LMFDB - Embedded newform 97.6.b.a.96.2

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			96.2
Character	$\chi$	$=$	97.96
Dual form			97.6.b.a.96.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-10.9603 q^{2} +12.4768 q^{3} +88.1276 q^{4} +77.3203i q^{5} -136.749 q^{6} +129.228i q^{7} -615.173 q^{8} -87.3297 q^{9} -847.452i q^{10} -350.587 q^{11} +1099.55 q^{12} +1085.83i q^{13} -1416.38i q^{14} +964.710i q^{15} +3922.38 q^{16} -1100.57i q^{17} +957.157 q^{18} -1031.75i q^{19} +6814.05i q^{20} +1612.35i q^{21} +3842.53 q^{22} -834.244i q^{23} -7675.39 q^{24} -2853.43 q^{25} -11901.0i q^{26} -4121.45 q^{27} +11388.6i q^{28} -7644.83i q^{29} -10573.5i q^{30} +4505.54 q^{31} -23304.9 q^{32} -4374.20 q^{33} +12062.5i q^{34} -9991.97 q^{35} -7696.15 q^{36} -2132.10i q^{37} +11308.3i q^{38} +13547.7i q^{39} -47565.4i q^{40} +9988.95i q^{41} -17671.8i q^{42} -500.775 q^{43} -30896.4 q^{44} -6752.36i q^{45} +9143.54i q^{46} -17980.2 q^{47} +48938.8 q^{48} +107.062 q^{49} +31274.4 q^{50} -13731.6i q^{51} +95691.9i q^{52} +30119.4 q^{53} +45172.3 q^{54} -27107.5i q^{55} -79497.8i q^{56} -12873.0i q^{57} +83789.4i q^{58} -7457.09i q^{59} +85017.5i q^{60} -47987.8 q^{61} -49381.9 q^{62} -11285.5i q^{63} +129911. q^{64} -83957.0 q^{65} +47942.4 q^{66} -3983.03i q^{67} -96990.5i q^{68} -10408.7i q^{69} +109515. q^{70} +39145.5i q^{71} +53722.9 q^{72} -21442.3 q^{73} +23368.4i q^{74} -35601.7 q^{75} -90925.8i q^{76} -45305.7i q^{77} -148487. i q^{78} -38480.9 q^{79} +303280. i q^{80} -30201.4 q^{81} -109482. i q^{82} +114812. i q^{83} +142093. i q^{84} +85096.4 q^{85} +5488.63 q^{86} -95382.9i q^{87} +215672. q^{88} -87567.0 q^{89} +74007.7i q^{90} -140320. q^{91} -73519.9i q^{92} +56214.6 q^{93} +197068. q^{94} +79775.4 q^{95} -290770. q^{96} +(89392.4 - 24420.2i) q^{97} -1173.43 q^{98} +30616.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.9603			−1.93752			−0.968760	−	0.247999i	$-0.920227\pi$
$2$	−10.9603			−1.93752			−0.968760	+	0.247999i	$0.920227\pi$
$3$	12.4768			0.800386			0.400193	−	0.916431i	$-0.368943\pi$
$3$	12.4768			0.800386			0.400193	+	0.916431i	$0.368943\pi$
$4$	88.1276			2.75399
$5$			77.3203i			1.38315i	0.722306	+	0.691574i	$0.243082\pi$
$5$			77.3203i			1.38315i	−0.722306	+	0.691574i	$0.756918\pi$
$6$	−136.749			−1.55077
$7$			129.228i			0.996810i	0.866944	+	0.498405i	$0.166081\pi$
$7$			129.228i			0.996810i	−0.866944	+	0.498405i	$0.833919\pi$
$8$	−615.173			−3.39838
$9$	−87.3297			−0.359381
$10$		−	847.452i		−	2.67988i
$11$	−350.587			−0.873603			−0.436801	−	0.899558i	$-0.643889\pi$
$11$	−350.587			−0.873603			−0.436801	+	0.899558i	$0.643889\pi$
$12$	1099.55			2.20425
$13$			1085.83i			1.78199i	0.454015	+	0.890994i	$0.349991\pi$
$13$			1085.83i			1.78199i	−0.454015	+	0.890994i	$0.650009\pi$
$14$		−	1416.38i		−	1.93134i
$15$			964.710i			1.10705i
$16$	3922.38			3.83045
$17$		−	1100.57i		−	0.923624i	−0.886978	−	0.461812i	$-0.847199\pi$
$17$		−	1100.57i		−	0.923624i	0.886978	−	0.461812i	$-0.152801\pi$
$18$	957.157			0.696309
$19$		−	1031.75i		−	0.655679i	−0.944733	−	0.327840i	$-0.893679\pi$
$19$		−	1031.75i		−	0.655679i	0.944733	−	0.327840i	$-0.106321\pi$
$20$			6814.05i			3.80917i
$21$			1612.35i			0.797833i
$22$	3842.53			1.69262
$23$		−	834.244i		−	0.328832i	−0.986391	−	0.164416i	$-0.947426\pi$
$23$		−	834.244i		−	0.328832i	0.986391	−	0.164416i	$-0.0525739\pi$
$24$	−7675.39			−2.72002
$25$	−2853.43			−0.913099
$26$		−	11901.0i		−	3.45264i
$27$	−4121.45			−1.08803
$28$			11388.6i			2.74520i
$29$		−	7644.83i		−	1.68800i	−0.536343	−	0.844000i	$-0.680195\pi$
$29$		−	7644.83i		−	1.68800i	0.536343	−	0.844000i	$-0.319805\pi$
$30$		−	10573.5i		−	2.14494i
$31$	4505.54			0.842059			0.421029	−	0.907047i	$-0.361669\pi$
$31$	4505.54			0.842059			0.421029	+	0.907047i	$0.361669\pi$
$32$	−23304.9			−4.02320
$33$	−4374.20			−0.699220
$34$			12062.5i			1.78954i
$35$	−9991.97			−1.37874
$36$	−7696.15			−0.989732
$37$		−	2132.10i		−	0.256037i	−0.991772	−	0.128018i	$-0.959138\pi$
$37$		−	2132.10i		−	0.256037i	0.991772	−	0.128018i	$-0.0408617\pi$
$38$			11308.3i			1.27039i
$39$			13547.7i			1.42628i
$40$		−	47565.4i		−	4.70047i
$41$			9988.95i			0.928026i	0.885828	+	0.464013i	$0.153591\pi$
$41$			9988.95i			0.928026i	−0.885828	+	0.464013i	$0.846409\pi$
$42$		−	17671.8i		−	1.54582i
$43$	−500.775			−0.0413021			−0.0206510	−	0.999787i	$-0.506574\pi$
$43$	−500.775			−0.0413021			−0.0206510	+	0.999787i	$0.506574\pi$
$44$	−30896.4			−2.40589
$45$		−	6752.36i		−	0.497078i
$46$			9143.54i			0.637118i
$47$	−17980.2			−1.18727			−0.593635	−	0.804734i	$-0.702308\pi$
$47$	−17980.2			−1.18727			−0.593635	+	0.804734i	$0.702308\pi$
$48$	48938.8			3.06584
$49$	107.062			0.00637007
$50$	31274.4			1.76915
$51$		−	13731.6i		−	0.739256i
$52$			95691.9i			4.90757i
$53$	30119.4			1.47285			0.736423	−	0.676521i	$-0.236513\pi$
$53$	30119.4			1.47285			0.736423	+	0.676521i	$0.236513\pi$
$54$	45172.3			2.10808
$55$		−	27107.5i		−	1.20832i
$56$		−	79497.8i		−	3.38754i
$57$		−	12873.0i		−	0.524797i
$58$			83789.4i			3.27054i
$59$		−	7457.09i		−	0.278894i	−0.990230	−	0.139447i	$-0.955467\pi$
$59$		−	7457.09i		−	0.278894i	0.990230	−	0.139447i	$-0.0445325\pi$
$60$			85017.5i			3.04881i
$61$	−47987.8			−1.65123			−0.825613	−	0.564238i	$-0.809170\pi$
$61$	−47987.8			−1.65123			−0.825613	+	0.564238i	$0.809170\pi$
$62$	−49381.9			−1.63151
$63$		−	11285.5i		−	0.358235i
$64$	129911.			3.96458
$65$	−83957.0			−2.46475
$66$	47942.4			1.35475
$67$		−	3983.03i		−	0.108399i	−0.998530	−	0.0541997i	$-0.982739\pi$
$67$		−	3983.03i		−	0.108399i	0.998530	−	0.0541997i	$-0.0172608\pi$
$68$		−	96990.5i		−	2.54365i
$69$		−	10408.7i		−	0.263192i
$70$	109515.			2.67133
$71$			39145.5i			0.921587i	0.887507	+	0.460793i	$0.152435\pi$
$71$			39145.5i			0.921587i	−0.887507	+	0.460793i	$0.847565\pi$
$72$	53722.9			1.22132
$73$	−21442.3			−0.470938			−0.235469	−	0.971882i	$-0.575663\pi$
$73$	−21442.3			−0.470938			−0.235469	+	0.971882i	$0.575663\pi$
$74$			23368.4i			0.496077i
$75$	−35601.7			−0.730832
$76$		−	90925.8i		−	1.80573i
$77$		−	45305.7i		−	0.870816i
$78$		−	148487.i		−	2.76345i
$79$	−38480.9			−0.693710			−0.346855	−	0.937919i	$-0.612750\pi$
$79$	−38480.9			−0.693710			−0.346855	+	0.937919i	$0.612750\pi$
$80$			303280.i			5.29809i
$81$	−30201.4			−0.511463
$82$		−	109482.i		−	1.79807i
$83$			114812.i			1.82934i	0.404205	+	0.914668i	$0.367548\pi$
