LMFDB - Embedded newform 273.2.cc.a.50.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(50,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

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

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

chi := DirichletCharacter("273.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cc (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.18
Character	$\chi$	$=$	273.50
Dual form			273.2.cc.a.71.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.751420 + 0.201342i) q^{2} +(-0.504568 - 1.65693i) q^{3} +(-1.20796 - 0.697414i) q^{4} +(-2.48091 + 2.48091i) q^{5} +(-0.0455330 - 1.34664i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-1.86742 - 1.86742i) q^{8} +(-2.49082 + 1.67207i) q^{9} +O(q^{10})$	\(q+(0.751420 + 0.201342i) q^{2} +(-0.504568 - 1.65693i) q^{3} +(-1.20796 - 0.697414i) q^{4} +(-2.48091 + 2.48091i) q^{5} +(-0.0455330 - 1.34664i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-1.86742 - 1.86742i) q^{8} +(-2.49082 + 1.67207i) q^{9} +(-2.36372 + 1.36469i) q^{10} +(-1.16287 + 4.33987i) q^{11} +(-0.546068 + 2.35339i) q^{12} +(-2.59448 - 2.50374i) q^{13} -0.777928i q^{14} +(5.36248 + 2.85890i) q^{15} +(0.367602 + 0.636705i) q^{16} +(2.53006 - 4.38220i) q^{17} +(-2.20831 + 0.754917i) q^{18} +(-4.15985 + 1.11463i) q^{19} +(4.72705 - 1.26661i) q^{20} +(-1.46988 + 0.916220i) q^{21} +(-1.74760 + 3.02693i) q^{22} +(-1.39149 - 2.41014i) q^{23} +(-2.15194 + 4.03642i) q^{24} -7.30982i q^{25} +(-1.44543 - 2.40374i) q^{26} +(4.02729 + 3.28344i) q^{27} +(-0.361008 + 1.34730i) q^{28} +(0.156921 - 0.0905985i) q^{29} +(3.45386 + 3.22793i) q^{30} +(-6.69080 - 6.69080i) q^{31} +(1.51507 + 5.65433i) q^{32} +(7.77760 - 0.262978i) q^{33} +(2.78347 - 2.78347i) q^{34} +(3.03848 + 1.75427i) q^{35} +(4.17493 - 0.282651i) q^{36} +(7.89628 + 2.11580i) q^{37} -3.35022 q^{38} +(-2.83942 + 5.56217i) q^{39} +9.26580 q^{40} +(-5.61219 - 1.50378i) q^{41} +(-1.28897 + 0.392518i) q^{42} +(0.515494 + 0.297621i) q^{43} +(4.43138 - 4.43138i) q^{44} +(2.03125 - 10.3277i) q^{45} +(-0.560334 - 2.09119i) q^{46} +(0.599020 + 0.599020i) q^{47} +(0.869495 - 0.930352i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(1.47178 - 5.49275i) q^{50} +(-8.53758 - 1.98102i) q^{51} +(1.38788 + 4.83383i) q^{52} -5.43018i q^{53} +(2.36509 + 3.27811i) q^{54} +(-7.88187 - 13.6518i) q^{55} +(-1.32047 + 2.28711i) q^{56} +(3.94578 + 6.33016i) q^{57} +(0.136155 - 0.0364827i) q^{58} +(-7.75661 + 2.07838i) q^{59} +(-4.48380 - 7.19330i) q^{60} +(1.75531 - 3.04029i) q^{61} +(-3.68046 - 6.37475i) q^{62} +(2.25976 + 1.97319i) q^{63} +3.08342i q^{64} +(12.6482 - 0.225122i) q^{65} +(5.89720 + 1.36835i) q^{66} +(-0.450145 + 1.67996i) q^{67} +(-6.11242 + 3.52901i) q^{68} +(-3.29132 + 3.52168i) q^{69} +(1.92997 + 1.92997i) q^{70} +(3.53048 + 13.1759i) q^{71} +(7.77386 + 1.52896i) q^{72} +(0.693304 - 0.693304i) q^{73} +(5.50742 + 3.17971i) q^{74} +(-12.1118 + 3.68830i) q^{75} +(5.80227 + 1.55471i) q^{76} +4.49297 q^{77} +(-3.25350 + 3.60783i) q^{78} +0.480977 q^{79} +(-2.49160 - 0.667621i) q^{80} +(3.40838 - 8.32964i) q^{81} +(-3.91434 - 2.25995i) q^{82} +(-8.15333 + 8.15333i) q^{83} +(2.41453 - 0.0816409i) q^{84} +(4.59498 + 17.1487i) q^{85} +(0.327429 + 0.327429i) q^{86} +(-0.229293 - 0.214294i) q^{87} +(10.2759 - 5.93281i) q^{88} +(-0.837175 + 3.12438i) q^{89} +(3.60574 - 7.35150i) q^{90} +(-1.74692 + 3.15409i) q^{91} +3.88179i q^{92} +(-7.71021 + 14.4621i) q^{93} +(0.329508 + 0.570724i) q^{94} +(7.55491 - 13.0855i) q^{95} +(8.60437 - 5.36337i) q^{96} +(-2.19811 + 0.588981i) q^{97} +(-0.751420 + 0.201342i) q^{98} +(-4.36007 - 12.7542i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{6}+O(q^{10}) $ 112 * q - 12 * q^6	$ 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) $ 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$1$

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 $

$2$	0.751420	+	0.201342i	0.531334	+	0.142371i	0.514504	−	0.857488i	$-0.327976\pi$
$2$	0.751420	+	0.201342i	0.531334	+	0.142371i	0.0168300	+	0.999858i	$0.494643\pi$
$3$	−0.504568	−	1.65693i	−0.291313	−	0.956628i
$3$	−0.504568	−	1.65693i	−0.291313	−	0.956628i
$4$	−1.20796	−	0.697414i	−0.603979	−	0.348707i
$5$	−2.48091	+	2.48091i	−1.10950	+	1.10950i	−0.116280	+	0.993217i	$0.537097\pi$
$5$	−2.48091	+	2.48091i	−1.10950	+	1.10950i	−0.993217	+	0.116280i	$0.962903\pi$
$6$	−0.0455330	−	1.34664i	−0.0185888	−	0.549764i
$7$	−0.258819	−	0.965926i	−0.0978244	−	0.365086i
$7$	−0.258819	−	0.965926i	−0.0978244	−	0.365086i
$8$	−1.86742	−	1.86742i	−0.660233	−	0.660233i
$9$	−2.49082	+	1.67207i	−0.830274	+	0.557356i
$10$	−2.36372	+	1.36469i	−0.747473	+	0.431554i
$11$	−1.16287	+	4.33987i	−0.350617	+	1.30852i	0.535294	+	0.844666i	$0.320201\pi$
$11$	−1.16287	+	4.33987i	−0.350617	+	1.30852i	−0.885911	+	0.463855i	$0.846466\pi$
$12$	−0.546068	+	2.35339i	−0.157636	+	0.679366i
$13$	−2.59448	−	2.50374i	−0.719578	−	0.694411i
$13$	−2.59448	−	2.50374i	−0.719578	−	0.694411i
$14$		−	0.777928i		−	0.207910i
$15$	5.36248	+	2.85890i	1.38459	+	0.738165i
$16$	0.367602	+	0.636705i	0.0919005	+	0.159176i
$17$	2.53006	−	4.38220i	0.613631	−	1.06284i	−0.376992	−	0.926216i	$-0.623042\pi$
$17$	2.53006	−	4.38220i	0.613631	−	1.06284i	0.990623	−	0.136623i	$-0.0436250\pi$
$18$	−2.20831	+	0.754917i	−0.520504	+	0.177936i
$19$	−4.15985	+	1.11463i	−0.954334	+	0.255713i	−0.702200	−	0.711979i	$-0.747799\pi$
$19$	−4.15985	+	1.11463i	−0.954334	+	0.255713i	−0.252134	+	0.967692i	$0.581132\pi$
$20$	4.72705	−	1.26661i	1.05700	−	0.283223i
$21$	−1.46988	+	0.916220i	−0.320754	+	0.199936i
$22$	−1.74760	+	3.02693i	−0.372590	+	0.645345i
$23$	−1.39149	−	2.41014i	−0.290147	−	0.502548i	0.683698	−	0.729765i	$-0.260371\pi$
$23$	−1.39149	−	2.41014i	−0.290147	−	0.502548i	−0.973844	+	0.227217i	$0.927037\pi$
$24$	−2.15194	+	4.03642i	−0.439263	+	0.823931i
$25$		−	7.30982i		−	1.46196i
$26$	−1.44543	−	2.40374i	−0.283473	−	0.471411i
$27$	4.02729	+	3.28344i	0.775051	+	0.631898i
$28$	−0.361008	+	1.34730i	−0.0682241	+	0.254616i
$29$	0.156921	−	0.0905985i	0.0291395	−	0.0168237i	−0.485359	−	0.874315i	$-0.661311\pi$
$29$	0.156921	−	0.0905985i	0.0291395	−	0.0168237i	0.514499	+	0.857491i	$0.327978\pi$
$30$	3.45386	+	3.22793i	0.630585	+	0.589337i
$31$	−6.69080	−	6.69080i	−1.20170	−	1.20170i	−0.973648	−	0.228055i	$-0.926763\pi$
$31$	−6.69080	−	6.69080i	−1.20170	−	1.20170i	−0.228055	−	0.973648i	$-0.573237\pi$
$32$	1.51507	+	5.65433i	0.267830	+	0.999555i
$33$	7.77760	−	0.262978i	1.35391	−	0.0457787i
$34$	2.78347	−	2.78347i	0.477360	−	0.477360i
$35$	3.03848	+	1.75427i	0.513597	+	0.296525i
$36$	4.17493	−	0.282651i	0.695821	−	0.0471085i
$37$	7.89628	+	2.11580i	1.29814	+	0.347836i	0.840747	−	0.541429i	$-0.182116\pi$
$37$	7.89628	+	2.11580i	1.29814	+	0.347836i	0.457394	+	0.889264i	$0.348783\pi$
$38$	−3.35022			−0.543477
$39$	−2.83942	+	5.56217i	−0.454671	+	0.890660i
$40$	9.26580			1.46505
$41$	−5.61219	−	1.50378i	−0.876477	−	0.234851i	−0.207591	−	0.978216i	$-0.566562\pi$
$41$	−5.61219	−	1.50378i	−0.876477	−	0.234851i	−0.668887	+	0.743364i	$0.733229\pi$
$42$	−1.28897	+	0.392518i	−0.198892	+	0.0605668i
$43$	0.515494	+	0.297621i	0.0786122	+	0.0453867i	0.538791	−	0.842440i	$-0.318881\pi$
$43$	0.515494	+	0.297621i	0.0786122	+	0.0453867i	−0.460179	+	0.887826i	$0.652215\pi$
$44$	4.43138	−	4.43138i	0.668056	−	0.668056i
$45$	2.03125	−	10.3277i	0.302802	−	1.53957i
$46$	−0.560334	−	2.09119i	−0.0826167	−	0.308330i
$47$	0.599020	+	0.599020i	0.0873760	+	0.0873760i	0.749444	−	0.662068i	$-0.230321\pi$
$47$	0.599020	+	0.599020i	0.0873760	+	0.0873760i	−0.662068	+	0.749444i	$0.730321\pi$
$48$	0.869495	−	0.930352i	0.125501	−	0.134285i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	1.47178	−	5.49275i	0.208141	−	0.776792i
$51$	−8.53758	−	1.98102i	−1.19550	−	0.277398i
$52$	1.38788	+	4.83383i	0.192464	+	0.670332i
$53$		−	5.43018i		−	0.745893i	−0.927853	−	0.372947i	$-0.878347\pi$
$53$		−	5.43018i		−	0.745893i	0.927853	−	0.372947i	$-0.121653\pi$
$54$	2.36509	+	3.27811i	0.321848	+	0.446094i
$55$	−7.88187	−	13.6518i	−1.06279	−	1.84081i
$56$	−1.32047	+	2.28711i	−0.176455	+	0.305628i
$57$	3.94578	+	6.33016i	0.522632	+	0.838450i
$58$	0.136155	−	0.0364827i	0.0178780	−	0.00479041i
$59$	−7.75661	+	2.07838i	−1.00982	+	0.270582i	−0.725556	−	0.688163i	$-0.758417\pi$
$59$	−7.75661	+	2.07838i	−1.00982	+	0.270582i	−0.284269	+	0.958745i	$0.591751\pi$
$60$	−4.48380	−	7.19330i	−0.578857	−	0.928650i
$61$	1.75531	−	3.04029i	0.224744	−	0.389269i	−0.731498	−	0.681843i	$-0.761179\pi$
$61$	1.75531	−	3.04029i	0.224744	−	0.389269i	0.956243	+	0.292574i	$0.0945119\pi$
$62$	−3.68046	−	6.37475i	−0.467419	−	0.809594i
$63$	2.25976	+	1.97319i	0.284704	+	0.248598i
$64$			3.08342i			0.385428i
$65$	12.6482	−	0.225122i	1.56882	−	0.0279229i
$66$	5.89720	+	1.36835i	0.725895	+	0.168433i
$67$	−0.450145	+	1.67996i	−0.0549939	+	0.205240i	−0.987956	−	0.154734i	$-0.950548\pi$
$67$	−0.450145	+	1.67996i	−0.0549939	+	0.205240i	0.932962	+	0.359974i	$0.117215\pi$
$68$	−6.11242	+	3.52901i	−0.741240	+	0.427955i
$69$	−3.29132	+	3.52168i	−0.396229	+	0.423961i
$70$	1.92997	+	1.92997i	0.230675	+	0.230675i
$71$	3.53048	+	13.1759i	0.418991	+	1.56370i	0.776705	+	0.629864i	$0.216889\pi$
