LMFDB - Embedded newform 1.56.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,56,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, 56, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 56);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 56 $
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:	$19.1581467685$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 149272663100531x^{2} + 190291401428579434725x + 325546600176957146615614350 $ x^4 - x^3 - 149272663100531x^2 + 190291401428579434725x + 325546600176957146615614350
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{20}\cdot 3^{9}\cdot 5^{2}\cdot 7\cdot 11 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-972934.$ 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)

$f(q)$	$=$	$q+2.88052e7 q^{2} +1.23937e13 q^{3} -3.51991e16 q^{4} -1.26520e19 q^{5} +3.57004e20 q^{6} +2.79909e23 q^{7} -2.05173e24 q^{8} -2.08450e25 q^{9} +O(q^{10})$	\(q+2.88052e7 q^{2} +1.23937e13 q^{3} -3.51991e16 q^{4} -1.26520e19 q^{5} +3.57004e20 q^{6} +2.79909e23 q^{7} -2.05173e24 q^{8} -2.08450e25 q^{9} -3.64445e26 q^{10} +4.43027e28 q^{11} -4.36247e29 q^{12} +1.55064e30 q^{13} +8.06283e30 q^{14} -1.56806e32 q^{15} +1.20908e33 q^{16} +8.73107e32 q^{17} -6.00444e32 q^{18} +1.64892e35 q^{19} +4.45340e35 q^{20} +3.46911e36 q^{21} +1.27615e36 q^{22} +5.17737e37 q^{23} -2.54286e37 q^{24} -1.17482e38 q^{25} +4.46665e37 q^{26} -2.42042e39 q^{27} -9.85253e39 q^{28} +1.58882e40 q^{29} -4.51682e39 q^{30} +5.89422e40 q^{31} +1.08749e41 q^{32} +5.49075e41 q^{33} +2.51500e40 q^{34} -3.54142e42 q^{35} +7.33724e41 q^{36} -1.50183e43 q^{37} +4.74974e42 q^{38} +1.92182e43 q^{39} +2.59586e43 q^{40} +2.49038e44 q^{41} +9.99285e43 q^{42} -2.64200e44 q^{43} -1.55941e45 q^{44} +2.63732e44 q^{45} +1.49135e45 q^{46} -1.75786e46 q^{47} +1.49850e46 q^{48} +4.81222e46 q^{49} -3.38408e45 q^{50} +1.08210e46 q^{51} -5.45811e46 q^{52} -7.37942e46 q^{53} -6.97207e46 q^{54} -5.60519e47 q^{55} -5.74298e47 q^{56} +2.04362e48 q^{57} +4.57662e47 q^{58} +2.54720e48 q^{59} +5.51942e48 q^{60} -1.07207e49 q^{61} +1.69784e48 q^{62} -5.83470e48 q^{63} -4.04291e49 q^{64} -1.96188e49 q^{65} +1.58162e49 q^{66} +1.06094e50 q^{67} -3.07325e49 q^{68} +6.41669e50 q^{69} -1.02011e50 q^{70} -1.17879e51 q^{71} +4.27683e49 q^{72} +2.92361e50 q^{73} -4.32604e50 q^{74} -1.45603e51 q^{75} -5.80404e51 q^{76} +1.24007e52 q^{77} +5.53584e50 q^{78} +2.26793e52 q^{79} -1.52973e52 q^{80} -2.63616e52 q^{81} +7.17360e51 q^{82} +3.10804e52 q^{83} -1.22109e53 q^{84} -1.10466e52 q^{85} -7.61035e51 q^{86} +1.96914e53 q^{87} -9.08973e52 q^{88} +4.89902e53 q^{89} +7.59684e51 q^{90} +4.34038e53 q^{91} -1.82239e54 q^{92} +7.30513e53 q^{93} -5.06356e53 q^{94} -2.08622e54 q^{95} +1.34781e54 q^{96} +4.57966e53 q^{97} +1.38617e54 q^{98} -9.23488e53 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 208622520 q^{2} - 6821470691280 q^{3} + 38\!\cdots\!72 q^{4}+ \cdots + 47\!\cdots\!28 q^{9}+O(q^{10}) $ 4 * q + 208622520 * q^2 - 6821470691280 * q^3 + 38727758778743872 * q^4 + 14396937963387167160 * q^5 + 201756545247712015008 * q^6 - 205529376090660565972000 * q^7 + 4549274472651430619082240 * q^8 + 47936416820074569958974228 * q^9	$ 4 q + 208622520 q^{2} - 6821470691280 q^{3} + 38\!\cdots\!72 q^{4}+ \cdots + 79\!