LMFDB - Embedded newform 1.52.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,52,Mod(1,1)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 52, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 52);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 52 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$16.4731353414$
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} - 2x^{3} - 495735060514x^{2} - 23954614981416598x + 48979992255622025570313 $ x^4 - 2x^3 - 495735060514x^2 - 23954614981416598*x + 48979992255622025570313
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{23}\cdot 3^{10}\cdot 5^{3}\cdot 7^{2}\cdot 13\cdot 17 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-511801.$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.13381e7 q^{2} +2.68083e12 q^{3} +3.83803e14 q^{4} +4.84667e17 q^{5} +1.37629e20 q^{6} +2.59004e21 q^{7} -9.58994e22 q^{8} +5.03313e24 q^{9} +O(q^{10})$	\(q+5.13381e7 q^{2} +2.68083e12 q^{3} +3.83803e14 q^{4} +4.84667e17 q^{5} +1.37629e20 q^{6} +2.59004e21 q^{7} -9.58994e22 q^{8} +5.03313e24 q^{9} +2.48819e25 q^{10} -4.45050e26 q^{11} +1.02891e27 q^{12} -1.37117e28 q^{13} +1.32968e29 q^{14} +1.29931e30 q^{15} -5.78755e30 q^{16} +2.62484e31 q^{17} +2.58392e32 q^{18} +1.11022e32 q^{19} +1.86017e32 q^{20} +6.94345e33 q^{21} -2.28480e34 q^{22} +2.36137e34 q^{23} -2.57090e35 q^{24} -2.09187e35 q^{25} -7.03932e35 q^{26} +7.71928e36 q^{27} +9.94066e35 q^{28} -2.25752e37 q^{29} +6.67040e37 q^{30} -4.11662e37 q^{31} -8.11754e37 q^{32} -1.19310e39 q^{33} +1.34754e39 q^{34} +1.25531e39 q^{35} +1.93173e39 q^{36} +5.65183e39 q^{37} +5.69965e39 q^{38} -3.67587e40 q^{39} -4.64793e40 q^{40} -5.54318e40 q^{41} +3.56464e41 q^{42} -5.70927e41 q^{43} -1.70812e41 q^{44} +2.43939e42 q^{45} +1.21229e42 q^{46} +1.49403e42 q^{47} -1.55154e43 q^{48} -5.88095e42 q^{49} -1.07393e43 q^{50} +7.03673e43 q^{51} -5.26259e42 q^{52} -1.42123e44 q^{53} +3.96293e44 q^{54} -2.15701e44 q^{55} -2.48383e44 q^{56} +2.97630e44 q^{57} -1.15897e45 q^{58} +2.24820e44 q^{59} +4.98678e44 q^{60} +2.34137e44 q^{61} -2.11340e45 q^{62} +1.30360e46 q^{63} +8.86500e45 q^{64} -6.64560e45 q^{65} -6.12516e46 q^{66} -2.65209e45 q^{67} +1.00742e46 q^{68} +6.33043e46 q^{69} +6.44450e46 q^{70} +7.64854e46 q^{71} -4.82675e47 q^{72} +5.90560e47 q^{73} +2.90154e47 q^{74} -5.60795e47 q^{75} +4.26105e46 q^{76} -1.15270e48 q^{77} -1.88712e48 q^{78} +3.15804e48 q^{79} -2.80503e48 q^{80} +9.85421e48 q^{81} -2.84576e48 q^{82} -1.40261e48 q^{83} +2.66492e48 q^{84} +1.27217e49 q^{85} -2.93103e49 q^{86} -6.05202e49 q^{87} +4.26801e49 q^{88} -1.71424e48 q^{89} +1.25234e50 q^{90} -3.55138e49 q^{91} +9.06303e48 q^{92} -1.10360e50 q^{93} +7.67005e49 q^{94} +5.38085e49 q^{95} -2.17617e50 q^{96} +6.68956e50 q^{97} -3.01917e50 q^{98} -2.24000e51 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32756040 q^{2} + 403863773040 q^{3} + 79\!\cdots\!12 q^{4}+ \cdots + 50\!\cdots\!28 q^{9}+O(q^{10}) $ 4 * q + 32756040 * q^2 + 403863773040 * q^3 + 7978103470875712 * q^4 + 1214113112967557880 * q^5 - 108315680321506869792 * q^6 + 6566332044151252469600 * q^7 - 139242173294665691205120 * q^8 + 5074459491561912905852628 * q^9	$ 4 q + 32756040 q^{2} + 403863773040 q^{3} + 79\!\cdots\!12 q^{4}+ \cdots - 17\!\cdots\!64 q^{99}+O(q^{100}) $ 4 * q + 32756040 * q^2 + 403863773040 * q^3 + 7978103470875712 * q^4 + 1214113112967557880 * q^5 - 108315680321506869792 * q^6 + 6566332044151252469600 * q^7 - 139242173294665691205120 * q^8 + 5074459491561912905852628 * q^9 - 26338767422633182993407120 * q^10 + 352319730227217761184247248 * q^11 - 4910848780592422991861233920 * q^12 + 30737495492092678036022901080 * q^13 + 116878411871248994844784530624 * q^14 + 1476946034741298295968992105760 * q^15 + 13655541308212814904424583532544 * q^16 + 48152025926602119975132578130120 * q^17 + 730659964110731978584225137598440 * q^18 + 817578654717102241686587953106480 * q^19 + 6688106698568613691058684703008640 * q^20 + 3140470390068165005119691106219648 * q^21 - 34873949046188270313389204382330720 * q^22 - 54442545328795748403982512519744480 * q^23 - 870683087493887261435021390762280960 * q^24 - 577962011134461749109509927876368100 * q^25 + 1509847347916659653711306190553689648 * q^26 + 3642253118748703704235871670153325920 * q^27 + 34411298173690719862562837156054996480 * q^28 + 24524817706178324469842039147126378520 * q^29 - 32614789988834827956259093871049954240 * q^30 - 74015080632891216448581759119415494272 * q^31 - 698885110517892283834830116511622594560 * q^32 - 1724079406359609582394466902199988121920 * q^33 + 599176354190711613816800945566309634064 * q^34 + 5459558934032100428649177266758776617280 * q^35 + 12554754321544086227706882021196271755584 * q^36 + 9223299799194559520674909690367653437560 * q^37 + 42209741287618122996397532876280940717920 * q^38 - 118792897816045747959690882363116779819104 * q^39 - 260218563144774091908833544090781982745600 * q^40 + 146626572441904135431040424870320811649768 * q^41 - 394089552887565758770180664977333719386880 * q^42 - 383253403750663564628750277915860311246000 * q^43 + 3919911265019437916289330658643948094246144 * q^44 + 2545472464534636601491522253941835784995160 * q^45 - 687622182810100175391810298681828635813312 * q^46 + 703242125794576181922406089648904926204480 * q^47 - 19921513489914046905912799321356910879457280 * q^48 - 21525353693695885888621049774661370126875228 * q^49 - 65550763083377103476240548536052846777230600 * q^50 + 69226097223174646745938497201257873367925728 * q^51 + 205575224727950383449569813934278240424406400 * q^52 - 46053881458574871528873628680364599519093960 * q^53 + 294401161348635890022909617885475632448012480 * q^54 + 288271437023082169121432211103105268991934560 * q^55 - 718413197664523425962520880364481249783828480 * q^56 - 887307836446731380883329853535980442723450560 * q^57 - 3260382815057328392932619475690091710393763920 * q^58 + 1119164779584192618652811959209270069996506640 * q^59 + 558043767811514977207202989845983481019937280 * q^60 + 3426848506305498355799302542081826532801316248 * q^61 + 9652948821672246376570757837225648817671719680 * q^62 + 21868523123734055667483988685251699312704411360 * q^63 - 3410402571656263891001355509990182780636233728 * q^64 + 10662663070585071183633914150857043524084084560 * q^65 - 156984231778185739728164366214465838456423999104 * q^66 + 30875136607724238160818607702139418169238276720 * q^67 - 92264980123003683860202361552579885626636888960 * q^68 + 156020595717735931080084316999827890833385237376 * q^69 - 127365497175284237875848441551548839150619662720 * q^70 + 396890633217178572952249989093970445513163336288 * q^71 + 501925030461922074943170888284533271860697602560 * q^72 + 1093181650202404127682760092563948835468903177320 * q^73 - 2446722614206037598896806276944107193380656941456 * q^74 + 724518911321762179312399215417368596720139638800 * q^75 - 1930298057964975808050160660816178333985982024960 * q^76 + 1379856740595107958858322062475643650952236464000 * q^77 - 9605787792912264070639160177141351698750561924800 * q^78 + 4057123342028363124154537966955503984273281629120 * q^79 + 6556705282035289158041818706914507044939664711680 * q^80 + 15818800845095699867974190511543023822607553099044 * q^81 + 2672741123252406904410297531162443665031405248080 * q^82 + 10514534101014085301175610601927458547806407366960 * q^83 - 18556852372864802601211458682882537051712984979456 * q^84 - 2214700921000481207852358003497850667551075883920 * q^85 - 43819383990098235110217468422860464230535375092832 * q^86 - 62935773893168085248047945604687939397070771225440 * q^87 - 25053936600673669378312978656608794916631597373440 * q^88 - 90777724780188979543741952283884054816841444724440 * q^89 + 319517252743833422678369782889855912186560337690160 * q^90 + 100567720661332633308233017957549269313038849882688 * q^91 + 192025202572015319809189966047000799088692638097920 * q^92 - 311055180320633222090977351600473435943779435025920 * q^93 + 639818007616166555781273040037466169910601363859584 * q^94 - 418719878951800677902105757696028542296429654882400 * q^95 - 246297662740859333859245239975410493322197215608832 * q^96 - 1321788056943507607869460465290134726019322989433720 * q^97 - 317844097908560926995320900303041587618753340105080 * q^98 - 1718121773684708507245882236398410835742486542126064 * 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 $

