LMFDB - Embedded newform 1.36.a.a.1.2

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			1.2
Root			$-3412.77$ 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)

$f(q)$	$=$	$q-26808.0 q^{2} +3.95729e8 q^{3} -3.36411e10 q^{4} +8.21401e11 q^{5} -1.06087e13 q^{6} +6.06942e14 q^{7} +1.82297e15 q^{8} +1.06570e17 q^{9} +O(q^{10})$	\(q-26808.0 q^{2} +3.95729e8 q^{3} -3.36411e10 q^{4} +8.21401e11 q^{5} -1.06087e13 q^{6} +6.06942e14 q^{7} +1.82297e15 q^{8} +1.06570e17 q^{9} -2.20201e16 q^{10} +1.23316e18 q^{11} -1.33127e19 q^{12} -8.46079e17 q^{13} -1.62709e19 q^{14} +3.25052e20 q^{15} +1.10703e21 q^{16} -3.92226e21 q^{17} -2.85692e21 q^{18} -3.52757e20 q^{19} -2.76328e22 q^{20} +2.40184e23 q^{21} -3.30584e22 q^{22} -8.58137e23 q^{23} +7.21400e23 q^{24} -2.23568e24 q^{25} +2.26817e22 q^{26} +2.23738e25 q^{27} -2.04182e25 q^{28} -1.38664e25 q^{29} -8.71400e24 q^{30} -3.33324e25 q^{31} -9.23139e25 q^{32} +4.87995e26 q^{33} +1.05148e26 q^{34} +4.98543e26 q^{35} -3.58512e27 q^{36} +1.99674e27 q^{37} +9.45671e24 q^{38} -3.34818e26 q^{39} +1.49739e27 q^{40} +2.10955e28 q^{41} -6.43887e27 q^{42} -4.57475e28 q^{43} -4.14847e28 q^{44} +8.75365e28 q^{45} +2.30049e28 q^{46} -1.72608e29 q^{47} +4.38083e29 q^{48} -1.04400e28 q^{49} +5.99342e28 q^{50} -1.55215e30 q^{51} +2.84630e28 q^{52} +1.81145e30 q^{53} -5.99797e29 q^{54} +1.01292e30 q^{55} +1.10643e30 q^{56} -1.39596e29 q^{57} +3.71730e29 q^{58} -5.02395e30 q^{59} -1.09351e31 q^{60} -3.25742e29 q^{61} +8.93574e29 q^{62} +6.46817e31 q^{63} -3.55625e31 q^{64} -6.94970e29 q^{65} -1.30822e31 q^{66} -4.01253e31 q^{67} +1.31949e32 q^{68} -3.39589e32 q^{69} -1.33649e31 q^{70} +3.85444e32 q^{71} +1.94273e32 q^{72} +9.93637e31 q^{73} -5.35285e31 q^{74} -8.84724e32 q^{75} +1.18671e31 q^{76} +7.48454e32 q^{77} +8.97580e30 q^{78} -2.62804e33 q^{79} +9.09314e32 q^{80} +3.52211e33 q^{81} -5.65527e32 q^{82} +6.17326e33 q^{83} -8.08006e33 q^{84} -3.22175e33 q^{85} +1.22640e33 q^{86} -5.48733e33 q^{87} +2.24800e33 q^{88} +6.75031e33 q^{89} -2.34668e33 q^{90} -5.13521e32 q^{91} +2.88686e34 q^{92} -1.31906e34 q^{93} +4.62727e33 q^{94} -2.89755e32 q^{95} -3.65313e34 q^{96} -8.10218e34 q^{97} +2.79875e32 q^{98} +1.31417e35 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−26808.0	−0.144624	−0.0723119	−	0.997382i	$-0.523038\pi$
$2$	−26808.0	−0.144624	−0.0723119	+	0.997382i	$0.523038\pi$
$3$	3.95729e8	1.76920	0.884598	−	0.466355i	$-0.154433\pi$
$3$	3.95729e8	1.76920	0.884598	+	0.466355i	$0.154433\pi$
$4$	−3.36411e10	−0.979084
$5$	8.21401e11	0.481482	0.240741	−	0.970589i	$-0.422610\pi$
$5$	8.21401e11	0.481482	0.240741	+	0.970589i	$0.422610\pi$
$6$	−1.06087e13	−0.255868
$7$	6.06942e14	0.986124	0.493062	−	0.869994i	$-0.335878\pi$
$7$	6.06942e14	0.986124	0.493062	+	0.869994i	$0.335878\pi$
$8$	1.82297e15	0.286223
$9$	1.06570e17	2.13005
$10$	−2.20201e16	−0.0696337
$11$	1.23316e18	0.735607	0.367804	−	0.929904i	$-0.380110\pi$
$11$	1.23316e18	0.735607	0.367804	+	0.929904i	$0.380110\pi$
$12$	−1.33127e19	−1.73219
$13$	−8.46079e17	−0.0271270	−0.0135635	−	0.999908i	$-0.504318\pi$
$13$	−8.46079e17	−0.0271270	−0.0135635	+	0.999908i	$0.504318\pi$
$14$	−1.62709e19	−0.142617
$15$	3.25052e20	0.851836
$16$	1.10703e21	0.937689
$17$	−3.92226e21	−1.14995	−0.574976	−	0.818170i	$-0.694989\pi$
$17$	−3.92226e21	−1.14995	−0.574976	+	0.818170i	$0.694989\pi$
$18$	−2.85692e21	−0.308056
$19$	−3.52757e20	−0.0147668	−0.00738342	−	0.999973i	$-0.502350\pi$
$19$	−3.52757e20	−0.0147668	−0.00738342	+	0.999973i	$0.502350\pi$
$20$	−2.76328e22	−0.471411
$21$	2.40184e23	1.74465
$22$	−3.30584e22	−0.106386
$23$	−8.58137e23	−1.26858	−0.634292	−	0.773093i	$-0.718708\pi$
$23$	−8.58137e23	−1.26858	−0.634292	+	0.773093i	$0.718708\pi$
$24$	7.21400e23	0.506384
$25$	−2.23568e24	−0.768175
$26$	2.26817e22	0.00392321
$27$	2.23738e25	1.99928
$28$	−2.04182e25	−0.965498
$29$	−1.38664e25	−0.354812	−0.177406	−	0.984138i	$-0.556771\pi$
$29$	−1.38664e25	−0.354812	−0.177406	+	0.984138i	$0.556771\pi$
$30$	−8.71400e24	−0.123196
$31$	−3.33324e25	−0.265483	−0.132741	−	0.991151i	$-0.542378\pi$
$31$	−3.33324e25	−0.265483	−0.132741	+	0.991151i	$0.542378\pi$
$32$	−9.23139e25	−0.421835
$33$	4.87995e26	1.30143
$34$	1.05148e26	0.166310
$35$	4.98543e26	0.474801
$36$	−3.58512e27	−2.08550
$37$	1.99674e27	0.719102	0.359551	−	0.933125i	$-0.382930\pi$
$37$	1.99674e27	0.719102	0.359551	+	0.933125i	$0.382930\pi$
$38$	9.45671e24	0.00213563
$39$	−3.34818e26	−0.0479930
$40$	1.49739e27	0.137811
$41$	2.10955e28	1.26029	0.630146	−	0.776476i	$-0.282995\pi$
$41$	2.10955e28	1.26029	0.630146	+	0.776476i	$0.282995\pi$
$42$	−6.43887e27	−0.252317
$43$	−4.57475e28	−1.18760	−0.593799	−	0.804614i	$-0.702372\pi$
$43$	−4.57475e28	−1.18760	−0.593799	+	0.804614i	$0.702372\pi$
$44$	−4.14847e28	−0.720221
$45$	8.75365e28	1.02558
$46$	2.30049e28	0.183467
$47$	−1.72608e29	−0.944816	−0.472408	−	0.881380i	$-0.656615\pi$
$47$	−1.72608e29	−0.944816	−0.472408	+	0.881380i	$0.656615\pi$
$48$	4.38083e29	1.65896
$49$	−1.04400e28	−0.0275593
$50$	5.99342e28	0.111096
$51$	−1.55215e30	−2.03449
$52$	2.84630e28	0.0265596
$53$	1.81145e30	1.21115	0.605577	−	0.795786i	$-0.292942\pi$
$53$	1.81145e30	1.21115	0.605577	+	0.795786i	$0.292942\pi$
$54$	−5.99797e29	−0.289144
$55$	1.01292e30	0.354182
$56$	1.10643e30	0.282251
$57$	−1.39596e29	−0.0261254
$58$	3.71730e29	0.0513143
$59$	−5.02395e30	−0.514204	−0.257102	−	0.966384i	$-0.582768\pi$
$59$	−5.02395e30	−0.514204	−0.257102	+	0.966384i	$0.582768\pi$
$60$	−1.09351e31	−0.834019
$61$	−3.25742e29	−0.0186038	−0.00930189	−	0.999957i	$-0.502961\pi$
$61$	−3.25742e29	−0.0186038	−0.00930189	+	0.999957i	$0.502961\pi$
$62$	8.93574e29	0.0383951
$63$	6.46817e31	2.10050
$64$	−3.55625e31	−0.876682
$65$	−6.94970e29	−0.0130612
$66$	−1.30822e31	−0.188218
$67$	−4.01253e31	−0.443720	−0.221860	−	0.975079i	$-0.571213\pi$
$67$	−4.01253e31	−0.443720	−0.221860	+	0.975079i	$0.571213\pi$
$68$	1.31949e32	1.12590
$69$	−3.39589e32	−2.24437
$70$	−1.33649e31	−0.0686675
$71$	3.85444e32	1.54504	0.772520	−	0.634990i	$-0.218996\pi$
$71$	3.85444e32	1.54504	0.772520	+	0.634990i	$0.218996\pi$
$72$	1.94273e32	0.609669
$73$	9.93637e31	0.244950	0.122475	−	0.992472i	$-0.460917\pi$
