LMFDB - Embedded newform 1.52.a.a.1.1

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			1.1
Root			$-457245.$ 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)

$f(q)$	$=$	$q-8.71140e7 q^{2} +6.49653e11 q^{3} +5.33705e15 q^{4} +8.70295e17 q^{5} -5.65939e19 q^{6} +3.14283e21 q^{7} -2.68769e23 q^{8} -1.73165e24 q^{9} +O(q^{10})$	\(q-8.71140e7 q^{2} +6.49653e11 q^{3} +5.33705e15 q^{4} +8.70295e17 q^{5} -5.65939e19 q^{6} +3.14283e21 q^{7} -2.68769e23 q^{8} -1.73165e24 q^{9} -7.58149e25 q^{10} +4.69985e26 q^{11} +3.46723e27 q^{12} +9.04757e27 q^{13} -2.73785e29 q^{14} +5.65389e29 q^{15} +1.13956e31 q^{16} -1.94276e30 q^{17} +1.50851e32 q^{18} -2.88440e32 q^{19} +4.64481e33 q^{20} +2.04175e33 q^{21} -4.09423e34 q^{22} +1.73996e34 q^{23} -1.74606e35 q^{24} +3.13324e35 q^{25} -7.88170e35 q^{26} -2.52412e36 q^{27} +1.67734e37 q^{28} +2.51798e37 q^{29} -4.92533e37 q^{30} -3.39978e37 q^{31} -3.87499e38 q^{32} +3.05327e38 q^{33} +1.69241e38 q^{34} +2.73519e39 q^{35} -9.24188e39 q^{36} +1.41519e40 q^{37} +2.51271e40 q^{38} +5.87778e39 q^{39} -2.33908e41 q^{40} +1.62359e41 q^{41} -1.77865e41 q^{42} -1.06168e41 q^{43} +2.50834e42 q^{44} -1.50704e42 q^{45} -1.51575e42 q^{46} -2.33100e42 q^{47} +7.40315e42 q^{48} -2.71188e42 q^{49} -2.72949e43 q^{50} -1.26212e42 q^{51} +4.82874e43 q^{52} -5.52737e43 q^{53} +2.19886e44 q^{54} +4.09026e44 q^{55} -8.44695e44 q^{56} -1.87386e44 q^{57} -2.19351e45 q^{58} +2.66580e45 q^{59} +3.01751e45 q^{60} -3.00082e45 q^{61} +2.96168e45 q^{62} -5.44227e45 q^{63} +8.09610e45 q^{64} +7.87405e45 q^{65} -2.65983e46 q^{66} +1.24565e45 q^{67} -1.03686e46 q^{68} +1.13037e46 q^{69} -2.38273e47 q^{70} +2.67507e47 q^{71} +4.65412e47 q^{72} +4.01968e47 q^{73} -1.23283e48 q^{74} +2.03552e47 q^{75} -1.53942e48 q^{76} +1.47708e48 q^{77} -5.12037e47 q^{78} -3.09063e48 q^{79} +9.91749e48 q^{80} +2.08963e48 q^{81} -1.41437e49 q^{82} +1.48588e48 q^{83} +1.08969e49 q^{84} -1.69077e48 q^{85} +9.24873e48 q^{86} +1.63581e49 q^{87} -1.26317e50 q^{88} -1.49141e49 q^{89} +1.31284e50 q^{90} +2.84350e49 q^{91} +9.28627e49 q^{92} -2.20867e49 q^{93} +2.03063e50 q^{94} -2.51028e50 q^{95} -2.51740e50 q^{96} -5.46477e50 q^{97} +2.36242e50 q^{98} -8.13847e50 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−8.71140e7	−1.83579	−0.917895	−	0.396823i	$-0.870113\pi$
$2$	−8.71140e7	−1.83579	−0.917895	+	0.396823i	$0.870113\pi$
$3$	6.49653e11	0.442679	0.221340	−	0.975197i	$-0.428957\pi$
$3$	6.49653e11	0.442679	0.221340	+	0.975197i	$0.428957\pi$
$4$	5.33705e15	2.37013
$5$	8.70295e17	1.30596	0.652982	−	0.757373i	$-0.273518\pi$
$5$	8.70295e17	1.30596	0.652982	+	0.757373i	$0.273518\pi$
$6$	−5.65939e19	−0.812667
$7$	3.14283e21	0.885770	0.442885	−	0.896578i	$-0.353955\pi$
$7$	3.14283e21	0.885770	0.442885	+	0.896578i	$0.353955\pi$
$8$	−2.68769e23	−2.51527
$9$	−1.73165e24	−0.804035
$10$	−7.58149e25	−2.39748
$11$	4.69985e26	1.30789	0.653944	−	0.756543i	$-0.273113\pi$
$11$	4.69985e26	1.30789	0.653944	+	0.756543i	$0.273113\pi$
$12$	3.46723e27	1.04921
$13$	9.04757e27	0.355612	0.177806	−	0.984066i	$-0.443100\pi$
$13$	9.04757e27	0.355612	0.177806	+	0.984066i	$0.443100\pi$
$14$	−2.73785e29	−1.62609
$15$	5.65389e29	0.578123
$16$	1.13956e31	2.24738
$17$	−1.94276e30	−0.0816527	−0.0408264	−	0.999166i	$-0.512999\pi$
$17$	−1.94276e30	−0.0816527	−0.0408264	+	0.999166i	$0.512999\pi$
$18$	1.50851e32	1.47604
$19$	−2.88440e32	−0.710949	−0.355474	−	0.934686i	$-0.615681\pi$
$19$	−2.88440e32	−0.710949	−0.355474	+	0.934686i	$0.615681\pi$
$20$	4.64481e33	3.09530
$21$	2.04175e33	0.392112
$22$	−4.09423e34	−2.40101
$23$	1.73996e34	0.328458	0.164229	−	0.986422i	$-0.447486\pi$
$23$	1.73996e34	0.328458	0.164229	+	0.986422i	$0.447486\pi$
$24$	−1.74606e35	−1.11346
$25$	3.13324e35	0.705542
$26$	−7.88170e35	−0.652829
$27$	−2.52412e36	−0.798609
$28$	1.67734e37	2.09939
$29$	2.51798e37	1.28796	0.643980	−	0.765042i	$-0.277282\pi$
$29$	2.51798e37	1.28796	0.643980	+	0.765042i	$0.277282\pi$
$30$	−4.92533e37	−1.06131
$31$	−3.39978e37	−0.317488	−0.158744	−	0.987320i	$-0.550744\pi$
$31$	−3.39978e37	−0.317488	−0.158744	+	0.987320i	$0.550744\pi$
$32$	−3.87499e38	−1.61045
$33$	3.05327e38	0.578975
$34$	1.69241e38	0.149897
$35$	2.73519e39	1.15678
$36$	−9.24188e39	−1.90567
$37$	1.41519e40	1.45101	0.725506	−	0.688216i	$-0.241606\pi$
$37$	1.41519e40	1.45101	0.725506	+	0.688216i	$0.241606\pi$
$38$	2.51271e40	1.30515
$39$	5.87778e39	0.157422
$40$	−2.33908e41	−3.28485
$41$	1.62359e41	1.21475	0.607375	−	0.794415i	$-0.292222\pi$
$41$	1.62359e41	1.21475	0.607375	+	0.794415i	$0.292222\pi$
$42$	−1.77865e41	−0.719835
$43$	−1.06168e41	−0.235802	−0.117901	−	0.993025i	$-0.537617\pi$
$43$	−1.06168e41	−0.235802	−0.117901	+	0.993025i	$0.537617\pi$
$44$	2.50834e42	3.09986
$45$	−1.50704e42	−1.05004
$46$	−1.51575e42	−0.602980
$47$	−2.33100e42	−0.535854	−0.267927	−	0.963439i	$-0.586339\pi$
$47$	−2.33100e42	−0.535854	−0.267927	+	0.963439i	$0.586339\pi$
$48$	7.40315e42	0.994867
$49$	−2.71188e42	−0.215412
$50$	−2.72949e43	−1.29523
$51$	−1.26212e42	−0.0361460
$52$	4.82874e43	0.842846
$53$	−5.52737e43	−0.593587	−0.296793	−	0.954942i	$-0.595917\pi$
$53$	−5.52737e43	−0.593587	−0.296793	+	0.954942i	$0.595917\pi$
$54$	2.19886e44	1.46608
$55$	4.09026e44	1.70805
$56$	−8.44695e44	−2.22795
$57$	−1.87386e44	−0.314722
$58$	−2.19351e45	−2.36443
$59$	2.66580e45	1.85824	0.929119	−	0.369782i	$-0.120567\pi$
$59$	2.66580e45	1.85824	0.929119	+	0.369782i	$0.120567\pi$
$60$	3.01751e45	1.37023
$61$	−3.00082e45	−0.893983	−0.446992	−	0.894538i	$-0.647505\pi$
$61$	−3.00082e45	−0.893983	−0.446992	+	0.894538i	$0.647505\pi$
$62$	2.96168e45	0.582842
$63$	−5.44227e45	−0.712190
$64$	8.09610e45	0.709066
$65$	7.87405e45	0.464417
$66$	−2.65983e46	−1.06288
$67$	1.24565e45	0.0339224	0.0169612	−	0.999856i	$-0.494601\pi$
$67$	1.24565e45	0.0339224	0.0169612	+	0.999856i	$0.494601\pi$
$68$	−1.03686e46	−0.193527
$69$	1.13037e46	0.145402
$70$	−2.38273e47	−2.12361
$71$	2.67507e47	1.66053	0.830266	−	0.557368i	$-0.188189\pi$
$71$	2.67507e47	1.66053	0.830266	+	0.557368i	$0.188189\pi$
$72$	4.65412e47	2.02236
