LMFDB - Embedded newform 97.6.b.a.96.19

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			96.19
Character	$\chi$	$=$	97.96
Dual form			97.6.b.a.96.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.466290 q^{2} -9.91982 q^{3} -31.7826 q^{4} -23.6226i q^{5} +4.62551 q^{6} -97.7284i q^{7} +29.7412 q^{8} -144.597 q^{9} +11.0150i q^{10} -176.630 q^{11} +315.277 q^{12} -592.622i q^{13} +45.5698i q^{14} +234.332i q^{15} +1003.17 q^{16} +1502.56i q^{17} +67.4242 q^{18} +1527.67i q^{19} +750.787i q^{20} +969.448i q^{21} +82.3609 q^{22} +1627.21i q^{23} -295.027 q^{24} +2566.97 q^{25} +276.334i q^{26} +3844.89 q^{27} +3106.06i q^{28} -561.146i q^{29} -109.267i q^{30} -2609.48 q^{31} -1419.49 q^{32} +1752.14 q^{33} -700.631i q^{34} -2308.60 q^{35} +4595.67 q^{36} +8546.03i q^{37} -712.336i q^{38} +5878.70i q^{39} -702.564i q^{40} -3786.09i q^{41} -452.044i q^{42} +871.908 q^{43} +5613.76 q^{44} +3415.76i q^{45} -758.752i q^{46} +8578.90 q^{47} -9951.31 q^{48} +7256.16 q^{49} -1196.95 q^{50} -14905.2i q^{51} +18835.1i q^{52} -14718.8 q^{53} -1792.84 q^{54} +4172.47i q^{55} -2906.56i q^{56} -15154.2i q^{57} +261.657i q^{58} +777.803i q^{59} -7447.67i q^{60} +17475.4 q^{61} +1216.77 q^{62} +14131.2i q^{63} -31439.7 q^{64} -13999.3 q^{65} -817.006 q^{66} -17153.0i q^{67} -47755.4i q^{68} -16141.6i q^{69} +1076.48 q^{70} -22581.9i q^{71} -4300.49 q^{72} -31207.8 q^{73} -3984.93i q^{74} -25463.9 q^{75} -48553.2i q^{76} +17261.8i q^{77} -2741.18i q^{78} +30670.3 q^{79} -23697.6i q^{80} -3003.56 q^{81} +1765.42i q^{82} +43519.9i q^{83} -30811.6i q^{84} +35494.5 q^{85} -406.562 q^{86} +5566.47i q^{87} -5253.19 q^{88} -18258.5 q^{89} -1592.74i q^{90} -57916.0 q^{91} -51716.9i q^{92} +25885.6 q^{93} -4000.25 q^{94} +36087.5 q^{95} +14081.1 q^{96} +(-45431.0 + 80767.4i) q^{97} -3383.47 q^{98} +25540.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.466290			−0.0824292			−0.0412146	−	0.999150i	$-0.513123\pi$
$2$	−0.466290			−0.0824292			−0.0412146	+	0.999150i	$0.513123\pi$
$3$	−9.91982			−0.636357			−0.318178	−	0.948031i	$-0.603071\pi$
$3$	−9.91982			−0.636357			−0.318178	+	0.948031i	$0.603071\pi$
$4$	−31.7826			−0.993205
$5$		−	23.6226i		−	0.422574i	−0.977424	−	0.211287i	$-0.932235\pi$
$5$		−	23.6226i		−	0.422574i	0.977424	−	0.211287i	$-0.0677655\pi$
$6$	4.62551			0.0524544
$7$		−	97.7284i		−	0.753834i	−0.926247	−	0.376917i	$-0.876984\pi$
$7$		−	97.7284i		−	0.753834i	0.926247	−	0.376917i	$-0.123016\pi$
$8$	29.7412			0.164298
$9$	−144.597			−0.595050
$10$			11.0150i			0.0348324i
$11$	−176.630			−0.440132			−0.220066	−	0.975485i	$-0.570627\pi$
$11$	−176.630			−0.440132			−0.220066	+	0.975485i	$0.570627\pi$
$12$	315.277			0.632033
$13$		−	592.622i		−	0.972567i	−0.873801	−	0.486283i	$-0.838352\pi$
$13$		−	592.622i		−	0.972567i	0.873801	−	0.486283i	$-0.161648\pi$
$14$			45.5698i			0.0621379i
$15$			234.332i			0.268908i
$16$	1003.17			0.979662
$17$			1502.56i			1.26099i	0.776194	+	0.630494i	$0.217148\pi$
$17$			1502.56i			1.26099i	−0.776194	+	0.630494i	$0.782852\pi$
$18$	67.4242			0.0490495
$19$			1527.67i			0.970833i	0.874283	+	0.485416i	$0.161332\pi$
$19$			1527.67i			0.970833i	−0.874283	+	0.485416i	$0.838668\pi$
$20$			750.787i			0.419703i
$21$			969.448i			0.479707i
$22$	82.3609			0.0362798
$23$			1627.21i			0.641393i	0.947182	+	0.320696i	$0.103917\pi$
$23$			1627.21i			0.641393i	−0.947182	+	0.320696i	$0.896083\pi$
$24$	−295.027			−0.104552
$25$	2566.97			0.821431
$26$			276.334i			0.0801679i
$27$	3844.89			1.01502
$28$			3106.06i			0.748712i
$29$		−	561.146i		−	0.123903i	−0.998079	−	0.0619513i	$-0.980268\pi$
$29$		−	561.146i		−	0.123903i	0.998079	−	0.0619513i	$-0.0197324\pi$
$30$		−	109.267i		−	0.0221659i
$31$	−2609.48			−0.487697			−0.243848	−	0.969813i	$-0.578410\pi$
$31$	−2609.48			−0.487697			−0.243848	+	0.969813i	$0.578410\pi$
$32$	−1419.49			−0.245051
$33$	1752.14			0.280081
$34$		−	700.631i		−	0.103942i
$35$	−2308.60			−0.318551
$36$	4595.67			0.591007
$37$			8546.03i			1.02627i	0.858309	+	0.513133i	$0.171515\pi$
$37$			8546.03i			1.02627i	−0.858309	+	0.513133i	$0.828485\pi$
$38$		−	712.336i		−	0.0800250i
$39$			5878.70i			0.618900i
$40$		−	702.564i		−	0.0694282i
$41$		−	3786.09i		−	0.351748i	−0.984413	−	0.175874i	$-0.943725\pi$
$41$		−	3786.09i		−	0.351748i	0.984413	−	0.175874i	$-0.0562751\pi$
$42$		−	452.044i		−	0.0395419i
$43$	871.908			0.0719117			0.0359559	−	0.999353i	$-0.488552\pi$
$43$	871.908			0.0719117			0.0359559	+	0.999353i	$0.488552\pi$
$44$	5613.76			0.437142
$45$			3415.76i			0.251453i
$46$		−	758.752i		−	0.0528695i
$47$	8578.90			0.566483			0.283241	−	0.959049i	$-0.408590\pi$
$47$	8578.90			0.566483			0.283241	+	0.959049i	$0.408590\pi$
$48$	−9951.31			−0.623415
$49$	7256.16			0.431734
$50$	−1196.95			−0.0677099
$51$		−	14905.2i		−	0.802438i
$52$			18835.1i			0.965959i
$53$	−14718.8			−0.719753			−0.359876	−	0.933000i	$-0.617181\pi$
$53$	−14718.8			−0.719753			−0.359876	+	0.933000i	$0.617181\pi$
$54$	−1792.84			−0.0836674
$55$			4172.47i			0.185988i
$56$		−	2906.56i		−	0.123854i
$57$		−	15154.2i		−	0.617796i
$58$			261.657i			0.0102132i
$59$			777.803i			0.0290897i	0.999894	+	0.0145449i	$0.00462994\pi$
$59$			777.803i			0.0290897i	−0.999894	+	0.0145449i	$0.995370\pi$
$60$		−	7447.67i		−	0.267081i
$61$	17475.4			0.601315			0.300658	−	0.953732i	$-0.402794\pi$
$61$	17475.4			0.601315			0.300658	+	0.953732i	$0.402794\pi$
$62$	1216.77			0.0402004
$63$			14131.2i			0.448569i
$64$	−31439.7			−0.959463
$65$	−13999.3			−0.410981
$66$	−817.006			−0.0230869
$67$		−	17153.0i		−	0.466824i	−0.972378	−	0.233412i	$-0.925011\pi$
$67$		−	17153.0i		−	0.466824i	0.972378	−	0.233412i	$-0.0749890\pi$
$68$		−	47755.4i		−	1.25242i
$69$		−	16141.6i		−	0.408155i
$70$	1076.48			0.0262579
$71$		−	22581.9i		−	0.531636i	−0.964023	−	0.265818i	$-0.914358\pi$
$71$		−	22581.9i		−	0.531636i	0.964023	−	0.265818i	$-0.0856421\pi$
$72$	−4300.49			−0.0977657
$73$	−31207.8			−0.685419			−0.342710	−	0.939441i	$-0.611345\pi$
$73$	−31207.8			−0.685419			−0.342710	+	0.939441i	$0.611345\pi$
$74$		−	3984.93i		−	0.0845944i
$75$	−25463.9			−0.522723
$76$		−	48553.2i		−	0.964237i
$77$			17261.8i			0.331787i
$78$		−	2741.18i		−	0.0510154i
$79$	30670.3			0.552905			0.276452	−	0.961028i	$-0.410841\pi$
$79$	30670.3			0.552905			0.276452	+	0.961028i	$0.410841\pi$
$80$		−	23697.6i		−	0.413980i
$81$	−3003.56			−0.0508655
$82$			1765.42i			0.0289943i
