LMFDB - Embedded newform 841.2.d.q.571.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(190,841)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			571.4
Character	$\chi$	$=$	841.571
Dual form			841.2.d.q.190.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0377915 + 0.0181994i) q^{2} +(-1.88776 - 2.36718i) q^{3} +(-1.24588 + 1.56229i) q^{4} +(1.56952 - 0.755841i) q^{5} +(0.114422 + 0.0551030i) q^{6} +(1.28043 + 1.60561i) q^{7} +(0.0373185 - 0.163503i) q^{8} +(-1.37232 + 6.01254i) q^{9} +(-0.0455587 + 0.0571287i) q^{10} +(-0.412076 - 1.80542i) q^{11} +6.05014 q^{12} +(-0.573636 - 2.51326i) q^{13} +(-0.0776107 - 0.0373753i) q^{14} +(-4.75209 - 2.28849i) q^{15} +(-0.887735 - 3.88942i) q^{16} -5.23359 q^{17} +(-0.0575626 - 0.252198i) q^{18} +(-0.236328 + 0.296346i) q^{19} +(-0.774597 + 3.39373i) q^{20} +(1.38362 - 6.06202i) q^{21} +(0.0484306 + 0.0607300i) q^{22} +(-3.27095 - 1.57521i) q^{23} +(-0.457489 + 0.220315i) q^{24} +(-1.22535 + 1.53654i) q^{25} +(0.0674185 + 0.0845401i) q^{26} +(8.63967 - 4.16065i) q^{27} -4.10370 q^{28} +0.221238 q^{30} +(2.13135 - 1.02641i) q^{31} +(0.313462 + 0.393069i) q^{32} +(-3.49585 + 4.38366i) q^{33} +(0.197785 - 0.0952483i) q^{34} +(3.22326 + 1.55224i) q^{35} +(-7.68356 - 9.63488i) q^{36} +(-1.46137 + 6.40269i) q^{37} +(0.00353786 - 0.0155004i) q^{38} +(-4.86645 + 6.10234i) q^{39} +(-0.0650102 - 0.284828i) q^{40} -9.44586 q^{41} +(0.0580363 + 0.254274i) q^{42} +(-0.896932 - 0.431940i) q^{43} +(3.33399 + 1.60556i) q^{44} +(2.39064 + 10.4741i) q^{45} +0.152282 q^{46} +(2.26249 + 9.91261i) q^{47} +(-7.53112 + 9.44372i) q^{48} +(0.619164 - 2.71274i) q^{49} +(0.0183436 - 0.0803687i) q^{50} +(9.87976 + 12.3888i) q^{51} +(4.64112 + 2.23505i) q^{52} +(-8.94664 + 4.30848i) q^{53} +(-0.250785 + 0.314474i) q^{54} +(-2.01137 - 2.52218i) q^{55} +(0.310306 - 0.149436i) q^{56} +1.14763 q^{57} -6.24449 q^{59} +(9.49582 - 4.57294i) q^{60} +(4.97874 + 6.24315i) q^{61} +(-0.0618670 + 0.0775788i) q^{62} +(-11.4110 + 5.49523i) q^{63} +(7.16973 + 3.45276i) q^{64} +(-2.79996 - 3.51104i) q^{65} +(0.0523334 - 0.229287i) q^{66} +(0.920842 - 4.03447i) q^{67} +(6.52044 - 8.17637i) q^{68} +(2.44598 + 10.7165i) q^{69} -0.150061 q^{70} +(0.507993 + 2.22566i) q^{71} +(0.931855 + 0.448757i) q^{72} +(-8.16639 - 3.93273i) q^{73} +(-0.0612978 - 0.268563i) q^{74} +5.95042 q^{75} +(-0.168540 - 0.738424i) q^{76} +(2.37117 - 2.97336i) q^{77} +(0.0728514 - 0.319183i) q^{78} +(2.28679 - 10.0191i) q^{79} +(-4.33311 - 5.43354i) q^{80} +(-9.48935 - 4.56983i) q^{81} +(0.356973 - 0.171909i) q^{82} +(-9.73931 + 12.2127i) q^{83} +(7.74680 + 9.71418i) q^{84} +(-8.21423 + 3.95576i) q^{85} +0.0417574 q^{86} -0.310570 q^{88} +(-8.66452 + 4.17261i) q^{89} +(-0.280968 - 0.352322i) q^{90} +(3.30082 - 4.13910i) q^{91} +(6.53614 - 3.14764i) q^{92} +(-6.45317 - 3.10768i) q^{93} +(-0.265906 - 0.333436i) q^{94} +(-0.146931 + 0.643747i) q^{95} +(0.338723 - 1.48404i) q^{96} +(-3.22829 + 4.04814i) q^{97} +(0.0259711 + 0.113787i) q^{98} +11.4207 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{2} + 6 q^{3} - 6 q^{4} + q^{5} - 3 q^{6} + 15 q^{8} - 8 q^{9} - 3 q^{10} + 5 q^{11} - 72 q^{12} + 4 q^{13} + 15 q^{14} - 7 q^{15} + 2 q^{16} - 54 q^{17} - 11 q^{18} + 17 q^{19} + 7 q^{20} + 25 q^{21}+ \cdots - 90 q^{99}+O(q^{100}) $ 48 * q + 4 * q^2 + 6 * q^3 - 6 * q^4 + q^5 - 3 * q^6 + 15 * q^8 - 8 * q^9 - 3 * q^10 + 5 * q^11 - 72 * q^12 + 4 * q^13 + 15 * q^14 - 7 * q^15 + 2 * q^16 - 54 * q^17 - 11 * q^18 + 17 * q^19 + 7 * q^20 + 25 * q^21 - 25 * q^22 + 7 * q^23 - 25 * q^24 + 13 * q^25 + 3 * q^26 + 18 * q^27 + 150 * q^28 - 156 * q^30 + q^31 - 6 * q^32 - 12 * q^34 + 5 * q^35 + 19 * q^36 + 6 * q^37 + 14 * q^38 + 27 * q^39 - 25 * q^40 - 36 * q^41 - 15 * q^42 - 5 * q^43 + 20 * q^44 + q^45 - 84 * q^46 + 31 * q^47 + 11 * q^48 - 4 * q^49 + 11 * q^50 - 23 * q^51 - 2 * q^52 - 19 * q^53 + 46 * q^54 + 20 * q^55 + 20 * q^56 - 36 * q^57 - 6 * q^59 - 9 * q^60 + 21 * q^61 + 12 * q^62 + 10 * q^63 - q^64 + 17 * q^65 + 5 * q^66 - 2 * q^67 + 8 * q^68 - 14 * q^69 + 30 * q^70 + 12 * q^71 - 34 * q^73 + 27 * q^74 - 24 * q^75 - 16 * q^76 - 10 * q^77 - 6 * q^78 + 29 * q^79 + 41 * q^80 - 12 * q^81 + 22 * q^82 + 3 * q^83 - 10 * q^84 + 2 * q^85 - 30 * q^86 - 90 * q^88 + 36 * q^89 - 38 * q^90 + 4 * q^92 - 2 * q^93 - 13 * q^94 + 11 * q^95 + 2 * q^96 - 18 * q^97 + 27 * q^98 - 90 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	−0.0377915	+	0.0181994i	−0.0267226	+	0.0128689i	−0.447197	−	0.894435i	$-0.647578\pi$
$2$	−0.0377915	+	0.0181994i	−0.0267226	+	0.0128689i	0.420475	+	0.907304i	$0.361864\pi$
$3$	−1.88776	−	2.36718i	−1.08990	−	1.36669i	−0.924818	−	0.380410i	$-0.875783\pi$
$3$	−1.88776	−	2.36718i	−1.08990	−	1.36669i	−0.165081	−	0.986280i	$-0.552788\pi$
$4$	−1.24588	+	1.56229i	−0.622941	+	0.781144i
$5$	1.56952	−	0.755841i	0.701911	−	0.338023i	−0.0486571	−	0.998816i	$-0.515494\pi$
$5$	1.56952	−	0.755841i	0.701911	−	0.338023i	0.750568	+	0.660793i	$0.229780\pi$
$6$	0.114422	+	0.0551030i	0.0467128	+	0.0224957i
$7$	1.28043	+	1.60561i	0.483958	+	0.606865i	0.962527	−	0.271186i	$-0.0874157\pi$
$7$	1.28043	+	1.60561i	0.483958	+	0.606865i	−0.478569	+	0.878050i	$0.658844\pi$
$8$	0.0373185	−	0.163503i	0.0131941	−	0.0578070i
$9$	−1.37232	+	6.01254i	−0.457441	+	2.00418i
$10$	−0.0455587	+	0.0571287i	−0.0144069	+	0.0180657i
$11$	−0.412076	−	1.80542i	−0.124245	−	0.544355i	−0.998287	−	0.0585041i	$-0.981367\pi$
$11$	−0.412076	−	1.80542i	−0.124245	−	0.544355i	0.874042	−	0.485851i	$-0.161490\pi$
$12$	6.05014			1.74652
$13$	−0.573636	−	2.51326i	−0.159098	−	0.697054i	−0.990051	−	0.140711i	$-0.955061\pi$
$13$	−0.573636	−	2.51326i	−0.159098	−	0.697054i	0.830953	−	0.556343i	$-0.187796\pi$
$14$	−0.0776107	−	0.0373753i	−0.0207423	−	0.00998898i
$15$	−4.75209	−	2.28849i	−1.22698	−	0.590884i
$16$	−0.887735	−	3.88942i	−0.221934	−	0.972356i
$17$	−5.23359			−1.26933			−0.634666	−	0.772787i	$-0.718862\pi$
$17$	−5.23359			−1.26933			−0.634666	+	0.772787i	$0.718862\pi$
$18$	−0.0575626	−	0.252198i	−0.0135676	−	0.0594437i
$19$	−0.236328	+	0.296346i	−0.0542173	+	0.0679863i	−0.808201	−	0.588907i	$-0.799558\pi$
$19$	−0.236328	+	0.296346i	−0.0542173	+	0.0679863i	0.753983	+	0.656893i	$0.228130\pi$
$20$	−0.774597	+	3.39373i	−0.173205	+	0.758862i
$21$	1.38362	−	6.06202i	0.301930	−	1.32284i
$22$	0.0484306	+	0.0607300i	0.0103254	+	0.0129477i
$23$	−3.27095	−	1.57521i	−0.682040	−	0.328453i	0.0605828	−	0.998163i	$-0.480704\pi$
$23$	−3.27095	−	1.57521i	−0.682040	−	0.328453i	−0.742623	+	0.669710i	$0.766418\pi$
$24$	−0.457489	+	0.220315i	−0.0933845	+	0.0449716i
$25$	−1.22535	+	1.53654i	−0.245070	+	0.307308i
$26$	0.0674185	+	0.0845401i	0.0132219	+	0.0165797i
$27$	8.63967	−	4.16065i	1.66271	−	0.800717i
$28$	−4.10370			−0.775526
$29$		0			0
$29$		0			0
$30$	0.221238			0.0403923
$31$	2.13135	−	1.02641i	0.382803	−	0.184348i	−0.232579	−	0.972578i	$-0.574716\pi$
$31$	2.13135	−	1.02641i	0.382803	−	0.184348i	0.615381	+	0.788230i	$0.289002\pi$
$32$	0.313462	+	0.393069i	0.0554128	+	0.0694855i
$33$	−3.49585	+	4.38366i	−0.608550	+	0.763097i
$34$	0.197785	−	0.0952483i	0.0339199	−	0.0163349i
$35$	3.22326	+	1.55224i	0.544830	+	0.262376i
$36$	−7.68356	−	9.63488i	−1.28059	−	1.60581i
$37$	−1.46137	+	6.40269i	−0.240248	+	1.05260i	0.700544	+	0.713610i	$0.252941\pi$
$37$	−1.46137	+	6.40269i	−0.240248	+	1.05260i	−0.940792	+	0.338986i	$0.889916\pi$
$38$	0.00353786	−	0.0155004i	0.000573916	−	0.00251449i
$39$	−4.86645	+	6.10234i	−0.779256	+	0.977156i
$40$	−0.0650102	−	0.284828i	−0.0102790	−	0.0450353i
$41$	−9.44586			−1.47520			−0.737598	−	0.675240i	$-0.764040\pi$
$41$	−9.44586			−1.47520			−0.737598	+	0.675240i	$0.764040\pi$
$42$	0.0580363	+	0.254274i	0.00895520	+	0.0392353i
$43$	−0.896932	−	0.431940i	−0.136781	−	0.0658702i	0.364241	−	0.931305i	$-0.381328\pi$
$43$	−0.896932	−	0.431940i	−0.136781	−	0.0658702i	−0.501022	+	0.865434i	$0.667043\pi$
$44$	3.33399	+	1.60556i	0.502617	+	0.242048i
$45$	2.39064	+	10.4741i	0.356375	+	1.56138i
$46$	0.152282			0.0224527
$47$	2.26249	+	9.91261i	0.330018	+	1.44590i	0.819093	+	0.573661i	$0.194477\pi$
$47$	2.26249	+	9.91261i	0.330018	+	1.44590i	−0.489075	+	0.872242i	$0.662666\pi$
$48$	−7.53112	+	9.44372i	−1.08702	+	1.36308i
$49$	0.619164	−	2.71274i	0.0884520	−	0.387534i
$50$	0.0183436	−	0.0803687i	0.00259418	−	0.0113659i
$51$	9.87976	+	12.3888i	1.38344	+	1.73478i
$52$	4.64112	+	2.23505i	0.643608	+	0.309945i
$53$	−8.94664	+	4.30848i	−1.22892	+	0.591815i	−0.931781	−	0.363021i	$-0.881745\pi$
$53$	−8.94664	+	4.30848i	−1.22892	+	0.591815i	−0.297135	+	0.954836i	$0.596031\pi$
$54$	−0.250785	+	0.314474i	−0.0341275	+	0.0427945i
$55$	−2.01137	−	2.52218i	−0.271214	−	0.340091i
$56$	0.310306	−	0.149436i	0.0414664	−	0.0199692i
$57$	1.14763			0.152008
$58$		0			0
$59$	−6.24449			−0.812963			−0.406482	−	0.913659i	$-0.633244\pi$
$59$	−6.24449			−0.812963			−0.406482	+	0.913659i	$0.633244\pi$
$60$	9.49582	−	4.57294i	1.22590	−	0.590365i
$61$	4.97874	+	6.24315i	0.637463	+	0.799353i	0.990683	−	0.136187i	$-0.0434848\pi$
$61$	4.97874	+	6.24315i	0.637463	+	0.799353i	−0.353220	+	0.935540i	$0.614913\pi$
$62$	−0.0618670	+	0.0775788i	−0.00785712	+	0.00985252i
$63$	−11.4110	+	5.49523i	−1.43765	+	0.692334i
$64$	7.16973	+	3.45276i	0.896217	+	0.431595i
$65$	−2.79996	−	3.51104i	−0.347293	−	0.435491i
$66$	0.0523334	−	0.229287i	0.00644179	−	0.0282233i
$67$	0.920842	−	4.03447i	0.112499	−	0.492889i	−0.887016	−	0.461739i	$-0.847226\pi$