$73$	9.93637e31	0.244950	0.122475	+	0.992472i	$0.460917\pi$
$74$	−5.35285e31	−0.103999
$75$	−8.84724e32	−1.35905
$76$	1.18671e31	0.0144580
$77$	7.48454e32	0.725400
$78$	8.97580e30	0.00694093
$79$	−2.62804e33	−1.62614	−0.813069	−	0.582167i	$-0.802205\pi$
$79$	−2.62804e33	−1.62614	−0.813069	+	0.582167i	$0.802205\pi$
$80$	9.09314e32	0.451481
$81$	3.52211e33	1.40707
$82$	−5.65527e32	−0.182268
$83$	6.17326e33	1.60934	0.804671	−	0.593722i	$-0.202342\pi$
$83$	6.17326e33	1.60934	0.804671	+	0.593722i	$0.202342\pi$
$84$	−8.08006e33	−1.70815
$85$	−3.22175e33	−0.553682
$86$	1.22640e33	0.171755
$87$	−5.48733e33	−0.627732
$88$	2.24800e33	0.210547
$89$	6.75031e33	0.518799	0.259399	−	0.965770i	$-0.416475\pi$
$89$	6.75031e33	0.518799	0.259399	+	0.965770i	$0.416475\pi$
$90$	−2.34668e33	−0.148323
$91$	−5.13521e32	−0.0267506
$92$	2.88686e34	1.24205
$93$	−1.31906e34	−0.469691
$94$	4.62727e33	0.136643
$95$	−2.89755e32	−0.00710997
$96$	−3.65313e34	−0.746308
$97$	−8.10218e34	−1.38069	−0.690346	−	0.723480i	$-0.742542\pi$
$97$	−8.10218e34	−1.38069	−0.690346	+	0.723480i	$0.742542\pi$
$98$	2.79875e32	0.00398573
$99$	1.31417e35	1.56688
$100$	7.52108e34	0.752108
$101$	−1.08776e35	−0.913923	−0.456962	−	0.889486i	$-0.651062\pi$
$101$	−1.08776e35	−0.913923	−0.456962	+	0.889486i	$0.651062\pi$
$102$	4.16101e34	0.294236
$103$	−2.99910e33	−0.0178788	−0.00893941	−	0.999960i	$-0.502846\pi$
$103$	−2.99910e33	−0.0178788	−0.00893941	+	0.999960i	$0.502846\pi$
$104$	−1.54237e33	−0.00776436
$105$	1.97288e35	0.840016
$106$	−4.85615e34	−0.175162
$107$	−3.51492e35	−1.07572	−0.537860	−	0.843034i	$-0.680767\pi$
$107$	−3.51492e35	−1.07572	−0.537860	+	0.843034i	$0.680767\pi$
$108$	−7.52679e35	−1.95746
$109$	6.20112e35	1.37248	0.686240	−	0.727375i	$-0.259260\pi$
$109$	6.20112e35	1.37248	0.686240	+	0.727375i	$0.259260\pi$
$110$	−2.71542e34	−0.0512231
$111$	7.90166e35	1.27223
$112$	6.71902e35	0.924678
$113$	−7.30280e35	−0.860234	−0.430117	−	0.902773i	$-0.641528\pi$
$113$	−7.30280e35	−0.860234	−0.430117	+	0.902773i	$0.641528\pi$
$114$	3.74229e33	0.00377835
$115$	−7.04874e35	−0.610801
$116$	4.66480e35	0.347391
$117$	−9.01664e34	−0.0577819
$118$	1.34682e35	0.0743661
$119$	−2.38058e36	−1.13400
$120$	5.92559e35	0.243815
$121$	−1.28957e36	−0.458882
$122$	8.73249e33	0.00269055
$123$	8.34808e36	2.22970
$124$	1.12134e36	0.259930
$125$	−4.22698e36	−0.851345
$126$	−1.73399e36	−0.303781
$127$	5.89251e35	0.0898949	0.0449475	−	0.998989i	$-0.485688\pi$
$127$	5.89251e35	0.0898949	0.0449475	+	0.998989i	$0.485688\pi$
$128$	4.12524e36	0.548624
$129$	−1.81036e37	−2.10109
$130$	1.86308e34	0.00188896
$131$	2.10664e37	1.86785	0.933925	−	0.357468i	$-0.116360\pi$
$131$	2.10664e37	1.86785	0.933925	+	0.357468i	$0.116360\pi$
$132$	−1.64167e37	−1.27421
$133$	−2.14103e35	−0.0145619
$134$	1.07568e36	0.0641725
$135$	1.83779e37	0.962618
$136$	−7.15014e36	−0.329142
$137$	2.66291e37	1.07832	0.539158	−	0.842204i	$-0.318742\pi$
$137$	2.66291e37	1.07832	0.539158	+	0.842204i	$0.318742\pi$
$138$	9.10372e36	0.324590
$139$	−1.89155e37	−0.594374	−0.297187	−	0.954819i	$-0.596048\pi$
$139$	−1.89155e37	−0.594374	−0.297187	+	0.954819i	$0.596048\pi$
$140$	−1.67715e37	−0.464870
$141$	−6.83058e37	−1.67156
$142$	−1.03330e37	−0.223449
$143$	−1.04335e36	−0.0199548
$144$	1.17976e38	1.99733
$145$	−1.13899e37	−0.170836
$146$	−2.66374e36	−0.0354256
$147$	−4.13140e36	−0.0487578
$148$	−6.71723e37	−0.704061
$149$	6.86254e37	0.639330	0.319665	−	0.947531i	$-0.396430\pi$
$149$	6.86254e37	0.639330	0.319665	+	0.947531i	$0.396430\pi$
$150$	2.37177e37	0.196551
$151$	1.75463e38	1.29446	0.647229	−	0.762295i	$-0.275928\pi$
$151$	1.75463e38	1.29446	0.647229	+	0.762295i	$0.275928\pi$
$152$	−6.43064e35	−0.00422660
$153$	−4.17994e38	−2.44946
$154$	−2.00646e37	−0.104910
$155$	−2.73792e37	−0.127825
$156$	1.12636e37	0.0469892
$157$	−1.13686e36	−0.00424096	−0.00212048	−	0.999998i	$-0.500675\pi$
$157$	−1.13686e36	−0.00424096	−0.00212048	+	0.999998i	$0.500675\pi$
$158$	7.04525e37	0.235178
$159$	7.16845e38	2.14277
$160$	−7.58267e37	−0.203106
$161$	−5.20839e38	−1.25098
$162$	−9.44207e37	−0.203495
$163$	7.96117e38	1.54061	0.770307	−	0.637673i	$-0.220103\pi$
$163$	7.96117e38	1.54061	0.770307	+	0.637673i	$0.220103\pi$
$164$	−7.09674e38	−1.23393
$165$	4.00840e38	0.626616
$166$	−1.65493e38	−0.232749
$167$	−9.18990e38	−1.16352	−0.581758	−	0.813362i	$-0.697635\pi$
$167$	−9.18990e38	−1.16352	−0.581758	+	0.813362i	$0.697635\pi$
$168$	4.37848e38	0.499357
$169$	−9.72070e38	−0.999264
$170$	8.63686e37	0.0800755
$171$	−3.75932e37	−0.0314541
$172$	1.53899e39	1.16276
$173$	1.70459e39	1.16363	0.581813	−	0.813323i	$-0.302344\pi$
$173$	1.70459e39	1.16363	0.581813	+	0.813323i	$0.302344\pi$
$174$	1.47104e38	0.0907849
$175$	−1.35693e39	−0.757516
$176$	1.36514e39	0.689771
$177$	−1.98812e39	−0.909727
$178$	−1.80962e38	−0.0750306
$179$	−9.48476e38	−0.356532	−0.178266	−	0.983982i	$-0.557049\pi$
$179$	−9.48476e38	−0.356532	−0.178266	+	0.983982i	$0.557049\pi$
$180$	−2.94482e39	−1.00413
$181$	3.12075e39	0.965791	0.482896	−	0.875678i	$-0.339585\pi$
$181$	3.12075e39	0.965791	0.482896	+	0.875678i	$0.339585\pi$
$182$	1.37665e37	0.00386877
$183$	−1.28905e38	−0.0329137
$184$	−1.56435e39	−0.363097
$185$	1.64012e39	0.346235
$186$	3.53613e38	0.0679285
$187$	−4.83675e39	−0.845913
$188$	5.80670e39	0.925054
$189$	1.35796e40	1.97154
$190$	7.76775e36	0.00102827
$191$	−3.57216e38	−0.0431367	−0.0215683	−	0.999767i	$-0.506866\pi$
$191$	−3.57216e38	−0.0431367	−0.0215683	+	0.999767i	$0.506866\pi$
$192$	−1.40731e40	−1.55102
$193$	−1.46241e40	−1.47169	−0.735847	−	0.677148i	$-0.763216\pi$
$193$	−1.46241e40	−1.47169	−0.735847	+	0.677148i	$0.763216\pi$
$194$	2.17203e39	0.199681
$195$	−2.75020e38	−0.0231078
$196$	3.51212e38	0.0269829
$197$	1.11047e40	0.780453	0.390226	−	0.920719i	$-0.372397\pi$
$197$	1.11047e40	0.780453	0.390226	+	0.920719i	$0.372397\pi$
$198$	−3.52303e39	−0.226608
$199$	1.81867e40	1.07109	0.535545	−	0.844507i	$-0.320106\pi$
$199$	1.81867e40	1.07109	0.535545	+	0.844507i	$0.320106\pi$
$200$	−4.07558e39	−0.219869
$201$	−1.58787e40	−0.785027
$202$	2.91607e39	0.132175
$203$	−8.41610e39	−0.349889
$204$	5.22160e40	1.99194