$83$			43519.9i			0.693414i	0.937973	+	0.346707i	$0.112700\pi$
$83$			43519.9i			0.693414i	−0.937973	+	0.346707i	$0.887300\pi$
$84$		−	30811.6i		−	0.476448i
$85$	35494.5			0.532860
$86$	−406.562			−0.00592763
$87$			5566.47i			0.0788463i
$88$	−5253.19			−0.0723130
$89$	−18258.5			−0.244337			−0.122169	−	0.992509i	$-0.538985\pi$
$89$	−18258.5			−0.244337			−0.122169	+	0.992509i	$0.538985\pi$
$90$		−	1592.74i		−	0.0207270i
$91$	−57916.0			−0.733154
$92$		−	51716.9i		−	0.637035i
$93$	25885.6			0.310349
$94$	−4000.25			−0.0466947
$95$	36087.5			0.410249
$96$	14081.1			0.155940
$97$	−45431.0	+	80767.4i	−0.490256	+	0.871579i
$97$	−45431.0	+	80767.4i	−0.490256	+	0.871579i
$98$	−3383.47			−0.0355875
$99$	25540.2			0.261901
$100$	−81585.0			−0.815850
$101$	−69711.1			−0.679984			−0.339992	−	0.940428i	$-0.610424\pi$
$101$	−69711.1			−0.679984			−0.339992	+	0.940428i	$0.610424\pi$
$102$			6950.13i			0.0661443i
$103$	100533.			0.933720			0.466860	−	0.884331i	$-0.345385\pi$
$103$	100533.			0.933720			0.466860	+	0.884331i	$0.345385\pi$
$104$		−	17625.3i		−	0.159791i
$105$	22900.9			0.202712
$106$	6863.24			0.0593286
$107$			214489.i			1.81111i	0.424227	+	0.905556i	$0.360546\pi$
$107$			214489.i			1.81111i	−0.424227	+	0.905556i	$0.639454\pi$
$108$	−122201.			−1.00812
$109$	67647.1			0.545359			0.272680	−	0.962105i	$-0.412090\pi$
$109$	67647.1			0.545359			0.272680	+	0.962105i	$0.412090\pi$
$110$		−	1945.58i		−	0.0153309i
$111$		−	84775.1i		−	0.653072i
$112$		−	98038.6i		−	0.738503i
$113$	186295.			1.37248			0.686238	−	0.727377i	$-0.259261\pi$
$113$	186295.			1.37248			0.686238	+	0.727377i	$0.259261\pi$
$114$			7066.24i			0.0509245i
$115$	38438.9			0.271036
$116$			17834.7i			0.123061i
$117$			85691.5i			0.578726i
$118$		−	362.682i		−	0.00239784i
$119$	146843.			0.950575
$120$			6969.31i			0.0441811i
$121$	−129853.			−0.806283
$122$	−8148.60			−0.0495660
$123$			37557.3i			0.223837i
$124$	82936.0			0.484383
$125$		−	134459.i		−	0.769689i
$126$		−	6589.26i		−	0.0369752i
$127$			240026.i			1.32053i	0.751031	+	0.660267i	$0.229557\pi$
$127$			240026.i			1.32053i	−0.751031	+	0.660267i	$0.770443\pi$
$128$	60083.6			0.324139
$129$	−8649.18			−0.0457615
$130$	6527.72			0.0338769
$131$			336513.i			1.71326i	0.515928	+	0.856632i	$0.327447\pi$
$131$			336513.i			1.71326i	−0.515928	+	0.856632i	$0.672553\pi$
$132$	−55687.5			−0.278178
$133$	149296.			0.731847
$134$			7998.27i			0.0384799i
$135$		−	90826.4i		−	0.428921i
$136$			44688.0i			0.207178i
$137$			215748.i			0.982077i	0.871138	+	0.491039i	$0.163383\pi$
$137$			215748.i			0.982077i	−0.871138	+	0.491039i	$0.836617\pi$
$138$			7526.68i			0.0336439i
$139$			64165.0i			0.281683i	0.990032	+	0.140842i	$0.0449809\pi$
$139$			64165.0i			0.281683i	−0.990032	+	0.140842i	$0.955019\pi$
$140$	73373.2			0.316386
$141$	−85101.1			−0.360485
$142$			10529.7i			0.0438224i
$143$			104675.i			0.428058i
$144$	−145056.			−0.582948
$145$	−13255.7			−0.0523580
$146$	14551.9			0.0564986
$147$	−71979.8			−0.274737
$148$		−	271615.i		−	1.01929i
$149$			219209.i			0.808896i	0.914561	+	0.404448i	$0.132536\pi$
$149$			219209.i			0.808896i	−0.914561	+	0.404448i	$0.867464\pi$
$150$	11873.6			0.0430877
$151$	123390.			0.440390			0.220195	−	0.975456i	$-0.429331\pi$
$151$	123390.			0.440390			0.220195	+	0.975456i	$0.429331\pi$
$152$			45434.6i			0.159506i
$153$		−	217267.i		−	0.750351i
$154$		−	8049.00i		−	0.0273489i
$155$			61642.7i			0.206088i
$156$		−	186840.i		−	0.614694i
$157$		−	361369.i		−	1.17004i	−0.811018	−	0.585021i	$-0.801086\pi$
$157$		−	361369.i		−	1.17004i	0.811018	−	0.585021i	$-0.198914\pi$
$158$	−14301.3			−0.0455755
$159$	146008.			0.458019
$160$			33532.0i			0.103552i
$161$	159025.			0.483504
$162$	1400.53			0.00419280
$163$	−391363.			−1.15375			−0.576873	−	0.816834i	$-0.695727\pi$
$163$	−391363.			−1.15375			−0.576873	+	0.816834i	$0.695727\pi$
$164$			120332.i			0.349358i
$165$		−	41390.1i		−	0.118355i
$166$		−	20292.9i		−	0.0571576i
$167$	9302.86			0.0258122			0.0129061	−	0.999917i	$-0.495892\pi$
$167$	9302.86			0.0258122			0.0129061	+	0.999917i	$0.495892\pi$
$168$			28832.5i			0.0788151i
$169$	20092.1			0.0541138
$170$	−16550.7			−0.0439233
$171$		−	220896.i		−	0.577694i
$172$	−27711.5			−0.0714231
$173$		−	132199.i		−	0.335824i	−0.985802	−	0.167912i	$-0.946297\pi$
$173$		−	132199.i		−	0.335824i	0.985802	−	0.167912i	$-0.0537025\pi$
$174$		−	2595.59i		−	0.00649924i
$175$		−	250866.i		−	0.619223i
$176$	−177191.			−0.431181
$177$		−	7715.67i		−	0.0185115i
$178$	8513.75			0.0201405
$179$			660241.i			1.54017i	0.637939	+	0.770087i	$0.279787\pi$
$179$			660241.i			1.54017i	−0.637939	+	0.770087i	$0.720213\pi$
$180$		−	108562.i		−	0.249744i
$181$		−	854614.i		−	1.93898i	−0.245128	−	0.969491i	$-0.578830\pi$
$181$		−	854614.i		−	1.93898i	0.245128	−	0.969491i	$-0.421170\pi$
$182$	27005.7			0.0604333
$183$	−173353.			−0.382651
$184$			48395.1i			0.105380i
$185$	201880.			0.433674
$186$	−12070.2			−0.0255818
$187$		−	265398.i		−	0.555001i
$188$	−272659.			−0.562634
$189$		−	375755.i		−	0.765157i
$190$	−16827.2			−0.0338165
$191$	−217228.			−0.430857			−0.215428	−	0.976520i	$-0.569115\pi$
$191$	−217228.			−0.430857			−0.215428	+	0.976520i	$0.569115\pi$
$192$	311876.			0.610561
$193$	−399450.			−0.771915			−0.385957	−	0.922517i	$-0.626129\pi$
$193$	−399450.			−0.771915			−0.385957	+	0.922517i	$0.626129\pi$
$194$	21184.0	−	37661.0i	0.0404114	−	0.0718435i
$195$	138870.			0.261531
$196$	−230619.			−0.428801
$197$	−447168.			−0.820929			−0.410464	−	0.911877i	$-0.634633\pi$
$197$	−447168.			−0.820929			−0.410464	+	0.911877i	$0.634633\pi$
$198$	−11909.2			−0.0215883
$199$			540987.i			0.968398i	0.874958	+	0.484199i	$0.160889\pi$
$199$			540987.i			0.968398i	−0.874958	+	0.484199i	$0.839111\pi$
$200$	76344.8			0.134960
$201$			170155.i			0.297066i
$202$	32505.6			0.0560506
$203$	−54839.9			−0.0934021
$204$			473725.i			0.796986i
$205$	−89437.3			−0.148639
$206$	−46877.7			−0.0769658
$207$		−	235290.i		−	0.381661i
$208$		−	594503.i		−	0.952787i
$209$		−	269832.i		−	0.427295i
$210$	−10678.5			−0.0167094
$211$			402116.i			0.621792i	0.950444	+	0.310896i	$0.100629\pi$
$211$			402116.i			0.621792i	−0.950444	+	0.310896i	$0.899371\pi$
$212$	467802.			0.714862
$213$			224008.i			0.338310i
$214$		−	100014.i		−	0.149289i
$215$		−	20596.7i		−	0.0303880i
$216$	114352.			0.166766
$217$			255020.i			0.367642i
$218$	−31543.1			−0.0449535
