LMFDB - Embedded newform 799.2.g.d.189.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [799,2,Mod(189,799)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(799, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("799.189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 799 = 17 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	799.g (of order $8$, 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:	$6.38004712150$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			189.1
Character	$\chi$	$=$	799.189
Dual form			799.2.g.d.706.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.88952 - 1.88952i) q^{2} +(-2.62295 + 1.08646i) q^{3} +5.14055i q^{4} +(0.619807 + 1.49635i) q^{5} +(7.00898 + 2.90322i) q^{6} +(0.0896722 - 0.216488i) q^{7} +(5.93412 - 5.93412i) q^{8} +(3.57813 - 3.57813i) q^{9} +O(q^{10})$	\(q+(-1.88952 - 1.88952i) q^{2} +(-2.62295 + 1.08646i) q^{3} +5.14055i q^{4} +(0.619807 + 1.49635i) q^{5} +(7.00898 + 2.90322i) q^{6} +(0.0896722 - 0.216488i) q^{7} +(5.93412 - 5.93412i) q^{8} +(3.57813 - 3.57813i) q^{9} +(1.65624 - 3.99851i) q^{10} +(1.86715 + 0.773397i) q^{11} +(-5.58500 - 13.4834i) q^{12} -2.30532i q^{13} +(-0.578495 + 0.239620i) q^{14} +(-3.25144 - 3.25144i) q^{15} -12.1442 q^{16} +(-3.50946 + 2.16418i) q^{17} -13.5219 q^{18} +(2.35820 + 2.35820i) q^{19} +(-7.69204 + 3.18615i) q^{20} +0.665261i q^{21} +(-2.06666 - 4.98935i) q^{22} +(-0.749724 - 0.310546i) q^{23} +(-9.11770 + 22.0121i) q^{24} +(1.68064 - 1.68064i) q^{25} +(-4.35593 + 4.35593i) q^{26} +(-2.23837 + 5.40389i) q^{27} +(1.11287 + 0.460964i) q^{28} +(-2.67055 - 6.44727i) q^{29} +12.2873i q^{30} +(8.93906 - 3.70268i) q^{31} +(11.0783 + 11.0783i) q^{32} -5.73769 q^{33} +(10.7204 + 2.54193i) q^{34} +0.379520 q^{35} +(18.3936 + 18.3936i) q^{36} +(-9.70869 + 4.02147i) q^{37} -8.91173i q^{38} +(2.50463 + 6.04672i) q^{39} +(12.5575 + 5.20149i) q^{40} +(0.675569 - 1.63097i) q^{41} +(1.25702 - 1.25702i) q^{42} +(5.66397 - 5.66397i) q^{43} +(-3.97569 + 9.59816i) q^{44} +(7.57187 + 3.13637i) q^{45} +(0.829835 + 2.00340i) q^{46} +1.00000i q^{47} +(31.8535 - 13.1941i) q^{48} +(4.91092 + 4.91092i) q^{49} -6.35121 q^{50} +(6.85383 - 9.48942i) q^{51} +11.8506 q^{52} +(-0.641136 - 0.641136i) q^{53} +(14.4402 - 5.98132i) q^{54} +3.27325i q^{55} +(-0.752540 - 1.81679i) q^{56} +(-8.74753 - 3.62335i) q^{57} +(-7.13618 + 17.2283i) q^{58} +(2.64940 - 2.64940i) q^{59} +(16.7142 - 16.7142i) q^{60} +(-2.12051 + 5.11937i) q^{61} +(-23.8868 - 9.89423i) q^{62} +(-0.453763 - 1.09548i) q^{63} -17.5771i q^{64} +(3.44955 - 1.42885i) q^{65} +(10.8415 + 10.8415i) q^{66} +6.89649 q^{67} +(-11.1251 - 18.0406i) q^{68} +2.30388 q^{69} +(-0.717110 - 0.717110i) q^{70} +(-4.61922 + 1.91334i) q^{71} -42.4661i q^{72} +(-1.33835 - 3.23107i) q^{73} +(25.9434 + 10.7461i) q^{74} +(-2.58229 + 6.23419i) q^{75} +(-12.1225 + 12.1225i) q^{76} +(0.334862 - 0.334862i) q^{77} +(6.69283 - 16.1579i) q^{78} +(10.3071 + 4.26932i) q^{79} +(-7.52703 - 18.1719i) q^{80} -1.42530i q^{81} +(-4.35824 + 1.80524i) q^{82} +(0.294084 + 0.294084i) q^{83} -3.41981 q^{84} +(-5.41355 - 3.91000i) q^{85} -21.4044 q^{86} +(14.0094 + 14.0094i) q^{87} +(15.6693 - 6.49044i) q^{88} -8.12564i q^{89} +(-8.38095 - 20.2334i) q^{90} +(-0.499073 - 0.206723i) q^{91} +(1.59638 - 3.85399i) q^{92} +(-19.4239 + 19.4239i) q^{93} +(1.88952 - 1.88952i) q^{94} +(-2.06706 + 4.99032i) q^{95} +(-41.0941 - 17.0217i) q^{96} +(5.10718 + 12.3298i) q^{97} -18.5585i q^{98} +(9.44821 - 3.91358i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 4 q^{2} + 4 q^{6} + 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) $ 152 * q - 4 * q^2 + 4 * q^6 + 4 * q^7 + 4 * q^8 - 8 * q^9	$ 152 q - 4 q^{2} + 4 q^{6} + 4 q^{7} + 4 q^{8} - 8 q^{9} - 8 q^{11} + 8 q^{12} - 12 q^{14} + 20 q^{15} - 160 q^{16} - 12 q^{17} + 96 q^{18} + 16 q^{19} + 96 q^{20} - 4 q^{22} - 16 q^{23} - 76 q^{24} - 12 q^{25} - 8 q^{26} + 8 q^{28} - 4 q^{29} - 4 q^{31} - 16 q^{32} - 72 q^{33} - 20 q^{34} + 48 q^{35} - 16 q^{36} + 16 q^{37} + 64 q^{40} - 68 q^{41} - 144 q^{42} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 12 q^{48} - 4 q^{49} + 96 q^{50} - 52 q^{51} + 168 q^{52} - 16 q^{53} + 168 q^{54} + 108 q^{56} - 104 q^{58} - 84 q^{59} - 4 q^{60} + 4 q^{61} - 28 q^{62} + 60 q^{63} + 60 q^{65} - 44 q^{66} - 160 q^{67} - 96 q^{68} + 160 q^{69} + 36 q^{70} + 40 q^{71} + 4 q^{73} + 76 q^{74} - 116 q^{75} - 148 q^{76} - 4 q^{77} + 68 q^{78} - 76 q^{80} + 64 q^{82} - 124 q^{83} + 208 q^{84} - 68 q^{85} + 80 q^{86} - 72 q^{87} + 188 q^{88} + 236 q^{90} - 32 q^{91} - 196 q^{92} - 152 q^{93} + 4 q^{94} - 48 q^{95} - 56 q^{96} - 20 q^{97} + 244 q^{99}+O(q^{100}) $ 152 * q - 4 * q^2 + 4 * q^6 + 4 * q^7 + 4 * q^8 - 8 * q^9 - 8 * q^11 + 8 * q^12 - 12 * q^14 + 20 * q^15 - 160 * q^16 - 12 * q^17 + 96 * q^18 + 16 * q^19 + 96 * q^20 - 4 * q^22 - 16 * q^23 - 76 * q^24 - 12 * q^25 - 8 * q^26 + 8 * q^28 - 4 * q^29 - 4 * q^31 - 16 * q^32 - 72 * q^33 - 20 * q^34 + 48 * q^35 - 16 * q^36 + 16 * q^37 + 64 * q^40 - 68 * q^41 - 144 * q^42 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 12 * q^48 - 4 * q^49 + 96 * q^50 - 52 * q^51 + 168 * q^52 - 16 * q^53 + 168 * q^54 + 108 * q^56 - 104 * q^58 - 84 * q^59 - 4 * q^60 + 4 * q^61 - 28 * q^62 + 60 * q^63 + 60 * q^65 - 44 * q^66 - 160 * q^67 - 96 * q^68 + 160 * q^69 + 36 * q^70 + 40 * q^71 + 4 * q^73 + 76 * q^74 - 116 * q^75 - 148 * q^76 - 4 * q^77 + 68 * q^78 - 76 * q^80 + 64 * q^82 - 124 * q^83 + 208 * q^84 - 68 * q^85 + 80 * q^86 - 72 * q^87 + 188 * q^88 + 236 * q^90 - 32 * q^91 - 196 * q^92 - 152 * q^93 + 4 * q^94 - 48 * q^95 - 56 * q^96 - 20 * q^97 + 244 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/799\mathbb{Z}\right)^\times$.

$n$	$52$	$377$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

Coefficient data

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

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

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

$2$	−1.88952	−	1.88952i	−1.33609	−	1.33609i	−0.899812	−	0.436279i	$-0.856296\pi$
$2$	−1.88952	−	1.88952i	−1.33609	−	1.33609i	−0.436279	−	0.899812i	$-0.643704\pi$
$3$	−2.62295	+	1.08646i	−1.51436	+	0.627268i	−0.976452	−	0.215737i	$-0.930785\pi$
$3$	−2.62295	+	1.08646i	−1.51436	+	0.627268i	−0.537907	+	0.843004i	$0.680785\pi$
$4$			5.14055i			2.57027i
$5$	0.619807	+	1.49635i	0.277186	+	0.669186i	0.999755	−	0.0221121i	$-0.00703907\pi$
$5$	0.619807	+	1.49635i	0.277186	+	0.669186i	−0.722570	+	0.691298i	$0.757039\pi$
$6$	7.00898	+	2.90322i	2.86141	+	1.18523i
$7$	0.0896722	−	0.216488i	0.0338929	−	0.0818247i	−0.906027	−	0.423220i	$-0.860900\pi$
$7$	0.0896722	−	0.216488i	0.0338929	−	0.0818247i	0.939920	+	0.341396i	$0.110900\pi$
$8$	5.93412	−	5.93412i	2.09803	−	2.09803i
$9$	3.57813	−	3.57813i	1.19271	−	1.19271i
$10$	1.65624	−	3.99851i	0.523748	−	1.26444i
$11$	1.86715	+	0.773397i	0.562966	+	0.233188i	0.645972	−	0.763361i	$-0.276452\pi$
$11$	1.86715	+	0.773397i	0.562966	+	0.233188i	−0.0830063	+	0.996549i	$0.526452\pi$
$12$	−5.58500	−	13.4834i	−1.61225	−	3.89232i
$13$		−	2.30532i		−	0.639379i	−0.947522	−	0.319690i	$-0.896421\pi$
$13$		−	2.30532i		−	0.639379i	0.947522	−	0.319690i	$-0.103579\pi$
$14$	−0.578495	+	0.239620i	−0.154609	+	0.0640412i
$15$	−3.25144	−	3.25144i	−0.839518	−	0.839518i
$16$	−12.1442			−3.03604
$17$	−3.50946	+	2.16418i	−0.851170	+	0.524891i
$17$	−3.50946	+	2.16418i	−0.851170	+	0.524891i
$18$	−13.5219			−3.18714
$19$	2.35820	+	2.35820i	0.541009	+	0.541009i	0.923825	−	0.382816i	$-0.125046\pi$
$19$	2.35820	+	2.35820i	0.541009	+	0.541009i	−0.382816	+	0.923825i	$0.625046\pi$
$20$	−7.69204	+	3.18615i	−1.71999	+	0.712444i
$21$			0.665261i			0.145172i
$22$	−2.06666	−	4.98935i	−0.440613	−	1.06373i
$23$	−0.749724	−	0.310546i	−0.156328	−	0.0647533i	0.303147	−	0.952944i	$-0.401963\pi$
$23$	−0.749724	−	0.310546i	−0.156328	−	0.0647533i	−0.459476	+	0.888190i	$0.651963\pi$
$24$	−9.11770	+	22.0121i	−1.86114	+	4.49319i
$25$	1.68064	−	1.68064i	0.336129	−	0.336129i
$26$	−4.35593	+	4.35593i	−0.854269	+	0.854269i
$27$	−2.23837	+	5.40389i	−0.430774	+	1.03998i
$28$	1.11287	+	0.460964i	0.210312	+	0.0871141i
$29$	−2.67055	−	6.44727i	−0.495908	−	1.19723i	−0.951669	−	0.307125i	$-0.900633\pi$
$29$	−2.67055	−	6.44727i	−0.495908	−	1.19723i	0.455761	−	0.890102i	$-0.349367\pi$
$30$			12.2873i			2.24334i
$31$	8.93906	−	3.70268i	1.60550	−	0.665021i	0.613323	−	0.789832i	$-0.289833\pi$
$31$	8.93906	−	3.70268i	1.60550	−	0.665021i	0.992180	+	0.124811i	$0.0398325\pi$
$32$	11.0783	+	11.0783i	1.95839	+	1.95839i
$33$	−5.73769			−0.998804
$34$	10.7204	+	2.54193i	1.83854	+	0.435938i
$35$	0.379520			0.0641506
$36$	18.3936	+	18.3936i	3.06559	+	3.06559i
$37$	−9.70869	+	4.02147i	−1.59610	+	0.661126i	−0.990857	−	0.134916i	$-0.956924\pi$
$37$	−9.70869	+	4.02147i	−1.59610	+	0.661126i	−0.605242	+	0.796042i	$0.706924\pi$
$38$		−	8.91173i		−	1.44567i
$39$	2.50463	+	6.04672i	0.401062	+	0.968250i
$40$	12.5575	+	5.20149i	1.98552	+	0.822428i
$41$	0.675569	−	1.63097i	0.105506	−	0.254714i	−0.862306	−	0.506387i	$-0.830981\pi$
$41$	0.675569	−	1.63097i	0.105506	−	0.254714i	0.967812	+	0.251673i	$0.0809807\pi$
$42$	1.25702	−	1.25702i	0.193963	−	0.193963i
$43$	5.66397	−	5.66397i	0.863748	−	0.863748i	−0.128023	−	0.991771i	$-0.540863\pi$
