LMFDB - Embedded newform 1.52.a.a.1.4

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			1.4
Root			$324949.$ 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)

$f(q)$	$=$	$q+8.12369e7 q^{2} -2.41142e12 q^{3} +4.34763e15 q^{4} +2.42754e17 q^{5} -1.95896e20 q^{6} +2.85586e21 q^{7} +1.70259e23 q^{8} +3.66124e24 q^{9} +O(q^{10})$	\(q+8.12369e7 q^{2} -2.41142e12 q^{3} +4.34763e15 q^{4} +2.42754e17 q^{5} -1.95896e20 q^{6} +2.85586e21 q^{7} +1.70259e23 q^{8} +3.66124e24 q^{9} +1.97206e25 q^{10} +3.52088e26 q^{11} -1.04840e28 q^{12} +3.67432e28 q^{13} +2.32001e29 q^{14} -5.85381e29 q^{15} +4.04130e30 q^{16} -6.54277e30 q^{17} +2.97427e32 q^{18} +2.55736e32 q^{19} +1.05541e33 q^{20} -6.88666e33 q^{21} +2.86025e34 q^{22} -1.69990e34 q^{23} -4.10565e35 q^{24} -3.85160e35 q^{25} +2.98490e36 q^{26} -3.63531e36 q^{27} +1.24162e37 q^{28} +3.94490e36 q^{29} -4.75545e37 q^{30} +9.38800e37 q^{31} -5.50861e37 q^{32} -8.49031e38 q^{33} -5.31514e38 q^{34} +6.93270e38 q^{35} +1.59177e40 q^{36} -1.74413e40 q^{37} +2.07752e40 q^{38} -8.86032e40 q^{39} +4.13310e40 q^{40} +2.14671e41 q^{41} -5.59451e41 q^{42} -2.13159e41 q^{43} +1.53075e42 q^{44} +8.88780e41 q^{45} -1.38095e42 q^{46} +4.04105e42 q^{47} -9.74526e42 q^{48} -4.43335e42 q^{49} -3.12892e43 q^{50} +1.57773e43 q^{51} +1.59746e44 q^{52} -4.94974e42 q^{53} -2.95321e44 q^{54} +8.54708e43 q^{55} +4.86235e44 q^{56} -6.16687e44 q^{57} +3.20472e44 q^{58} -1.20757e45 q^{59} -2.54502e45 q^{60} +2.20569e45 q^{61} +7.62652e45 q^{62} +1.04560e46 q^{63} -1.35752e46 q^{64} +8.91957e45 q^{65} -6.89726e46 q^{66} +4.56801e46 q^{67} -2.84456e46 q^{68} +4.09917e46 q^{69} +5.63191e46 q^{70} -1.91444e47 q^{71} +6.23358e47 q^{72} -8.49448e46 q^{73} -1.41688e48 q^{74} +9.28780e47 q^{75} +1.11185e48 q^{76} +1.00551e48 q^{77} -7.19785e48 q^{78} +2.35655e48 q^{79} +9.81042e47 q^{80} +8.81070e47 q^{81} +1.74392e49 q^{82} +5.38960e48 q^{83} -2.99406e49 q^{84} -1.58828e48 q^{85} -1.73164e49 q^{86} -9.51281e48 q^{87} +5.99461e49 q^{88} -7.58432e49 q^{89} +7.22017e49 q^{90} +1.04933e50 q^{91} -7.39055e49 q^{92} -2.26384e50 q^{93} +3.28282e50 q^{94} +6.20810e49 q^{95} +1.32835e50 q^{96} -8.33376e50 q^{97} -3.60151e50 q^{98} +1.28908e51 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	8.12369e7	1.71194	0.855970	−	0.517026i	$-0.172961\pi$
$2$	8.12369e7	1.71194	0.855970	+	0.517026i	$0.172961\pi$
$3$	−2.41142e12	−1.64316	−0.821581	−	0.570092i	$-0.806907\pi$
$3$	−2.41142e12	−1.64316	−0.821581	+	0.570092i	$0.806907\pi$
$4$	4.34763e15	1.93074
$5$	2.42754e17	0.364277	0.182138	−	0.983273i	$-0.441698\pi$
$5$	2.42754e17	0.364277	0.182138	+	0.983273i	$0.441698\pi$
$6$	−1.95896e20	−2.81299
$7$	2.85586e21	0.804889	0.402445	−	0.915444i	$-0.368161\pi$
$7$	2.85586e21	0.804889	0.402445	+	0.915444i	$0.368161\pi$
$8$	1.70259e23	1.59336
$9$	3.66124e24	1.69998
$10$	1.97206e25	0.623620
$11$	3.52088e26	0.979801	0.489900	−	0.871778i	$-0.337033\pi$
$11$	3.52088e26	0.979801	0.489900	+	0.871778i	$0.337033\pi$
$12$	−1.04840e28	−3.17251
$13$	3.67432e28	1.44418	0.722091	−	0.691798i	$-0.243181\pi$
$13$	3.67432e28	1.44418	0.722091	+	0.691798i	$0.243181\pi$
$14$	2.32001e29	1.37792
$15$	−5.85381e29	−0.598565
$16$	4.04130e30	0.797006
$17$	−6.54277e30	−0.274988	−0.137494	−	0.990503i	$-0.543905\pi$
$17$	−6.54277e30	−0.274988	−0.137494	+	0.990503i	$0.543905\pi$
$18$	2.97427e32	2.91026
$19$	2.55736e32	0.630341	0.315170	−	0.949035i	$-0.397938\pi$
$19$	2.55736e32	0.630341	0.315170	+	0.949035i	$0.397938\pi$
$20$	1.05541e33	0.703322
$21$	−6.88666e33	−1.32256
$22$	2.86025e34	1.67736
$23$	−1.69990e34	−0.320896	−0.160448	−	0.987044i	$-0.551294\pi$
$23$	−1.69990e34	−0.320896	−0.160448	+	0.987044i	$0.551294\pi$
$24$	−4.10565e35	−2.61815
$25$	−3.85160e35	−0.867302
$26$	2.98490e36	2.47235
$27$	−3.63531e36	−1.15018
$28$	1.24162e37	1.55403
$29$	3.94490e36	0.201784	0.100892	−	0.994897i	$-0.467830\pi$
$29$	3.94490e36	0.201784	0.100892	+	0.994897i	$0.467830\pi$
$30$	−4.75545e37	−1.02471
$31$	9.38800e37	0.876698	0.438349	−	0.898805i	$-0.355563\pi$
$31$	9.38800e37	0.876698	0.438349	+	0.898805i	$0.355563\pi$
$32$	−5.50861e37	−0.228938
$33$	−8.49031e38	−1.60997
$34$	−5.31514e38	−0.470763
$35$	6.93270e38	0.293202
$36$	1.59177e40	3.28221
$37$	−1.74413e40	−1.78828	−0.894140	−	0.447787i	$-0.852212\pi$
$37$	−1.74413e40	−1.78828	−0.894140	+	0.447787i	$0.852212\pi$
$38$	2.07752e40	1.07911
$39$	−8.86032e40	−2.37302
$40$	4.13310e40	0.580425
$41$	2.14671e41	1.60615	0.803074	−	0.595880i	$-0.203197\pi$
$41$	2.14671e41	1.60615	0.803074	+	0.595880i	$0.203197\pi$
$42$	−5.59451e41	−2.26415
$43$	−2.13159e41	−0.473432	−0.236716	−	0.971579i	$-0.576071\pi$
$43$	−2.13159e41	−0.473432	−0.236716	+	0.971579i	$0.576071\pi$
$44$	1.53075e42	1.89174
$45$	8.88780e41	0.619263
$46$	−1.38095e42	−0.549354
$47$	4.04105e42	0.928963	0.464481	−	0.885583i	$-0.346241\pi$
$47$	4.04105e42	0.928963	0.464481	+	0.885583i	$0.346241\pi$
$48$	−9.74526e42	−1.30961
$49$	−4.43335e42	−0.352153
$50$	−3.12892e43	−1.48477
$51$	1.57773e43	0.451850
$52$	1.59746e44	2.78833
$53$	−4.94974e42	−0.0531555	−0.0265777	−	0.999647i	$-0.508461\pi$
$53$	−4.94974e42	−0.0531555	−0.0265777	+	0.999647i	$0.508461\pi$
$54$	−2.95321e44	−1.96904
$55$	8.54708e43	0.356919
$56$	4.86235e44	1.28248
$57$	−6.16687e44	−1.03575
$58$	3.20472e44	0.345443
$59$	−1.20757e45	−0.841752	−0.420876	−	0.907118i	$-0.638277\pi$
$59$	−1.20757e45	−0.841752	−0.420876	+	0.907118i	$0.638277\pi$
$60$	−2.54502e45	−1.15567
$61$	2.20569e45	0.657104	0.328552	−	0.944486i	$-0.393439\pi$
$61$	2.20569e45	0.657104	0.328552	+	0.944486i	$0.393439\pi$
$62$	7.62652e45	1.50085
$63$	1.04560e46	1.36830
$64$	−1.35752e46	−1.18893
$65$	8.91957e45	0.526082
$66$	−6.89726e46	−2.75617
$67$	4.56801e46	1.24400	0.621999	−	0.783018i	$-0.286321\pi$
$67$	4.56801e46	1.24400	0.621999	+	0.783018i	$0.286321\pi$
$68$	−2.84456e46	−0.530930
$69$	4.09917e46	0.527284
$70$	5.63191e46	0.501945
$71$	−1.91444e47	−1.18838	−0.594189	−	0.804326i	$-0.702527\pi$
$71$	−1.91444e47	−1.18838	−0.594189	+	0.804326i	$0.702527\pi$
$72$	6.23358e47	2.70869