$2$	5.13381e7	1.08187	0.540935	−	0.841064i	$-0.318070\pi$
$2$	5.13381e7	1.08187	0.540935	+	0.841064i	$0.318070\pi$
$3$	2.68083e12	1.82674	0.913370	−	0.407131i	$-0.133471\pi$
$3$	2.68083e12	1.82674	0.913370	+	0.407131i	$0.133471\pi$
$4$	3.83803e14	0.170443
$5$	4.84667e17	0.727291	0.363645	−	0.931537i	$-0.381532\pi$
$5$	4.84667e17	0.727291	0.363645	+	0.931537i	$0.381532\pi$
$6$	1.37629e20	1.97629
$7$	2.59004e21	0.729972	0.364986	−	0.931013i	$-0.381074\pi$
$7$	2.59004e21	0.729972	0.364986	+	0.931013i	$0.381074\pi$
$8$	−9.58994e22	−0.897473
$9$	5.03313e24	2.33698
$10$	2.48819e25	0.786834
$11$	−4.45050e26	−1.23850	−0.619249	−	0.785194i	$-0.712563\pi$
$11$	−4.45050e26	−1.23850	−0.619249	+	0.785194i	$0.712563\pi$
$12$	1.02891e27	0.311355
$13$	−1.37117e28	−0.538934	−0.269467	−	0.963010i	$-0.586847\pi$
$13$	−1.37117e28	−0.538934	−0.269467	+	0.963010i	$0.586847\pi$
$14$	1.32968e29	0.789735
$15$	1.29931e30	1.32857
$16$	−5.78755e30	−1.14139
$17$	2.62484e31	1.10320	0.551601	−	0.834108i	$-0.314017\pi$
$17$	2.62484e31	1.10320	0.551601	+	0.834108i	$0.314017\pi$
$18$	2.58392e32	2.52831
$19$	1.11022e32	0.273647	0.136824	−	0.990595i	$-0.456311\pi$
$19$	1.11022e32	0.273647	0.136824	+	0.990595i	$0.456311\pi$
$20$	1.86017e32	0.123962
$21$	6.94345e33	1.33347
$22$	−2.28480e34	−1.33989
$23$	2.36137e34	0.445764	0.222882	−	0.974845i	$-0.428454\pi$
$23$	2.36137e34	0.445764	0.222882	+	0.974845i	$0.428454\pi$
$24$	−2.57090e35	−1.63945
$25$	−2.09187e35	−0.471048
$26$	−7.03932e35	−0.583056
$27$	7.71928e36	2.44231
$28$	9.94066e35	0.124419
$29$	−2.25752e37	−1.15474	−0.577368	−	0.816484i	$-0.695920\pi$
$29$	−2.25752e37	−1.15474	−0.577368	+	0.816484i	$0.695920\pi$
$30$	6.67040e37	1.43734
$31$	−4.11662e37	−0.384431	−0.192215	−	0.981353i	$-0.561567\pi$
$31$	−4.11662e37	−0.384431	−0.192215	+	0.981353i	$0.561567\pi$
$32$	−8.11754e37	−0.337365
$33$	−1.19310e39	−2.26241
$34$	1.34754e39	1.19352
$35$	1.25531e39	0.530902
$36$	1.93173e39	0.398321
$37$	5.65183e39	0.579488	0.289744	−	0.957104i	$-0.406430\pi$
$37$	5.65183e39	0.579488	0.289744	+	0.957104i	$0.406430\pi$
$38$	5.69965e39	0.296051
$39$	−3.67587e40	−0.984492
$40$	−4.64793e40	−0.652724
$41$	−5.54318e40	−0.414735	−0.207367	−	0.978263i	$-0.566490\pi$
$41$	−5.54318e40	−0.414735	−0.207367	+	0.978263i	$0.566490\pi$
$42$	3.56464e41	1.44264
$43$	−5.70927e41	−1.26805	−0.634023	−	0.773314i	$-0.718598\pi$
$43$	−5.70927e41	−1.26805	−0.634023	+	0.773314i	$0.718598\pi$
$44$	−1.70812e41	−0.211093
$45$	2.43939e42	1.69966
$46$	1.21229e42	0.482259
$47$	1.49403e42	0.343449	0.171725	−	0.985145i	$-0.445066\pi$
$47$	1.49403e42	0.343449	0.171725	+	0.985145i	$0.445066\pi$
$48$	−1.55154e43	−2.08503
$49$	−5.88095e42	−0.467140
$50$	−1.07393e43	−0.509613
$51$	7.03673e43	2.01526
$52$	−5.26259e42	−0.0918574
$53$	−1.42123e44	−1.52626	−0.763131	−	0.646244i	$-0.776339\pi$
$53$	−1.42123e44	−1.52626	−0.763131	+	0.646244i	$0.776339\pi$
$54$	3.96293e44	2.64226
$55$	−2.15701e44	−0.900749
$56$	−2.48383e44	−0.655131
$57$	2.97630e44	0.499882
$58$	−1.15897e45	−1.24927
$59$	2.24820e44	0.156714	0.0783572	−	0.996925i	$-0.475033\pi$
$59$	2.24820e44	0.156714	0.0783572	+	0.996925i	$0.475033\pi$
$60$	4.98678e44	0.226445
$61$	2.34137e44	0.0697524	0.0348762	−	0.999392i	$-0.488896\pi$
$61$	2.34137e44	0.0697524	0.0348762	+	0.999392i	$0.488896\pi$
$62$	−2.11340e45	−0.415904
$63$	1.30360e46	1.70593
$64$	8.86500e45	0.776407
$65$	−6.64560e45	−0.391962
$66$	−6.12516e46	−2.44764
$67$	−2.65209e45	−0.0722240	−0.0361120	−	0.999348i	$-0.511497\pi$
$67$	−2.65209e45	−0.0722240	−0.0361120	+	0.999348i	$0.511497\pi$
$68$	1.00742e46	0.188033
$69$	6.33043e46	0.814295
$70$	6.44450e46	0.574367
$71$	7.64854e46	0.474778	0.237389	−	0.971415i	$-0.423708\pi$
$71$	7.64854e46	0.474778	0.237389	+	0.971415i	$0.423708\pi$
$72$	−4.82675e47	−2.09737
$73$	5.90560e47	1.80522	0.902611	−	0.430456i	$-0.141647\pi$
$73$	5.90560e47	1.80522	0.902611	+	0.430456i	$0.141647\pi$
$74$	2.90154e47	0.626931
$75$	−5.60795e47	−0.860483
$76$	4.26105e46	0.0466412
$77$	−1.15270e48	−0.904070
$78$	−1.88712e48	−1.06509
$79$	3.15804e48	1.28803	0.644017	−	0.765011i	$-0.277267\pi$
$79$	3.15804e48	1.28803	0.644017	+	0.765011i	$0.277267\pi$
$80$	−2.80503e48	−0.830124
$81$	9.85421e48	2.12449
$82$	−2.84576e48	−0.448689
$83$	−1.40261e48	−0.162348	−0.0811739	−	0.996700i	$-0.525867\pi$
$83$	−1.40261e48	−0.162348	−0.0811739	+	0.996700i	$0.525867\pi$
$84$	2.66492e48	0.227280
$85$	1.27217e49	0.802348
$86$	−2.93103e49	−1.37186
$87$	−6.05202e49	−2.10940
$88$	4.26801e49	1.11152
$89$	−1.71424e48	−0.0334677	−0.0167338	−	0.999860i	$-0.505327\pi$
$89$	−1.71424e48	−0.0334677	−0.0167338	+	0.999860i	$0.505327\pi$
$90$	1.25234e50	1.83881
$91$	−3.55138e49	−0.393407
$92$	9.06303e48	0.0759773
$93$	−1.10360e50	−0.702255
$94$	7.67005e49	0.371568
$95$	5.38085e49	0.199021
$96$	−2.17617e50	−0.616278
$97$	6.68956e50	1.45451	0.727257	−	0.686365i	$-0.240795\pi$
$97$	6.68956e50	1.45451	0.727257	+	0.686365i	$0.240795\pi$
$98$	−3.01917e50	−0.505385
$99$	−2.24000e51	−2.89434
$100$	−8.02868e49	−0.0802868
$101$	2.03385e51	1.57806	0.789031	−	0.614354i	$-0.210583\pi$
$101$	2.03385e51	1.57806	0.789031	+	0.614354i	$0.210583\pi$
$102$	3.61253e51	2.18025
$103$	−2.62630e51	−1.23593	−0.617967	−	0.786204i	$-0.712043\pi$
$103$	−2.62630e51	−1.23593	−0.617967	+	0.786204i	$0.712043\pi$
$104$	1.31494e51	0.483679
$105$	3.36526e51	0.969820
$106$	−7.29632e51	−1.65122
$107$	−4.29375e51	−0.764804	−0.382402	−	0.923996i	$-0.624903\pi$
$107$	−4.29375e51	−0.764804	−0.382402	+	0.923996i	$0.624903\pi$
$108$	2.96268e51	0.416274
$109$	−4.62834e49	−0.00514103	−0.00257051	−	0.999997i	$-0.500818\pi$
$109$	−4.62834e49	−0.00514103	−0.00257051	+	0.999997i	$0.500818\pi$
$110$	−1.10737e52	−0.974493
$111$	1.51516e52	1.05857
$112$	−1.49900e52	−0.833185
$113$	2.75611e52	1.22123	0.610613	−	0.791929i	$-0.290923\pi$
$113$	2.75611e52	1.22123	0.610613	+	0.791929i	$0.290923\pi$
$114$	1.52798e52	0.540808
$115$	1.14448e52	0.324200
$116$	−8.66444e51	−0.196817
$117$	−6.90128e52	−1.25948
$118$	1.15418e52	0.169545
$119$	6.79843e52	0.805307
$120$	−1.24603e53	−1.19236
$121$	6.89398e52	0.533880
$122$	1.20202e52	0.0754630
$123$	−1.48603e53	−0.757613
$124$	−1.57997e52	−0.0655235
$125$	−3.16621e53	−1.06988
$126$	6.69245e53	1.84559
$127$	8.01732e53	1.80732	0.903659	−	0.428254i	$-0.140871\pi$
$127$	8.01732e53	1.80732	0.903659	+	0.428254i	$0.140871\pi$
$128$	6.37903e53	1.17734
$129$	−1.53056e54	−2.31639
$130$	−3.41173e53	−0.424051
$131$	−1.06837e54	−1.09220	−0.546102	−	0.837719i	$-0.683889\pi$
$131$	−1.06837e54	−1.09220	−0.546102	+	0.837719i	$0.683889\pi$
$132$	−4.57917e53	−0.385613
$133$	2.87551e53	0.199755
