LMFDB - Embedded newform 97.6.b.a.96.18

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			96.18
Character	$\chi$	$=$	97.96
Dual form			97.6.b.a.96.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.57129 q^{2} +15.1707 q^{3} -25.3885 q^{4} +24.3473i q^{5} -39.0083 q^{6} -87.8859i q^{7} +147.562 q^{8} -12.8494 q^{9} -62.6040i q^{10} +375.650 q^{11} -385.161 q^{12} +791.342i q^{13} +225.980i q^{14} +369.366i q^{15} +433.005 q^{16} -346.318i q^{17} +33.0395 q^{18} +2181.77i q^{19} -618.141i q^{20} -1333.29i q^{21} -965.905 q^{22} -401.963i q^{23} +2238.63 q^{24} +2532.21 q^{25} -2034.77i q^{26} -3881.42 q^{27} +2231.29i q^{28} +8186.13i q^{29} -949.747i q^{30} +8231.63 q^{31} -5835.38 q^{32} +5698.88 q^{33} +890.484i q^{34} +2139.79 q^{35} +326.226 q^{36} +4635.74i q^{37} -5609.97i q^{38} +12005.2i q^{39} +3592.75i q^{40} +15429.3i q^{41} +3428.28i q^{42} +10051.0 q^{43} -9537.18 q^{44} -312.848i q^{45} +1033.56i q^{46} -1002.30 q^{47} +6569.00 q^{48} +9083.07 q^{49} -6511.04 q^{50} -5253.89i q^{51} -20091.0i q^{52} +10085.9 q^{53} +9980.25 q^{54} +9146.07i q^{55} -12968.7i q^{56} +33099.1i q^{57} -21048.9i q^{58} -43554.4i q^{59} -9377.64i q^{60} -49923.9 q^{61} -21165.9 q^{62} +1129.28i q^{63} +1148.28 q^{64} -19267.0 q^{65} -14653.5 q^{66} -45710.3i q^{67} +8792.48i q^{68} -6098.07i q^{69} -5502.01 q^{70} -50043.1i q^{71} -1896.09 q^{72} -56338.0 q^{73} -11919.8i q^{74} +38415.4 q^{75} -55391.9i q^{76} -33014.3i q^{77} -30868.9i q^{78} -7796.78 q^{79} +10542.5i q^{80} -55761.5 q^{81} -39673.2i q^{82} +87350.6i q^{83} +33850.2i q^{84} +8431.91 q^{85} -25844.0 q^{86} +124189. i q^{87} +55431.8 q^{88} +133363. q^{89} +804.423i q^{90} +69547.8 q^{91} +10205.2i q^{92} +124880. q^{93} +2577.21 q^{94} -53120.3 q^{95} -88526.9 q^{96} +(-47035.9 + 79843.4i) q^{97} -23355.2 q^{98} -4826.87 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.57129			−0.454544			−0.227272	−	0.973831i	$-0.572981\pi$
$2$	−2.57129			−0.454544			−0.227272	+	0.973831i	$0.572981\pi$
$3$	15.1707			0.973202			0.486601	−	0.873624i	$-0.338237\pi$
$3$	15.1707			0.973202			0.486601	+	0.873624i	$0.338237\pi$
$4$	−25.3885			−0.793390
$5$			24.3473i			0.435538i	0.976000	+	0.217769i	$0.0698779\pi$
$5$			24.3473i			0.435538i	−0.976000	+	0.217769i	$0.930122\pi$
$6$	−39.0083			−0.442363
$7$		−	87.8859i		−	0.677913i	−0.940802	−	0.338957i	$-0.889926\pi$
$7$		−	87.8859i		−	0.677913i	0.940802	−	0.338957i	$-0.110074\pi$
$8$	147.562			0.815175
$9$	−12.8494			−0.0528781
$10$		−	62.6040i		−	0.197971i
$11$	375.650			0.936056			0.468028	−	0.883714i	$-0.344965\pi$
$11$	375.650			0.936056			0.468028	+	0.883714i	$0.344965\pi$
$12$	−385.161			−0.772128
$13$			791.342i			1.29869i	0.760494	+	0.649345i	$0.224957\pi$
$13$			791.342i			1.29869i	−0.760494	+	0.649345i	$0.775043\pi$
$14$			225.980i			0.308142i
$15$			369.366i			0.423866i
$16$	433.005			0.422857
$17$		−	346.318i		−	0.290638i	−0.989385	−	0.145319i	$-0.953579\pi$
$17$		−	346.318i		−	0.290638i	0.989385	−	0.145319i	$-0.0464209\pi$
$18$	33.0395			0.0240355
$19$			2181.77i			1.38652i	0.720688	+	0.693259i	$0.243826\pi$
$19$			2181.77i			1.38652i	−0.720688	+	0.693259i	$0.756174\pi$
$20$		−	618.141i		−	0.345551i
$21$		−	1333.29i		−	0.659746i
$22$	−965.905			−0.425479
$23$		−	401.963i		−	0.158441i	−0.996857	−	0.0792204i	$-0.974757\pi$
$23$		−	401.963i		−	0.158441i	0.996857	−	0.0792204i	$-0.0252431\pi$
$24$	2238.63			0.793330
$25$	2532.21			0.810307
$26$		−	2034.77i		−	0.590312i
$27$	−3881.42			−1.02466
$28$			2231.29i			0.537849i
$29$			8186.13i			1.80752i	0.428037	+	0.903761i	$0.359205\pi$
$29$			8186.13i			1.80752i	−0.428037	+	0.903761i	$0.640795\pi$
$30$		−	949.747i		−	0.192666i
$31$	8231.63			1.53844			0.769222	−	0.638982i	$-0.220644\pi$
$31$	8231.63			1.53844			0.769222	+	0.638982i	$0.220644\pi$
$32$	−5835.38			−1.00738
$33$	5698.88			0.910971
$34$			890.484i			0.132108i
$35$	2139.79			0.295257
$36$	326.226			0.0419530
$37$			4635.74i			0.556692i	0.960481	+	0.278346i	$0.0897862\pi$
$37$			4635.74i			0.556692i	−0.960481	+	0.278346i	$0.910214\pi$
$38$		−	5609.97i		−	0.630234i
$39$			12005.2i			1.26389i
$40$			3592.75i			0.355040i
$41$			15429.3i			1.43346i	0.697349	+	0.716731i	$0.254363\pi$
$41$			15429.3i			1.43346i	−0.697349	+	0.716731i	$0.745637\pi$
$42$			3428.28i			0.299884i
$43$	10051.0			0.828968			0.414484	−	0.910056i	$-0.363962\pi$
$43$	10051.0			0.828968			0.414484	+	0.910056i	$0.363962\pi$
$44$	−9537.18			−0.742657
$45$		−	312.848i		−	0.0230304i
$46$			1033.56i			0.0720183i
$47$	−1002.30			−0.0661843			−0.0330921	−	0.999452i	$-0.510535\pi$
$47$	−1002.30			−0.0661843			−0.0330921	+	0.999452i	$0.510535\pi$
$48$	6569.00			0.411525
$49$	9083.07			0.540434
$50$	−6511.04			−0.368320
$51$		−	5253.89i		−	0.282850i
$52$		−	20091.0i		−	1.03037i
$53$	10085.9			0.493203			0.246601	−	0.969117i	$-0.420686\pi$
$53$	10085.9			0.493203			0.246601	+	0.969117i	$0.420686\pi$
$54$	9980.25			0.465755
$55$			9146.07i			0.407688i
$56$		−	12968.7i		−	0.552618i
$57$			33099.1i			1.34936i
$58$		−	21048.9i		−	0.821599i
$59$		−	43554.4i		−	1.62893i	−0.580214	−	0.814464i	$-0.697031\pi$
$59$		−	43554.4i		−	1.62893i	0.580214	−	0.814464i	$-0.302969\pi$
$60$		−	9377.64i		−	0.336291i
$61$	−49923.9			−1.71785			−0.858923	−	0.512104i	$-0.828866\pi$
$61$	−49923.9			−1.71785			−0.858923	+	0.512104i	$0.828866\pi$
$62$	−21165.9			−0.699291
$63$			1129.28i			0.0358468i
$64$	1148.28			0.0350428
$65$	−19267.0			−0.565629
$66$	−14653.5			−0.414077
$67$		−	45710.3i		−	1.24402i	−0.783009	−	0.622010i	$-0.786316\pi$
$67$		−	45710.3i		−	1.24402i	0.783009	−	0.622010i	$-0.213684\pi$
$68$			8792.48i			0.230589i
$69$		−	6098.07i		−	0.154195i
$70$	−5502.01			−0.134207
$71$		−	50043.1i		−	1.17814i	−0.808080	−	0.589072i	$-0.799493\pi$
$71$		−	50043.1i		−	1.17814i	0.808080	−	0.589072i	$-0.200507\pi$
$72$	−1896.09			−0.0431049
$73$	−56338.0			−1.23736			−0.618678	−	0.785645i	$-0.712331\pi$
$73$	−56338.0			−1.23736			−0.618678	+	0.785645i	$0.712331\pi$
$74$		−	11919.8i		−	0.253041i
$75$	38415.4			0.788592
$76$		−	55391.9i		−	1.10005i
$77$		−	33014.3i		−	0.634565i
$78$		−	30868.9i		−	0.574493i
$79$	−7796.78			−0.140555			−0.0702777	−	0.997527i	$-0.522389\pi$
$79$	−7796.78			−0.140555			−0.0702777	+	0.997527i	$0.522389\pi$
$80$			10542.5i			0.184170i
$81$	−55761.5			−0.944326
$82$		−	39673.2i		−	0.651572i
$83$			87350.6i			1.39178i	0.718148	+	0.695890i	$0.244990\pi$
