LMFDB - Embedded newform 833.2.o.g.557.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(30,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("833.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.o (of order $12$, degree $4$, not 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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.4
Character	$\chi$	$=$	833.557
Dual form			833.2.o.g.667.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.615152 + 0.355158i) q^{2} +(-2.89474 + 0.775643i) q^{3} +(-0.747726 + 1.29510i) q^{4} +(-0.976053 + 3.64268i) q^{5} +(1.50523 - 1.50523i) q^{6} -2.48287i q^{8} +(5.17981 - 2.99057i) q^{9} +O(q^{10})$	\(q+(-0.615152 + 0.355158i) q^{2} +(-2.89474 + 0.775643i) q^{3} +(-0.747726 + 1.29510i) q^{4} +(-0.976053 + 3.64268i) q^{5} +(1.50523 - 1.50523i) q^{6} -2.48287i q^{8} +(5.17981 - 2.99057i) q^{9} +(-0.693306 - 2.58745i) q^{10} +(-0.679184 - 2.53475i) q^{11} +(1.15994 - 4.32894i) q^{12} -0.409675 q^{13} -11.3017i q^{15} +(-0.613639 - 1.06285i) q^{16} +(2.57292 - 3.22181i) q^{17} +(-2.12425 + 3.67930i) q^{18} +(-1.53144 + 0.884175i) q^{19} +(-3.98781 - 3.98781i) q^{20} +(1.31804 + 1.31804i) q^{22} +(-3.00200 - 0.804383i) q^{23} +(1.92582 + 7.18727i) q^{24} +(-7.98631 - 4.61090i) q^{25} +(0.252012 - 0.145499i) q^{26} +(-6.31730 + 6.31730i) q^{27} +(3.96073 + 3.96073i) q^{29} +(4.01388 + 6.95224i) q^{30} +(6.16845 - 1.65283i) q^{31} +(5.05543 + 2.91875i) q^{32} +(3.93212 + 6.81063i) q^{33} +(-0.438483 + 2.89570i) q^{34} +8.94449i q^{36} +(0.982858 - 3.66808i) q^{37} +(0.628043 - 1.08780i) q^{38} +(1.18590 - 0.317762i) q^{39} +(9.04432 + 2.42342i) q^{40} +(-5.30764 + 5.30764i) q^{41} -5.57516i q^{43} +(3.79059 + 1.01569i) q^{44} +(5.83790 + 21.7873i) q^{45} +(2.13237 - 0.571366i) q^{46} +(-5.93143 - 10.2735i) q^{47} +(2.60072 + 2.60072i) q^{48} +6.55039 q^{50} +(-4.94895 + 11.3220i) q^{51} +(0.306325 - 0.530570i) q^{52} +(3.50903 + 2.02594i) q^{53} +(1.64246 - 6.12974i) q^{54} +9.89619 q^{55} +(3.74730 - 3.74730i) q^{57} +(-3.84313 - 1.02976i) q^{58} +(-8.07738 - 4.66348i) q^{59} +(14.6368 + 8.45055i) q^{60} +(0.582819 + 0.156166i) q^{61} +(-3.20752 + 3.20752i) q^{62} -1.69192 q^{64} +(0.399865 - 1.49232i) q^{65} +(-4.83770 - 2.79305i) q^{66} +(-3.85103 + 6.67018i) q^{67} +(2.24873 + 5.74122i) q^{68} +9.31391 q^{69} +(-2.60890 - 2.60890i) q^{71} +(-7.42520 - 12.8608i) q^{72} +(-0.747623 + 0.200325i) q^{73} +(0.698140 + 2.60549i) q^{74} +(26.6947 + 7.15282i) q^{75} -2.64448i q^{76} +(-0.616654 + 0.616654i) q^{78} +(15.1631 + 4.06295i) q^{79} +(4.47058 - 1.19789i) q^{80} +(4.41526 - 7.64746i) q^{81} +(1.37995 - 5.15005i) q^{82} -2.28876i q^{83} +(9.22473 + 12.5170i) q^{85} +(1.98006 + 3.42957i) q^{86} +(-14.5374 - 8.39316i) q^{87} +(-6.29346 + 1.68633i) q^{88} +(-6.36829 - 11.0302i) q^{89} +(-11.3291 - 11.3291i) q^{90} +(3.28643 - 3.28643i) q^{92} +(-16.5740 + 9.56903i) q^{93} +(7.29746 + 4.21319i) q^{94} +(-1.72600 - 6.44153i) q^{95} +(-16.8980 - 4.52782i) q^{96} +(0.408884 + 0.408884i) q^{97} +(-11.0984 - 11.0984i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} + 24 q^{4} + 8 q^{5} + 8 q^{6}+O(q^{10}) $ 40 * q + 4 * q^3 + 24 * q^4 + 8 * q^5 + 8 * q^6	$ 40 q + 4 q^{3} + 24 q^{4} + 8 q^{5} + 8 q^{6} - 4 q^{10} + 4 q^{11} - 12 q^{12} - 16 q^{16} + 12 q^{17} + 8 q^{18} + 40 q^{20} - 40 q^{22} - 4 q^{24} + 16 q^{27} + 32 q^{29} + 36 q^{30} - 4 q^{31} + 16 q^{33} + 72 q^{34} + 28 q^{37} - 48 q^{38} - 20 q^{39} + 24 q^{40} - 48 q^{41} + 28 q^{44} - 36 q^{45} - 8 q^{46} - 40 q^{47} - 16 q^{48} - 56 q^{50} + 40 q^{51} + 28 q^{54} - 80 q^{55} + 72 q^{57} - 56 q^{58} + 16 q^{61} - 80 q^{62} + 64 q^{64} - 8 q^{65} + 32 q^{68} - 176 q^{69} - 16 q^{71} - 108 q^{72} - 8 q^{73} - 36 q^{74} - 8 q^{75} - 88 q^{78} + 4 q^{79} + 116 q^{80} - 4 q^{81} + 16 q^{82} + 32 q^{85} - 44 q^{86} - 72 q^{88} - 48 q^{89} + 112 q^{90} - 64 q^{92} - 44 q^{95} - 68 q^{96} - 48 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 + 24 * q^4 + 8 * q^5 + 8 * q^6 - 4 * q^10 + 4 * q^11 - 12 * q^12 - 16 * q^16 + 12 * q^17 + 8 * q^18 + 40 * q^20 - 40 * q^22 - 4 * q^24 + 16 * q^27 + 32 * q^29 + 36 * q^30 - 4 * q^31 + 16 * q^33 + 72 * q^34 + 28 * q^37 - 48 * q^38 - 20 * q^39 + 24 * q^40 - 48 * q^41 + 28 * q^44 - 36 * q^45 - 8 * q^46 - 40 * q^47 - 16 * q^48 - 56 * q^50 + 40 * q^51 + 28 * q^54 - 80 * q^55 + 72 * q^57 - 56 * q^58 + 16 * q^61 - 80 * q^62 + 64 * q^64 - 8 * q^65 + 32 * q^68 - 176 * q^69 - 16 * q^71 - 108 * q^72 - 8 * q^73 - 36 * q^74 - 8 * q^75 - 88 * q^78 + 4 * q^79 + 116 * q^80 - 4 * q^81 + 16 * q^82 + 32 * q^85 - 44 * q^86 - 72 * q^88 - 48 * q^89 + 112 * q^90 - 64 * q^92 - 44 * q^95 - 68 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.615152	+	0.355158i	−0.434978	+	0.251135i	−0.701465	−	0.712704i	$-0.747470\pi$
$2$	−0.615152	+	0.355158i	−0.434978	+	0.251135i	0.266487	+	0.963838i	$0.414137\pi$
$3$	−2.89474	+	0.775643i	−1.67128	+	0.447818i	−0.965455	−	0.260571i	$-0.916089\pi$
$3$	−2.89474	+	0.775643i	−1.67128	+	0.447818i	−0.705823	+	0.708388i	$0.749423\pi$
$4$	−0.747726	+	1.29510i	−0.373863	+	0.647549i
$5$	−0.976053	+	3.64268i	−0.436504	+	1.62906i	0.300937	+	0.953644i	$0.402701\pi$
$5$	−0.976053	+	3.64268i	−0.436504	+	1.62906i	−0.737441	+	0.675412i	$0.763966\pi$
$6$	1.50523	−	1.50523i	0.614506	−	0.614506i
$7$		0			0
$7$		0			0
$8$		−	2.48287i		−	0.877829i
$9$	5.17981	−	2.99057i	1.72660	−	0.996855i
$10$	−0.693306	−	2.58745i	−0.219243	−	0.818225i
$11$	−0.679184	−	2.53475i	−0.204782	−	0.764255i	−0.989516	−	0.144423i	$-0.953867\pi$
$11$	−0.679184	−	2.53475i	−0.204782	−	0.764255i	0.784734	−	0.619832i	$-0.212799\pi$
$12$	1.15994	−	4.32894i	0.334845	−	1.24966i
$13$	−0.409675			−0.113623			−0.0568117	−	0.998385i	$-0.518093\pi$
$13$	−0.409675			−0.113623			−0.0568117	+	0.998385i	$0.518093\pi$
$14$		0			0
$15$		−	11.3017i		−	2.91808i
$16$	−0.613639	−	1.06285i	−0.153410	−	0.265713i
$17$	2.57292	−	3.22181i	0.624025	−	0.781405i
$17$	2.57292	−	3.22181i	0.624025	−	0.781405i
$18$	−2.12425	+	3.67930i	−0.500690	+	0.867220i
$19$	−1.53144	+	0.884175i	−0.351335	+	0.202844i	−0.665273	−	0.746600i	$-0.731685\pi$
$19$	−1.53144	+	0.884175i	−0.351335	+	0.202844i	0.313938	+	0.949444i	$0.398352\pi$
$20$	−3.98781	−	3.98781i	−0.891702	−	0.891702i
$21$		0			0
$22$	1.31804	+	1.31804i	0.281006	+	0.281006i
$23$	−3.00200	−	0.804383i	−0.625960	−	0.167725i	−0.0681241	−	0.997677i	$-0.521701\pi$
$23$	−3.00200	−	0.804383i	−0.625960	−	0.167725i	−0.557836	+	0.829951i	$0.688368\pi$
$24$	1.92582	+	7.18727i	0.393107	+	1.46710i
$25$	−7.98631	−	4.61090i	−1.59726	−	0.922180i
$26$	0.252012	−	0.145499i	0.0494237	−	0.0285348i
$27$	−6.31730	+	6.31730i	−1.21576	+	1.21576i
$28$		0			0
$29$	3.96073	+	3.96073i	0.735489	+	0.735489i	0.971701	−	0.236213i	$-0.0759062\pi$
$29$	3.96073	+	3.96073i	0.735489	+	0.735489i	−0.236213	+	0.971701i	$0.575906\pi$
$30$	4.01388	+	6.95224i	0.732831	+	1.26930i
$31$	6.16845	−	1.65283i	1.10789	−	0.296857i	0.341914	−	0.939731i	$-0.388925\pi$
$31$	6.16845	−	1.65283i	1.10789	−	0.296857i	0.765972	+	0.642874i	$0.222258\pi$
$32$	5.05543	+	2.91875i	0.893682	+	0.515967i
$33$	3.93212	+	6.81063i	0.684494	+	1.18558i
$34$	−0.438483	+	2.89570i	−0.0751992	+	0.496608i
$35$		0			0
$36$			8.94449i			1.49075i
$37$	0.982858	−	3.66808i	0.161581	−	0.603028i	−0.836871	−	0.547401i	$-0.815617\pi$
$37$	0.982858	−	3.66808i	0.161581	−	0.603028i	0.998452	−	0.0556274i	$-0.0177159\pi$
$38$	0.628043	−	1.08780i	0.101882	−	0.176465i
$39$	1.18590	−	0.317762i	0.189896	−	0.0508826i
$40$	9.04432	+	2.42342i	1.43003	+	0.383176i
$41$	−5.30764	+	5.30764i	−0.828913	+	0.828913i	−0.987366	−	0.158453i	$-0.949349\pi$
$41$	−5.30764	+	5.30764i	−0.828913	+	0.828913i	0.158453	+	0.987366i	$0.449349\pi$
$42$		0			0
$43$		−	5.57516i		−	0.850204i	−0.905145	−	0.425102i	$-0.860238\pi$
$43$		−	5.57516i		−	0.850204i	0.905145	−	0.425102i	$-0.139762\pi$
$44$	3.79059	+	1.01569i	0.571453	+	0.153120i
$45$	5.83790	+	21.7873i	0.870263	+	3.24787i
$46$	2.13237	−	0.571366i	0.314400	−	0.0842433i
$47$	−5.93143	−	10.2735i	−0.865189	−	1.49855i	−0.866860	−	0.498552i	$-0.833865\pi$
$47$	−5.93143	−	10.2735i	−0.865189	−	1.49855i	0.00167131	−	0.999999i	$-0.499468\pi$
$48$	2.60072	+	2.60072i	0.375381	+	0.375381i
$49$		0			0
$50$	6.55039			0.926365
$51$	−4.94895	+	11.3220i	−0.692992	+	1.58539i
$52$	0.306325	−	0.530570i	0.0424796	−	0.0735768i
$53$	3.50903	+	2.02594i	0.482003	+	0.278285i	0.721251	−	0.692674i	$-0.243568\pi$
$53$	3.50903	+	2.02594i	0.482003	+	0.278285i	−0.239248	+	0.970959i	$0.576901\pi$
$54$	1.64246	−	6.12974i	0.223510	−	0.834151i
$55$	9.89619			1.33440
$56$		0			0
$57$	3.74730	−	3.74730i	0.496342	−	0.496342i
$58$	−3.84313	−	1.02976i	−0.504628	−	0.135215i
$59$	−8.07738	−	4.66348i	−1.05159	−	0.607133i	−0.128493	−	0.991710i	$-0.541014\pi$
