LMFDB - Embedded newform 3.42.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,42,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

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

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 42);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 42 $
Character orbit:	$[\chi]$	$=$	3.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:	$31.9415011369$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 196497525461x^{2} + 10360343667016365x + 6095744045744274504000 $ x^4 - x^3 - 196497525461x^2 + 10360343667016365x + 6095744045744274504000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{10}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$330995.$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00342e6 q^{2} +3.48678e9 q^{3} +1.81468e12 q^{4} -3.43221e14 q^{5} -6.98551e15 q^{6} -2.11939e17 q^{7} +7.69998e17 q^{8} +1.21577e19 q^{9} +O(q^{10})$	\(q-2.00342e6 q^{2} +3.48678e9 q^{3} +1.81468e12 q^{4} -3.43221e14 q^{5} -6.98551e15 q^{6} -2.11939e17 q^{7} +7.69998e17 q^{8} +1.21577e19 q^{9} +6.87617e20 q^{10} -2.68951e21 q^{11} +6.32741e21 q^{12} -4.84491e22 q^{13} +4.24604e23 q^{14} -1.19674e24 q^{15} -5.53316e24 q^{16} -2.66383e25 q^{17} -2.43570e25 q^{18} +4.14274e24 q^{19} -6.22838e26 q^{20} -7.38986e26 q^{21} +5.38824e27 q^{22} -6.80863e27 q^{23} +2.68482e27 q^{24} +7.23261e28 q^{25} +9.70641e28 q^{26} +4.23912e28 q^{27} -3.84602e29 q^{28} -1.53939e30 q^{29} +2.39757e30 q^{30} -6.13330e29 q^{31} +9.39202e30 q^{32} -9.37775e30 q^{33} +5.33678e31 q^{34} +7.27420e31 q^{35} +2.20623e31 q^{36} +1.47726e32 q^{37} -8.29967e30 q^{38} -1.68932e32 q^{39} -2.64280e32 q^{40} +1.43312e33 q^{41} +1.48050e33 q^{42} +1.93562e33 q^{43} -4.88061e33 q^{44} -4.17277e33 q^{45} +1.36406e34 q^{46} -1.54236e34 q^{47} -1.92929e34 q^{48} +3.50578e32 q^{49} -1.44900e35 q^{50} -9.28821e34 q^{51} -8.79197e34 q^{52} +2.77827e35 q^{53} -8.49274e34 q^{54} +9.23098e35 q^{55} -1.63193e35 q^{56} +1.44449e34 q^{57} +3.08404e36 q^{58} -2.82191e36 q^{59} -2.17170e36 q^{60} +3.86057e36 q^{61} +1.22876e36 q^{62} -2.57669e36 q^{63} -6.64865e36 q^{64} +1.66288e37 q^{65} +1.87876e37 q^{66} -4.59962e36 q^{67} -4.83401e37 q^{68} -2.37402e37 q^{69} -1.45733e38 q^{70} +9.12164e37 q^{71} +9.36137e36 q^{72} -6.94314e36 q^{73} -2.95957e38 q^{74} +2.52185e38 q^{75} +7.51776e36 q^{76} +5.70013e38 q^{77} +3.38441e38 q^{78} +5.97141e38 q^{79} +1.89910e39 q^{80} +1.47809e38 q^{81} -2.87114e39 q^{82} -3.36804e39 q^{83} -1.34103e39 q^{84} +9.14284e39 q^{85} -3.87787e39 q^{86} -5.36751e39 q^{87} -2.07092e39 q^{88} -1.32775e40 q^{89} +8.35982e39 q^{90} +1.02683e40 q^{91} -1.23555e40 q^{92} -2.13855e39 q^{93} +3.09000e40 q^{94} -1.42188e39 q^{95} +3.27479e40 q^{96} -9.71560e40 q^{97} -7.02357e38 q^{98} -3.26982e40 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 69822 q^{2} + 13947137604 q^{3} + 5352947588932 q^{4} + 118536963776280 q^{5} - 243454260446622 q^{6} + 15\!\cdots\!36 q^{7}+ \cdots + 48\!\cdots\!04 q^{9}+O(q^{10}) $ 4 * q - 69822 * q^2 + 13947137604 * q^3 + 5352947588932 * q^4 + 118536963776280 * q^5 - 243454260446622 * q^6 + 150256264888927136 * q^7 + 6279626248119395784 * q^8 + 48630661836227715204 * q^9	$ 4 q - 69822 q^{2} + 13947137604 q^{3} + 5352947588932 q^{4} + 118536963776280 q^{5} - 243454260446622 q^{6} + 15\!\cdots\!36 q^{7}+ \cdots + 88\!\cdots\!56 q^{99}+O(q^{100}) $ 4 * q - 69822 * q^2 + 13947137604 * q^3 + 5352947588932 * q^4 + 118536963776280 * q^5 - 243454260446622 * q^6 + 150256264888927136 * q^7 + 6279626248119395784 * q^8 + 48630661836227715204 * q^9 + 725751018728422700940 * q^10 + 724810647231440683056 * q^11 + 18664574152458657849732 * q^12 - 8843977274373065537608 * q^13 + 493449664223337937919568 * q^14 + 413312836237035157808280 * q^15 - 5962194966280197033033200 * q^16 - 38231582029295844707285688 * q^17 - 848872517682272882743422 * q^18 + 261842746845948075837831248 * q^19 + 785441926018305471679038360 * q^20 + 523911200567235135430405536 * q^21 - 6322149663566345845522943976 * q^22 - 15395573913207335266380880032 * q^23 + 21895702846052864805196365384 * q^24 + 117350921958371528604086683900 * q^25 - 62942545095927728709970694052 * q^26 + 169564633100864814057177732804 * q^27 + 684437536459146482218511575712 * q^28 - 1036098964520685524199931325064 * q^29 + 2530537331112123128971880036940 * q^30 + 9280613209905247622577480610304 * q^31 + 19645397922916950127447685511456 * q^32 + 2527258458445301210436445809456 * q^33 + 92420157643501864091330064020004 * q^34 + 207436667553525639419383641992640 * q^35 + 65079346006100643987841739630532 * q^36 + 200754880510048713109452091192856 * q^37 + 1146938682238729575315585266559528 * q^38 - 30837042003082501971082253252808 * q^39 + 2565083222429486590317315499815600 * q^40 + 2357905268481965433001096926030504 * q^41 + 1720552591892622502089456095058768 * q^42 + 3943358618915609696106480688157360 * q^43 - 18494278585991583572852191821764304 * q^44 + 1441132750124361726734484052640280 * q^45 - 44252120640849956767942988241684816 * q^46 - 8890000412230234893665157147040320 * q^47 - 20788888404146512009986643475113200 * q^48 - 33104900387055220681685954563991580 * q^49 - 216323679312314207800001999371642050 * q^50 - 133305283845300676339482147968952888 * q^51 - 596234086188669794371774262733483208 * q^52 + 95704753827317216756019399314791128 * q^53 - 2959835453092145761775065914960222 * q^54 + 1291057043675253444545805475556816160 * q^55 + 1940580325939766339139469085046208320 * q^56 + 912989205217443700887315001196762448 * q^57 + 3859053206955865617315425524661917116 * q^58 - 1809289331104083090977131835906657808 * q^59 + 2738666655532023559103418232328622360 * q^60 + 5381027332088000515346282395501157240 * q^61 + 14109494547714507002913033009898657152 * q^62 + 1826765401647017821917860444028843936 * q^63 - 389844533130084697385386794140537792 * q^64 - 9754648834359651370261564655441346480 * q^65 - 22043972827710532722740556743113718376 * q^66 - 73273159367285254897696664016673247728 * q^67 - 89019363361032581039655795923994746424 * q^68 - 53681046965013864485594032220229980832 * q^69 - 127374089191018487217525315519713602080 * q^70 - 84396091414708989106237239330896374752 * q^71 + 76345595132548433424120590562827574984 * q^72 - 44706579271813174655854382994714255832 * q^73 - 299692406925616462116506150539738813812 * q^74 + 409177364127418217299254754274337843900 * q^75 + 1128262001217587654782588548338718696272 * q^76 + 833312137190144115784050615522845895552 * q^77 - 219467084399719853089285669187657082852 * q^78 + 1416534390331633014953369475707893311680 * q^79 + 1539903590051088861086709486592809053280 * q^80 + 591235317657383693264332840825533190404 * q^81 + 613971248288365719286532695984150451412 * q^82 + 1526205590962076227407755639349783073104 * q^83 + 2386486125584620727973530035630532068512 * q^84 - 285377453319367852617718519171747770960 * q^85 - 12934468921257599734617599325958640634024 * q^86 - 3612653707382978727606828549504415526664 * q^87 - 13219976774504188013705589441700285953696 * q^88 - 39593715237961905051969833281675978558872 * q^89 + 8823438092269922908090462480445695772940 * q^90 - 8845052344004724172694600210873108791616 * q^91 - 65206363053810587386463980322833360400544 * q^92 + 32359497372012156098445494805887947067904 * q^93 + 98582759073905793403791649187553312740832 * q^94 + 7880313586718908134850457997267850706400 * q^95 + 68499267029064622122879551784898487597856 * q^96 + 36750128325858234547252025624989137001352 * q^97 - 68350119771260167200829379908744318383822 * q^98 + 8812005370202382972296217650292999095856 * 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 $