$43$	5.66397	−	5.66397i	0.863748	−	0.863748i	0.991771	+	0.128023i	$0.0408632\pi$
$44$	−3.97569	+	9.59816i	−0.599358	+	1.44698i
$45$	7.57187	+	3.13637i	1.12875	+	0.467542i
$46$	0.829835	+	2.00340i	0.122352	+	0.295385i
$47$			1.00000i			0.145865i
$47$			1.00000i			0.145865i
$48$	31.8535	−	13.1941i	4.59765	−	1.90441i
$49$	4.91092	+	4.91092i	0.701560	+	0.701560i
$50$	−6.35121			−0.898197
$51$	6.85383	−	9.48942i	0.959729	−	1.32878i
$52$	11.8506			1.64338
$53$	−0.641136	−	0.641136i	−0.0880669	−	0.0880669i	0.661701	−	0.749768i	$-0.269835\pi$
$53$	−0.641136	−	0.641136i	−0.0880669	−	0.0880669i	−0.749768	+	0.661701i	$0.769835\pi$
$54$	14.4402	−	5.98132i	1.96506	−	0.813954i
$55$			3.27325i			0.441365i
$56$	−0.752540	−	1.81679i	−0.100562	−	0.242779i
$57$	−8.74753	−	3.62335i	−1.15864	−	0.479924i
$58$	−7.13618	+	17.2283i	−0.937026	+	2.26218i
$59$	2.64940	−	2.64940i	0.344922	−	0.344922i	−0.513292	−	0.858214i	$-0.671574\pi$
$59$	2.64940	−	2.64940i	0.344922	−	0.344922i	0.858214	+	0.513292i	$0.171574\pi$
$60$	16.7142	−	16.7142i	2.15779	−	2.15779i
$61$	−2.12051	+	5.11937i	−0.271504	+	0.655468i	−0.999548	−	0.0300619i	$-0.990430\pi$
$61$	−2.12051	+	5.11937i	−0.271504	+	0.655468i	0.728044	+	0.685530i	$0.240430\pi$
$62$	−23.8868	−	9.89423i	−3.03363	−	1.25657i
$63$	−0.453763	−	1.09548i	−0.0571687	−	0.138018i
$64$		−	17.5771i		−	2.19714i
$65$	3.44955	−	1.42885i	0.427864	−	0.177227i
$66$	10.8415	+	10.8415i	1.33449	+	1.33449i
$67$	6.89649			0.842541			0.421270	−	0.906935i	$-0.361584\pi$
$67$	6.89649			0.842541			0.421270	+	0.906935i	$0.361584\pi$
$68$	−11.1251	−	18.0406i	−1.34911	−	2.18774i
$69$	2.30388			0.277355
$70$	−0.717110	−	0.717110i	−0.0857110	−	0.0857110i
$71$	−4.61922	+	1.91334i	−0.548201	+	0.227072i	−0.639554	−	0.768746i	$-0.720881\pi$
$71$	−4.61922	+	1.91334i	−0.548201	+	0.227072i	0.0913529	+	0.995819i	$0.470881\pi$
$72$		−	42.4661i		−	5.00468i
$73$	−1.33835	−	3.23107i	−0.156642	−	0.378168i	0.826002	−	0.563667i	$-0.190610\pi$
$73$	−1.33835	−	3.23107i	−0.156642	−	0.378168i	−0.982644	+	0.185499i	$0.940610\pi$
$74$	25.9434	+	10.7461i	3.01586	+	1.24921i
$75$	−2.58229	+	6.23419i	−0.298177	+	0.719862i
$76$	−12.1225	+	12.1225i	−1.39054	+	1.39054i
$77$	0.334862	−	0.334862i	0.0381611	−	0.0381611i
$78$	6.69283	−	16.1579i	0.757814	−	1.82952i
$79$	10.3071	+	4.26932i	1.15963	+	0.480336i	0.877753	−	0.479113i	$-0.159042\pi$
$79$	10.3071	+	4.26932i	1.15963	+	0.480336i	0.281881	+	0.959449i	$0.409042\pi$
$80$	−7.52703	−	18.1719i	−0.841547	−	2.03167i
$81$		−	1.42530i		−	0.158367i
$82$	−4.35824	+	1.80524i	−0.481287	+	0.199356i
$83$	0.294084	+	0.294084i	0.0322799	+	0.0322799i	0.723063	−	0.690783i	$-0.242734\pi$
$83$	0.294084	+	0.294084i	0.0322799	+	0.0322799i	−0.690783	+	0.723063i	$0.742734\pi$
$84$	−3.41981			−0.373132
$85$	−5.41355	−	3.91000i	−0.587182	−	0.424099i
$86$	−21.4044			−2.30809
$87$	14.0094	+	14.0094i	1.50196	+	1.50196i
$88$	15.6693	−	6.49044i	1.67035	−	0.691883i
$89$		−	8.12564i		−	0.861316i	−0.902515	−	0.430658i	$-0.858282\pi$
$89$		−	8.12564i		−	0.861316i	0.902515	−	0.430658i	$-0.141718\pi$
$90$	−8.38095	−	20.2334i	−0.883429	−	2.13279i
$91$	−0.499073	−	0.206723i	−0.0523170	−	0.0216704i
$92$	1.59638	−	3.85399i	0.166434	−	0.401807i
$93$	−19.4239	+	19.4239i	−2.01416	+	2.01416i
$94$	1.88952	−	1.88952i	0.194889	−	0.194889i
$95$	−2.06706	+	4.99032i	−0.212076	+	0.511996i
$96$	−41.0941	−	17.0217i	−4.19414	−	1.73727i
$97$	5.10718	+	12.3298i	0.518555	+	1.25190i	0.938791	+	0.344488i	$0.111947\pi$
$97$	5.10718	+	12.3298i	0.518555	+	1.25190i	−0.420236	+	0.907415i	$0.638053\pi$
$98$		−	18.5585i		−	1.87470i
$99$	9.44821	−	3.91358i	0.949581	−	0.393329i
$100$	8.63943	+	8.63943i	0.863943	+	0.863943i
$101$	14.7407			1.46675			0.733376	−	0.679823i	$-0.237944\pi$
$101$	14.7407			1.46675			0.733376	+	0.679823i	$0.237944\pi$
$102$	−30.8809	+	4.97998i	−3.05766	+	0.493091i
$103$	19.5245			1.92381			0.961904	−	0.273386i	$-0.0881436\pi$
$103$	19.5245			1.92381			0.961904	+	0.273386i	$0.0881436\pi$
$104$	−13.6800	−	13.6800i	−1.34144	−	1.34144i
$105$	−0.995461	+	0.412333i	−0.0971470	+	0.0402396i
$106$			2.42288i			0.235331i
$107$	2.60519	+	6.28947i	0.251853	+	0.608026i	0.998354	−	0.0573580i	$-0.0182676\pi$
$107$	2.60519	+	6.28947i	0.251853	+	0.608026i	−0.746501	+	0.665384i	$0.768268\pi$
$108$	−27.7790	−	11.5064i	−2.67303	−	1.10721i
$109$	−3.33512	+	8.05169i	−0.319446	+	0.771212i	0.679837	+	0.733363i	$0.262050\pi$
$109$	−3.33512	+	8.05169i	−0.319446	+	0.771212i	−0.999283	+	0.0378486i	$0.987950\pi$
$110$	6.18487	−	6.18487i	0.589704	−	0.589704i
$111$	21.0962	−	21.0962i	2.00236	−	2.00236i
$112$	−1.08899	+	2.62906i	−0.102900	+	0.248423i
$113$	−1.72489	−	0.714473i	−0.162264	−	0.0672119i	0.300073	−	0.953916i	$-0.402989\pi$
$113$	−1.72489	−	0.714473i	−0.162264	−	0.0672119i	−0.462337	+	0.886704i	$0.652989\pi$
$114$	9.68224	+	23.3750i	0.906824	+	2.18927i
$115$		−	1.31433i		−	0.122561i
$116$	33.1425	−	13.7281i	3.07720	−	1.27462i
$117$	−8.24872	−	8.24872i	−0.762594	−	0.762594i
$118$	−10.0122			−0.921694
$119$	0.153818	+	0.953823i	0.0141004	+	0.0874368i
$120$	−38.5889			−3.52267
$121$	−4.89008	−	4.89008i	−0.444553	−	0.444553i
$122$	13.6799	−	5.66639i	1.23852	−	0.513011i
$123$			5.01192i			0.451909i
$124$	19.0338	+	45.9517i	1.70929	+	4.12658i
$125$	11.0382	+	4.57218i	0.987289	+	0.408949i
$126$	−1.21254	+	2.92732i	−0.108021	+	0.260786i
$127$	8.10813	−	8.10813i	0.719480	−	0.719480i	−0.249019	−	0.968499i	$-0.580108\pi$
$127$	8.10813	−	8.10813i	0.719480	−	0.719480i	0.968499	+	0.249019i	$0.0801080\pi$
$128$	−11.0556	+	11.0556i	−0.977185	+	0.977185i
$129$	−8.70262	+	21.0100i	−0.766223	+	1.84983i
$130$	−9.21782	−	3.81815i	−0.808456	−	0.334874i
$131$	−1.84455	−	4.45314i	−0.161159	−	0.389072i	0.822587	−	0.568640i	$-0.192530\pi$
$131$	−1.84455	−	4.45314i	−0.161159	−	0.389072i	−0.983746	+	0.179568i	$0.942530\pi$
$132$		−	29.4949i		−	2.56720i
$133$	0.721987	−	0.299057i	0.0626043	−	0.0259315i
$134$	−13.0310	−	13.0310i	−1.12571	−	1.12571i
$135$	−9.47345			−0.815345
$136$	−7.98307	+	33.6681i	−0.684542	+	2.88701i
$137$	−11.4914			−0.981780			−0.490890	−	0.871222i	$-0.663328\pi$
$137$	−11.4914			−0.981780			−0.490890	+	0.871222i	$0.663328\pi$
$138$	−4.35322	−	4.35322i	−0.370571	−	0.370571i
$139$	−9.76763	+	4.04588i	−0.828479	+	0.343167i	−0.756300	−	0.654224i	$-0.772995\pi$
$139$	−9.76763	+	4.04588i	−0.828479	+	0.343167i	−0.0721787	+	0.997392i	$0.522995\pi$
$140$			1.95094i			0.164885i
$141$	−1.08646	−	2.62295i	−0.0914964	−	0.220892i
$142$	12.3434	+	5.11280i	1.03584	+	0.429057i
$143$	1.78293	−	4.30436i	0.149096	−	0.359949i
$144$	−43.4533	+	43.4533i	−3.62111	+	3.62111i
$145$	7.99212	−	7.99212i	0.663709	−	0.663709i
$146$	−3.57632	+	8.63401i	−0.295979	+	0.714556i
$147$	−18.2166	−	7.54556i	−1.50248	−	0.622347i
$148$	−20.6726	−	49.9080i	−1.69928	−	4.10241i
$149$			15.6282i			1.28031i	0.768246	+	0.640155i	$0.221130\pi$
$149$			15.6282i			1.28031i	−0.768246	+	0.640155i	$0.778870\pi$
$150$	16.6589	−	6.90033i	1.36019	−	0.563410i
$151$	2.36009	+	2.36009i	0.192062	+	0.192062i	0.796586	−	0.604525i	$-0.206637\pi$
$151$	2.36009	+	2.36009i	0.192062	+	0.192062i	−0.604525	+	0.796586i	$0.706637\pi$
$152$	27.9877			2.27010
$153$	−4.81359	+	20.3010i	−0.389156	+	1.64124i
$154$	−1.26546			−0.101973
$155$	11.0810	+	11.0810i	0.890046	+	0.890046i
$156$	−31.0835	+	12.8752i	−2.48867	+	1.03084i
$157$			12.0250i			0.959700i	0.877351	+	0.479850i	$0.159309\pi$
$157$			12.0250i			0.959700i	−0.877351	+	0.479850i	$0.840691\pi$
$158$	−11.4084	−	27.5423i	−0.907604	−	2.19115i
$159$	2.37823	+	0.985097i	0.188606	+	0.0781233i
$160$	−9.71060	+	23.4435i	−0.767690	+	1.85337i
$161$	−0.134459	+	0.134459i	−0.0105968	+	0.0105968i
$162$	−2.69313	+	2.69313i	−0.211592	+	0.211592i
$163$	−2.43170	+	5.87065i	−0.190466	+	0.459825i	−0.990048	−	0.140732i	$-0.955054\pi$
$163$	−2.43170	+	5.87065i	−0.190466	+	0.459825i	0.799582	+	0.600557i	$0.205054\pi$
$164$	8.38407	+	3.47280i	0.654686	+	0.271180i
$165$	−3.55626	−	8.58557i	−0.276854	−	0.668386i
$166$		−	1.11135i		−	0.0862577i
$167$	13.2356	−	5.48237i	1.02420	−	0.424238i	0.193586	−	0.981083i	$-0.437988\pi$
$167$	13.2356	−	5.48237i	1.02420	−	0.424238i	0.830616	+	0.556845i	$0.187988\pi$
$168$	3.94774	+	3.94774i	0.304575	+	0.304575i
$169$	7.68552			0.591194
$170$	2.84099	+	17.6170i	0.217894	+	1.35116i
$171$	16.8759			1.29053
$172$	29.1159	+	29.1159i	2.22007	+	2.22007i
$173$	19.1539	−	7.93379i	1.45624	−	0.603195i	0.492567	−	0.870275i	$-0.336059\pi$
$173$	19.1539	−	7.93379i	1.45624	−	0.603195i	0.963674	+	0.267080i	$0.0860588\pi$
$174$		−	52.9420i		−	4.01352i
$175$	−0.213132	−	0.514546i	−0.0161113	−	0.0388960i
$176$	−22.6749	−	9.39226i	−1.70919	−	0.707968i
$177$	−4.07076	+	9.82768i	−0.305977	+	0.738694i
$178$	−15.3535	+	15.3535i	−1.15080	+	1.15080i
$179$	−16.9414	+	16.9414i	−1.26626	+	1.26626i	−0.318257	+	0.948005i	$0.603097\pi$
$179$	−16.9414	+	16.9414i	−1.26626	+	1.26626i	−0.948005	+	0.318257i	$0.896903\pi$
$180$	−16.1227	+	38.9236i	−1.20171	+	2.90119i
$181$	−14.2647	−	5.90862i	−1.06028	−	0.439184i	−0.216732	−	0.976231i	$-0.569540\pi$
$181$	−14.2647	−	5.90862i	−1.06028	−	0.439184i	−0.843552	+	0.537047i	$0.819540\pi$
$182$	0.552400	+	1.33361i	0.0409466	+	0.0988539i
