LMFDB - Embedded newform 97.6.b.a.96.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [97,6,Mod(96,97)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(97, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("97.96"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 97 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	97.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$15.5572305219$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			96.23
Character	$\chi$	$=$	97.96
Dual form			97.6.b.a.96.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.99522 q^{2} +29.1171 q^{3} -28.0191 q^{4} -72.5916i q^{5} +58.0949 q^{6} -11.3700i q^{7} -119.751 q^{8} +604.804 q^{9} -144.836i q^{10} -24.9567 q^{11} -815.835 q^{12} -833.816i q^{13} -22.6857i q^{14} -2113.66i q^{15} +657.682 q^{16} -1845.68i q^{17} +1206.72 q^{18} +2655.07i q^{19} +2033.95i q^{20} -331.063i q^{21} -49.7941 q^{22} -1336.67i q^{23} -3486.80 q^{24} -2144.54 q^{25} -1663.64i q^{26} +10534.7 q^{27} +318.579i q^{28} +3986.45i q^{29} -4217.20i q^{30} -1548.28 q^{31} +5144.25 q^{32} -726.667 q^{33} -3682.53i q^{34} -825.370 q^{35} -16946.1 q^{36} -859.841i q^{37} +5297.43i q^{38} -24278.3i q^{39} +8692.93i q^{40} +10158.6i q^{41} -660.542i q^{42} +17391.3 q^{43} +699.266 q^{44} -43903.7i q^{45} -2666.94i q^{46} -4179.93 q^{47} +19149.8 q^{48} +16677.7 q^{49} -4278.82 q^{50} -53740.8i q^{51} +23362.8i q^{52} -33030.2 q^{53} +21019.0 q^{54} +1811.65i q^{55} +1361.58i q^{56} +77307.8i q^{57} +7953.83i q^{58} +9231.41i q^{59} +59222.7i q^{60} -5342.32 q^{61} -3089.15 q^{62} -6876.65i q^{63} -10781.9 q^{64} -60528.0 q^{65} -1449.86 q^{66} +55676.7i q^{67} +51714.3i q^{68} -38919.9i q^{69} -1646.79 q^{70} +46548.7i q^{71} -72426.0 q^{72} +81423.1 q^{73} -1715.57i q^{74} -62442.8 q^{75} -74392.6i q^{76} +283.759i q^{77} -48440.4i q^{78} +8898.89 q^{79} -47742.2i q^{80} +159772. q^{81} +20268.6i q^{82} +18263.0i q^{83} +9276.08i q^{84} -133981. q^{85} +34699.3 q^{86} +116074. i q^{87} +2988.60 q^{88} -82626.2 q^{89} -87597.4i q^{90} -9480.53 q^{91} +37452.3i q^{92} -45081.4 q^{93} -8339.87 q^{94} +192736. q^{95} +149786. q^{96} +(-31048.1 - 87311.8i) q^{97} +33275.7 q^{98} -15093.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} + 40 q^{3} + 638 q^{4} - 130 q^{6} + 180 q^{8} + 3300 q^{9} + 382 q^{11} + 2586 q^{12} + 10174 q^{16} + 4738 q^{18} + 1996 q^{22} - 3102 q^{24} - 25178 q^{25} + 3046 q^{27} + 14796 q^{31}+ \cdots - 562238 q^{99}+O(q^{100}) $ 40 * q - 2 * q^2 + 40 * q^3 + 638 * q^4 - 130 * q^6 + 180 * q^8 + 3300 * q^9 + 382 * q^11 + 2586 * q^12 + 10174 * q^16 + 4738 * q^18 + 1996 * q^22 - 3102 * q^24 - 25178 * q^25 + 3046 * q^27 + 14796 * q^31 + 8128 * q^32 - 9434 * q^33 - 2964 * q^35 + 18124 * q^36 - 45814 * q^43 - 60186 * q^44 - 17866 * q^47 + 69528 * q^48 - 64166 * q^49 + 78812 * q^50 + 117092 * q^53 - 53962 * q^54 - 33546 * q^61 - 148838 * q^62 + 215708 * q^64 + 89628 * q^65 - 17136 * q^66 + 218204 * q^70 - 127452 * q^72 + 25562 * q^73 - 52722 * q^75 - 193912 * q^79 + 175440 * q^81 - 243192 * q^85 + 108918 * q^86 + 155578 * q^88 - 434816 * q^89 - 483858 * q^91 - 66746 * q^93 - 245480 * q^94 + 97106 * q^95 - 306196 * q^96 - 251282 * q^97 - 310510 * q^98 - 562238 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/97\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$	1.99522			0.352708			0.176354	−	0.984327i	$-0.443570\pi$
$2$	1.99522			0.352708			0.176354	+	0.984327i	$0.443570\pi$
$3$	29.1171			1.86786			0.933931	−	0.357454i	$-0.116355\pi$
$3$	29.1171			1.86786			0.933931	+	0.357454i	$0.116355\pi$
$4$	−28.0191			−0.875597
$5$		−	72.5916i		−	1.29856i	−0.760550	−	0.649279i	$-0.775071\pi$
$5$		−	72.5916i		−	1.29856i	0.760550	−	0.649279i	$-0.224929\pi$
$6$	58.0949			0.658809
$7$		−	11.3700i		−	0.0877035i	−0.999038	−	0.0438518i	$-0.986037\pi$
$7$		−	11.3700i		−	0.0877035i	0.999038	−	0.0438518i	$-0.0139629\pi$
$8$	−119.751			−0.661538
$9$	604.804			2.48891
$10$		−	144.836i		−	0.458012i
$11$	−24.9567			−0.0621879			−0.0310940	−	0.999516i	$-0.509899\pi$
$11$	−24.9567			−0.0621879			−0.0310940	+	0.999516i	$0.509899\pi$
$12$	−815.835			−1.63549
$13$		−	833.816i		−	1.36840i	−0.729296	−	0.684198i	$-0.760152\pi$
$13$		−	833.816i		−	1.36840i	0.729296	−	0.684198i	$-0.239848\pi$
$14$		−	22.6857i		−	0.0309337i
$15$		−	2113.66i		−	2.42553i
$16$	657.682			0.642268
$17$		−	1845.68i		−	1.54894i	−0.632611	−	0.774469i	$-0.718017\pi$
$17$		−	1845.68i		−	1.54894i	0.632611	−	0.774469i	$-0.281983\pi$
$18$	1206.72			0.877857
$19$			2655.07i			1.68730i	0.536896	+	0.843648i	$0.319597\pi$
$19$			2655.07i			1.68730i	−0.536896	+	0.843648i	$0.680403\pi$
$20$			2033.95i			1.13701i
$21$		−	331.063i		−	0.163818i
$22$	−49.7941			−0.0219342
$23$		−	1336.67i		−	0.526871i	−0.964677	−	0.263435i	$-0.915144\pi$
$23$		−	1336.67i		−	0.526871i	0.964677	−	0.263435i	$-0.0848556\pi$
$24$	−3486.80			−1.23566
$25$	−2144.54			−0.686253
$26$		−	1663.64i		−	0.482644i
$27$	10534.7			2.78107
$28$			318.579i			0.0767930i
$29$			3986.45i			0.880220i	0.897944	+	0.440110i	$0.145061\pi$
$29$			3986.45i			0.880220i	−0.897944	+	0.440110i	$0.854939\pi$
$30$		−	4217.20i		−	0.855502i
$31$	−1548.28			−0.289364			−0.144682	−	0.989478i	$-0.546216\pi$
$31$	−1548.28			−0.289364			−0.144682	+	0.989478i	$0.546216\pi$
$32$	5144.25			0.888071
$33$	−726.667			−0.116158
$34$		−	3682.53i		−	0.546323i
$35$	−825.370			−0.113888
$36$	−16946.1			−2.17928
$37$		−	859.841i		−	0.103256i	−0.998666	−	0.0516278i	$-0.983559\pi$
$37$		−	859.841i		−	0.103256i	0.998666	−	0.0516278i	$-0.0164410\pi$
$38$			5297.43i			0.595123i
$39$		−	24278.3i		−	2.55597i
$40$			8692.93i			0.859045i
$41$			10158.6i			0.943789i	0.881655	+	0.471895i	$0.156430\pi$
$41$			10158.6i			0.943789i	−0.881655	+	0.471895i	$0.843570\pi$
$42$		−	660.542i		−	0.0577799i
$43$	17391.3			1.43437			0.717183	−	0.696885i	$-0.245431\pi$
$43$	17391.3			1.43437			0.717183	+	0.696885i	$0.245431\pi$
$44$	699.266			0.0544516
$45$		−	43903.7i		−	3.23199i
$46$		−	2666.94i		−	0.185831i
$47$	−4179.93			−0.276010			−0.138005	−	0.990432i	$-0.544069\pi$
$47$	−4179.93			−0.276010			−0.138005	+	0.990432i	$0.544069\pi$
$48$	19149.8			1.19967
$49$	16677.7			0.992308
$50$	−4278.82			−0.242047
$51$		−	53740.8i		−	2.89320i
$52$			23362.8i			1.19816i
$53$	−33030.2			−1.61518			−0.807590	−	0.589744i	$-0.799228\pi$
$53$	−33030.2			−1.61518			−0.807590	+	0.589744i	$0.799228\pi$
$54$	21019.0			0.980906
$55$			1811.65i			0.0807546i
$56$			1361.58i			0.0580192i
$57$			77307.8i			3.15164i
$58$			7953.83i			0.310461i
$59$			9231.41i			0.345253i	0.984987	+	0.172627i	$0.0552254\pi$
$59$			9231.41i			0.345253i	−0.984987	+	0.172627i	$0.944775\pi$