\cdots\!56 q^{99}+O(q^{100}) $ 4 * q + 208622520 * q^2 - 6821470691280 * q^3 + 38727758778743872 * q^4 + 14396937963387167160 * q^5 + 201756545247712015008 * q^6 - 205529376090660565972000 * q^7 + 4549274472651430619082240 * q^8 + 47936416820074569958974228 * q^9 + 4648305821937663379975180560 * q^10 + 19492148713537948248062043408 * q^11 + 512487561854224962046873117440 * q^12 - 4449970852951030370486873382760 * q^13 - 28356223847864660359303625873856 * q^14 + 248797810922527062710720195548320 * q^15 + 972748533533952319807553436258304 * q^16 + 8593971071724377583839140954773960 * q^17 + 38459068061903712495232732227386520 * q^18 + 339485321922051504109099704484079600 * q^19 + 2938981710383707492522432611899614080 * q^20 + 9223279286409457932469393248481185408 * q^21 + 38006076575943531891094535037919254240 * q^22 + 49808560358713761517710452453445612960 * q^23 + 190807152467783159198396962175734425600 * q^24 + 35720819629535961214417161732721803100 * q^25 - 2942801473325677064443328059884451887792 * q^26 - 8530982134391103993322927255258361598240 * q^27 - 14225688489857344137508473549032747368960 * q^28 - 18313921252535508838816178753292620581800 * q^29 + 81282391149812883221152750335721388925120 * q^30 + 228069689399145752868860523834729264526208 * q^31 + 633346612507316231430506989727883716689920 * q^32 + 847291303346996712726357318732333414939840 * q^33 + 896637942332031893460273084285964132034544 * q^34 - 4819663438502339394117495448236020975855040 * q^35 - 23127427661252023416447691458638107482530496 * q^36 - 32137889117062584203203089731106089299166920 * q^37 - 4952027966320588944657713384757782381142240 * q^38 + 66999829160538184499173080943184361764833056 * q^39 + 423453117316016459693780561000308646880691200 * q^40 + 246756563007211451240604479433521241061314408 * q^41 + 507527523766486022631274034521150794413218560 * q^42 - 860266067148440101585711757682636198922476400 * q^43 - 486680632760661386186662626683912868907405056 * q^44 - 9558583136774695571527888760209735674807045480 * q^45 - 12358385464441662606619414449724307588901916992 * q^46 + 4275321492760062770492681289130578251551314240 * q^47 + 19765938683883854374252413540295783983351644160 * q^48 + 51896265177052512954332052101694146860214382372 * q^49 + 174698296445912937700335126041507926720149534600 * q^50 + 114739625474091768829327173325517597576905389408 * q^51 - 262201419493851260177411503538061050352769552000 * q^52 - 488469552022263686716757080744643106633189705480 * q^53 - 1343912975841315509587669615741882301086568894400 * q^54 - 127591926326749967084952696035933816282025595680 * q^55 - 298136165704261759300184058675155027135738572800 * q^56 + 1638420796018602848713747835626091496488772083520 * q^57 + 6079853356051584053436052229523762232408341938640 * q^58 + 8189687634125713603536212764174920044680103250000 * q^59 + 10139666510723475640830884157120900147903797660160 * q^60 + 7023917261975601941077275556050474243839244469208 * q^61 - 30522733021551585983790682957575295692580599279360 * q^62 - 71978335814893755132347187478401614601601405967520 * q^63 - 98185742120493275625308720675268779449265392713728 * q^64 - 96029582501479027321081622269423947602394832060080 * q^65 + 64231534245847760638155838044250061298414536370816 * q^66 + 418567852430847740316243536772383918093566302547760 * q^67 + 