$183$		−	15.7317i		−	1.16292i
$184$	−6.29177	+	2.60614i	−0.463836	+	0.192127i
$185$	−12.0350	−	12.0350i	−0.884833	−	0.884833i
$186$	73.4034			5.38220
$187$	−8.22645	+	1.32663i	−0.601578	+	0.0970130i
$188$	−5.14055			−0.374913
$189$	0.969158	+	0.969158i	0.0704959	+	0.0704959i
$190$	13.3350	−	5.52355i	0.967425	−	0.400720i
$191$			4.64818i			0.336330i	0.985759	+	0.168165i	$0.0537842\pi$
$191$			4.64818i			0.336330i	−0.985759	+	0.168165i	$0.946216\pi$
$192$	19.0968	+	46.1038i	1.37820	+	3.32726i
$193$	18.4212	+	7.63029i	1.32598	+	0.549240i	0.929507	−	0.368804i	$-0.120233\pi$
$193$	18.4212	+	7.63029i	1.32598	+	0.549240i	0.396477	+	0.918045i	$0.370233\pi$
$194$	13.6473	−	32.9475i	0.979819	−	2.36549i
$195$	−7.49559	+	7.49559i	−0.536770	+	0.536770i
$196$	−25.2448	+	25.2448i	−1.80320	+	1.80320i
$197$	−8.91621	+	21.5256i	−0.635254	+	1.53364i	0.197681	+	0.980266i	$0.436659\pi$
$197$	−8.91621	+	21.5256i	−0.635254	+	1.53364i	−0.832935	+	0.553371i	$0.813341\pi$
$198$	−25.2473	−	10.4578i	−1.79425	−	0.743202i
$199$	10.6170	+	25.6317i	0.752618	+	1.81698i	0.544231	+	0.838935i	$0.316821\pi$
$199$	10.6170	+	25.6317i	0.752618	+	1.81698i	0.208387	+	0.978046i	$0.433179\pi$
$200$		−	19.9463i		−	1.41042i
$201$	−18.0891	+	7.49276i	−1.27591	+	0.528499i
$202$	−27.8528	−	27.8528i	−1.95971	−	1.95971i
$203$	−1.63523			−0.114771
$204$	48.7808	+	35.2325i	3.41534	+	2.46677i
$205$	2.85921			0.199696
$206$	−36.8919	−	36.8919i	−2.57038	−	2.57038i
$207$	−3.79378	+	1.57144i	−0.263686	+	0.109222i
$208$			27.9961i			1.94118i
$209$	2.57928	+	6.22694i	0.178413	+	0.430726i
$210$	2.66005	+	1.10183i	0.183561	+	0.0760334i
$211$	−3.88707	+	9.38423i	−0.267597	+	0.646037i	−0.999369	−	0.0355127i	$-0.988694\pi$
$211$	−3.88707	+	9.38423i	−0.267597	+	0.646037i	0.731772	+	0.681549i	$0.238694\pi$
$212$	3.29579	−	3.29579i	0.226356	−	0.226356i
$213$	10.0372	−	10.0372i	0.687738	−	0.687738i
$214$	6.96153	−	16.8066i	0.475880	−	1.14888i
$215$	11.9858	+	4.96469i	0.817427	+	0.338589i
$216$	18.7846	+	45.3501i	1.27813	+	3.08568i
$217$		−	2.26723i		−	0.153909i
$218$	21.5156	−	8.91204i	1.45722	−	0.603599i
$219$	7.02086	+	7.02086i	0.474426	+	0.474426i
$220$	−16.8263			−1.13443
$221$	4.98912	+	8.09042i	0.335604	+	0.544220i
$222$	−79.7233			−5.35068
$223$	−9.76875	−	9.76875i	−0.654164	−	0.654164i	0.299829	−	0.953993i	$-0.403070\pi$
$223$	−9.76875	−	9.76875i	−0.654164	−	0.654164i	−0.953993	+	0.299829i	$0.903070\pi$
$224$	3.39174	−	1.40491i	0.226620	−	0.0938693i
$225$		−	12.0271i		−	0.801808i
$226$	1.90920	+	4.60922i	0.126998	+	0.306601i
$227$	0.285875	+	0.118413i	0.0189742	+	0.00785936i	0.392150	−	0.919901i	$-0.371731\pi$
$227$	0.285875	+	0.118413i	0.0189742	+	0.00785936i	−0.373176	+	0.927760i	$0.621731\pi$
$228$	18.6260	−	44.9671i	1.23354	−	2.97802i
$229$	13.2545	−	13.2545i	0.875881	−	0.875881i	−0.117225	−	0.993105i	$-0.537400\pi$
$229$	13.2545	−	13.2545i	0.875881	−	0.875881i	0.993105	+	0.117225i	$0.0373998\pi$
$230$	−2.48344	+	2.48344i	−0.163753	+	0.163753i
$231$	−0.514511	+	1.24214i	−0.0338524	+	0.0817268i
$232$	−54.1062	−	22.4115i	−3.55225	−	1.47139i
$233$	−4.73220	−	11.4245i	−0.310017	−	0.748447i	−0.999704	−	0.0243391i	$-0.992252\pi$
$233$	−4.73220	−	11.4245i	−0.310017	−	0.748447i	0.689687	−	0.724108i	$-0.257748\pi$
$234$			31.1722i			2.03779i
$235$	−1.49635	+	0.619807i	−0.0976108	+	0.0404317i
$236$	13.6193	+	13.6193i	0.886544	+	0.886544i
$237$	−31.6733			−2.05740
$238$	1.51162	−	2.09291i	0.0979840	−	0.135663i
$239$	0.0226260			0.00146356			0.000731778	−	1.00000i	$-0.499767\pi$
$239$	0.0226260			0.00146356			0.000731778		1.00000i	$0.499767\pi$
$240$	39.4860	+	39.4860i	2.54881	+	2.54881i
$241$	11.5598	−	4.78822i	0.744630	−	0.308436i	0.0220819	−	0.999756i	$-0.492971\pi$
$241$	11.5598	−	4.78822i	0.744630	−	0.308436i	0.722549	+	0.691320i	$0.242971\pi$
$242$			18.4798i			1.18793i
$243$	−5.16657	−	12.4732i	−0.331436	−	0.800156i
$244$	−26.3164	−	10.9006i	−1.68473	−	0.697840i
$245$	−4.30461	+	10.3923i	−0.275012	+	0.663937i
$246$	9.47011	−	9.47011i	0.603792	−	0.603792i
$247$	5.43640	−	5.43640i	0.345910	−	0.345910i
$248$	31.0733	−	75.0177i	1.97316	−	4.76363i
$249$	−1.09088	−	0.451856i	−0.0691315	−	0.0286352i
$250$	−12.2177	−	29.4961i	−0.772715	−	1.86550i
$251$			10.9507i			0.691205i	0.938381	+	0.345602i	$0.112325\pi$
$251$			10.9507i			0.691205i	−0.938381	+	0.345602i	$0.887675\pi$
$252$	5.63137	−	2.33259i	0.354743	−	0.146939i
$253$	−1.15967	−	1.15967i	−0.0729078	−	0.0729078i
$254$	−30.6409			−1.92258
$255$	18.4475	+	4.37410i	1.15523	+	0.273917i
$256$	6.62521			0.414076
$257$	−18.1646	−	18.1646i	−1.13308	−	1.13308i	−0.989662	−	0.143417i	$-0.954191\pi$
$257$	−18.1646	−	18.1646i	−1.13308	−	1.13308i	−0.143417	−	0.989662i	$-0.545809\pi$
$258$	56.1425	−	23.2550i	3.49528	−	1.44779i
$259$			2.46243i			0.153008i
$260$	7.34507	+	17.7326i	0.455522	+	1.09973i
$261$	−32.6247	−	13.5136i	−2.01942	−	0.836471i
$262$	−4.92897	+	11.8996i	−0.304513	+	0.735159i
$263$	6.88669	−	6.88669i	0.424651	−	0.424651i	−0.462150	−	0.886802i	$-0.652922\pi$
$263$	6.88669	−	6.88669i	0.424651	−	0.424651i	0.886802	+	0.462150i	$0.152922\pi$
$264$	−34.0482	+	34.0482i	−2.09552	+	2.09552i
$265$	0.561981	−	1.35674i	0.0345222	−	0.0833440i
$266$	−1.92928	−	0.799134i	−0.118292	−	0.0489981i
$267$	8.82818	+	21.3131i	0.540276	+	1.30434i
$268$			35.4518i			2.16556i
$269$	−15.4765	+	6.41056i	−0.943617	+	0.390859i	−0.800828	−	0.598894i	$-0.795607\pi$
$269$	−15.4765	+	6.41056i	−0.943617	+	0.390859i	−0.142789	+	0.989753i	$0.545607\pi$
$270$	17.9002	+	17.9002i	1.08937	+	1.08937i
$271$	−15.5602			−0.945212			−0.472606	−	0.881274i	$-0.656687\pi$
$271$	−15.5602			−0.945212			−0.472606	+	0.881274i	$0.656687\pi$
$272$	42.6194	−	26.2821i	2.58418	−	1.59359i
$273$	1.53364			0.0928199
$274$	21.7133	+	21.7133i	1.31175	+	1.31175i
$275$	4.43781	−	1.83820i	0.267610	−	0.110848i
$276$			11.8432i			0.712878i
$277$	5.08563	+	12.2778i	0.305566	+	0.737701i	0.999838	+	0.0179889i	$0.00572636\pi$
$277$	5.08563	+	12.2778i	0.305566	+	0.737701i	−0.694272	+	0.719712i	$0.744274\pi$
$278$	26.1009	+	10.8113i	1.56543	+	0.648420i
$279$	18.7365	−	45.2338i	1.12172	−	2.70808i
$280$	2.25212	−	2.25212i	0.134590	−	0.134590i
$281$	4.66347	−	4.66347i	0.278199	−	0.278199i	−0.554191	−	0.832390i	$-0.686972\pi$
$281$	4.66347	−	4.66347i	0.278199	−	0.278199i	0.832390	+	0.554191i	$0.186972\pi$
$282$	−2.90322	+	7.00898i	−0.172884	+	0.417379i
$283$	6.51628	+	2.69913i	0.387353	+	0.160447i	0.567856	−	0.823128i	$-0.307773\pi$
$283$	6.51628	+	2.69913i	0.387353	+	0.160447i	−0.180504	+	0.983574i	$0.557773\pi$
$284$	−9.83564	−	23.7453i	−0.583638	−	1.40903i
$285$		−	15.3351i		−	0.908373i
$286$	−11.5020	+	4.76430i	−0.680129	+	0.281719i
$287$	−0.292505	−	0.292505i	−0.0172660	−	0.0172660i
$288$	79.2795			4.67159
$289$	7.63265	−	15.1902i	0.448979	−	0.893542i
$290$	−30.2025			−1.77355
$291$	−26.7917	−	26.7917i	−1.57056	−	1.57056i
$292$	16.6095	−	6.87987i	0.971997	−	0.402614i
$293$			20.9501i			1.22392i	0.790890	+	0.611958i	$0.209618\pi$
$293$			20.9501i			1.22392i	−0.790890	+	0.611958i	$0.790382\pi$
$294$	20.1631	+	48.6780i	1.17594	+	2.83896i
$295$	5.60652	+	2.32230i	0.326425	+	0.135209i
$296$	−33.7487	+	81.4765i	−1.96160	+	4.73572i
$297$	−8.35872	+	8.35872i	−0.485022	+	0.485022i
$298$	29.5297	−	29.5297i	1.71061	−	1.71061i
$299$	−0.715906	+	1.72835i	−0.0414019	+	0.0999531i
$300$	−32.0472	−	13.2744i	−1.85024	−	0.766396i
$301$	−0.718280	−	1.73408i	−0.0414010	−	0.0999509i
$302$		−	8.91887i		−	0.513224i
$303$	−38.6640	+	16.0151i	−2.22119	+	0.920046i
$304$	−28.6384	−	28.6384i	−1.64252	−	1.64252i
$305$	−8.97466			−0.513887
$306$	47.4545	−	29.2638i	2.71279	−	1.67290i
$307$	10.4876			0.598558			0.299279	−	0.954166i	$-0.403254\pi$
$307$	10.4876			0.598558			0.299279	+	0.954166i	$0.403254\pi$
$308$	1.72138	+	1.72138i	0.0980845	+	0.0980845i
$309$	−51.2118	+	21.2126i	−2.91334	+	1.20674i
$310$		−	41.8754i		−	2.37836i
$311$	1.06739	+	2.57690i	0.0605260	+	0.146123i	0.951249	−	0.308424i	$-0.0998014\pi$
$311$	1.06739	+	2.57690i	0.0605260	+	0.146123i	−0.890723	+	0.454546i	$0.849801\pi$
$312$	50.7448	+	21.0192i	2.87286	+	1.18998i
$313$	8.22796	−	19.8641i	0.465072	−	1.12278i	−0.501217	−	0.865322i	$-0.667114\pi$
$313$	8.22796	−	19.8641i	0.465072	−	1.12278i	0.966289	−	0.257461i	$-0.0828859\pi$
$314$	22.7215	−	22.7215i	1.28225	−	1.28225i
$315$	1.35797	−	1.35797i	0.0765130	−	0.0765130i
$316$	−21.9467	+	52.9839i	−1.23460	+	2.98058i
$317$	−13.2651	−	5.49458i	−0.745042	−	0.308606i	−0.0223250	−	0.999751i	$-0.507107\pi$
$317$	−13.2651	−	5.49458i	−0.745042	−	0.308606i	−0.722717	+	0.691144i	$0.757107\pi$
$318$	−2.63236	−	6.35507i	−0.147615	−	0.356375i
$319$		−	14.1034i		−	0.789638i
$320$	26.3015	−	10.8944i	1.47030	−	0.609016i
$321$	−13.6665	−	13.6665i	−0.762791	−	0.762791i
$322$	0.508125			0.0283167
$323$	−13.3796	−	3.17245i	−0.744461	−	0.176520i
$324$	7.32682			0.407046
$325$	−3.87441	−	3.87441i	−0.214914	−	0.214914i
$326$	15.6874	−	6.49795i	0.868847	−	0.359888i
$327$		−	24.7426i		−	1.36827i
$328$	−5.66945	−	13.6873i	−0.313043	−	0.755753i
$329$	0.216488	+	0.0896722i	0.0119354	+	0.00494379i
$330$	−9.50297	+	22.9422i	−0.523121	+	1.26293i
$331$	0.210813	−	0.210813i	0.0115873	−	0.0115873i	−0.701289	−	0.712877i	$-0.747392\pi$
