LMFDB - Embedded newform 14.48.a.c.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,48,Mod(1,14)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 48, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("14.1"); S:= CuspForms(chi, 48); N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 48 $
Character orbit:	$[\chi]$	$=$	14.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,50331648] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$195.870727717$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2 x^{5} + \cdots - 16\!\cdots\!84 $ x^6 - 2x^5 - 280483855999722656191x^4 - 492136456142149959522890667816x^3 + 13891946637162657775929491213298858350824x^2 + 14150461489541555473731650597670320328255623629568*x - 16057155296033027072903188810374434950926208872982575766384
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{36}\cdot 3^{15}\cdot 5^{6}\cdot 7^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.69579e9$ of defining polynomial
Character	$\chi$	$=$	14.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+8.38861e6 q^{2} +4.57489e10 q^{3} +7.03687e13 q^{4} +4.17176e16 q^{5} +3.83770e17 q^{6} -2.73687e19 q^{7} +5.90296e20 q^{8} -2.44958e22 q^{9} +3.49953e23 q^{10} -2.13199e24 q^{11} +3.21930e24 q^{12} -1.95138e25 q^{13} -2.29586e26 q^{14} +1.90854e27 q^{15} +4.95176e27 q^{16} -1.97729e28 q^{17} -2.05486e29 q^{18} +6.85888e29 q^{19} +2.93562e30 q^{20} -1.25209e30 q^{21} -1.78844e31 q^{22} -9.20825e31 q^{23} +2.70054e31 q^{24} +1.02982e33 q^{25} -1.63694e32 q^{26} -2.33707e33 q^{27} -1.92590e33 q^{28} +1.53180e34 q^{29} +1.60100e34 q^{30} -5.45750e34 q^{31} +4.15384e34 q^{32} -9.75364e34 q^{33} -1.65867e35 q^{34} -1.14176e36 q^{35} -1.72374e36 q^{36} -3.13590e36 q^{37} +5.75364e36 q^{38} -8.92737e35 q^{39} +2.46257e37 q^{40} -1.26888e38 q^{41} -1.05033e37 q^{42} -2.98527e38 q^{43} -1.50026e38 q^{44} -1.02191e39 q^{45} -7.72444e38 q^{46} -1.61389e39 q^{47} +2.26538e38 q^{48} +7.49048e38 q^{49} +8.63872e39 q^{50} -9.04588e38 q^{51} -1.37316e39 q^{52} +2.19473e39 q^{53} -1.96048e40 q^{54} -8.89416e40 q^{55} -1.61557e40 q^{56} +3.13786e40 q^{57} +1.28497e41 q^{58} -2.26203e41 q^{59} +1.34301e41 q^{60} +1.43967e42 q^{61} -4.57809e41 q^{62} +6.70421e41 q^{63} +3.48449e41 q^{64} -8.14071e41 q^{65} -8.18195e41 q^{66} -1.58039e43 q^{67} -1.39139e42 q^{68} -4.21268e42 q^{69} -9.57777e42 q^{70} -2.35793e42 q^{71} -1.44598e43 q^{72} +6.24780e43 q^{73} -2.63058e43 q^{74} +4.71130e43 q^{75} +4.82651e43 q^{76} +5.83500e43 q^{77} -7.48882e42 q^{78} -3.88095e44 q^{79} +2.06576e44 q^{80} +5.44397e44 q^{81} -1.06441e45 q^{82} +1.75777e45 q^{83} -8.81081e43 q^{84} -8.24877e44 q^{85} -2.50422e45 q^{86} +7.00784e44 q^{87} -1.25851e45 q^{88} -3.91769e45 q^{89} -8.57239e45 q^{90} +5.34069e44 q^{91} -6.47973e45 q^{92} -2.49675e45 q^{93} -1.35383e46 q^{94} +2.86136e46 q^{95} +1.90034e45 q^{96} +1.95504e45 q^{97} +6.28347e45 q^{98} +5.22250e46 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 50331648 q^{2} + 91348200216 q^{3} + 422212465065984 q^{4} - 30\!\cdots\!00 q^{5} + 76\!\cdots\!28 q^{6} - 16\!\cdots\!58 q^{7} + 35\!\cdots\!72 q^{8} + 23\!\cdots\!02 q^{9} - 25\!\cdots\!00 q^{10}+ \cdots - 22\!\cdots\!76 q^{99}+O(q^{100}) $ 6 * q + 50331648 * q^2 + 91348200216 * q^3 + 422212465065984 * q^4 - 30854924554017900 * q^5 + 766284243117539328 * q^6 - 164212484040485498058 * q^7 + 3541774862152233910272 * q^8 + 23611401481192331893902 * q^9 - 258829866953230988083200 * q^10 - 3041554928367556663244472 * q^11 + 6428058132089735347175424 * q^12 - 191570324075361446274867612 * q^13 - 1377514157321888972893323264 * q^14 + 2152872376393147160276606400 * q^15 + 29710560942849126597578981376 * q^16 + 182134574393674491978939242700 * q^17 + 198066791356341844863841468416 * q^18 + 105921872842145395281581529432 * q^19 - 2171222292562809092482636185600 * q^20 - 2500085811682828987741110530088 * q^21 - 25514412004543512765745883774976 * q^22 + 7899982928916455721382409846400 * q^23 + 53922459871313010651198539169792 * q^24 + 262683336957609462428869088912250 * q^25 - 1607008353101169631112924648964096 * q^26 - 5145497061786399782948702525214768 * q^27 - 11555426280223656413124714678976512 * q^28 - 1232522012314953851089211475650748 * q^29 + 18059602439590565413873622659891200 * q^30 + 72879381477193587191769574430120160 * q^31 + 249230249209671726169463823802564608 * q^32 + 650973340162559425050384304879402560 * q^33 + 1527855547835372992810465562827161600 * q^34 + 844460634316174754595838034424539700 * q^35 + 1661504670506140050559579452686204928 * q^36 - 2350829994343156615163160293570449164 * q^37 + 888537069898603600022237070445510656 * q^38 - 23749444470098095106267492597757308832 * q^39 - 18213532693170720855672581767613644800 * q^40 - 37574511477606821868284528556464112132 * q^41 - 20972239840569072709196981721580437504 * q^42 - 140317571620320602329291697555258434968 * q^43 - 214030400656609747534838046601833873408 * q^44 + 26295596306265329899718309281681956900 * q^45 + 66269859997372011796034254296789811200 * q^46 + 708002688958069624152534886966137104352 * q^47 + 452334378256175291652729275268030529536 * q^48 + 4494289985791117400966964616167386961894 * q^49 + 2203547541869298397406510670202011648000 * q^50 - 2727943917011418941975075709475285627248 * q^51 - 13480563126891296376910928613697407418368 * q^52 - 52279163845818199239402993035899030148076 * q^53 - 43163557816477887510441749592636804562944 * q^54 - 251960273873968093291926136296648972678000 * q^55 - 96933941337694405976389286553779800375296 * q^56 - 573477266714411774837109161637481283739792 * q^57 - 10339144012681320394877768098335669878784 * q^58 - 1154054456625062116390095979270500564117240 * q^59 + 151494925501568933755343582033744599449600 * q^60 - 1044005217659731085861156994850316373335676 * q^61 + 611356562494637943065575786221101415137280 * q^62 - 646214481483965241810590391497176813840386 * q^63 + 2090694862362245919518973588060783891185664 * q^64 + 3194584995357111391012342521501923033185800 * q^65 + 5460760169074367293453054182985795350036480 * q^66 - 933326469202418857699748343169593992036424 * q^67 + 12816581271416192570473813904056430415052800 * q^68 - 3891276550887494643219113510902717842230400 * q^69 + 7083849232709738075800683702277969123737600 * q^70 - 15354263243214256646706193660254232469772912 * q^71 + 13937711371045170477244492673439120148660224 * q^72 + 35097104101107095287360422807160923534046332 * q^73 - 19720191297186958327210607743927418420723712 * q^74 + 54253840923690951415133098526131371680829000 * q^75 + 7453589172847985347975338067035774253006848 * q^76 + 83243548355469568471308548464739505189205896 * q^77 - 199224779877420641393196338545487742926585856 * q^78 + 116083394738898838035318356572808875206583104 * q^79 - 152786186058193454335661864796457961678438400 * q^80 + 45644045361405935459098194557296623953436294 * q^81 - 315197847577144406778866542524983302743392256 * q^82 - 1650553357776207980536462167742742823540569160 * q^83 - 175927898904516447880951474445503430689554432 * q^84 - 6873331910637436173767195931321684421228903800 * q^85 - 1177069103834794367264314968445621349640044544 * q^86 - 11444858388565719560905086433015676826273466704 * q^87 - 1795417131191241781048722716428516445141336064 * q^88 - 6572746325824162151046522148908755018513654916 * q^89 + 220583449539507796519416206986791517106995200 * q^90 + 5243039797475987712325338969412905339972182916 * q^91 + 555911877732834837128307313868085384550809600 * q^92 + 10472287731311146814773470934954649411827909536 * q^93 + 5939157020615174513722947373083233442664022016 * q^94 - 6386150132253545069254818239614899940335103200 * q^95 + 3794455784114778100960418020347603044309925888 * q^96 - 34281171183200724766133718472300444680714638388 * q^97 + 37700836929127253758690687114898671607639703552 * q^98 - 226943335602453325836392523541612774950265114776 * q^99

