LMFDB - Embedded newform 2.42.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,42,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 42, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 42);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 42 $
Character orbit:	$[\chi]$	$=$	2.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:	$21.2943340913$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1139917559892 $ x^2 - x - 1139917559892
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{7}\cdot 3^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.06767e6$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.04858e6 q^{2} +1.05814e10 q^{3} +1.09951e12 q^{4} -2.54286e14 q^{5} +1.10955e16 q^{6} +2.96016e17 q^{7} +1.15292e18 q^{8} +7.54941e19 q^{9} +O(q^{10})$	\(q+1.04858e6 q^{2} +1.05814e10 q^{3} +1.09951e12 q^{4} -2.54286e14 q^{5} +1.10955e16 q^{6} +2.96016e17 q^{7} +1.15292e18 q^{8} +7.54941e19 q^{9} -2.66638e20 q^{10} -1.09620e21 q^{11} +1.16344e22 q^{12} +8.09333e22 q^{13} +3.10395e23 q^{14} -2.69071e24 q^{15} +1.20893e24 q^{16} -5.33128e24 q^{17} +7.91613e25 q^{18} -3.50762e25 q^{19} -2.79590e26 q^{20} +3.13228e27 q^{21} -1.14945e27 q^{22} +6.68932e27 q^{23} +1.21996e28 q^{24} +1.91866e28 q^{25} +8.48648e28 q^{26} +4.12899e29 q^{27} +3.25473e29 q^{28} -1.63586e30 q^{29} -2.82142e30 q^{30} +2.77961e30 q^{31} +1.26765e30 q^{32} -1.15993e31 q^{33} -5.59026e30 q^{34} -7.52726e31 q^{35} +8.30066e31 q^{36} +4.65417e31 q^{37} -3.67800e31 q^{38} +8.56392e32 q^{39} -2.93172e32 q^{40} -8.83679e32 q^{41} +3.28443e33 q^{42} -3.69256e32 q^{43} -1.20528e33 q^{44} -1.91971e34 q^{45} +7.01426e33 q^{46} -1.89619e34 q^{47} +1.27922e34 q^{48} +4.30577e34 q^{49} +2.01186e34 q^{50} -5.64127e34 q^{51} +8.89872e34 q^{52} -2.01460e35 q^{53} +4.32956e35 q^{54} +2.78747e35 q^{55} +3.41283e35 q^{56} -3.71157e35 q^{57} -1.71532e36 q^{58} +5.07603e34 q^{59} -2.95847e36 q^{60} -6.57027e36 q^{61} +2.91463e36 q^{62} +2.23474e37 q^{63} +1.32923e36 q^{64} -2.05802e37 q^{65} -1.21628e37 q^{66} +5.28414e37 q^{67} -5.86181e36 q^{68} +7.07827e37 q^{69} -7.89291e37 q^{70} -1.04768e38 q^{71} +8.70387e37 q^{72} -2.83453e38 q^{73} +4.88025e37 q^{74} +2.03022e38 q^{75} -3.85666e37 q^{76} -3.24491e38 q^{77} +8.97992e38 q^{78} -6.59452e38 q^{79} -3.07413e38 q^{80} +1.61558e39 q^{81} -9.26605e38 q^{82} +1.30773e39 q^{83} +3.44397e39 q^{84} +1.35567e39 q^{85} -3.87193e38 q^{86} -1.73098e40 q^{87} -1.26383e39 q^{88} +2.16819e39 q^{89} -2.01296e40 q^{90} +2.39575e40 q^{91} +7.35498e39 q^{92} +2.94123e40 q^{93} -1.98830e40 q^{94} +8.91937e39 q^{95} +1.34136e40 q^{96} -8.40052e39 q^{97} +4.51493e40 q^{98} -8.27563e40 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2097152 q^{2} + 8863347528 q^{3} + 2199023255552 q^{4} + 97599184325580 q^{5} + 92\!\cdots\!28 q^{6}+ \cdots + 41\!\cdots\!86 q^{9}+O(q^{10}) $ 2 * q + 2097152 * q^2 + 8863347528 * q^3 + 2199023255552 * q^4 + 97599184325580 * q^5 + 9293893497520128 * q^6 + 217106802373088656 * q^7 + 2305843009213693952 * q^8 + 41972929616872509786 * q^9	$ 2 q + 2097152 q^{2} + 8863347528 q^{3} + 2199023255552 q^{4} + 97599184325580 q^{5} + 92\!\cdots\!28 q^{6}+ \cdots - 12\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 2097152 * q^2 + 8863347528 * q^3 + 2199023255552 * q^4 + 97599184325580 * q^5 + 9293893497520128 * q^6 + 217106802373088656 * q^7 + 2305843009213693952 * q^8 + 41972929616872509786 * q^9 + 102340162303379374080 * q^10 + 110594481484939565784 * q^11 + 9745353668055665737728 * q^12 + 173293106838448696895068 * q^13 + 227652982405163810553856 * q^14 - 3295287287252802285241680 * q^15 + 2417851639229258349412352 * q^16 - 10287966260741677078429404 * q^17 + 44011806645941708821364736 * q^18 + 206254882139859790701457000 * q^19 + 107311438027428330555310080 * q^20 + 3267849131609686416057835584 * q^21 + 115966719017551990131523584 * q^22 + 14925421378885128304361915568 * q^23 + 10218743967835137756603875328 * q^24 + 97534966241249753807444705150 * q^25 + 181710992796233180795442823168 * q^26 + 533156288863055843864697754320 * q^27 + 238711453678477047815320109056 * q^28 - 1375143011941884388614889894020 * q^29 - 3455359162518394409049579847680 * q^30 - 3626496922711160469799126663616 * q^31 + 2535301200456458802993406410752 * q^32 - 13672735988327258412044854187424 * q^33 - 10787714509823464784191190728704 * q^34 - 103039524095905042910481769779360 * q^35 + 46149724165574973269071349415936 * q^36 + 120356679589378915210866994599436 * q^37 + 216273919294685619894570975232000 * q^38 + 697708668559917206762862430490352 * q^39 + 112524198441048689140364822446080 * q^40 + 1270177139906840106861139346878164 * q^41 + 3426588171026758543404261005328384 * q^42 - 6045433421160616098770468790853352 * q^43 + 121599918360548595604152473616384 * q^44 - 30992658299909156185379775337031460 * q^45 + 15650438647785852296874599978631168 * q^46 - 25416478966330542868882280891861664 * q^47 + 10715129674816697408268665175932928 * q^48 + 4716677344275473650585885334355954 * q^49 + 102272824761384701848395139147366400 * q^50 - 47896619495707425086522465903395056 * q^51 + 190537785982303003785762253746208768 * q^52 - 301376484284740318156836692232048852 * q^53 + 559054888750867644536269312433848320 * q^54 + 703399094180619772764269188861842960 * q^55 + 250307101252362748889997098673504256 * q^56 - 785787658029123941344672503009410400 * q^57 - 1441941958889973364676246785511915520 * q^58 - 3282010250697938085995473868454788040 * q^59 - 3623206689196887935863572238360903680 * q^60 - 4485157745840460017677520841591879236 * q^61 - 3802657637228777800780089040427810816 * q^62 + 24992547810032633572829803615671997008 * q^63 + 2658455991569831745807614120560689152 * q^64 + 11919812053150705903267451825832510120 * q^65 - 14336902811696243316668345024432308224 * q^66 + 55055736076082381526441630307313037256 * q^67 - 11311738529852649409548062009541525504 * q^68 + 56632222305135551516324020091548201152 * q^69 - 108044772018387726274901332228162191360 * q^70 - 48857884738531480102553331099997138416 * q^71 + 48391493166641943170589759285164507136 * q^72 - 485616958845162818165813572349849688812 * q^73 + 126203125657112585396150069729098203136 * q^74 + 68411444542067712502035991381122300600 * q^75 + 226779641198344268566569654924869632000 * q^76 - 419718086944271580508987308621981603648 * q^77 + 731600564843883744998575235913851338752 * q^78 - 905766854341990828970937020702446890080 * q^79 + 117990173904521070264047184061220782080 * q^80 + 2631580786121491108655810678136598411122 * q^81 + 1331877264654954771892026051792117694464 * q^82 + 1271755206567258248006583231290595969768 * q^83 + 3593038118022554366408666387923215581184 * q^84 - 388512546938141834318136915482004571560 * q^85 - 6339096395026914186384343082837844426752 * q^86 - 17757719150026706057484126704955838888080 * q^87 + 127506755994830604184219784174773469184 * q^88 + 2692414558304473820098690391828757436980 * q^89 - 32498157669485543356240783303803100200960 * q^90 + 16669534332125295311104493248216990683104 * q^91 + 16410674355540697858047580547193155616768 * q^92 + 40418607330508619745600934617627243192576 * q^93 - 26651109848599015319281106568464736190464 * q^94 + 93840167647611953736551449995129877215600 * q^95 + 11235627813900593301572723855519045910528 * q^96 - 31989468315501178009691057062669320691004 * q^97 + 4945794662950999058636745300357628821504 * q^98 - 123209315561064920195916977740234432814088 * 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 $