$134$	−1.36153e53	−0.0781369
$135$	3.74128e54	1.77627
$136$	−2.51720e54	−0.990094
$137$	1.78751e54	0.583274	0.291637	−	0.956529i	$-0.405800\pi$
$137$	1.78751e54	0.583274	0.291637	+	0.956529i	$0.405800\pi$
$138$	3.24993e54	0.880961
$139$	−5.89879e54	−1.33010	−0.665052	−	0.746797i	$-0.731591\pi$
$139$	−5.89879e54	−1.33010	−0.665052	+	0.746797i	$0.731591\pi$
$140$	4.81790e53	0.0904885
$141$	4.00522e54	0.627392
$142$	3.92662e54	0.513648
$143$	6.10239e54	0.667469
$144$	−2.91295e55	−2.66741
$145$	−1.09414e55	−0.839829
$146$	3.03182e55	1.95302
$147$	−1.57658e55	−0.853344
$148$	2.16919e54	0.0987697
$149$	2.84854e55	1.09238	0.546188	−	0.837663i	$-0.316078\pi$
$149$	2.84854e55	1.09238	0.546188	+	0.837663i	$0.316078\pi$
$150$	−2.87902e55	−0.930930
$151$	7.60980e54	0.207712	0.103856	−	0.994592i	$-0.466882\pi$
$151$	7.60980e54	0.207712	0.103856	+	0.994592i	$0.466882\pi$
$152$	−1.06469e55	−0.245591
$153$	1.32112e56	2.57816
$154$	−5.91774e55	−0.978086
$155$	−1.99519e55	−0.279593
$156$	−1.41081e55	−0.167800
$157$	−1.29871e56	−1.31242	−0.656209	−	0.754579i	$-0.727841\pi$
$157$	−1.29871e56	−1.31242	−0.656209	+	0.754579i	$0.727841\pi$
$158$	1.62128e56	1.39349
$159$	−3.81006e56	−2.78808
$160$	−3.93430e55	−0.245362
$161$	6.11605e55	0.325395
$162$	5.05897e56	2.29842
$163$	4.13179e56	1.60455	0.802277	−	0.596952i	$-0.203622\pi$
$163$	4.13179e56	1.60455	0.802277	+	0.596952i	$0.203622\pi$
$164$	−2.12749e55	−0.0706886
$165$	−5.78257e56	−1.64543
$166$	−7.20075e55	−0.175639
$167$	4.33151e56	0.906504	0.453252	−	0.891383i	$-0.350264\pi$
$167$	4.33151e56	0.906504	0.453252	+	0.891383i	$0.350264\pi$
$168$	−6.65873e56	−1.19675
$169$	−4.59298e56	−0.709550
$170$	6.53109e56	0.868037
$171$	5.58787e56	0.639508
$172$	−2.19124e56	−0.216130
$173$	4.65407e56	0.395966	0.197983	−	0.980205i	$-0.436561\pi$
$173$	4.65407e56	0.395966	0.197983	+	0.980205i	$0.436561\pi$
$174$	−3.10699e57	−2.28210
$175$	−5.41804e56	−0.343852
$176$	2.57575e57	1.41361
$177$	6.02704e56	0.286276
$178$	−8.80057e55	−0.0362077
$179$	5.11036e57	1.82263	0.911316	−	0.411708i	$-0.135068\pi$
$179$	5.11036e57	1.82263	0.911316	+	0.411708i	$0.135068\pi$
$180$	9.36247e56	0.289695
$181$	−4.70440e57	−1.26387	−0.631933	−	0.775023i	$-0.717738\pi$
$181$	−4.70440e57	−1.26387	−0.631933	+	0.775023i	$0.717738\pi$
$182$	−1.82321e57	−0.425615
$183$	6.27680e56	0.127419
$184$	−2.26454e57	−0.400061
$185$	2.73925e57	0.421457
$186$	−5.66565e57	−0.759748
$187$	−1.16818e58	−1.36631
$188$	5.73412e56	0.0585385
$189$	1.99932e58	1.78282
$190$	2.76243e57	0.215315
$191$	−2.06433e58	−1.40743	−0.703717	−	0.710481i	$-0.748478\pi$
$191$	−2.06433e58	−1.40743	−0.703717	+	0.710481i	$0.748478\pi$
$192$	2.37655e58	1.41829
$193$	6.31461e57	0.330092	0.165046	−	0.986286i	$-0.447223\pi$
$193$	6.31461e57	0.330092	0.165046	+	0.986286i	$0.447223\pi$
$194$	3.43429e58	1.57360
$195$	−1.78157e58	−0.716012
$196$	−2.25713e57	−0.0796207
$197$	−2.12414e58	−0.658104	−0.329052	−	0.944312i	$-0.606729\pi$
$197$	−2.12414e58	−0.658104	−0.329052	+	0.944312i	$0.606729\pi$
$198$	−1.14997e59	−3.13130
$199$	5.17721e58	1.23977	0.619887	−	0.784691i	$-0.287178\pi$
$199$	5.17721e58	1.23977	0.619887	+	0.784691i	$0.287178\pi$
$200$	2.00610e58	0.422753
$201$	−7.10980e57	−0.131934
$202$	1.04414e59	1.70726
$203$	−5.84707e58	−0.842925
$204$	2.70072e58	0.343487
$205$	−2.68659e58	−0.301633
$206$	−1.34829e59	−1.33712
$207$	1.18851e59	1.04174
$208$	7.93570e58	0.615135
$209$	−4.94103e58	−0.338912
$210$	1.72766e59	1.04922
$211$	−4.46281e57	−0.0240107	−0.0120054	−	0.999928i	$-0.503822\pi$
$211$	−4.46281e57	−0.0240107	−0.0120054	+	0.999928i	$0.503822\pi$
$212$	−5.45472e58	−0.260140
$213$	2.05044e59	0.867296
$214$	−2.20433e59	−0.827419
$215$	−2.76709e59	−0.922238
$216$	−7.40274e59	−2.19191
$217$	−1.06622e59	−0.280624
$218$	−2.37610e57	−0.00556192
$219$	1.58319e60	3.29767
$220$	−8.27868e58	−0.153526
$221$	−3.59910e59	−0.594553
$222$	7.77853e59	1.14524
$223$	5.20757e57	0.00683694	0.00341847	−	0.999994i	$-0.498912\pi$
$223$	5.20757e57	0.00683694	0.00341847	+	0.999994i	$0.498912\pi$
$224$	−2.10248e59	−0.246267
$225$	−1.05287e60	−1.10083
$226$	1.41493e60	1.32121
$227$	−5.70910e59	−0.476330	−0.238165	−	0.971225i	$-0.576546\pi$
$227$	−5.70910e59	−0.476330	−0.238165	+	0.971225i	$0.576546\pi$
$228$	1.14231e59	0.0852014
$229$	−1.79988e60	−1.20071	−0.600354	−	0.799734i	$-0.704974\pi$
$229$	−1.79988e60	−1.20071	−0.600354	+	0.799734i	$0.704974\pi$
$230$	5.87554e59	0.350742
$231$	−3.09018e60	−1.65150
$232$	2.16495e60	1.03634
$233$	2.07611e60	0.890581	0.445290	−	0.895386i	$-0.353100\pi$
$233$	2.07611e60	0.890581	0.445290	+	0.895386i	$0.353100\pi$
$234$	−3.54299e60	−1.36259
$235$	7.24104e59	0.249787
$236$	8.62867e58	0.0267109
$237$	8.46617e60	2.35290
$238$	3.49019e60	0.871237
$239$	−4.43052e60	−0.993822	−0.496911	−	0.867802i	$-0.665532\pi$
$239$	−4.43052e60	−0.993822	−0.496911	+	0.867802i	$0.665532\pi$
$240$	−7.51980e60	−1.51642
$241$	−4.39407e60	−0.796952	−0.398476	−	0.917179i	$-0.630461\pi$
$241$	−4.39407e60	−0.796952	−0.398476	+	0.917179i	$0.630461\pi$
$242$	3.53924e60	0.577588
$243$	9.79245e60	1.43857
$244$	8.98625e58	0.0118888
$245$	−2.85030e60	−0.339747
$246$	−7.62900e60	−0.819638
$247$	−1.52230e60	−0.147478
$248$	3.94782e60	0.345016
$249$	−3.76016e60	−0.296567
$250$	−1.62547e61	−1.15747
$251$	−2.03323e60	−0.130770	−0.0653849	−	0.997860i	$-0.520828\pi$
$251$	−2.03323e60	−0.130770	−0.0653849	+	0.997860i	$0.520828\pi$
$252$	5.00327e60	0.290763
$253$	−1.05093e61	−0.552078
$254$	4.11594e61	1.95528
$255$	3.41047e61	1.46568
$256$	1.27866e61	0.497318
$257$	3.10631e61	1.09383	0.546915	−	0.837188i	$-0.315802\pi$
$257$	3.10631e61	1.09383	0.546915	+	0.837188i	$0.315802\pi$
$258$	−7.85759e61	−2.50603
$259$	1.46385e61	0.423011
$260$	−2.55060e60	−0.0668071
$261$	−1.13624e62	−2.69859
$262$	−5.48481e61	−1.18162
$263$	7.24647e61	1.41663	0.708313	−	0.705899i	$-0.249457\pi$
$263$	7.24647e61	1.41663	0.708313	+	0.705899i	$0.249457\pi$
$264$	1.14418e62	2.03046
$265$	−6.88822e61	−1.11004
$266$	1.47623e61	0.216109
$267$	−4.59557e60	−0.0611368
$268$	−1.01788e60	−0.0123101
$269$	−5.04207e61	−0.554531	−0.277265	−	0.960793i	$-0.589428\pi$
$269$	−5.04207e61	−0.554531	−0.277265	+	0.960793i	$0.589428\pi$
$270$	1.92070e62	1.92169
$271$	5.33395e61	0.485660	0.242830	−	0.970069i	$-0.421924\pi$
$271$	5.33395e61	0.485660	0.242830	+	0.970069i	$0.421924\pi$
$272$	−1.51914e62	−1.25919
$273$	−9.52064e61	−0.718652
$274$	9.17672e61	0.631027
$275$	9.30990e61	0.583393
$276$	2.42964e61	0.138791
$277$	1.79274e62	0.933861	0.466931	−	0.884294i	$-0.345360\pi$
$277$	1.79274e62	0.933861	0.466931	+	0.884294i	$0.345360\pi$
$278$	−3.02833e62	−1.43900
$279$	−2.07195e62	−0.898406
$280$	−1.20383e62	−0.476470
$281$	−1.23411e62	−0.446006	−0.223003	−	0.974818i	$-0.571586\pi$
$281$	−1.23411e62	−0.446006	−0.223003	+	0.974818i	$0.571586\pi$
$282$	2.05621e62	0.678757
$283$	5.28631e61	0.159440	0.0797202	−	0.996817i	$-0.474597\pi$
$283$	5.28631e61	0.159440	0.0797202	+	0.996817i	$0.474597\pi$
$284$	2.93553e61	0.0809225
$285$	1.44251e62	0.363560
$286$	3.13285e62	0.722115
$287$	−1.43571e62	−0.302745
$288$	−4.08567e62	−0.788414
$289$	1.22875e62	0.217054
$290$	−5.61713e62	−0.908586
$291$	1.79335e63	2.65702
$292$	2.26659e62	0.307687
$293$	3.24054e62	0.403174	0.201587	−	0.979471i	$-0.435390\pi$
$293$	3.24054e62	0.403174	0.201587	+	0.979471i	$0.435390\pi$
$294$	−8.09387e62	−0.923207
$295$	1.08963e62	0.113977
$296$	−5.42007e62	−0.520075
$297$	−3.43547e63	−3.02480
$298$	1.46239e63	1.18181
$299$	−3.23784e62	−0.240237
$300$	−2.15235e62	−0.146663