$83$			87350.6i			1.39178i	−0.718148	+	0.695890i	$0.755010\pi$
$84$			33850.2i			0.523436i
$85$	8431.91			0.126584
$86$	−25844.0			−0.376803
$87$			124189.i			1.75908i
$88$	55431.8			0.763049
$89$	133363.			1.78468			0.892340	−	0.451364i	$-0.149063\pi$
$89$	133363.			1.78468			0.892340	+	0.451364i	$0.149063\pi$
$90$			804.423i			0.0104684i
$91$	69547.8			0.880400
$92$			10205.2i			0.125705i
$93$	124880.			1.49722
$94$	2577.21			0.0300837
$95$	−53120.3			−0.603881
$96$	−88526.9			−0.980386
$97$	−47035.9	+	79843.4i	−0.507575	+	0.861608i
$97$	−47035.9	+	79843.4i	−0.507575	+	0.861608i
$98$	−23355.2			−0.245651
$99$	−4826.87			−0.0494969
$100$	−64288.9			−0.642889
$101$	74871.0			0.730315			0.365157	−	0.930946i	$-0.381015\pi$
$101$	74871.0			0.730315			0.365157	+	0.930946i	$0.381015\pi$
$102$			13509.3i			0.128568i
$103$	−56654.4			−0.526187			−0.263094	−	0.964770i	$-0.584743\pi$
$103$	−56654.4			−0.526187			−0.263094	+	0.964770i	$0.584743\pi$
$104$			116772.i			1.05866i
$105$	32462.1			0.287345
$106$	−25933.8			−0.224182
$107$		−	157509.i		−	1.32998i	−0.746852	−	0.664991i	$-0.768435\pi$
$107$		−	157509.i		−	1.32998i	0.746852	−	0.664991i	$-0.231565\pi$
$108$	98543.3			0.812957
$109$	12968.0			0.104546			0.0522729	−	0.998633i	$-0.483353\pi$
$109$	12968.0			0.104546			0.0522729	+	0.998633i	$0.483353\pi$
$110$		−	23517.2i		−	0.185312i
$111$			70327.6i			0.541774i
$112$		−	38055.1i		−	0.286660i
$113$	−113394.			−0.835400			−0.417700	−	0.908585i	$-0.637164\pi$
$113$	−113394.			−0.835400			−0.417700	+	0.908585i	$0.637164\pi$
$114$		−	85107.3i		−	0.613345i
$115$	9786.72			0.0690069
$116$		−	207833.i		−	1.43407i
$117$		−	10168.3i		−	0.0686724i
$118$			111991.i			0.740420i
$119$	−30436.5			−0.197028
$120$			54504.5i			0.345525i
$121$	−19938.1			−0.123800
$122$	128369.			0.780837
$123$			234073.i			1.39505i
$124$	−208989.			−1.22059
$125$			137738.i			0.788457i
$126$		−	2903.71i		−	0.0162940i
$127$		−	170629.i		−	0.938736i	−0.883003	−	0.469368i	$-0.844482\pi$
$127$		−	170629.i		−	0.938736i	0.883003	−	0.469368i	$-0.155518\pi$
$128$	183780.			0.991453
$129$	152481.			0.806754
$130$	49541.2			0.257103
$131$			140568.i			0.715661i	0.933787	+	0.357830i	$0.116483\pi$
$131$			140568.i			0.715661i	−0.933787	+	0.357830i	$0.883517\pi$
$132$	−144686.			−0.722755
$133$	191747.			0.939939
$134$			117535.i			0.565462i
$135$		−	94502.1i		−	0.446280i
$136$		−	51103.5i		−	0.236921i
$137$			119157.i			0.542399i	0.962523	+	0.271199i	$0.0874203\pi$
$137$			119157.i			0.542399i	−0.962523	+	0.271199i	$0.912580\pi$
$138$			15679.9i			0.0700883i
$139$		−	367663.i		−	1.61403i	−0.590528	−	0.807017i	$-0.701080\pi$
$139$		−	367663.i		−	1.61403i	0.590528	−	0.807017i	$-0.298920\pi$
$140$	−54325.9			−0.234254
$141$	−15205.7			−0.0644107
$142$			128675.i			0.535519i
$143$			297268.i			1.21565i
$144$	−5563.85			−0.0223599
$145$	−199310.			−0.787244
$146$	144861.			0.562432
$147$	137797.			0.525951
$148$		−	117694.i		−	0.441674i
$149$			116429.i			0.429632i	0.976654	+	0.214816i	$0.0689153\pi$
$149$			116429.i			0.429632i	−0.976654	+	0.214816i	$0.931085\pi$
$150$	−98777.2			−0.358450
$151$	141257.			0.504158			0.252079	−	0.967707i	$-0.418886\pi$
$151$	141257.			0.504158			0.252079	+	0.967707i	$0.418886\pi$
$152$			321948.i			1.13025i
$153$			4449.97i			0.0153684i
$154$			84889.4i			0.288438i
$155$			200418.i			0.670051i
$156$		−	304794.i		−	1.00276i
$157$			494407.i			1.60080i	0.599469	+	0.800398i	$0.295378\pi$
$157$			494407.i			1.60080i	−0.599469	+	0.800398i	$0.704622\pi$
$158$	20047.8			0.0638886
$159$	153010.			0.479986
$160$		−	142076.i		−	0.438753i
$161$	−35326.9			−0.107409
$162$	143379.			0.429238
$163$	41646.6			0.122775			0.0613876	−	0.998114i	$-0.480447\pi$
$163$	41646.6			0.122775			0.0613876	+	0.998114i	$0.480447\pi$
$164$		−	391726.i		−	1.13729i
$165$			138752.i			0.396762i
$166$		−	224604.i		−	0.632625i
$167$	208299.			0.577958			0.288979	−	0.957335i	$-0.406684\pi$
$167$	208299.			0.577958			0.288979	+	0.957335i	$0.406684\pi$
$168$		−	196744.i		−	0.537809i
$169$	−254929.			−0.686598
$170$	−21680.9			−0.0575380
$171$		−	28034.5i		−	0.0733165i
$172$	−255179.			−0.657695
$173$			675745.i			1.71659i	0.513153	+	0.858297i	$0.328477\pi$
$173$			675745.i			1.71659i	−0.513153	+	0.858297i	$0.671523\pi$
$174$		−	319327.i		−	0.799581i
$175$		−	222545.i		−	0.549318i
$176$	162658.			0.395817
$177$		−	660752.i		−	1.58528i
$178$	−342915.			−0.811216
$179$			23383.5i			0.0545477i	0.999628	+	0.0272739i	$0.00868262\pi$
$179$			23383.5i			0.0545477i	−0.999628	+	0.0272739i	$0.991317\pi$
$180$			7942.73i			0.0182721i
$181$		−	559928.i		−	1.27039i	−0.772354	−	0.635193i	$-0.780921\pi$
$181$		−	559928.i		−	1.27039i	0.772354	−	0.635193i	$-0.219079\pi$
$182$	−178828.			−0.400181
$183$	−757382.			−1.67181
$184$		−	59314.7i		−	0.129157i
$185$	−112868.			−0.242461
$186$	−321102.			−0.680551
$187$		−	130094.i		−	0.272054i
$188$	25447.0			0.0525099
$189$			341122.i			0.694633i
$190$	136588.			0.274491
$191$	−441057.			−0.874804			−0.437402	−	0.899266i	$-0.644101\pi$
$191$	−441057.			−0.874804			−0.437402	+	0.899266i	$0.644101\pi$
$192$	17420.3			0.0341037
$193$	539185.			1.04194			0.520972	−	0.853574i	$-0.325569\pi$
$193$	539185.			1.04194			0.520972	+	0.853574i	$0.325569\pi$
$194$	120943.	−	205300.i	0.230715	−	0.391639i
$195$	−292295.			−0.550471
$196$	−230605.			−0.428774
$197$	640552.			1.17595			0.587975	−	0.808879i	$-0.299925\pi$
$197$	640552.			1.17595			0.587975	+	0.808879i	$0.299925\pi$
$198$	12411.3			0.0224985
$199$		−	641223.i		−	1.14783i	−0.818916	−	0.573913i	$-0.805425\pi$
$199$		−	641223.i		−	1.14783i	0.818916	−	0.573913i	$-0.194575\pi$
$200$	373659.			0.660542
$201$		−	693459.i		−	1.21068i
$202$	−192515.			−0.331960
$203$	719446.			1.22534
$204$			133388.i			0.224410i
$205$	−375662.			−0.624327
$206$	145675.			0.239175
$207$			5164.98i			0.00837805i
$208$			342655.i			0.549160i
$209$			819583.i			1.29786i
$210$	−83469.4			−0.130611
$211$		−	151679.i		−	0.234541i	−0.993100	−	0.117271i	$-0.962586\pi$
$211$		−	151679.i		−	0.234541i	0.993100	−	0.117271i	$-0.0374145\pi$
$212$	−256066.			−0.391302
$213$		−	759190.i		−	1.14657i
$214$			405001.i			0.604535i
$215$			244715.i			0.361047i
$216$	−572751.			−0.835279
$217$		−	723444.i		−	1.04293i
$218$	−33344.4			−0.0475206
$219$	−854688.			−1.20420
$220$		−	232205.i		−	0.323455i
$221$	274056.			0.377449