$205$	1.73278e40	0.606808
$206$	8.03998e37	0.00258570
$207$	−9.14514e40	−2.70215
$208$	−9.36633e38	−0.0254367
$209$	−4.35004e38	−0.0108626
$210$	−5.28889e39	−0.121486
$211$	−6.95408e39	−0.146993	−0.0734965	−	0.997295i	$-0.523416\pi$
$211$	−6.95408e39	−0.146993	−0.0734965	+	0.997295i	$0.523416\pi$
$212$	−6.09393e40	−1.18582
$213$	1.52531e41	2.73348
$214$	9.42280e39	0.155575
$215$	−3.75770e40	−0.571807
$216$	4.07867e40	0.572239
$217$	−2.02308e40	−0.261799
$218$	−1.66240e40	−0.198493
$219$	3.93211e40	0.433365
$220$	−3.40756e40	−0.346774
$221$	3.31854e39	0.0311948
$222$	−2.11828e40	−0.183995
$223$	7.64864e40	0.614115	0.307057	−	0.951691i	$-0.400656\pi$
$223$	7.64864e40	0.614115	0.307057	+	0.951691i	$0.400656\pi$
$224$	−5.60292e40	−0.415981
$225$	−2.38256e41	−1.63625
$226$	1.95773e40	0.124410
$227$	−1.63339e40	−0.0960808	−0.0480404	−	0.998845i	$-0.515298\pi$
$227$	−1.63339e40	−0.0960808	−0.0480404	+	0.998845i	$0.515298\pi$
$228$	4.69616e39	0.0255790
$229$	1.58770e41	0.801026	0.400513	−	0.916291i	$-0.368832\pi$
$229$	1.58770e41	0.801026	0.400513	+	0.916291i	$0.368832\pi$
$230$	1.88963e40	0.0883363
$231$	2.96185e41	1.28337
$232$	−2.52780e40	−0.101555
$233$	1.16673e41	0.434751	0.217375	−	0.976088i	$-0.430250\pi$
$233$	1.16673e41	0.434751	0.217375	+	0.976088i	$0.430250\pi$
$234$	2.41718e39	0.00835664
$235$	−1.41780e41	−0.454912
$236$	1.69011e41	0.503449
$237$	−1.03999e42	−2.87696
$238$	6.38187e40	0.164003
$239$	5.09777e41	1.21735	0.608677	−	0.793418i	$-0.291701\pi$
$239$	5.09777e41	1.21735	0.608677	+	0.793418i	$0.291701\pi$
$240$	3.59842e41	0.798757
$241$	−7.27282e41	−1.50108	−0.750541	−	0.660824i	$-0.770207\pi$
$241$	−7.27282e41	−1.50108	−0.750541	+	0.660824i	$0.770207\pi$
$242$	3.45708e40	0.0663653
$243$	2.74404e41	0.490096
$244$	1.09583e40	0.0182147
$245$	−8.57541e39	−0.0132693
$246$	−2.23795e41	−0.322468
$247$	2.98460e38	0.000400580 0
$248$	−6.07638e40	−0.0759872
$249$	2.44294e42	2.84724
$250$	1.13317e41	0.123125
$251$	4.56359e40	0.0462399	0.0231199	−	0.999733i	$-0.492640\pi$
$251$	4.56359e40	0.0462399	0.0231199	+	0.999733i	$0.492640\pi$
$252$	−2.17596e42	−2.05656
$253$	−1.05822e42	−0.933180
$254$	−1.57966e40	−0.0130009
$255$	−1.27494e42	−0.979571
$256$	1.11133e42	0.797338
$257$	2.36058e41	0.158194	0.0790968	−	0.996867i	$-0.474796\pi$
$257$	2.36058e41	0.158194	0.0790968	+	0.996867i	$0.474796\pi$
$258$	4.85321e41	0.303868
$259$	1.21190e42	0.709124
$260$	2.33795e40	0.0127880
$261$	−1.47774e42	−0.755768
$262$	−5.64748e41	−0.270136
$263$	7.96602e41	0.356464	0.178232	−	0.983988i	$-0.442962\pi$
$263$	7.96602e41	0.356464	0.178232	+	0.983988i	$0.442962\pi$
$264$	8.89599e41	0.372499
$265$	1.48793e42	0.583149
$266$	5.73967e39	0.00210600
$267$	2.67129e42	0.917856
$268$	1.34986e42	0.434439
$269$	−4.82372e42	−1.45451	−0.727256	−	0.686366i	$-0.759205\pi$
$269$	−4.82372e42	−1.45451	−0.727256	+	0.686366i	$0.759205\pi$
$270$	−4.92674e41	−0.139217
$271$	−2.22025e42	−0.588083	−0.294042	−	0.955793i	$-0.595000\pi$
$271$	−2.22025e42	−0.588083	−0.294042	+	0.955793i	$0.595000\pi$
$272$	−4.34205e42	−1.07830
$273$	−2.03215e41	−0.0473270
$274$	−7.13873e41	−0.155950
$275$	−2.75695e42	−0.565075
$276$	1.14242e43	2.19743
$277$	1.62622e42	0.293619	0.146809	−	0.989165i	$-0.453100\pi$
$277$	1.62622e42	0.293619	0.146809	+	0.989165i	$0.453100\pi$
$278$	5.07088e41	0.0859606
$279$	−3.55222e42	−0.565492
$280$	9.08827e41	0.135899
$281$	6.29076e42	0.883777	0.441888	−	0.897070i	$-0.354309\pi$
$281$	6.29076e42	0.883777	0.441888	+	0.897070i	$0.354309\pi$
$282$	1.83114e42	0.241748
$283$	4.07259e41	0.0505368	0.0252684	−	0.999681i	$-0.491956\pi$
$283$	4.07259e41	0.0505368	0.0252684	+	0.999681i	$0.491956\pi$
$284$	−1.29667e43	−1.51272
$285$	−1.14664e41	−0.0125789
$286$	2.79700e40	0.00288594
$287$	1.28037e43	1.24281
$288$	−9.83787e42	−0.898530
$289$	3.75055e42	0.322391
$290$	3.05340e41	0.0247069
$291$	−3.20627e43	−2.44271
$292$	−3.34270e42	−0.239827
$293$	2.65171e43	1.79202	0.896010	−	0.444033i	$-0.146453\pi$
$293$	2.65171e43	1.79202	0.896010	+	0.444033i	$0.146453\pi$
$294$	1.10755e41	0.00705154
$295$	−4.12668e42	−0.247580
$296$	3.63998e42	0.205823
$297$	2.75904e43	1.47069
$298$	−1.83971e42	−0.0924623
$299$	7.26051e41	0.0344129
$300$	2.97631e43	1.33063
$301$	−2.77661e43	−1.17112
$302$	−4.70380e42	−0.187209
$303$	−4.30459e43	−1.61691
$304$	−3.90512e41	−0.0138467
$305$	−2.67565e41	−0.00895739
$306$	1.12056e43	0.354250
$307$	2.04163e43	0.609615	0.304808	−	0.952414i	$-0.401408\pi$
$307$	2.04163e43	0.609615	0.304808	+	0.952414i	$0.401408\pi$
$308$	−2.51788e43	−0.710227
$309$	−1.18683e42	−0.0316311
$310$	7.33983e41	0.0184866
$311$	1.35407e43	0.322355	0.161178	−	0.986925i	$-0.448471\pi$
$311$	1.35407e43	0.322355	0.161178	+	0.986925i	$0.448471\pi$
$312$	−6.10361e41	−0.0137367
$313$	−6.11170e43	−1.30058	−0.650289	−	0.759687i	$-0.725352\pi$
$313$	−6.11170e43	−1.30058	−0.650289	+	0.759687i	$0.725352\pi$
$314$	3.04770e40	0.000613343 0
$315$	5.31296e43	1.01135
$316$	8.84100e43	1.59213
$317$	7.44500e43	1.26861	0.634305	−	0.773083i	$-0.281286\pi$
$317$	7.44500e43	1.26861	0.634305	+	0.773083i	$0.281286\pi$
$318$	−1.92172e43	−0.309895
$319$	−1.70994e43	−0.261002
$320$	−2.92110e43	−0.422107
$321$	−1.39095e44	−1.90316
$322$	1.39627e43	0.180922
$323$	1.38360e42	0.0169812
$324$	−1.18488e44	−1.37764
$325$	1.89156e42	0.0208383
$326$	−2.13423e43	−0.222809
$327$	2.45396e44	2.42819
$328$	3.84563e43	0.360724
$329$	−1.04763e44	−0.931706
$330$	−1.07457e43	−0.0906236
$331$	2.60186e43	0.208110	0.104055	−	0.994572i	$-0.466818\pi$
$331$	2.60186e43	0.208110	0.104055	+	0.994572i	$0.466818\pi$
$332$	−2.07675e44	−1.57568
$333$	2.12792e44	1.53172
$334$	2.46363e43	0.168272
$335$	−3.29590e43	−0.213643
$336$	2.65891e44	1.63594
$337$	−3.62826e43	−0.211921	−0.105961	−	0.994370i	$-0.533792\pi$
$337$	−3.62826e43	−0.211921	−0.105961	+	0.994370i	$0.533792\pi$
$338$	2.60593e43	0.144517
$339$	−2.88993e44	−1.52192
$340$	1.08383e44	0.542101
$341$	−4.11040e43	−0.195291
$342$	1.00780e42	0.00454901
$343$	−2.36257e44	−1.01330
$344$	−8.33961e43	−0.339917
$345$	−2.78939e44	−1.08063
$346$	−4.56967e43	−0.168288
$347$	3.83287e44	1.34202	0.671009	−	0.741449i	$-0.265861\pi$