$219$	309576.			0.436171
$220$		−	132612.i		−	0.184725i
$221$	890453.			1.22639
$222$			39529.8i			0.0538322i
$223$		−	1.10299e6i		−	1.48528i	−0.669689	−	0.742642i	$-0.733572\pi$
$223$		−	1.10299e6i		−	1.48528i	0.669689	−	0.742642i	$-0.266428\pi$
$224$			138724.i			0.184728i
$225$	−371177.			−0.488793
$226$	−86867.4			−0.113132
$227$	1.17876e6			1.51831			0.759154	−	0.650911i	$-0.225613\pi$
$227$	1.17876e6			1.51831			0.759154	+	0.650911i	$0.225613\pi$
$228$			481639.i			0.613599i
$229$	−1.19860e6			−1.51038			−0.755192	−	0.655504i	$-0.772456\pi$
$229$	−1.19860e6			−1.51038			−0.755192	+	0.655504i	$0.772456\pi$
$230$	−17923.7			−0.0223413
$231$		−	171234.i		−	0.211135i
$232$		−	16689.1i		−	0.0203570i
$233$		−	472989.i		−	0.570771i	−0.958413	−	0.285385i	$-0.907878\pi$
$233$		−	472989.i		−	0.570771i	0.958413	−	0.285385i	$-0.0921216\pi$
$234$		−	39957.1i		−	0.0477039i
$235$		−	202656.i		−	0.239381i
$236$		−	24720.6i		−	0.0288921i
$237$	−304244.			−0.351845
$238$	−68471.5			−0.0783552
$239$			22901.4i			0.0259339i	0.999916	+	0.0129669i	$0.00412762\pi$
$239$			22901.4i			0.0259339i	−0.999916	+	0.0129669i	$0.995872\pi$
$240$			235076.i			0.263439i
$241$	−1.03631e6			−1.14934			−0.574668	−	0.818386i	$-0.694869\pi$
$241$	−1.03631e6			−1.14934			−0.574668	+	0.818386i	$0.694869\pi$
$242$	60549.1			0.0664613
$243$	−904515.			−0.982652
$244$	−555413.			−0.597230
$245$		−	171409.i		−	0.182440i
$246$		−	17512.6i		−	0.0184507i
$247$	905329.			0.944200
$248$	−77609.0			−0.0801278
$249$		−	431710.i		−	0.441259i
$250$			62697.0i			0.0634449i
$251$			709938.i			0.711272i	0.934625	+	0.355636i	$0.115736\pi$
$251$			709938.i			0.711272i	−0.934625	+	0.355636i	$0.884264\pi$
$252$		−	449127.i		−	0.445521i
$253$		−	287414.i		−	0.282298i
$254$		−	111922.i		−	0.108851i
$255$	−352099.			−0.339089
$256$	978054.			0.932745
$257$			1.49260e6i			1.40965i	0.709382	+	0.704824i	$0.248974\pi$
$257$			1.49260e6i			1.40965i	−0.709382	+	0.704824i	$0.751026\pi$
$258$	4033.02			0.00377209
$259$	835190.			0.773635
$260$	444933.			0.408189
$261$			81140.1i			0.0737283i
$262$		−	156913.i		−	0.141223i
$263$			751114.i			0.669602i	0.942289	+	0.334801i	$0.108669\pi$
$263$			751114.i			0.669602i	−0.942289	+	0.334801i	$0.891331\pi$
$264$	52110.7			0.0460169
$265$			347697.i			0.304149i
$266$	−69615.4			−0.0603256
$267$	181121.			0.155486
$268$			545166.i			0.463652i
$269$	1.72309e6			1.45186			0.725932	−	0.687766i	$-0.241408\pi$
$269$	1.72309e6			1.45186			0.725932	+	0.687766i	$0.241408\pi$
$270$			42351.4i			0.0353557i
$271$			649646.i			0.537346i	0.963231	+	0.268673i	$0.0865850\pi$
$271$			649646.i			0.537346i	−0.963231	+	0.268673i	$0.913415\pi$
$272$			1.50733e6i			1.23534i
$273$	574516.			0.466548
$274$		−	100601.i		−	0.0809518i
$275$	−453405.			−0.361539
$276$			513023.i			0.405381i
$277$			1.56706e6i			1.22712i	0.789648	+	0.613560i	$0.210263\pi$
$277$			1.56706e6i			1.22712i	−0.789648	+	0.613560i	$0.789737\pi$
$278$		−	29919.5i		−	0.0232189i
$279$	377323.			0.290204
$280$	−68660.5			−0.0523373
$281$		−	159357.i		−	0.120394i	−0.998187	−	0.0601972i	$-0.980827\pi$
$281$		−	159357.i		−	0.120394i	0.998187	−	0.0601972i	$-0.0191729\pi$
$282$	39681.8			0.0297145
$283$	565938.			0.420052			0.210026	−	0.977696i	$-0.432645\pi$
$283$	565938.			0.420052			0.210026	+	0.977696i	$0.432645\pi$
$284$			717711.i			0.528024i
$285$	−357981.			−0.261065
$286$		−	48808.9i		−	0.0352845i
$287$	−370009.			−0.265159
$288$	205254.			0.145818
$289$	−837842.			−0.590089
$290$	6181.01			0.00431583
$291$	450667.	−	801198.i	0.311977	−	0.554635i
$292$	991865.			0.680762
$293$	−449425.			−0.305836			−0.152918	−	0.988239i	$-0.548867\pi$
$293$	−449425.			−0.305836			−0.152918	+	0.988239i	$0.548867\pi$
$294$	33563.5			0.0226464
$295$	18373.7			0.0122926
$296$			254169.i			0.168614i
$297$	−679125.			−0.446744
$298$		−	102215.i		−	0.0666767i
$299$	964321.			0.623797
$300$	809309.			0.519172
$301$		−	85210.2i		−	0.0542095i
$302$	−57535.5			−0.0363010
$303$	691522.			0.432712
$304$			1.53252e6i			0.951089i
$305$		−	412814.i		−	0.254100i
$306$			101309.i			0.0618508i
$307$	469544.			0.284335			0.142167	−	0.989843i	$-0.454593\pi$
$307$	469544.			0.284335			0.142167	+	0.989843i	$0.454593\pi$
$308$		−	548624.i		−	0.329532i
$309$	−997272.			−0.594179
$310$		−	28743.4i		−	0.0169877i
$311$			1.14896e6i			0.673600i	0.941576	+	0.336800i	$0.109345\pi$
$311$			1.14896e6i			0.673600i	−0.941576	+	0.336800i	$0.890655\pi$
$312$			174840.i			0.101684i
$313$	−35647.0			−0.0205666			−0.0102833	−	0.999947i	$-0.503273\pi$
$313$	−35647.0			−0.0205666			−0.0102833	+	0.999947i	$0.503273\pi$
$314$			168503.i			0.0964456i
$315$	333817.			0.189554
$316$	−974781.			−0.549148
$317$		−	1.30025e6i		−	0.726741i	−0.931645	−	0.363371i	$-0.881626\pi$
$317$		−	1.30025e6i		−	0.726741i	0.931645	−	0.363371i	$-0.118374\pi$
$318$	−68082.1			−0.0377542
$319$			99115.3i			0.0545336i
$320$			742687.i			0.405444i
$321$		−	2.12769e6i		−	1.15251i
$322$	−74151.6			−0.0398548
$323$	−2.29542e6			−1.22421
$324$	95460.7			0.0505199
$325$		−	1.52124e6i		−	0.798897i
$326$	182488.			0.0951024
$327$	−671047.			−0.347043
$328$		−	112603.i		−	0.0577916i
$329$		−	838402.i		−	0.427034i
$330$			19299.8i			0.00975591i
$331$			36154.1i			0.0181379i	0.999959	+	0.00906895i	$0.00288678\pi$
$331$			36154.1i			0.0181379i	−0.999959	+	0.00906895i	$0.997113\pi$
$332$		−	1.38317e6i		−	0.688703i
$333$		−	1.23573e6i		−	0.610680i
$334$	−4337.83			−0.00212768
$335$	−405198.			−0.197268
$336$			972526.i			0.469951i
$337$		−	2.16935e6i		−	1.04053i	−0.854004	−	0.520266i	$-0.825833\pi$
$337$		−	2.16935e6i		−	1.04053i	0.854004	−	0.520266i	$-0.174167\pi$
$338$	−9368.73			−0.00446055
$339$	−1.84801e6			−0.873384
$340$	−1.12811e6			−0.529240
$341$	460913.			0.214651
$342$			103002.i			0.0476189i
$343$		−	2.35165e6i		−	1.07929i
$344$	25931.6			0.0118150
$345$	−381307.			−0.172475
$346$			61643.0i			0.0276817i
$347$		−	1.79119e6i		−	0.798579i	−0.916825	−	0.399290i	$-0.869257\pi$
$347$		−	1.79119e6i		−	0.798579i	0.916825	−	0.399290i	$-0.130743\pi$
$348$		−	176917.i		−	0.0783106i
$349$		−	1.82482e6i		−	0.801965i	−0.916086	−	0.400983i	$-0.868669\pi$
$349$		−	1.82482e6i		−	0.801965i	0.916086	−	0.400983i	$-0.131331\pi$
$350$			116976.i			0.0510421i
$351$		−	2.27857e6i		−	0.987176i
$352$	250724.			0.107855
$353$	−1.51153e6			−0.645623			−0.322811	−	0.946463i	$-0.604628\pi$