$2$	1.04858e6	0.707107
$2$	1.04858e6	0.707107
$3$	1.05814e10	1.75210	0.876051	−	0.482218i	$-0.160169\pi$
$3$	1.05814e10	1.75210	0.876051	+	0.482218i	$0.160169\pi$
$4$	1.09951e12	0.500000
$5$	−2.54286e14	−1.19244	−0.596221	−	0.802820i	$-0.703332\pi$
$5$	−2.54286e14	−1.19244	−0.596221	+	0.802820i	$0.703332\pi$
$6$	1.10955e16	1.23892
$7$	2.96016e17	1.40218	0.701092	−	0.713071i	$-0.252696\pi$
$7$	2.96016e17	1.40218	0.701092	+	0.713071i	$0.252696\pi$
$8$	1.15292e18	0.353553
$9$	7.54941e19	2.06986
$10$	−2.66638e20	−0.843184
$11$	−1.09620e21	−0.491291	−0.245645	−	0.969360i	$-0.579000\pi$
$11$	−1.09620e21	−0.491291	−0.245645	+	0.969360i	$0.579000\pi$
$12$	1.16344e22	0.876051
$13$	8.09333e22	1.18111	0.590553	−	0.806999i	$-0.298910\pi$
$13$	8.09333e22	1.18111	0.590553	+	0.806999i	$0.298910\pi$
$14$	3.10395e23	0.991494
$15$	−2.69071e24	−2.08928
$16$	1.20893e24	0.250000
$17$	−5.33128e24	−0.318148	−0.159074	−	0.987267i	$-0.550851\pi$
$17$	−5.33128e24	−0.318148	−0.159074	+	0.987267i	$0.550851\pi$
$18$	7.91613e25	1.46361
$19$	−3.50762e25	−0.214074	−0.107037	−	0.994255i	$-0.534136\pi$
$19$	−3.50762e25	−0.214074	−0.107037	+	0.994255i	$0.534136\pi$
$20$	−2.79590e26	−0.596221
$21$	3.13228e27	2.45677
$22$	−1.14945e27	−0.347395
$23$	6.68932e27	0.812758	0.406379	−	0.913705i	$-0.366791\pi$
$23$	6.68932e27	0.812758	0.406379	+	0.913705i	$0.366791\pi$
$24$	1.21996e28	0.619462
$25$	1.91866e28	0.421917
$26$	8.48648e28	0.835168
$27$	4.12899e29	1.87451
$28$	3.25473e29	0.701092
$29$	−1.63586e30	−1.71628	−0.858139	−	0.513418i	$-0.828379\pi$
$29$	−1.63586e30	−1.71628	−0.858139	+	0.513418i	$0.828379\pi$
$30$	−2.82142e30	−1.47734
$31$	2.77961e30	0.743137	0.371568	−	0.928406i	$-0.378820\pi$
$31$	2.77961e30	0.743137	0.371568	+	0.928406i	$0.378820\pi$
$32$	1.26765e30	0.176777
$33$	−1.15993e31	−0.860791
$34$	−5.59026e30	−0.224964
$35$	−7.52726e31	−1.67202
$36$	8.30066e31	1.03493
$37$	4.65417e31	0.330908	0.165454	−	0.986218i	$-0.447091\pi$
$37$	4.65417e31	0.330908	0.165454	+	0.986218i	$0.447091\pi$
$38$	−3.67800e31	−0.151373
$39$	8.56392e32	2.06942
$40$	−2.93172e32	−0.421592
$41$	−8.83679e32	−0.765995	−0.382997	−	0.923749i	$-0.625108\pi$
$41$	−8.83679e32	−0.765995	−0.382997	+	0.923749i	$0.625108\pi$
$42$	3.28443e33	1.73720
$43$	−3.69256e32	−0.120566	−0.0602829	−	0.998181i	$-0.519200\pi$
$43$	−3.69256e32	−0.120566	−0.0602829	+	0.998181i	$0.519200\pi$
$44$	−1.20528e33	−0.245645
$45$	−1.91971e34	−2.46819
$46$	7.01426e33	0.574707
$47$	−1.89619e34	−0.999714	−0.499857	−	0.866108i	$-0.666614\pi$
$47$	−1.89619e34	−0.999714	−0.499857	+	0.866108i	$0.666614\pi$
$48$	1.27922e34	0.438026
$49$	4.30577e34	0.966120
$50$	2.01186e34	0.298341
$51$	−5.64127e34	−0.557427
$52$	8.89872e34	0.590553
$53$	−2.01460e35	−0.904761	−0.452380	−	0.891825i	$-0.649425\pi$
$53$	−2.01460e35	−0.904761	−0.452380	+	0.891825i	$0.649425\pi$
$54$	4.32956e35	1.32548
$55$	2.78747e35	0.585835
$56$	3.41283e35	0.495747
$57$	−3.71157e35	−0.375079
$58$	−1.71532e36	−1.21359
$59$	5.07603e34	0.0252964	0.0126482	−	0.999920i	$-0.495974\pi$
$59$	5.07603e34	0.0252964	0.0126482	+	0.999920i	$0.495974\pi$
$60$	−2.95847e36	−1.04464
$61$	−6.57027e36	−1.65319	−0.826593	−	0.562801i	$-0.809724\pi$
$61$	−6.57027e36	−1.65319	−0.826593	+	0.562801i	$0.809724\pi$
$62$	2.91463e36	0.525477
$63$	2.23474e37	2.90233
$64$	1.32923e36	0.125000
$65$	−2.05802e37	−1.40840
$66$	−1.21628e37	−0.608671
$67$	5.28414e37	1.94286	0.971429	−	0.237332i	$-0.0762729\pi$
$67$	5.28414e37	1.94286	0.971429	+	0.237332i	$0.0762729\pi$
$68$	−5.86181e36	−0.159074
$69$	7.07827e37	1.42403
$70$	−7.89291e37	−1.18230
$71$	−1.04768e38	−1.17337	−0.586684	−	0.809816i	$-0.699567\pi$
$71$	−1.04768e38	−1.17337	−0.586684	+	0.809816i	$0.699567\pi$
$72$	8.70387e37	0.731807
$73$	−2.83453e38	−1.79623	−0.898117	−	0.439756i	$-0.855065\pi$
$73$	−2.83453e38	−1.79623	−0.898117	+	0.439756i	$0.855065\pi$
$74$	4.88025e37	0.233987
$75$	2.03022e38	0.739242
$76$	−3.85666e37	−0.107037
$77$	−3.24491e38	−0.688880
$78$	8.97992e38	1.46330
$79$	−6.59452e38	−0.827614	−0.413807	−	0.910365i	$-0.635801\pi$
$79$	−6.59452e38	−0.827614	−0.413807	+	0.910365i	$0.635801\pi$
$80$	−3.07413e38	−0.298110
$81$	1.61558e39	1.21447
$82$	−9.26605e38	−0.541640
$83$	1.30773e39	0.596236	0.298118	−	0.954529i	$-0.403641\pi$
$83$	1.30773e39	0.596236	0.298118	+	0.954529i	$0.403641\pi$
$84$	3.44397e39	1.22838
$85$	1.35567e39	0.379373
$86$	−3.87193e38	−0.0852529
$87$	−1.73098e40	−3.00709
$88$	−1.26383e39	−0.173697
$89$	2.16819e39	0.236376	0.118188	−	0.992991i	$-0.462292\pi$
$89$	2.16819e39	0.236376	0.118188	+	0.992991i	$0.462292\pi$
$90$	−2.01296e40	−1.74527
$91$	2.39575e40	1.65613
$92$	7.35498e39	0.406379
$93$	2.94123e40	1.30205
$94$	−1.98830e40	−0.706905
$95$	8.91937e39	0.255270
$96$	1.34136e40	0.309731
$97$	−8.40052e39	−0.156850	−0.0784252	−	0.996920i	$-0.524989\pi$
$97$	−8.40052e39	−0.156850	−0.0784252	+	0.996920i	$0.524989\pi$
$98$	4.51493e40	0.683150
$99$	−8.27563e40	−1.01690
$100$	2.10959e40	0.210959
$101$	4.81454e40	0.392615	0.196308	−	0.980542i	$-0.437105\pi$
$101$	4.81454e40	0.392615	0.196308	+	0.980542i	$0.437105\pi$
$102$	−5.91530e40	−0.394161
$103$	8.87160e40	0.483992	0.241996	−	0.970277i	$-0.422198\pi$
$103$	8.87160e40	0.483992	0.241996	+	0.970277i	$0.422198\pi$
$104$	9.33098e40	0.417584
$105$	−7.96494e41	−2.92955
$106$	−2.11246e41	−0.639763
$107$	5.55682e41	1.38822	0.694111	−	0.719868i	$-0.255797\pi$
$107$	5.55682e41	1.38822	0.694111	+	0.719868i	$0.255797\pi$
$108$	4.53988e41	0.937253
$109$	−4.77382e41	−0.815873	−0.407936	−	0.913010i	$-0.633752\pi$
$109$	−4.77382e41	−0.815873	−0.407936	+	0.913010i	$0.633752\pi$
$110$	2.92288e41	0.414248
$111$	4.92479e41	0.579785
$112$	3.57861e41	0.350546
$113$	9.67742e41	0.790045	0.395022	−	0.918672i	$-0.370737\pi$
$113$	9.67742e41	0.790045	0.395022	+	0.918672i	$0.370737\pi$
$114$	−3.89186e41	−0.265221
$115$	−1.70100e42	−0.969167
$116$	−1.79865e42	−0.858139
$117$	6.10999e42	2.44473
$118$	5.32261e40	0.0178872
$119$	−1.57814e42	−0.446102
$120$	−3.10218e42	−0.738672
$121$	−3.77687e42	−0.758634
$122$	−6.88943e42	−1.16898
$123$	−9.35061e42	−1.34210
$124$	3.05621e42	0.371568
$125$	6.68471e42	0.689330
$126$	2.34330e43	2.05226
$127$	1.15659e43	0.861396	0.430698	−	0.902496i	$-0.358267\pi$
$127$	1.15659e43	0.861396	0.430698	+	0.902496i	$0.358267\pi$
$128$	1.39380e42	0.0883883
$129$	−3.90726e42	−0.211244
$130$	−2.15799e43	−0.995889
$131$	2.42843e43	0.957776	0.478888	−	0.877876i	$-0.341040\pi$
$131$	2.42843e43	0.957776	0.478888	+	0.877876i	$0.341040\pi$
$132$	−1.27536e43	−0.430396
$133$	−1.03831e43	−0.300171
$134$	5.54082e43	1.37381
$135$	−1.04994e44	−2.23524
$136$	−6.14655e42	−0.112482
$137$	−1.54500e43	−0.243308	−0.121654	−	0.992573i	$-0.538820\pi$
$137$	−1.54500e43	−0.243308	−0.121654	+	0.992573i	$0.538820\pi$
$138$	7.42210e43	1.00694
$139$	1.40766e44	1.64700	0.823501	−	0.567315i	$-0.192018\pi$
$139$	1.40766e44	1.64700	0.823501	+	0.567315i	$0.192018\pi$
$140$	−8.27631e43	−0.836011
$141$	−2.00644e44	−1.75160
$142$	−1.09858e44	−0.829696
$143$	−8.87189e43	−0.580266
$144$	9.12667e43	0.517465
$145$	4.15976e44	2.04656