$222$		−	180833.i		−	0.246260i
$223$			498802.i			0.671685i	0.941918	+	0.335843i	$0.109021\pi$
$223$			498802.i			0.671685i	−0.941918	+	0.335843i	$0.890979\pi$
$224$			512848.i			0.682918i
$225$	−32537.3			−0.0428475
$226$	291569.			0.379726
$227$	−196620.			−0.253258			−0.126629	−	0.991950i	$-0.540416\pi$
$227$	−196620.			−0.253258			−0.126629	+	0.991950i	$0.540416\pi$
$228$		−	840334.i		−	1.07057i
$229$	1.25697e6			1.58394			0.791968	−	0.610563i	$-0.209057\pi$
$229$	1.25697e6			1.58394			0.791968	+	0.610563i	$0.209057\pi$
$230$	−25164.5			−0.0313667
$231$		−	500851.i		−	0.617559i
$232$			1.20796e6i			1.47345i
$233$		−	745701.i		−	0.899860i	−0.893064	−	0.449930i	$-0.851449\pi$
$233$		−	745701.i		−	0.899860i	0.893064	−	0.449930i	$-0.148551\pi$
$234$			26145.5i			0.0312146i
$235$		−	24403.4i		−	0.0288258i
$236$			1.10578e6i			1.29238i
$237$	−118283.			−0.136789
$238$	78261.0			0.0895577
$239$			795496.i			0.900831i	0.892819	+	0.450416i	$0.148724\pi$
$239$			795496.i			0.900831i	−0.892819	+	0.450416i	$0.851276\pi$
$240$			159937.i			0.179235i
$241$	−1.02665e6			−1.13863			−0.569313	−	0.822121i	$-0.692791\pi$
$241$	−1.02665e6			−1.13863			−0.569313	+	0.822121i	$0.692791\pi$
$242$	51266.7			0.0562726
$243$	97242.9			0.105643
$244$	1.26749e6			1.36292
$245$			221148.i			0.235379i
$246$		−	601871.i		−	0.634111i
$247$	−1.72653e6			−1.80066
$248$	1.21468e6			1.25410
$249$			1.32517e6i			1.35448i
$250$		−	354164.i		−	0.358389i
$251$		−	478147.i		−	0.479046i	−0.970891	−	0.239523i	$-0.923009\pi$
$251$		−	478147.i		−	0.479046i	0.970891	−	0.239523i	$-0.0769911\pi$
$252$		−	28670.7i		−	0.0284405i
$253$		−	150997.i		−	0.148309i
$254$			438736.i			0.426697i
$255$	127918.			0.123192
$256$	−509296.			−0.485702
$257$		−	787316.i		−	0.743560i	−0.928321	−	0.371780i	$-0.878748\pi$
$257$		−	787316.i		−	0.743560i	0.928321	−	0.371780i	$-0.121252\pi$
$258$	−392072.			−0.366705
$259$	407417.			0.377389
$260$	489161.			0.448764
$261$		−	105187.i		−	0.0955784i
$262$		−	361440.i		−	0.325299i
$263$			856552.i			0.763598i	0.924245	+	0.381799i	$0.124695\pi$
$263$			856552.i			0.763598i	−0.924245	+	0.381799i	$0.875305\pi$
$264$	840940.			0.742601
$265$			245565.i			0.214808i
$266$	−493037.			−0.427244
$267$	2.02321e6			1.73685
$268$			1.16052e6i			0.986993i
$269$	−1.99953e6			−1.68480			−0.842399	−	0.538854i	$-0.818857\pi$
$269$	−1.99953e6			−1.68480			−0.842399	+	0.538854i	$0.818857\pi$
$270$			242992.i			0.202854i
$271$			592998.i			0.490490i	0.969461	+	0.245245i	$0.0788684\pi$
$271$			592998.i			0.490490i	−0.969461	+	0.245245i	$0.921132\pi$
$272$		−	149958.i		−	0.122898i
$273$	1.05509e6			0.856807
$274$		−	306388.i		−	0.246544i
$275$	951224.			0.758492
$276$			154821.i			0.122337i
$277$		−	1.28291e6i		−	1.00461i	−0.864691	−	0.502305i	$-0.832486\pi$
$277$		−	1.28291e6i		−	1.00461i	0.864691	−	0.502305i	$-0.167514\pi$
$278$			945368.i			0.733650i
$279$	−105771.			−0.0813501
$280$	315752.			0.240686
$281$			630665.i			0.476467i	0.971208	+	0.238233i	$0.0765683\pi$
$281$			630665.i			0.476467i	−0.971208	+	0.238233i	$0.923432\pi$
$282$	39098.2			0.0292775
$283$	−565144.			−0.419462			−0.209731	−	0.977759i	$-0.567259\pi$
$283$	−565144.			−0.419462			−0.209731	+	0.977759i	$0.567259\pi$
$284$			1.27052e6i			0.934727i
$285$	−805873.			−0.587698
$286$		−	764361.i		−	0.552565i
$287$	1.35602e6			0.971764
$288$	74981.1			0.0532685
$289$	1.29992e6			0.915529
$290$	512484.			0.357837
$291$	−713568.	+	1.21128e6i	−0.493973	+	0.838518i
$292$	1.43034e6			0.981705
$293$	−1.17160e6			−0.797281			−0.398641	−	0.917107i	$-0.630518\pi$
$293$	−1.17160e6			−0.797281			−0.398641	+	0.917107i	$0.630518\pi$
$294$	−354315.			−0.239068
$295$	1.06043e6			0.709460
$296$			684062.i			0.453801i
$297$	−1.45805e6			−0.959141
$298$		−	299374.i		−	0.195287i
$299$	318090.			0.205765
$300$	−975309.			−0.625661
$301$		−	883341.i		−	0.561969i
$302$	−363212.			−0.229162
$303$	1.13585e6			0.710744
$304$			944719.i			0.586299i
$305$		−	1.21551e6i		−	0.748187i
$306$		−	11442.2i		−	0.00698562i
$307$	−554500.			−0.335781			−0.167890	−	0.985806i	$-0.553695\pi$
$307$	−554500.			−0.335781			−0.167890	+	0.985806i	$0.553695\pi$
$308$			838183.i			0.503457i
$309$	−859487.			−0.512087
$310$		−	515333.i		−	0.304568i
$311$			1.14535e6i			0.671489i	0.941953	+	0.335744i	$0.108988\pi$
$311$			1.14535e6i			0.671489i	−0.941953	+	0.335744i	$0.891012\pi$
$312$			1.77152e6i			1.03029i
$313$	−2.50494e6			−1.44523			−0.722616	−	0.691250i	$-0.757060\pi$
$313$	−2.50494e6			−1.44523			−0.722616	+	0.691250i	$0.757060\pi$
$314$		−	1.27126e6i		−	0.727632i
$315$	−27494.9			−0.0156126
$316$	197948.			0.111515
$317$		−	2.90194e6i		−	1.62196i	−0.585073	−	0.810981i	$-0.698934\pi$
$317$		−	2.90194e6i		−	1.62196i	0.585073	−	0.810981i	$-0.301066\pi$
$318$	−393434.			−0.218175
$319$			3.07512e6i			1.69194i
$320$			27957.6i			0.0152625i
$321$		−	2.38952e6i		−	1.29434i
$322$	90835.7			0.0488222
$323$	755587.			0.402975
$324$	1.41570e6			0.749218
$325$			2.00384e6i			1.05234i
$326$	−107085.			−0.0558067
$327$	196734.			0.101744
$328$			2.27678e6i			1.16852i
$329$			88088.4i			0.0448672i
$330$		−	356773.i		−	0.180346i
$331$		−	770810.i		−	0.386703i	−0.981130	−	0.193351i	$-0.938064\pi$
$331$		−	770810.i		−	0.386703i	0.981130	−	0.193351i	$-0.0619358\pi$
$332$		−	2.21770e6i		−	1.10422i
$333$		−	59566.5i		−	0.0294369i
$334$	−535597.			−0.262707
$335$	1.11292e6			0.541818
$336$		−	577323.i		−	0.278978i
$337$			34775.1i			0.0166799i	0.999965	+	0.00833994i	$0.00265472\pi$
$337$			34775.1i			0.0166799i	−0.999965	+	0.00833994i	$0.997345\pi$
$338$	655496.			0.312089
$339$	−1.72027e6			−0.813013
$340$	−214073.			−0.100430
$341$	3.09221e6			1.44007
$342$			72084.7i			0.0333256i
$343$		−	2.27537e6i		−	1.04428i
$344$	1.48315e6			0.675754
$345$	148472.			0.0671577
$346$		−	1.73754e6i		−	0.780268i
$347$			210053.i			0.0936496i	0.998903	+	0.0468248i	$0.0149103\pi$
$347$			210053.i			0.0936496i	−0.998903	+	0.0468248i	$0.985090\pi$
$348$		−	3.15298e6i		−	1.39564i
$349$		−	591507.i		−	0.259954i	−0.991517	−	0.129977i	$-0.958510\pi$
$349$		−	591507.i		−	0.259954i	0.991517	−	0.129977i	$-0.0414903\pi$
$350$			572229.i			0.249689i
$351$		−	3.07153e6i		−	1.33072i
$352$	−2.19206e6			−0.942965
$353$	−2.37565e6			−1.01472			−0.507360	−	0.861734i	$-0.669379\pi$
$353$	−2.37565e6			−1.01472			−0.507360	+	0.861734i	$0.669379\pi$
$354$			1.69898e6i			0.720578i
