LMFDB - Embedded newform 14.48.a.c.1.3

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			1.3
Root			$6.87036e8$ 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)

$f(q)$	$=$	\(q+8.38861e6 q^{2} +2.85805e9 q^{3} +7.03687e13 q^{4} -4.96190e16 q^{5} +2.39750e16 q^{6} -2.73687e19 q^{7} +5.90296e20 q^{8} -2.65806e22 q^{9} -4.16234e23 q^{10} +2.75791e24 q^{11} +2.01117e23 q^{12} -1.47333e26 q^{13} -2.29586e26 q^{14} -1.41813e26 q^{15} +4.95176e27 q^{16} +1.61499e29 q^{17} -2.22975e29 q^{18} +9.03896e29 q^{19} -3.49162e30 q^{20} -7.82212e28 q^{21} +2.31350e31 q^{22} +4.22977e31 q^{23} +1.68709e30 q^{24} +1.75150e33 q^{25} -1.23591e33 q^{26} -1.51961e32 q^{27} -1.92590e33 q^{28} +3.47113e33 q^{29} -1.18962e33 q^{30} -1.81147e35 q^{31} +4.15384e34 q^{32} +7.88224e33 q^{33} +1.35475e36 q^{34} +1.35801e36 q^{35} -1.87045e36 q^{36} +1.12630e37 q^{37} +7.58243e36 q^{38} -4.21083e35 q^{39} -2.92899e37 q^{40} +5.45836e36 q^{41} -6.56167e35 q^{42} +2.20806e38 q^{43} +1.94071e38 q^{44} +1.31890e39 q^{45} +3.54819e38 q^{46} -1.06649e39 q^{47} +1.41524e37 q^{48} +7.49048e38 q^{49} +1.46926e40 q^{50} +4.61573e38 q^{51} -1.03676e40 q^{52} -3.12107e40 q^{53} -1.27474e39 q^{54} -1.36845e41 q^{55} -1.61557e40 q^{56} +2.58338e39 q^{57} +2.91180e40 q^{58} -7.68569e41 q^{59} -9.97923e39 q^{60} -2.46085e41 q^{61} -1.51957e42 q^{62} +7.27479e41 q^{63} +3.48449e41 q^{64} +7.31049e42 q^{65} +6.61210e40 q^{66} +7.21144e40 q^{67} +1.13645e43 q^{68} +1.20889e41 q^{69} +1.13918e43 q^{70} -1.56833e43 q^{71} -1.56904e43 q^{72} -4.53957e42 q^{73} +9.44813e43 q^{74} +5.00586e42 q^{75} +6.36060e43 q^{76} -7.54805e43 q^{77} -3.53230e42 q^{78} -7.66715e44 q^{79} -2.45701e44 q^{80} +7.06314e44 q^{81} +4.57881e43 q^{82} +4.38261e44 q^{83} -5.50433e42 q^{84} -8.01342e45 q^{85} +1.85226e45 q^{86} +9.92067e42 q^{87} +1.62798e45 q^{88} +8.80332e45 q^{89} +1.10638e46 q^{90} +4.03231e45 q^{91} +2.97643e45 q^{92} -5.17727e44 q^{93} -8.94640e45 q^{94} -4.48504e46 q^{95} +1.18719e44 q^{96} -4.24824e46 q^{97} +6.28347e45 q^{98} -7.33070e46 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.85805e9	0.0175275	0.00876375	−	0.999962i	$-0.497210\pi$
$3$	2.85805e9	0.0175275	0.00876375	+	0.999962i	$0.497210\pi$
$4$	7.03687e13	0.500000
$5$	−4.96190e16	−1.86145	−0.930727	−	0.365714i	$-0.880825\pi$
$5$	−4.96190e16	−1.86145	−0.930727	+	0.365714i	$0.880825\pi$
$6$	2.39750e16	0.0123938
$7$	−2.73687e19	−0.377964
$7$	−2.73687e19	−0.377964
$8$	5.90296e20	0.353553
$9$	−2.65806e22	−0.999693
$10$	−4.16234e23	−1.31625
$11$	2.75791e24	0.928650	0.464325	−	0.885665i	$-0.346297\pi$
$11$	2.75791e24	0.928650	0.464325	+	0.885665i	$0.346297\pi$
$12$	2.01117e23	0.00876375
$13$	−1.47333e26	−0.978656	−0.489328	−	0.872100i	$-0.662758\pi$
$13$	−1.47333e26	−0.978656	−0.489328	+	0.872100i	$0.662758\pi$
$14$	−2.29586e26	−0.267261
$15$	−1.41813e26	−0.0326267
$16$	4.95176e27	0.250000
$17$	1.61499e29	1.96165	0.980823	−	0.194899i	$-0.0624380\pi$
$17$	1.61499e29	1.96165	0.980823	+	0.194899i	$0.0624380\pi$
$18$	−2.22975e29	−0.706890
$19$	9.03896e29	0.804283	0.402141	−	0.915578i	$-0.368266\pi$
$19$	9.03896e29	0.804283	0.402141	+	0.915578i	$0.368266\pi$
$20$	−3.49162e30	−0.930727
$21$	−7.82212e28	−0.00662477
$22$	2.31350e31	0.656654
$23$	4.22977e31	0.422389	0.211194	−	0.977444i	$-0.432265\pi$
$23$	4.22977e31	0.422389	0.211194	+	0.977444i	$0.432265\pi$
$24$	1.68709e30	0.00619691
$25$	1.75150e33	2.46501
$26$	−1.23591e33	−0.692014
$27$	−1.51961e32	−0.0350496
$28$	−1.92590e33	−0.188982
$29$	3.47113e33	0.149320	0.0746601	−	0.997209i	$-0.476213\pi$
$29$	3.47113e33	0.149320	0.0746601	+	0.997209i	$0.476213\pi$
$30$	−1.18962e33	−0.0230705
$31$	−1.81147e35	−1.62567	−0.812834	−	0.582495i	$-0.802076\pi$
$31$	−1.81147e35	−1.62567	−0.812834	+	0.582495i	$0.802076\pi$
$32$	4.15384e34	0.176777
$33$	7.88224e33	0.0162769
$34$	1.35475e36	1.38709
$35$	1.35801e36	0.703564
$36$	−1.87045e36	−0.499846
$37$	1.12630e37	1.58094	0.790470	−	0.612501i	$-0.209836\pi$
$37$	1.12630e37	1.58094	0.790470	+	0.612501i	$0.209836\pi$
$38$	7.58243e36	0.568714
$39$	−4.21083e35	−0.0171534
$40$	−2.92899e37	−0.658124
$41$	5.45836e36	0.0686502	0.0343251	−	0.999411i	$-0.489072\pi$
$41$	5.45836e36	0.0686502	0.0343251	+	0.999411i	$0.489072\pi$
$42$	−6.56167e35	−0.00468442
$43$	2.20806e38	0.906781	0.453391	−	0.891312i	$-0.350214\pi$
$43$	2.20806e38	0.906781	0.453391	+	0.891312i	$0.350214\pi$
$44$	1.94071e38	0.464325
$45$	1.31890e39	1.86088
$46$	3.54819e38	0.298674
$47$	−1.06649e39	−0.541575	−0.270788	−	0.962639i	$-0.587284\pi$
$47$	−1.06649e39	−0.541575	−0.270788	+	0.962639i	$0.587284\pi$
$48$	1.41524e37	0.00438188
$49$	7.49048e38	0.142857
$50$	1.46926e40	1.74303
$51$	4.61573e38	0.0343828
$52$	−1.03676e40	−0.489328
$53$	−3.12107e40	−0.941501	−0.470751	−	0.882266i	$-0.656017\pi$
$53$	−3.12107e40	−0.941501	−0.470751	+	0.882266i	$0.656017\pi$
$54$	−1.27474e39	−0.0247838
$55$	−1.36845e41	−1.72864
$56$	−1.61557e40	−0.133631
$57$	2.58338e39	0.0140971
$58$	2.91180e40	0.105585
$59$	−7.68569e41	−1.86492	−0.932460	−	0.361272i	$-0.882343\pi$
$59$	−7.68569e41	−1.86492	−0.932460	+	0.361272i	$0.882343\pi$
$60$	−9.97923e39	−0.0163133
$61$	−2.46085e41	−0.272793	−0.136397	−	0.990654i	$-0.543552\pi$
$61$	−2.46085e41	−0.272793	−0.136397	+	0.990654i	$0.543552\pi$
$62$	−1.51957e42	−1.14952
$63$	7.27479e41	0.377848
$64$	3.48449e41	0.125000
$65$	7.31049e42	1.82172
$66$	6.61210e40	0.0115095
$67$	7.21144e40	0.00881585	0.00440792	−	0.999990i	$-0.498597\pi$
$67$	7.21144e40	0.00881585	0.00440792	+	0.999990i	$0.498597\pi$
$68$	1.13645e43	0.980823
$69$	1.20889e41	0.00740342
$70$	1.13918e43	0.497495
$71$	−1.56833e43	−0.490755	−0.245378	−	0.969428i	$-0.578912\pi$
$71$	−1.56833e43	−0.490755	−0.245378	+	0.969428i	$0.578912\pi$
$72$	−1.56904e43	−0.353445
$73$	−4.53957e42	−0.0739482	−0.0369741	−	0.999316i	$-0.511772\pi$
$73$	−4.53957e42	−0.0739482	−0.0369741	+	0.999316i	$0.511772\pi$
$74$	9.44813e43	1.11789
$75$	5.00586e42	0.0432055
$76$	6.36060e43	0.402141
$77$	−7.54805e43	−0.350997
$78$	−3.53230e42	−0.0121293
$79$	−7.66715e44	−1.95163	−0.975815	−	0.218598i	$-0.929852\pi$
