LMFDB - Embedded newform 841.2.d.o.190.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(190,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.190"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [36,2,2,-8,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			190.3
Character	$\chi$	$=$	841.190
Dual form			841.2.d.o.571.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.460625 + 0.221825i) q^{2} +(-1.67878 + 2.10513i) q^{3} +(-1.08401 - 1.35931i) q^{4} +(-1.98557 - 0.956199i) q^{5} +(-1.24026 + 0.597278i) q^{6} +(-0.811822 + 1.01799i) q^{7} +(-0.425324 - 1.86347i) q^{8} +(-0.945686 - 4.14332i) q^{9} +(-0.702494 - 0.880899i) q^{10} +(1.11450 - 4.88296i) q^{11} +4.68133 q^{12} +(-0.698231 + 3.05915i) q^{13} +(-0.599762 + 0.288830i) q^{14} +(5.34626 - 2.57462i) q^{15} +(-0.556308 + 2.43735i) q^{16} +1.37659 q^{17} +(0.483487 - 2.11830i) q^{18} +(3.71112 + 4.65360i) q^{19} +(0.852609 + 3.73552i) q^{20} +(-0.780131 - 3.41798i) q^{21} +(1.59653 - 2.00199i) q^{22} +(-0.779635 + 0.375453i) q^{23} +(4.63686 + 2.23299i) q^{24} +(-0.0892850 - 0.111960i) q^{25} +(-1.00022 + 1.25424i) q^{26} +(3.03208 + 1.46017i) q^{27} +2.26379 q^{28} +3.03374 q^{30} +(2.47226 + 1.19058i) q^{31} +(-3.18038 + 3.98807i) q^{32} +(8.40824 + 10.5436i) q^{33} +(0.634090 + 0.305362i) q^{34} +(2.58533 - 1.24503i) q^{35} +(-4.60691 + 5.77688i) q^{36} +(1.31287 + 5.75206i) q^{37} +(0.677149 + 2.96679i) q^{38} +(-5.26772 - 6.60551i) q^{39} +(-0.937335 + 4.10673i) q^{40} +1.90869 q^{41} +(0.398846 - 1.74746i) q^{42} +(9.92351 - 4.77891i) q^{43} +(-7.84557 + 3.77823i) q^{44} +(-2.08412 + 9.13111i) q^{45} -0.442405 q^{46} +(-0.640107 + 2.80449i) q^{47} +(-4.19700 - 5.26288i) q^{48} +(1.18039 + 5.17164i) q^{49} +(-0.0162914 - 0.0713773i) q^{50} +(-2.31099 + 2.89789i) q^{51} +(4.91521 - 2.36704i) q^{52} +(5.22834 + 2.51784i) q^{53} +(1.07275 + 1.34519i) q^{54} +(-6.88200 + 8.62976i) q^{55} +(2.24228 + 1.07983i) q^{56} -16.0266 q^{57} -4.35304 q^{59} +(-9.29510 - 4.47628i) q^{60} +(3.38895 - 4.24961i) q^{61} +(0.874684 + 1.09682i) q^{62} +(4.98560 + 2.40094i) q^{63} +(2.15528 - 1.03793i) q^{64} +(4.31154 - 5.40650i) q^{65} +(1.53421 + 6.72181i) q^{66} +(0.525768 + 2.30354i) q^{67} +(-1.49223 - 1.87120i) q^{68} +(0.518463 - 2.27154i) q^{69} +1.46705 q^{70} +(3.46904 - 15.1989i) q^{71} +(-7.31872 + 3.52451i) q^{72} +(3.06010 - 1.47367i) q^{73} +(-0.671212 + 2.94077i) q^{74} +0.385580 q^{75} +(2.30277 - 10.0891i) q^{76} +(4.06603 + 5.09865i) q^{77} +(-0.961175 - 4.21118i) q^{78} +(0.470882 + 2.06307i) q^{79} +(3.43518 - 4.30758i) q^{80} +(3.32295 - 1.60025i) q^{81} +(0.879192 + 0.423397i) q^{82} +(3.96481 + 4.97171i) q^{83} +(-3.80041 + 4.76556i) q^{84} +(-2.73330 - 1.31629i) q^{85} +5.63110 q^{86} -9.57325 q^{88} +(10.7511 + 5.17745i) q^{89} +(-2.98551 + 3.74371i) q^{90} +(-2.54735 - 3.19428i) q^{91} +(1.35549 + 0.652769i) q^{92} +(-6.65670 + 3.20570i) q^{93} +(-0.916957 + 1.14983i) q^{94} +(-2.91892 - 12.7886i) q^{95} +(-3.05623 - 13.3902i) q^{96} +(7.12247 + 8.93130i) q^{97} +(-0.603482 + 2.64403i) q^{98} -21.2856 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} + 2 q^{3} - 8 q^{4} + 2 q^{5} + 3 q^{6} + 4 q^{7} + 3 q^{8} - 6 q^{9} + 15 q^{10} + 13 q^{11} + 24 q^{12} + 6 q^{13} - 6 q^{14} + 19 q^{15} - 4 q^{16} - 18 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20}+ \cdots - 36 q^{99}+O(q^{100}) $ 36 * q + 2 * q^2 + 2 * q^3 - 8 * q^4 + 2 * q^5 + 3 * q^6 + 4 * q^7 + 3 * q^8 - 6 * q^9 + 15 * q^10 + 13 * q^11 + 24 * q^12 + 6 * q^13 - 6 * q^14 + 19 * q^15 - 4 * q^16 - 18 * q^17 + 17 * q^18 - 6 * q^19 + 5 * q^20 - 2 * q^21 + 4 * q^22 + 5 * q^23 + 10 * q^24 - 6 * q^25 + 9 * q^26 - q^27 - 30 * q^28 + 156 * q^30 + 16 * q^31 + 33 * q^32 - 27 * q^33 + 4 * q^35 + 21 * q^36 - 10 * q^37 - 41 * q^38 + 17 * q^39 + 7 * q^40 - 180 * q^41 + 21 * q^42 - 2 * q^43 + 16 * q^44 - 16 * q^45 + 120 * q^46 + 5 * q^47 - 30 * q^48 + 12 * q^49 - 8 * q^50 + 23 * q^51 + 13 * q^53 - 19 * q^54 + 10 * q^55 + 16 * q^56 - 96 * q^57 - 102 * q^59 - 9 * q^60 - 4 * q^61 + 9 * q^63 - q^64 - 32 * q^65 - 8 * q^66 + 9 * q^67 + 16 * q^68 + 26 * q^69 + 168 * q^70 - 21 * q^72 + 9 * q^73 + 36 * q^74 - 42 * q^75 + 24 * q^76 + 13 * q^77 + 6 * q^79 - 5 * q^80 + 22 * q^81 - 19 * q^82 + 24 * q^83 - 26 * q^85 + 102 * q^86 + 126 * q^88 + 9 * q^89 - 16 * q^90 - 16 * q^91 + 23 * q^92 + 12 * q^93 + 37 * q^94 + 31 * q^95 + 37 * q^96 - 10 * q^97 - 42 * q^98 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{7}\right)$

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 $

$2$	0.460625	+	0.221825i	0.325711	+	0.156854i	0.589592	−	0.807701i	$-0.299288\pi$
$2$	0.460625	+	0.221825i	0.325711	+	0.156854i	−0.263881	+	0.964555i	$0.585003\pi$
$3$	−1.67878	+	2.10513i	−0.969246	+	1.21540i	0.00727517	+	0.999974i	$0.497684\pi$
$3$	−1.67878	+	2.10513i	−0.969246	+	1.21540i	−0.976521	+	0.215422i	$0.930887\pi$
$4$	−1.08401	−	1.35931i	−0.542005	−	0.679653i
$5$	−1.98557	−	0.956199i	−0.887973	−	0.427625i	−0.0664428	−	0.997790i	$-0.521165\pi$
$5$	−1.98557	−	0.956199i	−0.887973	−	0.427625i	−0.821530	+	0.570165i	$0.806879\pi$
$6$	−1.24026	+	0.597278i	−0.506334	+	0.243838i
$7$	−0.811822	+	1.01799i	−0.306840	+	0.384765i	−0.911212	−	0.411937i	$-0.864852\pi$
$7$	−0.811822	+	1.01799i	−0.306840	+	0.384765i	0.604373	+	0.796702i	$0.293424\pi$
$8$	−0.425324	−	1.86347i	−0.150375	−	0.658835i
$9$	−0.945686	−	4.14332i	−0.315229	−	1.38111i
$10$	−0.702494	−	0.880899i	−0.222148	−	0.278565i
$11$	1.11450	−	4.88296i	0.336035	−	1.47227i	−0.471194	−	0.882030i	$-0.656177\pi$
$11$	1.11450	−	4.88296i	0.336035	−	1.47227i	0.807230	−	0.590238i	$-0.200966\pi$
$12$	4.68133			1.35138
$13$	−0.698231	+	3.05915i	−0.193654	+	0.848456i	0.780963	+	0.624578i	$0.214729\pi$
$13$	−0.698231	+	3.05915i	−0.193654	+	0.848456i	−0.974617	+	0.223878i	$0.928128\pi$
$14$	−0.599762	+	0.288830i	−0.160293	+	0.0771931i
$15$	5.34626	−	2.57462i	1.38040	−	0.664765i
$16$	−0.556308	+	2.43735i	−0.139077	+	0.609337i
$17$	1.37659			0.333871			0.166936	−	0.985968i	$-0.446613\pi$
$17$	1.37659			0.333871			0.166936	+	0.985968i	$0.446613\pi$
$18$	0.483487	−	2.11830i	0.113959	−	0.499287i
$19$	3.71112	+	4.65360i	0.851389	+	1.06761i	0.996933	+	0.0782567i	$0.0249354\pi$
$19$	3.71112	+	4.65360i	0.851389	+	1.06761i	−0.145544	+	0.989352i	$0.546493\pi$
$20$	0.852609	+	3.73552i	0.190649	+	0.835289i
$21$	−0.780131	−	3.41798i	−0.170238	−	0.745863i
$22$	1.59653	−	2.00199i	0.340382	−	0.426825i
$23$	−0.779635	+	0.375453i	−0.162565	+	0.0782873i	−0.513397	−	0.858151i	$-0.671613\pi$
$23$	−0.779635	+	0.375453i	−0.162565	+	0.0782873i	0.350832	+	0.936438i	$0.385899\pi$
$24$	4.63686	+	2.23299i	0.946495	+	0.455808i
$25$	−0.0892850	−	0.111960i	−0.0178570	−	0.0223920i
$26$	−1.00022	+	1.25424i	−0.196159	+	0.245976i
$27$	3.03208	+	1.46017i	0.583525	+	0.281011i
$28$	2.26379			0.427815
$29$		0			0
$29$		0			0
$30$	3.03374			0.553882
$31$	2.47226	+	1.19058i	0.444030	+	0.213834i	0.642520	−	0.766269i	$-0.277889\pi$
$31$	2.47226	+	1.19058i	0.444030	+	0.213834i	−0.198489	+	0.980103i	$0.563603\pi$
$32$	−3.18038	+	3.98807i	−0.562217	+	0.704998i
$33$	8.40824	+	10.5436i	1.46369	+	1.83540i
$34$	0.634090	+	0.305362i	0.108746	+	0.0523691i
$35$	2.58533	−	1.24503i	0.437001	−	0.210448i
$36$	−4.60691	+	5.77688i	−0.767818	+	0.962813i
$37$	1.31287	+	5.75206i	0.215835	+	0.945633i	0.960519	+	0.278216i	$0.0897431\pi$
$37$	1.31287	+	5.75206i	0.215835	+	0.945633i	−0.744684	+	0.667417i	$0.767400\pi$
$38$	0.677149	+	2.96679i	0.109848	+	0.481276i
$39$	−5.26772	−	6.60551i	−0.843511	−	1.05773i
$40$	−0.937335	+	4.10673i	−0.148206	+	0.649332i
$41$	1.90869			0.298088			0.149044	−	0.988831i	$-0.452380\pi$
$41$	1.90869			0.298088			0.149044	+	0.988831i	$0.452380\pi$
$42$	0.398846	−	1.74746i	0.0615433	−	0.269639i
$43$	9.92351	−	4.77891i	1.51332	−	0.728777i	0.521126	−	0.853480i	$-0.325512\pi$
$43$	9.92351	−	4.77891i	1.51332	−	0.728777i	0.992194	+	0.124703i	$0.0397977\pi$
$44$	−7.84557	+	3.77823i	−1.18276	+	0.569589i
$45$	−2.08412	+	9.13111i	−0.310682	+	1.36119i
$46$	−0.442405			−0.0652290
$47$	−0.640107	+	2.80449i	−0.0933691	+	0.409077i	−0.999915	−	0.0130302i	$-0.995852\pi$
$47$	−0.640107	+	2.80449i	−0.0933691	+	0.409077i	0.906546	+	0.422107i	$0.138709\pi$
$48$	−4.19700	−	5.26288i	−0.605785	−	0.759631i
$49$	1.18039	+	5.17164i	0.168628	+	0.738806i
$50$	−0.0162914	−	0.0713773i	−0.00230395	−	0.0100943i
$51$	−2.31099	+	2.89789i	−0.323603	+	0.405785i
$52$	4.91521	−	2.36704i	0.681617	−	0.328250i
$53$	5.22834	+	2.51784i	0.718167	+	0.345851i	0.757018	−	0.653394i	$-0.226655\pi$
$53$	5.22834	+	2.51784i	0.718167	+	0.345851i	−0.0388507	+	0.999245i	$0.512370\pi$
$54$	1.07275	+	1.34519i	0.145983	+	0.183057i
$55$	−6.88200	+	8.62976i	−0.927969	+	1.16364i
$56$	2.24228	+	1.07983i	0.299637	+	0.144298i
$57$	−16.0266			−2.12277
$58$		0			0
$59$	−4.35304			−0.566717			−0.283359	−	0.959014i	$-0.591449\pi$
$59$	−4.35304			−0.566717			−0.283359	+	0.959014i	$0.591449\pi$
$60$	−9.29510	−	4.47628i	−1.19999	−	0.577886i
$61$	3.38895	−	4.24961i	0.433911	−	0.544107i	−0.516016	−	0.856579i	$-0.672586\pi$
$61$	3.38895	−	4.24961i	0.433911	−	0.544107i	0.949927	+	0.312472i	$0.101157\pi$
$62$	0.874684	+	1.09682i	0.111085	+	0.139296i
$63$	4.98560	+	2.40094i	0.628126	+	0.302490i
$64$	2.15528	−	1.03793i	0.269409	−	0.129741i
$65$	4.31154	−	5.40650i	0.534781	−	0.670594i