$83$			114812.i			1.82934i	−0.404205	+	0.914668i	$0.632452\pi$
$84$			142093.i			2.19722i
$85$	85096.4			1.27751
$86$	5488.63			0.0800236
$87$		−	95382.9i		−	1.35105i
$88$	215672.			2.96884
$89$	−87567.0			−1.17183			−0.585916	−	0.810372i	$-0.699265\pi$
$89$	−87567.0			−1.17183			−0.585916	+	0.810372i	$0.699265\pi$
$90$			74007.7i			0.963099i
$91$	−140320.			−1.77630
$92$		−	73519.9i		−	0.905598i
$93$	56214.6			0.673972
$94$	197068.			2.30036
$95$	79775.4			0.906901
$96$	−290770.			−3.22011
$97$	89392.4	−	24420.2i	0.964653	−	0.263524i
$97$	89392.4	−	24420.2i	0.964653	−	0.263524i
$98$	−1173.43			−0.0123421
$99$	30616.6			0.313957
$100$	−251466.			−2.51466
$101$	−182389.			−1.77908			−0.889538	−	0.456861i	$-0.848974\pi$
$101$	−182389.			−1.77908			−0.889538	+	0.456861i	$0.848974\pi$
$102$			150502.i			1.43232i
$103$	56377.4			0.523615			0.261808	−	0.965120i	$-0.415681\pi$
$103$	56377.4			0.523615			0.261808	+	0.965120i	$0.415681\pi$
$104$		−	667976.i		−	6.05588i
$105$	−124668.			−1.10352
$106$	−330117.			−2.85367
$107$			109851.i			0.927562i	0.885950	+	0.463781i	$0.153508\pi$
$107$			109851.i			0.927562i	−0.885950	+	0.463781i	$0.846492\pi$
$108$	−363214.			−2.99642
$109$	69732.9			0.562175			0.281087	−	0.959682i	$-0.409305\pi$
$109$	69732.9			0.562175			0.281087	+	0.959682i	$0.409305\pi$
$110$			297105.i			2.34115i
$111$		−	26601.7i		−	0.204928i
$112$			506883.i			3.81823i
$113$	48853.0			0.359911			0.179956	−	0.983675i	$-0.442405\pi$
$113$	48853.0			0.359911			0.179956	+	0.983675i	$0.442405\pi$
$114$			141091.i			1.01680i
$115$	64504.0			0.454823
$116$		−	673720.i		−	4.64873i
$117$		−	94825.5i		−	0.640414i
$118$			81731.7i			0.540363i
$119$	142225.			0.920678
$120$		−	593464.i		−	3.76219i
$121$	−38139.8			−0.236818
$122$	525959.			3.19928
$123$			124630.i			0.742779i
$124$	397062.			2.31902
$125$			20997.6i			0.120197i
$126$			123692.i			0.694088i
$127$			42036.3i			0.231268i	0.993292	+	0.115634i	$0.0368900\pi$
$127$			42036.3i			0.231268i	−0.993292	+	0.115634i	$0.963110\pi$
$128$	−678107.			−3.65825
$129$	−6248.07			−0.0330576
$130$	920192.			4.77551
$131$			341215.i			1.73720i	0.495512	+	0.868601i	$0.334980\pi$
$131$			341215.i			1.73720i	−0.495512	+	0.868601i	$0.665020\pi$
$132$	−385487.			−1.92564
$133$	133332.			0.653587
$134$			43655.1i			0.210026i
$135$		−	318672.i		−	1.50491i
$136$			677041.i			3.13883i
$137$			220369.i			1.00311i	0.865126	+	0.501555i	$0.167238\pi$
$137$			220369.i			1.00311i	−0.865126	+	0.501555i	$0.832762\pi$
$138$			114082.i			0.509941i
$139$			17507.1i			0.0768559i	0.999261	+	0.0384279i	$0.0122350\pi$
$139$			17507.1i			0.0768559i	−0.999261	+	0.0384279i	$0.987765\pi$
$140$	−880568.			−3.79702
$141$	−224335.			−0.950275
$142$		−	429046.i		−	1.78559i
$143$		−	380679.i		−	1.55675i
$144$	−342541.			−1.37659
$145$	591100.			2.33475
$146$	235013.			0.912452
$147$	1335.79			0.00509852
$148$		−	187896.i		−	0.705122i
$149$		−	505750.i		−	1.86625i	−0.359551	−	0.933125i	$-0.617070\pi$
$149$		−	505750.i		−	1.86625i	0.359551	−	0.933125i	$-0.382930\pi$
$150$	390204.			1.41600
$151$	−126612.			−0.451890			−0.225945	−	0.974140i	$-0.572547\pi$
$151$	−126612.			−0.451890			−0.225945	+	0.974140i	$0.572547\pi$
$152$			634706.i			2.22825i
$153$			96112.4i			0.331933i
$154$			496563.i			1.68722i
$155$			348370.i			1.16469i
$156$			1.19393e6i			3.92795i
$157$			94283.9i			0.305273i	0.988282	+	0.152636i	$0.0487764\pi$
$157$			94283.9i			0.305273i	−0.988282	+	0.152636i	$0.951224\pi$
$158$	421761.			1.34408
$159$	375794.			1.17885
$160$		−	1.80194e6i		−	5.56468i
$161$	107808.			0.327783
$162$	331016.			0.990971
$163$	−132130.			−0.389523			−0.194762	−	0.980851i	$-0.562393\pi$
$163$	−132130.			−0.389523			−0.194762	+	0.980851i	$0.562393\pi$
$164$			880302.i			2.55577i
$165$		−	338215.i		−	0.967124i
$166$		−	1.25838e6i		−	3.54438i
$167$	33260.2			0.0922855			0.0461427	−	0.998935i	$-0.485307\pi$
$167$	33260.2			0.0922855			0.0461427	+	0.998935i	$0.485307\pi$
$168$		−	991877.i		−	2.71134i
$169$	−807742.			−2.17548
$170$	−932680.			−2.47520
$171$			90102.6i			0.235639i
$172$	−44132.1			−0.113745
$173$		−	158915.i		−	0.403692i	−0.979417	−	0.201846i	$-0.935306\pi$
$173$		−	158915.i		−	0.403692i	0.979417	−	0.201846i	$-0.0646941\pi$
$174$			1.04542e6i			2.61769i
$175$		−	368744.i		−	0.910186i
$176$	−1.37514e6			−3.34629
$177$		−	93040.5i		−	0.223223i
$178$	959758.			2.27045
$179$			219197.i			0.511331i	0.966765	+	0.255666i	$0.0822946\pi$
$179$			219197.i			0.511331i	−0.966765	+	0.255666i	$0.917705\pi$
$180$		−	595069.i		−	1.36895i
$181$			288008.i			0.653443i	0.945121	+	0.326721i	$0.105944\pi$
$181$			288008.i			0.653443i	−0.945121	+	0.326721i	$0.894056\pi$
$182$	1.53795e6			3.44163
$183$	−598734.			−1.32162
$184$			513205.i			1.11750i
$185$	164854.			0.354137
$186$	−616128.			−1.30584
$187$			385845.i			0.806880i
$188$	−1.58455e6			−3.26973
$189$		−	532608.i		−	1.08456i
$190$	−874360.			−1.75714
$191$	−121421.			−0.240830			−0.120415	−	0.992724i	$-0.538423\pi$
$191$	−121421.			−0.240830			−0.120415	+	0.992724i	$0.538423\pi$
$192$	1.62088e6			3.17319
$193$	−243573.			−0.470690			−0.235345	−	0.971912i	$-0.575622\pi$
$193$	−243573.			−0.470690			−0.235345	+	0.971912i	$0.575622\pi$
$194$	−979765.	+	267652.i	−1.86904	+	0.510582i
$195$	−1.04751e6			−1.97276
$196$	9435.09			0.0175431
$197$	357478.			0.656272			0.328136	−	0.944631i	$-0.393580\pi$
$197$	357478.			0.656272			0.328136	+	0.944631i	$0.393580\pi$
$198$	−335567.			−0.608297
$199$			796599.i			1.42596i	0.701185	+	0.712979i	$0.252655\pi$
$199$			796599.i			1.42596i	−0.701185	+	0.712979i	$0.747345\pi$
$200$	1.75536e6			3.10306
$201$		−	49695.5i		−	0.0867614i
$202$	1.99903e6			3.44700
$203$	987927.			1.68262
$204$		−	1.21013e6i		−	2.03590i
$205$	−772349.			−1.28360
$206$	−617912.			−1.01452
$207$			72854.3i			0.118176i
$208$			4.25906e6i			6.82583i
$209$			361719.i			0.572803i
$210$	1.36639e6			2.13810
$211$		−	230882.i		−	0.357013i	−0.983939	−	0.178506i	$-0.942873\pi$
$211$		−	230882.i		−	0.357013i	0.983939	−	0.178506i	$-0.0571266\pi$
$212$	2.65435e6			4.05620
$213$			488411.i			0.737626i
$214$		−	1.20399e6i		−	1.79717i
$215$		−	38720.1i		−	0.0571269i
$216$	2.53541e6			3.69755
$217$			582243.i			0.839372i
$218$	−764292.			−1.08923
$219$	−267531.			−0.376932
$220$		−	2.38892e6i		−	3.32770i
$221$	1.19504e6			1.64589