$79$	−7.66715e44	−1.95163	−0.975815	+	0.218598i	$0.929852\pi$
$80$	−2.45701e44	−0.465364
$81$	7.06314e44	0.999078
$82$	4.57881e43	0.0485430
$83$	4.38261e44	0.349460	0.174730	−	0.984616i	$-0.444095\pi$
$83$	4.38261e44	0.349460	0.174730	+	0.984616i	$0.444095\pi$
$84$	−5.50433e42	−0.00331239
$85$	−8.01342e45	−3.65152
$86$	1.85226e45	0.641191
$87$	9.92067e42	0.00261721
$88$	1.62798e45	0.328327
$89$	8.80332e45	1.36139	0.680693	−	0.732569i	$-0.261679\pi$
$89$	8.80332e45	1.36139	0.680693	+	0.732569i	$0.261679\pi$
$90$	1.10638e46	1.31584
$91$	4.03231e45	0.369897
$92$	2.97643e45	0.211194
$93$	−5.17727e44	−0.0284939
$94$	−8.94640e45	−0.382951
$95$	−4.48504e46	−1.49714
$96$	1.18719e44	0.00309845
$97$	−4.24824e46	−0.869108	−0.434554	−	0.900646i	$-0.643094\pi$
$97$	−4.24824e46	−0.869108	−0.434554	+	0.900646i	$0.643094\pi$
$98$	6.28347e45	0.101015
$99$	−7.33070e46	−0.928364
$100$	1.23251e47	1.23251
$101$	−1.03418e47	−0.818548	−0.409274	−	0.912411i	$-0.634218\pi$
$101$	−1.03418e47	−0.818548	−0.409274	+	0.912411i	$0.634218\pi$
$102$	3.87195e45	0.0243123
$103$	−1.36830e46	−0.0683133	−0.0341566	−	0.999416i	$-0.510875\pi$
$103$	−1.36830e46	−0.0683133	−0.0341566	+	0.999416i	$0.510875\pi$
$104$	−8.69698e46	−0.346007
$105$	3.88125e45	0.0123317
$106$	−2.61815e47	−0.665742
$107$	−3.91889e47	−0.799180	−0.399590	−	0.916694i	$-0.630848\pi$
$107$	−3.91889e47	−0.799180	−0.399590	+	0.916694i	$0.630848\pi$
$108$	−1.06933e46	−0.0175248
$109$	5.47798e47	0.722933	0.361466	−	0.932385i	$-0.382276\pi$
$109$	5.47798e47	0.722933	0.361466	+	0.932385i	$0.382276\pi$
$110$	−1.14794e48	−1.22233
$111$	3.21903e46	0.0277099
$112$	−1.35523e47	−0.0944911
$113$	1.62357e48	0.918605	0.459303	−	0.888280i	$-0.348099\pi$
$113$	1.62357e48	0.918605	0.459303	+	0.888280i	$0.348099\pi$
$114$	2.16709e46	0.00996813
$115$	−2.09877e48	−0.786257
$116$	2.44259e47	0.0746601
$117$	3.91619e48	0.978355
$118$	−6.44722e48	−1.31870
$119$	−4.42003e48	−0.741433
$120$	−8.37118e46	−0.0115353
$121$	−1.21368e48	−0.137610
$122$	−2.06431e48	−0.192894
$123$	1.56003e46	0.00120327
$124$	−1.27471e49	−0.812834
$125$	−5.16511e49	−2.72706
$126$	6.10254e48	0.267179
$127$	3.76428e49	1.36866	0.684329	−	0.729174i	$-0.260095\pi$
$127$	3.76428e49	1.36866	0.684329	+	0.729174i	$0.260095\pi$
$128$	2.92300e48	0.0883883
$129$	6.31075e47	0.0158936
$130$	6.13248e49	1.28815
$131$	7.15382e49	1.25505	0.627527	−	0.778595i	$-0.284067\pi$
$131$	7.15382e49	1.25505	0.627527	+	0.778595i	$0.284067\pi$
$132$	5.54663e47	0.00813845
$133$	−2.47385e49	−0.303990
$134$	6.04939e47	0.00623375
$135$	7.54014e48	0.0652433
$136$	9.53323e49	0.693547
$137$	−1.80580e50	−1.10595	−0.552977	−	0.833197i	$-0.686508\pi$
$137$	−1.80580e50	−1.10595	−0.552977	+	0.833197i	$0.686508\pi$
$138$	1.01409e48	0.00523501
$139$	2.72373e50	1.18663	0.593316	−	0.804970i	$-0.297819\pi$
$139$	2.72373e50	1.18663	0.593316	+	0.804970i	$0.297819\pi$
$140$	9.55614e49	0.351782
$141$	−3.04809e48	−0.00949246
$142$	−1.31561e50	−0.347016
$143$	−4.06330e50	−0.908828
$144$	−1.31621e50	−0.249923
$145$	−1.72234e50	−0.277953
$146$	−3.80807e49	−0.0522893
$147$	2.14082e48	0.00250393
$148$	7.92566e50	0.790470
$149$	9.74934e50	0.830038	0.415019	−	0.909813i	$-0.363775\pi$
$149$	9.74934e50	0.830038	0.415019	+	0.909813i	$0.363775\pi$
$150$	4.19922e49	0.0305509
$151$	4.36036e50	0.271372	0.135686	−	0.990752i	$-0.456676\pi$
$151$	4.36036e50	0.271372	0.135686	+	0.990752i	$0.456676\pi$
$152$	5.33566e50	0.284357
$153$	−4.29275e51	−1.96104
$154$	−6.33177e50	−0.248192
$155$	8.98834e51	3.02611
$156$	−2.96311e49	−0.00857669
$157$	4.28053e51	1.06624	0.533121	−	0.846039i	$-0.321019\pi$
$157$	4.28053e51	1.06624	0.533121	+	0.846039i	$0.321019\pi$
$158$	−6.43167e51	−1.38001
$159$	−8.92017e49	−0.0165022
$160$	−2.06109e51	−0.329062
$161$	−1.15763e51	−0.159648
$162$	5.92499e51	0.706455
$163$	−8.07644e51	−0.833319	−0.416660	−	0.909063i	$-0.636799\pi$
$163$	−8.07644e51	−0.833319	−0.416660	+	0.909063i	$0.636799\pi$
$164$	3.84098e50	0.0343251
$165$	−3.91108e50	−0.0302987
$166$	3.67640e51	0.247106
$167$	−2.27505e51	−0.132786	−0.0663932	−	0.997794i	$-0.521149\pi$
$167$	−2.27505e51	−0.132786	−0.0663932	+	0.997794i	$0.521149\pi$
$168$	−4.61736e49	−0.00234221
$169$	−9.57177e50	−0.0422333
$170$	−6.72215e52	−2.58201
$171$	−2.40261e52	−0.804036
$172$	1.55379e52	0.453391
$173$	−6.63394e52	−1.68923	−0.844613	−	0.535377i	$-0.820170\pi$
$173$	−6.63394e52	−1.68923	−0.844613	+	0.535377i	$0.820170\pi$
$174$	8.32206e49	0.00185065
$175$	−4.79363e52	−0.931688
$176$	1.36565e52	0.232162
$177$	−2.19661e51	−0.0326874
$178$	7.38476e52	0.962646
$179$	−4.94983e52	−0.565645	−0.282822	−	0.959172i	$-0.591271\pi$
$179$	−4.94983e52	−0.565645	−0.282822	+	0.959172i	$0.591271\pi$
$180$	9.28096e52	0.930441
$181$	1.68696e53	1.48477	0.742385	−	0.669974i	$-0.233695\pi$
$181$	1.68696e53	1.48477	0.742385	+	0.669974i	$0.233695\pi$
$182$	3.38254e52	0.261557
$183$	−7.03323e50	−0.00478139
$184$	2.49681e52	0.149337
$185$	−5.58861e53	−2.94285
$186$	−4.34301e51	−0.0201482
$187$	4.45400e53	1.82168
$188$	−7.50478e52	−0.270788
$189$	4.15898e51	0.0132475
$190$	−3.76232e53	−1.05863
$191$	9.00666e52	0.224016	0.112008	−	0.993707i	$-0.464272\pi$
$191$	9.00666e52	0.224016	0.112008	+	0.993707i	$0.464272\pi$
$192$	9.95884e50	0.00219094
$193$	−3.10384e53	−0.604369	−0.302185	−	0.953249i	$-0.597716\pi$
$193$	−3.10384e53	−0.604369	−0.302185	+	0.953249i	$0.597716\pi$
$194$	−3.56368e53	−0.614552
$195$	2.08937e52	0.0319303
$196$	5.27096e52	0.0714286
$197$	−8.17940e53	−0.983479	−0.491740	−	0.870742i	$-0.663639\pi$
$197$	−8.17940e53	−0.983479	−0.491740	+	0.870742i	$0.663639\pi$
$198$	−6.14944e53	−0.656453
$199$	−3.71278e53	−0.352089	−0.176044	−	0.984382i	$-0.556330\pi$
$199$	−3.71278e53	−0.352089	−0.176044	+	0.984382i	$0.556330\pi$
$200$	1.03390e54	0.871514
$201$	2.06106e50	0.000154520 0
$202$	−8.67534e53	−0.578801
$203$	−9.50006e52	−0.0564377
$204$	3.24803e52	0.0171914
$205$	−2.70838e53	−0.127789
$206$	−1.14781e53	−0.0483048
$207$	−1.12430e54	−0.422259
$208$	−7.29555e53	−0.244664
$209$	2.49286e54	0.746897
$210$	3.25583e52	0.00871984
$211$	1.01024e54	0.241985	0.120993	−	0.992653i	$-0.461392\pi$