$331$	0.210813	−	0.210813i	0.0115873	−	0.0115873i	0.712877	+	0.701289i	$0.247392\pi$
$332$	−1.51175	+	1.51175i	−0.0829682	+	0.0829682i
$333$	−20.3496	+	49.1283i	−1.11515	+	2.69221i
$334$	−35.3679	−	14.6499i	−1.93525	−	0.801606i
$335$	4.27449	+	10.3195i	0.233540	+	0.563817i
$336$		−	8.07903i		−	0.440747i
$337$	−8.78844	+	3.64029i	−0.478737	+	0.198299i	−0.608984	−	0.793182i	$-0.708423\pi$
$337$	−8.78844	+	3.64029i	−0.478737	+	0.198299i	0.130248	+	0.991482i	$0.458423\pi$
$338$	−14.5219	−	14.5219i	−0.789888	−	0.789888i
$339$	5.30054			0.287886
$340$	20.0995	−	27.8286i	1.09005	−	1.50922i
$341$	19.5542			1.05892
$342$	−31.8873	−	31.8873i	−1.72427	−	1.72427i
$343$	3.01894	−	1.25049i	0.163008	−	0.0675200i
$344$		−	67.2214i		−	3.62434i
$345$	1.42796	+	3.44740i	0.0768788	+	0.185602i
$346$	−51.1826	−	21.2005i	−2.75159	−	1.13975i
$347$	7.57351	−	18.2841i	0.406568	−	0.981541i	−0.579466	−	0.814996i	$-0.696739\pi$
$347$	7.57351	−	18.2841i	0.406568	−	0.981541i	0.986034	−	0.166545i	$-0.0532610\pi$
$348$	−72.0160	+	72.0160i	−3.86046	+	3.86046i
$349$	24.4693	−	24.4693i	1.30981	−	1.30981i	0.388262	−	0.921549i	$-0.373076\pi$
$349$	24.4693	−	24.4693i	1.30981	−	1.30981i	0.921549	−	0.388262i	$-0.126924\pi$
$350$	−0.569527	+	1.37496i	−0.0304425	+	0.0734947i
$351$	12.4577	+	5.16014i	0.664942	+	0.275428i
$352$	12.1169	+	29.2528i	0.645834	+	1.55918i
$353$			15.9517i			0.849023i	0.905422	+	0.424512i	$0.139554\pi$
$353$			15.9517i			0.849023i	−0.905422	+	0.424512i	$0.860446\pi$
$354$	26.2613	−	10.8778i	1.39577	−	0.578149i
$355$	−5.72605	−	5.72605i	−0.303907	−	0.303907i
$356$	41.7702			2.21382
$357$	−1.43974	−	2.33471i	−0.0761994	−	0.123566i
$358$	64.0222			3.38368
$359$	−18.9207	−	18.9207i	−0.998599	−	0.998599i	0.00140036	−	0.999999i	$-0.499554\pi$
$359$	−18.9207	−	18.9207i	−0.998599	−	0.998599i	−0.999999	+	0.00140036i	$0.999554\pi$
$360$	63.5440	−	26.3208i	3.34906	−	1.38723i
$361$		−	7.87776i		−	0.414619i
$362$	15.7889	+	38.1178i	0.829846	+	2.00343i
$363$	18.1393	+	7.51354i	0.952066	+	0.394359i
$364$	1.06267	−	2.56551i	0.0556990	−	0.134469i
$365$	4.00528	−	4.00528i	0.209646	−	0.209646i
$366$	−29.7253	+	29.7253i	−1.55377	+	1.55377i
$367$	−9.91325	+	23.9327i	−0.517467	+	1.24928i	0.421987	+	0.906602i	$0.361333\pi$
$367$	−9.91325	+	23.9327i	−0.517467	+	1.24928i	−0.939454	+	0.342675i	$0.888667\pi$
$368$	9.10477	+	3.77132i	0.474619	+	0.196594i
$369$	−3.41854	−	8.25309i	−0.177962	−	0.429639i
$370$			45.4808i			2.36443i
$371$	−0.196290	+	0.0813061i	−0.0101909	+	0.00422120i
$372$	−99.8493	−	99.8493i	−5.17695	−	5.17695i
$373$	31.0147			1.60588			0.802940	−	0.596059i	$-0.203268\pi$
$373$	31.0147			1.60588			0.802940	+	0.596059i	$0.203268\pi$
$374$	18.0507	+	13.0373i	0.933380	+	0.674144i
$375$	−33.9202			−1.75163
$376$	5.93412	+	5.93412i	0.306029	+	0.306029i
$377$	−14.8630	+	6.15645i	−0.765483	+	0.317073i
$378$		−	3.66248i		−	0.188378i
$379$	−7.23327	−	17.4627i	−0.371548	−	0.896997i	−0.993489	−	0.113932i	$-0.963655\pi$
$379$	−7.23327	−	17.4627i	−0.371548	−	0.896997i	0.621940	−	0.783065i	$-0.286345\pi$
$380$	−25.6530	−	10.6258i	−1.31597	−	0.545093i
$381$	−12.4580	+	30.0763i	−0.638244	+	1.54086i
$382$	8.78281	−	8.78281i	0.449368	−	0.449368i
$383$	16.7145	−	16.7145i	0.854069	−	0.854069i	−0.136562	−	0.990631i	$-0.543605\pi$
$383$	16.7145	−	16.7145i	0.854069	−	0.854069i	0.990631	+	0.136562i	$0.0436054\pi$
$384$	16.9868	−	41.0097i	0.866852	−	2.09277i
$385$	0.708620	+	0.293520i	0.0361146	+	0.0149592i
$386$	−20.3895	−	49.2247i	−1.03780	−	2.50547i
$387$		−	40.5329i		−	2.06040i
$388$	−63.3820	+	26.2537i	−3.21773	+	1.33283i
$389$	−1.74851	−	1.74851i	−0.0886528	−	0.0886528i	0.661390	−	0.750042i	$-0.269967\pi$
$389$	−1.74851	−	1.74851i	−0.0886528	−	0.0886528i	−0.750042	+	0.661390i	$0.769967\pi$
$390$	28.3261			1.43435
$391$	3.30321	−	0.532689i	0.167050	−	0.0269393i
$392$	58.2840			2.94379
$393$	9.67630	+	9.67630i	0.488105	+	0.488105i
$394$	57.5204	−	23.8257i	2.89783	−	1.20032i
$395$			18.0691i			0.909154i
$396$	20.1179	+	48.5690i	1.01096	+	2.44068i
$397$	−28.8961	−	11.9692i	−1.45025	−	0.600715i	−0.487994	−	0.872847i	$-0.662271\pi$
$397$	−28.8961	−	11.9692i	−1.45025	−	0.600715i	−0.962260	+	0.272132i	$0.912271\pi$
$398$	28.3705	−	68.4925i	1.42209	−	3.43322i
$399$	−1.56882	+	1.56882i	−0.0785393	+	0.0785393i
$400$	−20.4100	+	20.4100i	−1.02050	+	1.02050i
$401$	0.888275	−	2.14449i	0.0443583	−	0.107091i	−0.900147	−	0.435585i	$-0.856541\pi$
$401$	0.888275	−	2.14449i	0.0443583	−	0.107091i	0.944506	+	0.328495i	$0.106541\pi$
$402$	48.3374	+	20.0220i	2.41085	+	0.998607i
$403$	−8.53585	−	20.6074i	−0.425201	−	1.02653i
$404$			75.7752i			3.76996i
$405$	2.13274	−	0.883410i	0.105977	−	0.0438970i
$406$	3.08979	+	3.08979i	0.153344	+	0.153344i
$407$	−21.2377			−1.05272
$408$	−15.6399	−	96.9829i	−0.774289	−	4.80137i
$409$	16.4819			0.814978			0.407489	−	0.913210i	$-0.366404\pi$
$409$	16.4819			0.814978			0.407489	+	0.913210i	$0.366404\pi$
$410$	−5.40253	−	5.40253i	−0.266812	−	0.266812i
$411$	30.1414	−	12.4850i	1.48677	−	0.615839i
$412$			100.367i			4.94472i
$413$	−0.335985	−	0.811139i	−0.0165327	−	0.0399135i
$414$	10.1377	+	4.19916i	0.498240	+	0.206378i
$415$	−0.257776	+	0.622326i	−0.0126537	+	0.0305488i
$416$	25.5391	−	25.5391i	1.25216	−	1.25216i
$417$	21.2243	−	21.2243i	1.03936	−	1.03936i
$418$	6.89231	−	16.6395i	0.337114	−	0.813865i
$419$	29.7140	+	12.3079i	1.45162	+	0.601282i	0.962585	−	0.270981i	$-0.0873480\pi$
$419$	29.7140	+	12.3079i	1.45162	+	0.601282i	0.489038	+	0.872263i	$0.337348\pi$
$420$	−2.11962	−	5.11721i	−0.103427	−	0.249695i
$421$		−	24.0664i		−	1.17293i	−0.809976	−	0.586463i	$-0.800520\pi$
$421$		−	24.0664i		−	1.17293i	0.809976	−	0.586463i	$-0.199480\pi$
$422$	25.0763	−	10.3870i	1.22070	−	0.505629i
$423$	3.57813	+	3.57813i	0.173975	+	0.173975i
$424$	−7.60916			−0.369534
$425$	−2.26094	+	9.53537i	−0.109672	+	0.462533i
$426$	−37.9309			−1.83776
$427$	0.918131	+	0.918131i	0.0444315	+	0.0444315i
$428$	−32.3314	+	13.3921i	−1.56280	+	0.647331i
$429$			13.2272i			0.638614i
$430$	−13.2666	−	32.0283i	−0.639770	−	1.54454i
$431$	28.7342	+	11.9021i	1.38408	+	0.573303i	0.945568	−	0.325424i	$-0.105507\pi$
$431$	28.7342	+	11.9021i	1.38408	+	0.573303i	0.438508	+	0.898727i	$0.355507\pi$
$432$	27.1831	−	65.6257i	1.30785	−	3.15742i
$433$	−21.8302	+	21.8302i	−1.04909	+	1.04909i	−0.0503623	+	0.998731i	$0.516038\pi$
$433$	−21.8302	+	21.8302i	−1.04909	+	1.04909i	−0.998731	+	0.0503623i	$0.983962\pi$
$434$	−4.28396	+	4.28396i	−0.205637	+	0.205637i
$435$	−12.2798	+	29.6460i	−0.588770	+	1.42142i
$436$	−41.3901	−	17.1443i	−1.98223	−	0.821065i
$437$	−1.03567	−	2.50033i	−0.0495429	−	0.119607i
$438$		−	26.5321i		−	1.26775i
$439$	34.8832	−	14.4491i	1.66489	−	0.689619i	0.666452	−	0.745548i	$-0.267812\pi$
$439$	34.8832	−	14.4491i	1.66489	−	0.689619i	0.998435	+	0.0559295i	$0.0178122\pi$
$440$	19.4239	+	19.4239i	0.925998	+	0.925998i
$441$	35.1438			1.67352
$442$	5.85996	−	24.7140i	0.278730	−	1.17553i
$443$	10.4338			0.495723			0.247862	−	0.968795i	$-0.420272\pi$
$443$	10.4338			0.495723			0.247862	+	0.968795i	$0.420272\pi$
$444$	108.446	+	108.446i	5.14662	+	5.14662i
$445$	12.1588	−	5.03632i	0.576381	−	0.238745i
$446$			36.9165i			1.74804i
$447$	−16.9794	−	40.9918i	−0.803097	−	1.93885i
$448$	−3.80523	−	1.57618i	−0.179780	−	0.0744675i
$449$	5.91675	−	14.2843i	0.279229	−	0.674118i	−0.720586	−	0.693366i	$-0.756127\pi$
$449$	5.91675	−	14.2843i	0.279229	−	0.674118i	0.999815	+	0.0192476i	$0.00612707\pi$
$450$	−22.7254	+	22.7254i	−1.07129	+	1.07129i
$451$	2.52277	−	2.52277i	0.118793	−	0.118793i
$452$	3.67278	−	8.86688i	0.172753	−	0.417063i
$453$	−8.75454	−	3.62625i	−0.411324	−	0.170376i
$454$	−0.316421	−	0.763909i	−0.0148504	−	0.0358520i
$455$		−	0.874913i		−	0.0410166i
$456$	−73.4103	+	30.4075i	−3.43775	+	1.42396i
$457$	8.87502	+	8.87502i	0.415156	+	0.415156i	0.883530	−	0.468374i	$-0.155160\pi$
$457$	8.87502	+	8.87502i	0.415156	+	0.415156i	−0.468374	+	0.883530i	$0.655160\pi$
$458$	−50.0891			−2.34051
$459$	−3.83954	−	23.8090i	−0.179214	−	1.11131i
$460$	6.75635			0.315017
$461$	−19.3590	−	19.3590i	−0.901640	−	0.901640i	0.0939382	−	0.995578i	$-0.470054\pi$
$461$	−19.3590	−	19.3590i	−0.901640	−	0.901640i	−0.995578	+	0.0939382i	$0.970054\pi$
$462$	3.31922	−	1.37487i	0.154424	−	0.0639646i
$463$			31.1533i			1.44781i	0.689897	+	0.723907i	$0.257656\pi$
$463$			31.1533i			1.44781i	−0.689897	+	0.723907i	$0.742344\pi$
$464$	32.4315	+	78.2966i	1.50560	+	3.63483i
$465$	−41.1039	−	17.0258i	−1.90615	−	0.789551i
$466$	−12.6453	+	30.5284i	−0.585782	+	1.41420i
$467$	18.9227	−	18.9227i	0.875637	−	0.875637i	−0.117443	−	0.993080i	$-0.537470\pi$
$467$	18.9227	−	18.9227i	0.875637	−	0.875637i	0.993080	+	0.117443i	$0.0374697\pi$
$468$	42.4029	−	42.4029i	1.96008	−	1.96008i
$469$	0.618424	−	1.49301i	0.0285561	−	0.0689406i
$470$	3.99851	+	1.65624i	0.184437	+	0.0763965i
$471$	−13.0647	−	31.5409i	−0.601989	−	1.45333i
$472$		−	31.4437i		−	1.44731i
$473$	14.9560	−	6.19497i	0.687676	−	0.284845i
$474$	59.8472	+	59.8472i	2.74887	+	2.74887i
$475$	7.92660			0.363697
$476$	−4.90317	+	0.790707i	−0.224737	+	0.0362420i
$477$	−4.58814			−0.210076
$478$	−0.0427523	−	0.0427523i	−0.00195544	−	0.00195544i
$479$	−12.2308	+	5.06615i	−0.558838	+	0.231478i	−0.644180	−	0.764874i	$-0.722801\pi$