$66$	1.53421	+	6.72181i	0.188848	+	0.827398i
$67$	0.525768	+	2.30354i	0.0642328	+	0.281422i	0.996836	−	0.0794799i	$-0.0253260\pi$
$67$	0.525768	+	2.30354i	0.0642328	+	0.281422i	−0.932604	+	0.360902i	$0.882469\pi$
$68$	−1.49223	−	1.87120i	−0.180960	−	0.226916i
$69$	0.518463	−	2.27154i	0.0624156	−	0.273461i
$70$	1.46705			0.175346
$71$	3.46904	−	15.1989i	0.411700	−	1.80377i	−0.164398	−	0.986394i	$-0.552568\pi$
$71$	3.46904	−	15.1989i	0.411700	−	1.80377i	0.576098	−	0.817381i	$-0.304575\pi$
$72$	−7.31872	+	3.52451i	−0.862519	+	0.415367i
$73$	3.06010	−	1.47367i	0.358157	−	0.172480i	−0.246148	−	0.969232i	$-0.579165\pi$
$73$	3.06010	−	1.47367i	0.358157	−	0.172480i	0.604305	+	0.796753i	$0.293451\pi$
$74$	−0.671212	+	2.94077i	−0.0780269	+	0.341858i
$75$	0.385580			0.0445230
$76$	2.30277	−	10.0891i	0.264146	−	1.15730i
$77$	4.06603	+	5.09865i	0.463368	+	0.581045i
$78$	−0.961175	−	4.21118i	−0.108832	−	0.476822i
$79$	0.470882	+	2.06307i	0.0529784	+	0.232113i	0.994485	−	0.104882i	$-0.0334465\pi$
$79$	0.470882	+	2.06307i	0.0529784	+	0.232113i	−0.941506	+	0.336995i	$0.890589\pi$
$80$	3.43518	−	4.30758i	0.384064	−	0.481602i
$81$	3.32295	−	1.60025i	0.369217	−	0.177805i
$82$	0.879192	+	0.423397i	0.0970905	+	0.0467563i
$83$	3.96481	+	4.97171i	0.435194	+	0.545716i	0.950269	−	0.311429i	$-0.100808\pi$
$83$	3.96481	+	4.97171i	0.435194	+	0.545716i	−0.515075	+	0.857145i	$0.672236\pi$
$84$	−3.80041	+	4.76556i	−0.414658	+	0.519965i
$85$	−2.73330	−	1.31629i	−0.296469	−	0.142772i
$86$	5.63110			0.607217
$87$		0			0
$88$	−9.57325			−1.02051
$89$	10.7511	+	5.17745i	1.13961	+	0.548809i	0.905898	−	0.423496i	$-0.139197\pi$
$89$	10.7511	+	5.17745i	1.13961	+	0.548809i	0.233716	+	0.972305i	$0.424911\pi$
$90$	−2.98551	+	3.74371i	−0.314700	+	0.394622i
$91$	−2.54735	−	3.19428i	−0.267035	−	0.334851i
$92$	1.35549	+	0.652769i	0.141319	+	0.0680558i
$93$	−6.65670	+	3.20570i	−0.690267	+	0.332415i
$94$	−0.916957	+	1.14983i	−0.0945769	+	0.118596i
$95$	−2.91892	−	12.7886i	−0.299474	−	1.31208i
$96$	−3.05623	−	13.3902i	−0.311925	−	1.36663i
$97$	7.12247	+	8.93130i	0.723178	+	0.906836i	0.998513	−	0.0545120i	$-0.0173603\pi$
$97$	7.12247	+	8.93130i	0.723178	+	0.906836i	−0.275335	+	0.961348i	$0.588789\pi$
$98$	−0.603482	+	2.64403i	−0.0609609	+	0.267087i
$99$	−21.2856			−2.13929
$100$	−0.0554019	+	0.242731i	−0.00554019	+	0.0242731i
$101$	−0.878005	+	0.422825i	−0.0873648	+	0.0420727i	−0.477056	−	0.878873i	$-0.658296\pi$
$101$	−0.878005	+	0.422825i	−0.0873648	+	0.0420727i	0.389691	+	0.920946i	$0.372582\pi$
$102$	−1.70733	+	0.822204i	−0.169050	+	0.0814104i
$103$	1.73058	−	7.58218i	0.170520	−	0.747095i	−0.815266	−	0.579087i	$-0.803409\pi$
$103$	1.73058	−	7.58218i	0.170520	−	0.747095i	0.985786	−	0.168008i	$-0.0537335\pi$
$104$	5.99760			0.588113
$105$	−1.71926	+	7.53258i	−0.167783	+	0.735105i
$106$	1.84979	+	2.31956i	0.179667	+	0.225295i
$107$	1.21259	+	5.31270i	0.117225	+	0.513598i	0.999112	+	0.0421362i	$0.0134164\pi$
$107$	1.21259	+	5.31270i	0.117225	+	0.513598i	−0.881886	+	0.471462i	$0.843727\pi$
$108$	−1.30199	−	5.70437i	−0.125284	−	0.548903i
$109$	−4.92028	+	6.16983i	−0.471277	+	0.590963i	−0.959483	−	0.281766i	$-0.909080\pi$
$109$	−4.92028	+	6.16983i	−0.471277	+	0.590963i	0.488206	+	0.872728i	$0.337651\pi$
$110$	−5.08432	+	2.44848i	−0.484771	+	0.233454i
$111$	−14.3128	−	6.89270i	−1.35852	−	0.654227i
$112$	−2.02958	−	2.54501i	−0.191777	−	0.240481i
$113$	10.7869	−	13.5264i	1.01475	−	1.27246i	0.0529818	−	0.998595i	$-0.483127\pi$
$113$	10.7869	−	13.5264i	1.01475	−	1.27246i	0.961769	−	0.273862i	$-0.0883011\pi$
$114$	−7.38225	−	3.55510i	−0.691411	−	0.332966i
$115$	1.90703			0.177831
$116$		0			0
$117$	13.3353			1.23285
$118$	−2.00512	−	0.965615i	−0.184586	−	0.0888920i
$119$	−1.11754	+	1.40135i	−0.102445	+	0.128462i
$120$	−7.07162	−	8.86753i	−0.645547	−	0.809491i
$121$	−12.6905	−	6.11142i	−1.15368	−	0.555584i
$122$	2.50371	−	1.20572i	0.226675	−	0.109161i
$123$	−3.20428	+	4.01804i	−0.288920	+	0.362295i
$124$	−1.06159	−	4.65115i	−0.0953340	−	0.417686i
$125$	2.52220	+	11.0505i	0.225592	+	0.988385i
$126$	1.76390	+	2.21186i	0.157141	+	0.197048i
$127$	1.22746	−	5.37787i	0.108920	−	0.477209i	−0.890819	−	0.454358i	$-0.849869\pi$
$127$	1.22746	−	5.37787i	0.108920	−	0.477209i	0.999739	−	0.0228507i	$-0.00727424\pi$
$128$	11.4249			1.00983
$129$	−6.59920	+	28.9130i	−0.581027	+	2.54565i
$130$	3.18531	−	1.53396i	0.279370	−	0.134537i
$131$	−0.0254906	+	0.0122756i	−0.00222712	+	0.00107253i	−0.434997	−	0.900432i	$-0.643251\pi$
$131$	−0.0254906	+	0.0122756i	−0.00222712	+	0.00107253i	0.432770	+	0.901504i	$0.357536\pi$
$132$	5.21736	−	22.8587i	0.454113	−	1.98960i
$133$	−7.75009			−0.672018
$134$	−0.268802	+	1.17770i	−0.0232209	+	0.101738i
$135$	−4.62419	−	5.79855i	−0.397987	−	0.499060i
$136$	−0.585495	−	2.56522i	−0.0502058	−	0.219966i
$137$	1.36954	+	6.00036i	0.117008	+	0.512645i	0.999133	+	0.0416300i	$0.0132551\pi$
$137$	1.36954	+	6.00036i	0.117008	+	0.512645i	−0.882125	+	0.471015i	$0.843888\pi$
$138$	0.742702	−	0.931318i	0.0632230	−	0.0792791i
$139$	−11.1794	+	5.38369i	−0.948221	+	0.456639i	−0.843062	−	0.537816i	$-0.819249\pi$
$139$	−11.1794	+	5.38369i	−0.948221	+	0.456639i	−0.105159	+	0.994455i	$0.533535\pi$
$140$	−4.49490	−	2.16463i	−0.379888	−	0.182945i
$141$	−4.82921	−	6.05564i	−0.406693	−	0.509977i
$142$	4.96943	−	6.23146i	0.417025	−	0.522933i
$143$	14.1595	+	6.81887i	1.18408	+	0.570222i
$144$	10.6248			0.885400
$145$		0			0
$146$	1.73646			0.143710
$147$	−12.8686	−	6.19718i	−1.06138	−	0.511135i
$148$	6.39565	−	8.01989i	0.525719	−	0.659231i
$149$	−12.9734	−	16.2681i	−1.06282	−	1.33274i	−0.940328	−	0.340269i	$-0.889482\pi$
$149$	−12.9734	−	16.2681i	−1.06282	−	1.33274i	−0.122495	−	0.992469i	$-0.539089\pi$
$150$	0.177608	+	0.0855315i	0.0145016	+	0.00698362i
$151$	−18.0449	+	8.68996i	−1.46847	+	0.707179i	−0.985691	−	0.168561i	$-0.946088\pi$
$151$	−18.0449	+	8.68996i	−1.46847	+	0.707179i	−0.482782	+	0.875741i	$0.660374\pi$
$152$	7.09339	−	8.89484i	0.575350	−	0.721466i
$153$	−1.30182	−	5.70363i	−0.105246	−	0.461112i
$154$	0.741909	+	3.25052i	0.0597847	+	0.261934i
$155$	−3.77041	−	4.72794i	−0.302846	−	0.379757i
$156$	−3.26865	+	14.3209i	−0.261701	+	1.14659i
$157$	11.7893			0.940890			0.470445	−	0.882429i	$-0.344093\pi$
$157$	11.7893			0.940890			0.470445	+	0.882429i	$0.344093\pi$
$158$	−0.240741	+	1.05476i	−0.0191523	+	0.0839118i
$159$	−14.0776	+	6.77942i	−1.11643	+	0.537643i
$160$	10.1282	−	4.87751i	0.800708	−	0.385601i
$161$	0.250717	−	1.09846i	0.0197593	−	0.0865710i
$162$	1.88561			0.148148
$163$	−0.557775	+	2.44377i	−0.0436883	+	0.191411i	−0.992063	−	0.125741i	$-0.959869\pi$
$163$	−0.557775	+	2.44377i	−0.0436883	+	0.191411i	0.948375	+	0.317152i	$0.102726\pi$
$164$	−2.06904	−	2.59450i	−0.161565	−	0.202596i
$165$	−6.61335	−	28.9750i	−0.514849	−	2.25570i
$166$	0.723438	+	3.16959i	0.0561497	+	0.246008i
$167$	−1.66528	+	2.08820i	−0.128863	+	0.161589i	−0.842077	−	0.539357i	$-0.818667\pi$
$167$	−1.66528	+	2.08820i	−0.128863	+	0.161589i	0.713214	+	0.700946i	$0.247239\pi$
$168$	−6.03747	+	2.90749i	−0.465801	+	0.224318i
$169$	2.84172	+	1.36850i	0.218594	+	0.105269i
$170$	−0.967043	−	1.21263i	−0.0741688	−	0.0930047i
$171$	15.7718	−	19.7772i	1.20610	−	1.51240i
$172$	−17.2532	−	8.30870i	−1.31554	−	0.633532i
$173$	23.5982			1.79414			0.897071	−	0.441887i	$-0.145691\pi$
$173$	23.5982			1.79414			0.897071	+	0.441887i	$0.145691\pi$
$174$		0			0
$175$	0.186458			0.0140949
$176$	11.2815	+	5.43286i	0.850371	+	0.409517i
$177$	7.30781	−	9.16370i	0.549288	−	0.688786i
$178$	3.80374	+	4.76973i	0.285102	+	0.357507i
$179$	18.8829	+	9.09351i	1.41137	+	0.679681i	0.975433	−	0.220295i	$-0.0707020\pi$
$179$	18.8829	+	9.09351i	1.41137	+	0.679681i	0.435939	+	0.899976i	$0.356416\pi$
$180$	14.6712	−	7.06527i	1.09352	−	0.526614i
$181$	5.66995	−	7.10989i	0.421444	−	0.528474i	−0.525104	−	0.851038i	$-0.675973\pi$
$181$	5.66995	−	7.10989i	0.421444	−	0.528474i	0.946548	+	0.322564i	$0.104545\pi$
$182$	−0.464802	−	2.03643i	−0.0344534	−	0.150950i
$183$	3.25666	+	14.2683i	0.240739	+	1.05475i
$184$	1.03124	+	1.29314i	0.0760241	+	0.0953312i
$185$	2.89332	−	12.6765i	0.212721	−	0.931993i
$186$	−3.77735			−0.276969
$187$	1.53421	−	6.72181i	0.112192	−	0.491547i
$188$	4.50604	−	2.17000i	0.328637	−	0.158263i
$189$	−3.94796	+	1.90124i	−0.287171	+	0.138294i
$190$	1.49231	−	6.53825i	0.108264	−	0.474334i
$191$	−19.2700			−1.39433			−0.697163	−	0.716912i	$-0.745555\pi$
$191$	−19.2700			−1.39433			−0.697163	+	0.716912i	$0.745555\pi$
$192$	−1.43327	+	6.27958i	−0.103438	+	0.453190i
$193$	−3.31575	−	4.15782i	−0.238673	−	0.299287i	0.648040	−	0.761606i	$-0.275589\pi$
$193$	−3.31575	−	4.15782i	−0.238673	−	0.299287i	−0.886713	+	0.462319i	$0.847017\pi$
$194$	1.29960	+	5.69393i	0.0933060	+	0.408800i
$195$	4.14323	+	18.1527i	0.296703	+	1.29994i
$196$	5.75028	−	7.21063i	0.410735	−	0.515045i
$197$	8.98503	−	4.32696i	0.640157	−	0.308283i	−0.0855020	−	0.996338i	$-0.527249\pi$
$197$	8.98503	−	4.32696i	0.640157	−	0.308283i	0.725659	+	0.688055i	$0.241535\pi$
$198$	−9.80470	−	4.72169i	−0.696790	−	0.335556i
$199$	−13.8353	−	17.3490i	−0.980762	−	1.22984i	−0.973223	−	0.229865i	$-0.926172\pi$
$199$	−13.8353	−	17.3490i	−0.980762	−	1.22984i	−0.00753910	−	0.999972i	$-0.502400\pi$
$200$	−0.170658	+	0.213999i	−0.0120674	+	0.0151320i
