LMFDB - Embedded newform 3.42.a.b.1.2

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			1.2
Root			$263663.$ 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)

$f(q)$	$=$	$q-1.59943e6 q^{2} +3.48678e9 q^{3} +3.59152e11 q^{4} +3.20915e14 q^{5} -5.57687e15 q^{6} +2.35480e17 q^{7} +2.94274e18 q^{8} +1.21577e19 q^{9} +O(q^{10})$	\(q-1.59943e6 q^{2} +3.48678e9 q^{3} +3.59152e11 q^{4} +3.20915e14 q^{5} -5.57687e15 q^{6} +2.35480e17 q^{7} +2.94274e18 q^{8} +1.21577e19 q^{9} -5.13282e20 q^{10} +4.09335e21 q^{11} +1.25229e21 q^{12} +2.26252e22 q^{13} -3.76634e23 q^{14} +1.11896e24 q^{15} -5.49650e24 q^{16} -2.18147e25 q^{17} -1.94453e25 q^{18} -1.65269e26 q^{19} +1.15257e26 q^{20} +8.21069e26 q^{21} -6.54702e27 q^{22} +1.04809e28 q^{23} +1.02607e28 q^{24} +5.75119e28 q^{25} -3.61875e28 q^{26} +4.23912e28 q^{27} +8.45732e28 q^{28} -1.48336e29 q^{29} -1.78970e30 q^{30} +2.32552e30 q^{31} +2.32010e30 q^{32} +1.42726e31 q^{33} +3.48911e31 q^{34} +7.55692e31 q^{35} +4.36645e30 q^{36} -5.37090e31 q^{37} +2.64337e32 q^{38} +7.88894e31 q^{39} +9.44372e32 q^{40} -9.27726e32 q^{41} -1.31324e33 q^{42} +4.47072e33 q^{43} +1.47013e33 q^{44} +3.90158e33 q^{45} -1.67634e34 q^{46} -1.02491e34 q^{47} -1.91651e34 q^{48} +1.08833e34 q^{49} -9.19863e34 q^{50} -7.60632e34 q^{51} +8.12590e33 q^{52} -2.32449e35 q^{53} -6.78017e34 q^{54} +1.31362e36 q^{55} +6.92958e35 q^{56} -5.76258e35 q^{57} +2.37253e35 q^{58} -1.00765e35 q^{59} +4.01878e35 q^{60} +1.56573e36 q^{61} -3.71950e36 q^{62} +2.86289e36 q^{63} +8.37609e36 q^{64} +7.26079e36 q^{65} -2.28280e37 q^{66} -5.00920e36 q^{67} -7.83480e36 q^{68} +3.65446e37 q^{69} -1.20868e38 q^{70} -7.95732e37 q^{71} +3.57769e37 q^{72} -1.56377e38 q^{73} +8.59038e37 q^{74} +2.00532e38 q^{75} -5.93568e37 q^{76} +9.63902e38 q^{77} -1.26178e38 q^{78} +1.20235e39 q^{79} -1.76391e39 q^{80} +1.47809e38 q^{81} +1.48383e39 q^{82} +2.45813e39 q^{83} +2.94889e38 q^{84} -7.00068e39 q^{85} -7.15060e39 q^{86} -5.17216e38 q^{87} +1.20457e40 q^{88} -1.06301e40 q^{89} -6.24030e39 q^{90} +5.32780e39 q^{91} +3.76423e39 q^{92} +8.10858e39 q^{93} +1.63927e40 q^{94} -5.30374e40 q^{95} +8.08967e39 q^{96} +2.08674e40 q^{97} -1.74071e40 q^{98} +4.97655e40 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.59943e6	−1.07857	−0.539287	−	0.842122i	$-0.681306\pi$
$2$	−1.59943e6	−1.07857	−0.539287	+	0.842122i	$0.681306\pi$
$3$	3.48678e9	0.577350
$3$	3.48678e9	0.577350
$4$	3.59152e11	0.163323
$5$	3.20915e14	1.50489	0.752446	−	0.658654i	$-0.228874\pi$
$5$	3.20915e14	1.50489	0.752446	+	0.658654i	$0.228874\pi$
$6$	−5.57687e15	−0.622715
$7$	2.35480e17	1.11544	0.557718	−	0.830030i	$-0.311677\pi$
$7$	2.35480e17	1.11544	0.557718	+	0.830030i	$0.311677\pi$
$8$	2.94274e18	0.902418
$9$	1.21577e19	0.333333
$10$	−5.13282e20	−1.62314
$11$	4.09335e21	1.83455	0.917273	−	0.398260i	$-0.130386\pi$
$11$	4.09335e21	1.83455	0.917273	+	0.398260i	$0.130386\pi$
$12$	1.25229e21	0.0942948
$13$	2.26252e22	0.330183	0.165091	−	0.986278i	$-0.447208\pi$
$13$	2.26252e22	0.330183	0.165091	+	0.986278i	$0.447208\pi$
$14$	−3.76634e23	−1.20308
$15$	1.11896e24	0.868850
$16$	−5.49650e24	−1.13665
$17$	−2.18147e25	−1.30181	−0.650904	−	0.759160i	$-0.725610\pi$
$17$	−2.18147e25	−1.30181	−0.650904	+	0.759160i	$0.725610\pi$
$18$	−1.94453e25	−0.359525
$19$	−1.65269e26	−1.00866	−0.504328	−	0.863512i	$-0.668260\pi$
$19$	−1.65269e26	−1.00866	−0.504328	+	0.863512i	$0.668260\pi$
$20$	1.15257e26	0.245784
$21$	8.21069e26	0.643997
$22$	−6.54702e27	−1.97869
$23$	1.04809e28	1.27344	0.636718	−	0.771097i	$-0.280292\pi$
$23$	1.04809e28	1.27344	0.636718	+	0.771097i	$0.280292\pi$
$24$	1.02607e28	0.521011
$25$	5.75119e28	1.26470
$26$	−3.61875e28	−0.356127
$27$	4.23912e28	0.192450
$28$	8.45732e28	0.182177
$29$	−1.48336e29	−0.155628	−0.0778140	−	0.996968i	$-0.524794\pi$
$29$	−1.48336e29	−0.155628	−0.0778140	+	0.996968i	$0.524794\pi$
$30$	−1.78970e30	−0.937120
$31$	2.32552e30	0.621734	0.310867	−	0.950453i	$-0.399381\pi$
$31$	2.32552e30	0.621734	0.310867	+	0.950453i	$0.399381\pi$
$32$	2.32010e30	0.323542
$33$	1.42726e31	1.05918
$34$	3.48911e31	1.40410
$35$	7.55692e31	1.67861
$36$	4.36645e30	0.0544411
$37$	−5.37090e31	−0.381867	−0.190933	−	0.981603i	$-0.561151\pi$
$37$	−5.37090e31	−0.381867	−0.190933	+	0.981603i	$0.561151\pi$
$38$	2.64337e32	1.08791
$39$	7.88894e31	0.190631
$40$	9.44372e32	1.35804
$41$	−9.27726e32	−0.804176	−0.402088	−	0.915601i	$-0.631715\pi$
$41$	−9.27726e32	−0.804176	−0.402088	+	0.915601i	$0.631715\pi$
$42$	−1.31324e33	−0.694599
$43$	4.47072e33	1.45973	0.729867	−	0.683589i	$-0.239582\pi$
$43$	4.47072e33	1.45973	0.729867	+	0.683589i	$0.239582\pi$
$44$	1.47013e33	0.299624
$45$	3.90158e33	0.501631
$46$	−1.67634e34	−1.37350
$47$	−1.02491e34	−0.540355	−0.270177	−	0.962811i	$-0.587082\pi$
$47$	−1.02491e34	−0.540355	−0.270177	+	0.962811i	$0.587082\pi$
$48$	−1.91651e34	−0.656245
$49$	1.08833e34	0.244198
$50$	−9.19863e34	−1.36407
$51$	−7.60632e34	−0.751599
$52$	8.12590e33	0.0539266
$53$	−2.32449e35	−1.04393	−0.521966	−	0.852966i	$-0.674801\pi$
$53$	−2.32449e35	−1.04393	−0.521966	+	0.852966i	$0.674801\pi$
$54$	−6.78017e34	−0.207572
$55$	1.31362e36	2.76079
$56$	6.92958e35	1.00659
$57$	−5.76258e35	−0.582348
$58$	2.37253e35	0.167856
$59$	−1.00765e35	−0.0502159	−0.0251080	−	0.999685i	$-0.507993\pi$
$59$	−1.00765e35	−0.0502159	−0.0251080	+	0.999685i	$0.507993\pi$
$60$	4.01878e35	0.141904
$61$	1.56573e36	0.393964	0.196982	−	0.980407i	$-0.436886\pi$
$61$	1.56573e36	0.393964	0.196982	+	0.980407i	$0.436886\pi$
$62$	−3.71950e36	−0.670587
$63$	2.86289e36	0.371812
$64$	8.37609e36	0.787684
$65$	7.26079e36	0.496890
$66$	−2.28280e37	−1.14240
$67$	−5.00920e36	−0.184177	−0.0920883	−	0.995751i	$-0.529354\pi$
$67$	−5.00920e36	−0.184177	−0.0920883	+	0.995751i	$0.529354\pi$
$68$	−7.83480e36	−0.212616
$69$	3.65446e37	0.735218
$70$	−1.20868e38	−1.81051
$71$	−7.95732e37	−0.891191	−0.445596	−	0.895234i	$-0.647008\pi$
$71$	−7.95732e37	−0.891191	−0.445596	+	0.895234i	$0.647008\pi$
$72$	3.57769e37	0.300806
$73$	−1.56377e38	−0.990955	−0.495477	−	0.868621i	$-0.665007\pi$