$479$	−12.2308	+	5.06615i	−0.558838	+	0.231478i	0.0853429	+	0.996352i	$0.472801\pi$
$480$		−	72.0411i		−	3.28821i
$481$	9.27076	+	22.3816i	0.422710	+	1.02051i
$482$	−30.8898	−	12.7950i	−1.40699	−	0.582795i
$483$	0.206594	−	0.498762i	0.00940036	−	0.0226945i
$484$	25.1377	−	25.1377i	1.14262	−	1.14262i
$485$	−15.2842	+	15.2842i	−0.694020	+	0.694020i
$486$	−13.8060	+	33.3306i	−0.626253	+	1.51191i
$487$	21.1112	+	8.74453i	0.956638	+	0.396253i	0.805722	−	0.592294i	$-0.201778\pi$
$487$	21.1112	+	8.74453i	0.956638	+	0.396253i	0.150916	+	0.988547i	$0.451778\pi$
$488$	17.7956	+	42.9624i	0.805569	+	1.94481i
$489$		−	18.0403i		−	0.815813i
$490$	27.7700	−	11.5027i	1.25452	−	0.519639i
$491$	24.0849	+	24.0849i	1.08694	+	1.08694i	0.995842	+	0.0910927i	$0.0290359\pi$
$491$	24.0849	+	24.0849i	1.08694	+	1.08694i	0.0910927	+	0.995842i	$0.470964\pi$
$492$	−25.7640			−1.16153
$493$	23.3252	+	16.8469i	1.05052	+	0.758746i
$494$	−20.5443			−0.924334
$495$	11.7121	+	11.7121i	0.526421	+	0.526421i
$496$	−108.557	+	44.9659i	−4.87437	+	2.01903i
$497$			1.17158i			0.0525525i
$498$	1.20744	+	2.91502i	0.0541067	+	0.130625i
$499$	−24.7781	−	10.2634i	−1.10922	−	0.459455i	−0.248552	−	0.968619i	$-0.579955\pi$
$499$	−24.7781	−	10.2634i	−1.10922	−	0.459455i	−0.860670	+	0.509164i	$0.829955\pi$
$500$	−23.5035	+	56.7426i	−1.05111	+	2.53760i
$501$	−28.7599	+	28.7599i	−1.28490	+	1.28490i
$502$	20.6916	−	20.6916i	0.923512	−	0.923512i
$503$	−9.38284	+	22.6522i	−0.418360	+	1.01001i	0.564463	+	0.825458i	$0.309083\pi$
$503$	−9.38284	+	22.6522i	−0.418360	+	1.01001i	−0.982823	+	0.184552i	$0.940917\pi$
$504$	−9.19340	−	3.80803i	−0.409506	−	0.169623i
$505$	9.13637	+	22.0571i	0.406563	+	0.981530i
$506$			4.38243i			0.194823i
$507$	−20.1587	+	8.35001i	−0.895279	+	0.370837i
$508$	41.6802	+	41.6802i	1.84926	+	1.84926i
$509$	7.01131			0.310771			0.155385	−	0.987854i	$-0.450338\pi$
$509$	7.01131			0.310771			0.155385	+	0.987854i	$0.450338\pi$
$510$	−26.5919	−	43.1218i	−1.17751	−	1.90947i
$511$	−0.819501			−0.0362526
$512$	9.59273	+	9.59273i	0.423943	+	0.423943i
$513$	−18.0220	+	7.46496i	−0.795691	+	0.329586i
$514$			68.6448i			3.02779i
$515$	12.1014	+	29.2154i	0.533253	+	1.28739i
$516$	−108.003	−	44.7362i	−4.75456	−	1.96940i
$517$	−0.773397	+	1.86715i	−0.0340140	+	0.0821170i
$518$	4.65280	−	4.65280i	0.204432	−	0.204432i
$519$	−41.6198	+	41.6198i	−1.82691	+	1.82691i
$520$	11.9911	−	28.9490i	0.525843	−	1.26950i
$521$	27.1429	+	11.2430i	1.18915	+	0.492564i	0.887479	−	0.460847i	$-0.152454\pi$
$521$	27.1429	+	11.2430i	1.18915	+	0.492564i	0.301674	+	0.953411i	$0.402454\pi$
$522$	36.1108	+	87.1791i	1.58053	+	3.81573i
$523$			40.5891i			1.77484i	0.460966	+	0.887418i	$0.347503\pi$
$523$			40.5891i			1.77484i	−0.460966	+	0.887418i	$0.652497\pi$
$524$	22.8916	−	9.48200i	1.00002	−	0.414223i
$525$	1.11807	+	1.11807i	0.0487964	+	0.0487964i
$526$	−26.0250			−1.13474
$527$	−23.3580	+	32.3402i	−1.01749	+	1.40876i
$528$	69.6794			3.03241
$529$	−15.7978	−	15.7978i	−0.686861	−	0.686861i
$530$	−3.62546	+	1.50172i	−0.157480	+	0.0652303i
$531$		−	18.9598i		−	0.822783i
$532$	1.53732	+	3.71141i	0.0666512	+	0.160910i
$533$	−3.75990	−	1.55740i	−0.162859	−	0.0674585i
$534$	23.5905	−	56.9525i	1.02086	−	2.46457i
$535$	−7.79652	+	7.79652i	−0.337073	+	0.337073i
$536$	40.9246	−	40.9246i	1.76767	−	1.76767i
$537$	26.0303	−	62.8426i	1.12329	−	2.71186i
$538$	41.3559	+	17.1302i	1.78298	+	0.738535i
$539$	5.37132	+	12.9675i	0.231359	+	0.558550i
$540$		−	48.6987i		−	2.09566i
$541$	12.3510	−	5.11594i	0.531010	−	0.219952i	−0.101035	−	0.994883i	$-0.532216\pi$
$541$	12.3510	−	5.11594i	0.531010	−	0.219952i	0.632046	+	0.774931i	$0.282216\pi$
$542$	29.4012	+	29.4012i	1.26289	+	1.26289i
$543$	43.8349			1.88114
$544$	−62.8545	−	14.9035i	−2.69487	−	0.638982i
$545$	−14.1152			−0.604630
$546$	−2.89783	−	2.89783i	−0.124016	−	0.124016i
$547$	−14.0210	+	5.80769i	−0.599495	+	0.248319i	−0.661730	−	0.749743i	$-0.730177\pi$
$547$	−14.0210	+	5.80769i	−0.599495	+	0.248319i	0.0622347	+	0.998062i	$0.480177\pi$
$548$		−	59.0723i		−	2.52344i
$549$	10.7303	+	25.9052i	0.457958	+	1.10561i
$550$	−11.8586	−	4.91201i	−0.505654	−	0.209449i
$551$	8.90628	−	21.5017i	0.379420	−	0.916001i
$552$	13.6715	−	13.6715i	0.581898	−	0.581898i
$553$	1.84851	−	1.84851i	0.0786068	−	0.0786068i
$554$	13.5897	−	32.8085i	0.577372	−	1.39390i
$555$	44.6428	+	18.4916i	1.89498	+	0.784927i
$556$	−20.7981	−	50.2110i	−0.882034	−	2.12942i
$557$			0.334797i			0.0141858i	0.999975	+	0.00709290i	$0.00225776\pi$
$557$			0.334797i			0.0141858i	−0.999975	+	0.00709290i	$0.997742\pi$
$558$	−120.873	+	50.0672i	−5.11696	+	2.11951i
$559$	−13.0572	−	13.0572i	−0.552263	−	0.552263i
$560$	−4.60895			−0.194764
$561$	20.1362	−	12.4174i	0.850151	−	0.524263i
$562$	−17.6234			−0.743399
$563$	−13.4733	−	13.4733i	−0.567833	−	0.567833i	0.363688	−	0.931521i	$-0.381517\pi$
$563$	−13.4733	−	13.4733i	−0.567833	−	0.567833i	−0.931521	+	0.363688i	$0.881517\pi$
$564$	13.4834	−	5.58500i	0.567753	−	0.235171i
$565$		−	3.02387i		−	0.127215i
$566$	−7.21257	−	17.4127i	−0.303167	−	0.731909i
$567$	−0.308560	−	0.127810i	−0.0129583	−	0.00536750i
$568$	−16.0570	+	38.7651i	−0.673737	+	1.62655i
$569$	−19.7134	+	19.7134i	−0.826430	+	0.826430i	−0.987021	−	0.160591i	$-0.948660\pi$
$569$	−19.7134	+	19.7134i	−0.826430	+	0.826430i	0.160591	+	0.987021i	$0.448660\pi$
$570$	−28.9759	+	28.9759i	−1.21367	+	1.21367i
$571$	−1.38544	+	3.34475i	−0.0579789	+	0.139973i	−0.950214	−	0.311597i	$-0.899136\pi$
$571$	−1.38544	+	3.34475i	−0.0579789	+	0.139973i	0.892235	+	0.451571i	$0.149136\pi$
$572$	22.1268	+	9.16522i	0.925167	+	0.383217i
$573$	−5.05006	−	12.1919i	−0.210969	−	0.509325i
$574$			1.10539i			0.0461379i
$575$	−1.78194	+	0.738102i	−0.0743119	+	0.0307810i
$576$	−62.8932	−	62.8932i	−2.62055	−	2.62055i
$577$	−14.4882			−0.603152			−0.301576	−	0.953442i	$-0.597513\pi$
$577$	−14.4882			−0.603152			−0.301576	+	0.953442i	$0.597513\pi$
$578$	−43.1242	+	14.2802i	−1.79373	+	0.593976i
$579$	−56.6077			−2.35254
$580$	41.0839	+	41.0839i	1.70592	+	1.70592i
$581$	0.0900367	−	0.0372944i	0.00373535	−	0.00154723i
$582$			101.247i			4.19681i
$583$	−0.701242	−	1.69295i	−0.0290425	−	0.0701148i
$584$	−27.1155	−	11.2316i	−1.12205	−	0.464768i
$585$	7.23032	−	17.4555i	0.298937	−	0.721698i
$586$	39.5855	−	39.5855i	1.63526	−	1.63526i
$587$	−11.3393	+	11.3393i	−0.468022	+	0.468022i	−0.901273	−	0.433251i	$-0.857366\pi$
$587$	−11.3393	+	11.3393i	−0.468022	+	0.468022i	0.433251	+	0.901273i	$0.357366\pi$
$588$	38.7883	−	93.6433i	1.59960	−	3.86179i
$589$	29.8118	+	12.3485i	1.22837	+	0.508809i
$590$	−6.20560	−	14.9816i	−0.255481	−	0.616785i
$591$		−	66.1477i		−	2.72095i
$592$	117.904	−	48.8374i	4.84582	−	2.00720i
$593$	4.70068	+	4.70068i	0.193034	+	0.193034i	0.797006	−	0.603972i	$-0.206416\pi$
$593$	4.70068	+	4.70068i	0.193034	+	0.193034i	−0.603972	+	0.797006i	$0.706416\pi$
$594$	31.5879			1.29607
$595$	−1.33191	+	0.821350i	−0.0546030	+	0.0336721i
$596$	−80.3374			−3.29075
$597$	−55.6956	−	55.6956i	−2.27947	−	2.27947i
$598$	4.61847	−	1.91303i	0.188863	−	0.0782297i
$599$		−	36.3128i		−	1.48370i	−0.670564	−	0.741851i	$-0.733948\pi$
$599$		−	36.3128i		−	1.48370i	0.670564	−	0.741851i	$-0.266052\pi$
$600$	21.6708	+	52.3180i	0.884708	+	2.13587i
$601$	−35.1391	−	14.5551i	−1.43335	−	0.593714i	−0.475176	−	0.879891i	$-0.657615\pi$
$601$	−35.1391	−	14.5551i	−1.43335	−	0.593714i	−0.958177	+	0.286177i	$0.907615\pi$
$602$	−1.91938	+	4.63378i	−0.0782279	+	0.188859i
$603$	24.6765	−	24.6765i	1.00491	−	1.00491i
$604$	−12.1322	+	12.1322i	−0.493651	+	0.493651i
$605$	4.28635	−	10.3482i	0.174265	−	0.420712i
$606$	103.317	+	42.7954i	4.19697	+	1.73844i
$607$	−10.0203	−	24.1912i	−0.406713	−	0.981892i	−0.985997	−	0.166766i	$-0.946668\pi$
$607$	−10.0203	−	24.1912i	−0.406713	−	0.981892i	0.579284	−	0.815126i	$-0.303332\pi$
$608$			52.2500i			2.11902i
$609$	4.28912	−	1.77661i	0.173804	−	0.0719919i
$610$	16.9578	+	16.9578i	0.686600	+	0.686600i
$611$	2.30532			0.0932631
$612$	−104.358	−	24.7445i	−4.21844	−	1.00024i
$613$	6.87424			0.277648			0.138824	−	0.990317i	$-0.455668\pi$
$613$	6.87424			0.277648			0.138824	+	0.990317i	$0.455668\pi$
$614$	−19.8165	−	19.8165i	−0.799728	−	0.799728i
$615$	−7.49956	+	3.10642i	−0.302412	+	0.125263i
$616$		−	3.97423i		−	0.160126i
$617$	−9.84750	−	23.7740i	−0.396445	−	0.957104i	−0.988502	−	0.151207i	$-0.951684\pi$
$617$	−9.84750	−	23.7740i	−0.396445	−	0.957104i	0.592057	−	0.805896i	$-0.298316\pi$
$618$	136.847	+	56.6839i	5.50480	+	2.28016i
$619$	−1.79201	+	4.32628i	−0.0720268	+	0.173888i	−0.955793	−	0.294041i	$-0.905000\pi$
$619$	−1.79201	+	4.32628i	−0.0720268	+	0.173888i	0.883766	+	0.467929i	$0.155000\pi$
$620$	−56.9623	+	56.9623i	−2.28766	+	2.28766i
$621$	3.35631	−	3.35631i	0.134684	−	0.134684i
$622$	2.85225	−	6.88594i	0.114365	−	0.276101i
$623$	−1.75910	−	0.728644i	−0.0704769	−	0.0291925i
$624$	−30.4166	−	73.4323i	−1.21764	−	2.93964i
$625$			7.46693i			0.298677i
$626$	−53.0803	+	21.9866i	−2.12152	+	0.878761i
$627$	−13.5306	−	13.5306i	−0.540362	−	0.540362i
$628$	−61.8152			−2.46669
$629$	25.3691	−	35.1246i	1.01153	−	1.40051i
$630$	−5.13182			−0.204457
$631$	−20.3302	−	20.3302i	−0.809331	−	0.809331i	0.175201	−	0.984533i	$-0.443942\pi$
