	−3.36381	+	11.7237i	−0.309664	+	1.07925i
$119$			2.72281i			0.249600i
$120$	5.52817	−	9.45724i	0.504650	−	0.863324i
$121$		−	8.85533i		−	0.805030i
$122$	−18.9782	−	5.44532i	−1.71821	−	0.492996i
$123$	1.15526	+	16.9834i	0.104166	+	1.53134i
$124$	−5.49945	+	8.79447i	−0.493865	+	0.789767i
$125$	11.1593	+	0.685142i	0.998121	+	0.0612810i
$126$	5.42117	+	0.783774i	0.482956	+	0.0698241i
$127$	−4.03563	+	4.03563i	−0.358105	+	0.358105i	−0.863114	−	0.505009i	$-0.831489\pi$
$127$	−4.03563	+	4.03563i	−0.358105	+	0.358105i	0.505009	+	0.863114i	$0.331489\pi$
$128$	10.4194	−	4.40854i	0.920957	−	0.389664i
$129$	0.0957999	+	1.40835i	0.00843471	+	0.123998i
$130$	6.57694	+	0.250431i	0.576836	+	0.0219642i
$131$	12.4730	−	12.4730i	1.08977	−	1.08977i	0.0942236	−	0.995551i	$-0.469963\pi$
$131$	12.4730	−	12.4730i	1.08977	−	1.08977i	0.995551	−	0.0942236i	$-0.0300369\pi$
$132$	−1.47242	−	4.85470i	−0.128158	−	0.422547i
$133$	−4.29216			−0.372178
$134$	−13.3645	+	7.40516i	−1.15452	+	0.639708i
$135$	10.9527	+	3.87787i	0.942660	+	0.333754i
$136$	−4.43488	+	3.98919i	−0.380288	+	0.342071i
$137$	−2.68828	+	2.68828i	−0.229675	+	0.229675i	−0.812557	−	0.582882i	$-0.801925\pi$
$137$	−2.68828	+	2.68828i	−0.229675	+	0.229675i	0.582882	+	0.812557i	$0.301925\pi$
$138$	−3.10594	+	14.4657i	−0.264395	+	1.23140i
$139$	−4.14179	−	4.14179i	−0.351302	−	0.351302i	0.509292	−	0.860594i	$-0.329907\pi$
$139$	−4.14179	−	4.14179i	−0.351302	−	0.351302i	−0.860594	+	0.509292i	$0.829907\pi$
$140$	−1.80242	+	5.48529i	−0.152332	+	0.463592i
$141$	−10.6830	+	12.2425i	−0.899672	+	1.03100i
$142$	3.18616	−	1.76543i	0.267377	−	0.148151i
$143$	2.15528	−	2.15528i	0.180234	−	0.180234i
$144$	6.66596	+	9.97823i	0.555496	+	0.831519i
$145$	−7.92989	+	1.95201i	−0.658542	+	0.162105i
$146$	−4.08381	+	14.2330i	−0.337978	+	1.17793i
$147$	9.21598	−	0.626898i	0.760121	−	0.0517057i
$148$	18.4759	+	11.5535i	1.51871	+	0.949693i
$149$	−3.27529	+	3.27529i	−0.268322	+	0.268322i	−0.828424	−	0.560102i	$-0.810762\pi$
$149$	−3.27529	+	3.27529i	−0.268322	+	0.268322i	0.560102	+	0.828424i	$0.310762\pi$
$150$	−6.02354	+	10.6638i	−0.491820	+	0.870697i
$151$		−	11.4102i		−	0.928548i	−0.885692	−	0.464274i	$-0.846315\pi$
$151$		−	11.4102i		−	0.928548i	0.885692	−	0.464274i	$-0.153685\pi$
$152$	−6.28845	−	6.99101i	−0.510060	−	0.567046i
$153$	−5.03841	−	3.82674i	−0.407332	−	0.309373i
$154$	1.29594	+	2.33886i	0.104430	+	0.188471i
$155$	6.00240	−	9.92242i	0.482124	−	0.796988i
$156$	−3.39900	+	6.35841i	−0.272138	+	0.509080i
$157$	3.40961			0.272116			0.136058	−	0.990701i	$-0.456557\pi$
$157$	3.40961			0.272116			0.136058	+	0.990701i	$0.456557\pi$
$158$	−5.85979	−	10.5755i	−0.466180	−	0.841339i
$159$	−12.5461	+	0.853426i	−0.994973	+	0.0676811i
$160$	−11.5751	+	5.10074i	−0.915090	+	0.403249i
$161$		−	7.79828i		−	0.614591i
$162$	−9.06943	+	8.93003i	−0.712562	+	0.701609i
$163$			4.71686i			0.369453i	0.982790	+	0.184727i	$0.0591400\pi$
$163$			4.71686i			0.369453i	−0.982790	+	0.184727i	$0.940860\pi$
$164$	10.4216	−	16.6658i	0.813793	−	1.30138i
$165$	1.72635	+	5.40276i	0.134396	+	0.420604i
$166$	14.3043	−	7.92591i	1.11023	−	0.615170i
$167$	14.7875	−	14.7875i	1.14429	−	1.14429i	0.156635	−	0.987657i	$-0.449935\pi$
$167$	14.7875	−	14.7875i	1.14429	−	1.14429i	0.987657	−	0.156635i	$-0.0500647\pi$
$168$	−4.53924	−	4.40452i	−0.350210	−	0.339816i
$169$	8.66811			0.666778
$170$	4.89180	−	4.53294i	0.375184	−	0.347660i
$171$	6.03236	−	7.94240i	0.461306	−	0.607371i
$172$	0.864213	−	1.38201i	0.0658956	−	0.105377i
$173$	−20.6855			−1.57269			−0.786343	−	0.617790i	$-0.788028\pi$
$173$	−20.6855			−1.57269			−0.786343	+	0.617790i	$0.788028\pi$
$174$	1.87802	−	8.74673i	0.142372	−	0.663088i
$175$	1.92420	−	6.16189i	0.145456	−	0.465795i
$176$	−1.91081	+	5.53747i	−0.144033	+	0.417403i
$177$	11.2552	+	9.82146i	0.845989	+	0.738226i
$178$	−6.62905	−	11.9638i	−0.496868	−	0.896724i
$179$	15.0062	+	15.0062i	1.12162	+	1.12162i	0.991499	+	0.130118i	$0.0415355\pi$
$179$	15.0062	+	15.0062i	1.12162	+	1.12162i	0.130118	+	0.991499i	$0.458464\pi$
$180$	−7.61703	−	11.0445i	−0.567740	−	0.823208i
$181$	2.48233	−	2.48233i	0.184510	−	0.184510i	−0.608808	−	0.793318i	$-0.708352\pi$
$181$	2.48233	−	2.48233i	0.184510	−	0.184510i	0.793318	+	0.608808i	$0.208352\pi$
$182$	1.04807	−	3.65278i	0.0776883	−	0.270762i
$183$	−15.8989	+	18.2198i	−1.17528	+	1.34684i
$184$	12.7017	−	11.4253i	0.936383	−	0.842281i
$185$	−20.8455	−	12.6101i	−1.53259	−	0.927116i
$186$	6.89688	+	10.6683i	0.505703	+	0.782239i
$187$		−	3.08851i		−	0.225855i
$188$	18.2824	−	4.21444i	1.33338	−	0.307370i
$189$	3.68568	−	5.60543i	0.268094	−	0.407735i
$190$	7.14559	+	7.71129i	0.518395	+	0.559436i
$191$		−	14.6164i		−	1.05761i	−0.848744	−	0.528804i	$-0.822641\pi$
$191$		−	14.6164i		−	1.05761i	0.848744	−	0.528804i	$-0.177359\pi$
$192$	0.523579	−	13.8465i	0.0377860	−	0.999286i
$193$	−5.06820	−	5.06820i	−0.364817	−	0.364817i	0.500766	−	0.865583i	$-0.333052\pi$
$193$	−5.06820	−	5.06820i	−0.364817	−	0.364817i	−0.865583	+	0.500766i	$0.833052\pi$
$194$	3.63217	−	12.6590i	0.260775	−	0.908862i
$195$	3.69459	−	7.16437i	0.264575	−	0.513052i
$196$	−9.04365	−	5.65527i	−0.645975	−	0.403948i
$197$	−4.73103			−0.337072			−0.168536	−	0.985696i	$-0.553904\pi$
$197$	−4.73103			−0.337072			−0.168536	+	0.985696i	$0.553904\pi$
$198$	−6.14929	−	0.889042i	−0.437011	−	0.0631815i
$199$	−7.61133			−0.539553			−0.269776	−	0.962923i	$-0.586950\pi$
$199$	−7.61133			−0.539553			−0.269776	+	0.962923i	$0.586950\pi$
$200$	12.8555	−	5.89368i	0.909023	−	0.416746i
$201$	1.26997	+	18.6696i	0.0895764	+	1.31686i
$202$	9.36202	+	2.68620i	0.658710	+	0.189000i
$203$			4.71526i			0.330946i
$204$	2.12041	+	6.99118i	0.148459	+	0.489480i
$205$	−11.3747	+	18.8033i	−0.794447	+	1.31328i
$206$	−2.43453	+	8.48492i	−0.169622	+	0.591172i
$207$	14.4303	+	10.9600i	1.00297	+	0.761771i
$208$	7.48512	−	3.64460i	0.519000	−	0.252708i
$209$	4.86864			0.336771
$210$	5.14734	+	4.84877i	0.355200	+	0.334597i
$211$	−7.48648	−	7.48648i	−0.515391	−	0.515391i	0.400783	−	0.916173i	$-0.368738\pi$
$211$	−7.48648	−	7.48648i	−0.515391	−	0.515391i	−0.916173	+	0.400783i	$0.868738\pi$
$212$	12.3115	+	7.69878i	0.845560	+	0.528754i
$213$	−0.302766	−	4.45094i	−0.0207452	−	0.304973i
$214$	10.8476	−	6.01056i	0.741525	−	0.410874i
$215$	−0.943250	+	1.55926i	−0.0643291	+	0.106341i
$216$	14.5299	−	2.20934i	0.988636	−	0.150326i
$217$	−4.73460	−	4.73460i	−0.321405	−	0.321405i
$218$	−3.21407	+	11.2018i	−0.217684	+	0.758681i
$219$	13.6642	+	11.9237i	0.923343	+	0.805727i
$220$	2.04450	−	6.22202i	0.137840	−	0.419488i
$221$	−3.10379	+	3.10379i	−0.208784	+	0.208784i
$222$	22.4125	−	14.4893i	1.50423	−	0.972459i
$223$	14.9484	+	14.9484i	1.00102	+	1.00102i	0.999999	+	0.00101699i	$0.000323717\pi$
$223$	14.9484	+	14.9484i	1.00102	+	1.00102i	0.00101699	+	0.999999i	$0.499676\pi$
$224$	1.26226	+	7.19348i	0.0843385	+	0.480634i
$225$	8.69789	+	12.2208i	0.579859	+	0.814717i
$226$	3.68358	−	12.8381i	0.245028	−	0.853980i
$227$		−	5.12514i		−	0.340167i	−0.985430	−	0.170084i	$-0.945596\pi$
$227$		−	5.12514i		−	0.340167i	0.985430	−	0.170084i	$-0.0544038\pi$
$228$	−11.0207	+	3.34255i	−0.729862	+	0.221366i
$229$	−1.86356	−	1.86356i	−0.123148	−	0.123148i	0.642847	−	0.765995i	$-0.277753\pi$
$229$	−1.86356	−	1.86356i	−0.123148	−	0.123148i	−0.765995	+	0.642847i	$0.777753\pi$
$230$	−14.0104	+	12.9826i	−0.923817	+	0.856045i
$231$	3.26729	−	0.222251i	0.214972	−	0.0146230i
$232$	−7.68014	+	6.90833i	−0.504226	+	0.453554i
$233$	5.48648	+	5.48648i	0.359431	+	0.359431i	0.863603	−	0.504172i	$-0.168202\pi$