$211$	1.01024e54	0.241985	0.120993	+	0.992653i	$0.461392\pi$
$212$	−2.19626e54	−0.470751
$213$	−4.48235e52	−0.00860172
$214$	−3.28741e54	−0.565106
$215$	−1.09562e55	−1.68793
$216$	−8.97019e52	−0.0123919
$217$	4.95777e54	0.614445
$218$	4.59526e54	0.511191
$219$	−1.29743e52	−0.00129613
$220$	−9.62958e54	−0.864320
$221$	−2.37941e55	−1.91978
$222$	2.70032e53	0.0195939
$223$	−2.73824e55	−1.78775	−0.893874	−	0.448317i	$-0.852023\pi$
$223$	−2.73824e55	−1.78775	−0.893874	+	0.448317i	$0.852023\pi$
$224$	−1.13685e54	−0.0668153
$225$	−4.65559e55	−2.46426
$226$	1.36195e55	0.649552
$227$	−3.71604e55	−1.59762	−0.798808	−	0.601585i	$-0.794536\pi$
$227$	−3.71604e55	−1.59762	−0.798808	+	0.601585i	$0.794536\pi$
$228$	1.81789e53	0.00704853
$229$	−2.19337e55	−0.767322	−0.383661	−	0.923474i	$-0.625337\pi$
$229$	−2.19337e55	−0.767322	−0.383661	+	0.923474i	$0.625337\pi$
$230$	−1.76057e55	−0.555968
$231$	−2.15727e53	−0.00615209
$232$	2.04900e54	0.0527927
$233$	−4.19117e54	−0.0976048	−0.0488024	−	0.998808i	$-0.515540\pi$
$233$	−4.19117e54	−0.0976048	−0.0488024	+	0.998808i	$0.515540\pi$
$234$	3.28514e55	0.691801
$235$	5.29183e55	1.00812
$236$	−5.40832e55	−0.932460
$237$	−2.19131e54	−0.0342072
$238$	−3.70779e55	−0.524272
$239$	3.07194e55	0.393606	0.196803	−	0.980443i	$-0.436944\pi$
$239$	3.07194e55	0.393606	0.196803	+	0.980443i	$0.436944\pi$
$240$	−7.02226e53	−0.00815666
$241$	3.60139e55	0.379376	0.189688	−	0.981844i	$-0.439252\pi$
$241$	3.60139e55	0.379376	0.189688	+	0.981844i	$0.439252\pi$
$242$	−1.01811e55	−0.0973048
$243$	6.05914e54	0.0525610
$244$	−1.73167e55	−0.136397
$245$	−3.71670e55	−0.265922
$246$	1.30864e53	0.000850838 0
$247$	−1.33173e56	−0.787116
$248$	−1.06930e56	−0.574760
$249$	1.25257e54	0.00612517
$250$	−4.33281e56	−1.92832
$251$	−1.13914e56	−0.461576	−0.230788	−	0.973004i	$-0.574130\pi$
$251$	−1.13914e56	−0.461576	−0.230788	+	0.973004i	$0.574130\pi$
$252$	5.11918e55	0.188924
$253$	1.16653e56	0.392251
$254$	3.15771e56	0.967787
$255$	−2.29027e55	−0.0640020
$256$	2.45199e55	0.0625000
$257$	5.22610e56	1.21548	0.607742	−	0.794135i	$-0.292076\pi$
$257$	5.22610e56	1.21548	0.607742	+	0.794135i	$0.292076\pi$
$258$	5.29384e54	0.0112385
$259$	−3.08255e56	−0.597539
$260$	5.14430e56	0.910862
$261$	−9.22650e55	−0.149274
$262$	6.00106e56	0.887458
$263$	−1.04966e57	−1.41935	−0.709675	−	0.704529i	$-0.751158\pi$
$263$	−1.04966e57	−1.41935	−0.709675	+	0.704529i	$0.751158\pi$
$264$	4.65285e54	0.00575476
$265$	1.54864e57	1.75256
$266$	−2.07522e56	−0.214954
$267$	2.51603e55	0.0238617
$268$	5.07460e54	0.00440792
$269$	−1.70871e57	−1.35985	−0.679923	−	0.733284i	$-0.737987\pi$
$269$	−1.70871e57	−1.35985	−0.679923	+	0.733284i	$0.737987\pi$
$270$	6.32513e55	0.0461340
$271$	−1.27971e56	−0.0855722	−0.0427861	−	0.999084i	$-0.513623\pi$
$271$	−1.27971e56	−0.0855722	−0.0427861	+	0.999084i	$0.513623\pi$
$272$	7.99705e56	0.490412
$273$	1.15245e55	0.00648337
$274$	−1.51482e57	−0.782027
$275$	4.83047e57	2.28913
$276$	8.50679e54	0.00370171
$277$	−2.61228e57	−1.04411	−0.522054	−	0.852913i	$-0.674834\pi$
$277$	−2.61228e57	−1.04411	−0.522054	+	0.852913i	$0.674834\pi$
$278$	2.28483e57	0.839075
$279$	4.81501e57	1.62517
$280$	8.01627e56	0.248747
$281$	−1.82899e57	−0.521930	−0.260965	−	0.965348i	$-0.584041\pi$
$281$	−1.82899e57	−0.521930	−0.260965	+	0.965348i	$0.584041\pi$
$282$	−2.55692e55	−0.00671218
$283$	−7.06013e57	−1.70542	−0.852710	−	0.522385i	$-0.825043\pi$
$283$	−7.06013e57	−1.70542	−0.852710	+	0.522385i	$0.825043\pi$
$284$	−1.10361e57	−0.245378
$285$	−1.28184e56	−0.0262411
$286$	−3.40854e57	−0.642639
$287$	−1.49389e56	−0.0259473
$288$	−1.10412e57	−0.176722
$289$	1.93040e58	2.84806
$290$	−1.44480e57	−0.196542
$291$	−1.21417e56	−0.0152333
$292$	−3.19444e56	−0.0369741
$293$	−2.80215e57	−0.299297	−0.149648	−	0.988739i	$-0.547814\pi$
$293$	−2.80215e57	−0.299297	−0.149648	+	0.988739i	$0.547814\pi$
$294$	1.79585e55	0.00177055
$295$	3.81356e58	3.47147
$296$	6.64853e57	0.558947
$297$	−4.19094e56	−0.0325488
$298$	8.17834e57	0.586926
$299$	−6.23182e57	−0.413373
$300$	3.52256e56	0.0216028
$301$	−6.04319e57	−0.342731
$302$	3.65774e57	0.191889
$303$	−2.95574e56	−0.0143471
$304$	4.47587e57	0.201071
$305$	1.22105e58	0.507793
$306$	−3.60102e58	−1.38667
$307$	4.47679e58	1.59667	0.798334	−	0.602215i	$-0.205715\pi$
$307$	4.47679e58	1.59667	0.798334	+	0.602215i	$0.205715\pi$
$308$	−5.31147e57	−0.175498
$309$	−3.91065e55	−0.00119736
$310$	7.53996e58	2.13978
$311$	−1.28938e58	−0.339243	−0.169621	−	0.985509i	$-0.554254\pi$
$311$	−1.28938e58	−0.339243	−0.169621	+	0.985509i	$0.554254\pi$
$312$	−2.48564e56	−0.00606464
$313$	−7.64220e58	−1.72952	−0.864762	−	0.502182i	$-0.832531\pi$
$313$	−7.64220e58	−1.72952	−0.864762	+	0.502182i	$0.832531\pi$
$314$	3.59077e58	0.753946
$315$	−3.60967e58	−0.703348
$316$	−5.39528e58	−0.975815
$317$	6.89423e58	1.15769	0.578846	−	0.815437i	$-0.303503\pi$
$317$	6.89423e58	1.15769	0.578846	+	0.815437i	$0.303503\pi$
$318$	−7.48278e56	−0.0116688
$319$	9.57308e57	0.138666
$320$	−1.72897e58	−0.232682
$321$	−1.12004e57	−0.0140076
$322$	−9.71094e57	−0.112888
$323$	1.45978e59	1.57772
$324$	4.97024e58	0.499539
$325$	−2.58053e59	−2.41240
$326$	−6.77501e58	−0.589246
$327$	1.56563e57	0.0126712
$328$	3.22205e57	0.0242715
$329$	2.91886e58	0.204696
$330$	−3.28085e57	−0.0214244
$331$	1.30557e59	0.794042	0.397021	−	0.917810i	$-0.370044\pi$
$331$	1.30557e59	0.794042	0.397021	+	0.917810i	$0.370044\pi$
$332$	3.08399e58	0.174730
$333$	−2.99379e59	−1.58045
$334$	−1.90845e58	−0.0938942
$335$	−3.57824e57	−0.0164103
$336$	−3.87333e56	−0.00165619
$337$	−1.77600e59	−0.708174	−0.354087	−	0.935212i	$-0.615208\pi$
$337$	−1.77600e59	−0.708174	−0.354087	+	0.935212i	$0.615208\pi$
$338$	−8.02938e57	−0.0298634
$339$	4.64025e57	0.0161009
$340$	−5.63894e59	−1.82576
$341$	−4.99588e59	−1.50968
$342$	−2.01546e59	−0.568539
$343$	−2.05005e58	−0.0539949
$344$	1.30341e59	0.320596
$345$	−5.99837e57	−0.0137811
$346$	−5.56495e59	−1.19446
$347$	9.30629e58	0.186653	0.0933263	−	0.995636i	$-0.470250\pi$
$347$	9.30629e58	0.186653	0.0933263	+	0.995636i	$0.470250\pi$