$73$	4.01968e47	1.22874	0.614368	−	0.789020i	$-0.289411\pi$
$73$	4.01968e47	1.22874	0.614368	+	0.789020i	$0.289411\pi$
$74$	−1.23283e48	−2.66376
$75$	2.03552e47	0.312329
$76$	−1.53942e48	−1.68504
$77$	1.47708e48	1.15849
$78$	−5.12037e47	−0.288994
$79$	−3.09063e48	−1.26054	−0.630269	−	0.776377i	$-0.717056\pi$
$79$	−3.09063e48	−1.26054	−0.630269	+	0.776377i	$0.717056\pi$
$80$	9.91749e48	2.93499
$81$	2.08963e48	0.450507
$82$	−1.41437e49	−2.23003
$83$	1.48588e48	0.171986	0.0859929	−	0.996296i	$-0.472594\pi$
$83$	1.48588e48	0.171986	0.0859929	+	0.996296i	$0.472594\pi$
$84$	1.08969e49	0.929355
$85$	−1.69077e48	−0.106636
$86$	9.24873e48	0.432884
$87$	1.63581e49	0.570153
$88$	−1.26317e50	−3.28969
$89$	−1.49141e49	−0.291173	−0.145587	−	0.989346i	$-0.546507\pi$
$89$	−1.49141e49	−0.291173	−0.145587	+	0.989346i	$0.546507\pi$
$90$	1.31284e50	1.92766
$91$	2.84350e49	0.314990
$92$	9.28627e49	0.778487
$93$	−2.20867e49	−0.140545
$94$	2.03063e50	0.983716
$95$	−2.51028e50	−0.928473
$96$	−2.51740e50	−0.712911
$97$	−5.46477e50	−1.18821	−0.594105	−	0.804388i	$-0.702494\pi$
$97$	−5.46477e50	−1.18821	−0.594105	+	0.804388i	$0.702494\pi$
$98$	2.36242e50	0.395451
$99$	−8.13847e50	−1.05159
$100$	1.67223e51	1.67223
$101$	1.57367e51	1.22101	0.610503	−	0.792014i	$-0.290968\pi$
$101$	1.57367e51	1.22101	0.610503	+	0.792014i	$0.290968\pi$
$102$	1.09948e50	0.0663564
$103$	−2.10363e51	−0.989966	−0.494983	−	0.868903i	$-0.664826\pi$
$103$	−2.10363e51	−0.989966	−0.494983	+	0.868903i	$0.664826\pi$
$104$	−2.43170e51	−0.894459
$105$	1.77692e51	0.512084
$106$	4.81512e51	1.08970
$107$	2.77520e51	0.494319	0.247160	−	0.968975i	$-0.420503\pi$
$107$	2.77520e51	0.494319	0.247160	+	0.968975i	$0.420503\pi$
$108$	−1.34714e52	−1.89281
$109$	1.47283e52	1.63597	0.817986	−	0.575238i	$-0.195091\pi$
$109$	1.47283e52	1.63597	0.817986	+	0.575238i	$0.195091\pi$
$110$	−3.56319e52	−3.13563
$111$	9.19383e51	0.642333
$112$	3.58143e52	1.99066
$113$	−3.63164e52	−1.60917	−0.804586	−	0.593836i	$-0.797613\pi$
$113$	−3.63164e52	−1.60917	−0.804586	+	0.593836i	$0.797613\pi$
$114$	1.63239e52	0.577764
$115$	1.51428e52	0.428954
$116$	1.34386e53	3.05263
$117$	−1.56672e52	−0.285925
$118$	−2.32229e53	−3.41134
$119$	−6.10575e51	−0.0723255
$120$	−1.51959e53	−1.45413
$121$	9.17560e52	0.710571
$122$	2.61414e53	1.64117
$123$	1.05477e53	0.537745
$124$	−1.81448e53	−0.752487
$125$	−1.13805e53	−0.384551
$126$	4.74098e53	1.30743
$127$	−2.33329e53	−0.525986	−0.262993	−	0.964798i	$-0.584710\pi$
$127$	−2.33329e53	−0.525986	−0.262993	+	0.964798i	$0.584710\pi$
$128$	1.67287e53	0.308750
$129$	−6.89724e52	−0.104385
$130$	−6.85940e53	−0.852572
$131$	−3.64141e53	−0.372264	−0.186132	−	0.982525i	$-0.559595\pi$
$131$	−3.64141e53	−0.372264	−0.186132	+	0.982525i	$0.559595\pi$
$132$	1.62955e54	1.37224
$133$	−9.06517e53	−0.629737
$134$	−1.08513e53	−0.0622745
$135$	−2.19673e54	−1.04295
$136$	5.22152e53	0.205378
$137$	−4.42139e53	−0.144273	−0.0721364	−	0.997395i	$-0.522982\pi$
$137$	−4.42139e53	−0.144273	−0.0721364	+	0.997395i	$0.522982\pi$
$138$	−9.84711e53	−0.266927
$139$	6.82260e54	1.53841	0.769205	−	0.639002i	$-0.220652\pi$
$139$	6.82260e54	1.53841	0.769205	+	0.639002i	$0.220652\pi$
$140$	1.45978e55	2.74172
$141$	−1.51434e54	−0.237212
$142$	−2.33036e55	−3.04839
$143$	4.25222e54	0.465101
$144$	−1.97331e55	−1.80697
$145$	2.19138e55	1.68203
$146$	−3.50170e55	−2.25570
$147$	−1.76178e54	−0.0953584
$148$	7.55295e55	3.43908
$149$	−1.19546e55	−0.458441	−0.229221	−	0.973374i	$-0.573618\pi$
$149$	−1.19546e55	−0.458441	−0.229221	+	0.973374i	$0.573618\pi$
$150$	−1.77322e55	−0.573371
$151$	−1.21853e55	−0.332602	−0.166301	−	0.986075i	$-0.553182\pi$
$151$	−1.21853e55	−0.332602	−0.166301	+	0.986075i	$0.553182\pi$
$152$	7.75236e55	1.78823
$153$	3.36416e54	0.0656516
$154$	−1.28675e56	−2.12674
$155$	−2.95881e55	−0.414628
$156$	3.13700e55	0.373110
$157$	−3.87399e55	−0.391487	−0.195743	−	0.980655i	$-0.562712\pi$
$157$	−3.87399e55	−0.391487	−0.195743	+	0.980655i	$0.562712\pi$
$158$	2.69237e56	2.31409
$159$	−3.59087e55	−0.262768
$160$	−3.37238e56	−2.10319
$161$	5.46840e55	0.290938
$162$	−1.82036e56	−0.827037
$163$	−1.93511e56	−0.751487	−0.375743	−	0.926724i	$-0.622613\pi$
$163$	−1.93511e56	−0.751487	−0.375743	+	0.926724i	$0.622613\pi$
$164$	8.66517e56	2.87911
$165$	2.65724e56	0.756120
$166$	−1.29441e56	−0.315730
$167$	2.83095e56	0.592463	0.296232	−	0.955116i	$-0.404270\pi$
$167$	2.83095e56	0.592463	0.296232	+	0.955116i	$0.404270\pi$
$168$	−5.48758e56	−0.986266
$169$	−5.65449e56	−0.873540
$170$	1.47290e56	0.195760
$171$	4.99475e56	0.571628
$172$	−5.66625e56	−0.558882
$173$	−2.17979e57	−1.85455	−0.927275	−	0.374380i	$-0.877856\pi$
$173$	−2.17979e57	−1.85455	−0.927275	+	0.374380i	$0.877856\pi$
$174$	−1.42502e57	−1.04668
$175$	9.84723e56	0.624948
$176$	5.35574e57	2.93932
$177$	1.73184e57	0.822603
$178$	1.29923e57	0.534533
$179$	4.26922e56	0.152264	0.0761319	−	0.997098i	$-0.475743\pi$
$179$	4.26922e56	0.152264	0.0761319	+	0.997098i	$0.475743\pi$
$180$	−8.04316e57	−2.48873
$181$	2.18558e57	0.587168	0.293584	−	0.955933i	$-0.405152\pi$
$181$	2.18558e57	0.587168	0.293584	+	0.955933i	$0.405152\pi$
$182$	−2.47708e57	−0.578256
$183$	−1.94949e57	−0.395748
$184$	−4.67647e57	−0.826160
$185$	1.23163e58	1.89497
$186$	1.92407e57	0.258012
$187$	−9.13066e56	−0.106793
$188$	−1.24407e58	−1.27004
$189$	−7.93288e57	−0.707384
$190$	2.18680e58	1.70448
$191$	−1.12224e58	−0.765130	−0.382565	−	0.923929i	$-0.624959\pi$
$191$	−1.12224e58	−0.765130	−0.382565	+	0.923929i	$0.624959\pi$
$192$	5.25965e57	0.313889
$193$	−1.46948e58	−0.768159	−0.384080	−	0.923300i	$-0.625481\pi$
$193$	−1.46948e58	−0.768159	−0.384080	+	0.923300i	$0.625481\pi$
$194$	4.76058e58	2.18130
$195$	5.11540e57	0.205588
$196$	−1.44734e58	−0.510554
$197$	−3.80845e58	−1.17994	−0.589969	−	0.807426i	$-0.700860\pi$
$197$	−3.80845e58	−1.17994	−0.589969	+	0.807426i	$0.700860\pi$
$198$	7.08975e58	1.93050
$199$	−2.34549e58	−0.561669	−0.280834	−	0.959756i	$-0.590611\pi$
$199$	−2.34549e58	−0.561669	−0.280834	+	0.959756i	$0.590611\pi$
$200$	−8.42116e58	−1.77463