$73$	−8.49448e46	−0.259659	−0.129830	−	0.991536i	$-0.541443\pi$
$73$	−8.49448e46	−0.259659	−0.129830	+	0.991536i	$0.541443\pi$
$74$	−1.41688e48	−3.06143
$75$	9.28780e47	1.42512
$76$	1.11185e48	1.21702
$77$	1.00551e48	0.788631
$78$	−7.19785e48	−4.06247
$79$	2.35655e48	0.961139	0.480570	−	0.876957i	$-0.340430\pi$
$79$	2.35655e48	0.961139	0.480570	+	0.876957i	$0.340430\pi$
$80$	9.81042e47	0.290331
$81$	8.81070e47	0.189951
$82$	1.74392e49	2.74963
$83$	5.38960e48	0.623828	0.311914	−	0.950110i	$-0.399030\pi$
$83$	5.38960e48	0.623828	0.311914	+	0.950110i	$0.399030\pi$
$84$	−2.99406e49	−2.55352
$85$	−1.58828e48	−0.100172
$86$	−1.73164e49	−0.810487
$87$	−9.51281e48	−0.331564
$88$	5.99461e49	1.56118
$89$	−7.58432e49	−1.48071	−0.740357	−	0.672213i	$-0.765344\pi$
$89$	−7.58432e49	−1.48071	−0.740357	+	0.672213i	$0.765344\pi$
$90$	7.22017e49	1.06014
$91$	1.04933e50	1.16241
$92$	−7.39055e49	−0.619565
$93$	−2.26384e50	−1.44056
$94$	3.28282e50	1.59033
$95$	6.20810e49	0.229619
$96$	1.32835e50	0.376182
$97$	−8.33376e50	−1.81201	−0.906007	−	0.423263i	$-0.860885\pi$
$97$	−8.33376e50	−1.81201	−0.906007	+	0.423263i	$0.860885\pi$
$98$	−3.60151e50	−0.602865
$99$	1.28908e51	1.66564
$100$	−1.67453e51	−1.67453
$101$	3.60874e50	0.280001	0.140001	−	0.990151i	$-0.455290\pi$
$101$	3.60874e50	0.280001	0.140001	+	0.990151i	$0.455290\pi$
$102$	1.28170e51	0.773540
$103$	−5.92261e50	−0.278717	−0.139359	−	0.990242i	$-0.544504\pi$
$103$	−5.92261e50	−0.278717	−0.139359	+	0.990242i	$0.544504\pi$
$104$	6.25586e51	2.30111
$105$	−1.67176e51	−0.481779
$106$	−4.02102e50	−0.0909989
$107$	−2.68636e51	−0.478495	−0.239247	−	0.970959i	$-0.576901\pi$
$107$	−2.68636e51	−0.478495	−0.239247	+	0.970959i	$0.576901\pi$
$108$	−1.58050e52	−2.22069
$109$	−1.08273e52	−1.20267	−0.601335	−	0.798997i	$-0.705364\pi$
$109$	−1.08273e52	−1.20267	−0.601335	+	0.798997i	$0.705364\pi$
$110$	6.94338e51	0.611023
$111$	4.20583e52	2.93843
$112$	1.15414e52	0.641502
$113$	−1.18691e52	−0.525915	−0.262958	−	0.964807i	$-0.584698\pi$
$113$	−1.18691e52	−0.525915	−0.262958	+	0.964807i	$0.584698\pi$
$114$	−5.00977e52	−1.77314
$115$	−4.12658e51	−0.116895
$116$	1.71510e52	0.389592
$117$	1.34526e53	2.45508
$118$	−9.80988e52	−1.44103
$119$	−1.86852e52	−0.221335
$120$	−9.96663e52	−0.953733
$121$	−5.16394e51	−0.0399903
$122$	1.79184e53	1.12492
$123$	−5.17662e53	−2.63916
$124$	4.08156e53	1.69267
$125$	−2.01304e53	−0.680215
$126$	8.49410e53	2.34244
$127$	2.91976e53	0.658190	0.329095	−	0.944297i	$-0.393256\pi$
$127$	2.91976e53	0.658190	0.329095	+	0.944297i	$0.393256\pi$
$128$	−9.78766e53	−1.80644
$129$	5.14015e53	0.777925
$130$	7.24598e53	0.900620
$131$	−1.12031e54	−1.14530	−0.572651	−	0.819799i	$-0.694085\pi$
$131$	−1.12031e54	−1.14530	−0.572651	+	0.819799i	$0.694085\pi$
$132$	−3.69127e54	−3.10843
$133$	7.30346e53	0.507355
$134$	3.71091e54	2.12965
$135$	−8.82487e53	−0.418984
$136$	−1.11396e54	−0.438156
$137$	3.16309e54	1.03214	0.516068	−	0.856548i	$-0.327395\pi$
$137$	3.16309e54	1.03214	0.516068	+	0.856548i	$0.327395\pi$
$138$	3.33004e54	0.902678
$139$	−8.65660e53	−0.195196	−0.0975978	−	0.995226i	$-0.531116\pi$
$139$	−8.65660e53	−0.195196	−0.0975978	+	0.995226i	$0.531116\pi$
$140$	3.01408e54	0.566097
$141$	−9.74464e54	−1.52644
$142$	−1.55523e55	−2.03443
$143$	1.29368e55	1.41501
$144$	1.47962e55	1.35489
$145$	9.57641e53	0.0735053
$146$	−6.90065e54	−0.444521
$147$	1.06906e55	0.578645
$148$	−7.58285e55	−3.45270
$149$	−6.45813e54	−0.247661	−0.123830	−	0.992303i	$-0.539518\pi$
$149$	−6.45813e54	−0.247661	−0.123830	+	0.992303i	$0.539518\pi$
$150$	7.54512e55	2.43972
$151$	2.64453e55	0.721832	0.360916	−	0.932598i	$-0.382464\pi$
$151$	2.64453e55	0.721832	0.360916	+	0.932598i	$0.382464\pi$
$152$	4.35414e55	1.00436
$153$	−2.39546e55	−0.467474
$154$	8.16847e55	1.35009
$155$	2.27898e55	0.319361
$156$	−3.85214e56	−4.58168
$157$	−1.74550e55	−0.176392	−0.0881962	−	0.996103i	$-0.528110\pi$
$157$	−1.74550e55	−0.176392	−0.0881962	+	0.996103i	$0.528110\pi$
$158$	1.91439e56	1.64541
$159$	1.19359e55	0.0873430
$160$	−1.33724e55	−0.0833967
$161$	−4.85467e55	−0.258286
$162$	7.15754e55	0.325185
$163$	−2.44447e56	−0.949296	−0.474648	−	0.880176i	$-0.657425\pi$
$163$	−2.44447e56	−0.949296	−0.474648	+	0.880176i	$0.657425\pi$
$164$	9.33311e56	3.10105
$165$	−2.06106e56	−0.586475
$166$	4.37834e56	1.06796
$167$	−7.65512e56	−1.60207	−0.801036	−	0.598616i	$-0.795718\pi$
$167$	−7.65512e56	−1.60207	−0.801036	+	0.598616i	$0.795718\pi$
$168$	−1.17251e57	−2.10732
$169$	7.02756e56	1.08566
$170$	−1.29027e56	−0.171488
$171$	9.36311e56	1.07157
$172$	−9.26736e56	−0.914073
$173$	6.79321e56	0.577963	0.288981	−	0.957335i	$-0.406683\pi$
$173$	6.79321e56	0.577963	0.288981	+	0.957335i	$0.406683\pi$
$174$	−7.72791e56	−0.567618
$175$	−1.09996e57	−0.698082
$176$	1.42289e57	0.780907
$177$	2.91194e57	1.38313
$178$	−6.16126e57	−2.53489
$179$	2.98876e57	1.06596	0.532978	−	0.846129i	$-0.321073\pi$
$179$	2.98876e57	1.06596	0.532978	+	0.846129i	$0.321073\pi$
$180$	3.86409e57	1.19563
$181$	−1.29245e57	−0.347223	−0.173611	−	0.984814i	$-0.555544\pi$
$181$	−1.29245e57	−0.347223	−0.173611	+	0.984814i	$0.555544\pi$
$182$	8.52446e57	1.98997
$183$	−5.31885e57	−1.07973
$184$	−2.89423e57	−0.511304
$185$	−4.23395e57	−0.651429
$186$	−1.83907e58	−2.46614
$187$	−2.30363e57	−0.269434
$188$	1.75690e58	1.79358
$189$	−1.03819e58	−0.925767
$190$	5.04327e57	0.393093
$191$	2.79327e58	1.90442	0.952209	−	0.305446i	$-0.0988057\pi$
$191$	2.79327e58	1.90442	0.952209	+	0.305446i	$0.0988057\pi$
$192$	3.27355e58	1.95361
$193$	1.88817e58	0.987027	0.493514	−	0.869738i	$-0.335712\pi$
$193$	1.88817e58	0.987027	0.493514	+	0.869738i	$0.335712\pi$
$194$	−6.77008e58	−3.10206
$195$	−2.15088e58	−0.864437
$196$	−1.92746e58	−0.679915
$197$	−3.18961e58	−0.988209	−0.494104	−	0.869403i	$-0.664504\pi$
$197$	−3.18961e58	−0.988209	−0.494104	+	0.869403i	$0.664504\pi$
$198$	1.04721e59	2.85148
$199$	4.26943e58	1.02239	0.511195	−	0.859465i	$-0.329203\pi$
$199$	4.26943e58	1.02239	0.511195	+	0.859465i	$0.329203\pi$
$200$	−6.55768e58	−1.38193