$71$	3.53048	+	13.1759i	0.418991	+	1.56370i	−0.357714	+	0.933831i	$0.616444\pi$
$72$	7.77386	+	1.52896i	0.916158	+	0.180189i
$73$	0.693304	−	0.693304i	0.0811451	−	0.0811451i	−0.665369	−	0.746514i	$-0.731726\pi$
$73$	0.693304	−	0.693304i	0.0811451	−	0.0811451i	0.746514	+	0.665369i	$0.231726\pi$
$74$	5.50742	+	3.17971i	0.640225	+	0.369634i
$75$	−12.1118	+	3.68830i	−1.39856	+	0.425889i
$76$	5.80227	+	1.55471i	0.665566	+	0.178338i
$77$	4.49297			0.512021
$78$	−3.25350	+	3.60783i	−0.368386	+	0.408506i
$79$	0.480977			0.0541142			0.0270571	−	0.999634i	$-0.491386\pi$
$79$	0.480977			0.0541142			0.0270571	+	0.999634i	$0.491386\pi$
$80$	−2.49160	−	0.667621i	−0.278569	−	0.0746423i
$81$	3.40838	−	8.32964i	0.378709	−	0.925516i
$82$	−3.91434	−	2.25995i	−0.432267	−	0.249569i
$83$	−8.15333	+	8.15333i	−0.894944	+	0.894944i	−0.994984	−	0.100039i	$-0.968103\pi$
$83$	−8.15333	+	8.15333i	−0.894944	+	0.894944i	0.100039	+	0.994984i	$0.468103\pi$
$84$	2.41453	−	0.0816409i	0.263447	−	0.00890775i
$85$	4.59498	+	17.1487i	0.498396	+	1.86004i
$86$	0.327429	+	0.327429i	0.0353076	+	0.0353076i
$87$	−0.229293	−	0.214294i	−0.0245828	−	0.0229747i
$88$	10.2759	−	5.93281i	1.09542	−	0.632439i
$89$	−0.837175	+	3.12438i	−0.0887403	+	0.331183i	−0.995996	−	0.0893957i	$-0.971506\pi$
$89$	−0.837175	+	3.12438i	−0.0887403	+	0.331183i	0.907256	+	0.420579i	$0.138173\pi$
$90$	3.60574	−	7.35150i	0.380078	−	0.774916i
$91$	−1.74692	+	3.15409i	−0.183127	+	0.330638i
$92$			3.88179i			0.404705i
$93$	−7.71021	+	14.4621i	−0.799512	+	1.49965i
$94$	0.329508	+	0.570724i	0.0339861	+	0.0588657i
$95$	7.55491	−	13.0855i	0.775118	−	1.34254i
$96$	8.60437	−	5.36337i	0.878179	−	0.547396i
$97$	−2.19811	+	0.588981i	−0.223184	+	0.0598020i	−0.368678	−	0.929557i	$-0.620190\pi$
$97$	−2.19811	+	0.588981i	−0.223184	+	0.0598020i	0.145494	+	0.989359i	$0.453523\pi$
$98$	−0.751420	+	0.201342i	−0.0759049	+	0.0203387i
$99$	−4.36007	−	12.7542i	−0.438203	−	1.28185i
$100$	−5.09797	+	8.82995i	−0.509797	+	0.882995i
$101$	8.31306	+	14.3986i	0.827181	+	1.43272i	0.900241	+	0.435391i	$0.143390\pi$
$101$	8.31306	+	14.3986i	0.827181	+	1.43272i	−0.0730608	+	0.997327i	$0.523277\pi$
$102$	−6.01645	−	3.20755i	−0.595717	−	0.317595i
$103$		−	11.7781i		−	1.16053i	−0.814427	−	0.580266i	$-0.802949\pi$
$103$		−	11.7781i		−	1.16053i	0.814427	−	0.580266i	$-0.197051\pi$
$104$	0.169453	+	9.52050i	0.0166162	+	0.933562i
$105$	1.37357	−	5.91969i	0.134047	−	0.577703i
$106$	1.09333	−	4.08035i	0.106193	−	0.396319i
$107$	−6.54031	+	3.77605i	−0.632275	+	0.365044i	−0.781633	−	0.623739i	$-0.785613\pi$
$107$	−6.54031	+	3.77605i	−0.632275	+	0.365044i	0.149357	+	0.988783i	$0.452279\pi$
$108$	−2.57487	−	6.77494i	−0.247767	−	0.651919i
$109$	−3.51815	−	3.51815i	−0.336978	−	0.336978i	0.518251	−	0.855229i	$-0.326583\pi$
$109$	−3.51815	−	3.51815i	−0.336978	−	0.336978i	−0.855229	+	0.518251i	$0.826583\pi$
$110$	−3.17391	−	11.8452i	−0.302620	−	1.12939i
$111$	−0.478482	−	14.1511i	−0.0454155	−	1.34317i
$112$	0.519868	−	0.519868i	0.0491229	−	0.0491229i
$113$	−13.6298	−	7.86916i	−1.28218	−	0.740268i	−0.304935	−	0.952373i	$-0.598635\pi$
$113$	−13.6298	−	7.86916i	−1.28218	−	0.740268i	−0.977247	+	0.212105i	$0.931968\pi$
$114$	1.69041	+	5.55107i	0.158322	+	0.519905i
$115$	9.43150	+	2.52716i	0.879492	+	0.235659i
$116$	−0.252739			−0.0234662
$117$	10.6488	+	1.89822i	0.984481	+	0.175490i
$118$	−6.24694			−0.575078
$119$	−4.88771	−	1.30966i	−0.448056	−	0.120056i
$120$	−4.67523	−	15.3528i	−0.426788	−	1.40151i
$121$	−7.95596	−	4.59337i	−0.723269	−	0.417579i
$122$	1.93111	−	1.93111i	0.174835	−	0.174835i
$123$	0.340076	+	10.0578i	0.0306636	+	0.906878i
$124$	3.41594	+	12.7485i	0.306760	+	1.14485i
$125$	5.73045	+	5.73045i	0.512547	+	0.512547i
$126$	1.30075	+	1.93768i	0.115880	+	0.172622i
$127$	−18.0100	+	10.3981i	−1.59813	+	0.922681i	−0.606282	+	0.795250i	$0.707340\pi$
$127$	−18.0100	+	10.3981i	−1.59813	+	0.922681i	−0.991847	+	0.127431i	$0.959327\pi$
$128$	2.40932	−	8.99172i	0.212956	−	0.794763i
$129$	0.233034	−	1.00431i	0.0205175	−	0.0884243i
$130$	9.54944	+	2.37746i	0.837541	+	0.208517i
$131$		−	2.32681i		−	0.203294i	−0.994821	−	0.101647i	$-0.967589\pi$
$131$		−	2.32681i		−	0.203294i	0.994821	−	0.101647i	$-0.0324112\pi$
$132$	−9.57841	−	5.10654i	−0.833694	−	0.444468i
$133$	2.15330	+	3.72962i	0.186714	+	0.323399i
$134$	−0.676496	+	1.17172i	−0.0584403	+	0.101222i
$135$	−18.1372	+	1.84541i	−1.56101	+	0.158828i
$136$	−12.9081	+	3.45872i	−1.10686	+	0.296582i
$137$	−11.0253	+	2.95421i	−0.941951	+	0.252395i	−0.696943	−	0.717126i	$-0.745457\pi$
$137$	−11.0253	+	2.95421i	−0.941951	+	0.252395i	−0.245008	+	0.969521i	$0.578790\pi$
$138$	−3.18223	+	1.98358i	−0.270889	+	0.168854i
$139$	2.62925	−	4.55400i	0.223010	−	0.386265i	−0.732710	−	0.680540i	$-0.761745\pi$
$139$	2.62925	−	4.55400i	0.223010	−	0.386265i	0.955721	+	0.294276i	$0.0950784\pi$
$140$	−2.44690	−	4.23816i	−0.206801	−	0.358190i
$141$	0.690286	−	1.29478i	0.0581326	−	0.109040i
$142$			10.6115i			0.890497i
$143$	13.8829	−	8.34819i	1.16095	−	0.698111i
$144$	−1.98025	−	0.971264i	−0.165020	−	0.0809387i
$145$	−0.164541	+	0.614074i	−0.0136644	+	0.0509961i
$146$	0.660555	−	0.381371i	0.0546679	−	0.0315625i
$147$	1.26543	+	1.18266i	0.104371	+	0.0975440i
$148$	−8.06277	−	8.06277i	−0.662756	−	0.662756i
$149$	−1.83391	−	6.84424i	−0.150240	−	0.560702i	−0.999466	−	0.0326734i	$-0.989598\pi$
$149$	−1.83391	−	6.84424i	−0.150240	−	0.560702i	0.849226	−	0.528029i	$-0.177069\pi$
$150$	−9.84370	+	0.332838i	−0.803735	+	0.0271761i
$151$	12.7297	−	12.7297i	1.03593	−	1.03593i	0.0365972	−	0.999330i	$-0.488348\pi$
$151$	12.7297	−	12.7297i	1.03593	−	1.03593i	0.999330	−	0.0365972i	$-0.0116518\pi$
$152$	9.84966	+	5.68670i	0.798913	+	0.461253i
$153$	1.02539	+	15.1457i	0.0828983	+	1.22446i
$154$	3.37611	+	0.904625i	0.272054	+	0.0728968i
$155$	33.1985			2.66657
$156$	7.30903	−	4.73861i	0.585191	−	0.379392i
$157$	7.20282			0.574848			0.287424	−	0.957803i	$-0.407201\pi$
$157$	7.20282			0.574848			0.287424	+	0.957803i	$0.407201\pi$
$158$	0.361416	+	0.0968412i	0.0287527	+	0.00770427i
$159$	−8.99743	+	2.73990i	−0.713542	+	0.217288i
$160$	−17.7866	−	10.2691i	−1.40616	−	0.811846i
$161$	−1.96787	+	1.96787i	−0.155090	+	0.155090i
$162$	4.23824	−	5.57281i	0.332987	−	0.437841i
$163$	−1.93783	−	7.23206i	−0.151782	−	0.566459i	−0.999359	−	0.0357869i	$-0.988606\pi$
$163$	−1.93783	−	7.23206i	−0.151782	−	0.566459i	0.847577	−	0.530672i	$-0.178060\pi$
$164$	5.73053	+	5.73053i	0.447479	+	0.447479i
$165$	−18.6431	+	19.9479i	−1.45136	+	1.55295i
$166$	−7.76819	+	4.48497i	−0.602929	+	0.348101i
$167$	4.84548	−	18.0836i	0.374955	−	1.39935i	−0.478456	−	0.878112i	$-0.658803\pi$
$167$	4.84548	−	18.0836i	0.374955	−	1.39935i	0.853411	−	0.521239i	$-0.174530\pi$
$168$	4.45585	+	1.03391i	0.343776	+	0.0797680i
$169$	0.462621	+	12.9918i	0.0355862	+	0.999367i
$170$			13.8110i			1.05926i
$171$	8.49770	−	9.73188i	0.649836	−	0.744216i
$172$	−0.415130	−	0.719026i	−0.0316534	−	0.0548252i
$173$	0.999000	−	1.73032i	0.0759526	−	0.131554i	−0.825548	−	0.564333i	$-0.809134\pi$
$173$	0.999000	−	1.73032i	0.0759526	−	0.131554i	0.901500	+	0.432779i	$0.142467\pi$
$174$	−0.129149	−	0.207191i	−0.00979074	−	0.0157071i
$175$	−7.06074	+	1.89192i	−0.533742	+	0.143016i
$176$	−3.19069	+	0.854943i	−0.240507	+	0.0644438i
$177$	7.35747	+	11.8035i	0.553021	+	0.887203i
$178$	−1.25814	+	2.17916i	−0.0943016	+	0.163335i
$179$	−1.95622	−	3.38828i	−0.146215	−	0.253252i	0.783611	−	0.621252i	$-0.213376\pi$
$179$	−1.95622	−	3.38828i	−0.146215	−	0.253252i	−0.929826	+	0.368001i	$0.880042\pi$
$180$	−9.65639	+	11.0588i	−0.719745	+	0.824278i
$181$			0.828935i			0.0616142i	0.999525	+	0.0308071i	$0.00980776\pi$
$181$			0.828935i			0.0616142i	−0.999525	+	0.0308071i	$0.990192\pi$
$182$	−1.94772	+	2.01832i	−0.144375	+	0.149607i
$183$	−5.92321	−	1.37439i	−0.437856	−	0.101598i
$184$	−1.90224	+	7.09924i	−0.140235	+	0.523363i
$185$	−24.8391	+	14.3408i	−1.82620	+	1.05436i
$186$	−8.70545	+	9.31476i	−0.638315	+	0.682991i
$187$	16.0761	+	16.0761i	1.17560	+	1.17560i
$188$	−0.305825	−	1.14136i	−0.0223046	−	0.0832419i
$189$	2.12922	−	4.73988i	0.154878	−	0.344775i
$190$	8.31158	−	8.31158i	0.602985	−	0.602985i
$191$	−8.02535	−	4.63344i	−0.580694	−	0.335264i	0.180715	−	0.983535i	$-0.442159\pi$
$191$	−8.02535	−	4.63344i	−0.580694	−	0.335264i	−0.761409	+	0.648272i	$0.775492\pi$
$192$	5.10901	−	1.55580i	0.368711	−	0.112280i
$193$	7.97663	+	2.13733i	0.574170	+	0.153848i	0.534209	−	0.845353i	$-0.320610\pi$
$193$	7.97663	+	2.13733i	0.574170	+	0.153848i	0.0399618	+	0.999201i	$0.487276\pi$
$194$	−1.77029			−0.127099
$195$	−6.75489	−	20.8436i	−0.483728	−	1.49264i
$196$	1.39483			0.0996306
$197$	−9.34250	−	2.50331i	−0.665625	−	0.178354i	−0.0898420	−	0.995956i	$-0.528636\pi$
$197$	−9.34250	−	2.50331i	−0.665625	−	0.178354i	−0.575783	+	0.817602i	$0.695303\pi$
$198$	−0.708275	−	10.4617i	−0.0503349	−	0.743478i
$199$	−2.08418	−	1.20330i	−0.147744	−	0.0852998i	0.424306	−	0.905519i	$-0.360518\pi$
$199$	−2.08418	−	1.20330i	−0.147744	−	0.0852998i	−0.572049	+	0.820219i	$0.693851\pi$
$200$	−13.6505	+	13.6505i	−0.965236	+	0.965236i
$201$	3.01071	−	0.101799i	0.212359	−	0.00718034i
$202$	3.34754	+	12.4932i	0.235532	+	0.879019i
