LMFDB - Embedded newform 403.2.g.a.87.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(87,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("403.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.g (of order $3$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			87.11
Character	$\chi$	$=$	403.87
Dual form			403.2.g.a.315.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.770644 + 1.33479i) q^{2} +0.658984 q^{3} +(-0.187783 - 0.325250i) q^{4} +(-0.614094 + 1.06364i) q^{5} +(-0.507842 + 0.879608i) q^{6} +(-0.291650 + 0.505152i) q^{7} -2.50372 q^{8} -2.56574 q^{9} +O(q^{10})$	\(q+(-0.770644 + 1.33479i) q^{2} +0.658984 q^{3} +(-0.187783 - 0.325250i) q^{4} +(-0.614094 + 1.06364i) q^{5} +(-0.507842 + 0.879608i) q^{6} +(-0.291650 + 0.505152i) q^{7} -2.50372 q^{8} -2.56574 q^{9} +(-0.946495 - 1.63938i) q^{10} +(-1.06386 - 1.84267i) q^{11} +(-0.123746 - 0.214334i) q^{12} +(-2.05495 + 2.96263i) q^{13} +(-0.449516 - 0.778585i) q^{14} +(-0.404678 + 0.700923i) q^{15} +(2.30504 - 3.99245i) q^{16} +(0.814657 - 1.41103i) q^{17} +(1.97727 - 3.42473i) q^{18} +(-3.22086 + 5.57869i) q^{19} +0.461266 q^{20} +(-0.192193 + 0.332887i) q^{21} +3.27944 q^{22} +(-0.0727100 + 0.125937i) q^{23} -1.64991 q^{24} +(1.74578 + 3.02377i) q^{25} +(-2.37087 - 5.02606i) q^{26} -3.66773 q^{27} +0.219068 q^{28} +(1.56261 - 2.70652i) q^{29} +(-0.623725 - 1.08032i) q^{30} +(4.19465 + 3.66127i) q^{31} +(1.04901 + 1.81694i) q^{32} +(-0.701069 - 1.21429i) q^{33} +(1.25562 + 2.17480i) q^{34} +(-0.358201 - 0.620422i) q^{35} +(0.481802 + 0.834506i) q^{36} -10.1544 q^{37} +(-4.96427 - 8.59836i) q^{38} +(-1.35418 + 1.95233i) q^{39} +(1.53752 - 2.66306i) q^{40} +(-0.210039 - 0.363798i) q^{41} +(-0.296224 - 0.513075i) q^{42} +(0.113823 - 0.197148i) q^{43} +(-0.399551 + 0.692043i) q^{44} +(1.57561 - 2.72903i) q^{45} +(-0.112067 - 0.194106i) q^{46} +5.46942 q^{47} +(1.51899 - 2.63096i) q^{48} +(3.32988 + 5.76752i) q^{49} -5.38149 q^{50} +(0.536846 - 0.929844i) q^{51} +(1.34948 + 0.112039i) q^{52} +(0.615895 - 1.06676i) q^{53} +(2.82652 - 4.89567i) q^{54} +2.61325 q^{55} +(0.730209 - 1.26476i) q^{56} +(-2.12249 + 3.67627i) q^{57} +(2.40843 + 4.17153i) q^{58} +(1.83983 - 3.18668i) q^{59} +0.303967 q^{60} +(-2.45004 - 4.24359i) q^{61} +(-8.11962 + 2.77746i) q^{62} +(0.748298 - 1.29609i) q^{63} +5.98651 q^{64} +(-1.88925 - 4.00506i) q^{65} +2.16110 q^{66} +(0.939673 + 1.62756i) q^{67} -0.611915 q^{68} +(-0.0479148 + 0.0829908i) q^{69} +1.10418 q^{70} +2.64231 q^{71} +6.42389 q^{72} +(-1.40947 + 2.44127i) q^{73} +(7.82545 - 13.5541i) q^{74} +(1.15044 + 1.99262i) q^{75} +2.41929 q^{76} +1.24110 q^{77} +(-1.56237 - 3.31210i) q^{78} +(2.90930 + 5.03905i) q^{79} +(2.83102 + 4.90348i) q^{80} +5.28024 q^{81} +0.647460 q^{82} +(-7.89739 + 13.6787i) q^{83} +0.144362 q^{84} +(1.00055 + 1.73301i) q^{85} +(0.175435 + 0.303862i) q^{86} +(1.02974 - 1.78356i) q^{87} +(2.66362 + 4.61352i) q^{88} +(-8.66712 + 15.0119i) q^{89} +(2.42846 + 4.20622i) q^{90} +(-0.897256 - 1.90211i) q^{91} +0.0546148 q^{92} +(2.76421 + 2.41272i) q^{93} +(-4.21497 + 7.30055i) q^{94} +(-3.95582 - 6.85168i) q^{95} +(0.691282 + 1.19733i) q^{96} +(2.93445 + 5.08262i) q^{97} -10.2646 q^{98} +(2.72960 + 4.72780i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q - 2 q^{2} - 8 q^{3} - 34 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{8} + 58 q^{9}+O(q^{10}) $ 70 * q - 2 * q^2 - 8 * q^3 - 34 * q^4 - 2 * q^5 - 4 * q^7 - 6 * q^8 + 58 * q^9	\( 70 q - 2 q^{2} - 8 q^{3} - 34 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{8} + 58 q^{9} + 3 q^{10} + 2 q^{11} + 5 q^{12} + 4 q^{13} - 10 q^{14} + q^{15} - 28 q^{16} + 14 q^{17} - 20 q^{18} - 2 q^{19} - 50 q^{20} - 21 q^{21} - 8 q^{22} + 2 q^{23} - 8 q^{24} - 23 q^{25} + 6 q^{26} - 38 q^{27} + 42 q^{28} + 6 q^{29} + 31 q^{30} + 22 q^{31} + 14 q^{32} + 2 q^{33} - 11 q^{34} + 4 q^{35} - 28 q^{36} + 24 q^{37} - 7 q^{38} + 10 q^{39} - q^{40} - 2 q^{41} + 27 q^{42} - q^{43} + 2 q^{44} - 29 q^{45} + 14 q^{46} + q^{48} - 37 q^{49} - 14 q^{50} - 9 q^{51} - 19 q^{52} - 2 q^{53} + 24 q^{54} - 10 q^{55} - 13 q^{56} - q^{57} + 6 q^{58} + 21 q^{59} + 18 q^{60} - 3 q^{61} - 23 q^{62} - 32 q^{63} - 14 q^{64} + 23 q^{65} - 28 q^{66} - 2 q^{67} - 84 q^{68} + 32 q^{69} - 14 q^{70} - 86 q^{71} + 10 q^{72} + 11 q^{73} - 7 q^{74} + 37 q^{75} + 56 q^{76} - 10 q^{77} - 64 q^{78} + 2 q^{79} + 38 q^{80} + 22 q^{81} + 34 q^{82} + 56 q^{83} + 90 q^{84} - 5 q^{85} + 54 q^{86} - 24 q^{87} + 4 q^{88} + 30 q^{89} - 23 q^{90} - 36 q^{91} + 74 q^{92} + 19 q^{93} + 47 q^{94} - 9 q^{95} + 26 q^{96} + 29 q^{97} - 24 q^{98} + 3 q^{99}+O(q^{100}) \) 70 * q - 2 * q^2 - 8 * q^3 - 34 * q^4 - 2 * q^5 - 4 * q^7 - 6 * q^8 + 58 * q^9 + 3 * q^10 + 2 * q^11 + 5 * q^12 + 4 * q^13 - 10 * q^14 + q^15 - 28 * q^16 + 14 * q^17 - 20 * q^18 - 2 * q^19 - 50 * q^20 - 21 * q^21 - 8 * q^22 + 2 * q^23 - 8 * q^24 - 23 * q^25 + 6 * q^26 - 38 * q^27 + 42 * q^28 + 6 * q^29 + 31 * q^30 + 22 * q^31 + 14 * q^32 + 2 * q^33 - 11 * q^34 + 4 * q^35 - 28 * q^36 + 24 * q^37 - 7 * q^38 + 10 * q^39 - q^40 - 2 * q^41 + 27 * q^42 - q^43 + 2 * q^44 - 29 * q^45 + 14 * q^46 + q^48 - 37 * q^49 - 14 * q^50 - 9 * q^51 - 19 * q^52 - 2 * q^53 + 24 * q^54 - 10 * q^55 - 13 * q^56 - q^57 + 6 * q^58 + 21 * q^59 + 18 * q^60 - 3 * q^61 - 23 * q^62 - 32 * q^63 - 14 * q^64 + 23 * q^65 - 28 * q^66 - 2 * q^67 - 84 * q^68 + 32 * q^69 - 14 * q^70 - 86 * q^71 + 10 * q^72 + 11 * q^73 - 7 * q^74 + 37 * q^75 + 56 * q^76 - 10 * q^77 - 64 * q^78 + 2 * q^79 + 38 * q^80 + 22 * q^81 + 34 * q^82 + 56 * q^83 + 90 * q^84 - 5 * q^85 + 54 * q^86 - 24 * q^87 + 4 * q^88 + 30 * q^89 - 23 * q^90 - 36 * q^91 + 74 * q^92 + 19 * q^93 + 47 * q^94 - 9 * q^95 + 26 * q^96 + 29 * q^97 - 24 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.770644	+	1.33479i	−0.544927	+	0.943842i	0.453684	+	0.891163i	$0.350109\pi$
$2$	−0.770644	+	1.33479i	−0.544927	+	0.943842i	−0.998611	+	0.0526792i	$0.983224\pi$
$3$	0.658984			0.380465			0.190232	−	0.981739i	$-0.439076\pi$
$3$	0.658984			0.380465			0.190232	+	0.981739i	$0.439076\pi$
$4$	−0.187783	−	0.325250i	−0.0938915	−	0.162625i
$5$	−0.614094	+	1.06364i	−0.274631	+	0.475675i	−0.970042	−	0.242937i	$-0.921889\pi$
$5$	−0.614094	+	1.06364i	−0.274631	+	0.475675i	0.695411	+	0.718612i	$0.255222\pi$
$6$	−0.507842	+	0.879608i	−0.207326	+	0.359098i
$7$	−0.291650	+	0.505152i	−0.110233	+	0.190930i	−0.915864	−	0.401488i	$-0.868493\pi$
$7$	−0.291650	+	0.505152i	−0.110233	+	0.190930i	0.805631	+	0.592418i	$0.201826\pi$
$8$	−2.50372			−0.885198
$9$	−2.56574			−0.855247
$10$	−0.946495	−	1.63938i	−0.299308	−	0.518417i
$11$	−1.06386	−	1.84267i	−0.320767	−	0.555585i	0.659880	−	0.751371i	$-0.270607\pi$
$11$	−1.06386	−	1.84267i	−0.320767	−	0.555585i	−0.980646	+	0.195787i	$0.937274\pi$
$12$	−0.123746	−	0.214334i	−0.0357224	−	0.0618730i
$13$	−2.05495	+	2.96263i	−0.569940	+	0.821686i
$13$	−2.05495	+	2.96263i	−0.569940	+	0.821686i
$14$	−0.449516	−	0.778585i	−0.120138	−	0.208086i
$15$	−0.404678	+	0.700923i	−0.104487	+	0.180978i
$16$	2.30504	−	3.99245i	0.576260	−	0.998112i
$17$	0.814657	−	1.41103i	0.197583	−	0.342224i	−0.750161	−	0.661255i	$-0.770024\pi$
$17$	0.814657	−	1.41103i	0.197583	−	0.342224i	0.947744	+	0.319031i	$0.103357\pi$
$18$	1.97727	−	3.42473i	0.466047	−	0.807217i
$19$	−3.22086	+	5.57869i	−0.738915	+	1.27984i	0.214069	+	0.976819i	$0.431328\pi$
$19$	−3.22086	+	5.57869i	−0.738915	+	1.27984i	−0.952984	+	0.303020i	$0.902005\pi$
$20$	0.461266			0.103142
$21$	−0.192193	+	0.332887i	−0.0419399	+	0.0726420i
$22$	3.27944			0.699179
$23$	−0.0727100	+	0.125937i	−0.0151611	+	0.0262598i	−0.873506	−	0.486813i	$-0.838159\pi$
$23$	−0.0727100	+	0.125937i	−0.0151611	+	0.0262598i	0.858345	+	0.513072i	$0.171493\pi$
$24$	−1.64991			−0.336787
$25$	1.74578	+	3.02377i	0.349155	+	0.604755i
$26$	−2.37087	−	5.02606i	−0.464966	−	0.985692i
$27$	−3.66773			−0.705856
$28$	0.219068			0.0413999
$29$	1.56261	−	2.70652i	0.290170	−	0.502589i	−0.683680	−	0.729782i	$-0.739622\pi$
$29$	1.56261	−	2.70652i	0.290170	−	0.502589i	0.973850	+	0.227193i	$0.0729549\pi$
$30$	−0.623725	−	1.08032i	−0.113876	−	0.197239i
$31$	4.19465	+	3.66127i	0.753381	+	0.657584i
$31$	4.19465	+	3.66127i	0.753381	+	0.657584i
$32$	1.04901	+	1.81694i	0.185441	+	0.321193i
$33$	−0.701069	−	1.21429i	−0.122041	−	0.211380i
$34$	1.25562	+	2.17480i	0.215337	+	0.372975i
$35$	−0.358201	−	0.620422i	−0.0605470	−	0.104870i
$36$	0.481802	+	0.834506i	0.0803004	+	0.139084i
$37$	−10.1544			−1.66938			−0.834689	−	0.550721i	$-0.814353\pi$
$37$	−10.1544			−1.66938			−0.834689	+	0.550721i	$0.814353\pi$
$38$	−4.96427	−	8.59836i	−0.805310	−	1.39484i
$39$	−1.35418	+	1.95233i	−0.216842	+	0.312623i
$40$	1.53752	−	2.66306i	0.243103	−	0.421067i
$41$	−0.210039	−	0.363798i	−0.0328025	−	0.0568157i	0.849158	−	0.528139i	$-0.177110\pi$
$41$	−0.210039	−	0.363798i	−0.0328025	−	0.0568157i	−0.881961	+	0.471323i	$0.843777\pi$
$42$	−0.296224	−	0.513075i	−0.0457084	−	0.0791692i
$43$	0.113823	−	0.197148i	0.0173579	−	0.0300648i	−0.857216	−	0.514957i	$-0.827808\pi$
$43$	0.113823	−	0.197148i	0.0173579	−	0.0300648i	0.874574	+	0.484892i	$0.161141\pi$