$73$	−1.56377e38	−0.990955	−0.495477	+	0.868621i	$0.665007\pi$
$74$	8.59038e37	0.411872
$75$	2.00532e38	0.730175
$76$	−5.93568e37	−0.164737
$77$	9.63902e38	2.04632
$78$	−1.26178e38	−0.205610
$79$	1.20235e39	1.50895	0.754475	−	0.656329i	$-0.227892\pi$
$79$	1.20235e39	1.50895	0.754475	+	0.656329i	$0.227892\pi$
$80$	−1.76391e39	−1.71053
$81$	1.47809e38	0.111111
$82$	1.48383e39	0.867363
$83$	2.45813e39	1.12074	0.560369	−	0.828243i	$-0.310659\pi$
$83$	2.45813e39	1.12074	0.560369	+	0.828243i	$0.310659\pi$
$84$	2.94889e38	0.105180
$85$	−7.00068e39	−1.95908
$86$	−7.15060e39	−1.57443
$87$	−5.17216e38	−0.0898519
$88$	1.20457e40	1.65553
$89$	−1.06301e40	−1.15889	−0.579443	−	0.815012i	$-0.696730\pi$
$89$	−1.06301e40	−1.15889	−0.579443	+	0.815012i	$0.696730\pi$
$90$	−6.24030e39	−0.541046
$91$	5.32780e39	0.368298
$92$	3.76423e39	0.207982
$93$	8.10858e39	0.358958
$94$	1.63927e40	0.582813
$95$	−5.30374e40	−1.51792
$96$	8.08967e39	0.186797
$97$	2.08674e40	0.389626	0.194813	−	0.980840i	$-0.437590\pi$
$97$	2.08674e40	0.389626	0.194813	+	0.980840i	$0.437590\pi$
$98$	−1.74071e40	−0.263386
$99$	4.97655e40	0.611515
$100$	2.06555e40	0.206555
$101$	1.04865e41	0.855146	0.427573	−	0.903981i	$-0.359369\pi$
$101$	1.04865e41	0.855146	0.427573	+	0.903981i	$0.359369\pi$
$102$	1.21658e41	0.810656
$103$	−2.03937e41	−1.11258	−0.556292	−	0.830987i	$-0.687777\pi$
$103$	−2.03937e41	−1.11258	−0.556292	+	0.830987i	$0.687777\pi$
$104$	6.65803e40	0.297963
$105$	2.63494e41	0.969147
$106$	3.71786e41	1.12596
$107$	−7.60455e41	−1.89979	−0.949896	−	0.312567i	$-0.898811\pi$
$107$	−7.60455e41	−1.89979	−0.949896	+	0.312567i	$0.898811\pi$
$108$	1.52249e40	0.0314316
$109$	1.97252e41	0.337115	0.168557	−	0.985692i	$-0.446089\pi$
$109$	1.97252e41	0.337115	0.168557	+	0.985692i	$0.446089\pi$
$110$	−2.10104e42	−2.97772
$111$	−1.87272e41	−0.220471
$112$	−1.29432e42	−1.26786
$113$	7.19758e41	0.587595	0.293798	−	0.955868i	$-0.405081\pi$
$113$	7.19758e41	0.587595	0.293798	+	0.955868i	$0.405081\pi$
$114$	9.21685e41	0.628106
$115$	3.36347e42	1.91638
$116$	−5.32752e40	−0.0254177
$117$	2.75070e41	0.110061
$118$	1.61166e41	0.0541617
$119$	−5.13694e42	−1.45208
$120$	3.29282e42	0.784066
$121$	1.17770e43	2.36556
$122$	−2.50428e42	−0.424919
$123$	−3.23478e42	−0.464291
$124$	8.35214e41	0.101544
$125$	3.86292e42	0.398346
$126$	−4.57899e42	−0.401027
$127$	−7.84129e42	−0.583998	−0.291999	−	0.956419i	$-0.594320\pi$
$127$	−7.84129e42	−0.583998	−0.291999	+	0.956419i	$0.594320\pi$
$128$	−1.84989e43	−1.17312
$129$	1.55884e43	0.842778
$130$	−1.16131e43	−0.535933
$131$	1.88589e43	0.743799	0.371899	−	0.928273i	$-0.378707\pi$
$131$	1.88589e43	0.743799	0.371899	+	0.928273i	$0.378707\pi$
$132$	5.12604e42	0.172988
$133$	−3.89177e43	−1.12509
$134$	8.01186e42	0.198648
$135$	1.36040e43	0.289617
$136$	−6.41952e43	−1.17477
$137$	4.38524e43	0.690592	0.345296	−	0.938494i	$-0.387779\pi$
$137$	4.38524e43	0.690592	0.345296	+	0.938494i	$0.387779\pi$
$138$	−5.84504e43	−0.792988
$139$	2.01750e43	0.236054	0.118027	−	0.993010i	$-0.462343\pi$
$139$	2.01750e43	0.236054	0.118027	+	0.993010i	$0.462343\pi$
$140$	2.71408e43	0.274157
$141$	−3.57363e43	−0.311974
$142$	1.27272e44	0.961216
$143$	9.26130e43	0.605736
$144$	−6.68246e43	−0.378883
$145$	−4.76033e43	−0.234203
$146$	2.50114e44	1.06882
$147$	3.79479e43	0.140988
$148$	−1.92897e43	−0.0623677
$149$	3.54704e44	0.998958	0.499479	−	0.866326i	$-0.333525\pi$
$149$	3.54704e44	0.998958	0.499479	+	0.866326i	$0.333525\pi$
$150$	−3.20736e44	−0.787549
$151$	7.36078e44	1.57724	0.788618	−	0.614884i	$-0.210797\pi$
$151$	7.36078e44	1.57724	0.788618	+	0.614884i	$0.210797\pi$
$152$	−4.86345e44	−0.910230
$153$	−2.65216e44	−0.433936
$154$	−1.54169e45	−2.20711
$155$	7.46294e44	0.935643
$156$	2.83333e43	0.0311345
$157$	−1.20760e45	−1.16407	−0.582036	−	0.813163i	$-0.697744\pi$
$157$	−1.20760e45	−1.16407	−0.582036	+	0.813163i	$0.697744\pi$
$158$	−1.92307e45	−1.62752
$159$	−8.10499e44	−0.602714
$160$	7.44554e44	0.486897
$161$	2.46804e45	1.42044
$162$	−2.36410e44	−0.119842
$163$	3.84692e45	1.71897	0.859484	−	0.511163i	$-0.170785\pi$
$163$	3.84692e45	1.71897	0.859484	+	0.511163i	$0.170785\pi$
$164$	−3.33195e44	−0.131341
$165$	4.58030e45	1.59394
$166$	−3.93160e45	−1.20880
$167$	−1.57930e45	−0.429316	−0.214658	−	0.976689i	$-0.568864\pi$
$167$	−1.57930e45	−0.429316	−0.214658	+	0.976689i	$0.568864\pi$
$168$	2.41620e45	0.581155
$169$	−4.18355e45	−0.890979
$170$	1.11971e46	2.11301
$171$	−2.00929e45	−0.336219
$172$	1.60567e45	0.238409
$173$	−1.39579e46	−1.84024	−0.920122	−	0.391631i	$-0.871911\pi$
$173$	−1.39579e46	−1.84024	−0.920122	+	0.391631i	$0.871911\pi$
$174$	8.27250e44	0.0969120
$175$	1.35429e46	1.41069
$176$	−2.24991e46	−2.08523
$177$	−3.51344e44	−0.0289922
$178$	1.70021e46	1.24995
$179$	−4.81309e45	−0.315454	−0.157727	−	0.987483i	$-0.550417\pi$
$179$	−4.81309e45	−0.315454	−0.157727	+	0.987483i	$0.550417\pi$
$180$	1.40126e45	0.0819280
$181$	−1.02164e46	−0.533199	−0.266599	−	0.963807i	$-0.585900\pi$
$181$	−1.02164e46	−0.533199	−0.266599	+	0.963807i	$0.585900\pi$
$182$	−8.52144e45	−0.397237
$183$	5.45938e45	0.227455
$184$	3.08425e46	1.14917
$185$	−1.72360e46	−0.574668
$186$	−1.29691e46	−0.387164
$187$	−8.92952e46	−2.38822
$188$	−3.68098e45	−0.0882525
$189$	9.98228e45	0.214666
$190$	8.48297e46	1.63719
$191$	3.42603e46	0.593755	0.296878	−	0.954916i	$-0.404055\pi$
$191$	3.42603e46	0.593755	0.296878	+	0.954916i	$0.404055\pi$
$192$	2.92056e46	0.454770
$193$	1.60284e46	0.224370	0.112185	−	0.993687i	$-0.464215\pi$
$193$	1.60284e46	0.224370	0.112185	+	0.993687i	$0.464215\pi$
$194$	−3.33759e46	−0.420241
$195$	2.53168e46	0.286879
$196$	3.90877e45	0.0398833
$197$	1.67914e47	1.54358	0.771792	−	0.635875i	$-0.219361\pi$
$197$	1.67914e47	1.54358	0.771792	+	0.635875i	$0.219361\pi$
$198$	−7.95965e46	−0.659565
$199$	−5.27435e46	−0.394168	−0.197084	−	0.980387i	$-0.563147\pi$
$199$	−5.27435e46	−0.394168	−0.197084	+	0.980387i	$0.563147\pi$
$200$	1.69243e47	1.14129
$201$	−1.74660e46	−0.106334
$202$	−1.67723e47	−0.922339
$203$	−3.49302e46	−0.173593
$204$	−2.73183e46	−0.122754
$205$	−2.97722e47	−1.21020