$2$	−2.00342e6	−1.35101	−0.675504	−	0.737356i	$-0.736074\pi$
$2$	−2.00342e6	−1.35101	−0.675504	+	0.737356i	$0.736074\pi$
$3$	3.48678e9	0.577350
$3$	3.48678e9	0.577350
$4$	1.81468e12	0.825222
$5$	−3.43221e14	−1.60949	−0.804746	−	0.593619i	$-0.797699\pi$
$5$	−3.43221e14	−1.60949	−0.804746	+	0.593619i	$0.797699\pi$
$6$	−6.98551e15	−0.780005
$7$	−2.11939e17	−1.00393	−0.501963	−	0.864889i	$-0.667389\pi$
$7$	−2.11939e17	−1.00393	−0.501963	+	0.864889i	$0.667389\pi$
$8$	7.69998e17	0.236126
$9$	1.21577e19	0.333333
$10$	6.87617e20	2.17444
$11$	−2.68951e21	−1.20538	−0.602690	−	0.797976i	$-0.705904\pi$
$11$	−2.68951e21	−1.20538	−0.602690	+	0.797976i	$0.705904\pi$
$12$	6.32741e21	0.476442
$13$	−4.84491e22	−0.707045	−0.353522	−	0.935426i	$-0.615016\pi$
$13$	−4.84491e22	−0.707045	−0.353522	+	0.935426i	$0.615016\pi$
$14$	4.24604e23	1.35631
$15$	−1.19674e24	−0.929241
$16$	−5.53316e24	−1.14423
$17$	−2.66383e25	−1.58966	−0.794830	−	0.606833i	$-0.792440\pi$
$17$	−2.66383e25	−1.58966	−0.794830	+	0.606833i	$0.792440\pi$
$18$	−2.43570e25	−0.450336
$19$	4.14274e24	0.0252836	0.0126418	−	0.999920i	$-0.495976\pi$
$19$	4.14274e24	0.0252836	0.0126418	+	0.999920i	$0.495976\pi$
$20$	−6.22838e26	−1.32819
$21$	−7.38986e26	−0.579617
$22$	5.38824e27	1.62848
$23$	−6.80863e27	−0.827254	−0.413627	−	0.910446i	$-0.635738\pi$
$23$	−6.80863e27	−0.827254	−0.413627	+	0.910446i	$0.635738\pi$
$24$	2.68482e27	0.136328
$25$	7.23261e28	1.59047
$26$	9.70641e28	0.955223
$27$	4.23912e28	0.192450
$28$	−3.84602e29	−0.828461
$29$	−1.53939e30	−1.61506	−0.807530	−	0.589827i	$-0.799196\pi$
$29$	−1.53939e30	−1.61506	−0.807530	+	0.589827i	$0.799196\pi$
$30$	2.39757e30	1.25541
$31$	−6.13330e29	−0.163976	−0.0819878	−	0.996633i	$-0.526127\pi$
$31$	−6.13330e29	−0.163976	−0.0819878	+	0.996633i	$0.526127\pi$
$32$	9.39202e30	1.30974
$33$	−9.37775e30	−0.695926
$34$	5.33678e31	2.14764
$35$	7.27420e31	1.61581
$36$	2.20623e31	0.275074
$37$	1.47726e32	1.05032	0.525160	−	0.851004i	$-0.324006\pi$
$37$	1.47726e32	1.05032	0.525160	+	0.851004i	$0.324006\pi$
$38$	−8.29967e30	−0.0341584
$39$	−1.68932e32	−0.408213
$40$	−2.64280e32	−0.380044
$41$	1.43312e33	1.24226	0.621131	−	0.783707i	$-0.286674\pi$
$41$	1.43312e33	1.24226	0.621131	+	0.783707i	$0.286674\pi$
$42$	1.48050e33	0.783067
$43$	1.93562e33	0.632001	0.316000	−	0.948759i	$-0.397660\pi$
$43$	1.93562e33	0.632001	0.316000	+	0.948759i	$0.397660\pi$
$44$	−4.88061e33	−0.994706
$45$	−4.17277e33	−0.536498
$46$	1.36406e34	1.11763
$47$	−1.54236e34	−0.813168	−0.406584	−	0.913614i	$-0.633280\pi$
$47$	−1.54236e34	−0.813168	−0.406584	+	0.913614i	$0.633280\pi$
$48$	−1.92929e34	−0.660622
$49$	3.50578e32	0.00786621
$50$	−1.44900e35	−2.14873
$51$	−9.28821e34	−0.917790
$52$	−8.79197e34	−0.583469
$53$	2.77827e35	1.24773	0.623863	−	0.781534i	$-0.285562\pi$
$53$	2.77827e35	1.24773	0.623863	+	0.781534i	$0.285562\pi$
$54$	−8.49274e34	−0.260002
$55$	9.23098e35	1.94005
$56$	−1.63193e35	−0.237053
$57$	1.44449e34	0.0145975
$58$	3.08404e36	2.18196
$59$	−2.82191e36	−1.40630	−0.703148	−	0.711044i	$-0.748223\pi$
$59$	−2.82191e36	−1.40630	−0.703148	+	0.711044i	$0.748223\pi$
$60$	−2.17170e36	−0.766830
$61$	3.86057e36	0.971382	0.485691	−	0.874130i	$-0.338568\pi$
$61$	3.86057e36	0.971382	0.485691	+	0.874130i	$0.338568\pi$
$62$	1.22876e36	0.221532
$63$	−2.57669e36	−0.334642
$64$	−6.64865e36	−0.625236
$65$	1.66288e37	1.13798
$66$	1.87876e37	0.940202
$67$	−4.59962e36	−0.169118	−0.0845588	−	0.996418i	$-0.526948\pi$
$67$	−4.59962e36	−0.169118	−0.0845588	+	0.996418i	$0.526948\pi$
$68$	−4.83401e37	−1.31182
$69$	−2.37402e37	−0.477615
$70$	−1.45733e38	−2.18297
$71$	9.12164e37	1.02159	0.510795	−	0.859703i	$-0.329351\pi$
$71$	9.12164e37	1.02159	0.510795	+	0.859703i	$0.329351\pi$
$72$	9.36137e36	0.0787088
$73$	−6.94314e36	−0.0439985	−0.0219992	−	0.999758i	$-0.507003\pi$
$73$	−6.94314e36	−0.0439985	−0.0219992	+	0.999758i	$0.507003\pi$
$74$	−2.95957e38	−1.41899
$75$	2.52185e38	0.918257
$76$	7.51776e36	0.0208646
$77$	5.70013e38	1.21011
$78$	3.38441e38	0.551498
$79$	5.97141e38	0.749414	0.374707	−	0.927143i	$-0.377743\pi$
$79$	5.97141e38	0.749414	0.374707	+	0.927143i	$0.377743\pi$
$80$	1.89910e39	1.84163
$81$	1.47809e38	0.111111
$82$	−2.87114e39	−1.67830
$83$	−3.36804e39	−1.53559	−0.767797	−	0.640694i	$-0.778647\pi$
$83$	−3.36804e39	−1.53559	−0.767797	+	0.640694i	$0.778647\pi$
$84$	−1.34103e39	−0.478312
$85$	9.14284e39	2.55854
$86$	−3.87787e39	−0.853838
$87$	−5.36751e39	−0.932455
$88$	−2.07092e39	−0.284622
$89$	−1.32775e40	−1.44750	−0.723752	−	0.690060i	$-0.757584\pi$
$89$	−1.32775e40	−1.44750	−0.723752	+	0.690060i	$0.757584\pi$
$90$	8.35982e39	0.724812
$91$	1.02683e40	0.709820
$92$	−1.23555e40	−0.682668
$93$	−2.13855e39	−0.0946714
$94$	3.09000e40	1.09860
$95$	−1.42188e39	−0.0406938
$96$	3.27479e40	0.756178
$97$	−9.71560e40	−1.81405	−0.907025	−	0.421077i	$-0.861652\pi$
$97$	−9.71560e40	−1.81405	−0.907025	+	0.421077i	$0.861652\pi$
$98$	−7.02357e38	−0.0106273
$99$	−3.26982e40	−0.401793
$100$	1.31249e41	1.31249
$101$	−4.41832e40	−0.360304	−0.180152	−	0.983639i	$-0.557659\pi$
$101$	−4.41832e40	−0.360304	−0.180152	+	0.983639i	$0.557659\pi$
$102$	1.86082e41	1.23994
$103$	2.87560e41	1.56879	0.784395	−	0.620262i	$-0.212974\pi$
$103$	2.87560e41	1.56879	0.784395	+	0.620262i	$0.212974\pi$
$104$	−3.73057e40	−0.166952
$105$	2.53636e41	0.932889
$106$	−5.56605e41	−1.68569
$107$	−9.23802e40	−0.230787	−0.115394	−	0.993320i	$-0.536813\pi$
$107$	−9.23802e40	−0.230787	−0.115394	+	0.993320i	$0.536813\pi$
$108$	7.69265e40	0.158814
$109$	−7.45590e41	−1.27426	−0.637128	−	0.770758i	$-0.719878\pi$
$109$	−7.45590e41	−1.27426	−0.637128	+	0.770758i	$0.719878\pi$
$110$	−1.84936e42	−2.62102
$111$	5.15088e41	0.606402
$112$	1.17269e42	1.14872
$113$	−1.06665e42	−0.870791	−0.435396	−	0.900239i	$-0.643391\pi$
$113$	−1.06665e42	−0.870791	−0.435396	+	0.900239i	$0.643391\pi$
$114$	−2.89392e40	−0.0197213
$115$	2.33686e42	1.33146
$116$	−2.79350e42	−1.33278
$117$	−5.89028e41	−0.235682
$118$	5.65348e42	1.89992
$119$	5.64570e42	1.59590
$120$	−9.21486e41	−0.219418
$121$	2.25497e42	0.452939
$122$	−7.73436e42	−1.31235
$123$	4.99698e42	0.717220
$124$	−1.11300e42	−0.135316
$125$	−9.21595e42	−0.950353
$126$	5.16219e42	0.452104
$127$	3.83161e42	0.285368	0.142684	−	0.989768i	$-0.454427\pi$
$127$	3.83161e42	0.285368	0.142684	+	0.989768i	$0.454427\pi$
$128$	−7.33322e42	−0.465040
$129$	6.74910e42	0.364886
$130$	−3.33144e43	−1.53742
$131$	2.73831e43	1.07999	0.539996	−	0.841667i	$-0.318426\pi$
$131$	2.73831e43	1.07999	0.539996	+	0.841667i	$0.318426\pi$
$132$	−1.70176e43	−0.574294
$133$	−8.78010e41	−0.0253829
$134$	9.21500e42	0.228479
$135$	−1.45495e43	−0.309747
$136$	−2.05114e43	−0.375361
$137$	−4.47383e42	−0.0704544	−0.0352272	−	0.999379i	$-0.511215\pi$
$137$	−4.47383e42	−0.0704544	−0.0352272	+	0.999379i	$0.511215\pi$
$138$	4.75617e43	0.645262
$139$	−9.98093e43	−1.16780	−0.583899	−	0.811826i	$-0.698474\pi$
$139$	−9.98093e43	−1.16780	−0.583899	+	0.811826i	$0.698474\pi$