$44$	−0.399551	+	0.692043i	−0.0602346	+	0.104329i
$45$	1.57561	−	2.72903i	0.234877	−	0.406820i
$46$	−0.112067	−	0.194106i	−0.0165234	−	0.0286193i
$47$	5.46942			0.797797			0.398898	−	0.916995i	$-0.369393\pi$
$47$	5.46942			0.797797			0.398898	+	0.916995i	$0.369393\pi$
$48$	1.51899	−	2.63096i	0.219247	−	0.379746i
$49$	3.32988	+	5.76752i	0.475697	+	0.823932i
$50$	−5.38149			−0.761057
$51$	0.536846	−	0.929844i	0.0751735	−	0.130204i
$52$	1.34948	+	0.112039i	0.187139	+	0.0155370i
$53$	0.615895	−	1.06676i	0.0845997	−	0.146531i	−0.820621	−	0.571473i	$-0.806372\pi$
$53$	0.615895	−	1.06676i	0.0845997	−	0.146531i	0.905221	+	0.424942i	$0.139706\pi$
$54$	2.82652	−	4.89567i	0.384640	−	0.666216i
$55$	2.61325			0.352371
$56$	0.730209	−	1.26476i	0.0975783	−	0.169011i
$57$	−2.12249	+	3.67627i	−0.281131	+	0.486933i
$58$	2.40843	+	4.17153i	0.316243	+	0.547749i
$59$	1.83983	−	3.18668i	0.239525	−	0.414870i	−0.721053	−	0.692880i	$-0.756342\pi$
$59$	1.83983	−	3.18668i	0.239525	−	0.414870i	0.960578	+	0.278010i	$0.0896749\pi$
$60$	0.303967			0.0392420
$61$	−2.45004	−	4.24359i	−0.313695	−	0.543336i	0.665464	−	0.746430i	$-0.268234\pi$
$61$	−2.45004	−	4.24359i	−0.313695	−	0.543336i	−0.979159	+	0.203094i	$0.934900\pi$
$62$	−8.11962	+	2.77746i	−1.03119	+	0.352737i
$63$	0.748298	−	1.29609i	0.0942766	−	0.163292i
$64$	5.98651			0.748314
$65$	−1.88925	−	4.00506i	−0.234333	−	0.496767i
$66$	2.16110			0.266013
$67$	0.939673	+	1.62756i	0.114799	+	0.198838i	0.917700	−	0.397275i	$-0.130044\pi$
$67$	0.939673	+	1.62756i	0.114799	+	0.198838i	−0.802900	+	0.596113i	$0.796711\pi$
$68$	−0.611915			−0.0742056
$69$	−0.0479148	+	0.0829908i	−0.00576826	+	0.00999092i
$70$	1.10418			0.131975
$71$	2.64231			0.313585			0.156793	−	0.987632i	$-0.449885\pi$
$71$	2.64231			0.313585			0.156793	+	0.987632i	$0.449885\pi$
$72$	6.42389			0.757063
$73$	−1.40947	+	2.44127i	−0.164966	+	0.285729i	−0.936643	−	0.350285i	$-0.886085\pi$
$73$	−1.40947	+	2.44127i	−0.164966	+	0.285729i	0.771677	+	0.636014i	$0.219418\pi$
$74$	7.82545	−	13.5541i	0.909690	−	1.57563i
$75$	1.15044	+	1.99262i	0.132841	+	0.230088i
$76$	2.41929			0.277511
$77$	1.24110			0.141437
$78$	−1.56237	−	3.31210i	−0.176903	−	0.375021i
$79$	2.90930	+	5.03905i	0.327321	+	0.566937i	0.981979	−	0.188988i	$-0.0605207\pi$
$79$	2.90930	+	5.03905i	0.327321	+	0.566937i	−0.654658	+	0.755925i	$0.727187\pi$
$80$	2.83102	+	4.90348i	0.316518	+	0.548225i
$81$	5.28024			0.586693
$82$	0.647460			0.0715000
$83$	−7.89739	+	13.6787i	−0.866851	+	1.50143i	−0.00165351	+	0.999999i	$0.500526\pi$
$83$	−7.89739	+	13.6787i	−0.866851	+	1.50143i	−0.865197	+	0.501431i	$0.832807\pi$
$84$	0.144362			0.0157512
$85$	1.00055	+	1.73301i	0.108525	+	0.187971i
$86$	0.175435	+	0.303862i	0.0189176	+	0.0327663i
$87$	1.02974	−	1.78356i	0.110399	−	0.191217i
$88$	2.66362	+	4.61352i	0.283942	+	0.491803i
$89$	−8.66712	+	15.0119i	−0.918713	+	1.59126i	−0.117341	+	0.993092i	$0.537437\pi$
$89$	−8.66712	+	15.0119i	−0.918713	+	1.59126i	−0.801372	+	0.598166i	$0.795896\pi$
$90$	2.42846	+	4.20622i	0.255982	+	0.443374i
$91$	−0.897256	−	1.90211i	−0.0940580	−	0.199396i
$92$	0.0546148			0.00569399
$93$	2.76421	+	2.41272i	0.286635	+	0.250187i
$94$	−4.21497	+	7.30055i	−0.434741	+	0.752994i
$95$	−3.95582	−	6.85168i	−0.405858	−	0.702967i
$96$	0.691282	+	1.19733i	0.0705536	+	0.122202i
$97$	2.93445	+	5.08262i	0.297949	+	0.516062i	0.975666	−	0.219260i	$-0.0703643\pi$
$97$	2.93445	+	5.08262i	0.297949	+	0.516062i	−0.677718	+	0.735322i	$0.737031\pi$
$98$	−10.2646			−1.03688
$99$	2.72960	+	4.72780i	0.274335	+	0.475162i
$100$	0.655654	−	1.13563i	0.0655654	−	0.113563i
$101$	−0.106315	+	0.184143i	−0.0105787	+	0.0183229i	−0.871266	−	0.490811i	$-0.836701\pi$
$101$	−0.106315	+	0.184143i	−0.0105787	+	0.0183229i	0.860688	+	0.509133i	$0.170034\pi$
$102$	0.827434	+	1.43316i	0.0819281	+	0.141904i
$103$	−6.42073	+	11.1210i	−0.632653	+	1.09579i	0.354354	+	0.935111i	$0.384701\pi$
$103$	−6.42073	+	11.1210i	−0.632653	+	1.09579i	−0.987007	+	0.160676i	$0.948633\pi$
$104$	5.14501	−	7.41760i	0.504510	−	0.727356i
$105$	−0.236049	−	0.408848i	−0.0230360	−	0.0398995i
$106$	0.949271	+	1.64419i	0.0922013	+	0.159697i
$107$	16.5102			1.59611			0.798053	−	0.602588i	$-0.205864\pi$
$107$	16.5102			1.59611			0.798053	+	0.602588i	$0.205864\pi$
$108$	0.688738	+	1.19293i	0.0662739	+	0.114790i
$109$	18.7165			1.79272			0.896358	−	0.443332i	$-0.146204\pi$
$109$	18.7165			1.79272			0.896358	+	0.443332i	$0.146204\pi$
$110$	−2.01388	+	3.48815i	−0.192016	+	0.332582i
$111$	−6.69161			−0.635140
$112$	1.34453	+	2.32879i	0.127046	+	0.220050i
$113$	4.61352			0.434003			0.217002	−	0.976171i	$-0.430372\pi$
$113$	4.61352			0.434003			0.217002	+	0.976171i	$0.430372\pi$
$114$	−3.27137	−	5.66618i	−0.306392	−	0.530687i
$115$	−0.0893016	−	0.154675i	−0.00832742	−	0.0144235i
$116$	−1.17373			−0.108978
$117$	5.27246	−	7.60134i	0.487439	−	0.702745i
$118$	2.83570	+	4.91158i	0.261048	+	0.452148i
$119$	0.475189	+	0.823051i	0.0435605	+	0.0754490i
$120$	1.01320	−	1.75492i	0.0924922	−	0.160201i
$121$	3.23639	−	5.60559i	0.294217	−	0.509599i
$122$	7.55242			0.683764
$123$	−0.138412	−	0.239737i	−0.0124802	−	0.0216164i
$124$	0.403144	−	2.05183i	0.0362034	−	0.184260i
$125$	−10.4292			−0.932818
$126$	1.15334	+	1.99765i	0.102748	+	0.177964i
$127$	−14.7986			−1.31316			−0.656582	−	0.754255i	$-0.727998\pi$
$127$	−14.7986			−1.31316			−0.656582	+	0.754255i	$0.727998\pi$
$128$	−6.71149	+	11.6246i	−0.593217	+	1.02748i
$129$	0.0750079	−	0.129917i	0.00660408	−	0.0114386i
$130$	6.80187	+	0.564717i	0.596564	+	0.0495290i
$131$	−2.89935	−	5.02182i	−0.253317	−	0.438758i	0.711120	−	0.703071i	$-0.248188\pi$
$131$	−2.89935	−	5.02182i	−0.253317	−	0.438758i	−0.964437	+	0.264312i	$0.914855\pi$
$132$	−0.263298	+	0.456045i	−0.0229171	+	0.0396936i
$133$	−1.87872	−	3.25405i	−0.162906	−	0.282162i
$134$	−2.89661			−0.250229
$135$	2.25233	−	3.90116i	0.193850	−	0.335758i
$136$	−2.03967	+	3.53281i	−0.174900	+	0.302936i
$137$	15.3431			1.31085			0.655424	−	0.755261i	$-0.272490\pi$
$137$	15.3431			1.31085			0.655424	+	0.755261i	$0.272490\pi$
$138$	−0.0738504	−	0.127913i	−0.00628656	−	0.0108886i
$139$	−1.77751	−	3.07874i	−0.150766	−	0.261135i	0.780743	−	0.624852i	$-0.214841\pi$
$139$	−1.77751	−	3.07874i	−0.150766	−	0.261135i	−0.931509	+	0.363717i	$0.881507\pi$
$140$	−0.134528	+	0.233009i	−0.0113697	+	0.0196929i
$141$	3.60426			0.303534
$142$	−2.03628	+	3.52694i	−0.170881	+	0.295975i
$143$	7.64533	+	0.634744i	0.639334	+	0.0530800i
$144$	−5.91414	+	10.2436i	−0.492845	+	0.853632i
$145$	1.91918	+	3.32412i	0.159379	+	0.276053i
$146$	−2.17240	−	3.76270i	−0.179789	−	0.311403i
$147$	2.19434	+	3.80071i	0.180986	+	0.313477i
$148$	1.90683	+	3.30273i	0.156740	+	0.271482i
$149$	2.07784	−	3.59893i	0.170224	−	0.294836i	−0.768274	−	0.640121i	$-0.778884\pi$
$149$	2.07784	−	3.59893i	0.170224	−	0.294836i	0.938498	+	0.345285i	$0.112218\pi$
$150$	−3.54631			−0.289555
$151$	−0.226079			−0.0183981			−0.00919904	−	0.999958i	$-0.502928\pi$
$151$	−0.226079			−0.0183981			−0.00919904	+	0.999958i	$0.502928\pi$
$152$	8.06412	−	13.9675i	0.654087	−	1.13291i
$153$	−2.09020	+	3.62033i	−0.168982	+	0.292686i
$154$	−0.956448	+	1.65662i	−0.0770728	+	0.133494i
$155$	−6.47019	+	2.21324i	−0.519698	+	0.177772i
$156$	0.889286	+	0.0738319i	0.0711998	+	0.00591128i
$157$	17.1033			1.36499			0.682494	−	0.730891i	$-0.260895\pi$
$157$	17.1033			1.36499			0.682494	+	0.730891i	$0.260895\pi$
$158$	−8.96812			−0.713465
$159$	0.405865	−	0.702979i	0.0321872	−	0.0557498i
$160$	−2.57677			−0.203711
$161$	−0.0424117	−	0.0734593i	−0.00334251	−	0.00578940i
$162$	−4.06918	+	7.04803i	−0.319705	+	0.553746i
$163$	5.05236	+	8.75094i	0.395731	+	0.685427i	0.993194	−	0.116470i	$-0.0371578\pi$
$163$	5.05236	+	8.75094i	0.395731	+	0.685427i	−0.597463	+	0.801897i	$0.703824\pi$
$164$	−0.0788834	+	0.136630i	−0.00615976	+	0.0106690i
$165$	1.72209			0.134065
$166$	−12.1721	−	21.0828i	−0.944742	−	1.63634i
$167$	−21.1510			−1.63671			−0.818356	−	0.574712i	$-0.805114\pi$
$167$	−21.1510			−1.63671			−0.818356	+	0.574712i	$0.805114\pi$
$168$	0.481196	−	0.833456i	0.0371251	−	0.0643026i
$169$	−4.55438	−	12.1761i	−0.350337	−	0.936624i
$170$	−3.08427			−0.236553
$171$	8.26388	−	14.3135i	0.631955	−	1.09458i
$172$	−0.0854965			−0.00651905
$173$	−3.40740			−0.259060			−0.129530	−	0.991576i	$-0.541347\pi$
$173$	−3.40740			−0.259060			−0.129530	+	0.991576i	$0.541347\pi$
$174$	1.58712	+	2.74897i	0.120319	+	0.208399i
$175$	−2.03662			−0.153954
$176$	−9.80900			−0.739381
$177$	1.21242	−	2.09997i	0.0911309	−	0.157843i
$178$	−13.3585	−	23.1376i	−1.00126	−	1.73424i
$179$	−19.6735			−1.47046			−0.735232	−	0.677815i	$-0.762927\pi$
$179$	−19.6735			−1.47046			−0.735232	+	0.677815i	$0.762927\pi$
$180$	−1.18349			−0.0882120
$181$	9.47092	−	16.4041i	0.703968	−	1.21931i	−0.263094	−	0.964770i	$-0.584743\pi$
$181$	9.47092	−	16.4041i	0.703968	−	1.21931i	0.967063	−	0.254539i	$-0.0819236\pi$
$182$	3.23039	+	0.268199i	0.239453	+	0.0198803i
$183$	−1.61454	−	2.79646i	−0.119350	−	0.206720i
$184$	0.182045	−	0.315312i	0.0134206	−	0.0232451i
$185$	6.23578	−	10.8007i	0.458464	−	0.794082i