$67$	0.920842	−	4.03447i	0.112499	−	0.492889i	0.999515	−	0.0311504i	$-0.00991707\pi$
$68$	6.52044	−	8.17637i	0.790719	−	0.991531i
$69$	2.44598	+	10.7165i	0.294461	+	1.29012i
$70$	−0.150061			−0.0179358
$71$	0.507993	+	2.22566i	0.0602876	+	0.264137i	0.996085	−	0.0884011i	$-0.0281757\pi$
$71$	0.507993	+	2.22566i	0.0602876	+	0.264137i	−0.935797	+	0.352538i	$0.885319\pi$
$72$	0.931855	+	0.448757i	0.109820	+	0.0528866i
$73$	−8.16639	−	3.93273i	−0.955804	−	0.460291i	−0.110087	−	0.993922i	$-0.535113\pi$
$73$	−8.16639	−	3.93273i	−0.955804	−	0.460291i	−0.845717	+	0.533631i	$0.820827\pi$
$74$	−0.0612978	−	0.268563i	−0.00712572	−	0.0312198i
$75$	5.95042			0.687096
$76$	−0.168540	−	0.738424i	−0.0193329	−	0.0847030i
$77$	2.37117	−	2.97336i	0.270220	−	0.338845i
$78$	0.0728514	−	0.319183i	0.00824880	−	0.0361403i
$79$	2.28679	−	10.0191i	0.257284	−	1.12724i	−0.666857	−	0.745185i	$-0.732361\pi$
$79$	2.28679	−	10.0191i	0.257284	−	1.12724i	0.924142	−	0.382050i	$-0.124782\pi$
$80$	−4.33311	−	5.43354i	−0.484456	−	0.607489i
$81$	−9.48935	−	4.56983i	−1.05437	−	0.507759i
$82$	0.356973	−	0.171909i	0.0394211	−	0.0189842i
$83$	−9.73931	+	12.2127i	−1.06903	+	1.34052i	−0.132007	+	0.991249i	$0.542142\pi$
$83$	−9.73931	+	12.2127i	−1.06903	+	1.34052i	−0.937022	+	0.349271i	$0.886429\pi$
$84$	7.74680	+	9.71418i	0.845245	+	1.05990i
$85$	−8.21423	+	3.95576i	−0.890958	+	0.429063i
$86$	0.0417574			0.00450282
$87$		0			0
$88$	−0.310570			−0.0331069
$89$	−8.66452	+	4.17261i	−0.918437	+	0.442296i	−0.832513	−	0.554005i	$-0.813099\pi$
$89$	−8.66452	+	4.17261i	−0.918437	+	0.442296i	−0.0859244	+	0.996302i	$0.527384\pi$
$90$	−0.280968	−	0.352322i	−0.0296166	−	0.0371380i
$91$	3.30082	−	4.13910i	0.346020	−	0.433896i
$92$	6.53614	−	3.14764i	0.681440	−	0.328164i
$93$	−6.45317	−	3.10768i	−0.669162	−	0.322252i
$94$	−0.265906	−	0.333436i	−0.0274262	−	0.0343913i
$95$	−0.146931	+	0.643747i	−0.0150748	+	0.0660470i
$96$	0.338723	−	1.48404i	0.0345707	−	0.151464i
$97$	−3.22829	+	4.04814i	−0.327783	+	0.411027i	−0.918229	−	0.396050i	$-0.870381\pi$
$97$	−3.22829	+	4.04814i	−0.327783	+	0.411027i	0.590446	+	0.807077i	$0.298952\pi$
$98$	0.0259711	+	0.113787i	0.00262348	+	0.0114942i
$99$	11.4207			1.14782
$100$	−0.873875	−	3.82869i	−0.0873875	−	0.382869i
$101$	−7.62350	−	3.67128i	−0.758566	−	0.365306i	0.0142812	−	0.999898i	$-0.495454\pi$
$101$	−7.62350	−	3.67128i	−0.758566	−	0.365306i	−0.772848	+	0.634592i	$0.781168\pi$
$102$	−0.598840	−	0.288386i	−0.0592940	−	0.0285545i
$103$	−0.781959	−	3.42599i	−0.0770487	−	0.337573i	0.921682	−	0.387947i	$-0.126816\pi$
$103$	−0.781959	−	3.42599i	−0.0770487	−	0.337573i	−0.998730	+	0.0503745i	$0.983959\pi$
$104$	−0.432333			−0.0423938
$105$	−2.41031	−	10.5603i	−0.235222	−	1.03058i
$106$	0.259695	−	0.325647i	0.0252238	−	0.0316297i
$107$	0.988834	−	4.33236i	0.0955941	−	0.418825i	−0.904375	−	0.426740i	$-0.859662\pi$
$107$	0.988834	−	4.33236i	0.0955941	−	0.418825i	0.999969	+	0.00791429i	$0.00251922\pi$
$108$	−4.26389	+	18.6813i	−0.410293	+	1.79761i
$109$	−7.33397	−	9.19651i	−0.702467	−	0.880866i	0.294738	−	0.955578i	$-0.404768\pi$
$109$	−7.33397	−	9.19651i	−0.702467	−	0.880866i	−0.997205	+	0.0747120i	$0.976196\pi$
$110$	0.121915	+	0.0587112i	0.0116241	+	0.00559789i
$111$	17.9150	−	8.62741i	1.70042	−	0.818878i
$112$	5.10822	−	6.40551i	0.482681	−	0.605263i
$113$	−7.12008	−	8.92830i	−0.669801	−	0.839904i	0.324570	−	0.945862i	$-0.394781\pi$
$113$	−7.12008	−	8.92830i	−0.669801	−	0.839904i	−0.994371	+	0.105958i	$0.966209\pi$
$114$	−0.0433707	+	0.0208862i	−0.00406204	+	0.00195618i
$115$	−6.32443			−0.589756
$116$		0			0
$117$	15.8983			1.46980
$118$	0.235989	−	0.113646i	0.0217245	−	0.0104620i
$119$	−6.70126	−	8.40312i	−0.614304	−	0.770313i
$120$	−0.551515	+	0.691578i	−0.0503462	+	0.0631321i
$121$	6.82092	−	3.28478i	0.620083	−	0.298616i
$122$	−0.301776	−	0.145328i	−0.0273215	−	0.0131573i
$123$	17.8315	+	22.3600i	1.60781	+	2.01614i
$124$	−1.05188	+	4.60857i	−0.0944612	+	0.413862i
$125$	−2.70003	+	11.8296i	−0.241498	+	1.05807i
$126$	0.331227	−	0.415346i	0.0295081	−	0.0370020i
$127$	−2.68054	−	11.7442i	−0.237860	−	1.04213i	−0.942929	−	0.332993i	$-0.891941\pi$
$127$	−2.68054	−	11.7442i	−0.237860	−	1.04213i	0.705070	−	0.709138i	$-0.250916\pi$
$128$	−1.33930			−0.118379
$129$	0.670715	+	2.93859i	0.0590532	+	0.258729i
$130$	0.169714	+	0.0817298i	0.0148849	+	0.00716818i
$131$	13.1490	+	6.33224i	1.14884	+	0.553250i	0.908684	−	0.417485i	$-0.137088\pi$
$131$	13.1490	+	6.33224i	1.14884	+	0.553250i	0.240152	+	0.970735i	$0.422803\pi$
$132$	−2.49311	−	10.9230i	−0.216998	−	0.950729i
$133$	−0.778418			−0.0674974
$134$	0.0386251	+	0.169227i	0.00333670	+	0.0146190i
$135$	10.4154	−	13.0604i	0.896411	−	1.12406i
$136$	−0.195310	+	0.855707i	−0.0167477	+	0.0733763i
$137$	−0.636945	+	2.79064i	−0.0544179	+	0.238420i	−0.994821	−	0.101641i	$-0.967591\pi$
$137$	−0.636945	+	2.79064i	−0.0544179	+	0.238420i	0.940403	+	0.340061i	$0.110448\pi$
$138$	−0.287472	−	0.360478i	−0.0244712	−	0.0306859i
$139$	20.0631	+	9.66186i	1.70173	+	0.819509i	0.993540	+	0.113484i	$0.0362011\pi$
$139$	20.0631	+	9.66186i	1.70173	+	0.819509i	0.708187	+	0.706025i	$0.249513\pi$
$140$	−6.44084	+	3.10175i	−0.544350	+	0.262145i
$141$	19.1939	−	24.0683i	1.61641	−	2.02692i
$142$	−0.0597035	−	0.0748659i	−0.00501021	−	0.00628260i
$143$	−4.30112	+	2.07131i	−0.359678	+	0.173212i
$144$	24.6036			2.05030
$145$		0			0
$146$	0.380194			0.0314650
$147$	−7.59036	+	3.65532i	−0.626042	+	0.301486i
$148$	−8.18214	−	10.2601i	−0.672568	−	0.843373i
$149$	2.64125	−	3.31202i	0.216380	−	0.271332i	−0.661781	−	0.749697i	$-0.730199\pi$
$149$	2.64125	−	3.31202i	0.216380	−	0.271332i	0.878161	+	0.478366i	$0.158771\pi$
$150$	−0.224875	+	0.108294i	−0.0183610	+	0.00884219i
$151$	−7.02269	−	3.38195i	−0.571498	−	0.275219i	0.125735	−	0.992064i	$-0.459871\pi$
$151$	−7.02269	−	3.38195i	−0.571498	−	0.275219i	−0.697233	+	0.716845i	$0.745586\pi$
$152$	0.0396340	+	0.0496995i	0.00321474	+	0.00403116i
$153$	7.18217	−	31.4672i	0.580644	−	2.54397i
$154$	−0.0354968	+	0.155521i	−0.00286041	+	0.0125323i
$155$	2.56940	−	3.22193i	0.206380	−	0.258792i
$156$	−3.47058	−	15.2056i	−0.277868	−	1.21742i
$157$	−6.32741			−0.504982			−0.252491	−	0.967599i	$-0.581250\pi$
$157$	−6.32741			−0.504982			−0.252491	+	0.967599i	$0.581250\pi$
$158$	0.0959204	+	0.420255i	0.00763101	+	0.0334337i
$159$	27.0880	+	13.0449i	2.14822	+	1.03453i
$160$	0.789084	+	0.380003i	0.0623825	+	0.0300418i
$161$	−1.65906	−	7.26882i	−0.130752	−	0.572863i
$162$	0.441785			0.0347099
$163$	−0.391513	−	1.71533i	−0.0306656	−	0.134355i	0.957278	−	0.289170i	$-0.0933791\pi$
$163$	−0.391513	−	1.71533i	−0.0306656	−	0.134355i	−0.987944	+	0.154815i	$0.950522\pi$
$164$	11.7684	−	14.7572i	0.918961	−	1.15234i
$165$	−2.17346	+	9.52255i	−0.169204	+	0.741330i
$166$	0.145799	−	0.638786i	0.0113162	−	0.0495794i
$167$	−8.67915	−	10.8833i	−0.671613	−	0.842176i	0.322939	−	0.946420i	$-0.395329\pi$
$167$	−8.67915	−	10.8833i	−0.671613	−	0.842176i	−0.994552	+	0.104244i	$0.966758\pi$
$168$	−0.939524	−	0.452451i	−0.0724859	−	0.0349073i
$169$	5.72516	−	2.75709i	0.440397	−	0.212084i
$170$	0.238435	−	0.298988i	0.0182872	−	0.0229314i
$171$	−1.45747	−	1.82761i	−0.111456	−	0.139761i
$172$	1.79229	−	0.863119i	0.136661	−	0.0658122i
$173$	−8.38553			−0.637540			−0.318770	−	0.947832i	$-0.603270\pi$
$173$	−8.38553			−0.637540			−0.318770	+	0.947832i	$0.603270\pi$
$174$		0			0
$175$	−4.03606			−0.305098
$176$	−6.65623	+	3.20547i	−0.501732	+	0.241622i
$177$	11.7881	+	14.7818i	0.886048	+	1.11107i
$178$	0.251506	−	0.315379i	0.0188512	−	0.0236386i
$179$	17.7270	−	8.53688i	1.32498	−	0.638077i	0.368433	−	0.929654i	$-0.379895\pi$
$179$	17.7270	−	8.53688i	1.32498	−	0.638077i	0.956547	+	0.291578i	$0.0941802\pi$
$180$	−19.3419	−	9.31459i	−1.44166	−	0.694269i
$181$	7.51525	+	9.42383i	0.558604	+	0.700468i	0.978299	−	0.207198i	$-0.0664343\pi$
$181$	7.51525	+	9.42383i	0.558604	+	0.700468i	−0.419695	+	0.907665i	$0.637863\pi$
$182$	−0.0494138	+	0.216496i	−0.00366279	+	0.0160477i
$183$	5.37996	−	23.5711i	0.397698	−	1.74243i
$184$	−0.379618	+	0.476025i	−0.0279858	+	0.0350931i
$185$	2.54576	+	11.1537i	0.187168	+	0.820038i
$186$	0.300433			0.0220288
$187$	2.15664	+	9.44884i	0.157709	+	0.690967i
$188$	−18.3051	−	8.81529i	−1.33504	−	0.642921i
$189$	17.7429	+	8.54454i	1.29061	+	0.621523i
$190$	−0.00616308	−	0.0270022i	−0.000447117	−	0.00195895i
$191$	−11.6202			−0.840810			−0.420405	−	0.907337i	$-0.638112\pi$
$191$	−11.6202			−0.840810			−0.420405	+	0.907337i	$0.638112\pi$
$192$	−5.36144	−	23.4900i	−0.386929	−	1.69525i
$193$	−11.8790	+	14.8958i	−0.855072	+	1.07223i	0.141536	+	0.989933i	$0.454796\pi$
$193$	−11.8790	+	14.8958i	−0.855072	+	1.07223i	−0.996608	+	0.0822934i	$0.973776\pi$
$194$	0.0483279	−	0.211738i	0.00346974	−	0.0152019i
$195$	−3.02560	+	13.2560i	−0.216668	+	0.949283i
$196$	3.46667	+	4.34706i	0.247619	+	0.310504i
$197$	−15.0522	−	7.24876i	−1.07243	−	0.516453i	−0.187538	−	0.982257i	$-0.560051\pi$
$197$	−15.0522	−	7.24876i	−1.07243	−	0.516453i	−0.884888	+	0.465804i	$0.845765\pi$
$198$	−0.431604	+	0.207849i	−0.0306728	+	0.0147712i
$199$	−5.55438	+	6.96497i	−0.393739	+	0.493734i	−0.938703	−	0.344726i	$-0.887972\pi$
$199$	−5.55438	+	6.96497i	−0.393739	+	0.493734i	0.544964	+	0.838459i	$0.316543\pi$
$200$	0.205501	+	0.257690i	0.0145311	+	0.0182214i
$201$	−11.2886	+	5.43632i	−0.796239	+	0.383448i
$202$	0.354918			0.0249720
$203$		0			0
$204$	−31.6639			−2.21692