$233$	5.48648	+	5.48648i	0.359431	+	0.359431i	−0.504172	+	0.863603i	$0.668202\pi$
$234$	5.28626	+	7.07314i	0.345574	+	0.462386i
$235$	−20.3684	+	5.01384i	−1.32868	+	0.327067i
$236$	−3.87456	−	16.8079i	−0.252212	−	1.09410i
$237$	−14.7735	+	1.00494i	−0.959643	+	0.0652778i
$238$	−1.86627	−	3.36816i	−0.120972	−	0.218325i
$239$	−9.45252			−0.611433			−0.305716	−	0.952123i	$-0.598896\pi$
$239$	−9.45252			−0.611433			−0.305716	+	0.952123i	$0.598896\pi$
$240$	−0.356237	+	15.4878i	−0.0229950	+	0.999736i
$241$	10.3530			0.666894			0.333447	−	0.942769i	$-0.391788\pi$
$241$	10.3530			0.666894			0.333447	+	0.942769i	$0.391788\pi$
$242$	6.06961	+	10.9541i	0.390170	+	0.704159i
$243$	5.19255	+	14.6982i	0.333102	+	0.942891i
$244$	27.2086	−	6.27211i	1.74185	−	0.401531i
$245$	10.2036	+	6.17247i	0.651882	+	0.394345i
$246$	−13.0698	−	20.2168i	−0.833301	−	1.28898i
$247$	−4.89272	−	4.89272i	−0.311316	−	0.311316i
$248$	0.774982	−	14.6483i	0.0492114	−	0.930168i
$249$	−1.35927	−	19.9826i	−0.0861404	−	1.26634i
$250$	−14.2738	+	6.80129i	−0.902757	+	0.430151i
$251$	18.5502	+	18.5502i	1.17088	+	1.17088i	0.982001	+	0.188874i	$0.0604838\pi$
$251$	18.5502	+	18.5502i	1.17088	+	1.17088i	0.188874	+	0.982001i	$0.439516\pi$
$252$	−7.24327	+	2.74624i	−0.456283	+	0.172997i
$253$			8.84567i			0.556122i
$254$	2.22603	−	7.75823i	0.139673	−	0.486795i
$255$	−2.48610	−	7.78044i	−0.155685	−	0.487230i
$256$	−9.86728	+	12.5951i	−0.616705	+	0.787194i
$257$	5.32881	+	5.32881i	0.332402	+	0.332402i	0.853498	−	0.521096i	$-0.174477\pi$
$257$	5.32881	+	5.32881i	0.332402	+	0.332402i	−0.521096	+	0.853498i	$0.674477\pi$
$258$	−1.08381	−	1.67648i	−0.0674753	−	0.104373i
$259$	−9.94669	+	9.94669i	−0.618057	+	0.618057i
$260$	−8.30741	+	4.19818i	−0.515204	+	0.260360i
$261$	−8.72532	−	6.62699i	−0.540084	−	0.410201i
$262$	−6.88004	+	23.9786i	−0.425051	+	1.48140i
$263$	6.84521	+	6.84521i	0.422094	+	0.422094i	0.885924	−	0.463830i	$-0.153525\pi$
$263$	6.84521	+	6.84521i	0.422094	+	0.422094i	−0.463830	+	0.885924i	$0.653525\pi$
$264$	5.14891	+	4.99609i	0.316893	+	0.307488i
$265$	−13.8906	−	8.40287i	−0.853292	−	0.516184i
$266$	5.30946	−	2.94193i	0.325544	−	0.180381i
$267$	−16.7129	+	1.13686i	−1.02282	+	0.0695750i
$268$	11.4564	−	18.3205i	0.699810	−	1.11911i
$269$	−0.0586414	−	0.0586414i	−0.00357543	−	0.00357543i	0.705317	−	0.708892i	$-0.250805\pi$
$269$	−0.0586414	−	0.0586414i	−0.00357543	−	0.00357543i	−0.708892	+	0.705317i	$0.750805\pi$
$270$	−16.2066	+	2.71023i	−0.986304	+	0.164939i
$271$	14.7531			0.896185			0.448093	−	0.893987i	$-0.352103\pi$
$271$	14.7531			0.896185			0.448093	+	0.893987i	$0.352103\pi$
$272$	2.75173	−	7.97443i	0.166848	−	0.483521i
$273$	−3.50680	−	3.06010i	−0.212241	−	0.185206i
$274$	1.48284	−	5.16804i	0.0895815	−	0.312213i
$275$	−2.18264	+	6.98949i	−0.131618	+	0.421482i
$276$	−6.07297	−	20.0231i	−0.365550	−	1.20525i
$277$		−	12.2040i		−	0.733266i	−0.930366	−	0.366633i	$-0.880510\pi$
$277$		−	12.2040i		−	0.733266i	0.930366	−	0.366633i	$-0.119490\pi$
$278$	7.96232	+	2.28458i	0.477548	+	0.137020i
$279$	15.4153	−	2.10693i	0.922888	−	0.126139i
$280$	−1.53011	−	8.02079i	−0.0914414	−	0.479334i
$281$	2.18598			0.130404			0.0652022	−	0.997872i	$-0.479231\pi$
$281$	2.18598			0.130404			0.0652022	+	0.997872i	$0.479231\pi$
$282$	4.82379	−	22.4664i	0.287253	−	1.33786i
$283$	−10.8232			−0.643373			−0.321686	−	0.946846i	$-0.604250\pi$
$283$	−10.8232			−0.643373			−0.321686	+	0.946846i	$0.604250\pi$
$284$	−2.73126	+	4.36771i	−0.162071	+	0.259176i
$285$	12.2648	−	3.91901i	0.726507	−	0.232142i
$286$	−1.18884	+	4.14338i	−0.0702975	+	0.245003i
$287$	8.97222	+	8.97222i	0.529614	+	0.529614i
$288$	−15.0851	−	7.77421i	−0.888901	−	0.458100i
$289$		−	12.5523i		−	0.738369i
$290$	8.47143	−	7.84996i	0.497460	−	0.460965i
$291$	−12.1531	−	10.6050i	−0.712427	−	0.621677i
$292$	−4.70388	−	20.4056i	−0.275274	−	1.19415i
$293$		−	13.0105i		−	0.760084i	−0.924969	−	0.380042i	$-0.875910\pi$
$293$		−	13.0105i		−	0.760084i	0.924969	−	0.380042i	$-0.124090\pi$
$294$	−10.9706	+	7.09229i	−0.639818	+	0.413631i
$295$	4.60948	+	18.7257i	0.268375	+	1.09025i
$296$	−30.7739	−	1.62812i	−1.78870	−	0.0946327i
$297$	−4.18070	+	6.35830i	−0.242589	+	0.368946i
$298$	1.80663	−	6.29652i	0.104655	−	0.364747i
$299$	8.88942	−	8.88942i	0.514088	−	0.514088i
$300$	0.142010	−	17.3199i	0.00819894	−	0.999966i
$301$	0.744021	+	0.744021i	0.0428846	+	0.0428846i
$302$	7.82077	+	14.1145i	0.450035	+	0.812201i
$303$	7.84300	−	8.98789i	0.450568	−	0.516341i
$304$	12.5707	+	4.33774i	0.720977	+	0.248787i
$305$	−30.3131	+	7.46181i	−1.73572	+	0.427262i
$306$	8.85550	+	1.28030i	0.506235	+	0.0731897i
$307$	−34.3297			−1.95930			−0.979649	−	0.200718i	$-0.935672\pi$
$307$	−34.3297			−1.95930			−0.979649	+	0.200718i	$0.935672\pi$
$308$	−3.20620	−	2.00493i	−0.182690	−	0.114242i
$309$	8.14583	+	7.10820i	0.463400	+	0.404372i
$310$	−0.624019	+	16.3883i	−0.0354419	+	0.930794i
$311$	−19.7120			−1.11777			−0.558883	−	0.829247i	$-0.688770\pi$
$311$	−19.7120			−1.11777			−0.558883	+	0.829247i	$0.688770\pi$
$312$	−0.153568	−	10.1952i	−0.00869407	−	0.577188i
$313$	−8.82647	+	8.82647i	−0.498902	+	0.498902i	−0.911096	−	0.412194i	$-0.864763\pi$
$313$	−8.82647	+	8.82647i	−0.498902	+	0.498902i	0.412194	+	0.911096i	$0.364763\pi$
$314$	−4.21773	+	2.33701i	−0.238020	+	0.131885i
$315$	8.05190	−	3.18989i	0.453673	−	0.179730i
$316$	14.4973	+	9.06558i	0.815535	+	0.509979i
$317$		−	27.9576i		−	1.57026i	−0.619334	−	0.785128i	$-0.712597\pi$
$317$		−	27.9576i		−	1.57026i	0.619334	−	0.785128i	$-0.287403\pi$
$318$	14.9348	−	9.65506i	0.837501	−	0.541429i
$319$		−	5.34857i		−	0.299462i
$320$	10.8224	−	14.2435i	0.604989	−	0.796234i
$321$	−1.03080	−	15.1536i	−0.0575334	−	0.845794i
$322$	5.34510	+	9.64657i	0.297871	+	0.537583i
$323$	−7.01126			−0.390117
$324$	5.09819	−	17.2629i	0.283233	−	0.959051i
$325$	9.21749	−	4.83063i	0.511294	−	0.267955i
$326$	−3.23303	−	5.83482i	−0.179061	−	0.323161i
$327$	10.7541	+	9.38426i	0.594705	+	0.518951i
$328$	−1.46862	+	27.7590i	−0.0810909	+	1.53274i
$329$			12.1114i			0.667723i
$330$	−5.83868	−	5.50001i	−0.321409	−	0.302765i
$331$	−11.7945	+	11.7945i	−0.648285	+	0.648285i	−0.952578	−	0.304293i	$-0.901580\pi$
$331$	−11.7945	+	11.7945i	−0.648285	+	0.648285i	0.304293	+	0.952578i	$0.401580\pi$
$332$	−12.2620	+	19.6089i	−0.672967	+	1.07618i
$333$	−4.42636	−	32.3852i	−0.242563	−	1.77470i
$334$	−8.15669	+	28.4280i	−0.446314	+	1.55551i
$335$	−12.5041	+	20.6703i	−0.683174	+	1.12934i
$336$	8.63405	+	2.33717i	0.471026	+	0.127503i
$337$	1.70964	−	1.70964i	0.0931298	−	0.0931298i	−0.659007	−	0.752137i	$-0.729023\pi$
$337$	1.70964	−	1.70964i	0.0931298	−	0.0931298i	0.752137	+	0.659007i	$0.229023\pi$
$338$	−10.7226	+	5.94129i	−0.583231	+	0.323164i
$339$	−12.3251	−	10.7551i	−0.669407	−	0.584137i
$340$	−2.94426	+	8.96024i	−0.159675	+	0.485937i
$341$	5.37050	+	5.37050i	0.290829	+	0.290829i
$342$	−2.01822	+	13.9595i	−0.109133	+	0.754846i
$343$	11.2592	−	11.2592i	0.607940	−	0.607940i
$344$	−0.121785	+	2.30191i	−0.00656621	+	0.124111i
$345$	7.12031	+	22.2836i	0.383344	+	1.19971i
$346$	25.5882	−	14.1782i	1.37563	−	0.762226i
$347$	−19.6676			−1.05581			−0.527905	−	0.849304i	$-0.677022\pi$
$347$	−19.6676			−1.05581			−0.527905	+	0.849304i	$0.677022\pi$
$348$	3.67204	+	12.1070i	0.196842	+	0.649006i
$349$	−5.38375	+	5.38375i	−0.288186	+	0.288186i	−0.836362	−	0.548177i	$-0.815322\pi$
$349$	−5.38375	+	5.38375i	−0.288186	+	0.288186i	0.548177	+	0.836362i	$0.315322\pi$
$350$	1.84322	+	8.94122i	0.0985243	+	0.477928i
$351$	10.5911	−	2.18836i	0.565313	−	0.116806i
$352$	−1.43180	−	8.15963i	−0.0763150	−	0.434910i