$186$	−5.35070	+	1.83030i	−0.392333	+	0.134204i
$187$	−3.46673			−0.253513
$188$	−1.02706	−	1.77893i	−0.0749064	−	0.129742i
$189$	1.06969	−	1.85276i	0.0778088	−	0.134769i
$190$	12.1941			0.884653
$191$	−10.6409			−0.769946			−0.384973	−	0.922928i	$-0.625789\pi$
$191$	−10.6409			−0.769946			−0.384973	+	0.922928i	$0.625789\pi$
$192$	3.94502			0.284707
$193$	−17.4913			−1.25905			−0.629527	−	0.776978i	$-0.716751\pi$
$193$	−17.4913			−1.25905			−0.629527	+	0.776978i	$0.716751\pi$
$194$	−9.04567			−0.649441
$195$	−1.24499	−	2.63927i	−0.0891553	−	0.189002i
$196$	1.25059	−	2.16609i	0.0893279	−	0.154720i
$197$	−9.86434	−	17.0855i	−0.702805	−	1.21729i	−0.967478	−	0.252956i	$-0.918597\pi$
$197$	−9.86434	−	17.0855i	−0.702805	−	1.21729i	0.264673	−	0.964338i	$-0.414736\pi$
$198$	−8.41419			−0.597970
$199$	14.0400			0.995270			0.497635	−	0.867387i	$-0.334202\pi$
$199$	14.0400			0.995270			0.497635	+	0.867387i	$0.334202\pi$
$200$	−4.37094	−	7.57068i	−0.309072	−	0.535328i
$201$	0.619230	+	1.07254i	0.0436771	+	0.0756509i
$202$	−0.163862	−	0.283816i	−0.0115293	−	0.0199693i
$203$	0.911471	+	1.57871i	0.0639727	+	0.110804i
$204$	−0.403242			−0.0282326
$205$	0.515934			0.0360344
$206$	−9.89619	−	17.1407i	−0.689500	−	1.19425i
$207$	0.186555	−	0.323123i	0.0129665	−	0.0224586i
$208$	7.09142	+	15.0333i	0.491701	+	1.04237i
$209$	13.7062			0.948078
$210$	0.727638			0.0502118
$211$	1.95563			0.134631			0.0673157	−	0.997732i	$-0.478557\pi$
$211$	1.95563			0.134631			0.0673157	+	0.997732i	$0.478557\pi$
$212$	−0.462618			−0.0317728
$213$	1.74124			0.119308
$214$	−12.7235	+	22.0378i	−0.869761	+	1.50647i
$215$	0.139797	+	0.242135i	0.00953405	+	0.0165135i
$216$	9.18298			0.624822
$217$	−3.07287	+	1.05113i	−0.208600	+	0.0713552i
$218$	−14.4237	+	24.9827i	−0.976899	+	1.69204i
$219$	−0.928818	+	1.60876i	−0.0627637	+	0.108710i
$220$	−0.490724	−	0.849959i	−0.0330846	−	0.0573042i
$221$	2.50628	+	5.31311i	0.168590	+	0.357399i
$222$	5.15685	−	8.93192i	0.346105	−	0.599471i
$223$	−0.641900			−0.0429848			−0.0214924	−	0.999769i	$-0.506842\pi$
$223$	−0.641900			−0.0429848			−0.0214924	+	0.999769i	$0.506842\pi$
$224$	−1.22378			−0.0817669
$225$	−4.47921	−	7.75822i	−0.298614	−	0.517215i
$226$	−3.55538	+	6.15810i	−0.236500	+	0.409630i
$227$	−14.2769			−0.947589			−0.473795	−	0.880635i	$-0.657116\pi$
$227$	−14.2769			−0.947589			−0.473795	+	0.880635i	$0.657116\pi$
$228$	1.59427			0.105583
$229$	−2.56212	−	4.43771i	−0.169309	−	0.293252i	0.768868	−	0.639408i	$-0.220820\pi$
$229$	−2.56212	−	4.43771i	−0.169309	−	0.293252i	−0.938177	+	0.346155i	$0.887487\pi$
$230$	0.275279			0.0181513
$231$	0.817867			0.0538117
$232$	−3.91234	+	6.77638i	−0.256858	+	0.444891i
$233$	−2.85458			−0.187010			−0.0935050	−	0.995619i	$-0.529807\pi$
$233$	−2.85458			−0.187010			−0.0935050	+	0.995619i	$0.529807\pi$
$234$	6.08304	+	12.8956i	0.397661	+	0.843010i
$235$	−3.35874	+	5.81751i	−0.219100	+	0.379492i
$236$	−1.38195			−0.0899575
$237$	1.91718	+	3.32065i	0.124534	+	0.215700i
$238$	−1.46481			−0.0949492
$239$	3.03864	−	5.26308i	0.196553	−	0.340440i	−0.750855	−	0.660467i	$-0.770358\pi$
$239$	3.03864	−	5.26308i	0.196553	−	0.340440i	0.947409	+	0.320026i	$0.103692\pi$
$240$	1.86560	+	3.23131i	0.120424	+	0.208580i
$241$	9.40815	−	16.2954i	0.606032	−	1.04968i	−0.385856	−	0.922559i	$-0.626094\pi$
$241$	9.40815	−	16.2954i	0.606032	−	1.04968i	0.991887	−	0.127119i	$-0.0405730\pi$
$242$	4.98820	+	8.63982i	0.320654	+	0.555389i
$243$	14.4828			0.929072
$244$	−0.920150	+	1.59375i	−0.0589066	+	0.102029i
$245$	−8.17944			−0.522565
$246$	0.426666			0.0272032
$247$	−9.90891	−	21.0061i	−0.630489	−	1.33659i
$248$	−10.5022	−	9.16680i	−0.666892	−	0.582092i
$249$	−5.20425	+	9.01403i	−0.329806	+	0.571241i
$250$	8.03722	−	13.9209i	0.508318	−	0.880433i
$251$	−6.17477	+	10.6950i	−0.389748	+	0.675063i	−0.992415	−	0.122929i	$-0.960771\pi$
$251$	−6.17477	+	10.6950i	−0.389748	+	0.675063i	0.602668	+	0.797992i	$0.294104\pi$
$252$	−0.562070			−0.0354071
$253$	0.309414			0.0194527
$254$	11.4044	−	19.7531i	0.715578	−	1.23942i
$255$	0.659348	+	1.14202i	0.0412900	+	0.0715163i
$256$	−4.35782	−	7.54796i	−0.272364	−	0.471748i
$257$	4.91245	+	8.50861i	0.306430	+	0.530752i	0.977579	−	0.210570i	$-0.0675321\pi$
$257$	4.91245	+	8.50861i	0.306430	+	0.530752i	−0.671149	+	0.741323i	$0.734199\pi$
$258$	0.115609	+	0.200240i	0.00719748	+	0.0124664i
$259$	2.96154	−	5.12954i	0.184021	−	0.318734i
$260$	−0.947877	+	1.36656i	−0.0587848	+	0.0847505i
$261$	−4.00926	+	6.94424i	−0.248167	+	0.429838i
$262$	8.93746			0.552158
$263$	−10.9939	+	19.0420i	−0.677912	+	1.17418i	0.297697	+	0.954660i	$0.403782\pi$
$263$	−10.9939	+	19.0420i	−0.677912	+	1.17418i	−0.975609	+	0.219517i	$0.929552\pi$
$264$	1.75528	+	3.04024i	0.108030	+	0.187114i
$265$	0.756435	+	1.31018i	0.0464674	+	0.0804839i
$266$	5.79131			0.355088
$267$	−5.71150	+	9.89260i	−0.349538	+	0.605417i
$268$	0.352909	−	0.611257i	0.0215574	−	0.0373385i
$269$	−5.70090			−0.347590			−0.173795	−	0.984782i	$-0.555603\pi$
$269$	−5.70090			−0.347590			−0.173795	+	0.984782i	$0.555603\pi$
$270$	3.47149	+	6.01280i	0.211268	+	0.365928i
$271$	7.25778	−	12.5708i	0.440878	−	0.763624i	−0.556876	−	0.830595i	$-0.688000\pi$
$271$	7.25778	−	12.5708i	0.440878	−	0.763624i	0.997755	+	0.0669715i	$0.0213336\pi$
$272$	−3.75563	−	6.50495i	−0.227719	−	0.394420i
$273$	−0.591277	−	1.25346i	−0.0357857	−	0.0758630i
$274$	−11.8241	+	20.4799i	−0.714317	+	1.23723i
$275$	3.71454	−	6.43377i	0.223995	−	0.387971i
$276$	0.0359903			0.00216636
$277$	−2.16714	−	3.75360i	−0.130211	−	0.225532i	0.793547	−	0.608509i	$-0.208232\pi$
$277$	−2.16714	−	3.75360i	−0.130211	−	0.225532i	−0.923758	+	0.382977i	$0.874899\pi$
$278$	5.47930			0.328627
$279$	−10.7624	−	9.39387i	−0.644327	−	0.562396i
$280$	0.896834	+	1.55336i	0.0535961	+	0.0928312i
$281$	29.8617			1.78140			0.890700	−	0.454592i	$-0.150215\pi$
$281$	29.8617			1.78140			0.890700	+	0.454592i	$0.150215\pi$
$282$	−2.77760	+	4.81095i	−0.165404	+	0.286488i
$283$	4.34274	−	7.52185i	0.258149	−	0.447127i	−0.707597	−	0.706616i	$-0.750221\pi$
$283$	4.34274	−	7.52185i	0.258149	−	0.447127i	0.965746	+	0.259489i	$0.0835541\pi$
$284$	−0.496182	−	0.859412i	−0.0294430	−	0.0509967i
$285$	−2.60682	−	4.51515i	−0.154415	−	0.267454i
$286$	−6.73907	+	9.71577i	−0.398490	+	0.574506i
$287$	0.245031			0.0144637
$288$	−2.69149	−	4.66180i	−0.158598	−	0.274699i
$289$	7.17267	+	12.4234i	0.421922	+	0.730790i
$290$	−5.91602			−0.347401
$291$	1.93376	+	3.34937i	0.113359	+	0.196343i
$292$	1.05870			0.0619556
$293$	−3.40121	+	5.89106i	−0.198701	+	0.344160i	−0.948107	−	0.317950i	$-0.897005\pi$
$293$	−3.40121	+	5.89106i	−0.198701	+	0.344160i	0.749407	+	0.662110i	$0.230339\pi$
$294$	−6.76421			−0.394497
$295$	2.25965	+	3.91384i	0.131562	+	0.227872i
$296$	25.4239			1.47773
$297$	3.90197	+	6.75841i	0.226415	+	0.392163i
$298$	3.20255	+	5.54699i	0.185519	+	0.321328i
$299$	−0.223691	−	0.474208i	−0.0129364	−	0.0274242i
$300$	0.432066	−	0.748360i	0.0249453	−	0.0432066i
$301$	0.0663932	+	0.114996i	0.00382684	+	0.00662828i
$302$	0.174227	−	0.301769i	0.0100256	−	0.0173649i
$303$	−0.0700597	+	0.121347i	−0.00402483	+	0.00697120i
$304$	14.8484	+	25.7182i	0.851615	+	1.47504i
$305$	6.01821			0.344602
$306$	−3.22159	−	5.57996i	−0.184166	−	0.318985i
$307$	15.5831	+	26.9907i	0.889374	+	1.54044i	0.840617	+	0.541629i	$0.182192\pi$
$307$	15.5831	+	26.9907i	0.889374	+	1.54044i	0.0487562	+	0.998811i	$0.484474\pi$
$308$	−0.233058	−	0.403668i	−0.0132797	−	0.0230011i
$309$	−4.23116	+	7.32858i	−0.240702	+	0.416908i
$310$	2.03199	−	10.3420i	0.115409	−	0.587386i
$311$	1.98236			0.112410			0.0562048	−	0.998419i	$-0.482100\pi$
$311$	1.98236			0.112410			0.0562048	+	0.998419i	$0.482100\pi$
$312$	3.39048	−	4.88808i	0.191948	−	0.276733i
$313$	−5.24119	−	9.07800i	−0.296249	−	0.513119i	0.679025	−	0.734115i	$-0.262403\pi$
$313$	−5.24119	−	9.07800i	−0.296249	−	0.513119i	−0.975275	+	0.220996i	$0.929069\pi$
$314$	−13.1805	+	22.8293i	−0.743820	+	1.28833i
$315$	0.919050	+	1.59184i	0.0517826	+	0.0896901i
$316$	1.09263	−	1.89250i	0.0614654	−	0.106461i
$317$	−15.1197	−	26.1881i	−0.849208	−	1.47087i	−0.881916	−	0.471406i	$-0.843747\pi$
$317$	−15.1197	−	26.1881i	−0.849208	−	1.47087i	0.0327089	−	0.999465i	$-0.489587\pi$
$318$	0.625555	+	1.08349i	0.0350794	+	0.0607592i
$319$	−6.64963			−0.372308
$320$	−3.67628	+	6.36750i	−0.205510	+	0.355954i
$321$	10.8800			0.607262
$322$	0.130737			0.00728571
$323$	5.24779	+	9.08943i	0.291995	+	0.505749i
$324$	−0.991539	−	1.71740i	−0.0550855	−	0.0954109i
$325$	−12.5458	−	1.04160i	−0.695916	−	0.0577776i
$326$	−15.5743			−0.862579
$327$	12.3339			0.682065
$328$	0.525878	+	0.910847i	0.0290367	+	0.0502931i
$329$	−1.59516	+	2.76289i	−0.0879438	+	0.152323i
$330$	−1.32712	+	2.29864i	−0.0730554	+	0.126536i
$331$	6.36862			0.350051			0.175026	−	0.984564i	$-0.443999\pi$
$331$	6.36862			0.350051			0.175026	+	0.984564i	$0.443999\pi$
$332$	5.93198			0.325560
$333$	26.0536			1.42773
$334$	16.2999	−	28.2322i	0.891889	−	1.54480i
$335$	−2.30819			−0.126110
$336$	0.886024	+	1.53464i	0.0483366	+	0.0837214i
$337$	−27.0380			−1.47286			−0.736428	−	0.676516i	$-0.763489\pi$