$347$	3.83287e44	1.34202	0.671009	+	0.741449i	$0.265861\pi$
$348$	1.84600e44	0.614602
$349$	1.99513e44	0.631723	0.315862	−	0.948805i	$-0.397706\pi$
$349$	1.99513e44	0.631723	0.315862	+	0.948805i	$0.397706\pi$
$350$	3.63766e43	0.109555
$351$	−1.89300e43	−0.0542345
$352$	−1.13837e44	−0.310305
$353$	2.67595e44	0.694098	0.347049	−	0.937847i	$-0.387184\pi$
$353$	2.67595e44	0.694098	0.347049	+	0.937847i	$0.387184\pi$
$354$	5.32976e43	0.131568
$355$	3.16604e44	0.743909
$356$	−2.27088e44	−0.507947
$357$	−9.42065e44	−2.00626
$358$	2.54267e43	0.0515630
$359$	7.93674e44	1.53281	0.766407	−	0.642355i	$-0.222043\pi$
$359$	7.93674e44	1.53281	0.766407	+	0.642355i	$0.222043\pi$
$360$	1.59576e44	0.293545
$361$	−5.70534e44	−0.999782
$362$	−8.36610e43	−0.139676
$363$	−5.10320e44	−0.811852
$364$	1.72754e43	0.0261911
$365$	8.16175e43	0.117939
$366$	3.45570e42	0.00476011
$367$	−4.95841e44	−0.651158	−0.325579	−	0.945515i	$-0.605559\pi$
$367$	−4.95841e44	−0.651158	−0.325579	+	0.945515i	$0.605559\pi$
$368$	−9.49982e44	−1.18954
$369$	2.24814e45	2.68449
$370$	−4.39684e43	−0.0500738
$371$	1.09945e45	1.19435
$372$	4.43745e44	0.459867
$373$	1.46949e44	0.145299	0.0726496	−	0.997358i	$-0.476855\pi$
$373$	1.46949e44	0.145299	0.0726496	+	0.997358i	$0.476855\pi$
$374$	1.29664e44	0.122339
$375$	−1.67274e45	−1.50619
$376$	−3.14658e44	−0.270428
$377$	1.17321e43	0.00962500
$378$	−3.64042e44	−0.285131
$379$	−7.55442e44	−0.564956	−0.282478	−	0.959274i	$-0.591156\pi$
$379$	−7.55442e44	−0.564956	−0.282478	+	0.959274i	$0.591156\pi$
$380$	9.74766e42	0.00696125
$381$	2.33184e44	0.159042
$382$	9.57624e42	0.00623859
$383$	−5.97753e44	−0.372000	−0.186000	−	0.982550i	$-0.559552\pi$
$383$	−5.97753e44	−0.372000	−0.186000	+	0.982550i	$0.559552\pi$
$384$	1.63248e45	0.970622
$385$	6.14781e44	0.349267
$386$	3.92044e44	0.212842
$387$	−4.87530e45	−2.52964
$388$	2.72566e45	1.35181
$389$	−2.41609e45	−1.14550	−0.572750	−	0.819730i	$-0.694123\pi$
$389$	−2.41609e45	−1.14550	−0.572750	+	0.819730i	$0.694123\pi$
$390$	7.37273e42	0.00334193
$391$	3.36583e45	1.45881
$392$	−1.90317e43	−0.00788810
$393$	8.33657e45	3.30459
$394$	−2.97694e44	−0.112872
$395$	−2.15867e45	−0.782957
$396$	−4.42101e45	−1.53411
$397$	−1.25639e45	−0.417148	−0.208574	−	0.978007i	$-0.566882\pi$
$397$	−1.25639e45	−0.417148	−0.208574	+	0.978007i	$0.566882\pi$
$398$	−4.87550e44	−0.154905
$399$	−8.47267e43	−0.0257629
$400$	−2.47496e45	−0.720310
$401$	−3.77150e45	−1.05072	−0.525361	−	0.850880i	$-0.676070\pi$
$401$	−3.77150e45	−1.05072	−0.525361	+	0.850880i	$0.676070\pi$
$402$	4.25677e44	0.113534
$403$	2.82018e43	0.00720176
$404$	3.65935e45	0.894807
$405$	2.89306e45	0.677478
$406$	2.25619e44	0.0506022
$407$	2.46229e45	0.528977
$408$	−2.82952e45	−0.582317
$409$	−5.28767e45	−1.04257	−0.521286	−	0.853382i	$-0.674548\pi$
$409$	−5.28767e45	−1.04257	−0.521286	+	0.853382i	$0.674548\pi$
$410$	−4.64525e44	−0.0877589
$411$	1.05379e46	1.90775
$412$	1.00893e44	0.0175049
$413$	−3.04925e45	−0.507069
$414$	2.45163e45	0.390795
$415$	5.07072e45	0.774869
$416$	7.81048e43	0.0114431
$417$	−7.48542e45	−1.05156
$418$	1.16616e43	0.00157099
$419$	3.73280e45	0.482270	0.241135	−	0.970492i	$-0.422480\pi$
$419$	3.73280e45	0.482270	0.241135	+	0.970492i	$0.422480\pi$
$420$	−6.63697e45	−0.822446
$421$	−1.18084e45	−0.140364	−0.0701819	−	0.997534i	$-0.522358\pi$
$421$	−1.18084e45	−0.140364	−0.0701819	+	0.997534i	$0.522358\pi$
$422$	1.86425e44	0.0212587
$423$	−1.83947e46	−2.01251
$424$	3.30222e45	0.346660
$425$	8.76893e45	0.883365
$426$	−4.08906e45	−0.395326
$427$	−1.97706e44	−0.0183456
$428$	1.18246e46	1.05322
$429$	−4.12882e44	−0.0353040
$430$	1.00736e45	0.0826968
$431$	5.00269e45	0.394322	0.197161	−	0.980371i	$-0.436828\pi$
$431$	5.00269e45	0.394322	0.197161	+	0.980371i	$0.436828\pi$
$432$	2.47684e46	1.87471
$433$	−1.22691e46	−0.891817	−0.445909	−	0.895079i	$-0.647119\pi$
$433$	−1.22691e46	−0.891817	−0.445909	+	0.895079i	$0.647119\pi$
$434$	5.42348e44	0.0378624
$435$	−4.50730e45	−0.302242
$436$	−2.08612e46	−1.34377
$437$	3.02714e44	0.0187330
$438$	−1.05412e45	−0.0626748
$439$	1.91016e46	1.09129	0.545645	−	0.838016i	$-0.316285\pi$
$439$	1.91016e46	1.09129	0.545645	+	0.838016i	$0.316285\pi$
$440$	1.84651e45	0.101375
$441$	−1.11259e45	−0.0587027
$442$	−8.89634e43	−0.00451151
$443$	−1.54265e46	−0.751973	−0.375987	−	0.926625i	$-0.622696\pi$
$443$	−1.54265e46	−0.751973	−0.375987	+	0.926625i	$0.622696\pi$
$444$	−2.65820e46	−1.24562
$445$	5.54471e45	0.249792
$446$	−2.05045e45	−0.0888155
$447$	2.71570e46	1.13110
$448$	−2.15843e46	−0.864517
$449$	−3.71387e46	−1.43059	−0.715296	−	0.698822i	$-0.753708\pi$
$449$	−3.71387e46	−1.43059	−0.715296	+	0.698822i	$0.753708\pi$
$450$	6.38718e45	0.236641
$451$	2.60140e46	0.927080
$452$	2.45674e46	0.842241
$453$	6.94356e46	2.29015
$454$	4.37878e44	0.0138956
$455$	−4.21806e44	−0.0128799
$456$	−2.54479e44	−0.00747768
$457$	−1.10776e46	−0.313266	−0.156633	−	0.987657i	$-0.550064\pi$
$457$	−1.10776e46	−0.313266	−0.156633	+	0.987657i	$0.550064\pi$
$458$	−4.25630e45	−0.115847
$459$	−8.77558e46	−2.29908
$460$	2.37127e46	0.598025
$461$	−3.91769e46	−0.951183	−0.475592	−	0.879666i	$-0.657766\pi$
$461$	−3.91769e46	−0.951183	−0.475592	+	0.879666i	$0.657766\pi$
$462$	−7.94013e45	−0.185606
$463$	5.50481e46	1.23901	0.619505	−	0.784992i	$-0.287333\pi$
$463$	5.50481e46	1.23901	0.619505	+	0.784992i	$0.287333\pi$
$464$	−1.53505e46	−0.332704
$465$	−1.08348e46	−0.226148
$466$	−3.12776e45	−0.0628753
$467$	2.96872e46	0.574808	0.287404	−	0.957809i	$-0.407208\pi$
$467$	2.96872e46	0.574808	0.287404	+	0.957809i	$0.407208\pi$
$468$	3.03329e45	0.0565734
$469$	−2.43537e46	−0.437563
$470$	3.80084e45	0.0657911
$471$	−4.49889e44	−0.00750308
$472$	−9.15849e45	−0.147177
$473$	−5.64137e46	−0.873605
$474$	2.78801e46	0.416076
$475$	7.88652e44	0.0113435
$476$	8.00854e46	1.11028
$477$	1.93046e47	2.57982
$478$	−1.36661e46	−0.176058
$479$	−7.25716e46	−0.901354	−0.450677	−	0.892687i	$-0.648817\pi$
$479$	−7.25716e46	−0.901354	−0.450677	+	0.892687i	$0.648817\pi$
$480$	−3.00068e46	−0.359334
$481$	−1.68940e45	−0.0195071
$482$	1.94970e46	0.217092
$483$	−2.06111e47	−2.21323
$484$	4.33825e46	0.449284
$485$	−6.65514e46	−0.664778