$631$	−20.3302	−	20.3302i	−0.809331	−	0.809331i	−0.984533	+	0.175201i	$0.943942\pi$
$632$	86.4980	−	35.8287i	3.44071	−	1.42519i
$633$		−	28.8375i		−	1.14619i
$634$	14.6825	+	35.4467i	0.583117	+	1.40777i
$635$	17.1580	+	7.10709i	0.680896	+	0.282036i
$636$	−5.06394	+	12.2254i	−0.200798	+	0.484770i
$637$	11.3212	−	11.3212i	0.448563	−	0.448563i
$638$	−26.6486	+	26.6486i	−1.05503	+	1.05503i
$639$	−9.68198	+	23.3744i	−0.383013	+	0.924676i
$640$	−23.3953	−	9.69066i	−0.924781	−	0.383057i
$641$	12.7350	+	30.7450i	0.503002	+	1.21435i	0.947841	+	0.318743i	$0.103261\pi$
$641$	12.7350	+	30.7450i	0.503002	+	1.21435i	−0.444839	+	0.895610i	$0.646739\pi$
$642$			51.6463i			2.03831i
$643$	31.8151	−	13.1782i	1.25466	−	0.519698i	0.346396	−	0.938089i	$-0.387405\pi$
$643$	31.8151	−	13.1782i	1.25466	−	0.519698i	0.908267	+	0.418390i	$0.137405\pi$
$644$	−0.691192	−	0.691192i	−0.0272368	−	0.0272368i
$645$	−36.8321			−1.45026
$646$	19.2866	+	31.2754i	0.758821	+	1.23051i
$647$	38.6039			1.51767			0.758837	−	0.651280i	$-0.225768\pi$
$647$	38.6039			1.51767			0.758837	+	0.651280i	$0.225768\pi$
$648$	−8.45790	−	8.45790i	−0.332258	−	0.332258i
$649$	6.99585	−	2.89777i	0.274611	−	0.113748i
$650$			14.6415i			0.574289i
$651$	2.46325	+	5.94681i	0.0965424	+	0.233074i
$652$	−30.1784	−	12.5003i	−1.18188	−	0.489549i
$653$	−15.0279	+	36.2806i	−0.588088	+	1.41977i	0.297240	+	0.954803i	$0.403934\pi$
$653$	−15.0279	+	36.2806i	−0.588088	+	1.41977i	−0.885328	+	0.464967i	$0.846066\pi$
$654$	−46.7516	+	46.7516i	−1.82813	+	1.82813i
$655$	5.52017	−	5.52017i	0.215691	−	0.215691i
$656$	−8.20421	+	19.8067i	−0.320321	+	0.773323i
$657$	−16.3500	−	6.77239i	−0.637874	−	0.264216i
$658$	−0.239620	−	0.578495i	−0.00934137	−	0.0225521i
$659$			9.66360i			0.376440i	0.982127	+	0.188220i	$0.0602719\pi$
$659$			9.66360i			0.376440i	−0.982127	+	0.188220i	$0.939728\pi$
$660$	44.1345	−	18.2811i	1.71793	−	0.711592i
$661$	1.89134	+	1.89134i	0.0735646	+	0.0735646i	0.742932	−	0.669367i	$-0.233435\pi$
$661$	1.89134	+	1.89134i	0.0735646	+	0.0735646i	−0.669367	+	0.742932i	$0.733435\pi$
$662$	−0.796668			−0.0309634
$663$	−21.8761	−	15.8002i	−0.849597	−	0.613631i
$664$	3.49026			0.135448
$665$	0.894985	+	0.894985i	0.0347060	+	0.0347060i
$666$	131.280	−	54.3778i	5.08698	−	2.10710i
$667$			5.66300i			0.219272i
$668$	28.1824	+	68.0383i	1.09041	+	2.63248i
$669$	36.2363	+	15.0096i	1.40098	+	0.580303i
$670$	11.4222	−	27.5757i	0.441279	−	1.06534i
$671$	−7.91862	+	7.91862i	−0.305695	+	0.305695i
$672$	−7.36999	+	7.36999i	−0.284303	+	0.284303i
$673$	13.8777	−	33.5038i	0.534948	−	1.29148i	−0.393264	−	0.919425i	$-0.628654\pi$
$673$	13.8777	−	33.5038i	0.534948	−	1.29148i	0.928212	−	0.372052i	$-0.121346\pi$
$674$	23.4843	+	9.72752i	0.904581	+	0.374690i
$675$	5.32012	+	12.8439i	0.204772	+	0.494363i
$676$			39.5078i			1.51953i
$677$	−4.83631	+	2.00327i	−0.185875	+	0.0769918i	−0.473680	−	0.880697i	$-0.657075\pi$
$677$	−4.83631	+	2.00327i	−0.185875	+	0.0769918i	0.287805	+	0.957689i	$0.407075\pi$
$678$	−10.0155	−	10.0155i	−0.384641	−	0.384641i
$679$	3.12723			0.120012
$680$	−55.3271	+	8.92228i	−2.12170	+	0.342154i
$681$	−0.878485			−0.0336636
$682$	−36.9480	−	36.9480i	−1.41481	−	1.41481i
$683$	−0.842610	+	0.349021i	−0.0322416	+	0.0133549i	−0.398746	−	0.917061i	$-0.630554\pi$
$683$	−0.842610	+	0.349021i	−0.0322416	+	0.0133549i	0.366504	+	0.930416i	$0.380554\pi$
$684$			86.7515i			3.31702i
$685$	−7.12247	−	17.1952i	−0.272136	−	0.656993i
$686$	−8.06716	−	3.34153i	−0.308006	−	0.127580i
$687$	−20.3653	+	49.1662i	−0.776985	+	1.87581i
$688$	−68.7842	+	68.7842i	−2.62237	+	2.62237i
$689$	−1.47802	+	1.47802i	−0.0563081	+	0.0563081i
$690$	3.81577	−	9.21208i	0.145264	−	0.350698i
$691$	12.9897	+	5.38052i	0.494152	+	0.204685i	0.615821	−	0.787886i	$-0.288825\pi$
$691$	12.9897	+	5.38052i	0.494152	+	0.204685i	−0.121669	+	0.992571i	$0.538825\pi$
$692$	40.7840	+	98.4614i	1.55038	+	3.74294i
$693$		−	2.39636i		−	0.0910302i
$694$	−48.8584	+	20.2378i	−1.85464	+	0.768216i
$695$	−12.1081	−	12.1081i	−0.459286	−	0.459286i
$696$	166.267			6.30233
$697$	1.15882	+	7.18587i	0.0438936	+	0.272184i
$698$	−92.4703			−3.50005
$699$	24.8246	+	24.8246i	0.938953	+	0.938953i
$700$	2.64505	−	1.09562i	0.0999734	−	0.0414104i
$701$			14.4579i			0.546066i	0.962005	+	0.273033i	$0.0880269\pi$
$701$			14.4579i			0.546066i	−0.962005	+	0.273033i	$0.911973\pi$
$702$	−13.7888	−	33.2892i	−0.520426	−	1.25642i
$703$	−32.3785	−	13.4116i	−1.22118	−	0.505829i
$704$	13.5941	−	32.8191i	0.512347	−	1.23691i
$705$	3.25144	−	3.25144i	0.122456	−	0.122456i
$706$	30.1410	−	30.1410i	1.13437	−	1.13437i
$707$	1.32183	−	3.19118i	0.0497125	−	0.120017i
$708$	−50.5197	−	20.9259i	−1.89865	−	0.786445i
$709$	−17.3520	−	41.8915i	−0.651669	−	1.57327i	−0.810356	−	0.585938i	$-0.800726\pi$
$709$	−17.3520	−	41.8915i	−0.651669	−	1.57327i	0.158687	−	0.987329i	$-0.449274\pi$
$710$			21.6389i			0.812095i
$711$	52.1562	−	21.6038i	1.95601	−	0.810205i
$712$	−48.2185	−	48.2185i	−1.80707	−	1.80707i
$713$	−7.85168			−0.294048
$714$	−1.69105	+	7.13189i	−0.0632859	+	0.266904i
$715$	7.54588			0.282200
$716$	−87.0882	−	87.0882i	−3.25464	−	3.25464i
$717$	−0.0593468	+	0.0245823i	−0.00221635	+	0.000918041i
$718$			71.5021i			2.66844i
$719$	2.38061	+	5.74730i	0.0887818	+	0.214338i	0.962034	−	0.272931i	$-0.0879931\pi$
$719$	2.38061	+	5.74730i	0.0887818	+	0.214338i	−0.873252	+	0.487269i	$0.837993\pi$
$720$	−91.9539	−	38.0886i	−3.42692	−	1.41948i
$721$	1.75081	−	4.22682i	0.0652035	−	0.157415i
$722$	−14.8852	+	14.8852i	−0.553968	+	0.553968i
$723$	−25.1185	+	25.1185i	−0.934165	+	0.934165i
$724$	30.3735	−	73.3282i	1.12882	−	2.72522i
$725$	−15.3238	−	6.34732i	−0.569111	−	0.235734i
$726$	−20.0775	−	48.4715i	−0.745147	−	1.79895i
$727$		−	26.5614i		−	0.985109i	−0.870282	−	0.492554i	$-0.836063\pi$
$727$		−	26.5614i		−	0.985109i	0.870282	−	0.492554i	$-0.163937\pi$
$728$	−4.18828	+	1.73484i	−0.155228	+	0.0642975i
$729$	30.1268	+	30.1268i	1.11581	+	1.11581i
$730$	−15.1361			−0.560212
$731$	−7.61964	+	32.1354i	−0.281823	+	1.18857i
$732$	80.8695			2.98902
$733$	5.29870	+	5.29870i	0.195712	+	0.195712i	0.798159	−	0.602447i	$-0.205808\pi$
$733$	5.29870	+	5.29870i	0.195712	+	0.195712i	−0.602447	+	0.798159i	$0.705808\pi$
$734$	63.9525	−	26.4900i	2.36053	−	0.977763i
$735$		−	31.9351i		−	1.17794i
$736$	−4.86537	−	11.7460i	−0.179340	−	0.432965i
$737$	12.8768	+	5.33373i	0.474322	+	0.196470i
$738$	−9.13496	+	22.0537i	−0.336262	+	0.811809i
$739$	0.224526	−	0.224526i	0.00825932	−	0.00825932i	−0.702965	−	0.711224i	$-0.748141\pi$
$739$	0.224526	−	0.224526i	0.00825932	−	0.00825932i	0.711224	+	0.702965i	$0.248141\pi$
$740$	61.8666	−	61.8666i	2.27426	−	2.27426i
$741$	−8.35296	+	20.1658i	−0.306853	+	0.740810i
$742$	0.524523	+	0.217265i	0.0192559	+	0.00797604i
$743$	−6.16887	−	14.8930i	−0.226314	−	0.546370i	0.769409	−	0.638756i	$-0.220551\pi$
$743$	−6.16887	−	14.8930i	−0.226314	−	0.546370i	−0.995723	+	0.0923857i	$0.970551\pi$
$744$			230.527i			8.45154i
$745$	−23.3851	+	9.68645i	−0.856766	+	0.354884i
$746$	−58.6028	−	58.6028i	−2.14560	−	2.14560i
$747$	2.10454			0.0770011
$748$	−6.81962	−	42.2885i	−0.249350	−	1.54622i
$749$	1.59521			0.0582876
$750$	64.0927	+	64.0927i	2.34034	+	2.34034i
$751$	−13.1349	+	5.44065i	−0.479299	+	0.198532i	−0.609234	−	0.792990i	$-0.708523\pi$
$751$	−13.1349	+	5.44065i	−0.479299	+	0.198532i	0.129935	+	0.991522i	$0.458523\pi$
$752$		−	12.1442i		−	0.442852i
$753$	−11.8975	−	28.7232i	−0.433571	−	1.04673i
$754$	39.7166	+	16.4511i	1.44639	+	0.599115i
$755$	−2.06871	+	4.99432i	−0.0752882	+	0.181762i
$756$	−4.98201	+	4.98201i	−0.181194	+	0.181194i
$757$	−0.0565136	+	0.0565136i	−0.00205402	+	0.00205402i	−0.708133	−	0.706079i	$-0.750462\pi$
$757$	−0.0565136	+	0.0565136i	−0.00205402	+	0.00205402i	0.706079	+	0.708133i	$0.250462\pi$
$758$	−19.3286	+	46.6634i	−0.702047	+	1.69489i
$759$	4.30168	+	1.78182i	0.156141	+	0.0646758i
$760$	17.3470	+	41.8793i	0.629241	+	1.51912i
$761$		−	30.4594i		−	1.10415i	−0.833794	−	0.552076i	$-0.813836\pi$
$761$		−	30.4594i		−	1.10415i	0.833794	−	0.552076i	$-0.186164\pi$
$762$	80.3694	−	33.2901i	2.91148	−	1.20597i
$763$	1.44402	+	1.44402i	0.0522772	+	0.0522772i
$764$	−23.8942			−0.864461
$765$	−33.3608	+	5.37991i	−1.20616	+	0.194511i
$766$	−63.1645			−2.28223
$767$	−6.10769	−	6.10769i	−0.220536	−	0.220536i
$768$	−17.3776	+	7.19802i	−0.627059	+	0.259736i
$769$		−	42.2114i		−	1.52218i	−0.648646	−	0.761091i	$-0.724664\pi$
$769$		−	42.2114i		−	1.52218i	0.648646	−	0.761091i	$-0.275336\pi$
$770$	−0.784338	−	1.89356i	−0.0282656	−	0.0682392i
$771$	67.3800	+	27.9097i	2.42663	+	1.00514i
$772$	−39.2239	+	94.6949i	−1.41170	+	3.40814i
$773$	17.3923	−	17.3923i	0.625556	−	0.625556i	−0.321390	−	0.946947i	$-0.604150\pi$
$773$	17.3923	−	17.3923i	0.625556	−	0.625556i	0.946947	+	0.321390i	$0.104150\pi$
$774$	−76.5875	+	76.5875i	−2.75288	+	2.75288i
$775$	8.80049	−	21.2463i	0.316123	−	0.763188i
$776$	103.473	+	42.8600i	3.71447	+	1.53858i
$777$	−2.67533	−	6.45881i	−0.0959769	−	0.231709i
$778$			6.60766i			0.236896i
$779$	5.43928	−	2.25302i	0.194882	−	0.0807230i
$780$	−38.5315	−	38.5315i	−1.37965	−	1.37965i
$781$	−10.1045			−0.361569
$782$	−7.24799	−	5.23494i	−0.259188	−	0.187201i
$783$	40.8180			1.45872
$784$	−59.6390	−	59.6390i	−2.12996	−	2.12996i