$201$	−1.10154e59	−2.04409
$202$	2.93163e58	0.479346
$203$	1.12661e58	0.162414
$204$	6.85941e58	0.872403
$205$	5.21123e58	0.585082
$206$	−4.81134e58	−0.477147
$207$	−6.22374e58	−0.545517
$208$	1.48490e59	1.15102
$209$	9.00417e58	0.617609
$210$	−1.35809e59	−0.824776
$211$	−1.08128e59	−0.581748	−0.290874	−	0.956761i	$-0.593946\pi$
$211$	−1.08128e59	−0.581748	−0.290874	+	0.956761i	$0.593946\pi$
$212$	−2.15197e58	−0.102629
$213$	4.61652e59	1.95270
$214$	−2.18231e59	−0.819154
$215$	−5.17452e58	−0.172460
$216$	−6.18944e59	−1.83266
$217$	2.68108e59	0.705645
$218$	−8.79580e59	−2.05890
$219$	2.04837e59	0.426662
$220$	3.71596e59	0.689116
$221$	−2.40402e59	−0.397133
$222$	3.41669e60	5.03042
$223$	−6.98254e59	−0.916726	−0.458363	−	0.888765i	$-0.651564\pi$
$223$	−6.98254e59	−0.916726	−0.458363	+	0.888765i	$0.651564\pi$
$224$	−1.57318e59	−0.184270
$225$	−1.41016e60	−1.47440
$226$	−9.64205e59	−0.900335
$227$	1.84393e60	1.53846	0.769228	−	0.638975i	$-0.220641\pi$
$227$	1.84393e60	1.53846	0.769228	+	0.638975i	$0.220641\pi$
$228$	−2.68113e60	−1.99976
$229$	3.39685e59	0.226606	0.113303	−	0.993560i	$-0.463857\pi$
$229$	3.39685e59	0.226606	0.113303	+	0.993560i	$0.463857\pi$
$230$	−3.35231e59	−0.200117
$231$	−2.42471e60	−1.29585
$232$	6.71655e59	0.321516
$233$	−1.17691e60	−0.504854	−0.252427	−	0.967616i	$-0.581229\pi$
$233$	−1.17691e60	−0.504854	−0.252427	+	0.967616i	$0.581229\pi$
$234$	1.09284e61	4.20295
$235$	9.80980e59	0.338400
$236$	−5.25005e60	−1.62520
$237$	−5.68263e60	−1.57931
$238$	−1.51793e60	−0.378912
$239$	5.07807e60	1.13907	0.569537	−	0.821966i	$-0.307122\pi$
$239$	5.07807e60	1.13907	0.569537	+	0.821966i	$0.307122\pi$
$240$	−2.36570e60	−0.477060
$241$	4.94984e60	0.897752	0.448876	−	0.893594i	$-0.351824\pi$
$241$	4.94984e60	0.897752	0.448876	+	0.893594i	$0.351824\pi$
$242$	−4.19503e59	−0.0684609
$243$	5.70472e60	0.838059
$244$	9.58954e60	1.26870
$245$	−1.07621e60	−0.128281
$246$	−4.20532e61	−4.51808
$247$	9.39657e60	0.910327
$248$	1.59839e61	1.39690
$249$	−1.29966e61	−1.02505
$250$	−1.63533e61	−1.16449
$251$	−1.18124e60	−0.0759731	−0.0379866	−	0.999278i	$-0.512094\pi$
$251$	−1.18124e60	−0.0759731	−0.0379866	+	0.999278i	$0.512094\pi$
$252$	4.54587e61	2.64182
$253$	−5.98515e60	−0.314414
$254$	2.37192e61	1.12678
$255$	3.83001e60	0.164598
$256$	−4.89432e61	−1.90359
$257$	2.72008e61	0.957827	0.478914	−	0.877862i	$-0.341031\pi$
$257$	2.72008e61	0.957827	0.478914	+	0.877862i	$0.341031\pi$
$258$	4.17570e61	1.33176
$259$	−4.98099e61	−1.43937
$260$	3.87790e61	1.01572
$261$	1.44432e61	0.343029
$262$	−9.10105e61	−1.96069
$263$	−2.48007e61	−0.484834	−0.242417	−	0.970172i	$-0.577940\pi$
$263$	−2.48007e61	−0.484834	−0.242417	+	0.970172i	$0.577940\pi$
$264$	−1.44555e62	−2.56527
$265$	−1.20157e60	−0.0193633
$266$	5.93310e61	0.868560
$267$	1.82890e62	2.43305
$268$	1.98600e62	2.40183
$269$	−6.54289e61	−0.719592	−0.359796	−	0.933031i	$-0.617154\pi$
$269$	−6.54289e61	−0.719592	−0.359796	+	0.933031i	$0.617154\pi$
$270$	−7.16905e61	−0.717275
$271$	−6.85359e60	−0.0624024	−0.0312012	−	0.999513i	$-0.509933\pi$
$271$	−6.85359e60	−0.0624024	−0.0312012	+	0.999513i	$0.509933\pi$
$272$	−2.64413e61	−0.219167
$273$	−2.53038e62	−1.91002
$274$	2.56959e62	1.76695
$275$	−1.35610e62	−0.849784
$276$	1.78217e62	1.01805
$277$	−2.43203e62	−1.26688	−0.633438	−	0.773793i	$-0.718357\pi$
$277$	−2.43203e62	−1.26688	−0.633438	+	0.773793i	$0.718357\pi$
$278$	−7.03235e61	−0.334163
$279$	3.43717e62	1.49037
$280$	1.18035e62	0.467178
$281$	2.21655e62	0.801062	0.400531	−	0.916283i	$-0.368826\pi$
$281$	2.21655e62	0.801062	0.400531	+	0.916283i	$0.368826\pi$
$282$	−7.91624e62	−2.61317
$283$	1.63167e62	0.492127	0.246063	−	0.969254i	$-0.420863\pi$
$283$	1.63167e62	0.492127	0.246063	+	0.969254i	$0.420863\pi$
$284$	−8.32329e62	−2.29444
$285$	−1.49703e62	−0.377300
$286$	1.05095e63	2.42241
$287$	6.13070e62	1.29277
$288$	−2.01683e62	−0.389190
$289$	−5.23295e62	−0.924381
$290$	7.77958e61	0.125837
$291$	2.00962e63	2.97743
$292$	−3.69309e62	−0.501334
$293$	−7.35742e62	−0.915380	−0.457690	−	0.889112i	$-0.651323\pi$
$293$	−7.35742e62	−0.915380	−0.457690	+	0.889112i	$0.651323\pi$
$294$	8.68475e62	0.990605
$295$	−2.93141e62	−0.306631
$296$	−2.96954e63	−2.84938
$297$	−1.27995e63	−1.12695
$298$	−5.24638e62	−0.423980
$299$	−6.24599e62	−0.463432
$300$	4.03800e63	2.75153
$301$	−6.08751e62	−0.381060
$302$	2.14833e63	1.23573
$303$	−8.70217e62	−0.460088
$304$	1.03351e63	0.502386
$305$	5.35441e62	0.239368
$306$	−1.94600e63	−0.800288
$307$	−2.33959e63	−0.885341	−0.442671	−	0.896684i	$-0.645969\pi$
$307$	−2.33959e63	−0.885341	−0.442671	+	0.896684i	$0.645969\pi$
$308$	4.37160e63	1.52264
$309$	1.42819e63	0.457977
$310$	1.85137e63	0.546726
$311$	5.85752e63	1.59340	0.796698	−	0.604378i	$-0.206578\pi$
$311$	5.85752e63	1.59340	0.796698	+	0.604378i	$0.206578\pi$
$312$	−1.50855e64	−3.78109
$313$	−5.58306e63	−1.28971	−0.644855	−	0.764305i	$-0.723082\pi$
$313$	−5.58306e63	−1.28971	−0.644855	+	0.764305i	$0.723082\pi$
$314$	−1.41799e63	−0.301973
$315$	2.53823e63	0.498438
$316$	1.02454e64	1.85571
$317$	−2.94076e63	−0.491414	−0.245707	−	0.969344i	$-0.579020\pi$
$317$	−2.94076e63	−0.491414	−0.245707	+	0.969344i	$0.579020\pi$
$318$	9.69634e62	0.149526
$319$	1.38895e63	0.197708
$320$	−3.29544e63	−0.433101
$321$	6.47792e63	0.786244
$322$	−3.94379e63	−0.442169
$323$	−1.67322e63	−0.173336
$324$	3.83057e63	0.366746
$325$	−1.41520e64	−1.25254
$326$	−1.98582e64	−1.62514
$327$	2.61092e64	1.97618
$328$	3.65497e64	2.55918
$329$	1.15406e64	0.747712
$330$	−1.67434e64	−1.00401
$331$	8.27822e63	0.459540	0.229770	−	0.973245i	$-0.426203\pi$
$331$	8.27822e63	0.459540	0.229770	+	0.973245i	$0.426203\pi$
$332$	2.34320e64	1.20445
$333$	−6.38568e64	−3.04004
$334$	−6.21878e64	−2.74265
$335$	1.10890e64	0.453159
$336$	−2.78311e64	−1.05409
$337$	2.46670e63	0.0866070	0.0433035	−	0.999062i	$-0.486212\pi$
$337$	2.46670e63	0.0866070	0.0433035	+	0.999062i	$0.486212\pi$
$338$	5.70897e64	1.85858
$339$	2.86212e64	0.864164
$340$	−6.90527e63	−0.193405
$341$	3.30540e64	0.858989
$342$	7.60630e64	1.83446