$140$	1.32004e44	1.33340
$141$	−5.37788e43	−0.469482
$142$	−1.82745e44	−1.38018
$143$	1.30305e44	0.852257
$144$	−6.72703e43	−0.381410
$145$	5.28350e44	2.59943
$146$	1.39101e43	0.0594423
$147$	1.22239e42	0.00454156
$148$	2.68076e44	0.866746
$149$	2.04820e44	0.576837	0.288419	−	0.957504i	$-0.406870\pi$
$149$	2.04820e44	0.576837	0.288419	+	0.957504i	$0.406870\pi$
$150$	−5.05234e44	−1.24057
$151$	3.17569e43	0.0680472	0.0340236	−	0.999421i	$-0.489168\pi$
$151$	3.17569e43	0.0680472	0.0340236	+	0.999421i	$0.489168\pi$
$152$	3.18990e42	0.00597013
$153$	−3.23860e44	−0.529886
$154$	−1.14198e45	−1.63487
$155$	2.10508e44	0.263918
$156$	−3.06557e44	−0.336866
$157$	1.69451e44	0.163343	0.0816715	−	0.996659i	$-0.473974\pi$
$157$	1.69451e44	0.163343	0.0816715	+	0.996659i	$0.473974\pi$
$158$	−1.19633e45	−1.01246
$159$	9.68723e44	0.720375
$160$	−3.22354e45	−2.10801
$161$	1.44301e45	0.830501
$162$	−2.96124e44	−0.150112
$163$	4.18577e44	0.187038	0.0935189	−	0.995618i	$-0.470188\pi$
$163$	4.18577e44	0.187038	0.0935189	+	0.995618i	$0.470188\pi$
$164$	2.60065e45	1.02514
$165$	3.21864e45	1.12009
$166$	6.74761e45	2.07460
$167$	4.36373e45	1.18623	0.593117	−	0.805117i	$-0.297897\pi$
$167$	4.36373e45	1.18623	0.593117	+	0.805117i	$0.297897\pi$
$168$	−5.69018e44	−0.136863
$169$	−2.34814e45	−0.500088
$170$	−1.83170e46	−3.45661
$171$	5.03661e43	0.00842787
$172$	3.51254e45	0.521541
$173$	−4.54949e44	−0.0599815	−0.0299907	−	0.999550i	$-0.509548\pi$
$173$	−4.54949e44	−0.0599815	−0.0299907	+	0.999550i	$0.509548\pi$
$174$	1.07534e46	1.25975
$175$	−1.53287e46	−1.59671
$176$	1.48815e46	1.37923
$177$	−9.83939e45	−0.811925
$178$	2.66004e46	1.95559
$179$	−1.96397e46	−1.28720	−0.643601	−	0.765361i	$-0.722560\pi$
$179$	−1.96397e46	−1.28720	−0.643601	+	0.765361i	$0.722560\pi$
$180$	−7.57225e45	−0.442730
$181$	2.64903e45	0.138254	0.0691268	−	0.997608i	$-0.477979\pi$
$181$	2.64903e45	0.138254	0.0691268	+	0.997608i	$0.477979\pi$
$182$	−2.05717e46	−0.958973
$183$	1.34610e46	0.560828
$184$	−5.24262e45	−0.195336
$185$	−5.07027e46	−1.69048
$186$	4.28442e45	0.127902
$187$	7.16441e46	1.91614
$188$	−2.79890e46	−0.671044
$189$	−8.98435e45	−0.193206
$190$	2.84862e45	0.0549777
$191$	2.19040e46	0.379612	0.189806	−	0.981822i	$-0.439214\pi$
$191$	2.19040e46	0.379612	0.189806	+	0.981822i	$0.439214\pi$
$192$	−2.31824e46	−0.360980
$193$	−1.09612e47	−1.53438	−0.767189	−	0.641421i	$-0.778345\pi$
$193$	−1.09612e47	−1.53438	−0.767189	+	0.641421i	$0.778345\pi$
$194$	1.94645e47	2.45080
$195$	5.79809e46	0.657015
$196$	6.36189e44	0.00649137
$197$	6.57368e46	0.604297	0.302149	−	0.953261i	$-0.402296\pi$
$197$	6.57368e46	0.604297	0.302149	+	0.953261i	$0.402296\pi$
$198$	6.55084e46	0.542826
$199$	−1.41080e47	−1.05433	−0.527166	−	0.849762i	$-0.676745\pi$
$199$	−1.41080e47	−1.05433	−0.527166	+	0.849762i	$0.676745\pi$
$200$	5.56909e46	0.375551
$201$	−1.60379e46	−0.0976401
$202$	8.85177e46	0.486774
$203$	3.26256e47	1.62140
$204$	−1.68551e47	−0.757381
$205$	−4.91877e47	−1.99941
$206$	−5.76104e47	−2.11945
$207$	−8.27770e46	−0.275751
$208$	2.68077e47	0.809022
$209$	−1.11420e46	−0.0304764
$210$	−5.08140e47	−1.26034
$211$	−9.71826e46	−0.218675	−0.109337	−	0.994005i	$-0.534873\pi$
$211$	−9.71826e46	−0.218675	−0.109337	+	0.994005i	$0.534873\pi$
$212$	5.04168e47	1.02965
$213$	3.18052e47	0.589815
$214$	1.85077e47	0.311795
$215$	−6.64347e47	−1.01720
$216$	3.26411e46	0.0454426
$217$	1.29989e47	0.164619
$218$	1.49373e48	1.72153
$219$	−2.42092e46	−0.0254025
$220$	1.67513e48	1.60097
$221$	1.29060e48	1.12396
$222$	−1.03194e48	−0.819254
$223$	−1.08268e48	−0.783883	−0.391942	−	0.919990i	$-0.628197\pi$
$223$	−1.08268e48	−0.783883	−0.391942	+	0.919990i	$0.628197\pi$
$224$	−1.99054e48	−1.31488
$225$	8.79316e47	0.530156
$226$	2.13695e48	1.17645
$227$	−7.22684e47	−0.363428	−0.181714	−	0.983351i	$-0.558165\pi$
$227$	−7.22684e47	−0.363428	−0.181714	+	0.983351i	$0.558165\pi$
$228$	2.62128e46	0.0120462
$229$	−3.57660e48	−1.50260	−0.751299	−	0.659962i	$-0.770572\pi$
$229$	−3.57660e48	−1.50260	−0.751299	+	0.659962i	$0.770572\pi$
$230$	−4.68173e48	−1.79881
$231$	1.98751e48	0.698658
$232$	−1.18532e48	−0.381358
$233$	5.07597e48	1.49528	0.747640	−	0.664104i	$-0.231187\pi$
$233$	5.07597e48	1.49528	0.747640	+	0.664104i	$0.231187\pi$
$234$	1.18007e48	0.318408
$235$	5.29371e48	1.30879
$236$	−5.12087e48	−1.16051
$237$	2.08210e48	0.432674
$238$	−1.13107e49	−2.15607
$239$	−1.80945e48	−0.316512	−0.158256	−	0.987398i	$-0.550587\pi$
$239$	−1.80945e48	−0.316512	−0.158256	+	0.987398i	$0.550587\pi$
$240$	6.62175e48	1.06327
$241$	2.18958e48	0.322858	0.161429	−	0.986884i	$-0.448390\pi$
$241$	2.18958e48	0.322858	0.161429	+	0.986884i	$0.448390\pi$
$242$	−4.51765e48	−0.611924
$243$	5.15378e47	0.0641500
$244$	7.00571e48	0.801606
$245$	−1.20326e47	−0.0126606
$246$	−1.00111e49	−0.968970
$247$	−2.00712e47	−0.0178767
$248$	−4.72262e47	−0.0387190
$249$	−1.17436e49	−0.886575
$250$	1.84635e49	1.28393
$251$	1.23621e49	0.792100	0.396050	−	0.918229i	$-0.370381\pi$
$251$	1.23621e49	0.792100	0.396050	+	0.918229i	$0.370381\pi$
$252$	−4.67587e48	−0.276154
$253$	1.83119e49	0.997155
$254$	−7.67635e48	−0.385535
$255$	3.18791e49	1.47718
$256$	2.93121e49	1.25351
$257$	−7.95215e48	−0.313946	−0.156973	−	0.987603i	$-0.550174\pi$
$257$	−7.95215e48	−0.313946	−0.156973	+	0.987603i	$0.550174\pi$
$258$	−1.35213e49	−0.492963
$259$	−3.13089e49	−1.05444
$260$	3.01759e49	0.939089
$261$	−1.87153e49	−0.538353
$262$	−5.48599e49	−1.45908
$263$	−1.51702e49	−0.373162	−0.186581	−	0.982440i	$-0.559741\pi$
$263$	−1.51702e49	−0.373162	−0.186581	+	0.982440i	$0.559741\pi$
$264$	−7.22085e48	−0.164327
$265$	−9.53562e49	−2.00821
$266$	1.75903e48	0.0342925
$267$	−4.62956e49	−0.835717
$268$	−8.34686e48	−0.139560
$269$	7.09419e49	1.09896	0.549479	−	0.835508i	$-0.314826\pi$
$269$	7.09419e49	1.09896	0.549479	+	0.835508i	$0.314826\pi$
$270$	2.91489e49	0.418471
$271$	1.55633e49	0.207125	0.103563	−	0.994623i	$-0.466976\pi$
$271$	1.55633e49	0.207125	0.103563	+	0.994623i	$0.466976\pi$
$272$	1.47394e50	1.81894
$273$	3.58032e49	0.409815
$274$	8.96298e48	0.0951844
$275$	−1.94522e50	−1.91712
$276$	−4.30809e49	−0.394139
$277$	−3.47369e48	−0.0295091	−0.0147546	−	0.999891i	$-0.504697\pi$
$277$	−3.47369e48	−0.0295091	−0.0147546	+	0.999891i	$0.504697\pi$
$278$	1.99960e50	1.57770
$279$	−7.45666e48	−0.0546585
$280$	5.60112e49	0.381536
$281$	1.20363e50	0.762104	0.381052	−	0.924554i	$-0.375562\pi$
$281$	1.20363e50	0.762104	0.381052	+	0.924554i	$0.375562\pi$
$282$	1.07742e50	0.634275
$283$	6.17804e49	0.338243	0.169121	−	0.985595i	$-0.445907\pi$
$283$	6.17804e49	0.338243	0.169121	+	0.985595i	$0.445907\pi$
$284$	1.65529e50	0.843039
$285$	−4.95778e48	−0.0234946
$286$	−2.61055e50	−1.15141
$287$	−3.03734e50	−1.24714
$288$	1.14185e50	0.436579
$289$	4.28795e50	1.52702
$290$	−1.05851e51	−3.51185
$291$	−3.38762e50	−1.04734
$292$	−1.25996e49	−0.0363085
$293$	−6.08165e49	−0.163394	−0.0816968	−	0.996657i	$-0.526034\pi$
$293$	−6.08165e49	−0.163394	−0.0816968	+	0.996657i	$0.526034\pi$
$294$	−2.44897e48	−0.00613568
$295$	9.68539e50	2.26342
$296$	1.13749e50	0.248008
$297$	−1.14012e50	−0.231975
$298$	−4.10341e50	−0.779312
$299$	3.29872e50	0.584906
$300$	4.57637e50	0.757766
$301$	−4.10234e50	−0.634481
$302$	−6.36224e49	−0.0919323
$303$	−1.54057e50	−0.208022
$304$	−2.29225e49	−0.0289303
$305$	−1.32503e51	−1.56343
$306$	6.48828e50	0.715881