$201$	−5.73190	−	2.76034i	−0.404297	−	0.194699i
$202$	−0.498225			−0.0350550
$203$		0			0
$204$	6.44425			0.451188
$205$	−3.78984	−	1.82509i	−0.264694	−	0.127470i
$206$	2.47907	−	3.10866i	0.172725	−	0.216591i
$207$	2.29291	+	2.87522i	0.159368	+	0.199842i
$208$	−7.06778	−	3.40366i	−0.490062	−	0.236001i
$209$	26.8594	−	12.9348i	1.85790	−	0.894718i
$210$	−2.46285	+	3.08832i	−0.169953	+	0.213114i
$211$	1.62670	+	7.12705i	0.111987	+	0.490646i	0.999551	+	0.0299623i	$0.00953872\pi$
$211$	1.62670	+	7.12705i	0.111987	+	0.490646i	−0.887564	+	0.460684i	$0.847604\pi$
$212$	−2.24506	−	9.83627i	−0.154192	−	0.675558i
$213$	26.1718	+	32.8184i	1.79326	+	2.24868i
$214$	−0.619943	+	2.71615i	−0.0423784	+	0.185672i
$215$	−24.2734			−1.65543
$216$	1.43137	−	6.27123i	0.0973922	−	0.426703i
$217$	−3.21903	+	1.55020i	−0.218522	+	0.105235i
$218$	−3.63503	+	1.75054i	−0.246195	+	0.118561i
$219$	−2.03499	+	8.91586i	−0.137512	+	0.602478i
$220$	19.1906			1.29383
$221$	−0.961175	+	4.21118i	−0.0646556	+	0.283275i
$222$	−5.06388	−	6.34991i	−0.339866	−	0.426178i
$223$	−1.22390	−	5.36226i	−0.0819584	−	0.359083i	0.917274	−	0.398257i	$-0.130385\pi$
$223$	−1.22390	−	5.36226i	−0.0819584	−	0.359083i	−0.999232	+	0.0391734i	$0.987528\pi$
$224$	−1.47792	−	6.47520i	−0.0987478	−	0.432642i
$225$	−0.379450	+	0.475815i	−0.0252967	+	0.0317210i
$226$	7.96924	−	3.83779i	0.530106	−	0.255286i
$227$	−14.1912	−	6.83411i	−0.941901	−	0.453596i	−0.101062	−	0.994880i	$-0.532224\pi$
$227$	−14.1912	−	6.83411i	−0.941901	−	0.453596i	−0.840840	+	0.541284i	$0.817938\pi$
$228$	17.3730	+	21.7850i	1.15055	+	1.44275i
$229$	−9.24773	+	11.5963i	−0.611107	+	0.766304i	−0.987063	−	0.160333i	$-0.948743\pi$
$229$	−9.24773	+	11.5963i	−0.611107	+	0.766304i	0.375956	+	0.926638i	$0.377315\pi$
$230$	0.878425	+	0.423027i	0.0579216	+	0.0278936i
$231$	−17.5593			−1.15532
$232$		0			0
$233$	−15.8867			−1.04078			−0.520388	−	0.853930i	$-0.674213\pi$
$233$	−15.8867			−1.04078			−0.520388	+	0.853930i	$0.674213\pi$
$234$	6.14260	+	2.95812i	0.401554	+	0.193378i
$235$	3.95263	−	4.95644i	0.257841	−	0.323322i
$236$	4.71874	+	5.91711i	0.307164	+	0.385171i
$237$	−5.13353	−	2.47218i	−0.333459	−	0.160585i
$238$	−0.825624	+	0.397600i	−0.0535172	+	0.0257725i
$239$	5.86077	−	7.34917i	0.379102	−	0.475378i	−0.555274	−	0.831667i	$-0.687387\pi$
$239$	5.86077	−	7.34917i	0.379102	−	0.475378i	0.934376	+	0.356289i	$0.115958\pi$
$240$	3.30108	+	14.4630i	0.213084	+	0.933581i
$241$	2.32318	+	10.1785i	0.149649	+	0.655657i	0.992982	+	0.118265i	$0.0377332\pi$
$241$	2.32318	+	10.1785i	0.149649	+	0.655657i	−0.843333	+	0.537392i	$0.819410\pi$
$242$	−4.48990	−	5.63015i	−0.288622	−	0.361920i
$243$	−4.45637	+	19.5246i	−0.285876	+	1.25251i
$244$	−9.45018			−0.604986
$245$	2.60137	−	11.3973i	0.166195	−	0.728149i
$246$	−2.36728	+	1.14002i	−0.150932	+	0.0726851i
$247$	−16.8273	+	8.10359i	−1.07069	+	0.515619i
$248$	1.16709	−	5.11335i	0.0741102	−	0.324698i
$249$	−17.1221			−1.08507
$250$	−1.28949	+	5.64962i	−0.0815544	+	0.357313i
$251$	−9.21653	−	11.5572i	−0.581742	−	0.729482i	0.400667	−	0.916224i	$-0.368779\pi$
$251$	−9.21653	−	11.5572i	−0.581742	−	0.729482i	−0.982409	+	0.186742i	$0.940207\pi$
$252$	−2.14083	−	9.37959i	−0.134860	−	0.590859i
$253$	0.964413	+	4.22537i	0.0606321	+	0.265647i
$254$	1.75835	−	2.20490i	0.110329	−	0.138348i
$255$	7.35958	−	3.54419i	0.460875	−	0.221946i
$256$	0.952035	+	0.458476i	0.0595022	+	0.0286547i
$257$	1.07897	+	1.35299i	0.0673043	+	0.0843969i	0.814344	−	0.580383i	$-0.197097\pi$
$257$	1.07897	+	1.35299i	0.0673043	+	0.0843969i	−0.747040	+	0.664779i	$0.768526\pi$
$258$	−9.45340	+	11.8542i	−0.588543	+	0.738009i
$259$	−6.92137	−	3.33316i	−0.430073	−	0.207112i
$260$	−12.0228			−0.745625
$261$		0			0
$262$	−0.0144647			−0.000893630
$263$	12.1911	+	5.87091i	0.751734	+	0.362016i	0.770191	−	0.637814i	$-0.220161\pi$
$263$	12.1911	+	5.87091i	0.751734	+	0.362016i	−0.0184569	+	0.999830i	$0.505875\pi$
$264$	16.0714	−	20.1529i	0.989127	−	1.24033i
$265$	−7.97367	−	9.99867i	−0.489819	−	0.614213i
$266$	−3.56989	−	1.71917i	−0.218884	−	0.105409i
$267$	−28.9480	+	13.9406i	−1.77159	+	0.853151i
$268$	2.56128	−	3.21174i	0.156455	−	0.196188i
$269$	6.65101	+	29.1400i	0.405519	+	1.77669i	0.604410	+	0.796673i	$0.293409\pi$
$269$	6.65101	+	29.1400i	0.405519	+	1.77669i	−0.198891	+	0.980022i	$0.563734\pi$
$270$	−0.843753	−	3.69672i	−0.0513491	−	0.224975i
$271$	−5.83834	−	7.32105i	−0.354654	−	0.444722i	0.572217	−	0.820102i	$-0.306084\pi$
$271$	−5.83834	−	7.32105i	−0.354654	−	0.444722i	−0.926871	+	0.375380i	$0.877512\pi$
$272$	−0.765806	+	3.35522i	−0.0464338	+	0.203440i
$273$	11.0008			0.665799
$274$	−0.700186	+	3.06772i	−0.0422998	+	0.185327i
$275$	−0.646204	+	0.311195i	−0.0389676	+	0.0187658i
$276$	−3.64973	+	1.75762i	−0.219688	+	0.105796i
$277$	−4.98941	+	21.8600i	−0.299785	+	1.31344i	0.570664	+	0.821184i	$0.306686\pi$
$277$	−4.98941	+	21.8600i	−0.299785	+	1.31344i	−0.870449	+	0.492259i	$0.836171\pi$
$278$	−6.34374			−0.380472
$279$	2.59496	−	11.3693i	0.155356	−	0.680660i
$280$	−3.41967	−	4.28814i	−0.204365	−	0.256265i
$281$	1.93861	+	8.49362i	0.115648	+	0.506687i	0.999260	+	0.0384668i	$0.0122474\pi$
$281$	1.93861	+	8.49362i	0.115648	+	0.506687i	−0.883612	+	0.468220i	$0.844895\pi$
$282$	−0.881162	−	3.86062i	−0.0524724	−	0.229897i
$283$	−9.01447	+	11.3038i	−0.535855	+	0.671940i	−0.973891	−	0.227017i	$-0.927103\pi$
$283$	−9.01447	+	11.3038i	−0.535855	+	0.671940i	0.438036	+	0.898957i	$0.355674\pi$
$284$	−24.4204	+	11.7602i	−1.44908	+	0.697842i
$285$	31.8219	+	15.3246i	1.88496	+	0.907751i
$286$	5.00964	+	6.28188i	0.296226	+	0.371456i
$287$	−1.54952	+	1.94303i	−0.0914652	+	0.114694i
$288$	19.5315	+	9.40587i	1.15090	+	0.554246i
$289$	−15.1050			−0.888530
$290$		0			0
$291$	−30.7586			−1.80310
$292$	−5.32034	−	2.56214i	−0.311349	−	0.149938i
$293$	−20.4230	+	25.6097i	−1.19313	+	1.49613i	−0.369280	+	0.929318i	$0.620396\pi$
$293$	−20.4230	+	25.6097i	−1.19313	+	1.49613i	−0.823846	+	0.566814i	$0.808176\pi$
$294$	−4.55290	−	5.70916i	−0.265531	−	0.332965i
$295$	8.64325	+	4.16237i	0.503230	+	0.242343i
$296$	10.1604	−	4.89298i	0.590560	−	0.284399i
$297$	10.5092	−	13.1782i	0.609808	−	0.764674i
$298$	−2.36719	−	10.3713i	−0.137128	−	0.600796i
$299$	−0.604200	−	2.64717i	−0.0349418	−	0.153090i
$300$	−0.417973	−	0.524121i	−0.0241317	−	0.0302602i
$301$	−3.19123	+	13.9817i	−0.183939	+	0.805890i
$302$	−10.2396			−0.589222
$303$	0.583880	−	2.55814i	0.0335430	−	0.146962i
$304$	−13.4070	+	6.45645i	−0.768942	+	0.370303i
$305$	−10.7925	+	5.19738i	−0.617975	+	0.297601i
$306$	0.665561	−	2.91601i	0.0380476	−	0.166697i
$307$	28.4921			1.62613			0.813065	−	0.582173i	$-0.197798\pi$
$307$	28.4921			1.62613			0.813065	+	0.582173i	$0.197798\pi$
$308$	2.52300	−	11.0540i	0.143761	−	0.629858i
$309$	13.0562	+	16.3719i	0.742741	+	0.931367i
$310$	−0.687967	−	3.01418i	−0.0390739	−	0.171194i
$311$	−4.85265	−	21.2608i	−0.275168	−	1.20559i	−0.903823	−	0.427907i	$-0.859251\pi$
$311$	−4.85265	−	21.2608i	−0.275168	−	1.20559i	0.628654	−	0.777685i	$-0.283606\pi$
$312$	−10.0687	+	12.6257i	−0.570026	+	0.714790i
$313$	21.5580	−	10.3818i	1.21853	−	0.586814i	0.289630	−	0.957139i	$-0.406468\pi$
$313$	21.5580	−	10.3818i	1.21853	−	0.586814i	0.928902	+	0.370324i	$0.120754\pi$
$314$	5.43046	+	2.61517i	0.306458	+	0.147583i
$315$	−7.60347	−	9.53444i	−0.428407	−	0.537205i
$316$	2.29390	−	2.87646i	0.129042	−	0.161814i
$317$	8.42635	+	4.05792i	0.473271	+	0.227915i	0.655287	−	0.755380i	$-0.272548\pi$
$317$	8.42635	+	4.05792i	0.473271	+	0.227915i	−0.182016	+	0.983296i	$0.558262\pi$
$318$	−7.98835			−0.447964
$319$		0			0
$320$	−5.27191			−0.294709
$321$	−13.2196	−	6.36622i	−0.737845	−	0.355328i
$322$	0.359154	−	0.450365i	0.0200149	−	0.0250978i
$323$	5.10867	+	6.40608i	0.284254	+	0.356444i
$324$	−5.77734	−	2.78222i	−0.320963	−	0.154568i
$325$	0.404844	−	0.194962i	0.0224567	−	0.0108146i
$326$	−0.799016	+	1.00193i	−0.0442534	+	0.0554920i
$327$	−4.72820	−	20.7156i	−0.261470	−	1.14558i
$328$	−0.811813	−	3.55679i	−0.0448249	−	0.196391i
$329$	−2.33530	−	2.92837i	−0.128749	−	0.161446i
$330$	3.38111	−	14.8136i	0.186124	−	0.815463i
$331$	10.2474			0.563247			0.281623	−	0.959525i	$-0.409127\pi$
$331$	10.2474			0.563247			0.281623	+	0.959525i	$0.409127\pi$
$332$	2.46018	−	10.7788i	0.135020	−	0.591562i
$333$	22.5911	−	10.8793i	1.23798	−	0.596181i
$334$	−1.23029	+	0.592474i	−0.0673182	+	0.0324188i
$335$	1.15870	−	5.07658i	0.0633063	−	0.277363i
$336$	8.76478			0.478158
$337$	−3.54778	+	15.5438i	−0.193260	+	0.846726i	0.781577	+	0.623808i	$0.214415\pi$
$337$	−3.54778	+	15.5438i	−0.193260	+	0.846726i	−0.974837	+	0.222918i	$0.928442\pi$
$338$	1.00540	+	1.26073i	0.0546866	+	0.0685748i
$339$	10.3659	+	45.4158i	0.562996	+	2.46665i
$340$	1.17369	+	5.14227i	0.0636523	+	0.278879i
$341$	8.56887	−	10.7450i	0.464030	−	0.581876i
$342$	11.6520	−	5.61129i	0.630067	−	0.303424i
$343$	−14.4348	−	6.95142i	−0.779404	−	0.375341i
$344$	−13.1260	−	16.4595i	−0.707709	−	0.887439i
$345$	−3.20148	+	4.01453i	−0.172362	+	0.216135i
$346$	10.8699	+	5.23469i	0.584372	+	0.281419i
$347$	36.7925			1.97513			0.987563	−	0.157224i	$-0.0502544\pi$
$347$	36.7925			1.97513			0.987563	+	0.157224i	$0.0502544\pi$
$348$		0			0
$349$	32.4894			1.73912			0.869558	−	0.493831i	$-0.164404\pi$
$349$	32.4894			1.73912			0.869558	+	0.493831i	$0.164404\pi$
$350$	0.0858872	+	0.0413611i	0.00459086	+	0.00221084i