$222$			291562.i			0.397053i
$223$		−	846992.i		−	1.14056i	−0.821451	−	0.570279i	$-0.806835\pi$
$223$		−	846992.i		−	1.14056i	0.821451	−	0.570279i	$-0.193165\pi$
$224$		−	3.01165e6i		−	4.01036i
$225$	249190.			0.328151
$226$	−535442.			−0.697335
$227$	−211467.			−0.272382			−0.136191	−	0.990683i	$-0.543486\pi$
$227$	−211467.			−0.272382			−0.136191	+	0.990683i	$0.543486\pi$
$228$		−	1.13446e6i		−	1.44528i
$229$	338053.			0.425987			0.212994	−	0.977054i	$-0.431679\pi$
$229$	338053.			0.425987			0.212994	+	0.977054i	$0.431679\pi$
$230$	−706982.			−0.881229
$231$		−	565270.i		−	0.696989i
$232$			4.70289e6i			5.73647i
$233$		−	916406.i		−	1.10585i	−0.833229	−	0.552927i	$-0.813511\pi$
$233$		−	916406.i		−	1.10585i	0.833229	−	0.552927i	$-0.186489\pi$
$234$			1.03931e6i			1.24081i
$235$		−	1.39023e6i		−	1.64217i
$236$		−	657175.i		−	0.768071i
$237$	−480118.			−0.555236
$238$	−1.55882e6			−1.78383
$239$			746973.i			0.845883i	0.906157	+	0.422941i	$0.139002\pi$
$239$			746973.i			0.845883i	−0.906157	+	0.422941i	$0.860998\pi$
$240$			3.78396e6i			4.24052i
$241$	−934065.			−1.03594			−0.517970	−	0.855399i	$-0.673312\pi$
$241$	−934065.			−1.03594			−0.517970	+	0.855399i	$0.673312\pi$
$242$	418023.			0.458841
$243$	624697.			0.678662
$244$	−4.22905e6			−4.54745
$245$			8278.05i			0.00881075i
$246$		−	1.36598e6i		−	1.43915i
$247$	1.12031e6			1.16841
$248$	−2.77169e6			−2.86164
$249$			1.43249e6i			1.46418i
$250$		−	230139.i		−	0.232885i
$251$		−	1.19939e6i		−	1.20164i	−0.799383	−	0.600821i	$-0.794840\pi$
$251$		−	1.19939e6i		−	1.20164i	0.799383	−	0.600821i	$-0.205160\pi$
$252$		−	994560.i		−	0.986574i
$253$			292475.i			0.287268i
$254$		−	460730.i		−	0.448086i
$255$	1.06173e6			1.02250
$256$	3.27508e6			3.12336
$257$		−	49589.3i		−	0.0468333i	−0.999726	−	0.0234167i	$-0.992546\pi$
$257$		−	49589.3i		−	0.0468333i	0.999726	−	0.0234167i	$-0.00745444\pi$
$258$	68480.5			0.0640498
$259$	275527.			0.255220
$260$	−7.39893e6			−6.78790
$261$			667620.i			0.606636i
$262$		−	3.73981e6i		−	3.36587i
$263$		−	305867.i		−	0.272673i	−0.990663	−	0.136337i	$-0.956467\pi$
$263$		−	305867.i		−	0.272673i	0.990663	−	0.136337i	$-0.0435329\pi$
$264$	2.69089e6			2.37622
$265$			2.32885e6i			2.03716i
$266$	−1.46135e6			−1.26634
$267$	−1.09256e6			−0.937919
$268$		−	351015.i		−	0.298530i
$269$	565161.			0.476202			0.238101	−	0.971240i	$-0.423475\pi$
$269$	565161.			0.476202			0.238101	+	0.971240i	$0.423475\pi$
$270$			3.49273e6i			2.91579i
$271$		−	1.55966e6i		−	1.29005i	−0.764162	−	0.645024i	$-0.776847\pi$
$271$		−	1.55966e6i		−	1.29005i	0.764162	−	0.645024i	$-0.223153\pi$
$272$		−	4.31686e6i		−	3.53790i
$273$	−1.75075e6			−1.42173
$274$		−	2.41530e6i		−	1.94355i
$275$	1.00038e6			0.797686
$276$		−	917293.i		−	0.724828i
$277$			1.59463e6i			1.24870i	0.781143	+	0.624352i	$0.214637\pi$
$277$			1.59463e6i			1.24870i	−0.781143	+	0.624352i	$0.785363\pi$
$278$		−	191883.i		−	0.148910i
$279$	−393467.			−0.302620
$280$	6.14679e6			4.68547
$281$			743017.i			0.561349i	0.959803	+	0.280674i	$0.0905581\pi$
$281$			743017.i			0.561349i	−0.959803	+	0.280674i	$0.909442\pi$
$282$	2.45877e6			1.84118
$283$	−1.45519e6			−1.08007			−0.540036	−	0.841642i	$-0.681589\pi$
$283$	−1.45519e6			−1.08007			−0.540036	+	0.841642i	$0.681589\pi$
$284$			3.44980e6i			2.53804i
$285$	995341.			0.725872
$286$			4.17235e6i			3.01624i
$287$	−1.29085e6			−0.925066
$288$	2.03521e6			1.44586
$289$	208603.			0.146919
$290$	−6.47862e6			−4.52364
$291$	1.11533e6	−	304685.i	0.772095	−	0.210921i
$292$	−1.88965e6			−1.29696
$293$	45073.7			0.0306729			0.0153364	−	0.999882i	$-0.495118\pi$
$293$	45073.7			0.0306729			0.0153364	+	0.999882i	$0.495118\pi$
$294$	−14640.6			−0.00987848
$295$	576585.			0.385752
$296$			1.31161e6i			0.870112i
$297$	1.44493e6			0.950506
$298$			5.54315e6i			3.61590i
$299$	905850.			0.585974
$300$	−3.13749e6			−2.01270
$301$		−	64714.3i		−	0.0411703i
$302$	1.38770e6			0.875546
$303$	−2.27563e6			−1.42395
$304$		−	4.04693e6i		−	2.51155i
$305$		−	3.71043e6i		−	2.28389i
$306$		−	1.05342e6i		−	0.643128i
$307$	−2.45197e6			−1.48480			−0.742402	−	0.669954i	$-0.766314\pi$
$307$	−2.45197e6			−1.48480			−0.742402	+	0.669954i	$0.766314\pi$
$308$		−	3.99268e6i		−	2.39821i
$309$	703410.			0.419095
$310$		−	3.81823e6i		−	2.25661i
$311$		−	2.21710e6i		−	1.29982i	−0.760009	−	0.649912i	$-0.774806\pi$
$311$		−	2.21710e6i		−	1.29982i	0.760009	−	0.649912i	$-0.225194\pi$
$312$		−	8.33420e6i		−	4.84705i
$313$	2.98004e6			1.71934			0.859669	−	0.510852i	$-0.170670\pi$
$313$	2.98004e6			1.71934			0.859669	+	0.510852i	$0.170670\pi$
$314$		−	1.03338e6i		−	0.591473i
$315$	872596.			0.495492
$316$	−3.39123e6			−1.91047
$317$			2.66084e6i			1.48720i	0.668624	+	0.743601i	$0.266884\pi$
$317$			2.66084e6i			1.48720i	−0.668624	+	0.743601i	$0.733116\pi$
$318$	−4.11880e6			−2.28404
$319$			2.68018e6i			1.47464i
$320$			1.00448e7i			5.48360i
$321$			1.37058e6i			0.742408i
$322$	−1.18160e6			−0.635086
$323$	−1.13552e6			−0.605601
$324$	−2.66158e6			−1.40856
$325$		−	3.09835e6i		−	1.62713i
$326$	1.44818e6			0.754709
$327$	870043.			0.449957
$328$		−	6.14493e6i		−	3.15379i
$329$		−	2.32355e6i		−	1.18348i
$330$			3.70692e6i			1.87382i
$331$		−	354982.i		−	0.178089i	−0.996028	−	0.0890444i	$-0.971619\pi$
$331$		−	354982.i		−	0.178089i	0.996028	−	0.0890444i	$-0.0283813\pi$
$332$			1.01181e7i			5.03797i
$333$			186195.i			0.0920149i
$334$	−364541.			−0.178805
$335$	307969.			0.149932
$336$			6.32427e6i			3.05606i
$337$		−	1.20668e6i		−	0.578786i	−0.957210	−	0.289393i	$-0.906547\pi$
$337$		−	1.20668e6i		−	0.578786i	0.957210	−	0.289393i	$-0.0934534\pi$
$338$	8.85307e6			4.21504
$339$	609529.			0.288068
$340$	7.49934e6			3.51824
$341$	−1.57958e6			−0.735625
$342$		−	987549.i		−	0.456555i
$343$			2.18577e6i			1.00316i
$344$	308064.			0.140360
$345$	804803.			0.364034
$346$			1.74175e6i			0.782162i
$347$			2.70571e6i			1.20631i	0.797626	+	0.603153i	$0.206089\pi$
$347$			2.70571e6i			1.20631i	−0.797626	+	0.603153i	$0.793911\pi$
$348$		−	8.40586e6i		−	3.72078i
$349$		−	779832.i		−	0.342719i	−0.985209	−	0.171359i	$-0.945184\pi$
$349$		−	779832.i		−	0.342719i	0.985209	−	0.171359i	$-0.0548159\pi$
$350$			4.04154e6i			1.76350i
$351$		−	4.47521e6i		−	1.93886i
$352$	8.17038e6			3.51468
$353$	2.34517e6			1.00170			0.500850	−	0.865534i	$-0.333021\pi$
$353$	2.34517e6			1.00170			0.500850	+	0.865534i	$0.333021\pi$