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 $

$2$	8.38861e6	0.707107
$2$	8.38861e6	0.707107
$3$	4.57489e10	0.280564	0.140282	−	0.990112i	$-0.455199\pi$
$3$	4.57489e10	0.280564	0.140282	+	0.990112i	$0.455199\pi$
$4$	7.03687e13	0.500000
$5$	4.17176e16	1.56504	0.782518	−	0.622628i	$-0.213935\pi$
$5$	4.17176e16	1.56504	0.782518	+	0.622628i	$0.213935\pi$
$6$	3.83770e17	0.198389
$7$	−2.73687e19	−0.377964
$7$	−2.73687e19	−0.377964
$8$	5.90296e20	0.353553
$9$	−2.44958e22	−0.921284
$10$	3.49953e23	1.10665
$11$	−2.13199e24	−0.717889	−0.358945	−	0.933359i	$-0.616863\pi$
$11$	−2.13199e24	−0.717889	−0.358945	+	0.933359i	$0.616863\pi$
$12$	3.21930e24	0.140282
$13$	−1.95138e25	−0.129621	−0.0648103	−	0.997898i	$-0.520644\pi$
$13$	−1.95138e25	−0.129621	−0.0648103	+	0.997898i	$0.520644\pi$
$14$	−2.29586e26	−0.267261
$15$	1.90854e27	0.439092
$16$	4.95176e27	0.250000
$17$	−1.97729e28	−0.240171	−0.120085	−	0.992764i	$-0.538317\pi$
$17$	−1.97729e28	−0.240171	−0.120085	+	0.992764i	$0.538317\pi$
$18$	−2.05486e29	−0.651446
$19$	6.85888e29	0.610300	0.305150	−	0.952304i	$-0.401293\pi$
$19$	6.85888e29	0.610300	0.305150	+	0.952304i	$0.401293\pi$
$20$	2.93562e30	0.782518
$21$	−1.25209e30	−0.106043
$22$	−1.78844e31	−0.507625
$23$	−9.20825e31	−0.919545	−0.459773	−	0.888037i	$-0.652069\pi$
$23$	−9.20825e31	−0.919545	−0.459773	+	0.888037i	$0.652069\pi$
$24$	2.70054e31	0.0991943
$25$	1.02982e33	1.44934
$26$	−1.63694e32	−0.0916556
$27$	−2.33707e33	−0.539043
$28$	−1.92590e33	−0.188982
$29$	1.53180e34	0.658946	0.329473	−	0.944165i	$-0.393129\pi$
$29$	1.53180e34	0.658946	0.329473	+	0.944165i	$0.393129\pi$
$30$	1.60100e34	0.310485
$31$	−5.45750e34	−0.489772	−0.244886	−	0.969552i	$-0.578751\pi$
$31$	−5.45750e34	−0.489772	−0.244886	+	0.969552i	$0.578751\pi$
$32$	4.15384e34	0.176777
$33$	−9.75364e34	−0.201414
$34$	−1.65867e35	−0.169826
$35$	−1.14176e36	−0.591528
$36$	−1.72374e36	−0.460642
$37$	−3.13590e36	−0.440171	−0.220085	−	0.975481i	$-0.570634\pi$
$37$	−3.13590e36	−0.440171	−0.220085	+	0.975481i	$0.570634\pi$
$38$	5.75364e36	0.431547
$39$	−8.92737e35	−0.0363668
$40$	2.46257e37	0.553324
$41$	−1.26888e38	−1.59588	−0.797939	−	0.602739i	$-0.794076\pi$
$41$	−1.26888e38	−1.59588	−0.797939	+	0.602739i	$0.794076\pi$
$42$	−1.05033e37	−0.0749838
$43$	−2.98527e38	−1.22595	−0.612977	−	0.790101i	$-0.710028\pi$
$43$	−2.98527e38	−1.22595	−0.612977	+	0.790101i	$0.710028\pi$
$44$	−1.50026e38	−0.358945
$45$	−1.02191e39	−1.44184
$46$	−7.72444e38	−0.650217
$47$	−1.61389e39	−0.819546	−0.409773	−	0.912188i	$-0.634392\pi$
$47$	−1.61389e39	−0.819546	−0.409773	+	0.912188i	$0.634392\pi$
$48$	2.26538e38	0.0701409
$49$	7.49048e38	0.142857
$50$	8.63872e39	1.02484
$51$	−9.04588e38	−0.0673832
$52$	−1.37316e39	−0.0648103
$53$	2.19473e39	0.0662060	0.0331030	−	0.999452i	$-0.489461\pi$
$53$	2.19473e39	0.0662060	0.0331030	+	0.999452i	$0.489461\pi$
$54$	−1.96048e40	−0.381161
$55$	−8.89416e40	−1.12352
$56$	−1.61557e40	−0.133631
$57$	3.13786e40	0.171228
$58$	1.28497e41	0.465945
$59$	−2.26203e41	−0.548878	−0.274439	−	0.961604i	$-0.588492\pi$
$59$	−2.26203e41	−0.548878	−0.274439	+	0.961604i	$0.588492\pi$
$60$	1.34301e41	0.219546
$61$	1.43967e42	1.59592	0.797959	−	0.602711i	$-0.205913\pi$
$61$	1.43967e42	1.59592	0.797959	+	0.602711i	$0.205913\pi$
$62$	−4.57809e41	−0.346321
$63$	6.70421e41	0.348213
$64$	3.48449e41	0.125000
$65$	−8.14071e41	−0.202861
$66$	−8.18195e41	−0.142421
$67$	−1.58039e43	−1.93199	−0.965996	−	0.258556i	$-0.916754\pi$
$67$	−1.58039e43	−1.93199	−0.965996	+	0.258556i	$0.916754\pi$
$68$	−1.39139e42	−0.120085
$69$	−4.21268e42	−0.257991
$70$	−9.57777e42	−0.418273
$71$	−2.35793e42	−0.0737836	−0.0368918	−	0.999319i	$-0.511746\pi$
$71$	−2.35793e42	−0.0737836	−0.0368918	+	0.999319i	$0.511746\pi$
$72$	−1.44598e43	−0.325723
$73$	6.24780e43	1.01775	0.508873	−	0.860841i	$-0.330062\pi$
$73$	6.24780e43	1.01775	0.508873	+	0.860841i	$0.330062\pi$
$74$	−2.63058e43	−0.311248
$75$	4.71130e43	0.406631
$76$	4.82651e43	0.305150
$77$	5.83500e43	0.271337
$78$	−7.48882e42	−0.0257152
$79$	−3.88095e44	−0.987873	−0.493936	−	0.869498i	$-0.664442\pi$
$79$	−3.88095e44	−0.987873	−0.493936	+	0.869498i	$0.664442\pi$
$80$	2.06576e44	0.391259
$81$	5.44397e44	0.770048
$82$	−1.06441e45	−1.12846
$83$	1.75777e45	1.40161	0.700806	−	0.713352i	$-0.252824\pi$
$83$	1.75777e45	1.40161	0.700806	+	0.713352i	$0.252824\pi$
$84$	−8.81081e43	−0.0530216
$85$	−8.24877e44	−0.375876
$86$	−2.50422e45	−0.866880
$87$	7.00784e44	0.184876
$88$	−1.25851e45	−0.253812
$89$	−3.91769e45	−0.605850	−0.302925	−	0.953014i	$-0.597963\pi$
$89$	−3.91769e45	−0.605850	−0.302925	+	0.953014i	$0.597963\pi$
$90$	−8.57239e45	−1.01954
$91$	5.34069e44	0.0489920
$92$	−6.47973e45	−0.459773
$93$	−2.49675e45	−0.137412
$94$	−1.35383e46	−0.579506
$95$	2.86136e46	0.955142
$96$	1.90034e45	0.0495971
$97$	1.95504e45	0.0399963	0.0199981	−	0.999800i	$-0.493634\pi$
$97$	1.95504e45	0.0399963	0.0199981	+	0.999800i	$0.493634\pi$
$98$	6.28347e45	0.101015
$99$	5.22250e46	0.661380
$100$	7.24669e46	0.724669
$101$	−4.65881e46	−0.368742	−0.184371	−	0.982857i	$-0.559025\pi$
$101$	−4.65881e46	−0.368742	−0.184371	+	0.982857i	$0.559025\pi$
$102$	−7.58824e45	−0.0476471
$103$	2.53650e46	0.126637	0.0633183	−	0.997993i	$-0.479832\pi$
$103$	2.53650e46	0.126637	0.0633183	+	0.997993i	$0.479832\pi$
$104$	−1.15189e46	−0.0458278
$105$	−5.22342e46	−0.165961
$106$	1.84107e46	0.0468147
$107$	−5.36470e47	−1.09402	−0.547012	−	0.837125i	$-0.684235\pi$
$107$	−5.36470e47	−1.09402	−0.547012	+	0.837125i	$0.684235\pi$
$108$	−1.64457e47	−0.269521
$109$	−5.18261e47	−0.683952	−0.341976	−	0.939709i	$-0.611096\pi$
$109$	−5.18261e47	−0.683952	−0.341976	+	0.939709i	$0.611096\pi$
$110$	−7.46096e47	−0.794451
$111$	−1.43464e47	−0.123496
$112$	−1.35523e47	−0.0944911
$113$	−2.53933e48	−1.43673	−0.718365	−	0.695666i	$-0.755109\pi$
$113$	−2.53933e48	−1.43673	−0.718365	+	0.695666i	$0.755109\pi$
$114$	2.63223e47	0.121077
$115$	−3.84146e48	−1.43912
$116$	1.07791e48	0.329473
$117$	4.78008e47	0.119417
$118$	−1.89753e48	−0.388116
$119$	5.41159e47	0.0907761
$120$	1.12660e48	0.155243
$121$	−4.27436e48	−0.484635
$122$	1.20768e49	1.12848
$123$	−5.80499e48	−0.447745
$124$	−3.84038e48	−0.244886
$125$	1.33193e49	0.703229
$126$	5.62390e48	0.246224
$127$	2.49325e48	0.0906521	0.0453260	−	0.998972i	$-0.485567\pi$
$127$	2.49325e48	0.0906521	0.0453260	+	0.998972i	$0.485567\pi$
$128$	2.92300e48	0.0883883
$129$	−1.36573e49	−0.343958
$130$	−6.82892e48	−0.143444
$131$	6.29980e49	1.10523	0.552614	−	0.833438i	$-0.313631\pi$
$131$	6.29980e49	1.10523	0.552614	+	0.833438i	$0.313631\pi$
$132$	−6.86351e48	−0.100707
$133$	−1.87719e49	−0.230672
$134$	−1.32572e50	−1.36613
$135$	−9.74969e49	−0.843621
$136$	−1.16718e49	−0.0849132
$137$	1.45763e50	0.892718	0.446359	−	0.894854i	$-0.352721\pi$
$137$	1.45763e50	0.892718	0.446359	+	0.894854i	$0.352721\pi$
$138$	−3.53385e49	−0.182427