$59$	−8.07738	−	4.66348i	−1.05159	−	0.607133i	−0.923093	+	0.384577i	$0.874347\pi$
$60$	14.6368	+	8.45055i	1.88960	+	1.09096i
$61$	0.582819	+	0.156166i	0.0746224	+	0.0199950i	0.295937	−	0.955207i	$-0.404368\pi$
$61$	0.582819	+	0.156166i	0.0746224	+	0.0199950i	−0.221315	+	0.975202i	$0.571035\pi$
$62$	−3.20752	+	3.20752i	−0.407355	+	0.407355i
$63$		0			0
$64$	−1.69192			−0.211490
$65$	0.399865	−	1.49232i	0.0495971	−	0.185099i
$66$	−4.83770	−	2.79305i	−0.595479	−	0.343800i
$67$	−3.85103	+	6.67018i	−0.470479	+	0.814893i	−0.999430	−	0.0337593i	$-0.989252\pi$
$67$	−3.85103	+	6.67018i	−0.470479	+	0.814893i	0.528951	+	0.848652i	$0.322585\pi$
$68$	2.24873	+	5.74122i	0.272699	+	0.696225i
$69$	9.31391			1.12126
$70$		0			0
$71$	−2.60890	−	2.60890i	−0.309620	−	0.309620i	0.535142	−	0.844762i	$-0.320258\pi$
$71$	−2.60890	−	2.60890i	−0.309620	−	0.309620i	−0.844762	+	0.535142i	$0.820258\pi$
$72$	−7.42520	−	12.8608i	−0.875068	−	1.51566i
$73$	−0.747623	+	0.200325i	−0.0875026	+	0.0234463i	−0.302305	−	0.953211i	$-0.597756\pi$
$73$	−0.747623	+	0.200325i	−0.0875026	+	0.0234463i	0.214802	+	0.976658i	$0.431089\pi$
$74$	0.698140	+	2.60549i	0.0811571	+	0.302882i
$75$	26.6947	+	7.15282i	3.08244	+	0.825936i
$76$		−	2.64448i		−	0.303343i
$77$		0			0
$78$	−0.616654	+	0.616654i	−0.0698223	+	0.0698223i
$79$	15.1631	+	4.06295i	1.70598	+	0.457117i	0.974435	−	0.224671i	$-0.0721309\pi$
$79$	15.1631	+	4.06295i	1.70598	+	0.457117i	0.731549	+	0.681788i	$0.238798\pi$
$80$	4.47058	−	1.19789i	0.499826	−	0.133928i
$81$	4.41526	−	7.64746i	0.490585	−	0.849718i
$82$	1.37995	−	5.15005i	0.152390	−	0.568728i
$83$		−	2.28876i		−	0.251224i	−0.992079	−	0.125612i	$-0.959911\pi$
$83$		−	2.28876i		−	0.251224i	0.992079	−	0.125612i	$-0.0400895\pi$
$84$		0			0
$85$	9.22473	+	12.5170i	1.00056	+	1.35766i
$86$	1.98006	+	3.42957i	0.213516	+	0.369820i
$87$	−14.5374	−	8.39316i	−1.55857	−	0.899841i
$88$	−6.29346	+	1.68633i	−0.670885	+	0.179763i
$89$	−6.36829	−	11.0302i	−0.675037	−	1.16920i	−0.976458	−	0.215708i	$-0.930794\pi$
$89$	−6.36829	−	11.0302i	−0.675037	−	1.16920i	0.301421	−	0.953491i	$-0.402539\pi$
$90$	−11.3291	−	11.3291i	−1.19420	−	1.19420i
$91$		0			0
$92$	3.28643	−	3.28643i	0.342634	−	0.342634i
$93$	−16.5740	+	9.56903i	−1.71865	+	0.992262i
$94$	7.29746	+	4.21319i	0.752676	+	0.434558i
$95$	−1.72600	−	6.44153i	−0.177084	−	0.660887i
$96$	−16.8980	−	4.52782i	−1.72465	−	0.462118i
$97$	0.408884	+	0.408884i	0.0415159	+	0.0415159i	0.727560	−	0.686044i	$-0.240654\pi$
$97$	0.408884	+	0.408884i	0.0415159	+	0.0415159i	−0.686044	+	0.727560i	$0.740654\pi$
$98$		0			0
$99$	−11.0984	−	11.0984i	−1.11543	−	1.11543i
$100$	11.9431	−	6.89537i	1.19431	−	0.689537i
$101$	−0.678643	+	1.17544i	−0.0675275	+	0.116961i	−0.897812	−	0.440378i	$-0.854844\pi$
$101$	−0.678643	+	1.17544i	−0.0675275	+	0.116961i	0.830285	+	0.557339i	$0.188178\pi$
$102$	−0.976734	−	8.72239i	−0.0967111	−	0.863645i
$103$	2.99525	+	5.18792i	0.295130	+	0.511181i	0.975015	−	0.222138i	$-0.0713036\pi$
$103$	2.99525	+	5.18792i	0.295130	+	0.511181i	−0.679885	+	0.733319i	$0.737970\pi$
$104$			1.01717i			0.0997419i
$105$		0			0
$106$	−2.87812			−0.279547
$107$	0.856010	−	3.19467i	0.0827536	−	0.308841i	−0.912126	−	0.409911i	$-0.865560\pi$
$107$	0.856010	−	3.19467i	0.0827536	−	0.308841i	0.994879	+	0.101070i	$0.0322265\pi$
$108$	−3.45792	−	12.9051i	−0.332738	−	1.24180i
$109$	2.94398	+	10.9871i	0.281983	+	1.05237i	0.951016	+	0.309141i	$0.100042\pi$
$109$	2.94398	+	10.9871i	0.281983	+	1.05237i	−0.669034	+	0.743232i	$0.733292\pi$
$110$	−6.08766	+	3.51471i	−0.580436	+	0.335115i
$111$			11.3805i			1.08019i
$112$		0			0
$113$	−0.643322	+	0.643322i	−0.0605187	+	0.0605187i	−0.736718	−	0.676200i	$-0.763626\pi$
$113$	−0.643322	+	0.643322i	−0.0605187	+	0.0605187i	0.676200	+	0.736718i	$0.263626\pi$
$114$	−0.974275	+	3.63604i	−0.0912492	+	0.340547i
$115$	5.86022	−	10.1502i	0.546468	−	0.946511i
$116$	−8.09107	+	2.16800i	−0.751237	+	0.201293i
$117$	−2.12204	+	1.22516i	−0.196183	+	0.113266i
$118$	6.62509			0.609889
$119$		0			0
$120$	−28.0606			−2.56157
$121$	3.56262	−	2.05688i	0.323875	−	0.186989i
$122$	−0.413986	+	0.110927i	−0.0374805	+	0.0100429i
$123$	11.2474	−	19.4810i	1.01414	−	1.75655i
$124$	−2.47173	+	9.22462i	−0.221968	+	0.828395i
$125$	11.2580	−	11.2580i	1.00694	−	1.00694i
$126$		0			0
$127$		−	14.7826i		−	1.31175i	−0.754871	−	0.655873i	$-0.772300\pi$
$127$		−	14.7826i		−	1.31175i	0.754871	−	0.655873i	$-0.227700\pi$
$128$	−9.07007	+	5.23661i	−0.801688	+	0.462855i
$129$	4.32434	+	16.1386i	0.380736	+	1.42093i
$130$	0.284030	+	1.06002i	0.0249111	+	0.0929695i
$131$	−2.01673	+	7.52654i	−0.176203	+	0.657597i	0.820141	+	0.572161i	$0.193895\pi$
$131$	−2.01673	+	7.52654i	−0.176203	+	0.657597i	−0.996344	+	0.0854358i	$0.972772\pi$
$132$	−11.7606			−1.02363
$133$		0			0
$134$		−	5.47090i		−	0.472614i
$135$	−16.8459	−	29.1779i	−1.44986	−	2.51124i
$136$	−7.99936	−	6.38824i	−0.685939	−	0.547787i
$137$	7.64904	−	13.2485i	0.653501	−	1.13190i	−0.328766	−	0.944411i	$-0.606633\pi$
$137$	7.64904	−	13.2485i	0.653501	−	1.13190i	0.982267	−	0.187486i	$-0.0600339\pi$
$138$	−5.72947	+	3.30791i	−0.487725	+	0.281588i
$139$	8.93048	+	8.93048i	0.757473	+	0.757473i	0.975862	−	0.218389i	$-0.0700800\pi$
$139$	8.93048	+	8.93048i	0.757473	+	0.757473i	−0.218389	+	0.975862i	$0.570080\pi$
$140$		0			0
$141$	25.1385	+	25.1385i	2.11705	+	2.11705i
$142$	2.53145	+	0.678299i	0.212434	+	0.0569216i
$143$	0.278245	+	1.03842i	0.0232680	+	0.0868373i
$144$	−6.35706	−	3.67025i	−0.529755	−	0.305854i
$145$	−18.2935	+	10.5618i	−1.51920	+	0.877108i
$146$	0.388754	−	0.388754i	0.0321735	−	0.0321735i
$147$		0			0
$148$	4.01561	+	4.01561i	0.330081	+	0.330081i
$149$	8.19420	+	14.1928i	0.671295	+	1.16272i	0.977537	+	0.210763i	$0.0675949\pi$
$149$	8.19420	+	14.1928i	0.671295	+	1.16272i	−0.306242	+	0.951954i	$0.599072\pi$
$150$	−18.9617	+	5.08076i	−1.54821	+	0.414842i
$151$	−0.225684	−	0.130299i	−0.0183659	−	0.0106036i	0.490789	−	0.871278i	$-0.336709\pi$
$151$	−0.225684	−	0.130299i	−0.0183659	−	0.0106036i	−0.509155	+	0.860675i	$0.670042\pi$
$152$	2.19530	+	3.80236i	0.178062	+	0.308412i
$153$	3.69219	−	24.3829i	0.298496	−	1.97124i
$154$		0			0
$155$			24.0829i			1.93439i
$156$	−0.475197	+	1.77346i	−0.0380462	+	0.141990i
$157$	8.01434	−	13.8812i	0.639614	−	1.10784i	−0.345904	−	0.938270i	$-0.612428\pi$
$157$	8.01434	−	13.8812i	0.639614	−	1.10784i	0.985518	−	0.169573i	$-0.0542390\pi$
$158$	−10.7706	+	2.88597i	−0.856863	+	0.229596i
$159$	−11.7291	−	3.14281i	−0.930181	−	0.249241i
$160$	−15.5664	+	15.5664i	−1.23064	+	1.23064i
$161$		0			0
$162$			6.27246i			0.492811i
$163$	−3.43873	−	0.921404i	−0.269342	−	0.0721699i	0.121620	−	0.992577i	$-0.461191\pi$
$163$	−3.43873	−	0.921404i	−0.269342	−	0.0721699i	−0.390962	+	0.920407i	$0.627858\pi$
$164$	−2.90526	−	10.8426i	−0.226862	−	0.846662i
$165$	−28.6469	+	7.67591i	−2.23016	+	0.597569i
$166$	0.812872	+	1.40794i	0.0630911	+	0.109277i
$167$	−13.9205	−	13.9205i	−1.07720	−	1.07720i	−0.996759	−	0.0804404i	$-0.974367\pi$
$167$	−13.9205	−	13.9205i	−1.07720	−	1.07720i	−0.0804404	−	0.996759i	$-0.525633\pi$
$168$		0			0
$169$	−12.8322			−0.987090
$170$	−10.1201	−	4.42361i	−0.776177	−	0.339275i
$171$	−5.28836	+	9.15972i	−0.404411	+	0.700461i
$172$	7.22039	+	4.16869i	0.550549	+	0.317860i
$173$	1.68722	−	6.29677i	0.128277	−	0.478735i	−0.871659	−	0.490113i	$-0.836955\pi$
$173$	1.68722	−	6.29677i	0.128277	−	0.478735i	0.999935	+	0.0113786i	$0.00362200\pi$
$174$	11.9236			0.903925
$175$		0			0
$176$	−2.27729	+	2.27729i	−0.171657	+	0.171657i
$177$	26.9991	+	7.23439i	2.02938	+	0.543770i
$178$	7.83493	+	4.52350i	0.587252	+	0.339050i
$179$	−11.8561	−	6.84513i	−0.886168	−	0.511629i	−0.0134808	−	0.999909i	$-0.504291\pi$
$179$	−11.8561	−	6.84513i	−0.886168	−	0.511629i	−0.872687	+	0.488280i	$0.837625\pi$
$180$	−32.5819	−	8.73030i	−2.42851	−	0.650718i
$181$	6.75360	−	6.75360i	0.501991	−	0.501991i	−0.410065	−	0.912056i	$-0.634494\pi$
$181$	6.75360	−	6.75360i	0.501991	−	0.501991i	0.912056	+	0.410065i	$0.134494\pi$
$182$		0			0
$183$	−1.80824			−0.133669
$184$	−1.99718	+	7.45358i	−0.147234	+	0.549485i
$185$	12.4023	+	7.16047i	0.911835	+	0.526448i
$186$	6.79703	−	11.7728i	0.498383	−	0.863224i
$187$	−9.91397	−	4.33350i	−0.724981	−	0.316897i
$188$	17.7403			1.29385
$189$		0			0
$190$	3.34951	+	3.34951i	0.242999	+	0.242999i
$191$	−3.15027	−	5.45643i	−0.227946	−	0.394813i	0.729254	−	0.684244i	$-0.239868\pi$
$191$	−3.15027	−	5.45643i	−0.227946	−	0.394813i	−0.957199	+	0.289430i	$0.906534\pi$
$192$	4.89766	−	1.31232i	0.353458	−	0.0947088i
$193$	0.500895	+	1.86937i	0.0360552	+	0.134560i	0.981607	−	0.190910i	$-0.0611440\pi$
$193$	0.500895	+	1.86937i	0.0360552	+	0.134560i	−0.945552	+	0.325470i	$0.894477\pi$
$194$	−0.396745	−	0.106307i	−0.0284846	−	0.00763243i
$195$			4.63001i			0.331562i