$486$	−7.35623e45	−0.0708795
$487$	−1.32479e47	−1.23137	−0.615686	−	0.787992i	$-0.711121\pi$
$487$	−1.32479e47	−1.23137	−0.615686	+	0.787992i	$0.711121\pi$
$488$	−5.93816e44	−0.00532482
$489$	3.15046e47	2.72565
$490$	2.29890e44	0.00191906
$491$	5.04170e46	0.406117	0.203058	−	0.979167i	$-0.434912\pi$
$491$	5.04170e46	0.406117	0.203058	+	0.979167i	$0.434912\pi$
$492$	−2.80838e47	−2.18307
$493$	5.43876e46	0.408017
$494$	−8.00112e42	−5.79334e−5 0
$495$	1.07946e47	0.754425
$496$	−3.68999e46	−0.248941
$497$	2.33942e47	1.52360
$498$	−6.54903e46	−0.411778
$499$	3.13288e46	0.190189	0.0950944	−	0.995468i	$-0.469685\pi$
$499$	3.13288e46	0.190189	0.0950944	+	0.995468i	$0.469685\pi$
$500$	1.42200e47	0.833538
$501$	−3.63671e47	−2.05849
$502$	−1.22341e45	−0.00668738
$503$	2.79560e47	1.47582	0.737912	−	0.674897i	$-0.235812\pi$
$503$	2.79560e47	1.47582	0.737912	+	0.674897i	$0.235812\pi$
$504$	1.17913e47	0.601209
$505$	−8.93488e46	−0.440038
$506$	2.83687e46	0.134960
$507$	−3.84676e47	−1.76789
$508$	−1.98230e46	−0.0880147
$509$	−2.02483e47	−0.868614	−0.434307	−	0.900765i	$-0.643007\pi$
$509$	−2.02483e47	−0.868614	−0.434307	+	0.900765i	$0.643007\pi$
$510$	3.41785e46	0.141669
$511$	6.03080e46	0.241551
$512$	−1.71535e47	−0.663938
$513$	−7.89251e45	−0.0295231
$514$	−6.32824e45	−0.0228785
$515$	−2.46346e45	−0.00860833
$516$	6.09024e47	2.05714
$517$	−2.12852e47	−0.695014
$518$	−3.24887e46	−0.102556
$519$	6.74556e47	2.05868
$520$	−1.26691e45	−0.00373840
$521$	−7.62521e46	−0.217566	−0.108783	−	0.994066i	$-0.534695\pi$
$521$	−7.62521e46	−0.217566	−0.108783	+	0.994066i	$0.534695\pi$
$522$	3.96152e46	0.109302
$523$	2.14532e47	0.572417	0.286208	−	0.958167i	$-0.407605\pi$
$523$	2.14532e47	0.572417	0.286208	+	0.958167i	$0.407605\pi$
$524$	−7.08696e47	−1.82878
$525$	−5.36976e47	−1.34019
$526$	−2.13553e46	−0.0515532
$527$	1.30738e47	0.305293
$528$	5.40225e47	1.22034
$529$	2.78811e47	0.609307
$530$	−3.98884e46	−0.0843372
$531$	−5.35401e47	−1.09528
$532$	7.20265e45	0.0142574
$533$	−1.78484e46	−0.0341880
$534$	−7.16121e46	−0.132744
$535$	−2.88716e47	−0.517940
$536$	−7.31470e46	−0.127003
$537$	−3.75339e47	−0.630774
$538$	1.29314e47	0.210357
$539$	−1.28741e46	−0.0202728
$540$	−6.18251e47	−0.942484
$541$	1.23166e48	1.81777	0.908884	−	0.417049i	$-0.136936\pi$
$541$	1.23166e48	1.81777	0.908884	+	0.417049i	$0.136936\pi$
$542$	5.95204e46	0.0850508
$543$	1.23497e48	1.70867
$544$	3.62079e47	0.485090
$545$	5.09360e47	0.660825
$546$	5.44779e45	0.00684461
$547$	−7.20961e47	−0.877271	−0.438635	−	0.898665i	$-0.644538\pi$
$547$	−7.20961e47	−0.877271	−0.438635	+	0.898665i	$0.644538\pi$
$548$	−8.95831e47	−1.05576
$549$	−3.47142e46	−0.0396270
$550$	7.39082e46	0.0817233
$551$	4.89146e45	0.00523945
$552$	−6.19060e47	−0.642390
$553$	−1.59507e48	−1.60357
$554$	−4.35958e46	−0.0424642
$555$	6.49043e47	0.612557
$556$	6.36339e47	0.581942
$557$	5.88528e47	0.521556	0.260778	−	0.965399i	$-0.416021\pi$
$557$	5.88528e47	0.521556	0.260778	+	0.965399i	$0.416021\pi$
$558$	9.52280e46	0.0817836
$559$	3.87060e46	0.0322160
$560$	5.51901e47	0.445216
$561$	−1.91404e48	−1.49659
$562$	−1.68643e47	−0.127815
$563$	−1.44205e48	−1.05946	−0.529730	−	0.848166i	$-0.677707\pi$
$563$	−1.44205e48	−1.05946	−0.529730	+	0.848166i	$0.677707\pi$
$564$	2.29788e48	1.63660
$565$	−5.99852e47	−0.414187
$566$	−1.09178e46	−0.00730882
$567$	2.13772e48	1.38754
$568$	7.02651e47	0.442225
$569$	1.87904e48	1.14676	0.573379	−	0.819290i	$-0.305632\pi$
$569$	1.87904e48	1.14676	0.573379	+	0.819290i	$0.305632\pi$
$570$	3.07392e45	0.00181921
$571$	−1.57690e48	−0.905050	−0.452525	−	0.891752i	$-0.649477\pi$
$571$	−1.57690e48	−0.905050	−0.452525	+	0.891752i	$0.649477\pi$
$572$	3.50993e46	0.0195375
$573$	−1.41361e47	−0.0763172
$574$	−3.43242e47	−0.179739
$575$	1.91852e48	0.974495
$576$	−3.78988e48	−1.86738
$577$	−7.02869e47	−0.335968	−0.167984	−	0.985790i	$-0.553726\pi$
$577$	−7.02869e47	−0.335968	−0.167984	+	0.985790i	$0.553726\pi$
$578$	−1.00545e47	−0.0466254
$579$	−5.78720e48	−2.60371
$580$	3.83167e47	0.167263
$581$	3.74681e48	1.58701
$582$	8.59536e47	0.353274
$583$	2.23381e48	0.890934
$584$	1.81137e47	0.0701103
$585$	−7.40628e46	−0.0278210
$586$	−7.10871e47	−0.259169
$587$	−1.10752e48	−0.391908	−0.195954	−	0.980613i	$-0.562780\pi$
$587$	−1.10752e48	−0.391908	−0.195954	+	0.980613i	$0.562780\pi$
$588$	1.38985e47	0.0477380
$589$	1.17582e46	0.00392034
$590$	1.10628e47	0.0358059
$591$	4.39444e48	1.38077
$592$	2.21044e48	0.674294
$593$	−2.15841e48	−0.639258	−0.319629	−	0.947543i	$-0.603558\pi$
$593$	−2.15841e48	−0.639258	−0.319629	+	0.947543i	$0.603558\pi$
$594$	−7.39643e47	−0.212696
$595$	−1.95541e48	−0.545999
$596$	−2.30863e48	−0.625958
$597$	7.19701e48	1.89497
$598$	−1.94640e46	−0.00497692
$599$	−5.67895e48	−1.41026	−0.705129	−	0.709079i	$-0.749111\pi$
$599$	−5.67895e48	−1.41026	−0.705129	+	0.709079i	$0.749111\pi$
$600$	−1.61282e48	−0.388991
$601$	6.99029e48	1.63754	0.818770	−	0.574122i	$-0.194656\pi$
$601$	6.99029e48	1.63754	0.818770	+	0.574122i	$0.194656\pi$
$602$	7.44353e47	0.169371
$603$	−4.27614e48	−0.945147
$604$	−5.90275e48	−1.26738
$605$	−1.05925e48	−0.220944
$606$	1.15397e48	0.233843
$607$	−4.92572e48	−0.969768	−0.484884	−	0.874578i	$-0.661138\pi$
$607$	−4.92572e48	−0.969768	−0.484884	+	0.874578i	$0.661138\pi$
$608$	3.25643e46	0.00622916
$609$	−3.33049e48	−0.619022
$610$	7.17287e45	0.00129545
$611$	1.46040e47	0.0256300
$612$	1.40618e49	2.39823
$613$	3.59765e48	0.596295	0.298148	−	0.954520i	$-0.403631\pi$
$613$	3.59765e48	0.596295	0.298148	+	0.954520i	$0.403631\pi$
$614$	−5.47321e47	−0.0881649
$615$	6.85712e48	1.07356
$616$	1.36441e48	0.207626
$617$	−3.73363e48	−0.552257	−0.276128	−	0.961121i	$-0.589051\pi$
$617$	−3.73363e48	−0.552257	−0.276128	+	0.961121i	$0.589051\pi$
$618$	3.18165e46	0.00457461
$619$	2.84346e48	0.397430	0.198715	−	0.980057i	$-0.436323\pi$
$619$	2.84346e48	0.397430	0.198715	+	0.980057i	$0.436323\pi$
$620$	9.21067e47	0.125152
$621$	−1.91998e49	−2.53626
$622$	−3.62999e47	−0.0466202
$623$	4.09705e48	0.511600
$624$	−3.70653e47	−0.0450025
$625$	3.03465e48	0.358268
$626$	1.63843e48	0.188094
$627$	−1.72144e47	−0.0192180
$628$	3.82453e46	0.00415225