$201$	8.09237e56	0.0150168
$202$	−1.37088e59	−2.24151
$203$	7.91357e58	1.14084
$204$	−6.73598e57	−0.0856705
$205$	1.41300e59	1.58642
$206$	1.83256e59	1.81737
$207$	−3.01300e58	−0.264092
$208$	1.03102e59	0.799194
$209$	−1.35562e59	−0.929841
$210$	−1.54795e59	−0.940079
$211$	6.94465e58	0.373635	0.186818	−	0.982395i	$-0.440183\pi$
$211$	6.94465e58	0.373635	0.186818	+	0.982395i	$0.440183\pi$
$212$	−2.94999e59	−1.40688
$213$	1.73787e59	0.735083
$214$	−2.41759e59	−0.907466
$215$	−9.23975e58	−0.307950
$216$	6.78405e59	2.00872
$217$	−1.06849e59	−0.281221
$218$	−1.28304e60	−3.00330
$219$	2.61140e59	0.543936
$220$	2.18299e60	4.04831
$221$	−1.75772e58	−0.0290367
$222$	−8.00911e59	−1.17919
$223$	−7.27716e59	−0.955406	−0.477703	−	0.878521i	$-0.658530\pi$
$223$	−7.27716e59	−0.955406	−0.477703	+	0.878521i	$0.658530\pi$
$224$	−1.21784e60	−1.42648
$225$	−5.42566e59	−0.567281
$226$	3.16367e60	2.95410
$227$	1.77581e60	1.48162	0.740809	−	0.671716i	$-0.234442\pi$
$227$	1.77581e60	1.48162	0.740809	+	0.671716i	$0.234442\pi$
$228$	−1.00009e60	−0.745932
$229$	−5.95206e59	−0.397066	−0.198533	−	0.980094i	$-0.563618\pi$
$229$	−5.95206e59	−0.397066	−0.198533	+	0.980094i	$0.563618\pi$
$230$	−1.31915e60	−0.787470
$231$	9.59591e59	0.512838
$232$	−6.76753e60	−3.23957
$233$	−5.94034e59	−0.254821	−0.127410	−	0.991850i	$-0.540667\pi$
$233$	−5.94034e59	−0.254821	−0.127410	+	0.991850i	$0.540667\pi$
$234$	1.36483e60	0.524898
$235$	−2.02866e60	−0.699806
$236$	1.42275e61	4.40426
$237$	−2.00784e60	−0.558014
$238$	5.31896e59	0.132774
$239$	−6.11275e60	−1.37117	−0.685583	−	0.727995i	$-0.740453\pi$
$239$	−6.11275e60	−1.37117	−0.685583	+	0.727995i	$0.740453\pi$
$240$	6.44292e60	1.29926
$241$	5.01746e60	0.910016	0.455008	−	0.890487i	$-0.349636\pi$
$241$	5.01746e60	0.910016	0.455008	+	0.890487i	$0.349636\pi$
$242$	−7.99324e60	−1.30446
$243$	6.79372e60	0.998039
$244$	−1.60155e61	−2.11885
$245$	−2.36013e60	−0.281320
$246$	−9.18850e60	−0.987187
$247$	−2.60968e60	−0.252822
$248$	9.13754e60	0.798567
$249$	9.65307e59	0.0761346
$250$	9.91397e60	0.705956
$251$	2.83094e61	1.82075	0.910376	−	0.413783i	$-0.135793\pi$
$251$	2.83094e61	1.82075	0.910376	+	0.413783i	$0.135793\pi$
$252$	−2.90457e61	−1.68798
$253$	8.17756e60	0.429586
$254$	2.03263e61	0.965601
$255$	−1.09841e60	−0.0472053
$256$	−3.28038e61	−1.27587
$257$	−2.64892e61	−0.932769	−0.466384	−	0.884582i	$-0.654444\pi$
$257$	−2.64892e61	−0.932769	−0.466384	+	0.884582i	$0.654444\pi$
$258$	6.00846e60	0.191629
$259$	4.44771e61	1.28526
$260$	4.20242e61	1.10073
$261$	−4.36024e61	−1.03557
$262$	3.17217e61	0.683399
$263$	−3.49990e61	−0.684201	−0.342101	−	0.939663i	$-0.611138\pi$
$263$	−3.49990e61	−0.684201	−0.342101	+	0.939663i	$0.611138\pi$
$264$	−8.20624e61	−1.45628
$265$	−4.81044e61	−0.775203
$266$	7.89703e61	1.15606
$267$	−9.68897e60	−0.128896
$268$	6.64808e60	0.0804005
$269$	−1.25062e62	−1.37544	−0.687718	−	0.725978i	$-0.741388\pi$
$269$	−1.25062e62	−1.37544	−0.687718	+	0.725978i	$0.741388\pi$
$270$	1.91366e62	1.91465
$271$	8.34364e61	0.759694	0.379847	−	0.925049i	$-0.375977\pi$
$271$	8.34364e61	0.759694	0.379847	+	0.925049i	$0.375977\pi$
$272$	−2.21388e61	−0.183504
$273$	1.84729e61	0.139440
$274$	3.85165e61	0.264855
$275$	1.47257e62	0.922770
$276$	6.03285e61	0.344620
$277$	7.61658e61	0.396758	0.198379	−	0.980125i	$-0.436432\pi$
$277$	7.61658e61	0.396758	0.198379	+	0.980125i	$0.436432\pi$
$278$	−5.94344e62	−2.82420
$279$	5.88721e61	0.255272
$280$	−7.35133e62	−2.90962
$281$	1.57065e61	0.0567634	0.0283817	−	0.999597i	$-0.490965\pi$
$281$	1.57065e61	0.0567634	0.0283817	+	0.999597i	$0.490965\pi$
$282$	1.31920e62	0.435471
$283$	−2.43727e61	−0.0735104	−0.0367552	−	0.999324i	$-0.511702\pi$
$283$	−2.43727e61	−0.0735104	−0.0367552	+	0.999324i	$0.511702\pi$
$284$	1.42770e63	3.93567
$285$	−1.63081e62	−0.411016
$286$	−3.70428e62	−0.853828
$287$	5.10266e62	1.07599
$288$	6.71011e62	1.29486
$289$	−5.62328e62	−0.993333
$290$	−1.90900e63	−3.08786
$291$	−3.55020e62	−0.525996
$292$	2.14532e63	2.91226
$293$	−3.92051e62	−0.487773	−0.243887	−	0.969804i	$-0.578422\pi$
$293$	−3.92051e62	−0.487773	−0.243887	+	0.969804i	$0.578422\pi$
$294$	1.53475e62	0.175058
$295$	2.32003e63	2.42679
$296$	−3.80359e63	−3.64968
$297$	−1.18630e63	−1.04449
$298$	1.04141e63	0.841602
$299$	1.57424e62	0.116804
$300$	1.08637e63	0.740259
$301$	−3.33668e62	−0.208867
$302$	1.06151e63	0.610588
$303$	1.02234e63	0.540514
$304$	−3.28693e63	−1.59777
$305$	−2.61160e63	−1.16751
$306$	−2.93066e62	−0.120523
$307$	3.00029e63	1.13536	0.567682	−	0.823248i	$-0.307840\pi$
$307$	3.00029e63	1.13536	0.567682	+	0.823248i	$0.307840\pi$
$308$	7.88327e63	2.74576
$309$	−1.36663e63	−0.438237
$310$	2.57754e63	0.761170
$311$	−2.05385e63	−0.558700	−0.279350	−	0.960189i	$-0.590119\pi$
$311$	−2.05385e63	−0.558700	−0.279350	+	0.960189i	$0.590119\pi$
$312$	−1.57976e63	−0.395959
$313$	−3.26529e63	−0.754295	−0.377147	−	0.926153i	$-0.623095\pi$
$313$	−3.26529e63	−0.754295	−0.377147	+	0.926153i	$0.623095\pi$
$314$	3.37479e63	0.718688
$315$	−4.73638e63	−0.930094
$316$	−1.64949e64	−2.98764
$317$	−2.33370e63	−0.389972	−0.194986	−	0.980806i	$-0.562466\pi$
$317$	−2.33370e63	−0.389972	−0.194986	+	0.980806i	$0.562466\pi$
$318$	3.12815e63	0.482388
$319$	1.18341e64	1.68451
$320$	7.04599e63	0.926014
$321$	1.80291e63	0.218825
$322$	−4.76375e63	−0.534101
$323$	5.60368e62	0.0580509
$324$	1.11525e64	1.06776
$325$	2.83482e63	0.250899
$326$	1.68575e64	1.37957
$327$	9.56825e63	0.724211
$328$	−4.36369e64	−3.05542
$329$	−7.32593e63	−0.474644
$330$	−2.31483e64	−1.38808
$331$	3.40604e64	1.89076	0.945378	−	0.325977i	$-0.105693\pi$
$331$	3.40604e64	1.89076	0.945378	+	0.325977i	$0.105693\pi$
$332$	7.93023e63	0.407628
$333$	−2.45061e64	−1.16666
$334$	−2.46615e64	−1.08764
$335$	1.08408e63	0.0443015
$336$	2.32668e64	0.881223
$337$	2.02190e64	0.709899	0.354949	−	0.934885i	$-0.384498\pi$
$337$	2.02190e64	0.709899	0.354949	+	0.934885i	$0.384498\pi$
$338$	4.92586e64	1.60364
$339$	−2.35930e64	−0.712347
$340$	−9.02373e63	−0.252740
$341$	−1.59784e64	−0.415239
$342$	−4.35113e64	−1.04939
$343$	−4.80889e64	−1.07658