$343$	−4.86141e64	−1.08833
$344$	−3.62922e64	−0.754350
$345$	9.95091e63	0.192077
$346$	5.51860e64	0.989437
$347$	1.55920e64	0.259717	0.129858	−	0.991533i	$-0.458548\pi$
$347$	1.55920e64	0.259717	0.129858	+	0.991533i	$0.458548\pi$
$348$	−4.13582e64	−0.640163
$349$	−5.23164e64	−0.752644	−0.376322	−	0.926489i	$-0.622811\pi$
$349$	−5.23164e64	−0.752644	−0.376322	+	0.926489i	$0.622811\pi$
$350$	−8.93573e64	−1.19507
$351$	−1.33573e65	−1.66107
$352$	−1.93951e64	−0.224313
$353$	1.78259e65	1.91777	0.958885	−	0.283795i	$-0.0915934\pi$
$353$	1.78259e65	1.91777	0.958885	+	0.283795i	$0.0915934\pi$
$354$	2.36557e65	2.36784
$355$	−4.64739e64	−0.432898
$356$	−3.29738e65	−2.85887
$357$	4.50578e64	0.363689
$358$	2.42798e65	1.82485
$359$	−1.48533e65	−1.03972	−0.519858	−	0.854253i	$-0.674015\pi$
$359$	−1.48533e65	−1.03972	−0.519858	+	0.854253i	$0.674015\pi$
$360$	1.51323e65	0.986711
$361$	−9.92004e64	−0.602670
$362$	−1.04994e65	−0.594425
$363$	1.24524e64	0.0657105
$364$	4.56211e65	2.24430
$365$	−2.06207e64	−0.0945879
$366$	−4.32086e65	−1.84843
$367$	8.05130e64	0.321278	0.160639	−	0.987013i	$-0.448644\pi$
$367$	8.05130e64	0.321278	0.160639	+	0.987013i	$0.448644\pi$
$368$	−6.86982e64	−0.255756
$369$	7.85962e65	2.73042
$370$	−3.43953e65	−1.11521
$371$	−1.41357e64	−0.0427843
$372$	−9.84233e65	−2.78133
$373$	2.25234e64	0.0594372	0.0297186	−	0.999558i	$-0.490539\pi$
$373$	2.25234e64	0.0594372	0.0297186	+	0.999558i	$0.490539\pi$
$374$	−1.87140e65	−0.461254
$375$	4.85427e65	1.11770
$376$	6.88024e65	1.48018
$377$	1.44948e65	0.291413
$378$	−8.43395e65	−1.58486
$379$	−1.01382e66	−1.78098	−0.890491	−	0.455001i	$-0.849639\pi$
$379$	−1.01382e66	−1.78098	−0.890491	+	0.455001i	$0.849639\pi$
$380$	2.69905e65	0.443333
$381$	−7.04075e65	−1.08151
$382$	2.26917e66	3.26025
$383$	−3.69389e65	−0.496496	−0.248248	−	0.968697i	$-0.579855\pi$
$383$	−3.69389e65	−0.496496	−0.248248	+	0.968697i	$0.579855\pi$
$384$	2.36021e66	2.96828
$385$	2.44092e65	0.287280
$386$	1.53389e66	1.68973
$387$	−7.80425e65	−0.804825
$388$	−3.62321e66	−3.49852
$389$	−1.20048e66	−1.08552	−0.542762	−	0.839887i	$-0.682621\pi$
$389$	−1.20048e66	−1.08552	−0.542762	+	0.839887i	$0.682621\pi$
$390$	−1.74731e66	−1.47986
$391$	1.11221e65	0.0882426
$392$	−7.54816e65	−0.561108
$393$	2.70153e66	1.88192
$394$	−2.59114e66	−1.69175
$395$	5.72063e65	0.350121
$396$	5.60443e66	3.21591
$397$	−2.17708e66	−1.17143	−0.585714	−	0.810518i	$-0.699186\pi$
$397$	−2.17708e66	−1.17143	−0.585714	+	0.810518i	$0.699186\pi$
$398$	3.46835e66	1.75027
$399$	−1.76117e66	−0.833666
$400$	−1.55655e66	−0.691245
$401$	4.28565e66	1.78581	0.892905	−	0.450245i	$-0.148663\pi$
$401$	4.28565e66	1.78581	0.892905	+	0.450245i	$0.148663\pi$
$402$	−8.94854e66	−3.49935
$403$	3.44945e66	1.26611
$404$	1.56895e66	0.540609
$405$	2.13883e65	0.0691949
$406$	9.15221e65	0.278043
$407$	−6.14088e66	−1.75216
$408$	2.68623e66	0.719962
$409$	7.61605e66	1.91772	0.958860	−	0.283878i	$-0.0916211\pi$
$409$	7.61605e66	1.91772	0.958860	+	0.283878i	$0.0916211\pi$
$410$	4.23344e66	1.00162
$411$	−7.62752e66	−1.69597
$412$	−2.57493e66	−0.538129
$413$	−3.44863e66	−0.677517
$414$	−5.05598e66	−0.933891
$415$	1.30835e66	0.227246
$416$	−2.02404e66	−0.330628
$417$	2.08747e66	0.320738
$418$	7.31471e66	1.05731
$419$	3.51155e66	0.477574	0.238787	−	0.971072i	$-0.423250\pi$
$419$	3.51155e66	0.477574	0.238787	+	0.971072i	$0.423250\pi$
$420$	−7.26821e66	−0.930188
$421$	−3.18883e66	−0.384094	−0.192047	−	0.981386i	$-0.561513\pi$
$421$	−3.18883e66	−0.384094	−0.192047	+	0.981386i	$0.561513\pi$
$422$	−8.78397e66	−0.995917
$423$	1.47952e67	1.57922
$424$	−8.42737e65	−0.0846960
$425$	2.52001e66	0.238498
$426$	3.75031e67	3.34290
$427$	6.29914e66	0.528896
$428$	−1.16793e67	−0.923847
$429$	−3.11961e67	−2.32509
$430$	−4.20362e66	−0.295242
$431$	−2.27664e66	−0.150704	−0.0753519	−	0.997157i	$-0.524008\pi$
$431$	−2.27664e66	−0.150704	−0.0753519	+	0.997157i	$0.524008\pi$
$432$	−1.46914e67	−0.916700
$433$	−2.96559e66	−0.174449	−0.0872247	−	0.996189i	$-0.527800\pi$
$433$	−2.96559e66	−0.174449	−0.0872247	+	0.996189i	$0.527800\pi$
$434$	2.17802e67	1.20802
$435$	−2.30927e66	−0.120781
$436$	−4.70733e67	−2.32204
$437$	−4.34727e66	−0.202274
$438$	1.66404e67	0.730420
$439$	3.03815e67	1.25824	0.629121	−	0.777307i	$-0.283415\pi$
$439$	3.03815e67	1.25824	0.629121	+	0.777307i	$0.283415\pi$
$440$	1.45522e67	0.568701
$441$	−1.62315e67	−0.598653
$442$	−1.95295e67	−0.679867
$443$	−1.74549e67	−0.573619	−0.286810	−	0.957988i	$-0.592595\pi$
$443$	−1.74549e67	−0.573619	−0.286810	+	0.957988i	$0.592595\pi$
$444$	1.82854e68	5.67334
$445$	−1.84112e67	−0.539390
$446$	−5.67240e67	−1.56938
$447$	1.55732e67	0.406946
$448$	−3.87689e67	−0.956960
$449$	−2.54711e67	−0.593972	−0.296986	−	0.954882i	$-0.595981\pi$
$449$	−2.54711e67	−0.593972	−0.296986	+	0.954882i	$0.595981\pi$
$450$	−1.14557e68	−2.52408
$451$	7.55832e67	1.57370
$452$	−5.16023e67	−1.01540
$453$	−6.37706e67	−1.18609
$454$	1.49795e68	2.63374
$455$	2.54730e67	0.423437
$456$	−1.04996e68	−1.65033
$457$	8.96015e67	1.33184	0.665920	−	0.746023i	$-0.268039\pi$
$457$	8.96015e67	1.33184	0.665920	+	0.746023i	$0.268039\pi$
$458$	2.75949e67	0.387935
$459$	2.37850e67	0.316286
$460$	−1.79409e67	−0.225693
$461$	8.19688e67	0.975607	0.487804	−	0.872953i	$-0.337798\pi$
$461$	8.19688e67	0.975607	0.487804	+	0.872953i	$0.337798\pi$
$462$	−1.96976e68	−2.21841
$463$	−1.13766e68	−1.21254	−0.606269	−	0.795259i	$-0.707335\pi$
$463$	−1.13766e68	−1.21254	−0.606269	+	0.795259i	$0.707335\pi$
$464$	1.59425e67	0.160823
$465$	−5.49556e67	−0.524761
$466$	−9.56082e67	−0.864280
$467$	2.22344e67	0.190303	0.0951516	−	0.995463i	$-0.469666\pi$
$467$	2.22344e67	0.190303	0.0951516	+	0.995463i	$0.469666\pi$
$468$	5.84868e68	4.74011
$469$	1.30456e68	1.00128
$470$	7.96918e67	0.579319
$471$	4.20914e67	0.289841
$472$	−2.05599e68	−1.34122
$473$	−7.50507e67	−0.463869
$474$	−4.61639e68	−2.70368
$475$	−9.84993e67	−0.546696
$476$	−8.12364e67	−0.427340
$477$	−1.81222e67	−0.0903632
$478$	4.12527e68	1.95003
$479$	−1.15577e68	−0.517983	−0.258992	−	0.965880i	$-0.583390\pi$