$146$	−2.97222e44	−1.27013
$147$	4.55613e44	1.69274
$148$	5.11732e43	0.165454
$149$	1.57473e44	0.443493	0.221746	−	0.975104i	$-0.428824\pi$
$149$	1.57473e44	0.443493	0.221746	+	0.975104i	$0.428824\pi$
$150$	2.12884e44	0.522723
$151$	−2.82811e44	−0.605994	−0.302997	−	0.952992i	$-0.597987\pi$
$151$	−2.82811e44	−0.605994	−0.302997	+	0.952992i	$0.597987\pi$
$152$	−4.04401e43	−0.0756865
$153$	−4.02480e44	−0.658522
$154$	−3.40254e44	−0.487112
$155$	−7.06815e44	−0.886147
$156$	9.41613e44	1.03471
$157$	2.60906e44	0.251502	0.125751	−	0.992062i	$-0.459866\pi$
$157$	2.60906e44	0.251502	0.125751	+	0.992062i	$0.459866\pi$
$158$	−6.91486e44	−0.585212
$159$	−2.13174e45	−1.58523
$160$	−3.22346e44	−0.210796
$161$	1.98014e45	1.13964
$162$	1.69406e45	0.858757
$163$	−1.61270e45	−0.720621	−0.360310	−	0.932832i	$-0.617329\pi$
$163$	−1.61270e45	−0.720621	−0.360310	+	0.932832i	$0.617329\pi$
$164$	−9.71616e44	−0.382997
$165$	2.94955e45	1.02644
$166$	1.37126e45	0.421602
$167$	−1.22668e43	−0.00333459	−0.00166729	−	0.999999i	$-0.500531\pi$
$167$	−1.22668e43	−0.00333459	−0.00166729	+	0.999999i	$0.500531\pi$
$168$	3.61127e45	0.868599
$169$	1.85475e45	0.395011
$170$	1.42152e45	0.268257
$171$	−2.64804e45	−0.443103
$172$	−4.06001e44	−0.0602829
$173$	−6.97298e45	−0.919334	−0.459667	−	0.888091i	$-0.652031\pi$
$173$	−6.97298e45	−0.919334	−0.459667	+	0.888091i	$0.652031\pi$
$174$	−1.81506e46	−2.12634
$175$	5.67953e45	0.591606
$176$	−1.32522e45	−0.122823
$177$	5.37118e44	0.0443218
$178$	2.27351e45	0.167143
$179$	2.57092e46	1.68501	0.842504	−	0.538690i	$-0.181080\pi$
$179$	2.57092e46	1.68501	0.842504	+	0.538690i	$0.181080\pi$
$180$	−2.11074e46	−1.23409
$181$	1.71977e46	0.897553	0.448776	−	0.893644i	$-0.351860\pi$
$181$	1.71977e46	0.897553	0.448776	+	0.893644i	$0.351860\pi$
$182$	2.51213e46	1.17106
$183$	−6.95230e46	−2.89655
$184$	7.71226e45	0.287353
$185$	−1.18349e46	−0.394588
$186$	3.08410e46	0.920689
$187$	5.84413e45	0.156303
$188$	−2.08488e46	−0.499857
$189$	1.22225e47	2.62840
$190$	9.35264e45	0.180503
$191$	−2.15620e46	−0.373684	−0.186842	−	0.982390i	$-0.559825\pi$
$191$	−2.15620e46	−0.373684	−0.186842	+	0.982390i	$0.559825\pi$
$192$	1.40652e46	0.219013
$193$	2.03359e46	0.284668	0.142334	−	0.989819i	$-0.454539\pi$
$193$	2.03359e46	0.284668	0.142334	+	0.989819i	$0.454539\pi$
$194$	−8.80859e45	−0.110910
$195$	−2.17768e47	−2.46766
$196$	4.73424e46	0.483060
$197$	−1.48334e47	−1.36359	−0.681793	−	0.731545i	$-0.738800\pi$
$197$	−1.48334e47	−1.36359	−0.681793	+	0.731545i	$0.738800\pi$
$198$	−8.67763e46	−0.719059
$199$	−7.47977e46	−0.558985	−0.279493	−	0.960148i	$-0.590166\pi$
$199$	−7.47977e46	−0.558985	−0.279493	+	0.960148i	$0.590166\pi$
$200$	2.21206e46	0.149170
$201$	5.59139e47	3.40408
$202$	5.04842e46	0.277621
$203$	−4.84241e47	−2.40654
$204$	−6.20264e46	−0.278714
$205$	2.24707e47	0.913404
$206$	9.30254e46	0.342234
$207$	5.05004e47	1.68230
$208$	9.78424e46	0.295276
$209$	3.84504e46	0.105172
$210$	−8.35184e47	−2.07151
$211$	8.14889e47	1.83362	0.916808	−	0.399329i	$-0.130757\pi$
$211$	8.14889e47	1.83362	0.916808	+	0.399329i	$0.130757\pi$
$212$	−2.21508e47	−0.452380
$213$	−1.10860e48	−2.05586
$214$	5.82675e47	0.981622
$215$	9.38966e46	0.143768
$216$	4.76041e47	0.662738
$217$	8.22808e47	1.04201
$218$	−5.00571e47	−0.576909
$219$	−2.99935e48	−3.14719
$220$	3.06486e47	0.292918
$221$	−4.31479e47	−0.375766
$222$	5.16402e47	0.409970
$223$	−2.94601e45	−0.00213297	−0.00106648	−	0.999999i	$-0.500339\pi$
$223$	−2.94601e45	−0.00213297	−0.00106648	+	0.999999i	$0.500339\pi$
$224$	3.75245e47	0.247873
$225$	1.44847e48	0.873311
$226$	1.01475e48	0.558646
$227$	1.23961e48	0.623383	0.311691	−	0.950183i	$-0.399105\pi$
$227$	1.23961e48	0.623383	0.311691	+	0.950183i	$0.399105\pi$
$228$	−4.08091e47	−0.187539
$229$	2.51277e48	1.05567	0.527833	−	0.849348i	$-0.323005\pi$
$229$	2.51277e48	1.05567	0.527833	+	0.849348i	$0.323005\pi$
$230$	−1.78363e48	−0.685304
$231$	−3.43359e48	−1.20699
$232$	−1.88602e48	−0.606796
$233$	−3.44195e47	−0.101393	−0.0506966	−	0.998714i	$-0.516144\pi$
$233$	−3.44195e47	−0.101393	−0.0506966	+	0.998714i	$0.516144\pi$
$234$	6.40679e48	1.72868
$235$	4.82174e48	1.19210
$236$	5.58116e46	0.0126482
$237$	−6.97796e48	−1.45006
$238$	−1.65480e48	−0.315442
$239$	−1.24157e48	−0.217177	−0.108588	−	0.994087i	$-0.534633\pi$
$239$	−1.24157e48	−0.217177	−0.108588	+	0.994087i	$0.534633\pi$
$240$	−3.25287e48	−0.522320
$241$	8.53681e48	1.25877	0.629385	−	0.777094i	$-0.283307\pi$
$241$	8.53681e48	1.25877	0.629385	+	0.777094i	$0.283307\pi$
$242$	−3.96034e48	−0.536435
$243$	2.03549e48	0.253361
$244$	−7.22409e48	−0.826593
$245$	−1.09490e49	−1.15204
$246$	−9.80482e48	−0.949008
$247$	−2.83883e48	−0.252844
$248$	3.20467e48	0.262739
$249$	1.38377e49	1.04467
$250$	7.00942e48	0.487430
$251$	1.82523e49	1.16952	0.584759	−	0.811207i	$-0.301189\pi$
$251$	1.82523e49	1.16952	0.584759	+	0.811207i	$0.301189\pi$
$252$	2.45713e49	1.45116
$253$	−7.33281e48	−0.399300
$254$	1.21277e49	0.609099
$255$	1.43450e49	0.664700
$256$	1.46150e48	0.0625000
$257$	−3.84389e49	−1.51755	−0.758774	−	0.651354i	$-0.774201\pi$
$257$	−3.84389e49	−1.51755	−0.758774	+	0.651354i	$0.774201\pi$
$258$	−4.09706e48	−0.149372
$259$	1.37771e49	0.463994
$260$	−2.26282e49	−0.704200
$261$	−1.23498e50	−3.55246
$262$	2.54639e49	0.677250
$263$	5.88587e49	1.44783	0.723915	−	0.689889i	$-0.242341\pi$
$263$	5.88587e49	1.44783	0.723915	+	0.689889i	$0.242341\pi$
$264$	−1.33731e49	−0.304336
$265$	5.12285e49	1.07887
$266$	−1.08875e49	−0.212253
$267$	2.29426e49	0.414154
$268$	5.80997e49	0.971429
$269$	−6.22517e49	−0.964338	−0.482169	−	0.876078i	$-0.660151\pi$
$269$	−6.22517e49	−0.964338	−0.482169	+	0.876078i	$0.660151\pi$
$270$	−1.10095e50	−1.58055
$271$	−8.85718e49	−1.17876	−0.589380	−	0.807856i	$-0.700628\pi$
$271$	−8.85718e49	−1.17876	−0.589380	+	0.807856i	$0.700628\pi$
$272$	−6.44513e48	−0.0795369
$273$	2.53506e50	2.90170
$274$	−1.62005e49	−0.172045
$275$	−2.10323e49	−0.207284
$276$	7.78264e49	0.712017
$277$	−1.94293e50	−1.65053	−0.825264	−	0.564747i	$-0.808974\pi$
$277$	−1.94293e50	−1.65053	−0.825264	+	0.564747i	$0.808974\pi$
$278$	1.47604e50	1.16461
$279$	2.09844e50	1.53819
$280$	−8.67834e49	−0.591149
$281$	2.14728e50	1.35960	0.679798	−	0.733400i	$-0.262068\pi$
$281$	2.14728e50	1.35960	0.679798	+	0.733400i	$0.262068\pi$
$282$	−2.10391e50	−1.23857
$283$	−6.68644e49	−0.366078	−0.183039	−	0.983106i	$-0.558593\pi$
$283$	−6.68644e49	−0.366078	−0.183039	+	0.983106i	$0.558593\pi$
$284$	−1.15194e50	−0.586684
$285$	9.43799e49	0.447260
$286$	−9.30285e49	−0.410310
$287$	−2.61583e50	−1.07407
$288$	9.57001e49	0.365903
$289$	−2.52383e50	−0.898782
$290$	4.36183e50	1.44714
$291$	−8.88897e49	−0.274818
$292$	−3.11660e50	−0.898117
$293$	−2.93540e50	−0.788644	−0.394322	−	0.918972i	$-0.629021\pi$
$293$	−2.93540e50	−0.788644	−0.394322	+	0.918972i	$0.629021\pi$
$294$	4.77745e50	1.19695
$295$	−1.29076e49	−0.0301645
$296$	5.36590e49	0.116994
$297$	−4.52619e50	−0.920927
$298$	1.65122e50	0.313597
$299$	5.41389e50	0.959953
$300$	2.23225e50	0.369621
$301$	−1.09306e50	−0.169055
$302$	−2.96548e50	−0.428502
$303$	5.09449e50	0.687902
$304$	−4.24045e49	−0.0535184
$305$	1.67073e51	1.97133
$306$	−4.22031e50	−0.465645
$307$	−4.35932e50	−0.449864	−0.224932	−	0.974374i	$-0.572216\pi$
$307$	−4.35932e50	−0.449864	−0.224932	+	0.974374i	$0.572216\pi$