$355$	1.21842e6			0.513126
$356$	−3.38588e6			−1.41595
$357$	−461743.			−0.191748
$358$		−	60125.7i		−	0.0247944i
$359$			414310.i			0.169664i	0.996395	+	0.0848320i	$0.0270353\pi$
$359$			414310.i			0.169664i	−0.996395	+	0.0848320i	$0.972965\pi$
$360$		−	46164.6i		−	0.0187738i
$361$	−2.28404e6			−0.922433
$362$			1.43974e6i			0.577446i
$363$	−302475.			−0.120482
$364$	−1.76571e6			−0.698500
$365$		−	1.37168e6i		−	0.538915i
$366$	1.94745e6			0.759912
$367$		−	4.62883e6i		−	1.79393i	−0.442100	−	0.896966i	$-0.645766\pi$
$367$		−	4.62883e6i		−	1.79393i	0.442100	−	0.896966i	$-0.354234\pi$
$368$		−	174052.i		−	0.0669977i
$369$		−	198257.i		−	0.0757989i
$370$	290216.			0.110209
$371$		−	886409.i		−	0.334349i
$372$	−3.17051e6			−1.18788
$373$		−	1.62371e6i		−	0.604277i	−0.953264	−	0.302139i	$-0.902299\pi$
$373$		−	1.62371e6i		−	0.604277i	0.953264	−	0.302139i	$-0.0977005\pi$
$374$			334510.i			0.123660i
$375$			2.08958e6i			0.767328i
$376$	−147902.			−0.0539518
$377$	−6.47803e6			−2.34741
$378$		−	877124.i		−	0.315741i
$379$	−377022.			−0.134825			−0.0674123	−	0.997725i	$-0.521474\pi$
$379$	−377022.			−0.134825			−0.0674123	+	0.997725i	$0.521474\pi$
$380$	1.34864e6			0.479113
$381$		−	2.58856e6i		−	0.913579i
$382$	1.13408e6			0.397637
$383$			2.66711e6i			0.929060i	0.885557	+	0.464530i	$0.153777\pi$
$383$			2.66711e6i			0.929060i	−0.885557	+	0.464530i	$0.846223\pi$
$384$	2.78807e6			0.964884
$385$	803810.			0.276377
$386$	−1.38640e6			−0.473610
$387$	−129149.			−0.0438343
$388$	1.19417e6	−	2.02710e6i	0.402705	−	0.683591i
$389$	3.14086e6			1.05239			0.526193	−	0.850365i	$-0.323619\pi$
$389$	3.14086e6			1.05239			0.526193	+	0.850365i	$0.323619\pi$
$390$	751575.			0.250213
$391$	−139207.			−0.0460489
$392$	1.34032e6			0.440548
$393$			2.13251e6i			0.696482i
$394$	−1.64705e6			−0.534521
$395$		−	189831.i		−	0.0612172i
$396$	122547.			0.0392703
$397$	294384.			0.0937428			0.0468714	−	0.998901i	$-0.485075\pi$
$397$	294384.			0.0937428			0.0468714	+	0.998901i	$0.485075\pi$
$398$			1.64877e6i			0.521738i
$399$	2.90894e6			0.914751
$400$	1.09646e6			0.342644
$401$			2.41035e6i			0.748549i	0.927318	+	0.374274i	$0.122108\pi$
$401$			2.41035e6i			0.748549i	−0.927318	+	0.374274i	$0.877892\pi$
$402$			1.78308e6i			0.550309i
$403$			6.51403e6i			1.99796i
$404$	−1.90086e6			−0.579424
$405$		−	1.35764e6i		−	0.411290i
$406$	−1.84990e6			−0.556973
$407$			1.74142e6i			0.521095i
$408$		−	775277.i		−	0.230572i
$409$		−	4.55688e6i		−	1.34697i	−0.739200	−	0.673487i	$-0.764796\pi$
$409$		−	4.55688e6i		−	1.34697i	0.739200	−	0.673487i	$-0.235204\pi$
$410$	965936.			0.283784
$411$			1.80770e6i			0.527864i
$412$	1.43837e6			0.417472
$413$	−3.82782e6			−1.10427
$414$		−	13280.7i		−	0.00380819i
$415$	−2.12675e6			−0.606173
$416$		−	4.61778e6i		−	1.30828i
$417$		−	5.57771e6i		−	1.57078i
$418$		−	2.10739e6i		−	0.589934i
$419$	362869.			0.100975			0.0504877	−	0.998725i	$-0.483922\pi$
$419$	362869.			0.100975			0.0504877	+	0.998725i	$0.483922\pi$
$420$	−824162.			−0.227976
$421$	4.21847e6			1.15998			0.579989	−	0.814624i	$-0.303057\pi$
$421$	4.21847e6			1.15998			0.579989	+	0.814624i	$0.303057\pi$
$422$			390010.i			0.106609i
$423$	12879.0			0.00349970
$424$	1.48830e6			0.402046
$425$		−	876949.i		−	0.235506i
$426$			1.95210e6i			0.521168i
$427$			4.38761e6i			1.16455i
$428$			3.99891e6i			1.05519i
$429$			4.50976e6i			1.18307i
$430$		−	629233.i		−	0.164112i
$431$	6.16266e6			1.59799			0.798997	−	0.601336i	$-0.205365\pi$
$431$	6.16266e6			1.59799			0.798997	+	0.601336i	$0.205365\pi$
$432$	−1.68067e6			−0.433286
$433$		−	6.66190e6i		−	1.70757i	−0.520626	−	0.853785i	$-0.674302\pi$
$433$		−	6.66190e6i		−	1.70757i	0.520626	−	0.853785i	$-0.325698\pi$
$434$			1.86019e6i			0.474059i
$435$	−3.02368e6			−0.766148
$436$	−329237.			−0.0829455
$437$	876993.			0.219681
$438$	2.19765e6			0.547360
$439$			835315.i			0.206866i	0.994636	+	0.103433i	$0.0329827\pi$
$439$			835315.i			0.206866i	−0.994636	+	0.103433i	$0.967017\pi$
$440$			1.34962e6i			0.332337i
$441$	−116712.			−0.0285771
$442$	−704677.			−0.171567
$443$		−	674670.i		−	0.163336i	−0.996660	−	0.0816680i	$-0.973975\pi$
$443$		−	674670.i		−	0.163336i	0.996660	−	0.0816680i	$-0.0260247\pi$
$444$		−	1.78551e6i		−	0.429838i
$445$			3.24703e6i			0.777296i
$446$		−	1.28256e6i		−	0.305311i
$447$			1.76632e6i			0.418119i
$448$		−	100918.i		−	0.0237560i
$449$	2.57200e6			0.602081			0.301041	−	0.953611i	$-0.402666\pi$
$449$	2.57200e6			0.602081			0.301041	+	0.953611i	$0.402666\pi$
$450$	83662.9			0.0194761
$451$			5.79601e6i			1.34180i
$452$	2.87890e6			0.662798
$453$	2.14296e6			0.490647
$454$	505568.			0.115117
$455$			1.69330e6i			0.383447i
$456$			4.88418e6i			1.09997i
$457$			28944.3i			0.00648294i	0.999995	+	0.00324147i	$0.00103179\pi$
$457$			28944.3i			0.00648294i	−0.999995	+	0.00324147i	$0.998968\pi$
$458$	−3.23204e6			−0.719968
$459$			1.34420e6i			0.297806i
$460$	−248470.			−0.0547494
$461$	−1.79846e6			−0.394138			−0.197069	−	0.980390i	$-0.563142\pi$
$461$	−1.79846e6			−0.394138			−0.197069	+	0.980390i	$0.563142\pi$
$462$			1.28783e6i			0.280708i
$463$	2.99972e6			0.650321			0.325160	−	0.945659i	$-0.394582\pi$
$463$	2.99972e6			0.650321			0.325160	+	0.945659i	$0.394582\pi$
$464$			3.54464e6i			0.764323i
$465$			3.04049e6i			0.652095i
$466$			1.91741e6i			0.409026i
$467$	6.20467e6			1.31652			0.658258	−	0.752792i	$-0.271294\pi$
$467$	6.20467e6			1.31652			0.658258	+	0.752792i	$0.271294\pi$
$468$			258157.i			0.0544839i
$469$	−4.01729e6			−0.843338
$470$			62748.2i			0.0131026i
$471$			7.50051e6i			1.55790i
$472$		−	6.42699e6i		−	1.32786i
$473$	3.77566e6			0.775961
$474$	304139.			0.0621765
$475$			5.52470e6i			1.12351i
$476$	772735.			0.156320
$477$	−129598.			−0.0260796
$478$		−	2.04545e6i		−	0.409468i
$479$	1.94514e6			0.387357			0.193678	−	0.981065i	$-0.437958\pi$
$479$	1.94514e6			0.387357			0.193678	+	0.981065i	$0.437958\pi$
$480$		−	2.15539e6i		−	0.426995i
$481$	−3.66846e6			−0.722971
$482$	2.63982e6			0.517556
$483$	−535934.			−0.104531
$484$	506198.			0.0982216
$485$	−1.94397e6	−	1.14520e6i	−0.375263	−	0.221068i
$486$	−250040.			−0.0480196
$487$	−8.31786e6			−1.58924			−0.794620	−	0.607107i	$-0.792330\pi$
$487$	−8.31786e6			−1.58924			−0.794620	+	0.607107i	$0.792330\pi$
$488$	−7.36690e6			−1.40034
$489$	631808.			0.119485
$490$		−	568636.i		−	0.106990i