$348$	6.98105e56	0.00130860
$349$	−1.81707e59	−0.318400	−0.159200	−	0.987246i	$-0.550891\pi$
$349$	−1.81707e59	−0.318400	−0.159200	+	0.987246i	$0.550891\pi$
$350$	−4.02119e59	−0.658803
$351$	2.23888e58	0.0343015
$352$	1.14559e59	0.164164
$353$	−5.60444e59	−0.751324	−0.375662	−	0.926757i	$-0.622585\pi$
$353$	−5.60444e59	−0.751324	−0.375662	+	0.926757i	$0.622585\pi$
$354$	−1.84265e58	−0.0231135
$355$	7.78187e59	0.913519
$356$	6.19479e59	0.680693
$357$	−1.26327e58	−0.0129955
$358$	−4.15222e59	−0.399971
$359$	1.63871e60	1.47837	0.739185	−	0.673503i	$-0.235211\pi$
$359$	1.63871e60	1.47837	0.739185	+	0.673503i	$0.235211\pi$
$360$	7.78543e59	0.657921
$361$	−4.46019e59	−0.353129
$362$	1.41513e60	1.04989
$363$	−3.46877e57	−0.00241196
$364$	2.83748e59	0.184949
$365$	2.25249e59	0.137651
$366$	−5.89990e57	−0.00338095
$367$	−3.06220e60	−1.64582	−0.822909	−	0.568174i	$-0.807650\pi$
$367$	−3.06220e60	−1.64582	−0.822909	+	0.568174i	$0.807650\pi$
$368$	2.09448e59	0.105597
$369$	−1.45087e59	−0.0686291
$370$	−4.68806e60	−2.08091
$371$	8.54198e59	0.355854
$372$	−3.64318e58	−0.0142469
$373$	7.76030e59	0.284919	0.142459	−	0.989801i	$-0.454499\pi$
$373$	7.76030e59	0.284919	0.142459	+	0.989801i	$0.454499\pi$
$374$	3.73629e60	1.28812
$375$	−1.47621e59	−0.0477985
$376$	−6.29547e59	−0.191476
$377$	−5.11411e59	−0.146133
$378$	3.48880e58	0.00936740
$379$	2.95556e60	0.745794	0.372897	−	0.927873i	$-0.378365\pi$
$379$	2.95556e60	0.745794	0.372897	+	0.927873i	$0.378365\pi$
$380$	−3.15606e60	−0.748568
$381$	1.07585e59	0.0239891
$382$	7.55533e59	0.158403
$383$	4.65414e60	0.917632	0.458816	−	0.888531i	$-0.348274\pi$
$383$	4.65414e60	0.917632	0.458816	+	0.888531i	$0.348274\pi$
$384$	8.35408e57	0.00154923
$385$	3.74526e60	0.653364
$386$	−2.60369e60	−0.427354
$387$	−5.86917e60	−0.906503
$388$	−2.98944e60	−0.434554
$389$	8.28987e60	1.13431	0.567156	−	0.823611i	$-0.308044\pi$
$389$	8.28987e60	1.13431	0.567156	+	0.823611i	$0.308044\pi$
$390$	1.75269e59	0.0225781
$391$	6.83104e60	0.828577
$392$	4.42160e59	0.0505076
$393$	2.04460e59	0.0219980
$394$	−6.86138e60	−0.695425
$395$	3.80436e61	3.63287
$396$	−5.15852e60	−0.464182
$397$	−5.54339e60	−0.470109	−0.235054	−	0.971982i	$-0.575527\pi$
$397$	−5.54339e60	−0.470109	−0.235054	+	0.971982i	$0.575527\pi$
$398$	−3.11451e60	−0.248965
$399$	−7.07038e58	−0.00532819
$400$	8.67300e60	0.616254
$401$	−7.15209e60	−0.479226	−0.239613	−	0.970868i	$-0.577021\pi$
$401$	−7.15209e60	−0.479226	−0.239613	+	0.970868i	$0.577021\pi$
$402$	1.72895e57	0.000109262 0
$403$	2.66889e61	1.59097
$404$	−7.27740e60	−0.409274
$405$	−3.50465e61	−1.85974
$406$	−7.96923e59	−0.0399075
$407$	3.10625e61	1.46814
$408$	2.72464e59	0.0121561
$409$	−5.97660e60	−0.251743	−0.125871	−	0.992047i	$-0.540173\pi$
$409$	−5.97660e60	−0.251743	−0.125871	+	0.992047i	$0.540173\pi$
$410$	−2.27196e60	−0.0903606
$411$	−5.16107e59	−0.0193846
$412$	−9.62852e59	−0.0341566
$413$	2.10348e61	0.704874
$414$	−9.43131e60	−0.298582
$415$	−2.17461e61	−0.650505
$416$	−6.11995e60	−0.173003
$417$	7.78454e59	0.0207987
$418$	2.09116e61	0.528136
$419$	−5.61468e61	−1.34059	−0.670294	−	0.742095i	$-0.733832\pi$
$419$	−5.61468e61	−1.34059	−0.670294	+	0.742095i	$0.733832\pi$
$420$	2.73119e59	0.00616586
$421$	−5.24376e61	−1.11947	−0.559737	−	0.828670i	$-0.689098\pi$
$421$	−5.24376e61	−1.11947	−0.559737	+	0.828670i	$0.689098\pi$
$422$	8.47454e60	0.171109
$423$	2.83481e61	0.541409
$424$	−1.84236e61	−0.332871
$425$	2.82866e62	4.83549
$426$	−3.76007e59	−0.00608233
$427$	6.73504e60	0.103106
$428$	−2.75768e61	−0.399590
$429$	−1.16131e60	−0.0159295
$430$	−9.19071e61	−1.19355
$431$	2.89364e61	0.355818	0.177909	−	0.984047i	$-0.443067\pi$
$431$	2.89364e61	0.355818	0.177909	+	0.984047i	$0.443067\pi$
$432$	−7.52474e59	−0.00876240
$433$	9.60366e61	1.05918	0.529592	−	0.848253i	$-0.322345\pi$
$433$	9.60366e61	1.05918	0.529592	+	0.848253i	$0.322345\pi$
$434$	4.15888e61	0.434478
$435$	−4.92253e59	−0.00487182
$436$	3.85479e61	0.361466
$437$	3.82327e61	0.339720
$438$	−1.08836e59	−0.000916500 0
$439$	−1.42679e62	−1.13879	−0.569394	−	0.822065i	$-0.692822\pi$
$439$	−1.42679e62	−1.13879	−0.569394	+	0.822065i	$0.692822\pi$
$440$	−8.07788e61	−0.611166
$441$	−1.99102e61	−0.142813
$442$	−1.99599e62	−1.35749
$443$	−9.70171e61	−0.625692	−0.312846	−	0.949804i	$-0.601282\pi$
$443$	−9.70171e61	−0.625692	−0.312846	+	0.949804i	$0.601282\pi$
$444$	2.26519e60	0.0138550
$445$	−4.36812e62	−2.53416
$446$	−2.29700e62	−1.26413
$447$	2.78641e60	0.0145485
$448$	−9.53662e60	−0.0472456
$449$	3.07682e62	1.44648	0.723241	−	0.690595i	$-0.242651\pi$
$449$	3.07682e62	1.44648	0.723241	+	0.690595i	$0.242651\pi$
$450$	−3.90540e62	−1.74249
$451$	1.50537e61	0.0637520
$452$	1.14249e62	0.459303
$453$	1.24621e60	0.00475646
$454$	−3.11724e62	−1.12969
$455$	−2.00079e62	−0.688547
$456$	1.52496e60	0.00498407
$457$	6.26820e62	1.94586	0.972931	−	0.231098i	$-0.0742317\pi$
$457$	6.26820e62	1.94586	0.972931	+	0.231098i	$0.0742317\pi$
$458$	−1.83993e62	−0.542579
$459$	−2.45416e61	−0.0687550
$460$	−1.47688e62	−0.393129
$461$	−5.55866e61	−0.140604	−0.0703021	−	0.997526i	$-0.522396\pi$
$461$	−5.55866e61	−0.140604	−0.0703021	+	0.997526i	$0.522396\pi$
$462$	−1.80965e60	−0.00435019
$463$	−3.14206e62	−0.717896	−0.358948	−	0.933358i	$-0.616864\pi$
$463$	−3.14206e62	−0.717896	−0.358948	+	0.933358i	$0.616864\pi$
$464$	1.71882e61	0.0373300
$465$	2.56891e61	0.0530401
$466$	−3.51581e61	−0.0690171
$467$	−9.35089e62	−1.74545	−0.872723	−	0.488216i	$-0.837648\pi$
$467$	−9.35089e62	−1.74545	−0.872723	+	0.488216i	$0.837648\pi$
$468$	2.75578e62	0.489177
$469$	−1.97368e60	−0.00333208
$470$	4.43911e62	0.712847
$471$	1.22340e61	0.0186885
$472$	−4.53683e62	−0.659349
$473$	6.08964e62	0.842082
$474$	−1.83820e61	−0.0241881
$475$	1.58317e63	1.98257
$476$	−3.11032e62	−0.370716
$477$	8.29601e62	0.941212
$478$	2.57693e62	0.278321
$479$	−2.16694e62	−0.222824	−0.111412	−	0.993774i	$-0.535537\pi$
$479$	−2.16694e62	−0.222824	−0.111412	+	0.993774i	$0.535537\pi$
$480$	−5.89070e60	−0.00576763
$481$	−1.65941e63	−1.54720
$482$	3.02106e62	0.268259
$483$	−3.30857e60	−0.00279823
$484$	−8.54054e61	−0.0688049