$301$	−1.47872e63	−0.925639
$302$	3.90673e62	0.224717
$303$	5.45240e63	2.88271
$304$	−6.42543e62	−0.312339
$305$	1.13478e62	0.0507303
$306$	6.78236e63	2.78923
$307$	−4.26649e63	−1.61451	−0.807257	−	0.590200i	$-0.799049\pi$
$307$	−4.26649e63	−1.61451	−0.807257	+	0.590200i	$0.799049\pi$
$308$	−4.42409e62	−0.154092
$309$	−7.04065e63	−2.25773
$310$	−1.02429e63	−0.302483
$311$	2.40513e63	0.654258	0.327129	−	0.944980i	$-0.393919\pi$
$311$	2.40513e63	0.654258	0.327129	+	0.944980i	$0.393919\pi$
$312$	3.52513e63	0.883555
$313$	−4.21400e62	−0.0973451	−0.0486726	−	0.998815i	$-0.515499\pi$
$313$	−4.21400e62	−0.0973451	−0.0486726	+	0.998815i	$0.515499\pi$
$314$	−6.66736e63	−1.41987
$315$	6.31812e63	1.24071
$316$	1.21207e63	0.219536
$317$	3.76818e63	0.629681	0.314840	−	0.949145i	$-0.398049\pi$
$317$	3.76818e63	0.629681	0.314840	+	0.949145i	$0.398049\pi$
$318$	−1.95602e64	−3.01634
$319$	1.00471e64	1.43014
$320$	4.29657e63	0.564674
$321$	−1.15108e64	−1.39710
$322$	3.13987e63	0.352036
$323$	2.91414e63	0.301888
$324$	3.78208e63	0.362103
$325$	2.86831e63	0.253864
$326$	2.12118e64	1.73592
$327$	−1.24078e62	−0.00939132
$328$	5.31588e63	0.372213
$329$	3.86959e63	0.250709
$330$	−2.96866e64	−1.78014
$331$	−3.48200e64	−1.93293	−0.966463	−	0.256807i	$-0.917330\pi$
$331$	−3.48200e64	−1.93293	−0.966463	+	0.256807i	$0.917330\pi$
$332$	−5.38328e62	−0.0276710
$333$	2.84464e64	1.35425
$334$	2.22372e64	0.980719
$335$	−1.28538e63	−0.0525278
$336$	−4.01855e64	−1.52201
$337$	−3.75434e64	−1.31817	−0.659085	−	0.752068i	$-0.729056\pi$
$337$	−3.75434e64	−1.31817	−0.659085	+	0.752068i	$0.729056\pi$
$338$	−2.35795e64	−0.767641
$339$	7.38864e64	2.23086
$340$	4.88263e63	0.136755
$341$	1.83210e64	0.476117
$342$	2.86871e64	0.691864
$343$	−4.78386e64	−1.07097
$344$	5.47516e64	1.13804
$345$	3.06815e64	0.592229
$346$	2.38931e64	0.428383
$347$	1.26312e63	0.0210399	0.0105200	−	0.999945i	$-0.496651\pi$
$347$	1.26312e63	0.0210399	0.0105200	+	0.999945i	$0.496651\pi$
$348$	−2.32278e64	−0.359533
$349$	−6.61603e64	−0.951808	−0.475904	−	0.879497i	$-0.657879\pi$
$349$	−6.61603e64	−0.951808	−0.475904	+	0.879497i	$0.657879\pi$
$350$	−2.78152e64	−0.372004
$351$	−1.05844e65	−1.31624
$352$	3.61271e64	0.417826
$353$	−1.20269e65	−1.29390	−0.646949	−	0.762533i	$-0.723955\pi$
$353$	−1.20269e65	−1.29390	−0.646949	+	0.762533i	$0.723955\pi$
$354$	3.09417e64	0.309714
$355$	3.70699e64	0.345302
$356$	−6.57930e62	−0.00570433
$357$	1.82254e65	1.47109
$358$	2.62356e65	1.97185
$359$	1.83244e63	0.0128269	0.00641344	−	0.999979i	$-0.497959\pi$
$359$	1.83244e63	0.0128269	0.00641344	+	0.999979i	$0.497959\pi$
$360$	−2.33936e65	−1.52540
$361$	−1.52276e65	−0.925117
$362$	−2.41515e65	−1.36734
$363$	1.84816e65	0.975259
$364$	−1.36303e64	−0.0670534
$365$	2.86225e65	1.31292
$366$	3.22239e64	0.137851
$367$	3.73824e65	1.49170	0.745851	−	0.666112i	$-0.232043\pi$
$367$	3.73824e65	1.49170	0.745851	+	0.666112i	$0.232043\pi$
$368$	−1.36666e65	−0.508791
$369$	−2.78996e65	−0.969226
$370$	1.40628e65	0.455961
$371$	−3.68104e65	−1.11413
$372$	−4.23563e64	−0.119694
$373$	4.09981e65	1.08190	0.540952	−	0.841054i	$-0.318064\pi$
$373$	4.09981e65	1.08190	0.540952	+	0.841054i	$0.318064\pi$
$374$	−5.99724e65	−1.47817
$375$	−8.48807e65	−1.95439
$376$	−1.43276e65	−0.308236
$377$	3.09544e65	0.622326
$378$	1.02642e66	1.92878
$379$	−3.52556e65	−0.619338	−0.309669	−	0.950844i	$-0.600218\pi$
$379$	−3.52556e65	−0.619338	−0.309669	+	0.950844i	$0.600218\pi$
$380$	2.06519e64	0.0339217
$381$	2.14930e66	3.30150
$382$	−1.05979e66	−1.52266
$383$	−5.89561e65	−0.792429	−0.396214	−	0.918158i	$-0.629676\pi$
$383$	−5.89561e65	−0.792429	−0.396214	+	0.918158i	$0.629676\pi$
$384$	1.71011e66	2.15069
$385$	−5.58674e65	−0.657522
$386$	3.24180e65	0.357117
$387$	−2.87355e66	−2.96340
$388$	2.56747e65	0.247912
$389$	1.54980e66	1.40140	0.700698	−	0.713458i	$-0.252872\pi$
$389$	1.54980e66	1.40140	0.700698	+	0.713458i	$0.252872\pi$
$390$	−9.14624e65	−0.774632
$391$	6.19822e65	0.491768
$392$	5.63980e65	0.419246
$393$	−2.86412e66	−1.99517
$394$	−1.09049e66	−0.711983
$395$	1.53060e66	0.936775
$396$	−8.59718e65	−0.493320
$397$	−3.73577e65	−0.201012	−0.100506	−	0.994936i	$-0.532046\pi$
$397$	−3.73577e65	−0.201012	−0.100506	+	0.994936i	$0.532046\pi$
$398$	2.65788e66	1.34127
$399$	7.70874e65	0.364900
$400$	1.21068e66	0.537651
$401$	−2.11569e65	−0.0881600	−0.0440800	−	0.999028i	$-0.514036\pi$
$401$	−2.11569e65	−0.0881600	−0.0440800	+	0.999028i	$0.514036\pi$
$402$	−3.65004e65	−0.142736
$403$	5.64459e65	0.207183
$404$	7.80598e65	0.268969
$405$	4.77601e66	1.54512
$406$	−3.00177e66	−0.911936
$407$	−2.51535e66	−0.717696
$408$	−6.74819e66	−1.80864
$409$	1.06566e66	0.268332	0.134166	−	0.990959i	$-0.457164\pi$
$409$	1.06566e66	0.268332	0.134166	+	0.990959i	$0.457164\pi$
$410$	−1.37925e66	−0.326328
$411$	4.79199e66	1.06549
$412$	−1.00798e66	−0.210656
$413$	5.82293e65	0.114397
$414$	6.10159e66	1.12703
$415$	−6.79800e65	−0.118074
$416$	1.11305e66	0.181817
$417$	−1.58136e67	−2.42975
$418$	−2.53663e66	−0.366659
$419$	5.15077e65	0.0700511	0.0350255	−	0.999386i	$-0.488849\pi$
$419$	5.15077e65	0.0700511	0.0350255	+	0.999386i	$0.488849\pi$
$420$	1.29160e66	0.165299
$421$	5.05760e66	0.609187	0.304594	−	0.952482i	$-0.401479\pi$
$421$	5.05760e66	0.609187	0.304594	+	0.952482i	$0.401479\pi$
$422$	−2.29112e65	−0.0259765
$423$	7.51963e66	0.802633
$424$	1.36295e67	1.36978
$425$	−5.49083e66	−0.519661
$426$	1.05266e67	0.938301
$427$	6.06424e65	0.0509173
$428$	−1.64795e66	−0.130355
$429$	1.63594e67	1.21929
$430$	−1.42057e67	−0.997742
$431$	−6.54142e66	−0.433014	−0.216507	−	0.976281i	$-0.569466\pi$
$431$	−6.54142e66	−0.433014	−0.216507	+	0.976281i	$0.569466\pi$
$432$	−4.46757e67	−2.78763
$433$	3.67034e66	0.215906	0.107953	−	0.994156i	$-0.465570\pi$
$433$	3.67034e66	0.215906	0.107953	+	0.994156i	$0.465570\pi$
$434$	−5.47378e66	−0.303598
$435$	−2.93321e67	−1.53415
$436$	−1.77637e64	−0.000876252 0
$437$	2.62164e66	0.121982
$438$	8.12779e67	3.56765
$439$	7.98143e66	0.330549	0.165274	−	0.986248i	$-0.447149\pi$
$439$	7.98143e66	0.330549	0.165274	+	0.986248i	$0.447149\pi$
$440$	2.06856e67	0.808398
$441$	−2.95996e67	−1.09170
$442$	−1.84771e67	−0.643229
$443$	−1.14974e67	−0.377836	−0.188918	−	0.981993i	$-0.560498\pi$
$443$	−1.14974e67	−0.377836	−0.188918	+	0.981993i	$0.560498\pi$
$444$	5.81522e66	0.180426
$445$	−8.30834e65	−0.0243407
$446$	2.67347e65	0.00739668
$447$	7.63643e67	1.99549
$448$	2.29607e67	0.566756
$449$	−7.25393e67	−1.69158	−0.845789	−	0.533518i	$-0.820870\pi$
$449$	−7.25393e67	−1.69158	−0.845789	+	0.533518i	$0.820870\pi$
$450$	−5.40523e67	−1.19095
$451$	2.46699e67	0.513649
$452$	1.05780e67	0.208149
$453$	2.04005e67	0.379435
$454$	−2.93094e67	−0.515327
$455$	−1.72124e67	−0.286121
$456$	−2.85425e67	−0.448631
$457$	−3.92391e67	−0.583251	−0.291626	−	0.956533i	$-0.594196\pi$
$457$	−3.92391e67	−0.583251	−0.291626	+	0.956533i	$0.594196\pi$
$458$	−9.24022e67	−1.29901
$459$	2.02618e68	2.69436
$460$	4.39255e66	0.0552576
$461$	−2.24623e67	−0.267350	−0.133675	−	0.991025i	$-0.542678\pi$
$461$	−2.24623e67	−0.267350	−0.133675	+	0.991025i	$0.542678\pi$
$462$	−1.58644e68	−1.78671
$463$	8.68251e67	0.925401	0.462701	−	0.886515i	$-0.346880\pi$
$463$	8.68251e67	0.925401	0.462701	+	0.886515i	$0.346880\pi$
$464$	1.30655e68	1.31801
$465$	−5.34876e67	−0.510743
$466$	1.06583e68	0.963493
$467$	3.24322e67	0.277585	0.138792	−	0.990322i	$-0.455678\pi$
$467$	3.24322e67	0.277585	0.138792	+	0.990322i	$0.455678\pi$
$468$	−2.64873e67	−0.214669
$469$	−6.86903e66	−0.0527215
$470$	3.71742e67	0.270238