$491$	2.87535e6			0.538254			0.269127	−	0.963105i	$-0.413265\pi$
$491$	2.87535e6			0.538254			0.269127	+	0.963105i	$0.413265\pi$
$492$		−	5.94277e6i		−	1.10682i
$493$	2.83500e6			0.525335
$494$	4.43941e6			0.818479
$495$		−	117521.i		−	0.0215578i
$496$	3.56434e6			0.650541
$497$	−4.39808e6			−0.798680
$498$		−	3.40740e6i		−	0.615672i
$499$		−	1.09463e7i		−	1.96796i	−0.178281	−	0.983980i	$-0.557054\pi$
$499$		−	1.09463e7i		−	1.96796i	0.178281	−	0.983980i	$-0.442946\pi$
$500$		−	3.49695e6i		−	0.625554i
$501$	3.16005e6			0.562470
$502$			1.22946e6i			0.217748i
$503$	7.70213e6			1.35735			0.678674	−	0.734440i	$-0.262555\pi$
$503$	7.70213e6			1.35735			0.678674	+	0.734440i	$0.262555\pi$
$504$			166639.i			0.0292214i
$505$			1.82291e6i			0.318080i
$506$			388258.i			0.0674131i
$507$	−3.86745e6			−0.668198
$508$			4.33201e6i			0.744783i
$509$	−754034.			−0.129002			−0.0645010	−	0.997918i	$-0.520546\pi$
$509$	−754034.			−0.129002			−0.0645010	+	0.997918i	$0.520546\pi$
$510$	−328915.			−0.0559961
$511$			4.95132e6i			0.838819i
$512$	−4.57140e6			−0.770680
$513$		−	8.46837e6i		−	1.42071i
$514$			2.02442e6i			0.337981i
$515$		−	1.37938e6i		−	0.229175i
$516$	−3.87125e6			−0.640070
$517$	−376515.			−0.0619522
$518$	−1.04759e6			−0.171540
$519$			1.02515e7i			1.67059i
$520$	−2.84309e6			−0.461087
$521$	−1.49212e6			−0.240829			−0.120414	−	0.992724i	$-0.538422\pi$
$521$	−1.49212e6			−0.240829			−0.120414	+	0.992724i	$0.538422\pi$
$522$			270466.i			0.0434446i
$523$		−	5.49797e6i		−	0.878918i	−0.898263	−	0.439459i	$-0.855170\pi$
$523$		−	5.49797e6i		−	0.878918i	0.898263	−	0.439459i	$-0.144830\pi$
$524$		−	3.56880e6i		−	0.567798i
$525$		−	3.37617e6i		−	0.534597i
$526$		−	2.20244e6i		−	0.347089i
$527$		−	2.85076e6i		−	0.447131i
$528$	2.46764e6			0.385210
$529$	6.27477e6			0.974897
$530$		−	631418.i		−	0.0976399i
$531$			559648.i			0.0861347i
$532$	−4.86817e6			−0.745738
$533$	−1.22098e7			−1.86162
$534$	−5.20226e6			−0.789477
$535$	3.83492e6			0.579257
$536$		−	6.74513e6i		−	1.01409i
$537$			354744.i			0.0530860i
$538$	5.14138e6			0.765815
$539$	3.41205e6			0.505876
$540$			2.39926e6i			0.354074i
$541$			667061.i			0.0979878i	0.998799	+	0.0489939i	$0.0156015\pi$
$541$			667061.i			0.0979878i	−0.998799	+	0.0489939i	$0.984399\pi$
$542$		−	1.52477e6i		−	0.222949i
$543$		−	8.49450e6i		−	1.23634i
$544$			2.02090e6i			0.292784i
$545$			315736.i			0.0455336i
$546$	−2.71294e6			−0.389456
$547$	1.25496e7			1.79333			0.896665	−	0.442710i	$-0.145983\pi$
$547$	1.25496e7			1.79333			0.896665	+	0.442710i	$0.145983\pi$
$548$		−	3.02522e6i		−	0.430334i
$549$	641492.			0.0908365
$550$	−2.44587e6			−0.344768
$551$	−1.78603e7			−2.50616
$552$		−	899846.i		−	0.125696i
$553$			685227.i			0.0952843i
$554$			3.29874e6i			0.456639i
$555$	−1.71229e6			−0.235963
$556$			9.33440e6i			1.28056i
$557$	4.51817e6			0.617056			0.308528	−	0.951215i	$-0.400164\pi$
$557$	4.51817e6			0.617056			0.308528	+	0.951215i	$0.400164\pi$
$558$	271969.			0.0369772
$559$			7.95377e6i			1.07657i
$560$	926538.			0.124851
$561$		−	1.97362e6i		−	0.264763i
$562$		−	1.62162e6i		−	0.216575i
$563$		−	530832.i		−	0.0705807i	−0.999377	−	0.0352903i	$-0.988764\pi$
$563$		−	530832.i		−	0.0705807i	0.999377	−	0.0352903i	$-0.0112356\pi$
$564$	386049.			0.0511028
$565$		−	2.76084e6i		−	0.363849i
$566$	1.45315e6			0.190664
$567$			4.90065e6i			0.640171i
$568$		−	7.38448e6i		−	0.960393i
$569$			1.18565e6i			0.153524i	0.997049	+	0.0767618i	$0.0244581\pi$
$569$			1.18565e6i			0.153524i	−0.997049	+	0.0767618i	$0.975542\pi$
$570$	2.07213e6			0.267135
$571$	4.80573e6			0.616835			0.308417	−	0.951251i	$-0.400201\pi$
$571$	4.80573e6			0.616835			0.308417	+	0.951251i	$0.400201\pi$
$572$		−	7.54717e6i		−	0.964481i
$573$	−6.69114e6			−0.851361
$574$	−3.48671e6			−0.441709
$575$		−	1.01785e6i		−	0.128386i
$576$	−14754.7			−0.00185300
$577$		−	244609.i		−	0.0305867i	−0.999883	−	0.0152933i	$-0.995132\pi$
$577$		−	244609.i		−	0.0305867i	0.999883	−	0.0152933i	$-0.00486821\pi$
$578$	−3.34247e6			−0.416149
$579$	8.17983e6			1.01402
$580$	5.06018e6			0.624592
$581$	7.67689e6			0.943506
$582$	1.83479e6	−	3.11455e6i	0.224533	−	0.381143i
$583$	3.78877e6			0.461665
$584$	−8.31337e6			−1.00866
$585$	247570.			0.0299094
$586$	3.01253e6			0.362400
$587$			7.47122e6i			0.894945i	0.894298	+	0.447473i	$0.147676\pi$
$587$			7.47122e6i			0.894945i	−0.894298	+	0.447473i	$0.852324\pi$
$588$	−3.49845e6			−0.417284
$589$			1.79596e7i			2.13308i
$590$	−2.72668e6			−0.322481
$591$	9.71764e6			1.14444
$592$			2.00730e6i			0.235401i
$593$	−1.14284e7			−1.33459			−0.667294	−	0.744794i	$-0.732548\pi$
$593$	−1.14284e7			−1.33459			−0.667294	+	0.744794i	$0.732548\pi$
$594$	3.74908e6			0.435972
$595$		−	741046.i		−	0.0858129i
$596$		−	2.95597e6i		−	0.340866i
$597$		−	9.72781e6i		−	1.11707i
$598$	−817902.			−0.0935295
$599$			1.36625e7i			1.55584i	0.628366	+	0.777918i	$0.283724\pi$
$599$			1.36625e7i			1.55584i	−0.628366	+	0.777918i	$0.716276\pi$
$600$	5.66867e6			0.642840
$601$		−	5.07797e6i		−	0.573461i	−0.958011	−	0.286730i	$-0.907432\pi$
$601$		−	5.07797e6i		−	0.573461i	0.958011	−	0.286730i	$-0.0925684\pi$
$602$			2.27133e6i			0.255440i
$603$			587350.i			0.0657815i
$604$	−3.58629e6			−0.399993
$605$		−	485439.i		−	0.0539196i
$606$	−2.92059e6			−0.323064
$607$	−1.66710e7			−1.83649			−0.918246	−	0.396010i	$-0.870395\pi$
$607$	−1.66710e7			−1.83649			−0.918246	+	0.396010i	$0.870395\pi$
$608$		−	1.27315e7i		−	1.39675i
$609$	1.09145e7			1.19251
$610$			3.12544e6i			0.340084i
$611$		−	793165.i		−	0.0859529i
$612$		−	112978.i		−	0.0121931i
$613$	−1.76021e7			−1.89196			−0.945982	−	0.324220i	$-0.894898\pi$
$613$	−1.76021e7			−1.89196			−0.945982	+	0.324220i	$0.894898\pi$
$614$	1.42578e6			0.152627
$615$	−5.69906e6			−0.607597
$616$		−	4.87167e6i		−	0.517281i
$617$	−2.07301e6			−0.219224			−0.109612	−	0.993974i	$-0.534961\pi$
$617$	−2.07301e6			−0.219224			−0.109612	+	0.993974i	$0.534961\pi$
$618$	2.20999e6			0.232766
$619$		−	9.22938e6i		−	0.968158i	−0.875024	−	0.484079i	$-0.839155\pi$
$619$		−	9.22938e6i		−	0.968158i	0.875024	−	0.484079i	$-0.160845\pi$
$620$		−	5.08831e6i		−	0.531611i
$621$			1.56019e6i			0.162348i
$622$		−	2.94504e6i		−	0.305221i
$623$		−	1.17207e7i		−	1.20986i
$624$			5.19832e6i			0.534444i
$625$	4.55961e6			0.466904
$626$	6.44094e6			0.656921
$627$			1.24337e7i			1.26308i
$628$		−	1.25522e7i		−	1.27005i
$629$	1.60544e6			0.161796