$196$		0			0
$197$	−7.86389	+	7.86389i	−0.560279	+	0.560279i	−0.929387	−	0.369108i	$-0.879663\pi$
$197$	−7.86389	+	7.86389i	−0.560279	+	0.560279i	0.369108	+	0.929387i	$0.379663\pi$
$198$	10.7689	+	2.88551i	0.765309	+	0.205064i
$199$	17.3514	−	4.64930i	1.23001	−	0.329580i	0.415426	−	0.909627i	$-0.363633\pi$
$199$	17.3514	−	4.64930i	1.23001	−	0.329580i	0.814583	+	0.580047i	$0.196966\pi$
$200$	−11.4483	+	19.8290i	−0.809516	+	1.40212i
$201$	5.97405	−	22.2955i	0.421377	−	1.57260i
$202$		−	0.964102i		−	0.0678340i
$203$		0			0
$204$	−10.9626	−	14.8751i	−0.767537	−	1.04147i
$205$	−14.1535	−	24.5145i	−0.988522	−	1.71217i
$206$	−3.68506	−	2.12757i	−0.256750	−	0.148235i
$207$	−17.9553	+	4.81112i	−1.24798	+	0.334396i
$208$	0.251393	+	0.435425i	0.0174309	+	0.0301913i
$209$	3.28129	+	3.28129i	0.226971	+	0.226971i
$210$		0			0
$211$	8.77026	−	8.77026i	0.603770	−	0.603770i	−0.337541	−	0.941311i	$-0.609595\pi$
$211$	8.77026	−	8.77026i	0.603770	−	0.603770i	0.941311	+	0.337541i	$0.109595\pi$
$212$	−5.24759	+	3.02970i	−0.360406	+	0.208080i
$213$	9.57567	+	5.52852i	0.656114	+	0.378808i
$214$	0.608038	+	2.26923i	0.0415646	+	0.155121i
$215$	20.3085	+	5.44166i	1.38503	+	0.371118i
$216$	15.6851	+	15.6851i	1.06723	+	1.06723i
$217$		0			0
$218$	−5.71315	−	5.71315i	−0.386944	−	0.386944i
$219$	2.00879	−	1.15978i	0.135742	−	0.0783704i
$220$	−7.39964	+	12.8165i	−0.498883	+	0.864092i
$221$	−1.05406	+	1.31990i	−0.0709038	+	0.0887859i
$222$	−4.04186	−	7.00071i	−0.271272	−	0.469857i
$223$		−	28.6104i		−	1.91589i	−0.286950	−	0.957945i	$-0.592641\pi$
$223$		−	28.6104i		−	1.91589i	0.286950	−	0.957945i	$-0.407359\pi$
$224$		0			0
$225$	−55.1568			−3.67712
$226$	0.167260	−	0.624222i	0.0111260	−	0.0415226i
$227$	−2.41410	−	9.00954i	−0.160229	−	0.597984i	−0.998601	−	0.0528845i	$-0.983158\pi$
$227$	−2.41410	−	9.00954i	−0.160229	−	0.597984i	0.838371	−	0.545100i	$-0.183508\pi$
$228$	2.05117	+	7.65508i	0.135842	+	0.506970i
$229$	21.3882	−	12.3485i	1.41337	−	0.816012i	0.417670	−	0.908599i	$-0.362847\pi$
$229$	21.3882	−	12.3485i	1.41337	−	0.816012i	0.995705	+	0.0925867i	$0.0295135\pi$
$230$			8.32521i			0.548948i
$231$		0			0
$232$	9.83399	−	9.83399i	0.645633	−	0.645633i
$233$	−2.39323	+	8.93165i	−0.156786	+	0.585132i	0.842160	+	0.539227i	$0.181284\pi$
$233$	−2.39323	+	8.93165i	−0.156786	+	0.585132i	−0.998946	+	0.0459044i	$0.985383\pi$
$234$	0.870251	−	1.50732i	0.0568901	−	0.0985365i
$235$	43.2126	−	11.5788i	2.81888	−	0.755317i
$236$	12.0793	−	6.97401i	0.786298	−	0.453969i
$237$	−47.0446			−3.05588
$238$		0			0
$239$	−12.3284			−0.797455			−0.398728	−	0.917069i	$-0.630548\pi$
$239$	−12.3284			−0.797455			−0.398728	+	0.917069i	$0.630548\pi$
$240$	−12.0120	+	6.93514i	−0.775373	+	0.447662i
$241$	9.02859	−	2.41920i	0.581583	−	0.155835i	0.0439793	−	0.999032i	$-0.485996\pi$
$241$	9.02859	−	2.41920i	0.581583	−	0.155835i	0.537603	+	0.843198i	$0.319330\pi$
$242$	−1.46104	+	2.53059i	−0.0939189	+	0.162672i
$243$	0.0875419	−	0.326711i	0.00561581	−	0.0209585i
$244$	−0.638039	+	0.638039i	−0.0408463	+	0.0408463i
$245$		0			0
$246$			15.9784i			1.01875i
$247$	0.627391	−	0.362224i	0.0399199	−	0.0230478i
$248$	−4.10377	−	15.3155i	−0.260590	−	0.972535i
$249$	1.77526	+	6.62537i	0.112503	+	0.419866i
$250$	−2.92700	+	10.9237i	−0.185120	+	0.690876i
$251$	25.4353			1.60546			0.802732	−	0.596340i	$-0.203379\pi$
$251$	25.4353			1.60546			0.802732	+	0.596340i	$0.203379\pi$
$252$		0			0
$253$			8.15563i			0.512740i
$254$	5.25017	+	9.09356i	0.329425	+	0.570581i
$255$	−36.4119	−	29.0783i	−2.28020	−	1.82095i
$256$	5.41156	−	9.37310i	0.338223	−	0.585819i
$257$	8.89090	−	5.13317i	0.554599	−	0.320198i	−0.196376	−	0.980529i	$-0.562917\pi$
$257$	8.89090	−	5.13317i	0.554599	−	0.320198i	0.750975	+	0.660331i	$0.229584\pi$
$258$	−8.39189	−	8.39189i	−0.522456	−	0.522456i
$259$		0			0
$260$	1.63371	+	1.63371i	0.101318	+	0.101318i
$261$	32.3606	+	8.67101i	2.00307	+	0.536722i
$262$	−1.43252	−	5.34622i	−0.0885012	−	0.330291i
$263$	9.60674	+	5.54645i	0.592377	+	0.342009i	0.766037	−	0.642797i	$-0.222226\pi$
$263$	9.60674	+	5.54645i	0.592377	+	0.342009i	−0.173660	+	0.984806i	$0.555559\pi$
$264$	16.9099	−	9.76295i	1.04073	−	0.600868i
$265$	−10.8049	+	10.8049i	−0.663737	+	0.663737i
$266$		0			0
$267$	26.9900	+	26.9900i	1.65176	+	1.65176i
$268$	−5.75903	−	9.97494i	−0.351789	−	0.609316i
$269$	−13.9495	+	3.73775i	−0.850515	+	0.227895i	−0.657644	−	0.753329i	$-0.728447\pi$
$269$	−13.9495	+	3.73775i	−0.850515	+	0.227895i	−0.192871	+	0.981224i	$0.561780\pi$
$270$	20.7255	+	11.9659i	1.26132	+	0.728221i
$271$	10.5764	+	18.3189i	0.642472	+	1.11279i	0.984879	+	0.173242i	$0.0554244\pi$
$271$	10.5764	+	18.3189i	0.642472	+	1.11279i	−0.342407	+	0.939552i	$0.611242\pi$
$272$	−5.00316	−	0.757606i	−0.303361	−	0.0459366i
$273$		0			0
$274$			10.8665i			0.656467i
$275$	−6.26329	+	23.3749i	−0.377691	+	1.40956i
$276$	−6.96425	+	12.0624i	−0.419199	+	0.726073i
$277$	8.03887	−	2.15401i	0.483009	−	0.129422i	−0.00909442	−	0.999959i	$-0.502895\pi$
$277$	8.03887	−	2.15401i	0.483009	−	0.129422i	0.492103	+	0.870537i	$0.336228\pi$
$278$	−8.66533	−	2.32187i	−0.519712	−	0.139256i
$279$	27.0085	−	27.0085i	1.61696	−	1.61696i
$280$		0			0
$281$		−	12.0888i		−	0.721160i	−0.932728	−	0.360580i	$-0.882579\pi$
$281$		−	12.0888i		−	0.721160i	0.932728	−	0.360580i	$-0.117421\pi$
$282$	−24.3922	−	6.53586i	−1.45253	−	0.389205i
$283$	4.42123	+	16.5002i	0.262815	+	0.980837i	0.963574	+	0.267440i	$0.0861778\pi$
$283$	4.42123	+	16.5002i	0.262815	+	0.980837i	−0.700760	+	0.713397i	$0.747156\pi$
$284$	5.32953	−	1.42804i	0.316250	−	0.0847389i
$285$	9.99265	+	17.3078i	0.591914	+	1.02522i
$286$	−0.539967	−	0.539967i	−0.0319289	−	0.0319289i
$287$		0			0
$288$	34.9149			2.05738
$289$	−3.76017	−	16.5789i	−0.221187	−	0.975232i
$290$	7.50220	−	12.9942i	0.440544	−	0.763045i
$291$	−1.50076	−	0.866465i	−0.0879762	−	0.0507931i
$292$	0.299576	−	1.11803i	0.0175314	−	0.0654280i
$293$	2.86968			0.167649			0.0838243	−	0.996481i	$-0.473287\pi$
$293$	2.86968			0.167649			0.0838243	+	0.996481i	$0.473287\pi$
$294$		0			0
$295$	24.8715	−	24.8715i	1.44808	−	1.44808i
$296$	−9.10737	−	2.44031i	−0.529355	−	0.141840i
$297$	20.3034	+	11.7222i	1.17812	+	0.680188i
$298$	−10.0813	−	5.82047i	−0.583997	−	0.337171i
$299$	1.22984	+	0.329536i	0.0711237	+	0.0190575i
$300$	−29.2239	+	29.2239i	−1.68724	+	1.68724i
$301$		0			0
$302$	0.185106			0.0106517
$303$	1.05277	−	3.92899i	0.0604800	−	0.225714i
$304$	1.87950	+	1.08513i	0.107797	+	0.0622363i
$305$	−1.13773	+	1.97060i	−0.0651459	+	0.112836i
$306$	6.38851	+	16.3105i	0.365207	+	0.932408i
$307$	10.4120			0.594247			0.297123	−	0.954839i	$-0.403973\pi$
$307$	10.4120			0.594247			0.297123	+	0.954839i	$0.403973\pi$
$308$		0			0
$309$	−12.6944	−	12.6944i	−0.722160	−	0.722160i
$310$	−8.55325	−	14.8147i	−0.485792	−	0.841416i
$311$	−13.6357	+	3.65367i	−0.773209	+	0.207181i	−0.623789	−	0.781593i	$-0.714407\pi$
$311$	−13.6357	+	3.65367i	−0.773209	+	0.207181i	−0.149420	+	0.988774i	$0.547741\pi$
$312$	−0.788962	−	2.94445i	−0.0446662	−	0.166696i
$313$	−21.0299	−	5.63494i	−1.18868	−	0.318506i	−0.390316	−	0.920681i	$-0.627634\pi$
$313$	−21.0299	−	5.63494i	−1.18868	−	0.318506i	−0.798364	+	0.602175i	$0.794301\pi$
$314$			11.3854i			0.642517i
$315$		0			0
$316$	−16.5998	+	16.5998i	−0.933810	+	0.933810i
$317$	−16.6272	−	4.45523i	−0.933875	−	0.250231i	−0.240368	−	0.970682i	$-0.577268\pi$
$317$	−16.6272	−	4.45523i	−0.933875	−	0.250231i	−0.693506	+	0.720451i	$0.743935\pi$
$318$	8.33140	−	2.23239i	0.467201	−	0.125186i
$319$	7.34938	−	12.7295i	0.411487	−	0.712716i
$320$	1.65140	−	6.16311i	0.0923161	−	0.344528i
$321$			9.91170i			0.553217i
$322$		0			0
$323$	−1.09161	+	7.20891i	−0.0607390	+	0.401115i
$324$	6.60281	+	11.4364i	0.366823	+	0.635356i
$325$	3.27179	+	1.88897i	0.181486	+	0.104781i
$326$	2.44258	−	0.654488i	0.135282	−	0.0362487i
$327$	−17.0441	−	29.5213i	−0.942542	−	1.63253i
$328$	13.1782	+	13.1782i	0.727644	+	0.727644i
$329$		0			0
$330$	14.8960	−	14.8960i	0.819999	−	0.819999i
$331$	−0.862903	+	0.498197i	−0.0474294	+	0.0273834i	−0.523527	−	0.852009i	$-0.675384\pi$
$331$	−0.862903	+	0.498197i	−0.0474294	+	0.0273834i	0.476098	+	0.879392i	$0.342051\pi$
$332$	2.96417	+	1.71137i	0.162680	+	0.0939235i
$333$	−5.87860	−	21.9392i	−0.322145	−	1.20226i
$334$	13.5072	+	3.61924i	0.739080	+	0.198036i
$335$	−20.5385	−	20.5385i	−1.12214	−	1.12214i
$336$		0			0
$337$	10.9224	+	10.9224i	0.594979	+	0.594979i	0.938972	−	0.343993i	$-0.111780\pi$
$337$	10.9224	+	10.9224i	0.594979	+	0.594979i	−0.343993	+	0.938972i	$0.611780\pi$
$338$	7.89373	−	4.55745i	0.429362	−	0.247892i
$339$	1.36326	−	2.36124i	0.0740422	−	0.128245i
$340$	−23.1083	+	2.58767i	−1.25322	+	0.140336i
$341$	−8.37902	−	14.5129i	−0.453749	−	0.785917i
$342$		−	7.51282i		−	0.406247i
$343$		0			0