$337$	−27.0380			−1.47286			−0.736428	+	0.676516i	$0.763489\pi$
$338$	19.7624	+	3.30427i	1.07493	+	0.179729i
$339$	3.04024			0.165123
$340$	0.375773	−	0.650858i	0.0203792	−	0.0352977i
$341$	2.28396	−	11.6244i	0.123684	−	0.629498i
$342$	12.7370	+	22.0612i	0.688739	+	1.19293i
$343$	−7.96773			−0.430217
$344$	−0.284982	+	0.493603i	−0.0153652	+	0.0266133i
$345$	−0.0588483	−	0.101928i	−0.00316829	−	0.00548764i
$346$	2.62589	−	4.54817i	0.141169	−	0.244511i
$347$	−13.5057	+	23.3925i	−0.725023	+	1.25578i	0.233942	+	0.972251i	$0.424838\pi$
$347$	−13.5057	+	23.3925i	−0.725023	+	1.25578i	−0.958965	+	0.283526i	$0.908496\pi$
$348$	−0.773468			−0.0414623
$349$	−9.56795	+	16.5722i	−0.512161	+	0.887089i	0.487740	+	0.872989i	$0.337822\pi$
$349$	−9.56795	+	16.5722i	−0.512161	+	0.887089i	−0.999901	+	0.0140995i	$0.995512\pi$
$350$	1.56951	−	2.71847i	0.0838938	−	0.145308i
$351$	7.53700	−	10.8661i	0.402295	−	0.579992i
$352$	2.23201	−	3.86595i	0.118967	−	0.206056i
$353$	25.7704			1.37162			0.685811	−	0.727780i	$-0.259448\pi$
$353$	25.7704			1.37162			0.685811	+	0.727780i	$0.259448\pi$
$354$	1.86868	+	3.23665i	0.0993194	+	0.172026i
$355$	−1.62263	+	2.81048i	−0.0861202	+	0.149165i
$356$	6.51015			0.345037
$357$	0.313142	+	0.542378i	0.0165732	+	0.0287057i
$358$	15.1612	−	26.2600i	0.801296	−	1.38789i
$359$	−6.50919	+	11.2742i	−0.343542	+	0.595032i	−0.985088	−	0.172053i	$-0.944960\pi$
$359$	−6.50919	+	11.2742i	−0.343542	+	0.595032i	0.641546	+	0.767085i	$0.278293\pi$
$360$	−3.94487	+	6.83272i	−0.207913	+	0.360116i
$361$	−11.2478	−	19.4818i	−0.591992	−	1.02536i
$362$	14.5974	+	25.2835i	0.767223	+	1.32887i
$363$	2.13273	−	3.69399i	0.111939	−	0.193884i
$364$	−0.450172	+	0.649017i	−0.0235954	+	0.0340177i
$365$	−1.73109	−	2.99834i	−0.0906095	−	0.156940i
$366$	4.97692			0.260148
$367$	9.63637	+	16.6907i	0.503014	+	0.871246i	0.999994	+	0.00348410i	$0.00110902\pi$
$367$	9.63637	+	16.6907i	0.503014	+	0.871246i	−0.496980	+	0.867762i	$0.665558\pi$
$368$	0.335199	+	0.580582i	0.0174735	+	0.0302649i
$369$	0.538905	+	0.933410i	0.0280543	+	0.0485914i
$370$	9.61112	+	16.6470i	0.499659	+	0.865434i
$371$	0.359251	+	0.622241i	0.0186514	+	0.0323052i
$372$	0.265665	−	1.35213i	0.0137741	−	0.0701045i
$373$	0.157671	+	0.273094i	0.00816390	+	0.0141403i	0.870078	−	0.492913i	$-0.164068\pi$
$373$	0.157671	+	0.273094i	0.00816390	+	0.0141403i	−0.861915	+	0.507053i	$0.830735\pi$
$374$	2.67162	−	4.62738i	0.138146	−	0.239276i
$375$	−6.87269			−0.354904
$376$	−13.6939			−0.706209
$377$	4.80735	+	10.1912i	0.247591	+	0.524874i
$378$	1.64871	+	2.85564i	0.0848003	+	0.146878i
$379$	−21.3570			−1.09704			−0.548518	−	0.836139i	$-0.684808\pi$
$379$	−21.3570			−1.09704			−0.548518	+	0.836139i	$0.684808\pi$
$380$	−1.48567	+	2.57326i	−0.0762133	+	0.132005i
$381$	−9.75204			−0.499612
$382$	8.20031	−	14.2034i	0.419565	−	0.726707i
$383$	−14.3921			−0.735401			−0.367700	−	0.929944i	$-0.619855\pi$
$383$	−14.3921			−0.735401			−0.367700	+	0.929944i	$0.619855\pi$
$384$	−4.42276	+	7.66045i	−0.225698	+	0.390921i
$385$	−0.762154	+	1.32009i	−0.0388430	+	0.0672780i
$386$	13.4796	−	23.3473i	0.686093	−	1.18835i
$387$	−0.292041	+	0.505831i	−0.0148453	+	0.0257128i
$388$	1.10208	−	1.90886i	0.0559497	−	0.0969077i
$389$	2.63938	+	4.57153i	0.133822	+	0.231786i	0.925147	−	0.379610i	$-0.123942\pi$
$389$	2.63938	+	4.57153i	0.133822	+	0.231786i	−0.791325	+	0.611396i	$0.790608\pi$
$390$	4.48233	+	0.372140i	0.226971	+	0.0188440i
$391$	0.118467	+	0.205192i	0.00599115	+	0.0103770i
$392$	−8.33709	−	14.4403i	−0.421086	−	0.729343i
$393$	−1.91062	−	3.30930i	−0.0963783	−	0.166932i
$394$	30.4076			1.53191
$395$	−7.14633			−0.359571
$396$	1.02514	−	1.77560i	0.0515154	−	0.0892273i
$397$	8.29688	−	14.3706i	0.416409	−	0.721241i	−0.579167	−	0.815209i	$-0.696622\pi$
$397$	8.29688	−	14.3706i	0.416409	−	0.721241i	0.995575	+	0.0939683i	$0.0299552\pi$
$398$	−10.8198	+	18.7405i	−0.542350	+	0.939377i
$399$	−1.23805	−	2.14437i	−0.0619800	−	0.107353i
$400$	16.0963			0.804817
$401$	16.4834	−	28.5501i	0.823142	−	1.42572i	−0.0801892	−	0.996780i	$-0.525552\pi$
$401$	16.4834	−	28.5501i	0.823142	−	1.42572i	0.903331	−	0.428944i	$-0.141114\pi$
$402$	−1.90882			−0.0952034
$403$	−19.4668	+	4.90349i	−0.969710	+	0.244260i
$404$	0.0798564			0.00397300
$405$	−3.24256	+	5.61629i	−0.161124	+	0.279076i
$406$	−2.80968			−0.139442
$407$	10.8029	+	18.7112i	0.535482	+	0.927481i
$408$	−1.34411	+	2.32807i	−0.0665434	+	0.115257i
$409$	17.9051	−	31.0125i	0.885348	−	1.53347i	0.0400334	−	0.999198i	$-0.487254\pi$
$409$	17.9051	−	31.0125i	0.885348	−	1.53347i	0.845314	−	0.534269i	$-0.179413\pi$
$410$	−0.397601	+	0.688666i	−0.0196361	+	0.0340108i
$411$	10.1109			0.498732
$412$	4.82282			0.237603
$413$	1.07317	+	1.85879i	0.0528073	+	0.0914649i
$414$	0.287535	+	0.498025i	0.0141316	+	0.0244766i
$415$	−9.69948	−	16.8000i	−0.476129	−	0.824679i
$416$	−7.53859	−	0.625882i	−0.369610	−	0.0306864i
$417$	−1.17135	−	2.02884i	−0.0573613	−	0.0993526i
$418$	−10.5626	+	18.2950i	−0.516634	+	0.894836i
$419$	13.6690	−	23.6755i	0.667776	−	1.15662i	−0.310748	−	0.950492i	$-0.600580\pi$
$419$	13.6690	−	23.6755i	0.667776	−	1.15662i	0.978525	−	0.206130i	$-0.0660870\pi$
$420$	−0.0886519	+	0.153550i	−0.00432577	+	0.00749245i
$421$	2.62912	−	4.55376i	0.128135	−	0.221937i	−0.794819	−	0.606847i	$-0.792434\pi$
$421$	2.62912	−	4.55376i	0.128135	−	0.221937i	0.922954	+	0.384910i	$0.125767\pi$
$422$	−1.50710	+	2.61037i	−0.0733643	+	0.127071i
$423$	−14.0331			−0.682313
$424$	−1.54203	+	2.67087i	−0.0748875	+	0.129709i
$425$	5.68884			0.275949
$426$	−1.34188	+	2.32420i	−0.0650142	+	0.112608i
$427$	2.85821			0.138319
$428$	−3.10034	−	5.36995i	−0.149861	−	0.259566i
$429$	5.03815	+	0.418286i	0.243244	+	0.0201950i
$430$	−0.430934			−0.0207815
$431$	−23.0349			−1.10955			−0.554777	−	0.831999i	$-0.687196\pi$
$431$	−23.0349			−1.10955			−0.554777	+	0.831999i	$0.687196\pi$
$432$	−8.45428	+	14.6432i	−0.406757	+	0.704523i
$433$	17.7529	+	30.7489i	0.853149	+	1.47770i	0.878351	+	0.478015i	$0.158644\pi$
$433$	17.7529	+	30.7489i	0.853149	+	1.47770i	−0.0252023	+	0.999682i	$0.508023\pi$
$434$	0.965048	−	4.91169i	0.0463238	−	0.235769i
$435$	1.26471	+	2.19054i	0.0606382	+	0.105029i
$436$	−3.51464	−	6.08753i	−0.168321	−	0.291540i
$437$	−0.468377	−	0.811253i	−0.0224055	−	0.0388075i
$438$	−1.43157	−	2.47956i	−0.0684033	−	0.118478i
$439$	−10.0043	−	17.3279i	−0.477477	−	0.827015i	0.522189	−	0.852830i	$-0.325115\pi$
$439$	−10.0043	−	17.3279i	−0.477477	−	0.827015i	−0.999667	+	0.0258145i	$0.991782\pi$
$440$	−6.54284			−0.311918
$441$	−8.54361	−	14.7980i	−0.406838	−	0.704665i
$442$	−9.02336	−	0.749153i	−0.429197	−	0.0356336i
$443$	9.46794	−	16.3990i	0.449835	−	0.779138i	−0.548540	−	0.836125i	$-0.684816\pi$
$443$	9.46794	−	16.3990i	0.449835	−	0.779138i	0.998375	+	0.0569869i	$0.0181493\pi$
$444$	1.25657	+	2.17644i	0.0596342	+	0.103289i
$445$	−10.6449	−	18.4374i	−0.504615	−	0.874018i
$446$	0.494676	−	0.856804i	0.0234236	−	0.0405709i
$447$	1.36927	−	2.37164i	0.0647641	−	0.112175i
$448$	−1.74596	+	3.02410i	−0.0824891	+	0.142875i
$449$	7.96551	+	13.7967i	0.375915	+	0.651105i	0.990464	−	0.137775i	$-0.0439950\pi$
$449$	7.96551	+	13.7967i	0.375915	+	0.651105i	−0.614548	+	0.788879i	$0.710662\pi$
$450$	13.8075			0.650892
$451$	−0.446905	+	0.774062i	−0.0210439	+	0.0364492i
$452$	−0.866340	−	1.50055i	−0.0407492	−	0.0705797i
$453$	−0.148983			−0.00699982
$454$	11.0024	−	19.0567i	0.516367	−	0.894374i
$455$	2.57417	+	0.213717i	0.120679	+	0.0100192i
$456$	5.31413	−	9.20434i	0.248857	−	0.431033i
$457$	−11.1382	+	19.2919i	−0.521023	+	0.902438i	0.478679	+	0.877990i	$0.341116\pi$
$457$	−11.1382	+	19.2919i	−0.521023	+	0.902438i	−0.999701	+	0.0244474i	$0.992217\pi$
$458$	7.89791			0.369045
$459$	−2.98794	+	5.17527i	−0.139465	+	0.241561i
$460$	−0.0335386	+	0.0580906i	−0.00156375	+	0.00270849i
$461$	9.15862	+	15.8632i	0.426560	+	0.738823i	0.996565	−	0.0828182i	$-0.0263921\pi$
$461$	9.15862	+	15.8632i	0.426560	+	0.738823i	−0.570005	+	0.821641i	$0.693059\pi$
$462$	−0.630284	+	1.09168i	−0.0293235	+	0.0507897i
$463$	−24.4104			−1.13445			−0.567224	−	0.823563i	$-0.691983\pi$
$463$	−24.4104			−1.13445			−0.567224	+	0.823563i	$0.691983\pi$
$464$	−7.20377	−	12.4773i	−0.334427	−	0.579244i
$465$	−4.26375	+	1.45849i	−0.197727	+	0.0676359i
$466$	2.19987	−	3.81028i	0.101907	−	0.176508i
$467$	1.20582			0.0557986			0.0278993	−	0.999611i	$-0.491118\pi$
$467$	1.20582			0.0557986			0.0278993	+	0.999611i	$0.491118\pi$
$468$	−3.46241	−	0.287463i	−0.160050	−	0.0132880i
$469$	−1.09622			−0.0506188
$470$	−5.17678	−	8.96645i	−0.238787	−	0.413591i
$471$	11.2708			0.519330
$472$	−4.60641	+	7.97854i	−0.212027	+	0.367242i
$473$	−0.484371			−0.0222714
$474$	−5.90985			−0.271448
$475$	−22.4916			−1.03198
$476$	0.178465	−	0.309110i	0.00817992	−	0.0141680i
$477$	−1.58023	+	2.73703i	−0.0723536	+	0.125320i
$478$	4.68342	+	8.11192i	0.214215	+	0.371030i
$479$	33.2867			1.52091			0.760455	−	0.649391i	$-0.224976\pi$
$479$	33.2867			1.52091			0.760455	+	0.649391i	$0.224976\pi$
$480$	−1.69805			−0.0775049
$481$	20.8668	−	30.0839i	0.951445	−	1.37171i
$482$	14.5007	+	25.1159i	0.660487	+	1.14400i
