LMFDB - Embedded newform 43.5.b.b.42.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,5,Mod(42,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	43.b (of order $2$, degree $1$, 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:	$4.44490841261$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 142x^{10} + 7173x^{8} + 157368x^{6} + 1510016x^{4} + 5098688x^{2} + 90352 $ x^12 + 142x^10 + 7173x^8 + 157368x^6 + 1510016x^4 + 5098688*x^2 + 90352
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.3
Root			$-4.43775i$ of defining polynomial
Character	$\chi$	$=$	43.42
Dual form			43.5.b.b.42.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.43775i q^{2} +6.93950i q^{3} -3.69363 q^{4} -22.3554i q^{5} +30.7958 q^{6} -51.9837i q^{7} -54.6126i q^{8} +32.8434 q^{9} +O(q^{10})$	\(q-4.43775i q^{2} +6.93950i q^{3} -3.69363 q^{4} -22.3554i q^{5} +30.7958 q^{6} -51.9837i q^{7} -54.6126i q^{8} +32.8434 q^{9} -99.2077 q^{10} -25.0158 q^{11} -25.6320i q^{12} -38.7510 q^{13} -230.691 q^{14} +155.135 q^{15} -301.455 q^{16} +111.381 q^{17} -145.751i q^{18} +238.930i q^{19} +82.5727i q^{20} +360.741 q^{21} +111.014i q^{22} +823.523 q^{23} +378.984 q^{24} +125.236 q^{25} +171.967i q^{26} +790.016i q^{27} +192.009i q^{28} +424.840i q^{29} -688.452i q^{30} -1447.58 q^{31} +463.982i q^{32} -173.597i q^{33} -494.282i q^{34} -1162.12 q^{35} -121.311 q^{36} +626.677i q^{37} +1060.31 q^{38} -268.912i q^{39} -1220.89 q^{40} +580.694 q^{41} -1600.88i q^{42} +(-528.728 + 1771.79i) q^{43} +92.3990 q^{44} -734.227i q^{45} -3654.59i q^{46} -170.609 q^{47} -2091.95i q^{48} -301.309 q^{49} -555.765i q^{50} +772.930i q^{51} +143.132 q^{52} +4308.39 q^{53} +3505.89 q^{54} +559.237i q^{55} -2838.97 q^{56} -1658.05 q^{57} +1885.33 q^{58} -65.4372 q^{59} -573.013 q^{60} -3896.58i q^{61} +6423.99i q^{62} -1707.32i q^{63} -2764.25 q^{64} +866.294i q^{65} -770.379 q^{66} -5449.76 q^{67} -411.402 q^{68} +5714.84i q^{69} +5157.19i q^{70} +5845.23i q^{71} -1793.66i q^{72} -4773.87i q^{73} +2781.04 q^{74} +869.073i q^{75} -882.519i q^{76} +1300.41i q^{77} -1193.37 q^{78} +10139.3 q^{79} +6739.15i q^{80} -2822.00 q^{81} -2576.98i q^{82} +4438.95 q^{83} -1332.45 q^{84} -2489.97i q^{85} +(7862.77 + 2346.36i) q^{86} -2948.17 q^{87} +1366.18i q^{88} -9870.51i q^{89} -3258.32 q^{90} +2014.42i q^{91} -3041.79 q^{92} -10045.5i q^{93} +757.120i q^{94} +5341.37 q^{95} -3219.80 q^{96} -7761.47 q^{97} +1337.14i q^{98} -821.602 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9}+O(q^{10}) $ 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9	$ 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9} + 182 q^{10} - 180 q^{11} - 216 q^{13} + 732 q^{14} - 92 q^{15} + 1076 q^{16} + 678 q^{17} - 2392 q^{21} + 1566 q^{23} - 4234 q^{24} - 174 q^{25} + 5710 q^{31} + 936 q^{35} + 4210 q^{36} + 1242 q^{38} - 2618 q^{40} + 4878 q^{41} - 1108 q^{43} - 15168 q^{44} - 5526 q^{47} - 8544 q^{49} + 24084 q^{52} + 1212 q^{53} - 10004 q^{54} - 10152 q^{56} - 7692 q^{57} - 4666 q^{58} + 14016 q^{59} + 15848 q^{60} - 15580 q^{64} + 29808 q^{66} - 1088 q^{67} + 15186 q^{68} - 7674 q^{74} - 67708 q^{78} + 24302 q^{79} - 23660 q^{81} - 7032 q^{83} + 37180 q^{84} - 14412 q^{86} + 17850 q^{87} + 4268 q^{90} + 48354 q^{92} + 606 q^{95} + 50546 q^{96} - 5842 q^{97} - 25924 q^{99}+O(q^{100}) $ 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9 + 182 * q^10 - 180 * q^11 - 216 * q^13 + 732 * q^14 - 92 * q^15 + 1076 * q^16 + 678 * q^17 - 2392 * q^21 + 1566 * q^23 - 4234 * q^24 - 174 * q^25 + 5710 * q^31 + 936 * q^35 + 4210 * q^36 + 1242 * q^38 - 2618 * q^40 + 4878 * q^41 - 1108 * q^43 - 15168 * q^44 - 5526 * q^47 - 8544 * q^49 + 24084 * q^52 + 1212 * q^53 - 10004 * q^54 - 10152 * q^56 - 7692 * q^57 - 4666 * q^58 + 14016 * q^59 + 15848 * q^60 - 15580 * q^64 + 29808 * q^66 - 1088 * q^67 + 15186 * q^68 - 7674 * q^74 - 67708 * q^78 + 24302 * q^79 - 23660 * q^81 - 7032 * q^83 + 37180 * q^84 - 14412 * q^86 + 17850 * q^87 + 4268 * q^90 + 48354 * q^92 + 606 * q^95 + 50546 * q^96 - 5842 * q^97 - 25924 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$		−	4.43775i		−	1.10944i	−0.832038	−	0.554719i	$-0.812826\pi$
$2$		−	4.43775i		−	1.10944i	0.832038	−	0.554719i	$-0.187174\pi$
$3$			6.93950i			0.771055i	0.922696	+	0.385528i	$0.125981\pi$
$3$			6.93950i			0.771055i	−0.922696	+	0.385528i	$0.874019\pi$
$4$	−3.69363			−0.230852
$5$		−	22.3554i		−	0.894216i	−0.894480	−	0.447108i	$-0.852454\pi$
$5$		−	22.3554i		−	0.894216i	0.894480	−	0.447108i	$-0.147546\pi$
$6$	30.7958			0.855438
$7$		−	51.9837i		−	1.06089i	−0.847719	−	0.530446i	$-0.822024\pi$
$7$		−	51.9837i		−	1.06089i	0.847719	−	0.530446i	$-0.177976\pi$
$8$		−	54.6126i		−	0.853322i
$9$	32.8434			0.405474
$10$	−99.2077			−0.992077
$11$	−25.0158			−0.206742			−0.103371	−	0.994643i	$-0.532963\pi$
$11$	−25.0158			−0.206742			−0.103371	+	0.994643i	$0.532963\pi$
$12$		−	25.6320i		−	0.178000i
$13$	−38.7510			−0.229296			−0.114648	−	0.993406i	$-0.536574\pi$
$13$	−38.7510			−0.229296			−0.114648	+	0.993406i	$0.536574\pi$
$14$	−230.691			−1.17699
$15$	155.135			0.689490
$16$	−301.455			−1.17756
$17$	111.381			0.385402			0.192701	−	0.981257i	$-0.438275\pi$
$17$	111.381			0.385402			0.192701	+	0.981257i	$0.438275\pi$
$18$		−	145.751i		−	0.449848i
$19$			238.930i			0.661856i	0.943656	+	0.330928i	$0.107362\pi$
$19$			238.930i			0.661856i	−0.943656	+	0.330928i	$0.892638\pi$
$20$			82.5727i			0.206432i
$21$	360.741			0.818007
$22$			111.014i			0.229367i
$23$	823.523			1.55675			0.778377	−	0.627797i	$-0.216043\pi$
$23$	823.523			1.55675			0.778377	+	0.627797i	$0.216043\pi$
$24$	378.984			0.657958
$25$	125.236			0.200377
$26$			171.967i			0.254389i
$27$			790.016i			1.08370i
$28$			192.009i			0.244909i
$29$			424.840i			0.505160i	0.967576	+	0.252580i	$0.0812791\pi$
$29$			424.840i			0.505160i	−0.967576	+	0.252580i	$0.918721\pi$
$30$		−	688.452i		−	0.764946i
$31$	−1447.58			−1.50632			−0.753162	−	0.657835i	$-0.771472\pi$
$31$	−1447.58			−1.50632			−0.753162	+	0.657835i	$0.771472\pi$
$32$			463.982i			0.453107i
$33$		−	173.597i		−	0.159409i
$34$		−	494.282i		−	0.427580i
$35$	−1162.12			−0.948668
$36$	−121.311			−0.0936045
$37$			626.677i			0.457763i	0.973454	+	0.228881i	$0.0735068\pi$
$37$			626.677i			0.457763i	−0.973454	+	0.228881i	$0.926493\pi$
$38$	1060.31			0.734287
$39$		−	268.912i		−	0.176800i
$40$	−1220.89			−0.763054
$41$	580.694			0.345446			0.172723	−	0.984970i	$-0.444744\pi$
$41$	580.694			0.345446			0.172723	+	0.984970i	$0.444744\pi$
$42$		−	1600.88i		−	0.907528i
$43$	−528.728	+	1771.79i	−0.285953	+	0.958244i
$43$	−528.728	+	1771.79i	−0.285953	+	0.958244i
$44$	92.3990			0.0477268
$45$		−	734.227i		−	0.362581i
$46$		−	3654.59i		−	1.72712i
$47$	−170.609			−0.0772336			−0.0386168	−	0.999254i	$-0.512295\pi$