$307$	−2.16833e50	−0.223763	−0.111882	−	0.993722i	$-0.535688\pi$
$307$	−2.16833e50	−0.223763	−0.111882	+	0.993722i	$0.535688\pi$
$308$	1.03439e51	0.998610
$309$	1.00266e51	0.905741
$310$	−4.21736e50	−0.356555
$311$	4.74537e50	0.375563	0.187781	−	0.982211i	$-0.439870\pi$
$311$	4.74537e50	0.375563	0.187781	+	0.982211i	$0.439870\pi$
$312$	−1.30077e50	−0.0963898
$313$	−1.32823e51	−0.921749	−0.460875	−	0.887465i	$-0.652464\pi$
$313$	−1.32823e51	−0.921749	−0.460875	+	0.887465i	$0.652464\pi$
$314$	−3.39481e50	−0.220678
$315$	8.84373e50	0.538604
$316$	1.08362e51	0.618433
$317$	8.98401e50	0.480569	0.240284	−	0.970703i	$-0.422759\pi$
$317$	8.98401e50	0.480569	0.240284	+	0.970703i	$0.422759\pi$
$318$	−1.94076e51	−0.973232
$319$	4.14020e51	1.94676
$320$	2.28196e51	1.00631
$321$	−3.22110e50	−0.133245
$322$	−2.89097e51	−1.12201
$323$	−1.10356e50	−0.0401923
$324$	2.68226e50	0.0916913
$325$	−3.50413e51	−1.12453
$326$	−8.38587e50	−0.252690
$327$	−2.59971e51	−0.735692
$328$	1.10350e51	0.293331
$329$	3.26887e51	0.816360
$330$	−6.44831e51	−1.51325
$331$	−1.36487e51	−0.301036	−0.150518	−	0.988607i	$-0.548094\pi$
$331$	−1.36487e51	−0.301036	−0.150518	+	0.988607i	$0.548094\pi$
$332$	−6.11192e51	−1.26721
$333$	1.79600e51	0.350106
$334$	−8.74240e51	−1.60261
$335$	1.57869e51	0.272194
$336$	4.08893e51	0.663215
$337$	4.08797e51	0.623871	0.311936	−	0.950103i	$-0.399023\pi$
$337$	4.08797e51	0.623871	0.311936	+	0.950103i	$0.399023\pi$
$338$	4.70431e51	0.675622
$339$	−3.71918e51	−0.502751
$340$	1.65913e52	2.11137
$341$	1.64956e51	0.197653
$342$	−1.00905e50	−0.0113861
$343$	9.37133e51	0.996028
$344$	1.49043e51	0.149232
$345$	8.14814e51	0.768718
$346$	9.11455e50	0.0810354
$347$	−9.67986e50	−0.0811176	−0.0405588	−	0.999177i	$-0.512914\pi$
$347$	−9.67986e50	−0.0811176	−0.0405588	+	0.999177i	$0.512914\pi$
$348$	−9.74032e51	−0.769482
$349$	−1.20461e52	−0.897274	−0.448637	−	0.893714i	$-0.648090\pi$
$349$	−1.20461e52	−0.897274	−0.448637	+	0.893714i	$0.648090\pi$
$350$	3.07099e52	2.15717
$351$	−2.05381e51	−0.136071
$352$	−2.52600e52	−1.57873
$353$	−1.65328e52	−0.974912	−0.487456	−	0.873147i	$-0.662075\pi$
$353$	−1.65328e52	−0.974912	−0.487456	+	0.873147i	$0.662075\pi$
$354$	1.97125e52	1.09692
$355$	−3.13074e52	−1.64424
$356$	−2.40944e52	−1.19451
$357$	1.96854e52	0.921393
$358$	3.93465e52	1.73902
$359$	−3.30801e52	−1.38080	−0.690399	−	0.723429i	$-0.742565\pi$
$359$	−3.30801e52	−1.38080	−0.690399	+	0.723429i	$0.742565\pi$
$360$	−3.21302e51	−0.126681
$361$	−2.68300e52	−0.999361
$362$	−5.30714e51	−0.186782
$363$	7.86258e51	0.261505
$364$	1.86336e52	0.585759
$365$	2.38303e51	0.0708152
$366$	−2.69681e52	−0.757683
$367$	−5.27201e51	−0.140063	−0.0700313	−	0.997545i	$-0.522310\pi$
$367$	−5.27201e51	−0.140063	−0.0700313	+	0.997545i	$0.522310\pi$
$368$	3.76732e52	0.946569
$369$	1.74234e52	0.414087
$370$	1.01579e53	2.28385
$371$	−5.88825e52	−1.25262
$372$	−3.88079e51	−0.0781249
$373$	2.13564e52	0.406909	0.203455	−	0.979084i	$-0.434783\pi$
$373$	2.13564e52	0.406909	0.203455	+	0.979084i	$0.434783\pi$
$374$	−1.43534e53	−2.58872
$375$	−3.21340e52	−0.548687
$376$	−1.18761e52	−0.192010
$377$	7.45818e52	1.14192
$378$	1.79995e52	0.261022
$379$	1.38114e53	1.89729	0.948643	−	0.316349i	$-0.102457\pi$
$379$	1.38114e53	1.89729	0.948643	+	0.316349i	$0.102457\pi$
$380$	−2.58026e51	−0.0335814
$381$	1.33600e52	0.164757
$382$	−4.38831e52	−0.512859
$383$	1.09992e53	1.21839	0.609196	−	0.793020i	$-0.291492\pi$
$383$	1.09992e53	1.21839	0.609196	+	0.793020i	$0.291492\pi$
$384$	−2.55693e52	−0.268491
$385$	−1.95641e53	−1.94766
$386$	2.19599e53	2.07296
$387$	2.35327e52	0.210667
$388$	−1.76307e53	−1.49699
$389$	−6.95194e51	−0.0559937	−0.0279968	−	0.999608i	$-0.508913\pi$
$389$	−6.95194e51	−0.0559937	−0.0279968	+	0.999608i	$0.508913\pi$
$390$	−1.16160e53	−0.887633
$391$	1.81370e53	1.31505
$392$	2.69945e50	0.00185742
$393$	9.54789e52	0.623534
$394$	−1.31699e53	−0.816410
$395$	−2.04952e53	−1.20618
$396$	−5.93369e52	−0.331569
$397$	1.86384e53	0.989015	0.494508	−	0.869173i	$-0.335348\pi$
$397$	1.86384e53	0.989015	0.494508	+	0.869173i	$0.335348\pi$
$398$	2.82643e53	1.42441
$399$	−3.06143e51	−0.0146548
$400$	−4.00192e53	−1.81986
$401$	−7.71907e52	−0.333507	−0.166754	−	0.985999i	$-0.553328\pi$
$401$	−7.71907e52	−0.333507	−0.166754	+	0.985999i	$0.553328\pi$
$402$	3.21307e52	0.131913
$403$	2.97153e52	0.115938
$404$	−8.01785e52	−0.297331
$405$	−5.07311e52	−0.178833
$406$	−6.53629e53	−2.19052
$407$	−3.97311e53	−1.26603
$408$	−7.15190e52	−0.216714
$409$	−1.12970e52	−0.0325564	−0.0162782	−	0.999868i	$-0.505182\pi$
$409$	−1.12970e52	−0.0325564	−0.0162782	+	0.999868i	$0.505182\pi$
$410$	9.85437e53	2.70122
$411$	−1.55993e52	−0.0406768
$412$	5.21829e53	1.29460
$413$	5.98073e53	1.41182
$414$	1.65837e53	0.372542
$415$	1.15598e54	2.47153
$416$	−4.55035e53	−0.926044
$417$	−3.48014e53	−0.674228
$418$	2.23221e52	0.0411738
$419$	−2.36312e53	−0.415049	−0.207524	−	0.978230i	$-0.566541\pi$
$419$	−2.36312e53	−0.415049	−0.207524	+	0.978230i	$0.566541\pi$
$420$	4.60268e53	0.769840
$421$	2.89686e53	0.461471	0.230736	−	0.973016i	$-0.425887\pi$
$421$	2.89686e53	0.461471	0.230736	+	0.973016i	$0.425887\pi$
$422$	1.94698e53	0.295431
$423$	−1.87515e53	−0.271056
$424$	2.13926e53	0.294621
$425$	−1.92665e54	−2.52830
$426$	−6.37193e53	−0.796845
$427$	−8.18207e53	−0.975195
$428$	−1.67641e53	−0.190451
$429$	4.54344e53	0.492051
$430$	1.33097e54	1.37425
$431$	−1.78890e54	−1.76118	−0.880588	−	0.473883i	$-0.842852\pi$
$431$	−1.78890e54	−1.76118	−0.880588	+	0.473883i	$0.842852\pi$
$432$	−2.34557e53	−0.220207
$433$	3.17218e53	0.284025	0.142012	−	0.989865i	$-0.454643\pi$
$433$	3.17218e53	0.284025	0.142012	+	0.989865i	$0.454643\pi$
$434$	−2.60422e53	−0.222402
$435$	1.84224e54	1.50078
$436$	−1.35301e54	−1.05154
$437$	−2.82064e52	−0.0209160
$438$	4.85014e52	0.0343190
$439$	−2.40172e54	−1.62181	−0.810904	−	0.585180i	$-0.801024\pi$
$439$	−2.40172e54	−1.62181	−0.810904	+	0.585180i	$0.801024\pi$
$440$	7.10783e53	0.458097
$441$	4.26222e51	0.00262207
$442$	−2.58562e54	−1.51848
$443$	2.77202e54	1.55425	0.777124	−	0.629348i	$-0.216678\pi$
$443$	2.77202e54	1.55425	0.777124	+	0.629348i	$0.216678\pi$
$444$	9.34722e53	0.500416
$445$	4.55710e54	2.32975
$446$	2.16907e54	1.05903
$447$	7.14162e53	0.333037
$448$	1.40911e54	0.627690
$449$	−6.15902e53	−0.262097	−0.131048	−	0.991376i	$-0.541834\pi$
$449$	−6.15902e53	−0.262097	−0.131048	+	0.991376i	$0.541834\pi$
$450$	−1.76164e54	−0.716245
$451$	−3.85439e54	−1.49740
$452$	−1.93563e54	−0.718596
$453$	1.10729e53	0.0392871
$454$	1.44784e54	0.490994
$455$	−3.52429e54	−1.14245
$456$	1.11225e52	0.00344686
$457$	−1.23275e53	−0.0365253	−0.0182626	−	0.999833i	$-0.505813\pi$
$457$	−1.23275e53	−0.0365253	−0.0182626	+	0.999833i	$0.505813\pi$
$458$	7.16544e54	2.03002
$459$	−1.12923e54	−0.305930
$460$	4.24067e54	1.09875
$461$	−7.22256e54	−1.78987	−0.894936	−	0.446195i	$-0.852779\pi$
$461$	−7.22256e54	−1.78987	−0.894936	+	0.446195i	$0.852779\pi$
$462$	−3.98183e54	−0.943892
$463$	4.66005e54	1.05677	0.528385	−	0.849005i	$-0.322798\pi$
$463$	4.66005e54	1.05677	0.528385	+	0.849005i	$0.322798\pi$
$464$	8.51767e54	1.84800
$465$	7.33995e53	0.152373
$466$	−1.01693e55	−2.02014
$467$	9.30547e54	1.76906	0.884529	−	0.466485i	$-0.154480\pi$
$467$	9.30547e54	1.76906	0.884529	+	0.466485i	$0.154480\pi$
$468$	−1.06890e54	−0.194490