$485$	2.10793e63	1.61780
$486$	5.08277e61	0.0371662
$487$	3.19737e62	0.222773	0.111386	−	0.993777i	$-0.464471\pi$
$487$	3.19737e62	0.222773	0.111386	+	0.993777i	$0.464471\pi$
$488$	−1.45263e62	−0.0964470
$489$	−2.30829e61	−0.0146060
$490$	−3.11779e62	−0.188035
$491$	−2.48027e63	−1.42588	−0.712942	−	0.701223i	$-0.752638\pi$
$491$	−2.48027e63	−1.42588	−0.712942	+	0.701223i	$0.752638\pi$
$492$	1.09777e60	0.000601633 0
$493$	5.60586e62	0.292913
$494$	−1.11714e63	−0.556575
$495$	3.63742e63	1.72811
$496$	−8.96998e62	−0.406417
$497$	4.29231e62	0.185488
$498$	1.05073e61	0.00433115
$499$	4.39215e63	1.72709	0.863544	−	0.504274i	$-0.168240\pi$
$499$	4.39215e63	1.72709	0.863544	+	0.504274i	$0.168240\pi$
$500$	−3.63462e63	−1.36353
$501$	−6.50220e60	−0.00232742
$502$	−9.55578e62	−0.326384
$503$	5.36364e63	1.74828	0.874142	−	0.485670i	$-0.161424\pi$
$503$	5.36364e63	1.74828	0.874142	+	0.485670i	$0.161424\pi$
$504$	4.29428e62	0.133590
$505$	5.13150e63	1.52369
$506$	9.78557e62	0.277363
$507$	−2.73566e60	−0.000740244 0
$508$	2.64888e63	0.684329
$509$	3.48127e63	0.858757	0.429378	−	0.903125i	$-0.358733\pi$
$509$	3.48127e63	0.858757	0.429378	+	0.903125i	$0.358733\pi$
$510$	−1.92122e62	−0.0452562
$511$	1.24242e62	0.0279498
$512$	2.05688e62	0.0441942
$513$	−1.37357e62	−0.0281898
$514$	4.38397e63	0.859477
$515$	6.78934e62	0.127162
$516$	4.44079e61	0.00794681
$517$	−2.94129e63	−0.502933
$518$	−2.58583e63	−0.422524
$519$	−1.89601e62	−0.0296079
$520$	4.31535e63	0.644076
$521$	−4.33083e63	−0.617852	−0.308926	−	0.951086i	$-0.599970\pi$
$521$	−4.33083e63	−0.617852	−0.308926	+	0.951086i	$0.599970\pi$
$522$	−7.73975e62	−0.105553
$523$	−1.35148e64	−1.76206	−0.881031	−	0.473059i	$-0.843150\pi$
$523$	−1.35148e64	−1.76206	−0.881031	+	0.473059i	$0.843150\pi$
$524$	5.03405e63	0.627527
$525$	−1.37004e62	−0.0163302
$526$	−8.80521e63	−1.00363
$527$	−2.92551e64	−3.18899
$528$	3.90310e61	0.00406923
$529$	−8.23877e63	−0.821588
$530$	1.29910e64	1.23925
$531$	2.04291e64	1.86435
$532$	−1.74082e63	−0.151995
$533$	−8.04194e62	−0.0671849
$534$	2.11060e62	0.0168728
$535$	1.94451e64	1.48764
$536$	4.25688e61	0.00311687
$537$	−1.41468e62	−0.00991434
$538$	−1.43337e64	−0.961556
$539$	2.06581e63	0.132664
$540$	5.30590e62	0.0326216
$541$	−7.93957e63	−0.467370	−0.233685	−	0.972312i	$-0.575078\pi$
$541$	−7.93957e63	−0.467370	−0.233685	+	0.972312i	$0.575078\pi$
$542$	−1.07350e63	−0.0605087
$543$	4.82142e62	0.0260243
$544$	6.70841e63	0.346773
$545$	−2.71812e64	−1.34571
$546$	9.66747e61	0.00458444
$547$	−1.18369e64	−0.537696	−0.268848	−	0.963183i	$-0.586643\pi$
$547$	−1.18369e64	−0.537696	−0.268848	+	0.963183i	$0.586643\pi$
$548$	−1.27072e64	−0.552977
$549$	6.54110e63	0.272710
$550$	4.05209e64	1.61866
$551$	3.13754e63	0.120096
$552$	7.13601e61	0.00261750
$553$	2.09840e64	0.737647
$554$	−2.19134e64	−0.738295
$555$	−1.59725e63	−0.0515808
$556$	1.91665e64	0.593316
$557$	−2.94944e64	−0.875272	−0.437636	−	0.899152i	$-0.644184\pi$
$557$	−2.94944e64	−0.875272	−0.437636	+	0.899152i	$0.644184\pi$
$558$	4.03912e64	1.14917
$559$	−3.25319e64	−0.887427
$560$	6.72453e63	0.175891
$561$	1.27298e63	0.0319295
$562$	−1.53427e64	−0.369060
$563$	1.69796e64	0.391725	0.195863	−	0.980631i	$-0.437249\pi$
$563$	1.69796e64	0.391725	0.195863	+	0.980631i	$0.437249\pi$
$564$	−2.14490e62	−0.00474623
$565$	−8.05601e64	−1.70994
$566$	−5.92246e64	−1.20591
$567$	−1.93309e64	−0.377616
$568$	−9.25776e63	−0.173508
$569$	−7.10032e64	−1.27685	−0.638425	−	0.769684i	$-0.720414\pi$
$569$	−7.10032e64	−1.27685	−0.638425	+	0.769684i	$0.720414\pi$
$570$	−1.07529e63	−0.0185552
$571$	5.49938e64	0.910679	0.455340	−	0.890318i	$-0.349518\pi$
$571$	5.49938e64	0.910679	0.455340	+	0.890318i	$0.349518\pi$
$572$	−2.85929e64	−0.454414
$573$	2.57415e62	0.00392645
$574$	−1.25316e63	−0.0183475
$575$	7.40843e64	1.04119
$576$	−9.26200e63	−0.124962
$577$	−3.61792e64	−0.468628	−0.234314	−	0.972161i	$-0.575284\pi$
$577$	−3.61792e64	−0.468628	−0.234314	+	0.972161i	$0.575284\pi$
$578$	1.61934e65	2.01388
$579$	−8.87092e62	−0.0105931
$580$	−1.21199e64	−0.138976
$581$	−1.19947e64	−0.132084
$582$	−1.01852e63	−0.0107716
$583$	−8.60764e64	−0.874325
$584$	−2.67969e63	−0.0261446
$585$	−1.94317e65	−1.82116
$586$	−2.35061e64	−0.211635
$587$	−5.02884e64	−0.434983	−0.217492	−	0.976062i	$-0.569788\pi$
$587$	−5.02884e64	−0.434983	−0.217492	+	0.976062i	$0.569788\pi$
$588$	1.50647e62	0.00125196
$589$	−1.63738e65	−1.30750
$590$	3.19904e65	2.45470
$591$	−2.33771e63	−0.0172379
$592$	5.57719e64	0.395235
$593$	2.17891e65	1.48407	0.742035	−	0.670361i	$-0.233861\pi$
$593$	2.17891e65	1.48407	0.742035	+	0.670361i	$0.233861\pi$
$594$	−3.51562e63	−0.0230155
$595$	2.19317e65	1.38014
$596$	6.86049e64	0.415019
$597$	−1.06113e63	−0.00617124
$598$	−5.22763e64	−0.292299
$599$	−3.47392e65	−1.86762	−0.933812	−	0.357763i	$-0.883540\pi$
$599$	−3.47392e65	−1.86762	−0.933812	+	0.357763i	$0.883540\pi$
$600$	2.95494e63	0.0152755
$601$	1.55859e65	0.774784	0.387392	−	0.921915i	$-0.373376\pi$
$601$	1.55859e65	0.774784	0.387392	+	0.921915i	$0.373376\pi$
$602$	−5.06940e64	−0.242348
$603$	−1.91685e63	−0.00881314
$604$	3.06833e64	0.135686
$605$	6.02217e64	0.256154
$606$	−2.47945e63	−0.0101449
$607$	−1.72842e65	−0.680324	−0.340162	−	0.940367i	$-0.610482\pi$
$607$	−1.72842e65	−0.680324	−0.340162	+	0.940367i	$0.610482\pi$
$608$	3.75464e64	0.142178
$609$	−2.71516e62	−0.000989212 0
$610$	1.02429e65	0.359064
$611$	1.57129e65	0.530015
$612$	−3.02076e65	−0.980522
$613$	−2.97410e65	−0.929041	−0.464521	−	0.885562i	$-0.653773\pi$
$613$	−2.97410e65	−0.929041	−0.464521	+	0.885562i	$0.653773\pi$
$614$	3.75540e65	1.12901
$615$	−7.74069e62	−0.00223983
$616$	−4.45558e64	−0.124096
$617$	2.16734e65	0.581067	0.290534	−	0.956865i	$-0.406167\pi$
$617$	2.16734e65	0.581067	0.290534	+	0.956865i	$0.406167\pi$
$618$	−3.28049e62	−0.000846662 0
$619$	4.54166e65	1.12846	0.564228	−	0.825619i	$-0.309174\pi$
$619$	4.54166e65	1.12846	0.564228	+	0.825619i	$0.309174\pi$
$620$	6.32498e65	1.51305
$621$	−6.42759e63	−0.0148046
$622$	−1.08161e65	−0.239881
$623$	−2.40936e65	−0.514556
$624$	−2.08510e63	−0.00428835