627327947371921816104248533416688222149537051169920 * q^68 + 515735918068902691862050107073617954531351228253056 * q^69 - 471522968288511321788110491009215619195633708224640 * q^70 + 997985577607888605538672501225224229003742837277408 * q^71 - 4304125570291567284830418802698753913226780601899520 * q^72 - 898993596628095916013292323795403905388680301942040 * q^73 - 7967044320232055682477818350544716808849477162563056 * q^74 + 5296014974156672466059853856400507071088579916421200 * q^75 - 60907940015267454915614913374117951647840510009600 * q^76 + 14299054939611075432133092801777785333545282382563200 * q^77 + 396845629416952247715668693426892670455525504984000 * q^78 + 48721021140002244303635330301073120621076057627153600 * q^79 - 3558308494035098045228661758379879929555981454090240 * q^80 + 62764174850641400333291315844329697377153438426256804 * q^81 - 164154584875013842045822252535546173951453621276929360 * q^82 - 71840759606517399895238320212650236559070020961691920 * q^83 - 315751105587523254185006931474478000838644134120953856 * q^84 + 248899912487828257920888533066500872415304578192331760 * q^85 - 390961799675414150209662123589235297185712905683496992 * q^86 + 793070552989118953410697424048823657459134846084789280 * q^87 + 263660200754753376218335161392938332564087458967828480 * q^88 + 1567987214275383302209606514592359147814765036271890600 * q^89 - 1212078526300174060358044731623232837611704141954645680 * q^90 + 1660326344231373069708515805926098978407334056523187008 * q^91 - 2737928811190126698927829997086921657569438136581219840 * q^92 - 1148699655429559764317569984734958616523316649999439360 * q^93 - 4092215382133552783473757354682502518415689822573629056 * q^94 + 90834332415616009306267157723570331064559482078144800 * q^95 - 5408972861452632753807094701577513866193715960586043392 * q^96 + 5113732531532480760212291157301231295251404057238280840 * q^97 + 4361266856004358769699597237924757031028912315048682360 * q^98 + 7959889613481860830509059286387276732667315436102354256 * 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 $

$2$	2.88052e7	0.151756	0.0758780	−	0.997117i	$-0.475824\pi$
$2$	2.88052e7	0.151756	0.0758780	+	0.997117i	$0.475824\pi$
$3$	1.23937e13	0.938355	0.469177	−	0.883104i	$-0.344550\pi$
$3$	1.23937e13	0.938355	0.469177	+	0.883104i	$0.344550\pi$
$4$	−3.51991e16	−0.976970
$5$	−1.26520e19	−0.759426	−0.379713	−	0.925104i	$-0.623977\pi$
$5$	−1.26520e19	−0.759426	−0.379713	+	0.925104i	$0.623977\pi$
$6$	3.57004e20	0.142401
$7$	2.79909e23	1.60998	0.804990	−	0.593288i	$-0.202171\pi$
$7$	2.79909e23	1.60998	0.804990	+	0.593288i	$0.202171\pi$
$8$	−2.05173e24	−0.300017
$9$	−2.08450e25	−0.119490
$10$	−3.64445e26	−0.115247
$11$	4.43027e28	1.01890	0.509449	−	0.860501i	$-0.329849\pi$
$11$	4.43027e28	1.01890	0.509449	+	0.860501i	$0.329849\pi$
$12$	−4.36247e29	−0.916745
$13$	1.55064e30	0.360636	0.180318	−	0.983608i	$-0.442287\pi$
$13$	1.55064e30	0.360636	0.180318	+	0.983608i	$0.442287\pi$
$14$	8.06283e30	0.244324
$15$	−1.56806e32	−0.712611
$16$	1.20908e33	0.931441
$17$	8.73107e32	0.126976	0.0634881	−	0.997983i	$-0.479778\pi$
$17$	8.73107e32	0.126976	0.0634881	+	0.997983i	$0.479778\pi$
$18$	−6.00444e32	−0.0181334
$19$	1.64892e35	1.12584	0.562918	−	0.826513i	$-0.309679\pi$
$19$	1.64892e35	1.12584	0.562918	+	0.826513i	$0.309679\pi$