$139$	3.58465e50	1.56171	0.780853	−	0.624715i	$-0.214785\pi$
$139$	3.58465e50	1.56171	0.780853	+	0.624715i	$0.214785\pi$
$140$	−8.03441e49	−0.295764
$141$	−7.38336e49	−0.229935
$142$	−1.97797e49	−0.0521729
$143$	4.16034e49	0.0930533
$144$	−1.21298e50	−0.230321
$145$	6.39032e50	1.03127
$146$	5.24103e50	0.719656
$147$	3.42682e49	0.0400805
$148$	−2.20669e50	−0.220085
$149$	9.86272e50	0.839691	0.419845	−	0.907596i	$-0.362084\pi$
$149$	9.86272e50	0.839691	0.419845	+	0.907596i	$0.362084\pi$
$150$	3.95212e50	0.287532
$151$	−1.23599e50	−0.0769228	−0.0384614	−	0.999260i	$-0.512246\pi$
$151$	−1.23599e50	−0.0769228	−0.0384614	+	0.999260i	$0.512246\pi$
$152$	4.04877e50	0.215774
$153$	4.84354e50	0.221266
$154$	4.89475e50	0.191864
$155$	−2.27674e51	−0.766511
$156$	−6.28208e49	−0.0181834
$157$	−4.50074e51	−1.12109	−0.560547	−	0.828122i	$-0.689409\pi$
$157$	−4.50074e51	−1.12109	−0.560547	+	0.828122i	$0.689409\pi$
$158$	−3.25557e51	−0.698532
$159$	1.00406e50	0.0185750
$160$	1.73288e51	0.276662
$161$	2.52018e51	0.347555
$162$	4.56673e51	0.544506
$163$	−1.04851e52	−1.08184	−0.540920	−	0.841074i	$-0.681924\pi$
$163$	−1.04851e52	−1.08184	−0.540920	+	0.841074i	$0.681924\pi$
$164$	−8.92894e51	−0.797939
$165$	−4.06898e51	−0.315220
$166$	1.47453e52	0.991090
$167$	1.63921e52	0.956748	0.478374	−	0.878156i	$-0.341226\pi$
$167$	1.63921e52	0.956748	0.478374	+	0.878156i	$0.341226\pi$
$168$	−7.39104e50	−0.0374919
$169$	−2.22833e52	−0.983199
$170$	−6.91957e51	−0.265784
$171$	−1.68014e52	−0.562260
$172$	−2.10069e52	−0.612977
$173$	5.41837e52	1.37970	0.689851	−	0.723951i	$-0.257676\pi$
$173$	5.41837e52	1.37970	0.689851	+	0.723951i	$0.257676\pi$
$174$	5.87860e51	0.130727
$175$	−2.81848e52	−0.547798
$176$	−1.05571e52	−0.179472
$177$	−1.03485e52	−0.153995
$178$	−3.28640e52	−0.428400
$179$	−2.85957e52	−0.326779	−0.163390	−	0.986562i	$-0.552243\pi$
$179$	−2.85957e52	−0.326779	−0.163390	+	0.986562i	$0.552243\pi$
$180$	−7.19104e52	−0.720921
$181$	−1.29801e53	−1.14244	−0.571218	−	0.820799i	$-0.693529\pi$
$181$	−1.29801e53	−1.14244	−0.571218	+	0.820799i	$0.693529\pi$
$182$	4.48010e51	0.0346426
$183$	6.58632e52	0.447757
$184$	−5.43559e52	−0.325108
$185$	−1.30822e53	−0.688883
$186$	−2.09443e52	−0.0971652
$187$	4.21556e52	0.172416
$188$	−1.13567e53	−0.409773
$189$	6.39626e52	0.203739
$190$	2.40028e53	0.675387
$191$	−3.07810e52	−0.0765595	−0.0382797	−	0.999267i	$-0.512188\pi$
$191$	−3.07810e52	−0.0765595	−0.0382797	+	0.999267i	$0.512188\pi$
$192$	1.59412e52	0.0350705
$193$	−6.20236e53	−1.20770	−0.603852	−	0.797096i	$-0.706368\pi$
$193$	−6.20236e53	−1.20770	−0.603852	+	0.797096i	$0.706368\pi$
$194$	1.64001e52	0.0282816
$195$	−3.72429e52	−0.0569154
$196$	5.27096e52	0.0714286
$197$	6.54397e53	0.786837	0.393418	−	0.919360i	$-0.371292\pi$
$197$	6.54397e53	0.786837	0.393418	+	0.919360i	$0.371292\pi$
$198$	4.38095e53	0.467666
$199$	−3.49763e53	−0.331685	−0.165843	−	0.986152i	$-0.553034\pi$
$199$	−3.49763e53	−0.331685	−0.165843	+	0.986152i	$0.553034\pi$
$200$	6.07896e53	0.512418
$201$	−7.23010e53	−0.542047
$202$	−3.90810e53	−0.260740
$203$	−4.19235e53	−0.249058
$204$	−6.36547e52	−0.0336916
$205$	−5.29346e54	−2.49761
$206$	2.12777e53	0.0895456
$207$	2.25564e54	0.847162
$208$	−9.66279e52	−0.0324051
$209$	−1.46231e54	−0.438128
$210$	−4.38173e53	−0.117352
$211$	−1.11823e54	−0.267851	−0.133925	−	0.990991i	$-0.542758\pi$
$211$	−1.11823e54	−0.267851	−0.133925	+	0.990991i	$0.542758\pi$
$212$	1.54440e53	0.0331030
$213$	−1.07873e53	−0.0207010
$214$	−4.50024e54	−0.773592
$215$	−1.24538e55	−1.91866
$216$	−1.37956e54	−0.190580
$217$	1.49365e54	0.185117
$218$	−4.34749e54	−0.483627
$219$	2.85830e54	0.285543
$220$	−6.25871e54	−0.561761
$221$	3.85845e53	0.0311311
$222$	−1.20346e54	−0.0873248
$223$	1.98565e54	0.129640	0.0648198	−	0.997897i	$-0.479353\pi$
$223$	1.98565e54	0.129640	0.0648198	+	0.997897i	$0.479353\pi$
$224$	−1.13685e54	−0.0668153
$225$	−2.52262e55	−1.33525
$226$	−2.13014e55	−1.01592
$227$	−1.49272e55	−0.641759	−0.320880	−	0.947120i	$-0.603978\pi$
$227$	−1.49272e55	−0.641759	−0.320880	+	0.947120i	$0.603978\pi$
$228$	2.20808e54	0.0856140
$229$	−3.85021e55	−1.34695	−0.673473	−	0.739211i	$-0.735198\pi$
$229$	−3.85021e55	−1.34695	−0.673473	+	0.739211i	$0.735198\pi$
$230$	−3.22245e55	−1.01761
$231$	2.66945e54	0.0761272
$232$	9.04217e54	0.232973
$233$	−1.22980e55	−0.286399	−0.143199	−	0.989694i	$-0.545739\pi$
$233$	−1.22980e55	−0.286399	−0.143199	+	0.989694i	$0.545739\pi$
$234$	4.00982e54	0.0844408
$235$	−6.73274e55	−1.28262
$236$	−1.59176e55	−0.274439
$237$	−1.77549e55	−0.277161
$238$	4.53957e54	0.0641884
$239$	−1.38934e56	−1.78015	−0.890075	−	0.455815i	$-0.849348\pi$
$239$	−1.38934e56	−1.78015	−0.890075	+	0.455815i	$0.849348\pi$
$240$	9.45061e54	0.109773
$241$	4.25580e55	0.448313	0.224156	−	0.974553i	$-0.428037\pi$
$241$	4.25580e55	0.448313	0.224156	+	0.974553i	$0.428037\pi$
$242$	−3.58559e55	−0.342688
$243$	8.70455e55	0.755090
$244$	1.01308e56	0.797959
$245$	3.12485e55	0.223577
$246$	−4.86958e55	−0.316604
$247$	−1.33843e55	−0.0791075
$248$	−3.22154e55	−0.173161
$249$	8.04163e55	0.393242
$250$	1.11731e56	0.497258
$251$	−3.04781e56	−1.23497	−0.617484	−	0.786583i	$-0.711848\pi$
$251$	−3.04781e56	−1.23497	−0.617484	+	0.786583i	$0.711848\pi$
$252$	4.71767e55	0.174106
$253$	1.96319e56	0.660132
$254$	2.09149e55	0.0641007
$255$	−3.77373e55	−0.105457
$256$	2.45199e55	0.0625000
$257$	3.53878e56	0.823048	0.411524	−	0.911399i	$-0.364997\pi$
$257$	3.53878e56	0.823048	0.411524	+	0.911399i	$0.364997\pi$
$258$	−1.14565e56	−0.243215
$259$	8.58255e55	0.166369
$260$	−5.72851e55	−0.101430
$261$	−3.75228e56	−0.607077
$262$	5.28466e56	0.781514
$263$	−4.57231e56	−0.618267	−0.309133	−	0.951019i	$-0.600039\pi$
$263$	−4.57231e56	−0.618267	−0.309133	+	0.951019i	$0.600039\pi$
$264$	−5.75753e55	−0.0712105
$265$	9.15588e55	0.103615
$266$	−1.57470e56	−0.163110
$267$	−1.79230e56	−0.169979
$268$	−1.11210e57	−0.965996
$269$	4.54738e56	0.361895	0.180947	−	0.983493i	$-0.442084\pi$
$269$	4.54738e56	0.361895	0.180947	+	0.983493i	$0.442084\pi$
$270$	−8.17863e56	−0.596530
$271$	−1.57362e55	−0.0105226	−0.00526128	−	0.999986i	$-0.501675\pi$
$271$	−1.57362e55	−0.0105226	−0.00526128	+	0.999986i	$0.501675\pi$
$272$	−9.79106e55	−0.0600427
$273$	2.44331e55	0.0137454
$274$	1.22275e57	0.631247
$275$	−2.19556e57	−1.04046
$276$	−2.96441e56	−0.128995
$277$	3.72624e57	1.48935	0.744674	−	0.667428i	$-0.232605\pi$
$277$	3.72624e57	1.48935	0.744674	+	0.667428i	$0.232605\pi$
$278$	3.00702e57	1.10429
$279$	1.33686e57	0.451219
$280$	−6.73975e56	−0.209137
$281$	4.87014e57	1.38977	0.694885	−	0.719121i	$-0.255455\pi$
$281$	4.87014e57	1.38977	0.694885	+	0.719121i	$0.255455\pi$
$282$	−6.19361e56	−0.162588
$283$	7.65266e57	1.84855	0.924276	−	0.381726i	$-0.124670\pi$
$283$	7.65266e57	1.84855	0.924276	+	0.381726i	$0.124670\pi$
$284$	−1.65925e56	−0.0368918
$285$	1.30904e57	0.267978
$286$	3.48994e56	0.0657986
$287$	3.47276e57	0.603185
$288$	−1.01752e57	−0.162862
$289$	−6.38700e57	−0.942318
$290$	5.36059e57	0.729221
$291$	8.94410e55	0.0112215
$292$	4.39650e57	0.508873
$293$	−1.46527e58	−1.56505	−0.782525	−	0.622619i	$-0.786069\pi$
$293$	−1.46527e58	−1.56505	−0.782525	+	0.622619i	$0.786069\pi$
$294$	2.87462e56	0.0283412
$295$	−9.43665e57	−0.859014
$296$	−1.85111e57	−0.155624
$297$	4.98261e57	0.386973
$298$	8.27345e57	0.593751
$299$	1.79688e57	0.119192
$300$	3.31528e57	0.203316
$301$	8.17030e57	0.463367