$344$	−13.8424			−0.746334
$345$	−9.09087	+	33.9276i	−0.489436	+	1.82660i
$346$	1.19846	+	4.47270i	0.0644294	+	0.240454i
$347$	−3.32797	−	12.4202i	−0.178655	−	0.666749i	−0.995900	−	0.0904591i	$-0.971167\pi$
$347$	−3.32797	−	12.4202i	−0.178655	−	0.666749i	0.817245	−	0.576290i	$-0.195500\pi$
$348$	21.7399	−	12.5516i	1.16538	−	0.672834i
$349$			6.23304i			0.333647i	0.985987	+	0.166824i	$0.0533510\pi$
$349$			6.23304i			0.333647i	−0.985987	+	0.166824i	$0.946649\pi$
$350$		0			0
$351$	2.58804	−	2.58804i	0.138139	−	0.138139i
$352$	3.96474	−	14.7966i	0.211321	−	0.788661i
$353$	−6.17843	+	10.7014i	−0.328845	+	0.569576i	−0.982283	−	0.187404i	$-0.939993\pi$
$353$	−6.17843	+	10.7014i	−0.328845	+	0.569576i	0.653438	+	0.756980i	$0.273326\pi$
$354$	−19.1779	+	5.13870i	−1.01929	+	0.273119i
$355$	12.0498	−	6.95698i	0.639539	−	0.369238i
$356$	19.0469			1.00949
$357$		0			0
$358$	9.72441			0.513951
$359$	3.50680	−	2.02465i	0.185082	−	0.106857i	−0.404596	−	0.914495i	$-0.632588\pi$
$359$	3.50680	−	2.02465i	0.185082	−	0.106857i	0.589678	+	0.807638i	$0.299255\pi$
$360$	54.0952	−	14.4948i	2.85107	−	0.763942i
$361$	−7.93647	+	13.7464i	−0.417709	+	0.723493i
$362$	−1.75589	+	6.55309i	−0.0922877	+	0.344423i
$363$	−8.71746	+	8.71746i	−0.457548	+	0.457548i
$364$		0			0
$365$		−	2.91888i		−	0.152781i
$366$	1.11234	−	0.642210i	0.0581430	−	0.0335689i
$367$	−2.20868	−	8.24290i	−0.115292	−	0.430276i	0.884017	−	0.467456i	$-0.154829\pi$
$367$	−2.20868	−	8.24290i	−0.115292	−	0.430276i	−0.999309	+	0.0371799i	$0.988163\pi$
$368$	0.987201	+	3.68428i	0.0514614	+	0.192057i
$369$	−11.6197	+	43.3654i	−0.604898	+	2.25751i
$370$	−10.1724			−0.528838
$371$		0			0
$372$		−	28.6200i		−	1.48388i
$373$	6.62051	+	11.4671i	0.342797	+	0.593742i	0.984951	−	0.172834i	$-0.0552924\pi$
$373$	6.62051	+	11.4671i	0.342797	+	0.593742i	−0.642154	+	0.766576i	$0.721959\pi$
$374$	7.63767	−	0.855267i	0.394935	−	0.0442248i
$375$	−23.8567	+	41.3210i	−1.23195	+	2.13381i
$376$	−25.5079	+	14.7270i	−1.31547	+	0.759487i
$377$	−1.62261	−	1.62261i	−0.0835688	−	0.0835688i
$378$		0			0
$379$	6.55582	+	6.55582i	0.336750	+	0.336750i	0.855143	−	0.518393i	$-0.173469\pi$
$379$	6.55582	+	6.55582i	0.336750	+	0.336750i	−0.518393	+	0.855143i	$0.673469\pi$
$380$	9.63300	+	2.58115i	0.494162	+	0.132410i
$381$	11.4660	+	42.7919i	0.587423	+	2.19229i
$382$	3.87579	+	2.23769i	0.198303	+	0.114490i
$383$	15.7346	−	9.08437i	0.804000	−	0.464190i	−0.0408680	−	0.999165i	$-0.513012\pi$
$383$	15.7346	−	9.08437i	0.804000	−	0.464190i	0.844868	+	0.534975i	$0.179679\pi$
$384$	22.1937	−	22.1937i	1.13257	−	1.13257i
$385$		0			0
$386$	−0.972046	−	0.972046i	−0.0494759	−	0.0494759i
$387$	−16.6729	−	28.8783i	−0.847531	−	1.46797i
$388$	−0.835279	+	0.223812i	−0.0424049	+	0.0113624i
$389$	−7.01472	−	4.04995i	−0.355660	−	0.205341i	0.311515	−	0.950241i	$-0.399164\pi$
$389$	−7.01472	−	4.04995i	−0.355660	−	0.205341i	−0.667175	+	0.744901i	$0.732497\pi$
$390$	−1.64439	−	2.84816i	−0.0832667	−	0.144222i
$391$	−10.3155	+	7.60227i	−0.521676	+	0.384463i
$392$		0			0
$393$		−	23.3516i		−	1.17793i
$394$	2.04456	−	7.63041i	0.103004	−	0.384414i
$395$	−29.6000	+	51.2687i	−1.48934	+	2.57961i
$396$	22.6720	−	6.07495i	1.13931	−	0.305278i
$397$	−5.86792	−	1.57230i	−0.294502	−	0.0789117i	0.108543	−	0.994092i	$-0.465382\pi$
$397$	−5.86792	−	1.57230i	−0.294502	−	0.0789117i	−0.403045	+	0.915180i	$0.632048\pi$
$398$	−9.02251	+	9.02251i	−0.452258	+	0.452258i
$399$		0			0
$400$			11.3177i			0.565885i
$401$	38.5368	+	10.3259i	1.92443	+	0.515650i	0.984876	+	0.173258i	$0.0554295\pi$
$401$	38.5368	+	10.3259i	1.92443	+	0.515650i	0.939557	+	0.342392i	$0.111237\pi$
$402$	4.24346	+	15.8368i	0.211645	+	0.789869i
$403$	−2.52706	+	0.677124i	−0.125882	+	0.0337300i
$404$	−1.01488	−	1.75782i	−0.0504920	−	0.0874548i
$405$	23.5477	+	23.5477i	1.17010	+	1.17010i
$406$		0			0
$407$	−9.96519			−0.493956
$408$	28.1110	+	12.2876i	1.39170	+	0.608328i
$409$	7.92489	−	13.7263i	0.391860	−	0.678722i	−0.600835	−	0.799373i	$-0.705165\pi$
$409$	7.92489	−	13.7263i	0.391860	−	0.678722i	0.992695	+	0.120651i	$0.0384983\pi$
$410$	17.4131	+	10.0534i	0.859970	+	0.496504i
$411$	−11.8658	+	44.2839i	−0.585299	+	2.18436i
$412$	−8.95849			−0.441353
$413$		0			0
$414$	9.33655	−	9.33655i	0.458866	−	0.458866i
$415$	8.33723	+	2.23395i	0.409259	+	0.109660i
$416$	−2.07108	−	1.19574i	−0.101543	−	0.0586260i
$417$	−32.7783	−	18.9245i	−1.60516	−	0.926738i
$418$	−3.18386	−	0.853114i	−0.155728	−	0.0417272i
$419$	4.90962	−	4.90962i	0.239851	−	0.239851i	−0.576938	−	0.816788i	$-0.695752\pi$
$419$	4.90962	−	4.90962i	0.239851	−	0.239851i	0.816788	+	0.576938i	$0.195752\pi$
$420$		0			0
$421$	−0.950160			−0.0463079			−0.0231540	−	0.999732i	$-0.507371\pi$
$421$	−0.950160			−0.0463079			−0.0231540	+	0.999732i	$0.507371\pi$
$422$	−2.28021	+	8.50987i	−0.110999	+	0.414254i
$423$	−61.4474	−	35.4767i	−2.98768	−	1.72494i
$424$	5.03016	−	8.71249i	0.244286	−	0.423116i
$425$	−35.4036	+	13.8669i	−1.71733	+	0.672645i
$426$	−7.85399			−0.380527
$427$		0			0
$428$	3.49736	+	3.49736i	0.169051	+	0.169051i
$429$	−1.61089	−	2.79014i	−0.0777745	−	0.134709i
$430$	−14.4255	+	3.86529i	−0.695658	+	0.186401i
$431$	0.703755	+	2.62645i	0.0338987	+	0.126512i	0.980802	−	0.195008i	$-0.0624732\pi$
$431$	0.703755	+	2.62645i	0.0338987	+	0.126512i	−0.946903	+	0.321519i	$0.895807\pi$
$432$	10.5909	+	2.83782i	0.509555	+	0.136535i
$433$			38.1244i			1.83214i	0.401014	+	0.916072i	$0.368658\pi$
$433$			38.1244i			1.83214i	−0.401014	+	0.916072i	$0.631342\pi$
$434$		0			0
$435$	44.7629	−	44.7629i	2.14621	−	2.14621i
$436$	−16.4307	−	4.40259i	−0.786886	−	0.210846i
$437$	5.30858	−	1.42243i	0.253944	−	0.0680441i
$438$	−0.823808	+	1.42688i	−0.0393631	+	0.0681788i
$439$	−3.13730	+	11.7086i	−0.149735	+	0.558820i	0.849764	+	0.527164i	$0.176745\pi$
$439$	−3.13730	+	11.7086i	−0.149735	+	0.558820i	−0.999499	+	0.0316556i	$0.989922\pi$
$440$		−	24.5710i		−	1.17138i
$441$		0			0
$442$	0.179635	−	1.18630i	0.00854439	−	0.0564263i
$443$	4.56219	+	7.90195i	0.216756	+	0.375433i	0.953814	−	0.300396i	$-0.0971190\pi$
$443$	4.56219	+	7.90195i	0.216756	+	0.375433i	−0.737058	+	0.675829i	$0.763786\pi$
$444$	−14.7388	−	8.50946i	−0.699474	−	0.403841i
$445$	46.3953	−	12.4316i	2.19935	−	0.589313i
$446$	10.1612	+	17.5997i	0.481146	+	0.833370i
$447$	−34.7286	−	34.7286i	−1.64261	−	1.64261i
$448$		0			0
$449$	12.7040	−	12.7040i	0.599539	−	0.599539i	−0.340651	−	0.940190i	$-0.610647\pi$
$449$	12.7040	−	12.7040i	0.599539	−	0.599539i	0.940190	+	0.340651i	$0.110647\pi$
$450$	33.9298	−	19.5894i	1.59946	−	0.923451i
$451$	17.0584	+	9.84866i	0.803248	+	0.463755i
$452$	−0.352137	−	1.31419i	−0.0165631	−	0.0618145i
$453$	0.754361	+	0.202130i	0.0354430	+	0.00949691i
$454$	4.68485	+	4.68485i	0.219871	+	0.219871i
$455$		0			0
$456$	−9.30408	−	9.30408i	−0.435703	−	0.435703i
$457$	29.8357	−	17.2257i	1.39566	−	0.805782i	0.401722	−	0.915762i	$-0.368412\pi$
$457$	29.8357	−	17.2257i	1.39566	−	0.805782i	0.993934	+	0.109979i	$0.0350785\pi$
$458$	−8.77134	+	15.1924i	−0.409858	+	0.709894i
$459$	4.09926	+	36.6071i	0.191337	+	1.70867i
$460$	8.76367	+	15.1791i	0.408608	+	0.707730i
$461$			39.6206i			1.84531i	0.385621	+	0.922657i	$0.373987\pi$
$461$			39.6206i			1.84531i	−0.385621	+	0.922657i	$0.626013\pi$
$462$		0			0
$463$	−27.3322			−1.27024			−0.635118	−	0.772415i	$-0.719049\pi$
$463$	−27.3322			−1.27024			−0.635118	+	0.772415i	$0.719049\pi$
$464$	1.77922	−	6.64013i	0.0825981	−	0.308260i
$465$	−18.6798	−	69.7138i	−0.866253	−	3.23290i
$466$	−1.69995	−	6.34429i	−0.0787486	−	0.293894i
$467$	−2.76228	+	1.59480i	−0.127823	+	0.0737987i	−0.562548	−	0.826765i	$-0.690179\pi$
$467$	−2.76228	+	1.59480i	−0.127823	+	0.0737987i	0.434725	+	0.900563i	$0.356846\pi$
$468$		−	3.66434i		−	0.169384i
$469$		0			0
$470$	−22.4700	+	22.4700i	−1.03646	+	1.03646i
$471$	−12.4325	+	46.3988i	−0.572860	+	2.13794i
$472$	−11.5788	+	20.0551i	−0.532959	+	0.923112i
$473$	−14.1316	+	3.78656i	−0.649773	+	0.174106i
$474$	28.9396	−	16.7083i	1.32924	−	0.767437i
$475$	16.3074			0.748233
$476$		0			0
$477$	24.2348			1.10964
$478$	7.58381	−	4.37851i	0.346875	−	0.200269i
$479$	−6.42196	+	1.72076i	−0.293427	+	0.0786234i	−0.402529	−	0.915407i	$-0.631869\pi$
$479$	−6.42196	+	1.72076i	−0.293427	+	0.0786234i	0.109103	+	0.994030i	$0.465202\pi$
$480$	32.9868	−	57.1348i	1.50563	−	2.60783i
$481$	−0.402652	+	1.50272i	−0.0183594	+	0.0685181i
$482$	−4.69475	+	4.69475i	−0.213840	+	0.213840i
$483$		0			0
$484$			6.15193i			0.279633i
$485$	−1.88853	+	1.09034i	−0.0857537	+	0.0495099i
$486$	0.0621824	+	0.232068i	0.00282065	+	0.0105268i
$487$	−6.18652	−	23.0884i	−0.280338	−	1.04624i	−0.952179	−	0.305540i	$-0.901163\pi$
$487$	−6.18652	−	23.0884i	−0.280338	−	1.04624i	0.671841	−	0.740695i	$-0.265504\pi$
$488$	0.387740	−	1.44707i	0.0175522	−	0.0655057i
