LMFDB - Embedded newform 1.36.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,36,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 36, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 36);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 36 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$7.75951306336$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 12422194x - 2645665785 $ x^3 - 12422194*x - 2645665785
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3626.53$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+331573. q^{2} -1.54691e8 q^{3} +7.55810e10 q^{4} +2.12139e12 q^{5} -5.12913e13 q^{6} +3.96640e14 q^{7} +1.36679e16 q^{8} -2.61023e16 q^{9} +O(q^{10})$	\(q+331573. q^{2} -1.54691e8 q^{3} +7.55810e10 q^{4} +2.12139e12 q^{5} -5.12913e13 q^{6} +3.96640e14 q^{7} +1.36679e16 q^{8} -2.61023e16 q^{9} +7.03395e17 q^{10} -6.82681e17 q^{11} -1.16917e19 q^{12} -1.17949e19 q^{13} +1.31515e20 q^{14} -3.28159e20 q^{15} +1.93496e21 q^{16} -1.33083e21 q^{17} -8.65483e21 q^{18} -3.58945e22 q^{19} +1.60337e23 q^{20} -6.13565e22 q^{21} -2.26359e23 q^{22} +6.92195e23 q^{23} -2.11429e24 q^{24} +1.58990e24 q^{25} -3.91088e24 q^{26} +1.17772e25 q^{27} +2.99785e25 q^{28} -5.67568e25 q^{29} -1.08809e26 q^{30} +1.02960e26 q^{31} +1.71955e26 q^{32} +1.05604e26 q^{33} -4.41267e26 q^{34} +8.41427e26 q^{35} -1.97284e27 q^{36} +4.50412e27 q^{37} -1.19017e28 q^{38} +1.82456e27 q^{39} +2.89948e28 q^{40} -6.23104e27 q^{41} -2.03442e28 q^{42} -2.75822e27 q^{43} -5.15977e28 q^{44} -5.53731e28 q^{45} +2.29513e29 q^{46} +1.41103e29 q^{47} -2.99320e29 q^{48} -2.21495e29 q^{49} +5.27167e29 q^{50} +2.05867e29 q^{51} -8.91472e29 q^{52} -2.48503e30 q^{53} +3.90500e30 q^{54} -1.44823e30 q^{55} +5.42123e30 q^{56} +5.55255e30 q^{57} -1.88190e31 q^{58} +5.47495e30 q^{59} -2.48026e31 q^{60} +2.30979e31 q^{61} +3.41386e31 q^{62} -1.03532e31 q^{63} -9.46893e30 q^{64} -2.50216e31 q^{65} +3.50156e31 q^{66} +1.55814e31 q^{67} -1.00585e32 q^{68} -1.07076e32 q^{69} +2.78995e32 q^{70} -1.13262e32 q^{71} -3.56763e32 q^{72} +3.23524e32 q^{73} +1.49345e33 q^{74} -2.45942e32 q^{75} -2.71294e33 q^{76} -2.70778e32 q^{77} +6.04976e32 q^{78} -1.44166e32 q^{79} +4.10479e33 q^{80} -5.15885e32 q^{81} -2.06605e33 q^{82} +3.50421e33 q^{83} -4.63739e33 q^{84} -2.82320e33 q^{85} -9.14551e32 q^{86} +8.77975e33 q^{87} -9.33079e33 q^{88} +9.37543e33 q^{89} -1.83602e34 q^{90} -4.67833e33 q^{91} +5.23168e34 q^{92} -1.59269e34 q^{93} +4.67858e34 q^{94} -7.61461e34 q^{95} -2.65998e34 q^{96} +3.59603e33 q^{97} -7.34419e34 q^{98} +1.78195e34 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 139656 q^{2} - 104875308 q^{3} + 34841262144 q^{4} + 892652054010 q^{5} - 4786530564384 q^{6} + 878422149346056 q^{7} + 22\!\cdots\!00 q^{8}+ \cdots + 15\!\cdots\!51 q^{9}+O(q^{10}) $ 3 * q + 139656 * q^2 - 104875308 * q^3 + 34841262144 * q^4 + 892652054010 * q^5 - 4786530564384 * q^6 + 878422149346056 * q^7 + 22336009925337600 * q^8 + 150091978876243551 * q^9	$ 3 q + 139656 q^{2} - 104875308 q^{3} + 34841262144 q^{4} + 892652054010 q^{5} - 4786530564384 q^{6} + 878422149346056 q^{7} + 22\!\cdots\!00 q^{8}+ \cdots + 30\!\cdots\!52 q^{99}+O(q^{100}) $ 3 * q + 139656 * q^2 - 104875308 * q^3 + 34841262144 * q^4 + 892652054010 * q^5 - 4786530564384 * q^6 + 878422149346056 * q^7 + 22336009925337600 * q^8 + 150091978876243551 * q^9 + 1019870812729298160 * q^10 - 1157945428549987044 * q^11 - 22548891526776486144 * q^12 - 62139610550998650558 * q^13 + 135909343255071438528 * q^14 + 706062479352366674520 * q^15 + 2155694017285818421248 * q^16 - 3932636930193139724394 * q^17 - 23007400170989698594008 * q^18 - 32303396242934620550940 * q^19 + 147257059647928607018880 * q^20 + 222122458753667398807776 * q^21 + 22658809266113247402912 * q^22 - 514822069421375217224808 * q^23 - 3760729014923614708254720 * q^24 + 646885156836409574920725 * q^25 + 4284481859934908169468336 * q^26 + 27373531144823515220747400 * q^27 + 10448754713452503022622208 * q^28 - 38460399143984437598248110 * q^29 - 234613011392444285921119680 * q^30 + 103731594563724689730029856 * q^31 - 9222369125611166314758144 * q^32 + 1184565114402567148957069584 * q^33 - 554136735348503783026707312 * q^34 + 1596564453000564139676248560 * q^35 - 6052204716130590310531484352 * q^36 + 2464613172948888017021063706 * q^37 - 12543374691225905672793885600 * q^38 + 18611981954062877742706387512 * q^39 + 16458708947711983604007091200 * q^40 + 23522986584532768129037087406 * q^41 - 33931371616975894880367698688 * q^42 - 47516297135443858184325274308 * q^43 - 80954820698705302013923898112 * q^44 - 110576300682246572226345828030 * q^45 + 310121697020384938950505889856 * q^46 + 164346768841318947159729902256 * q^47 + 445342931723856383878644744192 * q^48 - 595089038084925731622037450821 * q^49 + 373669468267473207632799996600 * q^50 - 1803044074850794727352259927704 * q^51 - 511632617456400883939009686144 * q^52 - 1670480551111723484744458809558 * q^53 + 4424231404769003900494105901760 * q^54 + 3067178595313878889174894808520 * q^55 + 5670920217413056567252590243840 * q^56 + 4048712721984947152977307522800 * q^57 - 23757672063982901326871265032400 * q^58 + 4370528583092646699845243631180 * q^59 - 40771862895691439845448715210240 * q^60 + 23537078276516028947219080488306 * q^61 + 29401231764447267309574710842112 * q^62 + 45614247892704690123948892506792 * q^63 + 93510280736634320631093264384 * q^64 + 75762337609865790449417835274620 * q^65 - 75640417841065837797640948042368 * q^66 - 188845033384156918977315211921644 * q^67 + 21990159186015794982823459732608 * q^68 - 325983212396274250308653315934048 * q^69 + 223263426310223328568197933240960 * q^70 + 348774602295358210538621162006856 * q^71 + 314101495165322886769992842611200 * q^72 - 285174964854822786615792218987058 * q^73 + 2106337383176566865790045395789808 * q^74 - 1577819189216049218913461709237300 * q^75 - 2729074287668324197849535448894720 * q^76 + 691501421964810422051915307575712 * q^77 - 2213086042571083132613626950273216 * q^78 - 426212862591061661901736630874160 * q^79 + 6831119561623806264802413342351360 * q^80 + 1867221150796978455595408934723163 * q^81 - 4061181362173286538873115152234288 * q^82 + 14867187331664065317008883105766692 * q^83 - 13024788508690842242825242575869952 * q^84 - 8752040931978292430566755304420140 * q^85 + 148490750656470812540405098190496 * q^86 - 7833119385476156993771606256673800 * q^87 - 18777218849949122679898044025804800 * q^88 + 30583590846193751335205992418034270 * q^89 + 2860720282233327924484406809049520 * q^90 + 1003391702519487362566122156997296 * q^91 + 83662070125024358323030039384121856 * q^92 - 40914650682166972019906140161446016 * q^93 + 19076193270418512575422277142000768 * q^94 - 84521392849966457182141665888160200 * q^95 - 32392027865954425966997293222723584 * q^96 - 106165667044630951063328618701091994 * q^97 - 13202051562017808504422115585262392 * q^98 + 30288686341597731928441860752034252 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	331573.	1.78877	0.894385	−	0.447298i	$-0.147614\pi$
$2$	331573.	1.78877	0.894385	+	0.447298i	$0.147614\pi$
$3$	−1.54691e8	−0.691580	−0.345790	−	0.938312i	$-0.612389\pi$