$205$	−14.8255	+	7.13958i	−1.03546	+	0.498650i
$206$	0.0919024	+	0.115242i	0.00640314	+	0.00802929i
$207$	13.9598	−	17.5050i	0.970272	−	1.21668i
$208$	−9.26591	+	4.46223i	−0.642475	+	0.309400i
$209$	0.632414	+	0.304554i	0.0437450	+	0.0210665i
$210$	0.283280	+	0.355222i	0.0195482	+	0.0245126i
$211$	0.0565685	−	0.247843i	0.00389433	−	0.0170622i	−0.972943	−	0.231044i	$-0.925786\pi$
$211$	0.0565685	−	0.247843i	0.00389433	−	0.0170622i	0.976838	+	0.213981i	$0.0686432\pi$
$212$	4.41539	−	19.3451i	0.303250	−	1.32863i
$213$	4.30956	−	5.40402i	0.295286	−	0.370277i
$214$	0.0414770	+	0.181723i	0.00283531	+	0.0124223i
$215$	−1.73423			−0.118274
$216$	−0.357859	−	1.56788i	−0.0243492	−	0.106681i
$217$	4.37707	+	2.10788i	0.297135	+	0.143093i
$218$	0.444533	+	0.214076i	0.0301076	+	0.0144990i
$219$	6.10673	+	26.7553i	0.412655	+	1.80796i
$220$	6.44631			0.434610
$221$	3.00218	+	13.1534i	0.201948	+	0.884793i
$222$	−0.520021	+	0.652085i	−0.0349015	+	0.0437651i
$223$	−2.03757	+	8.92716i	−0.136445	+	0.597807i	0.859754	+	0.510708i	$0.170617\pi$
$223$	−2.03757	+	8.92716i	−0.136445	+	0.597807i	−0.996200	+	0.0870987i	$0.972240\pi$
$224$	−0.229749	+	1.00660i	−0.0153508	+	0.0672561i
$225$	−7.55692	−	9.47608i	−0.503795	−	0.631739i
$226$	0.431568	+	0.207832i	0.0287075	+	0.0138248i
$227$	4.33768	−	2.08892i	0.287902	−	0.138646i	−0.284359	−	0.958718i	$-0.591781\pi$
$227$	4.33768	−	2.08892i	0.287902	−	0.138646i	0.572261	+	0.820072i	$0.306066\pi$
$228$	−1.42982	+	1.79293i	−0.0946918	+	0.118740i
$229$	4.28089	+	5.36806i	0.282889	+	0.354732i	0.902892	−	0.429868i	$-0.141440\pi$
$229$	4.28089	+	5.36806i	0.282889	+	0.354732i	−0.620003	+	0.784600i	$0.712869\pi$
$230$	0.239010	−	0.115101i	0.0157598	−	0.00758953i
$231$	−11.5147			−0.757609
$232$		0			0
$233$	17.2302			1.12879			0.564393	−	0.825507i	$-0.309110\pi$
$233$	17.2302			1.12879			0.564393	+	0.825507i	$0.309110\pi$
$234$	−0.600820	+	0.289340i	−0.0392769	+	0.0189147i
$235$	11.0434	+	13.8480i	0.720391	+	0.903342i
$236$	7.77990	−	9.75569i	0.506428	−	0.635041i
$237$	−28.0339	+	13.5004i	−1.82100	+	0.876945i
$238$	0.406183	+	0.195607i	0.0263289	+	0.0126793i
$239$	−13.2829	−	16.6563i	−0.859201	−	1.07740i	−0.996223	−	0.0868358i	$-0.972324\pi$
$239$	−13.2829	−	16.6563i	−0.859201	−	1.07740i	0.137022	−	0.990568i	$-0.456247\pi$
$240$	−4.68229	+	20.5145i	−0.302241	+	1.32420i
$241$	2.00116	−	8.76764i	0.128906	−	0.564774i	−0.868683	−	0.495369i	$-0.835033\pi$
$241$	2.00116	−	8.76764i	0.128906	−	0.564774i	0.997589	−	0.0694047i	$-0.0221100\pi$
$242$	−0.197991	+	0.248273i	−0.0127274	+	0.0159596i
$243$	0.694555	+	3.04305i	0.0445557	+	0.195211i
$244$	−15.9565			−1.02151
$245$	−1.07861	−	4.72569i	−0.0689097	−	0.301913i
$246$	−1.08082	−	0.520495i	−0.0689105	−	0.0331856i
$247$	0.880361	+	0.423959i	0.0560160	+	0.0269759i
$248$	−0.0882815	−	0.386787i	−0.00560588	−	0.0245610i
$249$	47.2951			2.99721
$250$	−0.113254	−	0.496197i	−0.00716280	−	0.0313823i
$251$	4.05432	−	5.08396i	0.255906	−	0.320897i	−0.637237	−	0.770667i	$-0.719923\pi$
$251$	4.05432	−	5.08396i	0.255906	−	0.320897i	0.893144	+	0.449771i	$0.148494\pi$
$252$	5.63160	−	24.6736i	0.354757	−	1.55429i
$253$	−1.49603	+	6.55454i	−0.0940547	+	0.412081i
$254$	0.315040	+	0.395047i	0.0197673	+	0.0247875i
$255$	24.8705	+	11.9770i	1.55745	+	0.750028i
$256$	−14.2889	+	6.88115i	−0.893053	+	0.430072i
$257$	−3.60848	+	4.52490i	−0.225091	+	0.282255i	−0.881534	−	0.472120i	$-0.843489\pi$
$257$	−3.60848	+	4.52490i	−0.225091	+	0.282255i	0.656443	+	0.754376i	$0.272060\pi$
$258$	−0.0788280	−	0.0988472i	−0.00490762	−	0.00615396i
$259$	−12.1514	+	5.85182i	−0.755053	+	0.363614i
$260$	8.97368			0.556524
$261$		0			0
$262$	−0.612164			−0.0378196
$263$	27.2514	−	13.1236i	1.68039	−	0.809234i	0.683543	−	0.729910i	$-0.260438\pi$
$263$	27.2514	−	13.1236i	1.68039	−	0.809234i	0.996849	−	0.0793240i	$-0.0252762\pi$
$264$	0.586281	+	0.735173i	0.0360831	+	0.0452468i
$265$	−10.7854	+	13.5245i	−0.662543	+	0.830803i
$266$	0.0294176	−	0.0141668i	0.00180371	−	0.000868620i
$267$	26.2338	+	12.6336i	1.60549	+	0.773161i
$268$	5.15574	+	6.46510i	0.314937	+	0.394919i
$269$	2.65607	−	11.6370i	0.161943	−	0.709519i	−0.827120	−	0.562026i	$-0.810022\pi$
$269$	2.65607	−	11.6370i	0.161943	−	0.709519i	0.989063	−	0.147494i	$-0.0471206\pi$
$270$	−0.155919	+	0.683127i	−0.00948895	+	0.0415738i
$271$	10.9467	−	13.7267i	0.664964	−	0.833839i	−0.328909	−	0.944362i	$-0.606681\pi$
$271$	10.9467	−	13.7267i	0.664964	−	0.833839i	0.993874	+	0.110523i	$0.0352525\pi$
$272$	4.64604	+	20.3556i	0.281708	+	1.23424i
$273$	−16.0292			−0.970128
$274$	−0.0267169	−	0.117054i	−0.00161403	−	0.00707152i
$275$	3.27904	+	1.57910i	0.197733	+	0.0952234i
$276$	−19.7897	−	9.53021i	−1.19120	−	0.573651i
$277$	−0.239158	−	1.04782i	−0.0143696	−	0.0629574i	0.967235	−	0.253884i	$-0.0817080\pi$
$277$	−0.239158	−	1.04782i	−0.0143696	−	0.0629574i	−0.981604	+	0.190926i	$0.938851\pi$
$278$	−0.934053			−0.0560208
$279$	3.24640	+	14.2234i	0.194357	+	0.851533i
$280$	0.374083	−	0.469085i	0.0223557	−	0.0280332i
$281$	6.65038	−	29.1372i	0.396728	−	1.73818i	−0.243412	−	0.969923i	$-0.578267\pi$
$281$	6.65038	−	29.1372i	0.396728	−	1.73818i	0.640141	−	0.768258i	$-0.278876\pi$
$282$	−0.287335	+	1.25889i	−0.0171105	+	0.0749661i
$283$	16.6784	+	20.9141i	0.991430	+	1.24321i	0.969915	+	0.243446i	$0.0782778\pi$
$283$	16.6784	+	20.9141i	0.991430	+	1.24321i	0.0215158	+	0.999769i	$0.493151\pi$
$284$	−4.11002	−	1.97928i	−0.243885	−	0.117449i
$285$	1.80123	−	0.867428i	0.106696	−	0.0513820i
$286$	0.124849	−	0.156556i	0.00738248	−	0.00925733i
$287$	−12.0948	−	15.1664i	−0.713933	−	0.895244i
$288$	−2.79351	+	1.34529i	−0.164609	+	0.0792717i
$289$	10.3905			0.611204
$290$		0			0
$291$	15.6769			0.918996
$292$	16.3184	−	7.85854i	0.954963	−	0.459886i
$293$	3.62271	+	4.54273i	0.211641	+	0.265389i	0.876309	−	0.481749i	$-0.159998\pi$
$293$	3.62271	+	4.54273i	0.211641	+	0.265389i	−0.664668	+	0.747139i	$0.731427\pi$
$294$	0.220326	−	0.276280i	0.0128497	−	0.0161130i
$295$	−9.80086	+	4.71984i	−0.570628	+	0.274800i
$296$	0.992322	+	0.477877i	0.0576775	+	0.0277760i
$297$	−11.0719	−	13.8837i	−0.642458	−	0.805617i
$298$	−0.0395399	+	0.173236i	−0.00229048	+	0.0100353i
$299$	−2.08257	+	9.12435i	−0.120438	+	0.527675i
$300$	−7.41353	+	9.29627i	−0.428020	+	0.536721i
$301$	−0.454934	−	1.99320i	−0.0262220	−	0.114886i
$302$	0.326947			0.0188137
$303$	5.70076	+	24.9767i	0.327500	+	1.43487i
$304$	1.36241	+	0.656102i	0.0781396	+	0.0376300i
$305$	12.5331	+	6.03561i	0.717642	+	0.345598i
$306$	0.301259	+	1.31990i	0.0172218	+	0.0754538i
$307$	−5.15345			−0.294123			−0.147061	−	0.989127i	$-0.546982\pi$
$307$	−5.15345			−0.294123			−0.147061	+	0.989127i	$0.546982\pi$
$308$	1.69103	+	7.40890i	0.0963556	+	0.422162i
$309$	−6.63376	+	8.31848i	−0.377382	+	0.473222i
$310$	−0.0384643	+	0.168523i	−0.00218463	+	0.00957148i
$311$	−2.36415	+	10.3580i	−0.134058	+	0.587348i	0.862616	+	0.505860i	$0.168825\pi$
$311$	−2.36415	+	10.3580i	−0.134058	+	0.587348i	−0.996674	+	0.0814888i	$0.974033\pi$
$312$	0.816141	+	1.02341i	0.0462049	+	0.0579391i
$313$	−15.0555	−	7.25036i	−0.850988	−	0.409814i	−0.0430441	−	0.999073i	$-0.513706\pi$
$313$	−15.0555	−	7.25036i	−0.850988	−	0.409814i	−0.807944	+	0.589259i	$0.799420\pi$
$314$	0.239122	−	0.115155i	0.0134944	−	0.00649858i
$315$	−13.7562	+	17.2498i	−0.775076	+	0.971915i
$316$	12.8036	+	16.0552i	0.720260	+	0.903178i
$317$	−1.34356	+	0.647024i	−0.0754619	+	0.0363405i	−0.471234	−	0.882008i	$-0.656191\pi$
$317$	−1.34356	+	0.647024i	−0.0754619	+	0.0363405i	0.395772	+	0.918349i	$0.370477\pi$
$318$	−1.26111			−0.0707193
$319$		0			0
$320$	13.8628			0.774954
$321$	−12.1221	+	5.83772i	−0.676592	+	0.325830i
$322$	0.194987	+	0.244506i	0.0108662	+	0.0136258i
$323$	1.23684	−	1.55095i	0.0688198	−	0.0862972i
$324$	18.9620	−	9.13162i	1.05344	−	0.507312i
$325$	4.56463	+	2.19821i	0.253200	+	0.121935i
$326$	0.0460138	+	0.0576995i	0.00254847	+	0.00319568i
$327$	−7.92498	+	34.7216i	−0.438253	+	1.92011i
$328$	−0.352505	+	1.54443i	−0.0194638	+	0.0852767i
$329$	−13.0188	+	16.3251i	−0.717752	+	0.900033i
$330$	−0.0911666	−	0.399427i	−0.00501856	−	0.0219877i
$331$	29.8803			1.64237			0.821184	−	0.570663i	$-0.193314\pi$
$331$	29.8803			1.64237			0.821184	+	0.570663i	$0.193314\pi$
$332$	−6.94573	−	30.4312i	−0.381196	−	1.67013i
$333$	−36.4909	−	17.5731i	−1.99969	−	0.963000i
$334$	0.526068	+	0.253341i	0.0287852	+	0.0138622i
$335$	−1.60414	−	7.02820i	−0.0876435	−	0.383991i
$336$	−24.8061			−1.35328
$337$	−0.209469	−	0.917743i	−0.0114105	−	0.0499927i	0.968902	−	0.247444i	$-0.0795907\pi$
$337$	−0.209469	−	0.917743i	−0.0114105	−	0.0499927i	−0.980313	+	0.197451i	$0.936734\pi$
$338$	−0.166185	+	0.208389i	−0.00903926	+	0.0113349i
$339$	−7.69385	+	33.7090i	−0.417873	+	1.83082i
$340$	4.05392	−	17.7614i	0.219855	−	0.963247i
$341$	−2.73137	−	3.42504i	−0.147912	−	0.185476i
$342$	0.0883415	+	0.0425430i	0.00477696	+	0.00230046i
$343$	18.1004	−	8.71667i	0.977328	−	0.470656i
$344$	−0.104096	+	0.130532i	−0.00561246	+	0.00703780i
$345$	11.9390	+	14.9710i	0.642774	+	0.806013i
$346$	0.316902	−	0.152612i	0.0170367	−	0.00820446i
$347$	−8.65358			−0.464548			−0.232274	−	0.972650i	$-0.574617\pi$
$347$	−8.65358			−0.464548			−0.232274	+	0.972650i	$0.574617\pi$
$348$		0			0
$349$	−34.5616			−1.85004			−0.925021	−	0.379916i	$-0.875953\pi$
$349$	−34.5616			−1.85004			−0.925021	+	0.379916i	$0.875953\pi$
$350$	0.152529	−	0.0734540i	0.00815301	−	0.00392628i
$351$	−15.4128	−	19.3271i	−0.822676	−	1.03160i