$353$	−1.51153e6			−0.645623			−0.322811	+	0.946463i	$0.604628\pi$
$354$			3597.74i			0.00152588i
$355$	−533443.			−0.224656
$356$	580302.			0.242677
$357$	−1.45666e6			−0.604905
$358$		−	307864.i		−	0.126955i
$359$			2.52579e6i			1.03434i	0.855884	+	0.517168i	$0.173014\pi$
$359$			2.52579e6i			1.03434i	−0.855884	+	0.517168i	$0.826986\pi$
$360$			101589.i			0.0413133i
$361$	142334.			0.0574833
$362$			398498.i			0.159829i
$363$	1.28812e6			0.513084
$364$	1.84072e6			0.728172
$365$			737210.i			0.289640i
$366$	80832.7			0.0315416
$367$			896568.i			0.347471i	0.984792	+	0.173735i	$0.0555837\pi$
$367$			896568.i			0.347471i	−0.984792	+	0.173735i	$0.944416\pi$
$368$			1.63238e6i			0.628348i
$369$			547458.i			0.209307i
$370$	−94134.4			−0.0357474
$371$			1.43845e6i			0.542574i
$372$	−822710.			−0.308240
$373$		−	2.34116e6i		−	0.871281i	−0.900121	−	0.435641i	$-0.856522\pi$
$373$		−	2.34116e6i		−	0.871281i	0.900121	−	0.435641i	$-0.143478\pi$
$374$			123753.i			0.0457483i
$375$			1.33381e6i			0.489797i
$376$	255147.			0.0930722
$377$	−332547.			−0.120504
$378$			175211.i			0.0630713i
$379$	−255582.			−0.0913971			−0.0456985	−	0.998955i	$-0.514551\pi$
$379$	−255582.			−0.0913971			−0.0456985	+	0.998955i	$0.514551\pi$
$380$	−1.14695e6			−0.407461
$381$		−	2.38102e6i		−	0.840331i
$382$	101291.			0.0355152
$383$			3.75556e6i			1.30821i	0.756403	+	0.654106i	$0.226955\pi$
$383$			3.75556e6i			1.30821i	−0.756403	+	0.654106i	$0.773045\pi$
$384$	−596019.			−0.206268
$385$	407768.			0.140204
$386$	186260.			0.0636283
$387$	−126075.			−0.0427911
$388$	1.44391e6	−	2.56699e6i	0.486925	−	0.865657i
$389$	3.50781e6			1.17534			0.587668	−	0.809102i	$-0.300046\pi$
$389$	3.50781e6			1.17534			0.587668	+	0.809102i	$0.300046\pi$
$390$	−64753.8			−0.0215578
$391$	−2.44499e6			−0.808788
$392$	215807.			0.0709332
$393$		−	3.33815e6i		−	1.09025i
$394$	208510.			0.0676685
$395$		−	724512.i		−	0.233643i
$396$	−811734.			−0.260121
$397$	−18344.3			−0.00584150			−0.00292075	−	0.999996i	$-0.500930\pi$
$397$	−18344.3			−0.00584150			−0.00292075	+	0.999996i	$0.500930\pi$
$398$		−	252257.i		−	0.0798243i
$399$	−1.48099e6			−0.465716
$400$	2.57512e6			0.804725
$401$			3.81188e6i			1.18380i	0.806012	+	0.591900i	$0.201622\pi$
$401$			3.81188e6i			1.18380i	−0.806012	+	0.591900i	$0.798378\pi$
$402$		−	79341.4i		−	0.0244870i
$403$			1.54644e6i			0.474318i
$404$	2.21560e6			0.675364
$405$			70951.8i			0.0214944i
$406$	25571.3			0.00769906
$407$		−	1.50949e6i		−	0.451693i
$408$		−	443297.i		−	0.131839i
$409$			4.09227e6i			1.20964i	0.796362	+	0.604820i	$0.206755\pi$
$409$			4.09227e6i			1.20964i	−0.796362	+	0.604820i	$0.793245\pi$
$410$	41703.7			0.0122522
$411$		−	2.14018e6i		−	0.624951i
$412$	−3.19521e6			−0.927376
$413$	76013.5			0.0219288
$414$			109713.i			0.0314600i
$415$	1.02805e6			0.293019
$416$			841220.i			0.238329i
$417$		−	636506.i		−	0.179251i
$418$			125820.i			0.0352216i
$419$	1.34947e6			0.375516			0.187758	−	0.982215i	$-0.439878\pi$
$419$	1.34947e6			0.375516			0.187758	+	0.982215i	$0.439878\pi$
$420$	−727849.			−0.201334
$421$	−3.27848e6			−0.901504			−0.450752	−	0.892649i	$-0.648844\pi$
$421$	−3.27848e6			−0.901504			−0.450752	+	0.892649i	$0.648844\pi$
$422$		−	187503.i		−	0.0512539i
$423$	−1.24048e6			−0.337086
$424$	−437755.			−0.118254
$425$			3.85704e6i			1.03581i
$426$		−	104453.i		−	0.0278867i
$427$		−	1.70784e6i		−	0.453292i
$428$		−	6.81701e6i		−	1.79881i
$429$		−	1.03836e6i		−	0.272398i
$430$			9604.06i			0.00250486i
$431$	6.58840e6			1.70839			0.854195	−	0.519953i	$-0.174050\pi$
$431$	6.58840e6			1.70839			0.854195	+	0.519953i	$0.174050\pi$
$432$	3.85710e6			0.994378
$433$		−	3.71957e6i		−	0.953396i	−0.879067	−	0.476698i	$-0.841834\pi$
$433$		−	3.71957e6i		−	0.953396i	0.879067	−	0.476698i	$-0.158166\pi$
$434$		−	118913.i		−	0.0303045i
$435$	131494.			0.0333184
$436$	−2.15000e6			−0.541654
$437$	−2.48583e6			−0.622685
$438$	−144352.			−0.0359533
$439$			3.18701e6i			0.789263i	0.918840	+	0.394631i	$0.129128\pi$
$439$			3.18701e6i			0.789263i	−0.918840	+	0.394631i	$0.870872\pi$
$440$			124094.i			0.0305576i
$441$	−1.04922e6			−0.256903
$442$	−415209.			−0.101091
$443$			4.16494e6i			1.00832i	0.863609	+	0.504162i	$0.168198\pi$
$443$			4.16494e6i			1.00832i	−0.863609	+	0.504162i	$0.831802\pi$
$444$			2.69437e6i			0.648635i
$445$			431313.i			0.103251i
$446$			514313.i			0.122431i
$447$		−	2.17451e6i		−	0.514746i
$448$			3.07255e6i			0.723276i
$449$	−384436.			−0.0899928			−0.0449964	−	0.998987i	$-0.514328\pi$
$449$	−384436.			−0.0899928			−0.0449964	+	0.998987i	$0.514328\pi$
$450$	173076.			0.0402908
$451$			668738.i			0.154816i
$452$	−5.92093e6			−1.36315
$453$	−1.22401e6			−0.280245
$454$	−549643.			−0.125153
$455$			1.36813e6i			0.309812i
$456$		−	450703.i		−	0.101503i
$457$			2.29133e6i			0.513213i	0.966516	+	0.256606i	$0.0826044\pi$
$457$			2.29133e6i			0.513213i	−0.966516	+	0.256606i	$0.917396\pi$
$458$	558897.			0.124500
$459$			5.77720e6i			1.27993i
$460$	−1.22169e6			−0.269194
$461$	6.89986e6			1.51213			0.756063	−	0.654498i	$-0.227120\pi$
$461$	6.89986e6			1.51213			0.756063	+	0.654498i	$0.227120\pi$
$462$			79844.7i			0.0174037i
$463$	1.55515e6			0.337148			0.168574	−	0.985689i	$-0.446084\pi$
$463$	1.55515e6			0.337148			0.168574	+	0.985689i	$0.446084\pi$
$464$		−	562927.i		−	0.121383i
$465$		−	611485.i		−	0.131145i
$466$			220550.i			0.0470482i
$467$	4.17292e6			0.885417			0.442708	−	0.896666i	$-0.354018\pi$
$467$	4.17292e6			0.885417			0.442708	+	0.896666i	$0.354018\pi$
$468$		−	2.72350e6i		−	0.574794i
$469$	−1.67633e6			−0.351908
$470$			94496.4i			0.0197320i
$471$			3.58471e6i			0.744564i
$472$			23132.8i			0.00477940i
$473$	−154005.			−0.0316507
$474$	141866.			0.0290023
$475$			3.92148e6i			0.797473i
$476$	−4.66705e6			−0.944116
$477$	2.12830e6			0.428289
$478$		−	10678.7i		−	0.00213771i
$479$	8.50692e6			1.69408			0.847039	−	0.531531i	$-0.178383\pi$
$479$	8.50692e6			1.69408			0.847039	+	0.531531i	$0.178383\pi$
$480$		−	332631.i		−	0.0658962i
$481$	5.06457e6			0.998113
$482$	483221.			0.0947389
$483$	−1.57750e6			−0.307681
$484$	4.12705e6			0.800805
$485$	1.90794e6	+	1.07320e6i	0.368306	+	0.207169i
$486$	421766.			0.0809993
$487$	2.95564e6			0.564715			0.282358	−	0.959309i	$-0.408884\pi$
$487$	2.95564e6			0.564715			0.282358	+	0.959309i	$0.408884\pi$
$488$	519739.			0.0987951
$489$	3.88225e6			0.734194