$308$	−3.56782e50	−0.344440
$309$	9.38743e50	0.848004
$310$	−7.41149e50	−0.626601
$311$	−2.38798e50	−0.188992	−0.0944958	−	0.995525i	$-0.530124\pi$
$311$	−2.38798e50	−0.188992	−0.0944958	+	0.995525i	$0.530124\pi$
$312$	9.87353e50	0.731650
$313$	−2.03212e51	−1.41023	−0.705117	−	0.709091i	$-0.749106\pi$
$313$	−2.03212e51	−1.41023	−0.705117	+	0.709091i	$0.749106\pi$
$314$	2.73580e50	0.177839
$315$	−5.68264e51	−3.46086
$316$	−7.25075e50	−0.413807
$317$	2.68276e51	1.43505	0.717525	−	0.696532i	$-0.245275\pi$
$317$	2.68276e51	1.43505	0.717525	+	0.696532i	$0.245275\pi$
$318$	−2.23529e51	−1.12093
$319$	1.79323e51	0.843191
$320$	−3.38004e50	−0.149055
$321$	5.87993e51	2.43231
$322$	2.07633e51	0.805845
$323$	1.87001e50	0.0681071
$324$	1.77635e51	0.607233
$325$	1.55283e51	0.498329
$326$	−1.69103e51	−0.509556
$327$	−5.05139e51	−1.42949
$328$	−1.01881e51	−0.270820
$329$	−5.61302e51	−1.40178
$330$	3.09283e51	0.725805
$331$	7.54395e51	1.66389	0.831945	−	0.554858i	$-0.187227\pi$
$331$	7.54395e51	1.66389	0.831945	+	0.554858i	$0.187227\pi$
$332$	1.43787e51	0.298118
$333$	3.51362e51	0.684934
$334$	−1.28626e49	−0.00235791
$335$	−1.34368e52	−2.31674
$336$	3.78669e51	0.614192
$337$	−5.36454e51	−0.818689	−0.409345	−	0.912380i	$-0.634243\pi$
$337$	−5.36454e51	−0.818689	−0.409345	+	0.912380i	$0.634243\pi$
$338$	1.94485e51	0.279315
$339$	1.02401e52	1.38424
$340$	1.49058e51	0.189686
$341$	−3.04700e51	−0.365096
$342$	−2.77667e51	−0.313321
$343$	−4.46968e50	−0.0475059
$344$	−4.25723e50	−0.0426264
$345$	−1.79990e52	−1.69808
$346$	−7.31170e51	−0.650068
$347$	−1.60783e51	−0.134737	−0.0673684	−	0.997728i	$-0.521460\pi$
$347$	−1.60783e51	−0.134737	−0.0673684	+	0.997728i	$0.521460\pi$
$348$	−1.90323e52	−1.50355
$349$	1.51169e52	1.12601	0.563004	−	0.826454i	$-0.309646\pi$
$349$	1.51169e52	1.12601	0.563004	+	0.826454i	$0.309646\pi$
$350$	5.95542e51	0.418329
$351$	3.34173e52	2.21399
$352$	−1.38959e51	−0.0868487
$353$	8.96540e51	0.528675	0.264337	−	0.964430i	$-0.414847\pi$
$353$	8.96540e51	0.528675	0.264337	+	0.964430i	$0.414847\pi$
$354$	5.63209e50	0.0313403
$355$	2.66411e52	1.39917
$356$	2.38395e51	0.118188
$357$	−1.66990e52	−0.781616
$358$	2.69581e52	1.19148
$359$	−2.57092e52	−1.07313	−0.536565	−	0.843859i	$-0.680278\pi$
$359$	−2.57092e52	−1.07313	−0.536565	+	0.843859i	$0.680278\pi$
$360$	−2.21327e52	−0.872637
$361$	−2.56168e52	−0.954172
$362$	1.80331e52	0.634666
$363$	−3.99648e52	−1.32920
$364$	2.63416e52	0.828064
$365$	7.20782e52	2.14191
$366$	−7.29001e52	−2.04817
$367$	4.37801e52	1.16311	0.581557	−	0.813506i	$-0.302444\pi$
$367$	4.37801e52	1.16311	0.581557	+	0.813506i	$0.302444\pi$
$368$	8.08689e51	0.203189
$369$	−6.67125e52	−1.58550
$370$	−1.24098e52	−0.279016
$371$	−5.96354e52	−1.26864
$372$	3.23391e52	0.651026
$373$	−3.46418e52	−0.660039	−0.330020	−	0.943974i	$-0.607055\pi$
$373$	−3.46418e52	−0.660039	−0.330020	+	0.943974i	$0.607055\pi$
$374$	6.12802e51	0.110523
$375$	7.07339e52	1.20778
$376$	−2.18616e52	−0.353452
$377$	−1.32396e53	−2.02710
$378$	1.28162e53	1.85856
$379$	3.98009e52	0.546750	0.273375	−	0.961908i	$-0.411860\pi$
$379$	3.98009e52	0.546750	0.273375	+	0.961908i	$0.411860\pi$
$380$	9.80695e51	0.127635
$381$	1.22384e53	1.50925
$382$	−2.26094e52	−0.264235
$383$	4.24383e52	0.470092	0.235046	−	0.971984i	$-0.424476\pi$
$383$	4.24383e52	0.470092	0.235046	+	0.971984i	$0.424476\pi$
$384$	1.47484e52	0.154865
$385$	8.25136e52	0.821449
$386$	2.13237e52	0.201290
$387$	−2.78766e52	−0.249555
$388$	−9.23647e51	−0.0784252
$389$	−1.66821e53	−1.34364	−0.671821	−	0.740713i	$-0.734488\pi$
$389$	−1.66821e53	−1.34364	−0.671821	+	0.740713i	$0.734488\pi$
$390$	−2.28347e53	−1.74490
$391$	−3.56627e52	−0.258577
$392$	4.96421e52	0.341575
$393$	2.56963e53	1.67812
$394$	−1.55539e53	−0.964201
$395$	1.67689e53	0.986882
$396$	−9.09915e52	−0.508452
$397$	−2.90239e53	−1.54010	−0.770052	−	0.637981i	$-0.779770\pi$
$397$	−2.90239e53	−1.54010	−0.770052	+	0.637981i	$0.779770\pi$
$398$	−7.84311e52	−0.395262
$399$	−1.09868e53	−0.525930
$400$	2.31952e52	0.105479
$401$	1.04436e53	0.451222	0.225611	−	0.974217i	$-0.427562\pi$
$401$	1.04436e53	0.451222	0.225611	+	0.974217i	$0.427562\pi$
$402$	5.86299e53	2.40705
$403$	2.24963e53	0.877723
$404$	5.29365e52	0.196308
$405$	−4.10819e53	−1.44818
$406$	−5.07763e53	−1.70168
$407$	−5.10189e52	−0.162572
$408$	−6.50394e52	−0.197080
$409$	2.12912e53	0.613581	0.306790	−	0.951777i	$-0.400745\pi$
$409$	2.12912e53	0.613581	0.306790	+	0.951777i	$0.400745\pi$
$410$	2.35623e53	0.645874
$411$	−1.63483e53	−0.426301
$412$	9.75442e52	0.241996
$413$	1.50259e52	0.0354702
$414$	5.29535e53	1.18956
$415$	−3.32538e53	−0.710976
$416$	1.02595e53	0.208792
$417$	1.48951e54	2.88571
$418$	4.03181e52	0.0743681
$419$	−8.36673e53	−1.46950	−0.734748	−	0.678340i	$-0.762700\pi$
$419$	−8.36673e53	−1.46950	−0.734748	+	0.678340i	$0.762700\pi$
$420$	−8.75754e53	−1.46478
$421$	1.14983e54	1.83169	0.915845	−	0.401533i	$-0.131522\pi$
$421$	1.14983e54	1.83169	0.915845	+	0.401533i	$0.131522\pi$
$422$	8.54473e53	1.29656
$423$	−1.43151e54	−2.06927
$424$	−2.32268e53	−0.319881
$425$	−1.02289e53	−0.134232
$426$	−1.16245e54	−1.45371
$427$	−1.94490e54	−2.31807
$428$	6.10979e53	0.694111
$429$	−9.38774e53	−1.01669
$430$	9.84577e52	0.101659
$431$	1.32392e54	1.30340	0.651701	−	0.758476i	$-0.274056\pi$
$431$	1.32392e54	1.30340	0.651701	+	0.758476i	$0.274056\pi$
$432$	4.99165e53	0.468627
$433$	−1.08006e54	−0.967046	−0.483523	−	0.875332i	$-0.660643\pi$
$433$	−1.08006e54	−0.967046	−0.483523	+	0.875332i	$0.660643\pi$
$434$	8.62776e53	0.736816
$435$	4.40163e54	3.58578
$436$	−5.24887e53	−0.407936
$437$	−2.34636e53	−0.173990
$438$	−3.14504e54	−2.22540
$439$	1.14481e53	0.0773059	0.0386529	−	0.999253i	$-0.487693\pi$
$439$	1.14481e53	0.0773059	0.0386529	+	0.999253i	$0.487693\pi$
$440$	3.21374e53	0.207124
$441$	3.25060e54	1.99973
$442$	−4.52438e53	−0.265707
$443$	−9.71784e53	−0.544870	−0.272435	−	0.962174i	$-0.587829\pi$
$443$	−9.71784e53	−0.544870	−0.272435	+	0.962174i	$0.587829\pi$
$444$	5.41486e53	0.289892
$445$	−5.51341e53	−0.281864
$446$	−3.08911e51	−0.00150823
$447$	1.66629e54	0.777045
$448$	3.93472e53	0.175273
$449$	−3.40657e54	−1.44966	−0.724832	−	0.688926i	$-0.758083\pi$
$449$	−3.40657e54	−1.44966	−0.724832	+	0.688926i	$0.758083\pi$
$450$	1.51883e54	0.617524
$451$	9.68686e53	0.376326
$452$	1.06404e54	0.395022
$453$	−2.99255e54	−1.06176
$454$	1.29982e54	0.440798
$455$	−6.09207e54	−1.97484
$456$	−4.27914e53	−0.132610
$457$	1.58378e54	0.469258	0.234629	−	0.972085i	$-0.424612\pi$
$457$	1.58378e54	0.469258	0.234629	+	0.972085i	$0.424612\pi$
$458$	2.63484e54	0.746468
$459$	−2.20128e54	−0.596370
$460$	−1.87027e54	−0.484583
$461$	−2.93741e53	−0.0727939	−0.0363970	−	0.999337i	$-0.511588\pi$
$461$	−2.93741e53	−0.0727939	−0.0363970	+	0.999337i	$0.511588\pi$
$462$	−3.60038e54	−0.853469
$463$	7.57194e54	1.71711	0.858553	−	0.512725i	$-0.171364\pi$
$463$	7.57194e54	1.71711	0.858553	+	0.512725i	$0.171364\pi$
$464$	−1.97763e54	−0.429069
$465$	−7.47913e54	−1.55262
$466$	−3.60915e53	−0.0716958
$467$	−2.70909e54	−0.515024	−0.257512	−	0.966275i	$-0.582903\pi$
$467$	−2.70909e54	−0.515024	−0.257512	+	0.966275i	$0.582903\pi$
$468$	6.71800e54	1.22236
$469$	1.56419e55	2.72424
$470$	5.05597e54	0.842943
$471$	2.76077e54	0.440657
$472$	5.85227e52	0.00894362
$473$	4.04777e53	0.0592328
$474$	−7.31692e54	−1.02535