$353$	25.3482	−	25.3482i	1.34915	−	1.34915i	0.462556	−	0.886590i	$-0.346933\pi$
$353$	25.3482	−	25.3482i	1.34915	−	1.34915i	0.886590	−	0.462556i	$-0.153067\pi$
$354$	−20.6546	−	4.43477i	−1.09778	−	0.235705i
$355$	2.98105	−	4.92790i	0.158218	−	0.261546i
$356$	16.4004	+	10.2557i	0.869222	+	0.543550i
$357$	−4.70518	+	0.320060i	−0.249025	+	0.0169394i
$358$	−28.8484	−	8.27732i	−1.52469	−	0.437470i
$359$			22.5488i			1.19008i	0.803696	+	0.595040i	$0.202864\pi$
$359$			22.5488i			1.19008i	−0.803696	+	0.595040i	$0.797136\pi$
$360$	16.9925	+	8.44132i	0.895582	+	0.444896i
$361$			7.94766i			0.418298i
$362$	−1.36923	+	4.77211i	−0.0719654	+	0.250816i
$363$	15.3025	−	1.04092i	0.803174	−	0.0546343i
$364$	1.20721	+	5.23690i	0.0632749	+	0.274488i
$365$	5.59611	+	22.7338i	0.292914	+	1.18994i
$366$	7.17898	−	33.4355i	0.375251	−	1.74770i
$367$	16.5406	−	16.5406i	0.863411	−	0.863411i	−0.128322	−	0.991733i	$-0.540959\pi$
$367$	16.5406	−	16.5406i	0.863411	−	0.863411i	0.991733	+	0.128322i	$0.0409591\pi$
$368$	−7.88109	+	22.8392i	−0.410830	+	1.19058i
$369$	−29.2125	+	3.99271i	−1.52074	+	0.207852i
$370$	34.4294	+	1.31097i	1.78990	+	0.0681542i
$371$	−6.62805	+	6.62805i	−0.344111	+	0.344111i
$372$	−15.8438	−	8.46959i	−0.821462	−	0.439128i
$373$	−7.24873			−0.375325			−0.187663	−	0.982234i	$-0.560091\pi$
$373$	−7.24873			−0.375325			−0.187663	+	0.982234i	$0.560091\pi$
$374$	2.11693	+	3.82053i	0.109464	+	0.197555i
$375$	0.127788	+	19.3645i	0.00659892	+	0.999978i
$376$	−19.7269	+	17.7444i	−1.01734	+	0.915098i
$377$	−5.37502	+	5.37502i	−0.276828	+	0.276828i
$378$	−0.717160	+	9.46023i	−0.0368867	+	0.486582i
$379$	−6.48173	−	6.48173i	−0.332944	−	0.332944i	0.520759	−	0.853703i	$-0.325649\pi$
$379$	−6.48173	−	6.48173i	−0.332944	−	0.332944i	−0.853703	+	0.520759i	$0.825649\pi$
$380$	−14.1246	−	4.64124i	−0.724579	−	0.238091i
$381$	−7.44819	−	6.49943i	−0.381582	−	0.332976i
$382$	10.0184	+	18.0807i	0.512585	+	0.925089i
$383$	13.1911	−	13.1911i	0.674035	−	0.674035i	−0.284609	−	0.958644i	$-0.591864\pi$
$383$	13.1911	−	13.1911i	0.674035	−	0.674035i	0.958644	+	0.284609i	$0.0918636\pi$
$384$	8.84299	+	17.4872i	0.451267	+	0.892389i
$385$	3.61741	+	2.18829i	0.184361	+	0.111526i
$386$	9.74326	+	2.79558i	0.495919	+	0.142291i
$387$	−2.42244	+	0.331095i	−0.123140	+	0.0168305i
$388$	4.18367	+	18.1489i	0.212394	+	0.921370i
$389$	−1.04217	+	1.04217i	−0.0528401	+	0.0528401i	−0.733033	−	0.680193i	$-0.761896\pi$
$389$	−1.04217	+	1.04217i	−0.0528401	+	0.0528401i	0.680193	+	0.733033i	$0.261896\pi$
$390$	0.340345	+	11.3948i	0.0172340	+	0.576996i
$391$		−	12.7385i		−	0.644215i
$392$	15.0633	+	0.796941i	0.760814	+	0.0402516i
$393$	23.0203	+	20.0880i	1.16122	+	1.01330i
$394$	5.85234	−	3.24274i	0.294837	−	0.163367i
$395$	−16.3566	−	9.89467i	−0.822992	−	0.497855i
$396$	8.21611	−	3.11509i	0.412875	−	0.156539i
$397$	0.837780			0.0420470			0.0210235	−	0.999779i	$-0.493308\pi$
$397$	0.837780			0.0420470			0.0210235	+	0.999779i	$0.493308\pi$
$398$	9.41531	−	5.21695i	0.471947	−	0.261502i
$399$	−0.504534	−	7.41710i	−0.0252583	−	0.371320i
$400$	−11.8628	+	16.1020i	−0.593140	+	0.805099i
$401$			23.6742i			1.18223i	0.806587	+	0.591116i	$0.201312\pi$
$401$			23.6742i			1.18223i	−0.806587	+	0.591116i	$0.798688\pi$
$402$	−14.3675	−	22.2241i	−0.716586	−	1.10844i
$403$		−	10.7941i		−	0.537694i
$404$	−13.4221	+	3.09406i	−0.667775	+	0.153935i
$405$	−5.41372	+	19.3828i	−0.269010	+	0.963137i
$406$	−3.23193	−	5.83284i	−0.160398	−	0.289479i
$407$	11.2826	−	11.2826i	0.559259	−	0.559259i
$408$	−7.41487	−	7.19480i	−0.367091	−	0.356196i
$409$	25.7330			1.27242			0.636208	−	0.771517i	$-0.280502\pi$
$409$	25.7330			1.27242			0.636208	+	0.771517i	$0.280502\pi$
$410$	1.18254	−	31.0564i	0.0584014	−	1.53377i
$411$	−4.96151	−	4.32950i	−0.244733	−	0.213559i
$412$	−2.80418	−	12.1646i	−0.138152	−	0.599308i
$413$	11.1347			0.547900
$414$	−25.3626	−	3.66684i	−1.24650	−	0.180215i
$415$	13.3835	−	22.1239i	0.656968	−	1.08602i
$416$	−6.76111	+	9.63887i	−0.331491	+	0.472584i
$417$	6.67040	−	7.64411i	0.326651	−	0.374334i
$418$	−6.02257	+	3.33706i	−0.294574	+	0.163221i
$419$	−13.8036	−	13.8036i	−0.674351	−	0.674351i	0.284365	−	0.958716i	$-0.408217\pi$
$419$	−13.8036	−	13.8036i	−0.674351	−	0.674351i	−0.958716	+	0.284365i	$0.908217\pi$
$420$	−9.69077	−	2.46990i	−0.472861	−	0.120519i
$421$	13.7845	−	13.7845i	0.671817	−	0.671817i	−0.286318	−	0.958135i	$-0.592431\pi$
$421$	13.7845	−	13.7845i	0.671817	−	0.671817i	0.958135	+	0.286318i	$0.0924314\pi$
$422$	14.3923	+	4.12949i	0.700604	+	0.201021i
$423$	−22.4115	−	17.0218i	−1.08968	−	0.827628i
$424$	−20.5064	−	1.08491i	−0.995880	−	0.0526880i
$425$	3.14318	−	10.0655i	0.152467	−	0.488247i
$426$	3.42528	+	5.29834i	0.165956	+	0.256706i
$427$			18.0247i			0.872277i
$428$	−9.29884	+	14.8703i	−0.449476	+	0.718782i
$429$	3.97780	+	3.47110i	0.192050	+	0.167586i
$430$	0.0980619	−	2.57535i	0.00472896	−	0.124194i
$431$			2.16037i			0.104061i	0.998645	+	0.0520307i	$0.0165694\pi$
$431$			2.16037i			0.104061i	−0.998645	+	0.0520307i	$0.983431\pi$
$432$	−16.4594	+	12.6921i	−0.791902	+	0.610648i
$433$	−17.6860	−	17.6860i	−0.849935	−	0.849935i	0.140189	−	0.990125i	$-0.455229\pi$
$433$	−17.6860	−	17.6860i	−0.849935	−	0.849935i	−0.990125	+	0.140189i	$0.955229\pi$
$434$	9.10194	+	2.61157i	0.436907	+	0.125359i
$435$	−4.30532	−	13.4739i	−0.206424	−	0.646022i
$436$	−3.70208	−	16.0598i	−0.177298	−	0.769123i
$437$	20.0806			0.960586
$438$	−25.0755	−	5.38399i	−1.19816	−	0.257257i
$439$	−11.2105			−0.535049			−0.267525	−	0.963551i	$-0.586206\pi$
$439$	−11.2105			−0.535049			−0.267525	+	0.963551i	$0.586206\pi$
$440$	1.73562	+	9.09805i	0.0827422	+	0.433733i
$441$	2.16663	+	15.8521i	0.103173	+	0.754860i
$442$	1.71203	−	5.96683i	0.0814329	−	0.283813i
$443$		−	5.63824i		−	0.267881i	−0.990989	−	0.133940i	$-0.957237\pi$
$443$		−	5.63824i		−	0.267881i	0.990989	−	0.133940i	$-0.0427631\pi$
$444$	−17.7933	+	33.2855i	−0.844435	+	1.57966i
$445$	−18.5039	−	11.1936i	−0.877170	−	0.530629i
$446$	−28.7372	−	8.24541i	−1.36075	−	0.390432i
$447$	−6.04489	−	5.27488i	−0.285913	−	0.249493i
$448$	−6.49198	−	8.03324i	−0.306717	−	0.379535i
$449$	9.38457			0.442885			0.221443	−	0.975173i	$-0.428923\pi$
$449$	9.38457			0.442885			0.221443	+	0.975173i	$0.428923\pi$
$450$	−19.1357	−	9.15552i	−0.902067	−	0.431595i
$451$	−10.1773	−	10.1773i	−0.479229	−	0.479229i
$452$	4.24288	+	18.4057i	0.199568	+	0.865733i
$453$	19.7175	−	1.34124i	0.926407	−	0.0630170i
$454$	3.51287	+	6.33986i	0.164867	+	0.297544i
$455$	−1.43619	−	5.83442i	−0.0673297	−	0.273522i
$456$	11.3417	−	11.6886i	0.531122	−	0.547367i
$457$	16.2317	+	16.2317i	0.759289	+	0.759289i	0.976193	−	0.216904i	$-0.0695959\pi$
$457$	16.2317	+	16.2317i	0.759289	+	0.759289i	−0.216904	+	0.976193i	$0.569596\pi$
$458$	3.58258	+	1.02793i	0.167403	+	0.0480320i
$459$	6.02057	−	9.15649i	0.281016	−	0.427388i
$460$	8.43251	−	25.6626i	0.393168	−	1.19652i
$461$	−7.62591	+	7.62591i	−0.355174	+	0.355174i	−0.862030	−	0.506857i	$-0.830807\pi$
$461$	−7.62591	+	7.62591i	−0.355174	+	0.355174i	0.506857	+	0.862030i	$0.330807\pi$
$462$	−3.88935	+	2.51439i	−0.180949	+	0.116980i
$463$	10.9986	+	10.9986i	0.511149	+	0.511149i	0.914878	−	0.403730i	$-0.132286\pi$
$463$	10.9986	+	10.9986i	0.511149	+	0.511149i	−0.403730	+	0.914878i	$0.632286\pi$
$464$	4.76533	−	13.8098i	0.221225	−	0.641104i
$465$	17.8521	+	9.20613i	0.827870	+	0.426924i
$466$	−10.5474	−	3.02630i	−0.488598	−	0.140191i
$467$		−	9.64270i		−	0.446211i	−0.974794	−	0.223105i	$-0.928381\pi$
$467$		−	9.64270i		−	0.446211i	0.974794	−	0.223105i	$-0.0716194\pi$