$625$	1.31836e66	2.61128
$626$	−6.41074e65	−1.22296
$627$	7.12472e63	0.0130912
$628$	3.01215e65	0.533121
$629$	1.81897e66	3.10125
$630$	−3.02801e65	−0.497342
$631$	5.90112e65	0.933779	0.466890	−	0.884316i	$-0.345375\pi$
$631$	5.90112e65	0.933779	0.466890	+	0.884316i	$0.345375\pi$
$632$	−4.52589e65	−0.690005
$633$	2.88733e63	0.00424139
$634$	5.78330e65	0.818612
$635$	−1.86780e66	−2.54769
$636$	−6.27701e63	−0.00825108
$637$	−1.10359e65	−0.139808
$638$	8.03048e64	0.0980518
$639$	4.16871e65	0.490605
$640$	−1.45036e65	−0.164531
$641$	3.08794e65	0.337680	0.168840	−	0.985643i	$-0.445998\pi$
$641$	3.08794e65	0.337680	0.168840	+	0.985643i	$0.445998\pi$
$642$	−9.39556e63	−0.00990489
$643$	−1.70492e66	−1.73279	−0.866397	−	0.499356i	$-0.833570\pi$
$643$	−1.70492e66	−1.73279	−0.866397	+	0.499356i	$0.833570\pi$
$644$	−8.14613e64	−0.0798240
$645$	−3.13133e64	−0.0295852
$646$	1.22456e66	1.11562
$647$	8.74050e65	0.767866	0.383933	−	0.923361i	$-0.374569\pi$
$647$	8.74050e65	0.767866	0.383933	+	0.923361i	$0.374569\pi$
$648$	4.16934e65	0.353228
$649$	−2.11964e66	−1.73186
$650$	−2.16470e66	−1.70582
$651$	1.41696e64	0.0107697
$652$	−5.68329e65	−0.416660
$653$	−2.22673e65	−0.157474	−0.0787368	−	0.996895i	$-0.525089\pi$
$653$	−2.22673e65	−0.157474	−0.0787368	+	0.996895i	$0.525089\pi$
$654$	1.31335e64	0.00895990
$655$	−3.54965e66	−2.33623
$656$	2.70285e64	0.0171625
$657$	1.20665e65	0.0739255
$658$	2.44852e65	0.144742
$659$	2.55651e66	1.45828	0.729139	−	0.684366i	$-0.239921\pi$
$659$	2.55651e66	1.45828	0.729139	+	0.684366i	$0.239921\pi$
$660$	−2.75218e64	−0.0151494
$661$	−3.44639e65	−0.183076	−0.0915378	−	0.995802i	$-0.529178\pi$
$661$	−3.44639e65	−0.183076	−0.0915378	+	0.995802i	$0.529178\pi$
$662$	1.09519e66	0.561472
$663$	−6.80046e64	−0.0336489
$664$	2.58704e65	0.123553
$665$	1.22750e66	0.565864
$666$	−2.51137e66	−1.11755
$667$	1.46821e65	0.0630712
$668$	−1.60092e65	−0.0663932
$669$	−7.82601e64	−0.0313348
$670$	−3.00165e64	−0.0116038
$671$	−6.78680e65	−0.253330
$672$	−3.24918e63	−0.00117111
$673$	−5.27326e66	−1.83538	−0.917688	−	0.397302i	$-0.869947\pi$
$673$	−5.27326e66	−1.83538	−0.917688	+	0.397302i	$0.869947\pi$
$674$	−1.48982e66	−0.500755
$675$	−2.66159e65	−0.0863978
$676$	−6.73553e64	−0.0211166
$677$	−2.59424e66	−0.785554	−0.392777	−	0.919634i	$-0.628486\pi$
$677$	−2.59424e66	−0.785554	−0.392777	+	0.919634i	$0.628486\pi$
$678$	3.89253e64	0.0113850
$679$	1.16269e66	0.328492
$680$	−4.73029e66	−1.29101
$681$	−1.06206e65	−0.0280022
$682$	−4.19084e66	−1.06750
$683$	3.83200e66	0.943060	0.471530	−	0.881850i	$-0.343702\pi$
$683$	3.83200e66	0.943060	0.471530	+	0.881850i	$0.343702\pi$
$684$	−1.69069e66	−0.402018
$685$	8.96020e66	2.05868
$686$	−1.71971e65	−0.0381802
$687$	−6.26875e64	−0.0134492
$688$	1.09338e66	0.226695
$689$	4.59836e66	0.921405
$690$	−5.03180e64	−0.00974473
$691$	5.53236e66	1.03556	0.517781	−	0.855513i	$-0.326758\pi$
$691$	5.53236e66	1.03556	0.517781	+	0.855513i	$0.326758\pi$
$692$	−4.66822e66	−0.844613
$693$	2.00632e66	0.350889
$694$	7.80668e65	0.131983
$695$	−1.35148e67	−2.20886
$696$	5.85613e63	0.000925323 0
$697$	8.81521e65	0.134667
$698$	−1.52426e66	−0.225143
$699$	−1.19786e64	−0.00171077
$700$	−3.37322e66	−0.465844
$701$	−4.02185e66	−0.537097	−0.268549	−	0.963266i	$-0.586544\pi$
$701$	−4.02185e66	−0.537097	−0.268549	+	0.963266i	$0.586544\pi$
$702$	1.87811e65	0.0242548
$703$	1.01806e67	1.27152
$704$	9.60991e65	0.116081
$705$	1.51243e65	0.0176698
$706$	−4.70135e66	−0.531266
$707$	2.83042e66	0.309382
$708$	−1.54572e65	−0.0163437
$709$	−4.02893e66	−0.412100	−0.206050	−	0.978541i	$-0.566061\pi$
$709$	−4.02893e66	−0.412100	−0.206050	+	0.978541i	$0.566061\pi$
$710$	6.52790e66	0.645955
$711$	2.03798e67	1.95103
$712$	5.19656e66	0.481323
$713$	−7.66210e66	−0.686664
$714$	−1.05970e65	−0.00918918
$715$	2.01617e67	1.69174
$716$	−3.48313e66	−0.282822
$717$	8.77974e64	0.00689893
$718$	1.37465e67	1.04537
$719$	−6.32479e66	−0.465497	−0.232749	−	0.972537i	$-0.574772\pi$
$719$	−6.32479e66	−0.465497	−0.232749	+	0.972537i	$0.574772\pi$
$720$	6.53090e66	0.465221
$721$	3.74485e65	0.0258200
$722$	−3.74148e66	−0.249700
$723$	1.02929e65	0.00664951
$724$	1.18709e67	0.742385
$725$	6.07969e66	0.368076
$726$	−2.90981e64	−0.00170551
$727$	1.00068e67	0.567854	0.283927	−	0.958846i	$-0.408363\pi$
$727$	1.00068e67	0.567854	0.283927	+	0.958846i	$0.408363\pi$
$728$	2.38025e66	0.130778
$729$	−1.87627e67	−0.998157
$730$	1.88952e66	0.0973341
$731$	3.56600e67	1.77878
$732$	−4.94919e64	−0.00239069
$733$	8.44722e66	0.395158	0.197579	−	0.980287i	$-0.436692\pi$
$733$	8.44722e66	0.395158	0.197579	+	0.980287i	$0.436692\pi$
$734$	−2.56876e67	−1.16377
$735$	−1.06225e65	−0.00466095
$736$	1.75698e66	0.0746685
$737$	1.98885e65	0.00818683
$738$	−1.21708e66	−0.0485281
$739$	−2.08026e67	−0.803475	−0.401738	−	0.915755i	$-0.631594\pi$
$739$	−2.08026e67	−0.803475	−0.401738	+	0.915755i	$0.631594\pi$
$740$	−3.93263e67	−1.47142
$741$	−3.80616e65	−0.0137962
$742$	7.16554e66	0.251627
$743$	−1.93023e67	−0.656706	−0.328353	−	0.944555i	$-0.606494\pi$
$743$	−1.93023e67	−0.656706	−0.328353	+	0.944555i	$0.606494\pi$
$744$	−3.05612e65	−0.0100741
$745$	−4.83752e67	−1.54508
$746$	6.50981e66	0.201468
$747$	−1.16493e67	−0.349353
$748$	3.13423e67	0.910841
$749$	1.07255e67	0.302062
$750$	−1.23834e66	−0.0337986
$751$	3.43363e67	0.908269	0.454135	−	0.890933i	$-0.349949\pi$
$751$	3.43363e67	0.908269	0.454135	+	0.890933i	$0.349949\pi$
$752$	−5.28102e66	−0.135394
$753$	−3.25571e65	−0.00809028
$754$	−4.29003e66	−0.103332
$755$	−2.16357e67	−0.505146
$756$	2.92662e65	0.00662376
$757$	1.65846e67	0.363875	0.181938	−	0.983310i	$-0.441763\pi$
$757$	1.65846e67	0.363875	0.181938	+	0.983310i	$0.441763\pi$
$758$	2.47931e67	0.527356
$759$	3.33400e65	0.00687518
$760$	−2.64750e67	−0.529317
$761$	−1.18866e67	−0.230419	−0.115210	−	0.993341i	$-0.536754\pi$
$761$	−1.18866e67	−0.230419	−0.115210	+	0.993341i	$0.536754\pi$
$762$	9.02488e65	0.0169629
$763$	−1.49926e67	−0.273243
$764$	6.33787e66	0.112008
$765$	2.13002e68	3.65039
$766$	3.90418e67	0.648864
$767$	1.13235e68	1.82512
$768$	7.00791e64	0.00109547