$629$	−7.83171e48	−0.826933
$630$	−1.42430e48	−0.146265
$631$	8.72640e48	0.871608	0.435804	−	0.900041i	$-0.356464\pi$
$631$	8.72640e48	0.871608	0.435804	+	0.900041i	$0.356464\pi$
$632$	−4.79082e48	−0.465438
$633$	−2.75193e48	−0.260059
$634$	−1.99586e48	−0.183471
$635$	4.84011e47	0.0432828
$636$	−2.41154e49	−2.09795
$637$	8.83305e45	0.000747602 0
$638$	4.58401e47	0.0377471
$639$	4.10766e49	3.29101
$640$	3.38848e48	0.264153
$641$	1.94871e49	1.47820	0.739098	−	0.673598i	$-0.235252\pi$
$641$	1.94871e49	1.47820	0.739098	+	0.673598i	$0.235252\pi$
$642$	3.72887e48	0.275242
$643$	−2.20357e49	−1.58283	−0.791417	−	0.611277i	$-0.790656\pi$
$643$	−2.20357e49	−1.58283	−0.791417	+	0.611277i	$0.790656\pi$
$644$	1.75216e49	1.22482
$645$	−1.48703e49	−1.01164
$646$	−3.70916e46	−0.00245588
$647$	−1.15002e49	−0.741106	−0.370553	−	0.928811i	$-0.620832\pi$
$647$	−1.15002e49	−0.741106	−0.370553	+	0.928811i	$0.620832\pi$
$648$	6.42069e48	0.402734
$649$	−6.19531e48	−0.378252
$650$	−5.07091e46	−0.00301371
$651$	−8.00592e48	−0.463174
$652$	−2.67822e49	−1.50839
$653$	−3.36604e48	−0.184560	−0.0922801	−	0.995733i	$-0.529416\pi$
$653$	−3.36604e48	−0.184560	−0.0922801	+	0.995733i	$0.529416\pi$
$654$	−6.57858e48	−0.351173
$655$	1.73039e49	0.899337
$656$	2.33533e49	1.18176
$657$	1.05892e49	0.521757
$658$	2.80848e48	0.134747
$659$	−1.07733e49	−0.503334	−0.251667	−	0.967814i	$-0.580979\pi$
$659$	−1.07733e49	−0.503334	−0.251667	+	0.967814i	$0.580979\pi$
$660$	−1.34847e49	−0.613510
$661$	−1.67936e49	−0.744079	−0.372040	−	0.928217i	$-0.621341\pi$
$661$	−1.67936e49	−0.744079	−0.372040	+	0.928217i	$0.621341\pi$
$662$	−6.97506e47	−0.0300977
$663$	1.31324e48	0.0551897
$664$	1.12536e49	0.460630
$665$	−1.75864e47	−0.00701131
$666$	−5.70452e48	−0.221524
$667$	1.18993e49	0.450109
$668$	3.09158e49	1.13918
$669$	3.02679e49	1.08649
$670$	8.83564e47	0.0308979
$671$	−4.01690e47	−0.0136851
$672$	−2.21724e49	−0.735952
$673$	2.60356e49	0.841984	0.420992	−	0.907064i	$-0.361682\pi$
$673$	2.60356e49	0.841984	0.420992	+	0.907064i	$0.361682\pi$
$674$	9.72664e47	0.0306489
$675$	−5.00207e49	−1.53580
$676$	3.27015e49	0.978363
$677$	−5.14137e49	−1.49891	−0.749457	−	0.662053i	$-0.769685\pi$
$677$	−5.14137e49	−1.49891	−0.749457	+	0.662053i	$0.769685\pi$
$678$	7.74732e48	0.220106
$679$	−4.91756e49	−1.36153
$680$	−5.87313e48	−0.158476
$681$	−6.46378e48	−0.169986
$682$	1.10192e48	0.0282437
$683$	3.66408e47	0.00915382	0.00457691	−	0.999990i	$-0.498543\pi$
$683$	3.66408e47	0.00915382	0.00457691	+	0.999990i	$0.498543\pi$
$684$	1.26468e48	0.0307962
$685$	2.18732e49	0.519190
$686$	6.33359e48	0.146547
$687$	6.28298e49	1.41717
$688$	−5.06437e49	−1.11360
$689$	−1.53263e48	−0.0328550
$690$	7.47780e48	0.156284
$691$	8.07844e49	1.64612	0.823060	−	0.567954i	$-0.192265\pi$
$691$	8.07844e49	1.64612	0.823060	+	0.567954i	$0.192265\pi$
$692$	−5.73443e49	−1.13929
$693$	7.97626e49	1.54514
$694$	−1.02752e49	−0.194088
$695$	−1.55372e49	−0.286180
$696$	−1.00032e49	−0.179671
$697$	−8.27418e49	−1.44928
$698$	−5.34856e48	−0.0913622
$699$	4.61707e49	0.769159
$700$	4.56486e49	0.741672
$701$	1.36918e49	0.216968	0.108484	−	0.994098i	$-0.465400\pi$
$701$	1.36918e49	0.216968	0.108484	+	0.994098i	$0.465400\pi$
$702$	5.07476e47	0.00784360
$703$	−7.04362e47	−0.0106189
$704$	−4.38540e49	−0.644894
$705$	−5.61065e49	−0.804828
$706$	−7.17369e48	−0.100383
$707$	−6.60208e49	−0.901242
$708$	6.68826e49	0.890699
$709$	9.81931e49	1.27577	0.637884	−	0.770132i	$-0.279810\pi$
$709$	9.81931e49	1.27577	0.637884	+	0.770132i	$0.279810\pi$
$710$	−8.48752e48	−0.107587
$711$	−2.80069e50	−3.46376
$712$	1.23056e49	0.148492
$713$	2.86037e49	0.336787
$714$	2.52549e49	0.290153
$715$	−8.57006e47	−0.00960789
$716$	3.19077e49	0.349075
$717$	2.01733e50	2.15374
$718$	−2.12768e49	−0.221681
$719$	1.63037e50	1.65780	0.828899	−	0.559398i	$-0.188968\pi$
$719$	1.63037e50	1.65780	0.828899	+	0.559398i	$0.188968\pi$
$720$	9.69054e49	0.961677
$721$	−1.82028e48	−0.0176307
$722$	1.52949e49	0.144592
$723$	−2.87806e50	−2.65571
$724$	−1.04985e50	−0.945591
$725$	3.10009e49	0.272558
$726$	1.36807e49	0.117413
$727$	3.34890e49	0.280576	0.140288	−	0.990111i	$-0.455197\pi$
$727$	3.34890e49	0.280576	0.140288	+	0.990111i	$0.455197\pi$
$728$	−9.36131e47	−0.00765663
$729$	−6.76269e49	−0.539993
$730$	−2.18800e48	−0.0170568
$731$	1.79433e50	1.36568
$732$	4.33652e48	0.0322253
$733$	−2.00965e50	−1.45814	−0.729071	−	0.684438i	$-0.760048\pi$
$733$	−2.00965e50	−1.45814	−0.729071	+	0.684438i	$0.760048\pi$
$734$	1.32925e49	0.0941729
$735$	−3.39354e48	−0.0234760
$736$	7.92179e49	0.535133
$737$	−4.94807e49	−0.326404
$738$	−6.02681e49	−0.388241
$739$	−1.06372e50	−0.669190	−0.334595	−	0.942362i	$-0.608599\pi$
$739$	−1.06372e50	−0.669190	−0.334595	+	0.942362i	$0.608599\pi$
$740$	−5.51754e49	−0.338993
$741$	1.18109e47	0.000708704 0
$742$	−2.94740e49	−0.172731
$743$	7.25015e49	0.414995	0.207498	−	0.978236i	$-0.433468\pi$
$743$	7.25015e49	0.414995	0.207498	+	0.978236i	$0.433468\pi$
$744$	−2.40460e49	−0.134436
$745$	5.63690e49	0.307826
$746$	−3.93942e48	−0.0210137
$747$	6.57883e50	3.42798
$748$	1.62714e50	0.828220
$749$	−2.13335e50	−1.06079
$750$	4.48428e49	0.217832
$751$	−4.51226e49	−0.214139	−0.107069	−	0.994252i	$-0.534147\pi$
$751$	−4.51226e49	−0.214139	−0.107069	+	0.994252i	$0.534147\pi$
$752$	−1.91081e50	−0.885944
$753$	1.80595e49	0.0818074
$754$	−3.14513e47	−0.00139200
$755$	1.44125e50	0.623259
$756$	−4.56832e50	−1.93030
$757$	−1.21415e50	−0.501296	−0.250648	−	0.968078i	$-0.580644\pi$
$757$	−1.21415e50	−0.501296	−0.250648	+	0.968078i	$0.580644\pi$
$758$	2.02519e49	0.0817061
$759$	−4.18767e50	−1.65098
$760$	−5.28213e47	−0.00203503
$761$	3.14799e50	1.18523	0.592614	−	0.805486i	$-0.298096\pi$
$761$	3.14799e50	1.18523	0.592614	+	0.805486i	$0.298096\pi$
$762$	−6.25119e48	−0.0230012
$763$	3.76372e50	1.35344
$764$	1.20171e49	0.0422344
$765$	−3.43341e50	−1.17937
$766$	1.60246e49	0.0538000
$767$	4.25066e48	0.0139488
$768$	4.39784e50	1.41065
$769$	−5.16540e50	−1.61954	−0.809772	−	0.586744i	$-0.800409\pi$
$769$	−5.16540e50	−1.61954	−0.809772	+	0.586744i	$0.800409\pi$
$770$	−1.64811e49	−0.0505123
$771$	9.34149e49	0.279875
$772$	4.91972e50	1.44091