$475$	−6.72992e53	−0.0903214
$476$	−1.73519e54	−0.223051
$477$	−1.52090e55	−1.87273
$478$	−1.30188e54	−0.153567
$479$	−7.24145e53	−0.0818366	−0.0409183	−	0.999162i	$-0.513028\pi$
$479$	−7.24145e53	−0.0818366	−0.0409183	+	0.999162i	$0.513028\pi$
$480$	−3.41088e54	−0.369336
$481$	3.76678e54	0.390837
$482$	8.95149e54	0.890084
$483$	2.09528e55	1.99676
$484$	−4.15271e54	−0.379317
$485$	2.13613e54	0.187035
$486$	2.13436e54	0.179153
$487$	3.33837e54	0.268653	0.134326	−	0.990937i	$-0.457113\pi$
$487$	3.33837e54	0.268653	0.134326	+	0.990937i	$0.457113\pi$
$488$	−7.57500e54	−0.584489
$489$	−1.70647e55	−1.26260
$490$	−1.14808e55	−0.814617
$491$	−1.88223e55	−1.28086	−0.640430	−	0.768016i	$-0.721244\pi$
$491$	−1.88223e55	−1.28086	−0.640430	+	0.768016i	$0.721244\pi$
$492$	−1.02811e55	−0.671050
$493$	8.72124e54	0.546030
$494$	−2.97673e54	−0.178787
$495$	2.10438e55	1.21260
$496$	3.36034e54	0.185784
$497$	−3.10131e55	−1.64528
$498$	1.45099e55	0.738690
$499$	−6.93745e54	−0.338953	−0.169476	−	0.985534i	$-0.554208\pi$
$499$	−6.93745e54	−0.338953	−0.169476	+	0.985534i	$0.554208\pi$
$500$	7.34991e54	0.344665
$501$	−1.29800e53	−0.00584254
$502$	1.91390e55	0.826974
$503$	2.98925e55	1.23999	0.619995	−	0.784606i	$-0.287135\pi$
$503$	2.98925e55	1.23999	0.619995	+	0.784606i	$0.287135\pi$
$504$	2.57648e55	1.02613
$505$	−1.22427e55	−0.468171
$506$	−7.68901e54	−0.282348
$507$	1.96260e55	0.692099
$508$	1.27168e55	0.430698
$509$	5.65842e55	1.84069	0.920345	−	0.391108i	$-0.127908\pi$
$509$	5.65842e55	1.84069	0.920345	+	0.391108i	$0.127908\pi$
$510$	1.50418e55	0.470014
$511$	−8.39067e55	−2.51865
$512$	1.53250e54	0.0441942
$513$	−1.44829e55	−0.401282
$514$	−4.03061e55	−1.07307
$515$	−2.25592e55	−0.577133
$516$	−4.29608e54	−0.105622
$517$	2.07860e55	0.491150
$518$	1.44463e55	0.328093
$519$	−7.37843e55	−1.61077
$520$	−2.37274e55	−0.497945
$521$	3.31572e55	0.668967	0.334483	−	0.942402i	$-0.391438\pi$
$521$	3.31572e55	0.668967	0.334483	+	0.942402i	$0.391438\pi$
$522$	−1.29497e56	−2.51197
$523$	7.77683e55	1.45050	0.725250	−	0.688486i	$-0.241724\pi$
$523$	7.77683e55	1.45050	0.725250	+	0.688486i	$0.241724\pi$
$524$	2.67009e55	0.478888
$525$	6.00977e55	1.03655
$526$	6.17178e55	1.02377
$527$	−1.48189e55	−0.236427
$528$	−1.40228e55	−0.215198
$529$	−2.29924e55	−0.339424
$530$	5.37169e55	0.762880
$531$	3.83210e54	0.0523600
$532$	−1.14163e55	−0.150085
$533$	−7.15191e55	−0.904721
$534$	2.40571e55	0.292851
$535$	−1.41302e56	−1.65538
$536$	6.09220e55	0.686904
$537$	2.72041e56	2.95231
$538$	−6.52756e55	−0.681890
$539$	−4.71997e55	−0.474646
$540$	−1.15443e56	−1.11762
$541$	8.91733e55	0.831172	0.415586	−	0.909554i	$-0.363577\pi$
$541$	8.91733e55	0.831172	0.415586	+	0.909554i	$0.363577\pi$
$542$	−9.28743e55	−0.833509
$543$	1.81977e56	1.57260
$544$	−6.75820e54	−0.0562411
$545$	1.21391e56	0.972881
$546$	2.65820e56	2.05182
$547$	−8.97461e55	−0.667230	−0.333615	−	0.942709i	$-0.608268\pi$
$547$	−8.97461e55	−0.667230	−0.333615	+	0.942709i	$0.608268\pi$
$548$	−1.69875e55	−0.121654
$549$	−4.96016e56	−3.42186
$550$	−2.20539e55	−0.146572
$551$	5.73797e55	0.367410
$552$	8.16069e55	0.503472
$553$	−1.95208e56	−1.16047
$554$	−2.03731e56	−1.16710
$555$	−1.25230e56	−0.691359
$556$	1.54774e56	0.823501
$557$	3.47843e55	0.178382	0.0891911	−	0.996015i	$-0.471572\pi$
$557$	3.47843e55	0.178382	0.0891911	+	0.996015i	$0.471572\pi$
$558$	2.20037e56	1.08766
$559$	−2.98851e55	−0.142401
$560$	−9.09990e55	−0.418006
$561$	6.18394e55	0.273859
$562$	2.25159e56	0.961379
$563$	2.29948e55	0.0946688	0.0473344	−	0.998879i	$-0.484927\pi$
$563$	2.29948e55	0.0946688	0.0473344	+	0.998879i	$0.484927\pi$
$564$	−2.20611e56	−0.875801
$565$	−2.46083e56	−0.942082
$566$	−7.01124e55	−0.258856
$567$	4.78237e56	1.70290
$568$	−1.20790e56	−0.414848
$569$	3.18790e56	1.05610	0.528048	−	0.849214i	$-0.322924\pi$
$569$	3.18790e56	1.05610	0.528048	+	0.849214i	$0.322924\pi$
$570$	9.89645e55	0.316260
$571$	1.16154e54	0.00358091	0.00179046	−	0.999998i	$-0.499430\pi$
$571$	1.16154e54	0.00358091	0.00179046	+	0.999998i	$0.499430\pi$
$572$	−9.75474e55	−0.290133
$573$	−2.28157e56	−0.654733
$574$	−2.74290e56	−0.759479
$575$	1.28345e56	0.342917
$576$	1.00349e56	0.258733
$577$	6.45847e56	1.60703	0.803517	−	0.595281i	$-0.202959\pi$
$577$	6.45847e56	1.60703	0.803517	+	0.595281i	$0.202959\pi$
$578$	−2.64643e56	−0.635535
$579$	2.15183e56	0.498767
$580$	4.57371e56	1.02328
$581$	3.87109e56	0.836032
$582$	−9.32076e55	−0.194326
$583$	2.20840e56	0.444500
$584$	−3.26800e56	−0.635065
$585$	−1.55368e57	−2.91519
$586$	−3.07799e56	−0.557656
$587$	−1.53676e56	−0.268859	−0.134430	−	0.990923i	$-0.542920\pi$
$587$	−1.53676e56	−0.268859	−0.134430	+	0.990923i	$0.542920\pi$
$588$	5.00952e56	0.846371
$589$	−9.74980e55	−0.159086
$590$	−1.35346e55	−0.0213295
$591$	−1.56959e57	−2.38914
$592$	5.62655e55	0.0827270
$593$	7.79761e56	1.10749	0.553746	−	0.832686i	$-0.313198\pi$
$593$	7.79761e56	1.10749	0.553746	+	0.832686i	$0.313198\pi$
$594$	−4.74605e56	−0.651194
$595$	4.01300e56	0.531950
$596$	1.73143e56	0.221746
$597$	−7.91468e56	−0.979399
$598$	5.67687e56	0.678789
$599$	−9.18440e56	−1.06121	−0.530605	−	0.847619i	$-0.678035\pi$
$599$	−9.18440e56	−1.06121	−0.530605	+	0.847619i	$0.678035\pi$
$600$	2.34068e56	0.261362
$601$	1.34315e57	1.44943	0.724714	−	0.689050i	$-0.241972\pi$
$601$	1.34315e57	1.44943	0.724714	+	0.689050i	$0.241972\pi$
$602$	−1.14615e56	−0.119540
$603$	3.98921e57	4.02145
$604$	−3.10954e56	−0.302997
$605$	9.60405e56	0.904626
$606$	5.34196e56	0.486420
$607$	−1.37250e56	−0.120821	−0.0604105	−	0.998174i	$-0.519241\pi$
$607$	−1.37250e56	−0.120821	−0.0604105	+	0.998174i	$0.519241\pi$
$608$	−4.44643e55	−0.0378432
$609$	−5.12397e57	−4.21650
$610$	1.75188e57	1.39394
$611$	−1.53465e57	−1.18077
$612$	−4.42532e56	−0.329261
$613$	−4.58982e56	−0.330260	−0.165130	−	0.986272i	$-0.552804\pi$
$613$	−4.58982e56	−0.330260	−0.165130	+	0.986272i	$0.552804\pi$
$614$	−4.57107e56	−0.318102
$615$	2.37773e57	1.60038
$616$	−3.74113e56	−0.243556
$617$	−4.69500e56	−0.295658	−0.147829	−	0.989013i	$-0.547229\pi$
$617$	−4.69500e56	−0.295658	−0.147829	+	0.989013i	$0.547229\pi$
$618$	9.84344e56	0.599630
$619$	−8.01009e56	−0.472040	−0.236020	−	0.971748i	$-0.575843\pi$
$619$	−8.01009e56	−0.472040	−0.236020	+	0.971748i	$0.575843\pi$
$620$	−7.77151e56	−0.443074
$621$	2.76202e57	1.52352
$622$	−2.50398e56	−0.133637
$623$	6.41819e56	0.331442
$624$	1.03531e57	0.517354
$625$	−2.57233e57	−1.24390
$626$	−2.13084e57	−0.997187
$627$	4.06861e56	0.184273
$628$	2.86870e56	0.125751
$629$	−2.48127e56	−0.105278
$630$	−5.95868e57	−2.44719
$631$	−1.26000e57	−0.500920	−0.250460	−	0.968127i	$-0.580582\pi$
$631$	−1.26000e57	−0.500920	−0.250460	+	0.968127i	$0.580582\pi$
$632$	−7.60297e56	−0.292606
$633$	8.62271e57	3.21268
$634$	2.81308e57	1.01473
$635$	−2.94104e57	−1.02716
$636$	−2.34387e57	−0.792617
$637$	3.48480e57	1.14109
$638$	1.88033e57	0.596226
$639$	−7.90939e57	−2.42871
$640$	−3.54423e56	−0.105398
$641$	4.29334e57	1.23653	0.618267	−	0.785968i	$-0.287835\pi$
$641$	4.29334e57	1.23653	0.618267	+	0.785968i	$0.287835\pi$
$642$	6.16555e57	1.71990
$643$	−3.66649e57	−0.990662	−0.495331	−	0.868704i	$-0.664953\pi$
$643$	−3.66649e57	−0.990662	−0.495331	+	0.868704i	$0.664953\pi$
$644$	2.17719e57	0.569818
$645$	9.93562e56	0.251896
$646$	1.96085e56	0.0481590
$647$	7.19666e56	0.171235	0.0856177	−	0.996328i	$-0.472714\pi$