$479$	−1.15577e68	−0.517983	−0.258992	+	0.965880i	$0.583390\pi$
$480$	3.22464e67	0.137034
$481$	−6.40851e68	−2.58260
$482$	4.02110e68	1.53690
$483$	1.17066e68	0.424405
$484$	−2.24509e67	−0.0772107
$485$	−2.02305e68	−0.660074
$486$	4.63434e68	1.43471
$487$	2.20619e66	0.00648118	0.00324059	−	0.999995i	$-0.498968\pi$
$487$	2.20619e66	0.00648118	0.00324059	+	0.999995i	$0.498968\pi$
$488$	3.75539e68	1.04701
$489$	5.89465e68	1.55985
$490$	−8.74282e67	−0.219610
$491$	7.91071e68	1.88642	0.943208	−	0.332202i	$-0.107792\pi$
$491$	7.91071e68	1.88642	0.943208	+	0.332202i	$0.107792\pi$
$492$	−2.25060e69	−5.09552
$493$	−2.58106e67	−0.0554883
$494$	7.63348e68	1.55842
$495$	3.12929e68	0.606754
$496$	3.79397e68	0.698734
$497$	−5.46737e68	−0.956512
$498$	−1.05580e69	−1.75482
$499$	−9.62285e68	−1.51964	−0.759819	−	0.650135i	$-0.774712\pi$
$499$	−9.62285e68	−1.51964	−0.759819	+	0.650135i	$0.774712\pi$
$500$	−8.75194e68	−1.31332
$501$	1.84597e69	2.63246
$502$	−9.59607e67	−0.130061
$503$	5.82620e67	0.0750588	0.0375294	−	0.999296i	$-0.488051\pi$
$503$	5.82620e67	0.0750588	0.0375294	+	0.999296i	$0.488051\pi$
$504$	1.78022e69	2.18019
$505$	8.76036e67	0.101998
$506$	−4.86215e68	−0.538258
$507$	−1.69464e69	−1.78391
$508$	1.26940e69	1.27079
$509$	5.13252e68	0.488683	0.244342	−	0.969689i	$-0.421428\pi$
$509$	5.13252e68	0.488683	0.244342	+	0.969689i	$0.421428\pi$
$510$	3.11138e68	0.281783
$511$	−2.42590e68	−0.208997
$512$	−1.77201e69	−1.45239
$513$	−9.29681e68	−0.725005
$514$	2.20971e69	1.63974
$515$	−1.43774e68	−0.101530
$516$	2.23475e69	1.50197
$517$	1.42280e69	0.910199
$518$	−4.04640e69	−2.46411
$519$	−1.63813e69	−0.949686
$520$	1.51863e69	0.838240
$521$	1.75529e69	0.922545	0.461272	−	0.887259i	$-0.347393\pi$
$521$	1.75529e69	0.922545	0.461272	+	0.887259i	$0.347393\pi$
$522$	1.17332e69	0.587245
$523$	3.31068e68	0.157806	0.0789032	−	0.996882i	$-0.474858\pi$
$523$	3.31068e68	0.157806	0.0789032	+	0.996882i	$0.474858\pi$
$524$	−4.87069e69	−2.21128
$525$	2.65246e69	1.14706
$526$	−2.01473e69	−0.830006
$527$	−6.14235e68	−0.241082
$528$	−3.43119e69	−1.28316
$529$	−2.51724e69	−0.897026
$530$	−9.76118e67	−0.0331488
$531$	−4.42118e69	−1.43096
$532$	3.17527e69	0.979568
$533$	7.88771e69	2.31957
$534$	1.48574e70	4.16524
$535$	−6.52124e68	−0.174304
$536$	7.77744e69	1.98214
$537$	−7.20716e69	−1.75154
$538$	−5.31524e69	−1.23190
$539$	−1.56093e69	−0.345040
$540$	−3.83673e69	−0.808947
$541$	−8.41369e69	−1.69222	−0.846109	−	0.533009i	$-0.821061\pi$
$541$	−8.41369e69	−1.69222	−0.846109	+	0.533009i	$0.821061\pi$
$542$	−5.56764e68	−0.106829
$543$	3.11662e69	0.570543
$544$	3.60415e68	0.0629552
$545$	−2.62838e69	−0.438104
$546$	−2.05560e70	−3.26984
$547$	1.11230e70	1.68867	0.844334	−	0.535817i	$-0.179996\pi$
$547$	1.11230e70	1.68867	0.844334	+	0.535817i	$0.179996\pi$
$548$	1.37519e70	1.99278
$549$	8.07556e69	1.11706
$550$	−1.10165e70	−1.45478
$551$	1.00885e69	0.127193
$552$	6.97920e69	0.840155
$553$	6.72997e69	0.773611
$554$	−1.97570e70	−2.16882
$555$	1.02098e70	1.07040
$556$	−3.76357e69	−0.376871
$557$	−1.12523e70	−1.07630	−0.538152	−	0.842848i	$-0.680877\pi$
$557$	−1.12523e70	−1.07630	−0.538152	+	0.842848i	$0.680877\pi$
$558$	2.79225e70	2.55142
$559$	−7.83214e69	−0.683722
$560$	2.80171e69	0.233684
$561$	5.55501e69	0.442723
$562$	1.80065e70	1.37137
$563$	−2.06561e68	−0.0150344	−0.00751718	−	0.999972i	$-0.502393\pi$
$563$	−2.06561e68	−0.0150344	−0.00751718	+	0.999972i	$0.502393\pi$
$564$	−4.23661e70	−2.94715
$565$	−2.88126e69	−0.191579
$566$	1.32551e70	0.842491
$567$	2.51621e69	0.152890
$568$	−3.25951e70	−1.89352
$569$	1.15170e70	0.639698	0.319849	−	0.947469i	$-0.396368\pi$
$569$	1.15170e70	0.639698	0.319849	+	0.947469i	$0.396368\pi$
$570$	−1.21614e70	−0.645915
$571$	2.10280e70	1.06801	0.534007	−	0.845480i	$-0.320686\pi$
$571$	2.10280e70	1.06801	0.534007	+	0.845480i	$0.320686\pi$
$572$	5.62447e70	2.73201
$573$	−6.73574e70	−3.12927
$574$	4.98039e70	2.21315
$575$	6.54734e69	0.278314
$576$	−4.97021e70	−2.02116
$577$	5.78798e68	0.0225187	0.0112594	−	0.999937i	$-0.496416\pi$
$577$	5.78798e68	0.0225187	0.0112594	+	0.999937i	$0.496416\pi$
$578$	−4.25108e70	−1.58248
$579$	−4.55316e70	−1.62185
$580$	4.16347e69	0.141919
$581$	1.53919e70	0.502113
$582$	1.63255e71	5.09718
$583$	−1.74274e69	−0.0520818
$584$	−1.44626e70	−0.413732
$585$	3.26566e70	0.894328
$586$	−5.97694e70	−1.56707
$587$	−3.63201e70	−0.911748	−0.455874	−	0.890044i	$-0.650673\pi$
$587$	−3.63201e70	−0.911748	−0.455874	+	0.890044i	$0.650673\pi$
$588$	4.64790e70	1.11721
$589$	2.40085e70	0.552619
$590$	−2.38139e70	−0.524933
$591$	7.69148e70	1.62379
$592$	−7.04857e70	−1.42527
$593$	−2.80060e70	−0.542447	−0.271223	−	0.962516i	$-0.587428\pi$
$593$	−2.80060e70	−0.542447	−0.271223	+	0.962516i	$0.587428\pi$
$594$	−1.03979e71	−1.92927
$595$	−4.53591e69	−0.0806272
$596$	−2.80776e70	−0.478167
$597$	−1.02954e71	−1.67995
$598$	−5.07405e70	−0.793367
$599$	4.36080e70	0.653404	0.326702	−	0.945127i	$-0.394063\pi$
$599$	4.36080e70	0.653404	0.326702	+	0.945127i	$0.394063\pi$
$600$	1.58133e71	2.27073
$601$	3.82831e70	0.526875	0.263437	−	0.964676i	$-0.415144\pi$
$601$	3.82831e70	0.526875	0.263437	+	0.964676i	$0.415144\pi$
$602$	−4.94530e70	−0.652352
$603$	1.67246e71	2.11477
$604$	1.14974e71	1.39367
$605$	−1.25357e69	−0.0145675
$606$	−7.06937e70	−0.787642
$607$	−2.49833e70	−0.266894	−0.133447	−	0.991056i	$-0.542605\pi$
$607$	−2.49833e70	−0.266894	−0.133447	+	0.991056i	$0.542605\pi$
$608$	−1.40875e70	−0.144309
$609$	−2.71672e70	−0.266872
$610$	4.34976e70	0.409783
$611$	1.48481e71	1.34159
$612$	−1.04146e71	−0.902570
$613$	−1.99012e71	−1.65439	−0.827193	−	0.561919i	$-0.810063\pi$
$613$	−1.99012e71	−1.65439	−0.827193	+	0.561919i	$0.810063\pi$
$614$	−1.90061e71	−1.51565
$615$	−1.25664e71	−0.961384
$616$	1.71197e71	1.25658
$617$	5.04536e70	0.355321	0.177660	−	0.984092i	$-0.443147\pi$
$617$	5.04536e70	0.355321	0.177660	+	0.984092i	$0.443147\pi$
$618$	1.16021e71	0.784029
$619$	−8.80938e70	−0.571260	−0.285630	−	0.958340i	$-0.592203\pi$
$619$	−8.80938e70	−0.571260	−0.285630	+	0.958340i	$0.592203\pi$