$47$	−170.609			−0.0772336			−0.0386168	+	0.999254i	$0.512295\pi$
$48$		−	2091.95i		−	0.907963i
$49$	−301.309			−0.125493
$50$		−	555.765i		−	0.222306i
$51$			772.930i			0.297167i
$52$	143.132			0.0529334
$53$	4308.39			1.53378			0.766890	−	0.641779i	$-0.221803\pi$
$53$	4308.39			1.53378			0.766890	+	0.641779i	$0.221803\pi$
$54$	3505.89			1.20230
$55$			559.237i			0.184872i
$56$	−2838.97			−0.905283
$57$	−1658.05			−0.510327
$58$	1885.33			0.560444
$59$	−65.4372			−0.0187984			−0.00939919	−	0.999956i	$-0.502992\pi$
$59$	−65.4372			−0.0187984			−0.00939919	+	0.999956i	$0.502992\pi$
$60$	−573.013			−0.159170
$61$		−	3896.58i		−	1.04719i	−0.851968	−	0.523594i	$-0.824591\pi$
$61$		−	3896.58i		−	1.04719i	0.851968	−	0.523594i	$-0.175409\pi$
$62$			6423.99i			1.67117i
$63$		−	1707.32i		−	0.430164i
$64$	−2764.25			−0.674865
$65$			866.294i			0.205040i
$66$	−770.379			−0.176855
$67$	−5449.76			−1.21403			−0.607013	−	0.794692i	$-0.707632\pi$
$67$	−5449.76			−1.21403			−0.607013	+	0.794692i	$0.707632\pi$
$68$	−411.402			−0.0889709
$69$			5714.84i			1.20034i
$70$			5157.19i			1.05249i
$71$			5845.23i			1.15954i	0.814781	+	0.579769i	$0.196857\pi$
$71$			5845.23i			1.15954i	−0.814781	+	0.579769i	$0.803143\pi$
$72$		−	1793.66i		−	0.346000i
$73$		−	4773.87i		−	0.895828i	−0.894077	−	0.447914i	$-0.852167\pi$
$73$		−	4773.87i		−	0.895828i	0.894077	−	0.447914i	$-0.147833\pi$
$74$	2781.04			0.507859
$75$			869.073i			0.154502i
$76$		−	882.519i		−	0.152791i
$77$			1300.41i			0.219331i
$78$	−1193.37			−0.196148
$79$	10139.3			1.62463			0.812316	−	0.583217i	$-0.198206\pi$
$79$	10139.3			1.62463			0.812316	+	0.583217i	$0.198206\pi$
$80$			6739.15i			1.05299i
$81$	−2822.00			−0.430117
$82$		−	2576.98i		−	0.383250i
$83$	4438.95			0.644353			0.322176	−	0.946680i	$-0.395586\pi$
$83$	4438.95			0.644353			0.322176	+	0.946680i	$0.395586\pi$
$84$	−1332.45			−0.188839
$85$		−	2489.97i		−	0.344633i
$86$	7862.77	+	2346.36i	1.06311	+	0.317247i
$87$	−2948.17			−0.389506
$88$			1366.18i			0.176417i
$89$		−	9870.51i		−	1.24612i	−0.782174	−	0.623060i	$-0.785889\pi$
$89$		−	9870.51i		−	1.24612i	0.782174	−	0.623060i	$-0.214111\pi$
$90$	−3258.32			−0.402261
$91$			2014.42i			0.243258i
$92$	−3041.79			−0.359380
$93$		−	10045.5i		−	1.16146i
$94$			757.120i			0.0856858i
$95$	5341.37			0.591842
$96$	−3219.80			−0.349371
$97$	−7761.47			−0.824899			−0.412449	−	0.910981i	$-0.635327\pi$
$97$	−7761.47			−0.824899			−0.412449	+	0.910981i	$0.635327\pi$
$98$			1337.14i			0.139227i
$99$	−821.602			−0.0838284
$100$	−462.575			−0.0462575
$101$	−7907.71			−0.775190			−0.387595	−	0.921830i	$-0.626694\pi$
$101$	−7907.71			−0.775190			−0.387595	+	0.921830i	$0.626694\pi$
$102$	3430.07			0.329688
$103$	11579.3			1.09146			0.545728	−	0.837962i	$-0.316253\pi$
$103$	11579.3			1.09146			0.545728	+	0.837962i	$0.316253\pi$
$104$			2116.29i			0.195663i
$105$		−	8064.51i		−	0.731475i
$106$		−	19119.5i		−	1.70163i
$107$	−6463.42			−0.564540			−0.282270	−	0.959335i	$-0.591087\pi$
$107$	−6463.42			−0.564540			−0.282270	+	0.959335i	$0.591087\pi$
$108$		−	2918.03i		−	0.250174i
$109$	3408.56			0.286892			0.143446	−	0.989658i	$-0.454182\pi$
$109$	3408.56			0.286892			0.143446	+	0.989658i	$0.454182\pi$
$110$	2481.76			0.205104
$111$	−4348.82			−0.352960
$112$			15670.8i			1.24926i
$113$			11268.0i			0.882446i	0.897397	+	0.441223i	$0.145455\pi$
$113$			11268.0i			0.882446i	−0.897397	+	0.441223i	$0.854545\pi$
$114$			7358.03i			0.566176i
$115$		−	18410.2i		−	1.39208i
$116$		−	1569.20i		−	0.116617i
$117$	−1272.71			−0.0929734
$118$			290.394i			0.0208556i
$119$		−	5790.02i		−	0.408871i
$120$		−	8472.34i		−	0.588357i
$121$	−14015.2			−0.957258
$122$	−17292.1			−1.16179
$123$			4029.73i			0.266358i
$124$	5346.82			0.347738
$125$		−	16771.8i		−	1.07340i
$126$	−7576.67			−0.477240
$127$	13207.4			0.818860			0.409430	−	0.912342i	$-0.365728\pi$
$127$	13207.4			0.818860			0.409430	+	0.912342i	$0.365728\pi$
$128$			19690.8i			1.20183i
$129$	−12295.3	−	3669.10i	−0.738859	−	0.220486i
$130$	3844.40			0.227479
$131$			29457.5i			1.71653i	0.513203	+	0.858267i	$0.328459\pi$
$131$			29457.5i			1.71653i	−0.513203	+	0.858267i	$0.671541\pi$
$132$			641.203i			0.0368000i
$133$	12420.5			0.702158
$134$			24184.7i			1.34689i
$135$	17661.1			0.969060
$136$		−	6082.82i		−	0.328872i
$137$			14241.6i			0.758783i	0.925236	+	0.379392i	$0.123867\pi$
$137$			14241.6i			0.758783i	−0.925236	+	0.379392i	$0.876133\pi$
$138$	25361.0			1.33171
$139$	−18549.0			−0.960042			−0.480021	−	0.877257i	$-0.659371\pi$
$139$	−18549.0			−0.960042			−0.480021	+	0.877257i	$0.659371\pi$
$140$	4292.44			0.219002
$141$		−	1183.94i		−	0.0595513i
$142$	25939.7			1.28644
$143$	969.385			0.0474050
$144$	−9900.81			−0.477469
$145$	9497.46			0.451722
$146$	−21185.2			−0.993866
$147$		−	2090.94i		−	0.0967623i
$148$		−	2314.71i		−	0.105675i
$149$		−	31018.5i		−	1.39717i	−0.715528	−	0.698584i	$-0.753814\pi$
$149$		−	31018.5i		−	1.39717i	0.715528	−	0.698584i	$-0.246186\pi$
$150$	3856.73			0.171410
$151$			10079.5i			0.442063i	0.975267	+	0.221032i	$0.0709424\pi$
$151$			10079.5i			0.442063i	−0.975267	+	0.221032i	$0.929058\pi$
$152$	13048.6			0.564776
$153$	3658.14			0.156271
$154$	5770.91			0.243334
$155$			32361.2i			1.34698i
$156$			993.264i			0.0408146i
$157$			27782.4i			1.12712i	0.826075	+	0.563560i	$0.190569\pi$
$157$			27782.4i			1.12712i	−0.826075	+	0.563560i	$0.809431\pi$
$158$		−	44995.8i		−	1.80243i
$159$			29898.0i			1.18263i
$160$	10372.5			0.405176
$161$		−	42809.8i		−	1.65155i
$162$			12523.3i			0.477188i
$163$			23274.3i			0.875993i	0.898977	+	0.437996i	$0.144312\pi$
$163$			23274.3i			0.875993i	−0.898977	+	0.437996i	$0.855688\pi$
$164$	−2144.87			−0.0797469
$165$	−3880.83			−0.142546
$166$		−	19698.9i		−	0.714869i
$167$	−38477.5			−1.37967			−0.689833	−	0.723968i	$-0.742316\pi$
$167$	−38477.5			−1.37967			−0.689833	+	0.723968i	$0.742316\pi$
$168$		−	19701.0i		−	0.698023i
$169$	−27059.4			−0.947423
$170$	−11049.9			−0.382349
$171$			7847.26i			0.268365i
$172$	1952.93	−	6544.35i	0.0660129	−	0.221213i
$173$	26454.5			0.883909			0.441954	−	0.897038i	$-0.354285\pi$
$173$	26454.5			0.883909			0.441954	+	0.897038i	$0.354285\pi$
$174$			13083.3i			0.432133i
$175$		−	6510.22i		−	0.212579i
$176$	7541.13			0.243451
$177$		−	454.101i		−	0.0144946i
$178$	−43802.9			−1.38249
$179$		−	5807.25i		−	0.181244i	−0.995885	−	0.0906222i	$-0.971114\pi$
$179$		−	5807.25i		−	0.181244i	0.995885	−	0.0906222i	$-0.0288856\pi$
$180$			2711.97i			0.0837026i
$181$	−63912.2			−1.95086			−0.975431	−	0.220304i	$-0.929295\pi$
$181$	−63912.2			−1.95086			−0.975431	+	0.220304i	$0.929295\pi$
$182$	8939.50			0.269880
$183$	27040.3			0.807439
$184$		−	44974.7i		−	1.32841i
$185$	14009.6			0.409339