$354$			1.01975e6i			0.432499i
$355$	−3.02674e6			−1.27469
$356$	−7.71707e6			−3.22721
$357$	1.77451e6			0.736898
$358$		−	2.40246e6i		−	0.990715i
$359$			1.27800e6i			0.523351i	0.965156	+	0.261676i	$0.0842751\pi$
$359$			1.27800e6i			0.523351i	−0.965156	+	0.261676i	$0.915725\pi$
$360$			4.15387e6i			1.68926i
$361$	1.41159e6			0.570085
$362$		−	3.15664e6i		−	1.26606i
$363$	−475863.			−0.189546
$364$	−1.23661e7			−4.89192
$365$		−	1.65792e6i		−	0.651377i
$366$	6.56228e6			2.56066
$367$			2.43672e6i			0.944366i	0.881501	+	0.472183i	$0.156534\pi$
$367$			2.43672e6i			0.944366i	−0.881501	+	0.472183i	$0.843466\pi$
$368$		−	3.27223e6i		−	1.25957i
$369$		−	872332.i		−	0.333515i
$370$	−1.80685e6			−0.686148
$371$			3.89228e6i			1.46815i
$372$	4.95406e6			1.85611
$373$			707039.i			0.263130i	0.991308	+	0.131565i	$0.0420003\pi$
$373$			707039.i			0.263130i	−0.991308	+	0.131565i	$0.958000\pi$
$374$		−	4.22897e6i		−	1.56335i
$375$			261983.i			0.0962043i
$376$	1.10609e7			4.03480
$377$	8.30101e6			3.00800
$378$			5.83753e6i			2.10136i
$379$	−4.12298e6			−1.47439			−0.737197	−	0.675678i	$-0.763851\pi$
$379$	−4.12298e6			−1.47439			−0.737197	+	0.675678i	$0.763851\pi$
$380$	7.03041e6			2.49759
$381$			524478.i			0.185104i
$382$	1.33081e6			0.466614
$383$			1.06412e6i			0.370676i	0.982675	+	0.185338i	$0.0593379\pi$
$383$			1.06412e6i			0.370676i	−0.982675	+	0.185338i	$0.940662\pi$
$384$	−8.46060e6			−2.92801
$385$	3.50305e6			1.20447
$386$	2.66962e6			0.911972
$387$	43732.6			0.0148432
$388$	7.87793e6	−	2.15209e6i	2.65664	−	0.725740i
$389$	668424.			0.223964			0.111982	−	0.993710i	$-0.464280\pi$
$389$	668424.			0.223964			0.111982	+	0.993710i	$0.464280\pi$
$390$	1.14810e7			3.82226
$391$	−918144.			−0.303717
$392$	−65861.5			−0.0216479
$393$			4.25727e6i			1.39043i
$394$	−3.91806e6			−1.27154
$395$		−	2.97536e6i		−	0.959503i
$396$	2.69817e6			0.864632
$397$	−940056.			−0.299349			−0.149674	−	0.988735i	$-0.547823\pi$
$397$	−940056.			−0.299349			−0.149674	+	0.988735i	$0.547823\pi$
$398$		−	8.73094e6i		−	2.76282i
$399$	1.66355e6			0.523123
$400$	−1.11923e7			−3.49758
$401$			4.88928e6i			1.51839i	0.650862	+	0.759196i	$0.274408\pi$
$401$			4.88928e6i			1.51839i	−0.650862	+	0.759196i	$0.725592\pi$
$402$			544676.i			0.168102i
$403$			4.89226e6i			1.50054i
$404$	−1.60735e7			−4.89955
$405$		−	2.33518e6i		−	0.707430i
$406$	−1.08280e7			−3.26010
$407$			747485.i			0.223675i
$408$			8.44730e6i			2.51228i
$409$			2.95090e6i			0.872261i	0.899883	+	0.436130i	$0.143651\pi$
$409$			2.95090e6i			0.872261i	−0.899883	+	0.436130i	$0.856349\pi$
$410$	8.46515e6			2.48700
$411$			2.74949e6i			0.802875i
$412$	4.96841e6			1.44203
$413$	963667.			0.278004
$414$		−	798503.i		−	0.228968i
$415$	−8.87733e6			−2.53024
$416$		−	2.53052e7i		−	7.16929i
$417$			218432.i			0.0615144i
$418$		−	3.96454e6i		−	1.10982i
$419$	−1.92712e6			−0.536258			−0.268129	−	0.963383i	$-0.586405\pi$
$419$	−1.92712e6			−0.536258			−0.268129	+	0.963383i	$0.586405\pi$
$420$	−1.09867e7			−3.03908
$421$	1.39881e6			0.384639			0.192320	−	0.981332i	$-0.438399\pi$
$421$	1.39881e6			0.384639			0.192320	+	0.981332i	$0.438399\pi$
$422$			2.53053e6i			0.691720i
$423$	1.57020e6			0.426683
$424$	−1.85287e7			−5.00530
$425$			3.14040e6i			0.843360i
$426$		−	5.35311e6i		−	1.42916i
$427$		−	6.20138e6i		−	1.64596i
$428$			9.68086e6i			2.55449i
$429$		−	4.74965e6i		−	1.24600i
$430$			424383.i			0.110684i
$431$	−6.14094e6			−1.59236			−0.796181	−	0.605058i	$-0.793150\pi$
$431$	−6.14094e6			−1.59236			−0.796181	+	0.605058i	$0.793150\pi$
$432$	−1.61659e7			−4.16765
$433$		−	2.35234e6i		−	0.602949i	−0.953474	−	0.301474i	$-0.902521\pi$
$433$		−	2.35234e6i		−	0.602949i	0.953474	−	0.301474i	$-0.0974788\pi$
$434$		−	6.38154e6i		−	1.62630i
$435$	7.37504e6			1.86871
$436$	6.14539e6			1.54822
$437$	−860733.			−0.215608
$438$	2.93221e6			0.730314
$439$		−	3.76713e6i		−	0.932931i	−0.884539	−	0.466466i	$-0.845527\pi$
$439$		−	3.76713e6i		−	0.932931i	0.884539	−	0.466466i	$-0.154473\pi$
$440$			1.66758e7i			4.10634i
$441$	−9349.67			−0.00228929
$442$	−1.30979e7			−3.18894
$443$			4.16101e6i			1.00737i	0.863887	+	0.503686i	$0.168023\pi$
$443$			4.16101e6i			1.00737i	−0.863887	+	0.503686i	$0.831977\pi$
$444$		−	2.34434e6i		−	0.564370i
$445$		−	6.77071e6i		−	1.62082i
$446$			9.28326e6i			2.20985i
$447$		−	6.31013e6i		−	1.49372i
$448$			1.67882e7i			3.95193i
$449$	7.45106e6			1.74422			0.872112	−	0.489307i	$-0.162750\pi$
$449$	7.45106e6			1.74422			0.872112	+	0.489307i	$0.162750\pi$
$450$	−2.73118e6			−0.635799
$451$		−	3.50199e6i		−	0.810726i
$452$	4.30530e6			0.991190
$453$	−1.57971e6			−0.361687
$454$	2.31774e6			0.527746
$455$		−	1.08496e7i		−	2.45689i
$456$			7.91910e6i			1.78346i
$457$		−	3.08010e6i		−	0.689881i	−0.938625	−	0.344941i	$-0.887899\pi$
$457$		−	3.08010e6i		−	0.689881i	0.938625	−	0.344941i	$-0.112101\pi$
$458$	−3.70516e6			−0.825359
$459$			4.53595e6i			1.00493i
$460$	5.68458e6			1.25258
$461$	6.29148e6			1.37880			0.689399	−	0.724382i	$-0.257875\pi$
$461$	6.29148e6			1.37880			0.689399	+	0.724382i	$0.257875\pi$
$462$			6.19551e6i			1.35043i
$463$	−5.73564e6			−1.24345			−0.621727	−	0.783234i	$-0.713568\pi$
$463$	−5.73564e6			−1.24345			−0.621727	+	0.783234i	$0.713568\pi$
$464$		−	2.99859e7i		−	6.46581i
$465$			4.34653e6i			0.932204i
$466$			1.00441e7i			2.14262i
$467$	−4.02600e6			−0.854244			−0.427122	−	0.904194i	$-0.640473\pi$
$467$	−4.02600e6			−0.854244			−0.427122	+	0.904194i	$0.640473\pi$
$468$		−	8.35674e6i		−	1.76369i
$469$	514720.			0.108054
$470$			1.52373e7i			3.18174i
$471$			1.17636e6i			0.244336i
$472$			4.58740e6i			0.947789i
$473$	175565.			0.0360816
$474$	5.26223e6			1.07578
$475$			2.94404e6i			0.598700i
$476$	1.25339e7			2.53553
$477$	−2.63032e6			−0.529314
$478$		−	8.18703e6i		−	1.63892i
$479$	2.51906e6			0.501649			0.250825	−	0.968033i	$-0.419298\pi$
$479$	2.51906e6			0.501649			0.250825	+	0.968033i	$0.419298\pi$
$480$		−	2.24824e7i		−	4.45389i
$481$	2.31510e6			0.456255
$482$	1.02376e7			2.00715
$483$	1.34510e6			0.262353
$484$	−3.36117e6			−0.652195
$485$	1.88818e6	+	6.91185e6i	0.364492	+	1.33426i
$486$	−6.84685e6			−1.31492
$487$	6.01634e6			1.14950			0.574751	−	0.818328i	$-0.305099\pi$
$487$	6.01634e6			1.14950			0.574751	+	0.818328i	$0.305099\pi$
$488$	2.95208e7			5.61150
$489$	−1.64856e6			−0.311769
$490$		−	90729.7i		−	0.0170710i