$469$	9.74841e53	0.169781
$470$	−1.06055e55	−1.76818
$471$	5.90838e53	0.0943061
$472$	−2.17286e54	−0.332064
$473$	−5.20589e54	−0.761800
$474$	−4.17133e54	−0.584546
$475$	2.99628e53	0.0402128
$476$	1.02452e55	1.31697
$477$	3.37773e54	0.415909
$478$	3.62510e54	0.427610
$479$	−1.41559e55	−1.59977	−0.799887	−	0.600151i	$-0.795107\pi$
$479$	−1.41559e55	−1.59977	−0.799887	+	0.600151i	$0.795107\pi$
$480$	−1.12398e55	−1.21706
$481$	−7.15718e54	−0.742623
$482$	−4.38665e54	−0.436183
$483$	5.03148e54	0.479490
$484$	4.09205e54	0.373775
$485$	3.33460e55	2.91970
$486$	−1.03252e54	−0.0866672
$487$	−2.04972e55	−1.64949	−0.824746	−	0.565503i	$-0.808682\pi$
$487$	−2.04972e55	−1.64949	−0.824746	+	0.565503i	$0.808682\pi$
$488$	2.97263e54	0.229369
$489$	1.45949e54	0.107986
$490$	2.41064e53	0.0171046
$491$	−4.95694e54	−0.337321	−0.168660	−	0.985674i	$-0.553944\pi$
$491$	−4.95694e54	−0.337321	−0.168660	+	0.985674i	$0.553944\pi$
$492$	9.06792e54	0.591866
$493$	4.10067e55	2.56739
$494$	4.02112e53	0.0241515
$495$	1.12227e55	0.646683
$496$	3.39365e54	0.187626
$497$	−1.93323e55	−1.02560
$498$	2.35275e55	1.19777
$499$	−2.14720e55	−1.04909	−0.524543	−	0.851384i	$-0.675764\pi$
$499$	−2.14720e55	−1.04909	−0.524543	+	0.851384i	$0.675764\pi$
$500$	−1.67240e55	−0.784252
$501$	1.52154e55	0.684872
$502$	−2.47665e55	−1.07013
$503$	2.45440e55	1.01813	0.509063	−	0.860729i	$-0.329992\pi$
$503$	2.45440e55	1.01813	0.509063	+	0.860729i	$0.329992\pi$
$504$	−1.98404e54	−0.0790178
$505$	1.51646e55	0.579907
$506$	−3.66865e55	−1.34716
$507$	−8.18745e54	−0.288726
$508$	6.95316e54	0.235492
$509$	1.12858e55	0.367130	0.183565	−	0.983008i	$-0.441236\pi$
$509$	1.12858e55	0.367130	0.183565	+	0.983008i	$0.441236\pi$
$510$	−6.38673e55	−1.99568
$511$	1.47152e54	0.0441712
$512$	−4.25986e55	−1.22846
$513$	1.75616e53	0.00486584
$514$	1.59315e55	0.424144
$515$	−9.86966e55	−2.52496
$516$	1.22475e55	0.301112
$517$	4.14820e55	0.980175
$518$	6.27250e55	1.42456
$519$	−1.58631e54	−0.0346303
$520$	1.28041e55	0.268708
$521$	−3.43253e55	−0.692534	−0.346267	−	0.938136i	$-0.612551\pi$
$521$	−3.43253e55	−0.692534	−0.346267	+	0.938136i	$0.612551\pi$
$522$	3.74947e55	0.727319
$523$	−2.52587e54	−0.0471114	−0.0235557	−	0.999723i	$-0.507499\pi$
$523$	−2.52587e54	−0.0471114	−0.0235557	+	0.999723i	$0.507499\pi$
$524$	4.96916e55	0.891234
$525$	−5.34480e55	−0.921861
$526$	3.03922e55	0.504144
$527$	1.63381e55	0.260665
$528$	5.18886e55	0.796300
$529$	−2.13820e55	−0.315651
$530$	1.91039e56	2.71310
$531$	−3.43078e55	−0.468765
$532$	−1.59331e54	−0.0209465
$533$	−6.94333e55	−0.878335
$534$	9.27497e55	1.12906
$535$	3.17069e55	0.371450
$536$	−3.54170e54	−0.0399331
$537$	−6.84792e55	−0.743166
$538$	−1.42127e56	−1.48470
$539$	−9.42886e53	−0.00948177
$540$	−2.64028e55	−0.255610
$541$	−1.02690e56	−0.957158	−0.478579	−	0.878045i	$-0.658848\pi$
$541$	−1.02690e56	−0.957158	−0.478579	+	0.878045i	$0.658848\pi$
$542$	−3.11800e55	−0.279827
$543$	9.23661e54	0.0798208
$544$	−2.50188e56	−2.08204
$545$	2.55902e56	2.05091
$546$	−7.17290e55	−0.553663
$547$	6.01255e55	0.447011	0.223505	−	0.974703i	$-0.428250\pi$
$547$	6.01255e55	0.447011	0.223505	+	0.974703i	$0.428250\pi$
$548$	−8.11858e54	−0.0581405
$549$	4.69356e55	0.323794
$550$	3.89710e56	2.59004
$551$	−6.37728e54	−0.0408346
$552$	−1.82799e55	−0.112778
$553$	−1.26558e56	−0.752356
$554$	6.95928e54	0.0398671
$555$	−1.76789e56	−0.976000
$556$	−1.81122e56	−0.963693
$557$	3.06039e56	1.56944	0.784721	−	0.619849i	$-0.212806\pi$
$557$	3.06039e56	1.56944	0.784721	+	0.619849i	$0.212806\pi$
$558$	1.49388e55	0.0738441
$559$	−9.37792e55	−0.446853
$560$	−4.02493e56	−1.84886
$561$	2.49808e56	1.10629
$562$	−2.41139e56	−1.02961
$563$	−3.42167e56	−1.40869	−0.704346	−	0.709857i	$-0.748760\pi$
$563$	−3.42167e56	−1.40869	−0.704346	+	0.709857i	$0.748760\pi$
$564$	−9.75915e55	−0.387427
$565$	3.66097e56	1.40153
$566$	−1.23772e56	−0.456969
$567$	−3.13265e55	−0.111547
$568$	7.02364e55	0.241224
$569$	3.07296e56	1.01802	0.509008	−	0.860762i	$-0.330012\pi$
$569$	3.07296e56	1.01802	0.509008	+	0.860762i	$0.330012\pi$
$570$	9.93254e54	0.0317414
$571$	3.57289e56	1.10149	0.550743	−	0.834675i	$-0.314344\pi$
$571$	3.57289e56	1.10149	0.550743	+	0.834675i	$0.314344\pi$
$572$	2.36461e56	0.703301
$573$	7.63746e55	0.219169
$574$	6.08508e56	1.68489
$575$	−4.92441e56	−1.31572
$576$	−8.08320e55	−0.208412
$577$	−7.31817e55	−0.182095	−0.0910476	−	0.995847i	$-0.529022\pi$
$577$	−7.31817e55	−0.182095	−0.0910476	+	0.995847i	$0.529022\pi$
$578$	−8.59057e56	−2.06301
$579$	−3.82193e56	−0.885874
$580$	9.58787e56	2.14510
$581$	7.13819e56	1.54162
$582$	6.78684e56	1.41497
$583$	−7.47220e56	−1.50398
$584$	−5.34620e54	−0.0103892
$585$	2.02167e56	0.379328
$586$	1.21841e56	0.220746
$587$	7.85589e56	1.37440	0.687202	−	0.726466i	$-0.258839\pi$
$587$	7.85589e56	1.37440	0.687202	+	0.726466i	$0.258839\pi$
$588$	2.21825e54	0.00374779
$589$	−2.54087e54	−0.00414590
$590$	−1.94039e57	−3.05790
$591$	2.29210e56	0.348891
$592$	−8.17391e56	−1.20181
$593$	1.07054e57	1.52048	0.760240	−	0.649642i	$-0.225081\pi$
$593$	1.07054e57	1.52048	0.760240	+	0.649642i	$0.225081\pi$
$594$	2.28414e56	0.313401
$595$	−1.93773e57	−2.56859
$596$	3.71683e56	0.476019
$597$	−4.91916e56	−0.608719
$598$	−6.60873e56	−0.790212
$599$	−1.33866e57	−1.54675	−0.773374	−	0.633950i	$-0.781432\pi$
$599$	−1.33866e57	−1.54675	−0.773374	+	0.633950i	$0.781432\pi$
$600$	1.94182e56	0.216825
$601$	−3.44829e55	−0.0372115	−0.0186058	−	0.999827i	$-0.505923\pi$
$601$	−3.44829e55	−0.0372115	−0.0186058	+	0.999827i	$0.505923\pi$
$602$	8.21873e56	0.857189
$603$	−5.59207e55	−0.0563725
$604$	5.76286e55	0.0561540
$605$	−7.73952e56	−0.729003
$606$	3.08642e56	0.281039
$607$	1.12064e57	0.986505	0.493252	−	0.869886i	$-0.335808\pi$
$607$	1.12064e57	0.986505	0.493252	+	0.869886i	$0.335808\pi$
$608$	3.89087e55	0.0331149
$609$	1.13758e57	0.936115
$610$	2.65460e57	2.11221
$611$	7.47260e56	0.574946
$612$	−5.87703e56	−0.437274
$613$	7.02680e56	0.505612	0.252806	−	0.967517i	$-0.418646\pi$
$613$	7.02680e56	0.505612	0.252806	+	0.967517i	$0.418646\pi$
$614$	4.34408e56	0.302306
$615$	−1.71507e57	−1.15436
$616$	4.38909e56	0.285739
$617$	1.57026e57	0.988842	0.494421	−	0.869223i	$-0.335380\pi$
$617$	1.57026e57	0.988842	0.494421	+	0.869223i	$0.335380\pi$
$618$	−2.00875e57	−1.22366
$619$	−1.08061e57	−0.636813	−0.318406	−	0.947954i	$-0.603148\pi$
$619$	−1.08061e57	−0.636813	−0.318406	+	0.947954i	$0.603148\pi$
$620$	3.82005e56	0.217791
$621$	−2.88626e56	−0.159205
$622$	−9.50699e56	−0.507388
$623$	2.81401e57	1.45319
$624$	9.34725e56	0.467089
$625$	−1.25898e56	−0.0608807
$626$	2.66100e57	1.24529
$627$	−3.88496e55	−0.0175955
$628$	3.07499e56	0.134794
$629$	−3.93517e57	−1.66965
$630$	−1.77177e57	−0.727658
$631$	−1.40291e57	−0.557736	−0.278868	−	0.960329i	$-0.589959\pi$
$631$	−1.40291e57	−0.557736	−0.278868	+	0.960329i	$0.589959\pi$
$632$	4.59797e56	0.176956
$633$	−3.38855e56	−0.126252
$634$	−1.79988e57	−0.649252
$635$	−1.31509e57	−0.459298
$636$	1.75793e57	0.594469
$637$	−1.69852e55	−0.00556176
$638$	−8.29457e57	−2.63009
$639$	1.10898e57	0.340530
$640$	2.51692e57	0.748478
$641$	5.61783e57	1.61800	0.809001	−	0.587807i	$-0.200009\pi$
$641$	5.61783e57	1.61800	0.809001	+	0.587807i	$0.200009\pi$
$642$	6.45323e56	0.180015
$643$	−4.94656e57	−1.33653	−0.668265	−	0.743923i	$-0.732963\pi$
$643$	−4.94656e57	−1.33653	−0.668265	+	0.743923i	$0.732963\pi$