$630$	70697.5			0.00709663
$631$	7.80444e6			0.780312			0.390156	−	0.920749i	$-0.372421\pi$
$631$	7.80444e6			0.780312			0.390156	+	0.920749i	$0.372421\pi$
$632$	−1.15051e6			−0.114577
$633$		−	2.30108e6i		−	0.228256i
$634$			7.46173e6i			0.737253i
$635$	4.15435e6			0.408855
$636$	−3.88470e6			−0.380816
$637$			7.18781e6i			0.701856i
$638$		−	7.90702e6i		−	0.769062i
$639$			643023.i			0.0622981i
$640$			4.47454e6i			0.431815i
$641$		−	4.09193e6i		−	0.393354i	−0.980468	−	0.196677i	$-0.936985\pi$
$641$		−	4.09193e6i		−	0.393354i	0.980468	−	0.196677i	$-0.0630150\pi$
$642$			6.14415e6i			0.588335i
$643$	3.02431e6			0.288469			0.144235	−	0.989544i	$-0.453928\pi$
$643$	3.02431e6			0.288469			0.144235	+	0.989544i	$0.453928\pi$
$644$	896896.			0.0852172
$645$			3.71250e6i			0.351372i
$646$	−1.94283e6			−0.183170
$647$	−9.25208e6			−0.868918			−0.434459	−	0.900692i	$-0.643060\pi$
$647$	−9.25208e6			−0.868918			−0.434459	+	0.900692i	$0.643060\pi$
$648$	−8.22830e6			−0.769791
$649$		−	1.63612e7i		−	1.52477i
$650$		−	5.15246e6i		−	0.478334i
$651$		−	1.09752e7i		−	1.01498i
$652$	−1.05734e6			−0.0974085
$653$		−	6.50852e6i		−	0.597310i	−0.954361	−	0.298655i	$-0.903462\pi$
$653$		−	6.50852e6i		−	0.597310i	0.954361	−	0.298655i	$-0.0965379\pi$
$654$	−505859.			−0.0462472
$655$	−3.42244e6			−0.311697
$656$			6.68097e6i			0.606149i
$657$	723909.			0.0654290
$658$		−	226501.i		−	0.0203941i
$659$		−	8.25644e6i		−	0.740593i	−0.928914	−	0.370296i	$-0.879256\pi$
$659$		−	8.25644e6i		−	0.740593i	0.928914	−	0.370296i	$-0.120744\pi$
$660$		−	3.52271e6i		−	0.314787i
$661$	1.52658e7			1.35899			0.679495	−	0.733680i	$-0.262199\pi$
$661$	1.52658e7			1.35899			0.679495	+	0.733680i	$0.262199\pi$
$662$			1.98198e6i			0.175774i
$663$	4.15762e6			0.367334
$664$			1.28897e7i			1.13454i
$665$			4.66853e6i			0.409379i
$666$			153163.i			0.0133803i
$667$	3.29052e6			0.286385
$668$	−5.28840e6			−0.458546
$669$			7.56718e6i			0.653685i
$670$	−2.86165e6			−0.246280
$671$	−1.87539e7			−1.60800
$672$			7.78026e6i			0.664617i
$673$	−1.03502e7			−0.880872			−0.440436	−	0.897784i	$-0.645176\pi$
$673$	−1.03502e7			−0.880872			−0.440436	+	0.897784i	$0.645176\pi$
$674$		−	89416.8i		−	0.00758175i
$675$	−9.82856e6			−0.830291
$676$	6.47225e6			0.544739
$677$	1.98761e7			1.66671			0.833354	−	0.552740i	$-0.186418\pi$
$677$	1.98761e7			1.66671			0.833354	+	0.552740i	$0.186418\pi$
$678$	4.42332e6			0.369550
$679$	7.01711e6	+	4.13379e6i	0.584095	+	0.344092i
$680$	1.24423e6			0.103188
$681$	−2.98287e6			−0.246471
$682$	−7.95097e6			−0.654575
$683$	−4.85855e6			−0.398525			−0.199262	−	0.979946i	$-0.563855\pi$
$683$	−4.85855e6			−0.398525			−0.199262	+	0.979946i	$0.563855\pi$
$684$			711752.i			0.0581686i
$685$	−2.90116e6			−0.236235
$686$			5.85064e6i			0.474672i
$687$	1.90692e7			1.54149
$688$	4.35213e6			0.350535
$689$			7.98140e6i			0.640518i
$690$	−381764.			−0.0305261
$691$	1.13296e6			0.0902651			0.0451325	−	0.998981i	$-0.485629\pi$
$691$	1.13296e6			0.0902651			0.0451325	+	0.998981i	$0.485629\pi$
$692$		−	1.71561e7i		−	1.36193i
$693$			424214.i			0.0335546i
$694$		−	540108.i		−	0.0425679i
$695$	8.95160e6			0.702973
$696$			1.83257e7i			1.43396i
$697$	5.34344e6			0.416619
$698$			1.52094e6i			0.118161i
$699$		−	1.13128e7i		−	0.875745i
$700$			5.65009e6i			0.435823i
$701$	4.74384e6			0.364616			0.182308	−	0.983242i	$-0.441643\pi$
$701$	4.74384e6			0.364616			0.182308	+	0.983242i	$0.441643\pi$
$702$			7.89779e6i			0.604871i
$703$	−1.01141e7			−0.771864
$704$	431352.			0.0328020
$705$		−	370217.i		−	0.0280533i
$706$	6.10849e6			0.461235
$707$		−	6.58010e6i		−	0.495090i
$708$			1.67755e7i			1.25774i
$709$			1.60442e7i			1.19868i	0.800494	+	0.599340i	$0.204570\pi$
$709$			1.60442e7i			1.19868i	−0.800494	+	0.599340i	$0.795430\pi$
$710$	−3.13290e6			−0.233239
$711$	100184.			0.00743231
$712$	1.96794e7			1.45483
$713$		−	3.30881e6i		−	0.243752i
$714$	1.18728e6			0.0871577
$715$	−7.23766e6			−0.529460
$716$		−	593671.i		−	0.0432776i
$717$			1.20682e7i			0.876691i
$718$		−	1.06531e6i		−	0.0771198i
$719$			4.64749e6i			0.335271i	0.985849	+	0.167636i	$0.0536132\pi$
$719$			4.64749e6i			0.335271i	−0.985849	+	0.167636i	$0.946387\pi$
$720$		−	135465.i		−	0.00973858i
$721$			4.97912e6i			0.356709i
$722$	5.87292e6			0.419286
$723$	−1.55751e7			−1.10811
$724$			1.42157e7i			1.00791i
$725$			2.07290e7i			1.46465i
$726$	777752.			0.0547646
$727$	4.87644e6			0.342190			0.171095	−	0.985255i	$-0.445270\pi$
$727$	4.87644e6			0.342190			0.171095	+	0.985255i	$0.445270\pi$
$728$	1.02626e7			0.717680
$729$	1.50253e7			1.04714
$730$			3.52698e6i			0.244961i
$731$		−	3.48084e6i		−	0.240930i
$732$	1.92288e7			1.32640
$733$	−6.62004e6			−0.455093			−0.227547	−	0.973767i	$-0.573070\pi$
$733$	−6.62004e6			−0.455093			−0.227547	+	0.973767i	$0.573070\pi$
$734$			1.19021e7i			0.815421i
$735$			3.35498e6i			0.229072i
$736$			2.34561e6i			0.159610i
$737$		−	1.71711e7i		−	1.16447i
$738$			509776.i			0.0344539i
$739$			1.30312e7i			0.877753i	0.898547	+	0.438877i	$0.144623\pi$
$739$			1.30312e7i			0.877753i	−0.898547	+	0.438877i	$0.855377\pi$
$740$	2.86554e6			0.192366
$741$	−2.61927e7			−1.75240
$742$			2.27922e6i			0.151976i
$743$	3.14891e6			0.209261			0.104630	−	0.994511i	$-0.466634\pi$
$743$	3.14891e6			0.209261			0.104630	+	0.994511i	$0.466634\pi$
$744$	1.84276e7			1.22049
$745$	−2.83474e6			−0.187121
$746$			4.17503e6i			0.274671i
$747$		−	1.12240e6i		−	0.0735947i
$748$			3.30290e6i			0.215844i
$749$	−1.38428e7			−0.901612
$750$		−	5.37292e6i		−	0.348784i
$751$	−2.11967e7			−1.37141			−0.685706	−	0.727879i	$-0.740506\pi$
$751$	−2.11967e7			−1.37141			−0.685706	+	0.727879i	$0.740506\pi$
$752$	−434003.			−0.0279865
$753$		−	7.25384e6i		−	0.466209i
$754$	1.66569e7			1.06700
$755$			3.43922e6i			0.219580i
$756$		−	8.66056e6i		−	0.551114i
$757$			1.95552e7i			1.24029i	0.784489	+	0.620143i	$0.212925\pi$
$757$			1.95552e7i			1.24029i	−0.784489	+	0.620143i	$0.787075\pi$
$758$	969434.			0.0612837
$759$		−	2.29074e6i		−	0.144335i
$760$	−7.83856e6			−0.492269
$761$		−	2.02984e7i		−	1.27058i	−0.772275	−	0.635288i	$-0.780881\pi$
$761$		−	2.02984e7i		−	1.27058i	0.772275	−	0.635288i	$-0.219119\pi$
$762$			6.65594e6i			0.415262i
$763$		−	1.13970e6i		−	0.0708729i
$764$	1.11978e7			0.694061
$765$	−108345.			−0.00669353
$766$		−	6.85791e6i		−	0.422299i
$767$	3.44664e7			2.11547
$768$	−7.72638e6			−0.472686