$620$	9.90814e70	0.616601
$621$	6.17968e70	0.369088
$622$	4.75846e71	2.72780
$623$	−2.16597e71	−1.19181
$624$	−3.58072e71	−1.89131
$625$	1.22178e71	0.619516
$626$	−4.53551e71	−2.20790
$627$	−2.17128e71	−1.01483
$628$	−7.58881e70	−0.340567
$629$	1.14115e71	0.491756
$630$	2.06198e71	0.853296
$631$	3.58339e71	1.42411	0.712057	−	0.702121i	$-0.247764\pi$
$631$	3.58339e71	1.42411	0.712057	+	0.702121i	$0.247764\pi$
$632$	4.01224e71	1.53144
$633$	2.60741e71	0.955906
$634$	−2.38898e71	−0.841271
$635$	7.08782e70	0.239763
$636$	5.18928e70	0.168636
$637$	−1.62895e71	−0.508573
$638$	1.12834e71	0.338465
$639$	−7.00922e71	−2.02022
$640$	−2.37599e71	−0.658046
$641$	6.07769e71	1.61755	0.808777	−	0.588116i	$-0.200130\pi$
$641$	6.07769e71	1.61755	0.808777	+	0.588116i	$0.200130\pi$
$642$	5.26246e71	1.34600
$643$	−7.85977e71	−1.93210	−0.966050	−	0.258353i	$-0.916820\pi$
$643$	−7.85977e71	−1.93210	−0.966050	+	0.258353i	$0.916820\pi$
$644$	−2.11063e71	−0.498681
$645$	1.24779e71	0.283380
$646$	−1.35927e71	−0.296741
$647$	5.80462e71	1.21819	0.609095	−	0.793098i	$-0.291533\pi$
$647$	5.80462e71	1.21819	0.609095	+	0.793098i	$0.291533\pi$
$648$	1.50010e71	0.302662
$649$	−4.25169e71	−0.824750
$650$	−1.14966e72	−2.14428
$651$	−6.46519e71	−1.15949
$652$	−1.06277e72	−1.83284
$653$	9.50695e71	1.57672	0.788361	−	0.615213i	$-0.210930\pi$
$653$	9.50695e71	1.57672	0.788361	+	0.615213i	$0.210930\pi$
$654$	2.12103e72	3.38310
$655$	−2.71960e71	−0.417207
$656$	8.67551e71	1.28011
$657$	−3.11003e71	−0.441416
$658$	9.37526e71	1.28004
$659$	5.24300e71	0.688655	0.344327	−	0.938850i	$-0.388107\pi$
$659$	5.24300e71	0.688655	0.344327	+	0.938850i	$0.388107\pi$
$660$	−8.96072e71	−1.13233
$661$	1.48904e71	0.181038	0.0905189	−	0.995895i	$-0.471147\pi$
$661$	1.48904e71	0.181038	0.0905189	+	0.995895i	$0.471147\pi$
$662$	6.72497e71	0.786704
$663$	5.79710e71	0.652553
$664$	9.17627e71	0.993986
$665$	1.77294e71	0.184817
$666$	−5.18753e72	−5.20437
$667$	−6.70595e70	−0.0647518
$668$	−3.32817e72	−3.09318
$669$	1.68378e72	1.50633
$670$	9.00838e71	0.775781
$671$	7.76598e71	0.643831
$672$	3.79359e71	0.302785
$673$	−5.12793e70	−0.0394056	−0.0197028	−	0.999806i	$-0.506272\pi$
$673$	−5.12793e70	−0.0394056	−0.0197028	+	0.999806i	$0.506272\pi$
$674$	2.00387e71	0.148266
$675$	1.40018e72	0.997554
$676$	3.05533e72	2.09612
$677$	−2.88331e72	−1.90494	−0.952468	−	0.304639i	$-0.901464\pi$
$677$	−2.88331e72	−1.90494	−0.952468	+	0.304639i	$0.901464\pi$
$678$	2.32510e72	1.47940
$679$	−2.38000e72	−1.45847
$680$	−2.70419e71	−0.159610
$681$	−4.44648e72	−2.52793
$682$	2.68521e72	1.47054
$683$	1.21910e72	0.643150	0.321575	−	0.946884i	$-0.395788\pi$
$683$	1.21910e72	0.643150	0.321575	+	0.946884i	$0.395788\pi$
$684$	4.07073e72	2.06891
$685$	7.67852e71	0.375983
$686$	−3.94926e72	−1.86316
$687$	−8.19121e71	−0.372350
$688$	−8.61439e71	−0.377328
$689$	−1.81869e71	−0.0767661
$690$	8.08381e71	0.328824
$691$	−1.39481e72	−0.546794	−0.273397	−	0.961901i	$-0.588147\pi$
$691$	−1.39481e72	−0.546794	−0.273397	+	0.961901i	$0.588147\pi$
$692$	2.95344e72	1.11589
$693$	3.68142e72	1.34066
$694$	1.26665e72	0.444619
$695$	−2.10143e71	−0.0711052
$696$	−1.61964e72	−0.528302
$697$	−1.40454e72	−0.441672
$698$	−4.25002e72	−1.28848
$699$	2.83801e72	0.829557
$700$	−4.78222e72	−1.34781
$701$	5.63382e72	1.53106	0.765532	−	0.643397i	$-0.222476\pi$
$701$	5.63382e72	1.53106	0.765532	+	0.643397i	$0.222476\pi$
$702$	−1.08511e73	−2.84365
$703$	−4.46038e72	−1.12723
$704$	−4.77967e72	−1.16492
$705$	−2.36555e72	−0.556045
$706$	1.44812e73	3.28311
$707$	1.03060e72	0.225370
$708$	1.26601e73	2.67047
$709$	3.78104e72	0.769365	0.384682	−	0.923049i	$-0.374311\pi$
$709$	3.78104e72	0.769365	0.384682	+	0.923049i	$0.374311\pi$
$710$	−3.77539e72	−0.741095
$711$	8.62789e72	1.63392
$712$	−1.29130e73	−2.35932
$713$	−1.59587e72	−0.281329
$714$	3.66036e72	0.622614
$715$	3.14047e72	0.515455
$716$	1.29940e73	2.05808
$717$	−1.22453e73	−1.87168
$718$	−1.20664e73	−1.77993
$719$	6.26463e72	0.891885	0.445943	−	0.895062i	$-0.352869\pi$
$719$	6.26463e72	0.891885	0.445943	+	0.895062i	$0.352869\pi$
$720$	3.59183e72	0.493556
$721$	−1.69141e72	−0.224336
$722$	−8.05873e72	−1.03173
$723$	−1.19361e73	−1.47515
$724$	−5.61907e72	−0.670396
$725$	−1.51942e72	−0.175008
$726$	1.01160e72	0.112492
$727$	1.48516e73	1.59457	0.797287	−	0.603600i	$-0.206267\pi$
$727$	1.48516e73	1.59457	0.797287	+	0.603600i	$0.206267\pi$
$728$	1.78658e73	1.85214
$729$	−1.56540e73	−1.56702
$730$	−1.67516e72	−0.161929
$731$	1.39465e72	0.130188
$732$	−2.31244e73	−2.08467
$733$	5.93373e72	0.516627	0.258313	−	0.966061i	$-0.416833\pi$
$733$	5.93373e72	0.516627	0.258313	+	0.966061i	$0.416833\pi$
$734$	6.54063e72	0.550009
$735$	2.59520e72	0.210787
$736$	9.36409e71	0.0734652
$737$	1.60834e73	1.21887
$738$	6.38491e73	4.67431
$739$	1.50074e72	0.106138	0.0530692	−	0.998591i	$-0.483100\pi$
$739$	1.50074e72	0.106138	0.0530692	+	0.998591i	$0.483100\pi$
$740$	−1.84077e73	−1.25774
$741$	−2.26591e73	−1.49581
$742$	−1.14834e72	−0.0732441
$743$	−2.89489e73	−1.78409	−0.892047	−	0.451943i	$-0.850731\pi$
$743$	−2.89489e73	−1.78409	−0.892047	+	0.451943i	$0.850731\pi$
$744$	−3.85438e73	−2.29533
$745$	−1.56774e72	−0.0902170
$746$	1.82973e72	0.101753
$747$	1.97326e73	1.06050
$748$	−1.00153e73	−0.520205
$749$	−7.67184e72	−0.385135
$750$	3.94346e73	1.91344
$751$	1.40821e73	0.660462	0.330231	−	0.943900i	$-0.392873\pi$
$751$	1.40821e73	0.660462	0.330231	+	0.943900i	$0.392873\pi$
$752$	1.63311e73	0.740389
$753$	2.84847e72	0.124836
$754$	1.17752e73	0.498882
$755$	6.41970e72	0.262946
$756$	−4.51368e73	−1.78741
$757$	−9.83514e72	−0.376561	−0.188281	−	0.982115i	$-0.560291\pi$
$757$	−9.83514e72	−0.376561	−0.188281	+	0.982115i	$0.560291\pi$
$758$	−8.23593e73	−3.04893
$759$	1.44327e73	0.516633
$760$	1.05698e73	0.365866
$761$	4.56710e73	1.52873	0.764367	−	0.644782i	$-0.223052\pi$
$761$	4.56710e73	1.52873	0.764367	+	0.644782i	$0.223052\pi$
$762$	−5.71968e73	−1.85148
$763$	−3.09213e73	−0.968016
$764$	1.21441e74	3.67693
$765$	−5.81508e72	−0.170290