$344$	2.85347e64	0.593106
$345$	9.83755e63	0.189889
$346$	1.89890e65	3.40457
$347$	−9.66734e64	−1.61029	−0.805147	−	0.593075i	$-0.797914\pi$
$347$	−9.66734e64	−1.61029	−0.805147	+	0.593075i	$0.797914\pi$
$348$	8.73040e64	1.35134
$349$	5.19371e64	0.747187	0.373594	−	0.927593i	$-0.378126\pi$
$349$	5.19371e64	0.747187	0.373594	+	0.927593i	$0.378126\pi$
$350$	−8.57832e64	−1.14727
$351$	−2.28372e64	−0.283995
$352$	−1.82119e65	−2.10628
$353$	−3.23561e64	−0.348097	−0.174049	−	0.984737i	$-0.555685\pi$
$353$	−3.23561e64	−0.348097	−0.174049	+	0.984737i	$0.555685\pi$
$354$	−1.50868e65	−1.51013
$355$	2.32810e65	2.16859
$356$	−7.95972e64	−0.690117
$357$	−3.96662e63	−0.0320170
$358$	−3.71909e64	−0.279524
$359$	2.12862e63	0.0149001	0.00745005	−	0.999972i	$-0.497629\pi$
$359$	2.12862e63	0.0149001	0.00745005	+	0.999972i	$0.497629\pi$
$360$	4.05046e65	2.64113
$361$	−8.14040e64	−0.494552
$362$	−1.90394e65	−1.07792
$363$	5.96095e64	0.314555
$364$	1.51759e65	0.746567
$365$	3.49831e65	1.60468
$366$	1.69828e65	0.726510
$367$	−3.44041e65	−1.37286	−0.686429	−	0.727196i	$-0.740823\pi$
$367$	−3.44041e65	−1.37286	−0.686429	+	0.727196i	$0.740823\pi$
$368$	1.98278e65	0.738169
$369$	−2.81148e65	−0.976702
$370$	−1.07293e66	−3.47877
$371$	−1.73716e65	−0.525781
$372$	−1.17878e65	−0.333110
$373$	6.74887e65	1.78097	0.890484	−	0.455015i	$-0.150366\pi$
$373$	6.74887e65	1.78097	0.890484	+	0.455015i	$0.150366\pi$
$374$	7.95408e64	0.196049
$375$	−7.39334e64	−0.170233
$376$	6.26500e65	1.34782
$377$	2.27816e65	0.458014
$378$	6.91065e65	1.29861
$379$	−2.27327e65	−0.399348	−0.199674	−	0.979862i	$-0.563988\pi$
$379$	−2.27327e65	−0.399348	−0.199674	+	0.979862i	$0.563988\pi$
$380$	−1.33975e66	−2.20060
$381$	−1.51583e65	−0.232843
$382$	9.77629e65	1.40462
$383$	−1.15048e66	−1.54637	−0.773183	−	0.634183i	$-0.781336\pi$
$383$	−1.15048e66	−1.54637	−0.773183	+	0.634183i	$0.781336\pi$
$384$	1.08678e65	0.136677
$385$	1.28550e66	1.51294
$386$	1.28012e66	1.41018
$387$	1.83845e65	0.189593
$388$	−2.91658e66	−2.81621
$389$	7.64966e65	0.691715	0.345857	−	0.938287i	$-0.387588\pi$
$389$	7.64966e65	0.691715	0.345857	+	0.938287i	$0.387588\pi$
$390$	−4.45623e65	−0.377416
$391$	−3.38032e64	−0.0268195
$392$	7.28868e65	0.541819
$393$	−2.36565e65	−0.164794
$394$	3.31769e66	2.16612
$395$	−2.68976e66	−1.64622
$396$	−4.34355e66	−2.49240
$397$	−1.60215e66	−0.862074	−0.431037	−	0.902334i	$-0.641852\pi$
$397$	−1.60215e66	−0.862074	−0.431037	+	0.902334i	$0.641852\pi$
$398$	2.04325e66	1.03111
$399$	−5.88921e65	−0.278771
$400$	3.57050e66	1.58562
$401$	1.99632e65	0.0831857	0.0415929	−	0.999135i	$-0.486757\pi$
$401$	1.99632e65	0.0831857	0.0415929	+	0.999135i	$0.486757\pi$
$402$	−7.04959e64	−0.0275676
$403$	−3.07597e65	−0.112903
$404$	8.39874e66	2.89394
$405$	1.81860e66	0.588347
$406$	−6.89383e66	−2.09434
$407$	6.65119e66	1.89776
$408$	3.39217e65	0.0909168
$409$	−3.81426e66	−0.960430	−0.480215	−	0.877151i	$-0.659441\pi$
$409$	−3.81426e66	−0.960430	−0.480215	+	0.877151i	$0.659441\pi$
$410$	−1.23092e67	−2.91234
$411$	−2.87237e65	−0.0638666
$412$	−1.12272e67	−2.34635
$413$	8.37815e66	1.64597
$414$	2.62474e66	0.484817
$415$	1.29315e66	0.224607
$416$	−3.50593e66	−0.572694
$417$	4.43232e66	0.681022
$418$	1.18094e67	1.70699
$419$	−4.78644e66	−0.650961	−0.325480	−	0.945549i	$-0.605526\pi$
$419$	−4.78644e66	−0.650961	−0.325480	+	0.945549i	$0.605526\pi$
$420$	9.48353e66	1.21370
$421$	−8.14181e66	−0.980681	−0.490340	−	0.871531i	$-0.663128\pi$
$421$	−8.14181e66	−0.980681	−0.490340	+	0.871531i	$0.663128\pi$
$422$	−6.04977e66	−0.685916
$423$	4.03646e66	0.430846
$424$	1.48559e67	1.49303
$425$	−6.08711e65	−0.0576094
$426$	−1.51392e67	−1.34946
$427$	−9.43107e66	−0.791863
$428$	1.48114e67	1.17160
$429$	2.76247e66	0.205890
$430$	8.04912e66	0.565331
$431$	−5.75151e66	−0.380725	−0.190362	−	0.981714i	$-0.560966\pi$
$431$	−5.75151e66	−0.380725	−0.190362	+	0.981714i	$0.560966\pi$
$432$	−2.87638e67	−1.79478
$433$	−3.28347e67	−1.93148	−0.965742	−	0.259505i	$-0.916441\pi$
$433$	−3.28347e67	−1.93148	−0.965742	+	0.259505i	$0.916441\pi$
$434$	9.30807e66	0.516263
$435$	1.42364e67	0.744600
$436$	7.86055e67	3.87746
$437$	−5.01874e66	−0.233517
$438$	−2.27489e67	−0.998552
$439$	1.32507e67	0.548775	0.274388	−	0.961619i	$-0.411525\pi$
$439$	1.32507e67	0.548775	0.274388	+	0.961619i	$0.411525\pi$
$440$	−1.09933e68	−4.29621
$441$	4.69601e66	0.173199
$442$	1.53122e66	0.0533053
$443$	2.21195e67	0.726909	0.363454	−	0.931612i	$-0.381597\pi$
$443$	2.21195e67	0.726909	0.363454	+	0.931612i	$0.381597\pi$
$444$	4.90679e67	1.52241
$445$	−1.29796e67	−0.380262
$446$	6.33943e67	1.75393
$447$	−7.76631e66	−0.202943
$448$	2.54447e67	0.628069
$449$	2.50690e66	0.0584596	0.0292298	−	0.999573i	$-0.490695\pi$
$449$	2.50690e66	0.0584596	0.0292298	+	0.999573i	$0.490695\pi$
$450$	4.72651e67	1.04141
$451$	7.63061e67	1.58876
$452$	−1.93822e68	−3.81394
$453$	−7.91623e66	−0.147236
$454$	−1.54698e68	−2.71994
$455$	2.47468e67	0.411366
$456$	5.03634e67	0.791610
$457$	−6.35904e67	−0.945211	−0.472605	−	0.881274i	$-0.656686\pi$
$457$	−6.35904e67	−0.945211	−0.472605	+	0.881274i	$0.656686\pi$
$458$	5.18508e67	0.728930
$459$	4.90375e66	0.0652086
$460$	8.08179e67	1.01668
$461$	−2.39534e67	−0.285097	−0.142549	−	0.989788i	$-0.545530\pi$
$461$	−2.39534e67	−0.285097	−0.142549	+	0.989788i	$0.545530\pi$
$462$	−8.35938e67	−0.941464
$463$	−4.29264e67	−0.457519	−0.228759	−	0.973483i	$-0.573467\pi$
$463$	−4.29264e67	−0.457519	−0.228759	+	0.973483i	$0.573467\pi$
$464$	2.86937e68	2.89453
$465$	−1.92220e67	−0.183547
$466$	5.17487e67	0.467798
$467$	1.29125e68	1.10518	0.552588	−	0.833455i	$-0.313640\pi$
$467$	1.29125e68	1.10518	0.552588	+	0.833455i	$0.313640\pi$
$468$	−8.36166e67	−0.677678
$469$	3.91485e66	0.0300475
$470$	1.76724e68	1.28470
$471$	−2.51675e67	−0.173303
$472$	−7.16484e68	−4.67396
$473$	−4.98974e67	−0.308403
$474$	1.74911e68	1.02440
$475$	−9.03750e67	−0.501604
$476$	−3.25867e67	−0.171421
$477$	9.57145e67	0.477264
$478$	5.32506e68	2.51717
$479$	1.65481e67	0.0741637	0.0370819	−	0.999312i	$-0.488194\pi$