$186$	−44579.2			−1.28857
$187$	−2786.29			−0.0796788
$188$	630.167			0.0178295
$189$	41068.0			1.14969
$190$		−	23703.7i		−	0.656612i
$191$		−	58852.6i		−	1.61324i	−0.591071	−	0.806620i	$-0.701295\pi$
$191$		−	58852.6i		−	1.61324i	0.591071	−	0.806620i	$-0.298705\pi$
$192$		−	19182.5i		−	0.520358i
$193$	−4293.94			−0.115277			−0.0576384	−	0.998338i	$-0.518357\pi$
$193$	−4293.94			−0.115277			−0.0576384	+	0.998338i	$0.518357\pi$
$194$			34443.5i			0.915174i
$195$	−6011.65			−0.158097
$196$	1112.93			0.0289704
$197$	60627.5			1.56220			0.781101	−	0.624405i	$-0.214658\pi$
$197$	60627.5			1.56220			0.781101	+	0.624405i	$0.214658\pi$
$198$			3646.06i			0.0930023i
$199$			75910.5i			1.91688i	0.285290	+	0.958441i	$0.407910\pi$
$199$			75910.5i			1.91688i	−0.285290	+	0.958441i	$0.592090\pi$
$200$		−	6839.44i		−	0.170986i
$201$		−	37818.6i		−	0.936081i
$202$			35092.4i			0.860025i
$203$	22084.8			0.535921
$204$		−	2854.92i		−	0.0686015i
$205$		−	12981.7i		−	0.308903i
$206$		−	51385.9i		−	1.21090i
$207$	27047.3			0.631223
$208$	11681.7			0.270009
$209$		−	5977.01i		−	0.136833i
$210$	−35788.3			−0.811526
$211$		−	34858.4i		−	0.782964i	−0.920186	−	0.391482i	$-0.871962\pi$
$211$		−	34858.4i		−	0.782964i	0.920186	−	0.391482i	$-0.128038\pi$
$212$	−15913.6			−0.354076
$213$	−40563.0			−0.894068
$214$			28683.0i			0.626322i
$215$	39609.1	+	11819.9i	0.856877	+	0.255704i
$216$	43144.8			0.924743
$217$			75250.5i			1.59805i
$218$		−	15126.3i		−	0.318289i
$219$	33128.3			0.690733
$220$		−	2065.62i		−	0.0426781i
$221$	−4316.13			−0.0883711
$222$			19299.0i			0.391587i
$223$			69871.4i			1.40504i	0.711662	+	0.702522i	$0.247943\pi$
$223$			69871.4i			1.40504i	−0.711662	+	0.702522i	$0.752057\pi$
$224$	24119.5			0.480698
$225$	4113.16			0.0812476
$226$	50004.4			0.979019
$227$		−	5952.36i		−	0.115515i	−0.998331	−	0.0577574i	$-0.981605\pi$
$227$		−	5952.36i		−	0.115515i	0.998331	−	0.0577574i	$-0.0183950\pi$
$228$	6124.24			0.117810
$229$	−31808.4			−0.606556			−0.303278	−	0.952902i	$-0.598081\pi$
$229$	−31808.4			−0.606556			−0.303278	+	0.952902i	$0.598081\pi$
$230$	−81699.8			−1.54442
$231$	−9024.21			−0.169116
$232$	23201.6			0.431064
$233$		−	55507.2i		−	1.02244i	−0.859450	−	0.511220i	$-0.829194\pi$
$233$		−	55507.2i		−	1.02244i	0.859450	−	0.511220i	$-0.170806\pi$
$234$			5647.98i			0.103148i
$235$			3814.03i			0.0690635i
$236$	241.701			0.00433965
$237$			70361.9i			1.25268i
$238$	−25694.7			−0.453616
$239$	−62886.2			−1.10093			−0.550465	−	0.834859i	$-0.685549\pi$
$239$	−62886.2			−1.10093			−0.550465	+	0.834859i	$0.685549\pi$
$240$	−46766.3			−0.811916
$241$		−	19314.0i		−	0.332536i	−0.986081	−	0.166268i	$-0.946828\pi$
$241$		−	19314.0i		−	0.332536i	0.986081	−	0.166268i	$-0.0531717\pi$
$242$			62196.0i			1.06202i
$243$			44408.0i			0.752054i
$244$			14392.6i			0.241745i
$245$			6735.90i			0.112218i
$246$	17882.9			0.295507
$247$		−	9258.77i		−	0.151761i
$248$			79055.9i			1.28538i
$249$			30804.1i			0.496832i
$250$	−74429.2			−1.19087
$251$	−62983.5			−0.999723			−0.499862	−	0.866105i	$-0.666616\pi$
$251$	−62983.5			−0.999723			−0.499862	+	0.866105i	$0.666616\pi$
$252$			6306.22i			0.0993043i
$253$	−20601.0			−0.321846
$254$		−	58611.1i		−	0.908474i
$255$	17279.2			0.265731
$256$	43154.7			0.658488
$257$		−	53736.0i		−	0.813579i	−0.913522	−	0.406789i	$-0.866648\pi$
$257$		−	53736.0i		−	0.813579i	0.913522	−	0.406789i	$-0.133352\pi$
$258$	−16282.6	+	54563.7i	−0.244615	+	0.819718i
$259$	32577.0			0.485637
$260$		−	3199.77i		−	0.0473339i
$261$			13953.2i			0.204829i
$262$	130725.			1.90439
$263$		−	133357.i		−	1.92798i	−0.265932	−	0.963992i	$-0.585680\pi$
$263$		−	133357.i		−	1.92798i	0.265932	−	0.963992i	$-0.414320\pi$
$264$	−9480.57			−0.136027
$265$		−	96315.7i		−	1.37153i
$266$		−	55118.9i		−	0.779000i
$267$	68496.4			0.960827
$268$	20129.4			0.280260
$269$	61320.3			0.847421			0.423711	−	0.905798i	$-0.360727\pi$
$269$	61320.3			0.847421			0.423711	+	0.905798i	$0.360727\pi$
$270$		−	78375.7i		−	1.07511i
$271$	66120.9			0.900326			0.450163	−	0.892946i	$-0.351366\pi$
$271$	66120.9			0.900326			0.450163	+	0.892946i	$0.351366\pi$
$272$	−33576.5			−0.453834
$273$	−13979.1			−0.187565
$274$	63200.7			0.841823
$275$	−3132.86			−0.0414263
$276$		−	21108.5i		−	0.277102i
$277$		−	62649.4i		−	0.816502i	−0.912870	−	0.408251i	$-0.866139\pi$
$277$		−	62649.4i		−	0.816502i	0.912870	−	0.408251i	$-0.133861\pi$
$278$			82315.7i			1.06511i
$279$	−47543.3			−0.610775
$280$			63466.3i			0.809519i
$281$	110235.			1.39606			0.698032	−	0.716066i	$-0.254059\pi$
$281$	110235.			1.39606			0.698032	+	0.716066i	$0.254059\pi$
$282$	−5254.03			−0.0660685
$283$	−109263.			−1.36427			−0.682135	−	0.731226i	$-0.738948\pi$
$283$	−109263.			−1.36427			−0.682135	+	0.731226i	$0.738948\pi$
$284$		−	21590.1i		−	0.267682i
$285$			37066.5i			0.456343i
$286$		−	4301.89i		−	0.0525929i
$287$		−	30186.7i		−	0.366481i
$288$			15238.7i			0.183723i
$289$	−71115.2			−0.851465
$290$		−	42147.4i		−	0.501158i
$291$		−	53860.7i		−	0.636042i
$292$			17632.9i			0.206804i
$293$	−137382.			−1.60028			−0.800139	−	0.599814i	$-0.795241\pi$
$293$	−137382.			−1.60028			−0.800139	+	0.599814i	$0.795241\pi$
$294$	−9279.05			−0.107352
$295$			1462.88i			0.0168098i
$296$	34224.4			0.390619
$297$		−	19762.8i		−	0.224046i
$298$	−137653.			−1.55007
$299$	−31912.3			−0.356957
$300$		−	3210.04i		−	0.0356671i
$301$	92104.4	+	27485.2i	1.01659	+	0.303366i
$302$	44730.3			0.490442
$303$		−	54875.5i		−	0.597714i
$304$		−	72026.6i		−	0.779374i
$305$	−87109.7			−0.936412
$306$		−	16233.9i		−	0.173372i
$307$	−13056.1			−0.138528			−0.0692639	−	0.997598i	$-0.522065\pi$
$307$	−13056.1			−0.138528			−0.0692639	+	0.997598i	$0.522065\pi$
$308$		−	4803.25i		−	0.0506330i
$309$			80354.2i			0.841573i
$310$	143611.			1.49439
$311$	−190885.			−1.97356			−0.986781	−	0.162061i	$-0.948186\pi$
$311$	−190885.			−1.97356			−0.986781	+	0.162061i	$0.948186\pi$
$312$	−14686.0			−0.150867
$313$			31940.8i			0.326030i	0.986624	+	0.163015i	$0.0521219\pi$
$313$			31940.8i			0.326030i	−0.986624	+	0.163015i	$0.947878\pi$
$314$	123291.			1.25047
$315$	−38167.9			−0.384660
$316$	−37451.0			−0.375050
$317$	10721.3			0.106692			0.0533459	−	0.998576i	$-0.483011\pi$
$317$	10721.3			0.106692			0.0533459	+	0.998576i	$0.483011\pi$
$318$	132680.			1.31205
$319$		−	10627.7i		−	0.104438i
$320$			61795.9i			0.603476i
$321$		−	44852.9i		−	0.435291i
$322$	−189979.			−1.83229
$323$			26612.3i			0.255081i
$324$	10423.4			0.0992935
$325$	−4853.00			−0.0459456
$326$	103285.			0.971859
$327$			23653.7i			0.221209i
$328$		−	31713.2i		−	0.294776i
$329$			8868.89i			0.0819365i
$330$			17222.1i			0.158146i
$331$			49144.6i			0.448560i	0.974525	+	0.224280i	$0.0720030\pi$