$766$	−3.00081e73	−0.849971
$767$	−4.43698e73	−1.21564
$768$	1.18022e74	3.12791
$769$	3.75294e73	0.962167	0.481083	−	0.876675i	$-0.340243\pi$
$769$	3.75294e73	0.962167	0.481083	+	0.876675i	$0.340243\pi$
$770$	1.98293e73	0.491806
$771$	−6.55925e73	−1.57386
$772$	8.20906e73	1.90569
$773$	3.47460e73	0.780419	0.390210	−	0.920726i	$-0.372403\pi$
$773$	3.47460e73	0.780419	0.390210	+	0.920726i	$0.372403\pi$
$774$	−6.33993e73	−1.37781
$775$	−3.61588e73	−0.760362
$776$	−1.41890e74	−2.88720
$777$	1.20112e74	2.36511
$778$	−9.75230e73	−1.85835
$779$	5.48992e73	1.01242
$780$	−9.35123e73	−1.66900
$781$	−6.74052e73	−1.16437
$782$	9.03522e72	0.151066
$783$	−1.43410e73	−0.232088
$784$	−1.79165e73	−0.280668
$785$	−4.23728e72	−0.0642556
$786$	2.19464e74	3.22173
$787$	−5.13224e72	−0.0729376	−0.0364688	−	0.999335i	$-0.511611\pi$
$787$	−5.13224e72	−0.0729376	−0.0364688	+	0.999335i	$0.511611\pi$
$788$	−1.38672e74	−1.90797
$789$	5.98049e73	0.796660
$790$	4.64726e73	0.599385
$791$	−3.38963e73	−0.423304
$792$	2.19477e74	2.65397
$793$	8.10443e73	0.948978
$794$	−1.76859e74	−2.00541
$795$	2.89749e72	0.0318170
$796$	1.85619e74	1.97397
$797$	−5.49546e73	−0.566001	−0.283000	−	0.959120i	$-0.591330\pi$
$797$	−5.49546e73	−0.566001	−0.283000	+	0.959120i	$0.591330\pi$
$798$	−1.43072e74	−1.42719
$799$	−2.64396e73	−0.255454
$800$	2.12169e73	0.198558
$801$	−2.77680e74	−2.51719
$802$	3.48153e74	3.05720
$803$	−2.99081e73	−0.254414
$804$	−4.78908e74	−3.94659
$805$	−1.17849e73	−0.0940874
$806$	2.80223e74	2.16750
$807$	1.57776e74	1.18241
$808$	6.14420e73	0.446144
$809$	2.78397e73	0.195874	0.0979372	−	0.995193i	$-0.468776\pi$
$809$	2.78397e73	0.195874	0.0979372	+	0.995193i	$0.468776\pi$
$810$	1.73752e73	0.118457
$811$	−2.13458e74	−1.41020	−0.705099	−	0.709109i	$-0.749098\pi$
$811$	−2.13458e74	−1.41020	−0.705099	+	0.709109i	$0.749098\pi$
$812$	4.89807e73	0.313579
$813$	1.65269e73	0.102537
$814$	−4.98866e74	−2.99959
$815$	−5.93406e73	−0.345806
$816$	6.37610e73	0.360127
$817$	−5.45124e73	−0.298424
$818$	6.18704e74	3.28302
$819$	3.84186e74	1.97607
$820$	2.26565e74	1.12964
$821$	−1.21993e74	−0.589639	−0.294819	−	0.955553i	$-0.595259\pi$
$821$	−1.21993e74	−0.589639	−0.294819	+	0.955553i	$0.595259\pi$
$822$	−6.19636e74	−2.90339
$823$	−9.32706e72	−0.0423691	−0.0211845	−	0.999776i	$-0.506744\pi$
$823$	−9.32706e72	−0.0423691	−0.0211845	+	0.999776i	$0.506744\pi$
$824$	−1.00838e74	−0.444098
$825$	3.27012e74	1.39633
$826$	−2.80156e74	−1.15987
$827$	2.77630e73	0.111449	0.0557244	−	0.998446i	$-0.482253\pi$
$827$	2.77630e73	0.111449	0.0557244	+	0.998446i	$0.482253\pi$
$828$	−2.70585e74	−1.05325
$829$	3.61616e74	1.36492	0.682461	−	0.730922i	$-0.260910\pi$
$829$	3.61616e74	1.36492	0.682461	+	0.730922i	$0.260910\pi$
$830$	1.06286e74	0.389032
$831$	5.86463e74	2.08168
$832$	−4.98797e74	−1.71704
$833$	2.90064e73	0.0968380
$834$	1.69579e74	0.549084
$835$	−1.85831e74	−0.583598
$836$	3.91468e74	1.19244
$837$	−3.41283e74	−1.00836
$838$	2.85267e74	0.817578
$839$	−4.79920e74	−1.33425	−0.667127	−	0.744944i	$-0.732476\pi$
$839$	−4.79920e74	−1.33425	−0.667127	+	0.744944i	$0.732476\pi$
$840$	−2.84633e74	−0.767649
$841$	−3.66644e74	−0.959283
$842$	−2.59050e74	−0.657546
$843$	−5.34502e74	−1.31627
$844$	−4.70100e74	−1.12320
$845$	1.70597e74	0.395481
$846$	1.20192e75	2.70353
$847$	−1.47475e73	−0.0321877
$848$	−2.00034e73	−0.0423652
$849$	−3.93463e74	−0.808644
$850$	2.04718e74	0.408294
$851$	2.96486e74	0.573852
$852$	2.00709e75	3.77014
$853$	6.60846e74	1.20476	0.602379	−	0.798210i	$-0.294220\pi$
$853$	6.60846e74	1.20476	0.602379	+	0.798210i	$0.294220\pi$
$854$	5.11723e74	0.905438
$855$	2.27293e74	0.390347
$856$	−4.57376e74	−0.762416
$857$	−2.87199e74	−0.464699	−0.232349	−	0.972632i	$-0.574641\pi$
$857$	−2.87199e74	−0.464699	−0.232349	+	0.972632i	$0.574641\pi$
$858$	−2.53428e75	−3.98041
$859$	7.69360e74	1.17302	0.586508	−	0.809944i	$-0.300502\pi$
$859$	7.69360e74	1.17302	0.586508	+	0.809944i	$0.300502\pi$
$860$	−2.24969e74	−0.332975
$861$	−1.47837e75	−2.12423
$862$	−1.84947e74	−0.257996
$863$	−8.71585e74	−1.18041	−0.590207	−	0.807252i	$-0.700954\pi$
$863$	−8.71585e74	−1.18041	−0.590207	+	0.807252i	$0.700954\pi$
$864$	2.00255e74	0.263320
$865$	1.64908e74	0.210538
$866$	−2.40915e74	−0.298647
$867$	1.26188e75	1.51891
$868$	1.16563e75	1.36241
$869$	8.29714e74	0.941725
$870$	−1.87598e74	−0.206770
$871$	1.67843e75	1.79656
$872$	−1.84345e75	−1.91629
$873$	−3.05118e75	−3.08039
$874$	−3.53158e74	−0.346280
$875$	−5.74894e74	−0.547498
$876$	8.90557e74	0.823772
$877$	1.44865e75	1.30159	0.650797	−	0.759252i	$-0.274435\pi$
$877$	1.44865e75	1.30159	0.650797	+	0.759252i	$0.274435\pi$
$878$	2.46810e75	2.15403
$879$	1.77418e75	1.50412
$880$	3.45413e74	0.284466
$881$	−1.16519e75	−0.932207	−0.466103	−	0.884730i	$-0.654343\pi$
$881$	−1.16519e75	−0.932207	−0.466103	+	0.884730i	$0.654343\pi$
$882$	−1.31860e75	−1.02486
$883$	−1.52991e75	−1.15523	−0.577615	−	0.816309i	$-0.696016\pi$
$883$	−1.52991e75	−1.15523	−0.577615	+	0.816309i	$0.696016\pi$
$884$	−1.04518e75	−0.766759
$885$	7.06886e74	0.503844
$886$	−1.41799e75	−0.982001
$887$	−2.18618e75	−1.47107	−0.735535	−	0.677487i	$-0.763069\pi$
$887$	−2.18618e75	−1.47107	−0.735535	+	0.677487i	$0.763069\pi$
$888$	7.16080e75	4.68199
$889$	8.33840e74	0.529770
$890$	−1.49567e75	−0.923403
$891$	3.10214e74	0.186115
$892$	−3.03575e75	−1.76996
$893$	1.03344e75	0.585563
$894$	1.26512e75	0.696667
$895$	7.25535e74	0.388303
$896$	−2.79521e75	−1.45399
$897$	1.50617e75	0.761493
$898$	−2.06919e75	−1.01684
$899$	3.70348e74	0.176904
$900$	−6.13086e75	−2.84667
$901$	3.23850e73	0.0146171
$902$	6.14014e75	2.69409
$903$	1.46795e75	0.626144
$904$	−2.02081e75	−0.837975
$905$	−3.13746e74	−0.126485
$906$	−5.18052e75	−2.03051
$907$	−3.40042e75	−1.29583	−0.647914	−	0.761714i	$-0.724358\pi$
$907$	−3.40042e75	−1.29583	−0.647914	+	0.761714i	$0.724358\pi$
$908$	8.01672e75	2.97035
$909$	1.32124e75	0.475997
$910$	2.06935e75	0.724899
$911$	−4.11484e74	−0.140163	−0.0700817	−	0.997541i	$-0.522326\pi$
$911$	−4.11484e74	−0.140163	−0.0700817	+	0.997541i	$0.522326\pi$