$352$	0.580485	−	0.727906i	0.0309400	−	0.0387975i
$353$	12.9947	−	6.25794i	0.691640	−	0.333076i	−0.0548295	−	0.998496i	$-0.517462\pi$
$353$	12.9947	−	6.25794i	0.691640	−	0.333076i	0.746470	+	0.665419i	$0.231747\pi$
$354$	−0.714510	−	0.344090i	−0.0379758	−	0.0182882i
$355$	2.47955	+	3.10926i	0.131601	+	0.165022i
$356$	4.27616	−	18.7351i	0.226636	−	0.992956i
$357$	−7.24128	+	31.7261i	−0.383249	+	1.67913i
$358$	−0.514564	+	0.645243i	−0.0271956	+	0.0341022i
$359$	4.96020	+	21.7321i	0.261789	+	1.14697i	0.919309	+	0.393536i	$0.128748\pi$
$359$	4.96020	+	21.7321i	0.261789	+	1.14697i	−0.657520	+	0.753437i	$0.728394\pi$
$360$	1.80175			0.0949608
$361$	4.19593	+	18.3836i	0.220838	+	0.967556i
$362$	−0.455521	−	0.219367i	−0.0239416	−	0.0115297i
$363$	−20.6519	−	9.94543i	−1.08394	−	0.522000i
$364$	2.35403	+	10.3137i	0.123385	+	0.540583i
$365$	−15.7898			−0.826478
$366$	0.225664	+	0.988700i	0.0117957	+	0.0516802i
$367$	3.16762	−	3.97207i	0.165348	−	0.207340i	−0.692254	−	0.721654i	$-0.743382\pi$
$367$	3.16762	−	3.97207i	0.165348	−	0.207340i	0.857602	+	0.514314i	$0.171953\pi$
$368$	−3.22290	+	14.1205i	−0.168005	+	0.736080i
$369$	12.9628	−	56.7936i	0.674815	−	2.95656i
$370$	−0.299199	−	0.375184i	−0.0155546	−	0.0195049i
$371$	−18.3733	−	8.84812i	−0.953895	−	0.459372i
$372$	12.8950	−	6.20990i	0.668574	−	0.321968i
$373$	15.9051	−	19.9443i	0.823533	−	1.03268i	−0.175306	−	0.984514i	$-0.556092\pi$
$373$	15.9051	−	19.9443i	0.823533	−	1.03268i	0.998839	−	0.0481640i	$-0.0153370\pi$
$374$	−0.253466	−	0.317836i	−0.0131064	−	0.0164349i
$375$	33.0998	−	15.9400i	1.70926	−	0.823138i
$376$	1.70517			0.0879376
$377$		0			0
$378$	−0.826036			−0.0424867
$379$	−7.49536	+	3.60957i	−0.385011	+	0.185411i	−0.616369	−	0.787457i	$-0.711397\pi$
$379$	−7.49536	+	3.60957i	−0.385011	+	0.185411i	0.231359	+	0.972869i	$0.425683\pi$
$380$	−0.822659	−	1.03158i	−0.0422015	−	0.0529190i
$381$	−22.7404	+	28.5156i	−1.16503	+	1.46090i
$382$	0.439145	−	0.211481i	0.0224686	−	0.0108203i
$383$	−22.8146	−	10.9870i	−1.16577	−	0.561407i	−0.252039	−	0.967717i	$-0.581101\pi$
$383$	−22.8146	−	10.9870i	−1.16577	−	0.561407i	−0.913735	+	0.406310i	$0.866815\pi$
$384$	2.52828	+	3.17036i	0.129021	+	0.161787i
$385$	1.47422	−	6.45897i	0.0751331	−	0.329180i
$386$	0.177831	−	0.779128i	0.00905135	−	0.0396566i
$387$	3.82793	−	4.80008i	0.194585	−	0.244002i
$388$	−2.30230	−	10.0870i	−0.116881	−	0.512091i
$389$	27.3249			1.38543			0.692714	−	0.721212i	$-0.256415\pi$
$389$	27.3249			1.38543			0.692714	+	0.721212i	$0.256415\pi$
$390$	−0.126910	−	0.556028i	−0.00642633	−	0.0281556i
$391$	17.1188	+	8.24398i	0.865735	+	0.416916i
$392$	−0.420434	−	0.202470i	−0.0212351	−	0.0102263i
$393$	−9.83268	−	43.0798i	−0.495993	−	2.17309i
$394$	0.700769			0.0353042
$395$	−3.98368	−	17.4536i	−0.200441	−	0.878187i
$396$	−14.2288	+	17.8424i	−0.715024	+	0.896612i
$397$	−2.49786	+	10.9438i	−0.125364	+	0.549255i	0.872767	+	0.488137i	$0.162323\pi$
$397$	−2.49786	+	10.9438i	−0.125364	+	0.549255i	−0.998131	+	0.0611172i	$0.980534\pi$
$398$	0.0831498	−	0.364303i	0.00416792	−	0.0182609i
$399$	1.46947	+	1.84265i	0.0735653	+	0.0922480i
$400$	7.06404	+	3.40186i	0.353202	+	0.170093i
$401$	−30.0037	+	14.4490i	−1.49831	+	0.721549i	−0.990189	−	0.139736i	$-0.955375\pi$
$401$	−30.0037	+	14.4490i	−1.49831	+	0.721549i	−0.508123	+	0.861285i	$0.669660\pi$
$402$	0.327676	−	0.410893i	0.0163430	−	0.0204935i
$403$	−3.80225	−	4.76787i	−0.189404	−	0.237505i
$404$	15.2336	−	7.33611i	0.757899	−	0.364985i
$405$	−18.3478			−0.911710
$406$		0			0
$407$	12.1617			0.602835
$408$	2.39431	−	1.15304i	0.118536	−	0.0570839i
$409$	−10.0270	−	12.5734i	−0.495801	−	0.621715i	0.469475	−	0.882946i	$-0.344443\pi$
$409$	−10.0270	−	12.5734i	−0.495801	−	0.621715i	−0.965276	+	0.261231i	$0.915872\pi$
$410$	0.430341	−	0.539630i	0.0212530	−	0.0266504i
$411$	7.80833	−	3.76029i	0.385157	−	0.185482i
$412$	6.32661	+	3.04673i	0.311690	+	0.150102i
$413$	−7.99565	−	10.0262i	−0.393440	−	0.493359i
$414$	−0.208980	+	0.915600i	−0.0102708	+	0.0449993i
$415$	−6.05518	+	26.5295i	−0.297237	+	1.30228i
$416$	0.808073	−	1.01329i	0.0396190	−	0.0496807i
$417$	−15.0029	−	65.7321i	−0.734696	−	3.21891i
$418$	−0.0294426			−0.00144008
$419$	−6.24754	−	27.3723i	−0.305212	−	1.33722i	−0.862143	−	0.506664i	$-0.830878\pi$
$419$	−6.24754	−	27.3723i	−0.305212	−	1.33722i	0.556931	−	0.830559i	$-0.311979\pi$
$420$	19.5011	+	9.39125i	0.951558	+	0.458246i
$421$	−27.4778	−	13.2326i	−1.33919	−	0.644918i	−0.379291	−	0.925278i	$-0.623832\pi$
$421$	−27.4778	−	13.2326i	−1.33919	−	0.644918i	−0.959895	+	0.280360i	$0.909546\pi$
$422$	0.00237279	+	0.0103959i	0.000115505	+	0.000506062i
$423$	−62.7048			−3.04881
$424$	0.370573	+	1.62359i	0.0179966	+	0.0788484i
$425$	6.41297	−	8.04162i	0.311075	−	0.390076i
$426$	−0.0645147	+	0.282658i	−0.00312575	+	0.0136948i
$427$	−3.64913	+	15.9879i	−0.176594	+	0.773707i
$428$	5.53643	+	6.94246i	0.267613	+	0.335576i
$429$	13.0226	+	6.27137i	0.628739	+	0.302785i
$430$	0.0655392	−	0.0315620i	0.00316058	−	0.00152206i
$431$	−6.06385	+	7.60383i	−0.292086	+	0.366264i	−0.906124	−	0.423013i	$-0.860973\pi$
$431$	−6.06385	+	7.60383i	−0.292086	+	0.366264i	0.614038	+	0.789276i	$0.289544\pi$
$432$	−23.8523	−	29.9098i	−1.14759	−	1.43904i
$433$	20.9292	−	10.0790i	1.00580	−	0.484365i	0.142894	−	0.989738i	$-0.454359\pi$
$433$	20.9292	−	10.0790i	1.00580	−	0.484365i	0.862901	+	0.505373i	$0.168645\pi$
$434$	−0.203778			−0.00978166
$435$		0			0
$436$	23.5049			1.12568
$437$	1.23982	−	0.597066i	0.0593087	−	0.0285616i
$438$	−0.717714	−	0.899985i	−0.0342937	−	0.0430030i
$439$	−8.49672	+	10.6546i	−0.405526	+	0.508514i	−0.942097	−	0.335342i	$-0.891148\pi$
$439$	−8.49672	+	10.6546i	−0.405526	+	0.508514i	0.536570	+	0.843856i	$0.319720\pi$
$440$	−0.487446	+	0.234742i	−0.0232381	+	0.0111909i
$441$	15.4607	+	7.44550i	0.736225	+	0.354547i
$442$	−0.352841	−	0.442448i	−0.0167829	−	0.0210451i
$443$	2.04124	−	8.94324i	0.0969821	−	0.424906i	−0.903007	−	0.429626i	$-0.858645\pi$
$443$	2.04124	−	8.94324i	0.0969821	−	0.424906i	0.999989	+	0.00472000i	$0.00150243\pi$
$444$	−8.84150	+	38.7371i	−0.419599	+	1.83838i
$445$	−10.4453	+	13.0980i	−0.495155	+	0.620905i
$446$	−0.0854665	−	0.374453i	−0.00404695	−	0.0177309i
$447$	−12.8262			−0.606658
$448$	3.63657	+	15.9328i	0.171812	+	0.752756i
$449$	15.9872	+	7.69901i	0.754480	+	0.363339i	0.771260	−	0.636521i	$-0.219627\pi$
$449$	15.9872	+	7.69901i	0.754480	+	0.363339i	−0.0167793	+	0.999859i	$0.505341\pi$
$450$	0.458047	+	0.220584i	0.0215925	+	0.0103984i
$451$	3.89241	+	17.0538i	0.183286	+	0.803031i
$452$	22.8194			1.07333
$453$	5.25148	+	23.0082i	0.246736	+	1.08102i
$454$	−0.125910	+	0.157886i	−0.00590926	+	0.00740998i
$455$	2.05221	−	8.99131i	0.0962090	−	0.421519i
$456$	0.0428279	−	0.187641i	0.00200560	−	0.00878711i
$457$	1.57336	+	1.97293i	0.0735987	+	0.0922898i	0.817268	−	0.576258i	$-0.195488\pi$
$457$	1.57336	+	1.97293i	0.0735987	+	0.0922898i	−0.743669	+	0.668548i	$0.766916\pi$
$458$	−0.259477	−	0.124957i	−0.0121245	−	0.00583888i
$459$	−45.2165	+	21.7751i	−2.11053	+	1.01638i
$460$	7.87949	−	9.88057i	0.367383	−	0.460684i
$461$	−6.24287	−	7.82831i	−0.290759	−	0.364601i	0.614901	−	0.788604i	$-0.289196\pi$
$461$	−6.24287	−	7.82831i	−0.290759	−	0.364601i	−0.905661	+	0.424004i	$0.860624\pi$
$462$	0.435156	−	0.209560i	0.0202453	−	0.00974962i
$463$	27.8485			1.29423			0.647115	−	0.762393i	$-0.275976\pi$
$463$	27.8485			1.29423			0.647115	+	0.762393i	$0.275976\pi$
$464$		0			0
$465$	−12.4773			−0.578621
$466$	−0.651153	+	0.313579i	−0.0301641	+	0.0145263i
$467$	−12.6742	−	15.8929i	−0.586492	−	0.735438i	0.396713	−	0.917943i	$-0.370151\pi$
$467$	−12.6742	−	15.8929i	−0.586492	−	0.735438i	−0.983205	+	0.182505i	$0.941579\pi$
$468$	−19.8074	+	24.8377i	−0.915598	+	1.14812i
$469$	7.65687	−	3.68736i	0.353562	−	0.170266i
$470$	−0.669371	−	0.322352i	−0.0308758	−	0.0148690i
$471$	11.9446	+	14.9781i	0.550379	+	0.690154i
$472$	−0.233035	+	1.02099i	−0.0107263	+	0.0469950i
$473$	−0.410229	+	1.79733i	−0.0188624	+	0.0826414i
$474$	0.813742	−	1.02040i	0.0373764	−	0.0468685i
$475$	−0.165763	−	0.726254i	−0.00760571	−	0.0333228i
$476$	21.4771			0.984400
$477$	−13.6272	−	59.7046i	−0.623946	−	2.73369i
$478$	0.805116	+	0.387723i	0.0368251	+	0.0177340i
$479$	19.3266	+	9.30722i	0.883057	+	0.425258i	0.819740	−	0.572736i	$-0.194118\pi$
$479$	19.3266	+	9.30722i	0.883057	+	0.425258i	0.0633168	+	0.997993i	$0.479832\pi$
$480$	−0.590067	−	2.58525i	−0.0269328	−	0.118000i
$481$	16.9299			0.771939
$482$	0.0839393	+	0.367762i	0.00382333	+	0.0167511i
$483$	−14.0747	+	17.6491i	−0.640420	+	0.803061i
$484$	−3.36629	+	14.7487i	−0.153013	+	0.670395i
$485$	−2.00711	+	8.79372i	−0.0911382	+	0.399302i
$486$	−0.0816299	−	0.102361i	−0.00370281	−	0.00464318i
$487$	−14.7726	−	7.11409i	−0.669409	−	0.322370i	0.0681287	−	0.997677i	$-0.478297\pi$
$487$	−14.7726	−	7.11409i	−0.669409	−	0.322370i	−0.737537	+	0.675306i	$0.764011\pi$
$488$	1.20657	−	0.581055i	0.0546190	−	0.0263031i
$489$	−3.32140	+	4.16491i	−0.150199	+	0.188344i
$490$	0.126767	+	0.158961i	0.00572674	+	0.00718111i
$491$	26.3756	−	12.7018i	1.19031	−	0.573225i	0.269415	−	0.963024i	$-0.413170\pi$
$491$	26.3756	−	12.7018i	1.19031	−	0.573225i	0.920900	+	0.389799i	$0.127455\pi$
$492$	−57.1488			−2.57647
$493$		0			0
$494$	−0.0409860			−0.00184405
$495$	17.9250	−	8.63221i	0.805668	−	0.387989i
$496$	−5.88421	−	7.37856i	−0.264209	−	0.331307i
$497$	−2.92310	+	3.66545i	−0.131119	+	0.164418i