$773$	−4.51959e50	−1.29407	−0.647035	−	0.762460i	$-0.723991\pi$
$773$	−4.51959e50	−1.29407	−0.647035	+	0.762460i	$0.723991\pi$
$774$	1.30697e50	0.365846
$775$	7.45206e49	0.203937
$776$	−1.47700e50	−0.395185
$777$	4.79585e50	1.25458
$778$	6.47705e49	0.165666
$779$	−7.44157e48	−0.0186105
$780$	9.25195e48	0.0226244
$781$	4.75312e50	1.13654
$782$	−9.02313e49	−0.210979
$783$	−3.10244e50	−0.709369
$784$	−1.15574e49	−0.0258421
$785$	−9.33820e47	−0.00204195
$786$	−2.23487e50	−0.477923
$787$	−7.76649e50	−1.62430	−0.812151	−	0.583447i	$-0.801704\pi$
$787$	−7.76649e50	−1.62430	−0.812151	+	0.583447i	$0.801704\pi$
$788$	−3.73573e50	−0.764129
$789$	3.15238e50	0.630655
$790$	5.78697e49	0.113234
$791$	−4.43237e50	−0.848297
$792$	2.39569e50	0.448477
$793$	2.75603e47	0.000504665 0
$794$	3.36813e49	0.0603295
$795$	5.88817e50	1.03171
$796$	−6.11821e50	−1.04869
$797$	−7.96535e49	−0.133562	−0.0667812	−	0.997768i	$-0.521273\pi$
$797$	−7.96535e49	−0.133562	−0.0667812	+	0.997768i	$0.521273\pi$
$798$	2.27135e48	0.00372593
$799$	6.77011e50	1.08649
$800$	2.06385e50	0.324043
$801$	7.19379e50	1.10507
$802$	1.01106e50	0.151959
$803$	1.22531e50	0.180187
$804$	5.34178e50	0.768608
$805$	−4.27818e50	−0.602325
$806$	−7.56034e47	−0.00104155
$807$	−1.90889e51	−2.57332
$808$	−1.98295e50	−0.261585
$809$	8.80158e50	1.13622	0.568109	−	0.822954i	$-0.307675\pi$
$809$	8.80158e50	1.13622	0.568109	+	0.822954i	$0.307675\pi$
$810$	−7.75573e49	−0.0979794
$811$	1.29798e51	1.60473	0.802364	−	0.596835i	$-0.203575\pi$
$811$	1.29798e51	1.60473	0.802364	+	0.596835i	$0.203575\pi$
$812$	2.83126e50	0.342571
$813$	−8.78616e50	−1.04043
$814$	−6.60090e49	−0.0765026
$815$	6.53931e50	0.741778
$816$	−1.71827e51	−1.90772
$817$	1.61377e49	0.0175370
$818$	1.41752e50	0.150781
$819$	−5.47258e49	−0.0569802
$820$	−5.82927e50	−0.594116
$821$	8.37740e50	0.835804	0.417902	−	0.908492i	$-0.362766\pi$
$821$	8.37740e50	0.835804	0.417902	+	0.908492i	$0.362766\pi$
$822$	−2.82500e50	−0.275906
$823$	−1.79490e51	−1.71610	−0.858051	−	0.513564i	$-0.828325\pi$
$823$	−1.79490e51	−1.71610	−0.858051	+	0.513564i	$0.828325\pi$
$824$	−5.46725e48	−0.00511732
$825$	−1.09100e51	−0.999728
$826$	8.17442e49	0.0733342
$827$	6.78828e50	0.596230	0.298115	−	0.954530i	$-0.403642\pi$
$827$	6.78828e50	0.596230	0.298115	+	0.954530i	$0.403642\pi$
$828$	3.07652e51	2.64563
$829$	1.62563e51	1.36873	0.684363	−	0.729141i	$-0.260080\pi$
$829$	1.62563e51	1.36873	0.684363	+	0.729141i	$0.260080\pi$
$830$	−1.35936e50	−0.112064
$831$	6.43543e50	0.519469
$832$	3.00886e49	0.0237818
$833$	4.09483e49	0.0316919
$834$	2.00669e50	0.152081
$835$	−7.54860e50	−0.560213
$836$	1.46340e49	0.0106354
$837$	−7.45772e50	−0.530775
$838$	−1.00069e50	−0.0697476
$839$	−2.62276e51	−1.79029	−0.895147	−	0.445771i	$-0.852930\pi$
$839$	−2.62276e51	−1.79029	−0.895147	+	0.445771i	$0.852930\pi$
$840$	3.59649e50	0.240431
$841$	−1.33504e51	−0.874108
$842$	3.16560e49	0.0202999
$843$	2.48944e51	1.56357
$844$	2.33943e50	0.143918
$845$	−7.98459e50	−0.481128
$846$	4.93127e50	0.291056
$847$	−7.82695e50	−0.452515
$848$	2.00533e51	1.13569
$849$	1.61164e50	0.0894094
$850$	−2.35077e50	−0.127756
$851$	−1.71347e51	−0.912242
$852$	−5.13131e51	−2.67630
$853$	2.63497e51	1.34638	0.673191	−	0.739469i	$-0.264923\pi$
$853$	2.63497e51	1.34638	0.673191	+	0.739469i	$0.264923\pi$
$854$	5.30011e48	0.00265321
$855$	−3.08791e49	−0.0151446
$856$	−6.40758e50	−0.307895
$857$	1.21045e51	0.569880	0.284940	−	0.958545i	$-0.408026\pi$
$857$	1.21045e51	0.569880	0.284940	+	0.958545i	$0.408026\pi$
$858$	1.10686e49	0.00510579
$859$	1.22181e51	0.552234	0.276117	−	0.961124i	$-0.410952\pi$
$859$	1.22181e51	0.552234	0.276117	+	0.961124i	$0.410952\pi$
$860$	1.26413e51	0.559847
$861$	5.06680e51	2.19876
$862$	−1.34112e50	−0.0570283
$863$	−1.06383e51	−0.443284	−0.221642	−	0.975128i	$-0.571142\pi$
$863$	−1.06383e51	−0.443284	−0.221642	+	0.975128i	$0.571142\pi$
$864$	−2.06541e51	−0.843366
$865$	1.40015e51	0.560265
$866$	3.28911e50	0.128978
$867$	1.48420e51	0.570373
$868$	6.80586e50	0.256323
$869$	−3.24078e51	−1.19620
$870$	1.20832e50	0.0437113
$871$	3.39491e49	0.0120368
$872$	1.13044e51	0.392835
$873$	−8.63448e51	−2.94094
$874$	−8.11515e48	−0.00270923
$875$	−2.56553e51	−0.839531
$876$	−1.32280e51	−0.424301
$877$	2.07831e51	0.653459	0.326729	−	0.945118i	$-0.394053\pi$
$877$	2.07831e51	0.653459	0.326729	+	0.945118i	$0.394053\pi$
$878$	−5.12075e50	−0.157826
$879$	1.04936e52	3.17043
$880$	1.12133e51	0.332112
$881$	−5.23747e51	−1.52070	−0.760350	−	0.649514i	$-0.774973\pi$
$881$	−5.23747e51	−1.52070	−0.760350	+	0.649514i	$0.774973\pi$
$882$	2.98262e49	0.00848981
$883$	−2.39426e51	−0.668126	−0.334063	−	0.942551i	$-0.608420\pi$
$883$	−2.39426e51	−0.668126	−0.334063	+	0.942551i	$0.608420\pi$
$884$	−1.11639e50	−0.0305423
$885$	−1.63305e51	−0.438017
$886$	4.13554e50	0.108753
$887$	4.11591e51	1.06121	0.530606	−	0.847618i	$-0.321964\pi$
$887$	4.11591e51	1.06121	0.530606	+	0.847618i	$0.321964\pi$
$888$	1.44045e51	0.364141
$889$	3.57641e50	0.0886476
$890$	−1.48643e50	−0.0361259
$891$	4.34331e51	1.03505
$892$	−2.57309e51	−0.601270
$893$	6.08885e49	0.0139519
$894$	−7.28026e50	−0.163584
$895$	−7.79079e50	−0.171664
$896$	2.50378e51	0.541011
$897$	2.87319e50	0.0608832
$898$	9.95614e50	0.206898
$899$	4.62200e50	0.0941966
$900$	8.01520e51	1.60203
$901$	−7.10499e51	−1.39277
$902$	−6.97383e50	−0.134078
$903$	−1.09878e52	−2.07194
$904$	−1.33127e51	−0.246218
$905$	2.56338e51	0.465011
$906$	−1.86143e51	−0.331210
$907$	1.27732e51	0.222932	0.111466	−	0.993768i	$-0.464445\pi$
$907$	1.27732e51	0.222932	0.111466	+	0.993768i	$0.464445\pi$
$908$	5.49489e50	0.0940712
$909$	−1.15922e52	−1.94670
$910$	1.13078e49	0.00186274
$911$	4.62833e51	0.747915	0.373958	−	0.927446i	$-0.378001\pi$
$911$	4.62833e51	0.747915	0.373958	+	0.927446i	$0.378001\pi$
$912$	−1.54537e50	−0.0244975
$913$	7.61259e51	1.18384
$914$	2.96970e50	0.0453058
$915$	−1.05883e50	−0.0158474
$916$	−5.34118e51	−0.784272
$917$	1.27861e52	1.84193
$918$	2.35256e51	0.332501
$919$	3.73013e50	0.0517253	0.0258626	−	0.999666i	$-0.491767\pi$
$919$	3.73013e50	0.0517253	0.0258626	+	0.999666i	$0.491767\pi$
$920$	−1.28496e51	−0.174825