$491$	−3.49540e6			−0.654324			−0.327162	−	0.944968i	$-0.606092\pi$
$491$	−3.49540e6			−0.654324			−0.327162	+	0.944968i	$0.606092\pi$
$492$			1.09833e7i			2.04560i
$493$	−8.41366e6			−1.55908
$494$	−1.22789e7			−2.26382
$495$			2.36729e6i			0.434248i
$496$	1.76725e7			3.22547
$497$	−5.05871e6			−0.918647
$498$		−	1.57005e7i		−	2.83687i
$499$			6.49072e6i			1.16692i	0.812141	+	0.583461i	$0.198302\pi$
$499$			6.49072e6i			1.16692i	−0.812141	+	0.583461i	$0.801698\pi$
$500$			1.85047e6i			0.331022i
$501$	414980.			0.0738641
$502$			1.31456e7i			2.32821i
$503$	913450.			0.160977			0.0804886	−	0.996756i	$-0.474352\pi$
$503$	913450.			0.160977			0.0804886	+	0.996756i	$0.474352\pi$
$504$			6.94252e6i			1.21742i
$505$		−	1.41024e7i		−	2.46073i
$506$		−	3.20561e6i		−	0.556588i
$507$	−1.00780e7			−1.74123
$508$			3.70456e6i			0.636909i
$509$	−1.84137e6			−0.315027			−0.157513	−	0.987517i	$-0.550348\pi$
$509$	−1.84137e6			−0.315027			−0.157513	+	0.987517i	$0.550348\pi$
$510$	−1.16369e7			−1.98112
$511$		−	2.77095e6i		−	0.469435i
$512$	−1.41963e7			−2.39332
$513$			4.25232e6i			0.713399i
$514$			543512.i			0.0907406i
$515$			4.35912e6i			0.724238i
$516$	−550627.			−0.0910402
$517$	6.30362e6			1.03720
$518$	−3.01985e6			−0.494494
$519$		−	1.98275e6i		−	0.323110i
$520$	5.16481e7			8.37618
$521$	−1.19136e7			−1.92286			−0.961431	−	0.275047i	$-0.911307\pi$
$521$	−1.19136e7			−1.92286			−0.961431	+	0.275047i	$0.911307\pi$
$522$		−	7.31730e6i		−	1.17537i
$523$		−	6.55966e6i		−	1.04864i	−0.851521	−	0.524321i	$-0.824319\pi$
$523$		−	6.55966e6i		−	1.04864i	0.851521	−	0.524321i	$-0.175681\pi$
$524$			3.00705e7i			4.78423i
$525$		−	4.60074e6i		−	0.728500i
$526$			3.35238e6i			0.528310i
$527$		−	4.95866e6i		−	0.777746i
$528$	−1.71573e7			−2.67833
$529$	5.74038e6			0.891870
$530$		−	2.55248e7i		−	3.94705i
$531$			651225.i			0.100229i
$532$	1.17502e7			1.79997
$533$	−1.08463e7			−1.65373
$534$	1.19747e7			1.81724
$535$	−8.49368e6			−1.28296
$536$			2.45026e6i			0.368383i
$537$			2.73488e6i			0.409263i
$538$	−6.19432e6			−0.922651
$539$	−37534.4			−0.00556491
$540$		−	2.80838e7i		−	4.14449i
$541$			5.84285e6i			0.858285i	0.903237	+	0.429143i	$0.141184\pi$
$541$			5.84285e6i			0.858285i	−0.903237	+	0.429143i	$0.858816\pi$
$542$			1.70943e7i			2.49950i
$543$			3.59341e6i			0.523007i
$544$			2.56486e7i			3.71592i
$545$			5.39177e6i			0.777571i
$546$	1.91887e7			2.75463
$547$	−6.07402e6			−0.867976			−0.433988	−	0.900919i	$-0.642894\pi$
$547$	−6.07402e6			−0.867976			−0.433988	+	0.900919i	$0.642894\pi$
$548$			1.94206e7i			2.76255i
$549$	4.19076e6			0.593420
$550$	−1.09644e7			−1.54553
$551$	−7.88756e6			−1.10679
$552$			6.40315e6i			0.894429i
$553$		−	4.97282e6i		−	0.691497i
$554$		−	1.74775e7i		−	2.41939i
$555$	2.05685e6			0.283446
$556$			1.54286e6i			0.211660i
$557$	2.08445e6			0.284678			0.142339	−	0.989818i	$-0.454538\pi$
$557$	2.08445e6			0.284678			0.142339	+	0.989818i	$0.454538\pi$
$558$	4.31251e6			0.586333
$559$		−	543759.i		−	0.0735998i
$560$	−3.91924e7			−5.28118
$561$			4.81411e6i			0.645816i
$562$		−	8.14366e6i		−	1.08762i
$563$			8.27671e6i			1.10049i	0.835003	+	0.550246i	$0.185466\pi$
$563$			8.27671e6i			1.10049i	−0.835003	+	0.550246i	$0.814534\pi$
$564$	−1.97701e7			−2.61704
$565$			3.77733e6i			0.497810i
$566$	1.59493e7			2.09266
$567$		−	3.90287e6i		−	0.509832i
$568$		−	2.40813e7i		−	3.13191i
$569$			2.17889e6i			0.282134i	0.990000	+	0.141067i	$0.0450532\pi$
$569$			2.17889e6i			0.282134i	−0.990000	+	0.141067i	$0.954947\pi$
$570$	−1.09092e7			−1.40639
$571$	−603489.			−0.0774603			−0.0387302	−	0.999250i	$-0.512331\pi$
$571$	−603489.			−0.0774603			−0.0387302	+	0.999250i	$0.512331\pi$
$572$		−	3.35483e7i		−	4.28727i
$573$	−1.51495e6			−0.192757
$574$	1.41481e7			1.79233
$575$			2.38046e6i			0.300256i
$576$	−1.13451e7			−1.42480
$577$		−	307427.i		−	0.0384417i	−0.999815	−	0.0192208i	$-0.993881\pi$
$577$		−	307427.i		−	0.0384417i	0.999815	−	0.0192208i	$-0.00611856\pi$
$578$	−2.28635e6			−0.284658
$579$	−3.03900e6			−0.376734
$580$	5.20922e7			6.42988
$581$	−1.48370e7			−1.82350
$582$	−1.22243e7	+	3.33943e6i	−1.49595	+	0.408663i
$583$	−1.05595e7			−1.28668
$584$	1.31907e7			1.60043
$585$	7.33194e6			0.885787
$586$	−494020.			−0.0594293
$587$		−	7.87226e6i		−	0.942984i	−0.881870	−	0.471492i	$-0.843716\pi$
$587$		−	7.87226e6i		−	0.942984i	0.881870	−	0.471492i	$-0.156284\pi$
$588$	117720.			0.0140412
$589$		−	4.64860e6i		−	0.552120i
$590$	−6.31952e6			−0.747402
$591$	4.46018e6			0.525271
$592$		−	8.36290e6i		−	0.980738i
$593$	4.45994e6			0.520825			0.260413	−	0.965497i	$-0.416141\pi$
$593$	4.45994e6			0.520825			0.260413	+	0.965497i	$0.416141\pi$
$594$	−1.58368e7			−1.84163
$595$			1.09969e7i			1.27343i
$596$		−	4.45705e7i		−	5.13963i
$597$			9.93900e6i			1.14132i
$598$	−9.92837e6			−1.13534
$599$		−	1.68662e6i		−	0.192066i	−0.995378	−	0.0960330i	$-0.969385\pi$
$599$		−	1.68662e6i		−	0.192066i	0.995378	−	0.0960330i	$-0.0306154\pi$
$600$	2.19012e7			2.48365
$601$		−	3.02189e6i		−	0.341265i	−0.985335	−	0.170633i	$-0.945419\pi$
$601$		−	3.02189e6i		−	0.341265i	0.985335	−	0.170633i	$-0.0545811\pi$
$602$			709286.i			0.0797683i
$603$			347837.i			0.0389567i
$604$	−1.11580e7			−1.24450
$605$		−	2.94899e6i		−	0.327555i
$606$	2.49415e7			2.75893
$607$	4.42081e6			0.487001			0.243501	−	0.969901i	$-0.421704\pi$
$607$	4.42081e6			0.487001			0.243501	+	0.969901i	$0.421704\pi$
$608$			2.40448e7i			2.63793i
$609$	1.23262e7			1.34674
$610$			4.06674e7i			4.42508i
$611$		−	1.95235e7i		−	2.11570i
$612$			8.47015e6i			0.914140i
$613$	5.13001e6			0.551400			0.275700	−	0.961244i	$-0.411090\pi$
$613$	5.13001e6			0.551400			0.275700	+	0.961244i	$0.411090\pi$
$614$	2.68743e7			2.87684
$615$	−9.63643e6			−1.02737
$616$			2.78709e7i			2.95937i
$617$	5.10437e6			0.539795			0.269898	−	0.962889i	$-0.413010\pi$
$617$	5.10437e6			0.539795			0.269898	+	0.962889i	$0.413010\pi$
$618$	−7.70956e6			−0.812004
$619$		−	1.32209e7i		−	1.38687i	−0.720521	−	0.693433i	$-0.756097\pi$
$619$		−	1.32209e7i		−	1.38687i	0.720521	−	0.693433i	$-0.243903\pi$
$620$			3.07010e7i			3.20755i
$621$			3.43830e6i			0.357779i
$622$			2.43000e7i			2.51844i
$623$		−	1.13161e7i		−	1.16809i
$624$			5.31394e7i			5.46330i
$625$	−1.05405e7			−1.07935
$626$	−3.26620e7			−3.33125
$627$			4.51309e6i			0.458464i
$628$			8.30901e6i			0.840717i
$629$	−2.34652e6			−0.236482