$479$	1.65481e67	0.0741637	0.0370819	+	0.999312i	$0.488194\pi$
$480$	−2.19088e68	−0.931037
$481$	1.28040e68	0.515997
$482$	−4.37091e68	−1.67060
$483$	3.55256e67	0.128792
$484$	4.89707e68	1.68414
$485$	−4.75596e68	−1.55176
$486$	−5.91828e68	−1.83219
$487$	2.64354e68	0.776599	0.388300	−	0.921533i	$-0.373063\pi$
$487$	2.64354e68	0.776599	0.388300	+	0.921533i	$0.373063\pi$
$488$	8.06527e68	2.24861
$489$	−1.25715e68	−0.332668
$490$	2.05601e68	0.516445
$491$	−2.78351e68	−0.663766	−0.331883	−	0.943320i	$-0.607684\pi$
$491$	−2.78351e68	−0.663766	−0.331883	+	0.943320i	$0.607684\pi$
$492$	5.62935e68	1.27452
$493$	−4.89181e67	−0.105165
$494$	2.27340e68	0.464128
$495$	−7.08287e68	−1.37334
$496$	−3.87424e68	−0.713515
$497$	8.40729e68	1.47085
$498$	−8.40917e67	−0.139767
$499$	6.14422e67	0.0970293	0.0485147	−	0.998822i	$-0.484551\pi$
$499$	6.14422e67	0.0970293	0.0485147	+	0.998822i	$0.484551\pi$
$500$	−6.07381e68	−0.911436
$501$	1.83913e68	0.262271
$502$	−2.46614e69	−3.34252
$503$	−2.46940e68	−0.318133	−0.159066	−	0.987268i	$-0.550848\pi$
$503$	−2.46940e68	−0.318133	−0.159066	+	0.987268i	$0.550848\pi$
$504$	1.46271e69	1.79135
$505$	1.36955e69	1.59459
$506$	−7.12380e68	−0.788630
$507$	−3.67346e68	−0.386698
$508$	−1.24529e69	−1.24665
$509$	1.09348e69	1.04114	0.520570	−	0.853819i	$-0.325719\pi$
$509$	1.09348e69	1.04114	0.520570	+	0.853819i	$0.325719\pi$
$510$	9.56872e67	0.0866591
$511$	1.26332e69	1.08838
$512$	2.48098e69	2.03347
$513$	7.28057e68	0.567770
$514$	2.30758e69	1.71237
$515$	−1.83078e69	−1.29286
$516$	−3.68109e68	−0.247405
$517$	−1.09553e69	−0.700837
$518$	−3.87457e69	−2.35947
$519$	−1.41611e69	−0.820971
$520$	−2.11630e69	−1.16813
$521$	−1.75420e69	−0.921972	−0.460986	−	0.887407i	$-0.652504\pi$
$521$	−1.75420e69	−0.921972	−0.460986	+	0.887407i	$0.652504\pi$
$522$	3.79838e69	1.90108
$523$	1.24675e69	0.594272	0.297136	−	0.954835i	$-0.403969\pi$
$523$	1.24675e69	0.594272	0.297136	+	0.954835i	$0.403969\pi$
$524$	−1.94344e69	−0.882313
$525$	6.39728e68	0.276652
$526$	3.04890e69	1.25605
$527$	6.60494e67	0.0259238
$528$	3.47937e69	1.30118
$529$	−2.50346e69	−0.892115
$530$	4.19057e69	1.42311
$531$	−4.61622e69	−1.49409
$532$	−4.83813e69	−1.49256
$533$	1.46895e69	0.431980
$534$	8.44045e68	0.236627
$535$	2.41524e69	0.645563
$536$	−3.34791e68	−0.0853240
$537$	2.77351e68	0.0674040
$538$	1.08946e70	2.52501
$539$	−1.27454e69	−0.281735
$540$	−1.17241e70	−2.47194
$541$	1.90153e69	0.382449	0.191225	−	0.981546i	$-0.438754\pi$
$541$	1.90153e69	0.382449	0.191225	+	0.981546i	$0.438754\pi$
$542$	−7.26848e69	−1.39464
$543$	1.41986e69	0.259927
$544$	7.52816e68	0.131497
$545$	1.28179e70	2.13652
$546$	−1.60924e69	−0.255982
$547$	−1.93403e69	−0.293621	−0.146810	−	0.989165i	$-0.546901\pi$
$547$	−1.93403e69	−0.293621	−0.146810	+	0.989165i	$0.546901\pi$
$548$	−2.35972e69	−0.341945
$549$	5.19636e69	0.718794
$550$	−1.28282e70	−1.69401
$551$	−7.26284e69	−0.915674
$552$	−3.03808e69	−0.365724
$553$	−9.71332e69	−1.11655
$554$	−6.63511e69	−0.728365
$555$	8.00134e69	0.838864
$556$	3.64126e70	3.64623
$557$	−3.13526e69	−0.299893	−0.149946	−	0.988694i	$-0.547910\pi$
$557$	−3.13526e69	−0.299893	−0.149946	+	0.988694i	$0.547910\pi$
$558$	−5.12859e69	−0.468625
$559$	−9.60563e68	−0.0838542
$560$	3.11690e70	2.59973
$561$	−5.93176e68	−0.0472749
$562$	−1.36826e69	−0.104206
$563$	9.08297e69	0.661095	0.330547	−	0.943789i	$-0.392767\pi$
$563$	9.08297e69	0.661095	0.330547	+	0.943789i	$0.392767\pi$
$564$	−8.08211e69	−0.562222
$565$	−3.16060e70	−2.10152
$566$	2.12320e69	0.134950
$567$	6.56736e69	0.399046
$568$	−7.18975e70	−4.17668
$569$	7.13609e69	0.396367	0.198184	−	0.980165i	$-0.436496\pi$
$569$	7.13609e69	0.396367	0.198184	+	0.980165i	$0.436496\pi$
$570$	1.42066e70	0.754539
$571$	3.32172e70	1.68710	0.843552	−	0.537048i	$-0.180460\pi$
$571$	3.32172e70	1.68710	0.843552	+	0.537048i	$0.180460\pi$
$572$	2.26943e70	1.10235
$573$	−7.29067e69	−0.338707
$574$	−4.44513e70	−1.97529
$575$	5.45171e69	0.231741
$576$	−1.40196e70	−0.570114
$577$	−2.70924e70	−1.05406	−0.527028	−	0.849848i	$-0.676694\pi$
$577$	−2.70924e70	−1.05406	−0.527028	+	0.849848i	$0.676694\pi$
$578$	4.89867e70	1.82355
$579$	−9.54649e69	−0.340048
$580$	1.16955e71	3.98663
$581$	4.66987e69	0.152340
$582$	3.09273e70	0.965618
$583$	−2.59778e70	−0.776345
$584$	−1.08036e71	−3.09060
$585$	−1.36351e70	−0.373407
$586$	3.41531e70	0.895450
$587$	4.21203e70	1.05735	0.528676	−	0.848824i	$-0.322689\pi$
$587$	4.21203e70	1.05735	0.528676	+	0.848824i	$0.322689\pi$
$588$	−9.40270e69	−0.226012
$589$	9.80631e69	0.225718
$590$	−2.02107e71	−4.45508
$591$	−2.47417e70	−0.522334
$592$	1.61269e71	3.26097
$593$	−6.81213e68	−0.0131944	−0.00659718	−	0.999978i	$-0.502100\pi$
$593$	−6.81213e68	−0.0131944	−0.00659718	+	0.999978i	$0.502100\pi$
$594$	1.03343e71	1.91747
$595$	−5.31380e69	−0.0944545
$596$	−6.38021e70	−1.08656
$597$	−1.52375e70	−0.248639
$598$	−1.37139e70	−0.214427
$599$	6.95350e70	1.04188	0.520942	−	0.853592i	$-0.325581\pi$
$599$	6.95350e70	1.04188	0.520942	+	0.853592i	$0.325581\pi$
$600$	−5.47083e70	−0.785591
$601$	−1.18115e71	−1.62557	−0.812786	−	0.582563i	$-0.802050\pi$
$601$	−1.18115e71	−1.62557	−0.812786	+	0.582563i	$0.802050\pi$
$602$	2.90672e70	0.383436
$603$	−2.15702e69	−0.0272748
$604$	−6.50338e70	−0.788310
$605$	7.98548e70	0.927980
$606$	−8.90598e70	−0.992270
$607$	6.67421e70	0.712998	0.356499	−	0.934296i	$-0.383970\pi$
$607$	6.67421e70	0.712998	0.356499	+	0.934296i	$0.383970\pi$
$608$	1.11770e71	1.14494
$609$	5.14107e70	0.505025
$610$	2.27507e71	2.14330
$611$	−2.10899e70	−0.190556
$612$	1.79547e70	0.155603
$613$	1.23137e71	1.02364	0.511821	−	0.859092i	$-0.328971\pi$
$613$	1.23137e71	1.02364	0.511821	+	0.859092i	$0.328971\pi$
$614$	−2.61367e71	−2.08429
$615$	9.17958e70	0.702275
$616$	−3.96994e71	−2.91391
$617$	5.54308e70	0.390372	0.195186	−	0.980766i	$-0.437469\pi$
$617$	5.54308e70	0.390372	0.195186	+	0.980766i	$0.437469\pi$
$618$	1.19053e71	0.804512
$619$	−1.74222e71	−1.12978	−0.564888	−	0.825168i	$-0.691081\pi$
$619$	−1.74222e71	−1.12978	−0.564888	+	0.825168i	$0.691081\pi$
$620$	−1.57913e71	−0.982721