$471$	−3.48163e68	−2.39745
$472$	−2.15601e67	−0.140647
$473$	2.54091e68	1.57047
$474$	4.34637e68	2.54553
$475$	−2.32244e67	−0.128901
$476$	2.60926e67	0.137259
$477$	−7.15323e68	−3.56684
$478$	−2.27455e68	−1.07519
$479$	2.10847e68	0.944959	0.472479	−	0.881342i	$-0.343359\pi$
$479$	2.10847e68	0.944959	0.472479	+	0.881342i	$0.343359\pi$
$480$	−1.05472e68	−0.448213
$481$	−7.74961e67	−0.312306
$482$	−2.25583e68	−0.862199
$483$	1.63961e68	0.594413
$484$	2.64593e67	0.0909960
$485$	3.24220e68	1.05785
$486$	5.02726e68	1.55635
$487$	−1.64479e68	−0.483195	−0.241597	−	0.970377i	$-0.577671\pi$
$487$	−1.64479e68	−0.483195	−0.241597	+	0.970377i	$0.577671\pi$
$488$	−2.24536e67	−0.0626009
$489$	1.10766e69	2.93110
$490$	−1.46329e68	−0.367562
$491$	−2.01454e68	−0.480395	−0.240197	−	0.970724i	$-0.577212\pi$
$491$	−2.01454e68	−0.480395	−0.240197	+	0.970724i	$0.577212\pi$
$492$	−5.70343e67	−0.129130
$493$	−5.92562e68	−1.27391
$494$	−7.81518e67	−0.159552
$495$	−1.08565e69	−2.10503
$496$	2.38251e68	0.438786
$497$	1.98100e68	0.346575
$498$	−1.93040e68	−0.320847
$499$	−3.52023e68	−0.555914	−0.277957	−	0.960594i	$-0.589657\pi$
$499$	−3.52023e68	−0.555914	−0.277957	+	0.960594i	$0.589657\pi$
$500$	−1.21520e68	−0.182353
$501$	1.16120e69	1.65595
$502$	−1.04382e68	−0.141476
$503$	1.03779e69	1.33698	0.668492	−	0.743719i	$-0.266940\pi$
$503$	1.03779e69	1.33698	0.668492	+	0.743719i	$0.266940\pi$
$504$	−1.25015e69	−1.53103
$505$	9.85739e68	1.14771
$506$	−5.39528e68	−0.597277
$507$	−1.23130e69	−1.29616
$508$	3.07707e68	0.308044
$509$	−1.43270e69	−1.36411	−0.682057	−	0.731299i	$-0.738914\pi$
$509$	−1.43270e69	−1.36411	−0.682057	+	0.731299i	$0.738914\pi$
$510$	1.75087e69	1.58568
$511$	1.52957e69	1.31776
$512$	−7.79993e68	−0.639303
$513$	8.57008e68	0.668331
$514$	1.59472e69	1.18338
$515$	−1.27288e69	−0.898883
$516$	−5.87433e68	−0.394812
$517$	−6.64917e68	−0.425362
$518$	7.51511e68	0.457642
$519$	1.24768e69	0.723326
$520$	6.37309e68	0.351775
$521$	7.41512e67	0.0389723	0.0194862	−	0.999810i	$-0.493797\pi$
$521$	7.41512e67	0.0389723	0.0194862	+	0.999810i	$0.493797\pi$
$522$	−5.83324e69	−2.91953
$523$	−1.30708e69	−0.623030	−0.311515	−	0.950241i	$-0.600836\pi$
$523$	−1.30708e69	−0.623030	−0.311515	+	0.950241i	$0.600836\pi$
$524$	−4.10044e68	−0.186158
$525$	−1.45248e69	−0.628129
$526$	3.72020e69	1.53260
$527$	−1.08055e69	−0.424104
$528$	6.90513e69	2.58230
$529$	−2.24860e69	−0.801294
$530$	−3.53628e69	−1.20091
$531$	1.13155e69	0.366238
$532$	1.10363e68	0.0340468
$533$	7.60064e68	0.223515
$534$	−2.35928e68	−0.0661420
$535$	−2.08104e69	−0.556235
$536$	2.54334e68	0.0648191
$537$	1.37000e70	3.32947
$538$	−2.58850e69	−0.599930
$539$	2.61732e69	0.578553
$540$	1.43591e69	0.302752
$541$	−7.56485e69	−1.52149	−0.760746	−	0.649049i	$-0.775167\pi$
$541$	−7.56485e69	−1.52149	−0.760746	+	0.649049i	$0.775167\pi$
$542$	2.73835e69	0.525421
$543$	−1.26117e70	−2.30875
$544$	−2.13072e69	−0.372182
$545$	−2.24320e67	−0.00373902
$546$	−4.88772e69	−0.777488
$547$	−3.07662e68	−0.0467087	−0.0233543	−	0.999727i	$-0.507435\pi$
$547$	−3.07662e68	−0.0467087	−0.0233543	+	0.999727i	$0.507435\pi$
$548$	6.86050e68	0.0994150
$549$	1.17844e69	0.163010
$550$	4.77953e69	0.631155
$551$	−2.50634e69	−0.315990
$552$	−6.07085e69	−0.730807
$553$	8.17946e69	0.940229
$554$	9.20357e69	1.01032
$555$	7.34346e69	0.769891
$556$	−2.26398e69	−0.226707
$557$	2.02206e70	1.93414	0.967068	−	0.254519i	$-0.0819171\pi$
$557$	2.02206e70	1.93414	0.967068	+	0.254519i	$0.0819171\pi$
$558$	−1.06370e70	−0.971958
$559$	7.82838e69	0.683393
$560$	−7.26514e69	−0.605967
$561$	−3.13170e70	−2.49590
$562$	−6.33567e69	−0.482521
$563$	1.22868e69	0.0894285	0.0447142	−	0.999000i	$-0.485762\pi$
$563$	1.22868e69	0.0894285	0.0447142	+	0.999000i	$0.485762\pi$
$564$	1.53722e69	0.106935
$565$	1.33579e70	0.888186
$566$	2.71389e69	0.172494
$567$	2.55228e70	1.55082
$568$	−7.33491e69	−0.426100
$569$	−5.32852e69	−0.295967	−0.147984	−	0.988990i	$-0.547278\pi$
$569$	−5.32852e69	−0.295967	−0.147984	+	0.988990i	$0.547278\pi$
$570$	7.40559e69	0.393324
$571$	−6.57707e69	−0.334050	−0.167025	−	0.985953i	$-0.553416\pi$
$571$	−6.57707e69	−0.334050	−0.167025	+	0.985953i	$0.553416\pi$
$572$	2.34212e69	0.113765
$573$	−5.53410e70	−2.57101
$574$	−7.37064e69	−0.327531
$575$	−4.93970e69	−0.209976
$576$	4.46187e70	1.81445
$577$	−4.36043e70	−1.69647	−0.848235	−	0.529620i	$-0.822335\pi$
$577$	−4.36043e70	−1.69647	−0.848235	+	0.529620i	$0.822335\pi$
$578$	6.30816e69	0.234824
$579$	1.69284e70	0.602993
$580$	−4.19936e69	−0.143143
$581$	−3.63282e69	−0.118509
$582$	9.20674e70	2.87455
$583$	6.32518e70	1.89027
$584$	−5.66343e70	−1.62014
$585$	−3.34482e70	−0.916005
$586$	1.66363e70	0.436182
$587$	1.47836e70	0.371115	0.185557	−	0.982633i	$-0.440591\pi$
$587$	1.47836e70	0.371115	0.185557	+	0.982633i	$0.440591\pi$
$588$	−6.05097e69	−0.145446
$589$	−4.57035e69	−0.105198
$590$	5.59395e69	0.123308
$591$	−5.69445e70	−1.20218
$592$	−3.27102e70	−0.661424
$593$	4.45541e70	0.862964	0.431482	−	0.902122i	$-0.357991\pi$
$593$	4.45541e70	0.862964	0.431482	+	0.902122i	$0.357991\pi$
$594$	−1.76370e71	−3.27244
$595$	3.29497e70	0.585692
$596$	1.09328e70	0.186188
$597$	1.38792e71	2.26474
$598$	−1.66225e70	−0.259906
$599$	−2.36232e70	−0.353961	−0.176980	−	0.984214i	$-0.556633\pi$
$599$	−2.36232e70	−0.353961	−0.176980	+	0.984214i	$0.556633\pi$
$600$	5.37800e70	0.772260
$601$	−7.60000e70	−1.04596	−0.522979	−	0.852345i	$-0.675180\pi$
$601$	−7.60000e70	−1.04596	−0.522979	+	0.852345i	$0.675180\pi$
$602$	−7.59149e70	−1.00142
$603$	−1.33483e70	−0.168786
$604$	2.92067e69	0.0354030
$605$	3.34128e70	0.388286
$606$	2.79916e71	3.11871
$607$	7.81615e70	0.834990	0.417495	−	0.908679i	$-0.362908\pi$
$607$	7.81615e70	0.834990	0.417495	+	0.908679i	$0.362908\pi$
$608$	−9.01223e69	−0.0923190
$609$	−1.56750e71	−1.53981
$610$	5.82577e69	0.0548836
$611$	−2.04856e70	−0.185096
$612$	5.07049e70	0.439429
$613$	9.82908e70	0.817091	0.408546	−	0.912738i	$-0.366036\pi$
$613$	9.82908e70	0.817091	0.408546	+	0.912738i	$0.366036\pi$
$614$	−2.19033e71	−1.74669
$615$	−7.20229e70	−0.551005
$616$	1.10543e71	0.811378
$617$	6.23909e68	0.00439389	0.00219695	−	0.999998i	$-0.499301\pi$
$617$	6.23909e68	0.00439389	0.00219695	+	0.999998i	$0.499301\pi$
$618$	−3.61454e71	−2.44257
$619$	−3.87928e70	−0.251559	−0.125779	−	0.992058i	$-0.540143\pi$
$619$	−3.87928e70	−0.251559	−0.125779	+	0.992058i	$0.540143\pi$
$620$	−7.65760e69	−0.0476546
$621$	1.82281e71	1.08869
$622$	1.23475e71	0.707822
$623$	−4.43994e69	−0.0244305
$624$	2.12742e71	1.12369
$625$	−6.05579e70	−0.307065
$626$	−2.16339e70	−0.105315
$627$	−1.32460e71	−0.619104
$628$	−4.98451e70	−0.223692
$629$	1.48351e71	0.639293
$630$	3.24361e71	1.34228
$631$	−4.57404e71	−1.81782	−0.908911	−	0.416989i	$-0.863085\pi$
$631$	−4.57404e71	−1.81782	−0.908911	+	0.416989i	$0.863085\pi$
$632$	−3.02855e71	−1.15598
$633$	−1.19640e70	−0.0438614
$634$	1.93451e71	0.681233
$635$	3.88573e71	1.31444
$636$	−1.46232e71	−0.475209
$637$	8.06377e70	0.251758
$638$	5.15799e71	1.54723
$639$	3.84961e71	1.10955
$640$	3.09170e71	0.856266
$641$	−3.22553e71	−0.858463	−0.429231	−	0.903195i	$-0.641216\pi$
$641$	−3.22553e71	−0.858463	−0.429231	+	0.903195i	$0.641216\pi$
$642$	−5.90942e71	−1.51148
$643$	−7.02269e71	−1.72633	−0.863165	−	0.504922i	$-0.831521\pi$
$643$	−7.02269e71	−1.72633	−0.863165	+	0.504922i	$0.831521\pi$
$644$	2.34736e70	0.0554613
$645$	−7.41810e71	−1.68469
$646$	1.49606e71	0.326604
$647$	8.46993e71	1.77755	0.888773	−	0.458347i	$-0.151558\pi$
$647$	8.46993e71	1.77755	0.888773	+	0.458347i	$0.151558\pi$