$468$	−11.3872	−	5.12626i	−0.526376	−	0.236961i
$469$	9.86307	+	9.86307i	0.455434	+	0.455434i
$470$	21.7593	−	20.1630i	1.00368	−	0.930052i
$471$	0.400791	+	5.89200i	0.0184675	+	0.271489i
$472$	16.3134	+	18.1359i	0.750884	+	0.834775i
$473$	−0.843950	−	0.843950i	−0.0388049	−	0.0388049i
$474$	17.5862	−	11.3692i	0.807762	−	0.522204i
$475$	15.8669	+	4.95482i	0.728023	+	0.227343i
$476$	4.61720	+	2.88727i	0.211629	+	0.132338i
$477$	−2.94954	−	21.5801i	−0.135050	−	0.988086i
$478$	11.6929	−	6.47894i	0.534820	−	0.296340i
$479$	0.350518			0.0160156			0.00800779	−	0.999968i	$-0.497451\pi$
$479$	0.350518			0.0160156			0.00800779	+	0.999968i	$0.497451\pi$
$480$	−10.1750	−	19.4028i	−0.464423	−	0.885614i
$481$	−22.6769			−1.03398
$482$	−12.8068	+	7.09613i	−0.583332	+	0.323220i
$483$	13.4759	−	0.916670i	0.613174	−	0.0417099i
$484$	−15.0164	−	9.39019i	−0.682563	−	0.426827i
$485$	−4.97723	−	20.2196i	−0.226004	−	0.918126i
$486$	−16.4977	−	14.6228i	−0.748350	−	0.663304i
$487$	3.32822	+	3.32822i	0.150816	+	0.150816i	0.778482	−	0.627666i	$-0.215990\pi$
$487$	3.32822	+	3.32822i	0.150816	+	0.150816i	−0.627666	+	0.778482i	$0.715990\pi$
$488$	−29.3584	+	26.4080i	−1.32899	+	1.19543i
$489$	−8.15101	+	0.554456i	−0.368601	+	0.0250734i
$490$	−16.8527	−	0.641701i	−0.761326	−	0.0289891i
$491$	20.7903	+	20.7903i	0.938255	+	0.938255i	0.998202	−	0.0599467i	$-0.0190931\pi$
$491$	20.7903	+	20.7903i	0.938255	+	0.938255i	−0.0599467	+	0.998202i	$0.519093\pi$
$492$	30.0245	+	16.0502i	1.35361	+	0.723597i
$493$			7.70239i			0.346898i
$494$	9.40593	+	2.69879i	0.423193	+	0.121424i
$495$	−9.13335	+	3.61832i	−0.410514	+	0.162631i
$496$	9.08156	+	18.6513i	0.407774	+	0.837469i
$497$	−2.35140	−	2.35140i	−0.105475	−	0.105475i
$498$	15.3779	+	23.7870i	0.689099	+	1.06592i
$499$	2.98889	−	2.98889i	0.133801	−	0.133801i	−0.637034	−	0.770835i	$-0.719839\pi$
$499$	2.98889	−	2.98889i	0.133801	−	0.133801i	0.770835	+	0.637034i	$0.219839\pi$
$500$	12.9952	−	18.1968i	0.581162	−	0.813788i
$501$	27.2919	+	23.8154i	1.21931	+	1.06399i
$502$	−35.6614	−	10.2321i	−1.59165	−	0.456683i
$503$	−11.0899	−	11.0899i	−0.494475	−	0.494475i	0.415238	−	0.909713i	$-0.363698\pi$
$503$	−11.0899	−	11.0899i	−0.494475	−	0.494475i	−0.909713	+	0.415238i	$0.863698\pi$
$504$	7.07769	−	8.36181i	0.315265	−	0.372465i
$505$	14.9535	−	3.68094i	0.665424	−	0.163800i
$506$	−6.06299	−	10.9422i	−0.269533	−	0.486440i
$507$	1.01892	+	14.9790i	0.0452517	+	0.665241i
$508$	2.56402	+	11.1228i	0.113760	+	0.493494i
$509$	16.8263	+	16.8263i	0.745811	+	0.745811i	0.973690	−	0.227879i	$-0.0731789\pi$
$509$	16.8263	+	16.8263i	0.745811	+	0.745811i	−0.227879	+	0.973690i	$0.573179\pi$
$510$	8.40820	+	7.92048i	0.372321	+	0.350725i
$511$	13.5179			0.597998
$512$	3.57301	−	22.3435i	0.157906	−	0.987454i
$513$	14.4340	+	9.49065i	0.637277	+	0.419022i
$514$	−10.2443	−	2.93933i	−0.451855	−	0.129648i
$515$	3.33608	+	13.5526i	0.147005	+	0.597198i
$516$	2.48978	+	1.33096i	0.109606	+	0.0585921i
$517$		−	13.7381i		−	0.604200i
$518$	5.48652	−	19.1218i	0.241064	−	0.840165i
$519$	−2.43153	−	35.7457i	−0.106732	−	1.56906i
$520$	7.39886	−	10.8873i	0.324461	−	0.477438i
$521$	30.3997			1.33184			0.665918	−	0.746025i	$-0.268040\pi$
$521$	30.3997			1.33184			0.665918	+	0.746025i	$0.268040\pi$
$522$	15.3356	+	2.21717i	0.671221	+	0.0970428i
$523$	8.45346			0.369644			0.184822	−	0.982772i	$-0.440829\pi$
$523$	8.45346			0.369644			0.184822	+	0.982772i	$0.440829\pi$
$524$	−7.92468	−	34.3775i	−0.346191	−	1.50179i
$525$	10.8743	+	2.60081i	0.474593	+	0.113509i
$526$	−13.1595	−	3.77577i	−0.573779	−	0.164631i
$527$	−7.73398	−	7.73398i	−0.336897	−	0.336897i
$528$	−9.79368	−	2.65107i	−0.426215	−	0.115373i
$529$			13.4838i			0.586252i
$530$	22.9423	+	0.873576i	0.996550	+	0.0379457i
$531$	−15.6490	+	20.6040i	−0.679110	+	0.894139i
$532$	−4.55141	+	7.27841i	−0.197329	+	0.315559i
$533$			20.4552i			0.886015i
$534$	19.8949	−	12.8617i	0.860936	−	0.556580i
$535$	10.1493	−	16.7775i	0.438791	−	0.725355i
$536$	−1.61444	+	30.5152i	−0.0697330	+	1.31806i
$537$	−24.1676	+	27.6955i	−1.04291	+	1.19515i
$538$	0.112734	+	0.0323462i	0.00486031	+	0.00139454i
$539$	−5.52267	+	5.52267i	−0.237878	+	0.237878i
$540$	18.1902	−	14.4609i	0.782780	−	0.622299i
$541$	−7.99141	−	7.99141i	−0.343578	−	0.343578i	0.514133	−	0.857710i	$-0.328114\pi$
$541$	−7.99141	−	7.99141i	−0.343578	−	0.343578i	−0.857710	+	0.514133i	$0.828114\pi$
$542$	−18.2497	+	10.1120i	−0.783893	+	0.434349i
$543$	4.58140	+	3.99781i	0.196607	+	0.171563i
$544$	2.06191	+	11.7506i	0.0884037	+	0.503801i
$545$	4.40430	+	17.8921i	0.188659	+	0.766415i
$546$	6.43541	+	1.38175i	0.275410	+	0.0591336i
$547$	19.6579			0.840511			0.420255	−	0.907406i	$-0.361940\pi$
$547$	19.6579			0.840511			0.420255	+	0.907406i	$0.361940\pi$
$548$	1.70799	+	7.40929i	0.0729615	+	0.316509i
$549$	−33.3537	−	25.3326i	−1.42350	−	1.08117i
$550$	−2.09078	−	10.1421i	−0.0891513	−	0.432461i
$551$	−12.1418			−0.517259
$552$	21.2366	+	20.6063i	0.903888	+	0.877062i
$553$	−7.80476	+	7.80476i	−0.331892	+	0.331892i
$554$	8.36485	+	15.0965i	0.355388	+	0.641388i
$555$	19.3407	−	37.5046i	0.820967	−	1.59198i
$556$	−11.4154	+	2.63147i	−0.484120	+	0.111599i
$557$		−	32.6270i		−	1.38245i	−0.722640	−	0.691225i	$-0.757072\pi$
$557$		−	32.6270i		−	1.38245i	0.722640	−	0.691225i	$-0.242928\pi$
$558$	−17.6248	+	13.1722i	−0.746115	+	0.557625i
$559$			1.69625i			0.0717437i
$560$	7.39037	+	8.87305i	0.312300	+	0.374955i
$561$	5.33713	−	0.363048i	0.225334	−	0.0153279i
$562$	−2.70408	+	1.49831i	−0.114065	+	0.0632024i
$563$	22.9635			0.967798			0.483899	−	0.875124i	$-0.339220\pi$
$563$	22.9635			0.967798			0.483899	+	0.875124i	$0.339220\pi$
$564$	9.43184	+	31.0976i	0.397152	+	1.30944i
$565$	−5.04767	−	20.5058i	−0.212357	−	0.862685i
$566$	13.3884	−	7.41844i	0.562758	−	0.311820i
$567$	10.1198	+	5.71016i	0.424990	+	0.239804i
$568$	0.384890	−	7.27497i	0.0161496	−	0.305251i
$569$		−	42.0779i		−	1.76400i	−0.471254	−	0.881998i	$-0.656198\pi$
$569$		−	42.0779i		−	1.76400i	0.471254	−	0.881998i	$-0.343802\pi$
$570$	−12.4856	+	13.2544i	−0.522965	+	0.555167i
$571$	−12.9520	+	12.9520i	−0.542026	+	0.542026i	−0.924122	−	0.382096i	$-0.875202\pi$
$571$	−12.9520	+	12.9520i	−0.542026	+	0.542026i	0.382096	+	0.924122i	$0.375202\pi$
$572$	−1.36935	−	5.94027i	−0.0572553	−	0.248375i
$573$	25.2580	−	1.71813i	1.05517	−	0.0717758i
$574$	−17.2485	−	4.94902i	−0.719938	−	0.206568i
$575$	−9.00224	+	28.8280i	−0.375419	+	1.20221i
$576$	23.9891	−	0.722850i	0.999546	−	0.0301188i
$577$	6.79698	−	6.79698i	0.282962	−	0.282962i	−0.551327	−	0.834289i	$-0.685878\pi$
$577$	6.79698	−	6.79698i	0.282962	−	0.282962i	0.834289	+	0.551327i	$0.185878\pi$
$578$	8.60357	+	15.5273i	0.357861	+	0.645851i
$579$	8.16238	−	9.35389i	0.339217	−	0.388734i
$580$	−5.09875	+	15.5170i	−0.211714	+	0.644308i
$581$	−10.5567	−	10.5567i	−0.437964	−	0.437964i
$582$	22.3024	+	4.78857i	0.924465	+	0.198493i
$583$	7.51826	−	7.51826i	0.311375	−	0.311375i
$584$	19.8051	+	22.0178i	0.819542	+	0.911103i
$585$	12.8147	+	5.54231i	0.529824	+	0.229146i
$586$	8.91768	+	16.0942i	0.368386	+	0.664845i
$587$	−37.8077			−1.56049			−0.780245	−	0.625474i	$-0.784906\pi$
$587$	−37.8077			−1.56049			−0.780245	+	0.625474i	$0.784906\pi$
$588$	8.70957	−	16.2927i	0.359176	−	0.671900i
$589$	12.1916	−	12.1916i	0.502347	−	0.502347i
$590$	−18.5370	−	20.0045i	−0.763154	−	0.823572i
$591$	−0.556121	−	8.17549i	−0.0228758	−	0.336295i
$592$	39.1836	−	19.0790i	1.61044	−	0.784143i
$593$	21.2191	−	21.2191i	0.871365	−	0.871365i	−0.121256	−	0.992621i	$-0.538692\pi$