$206$	3.26183e47	1.20001
$207$	1.27423e47	0.424478
$208$	−1.24360e47	−0.375302
$209$	−6.76504e47	−1.85043
$210$	−4.21440e47	−1.04530
$211$	−4.70265e47	−1.05816	−0.529081	−	0.848571i	$-0.677463\pi$
$211$	−4.70265e47	−1.05816	−0.529081	+	0.848571i	$0.677463\pi$
$212$	−8.34844e46	−0.170498
$213$	−2.77455e47	−0.514530
$214$	1.21629e48	2.04907
$215$	1.43472e48	2.19674
$216$	1.24746e47	0.173670
$217$	5.47614e47	0.693505
$218$	−3.15490e47	−0.363603
$219$	−5.45252e47	−0.572128
$220$	4.71788e47	0.450902
$221$	−4.93564e47	−0.429835
$222$	2.99528e47	0.237794
$223$	6.26777e47	0.453799	0.226899	−	0.973918i	$-0.427141\pi$
$223$	6.26777e47	0.453799	0.226899	+	0.973918i	$0.427141\pi$
$224$	5.46337e47	0.360891
$225$	6.99211e47	0.421567
$226$	−1.15120e48	−0.633766
$227$	1.14299e48	0.574794	0.287397	−	0.957812i	$-0.407210\pi$
$227$	1.14299e48	0.574794	0.287397	+	0.957812i	$0.407210\pi$
$228$	−2.06964e47	−0.0951110
$229$	−2.06328e48	−0.866825	−0.433413	−	0.901196i	$-0.642691\pi$
$229$	−2.06328e48	−0.866825	−0.433413	+	0.901196i	$0.642691\pi$
$230$	−5.37964e48	−2.06696
$231$	3.36092e48	1.18144
$232$	−4.36515e47	−0.140442
$233$	−7.30911e47	−0.215312	−0.107656	−	0.994188i	$-0.534335\pi$
$233$	−7.30911e47	−0.215312	−0.107656	+	0.994188i	$0.534335\pi$
$234$	−4.39955e47	−0.118709
$235$	−3.28909e48	−0.813175
$236$	−3.61898e46	−0.00820144
$237$	4.19233e48	0.871193
$238$	8.21617e48	1.56618
$239$	3.57354e48	0.625089	0.312545	−	0.949903i	$-0.398819\pi$
$239$	3.57354e48	0.625089	0.312545	+	0.949903i	$0.398819\pi$
$240$	−6.15037e48	−0.987577
$241$	2.64837e47	0.0390507	0.0195254	−	0.999809i	$-0.493784\pi$
$241$	2.64837e47	0.0390507	0.0195254	+	0.999809i	$0.493784\pi$
$242$	−1.88364e49	−2.55143
$243$	5.15378e47	0.0641500
$244$	5.62336e47	0.0643435
$245$	3.49263e48	0.367492
$246$	5.17381e48	0.500773
$247$	−3.73926e48	−0.333041
$248$	6.84340e48	0.561064
$249$	8.57097e48	0.647058
$250$	−6.17847e48	−0.429646
$251$	1.94890e48	0.124876	0.0624380	−	0.998049i	$-0.480112\pi$
$251$	1.94890e48	0.124876	0.0624380	+	0.998049i	$0.480112\pi$
$252$	1.02821e48	0.0607256
$253$	4.29018e49	2.33617
$254$	1.25416e49	0.629886
$255$	−2.44099e49	−1.13108
$256$	1.11685e49	0.477612
$257$	9.44017e48	0.372692	0.186346	−	0.982484i	$-0.440335\pi$
$257$	9.44017e48	0.372692	0.186346	+	0.982484i	$0.440335\pi$
$258$	−2.49326e49	−0.908999
$259$	−1.26474e49	−0.425948
$260$	2.60773e48	0.0811537
$261$	−1.80342e48	−0.0518760
$262$	−3.01635e49	−0.802243
$263$	−5.72032e49	−1.40711	−0.703554	−	0.710641i	$-0.748405\pi$
$263$	−5.72032e49	−1.40711	−0.703554	+	0.710641i	$0.748405\pi$
$264$	4.20007e49	0.955819
$265$	−7.45964e49	−1.57100
$266$	6.22461e49	1.21350
$267$	−3.70648e49	−0.669084
$268$	−1.79906e48	−0.0300804
$269$	−2.68077e49	−0.415278	−0.207639	−	0.978206i	$-0.566578\pi$
$269$	−2.68077e49	−0.415278	−0.207639	+	0.978206i	$0.566578\pi$
$270$	−2.17586e49	−0.312373
$271$	−8.22411e49	−1.09451	−0.547253	−	0.836967i	$-0.684327\pi$
$271$	−8.22411e49	−1.09451	−0.547253	+	0.836967i	$0.684327\pi$
$272$	1.19905e50	1.47970
$273$	1.85769e49	0.212637
$274$	−7.01388e49	−0.744855
$275$	2.35416e50	2.32015
$276$	1.31250e49	0.120078
$277$	2.17515e49	0.184780	0.0923898	−	0.995723i	$-0.470549\pi$
$277$	2.17515e49	0.184780	0.0923898	+	0.995723i	$0.470549\pi$
$278$	−3.22685e49	−0.254601
$279$	2.82729e49	0.207245
$280$	2.22381e50	1.51481
$281$	−1.76875e50	−1.11992	−0.559961	−	0.828519i	$-0.689184\pi$
$281$	−1.76875e50	−1.11992	−0.559961	+	0.828519i	$0.689184\pi$
$282$	5.71578e49	0.336487
$283$	1.98156e50	1.08489	0.542444	−	0.840092i	$-0.317499\pi$
$283$	1.98156e50	1.08489	0.542444	+	0.840092i	$0.317499\pi$
$284$	−2.85789e49	−0.145552
$285$	−1.84930e50	−0.876371
$286$	−1.48128e50	−0.653331
$287$	−2.18461e50	−0.897007
$288$	2.82069e49	0.107847
$289$	1.95077e50	0.694703
$290$	7.61382e49	0.252606
$291$	7.27601e49	0.224951
$292$	−5.61630e49	−0.161846
$293$	−5.47637e50	−1.47132	−0.735659	−	0.677352i	$-0.763128\pi$
$293$	−5.47637e50	−1.47132	−0.735659	+	0.677352i	$0.763128\pi$
$294$	−6.06949e49	−0.152066
$295$	−3.23369e49	−0.0755696
$296$	−1.58052e50	−0.344603
$297$	1.73522e50	0.353058
$298$	−5.67323e50	−1.07745
$299$	2.37132e50	0.420467
$300$	7.20213e49	0.119255
$301$	1.05277e51	1.62824
$302$	−1.17731e51	−1.70117
$303$	3.65640e50	0.493719
$304$	9.08402e50	1.14649
$305$	5.02468e50	0.592873
$306$	4.24194e50	0.468032
$307$	−1.15018e51	−1.18694	−0.593468	−	0.804857i	$-0.702242\pi$
$307$	−1.15018e51	−1.18694	−0.593468	+	0.804857i	$0.702242\pi$
$308$	3.46187e50	0.334212
$309$	−7.11085e50	−0.642351
$310$	−1.19365e51	−1.00916
$311$	−9.25059e50	−0.732119	−0.366059	−	0.930592i	$-0.619293\pi$
$311$	−9.25059e50	−0.732119	−0.366059	+	0.930592i	$0.619293\pi$
$312$	2.32151e50	0.172029
$313$	1.36691e51	0.948597	0.474299	−	0.880364i	$-0.342702\pi$
$313$	1.36691e51	0.948597	0.474299	+	0.880364i	$0.342702\pi$
$314$	1.93147e51	1.25554
$315$	9.18746e50	0.559537
$316$	4.31826e50	0.246447
$317$	9.60481e49	0.0513776	0.0256888	−	0.999670i	$-0.491822\pi$
$317$	9.60481e49	0.0513776	0.0256888	+	0.999670i	$0.491822\pi$
$318$	1.29634e51	0.650072
$319$	−6.07191e50	−0.285507
$320$	2.68802e51	1.18538
$321$	−2.65154e51	−1.09685
$322$	−3.94746e51	−1.53205
$323$	3.60530e51	1.31308
$324$	5.30858e49	0.0181470
$325$	1.30122e51	0.417583
$326$	−6.15288e51	−1.85404
$327$	6.87774e50	0.194633
$328$	−2.73006e51	−0.725703
$329$	−2.41346e51	−0.602731
$330$	−7.32587e51	−1.71919
$331$	4.43023e51	0.977130	0.488565	−	0.872527i	$-0.337520\pi$
$331$	4.43023e51	0.977130	0.488565	+	0.872527i	$0.337520\pi$
$332$	8.82842e50	0.183043
$333$	−6.52976e50	−0.127289
$334$	2.52598e51	0.463050
$335$	−1.60753e51	−0.277166
$336$	−4.51300e51	−0.731999
$337$	−3.71004e50	−0.0566194	−0.0283097	−	0.999599i	$-0.509012\pi$
$337$	−3.71004e50	−0.0566194	−0.0283097	+	0.999599i	$0.509012\pi$
$338$	6.69129e51	0.960988
$339$	2.50964e51	0.339248
$340$	−2.51431e51	−0.319964
$341$	9.51915e51	1.14060
$342$	3.21372e51	0.362637
$343$	−7.93199e51	−0.843049
$344$	1.31562e52	1.31729
$345$	1.17277e52	1.10642
$346$	2.23247e52	1.98484
$347$	−2.30793e51	−0.193405	−0.0967025	−	0.995313i	$-0.530830\pi$