$921$	8.07933e51	1.07853
$922$	1.05026e51	0.137564
$923$	−3.26116e50	−0.0419123
$924$	−9.96398e51	−1.25653
$925$	−4.46407e51	−0.552396
$926$	−1.47573e51	−0.179190
$927$	−3.19613e50	−0.0380828
$928$	1.28006e51	0.149672
$929$	3.82307e51	0.438669	0.219334	−	0.975650i	$-0.429611\pi$
$929$	3.82307e51	0.438669	0.219334	+	0.975650i	$0.429611\pi$
$930$	2.90458e50	0.0327063
$931$	3.68277e48	0.000406964 0
$932$	−3.92499e51	−0.425658
$933$	5.35845e51	0.570309
$934$	−7.95853e50	−0.0831310
$935$	−3.97291e51	−0.407292
$936$	−1.64370e50	−0.0165385
$937$	1.21639e52	1.20124	0.600619	−	0.799536i	$-0.294921\pi$
$937$	1.21639e52	1.20124	0.600619	+	0.799536i	$0.294921\pi$
$938$	6.52875e50	0.0632820
$939$	−2.41858e52	−2.30098
$940$	4.76963e51	0.445397
$941$	−1.11091e52	−1.01827	−0.509133	−	0.860688i	$-0.670034\pi$
$941$	−1.11091e52	−1.01827	−0.509133	+	0.860688i	$0.670034\pi$
$942$	1.20606e49	0.00108512
$943$	−1.81028e52	−1.59879
$944$	−5.56166e51	−0.482163
$945$	1.11543e52	0.949261
$946$	1.51234e51	0.126344
$947$	3.07714e51	0.252362	0.126181	−	0.992007i	$-0.459728\pi$
$947$	3.07714e51	0.252362	0.126181	+	0.992007i	$0.459728\pi$
$948$	3.49864e52	2.81678
$949$	−8.40695e49	−0.00664477
$950$	−2.11422e49	−0.00164054
$951$	2.94620e52	2.24442
$952$	−4.33972e51	−0.324575
$953$	4.41309e50	0.0324053	0.0162027	−	0.999869i	$-0.494842\pi$
$953$	4.41309e50	0.0324053	0.0162027	+	0.999869i	$0.494842\pi$
$954$	−5.17519e51	−0.373104
$955$	−2.93417e50	−0.0207695
$956$	−1.71494e52	−1.19189
$957$	−6.76673e51	−0.461764
$958$	1.94550e51	0.130357
$959$	1.61623e52	1.06335
$960$	−1.15596e52	−0.746789
$961$	−1.46527e52	−0.929519
$962$	4.52893e49	0.00282119
$963$	−3.74584e52	−2.29134
$964$	2.44665e52	1.46969
$965$	−1.20123e52	−0.708594
$966$	5.52543e51	0.320086
$967$	2.95259e52	1.67973	0.839866	−	0.542795i	$-0.182634\pi$
$967$	2.95259e52	1.67973	0.839866	+	0.542795i	$0.182634\pi$
$968$	−2.35084e51	−0.131342
$969$	5.47532e50	0.0300430
$970$	1.78411e51	0.0961427
$971$	−8.31094e51	−0.439859	−0.219930	−	0.975516i	$-0.570583\pi$
$971$	−8.31094e51	−0.439859	−0.219930	+	0.975516i	$0.570583\pi$
$972$	−9.23125e51	−0.479845
$973$	−1.14806e52	−0.586126
$974$	3.55149e51	0.178086
$975$	7.48546e50	0.0368670
$976$	−3.60605e50	−0.0174446
$977$	−2.16398e52	−1.02825	−0.514125	−	0.857715i	$-0.671883\pi$
$977$	−2.16398e52	−1.02825	−0.514125	+	0.857715i	$0.671883\pi$
$978$	−8.44577e51	−0.394193
$979$	8.32419e51	0.381632
$980$	2.88486e50	0.0129918
$981$	6.60851e52	2.92345
$982$	−1.35158e51	−0.0587341
$983$	1.17980e51	0.0503643	0.0251822	−	0.999683i	$-0.491983\pi$
$983$	1.17980e51	0.0503643	0.0251822	+	0.999683i	$0.491983\pi$
$984$	1.52183e52	0.638192
$985$	9.12139e51	0.375774
$986$	−1.45802e51	−0.0590090
$987$	−4.14577e52	−1.64837
$988$	−1.00405e49	−0.000392202 0
$989$	3.92576e52	1.50657
$990$	−2.89382e51	−0.109108
$991$	−1.92041e52	−0.711387	−0.355694	−	0.934603i	$-0.615755\pi$
$991$	−1.92041e52	−0.711387	−0.355694	+	0.934603i	$0.615755\pi$
$992$	3.07704e51	0.111990
$993$	1.02963e52	0.368188
$994$	−6.27152e51	−0.220349
$995$	1.49386e52	0.515710
$996$	−8.21830e52	−2.78769
$997$	−4.51709e52	−1.50554	−0.752772	−	0.658281i	$-0.771284\pi$
$997$	−4.51709e52	−1.50554	−0.752772	+	0.658281i	$0.771284\pi$
$998$	−8.39864e50	−0.0275058
$999$	4.46746e52	1.43769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.36.a.a.1.2	✓	3
3.2	odd	2		9.36.a.b.1.2		3
4.3	odd	2		16.36.a.d.1.1		3
5.2	odd	4		25.36.b.a.24.3		6
5.3	odd	4		25.36.b.a.24.4		6
5.4	even	2		25.36.a.a.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.36.a.a.1.2	✓	3	1.1	even	1	trivial
9.36.a.b.1.2		3	3.2	odd	2
16.36.a.d.1.1		3	4.3	odd	2
25.36.a.a.1.2		3	5.4	even	2
25.36.b.a.24.3		6	5.2	odd	4
25.36.b.a.24.4		6	5.3	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)

\(f(q)\)	\(=\)	\(q-26808.0 q^{2} +3.95729e8 q^{3} -3.36411e10 q^{4} +8.21401e11 q^{5} -1.06087e13 q^{6} +6.06942e14 q^{7} +1.82297e15 q^{8} +1.06570e17 q^{9} +O(q^{10})\)	\(q-26808.0 q^{2} +3.95729e8 q^{3} -3.36411e10 q^{4} +8.21401e11 q^{5} -1.06087e13 q^{6} +6.06942e14 q^{7} +1.82297e15 q^{8} +1.06570e17 q^{9} -2.20201e16 q^{10} +1.23316e18 q^{11} -1.33127e19 q^{12} -8.46079e17 q^{13} -1.62709e19 q^{14} +3.25052e20 q^{15} +1.10703e21 q^{16} -3.92226e21 q^{17} -2.85692e21 q^{18} -3.52757e20 q^{19} -2.76328e22 q^{20} +2.40184e23 q^{21} -3.30584e22 q^{22} -8.58137e23 q^{23} +7.21400e23 q^{24} -2.23568e24 q^{25} +2.26817e22 q^{26} +2.23738e25 q^{27} -2.04182e25 q^{28} -1.38664e25 q^{29} -8.71400e24 q^{30} -3.33324e25 q^{31} -9.23139e25 q^{32} +4.87995e26 q^{33} +1.05148e26 q^{34} +4.98543e26 q^{35} -3.58512e27 q^{36} +1.99674e27 q^{37} +9.45671e24 q^{38} -3.34818e26 q^{39} +1.49739e27 q^{40} +2.10955e28 q^{41} -6.43887e27 q^{42} -4.57475e28 q^{43} -4.14847e28 q^{44} +8.75365e28 q^{45} +2.30049e28 q^{46} -1.72608e29 q^{47} +4.38083e29 q^{48} -1.04400e28 q^{49} +5.99342e28 q^{50} -1.55215e30 q^{51} +2.84630e28 q^{52} +1.81145e30 q^{53} -5.99797e29 q^{54} +1.01292e30 q^{55} +1.10643e30 q^{56} -1.39596e29 q^{57} +3.71730e29 q^{58} -5.02395e30 q^{59} -1.09351e31 q^{60} -3.25742e29 q^{61} +8.93574e29 q^{62} +6.46817e31 q^{63} -3.55625e31 q^{64} -6.94970e29 q^{65} -1.30822e31 q^{66} -4.01253e31 q^{67} +1.31949e32 q^{68} -3.39589e32 q^{69} -1.33649e31 q^{70} +3.85444e32 q^{71} +1.94273e32 q^{72} +9.93637e31 q^{73} -5.35285e31 q^{74} -8.84724e32 q^{75} +1.18671e31 q^{76} +7.48454e32 q^{77} +8.97580e30 q^{78} -2.62804e33 q^{79} +9.09314e32 q^{80} +3.52211e33 q^{81} -5.65527e32 q^{82} +6.17326e33 q^{83} -8.08006e33 q^{84} -3.22175e33 q^{85} +1.22640e33 q^{86} -5.48733e33 q^{87} +2.24800e33 q^{88} +6.75031e33 q^{89} -2.34668e33 q^{90} -5.13521e32 q^{91} +2.88686e34 q^{92} -1.31906e34 q^{93} +4.62727e33 q^{94} -2.89755e32 q^{95} -3.65313e34 q^{96} -8.10218e34 q^{97} +2.79875e32 q^{98} +1.31417e35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 139656 q^{2} - 104875308 q^{3} + 34841262144 q^{4} + 892652054010 q^{5} - 4786530564384 q^{6} + 878422149346056 q^{7} + 22\!\cdots\!00 q^{8}+ \cdots + 15\!\cdots\!51 q^{9}+O(q^{10}) \) 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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