$785$	−17.9936	+	7.45318i	−0.642218	+	0.266015i
$786$		−	36.5671i		−	1.30430i
$787$	11.8875	+	28.6991i	0.423745	+	1.02301i	0.981233	+	0.192826i	$0.0617653\pi$
$787$	11.8875	+	28.6991i	0.423745	+	1.02301i	−0.557488	+	0.830185i	$0.688235\pi$
$788$	−110.654	−	45.8342i	−3.94187	−	1.63278i
$789$	−10.5813	+	25.5455i	−0.376704	+	0.909444i
$790$	34.1418	−	34.1418i	1.21471	−	1.21471i
$791$	−0.309349	+	0.309349i	−0.0109992	+	0.0109992i
$792$	32.8432	−	79.2905i	1.16703	−	2.81746i
$793$	11.8018	+	4.88845i	0.419093	+	0.173594i
$794$	31.9837	+	77.2156i	1.13506	+	2.74028i
$795$			4.16923i			0.147867i
$796$	−131.761	+	54.5772i	−4.67014	+	1.93444i
$797$	−1.11916	−	1.11916i	−0.0396427	−	0.0396427i	0.687008	−	0.726650i	$-0.258924\pi$
$797$	−1.11916	−	1.11916i	−0.0396427	−	0.0396427i	−0.726650	+	0.687008i	$0.758924\pi$
$798$	5.92863			0.209871
$799$	−2.16418	−	3.50946i	−0.0765632	−	0.124156i
$800$	37.2375			1.31654
$801$	−29.0746	−	29.0746i	−1.02730	−	1.02730i
$802$	−5.73045	+	2.37363i	−0.202349	+	0.0838159i
$803$		−	7.06796i		−	0.249423i
$804$	−38.5169	−	92.9880i	−1.35839	−	3.27944i
$805$	−0.284535	−	0.117858i	−0.0100286	−	0.00415396i
$806$	−22.8093	+	55.0666i	−0.803424	+	1.93964i
$807$	33.6291	−	33.6291i	1.18380	−	1.18380i
$808$	87.4730	−	87.4730i	3.07729	−	3.07729i
$809$	3.20687	−	7.74206i	0.112747	−	0.272196i	−0.857426	−	0.514607i	$-0.827938\pi$
$809$	3.20687	−	7.74206i	0.112747	−	0.272196i	0.970174	+	0.242410i	$0.0779380\pi$
$810$	−5.69907	−	2.36063i	−0.200245	−	0.0829441i
$811$	1.48344	+	3.58135i	0.0520907	+	0.125758i	0.947783	−	0.318917i	$-0.103319\pi$
$811$	1.48344	+	3.58135i	0.0520907	+	0.125758i	−0.895692	+	0.444675i	$0.853319\pi$
$812$		−	8.40597i		−	0.294992i
$813$	40.8134	−	16.9055i	1.43139	−	0.592901i
$814$	40.1291	+	40.1291i	1.40652	+	1.40652i
$815$	−10.2917			−0.360503
$816$	−83.2340	+	115.241i	−2.91377	+	4.03424i
$817$	26.7136			0.934591
$818$	−31.1428	−	31.1428i	−1.08888	−	1.08888i
$819$	−2.52543	+	1.04607i	−0.0882456	+	0.0365525i
$820$			14.6979i			0.513274i
$821$	13.7824	+	33.2735i	0.481007	+	1.16125i	0.959131	+	0.282962i	$0.0913170\pi$
$821$	13.7824	+	33.2735i	0.481007	+	1.16125i	−0.478124	+	0.878292i	$0.658683\pi$
$822$	−80.5433	−	33.3621i	−2.80927	−	1.16364i
$823$	−11.6475	+	28.1196i	−0.406007	+	0.980189i	0.580170	+	0.814495i	$0.302986\pi$
$823$	−11.6475	+	28.1196i	−0.406007	+	0.980189i	−0.986177	+	0.165693i	$0.947014\pi$
$824$	115.861	−	115.861i	4.03621	−	4.03621i
$825$	−9.64301	+	9.64301i	−0.335727	+	0.335727i
$826$	−0.897812	+	2.16751i	−0.0312389	+	0.0754173i
$827$	24.1418	+	9.99985i	0.839492	+	0.347729i	0.760653	−	0.649159i	$-0.224879\pi$
$827$	24.1418	+	9.99985i	0.839492	+	0.347729i	0.0788385	+	0.996887i	$0.474879\pi$
$828$	−8.07805	−	19.5021i	−0.280732	−	0.677746i
$829$		−	1.06576i		−	0.0370154i	−0.999829	−	0.0185077i	$-0.994108\pi$
$829$		−	1.06576i		−	0.0370154i	0.999829	−	0.0185077i	$-0.00589152\pi$
$830$	1.66297	−	0.688824i	0.0577225	−	0.0239094i
$831$	−26.6787	−	26.6787i	−0.925473	−	0.925473i
$832$	−40.5208			−1.40481
$833$	−27.8628	−	6.60657i	−0.965389	−	0.228904i
$834$	−80.2072			−2.77735
$835$	16.4070	+	16.4070i	0.567789	+	0.567789i
$836$	−32.0099	+	13.2589i	−1.10709	+	0.458570i
$837$			56.5937i			1.95616i
$838$	−32.8890	−	79.4011i	−1.13613	−	2.74287i
$839$	29.2258	+	12.1057i	1.00899	+	0.417935i	0.825085	−	0.565009i	$-0.191127\pi$
$839$	29.2258	+	12.1057i	1.00899	+	0.417935i	0.183901	+	0.982945i	$0.441127\pi$
$840$	−3.46035	+	8.35402i	−0.119393	+	0.288241i
$841$	−13.9293	+	13.9293i	−0.480322	+	0.480322i
$842$	−45.4740	+	45.4740i	−1.56714	+	1.56714i
$843$	−7.16535	+	17.2987i	−0.246788	+	0.595799i
$844$	−48.2401	−	19.9817i	−1.66049	−	0.687798i
$845$	4.76354	+	11.5002i	0.163871	+	0.395619i
$846$		−	13.5219i		−	0.464892i
$847$	−1.49715	+	0.620139i	−0.0514426	+	0.0213082i
$848$	7.78606	+	7.78606i	0.267374	+	0.267374i
$849$	−20.0243			−0.687234
$850$	22.2893	−	13.7452i	0.764518	−	0.471455i
$851$	8.52769			0.292326
$852$	51.5967	+	51.5967i	1.76767	+	1.76767i
$853$	15.4412	−	6.39593i	0.528695	−	0.218993i	−0.102337	−	0.994750i	$-0.532632\pi$
$853$	15.4412	−	6.39593i	0.528695	−	0.218993i	0.631031	+	0.775757i	$0.282632\pi$
$854$		−	3.46965i		−	0.118729i
$855$	10.4598	+	25.2522i	0.357718	+	0.863607i
$856$	52.7820	+	21.8630i	1.80405	+	0.747263i
$857$	17.8408	−	43.0716i	0.609431	−	1.47130i	−0.254190	−	0.967154i	$-0.581809\pi$
$857$	17.8408	−	43.0716i	0.609431	−	1.47130i	0.863621	−	0.504142i	$-0.168191\pi$
$858$	24.9930	−	24.9930i	0.853247	−	0.853247i
$859$	−1.17990	+	1.17990i	−0.0402577	+	0.0402577i	−0.726949	−	0.686691i	$-0.759062\pi$
$859$	−1.17990	+	1.17990i	−0.0402577	+	0.0402577i	0.686691	+	0.726949i	$0.259062\pi$
$860$	−25.5213	+	61.6138i	−0.870268	+	2.10101i
$861$	1.08502	+	0.449430i	0.0369774	+	0.0153165i
$862$	−31.8045	−	76.7829i	−1.08327	−	2.61524i
$863$			10.1295i			0.344811i	0.985026	+	0.172405i	$0.0551539\pi$
$863$			10.1295i			0.344811i	−0.985026	+	0.172405i	$0.944846\pi$
$864$	−84.6636	+	35.0688i	−2.88031	+	1.19306i
$865$	23.7434	+	23.7434i	0.807299	+	0.807299i
$866$	82.4971			2.80337
$867$	−3.51646	+	48.1357i	−0.119425	+	1.63477i
$868$	11.6548			0.395589
$869$	15.9429	+	15.9429i	0.540826	+	0.540826i
$870$	79.2195	−	32.8138i	2.68579	−	1.11249i
$871$		−	15.8986i		−	0.538703i
$872$	27.9887	+	67.5707i	0.947817	+	2.28823i
$873$	62.3918	+	25.8435i	2.11164	+	0.874671i
$874$	−2.76750	+	6.68134i	−0.0936121	+	0.226000i
$875$	1.97964	−	1.97964i	0.0669242	−	0.0669242i
$876$	−36.0911	+	36.0911i	−1.21940	+	1.21940i
$877$	−13.8508	+	33.4388i	−0.467708	+	1.12915i	0.497453	+	0.867491i	$0.334269\pi$
$877$	−13.8508	+	33.4388i	−0.467708	+	1.12915i	−0.965161	+	0.261656i	$0.915731\pi$
$878$	−93.2143	−	38.6106i	−3.14583	−	1.30305i
$879$	−22.7614	−	54.9509i	−0.767723	−	1.85345i
$880$		−	39.7509i		−	1.34000i
$881$	−17.9189	+	7.42226i	−0.603704	+	0.250062i	−0.663534	−	0.748146i	$-0.730944\pi$
$881$	−17.9189	+	7.42226i	−0.603704	+	0.250062i	0.0598301	+	0.998209i	$0.480944\pi$
$882$	−66.4049	−	66.4049i	−2.23597	−	2.23597i
$883$	−1.29087			−0.0434411			−0.0217206	−	0.999764i	$-0.506914\pi$
$883$	−1.29087			−0.0434411			−0.0217206	+	0.999764i	$0.506914\pi$
$884$	−41.5892	+	25.6468i	−1.39880	+	0.862596i
$885$	−17.2287			−0.579136
$886$	−19.7148	−	19.7148i	−0.662331	−	0.662331i
$887$	37.0654	−	15.3530i	1.24454	−	0.515503i	0.339406	−	0.940640i	$-0.389774\pi$
$887$	37.0654	−	15.3530i	1.24454	−	0.515503i	0.905129	+	0.425137i	$0.139774\pi$
$888$		−	250.375i		−	8.40203i
$889$	−1.02824	−	2.48238i	−0.0344860	−	0.0832565i
$890$	−32.4904	−	13.4580i	−1.08908	−	0.451112i
$891$	1.10232	−	2.66124i	0.0369292	−	0.0891550i
$892$	50.2168	−	50.2168i	1.68138	−	1.68138i
$893$	−2.35820	+	2.35820i	−0.0789143	+	0.0789143i
$894$	−45.3720	+	109.538i	−1.51747	+	3.66349i
$895$	−35.8506	−	14.8498i	−1.19835	−	0.496375i
$896$	1.40202	+	3.38478i	0.0468383	+	0.113078i
$897$		−	5.31117i		−	0.177335i
$898$	−38.1702	+	15.8106i	−1.27376	+	0.527608i
$899$	−47.7444	−	47.7444i	−1.59236	−	1.59236i
$900$	61.8260			2.06087
$901$	3.63758	+	0.862509i	0.121185	+	0.0287343i
$902$	−9.53364			−0.317436
$903$	3.76802	+	3.76802i	0.125392	+	0.125392i
$904$	−14.4755	+	5.99594i	−0.481447	+	0.199422i
$905$		−	25.0071i		−	0.831263i
$906$	9.69000	+	23.3937i	0.321929	+	0.777204i
$907$	−28.5529	−	11.8270i	−0.948083	−	0.392709i	−0.145573	−	0.989348i	$-0.546503\pi$
$907$	−28.5529	−	11.8270i	−0.948083	−	0.392709i	−0.802510	+	0.596639i	$0.796503\pi$
$908$	−0.608709	+	1.46955i	−0.0202007	+	0.0487688i
$909$	52.7440	−	52.7440i	1.74941	−	1.74941i
$910$	−1.65316	+	1.65316i	−0.0548019	+	0.0548019i
$911$	10.6869	−	25.8004i	0.354072	−	0.854805i	−0.642037	−	0.766674i	$-0.721910\pi$
$911$	10.6869	−	25.8004i	0.354072	−	0.854805i	0.996109	−	0.0881314i	$-0.0280895\pi$
$912$	106.231	+	44.0025i	3.51767	+	1.45707i
$913$	0.321654	+	0.776541i	0.0106452	+	0.0256998i
$914$		−	33.5390i		−	1.10937i
$915$	23.5400	−	9.75060i	0.778210	−	0.322345i
$916$	68.1353	+	68.1353i	2.25125	+	2.25125i
$917$	−1.12945			−0.0372979
$918$	−37.7326	+	52.2424i	−1.24536	+	1.72426i
$919$	−13.8415			−0.456589			−0.228294	−	0.973592i	$-0.573315\pi$
$919$	−13.8415			−0.456589			−0.228294	+	0.973592i	$0.573315\pi$
$920$	−7.79937	−	7.79937i	−0.257138	−	0.257138i
$921$	−27.5084	+	11.3943i	−0.906432	+	0.375456i
$922$			73.1584i			2.40934i
$923$	4.41086	+	10.6488i	0.145185	+	0.350508i
$924$	−6.38528	−	2.64487i	−0.210060	−	0.0870099i
$925$	−9.55819	+	23.0755i	−0.314271	+	0.758718i
$926$	58.8646	−	58.8646i	1.93441	−	1.93441i
$927$	69.8613	−	69.8613i	2.29455	−	2.29455i
$928$	41.8398	−	101.010i	1.37346	−	3.31582i
$929$	−27.7560	−	11.4969i	−0.910646	−	0.377202i	−0.122342	−	0.992488i	$-0.539041\pi$
$929$	−27.7560	−	11.4969i	−0.910646	−	0.377202i	−0.788304	+	0.615286i	$0.789041\pi$
$930$	45.4959	+	109.837i	1.49187	+	3.60169i
$931$			23.1619i			0.759101i
$932$	58.7284	−	24.3261i	1.92371	−	0.796828i
$933$	−5.59940	−	5.59940i	−0.183316	−	0.183316i
$934$	−71.5094			−2.33986
$935$	−7.08391	−	11.4874i	−0.231669	−	0.375677i
$936$	−97.8978			−3.19989
$937$	9.80300	+	9.80300i	0.320250	+	0.320250i	0.848863	−	0.528613i	$-0.177288\pi$
$937$	9.80300	+	9.80300i	0.320250	+	0.320250i	−0.528613	+	0.848863i	$0.677288\pi$
$938$	−3.98958	+	1.65254i	−0.130265	+	0.0539573i