$347$	−2.30793e51	−0.193405	−0.0967025	+	0.995313i	$0.530830\pi$
$348$	−1.85759e50	−0.0146749
$349$	−1.85442e52	−1.38129	−0.690647	−	0.723192i	$-0.742674\pi$
$349$	−1.85442e52	−1.38129	−0.690647	+	0.723192i	$0.742674\pi$
$350$	−2.16610e52	−1.52154
$351$	9.59110e50	0.0635437
$352$	9.49695e51	0.593553
$353$	−5.30734e51	−0.312965	−0.156482	−	0.987681i	$-0.550015\pi$
$353$	−5.30734e51	−0.312965	−0.156482	+	0.987681i	$0.550015\pi$
$354$	5.61951e50	0.0312702
$355$	−2.55363e52	−1.34115
$356$	−3.81781e51	−0.189273
$357$	−1.79114e52	−0.838361
$358$	7.69820e51	0.340241
$359$	−6.85308e51	−0.286055	−0.143028	−	0.989719i	$-0.545684\pi$
$359$	−6.85308e51	−0.286055	−0.143028	+	0.989719i	$0.545684\pi$
$360$	1.14814e52	0.452681
$361$	4.66809e50	0.0173877
$362$	1.63405e52	0.575095
$363$	4.10637e52	1.36575
$364$	1.91349e51	0.0601517
$365$	−5.01837e52	−1.49128
$366$	−8.73189e51	−0.245327
$367$	3.14343e51	0.0835120	0.0417560	−	0.999128i	$-0.486705\pi$
$367$	3.14343e51	0.0835120	0.0417560	+	0.999128i	$0.486705\pi$
$368$	−5.76081e52	−1.44745
$369$	−1.12790e52	−0.268059
$370$	2.75678e52	0.619822
$371$	−5.47371e52	−1.16444
$372$	2.91221e51	0.0586263
$373$	9.77187e52	1.86186	0.930929	−	0.365199i	$-0.118999\pi$
$373$	9.77187e52	1.86186	0.930929	+	0.365199i	$0.118999\pi$
$374$	1.42821e53	2.57588
$375$	1.34692e52	0.229985
$376$	−3.01604e52	−0.487626
$377$	−3.35614e51	−0.0513857
$378$	−1.59660e52	−0.231533
$379$	−6.70476e52	−0.921042	−0.460521	−	0.887649i	$-0.652337\pi$
$379$	−6.70476e52	−0.921042	−0.460521	+	0.887649i	$0.652337\pi$
$380$	−1.90485e52	−0.247912
$381$	−2.73409e52	−0.337171
$382$	−5.47970e52	−0.640410
$383$	2.82438e52	0.312859	0.156429	−	0.987689i	$-0.450002\pi$
$383$	2.82438e52	0.312859	0.156429	+	0.987689i	$0.450002\pi$
$384$	−6.45017e52	−0.677300
$385$	3.09331e53	3.07949
$386$	−2.56363e52	−0.242000
$387$	5.43535e52	0.486578
$388$	7.49457e51	0.0636350
$389$	−1.90072e52	−0.153091	−0.0765457	−	0.997066i	$-0.524389\pi$
$389$	−1.90072e52	−0.153091	−0.0765457	+	0.997066i	$0.524389\pi$
$390$	−4.04925e52	−0.309421
$391$	−2.28637e53	−1.65777
$392$	3.20269e52	0.220369
$393$	6.57570e52	0.429433
$394$	−2.68567e53	−1.66487
$395$	3.85852e53	2.27081
$396$	1.78734e52	0.0998747
$397$	−1.59987e53	−0.848947	−0.424474	−	0.905440i	$-0.639541\pi$
$397$	−1.59987e53	−0.848947	−0.424474	+	0.905440i	$0.639541\pi$
$398$	8.43596e52	0.425139
$399$	−1.35697e53	−0.649572
$400$	−3.16114e53	−1.43752
$401$	−2.13645e53	−0.923067	−0.461534	−	0.887123i	$-0.652701\pi$
$401$	−2.13645e53	−0.923067	−0.461534	+	0.887123i	$0.652701\pi$
$402$	2.79356e52	0.114690
$403$	5.26154e52	0.205286
$404$	3.76623e52	0.139665
$405$	4.74341e52	0.167210
$406$	5.58684e52	0.187233
$407$	−2.19849e53	−0.700551
$408$	−2.23835e53	−0.678257
$409$	2.66798e53	0.768872	0.384436	−	0.923152i	$-0.374396\pi$
$409$	2.66798e53	0.768872	0.384436	+	0.923152i	$0.374396\pi$
$410$	4.76185e53	1.30529
$411$	1.52904e53	0.398713
$412$	−7.32444e52	−0.181711
$413$	−2.37281e52	−0.0560127
$414$	−2.03804e53	−0.457832
$415$	7.88851e53	1.68659
$416$	5.24927e52	0.106828
$417$	7.03459e52	0.136286
$418$	1.08202e54	1.99582
$419$	−4.29684e53	−0.754678	−0.377339	−	0.926075i	$-0.623161\pi$
$419$	−4.29684e53	−0.754678	−0.377339	+	0.926075i	$0.623161\pi$
$420$	9.46343e52	0.158284
$421$	−2.09315e53	−0.333439	−0.166720	−	0.986004i	$-0.553317\pi$
$421$	−2.09315e53	−0.333439	−0.166720	+	0.986004i	$0.553317\pi$
$422$	7.52156e53	1.14131
$423$	−1.24605e53	−0.180118
$424$	−6.84038e53	−0.942063
$425$	−1.25461e54	−1.64640
$426$	4.43769e53	0.554959
$427$	3.68700e53	0.439442
$428$	−2.73119e53	−0.310280
$429$	3.22921e53	0.349722
$430$	−2.29474e54	−2.36935
$431$	−1.17896e54	−1.16069	−0.580343	−	0.814372i	$-0.697081\pi$
$431$	−1.17896e54	−1.16069	−0.580343	+	0.814372i	$0.697081\pi$
$432$	−2.33003e53	−0.218748
$433$	9.09513e53	0.814342	0.407171	−	0.913352i	$-0.366515\pi$
$433$	9.09513e53	0.814342	0.407171	+	0.913352i	$0.366515\pi$
$434$	−8.75869e53	−0.747997
$435$	−1.65983e53	−0.135217
$436$	7.08433e52	0.0550587
$437$	−1.73217e54	−1.28446
$438$	8.72093e53	0.617083
$439$	2.37938e54	1.60673	0.803363	−	0.595490i	$-0.203042\pi$
$439$	2.37938e54	1.60673	0.803363	+	0.595490i	$0.203042\pi$
$440$	3.86564e54	2.49139
$441$	1.32316e53	0.0813994
$442$	7.89420e53	0.463609
$443$	−2.17243e54	−1.21806	−0.609030	−	0.793147i	$-0.708441\pi$
$443$	−2.17243e54	−1.21806	−0.609030	+	0.793147i	$0.708441\pi$
$444$	−6.72590e52	−0.0360080
$445$	−3.41135e54	−1.74400
$446$	−1.00249e54	−0.489456
$447$	1.23677e54	0.576748
$448$	1.97241e54	0.878612
$449$	4.64070e54	1.97485	0.987423	−	0.158100i	$-0.0505370\pi$
$449$	4.64070e54	1.97485	0.987423	+	0.158100i	$0.0505370\pi$
$450$	−1.11834e54	−0.454691
$451$	−3.79751e54	−1.47530
$452$	2.58502e53	0.0959681
$453$	2.56655e54	0.910617
$454$	−1.82813e54	−0.619959
$455$	1.70977e54	0.554249
$456$	−1.69578e54	−0.525521
$457$	2.01271e54	0.596346	0.298173	−	0.954512i	$-0.403623\pi$
$457$	2.01271e54	0.596346	0.298173	+	0.954512i	$0.403623\pi$
$458$	3.30008e54	0.934936
$459$	−9.24751e53	−0.250533
$460$	1.20800e54	0.312990
$461$	−4.15737e54	−1.03027	−0.515133	−	0.857110i	$-0.672258\pi$
$461$	−4.15737e54	−1.03027	−0.515133	+	0.857110i	$0.672258\pi$
$462$	−5.37555e54	−1.27427
$463$	5.22768e54	1.18549	0.592746	−	0.805390i	$-0.298044\pi$
$463$	5.22768e54	1.18549	0.592746	+	0.805390i	$0.298044\pi$
$464$	8.15329e53	0.176894
$465$	2.60217e54	0.540194
$466$	1.16904e54	0.232230
$467$	−9.76914e54	−1.85721	−0.928604	−	0.371073i	$-0.878990\pi$
$467$	−9.76914e54	−1.85721	−0.928604	+	0.371073i	$0.878990\pi$
$468$	9.87920e52	0.0179755
$469$	−1.17957e54	−0.205437
$470$	5.26066e54	0.877070
$471$	−4.21064e54	−0.672077
$472$	−2.96524e53	−0.0453158
$473$	1.83002e55	2.67795
$474$	−6.70533e54	−0.939646
$475$	−9.50495e54	−1.27565
$476$	−1.84494e54	−0.237159
$477$	−2.82603e54	−0.347977
$478$	−5.71563e54	−0.674205
$479$	−1.65944e55	−1.87536	−0.937678	−	0.347505i	$-0.887029\pi$
$479$	−1.65944e55	−1.87536	−0.937678	+	0.347505i	$0.887029\pi$
$480$	2.59610e54	0.281110
$481$	−1.21518e54	−0.126086
$482$	−4.23588e53	−0.0421191