$621$	−4.39187e70	−0.262309
$622$	1.78919e71	1.02566
$623$	−4.68724e70	−0.257912
$624$	6.69805e70	0.353787
$625$	−2.38187e71	−1.20775
$626$	2.84453e71	1.38473
$627$	−8.80684e70	−0.411621
$628$	−2.06757e71	−0.927874
$629$	−2.74937e70	−0.118479
$630$	4.12605e71	1.70746
$631$	3.02907e70	0.120382	0.0601909	−	0.998187i	$-0.480829\pi$
$631$	3.02907e70	0.120382	0.0601909	+	0.998187i	$0.480829\pi$
$632$	8.30665e71	3.17059
$633$	4.51161e70	0.165401
$634$	2.03298e71	0.715906
$635$	−2.03065e71	−0.686919
$636$	−1.91647e71	−0.622795
$637$	−2.45359e70	−0.0766031
$638$	−1.03092e72	−3.09240
$639$	−4.63227e71	−1.33513
$640$	1.45589e71	0.403217
$641$	4.16260e71	1.10786	0.553929	−	0.832564i	$-0.313128\pi$
$641$	4.16260e71	1.10786	0.553929	+	0.832564i	$0.313128\pi$
$642$	−1.57059e71	−0.401717
$643$	−1.46280e71	−0.359587	−0.179794	−	0.983704i	$-0.557543\pi$
$643$	−1.46280e71	−0.359587	−0.179794	+	0.983704i	$0.557543\pi$
$644$	2.91852e71	0.689560
$645$	−6.00263e70	−0.136323
$646$	−4.88159e70	−0.106569
$647$	4.77442e71	1.00199	0.500993	−	0.865451i	$-0.332968\pi$
$647$	4.77442e71	1.00199	0.500993	+	0.865451i	$0.332968\pi$
$648$	−5.61628e71	−1.13315
$649$	1.25289e72	2.43037
$650$	−2.46952e71	−0.460599
$651$	−6.94149e70	−0.124491
$652$	−1.03278e72	−1.78112
$653$	2.35120e71	0.389946	0.194973	−	0.980809i	$-0.437538\pi$
$653$	2.35120e71	0.389946	0.194973	+	0.980809i	$0.437538\pi$
$654$	−8.33529e71	−1.32950
$655$	−3.16910e71	−0.486163
$656$	1.85017e72	2.73000
$657$	−6.96066e71	−0.987947
$658$	6.38192e71	0.871346
$659$	3.04611e71	0.400099	0.200050	−	0.979786i	$-0.435890\pi$
$659$	3.04611e71	0.400099	0.200050	+	0.979786i	$0.435890\pi$
$660$	1.41819e72	1.79210
$661$	5.21186e71	0.633659	0.316830	−	0.948482i	$-0.397382\pi$
$661$	5.21186e71	0.633659	0.316830	+	0.948482i	$0.397382\pi$
$662$	−2.96713e72	−3.47103
$663$	−1.14191e70	−0.0128539
$664$	−3.99358e71	−0.432590
$665$	−7.88937e71	−0.822414
$666$	2.13482e72	2.14175
$667$	4.38118e71	0.423041
$668$	1.51089e72	1.40421
$669$	−4.72763e71	−0.422938
$670$	−9.44385e70	−0.0813283
$671$	−1.41034e72	−1.16923
$672$	−7.91175e71	−0.631475
$673$	6.60671e71	0.507693	0.253846	−	0.967245i	$-0.418304\pi$
$673$	6.60671e71	0.507693	0.253846	+	0.967245i	$0.418304\pi$
$674$	−1.76136e72	−1.30323
$675$	−7.90867e71	−0.563452
$676$	−3.01783e72	−2.07040
$677$	6.23542e71	0.411959	0.205980	−	0.978556i	$-0.433962\pi$
$677$	6.23542e71	0.411959	0.205980	+	0.978556i	$0.433962\pi$
$678$	2.05528e72	1.30772
$679$	−1.71749e72	−1.05248
$680$	4.54426e71	0.268217
$681$	1.15366e72	0.655882
$682$	1.39195e72	0.762292
$683$	3.27198e72	1.72617	0.863083	−	0.505062i	$-0.168530\pi$
$683$	3.27198e72	1.72617	0.863083	+	0.505062i	$0.168530\pi$
$684$	2.66573e72	1.35483
$685$	−3.84792e71	−0.188415
$686$	4.18921e72	1.97637
$687$	−3.86677e71	−0.175773
$688$	−1.20984e72	−0.529937
$689$	−5.00093e71	−0.211087
$690$	−8.56989e71	−0.348597
$691$	−2.74210e72	−1.07496	−0.537481	−	0.843276i	$-0.680624\pi$
$691$	−2.74210e72	−1.07496	−0.537481	+	0.843276i	$0.680624\pi$
$692$	−1.16336e73	−4.39552
$693$	−2.55778e72	−0.931465
$694$	8.42161e72	2.95616
$695$	5.93767e72	2.00911
$696$	−4.39655e72	−1.43409
$697$	−3.15423e71	−0.0991877
$698$	−4.52445e72	−1.37168
$699$	−3.85915e71	−0.112804
$700$	5.25552e72	1.48121
$701$	−2.11073e72	−0.573619	−0.286810	−	0.957988i	$-0.592595\pi$
$701$	−2.11073e72	−0.573619	−0.286810	+	0.957988i	$0.592595\pi$
$702$	1.98944e72	0.521355
$703$	−4.08197e72	−1.03160
$704$	3.80505e72	0.927379
$705$	−1.31792e72	−0.309790
$706$	2.81867e72	0.639034
$707$	4.94576e72	1.08153
$708$	9.24294e72	1.94967
$709$	−1.26460e72	−0.257321	−0.128661	−	0.991689i	$-0.541068\pi$
$709$	−1.26460e72	−0.257321	−0.128661	+	0.991689i	$0.541068\pi$
$710$	−2.02810e73	−3.98108
$711$	5.35188e72	1.01352
$712$	4.00844e72	0.732378
$713$	−5.91548e71	−0.104281
$714$	3.45548e71	0.0587765
$715$	3.70069e72	0.607405
$716$	2.27851e72	0.360884
$717$	−3.97116e72	−0.606987
$718$	−1.85432e71	−0.0273535
$719$	5.81095e72	0.827296	0.413648	−	0.910437i	$-0.364254\pi$
$719$	5.81095e72	0.827296	0.413648	+	0.910437i	$0.364254\pi$
$720$	−1.71736e73	−2.35984
$721$	−6.61135e72	−0.876882
$722$	7.09143e72	0.907894
$723$	3.25960e72	0.402845
$724$	1.16645e73	1.39166
$725$	7.88941e72	0.908711
$726$	−5.19283e72	−0.577457
$727$	3.02801e72	0.325110	0.162555	−	0.986700i	$-0.448027\pi$
$727$	3.02801e72	0.325110	0.162555	+	0.986700i	$0.448027\pi$
$728$	−7.64243e72	−0.792285
$729$	−8.68717e70	−0.00869614
$730$	−3.04751e73	−2.94587
$731$	2.06259e71	0.0192539
$732$	−1.04045e73	−0.937973
$733$	−1.84067e72	−0.160259	−0.0801297	−	0.996784i	$-0.525533\pi$
$733$	−1.84067e72	−0.160259	−0.0801297	+	0.996784i	$0.525533\pi$
$734$	2.99708e73	2.52028
$735$	−1.53327e72	−0.124535
$736$	−6.74234e72	−0.528964
$737$	5.85435e71	0.0443668
$738$	2.44919e73	1.79302
$739$	−2.72537e73	−1.92749	−0.963746	−	0.266820i	$-0.914027\pi$
$739$	−2.72537e73	−1.92749	−0.963746	+	0.266820i	$0.914027\pi$
$740$	6.57329e73	4.49132
$741$	−1.69538e72	−0.111919
$742$	1.51331e73	0.965224
$743$	−1.44844e73	−0.892662	−0.446331	−	0.894868i	$-0.647270\pi$
$743$	−1.44844e73	−0.892662	−0.446331	+	0.894868i	$0.647270\pi$
$744$	5.93623e72	0.353509
$745$	−1.04040e73	−0.598708
$746$	−5.87922e73	−3.26948
$747$	−2.57302e72	−0.138283
$748$	−4.87308e72	−0.253112
$749$	8.72197e72	0.437853
$750$	6.44064e72	0.312512
$751$	1.83054e73	0.858539	0.429270	−	0.903176i	$-0.358771\pi$
$751$	1.83054e73	0.858539	0.429270	+	0.903176i	$0.358771\pi$
$752$	−2.65630e73	−1.20427
$753$	1.83913e73	0.806009
$754$	−1.98459e73	−0.840818
$755$	−1.06048e73	−0.434367
$756$	−4.23382e73	−1.67659
$757$	−3.21435e73	−1.23069	−0.615344	−	0.788259i	$-0.710983\pi$
$757$	−3.21435e73	−1.23069	−0.615344	+	0.788259i	$0.710983\pi$
$758$	1.98034e73	0.733120
$759$	5.31257e72	0.190169
$760$	6.74684e73	2.33536
$761$	2.98468e73	0.999055	0.499527	−	0.866298i	$-0.333507\pi$
$761$	2.98468e73	0.999055	0.499527	+	0.866298i	$0.333507\pi$
$762$	1.32050e73	0.427452
$763$	4.62884e73	1.44909
$764$	−5.98946e73	−1.81346
$765$	2.92781e72	0.0857387
$766$	1.00223e74	2.83880
$767$	2.41190e73	0.660812