$630$	−9.56389e6			−0.960026
$631$	−9.93999e6			−0.993831			−0.496916	−	0.867799i	$-0.665534\pi$
$631$	−9.93999e6			−0.993831			−0.496916	+	0.867799i	$0.665534\pi$
$632$	2.36724e7			2.35749
$633$		−	2.88067e6i		−	0.285748i
$634$		−	2.91635e7i		−	2.88148i
$635$	−3.25026e6			−0.319878
$636$	3.31178e7			3.24653
$637$			116251.i			0.0113514i
$638$		−	2.93755e7i		−	2.85715i
$639$		−	3.41857e6i		−	0.331201i
$640$		−	5.24315e7i		−	5.05990i
$641$		−	1.19932e7i		−	1.15289i	−0.817135	−	0.576446i	$-0.804439\pi$
$641$		−	1.19932e7i		−	1.15289i	0.817135	−	0.576446i	$-0.195561\pi$
$642$		−	1.50220e7i		−	1.43843i
$643$	8.00379e6			0.763428			0.381714	−	0.924280i	$-0.375334\pi$
$643$	8.00379e6			0.763428			0.381714	+	0.924280i	$0.375334\pi$
$644$	9.50085e6			0.902709
$645$		−	483103.i		−	0.0457236i
$646$	1.24456e7			1.17336
$647$	1.76907e7			1.66144			0.830721	−	0.556688i	$-0.187928\pi$
$647$	1.76907e7			1.66144			0.830721	+	0.556688i	$0.187928\pi$
$648$	1.85791e7			1.73815
$649$			2.61436e6i			0.243643i
$650$			3.39588e7i			3.15260i
$651$			7.26452e6i			0.671822i
$652$	−1.16443e7			−1.07274
$653$			6.53143e6i			0.599412i	0.954032	+	0.299706i	$0.0968885\pi$
$653$			6.53143e6i			0.599412i	−0.954032	+	0.299706i	$0.903111\pi$
$654$	−9.53591e6			−0.871801
$655$	−2.63829e7			−2.40281
$656$			3.91805e7i			3.55476i
$657$	1.87255e6			0.169246
$658$			2.54667e7i			2.29302i
$659$			2.75274e6i			0.246918i	0.992350	+	0.123459i	$0.0393987\pi$
$659$			2.75274e6i			0.246918i	−0.992350	+	0.123459i	$0.960601\pi$
$660$		−	2.98060e7i		−	2.66345i
$661$	827167.			0.0736359			0.0368179	−	0.999322i	$-0.488278\pi$
$661$	827167.			0.0736359			0.0368179	+	0.999322i	$0.488278\pi$
$662$			3.89070e6i			0.345051i
$663$	1.49102e7			1.31735
$664$		−	7.06295e7i		−	6.21679i
$665$			1.03092e7i			0.904008i
$666$		−	2.04075e6i		−	0.178281i
$667$	−6.37765e6			−0.555068
$668$	2.93114e6			0.254153
$669$		−	1.05677e7i		−	0.912887i
$670$	−3.37543e6			−0.290497
$671$	1.68239e7			1.44251
$672$		−	3.75757e7i		−	3.20984i
$673$	−1.38566e7			−1.17929			−0.589645	−	0.807663i	$-0.700732\pi$
$673$	−1.38566e7			−1.17929			−0.589645	+	0.807663i	$0.700732\pi$
$674$			1.32256e7i			1.12141i
$675$	1.17603e7			0.993479
$676$	−7.11843e7			−5.99125
$677$	234072.			0.0196281			0.00981403	−	0.999952i	$-0.496876\pi$
$677$	234072.			0.0196281			0.00981403	+	0.999952i	$0.496876\pi$
$678$	−6.68060e6			−0.558138
$679$	3.15578e6	+	1.15520e7i	0.262683	+	0.961576i
$680$	−5.23490e7			−4.34147
$681$	−2.63844e6			−0.218011
$682$	1.73127e7			1.42529
$683$	−7.47804e6			−0.613389			−0.306695	−	0.951808i	$-0.599223\pi$
$683$	−7.47804e6			−0.613389			−0.306695	+	0.951808i	$0.599223\pi$
$684$			7.94052e6i			0.648946i
$685$	−1.70390e7			−1.38745
$686$		−	2.39567e7i		−	1.94364i
$687$	4.21782e6			0.340955
$688$	−1.96423e6			−0.158206
$689$			3.27047e7i			2.62459i
$690$	−8.82086e6			−0.705324
$691$	1.99730e7			1.59129			0.795643	−	0.605766i	$-0.207133\pi$
$691$	1.99730e7			1.59129			0.795643	+	0.605766i	$0.207133\pi$
$692$		−	1.40048e7i		−	1.11176i
$693$			3.95654e6i			0.312955i
$694$		−	2.96553e7i		−	2.33724i
$695$	−1.35365e6			−0.106303
$696$			5.86770e7i			4.59140i
$697$	1.09935e7			0.857147
$698$			8.54718e6i			0.664024i
$699$		−	1.14338e7i		−	0.885111i
$700$		−	3.24965e7i		−	2.50664i
$701$	2.27019e7			1.74489			0.872443	−	0.488717i	$-0.162535\pi$
$701$	2.27019e7			1.74489			0.872443	+	0.488717i	$0.162535\pi$
$702$			4.90496e7i			3.75658i
$703$	−2.19980e6			−0.167878
$704$	−4.55452e7			−3.46347
$705$		−	1.73457e7i		−	1.31437i
$706$	−2.57037e7			−1.94081
$707$		−	2.35698e7i		−	1.77340i
$708$		−	8.19944e6i		−	0.614753i
$709$			1.78961e7i			1.33704i	0.743696	+	0.668518i	$0.233071\pi$
$709$			1.78961e7i			1.33704i	−0.743696	+	0.668518i	$0.766929\pi$
$710$	3.31739e7			2.46974
$711$	3.36053e6			0.249306
$712$	5.38689e7			3.98234
$713$		−	3.75872e6i		−	0.276896i
$714$	−1.94491e7			−1.42775
$715$	2.94342e7			2.15322
$716$			1.93173e7i			1.40820i
$717$			9.31982e6i			0.677033i
$718$		−	1.40072e7i		−	1.01400i
$719$		−	2.24722e7i		−	1.62115i	−0.585633	−	0.810576i	$-0.699154\pi$
$719$		−	2.24722e7i		−	1.62115i	0.585633	−	0.810576i	$-0.300846\pi$
$720$		−	2.64854e7i		−	1.90403i
$721$			7.28556e6i			0.521945i
$722$	−1.54714e7			−1.10455
$723$	−1.16541e7			−0.829152
$724$			2.53814e7i			1.79957i
$725$			2.18140e7i			1.54131i
$726$	5.21559e6			0.367250
$727$	1.85580e7			1.30225			0.651127	−	0.758969i	$-0.274296\pi$
$727$	1.85580e7			1.30225			0.651127	+	0.758969i	$0.274296\pi$
$728$	8.63213e7			6.03656
$729$	1.51332e7			1.05466
$730$			1.81713e7i			1.26206i
$731$			551138.i			0.0381476i
$732$	−5.27649e7			−3.63972
$733$	1.17957e7			0.810894			0.405447	−	0.914118i	$-0.367116\pi$
$733$	1.17957e7			0.810894			0.405447	+	0.914118i	$0.367116\pi$
$734$		−	2.67071e7i		−	1.82973i
$735$			103284.i			0.00705201i
$736$			1.94419e7i			1.32296i
$737$			1.39640e6i			0.0946980i
$738$			9.56099e6i			0.646193i
$739$			2.43126e7i			1.63765i	0.574046	+	0.818823i	$0.305373\pi$
$739$			2.43126e7i			1.63765i	−0.574046	+	0.818823i	$0.694627\pi$
$740$	1.45282e7			0.975288
$741$	1.39779e7			0.935182
$742$		−	4.26605e7i		−	2.84457i
$743$	−5.95531e6			−0.395760			−0.197880	−	0.980226i	$-0.563406\pi$
$743$	−5.95531e6			−0.395760			−0.197880	+	0.980226i	$0.563406\pi$
$744$	−3.45817e7			−2.29042
$745$	3.91047e7			2.58130
$746$		−	7.74934e6i		−	0.509821i
$747$		−	1.00265e7i		−	0.657430i
$748$			3.40036e7i			2.22214i
$749$	−1.41958e7			−0.924603
$750$		−	2.87140e6i		−	0.186398i
$751$	−4.81446e6			−0.311493			−0.155746	−	0.987797i	$-0.549778\pi$
$751$	−4.81446e6			−0.311493			−0.155746	+	0.987797i	$0.549778\pi$
$752$	−7.05252e7			−4.54778
$753$		−	1.49645e7i		−	0.961778i
$754$	−9.09813e7			−5.82806
$755$		−	9.78968e6i		−	0.625031i
$756$		−	4.69375e7i		−	2.98686i
$757$			1.21358e7i			0.769712i	0.922977	+	0.384856i	$0.125749\pi$
$757$			1.21358e7i			0.769712i	−0.922977	+	0.384856i	$0.874251\pi$
$758$	4.51890e7			2.85667
$759$			3.64915e6i			0.229926i
$760$	−4.90757e7			−3.08200
$761$			8.94667e6i			0.560015i	0.959998	+	0.280008i	$0.0903370\pi$
$761$			8.94667e6i			0.560015i	−0.959998	+	0.280008i	$0.909663\pi$
$762$		−	5.74843e6i		−	0.358642i
$763$			9.01146e6i			0.560382i
$764$	−1.07006e7			−0.663243
$765$	−7.43144e6			−0.459113
$766$		−	1.16631e7i		−	0.718192i
$767$	8.09716e6			0.496986
$768$	4.08625e7			2.49990