$912$	−2.49222e75	−0.825501
$913$	1.89761e75	0.611228
$914$	7.27895e75	2.28003
$915$	−1.29117e75	−0.393320
$916$	1.47682e75	0.437516
$917$	−3.19944e75	−0.921841
$918$	1.93222e75	0.541462
$919$	−4.75576e75	−1.29621	−0.648104	−	0.761552i	$-0.724438\pi$
$919$	−4.75576e75	−1.29621	−0.648104	+	0.761552i	$0.724438\pi$
$920$	−7.02587e74	−0.186256
$921$	5.64172e75	1.45476
$922$	6.65889e75	1.67018
$923$	−7.03428e75	−1.71623
$924$	−1.05417e76	−2.50194
$925$	6.71770e75	1.55098
$926$	−9.24196e75	−2.07579
$927$	−2.16841e75	−0.473814
$928$	−2.17309e74	−0.0461960
$929$	7.98781e75	1.65207	0.826033	−	0.563622i	$-0.190593\pi$
$929$	7.98781e75	1.65207	0.826033	+	0.563622i	$0.190593\pi$
$930$	−4.46442e75	−0.898359
$931$	−1.13377e75	−0.221977
$932$	−5.11675e75	−0.974740
$933$	−1.41249e76	−2.61821
$934$	1.80626e75	0.325787
$935$	−5.59216e74	−0.0981484
$936$	2.29042e76	3.91183
$937$	−3.77230e75	−0.626970	−0.313485	−	0.949593i	$-0.601497\pi$
$937$	−3.77230e75	−0.626970	−0.313485	+	0.949593i	$0.601497\pi$
$938$	1.05978e76	1.71413
$939$	1.34631e76	2.11920
$940$	4.26494e75	0.653360
$941$	−1.08168e75	−0.161274	−0.0806371	−	0.996744i	$-0.525695\pi$
$941$	−1.08168e75	−0.161274	−0.0806371	+	0.996744i	$0.525695\pi$
$942$	3.41937e75	0.496191
$943$	−3.64920e75	−0.515406
$944$	−4.88014e75	−0.670882
$945$	−2.52025e75	−0.337235
$946$	−6.09688e75	−0.794116
$947$	2.23798e75	0.283747	0.141873	−	0.989885i	$-0.454687\pi$
$947$	2.23798e75	0.283747	0.141873	+	0.989885i	$0.454687\pi$
$948$	−2.47060e76	−3.04922
$949$	−3.12115e75	−0.374995
$950$	−8.00178e75	−0.935911
$951$	7.09139e75	0.807473
$952$	−3.18132e75	−0.352667
$953$	1.63024e76	1.75947	0.879737	−	0.475461i	$-0.157719\pi$
$953$	1.63024e76	1.75947	0.879737	+	0.475461i	$0.157719\pi$
$954$	−1.47219e75	−0.154696
$955$	6.78078e75	0.693735
$956$	2.20776e76	2.19925
$957$	−3.34935e75	−0.324867
$958$	−9.38912e75	−0.886756
$959$	9.03332e75	0.830755
$960$	7.94668e75	0.711655
$961$	−2.65345e75	−0.231401
$962$	−5.20607e76	−4.42126
$963$	−9.83538e75	−0.813431
$964$	2.15201e76	1.73332
$965$	4.58360e75	0.359551
$966$	9.51011e75	0.726556
$967$	−1.19422e76	−0.888609	−0.444305	−	0.895876i	$-0.646549\pi$
$967$	−1.19422e76	−0.888609	−0.444305	+	0.895876i	$0.646549\pi$
$968$	−8.79207e74	−0.0637191
$969$	4.03484e75	0.284820
$970$	−1.64347e76	−1.13001
$971$	−9.57238e75	−0.641106	−0.320553	−	0.947231i	$-0.603869\pi$
$971$	−9.57238e75	−0.641106	−0.320553	+	0.947231i	$0.603869\pi$
$972$	2.48020e76	1.61807
$973$	−2.47220e75	−0.157111
$974$	1.79224e74	0.0110954
$975$	3.41264e76	2.05813
$976$	8.91387e75	0.523716
$977$	−3.03295e75	−0.173602	−0.0868008	−	0.996226i	$-0.527664\pi$
$977$	−3.03295e75	−0.173602	−0.0868008	+	0.996226i	$0.527664\pi$
$978$	4.78863e76	2.67036
$979$	−2.67035e76	−1.45081
$980$	−4.67898e75	−0.247677
$981$	−3.96415e76	−2.04451
$982$	6.42642e76	3.22943
$983$	7.25776e75	0.355376	0.177688	−	0.984087i	$-0.443138\pi$
$983$	7.25776e75	0.355376	0.177688	+	0.984087i	$0.443138\pi$
$984$	−8.81365e76	−4.20514
$985$	−7.74291e75	−0.359981
$986$	−2.09677e75	−0.0949926
$987$	−2.78293e76	−1.22861
$988$	4.08528e76	1.75760
$989$	3.62349e75	0.151922
$990$	2.54214e76	1.03873
$991$	−1.83886e74	−0.00732268	−0.00366134	−	0.999993i	$-0.501165\pi$
$991$	−1.83886e74	−0.00732268	−0.00366134	+	0.999993i	$0.501165\pi$
$992$	−5.17148e75	−0.200709
$993$	−1.99622e76	−0.755098
$994$	−4.44152e76	−1.63749
$995$	1.03642e76	0.372433
$996$	−5.65043e76	−1.97910
$997$	4.30923e76	1.47120	0.735602	−	0.677414i	$-0.236900\pi$
$997$	4.30923e76	1.47120	0.735602	+	0.677414i	$0.236900\pi$
$998$	−7.81731e76	−2.60153
$999$	6.34047e76	2.05684

Twists

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

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

\(f(q)\)	\(=\)	\(q+8.12369e7 q^{2} -2.41142e12 q^{3} +4.34763e15 q^{4} +2.42754e17 q^{5} -1.95896e20 q^{6} +2.85586e21 q^{7} +1.70259e23 q^{8} +3.66124e24 q^{9} +O(q^{10})\)	\(q+8.12369e7 q^{2} -2.41142e12 q^{3} +4.34763e15 q^{4} +2.42754e17 q^{5} -1.95896e20 q^{6} +2.85586e21 q^{7} +1.70259e23 q^{8} +3.66124e24 q^{9} +1.97206e25 q^{10} +3.52088e26 q^{11} -1.04840e28 q^{12} +3.67432e28 q^{13} +2.32001e29 q^{14} -5.85381e29 q^{15} +4.04130e30 q^{16} -6.54277e30 q^{17} +2.97427e32 q^{18} +2.55736e32 q^{19} +1.05541e33 q^{20} -6.88666e33 q^{21} +2.86025e34 q^{22} -1.69990e34 q^{23} -4.10565e35 q^{24} -3.85160e35 q^{25} +2.98490e36 q^{26} -3.63531e36 q^{27} +1.24162e37 q^{28} +3.94490e36 q^{29} -4.75545e37 q^{30} +9.38800e37 q^{31} -5.50861e37 q^{32} -8.49031e38 q^{33} -5.31514e38 q^{34} +6.93270e38 q^{35} +1.59177e40 q^{36} -1.74413e40 q^{37} +2.07752e40 q^{38} -8.86032e40 q^{39} +4.13310e40 q^{40} +2.14671e41 q^{41} -5.59451e41 q^{42} -2.13159e41 q^{43} +1.53075e42 q^{44} +8.88780e41 q^{45} -1.38095e42 q^{46} +4.04105e42 q^{47} -9.74526e42 q^{48} -4.43335e42 q^{49} -3.12892e43 q^{50} +1.57773e43 q^{51} +1.59746e44 q^{52} -4.94974e42 q^{53} -2.95321e44 q^{54} +8.54708e43 q^{55} +4.86235e44 q^{56} -6.16687e44 q^{57} +3.20472e44 q^{58} -1.20757e45 q^{59} -2.54502e45 q^{60} +2.20569e45 q^{61} +7.62652e45 q^{62} +1.04560e46 q^{63} -1.35752e46 q^{64} +8.91957e45 q^{65} -6.89726e46 q^{66} +4.56801e46 q^{67} -2.84456e46 q^{68} +4.09917e46 q^{69} +5.63191e46 q^{70} -1.91444e47 q^{71} +6.23358e47 q^{72} -8.49448e46 q^{73} -1.41688e48 q^{74} +9.28780e47 q^{75} +1.11185e48 q^{76} +1.00551e48 q^{77} -7.19785e48 q^{78} +2.35655e48 q^{79} +9.81042e47 q^{80} +8.81070e47 q^{81} +1.74392e49 q^{82} +5.38960e48 q^{83} -2.99406e49 q^{84} -1.58828e48 q^{85} -1.73164e49 q^{86} -9.51281e48 q^{87} +5.99461e49 q^{88} -7.58432e49 q^{89} +7.22017e49 q^{90} +1.04933e50 q^{91} -7.39055e49 q^{92} -2.26384e50 q^{93} +3.28282e50 q^{94} +6.20810e49 q^{95} +1.32835e50 q^{96} -8.33376e50 q^{97} -3.60151e50 q^{98} +1.28908e51 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32756040 q^{2} + 403863773040 q^{3} + 79\!\cdots\!12 q^{4}+ \cdots + 50\!\cdots\!28 q^{9}+O(q^{10}) \) 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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