$768$	−2.13111e73	−0.564800
$769$	−2.25014e73	−0.576883	−0.288442	−	0.957498i	$-0.593137\pi$
$769$	−2.25014e73	−0.576883	−0.288442	+	0.957498i	$0.593137\pi$
$770$	−1.11985e74	−2.77745
$771$	−1.72088e73	−0.412917
$772$	−7.84267e73	−1.82064
$773$	1.94895e73	0.437746	0.218873	−	0.975753i	$-0.429762\pi$
$773$	1.94895e73	0.437746	0.218873	+	0.975753i	$0.429762\pi$
$774$	−1.60155e73	−0.348054
$775$	−1.06523e73	−0.224001
$776$	1.46876e74	2.98866
$777$	2.88946e73	0.568959
$778$	−6.66392e73	−1.26984
$779$	−4.68307e73	−0.863625
$780$	2.73012e73	0.487269
$781$	1.25724e74	2.17179
$782$	2.94473e72	0.0492350
$783$	−6.35567e73	−1.02858
$784$	−3.09033e73	−0.484112
$785$	−3.37151e73	−0.511268
$786$	2.06081e73	0.302526
$787$	−5.33534e73	−0.758240	−0.379120	−	0.925348i	$-0.623773\pi$
$787$	−5.33534e73	−0.758240	−0.379120	+	0.925348i	$0.623773\pi$
$788$	−2.03259e74	−2.79660
$789$	−2.27372e73	−0.302882
$790$	2.34316e74	3.02211
$791$	−1.14136e74	−1.42536
$792$	2.18737e74	2.64502
$793$	−2.71501e73	−0.317911
$794$	1.39569e74	1.58259
$795$	−3.12512e73	−0.343166
$796$	−1.25180e74	−1.33123
$797$	6.56993e73	0.676664	0.338332	−	0.941027i	$-0.390137\pi$
$797$	6.56993e73	0.676664	0.338332	+	0.941027i	$0.390137\pi$
$798$	5.13033e73	0.511766
$799$	4.52856e72	0.0437540
$800$	−1.21413e74	−1.13624
$801$	2.58259e73	0.234113
$802$	−1.73908e73	−0.152712
$803$	1.88919e74	1.60705
$804$	4.31894e72	0.0355916
$805$	4.75912e73	0.379955
$806$	2.67960e73	0.207265
$807$	−8.12466e73	−0.608877
$808$	−4.22952e74	−3.07115
$809$	−1.11962e74	−0.787738	−0.393869	−	0.919167i	$-0.628864\pi$
$809$	−1.11962e74	−0.787738	−0.393869	+	0.919167i	$0.628864\pi$
$810$	−1.58425e74	−1.08008
$811$	1.56076e74	1.03111	0.515553	−	0.856858i	$-0.327587\pi$
$811$	1.56076e74	1.03111	0.515553	+	0.856858i	$0.327587\pi$
$812$	4.22351e74	2.70393
$813$	5.42047e73	0.336301
$814$	−5.79412e74	−3.48389
$815$	−1.68411e74	−0.981414
$816$	−1.43825e73	−0.0812336
$817$	3.06231e73	0.167643
$818$	3.32275e74	1.76315
$819$	−4.92393e73	−0.253263
$820$	7.54125e74	3.76002
$821$	−2.63166e74	−1.27198	−0.635989	−	0.771698i	$-0.719408\pi$
$821$	−2.63166e74	−1.27198	−0.635989	+	0.771698i	$0.719408\pi$
$822$	2.50224e73	0.117246
$823$	3.49608e74	1.58813	0.794063	−	0.607835i	$-0.207962\pi$
$823$	3.49608e74	1.58813	0.794063	+	0.607835i	$0.207962\pi$
$824$	5.65390e74	2.49003
$825$	9.56662e73	0.408491
$826$	−7.29855e74	−3.02166
$827$	−3.08226e74	−1.23731	−0.618656	−	0.785662i	$-0.712322\pi$
$827$	−3.08226e74	−1.23731	−0.618656	+	0.785662i	$0.712322\pi$
$828$	−1.60805e74	−0.625931
$829$	−3.63825e73	−0.137326	−0.0686629	−	0.997640i	$-0.521873\pi$
$829$	−3.63825e73	−0.137326	−0.0686629	+	0.997640i	$0.521873\pi$
$830$	−1.12652e74	−0.412332
$831$	4.94813e73	0.175637
$832$	7.32500e73	0.252152
$833$	5.26851e72	0.0175890
$834$	−3.86117e74	−1.25021
$835$	2.46376e74	0.773736
$836$	−7.23503e74	−2.20384
$837$	8.58145e73	0.253549
$838$	4.16966e74	1.19503
$839$	1.84060e74	0.511717	0.255859	−	0.966714i	$-0.417642\pi$
$839$	1.84060e74	0.511717	0.255859	+	0.966714i	$0.417642\pi$
$840$	−4.77581e74	−1.28803
$841$	2.51814e74	0.658842
$842$	7.09266e74	1.80032
$843$	1.02038e73	0.0251280
$844$	3.70640e74	0.885564
$845$	−4.92108e74	−1.14081
$846$	−3.51633e74	−0.790942
$847$	2.88374e74	0.629402
$848$	−6.29875e74	−1.33401
$849$	−1.58338e73	−0.0325415
$850$	5.30273e73	0.105759
$851$	2.46238e74	0.476597
$852$	9.27508e74	1.74224
$853$	−8.40007e74	−1.53138	−0.765689	−	0.643211i	$-0.777602\pi$
$853$	−8.40007e74	−1.53138	−0.765689	+	0.643211i	$0.777602\pi$
$854$	8.21578e74	1.45370
$855$	4.34691e74	0.746525
$856$	−7.45886e74	−1.24334
$857$	2.87444e74	0.465095	0.232548	−	0.972585i	$-0.425294\pi$
$857$	2.87444e74	0.465095	0.232548	+	0.972585i	$0.425294\pi$
$858$	−2.40650e74	−0.377972
$859$	−9.96707e74	−1.51964	−0.759822	−	0.650131i	$-0.774714\pi$
$859$	−9.96707e74	−1.51964	−0.759822	+	0.650131i	$0.774714\pi$
$860$	−4.93130e74	−0.729880
$861$	3.31495e74	0.476318
$862$	5.01037e74	0.698931
$863$	9.87545e74	1.33746	0.668732	−	0.743504i	$-0.266838\pi$
$863$	9.87545e74	1.33746	0.668732	+	0.743504i	$0.266838\pi$
$864$	9.78095e74	1.28612
$865$	−1.89706e75	−2.42198
$866$	2.86036e75	3.54580
$867$	−3.65318e74	−0.439728
$868$	−5.70260e74	−0.666530
$869$	−1.45255e75	−1.64864
$870$	−1.24019e75	−1.36693
$871$	1.12701e73	0.0120632
$872$	−3.95850e75	−4.11491
$873$	9.46305e74	0.955362
$874$	4.37202e74	0.428688
$875$	−3.57668e74	−0.340624
$876$	1.39372e75	1.28920
$877$	1.76322e75	1.58422	0.792112	−	0.610375i	$-0.208981\pi$
$877$	1.76322e75	1.58422	0.792112	+	0.610375i	$0.208981\pi$
$878$	−1.15432e75	−1.00744
$879$	−2.54697e74	−0.215927
$880$	4.66107e75	3.83864
$881$	3.09062e74	0.247263	0.123632	−	0.992328i	$-0.460546\pi$
$881$	3.09062e74	0.247263	0.123632	+	0.992328i	$0.460546\pi$
$882$	−4.09088e74	−0.317957
$883$	1.81758e75	1.37245	0.686223	−	0.727392i	$-0.259268\pi$
$883$	1.81758e75	1.37245	0.686223	+	0.727392i	$0.259268\pi$
$884$	−9.38105e73	−0.0688206
$885$	1.50721e75	1.07429
$886$	−1.92692e75	−1.33445
$887$	−1.25497e75	−0.844461	−0.422230	−	0.906489i	$-0.638753\pi$
$887$	−1.25497e75	−0.844461	−0.422230	+	0.906489i	$0.638753\pi$
$888$	−2.47101e75	−1.61564
$889$	−7.33315e74	−0.465903
$890$	1.13071e75	0.698081
$891$	9.82096e74	0.589213
$892$	−3.88386e75	−2.26443
$893$	6.72353e74	0.380965
$894$	6.76555e74	0.372560
$895$	3.71548e74	0.198851
$896$	5.25754e74	0.273482
$897$	1.02271e74	0.0517065
$898$	−2.18386e74	−0.107320
$899$	−8.56056e74	−0.408912
$900$	−2.89570e75	−1.34453
$901$	1.07383e74	0.0484680
$902$	−6.64733e75	−2.91663
$903$	−2.16768e74	−0.0924610
$904$	9.76071e75	4.04750
$905$	1.90209e75	0.766820
$906$	6.89615e74	0.270295
$907$	−1.93095e75	−0.735845	−0.367922	−	0.929857i	$-0.619931\pi$
$907$	−1.93095e75	−0.735845	−0.367922	+	0.929857i	$0.619931\pi$
$908$	9.47757e75	3.51162
$909$	−2.72503e75	−0.981731
$910$	−2.15579e75	−0.755182
$911$	−9.00047e74	−0.306582	−0.153291	−	0.988181i	$-0.548987\pi$
$911$	−9.00047e74	−0.306582	−0.153291	+	0.988181i	$0.548987\pi$
$912$	−2.13536e75	−0.707299
$913$	6.98342e74	0.224938