$489$	10.6689			0.482464
$490$		0			0
$491$		−	37.9028i		−	1.71053i	−0.518192	−	0.855264i	$-0.673395\pi$
$491$		−	37.9028i		−	1.71053i	0.518192	−	0.855264i	$-0.326605\pi$
$492$	16.8199	+	29.1330i	0.758300	+	1.31341i
$493$	22.9514	−	2.57010i	1.03368	−	0.115751i
$494$	−0.257294	+	0.445646i	−0.0115762	+	0.0200506i
$495$	51.2604	−	29.5952i	2.30398	−	1.33021i
$496$	−5.54192	−	5.54192i	−0.248839	−	0.248839i
$497$		0			0
$498$	−3.44511	−	3.44511i	−0.154379	−	0.154379i
$499$	−12.4493	−	3.33577i	−0.557306	−	0.149330i	−0.0308376	−	0.999524i	$-0.509817\pi$
$499$	−12.4493	−	3.33577i	−0.557306	−	0.149330i	−0.526468	+	0.850195i	$0.676484\pi$
$500$	6.16230	+	22.9980i	0.275587	+	1.02850i
$501$	51.0935	+	29.4988i	2.28269	+	1.31791i
$502$	−15.6466	+	9.03356i	−0.698341	+	0.403188i
$503$	11.9184	−	11.9184i	0.531414	−	0.531414i	−0.389579	−	0.920993i	$-0.627380\pi$
$503$	11.9184	−	11.9184i	0.531414	−	0.531414i	0.920993	+	0.389579i	$0.127380\pi$
$504$		0			0
$505$	−3.61937	−	3.61937i	−0.161060	−	0.161060i
$506$	−2.89654	−	5.01695i	−0.128767	−	0.223031i
$507$	37.1458	−	9.95318i	1.64970	−	0.442036i
$508$	19.1450	+	11.0534i	0.849421	+	0.490413i
$509$	−14.9503	−	25.8947i	−0.662662	−	1.14776i	−0.979914	−	0.199423i	$-0.936093\pi$
$509$	−14.9503	−	25.8947i	−0.662662	−	1.14776i	0.317252	−	0.948341i	$-0.397240\pi$
$510$	32.7262	+	4.95559i	1.44914	+	0.219437i
$511$		0			0
$512$		−	13.2586i		−	0.585952i
$513$	4.08894	−	15.2601i	0.180531	−	0.673751i
$514$	−3.64617	+	6.31535i	−0.160826	+	0.278558i
$515$	−21.8214	+	5.84704i	−0.961568	+	0.257651i
$516$	−24.1345	−	6.46683i	−1.06246	−	0.284686i
$517$	−22.0123	+	22.0123i	−0.968100	+	0.968100i
$518$		0			0
$519$			19.5362i			0.857543i
$520$	−3.70523	−	0.992814i	−0.162485	−	0.0435378i
$521$	2.78827	+	10.4060i	0.122157	+	0.455894i	0.999722	−	0.0235618i	$-0.00750064\pi$
$521$	2.78827	+	10.4060i	0.122157	+	0.455894i	−0.877566	+	0.479456i	$0.840834\pi$
$522$	−22.9863	+	6.15915i	−1.00608	+	0.269579i
$523$	−7.97760	−	13.8176i	−0.348836	−	0.604202i	0.637207	−	0.770693i	$-0.280090\pi$
$523$	−7.97760	−	13.8176i	−0.348836	−	0.604202i	−0.986043	+	0.166491i	$0.946756\pi$
$524$	−8.23966	−	8.23966i	−0.359951	−	0.359951i
$525$		0			0
$526$	−7.87947			−0.343561
$527$	10.5458	−	24.1262i	0.459383	−	1.05095i
$528$	4.82580	−	8.35853i	0.210016	−	0.363758i
$529$	−11.5536	−	6.67049i	−0.502332	−	0.290021i
$530$	2.80920	−	10.4841i	0.122024	−	0.455398i
$531$	−55.7858			−2.42090
$532$		0			0
$533$	2.17441	−	2.17441i	0.0941840	−	0.0941840i
$534$	−26.1887	−	7.01723i	−1.13329	−	0.303665i
$535$	10.8017	+	6.23634i	0.466997	+	0.269621i
$536$	16.5612	+	9.56163i	0.715336	+	0.413000i
$537$	39.6297	+	10.6188i	1.71015	+	0.458233i
$538$	7.25355	−	7.25355i	0.312723	−	0.312723i
$539$		0			0
$540$	50.3844			2.16820
$541$	6.32277	−	23.5969i	0.271837	−	1.01451i	−0.686094	−	0.727512i	$-0.740676\pi$
$541$	6.32277	−	23.5969i	0.271837	−	1.01451i	0.957931	−	0.286997i	$-0.0926570\pi$
$542$	−13.0122	−	7.51260i	−0.558922	−	0.322694i
$543$	−14.3115	+	24.7883i	−0.614166	+	1.06377i
$544$	22.4109	−	8.77793i	0.960859	−	0.376351i
$545$	−42.8960			−1.83746
$546$		0			0
$547$	−0.0381169	−	0.0381169i	−0.00162976	−	0.00162976i	0.706291	−	0.707921i	$-0.250367\pi$
$547$	−0.0381169	−	0.0381169i	−0.00162976	−	0.00162976i	−0.707921	+	0.706291i	$0.750367\pi$
$548$	11.4388	+	19.8125i	0.488640	+	0.846349i
$549$	3.48592	−	0.934049i	0.148775	−	0.0398642i
$550$	−4.44892	−	16.6036i	−0.189702	−	0.707979i
$551$	−9.56758	−	2.56362i	−0.407592	−	0.109214i
$552$		−	23.1253i		−	0.984277i
$553$		0			0
$554$	−4.18011	+	4.18011i	−0.177596	+	0.177596i
$555$	−41.4554	−	11.1079i	−1.75968	−	0.471506i
$556$	−18.2434	+	4.88830i	−0.773693	+	0.207310i
$557$	−13.6274	+	23.6033i	−0.577411	+	1.00011i	0.418364	+	0.908279i	$0.362604\pi$
$557$	−13.6274	+	23.6033i	−0.577411	+	1.00011i	−0.995775	+	0.0918258i	$0.970730\pi$
$558$	−7.02204	+	26.2066i	−0.297267	+	1.10941i
$559$			2.28401i			0.0966032i
$560$		0			0
$561$	32.0596	+	4.85464i	1.35356	+	0.204963i
$562$	4.29345	+	7.43647i	0.181108	+	0.313689i
$563$	18.0621	+	10.4281i	0.761225	+	0.439494i	0.829736	−	0.558157i	$-0.188491\pi$
$563$	18.0621	+	10.4281i	0.761225	+	0.439494i	−0.0685102	+	0.997650i	$0.521825\pi$
$564$	−51.3536	+	13.7602i	−2.16238	+	0.579408i
$565$	−1.71550	−	2.97133i	−0.0721716	−	0.125005i
$566$	−8.57992	−	8.57992i	−0.360641	−	0.360641i
$567$		0			0
$568$	−6.47758	+	6.47758i	−0.271793	+	0.271793i
$569$	−14.9493	+	8.63097i	−0.626707	+	0.361829i	−0.779476	−	0.626433i	$-0.784514\pi$
$569$	−14.9493	+	8.63097i	−0.626707	+	0.361829i	0.152769	+	0.988262i	$0.451181\pi$
$570$	−12.2940	−	7.09794i	−0.514939	−	0.297300i
$571$	9.01148	+	33.6313i	0.377119	+	1.40743i	0.850225	+	0.526420i	$0.176466\pi$
$571$	9.01148	+	33.6313i	0.377119	+	1.40743i	−0.473106	+	0.881005i	$0.656867\pi$
$572$	−1.55291	−	0.416101i	−0.0649305	−	0.0173981i
$573$	13.3514	+	13.3514i	0.557765	+	0.557765i
$574$		0			0
$575$	20.2660	+	20.2660i	0.845149	+	0.845149i
$576$	−8.76381	+	5.05979i	−0.365159	+	0.210825i
$577$	−11.2200	+	19.4335i	−0.467093	+	0.809029i	−0.999293	−	0.0375897i	$-0.988032\pi$
$577$	−11.2200	+	19.4335i	−0.467093	+	0.809029i	0.532200	+	0.846618i	$0.321365\pi$
$578$	8.20122	+	8.86310i	0.341126	+	0.368657i
$579$	−2.89992	−	5.02281i	−0.120517	−	0.208741i
$580$		−	31.5893i		−	1.31167i
$581$		0			0
$582$	1.23093			0.0510236
$583$	2.75197	−	10.2705i	0.113975	−	0.425361i
$584$	0.497382	+	1.85625i	0.0205818	+	0.0768123i
$585$	−2.39164	−	8.92573i	−0.0988823	−	0.369034i
$586$	−1.76529	+	1.01919i	−0.0729234	+	0.0421024i
$587$			4.91137i			0.202714i	0.994850	+	0.101357i	$0.0323184\pi$
$587$			4.91137i			0.202714i	−0.994850	+	0.101357i	$0.967682\pi$
$588$		0			0
$589$	−7.98520	+	7.98520i	−0.329024	+	0.329024i
$590$	−6.46644	+	24.1331i	−0.266219	+	0.993543i
$591$	16.6643	−	28.8635i	0.685479	−	1.18728i
$592$	−4.50175	+	1.20624i	−0.185021	+	0.0495761i
$593$	−11.8833	+	6.86085i	−0.487990	+	0.281741i	−0.723740	−	0.690072i	$-0.757579\pi$
$593$	−11.8833	+	6.86085i	−0.487990	+	0.281741i	0.235750	+	0.971814i	$0.424245\pi$
$594$	−16.6529			−0.683275
$595$		0			0
$596$	−24.5081			−1.00389
$597$	−46.6216	+	26.9170i	−1.90809	+	1.10164i
$598$	−0.873578	+	0.234074i	−0.0357232	+	0.00957202i
$599$	9.99531	−	17.3124i	0.408397	−	0.707365i	−0.586313	−	0.810085i	$-0.699421\pi$
$599$	9.99531	−	17.3124i	0.408397	−	0.707365i	0.994710	+	0.102720i	$0.0327544\pi$
$600$	17.7596	−	66.2796i	0.725031	−	2.70585i
$601$	18.4941	−	18.4941i	0.754391	−	0.754391i	−0.220904	−	0.975295i	$-0.570901\pi$
$601$	18.4941	−	18.4941i	0.754391	−	0.754391i	0.975295	+	0.220904i	$0.0709008\pi$
$602$		0			0
$603$			46.0671i			1.87600i
$604$	0.337499	−	0.194855i	0.0137326	−	0.00792855i
$605$	4.01525	+	14.9851i	0.163243	+	0.609232i
$606$	0.747798	+	2.79082i	0.0303772	+	0.113369i
$607$	10.2561	−	38.2761i	0.416280	−	1.55358i	−0.365977	−	0.930624i	$-0.619265\pi$
$607$	10.2561	−	38.2761i	0.416280	−	1.55358i	0.782257	−	0.622956i	$-0.214068\pi$
$608$	−10.3227			−0.418643
$609$		0			0
$610$		−	1.61629i		−	0.0654416i
$611$	2.42996	+	4.20882i	0.0983057	+	0.170270i
$612$	28.8175	+	23.0134i	1.16488	+	0.930264i
$613$	10.8330	−	18.7633i	0.437541	−	0.757844i	−0.559958	−	0.828521i	$-0.689183\pi$
$613$	10.8330	−	18.7633i	0.437541	−	0.757844i	0.997499	+	0.0706773i	$0.0225161\pi$
$614$	−6.40499	+	3.69792i	−0.258484	+	0.149236i
$615$	59.9852	+	59.9852i	2.41883	+	2.41883i
$616$		0			0
$617$	−24.0750	−	24.0750i	−0.969222	−	0.969222i	0.0303184	−	0.999540i	$-0.490348\pi$
$617$	−24.0750	−	24.0750i	−0.969222	−	0.969222i	−0.999540	+	0.0303184i	$0.990348\pi$
$618$	12.3175	+	3.30047i	0.495483	+	0.132764i
$619$	−4.29924	−	16.0450i	−0.172801	−	0.644902i	−0.996916	−	0.0784791i	$-0.974994\pi$
$619$	−4.29924	−	16.0450i	−0.172801	−	0.644902i	0.824115	−	0.566423i	$-0.191673\pi$
$620$	−31.1898	−	18.0074i	−1.25261	−	0.723196i
$621$	24.0460	−	13.8830i	0.964934	−	0.557105i
$622$	7.09038	−	7.09038i	0.284298	−	0.284298i
$623$		0			0
$624$	−1.06545	−	1.06545i	−0.0426521	−	0.0426521i
$625$	6.96627	+	12.0659i	0.278651	+	0.482638i
$626$	14.9379	−	4.00259i	0.597037	−	0.159976i
$627$	−12.0436	−	6.95336i	−0.480974	−	0.277690i
$628$	11.9851	+	20.7587i	0.478256	+	0.828363i
$629$	−9.28904	−	12.6042i	−0.370378	−	0.502564i
$630$		0			0
$631$		−	2.07847i		−	0.0827427i	−0.999144	−	0.0413714i	$-0.986827\pi$
$631$		−	2.07847i		−	0.0827427i	0.999144	−	0.0413714i	$-0.0131727\pi$
$632$	10.0878	−	37.6481i	0.401270	−	1.49756i
$633$	−18.5850	+	32.1902i	−0.738688	+	1.27945i
$634$	11.8105	−	3.16462i	0.469056	−	0.125683i
$635$	53.8484	+	14.4286i	2.13691	+	0.572583i
$636$	12.8404	−	12.8404i	0.509156	−	0.509156i
$637$		0			0
$638$			10.4408i			0.413354i
$639$	−21.3157	−	5.71153i	−0.843237	−	0.225945i
$640$	−10.2224	−	38.1506i	−0.404076	−	1.50803i