$593$	21.2191	−	21.2191i	0.871365	−	0.871365i	0.992621	+	0.121256i	$0.0386923\pi$
$594$	0.813482	−	10.7308i	0.0333776	−	0.440291i
$595$	−5.20939	−	3.15133i	−0.213564	−	0.129192i
$596$	2.08094	+	9.02717i	0.0852385	+	0.369767i
$597$	−0.894694	−	13.1528i	−0.0366174	−	0.538309i
$598$	−4.90334	+	17.0893i	−0.200513	+	0.698834i
$599$			17.6257i			0.720165i	0.932920	+	0.360083i	$0.117251\pi$
$599$			17.6257i			0.720165i	−0.932920	+	0.360083i	$0.882749\pi$
$600$	11.6957	+	21.5223i	0.477477	+	0.878644i
$601$			1.46847i			0.0599003i	0.999551	+	0.0299501i	$0.00953485\pi$
$601$			1.46847i			0.0599003i	−0.999551	+	0.0299501i	$0.990465\pi$
$602$	−1.43033	−	0.410397i	−0.0582959	−	0.0167265i
$603$	−32.1129	+	4.38915i	−1.30774	+	0.178740i
$604$	−19.3488	−	12.0994i	−0.787290	−	0.492316i
$605$	16.9423	+	10.2490i	0.688804	+	0.416680i
$606$	−3.54142	+	16.4939i	−0.143860	+	0.670018i
$607$	−12.7986	+	12.7986i	−0.519479	+	0.519479i	−0.917414	−	0.397935i	$-0.869727\pi$
$607$	−12.7986	+	12.7986i	−0.519479	+	0.519479i	0.397935	+	0.917414i	$0.369727\pi$
$608$	−18.5232	+	3.25033i	−0.751216	+	0.131818i
$609$	−8.14824	+	0.554268i	−0.330183	+	0.0224601i
$610$	32.3832	−	30.0075i	1.31116	−	1.21497i
$611$	−13.8060	+	13.8060i	−0.558532	+	0.558532i
$612$	−11.8319	+	4.48599i	−0.478276	+	0.181335i
$613$	−8.91389			−0.360029			−0.180014	−	0.983664i	$-0.557614\pi$
$613$	−8.91389			−0.360029			−0.180014	+	0.983664i	$0.557614\pi$
$614$	42.4662	−	23.5302i	1.71380	−	0.949603i
$615$	−33.8303	−	17.4459i	−1.36417	−	0.703488i
$616$	5.34033	+	0.282535i	0.215168	+	0.0113837i
$617$	−1.81921	+	1.81921i	−0.0732388	+	0.0732388i	−0.742777	−	0.669539i	$-0.766492\pi$
$617$	−1.81921	+	1.81921i	−0.0732388	+	0.0732388i	0.669539	+	0.742777i	$0.266492\pi$
$618$	−14.9486	−	3.20963i	−0.601321	−	0.129110i
$619$	−0.786785	−	0.786785i	−0.0316236	−	0.0316236i	0.691118	−	0.722742i	$-0.257118\pi$
$619$	−0.786785	−	0.786785i	−0.0316236	−	0.0316236i	−0.722742	+	0.691118i	$0.757118\pi$
$620$	−10.4610	−	20.7003i	−0.420122	−	0.831343i
$621$	−17.2432	+	26.2247i	−0.691947	+	1.05236i
$622$	24.3840	−	13.5110i	0.977710	−	0.541742i
$623$	−8.82935	+	8.82935i	−0.353741	+	0.353741i
$624$	7.17794	+	12.5063i	0.287348	+	0.500653i
$625$	−14.2264	+	20.5575i	−0.569056	+	0.822298i
$626$	4.86862	−	16.9683i	0.194589	−	0.678190i
$627$	0.572297	+	8.41329i	0.0228554	+	0.335995i
$628$	3.61555	−	5.78183i	0.144276	−	0.230720i
$629$	−16.2479	+	16.2479i	−0.647848	+	0.647848i
$630$	−7.77390	+	9.46486i	−0.309719	+	0.377089i
$631$			39.2718i			1.56339i	0.623663	+	0.781693i	$0.285644\pi$
$631$			39.2718i			1.56339i	−0.623663	+	0.781693i	$0.714356\pi$
$632$	−24.1470	−	1.27752i	−0.960517	−	0.0508171i
$633$	12.0571	−	13.8171i	0.479225	−	0.549180i
$634$	19.1627	+	34.5839i	0.761048	+	1.37350i
$635$	−3.05036	−	12.3919i	−0.121050	−	0.491757i
$636$	−11.8567	+	22.1800i	−0.470150	+	0.879495i
$637$	11.1000			0.439797
$638$	3.66601	+	6.61624i	0.145139	+	0.261940i
$639$	7.65589	−	1.04639i	0.302862	−	0.0413947i
$640$	−3.62466	+	25.0372i	−0.143277	+	0.989683i
$641$		−	26.9846i		−	1.06583i	−0.846170	−	0.532914i	$-0.821097\pi$
$641$		−	26.9846i		−	1.06583i	0.846170	−	0.532914i	$-0.178903\pi$
$642$	11.6617	+	18.0387i	0.460251	+	0.711931i
$643$		−	18.7886i		−	0.740949i	−0.928843	−	0.370474i	$-0.879195\pi$
$643$		−	18.7886i		−	0.740949i	0.928843	−	0.370474i	$-0.120805\pi$
$644$	−13.2239	−	8.26930i	−0.521095	−	0.325856i
$645$	−2.80537	−	1.44670i	−0.110462	−	0.0569638i
$646$	8.67302	−	4.80566i	0.341235	−	0.189076i
$647$	−4.74385	+	4.74385i	−0.186500	+	0.186500i	−0.794181	−	0.607681i	$-0.792100\pi$
$647$	−4.74385	+	4.74385i	−0.186500	+	0.186500i	0.607681	+	0.794181i	$0.292100\pi$
$648$	5.52582	+	24.8488i	0.217075	+	0.976155i
$649$	−12.6301			−0.495776
$650$	−8.09115	+	12.2934i	−0.317361	+	0.482187i
$651$	7.62512	−	8.73820i	0.298852	−	0.342477i
$652$	7.99860	+	5.00176i	0.313249	+	0.195884i
$653$	−37.7676			−1.47796			−0.738981	−	0.673726i	$-0.764693\pi$
$653$	−37.7676			−1.47796			−0.738981	+	0.673726i	$0.764693\pi$
$654$	−19.7352	−	4.23736i	−0.771706	−	0.165694i
$655$	9.42784	+	38.2999i	0.368376	+	1.49650i
$656$	−17.2099	−	35.3449i	−0.671933	−	1.37999i
$657$	−18.9986	+	25.0142i	−0.741205	+	0.975896i
$658$	−8.30139	−	14.9820i	−0.323622	−	0.584058i
$659$	−13.5538	−	13.5538i	−0.527980	−	0.527980i	0.391990	−	0.919970i	$-0.371787\pi$
$659$	−13.5538	−	13.5538i	−0.527980	−	0.527980i	−0.919970	+	0.391990i	$0.871787\pi$
$660$	10.9923	+	2.80163i	0.427876	+	0.109053i
$661$	−16.9462	+	16.9462i	−0.659132	+	0.659132i	−0.955175	−	0.296043i	$-0.904333\pi$
$661$	−16.9462	+	16.9462i	−0.659132	+	0.659132i	0.296043	+	0.955175i	$0.404333\pi$
$662$	6.50577	−	22.6741i	0.252854	−	0.881256i
$663$	−5.72837	−	4.99869i	−0.222472	−	0.194133i
$664$	1.72797	−	32.6611i	0.0670582	−	1.26750i
$665$	4.96766	−	8.21192i	0.192638	−	0.318445i
$666$	27.6729	+	37.0270i	1.07230	+	1.43477i
$667$		−	22.0601i		−	0.854169i
$668$	−9.39517	−	40.7565i	−0.363510	−	1.57692i
$669$	−24.0745	+	27.5888i	−0.930773	+	1.06664i
$670$	1.29995	−	34.1400i	0.0502215	−	1.31894i
$671$		−	20.4456i		−	0.789294i
$672$	−12.2824	+	3.02684i	−0.473802	+	0.116763i
$673$	26.0839	+	26.0839i	1.00546	+	1.00546i	0.999985	+	0.00547515i	$0.00174280\pi$
$673$	26.0839	+	26.0839i	1.00546	+	1.00546i	0.00547515	+	0.999985i	$0.498257\pi$
$674$	−0.943023	+	3.28666i	−0.0363239	+	0.126597i
$675$	−20.0957	+	16.4670i	−0.773485	+	0.633814i
$676$	9.19167	−	14.6989i	0.353526	−	0.565343i
$677$	6.41910			0.246706			0.123353	−	0.992363i	$-0.460635\pi$
$677$	6.41910			0.246706			0.123353	+	0.992363i	$0.460635\pi$
$678$	22.6180	+	4.85634i	0.868641	+	0.186507i
$679$	−12.0230			−0.461399
$680$	−2.49944	−	13.1020i	−0.0958490	−	0.502438i
$681$	8.85653	−	0.602448i	0.339383	−	0.0230858i
$682$	−10.3244	−	2.96233i	−0.395343	−	0.113433i
$683$			14.6529i			0.560679i	0.959901	+	0.280340i	$0.0904471\pi$
$683$			14.6529i			0.560679i	−0.959901	+	0.280340i	$0.909553\pi$
$684$	−7.07158	−	18.6515i	−0.270389	−	0.713156i
$685$	−2.03196	−	8.25468i	−0.0776371	−	0.315395i
$686$	−6.21050	+	21.6451i	−0.237118	+	0.826412i
$687$	3.00129	−	3.43940i	0.114506	−	0.131221i
$688$	−1.42713	−	2.93097i	−0.0544087	−	0.111742i
$689$	−15.1109			−0.575679
$690$	−24.0815	−	22.6847i	−0.916767	−	0.863591i
$691$	28.3072	+	28.3072i	1.07686	+	1.07686i	0.996789	+	0.0800692i	$0.0255141\pi$
$691$	28.3072	+	28.3072i	1.07686	+	1.07686i	0.0800692	+	0.996789i	$0.474486\pi$
$692$	−21.9349	+	35.0773i	−0.833839	+	1.33344i
$693$	0.768125	+	5.61994i	0.0291786	+	0.213484i
$694$	24.3290	−	13.4805i	0.923517	−	0.511714i
$695$	12.7179	−	3.13060i	0.482416	−	0.118751i
$696$	−12.8408	−	12.4597i	−0.486728	−	0.472283i
$697$	14.6562	+	14.6562i	0.555141	+	0.555141i
$698$	2.96964	−	10.3499i	0.112403	−	0.391749i
$699$	−8.83603	+	10.1259i	−0.334209	+	0.382996i
$700$	−8.40857	−	9.79702i	−0.317814	−	0.370292i
$701$	23.7655	−	23.7655i	0.897612	−	0.897612i	−0.0976124	−	0.995225i	$-0.531121\pi$
$701$	23.7655	−	23.7655i	0.897612	−	0.897612i	0.995225	+	0.0976124i	$0.0311205\pi$
$702$	−11.6014	+	9.96640i	−0.437867	+	0.376157i
$703$	−25.6128	−	25.6128i	−0.966004	−	0.966004i
$704$	7.36392	+	9.11218i	0.277538	+	0.343428i
$705$	−11.0584	−	34.6083i	−0.416485	−	1.30342i
$706$	−13.9819	+	48.7301i	−0.526214	+	1.83398i
$707$		−	8.89166i		−	0.334405i
$708$	28.5897	−	8.67119i	1.07447	−	0.325883i
$709$	−5.81334	−	5.81334i	−0.218325	−	0.218325i	0.589468	−	0.807792i	$-0.299338\pi$
$709$	−5.81334	−	5.81334i	−0.218325	−	0.218325i	−0.807792	+	0.589468i	$0.799338\pi$
$710$	−0.309915	+	8.13914i	−0.0116309	+	0.305457i
$711$	−3.47318	−	25.4114i	−0.130255	−	0.953000i