$769$		−	2.47299e7i		−	1.50802i	−0.656864	−	0.754009i	$-0.728117\pi$
$769$		−	2.47299e7i		−	1.50802i	0.656864	−	0.754009i	$-0.271883\pi$
$770$	−2.06683e6			−0.125626
$771$		−	1.19441e7i		−	0.723634i
$772$	−1.36891e7			−0.826668
$773$	2.10848e7			1.26917			0.634587	−	0.772851i	$-0.281170\pi$
$773$	2.10848e7			1.26917			0.634587	+	0.772851i	$0.281170\pi$
$774$	332080.			0.0199246
$775$	2.08442e7			1.24661
$776$	−6.94073e6	+	1.17819e7i	−0.413762	+	0.702361i
$777$	6.18080e6			0.367276
$778$	−8.07607e6			−0.478356
$779$	−3.36632e7			−1.98752
$780$	7.42092e6			0.436738
$781$		−	1.87987e7i		−	1.10281i
$782$	357942.			0.0209313
$783$		−	3.17738e7i		−	1.85210i
$784$	3.93302e6			0.228526
$785$	−1.20375e7			−0.697207
$786$		−	5.48331e6i		−	0.316582i
$787$	1.34144e6			0.0772030			0.0386015	−	0.999255i	$-0.487710\pi$
$787$	1.34144e6			0.0772030			0.0386015	+	0.999255i	$0.487710\pi$
$788$	−1.62626e7			−0.932987
$789$			1.29945e7i			0.743135i
$790$			488109.i			0.0278259i
$791$			9.96575e6i			0.566329i
$792$	−712265.			−0.0403486
$793$		−	3.95069e7i		−	2.23095i
$794$	−756946.			−0.0426102
$795$			3.72539e6i			0.209052i
$796$			1.62797e7i			0.910674i
$797$		−	1.88645e7i		−	1.05196i	−0.850497	−	0.525979i	$-0.823699\pi$
$797$		−	1.88645e7i		−	1.05196i	0.850497	−	0.525979i	$-0.176301\pi$
$798$	−7.47973e6			−0.415795
$799$			347116.i			0.0192357i
$800$	−1.47764e7			−0.816288
$801$	−1.71363e6			−0.0943705
$802$		−	6.19772e6i		−	0.340248i
$803$	−2.11634e7			−1.15823
$804$			1.76059e7i			0.960543i
$805$		−	860115.i		−	0.0467807i
$806$		−	1.67495e7i		−	0.908162i
$807$	−3.03344e7			−1.63965
$808$	1.10481e7			0.595334
$809$	5.74554e6			0.308645			0.154323	−	0.988021i	$-0.450680\pi$
$809$	5.74554e6			0.308645			0.154323	+	0.988021i	$0.450680\pi$
$810$			3.49089e6i			0.186949i
$811$	−1.40167e7			−0.748329			−0.374165	−	0.927362i	$-0.622071\pi$
$811$	−1.40167e7			−0.748329			−0.374165	+	0.927362i	$0.622071\pi$
$812$	−1.82656e7			−0.972175
$813$			8.99621e6i			0.477346i
$814$		−	4.47769e6i		−	0.236861i
$815$			1.01398e6i			0.0534732i
$816$		−	2.27496e6i		−	0.119605i
$817$			2.19290e7i			1.14938i
$818$			1.17170e7i			0.612259i
$819$	−893647.			−0.0465539
$820$	9.53748e6			0.495335
$821$		−	3.27780e7i		−	1.69717i	−0.529062	−	0.848583i	$-0.677456\pi$
$821$		−	3.27780e7i		−	1.69717i	0.529062	−	0.848583i	$-0.322544\pi$
$822$		−	4.64812e6i		−	0.239937i
$823$	1.61869e7			0.833034			0.416517	−	0.909128i	$-0.363251\pi$
$823$	1.61869e7			0.833034			0.416517	+	0.909128i	$0.363251\pi$
$824$	−8.36006e6			−0.428935
$825$	1.44307e7			0.738166
$826$	9.84243e6			0.501941
$827$			5.32434e6i			0.270709i	0.990797	+	0.135354i	$0.0432173\pi$
$827$			5.32434e6i			0.270709i	−0.990797	+	0.135354i	$0.956783\pi$
$828$		−	131131.i		−	0.00664706i
$829$	3.38643e7			1.71142			0.855709	−	0.517457i	$-0.173121\pi$
$829$	3.38643e7			1.71142			0.855709	+	0.517457i	$0.173121\pi$
$830$	5.46850e6			0.275532
$831$		−	1.94627e7i		−	0.977688i
$832$			908683.i			0.0455097i
$833$		−	3.14563e6i		−	0.157071i
$834$			1.43419e7i			0.713990i
$835$			5.07152e6i			0.251723i
$836$		−	2.08080e7i		−	1.02971i
$837$	−3.19504e7			−1.57639
$838$	−933043.			−0.0458978
$839$		−	2.67032e7i		−	1.30966i	−0.755775	−	0.654831i	$-0.772740\pi$
$839$		−	2.67032e7i		−	1.30966i	0.755775	−	0.654831i	$-0.227260\pi$
$840$	4.79018e6			0.234236
$841$	−4.65016e7			−2.26714
$842$	−1.08469e7			−0.527262
$843$			9.56763e6i			0.463698i
$844$			3.85090e6i			0.186083i
$845$		−	6.20683e6i		−	0.299039i
$846$	−33115.6			−0.00159077
$847$			1.75228e6i			0.0839257i
$848$	4.36725e6			0.208554
$849$	−8.57364e6			−0.408221
$850$			2.25489e6i			0.107048i
$851$	1.86340e6			0.0882027
$852$			1.92747e7i			0.909678i
$853$			8.97404e6i			0.422294i	0.977454	+	0.211147i	$0.0677199\pi$
$853$			8.97404e6i			0.422294i	−0.977454	+	0.211147i	$0.932280\pi$
$854$		−	1.12818e7i		−	0.529340i
$855$	682564.			0.0319321
$856$		−	2.32424e7i		−	1.08417i
$857$	−3.24570e7			−1.50958			−0.754791	−	0.655966i	$-0.772262\pi$
$857$	−3.24570e7			−1.50958			−0.754791	+	0.655966i	$0.772262\pi$
$858$		−	1.15959e7i		−	0.537757i
$859$		−	1.84931e7i		−	0.855121i	−0.903987	−	0.427560i	$-0.859373\pi$
$859$		−	1.84931e7i		−	0.855121i	0.903987	−	0.427560i	$-0.140627\pi$
$860$		−	6.21293e6i		−	0.286451i
$861$	2.05718e7			0.945722
$862$	−1.58460e7			−0.726358
$863$		−	4.44853e6i		−	0.203325i	−0.994819	−	0.101662i	$-0.967584\pi$
$863$		−	4.44853e6i		−	0.203325i	0.994819	−	0.101662i	$-0.0324161\pi$
$864$	2.26495e7			1.03223
$865$	−1.64526e7			−0.747642
$866$			1.71297e7i			0.776166i
$867$	1.97207e7			0.890995
$868$			1.83671e7i			0.827451i
$869$	−2.92886e6			−0.131568
$870$	7.77476e6			0.348248
$871$	3.61725e7			1.61560
$872$	1.91359e6			0.0852230
$873$	604383.	−	1.02594e6i	0.0268396	−	0.0455602i
$874$	−2.25500e6			−0.0998547
$875$	1.21052e7			0.534506
$876$	2.16992e7			0.955397
$877$	2.80744e7			1.23257			0.616285	−	0.787523i	$-0.288637\pi$
$877$	2.80744e7			1.23257			0.616285	+	0.787523i	$0.288637\pi$
$878$		−	2.14784e6i		−	0.0940297i
$879$	−1.77741e7			−0.775916
$880$			3.96029e6i			0.172393i
$881$	−414085.			−0.0179742			−0.00898711	−	0.999960i	$-0.502861\pi$
$881$	−414085.			−0.0179742			−0.00898711	+	0.999960i	$0.502861\pi$
$882$	300100.			0.0129896
$883$		−	4.39361e7i		−	1.89636i	−0.317739	−	0.948178i	$-0.602924\pi$
$883$		−	4.39361e7i		−	1.89636i	0.317739	−	0.948178i	$-0.397076\pi$
$884$	−6.95786e6			−0.299464
$885$	1.60875e7			0.690448
$886$			1.73477e6i			0.0742435i
$887$			2.38336e7i			1.01714i	0.861021	+	0.508570i	$0.169826\pi$
$887$			2.38336e7i			1.01714i	−0.861021	+	0.508570i	$0.830174\pi$
$888$			1.03777e7i			0.441640i
$889$	−1.49959e7			−0.636381
$890$		−	8.34905e6i		−	0.353315i
$891$	−2.09468e7			−0.883941
$892$		−	1.26638e7i		−	0.532908i
$893$		−	2.18680e6i		−	0.0917657i
$894$		−	4.54172e6i		−	0.190054i
$895$	−569325.			−0.0237576
$896$		−	1.61516e7i		−	0.672119i
$897$	4.82566e6			0.200251
$898$	−6.61336e6			−0.273672
$899$			6.73852e7i			2.78077i
$900$	826073.			0.0339948
$901$		−	3.49293e6i		−	0.143344i
$902$		−	1.49032e7i		−	0.609908i
$903$		−	1.34009e7i		−	0.546909i
$904$	−1.67327e7			−0.680997
$905$	1.36327e7			0.553301
$906$	−5.51018e6			−0.223021
$907$			939045.i			0.0379025i	0.999820	+	0.0189513i	$0.00603274\pi$
$907$			939045.i			0.0379025i	−0.999820	+	0.0189513i	$0.993967\pi$
$908$	4.99189e6			0.200932
$909$	−962046.			−0.0386177
$910$		−	4.35397e6i		−	0.174294i