$3$	−1.54691e8	−0.691580	−0.345790	+	0.938312i	$0.612389\pi$
$4$	7.55810e10	2.19970
$5$	2.12139e12	1.24350	0.621748	−	0.783217i	$-0.286423\pi$
$5$	2.12139e12	1.24350	0.621748	+	0.783217i	$0.286423\pi$
$6$	−5.12913e13	−1.23708
$7$	3.96640e14	0.644438	0.322219	−	0.946665i	$-0.395571\pi$
$7$	3.96640e14	0.644438	0.322219	+	0.946665i	$0.395571\pi$
$8$	1.36679e16	2.14598
$9$	−2.61023e16	−0.521717
$10$	7.03395e17	2.22433
$11$	−6.82681e17	−0.407236	−0.203618	−	0.979050i	$-0.565270\pi$
$11$	−6.82681e17	−0.407236	−0.203618	+	0.979050i	$0.565270\pi$
$12$	−1.16917e19	−1.52127
$13$	−1.17949e19	−0.378169	−0.189085	−	0.981961i	$-0.560552\pi$
$13$	−1.17949e19	−0.378169	−0.189085	+	0.981961i	$0.560552\pi$
$14$	1.31515e20	1.15275
$15$	−3.28159e20	−0.859977
$16$	1.93496e21	1.63897
$17$	−1.33083e21	−0.390181	−0.195090	−	0.980785i	$-0.562500\pi$
$17$	−1.33083e21	−0.390181	−0.195090	+	0.980785i	$0.562500\pi$
$18$	−8.65483e21	−0.933232
$19$	−3.58945e22	−1.50259	−0.751294	−	0.659967i	$-0.770570\pi$
$19$	−3.58945e22	−1.50259	−0.751294	+	0.659967i	$0.770570\pi$
$20$	1.60337e23	2.73532
$21$	−6.13565e22	−0.445680
$22$	−2.26359e23	−0.728451
$23$	6.92195e23	1.02327	0.511636	−	0.859202i	$-0.329039\pi$
$23$	6.92195e23	1.02327	0.511636	+	0.859202i	$0.329039\pi$
$24$	−2.11429e24	−1.48412
$25$	1.58990e24	0.546284
$26$	−3.91088e24	−0.676457
$27$	1.17772e25	1.05239
$28$	2.99785e25	1.41757
$29$	−5.67568e25	−1.45229	−0.726144	−	0.687542i	$-0.758690\pi$
$29$	−5.67568e25	−1.45229	−0.726144	+	0.687542i	$0.758690\pi$
$30$	−1.08809e26	−1.53830
$31$	1.02960e26	0.820043	0.410022	−	0.912076i	$-0.365521\pi$
$31$	1.02960e26	0.820043	0.410022	+	0.912076i	$0.365521\pi$
$32$	1.71955e26	0.785760
$33$	1.05604e26	0.281636
$34$	−4.41267e26	−0.697943
$35$	8.41427e26	0.801356
$36$	−1.97284e27	−1.14762
$37$	4.50412e27	1.62211	0.811054	−	0.584971i	$-0.198894\pi$
$37$	4.50412e27	1.62211	0.811054	+	0.584971i	$0.198894\pi$
$38$	−1.19017e28	−2.68779
$39$	1.82456e27	0.261534
$40$	2.89948e28	2.66852
$41$	−6.23104e27	−0.372257	−0.186129	−	0.982525i	$-0.559594\pi$
$41$	−6.23104e27	−0.372257	−0.186129	+	0.982525i	$0.559594\pi$
$42$	−2.03442e28	−0.797219
$43$	−2.75822e27	−0.0716029	−0.0358014	−	0.999359i	$-0.511398\pi$
$43$	−2.75822e27	−0.0716029	−0.0358014	+	0.999359i	$0.511398\pi$
$44$	−5.15977e28	−0.895795
$45$	−5.53731e28	−0.648754
$46$	2.29513e29	1.83040
$47$	1.41103e29	0.772365	0.386182	−	0.922422i	$-0.373793\pi$
$47$	1.41103e29	0.772365	0.386182	+	0.922422i	$0.373793\pi$
$48$	−2.99320e29	−1.13348
$49$	−2.21495e29	−0.584700
$50$	5.27167e29	0.977177
$51$	2.05867e29	0.269841
$52$	−8.91472e29	−0.831858
$53$	−2.48503e30	−1.66151	−0.830755	−	0.556638i	$-0.812091\pi$
$53$	−2.48503e30	−1.66151	−0.830755	+	0.556638i	$0.812091\pi$
$54$	3.90500e30	1.88248
$55$	−1.44823e30	−0.506396
$56$	5.42123e30	1.38295
$57$	5.55255e30	1.03916
$58$	−1.88190e31	−2.59781
$59$	5.47495e30	0.560364	0.280182	−	0.959947i	$-0.409605\pi$
$59$	5.47495e30	0.560364	0.280182	+	0.959947i	$0.409605\pi$
$60$	−2.48026e31	−1.89169
$61$	2.30979e31	1.31917	0.659585	−	0.751630i	$-0.270732\pi$
$61$	2.30979e31	1.31917	0.659585	+	0.751630i	$0.270732\pi$
$62$	3.41386e31	1.46687
$63$	−1.03532e31	−0.336214
$64$	−9.46893e30	−0.233427
$65$	−2.50216e31	−0.470252
$66$	3.50156e31	0.503782
$67$	1.55814e31	0.172304	0.0861522	−	0.996282i	$-0.472543\pi$
$67$	1.55814e31	0.172304	0.0861522	+	0.996282i	$0.472543\pi$
$68$	−1.00585e32	−0.858279
$69$	−1.07076e32	−0.707675
$70$	2.78995e32	1.43344
$71$	−1.13262e32	−0.454008	−0.227004	−	0.973894i	$-0.572893\pi$
$71$	−1.13262e32	−0.454008	−0.227004	+	0.973894i	$0.572893\pi$
$72$	−3.56763e32	−1.11960
$73$	3.23524e32	0.797548	0.398774	−	0.917049i	$-0.369436\pi$
$73$	3.23524e32	0.797548	0.398774	+	0.917049i	$0.369436\pi$
$74$	1.49345e33	2.90158
$75$	−2.45942e32	−0.377799
$76$	−2.71294e33	−3.30524
$77$	−2.70778e32	−0.262438
$78$	6.04976e32	0.467824
$79$	−1.44166e32	−0.0892050	−0.0446025	−	0.999005i	$-0.514202\pi$
$79$	−1.44166e32	−0.0892050	−0.0446025	+	0.999005i	$0.514202\pi$
$80$	4.10479e33	2.03806
$81$	−5.15885e32	−0.206094
$82$	−2.06605e33	−0.665882
$83$	3.50421e33	0.913532	0.456766	−	0.889587i	$-0.349008\pi$
$83$	3.50421e33	0.913532	0.456766	+	0.889587i	$0.349008\pi$
$84$	−4.63739e33	−0.980361
$85$	−2.82320e33	−0.485188
$86$	−9.14551e32	−0.128081
$87$	8.77975e33	1.00437
$88$	−9.33079e33	−0.873920
$89$	9.37543e33	0.720553	0.360277	−	0.932846i	$-0.382682\pi$
$89$	9.37543e33	0.720553	0.360277	+	0.932846i	$0.382682\pi$
$90$	−1.83602e34	−1.16047
$91$	−4.67833e33	−0.243706
$92$	5.23168e34	2.25089
$93$	−1.59269e34	−0.567126
$94$	4.67858e34	1.38158
$95$	−7.61461e34	−1.86846
$96$	−2.65998e34	−0.543416
$97$	3.59603e33	0.0612799	0.0306399	−	0.999530i	$-0.490245\pi$
$97$	3.59603e33	0.0612799	0.0306399	+	0.999530i	$0.490245\pi$
$98$	−7.34419e34	−1.04589
$99$	1.78195e34	0.212462
$100$	1.20166e35	1.20166
$101$	7.27571e34	0.611296	0.305648	−	0.952145i	$-0.401127\pi$
$101$	7.27571e34	0.611296	0.305648	+	0.952145i	$0.401127\pi$
$102$	6.82599e34	0.482683
$103$	9.48038e34	0.565164	0.282582	−	0.959243i	$-0.408809\pi$
$103$	9.48038e34	0.565164	0.282582	+	0.959243i	$0.408809\pi$
$104$	−1.61211e35	−0.811544
$105$	−1.30161e35	−0.554202
$106$	−8.23968e35	−2.97206
$107$	5.43957e35	1.66475	0.832374	−	0.554214i	$-0.186981\pi$
$107$	5.43957e35	1.66475	0.832374	+	0.554214i	$0.186981\pi$
$108$	8.90133e35	2.31494
$109$	−2.19201e35	−0.485153	−0.242577	−	0.970132i	$-0.577993\pi$
$109$	−2.19201e35	−0.485153	−0.242577	+	0.970132i	$0.577993\pi$
$110$	−4.80194e35	−0.905826
$111$	−6.96746e35	−1.12182
$112$	7.67481e35	1.05621
$113$	−3.57083e35	−0.420627	−0.210313	−	0.977634i	$-0.567448\pi$
$113$	−3.57083e35	−0.420627	−0.210313	+	0.977634i	$0.567448\pi$
$114$	1.84108e36	1.85882
$115$	1.46841e36	1.27244
$116$	−4.28974e36	−3.19460
$117$	3.07875e35	0.197297
$118$	1.81535e36	1.00236
$119$	−5.27859e35	−0.251447
$120$	−4.48523e36	−1.84550
$121$	−2.34419e36	−0.834159
$122$	7.65865e36	2.35969
$123$	9.63884e35	0.257446
$124$	7.78179e36	1.80385
$125$	−2.80126e36	−0.564194
$126$	−3.43285e36	−0.601410
$127$	−2.98205e36	−0.454935	−0.227467	−	0.973786i	$-0.573045\pi$
$127$	−2.98205e36	−0.454935	−0.227467	+	0.973786i	$0.573045\pi$
$128$	−9.04797e36	−1.20331
$129$	4.26671e35	0.0495191
$130$	−8.29648e36	−0.841173
$131$	1.67513e37	1.48525	0.742627	−	0.669705i	$-0.233579\pi$
$131$	1.67513e37	1.48525	0.742627	+	0.669705i	$0.233579\pi$
$132$	7.98169e36	0.619514
$133$	−1.42372e37	−0.968325
$134$	5.16636e36	0.308213
$135$	2.49840e37	1.30864
$136$	−1.81896e37	−0.837321
$137$	7.05739e36	0.285782	0.142891	−	0.989738i	$-0.454360\pi$
$137$	7.05739e36	0.285782	0.142891	+	0.989738i	$0.454360\pi$
$138$	−3.55036e37	−1.26587
$139$	5.54070e36	0.174103	0.0870514	−	0.996204i	$-0.472256\pi$
$139$	5.54070e36	0.174103	0.0870514	+	0.996204i	$0.472256\pi$
$140$	6.35959e37	1.76274
$141$	−2.18273e37	−0.534152
$142$	−3.75546e37	−0.812115
$143$	8.05216e36	0.154004
$144$	−5.05068e37	−0.855080
$145$	−1.20403e38	−1.80592
$146$	1.07272e38	1.42663
$147$	3.42633e37	0.404367
$148$	3.40426e38	3.56815
$149$	−1.26594e38	−1.17938	−0.589689	−	0.807631i	$-0.700750\pi$
$149$	−1.26594e38	−1.17938	−0.589689	+	0.807631i	$0.700750\pi$
$150$	−8.15479e37	−0.675796