$60$			59222.7i			2.12378i
$61$	−5342.32			−0.183825			−0.0919126	−	0.995767i	$-0.529298\pi$
$61$	−5342.32			−0.183825			−0.0919126	+	0.995767i	$0.529298\pi$
$62$	−3089.15			−0.102061
$63$		−	6876.65i		−	0.218286i
$64$	−10781.9			−0.329038
$65$	−60528.0			−1.77694
$66$	−1449.86			−0.0409700
$67$			55676.7i			1.51526i	0.652685	+	0.757629i	$0.273642\pi$
$67$			55676.7i			1.51526i	−0.652685	+	0.757629i	$0.726358\pi$
$68$			51714.3i			1.35625i
$69$		−	38919.9i		−	0.984122i
$70$	−1646.79			−0.0401692
$71$			46548.7i			1.09588i	0.836518	+	0.547939i	$0.184587\pi$
$71$			46548.7i			1.09588i	−0.836518	+	0.547939i	$0.815413\pi$
$72$	−72426.0			−1.64651
$73$	81423.1			1.78830			0.894151	−	0.447766i	$-0.147780\pi$
$73$	81423.1			1.78830			0.894151	+	0.447766i	$0.147780\pi$
$74$		−	1715.57i		−	0.0364191i
$75$	−62442.8			−1.28183
$76$		−	74392.6i		−	1.47739i
$77$			283.759i			0.00545410i
$78$		−	48440.4i		−	0.901512i
$79$	8898.89			0.160424			0.0802118	−	0.996778i	$-0.474440\pi$
$79$	8898.89			0.160424			0.0802118	+	0.996778i	$0.474440\pi$
$80$		−	47742.2i		−	0.834022i
$81$	159772.			2.70575
$82$			20268.6i			0.332882i
$83$			18263.0i			0.290990i	0.989359	+	0.145495i	$0.0464774\pi$
$83$			18263.0i			0.290990i	−0.989359	+	0.145495i	$0.953523\pi$
$84$			9276.08i			0.143439i
$85$	−133981.			−2.01139
$86$	34699.3			0.505912
$87$			116074.i			1.64413i
$88$	2988.60			0.0411397
$89$	−82626.2			−1.10571			−0.552857	−	0.833276i	$-0.686462\pi$
$89$	−82626.2			−1.10571			−0.552857	+	0.833276i	$0.686462\pi$
$90$		−	87597.4i		−	1.13995i
$91$	−9480.53			−0.120013
$92$			37452.3i			0.461327i
$93$	−45081.4			−0.540492
$94$	−8339.87			−0.0973508
$95$	192736.			2.19105
$96$	149786.			1.65879
$97$	−31048.1	−	87311.8i	−0.335047	−	0.942201i
$97$	−31048.1	−	87311.8i	−0.335047	−	0.942201i
$98$	33275.7			0.349995
$99$	−15093.9			−0.154780
$100$	60088.1			0.600881
$101$	−69826.8			−0.681112			−0.340556	−	0.940224i	$-0.610615\pi$
$101$	−69826.8			−0.681112			−0.340556	+	0.940224i	$0.610615\pi$
$102$		−	107225.i		−	1.02046i
$103$	98055.0			0.910703			0.455352	−	0.890312i	$-0.349514\pi$
$103$	98055.0			0.910703			0.455352	+	0.890312i	$0.349514\pi$
$104$			99850.4i			0.905246i
$105$	−24032.4			−0.212727
$106$	−65902.3			−0.569687
$107$			37969.8i			0.320611i	0.987067	+	0.160306i	$0.0512480\pi$
$107$			37969.8i			0.320611i	−0.987067	+	0.160306i	$0.948752\pi$
$108$	−295173.			−2.43510
$109$	13428.2			0.108256			0.0541281	−	0.998534i	$-0.482762\pi$
$109$	13428.2			0.108256			0.0541281	+	0.998534i	$0.482762\pi$
$110$			3614.63i			0.0284828i
$111$		−	25036.1i		−	0.192867i
$112$		−	7477.88i		−	0.0563291i
$113$	154323.			1.13693			0.568467	−	0.822706i	$-0.307537\pi$
$113$	154323.			1.13693			0.568467	+	0.822706i	$0.307537\pi$
$114$			154246.i			1.11161i
$115$	−97030.9			−0.684172
$116$		−	111697.i		−	0.770718i
$117$		−	504296.i		−	3.40581i
$118$			18418.7i			0.121774i
$119$	−20985.5			−0.135847
$120$			253113.i			1.60458i
$121$	−160428.			−0.996133
$122$	−10659.1			−0.0648366
$123$			295789.i			1.76287i
$124$	43381.4			0.253367
$125$		−	71173.1i		−	0.407419i
$126$		−	13720.4i		−	0.0769912i
$127$			232834.i			1.28097i	0.767973	+	0.640483i	$0.221266\pi$
$127$			232834.i			1.28097i	−0.767973	+	0.640483i	$0.778734\pi$
$128$	−186128.			−1.00412
$129$	506383.			2.67920
$130$	−120767.			−0.626741
$131$			126240.i			0.642714i	0.946958	+	0.321357i	$0.104139\pi$
$131$			126240.i			0.642714i	−0.946958	+	0.321357i	$0.895861\pi$
$132$	20360.6			0.101708
$133$	30188.2			0.147982
$134$			111087.i			0.534444i
$135$		−	764730.i		−	3.61138i
$136$			221022.i			1.02468i
$137$		−	239969.i		−	1.09233i	−0.837677	−	0.546165i	$-0.816087\pi$
$137$		−	239969.i		−	1.09233i	0.837677	−	0.546165i	$-0.183913\pi$
$138$		−	77653.6i		−	0.347107i
$139$		−	255909.i		−	1.12344i	−0.827329	−	0.561718i	$-0.810141\pi$
$139$		−	255909.i		−	1.12344i	0.827329	−	0.561718i	$-0.189859\pi$
$140$	23126.1			0.0997201
$141$	−121707.			−0.515548
$142$			92874.8i			0.386525i
$143$			20809.3i			0.0850977i
$144$	397769.			1.59854
$145$	289383.			1.14302
$146$	162457.			0.630748
$147$	485607.			1.85349
$148$			24092.0i			0.0904104i
$149$		−	403461.i		−	1.48880i	−0.667735	−	0.744399i	$-0.732736\pi$
$149$		−	403461.i		−	1.48880i	0.667735	−	0.744399i	$-0.267264\pi$
$150$	−124587.			−0.452110
$151$	−386858.			−1.38073			−0.690366	−	0.723461i	$-0.742550\pi$
$151$	−386858.			−1.38073			−0.690366	+	0.723461i	$0.742550\pi$
$152$		−	317947.i		−	1.11621i
$153$		−	1.11628e6i		−	3.85516i
$154$			566.161i			0.00192370i
$155$			112392.i			0.375756i
$156$			680256.i			2.23800i
$157$			311504.i			1.00859i	0.863531	+	0.504295i	$0.168248\pi$
$157$			311504.i			1.00859i	−0.863531	+	0.504295i	$0.831752\pi$
$158$	17755.2			0.0565827
$159$	−961742.			−3.01693
$160$		−	373430.i		−	1.15321i
$161$	−15198.0			−0.0462084
$162$	318780.			0.954339
$163$	339867.			1.00194			0.500969	−	0.865465i	$-0.332977\pi$
$163$	339867.			1.00194			0.500969	+	0.865465i	$0.332977\pi$
$164$		−	284635.i		−	0.826379i
$165$			52749.9i			0.150838i
$166$			36438.7i			0.102634i
$167$	326766.			0.906664			0.453332	−	0.891342i	$-0.350235\pi$
$167$	326766.			0.906664			0.453332	+	0.891342i	$0.350235\pi$
$168$			39645.1i			0.108372i
$169$	−323956.			−0.872508
$170$	−267321.			−0.709432
$171$			1.60580e6i			4.19952i
$172$	−487288.			−1.25593
$173$		−	334893.i		−	0.850728i	−0.905022	−	0.425364i	$-0.860146\pi$
$173$		−	334893.i		−	0.850728i	0.905022	−	0.425364i	$-0.139854\pi$
$174$			231592.i			0.579897i
$175$			24383.5i			0.0601868i
$176$	−16413.6			−0.0399413
$177$			268792.i			0.644885i
$178$	−164857.			−0.389994
$179$		−	8397.70i		−	0.0195897i	−0.999952	−	0.00979485i	$-0.996882\pi$
$179$		−	8397.70i		−	0.0195897i	0.999952	−	0.00979485i	$-0.00311785\pi$
$180$			1.23014e6i			2.82992i
$181$			145823.i			0.330848i	0.986223	+	0.165424i	$0.0528993\pi$
$181$			145823.i			0.330848i	−0.986223	+	0.165424i	$0.947101\pi$
$182$	−18915.7			−0.0423296
$183$	−155553.			−0.343360
$184$			160068.i			0.348545i
$185$	−62417.2			−0.134083
$186$	−89947.1			−0.190636
$187$			46062.2i			0.0963253i
$188$	117118.			0.241673
$189$		−	119780.i		−	0.243910i
$190$	384549.			0.772801
$191$	500958.			0.993614			0.496807	−	0.867861i	$-0.334506\pi$
$191$	500958.			0.993614			0.496807	+	0.867861i	$0.334506\pi$
$192$	−313938.			−0.614598
$193$	582971.			1.12656			0.563279	−	0.826267i	$-0.309540\pi$
$193$	582971.			1.12656			0.563279	+	0.826267i	$0.309540\pi$
$194$	−61947.7	−	174206.i	−0.118174	−	0.332322i
$195$	−1.76240e6			−3.31908
$196$	−467295.			−0.868862
$197$	526473.			0.966519			0.483259	−	0.875477i	$-0.339453\pi$
$197$	526473.			0.966519			0.483259	+	0.875477i	$0.339453\pi$