$351$	−6.58398	+	8.25606i	−0.351427	+	0.440676i
$352$	15.9290	+	19.9744i	0.849020	+	1.06464i
$353$	10.8270	+	5.21401i	0.576264	+	0.277514i	0.699230	−	0.714897i	$-0.253526\pi$
$353$	10.8270	+	5.21401i	0.576264	+	0.277514i	−0.122966	+	0.992411i	$0.539241\pi$
$354$	5.39890	−	2.59997i	0.286948	−	0.138187i
$355$	−21.4212	+	26.8613i	−1.13692	+	1.42565i
$356$	−4.61655	−	20.2264i	−0.244677	−	1.07200i
$357$	−1.07392	−	4.70514i	−0.0568377	−	0.249022i
$358$	6.68076	+	8.37741i	0.353089	+	0.442760i
$359$	0.869747	−	3.81061i	0.0459035	−	0.201116i	−0.946776	−	0.321892i	$-0.895681\pi$
$359$	0.869747	−	3.81061i	0.0459035	−	0.201116i	0.992680	+	0.120776i	$0.0385383\pi$
$360$	17.9019			0.943515
$361$	−3.65566	+	16.0165i	−0.192403	+	0.842973i
$362$	4.18888	−	2.01726i	0.220162	−	0.106025i
$363$	34.1699	−	16.4554i	1.79346	−	0.863683i
$364$	−1.58065	+	6.92526i	−0.0828483	+	0.362982i
$365$	−7.48515			−0.391791
$366$	−1.66498	+	7.29477i	−0.0870301	+	0.381304i
$367$	7.97279	+	9.99756i	0.416176	+	0.521868i	0.945091	−	0.326806i	$-0.105973\pi$
$367$	7.97279	+	9.99756i	0.416176	+	0.521868i	−0.528915	+	0.848675i	$0.677401\pi$
$368$	−0.481390	−	2.10911i	−0.0250942	−	0.109945i
$369$	−1.80502	−	7.90833i	−0.0939658	−	0.411691i
$370$	4.14470	−	5.19729i	0.215473	−	0.270194i
$371$	−6.80761	+	3.27837i	−0.353434	+	0.170205i
$372$	11.5735	+	5.57348i	0.600056	+	0.288972i
$373$	15.5788	+	19.5352i	0.806641	+	1.01150i	0.999542	+	0.0302771i	$0.00963898\pi$
$373$	15.5788	+	19.5352i	0.806641	+	1.01150i	−0.192901	+	0.981218i	$0.561790\pi$
$374$	2.19776	−	2.75591i	0.113644	−	0.142505i
$375$	−27.4969	−	13.2418i	−1.41993	−	0.683804i
$376$	5.49833			0.283555
$377$		0			0
$378$	−2.24027			−0.115227
$379$	−11.7443	−	5.65577i	−0.603265	−	0.290517i	0.107213	−	0.994236i	$-0.465807\pi$
$379$	−11.7443	−	5.65577i	−0.603265	−	0.290517i	−0.710479	+	0.703719i	$0.751521\pi$
$380$	−14.2195	+	17.8307i	−0.729445	+	0.914695i
$381$	9.26046	+	11.6122i	0.474428	+	0.594913i
$382$	−8.87624	−	4.27457i	−0.454148	−	0.218706i
$383$	−21.6548	+	10.4284i	−1.10651	+	0.532867i	−0.895699	−	0.444660i	$-0.853324\pi$
$383$	−21.6548	+	10.4284i	−1.10651	+	0.532867i	−0.210810	+	0.977527i	$0.567610\pi$
$384$	−19.1799	+	24.0508i	−0.978769	+	1.22734i
$385$	−3.19807	−	14.0116i	−0.162989	−	0.714100i
$386$	−0.605009	−	2.65072i	−0.0307941	−	0.134918i
$387$	−29.1851	−	36.5969i	−1.48356	−	1.86033i
$388$	4.41953	−	19.3632i	0.224368	−	0.983020i
$389$	−17.6717			−0.895991			−0.447995	−	0.894036i	$-0.647862\pi$
$389$	−17.6717			−0.895991			−0.447995	+	0.894036i	$0.647862\pi$
$390$	−2.11825	+	9.28066i	−0.107262	+	0.469945i
$391$	−1.07323	+	0.516843i	−0.0542758	+	0.0261379i
$392$	9.13513	−	4.39925i	0.461394	−	0.222195i
$393$	0.0169514	−	0.0742691i	0.000855087	−	0.00374638i
$394$	5.09856			0.256862
$395$	1.03774	−	4.54662i	0.0522142	−	0.228765i
$396$	23.0738	+	28.9337i	1.15950	+	1.45397i
$397$	−6.73183	−	29.4941i	−0.337861	−	1.48027i	−0.803507	−	0.595295i	$-0.797035\pi$
$397$	−6.73183	−	29.4941i	−0.337861	−	1.48027i	0.465646	−	0.884971i	$-0.345822\pi$
$398$	−2.52447	−	11.0604i	−0.126540	−	0.554408i
$399$	13.0107	−	16.3149i	0.651351	−	0.816768i
$400$	0.322555	−	0.155334i	0.0161278	−	0.00776672i
$401$	11.1335	+	5.36161i	0.555981	+	0.267746i	0.690705	−	0.723137i	$-0.257300\pi$
$401$	11.1335	+	5.36161i	0.555981	+	0.267746i	−0.134724	+	0.990883i	$0.543015\pi$
$402$	−2.02794	−	2.54296i	−0.101145	−	0.126831i
$403$	−5.36836	+	6.73171i	−0.267417	+	0.335330i
$404$	1.52652	+	0.735131i	0.0759470	+	0.0365741i
$405$	−8.12810			−0.403889
$406$		0			0
$407$	29.5503			1.46475
$408$	6.38304	+	3.07391i	0.316007	+	0.152181i
$409$	−3.80764	+	4.77463i	−0.188276	+	0.236090i	−0.867006	−	0.498297i	$-0.833959\pi$
$409$	−3.80764	+	4.77463i	−0.188276	+	0.236090i	0.678731	+	0.734387i	$0.262530\pi$
$410$	−1.34084	−	1.68137i	−0.0662196	−	0.0830368i
$411$	−14.9307	−	7.19024i	−0.736476	−	0.354668i
$412$	−12.1825	+	5.86677i	−0.600188	+	0.289035i
$413$	3.53389	−	4.43136i	0.173891	−	0.218053i
$414$	0.418376	+	1.83302i	0.0205621	+	0.0900882i
$415$	−3.11845	−	13.6628i	−0.153079	−	0.670681i
$416$	−9.97946	−	12.5138i	−0.489283	−	0.613542i
$417$	7.43435	−	32.5720i	0.364062	−	1.59506i
$418$	15.2414			0.745480
$419$	−2.58290	+	11.3164i	−0.126183	+	0.552845i	0.871828	+	0.489812i	$0.162934\pi$
$419$	−2.58290	+	11.3164i	−0.126183	+	0.552845i	−0.998011	+	0.0630329i	$0.979923\pi$
$420$	12.1028	−	5.82839i	0.590555	−	0.284397i
$421$	18.2777	−	8.80208i	0.890801	−	0.428987i	0.0682433	−	0.997669i	$-0.478261\pi$
$421$	18.2777	−	8.80208i	0.890801	−	0.428987i	0.822558	+	0.568682i	$0.192546\pi$
$422$	−0.831661	+	3.64374i	−0.0404846	+	0.177375i
$423$	12.2252			0.594412
$424$	2.46816	−	10.8137i	0.119865	−	0.525161i
$425$	−0.122909	−	0.154122i	−0.00596194	−	0.00747603i
$426$	4.77544	+	20.9226i	0.231371	+	1.01370i
$427$	1.57485	+	6.89985i	0.0762121	+	0.333907i
$428$	5.90713	−	7.40730i	0.285532	−	0.358045i
$429$	−38.1253	+	18.3602i	−1.84071	+	0.886439i
$430$	−11.1809	−	5.38446i	−0.539193	−	0.259661i
$431$	10.5892	+	13.2784i	0.510063	+	0.639598i	0.968466	−	0.249146i	$-0.0801499\pi$
$431$	10.5892	+	13.2784i	0.510063	+	0.639598i	−0.458403	+	0.888744i	$0.651578\pi$
$432$	−5.24572	+	6.57793i	−0.252385	+	0.316481i
$433$	14.3572	+	6.91405i	0.689962	+	0.332268i	0.745798	−	0.666172i	$-0.232068\pi$
$433$	14.3572	+	6.91405i	0.689962	+	0.332268i	−0.0558365	+	0.998440i	$0.517783\pi$
$434$	−1.82664			−0.0876815
$435$		0			0
$436$	13.7203			0.657084
$437$	−4.64053	−	2.23476i	−0.221986	−	0.106903i
$438$	−2.91513	+	3.65546i	−0.139290	+	0.174665i
$439$	−3.36904	−	4.22464i	−0.160795	−	0.201631i	0.694907	−	0.719100i	$-0.255446\pi$
$439$	−3.36904	−	4.22464i	−0.160795	−	0.201631i	−0.855702	+	0.517469i	$0.826874\pi$
$440$	19.0083	+	9.15394i	0.906187	+	0.436397i
$441$	20.3115	−	9.78149i	0.967213	−	0.465785i
$442$	−1.37689	+	1.72656i	−0.0654919	+	0.0821243i
$443$	4.23933	+	18.5737i	0.201417	+	0.882465i	0.970075	+	0.242805i	$0.0780675\pi$
$443$	4.23933	+	18.5737i	0.201417	+	0.882465i	−0.768658	+	0.639660i	$0.779075\pi$
$444$	6.14598	+	26.9273i	0.291675	+	1.27791i
$445$	−16.3964	−	20.5604i	−0.777262	−	0.974655i
$446$	0.625726	−	2.74148i	0.0296290	−	0.129813i
$447$	56.0260			2.64994
$448$	−0.693099	+	3.03666i	−0.0327458	+	0.143469i
$449$	15.9358	−	7.67428i	0.752058	−	0.362172i	−0.0182592	−	0.999833i	$-0.505812\pi$
$449$	15.9358	−	7.67428i	0.752058	−	0.362172i	0.770317	+	0.637661i	$0.220098\pi$
$450$	−0.280332	+	0.135001i	−0.0132150	+	0.00636400i
$451$	2.12724	−	9.32007i	0.100168	−	0.438865i
$452$	−30.0797			−1.41483
$453$	12.0000	−	52.5754i	0.563808	−	2.47021i
$454$	−5.02083	−	6.29593i	−0.235639	−	0.295483i
$455$	2.00357	+	8.77823i	0.0939290	+	0.411530i
$456$	6.81649	+	29.8650i	0.319211	+	1.39856i
$457$	−9.41345	+	11.8041i	−0.440343	+	0.552172i	−0.951634	−	0.307235i	$-0.900596\pi$
$457$	−9.41345	+	11.8041i	−0.440343	+	0.552172i	0.511291	+	0.859408i	$0.329168\pi$
$458$	−6.83209	+	3.29016i	−0.319243	+	0.153739i
$459$	4.17392	+	2.01005i	0.194822	+	0.0938213i
$460$	−2.06724	−	2.59223i	−0.0963854	−	0.120864i
$461$	13.9049	−	17.4362i	0.647617	−	0.812087i	−0.344315	−	0.938854i	$-0.611889\pi$
$461$	13.9049	−	17.4362i	0.647617	−	0.812087i	0.991932	+	0.126768i	$0.0404603\pi$
$462$	−8.08825	−	3.89510i	−0.376300	−	0.181216i
$463$	−26.7391			−1.24267			−0.621335	−	0.783545i	$-0.713409\pi$
$463$	−26.7391			−1.24267			−0.621335	+	0.783545i	$0.713409\pi$
$464$		0			0
$465$	16.2826			0.755088
$466$	−7.31784	−	3.52408i	−0.338992	−	0.163250i
$467$	−7.20832	+	9.03895i	−0.333561	+	0.418273i	−0.920122	−	0.391633i	$-0.871910\pi$
$467$	−7.20832	+	9.03895i	−0.333561	+	0.418273i	0.586560	+	0.809906i	$0.300482\pi$
$468$	−14.4557	−	18.1268i	−0.668213	−	0.837912i
$469$	−2.77182	−	1.33484i	−0.127991	−	0.0616370i
$470$	2.92014	−	1.40627i	0.134696	−	0.0648663i
$471$	−19.7917	+	24.8180i	−0.911953	+	1.14355i
$472$	1.85145	+	8.11174i	0.0852200	+	0.373373i
$473$	−12.2754	−	53.7822i	−0.564425	−	2.47291i
$474$	−1.81624	−	2.27750i	−0.0834228	−	0.104609i
$475$	0.189669	−	0.830993i	0.00870260	−	0.0381286i
$476$	3.11630			0.142835
$477$	5.48783	−	24.0438i	0.251271	−	1.10089i
$478$	4.32985	−	2.08515i	0.198043	−	0.0953724i
$479$	21.9188	−	10.5555i	1.00149	−	0.482294i	0.140049	−	0.990145i	$-0.455274\pi$
$479$	21.9188	−	10.5555i	1.00149	−	0.482294i	0.861445	+	0.507850i	$0.169560\pi$
$480$	−6.73536	+	29.5095i	−0.307426	+	1.34692i
$481$	−18.5131			−0.844125
$482$	−1.18774	+	5.20383i	−0.0541001	+	0.237028i
$483$	1.89151	+	2.37187i	0.0860665	+	0.107924i
$484$	5.44934	+	23.8751i	0.247697	+	1.08523i
$485$	−5.60206	−	24.5442i	−0.254376	−	1.11450i
$486$	−6.38378	+	8.00501i	−0.289574	+	0.363115i
$487$	−1.15944	+	0.558359i	−0.0525395	+	0.0253017i	−0.459969	−	0.887935i	$-0.652139\pi$
$487$	−1.15944	+	0.558359i	−0.0525395	+	0.0253017i	0.407430	+	0.913237i	$0.366425\pi$
$488$	−9.36041	−	4.50773i	−0.423726	−	0.204056i
$489$	−4.20807	−	5.27675i	−0.190295	−	0.238623i
$490$	3.72647	−	4.67285i	0.168345	−	0.211098i
$491$	29.4242	+	14.1700i	1.32790	+	0.639481i	0.957242	−	0.289289i	$-0.0934189\pi$
$491$	29.4242	+	14.1700i	1.32790	+	0.639481i	0.370655	+	0.928771i	$0.379133\pi$
$492$	8.93522			0.402831
$493$		0			0
$494$	−9.54865			−0.429614
$495$	42.2641	+	20.3533i	1.89963	+	0.914813i
$496$	−4.27718	+	5.36342i	−0.192051	+	0.240825i