$302$	−1.03682e57	−0.0543926
$303$	−2.13136e57	−0.103456
$304$	3.39635e57	0.152575
$305$	6.00594e58	2.49767
$306$	4.06305e57	0.156458
$307$	2.81687e58	1.00465	0.502325	−	0.864679i	$-0.332478\pi$
$307$	2.81687e58	1.00465	0.502325	+	0.864679i	$0.332478\pi$
$308$	4.10601e57	0.135668
$309$	1.16042e57	0.0355297
$310$	−1.90987e58	−0.542005
$311$	3.17533e58	0.835449	0.417725	−	0.908574i	$-0.362828\pi$
$311$	3.17533e58	0.835449	0.417725	+	0.908574i	$0.362828\pi$
$312$	−5.26979e56	−0.0128576
$313$	6.80203e58	1.53938	0.769692	−	0.638416i	$-0.220410\pi$
$313$	6.80203e58	1.53938	0.769692	+	0.638416i	$0.220410\pi$
$314$	−3.77550e58	−0.792734
$315$	2.79683e58	0.544965
$316$	−2.73097e58	−0.493936
$317$	−6.30005e58	−1.05792	−0.528958	−	0.848648i	$-0.677417\pi$
$317$	−6.30005e58	−1.05792	−0.528958	+	0.848648i	$0.677417\pi$
$318$	8.42270e56	0.0131345
$319$	−3.26579e58	−0.473051
$320$	1.45365e58	0.195629
$321$	−2.45429e58	−0.306944
$322$	2.11408e58	0.245759
$323$	−1.35620e58	−0.146576
$324$	3.83085e58	0.385024
$325$	−2.00957e58	−0.187864
$326$	−8.79552e58	−0.764976
$327$	−2.37099e58	−0.191892
$328$	−7.49014e58	−0.564228
$329$	4.41700e58	0.309759
$330$	−3.41331e58	−0.222894
$331$	−2.82332e59	−1.71713	−0.858563	−	0.512709i	$-0.828642\pi$
$331$	−2.82332e59	−1.71713	−0.858563	+	0.512709i	$0.828642\pi$
$332$	1.23692e59	0.700806
$333$	7.68164e58	0.405522
$334$	1.37507e59	0.676523
$335$	−6.59300e59	−3.02364
$336$	−6.20005e57	−0.0265108
$337$	−1.36123e59	−0.542784	−0.271392	−	0.962469i	$-0.587484\pi$
$337$	−1.36123e59	−0.542784	−0.271392	+	0.962469i	$0.587484\pi$
$338$	−1.86926e59	−0.695226
$339$	−1.16172e59	−0.403094
$340$	−5.80456e58	−0.187938
$341$	1.16354e59	0.351602
$342$	−1.40940e59	−0.397578
$343$	−2.05005e58	−0.0539949
$344$	−1.76219e59	−0.433440
$345$	−1.75743e59	−0.403765
$346$	4.54526e59	0.975597
$347$	1.32848e59	0.266448	0.133224	−	0.991086i	$-0.457467\pi$
$347$	1.32848e59	0.266448	0.133224	+	0.991086i	$0.457467\pi$
$348$	4.93133e58	0.0924382
$349$	5.10481e59	0.894504	0.447252	−	0.894408i	$-0.352403\pi$
$349$	5.10481e59	0.894504	0.447252	+	0.894408i	$0.352403\pi$
$350$	−2.36431e59	−0.387352
$351$	4.56052e58	0.0698710
$352$	−8.85595e58	−0.126906
$353$	−2.62873e59	−0.352403	−0.176202	−	0.984354i	$-0.556381\pi$
$353$	−2.62873e59	−0.352403	−0.176202	+	0.984354i	$0.556381\pi$
$354$	−8.68099e58	−0.108891
$355$	−9.83672e58	−0.115474
$356$	−2.75683e59	−0.302925
$357$	2.47574e58	0.0254685
$358$	−2.39878e59	−0.231068
$359$	−1.74617e60	−1.57531	−0.787656	−	0.616116i	$-0.788705\pi$
$359$	−1.74617e60	−1.57531	−0.787656	+	0.616116i	$0.788705\pi$
$360$	−6.03228e59	−0.509768
$361$	−7.92604e59	−0.627534
$362$	−1.08885e60	−0.807824
$363$	−1.95547e59	−0.135971
$364$	3.75818e58	0.0244960
$365$	2.60643e60	1.59281
$366$	5.52501e59	0.316612
$367$	−2.43269e59	−0.130748	−0.0653738	−	0.997861i	$-0.520824\pi$
$367$	−2.43269e59	−0.130748	−0.0653738	+	0.997861i	$0.520824\pi$
$368$	−4.55971e59	−0.229886
$369$	3.10823e60	1.47026
$370$	−1.09742e60	−0.487114
$371$	−6.00669e58	−0.0250235
$372$	−1.75693e59	−0.0687062
$373$	5.29913e60	1.94557	0.972786	−	0.231705i	$-0.0744304\pi$
$373$	5.29913e60	1.94557	0.972786	+	0.231705i	$0.0744304\pi$
$374$	3.53627e59	0.121917
$375$	6.09344e59	0.197300
$376$	−9.52670e59	−0.289753
$377$	−2.98914e59	−0.0854130
$378$	5.36558e59	0.144065
$379$	1.77237e60	0.447231	0.223615	−	0.974677i	$-0.428214\pi$
$379$	1.77237e60	0.447231	0.223615	+	0.974677i	$0.428214\pi$
$380$	2.01350e60	0.477571
$381$	1.14063e59	0.0254337
$382$	−2.58210e59	−0.0541357
$383$	−1.65136e60	−0.325590	−0.162795	−	0.986660i	$-0.552051\pi$
$383$	−1.65136e60	−0.325590	−0.162795	+	0.986660i	$0.552051\pi$
$384$	1.33724e59	0.0247986
$385$	2.43422e60	0.424652
$386$	−5.20292e60	−0.853976
$387$	7.31266e60	1.12945
$388$	1.37574e59	0.0199981
$389$	−3.20749e60	−0.438884	−0.219442	−	0.975626i	$-0.570424\pi$
$389$	−3.20749e60	−0.438884	−0.219442	+	0.975626i	$0.570424\pi$
$390$	−3.12416e59	−0.0402453
$391$	1.82074e60	0.220848
$392$	4.42160e59	0.0505076
$393$	2.88209e60	0.310087
$394$	5.48948e60	0.556378
$395$	−1.61904e61	−1.54606
$396$	3.67501e60	0.330690
$397$	−4.14935e60	−0.351887	−0.175943	−	0.984400i	$-0.556298\pi$
$397$	−4.14935e60	−0.351887	−0.175943	+	0.984400i	$0.556298\pi$
$398$	−2.93402e60	−0.234537
$399$	−8.58794e59	−0.0647181
$400$	5.09940e60	0.362334
$401$	2.16421e61	1.45013	0.725065	−	0.688680i	$-0.241810\pi$
$401$	2.16421e61	1.45013	0.725065	+	0.688680i	$0.241810\pi$
$402$	−6.06505e60	−0.383285
$403$	1.06497e60	0.0634846
$404$	−3.27835e60	−0.184371
$405$	2.27109e61	1.20515
$406$	−3.51680e60	−0.176111
$407$	6.68571e60	0.315994
$408$	−5.33975e59	−0.0238236
$409$	3.89301e60	0.163979	0.0819895	−	0.996633i	$-0.473873\pi$
$409$	3.89301e60	0.163979	0.0819895	+	0.996633i	$0.473873\pi$
$410$	−4.44048e61	−1.76607
$411$	6.66850e60	0.250464
$412$	1.78490e60	0.0633183
$413$	6.19089e60	0.207457
$414$	1.89217e61	0.599034
$415$	7.33302e61	2.19357
$416$	−8.10573e59	−0.0229139
$417$	1.63994e61	0.438158
$418$	−1.22667e61	−0.309803
$419$	7.94187e60	0.189624	0.0948120	−	0.995495i	$-0.469775\pi$
$419$	7.94187e60	0.189624	0.0948120	+	0.995495i	$0.469775\pi$
$420$	−3.67566e60	−0.0829806
$421$	5.68598e61	1.21388	0.606941	−	0.794747i	$-0.292396\pi$
$421$	5.68598e61	1.21388	0.606941	+	0.794747i	$0.292396\pi$
$422$	−9.38038e60	−0.189399
$423$	3.95335e61	0.755034
$424$	1.29554e60	0.0234074
$425$	−2.03624e61	−0.348089
$426$	−9.04902e59	−0.0146378
$427$	−3.94019e61	−0.603201
$428$	−3.77507e61	−0.547012
$429$	1.90331e60	0.0261074
$430$	−1.04470e62	−1.35670
$431$	−3.38663e60	−0.0416439	−0.0208219	−	0.999783i	$-0.506628\pi$
$431$	−3.38663e60	−0.0416439	−0.0208219	+	0.999783i	$0.506628\pi$
$432$	−1.15726e61	−0.134761
$433$	−2.99996e61	−0.330864	−0.165432	−	0.986221i	$-0.552902\pi$
$433$	−2.99996e61	−0.330864	−0.165432	+	0.986221i	$0.552902\pi$
$434$	1.25296e61	0.130897
$435$	2.92350e61	0.289338
$436$	−3.64694e61	−0.341976
$437$	−6.31583e61	−0.561198
$438$	2.39772e61	0.201909
$439$	7.61907e61	0.608115	0.304057	−	0.952654i	$-0.401659\pi$
$439$	7.61907e61	0.608115	0.304057	+	0.952654i	$0.401659\pi$
$440$	−5.25019e61	−0.397225
$441$	−1.83486e61	−0.131612
$442$	3.23670e60	0.0220130
$443$	−6.03416e61	−0.389161	−0.194581	−	0.980887i	$-0.562335\pi$
$443$	−6.03416e61	−0.389161	−0.194581	+	0.980887i	$0.562335\pi$
$444$	−1.00954e61	−0.0617480
$445$	−1.63437e62	−0.948176
$446$	1.66568e61	0.0916691
$447$	4.51209e61	0.235587
$448$	−9.53662e60	−0.0472456
$449$	−1.48223e62	−0.696828	−0.348414	−	0.937341i	$-0.613280\pi$
$449$	−1.48223e62	−0.696828	−0.348414	+	0.937341i	$0.613280\pi$
$450$	−2.11613e62	−0.944165
$451$	2.70524e62	1.14566
$452$	−1.78689e62	−0.718365
$453$	−5.65450e60	−0.0215817
$454$	−1.25219e62	−0.453792
$455$	2.22801e61	0.0766742
$456$	1.85227e61	0.0605383
$457$	1.23134e62	0.382250	0.191125	−	0.981566i	$-0.438786\pi$
$457$	1.23134e62	0.382250	0.191125	+	0.981566i	$0.438786\pi$
$458$	−3.22979e62	−0.952435
$459$	4.62106e61	0.129462
$460$	−2.70319e62	−0.719561
$461$	−5.68520e62	−1.43805	−0.719025	−	0.694984i	$-0.755411\pi$
$461$	−5.68520e62	−1.43805	−0.719025	+	0.694984i	$0.755411\pi$
$462$	2.23930e61	0.0538301
$463$	−7.15046e62	−1.63373	−0.816866	−	0.576828i	$-0.804290\pi$
$463$	−7.15046e62	−1.63373	−0.816866	+	0.576828i	$0.804290\pi$
$464$	7.58512e61	0.164737
$465$	−1.04158e62	−0.215055
$466$	−1.03163e62	−0.202514
$467$	6.59199e62	1.23047	0.615233	−	0.788345i	$-0.289062\pi$