$647$	7.19666e56	0.171235	0.0856177	+	0.996328i	$0.472714\pi$
$648$	1.86264e57	0.429378
$649$	−5.56433e55	−0.0124279
$650$	1.62827e57	0.352372
$651$	8.70650e57	1.82572
$652$	−1.77318e57	−0.360310
$653$	1.77671e56	0.0349862	0.0174931	−	0.999847i	$-0.494431\pi$
$653$	1.77671e56	0.0349862	0.0174931	+	0.999847i	$0.494431\pi$
$654$	−5.29677e57	−1.01080
$655$	−6.17515e57	−1.14209
$656$	−1.06830e57	−0.191499
$657$	−2.13990e58	−3.71796
$658$	−5.88568e57	−0.991210
$659$	5.94098e57	0.969855	0.484928	−	0.874554i	$-0.338846\pi$
$659$	5.94098e57	0.969855	0.484928	+	0.874554i	$0.338846\pi$
$660$	3.24307e57	0.513222
$661$	8.22733e57	1.26220	0.631101	−	0.775700i	$-0.282603\pi$
$661$	8.22733e57	1.26220	0.631101	+	0.775700i	$0.282603\pi$
$662$	7.91040e57	1.17655
$663$	−4.56567e57	−0.658381
$664$	1.50771e57	0.210801
$665$	2.64027e57	0.357936
$666$	3.68430e57	0.484321
$667$	−1.09428e58	−1.39492
$668$	−1.34874e55	−0.00166729
$669$	−3.11730e55	−0.00373717
$670$	−1.40895e58	−1.63819
$671$	7.20231e57	0.812194
$672$	3.97063e57	0.434300
$673$	3.40645e57	0.361404	0.180702	−	0.983538i	$-0.442163\pi$
$673$	3.40645e57	0.361404	0.180702	+	0.983538i	$0.442163\pi$
$674$	−5.62512e57	−0.578901
$675$	7.92213e57	0.790887
$676$	2.03932e57	0.197505
$677$	−3.42769e57	−0.322058	−0.161029	−	0.986950i	$-0.551481\pi$
$677$	−3.42769e57	−0.322058	−0.161029	+	0.986950i	$0.551481\pi$
$678$	1.07375e58	0.978805
$679$	−2.48669e57	−0.219933
$680$	1.56298e57	0.134129
$681$	1.31169e58	1.09223
$682$	−3.19501e57	−0.258162
$683$	8.22982e57	0.645306	0.322653	−	0.946517i	$-0.395425\pi$
$683$	8.22982e57	0.645306	0.322653	+	0.946517i	$0.395425\pi$
$684$	−2.91155e57	−0.221551
$685$	3.92872e57	0.290131
$686$	−4.68680e56	−0.0335917
$687$	2.65888e58	1.84963
$688$	−4.46403e56	−0.0301414
$689$	−1.63048e58	−1.06862
$690$	−1.88734e58	−1.20072
$691$	1.60618e58	0.991960	0.495980	−	0.868334i	$-0.334809\pi$
$691$	1.60618e58	0.991960	0.495980	+	0.868334i	$0.334809\pi$
$692$	−7.66688e57	−0.459667
$693$	−2.44972e58	−1.42589
$694$	−1.68593e57	−0.0952733
$695$	−3.57948e58	−1.96395
$696$	−1.99568e58	−1.06317
$697$	4.71115e57	0.243699
$698$	1.58512e58	0.796208
$699$	−3.64208e57	−0.177651
$700$	6.24471e57	0.295803
$701$	−3.61228e58	−1.66174	−0.830869	−	0.556468i	$-0.812156\pi$
$701$	−3.61228e58	−1.66174	−0.830869	+	0.556468i	$0.812156\pi$
$702$	3.50406e58	1.56553
$703$	−1.63251e57	−0.0708387
$704$	−1.45710e57	−0.0614113
$705$	5.10210e58	2.08868
$706$	9.40091e57	0.373829
$707$	1.42518e58	0.550519
$708$	5.90567e56	0.0221609
$709$	−2.71836e58	−0.990965	−0.495483	−	0.868618i	$-0.665009\pi$
$709$	−2.71836e58	−0.990965	−0.495483	+	0.868618i	$0.665009\pi$
$710$	2.79352e58	0.989364
$711$	−4.97847e58	−1.71305
$712$	2.49976e57	0.0835714
$713$	1.85937e58	0.603990
$714$	−1.75102e58	−0.552686
$715$	2.25600e58	0.691934
$716$	2.82676e58	0.842504
$717$	−1.31376e58	−0.380516
$718$	−2.69580e58	−0.758817
$719$	−1.95054e58	−0.533595	−0.266797	−	0.963753i	$-0.585965\pi$
$719$	−1.95054e58	−0.533595	−0.266797	+	0.963753i	$0.585965\pi$
$720$	−2.32078e58	−0.617047
$721$	2.62613e58	0.678647
$722$	−2.68611e58	−0.674702
$723$	9.03318e58	2.20549
$724$	1.89091e58	0.448776
$725$	−3.13866e58	−0.724127
$726$	−4.19061e58	−0.939889
$727$	6.41681e58	1.39915	0.699575	−	0.714560i	$-0.253373\pi$
$727$	6.41681e58	1.39915	0.699575	+	0.714560i	$0.253373\pi$
$728$	2.76212e58	0.585530
$729$	−3.73866e58	−0.770552
$730$	7.55795e58	1.51456
$731$	1.96861e57	0.0383577
$732$	−7.64413e58	−1.44827
$733$	1.98495e58	0.365695	0.182847	−	0.983141i	$-0.441469\pi$
$733$	1.98495e58	0.365695	0.182847	+	0.983141i	$0.441469\pi$
$734$	4.59067e58	0.822445
$735$	−1.15856e59	−2.01850
$736$	8.47972e57	0.143677
$737$	−5.79246e58	−0.954507
$738$	−6.99532e58	−1.12112
$739$	9.09593e58	1.41787	0.708934	−	0.705275i	$-0.249176\pi$
$739$	9.09593e58	1.41787	0.708934	+	0.705275i	$0.249176\pi$
$740$	−1.30126e58	−0.197294
$741$	−3.00389e58	−0.443008
$742$	−6.25322e58	−0.897065
$743$	−1.22229e59	−1.70570	−0.852849	−	0.522158i	$-0.825127\pi$
$743$	−1.22229e59	−1.70570	−0.852849	+	0.522158i	$0.825127\pi$
$744$	3.39100e58	0.460345
$745$	−4.00431e58	−0.528839
$746$	−3.63246e58	−0.466718
$747$	9.87260e58	1.23413
$748$	6.42569e57	0.0781515
$749$	1.64491e59	1.94654
$750$	7.41698e58	0.854027
$751$	−3.17979e57	−0.0356270	−0.0178135	−	0.999841i	$-0.505671\pi$
$751$	−3.17979e57	−0.0356270	−0.0178135	+	0.999841i	$0.505671\pi$
$752$	−2.29235e58	−0.249929
$753$	1.93136e59	2.04912
$754$	−1.38827e59	−1.43338
$755$	7.19147e58	0.722612
$756$	1.34387e59	1.31420
$757$	−5.74234e58	−0.546542	−0.273271	−	0.961937i	$-0.588106\pi$
$757$	−5.74234e58	−0.546542	−0.273271	+	0.961937i	$0.588106\pi$
$758$	4.17343e58	0.386611
$759$	−7.75917e58	−0.699615
$760$	1.02833e58	0.0902517
$761$	−1.47303e59	−1.25842	−0.629209	−	0.777236i	$-0.716621\pi$
$761$	−1.47303e59	−1.25842	−0.629209	+	0.777236i	$0.716621\pi$
$762$	1.28329e59	1.06720
$763$	−1.41313e59	−1.14400
$764$	−2.37077e58	−0.186842
$765$	1.02345e59	0.785249
$766$	4.44998e58	0.332405
$767$	4.10820e57	0.0298777
$768$	1.54648e58	0.109506
$769$	−1.33564e59	−0.920873	−0.460437	−	0.887693i	$-0.652307\pi$
$769$	−1.33564e59	−0.920873	−0.460437	+	0.887693i	$0.652307\pi$
$770$	8.65218e58	0.580852
$771$	−4.06740e59	−2.65890
$772$	2.23595e58	0.142334
$773$	2.25801e59	1.39974	0.699868	−	0.714272i	$-0.253242\pi$
$773$	2.25801e59	1.39974	0.699868	+	0.714272i	$0.253242\pi$
$774$	−2.92308e58	−0.176462
$775$	5.33312e58	0.313542
$776$	−9.68514e57	−0.0554550
$777$	1.45782e59	0.812965
$778$	−1.74924e59	−0.950099
$779$	3.09961e58	0.163979
$780$	−2.39439e59	−1.23383
$781$	1.14847e59	0.576464
$782$	−3.73950e58	−0.182842
$783$	−6.75446e59	−3.21717
$784$	5.20536e58	0.241530
$785$	−6.63448e58	−0.299902
$786$	2.69445e59	1.18661
$787$	3.77733e59	1.62070	0.810351	−	0.585945i	$-0.199277\pi$
$787$	3.77733e59	1.62070	0.810351	+	0.585945i	$0.199277\pi$
$788$	−1.63095e59	−0.681793
$789$	6.22810e59	2.53675
$790$	1.75835e59	0.697831
$791$	2.86467e59	1.10779
$792$	−9.54115e58	−0.359530
$793$	−5.31754e59	−1.95259
$794$	−3.04337e59	−1.08902
$795$	5.42071e59	1.89030
$796$	−8.22410e58	−0.279493
$797$	−1.32373e59	−0.438433	−0.219217	−	0.975676i	$-0.570350\pi$
$797$	−1.32373e59	−0.438433	−0.219217	+	0.975676i	$0.570350\pi$
$798$	−1.15205e59	−0.371888
$799$	1.01091e59	0.318057
$800$	2.43219e58	0.0745852
$801$	1.63686e59	0.489265
$802$	1.09509e59	0.319062
$803$	3.10721e59	0.882473
$804$	6.14779e59	1.70204
$805$	−5.03523e59	−1.35895
$806$	2.35891e59	0.620644
$807$	−6.58713e59	−1.68962
$808$	5.55079e58	0.138810
$809$	8.51729e58	0.207662	0.103831	−	0.994595i	$-0.466890\pi$
$809$	8.51729e58	0.207662	0.103831	+	0.994595i	$0.466890\pi$
$810$	−4.30775e59	−1.02402
$811$	−1.20156e59	−0.278496	−0.139248	−	0.990258i	$-0.544469\pi$
$811$	−1.20156e59	−0.278496	−0.139248	+	0.990258i	$0.544469\pi$
$812$	−5.32428e59	−1.20327
$813$	−9.37218e59	−2.06531
$814$	−5.34972e58	−0.114956
$815$	4.10086e59	0.859298
$816$	−6.81988e58	−0.139357
$817$	1.29521e58	0.0258100
$818$	2.23254e59	0.433867
$819$	1.80865e60	3.42796
$820$	2.47068e59	0.456702
$821$	−1.35794e59	−0.244820	−0.122410	−	0.992480i	$-0.539062\pi$
$821$	−1.35794e59	−0.244820	−0.122410	+	0.992480i	$0.539062\pi$
$822$	−1.71425e59	−0.301440
$823$	−8.83563e59	−1.51545	−0.757724	−	0.652575i	$-0.773689\pi$