$203$	−0.128126	−	0.128126i	−0.00899266	−	0.00899266i
$204$	8.93144	+	8.34721i	0.625326	+	0.584422i
$205$	17.6541	−	10.1926i	1.23301	−	0.711882i
$206$	2.37144	−	8.85032i	0.165226	−	0.616631i
$207$	7.49587	+	3.67655i	0.520999	+	0.255538i
$208$	0.640407	−	2.57230i	0.0444042	−	0.178357i
$209$		−	19.3494i		−	1.33842i
$210$	2.22402	−	4.17162i	0.153472	−	0.287869i
$211$	−0.518546	−	0.898148i	−0.0356982	−	0.0618311i	0.847624	−	0.530597i	$-0.178032\pi$
$211$	−0.518546	−	0.898148i	−0.0356982	−	0.0618311i	−0.883323	+	0.468766i	$0.844699\pi$
$212$	−3.78709	+	6.55943i	−0.260098	+	0.450503i
$213$	20.0502	−	12.4979i	1.37382	−	0.856343i
$214$	−5.67480	+	1.52056i	−0.387921	+	0.103943i
$215$	−2.01726	+	0.540524i	−0.137576	+	0.0368635i
$216$	−1.38907	−	13.6522i	−0.0945144	−	0.928914i
$217$	−4.73111	+	8.19453i	−0.321169	+	0.556281i
$218$	−1.93526	−	3.35196i	−0.131072	−	0.227023i
$219$	−1.49857	−	0.798936i	−0.101264	−	0.0539871i
$220$			21.9877i			1.48241i
$221$	−17.5361	+	5.03491i	−1.17960	+	0.338684i
$222$	2.48968	−	10.7298i	0.167097	−	0.720136i
$223$	−6.10194	+	22.7727i	−0.408616	+	1.52498i	0.388672	+	0.921376i	$0.372934\pi$
$223$	−6.10194	+	22.7727i	−0.408616	+	1.52498i	−0.797288	+	0.603599i	$0.793733\pi$
$224$	5.06954	−	2.92690i	0.338723	−	0.195562i
$225$	12.2225	+	18.2075i	0.814834	+	1.21383i
$226$	−8.65730	−	8.65730i	−0.575875	−	0.575875i
$227$	−6.46981	−	24.1457i	−0.429416	−	1.60260i	−0.754086	−	0.656776i	$-0.771920\pi$
$227$	−6.46981	−	24.1457i	−0.429416	−	1.60260i	0.324670	−	0.945828i	$-0.394747\pi$
$228$	−0.351594	−	10.3984i	−0.0232849	−	0.688651i
$229$	16.6026	−	16.6026i	1.09713	−	1.09713i	0.102384	−	0.994745i	$-0.467353\pi$
$229$	16.6026	−	16.6026i	1.09713	−	1.09713i	0.994745	−	0.102384i	$-0.0326471\pi$
$230$	6.57820	+	3.79792i	0.433753	+	0.250428i
$231$	−2.26701	−	7.44452i	−0.149158	−	0.489814i
$232$	−0.462223	−	0.123852i	−0.0303465	−	0.00813131i
$233$	−2.65471			−0.173916			−0.0869579	−	0.996212i	$-0.527715\pi$
$233$	−2.65471			−0.173916			−0.0869579	+	0.996212i	$0.527715\pi$
$234$	7.61953	+	3.57041i	0.498104	+	0.233405i
$235$	−2.97223			−0.193887
$236$	10.8191	+	2.89898i	0.704266	+	0.188708i
$237$	−0.242686	−	0.796945i	−0.0157642	−	0.0517671i
$238$	−3.40904	−	1.96821i	−0.220975	−	0.127580i
$239$	9.53436	−	9.53436i	0.616726	−	0.616726i	−0.327964	−	0.944690i	$-0.606362\pi$
$239$	9.53436	−	9.53436i	0.616726	−	0.616726i	0.944690	+	0.327964i	$0.106362\pi$
$240$	0.150980	+	4.46525i	0.00974575	+	0.288231i
$241$	−3.48866	−	13.0198i	−0.224724	−	0.838682i	−0.982515	−	0.186184i	$-0.940388\pi$
$241$	−3.48866	−	13.0198i	−0.224724	−	0.838682i	0.757791	−	0.652498i	$-0.226279\pi$
$242$	−5.05343	−	5.05343i	−0.324847	−	0.324847i
$243$	−15.5214	−	1.44457i	−0.995697	−	0.0926692i
$244$	−4.24068	+	2.44836i	−0.271482	+	0.156740i
$245$	0.908076	−	3.38898i	0.0580148	−	0.216514i
$246$	−1.76951	+	7.62608i	−0.112820	+	0.486221i
$247$	13.5834	+	7.52328i	0.864288	+	0.478695i
$248$			24.9891i			1.58681i
$249$	17.6234	+	9.39557i	1.11684	+	0.595420i
$250$	3.15219	+	5.45976i	0.199362	+	0.345306i
$251$	−10.2809	+	17.8070i	−0.648922	+	1.12397i	0.334459	+	0.942410i	$0.391447\pi$
$251$	−10.2809	+	17.8070i	−0.648922	+	1.12397i	−0.983381	+	0.181555i	$0.941887\pi$
$252$	−1.35357	−	3.95952i	−0.0852669	−	0.249426i
$253$	12.0778	−	3.23624i	0.759325	−	0.203461i
$254$	−15.6267	+	4.18715i	−0.980504	+	0.262725i
$255$	26.0957	−	16.2662i	1.63418	−	1.01863i
$256$	6.70425	−	11.6121i	0.419016	−	0.725757i
$257$	14.3294	+	24.8193i	0.893844	+	1.54818i	0.835229	+	0.549902i	$0.185335\pi$
$257$	14.3294	+	24.8193i	0.893844	+	1.54818i	0.0586143	+	0.998281i	$0.481332\pi$
$258$	0.377316	−	0.707737i	0.0234907	−	0.0440618i
$259$		−	8.17483i		−	0.507959i
$260$	−15.4355	−	8.54910i	−0.957268	−	0.530193i
$261$	−0.239376	+	0.488048i	−0.0148170	+	0.0302094i
$262$	0.468485	−	1.74841i	0.0289431	−	0.108017i
$263$	7.02527	−	4.05604i	0.433197	−	0.250106i	−0.267511	−	0.963555i	$-0.586201\pi$
$263$	7.02527	−	4.05604i	0.433197	−	0.250106i	0.700708	+	0.713448i	$0.252868\pi$
$264$	−15.0151	−	14.0330i	−0.924118	−	0.863669i
$265$	13.4718	+	13.4718i	0.827566	+	0.827566i
$266$	0.867100	+	3.23606i	0.0531653	+	0.198416i
$267$	5.59928	−	0.189325i	0.342671	−	0.0115865i
$268$	1.71539	−	1.71539i	0.104784	−	0.104784i
$269$	11.7464	+	6.78177i	0.716189	+	0.413492i	0.813348	−	0.581777i	$-0.197642\pi$
$269$	11.7464	+	6.78177i	0.716189	+	0.413492i	−0.0971595	+	0.995269i	$0.530976\pi$
$270$	−14.0003	−	2.26512i	−0.852028	−	0.137851i
$271$	7.09262	+	1.90046i	0.430846	+	0.115445i	0.467723	−	0.883875i	$-0.345074\pi$
$271$	7.09262	+	1.90046i	0.430846	+	0.115445i	−0.0368772	+	0.999320i	$0.511741\pi$
$272$	3.72023			0.225572
$273$	6.10754	+	1.30307i	0.369645	+	0.0788655i
$274$	−8.87941			−0.536425
$275$	31.7237	+	8.50033i	1.91301	+	0.512589i
$276$	6.43185	−	1.95863i	0.387152	−	0.117896i
$277$	9.42219	+	5.43990i	0.566124	+	0.326852i	0.755600	−	0.655033i	$-0.227345\pi$
$277$	9.42219	+	5.43990i	0.566124	+	0.326852i	−0.189475	+	0.981885i	$0.560679\pi$
$278$	2.89259	−	2.89259i	0.173486	−	0.173486i
$279$	27.8531	+	5.47812i	1.66752	+	0.327967i
$280$	−2.39817	−	8.95007i	−0.143318	−	0.534869i
$281$	−10.2652	−	10.2652i	−0.612373	−	0.612373i	0.331191	−	0.943564i	$-0.392550\pi$
$281$	−10.2652	−	10.2652i	−0.612373	−	0.612373i	−0.943564	+	0.331191i	$0.892550\pi$
$282$	0.779389	−	0.833940i	0.0464120	−	0.0496604i
$283$	−3.03747	+	1.75369i	−0.180559	+	0.104246i	−0.587555	−	0.809184i	$-0.699910\pi$
$283$	−3.03747	+	1.75369i	−0.180559	+	0.104246i	0.406996	+	0.913430i	$0.366576\pi$
$284$	4.92441	−	18.3782i	0.292210	−	1.09054i
$285$	−25.4937	−	5.91542i	−1.51012	−	0.350399i
$286$	12.1128	−	3.47778i	0.716242	−	0.205645i
$287$			5.81017i			0.342963i
$288$	−13.2282	−	11.5506i	−0.779480	−	0.680627i
$289$	−4.30246	−	7.45207i	−0.253086	−	0.438357i
$290$	−0.247278	+	0.428299i	−0.0145207	+	0.0251506i
$291$	2.08499	+	3.34492i	0.122225	+	0.196083i
$292$	−1.32100	+	0.353961i	−0.0773058	+	0.0207140i
$293$	16.8739	−	4.52134i	0.985782	−	0.264139i	0.270304	−	0.962775i	$-0.412876\pi$
$293$	16.8739	−	4.52134i	0.985782	−	0.264139i	0.715478	+	0.698635i	$0.246209\pi$
$294$	0.712753	+	1.14346i	0.0415686	+	0.0666879i
$295$	14.0872	−	24.3997i	0.820188	−	1.42061i
$296$	−10.7946	−	18.6968i	−0.627422	−	1.08673i
$297$	−18.9329	+	13.6597i	−1.09860	+	0.792616i
$298$		−	5.51215i		−	0.319310i
$299$	−2.42415	+	9.73698i	−0.140192	+	0.563104i
$300$	17.2029	+	3.99166i	0.993208	+	0.230459i
$301$	0.154060	−	0.574959i	0.00887986	−	0.0331401i
$302$	12.1284	−	7.00232i	0.697909	−	0.402938i
$303$	19.6630	−	21.0392i	1.12961	−	1.20867i
$304$	−2.23886	−	2.23886i	−0.128407	−	0.128407i
$305$	3.18791	+	11.8974i	0.182539	+	0.681245i
$306$	−2.27897	+	11.5873i	−0.130280	+	0.662399i
$307$	−21.2970	+	21.2970i	−1.21548	+	1.21548i	−0.246283	+	0.969198i	$0.579209\pi$
$307$	−21.2970	+	21.2970i	−1.21548	+	1.21548i	−0.969198	+	0.246283i	$0.920791\pi$
$308$	−5.42731	−	3.13346i	−0.309250	−	0.178545i
$309$	−19.5155	+	5.94287i	−1.11020	+	0.338078i
$310$	24.9461	+	6.68428i	1.41684	+	0.379641i
$311$	−31.6210			−1.79306			−0.896532	−	0.442978i	$-0.853922\pi$
$311$	−31.6210			−1.79306			−0.896532	+	0.442978i	$0.853922\pi$
$312$	15.6893	−	5.08452i	0.888231	−	0.287854i
$313$	−0.406180			−0.0229586			−0.0114793	−	0.999934i	$-0.503654\pi$
$313$	−0.406180			−0.0229586			−0.0114793	+	0.999934i	$0.503654\pi$
$314$	5.41235	+	1.45023i	0.305436	+	0.0818414i
$315$	−10.5016	+	0.710977i	−0.591696	+	0.0400590i
$316$	−0.581000	−	0.335441i	−0.0326838	−	0.0188700i
$317$	19.4304	−	19.4304i	1.09132	−	1.09132i	0.0959323	−	0.995388i	$-0.469417\pi$
$317$	19.4304	−	19.4304i	1.09132	−	1.09132i	0.995388	−	0.0959323i	$-0.0305832\pi$
$318$	−7.31251	+	0.247253i	−0.410065	+	0.0138652i
$319$	0.210708	+	0.786372i	0.0117974	+	0.0440284i
$320$	−7.64969	−	7.64969i	−0.427631	−	0.427631i
$321$	9.55667	+	8.93154i	0.533401	+	0.498510i
$322$	−1.87491	+	1.08248i	−0.104485	+	0.0603243i
$323$	−5.64016	+	21.0494i	−0.313827	+	1.17122i
$324$	−9.92639	+	7.68479i	−0.551466	+	0.426933i
$325$	−18.3019	+	18.9652i	−1.01520	+	1.05200i
$326$		−	5.82449i		−	0.322588i
$327$	−4.05417	+	7.60447i	−0.224196	+	0.420528i
$328$	7.67213	+	13.2885i	0.423622	+	0.733736i
$329$	0.423571	−	0.733647i	0.0233522	−	0.0404472i
$330$	−18.0252	+	11.2356i	−0.992253	+	0.618502i
$331$	5.34167	−	1.43130i	0.293605	−	0.0786712i	−0.109010	−	0.994041i	$-0.534768\pi$
$331$	5.34167	−	1.43130i	0.293605	−	0.0786712i	0.402615	+	0.915369i	$0.368101\pi$
$332$	15.5351	−	4.16262i	0.852601	−	0.228454i
$333$	−23.2060	+	7.93302i	−1.27168	+	0.434727i
$334$	7.28199	−	12.6128i	0.398453	−	0.690141i
$335$	−3.05107	−	5.28460i	−0.166698	−	0.288729i
$336$	−1.12369	−	0.599075i	−0.0613024	−	0.0326822i
$337$			1.45460i			0.0792370i	0.999215	+	0.0396185i	$0.0126143\pi$
$337$			1.45460i			0.0792370i	−0.999215	+	0.0396185i	$0.987386\pi$
$338$	−2.26817	+	9.85542i	−0.123372	+	0.536064i
$339$	−6.16147	+	26.5541i	−0.334645	+	1.44222i
$340$	6.40921	−	23.9195i	0.347588	−	1.29722i
$341$	36.8177	−	21.2567i	1.99379	−	1.15112i
$342$	8.34479	−	5.60179i	0.451234	−	0.302910i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−0.406861	−	1.51843i	−0.0219365	−	0.0818681i
$345$	−0.571510	−	16.9024i	−0.0307691	−	0.909997i
