LMFDB - Embedded newform 2.42.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 42);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.1
Root			$1.06767e6$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.04858e6 q^{2} -1.71810e9 q^{3} +1.09951e12 q^{4} +3.51885e14 q^{5} -1.80156e15 q^{6} -7.89090e16 q^{7} +1.15292e18 q^{8} -3.35211e19 q^{9} +O(q^{10})$	\(q+1.04858e6 q^{2} -1.71810e9 q^{3} +1.09951e12 q^{4} +3.51885e14 q^{5} -1.80156e15 q^{6} -7.89090e16 q^{7} +1.15292e18 q^{8} -3.35211e19 q^{9} +3.68978e20 q^{10} +1.20679e21 q^{11} -1.88907e21 q^{12} +9.23598e22 q^{13} -8.27420e22 q^{14} -6.04574e23 q^{15} +1.20893e24 q^{16} -4.95668e24 q^{17} -3.51494e25 q^{18} +2.41331e26 q^{19} +3.86902e26 q^{20} +1.35574e26 q^{21} +1.26541e27 q^{22} +8.23610e27 q^{23} -1.98084e27 q^{24} +7.83484e28 q^{25} +9.68462e28 q^{26} +1.20257e29 q^{27} -8.67613e28 q^{28} +2.60718e29 q^{29} -6.33942e29 q^{30} -6.40610e30 q^{31} +1.26765e30 q^{32} -2.07339e30 q^{33} -5.19746e30 q^{34} -2.77669e31 q^{35} -3.68569e31 q^{36} +7.38149e31 q^{37} +2.53054e32 q^{38} -1.58683e32 q^{39} +4.05696e32 q^{40} +2.15386e33 q^{41} +1.42159e32 q^{42} -5.67618e33 q^{43} +1.32688e33 q^{44} -1.17956e34 q^{45} +8.63618e33 q^{46} -6.45458e33 q^{47} -2.07706e33 q^{48} -3.83410e34 q^{49} +8.21542e34 q^{50} +8.51608e33 q^{51} +1.01551e35 q^{52} -9.99163e34 q^{53} +1.26099e35 q^{54} +4.24652e35 q^{55} -9.09758e34 q^{56} -4.14631e35 q^{57} +2.73383e35 q^{58} -3.33277e36 q^{59} -6.64736e35 q^{60} +2.08511e36 q^{61} -6.71729e36 q^{62} +2.64512e36 q^{63} +1.32923e36 q^{64} +3.25000e37 q^{65} -2.17411e36 q^{66} +2.21433e36 q^{67} -5.44993e36 q^{68} -1.41505e37 q^{69} -2.91157e37 q^{70} +5.59105e37 q^{71} -3.86472e37 q^{72} -2.02164e38 q^{73} +7.74006e37 q^{74} -1.34610e38 q^{75} +2.65346e38 q^{76} -9.52266e37 q^{77} -1.66392e38 q^{78} -2.46315e38 q^{79} +4.25403e38 q^{80} +1.01600e39 q^{81} +2.25848e39 q^{82} -3.59771e37 q^{83} +1.49065e38 q^{84} -1.74418e39 q^{85} -5.95190e39 q^{86} -4.47940e38 q^{87} +1.39134e39 q^{88} +5.24223e38 q^{89} -1.23686e40 q^{90} -7.28801e39 q^{91} +9.05569e39 q^{92} +1.10063e40 q^{93} -6.76812e39 q^{94} +8.49208e40 q^{95} -2.17795e39 q^{96} -2.35889e40 q^{97} -4.02035e40 q^{98} -4.04530e40 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2097152 q^{2} + 8863347528 q^{3} + 2199023255552 q^{4} + 97599184325580 q^{5} + 92\!\cdots\!28 q^{6}+ \cdots + 41\!\cdots\!86 q^{9}+O(q^{10}) $ 2 * q + 2097152 * q^2 + 8863347528 * q^3 + 2199023255552 * q^4 + 97599184325580 * q^5 + 9293893497520128 * q^6 + 217106802373088656 * q^7 + 2305843009213693952 * q^8 + 41972929616872509786 * q^9	$ 2 q + 2097152 q^{2} + 8863347528 q^{3} + 2199023255552 q^{4} + 97599184325580 q^{5} + 92\!\cdots\!28 q^{6}+ \cdots - 12\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 2097152 * q^2 + 8863347528 * q^3 + 2199023255552 * q^4 + 97599184325580 * q^5 + 9293893497520128 * q^6 + 217106802373088656 * q^7 + 2305843009213693952 * q^8 + 41972929616872509786 * q^9 + 102340162303379374080 * q^10 + 110594481484939565784 * q^11 + 9745353668055665737728 * q^12 + 173293106838448696895068 * q^13 + 227652982405163810553856 * q^14 - 3295287287252802285241680 * q^15 + 2417851639229258349412352 * q^16 - 10287966260741677078429404 * q^17 + 44011806645941708821364736 * q^18 + 206254882139859790701457000 * q^19 + 107311438027428330555310080 * q^20 + 3267849131609686416057835584 * q^21 + 115966719017551990131523584 * q^22 + 14925421378885128304361915568 * q^23 + 10218743967835137756603875328 * q^24 + 97534966241249753807444705150 * q^25 + 181710992796233180795442823168 * q^26 + 533156288863055843864697754320 * q^27 + 238711453678477047815320109056 * q^28 - 1375143011941884388614889894020 * q^29 - 3455359162518394409049579847680 * q^30 - 3626496922711160469799126663616 * q^31 + 2535301200456458802993406410752 * q^32 - 13672735988327258412044854187424 * q^33 - 10787714509823464784191190728704 * q^34 - 103039524095905042910481769779360 * q^35 + 46149724165574973269071349415936 * q^36 + 120356679589378915210866994599436 * q^37 + 216273919294685619894570975232000 * q^38 + 697708668559917206762862430490352 * q^39 + 112524198441048689140364822446080 * q^40 + 1270177139906840106861139346878164 * q^41 + 3426588171026758543404261005328384 * q^42 - 6045433421160616098770468790853352 * q^43 + 121599918360548595604152473616384 * q^44 - 30992658299909156185379775337031460 * q^45 + 15650438647785852296874599978631168 * q^46 - 25416478966330542868882280891861664 * q^47 + 10715129674816697408268665175932928 * q^48 + 4716677344275473650585885334355954 * q^49 + 102272824761384701848395139147366400 * q^50 - 47896619495707425086522465903395056 * q^51 + 190537785982303003785762253746208768 * q^52 - 301376484284740318156836692232048852 * q^53 + 559054888750867644536269312433848320 * q^54 + 703399094180619772764269188861842960 * q^55 + 250307101252362748889997098673504256 * q^56 - 785787658029123941344672503009410400 * q^57 - 1441941958889973364676246785511915520 * q^58 - 3282010250697938085995473868454788040 * q^59 - 3623206689196887935863572238360903680 * q^60 - 4485157745840460017677520841591879236 * q^61 - 3802657637228777800780089040427810816 * q^62 + 24992547810032633572829803615671997008 * q^63 + 2658455991569831745807614120560689152 * q^64 + 11919812053150705903267451825832510120 * q^65 - 14336902811696243316668345024432308224 * q^66 + 55055736076082381526441630307313037256 * q^67 - 11311738529852649409548062009541525504 * q^68 + 56632222305135551516324020091548201152 * q^69 - 108044772018387726274901332228162191360 * q^70 - 48857884738531480102553331099997138416 * q^71 + 48391493166641943170589759285164507136 * q^72 - 485616958845162818165813572349849688812 * q^73 + 126203125657112585396150069729098203136 * q^74 + 68411444542067712502035991381122300600 * q^75 + 226779641198344268566569654924869632000 * q^76 - 419718086944271580508987308621981603648 * q^77 + 731600564843883744998575235913851338752 * q^78 - 905766854341990828970937020702446890080 * q^79 + 117990173904521070264047184061220782080 * q^80 + 2631580786121491108655810678136598411122 * q^81 + 1331877264654954771892026051792117694464 * q^82 + 1271755206567258248006583231290595969768 * q^83 + 3593038118022554366408666387923215581184 * q^84 - 388512546938141834318136915482004571560 * q^85 - 6339096395026914186384343082837844426752 * q^86 - 17757719150026706057484126704955838888080 * q^87 + 127506755994830604184219784174773469184 * q^88 + 2692414558304473820098690391828757436980 * q^89 - 32498157669485543356240783303803100200960 * q^90 + 16669534332125295311104493248216990683104 * q^91 + 16410674355540697858047580547193155616768 * q^92 + 40418607330508619745600934617627243192576 * q^93 - 26651109848599015319281106568464736190464 * q^94 + 93840167647611953736551449995129877215600 * q^95 + 11235627813900593301572723855519045910528 * q^96 - 31989468315501178009691057062669320691004 * q^97 + 4945794662950999058636745300357628821504 * q^98 - 123209315561064920195916977740234432814088 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.04858e6	0.707107
$2$	1.04858e6	0.707107
$3$	−1.71810e9	−0.284487	−0.142244	−	0.989832i	$-0.545432\pi$