$483$	−0.0279487	−	0.0484085i	−0.00127171	−	0.00220266i
$484$	−2.43095			−0.110498
$485$	−7.20812			−0.327304
$486$	−11.1611	+	19.3315i	−0.506277	+	0.876897i
$487$	17.1145			0.775531			0.387765	−	0.921758i	$-0.373247\pi$
$487$	17.1145			0.775531			0.387765	+	0.921758i	$0.373247\pi$
$488$	6.13420	+	10.6248i	0.277682	+	0.480960i
$489$	3.32943	+	5.76673i	0.150562	+	0.260781i
$490$	6.30343	−	10.9179i	0.284760	−	0.493219i
$491$	−6.41967	−	11.1192i	−0.289716	−	0.501802i	0.684026	−	0.729457i	$-0.260227\pi$
$491$	−6.41967	−	11.1192i	−0.289716	−	0.501802i	−0.973742	+	0.227655i	$0.926894\pi$
$492$	−0.0519829	+	0.0900370i	−0.00234357	+	0.00405918i
$493$	−2.54599	−	4.40978i	−0.114665	−	0.198606i
$494$	35.6751	+	2.96188i	1.60510	+	0.133261i
$495$	−6.70492			−0.301364
$496$	24.2863	−	8.30754i	1.09049	−	0.373020i
$497$	−0.770630	+	1.33477i	−0.0345675	+	0.0598727i
$498$	−8.02125	−	13.8932i	−0.359441	−	0.622570i
$499$	−9.33960	−	16.1767i	−0.418098	−	0.724167i	0.577650	−	0.816284i	$-0.303970\pi$
$499$	−9.33960	−	16.1767i	−0.418098	−	0.724167i	−0.995748	+	0.0921174i	$0.970636\pi$
$500$	1.95843	+	3.39210i	0.0875837	+	0.151699i
$501$	−13.9382			−0.622711
$502$	−9.51709	−	16.4841i	−0.424768	−	0.735720i
$503$	−15.9943	+	27.7030i	−0.713153	+	1.23522i	0.250515	+	0.968113i	$0.419400\pi$
$503$	−15.9943	+	27.7030i	−0.713153	+	1.23522i	−0.963668	+	0.267104i	$0.913933\pi$
$504$	−1.87353	+	3.24504i	−0.0834535	+	0.144546i
$505$	−0.130574	−	0.226162i	−0.00581049	−	0.0100641i
$506$	−0.238448	+	0.413004i	−0.0106003	+	0.0183603i
$507$	−3.00127	−	8.02386i	−0.133291	−	0.356352i
$508$	2.77893	+	4.81324i	0.123295	+	0.213553i
$509$	−1.85777	−	3.21775i	−0.0823442	−	0.142624i	0.821912	−	0.569614i	$-0.192907\pi$
$509$	−1.85777	−	3.21775i	−0.0823442	−	0.142624i	−0.904256	+	0.426990i	$0.859574\pi$
$510$	−2.03249			−0.0900001
$511$	−0.822143	−	1.42399i	−0.0363694	−	0.0629937i
$512$	−13.4126			−0.592761
$513$	11.8132	−	20.4611i	0.521568	−	0.903382i
$514$	−15.1430			−0.667928
$515$	−7.88586	−	13.6587i	−0.347493	−	0.601875i
$516$	−0.0563408			−0.00248027
$517$	−5.81872	−	10.0783i	−0.255907	−	0.443244i
$518$	4.56458	+	7.90609i	0.200556	+	0.347374i
$519$	−2.24542			−0.0985630
$520$	4.73015	+	10.0276i	0.207431	+	0.439737i
$521$	6.63403	+	11.4905i	0.290642	+	0.503407i	0.973962	−	0.226712i	$-0.0727977\pi$
$521$	6.63403	+	11.4905i	0.290642	+	0.503407i	−0.683320	+	0.730119i	$0.739464\pi$
$522$	−6.17942	−	10.7031i	−0.270466	−	0.468460i
$523$	4.55031	−	7.88136i	0.198971	−	0.344628i	−0.749224	−	0.662317i	$-0.769573\pi$
$523$	4.55031	−	7.88136i	0.198971	−	0.344628i	0.948195	+	0.317689i	$0.102907\pi$
$524$	−1.08890	+	1.88602i	−0.0475687	+	0.0823914i
$525$	−1.34210			−0.0585741
$526$	−16.9447	−	29.3491i	−0.738825	−	1.27968i
$527$	8.58335	−	2.93608i	0.373897	−	0.127898i
$528$	−6.46397			−0.281308
$529$	11.4894	+	19.9003i	0.499540	+	0.865229i
$530$	−2.33177			−0.101285
$531$	−4.72052	+	8.17618i	−0.204853	+	0.354816i
$532$	−0.705585	+	1.22211i	−0.0305910	+	0.0529852i
$533$	1.50942	+	0.125318i	0.0653801	+	0.00542811i
$534$	−8.80305	−	15.2473i	−0.380945	−	0.659817i
$535$	−10.1388	+	17.5610i	−0.438340	+	0.759228i
$536$	−2.35268	−	4.07496i	−0.101620	−	0.176011i
$537$	−12.9645			−0.559460
$538$	4.39336	−	7.60953i	0.189411	−	0.328070i
$539$	7.08508	−	12.2717i	0.305176	−	0.528580i
$540$	−1.69180			−0.0728035
$541$	0.704181	+	1.21968i	0.0302751	+	0.0524380i	0.880766	−	0.473552i	$-0.157028\pi$
$541$	0.704181	+	1.21968i	0.0302751	+	0.0524380i	−0.850491	+	0.525990i	$0.823695\pi$
$542$	11.1863	+	19.3753i	0.480493	+	0.832239i
$543$	6.24119	−	10.8101i	0.267835	−	0.463904i
$544$	3.41834			0.146560
$545$	−11.4937	+	19.9077i	−0.492336	+	0.852750i
$546$	2.12878	+	0.176739i	0.0911033	+	0.00756374i
$547$	−6.96659	+	12.0665i	−0.297870	+	0.515926i	−0.975648	−	0.219340i	$-0.929610\pi$
$547$	−6.96659	+	12.0665i	−0.297870	+	0.515926i	0.677778	+	0.735266i	$0.262943\pi$
$548$	−2.88117	−	4.99034i	−0.123078	−	0.213177i
$549$	6.28616	+	10.8879i	0.268287	+	0.464686i
$550$	5.72517	+	9.91628i	0.244122	+	0.422832i
$551$	10.0659	+	17.4347i	0.428822	+	0.742741i
$552$	0.119965	−	0.207786i	0.00510605	−	0.00884394i
$553$	−3.39398			−0.144327
$554$	6.68038			0.283822
$555$	4.10928	−	7.11748i	0.174429	−	0.302120i
$556$	−0.667572	+	1.15627i	−0.0283114	+	0.0490367i
$557$	8.29630	−	14.3696i	0.351526	−	0.608860i	−0.634991	−	0.772519i	$-0.718996\pi$
$557$	8.29630	−	14.3696i	0.351526	−	0.608860i	0.986517	+	0.163659i	$0.0523297\pi$
$558$	20.8328	−	7.12623i	0.881924	−	0.301678i
$559$	0.350176	+	0.742346i	0.0148109	+	0.0313979i
$560$	−3.30267			−0.139563
$561$	−2.28452			−0.0964526
$562$	−23.0127	+	39.8592i	−0.970733	+	1.68136i
$563$	−9.31343			−0.392514			−0.196257	−	0.980552i	$-0.562879\pi$
$563$	−9.31343			−0.392514			−0.196257	+	0.980552i	$0.562879\pi$
$564$	−0.676819	−	1.17229i	−0.0284992	−	0.0493621i
$565$	−2.83313	+	4.90713i	−0.119191	+	0.206445i
$566$	6.69341	+	11.5933i	0.281345	+	0.487304i
$567$	−1.53998	+	2.66733i	−0.0646731	+	0.112017i
$568$	−6.61561			−0.277585
$569$	9.45514	+	16.3768i	0.396380	+	0.686550i	0.993276	−	0.115768i	$-0.0369329\pi$
$569$	9.45514	+	16.3768i	0.396380	+	0.686550i	−0.596896	+	0.802318i	$0.703600\pi$
$570$	8.03572			0.336579
$571$	3.26736	−	5.65923i	0.136735	−	0.236831i	−0.789524	−	0.613720i	$-0.789673\pi$
$571$	3.26736	−	5.65923i	0.136735	−	0.236831i	0.926259	+	0.376888i	$0.123006\pi$
$572$	−1.22921	−	2.60583i	−0.0513959	−	0.108955i
$573$	−7.01216			−0.292937
$574$	−0.188832	+	0.327066i	−0.00788168	+	0.0136515i
$575$	−0.507742			−0.0211743
$576$	−15.3598			−0.639993
$577$	2.89030	+	5.00615i	0.120325	+	0.208409i	0.919896	−	0.392163i	$-0.128273\pi$
$577$	2.89030	+	5.00615i	0.120325	+	0.208409i	−0.799571	+	0.600572i	$0.794940\pi$
$578$	−22.1103			−0.919667
$579$	−11.5265			−0.479026
$580$	0.720780	−	1.24843i	0.0299287	−	0.0518381i
$581$	−4.60654	−	7.97877i	−0.191112	−	0.331015i
$582$	−5.96095			−0.247089
$583$	−2.62091			−0.108547
$584$	3.52891	−	6.11226i	0.146027	−	0.252927i
$585$	4.84732	+	10.2760i	0.200412	+	0.424858i
$586$	−5.24224	−	9.07982i	−0.216555	−	0.375084i
$587$	3.15636	−	5.46697i	0.130277	−	0.225646i	−0.793506	−	0.608562i	$-0.791747\pi$
$587$	3.15636	−	5.46697i	0.130277	−	0.225646i	0.923783	+	0.382916i	$0.125080\pi$
$588$	0.824119	−	1.42742i	0.0339861	−	0.0588656i
$589$	−33.9355	+	11.6082i	−1.39829	+	0.478308i
$590$	−6.96555			−0.286767
$591$	−6.50044	−	11.2591i	−0.267392	−	0.463137i
$592$	−23.4064	+	40.5411i	−0.961997	+	1.66623i
$593$	25.8994			1.06356			0.531780	−	0.846882i	$-0.321523\pi$
$593$	25.8994			1.06356			0.531780	+	0.846882i	$0.321523\pi$
$594$	−12.0281			−0.493519
$595$	−1.16724			−0.0478523
$596$	−1.56074			−0.0639302
$597$	9.25214			0.378665
$598$	0.805356	+	0.0668637i	0.0329335	+	0.00273426i
$599$	−5.60704	+	9.71167i	−0.229097	+	0.396808i	−0.957541	−	0.288298i	$-0.906911\pi$
$599$	−5.60704	+	9.71167i	−0.229097	+	0.396808i	0.728444	+	0.685106i	$0.240244\pi$
$600$	−2.88038	−	4.98896i	−0.117591	−	0.203673i
$601$	5.76703			0.235242			0.117621	−	0.993059i	$-0.462473\pi$
$601$	5.76703			0.235242			0.117621	+	0.993059i	$0.462473\pi$
$602$	−0.204662			−0.00834140
$603$	−2.41096	−	4.17590i	−0.0981817	−	0.170056i
$604$	0.0424539	+	0.0735322i	0.00172742	+	0.00299198i
$605$	3.97489	+	6.88472i	0.161602	+	0.279904i
$606$	−0.107982	−	0.187031i	−0.00438648	−	0.00759760i
$607$	3.48540			0.141468			0.0707340	−	0.997495i	$-0.477466\pi$
$607$	3.48540			0.141468			0.0707340	+	0.997495i	$0.477466\pi$
$608$	−13.5149			−0.548100
$609$	0.600645	+	1.04035i	0.0243394	+	0.0421570i
$610$	−4.63790	+	8.03307i	−0.187783	+	0.325250i
$611$	−11.2394	+	16.2039i	−0.454696	+	0.655539i
$612$	1.57001			0.0634641
$613$	7.33725			0.296349			0.148174	−	0.988961i	$-0.452660\pi$
$613$	7.33725			0.296349			0.148174	+	0.988961i	$0.452660\pi$
$614$	−48.0360			−1.93858
$615$	0.339992			0.0137098
$616$	−3.10737			−0.125200
$617$	21.7881	−	37.7381i	0.877156	−	1.51928i	0.0227081	−	0.999742i	$-0.492771\pi$
$617$	21.7881	−	37.7381i	0.877156	−	1.51928i	0.854448	−	0.519537i	$-0.173895\pi$
$618$	−6.52143	−	11.2954i	−0.262330	−	0.454370i
$619$	5.90577			0.237373			0.118687	−	0.992932i	$-0.462132\pi$
$619$	5.90577			0.237373			0.118687	+	0.992932i	$0.462132\pi$
$620$	1.93485	+	1.68882i	0.0777054	+	0.0678246i
$621$	0.266681	−	0.461905i	0.0107015	−	0.0185356i
$622$	−1.52770	+	2.64605i	−0.0612550	+	0.106097i
$623$	−5.05553	−	8.75643i	−0.202545	−	0.350819i
$624$	4.67313	+	9.90668i	0.187075	+	0.396585i
$625$	−2.32436	+	4.02591i	−0.0929743	+	0.161036i
$626$	16.1563			0.645737
$627$	9.03218			0.360710
$628$	−3.21170	−	5.56283i	−0.128161	−	0.221981i
$629$	−8.27238	+	14.3282i	−0.329841	+	0.571302i
$630$	−2.83304			−0.112871
$631$	−13.9779			−0.556453			−0.278227	−	0.960515i	$-0.589747\pi$
$631$	−13.9779			−0.556453			−0.278227	+	0.960515i	$0.589747\pi$
$632$	−7.28406	−	12.6164i	−0.289744	−	0.501852i
$633$	1.28873			0.0512225
$634$	46.6076			1.85103
$635$	9.08773	−	15.7404i	0.360636	−	0.624639i
$636$	−0.304858			−0.0120884
$637$	−23.9298	−	1.98674i	−0.948132	−	0.0787175i
$638$	5.12449	−	8.87588i	0.202881	−	0.351399i