$490$			79926.5i			0.0150384i
$491$	−632440.			−0.118390			−0.0591951	−	0.998246i	$-0.518853\pi$
$491$	−632440.			−0.118390			−0.0591951	+	0.998246i	$0.518853\pi$
$492$		−	1.19367e6i		−	0.222316i
$493$	843158.			0.156240
$494$	−422146.			−0.0778297
$495$		−	603327.i		−	0.110672i
$496$	−2.61776e6			−0.477778
$497$	−2.20689e6			−0.400766
$498$			201302.i			0.0363726i
$499$			7.14474e6i			1.28450i	0.766494	+	0.642251i	$0.221999\pi$
$499$			7.14474e6i			1.28450i	−0.766494	+	0.642251i	$0.778001\pi$
$500$			4.27346e6i			0.764460i
$501$	−92282.8			−0.0164258
$502$		−	331037.i		−	0.0586296i
$503$	−7.26339e6			−1.28003			−0.640014	−	0.768363i	$-0.721071\pi$
$503$	−7.26339e6			−1.28003			−0.640014	+	0.768363i	$0.721071\pi$
$504$			420280.i			0.0736991i
$505$			1.64676e6i			0.287344i
$506$			134019.i			0.0232696i
$507$	−199310.			−0.0344357
$508$		−	7.62866e6i		−	1.31156i
$509$	−2.15850e6			−0.369281			−0.184641	−	0.982806i	$-0.559112\pi$
$509$	−2.15850e6			−0.369281			−0.184641	+	0.982806i	$0.559112\pi$
$510$	164180.			0.0279509
$511$			3.04989e6i			0.516692i
$512$	−2.37873e6			−0.401024
$513$			5.87372e6i			0.985416i
$514$		−	695985.i		−	0.116196i
$515$		−	2.37486e6i		−	0.394566i
$516$	274893.			0.0454506
$517$	−1.51529e6			−0.249328
$518$	−389441.			−0.0637701
$519$			1.31139e6i			0.213704i
$520$	−416355.			−0.0675236
$521$	−1.13928e6			−0.183881			−0.0919403	−	0.995765i	$-0.529307\pi$
$521$	−1.13928e6			−0.183881			−0.0919403	+	0.995765i	$0.529307\pi$
$522$		−	37834.8i		−	0.00607736i
$523$			1.65131e6i			0.263982i	0.991251	+	0.131991i	$0.0421371\pi$
$523$			1.65131e6i			0.263982i	−0.991251	+	0.131991i	$0.957863\pi$
$524$		−	1.06953e7i		−	1.70162i
$525$			2.48855e6i			0.394047i
$526$		−	350237.i		−	0.0551947i
$527$		−	3.92091e6i		−	0.614979i
$528$	1.75770e6			0.274385
$529$	3.78853e6			0.588615
$530$		−	162128.i		−	0.0250707i
$531$		−	112468.i		−	0.0173099i
$532$	−4.74502e6			−0.726874
$533$	−2.24372e6			−0.342098
$534$	−84454.9			−0.0128166
$535$	5.06678e6			0.765329
$536$		−	510150.i		−	0.0766984i
$537$		−	6.54947e6i		−	0.980100i
$538$	−803458.			−0.119676
$539$	−1.28166e6			−0.190020
$540$			2.88670e6i			0.426007i
$541$		−	8.47691e6i		−	1.24522i	−0.782534	−	0.622608i	$-0.786073\pi$
$541$		−	8.47691e6i		−	1.24522i	0.782534	−	0.622608i	$-0.213927\pi$
$542$		−	302924.i		−	0.0442930i
$543$			8.47762e6i			1.23388i
$544$		−	2.13287e6i		−	0.309006i
$545$		−	1.59800e6i		−	0.230455i
$546$	−267891.			−0.0384571
$547$	−5.24828e6			−0.749979			−0.374989	−	0.927029i	$-0.622354\pi$
$547$	−5.24828e6			−0.749979			−0.374989	+	0.927029i	$0.622354\pi$
$548$		−	6.85703e6i		−	0.975404i
$549$	−2.52689e6			−0.357813
$550$	211418.			0.0298013
$551$	857244.			0.120289
$552$		−	480071.i		−	0.0670591i
$553$		−	2.99736e6i		−	0.416798i
$554$		−	730706.i		−	0.101151i
$555$	−2.00261e6			−0.275971
$556$		−	2.03933e6i		−	0.279770i
$557$	−1.17188e7			−1.60046			−0.800228	−	0.599696i	$-0.795288\pi$
$557$	−1.17188e7			−1.60046			−0.800228	+	0.599696i	$0.795288\pi$
$558$	−175942.			−0.0239213
$559$		−	516712.i		−	0.0699390i
$560$	−2.31593e6			−0.312072
$561$			2.63270e6i			0.353179i
$562$			74306.7i			0.00992401i
$563$		−	6.71582e6i		−	0.892952i	−0.894796	−	0.446476i	$-0.852679\pi$
$563$		−	6.71582e6i		−	0.892952i	0.894796	−	0.446476i	$-0.147321\pi$
$564$	2.70473e6			0.358036
$565$		−	4.40077e6i		−	0.579972i
$566$	−263891.			−0.0346246
$567$			293533.i			0.0383441i
$568$		−	671612.i		−	0.0873470i
$569$		−	4.99269e6i		−	0.646479i	−0.946317	−	0.323239i	$-0.895228\pi$
$569$		−	4.99269e6i		−	0.646479i	0.946317	−	0.323239i	$-0.104772\pi$
$570$	166923.			0.0215193
$571$	−9.70480e6			−1.24565			−0.622825	−	0.782361i	$-0.714015\pi$
$571$	−9.70480e6			−1.24565			−0.622825	+	0.782361i	$0.714015\pi$
$572$		−	3.32684e6i		−	0.425150i
$573$	2.15487e6			0.274179
$574$	172531.			0.0218569
$575$			4.17700e6i			0.526860i
$576$	4.54609e6			0.570929
$577$			1.63251e6i			0.204135i	0.994777	+	0.102067i	$0.0325458\pi$
$577$			1.63251e6i			0.204135i	−0.994777	+	0.102067i	$0.967454\pi$
$578$	390677.			0.0486406
$579$	3.96248e6			0.491213
$580$	421301.			0.0520023
$581$	4.25313e6			0.522719
$582$	−210142.	+	373591.i	−0.0257161	+	0.0457181i
$583$	2.59979e6			0.316786
$584$	−928158.			−0.112613
$585$	2.02426e6			0.244554
$586$	209563.			0.0252098
$587$		−	7.24173e6i		−	0.867456i	−0.901044	−	0.433728i	$-0.857198\pi$
$587$		−	7.24173e6i		−	0.867456i	0.901044	−	0.433728i	$-0.142802\pi$
$588$	2.28770e6			0.272870
$589$		−	3.98641e6i		−	0.473472i
$590$	−8567.49			−0.00101327
$591$	4.43583e6			0.522403
$592$			8.57316e6i			1.00540i
$593$	−9.11270e6			−1.06417			−0.532084	−	0.846692i	$-0.678591\pi$
$593$	−9.11270e6			−1.06417			−0.532084	+	0.846692i	$0.678591\pi$
$594$	316669.			0.0368247
$595$		−	3.46882e6i		−	0.401688i
$596$		−	6.96703e6i		−	0.803400i
$597$		−	5.36649e6i		−	0.616247i
$598$	−449653.			−0.0514191
$599$		−	2.16685e6i		−	0.246753i	−0.992360	−	0.123376i	$-0.960628\pi$
$599$		−	2.16685e6i		−	0.246753i	0.992360	−	0.123376i	$-0.0393723\pi$
$600$	−757327.			−0.0858826
$601$		−	3.47129e6i		−	0.392017i	−0.980602	−	0.196008i	$-0.937202\pi$
$601$		−	3.47129e6i		−	0.392017i	0.980602	−	0.196008i	$-0.0627979\pi$
$602$			39732.7i			0.00446845i
$603$			2.48027e6i			0.277783i
$604$	−3.92165e6			−0.437398
$605$			3.06746e6i			0.340714i
$606$	−322450.			−0.0356682
$607$	1.18808e7			1.30880			0.654399	−	0.756149i	$-0.272922\pi$
$607$	1.18808e7			1.30880			0.654399	+	0.756149i	$0.272922\pi$
$608$		−	2.16850e6i		−	0.237904i
$609$	544002.			0.0594370
$610$			192491.i			0.0209453i
$611$		−	5.08404e6i		−	0.550943i
$612$			6.90529e6i			0.745252i
$613$	−921903.			−0.0990910			−0.0495455	−	0.998772i	$-0.515777\pi$
$613$	−921903.			−0.0990910			−0.0495455	+	0.998772i	$0.515777\pi$
$614$	−218943.			−0.0234375
$615$	887202.			0.0945877
$616$			513386.i			0.0545120i
$617$	−1.35922e7			−1.43740			−0.718700	−	0.695320i	$-0.755263\pi$
$617$	−1.35922e7			−1.43740			−0.718700	+	0.695320i	$0.755263\pi$
$618$	465018.			0.0489777
$619$			1.85507e7i			1.94596i	0.230888	+	0.972980i	$0.425837\pi$
$619$			1.85507e7i			1.94596i	−0.230888	+	0.972980i	$0.574163\pi$
$620$		−	1.95916e6i		−	0.204688i
$621$			6.25645e6i			0.651027i
$622$		−	535747.i		−	0.0555243i
$623$			1.78437e6i			0.184190i
$624$			5.89737e6i			0.606313i
$625$	4.84551e6			0.496181
$626$	16621.8			0.00169529
$627$			2.67669e6i			0.271912i
$628$			1.14852e7i			1.16209i