$648$	−9.45013e71	−1.90667
$649$	−1.00056e71	−0.194091
$650$	1.47254e71	0.274648
$651$	−2.85836e71	−0.512626
$652$	1.58580e71	0.273485
$653$	7.34453e71	1.21809	0.609043	−	0.793137i	$-0.291554\pi$
$653$	7.34453e71	1.21809	0.609043	+	0.793137i	$0.291554\pi$
$654$	−6.36992e69	−0.0101602
$655$	−5.17803e71	−0.794350
$656$	3.20814e71	0.473375
$657$	2.97237e72	4.21876
$658$	1.98657e71	0.271234
$659$	5.48627e70	0.0720608	0.0360304	−	0.999351i	$-0.488529\pi$
$659$	5.48627e70	0.0720608	0.0360304	+	0.999351i	$0.488529\pi$
$660$	−2.21937e71	−0.280452
$661$	−9.86251e71	−1.19909	−0.599543	−	0.800343i	$-0.704651\pi$
$661$	−9.86251e71	−1.19909	−0.599543	+	0.800343i	$0.704651\pi$
$662$	−1.78759e72	−2.09117
$663$	−9.64855e71	−1.08609
$664$	1.34510e71	0.145703
$665$	1.39366e71	0.145280
$666$	1.46038e72	1.46512
$667$	−5.33085e71	−0.514740
$668$	1.66245e71	0.154507
$669$	1.39606e70	0.0124893
$670$	−6.59890e70	−0.0568283
$671$	−1.04203e71	−0.0863883
$672$	−5.63637e71	−0.449866
$673$	1.21639e72	0.934739	0.467369	−	0.884062i	$-0.345202\pi$
$673$	1.21639e72	0.934739	0.467369	+	0.884062i	$0.345202\pi$
$674$	−1.92741e72	−1.42609
$675$	−1.61478e72	−1.15045
$676$	−1.76280e71	−0.120938
$677$	−9.64935e71	−0.637510	−0.318755	−	0.947837i	$-0.603265\pi$
$677$	−9.64935e71	−0.637510	−0.318755	+	0.947837i	$0.603265\pi$
$678$	3.79319e72	2.41350
$679$	1.73262e72	1.06176
$680$	−1.22000e72	−0.720086
$681$	−1.53051e72	−0.870131
$682$	9.40568e71	0.515097
$683$	3.44340e72	1.81660	0.908299	−	0.418321i	$-0.137381\pi$
$683$	3.44340e72	1.81660	0.908299	+	0.418321i	$0.137381\pi$
$684$	2.14464e71	0.109000
$685$	8.66344e71	0.424210
$686$	−2.45594e72	−1.15865
$687$	−4.82515e72	−2.19338
$688$	3.30427e72	1.44734
$689$	1.94874e72	0.822554
$690$	1.57513e72	0.640715
$691$	−1.61159e70	−0.00631779	−0.00315889	−	0.999995i	$-0.501006\pi$
$691$	−1.61159e70	−0.00631779	−0.00315889	+	0.999995i	$0.501006\pi$
$692$	1.78625e71	0.0674895
$693$	−5.80168e72	−2.11279
$694$	6.48463e70	0.0227624
$695$	−2.85895e72	−0.967373
$696$	5.80385e72	1.89313
$697$	−1.45499e72	−0.457536
$698$	−3.39655e72	−1.02973
$699$	5.56568e72	1.62686
$700$	−2.07946e71	−0.0586072
$701$	7.31953e71	0.198918	0.0994589	−	0.995042i	$-0.468289\pi$
$701$	7.31953e71	0.198918	0.0994589	+	0.995042i	$0.468289\pi$
$702$	−5.43385e72	−1.42400
$703$	6.27476e71	0.158575
$704$	−3.94537e72	−0.961579
$705$	1.94120e72	0.456297
$706$	−6.17440e72	−1.39983
$707$	5.26775e72	1.15194
$708$	2.31320e71	0.0487938
$709$	−4.60802e72	−0.937637	−0.468819	−	0.883294i	$-0.655320\pi$
$709$	−4.60802e72	−0.937637	−0.468819	+	0.883294i	$0.655320\pi$
$710$	1.90310e72	0.373571
$711$	1.58949e73	3.01011
$712$	1.64394e71	0.0300364
$713$	−9.72089e71	−0.171365
$714$	9.35659e72	1.59152
$715$	2.95763e72	0.485444
$716$	1.96137e72	0.310655
$717$	−1.18775e73	−1.81545
$718$	9.40739e70	0.0138770
$719$	8.14014e72	1.15890	0.579449	−	0.815009i	$-0.303268\pi$
$719$	8.14014e72	1.15890	0.579449	+	0.815009i	$0.303268\pi$
$720$	−1.41181e73	−1.93998
$721$	−6.80222e72	−0.902197
$722$	−7.81754e72	−1.00086
$723$	−1.17797e73	−1.45582
$724$	−1.80557e72	−0.215417
$725$	4.72245e72	0.543937
$726$	9.48809e72	1.05510
$727$	−8.09226e72	−0.868845	−0.434423	−	0.900709i	$-0.643048\pi$
$727$	−8.09226e72	−0.868845	−0.434423	+	0.900709i	$0.643048\pi$
$728$	3.40576e72	0.353072
$729$	5.02892e72	0.503411
$730$	1.46942e73	1.42041
$731$	−1.49859e73	−1.39891
$732$	2.40906e71	0.0217177
$733$	1.72167e73	1.49899	0.749495	−	0.662010i	$-0.230297\pi$
$733$	1.72167e73	1.49899	0.749495	+	0.662010i	$0.230297\pi$
$734$	1.91914e73	1.61383
$735$	−7.64116e72	−0.620629
$736$	−1.91685e72	−0.150385
$737$	1.18031e72	0.0894493
$738$	−1.43231e73	−1.04858
$739$	−4.89392e72	−0.346118	−0.173059	−	0.984911i	$-0.555365\pi$
$739$	−4.89392e72	−0.346118	−0.173059	+	0.984911i	$0.555365\pi$
$740$	1.05133e72	0.0718343
$741$	−4.08101e72	−0.269404
$742$	−1.88978e73	−1.20534
$743$	1.78935e73	1.10276	0.551379	−	0.834255i	$-0.314102\pi$
$743$	1.78935e73	1.10276	0.551379	+	0.834255i	$0.314102\pi$
$744$	1.05834e73	0.630254
$745$	1.38059e73	0.794475
$746$	2.10477e73	1.17048
$747$	−7.05954e72	−0.379403
$748$	−4.48353e72	−0.232879
$749$	−1.11210e73	−0.558286
$750$	−4.35762e73	−2.11440
$751$	1.11871e73	0.524685	0.262343	−	0.964975i	$-0.415505\pi$
$751$	1.11871e73	0.524685	0.262343	+	0.964975i	$0.415505\pi$
$752$	−8.64674e72	−0.392010
$753$	−5.45075e72	−0.238882
$754$	1.58914e73	0.673276
$755$	3.68822e72	0.151067
$756$	7.67347e72	0.303869
$757$	−7.85188e72	−0.300628	−0.150314	−	0.988638i	$-0.548028\pi$
$757$	−7.85188e72	−0.300628	−0.150314	+	0.988638i	$0.548028\pi$
$758$	−1.80995e73	−0.670043
$759$	−2.81736e73	−1.00850
$760$	−5.16021e72	−0.178616
$761$	−3.37728e73	−1.13047	−0.565234	−	0.824931i	$-0.691214\pi$
$761$	−3.37728e73	−1.13047	−0.565234	+	0.824931i	$0.691214\pi$
$762$	1.10341e74	3.57179
$763$	−1.19876e71	−0.00375281
$764$	−7.92296e72	−0.239887
$765$	6.40301e73	1.87507
$766$	−3.02670e73	−0.857305
$767$	−3.08266e72	−0.0844587
$768$	3.42785e73	0.908471
$769$	−7.30333e73	−1.87240	−0.936202	−	0.351464i	$-0.885684\pi$
$769$	−7.30333e73	−1.87240	−0.936202	+	0.351464i	$0.885684\pi$
$770$	−2.86813e73	−0.711353
$771$	8.32747e73	1.99814
$772$	2.42357e72	0.0562619
$773$	8.48856e73	1.90659	0.953294	−	0.302043i	$-0.0976687\pi$
$773$	8.48856e73	1.90659	0.953294	+	0.302043i	$0.0976687\pi$
$774$	−1.47523e74	−3.20601
$775$	8.61146e72	0.181085
$776$	−6.41525e73	−1.30539
$777$	3.92431e73	0.772730
$778$	7.95638e73	1.51613
$779$	−6.15414e72	−0.113491
$780$	−6.83772e72	−0.122039
$781$	−3.40398e73	−0.588012
$782$	3.18205e73	0.532029
$783$	−1.74264e74	−2.82022
$784$	3.40363e73	0.533190
$785$	−6.29443e73	−0.954510
$786$	−1.47038e74	−2.15852
$787$	5.38760e73	0.765667	0.382833	−	0.923817i	$-0.374948\pi$
$787$	5.38760e73	0.765667	0.382833	+	0.923817i	$0.374948\pi$
$788$	−8.15252e72	−0.112169
$789$	1.94265e74	2.58781
$790$	7.85780e73	1.01347
$791$	7.13843e73	0.891461
$792$	2.14815e74	2.59760
$793$	−3.21041e72	−0.0375919
$794$	−1.91788e73	−0.217469
$795$	−1.84661e74	−2.02775
$796$	1.98703e73	0.211311
$797$	−6.28418e73	−0.647234	−0.323617	−	0.946188i	$-0.604899\pi$
$797$	−6.28418e73	−0.647234	−0.323617	+	0.946188i	$0.604899\pi$
$798$	3.95752e73	0.394775
$799$	3.92157e73	0.378894
$800$	1.69809e73	0.158915
$801$	−8.62799e72	−0.0782132
$802$	−1.08616e73	−0.0953776
$803$	−2.62829e74	−2.23577
$804$	−2.72876e72	−0.0224873
$805$	2.96425e73	0.236657
$806$	2.89782e73	0.224145
$807$	−1.35169e74	−1.01298
$808$	−1.95045e74	−1.41627
$809$	9.71872e73	0.683788	0.341894	−	0.939738i	$-0.388932\pi$
$809$	9.71872e73	0.683788	0.341894	+	0.939738i	$0.388932\pi$
$810$	2.45191e74	1.67162
$811$	1.93558e74	1.27873	0.639366	−	0.768903i	$-0.279197\pi$
$811$	1.93558e74	1.27873	0.639366	+	0.768903i	$0.279197\pi$
$812$	−2.24412e73	−0.143671
$813$	1.42994e74	0.887174
$814$	−1.29133e74	−0.776454
$815$	2.00254e74	1.16698
$816$	−4.07254e74	−2.30020
$817$	−6.33853e73	−0.346998
$818$	5.47088e73	0.290300
$819$	−1.78746e74	−0.919383
$820$	−1.03112e73	−0.0514112
$821$	−8.81688e73	−0.426152	−0.213076	−	0.977036i	$-0.568348\pi$
$821$	−8.81688e73	−0.426152	−0.213076	+	0.977036i	$0.568348\pi$
$822$	2.46012e74	1.15272
$823$	−1.57751e74	−0.716600	−0.358300	−	0.933606i	$-0.616644\pi$
$823$	−1.57751e74	−0.716600	−0.358300	+	0.933606i	$0.616644\pi$
$824$	2.51861e74	1.10922
$825$	2.49582e74	1.06571
$826$	2.98938e73	0.123763
$827$	4.29357e74	1.72357	0.861784	−	0.507276i	$-0.169347\pi$
$827$	4.29357e74	1.72357	0.861784	+	0.507276i	$0.169347\pi$
$828$	4.56154e73	0.177557
$829$	−4.05215e74	−1.52949	−0.764743	−	0.644336i	$-0.777134\pi$