$467$	6.59199e62	1.23047	0.615233	+	0.788345i	$0.289062\pi$
$468$	3.36368e61	0.0597087
$469$	4.32532e62	0.730225
$470$	−5.64784e62	−0.906948
$471$	−2.05904e62	−0.314538
$472$	−1.33527e62	−0.194058
$473$	6.36456e62	0.880100
$474$	−1.48939e62	−0.195983
$475$	7.06338e62	0.884531
$476$	3.80807e61	0.0453880
$477$	−5.37617e61	−0.0609946
$478$	−1.16546e63	−1.25876
$479$	1.31263e63	1.34977	0.674883	−	0.737924i	$-0.264194\pi$
$479$	1.31263e63	1.34977	0.674883	+	0.737924i	$0.264194\pi$
$480$	7.92775e61	0.0776213
$481$	6.11934e61	0.0570552
$482$	3.57003e62	0.317005
$483$	1.15296e62	0.0975114
$484$	−3.00781e62	−0.242317
$485$	8.15595e61	0.0625956
$486$	7.30190e62	0.533929
$487$	2.77178e63	1.93121	0.965603	−	0.260020i	$-0.0837290\pi$
$487$	2.77178e63	1.93121	0.965603	+	0.260020i	$0.0837290\pi$
$488$	8.49829e62	0.564242
$489$	−4.79681e62	−0.303525
$490$	2.62131e62	0.158092
$491$	8.05956e62	0.463336	0.231668	−	0.972795i	$-0.425582\pi$
$491$	8.05956e62	0.463336	0.231668	+	0.972795i	$0.425582\pi$
$492$	−4.08490e62	−0.223873
$493$	−3.02882e62	−0.158260
$494$	−1.12276e62	−0.0559374
$495$	2.17870e63	1.03508
$496$	−2.70242e62	−0.122443
$497$	6.45336e61	0.0278876
$498$	6.74581e62	0.278064
$499$	−2.95377e63	−1.16149	−0.580744	−	0.814086i	$-0.697238\pi$
$499$	−2.95377e63	−1.16149	−0.580744	+	0.814086i	$0.697238\pi$
$500$	9.37263e62	0.351614
$501$	7.49921e62	0.268429
$502$	−2.55669e63	−0.873255
$503$	3.50183e63	1.14143	0.570713	−	0.821150i	$-0.306667\pi$
$503$	3.50183e63	1.14143	0.570713	+	0.821150i	$0.306667\pi$
$504$	3.95747e62	0.123112
$505$	−1.94355e63	−0.577095
$506$	1.64685e63	0.466784
$507$	−1.01944e63	−0.275850
$508$	1.75447e62	0.0453260
$509$	4.46958e63	1.10255	0.551276	−	0.834323i	$-0.314141\pi$
$509$	4.46958e63	1.10255	0.551276	+	0.834323i	$0.314141\pi$
$510$	−3.16563e62	−0.0745695
$511$	−1.70994e63	−0.384672
$512$	2.05688e62	0.0441942
$513$	−1.60297e63	−0.328978
$514$	2.96854e63	0.581983
$515$	1.05817e63	0.198191
$516$	−9.61045e62	−0.171979
$517$	3.44079e63	0.588343
$518$	7.19957e62	0.117641
$519$	2.47885e63	0.387095
$520$	−4.80543e62	−0.0717221
$521$	8.71875e63	1.24385	0.621925	−	0.783077i	$-0.286351\pi$
$521$	8.71875e63	1.24385	0.621925	+	0.783077i	$0.286351\pi$
$522$	−3.14764e63	−0.429268
$523$	−4.57676e63	−0.596717	−0.298358	−	0.954454i	$-0.596439\pi$
$523$	−4.57676e63	−0.596717	−0.298358	+	0.954454i	$0.596439\pi$
$524$	4.43309e63	0.552614
$525$	−1.28942e63	−0.153692
$526$	−3.83553e63	−0.437180
$527$	1.07911e63	0.117629
$528$	−4.82977e62	−0.0503534
$529$	−1.54867e63	−0.154437
$530$	7.68051e62	0.0732667
$531$	5.54104e63	0.505673
$532$	−1.32095e63	−0.115336
$533$	2.47607e63	0.206859
$534$	−1.50349e63	−0.120194
$535$	−2.23803e64	−1.71219
$536$	−9.32896e63	−0.683063
$537$	−1.30822e63	−0.0916824
$538$	3.81462e63	0.255898
$539$	−1.59697e63	−0.102556
$540$	−6.86074e63	−0.421810
$541$	2.25060e64	1.32483	0.662417	−	0.749135i	$-0.269531\pi$
$541$	2.25060e64	1.32483	0.662417	+	0.749135i	$0.269531\pi$
$542$	−1.32005e62	−0.00744057
$543$	−5.93826e63	−0.320526
$544$	−8.21333e62	−0.0424566
$545$	−2.16206e64	−1.07041
$546$	2.04960e62	0.00971944
$547$	−3.73451e64	−1.69641	−0.848205	−	0.529668i	$-0.822317\pi$
$547$	−3.73451e64	−1.69641	−0.848205	+	0.529668i	$0.822317\pi$
$548$	1.02572e64	0.446359
$549$	−3.52659e64	−1.47029
$550$	−1.84177e64	−0.735719
$551$	1.05065e64	0.402155
$552$	−2.48673e63	−0.0912136
$553$	1.06217e64	0.373381
$554$	3.12580e64	1.05313
$555$	−5.98497e63	−0.193276
$556$	2.52247e64	0.780853
$557$	1.81240e63	0.0537844	0.0268922	−	0.999638i	$-0.491439\pi$
$557$	1.81240e63	0.0537844	0.0268922	+	0.999638i	$0.491439\pi$
$558$	1.12144e64	0.319060
$559$	5.82540e63	0.158909
$560$	−5.65371e63	−0.147882
$561$	1.92858e63	0.0483737
$562$	4.08537e64	0.982716
$563$	−6.54978e64	−1.51105	−0.755526	−	0.655119i	$-0.772619\pi$
$563$	−6.54978e64	−1.51105	−0.755526	+	0.655119i	$0.772619\pi$
$564$	−5.19557e63	−0.114967
$565$	−1.05935e65	−2.24853
$566$	6.41952e64	1.30712
$567$	−1.48995e64	−0.291051
$568$	−1.39188e63	−0.0260864
$569$	8.42527e64	1.51512	0.757558	−	0.652768i	$-0.226392\pi$
$569$	8.42527e64	1.51512	0.757558	+	0.652768i	$0.226392\pi$
$570$	1.09810e64	0.189489
$571$	4.73298e64	0.783766	0.391883	−	0.920015i	$-0.371824\pi$
$571$	4.73298e64	0.783766	0.391883	+	0.920015i	$0.371824\pi$
$572$	2.92758e63	0.0465266
$573$	−1.40820e63	−0.0214798
$574$	2.91316e64	0.426516
$575$	−9.48280e64	−1.33273
$576$	−8.53556e63	−0.115161
$577$	−2.33941e64	−0.303023	−0.151511	−	0.988456i	$-0.548414\pi$
$577$	−2.33941e64	−0.303023	−0.151511	+	0.988456i	$0.548414\pi$
$578$	−5.35780e64	−0.666319
$579$	−2.83752e64	−0.338838
$580$	4.49679e64	0.515637
$581$	−4.81081e64	−0.529760
$582$	7.50285e62	0.00793480
$583$	−4.67914e63	−0.0475286
$584$	3.68805e64	0.359828
$585$	1.99414e64	0.186892
$586$	−1.22916e65	−1.10666
$587$	−1.35444e65	−1.17156	−0.585782	−	0.810469i	$-0.699212\pi$
$587$	−1.35444e65	−1.17156	−0.585782	+	0.810469i	$0.699212\pi$
$588$	2.41141e63	0.0200403
$589$	−3.74323e64	−0.298908
$590$	−7.91603e64	−0.607415
$591$	2.99379e64	0.220758
$592$	−1.55282e64	−0.110043
$593$	7.56604e64	0.515327	0.257664	−	0.966235i	$-0.417047\pi$
$593$	7.56604e64	0.515327	0.257664	+	0.966235i	$0.417047\pi$
$594$	4.17972e64	0.273631
$595$	2.25759e64	0.142068
$596$	6.94027e64	0.419845
$597$	−1.60013e64	−0.0930588
$598$	1.50734e64	0.0842815
$599$	−5.32759e63	−0.0286418	−0.0143209	−	0.999897i	$-0.504559\pi$
$599$	−5.32759e63	−0.0286418	−0.0143209	+	0.999897i	$0.504559\pi$
$600$	2.78106e64	0.143766
$601$	−2.98566e65	−1.48419	−0.742095	−	0.670294i	$-0.766168\pi$
$601$	−2.98566e65	−1.48419	−0.742095	+	0.670294i	$0.766168\pi$
$602$	6.85374e64	0.327650
$603$	3.87129e65	1.77991
$604$	−8.69748e63	−0.0384614
$605$	−1.78316e65	−0.758471
$606$	−1.78791e64	−0.0731542
$607$	4.40767e65	1.73490	0.867451	−	0.497523i	$-0.165757\pi$
$607$	4.40767e65	1.73490	0.867451	+	0.497523i	$0.165757\pi$
$608$	2.84907e64	0.107887
$609$	−1.91796e64	−0.0698767
$610$	5.03815e65	1.76612
$611$	3.14931e64	0.106230
$612$	3.40833e64	0.110633
$613$	5.99582e65	1.87295	0.936477	−	0.350729i	$-0.114066\pi$
$613$	5.99582e65	1.87295	0.936477	+	0.350729i	$0.114066\pi$
$614$	2.36296e65	0.710395
$615$	−2.42170e65	−0.700737
$616$	3.44437e64	0.0959320
$617$	−7.25982e65	−1.94637	−0.973183	−	0.230032i	$-0.926117\pi$
$617$	−7.25982e65	−1.94637	−0.973183	+	0.230032i	$0.926117\pi$
$618$	9.73431e63	0.0251233
$619$	5.68633e65	1.41287	0.706434	−	0.707779i	$-0.250303\pi$
$619$	5.68633e65	1.41287	0.706434	+	0.707779i	$0.250303\pi$
$620$	−1.60211e65	−0.383256
$621$	2.15203e65	0.495674
$622$	2.66366e65	0.590752
$623$	1.07222e65	0.228990
$624$	−4.42062e63	−0.00909171
$625$	−1.76078e65	−0.348759
$626$	5.70596e65	1.08851
$627$	−6.68990e64	−0.122923
$628$	−3.16712e65	−0.560547
$629$	6.20057e64	0.105716
$630$	2.34616e65	0.385349
$631$	2.05639e65	0.325398	0.162699	−	0.986676i	$-0.447980\pi$
$631$	2.05639e65	0.325398	0.162699	+	0.986676i	$0.447980\pi$
$632$	−2.29091e65	−0.349266
$633$	−5.11578e64	−0.0751492
$634$	−5.28486e65	−0.748059
$635$	1.04012e65	0.141874
$636$	7.06547e63	0.00928751
$637$	−1.46168e64	−0.0185172
$638$	−2.73955e65	−0.334497
$639$	5.77595e64	0.0679756
$640$	1.21941e65	0.138331
$641$	3.57747e65	0.391212	0.195606	−	0.980683i	$-0.437333\pi$
$641$	3.57747e65	0.391212	0.195606	+	0.980683i	$0.437333\pi$
$642$	−2.05881e65	−0.217042
$643$	−4.28331e65	−0.435333	−0.217666	−	0.976023i	$-0.569844\pi$