$151$	1.46030e38	1.07732	0.538661	−	0.842523i	$-0.318930\pi$
$151$	1.46030e38	1.07732	0.538661	+	0.842523i	$0.318930\pi$
$152$	−4.90602e38	−3.22453
$153$	3.47377e37	0.203564
$154$	−8.97829e37	−0.469441
$155$	2.18417e38	1.01972
$156$	1.37902e38	0.575296
$157$	−2.57702e38	−0.961332	−0.480666	−	0.876904i	$-0.659605\pi$
$157$	−2.57702e38	−0.961332	−0.480666	+	0.876904i	$0.659605\pi$
$158$	−4.78016e37	−0.159567
$159$	3.84410e38	1.14907
$160$	3.64783e38	0.977091
$161$	2.74552e38	0.659436
$162$	−1.71054e38	−0.368655
$163$	−1.00523e39	−1.94529	−0.972643	−	0.232306i	$-0.925373\pi$
$163$	−1.00523e39	−1.94529	−0.972643	+	0.232306i	$0.925373\pi$
$164$	−4.70948e38	−0.818853
$165$	2.24028e38	0.350213
$166$	1.16190e39	1.63410
$167$	4.87583e38	0.617320	0.308660	−	0.951172i	$-0.400119\pi$
$167$	4.87583e38	0.617320	0.308660	+	0.951172i	$0.400119\pi$
$168$	−8.38614e38	−0.956422
$169$	−8.33666e38	−0.856988
$170$	−9.36097e38	−0.867890
$171$	9.36930e38	0.783926
$172$	−2.08469e38	−0.157505
$173$	−3.15688e37	−0.0215502	−0.0107751	−	0.999942i	$-0.503430\pi$
$173$	−3.15688e37	−0.0215502	−0.0107751	+	0.999942i	$0.503430\pi$
$174$	2.91113e39	1.79659
$175$	6.30617e38	0.352046
$176$	−1.32096e39	−0.667447
$177$	−8.46924e38	−0.387536
$178$	3.10864e39	1.28890
$179$	−4.86041e38	−0.182702	−0.0913512	−	0.995819i	$-0.529119\pi$
$179$	−4.86041e38	−0.182702	−0.0913512	+	0.995819i	$0.529119\pi$
$180$	−4.18516e39	−1.42706
$181$	−4.89892e39	−1.51609	−0.758045	−	0.652202i	$-0.773845\pi$
$181$	−4.89892e39	−1.51609	−0.758045	+	0.652202i	$0.773845\pi$
$182$	−1.55121e39	−0.435935
$183$	−3.57303e39	−0.912311
$184$	9.46084e39	2.19593
$185$	9.55498e39	2.01709
$186$	−5.28093e39	−1.01446
$187$	9.08530e38	0.158895
$188$	1.06647e40	1.69897
$189$	4.67131e39	0.678199
$190$	−2.52480e40	−3.34225
$191$	−8.79853e39	−1.06249	−0.531246	−	0.847217i	$-0.678276\pi$
$191$	−8.79853e39	−1.06249	−0.531246	+	0.847217i	$0.678276\pi$
$192$	1.46476e39	0.161434
$193$	1.65403e40	1.66452	0.832262	−	0.554383i	$-0.187046\pi$
$193$	1.65403e40	1.66452	0.832262	+	0.554383i	$0.187046\pi$
$194$	1.19235e39	0.109616
$195$	3.87060e39	0.325217
$196$	−1.67408e40	−1.28616
$197$	3.96581e36	0.000278723 0	0.000139362	−	1.00000i	$-0.499956\pi$
$197$	3.96581e36	0.000278723 0	0.000139362		1.00000i	$0.499956\pi$
$198$	5.90848e39	0.380045
$199$	−1.61546e40	−0.951409	−0.475705	−	0.879605i	$-0.657807\pi$
$199$	−1.61546e40	−0.951409	−0.475705	+	0.879605i	$0.657807\pi$
$200$	2.17305e40	1.17232
$201$	−2.41029e39	−0.119162
$202$	2.41243e40	1.09347
$203$	−2.25120e40	−0.935909
$204$	1.55596e40	0.593569
$205$	−1.32184e40	−0.462901
$206$	3.14344e40	1.01095
$207$	−1.80679e40	−0.533859
$208$	−2.28226e40	−0.619808
$209$	2.45045e40	0.611908
$210$	−4.31579e40	−0.991339
$211$	2.70344e40	0.571444	0.285722	−	0.958313i	$-0.407767\pi$
$211$	2.70344e40	0.571444	0.285722	+	0.958313i	$0.407767\pi$
$212$	−1.87821e41	−3.65482
$213$	1.75206e40	0.313983
$214$	1.80362e41	2.97785
$215$	−5.85124e39	−0.0890379
$216$	1.60969e41	2.25841
$217$	4.08379e40	0.528467
$218$	−7.26812e40	−0.867827
$219$	−5.00462e40	−0.551569
$220$	−1.09459e41	−1.11392
$221$	1.56970e40	0.147554
$222$	−2.31022e41	−2.00667
$223$	1.60448e41	1.28825	0.644124	−	0.764921i	$-0.277222\pi$
$223$	1.60448e41	1.28825	0.644124	+	0.764921i	$0.277222\pi$
$224$	6.82042e40	0.506374
$225$	−4.15000e40	−0.285006
$226$	−1.18399e41	−0.752405
$227$	−1.32023e41	−0.776597	−0.388299	−	0.921534i	$-0.626937\pi$
$227$	−1.32023e41	−0.776597	−0.388299	+	0.921534i	$0.626937\pi$
$228$	4.19667e41	2.28584
$229$	−1.27675e41	−0.644147	−0.322073	−	0.946715i	$-0.604380\pi$
$229$	−1.27675e41	−0.644147	−0.322073	+	0.946715i	$0.604380\pi$
$230$	4.86887e41	2.27610
$231$	4.18869e40	0.181497
$232$	−7.75745e41	−3.11659
$233$	−1.15249e41	−0.429445	−0.214722	−	0.976675i	$-0.568885\pi$
$233$	−1.15249e41	−0.429445	−0.214722	+	0.976675i	$0.568885\pi$
$234$	1.02083e41	0.352919
$235$	2.99333e41	0.960433
$236$	4.13802e41	1.23263
$237$	2.23012e40	0.0616924
$238$	−1.75024e41	−0.449781
$239$	1.42881e41	0.341201	0.170601	−	0.985340i	$-0.445429\pi$
$239$	1.42881e41	0.341201	0.170601	+	0.985340i	$0.445429\pi$
$240$	−6.34973e41	−1.40948
$241$	−1.47367e41	−0.304160	−0.152080	−	0.988368i	$-0.548597\pi$
$241$	−1.47367e41	−0.304160	−0.152080	+	0.988368i	$0.548597\pi$
$242$	−7.77271e41	−1.49212
$243$	−5.09429e41	−0.909859
$244$	1.74576e42	2.90177
$245$	−4.69877e41	−0.727073
$246$	3.19598e41	0.460511
$247$	4.23373e41	0.568233
$248$	1.40724e42	1.75980
$249$	−5.42069e41	−0.631781
$250$	−9.28823e41	−1.00921
$251$	1.16925e42	1.18473	0.592363	−	0.805671i	$-0.298195\pi$
$251$	1.16925e42	1.18473	0.592363	+	0.805671i	$0.298195\pi$
$252$	−7.82507e41	−0.739569
$253$	−4.72548e41	−0.416713
$254$	−9.88766e41	−0.813773
$255$	4.36723e41	0.335546
$256$	−2.67471e42	−1.91901
$257$	6.14627e41	0.411890	0.205945	−	0.978564i	$-0.433973\pi$
$257$	6.14627e41	0.411890	0.205945	+	0.978564i	$0.433973\pi$
$258$	1.41473e41	0.0885783
$259$	1.78651e42	1.04535
$260$	−1.89116e42	−1.03441
$261$	1.48148e42	0.757684
$262$	5.55428e42	2.65678
$263$	5.29428e41	0.236909	0.118454	−	0.992959i	$-0.462206\pi$
$263$	5.29428e41	0.236909	0.118454	+	0.992959i	$0.462206\pi$
$264$	1.44339e42	0.604386
$265$	−5.27170e42	−2.06608
$266$	−4.72067e42	−1.73211
$267$	−1.45029e42	−0.498320
$268$	1.17766e42	0.379018
$269$	2.61222e42	0.787670	0.393835	−	0.919181i	$-0.371148\pi$
$269$	2.61222e42	0.787670	0.393835	+	0.919181i	$0.371148\pi$
$270$	8.28402e42	2.34086
$271$	−6.35646e42	−1.68365	−0.841827	−	0.539748i	$-0.818520\pi$
$271$	−6.35646e42	−1.68365	−0.841827	+	0.539748i	$0.818520\pi$
$272$	−2.57509e42	−0.639495
$273$	7.23695e41	0.168542
$274$	2.34004e42	0.511197
$275$	−1.08539e42	−0.222466
$276$	−8.09293e42	−1.55667
$277$	1.32088e41	0.0238488	0.0119244	−	0.999929i	$-0.496204\pi$
$277$	1.32088e41	0.0238488	0.0119244	+	0.999929i	$0.496204\pi$
$278$	1.83715e42	0.311430
$279$	−2.68748e42	−0.427831
$280$	1.15005e43	1.71970
$281$	1.21053e43	1.70065	0.850324	−	0.526260i	$-0.176406\pi$
$281$	1.21053e43	1.70065	0.850324	+	0.526260i	$0.176406\pi$
$282$	−7.23734e42	−0.955475
$283$	1.08291e41	0.0134378	0.00671891	−	0.999977i	$-0.497861\pi$
$283$	1.08291e41	0.0134378	0.00671891	+	0.999977i	$0.497861\pi$
$284$	−8.56046e42	−0.998680
$285$	1.17791e43	1.29219
$286$	2.66988e42	0.275477
$287$	−2.47148e42	−0.239896
$288$	−4.48842e42	−0.409945
$289$	−9.86245e42	−0.847759
$290$	−3.99224e43	−3.23037
$291$	−5.56273e41	−0.0423799
$292$	2.44523e43	1.75437
$293$	−2.38381e42	−0.161097	−0.0805486	−	0.996751i	$-0.525667\pi$
$293$	−2.38381e42	−0.161097	−0.0805486	+	0.996751i	$0.525667\pi$
$294$	1.13608e43	0.723319
$295$	1.16145e43	0.696811
$296$	6.15617e43	3.48102
$297$	−8.04007e42	−0.428570
$298$	−4.19751e43	−2.10963
$299$	−8.16438e42	−0.386970
$300$	−1.85886e43	−0.831044
$301$	−1.09402e42	−0.0461436
$302$	4.84196e43	1.92708
$303$	−1.12548e43	−0.422760
$304$	−6.94543e43	−2.46270
$305$	4.89996e43	1.64038
$306$	1.15181e43	0.364129
$307$	−4.84424e43	−1.44645	−0.723226	−	0.690611i	$-0.757342\pi$
$307$	−4.84424e43	−1.44645	−0.723226	+	0.690611i	$0.757342\pi$
$308$	−2.04657e43	−0.577284
$309$	−1.46653e43	−0.390856
$310$	7.24212e43	1.82405
$311$	1.85715e43	0.442119	0.221060	−	0.975260i	$-0.429048\pi$
$311$	1.85715e43	0.442119	0.221060	+	0.975260i	$0.429048\pi$