$629$	−1.28410e7			−1.29411
$630$	−155655.			−0.0156247
$631$	−1.98710e6			−0.198676			−0.0993380	−	0.995054i	$-0.531673\pi$
$631$	−1.98710e6			−0.198676			−0.0993380	+	0.995054i	$0.531673\pi$
$632$	912171.			0.0908413
$633$		−	3.98892e6i		−	0.395682i
$634$			606295.i			0.0599047i
$635$	5.67005e6			0.558023
$636$	−4.64051e6			−0.454907
$637$		−	4.30016e6i		−	0.419890i
$638$		−	46216.5i		−	0.00449516i
$639$			3.26528e6i			0.316350i
$640$		−	1.41933e6i		−	0.136973i
$641$		−	7.60605e6i		−	0.731163i	−0.930779	−	0.365581i	$-0.880870\pi$
$641$		−	7.60605e6i		−	0.731163i	0.930779	−	0.365581i	$-0.119130\pi$
$642$			992121.i			0.0950008i
$643$	−1.42591e7			−1.36008			−0.680041	−	0.733174i	$-0.738038\pi$
$643$	−1.42591e7			−1.36008			−0.680041	+	0.733174i	$0.738038\pi$
$644$	−5.05421e6			−0.480218
$645$			204316.i			0.0193376i
$646$	1.07033e6			0.100911
$647$	1.88917e7			1.77423			0.887114	−	0.461551i	$-0.152707\pi$
$647$	1.88917e7			1.77423			0.887114	+	0.461551i	$0.152707\pi$
$648$	−89329.3			−0.00835711
$649$		−	137384.i		−	0.0128033i
$650$			709341.i			0.0658524i
$651$		−	2.52976e6i		−	0.233952i
$652$	1.24385e7			1.14591
$653$		−	2.04065e7i		−	1.87277i	−0.350973	−	0.936386i	$-0.614149\pi$
$653$		−	2.04065e7i		−	1.87277i	0.350973	−	0.936386i	$-0.385851\pi$
$654$	312902.			0.0286065
$655$	7.94932e6			0.723980
$656$		−	3.79811e6i		−	0.344594i
$657$	4.51256e6			0.407859
$658$			390939.i			0.0352001i
$659$			4.40356e6i			0.394994i	0.980304	+	0.197497i	$0.0632812\pi$
$659$			4.40356e6i			0.394994i	−0.980304	+	0.197497i	$0.936719\pi$
$660$			1.31548e6i			0.117551i
$661$	−1.32658e7			−1.18095			−0.590473	−	0.807057i	$-0.701059\pi$
$661$	−1.32658e7			−1.18095			−0.590473	+	0.807057i	$0.701059\pi$
$662$		−	16858.3i		−	0.00149509i
$663$	−8.83313e6			−0.780424
$664$			1.29433e6i			0.113927i
$665$		−	3.52677e6i		−	0.309259i
$666$			576210.i			0.0503379i
$667$	913102.			0.0794703
$668$	−295669.			−0.0256368
$669$			1.09415e7i			0.945171i
$670$	188940.			0.0162606
$671$	−3.08668e6			−0.264658
$672$		−	1.37612e6i		−	0.117553i
$673$	2.11276e7			1.79809			0.899047	−	0.437853i	$-0.144261\pi$
$673$	2.11276e7			1.79809			0.899047	+	0.437853i	$0.144261\pi$
$674$			1.01155e6i			0.0857702i
$675$	9.86974e6			0.833770
$676$	−638577.			−0.0537461
$677$	−1.55509e7			−1.30402			−0.652010	−	0.758210i	$-0.726074\pi$
$677$	−1.55509e7			−1.30402			−0.652010	+	0.758210i	$0.726074\pi$
$678$	861709.			0.0719924
$679$	7.89327e6	+	4.43990e6i	0.657026	+	0.369571i
$680$	1.05565e6			0.0875481
$681$	−1.16931e7			−0.966185
$682$	−214919.			−0.0176935
$683$	2.03835e6			0.167196			0.0835981	−	0.996500i	$-0.473359\pi$
$683$	2.03835e6			0.167196			0.0835981	+	0.996500i	$0.473359\pi$
$684$			7.02065e6i			0.573769i
$685$	5.09653e6			0.415000
$686$			1.09655e6i			0.0889650i
$687$	1.18899e7			0.961143
$688$	874676.			0.0704492
$689$			8.72270e6i			0.700008i
$690$	177800.			0.0142170
$691$	1.84540e7			1.47026			0.735131	−	0.677925i	$-0.237121\pi$
$691$	1.84540e7			1.47026			0.735131	+	0.677925i	$0.237121\pi$
$692$			4.20162e6i			0.333543i
$693$		−	2.49601e6i		−	0.197430i
$694$			835214.i			0.0658263i
$695$	1.51574e6			0.119032
$696$			165553.i			0.0129543i
$697$	5.68884e6			0.443549
$698$			850894.i			0.0661054i
$699$			4.69197e6i			0.363214i
$700$			7.97317e6i			0.615015i
$701$	−1.84195e7			−1.41574			−0.707868	−	0.706344i	$-0.750343\pi$
$701$	−1.84195e7			−1.41574			−0.707868	+	0.706344i	$0.750343\pi$
$702$			1.06247e6i			0.0813721i
$703$	−1.30555e7			−0.996334
$704$	5.55320e6			0.422291
$705$			2.01031e6i			0.152332i
$706$	704809.			0.0532182
$707$			6.81276e6i			0.512595i
$708$			245224.i			0.0183857i
$709$			8.20204e6i			0.612782i	0.951906	+	0.306391i	$0.0991216\pi$
$709$			8.20204e6i			0.612782i	−0.951906	+	0.306391i	$0.900878\pi$
$710$	248739.			0.0185182
$711$	−4.43484e6			−0.329006
$712$	−543029.			−0.0401442
$713$		−	4.24617e6i		−	0.312805i
$714$	679225.			0.0498618
$715$	2.47270e6			0.180886
$716$		−	2.09842e7i		−	1.52971i
$717$		−	227178.i		−	0.0165032i
$718$		−	1.17775e6i		−	0.0852594i
$719$			1.93499e7i			1.39591i	0.716143	+	0.697954i	$0.245906\pi$
$719$			1.93499e7i			1.39591i	−0.716143	+	0.697954i	$0.754094\pi$
$720$			3.42660e6i			0.246339i
$721$		−	9.82496e6i		−	0.703870i
$722$	−66369.1			−0.00473830
$723$	1.02800e7			0.731388
$724$			2.71618e7i			1.92581i
$725$		−	1.44045e6i		−	0.101778i
$726$	−600636.			−0.0422931
$727$	−1.34628e6			−0.0944711			−0.0472356	−	0.998884i	$-0.515041\pi$
$727$	−1.34628e6			−0.0944711			−0.0472356	+	0.998884i	$0.515041\pi$
$728$	−1.72249e6			−0.120456
$729$	9.70249e6			0.676183
$730$		−	343754.i		−	0.0238748i
$731$			1.31010e6i			0.0906798i
$732$	5.50960e6			0.380051
$733$	−7.66144e6			−0.526684			−0.263342	−	0.964702i	$-0.584825\pi$
$733$	−7.66144e6			−0.526684			−0.263342	+	0.964702i	$0.584825\pi$
$734$		−	418061.i		−	0.0286417i
$735$			1.70035e6i			0.116097i
$736$		−	2.30981e6i		−	0.157174i
$737$			3.02974e6i			0.205464i
$738$		−	255274.i		−	0.0172531i
$739$		−	1.25070e7i		−	0.842446i	−0.906957	−	0.421223i	$-0.861601\pi$
$739$		−	1.25070e7i		−	0.842446i	0.906957	−	0.421223i	$-0.138399\pi$
$740$	−6.41625e6			−0.430727
$741$	−8.98070e6			−0.600848
$742$		−	670733.i		−	0.0447239i
$743$	−4.17158e6			−0.277223			−0.138611	−	0.990347i	$-0.544264\pi$
$743$	−4.17158e6			−0.277223			−0.138611	+	0.990347i	$0.544264\pi$
$744$	769867.			0.0509898
$745$	5.17829e6			0.341818
$746$			1.09166e6i			0.0718190i
$747$		−	6.29286e6i		−	0.412616i
$748$			8.43504e6i			0.551230i
$749$	2.09617e7			1.36528
$750$		−	621943.i		−	0.0403736i
$751$	−1.94965e7			−1.26141			−0.630706	−	0.776022i	$-0.717235\pi$
$751$	−1.94965e7			−1.26141			−0.630706	+	0.776022i	$0.717235\pi$
$752$	8.60613e6			0.554962
$753$		−	7.04245e6i		−	0.452623i
$754$	155064.			0.00993302
$755$		−	2.91479e6i		−	0.186097i
$756$			1.19425e7i			0.759958i
$757$		−	1.50001e6i		−	0.0951379i	−0.998868	−	0.0475689i	$-0.984853\pi$
$757$		−	1.50001e6i		−	0.0951379i	0.998868	−	0.0475689i	$-0.0151474\pi$
$758$	119175.			0.00753379
$759$			2.85110e6i			0.179642i
$760$	1.07328e6			0.0674032
$761$			1.19231e7i			0.746327i	0.927766	+	0.373164i	$0.121727\pi$
$761$			1.19231e7i			0.746327i	−0.927766	+	0.373164i	$0.878273\pi$
$762$			1.11025e6i			0.0692678i
$763$		−	6.61104e6i		−	0.411110i
$764$	6.90407e6			0.427929
$765$	−5.13240e6			−0.317079
$766$		−	1.75118e6i		−	0.107835i