$769$	−8.48937e67	−1.28708	−0.643542	−	0.765411i	$-0.722536\pi$
$769$	−8.48937e67	−1.28708	−0.643542	+	0.765411i	$0.722536\pi$
$770$	3.14176e67	0.461998
$771$	1.49364e66	0.0213044
$772$	−2.18413e67	−0.302185
$773$	3.31439e67	0.444821	0.222411	−	0.974953i	$-0.428607\pi$
$773$	3.31439e67	0.444821	0.222411	+	0.974953i	$0.428607\pi$
$774$	−4.92342e67	−0.640994
$775$	−3.17279e68	−4.00729
$776$	−2.50772e67	−0.307276
$777$	−8.81009e65	−0.0104734
$778$	6.95405e67	0.802079
$779$	4.93379e66	0.0552141
$780$	1.47026e66	0.0159651
$781$	−4.32530e67	−0.455740
$782$	5.73029e67	0.585893
$783$	−5.27477e65	−0.00523362
$784$	3.70911e66	0.0357143
$785$	−2.12395e68	−1.98476
$786$	1.71513e66	0.0155549
$787$	−1.80792e68	−1.59138	−0.795690	−	0.605704i	$-0.792892\pi$
$787$	−1.80792e68	−1.59138	−0.795690	+	0.605704i	$0.792892\pi$
$788$	−5.75574e67	−0.491740
$789$	−2.99999e66	−0.0248777
$790$	3.19133e68	2.56883
$791$	−4.44352e67	−0.347200
$792$	−4.32728e67	−0.328226
$793$	3.62563e67	0.266971
$794$	−4.65013e67	−0.332417
$795$	4.42610e66	0.0307180
$796$	−2.61264e67	−0.176044
$797$	−1.01561e68	−0.664441	−0.332221	−	0.943202i	$-0.607798\pi$
$797$	−1.01561e68	−0.664441	−0.332221	+	0.943202i	$0.607798\pi$
$798$	−5.93106e65	−0.00376760
$799$	−1.72238e68	−1.06238
$800$	7.27544e67	0.435757
$801$	−2.33998e68	−1.36097
$802$	−5.99961e67	−0.338864
$803$	−1.25197e67	−0.0686720
$804$	1.45034e64	7.72599e−5 0
$805$	5.74406e67	0.297177
$806$	2.23883e68	1.12498
$807$	−4.88357e66	−0.0238347
$808$	−6.10473e67	−0.289401
$809$	3.37468e68	1.55397	0.776985	−	0.629520i	$-0.216748\pi$
$809$	3.37468e68	1.55397	0.776985	+	0.629520i	$0.216748\pi$
$810$	−2.93992e68	−1.31503
$811$	−3.80483e68	−1.65328	−0.826638	−	0.562734i	$-0.809750\pi$
$811$	−3.80483e68	−1.65328	−0.826638	+	0.562734i	$0.809750\pi$
$812$	−6.68507e66	−0.0282189
$813$	−3.65747e65	−0.00149987
$814$	2.60571e68	1.03813
$815$	4.00745e68	1.55119
$816$	2.28560e66	0.00859569
$817$	1.99586e68	0.729309
$818$	−5.01354e67	−0.178009
$819$	−1.07181e68	−0.369783
$820$	−1.90585e67	−0.0638946
$821$	−1.34877e68	−0.439414	−0.219707	−	0.975566i	$-0.570510\pi$
$821$	−1.34877e68	−0.439414	−0.219707	+	0.975566i	$0.570510\pi$
$822$	−4.32942e66	−0.0137070
$823$	4.49698e66	0.0138365	0.00691823	−	0.999976i	$-0.497798\pi$
$823$	4.49698e66	0.0138365	0.00691823	+	0.999976i	$0.497798\pi$
$824$	−8.07699e66	−0.0241524
$825$	1.38057e67	0.0401228
$826$	1.76452e68	0.498421
$827$	3.01096e68	0.826657	0.413329	−	0.910582i	$-0.364366\pi$
$827$	3.01096e68	0.826657	0.413329	+	0.910582i	$0.364366\pi$
$828$	−7.91155e67	−0.211129
$829$	−1.22710e68	−0.318308	−0.159154	−	0.987254i	$-0.550877\pi$
$829$	−1.22710e68	−0.318308	−0.159154	+	0.987254i	$0.550877\pi$
$830$	−1.82419e68	−0.459976
$831$	−7.46602e66	−0.0183006
$832$	−5.13379e67	−0.122332
$833$	1.20971e68	0.280235
$834$	6.53015e66	0.0147069
$835$	1.12886e68	0.247176
$836$	1.75420e68	0.373448
$837$	2.75273e67	0.0569790
$838$	−4.70994e68	−0.947939
$839$	−2.49800e68	−0.488863	−0.244431	−	0.969667i	$-0.578601\pi$
$839$	−2.49800e68	−0.488863	−0.244431	+	0.969667i	$0.578601\pi$
$840$	2.29109e66	0.00435992
$841$	−5.28339e68	−0.977703
$842$	−4.39879e68	−0.791587
$843$	−5.22733e66	−0.00914813
$844$	7.10896e67	0.120993
$845$	4.74941e67	0.0786153
$846$	2.37801e68	0.382834
$847$	3.32170e67	0.0520116
$848$	−1.54548e68	−0.235375
$849$	−2.01782e67	−0.0298918
$850$	2.37285e69	3.41921
$851$	4.76401e68	0.667771
$852$	−3.15417e66	−0.00430086
$853$	3.88675e68	0.515566	0.257783	−	0.966203i	$-0.417008\pi$
$853$	3.88675e68	0.515566	0.257783	+	0.966203i	$0.417008\pi$
$854$	5.64976e67	0.0729071
$855$	1.19215e69	1.49668
$856$	−2.31331e68	−0.282553
$857$	7.74068e68	0.919877	0.459939	−	0.887951i	$-0.347871\pi$
$857$	7.74068e68	0.919877	0.459939	+	0.887951i	$0.347871\pi$
$858$	−9.74177e66	−0.0112638
$859$	−7.32436e68	−0.824006	−0.412003	−	0.911182i	$-0.635171\pi$
$859$	−7.32436e68	−0.824006	−0.412003	+	0.911182i	$0.635171\pi$
$860$	−7.70972e68	−0.843966
$861$	−4.26960e65	−0.000454792 0
$862$	2.42736e68	0.251601
$863$	−1.68558e68	−0.170018	−0.0850091	−	0.996380i	$-0.527092\pi$
$863$	−1.68558e68	−0.170018	−0.0850091	+	0.996380i	$0.527092\pi$
$864$	−6.31221e66	−0.00619596
$865$	3.29169e69	3.14442
$866$	8.05614e68	0.748956
$867$	5.51718e67	0.0499193
$868$	3.48872e68	0.307222
$869$	−2.11453e69	−1.81238
$870$	−4.12932e66	−0.00344490
$871$	−1.06248e67	−0.00862768
$872$	3.23363e68	0.255595
$873$	1.12921e69	0.868841
$874$	3.20719e68	0.240218
$875$	1.41363e69	1.03073
$876$	−9.12986e65	−0.000648063 0
$877$	4.63355e68	0.320201	0.160101	−	0.987101i	$-0.448818\pi$
$877$	4.63355e68	0.320201	0.160101	+	0.987101i	$0.448818\pi$
$878$	−1.19688e69	−0.805245
$879$	−8.00868e66	−0.00524593
$880$	−6.77622e68	−0.432160
$881$	−1.21977e69	−0.757435	−0.378718	−	0.925512i	$-0.623635\pi$
$881$	−1.21977e69	−0.757435	−0.378718	+	0.925512i	$0.623635\pi$
$882$	−1.67019e68	−0.100984
$883$	−2.10590e69	−1.23983	−0.619914	−	0.784670i	$-0.712832\pi$
$883$	−2.10590e69	−1.23983	−0.619914	+	0.784670i	$0.712832\pi$
$884$	−1.67436e69	−0.959888
$885$	1.08993e68	0.0608461
$886$	−8.13838e68	−0.442431
$887$	2.39710e69	1.26906	0.634528	−	0.772900i	$-0.281195\pi$
$887$	2.39710e69	1.26906	0.634528	+	0.772900i	$0.281195\pi$
$888$	1.90018e67	0.00979694
$889$	−1.03024e69	−0.517304
$890$	−3.66424e69	−1.79192
$891$	1.94795e69	0.927794
$892$	−1.92686e69	−0.893874
$893$	−9.63999e68	−0.435579
$894$	2.33741e67	0.0102873
$895$	2.45605e69	1.05292
$896$	−7.99989e67	−0.0334077
$897$	−1.78108e67	−0.00724540
$898$	2.58102e69	1.02282
$899$	−6.28786e68	−0.242745
$900$	−3.27608e69	−1.23213
$901$	−5.04051e69	−1.84689
$902$	1.26279e68	0.0450794
$903$	−1.72717e67	−0.00600722
$904$	9.58389e68	0.324776
$905$	−8.37053e69	−2.76383
$906$	1.04540e67	0.00336333
$907$	−3.76696e68	−0.118092	−0.0590460	−	0.998255i	$-0.518806\pi$
$907$	−3.76696e68	−0.118092	−0.0590460	+	0.998255i	$0.518806\pi$
$908$	−2.61493e69	−0.798808
$909$	2.74892e69	0.818297
$910$	−1.67838e69	−0.486876
$911$	−4.72660e68	−0.133619	−0.0668094	−	0.997766i	$-0.521282\pi$
$911$	−4.72660e68	−0.133619	−0.0668094	+	0.997766i	$0.521282\pi$
$912$	1.27923e67	0.00352427