$312$	2.49379e43	0.561248
$313$	2.67734e43	0.569740	0.284870	−	0.958566i	$-0.408049\pi$
$313$	2.67734e43	0.569740	0.284870	+	0.958566i	$0.408049\pi$
$314$	−8.54470e43	−1.71960
$315$	−2.19632e43	−0.418081
$316$	−1.08962e43	−0.196224
$317$	−2.42612e43	−0.413405	−0.206703	−	0.978404i	$-0.566273\pi$
$317$	−2.42612e43	−0.413405	−0.206703	+	0.978404i	$0.566273\pi$
$318$	1.27460e44	2.05542
$319$	3.87468e43	0.591423
$320$	−2.00873e43	−0.290266
$321$	−8.41452e43	−1.15131
$322$	9.10342e43	1.17958
$323$	4.77694e43	0.586281
$324$	−3.89911e43	−0.453344
$325$	−1.87527e43	−0.206588
$326$	−3.33308e44	−3.47967
$327$	3.39084e43	0.335522
$328$	−8.51651e43	−0.798857
$329$	5.59669e43	0.497741
$330$	7.42816e43	0.626451
$331$	1.83689e44	1.46924	0.734620	−	0.678479i	$-0.237361\pi$
$331$	1.83689e44	1.46924	0.734620	+	0.678479i	$0.237361\pi$
$332$	2.64852e44	2.00950
$333$	−1.17568e44	−0.846282
$334$	1.61669e44	1.10424
$335$	3.30541e43	0.214260
$336$	−1.18722e44	−0.730457
$337$	9.63203e42	0.0562593	0.0281297	−	0.999604i	$-0.491045\pi$
$337$	9.63203e42	0.0562593	0.0281297	+	0.999604i	$0.491045\pi$
$338$	−2.76421e44	−1.53295
$339$	5.52375e43	0.290897
$340$	−2.13380e44	−1.06727
$341$	−7.02885e43	−0.333951
$342$	3.10661e44	1.40226
$343$	−2.38109e44	−1.02124
$344$	−3.76990e43	−0.153659
$345$	−2.27150e44	−0.879992
$346$	−1.04674e43	−0.0385483
$347$	2.05198e44	0.718468	0.359234	−	0.933247i	$-0.383038\pi$
$347$	2.05198e44	0.718468	0.359234	+	0.933247i	$0.383038\pi$
$348$	6.63583e44	2.20932
$349$	−1.00117e44	−0.317003	−0.158501	−	0.987359i	$-0.550666\pi$
$349$	−1.00117e44	−0.317003	−0.158501	+	0.987359i	$0.550666\pi$
$350$	2.09096e44	0.629730
$351$	−1.38911e44	−0.397981
$352$	−1.17390e44	−0.319990
$353$	−2.71539e44	−0.704328	−0.352164	−	0.935938i	$-0.614554\pi$
$353$	−2.71539e44	−0.704328	−0.352164	+	0.935938i	$0.614554\pi$
$354$	−2.80817e44	−0.693213
$355$	−2.40272e44	−0.564557
$356$	7.08605e44	1.58500
$357$	8.16550e43	0.173896
$358$	−1.61158e44	−0.326813
$359$	8.81356e44	1.70215	0.851076	−	0.525043i	$-0.175951\pi$
$359$	8.81356e44	1.70215	0.851076	+	0.525043i	$0.175951\pi$
$360$	−7.56833e44	−1.39221
$361$	7.17758e44	1.25777
$362$	−1.62435e45	−2.71194
$363$	3.62625e44	0.576888
$364$	−3.53593e44	−0.536080
$365$	6.86320e44	0.991749
$366$	−1.18472e45	−1.63191
$367$	−1.11298e45	−1.46161	−0.730806	−	0.682585i	$-0.760856\pi$
$367$	−1.11298e45	−1.46161	−0.730806	+	0.682585i	$0.760856\pi$
$368$	1.33937e45	1.67712
$369$	1.62645e44	0.194213
$370$	3.16817e45	3.60810
$371$	−9.85661e44	−1.07074
$372$	−1.20377e45	−1.24750
$373$	−5.50495e44	−0.544313	−0.272157	−	0.962253i	$-0.587737\pi$
$373$	−5.50495e44	−0.544313	−0.272157	+	0.962253i	$0.587737\pi$
$374$	3.01244e44	0.284227
$375$	4.33329e44	0.390185
$376$	1.92857e45	1.65748
$377$	6.69441e44	0.549211
$378$	1.54888e45	1.21314
$379$	−1.81534e45	−1.35760	−0.678799	−	0.734325i	$-0.737499\pi$
$379$	−1.81534e45	−1.35760	−0.678799	+	0.734325i	$0.737499\pi$
$380$	−5.75520e45	−4.11006
$381$	4.61295e44	0.314624
$382$	−2.91736e45	−1.90056
$383$	5.42819e44	0.337813	0.168907	−	0.985632i	$-0.445976\pi$
$383$	5.42819e44	0.337813	0.168907	+	0.985632i	$0.445976\pi$
$384$	1.39964e45	0.832184
$385$	−5.74426e44	−0.326341
$386$	5.48431e45	2.97745
$387$	7.19958e43	0.0373564
$388$	2.71792e44	0.134797
$389$	2.27596e45	1.07906	0.539532	−	0.841965i	$-0.318601\pi$
$389$	2.27596e45	1.07906	0.539532	+	0.841965i	$0.318601\pi$
$390$	1.28339e45	0.581738
$391$	−9.21192e44	−0.399261
$392$	−3.02737e45	−1.25476
$393$	−2.59127e45	−1.02717
$394$	1.31496e42	0.000498572 0
$395$	−3.05832e44	−0.110926
$396$	1.34682e45	0.467352
$397$	2.97575e45	0.988013	0.494006	−	0.869458i	$-0.335532\pi$
$397$	2.97575e45	0.988013	0.494006	+	0.869458i	$0.335532\pi$
$398$	−5.35643e45	−1.70185
$399$	2.20236e45	0.669674
$400$	3.07638e45	0.895345
$401$	−3.35408e45	−0.934429	−0.467215	−	0.884144i	$-0.654742\pi$
$401$	−3.35408e45	−0.934429	−0.467215	+	0.884144i	$0.654742\pi$
$402$	−7.99189e44	−0.213154
$403$	−1.21440e45	−0.310115
$404$	5.49906e45	1.34467
$405$	−1.09439e45	−0.256277
$406$	−7.46438e45	−1.67413
$407$	−3.07488e45	−0.660580
$408$	2.81376e45	0.579074
$409$	8.75180e45	1.72560	0.862799	−	0.505547i	$-0.168709\pi$
$409$	8.75180e45	1.72560	0.862799	+	0.505547i	$0.168709\pi$
$410$	−4.38288e45	−0.828022
$411$	−1.09171e45	−0.197641
$412$	7.16537e45	1.24319
$413$	2.17158e45	0.361119
$414$	−5.99083e45	−0.954951
$415$	7.43379e45	1.13597
$416$	−2.02819e45	−0.297150
$417$	−8.57095e44	−0.120406
$418$	8.12503e45	1.09456
$419$	1.99625e45	0.257911	0.128955	−	0.991650i	$-0.458838\pi$
$419$	1.99625e45	0.257911	0.128955	+	0.991650i	$0.458838\pi$
$420$	−9.83770e45	−1.21908
$421$	−1.23389e46	−1.46670	−0.733348	−	0.679854i	$-0.762043\pi$
$421$	−1.23389e46	−1.46670	−0.733348	+	0.679854i	$0.762043\pi$
$422$	8.96388e45	1.02218
$423$	−3.68311e45	−0.402956
$424$	−3.39650e46	−3.56557
$425$	−2.11588e45	−0.213150
$426$	5.80936e45	0.561643
$427$	9.16156e45	0.850122
$428$	4.11129e46	3.66194
$429$	−1.24559e45	−0.106506
$430$	−1.94012e45	−0.159268
$431$	−1.20357e46	−0.948677	−0.474339	−	0.880343i	$-0.657313\pi$
$431$	−1.20357e46	−0.948677	−0.474339	+	0.880343i	$0.657313\pi$
$432$	2.27884e46	1.72484
$433$	−2.06332e46	−1.49979	−0.749893	−	0.661559i	$-0.769895\pi$
$433$	−2.06332e46	−1.49979	−0.749893	+	0.661559i	$0.769895\pi$
$434$	1.35407e46	0.945305
$435$	1.86252e46	1.24894
$436$	−1.65674e46	−1.06719
$437$	−2.48460e46	−1.53756
$438$	−1.65940e46	−0.986629
$439$	3.14998e46	1.79961	0.899805	−	0.436293i	$-0.143709\pi$
$439$	3.14998e46	1.79961	0.899805	+	0.436293i	$0.143709\pi$
$440$	−1.97942e46	−1.08672
$441$	5.78154e45	0.305048
$442$	5.20470e45	0.263941
$443$	−2.49595e46	−1.21667	−0.608333	−	0.793682i	$-0.708161\pi$
$443$	−2.49595e46	−1.21667	−0.608333	+	0.793682i	$0.708161\pi$
$444$	−5.26608e46	−2.46766
$445$	1.98889e46	0.896006
$446$	5.32003e46	2.30438
$447$	1.95829e46	0.815634
$448$	−3.75576e45	−0.150429
$449$	3.14792e46	1.21259	0.606294	−	0.795241i	$-0.292656\pi$
$449$	3.14792e46	1.21259	0.606294	+	0.795241i	$0.292656\pi$
$450$	−1.37603e46	−0.509810
$451$	4.25381e45	0.151596
$452$	−2.69887e46	−0.925252
$453$	−2.25895e46	−0.745054
$454$	−4.37752e46	−1.38915
$455$	−9.92455e45	−0.303048
$456$	7.58916e46	2.23002
$457$	3.21994e46	0.910572	0.455286	−	0.890345i	$-0.349537\pi$
$457$	3.21994e46	0.910572	0.455286	+	0.890345i	$0.349537\pi$
$458$	−4.23336e46	−1.15223
$459$	−1.56734e46	−0.410622
$460$	1.10984e47	2.79898
$461$	8.96567e45	0.217679	0.108840	−	0.994059i	$-0.465287\pi$
$461$	8.96567e45	0.217679	0.108840	+	0.994059i	$0.465287\pi$
$462$	1.38886e46	0.324656
$463$	−2.74379e46	−0.617566	−0.308783	−	0.951133i	$-0.599922\pi$
$463$	−2.74379e46	−0.617566	−0.308783	+	0.951133i	$0.599922\pi$
$464$	−1.09822e47	−2.38026
$465$	−3.37871e46	−0.705219
$466$	−3.82134e46	−0.768178
$467$	−8.40024e46	−1.62647	−0.813235	−	0.581935i	$-0.802296\pi$
$467$	−8.40024e46	−1.62647	−0.813235	+	0.581935i	$0.802296\pi$
$468$	2.32695e46	0.433994
$469$	6.18019e45	0.111039
$470$	9.92509e46	1.71799
$471$	3.98641e46	0.664838
$472$	7.48309e46	1.20253
$473$	1.88298e45	0.0291592
$474$	7.39447e45	0.110353
$475$	−5.70686e46	−0.820841
$476$	−3.98962e46	−0.553107
$477$	6.48649e46	0.866839
$478$	4.73755e46	0.610331