$639$	−6.77949			−0.268193
$640$	−8.24297	−	14.2772i	−0.325832	−	0.564358i
$641$	11.2126			0.442869			0.221435	−	0.975175i	$-0.428926\pi$
$641$	11.2126			0.442869			0.221435	+	0.975175i	$0.428926\pi$
$642$	−8.38459	+	14.5225i	−0.330913	+	0.573159i
$643$	−6.39985	−	11.0849i	−0.252386	−	0.437145i	0.711797	−	0.702386i	$-0.247882\pi$
$643$	−6.39985	−	11.0849i	−0.252386	−	0.437145i	−0.964182	+	0.265241i	$0.914548\pi$
$644$	−0.0159284	+	0.0275888i	−0.000627667	+	0.00108715i
$645$	0.0921238	+	0.159563i	0.00362737	+	0.00628279i
$646$	−16.1767			−0.636463
$647$	−19.6628	+	34.0571i	−0.773026	+	1.33892i	0.162871	+	0.986647i	$0.447925\pi$
$647$	−19.6628	+	34.0571i	−0.773026	+	1.33892i	−0.935897	+	0.352273i	$0.885409\pi$
$648$	−13.2202			−0.519340
$649$	−7.82930			−0.307327
$650$	11.0587	−	15.9434i	0.433757	−	0.625350i
$651$	−2.02497	+	0.692677i	−0.0793649	+	0.0271481i
$652$	1.89749	−	3.28656i	0.0743116	−	0.128712i
$653$	10.7462	−	18.6130i	0.420533	−	0.728385i	−0.575459	−	0.817831i	$-0.695176\pi$
$653$	10.7462	−	18.6130i	0.420533	−	0.728385i	0.995992	+	0.0894463i	$0.0285097\pi$
$654$	−9.50502	+	16.4632i	−0.371676	+	0.643761i
$655$	7.12189			0.278275
$656$	−1.93659			−0.0756112
$657$	3.61633	−	6.26367i	0.141086	−	0.244369i
$658$	−2.45859	−	4.25841i	−0.0958459	−	0.166010i
$659$	16.9789	+	29.4083i	0.661403	+	1.14558i	0.980247	+	0.197777i	$0.0633721\pi$
$659$	16.9789	+	29.4083i	0.661403	+	1.14558i	−0.318844	+	0.947807i	$0.603295\pi$
$660$	−0.323379	−	0.560109i	−0.0125875	−	0.0218022i
$661$	−5.20203	−	9.01018i	−0.202336	−	0.350456i	0.746945	−	0.664886i	$-0.231520\pi$
$661$	−5.20203	−	9.01018i	−0.202336	−	0.350456i	−0.949281	+	0.314430i	$0.898187\pi$
$662$	−4.90794	+	8.50080i	−0.190752	+	0.330393i
$663$	1.65160	+	3.50126i	0.0641427	+	0.135978i
$664$	19.7728	−	34.2476i	0.767335	−	1.32906i
$665$	4.61485			0.178956
$666$	−20.0781	+	34.7762i	−0.778009	+	1.34755i
$667$	0.227235	+	0.393583i	0.00879858	+	0.0152396i
$668$	3.97179	+	6.87935i	0.153673	+	0.266170i
$669$	−0.423002			−0.0163542
$670$	1.77879	−	3.08096i	0.0687207	−	0.119028i
$671$	−5.21301	+	9.02920i	−0.201246	+	0.348568i
$672$	−0.806449			−0.0311094
$673$	5.56739	+	9.64301i	0.214607	+	0.371711i	0.953151	−	0.302495i	$-0.0978195\pi$
$673$	5.56739	+	9.64301i	0.214607	+	0.371711i	−0.738544	+	0.674206i	$0.764486\pi$
$674$	20.8367	−	36.0902i	0.802599	−	1.39014i
$675$	−6.40305	−	11.0904i	−0.246453	−	0.426870i
$676$	−3.10504	+	3.76778i	−0.119425	+	0.144915i
$677$	−9.57405	+	16.5827i	−0.367961	+	0.637327i	−0.989247	−	0.146257i	$-0.953277\pi$
$677$	−9.57405	+	16.5827i	−0.367961	+	0.637327i	0.621286	+	0.783584i	$0.286611\pi$
$678$	−2.34294	+	4.05809i	−0.0899800	+	0.155850i
$679$	−3.42333			−0.131375
$680$	−2.50510	−	4.33896i	−0.0960662	−	0.166392i
$681$	−9.40823			−0.360524
$682$	13.7561	+	12.0069i	0.526748	+	0.459769i
$683$	16.5140	+	28.6030i	0.631889	+	1.09446i	0.987165	+	0.159703i	$0.0510537\pi$
$683$	16.5140	+	28.6030i	0.631889	+	1.09446i	−0.355276	+	0.934762i	$0.615613\pi$
$684$	−6.20727			−0.237341
$685$	−9.42210	+	16.3196i	−0.360000	+	0.623538i
$686$	6.14028	−	10.6353i	0.234437	−	0.406057i
$687$	−1.68839	−	2.92438i	−0.0644162	−	0.111572i
$688$	−0.524736	−	0.908869i	−0.0200054	−	0.0346503i
$689$	1.89479	+	4.01681i	0.0721858	+	0.153028i
$690$	0.181404			0.00690595
$691$	19.3100	+	33.4460i	0.734589	+	1.27234i	0.954904	+	0.296916i	$0.0959582\pi$
$691$	19.3100	+	33.4460i	0.734589	+	1.27234i	−0.220315	+	0.975429i	$0.570708\pi$
$692$	0.639851	+	1.10825i	0.0243235	+	0.0421295i
$693$	−3.18435			−0.120963
$694$	−20.8161	−	36.0546i	−0.790170	−	1.36861i
$695$	4.36623			0.165621
$696$	−2.57817	+	4.46553i	−0.0977254	+	0.169265i
$697$	−0.684438			−0.0259249
$698$	−14.7470	−	25.5425i	−0.558181	−	0.966798i
$699$	−1.88113			−0.0711507
$700$	0.382443	+	0.662411i	0.0144550	+	0.0250368i
$701$	−13.9037	−	24.0819i	−0.525134	−	0.909560i	−0.999572	−	0.0292702i	$-0.990682\pi$
$701$	−13.9037	−	24.0819i	−0.525134	−	0.909560i	0.474437	−	0.880289i	$-0.342652\pi$
$702$	8.69573	+	18.4343i	0.328199	+	0.695757i
$703$	32.7060	−	56.6484i	1.23353	−	2.13654i
$704$	−6.36883	−	11.0311i	−0.240034	−	0.415752i
$705$	−2.21336	+	3.83364i	−0.0833598	+	0.144383i
$706$	−19.8598	+	34.3982i	−0.747434	+	1.29459i
$707$	−0.0620133	−	0.107410i	−0.00233225	−	0.00403958i
$708$	−0.910686			−0.0342257
$709$	−13.4659	−	23.3237i	−0.505724	−	0.875940i	−0.999978	−	0.00662256i	$-0.997892\pi$
$709$	−13.4659	−	23.3237i	−0.505724	−	0.875940i	0.494254	−	0.869318i	$-0.335441\pi$
$710$	−2.50094	−	4.33175i	−0.0938585	−	0.162568i
$711$	−7.46450	−	12.9289i	−0.279941	−	0.484871i
$712$	21.7000	−	37.5856i	0.813243	−	1.40858i
$713$	−0.766084	+	0.262052i	−0.0286901	+	0.00981394i
$714$	−0.965283			−0.0361248
$715$	−5.37009	+	7.74210i	−0.200830	+	0.289538i
$716$	3.69434	+	6.39879i	0.138064	+	0.239134i
$717$	2.00242	−	3.46829i	0.0747816	−	0.129526i
$718$	−10.0325	−	17.3768i	−0.374411	−	0.648498i
$719$	−13.8629	+	24.0112i	−0.516998	+	0.895467i	0.482807	+	0.875727i	$0.339617\pi$
$719$	−13.8629	+	24.0112i	−0.516998	+	0.895467i	−0.999805	+	0.0197403i	$0.993716\pi$
$720$	−7.26367	−	12.5810i	−0.270701	−	0.468868i
$721$	−3.74521	−	6.48689i	−0.139479	−	0.241584i
$722$	34.6723			1.29037
$723$	6.19982	−	10.7384i	0.230574	−	0.399365i
$724$	−7.11391			−0.264387
$725$	10.9119			0.405257
$726$	3.28715	+	5.69351i	0.121997	+	0.211306i
$727$	25.4822	+	44.1365i	0.945082	+	1.63693i	0.755586	+	0.655049i	$0.227352\pi$
$727$	25.4822	+	44.1365i	0.945082	+	1.63693i	0.189496	+	0.981882i	$0.439315\pi$
$728$	2.24648	+	4.76236i	0.0832599	+	0.176505i
$729$	−6.29679			−0.233214
$730$	5.33622			0.197502
$731$	−0.185454	−	0.321216i	−0.00685927	−	0.0118806i
$732$	−0.606365	+	1.05025i	−0.0224119	+	0.0388185i
$733$	4.72905	−	8.19095i	0.174671	−	0.302540i	−0.765376	−	0.643583i	$-0.777447\pi$
$733$	4.72905	−	8.19095i	0.174671	−	0.302540i	0.940048	+	0.341044i	$0.110780\pi$
$734$	−29.7048			−1.09642
$735$	−5.39012			−0.198818
$736$	−0.305094			−0.0112459
$737$	1.99937	−	3.46301i	0.0736477	−	0.127562i
$738$	−1.66121			−0.0611501
$739$	17.2520	+	29.8813i	0.634625	+	1.09920i	0.986594	+	0.163192i	$0.0521789\pi$
$739$	17.2520	+	29.8813i	0.634625	+	1.09920i	−0.351969	+	0.936012i	$0.614488\pi$
$740$	−4.68389			−0.172183
$741$	−6.52982	−	13.8427i	−0.239879	−	0.508524i
$742$	−1.10742			−0.0406546
$743$	5.40465	−	9.36112i	0.198277	−	0.343426i	−0.749693	−	0.661786i	$-0.769799\pi$
$743$	5.40465	−	9.36112i	0.198277	−	0.343426i	0.947970	+	0.318360i	$0.103132\pi$
$744$	−6.92080	−	6.04077i	−0.253729	−	0.221466i
$745$	2.55198	+	4.42016i	0.0934974	+	0.161942i
$746$	−0.486033			−0.0177949
$747$	20.2626	−	35.0959i	0.741371	−	1.28409i
$748$	0.650994	+	1.12755i	0.0238027	+	0.0412275i
$749$	−4.81521	+	8.34019i	−0.175944	+	0.304744i
$750$	5.29640	−	9.17363i	0.193397	−	0.334974i
$751$	−12.8376			−0.468450			−0.234225	−	0.972182i	$-0.575255\pi$
$751$	−12.8376			−0.468450			−0.234225	+	0.972182i	$0.575255\pi$
$752$	12.6072	−	21.8364i	0.459739	−	0.796291i
$753$	−4.06907	+	7.04784i	−0.148285	+	0.256838i
$754$	−17.3079	−	1.43697i	−0.630317	−	0.0523313i
$755$	0.138834	−	0.240468i	0.00505269	−	0.00875151i
$756$	−0.803482			−0.0292223
$757$	7.62288	+	13.2032i	0.277058	+	0.479879i	0.970652	−	0.240487i	$-0.0773072\pi$
$757$	7.62288	+	13.2032i	0.277058	+	0.479879i	−0.693594	+	0.720366i	$0.743974\pi$
$758$	16.4586	−	28.5072i	0.597805	−	1.03543i
$759$	0.203899			0.00740107
$760$	9.90426	+	17.1547i	0.359265	+	0.622266i
$761$	12.8480	−	22.2534i	0.465741	−	0.806687i	−0.533494	−	0.845804i	$-0.679121\pi$
$761$	12.8480	−	22.2534i	0.465741	−	0.806687i	0.999235	+	0.0391173i	$0.0124546\pi$
$762$	7.51535	−	13.0170i	0.272252	−	0.471555i
$763$	−5.45866	+	9.45468i	−0.197617	+	0.342282i
$764$	1.99817	+	3.46094i	0.0722914	+	0.125212i
$765$	−2.56716	−	4.44644i	−0.0928157	−	0.160762i
$766$	11.0912	−	19.2105i	0.400740	−	0.694102i
$767$	5.66020	+	11.9992i	0.204378	+	0.433265i
$768$	−2.87173	−	4.97399i	−0.103625	−	0.179483i
$769$	−41.6408			−1.50160			−0.750802	−	0.660527i	$-0.770333\pi$
$769$	−41.6408			−1.50160			−0.750802	+	0.660527i	$0.770333\pi$
$770$	−1.17470	−	2.03464i	−0.0423332	−	0.0733232i
$771$	3.23723	+	5.60704i	0.116586	+	0.201933i
$772$	3.28458	+	5.68906i	0.118215	+	0.204754i
$773$	−2.54959	−	4.41603i	−0.0917025	−	0.158833i	0.816525	−	0.577310i	$-0.195898\pi$
$773$	−2.54959	−	4.41603i	−0.0917025	−	0.158833i	−0.908228	+	0.418477i	$0.862564\pi$
$774$	−0.450120	−	0.779630i	−0.0161792	−	0.0280232i
$775$	−3.74794	+	19.0754i	−0.134630	+	0.685210i
$776$	−7.34705	−	12.7255i	−0.263744	−	0.456817i
$777$	1.95161	−	3.38028i	0.0700135	−	0.121267i
$778$	−8.13607			−0.291692
$779$	2.70602			0.0969532
$780$	−0.624636	+	0.900542i	−0.0223655	+	0.0322446i
$781$	−2.81106	−	4.86890i	−0.100588	−	0.174223i
$782$	−0.365185			−0.0130590
$783$	−5.73125	+	9.92681i	−0.204818	+	0.354755i
$784$	30.7020			1.09650
$785$	−10.5030	+	18.1917i	−0.374868	+	0.649291i
$786$	5.88964			0.210077
$787$	16.1268	−	27.9324i	0.574857	−	0.995682i	−0.421200	−	0.906968i	$-0.638391\pi$
$787$	16.1268	−	27.9324i	0.574857	−	0.995682i	0.996057	−	0.0887142i	$-0.0282758\pi$