$829$	−4.05215e74	−1.52949	−0.764743	+	0.644336i	$0.777134\pi$
$830$	−3.48996e73	−0.127741
$831$	4.80601e74	1.70592
$832$	−1.21554e74	−0.418432
$833$	−1.54365e74	−0.515350
$834$	−8.11843e74	−2.62868
$835$	2.09934e74	0.659292
$836$	−1.89638e73	−0.0577651
$837$	−3.17774e74	−0.938898
$838$	2.64431e73	0.0757862
$839$	3.20891e73	0.0892128	0.0446064	−	0.999005i	$-0.485797\pi$
$839$	3.20891e73	0.0892128	0.0446064	+	0.999005i	$0.485797\pi$
$840$	−3.22726e74	−0.870387
$841$	1.27433e74	0.333415
$842$	2.59647e74	0.659061
$843$	−3.30842e74	−0.814738
$844$	−1.71284e72	−0.00409246
$845$	−2.22606e74	−0.516049
$846$	3.86044e74	0.868345
$847$	1.78557e74	0.389717
$848$	8.22542e74	1.74206
$849$	1.41717e74	0.291256
$850$	−2.81889e74	−0.562206
$851$	1.33461e74	0.258315
$852$	7.86966e73	0.147824
$853$	−3.28210e74	−0.598345	−0.299172	−	0.954199i	$-0.596711\pi$
$853$	−3.28210e74	−0.598345	−0.299172	+	0.954199i	$0.596711\pi$
$854$	3.11327e73	0.0550859
$855$	2.70826e74	0.465108
$856$	4.11768e74	0.686391
$857$	−1.05278e75	−1.70344	−0.851719	−	0.523999i	$-0.824440\pi$
$857$	−1.05278e75	−1.70344	−0.851719	+	0.523999i	$0.824440\pi$
$858$	8.39863e74	1.31912
$859$	7.91408e74	1.20663	0.603316	−	0.797502i	$-0.293846\pi$
$859$	7.91408e74	1.20663	0.603316	+	0.797502i	$0.293846\pi$
$860$	−1.06202e74	−0.157189
$861$	−3.84888e74	−0.553036
$862$	−3.35824e74	−0.468465
$863$	−9.98167e74	−1.35185	−0.675924	−	0.736971i	$-0.736255\pi$
$863$	−9.98167e74	−1.35185	−0.675924	+	0.736971i	$0.736255\pi$
$864$	−6.26615e74	−0.823950
$865$	2.25567e74	0.287982
$866$	1.88428e74	0.233582
$867$	3.29406e74	0.396501
$868$	−4.09219e73	−0.0478303
$869$	−1.40549e75	−1.59523
$870$	−1.50586e75	−1.65975
$871$	3.63647e73	0.0389239
$872$	4.43856e72	0.00461393
$873$	3.36694e75	3.39917
$874$	1.34590e74	0.131969
$875$	−8.20062e74	−0.780983
$876$	6.07633e74	0.562065
$877$	8.86567e73	0.0796567	0.0398283	−	0.999207i	$-0.487319\pi$
$877$	8.86567e73	0.0796567	0.0398283	+	0.999207i	$0.487319\pi$
$878$	4.09752e74	0.357611
$879$	8.68732e74	0.736494
$880$	1.24838e75	1.02811
$881$	−4.12425e74	−0.329958	−0.164979	−	0.986297i	$-0.552756\pi$
$881$	−4.12425e74	−0.329958	−0.164979	+	0.986297i	$0.552756\pi$
$882$	−1.51959e75	−1.18107
$883$	−3.74600e74	−0.282859	−0.141429	−	0.989948i	$-0.545170\pi$
$883$	−3.74600e74	−0.282859	−0.141429	+	0.989948i	$0.545170\pi$
$884$	−1.38134e74	−0.101337
$885$	2.92110e74	0.208206
$886$	−5.90253e74	−0.408770
$887$	7.25014e74	0.487859	0.243929	−	0.969793i	$-0.421563\pi$
$887$	7.25014e74	0.487859	0.243929	+	0.969793i	$0.421563\pi$
$888$	−1.45303e75	−0.950042
$889$	2.07652e75	1.31929
$890$	−4.26534e73	−0.0263335
$891$	−4.38562e75	−2.63117
$892$	1.99868e72	0.00116531
$893$	1.65869e74	0.0939840
$894$	3.92040e75	2.15886
$895$	2.47682e75	1.32558
$896$	1.65219e75	0.859423
$897$	−8.68009e74	−0.438851
$898$	−3.72403e75	−1.83007
$899$	9.29336e74	0.443916
$900$	−4.04094e74	−0.187629
$901$	−3.73049e75	−1.68377
$902$	1.26651e75	0.555701
$903$	−3.96420e75	−1.69090
$904$	−2.64309e75	−1.09602
$905$	−2.28007e75	−0.919198
$906$	1.04733e75	0.410500
$907$	2.49801e75	0.951936	0.475968	−	0.879463i	$-0.342098\pi$
$907$	2.49801e75	0.951936	0.475968	+	0.879463i	$0.342098\pi$
$908$	−2.19117e74	−0.0811871
$909$	1.02366e76	3.68789
$910$	−8.83650e74	−0.309546
$911$	4.96282e75	1.69048	0.845240	−	0.534387i	$-0.179457\pi$
$911$	4.96282e75	1.69048	0.845240	+	0.534387i	$0.179457\pi$
$912$	−1.72255e75	−0.570562
$913$	6.24233e74	0.201068
$914$	−2.01446e75	−0.631002
$915$	3.04216e74	0.0926710
$916$	−6.90798e74	−0.204652
$917$	−2.76712e75	−0.797279
$918$	1.04021e76	2.91495
$919$	8.27126e74	0.225437	0.112719	−	0.993627i	$-0.464044\pi$
$919$	8.27126e74	0.225437	0.112719	+	0.993627i	$0.464044\pi$
$920$	−1.09755e75	−0.290961
$921$	−1.14377e76	−2.94930
$922$	−1.15317e75	−0.289238
$923$	−1.04874e75	−0.255874
$924$	−1.18602e75	−0.281487
$925$	−1.18229e75	−0.272967
$926$	4.45744e75	1.00116
$927$	−1.32185e76	−2.88835
$928$	1.83255e75	0.389567
$929$	6.26908e75	1.29659	0.648296	−	0.761389i	$-0.275482\pi$
$929$	6.26908e75	1.29659	0.648296	+	0.761389i	$0.275482\pi$
$930$	−2.74595e75	−0.552558
$931$	−6.52913e74	−0.127832
$932$	7.96816e74	0.151793
$933$	6.44774e75	1.19516
$934$	1.66501e75	0.300311
$935$	−5.66180e75	−0.993707
$936$	6.61829e75	1.13035
$937$	4.04271e75	0.671913	0.335956	−	0.941878i	$-0.390941\pi$
$937$	4.04271e75	0.671913	0.335956	+	0.941878i	$0.390941\pi$
$938$	−3.52643e74	−0.0570378
$939$	−1.12970e75	−0.177824
$940$	2.77914e74	0.0425745
$941$	5.70557e75	0.850675	0.425337	−	0.905035i	$-0.360155\pi$
$941$	5.70557e75	0.850675	0.425337	+	0.905035i	$0.360155\pi$
$942$	−1.78740e76	−2.59373
$943$	−1.30895e75	−0.184874
$944$	−1.30116e75	−0.178873
$945$	9.69005e75	1.29663
$946$	1.30446e76	1.69905
$947$	9.10957e75	1.15498	0.577489	−	0.816399i	$-0.304033\pi$
$947$	9.10957e75	1.15498	0.577489	+	0.816399i	$0.304033\pi$
$948$	3.24934e75	0.401035
$949$	−8.09757e75	−0.972896
$950$	−1.19230e75	−0.139454
$951$	1.01018e76	1.15026
$952$	−6.51966e75	−0.722741
$953$	−8.74403e75	−0.943719	−0.471859	−	0.881674i	$-0.656417\pi$
$953$	−8.74403e75	−0.943719	−0.471859	+	0.881674i	$0.656417\pi$
$954$	−3.67233e76	−3.85886
$955$	−1.00051e76	−1.02361
$956$	−1.70045e75	−0.169390
$957$	2.69345e76	2.61249
$958$	1.08245e76	1.02232
$959$	4.62971e75	0.425774
$960$	1.15184e76	1.03151
$961$	−9.77225e75	−0.852213
$962$	−3.97850e75	−0.337874
$963$	−2.16110e76	−1.78733
$964$	−1.68646e75	−0.135835
$965$	3.06048e75	0.240073
$966$	8.41744e75	0.643077
$967$	8.14685e75	0.606198	0.303099	−	0.952959i	$-0.401979\pi$
$967$	8.14685e75	0.606198	0.303099	+	0.952959i	$0.401979\pi$
$968$	−6.61129e75	−0.479143
$969$	7.81230e75	0.551471
$970$	1.66449e76	1.14446
$971$	−7.24090e75	−0.484956	−0.242478	−	0.970157i	$-0.577960\pi$
$971$	−7.24090e75	−0.484956	−0.242478	+	0.970157i	$0.577960\pi$
$972$	3.75838e75	0.245194
$973$	−1.52781e76	−0.970940
$974$	−8.44405e75	−0.522754
$975$	7.68945e75	0.463743
$976$	−1.35508e75	−0.0796148
$977$	−2.93870e76	−1.68207	−0.841034	−	0.540982i	$-0.818053\pi$
$977$	−2.93870e76	−1.68207	−0.841034	+	0.540982i	$0.818053\pi$
$978$	5.68653e76	3.17107
$979$	7.62922e74	0.0414497
$980$	−1.09395e75	−0.0579074
$981$	−2.32951e74	−0.0120145
$982$	−1.03423e76	−0.519725
$983$	3.52481e76	1.72592	0.862961	−	0.505271i	$-0.168607\pi$
$983$	3.52481e76	1.72592	0.862961	+	0.505271i	$0.168607\pi$
$984$	1.42509e76	0.679937
$985$	−1.02950e76	−0.478633
$986$	−3.04210e76	−1.37820
$987$	1.03737e76	0.457979
$988$	−5.84262e74	−0.0251365
$989$	−1.34817e76	−0.565249
$990$	−5.57353e76	−2.27737
$991$	1.68555e76	0.671218	0.335609	−	0.942001i	$-0.391058\pi$
$991$	1.68555e76	0.671218	0.335609	+	0.942001i	$0.391058\pi$
$992$	3.34169e75	0.129693
$993$	−9.33464e76	−3.53095
$994$	1.01701e76	0.374949
$995$	2.50922e76	0.901676
$996$	−1.44316e75	−0.0505478
$997$	8.12879e75	0.277523	0.138762	−	0.990326i	$-0.455688\pi$
$997$	8.12879e75	0.277523	0.138762	+	0.990326i	$0.455688\pi$
$998$	−1.80722e76	−0.601426
$999$	4.36280e76	1.41529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.52.a.a.1.3	✓	4
3.2	odd	2		9.52.a.b.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.52.a.a.1.3	✓	4	1.1	even	1	trivial