$479$	1.51913e47	1.88679	0.943395	−	0.331671i	$-0.107612\pi$
$479$	1.51913e47	1.88679	0.943395	+	0.331671i	$0.107612\pi$
$480$	−5.64286e46	−0.675736
$481$	−5.31257e46	−0.613431
$482$	−4.88629e46	−0.544072
$483$	−4.24707e46	−0.456052
$484$	−1.77176e47	−1.83490
$485$	7.62857e45	0.0762014
$486$	−1.68913e47	−1.62753
$487$	−9.57009e46	−0.889527	−0.444764	−	0.895648i	$-0.646712\pi$
$487$	−9.57009e46	−0.889527	−0.444764	+	0.895648i	$0.646712\pi$
$488$	3.15699e47	2.83091
$489$	1.55500e47	1.34532
$490$	−1.55799e47	−1.30057
$491$	−9.00218e46	−0.725139	−0.362570	−	0.931957i	$-0.618100\pi$
$491$	−9.00218e46	−0.725139	−0.362570	+	0.931957i	$0.618100\pi$
$492$	7.28514e46	0.566302
$493$	7.55335e46	0.566655
$494$	1.40379e47	1.01644
$495$	3.78021e46	0.264196
$496$	1.99222e47	1.34403
$497$	−4.49242e46	−0.292580
$498$	−1.79736e47	−1.13011
$499$	−1.31845e47	−0.800394	−0.400197	−	0.916429i	$-0.631058\pi$
$499$	−1.31845e47	−0.800394	−0.400197	+	0.916429i	$0.631058\pi$
$500$	−2.11722e47	−1.24106
$501$	−7.54246e46	−0.426926
$502$	3.87693e47	2.11920
$503$	3.29261e46	0.173820	0.0869101	−	0.996216i	$-0.472301\pi$
$503$	3.29261e46	0.173820	0.0869101	+	0.996216i	$0.472301\pi$
$504$	−1.41507e47	−0.721510
$505$	1.54346e47	0.760144
$506$	−1.56684e47	−0.745404
$507$	1.28960e47	0.592676
$508$	−2.25386e47	−1.00072
$509$	1.43449e47	0.615370	0.307685	−	0.951488i	$-0.400446\pi$
$509$	1.43449e47	0.615370	0.307685	+	0.951488i	$0.400446\pi$
$510$	1.44806e47	0.600215
$511$	1.28323e47	0.513970
$512$	−5.75978e47	−2.22937
$513$	−4.22737e47	−1.58131
$514$	2.03794e47	0.736777
$515$	2.01115e47	0.702779
$516$	3.22482e46	0.108927
$517$	−9.63280e46	−0.314534
$518$	5.92360e47	1.86989
$519$	4.88340e45	0.0149037
$520$	−3.41992e47	−1.00915
$521$	−2.33055e47	−0.664966	−0.332483	−	0.943109i	$-0.607886\pi$
$521$	−2.33055e47	−0.664966	−0.332483	+	0.943109i	$0.607886\pi$
$522$	4.91220e47	1.35532
$523$	−4.26380e47	−1.13767	−0.568836	−	0.822451i	$-0.692606\pi$
$523$	−4.26380e47	−1.13767	−0.568836	+	0.822451i	$0.692606\pi$
$524$	1.26608e48	3.26711
$525$	−9.75506e46	−0.243468
$526$	1.75544e47	0.423776
$527$	−1.37021e47	−0.319965
$528$	2.04340e47	0.461593
$529$	2.15467e46	0.0470875
$530$	−1.74795e48	−3.69575
$531$	−1.42909e47	−0.292351
$532$	−1.07606e48	−2.13002
$533$	7.34945e46	0.140776
$534$	−4.80878e47	−0.891380
$535$	1.15394e48	2.07011
$536$	2.12964e47	0.369762
$537$	7.51860e46	0.126353
$538$	8.66140e47	1.40896
$539$	1.51211e47	0.238111
$540$	1.88832e48	2.87862
$541$	−5.43835e45	−0.00802629	−0.00401314	−	0.999992i	$-0.501277\pi$
$541$	−5.43835e45	−0.00802629	−0.00401314	+	0.999992i	$0.501277\pi$
$542$	−2.10763e48	−3.01167
$543$	7.57817e47	1.04850
$544$	−2.28842e47	−0.306588
$545$	−4.65010e47	−0.603286
$546$	2.39958e47	0.301484
$547$	−4.15694e47	−0.505820	−0.252910	−	0.967490i	$-0.581388\pi$
$547$	−4.15694e47	−0.505820	−0.252910	+	0.967490i	$0.581388\pi$
$548$	5.33405e47	0.628633
$549$	−6.02909e47	−0.688233
$550$	−3.59887e47	−0.397941
$551$	2.03726e48	2.18219
$552$	−1.46350e48	−1.51866
$553$	−5.71821e46	−0.0574871
$554$	4.37967e46	0.0426600
$555$	−1.47807e48	−1.39498
$556$	4.18772e47	0.382973
$557$	1.81613e45	0.00160947	0.000804733	−	1.00000i	$-0.499744\pi$
$557$	1.81613e45	0.00160947	0.000804733		1.00000i	$0.499744\pi$
$558$	−8.91097e47	−0.765291
$559$	3.25329e46	0.0270780
$560$	1.62812e48	1.31340
$561$	−1.40541e47	−0.109889
$562$	4.01379e48	3.04207
$563$	−2.19502e48	−1.61266	−0.806329	−	0.591468i	$-0.798549\pi$
$563$	−2.19502e48	−1.61266	−0.806329	+	0.591468i	$0.798549\pi$
$564$	−1.64973e48	−1.17497
$565$	−7.57512e47	−0.523048
$566$	3.59063e46	0.0240372
$567$	−2.04621e47	−0.132815
$568$	−1.54805e48	−0.974293
$569$	1.19614e48	0.729993	0.364996	−	0.931009i	$-0.381070\pi$
$569$	1.19614e48	0.729993	0.364996	+	0.931009i	$0.381070\pi$
$570$	3.90564e48	2.31143
$571$	−1.26426e48	−0.725610	−0.362805	−	0.931865i	$-0.618181\pi$
$571$	−1.26426e48	−0.725610	−0.362805	+	0.931865i	$0.618181\pi$
$572$	6.08590e47	0.338762
$573$	1.36105e48	0.734799
$574$	−8.19476e47	−0.429120
$575$	1.10052e48	0.558998
$576$	2.47161e47	0.121783
$577$	2.42022e48	1.15686	0.578428	−	0.815734i	$-0.303667\pi$
$577$	2.42022e48	1.15686	0.578428	+	0.815734i	$0.303667\pi$
$578$	−3.27012e48	−1.51645
$579$	−2.55863e48	−1.15115
$580$	−9.10019e48	−3.97247
$581$	1.38991e48	0.588715
$582$	−1.84445e47	−0.0758080
$583$	1.69648e48	0.676626
$584$	4.42189e48	1.71153
$585$	6.53121e47	0.245339
$586$	−7.90407e47	−0.288166
$587$	−1.04500e48	−0.369787	−0.184893	−	0.982759i	$-0.559194\pi$
$587$	−1.04500e48	−0.369787	−0.184893	+	0.982759i	$0.559194\pi$
$588$	2.58965e48	0.889485
$589$	−3.69568e48	−1.23219
$590$	3.85105e48	1.24643
$591$	−6.13475e44	−0.000192760 0
$592$	8.71527e48	2.65859
$593$	4.87793e48	1.44470	0.722351	−	0.691526i	$-0.243061\pi$
$593$	4.87793e48	1.44470	0.722351	+	0.691526i	$0.243061\pi$
$594$	−2.66587e48	−0.766613
$595$	−1.11979e48	−0.312674
$596$	−9.56809e48	−2.59427
$597$	2.49897e48	0.657976
$598$	−2.70709e48	−0.692201
$599$	8.48111e47	0.210612	0.105306	−	0.994440i	$-0.466418\pi$
$599$	8.48111e47	0.210612	0.105306	+	0.994440i	$0.466418\pi$
$600$	−3.36151e48	−0.810751
$601$	−6.23099e48	−1.45967	−0.729834	−	0.683624i	$-0.760403\pi$
$601$	−6.23099e48	−1.45967	−0.729834	+	0.683624i	$0.760403\pi$
$602$	−3.62747e47	−0.0825402
$603$	−4.06710e47	−0.0898942
$604$	1.10371e49	2.36978
$605$	−4.97293e48	−1.03727
$606$	−3.73181e48	−0.756220
$607$	2.65746e48	0.523197	0.261598	−	0.965177i	$-0.415750\pi$
$607$	2.65746e48	0.523197	0.261598	+	0.965177i	$0.415750\pi$
$608$	−6.17224e48	−1.18067
$609$	3.48240e48	0.647256
$610$	1.62470e49	2.93427
$611$	−1.66429e48	−0.292085
$612$	2.62551e48	0.447779
$613$	5.89105e48	0.976415	0.488208	−	0.872727i	$-0.337651\pi$
$613$	5.89105e48	0.976415	0.488208	+	0.872727i	$0.337651\pi$
$614$	−1.60622e49	−2.58737
$615$	2.04477e48	0.320133
$616$	−3.70097e48	−0.563187
$617$	−2.86204e48	−0.423337	−0.211668	−	0.977342i	$-0.567890\pi$
$617$	−2.86204e48	−0.423337	−0.211668	+	0.977342i	$0.567890\pi$
$618$	−4.86261e48	−0.699151
$619$	−9.42149e48	−1.31684	−0.658420	−	0.752651i	$-0.728775\pi$
$619$	−9.42149e48	−1.31684	−0.658420	+	0.752651i	$0.728775\pi$
$620$	1.65082e49	2.24308
$621$	8.15212e48	1.07688
$622$	6.15780e48	0.790850
$623$	3.71867e48	0.464352
$624$	3.53045e48	0.428647
$625$	−1.05698e49	−1.24786
$626$	8.87733e48	1.01913
$627$	−3.79062e48	−0.423183
$628$	−1.94774e49	−2.11464
$629$	−5.99421e48	−0.632915
$630$	−7.28240e48	−0.747851
$631$	8.74950e48	0.873915	0.436958	−	0.899482i	$-0.356056\pi$
$631$	8.74950e48	0.873915	0.436958	+	0.899482i	$0.356056\pi$
$632$	−1.97045e48	−0.191432
$633$	−4.18197e48	−0.395199
$634$	−8.04438e48	−0.739487
$635$	−6.32607e48	−0.565710
$636$	2.90541e49	2.52760
$637$	2.61252e48	0.221116
$638$	1.28474e49	1.05792
$639$	2.95640e48	0.236864
$640$	−1.91942e49	−1.49631
$641$	5.35983e48	0.406571	0.203285	−	0.979120i	$-0.434838\pi$
$641$	5.35983e48	0.406571	0.203285	+	0.979120i	$0.434838\pi$
$642$	−2.79003e49	−2.05942
$643$	2.04799e49	1.47108	0.735538	−	0.677483i	$-0.236929\pi$
$643$	2.04799e49	1.47108	0.735538	+	0.677483i	$0.236929\pi$
$644$	2.07509e49	1.45056
$645$	9.05133e47	0.0615768
$646$	1.58391e49	1.04872
$647$	2.13324e49	1.37472	0.687360	−	0.726317i	$-0.258769\pi$