$788$	−3.70471	+	6.41675i	−0.131975	+	0.228587i
$789$	−7.24479	+	12.5483i	−0.257921	+	0.446733i
$790$	5.50727	−	9.53887i	0.195940	−	0.339378i
$791$	−1.34553	+	2.33053i	−0.0478416	+	0.0828641i
$792$	−6.83415	−	11.8371i	−0.242841	−	0.420613i
$793$	17.6069	+	1.46179i	0.625239	+	0.0519097i
$794$	12.7879	+	22.1493i	0.453825	+	0.786048i
$795$	0.498479	+	0.863390i	0.0176792	+	0.0306213i
$796$	−2.63648	−	4.56651i	−0.0934474	−	0.161856i
$797$	16.0176			0.567373			0.283687	−	0.958917i	$-0.408442\pi$
$797$	16.0176			0.567373			0.283687	+	0.958917i	$0.408442\pi$
$798$	3.81638			0.135098
$799$	4.45570	−	7.71750i	0.157631	−	0.273025i
$800$	−3.66268	+	6.34395i	−0.129495	+	0.224292i
$801$	22.2376	−	38.5166i	0.785726	−	1.36092i
$802$	25.4057	+	44.0039i	0.897105	+	1.55383i
$803$	5.99793			0.211662
$804$	0.232562	−	0.402809i	0.00820182	−	0.0142060i
$805$	0.104179			0.00367183
$806$	8.45681	−	29.7630i	0.297878	−	1.04836i
$807$	−3.75680			−0.132246
$808$	0.266182	−	0.461041i	0.00936426	−	0.0162194i
$809$	−16.1718			−0.568572			−0.284286	−	0.958740i	$-0.591756\pi$
$809$	−16.1718			−0.568572			−0.284286	+	0.958740i	$0.591756\pi$
$810$	−4.99772	−	8.65631i	−0.175602	−	0.304152i
$811$	16.3526	−	28.3235i	0.574216	−	0.994572i	−0.421910	−	0.906638i	$-0.638640\pi$
$811$	16.3526	−	28.3235i	0.574216	−	0.994572i	0.996126	−	0.0879339i	$-0.0280264\pi$
$812$	0.342318	−	0.592912i	0.0120130	−	0.0208071i
$813$	4.78276	−	8.28398i	0.167739	−	0.290532i
$814$	−33.3008			−1.16719
$815$	−12.4105			−0.434721
$816$	−2.47490	−	4.28666i	−0.0866390	−	0.150063i
$817$	0.733218	+	1.26997i	0.0256521	+	0.0444307i
$818$	27.5968	+	47.7991i	0.964900	+	1.67126i
$819$	2.30212	+	4.88033i	0.0804427	+	0.170532i
$820$	−0.0968837	−	0.167807i	−0.00338332	−	0.00586009i
$821$	−7.78245	+	13.4796i	−0.271609	+	0.470441i	−0.969274	−	0.245983i	$-0.920889\pi$
$821$	−7.78245	+	13.4796i	−0.271609	+	0.470441i	0.697665	+	0.716424i	$0.254222\pi$
$822$	−7.79186	+	13.4959i	−0.271772	+	0.470724i
$823$	3.85000	−	6.66839i	0.134202	−	0.232446i	−0.791090	−	0.611700i	$-0.790486\pi$
$823$	3.85000	−	6.66839i	0.134202	−	0.232446i	0.925293	+	0.379254i	$0.123819\pi$
$824$	16.0757	−	27.8439i	0.560024	−	0.969989i
$825$	2.44782	−	4.23975i	0.0852222	−	0.147609i
$826$	−3.30813			−0.115105
$827$	5.34883	−	9.26444i	0.185997	−	0.322156i	−0.757915	−	0.652353i	$-0.773782\pi$
$827$	5.34883	−	9.26444i	0.185997	−	0.322156i	0.943912	+	0.330197i	$0.107115\pi$
$828$	−0.140127			−0.00486977
$829$	−2.53419	+	4.38935i	−0.0880162	+	0.152449i	−0.906672	−	0.421835i	$-0.861386\pi$
$829$	−2.53419	+	4.38935i	−0.0880162	+	0.152449i	0.818656	+	0.574284i	$0.194719\pi$
$830$	29.8994			1.03782
$831$	−1.42811	−	2.47356i	−0.0495407	−	0.0858070i
$832$	−12.3020	+	17.7358i	−0.426494	+	0.614879i
$833$	10.8508			0.375959
$834$	3.61077			0.125031
$835$	12.9887	−	22.4971i	0.449492	−	0.778543i
$836$	−2.57379	−	4.45794i	−0.0890165	−	0.154181i
$837$	−15.3849	−	13.4286i	−0.531779	−	0.464159i
$838$	21.0679	+	36.4907i	0.727779	+	1.26055i
$839$	25.3020	+	43.8243i	0.873521	+	1.51298i	0.858330	+	0.513099i	$0.171503\pi$
$839$	25.3020	+	43.8243i	0.873521	+	1.51298i	0.0151917	+	0.999885i	$0.495164\pi$
$840$	0.591000	+	1.02364i	0.0203914	+	0.0353190i
$841$	9.61648	+	16.6562i	0.331603	+	0.574353i
$842$	4.05222	+	7.01866i	0.139649	+	0.241879i
$843$	19.6784			0.677760
$844$	−0.367235	−	0.636070i	−0.0126407	−	0.0218944i
$845$	15.7478	+	2.63304i	0.541742	+	0.0905793i
$846$	10.8145	−	18.7313i	0.371811	−	0.643996i
$847$	1.88778	+	3.26974i	0.0648650	+	0.112350i
$848$	−2.83933	−	4.91786i	−0.0975029	−	0.168880i
$849$	2.86180	−	4.95678i	0.0982166	−	0.170116i
$850$	−4.38406	+	7.59342i	−0.150372	+	0.260452i
$851$	0.738329	−	1.27882i	0.0253096	−	0.0438375i
$852$	−0.326976	−	0.566339i	−0.0112020	−	0.0194025i
$853$	−11.5041			−0.393891			−0.196946	−	0.980414i	$-0.563102\pi$
$853$	−11.5041			−0.393891			−0.196946	+	0.980414i	$0.563102\pi$
$854$	−2.20266	+	3.81512i	−0.0753735	+	0.130551i
$855$	10.1496	+	17.5796i	0.347109	+	0.601210i
$856$	−41.3370			−1.41287
$857$	−14.5877	+	25.2667i	−0.498307	+	0.863093i	−0.999998	−	0.00195414i	$-0.999378\pi$
$857$	−14.5877	+	25.2667i	−0.498307	+	0.863093i	0.501691	+	0.865047i	$0.332711\pi$
$858$	−4.44094	+	6.40254i	−0.151611	+	0.218579i
$859$	−25.1594	+	43.5773i	−0.858427	+	1.48684i	0.0150023	+	0.999887i	$0.495224\pi$
$859$	−25.1594	+	43.5773i	−0.858427	+	1.48684i	−0.873429	+	0.486951i	$0.838109\pi$
$860$	0.0525029	−	0.0909377i	0.00179033	−	0.00310095i
$861$	0.161472			0.00550294
$862$	17.7517	−	30.7469i	0.604626	−	1.04724i
$863$	13.0118	−	22.5371i	0.442926	−	0.767171i	−0.554979	−	0.831865i	$-0.687274\pi$
$863$	13.0118	−	22.5371i	0.442926	−	0.767171i	0.997905	+	0.0646934i	$0.0206069\pi$
$864$	−3.84749	−	6.66405i	−0.130894	−	0.226716i
$865$	2.09246	−	3.62425i	0.0711458	−	0.123228i
$866$	−54.7246			−1.85962
$867$	4.72668	+	8.18684i	0.160526	+	0.278040i
$868$	0.918912	+	0.802066i	0.0311899	+	0.0272239i
$869$	6.19019	−	10.7217i	0.209988	−	0.363709i
$870$	−3.89856			−0.132174
$871$	−6.75285	−	0.560647i	−0.228811	−	0.0189968i
$872$	−46.8608			−1.58691
$873$	−7.52904	−	13.0407i	−0.254819	−	0.441360i
$874$	1.44381			0.0488375
$875$	3.04168	−	5.26835i	0.102828	−	0.178103i
$876$	0.697665			0.0235719
$877$	−44.7547			−1.51126			−0.755630	−	0.654999i	$-0.772669\pi$
$877$	−44.7547			−1.51126			−0.755630	+	0.654999i	$0.772669\pi$
$878$	30.8389			1.04076
$879$	−2.24134	+	3.88212i	−0.0755986	+	0.130941i
$880$	6.02365	−	10.4333i	0.203057	−	0.351705i
$881$	26.2345	+	45.4394i	0.883862	+	1.53089i	0.847013	+	0.531573i	$0.178399\pi$
$881$	26.2345	+	45.4394i	0.883862	+	1.53089i	0.0368490	+	0.999321i	$0.488268\pi$
$882$	26.3363			0.886790
$883$	33.1798			1.11659			0.558294	−	0.829643i	$-0.311456\pi$
$883$	33.1798			1.11659			0.558294	+	0.829643i	$0.311456\pi$
$884$	1.25745	−	1.81288i	0.0422927	−	0.0609737i
$885$	1.48908	+	2.57916i	0.0500548	+	0.0866974i
$886$	14.5928	+	25.2755i	0.490255	+	0.849147i
$887$	33.6411			1.12956			0.564779	−	0.825242i	$-0.308961\pi$
$887$	33.6411			1.12956			0.564779	+	0.825242i	$0.308961\pi$
$888$	16.7539			0.562225
$889$	4.31601	−	7.47555i	0.144754	−	0.250722i
$890$	32.8136			1.09991
$891$	−5.61746	−	9.72972i	−0.188192	−	0.325958i
$892$	0.120538	+	0.208778i	0.00403591	+	0.00699040i
$893$	−17.6162	+	30.5122i	−0.589504	+	1.02105i
$894$	2.11043	+	3.65538i	0.0705834	+	0.122254i
$895$	12.0814	−	20.9255i	0.403835	−	0.699464i
$896$	−3.91481	−	6.78065i	−0.130785	−	0.226525i
$897$	−0.147409	−	0.312496i	−0.00492184	−	0.0104339i
$898$	−24.5543			−0.819386
$899$	16.4639	−	5.63177i	0.549103	−	0.187830i
$900$	−1.68224	+	2.91372i	−0.0560746	+	0.0971241i
$901$	−1.00349	−	1.73809i	−0.0334310	−	0.0579041i
$902$	−0.688809	−	1.19305i	−0.0229348	−	0.0397243i
$903$	0.0437521	+	0.0757808i	0.00145598	+	0.00252183i
$904$	−11.5510			−0.384179
$905$	11.6321	+	20.1473i	0.386663	+	0.669721i
$906$	0.114813	−	0.198861i	0.00381439	−	0.00660672i
$907$	2.59313	−	4.49144i	0.0861036	−	0.149136i	−0.819757	−	0.572711i	$-0.805892\pi$
$907$	2.59313	−	4.49144i	0.0861036	−	0.149136i	0.905861	+	0.423575i	$0.139225\pi$
$908$	2.68095	+	4.64355i	0.0889706	+	0.154102i
$909$	0.272776	−	0.472462i	0.00904741	−	0.0156706i
$910$	−2.26903	+	3.27128i	−0.0752177	+	0.108442i
$911$	19.9285	+	34.5172i	0.660261	+	1.14361i	0.980547	+	0.196285i	$0.0628878\pi$
$911$	19.9285	+	34.5172i	0.660261	+	1.14361i	−0.320286	+	0.947321i	$0.603779\pi$
$912$	9.78487	+	16.9479i	0.324009	+	0.561201i
$913$	33.6070			1.11223
$914$	−17.1672	−	29.7344i	−0.567839	−	0.983526i
$915$	3.96591			0.131109
$916$	−0.962243	+	1.66665i	−0.0317934	+	0.0550678i
$917$	3.38238			0.111696
$918$	−4.60528	−	7.97658i	−0.151997	−	0.263266i
$919$	55.5797			1.83341			0.916703	−	0.399570i	$-0.130840\pi$
$919$	55.5797			1.83341			0.916703	+	0.399570i	$0.130840\pi$
$920$	0.223586	+	0.387263i	0.00737142	+	0.0127677i
$921$	10.2690	+	17.7864i	0.338375	+	0.586083i
$922$	−28.2321			−0.929776
$923$	−5.42982	+	7.82821i	−0.178725	+	0.257669i
$924$	−0.153582	−	0.266011i	−0.00505246	−	0.00875112i
$925$	−17.7274	−	30.7047i	−0.582873	−	1.00956i
$926$	18.8117	−	32.5829i	0.618192	−	1.07074i
$927$	16.4739	−	28.5337i	0.541075	−	0.937169i
$928$	6.55679			0.215237
$929$	4.56660	+	7.90958i	0.149825	+	0.259505i	0.931163	−	0.364604i	$-0.118796\pi$
$929$	4.56660	+	7.90958i	0.149825	+	0.259505i	−0.781338	+	0.624109i	$0.785462\pi$
$930$	1.33905	−	6.81521i	0.0439092	−	0.223480i
$931$	−42.9003			−1.40600
$932$	0.536042	+	0.928453i	0.0175587	+	0.0304125i
$933$	1.30635			0.0427679
$934$	−0.929255	+	1.60952i	−0.0304062	+	0.0526650i
$935$	2.12890	−	3.68737i	0.0696225	−	0.120590i
$936$	−13.2008	+	19.0316i	−0.431480	+	0.622068i
$937$	24.5211	+	42.4718i	0.801070	+	1.38749i	0.918913	+	0.394461i	$0.129069\pi$
$937$	24.5211	+	42.4718i	0.801070	+	1.38749i	−0.117843	+	0.993032i	$0.537598\pi$
$938$	0.844796	−	1.46323i	0.0275836	−	0.0477762i
$939$	−3.45386	−	5.98226i	−0.112712	−	0.195224i
$940$	2.52286			0.0822865
$941$	−14.1161	+	24.4498i	−0.460172	+	0.797041i	−0.998969	−	0.0453944i	$-0.985546\pi$
$941$	−14.1161	+	24.4498i	−0.460172	+	0.797041i	0.538797	+	0.842435i	$0.318879\pi$