$769$		−	1.13075e7i		−	0.689529i	−0.938689	−	0.344765i	$-0.887959\pi$
$769$		−	1.13075e7i		−	0.689529i	0.938689	−	0.344765i	$-0.112041\pi$
$770$	−3.83944e7			−2.33368
$771$		−	618715.i		−	0.0374848i
$772$	−2.14655e7			−1.29627
$773$	−2.30217e6			−0.138576			−0.0692882	−	0.997597i	$-0.522073\pi$
$773$	−2.30217e6			−0.138576			−0.0692882	+	0.997597i	$0.522073\pi$
$774$	−479321.			−0.0287590
$775$	−1.28563e7			−0.768883
$776$	−5.49918e7	+	1.50226e7i	−3.27826	+	0.895554i
$777$	3.43769e6			0.204275
$778$	−7.32610e6			−0.433934
$779$	1.03061e7			0.608487
$780$	−9.23149e7			−5.43294
$781$		−	1.37239e7i		−	0.805101i
$782$	1.00631e7			0.588458
$783$			3.15078e7i			1.83660i
$784$	419937.			0.0244003
$785$	−7.29006e6			−0.422238
$786$		−	4.66609e7i		−	2.69399i
$787$	1.70451e7			0.980985			0.490492	−	0.871446i	$-0.336817\pi$
$787$	1.70451e7			0.980985			0.490492	+	0.871446i	$0.336817\pi$
$788$	3.15037e7			1.80736
$789$		−	3.81623e6i		−	0.218244i
$790$			3.26107e7i			1.85906i
$791$			6.31319e6i			0.358763i
$792$	−1.88345e7			−1.06695
$793$		−	5.21068e7i		−	2.94246i
$794$	1.03033e7			0.579994
$795$			2.90565e7i			1.63052i
$796$			7.02023e7i			3.92707i
$797$			2.82937e7i			1.57777i	0.614539	+	0.788887i	$0.289342\pi$
$797$			2.82937e7i			1.57777i	−0.614539	+	0.788887i	$0.710658\pi$
$798$	−1.82330e7			−1.01356
$799$			1.97885e7i			1.09659i
$800$	6.64989e7			3.67358
$801$	7.64720e6			0.421135
$802$		−	5.35878e7i		−	2.94192i
$803$	7.51738e6			0.411412
$804$		−	4.37954e6i		−	0.238940i
$805$			8.33574e6i			0.453372i
$806$		−	5.36205e7i		−	2.90733i
$807$	7.05139e6			0.381146
$808$	1.12201e8			6.04599
$809$	2.96599e7			1.59330			0.796651	−	0.604440i	$-0.206603\pi$
$809$	2.96599e7			1.59330			0.796651	+	0.604440i	$0.206603\pi$
$810$			2.55942e7i			1.37066i
$811$	−2.03879e7			−1.08848			−0.544240	−	0.838929i	$-0.683182\pi$
$811$	−2.03879e7			−1.08848			−0.544240	+	0.838929i	$0.683182\pi$
$812$	8.70636e7			4.63390
$813$		−	1.94595e7i		−	1.03254i
$814$		−	8.19264e6i		−	0.433374i
$815$		−	1.02164e7i		−	0.538768i
$816$		−	5.38605e7i		−	2.83169i
$817$			516676.i			0.0270809i
$818$		−	3.23427e7i		−	1.69002i
$819$	1.22541e7			0.638371
$820$	−6.80652e7			−3.53501
$821$		−	1.62008e7i		−	0.838840i	−0.907792	−	0.419420i	$-0.862233\pi$
$821$		−	1.62008e7i		−	0.838840i	0.907792	−	0.419420i	$-0.137767\pi$
$822$		−	3.01352e7i		−	1.55559i
$823$	−1.27062e7			−0.653907			−0.326954	−	0.945040i	$-0.606022\pi$
$823$	−1.27062e7			−0.653907			−0.326954	+	0.945040i	$0.606022\pi$
$824$	−3.46819e7			−1.77945
$825$	1.24815e7			0.638457
$826$	−1.05620e7			−0.538639
$827$			3.08158e7i			1.56679i	0.621526	+	0.783394i	$0.286513\pi$
$827$			3.08158e7i			1.56679i	−0.621526	+	0.783394i	$0.713487\pi$
$828$			6.42047e6i			0.325455i
$829$	1.34381e7			0.679126			0.339563	−	0.940583i	$-0.389721\pi$
$829$	1.34381e7			0.679126			0.339563	+	0.940583i	$0.389721\pi$
$830$	9.72980e7			4.90240
$831$			1.98958e7i			0.999445i
$832$			1.41062e8i			7.06483i
$833$		−	117829.i		−	0.00588355i
$834$		−	2.39408e6i		−	0.119185i
$835$			2.57169e6i			0.127644i
$836$			3.18774e7i			1.57749i
$837$	−1.85694e7			−0.916186
$838$	2.11218e7			1.03901
$839$			2.02403e7i			0.992684i	0.868127	+	0.496342i	$0.165324\pi$
$839$			2.02403e7i			0.992684i	−0.868127	+	0.496342i	$0.834676\pi$
$840$	7.66923e7			3.75019
$841$	−3.79322e7			−1.84935
$842$	−1.53313e7			−0.745247
$843$			9.27046e6i			0.449296i
$844$		−	2.03471e7i		−	0.983209i
$845$		−	6.24549e7i		−	3.00902i
$846$	−1.72099e7			−0.826707
$847$		−	4.92874e6i		−	0.236063i
$848$	1.18140e8			5.64167
$849$	−1.81561e7			−0.864475
$850$		−	3.44197e7i		−	1.63403i
$851$	−1.77869e6			−0.0841930
$852$			4.30424e7i			2.03141i
$853$		−	5.05236e6i		−	0.237751i	−0.992909	−	0.118875i	$-0.962071\pi$
$853$		−	5.05236e6i		−	0.237751i	0.992909	−	0.118875i	$-0.0379289\pi$
$854$			6.79688e7i			3.18908i
$855$	−6.96676e6			−0.325924
$856$		−	6.75771e7i		−	3.15221i
$857$	−4.11264e7			−1.91280			−0.956398	−	0.292066i	$-0.905657\pi$
$857$	−4.11264e7			−1.91280			−0.956398	+	0.292066i	$0.905657\pi$
$858$			5.20575e7i			2.41415i
$859$		−	6.49889e6i		−	0.300508i	−0.988647	−	0.150254i	$-0.951991\pi$
$859$		−	6.49889e6i		−	0.300508i	0.988647	−	0.150254i	$-0.0480092\pi$
$860$		−	3.41231e6i		−	0.157327i
$861$	−1.61057e7			−0.740410
$862$	6.73064e7			3.08524
$863$			1.41643e7i			0.647393i	0.946161	+	0.323696i	$0.104926\pi$
$863$			1.41643e7i			0.647393i	−0.946161	+	0.323696i	$0.895074\pi$
$864$	9.60499e7			4.37736
$865$	1.22874e7			0.558366
$866$			2.57823e7i			1.16823i
$867$	2.60270e6			0.117592
$868$			5.13116e7i			2.31162i
$869$	1.34909e7			0.606027
$870$	−8.08324e7			−3.62066
$871$	4.32491e6			0.193166
$872$	−4.28978e7			−1.91049
$873$	−7.80661e6	+	2.13261e6i	−0.346678	+	0.0947055i
$874$	9.43387e6			0.417745
$875$	−2.71348e6			−0.119814
$876$	−2.35768e7			−1.03807
$877$	−1.64644e7			−0.722846			−0.361423	−	0.932402i	$-0.617709\pi$
$877$	−1.64644e7			−0.722846			−0.361423	+	0.932402i	$0.617709\pi$
$878$			4.12888e7i			1.80757i
$879$	562376.			0.0245502
$880$		−	1.06326e8i		−	4.62842i
$881$	1.98872e6			0.0863243			0.0431621	−	0.999068i	$-0.486257\pi$
$881$	1.98872e6			0.0863243			0.0431621	+	0.999068i	$0.486257\pi$
$882$	102475.			0.00443554
$883$		−	3.28725e6i		−	0.141883i	−0.997480	−	0.0709415i	$-0.977400\pi$
$883$		−	3.28725e6i		−	0.141883i	0.997480	−	0.0709415i	$-0.0226004\pi$
$884$	1.05316e8			4.53275
$885$	7.19393e6			0.308751
$886$		−	4.56058e7i		−	1.95180i
$887$			5.39047e6i			0.230047i	0.993363	+	0.115024i	$0.0366944\pi$
$887$			5.39047e6i			0.230047i	−0.993363	+	0.115024i	$0.963306\pi$
$888$			1.63647e7i			0.696426i
$889$	−5.43228e6			−0.230530
$890$			7.42088e7i			3.14037i
$891$	1.05882e7			0.446816
$892$		−	7.46434e7i		−	3.14108i
$893$			1.85511e7i			0.778468i
$894$			6.91608e7i			2.89412i
$895$	−1.69484e7			−0.707247
$896$		−	8.76306e7i		−	3.64658i
$897$	1.13021e7			0.469006
$898$	−8.16656e7			−3.37947
$899$		−	3.44440e7i		−	1.42140i
$900$	2.19605e7			0.903723
$901$		−	3.31485e7i		−	1.36036i
$902$			3.83828e7i			1.57080i
$903$		−	807427.i		−	0.0329522i
$904$	−3.00531e7			−1.22312
$905$	−2.22689e7			−0.903808
$906$	1.73141e7			0.700775
$907$			3.72525e7i			1.50362i	0.659382	+	0.751808i	$0.270818\pi$
$907$			3.72525e7i			1.50362i	−0.659382	+	0.751808i	$0.729182\pi$
$908$	−1.86361e7			−0.750137
$909$	1.59280e7			0.639367
$910$			1.18915e8i			4.76028i