$643$	−4.28331e65	−0.435333	−0.217666	+	0.976023i	$0.569844\pi$
$644$	1.77342e65	0.173778
$645$	−5.69749e65	−0.538307
$646$	−1.13766e65	−0.103645
$647$	2.86624e65	0.251804	0.125902	−	0.992043i	$-0.459818\pi$
$647$	2.86624e65	0.251804	0.125902	+	0.992043i	$0.459818\pi$
$648$	3.21355e65	0.272253
$649$	4.82263e65	0.394034
$650$	−1.68575e65	−0.132840
$651$	6.83329e64	0.0519370
$652$	−7.37822e65	−0.540920
$653$	1.13751e65	0.0804442	0.0402221	−	0.999191i	$-0.487193\pi$
$653$	1.13751e65	0.0804442	0.0402221	+	0.999191i	$0.487193\pi$
$654$	−1.98893e65	−0.135688
$655$	2.62813e66	1.72972
$656$	−6.28318e65	−0.398969
$657$	−1.53045e66	−0.937634
$658$	3.70525e65	0.219033
$659$	−1.57436e66	−0.898042	−0.449021	−	0.893521i	$-0.648227\pi$
$659$	−1.57436e66	−0.898042	−0.449021	+	0.893521i	$0.648227\pi$
$660$	−2.86329e65	−0.157610
$661$	3.95877e65	0.210294	0.105147	−	0.994457i	$-0.466469\pi$
$661$	3.95877e65	0.210294	0.105147	+	0.994457i	$0.466469\pi$
$662$	−2.36837e66	−1.21419
$663$	1.76520e64	0.00873425
$664$	1.03761e66	0.495545
$665$	−7.83118e65	−0.361010
$666$	6.44383e65	0.286748
$667$	−1.41052e66	−0.605931
$668$	1.15349e66	0.478374
$669$	9.08413e64	0.0363722
$670$	−5.53061e66	−2.13803
$671$	−3.06936e66	−1.14569
$672$	−5.20098e64	−0.0187460
$673$	1.13042e66	0.393446	0.196723	−	0.980459i	$-0.436970\pi$
$673$	1.13042e66	0.393446	0.196723	+	0.980459i	$0.436970\pi$
$674$	−1.14188e66	−0.383807
$675$	−2.40675e66	−0.781254
$676$	−1.56805e66	−0.491599
$677$	−5.89355e66	−1.78461	−0.892304	−	0.451434i	$-0.850912\pi$
$677$	−5.89355e66	−1.78461	−0.892304	+	0.451434i	$0.850912\pi$
$678$	−9.74517e65	−0.285031
$679$	−5.35070e64	−0.0151172
$680$	−4.86922e65	−0.132892
$681$	−6.82906e65	−0.180054
$682$	9.76044e65	0.248620
$683$	4.65402e66	1.14536	0.572679	−	0.819780i	$-0.305904\pi$
$683$	4.65402e66	1.14536	0.572679	+	0.819780i	$0.305904\pi$
$684$	−1.18229e66	−0.281130
$685$	6.08089e66	1.39714
$686$	−1.71971e65	−0.0381802
$687$	−1.76143e66	−0.377904
$688$	−1.47823e66	−0.306489
$689$	−4.28276e64	−0.00858167
$690$	−1.47424e66	−0.285505
$691$	−4.06640e66	−0.761159	−0.380580	−	0.924748i	$-0.624276\pi$
$691$	−4.06640e66	−0.761159	−0.380580	+	0.924748i	$0.624276\pi$
$692$	3.81284e66	0.689851
$693$	−1.42933e66	−0.249978
$694$	1.11441e66	0.188407
$695$	1.49543e67	2.44413
$696$	4.13670e65	0.0653637
$697$	2.50894e66	0.383283
$698$	4.28223e66	0.632510
$699$	−5.62621e65	−0.0803531
$700$	−1.98333e66	−0.273899
$701$	1.18836e67	1.58699	0.793497	−	0.608574i	$-0.208258\pi$
$701$	1.18836e67	1.58699	0.793497	+	0.608574i	$0.208258\pi$
$702$	3.82564e65	0.0494063
$703$	−2.15087e66	−0.268636
$704$	−7.42891e65	−0.0897362
$705$	−3.08016e66	−0.359856
$706$	−2.20514e66	−0.249187
$707$	1.27506e66	0.139371
$708$	−7.28214e65	−0.0769977
$709$	6.73526e66	0.688919	0.344459	−	0.938801i	$-0.388062\pi$
$709$	6.73526e66	0.688919	0.344459	+	0.938801i	$0.388062\pi$
$710$	−8.25164e65	−0.0816524
$711$	9.50671e66	0.910111
$712$	−2.31260e66	−0.214200
$713$	5.02541e66	0.450368
$714$	2.07681e65	0.0180089
$715$	1.73559e66	0.145632
$716$	−2.01224e66	−0.163390
$717$	−6.35606e66	−0.499445
$718$	−1.46479e67	−1.11391
$719$	−3.71757e66	−0.273609	−0.136805	−	0.990598i	$-0.543683\pi$
$719$	−3.71757e66	−0.273609	−0.136805	+	0.990598i	$0.543683\pi$
$720$	−5.06024e66	−0.360461
$721$	−6.94207e65	−0.0478642
$722$	−6.64885e66	−0.443733
$723$	1.94698e66	0.125780
$724$	−9.13393e66	−0.571218
$725$	1.57748e67	0.955036
$726$	−1.64037e66	−0.0961460
$727$	1.48214e67	0.841065	0.420532	−	0.907278i	$-0.361843\pi$
$727$	1.48214e67	0.841065	0.420532	+	0.907278i	$0.361843\pi$
$728$	3.15259e65	0.0173213
$729$	−1.04926e67	−0.558197
$730$	2.18643e67	1.12629
$731$	5.90273e66	0.294438
$732$	4.63471e66	0.223878
$733$	7.51173e66	0.351396	0.175698	−	0.984444i	$-0.443782\pi$
$733$	7.51173e66	0.351396	0.175698	+	0.984444i	$0.443782\pi$
$734$	−2.04069e66	−0.0924525
$735$	1.42959e66	0.0627275
$736$	−3.82496e66	−0.162554
$737$	3.36937e67	1.38696
$738$	2.60737e67	1.03963
$739$	−8.53564e66	−0.329679	−0.164840	−	0.986320i	$-0.552711\pi$
$739$	−8.53564e66	−0.329679	−0.164840	+	0.986320i	$0.552711\pi$
$740$	−9.20579e66	−0.344441
$741$	−6.12318e65	−0.0221947
$742$	−5.03878e65	−0.0176943
$743$	−4.79074e67	−1.62992	−0.814958	−	0.579519i	$-0.803240\pi$
$743$	−4.79074e67	−1.62992	−0.814958	+	0.579519i	$0.803240\pi$
$744$	−1.47382e66	−0.0485826
$745$	4.11449e67	1.31415
$746$	4.44524e67	1.37573
$747$	−4.30582e67	−1.29128
$748$	2.96644e66	0.0862081
$749$	1.46825e67	0.413502
$750$	5.11155e66	0.139512
$751$	−3.91615e67	−1.03591	−0.517953	−	0.855409i	$-0.673306\pi$
$751$	−3.91615e67	−1.03591	−0.517953	+	0.855409i	$0.673306\pi$
$752$	−7.99158e66	−0.204886
$753$	−1.39434e67	−0.346487
$754$	−2.50747e66	−0.0603961
$755$	−5.15624e66	−0.120387
$756$	4.50097e66	0.101869
$757$	2.30362e67	0.505426	0.252713	−	0.967541i	$-0.418677\pi$
$757$	2.30362e67	0.505426	0.252713	+	0.967541i	$0.418677\pi$
$758$	1.48677e67	0.316240
$759$	8.98140e66	0.185209
$760$	1.68905e67	0.337694
$761$	−3.02172e67	−0.585754	−0.292877	−	0.956150i	$-0.594613\pi$
$761$	−3.02172e67	−0.585754	−0.292877	+	0.956150i	$0.594613\pi$
$762$	9.56833e65	0.0179843
$763$	1.41842e67	0.258510
$764$	−2.16602e66	−0.0382797
$765$	2.02061e67	0.346289
$766$	−1.38526e67	−0.230227
$767$	4.41409e66	0.0711459
$768$	1.12176e66	0.0175352
$769$	−9.59373e67	−1.45452	−0.727258	−	0.686364i	$-0.759206\pi$
$769$	−9.59373e67	−1.45452	−0.727258	+	0.686364i	$0.759206\pi$
$770$	2.04197e67	0.300274
$771$	1.61895e67	0.230917
$772$	−4.36453e67	−0.603852
$773$	1.92111e67	0.257831	0.128915	−	0.991656i	$-0.458850\pi$
$773$	1.92111e67	0.257831	0.128915	+	0.991656i	$0.458850\pi$
$774$	6.13430e67	0.798643
$775$	−5.62022e67	−0.709845
$776$	1.15405e66	0.0141408
$777$	3.92643e66	0.0466771
$778$	−2.69064e67	−0.310338
$779$	−8.70309e67	−0.973964
$780$	−2.62073e66	−0.0284577
$781$	5.02709e66	0.0529684
$782$	1.52734e67	0.156163
$783$	−3.57993e67	−0.355200
$784$	3.70911e66	0.0357143
$785$	−1.87760e68	−1.75455
$786$	2.41767e67	0.219264
$787$	1.53889e68	1.35457	0.677287	−	0.735719i	$-0.263156\pi$
$787$	1.53889e68	1.35457	0.677287	+	0.735719i	$0.263156\pi$
$788$	4.60491e67	0.393418
$789$	−2.09178e67	−0.173463
$790$	−1.35815e68	−1.09323
$791$	6.94982e67	0.543033
$792$	3.08282e67	0.233833
$793$	−2.80934e67	−0.206864
$794$	−3.48073e67	−0.248822
$795$	4.18872e66	0.0290706
$796$	−2.46123e67	−0.165843
$797$	−1.74415e68	−1.14107	−0.570535	−	0.821273i	$-0.693264\pi$
$797$	−1.74415e68	−1.14107	−0.570535	+	0.821273i	$0.693264\pi$
$798$	−7.20409e66	−0.0457626
$799$	3.19112e67	0.196831
$800$	4.27769e67	0.256209
$801$	9.59671e67	0.558160
$802$	1.81547e68	1.02540
$803$	−1.33203e68	−0.730630
$804$	−5.08773e67	−0.271024
$805$	1.05136e68	0.543937
$806$	8.93360e66	0.0448904
$807$	2.08038e67	0.101535
$808$	−2.75008e67	−0.130370
$809$	−4.21527e68	−1.94104	−0.970520	−	0.241019i	$-0.922518\pi$
$809$	−4.21527e68	−1.94104	−0.970520	+	0.241019i	$0.922518\pi$
$810$	1.90513e68	0.852172
$811$	1.23406e68	0.536223	0.268112	−	0.963388i	$-0.413600\pi$
$811$	1.23406e68	0.536223	0.268112	+	0.963388i	$0.413600\pi$
$812$	−2.95011e67	−0.124529
$813$	−7.19914e65	−0.00295225
$814$	5.60838e67	0.223441
$815$	−4.37412e68	−1.69312
$816$	−4.47930e66	−0.0168458
$817$	−2.04756e68	−0.748200
$818$	3.26569e67	0.115951
$819$	−1.30825e67	−0.0451355
$820$	−3.72494e68	−1.24880
$821$	−1.35533e68	−0.441550	−0.220775	−	0.975325i	$-0.570859\pi$