$198$	−30115.7			−0.0545921
$199$		−	690511.i		−	1.23606i	−0.786156	−	0.618028i	$-0.787932\pi$
$199$		−	690511.i		−	1.23606i	0.786156	−	0.618028i	$-0.212068\pi$
$200$	256811.			0.453982
$201$			1.62114e6i			2.83029i
$202$	−139320.			−0.240233
$203$	45326.1			0.0771984
$204$			1.50577e6i			2.53328i
$205$	737431.			1.22557
$206$	195641.			0.321212
$207$		−	808423.i		−	1.31133i
$208$		−	548386.i		−	0.878877i
$209$		−	66261.8i		−	0.104929i
$210$	−47949.8			−0.0750306
$211$			506320.i			0.782923i	0.920195	+	0.391461i	$0.128030\pi$
$211$			506320.i			0.782923i	−0.920195	+	0.391461i	$0.871970\pi$
$212$	925475.			1.41425
$213$			1.35536e6i			2.04695i
$214$			75758.0i			0.113082i
$215$		−	1.26246e6i		−	1.86261i
$216$	−1.26154e6			−1.83978
$217$			17604.0i			0.0253783i
$218$	26792.3			0.0381828
$219$	2.37080e6			3.34030
$220$		−	50760.8i		−	0.0707085i
$221$	−1.53896e6			−2.11956
$222$		−	49952.4i		−	0.0680258i
$223$			358548.i			0.482819i	0.970423	+	0.241410i	$0.0776098\pi$
$223$			358548.i			0.482819i	−0.970423	+	0.241410i	$0.922390\pi$
$224$		−	58490.4i		−	0.0778869i
$225$	−1.29703e6			−1.70802
$226$	307908.			0.401006
$227$	−859830.			−1.10751			−0.553755	−	0.832680i	$-0.686806\pi$
$227$	−859830.			−1.10751			−0.553755	+	0.832680i	$0.686806\pi$
$228$		−	2.16610e6i		−	2.75956i
$229$	−348458.			−0.439098			−0.219549	−	0.975601i	$-0.570459\pi$
$229$	−348458.			−0.439098			−0.219549	+	0.975601i	$0.570459\pi$
$230$	−193598.			−0.241313
$231$			8262.24i			0.0101875i
$232$		−	477382.i		−	0.582299i
$233$		−	1.31789e6i		−	1.59034i	−0.606386	−	0.795170i	$-0.707382\pi$
$233$		−	1.31789e6i		−	1.59034i	0.606386	−	0.795170i	$-0.292618\pi$
$234$		−	1.00618e6i		−	1.20126i
$235$			303428.i			0.358415i
$236$		−	258656.i		−	0.302303i
$237$	259110.			0.299649
$238$	−41870.6			−0.0479144
$239$		−	859363.i		−	0.973154i	−0.873638	−	0.486577i	$-0.838245\pi$
$239$		−	859363.i		−	0.973154i	0.873638	−	0.486577i	$-0.161755\pi$
$240$		−	1.39011e6i		−	1.55784i
$241$	747922.			0.829495			0.414748	−	0.909937i	$-0.363870\pi$
$241$	747922.			0.829495			0.414748	+	0.909937i	$0.363870\pi$
$242$	−320089.			−0.351344
$243$	2.09216e6			2.27290
$244$	149687.			0.160957
$245$		−	1.21066e6i		−	1.28857i
$246$			590164.i			0.621777i
$247$	2.21384e6			2.30889
$248$	185408.			0.191425
$249$			531766.i			0.543529i
$250$		−	142006.i		−	0.143700i
$251$			583583.i			0.584680i	0.956314	+	0.292340i	$0.0944339\pi$
$251$			583583.i			0.584680i	−0.956314	+	0.292340i	$0.905566\pi$
$252$			192678.i			0.191131i
$253$			33358.9i			0.0327650i
$254$			464554.i			0.451806i
$255$	−3.90113e6			−3.75699
$256$	−26345.0			−0.0251245
$257$			1.08631e6i			1.02594i	0.858408	+	0.512968i	$0.171454\pi$
$257$			1.08631e6i			1.02594i	−0.858408	+	0.512968i	$0.828546\pi$
$258$	1.01034e6			0.944974
$259$	−9776.43			−0.00905589
$260$	1.69594e6			1.55589
$261$			2.41102e6i			2.19079i
$262$			251876.i			0.226690i
$263$		−	320911.i		−	0.286085i	−0.989717	−	0.143043i	$-0.954311\pi$
$263$		−	320911.i		−	0.286085i	0.989717	−	0.143043i	$-0.0456886\pi$
$264$	87019.2			0.0768432
$265$			2.39771e6i			2.09740i
$266$	60232.1			0.0521944
$267$	−2.40583e6			−2.06532
$268$		−	1.56001e6i		−	1.32676i
$269$	−155007.			−0.130608			−0.0653041	−	0.997865i	$-0.520802\pi$
$269$	−155007.			−0.130608			−0.0653041	+	0.997865i	$0.520802\pi$
$270$		−	1.52580e6i		−	1.27376i
$271$			2.23692e6i			1.85024i	0.379676	+	0.925119i	$0.376035\pi$
$271$			2.23692e6i			1.85024i	−0.379676	+	0.925119i	$0.623965\pi$
$272$		−	1.21387e6i		−	0.994833i
$273$	−276045.			−0.224168
$274$		−	478791.i		−	0.385274i
$275$	53520.7			0.0426767
$276$			1.09050e6i			0.861694i
$277$		−	1.64351e6i		−	1.28698i	−0.765454	−	0.643491i	$-0.777485\pi$
$277$		−	1.64351e6i		−	1.28698i	0.765454	−	0.643491i	$-0.222515\pi$
$278$		−	510594.i		−	0.396245i
$279$	−936406.			−0.720201
$280$	98839.0			0.0753413
$281$			659197.i			0.498023i	0.968501	+	0.249012i	$0.0801057\pi$
$281$			659197.i			0.498023i	−0.968501	+	0.249012i	$0.919894\pi$
$282$	−242833.			−0.181838
$283$	−238830.			−0.177265			−0.0886324	−	0.996064i	$-0.528250\pi$
$283$	−238830.			−0.177265			−0.0886324	+	0.996064i	$0.528250\pi$
$284$		−	1.30425e6i		−	0.959547i
$285$	5.61190e6			4.09258
$286$			41519.1i			0.0300146i
$287$	115504.			0.0827737
$288$	3.11127e6			2.21033
$289$	−1.98668e6			−1.39921
$290$	577381.			0.403151
$291$	−904030.	−	2.54227e6i	−0.625821	−	1.75990i
$292$	−2.28140e6			−1.56583
$293$	−660970.			−0.449793			−0.224897	−	0.974383i	$-0.572204\pi$
$293$	−660970.			−0.449793			−0.224897	+	0.974383i	$0.572204\pi$
$294$	968890.			0.653742
$295$	670123.			0.448332
$296$			102967.i			0.0683075i
$297$	−262911.			−0.172949
$298$		−	804992.i		−	0.525111i
$299$	−1.11454e6			−0.720968
$300$	1.74959e6			1.12236
$301$		−	197739.i		−	0.125799i
$302$	−771865.			−0.486995
$303$	−2.03315e6			−1.27222
$304$			1.74619e6i			1.08370i
$305$			387807.i			0.238708i
$306$		−	2.22721e6i		−	1.35975i
$307$	−2.89041e6			−1.75031			−0.875153	−	0.483846i	$-0.839240\pi$
$307$	−2.89041e6			−1.75031			−0.875153	+	0.483846i	$0.839240\pi$
$308$		−	7950.68i		−	0.00477560i
$309$	2.85508e6			1.70107
$310$			224246.i			0.132532i
$311$		−	2.55348e6i		−	1.49703i	−0.663115	−	0.748517i	$-0.730766\pi$
$311$		−	2.55348e6i		−	1.49703i	0.663115	−	0.748517i	$-0.269234\pi$
$312$			2.90735e6i			1.69087i
$313$	−2.50658e6			−1.44618			−0.723088	−	0.690756i	$-0.757278\pi$
$313$	−2.50658e6			−1.44618			−0.723088	+	0.690756i	$0.757278\pi$
$314$			621518.i			0.355738i
$315$	−499187.			−0.283457
$316$	−249339.			−0.140466
$317$			497832.i			0.278250i	0.990275	+	0.139125i	$0.0444289\pi$
$317$			497832.i			0.278250i	−0.990275	+	0.139125i	$0.955571\pi$
$318$	−1.91888e6			−1.06410
$319$		−	99488.8i		−	0.0547391i
$320$			782677.i			0.427275i
$321$			1.10557e6i			0.598857i
$322$	−30323.3			−0.0162981
$323$	4.90041e6			2.61352
$324$	−4.47667e6			−2.36915
$325$			1.78815e6i			0.939066i
$326$	678109.			0.353391
$327$	390991.			0.202208
$328$		−	1.21651e6i		−	0.624352i
$329$			47526.0i			0.0242070i
$330$			105248.i			0.0532019i
$331$			1.66555e6i			0.835582i	0.908543	+	0.417791i	$0.137196\pi$
$331$			1.66555e6i			0.835582i	−0.908543	+	0.417791i	$0.862804\pi$
$332$		−	511714.i		−	0.254790i
$333$		−	520036.i		−	0.256994i
$334$	651970.			0.319787
$335$	4.04166e6			1.96765
$336$		−	217734.i		−	0.105215i
$337$		−	629783.i		−	0.302076i	−0.988528	−	0.151038i	$-0.951738\pi$
$337$		−	629783.i		−	0.302076i	0.988528	−	0.151038i	$-0.0482616\pi$
$338$	−646363.			−0.307740
$339$	4.49344e6			2.12364
$340$	3.75403e6			1.76116
$341$	38640.0			0.0179950
$342$			3.20391e6i			1.48120i
$343$		−	380723.i		−	0.174732i