$913$	1.20868e69	0.324526
$914$	5.25814e69	1.37593
$915$	3.48981e67	0.00890034
$916$	−1.54345e69	−0.383661
$917$	−1.95791e69	−0.474366
$918$	−2.05870e68	−0.0486171
$919$	2.71709e69	0.625445	0.312722	−	0.949845i	$-0.398759\pi$
$919$	2.71709e69	0.625445	0.312722	+	0.949845i	$0.398759\pi$
$920$	−1.23889e69	−0.277984
$921$	1.27949e68	0.0279856
$922$	−4.66294e68	−0.0994222
$923$	2.31065e69	0.480280
$924$	−1.51804e67	−0.00307605
$925$	1.97272e70	3.89704
$926$	−2.63575e69	−0.507629
$927$	3.63702e68	0.0682923
$928$	1.44185e68	0.0263963
$929$	−5.48153e69	−0.978436	−0.489218	−	0.872161i	$-0.662718\pi$
$929$	−5.48153e69	−0.978436	−0.489218	+	0.872161i	$0.662718\pi$
$930$	2.15496e68	0.0375050
$931$	6.77062e68	0.114898
$932$	−2.94928e68	−0.0488024
$933$	−3.68510e67	−0.00594608
$934$	−7.84410e69	−1.23422
$935$	−2.21003e70	−3.39098
$936$	2.31171e69	0.345901
$937$	−7.02329e69	−1.02485	−0.512425	−	0.858732i	$-0.671253\pi$
$937$	−7.02329e69	−1.02485	−0.512425	+	0.858732i	$0.671253\pi$
$938$	−1.65564e67	−0.00235613
$939$	−2.18418e68	−0.0303142
$940$	3.72379e69	0.504059
$941$	1.44920e69	0.191325	0.0956624	−	0.995414i	$-0.469503\pi$
$941$	1.44920e69	0.191325	0.0956624	+	0.995414i	$0.469503\pi$
$942$	1.02626e68	0.0132148
$943$	2.30876e68	0.0289971
$944$	−3.80577e69	−0.466230
$945$	−2.06364e68	−0.0246596
$946$	5.10836e69	0.595442
$947$	1.34230e70	1.52625	0.763124	−	0.646252i	$-0.223664\pi$
$947$	1.34230e70	1.52625	0.763124	+	0.646252i	$0.223664\pi$
$948$	−1.54200e68	−0.0171036
$949$	6.68826e68	0.0723698
$950$	1.32806e70	1.40189
$951$	1.97040e68	0.0202914
$952$	−2.60913e69	−0.262136
$953$	−8.38184e69	−0.821592	−0.410796	−	0.911727i	$-0.634749\pi$
$953$	−8.38184e69	−0.821592	−0.410796	+	0.911727i	$0.634749\pi$
$954$	6.95920e69	0.665537
$955$	−4.46901e69	−0.416996
$956$	2.16168e69	0.196803
$957$	2.73603e67	0.00243047
$958$	−1.81776e69	−0.157560
$959$	4.94225e69	0.418011
$960$	−4.94147e67	−0.00407833
$961$	2.03978e70	1.64280
$962$	−1.39202e70	−1.09403
$963$	1.04167e70	0.798935
$964$	2.53425e69	0.189688
$965$	1.54009e70	1.12501
$966$	−2.77543e67	−0.00197865
$967$	−3.98935e69	−0.277575	−0.138788	−	0.990322i	$-0.544321\pi$
$967$	−3.98935e69	−0.277575	−0.138788	+	0.990322i	$0.544321\pi$
$968$	−7.16432e68	−0.0486524
$969$	4.17213e68	0.0276535
$970$	1.76826e70	1.14396
$971$	−4.66403e69	−0.294516	−0.147258	−	0.989098i	$-0.547045\pi$
$971$	−4.66403e69	−0.294516	−0.147258	+	0.989098i	$0.547045\pi$
$972$	4.26374e68	0.0262805
$973$	−7.45450e69	−0.448504
$974$	2.68215e69	0.157524
$975$	−7.37527e68	−0.0422833
$976$	−1.21855e69	−0.0681984
$977$	−1.29371e70	−0.706830	−0.353415	−	0.935467i	$-0.614980\pi$
$977$	−1.29371e70	−0.706830	−0.353415	+	0.935467i	$0.614980\pi$
$978$	−1.93633e68	−0.0103280
$979$	2.42788e70	1.26425
$980$	−2.61539e69	−0.132961
$981$	−1.45608e70	−0.722711
$982$	−2.08060e70	−1.00825
$983$	1.34733e70	0.637478	0.318739	−	0.947843i	$-0.396741\pi$
$983$	1.34733e70	0.637478	0.318739	+	0.947843i	$0.396741\pi$
$984$	9.20877e66	0.000425419 0
$985$	4.05853e70	1.83070
$986$	4.70253e69	0.207121
$987$	8.34224e67	0.00358781
$988$	−9.37123e69	−0.393558
$989$	9.33959e69	0.383014
$990$	3.05129e70	1.22196
$991$	−4.96910e70	−1.94333	−0.971665	−	0.236363i	$-0.924045\pi$
$991$	−4.96910e70	−1.94333	−0.971665	+	0.236363i	$0.924045\pi$
$992$	−7.52456e69	−0.287380
$993$	3.73139e68	0.0139176
$994$	3.60065e69	0.131160
$995$	1.84224e70	0.655398
$996$	8.81419e67	0.00306258
$997$	−1.54373e70	−0.523885	−0.261943	−	0.965083i	$-0.584363\pi$
$997$	−1.54373e70	−0.523885	−0.261943	+	0.965083i	$0.584363\pi$
$998$	3.68440e70	1.22124
$999$	−1.71154e69	−0.0554113

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.48.a.c.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.48.a.c.1.3	✓	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)

\(f(q)\)	\(=\)	\(q+8.38861e6 q^{2} +2.85805e9 q^{3} +7.03687e13 q^{4} -4.96190e16 q^{5} +2.39750e16 q^{6} -2.73687e19 q^{7} +5.90296e20 q^{8} -2.65806e22 q^{9} -4.16234e23 q^{10} +2.75791e24 q^{11} +2.01117e23 q^{12} -1.47333e26 q^{13} -2.29586e26 q^{14} -1.41813e26 q^{15} +4.95176e27 q^{16} +1.61499e29 q^{17} -2.22975e29 q^{18} +9.03896e29 q^{19} -3.49162e30 q^{20} -7.82212e28 q^{21} +2.31350e31 q^{22} +4.22977e31 q^{23} +1.68709e30 q^{24} +1.75150e33 q^{25} -1.23591e33 q^{26} -1.51961e32 q^{27} -1.92590e33 q^{28} +3.47113e33 q^{29} -1.18962e33 q^{30} -1.81147e35 q^{31} +4.15384e34 q^{32} +7.88224e33 q^{33} +1.35475e36 q^{34} +1.35801e36 q^{35} -1.87045e36 q^{36} +1.12630e37 q^{37} +7.58243e36 q^{38} -4.21083e35 q^{39} -2.92899e37 q^{40} +5.45836e36 q^{41} -6.56167e35 q^{42} +2.20806e38 q^{43} +1.94071e38 q^{44} +1.31890e39 q^{45} +3.54819e38 q^{46} -1.06649e39 q^{47} +1.41524e37 q^{48} +7.49048e38 q^{49} +1.46926e40 q^{50} +4.61573e38 q^{51} -1.03676e40 q^{52} -3.12107e40 q^{53} -1.27474e39 q^{54} -1.36845e41 q^{55} -1.61557e40 q^{56} +2.58338e39 q^{57} +2.91180e40 q^{58} -7.68569e41 q^{59} -9.97923e39 q^{60} -2.46085e41 q^{61} -1.51957e42 q^{62} +7.27479e41 q^{63} +3.48449e41 q^{64} +7.31049e42 q^{65} +6.61210e40 q^{66} +7.21144e40 q^{67} +1.13645e43 q^{68} +1.20889e41 q^{69} +1.13918e43 q^{70} -1.56833e43 q^{71} -1.56904e43 q^{72} -4.53957e42 q^{73} +9.44813e43 q^{74} +5.00586e42 q^{75} +6.36060e43 q^{76} -7.54805e43 q^{77} -3.53230e42 q^{78} -7.66715e44 q^{79} -2.45701e44 q^{80} +7.06314e44 q^{81} +4.57881e43 q^{82} +4.38261e44 q^{83} -5.50433e42 q^{84} -8.01342e45 q^{85} +1.85226e45 q^{86} +9.92067e42 q^{87} +1.62798e45 q^{88} +8.80332e45 q^{89} +1.10638e46 q^{90} +4.03231e45 q^{91} +2.97643e45 q^{92} -5.17727e44 q^{93} -8.94640e45 q^{94} -4.48504e46 q^{95} +1.18719e44 q^{96} -4.24824e46 q^{97} +6.28347e45 q^{98} -7.33070e46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 50331648 q^{2} + 91348200216 q^{3} + 422212465065984 q^{4} - 30\!\cdots\!00 q^{5} + 76\!\cdots\!28 q^{6} - 16\!\cdots\!58 q^{7} + 35\!\cdots\!72 q^{8} + 23\!\cdots\!02 q^{9} - 25\!\cdots\!00 q^{10}+ \cdots - 22\!\cdots\!76 q^{99}+O(q^{100}) \) 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

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