$911$			2.28020e7i			0.910284i	0.890419	+	0.455142i	$0.150412\pi$
$911$			2.28020e7i			0.910284i	−0.890419	+	0.455142i	$0.849588\pi$
$912$			1.43321e7i			0.570587i
$913$			3.28132e7i			1.30278i
$914$		−	74424.1i		−	0.00294678i
$915$		−	1.84402e7i		−	0.728137i
$916$	−3.19126e7			−1.25668
$917$	1.23539e7			0.485156
$918$		−	3.45634e6i		−	0.135366i
$919$			1.95364e7i			0.763054i	0.924358	+	0.381527i	$0.124602\pi$
$919$			1.95364e7i			0.763054i	−0.924358	+	0.381527i	$0.875398\pi$
$920$	1.44415e6			0.0562527
$921$	−8.41217e6			−0.326782
$922$	4.62436e6			0.179153
$923$	3.96012e7			1.53004
$924$			1.27158e7i			0.489965i
$925$			1.17387e7i			0.451091i
$926$	−7.71314e6			−0.295599
$927$	727974.			0.0278238
$928$		−	4.77692e7i		−	1.82087i
$929$			3.68087e7i			1.39930i	0.714485	+	0.699650i	$0.246661\pi$
$929$			3.68087e7i			1.39930i	−0.714485	+	0.699650i	$0.753339\pi$
$930$		−	7.81797e6i		−	0.296406i
$931$			1.98172e7i			0.749321i
$932$			1.89322e7i			0.713940i
$933$			1.73758e7i			0.653494i
$934$	−1.59540e7			−0.598415
$935$	3.16745e6			0.118490
$936$		−	1.50045e6i		−	0.0559800i
$937$	−5.99307e6			−0.222998			−0.111499	−	0.993765i	$-0.535565\pi$
$937$	−5.99307e6			−0.222998			−0.111499	+	0.993765i	$0.535565\pi$
$938$	1.03296e7			0.383334
$939$	−3.80018e7			−1.40650
$940$			619565.i			0.0228701i
$941$			1.54215e7i			0.567744i	0.958862	+	0.283872i	$0.0916191\pi$
$941$			1.54215e7i			0.567744i	−0.958862	+	0.283872i	$0.908381\pi$
$942$		−	1.92860e7i		−	0.708133i
$943$	6.20201e6			0.227119
$944$		−	1.88593e7i		−	0.688803i
$945$	−8.30540e6			−0.302539
$946$	−9.70831e6			−0.352708
$947$		−	4.13797e7i		−	1.49938i	−0.661789	−	0.749690i	$-0.730202\pi$
$947$		−	4.13797e7i		−	1.49938i	0.661789	−	0.749690i	$-0.269798\pi$
$948$	3.00302e6			0.108527
$949$		−	4.45826e7i		−	1.60694i
$950$		−	1.42056e7i		−	0.510683i
$951$		−	4.40245e7i		−	1.57850i
$952$	−4.49128e6			−0.160612
$953$			3.14677e7i			1.12236i	0.827693	+	0.561182i	$0.189653\pi$
$953$			3.14677e7i			1.12236i	−0.827693	+	0.561182i	$0.810347\pi$
$954$	333233.			0.0118543
$955$		−	1.07385e7i		−	0.381010i
$956$		−	2.01964e7i		−	0.714710i
$957$			4.66518e7i			1.64660i
$958$	−5.00151e6			−0.176071
$959$	1.04722e7			0.367699
$960$			424136.i			0.0148535i
$961$	3.91306e7			1.36681
$962$	9.43267e6			0.328622
$963$			2.02389e6i			0.0703270i
$964$	2.60651e7			0.903374
$965$			1.31277e7i			0.453806i
$966$	1.37804e6			0.0475138
$967$	9.96199e6			0.342594			0.171297	−	0.985219i	$-0.445204\pi$
$967$	9.96199e6			0.342594			0.171297	+	0.985219i	$0.445204\pi$
$968$	−2.94212e6			−0.100919
$969$	1.14628e7			0.392176
$970$	4.99851e6	+	2.94464e6i	0.170573	+	0.100485i
$971$	−4.70460e7			−1.60131			−0.800653	−	0.599129i	$-0.795514\pi$
$971$	−4.70460e7			−1.60131			−0.800653	+	0.599129i	$0.795514\pi$
$972$	−2.46885e6			−0.0838164
$973$	−3.23124e7			−1.09418
$974$	2.13876e7			0.722380
$975$			3.03997e7i			1.02414i
$976$	−2.16173e7			−0.726403
$977$		−	39607.4i		−	0.00132752i	−1.00000		0.000663758i	$-0.999789\pi$
$977$		−	39607.4i		−	0.00132752i	1.00000		0.000663758i	$-0.000211281\pi$
$978$	−1.62456e6			−0.0543112
$979$	5.00978e7			1.67056
$980$		−	5.61461e6i		−	0.186747i
$981$	−166631.			−0.00552818
$982$	−7.39336e6			−0.244660
$983$			2.73256e7i			0.901957i	0.892535	+	0.450979i	$0.148925\pi$
$983$			2.73256e7i			0.901957i	−0.892535	+	0.450979i	$0.851075\pi$
$984$			3.45404e7i			1.13721i
$985$			1.55957e7i			0.512171i
$986$	−7.28962e6			−0.238788
$987$			1.33636e6i			0.0436648i
$988$	4.38339e7			1.42862
$989$		−	4.04013e6i		−	0.131342i
$990$			302181.i			0.00979896i
$991$			2.55110e7i			0.825170i	0.910919	+	0.412585i	$0.135374\pi$
$991$			2.55110e7i			0.825170i	−0.910919	+	0.412585i	$0.864626\pi$
$992$	−4.80347e7			−1.54980
$993$		−	1.16937e7i		−	0.376340i
$994$	1.13088e7			0.363035
$995$	1.56121e7			0.499922
$996$		−	3.36441e7i		−	1.07463i
$997$	−1.25435e7			−0.399651			−0.199826	−	0.979831i	$-0.564038\pi$
$997$	−1.25435e7			−0.399651			−0.199826	+	0.979831i	$0.564038\pi$
$998$			2.81461e7i			0.894524i
$999$		−	1.79933e7i		−	0.570422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.6.b.a.96.18	yes	40
97.96	even	2	inner	97.6.b.a.96.17	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.6.b.a.96.17	✓	40	97.96	even	2	inner
97.6.b.a.96.18	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)

\(f(q)\)	\(=\)	\(q-2.57129 q^{2} +15.1707 q^{3} -25.3885 q^{4} +24.3473i q^{5} -39.0083 q^{6} -87.8859i q^{7} +147.562 q^{8} -12.8494 q^{9} -62.6040i q^{10} +375.650 q^{11} -385.161 q^{12} +791.342i q^{13} +225.980i q^{14} +369.366i q^{15} +433.005 q^{16} -346.318i q^{17} +33.0395 q^{18} +2181.77i q^{19} -618.141i q^{20} -1333.29i q^{21} -965.905 q^{22} -401.963i q^{23} +2238.63 q^{24} +2532.21 q^{25} -2034.77i q^{26} -3881.42 q^{27} +2231.29i q^{28} +8186.13i q^{29} -949.747i q^{30} +8231.63 q^{31} -5835.38 q^{32} +5698.88 q^{33} +890.484i q^{34} +2139.79 q^{35} +326.226 q^{36} +4635.74i q^{37} -5609.97i q^{38} +12005.2i q^{39} +3592.75i q^{40} +15429.3i q^{41} +3428.28i q^{42} +10051.0 q^{43} -9537.18 q^{44} -312.848i q^{45} +1033.56i q^{46} -1002.30 q^{47} +6569.00 q^{48} +9083.07 q^{49} -6511.04 q^{50} -5253.89i q^{51} -20091.0i q^{52} +10085.9 q^{53} +9980.25 q^{54} +9146.07i q^{55} -12968.7i q^{56} +33099.1i q^{57} -21048.9i q^{58} -43554.4i q^{59} -9377.64i q^{60} -49923.9 q^{61} -21165.9 q^{62} +1129.28i q^{63} +1148.28 q^{64} -19267.0 q^{65} -14653.5 q^{66} -45710.3i q^{67} +8792.48i q^{68} -6098.07i q^{69} -5502.01 q^{70} -50043.1i q^{71} -1896.09 q^{72} -56338.0 q^{73} -11919.8i q^{74} +38415.4 q^{75} -55391.9i q^{76} -33014.3i q^{77} -30868.9i q^{78} -7796.78 q^{79} +10542.5i q^{80} -55761.5 q^{81} -39673.2i q^{82} +87350.6i q^{83} +33850.2i q^{84} +8431.91 q^{85} -25844.0 q^{86} +124189. i q^{87} +55431.8 q^{88} +133363. q^{89} +804.423i q^{90} +69547.8 q^{91} +10205.2i q^{92} +124880. q^{93} +2577.21 q^{94} -53120.3 q^{95} -88526.9 q^{96} +(-47035.9 + 79843.4i) q^{97} -23355.2 q^{98} -4826.87 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} + 40 q^{3} + 638 q^{4} - 130 q^{6} + 180 q^{8} + 3300 q^{9} + 382 q^{11} + 2586 q^{12} + 10174 q^{16} + 4738 q^{18} + 1996 q^{22} - 3102 q^{24} - 25178 q^{25} + 3046 q^{27} + 14796 q^{31}+ \cdots - 562238 q^{99}+O(q^{100}) \) 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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