$331$			49144.6i			0.448560i	−0.974525	+	0.224280i	$0.927997\pi$
$332$	−16395.8			−0.148750
$333$			20582.2i			0.185611i
$334$			170754.i			1.53065i
$335$			121832.i			1.08560i
$336$	−108747.			−0.963252
$337$	113598.			1.00025			0.500127	−	0.865952i	$-0.333287\pi$
$337$	113598.			1.00025			0.500127	+	0.865952i	$0.333287\pi$
$338$			120083.i			1.05111i
$339$	−78194.0			−0.680415
$340$			9197.05i			0.0795593i
$341$	36212.2			0.311420
$342$	34824.2			0.297734
$343$		−	109150.i		−	0.927758i
$344$	96762.2	+	28875.2i	0.817690	+	0.244010i
$345$	127757.			1.07337
$346$		−	117399.i		−	0.980642i
$347$			25603.4i			0.212637i	0.994332	+	0.106319i	$0.0339063\pi$
$347$			25603.4i			0.212637i	−0.994332	+	0.106319i	$0.966094\pi$
$348$	10889.5			0.0899183
$349$			4308.53i			0.0353735i	0.999844	+	0.0176867i	$0.00563016\pi$
$349$			4308.53i			0.0353735i	−0.999844	+	0.0176867i	$0.994370\pi$
$350$	−28890.7			−0.235843
$351$		−	30613.9i		−	0.248487i
$352$		−	11606.9i		−	0.0936762i
$353$	101165.			0.811856			0.405928	−	0.913905i	$-0.366948\pi$
$353$	101165.			0.811856			0.405928	+	0.913905i	$0.366948\pi$
$354$	−2015.19			−0.0160809
$355$	130673.			1.03688
$356$			36458.0i			0.287669i
$357$	40179.8			0.315262
$358$	−25771.2			−0.201079
$359$	3103.18			0.0240779			0.0120389	−	0.999928i	$-0.496168\pi$
$359$	3103.18			0.0240779			0.0120389	+	0.999928i	$0.496168\pi$
$360$	−40098.0			−0.309398
$361$	73233.5			0.561947
$362$			283626.i			2.16436i
$363$		−	97258.5i		−	0.738099i
$364$		−	7440.53i		−	0.0561567i
$365$	−106722.			−0.801064
$366$		−	119998.i		−	0.895804i
$367$	158319.			1.17544			0.587722	−	0.809063i	$-0.300025\pi$
$367$	158319.			1.17544			0.587722	+	0.809063i	$0.300025\pi$
$368$	−248255.			−1.83317
$369$	19072.0			0.140069
$370$		−	62171.2i		−	0.454136i
$371$		−	223966.i		−	1.62718i
$372$			37104.2i			0.268125i
$373$			186262.i			1.33877i	0.742914	+	0.669387i	$0.233443\pi$
$373$			186262.i			1.33877i	−0.742914	+	0.669387i	$0.766557\pi$
$374$			12364.8i			0.0883986i
$375$	116388.			0.827648
$376$			9317.40i			0.0659051i
$377$		−	16463.0i		−	0.115831i
$378$		−	182249.i		−	1.27551i
$379$	31309.9			0.217973			0.108987	−	0.994043i	$-0.465239\pi$
$379$	31309.9			0.217973			0.108987	+	0.994043i	$0.465239\pi$
$380$	−19729.1			−0.136628
$381$			91652.6i			0.631386i
$382$	−261173.			−1.78979
$383$			18588.7i			0.126722i	0.997991	+	0.0633609i	$0.0201819\pi$
$383$			18588.7i			0.126722i	−0.997991	+	0.0633609i	$0.979818\pi$
$384$	−136644.			−0.926676
$385$	29071.3			0.196129
$386$			19055.4i			0.127892i
$387$	−17365.2	+	58191.6i	−0.115947	+	0.388543i
$388$	28668.0			0.190430
$389$			158939.i			1.05034i	0.850997	+	0.525170i	$0.175998\pi$
$389$			158939.i			1.05034i	−0.850997	+	0.525170i	$0.824002\pi$
$390$			26678.2i			0.175399i
$391$	91725.1			0.599977
$392$			16455.3i			0.107086i
$393$	−204420.			−1.32354
$394$		−	269050.i		−	1.73317i
$395$		−	226669.i		−	1.45277i
$396$	3034.70			0.0193520
$397$	97945.4			0.621445			0.310723	−	0.950501i	$-0.399429\pi$
$397$	97945.4			0.621445			0.310723	+	0.950501i	$0.399429\pi$
$398$	336872.			2.12666
$399$			86191.8i			0.541402i
$400$	−37752.9			−0.235956
$401$	−252905.			−1.57278			−0.786392	−	0.617727i	$-0.788054\pi$
$401$	−252905.			−1.57278			−0.786392	+	0.617727i	$0.788054\pi$
$402$	−167830.			−1.03852
$403$	56095.0			0.345394
$404$	29208.2			0.178954
$405$			63086.9i			0.384618i
$406$		−	98006.6i		−	0.594571i
$407$		−	15676.8i		−	0.0946386i
$408$	42211.7			0.253579
$409$		−	134853.i		−	0.806149i	−0.915167	−	0.403074i	$-0.867942\pi$
$409$		−	134853.i		−	0.806149i	0.915167	−	0.403074i	$-0.132058\pi$
$410$	−57609.4			−0.342709
$411$	−98829.6			−0.585064
$412$	−42769.5			−0.251965
$413$			3401.67i			0.0199431i
$414$		−	120029.i		−	0.700303i
$415$		−	99234.5i		−	0.576191i
$416$		−	17979.7i		−	0.103896i
$417$		−	128720.i		−	0.740245i
$418$	−26524.5			−0.151808
$419$		−	10482.5i		−	0.0597086i	−0.999554	−	0.0298543i	$-0.990496\pi$
$419$		−	10482.5i		−	0.0597086i	0.999554	−	0.0298543i	$-0.00950433\pi$
$420$			29787.4i			0.168863i
$421$			241369.i			1.36181i	0.732371	+	0.680906i	$0.238414\pi$
$421$			241369.i			1.36181i	−0.732371	+	0.680906i	$0.761586\pi$
$422$	−154693.			−0.868650
$423$	−5603.37			−0.0313162
$424$		−	235292.i		−	1.30881i
$425$	13948.9			0.0772258
$426$			180008.i			0.991913i
$427$	−202559.			−1.11095
$428$	23873.5			0.130325
$429$			6727.04i			0.0365519i
$430$	52453.9	−	175776.i	0.283688	−	0.950652i
$431$	59107.4			0.318191			0.159095	−	0.987263i	$-0.449142\pi$
$431$	59107.4			0.318191			0.159095	+	0.987263i	$0.449142\pi$
$432$		−	238154.i		−	1.27612i
$433$			193520.i			1.03216i	0.856539	+	0.516082i	$0.172610\pi$
$433$			193520.i			1.03216i	−0.856539	+	0.516082i	$0.827390\pi$
$434$	333943.			1.77293
$435$			65907.6i			0.348303i
$436$	−12590.0			−0.0662296
$437$			196764.i			1.03035i
$438$		−	147015.i		−	0.766325i
$439$	−4663.78			−0.0241997			−0.0120998	−	0.999927i	$-0.503852\pi$
$439$	−4663.78			−0.0241997			−0.0120998	+	0.999927i	$0.503852\pi$
$440$	30541.4			0.157755
$441$	−9896.02			−0.0508843
$442$			19153.9i			0.0980423i
$443$	102777.			0.523708			0.261854	−	0.965107i	$-0.415666\pi$
$443$	102777.			0.523708			0.261854	+	0.965107i	$0.415666\pi$
$444$	16063.0			0.0814816
$445$	−220659.			−1.11430
$446$	310072.			1.55881
$447$	215253.			1.07729
$448$			143696.i			0.715960i
$449$			222984.i			1.10606i	0.833160	+	0.553032i	$0.186529\pi$
$449$			222984.i			1.10606i	−0.833160	+	0.553032i	$0.813471\pi$
$450$		−	18253.2i		−	0.0901392i
$451$	−14526.5			−0.0714180
$452$		−	41619.7i		−	0.203715i
$453$	−69946.6			−0.340855
$454$	−26415.1			−0.128156
$455$	45033.2			0.217525
$456$			90550.6i			0.435473i
$457$		−	239772.i		−	1.14806i	−0.818833	−	0.574032i	$-0.805378\pi$
$457$		−	239772.i		−	1.14806i	0.818833	−	0.574032i	$-0.194622\pi$
$458$			141158.i			0.672936i
$459$			87993.0i			0.417660i
$460$			68000.5i			0.321363i
$461$	234784.			1.10476			0.552378	−	0.833593i	$-0.313720\pi$
$461$	234784.			1.10476			0.552378	+	0.833593i	$0.313720\pi$
$462$			40047.2i			0.187624i
$463$		−	323705.i		−	1.51004i	−0.655704	−	0.755018i	$-0.727628\pi$
$463$		−	323705.i		−	1.51004i	0.655704	−	0.755018i	$-0.272372\pi$
$464$		−	128070.i		−	0.594856i
$465$	−224570.			−1.03860
$466$	−246327.			−1.13433
$467$			158850.i			0.728372i	0.931326	+	0.364186i	$0.118653\pi$
$467$			158850.i			0.728372i	−0.931326	+	0.364186i	$0.881347\pi$
$468$	4700.94			0.0214631
$469$			283299.i			1.28795i
$470$	16925.7			0.0766217
$471$	−192796.			−0.869072
$472$			3573.69i			0.0160411i
$473$	13226.5	−	44322.7i	0.0591185	−	0.198109i
$474$	312248.			1.38977
$475$			29922.5i			0.132621i
$476$			21386.2i			0.0943886i
$477$	141502.			0.621907
$478$			279073.i			1.22141i
$479$	−50616.7			−0.220609			−0.110304	−	0.993898i	$-0.535183\pi$