$498$	−1.78735	+	0.860744i	−0.0800932	+	0.0385709i
$499$	4.21115	+	2.02798i	0.188517	+	0.0907849i	0.525761	−	0.850632i	$-0.323781\pi$
$499$	4.21115	+	2.02798i	0.188517	+	0.0907849i	−0.337244	+	0.941417i	$0.609495\pi$
$500$	−15.1173	−	18.9565i	−0.676067	−	0.847761i
$501$	−9.37856	+	41.0902i	−0.419003	+	1.83577i
$502$	−0.0606937	+	0.265917i	−0.00270889	+	0.0118684i
$503$	−6.92526	+	8.68400i	−0.308782	+	0.387201i	−0.911873	−	0.410472i	$-0.865364\pi$
$503$	−6.92526	+	8.68400i	−0.308782	+	0.387201i	0.603091	+	0.797672i	$0.293935\pi$
$504$	0.472647	+	2.07080i	0.0210534	+	0.0922408i
$505$	−14.7401			−0.655928
$506$	−0.0627516	−	0.274933i	−0.00278965	−	0.0122223i
$507$	−17.3342	−	8.34773i	−0.769841	−	0.370736i
$508$	21.6875	+	10.4441i	0.962227	+	0.463384i
$509$	7.39923	+	32.4181i	0.327965	+	1.43691i	0.823003	+	0.568037i	$0.192297\pi$
$509$	7.39923	+	32.4181i	0.327965	+	1.43691i	−0.495038	+	0.868871i	$0.664846\pi$
$510$	−1.15787			−0.0512712
$511$	−4.14209	−	18.1477i	−0.183235	−	0.802805i
$512$	2.08485	−	2.61431i	0.0921381	−	0.115537i
$513$	−0.808805	+	3.54361i	−0.0357096	+	0.156454i
$514$	0.0540195	−	0.236675i	0.00238270	−	0.0104393i
$515$	−3.81681	−	4.78612i	−0.168189	−	0.210902i
$516$	−5.42656	−	2.61329i	−0.238891	−	0.115044i
$517$	16.9641	−	8.16949i	0.746081	−	0.359294i
$518$	0.352721	−	0.442298i	0.0154977	−	0.0194334i
$519$	15.8299	+	19.8500i	0.694854	+	0.871320i
$520$	−0.678556	+	0.326775i	−0.0297567	+	0.0143300i
$521$	−11.6310			−0.509565			−0.254783	−	0.966998i	$-0.582004\pi$
$521$	−11.6310			−0.509565			−0.254783	+	0.966998i	$0.582004\pi$
$522$		0			0
$523$	−0.747202			−0.0326728			−0.0163364	−	0.999867i	$-0.505200\pi$
$523$	−0.747202			−0.0326728			−0.0163364	+	0.999867i	$0.505200\pi$
$524$	−26.2749	+	12.6533i	−1.14782	+	0.552763i
$525$	7.61912	+	9.55408i	0.332526	+	0.416974i
$526$	−0.791029	+	0.991919i	−0.0344905	+	0.0432497i
$527$	−11.1546	+	5.37179i	−0.485903	+	0.233999i
$528$	20.1533	+	9.70531i	0.877059	+	0.422370i
$529$	−6.12244	−	7.67729i	−0.266193	−	0.333795i
$530$	0.161459	−	0.707399i	0.00701334	−	0.0307274i
$531$	8.56945	−	37.5452i	0.371883	−	1.62932i
$532$	0.969818	−	1.21611i	0.0420469	−	0.0527252i
$533$	5.41849	+	23.7399i	0.234701	+	1.02829i
$534$	−1.22134			−0.0528525
$535$	−1.72258	−	7.54714i	−0.0744738	−	0.326291i
$536$	−0.625283	−	0.301121i	−0.0270081	−	0.0130064i
$537$	−53.6727	−	25.8474i	−2.31615	−	1.11540i
$538$	0.111410	+	0.488118i	0.00480321	+	0.0210442i
$539$	−5.15277			−0.221946
$540$	7.42786	+	32.5436i	0.319644	+	1.40045i
$541$	−12.0004	+	15.0480i	−0.515938	+	0.646965i	−0.969741	−	0.244136i	$-0.921496\pi$
$541$	−12.0004	+	15.0480i	−0.515938	+	0.646965i	0.453803	+	0.891102i	$0.350067\pi$
$542$	−0.163873	+	0.717977i	−0.00703897	+	0.0308397i
$543$	8.12087	−	35.5798i	0.348500	−	1.52688i
$544$	−1.64053	−	2.05716i	−0.0703373	−	0.0882001i
$545$	−18.4619	−	8.89080i	−0.790822	−	0.380840i
$546$	0.605765	−	0.291721i	0.0259244	−	0.0124845i
$547$	−15.7724	+	19.7779i	−0.674377	+	0.845642i	−0.994823	−	0.101624i	$-0.967596\pi$
$547$	−15.7724	+	19.7779i	−0.674377	+	0.845642i	0.320445	+	0.947267i	$0.396167\pi$
$548$	−3.56622	−	4.47190i	−0.152341	−	0.191030i
$549$	−44.3696	+	21.3673i	−1.89365	+	0.911933i
$550$	−0.152658			−0.00650938
$551$		0			0
$552$	1.84346			0.0784630
$553$	19.0149	−	9.15708i	0.808594	−	0.389398i
$554$	0.0281078	+	0.0352461i	0.00119419	+	0.00149746i
$555$	21.5970	−	27.0818i	0.916742	−	1.14956i
$556$	−40.0908	+	19.3067i	−1.70023	+	0.818788i
$557$	−32.5644	−	15.6822i	−1.37980	−	0.664476i	−0.410843	−	0.911706i	$-0.634765\pi$
$557$	−32.5644	−	15.6822i	−1.37980	−	0.664476i	−0.968957	+	0.247230i	$0.920480\pi$
$558$	−0.381544	−	0.478441i	−0.0161520	−	0.0202540i
$559$	−0.571066	+	2.50200i	−0.0241535	+	0.105823i
$560$	3.17591	−	13.9146i	0.134207	−	0.587998i
$561$	18.2958	−	22.9423i	0.772451	−	0.968623i
$562$	0.278953	+	1.22217i	0.0117669	+	0.0515542i
$563$	−8.84332			−0.372701			−0.186351	−	0.982483i	$-0.559666\pi$
$563$	−8.84332			−0.372701			−0.186351	+	0.982483i	$0.559666\pi$
$564$	13.6884	+	59.9726i	0.576384	+	2.52530i
$565$	−17.9235	−	8.63150i	−0.754047	−	0.363130i
$566$	−1.01093	−	0.486837i	−0.0424925	−	0.0204633i
$567$	−4.81310	−	21.0876i	−0.202131	−	0.885595i
$568$	0.382860			0.0160644
$569$	−3.66937	−	16.0766i	−0.153828	−	0.673964i	−0.991751	−	0.128177i	$-0.959088\pi$
$569$	−3.66937	−	16.0766i	−0.153828	−	0.673964i	0.837923	−	0.545788i	$-0.183770\pi$
$570$	−0.0522846	+	0.0655628i	−0.00218996	+	0.00274612i
$571$	5.03592	−	22.0638i	0.210747	−	0.923341i	−0.753315	−	0.657660i	$-0.771546\pi$
$571$	5.03592	−	22.0638i	0.210747	−	0.923341i	0.964061	−	0.265681i	$-0.0855967\pi$
$572$	2.12271	−	9.30019i	0.0887549	−	0.388861i
$573$	21.9362	+	27.5071i	0.916397	+	1.14913i
$574$	0.733100	+	0.353042i	0.0305990	+	0.0147357i
$575$	6.42842	−	3.09576i	0.268084	−	0.129102i
$576$	−30.5990	+	38.3700i	−1.27496	+	1.59875i
$577$	25.6504	+	32.1646i	1.06784	+	1.33903i	0.937665	+	0.347540i	$0.112983\pi$
$577$	25.6504	+	32.1646i	1.06784	+	1.33903i	0.130176	+	0.991491i	$0.458446\pi$
$578$	−0.392671	+	0.189100i	−0.0163330	+	0.00786554i
$579$	57.6859			2.39734
$580$		0			0
$581$	−32.0794			−1.33088
$582$	−0.592453	+	0.285311i	−0.0245580	+	0.0118265i
$583$	11.4653	+	14.3770i	0.474845	+	0.595436i
$584$	−0.947770	+	1.18847i	−0.0392190	+	0.0491791i
$585$	24.9527	−	12.0166i	1.03167	−	0.496825i
$586$	−0.219583	−	0.105745i	−0.00907087	−	0.00436830i
$587$	−16.3278	−	20.4744i	−0.673921	−	0.845070i	0.320857	−	0.947128i	$-0.396029\pi$
$587$	−16.3278	−	20.4744i	−0.673921	−	0.845070i	−0.994779	+	0.102057i	$0.967458\pi$
$588$	3.74603	−	16.4124i	0.154484	−	0.676837i
$589$	−0.199527	+	0.874186i	−0.00822137	+	0.0360202i
$590$	0.284491	−	0.356740i	0.0117123	−	0.0146867i
$591$	11.2559	+	49.3152i	0.463004	+	2.02855i
$592$	26.2001			1.07682
$593$	7.00624	+	30.6963i	0.287712	+	1.26055i	0.887657	+	0.460506i	$0.152332\pi$
$593$	7.00624	+	30.6963i	0.287712	+	1.26055i	−0.599945	+	0.800041i	$0.704811\pi$
$594$	0.671100	+	0.323185i	0.0275356	+	0.0132604i
$595$	−16.8692	−	8.12378i	−0.691570	−	0.333042i
$596$	1.88364	+	8.25279i	0.0771571	+	0.338047i
$597$	26.9726			1.10392
$598$	−0.0873543	−	0.382724i	−0.00357218	−	0.0156508i
$599$	−8.84051	+	11.0857i	−0.361214	+	0.452947i	−0.928918	−	0.370285i	$-0.879260\pi$
$599$	−8.84051	+	11.0857i	−0.361214	+	0.452947i	0.567705	+	0.823232i	$0.307832\pi$
$600$	0.222061	−	0.972912i	0.00906559	−	0.0397190i
$601$	−3.12047	+	13.6717i	−0.127287	+	0.557679i	0.870558	+	0.492065i	$0.163758\pi$
$601$	−3.12047	+	13.6717i	−0.127287	+	0.557679i	−0.997845	+	0.0656141i	$0.979099\pi$
$602$	0.0534676	+	0.0670463i	0.00217918	+	0.00273260i
$603$	22.9937	+	11.0732i	0.936376	+	0.450935i
$604$	14.0330	−	6.75794i	0.570995	−	0.274977i
$605$	8.22280	−	10.3111i	0.334304	−	0.419204i
$606$	−0.670001	−	0.840155i	−0.0272169	−	0.0341289i
$607$	16.4878	−	7.94009i	0.669218	−	0.322278i	−0.0682425	−	0.997669i	$-0.521739\pi$
$607$	16.4878	−	7.94009i	0.669218	−	0.322278i	0.737460	+	0.675390i	$0.236025\pi$
$608$	−0.190564			−0.00772840
$609$		0			0
$610$	−0.583488			−0.0236247
$611$	23.6152	−	11.3725i	0.955367	−	0.460080i
$612$	40.2126	+	50.4250i	1.62550	+	2.03831i
$613$	18.6106	−	23.3369i	0.751673	−	0.942568i	−0.247984	−	0.968764i	$-0.579768\pi$
$613$	18.6106	−	23.3369i	0.751673	−	0.942568i	0.999657	+	0.0261960i	$0.00833939\pi$
$614$	0.194757	−	0.0937898i	0.00785973	−	0.00378505i
$615$	44.8876	+	21.6167i	1.81004	+	0.871670i
$616$	−0.397664	−	0.498655i	−0.0160223	−	0.0200914i
$617$	1.02220	−	4.47857i	0.0411524	−	0.180300i	−0.950175	−	0.311718i	$-0.899096\pi$
$617$	1.02220	−	4.47857i	0.0411524	−	0.180300i	0.991327	+	0.131417i	$0.0419528\pi$
$618$	0.0993083	−	0.435098i	0.00399477	−	0.0175022i
$619$	−3.91899	+	4.91425i	−0.157517	+	0.197521i	−0.854327	−	0.519735i	$-0.826031\pi$
$619$	−3.91899	+	4.91425i	−0.157517	+	0.197521i	0.696810	+	0.717256i	$0.254602\pi$
$620$	1.83241	+	8.02830i	0.0735912	+	0.322424i
$621$	−34.8138			−1.39703
$622$	−0.0991650	−	0.434470i	−0.00397616	−	0.0174207i
$623$	−17.7939	−	8.56911i	−0.712899	−	0.343314i
$624$	28.0547	+	13.5104i	1.12309	+	0.540850i
$625$	2.51694	+	11.0274i	0.100678	+	0.441098i
$626$	0.700923			0.0280145
$627$	−0.472911	−	2.07196i	−0.0188863	−	0.0827461i
$628$	7.88320	−	9.88523i	0.314574	−	0.394463i
$629$	7.64822	−	33.5090i	0.304954	−	1.33609i
$630$	0.205933	−	0.902250i	0.00820455	−	0.0359465i
$631$	6.03968	+	7.57352i	0.240436	+	0.301497i	0.887378	−	0.461042i	$-0.152524\pi$
$631$	6.03968	+	7.57352i	0.240436	+	0.301497i	−0.646943	+	0.762539i	$0.723953\pi$
$632$	−1.55281	−	0.747795i	−0.0617675	−	0.0297457i
$633$	−0.693475	+	0.333960i	−0.0275632	+	0.0132737i
$634$	0.0389997	−	0.0489040i	0.00154887	−	0.00194223i
$635$	−13.0839	−	16.4067i	−0.519220	−	0.651082i
$636$	−54.1284	+	26.0669i	−2.14633	+	1.03362i
$637$	−7.17299			−0.284204
$638$		0			0
$639$	−14.0790			−0.556956
$640$	−2.10206	+	1.01230i	−0.0830913	+	0.0400147i
$641$	2.99201	+	3.75186i	0.118177	+	0.148189i	0.837401	−	0.546589i	$-0.184074\pi$
$641$	2.99201	+	3.75186i	0.118177	+	0.148189i	−0.719224	+	0.694778i	$0.755503\pi$
$642$	0.351871	−	0.441232i	0.0138872	−	0.0174140i
$643$	−11.0564	+	5.32449i	−0.436022	+	0.209977i	−0.639001	−	0.769206i	$-0.720652\pi$
$643$	−11.0564	+	5.32449i	−0.436022	+	0.209977i	0.202979	+	0.979183i	$0.434938\pi$
$644$	13.4230	+	6.46417i	0.528940	+	0.254724i
$645$	3.27381	+	4.10523i	0.128906	+	0.161643i
$646$	−0.0185157	+	0.0811226i	−0.000728490	+	0.00319172i