$3$	−1.71810e9	−0.284487	−0.142244	+	0.989832i	$0.545432\pi$
$4$	1.09951e12	0.500000
$5$	3.51885e14	1.65012	0.825060	−	0.565044i	$-0.191141\pi$
$5$	3.51885e14	1.65012	0.825060	+	0.565044i	$0.191141\pi$
$6$	−1.80156e15	−0.201163
$7$	−7.89090e16	−0.373780	−0.186890	−	0.982381i	$-0.559841\pi$
$7$	−7.89090e16	−0.373780	−0.186890	+	0.982381i	$0.559841\pi$
$8$	1.15292e18	0.353553
$9$	−3.35211e19	−0.919067
$10$	3.68978e20	1.16681
$11$	1.20679e21	0.540856	0.270428	−	0.962740i	$-0.412835\pi$
$11$	1.20679e21	0.540856	0.270428	+	0.962740i	$0.412835\pi$
$12$	−1.88907e21	−0.142244
$13$	9.23598e22	1.34786	0.673929	−	0.738796i	$-0.264605\pi$
$13$	9.23598e22	1.34786	0.673929	+	0.738796i	$0.264605\pi$
$14$	−8.27420e22	−0.264303
$15$	−6.04574e23	−0.469439
$16$	1.20893e24	0.250000
$17$	−4.95668e24	−0.295793	−0.147897	−	0.989003i	$-0.547250\pi$
$17$	−4.95668e24	−0.295793	−0.147897	+	0.989003i	$0.547250\pi$
$18$	−3.51494e25	−0.649878
$19$	2.41331e26	1.47287	0.736435	−	0.676508i	$-0.236508\pi$
$19$	2.41331e26	1.47287	0.736435	+	0.676508i	$0.236508\pi$
$20$	3.86902e26	0.825060
$21$	1.35574e26	0.106336
$22$	1.26541e27	0.382443
$23$	8.23610e27	1.00069	0.500347	−	0.865825i	$-0.333206\pi$
$23$	8.23610e27	1.00069	0.500347	+	0.865825i	$0.333206\pi$
$24$	−1.98084e27	−0.100581
$25$	7.83484e28	1.72290
$26$	9.68462e28	0.953079
$27$	1.20257e29	0.545950
$28$	−8.67613e28	−0.186890
$29$	2.60718e29	0.273534	0.136767	−	0.990603i	$-0.456329\pi$
$29$	2.60718e29	0.273534	0.136767	+	0.990603i	$0.456329\pi$
$30$	−6.33942e29	−0.331943
$31$	−6.40610e30	−1.71269	−0.856346	−	0.516402i	$-0.827271\pi$
$31$	−6.40610e30	−1.71269	−0.856346	+	0.516402i	$0.827271\pi$
$32$	1.26765e30	0.176777
$33$	−2.07339e30	−0.153867
$34$	−5.19746e30	−0.209157
$35$	−2.77669e31	−0.616783
$36$	−3.68569e31	−0.459533
$37$	7.38149e31	0.524818	0.262409	−	0.964957i	$-0.415483\pi$
$37$	7.38149e31	0.524818	0.262409	+	0.964957i	$0.415483\pi$
$38$	2.53054e32	1.04148
$39$	−1.58683e32	−0.383448
$40$	4.05696e32	0.583406
$41$	2.15386e33	1.86701	0.933507	−	0.358558i	$-0.116732\pi$
$41$	2.15386e33	1.86701	0.933507	+	0.358558i	$0.116732\pi$
$42$	1.42159e32	0.0751908
$43$	−5.67618e33	−1.85333	−0.926665	−	0.375889i	$-0.877337\pi$
$43$	−5.67618e33	−1.85333	−0.926665	+	0.375889i	$0.877337\pi$
$44$	1.32688e33	0.270428
$45$	−1.17956e34	−1.51657
$46$	8.63618e33	0.707597
$47$	−6.45458e33	−0.340300	−0.170150	−	0.985418i	$-0.554425\pi$
$47$	−6.45458e33	−0.340300	−0.170150	+	0.985418i	$0.554425\pi$
$48$	−2.07706e33	−0.0711218
$49$	−3.83410e34	−0.860288
$50$	8.21542e34	1.21827
$51$	8.51608e33	0.0841494
$52$	1.01551e35	0.673929
$53$	−9.99163e34	−0.448726	−0.224363	−	0.974506i	$-0.572030\pi$
$53$	−9.99163e34	−0.448726	−0.224363	+	0.974506i	$0.572030\pi$
$54$	1.26099e35	0.386045
$55$	4.24652e35	0.892479
$56$	−9.09758e34	−0.132151
$57$	−4.14631e35	−0.419013
$58$	2.73383e35	0.193418
$59$	−3.33277e36	−1.66088	−0.830442	−	0.557105i	$-0.811912\pi$
$59$	−3.33277e36	−1.66088	−0.830442	+	0.557105i	$0.811912\pi$
$60$	−6.64736e35	−0.234719
$61$	2.08511e36	0.524648	0.262324	−	0.964980i	$-0.415511\pi$
$61$	2.08511e36	0.524648	0.262324	+	0.964980i	$0.415511\pi$
$62$	−6.71729e36	−1.21106
$63$	2.64512e36	0.343529
$64$	1.32923e36	0.125000
$65$	3.25000e37	2.22413
$66$	−2.17411e36	−0.108800
$67$	2.21433e36	0.0814159	0.0407080	−	0.999171i	$-0.487039\pi$
$67$	2.21433e36	0.0814159	0.0407080	+	0.999171i	$0.487039\pi$
$68$	−5.44993e36	−0.147897
$69$	−1.41505e37	−0.284685
$70$	−2.91157e37	−0.436131
$71$	5.59105e37	0.626177	0.313089	−	0.949724i	$-0.398636\pi$
$71$	5.59105e37	0.626177	0.313089	+	0.949724i	$0.398636\pi$
$72$	−3.86472e37	−0.324939
$73$	−2.02164e38	−1.28110	−0.640552	−	0.767915i	$-0.721294\pi$
$73$	−2.02164e38	−1.28110	−0.640552	+	0.767915i	$0.721294\pi$
$74$	7.74006e37	0.371103
$75$	−1.34610e38	−0.490143
$76$	2.65346e38	0.736435
$77$	−9.52266e37	−0.202162
$78$	−1.66392e38	−0.271139
$79$	−2.46315e38	−0.309126	−0.154563	−	0.987983i	$-0.549397\pi$
$79$	−2.46315e38	−0.309126	−0.154563	+	0.987983i	$0.549397\pi$
$80$	4.25403e38	0.412530
$81$	1.01600e39	0.763751
$82$	2.25848e39	1.32018
$83$	−3.59771e37	−0.0164031	−0.00820154	−	0.999966i	$-0.502611\pi$
$83$	−3.59771e37	−0.0164031	−0.00820154	+	0.999966i	$0.502611\pi$
$84$	1.49065e38	0.0531679
$85$	−1.74418e39	−0.488095
$86$	−5.95190e39	−1.31050
$87$	−4.47940e38	−0.0778171
$88$	1.39134e39	0.191222
$89$	5.24223e38	0.0571506	0.0285753	−	0.999592i	$-0.490903\pi$
$89$	5.24223e38	0.0571506	0.0285753	+	0.999592i	$0.490903\pi$
$90$	−1.23686e40	−1.07238
$91$	−7.28801e39	−0.503803
$92$	9.05569e39	0.500347
$93$	1.10063e40	0.487239
$94$	−6.76812e39	−0.240628
$95$	8.49208e40	2.43041
$96$	−2.17795e39	−0.0502907
$97$	−2.35889e40	−0.440441	−0.220221	−	0.975450i	$-0.570678\pi$
$97$	−2.35889e40	−0.440441	−0.220221	+	0.975450i	$0.570678\pi$
$98$	−4.02035e40	−0.608316
$99$	−4.04530e40	−0.497083
$100$	8.61450e40	0.861450
$101$	−1.92595e40	−0.157057	−0.0785284	−	0.996912i	$-0.525022\pi$
$101$	−1.92595e40	−0.157057	−0.0785284	+	0.996912i	$0.525022\pi$
$102$	8.92976e39	0.0595026
$103$	−2.65701e41	−1.44954	−0.724770	−	0.688991i	$-0.758054\pi$
$103$	−2.65701e41	−1.44954	−0.724770	+	0.688991i	$0.758054\pi$
$104$	1.06484e41	0.476540
$105$	4.77063e40	0.175467
$106$	−1.04770e41	−0.317297
$107$	−2.47756e41	−0.618951	−0.309476	−	0.950907i	$-0.600154\pi$
$107$	−2.47756e41	−0.618951	−0.309476	+	0.950907i	$0.600154\pi$
$108$	1.32224e41	0.272975
$109$	−5.73631e40	−0.0980369	−0.0490184	−	0.998798i	$-0.515609\pi$
$109$	−5.73631e40	−0.0980369	−0.0490184	+	0.998798i	$0.515609\pi$
$110$	4.45280e41	0.631078
$111$	−1.26822e41	−0.149304
$112$	−9.53951e40	−0.0934451
$113$	1.51047e42	1.23312	0.616558	−	0.787310i	$-0.288527\pi$
$113$	1.51047e42	1.23312	0.616558	+	0.787310i	$0.288527\pi$
$114$	−4.34772e41	−0.296287
$115$	2.89816e42	1.65127
$116$	2.86663e41	0.136767
$117$	−3.09600e42	−1.23877
$118$	−3.49466e42	−1.17442
$119$	3.91127e41	0.110562
$120$	−6.97026e41	−0.165972
$121$	−3.52217e42	−0.707474
$122$	2.18640e42	0.370982
$123$	−3.70054e42	−0.531142
$124$	−7.04359e42	−0.856346
$125$	1.15677e43	1.19287
$126$	2.77361e42	0.242912
$127$	7.49737e42	0.558384	0.279192	−	0.960235i	$-0.409933\pi$
$127$	7.49737e42	0.558384	0.279192	+	0.960235i	$0.409933\pi$
$128$	1.39380e42	0.0883883
$129$	9.75225e42	0.527249
$130$	3.40787e43	1.57270
$131$	−4.11904e43	−1.62456	−0.812278	−	0.583271i	$-0.801773\pi$
$131$	−4.11904e43	−1.62456	−0.812278	+	0.583271i	$0.801773\pi$
$132$	−2.27972e42	−0.0769334
$133$	−1.90432e43	−0.550530
$134$	2.32190e42	0.0575698
$135$	4.23166e43	0.900884
$136$	−5.71467e42	−0.104579
$137$	−3.66801e43	−0.577643	−0.288821	−	0.957383i	$-0.593263\pi$
$137$	−3.66801e43	−0.577643	−0.288821	+	0.957383i	$0.593263\pi$
$138$	−1.48378e43	−0.201302
$139$	−8.88436e43	−1.03950	−0.519748	−	0.854320i	$-0.673974\pi$
$139$	−8.88436e43	−1.03950	−0.519748	+	0.854320i	$0.673974\pi$
$140$	−3.05300e43	−0.308391
$141$	1.10896e43	0.0968110
$142$	5.86264e43	0.442774
$143$	1.11459e44	0.728998
$144$	−4.05246e43	−0.229767
$145$	9.17428e43	0.451365
$146$	−2.11984e44	−0.905877
$147$	6.58737e43	0.244741
$148$	8.11604e43	0.262409
$149$	3.54730e44	0.999033	0.499517	−	0.866304i	$-0.333511\pi$
$149$	3.54730e44	0.999033	0.499517	+	0.866304i	$0.333511\pi$
$150$	−1.41149e44	−0.346583