$942$	−8.68575	+	15.0442i	−0.282997	+	0.490165i
$943$	0.0610877			0.00198929
$944$	−8.48176	−	14.6908i	−0.276058	−	0.478146i
$945$	1.31379	+	2.27554i	0.0427374	+	0.0740234i
$946$	0.373277	−	0.646535i	0.0121363	−	0.0210207i
$947$	1.10562			0.0359279			0.0179640	−	0.999839i	$-0.494282\pi$
$947$	1.10562			0.0359279			0.0179640	+	0.999839i	$0.494282\pi$
$948$	0.720028	−	1.24712i	0.0233854	−	0.0405047i
$949$	−4.33621	−	9.19242i	−0.140759	−	0.298399i
$950$	17.3330	−	30.0216i	0.562357	−	0.974030i
$951$	−9.96365	−	17.2575i	−0.323093	−	0.559614i
$952$	−1.18974	−	2.06069i	−0.0385597	−	0.0667873i
$953$	−13.2934	−	23.0248i	−0.430615	−	0.745847i	0.566312	−	0.824191i	$-0.308370\pi$
$953$	−13.2934	−	23.0248i	−0.430615	−	0.745847i	−0.996926	+	0.0783446i	$0.975037\pi$
$954$	−2.43558	−	4.21855i	−0.0788549	−	0.136581i
$955$	6.53449	−	11.3181i	0.211451	−	0.366244i
$956$	−2.28242			−0.0738187
$957$	−4.38200			−0.141650
$958$	−25.6522	+	44.4309i	−0.828785	+	1.43550i
$959$	−4.47481	+	7.75060i	−0.144499	+	0.250280i
$960$	−2.42261	+	4.19608i	−0.0781894	+	0.135428i
$961$	4.19018	+	30.7155i	0.135167	+	0.990823i
$962$	24.0749	+	51.0368i	0.776205	+	1.64549i
$963$	−42.3610			−1.36506
$964$	−7.06676			−0.227605
$965$	10.7413	−	18.6045i	0.345776	−	0.598901i
$966$	0.0861538			0.00277195
$967$	5.64972	+	9.78561i	0.181683	+	0.314684i	0.942454	−	0.334337i	$-0.108512\pi$
$967$	5.64972	+	9.78561i	0.181683	+	0.314684i	−0.760771	+	0.649021i	$0.775179\pi$
$968$	−8.10301	+	14.0348i	−0.260441	+	0.451096i
$969$	3.45821	+	5.98979i	0.111094	+	0.192420i
$970$	5.55489	−	9.62136i	0.178357	−	0.308923i
$971$	6.64577			0.213273			0.106636	−	0.994298i	$-0.465992\pi$
$971$	6.64577			0.213273			0.106636	+	0.994298i	$0.465992\pi$
$972$	−2.71962	−	4.71053i	−0.0872320	−	0.151090i
$973$	2.07364			0.0664779
$974$	−13.1892	+	22.8443i	−0.422608	+	0.731978i
$975$	−8.26749	−	0.686398i	−0.264772	−	0.0219823i
$976$	−22.5897			−0.723080
$977$	−9.08273	+	15.7317i	−0.290582	+	0.503303i	−0.973948	−	0.226774i	$-0.927182\pi$
$977$	−9.08273	+	15.7317i	−0.290582	+	0.503303i	0.683365	+	0.730077i	$0.260516\pi$
$978$	−10.2632			−0.328181
$979$	36.8825			1.17877
$980$	1.53596	+	2.66036i	0.0490644	+	0.0849821i
$981$	−48.0217			−1.53321
$982$	19.7891			0.631496
$983$	7.90826	−	13.6975i	0.252234	−	0.436883i	−0.711906	−	0.702274i	$-0.752168\pi$
$983$	7.90826	−	13.6975i	0.252234	−	0.436883i	0.964141	+	0.265392i	$0.0855013\pi$
$984$	0.346545	+	0.600234i	0.0110475	+	0.0191348i
$985$	24.2305			0.772049
$986$	7.84819			0.249937
$987$	−1.05118	+	1.82070i	−0.0334595	+	0.0579535i
$988$	−4.97151	+	7.16746i	−0.158165	+	0.228027i
$989$	0.0165522	+	0.0286693i	0.000526330	+	0.000911630i
$990$	5.16710	−	8.94968i	0.164221	−	0.284440i
$991$	−21.8499	+	37.8451i	−0.694084	+	1.20219i	0.276404	+	0.961042i	$0.410857\pi$
$991$	−21.8499	+	37.8451i	−0.694084	+	1.20219i	−0.970488	+	0.241148i	$0.922476\pi$
$992$	−2.25208	+	11.4621i	−0.0715036	+	0.363923i
$993$	4.19682			0.133182
$994$	−1.18776	−	2.05727i	−0.0376735	−	0.0652525i
$995$	−8.62189	+	14.9335i	−0.273332	+	0.473425i
$996$	3.90908			0.123864
$997$	−52.9523			−1.67701			−0.838507	−	0.544890i	$-0.816571\pi$
$997$	−52.9523			−1.67701			−0.838507	+	0.544890i	$0.816571\pi$
$998$	28.7900			0.911332
$999$	37.2438			1.17834

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.g.a.87.11	yes	70
13.3	even	3		403.2.e.a.211.11	yes	70
31.5	even	3		403.2.e.a.191.11	✓	70
403.315	even	3	inner	403.2.g.a.315.11	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.e.a.191.11	✓	70	31.5	even	3
403.2.e.a.211.11	yes	70	13.3	even	3
403.2.g.a.87.11	yes	70	1.1	even	1	trivial
403.2.g.a.315.11	yes	70	403.315	even	3	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.770644 + 1.33479i) q^{2} +0.658984 q^{3} +(-0.187783 - 0.325250i) q^{4} +(-0.614094 + 1.06364i) q^{5} +(-0.507842 + 0.879608i) q^{6} +(-0.291650 + 0.505152i) q^{7} -2.50372 q^{8} -2.56574 q^{9} +O(q^{10})\)	\(q+(-0.770644 + 1.33479i) q^{2} +0.658984 q^{3} +(-0.187783 - 0.325250i) q^{4} +(-0.614094 + 1.06364i) q^{5} +(-0.507842 + 0.879608i) q^{6} +(-0.291650 + 0.505152i) q^{7} -2.50372 q^{8} -2.56574 q^{9} +(-0.946495 - 1.63938i) q^{10} +(-1.06386 - 1.84267i) q^{11} +(-0.123746 - 0.214334i) q^{12} +(-2.05495 + 2.96263i) q^{13} +(-0.449516 - 0.778585i) q^{14} +(-0.404678 + 0.700923i) q^{15} +(2.30504 - 3.99245i) q^{16} +(0.814657 - 1.41103i) q^{17} +(1.97727 - 3.42473i) q^{18} +(-3.22086 + 5.57869i) q^{19} +0.461266 q^{20} +(-0.192193 + 0.332887i) q^{21} +3.27944 q^{22} +(-0.0727100 + 0.125937i) q^{23} -1.64991 q^{24} +(1.74578 + 3.02377i) q^{25} +(-2.37087 - 5.02606i) q^{26} -3.66773 q^{27} +0.219068 q^{28} +(1.56261 - 2.70652i) q^{29} +(-0.623725 - 1.08032i) q^{30} +(4.19465 + 3.66127i) q^{31} +(1.04901 + 1.81694i) q^{32} +(-0.701069 - 1.21429i) q^{33} +(1.25562 + 2.17480i) q^{34} +(-0.358201 - 0.620422i) q^{35} +(0.481802 + 0.834506i) q^{36} -10.1544 q^{37} +(-4.96427 - 8.59836i) q^{38} +(-1.35418 + 1.95233i) q^{39} +(1.53752 - 2.66306i) q^{40} +(-0.210039 - 0.363798i) q^{41} +(-0.296224 - 0.513075i) q^{42} +(0.113823 - 0.197148i) q^{43} +(-0.399551 + 0.692043i) q^{44} +(1.57561 - 2.72903i) q^{45} +(-0.112067 - 0.194106i) q^{46} +5.46942 q^{47} +(1.51899 - 2.63096i) q^{48} +(3.32988 + 5.76752i) q^{49} -5.38149 q^{50} +(0.536846 - 0.929844i) q^{51} +(1.34948 + 0.112039i) q^{52} +(0.615895 - 1.06676i) q^{53} +(2.82652 - 4.89567i) q^{54} +2.61325 q^{55} +(0.730209 - 1.26476i) q^{56} +(-2.12249 + 3.67627i) q^{57} +(2.40843 + 4.17153i) q^{58} +(1.83983 - 3.18668i) q^{59} +0.303967 q^{60} +(-2.45004 - 4.24359i) q^{61} +(-8.11962 + 2.77746i) q^{62} +(0.748298 - 1.29609i) q^{63} +5.98651 q^{64} +(-1.88925 - 4.00506i) q^{65} +2.16110 q^{66} +(0.939673 + 1.62756i) q^{67} -0.611915 q^{68} +(-0.0479148 + 0.0829908i) q^{69} +1.10418 q^{70} +2.64231 q^{71} +6.42389 q^{72} +(-1.40947 + 2.44127i) q^{73} +(7.82545 - 13.5541i) q^{74} +(1.15044 + 1.99262i) q^{75} +2.41929 q^{76} +1.24110 q^{77} +(-1.56237 - 3.31210i) q^{78} +(2.90930 + 5.03905i) q^{79} +(2.83102 + 4.90348i) q^{80} +5.28024 q^{81} +0.647460 q^{82} +(-7.89739 + 13.6787i) q^{83} +0.144362 q^{84} +(1.00055 + 1.73301i) q^{85} +(0.175435 + 0.303862i) q^{86} +(1.02974 - 1.78356i) q^{87} +(2.66362 + 4.61352i) q^{88} +(-8.66712 + 15.0119i) q^{89} +(2.42846 + 4.20622i) q^{90} +(-0.897256 - 1.90211i) q^{91} +0.0546148 q^{92} +(2.76421 + 2.41272i) q^{93} +(-4.21497 + 7.30055i) q^{94} +(-3.95582 - 6.85168i) q^{95} +(0.691282 + 1.19733i) q^{96} +(2.93445 + 5.08262i) q^{97} -10.2646 q^{98} +(2.72960 + 4.72780i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 2 q^{2} - 8 q^{3} - 34 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{8} + 58 q^{9}+O(q^{10}) \) 70 * q - 2 * q^2 - 8 * q^3 - 34 * q^4 - 2 * q^5 - 4 * q^7 - 6 * q^8 + 58 * q^9	\( 70 q - 2 q^{2} - 8 q^{3} - 34 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{8} + 58 q^{9} + 3 q^{10} + 2 q^{11} + 5 q^{12} + 4 q^{13} - 10 q^{14} + q^{15} - 28 q^{16} + 14 q^{17} - 20 q^{18} - 2 q^{19} - 50 q^{20} - 21 q^{21} - 8 q^{22} + 2 q^{23} - 8 q^{24} - 23 q^{25} + 6 q^{26} - 38 q^{27} + 42 q^{28} + 6 q^{29} + 31 q^{30} + 22 q^{31} + 14 q^{32} + 2 q^{33} - 11 q^{34} + 4 q^{35} - 28 q^{36} + 24 q^{37} - 7 q^{38} + 10 q^{39} - q^{40} - 2 q^{41} + 27 q^{42} - q^{43} + 2 q^{44} - 29 q^{45} + 14 q^{46} + q^{48} - 37 q^{49} - 14 q^{50} - 9 q^{51} - 19 q^{52} - 2 q^{53} + 24 q^{54} - 10 q^{55} - 13 q^{56} - q^{57} + 6 q^{58} + 21 q^{59} + 18 q^{60} - 3 q^{61} - 23 q^{62} - 32 q^{63} - 14 q^{64} + 23 q^{65} - 28 q^{66} - 2 q^{67} - 84 q^{68} + 32 q^{69} - 14 q^{70} - 86 q^{71} + 10 q^{72} + 11 q^{73} - 7 q^{74} + 37 q^{75} + 56 q^{76} - 10 q^{77} - 64 q^{78} + 2 q^{79} + 38 q^{80} + 22 q^{81} + 34 q^{82} + 56 q^{83} + 90 q^{84} - 5 q^{85} + 54 q^{86} - 24 q^{87} + 4 q^{88} + 30 q^{89} - 23 q^{90} - 36 q^{91} + 74 q^{92} + 19 q^{93} + 47 q^{94} - 9 q^{95} + 26 q^{96} + 29 q^{97} - 24 q^{98} + 3 q^{99}+O(q^{100}) \) 70 * q - 2 * q^2 - 8 * q^3 - 34 * q^4 - 2 * q^5 - 4 * q^7 - 6 * q^8 + 58 * q^9 + 3 * q^10 + 2 * q^11 + 5 * q^12 + 4 * q^13 - 10 * q^14 + q^15 - 28 * q^16 + 14 * q^17 - 20 * q^18 - 2 * q^19 - 50 * q^20 - 21 * q^21 - 8 * q^22 + 2 * q^23 - 8 * q^24 - 23 * q^25 + 6 * q^26 - 38 * q^27 + 42 * q^28 + 6 * q^29 + 31 * q^30 + 22 * q^31 + 14 * q^32 + 2 * q^33 - 11 * q^34 + 4 * q^35 - 28 * q^36 + 24 * q^37 - 7 * q^38 + 10 * q^39 - q^40 - 2 * q^41 + 27 * q^42 - q^43 + 2 * q^44 - 29 * q^45 + 14 * q^46 + q^48 - 37 * q^49 - 14 * q^50 - 9 * q^51 - 19 * q^52 - 2 * q^53 + 24 * q^54 - 10 * q^55 - 13 * q^56 - q^57 + 6 * q^58 + 21 * q^59 + 18 * q^60 - 3 * q^61 - 23 * q^62 - 32 * q^63 - 14 * q^64 + 23 * q^65 - 28 * q^66 - 2 * q^67 - 84 * q^68 + 32 * q^69 - 14 * q^70 - 86 * q^71 + 10 * q^72 + 11 * q^73 - 7 * q^74 + 37 * q^75 + 56 * q^76 - 10 * q^77 - 64 * q^78 + 2 * q^79 + 38 * q^80 + 22 * q^81 + 34 * q^82 + 56 * q^83 + 90 * q^84 - 5 * q^85 + 54 * q^86 - 24 * q^87 + 4 * q^88 + 30 * q^89 - 23 * q^90 - 36 * q^91 + 74 * q^92 + 19 * q^93 + 47 * q^94 - 9 * q^95 + 26 * q^96 + 29 * q^97 - 24 * q^98 + 3 * q^99

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