$344$	−2.08262e6			−0.948887
$345$	−2.82526e6			−1.27794
$346$		−	668184.i		−	0.300058i
$347$			2.52850e6i			1.12730i	0.826013	+	0.563651i	$0.190604\pi$
$347$			2.52850e6i			1.12730i	−0.826013	+	0.563651i	$0.809396\pi$
$348$		−	3.25228e6i		−	1.43960i
$349$			1.29822e6i			0.570539i	0.958447	+	0.285269i	$0.0920831\pi$
$349$			1.29822e6i			0.570539i	−0.958447	+	0.285269i	$0.907917\pi$
$350$			48650.4i			0.0212284i
$351$		−	8.78399e6i		−	3.80561i
$352$	−128384.			−0.0552273
$353$	−3.43592e6			−1.46759			−0.733797	−	0.679369i	$-0.762254\pi$
$353$	−3.43592e6			−1.46759			−0.733797	+	0.679369i	$0.762254\pi$
$354$			536298.i			0.227456i
$355$	3.37905e6			1.42306
$356$	2.31511e6			0.968160
$357$	−611036.			−0.253744
$358$		−	16755.2i		−	0.00690944i
$359$		−	889441.i		−	0.364234i	−0.983277	−	0.182117i	$-0.941705\pi$
$359$		−	889441.i		−	0.364234i	0.983277	−	0.182117i	$-0.0582950\pi$
$360$			5.25752e6i			2.13808i
$361$	−4.57328e6			−1.84697
$362$			290948.i			0.116693i
$363$	−4.67120e6			−1.86064
$364$	265636.			0.105083
$365$		−	5.91064e6i		−	2.32221i
$366$	−310361.			−0.121106
$367$			4.03111e6i			1.56228i	0.624354	+	0.781141i	$0.285362\pi$
$367$			4.03111e6i			1.56228i	−0.624354	+	0.781141i	$0.714638\pi$
$368$		−	879103.i		−	0.338392i
$369$			6.14398e6i			2.34900i
$370$	−124536.			−0.0472923
$371$			375554.i			0.141657i
$372$	1.26314e6			0.473254
$373$			1.60552e6i			0.597506i	0.954330	+	0.298753i	$0.0965707\pi$
$373$			1.60552e6i			0.597506i	−0.954330	+	0.298753i	$0.903429\pi$
$374$			91904.0i			0.0339747i
$375$		−	2.07235e6i		−	0.761002i
$376$	500552.			0.182591
$377$	3.32397e6			1.20449
$378$		−	238987.i		−	0.0860289i
$379$	−581217.			−0.207845			−0.103923	−	0.994585i	$-0.533139\pi$
$379$	−581217.			−0.207845			−0.103923	+	0.994585i	$0.533139\pi$
$380$	−5.40028e6			−1.91848
$381$			6.77945e6i			2.39267i
$382$	999519.			0.350455
$383$			4.03085e6i			1.40411i	0.712125	+	0.702053i	$0.247733\pi$
$383$			4.03085e6i			1.40411i	−0.712125	+	0.702053i	$0.752267\pi$
$384$	−5.41952e6			−1.87557
$385$	20598.5			0.00708247
$386$	1.16315e6			0.397346
$387$	1.05183e7			3.57000
$388$	869940.	+	2.44640e6i	0.293366	+	0.824989i
$389$	−1.94850e6			−0.652870			−0.326435	−	0.945220i	$-0.605847\pi$
$389$	−1.94850e6			−0.652870			−0.326435	+	0.945220i	$0.605847\pi$
$390$	−3.51637e6			−1.17067
$391$	−2.46706e6			−0.816091
$392$	−1.99718e6			−0.656449
$393$			3.67573e6i			1.20050i
$394$	1.05043e6			0.340899
$395$		−	645985.i		−	0.208319i
$396$	422919.			0.135525
$397$	−4.13875e6			−1.31793			−0.658965	−	0.752173i	$-0.729006\pi$
$397$	−4.13875e6			−1.31793			−0.658965	+	0.752173i	$0.729006\pi$
$398$		−	1.37772e6i		−	0.435966i
$399$	878993.			0.276410
$400$	−1.41043e6			−0.440758
$401$			5.40237e6i			1.67774i	0.544336	+	0.838868i	$0.316782\pi$
$401$			5.40237e6i			1.67774i	−0.544336	+	0.838868i	$0.683218\pi$
$402$			3.23453e6i			0.998267i
$403$			1.29098e6i			0.395965i
$404$	1.95648e6			0.596380
$405$		−	1.15981e7i		−	3.51357i
$406$	90435.4			0.0272285
$407$			21458.8i			0.00642126i
$408$			6.43553e6i			1.91396i
$409$		−	1.02617e6i		−	0.303328i	−0.988432	−	0.151664i	$-0.951537\pi$
$409$		−	1.02617e6i		−	0.303328i	0.988432	−	0.151664i	$-0.0484632\pi$
$410$	1.47133e6			0.432266
$411$		−	6.98720e6i		−	2.04032i
$412$	−2.74741e6			−0.797409
$413$	104962.			0.0302799
$414$		−	1.61298e6i		−	0.462517i
$415$	1.32574e6			0.377867
$416$		−	4.28936e6i		−	1.21523i
$417$		−	7.45132e6i		−	2.09842i
$418$		−	132207.i		−	0.0370094i
$419$	−4.26053e6			−1.18557			−0.592787	−	0.805360i	$-0.701972\pi$
$419$	−4.26053e6			−1.18557			−0.592787	+	0.805360i	$0.701972\pi$
$420$	673365.			0.186263
$421$	−3.85677e6			−1.06052			−0.530260	−	0.847835i	$-0.677906\pi$
$421$	−3.85677e6			−1.06052			−0.530260	+	0.847835i	$0.677906\pi$
$422$			1.01022e6i			0.276143i
$423$	−2.52804e6			−0.686963
$424$	3.95540e6			1.06850
$425$			3.95814e6i			1.06296i
$426$			2.70424e6i			0.721974i
$427$			60742.4i			0.0161221i
$428$		−	1.06388e6i		−	0.280726i
$429$			605907.i			0.158951i
$430$		−	2.51888e6i		−	0.656956i
$431$	4.34436e6			1.12650			0.563252	−	0.826285i	$-0.309550\pi$
$431$	4.34436e6			1.12650			0.563252	+	0.826285i	$0.309550\pi$
$432$	6.92848e6			1.78619
$433$			6.07134e6i			1.55620i	0.628142	+	0.778099i	$0.283816\pi$
$433$			6.07134e6i			1.55620i	−0.628142	+	0.778099i	$0.716184\pi$
$434$			35123.8i			0.00895111i
$435$	8.42598e6			2.13500
$436$	−376248.			−0.0947889
$437$	3.54894e6			0.888987
$438$	4.73027e6			1.17815
$439$		−	96532.4i		−	0.0239063i	−0.999929	−	0.0119531i	$-0.996195\pi$
$439$		−	96532.4i		−	0.0239063i	0.999929	−	0.0119531i	$-0.00380489\pi$
$440$		−	216947.i		−	0.0534222i
$441$	1.00868e7			2.46976
$442$	−3.07056e6			−0.747586
$443$		−	7.95372e6i		−	1.92558i	−0.270255	−	0.962789i	$-0.587108\pi$
$443$		−	7.95372e6i		−	1.92558i	0.270255	−	0.962789i	$-0.412892\pi$
$444$			701488.i			0.168874i
$445$			5.99797e6i			1.43583i
$446$			715380.i			0.170294i
$447$		−	1.17476e7i		−	2.78087i
$448$			122591.i			0.0288578i
$449$	−1.01396e6			−0.237358			−0.118679	−	0.992933i	$-0.537866\pi$
$449$	−1.01396e6			−0.237358			−0.118679	+	0.992933i	$0.537866\pi$
$450$	−2.58785e6			−0.602432
$451$		−	253526.i		−	0.0586923i
$452$	−4.32400e6			−0.995497
$453$	−1.12642e7			−2.57901
$454$	−1.71555e6			−0.390628
$455$			688207.i			0.155844i
$456$		−	9.25770e6i		−	2.08493i
$457$		−	2.20788e6i		−	0.494522i	−0.968949	−	0.247261i	$-0.920469\pi$
$457$		−	2.20788e6i		−	0.494522i	0.968949	−	0.247261i	$-0.0795306\pi$
$458$	−695249.			−0.154873
$459$		−	1.94437e7i		−	4.30771i
$460$	2.71872e6			0.599059
$461$	−433567.			−0.0950176			−0.0475088	−	0.998871i	$-0.515128\pi$
$461$	−433567.			−0.0950176			−0.0475088	+	0.998871i	$0.515128\pi$
$462$			16485.0i			0.00359321i
$463$	2.40559e6			0.521517			0.260759	−	0.965404i	$-0.416027\pi$
$463$	2.40559e6			0.521517			0.260759	+	0.965404i	$0.416027\pi$
$464$			2.62182e6i			0.565337i
$465$			3.27253e6i			0.701861i
$466$		−	2.62948e6i		−	0.560925i
$467$	3.94418e6			0.836882			0.418441	−	0.908244i	$-0.362577\pi$
$467$	3.94418e6			0.836882			0.418441	+	0.908244i	$0.362577\pi$
$468$			1.41299e7i			2.98212i
$469$	633047.			0.132894
$470$			605405.i			0.126416i
$471$			9.07009e6i			1.88391i
$472$		−	1.10547e6i		−	0.228398i
$473$	−434029.			−0.0892002
$474$	516980.			0.105689
$475$		−	5.69390e6i		−	1.15791i
$476$	587994.			0.118948
$477$	−1.99768e7			−4.02003
$478$		−	1.71461e6i		−	0.343239i
$479$	−6.35821e6			−1.26618			−0.633091	−	0.774078i	$-0.718214\pi$
$479$	−6.35821e6			−1.26618			−0.633091	+	0.774078i	$0.718214\pi$
$480$		−	1.08732e7i		−	2.15404i
$481$	−716949.			−0.141295
$482$	1.49227e6			0.292569
$483$	−442521.			−0.0863110