$712$	−27.3170	−	1.44523i	−1.02375	−	0.0541624i
$713$	22.1505	+	22.1505i	0.829544	+	0.829544i
$714$	5.60099	−	3.62094i	0.209612	−	0.135510i
$715$	1.62909	+	6.61804i	0.0609243	+	0.247501i
$716$	41.3593	−	9.53411i	1.54567	−	0.356307i
$717$	−1.11112	−	16.3345i	−0.0414956	−	0.610023i
$718$	−15.4554	−	27.8931i	−0.576790	−	1.04096i
$719$	2.88200			0.107480			0.0537402	−	0.998555i	$-0.482886\pi$
$719$	2.88200			0.107480			0.0537402	+	0.998555i	$0.482886\pi$
$720$	−26.8057	+	1.20496i	−0.998991	+	0.0449062i
$721$	8.05862			0.300119
$722$	−5.44748	−	9.83135i	−0.202734	−	0.365885i
$723$	1.21697	+	17.8905i	0.0452595	+	0.665356i
$724$	−1.57713	−	6.84166i	−0.0586137	−	0.254268i
$725$	5.44324	−	17.4310i	0.202157	−	0.647370i
$726$	−18.2159	+	11.7763i	−0.676057	+	0.437059i
$727$	−24.4474	−	24.4474i	−0.906704	−	0.906704i	0.0893004	−	0.996005i	$-0.471537\pi$
$727$	−24.4474	−	24.4474i	−0.906704	−	0.906704i	−0.996005	+	0.0893004i	$0.971537\pi$
$728$	−5.08281	−	5.65067i	−0.188381	−	0.209428i
$729$	−24.7890	+	10.7008i	−0.918110	+	0.396325i
$730$	−22.5046	−	24.2863i	−0.832934	−	0.898876i
$731$	1.21536	+	1.21536i	0.0449517	+	0.0449517i
$732$	14.0369	+	46.2808i	0.518818	+	1.71059i
$733$			17.2734i			0.638007i	0.947754	+	0.319003i	$0.103348\pi$
$733$			17.2734i			0.638007i	−0.947754	+	0.319003i	$0.896652\pi$
$734$	−9.12366	+	31.7981i	−0.336761	+	1.17369i
$735$	−9.46698	+	18.3579i	−0.349195	+	0.677142i
$736$	−5.90542	−	33.6542i	−0.217677	−	1.24051i
$737$	−11.1878	−	11.1878i	−0.412107	−	0.412107i
$738$	33.3995	−	24.9618i	1.22945	−	0.918857i
$739$	−7.62856	+	7.62856i	−0.280621	+	0.280621i	−0.833357	−	0.552736i	$-0.813584\pi$
$739$	−7.62856	+	7.62856i	−0.280621	+	0.280621i	0.552736	+	0.833357i	$0.313584\pi$
$740$	−43.4882	+	21.9769i	−1.59866	+	0.807887i
$741$	7.87978	−	9.03003i	0.289471	−	0.331727i
$742$	3.65599	−	12.7420i	0.134216	−	0.467773i
$743$	21.3182	+	21.3182i	0.782090	+	0.782090i	0.980183	−	0.198093i	$-0.0634749\pi$
$743$	21.3182	+	21.3182i	0.782090	+	0.782090i	−0.198093	+	0.980183i	$0.563475\pi$
$744$	25.4042	−	0.382658i	0.931363	−	0.0140289i
$745$	−2.47565	−	10.0571i	−0.0907008	−	0.368465i
$746$	8.96677	−	4.96842i	0.328297	−	0.181907i
$747$	34.3712	−	4.69780i	1.25758	−	0.171884i
$748$	−5.23733	−	3.27506i	−0.191496	−	0.119748i
$749$	−8.00558	−	8.00558i	−0.292518	−	0.292518i
$750$	−13.4309	−	23.8665i	−0.490426	−	0.871483i
$751$	−26.1007			−0.952430			−0.476215	−	0.879329i	$-0.657992\pi$
$751$	−26.1007			−0.952430			−0.476215	+	0.879329i	$0.657992\pi$
$752$	12.2400	−	35.4712i	0.446347	−	1.29350i
$753$	−29.8752	+	34.2363i	−1.08871	+	1.24764i
$754$	2.96482	−	10.3331i	0.107973	−	0.376310i
$755$	21.8304	+	13.2059i	0.794489	+	0.480612i
$756$	−5.59709	−	12.1940i	−0.203564	−	0.443491i
$757$			42.5694i			1.54721i	0.633668	+	0.773605i	$0.281548\pi$
$757$			42.5694i			1.54721i	−0.633668	+	0.773605i	$0.718452\pi$
$758$	12.4607	+	3.57528i	0.452592	+	0.129860i
$759$	−15.2858	+	1.03979i	−0.554840	+	0.0377419i
$760$	20.6536	−	3.94004i	0.749184	−	0.142920i
$761$	−51.8643			−1.88008			−0.940040	−	0.341065i	$-0.889212\pi$
$761$	−51.8643			−1.88008			−0.940040	+	0.341065i	$0.889212\pi$
$762$	13.6683	+	2.93474i	0.495152	+	0.106314i
$763$	10.6390			0.385158
$764$	−24.7857	−	15.4993i	−0.896716	−	0.560744i
$765$	13.1528	−	5.21069i	0.475541	−	0.188393i
$766$	−7.27614	+	25.3591i	−0.262897	+	0.916260i
$767$	12.6926	+	12.6926i	0.458304	+	0.458304i
$768$	−22.9249	−	15.5707i	−0.827233	−	0.561859i
$769$			4.33991i			0.156501i	0.996934	+	0.0782506i	$0.0249334\pi$
$769$			4.33991i			0.156501i	−0.996934	+	0.0782506i	$0.975067\pi$
$770$	−5.97469	−	0.227499i	−0.215313	−	0.00819848i
$771$	−8.58210	+	9.83487i	−0.309077	+	0.354194i
$772$	−13.9687	+	3.22005i	−0.502744	+	0.115892i
$773$		−	39.7001i		−	1.42791i	−0.700190	−	0.713957i	$-0.746901\pi$
$773$		−	39.7001i		−	1.42791i	0.700190	−	0.713957i	$-0.253099\pi$
$774$	2.76965	−	2.06996i	0.0995530	−	0.0744031i
$775$	12.0369	+	22.9680i	0.432378	+	0.825035i
$776$	−17.6149	−	19.5828i	−0.632336	−	0.702983i
$777$	−18.3577	−	16.0192i	−0.658577	−	0.574687i
$778$	0.574853	−	2.00350i	0.0206095	−	0.0718289i
$779$	−23.1035	+	23.1035i	−0.827769	+	0.827769i
$780$	−8.23121	−	13.8622i	−0.294724	−	0.496346i
$781$	2.66722	+	2.66722i	0.0954407	+	0.0954407i
$782$	8.73123	+	15.7577i	0.312228	+	0.563495i
$783$	10.4262	−	15.8568i	0.372601	−	0.566677i
$784$	−19.1798	+	9.33888i	−0.684992	+	0.333532i
$785$	−3.94621	+	6.52339i	−0.140846	+	0.232830i
$786$	−42.2451	−	9.07049i	−1.50683	−	0.323534i
$787$	−5.30056			−0.188945			−0.0944723	−	0.995527i	$-0.530116\pi$
$787$	−5.30056			−0.188945			−0.0944723	+	0.995527i	$0.530116\pi$
$788$	−5.01678	+	8.02262i	−0.178716	+	0.285794i
$789$	−11.0243	+	12.6336i	−0.392475	+	0.449767i
$790$	27.0154	+	1.02867i	0.961164	+	0.0365983i
$791$	−12.1931			−0.433538
$792$	−8.02829	+	9.48488i	−0.285273	+	0.337031i
$793$	−20.5467	+	20.5467i	−0.729636	+	0.729636i
$794$	−1.03634	+	0.574231i	−0.0367785	+	0.0203787i
$795$	12.8878	−	24.9915i	0.457084	−	0.886356i
$796$	−8.07105	+	12.9069i	−0.286071	+	0.457472i
$797$			17.4862i			0.619394i	0.950835	+	0.309697i	$0.100228\pi$
$797$			17.4862i			0.619394i	−0.950835	+	0.309697i	$0.899772\pi$
$798$	5.70794	+	8.82923i	0.202059	+	0.312551i
$799$			19.7840i			0.699908i
$800$	3.63783	−	28.0494i	0.128617	−	0.991694i
$801$	−3.92914	−	28.7473i	−0.138829	−	1.01574i
$802$	−16.2267	−	29.2852i	−0.572986	−	1.03410i
$803$	−15.3335			−0.541108
$804$	33.0056	+	17.6438i	1.16402	+	0.622247i
$805$	14.9200	+	9.02557i	0.525859	+	0.318110i
$806$	7.39851	+	13.3525i	0.260601	+	0.470321i
$807$	0.0944426	−	0.108229i	0.00332454	−	0.00380984i
$808$	14.4826	−	13.0272i	0.509496	−	0.458294i
$809$		−	37.4327i		−	1.31606i	−0.752991	−	0.658031i	$-0.771389\pi$
$809$		−	37.4327i		−	1.31606i	0.752991	−	0.658031i	$-0.228611\pi$
$810$	−6.58848	−	27.6874i	−0.231496	−	0.972836i
$811$	7.78970	−	7.78970i	0.273533	−	0.273533i	−0.556987	−	0.830521i	$-0.688043\pi$
$811$	7.78970	−	7.78970i	0.273533	−	0.273533i	0.830521	+	0.556987i	$0.188043\pi$
$812$	7.99588	+	5.00006i	0.280600	+	0.175468i
$813$	1.73419	+	25.4942i	0.0608206	+	0.894119i
$814$	−6.22342	+	21.6901i	−0.218131	+	0.760237i
$815$	−9.02447	−	5.45920i	−0.316113	−	0.191227i
$816$	14.1037	+	3.81777i	0.493730	+	0.133649i
$817$	−1.91586	+	1.91586i	−0.0670274	+	0.0670274i
$818$	−31.8321	+	17.6379i	−1.11298	+	0.616696i
$819$	4.87582	−	6.41966i	0.170375	−	0.224321i
$820$	19.8239	+	39.2277i	0.692279	+	1.36989i
$821$	−12.3460	−	12.3460i	−0.430879	−	0.430879i	0.458049	−	0.888927i	$-0.348549\pi$
$821$	−12.3460	−	12.3460i	−0.430879	−	0.430879i	−0.888927	+	0.458049i	$0.848549\pi$
$822$	9.10497	+	1.95494i	0.317572	+	0.0681863i
$823$	−10.6014	+	10.6014i	−0.369542	+	0.369542i	−0.867310	−	0.497768i	$-0.834153\pi$
$823$	−10.6014	+	10.6014i	−0.369542	+	0.369542i	0.497768	+	0.867310i	$0.334153\pi$
$824$	11.8067	+	13.1258i	0.411305	+	0.457257i
$825$	−12.3348	−	2.95012i	−0.429443	−	0.102710i
$826$	−13.7737	+	7.63191i	−0.479248	+	0.265548i
$827$	18.5764			0.645966			0.322983	−	0.946405i	$-0.395314\pi$
$827$	18.5764			0.645966			0.322983	+	0.946405i	$0.395314\pi$
$828$	33.8872	−	12.8481i	1.17766	−	0.446503i
$829$	−14.7854	+	14.7854i	−0.513517	+	0.513517i	−0.915602	−	0.402085i	$-0.868286\pi$
$829$	−14.7854	+	14.7854i	−0.513517	+	0.513517i	0.402085	+	0.915602i	$0.368286\pi$
$830$	−1.39137	+	36.5408i	−0.0482951	+	1.26835i
$831$	21.0892	−	1.43455i	0.731575	−	0.0497640i
$832$	1.75691	−	16.5576i	0.0609099	−	0.574031i
$833$	7.95312	−	7.95312i	0.275559	−	0.275559i
$834$	−3.01194	+	14.0279i	−0.104295	+	0.485746i