$346$	1.09906	−	1.09906i	0.0590856	−	0.0590856i
$347$	3.72070	+	2.14814i	0.199737	+	0.115318i	0.596533	−	0.802589i	$-0.296544\pi$
$347$	3.72070	+	2.14814i	0.199737	+	0.115318i	−0.396796	+	0.917907i	$0.629878\pi$
$348$	0.127524	+	0.418770i	0.00683601	+	0.0224484i
$349$	16.3054	+	4.36902i	0.872809	+	0.233868i	0.667302	−	0.744787i	$-0.267449\pi$
$349$	16.3054	+	4.36902i	0.872809	+	0.233868i	0.205507	+	0.978656i	$0.434116\pi$
$350$	−5.68651			−0.303957
$351$	−2.22783	−	18.6021i	−0.118913	−	0.992905i
$352$	−26.3009			−1.40184
$353$	−19.3490	−	5.18454i	−1.02984	−	0.275945i	−0.295945	−	0.955205i	$-0.595634\pi$
$353$	−19.3490	−	5.18454i	−1.02984	−	0.275945i	−0.733898	+	0.679260i	$0.762301\pi$
$354$	3.15201	+	10.3507i	0.167527	+	0.550135i
$355$	−41.4471	−	23.9295i	−2.19978	−	1.27005i
$356$	3.19026	−	3.19026i	0.169083	−	0.169083i
$357$	0.296175	+	8.75940i	0.0156753	+	0.463596i
$358$	−0.787741	−	2.93989i	−0.0416334	−	0.155378i
$359$	−7.53985	−	7.53985i	−0.397938	−	0.397938i	0.479567	−	0.877505i	$-0.340794\pi$
$359$	−7.53985	−	7.53985i	−0.397938	−	0.397938i	−0.877505	+	0.479567i	$0.840794\pi$
$360$	−23.0795	+	15.4930i	−1.21639	+	0.816555i
$361$	−0.392554	+	0.226641i	−0.0206607	+	0.0119285i
$362$	−0.166900	+	0.622878i	−0.00877206	+	0.0327378i
$363$	−3.59656	+	15.5001i	−0.188771	+	0.813545i
$364$	4.30991	−	2.59167i	0.225901	−	0.135841i
$365$			3.44005i			0.180060i
$366$	−4.17410	−	2.22534i	−0.218184	−	0.116320i
$367$	−7.46522	−	12.9301i	−0.389681	−	0.674948i	0.602725	−	0.797949i	$-0.294082\pi$
$367$	−7.46522	−	12.9301i	−0.389681	−	0.674948i	−0.992407	+	0.123001i	$0.960748\pi$
$368$	1.02303	−	1.77194i	0.0533292	−	0.0923689i
$369$	16.4934	−	5.63831i	0.858612	−	0.293519i
$370$	−21.5520	+	5.77484i	−1.12043	+	0.300220i
$371$	−5.24516	+	1.40544i	−0.272315	+	0.0729666i
$372$	19.3997	−	12.0924i	1.00583	−	0.626964i
$373$	5.21339	−	9.02985i	0.269939	−	0.467548i	−0.698907	−	0.715213i	$-0.746330\pi$
$373$	5.21339	−	9.02985i	0.269939	−	0.467548i	0.968846	+	0.247665i	$0.0796631\pi$
$374$	8.84309	+	15.3167i	0.457265	+	0.792007i
$375$	6.60354	−	12.3863i	0.341005	−	0.639628i
$376$		−	2.23724i		−	0.115377i
$377$	−0.633963	−	0.157833i	−0.0326508	−	0.00812884i
$378$	2.55428	−	3.13294i	0.131378	−	0.161141i
$379$	−4.53057	+	16.9083i	−0.232720	+	0.868522i	0.746444	+	0.665448i	$0.231760\pi$
$379$	−4.53057	+	16.9083i	−0.232720	+	0.868522i	−0.979164	+	0.203073i	$0.934907\pi$
$380$	−18.2520	+	10.5378i	−0.936309	+	0.540578i
$381$	26.3162	+	24.5947i	1.34822	+	1.26003i
$382$	−5.09750	−	5.09750i	−0.260811	−	0.260811i
$383$	5.82855	+	21.7524i	0.297825	+	1.11150i	0.938948	+	0.344059i	$0.111802\pi$
$383$	5.82855	+	21.7524i	0.297825	+	1.11150i	−0.641123	+	0.767438i	$0.721531\pi$
$384$	−16.1143	+	0.544861i	−0.822330	+	0.0278048i
$385$	−11.1466	+	11.1466i	−0.568085	+	0.568085i
$386$	5.56347	+	3.21207i	0.283173	+	0.163490i
$387$	−1.78165	+	0.120621i	−0.0905662	+	0.00613151i
$388$	3.06598	+	0.821528i	0.155652	+	0.0417067i
$389$	−3.03623			−0.153943			−0.0769716	−	0.997033i	$-0.524525\pi$
$389$	−3.03623			−0.153943			−0.0769716	+	0.997033i	$0.524525\pi$
$390$	−0.879069	−	17.0223i	−0.0445134	−	0.861959i
$391$	−14.0823			−0.712171
$392$	2.55094	+	0.683523i	0.128842	+	0.0345231i
$393$	−3.85535	+	1.17403i	−0.194477	+	0.0592222i
$394$	−6.51612	−	3.76208i	−0.328277	−	0.189531i
$395$	−1.19326	+	1.19326i	−0.0600395	+	0.0600395i
$396$	−3.62821	+	18.4473i	−0.182324	+	0.927014i
$397$	−2.69287	−	10.0499i	−0.135151	−	0.504392i	−0.999997	−	0.00235427i	$-0.999251\pi$
$397$	−2.69287	−	10.0499i	−0.135151	−	0.504392i	0.864846	−	0.502037i	$-0.167416\pi$
$398$	−1.32382	−	1.32382i	−0.0663571	−	0.0663571i
$399$	5.09322	−	5.44970i	0.254980	−	0.272826i
$400$	4.65420	−	2.68710i	0.232710	−	0.134355i
$401$	−6.76497	+	25.2472i	−0.337827	+	1.26079i	0.562946	+	0.826494i	$0.309668\pi$
$401$	−6.76497	+	25.2472i	−0.337827	+	1.26079i	−0.900772	+	0.434292i	$0.856999\pi$
$402$	2.28280	+	0.529689i	0.113856	+	0.0264185i
$403$	0.607135	+	34.1111i	0.0302436	+	1.69920i
$404$		−	23.1906i		−	1.15378i
$405$	12.2092	+	29.1210i	0.606680	+	1.44703i
$406$	−0.0704791	−	0.122073i	−0.00349782	−	0.00605840i
$407$	−18.3646	+	31.8084i	−0.910300	+	1.57669i
$408$	12.2439	+	19.6426i	0.606162	+	0.972456i
$409$	−21.1087	+	5.65606i	−1.04376	+	0.279674i	−0.739670	−	0.672969i	$-0.765019\pi$
$409$	−21.1087	+	5.65606i	−1.04376	+	0.279674i	−0.304089	+	0.952644i	$0.598352\pi$
$410$	15.3178	−	4.10440i	0.756494	−	0.202702i
$411$	10.4579	+	16.7775i	0.515850	+	0.827571i
$412$	−8.21423	+	14.2275i	−0.404686	+	0.700937i
$413$	4.01512	+	6.95439i	0.197571	+	0.342203i
$414$	4.89231	+	4.27187i	0.240444	+	0.209951i
$415$		−	40.4553i		−	1.98587i
$416$	10.2261	−	18.4634i	0.501377	−	0.905242i
$417$	−8.87228	−	2.05868i	−0.434477	−	0.100814i
$418$	3.89585	−	14.5395i	0.190552	−	0.711151i
$419$	−3.28067	+	1.89410i	−0.160271	+	0.0925327i	−0.577990	−	0.816044i	$-0.696163\pi$
$419$	−3.28067	+	1.89410i	−0.160271	+	0.0925327i	0.417719	+	0.908576i	$0.362830\pi$
$420$	−5.78770	+	6.19278i	−0.282411	+	0.302177i
$421$	−26.6573	−	26.6573i	−1.29920	−	1.29920i	−0.928921	−	0.370278i	$-0.879262\pi$
$421$	−26.6573	−	26.6573i	−1.29920	−	1.29920i	−0.370278	−	0.928921i	$-0.620738\pi$
$422$	−0.208811	−	0.779292i	−0.0101647	−	0.0379354i
$423$	−2.49365	−	0.490450i	−0.121246	−	0.0238465i
$424$	−10.1404	+	10.1404i	−0.492463	+	0.492463i
$425$	−32.0331	−	18.4943i	−1.55383	−	0.897106i
$426$	17.5825	−	5.35423i	0.851874	−	0.259413i
$427$	−3.39100	−	0.908616i	−0.164102	−	0.0439710i
$428$	10.5339			0.509174
$429$	−20.8372	−	18.7908i	−1.00603	−	0.907227i
$430$	−1.62464			−0.0783473
$431$	−1.34467	−	0.360304i	−0.0647706	−	0.0173552i	0.226288	−	0.974060i	$-0.427341\pi$
$431$	−1.34467	−	0.360304i	−0.0647706	−	0.0173552i	−0.291059	+	0.956705i	$0.594008\pi$
$432$	−0.610146	+	3.77119i	−0.0293556	+	0.181442i
$433$	14.0773	+	8.12751i	0.676510	+	0.390583i	0.798539	−	0.601943i	$-0.205607\pi$
$433$	14.0773	+	8.12751i	0.676510	+	0.390583i	−0.122029	+	0.992527i	$0.538940\pi$
$434$	−5.20496	+	5.20496i	−0.249846	+	0.249846i
$435$	1.10050	−	0.0372104i	0.0527649	−	0.00178410i
$436$	1.79617	+	6.70338i	0.0860207	+	0.321034i
$437$	8.47481	+	8.47481i	0.405405	+	0.405405i
$438$	−0.965200	−	0.902063i	−0.0461190	−	0.0431023i
$439$	−21.0565	+	12.1570i	−1.00497	+	0.580222i	−0.909716	−	0.415231i	$-0.863701\pi$
$439$	−21.0565	+	12.1570i	−1.00497	+	0.580222i	−0.0952576	+	0.995453i	$0.530367\pi$
$440$	−10.7749	+	40.2124i	−0.513672	+	1.91705i
$441$	1.32108	−	2.69346i	0.0629086	−	0.128260i
$442$	−14.1907	+	0.252577i	−0.674983	+	0.0120138i
$443$		−	19.7974i		−	0.940603i	−0.882506	−	0.470302i	$-0.844145\pi$
$443$		−	19.7974i		−	0.940603i	0.882506	−	0.470302i	$-0.155855\pi$
$444$	−9.29122	+	17.4277i	−0.440942	+	0.827080i
$445$	−5.67434	−	9.82825i	−0.268990	−	0.465904i
$446$	−9.17024	+	15.8833i	−0.434223	+	0.752097i
$447$	−10.4151	+	6.49205i	−0.492617	+	0.307063i
$448$	2.97836	−	0.798048i	0.140714	−	0.0377042i
$449$	22.2109	−	5.95139i	1.04820	−	0.280863i	0.306690	−	0.951809i	$-0.400779\pi$
$449$	22.2109	−	5.95139i	1.04820	−	0.280863i	0.741506	+	0.670946i	$0.234112\pi$
$450$	5.51831	+	16.1424i	0.260136	+	0.760958i
$451$	13.0524	−	22.6075i	0.614616	−	1.06455i
$452$	10.9761	+	19.0112i	0.516273	+	0.894212i
$453$	−27.5152	−	14.6692i	−1.29278	−	0.689218i
$454$		−	19.4462i		−	0.912655i
$455$	−3.49105	−	12.1590i	−0.163663	−	0.570021i
$456$	4.45263	−	19.1895i	0.208514	−	0.898631i
$457$	2.81689	−	10.5128i	0.131769	−	0.491767i	−0.868222	−	0.496177i	$-0.834737\pi$
$457$	2.81689	−	10.5128i	0.131769	−	0.491767i	0.999990	+	0.00440926i	$0.00140351\pi$
$458$	15.8183	−	9.13271i	0.739141	−	0.426744i
$459$	24.5780	−	9.34106i	1.14720	−	0.436003i
$460$	−9.63037	−	9.63037i	−0.449018	−	0.449018i
$461$	−3.11425	−	11.6225i	−0.145045	−	0.541316i	−0.999753	−	0.0222070i	$-0.992931\pi$
$461$	−3.11425	−	11.6225i	−0.145045	−	0.541316i	0.854708	−	0.519109i	$-0.173736\pi$
$462$	−0.204578	−	6.05041i	−0.00951784	−	0.281491i
$463$	28.0743	−	28.0743i	1.30472	−	1.30472i	0.379551	−	0.925171i	$-0.376079\pi$
$463$	28.0743	−	28.0743i	1.30472	−	1.30472i	0.925171	−	0.379551i	$-0.123921\pi$
$464$	0.115369	+	0.0666084i	0.00535588	+	0.00309222i
$465$	−16.7509	−	55.0076i	−0.776806	−	2.55092i
$466$	−1.99480	−	0.534506i	−0.0924075	−	0.0247605i
$467$	−27.3292			−1.26464			−0.632321	−	0.774706i	$-0.717898\pi$
$467$	−27.3292			−1.26464			−0.632321	+	0.774706i	$0.717898\pi$
$468$	−11.5394	−	9.71958i	−0.533411	−	0.449288i
$469$	1.73923			0.0803100
$470$	−2.23339	−	0.598436i	−0.103019	−	0.0276038i
$471$	−3.63432	−	11.9346i	−0.167460	−	0.549915i
$472$	18.3661	+	10.6037i	0.845366	+	0.488073i
$473$	−1.89109	+	1.89109i	−0.0869523	+	0.0869523i
$474$	−0.0219003	−	0.647704i	−0.00100592	−	0.0297500i
$475$	8.14773	+	30.4077i	0.373843	+	1.39520i
$476$	4.99077	+	4.99077i	0.228752	+	0.228752i
$477$	9.07963	+	13.5256i	0.415728	+	0.619296i
$478$	9.08398	−	5.24464i	0.415492	−	0.239884i
$479$	3.92086	−	14.6328i	0.179149	−	0.668591i	−0.816659	−	0.577120i	$-0.804176\pi$
$479$	3.92086	−	14.6328i	0.179149	−	0.668591i	0.995808	−	0.0914712i	$-0.0291569\pi$
$480$	−8.04062	+	34.6527i	−0.367003	+	1.58167i
$481$	−15.1893	−	25.2596i	−0.692573	−	1.15174i
$482$		−	10.4858i		−	0.477615i