$479$	−50616.7			−0.220609			−0.110304	+	0.993898i	$0.535183\pi$
$480$			71979.9i			0.312413i
$481$		−	24284.3i		−	0.104963i
$482$	−85710.8			−0.368928
$483$	297079.			1.27344
$484$	51767.1			0.220985
$485$			173511.i			0.737638i
$486$	197072.			0.834357
$487$	−414555.			−1.74793			−0.873966	−	0.485987i	$-0.838460\pi$
$487$	−414555.			−1.74793			−0.873966	+	0.485987i	$0.838460\pi$
$488$	−212803.			−0.893588
$489$	−161512.			−0.675439
$490$	29892.2			0.124499
$491$			162691.i			0.674841i	0.941354	+	0.337421i	$0.109554\pi$
$491$			162691.i			0.674841i	−0.941354	+	0.337421i	$0.890446\pi$
$492$		−	14884.3i		−	0.0614892i
$493$			47319.2i			0.194690i
$494$	−41088.1			−0.168369
$495$			18367.2i			0.0749607i
$496$	436380.			1.77379
$497$	303857.			1.23015
$498$	136701.			0.551204
$499$		−	202146.i		−	0.811829i	−0.913911	−	0.405914i	$-0.866953\pi$
$499$		−	202146.i		−	0.811829i	0.913911	−	0.405914i	$-0.133047\pi$
$500$			61949.0i			0.247796i
$501$		−	267015.i		−	1.06380i
$502$			279505.i			1.10913i
$503$		−	142571.i		−	0.563501i	−0.959488	−	0.281751i	$-0.909085\pi$
$503$		−	142571.i		−	0.563501i	0.959488	−	0.281751i	$-0.0909151\pi$
$504$	−93241.3			−0.367068
$505$			176780.i			0.693187i
$506$			91422.3i			0.357068i
$507$		−	187778.i		−	0.730516i
$508$	−48783.3			−0.189035
$509$	−132370.			−0.510922			−0.255461	−	0.966819i	$-0.582227\pi$
$509$	−132370.			−0.510922			−0.255461	+	0.966819i	$0.582227\pi$
$510$		−	76680.7i		−	0.294812i
$511$	−248164.			−0.950378
$512$			123542.i			0.471276i
$513$	−188758.			−0.717251
$514$	−238467.			−0.902615
$515$		−	258859.i		−	0.975998i
$516$	45414.5	+	13552.3i	0.170567	+	0.0508996i
$517$	4267.91			0.0159674
$518$		−	144569.i		−	0.538784i
$519$			183581.i			0.681542i
$520$	47310.6			0.174965
$521$		−	222159.i		−	0.818444i	−0.912435	−	0.409222i	$-0.865800\pi$
$521$		−	222159.i		−	0.818444i	0.912435	−	0.409222i	$-0.134200\pi$
$522$	61920.7			0.227245
$523$			426785.i			1.56029i	0.625599	+	0.780145i	$0.284855\pi$
$523$			426785.i			1.56029i	−0.625599	+	0.780145i	$0.715145\pi$
$524$		−	108805.i		−	0.396266i
$525$	45177.6			0.163910
$526$	−591804.			−2.13898
$527$	−161233.			−0.580541
$528$			52331.6i			0.187714i
$529$	398349.			1.42348
$530$	−427425.			−1.52163
$531$	−2149.18			−0.00762225
$532$	−45876.7			−0.162095
$533$	−22502.5			−0.0792092
$534$		−	303970.i		−	1.06598i
$535$			144492.i			0.504821i
$536$			297626.i			1.03595i
$537$	40299.4			0.139750
$538$		−	272124.i		−	0.940161i
$539$	7537.48			0.0259447
$540$	−65233.7			−0.223710
$541$	225636.			0.770927			0.385463	−	0.922723i	$-0.374042\pi$
$541$	225636.			0.770927			0.385463	+	0.922723i	$0.374042\pi$
$542$		−	293428.i		−	0.998856i
$543$		−	443519.i		−	1.50422i
$544$			51678.9i			0.174629i
$545$		−	76199.8i		−	0.256543i
$546$			62035.6i			0.208092i
$547$	45128.1			0.150825			0.0754124	−	0.997152i	$-0.475973\pi$
$547$	45128.1			0.150825			0.0754124	+	0.997152i	$0.475973\pi$
$548$		−	52603.3i		−	0.175167i
$549$		−	127977.i		−	0.424607i
$550$			13902.9i			0.0459599i
$551$	−101507.			−0.334343
$552$	312102.			1.02428
$553$		−	527080.i		−	1.72356i
$554$	−278022.			−0.905858
$555$			97219.7i			0.315623i
$556$	68513.1			0.221628
$557$	561545.			1.80998			0.904991	−	0.425430i	$-0.139877\pi$
$557$	561545.			1.80998			0.904991	+	0.425430i	$0.139877\pi$
$558$			210985.i			0.677617i
$559$	20488.7	−	68658.7i	0.0655679	−	0.219721i
$560$	350326.			1.11711
$561$		−	19335.4i		−	0.0614367i
$562$		−	489194.i		−	1.54885i
$563$	140409.			0.442975			0.221487	−	0.975163i	$-0.428909\pi$
$563$	140409.			0.442975			0.221487	+	0.975163i	$0.428909\pi$
$564$			4373.04i			0.0137476i
$565$	251900.			0.789098
$566$			484882.i			1.51357i
$567$			146698.i			0.456308i
$568$	319223.			0.989459
$569$	−434476.			−1.34197			−0.670983	−	0.741473i	$-0.734128\pi$
$569$	−434476.			−1.34197			−0.670983	+	0.741473i	$0.734128\pi$
$570$	164492.			0.506284
$571$		−	63191.7i		−	0.193815i	−0.995293	−	0.0969076i	$-0.969105\pi$
$571$		−	63191.7i		−	0.193815i	0.995293	−	0.0969076i	$-0.0308951\pi$
$572$	−3580.55			−0.0109435
$573$	408407.			1.24390
$574$	−133961.			−0.406588
$575$	103134.			0.311938
$576$	−90787.2			−0.273640
$577$		−	524185.i		−	1.57447i	−0.616656	−	0.787233i	$-0.711513\pi$
$577$		−	524185.i		−	1.57447i	0.616656	−	0.787233i	$-0.288487\pi$
$578$			315592.i			0.944647i
$579$		−	29797.8i		−	0.0888847i
$580$	−35080.1			−0.104281
$581$		−	230753.i		−	0.683589i
$582$	−239020.			−0.705650
$583$	−107778.			−0.317096
$584$	−260713.			−0.764430
$585$			28452.0i			0.0831383i
$586$			609669.i			1.77541i
$587$		−	653761.i		−	1.89733i	−0.316284	−	0.948665i	$-0.602435\pi$
$587$		−	653761.i		−	1.89733i	0.316284	−	0.948665i	$-0.397565\pi$
$588$			7723.15i			0.0223378i
$589$		−	345869.i		−	0.996969i
$590$	6491.88			0.0186495
$591$			420724.i			1.20454i
$592$		−	188915.i		−	0.539043i
$593$		−	73594.7i		−	0.209285i	−0.994510	−	0.104642i	$-0.966630\pi$
$593$		−	73594.7i		−	0.209285i	0.994510	−	0.104642i	$-0.0333698\pi$
$594$	−87702.6			−0.248565
$595$	−129438.			−0.365619
$596$			114571.i			0.322539i
$597$	−526781.			−1.47802
$598$			141619.i			0.396022i
$599$	−219023.			−0.610430			−0.305215	−	0.952283i	$-0.598728\pi$
$599$	−219023.			−0.610430			−0.305215	+	0.952283i	$0.598728\pi$
$600$	47462.3			0.131840
$601$			350767.i			0.971112i	0.874206	+	0.485556i	$0.161383\pi$
$601$			350767.i			0.971112i	−0.874206	+	0.485556i	$0.838617\pi$
$602$	121973.	−	408736.i	0.336565	−	1.12785i
$603$	−178989.			−0.492256
$604$		−	37229.9i		−	0.102051i
$605$			313316.i			0.855996i
$606$	−243524.			−0.663126
$607$			93560.7i			0.253931i	0.991907	+	0.126966i	$0.0405238\pi$
$607$			93560.7i			0.253931i	−0.991907	+	0.126966i	$0.959476\pi$
$608$	−110859.			−0.299891
$609$			153257.i			0.413224i
$610$			386571.i			1.03889i
$611$	6611.26			0.0177093
$612$	−13511.8			−0.0360754
$613$	385616.			1.02620			0.513102	−	0.858327i	$-0.328496\pi$
$613$	385616.			1.02620			0.513102	+	0.858327i	$0.328496\pi$
$614$			57939.8i			0.153688i
$615$	90086.2			0.238181
$616$	71018.9			0.187160
$617$	−262907.			−0.690609			−0.345304	−	0.938491i	$-0.612224\pi$
$617$	−262907.			−0.690609			−0.345304	+	0.938491i	$0.612224\pi$
$618$	356592.			0.933673
$619$	105010.			0.274063			0.137031	−	0.990567i	$-0.456244\pi$
$619$	105010.			0.274063			0.137031	+	0.990567i	$0.456244\pi$
$620$		−	119530.i		−	0.310953i
$621$			650596.i			1.68705i
$622$			847099.i			2.18954i
$623$	−513106.			−1.32200
$624$			81065.0i			0.208192i
$625$	−296669.			−0.759472
$626$	141745.			0.361710
$627$	41477.4			0.105506
$628$		−	102618.i		−	0.260198i
$629$			69800.1i			0.176423i
$630$			169380.i			0.426756i
$631$			584197.i			1.46724i	0.679561	+	0.733619i	$0.262170\pi$