$151$	4.26711e44	0.914338	0.457169	−	0.889380i	$-0.348863\pi$
$151$	4.26711e44	0.914338	0.457169	+	0.889380i	$0.348863\pi$
$152$	2.78236e44	0.520738
$153$	1.66154e44	0.271854
$154$	−9.98524e43	−0.142950
$155$	−2.25421e45	−2.82615
$156$	−1.74474e44	−0.191724
$157$	−8.24494e43	−0.0794776	−0.0397388	−	0.999210i	$-0.512653\pi$
$157$	−8.24494e43	−0.0794776	−0.0397388	+	0.999210i	$0.512653\pi$
$158$	−2.58280e44	−0.218585
$159$	1.71666e44	0.127657
$160$	4.46067e44	0.291703
$161$	−6.49902e44	−0.374040
$162$	1.06536e45	0.540054
$163$	1.78991e44	0.0799806	0.0399903	−	0.999200i	$-0.487267\pi$
$163$	1.78991e44	0.0799806	0.0399903	+	0.999200i	$0.487267\pi$
$164$	2.36819e45	0.933507
$165$	−7.29595e44	−0.253899
$166$	−3.77248e43	−0.0115987
$167$	3.96773e45	1.07859	0.539293	−	0.842118i	$-0.318692\pi$
$167$	3.96773e45	1.07859	0.539293	+	0.842118i	$0.318692\pi$
$168$	1.56306e44	0.0375954
$169$	3.83487e45	0.816721
$170$	−1.82891e45	−0.345135
$171$	−8.08969e45	−1.35367
$172$	−6.24102e45	−0.926665
$173$	6.93399e45	0.914193	0.457097	−	0.889417i	$-0.348889\pi$
$173$	6.93399e45	0.914193	0.457097	+	0.889417i	$0.348889\pi$
$174$	−4.69699e44	−0.0550250
$175$	−6.18239e45	−0.643986
$176$	1.45892e45	0.135214
$177$	5.72604e45	0.472500
$178$	5.49687e44	0.0404116
$179$	−1.62403e46	−1.06441	−0.532203	−	0.846617i	$-0.678636\pi$
$179$	−1.62403e46	−1.06441	−0.532203	+	0.846617i	$0.678636\pi$
$180$	−1.29694e46	−0.758286
$181$	2.21915e46	1.15818	0.579090	−	0.815264i	$-0.303408\pi$
$181$	2.21915e46	1.15818	0.579090	+	0.815264i	$0.303408\pi$
$182$	−7.64204e45	−0.356242
$183$	−3.58243e45	−0.149256
$184$	9.49558e45	0.353799
$185$	2.59744e46	0.866014
$186$	1.15410e46	0.344530
$187$	−5.98168e45	−0.159982
$188$	−7.09688e45	−0.170150
$189$	−9.48935e45	−0.204066
$190$	8.90459e46	1.71856
$191$	−4.97685e46	−0.862523	−0.431262	−	0.902227i	$-0.641931\pi$
$191$	−4.97685e46	−0.862523	−0.431262	+	0.902227i	$0.641931\pi$
$192$	−2.28375e45	−0.0355609
$193$	4.02520e46	0.563459	0.281730	−	0.959494i	$-0.409092\pi$
$193$	4.02520e46	0.563459	0.281730	+	0.959494i	$0.409092\pi$
$194$	−2.47348e46	−0.311439
$195$	−5.58383e46	−0.632736
$196$	−4.21564e46	−0.430144
$197$	−7.00300e46	−0.643764	−0.321882	−	0.946780i	$-0.604315\pi$
$197$	−7.00300e46	−0.643764	−0.321882	+	0.946780i	$0.604315\pi$
$198$	−4.24180e46	−0.351491
$199$	−1.17193e47	−0.875818	−0.437909	−	0.899019i	$-0.644281\pi$
$199$	−1.17193e47	−0.875818	−0.437909	+	0.899019i	$0.644281\pi$
$200$	9.03295e46	0.609137
$201$	−3.80445e45	−0.0231618
$202$	−2.01950e46	−0.111056
$203$	−2.05730e46	−0.102242
$204$	9.36353e45	0.0420747
$205$	7.57910e47	3.08080
$206$	−2.78608e47	−1.02498
$207$	−2.76083e47	−0.919704
$208$	1.11656e47	0.336964
$209$	2.91236e47	0.796611
$210$	5.00237e46	0.124074
$211$	5.52367e47	1.24290	0.621452	−	0.783452i	$-0.286543\pi$
$211$	5.52367e47	1.24290	0.621452	+	0.783452i	$0.286543\pi$
$212$	−1.09859e47	−0.224363
$213$	−9.60599e46	−0.178139
$214$	−2.59791e47	−0.437665
$215$	−1.99736e48	−3.05822
$216$	1.38647e47	0.193023
$217$	5.05499e47	0.640171
$218$	−6.01496e46	−0.0693225
$219$	3.47337e47	0.364458
$220$	4.66910e47	0.446239
$221$	−4.57798e47	−0.398687
$222$	−1.32982e47	−0.105574
$223$	1.20926e48	0.875531	0.437765	−	0.899089i	$-0.355770\pi$
$223$	1.20926e48	0.875531	0.437765	+	0.899089i	$0.355770\pi$
$224$	−1.00029e47	−0.0660757
$225$	−2.62633e48	−1.58346
$226$	1.58384e48	0.871944
$227$	−1.02944e48	−0.517690	−0.258845	−	0.965919i	$-0.583342\pi$
$227$	−1.02944e48	−0.517690	−0.258845	+	0.965919i	$0.583342\pi$
$228$	−4.55892e47	−0.209506
$229$	2.04406e48	0.858750	0.429375	−	0.903126i	$-0.358734\pi$
$229$	2.04406e48	0.858750	0.429375	+	0.903126i	$0.358734\pi$
$230$	3.03894e48	1.16762
$231$	1.63609e47	0.0575124
$232$	3.00587e47	0.0967090
$233$	4.38442e48	1.29156	0.645781	−	0.763523i	$-0.276532\pi$
$233$	4.38442e48	1.29156	0.645781	+	0.763523i	$0.276532\pi$
$234$	−3.24639e48	−0.875944
$235$	−2.27127e48	−0.561536
$236$	−3.66442e48	−0.830442
$237$	4.23194e47	0.0879423
$238$	4.10126e47	0.0781789
$239$	4.33337e48	0.757999	0.379000	−	0.925397i	$-0.376268\pi$
$239$	4.33337e48	0.757999	0.379000	+	0.925397i	$0.376268\pi$
$240$	−7.30885e47	−0.117360
$241$	−3.97635e48	−0.586320	−0.293160	−	0.956063i	$-0.594707\pi$
$241$	−3.97635e48	−0.586320	−0.293160	+	0.956063i	$0.594707\pi$
$242$	−3.69327e48	−0.500260
$243$	−6.13173e48	−0.763228
$244$	2.29260e48	0.262324
$245$	−1.34916e49	−1.41958
$246$	−3.88030e48	−0.375574
$247$	2.22893e49	1.98522
$248$	−7.38574e48	−0.605528
$249$	6.18123e46	0.00466647
$250$	1.21297e49	0.843487
$251$	1.35701e49	0.869507	0.434754	−	0.900549i	$-0.356835\pi$
$251$	1.35701e49	0.869507	0.434754	+	0.900549i	$0.356835\pi$
$252$	2.90834e48	0.171765
$253$	9.93926e48	0.541232
$254$	7.86156e48	0.394837
$255$	2.99668e48	0.138857
$256$	1.46150e48	0.0625000
$257$	−4.30252e49	−1.69861	−0.849304	−	0.527903i	$-0.822978\pi$
$257$	−4.30252e49	−1.69861	−0.849304	+	0.527903i	$0.822978\pi$
$258$	1.02260e49	0.372821
$259$	−5.82466e48	−0.196167
$260$	3.57342e49	1.11206
$261$	−8.73956e48	−0.251397
$262$	−4.31913e49	−1.14873
$263$	−1.54140e49	−0.379160	−0.189580	−	0.981865i	$-0.560713\pi$
$263$	−1.54140e49	−0.379160	−0.189580	+	0.981865i	$0.560713\pi$
$264$	−2.39045e48	−0.0544001
$265$	−3.51591e49	−0.740452
$266$	−1.99682e49	−0.389283
$267$	−9.00667e47	−0.0162586
$268$	2.43468e48	0.0407080
$269$	2.17495e49	0.336920	0.168460	−	0.985708i	$-0.446121\pi$
$269$	2.17495e49	0.336920	0.168460	+	0.985708i	$0.446121\pi$
$270$	4.43722e49	0.637021
$271$	5.12539e49	0.682113	0.341056	−	0.940043i	$-0.389215\pi$
$271$	5.12539e49	0.682113	0.341056	+	0.940043i	$0.389215\pi$
$272$	−5.99226e48	−0.0739483
$273$	1.25215e49	0.143326
$274$	−3.84619e49	−0.408455
$275$	9.45501e49	0.931841
$276$	−1.55586e49	−0.142342
$277$	−5.73007e49	−0.486771	−0.243385	−	0.969930i	$-0.578258\pi$
$277$	−5.73007e49	−0.486771	−0.243385	+	0.969930i	$0.578258\pi$
$278$	−9.31592e49	−0.735034
$279$	2.14740e50	1.57408
$280$	−3.20130e49	−0.218066
$281$	1.97230e49	0.124880	0.0624400	−	0.998049i	$-0.480112\pi$
$281$	1.97230e49	0.124880	0.0624400	+	0.998049i	$0.480112\pi$
$282$	1.16283e49	0.0684557
$283$	−1.39119e49	−0.0761663	−0.0380832	−	0.999275i	$-0.512125\pi$
$283$	−1.39119e49	−0.0761663	−0.0380832	+	0.999275i	$0.512125\pi$
$284$	6.14742e49	0.313089
$285$	−1.45902e50	−0.691422
$286$	1.16873e50	0.515479
$287$	−1.69959e50	−0.697853
$288$	−4.24931e49	−0.162470
$289$	−2.56237e50	−0.912506
$290$	9.61993e49	0.319163
$291$	4.05282e49	0.125300
$292$	−2.22281e50	−0.640552
$293$	3.84683e50	1.03351	0.516757	−	0.856132i	$-0.327139\pi$
$293$	3.84683e50	1.03351	0.516757	+	0.856132i	$0.327139\pi$
$294$	6.90736e49	0.173058
$295$	−1.17275e51	−2.74066
$296$	8.51028e49	0.185551
$297$	1.45125e50	0.295281
$298$	3.71962e50	0.706423
$299$	7.60684e50	1.34879
$300$	−1.48006e50	−0.245071
$301$	4.47901e50	0.692738
$302$	4.47439e50	0.646535
$303$	3.30897e49	0.0446807
$304$	2.91751e50	0.368217
$305$	7.33720e50	0.865732
$306$	1.74225e50	0.192230
$307$	−1.33309e51	−1.37569	−0.687846	−	0.725856i	$-0.741444\pi$
$307$	−1.33309e51	−1.37569	−0.687846	+	0.725856i	$0.741444\pi$
$308$	−1.04703e50	−0.101081
$309$	4.56501e50	0.412376
$310$	−2.36371e51	−1.99839
$311$	−3.42217e50	−0.270841	−0.135420	−	0.990788i	$-0.543239\pi$
$311$	−3.42217e50	−0.270841	−0.135420	+	0.990788i	$0.543239\pi$