$647$	2.36528	−	10.3630i	0.0929888	−	0.407411i	−0.906914	−	0.421315i	$-0.861569\pi$
$647$	2.36528	−	10.3630i	0.0929888	−	0.407411i	0.999903	+	0.0139040i	$0.00442592\pi$
$648$	−1.10131	+	1.38100i	−0.0432635	+	0.0542507i
$649$	2.57320	+	11.2739i	0.101007	+	0.442541i
$650$	−0.212510			−0.00833534
$651$	−3.27312	−	14.3405i	−0.128284	−	0.562047i
$652$	3.16762	+	1.52544i	0.124053	+	0.0597410i
$653$	25.2655	+	12.1672i	0.988715	+	0.476140i	0.857094	−	0.515160i	$-0.172268\pi$
$653$	25.2655	+	12.1672i	0.988715	+	0.476140i	0.131621	+	0.991300i	$0.457982\pi$
$654$	−0.332416	−	1.45641i	−0.0129985	−	0.0569502i
$655$	25.4238			0.993391
$656$	8.38543	+	36.7390i	0.327396	+	1.43442i
$657$	34.8526	−	43.7038i	1.35973	−	1.70505i
$658$	0.194894	−	0.853886i	0.00759775	−	0.0332879i
$659$	−4.51304	+	19.7729i	−0.175803	+	0.770243i	0.807736	+	0.589545i	$0.200693\pi$
$659$	−4.51304	+	19.7729i	−0.175803	+	0.770243i	−0.983539	+	0.180698i	$0.942164\pi$
$660$	−12.1691	−	15.2596i	−0.473681	−	0.593977i
$661$	28.2268	+	13.5933i	1.09790	+	0.528719i	0.892996	−	0.450064i	$-0.148599\pi$
$661$	28.2268	+	13.5933i	1.09790	+	0.528719i	0.204900	+	0.978783i	$0.434313\pi$
$662$	−1.12922	+	0.543804i	−0.0438884	+	0.0211355i
$663$	25.4690	−	31.9371i	0.989134	−	1.24034i
$664$	1.63336	+	2.04817i	0.0633866	+	0.0794843i
$665$	−1.22174	+	0.588361i	−0.0473772	+	0.0228157i
$666$	1.69887			0.0658297
$667$		0			0
$668$	27.8161			1.07624
$669$	24.9786	−	12.0291i	0.965728	−	0.465070i
$670$	0.188532	+	0.236412i	0.00728362	+	0.00913338i
$671$	9.21989	−	11.5614i	0.355930	−	0.446322i
$672$	2.81651	−	1.35636i	0.108649	−	0.0523226i
$673$	−36.6770	−	17.6627i	−1.41379	−	0.680848i	−0.437887	−	0.899030i	$-0.644273\pi$
$673$	−36.6770	−	17.6627i	−1.41379	−	0.680848i	−0.975908	+	0.218183i	$0.929987\pi$
$674$	0.0246185	+	0.0308707i	0.000948271	+	0.00118909i
$675$	−4.19362	+	18.3734i	−0.161412	+	0.707194i
$676$	−2.82551	+	12.3794i	−0.108673	+	0.476129i
$677$	−5.16340	+	6.47470i	−0.198445	+	0.248843i	−0.871090	−	0.491123i	$-0.836587\pi$
$677$	−5.16340	+	6.47470i	−0.198445	+	0.248843i	0.672645	+	0.739965i	$0.265158\pi$
$678$	−0.322722	−	1.41394i	−0.0123941	−	0.0543019i
$679$	−10.6334			−0.408071
$680$	0.340237	+	1.49067i	0.0130475	+	0.0571647i
$681$	−13.1333	−	6.32468i	−0.503270	−	0.242362i
$682$	0.165556	+	0.0797277i	0.00633948	+	0.00305293i
$683$	−0.748879	−	3.28106i	−0.0286551	−	0.125546i	0.958577	−	0.284832i	$-0.0919379\pi$
$683$	−0.748879	−	3.28106i	−0.0286551	−	0.125546i	−0.987232	+	0.159286i	$0.949081\pi$
$684$	4.67109			0.178604
$685$	1.10958	+	4.86140i	0.0423949	+	0.185744i
$686$	−0.525401	+	0.658832i	−0.0200599	+	0.0251543i
$687$	4.62586	−	20.2672i	0.176488	−	0.773243i
$688$	−0.883758	+	3.87200i	−0.0336930	+	0.147618i
$689$	15.9604	+	20.0138i	0.608045	+	0.762464i
$690$	−0.723657	−	0.348495i	−0.0275491	−	0.0132670i
$691$	−0.950641	+	0.457805i	−0.0361641	+	0.0174157i	−0.451878	−	0.892080i	$-0.649246\pi$
$691$	−0.950641	+	0.457805i	−0.0361641	+	0.0174157i	0.415714	+	0.909495i	$0.363532\pi$
$692$	10.4474	−	13.1006i	0.397150	−	0.498011i
$693$	14.6234	+	18.3372i	0.555497	+	0.696571i
$694$	0.327032	−	0.157490i	0.0124139	−	0.00597824i
$695$	38.7922			1.47147
$696$		0			0
$697$	49.4358			1.87251
$698$	1.30614	−	0.629002i	0.0494380	−	0.0238081i
$699$	−32.5264	−	40.7868i	−1.23026	−	1.54270i
$700$	5.02846	−	6.30549i	0.190058	−	0.238325i
$701$	−12.6726	+	6.10279i	−0.478637	+	0.230499i	−0.657616	−	0.753354i	$-0.728435\pi$
$701$	−12.6726	+	6.10279i	−0.478637	+	0.230499i	0.178979	+	0.983853i	$0.442721\pi$
$702$	0.934215	+	0.449894i	0.0352597	+	0.0169802i
$703$	−1.55205	−	1.94620i	−0.0585365	−	0.0734025i
$704$	3.27922	−	14.3672i	0.123590	−	0.541484i
$705$	11.9333	−	52.2833i	0.449435	−	1.96910i
$706$	−0.377200	+	0.472994i	−0.0141961	+	0.0178013i
$707$	−3.86672	−	16.9412i	−0.145423	−	0.637140i
$708$	−37.7800			−1.41986
$709$	−0.907390	−	3.97553i	−0.0340777	−	0.149304i	0.955027	−	0.296520i	$-0.0958261\pi$
$709$	−0.907390	−	3.97553i	−0.0340777	−	0.149304i	−0.989104	+	0.147215i	$0.952969\pi$
$710$	−0.150293	−	0.0723771i	−0.00564038	−	0.00271627i
$711$	57.1019	+	27.4988i	2.14149	+	1.03129i
$712$	0.358888	+	1.57239i	0.0134499	+	0.0589278i
$713$	−8.58835			−0.321636
$714$	−0.303738	−	1.33076i	−0.0113671	−	0.0498026i
$715$	−5.18511	+	6.50193i	−0.193912	+	0.243158i
$716$	−8.74872	+	38.3307i	−0.326955	+	1.43248i
$717$	−14.3533	+	62.8860i	−0.536035	+	2.34852i
$718$	−0.582964	−	0.731014i	−0.0217560	−	0.0272812i
$719$	−7.50095	−	3.61226i	−0.279738	−	0.134715i	0.288754	−	0.957403i	$-0.406759\pi$
$719$	−7.50095	−	3.61226i	−0.279738	−	0.134715i	−0.568493	+	0.822688i	$0.692473\pi$
$720$	38.6158	−	18.5964i	1.43913	−	0.693047i
$721$	4.49956	−	5.64227i	0.167572	−	0.210129i
$722$	−0.493140	−	0.618379i	−0.0183528	−	0.0230137i
$723$	−24.5323	+	11.8141i	−0.912365	+	0.439372i
$724$	−24.0858			−0.895144
$725$		0			0
$726$	0.961467			0.0356834
$727$	−33.2338	+	16.0046i	−1.23258	+	0.593577i	−0.932787	−	0.360429i	$-0.882630\pi$
$727$	−33.2338	+	16.0046i	−1.23258	+	0.593577i	−0.299788	+	0.954006i	$0.596916\pi$
$728$	−0.553574	−	0.694160i	−0.0205168	−	0.0257273i
$729$	−13.8082	+	17.3150i	−0.511416	+	0.641296i
$730$	0.596722	−	0.287366i	0.0220857	−	0.0106359i
$731$	4.69417	+	2.26060i	0.173620	+	0.0836111i
$732$	30.1221	+	37.7719i	1.11334	+	1.39609i
$733$	−2.25639	+	9.88588i	−0.0833416	+	0.365143i	−0.999351	−	0.0360127i	$-0.988534\pi$
$733$	−2.25639	+	9.88588i	−0.0833416	+	0.365143i	0.916010	+	0.401156i	$0.131391\pi$
$734$	−0.0474197	+	0.207759i	−0.00175029	+	0.00766853i
$735$	−9.15038	+	11.4742i	−0.337517	+	0.423233i
$736$	−0.406154	−	1.77948i	−0.0149710	−	0.0655924i
$737$	−7.66338			−0.282284
$738$	0.543728	+	2.38223i	0.0200149	+	0.0876911i
$739$	10.9875	+	5.29132i	0.404183	+	0.194644i	0.624920	−	0.780689i	$-0.285132\pi$
$739$	10.9875	+	5.29132i	0.404183	+	0.194644i	−0.220736	+	0.975334i	$0.570846\pi$
$740$	−20.5970	−	9.91901i	−0.757162	−	0.364630i
$741$	−0.658323	−	2.88430i	−0.0241841	−	0.105957i
$742$	0.855386			0.0314022
$743$	−7.28664	−	31.9248i	−0.267321	−	1.17121i	−0.913117	−	0.407699i	$-0.866331\pi$
$743$	−7.28664	−	31.9248i	−0.267321	−	1.17121i	0.645796	−	0.763510i	$-0.276526\pi$
$744$	−0.748938	+	0.939138i	−0.0274574	+	0.0344305i
$745$	1.64213	−	7.19466i	0.0601631	−	0.263592i
$746$	−0.238101	+	1.04319i	−0.00871750	+	0.0381939i
$747$	−60.0639	−	75.3178i	−2.19762	−	2.75573i
$748$	−17.4487	−	8.40286i	−0.637988	−	0.307239i
$749$	8.22223	−	3.95962i	0.300434	−	0.144681i
$750$	−0.960790	+	1.20479i	−0.0350831	+	0.0439928i
$751$	−29.8089	−	37.3791i	−1.08774	−	1.36398i	−0.926163	−	0.377124i	$-0.876913\pi$
$751$	−29.8089	−	37.3791i	−1.08774	−	1.36398i	−0.161579	−	0.986860i	$-0.551659\pi$
$752$	36.5458	−	17.5995i	1.33269	−	0.641789i
$753$	−19.6882			−0.717478
$754$		0			0
$755$	−13.5785			−0.494171
$756$	−35.4546	+	17.0740i	−1.28947	+	0.620977i
$757$	9.26322	+	11.6157i	0.336678	+	0.422180i	0.921135	−	0.389244i	$-0.127264\pi$
$757$	9.26322	+	11.6157i	0.336678	+	0.422180i	−0.584457	+	0.811425i	$0.698692\pi$
$758$	0.217569	−	0.272822i	0.00790244	−	0.00990935i
$759$	18.3399	−	8.83204i	0.665697	−	0.320583i
$760$	0.0997713	+	0.0480473i	0.00361909	+	0.00174286i
$761$	11.4441	+	14.3504i	0.414847	+	0.520201i	0.944721	−	0.327875i	$-0.106332\pi$
$761$	11.4441	+	14.3504i	0.414847	+	0.520201i	−0.529875	+	0.848076i	$0.677761\pi$
$762$	0.340427	−	1.49151i	0.0123324	−	0.0540317i
$763$	5.37537	−	23.5510i	0.194602	−	0.852605i
$764$	14.4774	−	18.1541i	0.523775	−	0.656793i
$765$	−12.5116	−	54.8169i	−0.452358	−	1.98191i
$766$	1.06216			0.0383772
$767$	3.58206	+	15.6940i	0.129341	+	0.566679i
$768$	43.2628	+	20.8343i	1.56111	+	0.751792i
$769$	−11.7658	−	5.66609i	−0.424284	−	0.204324i	0.209543	−	0.977799i	$-0.432802\pi$
$769$	−11.7658	−	5.66609i	−0.424284	−	0.204324i	−0.633827	+	0.773475i	$0.718517\pi$
$770$	0.0618367	+	0.270924i	0.00222844	+	0.00976343i
$771$	17.5232			0.631082
$772$	−8.47170	−	37.1170i	−0.304903	−	1.33587i
$773$	18.8830	−	23.6785i	0.679174	−	0.851658i	−0.316104	−	0.948725i	$-0.602375\pi$
$773$	18.8830	−	23.6785i	0.679174	−	0.851658i	0.995278	+	0.0970671i	$0.0309461\pi$
$774$	−0.0573047	+	0.251068i	−0.00205977	+	0.00902446i
$775$	−1.03454	+	4.53261i	−0.0371618	+	0.162816i
$776$	0.541409	+	0.678905i	0.0194354	+	0.0243713i
$777$	36.7912	+	17.7177i	1.31988	+	0.635620i
$778$	−1.03265	+	0.497298i	−0.0370223	+	0.0178290i
$779$	2.23232	−	2.79924i	0.0799812	−	0.100293i
$780$	−16.9402	−	21.2423i	−0.606555	−	0.760596i
$781$	3.80892	−	1.83428i	0.136294	−	0.0656357i
$782$	−0.796981			−0.0285000
$783$		0			0
$784$	−11.1006			−0.396451
$785$	−9.93100	+	4.78252i	−0.354452	+	0.170695i
$786$	1.15562	+	1.44910i	0.0412196	+	0.0516877i
$787$	−1.84797	+	2.31728i	−0.0658730	+	0.0826021i	−0.813676	−	0.581318i	$-0.802537\pi$
$787$	−1.84797	+	2.31728i	−0.0658730	+	0.0826021i	0.747803	+	0.663920i	$0.231109\pi$
$788$	30.0779	−	14.4848i	1.07148	−	0.515999i
$789$	−82.5099	−	39.7347i	−2.93743	−	1.41459i
$790$	0.468195	+	0.587098i	0.0166576	+	0.0208880i
$791$	5.21860	−	22.8642i	0.185552	−	0.812957i
$792$	0.426202	−	1.86731i	0.0151444	−	0.0663521i
$793$	12.8347	−	16.0942i	0.455773	−	0.571521i
$794$	−0.104774	−	0.459043i	−0.00371827	−	0.0162908i
$795$	52.3751			1.85755
$796$	−3.96118	−	17.3551i	−0.140400	−	0.615134i
$797$	21.5892	+	10.3968i	0.764729	+	0.368274i	0.775237	−	0.631670i	$-0.217630\pi$
$797$	21.5892	+	10.3968i	0.764729	+	0.368274i	−0.0105075	+	0.999945i	$0.503345\pi$