$483$	8.60552e54	0.820089
$484$	4.22972e54	0.386351
$485$	6.69667e54	0.586345
$486$	−8.24310e53	−0.0691906
$487$	4.75101e54	0.382333	0.191167	−	0.981558i	$-0.438773\pi$
$487$	4.75101e54	0.382333	0.191167	+	0.981558i	$0.438773\pi$
$488$	4.60756e54	0.355520
$489$	1.34134e55	0.992447
$490$	−5.58622e54	−0.396368
$491$	1.29983e55	0.884538	0.442269	−	0.896883i	$-0.354174\pi$
$491$	1.29983e55	0.884538	0.442269	+	0.896883i	$0.354174\pi$
$492$	−1.16178e54	−0.0758296
$493$	3.23591e54	0.202598
$494$	5.98068e54	0.359210
$495$	1.59705e55	0.920264
$496$	−1.27822e55	−0.706694
$497$	−1.87379e55	−0.994067
$498$	−1.37087e55	−0.697900
$499$	3.12552e55	1.52708	0.763539	−	0.645762i	$-0.223460\pi$
$499$	3.12552e55	1.52708	0.763539	+	0.645762i	$0.223460\pi$
$500$	1.38737e54	0.0650592
$501$	−5.50669e54	−0.247866
$502$	−3.11713e54	−0.134688
$503$	1.38978e55	0.576504	0.288252	−	0.957555i	$-0.406926\pi$
$503$	1.38978e55	0.576504	0.288252	+	0.957555i	$0.406926\pi$
$504$	8.42476e54	0.335530
$505$	3.36526e55	1.28690
$506$	−6.86185e55	−2.51974
$507$	−1.45871e55	−0.514407
$508$	−2.81622e54	−0.0953806
$509$	−4.24927e55	−1.38229	−0.691146	−	0.722715i	$-0.742894\pi$
$509$	−4.24927e55	−1.38229	−0.691146	+	0.722715i	$0.742894\pi$
$510$	3.90419e55	1.21995
$511$	−3.68237e55	−1.10535
$512$	2.28163e55	0.657978
$513$	−7.00595e54	−0.194116
$514$	−1.50989e55	−0.401977
$515$	−6.54465e55	−1.67432
$516$	5.59861e54	0.137645
$517$	−4.19530e55	−0.991305
$518$	2.02286e55	0.459417
$519$	−4.86683e55	−1.06247
$520$	2.13666e55	0.448402
$521$	7.63345e55	1.54009	0.770047	−	0.637987i	$-0.220233\pi$
$521$	7.63345e55	1.54009	0.770047	+	0.637987i	$0.220233\pi$
$522$	2.88444e54	0.0559521
$523$	8.49813e55	1.58504	0.792518	−	0.609849i	$-0.208770\pi$
$523$	8.49813e55	1.58504	0.792518	+	0.609849i	$0.208770\pi$
$524$	6.77322e54	0.121480
$525$	4.72213e55	0.814464
$526$	9.14925e55	1.51767
$527$	−5.07305e55	−0.809379
$528$	−7.84494e55	−1.20391
$529$	4.21094e55	0.621638
$530$	1.19312e56	1.69445
$531$	−1.22506e54	−0.0167386
$532$	−1.39774e55	−0.183754
$533$	−2.09900e55	−0.265525
$534$	5.92825e55	0.721657
$535$	−2.44042e56	−2.85898
$536$	−1.47408e55	−0.166204
$537$	−1.67822e55	−0.182128
$538$	4.28771e55	0.447908
$539$	4.45493e55	0.447993
$540$	4.88589e54	0.0473012
$541$	8.87529e54	0.0827254	0.0413627	−	0.999144i	$-0.486830\pi$
$541$	8.87529e54	0.0827254	0.0413627	+	0.999144i	$0.486830\pi$
$542$	1.31539e56	1.18051
$543$	−3.56226e55	−0.307842
$544$	−5.06122e55	−0.421190
$545$	6.33011e55	0.507321
$546$	−2.97124e55	−0.229345
$547$	−1.64997e56	−1.22669	−0.613345	−	0.789815i	$-0.710177\pi$
$547$	−1.64997e56	−1.22669	−0.613345	+	0.789815i	$0.710177\pi$
$548$	1.57497e55	0.112790
$549$	1.90357e55	0.131321
$550$	−3.76532e56	−2.50246
$551$	2.45154e55	0.156975
$552$	1.07541e56	0.663474
$553$	2.83129e56	1.68314
$554$	−3.47900e55	−0.199299
$555$	−6.00984e55	−0.331785
$556$	7.24590e54	0.0385531
$557$	2.56239e56	1.31405	0.657027	−	0.753867i	$-0.271814\pi$
$557$	2.56239e56	1.31405	0.657027	+	0.753867i	$0.271814\pi$
$558$	−4.52205e55	−0.223529
$559$	1.01151e56	0.481979
$560$	−4.15366e56	−1.90799
$561$	−3.11353e56	−1.37884
$562$	2.82900e56	1.20792
$563$	−1.39228e55	−0.0573196	−0.0286598	−	0.999589i	$-0.509124\pi$
$563$	−1.39228e55	−0.0573196	−0.0286598	+	0.999589i	$0.509124\pi$
$564$	−1.28348e55	−0.0509526
$565$	2.30981e56	0.884268
$566$	−3.16936e56	−1.17013
$567$	3.48061e55	0.123937
$568$	−2.34164e56	−0.804227
$569$	−2.49708e56	−0.827239	−0.413620	−	0.910450i	$-0.635736\pi$
$569$	−2.49708e56	−0.827239	−0.413620	+	0.910450i	$0.635736\pi$
$570$	2.95783e56	0.945232
$571$	−1.43957e56	−0.443805	−0.221902	−	0.975069i	$-0.571227\pi$
$571$	−1.43957e56	−0.443805	−0.221902	+	0.975069i	$0.571227\pi$
$572$	3.32621e55	0.0989308
$573$	1.19458e56	0.342805
$574$	3.49414e56	0.967489
$575$	6.02775e56	1.61051
$576$	1.01834e56	0.262561
$577$	7.48240e56	1.86181	0.930907	−	0.365255i	$-0.119018\pi$
$577$	7.48240e56	1.86181	0.930907	+	0.365255i	$0.119018\pi$
$578$	−3.12011e56	−0.749289
$579$	5.58876e55	0.129540
$580$	−1.70968e55	−0.0382509
$581$	5.78841e56	1.25011
$582$	−1.16375e56	−0.242626
$583$	−9.51493e56	−1.91514
$584$	−4.60177e56	−0.894255
$585$	8.82742e55	0.165630
$586$	8.75907e56	1.58693
$587$	−5.43255e56	−0.950435	−0.475217	−	0.879868i	$-0.657631\pi$
$587$	−5.43255e56	−0.950435	−0.475217	+	0.879868i	$0.657631\pi$
$588$	1.36290e55	0.0230266
$589$	−3.84337e56	−0.627116
$590$	5.17206e55	0.0815074
$591$	5.85481e56	0.891188
$592$	2.95211e56	0.434048
$593$	−9.45252e56	−1.34254	−0.671269	−	0.741214i	$-0.734250\pi$
$593$	−9.45252e56	−1.34254	−0.671269	+	0.741214i	$0.734250\pi$
$594$	−2.77536e56	−0.380800
$595$	−1.64852e57	−2.18523
$596$	1.27392e56	0.163153
$597$	−1.83905e56	−0.227573
$598$	−3.79277e56	−0.453505
$599$	−3.47722e56	−0.401775	−0.200887	−	0.979614i	$-0.564383\pi$
$599$	−3.47722e56	−0.401775	−0.200887	+	0.979614i	$0.564383\pi$
$600$	5.90114e56	0.658923
$601$	6.30772e56	0.680684	0.340342	−	0.940302i	$-0.389457\pi$
$601$	6.30772e56	0.680684	0.340342	+	0.940302i	$0.389457\pi$
$602$	−1.68382e57	−1.75618
$603$	−6.09001e55	−0.0613922
$604$	2.64364e56	0.257599
$605$	3.77941e57	3.55991
$606$	−5.84815e56	−0.532513
$607$	−3.56157e56	−0.313526	−0.156763	−	0.987636i	$-0.550106\pi$
$607$	−3.56157e56	−0.313526	−0.156763	+	0.987636i	$0.550106\pi$
$608$	−3.83440e56	−0.326343
$609$	−1.21794e56	−0.100224
$610$	−8.03662e56	−0.639458
$611$	−2.31888e56	−0.178416
$612$	−9.52529e55	−0.0708719
$613$	−4.16993e56	−0.300047	−0.150023	−	0.988682i	$-0.547935\pi$
$613$	−4.16993e56	−0.300047	−0.150023	+	0.988682i	$0.547935\pi$
$614$	1.83963e57	1.28020
$615$	−1.03809e57	−0.698708
$616$	2.83652e57	1.84663
$617$	2.42342e57	1.52610	0.763051	−	0.646338i	$-0.223701\pi$
$617$	2.42342e57	1.52610	0.763051	+	0.646338i	$0.223701\pi$
$618$	1.13733e57	0.692824
$619$	−1.32231e56	−0.0779246	−0.0389623	−	0.999241i	$-0.512405\pi$
$619$	−1.32231e56	−0.0779246	−0.0389623	+	0.999241i	$0.512405\pi$
$620$	2.68033e56	0.152812
$621$	4.44296e56	0.245073
$622$	1.47957e57	0.789645
$623$	−2.50317e57	−1.29266
$624$	−4.33615e56	−0.216681
$625$	−1.37567e57	−0.665233