$647$	2.13324e49	1.37472	0.687360	+	0.726317i	$0.258769\pi$
$648$	−7.05105e48	−0.442274
$649$	−3.73764e48	−0.228200
$650$	−6.21789e48	−0.369538
$651$	−6.31724e48	−0.365477
$652$	−7.59765e49	−4.27904
$653$	−2.78018e49	−1.52438	−0.762189	−	0.647354i	$-0.775876\pi$
$653$	−2.78018e49	−1.52438	−0.762189	+	0.647354i	$0.775876\pi$
$654$	1.12431e49	0.600172
$655$	3.55360e49	1.84691
$656$	−1.20568e49	−0.610119
$657$	−8.44474e48	−0.416095
$658$	1.85571e49	0.890344
$659$	−2.64746e49	−1.23690	−0.618450	−	0.785824i	$-0.712239\pi$
$659$	−2.64746e49	−1.23690	−0.618450	+	0.785824i	$0.712239\pi$
$660$	1.69322e49	0.770363
$661$	2.31405e49	1.02529	0.512646	−	0.858600i	$-0.328665\pi$
$661$	2.31405e49	1.02529	0.512646	+	0.858600i	$0.328665\pi$
$662$	6.09062e49	2.62813
$663$	−2.42818e48	−0.102046
$664$	4.78952e49	1.96042
$665$	−3.02026e49	−1.20411
$666$	−3.89824e49	−1.51380
$667$	−3.92868e49	−1.48609
$668$	3.68520e49	1.35792
$669$	−2.48198e49	−0.890927
$670$	1.09599e49	0.383262
$671$	−1.57685e49	−0.537213
$672$	−1.05506e49	−0.350198
$673$	3.41502e49	1.10441	0.552204	−	0.833709i	$-0.313787\pi$
$673$	3.41502e49	1.10441	0.552204	+	0.833709i	$0.313787\pi$
$674$	3.19372e48	0.100635
$675$	1.87245e49	0.574904
$676$	−6.30093e49	−1.88511
$677$	1.81760e49	0.529903	0.264951	−	0.964262i	$-0.414644\pi$
$677$	1.81760e49	0.529903	0.264951	+	0.964262i	$0.414644\pi$
$678$	1.83153e49	0.520348
$679$	1.42633e48	0.0394911
$680$	−3.85871e49	−1.04121
$681$	2.04227e49	0.537079
$682$	−2.33058e49	−0.597361
$683$	−1.52341e49	−0.380587	−0.190294	−	0.981727i	$-0.560944\pi$
$683$	−1.52341e49	−0.380587	−0.190294	+	0.981727i	$0.560944\pi$
$684$	7.08142e49	1.72440
$685$	1.49715e49	0.355368
$686$	−7.89504e49	−1.82676
$687$	1.97501e49	0.445479
$688$	−5.33703e48	−0.117355
$689$	2.93107e49	0.628332
$690$	−7.53168e49	−1.57410
$691$	−1.25243e49	−0.255203	−0.127602	−	0.991825i	$-0.540728\pi$
$691$	−1.25243e49	−0.255203	−0.127602	+	0.991825i	$0.540728\pi$
$692$	−2.38600e48	−0.0474039
$693$	7.06795e48	0.136918
$694$	6.80382e49	1.28517
$695$	1.17540e49	0.216496
$696$	1.20001e50	2.15537
$697$	8.29244e48	0.145247
$698$	−3.31961e49	−0.567045
$699$	1.78279e49	0.296995
$700$	4.76627e49	0.774395
$701$	4.20207e49	0.665883	0.332942	−	0.942947i	$-0.391959\pi$
$701$	4.20207e49	0.665883	0.332942	+	0.942947i	$0.391959\pi$
$702$	−4.60592e49	−0.711896
$703$	−1.61673e50	−2.43736
$704$	6.46426e48	0.0950598
$705$	−4.63041e49	−0.664216
$706$	−9.00351e49	−1.25988
$707$	2.88584e49	0.393942
$708$	−6.40114e49	−0.852463
$709$	9.39998e48	0.122129	0.0610644	−	0.998134i	$-0.480551\pi$
$709$	9.39998e48	0.122129	0.0610644	+	0.998134i	$0.480551\pi$
$710$	−7.96679e49	−1.00986
$711$	3.76307e48	0.0465398
$712$	1.28142e50	1.54629
$713$	7.12681e49	0.839128
$714$	2.70746e49	0.311059
$715$	1.70817e49	0.191503
$716$	−3.67354e49	−0.401890
$717$	−2.21023e49	−0.235968
$718$	2.92234e50	3.04476
$719$	−7.29315e49	−0.741583	−0.370792	−	0.928716i	$-0.620914\pi$
$719$	−7.29315e49	−0.741583	−0.370792	+	0.928716i	$0.620914\pi$
$720$	−1.07145e50	−1.06329
$721$	3.76030e49	0.364213
$722$	2.37989e50	2.24987
$723$	2.27963e49	0.210351
$724$	−3.70265e50	−3.33494
$725$	−9.02375e49	−0.793363
$726$	1.20237e50	1.03192
$727$	−4.92620e49	−0.412724	−0.206362	−	0.978476i	$-0.566162\pi$
$727$	−4.92620e49	−0.412724	−0.206362	+	0.978476i	$0.566162\pi$
$728$	−6.39429e49	−0.522990
$729$	1.04614e50	0.835334
$730$	2.27565e50	1.77401
$731$	3.67071e48	0.0279380
$732$	−2.70054e50	−2.00681
$733$	−1.28080e50	−0.929310	−0.464655	−	0.885492i	$-0.653822\pi$
$733$	−1.28080e50	−0.929310	−0.464655	+	0.885492i	$0.653822\pi$
$734$	−3.69035e50	−2.61449
$735$	7.26857e49	0.502829
$736$	1.19026e50	0.804047
$737$	−1.06371e49	−0.0701685
$738$	5.39286e49	0.347402
$739$	1.99479e50	1.25493	0.627466	−	0.778644i	$-0.284092\pi$
$739$	1.99479e50	1.25493	0.627466	+	0.778644i	$0.284092\pi$
$740$	7.22175e50	4.43698
$741$	−6.54918e49	−0.392978
$742$	−3.26819e50	−1.91531
$743$	1.05855e50	0.605907	0.302954	−	0.953005i	$-0.402027\pi$
$743$	1.05855e50	0.605907	0.302954	+	0.953005i	$0.402027\pi$
$744$	−2.17687e50	−1.21704
$745$	−2.68554e50	−1.46655
$746$	−1.82529e50	−0.973651
$747$	−9.14681e49	−0.476606
$748$	6.86676e49	0.349522
$749$	2.15755e50	1.07283
$750$	1.43680e50	0.697951
$751$	−1.20549e50	−0.572090	−0.286045	−	0.958216i	$-0.592341\pi$
$751$	−1.20549e50	−0.572090	−0.286045	+	0.958216i	$0.592341\pi$
$752$	2.73027e50	1.26588
$753$	−1.80872e50	−0.819333
$754$	2.21969e50	0.982411
$755$	3.09786e50	1.33965
$756$	3.53062e50	1.49183
$757$	1.18495e50	0.489240	0.244620	−	0.969619i	$-0.421337\pi$
$757$	1.18495e50	0.489240	0.244620	+	0.969619i	$0.421337\pi$
$758$	−6.01917e50	−2.42843
$759$	7.30989e49	0.288190
$760$	−1.04076e51	−4.00969
$761$	2.89900e50	1.09148	0.545741	−	0.837954i	$-0.316248\pi$
$761$	2.89900e50	1.09148	0.545741	+	0.837954i	$0.316248\pi$
$762$	1.52953e50	0.562789
$763$	−8.69439e49	−0.312651
$764$	−6.65002e50	−2.33716
$765$	7.36920e49	0.253131
$766$	1.79984e50	0.604270
$767$	−6.45766e49	−0.211912
$768$	4.13754e50	1.32715
$769$	6.18664e49	0.193974	0.0969870	−	0.995286i	$-0.469079\pi$
$769$	6.18664e49	0.193974	0.0969870	+	0.995286i	$0.469079\pi$
$770$	−1.90464e50	−0.583748
$771$	−9.50771e49	−0.284855
$772$	1.25013e51	3.66145
$773$	−6.37753e50	−1.82604	−0.913022	−	0.407911i	$-0.866257\pi$
$773$	−6.37753e50	−1.82604	−0.913022	+	0.407911i	$0.866257\pi$
$774$	2.38719e49	0.0668221
$775$	1.63695e50	0.447977
$776$	4.91501e49	0.131506
$777$	−2.76357e50	−0.722941
$778$	7.54649e50	1.93020
$779$	2.23660e50	0.559349
$780$	2.92544e50	0.715379
$781$	7.73218e49	0.184888
$782$	−3.05443e50	−0.714186
$783$	−6.68436e50	−1.52837
$784$	−4.28584e50	−0.958307
$785$	−5.46685e50	−1.19541
$786$	−8.59196e50	−1.83737
$787$	6.23653e50	1.30432	0.652161	−	0.758080i	$-0.273862\pi$
$787$	6.23653e50	1.30432	0.652161	+	0.758080i	$0.273862\pi$
$788$	2.99740e47	0.000613107 0
$789$	−8.18976e49	−0.163841
$790$	−1.01406e50	−0.198421
$791$	−1.41634e50	−0.271068
$792$	2.43555e50	0.455939
$793$	−2.72438e50	−0.498869
$794$	9.86679e50	1.76733
$795$	8.15483e50	1.42886
$796$	−1.22098e51	−2.09281
$797$	9.07097e50	1.52101	0.760507	−	0.649329i	$-0.224950\pi$
$797$	9.07097e50	1.52101	0.760507	+	0.649329i	$0.224950\pi$
$798$	7.30245e50	1.19789
$799$	−1.87783e50	−0.301362
$800$	2.73391e50	0.429249
$801$	−2.44720e50	−0.375925
$802$	−1.11212e51	−1.67148
$803$	−2.20864e50	−0.324790
$804$	−1.82172e50	−0.262121
$805$	5.82432e50	0.820006
$806$	−4.02662e50	−0.554724
$807$	−4.04086e50	−0.544736
$808$	9.94435e50	1.31183
$809$	1.43609e51	1.85389	0.926943	−	0.375202i	$-0.122427\pi$
$809$	1.43609e51	1.85389	0.926943	+	0.375202i	$0.122427\pi$
$810$	−3.62871e50	−0.458421
$811$	6.18627e50	0.764828	0.382414	−	0.923991i	$-0.375093\pi$
$811$	6.18627e50	0.764828	0.382414	+	0.923991i	$0.375093\pi$
$812$	−1.70148e51	−2.05872
$813$	9.83286e50	1.16438
$814$	−1.01955e51	−1.18163
$815$	−2.13249e51	−2.41896
$816$	3.98343e50	0.442262
$817$	9.90049e49	0.107590
$818$	2.90186e51	3.08670
$819$	1.22115e50	0.127146
$820$	−9.99063e50	−1.01824
$821$	−9.87204e50	−0.984922	−0.492461	−	0.870335i	$-0.663903\pi$
$821$	−9.87204e50	−0.984922	−0.492461	+	0.870335i	$0.663903\pi$
$822$	−3.61983e50	−0.353534
$823$	−1.56871e51	−1.49985	−0.749923	−	0.661525i	$-0.769909\pi$