$483$	4.25354	+	2.26769i	0.193543	+	0.103184i
$484$	6.40697	+	11.0972i	0.291226	+	0.504418i
$485$	3.99210	−	6.91451i	0.181272	−	0.313972i
$486$	−11.3722	−	4.21059i	−0.515855	−	0.190996i
$487$	3.68481	−	0.987342i	0.166975	−	0.0447407i	−0.174363	−	0.984681i	$-0.555787\pi$
$487$	3.68481	−	0.987342i	0.166975	−	0.0447407i	0.341338	+	0.939941i	$0.389120\pi$
$488$	−8.95539	+	2.39959i	−0.405392	+	0.108624i
$489$	−11.0052	+	6.85991i	−0.497674	+	0.310216i
$490$	1.36469	−	2.36372i	0.0616506	−	0.106782i
$491$	−9.73797	−	16.8667i	−0.439468	−	0.761182i	0.558180	−	0.829720i	$-0.311500\pi$
$491$	−9.73797	−	16.8667i	−0.439468	−	0.761182i	−0.997648	+	0.0685383i	$0.978166\pi$
$492$	6.60363	−	12.3865i	0.297715	−	0.558427i
$493$		−	0.916881i		−	0.0412942i
$494$	8.69206	+	8.38805i	0.391074	+	0.377396i
$495$	42.4590	+	20.8252i	1.90839	+	0.936022i
$496$	1.80052	−	6.71962i	0.0808456	−	0.301720i
$497$	11.8132	−	6.82036i	0.529895	−	0.305935i
$498$	11.3509	+	10.6084i	0.508644	+	0.475372i
$499$	4.22889	+	4.22889i	0.189311	+	0.189311i	0.795398	−	0.606087i	$-0.207262\pi$
$499$	4.22889	+	4.22889i	0.189311	+	0.189311i	−0.606087	+	0.795398i	$0.707262\pi$
$500$	−2.92564	−	10.9186i	−0.130839	−	0.488296i
$501$	−32.4081	+	1.09579i	−1.44789	+	0.0489564i
$502$	−11.3105	+	11.3105i	−0.504814	+	0.504814i
$503$	2.60705	+	1.50518i	0.116243	+	0.0671128i	0.556994	−	0.830516i	$-0.311955\pi$
$503$	2.60705	+	1.50518i	0.116243	+	0.0671128i	−0.440751	+	0.897629i	$0.645288\pi$
$504$	−0.535164	−	7.90470i	−0.0238381	−	0.352103i
$505$	−56.3457	−	15.0978i	−2.50735	−	0.671842i
$506$	9.72711			0.432423
$507$	21.2930	−	7.32176i	0.945655	−	0.325171i
$508$	29.0071			1.28698
$509$	−9.82903	−	2.63368i	−0.435664	−	0.116736i	0.0343197	−	0.999411i	$-0.489074\pi$
$509$	−9.82903	−	2.63368i	−0.435664	−	0.116736i	−0.469984	+	0.882675i	$0.655740\pi$
$510$	22.8839	−	6.96862i	1.01332	−	0.308576i
$511$	−0.849121	−	0.490240i	−0.0375629	−	0.0216869i
$512$	−5.78907	+	5.78907i	−0.255843	+	0.255843i
$513$	−20.4127	−	9.16968i	−0.901243	−	0.404851i
$514$	5.77024	+	21.5348i	0.254514	+	0.949860i
$515$	29.2204	+	29.2204i	1.28761	+	1.28761i
$516$	−0.981913	+	1.05064i	−0.0432263	+	0.0462518i
$517$	−3.29625	+	1.90309i	−0.144969	+	0.0836978i
$518$	1.64594	−	6.14273i	0.0723185	−	0.269896i
$519$	−3.37108	−	0.782207i	−0.147974	−	0.0343351i
$520$	−24.0399	−	23.1991i	−1.05422	−	1.01735i
$521$		−	21.2194i		−	0.929637i	−0.885406	−	0.464818i	$-0.846120\pi$
$521$		−	21.2194i		−	0.929637i	0.885406	−	0.464818i	$-0.153880\pi$
$522$	−0.278137	+	0.318532i	−0.0121737	+	0.0139418i
$523$	15.9463	+	27.6198i	0.697283	+	1.20773i	0.969405	+	0.245466i	$0.0789411\pi$
$523$	15.9463	+	27.6198i	0.697283	+	1.20773i	−0.272122	+	0.962263i	$0.587726\pi$
$524$	−1.62275	+	2.81068i	−0.0708901	+	0.122785i
$525$	6.69740	+	10.7445i	0.292299	+	0.468930i
$526$	6.09559	−	1.63331i	0.265780	−	0.0712156i
$527$	−46.2486	+	12.3923i	−2.01462	+	0.539816i
$528$	3.02650	+	4.85537i	0.131712	+	0.211303i
$529$	7.62749	−	13.2112i	0.331630	−	0.574400i
$530$	7.41054	+	12.8354i	0.321893	+	0.557535i
$531$	15.8451	−	18.1464i	0.687621	−	0.787489i
$532$		−	6.00695i		−	0.260435i
$533$	10.7956	+	17.9530i	0.467611	+	0.777630i
$534$	4.24553	+	0.985111i	0.183722	+	0.0426299i
$535$	6.85787	−	25.5939i	0.296492	−	1.10652i
$536$	3.97781	−	2.29659i	0.171815	−	0.0991975i
$537$	−4.62708	+	4.95094i	−0.199673	+	0.213649i
$538$	7.46100	+	7.46100i	0.321667	+	0.321667i
$539$	−1.16287	−	4.33987i	−0.0500882	−	0.186932i
$540$	23.1960	+	10.4200i	0.998198	+	0.448405i
$541$	−24.9062	+	24.9062i	−1.07080	+	1.07080i	−0.0735064	+	0.997295i	$0.523419\pi$
$541$	−24.9062	+	24.9062i	−1.07080	+	1.07080i	−0.997295	+	0.0735064i	$0.976581\pi$
$542$	4.94690	+	2.85609i	0.212487	+	0.122680i
$543$	1.37349	−	0.418254i	0.0589419	−	0.0179490i
$544$	28.6117	+	7.66647i	1.22672	+	0.328697i
$545$	17.4564			0.747751
$546$	4.32696	+	2.20886i	0.185177	+	0.0945306i
$547$	−39.4776			−1.68794			−0.843970	−	0.536390i	$-0.819788\pi$
$547$	−39.4776			−1.68794			−0.843970	+	0.536390i	$0.819788\pi$
$548$	15.3783	+	4.12061i	0.656930	+	0.176024i
$549$	0.711399	+	10.5078i	0.0303618	+	0.448462i
$550$	22.1263	+	12.7746i	0.943470	+	0.544713i
$551$	−0.551785	+	0.551785i	−0.0235068	+	0.0235068i
$552$	12.7227	−	0.430185i	0.541516	−	0.0183099i
$553$	−0.124486	−	0.464588i	−0.00529369	−	0.0197563i
$554$	5.98474	+	5.98474i	0.254267	+	0.254267i
$555$	36.2947	+	33.9206i	1.54063	+	1.43985i
$556$	−6.35204	+	3.66735i	−0.269387	+	0.155530i
$557$	−2.15704	+	8.05019i	−0.0913968	+	0.341097i	−0.996449	−	0.0842040i	$-0.973165\pi$
$557$	−2.15704	+	8.05019i	−0.0913968	+	0.341097i	0.905052	+	0.425301i	$0.139832\pi$
$558$	19.8264	+	9.72438i	0.839318	+	0.411666i
$559$	−0.592275	−	2.06283i	−0.0250505	−	0.0872485i
$560$			2.57949i			0.109003i
$561$	18.5254	−	34.7484i	0.782144	−	1.46708i
$562$	−5.64668	−	9.78034i	−0.238191	−	0.412559i
$563$	4.81351	−	8.33724i	0.202865	−	0.351373i	−0.746585	−	0.665290i	$-0.768308\pi$
$563$	4.81351	−	8.33724i	0.202865	−	0.351373i	0.949450	+	0.313917i	$0.101641\pi$
$564$	−1.73683	+	1.08262i	−0.0731339	+	0.0455866i
$565$	53.3369	−	14.2916i	2.24390	−	0.601251i
$566$	−2.63551	+	0.706183i	−0.110779	+	0.0296831i
$567$	−8.92797	−	1.13637i	−0.374940	−	0.0477233i
$568$	18.0121	−	31.1979i	0.755771	−	1.30903i
$569$	15.3876	+	26.6521i	0.645081	+	1.11731i	0.984283	+	0.176599i	$0.0565097\pi$
$569$	15.3876	+	26.6521i	0.645081	+	1.11731i	−0.339202	+	0.940714i	$0.610157\pi$
$570$	−17.9654	−	9.57793i	−0.752490	−	0.401175i
$571$			19.4625i			0.814482i	0.913321	+	0.407241i	$0.133509\pi$
$571$			19.4625i			0.814482i	−0.913321	+	0.407241i	$0.866491\pi$
$572$	−22.5921	+	0.402111i	−0.944624	+	0.0168131i
$573$	−3.62794	+	15.6353i	−0.151559	+	0.653175i
$574$	−1.16983	+	4.36588i	−0.0488279	+	0.182228i
$575$	−17.6177	+	10.1716i	−0.734708	+	0.424184i
$576$	−5.15569	−	7.68025i	−0.214820	−	0.320011i
$577$	7.38296	+	7.38296i	0.307357	+	0.307357i	0.843883	−	0.536527i	$-0.180264\pi$
$577$	7.38296	+	7.38296i	0.307357	+	0.307357i	−0.536527	+	0.843883i	$0.680264\pi$
$578$	−1.73253	−	6.46591i	−0.0720640	−	0.268946i
$579$	−0.483351	−	14.2951i	−0.0200874	−	0.594085i
$580$	0.627022	−	0.627022i	0.0260357	−	0.0260357i
$581$	9.98575	+	5.76528i	0.414279	+	0.239184i
$582$	0.893232	+	2.93324i	0.0370257	+	0.121587i
$583$	23.5663	+	6.31457i	0.976017	+	0.261523i
$584$	−2.58938			−0.107149
$585$	−31.1280	+	21.7094i	−1.28698	+	0.897572i
$586$	13.5897			0.561386
$587$	−12.6654	−	3.39369i	−0.522758	−	0.140072i	−0.0122157	−	0.999925i	$-0.503888\pi$
$587$	−12.6654	−	3.39369i	−0.522758	−	0.140072i	−0.510542	+	0.859853i	$0.670555\pi$
$588$	−0.703786	−	2.31113i	−0.0290237	−	0.0953094i
$589$	35.2905	+	20.3750i	1.45412	+	0.839536i
$590$	15.4981	−	15.4981i	0.638047	−	0.638047i
$591$	0.566117	+	16.7429i	0.0232869	+	0.688713i
$592$	1.55555	+	5.80538i	0.0639325	+	0.238599i
$593$	−9.76489	−	9.76489i	−0.400996	−	0.400996i	0.477588	−	0.878584i	$-0.341511\pi$
$593$	−9.76489	−	9.76489i	−0.400996	−	0.400996i	−0.878584	+	0.477588i	$0.841511\pi$
$594$	−16.9768	+	6.45218i	−0.696568	+	0.264736i
$595$	15.3751	−	8.87682i	0.630318	−	0.363914i
$596$	−2.55799	+	9.54655i	−0.104779	+	0.391042i
$597$	−0.942173	+	4.06048i	−0.0385606	+	0.166185i
$598$	−3.78202	+	6.82848i	−0.154658	+	0.279237i
$599$		−	11.5553i		−	0.472135i	−0.971737	−	0.236067i	$-0.924141\pi$
$599$		−	11.5553i		−	0.472135i	0.971737	−	0.236067i	$-0.0758586\pi$
$600$	29.5055	+	15.7303i	1.20456	+	0.642186i
$601$	12.4061	+	21.4880i	0.506055	+	0.876514i	0.999975	+	0.00700628i	$0.00223019\pi$
$601$	12.4061	+	21.4880i	0.506055	+	0.876514i	−0.493920	+	0.869507i	$0.664436\pi$
$602$	0.231527	−	0.401017i	0.00943635	−	0.0163442i
$603$	−1.68778	−	4.93716i	−0.0687317	−	0.201057i
$604$	−24.2548	+	6.49905i	−0.986913	+	0.264443i
$605$	31.1337	−	8.34226i	1.26577	−	0.339161i
$606$	19.0113	−	11.8503i	0.772280	−	0.481386i
$607$	−10.4788	+	18.1499i	−0.425323	+	0.736681i	−0.996451	−	0.0841805i	$-0.973173\pi$
$607$	−10.4788	+	18.1499i	−0.425323	+	0.736681i	0.571128	+	0.820861i	$0.306506\pi$
$608$	−12.6050	−	21.8324i	−0.511198	−	0.885422i
$609$	−0.147647	+	0.276943i	−0.00598295	+	0.0112223i
$610$			9.58184i			0.387957i
$611$	−0.0543561	−	3.05393i	−0.00219901	−	0.123549i
$612$	9.32421	−	19.0105i	0.376909	−	0.768454i
$613$	1.35054	−	5.04028i	0.0545477	−	0.203575i	−0.933274	−	0.359165i	$-0.883061\pi$
$613$	1.35054	−	5.04028i	0.0545477	−	0.203575i	0.987822	+	0.155591i	$0.0497280\pi$
$614$	−20.2909	+	11.7150i	−0.818876	+	0.472778i
$615$	−25.7961	−	24.1087i	−1.04020	−	0.972156i
$616$	−8.39026	−	8.39026i	−0.338053	−	0.338053i
$617$	−6.09399	−	22.7431i	−0.245335	−	0.915602i	−0.973215	−	0.229898i	$-0.926161\pi$
$617$	−6.09399	−	22.7431i	−0.245335	−	0.915602i	0.727880	−	0.685705i	$-0.240506\pi$
$618$	−15.8609	+	0.536293i	−0.638019	+	0.0215729i
$619$	−16.2097	+	16.2097i	−0.651524	+	0.651524i	−0.953360	−	0.301836i	$-0.902401\pi$
$619$	−16.2097	+	16.2097i	−0.651524	+	0.651524i	0.301836	+	0.953360i	$0.402401\pi$
$620$	−40.1024	−	23.1531i	−1.61055	−	0.929852i
$621$	2.30960	−	14.2752i	0.0926811	−	0.572844i
$622$	−23.7607	−	6.36666i	−0.952717	−	0.255280i
$623$	3.23459			0.129591
$624$	−4.58524	+	0.236791i	−0.183556	+	0.00947924i
$625$	8.11564			0.324626