$626$	−2.18628e57	−1.02313
$627$	−2.35882e57	−1.06834
$628$	−4.33711e56	−0.190120
$629$	1.17165e57	0.497117
$630$	−1.46947e57	−0.603503
$631$	1.32515e57	0.526822	0.263411	−	0.964684i	$-0.415153\pi$
$631$	1.32515e57	0.526822	0.263411	+	0.964684i	$0.415153\pi$
$632$	3.53820e57	1.36170
$633$	−1.63971e57	−0.610930
$634$	−1.53622e56	−0.0554146
$635$	−2.51639e57	−0.878854
$636$	−2.91092e56	−0.0984373
$637$	2.46238e56	0.0806301
$638$	9.71159e56	0.307940
$639$	−9.67425e56	−0.297064
$640$	−5.93659e57	−1.76542
$641$	−5.79020e56	−0.166765	−0.0833824	−	0.996518i	$-0.526572\pi$
$641$	−5.79020e56	−0.166765	−0.0833824	+	0.996518i	$0.526572\pi$
$642$	4.24095e57	1.18303
$643$	9.70178e56	0.262136	0.131068	−	0.991373i	$-0.458159\pi$
$643$	9.70178e56	0.262136	0.131068	+	0.991373i	$0.458159\pi$
$644$	8.86401e56	0.231990
$645$	5.00256e57	1.26829
$646$	−5.76643e57	−1.41625
$647$	−2.04507e57	−0.486598	−0.243299	−	0.969951i	$-0.578230\pi$
$647$	−2.04507e57	−0.486598	−0.243299	+	0.969951i	$0.578230\pi$
$648$	4.34964e56	0.100269
$649$	−4.12464e56	−0.0921234
$650$	−2.08121e57	−0.450394
$651$	1.90941e57	0.400395
$652$	1.38163e57	0.280748
$653$	−6.17960e56	−0.121686	−0.0608430	−	0.998147i	$-0.519379\pi$
$653$	−6.17960e56	−0.121686	−0.0608430	+	0.998147i	$0.519379\pi$
$654$	−1.10005e57	−0.209926
$655$	6.05212e57	1.11934
$656$	5.09925e57	0.914065
$657$	−1.90118e57	−0.330318
$658$	3.86015e57	0.650091
$659$	2.52320e57	0.411909	0.205955	−	0.978562i	$-0.433970\pi$
$659$	2.52320e57	0.411909	0.205955	+	0.978562i	$0.433970\pi$
$660$	1.64502e57	0.260328
$661$	−4.49723e57	−0.689946	−0.344973	−	0.938613i	$-0.612112\pi$
$661$	−4.49723e57	−0.689946	−0.344973	+	0.938613i	$0.612112\pi$
$662$	−7.08584e57	−1.05391
$663$	−1.72095e57	−0.248165
$664$	7.23365e57	1.01137
$665$	−1.24893e58	−1.69314
$666$	1.04439e57	0.137291
$667$	−1.55469e57	−0.198182
$668$	−5.67209e56	−0.0701174
$669$	2.18544e57	0.262001
$670$	2.57113e57	0.298944
$671$	6.40909e57	0.722745
$672$	1.90496e57	0.208361
$673$	1.53837e58	1.63212	0.816061	−	0.577966i	$-0.196153\pi$
$673$	1.53837e58	1.63212	0.816061	+	0.577966i	$0.196153\pi$
$674$	5.93395e56	0.0610683
$675$	2.43800e57	0.243392
$676$	−1.50253e57	−0.145518
$677$	1.37721e58	1.29399	0.646997	−	0.762492i	$-0.276024\pi$
$677$	1.37721e58	1.29399	0.646997	+	0.762492i	$0.276024\pi$
$678$	−4.01399e57	−0.365905
$679$	4.91386e57	0.434603
$680$	−2.06012e58	−1.76791
$681$	3.98536e57	0.331858
$682$	−1.52252e58	−1.23022
$683$	−1.94435e58	−1.52458	−0.762290	−	0.647236i	$-0.775925\pi$
$683$	−1.94435e58	−1.52458	−0.762290	+	0.647236i	$0.775925\pi$
$684$	−7.21640e56	−0.0549124
$685$	1.40729e58	1.03927
$686$	1.26867e58	0.909291
$687$	−7.19423e57	−0.500462
$688$	−2.45733e58	−1.65921
$689$	−5.25921e57	−0.344688
$690$	−1.87576e58	−1.19336
$691$	−2.44962e58	−1.51286	−0.756430	−	0.654074i	$-0.773058\pi$
$691$	−2.44962e58	−1.51286	−0.756430	+	0.654074i	$0.773058\pi$
$692$	−5.01301e57	−0.300555
$693$	1.17188e58	0.682106
$694$	3.69137e57	0.208602
$695$	6.47447e57	0.355235
$696$	−1.52203e57	−0.0810840
$697$	2.02381e58	1.04688
$698$	2.96601e58	1.48983
$699$	−2.54853e57	−0.124310
$700$	4.86397e57	0.230399
$701$	−1.67730e58	−0.771599	−0.385799	−	0.922583i	$-0.626074\pi$
$701$	−1.67730e58	−0.771599	−0.385799	+	0.922583i	$0.626074\pi$
$702$	−1.53403e57	−0.0685367
$703$	8.87644e57	0.385172
$704$	3.42863e58	1.44504
$705$	−1.14683e58	−0.469487
$706$	8.48872e57	0.337556
$707$	2.46935e58	0.953861
$708$	−1.26186e56	−0.00473510
$709$	−4.58084e58	−1.66993	−0.834963	−	0.550306i	$-0.814511\pi$
$709$	−4.58084e58	−1.66993	−0.834963	+	0.550306i	$0.814511\pi$
$710$	4.08435e58	1.44653
$711$	1.46177e58	0.502983
$712$	−3.12816e58	−1.04580
$713$	2.43735e58	0.791739
$714$	2.86480e58	0.904235
$715$	2.97209e58	0.911567
$716$	−1.72863e57	−0.0515211
$717$	1.24602e58	0.360895
$718$	1.09610e58	0.308532
$719$	−4.86766e58	−1.33161	−0.665807	−	0.746124i	$-0.731912\pi$
$719$	−4.86766e58	−1.33161	−0.665807	+	0.746124i	$0.731912\pi$
$720$	−2.14450e58	−0.570178
$721$	−4.80232e58	−1.24102
$722$	−7.46628e56	−0.0187539
$723$	9.23429e56	0.0225460
$724$	−3.66926e57	−0.0870838
$725$	−8.53109e57	−0.196823
$726$	−6.56785e58	−1.47307
$727$	−1.73618e58	−0.378563	−0.189282	−	0.981923i	$-0.560616\pi$
$727$	−1.73618e58	−0.378563	−0.189282	+	0.981923i	$0.560616\pi$
$728$	1.56784e58	0.332359
$729$	1.79701e57	0.0370370
$730$	8.02653e58	1.60846
$731$	−9.75274e58	−1.90029
$732$	1.96075e57	0.0371487
$733$	−2.87695e58	−0.530031	−0.265015	−	0.964244i	$-0.585377\pi$
$733$	−2.87695e58	−0.530031	−0.265015	+	0.964244i	$0.585377\pi$
$734$	−5.02769e57	−0.0900739
$735$	1.21781e58	0.212172
$736$	2.43166e58	0.412010
$737$	−2.05044e58	−0.337880
$738$	1.80399e58	0.289121
$739$	−9.32596e57	−0.145373	−0.0726863	−	0.997355i	$-0.523157\pi$
$739$	−9.32596e57	−0.145373	−0.0726863	+	0.997355i	$0.523157\pi$
$740$	−6.19036e57	−0.0938567
$741$	−1.30380e58	−0.192281
$742$	8.75482e58	1.25593
$743$	6.98846e58	0.975239	0.487619	−	0.873056i	$-0.337865\pi$
$743$	6.98846e58	0.975239	0.487619	+	0.873056i	$0.337865\pi$
$744$	2.38615e58	0.323931
$745$	1.13830e59	1.50332
$746$	−1.56294e59	−2.00815
$747$	2.98851e58	0.373579
$748$	−3.20705e58	−0.390053
$749$	−1.79072e59	−2.11910
$750$	−2.15430e58	−0.248056
$751$	1.15523e58	0.129434	0.0647172	−	0.997904i	$-0.479385\pi$
$751$	1.15523e58	0.129434	0.0647172	+	0.997904i	$0.479385\pi$
$752$	5.63340e58	0.614193
$753$	6.79541e57	0.0720972
$754$	5.36791e57	0.0554233
$755$	2.36219e59	2.37357
$756$	3.58516e57	0.0350599
$757$	−8.37064e58	−0.796697	−0.398348	−	0.917234i	$-0.630417\pi$
$757$	−8.37064e58	−0.796697	−0.398348	+	0.917234i	$0.630417\pi$
$758$	1.07238e59	0.993412
$759$	1.49589e59	1.34879
$760$	−1.56076e59	−1.36980
$761$	−2.09392e58	−0.178885	−0.0894425	−	0.995992i	$-0.528509\pi$
$761$	−2.09392e58	−0.178885	−0.0894425	+	0.995992i	$0.528509\pi$
$762$	4.37298e58	0.363665
$763$	4.64489e58	0.376030
$764$	1.23047e58	0.0969741
$765$	−8.51119e58	−0.653027
$766$	−4.51740e58	−0.337441
$767$	−2.27982e57	−0.0165805
$768$	3.89421e58	0.275749
$769$	1.28539e59	0.886229	0.443114	−	0.896465i	$-0.353874\pi$