$497$	12.6561	+	15.8702i	0.567703	+	0.711877i
$498$	−7.88689	−	3.79812i	−0.353420	−	0.170198i
$499$	9.44501	−	4.54848i	0.422817	−	0.203618i	−0.210362	−	0.977624i	$-0.567464\pi$
$499$	9.44501	−	4.54848i	0.422817	−	0.203618i	0.633179	+	0.774006i	$0.281750\pi$
$500$	12.2869	−	15.4073i	0.549487	−	0.689034i
$501$	−1.60027	−	7.01126i	−0.0714949	−	0.313240i
$502$	−1.68169	−	7.36798i	−0.0750577	−	0.328849i
$503$	2.36325	+	2.96342i	0.105372	+	0.132133i	0.831721	−	0.555193i	$-0.187356\pi$
$503$	2.36325	+	2.96342i	0.105372	+	0.132133i	−0.726349	+	0.687326i	$0.758784\pi$
$504$	2.35357	−	10.3117i	0.104836	−	0.459318i
$505$	2.14764			0.0955689
$506$	−0.493062	+	2.16024i	−0.0219193	+	0.0960346i
$507$	−7.65151	+	3.68477i	−0.339815	+	0.163646i
$508$	−8.64076	+	4.16117i	−0.383372	+	0.184622i
$509$	1.78424	−	7.81725i	0.0790849	−	0.346494i	−0.919869	−	0.392226i	$-0.871705\pi$
$509$	1.78424	−	7.81725i	0.0790849	−	0.346494i	0.998954	+	0.0457326i	$0.0145622\pi$
$510$	4.17620			0.184925
$511$	−0.984074	+	4.31151i	−0.0435329	+	0.190730i
$512$	−13.9098	−	17.4423i	−0.614730	−	0.770847i
$513$	4.45736	+	19.5290i	0.196797	+	0.862225i
$514$	0.196874	+	0.862562i	0.00868375	+	0.0380460i
$515$	−10.6863	+	13.4002i	−0.470893	+	0.590482i
$516$	46.4552	−	22.3717i	2.04508	−	0.984857i
$517$	12.9808	+	6.25123i	0.570895	+	0.274929i
$518$	−2.44878	−	3.07067i	−0.107593	−	0.134918i
$519$	−39.6163	+	49.6773i	−1.73896	+	2.18059i
$520$	−11.9086	−	5.73490i	−0.522228	−	0.251492i
$521$	−6.39024			−0.279962			−0.139981	−	0.990154i	$-0.544704\pi$
$521$	−6.39024			−0.279962			−0.139981	+	0.990154i	$0.544704\pi$
$522$		0			0
$523$	−16.3261			−0.713891			−0.356946	−	0.934125i	$-0.616182\pi$
$523$	−16.3261			−0.713891			−0.356946	+	0.934125i	$0.616182\pi$
$524$	0.0443184	+	0.0213426i	0.00193606	+	0.000932357i
$525$	−0.313022	+	0.392517i	−0.0136614	+	0.0171309i
$526$	4.31320	+	5.40858i	0.188064	+	0.235825i
$527$	3.40327	+	1.63893i	0.148249	+	0.0713929i
$528$	−30.3760	+	14.6283i	−1.32194	+	0.636615i
$529$	−13.8734	+	17.3967i	−0.603191	+	0.756378i
$530$	−1.45492	−	6.37440i	−0.0631975	−	0.276886i
$531$	4.11661	+	18.0360i	0.178645	+	0.782697i
$532$	8.40118	+	10.5347i	0.364237	+	0.456739i
$533$	−1.33271	+	5.83898i	−0.0577260	+	0.252914i
$534$	−16.4265			−0.710846
$535$	2.67232	−	11.7082i	0.115535	−	0.506190i
$536$	4.06895	−	1.95950i	0.175752	−	0.0846376i
$537$	−50.8433	+	24.4848i	−2.19405	+	1.05660i
$538$	−3.40036	+	14.8980i	−0.146600	+	0.642297i
$539$	26.5684			1.14438
$540$	−2.86933	+	12.5714i	−0.123477	+	0.540986i
$541$	13.6925	+	17.1699i	0.588688	+	0.738191i	0.983567	−	0.180542i	$-0.0577851\pi$
$541$	13.6925	+	17.1699i	0.588688	+	0.738191i	−0.394880	+	0.918733i	$0.629214\pi$
$542$	−1.06529	−	4.66735i	−0.0457582	−	0.200480i
$543$	5.44861	+	23.8719i	0.233822	+	1.02444i
$544$	−4.37806	+	5.48992i	−0.187708	+	0.235378i
$545$	15.6691	−	7.54586i	0.671192	−	0.323229i
$546$	5.06725	+	2.44026i	0.216858	+	0.104433i
$547$	2.55954	+	3.20956i	0.109438	+	0.137231i	0.833534	−	0.552468i	$-0.186314\pi$
$547$	2.55954	+	3.20956i	0.109438	+	0.137231i	−0.724096	+	0.689700i	$0.757743\pi$
$548$	6.67172	−	8.36608i	0.285002	−	0.357381i
$549$	−20.8124	−	10.0227i	−0.888250	−	0.427759i
$550$	−0.366689			−0.0156357
$551$		0			0
$552$	−4.45344			−0.189551
$553$	−2.48246	−	1.19549i	−0.105565	−	0.0508374i
$554$	−7.14736	+	8.96251i	−0.303662	+	0.380781i
$555$	21.8283	+	27.3719i	0.926561	+	1.16187i
$556$	19.4366	+	9.36019i	0.824297	+	0.396960i
$557$	22.4262	−	10.7999i	0.950229	−	0.457606i	0.106463	−	0.994317i	$-0.466048\pi$
$557$	22.4262	−	10.7999i	0.950229	−	0.457606i	0.843766	+	0.536711i	$0.180333\pi$
$558$	3.71730	−	4.66134i	0.157366	−	0.197330i
$559$	7.69050	+	33.6943i	0.325273	+	1.42512i
$560$	1.59633	+	6.99397i	0.0674571	+	0.295549i
$561$	11.5747	+	14.5142i	0.488683	+	0.612789i
$562$	−0.991127	+	4.34241i	−0.0418082	+	0.183174i
$563$	−22.6338			−0.953902			−0.476951	−	0.878930i	$-0.658258\pi$
$563$	−22.6338			−0.953902			−0.476951	+	0.878930i	$0.658258\pi$
$564$	−2.99655	+	13.1287i	−0.126178	+	0.552820i
$565$	−34.3522	+	16.5431i	−1.44521	+	0.695975i
$566$	−6.65976	+	3.20717i	−0.279931	+	0.134807i
$567$	−1.06860	+	4.68185i	−0.0448771	+	0.196619i
$568$	−29.7981			−1.25030
$569$	2.31372	−	10.1371i	0.0969961	−	0.424968i	−0.902993	−	0.429656i	$-0.858635\pi$
$569$	2.31372	−	10.1371i	0.0969961	−	0.424968i	0.999989	+	0.00468769i	$0.00149214\pi$
$570$	11.2586	+	14.1178i	0.471570	+	0.591330i
$571$	−7.93883	−	34.7823i	−0.332230	−	1.45559i	−0.814803	−	0.579738i	$-0.803155\pi$
$571$	−7.93883	−	34.7823i	−0.332230	−	1.45559i	0.482573	−	0.875856i	$-0.339702\pi$
$572$	−6.08014	−	26.6388i	−0.254224	−	1.11383i
$573$	32.3501	−	40.5658i	1.35145	−	1.69466i
$574$	−1.14476	+	0.551288i	−0.0477814	+	0.0230103i
$575$	0.111645	+	0.0537656i	0.00465594	+	0.00224218i
$576$	−6.33867	−	7.94845i	−0.264111	−	0.331185i
$577$	−1.00307	+	1.25781i	−0.0417582	+	0.0523632i	−0.802272	−	0.596959i	$-0.796376\pi$
$577$	−1.00307	+	1.25781i	−0.0417582	+	0.0523632i	0.760514	+	0.649322i	$0.224947\pi$
$578$	−6.95775	−	3.35068i	−0.289404	−	0.139370i
$579$	14.3192			0.595085
$580$		0			0
$581$	−8.27988			−0.343507
$582$	−14.1682	−	6.82304i	−0.587291	−	0.282824i
$583$	18.1215	−	22.7236i	0.750515	−	0.941116i
$584$	−4.04766	−	5.07561i	−0.167493	−	0.210030i
$585$	−26.4782	−	12.7512i	−1.09474	−	0.527199i
$586$	−15.0882	+	7.26611i	−0.623289	+	0.300160i
$587$	15.4340	−	19.3537i	0.637031	−	0.798812i	−0.353597	−	0.935398i	$-0.615042\pi$
$587$	15.4340	−	19.3537i	0.637031	−	0.798812i	0.990628	+	0.136586i	$0.0436131\pi$
$588$	5.52581	+	24.2102i	0.227881	+	0.998410i
$589$	3.63438	+	15.9233i	0.149752	+	0.656107i
$590$	3.05798	+	3.83459i	0.125895	+	0.157867i
$591$	−5.97511	+	26.1787i	−0.245783	+	1.07685i
$592$	−14.7501			−0.606227
$593$	2.27138	−	9.95156i	0.0932743	−	0.408662i	−0.906638	−	0.421910i	$-0.861360\pi$
$593$	2.27138	−	9.95156i	0.0932743	−	0.408662i	0.999912	+	0.0132481i	$0.00421711\pi$
$594$	7.76407	−	3.73898i	0.318564	−	0.153412i
$595$	3.55893	−	1.71389i	0.145902	−	0.0702626i
$596$	−8.05007	+	35.2697i	−0.329744	+	1.44470i
$597$	59.7483			2.44534
$598$	0.308901	−	1.35338i	0.0126319	−	0.0553439i
$599$	−11.7055	−	14.6783i	−0.478274	−	0.599737i	0.482901	−	0.875675i	$-0.339583\pi$
$599$	−11.7055	−	14.6783i	−0.478274	−	0.599737i	−0.961176	+	0.275938i	$0.911012\pi$
$600$	−0.163996	−	0.718516i	−0.00669513	−	0.0293333i
$601$	−9.08127	−	39.7876i	−0.370433	−	1.62297i	−0.725564	−	0.688155i	$-0.758421\pi$
$601$	−9.08127	−	39.7876i	−0.370433	−	1.62297i	0.355131	−	0.934817i	$-0.384436\pi$
$602$	−4.57145	+	5.73242i	−0.186318	+	0.233636i
$603$	9.04709	−	4.35685i	0.368426	−	0.177425i
$604$	31.3732	+	15.1085i	1.27656	+	0.614757i
$605$	19.3541	+	24.2693i	0.786857	+	0.986687i
$606$	0.836411	−	1.04883i	0.0339769	−	0.0426057i
$607$	10.5448	+	5.07809i	0.427999	+	0.206113i	0.635467	−	0.772128i	$-0.280808\pi$
$607$	10.5448	+	5.07809i	0.427999	+	0.206113i	−0.207467	+	0.978242i	$0.566522\pi$
$608$	−30.3616			−1.23133
$609$		0			0
$610$	−6.12419			−0.247961
$611$	−8.13241	−	3.91636i	−0.329002	−	0.158439i
$612$	−6.34180	+	7.95237i	−0.256352	+	0.321455i
$613$	8.64754	+	10.8437i	0.349271	+	0.437972i	0.925172	−	0.379547i	$-0.123920\pi$
$613$	8.64754	+	10.8437i	0.349271	+	0.437972i	−0.575901	+	0.817519i	$0.695349\pi$
$614$	13.1242	+	6.32027i	0.529649	+	0.255065i
$615$	10.2044	−	4.91416i	0.411480	−	0.198158i
$616$	7.77177	−	9.74550i	0.313134	−	0.392657i
$617$	−5.61426	−	24.5977i	−0.226021	−	0.990265i	−0.952849	−	0.303445i	$-0.901863\pi$
$617$	−5.61426	−	24.5977i	−0.226021	−	0.990265i	0.726828	−	0.686820i	$-0.240994\pi$
$618$	2.38230	+	10.4375i	0.0958301	+	0.419859i
$619$	18.0210	+	22.5976i	0.724325	+	0.908275i	0.998574	−	0.0533840i	$-0.0170007\pi$
$619$	18.0210	+	22.5976i	0.724325	+	0.908275i	−0.274249	+	0.961659i	$0.588429\pi$
$620$	−2.33956	+	10.2503i	−0.0939589	+	0.411661i
$621$	−2.91215			−0.116860
$622$	2.48094	−	10.8697i	0.0994768	−	0.435836i
$623$	−13.9986	+	6.74136i	−0.560841	+	0.270087i
$624$	19.0304	−	9.16456i	0.761826	−	0.366876i
$625$	5.39913	−	23.6551i	0.215965	−	0.946206i
$626$	12.2331			0.488934
$627$	−17.8617	+	78.2571i	−0.713327	+	3.12529i
$628$	−12.7797	−	16.0253i	−0.509967	−	0.639479i
$629$	1.80728	+	7.91821i	0.0720609	+	0.315720i
$630$	−1.38737	−	6.07845i	−0.0552740	−	0.242171i
$631$	9.78694	−	12.2724i	0.389612	−	0.488558i	−0.547884	−	0.836554i	$-0.684566\pi$
$631$	9.78694	−	12.2724i	0.389612	−	0.488558i	0.937496	+	0.347996i	$0.113138\pi$
$632$	3.64418	−	1.75495i	0.144958	−	0.0698080i
$633$	−17.7342	−	8.54035i	−0.704872	−	0.339449i
$634$	2.98124	+	3.73836i	0.118400	+	0.148469i
$635$	−7.57953	+	9.50443i	−0.300784	+	0.377172i
$636$	24.4756	+	11.7868i	0.970520	+	0.467378i
$637$	−16.6450			−0.659499
$638$		0			0
$639$	−66.2544			−2.62098
$640$	−22.6849	−	10.9245i	−0.896698	−	0.431827i
$641$	20.2918	−	25.4452i	0.801480	−	1.00502i	−0.198211	−	0.980159i	$-0.563513\pi$
$641$	20.2918	−	25.4452i	0.801480	−	1.00502i	0.999691	−	0.0248642i	$-0.00791535\pi$
$642$	−4.67709	−	5.86488i	−0.184590	−	0.231468i
$643$	−22.1327	−	10.6586i	−0.872830	−	0.420333i	−0.0568293	−	0.998384i	$-0.518099\pi$
$643$	−22.1327	−	10.6586i	−0.872830	−	0.420333i	−0.816000	+	0.578051i	$0.803813\pi$
$644$	−1.76493	+	0.849944i	−0.0695479	+	0.0334925i
$645$	40.7497	−	51.0986i	1.60452	−	2.01200i