$644$	2.61861e57	0.685348
$645$	−2.31643e57	−0.587281
$646$	2.21089e56	0.0543002
$647$	−2.45422e57	−0.583951	−0.291976	−	0.956426i	$-0.594313\pi$
$647$	−2.45422e57	−0.583951	−0.291976	+	0.956426i	$0.594313\pi$
$648$	1.13812e56	0.0262363
$649$	7.58956e57	1.69512
$650$	7.02026e57	1.51925
$651$	4.53242e56	0.0950430
$652$	7.59584e56	0.154348
$653$	−3.19886e57	−0.629906	−0.314953	−	0.949107i	$-0.601989\pi$
$653$	−3.19886e57	−0.629906	−0.314953	+	0.949107i	$0.601989\pi$
$654$	5.20832e57	0.993926
$655$	−9.39846e57	−1.73824
$656$	−7.92967e57	−1.42143
$657$	−8.44124e55	−0.0146662
$658$	−6.54893e57	−1.10291
$659$	−1.37754e57	−0.224882	−0.112441	−	0.993658i	$-0.535867\pi$
$659$	−1.37754e57	−0.224882	−0.112441	+	0.993658i	$0.535867\pi$
$660$	5.84082e57	0.924321
$661$	7.48119e57	1.14773	0.573867	−	0.818949i	$-0.305443\pi$
$661$	7.48119e57	1.14773	0.573867	+	0.818949i	$0.305443\pi$
$662$	2.73441e57	0.406701
$663$	4.50005e57	0.648919
$664$	−2.59338e57	−0.362594
$665$	3.01352e56	0.0408536
$666$	−3.59815e57	−0.472996
$667$	1.04811e58	1.33606
$668$	7.91878e57	0.978906
$669$	−3.77508e57	−0.452575
$670$	−3.16278e57	−0.367736
$671$	−1.03831e58	−1.17088
$672$	−6.94057e57	−0.759146
$673$	1.60993e58	1.70804	0.854022	−	0.520237i	$-0.174156\pi$
$673$	1.60993e58	1.70804	0.854022	+	0.520237i	$0.174156\pi$
$674$	−8.18994e57	−0.842855
$675$	3.06599e57	0.306086
$676$	−4.26112e57	−0.412683
$677$	5.61289e57	0.527374	0.263687	−	0.964608i	$-0.415061\pi$
$677$	5.61289e57	0.527374	0.263687	+	0.964608i	$0.415061\pi$
$678$	7.45109e57	0.679221
$679$	2.05912e58	1.82117
$680$	7.03996e57	0.604140
$681$	−2.51984e57	−0.209825
$682$	−3.30476e57	−0.267030
$683$	−2.16339e58	−1.69633	−0.848164	−	0.529733i	$-0.822292\pi$
$683$	−2.16339e58	−1.69633	−0.848164	+	0.529733i	$0.822292\pi$
$684$	9.13985e55	0.00695487
$685$	1.53551e57	0.113396
$686$	−1.87747e58	−1.34564
$687$	−1.24708e58	−0.867525
$688$	−1.07101e58	−0.723154
$689$	−1.34605e58	−0.882198
$690$	−1.63242e58	−1.03854
$691$	−9.86473e57	−0.609236	−0.304618	−	0.952475i	$-0.598529\pi$
$691$	−9.86473e57	−0.609236	−0.304618	+	0.952475i	$0.598529\pi$
$692$	−8.25587e56	−0.0494980
$693$	6.93003e57	0.403370
$694$	1.93929e57	0.109590
$695$	3.42567e58	1.87956
$696$	−4.13297e57	−0.220177
$697$	−3.81759e58	−1.97477
$698$	2.41334e58	1.21222
$699$	1.76988e58	0.863300
$700$	−2.78168e58	−1.31764
$701$	2.34581e58	1.07913	0.539564	−	0.841944i	$-0.318589\pi$
$701$	2.34581e58	1.07913	0.539564	+	0.841944i	$0.318589\pi$
$702$	4.11466e57	0.183833
$703$	6.11991e56	0.0265559
$704$	1.78816e58	0.753646
$705$	1.84580e58	0.755629
$706$	3.31222e58	1.31711
$707$	9.36416e57	0.361719
$708$	−1.78554e58	−0.670019
$709$	2.11154e58	0.769754	0.384877	−	0.922968i	$-0.374244\pi$
$709$	2.11154e58	0.769754	0.384877	+	0.922968i	$0.374244\pi$
$710$	6.27220e58	2.22138
$711$	7.25985e57	0.249805
$712$	−1.02236e58	−0.341794
$713$	4.17593e57	0.135649
$714$	−3.94381e58	−1.24481
$715$	−4.47233e58	−1.37170
$716$	−3.56397e58	−1.06223
$717$	−6.30917e57	−0.182738
$718$	6.62734e58	1.86547
$719$	−3.21690e58	−0.880024	−0.440012	−	0.897992i	$-0.645026\pi$
$719$	−3.21690e58	−0.880024	−0.440012	+	0.897992i	$0.645026\pi$
$720$	2.30886e58	0.613877
$721$	−6.09451e58	−1.57495
$722$	5.37518e58	1.35014
$723$	7.63459e57	0.186402
$724$	4.80715e57	0.114090
$725$	−1.11338e59	−2.56870
$726$	−1.57521e58	−0.353295
$727$	1.46981e58	0.320484	0.160242	−	0.987078i	$-0.448773\pi$
$727$	1.46981e58	0.320484	0.160242	+	0.987078i	$0.448773\pi$
$728$	7.90654e57	0.167607
$729$	1.79701e57	0.0370370
$730$	−4.77423e57	−0.0956719
$731$	−5.15618e58	−1.00467
$732$	2.44274e58	0.462807
$733$	4.14987e58	0.764545	0.382273	−	0.924050i	$-0.375141\pi$
$733$	4.14987e58	0.764545	0.382273	+	0.924050i	$0.375141\pi$
$734$	1.05621e58	0.189226
$735$	−4.19551e56	−0.00730961
$736$	−6.39467e58	−1.08349
$737$	1.23708e58	0.203851
$738$	−3.49064e58	−0.559435
$739$	4.59350e57	0.0716033	0.0358016	−	0.999359i	$-0.488602\pi$
$739$	4.59350e57	0.0716033	0.0358016	+	0.999359i	$0.488602\pi$
$740$	−9.20092e58	−1.39502
$741$	−6.99840e56	−0.0103211
$742$	1.17966e59	1.69230
$743$	8.66038e58	1.20855	0.604277	−	0.796774i	$-0.293462\pi$
$743$	8.66038e58	1.20855	0.604277	+	0.796774i	$0.293462\pi$
$744$	−1.64668e57	−0.0223544
$745$	−7.02985e58	−0.928416
$746$	−4.27860e58	−0.549738
$747$	−4.09475e58	−0.511864
$748$	1.30011e59	1.58124
$749$	1.95790e58	0.231693
$750$	6.43781e58	0.741280
$751$	1.41094e59	1.58085	0.790426	−	0.612557i	$-0.209859\pi$
$751$	1.41094e59	1.58085	0.790426	+	0.612557i	$0.209859\pi$
$752$	8.53413e58	0.930451
$753$	4.31039e58	0.457319
$754$	−1.49419e59	−1.54274
$755$	−1.08996e58	−0.109521
$756$	−1.63037e58	−0.159437
$757$	3.70705e58	0.352828	0.176414	−	0.984316i	$-0.443550\pi$
$757$	3.70705e58	0.352828	0.176414	+	0.984316i	$0.443550\pi$
$758$	−2.76700e59	−2.56325
$759$	6.38496e58	0.575707
$760$	−1.09484e57	−0.00960888
$761$	−1.86135e59	−1.59017	−0.795084	−	0.606500i	$-0.792573\pi$
$761$	−1.86135e59	−1.59017	−0.795084	+	0.606500i	$0.792573\pi$
$762$	−2.67658e58	−0.222588
$763$	1.58020e59	1.27926
$764$	3.97489e58	0.313264
$765$	1.11156e59	0.852848
$766$	−2.20361e59	−1.64606
$767$	1.36719e59	0.994314
$768$	1.02205e59	0.723713
$769$	−6.59899e58	−0.454975	−0.227487	−	0.973781i	$-0.573051\pi$
$769$	−6.59899e58	−0.454975	−0.227487	+	0.973781i	$0.573051\pi$
$770$	3.91951e59	2.63131
$771$	−2.77274e58	−0.181257
$772$	−1.98911e59	−1.26620
$773$	1.95752e59	1.21347	0.606733	−	0.794906i	$-0.292480\pi$
$773$	1.95752e59	1.21347	0.606733	+	0.794906i	$0.292480\pi$
$774$	−4.71459e58	−0.284613
$775$	−4.43597e58	−0.260798
$776$	−7.48099e58	−0.428345
$777$	−1.09167e59	−0.608782
$778$	1.39277e58	0.0756479
$779$	5.93704e57	0.0314089
$780$	1.05217e59	0.542183
$781$	−2.45328e59	−1.23140
$782$	−3.63362e59	−1.77664
$783$	−6.52563e58	−0.310818
$784$	−1.93981e57	−0.00900076
$785$	−5.81591e58	−0.262899
$786$	−1.91285e59	−0.842399
$787$	2.07905e59	0.892038	0.446019	−	0.895024i	$-0.352841\pi$
$787$	2.07905e59	0.892038	0.446019	+	0.895024i	$0.352841\pi$
$788$	1.19291e59	0.498679
$789$	−5.28950e58	−0.215445
$790$	4.10605e59	1.62955
$791$	2.26065e59	0.874209
$792$	−2.51775e58	−0.0948740
$793$	−1.87041e59	−0.686811
$794$	−3.73406e59	−1.33617
$795$	−3.32486e59	−1.15944
$796$	−2.56015e59	−0.870058
$797$	1.24780e58	0.0413283	0.0206642	−	0.999786i	$-0.493422\pi$
$797$	1.24780e58	0.0413283	0.0206642	+	0.999786i	$0.493422\pi$
$798$	6.13334e57	0.0197988
$799$	4.10859e59	1.29266
$800$	6.79288e59	2.08310
$801$	−1.61423e59	−0.482501
$802$	1.54646e59	0.450571
$803$	1.86737e58	0.0530348
$804$	−2.91037e58	−0.0805748
$805$	−4.95273e59	−1.33669
$806$	−5.95323e58	−0.156633
$807$	2.47359e59	0.634483
$808$	−3.40210e58	−0.0850774
$809$	−1.93365e58	−0.0471448	−0.0235724	−	0.999722i	$-0.507504\pi$
$809$	−1.93365e58	−0.0471448	−0.0235724	+	0.999722i	$0.507504\pi$
$810$	1.01636e59	0.241604
$811$	6.76399e59	1.56775	0.783873	−	0.620921i	$-0.213241\pi$
$811$	6.76399e59	1.56775	0.783873	+	0.620921i	$0.213241\pi$
$812$	5.92051e59	1.33801
$813$	5.42660e58	0.119584
$814$	7.95982e59	1.71042
$815$	−1.43665e59	−0.301036
$816$	5.13931e59	1.05016
$817$	8.01879e57	0.0159793
$818$	2.26327e58	0.0439839
$819$	1.24838e59	0.236607
$820$	−8.92600e59	−1.64996
$821$	−6.71492e59	−1.21061	−0.605307	−	0.795992i	$-0.706950\pi$
$821$	−6.71492e59	−1.21061	−0.605307	+	0.795992i	$0.706950\pi$