$631$			584197.i			1.46724i	−0.679561	+	0.733619i	$0.737830\pi$
$632$		−	553735.i		−	1.38633i
$633$	241899.			0.603709
$634$		−	47578.7i		−	0.118368i
$635$		−	295257.i		−	0.732238i
$636$		−	110432.i		−	0.273012i
$637$	11676.0			0.0287751
$638$	−47163.0			−0.115867
$639$			191977.i			0.470162i
$640$	440195.			1.07469
$641$		−	230667.i		−	0.561397i	−0.959796	−	0.280699i	$-0.909434\pi$
$641$		−	230667.i		−	0.561397i	0.959796	−	0.280699i	$-0.0905661\pi$
$642$	−199046.			−0.482929
$643$	205024.			0.495886			0.247943	−	0.968775i	$-0.420245\pi$
$643$	205024.			0.495886			0.247943	+	0.968775i	$0.420245\pi$
$644$			158124.i			0.381264i
$645$	−82024.3	+	274868.i	−0.197162	+	0.660700i
$646$	118099.			0.282996
$647$		−	151853.i		−	0.362757i	−0.983413	−	0.181379i	$-0.941944\pi$
$647$		−	151853.i		−	0.362757i	0.983413	−	0.181379i	$-0.0580560\pi$
$648$			154117.i			0.367028i
$649$	1636.96			0.00388641
$650$			21536.4i			0.0509738i
$651$	−522200.			−1.23218
$652$		−	85966.5i		−	0.202225i
$653$		−	165779.i		−	0.388780i	−0.980924	−	0.194390i	$-0.937727\pi$
$653$		−	165779.i		−	0.388780i	0.980924	−	0.194390i	$-0.0622727\pi$
$654$	104969.			0.245418
$655$	658533.			1.53495
$656$	−175053.			−0.406783
$657$		−	156790.i		−	0.363235i
$658$	39357.9			0.0909035
$659$	461726.			1.06320			0.531599	−	0.846996i	$-0.321592\pi$
$659$	461726.			1.06320			0.531599	+	0.846996i	$0.321592\pi$
$660$	14334.3			0.0329071
$661$	−206270.			−0.472099			−0.236050	−	0.971741i	$-0.575853\pi$
$661$	−206270.			−0.472099			−0.236050	+	0.971741i	$0.575853\pi$
$662$	218092.			0.497649
$663$		−	29951.8i		−	0.0681390i
$664$		−	242422.i		−	0.549840i
$665$		−	277665.i		−	0.627881i
$666$	91338.6			0.205924
$667$			349865.i			0.786410i
$668$	142122.			0.318499
$669$	−484873.			−1.08337
$670$	540659.			1.20441
$671$			97476.0i			0.216497i
$672$			167377.i			0.370645i
$673$		−	739539.i		−	1.63279i	−0.577492	−	0.816397i	$-0.695968\pi$
$673$		−	739539.i		−	1.63279i	0.577492	−	0.816397i	$-0.304032\pi$
$674$		−	504119.i		−	1.10972i
$675$			98938.2i			0.217148i
$676$	99947.4			0.218715
$677$			248420.i			0.542012i	0.962578	+	0.271006i	$0.0873563\pi$
$677$			248420.i			0.542012i	−0.962578	+	0.271006i	$0.912644\pi$
$678$			347005.i			0.754878i
$679$			403470.i			0.875129i
$680$	−135984.			−0.294083
$681$	41306.4			0.0890682
$682$		−	160701.i		−	0.345501i
$683$	536792.			1.15071			0.575354	−	0.817905i	$-0.304864\pi$
$683$	536792.			1.15071			0.575354	+	0.817905i	$0.304864\pi$
$684$		−	28984.9i		−	0.0619526i
$685$	318377.			0.678517
$686$	−484379.			−1.02929
$687$		−	220734.i		−	0.467688i
$688$	159388.	−	534116.i	0.336727	−	1.12839i
$689$	−166954.			−0.351689
$690$		−	566956.i		−	1.19083i
$691$			253638.i			0.531199i	0.964083	+	0.265600i	$0.0855699\pi$
$691$			253638.i			0.531199i	−0.964083	+	0.265600i	$0.914430\pi$
$692$	−97713.2			−0.204052
$693$			42709.9i			0.0889329i
$694$	113622.			0.235908
$695$			414670.i			0.858485i
$696$			161007.i			0.332374i
$697$	64678.5			0.133136
$698$	19120.2			0.0392447
$699$	385192.			0.788358
$700$			24046.4i			0.0490742i
$701$	−64810.3			−0.131889			−0.0659444	−	0.997823i	$-0.521006\pi$
$701$	−64810.3			−0.131889			−0.0659444	+	0.997823i	$0.521006\pi$
$702$	−135857.			−0.275681
$703$	−149732.			−0.302973
$704$	69149.8			0.139523
$705$	−26467.5			−0.0532518
$706$		−	448943.i		−	0.900704i
$707$			411072.i			0.822393i
$708$			1677.28i			0.00334611i
$709$	−120036.			−0.238792			−0.119396	−	0.992847i	$-0.538096\pi$
$709$	−120036.			−0.238792			−0.119396	+	0.992847i	$0.538096\pi$
$710$		−	579892.i		−	1.15035i
$711$	333010.			0.658746
$712$	−539054.			−1.06334
$713$	−1.19211e6			−2.34498
$714$		−	178308.i		−	0.349763i
$715$		−	21671.0i		−	0.0423903i
$716$			21449.9i			0.0418407i
$717$		−	436398.i		−	0.848877i
$718$		−	13771.2i		−	0.0267129i
$719$	−332719.			−0.643605			−0.321802	−	0.946807i	$-0.604289\pi$
$719$	−332719.			−0.643605			−0.321802	+	0.946807i	$0.604289\pi$
$720$			221337.i			0.426961i
$721$		−	601933.i		−	1.15792i
$722$		−	324992.i		−	0.623446i
$723$	134030.			0.256404
$724$	236068.			0.450361
$725$			53205.1i			0.101222i
$726$	−431609.			−0.818875
$727$		−	582297.i		−	1.10173i	−0.834594	−	0.550866i	$-0.814298\pi$
$727$		−	582297.i		−	1.10173i	0.834594	−	0.550866i	$-0.185702\pi$
$728$	110013.			0.207577
$729$	−536751.			−1.00999
$730$			473605.i			0.888731i
$731$	−58890.4	+	197345.i	−0.110207	+	0.369309i
$732$	−99877.1			−0.186399
$733$			469633.i			0.874079i	0.899442	+	0.437039i	$0.143973\pi$
$733$			469633.i			0.874079i	−0.899442	+	0.437039i	$0.856027\pi$
$734$		−	702582.i		−	1.30408i
$735$	−46743.7			−0.0865264
$736$			382100.i			0.705376i
$737$	136330.			0.250990
$738$		−	84636.6i		−	0.155398i
$739$			755334.i			1.38309i	0.722334	+	0.691545i	$0.243070\pi$
$739$			755334.i			1.38309i	−0.722334	+	0.691545i	$0.756930\pi$
$740$	−51746.4			−0.0944967
$741$	64251.2			0.117016
$742$	−993906.			−1.80525
$743$		−	18481.9i		−	0.0334788i	−0.999860	−	0.0167394i	$-0.994671\pi$
$743$		−	18481.9i		−	0.0334788i	0.999860	−	0.0167394i	$-0.00532857\pi$
$744$	−548608.			−0.991098
$745$	−693432.			−1.24937
$746$	826585.			1.48529
$747$	145790.			0.261268
$748$	10291.5			0.0183940
$749$			335993.i			0.598916i
$750$		−	516501.i		−	0.918224i
$751$		−	62072.3i		−	0.110057i	−0.998485	−	0.0550286i	$-0.982475\pi$
$751$		−	62072.3i		−	0.110057i	0.998485	−	0.0550286i	$-0.0175250\pi$
$752$	51431.0			0.0909471
$753$		−	437074.i		−	0.770842i
$754$	−73058.5			−0.128507
$755$	225331.			0.395300
$756$	−151690.			−0.265408
$757$			452452.i			0.789551i	0.918778	+	0.394776i	$0.129178\pi$
$757$			452452.i			0.789551i	−0.918778	+	0.394776i	$0.870822\pi$
$758$		−	138946.i		−	0.241828i
$759$		−	142961.i		−	0.248161i
$760$		−	291706.i		−	0.505032i
$761$		−	239204.i		−	0.413047i	−0.978442	−	0.206523i	$-0.933785\pi$
$761$		−	239204.i		−	0.413047i	0.978442	−	0.206523i	$-0.0662150\pi$
$762$	406732.			0.700484
$763$		−	177190.i		−	0.304361i
$764$			217380.i			0.372420i
$765$		−	81779.2i		−	0.139740i
$766$	82491.9			0.140590
$767$	2535.76			0.00431039
$768$			299472.i			0.507731i
$769$	838340.			1.41765			0.708823	−	0.705386i	$-0.249227\pi$
$769$	838340.			1.41765			0.708823	+	0.705386i	$0.249227\pi$
$770$		−	129011.i		−	0.217593i
$771$	372901.			0.627314
$772$	15860.2			0.0266119
$773$			520027.i			0.870295i	0.900359	+	0.435148i	$0.143304\pi$
$773$			520027.i			0.870295i	−0.900359	+	0.435148i	$0.856696\pi$
$774$	258240.	+	77062.4i	0.431064	+	0.128635i
$775$	−181288.			−0.301833
$776$			423874.i			0.703904i
$777$			226068.i			0.374453i
$778$	705330.			1.16529
$779$			138745.i			0.228635i
$780$	22204.8			0.0364971
$781$		−	146223.i		−	0.239725i
$782$		−	407053.i		−	0.665637i
$783$	−335630.			−0.547441
$784$	90831.3			0.147776