$769$	1.28539e59	0.886229	0.443114	+	0.896465i	$0.353874\pi$
$770$	−4.94753e59	−3.32146
$771$	3.29158e58	0.215174
$772$	5.75663e57	0.0366449
$773$	1.59781e59	0.990478	0.495239	−	0.868757i	$-0.335080\pi$
$773$	1.59781e59	0.990478	0.495239	+	0.868757i	$0.335080\pi$
$774$	−8.69346e58	−0.524811
$775$	1.33745e59	0.786308
$776$	6.14074e58	0.351605
$777$	−4.40988e58	−0.245921
$778$	3.04006e58	0.165120
$779$	1.53325e59	0.811137
$780$	9.09258e57	0.0468541
$781$	−3.25721e59	−1.63493
$782$	3.65689e59	1.78803
$783$	−6.28814e57	−0.0299506
$784$	−5.98203e58	−0.277568
$785$	−3.87537e59	−1.75180
$786$	−1.05174e59	−0.463175
$787$	7.76783e58	0.333286	0.166643	−	0.986017i	$-0.446707\pi$
$787$	7.76783e58	0.333286	0.166643	+	0.986017i	$0.446707\pi$
$788$	6.03068e58	0.252103
$789$	−1.99455e59	−0.812395
$790$	−6.17143e59	−2.44923
$791$	1.69489e59	0.655425
$792$	1.46447e59	0.551842
$793$	3.54251e58	0.130080
$794$	2.55889e59	0.915653
$795$	−2.60102e59	−0.907020
$796$	−1.89429e58	−0.0643768
$797$	1.52749e58	0.0505920	0.0252960	−	0.999680i	$-0.491947\pi$
$797$	1.52749e58	0.0505920	0.0252960	+	0.999680i	$0.491947\pi$
$798$	2.17039e59	0.700612
$799$	2.23581e59	0.703438
$800$	1.33433e59	0.409184
$801$	−1.29237e59	−0.386296
$802$	3.41710e59	0.995597
$803$	−6.40104e59	−1.81795
$804$	−6.27294e57	−0.0173669
$805$	7.92032e59	2.13760
$806$	−8.41546e58	−0.221416
$807$	−9.34728e58	−0.239761
$808$	3.08589e59	0.771699
$809$	5.87620e59	1.43269	0.716345	−	0.697747i	$-0.245814\pi$
$809$	5.87620e59	1.43269	0.716345	+	0.697747i	$0.245814\pi$
$810$	−7.58675e58	−0.180349
$811$	−2.60886e59	−0.604676	−0.302338	−	0.953201i	$-0.597767\pi$
$811$	−2.60886e59	−0.604676	−0.302338	+	0.953201i	$0.597767\pi$
$812$	−1.25453e58	−0.0283518
$813$	−2.86757e59	−0.631914
$814$	3.51634e59	0.755597
$815$	1.23454e60	2.58686
$816$	4.18081e59	0.854304
$817$	−7.38872e59	−1.47237
$818$	−4.26724e59	−0.829286
$819$	6.47736e58	0.122766
$820$	−1.06927e59	−0.197654
$821$	−2.68738e59	−0.484502	−0.242251	−	0.970214i	$-0.577886\pi$
$821$	−2.68738e59	−0.484502	−0.242251	+	0.970214i	$0.577886\pi$
$822$	−2.44559e59	−0.430042
$823$	−6.91646e59	−1.18628	−0.593140	−	0.805099i	$-0.702112\pi$
$823$	−6.91646e59	−1.18628	−0.593140	+	0.805099i	$0.702112\pi$
$824$	−6.00135e59	−1.00402
$825$	8.20846e59	1.33954
$826$	3.79514e58	0.0604139
$827$	−1.66543e58	−0.0258621	−0.0129310	−	0.999916i	$-0.504116\pi$
$827$	−1.66543e58	−0.0258621	−0.0129310	+	0.999916i	$0.504116\pi$
$828$	4.57642e58	0.0693273
$829$	−8.91805e59	−1.31796	−0.658980	−	0.752161i	$-0.729012\pi$
$829$	−8.91805e59	−1.31796	−0.658980	+	0.752161i	$0.729012\pi$
$830$	−1.26171e60	−1.81911
$831$	7.58428e58	0.106683
$832$	1.89511e59	0.260080
$833$	−2.37417e59	−0.317899
$834$	−1.12513e59	−0.146994
$835$	−5.06822e59	−0.646075
$836$	−2.42968e59	−0.302218
$837$	9.85814e58	0.119653
$838$	6.87250e59	0.813977
$839$	6.04271e59	0.698411	0.349206	−	0.937046i	$-0.386451\pi$
$839$	6.04271e59	0.698411	0.349206	+	0.937046i	$0.386451\pi$
$840$	7.75395e59	0.874576
$841$	−8.86482e59	−0.975780
$842$	3.34784e59	0.359639
$843$	−6.16727e59	−0.646588
$844$	−1.68897e59	−0.172823
$845$	−1.34257e60	−1.34083
$846$	1.99297e59	0.194271
$847$	2.77324e60	2.63863
$848$	1.27765e60	1.18658
$849$	6.90927e59	0.626361
$850$	2.00666e60	1.77576
$851$	−5.62917e59	−0.486282
$852$	−9.96484e58	−0.0840347
$853$	1.07100e60	0.881727	0.440863	−	0.897574i	$-0.354672\pi$
$853$	1.07100e60	0.881727	0.440863	+	0.897574i	$0.354672\pi$
$854$	−5.89709e59	−0.473971
$855$	−6.44811e59	−0.505973
$856$	−2.23782e60	−1.71441
$857$	−1.09608e59	−0.0819855	−0.0409927	−	0.999159i	$-0.513052\pi$
$857$	−1.09608e59	−0.0819855	−0.0409927	+	0.999159i	$0.513052\pi$
$858$	−5.16490e59	−0.377201
$859$	1.21084e60	0.863430	0.431715	−	0.902010i	$-0.357909\pi$
$859$	1.21084e60	0.863430	0.431715	+	0.902010i	$0.357909\pi$
$860$	5.15283e59	0.358779
$861$	−7.61728e59	−0.517887
$862$	1.88566e60	1.25189
$863$	−1.35388e60	−0.877728	−0.438864	−	0.898554i	$-0.644619\pi$
$863$	−1.35388e60	−0.877728	−0.438864	+	0.898554i	$0.644619\pi$
$864$	9.83515e58	0.0622658
$865$	−4.47931e60	−2.76937
$866$	−1.45470e60	−0.878329
$867$	6.80190e59	0.401087
$868$	1.96676e59	0.113266
$869$	4.92163e60	2.76824
$870$	2.65477e59	0.145842
$871$	−1.13334e59	−0.0608120
$872$	5.80462e59	0.304218
$873$	2.53699e59	0.129875
$874$	2.77048e60	1.38538
$875$	9.09641e59	0.444329
$876$	−1.95828e59	−0.0934419
$877$	1.82892e60	0.852517	0.426259	−	0.904601i	$-0.359831\pi$
$877$	1.82892e60	0.852517	0.426259	+	0.904601i	$0.359831\pi$
$878$	−3.80566e60	−1.73297
$879$	−1.90949e60	−0.849466
$880$	−7.22029e60	−3.13805
$881$	9.73145e59	0.413210	0.206605	−	0.978424i	$-0.433758\pi$
$881$	9.73145e59	0.413210	0.206605	+	0.978424i	$0.433758\pi$
$882$	−2.11630e59	−0.0877954
$883$	−2.26914e60	−0.919742	−0.459871	−	0.887986i	$-0.652104\pi$
$883$	−2.26914e60	−0.919742	−0.459871	+	0.887986i	$0.652104\pi$
$884$	−1.77264e59	−0.0702021
$885$	−1.12752e59	−0.0436301
$886$	3.47464e60	1.31377
$887$	9.48427e59	0.350404	0.175202	−	0.984532i	$-0.443942\pi$
$887$	9.48427e59	0.350404	0.175202	+	0.984532i	$0.443942\pi$
$888$	−5.51093e59	−0.198957
$889$	−1.84647e60	−0.651413
$890$	5.45622e60	1.88103
$891$	6.05033e59	0.203838
$892$	2.25108e59	0.0741160
$893$	1.69386e60	0.545032
$894$	−1.97813e60	−0.622066
$895$	−1.54459e60	−0.474725
$896$	−4.35613e60	−1.30854
$897$	8.26830e59	0.242757
$898$	−7.42247e60	−2.13002
$899$	−3.44958e59	−0.0967593
$900$	2.51123e59	0.0688517
$901$	5.07081e60	1.35900
$902$	6.07384e60	1.59122
$903$	3.67077e60	0.940065
$904$	2.11806e60	0.530257
$905$	−3.27862e60	−0.802407
$906$	−4.10501e60	−0.982169
$907$	−6.87953e59	−0.160920	−0.0804599	−	0.996758i	$-0.525639\pi$
$907$	−6.87953e59	−0.160920	−0.0804599	+	0.996758i	$0.525639\pi$
$908$	4.10507e59	0.0938774
$909$	1.27491e60	0.285049
$910$	−2.73466e60	−0.597799
$911$	−1.32323e60	−0.282819	−0.141409	−	0.989951i	$-0.545163\pi$
$911$	−1.32323e60	−0.282819	−0.141409	+	0.989951i	$0.545163\pi$
$912$	3.16740e60	0.661925
$913$	1.00620e61	2.05604
$914$	−3.21918e60	−0.643204
$915$	1.75200e60	0.342295
$916$	−7.41032e59	−0.141573