$626$	−0.305212	−	0.0817813i	−0.0121987	−	0.00326864i
$627$	−32.0605	+	9.76308i	−1.28037	+	0.389900i
$628$	−8.70070	−	5.02335i	−0.347196	−	0.200454i
$629$	29.2500	−	29.2500i	1.16627	−	1.16627i
$630$	−8.03424	−	1.58017i	−0.320092	−	0.0629554i
$631$	8.86996	+	33.1031i	0.353108	+	1.31782i	0.882849	+	0.469656i	$0.155622\pi$
$631$	8.86996	+	33.1031i	0.353108	+	1.31782i	−0.529742	+	0.848159i	$0.677711\pi$
$632$	−0.898187	−	0.898187i	−0.0357280	−	0.0357280i
$633$	−1.22653	+	1.31237i	−0.0487500	+	0.0521621i
$634$	18.5126	−	10.6882i	0.735228	−	0.424484i
$635$	18.8845	−	70.4779i	0.749408	−	2.79683i
$636$	12.7793	+	2.96525i	0.506734	+	0.117580i
$637$	3.49875	+	0.871060i	0.138626	+	0.0345126i
$638$			0.633320i			0.0250734i
$639$	−30.8248	−	26.9157i	−1.21941	−	1.06477i
$640$	16.3303	+	28.2850i	0.645513	+	1.11806i
$641$	18.2550	−	31.6186i	0.721029	−	1.24886i	−0.239559	−	0.970882i	$-0.577003\pi$
$641$	18.2550	−	31.6186i	0.721029	−	1.24886i	0.960588	−	0.277977i	$-0.0896638\pi$
$642$	5.38278	+	8.63551i	0.212441	+	0.340816i
$643$	−11.5608	+	3.09770i	−0.455912	+	0.122161i	−0.479464	−	0.877561i	$-0.659169\pi$
$643$	−11.5608	+	3.09770i	−0.455912	+	0.122161i	0.0235522	+	0.999723i	$0.492502\pi$
$644$	3.74952	−	1.00468i	0.147752	−	0.0395900i
$645$	1.91346	+	3.06973i	0.0753423	+	0.120871i
$646$	−8.47626	+	14.6813i	−0.333494	+	0.577629i
$647$	−0.357320	−	0.618896i	−0.0140477	−	0.0243313i	0.858916	−	0.512116i	$-0.171138\pi$
$647$	−0.357320	−	0.618896i	−0.0140477	−	0.0243313i	−0.872964	+	0.487785i	$0.837805\pi$
$648$	−21.9198	+	9.19006i	−0.861092	+	0.361020i
$649$		−	36.0796i		−	1.41625i
$650$	−17.5709	+	10.5659i	−0.689186	+	0.414427i
$651$	15.9649	+	3.70441i	0.625714	+	0.145187i
$652$	−2.70293	+	10.0875i	−0.105855	+	0.395057i
$653$	−30.5471	+	17.6364i	−1.19540	+	0.690165i	−0.959527	−	0.281618i	$-0.909129\pi$
$653$	−30.5471	+	17.6364i	−1.19540	+	0.690165i	−0.235875	+	0.971783i	$0.575796\pi$
$654$	−4.57749	+	4.89787i	−0.178994	+	0.191522i
$655$	5.77260	+	5.77260i	0.225554	+	0.225554i
$656$	−1.10559	−	4.12611i	−0.0431659	−	0.161097i
$657$	−0.567646	+	2.88615i	−0.0221460	+	0.112599i
$658$	0.465994	−	0.465994i	0.0181663	−	0.0181663i
$659$	−2.45622	−	1.41810i	−0.0956806	−	0.0552412i	0.451396	−	0.892324i	$-0.350926\pi$
$659$	−2.45622	−	1.41810i	−0.0956806	−	0.0552412i	−0.547077	+	0.837082i	$0.684259\pi$
$660$	36.4320	−	11.0943i	1.41812	−	0.431845i
$661$	−6.27813	−	1.68222i	−0.244191	−	0.0654308i	0.134648	−	0.990894i	$-0.457010\pi$
$661$	−6.27813	−	1.68222i	−0.244191	−	0.0654308i	−0.378839	+	0.925463i	$0.623676\pi$
$662$	4.30202			0.167203
$663$	17.1906	+	26.5155i	0.667629	+	1.02978i
$664$	30.4514			1.18174
$665$	−14.5950	−	3.91071i	−0.565969	−	0.151651i
$666$	−19.0347	+	1.28869i	−0.737580	+	0.0499356i
$667$	−0.436710	−	0.252135i	−0.0169095	−	0.00976269i
$668$	−18.4649	+	18.4649i	−0.714428	+	0.714428i
$669$	40.8116	−	1.37993i	1.57787	−	0.0533514i
$670$	−1.22862	−	4.58527i	−0.0474657	−	0.177144i
$671$	11.1533	+	11.1533i	0.430567	+	0.430567i
$672$	−7.40759	−	6.92304i	−0.285754	−	0.267062i
$673$	34.1938	−	19.7418i	1.31807	−	0.760989i	0.334654	−	0.942341i	$-0.391381\pi$
$673$	34.1938	−	19.7418i	1.31807	−	0.760989i	0.983418	+	0.181352i	$0.0580472\pi$
$674$	−0.292873	+	1.09302i	−0.0112810	+	0.0421014i
$675$	24.0013	−	29.4387i	0.923812	−	1.13310i
$676$	8.50182	−	16.0161i	0.326993	−	0.616005i
$677$			22.2942i			0.856836i	0.903581	+	0.428418i	$0.140929\pi$
$677$			22.2942i			0.856836i	−0.903581	+	0.428418i	$0.859071\pi$
$678$	−9.97632	+	18.7127i	−0.383138	+	0.718658i
$679$	1.13782	+	1.97077i	0.0436657	+	0.0756312i
$680$	23.4431	−	40.6046i	0.899001	−	1.55712i
$681$	−36.7432	+	22.9031i	−1.40800	+	0.877650i
$682$	31.9455	−	8.55976i	1.22326	−	0.327770i
$683$	−8.79388	+	2.35631i	−0.336488	+	0.0901618i	−0.423107	−	0.906080i	$-0.639061\pi$
$683$	−8.79388	+	2.35631i	−0.336488	+	0.0901618i	0.0866185	+	0.996242i	$0.472394\pi$
$684$	−17.0520	+	5.82927i	−0.652000	+	0.222888i
$685$	20.0235	−	34.6818i	0.765060	−	1.32512i
$686$	0.388964	+	0.673705i	0.0148507	+	0.0257222i
$687$	−35.8864	−	19.1321i	−1.36915	−	0.729937i
$688$			0.437624i			0.0166843i
$689$	−13.5957	+	14.0885i	−0.517957	+	0.536729i
$690$	2.97374	−	12.8159i	0.113208	−	0.487893i
$691$	−4.37461	+	16.3263i	−0.166418	+	0.621081i	0.831437	+	0.555619i	$0.187519\pi$
$691$	−4.37461	+	16.3263i	−0.166418	+	0.621081i	−0.997855	+	0.0654616i	$0.979148\pi$
$692$	−2.41350	+	1.39343i	−0.0917475	+	0.0529704i
$693$	−11.1912	+	7.51254i	−0.425118	+	0.285378i
$694$	2.36329	+	2.36329i	0.0897094	+	0.0897094i
$695$	4.77512	+	17.8210i	0.181131	+	0.675988i
$696$	0.0280088	+	0.828363i	0.00106167	+	0.0313990i
$697$	−20.7891	+	20.7891i	−0.787443	+	0.787443i
$698$	11.3726	+	6.56595i	0.430457	+	0.248525i
$699$	1.33948	+	4.39866i	0.0506639	+	0.166373i
$700$	9.84853	+	2.63890i	0.372239	+	0.0997412i
$701$	−38.7119			−1.46213			−0.731063	−	0.682310i	$-0.760976\pi$
$701$	−38.7119			−1.46213			−0.731063	+	0.682310i	$0.760976\pi$
$702$	2.07135	−	14.4265i	0.0781779	−	0.544494i
$703$	−35.2056			−1.32781
$704$	−13.3817	−	3.58560i	−0.504340	−	0.135138i
$705$	1.49969	+	4.92477i	0.0564817	+	0.185478i
$706$	−13.4954	−	7.79155i	−0.507904	−	0.293239i
$707$	11.7564	−	11.7564i	0.442147	−	0.442147i
$708$	−0.655596	−	19.3893i	−0.0246388	−	0.728694i
$709$	−5.05872	−	18.8794i	−0.189984	−	0.709031i	−0.993508	−	0.113759i	$-0.963711\pi$
$709$	−5.05872	−	18.8794i	−0.189984	−	0.709031i	0.803524	−	0.595272i	$-0.202956\pi$
$710$	−26.3262	−	26.3262i	−0.988003	−	0.988003i
$711$	−1.19803	+	0.804227i	−0.0449296	+	0.0301609i
$712$	7.39788	−	4.27117i	0.277247	−	0.160069i
$713$	−6.81555	+	25.4360i	−0.255244	+	0.952584i
$714$	−1.54109	+	6.64162i	−0.0576737	+	0.248556i
$715$	−13.7312	+	55.1534i	−0.513516	+	2.06262i
$716$			5.45719i			0.203945i
$717$	−20.6085	−	10.9870i	−0.769638	−	0.410317i
$718$	−4.14750	−	7.18369i	−0.154783	−	0.268093i
$719$	−0.214709	+	0.371886i	−0.00800729	+	0.0138690i	−0.870001	−	0.493049i	$-0.835882\pi$
$719$	−0.214709	+	0.371886i	−0.00800729	+	0.0138690i	0.861994	+	0.506918i	$0.169215\pi$
$720$	7.32243	−	2.50319i	0.272891	−	0.0932884i
$721$	−11.3768	+	3.04840i	−0.423694	+	0.113528i
$722$	−0.340606	+	0.0912650i	−0.0126760	+	0.00339653i
$723$	−19.8127	+	12.3499i	−0.736842	+	0.459296i
$724$	0.578111	−	1.00132i	0.0214853	−	0.0372137i
$725$	−0.662259	−	1.14707i	−0.0245957	−	0.0426010i
$726$	−5.82336	+	10.9230i	−0.216125	+	0.405389i
$727$		−	43.8176i		−	1.62511i	−0.582888	−	0.812553i	$-0.698077\pi$
$727$		−	43.8176i		−	1.62511i	0.582888	−	0.812553i	$-0.301923\pi$
$728$	9.15224	−	2.62777i	0.339205	−	0.0973915i
$729$	5.43805	+	26.4467i	0.201409	+	0.979507i
$730$	−0.692628	+	2.58492i	−0.0256353	+	0.0956723i
$731$	2.60847	−	1.50600i	0.0964777	−	0.0557014i
$732$	6.19646	+	5.79114i	0.229028	+	0.214047i
$733$	34.6540	+	34.6540i	1.27998	+	1.27998i	0.940679	+	0.339297i	$0.110189\pi$
$733$	34.6540	+	34.6540i	1.27998	+	1.27998i	0.339297	+	0.940679i	$0.389811\pi$
$734$	−3.00613	−	11.2190i	−0.110958	−	0.414102i
$735$	−6.07349	+	0.205359i	−0.224024	+	0.00757476i
$736$	11.5195	−	11.5195i	0.424615	−	0.424615i
$737$	−6.76737	−	3.90714i	−0.249279	−	0.143921i
$738$	13.5287	−	0.915920i	0.497999	−	0.0337155i
$739$	−2.52567	−	0.676752i	−0.0929083	−	0.0248947i	0.212065	−	0.977255i	$-0.431981\pi$
$739$	−2.52567	−	0.676752i	−0.0929083	−	0.0248947i	−0.304974	+	0.952361i	$0.598648\pi$
$740$	40.0060			1.47065
$741$	5.61180	−	26.3027i	0.206155	−	0.966252i
$742$	−4.22429			−0.155079
$743$	−12.4271	−	3.32983i	−0.455906	−	0.122160i	0.0235556	−	0.999723i	$-0.492501\pi$
$743$	−12.4271	−	3.32983i	−0.455906	−	0.122160i	−0.479462	+	0.877563i	$0.659168\pi$
$744$	41.4051	−	12.6087i	1.51798	−	0.462257i
$745$	21.5297	+	12.4302i	0.788788	+	0.455407i
$746$	5.73554	−	5.73554i	0.209993	−	0.209993i
$747$	6.67557	−	33.9414i	0.244246	−	1.24185i
$748$	−8.20752	−	30.6309i	−0.300097	−	1.11998i
$749$	5.34014	+	5.34014i	0.195124	+	0.195124i
$750$	7.45593	−	7.97778i	0.272252	−	0.291307i
$751$	−2.01789	+	1.16503i	−0.0736339	+	0.0425126i	−0.536365	−	0.843986i	$-0.680203\pi$
$751$	−2.01789	+	1.16503i	−0.0736339	+	0.0425126i	0.462731	+	0.886499i	$0.346870\pi$
$752$	−0.161198	+	0.601600i	−0.00587830	+	0.0219381i
$753$	34.6923	+	8.04981i	1.26426	+	0.293351i
$754$	−0.444594	−	0.246243i	−0.0161912	−	0.00896764i
$755$			63.1624i			2.29871i
$756$	−5.87766	+	4.24062i	−0.213769	+	0.154230i
$757$	7.22715	+	12.5178i	0.262675	+	0.454967i	0.966952	−	0.254959i	$-0.0820619\pi$
$757$	7.22715	+	12.5178i	0.262675	+	0.454967i	−0.704277	+	0.709926i	$0.748729\pi$
$758$	−6.80872	+	11.7931i	−0.247304	+	0.428343i
$759$	−11.4563	−	18.3792i	−0.415837	−	0.667121i
$760$	−38.5443	+	10.3279i	−1.39815	+	0.374633i
$761$	37.8495	−	10.1417i	1.37204	−	0.367638i	0.503819	−	0.863809i	$-0.331928\pi$
$761$	37.8495	−	10.1417i	1.37204	−	0.367638i	0.868225	+	0.496171i	$0.165261\pi$
$762$	14.8225	+	23.7796i	0.536964	+	0.861442i
$763$	−2.48771	+	4.30883i	−0.0900610	+	0.155990i
$764$	6.46285	+	11.1940i	0.233818	+	0.404984i
$765$	−40.1191	−	35.0312i	−1.45051	−	1.26656i
$766$			17.5188i			0.632978i
$767$	25.3281	+	14.0282i	0.914543	+	0.506529i
$768$	−22.6232	−	5.24936i	−0.816344	−	0.189420i
$769$	4.61632	−	17.2283i	0.166469	−	0.621270i	−0.831380	−	0.555705i	$-0.812448\pi$