$822$	3.12520e58	0.0549547
$823$	−8.16687e59	−1.40074	−0.700372	−	0.713778i	$-0.746983\pi$
$823$	−8.16687e59	−1.40074	−0.700372	+	0.713778i	$0.746983\pi$
$824$	2.21420e59	0.370433
$825$	−6.78256e59	−1.10685
$826$	−1.19819e60	−1.90737
$827$	6.61685e59	1.02752	0.513758	−	0.857935i	$-0.328253\pi$
$827$	6.61685e59	1.02752	0.513758	+	0.857935i	$0.328253\pi$
$828$	−1.50214e59	−0.227556
$829$	8.11669e59	1.19953	0.599765	−	0.800176i	$-0.295261\pi$
$829$	8.11669e59	1.19953	0.599765	+	0.800176i	$0.295261\pi$
$830$	−2.31592e60	−3.33905
$831$	−1.21120e58	−0.0170371
$832$	3.22121e59	0.442070
$833$	−9.33882e57	−0.0125046
$834$	6.97219e59	0.910888
$835$	−1.49772e60	−1.90923
$836$	−2.02191e58	−0.0251498
$837$	−2.59998e58	−0.0315571
$838$	4.73434e59	0.560734
$839$	8.50436e59	0.982927	0.491463	−	0.870898i	$-0.336462\pi$
$839$	8.50436e59	0.982927	0.491463	+	0.870898i	$0.336462\pi$
$840$	1.95299e59	0.220280
$841$	1.46122e60	1.60842
$842$	−5.80364e59	−0.623451
$843$	4.19681e59	0.440001
$844$	−1.76356e59	−0.180455
$845$	8.05931e59	0.804888
$846$	3.75672e59	0.366199
$847$	−4.77916e59	−0.454717
$848$	−1.53726e60	−1.42769
$849$	2.15415e59	0.195285
$850$	3.85989e60	3.41575
$851$	−1.00581e60	−0.868880
$852$	5.77163e59	0.486729
$853$	−2.06137e60	−1.69708	−0.848538	−	0.529135i	$-0.822516\pi$
$853$	−2.06137e60	−1.69708	−0.848538	+	0.529135i	$0.822516\pi$
$854$	1.63921e60	1.31750
$855$	−1.72867e58	−0.0135646
$856$	−7.11325e58	−0.0544949
$857$	1.32928e60	0.994285	0.497142	−	0.867669i	$-0.334383\pi$
$857$	1.32928e60	0.994285	0.497142	+	0.867669i	$0.334383\pi$
$858$	−9.10243e59	−0.664765
$859$	−1.38551e60	−0.987987	−0.493994	−	0.869466i	$-0.664463\pi$
$859$	−1.38551e60	−0.987987	−0.493994	+	0.869466i	$0.664463\pi$
$860$	−1.20558e60	−0.839416
$861$	−1.05905e60	−0.720035
$862$	3.58393e60	2.37936
$863$	−7.45819e59	−0.483517	−0.241759	−	0.970336i	$-0.577724\pi$
$863$	−7.45819e59	−0.483517	−0.241759	+	0.970336i	$0.577724\pi$
$864$	3.98139e59	0.252059
$865$	1.56148e59	0.0965398
$866$	−6.35522e59	−0.383719
$867$	1.49511e60	0.881623
$868$	2.35888e59	0.135847
$869$	−1.60602e60	−0.903328
$870$	−3.69079e60	−2.02757
$871$	2.22848e59	0.119574
$872$	−5.74102e59	−0.300885
$873$	−1.18119e60	−0.604683
$874$	5.65093e58	0.0282576
$875$	1.95322e60	0.954084
$876$	−4.39321e58	−0.0209627
$877$	2.15621e60	1.00508	0.502538	−	0.864555i	$-0.332400\pi$
$877$	2.15621e60	1.00508	0.502538	+	0.864555i	$0.332400\pi$
$878$	4.81166e60	2.19107
$879$	−2.12054e59	−0.0943353
$880$	−5.10765e60	−2.21986
$881$	2.09977e60	0.891589	0.445795	−	0.895135i	$-0.352921\pi$
$881$	2.09977e60	0.891589	0.445795	+	0.895135i	$0.352921\pi$
$882$	−8.53902e57	−0.00354244
$883$	−2.55719e60	−1.03650	−0.518249	−	0.855230i	$-0.673416\pi$
$883$	−2.55719e60	−1.03650	−0.518249	+	0.855230i	$0.673416\pi$
$884$	2.34203e60	0.927517
$885$	3.37709e60	1.30679
$886$	−5.55353e60	−2.09980
$887$	1.55710e60	0.575285	0.287642	−	0.957738i	$-0.407129\pi$
$887$	1.55710e60	0.575285	0.287642	+	0.957738i	$0.407129\pi$
$888$	3.96617e59	0.143188
$889$	−8.12069e59	−0.286488
$890$	−9.12981e60	−3.14751
$891$	−3.97534e59	−0.133931
$892$	−1.96473e60	−0.646878
$893$	−6.38961e58	−0.0205598
$894$	−1.43077e60	−0.449936
$895$	6.74075e60	2.07174
$896$	1.55420e60	0.466865
$897$	1.15019e60	0.337695
$898$	1.23391e60	0.354095
$899$	9.44151e59	0.264830
$900$	1.59568e60	0.437496
$901$	−7.40085e60	−1.98346
$902$	7.72198e60	2.02299
$903$	−1.43040e60	−0.366318
$904$	−8.21318e59	−0.205617
$905$	−9.09204e59	−0.222518
$906$	−2.21838e59	−0.0530771
$907$	−1.66650e60	−0.389814	−0.194907	−	0.980822i	$-0.562440\pi$
$907$	−1.66650e60	−0.389814	−0.194907	+	0.980822i	$0.562440\pi$
$908$	−1.31144e60	−0.299909
$909$	−5.37165e59	−0.120101
$910$	7.06064e60	1.54346
$911$	3.26737e60	0.698348	0.349174	−	0.937058i	$-0.386462\pi$
$911$	3.26737e60	0.698348	0.349174	+	0.937058i	$0.386462\pi$
$912$	−7.99257e58	−0.0167029
$913$	9.05839e60	1.85097
$914$	2.46972e59	0.0493459
$915$	−4.62010e60	−0.902648
$916$	−6.49039e60	−1.23998
$917$	−5.80355e60	−1.08423
$918$	2.26232e60	0.413314
$919$	3.23443e60	0.577869	0.288934	−	0.957349i	$-0.406699\pi$
$919$	3.23443e60	0.577869	0.288934	+	0.957349i	$0.406699\pi$
$920$	1.79938e60	0.314393
$921$	−7.56050e59	−0.129190
$922$	1.44698e61	2.41813
$923$	−4.41935e60	−0.722310
$924$	3.60671e60	0.576548
$925$	1.06844e61	1.67050
$926$	−9.33606e60	−1.42770
$927$	3.49605e60	0.522930
$928$	−1.44579e61	−2.11530
$929$	3.84037e60	0.549606	0.274803	−	0.961501i	$-0.411387\pi$
$929$	3.84037e60	0.549606	0.274803	+	0.961501i	$0.411387\pi$
$930$	−1.47050e60	−0.205857
$931$	1.45236e57	0.000198886 0
$932$	9.21127e60	1.23394
$933$	1.65461e60	0.216831
$934$	−1.86428e61	−2.39001
$935$	−2.45898e61	−3.08402
$936$	−4.53550e59	−0.0556507
$937$	2.56852e60	0.308334	0.154167	−	0.988045i	$-0.450731\pi$
$937$	2.56852e60	0.308334	0.154167	+	0.988045i	$0.450731\pi$
$938$	−1.95302e60	−0.229376
$939$	−4.63124e60	−0.532172
$940$	9.60641e60	1.08004
$941$	−1.47165e61	−1.61889	−0.809444	−	0.587197i	$-0.800231\pi$
$941$	−1.47165e61	−1.61889	−0.809444	+	0.587197i	$0.800231\pi$
$942$	−1.18370e60	−0.127408
$943$	−9.75757e60	−1.02767
$944$	1.56141e61	1.60913
$945$	3.08362e60	0.310963
$946$	1.04296e61	1.02920
$947$	−1.41745e61	−1.36878	−0.684388	−	0.729118i	$-0.739930\pi$
$947$	−1.41745e61	−1.36878	−0.684388	+	0.729118i	$0.739930\pi$
$948$	3.77836e60	0.357052
$949$	3.36389e59	0.0311089
$950$	−6.00283e59	−0.0543278
$951$	3.13253e60	0.277456
$952$	4.34718e60	0.376834
$953$	1.56903e61	1.33115	0.665573	−	0.746332i	$-0.268187\pi$
$953$	1.56903e61	1.33115	0.665573	+	0.746332i	$0.268187\pi$
$954$	−6.76702e60	−0.561896
$955$	−7.51793e60	−0.610983
$956$	−3.28358e60	−0.261193
$957$	1.44360e61	1.12396
$958$	2.83602e61	2.16131
$959$	9.48180e59	0.0707309
$960$	7.95669e60	0.580995
$961$	−1.36142e61	−0.973112
$962$	1.43389e61	1.00329
$963$	−1.12313e60	−0.0769290
$964$	3.97339e60	0.266429
$965$	3.76211e61	2.46957
$966$	−1.00802e61	−0.647795
$967$	−8.55928e60	−0.538511	−0.269256	−	0.963069i	$-0.586778\pi$
$967$	−8.55928e60	−0.538511	−0.269256	+	0.963069i	$0.586778\pi$
$968$	1.73632e60	0.106951
$969$	−3.84787e59	−0.0232051
$970$	−6.68062e61	−3.94454
$971$	−1.94026e61	−1.12167	−0.560835	−	0.827928i	$-0.689520\pi$
$971$	−1.94026e61	−1.12167	−0.560835	+	0.827928i	$0.689520\pi$
$972$	9.35247e59	0.0529380
$973$	2.11535e61	1.17238
$974$	4.10645e61	2.22848
$975$	−1.22182e61	−0.649249
$976$	−2.13612e61	−1.11149
$977$	6.21621e60	0.316729	0.158364	−	0.987381i	$-0.449378\pi$
$977$	6.21621e60	0.316729	0.158364	+	0.987381i	$0.449378\pi$
$978$	−2.92397e60	−0.145890
$979$	3.57099e61	1.74479
$980$	−2.18353e59	−0.0104478
$981$	−9.06463e60	−0.424752
$982$	9.93085e60	0.455723
$983$	−6.48229e60	−0.291327	−0.145664	−	0.989334i	$-0.546532\pi$
$983$	−6.48229e60	−0.291327	−0.145664	+	0.989334i	$0.546532\pi$
$984$	3.84766e60	0.169355
$985$	−2.25623e61	−0.972612
$986$	−8.21537e61	−3.46857
$987$	1.13978e61	0.471325
$988$	−3.64229e59	−0.0147522
$989$	−1.31789e61	−0.522825
$990$	−2.24839e61	−0.873674
$991$	−2.42504e60	−0.0923016	−0.0461508	−	0.998934i	$-0.514695\pi$
$991$	−2.42504e60	−0.0923016	−0.0461508	+	0.998934i	$0.514695\pi$
$992$	−5.76040e60	−0.214765
$993$	−4.75901e60	−0.173803
$994$	3.87308e61	1.38559
$995$	4.84217e61	1.69694
$996$	−2.13110e61	−0.731621
$997$	2.46785e61	0.829979	0.414990	−	0.909826i	$-0.363785\pi$