$939$			61.0417i			1.99202i
$940$	−3.18615	−	7.69204i	−0.103921	−	0.250887i
$941$	12.7322	+	5.27383i	0.415057	+	0.171922i	0.580432	−	0.814309i	$-0.302884\pi$
$941$	12.7322	+	5.27383i	0.415057	+	0.171922i	−0.165376	+	0.986231i	$0.552884\pi$
$942$	−34.9112	+	84.2831i	−1.13747	+	2.74609i
$943$	−1.01298	+	1.01298i	−0.0329872	+	0.0329872i
$944$	−32.1747	+	32.1747i	−1.04720	+	1.04720i
$945$	−0.849505	+	2.05089i	−0.0276344	+	0.0667153i
$946$	−39.9651	−	16.5541i	−1.29938	−	0.538219i
$947$	1.18502	+	2.86088i	0.0385078	+	0.0929661i	0.941963	−	0.335716i	$-0.108978\pi$
$947$	1.18502	+	2.86088i	0.0385078	+	0.0929661i	−0.903456	+	0.428682i	$0.858978\pi$
$948$		−	162.818i		−	5.28809i
$949$	−7.44864	+	3.08533i	−0.241793	+	0.100154i
$950$	−14.9774	−	14.9774i	−0.485932	−	0.485932i
$951$	40.7633			1.32184
$952$	6.57287	+	4.74733i	0.213028	+	0.153862i
$953$	−11.4361			−0.370452			−0.185226	−	0.982696i	$-0.559302\pi$
$953$	−11.4361			−0.370452			−0.185226	+	0.982696i	$0.559302\pi$
$954$	8.66936	+	8.66936i	0.280681	+	0.280681i
$955$	−6.95528	+	2.88097i	−0.225068	+	0.0932260i
$956$			0.116310i			0.00376174i
$957$	15.3228	+	36.9924i	0.495315	+	1.19580i
$958$	32.6828	+	13.5377i	1.05593	+	0.437382i
$959$	−1.03046	+	2.48776i	−0.0332754	+	0.0803338i
$960$	−57.1509	+	57.1509i	−1.84454	+	1.84454i
$961$	44.2767	−	44.2767i	1.42828	−	1.42828i
$962$	24.7731	−	59.8077i	0.798718	−	1.92828i
$963$	31.8262	+	13.1829i	1.02559	+	0.424812i
$964$	24.6141	+	59.4236i	0.792765	+	1.91391i
$965$			32.2937i			1.03957i
$966$	−1.33278	+	0.552057i	−0.0428816	+	0.0177621i
$967$	−7.31199	−	7.31199i	−0.235138	−	0.235138i	0.579696	−	0.814833i	$-0.303171\pi$
$967$	−7.31199	−	7.31199i	−0.235138	−	0.235138i	−0.814833	+	0.579696i	$0.803171\pi$
$968$	−58.0367			−1.86537
$969$	38.5407	−	6.21524i	1.23811	−	0.199662i
$970$	57.7595			1.85455
$971$	−19.8985	−	19.8985i	−0.638574	−	0.638574i	0.311629	−	0.950204i	$-0.399125\pi$
$971$	−19.8985	−	19.8985i	−0.638574	−	0.638574i	−0.950204	+	0.311629i	$0.899125\pi$
$972$	64.1191	−	26.5590i	2.05662	−	0.851880i
$973$			2.47738i			0.0794210i
$974$	−23.3670	−	56.4129i	−0.748726	−	1.80758i
$975$	14.3718	+	5.95298i	0.460265	+	0.190648i
$976$	25.7518	−	62.1704i	0.824296	−	1.99003i
$977$	−37.4017	+	37.4017i	−1.19659	+	1.19659i	−0.221404	+	0.975182i	$0.571064\pi$
$977$	−37.4017	+	37.4017i	−1.19659	+	1.19659i	−0.975182	+	0.221404i	$0.928936\pi$
$978$	−34.0875	+	34.0875i	−1.09000	+	1.09000i
$979$	6.28435	−	15.1718i	0.200849	−	0.484891i
$980$	−53.4219	−	22.1281i	−1.70650	−	0.706856i
$981$	16.8765	+	40.7435i	0.538825	+	1.30084i
$982$		−	91.0176i		−	2.90449i
$983$	37.3195	−	15.4583i	1.19031	−	0.493042i	0.302453	−	0.953164i	$-0.402195\pi$
$983$	37.3195	−	15.4583i	1.19031	−	0.493042i	0.887855	+	0.460122i	$0.152195\pi$
$984$	29.7413	+	29.7413i	0.948119	+	0.948119i
$985$	−37.7361			−1.20237
$986$	−12.2409	−	75.9059i	−0.389830	−	2.41734i
$987$	−0.665261			−0.0211755
$988$	27.9461	+	27.9461i	0.889084	+	0.889084i
$989$	−6.00534	+	2.48749i	−0.190959	+	0.0790977i
$990$		−	44.2605i		−	1.40669i
$991$	1.59765	+	3.85706i	0.0507509	+	0.122523i	0.947222	−	0.320579i	$-0.103878\pi$
$991$	1.59765	+	3.85706i	0.0507509	+	0.122523i	−0.896471	+	0.443103i	$0.853878\pi$
$992$	140.050	+	58.0104i	4.44658	+	1.84183i
$993$	−0.323911	+	0.781989i	−0.0102790	+	0.0248157i
$994$	2.21372	−	2.21372i	0.0702149	−	0.0702149i
$995$	−31.7734	+	31.7734i	−1.00728	+	1.00728i
$996$	2.32279	−	5.60770i	0.0736003	−	0.177687i
$997$	16.9222	+	7.00942i	0.535933	+	0.221991i	0.634199	−	0.773170i	$-0.281330\pi$
$997$	16.9222	+	7.00942i	0.535933	+	0.221991i	−0.0982667	+	0.995160i	$0.531330\pi$
$998$	27.4258	+	66.2117i	0.868148	+	2.09589i
$999$		−	61.4663i		−	1.94471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.g.d.189.1	✓	152
17.9	even	8	inner	799.2.g.d.706.1	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.g.d.189.1	✓	152	1.1	even	1	trivial
799.2.g.d.706.1	yes	152	17.9	even	8	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:	\( N \)	\(=\)	\( 799 = 17 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	799.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.88952 - 1.88952i) q^{2} +(-2.62295 + 1.08646i) q^{3} +5.14055i q^{4} +(0.619807 + 1.49635i) q^{5} +(7.00898 + 2.90322i) q^{6} +(0.0896722 - 0.216488i) q^{7} +(5.93412 - 5.93412i) q^{8} +(3.57813 - 3.57813i) q^{9} +O(q^{10})\)	\(q+(-1.88952 - 1.88952i) q^{2} +(-2.62295 + 1.08646i) q^{3} +5.14055i q^{4} +(0.619807 + 1.49635i) q^{5} +(7.00898 + 2.90322i) q^{6} +(0.0896722 - 0.216488i) q^{7} +(5.93412 - 5.93412i) q^{8} +(3.57813 - 3.57813i) q^{9} +(1.65624 - 3.99851i) q^{10} +(1.86715 + 0.773397i) q^{11} +(-5.58500 - 13.4834i) q^{12} -2.30532i q^{13} +(-0.578495 + 0.239620i) q^{14} +(-3.25144 - 3.25144i) q^{15} -12.1442 q^{16} +(-3.50946 + 2.16418i) q^{17} -13.5219 q^{18} +(2.35820 + 2.35820i) q^{19} +(-7.69204 + 3.18615i) q^{20} +0.665261i q^{21} +(-2.06666 - 4.98935i) q^{22} +(-0.749724 - 0.310546i) q^{23} +(-9.11770 + 22.0121i) q^{24} +(1.68064 - 1.68064i) q^{25} +(-4.35593 + 4.35593i) q^{26} +(-2.23837 + 5.40389i) q^{27} +(1.11287 + 0.460964i) q^{28} +(-2.67055 - 6.44727i) q^{29} +12.2873i q^{30} +(8.93906 - 3.70268i) q^{31} +(11.0783 + 11.0783i) q^{32} -5.73769 q^{33} +(10.7204 + 2.54193i) q^{34} +0.379520 q^{35} +(18.3936 + 18.3936i) q^{36} +(-9.70869 + 4.02147i) q^{37} -8.91173i q^{38} +(2.50463 + 6.04672i) q^{39} +(12.5575 + 5.20149i) q^{40} +(0.675569 - 1.63097i) q^{41} +(1.25702 - 1.25702i) q^{42} +(5.66397 - 5.66397i) q^{43} +(-3.97569 + 9.59816i) q^{44} +(7.57187 + 3.13637i) q^{45} +(0.829835 + 2.00340i) q^{46} +1.00000i q^{47} +(31.8535 - 13.1941i) q^{48} +(4.91092 + 4.91092i) q^{49} -6.35121 q^{50} +(6.85383 - 9.48942i) q^{51} +11.8506 q^{52} +(-0.641136 - 0.641136i) q^{53} +(14.4402 - 5.98132i) q^{54} +3.27325i q^{55} +(-0.752540 - 1.81679i) q^{56} +(-8.74753 - 3.62335i) q^{57} +(-7.13618 + 17.2283i) q^{58} +(2.64940 - 2.64940i) q^{59} +(16.7142 - 16.7142i) q^{60} +(-2.12051 + 5.11937i) q^{61} +(-23.8868 - 9.89423i) q^{62} +(-0.453763 - 1.09548i) q^{63} -17.5771i q^{64} +(3.44955 - 1.42885i) q^{65} +(10.8415 + 10.8415i) q^{66} +6.89649 q^{67} +(-11.1251 - 18.0406i) q^{68} +2.30388 q^{69} +(-0.717110 - 0.717110i) q^{70} +(-4.61922 + 1.91334i) q^{71} -42.4661i q^{72} +(-1.33835 - 3.23107i) q^{73} +(25.9434 + 10.7461i) q^{74} +(-2.58229 + 6.23419i) q^{75} +(-12.1225 + 12.1225i) q^{76} +(0.334862 - 0.334862i) q^{77} +(6.69283 - 16.1579i) q^{78} +(10.3071 + 4.26932i) q^{79} +(-7.52703 - 18.1719i) q^{80} -1.42530i q^{81} +(-4.35824 + 1.80524i) q^{82} +(0.294084 + 0.294084i) q^{83} -3.41981 q^{84} +(-5.41355 - 3.91000i) q^{85} -21.4044 q^{86} +(14.0094 + 14.0094i) q^{87} +(15.6693 - 6.49044i) q^{88} -8.12564i q^{89} +(-8.38095 - 20.2334i) q^{90} +(-0.499073 - 0.206723i) q^{91} +(1.59638 - 3.85399i) q^{92} +(-19.4239 + 19.4239i) q^{93} +(1.88952 - 1.88952i) q^{94} +(-2.06706 + 4.99032i) q^{95} +(-41.0941 - 17.0217i) q^{96} +(5.10718 + 12.3298i) q^{97} -18.5585i q^{98} +(9.44821 - 3.91358i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 4 q^{2} + 4 q^{6} + 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) \) 152 * q - 4 * q^2 + 4 * q^6 + 4 * q^7 + 4 * q^8 - 8 * q^9	\( 152 q - 4 q^{2} + 4 q^{6} + 4 q^{7} + 4 q^{8} - 8 q^{9} - 8 q^{11} + 8 q^{12} - 12 q^{14} + 20 q^{15} - 160 q^{16} - 12 q^{17} + 96 q^{18} + 16 q^{19} + 96 q^{20} - 4 q^{22} - 16 q^{23} - 76 q^{24} - 12 q^{25} - 8 q^{26} + 8 q^{28} - 4 q^{29} - 4 q^{31} - 16 q^{32} - 72 q^{33} - 20 q^{34} + 48 q^{35} - 16 q^{36} + 16 q^{37} + 64 q^{40} - 68 q^{41} - 144 q^{42} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 12 q^{48} - 4 q^{49} + 96 q^{50} - 52 q^{51} + 168 q^{52} - 16 q^{53} + 168 q^{54} + 108 q^{56} - 104 q^{58} - 84 q^{59} - 4 q^{60} + 4 q^{61} - 28 q^{62} + 60 q^{63} + 60 q^{65} - 44 q^{66} - 160 q^{67} - 96 q^{68} + 160 q^{69} + 36 q^{70} + 40 q^{71} + 4 q^{73} + 76 q^{74} - 116 q^{75} - 148 q^{76} - 4 q^{77} + 68 q^{78} - 76 q^{80} + 64 q^{82} - 124 q^{83} + 208 q^{84} - 68 q^{85} + 80 q^{86} - 72 q^{87} + 188 q^{88} + 236 q^{90} - 32 q^{91} - 196 q^{92} - 152 q^{93} + 4 q^{94} - 48 q^{95} - 56 q^{96} - 20 q^{97} + 244 q^{99}+O(q^{100}) \) 152 * q - 4 * q^2 + 4 * q^6 + 4 * q^7 + 4 * q^8 - 8 * q^9 - 8 * q^11 + 8 * q^12 - 12 * q^14 + 20 * q^15 - 160 * q^16 - 12 * q^17 + 96 * q^18 + 16 * q^19 + 96 * q^20 - 4 * q^22 - 16 * q^23 - 76 * q^24 - 12 * q^25 - 8 * q^26 + 8 * q^28 - 4 * q^29 - 4 * q^31 - 16 * q^32 - 72 * q^33 - 20 * q^34 + 48 * q^35 - 16 * q^36 + 16 * q^37 + 64 * q^40 - 68 * q^41 - 144 * q^42 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 12 * q^48 - 4 * q^49 + 96 * q^50 - 52 * q^51 + 168 * q^52 - 16 * q^53 + 168 * q^54 + 108 * q^56 - 104 * q^58 - 84 * q^59 - 4 * q^60 + 4 * q^61 - 28 * q^62 + 60 * q^63 + 60 * q^65 - 44 * q^66 - 160 * q^67 - 96 * q^68 + 160 * q^69 + 36 * q^70 + 40 * q^71 + 4 * q^73 + 76 * q^74 - 116 * q^75 - 148 * q^76 - 4 * q^77 + 68 * q^78 - 76 * q^80 + 64 * q^82 - 124 * q^83 + 208 * q^84 - 68 * q^85 + 80 * q^86 - 72 * q^87 + 188 * q^88 + 236 * q^90 - 32 * q^91 - 196 * q^92 - 152 * q^93 + 4 * q^94 - 48 * q^95 - 56 * q^96 - 20 * q^97 + 244 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more