$769$	4.61632	−	17.2283i	0.166469	−	0.621270i	0.997848	−	0.0655648i	$-0.0208849\pi$
$770$	−10.6201	+	6.13152i	−0.382722	+	0.220965i
$771$	33.8936	−	36.2658i	1.22065	−	1.30608i
$772$	−8.14482	−	8.14482i	−0.293138	−	0.293138i
$773$	10.0848	+	37.6369i	0.362724	+	1.35371i	0.870480	+	0.492205i	$0.163809\pi$
$773$	10.0848	+	37.6369i	0.362724	+	1.35371i	−0.507755	+	0.861501i	$0.669525\pi$
$774$	−1.36305	−	0.268084i	−0.0489939	−	0.00963608i
$775$	−48.9086	+	48.9086i	−1.75685	+	1.75685i
$776$	5.20466	+	3.00491i	0.186837	+	0.107870i
$777$	−13.5451	+	4.12476i	−0.485928	+	0.147975i
$778$	−2.28149	−	0.611323i	−0.0817953	−	0.0219170i
$779$	25.0220			0.896507
$780$	−6.37698	+	29.8891i	−0.228333	+	1.07020i
$781$	−61.2873			−2.19303
$782$	−10.5817	−	2.83536i	−0.378401	−	0.101392i
$783$	0.929441	+	0.150375i	0.0332155	+	0.00537398i
$784$	−0.636705	−	0.367602i	−0.0227395	−	0.0131286i
$785$	−17.8695	+	17.8695i	−0.637791	+	0.637791i
$786$	−3.13337	+	0.105947i	−0.111764	+	0.00377899i
$787$	3.17668	+	11.8555i	0.113237	+	0.422605i	0.999149	−	0.0412480i	$-0.0131334\pi$
$787$	3.17668	+	11.8555i	0.113237	+	0.422605i	−0.885912	+	0.463853i	$0.846467\pi$
$788$	9.53949	+	9.53949i	0.339830	+	0.339830i
$789$	−10.2653	−	9.59382i	−0.365455	−	0.341549i
$790$	−1.13689	+	0.656387i	−0.0404489	+	0.0233532i
$791$	−4.07337	+	15.2020i	−0.144833	+	0.540522i
$792$	−15.6754	+	31.9596i	−0.557002	+	1.13563i
$793$	−12.1662	+	3.49312i	−0.432034	+	0.124044i
$794$		−	8.09392i		−	0.287242i
$795$	15.5244	−	29.1192i	0.550592	−	1.03275i
$796$	1.67840	+	2.90707i	0.0594893	+	0.103038i
$797$	−15.7312	+	27.2472i	−0.557226	+	0.965144i	0.440501	+	0.897752i	$0.354801\pi$
$797$	−15.7312	+	27.2472i	−0.557226	+	0.965144i	−0.997727	+	0.0673915i	$0.978532\pi$
$798$	4.92441	−	3.06954i	0.174322	−	0.108660i
$799$	4.14059	−	1.10947i	0.146483	−	0.0392501i
$800$	41.3322	−	11.0749i	1.46131	−	0.391557i
$801$	−3.13892	−	9.18208i	−0.110908	−	0.324433i
$802$	−10.1667	+	17.6092i	−0.358998	+	0.621802i
$803$	2.20263	+	3.81507i	0.0777292	+	0.134631i
$804$	−3.70780	−	1.97674i	−0.130764	−	0.0697143i
$805$		−	9.76421i		−	0.344143i
$806$	−6.41181	+	25.7540i	−0.225846	+	0.907147i
$807$	5.31006	−	22.8848i	0.186923	−	0.805582i
$808$	11.3643	−	42.4123i	0.399796	−	1.49206i
$809$	13.8418	−	7.99158i	0.486653	−	0.280969i	−0.236532	−	0.971624i	$-0.576011\pi$
$809$	13.8418	−	7.99158i	0.486653	−	0.280969i	0.723185	+	0.690655i	$0.242677\pi$
$810$	3.31095	+	24.3403i	0.116335	+	0.855232i
$811$	8.86374	+	8.86374i	0.311248	+	0.311248i	0.845393	−	0.534145i	$-0.179366\pi$
$811$	8.86374	+	8.86374i	0.311248	+	0.311248i	−0.534145	+	0.845393i	$0.679366\pi$
$812$	0.0654136	+	0.244127i	0.00229557	+	0.00856718i
$813$	−0.429784	−	12.7109i	−0.0150732	−	0.445790i
$814$	−20.2039	+	20.2039i	−0.708148	+	0.708148i
$815$	22.7497	+	13.1345i	0.796886	+	0.460082i
$816$	−1.87711	−	6.16415i	−0.0657120	−	0.215788i
$817$	−2.47611	−	0.663473i	−0.0866283	−	0.0232120i
$818$	−17.0003			−0.594403
$819$	−0.922573	−	10.7772i	−0.0322373	−	0.376587i
$820$	−28.4338			−0.992953
$821$	−4.45268	−	1.19309i	−0.155400	−	0.0416392i	0.180280	−	0.983615i	$-0.442299\pi$
$821$	−4.45268	−	1.19309i	−0.155400	−	0.0416392i	−0.335680	+	0.941976i	$0.608966\pi$
$822$	4.48027	+	14.7125i	0.156267	+	0.513159i
$823$	−33.5844	−	19.3899i	−1.17068	−	0.675891i	−0.216838	−	0.976208i	$-0.569574\pi$
$823$	−33.5844	−	19.3899i	−1.17068	−	0.675891i	−0.953840	+	0.300316i	$0.902908\pi$
$824$	−21.9947	+	21.9947i	−0.766221	+	0.766221i
$825$	−1.92232	−	56.8529i	−0.0669268	−	1.97936i
$826$	1.61683	+	6.03408i	0.0562566	+	0.209953i
$827$	2.94012	+	2.94012i	0.102238	+	0.102238i	0.756376	−	0.654138i	$-0.226968\pi$
$827$	2.94012	+	2.94012i	0.102238	+	0.102238i	−0.654138	+	0.756376i	$0.726968\pi$
$828$	−6.49061	−	9.66885i	−0.225564	−	0.336016i
$829$	−9.37700	+	5.41381i	−0.325677	+	0.188030i	−0.653920	−	0.756564i	$-0.726877\pi$
$829$	−9.37700	+	5.41381i	−0.325677	+	0.188030i	0.328243	+	0.944593i	$0.393543\pi$
$830$	8.14538	−	30.3990i	0.282730	−	1.05516i
$831$	4.25939	−	18.3567i	0.147757	−	0.636787i
$832$	7.72007	−	7.99987i	0.267645	−	0.277346i
$833$			5.06013i			0.175323i
$834$	−6.25231	−	3.33330i	−0.216500	−	0.115423i
$835$	32.8425	+	56.8850i	1.13656	+	1.96859i
$836$	−13.4945	+	23.3732i	−0.466718	+	0.808379i
$837$	−4.97692	−	48.9146i	−0.172028	−	1.69074i
$838$	−2.84653	+	0.762724i	−0.0983316	+	0.0263479i
$839$	−13.3696	+	3.58236i	−0.461569	+	0.123677i	−0.482107	−	0.876112i	$-0.660129\pi$
$839$	−13.3696	+	3.58236i	−0.461569	+	0.123677i	0.0205388	+	0.999789i	$0.493462\pi$
$840$	−13.6196	+	8.48951i	−0.469921	+	0.292916i
$841$	−14.4836	+	25.0863i	−0.499434	+	0.865045i
$842$	−14.6636	−	25.3981i	−0.505341	−	0.875277i
$843$	−11.8293	+	22.1883i	−0.407421	+	0.764205i
$844$			1.44657i			0.0497929i
$845$	−33.3791	−	31.0837i	−1.14828	−	1.06931i
$846$	−1.77503	−	0.870613i	−0.0610269	−	0.0299323i
$847$	−2.37770	+	8.87372i	−0.0816989	+	0.304904i
$848$	3.45743	−	1.99615i	0.118729	−	0.0685480i
$849$	4.43835	+	4.14802i	0.152324	+	0.142360i
$850$	−20.3466	−	20.3466i	−0.697884	−	0.697884i
$851$	−5.88825	−	21.9752i	−0.201847	−	0.753302i
$852$	−32.9360	+	1.11364i	−1.12837	+	0.0381527i
$853$	−30.6895	+	30.6895i	−1.05079	+	1.05079i	−0.0521481	+	0.998639i	$0.516607\pi$
$853$	−30.6895	+	30.6895i	−1.05079	+	1.05079i	−0.998639	+	0.0521481i	$0.983393\pi$
$854$	−2.36512	−	1.36550i	−0.0809328	−	0.0467266i
$855$	3.06188	+	45.2259i	0.104714	+	1.54669i
$856$	19.2650	+	5.16203i	0.658463	+	0.176435i
$857$	49.2792			1.68334			0.841672	−	0.539989i	$-0.181572\pi$
$857$	49.2792			1.68334			0.841672	+	0.539989i	$0.181572\pi$
$858$	−11.8741	−	18.3152i	−0.405377	−	0.625270i
$859$	−20.7729			−0.708762			−0.354381	−	0.935101i	$-0.615308\pi$
$859$	−20.7729			−0.708762			−0.354381	+	0.935101i	$0.615308\pi$
$860$	2.81374	+	0.753939i	0.0959477	+	0.0257091i
$861$	9.62703	−	2.93163i	0.328088	−	0.0999096i
$862$	−0.937870	−	0.541479i	−0.0319440	−	0.0184429i
$863$	−2.07454	+	2.07454i	−0.0706180	+	0.0706180i	−0.741534	−	0.670916i	$-0.765901\pi$
$863$	−2.07454	+	2.07454i	−0.0706180	+	0.0706180i	0.670916	+	0.741534i	$0.265901\pi$
$864$	−12.4640	+	27.7463i	−0.424035	+	0.943947i
$865$	1.81434	+	6.77119i	0.0616893	+	0.230227i
$866$	8.94153	+	8.94153i	0.303846	+	0.303846i
$867$	−10.1767	+	10.8889i	−0.345618	+	0.369808i
$868$	11.4300	−	6.59909i	0.387958	−	0.223988i
$869$	−0.559312	+	2.08738i	−0.0189734	+	0.0708095i
$870$	0.834429	+	0.193616i	0.0282898	+	0.00656421i
$871$	5.37407	−	3.23158i	0.182093	−	0.109498i
$872$			13.1397i			0.444967i
$873$	4.49028	−	5.14243i	0.151973	−	0.174045i
$874$	4.66180	+	8.07448i	0.157688	+	0.273123i
$875$	4.05204	−	7.01834i	0.136984	−	0.237263i
$876$	1.25302	+	2.01021i	0.0423358	+	0.0679186i
$877$	52.0706	−	13.9523i	1.75830	−	0.471135i	0.771934	−	0.635702i	$-0.219289\pi$
$877$	52.0706	−	13.9523i	1.75830	−	0.471135i	0.986366	+	0.164567i	$0.0526227\pi$
$878$	−18.2700	+	4.89544i	−0.616584	+	0.165213i
$879$	−16.0056	−	25.6775i	−0.539854	−	0.866079i
$880$	5.79478	−	10.0369i	0.195342	−	0.338342i
$881$	−16.7291	−	28.9756i	−0.563616	−	0.976212i	−0.997177	−	0.0750874i	$-0.976076\pi$
$881$	−16.7291	−	28.9756i	−0.563616	−	0.976212i	0.433561	−	0.901124i	$-0.357257\pi$
$882$	1.53500	−	1.75793i	0.0516860	−	0.0591927i
$883$			32.6502i			1.09877i	0.835571	+	0.549383i	$0.185137\pi$
$883$			32.6502i			1.09877i	−0.835571	+	0.549383i	$0.814863\pi$
$884$	24.6942	+	6.14795i	0.830557	+	0.206778i
$885$	−47.5365	−	11.0301i	−1.59792	−	0.370774i
$886$	3.98606	−	14.8762i	0.133914	−	0.499775i
$887$	31.7441	−	18.3274i	1.06586	−	0.615375i	0.138814	−	0.990319i	$-0.455671\pi$
$887$	31.7441	−	18.3274i	1.06586	−	0.615375i	0.927048	+	0.374943i	$0.122338\pi$
$888$	−25.5326	+	27.3196i	−0.856817	+	0.916787i
$889$	14.7051	+	14.7051i	0.493194	+	0.493194i
$890$	−2.28497	−	8.52764i	−0.0765925	−	0.285847i
$891$	32.1861	+	24.4782i	1.07827	+	0.820050i
$892$	23.2529	−	23.2529i	0.778565	−	0.778565i
$893$	−3.15952	−	1.82415i	−0.105729	−	0.0610428i
$894$	−9.13323	+	2.78126i	−0.305461	+	0.0930191i
$895$	13.2592	+	3.55280i	0.443207	+	0.118757i
$896$	−9.30892			−0.310989
$897$	17.3566	−	0.896332i	0.579521	−	0.0299277i
$898$	17.8880			0.596929
$899$	−1.65611	−	0.443752i	−0.0552342	−	0.0148000i
$900$	−2.06613	−	30.5180i	−0.0688709	−	1.01727i
$901$	−23.7962	−	13.7387i	−0.792765	−	0.457703i
$902$	14.3597	−	14.3597i	0.478127	−	0.478127i
$903$	−1.03040	+	0.0348402i	−0.0342896	+	0.00115941i
$904$	10.7575	+	40.1475i	0.357789	+	1.33529i
$905$	−2.05651	−	2.05651i	−0.0683608	−	0.0683608i
$906$	−17.7219	−	16.5627i	−0.588772	−	0.550259i
$907$	13.4532	−	7.76719i	0.446705	−	0.257905i	−0.259733	−	0.965681i	$-0.583634\pi$
$907$	13.4532	−	7.76719i	0.446705	−	0.257905i	0.706438	+	0.707775i	$0.250301\pi$
$908$	−9.02427	+	33.6790i	−0.299481	+	1.11768i
$909$	−44.7819	−	21.9645i	−1.48532	−	0.728515i
$910$	−0.175129	−	9.83938i	−0.00580546	−	0.326172i
$911$		−	15.1851i		−	0.503104i	−0.967844	−	0.251552i	$-0.919059\pi$
$911$		−	15.1851i		−	0.503104i	0.967844	−	0.251552i	$-0.0809410\pi$
$912$	−2.57997	+	4.83928i	−0.0854313	+	0.160245i
$913$	−25.9032	−	44.8656i	−0.857270	−	1.48484i
$914$	4.23334	−	7.33236i	0.140026	−	0.242533i
$915$	18.1047	−	11.2852i	0.598522	−	0.373078i