$646$	0.932154	+	4.08403i	0.0366751	+	0.160684i
$647$	−2.89762	−	12.6953i	−0.113917	−	0.499104i	−0.999407	−	0.0344444i	$-0.989034\pi$
$647$	−2.89762	−	12.6953i	−0.113917	−	0.499104i	0.885489	−	0.464660i	$-0.153823\pi$
$648$	−4.39534	−	5.51158i	−0.172665	−	0.216515i
$649$	−4.85147	+	21.2557i	−0.190437	+	0.834359i
$650$	0.229729			0.00901071
$651$	2.14068	−	9.37892i	0.0838997	−	0.367589i
$652$	3.92647	−	1.89089i	0.153772	−	0.0740529i
$653$	−26.9922	+	12.9988i	−1.05629	+	0.508681i	−0.879663	−	0.475597i	$-0.842232\pi$
$653$	−26.9922	+	12.9988i	−1.05629	+	0.508681i	−0.176624	+	0.984278i	$0.556518\pi$
$654$	2.41732	−	10.5910i	0.0945247	−	0.414140i
$655$	0.0623513			0.00243627
$656$	−1.06182	+	4.65215i	−0.0414572	+	0.181636i
$657$	−8.99976	−	11.2853i	−0.351114	−	0.440283i
$658$	−0.426110	−	1.86691i	−0.0166115	−	0.0727797i
$659$	3.16010	+	13.8453i	0.123100	+	0.539336i	0.998440	+	0.0558290i	$0.0177802\pi$
$659$	3.16010	+	13.8453i	0.123100	+	0.539336i	−0.875340	+	0.483507i	$0.839363\pi$
$660$	−32.2169	+	40.3988i	−1.25404	+	1.57252i
$661$	−36.3824	+	17.5209i	−1.41511	+	0.681482i	−0.976165	−	0.217031i	$-0.930363\pi$
$661$	−36.3824	+	17.5209i	−1.41511	+	0.681482i	−0.438947	+	0.898513i	$0.644649\pi$
$662$	4.72020	+	2.27313i	0.183456	+	0.0883477i
$663$	−7.25147	−	9.09306i	−0.281624	−	0.353145i
$664$	7.57829	−	9.50287i	0.294095	−	0.368783i
$665$	15.3883	+	7.41063i	0.596734	+	0.287372i
$666$	12.8193			0.496739
$667$		0			0
$668$	4.64368			0.179669
$669$	13.3429	+	6.42560i	0.515866	+	0.248428i
$670$	1.65984	−	2.08137i	0.0641251	−	0.0804104i
$671$	−16.9737	−	21.2843i	−0.655261	−	0.821671i
$672$	16.1122	+	7.75924i	0.621543	+	0.299319i
$673$	36.7542	−	17.6999i	1.41677	−	0.682281i	0.440285	−	0.897858i	$-0.354878\pi$
$673$	36.7542	−	17.6999i	1.41677	−	0.682281i	0.976487	+	0.215577i	$0.0691632\pi$
$674$	−5.08221	+	6.37289i	−0.195760	+	0.245475i
$675$	−0.107239	−	0.469843i	−0.00412762	−	0.0180843i
$676$	−1.22024	−	5.34624i	−0.0469325	−	0.205625i
$677$	−12.8368	−	16.0969i	−0.493360	−	0.618654i	0.471357	−	0.881942i	$-0.343764\pi$
$677$	−12.8368	−	16.0969i	−0.493360	−	0.618654i	−0.964717	+	0.263289i	$0.915193\pi$
$678$	−5.29960	+	23.2191i	−0.203530	+	0.891723i
$679$	−14.8742			−0.570818
$680$	−1.29032	+	5.65327i	−0.0494816	+	0.216793i
$681$	38.2106	−	18.4012i	1.46423	−	0.705137i
$682$	6.33056	−	3.04864i	0.242410	−	0.116738i
$683$	−2.81208	+	12.3205i	−0.107601	+	0.471432i	0.892203	+	0.451635i	$0.149159\pi$
$683$	−2.81208	+	12.3205i	−0.107601	+	0.471432i	−0.999804	+	0.0197967i	$0.993698\pi$
$684$	−43.9801			−1.68162
$685$	3.01822	−	13.2237i	0.115320	−	0.505251i
$686$	−5.10702	−	6.40400i	−0.194987	−	0.244506i
$687$	−8.88673	−	38.9353i	−0.339050	−	1.48547i
$688$	6.12733	+	26.8456i	0.233602	+	1.02348i
$689$	−11.3530	+	14.2362i	−0.432516	+	0.542358i
$690$	−2.36521	+	1.13903i	−0.0900420	+	0.0433620i
$691$	19.9271	+	9.59637i	0.758061	+	0.365063i	0.772651	−	0.634830i	$-0.218930\pi$
$691$	19.9271	+	9.59637i	0.758061	+	0.365063i	−0.0145902	+	0.999894i	$0.504644\pi$
$692$	−25.5807	−	32.0772i	−0.972434	−	1.21939i
$693$	17.2801	−	21.6686i	0.656418	−	0.823122i
$694$	16.9476	+	8.16152i	0.643321	+	0.309807i
$695$	27.3453			1.03726
$696$		0			0
$697$	2.62748			0.0995229
$698$	14.9654	+	7.20697i	0.566449	+	0.272788i
$699$	26.6704	−	33.4436i	1.00877	−	1.26495i
$700$	−0.202122	−	0.253453i	−0.00763950	−	0.00957963i
$701$	−1.97108	−	0.949223i	−0.0744467	−	0.0358516i	0.396290	−	0.918125i	$-0.370298\pi$
$701$	−1.97108	−	0.949223i	−0.0744467	−	0.0358516i	−0.470737	+	0.882274i	$0.656012\pi$
$702$	−4.86415	+	2.34245i	−0.183586	+	0.0884102i
$703$	−21.8956	+	27.4562i	−0.825807	+	1.03553i
$704$	−2.66609	−	11.6809i	−0.100482	−	0.440240i
$705$	3.79833	+	16.6416i	0.143053	+	0.626758i
$706$	3.83059	+	4.80341i	0.144166	+	0.180779i
$707$	0.282351	−	1.23706i	0.0106189	−	0.0465245i
$708$	−20.3780			−0.765852
$709$	−6.63065	+	29.0508i	−0.249019	+	1.09102i	0.683513	+	0.729938i	$0.260451\pi$
$709$	−6.63065	+	29.0508i	−0.249019	+	1.09102i	−0.932532	+	0.361086i	$0.882406\pi$
$710$	−15.8257	+	7.62124i	−0.593926	+	0.286020i
$711$	8.10265	−	3.90203i	0.303873	−	0.146338i
$712$	5.07531	−	22.2364i	0.190205	−	0.833344i
$713$	−2.37446			−0.0889244
$714$	0.549046	−	2.40553i	0.0205475	−	0.0900246i
$715$	−21.5945	−	27.0786i	−0.807588	−	1.01268i
$716$	−8.10837	−	35.5251i	−0.303024	−	1.32763i
$717$	5.63198	+	24.6753i	0.210330	+	0.921517i
$718$	1.24592	−	1.56233i	0.0464972	−	0.0583057i
$719$	−7.32614	+	3.52808i	−0.273219	+	0.131575i	−0.565477	−	0.824764i	$-0.691308\pi$
$719$	−7.32614	+	3.52808i	−0.273219	+	0.131575i	0.292258	+	0.956340i	$0.405593\pi$
$720$	−21.0963	−	10.1594i	−0.786211	−	0.378619i
$721$	6.31368	+	7.91710i	0.235134	+	0.294848i
$722$	−5.23675	+	6.56668i	−0.194892	+	0.244387i
$723$	−25.3272	−	12.1969i	−0.941930	−	0.453609i
$724$	−15.8108			−0.587604
$725$		0			0
$726$	19.3898			0.719621
$727$	9.19352	+	4.42737i	0.340969	+	0.164202i	0.596530	−	0.802591i	$-0.296546\pi$
$727$	9.19352	+	4.42737i	0.340969	+	0.164202i	−0.255561	+	0.966793i	$0.582260\pi$
$728$	−4.86898	+	6.10551i	−0.180456	+	0.226285i
$729$	−26.7219	−	33.5082i	−0.989701	−	1.24105i
$730$	−3.44785	−	1.66040i	−0.127611	−	0.0614541i
$731$	13.6606	−	6.57858i	0.505254	−	0.243317i
$732$	15.8648	−	19.8938i	0.586380	−	0.735297i
$733$	−5.48731	−	24.0415i	−0.202679	−	0.887993i	−0.969298	−	0.245891i	$-0.920920\pi$
$733$	−5.48731	−	24.0415i	−0.202679	−	0.887993i	0.766619	−	0.642102i	$-0.221938\pi$
$734$	1.45475	+	6.37369i	0.0536960	+	0.235257i
$735$	19.6257	+	24.6099i	0.723905	+	0.907748i
$736$	0.982205	−	4.30332i	0.0362046	−	0.158623i
$737$	11.8341			0.435913
$738$	0.922828	−	4.04318i	0.0339698	−	0.148831i
$739$	−3.75853	+	1.81001i	−0.138260	+	0.0665823i	−0.501734	−	0.865022i	$-0.667305\pi$
$739$	−3.75853	+	1.81001i	−0.138260	+	0.0665823i	0.363475	+	0.931604i	$0.381590\pi$
$740$	−20.3676	+	9.80852i	−0.748728	+	0.360568i
$741$	11.1903	−	49.0277i	0.411084	−	1.80108i
$742$	−3.86299			−0.141815
$743$	−0.622733	+	2.72837i	−0.0228459	+	0.100094i	−0.985065	−	0.172180i	$-0.944919\pi$
$743$	−0.622733	+	2.72837i	−0.0228459	+	0.100094i	0.962220	+	0.272275i	$0.0877759\pi$
$744$	8.80496	+	11.0411i	0.322806	+	0.404785i
$745$	10.2040	+	44.7067i	0.373846	+	1.63793i
$746$	2.84259	+	12.4542i	0.104075	+	0.455980i
$747$	16.8499	−	21.1291i	0.616506	−	0.773075i
$748$	−10.8001	+	5.20105i	−0.394891	+	0.190169i
$749$	−6.39269	−	3.07856i	−0.233584	−	0.112488i
$750$	−9.72839	−	12.1990i	−0.355231	−	0.445445i
$751$	9.16581	−	11.4936i	0.334465	−	0.419406i	−0.585951	−	0.810347i	$-0.699279\pi$
$751$	9.16581	−	11.4936i	0.334465	−	0.419406i	0.920416	+	0.390941i	$0.127850\pi$
$752$	−6.47942	−	3.12032i	−0.236280	−	0.113786i
$753$	39.8019			1.45046
$754$		0			0
$755$	44.1387			1.60637
$756$	6.86399	+	3.30552i	0.249641	+	0.120221i
$757$	−14.3004	+	17.9321i	−0.519755	+	0.651753i	−0.970557	−	0.240872i	$-0.922567\pi$
$757$	−14.3004	+	17.9321i	−0.519755	+	0.651753i	0.450802	+	0.892624i	$0.351138\pi$
$758$	−4.15514	−	5.21038i	−0.150921	−	0.189249i
$759$	−10.5140	−	5.06327i	−0.381633	−	0.183785i
$760$	−22.5897	+	10.8786i	−0.819413	+	0.394608i
$761$	−7.86979	+	9.86841i	−0.285280	+	0.357729i	−0.903736	−	0.428089i	$-0.859187\pi$
$761$	−7.86979	+	9.86841i	−0.285280	+	0.357729i	0.618457	+	0.785819i	$0.287758\pi$
$762$	1.68971	+	7.40310i	0.0612117	+	0.268186i
$763$	−2.28645	−	10.0176i	−0.0827751	−	0.362662i
$764$	20.8889	+	26.1938i	0.755733	+	0.947659i
$765$	−2.86896	+	12.5698i	−0.103728	+	0.454460i
$766$	−12.2880			−0.443985
$767$	3.03943	−	13.3166i	0.109747	−	0.480834i
$768$	−2.56341	+	1.23447i	−0.0924991	+	0.0445452i
$769$	3.17809	−	1.53049i	0.114605	−	0.0551908i	−0.375703	−	0.926740i	$-0.622599\pi$
$769$	3.17809	−	1.53049i	0.114605	−	0.0551908i	0.490308	+	0.871549i	$0.336884\pi$
$770$	1.63503	−	7.16353i	0.0589224	−	0.258156i
$771$	−4.65956			−0.167810
$772$	−2.05744	+	9.01425i	−0.0740490	+	0.324430i
$773$	16.3402	+	20.4899i	0.587716	+	0.736972i	0.983407	−	0.181411i	$-0.0580665\pi$
$773$	16.3402	+	20.4899i	0.587716	+	0.736972i	−0.395692	+	0.918383i	$0.629495\pi$
$774$	−5.32525	−	23.3315i	−0.191412	−	0.838632i
$775$	−0.0874388	−	0.383094i	−0.00314089	−	0.0137612i
$776$	13.6138	−	17.0712i	0.488708	−	0.612820i
$777$	18.6362	−	8.97472i	0.668570	−	0.321966i
$778$	−8.14003	−	3.92003i	−0.291834	−	0.140540i
$779$	7.08339	+	8.88229i	0.253789	+	0.318241i
$780$	20.1838	−	25.3096i	0.722694	−	0.906230i
$781$	−70.3492	−	33.8784i	−2.51729	−	1.21226i
$782$	−0.609008			−0.0217781
$783$		0			0
$784$	−13.2617			−0.473634
$785$	−23.4085	−	11.2729i	−0.835485	−	0.402348i
$786$	0.0242830	−	0.0304500i	0.000866147	−	0.00108611i
$787$	−11.2304	−	14.0824i	−0.400319	−	0.501984i	0.540289	−	0.841480i	$-0.318315\pi$
$787$	−11.2304	−	14.0824i	−0.400319	−	0.501984i	−0.940608	+	0.339496i	$0.889744\pi$
$788$	−15.6215	−	7.52293i	−0.556494	−	0.267993i
$789$	−32.8252	+	15.8078i	−1.16861	+	0.562772i
$790$	1.48656	−	1.86409i	0.0528896	−	0.0663214i
$791$	5.01270	+	21.9621i	0.178231	+	0.780881i
$792$	9.05329	+	39.6651i	0.321695	+	1.40944i
$793$	10.6339	+	13.3345i	0.377622	+	0.473523i
$794$	3.44169	−	15.0790i	0.122141	−	0.535134i
$795$	34.4345			1.22127
$796$	−8.58491	+	37.6129i	−0.304284	+	1.33316i
$797$	−31.5103	+	15.1746i	−1.11615	+	0.537511i	−0.898702	−	0.438560i	$-0.855489\pi$