$767$	460944.			0.0282917
$768$	−9.70212e6			−0.593558
$769$			1.66689e7i			1.01646i	0.861221	+	0.508231i	$0.169700\pi$
$769$			1.66689e7i			1.01646i	−0.861221	+	0.508231i	$0.830300\pi$
$770$	−190138.			−0.0115569
$771$		−	1.48063e7i		−	0.897039i
$772$	1.26956e7			0.766670
$773$	1.24060e7			0.746762			0.373381	−	0.927678i	$-0.378198\pi$
$773$	1.24060e7			0.746762			0.373381	+	0.927678i	$0.378198\pi$
$774$	58787.7			0.00352723
$775$	−6.69846e6			−0.400609
$776$	−1.35117e6	+	2.40212e6i	−0.0805482	+	0.143199i
$777$	−8.28494e6			−0.492308
$778$	−1.63566e6			−0.0968820
$779$	5.78388e6			0.341488
$780$	−4.41366e6			−0.259754
$781$			3.98865e6i			0.233990i
$782$	1.14007e6			0.0666678
$783$		−	2.15755e6i		−	0.125764i
$784$	7.27919e6			0.422954
$785$	−8.53647e6			−0.494429
$786$			1.55655e6i			0.0898682i
$787$	−1.68974e7			−0.972485			−0.486243	−	0.873824i	$-0.661633\pi$
$787$	−1.68974e7			−0.972485			−0.486243	+	0.873824i	$0.661633\pi$
$788$	1.42122e7			0.815351
$789$		−	7.45092e6i		−	0.426106i
$790$			337833.i			0.0192590i
$791$		−	1.82063e7i		−	1.03462i
$792$	759597.			0.0430299
$793$		−	1.03563e7i		−	0.584819i
$794$	8553.75			0.000481510
$795$		−	3.44909e6i		−	0.193547i
$796$		−	1.71939e7i		−	0.961818i
$797$		−	7.35156e6i		−	0.409953i	−0.978767	−	0.204976i	$-0.934288\pi$
$797$		−	7.35156e6i		−	0.409953i	0.978767	−	0.204976i	$-0.0657117\pi$
$798$	690573.			0.0383886
$799$			1.28903e7i			0.714328i
$800$	−3.64379e6			−0.201293
$801$	2.64013e6			0.145393
$802$		−	1.77744e6i		−	0.0975796i
$803$	5.51225e6			0.301675
$804$		−	5.40795e6i		−	0.295048i
$805$		−	3.75658e6i		−	0.204316i
$806$		−	721087.i		−	0.0390976i
$807$	−1.70927e7			−0.923904
$808$	−2.07329e6			−0.111720
$809$	283044.			0.0152049			0.00760244	−	0.999971i	$-0.497580\pi$
$809$	283044.			0.0152049			0.00760244	+	0.999971i	$0.497580\pi$
$810$		−	33084.1i		−	0.00177177i
$811$	−1.97671e7			−1.05534			−0.527669	−	0.849450i	$-0.676934\pi$
$811$	−1.97671e7			−1.05534			−0.527669	+	0.849450i	$0.676934\pi$
$812$	1.74295e6			0.0927674
$813$		−	6.44438e6i		−	0.341944i
$814$			703859.i			0.0372327i
$815$			9.24500e6i			0.487543i
$816$		−	1.49525e7i		−	0.786118i
$817$			1.33199e6i			0.0698143i
$818$		−	1.90819e6i		−	0.0997097i
$819$	8.37449e6			0.436263
$820$	2.84255e6			0.147629
$821$		−	3.01579e7i		−	1.56151i	−0.624840	−	0.780753i	$-0.714836\pi$
$821$		−	3.01579e7i		−	1.56151i	0.624840	−	0.780753i	$-0.285164\pi$
$822$			997946.i			0.0515143i
$823$	−3.47753e7			−1.78966			−0.894831	−	0.446406i	$-0.852704\pi$
$823$	−3.47753e7			−1.78966			−0.894831	+	0.446406i	$0.852704\pi$
$824$	2.98998e6			0.153409
$825$	4.49770e6			0.230067
$826$	−35444.3			−0.00180758
$827$		−	1.76944e7i		−	0.899647i	−0.893117	−	0.449824i	$-0.851487\pi$
$827$		−	1.76944e7i		−	0.899647i	0.893117	−	0.449824i	$-0.148513\pi$
$828$			7.47812e6i			0.379068i
$829$	1.25566e7			0.634581			0.317290	−	0.948328i	$-0.397227\pi$
$829$	1.25566e7			0.634581			0.317290	+	0.948328i	$0.397227\pi$
$830$	−479371.			−0.0241533
$831$		−	1.55450e7i		−	0.780886i
$832$			1.86319e7i			0.933142i
$833$			1.09028e7i			0.544411i
$834$			296796.i			0.0147755i
$835$		−	219758.i		−	0.0109076i
$836$			8.57596e6i			0.424392i
$837$	−1.00332e7			−0.495022
$838$	−629244.			−0.0309535
$839$			2.45300e7i			1.20307i	0.798845	+	0.601536i	$0.205445\pi$
$839$			2.45300e7i			1.20307i	−0.798845	+	0.601536i	$0.794555\pi$
$840$	681099.			0.0333052
$841$	2.01963e7			0.984648
$842$	1.52872e6			0.0743102
$843$			1.58080e6i			0.0766137i
$844$		−	1.27803e7i		−	0.617568i
$845$		−	474627.i		−	0.0228671i
$846$	578425.			0.0277857
$847$			1.26903e7i			0.607804i
$848$	−1.47655e7			−0.705115
$849$	−5.61401e6			−0.267303
$850$		−	1.79850e6i		−	0.0853814i
$851$	−1.39062e7			−0.658240
$852$		−	7.11956e6i		−	0.336012i
$853$		−	2.33868e7i		−	1.10052i	−0.834994	−	0.550260i	$-0.814529\pi$
$853$		−	2.33868e7i		−	1.10052i	0.834994	−	0.550260i	$-0.185471\pi$
$854$			796350.i			0.0373645i
$855$	−5.21814e6			−0.244118
$856$			6.37915e6i			0.297563i
$857$	1.59207e7			0.740473			0.370237	−	0.928937i	$-0.379277\pi$
$857$	1.59207e7			0.740473			0.370237	+	0.928937i	$0.379277\pi$
$858$			484176.i			0.0224535i
$859$		−	1.83520e6i		−	0.0848594i	−0.999099	−	0.0424297i	$-0.986490\pi$
$859$		−	1.83520e6i		−	0.0848594i	0.999099	−	0.0424297i	$-0.0135098\pi$
$860$			654618.i			0.0301815i
$861$	3.67042e6			0.168736
$862$	−3.07211e6			−0.140821
$863$		−	2.25018e7i		−	1.02847i	−0.857650	−	0.514234i	$-0.828076\pi$
$863$		−	2.25018e7i		−	1.02847i	0.857650	−	0.514234i	$-0.171924\pi$
$864$	−5.45778e6			−0.248732
$865$	−3.12288e6			−0.141911
$866$			1.73440e6i			0.0785877i
$867$	8.31124e6			0.375507
$868$		−	8.10520e6i		−	0.365144i
$869$	−5.41730e6			−0.243351
$870$	−61314.5			−0.00274641
$871$	−1.01652e7			−0.454017
$872$	2.01190e6			0.0896016
$873$	6.56919e6	−	1.16787e7i	0.291727	−	0.518633i
$874$	1.15912e6			0.0513275
$875$	−1.31405e7			−0.580218
$876$	−9.83912e6			−0.433208
$877$	−1.37558e7			−0.603929			−0.301965	−	0.953319i	$-0.597642\pi$
$877$	−1.37558e7			−0.603929			−0.301965	+	0.953319i	$0.597642\pi$
$878$		−	1.48607e6i		−	0.0650583i
$879$	4.45822e6			0.194621
$880$			4.18571e6i			0.182206i
$881$	2.22513e7			0.965863			0.482932	−	0.875658i	$-0.339572\pi$
$881$	2.22513e7			0.965863			0.482932	+	0.875658i	$0.339572\pi$
$882$	489241.			0.0211764
$883$		−	3.03062e7i		−	1.30807i	−0.756465	−	0.654034i	$-0.773075\pi$
$883$		−	3.03062e7i		−	1.30807i	0.756465	−	0.654034i	$-0.226925\pi$
$884$	−2.83009e7			−1.21806
$885$	−182264.			−0.00782246
$886$		−	1.94207e6i		−	0.0831153i
$887$			1.47585e7i			0.629845i	0.949117	+	0.314923i	$0.101979\pi$
$887$			1.47585e7i			0.629845i	−0.949117	+	0.314923i	$0.898021\pi$
$888$		−	2.52131e6i		−	0.107299i
$889$	2.34574e7			0.995464
$890$		−	201117.i		−	0.00851087i
$891$	530519.			0.0223875
$892$			3.50559e7i			1.47519i
$893$			1.31057e7i			0.549960i
$894$			1.01395e6i			0.0424301i
$895$	1.55966e7			0.650838
$896$		−	5.87188e6i		−	0.244347i
$897$	−9.56589e6			−0.396958
$898$	179259.			0.00741804
$899$			1.46430e6i			0.0604269i
$900$	1.17970e7			0.485472
$901$		−	2.21160e7i		−	0.907599i
$902$		−	311826.i		−	0.0127613i
$903$			845270.i			0.0344966i
$904$	5.54063e6			0.225495
$905$	−2.01882e7			−0.819363
$906$	570742.			0.0231004
$907$			4.20540e6i			0.169742i	0.996392	+	0.0848710i	$0.0270478\pi$
$907$			4.20540e6i			0.169742i	−0.996392	+	0.0848710i	$0.972952\pi$