$484$	4.49505e6			0.872211
$485$	−6.33811e6	+	2.25383e6i	−1.22350	+	0.435078i
$486$	4.17432e6			0.801668
$487$	5.20333e6			0.994165			0.497083	−	0.867703i	$-0.334405\pi$
$487$	5.20333e6			0.994165			0.497083	+	0.867703i	$0.334405\pi$
$488$	639748.			0.121607
$489$	9.89595e6			1.87148
$490$		−	2.41553e6i		−	0.454489i
$491$	1.52023e6			0.284581			0.142291	−	0.989825i	$-0.454553\pi$
$491$	1.52023e6			0.284581			0.142291	+	0.989825i	$0.454553\pi$
$492$		−	8.28775e6i		−	1.54356i
$493$	7.35771e6			1.36341
$494$	4.41709e6			0.814364
$495$			1.09569e6i			0.200991i
$496$	−1.01828e6			−0.185849
$497$	529261.			0.0961123
$498$			1.06099e6i			0.191707i
$499$			3.86501e6i			0.694864i	0.937705	+	0.347432i	$0.112946\pi$
$499$			3.86501e6i			0.694864i	−0.937705	+	0.347432i	$0.887054\pi$
$500$			1.99421e6i			0.356735i
$501$	9.51448e6			1.69352
$502$			1.16437e6i			0.206221i
$503$	−7.98633e6			−1.40743			−0.703716	−	0.710481i	$-0.748477\pi$
$503$	−7.98633e6			−1.40743			−0.703716	+	0.710481i	$0.748477\pi$
$504$			823487.i			0.144404i
$505$			5.06884e6i			0.884463i
$506$			66558.2i			0.0115565i
$507$	−9.43266e6			−1.62972
$508$		−	6.52380e6i		−	1.12161i
$509$	4.44864e6			0.761085			0.380543	−	0.924763i	$-0.375737\pi$
$509$	4.44864e6			0.761085			0.380543	+	0.924763i	$0.375737\pi$
$510$	−7.78361e6			−1.32512
$511$		−	925785.i		−	0.156840i
$512$	5.90355e6			0.995263
$513$			2.79703e7i			4.69249i
$514$			2.16742e6i			0.361855i
$515$		−	7.11797e6i		−	1.18260i
$516$	−1.41884e7			−2.34590
$517$	104317.			0.0171645
$518$	−19506.1			−0.00319408
$519$		−	9.75111e6i		−	1.58904i
$520$	7.24830e6			1.17551
$521$	−5.99246e6			−0.967188			−0.483594	−	0.875292i	$-0.660669\pi$
$521$	−5.99246e6			−0.967188			−0.483594	+	0.875292i	$0.660669\pi$
$522$			4.81051e6i			0.772707i
$523$			576600.i			0.0921765i	0.998937	+	0.0460883i	$0.0146755\pi$
$523$			576600.i			0.0921765i	−0.998937	+	0.0460883i	$0.985324\pi$
$524$		−	3.53713e6i		−	0.562759i
$525$			709977.i			0.112421i
$526$		−	640287.i		−	0.100905i
$527$			2.85763e6i			0.448207i
$528$	−477916.			−0.0746048
$529$	4.64966e6			0.722407
$530$			4.78395e6i			0.739771i
$531$			5.58320e6i			0.859303i
$532$	−845847.			−0.129573
$533$	8.47042e6			1.29148
$534$	−4.80016e6			−0.728455
$535$	2.75629e6			0.416332
$536$		−	6.66735e6i		−	1.00240i
$537$		−	244517.i		−	0.0365909i
$538$	−309273.			−0.0460666
$539$	−416222.			−0.0617096
$540$			2.14270e7i			3.16212i
$541$			3.16338e6i			0.464685i	0.972634	+	0.232342i	$0.0746389\pi$
$541$			3.16338e6i			0.464685i	−0.972634	+	0.232342i	$0.925361\pi$
$542$			4.46315e6i			0.652594i
$543$			4.24594e6i			0.617979i
$544$		−	9.49465e6i		−	1.37557i
$545$		−	974778.i		−	0.140577i
$546$	−550770.			−0.0790658
$547$	1.03552e6			0.147975			0.0739875	−	0.997259i	$-0.476427\pi$
$547$	1.03552e6			0.147975			0.0739875	+	0.997259i	$0.476427\pi$
$548$			6.72372e6i			0.956442i
$549$	−3.23106e6			−0.457524
$550$	106785.			0.0150524
$551$	−1.05843e7			−1.48519
$552$			4.66070e6i			0.651034i
$553$		−	101181.i		−	0.0140697i
$554$		−	3.27915e6i		−	0.453929i
$555$	−1.81741e6			−0.250449
$556$			7.17034e6i			0.983677i
$557$	9.37276e6			1.28006			0.640029	−	0.768351i	$-0.278922\pi$
$557$	9.37276e6			1.28006			0.640029	+	0.768351i	$0.278922\pi$
$558$	−1.86833e6			−0.254020
$559$		−	1.45011e7i		−	1.96278i
$560$	−542831.			−0.0731467
$561$			1.34120e6i			0.179922i
$562$			1.31524e6i			0.175657i
$563$		−	7.31437e6i		−	0.972537i	−0.873809	−	0.486268i	$-0.838358\pi$
$563$		−	7.31437e6i		−	0.972537i	0.873809	−	0.486268i	$-0.161642\pi$
$564$	3.41013e6			0.451413
$565$		−	1.12026e7i		−	1.47638i
$566$	−476517.			−0.0625226
$567$		−	1.81661e6i		−	0.237304i
$568$		−	5.57426e6i		−	0.724964i
$569$		−	7.38802e6i		−	0.956638i	−0.878186	−	0.478319i	$-0.841246\pi$
$569$		−	7.38802e6i		−	0.956638i	0.878186	−	0.478319i	$-0.158754\pi$
$570$	1.11969e7			1.44349
$571$	−6.07542e6			−0.779805			−0.389902	−	0.920856i	$-0.627491\pi$
$571$	−6.07542e6			−0.779805			−0.389902	+	0.920856i	$0.627491\pi$
$572$		−	583059.i		−	0.0745113i
$573$	1.45864e7			1.85593
$574$	230455.			0.0291949
$575$			2.86654e6i			0.361567i
$576$	−6.52095e6			−0.818945
$577$			4.84527e6i			0.605868i	0.953011	+	0.302934i	$0.0979663\pi$
$577$			4.84527e6i			0.605868i	−0.953011	+	0.302934i	$0.902034\pi$
$578$	−3.96386e6			−0.493513
$579$	1.69744e7			2.10425
$580$	−8.10825e6			−1.00082
$581$	207652.			0.0255208
$582$	−1.80373e6	−	5.07237e6i	−0.220732	−	0.620731i
$583$	824325.			0.100445
$584$	−9.75051e6			−1.18303
$585$	−3.66076e7			−4.42264
$586$	−1.31878e6			−0.158646
$587$			1.43096e6i			0.171409i	0.996321	+	0.0857043i	$0.0273140\pi$
$587$			1.43096e6i			0.171409i	−0.996321	+	0.0857043i	$0.972686\pi$
$588$	−1.36063e7			−1.62291
$589$		−	4.11078e6i		−	0.488243i
$590$	1.33704e6			0.158130
$591$	1.53293e7			1.80532
$592$		−	565502.i		−	0.0663178i
$593$	2.93816e6			0.343114			0.171557	−	0.985174i	$-0.445120\pi$
$593$	2.93816e6			0.343114			0.171557	+	0.985174i	$0.445120\pi$
$594$	−524565.			−0.0610005
$595$			1.52337e6i			0.176406i
$596$			1.13046e7i			1.30359i
$597$		−	2.01057e7i		−	2.30878i
$598$	−2.22374e6			−0.254291
$599$			8.81482e6i			1.00380i	0.864926	+	0.501899i	$0.167365\pi$
$599$			8.81482e6i			1.00380i	−0.864926	+	0.501899i	$0.832635\pi$
$600$	7.47759e6			0.847976
$601$		−	1.73019e7i		−	1.95392i	−0.213421	−	0.976960i	$-0.568461\pi$
$601$		−	1.73019e7i		−	1.95392i	0.213421	−	0.976960i	$-0.431539\pi$
$602$		−	394533.i		−	0.0443703i
$603$			3.36735e7i			3.77134i
$604$	1.08394e7			1.20896
$605$			1.16457e7i			1.29354i
$606$	−4.05658e6			−0.448723
$607$	−2.23416e6			−0.246117			−0.123059	−	0.992399i	$-0.539270\pi$
$607$	−2.23416e6			−0.246117			−0.123059	+	0.992399i	$0.539270\pi$
$608$			1.36583e7i			1.49844i
$609$	1.31976e6			0.144196
$610$			773760.i			0.0841941i
$611$			3.48529e6i			0.377691i
$612$			3.12771e7i			3.37557i
$613$	99675.7			0.0107137			0.00535683	−	0.999986i	$-0.498295\pi$
$613$	99675.7			0.0107137			0.00535683	+	0.999986i	$0.498295\pi$
$614$	−5.76700e6			−0.617347
$615$	2.14718e7			2.28919
$616$		−	33980.5i		−	0.00360809i
$617$	−7.93517e6			−0.839157			−0.419579	−	0.907719i	$-0.637822\pi$
$617$	−7.93517e6			−0.839157			−0.419579	+	0.907719i	$0.637822\pi$
$618$	5.69650e6			0.599980
$619$		−	9.05446e6i		−	0.949808i	−0.880038	−	0.474904i	$-0.842483\pi$
$619$		−	9.05446e6i		−	0.949808i	0.880038	−	0.474904i	$-0.157517\pi$
$620$		−	3.14912e6i		−	0.329011i
$621$		−	1.40814e7i		−	1.46527i
$622$		−	5.09475e6i		−	0.528016i
$623$			939464.i			0.0969750i
$624$		−	1.59674e7i		−	1.64162i
$625$	−1.18683e7			−1.21531
$626$	−5.00118e6			−0.510078
$627$		−	1.92935e6i		−	0.195994i