$312$	−1.82949e50	−0.135570
$313$	8.29482e50	0.575636	0.287818	−	0.957685i	$-0.407070\pi$
$313$	8.29482e50	0.575636	0.287818	+	0.957685i	$0.407070\pi$
$314$	−8.64544e49	−0.0561991
$315$	9.30777e50	0.566865
$316$	−2.70826e50	−0.154563
$317$	−2.94058e51	−1.57296	−0.786481	−	0.617615i	$-0.788099\pi$
$317$	−2.94058e51	−1.57296	−0.786481	+	0.617615i	$0.788099\pi$
$318$	1.80005e50	0.0902670
$319$	3.14632e50	0.147943
$320$	4.67736e50	0.206265
$321$	4.25670e50	0.176084
$322$	−6.81472e50	−0.264486
$323$	−1.19620e51	−0.435665
$324$	1.11711e51	0.381876
$325$	7.23624e51	2.32222
$326$	1.87685e50	0.0565548
$327$	9.85556e49	0.0278902
$328$	2.48323e51	0.660089
$329$	5.09324e50	0.127197
$330$	−7.65035e50	−0.179534
$331$	−8.47531e51	−1.86931	−0.934656	−	0.355554i	$-0.884292\pi$
$331$	−8.47531e51	−1.86931	−0.934656	+	0.355554i	$0.884292\pi$
$332$	−3.95573e49	−0.00820154
$333$	−2.47436e51	−0.482343
$334$	4.16047e51	0.762675
$335$	7.79191e50	0.134346
$336$	1.63898e50	0.0265839
$337$	2.49054e51	0.380085	0.190042	−	0.981776i	$-0.439137\pi$
$337$	2.49054e51	0.380085	0.190042	+	0.981776i	$0.439137\pi$
$338$	4.02116e51	0.577509
$339$	−2.59514e51	−0.350806
$340$	−1.91775e51	−0.244047
$341$	−7.73083e51	−0.926321
$342$	−8.48265e51	−0.957186
$343$	6.54224e51	0.695339
$344$	−6.54419e51	−0.655251
$345$	−4.97933e51	−0.469764
$346$	7.27082e51	0.646432
$347$	−1.02424e51	−0.0858314	−0.0429157	−	0.999079i	$-0.513665\pi$
$347$	−1.02424e51	−0.0858314	−0.0429157	+	0.999079i	$0.513665\pi$
$348$	−4.92515e50	−0.0389086
$349$	7.39758e51	0.551022	0.275511	−	0.961298i	$-0.411153\pi$
$349$	7.39758e51	0.551022	0.275511	+	0.961298i	$0.411153\pi$
$350$	−6.48271e51	−0.455367
$351$	1.11069e52	0.735863
$352$	1.52979e51	0.0956108
$353$	−6.47846e51	−0.382024	−0.191012	−	0.981588i	$-0.561177\pi$
$353$	−6.47846e51	−0.382024	−0.191012	+	0.981588i	$0.561177\pi$
$354$	6.00418e51	0.334108
$355$	1.96741e52	1.03327
$356$	5.76389e50	0.0285753
$357$	−6.71995e50	−0.0314534
$358$	−1.70292e52	−0.752648
$359$	2.46025e52	1.02693	0.513467	−	0.858109i	$-0.328361\pi$
$359$	2.46025e52	1.02693	0.513467	+	0.858109i	$0.328361\pi$
$360$	−1.35994e52	−0.536189
$361$	3.13936e52	1.16935
$362$	2.32695e52	0.818957
$363$	6.05145e51	0.201267
$364$	−8.01325e51	−0.251901
$365$	−7.11383e52	−2.11398
$366$	−3.75645e51	−0.105540
$367$	−4.93112e52	−1.31006	−0.655030	−	0.755603i	$-0.727344\pi$
$367$	−4.93112e52	−1.31006	−0.655030	+	0.755603i	$0.727344\pi$
$368$	9.95684e51	0.250173
$369$	−7.21997e52	−1.71591
$370$	2.72361e52	0.612364
$371$	7.88429e51	0.167725
$372$	1.21016e52	0.243620
$373$	3.70443e52	0.705815	0.352907	−	0.935658i	$-0.385193\pi$
$373$	3.70443e52	0.705815	0.352907	+	0.935658i	$0.385193\pi$
$374$	−6.27225e51	−0.113124
$375$	−1.98746e52	−0.339357
$376$	−7.44162e51	−0.120314
$377$	2.40799e52	0.368686
$378$	−9.95031e51	−0.144296
$379$	1.03809e53	1.42604	0.713021	−	0.701143i	$-0.247327\pi$
$379$	1.03809e53	1.42604	0.713021	+	0.701143i	$0.247327\pi$
$380$	9.33714e52	1.21521
$381$	−1.28812e52	−0.158853
$382$	−5.21861e52	−0.609896
$383$	−1.27369e52	−0.141088	−0.0705440	−	0.997509i	$-0.522474\pi$
$383$	−1.27369e52	−0.141088	−0.0705440	+	0.997509i	$0.522474\pi$
$384$	−2.39468e51	−0.0251454
$385$	−3.35088e52	−0.333591
$386$	4.22073e52	0.398426
$387$	1.90272e53	1.70333
$388$	−2.59363e52	−0.220221
$389$	−1.61862e53	−1.30371	−0.651853	−	0.758346i	$-0.726008\pi$
$389$	−1.61862e53	−1.30371	−0.651853	+	0.758346i	$0.726008\pi$
$390$	−5.85507e52	−0.447412
$391$	−4.08237e52	−0.295998
$392$	−4.42042e52	−0.304158
$393$	7.07693e52	0.462166
$394$	−7.34318e52	−0.455210
$395$	−8.66745e52	−0.510095
$396$	−4.44785e52	−0.248542
$397$	2.20821e53	1.17175	0.585876	−	0.810401i	$-0.300751\pi$
$397$	2.20821e53	1.17175	0.585876	+	0.810401i	$0.300751\pi$
$398$	−1.22886e53	−0.619297
$399$	3.27181e52	0.156619
$400$	9.47174e52	0.430725
$401$	−1.18852e52	−0.0513509	−0.0256755	−	0.999670i	$-0.508174\pi$
$401$	−1.18852e52	−0.0513509	−0.0256755	+	0.999670i	$0.508174\pi$
$402$	−3.98925e51	−0.0163779
$403$	−5.91666e53	−2.30847
$404$	−2.11760e52	−0.0785284
$405$	3.57516e53	1.26028
$406$	−2.15723e52	−0.0722959
$407$	8.90792e52	0.283851
$408$	9.81837e51	0.0297513
$409$	−9.36392e52	−0.269855	−0.134927	−	0.990856i	$-0.543080\pi$
$409$	−9.36392e52	−0.269855	−0.134927	+	0.990856i	$0.543080\pi$
$410$	7.94726e53	2.17845
$411$	6.30202e52	0.164332
$412$	−2.92141e53	−0.724770
$413$	2.62985e53	0.620806
$414$	−2.89494e53	−0.650329
$415$	−1.26598e52	−0.0270671
$416$	1.17080e53	0.238270
$417$	1.52642e53	0.295723
$418$	3.05383e53	0.563289
$419$	−4.45575e53	−0.782588	−0.391294	−	0.920266i	$-0.627972\pi$
$419$	−4.45575e53	−0.782588	−0.391294	+	0.920266i	$0.627972\pi$
$420$	5.24536e52	0.0877335
$421$	−5.72623e53	−0.912191	−0.456096	−	0.889931i	$-0.650752\pi$
$421$	−5.72623e53	−0.912191	−0.456096	+	0.889931i	$0.650752\pi$
$422$	5.79199e53	0.878866
$423$	2.16365e53	0.312758
$424$	−1.15196e53	−0.158649
$425$	−3.88348e53	−0.509622
$426$	−1.00726e53	−0.125964
$427$	−1.64534e53	−0.196103
$428$	−2.72410e53	−0.309476
$429$	−1.91498e53	−0.207391
$430$	−2.09439e54	−2.16249
$431$	−7.99569e53	−0.787176	−0.393588	−	0.919287i	$-0.628766\pi$
$431$	−7.99569e53	−0.787176	−0.393588	+	0.919287i	$0.628766\pi$
$432$	1.45382e53	0.136488
$433$	1.41016e54	1.26261	0.631303	−	0.775536i	$-0.282520\pi$
$433$	1.41016e54	1.26261	0.631303	+	0.775536i	$0.282520\pi$
$434$	5.30054e53	0.452669
$435$	−1.57623e53	−0.128408
$436$	−6.30714e52	−0.0490184
$437$	1.98763e54	1.47389
$438$	3.64210e53	0.257711
$439$	9.48293e53	0.640353	0.320177	−	0.947358i	$-0.396258\pi$
$439$	9.48293e53	0.640353	0.320177	+	0.947358i	$0.396258\pi$
$440$	4.89590e53	0.315539
$441$	1.28523e54	0.790662
$442$	−4.80036e53	−0.281914
$443$	−1.15125e54	−0.645494	−0.322747	−	0.946485i	$-0.604606\pi$
$443$	−1.15125e54	−0.645494	−0.322747	+	0.946485i	$0.604606\pi$
$444$	−1.39442e53	−0.0746521
$445$	1.84466e53	0.0943054
$446$	1.26801e54	0.619094
$447$	−6.09463e53	−0.284212
$448$	−1.04888e53	−0.0467225
$449$	−1.29162e54	−0.549649	−0.274824	−	0.961494i	$-0.588620\pi$
$449$	−1.29162e54	−0.549649	−0.274824	+	0.961494i	$0.588620\pi$
$450$	−2.75390e54	−1.11968
$451$	2.59925e54	1.00979
$452$	1.66078e54	0.616558
$453$	−7.33133e53	−0.260118
$454$	−1.07944e54	−0.366062
$455$	−2.56454e54	−0.831336
$456$	−4.78037e53	−0.148143
$457$	−5.70144e54	−1.68928	−0.844641	−	0.535332i	$-0.820186\pi$
$457$	−5.70144e54	−1.68928	−0.844641	+	0.535332i	$0.820186\pi$
$458$	2.14335e54	0.607228
$459$	−5.96076e53	−0.161488
$460$	3.18656e54	0.825633
$461$	−5.36766e54	−1.33020	−0.665098	−	0.746756i	$-0.731610\pi$
$461$	−5.36766e54	−1.33020	−0.665098	+	0.746756i	$0.731610\pi$
$462$	1.71556e53	0.0406674
$463$	6.24453e54	1.41609	0.708043	−	0.706170i	$-0.249578\pi$
$463$	6.24453e54	1.41609	0.708043	+	0.706170i	$0.249578\pi$
$464$	3.15189e53	0.0683836
$465$	3.87296e54	0.804004
$466$	4.59739e54	0.913272
$467$	−8.52716e53	−0.162109	−0.0810547	−	0.996710i	$-0.525829\pi$
$467$	−8.52716e53	−0.162109	−0.0810547	+	0.996710i	$0.525829\pi$
$468$	−3.40409e54	−0.619386
$469$	−1.74731e53	−0.0304317
$470$	−2.38160e54	−0.397066
$471$	1.41656e53	0.0226104
$472$	−3.84242e54	−0.587211
$473$	−6.84996e54	−1.00239
$474$	4.43751e53	0.0621846
$475$	1.89079e55	2.53761