$908$	−3.74639e7			−1.50799
$909$	1.00800e7			0.404625
$910$		−	637944.i		−	0.0255375i
$911$		−	1.65850e7i		−	0.662094i	−0.943614	−	0.331047i	$-0.892598\pi$
$911$		−	1.65850e7i		−	0.662094i	0.943614	−	0.331047i	$-0.107402\pi$
$912$		−	1.52023e7i		−	0.605232i
$913$		−	7.68693e6i		−	0.305194i
$914$		−	1.06843e6i		−	0.0423037i
$915$			4.09504e6i			0.161698i
$916$	3.80947e7			1.50012
$917$	3.28869e7			1.29152
$918$		−	2.69385e6i		−	0.105504i
$919$		−	4.47618e7i		−	1.74831i	−0.485645	−	0.874156i	$-0.661415\pi$
$919$		−	4.47618e7i		−	1.74831i	0.485645	−	0.874156i	$-0.338585\pi$
$920$	1.14322e6			0.0445307
$921$	−4.65779e6			−0.180938
$922$	−3.21734e6			−0.124643
$923$	−1.33825e7			−0.517052
$924$			5.44225e6i			0.209700i
$925$			2.19374e7i			0.843008i
$926$	−725152.			−0.0277908
$927$	−1.45368e7			−0.555610
$928$			796540.i			0.0303625i
$929$			1.28854e7i			0.489846i	0.969543	+	0.244923i	$0.0787626\pi$
$929$			1.28854e7i			0.489846i	−0.969543	+	0.244923i	$0.921237\pi$
$930$			285129.i			0.0108102i
$931$			1.10850e7i			0.419142i
$932$			1.50328e7i			0.566893i
$933$		−	1.13974e7i		−	0.428650i
$934$	−1.94579e6			−0.0729842
$935$	−6.26940e6			−0.234529
$936$			2.54857e6i			0.0950837i
$937$	−3.36388e7			−1.25167			−0.625837	−	0.779954i	$-0.715243\pi$
$937$	−3.36388e7			−1.25167			−0.625837	+	0.779954i	$0.715243\pi$
$938$	781658.			0.0290075
$939$	353612.			0.0130877
$940$			6.44093e6i			0.237754i
$941$			2.57789e7i			0.949052i	0.880242	+	0.474526i	$0.157380\pi$
$941$			2.57789e7i			0.949052i	−0.880242	+	0.474526i	$0.842620\pi$
$942$		−	1.67152e6i		−	0.0613738i
$943$	6.16076e6			0.225608
$944$			780272.i			0.0284981i
$945$	−8.87632e6			−0.323336
$946$	71811.2			0.00260894
$947$		−	6.74925e6i		−	0.244557i	−0.992496	−	0.122279i	$-0.960980\pi$
$947$		−	6.74925e6i		−	0.244557i	0.992496	−	0.122279i	$-0.0390201\pi$
$948$	9.66965e6			0.349454
$949$			1.84944e7i			0.666616i
$950$		−	1.82855e6i		−	0.0657350i
$951$			1.28983e7i			0.462467i
$952$	4.36729e6			0.156178
$953$			5.12384e7i			1.82752i	0.406249	+	0.913762i	$0.366837\pi$
$953$			5.12384e7i			1.82752i	−0.406249	+	0.913762i	$0.633163\pi$
$954$	−992405.			−0.0353035
$955$			5.13150e6i			0.182069i
$956$		−	727865.i		−	0.0257577i
$957$		−	983206.i		−	0.0347028i
$958$	−3.96669e6			−0.139642
$959$	2.10847e7			0.740323
$960$		−	7.36732e6i		−	0.258007i
$961$	−2.18198e7			−0.762152
$962$	−2.36156e6			−0.0822737
$963$		−	3.10145e7i		−	1.07770i
$964$	3.29366e7			1.14153
$965$			9.43605e6i			0.326191i
$966$	735571.			0.0253619
$967$	1.49450e7			0.513961			0.256981	−	0.966417i	$-0.417272\pi$
$967$	1.49450e7			0.513961			0.256981	+	0.966417i	$0.417272\pi$
$968$	−3.86197e6			−0.132471
$969$	2.27701e7			0.779033
$970$	−889651.	−	500421.i	−0.0303592	−	0.0170768i
$971$	3.58565e7			1.22045			0.610225	−	0.792228i	$-0.291079\pi$
$971$	3.58565e7			1.22045			0.610225	+	0.792228i	$0.291079\pi$
$972$	2.87478e7			0.975976
$973$	6.27075e6			0.212343
$974$	−1.37819e6			−0.0465490
$975$			1.50905e7i			0.508383i
$976$	1.75309e7			0.589086
$977$			4.06130e7i			1.36122i	0.732645	+	0.680611i	$0.238285\pi$
$977$			4.06130e7i			1.36122i	−0.732645	+	0.680611i	$0.761715\pi$
$978$	−1.81025e6			−0.0605190
$979$	3.22500e6			0.107541
$980$			5.44783e6i			0.181200i
$981$	−9.78157e6			−0.324516
$982$	294901.			0.00975881
$983$			1.42860e7i			0.471549i	0.971808	+	0.235774i	$0.0757627\pi$
$983$			1.42860e7i			0.471549i	−0.971808	+	0.235774i	$0.924237\pi$
$984$			1.11700e6i			0.0367761i
$985$			1.05633e7i			0.346903i
$986$	−393156.			−0.0128787
$987$			8.31680e6i			0.271746i
$988$	−2.87737e7			−0.937785
$989$			1.41878e6i			0.0461237i
$990$			281325.i			0.00912264i
$991$		−	2.07465e7i		−	0.671058i	−0.942030	−	0.335529i	$-0.891085\pi$
$991$		−	2.07465e7i		−	0.671058i	0.942030	−	0.335529i	$-0.108915\pi$
$992$	3.70413e6			0.119511
$993$		−	358642.i		−	0.0115422i
$994$	1.02905e6			0.0330348
$995$	1.27795e7			0.409220
$996$			1.37208e7i			0.438261i
$997$	1.53883e7			0.490291			0.245146	−	0.969486i	$-0.421164\pi$
$997$	1.53883e7			0.490291			0.245146	+	0.969486i	$0.421164\pi$
$998$		−	3.33152e6i		−	0.105881i
$999$			3.28586e7i			1.04168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.6.b.a.96.19	✓	40
97.96	even	2	inner	97.6.b.a.96.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.6.b.a.96.19	✓	40	1.1	even	1	trivial
97.6.b.a.96.20	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)

\(f(q)\)	\(=\)	\(q-0.466290 q^{2} -9.91982 q^{3} -31.7826 q^{4} -23.6226i q^{5} +4.62551 q^{6} -97.7284i q^{7} +29.7412 q^{8} -144.597 q^{9} +11.0150i q^{10} -176.630 q^{11} +315.277 q^{12} -592.622i q^{13} +45.5698i q^{14} +234.332i q^{15} +1003.17 q^{16} +1502.56i q^{17} +67.4242 q^{18} +1527.67i q^{19} +750.787i q^{20} +969.448i q^{21} +82.3609 q^{22} +1627.21i q^{23} -295.027 q^{24} +2566.97 q^{25} +276.334i q^{26} +3844.89 q^{27} +3106.06i q^{28} -561.146i q^{29} -109.267i q^{30} -2609.48 q^{31} -1419.49 q^{32} +1752.14 q^{33} -700.631i q^{34} -2308.60 q^{35} +4595.67 q^{36} +8546.03i q^{37} -712.336i q^{38} +5878.70i q^{39} -702.564i q^{40} -3786.09i q^{41} -452.044i q^{42} +871.908 q^{43} +5613.76 q^{44} +3415.76i q^{45} -758.752i q^{46} +8578.90 q^{47} -9951.31 q^{48} +7256.16 q^{49} -1196.95 q^{50} -14905.2i q^{51} +18835.1i q^{52} -14718.8 q^{53} -1792.84 q^{54} +4172.47i q^{55} -2906.56i q^{56} -15154.2i q^{57} +261.657i q^{58} +777.803i q^{59} -7447.67i q^{60} +17475.4 q^{61} +1216.77 q^{62} +14131.2i q^{63} -31439.7 q^{64} -13999.3 q^{65} -817.006 q^{66} -17153.0i q^{67} -47755.4i q^{68} -16141.6i q^{69} +1076.48 q^{70} -22581.9i q^{71} -4300.49 q^{72} -31207.8 q^{73} -3984.93i q^{74} -25463.9 q^{75} -48553.2i q^{76} +17261.8i q^{77} -2741.18i q^{78} +30670.3 q^{79} -23697.6i q^{80} -3003.56 q^{81} +1765.42i q^{82} +43519.9i q^{83} -30811.6i q^{84} +35494.5 q^{85} -406.562 q^{86} +5566.47i q^{87} -5253.19 q^{88} -18258.5 q^{89} -1592.74i q^{90} -57916.0 q^{91} -51716.9i q^{92} +25885.6 q^{93} -4000.25 q^{94} +36087.5 q^{95} +14081.1 q^{96} +(-45431.0 + 80767.4i) q^{97} -3383.47 q^{98} +25540.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} + 40 q^{3} + 638 q^{4} - 130 q^{6} + 180 q^{8} + 3300 q^{9} + 382 q^{11} + 2586 q^{12} + 10174 q^{16} + 4738 q^{18} + 1996 q^{22} - 3102 q^{24} - 25178 q^{25} + 3046 q^{27} + 14796 q^{31}+ \cdots - 562238 q^{99}+O(q^{100}) \) 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