$798$	−0.0890685	−	0.0428931i	−0.00315299	−	0.00151840i
$799$	−11.8409	−	51.8785i	−0.418902	−	1.83533i
$800$	−0.988067			−0.0349334
$801$	−13.1975	−	57.8219i	−0.466310	−	2.04304i
$802$	0.870920	−	1.09210i	0.0307532	−	0.0385633i
$803$	−3.73506	+	16.3644i	−0.131807	+	0.577486i
$804$	5.57122	−	24.4091i	0.196482	−	0.860843i
$805$	−8.09801	−	10.1546i	−0.285417	−	0.357902i
$806$	0.230465	+	0.110986i	0.00811779	+	0.00390932i
$807$	−32.5608	+	15.6805i	−1.14619	+	0.551978i
$808$	−0.884763	+	1.10946i	−0.0311258	+	0.0390306i
$809$	30.4028	+	38.1238i	1.06890	+	1.34036i	0.937090	+	0.349089i	$0.113509\pi$
$809$	30.4028	+	38.1238i	1.06890	+	1.34036i	0.131814	+	0.991274i	$0.457920\pi$
$810$	0.693391	−	0.333919i	0.0243633	−	0.0117327i
$811$	23.3346			0.819389			0.409695	−	0.912223i	$-0.365635\pi$
$811$	23.3346			0.819389			0.409695	+	0.912223i	$0.365635\pi$
$812$		0			0
$813$	−53.1583			−1.86434
$814$	−0.459610	+	0.221337i	−0.0161093	+	0.00775785i
$815$	−1.91100	−	2.39632i	−0.0669396	−	0.0839396i
$816$	39.4148	−	49.4246i	1.37979	−	1.73021i
$817$	0.339973	−	0.163723i	0.0118942	−	0.00572793i
$818$	0.607762	+	0.292683i	0.0212499	+	0.0102334i
$819$	20.3567	+	25.5265i	0.711321	+	0.891969i
$820$	7.31674	−	32.0567i	0.255512	−	1.11947i
$821$	−8.15157	+	35.7144i	−0.284492	+	1.24644i	0.607475	+	0.794339i	$0.292182\pi$
$821$	−8.15157	+	35.7144i	−0.284492	+	1.24644i	−0.891967	+	0.452101i	$0.850675\pi$
$822$	−0.226653	+	0.284214i	−0.00790544	+	0.00991311i
$823$	−5.97881	−	26.1949i	−0.208408	−	0.913096i	−0.965626	−	0.259934i	$-0.916299\pi$
$823$	−5.97881	−	26.1949i	−0.208408	−	0.913096i	0.757218	−	0.653162i	$-0.226558\pi$
$824$	−0.589341			−0.0205307
$825$	−2.45202	−	10.7430i	−0.0853686	−	0.374024i
$826$	0.484639	+	0.233390i	0.0168628	+	0.00812067i
$827$	2.29776	+	1.10654i	0.0799010	+	0.0384783i	0.473407	−	0.880844i	$-0.343024\pi$
$827$	2.29776	+	1.10654i	0.0799010	+	0.0384783i	−0.393507	+	0.919322i	$0.628738\pi$
$828$	9.95561	+	43.6184i	0.345981	+	1.51584i
$829$	−29.2663			−1.01646			−0.508230	−	0.861221i	$-0.669700\pi$
$829$	−29.2663			−1.01646			−0.508230	+	0.861221i	$0.669700\pi$
$830$	−0.253987	−	1.11279i	−0.00881602	−	0.0386255i
$831$	−2.02890	+	2.54416i	−0.0703818	+	0.0882560i
$832$	4.56488	−	20.0001i	0.158259	−	0.693377i
$833$	−3.24045	+	14.1973i	−0.112275	+	0.491909i
$834$	1.76327	+	2.21107i	0.0610570	+	0.0765631i
$835$	−21.8482	−	10.5215i	−0.756087	−	0.364112i
$836$	−1.26371	+	0.608573i	−0.0437065	+	0.0210479i
$837$	14.1437	−	17.7356i	0.488877	−	0.613033i
$838$	0.734264	+	0.920737i	0.0253647	+	0.0318063i
$839$	−41.7931	+	20.1265i	−1.44286	+	0.694843i	−0.981339	−	0.192288i	$-0.938409\pi$
$839$	−41.7931	+	20.1265i	−1.44286	+	0.694843i	−0.461518	+	0.887131i	$0.652695\pi$
$840$	−1.81658			−0.0626781
$841$		0			0
$842$	1.27925			0.0440860
$843$	−81.5272	+	39.2615i	−2.80795	+	1.35224i
$844$	0.316724	+	0.397159i	0.0109021	+	0.0136708i
$845$	6.90183	−	8.65463i	0.237430	−	0.297728i
$846$	2.36971	−	1.14119i	0.0814722	−	0.0392349i
$847$	14.0078	+	6.74581i	0.481314	+	0.231789i
$848$	24.6997	+	30.9725i	0.848192	+	1.06360i
$849$	18.0225	−	78.9616i	0.618530	−	2.70996i
$850$	−0.0960031	+	0.420617i	−0.00329288	+	0.0144270i
$851$	14.8656	−	18.6409i	0.509587	−	0.639002i
$852$	3.07342	+	13.4656i	0.105294	+	0.461322i
$853$	51.5353			1.76453			0.882267	−	0.470749i	$-0.156016\pi$
$853$	51.5353			1.76453			0.882267	+	0.470749i	$0.156016\pi$
$854$	−0.153064	−	0.670617i	−0.00523774	−	0.0229481i
$855$	−3.66892	−	1.76686i	−0.125474	−	0.0604252i
$856$	−0.671452	−	0.323354i	−0.0229498	−	0.0110520i
$857$	−3.83189	−	16.7886i	−0.130895	−	0.573488i	−0.997253	−	0.0740653i	$-0.976403\pi$
$857$	−3.83189	−	16.7886i	−0.130895	−	0.573488i	0.866359	−	0.499423i	$-0.166454\pi$
$858$	−0.606280			−0.0206981
$859$	3.14784	+	13.7916i	0.107403	+	0.470563i	0.999813	+	0.0193380i	$0.00615585\pi$
$859$	3.14784	+	13.7916i	0.107403	+	0.470563i	−0.892410	+	0.451226i	$0.850987\pi$
$860$	2.16065	−	2.70937i	0.0736775	−	0.0923887i
$861$	−13.0695	+	57.2610i	−0.445406	+	1.95145i
$862$	0.0907767	−	0.397719i	0.00309187	−	0.0135464i
$863$	−11.6034	−	14.5502i	−0.394986	−	0.495296i	0.544080	−	0.839033i	$-0.316879\pi$
$863$	−11.6034	−	14.5502i	−0.394986	−	0.495296i	−0.939066	+	0.343737i	$0.888307\pi$
$864$	4.34363	+	2.09178i	0.147773	+	0.0711639i
$865$	−13.1613	+	6.33813i	−0.447497	+	0.215503i
$866$	−0.607515	+	0.761800i	−0.0206442	+	0.0258870i
$867$	−19.6147	−	24.5961i	−0.666150	−	0.835326i
$868$	−8.74643	+	4.21206i	−0.296873	+	0.142967i
$869$	−19.0310			−0.645583
$870$		0			0
$871$	−10.6679			−0.361469
$872$	−1.77735	+	0.855927i	−0.0601887	+	0.0289853i
$873$	−19.9094	−	24.9656i	−0.673830	−	0.844956i
$874$	−0.0359884	+	0.0451280i	−0.00121733	+	0.00152648i
$875$	−22.4510	+	10.8118i	−0.758981	+	0.365506i
$876$	−49.4078	−	23.7935i	−1.66934	−	0.803909i
$877$	5.30368	+	6.65061i	0.179093	+	0.224575i	0.863272	−	0.504738i	$-0.168411\pi$
$877$	5.30368	+	6.65061i	0.179093	+	0.224575i	−0.684180	+	0.729313i	$0.739840\pi$
$878$	0.127197	−	0.557287i	0.00429269	−	0.0188075i
$879$	3.91464	−	17.1512i	0.132038	−	0.578495i
$880$	−8.02427	+	10.0621i	−0.270498	+	0.339194i
$881$	−6.93518	−	30.3850i	−0.233652	−	1.02370i	−0.946582	−	0.322462i	$-0.895490\pi$
$881$	−6.93518	−	30.3850i	−0.233652	−	1.02370i	0.712930	−	0.701235i	$-0.247368\pi$
$882$	−0.719788			−0.0242365
$883$	−4.52792	−	19.8381i	−0.152377	−	0.667606i	−0.992191	−	0.124732i	$-0.960193\pi$
$883$	−4.52792	−	19.8381i	−0.152377	−	0.667606i	0.839814	−	0.542875i	$-0.182664\pi$
$884$	−24.2897	−	11.6973i	−0.816952	−	0.393423i
$885$	29.6744	+	14.2904i	0.997493	+	0.480367i
$886$	0.0856205	+	0.375128i	0.00287648	+	0.0126027i
$887$	−11.2240			−0.376866			−0.188433	−	0.982086i	$-0.560341\pi$
$887$	−11.2240			−0.376866			−0.188433	+	0.982086i	$0.560341\pi$
$888$	−0.742046	−	3.25112i	−0.0249014	−	0.109100i
$889$	15.4244	−	19.3416i	0.517318	−	0.648697i
$890$	0.156368	−	0.685092i	0.00524146	−	0.0229643i
$891$	−4.34014	+	19.0154i	−0.145400	+	0.637040i
$892$	−11.4082	−	14.3055i	−0.381975	−	0.478982i
$893$	−3.47225	−	1.67215i	−0.116194	−	0.0559562i
$894$	0.484721	−	0.233429i	0.0162115	−	0.00780704i
$895$	21.3704	−	26.7976i	0.714334	−	0.895746i
$896$	−1.71489	−	2.15040i	−0.0572903	−	0.0718398i
$897$	25.5303	−	12.2948i	0.852433	−	0.410510i
$898$	−0.744296			−0.0248375
$899$		0			0
$900$	24.2194			0.807314
$901$	46.8230	−	22.5488i	1.55990	−	0.751209i
$902$	−0.457469	−	0.573648i	−0.0152320	−	0.0191004i
$903$	−3.85944	+	4.83958i	−0.128434	+	0.161051i
$904$	−1.72551	+	0.830964i	−0.0573898	+	0.0276374i
$905$	18.9183	+	9.11056i	0.628864	+	0.302845i
$906$	−0.617198	−	0.773942i	−0.0205050	−	0.0257125i
$907$	−9.07758	+	39.7715i	−0.301416	+	1.32059i	0.566575	+	0.824010i	$0.308268\pi$
$907$	−9.07758	+	39.7715i	−0.301416	+	1.32059i	−0.867991	+	0.496580i	$0.834589\pi$
$908$	−2.14075	+	9.37924i	−0.0710433	+	0.311261i
$909$	32.5356	−	40.7984i	1.07914	−	1.35320i
$910$	0.0860806	+	0.377144i	0.00285355	+	0.0125022i
$911$	−30.2991			−1.00385			−0.501926	−	0.864910i	$-0.667375\pi$
$911$	−30.2991			−1.00385			−0.501926	+	0.864910i	$0.667375\pi$
$912$	−1.01879	−	4.46363i	−0.0337356	−	0.147805i
$913$	26.0624	+	12.5510i	0.862541	+	0.415378i
$914$	−0.0953658	−	0.0459257i	−0.00315442	−	0.00151909i
$915$	−9.37208	−	41.0618i	−0.309831	−	1.35746i
$916$	−13.7199			−0.453320
$917$	6.66933	+	29.2202i	0.220241	+	0.964937i
$918$	1.31250	−	1.64583i	0.0433191	−	0.0543204i
$919$	−5.90500	+	25.8715i	−0.194788	+	0.853422i	0.779192	+	0.626786i	$0.215630\pi$
$919$	−5.90500	+	25.8715i	−0.194788	+	0.853422i	−0.973980	+	0.226636i	$0.927227\pi$
$920$	−0.236018	+	1.03406i	−0.00778128	+	0.0340920i
$921$	9.72848	+	12.1991i	0.320564	+	0.401975i
$922$	0.378398	+	0.182227i	0.0124619	+	0.00600132i
$923$	5.30227	−	2.55344i	0.174526	−	0.0840474i
$924$	14.3459	−	17.9892i	0.471946	−	0.591802i
$925$	−8.04729	−	10.0910i	−0.264593	−	0.331789i
$926$	−1.05244	+	0.506826i	−0.0345852	+	0.0166553i
$927$	21.6720			0.711801
$928$		0			0
$929$	4.73988			0.155510			0.0777551	−	0.996972i	$-0.475225\pi$
$929$	4.73988			0.155510			0.0777551	+	0.996972i	$0.475225\pi$
$930$	0.471536	−	0.227080i	0.0154623	−	0.00744623i
$931$	0.657582	+	0.824581i	0.0215514	+	0.0270246i
$932$	−21.4668	+	26.9185i	−0.703167	+	0.881743i
$933$	28.9822	−	13.9571i	0.948833	−	0.456934i
$934$	0.768219	+	0.369955i	0.0251369	+	0.0121053i
$935$	10.5267	+	13.2001i	0.344260	+	0.431689i
$936$	0.593301	−	2.59942i	0.0193926	−	0.0849647i
$937$	4.15188	−	18.1906i	0.135636	−	0.594260i	−0.860728	−	0.509065i	$-0.829991\pi$
$937$	4.15188	−	18.1906i	0.135636	−	0.594260i	0.996364	−	0.0851954i	$-0.0271514\pi$
$938$	−0.222257	+	0.278701i	−0.00725694	+	0.00909992i
$939$	11.2583	+	49.3260i	0.367402	+	1.60969i
$940$	−35.3933			−1.15440
$941$	5.02127	+	21.9996i	0.163689	+	0.717167i	0.988433	+	0.151661i	$0.0484622\pi$
$941$	5.02127	+	21.9996i	0.163689	+	0.717167i	−0.824744	+	0.565507i	$0.808681\pi$
$942$	−0.723997	−	0.348659i	−0.0235891	−	0.0113599i
$943$	30.8969	+	14.8792i	1.00614	+	0.484533i
$944$	5.54345	+	24.2875i	0.180424	+	0.790489i
$945$	34.3062			1.11598
$946$	−0.0172072	−	0.0753898i	−0.000559455	−	0.00245113i
$947$	−17.2315	+	21.6077i	−0.559950	+	0.702155i	−0.978549	−	0.206016i	$-0.933950\pi$
$947$	−17.2315	+	21.6077i	−0.559950	+	0.702155i	0.418599	+	0.908171i	$0.362521\pi$
$948$	13.8354	−	60.6169i	0.449353	−	1.96874i
$949$	−5.19945	+	22.7803i	−0.168781	+	0.739478i