$641$	39.0838	−	10.4725i	1.54372	−	0.413638i	0.616253	−	0.787549i	$-0.288650\pi$
$641$	39.0838	−	10.4725i	1.54372	−	0.413638i	0.927465	+	0.373911i	$0.121983\pi$
$642$	−3.52022	−	6.09720i	−0.138932	−	0.240637i
$643$	21.4678	+	21.4678i	0.846607	+	0.846607i	0.989708	−	0.143101i	$-0.0457073\pi$
$643$	21.4678	+	21.4678i	0.846607	+	0.846607i	−0.143101	+	0.989708i	$0.545707\pi$
$644$		0			0
$645$	−63.0087			−2.48096
$646$	−1.88879	−	4.82227i	−0.0743136	−	0.189730i
$647$	7.62353	−	13.2043i	0.299712	−	0.519116i	−0.676358	−	0.736573i	$-0.736443\pi$
$647$	7.62353	−	13.2043i	0.299712	−	0.519116i	0.976070	+	0.217457i	$0.0697761\pi$
$648$	−18.9877	−	10.9625i	−0.745907	−	0.430649i
$649$	−6.33472	+	23.6415i	−0.248659	+	0.928010i
$650$	−2.68353			−0.105257
$651$		0			0
$652$	3.76453	−	3.76453i	0.147430	−	0.147430i
$653$	−35.8689	−	9.61103i	−1.40366	−	0.376109i	−0.524000	−	0.851718i	$-0.675561\pi$
$653$	−35.8689	−	9.61103i	−1.40366	−	0.376109i	−0.879656	+	0.475610i	$0.842228\pi$
$654$	20.9694	+	12.1067i	0.819970	+	0.473410i
$655$	−25.4484	−	14.6926i	−0.994349	−	0.574088i
$656$	8.89821	+	2.38427i	0.347417	+	0.0930900i
$657$	−3.27346	+	3.27346i	−0.127710	+	0.127710i
$658$		0			0
$659$	−19.0915			−0.743697			−0.371849	−	0.928293i	$-0.621276\pi$
$659$	−19.0915			−0.743697			−0.371849	+	0.928293i	$0.621276\pi$
$660$	11.4790	−	42.8400i	0.446818	−	1.66755i
$661$	−37.9339	−	21.9012i	−1.47546	−	0.851857i	−0.475842	−	0.879531i	$-0.657857\pi$
$661$	−37.9339	−	21.9012i	−1.47546	−	0.851857i	−0.999617	+	0.0276741i	$0.991190\pi$
$662$	0.353877	−	0.612934i	0.0137538	−	0.0238223i
$663$	2.02746	−	4.63833i	0.0787401	−	0.180138i
$664$	−5.68271			−0.220532
$665$		0			0
$666$	11.4081	+	11.4081i	0.442056	+	0.442056i
$667$	−8.70415	−	15.0760i	−0.337026	−	0.583746i
$668$	28.4371	−	7.61970i	1.10027	−	0.294815i
$669$	22.1914	+	82.8195i	0.857970	+	3.20199i
$670$	19.9287	+	5.33989i	0.769914	+	0.206298i
$671$		−	1.58337i		−	0.0611251i
$672$		0			0
$673$	−7.02754	+	7.02754i	−0.270892	+	0.270892i	−0.829459	−	0.558567i	$-0.811351\pi$
$673$	−7.02754	+	7.02754i	−0.270892	+	0.270892i	0.558567	+	0.829459i	$0.311351\pi$
$674$	−10.5981	−	2.83974i	−0.408222	−	0.109383i
$675$	79.5803	−	21.3235i	3.06305	−	0.820741i
$676$	9.59494	−	16.6189i	0.369036	−	0.639189i
$677$	7.86985	−	29.3707i	0.302463	−	1.12881i	−0.632644	−	0.774442i	$-0.718031\pi$
$677$	7.86985	−	29.3707i	0.302463	−	1.12881i	0.935107	−	0.354365i	$-0.115303\pi$
$678$			1.93669i			0.0743782i
$679$		0			0
$680$	31.0781	−	22.9039i	1.19179	−	0.878323i
$681$	13.9764	+	24.2078i	0.535575	+	0.927644i
$682$	10.3087	+	5.95175i	0.394742	+	0.227904i
$683$	4.87189	−	1.30542i	0.186418	−	0.0499504i	−0.164402	−	0.986393i	$-0.552570\pi$
$683$	4.87189	−	1.30542i	0.186418	−	0.0499504i	0.350820	+	0.936443i	$0.385903\pi$
$684$	−7.90849	−	13.6979i	−0.302389	−	0.523753i
$685$	40.7942	+	40.7942i	1.55867	+	1.55867i
$686$		0			0
$687$	−52.3353	+	52.3353i	−1.99672	+	1.99672i
$688$	−5.92558	+	3.42114i	−0.225911	+	0.130430i
$689$	−1.43756	−	0.829978i	−0.0547668	−	0.0316196i
$690$	−6.45739	−	24.0993i	−0.245829	−	0.917445i
$691$	−11.3053	−	3.02925i	−0.430075	−	0.115238i	0.0372865	−	0.999305i	$-0.488129\pi$
$691$	−11.3053	−	3.02925i	−0.430075	−	0.115238i	−0.467361	+	0.884066i	$0.654795\pi$
$692$	6.89337	+	6.89337i	0.262047	+	0.262047i
$693$		0			0
$694$	6.45832	+	6.45832i	0.245155	+	0.245155i
$695$	−41.2475	+	23.8143i	−1.56461	+	0.903326i
$696$	−20.8392	+	36.0945i	−0.789906	+	1.36816i
$697$	3.44410	+	30.7563i	0.130454	+	1.16498i
$698$	−2.21371	−	3.83427i	−0.0837903	−	0.145129i
$699$		−	27.7111i		−	1.04813i
$700$		0			0
$701$	31.0131			1.17135			0.585673	−	0.810547i	$-0.300830\pi$
$701$	31.0131			1.17135			0.585673	+	0.810547i	$0.300830\pi$
$702$	−0.672874	+	2.51120i	−0.0253960	+	0.0947792i
$703$	1.73804	+	6.48644i	0.0655513	+	0.244641i
$704$	1.14912	+	4.28858i	0.0433092	+	0.161632i
$705$	−116.108	+	67.0351i	−4.37289	+	2.52469i
$706$		−	8.77727i		−	0.330337i
$707$		0			0
$708$	−29.5572	+	29.5572i	−1.11083	+	1.11083i
$709$	−4.66254	+	17.4009i	−0.175106	+	0.653503i	0.821428	+	0.570312i	$0.193178\pi$
$709$	−4.66254	+	17.4009i	−0.175106	+	0.653503i	−0.996534	+	0.0831907i	$0.973489\pi$
$710$	−4.94165	+	8.55919i	−0.185457	+	0.321221i
$711$	90.6926	−	24.3010i	3.40124	−	0.911359i
$712$	−27.3866	+	15.8117i	−1.02636	+	0.592567i
$713$	−19.8472			−0.743283
$714$		0			0
$715$	−4.05422			−0.151619
$716$	17.7302	−	10.2366i	0.662611	−	0.382558i
$717$	35.6874	−	9.56240i	1.33277	−	0.357114i
$718$	−1.43814	+	2.49093i	−0.0536709	+	0.0929608i
$719$	−7.40683	+	27.6427i	−0.276228	+	1.03090i	0.678786	+	0.734336i	$0.262507\pi$
$719$	−7.40683	+	27.6427i	−0.276228	+	1.03090i	−0.955014	+	0.296561i	$0.904160\pi$
$720$	19.5744	−	19.5744i	0.729494	−	0.729494i
$721$		0			0
$722$		−	11.2748i		−	0.419605i
$723$	−24.2590	+	14.0059i	−0.902201	+	0.520886i
$724$	3.69674	+	13.7964i	0.137388	+	0.512740i
$725$	−13.3691	−	49.8941i	−0.496515	−	1.85302i
$726$	2.26648	−	8.45863i	0.0841171	−	0.313929i
$727$	18.0516			0.669498			0.334749	−	0.942307i	$-0.391348\pi$
$727$	18.0516			0.669498			0.334749	+	0.942307i	$0.391348\pi$
$728$		0			0
$729$			27.5052i			1.01871i
$730$	1.03666	+	1.79555i	0.0383686	+	0.0664564i
$731$	−17.9621	−	14.3444i	−0.664354	−	0.530549i
$732$	1.35207	−	2.34185i	0.0499738	−	0.0865572i
$733$	43.5861	−	25.1645i	1.60989	−	0.929470i	0.620496	−	0.784209i	$-0.286931\pi$
$733$	43.5861	−	25.1645i	1.60989	−	0.929470i	0.989393	−	0.145261i	$-0.0464022\pi$
$734$	4.28620	+	4.28620i	0.158207	+	0.158207i
$735$		0			0
$736$	−12.8286	−	12.8286i	−0.472868	−	0.472868i
$737$	19.5228	+	5.23112i	0.719131	+	0.192691i
$738$	−8.25367	−	30.8031i	−0.303822	−	1.13388i
$739$	−44.3562	−	25.6091i	−1.63167	−	0.942045i	−0.983578	−	0.180484i	$-0.942234\pi$
$739$	−44.3562	−	25.6091i	−1.63167	−	0.942045i	−0.648093	−	0.761562i	$-0.724433\pi$
$740$	−18.5470	+	10.7081i	−0.681803	+	0.393639i
$741$	−1.53518	+	1.53518i	−0.0563961	+	0.0563961i
$742$		0			0
$743$	6.02128	+	6.02128i	0.220899	+	0.220899i	0.808877	−	0.587978i	$-0.200076\pi$
$743$	6.02128	+	6.02128i	0.220899	+	0.220899i	−0.587978	+	0.808877i	$0.700076\pi$
$744$	23.7587	+	41.1513i	0.871036	+	1.50868i
$745$	−59.6977	+	15.9959i	−2.18715	+	0.586046i
$746$	−8.14523	−	4.70265i	−0.298218	−	0.172176i
$747$	−6.84469	−	11.8554i	−0.250434	−	0.433765i
$748$	13.0252	−	9.59930i	0.476250	−	0.350985i
$749$		0			0
$750$		−	33.8916i		−	1.23754i
$751$	−3.20080	+	11.9456i	−0.116799	+	0.435900i	−0.999415	−	0.0341945i	$-0.989113\pi$
$751$	−3.20080	+	11.9456i	−0.116799	+	0.435900i	0.882616	+	0.470094i	$0.155780\pi$
$752$	−7.27951	+	12.6085i	−0.265457	+	0.459784i
$753$	−73.6286	+	19.7287i	−2.68318	+	0.718955i
$754$	1.57444	+	0.421869i	0.0573376	+	0.0153636i
$755$	0.694916	−	0.694916i	0.0252906	−	0.0252906i
$756$		0			0
$757$		−	1.96401i		−	0.0713832i	−0.999363	−	0.0356916i	$-0.988637\pi$
$757$		−	1.96401i		−	0.0713832i	0.999363	−	0.0356916i	$-0.0113634\pi$
$758$	−6.36117	−	1.70447i	−0.231048	−	0.0619092i
$759$	−6.32585	−	23.6084i	−0.229614	−	0.856931i
$760$	−15.9935	+	4.28545i	−0.580146	+	0.155450i
$761$	−0.291188	−	0.504352i	−0.0105556	−	0.0182828i	0.860699	−	0.509114i	$-0.170027\pi$
$761$	−0.291188	−	0.504352i	−0.0105556	−	0.0182828i	−0.871255	+	0.490831i	$0.836693\pi$
$762$	−22.2512	−	22.2512i	−0.806077	−	0.806077i
$763$		0			0
$764$	9.42215			0.340882
$765$	85.2152	+	37.2484i	3.08096	+	1.34672i
$766$	−6.45277	+	11.1765i	−0.233148	+	0.403824i
$767$	3.30910	+	1.91051i	0.119485	+	0.0689846i
$768$	−8.39488	+	31.3301i	−0.302924	+	1.13053i
$769$	−47.7776			−1.72290			−0.861452	−	0.507838i	$-0.830445\pi$
$769$	−47.7776			−1.72290			−0.861452	+	0.507838i	$0.830445\pi$
$770$		0			0
$771$	−21.7553	+	21.7553i	−0.783499	+	0.783499i
$772$	−2.79555	−	0.749064i	−0.100614	−	0.0269594i
$773$	−25.7762	−	14.8819i	−0.927106	−	0.535265i	−0.0412107	−	0.999150i	$-0.513121\pi$
$773$	−25.7762	−	14.8819i	−0.927106	−	0.535265i	−0.885895	+	0.463886i	$0.846455\pi$
$774$	20.5127	+	11.8430i	0.737314	+	0.425689i
$775$	−56.8842	−	15.2421i	−2.04334	−	0.547512i
$776$	1.01521	−	1.01521i	0.0364439	−	0.0364439i
$777$		0			0
$778$	5.75349			0.206273
$779$	3.43542	−	12.8212i	0.123087	−	0.459366i
$780$	−5.99633	−	3.46198i	−0.214703	−	0.123959i
$781$	−4.84099	+	8.38484i	−0.173224	+	0.300033i
$782$	3.64557	−	8.34017i	0.130365	−	0.298244i
$783$	−50.0422			−1.78836
$784$		0			0
$785$	42.7425	+	42.7425i	1.52554	+	1.52554i
$786$	8.29352	+	14.3648i	0.295820	+	0.512375i
$787$	−8.61839	+	2.30929i	−0.307213	+	0.0823174i	−0.409132	−	0.912475i	$-0.634168\pi$
$787$	−8.61839	+	2.30929i	−0.307213	+	0.0823174i	0.101919	+	0.994793i	$0.467502\pi$
$788$	−4.30448	−	16.0645i	−0.153341	−	0.572276i
$789$	−32.1111	−	8.60413i	−1.14318	−	0.306315i
$790$		−	42.0507i		−	1.49610i
$791$		0			0
$792$	−27.5559	+	27.5559i	−0.979155	+	0.979155i