$823$	−8.83563e59	−1.51545	−0.757724	+	0.652575i	$0.773689\pi$
$824$	1.02283e59	0.171117
$825$	−2.22552e59	−0.363183
$826$	1.57558e58	0.0250812
$827$	−2.24391e59	−0.348451	−0.174226	−	0.984706i	$-0.555742\pi$
$827$	−2.24391e59	−0.348451	−0.174226	+	0.984706i	$0.555742\pi$
$828$	5.55258e59	0.841148
$829$	−8.39406e58	−0.124052	−0.0620260	−	0.998075i	$-0.519756\pi$
$829$	−8.39406e58	−0.124052	−0.0620260	+	0.998075i	$0.519756\pi$
$830$	−3.48691e59	−0.502736
$831$	−2.05591e60	−2.89189
$832$	1.07579e59	0.147638
$833$	−2.29553e59	−0.307369
$834$	1.56186e60	2.04051
$835$	3.11926e57	0.00397630
$836$	4.22766e58	0.0525862
$837$	1.14770e60	1.39301
$838$	−8.77315e59	−1.03909
$839$	7.27294e59	0.840600	0.420300	−	0.907385i	$-0.361925\pi$
$839$	7.27294e59	0.840600	0.420300	+	0.907385i	$0.361925\pi$
$840$	−9.18295e59	−1.03575
$841$	1.76756e60	1.94561
$842$	1.20569e60	1.29520
$843$	2.27214e60	2.38215
$844$	8.95980e59	0.916808
$845$	−4.71638e59	−0.471027
$846$	−1.50105e60	−1.46319
$847$	−1.11801e60	−1.06374
$848$	−2.43550e59	−0.226190
$849$	−7.07522e59	−0.641405
$850$	−1.07258e59	−0.0949164
$851$	3.11332e59	0.268948
$852$	−1.21892e60	−1.02793
$853$	9.33512e58	0.0768537	0.0384269	−	0.999261i	$-0.487765\pi$
$853$	9.33512e58	0.0768537	0.0384269	+	0.999261i	$0.487765\pi$
$854$	−2.03938e60	−1.63912
$855$	6.73360e59	0.528374
$856$	6.40658e59	0.490811
$857$	−1.10562e60	−0.826990	−0.413495	−	0.910506i	$-0.635692\pi$
$857$	−1.10562e60	−0.826990	−0.413495	+	0.910506i	$0.635692\pi$
$858$	−9.84376e59	−0.718905
$859$	−6.75499e59	−0.481687	−0.240844	−	0.970564i	$-0.577424\pi$
$859$	−6.75499e59	−0.481687	−0.240844	+	0.970564i	$0.577424\pi$
$860$	1.03240e59	0.0718838
$861$	−2.76793e60	−1.88187
$862$	1.38823e60	0.921644
$863$	5.90285e59	0.382684	0.191342	−	0.981523i	$-0.438716\pi$
$863$	5.90285e59	0.382684	0.191342	+	0.981523i	$0.438716\pi$
$864$	5.23412e59	0.331369
$865$	1.77313e60	1.09625
$866$	−1.13253e60	−0.683805
$867$	−2.67058e60	−1.57476
$868$	9.04687e59	0.521007
$869$	7.22889e59	0.406599
$870$	4.61545e60	2.53553
$871$	4.27663e60	2.29472
$872$	−5.50384e59	−0.288455
$873$	−6.34190e59	−0.324659
$874$	−2.46033e59	−0.123030
$875$	1.97878e60	0.966567
$876$	−3.29782e60	−1.57359
$877$	−2.63402e60	−1.22780	−0.613900	−	0.789384i	$-0.710400\pi$
$877$	−2.63402e60	−1.22780	−0.613900	+	0.789384i	$0.710400\pi$
$878$	1.20042e59	0.0546635
$879$	−3.10608e60	−1.38179
$880$	3.36985e59	0.146459
$881$	1.68258e60	0.714445	0.357223	−	0.934019i	$-0.383724\pi$
$881$	1.68258e60	0.714445	0.357223	+	0.934019i	$0.383724\pi$
$882$	3.40850e60	1.41403
$883$	2.43606e60	0.987400	0.493700	−	0.869632i	$-0.335644\pi$
$883$	2.43606e60	0.987400	0.493700	+	0.869632i	$0.335644\pi$
$884$	−4.74416e59	−0.187883
$885$	−1.36582e59	−0.0528512
$886$	−1.01899e60	−0.385282
$887$	−2.73192e60	−1.00933	−0.504666	−	0.863315i	$-0.668384\pi$
$887$	−2.73192e60	−1.00933	−0.504666	+	0.863315i	$0.668384\pi$
$888$	5.67790e59	0.204985
$889$	3.42369e60	1.20784
$890$	−5.78123e59	−0.199308
$891$	−1.77099e60	−0.596655
$892$	−3.23917e57	−0.00106648
$893$	6.65111e59	0.214012
$894$	1.74723e60	0.549454
$895$	−6.53750e60	−2.00927
$896$	4.12586e59	0.123937
$897$	5.72868e60	1.68194
$898$	−3.57205e60	−1.02507
$899$	−4.54705e60	−1.27543
$900$	1.59261e60	0.436655
$901$	1.07404e60	0.287848
$902$	1.01574e60	0.266103
$903$	−1.15661e60	−0.296202
$904$	1.11573e60	0.279323
$905$	−4.37314e60	−1.07028
$906$	−3.13791e60	−0.750780
$907$	−9.66132e59	−0.225989	−0.112994	−	0.993596i	$-0.536044\pi$
$907$	−9.66132e59	−0.225989	−0.112994	+	0.993596i	$0.536044\pi$
$908$	1.36296e60	0.311691
$909$	3.63469e60	0.812659
$910$	−6.38799e60	−1.39642
$911$	−3.27643e60	−0.700284	−0.350142	−	0.936697i	$-0.613867\pi$
$911$	−3.27643e60	−0.700284	−0.350142	+	0.936697i	$0.613867\pi$
$912$	−4.48701e59	−0.0937697
$913$	−1.43353e60	−0.292925
$914$	1.66071e60	0.331815
$915$	1.76787e61	3.45397
$916$	2.76283e60	0.527833
$917$	7.18853e60	1.34298
$918$	−2.30821e60	−0.421697
$919$	2.29076e60	0.409271	0.204636	−	0.978838i	$-0.434399\pi$
$919$	2.29076e60	0.409271	0.204636	+	0.978838i	$0.434399\pi$
$920$	−1.96112e60	−0.342652
$921$	−4.61279e60	−0.788208
$922$	−3.08009e59	−0.0514731
$923$	−8.47926e60	−1.38587
$924$	−3.77527e60	−0.603494
$925$	8.92977e59	0.139616
$926$	7.93976e60	1.21418
$927$	6.69753e60	1.00180
$928$	−2.07370e60	−0.303398
$929$	6.62994e60	0.948828	0.474414	−	0.880302i	$-0.342660\pi$
$929$	6.62994e60	0.948828	0.474414	+	0.880302i	$0.342660\pi$
$930$	−7.84243e60	−1.09787
$931$	−1.51030e60	−0.206821
$932$	−3.78447e59	−0.0506966
$933$	−2.52683e60	−0.331133
$934$	−2.84069e60	−0.364177
$935$	−1.48608e60	−0.186382
$936$	7.04434e60	0.864341
$937$	−2.63986e60	−0.316898	−0.158449	−	0.987367i	$-0.550649\pi$
$937$	−2.63986e60	−0.316898	−0.158449	+	0.987367i	$0.550649\pi$
$938$	1.64017e61	1.92633
$939$	−2.15028e61	−2.47088
$940$	5.30156e60	0.596050
$941$	1.40617e61	1.54685	0.773427	−	0.633885i	$-0.218541\pi$
$941$	1.40617e61	1.54685	0.773427	+	0.633885i	$0.218541\pi$
$942$	2.89487e60	0.311592
$943$	−5.91121e60	−0.622568
$944$	6.13655e58	0.00632409
$945$	−3.10800e61	−3.13422
$946$	4.24439e59	0.0418839
$947$	1.18800e61	1.14721	0.573606	−	0.819131i	$-0.305544\pi$
$947$	1.18800e61	1.14721	0.573606	+	0.819131i	$0.305544\pi$
$948$	−7.67235e60	−0.725032
$949$	−2.29408e61	−2.12154
$950$	−7.05683e59	−0.0638669
$951$	2.83875e61	2.51436
$952$	−1.81948e60	−0.157721
$953$	−1.12712e61	−0.956235	−0.478117	−	0.878296i	$-0.658681\pi$
$953$	−1.12712e61	−0.956235	−0.478117	+	0.878296i	$0.658681\pi$
$954$	−1.59478e61	−1.32422
$955$	5.48291e60	0.445597
$956$	−1.36512e60	−0.108588
$957$	1.89749e61	1.47736
$958$	−7.59321e59	−0.0578672
$959$	−4.57345e60	−0.341163
$960$	−3.57657e60	−0.261160
$961$	−6.26416e60	−0.447748
$962$	3.94975e60	0.276364
$963$	4.19507e61	2.87343
$964$	9.38632e60	0.629385
$965$	−5.17113e60	−0.339450
$966$	2.19706e61	1.41192
$967$	−6.94733e60	−0.437095	−0.218547	−	0.975826i	$-0.570132\pi$
$967$	−6.94733e60	−0.437095	−0.218547	+	0.975826i	$0.570132\pi$
$968$	−4.35444e60	−0.268217
$969$	1.97874e60	0.119331
$970$	2.23990e60	0.132254
$971$	−2.12424e61	−1.22803	−0.614016	−	0.789294i	$-0.710447\pi$
$971$	−2.12424e61	−1.22803	−0.614016	+	0.789294i	$0.710447\pi$
$972$	2.23804e60	0.126680
$973$	4.16689e61	2.30940
$974$	3.50054e60	0.189966
$975$	1.64312e61	0.873124
$976$	−7.94297e60	−0.413296
$977$	−2.72440e61	−1.38814	−0.694068	−	0.719909i	$-0.744183\pi$
$977$	−2.72440e61	−1.38814	−0.694068	+	0.719909i	$0.744183\pi$
$978$	−1.78936e61	−0.892794
$979$	−2.37676e60	−0.116129
$980$	−1.20385e61	−0.576021
$981$	−3.60395e61	−1.68874
$982$	−1.97366e61	−0.905705
$983$	−6.88350e60	−0.309359	−0.154679	−	0.987965i	$-0.549434\pi$
$983$	−6.88350e60	−0.309359	−0.154679	+	0.987965i	$0.549434\pi$
$984$	−1.07805e61	−0.474504
$985$	3.77192e61	1.62600
$986$	9.14488e60	0.386101
$987$	−5.93939e61	−2.45607
$988$	−3.12133e60	−0.126422
$989$	−2.47007e60	−0.0979908
$990$	2.20660e61	0.857436
$991$	−1.65448e60	−0.0629727	−0.0314864	−	0.999504i	$-0.510024\pi$
$991$	−1.65448e60	−0.0629727	−0.0314864	+	0.999504i	$0.510024\pi$
$992$	3.52357e60	0.131369
$993$	7.98259e61	2.91531
$994$	−3.25196e61	−1.16339
$995$	1.90200e61	0.666557
$996$	1.52147e61	0.522333
$997$	3.62868e60	0.122039	0.0610193	−	0.998137i	$-0.480565\pi$
$997$	3.62868e60	0.122039	0.0610193	+	0.998137i	$0.480565\pi$
$998$	−7.27445e60	−0.239676