$823$	−1.56871e51	−1.49985	−0.749923	+	0.661525i	$0.769909\pi$
$824$	1.29577e51	1.21283
$825$	1.67900e50	0.153853
$826$	7.20039e50	0.645960
$827$	−3.34712e49	−0.0293985	−0.0146992	−	0.999892i	$-0.504679\pi$
$827$	−3.34712e49	−0.0293985	−0.0146992	+	0.999892i	$0.504679\pi$
$828$	−1.36559e51	−1.17433
$829$	−1.24277e51	−1.04638	−0.523188	−	0.852217i	$-0.675257\pi$
$829$	−1.24277e51	−1.04638	−0.523188	+	0.852217i	$0.675257\pi$
$830$	2.46485e51	2.03200
$831$	−2.04327e49	−0.0164933
$832$	1.11685e50	0.0882749
$833$	2.94772e50	0.228139
$834$	−2.84190e50	−0.215379
$835$	1.03435e51	0.767635
$836$	1.85208e51	1.34601
$837$	1.21258e51	0.863005
$838$	6.61903e50	0.461343
$839$	7.06560e50	0.482297	0.241149	−	0.970488i	$-0.422476\pi$
$839$	7.06560e50	0.482297	0.241149	+	0.970488i	$0.422476\pi$
$840$	−1.77902e51	−1.18931
$841$	1.69401e51	1.10914
$842$	−4.09125e51	−2.62358
$843$	−1.87258e51	−1.17613
$844$	2.04329e51	1.25700
$845$	−1.76853e51	−1.06566
$846$	−1.22122e51	−0.720796
$847$	−9.29800e50	−0.537564
$848$	−4.80842e51	−2.72317
$849$	−1.67516e49	−0.00929333
$850$	−7.01568e50	−0.381275
$851$	3.11773e51	1.65986
$852$	1.32422e51	0.690667
$853$	−4.40952e50	−0.225311	−0.112656	−	0.993634i	$-0.535936\pi$
$853$	−4.40952e50	−0.225311	−0.112656	+	0.993634i	$0.535936\pi$
$854$	3.03773e51	1.52067
$855$	1.98759e51	0.974810
$856$	7.43474e51	3.57252
$857$	−2.01998e51	−0.951004	−0.475502	−	0.879715i	$-0.657733\pi$
$857$	−2.01998e51	−0.951004	−0.475502	+	0.879715i	$0.657733\pi$
$858$	−4.13006e50	−0.190515
$859$	−2.47558e51	−1.11891	−0.559456	−	0.828860i	$-0.688990\pi$
$859$	−2.47558e51	−1.11891	−0.559456	+	0.828860i	$0.688990\pi$
$860$	−4.42243e50	−0.195857
$861$	3.82315e50	0.165908
$862$	−3.99071e51	−1.69696
$863$	1.15182e51	0.479948	0.239974	−	0.970779i	$-0.422861\pi$
$863$	1.15182e51	0.479948	0.239974	+	0.970779i	$0.422861\pi$
$864$	2.02515e51	0.826926
$865$	−6.69696e49	−0.0267976
$866$	−6.84143e51	−2.68277
$867$	1.52563e51	0.586293
$868$	3.08657e51	1.16247
$869$	9.84195e49	0.0363274
$870$	6.17563e51	2.23406
$871$	−1.83781e50	−0.0651602
$872$	−2.99601e51	−1.04113
$873$	−9.38647e49	−0.0319708
$874$	−8.23827e51	−2.75034
$875$	−1.11109e51	−0.363588
$876$	−3.78255e51	−1.21328
$877$	1.21793e50	0.0382938	0.0191469	−	0.999817i	$-0.493905\pi$
$877$	1.21793e50	0.0382938	0.0191469	+	0.999817i	$0.493905\pi$
$878$	1.04445e52	3.21909
$879$	3.68753e50	0.111412
$880$	−2.80226e51	−0.829969
$881$	1.43159e51	0.415663	0.207832	−	0.978165i	$-0.433359\pi$
$881$	1.43159e51	0.415663	0.207832	+	0.978165i	$0.433359\pi$
$882$	1.91700e51	0.545661
$883$	4.21625e51	1.17656	0.588280	−	0.808658i	$-0.299805\pi$
$883$	4.21625e51	1.17656	0.588280	+	0.808658i	$0.299805\pi$
$884$	1.18639e51	0.324575
$885$	−1.79665e51	−0.481900
$886$	−8.27591e51	−2.17634
$887$	1.06484e51	0.274549	0.137274	−	0.990533i	$-0.456166\pi$
$887$	1.06484e51	0.274549	0.137274	+	0.990533i	$0.456166\pi$
$888$	−9.52303e51	−2.40740
$889$	−1.18280e51	−0.293177
$890$	6.59463e51	1.60275
$891$	3.52185e50	0.0839288
$892$	1.21268e52	2.83376
$893$	−5.06481e51	−1.16055
$894$	6.49316e51	1.45898
$895$	−1.03108e51	−0.227190
$896$	−3.58879e51	−0.775457
$897$	1.26295e51	0.267621
$898$	1.04377e52	2.16904
$899$	−5.84365e51	−1.19094
$900$	−3.13661e51	−0.626927
$901$	3.30714e51	0.648289
$902$	1.41045e51	0.271171
$903$	1.69235e50	0.0319120
$904$	−4.88057e51	−0.902658
$905$	−1.03925e52	−1.88525
$906$	−7.49007e51	−1.33273
$907$	5.18332e51	0.904649	0.452325	−	0.891853i	$-0.350595\pi$
$907$	5.18332e51	0.904649	0.452325	+	0.891853i	$0.350595\pi$
$908$	−9.97841e51	−1.70828
$909$	−1.89913e51	−0.318923
$910$	−3.29072e51	−0.542083
$911$	9.24676e51	1.49423	0.747116	−	0.664694i	$-0.231438\pi$
$911$	9.24676e51	1.49423	0.747116	+	0.664694i	$0.231438\pi$
$912$	1.07439e52	1.70315
$913$	−2.39226e51	−0.372023
$914$	1.06765e52	1.62880
$915$	−7.57978e51	−1.13446
$916$	−9.64981e51	−1.41693
$917$	6.64424e51	0.957154
$918$	−5.19689e51	−0.734508
$919$	−4.29279e51	−0.595275	−0.297638	−	0.954679i	$-0.596199\pi$
$919$	−4.29279e51	−0.595275	−0.297638	+	0.954679i	$0.596199\pi$
$920$	2.00701e52	2.73063
$921$	7.49359e51	1.00034
$922$	2.97278e51	0.389378
$923$	1.33592e51	0.171692
$924$	3.16586e51	0.399238
$925$	7.16109e51	0.886132
$926$	−9.09766e51	−1.10468
$927$	−2.47460e51	−0.294856
$928$	−9.75961e51	−1.14115
$929$	4.47733e51	0.513740	0.256870	−	0.966446i	$-0.417309\pi$
$929$	4.47733e51	0.513740	0.256870	+	0.966446i	$0.417309\pi$
$930$	−1.12029e52	−1.26147
$931$	7.95047e51	0.878564
$932$	−8.71061e51	−0.944649
$933$	−2.87284e51	−0.305761
$934$	−2.78529e52	−2.90938
$935$	1.92734e51	0.197586
$936$	4.20799e51	0.423397
$937$	−1.28073e50	−0.0126478	−0.00632388	−	0.999980i	$-0.502013\pi$
$937$	−1.28073e50	−0.0126478	−0.00632388	+	0.999980i	$0.502013\pi$
$938$	2.04919e51	0.198624
$939$	−4.14159e51	−0.394021
$940$	2.26239e52	2.11266
$941$	3.26378e50	0.0299160	0.0149580	−	0.999888i	$-0.495239\pi$
$941$	3.26378e50	0.0299160	0.0149580	+	0.999888i	$0.495239\pi$
$942$	1.32179e52	1.18924
$943$	−4.31310e51	−0.380921
$944$	1.05938e52	0.918420
$945$	9.90965e51	0.843338
$946$	6.24346e50	0.0521591
$947$	−1.57573e52	−1.29228	−0.646140	−	0.763219i	$-0.723618\pi$
$947$	−1.57573e52	−1.29228	−0.646140	+	0.763219i	$0.723618\pi$
$948$	1.68555e51	0.135705
$949$	−3.81594e51	−0.301608
$950$	−1.89224e52	−1.46830
$951$	3.75299e51	0.285903
$952$	−7.21472e51	−0.539601
$953$	−9.47096e51	−0.695454	−0.347727	−	0.937596i	$-0.613046\pi$
$953$	−9.47096e51	−0.695454	−0.347727	+	0.937596i	$0.613046\pi$
$954$	2.15075e52	1.55057
$955$	−1.86651e52	−1.32121
$956$	1.07991e52	0.750540
$957$	−5.99377e51	−0.409017
$958$	5.03703e52	3.37503
$959$	2.79924e51	0.184168
$960$	3.10731e51	0.200742
$961$	−5.16308e51	−0.327529
$962$	−1.76151e52	−1.09729
$963$	−1.41985e52	−0.868528
$964$	−1.11381e52	−0.669059
$965$	3.50883e52	2.06983
$966$	−1.40821e52	−0.815773
$967$	1.42806e52	0.812424	0.406212	−	0.913779i	$-0.366849\pi$
$967$	1.42806e52	0.812424	0.406212	+	0.913779i	$0.366849\pi$
$968$	−3.20401e52	−1.79009
$969$	−7.38949e51	−0.405460
$970$	2.52943e51	0.136307
$971$	−4.08920e51	−0.216422	−0.108211	−	0.994128i	$-0.534512\pi$
$971$	−4.08920e51	−0.216422	−0.108211	+	0.994128i	$0.534512\pi$
$972$	−3.85032e52	−2.00141
$973$	2.19766e51	0.112198
$974$	−3.17319e52	−1.59116
$975$	2.90087e51	0.142872
$976$	4.46934e52	2.16208
$977$	2.55940e52	1.21614	0.608071	−	0.793883i	$-0.291944\pi$
$977$	2.55940e52	1.21614	0.608071	+	0.793883i	$0.291944\pi$
$978$	5.15597e52	2.40647
$979$	−6.40042e51	−0.293435
$980$	−3.55138e52	−1.59934
$981$	5.72166e51	0.253113
$982$	−2.98488e52	−1.29711
$983$	1.82270e52	0.778087	0.389044	−	0.921219i	$-0.372806\pi$
$983$	1.82270e52	0.778087	0.389044	+	0.921219i	$0.372806\pi$
$984$	1.31742e52	0.552474
$985$	8.41302e48	0.000346592 0
$986$	2.50449e52	1.01361
$987$	−8.65757e51	−0.344228
$988$	3.19989e52	1.24994
$989$	−1.90922e51	−0.0732693
$990$	1.25342e52	0.472585
$991$	8.47738e51	0.314031	0.157015	−	0.987596i	$-0.449813\pi$
$991$	8.47738e51	0.314031	0.157015	+	0.987596i	$0.449813\pi$
$992$	1.77044e52	0.644358
$993$	−2.84149e52	−1.01610
$994$	−1.48957e52	−0.523358
$995$	−3.42702e52	−1.18307
$996$	−4.09702e52	−1.38973
$997$	−4.09490e52	−1.36483	−0.682414	−	0.730966i	$-0.739070\pi$