$797$	−31.5103	+	15.1746i	−1.11615	+	0.537511i	−0.217452	+	0.976071i	$0.569774\pi$
$798$	9.61214	−	4.62896i	0.340266	−	0.163863i
$799$	−0.881162	+	3.86062i	−0.0311733	+	0.136579i
$800$	0.730464			0.0258258
$801$	11.2847	−	49.4415i	0.398725	−	1.74693i
$802$	3.93903	+	4.93939i	0.139092	+	0.174416i
$803$	−3.78536	−	16.5847i	−0.133582	−	0.585263i
$804$	2.46129	+	10.7836i	0.0868032	+	0.380309i
$805$	−1.54817	+	1.94134i	−0.0545657	+	0.0684232i
$806$	−3.96607	+	1.90996i	−0.139699	+	0.0672753i
$807$	−72.5089	−	34.9185i	−2.55243	−	1.22919i
$808$	1.16136	+	1.45630i	0.0408564	+	0.0512323i
$809$	23.8557	−	29.9141i	0.838723	−	1.05173i	−0.159196	−	0.987247i	$-0.550890\pi$
$809$	23.8557	−	29.9141i	0.838723	−	1.05173i	0.997919	−	0.0644781i	$-0.0205383\pi$
$810$	−3.74401	−	1.80302i	−0.131551	−	0.0633517i
$811$	31.7116			1.11354			0.556772	−	0.830665i	$-0.312040\pi$
$811$	31.7116			1.11354			0.556772	+	0.830665i	$0.312040\pi$
$812$		0			0
$813$	25.2130			0.884260
$814$	13.6116	+	6.55500i	0.477087	+	0.229753i
$815$	3.44423	−	4.31893i	0.120646	−	0.151286i
$816$	−5.77753	−	7.24480i	−0.202254	−	0.253619i
$817$	59.0664	+	28.4449i	2.06647	+	0.995161i
$818$	−2.81303	+	1.35468i	−0.0983553	+	0.0473654i
$819$	−10.8259	+	13.5753i	−0.378288	+	0.474358i
$820$	1.62737	+	7.12997i	0.0568302	+	0.248989i
$821$	4.78154	+	20.9493i	0.166877	+	0.731135i	0.987233	+	0.159282i	$0.0509181\pi$
$821$	4.78154	+	20.9493i	0.166877	+	0.731135i	−0.820356	+	0.571853i	$0.806225\pi$
$822$	−5.28247	−	6.62401i	−0.184247	−	0.231039i
$823$	1.98107	−	8.67963i	0.0690558	−	0.302553i	−0.928592	−	0.371102i	$-0.878980\pi$
$823$	1.98107	−	8.67963i	0.0690558	−	0.302553i	0.997648	+	0.0685493i	$0.0218370\pi$
$824$	−14.8652			−0.517854
$825$	0.429730	−	1.88277i	0.0149613	−	0.0655497i
$826$	2.61079	−	1.25729i	0.0908409	−	0.0437467i
$827$	24.7172	−	11.9032i	0.859503	−	0.413915i	0.0484067	−	0.998828i	$-0.484586\pi$
$827$	24.7172	−	11.9032i	0.859503	−	0.413915i	0.811096	+	0.584913i	$0.198871\pi$
$828$	1.42276	−	6.23354i	0.0494445	−	0.216630i
$829$	−40.4211			−1.40388			−0.701942	−	0.712234i	$-0.747683\pi$
$829$	−40.4211			−1.40388			−0.701942	+	0.712234i	$0.747683\pi$
$830$	1.59432	−	6.98519i	0.0553398	−	0.242459i
$831$	−37.6420	−	47.2016i	−1.30579	−	1.63741i
$832$	1.67029	+	7.31802i	0.0579069	+	0.253707i
$833$	1.62491	+	7.11920i	0.0562999	+	0.246666i
$834$	10.6498	−	13.3544i	0.368771	−	0.462424i
$835$	5.30326	−	2.55392i	0.183527	−	0.0883819i
$836$	−46.6982	−	22.4887i	−1.61509	−	0.777787i
$837$	5.75764	+	7.21985i	0.199013	+	0.249555i
$838$	−3.70003	+	4.63969i	−0.127815	+	0.160275i
$839$	−7.30269	−	3.51679i	−0.252117	−	0.121413i	0.303557	−	0.952813i	$-0.401826\pi$
$839$	−7.30269	−	3.51679i	−0.252117	−	0.121413i	−0.555674	+	0.831400i	$0.687540\pi$
$840$	14.7680			0.509543
$841$		0			0
$842$	10.3717			0.357432
$843$	−21.1347	−	10.1779i	−0.727916	−	0.350546i
$844$	7.92448	−	9.93698i	0.272772	−	0.342045i
$845$	−4.33388	−	5.43451i	−0.149090	−	0.186953i
$846$	5.63126	+	2.71187i	0.193607	+	0.0932360i
$847$	16.5238	−	7.95744i	0.567765	−	0.273421i
$848$	−9.04541	+	11.3426i	−0.310620	+	0.389506i
$849$	−8.66257	−	37.9532i	−0.297299	−	1.30255i
$850$	−0.0224265	−	0.0982569i	−0.000769223	−	0.00337018i
$851$	−3.18319	−	3.99159i	−0.109118	−	0.136830i
$852$	16.2397	−	71.1510i	0.556364	−	2.43759i
$853$	−12.7043			−0.434988			−0.217494	−	0.976062i	$-0.569788\pi$
$853$	−12.7043			−0.434988			−0.217494	+	0.976062i	$0.569788\pi$
$854$	−0.805148	+	3.52759i	−0.0275516	+	0.120711i
$855$	−50.2269	+	24.1880i	−1.71772	+	0.827212i
$856$	9.38429	−	4.51924i	0.320749	−	0.154464i
$857$	10.2847	−	45.0600i	0.351317	−	1.53922i	−0.422826	−	0.906211i	$-0.638962\pi$
$857$	10.2847	−	45.0600i	0.351317	−	1.53922i	0.774143	−	0.633011i	$-0.218181\pi$
$858$	−21.6343			−0.738581
$859$	1.34676	−	5.90054i	0.0459508	−	0.201324i	−0.946742	−	0.321994i	$-0.895647\pi$
$859$	1.34676	−	5.90054i	0.0459508	−	0.201324i	0.992693	+	0.120670i	$0.0385042\pi$
$860$	26.3126	+	32.9950i	0.897252	+	1.12512i
$861$	−1.48903	−	6.52387i	−0.0507460	−	0.222333i
$862$	1.93215	+	8.46532i	0.0658094	+	0.288330i
$863$	−8.18740	+	10.2667i	−0.278702	+	0.349482i	−0.901405	−	0.432977i	$-0.857463\pi$
$863$	−8.18740	+	10.2667i	−0.278702	+	0.349482i	0.622703	+	0.782458i	$0.286035\pi$
$864$	−15.4664	+	7.44825i	−0.526179	+	0.253394i
$865$	−46.8559	−	22.5646i	−1.59315	−	0.767220i
$866$	5.07957	+	6.36957i	0.172611	+	0.216447i
$867$	25.3580	−	31.7980i	0.861204	−	1.07992i
$868$	5.59666	+	2.69521i	0.189963	+	0.0914814i
$869$	10.5987			0.359536
$870$		0			0
$871$	−7.41398			−0.251213
$872$	13.5900	+	6.54459i	0.460215	+	0.221628i
$873$	30.2696	−	37.9569i	1.02447	−	1.28465i
$874$	−1.64182	−	2.05877i	−0.0555353	−	0.0696391i
$875$	−13.2969	−	6.40344i	−0.449516	−	0.216476i
$876$	14.3253	−	6.89872i	0.484008	−	0.233086i
$877$	19.1884	−	24.0615i	0.647946	−	0.812499i	−0.344025	−	0.938960i	$-0.611791\pi$
$877$	19.1884	−	24.0615i	0.647946	−	0.812499i	0.991972	+	0.126461i	$0.0403620\pi$
$878$	−0.614732	−	2.69332i	−0.0207462	−	0.0908950i
$879$	−19.6258	−	85.9861i	−0.661961	−	2.90024i
$880$	−17.2052	−	21.5746i	−0.579987	−	0.727281i
$881$	6.56895	−	28.7805i	0.221314	−	0.969638i	−0.735177	−	0.677875i	$-0.762901\pi$
$881$	6.56895	−	28.7805i	0.221314	−	0.969638i	0.956491	−	0.291763i	$-0.0942419\pi$
$882$	11.5258			0.388093
$883$	−8.01550	+	35.1182i	−0.269743	+	1.18182i	0.640569	+	0.767900i	$0.278698\pi$
$883$	−8.01550	+	35.1182i	−0.269743	+	1.18182i	−0.910313	+	0.413922i	$0.864159\pi$
$884$	6.76621	−	3.25843i	0.227572	−	0.109593i
$885$	−23.2725	+	11.2074i	−0.782295	+	0.376734i
$886$	−2.16738	+	9.49592i	−0.0728146	+	0.319022i
$887$	14.2942			0.479952			0.239976	−	0.970779i	$-0.422860\pi$
$887$	14.2942			0.479952			0.239976	+	0.970779i	$0.422860\pi$
$888$	−6.75672	+	29.6031i	−0.226741	+	0.993417i
$889$	4.47815	+	5.61542i	0.150192	+	0.188335i
$890$	−2.99176	−	13.1078i	−0.100284	−	0.439373i
$891$	−4.11051	−	18.0093i	−0.137707	−	0.603335i
$892$	−5.96223	+	7.47640i	−0.199630	+	0.250328i
$893$	−15.4265	+	7.42900i	−0.516228	+	0.248602i
$894$	25.8070	+	12.4280i	0.863115	+	0.415655i
$895$	−28.7980	−	36.1116i	−0.962612	−	1.20708i
$896$	−9.27496	+	11.6304i	−0.309855	+	0.388545i
$897$	6.58696	+	3.17211i	0.219932	+	0.105914i
$898$	9.04279			0.301762
$899$		0			0
$900$	1.05811			0.0352702
$901$	7.19726	+	3.46602i	0.239775	+	0.115470i
$902$	3.04729	−	3.82118i	0.101464	−	0.127231i
$903$	−24.0758	−	30.1901i	−0.801193	−	1.00466i
$904$	−29.7940	−	14.3480i	−0.990932	−	0.477208i
$905$	−18.0565	+	8.69557i	−0.600220	+	0.289051i
$906$	17.1901	−	21.5556i	0.571101	−	0.716138i
$907$	−4.48370	−	19.6444i	−0.148879	−	0.652281i	−0.993198	−	0.116440i	$-0.962852\pi$
$907$	−4.48370	−	19.6444i	−0.148879	−	0.652281i	0.844319	−	0.535841i	$-0.180005\pi$
$908$	6.09373	+	26.6984i	0.202228	+	0.886017i
$909$	2.58222	+	3.23800i	0.0856467	+	0.107398i
$910$	−1.02434	+	4.48792i	−0.0339565	+	0.148773i
$911$	18.4045			0.609769			0.304885	−	0.952389i	$-0.401382\pi$
$911$	18.4045			0.609769			0.304885	+	0.952389i	$0.401382\pi$
$912$	8.91572	−	39.0623i	0.295229	−	1.29348i
$913$	28.6954	−	13.8190i	0.949680	−	0.457342i
$914$	−6.95452	+	3.34912i	−0.230035	+	0.110779i
$915$	7.17707	−	31.4448i	0.237266	−	1.03953i
$916$	25.7875			0.852044
$917$	0.00819733	−	0.0359149i	0.000270700	−	0.00118601i
$918$	1.47673	+	1.85176i	0.0487394	+	0.0611173i
$919$	−1.18329	−	5.18431i	−0.0390330	−	0.171015i	0.951654	−	0.307171i	$-0.0993823\pi$
$919$	−1.18329	−	5.18431i	−0.0390330	−	0.171015i	−0.990687	+	0.136156i	$0.956525\pi$
$920$	−0.811104	−	3.55368i	−0.0267413	−	0.117161i
$921$	−47.8320	+	59.9795i	−1.57612	+	1.97639i
$922$	10.2728	−	4.94710i	0.338316	−	0.162924i
$923$	44.0734	+	21.2247i	1.45070	+	0.698618i
$924$	19.0345	+	23.8684i	0.626188	+	0.785214i
$925$	0.526781	−	0.660562i	0.0173204	−	0.0217191i
$926$	−12.3167	−	5.93140i	−0.404751	−	0.194918i
$927$	−33.0520			−1.08557
$928$		0			0
$929$	−1.90689			−0.0625630			−0.0312815	−	0.999511i	$-0.509959\pi$
$929$	−1.90689			−0.0625630			−0.0312815	+	0.999511i	$0.509959\pi$
$930$	7.50018	+	3.61190i	0.245941	+	0.118439i
$931$	−19.6861	+	24.6857i	−0.645187	+	0.809040i
$932$	17.2214	+	21.5950i	0.564106	+	0.707366i
$933$	52.9033	+	25.4769i	1.73198	+	0.834076i
$934$	−5.32541	+	2.56458i	−0.174253	+	0.0839156i
$935$	−9.47367	+	11.8796i	−0.309822	+	0.388504i
$936$	−5.67184	−	24.8500i	−0.185390	−	0.812247i
$937$	0.750582	+	3.28851i	0.0245204	+	0.107431i	0.985707	−	0.168467i	$-0.0538818\pi$
$937$	0.750582	+	3.28851i	0.0245204	+	0.107431i	−0.961187	+	0.275898i	$0.911025\pi$
$938$	−0.980668	−	1.22972i	−0.0320199	−	0.0401517i
$939$	−14.3362	+	62.8112i	−0.467846	+	2.04977i
$940$	−11.0220			−0.359498
$941$	4.41270	−	19.3333i	0.143850	−	0.630248i	−0.850670	−	0.525700i	$-0.823803\pi$
$941$	4.41270	−	19.3333i	0.143850	−	0.630248i	0.994520	−	0.104548i	$-0.0333395\pi$
$942$	−14.6218	+	7.04150i	−0.476405	+	0.229424i
$943$	−1.48808	+	0.716624i	−0.0484587	+	0.0233365i
$944$	2.42163	−	10.6099i	0.0788174	−	0.345322i
$945$	9.65689			0.314139
$946$	6.27588	−	27.4964i	0.204047	−	0.893986i
$947$	−25.2605	−	31.6756i	−0.820855	−	1.02932i	−0.998973	−	0.0453108i	$-0.985572\pi$
$947$	−25.2605	−	31.6756i	−0.820855	−	1.02932i	0.178118	−	0.984009i	$-0.442999\pi$
$948$	2.20435	+	9.65791i	0.0715941	+	0.313674i
$949$	2.37151	+	10.3903i	0.0769824	+	0.337282i
$950$	0.271702	−	0.340703i	0.00881517	−	0.0110539i