$793$	−0.238767	−	0.0639773i	−0.00847885	−	0.00227190i
$794$	4.16808	−	1.11683i	0.147919	−	0.0396349i
$795$	22.8965	−	39.6580i	0.812056	−	1.40652i
$796$	−6.95280	+	25.9482i	−0.246435	+	0.919709i
$797$		−	18.3449i		−	0.649810i	−0.945747	−	0.324905i	$-0.894668\pi$
$797$		−	18.3449i		−	0.649810i	0.945747	−	0.324905i	$-0.105332\pi$
$798$		0			0
$799$	−48.3606	−	7.32303i	−1.71087	−	0.259070i
$800$	−26.9161	−	46.6201i	−0.951629	−	1.64827i
$801$	−65.9731	−	38.0896i	−2.33104	−	1.34583i
$802$	−27.3733	+	7.33464i	−0.966584	+	0.258995i
$803$	1.01555	+	1.75898i	0.0358379	+	0.0620730i
$804$	24.4079	+	24.4079i	0.860799	+	0.860799i
$805$		0			0
$806$	1.31404	−	1.31404i	0.0462851	−	0.0462851i
$807$	37.4809	−	21.6396i	1.31939	−	0.761751i
$808$	2.91848	+	1.68499i	0.102672	+	0.0592776i
$809$	−9.51818	−	35.5223i	−0.334641	−	1.24890i	−0.904257	−	0.426988i	$-0.859575\pi$
$809$	−9.51818	−	35.5223i	−0.334641	−	1.24890i	0.569616	−	0.821911i	$-0.307092\pi$
$810$	−22.8486	−	6.12226i	−0.802817	−	0.215114i
$811$	−12.7177	−	12.7177i	−0.446580	−	0.446580i	0.447636	−	0.894216i	$-0.352266\pi$
$811$	−12.7177	−	12.7177i	−0.446580	−	0.446580i	−0.894216	+	0.447636i	$0.852266\pi$
$812$		0			0
$813$	−44.8249	−	44.8249i	−1.57208	−	1.57208i
$814$	6.13010	−	3.53922i	0.214860	−	0.124049i
$815$	6.71276	−	11.6268i	0.235138	−	0.407270i
$816$	15.0705	−	1.68759i	0.527572	−	0.0590775i
$817$	4.92942	+	8.53801i	0.172459	+	0.298707i
$818$			11.2583i			0.393639i
$819$		0			0
$820$	42.3317			1.47829
$821$	6.94886	−	25.9335i	0.242517	−	0.905085i	−0.732099	−	0.681199i	$-0.761459\pi$
$821$	6.94886	−	25.9335i	0.242517	−	0.905085i	0.974615	−	0.223886i	$-0.0718744\pi$
$822$	−8.42849	−	31.4556i	−0.293977	−	1.09714i
$823$	6.70223	+	25.0131i	0.233625	+	0.871901i	0.978764	+	0.204991i	$0.0657166\pi$
$823$	6.70223	+	25.0131i	0.233625	+	0.871901i	−0.745139	+	0.666910i	$0.767617\pi$
$824$	12.8809	−	7.43682i	0.448729	−	0.259074i
$825$		−	72.5224i		−	2.52490i
$826$		0			0
$827$	33.8532	−	33.8532i	1.17719	−	1.17719i	0.196733	−	0.980457i	$-0.436967\pi$
$827$	33.8532	−	33.8532i	1.17719	−	1.17719i	0.980457	−	0.196733i	$-0.0630332\pi$
$828$	7.19479	−	26.8513i	0.250036	−	0.933148i
$829$	20.7357	−	35.9154i	0.720182	−	1.24739i	−0.240744	−	0.970589i	$-0.577391\pi$
$829$	20.7357	−	35.9154i	0.720182	−	1.24739i	0.960926	−	0.276804i	$-0.0892752\pi$
$830$	−5.92207	+	1.58681i	−0.205558	+	0.0550791i
$831$	−21.5997	+	12.4706i	−0.749285	+	0.432600i
$832$	0.693137			0.0240302
$833$		0			0
$834$	26.8848			0.930944
$835$	64.2950	−	37.1208i	2.22502	−	1.28462i
$836$	−6.70309	+	1.79609i	−0.231831	+	0.0621190i
$837$	−28.5265	+	49.4094i	−0.986021	+	1.70784i
$838$	−1.27647	+	4.76385i	−0.0440950	+	0.164565i
$839$	−2.00167	+	2.00167i	−0.0691053	+	0.0691053i	−0.740815	−	0.671709i	$-0.765560\pi$
$839$	−2.00167	+	2.00167i	−0.0691053	+	0.0691053i	0.671709	+	0.740815i	$0.265560\pi$
$840$		0			0
$841$			2.37473i			0.0818873i
$842$	0.584492	−	0.337457i	0.0201429	−	0.0116295i
$843$	9.37662	+	34.9940i	0.322948	+	1.20526i
$844$	4.80061	+	17.9161i	0.165244	+	0.616698i
$845$	12.5249	−	46.7435i	0.430869	−	1.60802i
$846$	50.3993			1.73276
$847$		0			0
$848$		−	4.97278i		−	0.170766i
$849$	−25.5966	−	44.3346i	−0.878472	−	1.52156i
$850$	16.8536	−	21.1041i	0.578074	−	0.723866i
$851$	−5.90107	+	10.2210i	−0.202286	+	0.350370i
$852$	−14.3200	+	8.26763i	−0.490594	+	0.283244i
$853$	−27.6517	−	27.6517i	−0.946776	−	0.946776i	0.0518773	−	0.998653i	$-0.483480\pi$
$853$	−27.6517	−	27.6517i	−0.946776	−	0.946776i	−0.998653	+	0.0518773i	$0.983480\pi$
$854$		0			0
$855$	−28.2042	−	28.2042i	−0.964563	−	0.964563i
$856$	−7.93198	−	2.12537i	−0.271109	−	0.0726435i
$857$	−12.5673	−	46.9017i	−0.429289	−	1.60213i	−0.754374	−	0.656445i	$-0.772059\pi$
$857$	−12.5673	−	46.9017i	−0.429289	−	1.60213i	0.325084	−	0.945685i	$-0.394607\pi$
$858$	1.98188	+	1.14424i	0.0676604	+	0.0390638i
$859$	−13.7524	+	7.93995i	−0.469226	+	0.270908i	−0.715916	−	0.698187i	$-0.753990\pi$
$859$	−13.7524	+	7.93995i	−0.469226	+	0.270908i	0.246690	+	0.969094i	$0.420657\pi$
$860$	−22.2327	+	22.2327i	−0.758129	+	0.758129i
$861$		0			0
$862$	−1.36572	−	1.36572i	−0.0465166	−	0.0465166i
$863$	−22.9989	−	39.8352i	−0.782891	−	1.35601i	−0.930251	−	0.366924i	$-0.880411\pi$
$863$	−22.9989	−	39.8352i	−0.782891	−	1.35601i	0.147360	−	0.989083i	$-0.452923\pi$
$864$	−50.3753	+	13.4980i	−1.71380	+	0.459212i
$865$	21.2903	+	12.2920i	0.723893	+	0.417940i
$866$	−13.5402	−	23.4523i	−0.460115	−	0.796942i
$867$	23.7440	+	45.0751i	0.806390	+	1.53083i
$868$		0			0
$869$		−	41.1942i		−	1.39742i
$870$	−11.6381	+	43.4338i	−0.394567	+	1.47254i
$871$	1.57767	−	2.73261i	0.0534574	−	0.0925909i
$872$	27.2796	−	7.30954i	0.923803	−	0.247532i
$873$	3.34074	+	0.895149i	0.113067	+	0.0302962i
$874$	−2.76040	+	2.76040i	−0.0933718	+	0.0933718i
$875$		0			0
$876$			3.46878i			0.117199i
$877$	−38.9199	−	10.4285i	−1.31423	−	0.352147i	−0.467417	−	0.884037i	$-0.654815\pi$
$877$	−38.9199	−	10.4285i	−1.31423	−	0.352147i	−0.846813	+	0.531890i	$0.821482\pi$
$878$	−2.22848	−	8.31678i	−0.0752074	−	0.280678i
$879$	−8.30698	+	2.22585i	−0.280187	+	0.0750760i
$880$	−6.07269	−	10.5182i	−0.204710	−	0.354569i
$881$	−3.34499	−	3.34499i	−0.112696	−	0.112696i	0.648510	−	0.761206i	$-0.275392\pi$
$881$	−3.34499	−	3.34499i	−0.112696	−	0.112696i	−0.761206	+	0.648510i	$0.775392\pi$
$882$		0			0
$883$	−49.7125			−1.67296			−0.836480	−	0.547998i	$-0.815390\pi$
$883$	−49.7125			−1.67296			−0.836480	+	0.547998i	$0.815390\pi$
$884$	−0.921249	−	2.35203i	−0.0309849	−	0.0791075i
$885$	−52.7051	+	91.2880i	−1.77166	+	3.06861i
$886$	−5.61288	−	3.24060i	−0.188568	−	0.108870i
$887$	−10.9982	+	41.0460i	−0.369285	+	1.37819i	0.492233	+	0.870463i	$0.336181\pi$
$887$	−10.9982	+	41.0460i	−0.369285	+	1.37819i	−0.861518	+	0.507727i	$0.830486\pi$
$888$	28.2563			0.948218
$889$		0			0
$890$	−24.1250	+	24.1250i	−0.808670	+	0.808670i
$891$	−22.3832	−	5.99755i	−0.749864	−	0.200925i
$892$	37.0532	+	21.3927i	1.24063	+	0.716280i
$893$	18.1672	+	10.4888i	0.607943	+	0.350996i
$894$	33.6975	+	9.02921i	1.12701	+	0.301982i
$895$	36.5068	−	36.5068i	1.22029	−	1.22029i
$896$		0			0
$897$	−3.81568			−0.127402
$898$	−3.30296	+	12.3268i	−0.110221	+	0.411351i
$899$	30.9780	+	17.8851i	1.03317	+	0.596503i
$900$	41.2421	−	71.4335i	1.37474	−	2.38112i
$901$	15.5557	−	6.09287i	0.518235	−	0.202983i
$902$	−13.9913			−0.465860
$903$		0			0
$904$	1.59729	+	1.59729i	0.0531250	+	0.0531250i
$905$	18.0093	+	31.1931i	0.598651	+	1.03689i
$906$	−0.535834	+	0.143576i	−0.0178019	+	0.00477001i
$907$	−2.18246	−	8.14504i	−0.0724673	−	0.270452i	0.920180	−	0.391496i	$-0.128042\pi$
$907$	−2.18246	−	8.14504i	−0.0724673	−	0.270452i	−0.992647	+	0.121044i	$0.961376\pi$
$908$	13.4733	+	3.61017i	0.447128	+	0.119808i
$909$			8.11810i			0.269260i
$910$		0			0
$911$	−4.86385	+	4.86385i	−0.161146	+	0.161146i	−0.783074	−	0.621928i	$-0.786350\pi$
$911$	−4.86385	+	4.86385i	−0.161146	+	0.161146i	0.621928	+	0.783074i	$0.286350\pi$
$912$	−6.28232	−	1.68334i	−0.208028	−	0.0557411i
$913$	−5.80144	+	1.55449i	−0.192000	+	0.0514461i
$914$	−12.2357	+	21.1928i	−0.404720	+	0.700995i
$915$	1.76494	−	6.58683i	0.0583470	−	0.217754i
$916$			36.9332i			1.22031i
$917$		0			0
$918$	−15.5230	−	21.0630i	−0.512334	−	0.695183i
$919$	−15.9109	−	27.5585i	−0.524853	−	0.909072i	−0.999581	−	0.0289399i	$-0.990787\pi$
$919$	−15.9109	−	27.5585i	−0.524853	−	0.909072i	0.474728	−	0.880133i	$-0.342546\pi$
$920$	−25.2017	−	14.5502i	−0.830874	−	0.479705i
$921$	−30.1401	+	8.07603i	−0.993151	+	0.266114i
$922$	−14.0716	−	24.3727i	−0.463422	−	0.802671i
$923$	1.06880	+	1.06880i	0.0351801	+	0.0351801i
$924$		0			0
$925$	−24.7625	+	24.7625i	−0.814187	+	0.814187i
$926$	16.8135	−	9.70726i	0.552525	−	0.319000i
$927$	31.0296	+	17.9150i	1.01915	+	0.588404i
$928$	8.46279	+	31.5836i	0.277805	+	1.03678i
$929$	−53.1670	−	14.2461i	−1.74435	−	0.467398i	−0.760947	−	0.648815i	$-0.775265\pi$
$929$	−53.1670	−	14.2461i	−1.74435	−	0.467398i	−0.983406	+	0.181417i	$0.941932\pi$
$930$	36.2503	+	36.2503i	1.18869	+	1.18869i
$931$		0			0
$932$	−9.77789	−	9.77789i	−0.320285	−	0.320285i
$933$	36.6378	−	21.1528i	1.19947	−	0.692513i
$934$	1.13281	−	1.96209i	0.0370668	−	0.0642016i
$935$	25.4621	−	31.8837i	0.832700	−	1.04271i
$936$	3.04192	+	5.26876i	0.0994282	+	0.172215i
$937$			4.92438i			0.160873i	0.996760	+	0.0804363i	$0.0256313\pi$
$937$			4.92438i			0.160873i	−0.996760	+	0.0804363i	$0.974369\pi$
$938$		0			0
$939$	65.2467			2.12925
$940$	−17.3155	+	64.6224i	−0.564770	+	2.10775i
$941$	0.0418102	+	0.156038i	0.00136297	+	0.00508668i	0.966604	−	0.256275i	$-0.0824952\pi$
$941$	0.0418102	+	0.156038i	0.00136297	+	0.00508668i	−0.965241	+	0.261361i	$0.915829\pi$
$942$	−8.83102	−	32.9578i	−0.287730	−	1.07382i
$943$	20.2029	−	11.6641i	0.657896	−	0.379837i
$944$			11.4468i			0.372561i