$997$	−4.09490e52	−1.36483	−0.682414	+	0.730966i	$0.739070\pi$
$998$	−4.37162e52	−1.43172
$999$	5.30459e52	1.70709

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.36.a.a.1.3	✓	3
3.2	odd	2		9.36.a.b.1.1		3
4.3	odd	2		16.36.a.d.1.2		3
5.2	odd	4		25.36.b.a.24.6		6
5.3	odd	4		25.36.b.a.24.1		6
5.4	even	2		25.36.a.a.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.36.a.a.1.3	✓	3	1.1	even	1	trivial
9.36.a.b.1.1		3	3.2	odd	2
16.36.a.d.1.2		3	4.3	odd	2
25.36.a.a.1.1		3	5.4	even	2
25.36.b.a.24.1		6	5.3	odd	4
25.36.b.a.24.6		6	5.2	odd	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 36 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+331573. q^{2} -1.54691e8 q^{3} +7.55810e10 q^{4} +2.12139e12 q^{5} -5.12913e13 q^{6} +3.96640e14 q^{7} +1.36679e16 q^{8} -2.61023e16 q^{9} +O(q^{10})\)	\(q+331573. q^{2} -1.54691e8 q^{3} +7.55810e10 q^{4} +2.12139e12 q^{5} -5.12913e13 q^{6} +3.96640e14 q^{7} +1.36679e16 q^{8} -2.61023e16 q^{9} +7.03395e17 q^{10} -6.82681e17 q^{11} -1.16917e19 q^{12} -1.17949e19 q^{13} +1.31515e20 q^{14} -3.28159e20 q^{15} +1.93496e21 q^{16} -1.33083e21 q^{17} -8.65483e21 q^{18} -3.58945e22 q^{19} +1.60337e23 q^{20} -6.13565e22 q^{21} -2.26359e23 q^{22} +6.92195e23 q^{23} -2.11429e24 q^{24} +1.58990e24 q^{25} -3.91088e24 q^{26} +1.17772e25 q^{27} +2.99785e25 q^{28} -5.67568e25 q^{29} -1.08809e26 q^{30} +1.02960e26 q^{31} +1.71955e26 q^{32} +1.05604e26 q^{33} -4.41267e26 q^{34} +8.41427e26 q^{35} -1.97284e27 q^{36} +4.50412e27 q^{37} -1.19017e28 q^{38} +1.82456e27 q^{39} +2.89948e28 q^{40} -6.23104e27 q^{41} -2.03442e28 q^{42} -2.75822e27 q^{43} -5.15977e28 q^{44} -5.53731e28 q^{45} +2.29513e29 q^{46} +1.41103e29 q^{47} -2.99320e29 q^{48} -2.21495e29 q^{49} +5.27167e29 q^{50} +2.05867e29 q^{51} -8.91472e29 q^{52} -2.48503e30 q^{53} +3.90500e30 q^{54} -1.44823e30 q^{55} +5.42123e30 q^{56} +5.55255e30 q^{57} -1.88190e31 q^{58} +5.47495e30 q^{59} -2.48026e31 q^{60} +2.30979e31 q^{61} +3.41386e31 q^{62} -1.03532e31 q^{63} -9.46893e30 q^{64} -2.50216e31 q^{65} +3.50156e31 q^{66} +1.55814e31 q^{67} -1.00585e32 q^{68} -1.07076e32 q^{69} +2.78995e32 q^{70} -1.13262e32 q^{71} -3.56763e32 q^{72} +3.23524e32 q^{73} +1.49345e33 q^{74} -2.45942e32 q^{75} -2.71294e33 q^{76} -2.70778e32 q^{77} +6.04976e32 q^{78} -1.44166e32 q^{79} +4.10479e33 q^{80} -5.15885e32 q^{81} -2.06605e33 q^{82} +3.50421e33 q^{83} -4.63739e33 q^{84} -2.82320e33 q^{85} -9.14551e32 q^{86} +8.77975e33 q^{87} -9.33079e33 q^{88} +9.37543e33 q^{89} -1.83602e34 q^{90} -4.67833e33 q^{91} +5.23168e34 q^{92} -1.59269e34 q^{93} +4.67858e34 q^{94} -7.61461e34 q^{95} -2.65998e34 q^{96} +3.59603e33 q^{97} -7.34419e34 q^{98} +1.78195e34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 139656 q^{2} - 104875308 q^{3} + 34841262144 q^{4} + 892652054010 q^{5} - 4786530564384 q^{6} + 878422149346056 q^{7} + 22\!\cdots\!00 q^{8}+ \cdots + 15\!\cdots\!51 q^{9}+O(q^{10}) \) 3 * q + 139656 * q^2 - 104875308 * q^3 + 34841262144 * q^4 + 892652054010 * q^5 - 4786530564384 * q^6 + 878422149346056 * q^7 + 22336009925337600 * q^8 + 150091978876243551 * q^9	\( 3 q + 139656 q^{2} - 104875308 q^{3} + 34841262144 q^{4} + 892652054010 q^{5} - 4786530564384 q^{6} + 878422149346056 q^{7} + 22\!\cdots\!00 q^{8}+ \cdots + 30\!\cdots\!52 q^{99}+O(q^{100}) \) 3 * q + 139656 * q^2 - 104875308 * q^3 + 34841262144 * q^4 + 892652054010 * q^5 - 4786530564384 * q^6 + 878422149346056 * q^7 + 22336009925337600 * q^8 + 150091978876243551 * q^9 + 1019870812729298160 * q^10 - 1157945428549987044 * q^11 - 22548891526776486144 * q^12 - 62139610550998650558 * q^13 + 135909343255071438528 * q^14 + 706062479352366674520 * q^15 + 2155694017285818421248 * q^16 - 3932636930193139724394 * q^17 - 23007400170989698594008 * q^18 - 32303396242934620550940 * q^19 + 147257059647928607018880 * q^20 + 222122458753667398807776 * q^21 + 22658809266113247402912 * q^22 - 514822069421375217224808 * q^23 - 3760729014923614708254720 * q^24 + 646885156836409574920725 * q^25 + 4284481859934908169468336 * q^26 + 27373531144823515220747400 * q^27 + 10448754713452503022622208 * q^28 - 38460399143984437598248110 * q^29 - 234613011392444285921119680 * q^30 + 103731594563724689730029856 * q^31 - 9222369125611166314758144 * q^32 + 1184565114402567148957069584 * q^33 - 554136735348503783026707312 * q^34 + 1596564453000564139676248560 * q^35 - 6052204716130590310531484352 * q^36 + 2464613172948888017021063706 * q^37 - 12543374691225905672793885600 * q^38 + 18611981954062877742706387512 * q^39 + 16458708947711983604007091200 * q^40 + 23522986584532768129037087406 * q^41 - 33931371616975894880367698688 * q^42 - 47516297135443858184325274308 * q^43 - 80954820698705302013923898112 * q^44 - 110576300682246572226345828030 * q^45 + 310121697020384938950505889856 * q^46 + 164346768841318947159729902256 * q^47 + 445342931723856383878644744192 * q^48 - 595089038084925731622037450821 * q^49 + 373669468267473207632799996600 * q^50 - 1803044074850794727352259927704 * q^51 - 511632617456400883939009686144 * q^52 - 1670480551111723484744458809558 * q^53 + 4424231404769003900494105901760 * q^54 + 3067178595313878889174894808520 * q^55 + 5670920217413056567252590243840 * q^56 + 4048712721984947152977307522800 * q^57 - 23757672063982901326871265032400 * q^58 + 4370528583092646699845243631180 * q^59 - 40771862895691439845448715210240 * q^60 + 23537078276516028947219080488306 * q^61 + 29401231764447267309574710842112 * q^62 + 45614247892704690123948892506792 * q^63 + 93510280736634320631093264384 * q^64 + 75762337609865790449417835274620 * q^65 - 75640417841065837797640948042368 * q^66 - 188845033384156918977315211921644 * q^67 + 21990159186015794982823459732608 * q^68 - 325983212396274250308653315934048 * q^69 + 223263426310223328568197933240960 * q^70 + 348774602295358210538621162006856 * q^71 + 314101495165322886769992842611200 * q^72 - 285174964854822786615792218987058 * q^73 + 2106337383176566865790045395789808 * q^74 - 1577819189216049218913461709237300 * q^75 - 2729074287668324197849535448894720 * q^76 + 691501421964810422051915307575712 * q^77 - 2213086042571083132613626950273216 * q^78 - 426212862591061661901736630874160 * q^79 + 6831119561623806264802413342351360 * q^80 + 1867221150796978455595408934723163 * q^81 - 4061181362173286538873115152234288 * q^82 + 14867187331664065317008883105766692 * q^83 - 13024788508690842242825242575869952 * q^84 - 8752040931978292430566755304420140 * q^85 + 148490750656470812540405098190496 * q^86 - 7833119385476156993771606256673800 * q^87 - 18777218849949122679898044025804800 * q^88 + 30583590846193751335205992418034270 * q^89 + 2860720282233327924484406809049520 * q^90 + 1003391702519487362566122156997296 * q^91 + 83662070125024358323030039384121856 * q^92 - 40914650682166972019906140161446016 * q^93 + 19076193270418512575422277142000768 * q^94 - 84521392849966457182141665888160200 * q^95 - 32392027865954425966997293222723584 * q^96 - 106165667044630951063328618701091994 * q^97 - 13202051562017808504422115585262392 * q^98 + 30288686341597731928441860752034252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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