$911$		−	2.39819e7i		−	0.957385i	−0.877983	−	0.478693i	$-0.841111\pi$
$911$		−	2.39819e7i		−	0.957385i	0.877983	−	0.478693i	$-0.158889\pi$
$912$		−	5.04927e7i		−	2.01021i
$913$		−	4.02517e7i		−	1.59811i
$914$			3.37587e7i			1.33666i
$915$		−	4.62943e7i		−	1.82799i
$916$	2.97918e7			1.17316
$917$	−4.40947e7			−1.73166
$918$		−	4.97152e7i		−	1.94707i
$919$			3.25978e7i			1.27321i	0.771190	+	0.636605i	$0.219662\pi$
$919$			3.25978e7i			1.27321i	−0.771190	+	0.636605i	$0.780338\pi$
$920$	−3.96812e7			−1.54566
$921$	−3.05927e7			−1.18842
$922$	−6.89563e7			−2.67145
$923$	−4.25055e7			−1.64226
$924$		−	4.98159e7i		−	1.91950i
$925$			6.08380e6i			0.233787i
$926$	6.28642e7			2.40922
$927$	−4.92343e6			−0.188178
$928$			1.78162e8i			6.79116i
$929$		−	2.96689e7i		−	1.12788i	−0.825817	−	0.563939i	$-0.809285\pi$
$929$		−	2.96689e7i		−	1.12788i	0.825817	−	0.563939i	$-0.190715\pi$
$930$		−	4.76392e7i		−	1.80616i
$931$		−	110461.i		−	0.00417672i
$932$		−	8.07606e7i		−	3.04551i
$933$		−	2.76623e7i		−	1.04036i
$934$	4.41261e7			1.65512
$935$	−2.98337e7			−1.11604
$936$			5.83341e7i			2.17637i
$937$	2.25654e7			0.839640			0.419820	−	0.907607i	$-0.362093\pi$
$937$	2.25654e7			0.839640			0.419820	+	0.907607i	$0.362093\pi$
$938$	−5.64147e6			−0.209356
$939$	3.71813e7			1.37613
$940$		−	1.22518e8i		−	4.52252i
$941$			2.48205e7i			0.913770i	0.889526	+	0.456885i	$0.151035\pi$
$941$			2.48205e7i			0.913770i	−0.889526	+	0.456885i	$0.848965\pi$
$942$		−	1.28932e7i		−	0.473407i
$943$	8.33322e6			0.305164
$944$		−	2.92496e7i		−	1.06829i
$945$	4.11815e7			1.50011
$946$	−1.92424e6			−0.0699088
$947$		−	4.69323e7i		−	1.70058i	−0.526316	−	0.850289i	$-0.676427\pi$
$947$		−	4.69323e7i		−	1.70058i	0.526316	−	0.850289i	$-0.323573\pi$
$948$	−4.23117e7			−1.52911
$949$		−	2.32827e7i		−	0.839206i
$950$		−	3.22674e7i		−	1.15999i
$951$			3.31987e7i			1.19034i
$952$	−8.74928e7			−3.12882
$953$			4.50650e7i			1.60734i	0.595078	+	0.803668i	$0.297121\pi$
$953$			4.50650e7i			1.60734i	−0.595078	+	0.803668i	$0.702879\pi$
$954$	2.88290e7			1.02556
$955$		−	9.38833e6i		−	0.333104i
$956$			6.58289e7i			2.32955i
$957$			3.34400e7i			1.18028i
$958$	−2.76096e7			−0.971956
$959$	−2.84779e7			−0.999910
$960$			1.25327e8i			4.38900i
$961$	−8.32928e6			−0.290937
$962$	−2.53742e7			−0.884003
$963$		−	9.59322e6i		−	0.333349i
$964$	−8.23169e7			−2.85296
$965$		−	1.88331e7i		−	0.651034i
$966$	−1.47426e7			−0.508314
$967$	−2.67456e7			−0.919784			−0.459892	−	0.887975i	$-0.652112\pi$
$967$	−2.67456e7			−0.919784			−0.459892	+	0.887975i	$0.652112\pi$
$968$	2.34626e7			0.804800
$969$	−1.41676e7			−0.484715
$970$	−2.06949e7	−	7.57557e7i	−0.706211	−	2.58515i
$971$	−3.90194e6			−0.132811			−0.0664053	−	0.997793i	$-0.521153\pi$
$971$	−3.90194e6			−0.132811			−0.0664053	+	0.997793i	$0.521153\pi$
$972$	5.50530e7			1.86903
$973$	−2.26241e6			−0.0766107
$974$	−6.59407e7			−2.22718
$975$		−	3.86575e7i		−	1.30233i
$976$	−1.88227e8			−6.32494
$977$			4.70491e7i			1.57694i	0.615074	+	0.788469i	$0.289126\pi$
$977$			4.70491e7i			1.57694i	−0.615074	+	0.788469i	$0.710874\pi$
$978$	1.80687e7			0.604059
$979$	3.06998e7			1.02372
$980$			729524.i			0.0242647i
$981$	−6.08975e6			−0.202035
$982$	3.83105e7			1.26777
$983$		−	2.16849e7i		−	0.715769i	−0.933766	−	0.357885i	$-0.883498\pi$
$983$		−	2.16849e7i		−	0.715769i	0.933766	−	0.357885i	$-0.116502\pi$
$984$		−	7.66691e7i		−	2.52425i
$985$			2.76403e7i			0.907721i
$986$	9.22160e7			3.02075
$987$		−	2.89904e7i		−	0.947244i
$988$	9.87303e7			3.21779
$989$			417769.i			0.0135814i
$990$		−	2.59461e7i		−	0.841365i
$991$			3.97245e7i			1.28491i	0.766322	+	0.642457i	$0.222085\pi$
$991$			3.97245e7i			1.28491i	−0.766322	+	0.642457i	$0.777915\pi$
$992$	−1.05001e8			−3.38777
$993$		−	4.42904e6i		−	0.142540i
$994$	5.54448e7			1.77990
$995$	−6.15933e7			−1.97231
$996$			1.26242e8i			4.03232i
$997$	−4.82543e6			−0.153744			−0.0768720	−	0.997041i	$-0.524493\pi$
$997$	−4.82543e6			−0.153744			−0.0768720	+	0.997041i	$0.524493\pi$
$998$		−	7.11401e7i		−	2.26094i
$999$			8.78734e6i			0.278576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.6.b.a.96.2	yes	40
97.96	even	2	inner	97.6.b.a.96.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.6.b.a.96.1	✓	40	97.96	even	2	inner
97.6.b.a.96.2	yes	40	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-10.9603 q^{2} +12.4768 q^{3} +88.1276 q^{4} +77.3203i q^{5} -136.749 q^{6} +129.228i q^{7} -615.173 q^{8} -87.3297 q^{9} -847.452i q^{10} -350.587 q^{11} +1099.55 q^{12} +1085.83i q^{13} -1416.38i q^{14} +964.710i q^{15} +3922.38 q^{16} -1100.57i q^{17} +957.157 q^{18} -1031.75i q^{19} +6814.05i q^{20} +1612.35i q^{21} +3842.53 q^{22} -834.244i q^{23} -7675.39 q^{24} -2853.43 q^{25} -11901.0i q^{26} -4121.45 q^{27} +11388.6i q^{28} -7644.83i q^{29} -10573.5i q^{30} +4505.54 q^{31} -23304.9 q^{32} -4374.20 q^{33} +12062.5i q^{34} -9991.97 q^{35} -7696.15 q^{36} -2132.10i q^{37} +11308.3i q^{38} +13547.7i q^{39} -47565.4i q^{40} +9988.95i q^{41} -17671.8i q^{42} -500.775 q^{43} -30896.4 q^{44} -6752.36i q^{45} +9143.54i q^{46} -17980.2 q^{47} +48938.8 q^{48} +107.062 q^{49} +31274.4 q^{50} -13731.6i q^{51} +95691.9i q^{52} +30119.4 q^{53} +45172.3 q^{54} -27107.5i q^{55} -79497.8i q^{56} -12873.0i q^{57} +83789.4i q^{58} -7457.09i q^{59} +85017.5i q^{60} -47987.8 q^{61} -49381.9 q^{62} -11285.5i q^{63} +129911. q^{64} -83957.0 q^{65} +47942.4 q^{66} -3983.03i q^{67} -96990.5i q^{68} -10408.7i q^{69} +109515. q^{70} +39145.5i q^{71} +53722.9 q^{72} -21442.3 q^{73} +23368.4i q^{74} -35601.7 q^{75} -90925.8i q^{76} -45305.7i q^{77} -148487. i q^{78} -38480.9 q^{79} +303280. i q^{80} -30201.4 q^{81} -109482. i q^{82} +114812. i q^{83} +142093. i q^{84} +85096.4 q^{85} +5488.63 q^{86} -95382.9i q^{87} +215672. q^{88} -87567.0 q^{89} +74007.7i q^{90} -140320. q^{91} -73519.9i q^{92} +56214.6 q^{93} +197068. q^{94} +79775.4 q^{95} -290770. q^{96} +(89392.4 - 24420.2i) q^{97} -1173.43 q^{98} +30616.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} + 40 q^{3} + 638 q^{4} - 130 q^{6} + 180 q^{8} + 3300 q^{9} + 382 q^{11} + 2586 q^{12} + 10174 q^{16} + 4738 q^{18} + 1996 q^{22} - 3102 q^{24} - 25178 q^{25} + 3046 q^{27} + 14796 q^{31}+ \cdots - 562238 q^{99}+O(q^{100}) \) 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

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