$917$	4.44091e60	0.829660
$918$	1.47907e60	0.270219
$919$	−2.10890e60	−0.376780	−0.188390	−	0.982094i	$-0.560327\pi$
$919$	−2.10890e60	−0.376780	−0.188390	+	0.982094i	$0.560327\pi$
$920$	9.89784e60	1.72938
$921$	−4.01042e60	−0.685278
$922$	6.64942e60	1.11122
$923$	−1.80036e60	−0.294256
$924$	1.20708e60	0.192957
$925$	−3.08891e60	−0.482947
$926$	−8.36130e60	−1.27864
$927$	−2.47940e60	−0.370862
$928$	−3.44154e59	−0.0503523
$929$	−8.23760e60	−1.17890	−0.589452	−	0.807803i	$-0.700656\pi$
$929$	−8.23760e60	−1.17890	−0.589452	+	0.807803i	$0.700656\pi$
$930$	−4.16198e60	−0.582639
$931$	−1.79868e60	−0.246312
$932$	−2.62508e59	−0.0351655
$933$	−3.22548e60	−0.422689
$934$	1.56251e61	2.00314
$935$	−2.86562e61	−3.59402
$936$	8.09461e59	0.0993210
$937$	1.44081e61	1.72960	0.864801	−	0.502115i	$-0.167445\pi$
$937$	1.44081e61	1.72960	0.864801	+	0.502115i	$0.167445\pi$
$938$	1.88663e60	0.221580
$939$	4.76613e60	0.547673
$940$	−1.18128e60	−0.132811
$941$	−1.04517e61	−1.14974	−0.574870	−	0.818245i	$-0.694947\pi$
$941$	−1.04517e61	−1.14974	−0.574870	+	0.818245i	$0.694947\pi$
$942$	6.73462e60	0.724885
$943$	−9.72339e60	−1.02407
$944$	5.53852e59	0.0570779
$945$	3.20347e60	0.323049
$946$	−2.92699e61	−2.88837
$947$	9.09242e60	0.878021	0.439011	−	0.898482i	$-0.355329\pi$
$947$	9.09242e60	0.878021	0.439011	+	0.898482i	$0.355329\pi$
$948$	1.50568e60	0.142286
$949$	−3.53806e60	−0.327196
$950$	1.52025e61	1.37588
$951$	3.34899e59	0.0296629
$952$	−1.51167e61	−1.31039
$953$	8.38627e60	0.711483	0.355742	−	0.934584i	$-0.384228\pi$
$953$	8.38627e60	0.711483	0.355742	+	0.934584i	$0.384228\pi$
$954$	4.52004e60	0.375319
$955$	1.09947e61	0.893538
$956$	1.28344e60	0.102092
$957$	−2.11714e60	−0.164837
$958$	2.65416e61	2.02271
$959$	1.03264e61	0.770311
$960$	9.37254e60	0.684379
$961$	−8.58235e60	−0.613446
$962$	1.94359e60	0.135993
$963$	−9.24535e60	−0.633264
$964$	9.51167e58	0.00637790
$965$	5.14376e60	0.337653
$966$	−1.37639e61	−0.884527
$967$	2.28385e61	1.43689	0.718447	−	0.695581i	$-0.244853\pi$
$967$	2.28385e61	1.43689	0.718447	+	0.695581i	$0.244853\pi$
$968$	3.46566e61	2.13472
$969$	1.25709e61	0.758105
$970$	−1.07109e61	−0.632417
$971$	−2.76347e61	−1.59757	−0.798786	−	0.601616i	$-0.794524\pi$
$971$	−2.76347e61	−1.59757	−0.798786	+	0.601616i	$0.794524\pi$
$972$	1.85099e59	0.0104772
$973$	4.75082e60	0.263303
$974$	−7.59891e60	−0.412375
$975$	4.53708e60	0.241091
$976$	−8.60605e60	−0.447799
$977$	−2.22641e61	−1.13440	−0.567199	−	0.823581i	$-0.691973\pi$
$977$	−2.22641e61	−1.13440	−0.567199	+	0.823581i	$0.691973\pi$
$978$	−2.14538e61	−1.07043
$979$	−4.35126e61	−2.12603
$980$	1.25439e60	0.0600201
$981$	2.39812e60	0.112372
$982$	−2.07899e61	−0.954040
$983$	2.36280e61	1.06189	0.530945	−	0.847407i	$-0.321837\pi$
$983$	2.36280e61	1.06189	0.530945	+	0.847407i	$0.321837\pi$
$984$	−9.51914e60	−0.418985
$985$	5.38863e61	2.32293
$986$	−5.17561e60	−0.218517
$987$	−8.41520e60	−0.347987
$988$	−1.34296e60	−0.0543934
$989$	4.68570e61	1.85888
$990$	−2.55437e61	−0.992574
$991$	−4.84850e61	−1.84543	−0.922716	−	0.385481i	$-0.874035\pi$
$991$	−4.84850e61	−1.84543	−0.922716	+	0.385481i	$0.874035\pi$
$992$	5.39542e60	0.201157
$993$	1.54473e61	0.564146
$994$	2.99700e61	1.07218
$995$	−1.69262e61	−0.593180
$996$	3.07828e60	0.105680
$997$	3.96621e60	0.133391	0.0666953	−	0.997773i	$-0.478754\pi$
$997$	3.96621e60	0.133391	0.0666953	+	0.997773i	$0.478754\pi$
$998$	−4.99905e61	−1.64707
$999$	−2.27679e60	−0.0734903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.42.a.b.1.2	✓	4
3.2	odd	2		9.42.a.c.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.42.a.b.1.2	✓	4	1.1	even	1	trivial
9.42.a.c.1.3		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)

\(f(q)\)	\(=\)	\(q-1.59943e6 q^{2} +3.48678e9 q^{3} +3.59152e11 q^{4} +3.20915e14 q^{5} -5.57687e15 q^{6} +2.35480e17 q^{7} +2.94274e18 q^{8} +1.21577e19 q^{9} +O(q^{10})\)	\(q-1.59943e6 q^{2} +3.48678e9 q^{3} +3.59152e11 q^{4} +3.20915e14 q^{5} -5.57687e15 q^{6} +2.35480e17 q^{7} +2.94274e18 q^{8} +1.21577e19 q^{9} -5.13282e20 q^{10} +4.09335e21 q^{11} +1.25229e21 q^{12} +2.26252e22 q^{13} -3.76634e23 q^{14} +1.11896e24 q^{15} -5.49650e24 q^{16} -2.18147e25 q^{17} -1.94453e25 q^{18} -1.65269e26 q^{19} +1.15257e26 q^{20} +8.21069e26 q^{21} -6.54702e27 q^{22} +1.04809e28 q^{23} +1.02607e28 q^{24} +5.75119e28 q^{25} -3.61875e28 q^{26} +4.23912e28 q^{27} +8.45732e28 q^{28} -1.48336e29 q^{29} -1.78970e30 q^{30} +2.32552e30 q^{31} +2.32010e30 q^{32} +1.42726e31 q^{33} +3.48911e31 q^{34} +7.55692e31 q^{35} +4.36645e30 q^{36} -5.37090e31 q^{37} +2.64337e32 q^{38} +7.88894e31 q^{39} +9.44372e32 q^{40} -9.27726e32 q^{41} -1.31324e33 q^{42} +4.47072e33 q^{43} +1.47013e33 q^{44} +3.90158e33 q^{45} -1.67634e34 q^{46} -1.02491e34 q^{47} -1.91651e34 q^{48} +1.08833e34 q^{49} -9.19863e34 q^{50} -7.60632e34 q^{51} +8.12590e33 q^{52} -2.32449e35 q^{53} -6.78017e34 q^{54} +1.31362e36 q^{55} +6.92958e35 q^{56} -5.76258e35 q^{57} +2.37253e35 q^{58} -1.00765e35 q^{59} +4.01878e35 q^{60} +1.56573e36 q^{61} -3.71950e36 q^{62} +2.86289e36 q^{63} +8.37609e36 q^{64} +7.26079e36 q^{65} -2.28280e37 q^{66} -5.00920e36 q^{67} -7.83480e36 q^{68} +3.65446e37 q^{69} -1.20868e38 q^{70} -7.95732e37 q^{71} +3.57769e37 q^{72} -1.56377e38 q^{73} +8.59038e37 q^{74} +2.00532e38 q^{75} -5.93568e37 q^{76} +9.63902e38 q^{77} -1.26178e38 q^{78} +1.20235e39 q^{79} -1.76391e39 q^{80} +1.47809e38 q^{81} +1.48383e39 q^{82} +2.45813e39 q^{83} +2.94889e38 q^{84} -7.00068e39 q^{85} -7.15060e39 q^{86} -5.17216e38 q^{87} +1.20457e40 q^{88} -1.06301e40 q^{89} -6.24030e39 q^{90} +5.32780e39 q^{91} +3.76423e39 q^{92} +8.10858e39 q^{93} +1.63927e40 q^{94} -5.30374e40 q^{95} +8.08967e39 q^{96} +2.08674e40 q^{97} -1.74071e40 q^{98} +4.97655e40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 69822 q^{2} + 13947137604 q^{3} + 5352947588932 q^{4} + 118536963776280 q^{5} - 243454260446622 q^{6} + 15\!\cdots\!36 q^{7}+ \cdots + 48\!\cdots\!04 q^{9}+O(q^{10}) \) 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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