$785$	621087.			1.00789
$786$			907165.i			1.46839i
$787$	−297689.			−0.480633			−0.240316	−	0.970695i	$-0.577251\pi$
$787$	−297689.			−0.480633			−0.240316	+	0.970695i	$0.577251\pi$
$788$	−223936.			−0.360638
$789$	925429.			1.48658
$790$	−1.00590e6			−1.61176
$791$	585751.			0.936181
$792$			44869.8i			0.0715326i
$793$			150996.i			0.240116i
$794$		−	434657.i		−	0.689455i
$795$	668383.			1.05753
$796$		−	280385.i		−	0.442516i
$797$	943410.			1.48520			0.742598	−	0.669737i	$-0.233593\pi$
$797$	943410.			1.48520			0.742598	+	0.669737i	$0.233593\pi$
$798$	382498.			0.600652
$799$	−19002.6			−0.0297660
$800$			58107.1i			0.0907923i
$801$		−	324181.i		−	0.505269i
$802$			1.12233e6i			1.74491i
$803$			119422.i			0.185205i
$804$			139688.i			0.216096i
$805$	−957031.			−1.47684
$806$		−	248936.i		−	0.383193i
$807$			425532.i			0.653409i
$808$			431860.i			0.661486i
$809$	365446.			0.558375			0.279187	−	0.960237i	$-0.409935\pi$
$809$	365446.			0.558375			0.279187	+	0.960237i	$0.409935\pi$
$810$	279964.			0.426710
$811$		−	465367.i		−	0.707544i	−0.935332	−	0.353772i	$-0.884899\pi$
$811$		−	465367.i		−	0.707544i	0.935332	−	0.353772i	$-0.115101\pi$
$812$	−81573.0			−0.123718
$813$			458846.i			0.694201i
$814$	−69569.7			−0.104996
$815$	520305.			0.783327
$816$		−	233004.i		−	0.349931i
$817$	−423334.	−	126329.i	−0.634219	−	0.189260i
$818$	−598445.			−0.894372
$819$			66160.4i			0.0986348i
$820$			47949.5i			0.0713109i
$821$	−391246.			−0.580449			−0.290224	−	0.956959i	$-0.593730\pi$
$821$	−391246.			−0.580449			−0.290224	+	0.956959i	$0.593730\pi$
$822$			438581.i			0.649092i
$823$	−329039.			−0.485789			−0.242895	−	0.970053i	$-0.578097\pi$
$823$	−329039.			−0.485789			−0.242895	+	0.970053i	$0.578097\pi$
$824$		−	632373.i		−	0.931363i
$825$		−	21740.5i		−	0.0319420i
$826$	15095.8			0.0221256
$827$	−42044.1			−0.0614744			−0.0307372	−	0.999528i	$-0.509785\pi$
$827$	−42044.1			−0.0614744			−0.0307372	+	0.999528i	$0.509785\pi$
$828$	−99902.7			−0.145719
$829$		−	591458.i		−	0.860626i	−0.902680	−	0.430313i	$-0.858403\pi$
$829$		−	591458.i		−	0.860626i	0.902680	−	0.430313i	$-0.141597\pi$
$830$	−440378.			−0.639248
$831$	434755.			0.629568
$832$	107117.			0.154744
$833$	−33560.2			−0.0483654
$834$	−571229.			−0.821256
$835$			860181.i			1.23372i
$836$			22076.9i			0.0315882i
$837$		−	1.14361e6i		−	1.63240i
$838$	−46518.7			−0.0662430
$839$			1.21494e6i			1.72597i	0.505233	+	0.862983i	$0.331407\pi$
$839$			1.21494e6i			1.72597i	−0.505233	+	0.862983i	$0.668593\pi$
$840$	−440424.			−0.624184
$841$	526792.			0.744813
$842$	1.07113e6			1.51085
$843$			764973.i			1.07644i
$844$			128754.i			0.180749i
$845$			604923.i			0.847202i
$846$			24866.4i			0.0347434i
$847$			728563.i			1.01555i
$848$	−1.29879e6			−1.80612
$849$		−	758230.i		−	1.05193i
$850$		−	61901.8i		−	0.0856772i
$851$			516083.i			0.712624i
$852$	149825.			0.206397
$853$	−1.22261e6			−1.68031			−0.840154	−	0.542347i	$-0.817536\pi$
$853$	−1.22261e6			−1.68031			−0.840154	+	0.542347i	$0.817536\pi$
$854$			898906.i			1.23253i
$855$	175429.			0.239976
$856$			352984.i			0.481734i
$857$	−25443.6			−0.0346432			−0.0173216	−	0.999850i	$-0.505514\pi$
$857$	−25443.6			−0.0346432			−0.0173216	+	0.999850i	$0.505514\pi$
$858$	29852.9			0.0405520
$859$		−	853100.i		−	1.15615i	−0.815984	−	0.578074i	$-0.803804\pi$
$859$		−	853100.i		−	1.15615i	0.815984	−	0.578074i	$-0.196196\pi$
$860$	−146302.	−	43658.5i	−0.197812	−	0.0590298i
$861$	209480.			0.282577
$862$		−	262304.i		−	0.353013i
$863$		−	657351.i		−	0.882624i	−0.897354	−	0.441312i	$-0.854513\pi$
$863$		−	657351.i		−	0.882624i	0.897354	−	0.441312i	$-0.145487\pi$
$864$	−366553.			−0.491031
$865$		−	591401.i		−	0.790406i
$866$	858792.			1.14512
$867$		−	493504.i		−	0.656527i
$868$		−	277948.i		−	0.368913i
$869$	−253643.			−0.335879
$870$	292482.			0.386420
$871$	211184.			0.278371
$872$		−	186150.i		−	0.244811i
$873$	−254913.			−0.334475
$874$	873191.			1.14311
$875$	−871862.			−1.13876
$876$	−122364.			−0.159457
$877$	−853878.			−1.11019			−0.555094	−	0.831788i	$-0.687318\pi$
$877$	−853878.			−1.11019			−0.555094	+	0.831788i	$0.687318\pi$
$878$			20696.7i			0.0268480i
$879$		−	953364.i		−	1.23390i
$880$		−	168585.i		−	0.217698i
$881$	170801.			0.220059			0.110030	−	0.993928i	$-0.464905\pi$
$881$	170801.			0.220059			0.110030	+	0.993928i	$0.464905\pi$
$882$			43916.1i			0.0564529i
$883$	−608395.			−0.780304			−0.390152	−	0.920750i	$-0.627578\pi$
$883$	−608395.			−0.780304			−0.390152	+	0.920750i	$0.627578\pi$
$884$	15942.2			0.0204007
$885$	−10151.6			−0.0129613
$886$		−	456100.i		−	0.581022i
$887$		−	433884.i		−	0.551476i	−0.961233	−	0.275738i	$-0.911078\pi$
$887$		−	433884.i		−	0.551476i	0.961233	−	0.275738i	$-0.0889222\pi$
$888$			237500.i			0.301189i
$889$		−	686570.i		−	0.868722i
$890$			979231.i			1.23625i
$891$	70594.4			0.0889232
$892$		−	258079.i		−	0.324357i
$893$		−	40763.6i		−	0.0511175i
$894$		−	955239.i		−	1.19519i
$895$	−129824.			−0.162072
$896$	1.02360e6			1.27501
$897$		−	221455.i		−	0.275234i
$898$	989546.			1.22711
$899$		−	614988.i		−	0.760935i
$900$	−15192.5			−0.0187562
$901$	479874.			0.591122
$902$			64465.0i			0.0792339i
$903$	−190734.	+	639158.i	−0.233912	+	0.783850i
$904$	615372.			0.753011
$905$			1.42878e6i			1.74449i
$906$			310406.i			0.378158i
$907$	−1.51273e6			−1.83885			−0.919425	−	0.393265i	$-0.871345\pi$
$907$	−1.51273e6			−1.83885			−0.919425	+	0.393265i	$0.871345\pi$
$908$			21985.8i			0.0266668i
$909$	−259716.			−0.314319
$910$		−	199846.i		−	0.241331i
$911$		−	1.18401e6i		−	1.42665i	−0.700831	−	0.713327i	$-0.747187\pi$
$911$		−	1.18401e6i		−	1.42665i	0.700831	−	0.713327i	$-0.252813\pi$
$912$	499829.			0.600941
$913$	−111044.			−0.133215
$914$	−1.06405e6			−1.27371
$915$		−	604498.i		−	0.722025i
$916$	117489.			0.140025
$917$	1.53131e6			1.82106
$918$	390491.			0.463368
$919$	367164.			0.434740			0.217370	−	0.976089i	$-0.430252\pi$
$919$	367164.			0.434740			0.217370	+	0.976089i	$0.430252\pi$
$920$	−1.00543e6			−1.18789
$921$		−	90602.9i		−	0.106813i
$922$		−	1.04191e6i		−	1.22566i
$923$		−	226508.i		−	0.265877i
$924$	33332.1			0.0390408
$925$			78482.3i			0.0917251i
$926$	−1.43652e6			−1.67529
$927$	380302.			0.442557
$928$	−197118.			−0.228892
$929$			1.60017e6i			1.85410i	0.374936	+	0.927051i	$0.377665\pi$
$929$			1.60017e6i			1.85410i	−0.374936	+	0.927051i	$0.622335\pi$
$930$			996587.i			1.15226i
$931$		−	71991.8i		−	0.0830585i
$932$			205023.i			0.236032i
$933$		−	1.32464e6i		−	1.52173i
$934$	704936.			0.808083
$935$			62288.6i			0.0712501i
$936$			69506.2i			0.0793362i
$937$		−	241683.i		−	0.275275i	−0.990483	−	0.137638i	$-0.956049\pi$
$937$		−	241683.i		−	0.275275i	0.990483	−	0.137638i	$-0.0439510\pi$
$938$	1.25721e6			1.42890