$945$		0			0
$946$	7.34827	−	7.34827i	0.238913	−	0.238913i
$947$	−11.8156	+	44.0963i	−0.383954	+	1.43294i	0.455855	+	0.890054i	$0.349334\pi$
$947$	−11.8156	+	44.0963i	−0.383954	+	1.43294i	−0.839809	+	0.542882i	$0.817333\pi$
$948$	35.1765	−	60.9275i	1.14248	−	1.97883i
$949$	0.306283	−	0.0820682i	0.00994235	−	0.00266404i
$950$	−10.0315	+	5.79169i	−0.325465	+	0.187907i
$951$	51.5870			1.67282
$952$		0			0
$953$	48.4329			1.56889			0.784447	−	0.620195i	$-0.212947\pi$
$953$	48.4329			1.56889			0.784447	+	0.620195i	$0.212947\pi$
$954$	−14.9081	+	8.60720i	−0.482668	+	0.278668i
$955$	22.9509	−	6.14966i	0.742672	−	0.198998i
$956$	9.21823	−	15.9664i	0.298139	−	0.516392i
$957$	−11.4010	+	42.5491i	−0.368542	+	1.37542i
$958$	3.33934	−	3.33934i	0.107889	−	0.107889i
$959$		0			0
$960$			19.1215i			0.617144i
$961$	8.47115	−	4.89082i	0.273263	−	0.157768i
$962$	−0.286010	−	1.06741i	−0.00922135	−	0.0344145i
$963$	−5.11991	−	19.1078i	−0.164987	−	0.615739i
$964$	−3.61780	+	13.5018i	−0.116522	+	0.434864i
$965$	−7.29840			−0.234944
$966$		0			0
$967$			22.1661i			0.712814i	0.934331	+	0.356407i	$0.115998\pi$
$967$			22.1661i			0.712814i	−0.934331	+	0.356407i	$0.884002\pi$
$968$	−5.10698	−	8.84555i	−0.164145	−	0.284307i
$969$	−2.43160	−	21.7146i	−0.0781144	−	0.697574i
$970$	0.774487	−	1.34145i	0.0248673	−	0.0430714i
$971$	−33.8584	+	19.5482i	−1.08657	+	0.627330i	−0.932661	−	0.360755i	$-0.882519\pi$
$971$	−33.8584	+	19.5482i	−1.08657	+	0.627330i	−0.153908	+	0.988085i	$0.549186\pi$
$972$	0.357665	+	0.357665i	0.0114721	+	0.0114721i
$973$		0			0
$974$	12.0057	+	12.0057i	0.384687	+	0.384687i
$975$	−10.9361	−	2.93033i	−0.350237	−	0.0938457i
$976$	−0.191659	−	0.715281i	−0.00613485	−	0.0228956i
$977$	26.9801	+	15.5769i	0.863168	+	0.498350i	0.865072	−	0.501648i	$-0.167273\pi$
$977$	26.9801	+	15.5769i	0.863168	+	0.498350i	−0.00190370	+	0.999998i	$0.500606\pi$
$978$	−6.56299	+	3.78914i	−0.209861	+	0.121163i
$979$	−23.6335	+	23.6335i	−0.755331	+	0.755331i
$980$		0			0
$981$	48.1069	+	48.1069i	1.53594	+	1.53594i
$982$	13.4615	+	23.3160i	0.429573	+	0.744042i
$983$	−27.1312	+	7.26977i	−0.865350	+	0.231870i	−0.664076	−	0.747665i	$-0.731175\pi$
$983$	−27.1312	+	7.26977i	−0.865350	+	0.231870i	−0.201274	+	0.979535i	$0.564508\pi$
$984$	−48.3690	−	27.9258i	−1.54195	−	0.890243i
$985$	−20.9701	−	36.3212i	−0.668162	−	1.15729i
$986$	−13.2058	+	9.73236i	−0.420558	+	0.309941i
$987$		0			0
$988$			1.08338i			0.0344669i
$989$	−4.48457	+	16.7366i	−0.142601	+	0.532194i
$990$	−21.0219	+	36.4111i	−0.668121	+	1.15722i
$991$	11.9720	−	3.20788i	0.380302	−	0.101902i	−0.0636032	−	0.997975i	$-0.520259\pi$
$991$	11.9720	−	3.20788i	0.380302	−	0.101902i	0.443906	+	0.896074i	$0.353593\pi$
$992$	36.0084	+	9.64841i	1.14327	+	0.306337i
$993$	2.11146	−	2.11146i	0.0670050	−	0.0670050i
$994$		0			0
$995$			67.7436i			2.14762i
$996$	−9.90792	−	2.65482i	−0.313944	−	0.0841211i
$997$	8.06438	+	30.0967i	0.255401	+	0.953171i	0.967867	+	0.251464i	$0.0809119\pi$
$997$	8.06438	+	30.0967i	0.255401	+	0.953171i	−0.712465	+	0.701707i	$0.752421\pi$
$998$	8.84292	−	2.36945i	0.279918	−	0.0750037i
$999$	16.9633	+	29.3813i	0.536696	+	0.929584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.o.g.557.4		40
7.2	even	3	inner	833.2.o.g.30.7		40
7.3	odd	6		833.2.g.h.540.4		20
7.4	even	3		119.2.g.a.64.4	✓	20
7.5	odd	6		833.2.o.f.30.7		40
7.6	odd	2		833.2.o.f.557.4		40
17.4	even	4	inner	833.2.o.g.361.7		40
21.11	odd	6		1071.2.n.c.64.7		20
119.4	even	12		119.2.g.a.106.7	yes	20
119.32	even	24		2023.2.a.m.1.7		10
119.38	odd	12		833.2.g.h.344.7		20
119.53	even	24		2023.2.a.n.1.7		10
119.55	odd	4		833.2.o.f.361.7		40
119.72	even	12	inner	833.2.o.g.667.4		40
119.89	odd	12		833.2.o.f.667.4		40
357.242	odd	12		1071.2.n.c.820.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.g.a.64.4	✓	20	7.4	even	3
119.2.g.a.106.7	yes	20	119.4	even	12
833.2.g.h.344.7		20	119.38	odd	12
833.2.g.h.540.4		20	7.3	odd	6
833.2.o.f.30.7		40	7.5	odd	6
833.2.o.f.361.7		40	119.55	odd	4
833.2.o.f.557.4		40	7.6	odd	2
833.2.o.f.667.4		40	119.89	odd	12
833.2.o.g.30.7		40	7.2	even	3	inner
833.2.o.g.361.7		40	17.4	even	4	inner
833.2.o.g.557.4		40	1.1	even	1	trivial
833.2.o.g.667.4		40	119.72	even	12	inner
1071.2.n.c.64.7		20	21.11	odd	6
1071.2.n.c.820.4		20	357.242	odd	12
2023.2.a.m.1.7		10	119.32	even	24
2023.2.a.n.1.7		10	119.53	even	24

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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.615152 + 0.355158i) q^{2} +(-2.89474 + 0.775643i) q^{3} +(-0.747726 + 1.29510i) q^{4} +(-0.976053 + 3.64268i) q^{5} +(1.50523 - 1.50523i) q^{6} -2.48287i q^{8} +(5.17981 - 2.99057i) q^{9} +O(q^{10})\)	\(q+(-0.615152 + 0.355158i) q^{2} +(-2.89474 + 0.775643i) q^{3} +(-0.747726 + 1.29510i) q^{4} +(-0.976053 + 3.64268i) q^{5} +(1.50523 - 1.50523i) q^{6} -2.48287i q^{8} +(5.17981 - 2.99057i) q^{9} +(-0.693306 - 2.58745i) q^{10} +(-0.679184 - 2.53475i) q^{11} +(1.15994 - 4.32894i) q^{12} -0.409675 q^{13} -11.3017i q^{15} +(-0.613639 - 1.06285i) q^{16} +(2.57292 - 3.22181i) q^{17} +(-2.12425 + 3.67930i) q^{18} +(-1.53144 + 0.884175i) q^{19} +(-3.98781 - 3.98781i) q^{20} +(1.31804 + 1.31804i) q^{22} +(-3.00200 - 0.804383i) q^{23} +(1.92582 + 7.18727i) q^{24} +(-7.98631 - 4.61090i) q^{25} +(0.252012 - 0.145499i) q^{26} +(-6.31730 + 6.31730i) q^{27} +(3.96073 + 3.96073i) q^{29} +(4.01388 + 6.95224i) q^{30} +(6.16845 - 1.65283i) q^{31} +(5.05543 + 2.91875i) q^{32} +(3.93212 + 6.81063i) q^{33} +(-0.438483 + 2.89570i) q^{34} +8.94449i q^{36} +(0.982858 - 3.66808i) q^{37} +(0.628043 - 1.08780i) q^{38} +(1.18590 - 0.317762i) q^{39} +(9.04432 + 2.42342i) q^{40} +(-5.30764 + 5.30764i) q^{41} -5.57516i q^{43} +(3.79059 + 1.01569i) q^{44} +(5.83790 + 21.7873i) q^{45} +(2.13237 - 0.571366i) q^{46} +(-5.93143 - 10.2735i) q^{47} +(2.60072 + 2.60072i) q^{48} +6.55039 q^{50} +(-4.94895 + 11.3220i) q^{51} +(0.306325 - 0.530570i) q^{52} +(3.50903 + 2.02594i) q^{53} +(1.64246 - 6.12974i) q^{54} +9.89619 q^{55} +(3.74730 - 3.74730i) q^{57} +(-3.84313 - 1.02976i) q^{58} +(-8.07738 - 4.66348i) q^{59} +(14.6368 + 8.45055i) q^{60} +(0.582819 + 0.156166i) q^{61} +(-3.20752 + 3.20752i) q^{62} -1.69192 q^{64} +(0.399865 - 1.49232i) q^{65} +(-4.83770 - 2.79305i) q^{66} +(-3.85103 + 6.67018i) q^{67} +(2.24873 + 5.74122i) q^{68} +9.31391 q^{69} +(-2.60890 - 2.60890i) q^{71} +(-7.42520 - 12.8608i) q^{72} +(-0.747623 + 0.200325i) q^{73} +(0.698140 + 2.60549i) q^{74} +(26.6947 + 7.15282i) q^{75} -2.64448i q^{76} +(-0.616654 + 0.616654i) q^{78} +(15.1631 + 4.06295i) q^{79} +(4.47058 - 1.19789i) q^{80} +(4.41526 - 7.64746i) q^{81} +(1.37995 - 5.15005i) q^{82} -2.28876i q^{83} +(9.22473 + 12.5170i) q^{85} +(1.98006 + 3.42957i) q^{86} +(-14.5374 - 8.39316i) q^{87} +(-6.29346 + 1.68633i) q^{88} +(-6.36829 - 11.0302i) q^{89} +(-11.3291 - 11.3291i) q^{90} +(3.28643 - 3.28643i) q^{92} +(-16.5740 + 9.56903i) q^{93} +(7.29746 + 4.21319i) q^{94} +(-1.72600 - 6.44153i) q^{95} +(-16.8980 - 4.52782i) q^{96} +(0.408884 + 0.408884i) q^{97} +(-11.0984 - 11.0984i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} + 24 q^{4} + 8 q^{5} + 8 q^{6}+O(q^{10}) \) 40 * q + 4 * q^3 + 24 * q^4 + 8 * q^5 + 8 * q^6	\( 40 q + 4 q^{3} + 24 q^{4} + 8 q^{5} + 8 q^{6} - 4 q^{10} + 4 q^{11} - 12 q^{12} - 16 q^{16} + 12 q^{17} + 8 q^{18} + 40 q^{20} - 40 q^{22} - 4 q^{24} + 16 q^{27} + 32 q^{29} + 36 q^{30} - 4 q^{31} + 16 q^{33} + 72 q^{34} + 28 q^{37} - 48 q^{38} - 20 q^{39} + 24 q^{40} - 48 q^{41} + 28 q^{44} - 36 q^{45} - 8 q^{46} - 40 q^{47} - 16 q^{48} - 56 q^{50} + 40 q^{51} + 28 q^{54} - 80 q^{55} + 72 q^{57} - 56 q^{58} + 16 q^{61} - 80 q^{62} + 64 q^{64} - 8 q^{65} + 32 q^{68} - 176 q^{69} - 16 q^{71} - 108 q^{72} - 8 q^{73} - 36 q^{74} - 8 q^{75} - 88 q^{78} + 4 q^{79} + 116 q^{80} - 4 q^{81} + 16 q^{82} + 32 q^{85} - 44 q^{86} - 72 q^{88} - 48 q^{89} + 112 q^{90} - 64 q^{92} - 44 q^{95} - 68 q^{96} - 48 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 + 24 * q^4 + 8 * q^5 + 8 * q^6 - 4 * q^10 + 4 * q^11 - 12 * q^12 - 16 * q^16 + 12 * q^17 + 8 * q^18 + 40 * q^20 - 40 * q^22 - 4 * q^24 + 16 * q^27 + 32 * q^29 + 36 * q^30 - 4 * q^31 + 16 * q^33 + 72 * q^34 + 28 * q^37 - 48 * q^38 - 20 * q^39 + 24 * q^40 - 48 * q^41 + 28 * q^44 - 36 * q^45 - 8 * q^46 - 40 * q^47 - 16 * q^48 - 56 * q^50 + 40 * q^51 + 28 * q^54 - 80 * q^55 + 72 * q^57 - 56 * q^58 + 16 * q^61 - 80 * q^62 + 64 * q^64 - 8 * q^65 + 32 * q^68 - 176 * q^69 - 16 * q^71 - 108 * q^72 - 8 * q^73 - 36 * q^74 - 8 * q^75 - 88 * q^78 + 4 * q^79 + 116 * q^80 - 4 * q^81 + 16 * q^82 + 32 * q^85 - 44 * q^86 - 72 * q^88 - 48 * q^89 + 112 * q^90 - 64 * q^92 - 44 * q^95 - 68 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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