$476$	4.30048e53	0.0552809
$477$	3.34931e54	0.412409
$478$	4.54387e54	0.535986
$479$	−6.54754e54	−0.739947	−0.369973	−	0.929042i	$-0.620633\pi$
$479$	−6.54754e54	−0.739947	−0.369973	+	0.929042i	$0.620633\pi$
$480$	−7.66389e53	−0.0829858
$481$	6.81753e54	0.707380
$482$	−4.16950e54	−0.414591
$483$	1.11660e54	0.106410
$484$	−3.87267e54	−0.353737
$485$	−8.30060e54	−0.726781
$486$	−6.42958e54	−0.539684
$487$	−4.90744e54	−0.394922	−0.197461	−	0.980311i	$-0.563270\pi$
$487$	−4.90744e54	−0.394922	−0.197461	+	0.980311i	$0.563270\pi$
$488$	2.40397e54	0.185491
$489$	−3.07524e53	−0.0227535
$490$	−1.41470e55	−1.00379
$491$	2.65373e54	0.180587	0.0902935	−	0.995915i	$-0.471219\pi$
$491$	2.65373e54	0.180587	0.0902935	+	0.995915i	$0.471219\pi$
$492$	−4.06879e54	−0.265571
$493$	−1.29230e54	−0.0809097
$494$	2.33720e55	1.40376
$495$	−1.42348e55	−0.820248
$496$	−7.74451e54	−0.428173
$497$	−4.41184e54	−0.234053
$498$	6.48149e52	0.00329969
$499$	6.02973e53	0.0294603	0.0147301	−	0.999892i	$-0.495311\pi$
$499$	6.02973e53	0.0294603	0.0147301	+	0.999892i	$0.495311\pi$
$500$	1.27189e55	0.596435
$501$	−6.81696e54	−0.306844
$502$	1.42293e55	0.614834
$503$	4.08674e55	1.69525	0.847625	−	0.530596i	$-0.178032\pi$
$503$	4.08674e55	1.69525	0.847625	+	0.530596i	$0.178032\pi$
$504$	3.04961e54	0.121456
$505$	−6.77713e54	−0.259163
$506$	1.04221e55	0.382709
$507$	−6.58870e54	−0.232347
$508$	8.24344e54	0.279192
$509$	4.17871e54	0.135934	0.0679670	−	0.997688i	$-0.478349\pi$
$509$	4.17871e54	0.135934	0.0679670	+	0.997688i	$0.478349\pi$
$510$	3.14225e54	0.0981865
$511$	1.59525e55	0.478851
$512$	1.53250e54	0.0441942
$513$	2.90217e55	0.804114
$514$	−4.51151e55	−1.20110
$515$	−9.34962e55	−2.39192
$516$	1.07227e55	0.263624
$517$	−7.78933e54	−0.184053
$518$	−6.10760e54	−0.138711
$519$	−1.19133e55	−0.260076
$520$	3.74700e55	0.786348
$521$	2.55519e55	0.515525	0.257763	−	0.966208i	$-0.417015\pi$
$521$	2.55519e55	0.515525	0.257763	+	0.966208i	$0.417015\pi$
$522$	−9.16409e54	−0.177764
$523$	−6.45058e55	−1.20314	−0.601568	−	0.798822i	$-0.705457\pi$
$523$	−6.45058e55	−1.20314	−0.601568	+	0.798822i	$0.705457\pi$
$524$	−4.52893e55	−0.812278
$525$	1.06220e55	0.183206
$526$	−1.61627e55	−0.268107
$527$	3.17530e55	0.506603
$528$	−2.50657e54	−0.0384667
$529$	9.40022e52	0.00138770
$530$	−3.68670e55	−0.523579
$531$	1.11718e56	1.52646
$532$	−2.09382e55	−0.275265
$533$	1.98930e56	2.51647
$534$	−9.44418e53	−0.0114966
$535$	−8.71816e55	−1.02134
$536$	2.55295e54	0.0287849
$537$	2.79025e55	0.302810
$538$	2.28060e55	0.238238
$539$	−4.62696e55	−0.465292
$540$	4.65276e55	0.450442
$541$	−1.14581e56	−1.06799	−0.533995	−	0.845488i	$-0.679310\pi$
$541$	−1.14581e56	−1.06799	−0.533995	+	0.845488i	$0.679310\pi$
$542$	5.37436e55	0.482327
$543$	−3.81273e55	−0.329488
$544$	−6.28334e54	−0.0522894
$545$	−2.01852e55	−0.161773
$546$	1.31298e55	0.101346
$547$	6.76717e55	0.503114	0.251557	−	0.967842i	$-0.419057\pi$
$547$	6.76717e55	0.503114	0.251557	+	0.967842i	$0.419057\pi$
$548$	−4.03302e55	−0.288821
$549$	−6.98953e55	−0.482186
$550$	9.91430e55	0.658911
$551$	6.29194e55	0.402881
$552$	−1.63144e55	−0.100651
$553$	1.94364e55	0.115545
$554$	−6.00841e55	−0.344199
$555$	−4.46266e55	−0.246370
$556$	−9.76845e55	−0.519748
$557$	−1.91017e56	−0.979584	−0.489792	−	0.871839i	$-0.662927\pi$
$557$	−1.91017e56	−0.979584	−0.489792	+	0.871839i	$0.662927\pi$
$558$	2.25171e56	1.11304
$559$	−5.24250e56	−2.49802
$560$	−3.35681e55	−0.154196
$561$	1.02771e55	0.0455128
$562$	2.06810e55	0.0883035
$563$	2.46904e56	1.01650	0.508249	−	0.861210i	$-0.330293\pi$
$563$	2.46904e56	1.01650	0.508249	+	0.861210i	$0.330293\pi$
$564$	1.21932e55	0.0484055
$565$	5.31511e56	2.03479
$566$	−1.45876e55	−0.0538577
$567$	−8.01717e55	−0.285475
$568$	6.44604e55	0.221387
$569$	−4.36145e56	−1.44487	−0.722437	−	0.691437i	$-0.756978\pi$
$569$	−4.36145e56	−1.44487	−0.722437	+	0.691437i	$0.756978\pi$
$570$	−1.52990e56	−0.488909
$571$	3.87246e56	1.19384	0.596920	−	0.802300i	$-0.296391\pi$
$571$	3.87246e56	1.19384	0.596920	+	0.802300i	$0.296391\pi$
$572$	1.22550e56	0.364499
$573$	8.55074e55	0.245377
$574$	−1.78214e56	−0.493457
$575$	6.45285e56	1.72409
$576$	−4.45572e55	−0.114883
$577$	3.88180e56	0.965893	0.482947	−	0.875650i	$-0.339567\pi$
$577$	3.88180e56	0.965893	0.482947	+	0.875650i	$0.339567\pi$
$578$	−2.68684e56	−0.645239
$579$	−6.91570e55	−0.160297
$580$	1.00872e56	0.225682
$581$	2.83892e54	0.00613115
$582$	4.24969e55	0.0886004
$583$	−1.20578e56	−0.242696
$584$	−2.33079e56	−0.452938
$585$	−1.08944e57	−2.04412
$586$	4.03369e56	0.730805
$587$	5.00890e56	0.876317	0.438158	−	0.898898i	$-0.355631\pi$
$587$	5.00890e56	0.876317	0.438158	+	0.898898i	$0.355631\pi$
$588$	7.24289e55	0.122371
$589$	−1.54599e57	−2.52257
$590$	−1.22972e57	−1.93794
$591$	1.20319e56	0.183143
$592$	8.92368e55	0.131205
$593$	9.63914e56	1.36904	0.684521	−	0.728993i	$-0.260011\pi$
$593$	9.63914e56	1.36904	0.684521	+	0.728993i	$0.260011\pi$
$594$	1.52175e56	0.208795
$595$	1.37632e56	0.182440
$596$	3.90030e56	0.499517
$597$	2.01350e56	0.249159
$598$	7.97635e56	0.953740
$599$	−1.39170e56	−0.160803	−0.0804016	−	0.996763i	$-0.525620\pi$
$599$	−1.39170e56	−0.160803	−0.0804016	+	0.996763i	$0.525620\pi$
$600$	−1.55195e56	−0.173292
$601$	−1.72237e56	−0.185866	−0.0929330	−	0.995672i	$-0.529624\pi$
$601$	−1.72237e56	−0.185866	−0.0929330	+	0.995672i	$0.529624\pi$
$602$	4.69659e56	0.489840
$603$	−7.42269e55	−0.0748267
$604$	4.69174e56	0.457169
$605$	−1.23940e57	−1.16742
$606$	3.46971e55	0.0315940
$607$	1.22974e57	1.08254	0.541270	−	0.840849i	$-0.317944\pi$
$607$	1.22974e57	1.08254	0.541270	+	0.840849i	$0.317944\pi$
$608$	3.05923e56	0.260369
$609$	3.53465e55	0.0290865
$610$	7.69361e56	0.612165
$611$	−5.96143e56	−0.458676
$612$	1.82688e56	0.135927
$613$	2.53270e57	1.82240	0.911199	−	0.411966i	$-0.135158\pi$
$613$	2.53270e57	1.82240	0.911199	+	0.411966i	$0.135158\pi$
$614$	−1.39784e57	−0.972762
$615$	−1.30217e57	−0.876449
$616$	−1.09789e56	−0.0714749
$617$	−2.74089e56	−0.172602	−0.0863011	−	0.996269i	$-0.527505\pi$
$617$	−2.74089e56	−0.172602	−0.0863011	+	0.996269i	$0.527505\pi$
$618$	4.78676e56	0.291594
$619$	−1.90431e57	−1.12222	−0.561112	−	0.827740i	$-0.689626\pi$
$619$	−1.90431e57	−1.12222	−0.561112	+	0.827740i	$0.689626\pi$
$620$	−2.47853e57	−1.41307
$621$	9.90449e56	0.546329
$622$	−3.58841e56	−0.191513
$623$	−4.13659e55	−0.0213618
$624$	−1.91836e56	−0.0958621
$625$	5.07645e56	0.245482
$626$	8.69774e56	0.407036
$627$	−5.00373e56	−0.226626
$628$	−9.06541e55	−0.0397388
$629$	−3.65877e56	−0.155238
$630$	9.75991e56	0.400834
$631$	1.91059e57	0.759565	0.379782	−	0.925076i	$-0.375999\pi$
$631$	1.91059e57	0.759565	0.379782	+	0.925076i	$0.375999\pi$
$632$	−2.83982e56	−0.109292
$633$	−9.49023e56	−0.353590
$634$	−3.08342e57	−1.11225
$635$	2.63821e57	0.921400
$636$	1.88749e56	0.0638284
$637$	−3.54117e57	−1.15955
$638$	3.29916e56	0.104611
$639$	−1.87418e57	−0.575499
$640$	4.90456e56	0.145851
$641$	6.02067e57	1.73403	0.867013	−	0.498286i	$-0.166037\pi$
$641$	6.02067e57	1.73403	0.867013	+	0.498286i	$0.166037\pi$
$642$	4.46347e56	0.124510
$643$	5.41099e57	1.46201	0.731007	−	0.682370i	$-0.239051\pi$
$643$	5.41099e57	1.46201	0.731007	+	0.682370i	$0.239051\pi$
$644$	−7.14575e56	−0.187020
$645$	3.43167e57	0.870024
$646$	−1.25431e57	−0.308062