$939$	−221653.			−0.251387
$940$		−	14087.6i		−	0.0159435i
$941$	−586773.			−0.662660			−0.331330	−	0.943515i	$-0.607497\pi$
$941$	−586773.			−0.662660			−0.331330	+	0.943515i	$0.607497\pi$
$942$			855580.i			0.964181i
$943$	478215.			0.537774
$944$	19726.4			0.0221362
$945$		−	918091.i		−	1.02807i
$946$	−196693.	−	58696.0i	−0.219790	−	0.0655883i
$947$	−1.14388e6			−1.27550			−0.637748	−	0.770245i	$-0.720134\pi$
$947$	−1.14388e6			−1.27550			−0.637748	+	0.770245i	$0.720134\pi$
$948$		−	259891.i		−	0.289184i
$949$			184992.i			0.205410i
$950$	132789.			0.147134
$951$			74400.7i			0.0822652i
$952$	−316208.			−0.348898
$953$		−	1.25121e6i		−	1.37766i	−0.724922	−	0.688831i	$-0.758124\pi$
$953$		−	1.25121e6i		−	1.37766i	0.724922	−	0.688831i	$-0.241876\pi$
$954$		−	627950.i		−	0.689968i
$955$	−1.31567e6			−1.44259
$956$	232278.			0.254152
$957$	73750.8			0.0805272
$958$			224624.i			0.244752i
$959$	740332.			0.804988
$960$	−428832.			−0.465313
$961$	1.17196e6			1.26901
$962$	−107768.			−0.116450
$963$	−212280.			−0.228906
$964$			71338.9i			0.0767666i
$965$			95992.8i			0.103082i
$966$		−	1.31836e6i		−	1.41280i
$967$	687143.			0.734843			0.367421	−	0.930055i	$-0.380241\pi$
$967$	687143.			0.734843			0.367421	+	0.930055i	$0.380241\pi$
$968$			765407.i			0.816849i
$969$	−184676.			−0.196681
$970$	769998.			0.818363
$971$	−288966.			−0.306484			−0.153242	−	0.988189i	$-0.548971\pi$
$971$	−288966.			−0.306484			−0.153242	+	0.988189i	$0.548971\pi$
$972$		−	164027.i		−	0.173613i
$973$			964245.i			1.01850i
$974$			1.83969e6i			1.93922i
$975$		−	33677.4i		−	0.0354266i
$976$			1.17465e6i			1.23313i
$977$	1.40399e6			1.47087			0.735434	−	0.677597i	$-0.236978\pi$
$977$	1.40399e6			1.47087			0.735434	+	0.677597i	$0.236978\pi$
$978$			716748.i			0.749357i
$979$			246918.i			0.257625i
$980$		−	24879.9i		−	0.0259058i
$981$	111949.			0.116327
$982$	721984.			0.748694
$983$		−	308569.i		−	0.319334i	−0.987171	−	0.159667i	$-0.948958\pi$
$983$		−	308569.i		−	0.319334i	0.987171	−	0.159667i	$-0.0510421\pi$
$984$	220074.			0.227289
$985$		−	1.35535e6i		−	1.39695i
$986$	209991.			0.215996
$987$	−61545.6			−0.0631776
$988$			34198.5i			0.0350343i
$989$	−435419.	+	1.45911e6i	−0.445159	+	1.49175i
$990$	81509.3			0.0831642
$991$			630206.i			0.641705i	0.947129	+	0.320853i	$0.103969\pi$
$991$			630206.i			0.641705i	−0.947129	+	0.320853i	$0.896031\pi$
$992$		−	671649.i		−	0.682526i
$993$	−341039.			−0.345864
$994$		−	1.34844e6i		−	1.36477i
$995$	1.69701e6			1.71411
$996$		−	113779.i		−	0.114695i
$997$			1.44327e6i			1.45197i	0.687713	+	0.725983i	$0.258615\pi$
$997$			1.44327e6i			1.45197i	−0.687713	+	0.725983i	$0.741385\pi$
$998$	−897074.			−0.900673
$999$	−495085.			−0.496076

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.5.b.b.42.3	✓	12
3.2	odd	2		387.5.b.c.343.10		12
4.3	odd	2		688.5.b.d.257.5		12
43.42	odd	2	inner	43.5.b.b.42.10	yes	12
129.128	even	2		387.5.b.c.343.3		12
172.171	even	2		688.5.b.d.257.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.5.b.b.42.3	✓	12	1.1	even	1	trivial
43.5.b.b.42.10	yes	12	43.42	odd	2	inner
387.5.b.c.343.3		12	129.128	even	2
387.5.b.c.343.10		12	3.2	odd	2
688.5.b.d.257.5		12	4.3	odd	2
688.5.b.d.257.8		12	172.171	even	2

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.43775i q^{2} +6.93950i q^{3} -3.69363 q^{4} -22.3554i q^{5} +30.7958 q^{6} -51.9837i q^{7} -54.6126i q^{8} +32.8434 q^{9} +O(q^{10})\)	\(q-4.43775i q^{2} +6.93950i q^{3} -3.69363 q^{4} -22.3554i q^{5} +30.7958 q^{6} -51.9837i q^{7} -54.6126i q^{8} +32.8434 q^{9} -99.2077 q^{10} -25.0158 q^{11} -25.6320i q^{12} -38.7510 q^{13} -230.691 q^{14} +155.135 q^{15} -301.455 q^{16} +111.381 q^{17} -145.751i q^{18} +238.930i q^{19} +82.5727i q^{20} +360.741 q^{21} +111.014i q^{22} +823.523 q^{23} +378.984 q^{24} +125.236 q^{25} +171.967i q^{26} +790.016i q^{27} +192.009i q^{28} +424.840i q^{29} -688.452i q^{30} -1447.58 q^{31} +463.982i q^{32} -173.597i q^{33} -494.282i q^{34} -1162.12 q^{35} -121.311 q^{36} +626.677i q^{37} +1060.31 q^{38} -268.912i q^{39} -1220.89 q^{40} +580.694 q^{41} -1600.88i q^{42} +(-528.728 + 1771.79i) q^{43} +92.3990 q^{44} -734.227i q^{45} -3654.59i q^{46} -170.609 q^{47} -2091.95i q^{48} -301.309 q^{49} -555.765i q^{50} +772.930i q^{51} +143.132 q^{52} +4308.39 q^{53} +3505.89 q^{54} +559.237i q^{55} -2838.97 q^{56} -1658.05 q^{57} +1885.33 q^{58} -65.4372 q^{59} -573.013 q^{60} -3896.58i q^{61} +6423.99i q^{62} -1707.32i q^{63} -2764.25 q^{64} +866.294i q^{65} -770.379 q^{66} -5449.76 q^{67} -411.402 q^{68} +5714.84i q^{69} +5157.19i q^{70} +5845.23i q^{71} -1793.66i q^{72} -4773.87i q^{73} +2781.04 q^{74} +869.073i q^{75} -882.519i q^{76} +1300.41i q^{77} -1193.37 q^{78} +10139.3 q^{79} +6739.15i q^{80} -2822.00 q^{81} -2576.98i q^{82} +4438.95 q^{83} -1332.45 q^{84} -2489.97i q^{85} +(7862.77 + 2346.36i) q^{86} -2948.17 q^{87} +1366.18i q^{88} -9870.51i q^{89} -3258.32 q^{90} +2014.42i q^{91} -3041.79 q^{92} -10045.5i q^{93} +757.120i q^{94} +5341.37 q^{95} -3219.80 q^{96} -7761.47 q^{97} +1337.14i q^{98} -821.602 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9}+O(q^{10}) \) 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9	\( 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9} + 182 q^{10} - 180 q^{11} - 216 q^{13} + 732 q^{14} - 92 q^{15} + 1076 q^{16} + 678 q^{17} - 2392 q^{21} + 1566 q^{23} - 4234 q^{24} - 174 q^{25} + 5710 q^{31} + 936 q^{35} + 4210 q^{36} + 1242 q^{38} - 2618 q^{40} + 4878 q^{41} - 1108 q^{43} - 15168 q^{44} - 5526 q^{47} - 8544 q^{49} + 24084 q^{52} + 1212 q^{53} - 10004 q^{54} - 10152 q^{56} - 7692 q^{57} - 4666 q^{58} + 14016 q^{59} + 15848 q^{60} - 15580 q^{64} + 29808 q^{66} - 1088 q^{67} + 15186 q^{68} - 7674 q^{74} - 67708 q^{78} + 24302 q^{79} - 23660 q^{81} - 7032 q^{83} + 37180 q^{84} - 14412 q^{86} + 17850 q^{87} + 4268 q^{90} + 48354 q^{92} + 606 q^{95} + 50546 q^{96} - 5842 q^{97} - 25924 q^{99}+O(q^{100}) \) 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9 + 182 * q^10 - 180 * q^11 - 216 * q^13 + 732 * q^14 - 92 * q^15 + 1076 * q^16 + 678 * q^17 - 2392 * q^21 + 1566 * q^23 - 4234 * q^24 - 174 * q^25 + 5710 * q^31 + 936 * q^35 + 4210 * q^36 + 1242 * q^38 - 2618 * q^40 + 4878 * q^41 - 1108 * q^43 - 15168 * q^44 - 5526 * q^47 - 8544 * q^49 + 24084 * q^52 + 1212 * q^53 - 10004 * q^54 - 10152 * q^56 - 7692 * q^57 - 4666 * q^58 + 14016 * q^59 + 15848 * q^60 - 15580 * q^64 + 29808 * q^66 - 1088 * q^67 + 15186 * q^68 - 7674 * q^74 - 67708 * q^78 + 24302 * q^79 - 23660 * q^81 - 7032 * q^83 + 37180 * q^84 - 14412 * q^86 + 17850 * q^87 + 4268 * q^90 + 48354 * q^92 + 606 * q^95 + 50546 * q^96 - 5842 * q^97 - 25924 * q^99

Introduction

L-functions

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