$914$	5.53962e75	1.73521
$915$	−1.69663e75	−0.516832
$916$	−3.17665e75	−0.941097
$917$	−1.14443e75	−0.329740
$918$	−4.27185e74	−0.119709
$919$	−6.41329e75	−1.74798	−0.873988	−	0.485948i	$-0.838475\pi$
$919$	−6.41329e75	−1.74798	−0.873988	+	0.485948i	$0.838475\pi$
$920$	−4.06991e75	−1.07893
$921$	1.94915e75	0.502602
$922$	2.08667e75	0.523379
$923$	2.42029e75	0.590505
$924$	5.12139e75	1.21549
$925$	4.43413e75	1.02375
$926$	3.73949e75	0.839909
$927$	3.64274e75	0.795967
$928$	−9.75713e75	−2.07419
$929$	−6.16892e75	−1.27588	−0.637938	−	0.770088i	$-0.720212\pi$
$929$	−6.16892e75	−1.27588	−0.637938	+	0.770088i	$0.720212\pi$
$930$	1.67450e75	0.336954
$931$	7.82212e74	0.153147
$932$	−3.17039e75	−0.603958
$933$	−1.33429e75	−0.247325
$934$	−1.12486e76	−2.02887
$935$	−7.94636e74	−0.139467
$936$	4.21085e75	0.719177
$937$	1.06049e76	1.76258	0.881290	−	0.472575i	$-0.156675\pi$
$937$	1.06049e76	1.76258	0.881290	+	0.472575i	$0.156675\pi$
$938$	−3.41039e74	−0.0551609
$939$	−2.12130e75	−0.333911
$940$	−1.08270e76	−1.65863
$941$	3.41799e75	0.509608	0.254804	−	0.966993i	$-0.417989\pi$
$941$	3.41799e75	0.509608	0.254804	+	0.966993i	$0.417989\pi$
$942$	2.19244e75	0.318148
$943$	2.82498e75	0.398994
$944$	3.03783e76	4.17616
$945$	−6.90395e75	−0.923818
$946$	4.34676e75	0.566164
$947$	−6.63593e75	−0.841351	−0.420675	−	0.907211i	$-0.638207\pi$
$947$	−6.63593e75	−0.841351	−0.420675	+	0.907211i	$0.638207\pi$
$948$	−1.07159e76	−1.32257
$949$	3.63683e75	0.436953
$950$	7.87293e75	0.920840
$951$	−1.51609e75	−0.172632
$952$	1.64103e75	0.181918
$953$	1.31580e76	1.42010	0.710052	−	0.704149i	$-0.248671\pi$
$953$	1.31580e76	1.42010	0.710052	+	0.704149i	$0.248671\pi$
$954$	−8.33808e75	−0.876158
$955$	−9.76680e75	−0.999232
$956$	−3.26241e76	−3.24984
$957$	7.68806e75	0.745697
$958$	−1.44157e75	−0.136149
$959$	−1.38957e75	−0.127793
$960$	4.57745e75	0.409927
$961$	−1.03111e76	−0.899201
$962$	−1.11541e76	−0.947263
$963$	−4.80566e75	−0.397450
$964$	2.67784e76	2.15685
$965$	−1.27888e76	−1.00319
$966$	−3.09478e75	−0.236436
$967$	1.67049e76	1.24299	0.621496	−	0.783417i	$-0.286525\pi$
$967$	1.67049e76	1.24299	0.621496	+	0.783417i	$0.286525\pi$
$968$	−2.46612e76	−1.78728
$969$	3.64044e74	0.0256979
$970$	4.14311e76	2.84870
$971$	1.63388e76	1.09428	0.547142	−	0.837040i	$-0.315716\pi$
$971$	1.63388e76	1.09428	0.547142	+	0.837040i	$0.315716\pi$
$972$	3.62584e76	2.36548
$973$	2.14423e76	1.36268
$974$	−2.30289e76	−1.42567
$975$	1.84165e75	0.111068
$976$	−3.41960e76	−2.00912
$977$	−2.38186e76	−1.36334	−0.681672	−	0.731658i	$-0.738747\pi$
$977$	−2.38186e76	−1.36334	−0.681672	+	0.731658i	$0.738747\pi$
$978$	1.09515e76	0.610708
$979$	−7.00939e75	−0.380822
$980$	−1.25961e76	−0.666765
$981$	−2.55041e76	−1.31538
$982$	2.42483e76	1.21854
$983$	3.78819e76	1.85488	0.927442	−	0.373966i	$-0.122002\pi$
$983$	3.78819e76	1.85488	0.927442	+	0.373966i	$0.122002\pi$
$984$	−2.83488e76	−1.35257
$985$	−3.31447e76	−1.54096
$986$	4.26145e75	0.193062
$987$	−4.75931e75	−0.210115
$988$	−1.39280e76	−0.599220
$989$	−1.84728e75	−0.0774512
$990$	6.17017e76	2.52116
$991$	2.49197e76	0.992349	0.496175	−	0.868223i	$-0.334738\pi$
$991$	2.49197e76	0.992349	0.496175	+	0.868223i	$0.334738\pi$
$992$	1.31741e76	0.511298
$993$	2.21274e76	0.836998
$994$	−7.32392e76	−2.70017
$995$	−2.04127e76	−0.733519
$996$	5.15189e75	0.180449
$997$	−2.96256e76	−1.01144	−0.505721	−	0.862697i	$-0.668773\pi$
$997$	−2.96256e76	−1.01144	−0.505721	+	0.862697i	$0.668773\pi$
$998$	−5.35248e75	−0.178126
$999$	−3.57211e76	−1.15879

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.52.a.a.1.1	✓	4
3.2	odd	2		9.52.a.b.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.52.a.a.1.1	✓	4	1.1	even	1	trivial
9.52.a.b.1.4		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-8.71140e7 q^{2} +6.49653e11 q^{3} +5.33705e15 q^{4} +8.70295e17 q^{5} -5.65939e19 q^{6} +3.14283e21 q^{7} -2.68769e23 q^{8} -1.73165e24 q^{9} +O(q^{10})\)	\(q-8.71140e7 q^{2} +6.49653e11 q^{3} +5.33705e15 q^{4} +8.70295e17 q^{5} -5.65939e19 q^{6} +3.14283e21 q^{7} -2.68769e23 q^{8} -1.73165e24 q^{9} -7.58149e25 q^{10} +4.69985e26 q^{11} +3.46723e27 q^{12} +9.04757e27 q^{13} -2.73785e29 q^{14} +5.65389e29 q^{15} +1.13956e31 q^{16} -1.94276e30 q^{17} +1.50851e32 q^{18} -2.88440e32 q^{19} +4.64481e33 q^{20} +2.04175e33 q^{21} -4.09423e34 q^{22} +1.73996e34 q^{23} -1.74606e35 q^{24} +3.13324e35 q^{25} -7.88170e35 q^{26} -2.52412e36 q^{27} +1.67734e37 q^{28} +2.51798e37 q^{29} -4.92533e37 q^{30} -3.39978e37 q^{31} -3.87499e38 q^{32} +3.05327e38 q^{33} +1.69241e38 q^{34} +2.73519e39 q^{35} -9.24188e39 q^{36} +1.41519e40 q^{37} +2.51271e40 q^{38} +5.87778e39 q^{39} -2.33908e41 q^{40} +1.62359e41 q^{41} -1.77865e41 q^{42} -1.06168e41 q^{43} +2.50834e42 q^{44} -1.50704e42 q^{45} -1.51575e42 q^{46} -2.33100e42 q^{47} +7.40315e42 q^{48} -2.71188e42 q^{49} -2.72949e43 q^{50} -1.26212e42 q^{51} +4.82874e43 q^{52} -5.52737e43 q^{53} +2.19886e44 q^{54} +4.09026e44 q^{55} -8.44695e44 q^{56} -1.87386e44 q^{57} -2.19351e45 q^{58} +2.66580e45 q^{59} +3.01751e45 q^{60} -3.00082e45 q^{61} +2.96168e45 q^{62} -5.44227e45 q^{63} +8.09610e45 q^{64} +7.87405e45 q^{65} -2.65983e46 q^{66} +1.24565e45 q^{67} -1.03686e46 q^{68} +1.13037e46 q^{69} -2.38273e47 q^{70} +2.67507e47 q^{71} +4.65412e47 q^{72} +4.01968e47 q^{73} -1.23283e48 q^{74} +2.03552e47 q^{75} -1.53942e48 q^{76} +1.47708e48 q^{77} -5.12037e47 q^{78} -3.09063e48 q^{79} +9.91749e48 q^{80} +2.08963e48 q^{81} -1.41437e49 q^{82} +1.48588e48 q^{83} +1.08969e49 q^{84} -1.69077e48 q^{85} +9.24873e48 q^{86} +1.63581e49 q^{87} -1.26317e50 q^{88} -1.49141e49 q^{89} +1.31284e50 q^{90} +2.84350e49 q^{91} +9.28627e49 q^{92} -2.20867e49 q^{93} +2.03063e50 q^{94} -2.51028e50 q^{95} -2.51740e50 q^{96} -5.46477e50 q^{97} +2.36242e50 q^{98} -8.13847e50 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32756040 q^{2} + 403863773040 q^{3} + 79\!\cdots\!12 q^{4}+ \cdots + 50\!\cdots\!28 q^{9}+O(q^{10}) \) 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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