$647$	−6.44976e57	−1.53464	−0.767319	−	0.641266i	$-0.778410\pi$
$647$	−6.44976e57	−1.53464	−0.767319	+	0.641266i	$0.778410\pi$
$648$	1.17137e57	0.270027
$649$	−4.02196e57	−0.898300
$650$	7.58774e57	1.64206
$651$	−8.68498e56	−0.182120
$652$	1.96802e56	0.0399903
$653$	5.84519e57	1.15101	0.575504	−	0.817799i	$-0.304806\pi$
$653$	5.84519e57	1.15101	0.575504	+	0.817799i	$0.304806\pi$
$654$	1.03343e56	0.0197214
$655$	−1.44943e58	−2.68071
$656$	2.60385e57	0.466754
$657$	6.77675e57	1.17742
$658$	5.34065e56	0.0899422
$659$	−3.68490e57	−0.601554	−0.300777	−	0.953694i	$-0.597246\pi$
$659$	−3.68490e57	−0.601554	−0.300777	+	0.953694i	$0.597246\pi$
$660$	−8.02198e56	−0.126949
$661$	−6.04679e57	−0.927672	−0.463836	−	0.885921i	$-0.653527\pi$
$661$	−6.04679e57	−0.927672	−0.463836	+	0.885921i	$0.653527\pi$
$662$	−8.88701e57	−1.32180
$663$	7.86543e56	0.113421
$664$	−4.14788e55	−0.00579937
$665$	−6.70101e57	−0.908441
$666$	−2.59455e57	−0.341068
$667$	2.14730e57	0.273724
$668$	4.36257e57	0.539293
$669$	−2.07764e57	−0.249077
$670$	8.17041e56	0.0949971
$671$	2.51629e57	0.283759
$672$	1.71860e56	0.0187977
$673$	6.56510e57	0.696518	0.348259	−	0.937398i	$-0.386773\pi$
$673$	6.56510e57	0.696518	0.348259	+	0.937398i	$0.386773\pi$
$674$	2.61152e57	0.268761
$675$	9.42194e57	0.940617
$676$	4.21649e57	0.408360
$677$	1.10721e58	1.04031	0.520155	−	0.854072i	$-0.325874\pi$
$677$	1.10721e58	1.04031	0.520155	+	0.854072i	$0.325874\pi$
$678$	−2.72120e57	−0.248057
$679$	1.86138e57	0.164628
$680$	−2.01091e57	−0.172568
$681$	1.76868e57	0.147276
$682$	−8.10636e57	−0.655008
$683$	1.97103e58	1.54550	0.772749	−	0.634711i	$-0.218881\pi$
$683$	1.97103e58	1.54550	0.772749	+	0.634711i	$0.218881\pi$
$684$	−8.89471e57	−0.676833
$685$	−1.29072e58	−0.953180
$686$	6.86003e57	0.491679
$687$	−3.51190e57	−0.244303
$688$	−6.86208e57	−0.463332
$689$	−9.22825e57	−0.604819
$690$	−5.22121e57	−0.332173
$691$	1.78821e58	1.10438	0.552191	−	0.833718i	$-0.313792\pi$
$691$	1.78821e58	1.10438	0.552191	+	0.833718i	$0.313792\pi$
$692$	7.62400e57	0.457097
$693$	3.19210e57	0.185800
$694$	−1.07399e57	−0.0606920
$695$	−3.12627e58	−1.71529
$696$	−5.16440e56	−0.0275125
$697$	−1.06760e58	−0.552250
$698$	7.75693e57	0.389631
$699$	−7.53287e57	−0.367433
$700$	−6.79761e57	−0.321993
$701$	−2.83192e58	−1.30275	−0.651375	−	0.758756i	$-0.725807\pi$
$701$	−2.83192e58	−1.30275	−0.651375	+	0.758756i	$0.725807\pi$
$702$	1.16464e58	0.520334
$703$	1.78138e58	0.772989
$704$	1.60410e57	0.0676071
$705$	3.90227e57	0.159750
$706$	−6.79315e57	−0.270131
$707$	1.51975e57	0.0587047
$708$	6.29584e57	0.236250
$709$	3.01107e58	1.09767	0.548836	−	0.835930i	$-0.315071\pi$
$709$	3.01107e58	1.09767	0.548836	+	0.835930i	$0.315071\pi$
$710$	2.06298e58	0.730631
$711$	8.25675e57	0.284107
$712$	6.04388e56	0.0202058
$713$	−5.27613e58	−1.71388
$714$	−7.04638e56	−0.0222409
$715$	3.92207e58	1.20293
$716$	−1.78564e58	−0.532203
$717$	−7.44516e57	−0.215641
$718$	2.57976e58	0.726153
$719$	−3.81485e58	−1.04360	−0.521802	−	0.853067i	$-0.674740\pi$
$719$	−3.81485e58	−1.04360	−0.521802	+	0.853067i	$0.674740\pi$
$720$	−1.42600e58	−0.379143
$721$	2.09662e58	0.541809
$722$	3.29185e58	0.826852
$723$	6.83176e57	0.166801
$724$	2.43998e58	0.579090
$725$	2.04268e58	0.471272
$726$	6.34540e57	0.142318
$727$	3.32784e58	0.725617	0.362808	−	0.931864i	$-0.381818\pi$
$727$	3.32784e58	0.725617	0.362808	+	0.931864i	$0.381818\pi$
$728$	−8.40251e57	−0.178121
$729$	−2.65217e58	−0.546622
$730$	−7.45939e58	−1.49481
$731$	2.81350e58	0.548202
$732$	−3.93893e57	−0.0746278
$733$	−2.73207e58	−0.503338	−0.251669	−	0.967813i	$-0.580979\pi$
$733$	−2.73207e58	−0.503338	−0.251669	+	0.967813i	$0.580979\pi$
$734$	−5.17065e58	−0.926352
$735$	2.31800e58	0.403852
$736$	1.04405e58	0.176899
$737$	2.67224e57	0.0440343
$738$	−7.57069e58	−1.21333
$739$	−2.78923e58	−0.434784	−0.217392	−	0.976084i	$-0.569755\pi$
$739$	−2.78923e58	−0.434784	−0.217392	+	0.976084i	$0.569755\pi$
$740$	2.85591e58	0.433007
$741$	−3.82952e58	−0.564770
$742$	8.26728e57	0.118599
$743$	−5.29149e58	−0.738427	−0.369214	−	0.929345i	$-0.620373\pi$
$743$	−5.29149e58	−0.738427	−0.369214	+	0.929345i	$0.620373\pi$
$744$	1.26894e58	0.172265
$745$	1.24824e59	1.64853
$746$	3.88438e58	0.499086
$747$	1.20599e57	0.0150755
$748$	−6.57693e57	−0.0799908
$749$	1.95502e58	0.231352
$750$	−2.08400e58	−0.239961
$751$	−1.65688e59	−1.85641	−0.928203	−	0.372075i	$-0.878647\pi$
$751$	−1.65688e59	−1.85641	−0.928203	+	0.372075i	$0.878647\pi$
$752$	−7.80311e57	−0.0850750
$753$	−2.33149e58	−0.247364
$754$	2.52496e58	0.260700
$755$	1.50153e59	1.50877
$756$	−1.04337e58	−0.102033
$757$	1.30792e59	1.24485	0.622424	−	0.782680i	$-0.286148\pi$
$757$	1.30792e59	1.24485	0.622424	+	0.782680i	$0.286148\pi$
$758$	1.08852e59	1.00836
$759$	−1.70766e58	−0.153974
$760$	9.79070e58	0.859281
$761$	8.10267e58	0.692218	0.346109	−	0.938194i	$-0.387503\pi$
$761$	8.10267e58	0.692218	0.346109	+	0.938194i	$0.387503\pi$
$762$	−1.35070e58	−0.112326
$763$	4.52646e57	0.0366443
$764$	−5.47211e58	−0.431262
$765$	5.84670e58	0.448592
$766$	−1.33556e58	−0.0997643
$767$	−3.07814e59	−2.23863
$768$	−2.51101e57	−0.0177805
$769$	−5.87182e58	−0.404839	−0.202420	−	0.979299i	$-0.564881\pi$
$769$	−5.87182e58	−0.404839	−0.202420	+	0.979299i	$0.564881\pi$
$770$	−3.51366e58	−0.235884
$771$	7.39216e58	0.483233
$772$	4.42575e58	0.281730
$773$	−2.32645e59	−1.44216	−0.721081	−	0.692850i	$-0.756355\pi$
$773$	−2.32645e59	−1.44216	−0.721081	+	0.692850i	$0.756355\pi$
$774$	1.99515e59	1.20444
$775$	−5.01908e59	−2.95080
$776$	−2.71962e58	−0.155719
$777$	1.00074e58	0.0558070
$778$	−1.69725e59	−0.921859
$779$	5.19792e59	2.74987
$780$	−6.13949e58	−0.316368
$781$	6.74723e58	0.338672
$782$	−4.28068e58	−0.209302
$783$	3.13532e58	0.149336
$784$	−4.63514e58	−0.215072
$785$	−2.90127e58	−0.131148
$786$	7.42070e58	0.326800
$787$	2.24048e59	0.961299	0.480649	−	0.876913i	$-0.340401\pi$
$787$	2.24048e59	0.961299	0.480649	+	0.876913i	$0.340401\pi$
$788$	−7.69988e58	−0.321882
$789$	2.64828e58	0.107866
$790$	−9.08848e58	−0.360691
$791$	−1.19190e59	−0.460914
$792$	−4.66391e58	−0.175745
$793$	1.92580e59	0.707150
$794$	2.31548e59	0.828553
$795$	6.04068e58	0.210649
$796$	−1.28855e59	−0.437909
$797$	3.32067e59	1.09984	0.549921	−	0.835217i	$-0.314658\pi$
$797$	3.32067e59	1.09984	0.549921	+	0.835217i	$0.314658\pi$
$798$	3.43074e58	0.110746
$799$	3.19933e58	0.100658
$800$	9.93184e58	0.304568
$801$	−1.75725e58	−0.0525252
$802$	−1.24626e58	−0.0363106
$803$	−2.43969e59	−0.692893
$804$	−4.18303e57	−0.0115809
$805$	−2.28691e59	−0.617211
$806$	−6.20407e59	−1.63233
$807$	−3.73678e58	−0.0958495
$808$	−2.22047e58	−0.0555279
$809$	7.35141e59	1.79236	0.896182	−	0.443687i	$-0.146330\pi$
$809$	7.35141e59	1.79236	0.896182	+	0.443687i	$0.146330\pi$
$810$	3.74883e59	0.891154
$811$	−7.34195e58	−0.170170	−0.0850852	−	0.996374i	$-0.527116\pi$
$811$	−7.34195e58	−0.170170	−0.0850852	+	0.996374i	$0.527116\pi$
$812$	−2.26202e58	−0.0511209
$813$	−8.80593e58	−0.194053
$814$	9.34063e58	0.200713
$815$	6.29842e58	0.131978
$816$	1.02953e58	0.0210374
$817$	−1.36984e60	−2.72971
$818$	−9.81878e58	−0.190816
$819$	2.44302e59	0.463029
$820$	8.33331e59	1.54040
$821$	−7.00875e59	−1.26359	−0.631794	−	0.775136i	$-0.717681\pi$
$821$	−7.00875e59	−1.26359	−0.631794	+	0.775136i	$0.717681\pi$