$628$		−	8.72807e6i		−	0.883119i
$629$	−1.58699e6			−0.159937
$630$	−995987.			−0.0999775
$631$	−7.82386e6			−0.782253			−0.391127	−	0.920337i	$-0.627915\pi$
$631$	−7.82386e6			−0.782253			−0.391127	+	0.920337i	$0.627915\pi$
$632$	−1.06565e6			−0.106126
$633$			1.47426e7i			1.46239i
$634$			993283.i			0.0981409i
$635$	1.69018e7			1.66341
$636$	2.69471e7			2.64162
$637$		−	1.39062e7i		−	1.35787i
$638$		−	198502.i		−	0.0193069i
$639$			2.81529e7i			2.72754i
$640$			1.35114e7i			1.30391i
$641$			6.05239e6i			0.581811i	0.956752	+	0.290905i	$0.0939565\pi$
$641$			6.05239e6i			0.581811i	−0.956752	+	0.290905i	$0.906044\pi$
$642$			2.20585e6i			0.211222i
$643$	−1.09121e7			−1.04083			−0.520417	−	0.853912i	$-0.674223\pi$
$643$	−1.09121e7			−1.04083			−0.520417	+	0.853912i	$0.674223\pi$
$644$	425834.			0.0404600
$645$		−	3.67591e7i		−	3.47909i
$646$	9.77737e6			0.921809
$647$	−1.39398e7			−1.30917			−0.654584	−	0.755990i	$-0.727156\pi$
$647$	−1.39398e7			−1.30917			−0.654584	+	0.755990i	$0.727156\pi$
$648$	−1.91329e7			−1.78996
$649$		−	230386.i		−	0.0214706i
$650$			3.56775e6i			0.331216i
$651$			512577.i			0.0474031i
$652$	−9.52278e6			−0.877293
$653$			4.73716e6i			0.434745i	0.976089	+	0.217373i	$0.0697486\pi$
$653$			4.73716e6i			0.434745i	−0.976089	+	0.217373i	$0.930251\pi$
$654$	780112.			0.0713202
$655$	9.16395e6			0.834602
$656$			6.68114e6i			0.606165i
$657$	4.92451e7			4.45091
$658$			94824.7i			0.00853801i
$659$		−	624376.i		−	0.0560057i	−0.999608	−	0.0280029i	$-0.991085\pi$
$659$		−	624376.i		−	0.0560057i	0.999608	−	0.0280029i	$-0.00891476\pi$
$660$		−	1.47801e6i		−	0.132074i
$661$	6.38690e6			0.568573			0.284287	−	0.958739i	$-0.408243\pi$
$661$	6.38690e6			0.568573			0.284287	+	0.958739i	$0.408243\pi$
$662$			3.32314e6i			0.294716i
$663$	−4.48100e7			−3.95905
$664$		−	2.18702e6i		−	0.192501i
$665$		−	2.19141e6i		−	0.192163i
$666$		−	1.03758e6i		−	0.0906437i
$667$	5.32856e6			0.463762
$668$	−9.15570e6			−0.793872
$669$			1.04399e7i			0.901840i
$670$	8.06399e6			0.694006
$671$	133327.			0.0114317
$672$		−	1.70307e6i		−	0.145482i
$673$	−1.24911e7			−1.06307			−0.531536	−	0.847036i	$-0.678385\pi$
$673$	−1.24911e7			−1.06307			−0.531536	+	0.847036i	$0.678385\pi$
$674$		−	1.25655e6i		−	0.106545i
$675$	−2.25921e7			−1.90852
$676$	9.07697e6			0.763966
$677$	2.00378e7			1.68027			0.840135	−	0.542377i	$-0.182476\pi$
$677$	2.00378e7			1.68027			0.840135	+	0.542377i	$0.182476\pi$
$678$	8.96539e6			0.749023
$679$	−992740.	+	353018.i	−0.0826344	+	0.0293848i
$680$	1.60444e7			1.33061
$681$	−2.50357e7			−2.06868
$682$	77095.1			0.00634696
$683$	1.44633e7			1.18635			0.593177	−	0.805072i	$-0.297873\pi$
$683$	1.44633e7			1.18635			0.593177	+	0.805072i	$0.297873\pi$
$684$		−	4.49930e7i		−	3.67709i
$685$	−1.74198e7			−1.41845
$686$		−	759625.i		−	0.0616295i
$687$	−1.01461e7			−0.820174
$688$	1.14379e7			0.921247
$689$			2.75411e7i			2.21021i
$690$	−5.63700e6			−0.450739
$691$	−7.06083e6			−0.562549			−0.281275	−	0.959627i	$-0.590757\pi$
$691$	−7.06083e6			−0.562549			−0.281275	+	0.959627i	$0.590757\pi$
$692$			9.38340e6i			0.744895i
$693$			171619.i			0.0135748i
$694$			5.04491e6i			0.397608i
$695$	−1.85768e7			−1.45885
$696$		−	1.39000e7i		−	1.08765i
$697$	1.87496e7			1.46187
$698$			2.59023e6i			0.201234i
$699$		−	3.83732e7i		−	2.97054i
$700$		−	683205.i		−	0.0526994i
$701$	8.98565e6			0.690644			0.345322	−	0.938484i	$-0.387770\pi$
$701$	8.98565e6			0.690644			0.345322	+	0.938484i	$0.387770\pi$
$702$		−	1.75260e7i		−	1.34227i
$703$	2.28294e6			0.174223
$704$	269082.			0.0204622
$705$			8.83494e6i			0.669469i
$706$	−6.85540e6			−0.517632
$707$			793934.i			0.0597359i
$708$		−	7.53130e6i		−	0.564660i
$709$		−	3.87999e6i		−	0.289878i	−0.989441	−	0.144939i	$-0.953701\pi$
$709$		−	3.87999e6i		−	0.289878i	0.989441	−	0.144939i	$-0.0462986\pi$
$710$	6.74193e6			0.501925
$711$	5.38209e6			0.399279
$712$	9.89458e6			0.731472
$713$			2.06954e6i			0.152458i
$714$	−1.21915e6			−0.0894976
$715$	1.51058e6			0.110504
$716$			235296.i			0.0171527i
$717$		−	2.50221e7i		−	1.81772i
$718$		−	1.77463e6i		−	0.128468i
$719$		−	9.98891e6i		−	0.720603i	−0.932836	−	0.360301i	$-0.882674\pi$
$719$		−	9.98891e6i		−	0.720603i	0.932836	−	0.360301i	$-0.117326\pi$
$720$		−	2.88747e7i		−	2.07580i
$721$		−	1.11489e6i		−	0.0798719i
$722$	−9.12468e6			−0.651441
$723$	2.17773e7			1.54938
$724$		−	4.08583e6i		−	0.289690i
$725$		−	8.54911e6i		−	0.604054i
$726$	−9.32006e6			−0.656262
$727$	−1.73293e7			−1.21603			−0.608017	−	0.793924i	$-0.708035\pi$
$727$	−1.73293e7			−1.21603			−0.608017	+	0.793924i	$0.708035\pi$
$728$	1.13530e6			0.0793933
$729$	2.20931e7			1.53970
$730$		−	1.17930e7i		−	0.819063i
$731$		−	3.20987e7i		−	2.22174i
$732$	4.35845e6			0.300645
$733$	2.85272e7			1.96110			0.980548	−	0.196281i	$-0.0628863\pi$
$733$	2.85272e7			1.96110			0.980548	+	0.196281i	$0.0628863\pi$
$734$			8.04294e6i			0.551029i
$735$		−	3.52510e7i		−	2.40687i
$736$		−	6.87616e6i		−	0.467898i
$737$		−	1.38951e6i		−	0.0942308i
$738$			1.22586e7i			0.828512i
$739$			2.47307e7i			1.66581i	0.553414	+	0.832906i	$0.313325\pi$
$739$			2.47307e7i			1.66581i	−0.553414	+	0.832906i	$0.686675\pi$
$740$	1.74888e6			0.117403
$741$	6.44605e7			4.31269
$742$			749312.i			0.0499635i
$743$	−9.73513e6			−0.646948			−0.323474	−	0.946237i	$-0.604851\pi$
$743$	−9.73513e6			−0.646948			−0.323474	+	0.946237i	$0.604851\pi$
$744$	5.39854e6			0.357556
$745$	−2.92879e7			−1.93329
$746$			3.20335e6i			0.210745i
$747$			1.10456e7i			0.724247i
$748$		−	1.29062e6i		−	0.0843422i
$749$	431718.			0.0281187
$750$		−	4.13479e6i		−	0.268411i
$751$	2.05585e7			1.33012			0.665061	−	0.746789i	$-0.268406\pi$
$751$	2.05585e7			1.33012			0.665061	+	0.746789i	$0.268406\pi$
$752$	−2.74907e6			−0.177272
$753$			1.69922e7i			1.09210i
$754$	6.63203e6			0.424833
$755$			2.80826e7i			1.79296i
$756$			3.35613e6i			0.213567i
$757$			1.58872e7i			1.00764i	0.863808	+	0.503822i	$0.168073\pi$
$757$			1.58872e7i			1.00764i	−0.863808	+	0.503822i	$0.831927\pi$
$758$	−1.15965e6			−0.0733086
$759$			971313.i			0.0612005i
$760$	−2.30803e7			−1.44946
$761$			6.63090e6i			0.415060i	0.978229	+	0.207530i	$0.0665425\pi$
$761$			6.63090e6i			0.415060i	−0.978229	+	0.207530i	$0.933458\pi$
$762$			1.35265e7i			0.843912i
$763$		−	152680.i		−	0.00949446i
$764$	−1.40364e7			−0.870006
$765$	−8.10322e7			−5.00616
$766$			8.04242e6i			0.495239i
$767$	7.69730e6			0.472443
$768$	−767088.			−0.0469291
$769$		−	1.10337e7i		−	0.672831i	−0.941714	−	0.336415i	$-0.890785\pi$
$769$		−	1.10337e7i		−	0.672831i	0.941714	−	0.336415i	$-0.109215\pi$
$770$	41098.5			0.00249804
$771$			3.16301e7i			1.91630i
$772$	−1.63343e7			−0.986411