$997$	2.46785e61	0.829979	0.414990	+	0.909826i	$0.363785\pi$
$998$	4.30175e61	1.41732
$999$	6.26227e60	0.202134

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.42.a.b.1.1	✓	4
3.2	odd	2		9.42.a.c.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.42.a.b.1.1	✓	4	1.1	even	1	trivial
9.42.a.c.1.4		4	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00342e6 q^{2} +3.48678e9 q^{3} +1.81468e12 q^{4} -3.43221e14 q^{5} -6.98551e15 q^{6} -2.11939e17 q^{7} +7.69998e17 q^{8} +1.21577e19 q^{9} +O(q^{10})\)	\(q-2.00342e6 q^{2} +3.48678e9 q^{3} +1.81468e12 q^{4} -3.43221e14 q^{5} -6.98551e15 q^{6} -2.11939e17 q^{7} +7.69998e17 q^{8} +1.21577e19 q^{9} +6.87617e20 q^{10} -2.68951e21 q^{11} +6.32741e21 q^{12} -4.84491e22 q^{13} +4.24604e23 q^{14} -1.19674e24 q^{15} -5.53316e24 q^{16} -2.66383e25 q^{17} -2.43570e25 q^{18} +4.14274e24 q^{19} -6.22838e26 q^{20} -7.38986e26 q^{21} +5.38824e27 q^{22} -6.80863e27 q^{23} +2.68482e27 q^{24} +7.23261e28 q^{25} +9.70641e28 q^{26} +4.23912e28 q^{27} -3.84602e29 q^{28} -1.53939e30 q^{29} +2.39757e30 q^{30} -6.13330e29 q^{31} +9.39202e30 q^{32} -9.37775e30 q^{33} +5.33678e31 q^{34} +7.27420e31 q^{35} +2.20623e31 q^{36} +1.47726e32 q^{37} -8.29967e30 q^{38} -1.68932e32 q^{39} -2.64280e32 q^{40} +1.43312e33 q^{41} +1.48050e33 q^{42} +1.93562e33 q^{43} -4.88061e33 q^{44} -4.17277e33 q^{45} +1.36406e34 q^{46} -1.54236e34 q^{47} -1.92929e34 q^{48} +3.50578e32 q^{49} -1.44900e35 q^{50} -9.28821e34 q^{51} -8.79197e34 q^{52} +2.77827e35 q^{53} -8.49274e34 q^{54} +9.23098e35 q^{55} -1.63193e35 q^{56} +1.44449e34 q^{57} +3.08404e36 q^{58} -2.82191e36 q^{59} -2.17170e36 q^{60} +3.86057e36 q^{61} +1.22876e36 q^{62} -2.57669e36 q^{63} -6.64865e36 q^{64} +1.66288e37 q^{65} +1.87876e37 q^{66} -4.59962e36 q^{67} -4.83401e37 q^{68} -2.37402e37 q^{69} -1.45733e38 q^{70} +9.12164e37 q^{71} +9.36137e36 q^{72} -6.94314e36 q^{73} -2.95957e38 q^{74} +2.52185e38 q^{75} +7.51776e36 q^{76} +5.70013e38 q^{77} +3.38441e38 q^{78} +5.97141e38 q^{79} +1.89910e39 q^{80} +1.47809e38 q^{81} -2.87114e39 q^{82} -3.36804e39 q^{83} -1.34103e39 q^{84} +9.14284e39 q^{85} -3.87787e39 q^{86} -5.36751e39 q^{87} -2.07092e39 q^{88} -1.32775e40 q^{89} +8.35982e39 q^{90} +1.02683e40 q^{91} -1.23555e40 q^{92} -2.13855e39 q^{93} +3.09000e40 q^{94} -1.42188e39 q^{95} +3.27479e40 q^{96} -9.71560e40 q^{97} -7.02357e38 q^{98} -3.26982e40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 69822 q^{2} + 13947137604 q^{3} + 5352947588932 q^{4} + 118536963776280 q^{5} - 243454260446622 q^{6} + 15\!\cdots\!36 q^{7}+ \cdots + 48\!\cdots\!04 q^{9}+O(q^{10}) \) 4 * q - 69822 * q^2 + 13947137604 * q^3 + 5352947588932 * q^4 + 118536963776280 * q^5 - 243454260446622 * q^6 + 150256264888927136 * q^7 + 6279626248119395784 * q^8 + 48630661836227715204 * q^9	\( 4 q - 69822 q^{2} + 13947137604 q^{3} + 5352947588932 q^{4} + 118536963776280 q^{5} - 243454260446622 q^{6} + 15\!\cdots\!36 q^{7}+ \cdots + 88\!\cdots\!56 q^{99}+O(q^{100}) \) 4 * q - 69822 * q^2 + 13947137604 * q^3 + 5352947588932 * q^4 + 118536963776280 * q^5 - 243454260446622 * q^6 + 150256264888927136 * q^7 + 6279626248119395784 * q^8 + 48630661836227715204 * q^9 + 725751018728422700940 * q^10 + 724810647231440683056 * q^11 + 18664574152458657849732 * q^12 - 8843977274373065537608 * q^13 + 493449664223337937919568 * q^14 + 413312836237035157808280 * q^15 - 5962194966280197033033200 * q^16 - 38231582029295844707285688 * q^17 - 848872517682272882743422 * q^18 + 261842746845948075837831248 * q^19 + 785441926018305471679038360 * q^20 + 523911200567235135430405536 * q^21 - 6322149663566345845522943976 * q^22 - 15395573913207335266380880032 * q^23 + 21895702846052864805196365384 * q^24 + 117350921958371528604086683900 * q^25 - 62942545095927728709970694052 * q^26 + 169564633100864814057177732804 * q^27 + 684437536459146482218511575712 * q^28 - 1036098964520685524199931325064 * q^29 + 2530537331112123128971880036940 * q^30 + 9280613209905247622577480610304 * q^31 + 19645397922916950127447685511456 * q^32 + 2527258458445301210436445809456 * q^33 + 92420157643501864091330064020004 * q^34 + 207436667553525639419383641992640 * q^35 + 65079346006100643987841739630532 * q^36 + 200754880510048713109452091192856 * q^37 + 1146938682238729575315585266559528 * q^38 - 30837042003082501971082253252808 * q^39 + 2565083222429486590317315499815600 * q^40 + 2357905268481965433001096926030504 * q^41 + 1720552591892622502089456095058768 * q^42 + 3943358618915609696106480688157360 * q^43 - 18494278585991583572852191821764304 * q^44 + 1441132750124361726734484052640280 * q^45 - 44252120640849956767942988241684816 * q^46 - 8890000412230234893665157147040320 * q^47 - 20788888404146512009986643475113200 * q^48 - 33104900387055220681685954563991580 * q^49 - 216323679312314207800001999371642050 * q^50 - 133305283845300676339482147968952888 * q^51 - 596234086188669794371774262733483208 * q^52 + 95704753827317216756019399314791128 * q^53 - 2959835453092145761775065914960222 * q^54 + 1291057043675253444545805475556816160 * q^55 + 1940580325939766339139469085046208320 * q^56 + 912989205217443700887315001196762448 * q^57 + 3859053206955865617315425524661917116 * q^58 - 1809289331104083090977131835906657808 * q^59 + 2738666655532023559103418232328622360 * q^60 + 5381027332088000515346282395501157240 * q^61 + 14109494547714507002913033009898657152 * q^62 + 1826765401647017821917860444028843936 * q^63 - 389844533130084697385386794140537792 * q^64 - 9754648834359651370261564655441346480 * q^65 - 22043972827710532722740556743113718376 * q^66 - 73273159367285254897696664016673247728 * q^67 - 89019363361032581039655795923994746424 * q^68 - 53681046965013864485594032220229980832 * q^69 - 127374089191018487217525315519713602080 * q^70 - 84396091414708989106237239330896374752 * q^71 + 76345595132548433424120590562827574984 * q^72 - 44706579271813174655854382994714255832 * q^73 - 299692406925616462116506150539738813812 * q^74 + 409177364127418217299254754274337843900 * q^75 + 1128262001217587654782588548338718696272 * q^76 + 833312137190144115784050615522845895552 * q^77 - 219467084399719853089285669187657082852 * q^78 + 1416534390331633014953369475707893311680 * q^79 + 1539903590051088861086709486592809053280 * q^80 + 591235317657383693264332840825533190404 * q^81 + 613971248288365719286532695984150451412 * q^82 + 1526205590962076227407755639349783073104 * q^83 + 2386486125584620727973530035630532068512 * q^84 - 285377453319367852617718519171747770960 * q^85 - 12934468921257599734617599325958640634024 * q^86 - 3612653707382978727606828549504415526664 * q^87 - 13219976774504188013705589441700285953696 * q^88 - 39593715237961905051969833281675978558872 * q^89 + 8823438092269922908090462480445695772940 * q^90 - 8845052344004724172694600210873108791616 * q^91 - 65206363053810587386463980322833360400544 * q^92 + 32359497372012156098445494805887947067904 * q^93 + 98582759073905793403791649187553312740832 * q^94 + 7880313586718908134850457997267850706400 * q^95 + 68499267029064622122879551784898487597856 * q^96 + 36750128325858234547252025624989137001352 * q^97 - 68350119771260167200829379908744318383822 * q^98 + 8812005370202382972296217650292999095856 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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