$821$	−1.35533e68	−0.441550	−0.220775	+	0.975325i	$0.570859\pi$
$822$	5.59395e67	0.177105
$823$	−2.10249e68	−0.646901	−0.323450	−	0.946245i	$-0.604843\pi$
$823$	−2.10249e68	−0.646901	−0.323450	+	0.946245i	$0.604843\pi$
$824$	1.49728e67	0.0447728
$825$	−1.00445e68	−0.291916
$826$	5.19330e67	0.146694
$827$	6.21881e67	0.170737	0.0853685	−	0.996349i	$-0.472793\pi$
$827$	6.21881e67	0.170737	0.0853685	+	0.996349i	$0.472793\pi$
$828$	1.58727e68	0.423581
$829$	8.82520e67	0.228925	0.114462	−	0.993428i	$-0.463485\pi$
$829$	8.82520e67	0.228925	0.114462	+	0.993428i	$0.463485\pi$
$830$	6.15138e68	1.55109
$831$	1.70472e68	0.417857
$832$	−6.79958e66	−0.0162026
$833$	−1.48108e67	−0.0343101
$834$	1.37568e68	0.309824
$835$	6.83839e68	1.49735
$836$	−1.02901e68	−0.219064
$837$	1.27546e68	0.264008
$838$	6.66212e67	0.134084
$839$	7.60277e68	1.48787	0.743937	−	0.668250i	$-0.232956\pi$
$839$	7.60277e68	1.48787	0.743937	+	0.668250i	$0.232956\pi$
$840$	−3.08337e67	−0.0586762
$841$	−3.05746e68	−0.565790
$842$	4.76975e68	0.858344
$843$	2.22804e68	0.389919
$844$	−7.86884e67	−0.133925
$845$	−9.29604e68	−1.53874
$846$	3.31631e68	0.533890
$847$	1.16984e68	0.183175
$848$	1.08678e67	0.0165515
$849$	3.50101e68	0.518636
$850$	−1.70812e68	−0.246136
$851$	2.88761e68	0.404757
$852$	−7.59087e66	−0.0103505
$853$	1.29663e69	1.71994	0.859968	−	0.510347i	$-0.170483\pi$
$853$	1.29663e69	1.71994	0.859968	+	0.510347i	$0.170483\pi$
$854$	−3.30527e68	−0.426527
$855$	−7.00914e68	−0.879957
$856$	−3.16676e68	−0.386796
$857$	7.27586e68	0.864639	0.432320	−	0.901720i	$-0.357695\pi$
$857$	7.27586e68	0.864639	0.432320	+	0.901720i	$0.357695\pi$
$858$	1.59661e67	0.0184607
$859$	−1.03789e69	−1.16765	−0.583825	−	0.811880i	$-0.698445\pi$
$859$	−1.03789e69	−1.16765	−0.583825	+	0.811880i	$0.698445\pi$
$860$	−8.76359e68	−0.959331
$861$	1.58875e68	0.169232
$862$	−2.84091e67	−0.0294467
$863$	8.82493e68	0.890139	0.445069	−	0.895496i	$-0.353179\pi$
$863$	8.82493e68	0.890139	0.445069	+	0.895496i	$0.353179\pi$
$864$	−9.70780e67	−0.0952902
$865$	2.26042e69	2.15928
$866$	−2.51655e68	−0.233956
$867$	−2.92198e68	−0.264380
$868$	1.05106e68	0.0925583
$869$	8.27415e68	0.709183
$870$	2.45241e68	0.204593
$871$	3.08394e68	0.250426
$872$	−3.05927e68	−0.241814
$873$	−4.78903e67	−0.0368479
$874$	−5.29810e68	−0.396827
$875$	−3.64533e68	−0.265795
$876$	2.01135e68	0.142771
$877$	2.70944e69	1.87236	0.936180	−	0.351522i	$-0.114336\pi$
$877$	2.70944e69	1.87236	0.936180	+	0.351522i	$0.114336\pi$
$878$	6.39134e68	0.430002
$879$	−6.70345e68	−0.439096
$880$	−4.40418e68	−0.280881
$881$	−2.86512e68	−0.177914	−0.0889568	−	0.996035i	$-0.528353\pi$
$881$	−2.86512e68	−0.177914	−0.0889568	+	0.996035i	$0.528353\pi$
$882$	−1.53919e68	−0.0930637
$883$	2.36022e69	1.38956	0.694778	−	0.719224i	$-0.255502\pi$
$883$	2.36022e69	1.38956	0.694778	+	0.719224i	$0.255502\pi$
$884$	2.71514e67	0.0155655
$885$	−4.31717e68	−0.241008
$886$	−5.06182e68	−0.275178
$887$	−2.14853e69	−1.13746	−0.568731	−	0.822524i	$-0.692565\pi$
$887$	−2.14853e69	−1.13746	−0.568731	+	0.822524i	$0.692565\pi$
$888$	−8.46861e67	−0.0436624
$889$	−6.82370e67	−0.0342633
$890$	−1.37101e69	−0.670462
$891$	−1.16065e69	−0.552810
$892$	1.39728e68	0.0648198
$893$	−1.10694e69	−0.500169
$894$	3.78501e68	0.166585
$895$	−1.19294e69	−0.511421
$896$	−7.99989e67	−0.0334077
$897$	8.22055e67	0.0334409
$898$	−1.24338e69	−0.492732
$899$	−8.35982e68	−0.322734
$900$	−1.77514e69	−0.667626
$901$	−4.33961e67	−0.0159008
$902$	2.26932e69	0.810107
$903$	3.73782e68	0.130004
$904$	−1.49895e69	−0.507961
$905$	−5.41499e69	−1.78795
$906$	−4.74334e67	−0.0152606
$907$	−1.96925e67	−0.00617348	−0.00308674	−	0.999995i	$-0.500983\pi$
$907$	−1.96925e67	−0.00617348	−0.00308674	+	0.999995i	$0.500983\pi$
$908$	−1.05041e69	−0.320880
$909$	1.14122e69	0.339716
$910$	1.86899e68	0.0542168
$911$	−1.28070e69	−0.362047	−0.181024	−	0.983479i	$-0.557941\pi$
$911$	−1.28070e69	−0.362047	−0.181024	+	0.983479i	$0.557941\pi$
$912$	1.55379e68	0.0428070
$913$	−3.74756e69	−1.00620
$914$	1.03292e69	0.270291
$915$	2.74766e69	0.700756
$916$	−2.70934e69	−0.673473
$917$	−1.72418e69	−0.417737
$918$	3.87642e68	0.0915437
$919$	−3.17051e69	−0.729818	−0.364909	−	0.931043i	$-0.618900\pi$
$919$	−3.17051e69	−0.729818	−0.364909	+	0.931043i	$0.618900\pi$
$920$	−2.26760e69	−0.508806
$921$	1.28869e69	0.281868
$922$	−4.76909e69	−1.01685
$923$	4.60123e67	0.00956387
$924$	1.87846e68	0.0380636
$925$	−3.22940e69	−0.637956
$926$	−5.99824e69	−1.15522
$927$	−6.21336e68	−0.116668
$928$	6.36286e68	0.116486
$929$	8.21111e69	1.46566	0.732829	−	0.680413i	$-0.238199\pi$
$929$	8.21111e69	1.46566	0.732829	+	0.680413i	$0.238199\pi$
$930$	−8.73744e68	−0.152067
$931$	5.13763e68	0.0871857
$932$	−8.65396e68	−0.143199
$933$	1.45268e69	0.234397
$934$	5.52976e69	0.870071
$935$	1.75863e69	0.269837
$936$	2.82166e68	0.0422204
$937$	−6.83105e68	−0.0996798	−0.0498399	−	0.998757i	$-0.515871\pi$
$937$	−6.83105e68	−0.0996798	−0.0498399	+	0.998757i	$0.515871\pi$
$938$	3.62834e69	0.516347
$939$	3.11186e69	0.431895
$940$	−4.73775e69	−0.641309
$941$	1.23580e70	1.63151	0.815756	−	0.578395i	$-0.196321\pi$
$941$	1.23580e70	1.63151	0.815756	+	0.578395i	$0.196321\pi$
$942$	−1.72725e69	−0.222412
$943$	1.16842e70	1.46748
$944$	−1.12010e69	−0.137220
$945$	2.66837e69	0.318859
$946$	5.33898e69	0.622324
$947$	3.76469e69	0.428060	0.214030	−	0.976827i	$-0.431341\pi$
$947$	3.76469e69	0.428060	0.214030	+	0.976827i	$0.431341\pi$
$948$	−1.24939e69	−0.138581
$949$	−1.21919e69	−0.131921
$950$	5.92519e69	0.625458
$951$	−2.88220e69	−0.296813
$952$	3.19444e68	0.0320942
$953$	−2.51591e69	−0.246611	−0.123305	−	0.992369i	$-0.539349\pi$
$953$	−2.51591e69	−0.246611	−0.123305	+	0.992369i	$0.539349\pi$
$954$	−4.50986e68	−0.0431297
$955$	−1.28411e69	−0.119818
$956$	−9.77658e69	−0.890075
$957$	−1.49407e69	−0.132721
$958$	1.10112e70	0.954429
$959$	−3.98935e69	−0.337416
$960$	6.65028e68	0.0548865
$961$	−9.43808e69	−0.760123
$962$	5.13327e68	0.0403441
$963$	1.31413e70	1.00791
$964$	2.99475e69	0.224156
$965$	−2.58748e70	−1.89010
$966$	9.67170e68	0.0689510
$967$	7.97343e68	0.0554783	0.0277391	−	0.999615i	$-0.491169\pi$
$967$	7.97343e68	0.0554783	0.0277391	+	0.999615i	$0.491169\pi$
$968$	−2.52313e69	−0.171344
$969$	−6.20446e68	−0.0411240
$970$	6.84171e68	0.0442618
$971$	−1.32156e70	−0.834516	−0.417258	−	0.908788i	$-0.637009\pi$
$971$	−1.32156e70	−0.834516	−0.417258	+	0.908788i	$0.637009\pi$
$972$	6.12528e69	0.377545
$973$	−9.81074e69	−0.590269
$974$	2.32514e70	1.36557
$975$	−9.19355e68	−0.0527078
$976$	7.12888e69	0.398980
$977$	−9.48252e69	−0.518086	−0.259043	−	0.965866i	$-0.583407\pi$
$977$	−9.48252e69	−0.518086	−0.259043	+	0.965866i	$0.583407\pi$
$978$	−4.02386e69	−0.214625
$979$	8.35248e69	0.434933
$980$	2.19892e69	0.111788
$981$	1.26952e70	0.630114
$982$	6.76085e69	0.327628
$983$	2.31221e69	0.109400	0.0547002	−	0.998503i	$-0.482580\pi$
$983$	2.31221e69	0.109400	0.0547002	+	0.998503i	$0.482580\pi$
$984$	−3.42666e69	−0.158302
$985$	2.72999e70	1.23143
$986$	−2.54076e69	−0.111907
$987$	2.02073e69	0.0869072
$988$	−9.41837e68	−0.0395537
$989$	2.74891e70	1.12732
$990$	1.82763e70	0.731915
$991$	3.87403e70	1.51507	0.757533	−	0.652797i	$-0.226404\pi$
$991$	3.87403e70	1.51507	0.757533	+	0.652797i	$0.226404\pi$
$992$	−2.26696e69	−0.0865803
$993$	−1.29164e70	−0.481763
$994$	5.41347e68	0.0197195
$995$	−1.45913e70	−0.519099
$996$	5.65880e69	0.196621
$997$	−5.34728e70	−1.81466	−0.907332	−	0.420414i	$-0.861885\pi$