$773$	−1.48462e7			−0.893645			−0.446823	−	0.894623i	$-0.647444\pi$
$773$	−1.48462e7			−0.893645			−0.446823	+	0.894623i	$0.647444\pi$
$774$	2.09863e7			1.25917
$775$	3.32035e6			0.198577
$776$	3.71804e6	+	1.04557e7i	0.221646	+	0.623302i
$777$	−284661.			−0.0169151
$778$	−3.88768e6			−0.230272
$779$	−2.69718e7			−1.59245
$780$	4.93809e7			2.90618
$781$		−	1.16170e6i		−	0.0681503i
$782$	−4.92233e6			−0.287842
$783$			4.19960e7i			2.44796i
$784$	1.09686e7			0.637327
$785$	2.26126e7			1.30971
$786$			7.33388e6i			0.423426i
$787$	−7.77655e6			−0.447559			−0.223780	−	0.974640i	$-0.571840\pi$
$787$	−7.77655e6			−0.447559			−0.223780	+	0.974640i	$0.571840\pi$
$788$	−1.47513e7			−0.846281
$789$		−	9.34400e6i		−	0.534368i
$790$		−	1.28888e6i		−	0.0734759i
$791$		−	1.75466e6i		−	0.0997132i
$792$	1.80752e6			0.102393
$793$			4.45451e6i			0.251546i
$794$	−8.25770e6			−0.464844
$795$			6.98144e7i			3.91766i
$796$			1.93475e7i			1.08229i
$797$		−	2.97502e7i		−	1.65899i	−0.558514	−	0.829495i	$-0.688628\pi$
$797$		−	2.97502e7i		−	1.65899i	0.558514	−	0.829495i	$-0.311372\pi$
$798$	1.75378e6			0.0974919
$799$			7.71482e6i			0.427522i
$800$	−1.10321e7			−0.609441
$801$	−4.99727e7			−2.75202
$802$			1.07789e7i			0.591750i
$803$	−2.03206e6			−0.111211
$804$		−	4.54230e7i		−	2.47820i
$805$			1.10325e6i			0.0600043i
$806$			2.57578e6i			0.139660i
$807$	−4.51335e6			−0.243958
$808$	8.36183e6			0.450581
$809$	2.58345e7			1.38781			0.693903	−	0.720068i	$-0.255890\pi$
$809$	2.58345e7			1.38781			0.693903	+	0.720068i	$0.255890\pi$
$810$		−	2.31407e7i		−	1.23927i
$811$	4.56383e6			0.243656			0.121828	−	0.992551i	$-0.461124\pi$
$811$	4.56383e6			0.243656			0.121828	+	0.992551i	$0.461124\pi$
$812$	−1.27000e6			−0.0675947
$813$			6.51327e7i			3.45599i
$814$			42815.0i			0.00226483i
$815$		−	2.46715e7i		−	1.30107i
$816$		−	3.53444e7i		−	1.85821i
$817$			4.61750e7i			2.42020i
$818$		−	2.04744e6i		−	0.106986i
$819$	−5.73386e6			−0.298702
$820$	−2.06621e7			−1.07310
$821$			3.60552e6i			0.186685i	0.995634	+	0.0933426i	$0.0297552\pi$
$821$			3.60552e6i			0.186685i	−0.995634	+	0.0933426i	$0.970245\pi$
$822$		−	1.39410e7i		−	0.719638i
$823$	1.94009e7			0.998441			0.499221	−	0.866475i	$-0.333620\pi$
$823$	1.94009e7			0.998441			0.499221	+	0.866475i	$0.333620\pi$
$824$	−1.17422e7			−0.602465
$825$	1.55837e6			0.0797141
$826$	209421.			0.0106800
$827$			7.54254e6i			0.383490i	0.981445	+	0.191745i	$0.0614147\pi$
$827$			7.54254e6i			0.383490i	−0.981445	+	0.191745i	$0.938585\pi$
$828$			2.26513e7i			1.14820i
$829$	−9.04398e6			−0.457060			−0.228530	−	0.973537i	$-0.573392\pi$
$829$	−9.04398e6			−0.457060			−0.228530	+	0.973537i	$0.573392\pi$
$830$	2.64515e6			0.133277
$831$		−	4.78542e7i		−	2.40390i
$832$			8.99014e6i			0.450255i
$833$		−	3.07817e7i		−	1.53702i
$834$		−	1.48670e7i		−	0.740130i
$835$		−	2.37205e7i		−	1.17736i
$836$			1.85660e6i			0.0918760i
$837$	−1.63106e7			−0.804743
$838$	−8.50068e6			−0.418161
$839$			2.46864e7i			1.21075i	0.795942	+	0.605373i	$0.206976\pi$
$839$			2.46864e7i			1.21075i	−0.795942	+	0.605373i	$0.793024\pi$
$840$	2.87790e6			0.140727
$841$	4.61936e6			0.225212
$842$	−7.69509e6			−0.374053
$843$			1.91939e7i			0.930238i
$844$		−	1.41866e7i		−	0.685525i
$845$			2.35165e7i			1.13300i
$846$	−5.04399e6			−0.242297
$847$			1.82408e6i			0.0873644i
$848$	−2.17233e7			−1.03738
$849$	−6.95402e6			−0.331106
$850$			7.89734e6i			0.374916i
$851$	−1.14932e6			−0.0544024
$852$		−	3.79761e7i		−	1.79230i
$853$			2.18992e7i			1.03052i	0.857034	+	0.515260i	$0.172305\pi$
$853$			2.18992e7i			1.03052i	−0.857034	+	0.515260i	$0.827695\pi$
$854$			121194.i			0.00568640i
$855$	1.16567e8			5.45333
$856$		−	4.54693e6i		−	0.212096i
$857$	−3.74254e6			−0.174066			−0.0870330	−	0.996205i	$-0.527739\pi$
$857$	−3.74254e6			−0.174066			−0.0870330	+	0.996205i	$0.527739\pi$
$858$			1.20892e6i			0.0560632i
$859$			2.40580e7i			1.11244i	0.831035	+	0.556220i	$0.187749\pi$
$859$			2.40580e7i			1.11244i	−0.831035	+	0.556220i	$0.812251\pi$
$860$			3.53730e7i			1.63089i
$861$	3.36314e6			0.154610
$862$	8.66794e6			0.397327
$863$		−	2.24494e7i		−	1.02607i	−0.858368	−	0.513035i	$-0.828521\pi$
$863$		−	2.24494e7i		−	1.02607i	0.858368	−	0.513035i	$-0.171479\pi$
$864$	5.41931e7			2.46979
$865$	−2.43104e7			−1.10472
$866$			1.21136e7i			0.548883i
$867$	−5.78463e7			−2.61353
$868$		−	493248.i		−	0.0222211i
$869$	−222087.			−0.00997641
$870$	1.68117e7			0.753030
$871$	4.64242e7			2.07347
$872$	−1.60805e6			−0.0716156
$873$	−1.87780e7	−	5.28066e7i	−0.833900	−	2.34505i
$874$	7.08091e6			0.313553
$875$	−809241.			−0.0357321
$876$	−6.64278e7			−2.92476
$877$	3.18309e7			1.39750			0.698748	−	0.715368i	$-0.253741\pi$
$877$	3.18309e7			1.39750			0.698748	+	0.715368i	$0.253741\pi$
$878$		−	192603.i		−	0.00843193i
$879$	−1.92455e7			−0.840151
$880$			1.19149e6i			0.0518661i
$881$	−1.98695e7			−0.862475			−0.431237	−	0.902239i	$-0.641923\pi$
$881$	−1.98695e7			−0.862475			−0.431237	+	0.902239i	$0.641923\pi$
$882$	2.01253e7			0.871105
$883$		−	2.95149e7i		−	1.27391i	−0.770899	−	0.636957i	$-0.780193\pi$
$883$		−	2.95149e7i		−	1.27391i	0.770899	−	0.636957i	$-0.219807\pi$
$884$	4.31202e7			1.85588
$885$	1.95120e7			0.837421
$886$		−	1.58694e7i		−	0.679166i
$887$		−	2.04148e7i		−	0.871237i	−0.900131	−	0.435619i	$-0.856530\pi$
$887$		−	2.04148e7i		−	0.871237i	0.900131	−	0.435619i	$-0.143470\pi$
$888$			2.99810e6i			0.127589i
$889$	2.64733e6			0.112345
$890$			1.19672e7i			0.506430i
$891$	−3.98738e6			−0.168265
$892$		−	1.00462e7i		−	0.422755i
$893$		−	1.10980e7i		−	0.465711i
$894$		−	2.34390e7i		−	0.980834i
$895$	−609603.			−0.0254384
$896$			2.11629e6i			0.0880653i
$897$	−3.24520e7			−1.34667
$898$	−2.02307e6			−0.0837181
$899$		−	6.17214e6i		−	0.254704i
$900$	3.63416e7			1.49554
$901$			6.09631e7i			2.50181i
$902$		−	505839.i		−	0.0207012i
$903$		−	5.75759e6i		−	0.234975i
$904$	−1.84804e7			−0.752125
$905$	1.05855e7			0.429626
$906$	−2.24745e7			−0.909639
$907$		−	2.32820e7i		−	0.939726i	−0.882739	−	0.469863i	$-0.844303\pi$
$907$		−	2.32820e7i		−	0.939726i	0.882739	−	0.469863i	$-0.155697\pi$
$908$	2.40917e7			0.969733
$909$	−4.22315e7			−1.69522
$910$			1.37312e6i			0.0549674i
$911$		−	3.71188e7i		−	1.48183i	−0.671599	−	0.740915i	$-0.734392\pi$
$911$		−	3.71188e7i		−	1.48183i	0.671599	−	0.740915i	$-0.265608\pi$
$912$			5.08439e7i			2.02419i
$913$		−	455786.i		−	0.0180961i
$914$		−	4.40521e6i		−	0.174422i
$915$			1.12918e7i			0.445873i
$916$	9.76348e6			0.384473
$917$	1.43535e6			0.0563683
$918$		−	3.87943e7i		−	1.51936i
$919$			1.55502e7i			0.607362i	0.952774	+	0.303681i	$0.0982157\pi$
$919$			1.55502e7i			0.607362i	−0.952774	+	0.303681i	$0.901784\pi$