$822$	6.60814e58	0.116200
$823$	−4.10799e59	−0.704584	−0.352292	−	0.935890i	$-0.614598\pi$
$823$	−4.10799e59	−0.704584	−0.352292	+	0.935890i	$0.614598\pi$
$824$	−3.06332e59	−0.512490
$825$	−1.62447e59	−0.265097
$826$	2.75760e59	0.438976
$827$	2.98123e59	0.462949	0.231474	−	0.972841i	$-0.425645\pi$
$827$	2.98123e59	0.462949	0.231474	+	0.972841i	$0.425645\pi$
$828$	−3.03557e59	−0.459852
$829$	3.83752e59	0.567130	0.283565	−	0.958953i	$-0.408483\pi$
$829$	3.83752e59	0.567130	0.283565	+	0.958953i	$0.408483\pi$
$830$	−1.32748e58	−0.0191393
$831$	9.84484e58	0.138480
$832$	1.22767e59	0.168482
$833$	1.90044e59	0.254467
$834$	1.60057e59	0.209108
$835$	1.39618e60	1.77980
$836$	3.20218e59	0.398306
$837$	−7.70379e59	−0.935045
$838$	−4.67219e59	−0.553373
$839$	9.98054e59	1.15354	0.576772	−	0.816905i	$-0.304312\pi$
$839$	9.98054e59	1.15354	0.576772	+	0.816905i	$0.304312\pi$
$840$	5.50016e58	0.0620369
$841$	−8.40511e59	−0.925179
$842$	−6.00439e59	−0.645017
$843$	−3.38861e58	−0.0355268
$844$	6.07334e59	0.621452
$845$	1.34943e60	1.34769
$846$	2.26875e59	0.221154
$847$	2.77931e59	0.264440
$848$	−1.20791e59	−0.112181
$849$	2.39020e58	0.0216684
$850$	−4.07212e59	−0.360357
$851$	6.07948e59	0.525182
$852$	−1.05619e59	−0.0890697
$853$	−1.04133e60	−0.857302	−0.428651	−	0.903470i	$-0.641011\pi$
$853$	−1.04133e60	−0.857302	−0.428651	+	0.903470i	$0.641011\pi$
$854$	−1.72526e59	−0.138666
$855$	−2.84664e60	−2.23371
$856$	−2.85643e59	−0.218832
$857$	−2.22118e59	−0.166141	−0.0830705	−	0.996544i	$-0.526473\pi$
$857$	−2.22118e59	−0.166141	−0.0830705	+	0.996544i	$0.526473\pi$
$858$	−2.00800e59	−0.146647
$859$	1.83508e60	1.30856	0.654282	−	0.756250i	$-0.272971\pi$
$859$	1.83508e60	1.30856	0.654282	+	0.756250i	$0.272971\pi$
$860$	−2.19612e60	−1.52911
$861$	2.92006e59	0.198530
$862$	−8.38409e59	−0.556618
$863$	−2.51134e60	−1.62811	−0.814055	−	0.580788i	$-0.802744\pi$
$863$	−2.51134e60	−1.62811	−0.814055	+	0.580788i	$0.802744\pi$
$864$	1.52444e59	0.0965113
$865$	2.43997e60	1.50853
$866$	1.47866e60	0.892797
$867$	4.40241e59	0.259597
$868$	5.55802e59	0.320085
$869$	−2.97250e59	−0.167193
$870$	−1.65280e59	−0.0907979
$871$	2.04515e59	0.109737
$872$	−6.61351e58	−0.0346613
$873$	7.90728e59	0.404795
$874$	2.08418e60	1.04220
$875$	−9.12799e59	−0.445872
$876$	3.81901e59	0.182229
$877$	1.15614e60	0.538913	0.269457	−	0.963013i	$-0.413156\pi$
$877$	1.15614e60	0.538913	0.269457	+	0.963013i	$0.413156\pi$
$878$	9.94357e59	0.452798
$879$	−6.60924e59	−0.294022
$880$	5.13372e59	0.223120
$881$	−2.91398e60	−1.23732	−0.618658	−	0.785661i	$-0.712323\pi$
$881$	−2.91398e60	−1.23732	−0.618658	+	0.785661i	$0.712323\pi$
$882$	1.34767e60	0.559083
$883$	1.84407e60	0.747452	0.373726	−	0.927539i	$-0.378080\pi$
$883$	1.84407e60	0.747452	0.373726	+	0.927539i	$0.378080\pi$
$884$	−5.03354e59	−0.199344
$885$	2.01491e60	0.779683
$886$	−1.20717e60	−0.456433
$887$	−4.08939e59	−0.151086	−0.0755431	−	0.997143i	$-0.524069\pi$
$887$	−4.08939e59	−0.151086	−0.0755431	+	0.997143i	$0.524069\pi$
$888$	−1.46215e59	−0.0527870
$889$	−5.91610e59	−0.208713
$890$	1.93427e59	0.0666840
$891$	1.22610e60	0.413080
$892$	1.32960e60	0.437765
$893$	−1.55769e60	−0.501217
$894$	−6.39068e59	−0.200968
$895$	−5.71472e60	−1.75640
$896$	−1.09983e59	−0.0330378
$897$	−1.30693e60	−0.383714
$898$	−1.35436e60	−0.388660
$899$	−1.67019e60	−0.468480
$900$	−2.88768e60	−0.791730
$901$	4.95254e59	0.132730
$902$	2.72552e60	0.714027
$903$	−7.69540e59	−0.197075
$904$	1.74145e60	0.435972
$905$	7.80886e60	1.91114
$906$	−7.68746e59	−0.183931
$907$	1.20769e60	0.282492	0.141246	−	0.989975i	$-0.454889\pi$
$907$	1.20769e60	0.282492	0.141246	+	0.989975i	$0.454889\pi$
$908$	−1.13188e60	−0.258845
$909$	6.45600e59	0.144346
$910$	−2.68912e60	−0.587843
$911$	5.09758e59	0.108953	0.0544763	−	0.998515i	$-0.482651\pi$
$911$	5.09758e59	0.108953	0.0544763	+	0.998515i	$0.482651\pi$
$912$	−5.01258e59	−0.104753
$913$	−4.34169e58	−0.00887172
$914$	−5.97839e60	−1.19450
$915$	−1.26060e60	−0.246290
$916$	2.24747e60	0.429375
$917$	3.25029e60	0.607227
$918$	−6.25031e59	−0.114190
$919$	−5.01795e60	−0.896517	−0.448259	−	0.893904i	$-0.647956\pi$
$919$	−5.01795e60	−0.896517	−0.448259	+	0.893904i	$0.647956\pi$
$920$	3.34135e60	0.583811
$921$	2.29038e60	0.391367
$922$	−5.62840e60	−0.940591
$923$	5.16388e60	0.843998
$924$	1.79890e59	0.0287562
$925$	5.78328e60	0.904209
$926$	6.54787e60	1.00132
$927$	8.90660e60	1.33222
$928$	3.30499e59	0.0483545
$929$	−3.15656e60	−0.451744	−0.225872	−	0.974157i	$-0.572523\pi$
$929$	−3.15656e60	−0.451744	−0.225872	+	0.974157i	$0.572523\pi$
$930$	4.06110e60	0.568516
$931$	−9.25288e60	−1.26709
$932$	4.82072e60	0.645781
$933$	5.87964e59	0.0770508
$934$	−8.94138e59	−0.114629
$935$	−2.10486e60	−0.263989
$936$	−3.56945e60	−0.437972
$937$	−5.64418e60	−0.677547	−0.338773	−	0.940868i	$-0.610012\pi$
$937$	−5.64418e60	−0.677547	−0.338773	+	0.940868i	$0.610012\pi$
$938$	−1.83218e59	−0.0215185
$939$	−1.42513e60	−0.163761
$940$	−2.49729e60	−0.280768
$941$	−1.57154e61	−1.72877	−0.864385	−	0.502831i	$-0.832292\pi$
$941$	−1.57154e61	−1.72877	−0.864385	+	0.502831i	$0.832292\pi$
$942$	1.48537e59	0.0159879
$943$	1.77394e61	1.86831
$944$	−4.02907e60	−0.415221
$945$	−3.33916e60	−0.336733
$946$	−7.18270e60	−0.708793
$947$	−3.54084e60	−0.341926	−0.170963	−	0.985277i	$-0.554688\pi$
$947$	−3.54084e60	−0.341926	−0.170963	+	0.985277i	$0.554688\pi$
$948$	4.65306e59	0.0439712
$949$	−1.86718e61	−1.72675
$950$	1.98264e61	1.79436
$951$	5.05221e60	0.447488
$952$	4.50938e59	0.0390895
$953$	−3.82394e60	−0.324420	−0.162210	−	0.986756i	$-0.551862\pi$
$953$	−3.82394e60	−0.324420	−0.162210	+	0.986756i	$0.551862\pi$
$954$	3.51200e60	0.291617
$955$	−1.75128e61	−1.42327
$956$	4.76459e60	0.379000
$957$	−5.40570e59	−0.0420879
$958$	−6.86560e60	−0.523221
$959$	2.89439e60	0.215912
$960$	−8.03617e59	−0.0586798
$961$	2.70478e61	1.93331
$962$	7.14870e60	0.500193
$963$	8.30505e60	0.568858
$964$	−4.37204e60	−0.293160
$965$	1.41641e61	0.929776
$966$	1.17084e60	0.0752429
$967$	1.08706e61	0.683930	0.341965	−	0.939713i	$-0.388908\pi$
$967$	1.08706e61	0.683930	0.341965	+	0.939713i	$0.388908\pi$
$968$	−4.06079e60	−0.250130
$969$	2.05519e60	0.123941
$970$	−8.70381e60	−0.513912
$971$	1.86961e61	1.08083	0.540416	−	0.841398i	$-0.318267\pi$
$971$	1.86961e61	1.08083	0.540416	+	0.841398i	$0.318267\pi$
$972$	−6.74190e60	−0.381614
$973$	7.01055e60	0.388543
$974$	−5.14582e60	−0.279252
$975$	−1.24326e61	−0.660643
$976$	2.52075e60	0.131162
$977$	−2.93813e61	−1.49704	−0.748518	−	0.663115i	$-0.769234\pi$
$977$	−2.93813e61	−1.49704	−0.748518	+	0.663115i	$0.769234\pi$
$978$	−3.22462e59	−0.0160891
$979$	6.32627e59	0.0309103
$980$	−1.48342e61	−0.709790
$981$	1.92288e60	0.0901024
$982$	2.78264e60	0.127694
$983$	2.55719e61	1.14925	0.574626	−	0.818416i	$-0.305148\pi$
$983$	2.55719e61	1.14925	0.574626	+	0.818416i	$0.305148\pi$
$984$	−4.26644e60	−0.187787
$985$	−2.46425e61	−1.06229
$986$	−1.35507e60	−0.0572118
$987$	−8.75070e59	−0.0361861
$988$	2.45073e61	0.992610
$989$	−4.67496e61	−1.85461
$990$	−1.49263e61	−0.580003
$991$	1.53747e61	0.585188	0.292594	−	0.956237i	$-0.405482\pi$
$991$	1.53747e61	0.585188	0.292594	+	0.956237i	$0.405482\pi$
$992$	−8.12070e60	−0.302764
$993$	1.45614e61	0.531796
$994$	−4.62615e60	−0.165500