$835$	11.1772	+	45.4067i	0.386804	+	1.57137i
$836$	5.16271	−	8.25597i	0.178556	−	0.285539i
$837$	5.45293	+	26.3908i	0.188481	+	0.912200i
$838$	26.5365	+	7.61398i	0.916689	+	0.263021i
$839$			33.8653i			1.16916i	0.811336	+	0.584580i	$0.198741\pi$
$839$			33.8653i			1.16916i	−0.811336	+	0.584580i	$0.801259\pi$
$840$	13.6805	−	3.58694i	0.472023	−	0.123761i
$841$		−	15.6613i		−	0.540045i
$842$	−7.60345	+	26.4998i	−0.262032	+	0.913244i
$843$	0.256956	+	3.77749i	0.00885004	+	0.130104i
$844$	−20.6338	+	4.75650i	−0.710246	+	0.163725i
$845$	−10.0323	+	16.5842i	−0.345121	+	0.570512i
$846$	39.3903	+	5.69491i	1.35427	+	0.195795i
$847$	8.08423	−	8.08423i	0.277777	−	0.277777i
$848$	26.1103	−	12.7135i	0.896632	−	0.436582i
$849$	−1.27224	−	18.7031i	−0.0436632	−	0.641889i
$850$	3.01091	+	14.6055i	0.103273	+	0.500965i
$851$	46.5350	−	46.5350i	1.59520	−	1.59520i
$852$	−7.86871	−	4.20636i	−0.269578	−	0.144108i
$853$	27.4595			0.940194			0.470097	−	0.882615i	$-0.344219\pi$
$853$	27.4595			0.940194			0.470097	+	0.882615i	$0.344219\pi$
$854$	−12.3545	−	22.2968i	−0.422762	−	0.762981i
$855$	8.21397	+	20.7337i	0.280912	+	0.709077i
$856$	1.31039	−	24.7683i	0.0447883	−	0.846564i
$857$	−17.7906	+	17.7906i	−0.607715	+	0.607715i	−0.942348	−	0.334634i	$-0.891387\pi$
$857$	−17.7906	+	17.7906i	−0.607715	+	0.607715i	0.334634	+	0.942348i	$0.391387\pi$
$858$	−7.29975	−	1.56734i	−0.249209	−	0.0535080i
$859$	4.90738	+	4.90738i	0.167438	+	0.167438i	0.785852	−	0.618414i	$-0.212225\pi$
$859$	4.90738	+	4.90738i	0.167438	+	0.167438i	−0.618414	+	0.785852i	$0.712225\pi$
$860$	1.64389	+	3.25295i	0.0560562	+	0.110925i
$861$	−14.4499	+	16.5592i	−0.492450	+	0.564335i
$862$	−1.48076	−	2.67241i	−0.0504349	−	0.0910226i
$863$	4.91101	−	4.91101i	0.167173	−	0.167173i	−0.618563	−	0.785735i	$-0.712285\pi$
$863$	4.91101	−	4.91101i	0.167173	−	0.167173i	0.785735	+	0.618563i	$0.212285\pi$
$864$	11.6611	−	26.9818i	0.396718	−	0.917941i
$865$	23.9409	−	39.5762i	0.814016	−	1.34563i
$866$	34.0002	+	9.75548i	1.15537	+	0.331505i
$867$	21.6911	−	1.47549i	0.736667	−	0.0501103i
$868$	−13.0492	+	3.00810i	−0.442920	+	0.102102i
$869$	8.85302	−	8.85302i	0.300318	−	0.300318i
$870$	14.5610	+	13.7164i	0.493663	+	0.465029i
$871$			22.4862i			0.761916i
$872$	15.5872	+	17.3286i	0.527849	+	0.586822i
$873$	16.8975	−	22.2478i	0.571894	−	0.752975i
$874$	−24.8400	+	13.7636i	−0.840225	+	0.465562i
$875$	9.56212	+	10.8131i	0.323259	+	0.365549i
$876$	34.7091	−	10.5272i	1.17271	−	0.355681i
$877$	20.1399			0.680076			0.340038	−	0.940412i	$-0.389560\pi$
$877$	20.1399			0.680076			0.340038	+	0.940412i	$0.389560\pi$
$878$	13.8676	−	7.68392i	0.468008	−	0.259320i
$879$	22.4830	−	1.52936i	0.758331	−	0.0515840i
$880$	−8.38296	−	10.0648i	−0.282590	−	0.339284i
$881$			36.5232i			1.23050i	0.788333	+	0.615249i	$0.210944\pi$
$881$			36.5232i			1.23050i	−0.788333	+	0.615249i	$0.789056\pi$
$882$	−13.5455	−	18.1241i	−0.456099	−	0.610271i
$883$		−	28.7937i		−	0.968985i	−0.874795	−	0.484493i	$-0.839004\pi$
$883$		−	28.7937i		−	0.968985i	0.874795	−	0.484493i	$-0.160996\pi$
$884$	1.97198	+	8.55450i	0.0663248	+	0.287719i
$885$	−31.8173	+	10.1666i	−1.06953	+	0.341747i
$886$	3.86456	+	6.97457i	0.129832	+	0.234315i
$887$	28.4788	−	28.4788i	0.956224	−	0.956224i	−0.0428570	−	0.999081i	$-0.513646\pi$
$887$	28.4788	−	28.4788i	0.956224	−	0.956224i	0.999081	+	0.0428570i	$0.0136460\pi$
$888$	−0.803908	−	53.3704i	−0.0269774	−	1.79099i
$889$	−7.36844			−0.247130
$890$	30.5619	+	1.16371i	1.02444	+	0.0390076i
$891$	−11.4789	−	6.47709i	−0.384559	−	0.216991i
$892$	41.1999	−	9.49737i	1.37947	−	0.317995i
$893$	−31.1869			−1.04363
$894$	11.0931	+	2.38181i	0.371009	+	0.0796597i
$895$	−46.0783	+	11.3425i	−1.54023	+	0.379139i
$896$	13.5368	+	5.48749i	0.452233	+	0.183324i
$897$	16.4064	+	14.3165i	0.547792	+	0.478014i
$898$	−11.6088	+	6.43237i	−0.387392	+	0.214651i
$899$	−13.3934	−	13.3934i	−0.446695	−	0.446695i
$900$	29.9465	−	1.79052i	0.998217	−	0.0596838i
$901$	−10.8269	+	10.8269i	−0.360698	+	0.360698i
$902$	19.5651	+	5.61372i	0.651447	+	0.186916i
$903$	−1.19825	+	1.37317i	−0.0398754	+	0.0456962i
$904$	−17.8641	−	19.8600i	−0.594153	−	0.660533i
$905$	1.87629	+	7.62227i	0.0623698	+	0.253373i
$906$	−23.4714	+	15.1739i	−0.779786	+	0.504118i
$907$		−	21.8599i		−	0.725846i	−0.931819	−	0.362923i	$-0.881779\pi$
$907$		−	21.8599i		−	0.725846i	0.931819	−	0.362923i	$-0.118221\pi$
$908$	−8.69093	−	5.43470i	−0.288418	−	0.180357i
$909$	16.4535	+	12.4966i	0.545728	+	0.414488i
$910$	5.77561	+	6.23286i	0.191460	+	0.206617i
$911$		−	26.5894i		−	0.880945i	−0.897766	−	0.440473i	$-0.854811\pi$
$911$		−	26.5894i		−	0.880945i	0.897766	−	0.440473i	$-0.145189\pi$
$912$	−6.01822	+	22.2327i	−0.199283	+	0.736199i
$913$	11.9745	+	11.9745i	0.396299	+	0.396299i
$914$	−31.2044	−	8.95331i	−1.03215	−	0.296149i
$915$	−16.4577	−	51.5056i	−0.544073	−	1.70272i
$916$	−5.13625	+	1.18401i	−0.169707	+	0.0391207i
$917$	22.7738			0.752059
$918$	−1.17148	+	15.4533i	−0.0386647	+	0.510035i
$919$	46.8512			1.54548			0.772739	−	0.634723i	$-0.218886\pi$
$919$	46.8512			1.54548			0.772739	+	0.634723i	$0.218886\pi$
$920$	7.15851	+	37.5248i	0.236009	+	1.23715i
$921$	−4.03537	−	59.3237i	−0.132970	−	1.95478i
$922$	4.20640	−	14.6603i	0.138530	−	0.482811i
$923$		−	5.36083i		−	0.176454i
$924$	3.08776	−	5.77617i	0.101580	−	0.190022i
$925$	48.2524	−	25.2877i	1.58653	−	0.831455i
$926$	−21.1441	−	6.06676i	−0.694838	−	0.199366i
$927$	−11.3259	+	14.9120i	−0.371990	+	0.489775i
$928$	3.57073	+	20.3492i	0.117215	+	0.667994i
$929$	20.5659			0.674747			0.337373	−	0.941371i	$-0.390462\pi$
$929$	20.5659			0.674747			0.337373	+	0.941371i	$0.390462\pi$
$930$	−28.3933	+	0.848067i	−0.931053	+	0.0278092i
$931$	12.5371	+	12.5371i	0.410885	+	0.410885i
$932$	15.1215	−	3.48581i	0.495322	−	0.114181i
$933$	−2.31710	−	34.0635i	−0.0758585	−	1.11519i
$934$	6.60929	+	11.9281i	0.216263	+	0.390301i
$935$	5.90906	+	3.57458i	0.193247	+	0.116901i
$936$	17.5998	−	1.46379i	0.575268	−	0.0478456i
$937$	−34.0136	−	34.0136i	−1.11118	−	1.11118i	−0.992992	−	0.118184i	$-0.962293\pi$
$937$	−34.0136	−	34.0136i	−1.11118	−	1.11118i	−0.118184	−	0.992992i	$-0.537707\pi$
$938$	−18.9611	−	5.44040i	−0.619101	−	0.177635i
$939$	−16.2902	−	14.2151i	−0.531610	−	0.463893i
$940$	−13.0964	+	39.8562i	−0.427158	+	1.29997i
$941$	−12.2462	+	12.2462i	−0.399216	+	0.399216i	−0.877956	−	0.478741i	$-0.841093\pi$
$941$	−12.2462	+	12.2462i	−0.399216	+	0.399216i	0.478741	+	0.877956i	$0.341093\pi$
$942$	−4.53427	−	7.01377i	−0.147735	−	0.228521i
$943$	−41.9760	−	41.9760i	−1.36693	−	1.36693i
$944$	−32.6106	−	11.2529i	−1.06138	−	0.366250i
$945$	6.45879	+	13.5392i	0.210104	+	0.440430i
$946$	1.62244	+	0.465517i	0.0527500	+	0.0151353i
$947$			47.5663i			1.54570i	0.634592	+	0.772848i	$0.281168\pi$
$947$			47.5663i			1.54570i	−0.634592	+	0.772848i	$0.718832\pi$
$948$	−13.9617	+	26.1178i	−0.453456	+	0.848265i
$949$	15.4094	+	15.4094i	0.500209	+	0.500209i
$950$	−23.0237	+	4.74630i	−0.746987	+	0.153990i
$951$	48.3124	−	3.28635i	1.56664	−	0.106567i
$952$	−7.69053	−	0.406875i	−0.249251	−	0.0131869i
$953$	−22.3066	−	22.3066i	−0.722582	−	0.722582i	0.246548	−	0.969131i	$-0.420704\pi$
$953$	−22.3066	−	22.3066i	−0.722582	−	0.722582i	−0.969131	+	0.246548i	$0.920704\pi$
$954$	18.4401	+	24.6732i	0.597019	+	0.798825i
$955$	27.9647	+	16.9167i	0.904916	+	0.547413i
$956$	−10.0235	+	16.0291i	−0.324182	+	0.518417i
$957$	9.24263	−	0.628711i	0.298772	−	0.0203233i
$958$	−0.433595	+	0.240252i	−0.0140088	+	0.00776219i
$959$	−4.90839			−0.158500
$960$	25.8857	+	17.0274i	0.835456	+	0.549557i