$916$	−31.6341	+	8.47632i	−1.04522	+	0.280066i
$917$	−2.24752	+	0.602222i	−0.0742198	+	0.0198871i
$918$	20.3492	−	2.07047i	0.671622	−	0.0683356i
$919$	26.0736	−	45.1609i	0.860090	−	1.48972i	−0.0117519	−	0.999931i	$-0.503741\pi$
$919$	26.0736	−	45.1609i	0.860090	−	1.48972i	0.871842	−	0.489788i	$-0.162926\pi$
$920$	−12.8933	−	22.3319i	−0.425080	−	0.736259i
$921$	46.0333	+	24.5417i	1.51685	+	0.808678i
$922$		−	9.36044i		−	0.308270i
$923$	23.8293	−	43.0240i	0.784351	−	1.41615i
$924$	−2.45347	+	10.5737i	−0.0807131	+	0.347849i
$925$	15.4661	−	57.7204i	0.508523	−	1.89783i
$926$	26.7481	−	15.4430i	0.878998	−	0.507489i
$927$	19.6938	+	29.3372i	0.646829	+	0.963560i
$928$	0.750022	+	0.750022i	0.0246207	+	0.0246207i
$929$	8.38590	+	31.2966i	0.275132	+	1.02681i	0.955753	+	0.294172i	$0.0950437\pi$
$929$	8.38590	+	31.2966i	0.275132	+	1.02681i	−0.680620	+	0.732636i	$0.738290\pi$
$930$	−1.51163	−	44.7065i	−0.0495683	−	1.46598i
$931$	3.04522	−	3.04522i	0.0998030	−	0.0998030i
$932$	3.20678	+	1.85143i	0.105041	+	0.0606457i
$933$	15.9550	+	52.3938i	0.522343	+	1.71530i
$934$	−20.5357	−	5.50252i	−0.671948	−	0.180048i
$935$	−79.7665			−2.60864
$936$	−16.3410	−	23.4305i	−0.534122	−	0.765851i
$937$	26.0509			0.851046			0.425523	−	0.904948i	$-0.360090\pi$
$937$	26.0509			0.851046			0.425523	+	0.904948i	$0.360090\pi$
$938$	1.30689	+	0.350180i	0.0426715	+	0.0114338i
$939$	0.204946	+	0.673011i	0.00668814	+	0.0219629i
$940$	3.59032	+	2.07287i	0.117103	+	0.0676097i
$941$	−33.4066	+	33.4066i	−1.08902	+	1.08902i	−0.0933958	+	0.995629i	$0.529772\pi$
$941$	−33.4066	+	33.4066i	−1.08902	+	1.08902i	−0.995629	+	0.0933958i	$0.970228\pi$
$942$	−0.327966	−	9.69961i	−0.0106857	−	0.316030i
$943$	4.18501	+	15.6187i	0.136283	+	0.508614i
$944$	−4.17466	−	4.17466i	−0.135874	−	0.135874i
$945$	6.47680	+	17.0416i	0.210690	+	0.554363i
$946$	−1.80176	+	1.04024i	−0.0585802	+	0.0338213i
$947$	−2.95823	+	11.0403i	−0.0961296	+	0.358761i	−0.997188	−	0.0749365i	$-0.976125\pi$
$947$	−2.95823	+	11.0403i	−0.0961296	+	0.358761i	0.901059	+	0.433697i	$0.142791\pi$
$948$	−0.262647	+	1.13193i	−0.00853036	+	0.0367633i
$949$	−3.53461	+	0.0629116i	−0.114738	+	0.00204220i
$950$			24.4895i			0.794543i
$951$	−41.9987	−	22.3908i	−1.36190	−	0.726072i
$952$	6.68173	+	11.5731i	0.216556	+	0.375086i
$953$	15.4255	−	26.7177i	0.499680	−	0.865471i	−0.500320	−	0.865841i	$-0.666784\pi$
$953$	15.4255	−	26.7177i	0.499680	−	0.865471i	1.00000		0.000369668i	$0.000117669\pi$
$954$	4.09934	+	11.9915i	0.132721	+	0.388241i
$955$	31.4053	−	8.41503i	1.01625	−	0.272304i
$956$	−18.1665	+	4.86770i	−0.587546	+	0.157433i
$957$	1.19665	−	0.745906i	0.0386821	−	0.0241117i
$958$	5.89242	−	10.2060i	0.190376	−	0.329740i
$959$	5.70709	+	9.88497i	0.184292	+	0.319202i
$960$	−8.81520	+	16.5348i	−0.284509	+	0.533658i
$961$			58.5337i			1.88818i
$962$	−6.32773	−	22.0388i	−0.204014	−	0.710560i
$963$	9.97693	−	20.3413i	0.321502	−	0.655489i
$964$	−4.86608	+	18.1605i	−0.156726	+	0.584909i
$965$	−25.0918	+	14.4868i	−0.807734	+	0.466345i
$966$	2.73962	+	2.56041i	0.0881457	+	0.0823798i
$967$	1.58014	+	1.58014i	0.0508139	+	0.0508139i	0.732057	−	0.681243i	$-0.238560\pi$
$967$	1.58014	+	1.58014i	0.0508139	+	0.0508139i	−0.681243	+	0.732057i	$0.738560\pi$
$968$	6.27935	+	23.4349i	0.201826	+	0.753225i
$969$	37.7231	−	1.27550i	1.21184	−	0.0409751i
$970$	4.39193	−	4.39193i	0.141016	−	0.141016i
$971$	27.1454	+	15.6724i	0.871136	+	0.502951i	0.867726	−	0.497043i	$-0.165581\pi$
$971$	27.1454	+	15.6724i	0.871136	+	0.502951i	0.00341055	+	0.999994i	$0.498914\pi$
$972$	17.7417	+	12.5698i	0.569065	+	0.403177i
$973$	−5.07932	−	1.36100i	−0.162836	−	0.0436317i
$974$	2.96763			0.0950892
$975$	40.6584	+	20.7556i	1.30211	+	0.664712i
$976$	2.58102			0.0826165
$977$	39.0767	+	10.4706i	1.25018	+	0.334984i	0.822404	−	0.568903i	$-0.192632\pi$
$977$	39.0767	+	10.4706i	1.25018	+	0.334984i	0.427771	+	0.903887i	$0.359299\pi$
$978$	−9.65076	+	2.93885i	−0.308597	+	0.0939741i
$979$	−12.5859	−	7.26646i	−0.402247	−	0.232237i
$980$	−3.46044	+	3.46044i	−0.110540	+	0.110540i
$981$	14.6457	+	2.88050i	0.467600	+	0.0919672i
$982$	−3.92133	−	14.6346i	−0.125135	−	0.467009i
$983$	−5.93903	−	5.93903i	−0.189426	−	0.189426i	0.606022	−	0.795448i	$-0.292764\pi$
$983$	−5.93903	−	5.93903i	−0.189426	−	0.189426i	−0.795448	+	0.606022i	$0.792764\pi$
$984$	18.1470	−	19.4171i	0.578505	−	0.618996i
$985$	29.3884	−	16.9674i	0.936392	−	0.540626i
$986$	0.184607	−	0.688963i	0.00587909	−	0.0219410i
$987$	−1.42932	−	0.331652i	−0.0454958	−	0.0105566i
$988$	−11.1613	−	18.5610i	−0.355087	−	0.590505i
$989$		−	1.65655i		−	0.0526752i
$990$	27.7116	+	24.1973i	0.880732	+	0.769039i
$991$	26.1869	+	45.3571i	0.831855	+	1.44082i	0.896565	+	0.442912i	$0.146055\pi$
$991$	26.1869	+	45.3571i	0.831855	+	1.44082i	−0.0647097	+	0.997904i	$0.520612\pi$
$992$	27.6950	−	47.9691i	0.879316	−	1.52302i
$993$	−5.06679	−	8.12858i	−0.160790	−	0.257953i
$994$	10.2499	−	2.74646i	0.325108	−	0.0871124i
$995$	8.15594	−	2.18538i	0.258561	−	0.0692811i
$996$	−14.7357	−	23.6403i	−0.466919	−	0.749070i
$997$	10.9459	−	18.9589i	0.346661	−	0.600435i	−0.638993	−	0.769213i	$-0.720649\pi$
$997$	10.9459	−	18.9589i	0.346661	−	0.600435i	0.985654	+	0.168778i	$0.0539820\pi$
$998$	2.32622	+	4.02913i	0.0736352	+	0.127540i
$999$	24.8535	+	34.4479i	0.786329	+	1.08988i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cc.a.50.18	yes	112
3.2	odd	2	inner	273.2.cc.a.50.11	✓	112
13.6	odd	12	inner	273.2.cc.a.71.11	yes	112
39.32	even	12	inner	273.2.cc.a.71.18	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cc.a.50.11	✓	112	3.2	odd	2	inner
273.2.cc.a.50.18	yes	112	1.1	even	1	trivial
273.2.cc.a.71.11	yes	112	13.6	odd	12	inner
273.2.cc.a.71.18	yes	112	39.32	even	12	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.751420 + 0.201342i) q^{2} +(-0.504568 - 1.65693i) q^{3} +(-1.20796 - 0.697414i) q^{4} +(-2.48091 + 2.48091i) q^{5} +(-0.0455330 - 1.34664i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-1.86742 - 1.86742i) q^{8} +(-2.49082 + 1.67207i) q^{9} +O(q^{10})\)	\(q+(0.751420 + 0.201342i) q^{2} +(-0.504568 - 1.65693i) q^{3} +(-1.20796 - 0.697414i) q^{4} +(-2.48091 + 2.48091i) q^{5} +(-0.0455330 - 1.34664i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-1.86742 - 1.86742i) q^{8} +(-2.49082 + 1.67207i) q^{9} +(-2.36372 + 1.36469i) q^{10} +(-1.16287 + 4.33987i) q^{11} +(-0.546068 + 2.35339i) q^{12} +(-2.59448 - 2.50374i) q^{13} -0.777928i q^{14} +(5.36248 + 2.85890i) q^{15} +(0.367602 + 0.636705i) q^{16} +(2.53006 - 4.38220i) q^{17} +(-2.20831 + 0.754917i) q^{18} +(-4.15985 + 1.11463i) q^{19} +(4.72705 - 1.26661i) q^{20} +(-1.46988 + 0.916220i) q^{21} +(-1.74760 + 3.02693i) q^{22} +(-1.39149 - 2.41014i) q^{23} +(-2.15194 + 4.03642i) q^{24} -7.30982i q^{25} +(-1.44543 - 2.40374i) q^{26} +(4.02729 + 3.28344i) q^{27} +(-0.361008 + 1.34730i) q^{28} +(0.156921 - 0.0905985i) q^{29} +(3.45386 + 3.22793i) q^{30} +(-6.69080 - 6.69080i) q^{31} +(1.51507 + 5.65433i) q^{32} +(7.77760 - 0.262978i) q^{33} +(2.78347 - 2.78347i) q^{34} +(3.03848 + 1.75427i) q^{35} +(4.17493 - 0.282651i) q^{36} +(7.89628 + 2.11580i) q^{37} -3.35022 q^{38} +(-2.83942 + 5.56217i) q^{39} +9.26580 q^{40} +(-5.61219 - 1.50378i) q^{41} +(-1.28897 + 0.392518i) q^{42} +(0.515494 + 0.297621i) q^{43} +(4.43138 - 4.43138i) q^{44} +(2.03125 - 10.3277i) q^{45} +(-0.560334 - 2.09119i) q^{46} +(0.599020 + 0.599020i) q^{47} +(0.869495 - 0.930352i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(1.47178 - 5.49275i) q^{50} +(-8.53758 - 1.98102i) q^{51} +(1.38788 + 4.83383i) q^{52} -5.43018i q^{53} +(2.36509 + 3.27811i) q^{54} +(-7.88187 - 13.6518i) q^{55} +(-1.32047 + 2.28711i) q^{56} +(3.94578 + 6.33016i) q^{57} +(0.136155 - 0.0364827i) q^{58} +(-7.75661 + 2.07838i) q^{59} +(-4.48380 - 7.19330i) q^{60} +(1.75531 - 3.04029i) q^{61} +(-3.68046 - 6.37475i) q^{62} +(2.25976 + 1.97319i) q^{63} +3.08342i q^{64} +(12.6482 - 0.225122i) q^{65} +(5.89720 + 1.36835i) q^{66} +(-0.450145 + 1.67996i) q^{67} +(-6.11242 + 3.52901i) q^{68} +(-3.29132 + 3.52168i) q^{69} +(1.92997 + 1.92997i) q^{70} +(3.53048 + 13.1759i) q^{71} +(7.77386 + 1.52896i) q^{72} +(0.693304 - 0.693304i) q^{73} +(5.50742 + 3.17971i) q^{74} +(-12.1118 + 3.68830i) q^{75} +(5.80227 + 1.55471i) q^{76} +4.49297 q^{77} +(-3.25350 + 3.60783i) q^{78} +0.480977 q^{79} +(-2.49160 - 0.667621i) q^{80} +(3.40838 - 8.32964i) q^{81} +(-3.91434 - 2.25995i) q^{82} +(-8.15333 + 8.15333i) q^{83} +(2.41453 - 0.0816409i) q^{84} +(4.59498 + 17.1487i) q^{85} +(0.327429 + 0.327429i) q^{86} +(-0.229293 - 0.214294i) q^{87} +(10.2759 - 5.93281i) q^{88} +(-0.837175 + 3.12438i) q^{89} +(3.60574 - 7.35150i) q^{90} +(-1.74692 + 3.15409i) q^{91} +3.88179i q^{92} +(-7.71021 + 14.4621i) q^{93} +(0.329508 + 0.570724i) q^{94} +(7.55491 - 13.0855i) q^{95} +(8.60437 - 5.36337i) q^{96} +(-2.19811 + 0.588981i) q^{97} +(-0.751420 + 0.201342i) q^{98} +(-4.36007 - 12.7542i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{6}+O(q^{10}) \) 112 * q - 12 * q^6	\( 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) \) 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Introduction

L-functions

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