$995$	−4.12385e61	−1.44521
$996$	6.79634e58	0.00233324
$997$	4.42141e61	1.48700	0.743499	−	0.668737i	$-0.233165\pi$
$997$	4.42141e61	1.48700	0.743499	+	0.668737i	$0.233165\pi$
$998$	6.32263e59	0.0208316
$999$	8.87676e60	0.286525

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.04858e6 q^{2} -1.71810e9 q^{3} +1.09951e12 q^{4} +3.51885e14 q^{5} -1.80156e15 q^{6} -7.89090e16 q^{7} +1.15292e18 q^{8} -3.35211e19 q^{9} +O(q^{10})\)	\(q+1.04858e6 q^{2} -1.71810e9 q^{3} +1.09951e12 q^{4} +3.51885e14 q^{5} -1.80156e15 q^{6} -7.89090e16 q^{7} +1.15292e18 q^{8} -3.35211e19 q^{9} +3.68978e20 q^{10} +1.20679e21 q^{11} -1.88907e21 q^{12} +9.23598e22 q^{13} -8.27420e22 q^{14} -6.04574e23 q^{15} +1.20893e24 q^{16} -4.95668e24 q^{17} -3.51494e25 q^{18} +2.41331e26 q^{19} +3.86902e26 q^{20} +1.35574e26 q^{21} +1.26541e27 q^{22} +8.23610e27 q^{23} -1.98084e27 q^{24} +7.83484e28 q^{25} +9.68462e28 q^{26} +1.20257e29 q^{27} -8.67613e28 q^{28} +2.60718e29 q^{29} -6.33942e29 q^{30} -6.40610e30 q^{31} +1.26765e30 q^{32} -2.07339e30 q^{33} -5.19746e30 q^{34} -2.77669e31 q^{35} -3.68569e31 q^{36} +7.38149e31 q^{37} +2.53054e32 q^{38} -1.58683e32 q^{39} +4.05696e32 q^{40} +2.15386e33 q^{41} +1.42159e32 q^{42} -5.67618e33 q^{43} +1.32688e33 q^{44} -1.17956e34 q^{45} +8.63618e33 q^{46} -6.45458e33 q^{47} -2.07706e33 q^{48} -3.83410e34 q^{49} +8.21542e34 q^{50} +8.51608e33 q^{51} +1.01551e35 q^{52} -9.99163e34 q^{53} +1.26099e35 q^{54} +4.24652e35 q^{55} -9.09758e34 q^{56} -4.14631e35 q^{57} +2.73383e35 q^{58} -3.33277e36 q^{59} -6.64736e35 q^{60} +2.08511e36 q^{61} -6.71729e36 q^{62} +2.64512e36 q^{63} +1.32923e36 q^{64} +3.25000e37 q^{65} -2.17411e36 q^{66} +2.21433e36 q^{67} -5.44993e36 q^{68} -1.41505e37 q^{69} -2.91157e37 q^{70} +5.59105e37 q^{71} -3.86472e37 q^{72} -2.02164e38 q^{73} +7.74006e37 q^{74} -1.34610e38 q^{75} +2.65346e38 q^{76} -9.52266e37 q^{77} -1.66392e38 q^{78} -2.46315e38 q^{79} +4.25403e38 q^{80} +1.01600e39 q^{81} +2.25848e39 q^{82} -3.59771e37 q^{83} +1.49065e38 q^{84} -1.74418e39 q^{85} -5.95190e39 q^{86} -4.47940e38 q^{87} +1.39134e39 q^{88} +5.24223e38 q^{89} -1.23686e40 q^{90} -7.28801e39 q^{91} +9.05569e39 q^{92} +1.10063e40 q^{93} -6.76812e39 q^{94} +8.49208e40 q^{95} -2.17795e39 q^{96} -2.35889e40 q^{97} -4.02035e40 q^{98} -4.04530e40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2097152 q^{2} + 8863347528 q^{3} + 2199023255552 q^{4} + 97599184325580 q^{5} + 92\!\cdots\!28 q^{6}+ \cdots + 41\!\cdots\!86 q^{9}+O(q^{10}) \) 2 * q + 2097152 * q^2 + 8863347528 * q^3 + 2199023255552 * q^4 + 97599184325580 * q^5 + 9293893497520128 * q^6 + 217106802373088656 * q^7 + 2305843009213693952 * q^8 + 41972929616872509786 * q^9	\( 2 q + 2097152 q^{2} + 8863347528 q^{3} + 2199023255552 q^{4} + 97599184325580 q^{5} + 92\!\cdots\!28 q^{6}+ \cdots - 12\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 2097152 * q^2 + 8863347528 * q^3 + 2199023255552 * q^4 + 97599184325580 * q^5 + 9293893497520128 * q^6 + 217106802373088656 * q^7 + 2305843009213693952 * q^8 + 41972929616872509786 * q^9 + 102340162303379374080 * q^10 + 110594481484939565784 * q^11 + 9745353668055665737728 * q^12 + 173293106838448696895068 * q^13 + 227652982405163810553856 * q^14 - 3295287287252802285241680 * q^15 + 2417851639229258349412352 * q^16 - 10287966260741677078429404 * q^17 + 44011806645941708821364736 * q^18 + 206254882139859790701457000 * q^19 + 107311438027428330555310080 * q^20 + 3267849131609686416057835584 * q^21 + 115966719017551990131523584 * q^22 + 14925421378885128304361915568 * q^23 + 10218743967835137756603875328 * q^24 + 97534966241249753807444705150 * q^25 + 181710992796233180795442823168 * q^26 + 533156288863055843864697754320 * q^27 + 238711453678477047815320109056 * q^28 - 1375143011941884388614889894020 * q^29 - 3455359162518394409049579847680 * q^30 - 3626496922711160469799126663616 * q^31 + 2535301200456458802993406410752 * q^32 - 13672735988327258412044854187424 * q^33 - 10787714509823464784191190728704 * q^34 - 103039524095905042910481769779360 * q^35 + 46149724165574973269071349415936 * q^36 + 120356679589378915210866994599436 * q^37 + 216273919294685619894570975232000 * q^38 + 697708668559917206762862430490352 * q^39 + 112524198441048689140364822446080 * q^40 + 1270177139906840106861139346878164 * q^41 + 3426588171026758543404261005328384 * q^42 - 6045433421160616098770468790853352 * q^43 + 121599918360548595604152473616384 * q^44 - 30992658299909156185379775337031460 * q^45 + 15650438647785852296874599978631168 * q^46 - 25416478966330542868882280891861664 * q^47 + 10715129674816697408268665175932928 * q^48 + 4716677344275473650585885334355954 * q^49 + 102272824761384701848395139147366400 * q^50 - 47896619495707425086522465903395056 * q^51 + 190537785982303003785762253746208768 * q^52 - 301376484284740318156836692232048852 * q^53 + 559054888750867644536269312433848320 * q^54 + 703399094180619772764269188861842960 * q^55 + 250307101252362748889997098673504256 * q^56 - 785787658029123941344672503009410400 * q^57 - 1441941958889973364676246785511915520 * q^58 - 3282010250697938085995473868454788040 * q^59 - 3623206689196887935863572238360903680 * q^60 - 4485157745840460017677520841591879236 * q^61 - 3802657637228777800780089040427810816 * q^62 + 24992547810032633572829803615671997008 * q^63 + 2658455991569831745807614120560689152 * q^64 + 11919812053150705903267451825832510120 * q^65 - 14336902811696243316668345024432308224 * q^66 + 55055736076082381526441630307313037256 * q^67 - 11311738529852649409548062009541525504 * q^68 + 56632222305135551516324020091548201152 * q^69 - 108044772018387726274901332228162191360 * q^70 - 48857884738531480102553331099997138416 * q^71 + 48391493166641943170589759285164507136 * q^72 - 485616958845162818165813572349849688812 * q^73 + 126203125657112585396150069729098203136 * q^74 + 68411444542067712502035991381122300600 * q^75 + 226779641198344268566569654924869632000 * q^76 - 419718086944271580508987308621981603648 * q^77 + 731600564843883744998575235913851338752 * q^78 - 905766854341990828970937020702446890080 * q^79 + 117990173904521070264047184061220782080 * q^80 + 2631580786121491108655810678136598411122 * q^81 + 1331877264654954771892026051792117694464 * q^82 + 1271755206567258248006583231290595969768 * q^83 + 3593038118022554366408666387923215581184 * q^84 - 388512546938141834318136915482004571560 * q^85 - 6339096395026914186384343082837844426752 * q^86 - 17757719150026706057484126704955838888080 * q^87 + 127506755994830604184219784174773469184 * q^88 + 2692414558304473820098690391828757436980 * q^89 - 32498157669485543356240783303803100200960 * q^90 + 16669534332125295311104493248216990683104 * q^91 + 16410674355540697858047580547193155616768 * q^92 + 40418607330508619745600934617627243192576 * q^93 - 26651109848599015319281106568464736190464 * q^94 + 93840167647611953736551449995129877215600 * q^95 + 11235627813900593301572723855519045910528 * q^96 - 31989468315501178009691057062669320691004 * q^97 + 4945794662950999058636745300357628821504 * q^98 - 123209315561064920195916977740234432814088 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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