9.52.a.b.1.2		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:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 52 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+5.13381e7 q^{2} +2.68083e12 q^{3} +3.83803e14 q^{4} +4.84667e17 q^{5} +1.37629e20 q^{6} +2.59004e21 q^{7} -9.58994e22 q^{8} +5.03313e24 q^{9} +O(q^{10})\)	\(q+5.13381e7 q^{2} +2.68083e12 q^{3} +3.83803e14 q^{4} +4.84667e17 q^{5} +1.37629e20 q^{6} +2.59004e21 q^{7} -9.58994e22 q^{8} +5.03313e24 q^{9} +2.48819e25 q^{10} -4.45050e26 q^{11} +1.02891e27 q^{12} -1.37117e28 q^{13} +1.32968e29 q^{14} +1.29931e30 q^{15} -5.78755e30 q^{16} +2.62484e31 q^{17} +2.58392e32 q^{18} +1.11022e32 q^{19} +1.86017e32 q^{20} +6.94345e33 q^{21} -2.28480e34 q^{22} +2.36137e34 q^{23} -2.57090e35 q^{24} -2.09187e35 q^{25} -7.03932e35 q^{26} +7.71928e36 q^{27} +9.94066e35 q^{28} -2.25752e37 q^{29} +6.67040e37 q^{30} -4.11662e37 q^{31} -8.11754e37 q^{32} -1.19310e39 q^{33} +1.34754e39 q^{34} +1.25531e39 q^{35} +1.93173e39 q^{36} +5.65183e39 q^{37} +5.69965e39 q^{38} -3.67587e40 q^{39} -4.64793e40 q^{40} -5.54318e40 q^{41} +3.56464e41 q^{42} -5.70927e41 q^{43} -1.70812e41 q^{44} +2.43939e42 q^{45} +1.21229e42 q^{46} +1.49403e42 q^{47} -1.55154e43 q^{48} -5.88095e42 q^{49} -1.07393e43 q^{50} +7.03673e43 q^{51} -5.26259e42 q^{52} -1.42123e44 q^{53} +3.96293e44 q^{54} -2.15701e44 q^{55} -2.48383e44 q^{56} +2.97630e44 q^{57} -1.15897e45 q^{58} +2.24820e44 q^{59} +4.98678e44 q^{60} +2.34137e44 q^{61} -2.11340e45 q^{62} +1.30360e46 q^{63} +8.86500e45 q^{64} -6.64560e45 q^{65} -6.12516e46 q^{66} -2.65209e45 q^{67} +1.00742e46 q^{68} +6.33043e46 q^{69} +6.44450e46 q^{70} +7.64854e46 q^{71} -4.82675e47 q^{72} +5.90560e47 q^{73} +2.90154e47 q^{74} -5.60795e47 q^{75} +4.26105e46 q^{76} -1.15270e48 q^{77} -1.88712e48 q^{78} +3.15804e48 q^{79} -2.80503e48 q^{80} +9.85421e48 q^{81} -2.84576e48 q^{82} -1.40261e48 q^{83} +2.66492e48 q^{84} +1.27217e49 q^{85} -2.93103e49 q^{86} -6.05202e49 q^{87} +4.26801e49 q^{88} -1.71424e48 q^{89} +1.25234e50 q^{90} -3.55138e49 q^{91} +9.06303e48 q^{92} -1.10360e50 q^{93} +7.67005e49 q^{94} +5.38085e49 q^{95} -2.17617e50 q^{96} +6.68956e50 q^{97} -3.01917e50 q^{98} -2.24000e51 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32756040 q^{2} + 403863773040 q^{3} + 79\!\cdots\!12 q^{4}+ \cdots + 50\!\cdots\!28 q^{9}+O(q^{10}) \) 4 * q + 32756040 * q^2 + 403863773040 * q^3 + 7978103470875712 * q^4 + 1214113112967557880 * q^5 - 108315680321506869792 * q^6 + 6566332044151252469600 * q^7 - 139242173294665691205120 * q^8 + 5074459491561912905852628 * q^9	\( 4 q + 32756040 q^{2} + 403863773040 q^{3} + 79\!\cdots\!12 q^{4}+ \cdots - 17\!\cdots\!64 q^{99}+O(q^{100}) \) 4 * q + 32756040 * q^2 + 403863773040 * q^3 + 7978103470875712 * q^4 + 1214113112967557880 * q^5 - 108315680321506869792 * q^6 + 6566332044151252469600 * q^7 - 139242173294665691205120 * q^8 + 5074459491561912905852628 * q^9 - 26338767422633182993407120 * q^10 + 352319730227217761184247248 * q^11 - 4910848780592422991861233920 * q^12 + 30737495492092678036022901080 * q^13 + 116878411871248994844784530624 * q^14 + 1476946034741298295968992105760 * q^15 + 13655541308212814904424583532544 * q^16 + 48152025926602119975132578130120 * q^17 + 730659964110731978584225137598440 * q^18 + 817578654717102241686587953106480 * q^19 + 6688106698568613691058684703008640 * q^20 + 3140470390068165005119691106219648 * q^21 - 34873949046188270313389204382330720 * q^22 - 54442545328795748403982512519744480 * q^23 - 870683087493887261435021390762280960 * q^24 - 577962011134461749109509927876368100 * q^25 + 1509847347916659653711306190553689648 * q^26 + 3642253118748703704235871670153325920 * q^27 + 34411298173690719862562837156054996480 * q^28 + 24524817706178324469842039147126378520 * q^29 - 32614789988834827956259093871049954240 * q^30 - 74015080632891216448581759119415494272 * q^31 - 698885110517892283834830116511622594560 * q^32 - 1724079406359609582394466902199988121920 * q^33 + 599176354190711613816800945566309634064 * q^34 + 5459558934032100428649177266758776617280 * q^35 + 12554754321544086227706882021196271755584 * q^36 + 9223299799194559520674909690367653437560 * q^37 + 42209741287618122996397532876280940717920 * q^38 - 118792897816045747959690882363116779819104 * q^39 - 260218563144774091908833544090781982745600 * q^40 + 146626572441904135431040424870320811649768 * q^41 - 394089552887565758770180664977333719386880 * q^42 - 383253403750663564628750277915860311246000 * q^43 + 3919911265019437916289330658643948094246144 * q^44 + 2545472464534636601491522253941835784995160 * q^45 - 687622182810100175391810298681828635813312 * q^46 + 703242125794576181922406089648904926204480 * q^47 - 19921513489914046905912799321356910879457280 * q^48 - 21525353693695885888621049774661370126875228 * q^49 - 65550763083377103476240548536052846777230600 * q^50 + 69226097223174646745938497201257873367925728 * q^51 + 205575224727950383449569813934278240424406400 * q^52 - 46053881458574871528873628680364599519093960 * q^53 + 294401161348635890022909617885475632448012480 * q^54 + 288271437023082169121432211103105268991934560 * q^55 - 718413197664523425962520880364481249783828480 * q^56 - 887307836446731380883329853535980442723450560 * q^57 - 3260382815057328392932619475690091710393763920 * q^58 + 1119164779584192618652811959209270069996506640 * q^59 + 558043767811514977207202989845983481019937280 * q^60 + 3426848506305498355799302542081826532801316248 * q^61 + 9652948821672246376570757837225648817671719680 * q^62 + 21868523123734055667483988685251699312704411360 * q^63 - 3410402571656263891001355509990182780636233728 * q^64 + 10662663070585071183633914150857043524084084560 * q^65 - 156984231778185739728164366214465838456423999104 * q^66 + 30875136607724238160818607702139418169238276720 * q^67 - 92264980123003683860202361552579885626636888960 * q^68 + 156020595717735931080084316999827890833385237376 * q^69 - 127365497175284237875848441551548839150619662720 * q^70 + 396890633217178572952249989093970445513163336288 * q^71 + 501925030461922074943170888284533271860697602560 * q^72 + 1093181650202404127682760092563948835468903177320 * q^73 - 2446722614206037598896806276944107193380656941456 * q^74 + 724518911321762179312399215417368596720139638800 * q^75 - 1930298057964975808050160660816178333985982024960 * q^76 + 1379856740595107958858322062475643650952236464000 * q^77 - 9605787792912264070639160177141351698750561924800 * q^78 + 4057123342028363124154537966955503984273281629120 * q^79 + 6556705282035289158041818706914507044939664711680 * q^80 + 15818800845095699867974190511543023822607553099044 * q^81 + 2672741123252406904410297531162443665031405248080 * q^82 + 10514534101014085301175610601927458547806407366960 * q^83 - 18556852372864802601211458682882537051712984979456 * q^84 - 2214700921000481207852358003497850667551075883920 * q^85 - 43819383990098235110217468422860464230535375092832 * q^86 - 62935773893168085248047945604687939397070771225440 * q^87 - 25053936600673669378312978656608794916631597373440 * q^88 - 90777724780188979543741952283884054816841444724440 * q^89 + 319517252743833422678369782889855912186560337690160 * q^90 + 100567720661332633308233017957549269313038849882688 * q^91 + 192025202572015319809189966047000799088692638097920 * q^92 - 311055180320633222090977351600473435943779435025920 * q^93 + 639818007616166555781273040037466169910601363859584 * q^94 - 418719878951800677902105757696028542296429654882400 * q^95 - 246297662740859333859245239975410493322197215608832 * q^96 - 1321788056943507607869460465290134726019322989433720 * q^97 - 317844097908560926995320900303041587618753340105080 * q^98 - 1718121773684708507245882236398410835742486542126064 * q^99

Introduction

L-functions

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