$920$	1.16196e7			0.452606
$921$	−8.41604e7			−3.26933
$922$	−865061.			−0.0335135
$923$	3.88131e7			1.49959
$924$		−	231501.i		−	0.00892015i
$925$			1.84396e6i			0.0708595i
$926$	4.79967e6			0.183943
$927$	5.93041e7			2.26666
$928$			2.05073e7i			0.781698i
$929$			4.40630e6i			0.167508i	0.996486	+	0.0837538i	$0.0266909\pi$
$929$			4.40630e6i			0.167508i	−0.996486	+	0.0837538i	$0.973309\pi$
$930$			6.52940e6i			0.247552i
$931$			4.42805e7i			1.67432i
$932$			3.69262e7i			1.39250i
$933$		−	7.43499e7i		−	2.79625i
$934$	7.86949e6			0.295175
$935$	3.34373e6			0.125084
$936$			6.03900e7i			2.25307i
$937$	−2.32408e7			−0.864773			−0.432387	−	0.901688i	$-0.642328\pi$
$937$	−2.32408e7			−0.864773			−0.432387	+	0.901688i	$0.642328\pi$
$938$	1.26307e6			0.0468726
$939$	−7.29844e7			−2.70126
$940$		−	8.50178e6i		−	0.313827i
$941$			1.76935e7i			0.651387i	0.945475	+	0.325694i	$0.105598\pi$
$941$			1.76935e7i			0.651387i	−0.945475	+	0.325694i	$0.894402\pi$
$942$			1.80968e7i			0.664469i
$943$	1.35787e7			0.497255
$944$			6.07133e6i			0.221745i
$945$	−8.69501e6			−0.316731
$946$	−865982.			−0.0314616
$947$			3.43945e6i			0.124627i	0.998057	+	0.0623137i	$0.0198479\pi$
$947$			3.43945e6i			0.124627i	−0.998057	+	0.0623137i	$0.980152\pi$
$948$	−7.26003e6			−0.262372
$949$		−	6.78919e7i		−	2.44710i
$950$		−	1.13606e7i		−	0.408405i
$951$			1.44954e7i			0.519732i
$952$	2.51303e6			0.0898682
$953$			2.35757e7i			0.840876i	0.907321	+	0.420438i	$0.138124\pi$
$953$			2.35757e7i			0.840876i	−0.907321	+	0.420438i	$0.861876\pi$
$954$	−3.98580e7			−1.41790
$955$		−	3.63653e7i		−	1.29027i
$956$			2.40786e7i			0.852091i
$957$		−	2.89682e6i		−	0.102245i
$958$	−1.26860e7			−0.446592
$959$	−2.72846e6			−0.0958013
$960$			2.27893e7i			0.798091i
$961$	−2.62320e7			−0.916268
$962$	−1.43047e6			−0.0498357
$963$			2.29643e7i			0.797972i
$964$	−2.09561e7			−0.726304
$965$		−	4.23188e7i		−	1.46290i
$966$	−882925.			−0.0304425
$967$	1.55092e7			0.533363			0.266681	−	0.963785i	$-0.414073\pi$
$967$	1.55092e7			0.533363			0.266681	+	0.963785i	$0.414073\pi$
$968$	1.92115e7			0.658979
$969$	1.42685e8			4.88169
$970$	−1.26459e7	+	4.49688e6i	−0.431539	+	0.153455i
$971$	−3.77320e6			−0.128428			−0.0642142	−	0.997936i	$-0.520454\pi$
$971$	−3.77320e6			−0.128428			−0.0642142	+	0.997936i	$0.520454\pi$
$972$	−5.86205e7			−1.99014
$973$	−2.90970e6			−0.0985293
$974$	1.03818e7			0.350650
$975$			5.20658e7i			1.75405i
$976$	−3.51355e6			−0.118065
$977$		−	1.69465e6i		−	0.0567993i	−0.999597	−	0.0283996i	$-0.990959\pi$
$977$		−	1.69465e6i		−	0.0567993i	0.999597	−	0.0283996i	$-0.00904110\pi$
$978$	1.97446e7			0.660086
$979$	2.06208e6			0.0687621
$980$			3.39217e7i			1.12827i
$981$	8.12146e6			0.269440
$982$	3.03319e6			0.100374
$983$		−	3.64667e7i		−	1.20368i	−0.798615	−	0.601842i	$-0.794434\pi$
$983$		−	3.64667e7i		−	1.20368i	0.798615	−	0.601842i	$-0.205566\pi$
$984$		−	3.54211e7i		−	1.16620i
$985$		−	3.82175e7i		−	1.25508i
$986$	1.46802e7			0.480884
$987$			1.38382e6i			0.0452154i
$988$	−6.20297e7			−2.02166
$989$		−	2.32463e7i		−	0.755725i
$990$			2.18615e6i			0.0708910i
$991$			8.64246e6i			0.279546i	0.990184	+	0.139773i	$0.0446373\pi$
$991$			8.64246e6i			0.279546i	−0.990184	+	0.139773i	$0.955363\pi$
$992$	−7.96474e6			−0.256976
$993$			4.84961e7i			1.56075i
$994$	1.05599e6			0.0338996
$995$	−5.01253e7			−1.60509
$996$		−	1.48996e7i		−	0.475912i
$997$	−4.45178e6			−0.141839			−0.0709195	−	0.997482i	$-0.522593\pi$
$997$	−4.45178e6			−0.141839			−0.0709195	+	0.997482i	$0.522593\pi$
$998$			7.71154e6i			0.245084i
$999$		−	9.05816e6i		−	0.287161i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.6.b.a.96.23	✓	40
97.96	even	2	inner	97.6.b.a.96.24	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.6.b.a.96.23	✓	40	1.1	even	1	trivial
97.6.b.a.96.24	yes	40	97.96	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	97.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.99522 q^{2} +29.1171 q^{3} -28.0191 q^{4} -72.5916i q^{5} +58.0949 q^{6} -11.3700i q^{7} -119.751 q^{8} +604.804 q^{9} -144.836i q^{10} -24.9567 q^{11} -815.835 q^{12} -833.816i q^{13} -22.6857i q^{14} -2113.66i q^{15} +657.682 q^{16} -1845.68i q^{17} +1206.72 q^{18} +2655.07i q^{19} +2033.95i q^{20} -331.063i q^{21} -49.7941 q^{22} -1336.67i q^{23} -3486.80 q^{24} -2144.54 q^{25} -1663.64i q^{26} +10534.7 q^{27} +318.579i q^{28} +3986.45i q^{29} -4217.20i q^{30} -1548.28 q^{31} +5144.25 q^{32} -726.667 q^{33} -3682.53i q^{34} -825.370 q^{35} -16946.1 q^{36} -859.841i q^{37} +5297.43i q^{38} -24278.3i q^{39} +8692.93i q^{40} +10158.6i q^{41} -660.542i q^{42} +17391.3 q^{43} +699.266 q^{44} -43903.7i q^{45} -2666.94i q^{46} -4179.93 q^{47} +19149.8 q^{48} +16677.7 q^{49} -4278.82 q^{50} -53740.8i q^{51} +23362.8i q^{52} -33030.2 q^{53} +21019.0 q^{54} +1811.65i q^{55} +1361.58i q^{56} +77307.8i q^{57} +7953.83i q^{58} +9231.41i q^{59} +59222.7i q^{60} -5342.32 q^{61} -3089.15 q^{62} -6876.65i q^{63} -10781.9 q^{64} -60528.0 q^{65} -1449.86 q^{66} +55676.7i q^{67} +51714.3i q^{68} -38919.9i q^{69} -1646.79 q^{70} +46548.7i q^{71} -72426.0 q^{72} +81423.1 q^{73} -1715.57i q^{74} -62442.8 q^{75} -74392.6i q^{76} +283.759i q^{77} -48440.4i q^{78} +8898.89 q^{79} -47742.2i q^{80} +159772. q^{81} +20268.6i q^{82} +18263.0i q^{83} +9276.08i q^{84} -133981. q^{85} +34699.3 q^{86} +116074. i q^{87} +2988.60 q^{88} -82626.2 q^{89} -87597.4i q^{90} -9480.53 q^{91} +37452.3i q^{92} -45081.4 q^{93} -8339.87 q^{94} +192736. q^{95} +149786. q^{96} +(-31048.1 - 87311.8i) q^{97} +33275.7 q^{98} -15093.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} + 40 q^{3} + 638 q^{4} - 130 q^{6} + 180 q^{8} + 3300 q^{9} + 382 q^{11} + 2586 q^{12} + 10174 q^{16} + 4738 q^{18} + 1996 q^{22} - 3102 q^{24} - 25178 q^{25} + 3046 q^{27} + 14796 q^{31}+ \cdots - 562238 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 + 40 * q^3 + 638 * q^4 - 130 * q^6 + 180 * q^8 + 3300 * q^9 + 382 * q^11 + 2586 * q^12 + 10174 * q^16 + 4738 * q^18 + 1996 * q^22 - 3102 * q^24 - 25178 * q^25 + 3046 * q^27 + 14796 * q^31 + 8128 * q^32 - 9434 * q^33 - 2964 * q^35 + 18124 * q^36 - 45814 * q^43 - 60186 * q^44 - 17866 * q^47 + 69528 * q^48 - 64166 * q^49 + 78812 * q^50 + 117092 * q^53 - 53962 * q^54 - 33546 * q^61 - 148838 * q^62 + 215708 * q^64 + 89628 * q^65 - 17136 * q^66 + 218204 * q^70 - 127452 * q^72 + 25562 * q^73 - 52722 * q^75 - 193912 * q^79 + 175440 * q^81 - 243192 * q^85 + 108918 * q^86 + 155578 * q^88 - 434816 * q^89 - 483858 * q^91 - 66746 * q^93 - 245480 * q^94 + 97106 * q^95 - 306196 * q^96 - 251282 * q^97 - 310510 * q^98 - 562238 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more