$951$	−22.6884	+	10.9262i	−0.735723	+	0.354306i
$952$	3.08669	+	1.48647i	0.100040	+	0.0481769i
$953$	−1.46017	−	1.83099i	−0.0472994	−	0.0593116i	0.757619	−	0.652697i	$-0.226362\pi$
$953$	−1.46017	−	1.83099i	−0.0472994	−	0.0593116i	−0.804919	+	0.593385i	$0.797791\pi$
$954$	7.86135	−	9.85782i	0.254521	−	0.319159i
$955$	38.2619	+	18.4259i	1.23812	+	0.596249i
$956$	−16.3429			−0.528567
$957$		0			0
$958$	12.4378			0.401848
$959$	−7.22014	−	3.47704i	−0.233150	−	0.112279i
$960$	8.85040	−	11.0980i	0.285645	−	0.358188i
$961$	−14.6336	−	18.3500i	−0.472052	−	0.591934i
$962$	−8.52761	−	4.10668i	−0.274941	−	0.132405i
$963$	20.8655	−	10.0483i	0.672381	−	0.323802i
$964$	11.3174	−	14.1916i	0.364508	−	0.457079i
$965$	2.60795	+	11.4262i	0.0839528	+	0.367821i
$966$	0.345134	+	1.51213i	0.0111045	+	0.0486519i
$967$	−8.24797	−	10.3426i	−0.265237	−	0.332596i	0.631322	−	0.775521i	$-0.282513\pi$
$967$	−8.24797	−	10.3426i	−0.265237	−	0.332596i	−0.896559	+	0.442924i	$0.853941\pi$
$968$	−5.99086	+	26.2477i	−0.192553	+	0.843632i
$969$	−22.0620			−0.708732
$970$	2.86408	−	12.5484i	0.0919601	−	0.402904i
$971$	18.5961	−	8.95543i	0.596778	−	0.287393i	−0.111008	−	0.993819i	$-0.535408\pi$
$971$	18.5961	−	8.95543i	0.596778	−	0.287393i	0.707787	+	0.706426i	$0.249694\pi$
$972$	31.3707	−	15.1073i	1.00622	−	0.484568i
$973$	3.59509	−	15.7511i	0.115253	−	0.504957i
$974$	−0.657928			−0.0210814
$975$	−0.269224	+	1.17955i	−0.00862207	+	0.0377757i
$976$	8.47247	+	10.6241i	0.271197	+	0.340070i
$977$	0.601379	+	2.63481i	0.0192398	+	0.0842952i	0.983636	−	0.180165i	$-0.0576633\pi$
$977$	0.601379	+	2.63481i	0.0192398	+	0.0842952i	−0.964397	+	0.264460i	$0.914806\pi$
$978$	−0.767825	−	3.36406i	−0.0245523	−	0.107571i
$979$	37.2634	−	46.7269i	1.19094	−	1.49340i
$980$	−18.3124	+	8.81877i	−0.584967	+	0.281705i
$981$	30.2166	+	14.5516i	0.964742	+	0.464595i
$982$	10.4103	+	13.0541i	0.332206	+	0.416573i
$983$	−9.09394	+	11.4034i	−0.290052	+	0.363713i	−0.905413	−	0.424532i	$-0.860439\pi$
$983$	−9.09394	+	11.4034i	−0.290052	+	0.363713i	0.615361	+	0.788245i	$0.289010\pi$
$984$	8.85034	+	4.26210i	0.282139	+	0.135871i
$985$	−21.9778			−0.700272
$986$		0			0
$987$	10.0850			0.321011
$988$	29.2562	+	14.0890i	0.930764	+	0.448232i
$989$	−5.94246	+	7.45161i	−0.188959	+	0.236948i
$990$	14.9530	+	18.7505i	0.475238	+	0.595930i
$991$	−20.1359	−	9.69695i	−0.639639	−	0.308034i	0.0858084	−	0.996312i	$-0.472653\pi$
$991$	−20.1359	−	9.69695i	−0.639639	−	0.308034i	−0.725447	+	0.688278i	$0.758367\pi$
$992$	−12.6108	+	6.07305i	−0.400394	+	0.192819i
$993$	−17.2031	+	21.5720i	−0.545925	+	0.684568i
$994$	2.30929	+	10.1177i	0.0732463	+	0.320913i
$995$	10.8819	+	47.6769i	0.344981	+	1.51146i
$996$	18.5606	+	23.2742i	0.588114	+	0.737472i
$997$	−12.1091	+	53.0535i	−0.383499	+	1.68022i	0.302921	+	0.953016i	$0.402038\pi$
$997$	−12.1091	+	53.0535i	−0.383499	+	1.68022i	−0.686421	+	0.727205i	$0.740819\pi$
$998$	5.35958			0.169655
$999$	−4.41828	+	19.3577i	−0.139788	+	0.612452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.o.190.3		36
29.2	odd	28		841.2.e.l.267.7		72
29.3	odd	28		841.2.b.d.840.7		12
29.4	even	14		841.2.d.n.778.3		36
29.5	even	14		841.2.d.n.574.3		36
29.6	even	14		841.2.d.n.605.4		36
29.7	even	7		841.2.a.g.1.4	✓	6
29.8	odd	28		841.2.e.l.270.7		72
29.9	even	14		841.2.d.n.571.4		36
29.10	odd	28		841.2.e.l.63.7		72
29.11	odd	28		841.2.e.l.196.7		72
29.12	odd	4		841.2.e.l.651.6		72
29.13	even	14		841.2.d.n.645.4		36
29.14	odd	28		841.2.e.l.236.6		72
29.15	odd	28		841.2.e.l.236.7		72
29.16	even	7	inner	841.2.d.o.645.3		36
29.17	odd	4		841.2.e.l.651.7		72
29.18	odd	28		841.2.e.l.196.6		72
29.19	odd	28		841.2.e.l.63.6		72
29.20	even	7	inner	841.2.d.o.571.3		36
29.21	odd	28		841.2.e.l.270.6		72
29.22	even	14		841.2.a.h.1.3	yes	6
29.23	even	7	inner	841.2.d.o.605.3		36
29.24	even	7	inner	841.2.d.o.574.4		36
29.25	even	7	inner	841.2.d.o.778.4		36
29.26	odd	28		841.2.b.d.840.6		12
29.27	odd	28		841.2.e.l.267.6		72
29.28	even	2		841.2.d.n.190.4		36
87.65	odd	14		7569.2.a.bc.1.3		6
87.80	odd	14		7569.2.a.y.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.g.1.4	✓	6	29.7	even	7
841.2.a.h.1.3	yes	6	29.22	even	14
841.2.b.d.840.6		12	29.26	odd	28
841.2.b.d.840.7		12	29.3	odd	28
841.2.d.n.190.4		36	29.28	even	2
841.2.d.n.571.4		36	29.9	even	14
841.2.d.n.574.3		36	29.5	even	14
841.2.d.n.605.4		36	29.6	even	14
841.2.d.n.645.4		36	29.13	even	14
841.2.d.n.778.3		36	29.4	even	14
841.2.d.o.190.3		36	1.1	even	1	trivial
841.2.d.o.571.3		36	29.20	even	7	inner
841.2.d.o.574.4		36	29.24	even	7	inner
841.2.d.o.605.3		36	29.23	even	7	inner
841.2.d.o.645.3		36	29.16	even	7	inner
841.2.d.o.778.4		36	29.25	even	7	inner
841.2.e.l.63.6		72	29.19	odd	28
841.2.e.l.63.7		72	29.10	odd	28
841.2.e.l.196.6		72	29.18	odd	28
841.2.e.l.196.7		72	29.11	odd	28
841.2.e.l.236.6		72	29.14	odd	28
841.2.e.l.236.7		72	29.15	odd	28
841.2.e.l.267.6		72	29.27	odd	28
841.2.e.l.267.7		72	29.2	odd	28
841.2.e.l.270.6		72	29.21	odd	28
841.2.e.l.270.7		72	29.8	odd	28
841.2.e.l.651.6		72	29.12	odd	4
841.2.e.l.651.7		72	29.17	odd	4
7569.2.a.y.1.4		6	87.80	odd	14
7569.2.a.bc.1.3		6	87.65	odd	14

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.460625 + 0.221825i) q^{2} +(-1.67878 + 2.10513i) q^{3} +(-1.08401 - 1.35931i) q^{4} +(-1.98557 - 0.956199i) q^{5} +(-1.24026 + 0.597278i) q^{6} +(-0.811822 + 1.01799i) q^{7} +(-0.425324 - 1.86347i) q^{8} +(-0.945686 - 4.14332i) q^{9} +(-0.702494 - 0.880899i) q^{10} +(1.11450 - 4.88296i) q^{11} +4.68133 q^{12} +(-0.698231 + 3.05915i) q^{13} +(-0.599762 + 0.288830i) q^{14} +(5.34626 - 2.57462i) q^{15} +(-0.556308 + 2.43735i) q^{16} +1.37659 q^{17} +(0.483487 - 2.11830i) q^{18} +(3.71112 + 4.65360i) q^{19} +(0.852609 + 3.73552i) q^{20} +(-0.780131 - 3.41798i) q^{21} +(1.59653 - 2.00199i) q^{22} +(-0.779635 + 0.375453i) q^{23} +(4.63686 + 2.23299i) q^{24} +(-0.0892850 - 0.111960i) q^{25} +(-1.00022 + 1.25424i) q^{26} +(3.03208 + 1.46017i) q^{27} +2.26379 q^{28} +3.03374 q^{30} +(2.47226 + 1.19058i) q^{31} +(-3.18038 + 3.98807i) q^{32} +(8.40824 + 10.5436i) q^{33} +(0.634090 + 0.305362i) q^{34} +(2.58533 - 1.24503i) q^{35} +(-4.60691 + 5.77688i) q^{36} +(1.31287 + 5.75206i) q^{37} +(0.677149 + 2.96679i) q^{38} +(-5.26772 - 6.60551i) q^{39} +(-0.937335 + 4.10673i) q^{40} +1.90869 q^{41} +(0.398846 - 1.74746i) q^{42} +(9.92351 - 4.77891i) q^{43} +(-7.84557 + 3.77823i) q^{44} +(-2.08412 + 9.13111i) q^{45} -0.442405 q^{46} +(-0.640107 + 2.80449i) q^{47} +(-4.19700 - 5.26288i) q^{48} +(1.18039 + 5.17164i) q^{49} +(-0.0162914 - 0.0713773i) q^{50} +(-2.31099 + 2.89789i) q^{51} +(4.91521 - 2.36704i) q^{52} +(5.22834 + 2.51784i) q^{53} +(1.07275 + 1.34519i) q^{54} +(-6.88200 + 8.62976i) q^{55} +(2.24228 + 1.07983i) q^{56} -16.0266 q^{57} -4.35304 q^{59} +(-9.29510 - 4.47628i) q^{60} +(3.38895 - 4.24961i) q^{61} +(0.874684 + 1.09682i) q^{62} +(4.98560 + 2.40094i) q^{63} +(2.15528 - 1.03793i) q^{64} +(4.31154 - 5.40650i) q^{65} +(1.53421 + 6.72181i) q^{66} +(0.525768 + 2.30354i) q^{67} +(-1.49223 - 1.87120i) q^{68} +(0.518463 - 2.27154i) q^{69} +1.46705 q^{70} +(3.46904 - 15.1989i) q^{71} +(-7.31872 + 3.52451i) q^{72} +(3.06010 - 1.47367i) q^{73} +(-0.671212 + 2.94077i) q^{74} +0.385580 q^{75} +(2.30277 - 10.0891i) q^{76} +(4.06603 + 5.09865i) q^{77} +(-0.961175 - 4.21118i) q^{78} +(0.470882 + 2.06307i) q^{79} +(3.43518 - 4.30758i) q^{80} +(3.32295 - 1.60025i) q^{81} +(0.879192 + 0.423397i) q^{82} +(3.96481 + 4.97171i) q^{83} +(-3.80041 + 4.76556i) q^{84} +(-2.73330 - 1.31629i) q^{85} +5.63110 q^{86} -9.57325 q^{88} +(10.7511 + 5.17745i) q^{89} +(-2.98551 + 3.74371i) q^{90} +(-2.54735 - 3.19428i) q^{91} +(1.35549 + 0.652769i) q^{92} +(-6.65670 + 3.20570i) q^{93} +(-0.916957 + 1.14983i) q^{94} +(-2.91892 - 12.7886i) q^{95} +(-3.05623 - 13.3902i) q^{96} +(7.12247 + 8.93130i) q^{97} +(-0.603482 + 2.64403i) q^{98} -21.2856 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} + 2 q^{3} - 8 q^{4} + 2 q^{5} + 3 q^{6} + 4 q^{7} + 3 q^{8} - 6 q^{9} + 15 q^{10} + 13 q^{11} + 24 q^{12} + 6 q^{13} - 6 q^{14} + 19 q^{15} - 4 q^{16} - 18 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20}+ \cdots - 36 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 + 2 * q^3 - 8 * q^4 + 2 * q^5 + 3 * q^6 + 4 * q^7 + 3 * q^8 - 6 * q^9 + 15 * q^10 + 13 * q^11 + 24 * q^12 + 6 * q^13 - 6 * q^14 + 19 * q^15 - 4 * q^16 - 18 * q^17 + 17 * q^18 - 6 * q^19 + 5 * q^20 - 2 * q^21 + 4 * q^22 + 5 * q^23 + 10 * q^24 - 6 * q^25 + 9 * q^26 - q^27 - 30 * q^28 + 156 * q^30 + 16 * q^31 + 33 * q^32 - 27 * q^33 + 4 * q^35 + 21 * q^36 - 10 * q^37 - 41 * q^38 + 17 * q^39 + 7 * q^40 - 180 * q^41 + 21 * q^42 - 2 * q^43 + 16 * q^44 - 16 * q^45 + 120 * q^46 + 5 * q^47 - 30 * q^48 + 12 * q^49 - 8 * q^50 + 23 * q^51 + 13 * q^53 - 19 * q^54 + 10 * q^55 + 16 * q^56 - 96 * q^57 - 102 * q^59 - 9 * q^60 - 4 * q^61 + 9 * q^63 - q^64 - 32 * q^65 - 8 * q^66 + 9 * q^67 + 16 * q^68 + 26 * q^69 + 168 * q^70 - 21 * q^72 + 9 * q^73 + 36 * q^74 - 42 * q^75 + 24 * q^76 + 13 * q^77 + 6 * q^79 - 5 * q^80 + 22 * q^81 - 19 * q^82 + 24 * q^83 - 26 * q^85 + 102 * q^86 + 126 * q^88 + 9 * q^89 - 16 * q^90 - 16 * q^91 + 23 * q^92 + 12 * q^93 + 37 * q^94 + 31 * q^95 + 37 * q^96 - 10 * q^97 - 42 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more