$961$	−4.10336			−0.132366
$962$	28.0516	−	15.5432i	0.904419	−	0.501132i
$963$	26.0652	−	3.56255i	0.839939	−	0.114802i
$964$	10.9783	−	17.5560i	0.353587	−	0.565441i
$965$	15.5625	−	3.83083i	0.500974	−	0.123319i
$966$	−16.0415	+	10.3706i	−0.516128	+	0.333667i
$967$	9.83196	+	9.83196i	0.316175	+	0.316175i	0.847296	−	0.531121i	$-0.178229\pi$
$967$	9.83196	+	9.83196i	0.316175	+	0.316175i	−0.531121	+	0.847296i	$0.678229\pi$
$968$	25.0117	+	1.32327i	0.803905	+	0.0425314i
$969$	−0.824157	−	12.1159i	−0.0264757	−	0.389218i
$970$	20.0158	+	21.6005i	0.642670	+	0.693549i
$971$	27.1430	+	27.1430i	0.871059	+	0.871059i	0.992588	−	0.121529i	$-0.0387798\pi$
$971$	27.1430	+	27.1430i	0.871059	+	0.871059i	−0.121529	+	0.992588i	$0.538780\pi$
$972$	30.4306	+	6.78075i	0.976062	+	0.217493i
$973$		−	7.56227i		−	0.242435i
$974$	−6.39827	−	1.83582i	−0.205014	−	0.0588235i
$975$	9.43110	+	15.3605i	0.302037	+	0.491931i
$976$	18.2161	−	52.7898i	0.583084	−	1.68976i
$977$	27.0368	+	27.0368i	0.864984	+	0.864984i	0.991912	−	0.126928i	$-0.0405116\pi$
$977$	27.0368	+	27.0368i	0.864984	+	0.864984i	−0.126928	+	0.991912i	$0.540512\pi$
$978$	9.70287	−	6.27273i	0.310263	−	0.200580i
$979$	10.0152	−	10.0152i	0.320088	−	0.320088i
$980$	21.2868	−	10.7574i	0.679982	−	0.343631i
$981$	−14.9524	+	19.6869i	−0.477394	+	0.628553i
$982$	−39.9680	−	11.4678i	−1.27543	−	0.365952i
$983$	15.4408	+	15.4408i	0.492484	+	0.492484i	0.909088	−	0.416604i	$-0.136780\pi$
$983$	15.4408	+	15.4408i	0.492484	+	0.492484i	−0.416604	+	0.909088i	$0.636780\pi$
$984$	−48.1418	+	0.725150i	−1.53470	+	0.0231169i
$985$	5.47559	−	9.05158i	0.174467	−	0.288407i
$986$	−5.27937	−	9.52796i	−0.168129	−	0.303432i
$987$	−20.9292	+	1.42367i	−0.666184	+	0.0453158i
$988$	−13.4851	+	3.10857i	−0.429017	+	0.0988967i
$989$	−3.48086	−	3.48086i	−0.110685	−	0.110685i
$990$	8.81800	−	10.7361i	0.280255	−	0.341215i
$991$	−9.30144			−0.295470			−0.147735	−	0.989027i	$-0.547198\pi$
$991$	−9.30144			−0.295470			−0.147735	+	0.989027i	$0.547198\pi$
$992$	−24.0180	−	16.8472i	−0.762572	−	0.534900i
$993$	−21.7680	−	18.9952i	−0.690787	−	0.602794i
$994$	4.52042	+	1.29702i	0.143379	+	0.0411389i
$995$	8.80919	−	14.5623i	0.279270	−	0.461655i
$996$	−35.3267	−	18.8845i	−1.11937	−	0.598379i
$997$			14.4349i			0.457158i	0.973525	+	0.228579i	$0.0734080\pi$
$997$			14.4349i			0.457158i	−0.973525	+	0.228579i	$0.926592\pi$
$998$	−1.64865	+	5.74594i	−0.0521871	+	0.181884i
$999$	55.4432	−	11.4558i	1.75414	−	0.362446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bb.a.173.8	✓	88
3.2	odd	2	inner	240.2.bb.a.173.37	yes	88
4.3	odd	2		960.2.bb.a.593.21		88
5.2	odd	4		240.2.bf.a.77.15	yes	88
12.11	even	2		960.2.bb.a.593.24		88
15.2	even	4		240.2.bf.a.77.30	yes	88
16.5	even	4		240.2.bf.a.53.30	yes	88
16.11	odd	4		960.2.bf.a.113.4		88
20.7	even	4		960.2.bf.a.17.4		88
48.5	odd	4		240.2.bf.a.53.15	yes	88
48.11	even	4		960.2.bf.a.113.3		88
60.47	odd	4		960.2.bf.a.17.3		88
80.27	even	4		960.2.bb.a.497.24		88
80.37	odd	4	inner	240.2.bb.a.197.37	yes	88
240.107	odd	4		960.2.bb.a.497.21		88
240.197	even	4	inner	240.2.bb.a.197.8	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bb.a.173.8	✓	88	1.1	even	1	trivial
240.2.bb.a.173.37	yes	88	3.2	odd	2	inner
240.2.bb.a.197.8	yes	88	240.197	even	4	inner
240.2.bb.a.197.37	yes	88	80.37	odd	4	inner
240.2.bf.a.53.15	yes	88	48.5	odd	4
240.2.bf.a.53.30	yes	88	16.5	even	4
240.2.bf.a.77.15	yes	88	5.2	odd	4
240.2.bf.a.77.30	yes	88	15.2	even	4
960.2.bb.a.497.21		88	240.107	odd	4
960.2.bb.a.497.24		88	80.27	even	4
960.2.bb.a.593.21		88	4.3	odd	2
960.2.bb.a.593.24		88	12.11	even	2
960.2.bf.a.17.3		88	60.47	odd	4
960.2.bf.a.17.4		88	20.7	even	4
960.2.bf.a.113.3		88	48.11	even	4
960.2.bf.a.113.4		88	16.11	odd	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23701 + 0.685419i) q^{2} +(0.117548 + 1.72806i) q^{3} +(1.06040 - 1.69575i) q^{4} +(-1.15738 + 1.91324i) q^{5} +(-1.32985 - 2.05706i) q^{6} +(0.912923 + 0.912923i) q^{7} +(-0.149432 + 2.82448i) q^{8} +(-2.97237 + 0.406258i) q^{9} +(0.120323 - 3.15999i) q^{10} +(-1.03554 - 1.03554i) q^{11} +(3.05499 + 1.63310i) q^{12} +2.08132i q^{13} +(-1.75503 - 0.503562i) q^{14} +(-3.44223 - 1.77512i) q^{15} +(-1.75110 - 3.59634i) q^{16} +(1.49126 + 1.49126i) q^{17} +(3.39840 - 2.53986i) q^{18} +(-2.35078 + 2.35078i) q^{19} +(2.01708 + 3.99142i) q^{20} +(-1.47027 + 1.68489i) q^{21} +(1.99075 + 0.571195i) q^{22} +(-4.27105 - 4.27105i) q^{23} +(-4.89842 + 0.0737840i) q^{24} +(-2.32095 - 4.42868i) q^{25} +(-1.42658 - 2.57462i) q^{26} +(-1.05143 - 5.08866i) q^{27} +(2.51615 - 0.580021i) q^{28} +(2.58251 + 2.58251i) q^{29} +(5.47478 - 0.163524i) q^{30} -5.18620 q^{31} +(4.63114 + 3.24847i) q^{32} +(1.66774 - 1.91119i) q^{33} +(-2.86685 - 0.822570i) q^{34} +(-2.80323 + 0.690039i) q^{35} +(-2.46299 + 5.47117i) q^{36} +10.8954i q^{37} +(1.29667 - 4.51922i) q^{38} +(-3.59664 + 0.244654i) q^{39} +(-5.23094 - 3.55489i) q^{40} +9.82802 q^{41} +(0.663884 - 3.09199i) q^{42} +0.814988 q^{43} +(-2.85409 + 0.657923i) q^{44} +(2.66289 - 6.15703i) q^{45} +(8.21081 + 2.35588i) q^{46} +(6.63331 + 6.63331i) q^{47} +(6.00884 - 3.44875i) q^{48} -5.33314i q^{49} +(5.90654 + 3.88751i) q^{50} +(-2.40169 + 2.75228i) q^{51} +(3.52938 + 2.20703i) q^{52} +7.26025i q^{53} +(4.78850 + 5.57407i) q^{54} +(3.17974 - 0.782718i) q^{55} +(-2.71495 + 2.44211i) q^{56} +(-4.33861 - 3.78596i) q^{57} +(-4.96470 - 1.42449i) q^{58} +(6.09835 - 6.09835i) q^{59} +(-6.66029 + 3.95480i) q^{60} +(9.87198 + 9.87198i) q^{61} +(6.41539 - 3.55472i) q^{62} +(-3.08442 - 2.34266i) q^{63} +(-7.95534 - 0.844133i) q^{64} +(-3.98205 - 2.40887i) q^{65} +(-0.753050 + 3.50727i) q^{66} +10.8038 q^{67} +(4.11014 - 0.947466i) q^{68} +(6.87857 - 7.88268i) q^{69} +(2.99467 - 2.77498i) q^{70} -2.57569 q^{71} +(-0.703301 - 8.45608i) q^{72} +(7.40366 - 7.40366i) q^{73} +(-7.46794 - 13.4778i) q^{74} +(7.38019 - 4.53131i) q^{75} +(1.49356 + 6.47909i) q^{76} -1.89073i q^{77} +(4.28139 - 2.76785i) q^{78} +8.54920i q^{79} +(8.90733 + 0.812052i) q^{80} +(8.66991 - 2.41509i) q^{81} +(-12.1574 + 6.73632i) q^{82} -11.5636 q^{83} +(1.29808 + 4.27987i) q^{84} +(-4.57909 + 1.12718i) q^{85} +(-1.00815 + 0.558608i) q^{86} +(-4.15916 + 4.76629i) q^{87} +(3.07959 - 2.77011i) q^{88} +9.67152i q^{89} +(0.926126 + 9.44152i) q^{90} +(-1.90008 + 1.90008i) q^{91} +(-11.7716 + 2.71359i) q^{92} +(-0.609625 - 8.96205i) q^{93} +(-12.7521 - 3.65889i) q^{94} +(-1.77685 - 7.21834i) q^{95} +(-5.06917 + 8.38472i) q^{96} +(-6.58488 + 6.58488i) q^{97} +(3.65544 + 6.59717i) q^{98} +(3.49869 + 2.65730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{4} - 4 q^{6} - 12 q^{10} + 4 q^{12} - 4 q^{15} - 12 q^{16} + 16 q^{18} - 8 q^{19} - 4 q^{21} - 20 q^{22} - 12 q^{24} - 36 q^{28} - 16 q^{30} - 16 q^{31} - 4 q^{33} + 28 q^{34} - 20 q^{36} + 24 q^{39}+ \cdots - 32 q^{99}+O(q^{100}) \) 88 * q - 4 * q^4 - 4 * q^6 - 12 * q^10 + 4 * q^12 - 4 * q^15 - 12 * q^16 + 16 * q^18 - 8 * q^19 - 4 * q^21 - 20 * q^22 - 12 * q^24 - 36 * q^28 - 16 * q^30 - 16 * q^31 - 4 * q^33 + 28 * q^34 - 20 * q^36 + 24 * q^39 - 4 * q^40 - 20 * q^42 - 40 * q^43 + 8 * q^45 - 36 * q^46 + 16 * q^48 - 4 * q^51 + 24 * q^52 - 24 * q^54 + 12 * q^57 + 44 * q^58 - 56 * q^60 - 24 * q^61 - 32 * q^63 - 28 * q^64 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 28 * q^70 + 64 * q^72 - 24 * q^75 - 36 * q^76 + 20 * q^78 - 8 * q^81 - 48 * q^82 + 48 * q^84 - 24 * q^85 - 12 * q^87 + 60 * q^88 + 76 * q^90 - 8 * q^91 - 20 * q^94 + 48 * q^96 - 8 * q^97 - 32 * q^99

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