$950$	0.0194818	+	0.0244294i	0.000632073	+	0.000792595i
$951$	4.06794	+	1.95902i	0.131912	+	0.0635255i
$952$	−1.62402	+	0.782085i	−0.0526346	+	0.0253475i
$953$	−23.2906	+	29.2055i	−0.754458	+	0.946060i	−0.999726	−	0.0233952i	$-0.992552\pi$
$953$	−23.2906	+	29.2055i	−0.754458	+	0.946060i	0.245269	+	0.969455i	$0.421124\pi$
$954$	1.60158	+	2.00832i	0.0518531	+	0.0650217i
$955$	−18.2382	+	8.78305i	−0.590174	+	0.284213i
$956$	42.5708			1.37684
$957$		0			0
$958$	−0.899769			−0.0290702
$959$	−5.29625	+	2.55054i	−0.171025	+	0.0823612i
$960$	−26.1696	−	32.8157i	−0.844621	−	1.05912i
$961$	−15.8390	+	19.8615i	−0.510936	+	0.640694i
$962$	−0.639807	+	0.308115i	−0.0206282	+	0.00993403i
$963$	24.6915	+	11.8908i	0.795672	+	0.383176i
$964$	11.2044	+	14.0498i	0.360869	+	0.452515i
$965$	−7.38551	+	32.3580i	−0.237748	+	1.04164i
$966$	0.210700	−	0.923136i	0.00677915	−	0.0297014i
$967$	−24.9098	+	31.2359i	−0.801046	+	1.00448i	0.198656	+	0.980069i	$0.436342\pi$
$967$	−24.9098	+	31.2359i	−0.801046	+	1.00448i	−0.999702	+	0.0244104i	$0.992229\pi$
$968$	−0.282525	−	1.23782i	−0.00908070	−	0.0397851i
$969$	−6.00624			−0.192948
$970$	−0.0841890	−	0.368856i	−0.00270315	−	0.0118433i
$971$	13.3182	+	6.41370i	0.427401	+	0.205825i	0.635203	−	0.772346i	$-0.280917\pi$
$971$	13.3182	+	6.41370i	0.427401	+	0.205825i	−0.207802	+	0.978171i	$0.566631\pi$
$972$	−5.61945	−	2.70618i	−0.180244	−	0.0868008i
$973$	10.1762	+	44.5849i	0.326234	+	1.42933i
$974$	0.687749			0.0220369
$975$	−3.41338	−	14.9550i	−0.109316	−	0.478943i
$976$	19.8624	−	24.9067i	0.635781	−	0.797244i
$977$	2.18704	−	9.58204i	0.0699695	−	0.306556i	−0.927819	−	0.373032i	$-0.878318\pi$
$977$	2.18704	−	9.58204i	0.0699695	−	0.306556i	0.997788	+	0.0664753i	$0.0211754\pi$
$978$	0.0497219	−	0.217846i	0.00158993	−	0.00696594i
$979$	11.1038	+	13.9237i	0.354878	+	0.445003i
$980$	8.72670	+	4.20256i	0.278764	+	0.134246i
$981$	65.3589	−	31.4752i	2.08675	−	1.00493i
$982$	−0.765608	+	0.960042i	−0.0244315	+	0.0306362i
$983$	29.5339	+	37.0344i	0.941985	+	1.18121i	0.983286	+	0.182066i	$0.0582783\pi$
$983$	29.5339	+	37.0344i	0.941985	+	1.18121i	−0.0413009	+	0.999147i	$0.513150\pi$
$984$	4.32138	−	2.08106i	0.137760	−	0.0663419i
$985$	−29.1037			−0.927320
$986$		0			0
$987$	63.2209			2.01234
$988$	−1.75917	+	0.847173i	−0.0559667	+	0.0269522i
$989$	2.25342	+	2.82570i	0.0716547	+	0.0898522i
$990$	−0.520310	+	0.652448i	−0.0165365	+	0.0207362i
$991$	44.1305	−	21.2521i	1.40185	−	0.675096i	0.428316	−	0.903629i	$-0.359107\pi$
$991$	44.1305	−	21.2521i	1.40185	−	0.675096i	0.973536	+	0.228533i	$0.0733928\pi$
$992$	1.07155	+	0.516030i	0.0340217	+	0.0163840i
$993$	−56.4068	−	70.7319i	−1.79002	−	2.24461i
$994$	0.0437592	−	0.191721i	0.00138796	−	0.00608104i
$995$	−3.45330	+	15.1299i	−0.109477	+	0.479650i
$996$	−58.9242	+	73.8886i	−1.86708	+	2.34125i
$997$	−0.258554	−	1.13280i	−0.00818850	−	0.0358762i	0.970669	−	0.240421i	$-0.0772856\pi$
$997$	−0.258554	−	1.13280i	−0.00818850	−	0.0358762i	−0.978857	+	0.204545i	$0.934428\pi$
$998$	−0.196054			−0.00620597
$999$	14.0135	+	61.3974i	0.443369	+	1.94253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.q.571.4		48
29.2	odd	28		841.2.e.m.196.8		96
29.3	odd	28		841.2.e.m.267.8		96
29.4	even	14		841.2.a.j.1.4	yes	8
29.5	even	14		841.2.d.p.645.5		48
29.6	even	14		841.2.d.p.778.4		48
29.7	even	7	inner	841.2.d.q.574.5		48
29.8	odd	28		841.2.e.m.236.8		96
29.9	even	14		841.2.d.p.605.5		48
29.10	odd	28		841.2.b.f.840.9		16
29.11	odd	28		841.2.e.m.651.8		96
29.12	odd	4		841.2.e.m.270.8		96
29.13	even	14		841.2.d.p.190.5		48
29.14	odd	28		841.2.e.m.63.9		96
29.15	odd	28		841.2.e.m.63.8		96
29.16	even	7	inner	841.2.d.q.190.4		48
29.17	odd	4		841.2.e.m.270.9		96
29.18	odd	28		841.2.e.m.651.9		96
29.19	odd	28		841.2.b.f.840.8		16
29.20	even	7	inner	841.2.d.q.605.4		48
29.21	odd	28		841.2.e.m.236.9		96
29.22	even	14		841.2.d.p.574.4		48
29.23	even	7	inner	841.2.d.q.778.5		48
29.24	even	7	inner	841.2.d.q.645.4		48
29.25	even	7		841.2.a.i.1.5	✓	8
29.26	odd	28		841.2.e.m.267.9		96
29.27	odd	28		841.2.e.m.196.9		96
29.28	even	2		841.2.d.p.571.5		48
87.62	odd	14		7569.2.a.bd.1.5		8
87.83	odd	14		7569.2.a.bi.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.i.1.5	✓	8	29.25	even	7
841.2.a.j.1.4	yes	8	29.4	even	14
841.2.b.f.840.8		16	29.19	odd	28
841.2.b.f.840.9		16	29.10	odd	28
841.2.d.p.190.5		48	29.13	even	14
841.2.d.p.571.5		48	29.28	even	2
841.2.d.p.574.4		48	29.22	even	14
841.2.d.p.605.5		48	29.9	even	14
841.2.d.p.645.5		48	29.5	even	14
841.2.d.p.778.4		48	29.6	even	14
841.2.d.q.190.4		48	29.16	even	7	inner
841.2.d.q.571.4		48	1.1	even	1	trivial
841.2.d.q.574.5		48	29.7	even	7	inner
841.2.d.q.605.4		48	29.20	even	7	inner
841.2.d.q.645.4		48	29.24	even	7	inner
841.2.d.q.778.5		48	29.23	even	7	inner
841.2.e.m.63.8		96	29.15	odd	28
841.2.e.m.63.9		96	29.14	odd	28
841.2.e.m.196.8		96	29.2	odd	28
841.2.e.m.196.9		96	29.27	odd	28
841.2.e.m.236.8		96	29.8	odd	28
841.2.e.m.236.9		96	29.21	odd	28
841.2.e.m.267.8		96	29.3	odd	28
841.2.e.m.267.9		96	29.26	odd	28
841.2.e.m.270.8		96	29.12	odd	4
841.2.e.m.270.9		96	29.17	odd	4
841.2.e.m.651.8		96	29.11	odd	28
841.2.e.m.651.9		96	29.18	odd	28
7569.2.a.bd.1.5		8	87.62	odd	14
7569.2.a.bi.1.4		8	87.83	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.0377915 + 0.0181994i) q^{2} +(-1.88776 - 2.36718i) q^{3} +(-1.24588 + 1.56229i) q^{4} +(1.56952 - 0.755841i) q^{5} +(0.114422 + 0.0551030i) q^{6} +(1.28043 + 1.60561i) q^{7} +(0.0373185 - 0.163503i) q^{8} +(-1.37232 + 6.01254i) q^{9} +(-0.0455587 + 0.0571287i) q^{10} +(-0.412076 - 1.80542i) q^{11} +6.05014 q^{12} +(-0.573636 - 2.51326i) q^{13} +(-0.0776107 - 0.0373753i) q^{14} +(-4.75209 - 2.28849i) q^{15} +(-0.887735 - 3.88942i) q^{16} -5.23359 q^{17} +(-0.0575626 - 0.252198i) q^{18} +(-0.236328 + 0.296346i) q^{19} +(-0.774597 + 3.39373i) q^{20} +(1.38362 - 6.06202i) q^{21} +(0.0484306 + 0.0607300i) q^{22} +(-3.27095 - 1.57521i) q^{23} +(-0.457489 + 0.220315i) q^{24} +(-1.22535 + 1.53654i) q^{25} +(0.0674185 + 0.0845401i) q^{26} +(8.63967 - 4.16065i) q^{27} -4.10370 q^{28} +0.221238 q^{30} +(2.13135 - 1.02641i) q^{31} +(0.313462 + 0.393069i) q^{32} +(-3.49585 + 4.38366i) q^{33} +(0.197785 - 0.0952483i) q^{34} +(3.22326 + 1.55224i) q^{35} +(-7.68356 - 9.63488i) q^{36} +(-1.46137 + 6.40269i) q^{37} +(0.00353786 - 0.0155004i) q^{38} +(-4.86645 + 6.10234i) q^{39} +(-0.0650102 - 0.284828i) q^{40} -9.44586 q^{41} +(0.0580363 + 0.254274i) q^{42} +(-0.896932 - 0.431940i) q^{43} +(3.33399 + 1.60556i) q^{44} +(2.39064 + 10.4741i) q^{45} +0.152282 q^{46} +(2.26249 + 9.91261i) q^{47} +(-7.53112 + 9.44372i) q^{48} +(0.619164 - 2.71274i) q^{49} +(0.0183436 - 0.0803687i) q^{50} +(9.87976 + 12.3888i) q^{51} +(4.64112 + 2.23505i) q^{52} +(-8.94664 + 4.30848i) q^{53} +(-0.250785 + 0.314474i) q^{54} +(-2.01137 - 2.52218i) q^{55} +(0.310306 - 0.149436i) q^{56} +1.14763 q^{57} -6.24449 q^{59} +(9.49582 - 4.57294i) q^{60} +(4.97874 + 6.24315i) q^{61} +(-0.0618670 + 0.0775788i) q^{62} +(-11.4110 + 5.49523i) q^{63} +(7.16973 + 3.45276i) q^{64} +(-2.79996 - 3.51104i) q^{65} +(0.0523334 - 0.229287i) q^{66} +(0.920842 - 4.03447i) q^{67} +(6.52044 - 8.17637i) q^{68} +(2.44598 + 10.7165i) q^{69} -0.150061 q^{70} +(0.507993 + 2.22566i) q^{71} +(0.931855 + 0.448757i) q^{72} +(-8.16639 - 3.93273i) q^{73} +(-0.0612978 - 0.268563i) q^{74} +5.95042 q^{75} +(-0.168540 - 0.738424i) q^{76} +(2.37117 - 2.97336i) q^{77} +(0.0728514 - 0.319183i) q^{78} +(2.28679 - 10.0191i) q^{79} +(-4.33311 - 5.43354i) q^{80} +(-9.48935 - 4.56983i) q^{81} +(0.356973 - 0.171909i) q^{82} +(-9.73931 + 12.2127i) q^{83} +(7.74680 + 9.71418i) q^{84} +(-8.21423 + 3.95576i) q^{85} +0.0417574 q^{86} -0.310570 q^{88} +(-8.66452 + 4.17261i) q^{89} +(-0.280968 - 0.352322i) q^{90} +(3.30082 - 4.13910i) q^{91} +(6.53614 - 3.14764i) q^{92} +(-6.45317 - 3.10768i) q^{93} +(-0.265906 - 0.333436i) q^{94} +(-0.146931 + 0.643747i) q^{95} +(0.338723 - 1.48404i) q^{96} +(-3.22829 + 4.04814i) q^{97} +(0.0259711 + 0.113787i) q^{98} +11.4207 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 6 q^{3} - 6 q^{4} + q^{5} - 3 q^{6} + 15 q^{8} - 8 q^{9} - 3 q^{10} + 5 q^{11} - 72 q^{12} + 4 q^{13} + 15 q^{14} - 7 q^{15} + 2 q^{16} - 54 q^{17} - 11 q^{18} + 17 q^{19} + 7 q^{20} + 25 q^{21}+ \cdots - 90 q^{99}+O(q^{100}) \) 48 * q + 4 * q^2 + 6 * q^3 - 6 * q^4 + q^5 - 3 * q^6 + 15 * q^8 - 8 * q^9 - 3 * q^10 + 5 * q^11 - 72 * q^12 + 4 * q^13 + 15 * q^14 - 7 * q^15 + 2 * q^16 - 54 * q^17 - 11 * q^18 + 17 * q^19 + 7 * q^20 + 25 * q^21 - 25 * q^22 + 7 * q^23 - 25 * q^24 + 13 * q^25 + 3 * q^26 + 18 * q^27 + 150 * q^28 - 156 * q^30 + q^31 - 6 * q^32 - 12 * q^34 + 5 * q^35 + 19 * q^36 + 6 * q^37 + 14 * q^38 + 27 * q^39 - 25 * q^40 - 36 * q^41 - 15 * q^42 - 5 * q^43 + 20 * q^44 + q^45 - 84 * q^46 + 31 * q^47 + 11 * q^48 - 4 * q^49 + 11 * q^50 - 23 * q^51 - 2 * q^52 - 19 * q^53 + 46 * q^54 + 20 * q^55 + 20 * q^56 - 36 * q^57 - 6 * q^59 - 9 * q^60 + 21 * q^61 + 12 * q^62 + 10 * q^63 - q^64 + 17 * q^65 + 5 * q^66 - 2 * q^67 + 8 * q^68 - 14 * q^69 + 30 * q^70 + 12 * q^71 - 34 * q^73 + 27 * q^74 - 24 * q^75 - 16 * q^76 - 10 * q^77 - 6 * q^78 + 29 * q^79 + 41 * q^80 - 12 * q^81 + 22 * q^82 + 3 * q^83 - 10 * q^84 + 2 * q^85 - 30 * q^86 - 90 * q^88 + 36 * q^89 - 38 * q^90 + 4 * q^92 - 2 * q^93 - 13 * q^94 + 11 * q^95 + 2 * q^96 - 18 * q^97 + 27 * q^98 - 90 * q^99

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