$999$	1.92170e61	0.620289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.42.a.b.1.2	✓	2
3.2	odd	2		18.42.a.c.1.2		2
4.3	odd	2		16.42.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.42.a.b.1.2	✓	2	1.1	even	1	trivial
16.42.a.b.1.1		2	4.3	odd	2
18.42.a.c.1.2		2	3.2	odd	2

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:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q+1.04858e6 q^{2} +1.05814e10 q^{3} +1.09951e12 q^{4} -2.54286e14 q^{5} +1.10955e16 q^{6} +2.96016e17 q^{7} +1.15292e18 q^{8} +7.54941e19 q^{9} +O(q^{10})\)	\(q+1.04858e6 q^{2} +1.05814e10 q^{3} +1.09951e12 q^{4} -2.54286e14 q^{5} +1.10955e16 q^{6} +2.96016e17 q^{7} +1.15292e18 q^{8} +7.54941e19 q^{9} -2.66638e20 q^{10} -1.09620e21 q^{11} +1.16344e22 q^{12} +8.09333e22 q^{13} +3.10395e23 q^{14} -2.69071e24 q^{15} +1.20893e24 q^{16} -5.33128e24 q^{17} +7.91613e25 q^{18} -3.50762e25 q^{19} -2.79590e26 q^{20} +3.13228e27 q^{21} -1.14945e27 q^{22} +6.68932e27 q^{23} +1.21996e28 q^{24} +1.91866e28 q^{25} +8.48648e28 q^{26} +4.12899e29 q^{27} +3.25473e29 q^{28} -1.63586e30 q^{29} -2.82142e30 q^{30} +2.77961e30 q^{31} +1.26765e30 q^{32} -1.15993e31 q^{33} -5.59026e30 q^{34} -7.52726e31 q^{35} +8.30066e31 q^{36} +4.65417e31 q^{37} -3.67800e31 q^{38} +8.56392e32 q^{39} -2.93172e32 q^{40} -8.83679e32 q^{41} +3.28443e33 q^{42} -3.69256e32 q^{43} -1.20528e33 q^{44} -1.91971e34 q^{45} +7.01426e33 q^{46} -1.89619e34 q^{47} +1.27922e34 q^{48} +4.30577e34 q^{49} +2.01186e34 q^{50} -5.64127e34 q^{51} +8.89872e34 q^{52} -2.01460e35 q^{53} +4.32956e35 q^{54} +2.78747e35 q^{55} +3.41283e35 q^{56} -3.71157e35 q^{57} -1.71532e36 q^{58} +5.07603e34 q^{59} -2.95847e36 q^{60} -6.57027e36 q^{61} +2.91463e36 q^{62} +2.23474e37 q^{63} +1.32923e36 q^{64} -2.05802e37 q^{65} -1.21628e37 q^{66} +5.28414e37 q^{67} -5.86181e36 q^{68} +7.07827e37 q^{69} -7.89291e37 q^{70} -1.04768e38 q^{71} +8.70387e37 q^{72} -2.83453e38 q^{73} +4.88025e37 q^{74} +2.03022e38 q^{75} -3.85666e37 q^{76} -3.24491e38 q^{77} +8.97992e38 q^{78} -6.59452e38 q^{79} -3.07413e38 q^{80} +1.61558e39 q^{81} -9.26605e38 q^{82} +1.30773e39 q^{83} +3.44397e39 q^{84} +1.35567e39 q^{85} -3.87193e38 q^{86} -1.73098e40 q^{87} -1.26383e39 q^{88} +2.16819e39 q^{89} -2.01296e40 q^{90} +2.39575e40 q^{91} +7.35498e39 q^{92} +2.94123e40 q^{93} -1.98830e40 q^{94} +8.91937e39 q^{95} +1.34136e40 q^{96} -8.40052e39 q^{97} +4.51493e40 q^{98} -8.27563e40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2097152 q^{2} + 8863347528 q^{3} + 2199023255552 q^{4} + 97599184325580 q^{5} + 92\!\cdots\!28 q^{6}+ \cdots + 41\!\cdots\!86 q^{9}+O(q^{10}) \) 2 * q + 2097152 * q^2 + 8863347528 * q^3 + 2199023255552 * q^4 + 97599184325580 * q^5 + 9293893497520128 * q^6 + 217106802373088656 * q^7 + 2305843009213693952 * q^8 + 41972929616872509786 * q^9	\( 2 q + 2097152 q^{2} + 8863347528 q^{3} + 2199023255552 q^{4} + 97599184325580 q^{5} + 92\!\cdots\!28 q^{6}+ \cdots - 12\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 2097152 * q^2 + 8863347528 * q^3 + 2199023255552 * q^4 + 97599184325580 * q^5 + 9293893497520128 * q^6 + 217106802373088656 * q^7 + 2305843009213693952 * q^8 + 41972929616872509786 * q^9 + 102340162303379374080 * q^10 + 110594481484939565784 * q^11 + 9745353668055665737728 * q^12 + 173293106838448696895068 * q^13 + 227652982405163810553856 * q^14 - 3295287287252802285241680 * q^15 + 2417851639229258349412352 * q^16 - 10287966260741677078429404 * q^17 + 44011806645941708821364736 * q^18 + 206254882139859790701457000 * q^19 + 107311438027428330555310080 * q^20 + 3267849131609686416057835584 * q^21 + 115966719017551990131523584 * q^22 + 14925421378885128304361915568 * q^23 + 10218743967835137756603875328 * q^24 + 97534966241249753807444705150 * q^25 + 181710992796233180795442823168 * q^26 + 533156288863055843864697754320 * q^27 + 238711453678477047815320109056 * q^28 - 1375143011941884388614889894020 * q^29 - 3455359162518394409049579847680 * q^30 - 3626496922711160469799126663616 * q^31 + 2535301200456458802993406410752 * q^32 - 13672735988327258412044854187424 * q^33 - 10787714509823464784191190728704 * q^34 - 103039524095905042910481769779360 * q^35 + 46149724165574973269071349415936 * q^36 + 120356679589378915210866994599436 * q^37 + 216273919294685619894570975232000 * q^38 + 697708668559917206762862430490352 * q^39 + 112524198441048689140364822446080 * q^40 + 1270177139906840106861139346878164 * q^41 + 3426588171026758543404261005328384 * q^42 - 6045433421160616098770468790853352 * q^43 + 121599918360548595604152473616384 * q^44 - 30992658299909156185379775337031460 * q^45 + 15650438647785852296874599978631168 * q^46 - 25416478966330542868882280891861664 * q^47 + 10715129674816697408268665175932928 * q^48 + 4716677344275473650585885334355954 * q^49 + 102272824761384701848395139147366400 * q^50 - 47896619495707425086522465903395056 * q^51 + 190537785982303003785762253746208768 * q^52 - 301376484284740318156836692232048852 * q^53 + 559054888750867644536269312433848320 * q^54 + 703399094180619772764269188861842960 * q^55 + 250307101252362748889997098673504256 * q^56 - 785787658029123941344672503009410400 * q^57 - 1441941958889973364676246785511915520 * q^58 - 3282010250697938085995473868454788040 * q^59 - 3623206689196887935863572238360903680 * q^60 - 4485157745840460017677520841591879236 * q^61 - 3802657637228777800780089040427810816 * q^62 + 24992547810032633572829803615671997008 * q^63 + 2658455991569831745807614120560689152 * q^64 + 11919812053150705903267451825832510120 * q^65 - 14336902811696243316668345024432308224 * q^66 + 55055736076082381526441630307313037256 * q^67 - 11311738529852649409548062009541525504 * q^68 + 56632222305135551516324020091548201152 * q^69 - 108044772018387726274901332228162191360 * q^70 - 48857884738531480102553331099997138416 * q^71 + 48391493166641943170589759285164507136 * q^72 - 485616958845162818165813572349849688812 * q^73 + 126203125657112585396150069729098203136 * q^74 + 68411444542067712502035991381122300600 * q^75 + 226779641198344268566569654924869632000 * q^76 - 419718086944271580508987308621981603648 * q^77 + 731600564843883744998575235913851338752 * q^78 - 905766854341990828970937020702446890080 * q^79 + 117990173904521070264047184061220782080 * q^80 + 2631580786121491108655810678136598411122 * q^81 + 1331877264654954771892026051792117694464 * q^82 + 1271755206567258248006583231290595969768 * q^83 + 3593038118022554366408666387923215581184 * q^84 - 388512546938141834318136915482004571560 * q^85 - 6339096395026914186384343082837844426752 * q^86 - 17757719150026706057484126704955838888080 * q^87 + 127506755994830604184219784174773469184 * q^88 + 2692414558304473820098690391828757436980 * q^89 - 32498157669485543356240783303803100200960 * q^90 + 16669534332125295311104493248216990683104 * q^91 + 16410674355540697858047580547193155616768 * q^92 + 40418607330508619745600934617627243192576 * q^93 - 26651109848599015319281106568464736190464 * q^94 + 93840167647611953736551449995129877215600 * q^95 + 11235627813900593301572723855519045910528 * q^96 - 31989468315501178009691057062669320691004 * q^97 + 4945794662950999058636745300357628821504 * q^98 - 123209315561064920195916977740234432814088 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more