$997$	−5.34728e70	−1.81466	−0.907332	+	0.420414i	$0.861885\pi$
$998$	−2.47781e70	−0.821296
$999$	7.32881e69	0.237271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.48.a.c.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.48.a.c.1.4	✓	6	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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 48 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

\(f(q)\)	\(=\)	\(q+8.38861e6 q^{2} +4.57489e10 q^{3} +7.03687e13 q^{4} +4.17176e16 q^{5} +3.83770e17 q^{6} -2.73687e19 q^{7} +5.90296e20 q^{8} -2.44958e22 q^{9} +3.49953e23 q^{10} -2.13199e24 q^{11} +3.21930e24 q^{12} -1.95138e25 q^{13} -2.29586e26 q^{14} +1.90854e27 q^{15} +4.95176e27 q^{16} -1.97729e28 q^{17} -2.05486e29 q^{18} +6.85888e29 q^{19} +2.93562e30 q^{20} -1.25209e30 q^{21} -1.78844e31 q^{22} -9.20825e31 q^{23} +2.70054e31 q^{24} +1.02982e33 q^{25} -1.63694e32 q^{26} -2.33707e33 q^{27} -1.92590e33 q^{28} +1.53180e34 q^{29} +1.60100e34 q^{30} -5.45750e34 q^{31} +4.15384e34 q^{32} -9.75364e34 q^{33} -1.65867e35 q^{34} -1.14176e36 q^{35} -1.72374e36 q^{36} -3.13590e36 q^{37} +5.75364e36 q^{38} -8.92737e35 q^{39} +2.46257e37 q^{40} -1.26888e38 q^{41} -1.05033e37 q^{42} -2.98527e38 q^{43} -1.50026e38 q^{44} -1.02191e39 q^{45} -7.72444e38 q^{46} -1.61389e39 q^{47} +2.26538e38 q^{48} +7.49048e38 q^{49} +8.63872e39 q^{50} -9.04588e38 q^{51} -1.37316e39 q^{52} +2.19473e39 q^{53} -1.96048e40 q^{54} -8.89416e40 q^{55} -1.61557e40 q^{56} +3.13786e40 q^{57} +1.28497e41 q^{58} -2.26203e41 q^{59} +1.34301e41 q^{60} +1.43967e42 q^{61} -4.57809e41 q^{62} +6.70421e41 q^{63} +3.48449e41 q^{64} -8.14071e41 q^{65} -8.18195e41 q^{66} -1.58039e43 q^{67} -1.39139e42 q^{68} -4.21268e42 q^{69} -9.57777e42 q^{70} -2.35793e42 q^{71} -1.44598e43 q^{72} +6.24780e43 q^{73} -2.63058e43 q^{74} +4.71130e43 q^{75} +4.82651e43 q^{76} +5.83500e43 q^{77} -7.48882e42 q^{78} -3.88095e44 q^{79} +2.06576e44 q^{80} +5.44397e44 q^{81} -1.06441e45 q^{82} +1.75777e45 q^{83} -8.81081e43 q^{84} -8.24877e44 q^{85} -2.50422e45 q^{86} +7.00784e44 q^{87} -1.25851e45 q^{88} -3.91769e45 q^{89} -8.57239e45 q^{90} +5.34069e44 q^{91} -6.47973e45 q^{92} -2.49675e45 q^{93} -1.35383e46 q^{94} +2.86136e46 q^{95} +1.90034e45 q^{96} +1.95504e45 q^{97} +6.28347e45 q^{98} +5.22250e46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 50331648 q^{2} + 91348200216 q^{3} + 422212465065984 q^{4} - 30\!\cdots\!00 q^{5} + 76\!\cdots\!28 q^{6} - 16\!\cdots\!58 q^{7} + 35\!\cdots\!72 q^{8} + 23\!\cdots\!02 q^{9} - 25\!\cdots\!00 q^{10}+ \cdots - 22\!\cdots\!76 q^{99}+O(q^{100}) \) 6 * q + 50331648 * q^2 + 91348200216 * q^3 + 422212465065984 * q^4 - 30854924554017900 * q^5 + 766284243117539328 * q^6 - 164212484040485498058 * q^7 + 3541774862152233910272 * q^8 + 23611401481192331893902 * q^9 - 258829866953230988083200 * q^10 - 3041554928367556663244472 * q^11 + 6428058132089735347175424 * q^12 - 191570324075361446274867612 * q^13 - 1377514157321888972893323264 * q^14 + 2152872376393147160276606400 * q^15 + 29710560942849126597578981376 * q^16 + 182134574393674491978939242700 * q^17 + 198066791356341844863841468416 * q^18 + 105921872842145395281581529432 * q^19 - 2171222292562809092482636185600 * q^20 - 2500085811682828987741110530088 * q^21 - 25514412004543512765745883774976 * q^22 + 7899982928916455721382409846400 * q^23 + 53922459871313010651198539169792 * q^24 + 262683336957609462428869088912250 * q^25 - 1607008353101169631112924648964096 * q^26 - 5145497061786399782948702525214768 * q^27 - 11555426280223656413124714678976512 * q^28 - 1232522012314953851089211475650748 * q^29 + 18059602439590565413873622659891200 * q^30 + 72879381477193587191769574430120160 * q^31 + 249230249209671726169463823802564608 * q^32 + 650973340162559425050384304879402560 * q^33 + 1527855547835372992810465562827161600 * q^34 + 844460634316174754595838034424539700 * q^35 + 1661504670506140050559579452686204928 * q^36 - 2350829994343156615163160293570449164 * q^37 + 888537069898603600022237070445510656 * q^38 - 23749444470098095106267492597757308832 * q^39 - 18213532693170720855672581767613644800 * q^40 - 37574511477606821868284528556464112132 * q^41 - 20972239840569072709196981721580437504 * q^42 - 140317571620320602329291697555258434968 * q^43 - 214030400656609747534838046601833873408 * q^44 + 26295596306265329899718309281681956900 * q^45 + 66269859997372011796034254296789811200 * q^46 + 708002688958069624152534886966137104352 * q^47 + 452334378256175291652729275268030529536 * q^48 + 4494289985791117400966964616167386961894 * q^49 + 2203547541869298397406510670202011648000 * q^50 - 2727943917011418941975075709475285627248 * q^51 - 13480563126891296376910928613697407418368 * q^52 - 52279163845818199239402993035899030148076 * q^53 - 43163557816477887510441749592636804562944 * q^54 - 251960273873968093291926136296648972678000 * q^55 - 96933941337694405976389286553779800375296 * q^56 - 573477266714411774837109161637481283739792 * q^57 - 10339144012681320394877768098335669878784 * q^58 - 1154054456625062116390095979270500564117240 * q^59 + 151494925501568933755343582033744599449600 * q^60 - 1044005217659731085861156994850316373335676 * q^61 + 611356562494637943065575786221101415137280 * q^62 - 646214481483965241810590391497176813840386 * q^63 + 2090694862362245919518973588060783891185664 * q^64 + 3194584995357111391012342521501923033185800 * q^65 + 5460760169074367293453054182985795350036480 * q^66 - 933326469202418857699748343169593992036424 * q^67 + 12816581271416192570473813904056430415052800 * q^68 - 3891276550887494643219113510902717842230400 * q^69 + 7083849232709738075800683702277969123737600 * q^70 - 15354263243214256646706193660254232469772912 * q^71 + 13937711371045170477244492673439120148660224 * q^72 + 35097104101107095287360422807160923534046332 * q^73 - 19720191297186958327210607743927418420723712 * q^74 + 54253840923690951415133098526131371680829000 * q^75 + 7453589172847985347975338067035774253006848 * q^76 + 83243548355469568471308548464739505189205896 * q^77 - 199224779877420641393196338545487742926585856 * q^78 + 116083394738898838035318356572808875206583104 * q^79 - 152786186058193454335661864796457961678438400 * q^80 + 45644045361405935459098194557296623953436294 * q^81 - 315197847577144406778866542524983302743392256 * q^82 - 1650553357776207980536462167742742823540569160 * q^83 - 175927898904516447880951474445503430689554432 * q^84 - 6873331910637436173767195931321684421228903800 * q^85 - 1177069103834794367264314968445621349640044544 * q^86 - 11444858388565719560905086433015676826273466704 * q^87 - 1795417131191241781048722716428516445141336064 * q^88 - 6572746325824162151046522148908755018513654916 * q^89 + 220583449539507796519416206986791517106995200 * q^90 + 5243039797475987712325338969412905339972182916 * q^91 + 555911877732834837128307313868085384550809600 * q^92 + 10472287731311146814773470934954649411827909536 * q^93 + 5939157020615174513722947373083233442664022016 * q^94 - 6386150132253545069254818239614899940335103200 * q^95 + 3794455784114778100960418020347603044309925888 * q^96 - 34281171183200724766133718472300444680714638388 * q^97 + 37700836929127253758690687114898671607639703552 * q^98 - 226943335602453325836392523541612774950265114776 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more