$20$	4.45340e35	0.741936
$21$	3.46911e36	1.51073
$22$	1.27615e36	0.154624
$23$	5.17737e37	1.84754	0.923770	−	0.382948i	$-0.125091\pi$
$23$	5.17737e37	1.84754	0.923770	+	0.382948i	$0.125091\pi$
$24$	−2.54286e37	−0.281523
$25$	−1.17482e38	−0.423272
$26$	4.46665e37	0.0547287
$27$	−2.42042e39	−1.05048
$28$	−9.85253e39	−1.57290
$29$	1.58882e40	0.966338	0.483169	−	0.875527i	$-0.339486\pi$
$29$	1.58882e40	0.966338	0.483169	+	0.875527i	$0.339486\pi$
$30$	−4.51682e39	−0.108143
$31$	5.89422e40	0.572770	0.286385	−	0.958115i	$-0.407546\pi$
$31$	5.89422e40	0.572770	0.286385	+	0.958115i	$0.407546\pi$
$32$	1.08749e41	0.441369
$33$	5.49075e41	0.956089
$34$	2.51500e40	0.0192694
$35$	−3.54142e42	−1.22266
$36$	7.33724e41	0.116738
$37$	−1.50183e43	−1.12479	−0.562396	−	0.826868i	$-0.690120\pi$
$37$	−1.50183e43	−1.12479	−0.562396	+	0.826868i	$0.690120\pi$
$38$	4.74974e42	0.170853
$39$	1.92182e43	0.338404
$40$	2.59586e43	0.227841
$41$	2.49038e44	1.10843	0.554217	−	0.832372i	$-0.313018\pi$
$41$	2.49038e44	1.10843	0.554217	+	0.832372i	$0.313018\pi$
$42$	9.99285e43	0.229263
$43$	−2.64200e44	−0.317359	−0.158680	−	0.987330i	$-0.550724\pi$
$43$	−2.64200e44	−0.317359	−0.158680	+	0.987330i	$0.550724\pi$
$44$	−1.55941e45	−0.995434
$45$	2.63732e44	0.0907440
$46$	1.49135e45	0.280375
$47$	−1.75786e46	−1.82934	−0.914669	−	0.404204i	$-0.867549\pi$
$47$	−1.75786e46	−1.82934	−0.914669	+	0.404204i	$0.867549\pi$
$48$	1.49850e46	0.874022
$49$	4.81222e46	1.59204
$50$	−3.38408e45	−0.0642341
$51$	1.08210e46	0.119149
$52$	−5.45811e46	−0.352330
$53$	−7.37942e46	−0.282121	−0.141061	−	0.990001i	$-0.545051\pi$
$53$	−7.37942e46	−0.282121	−0.141061	+	0.990001i	$0.545051\pi$
$54$	−6.97207e46	−0.159417
$55$	−5.60519e47	−0.773778
$56$	−5.74298e47	−0.483022
$57$	2.04362e48	1.05643
$58$	4.57662e47	0.146648
$59$	2.54720e48	0.510073	0.255036	−	0.966931i	$-0.417913\pi$
$59$	2.54720e48	0.510073	0.255036	+	0.966931i	$0.417913\pi$
$60$	5.51942e48	0.696200
$61$	−1.07207e49	−0.858325	−0.429162	−	0.903227i	$-0.641191\pi$
$61$	−1.07207e49	−0.858325	−0.429162	+	0.903227i	$0.641191\pi$
$62$	1.69784e48	0.0869213
$63$	−5.83470e48	−0.192377
$64$	−4.04291e49	−0.864460
$65$	−1.96188e49	−0.273876
$66$	1.58162e49	0.145092
$67$	1.06094e50	0.643627	0.321814	−	0.946803i	$-0.395708\pi$
$67$	1.06094e50	0.643627	0.321814	+	0.946803i	$0.395708\pi$
$68$	−3.07325e49	−0.124052
$69$	6.41669e50	1.73365
$70$	−1.02011e50	−0.185546
$71$	−1.17879e51	−1.45156	−0.725778	−	0.687929i	$-0.758520\pi$
$71$	−1.17879e51	−1.45156	−0.725778	+	0.687929i	$0.758520\pi$
$72$	4.27683e49	0.0358491
$73$	2.92361e50	0.167703	0.0838516	−	0.996478i	$-0.473278\pi$
$73$	2.92361e50	0.167703	0.0838516	+	0.996478i	$0.473278\pi$
$74$	−4.32604e50	−0.170694
$75$	−1.45603e51	−0.397180
$76$	−5.80404e51	−1.09991
$77$	1.24007e52	1.64041
$78$	5.53584e50	0.0513549
$79$	2.26793e52	1.48212	0.741062	−	0.671436i	$-0.234322\pi$
$79$	2.26793e52	1.48212	0.741062	+	0.671436i	$0.234322\pi$
$80$	−1.52973e52	−0.707360
$81$	−2.63616e52	−0.866232
$82$	7.17360e51	0.168212
$83$	3.10804e52	0.522203	0.261101	−	0.965311i	$-0.415914\pi$
$83$	3.10804e52	0.522203	0.261101	+	0.965311i	$0.415914\pi$
$84$	−1.22109e53	−1.47594
$85$	−1.10466e52	−0.0964290
$86$	−7.61035e51	−0.0481612
$87$	1.96914e53	0.906768
$88$	−9.08973e52	−0.305687
$89$	4.89902e53	1.20749	0.603745	−	0.797177i	$-0.293674\pi$
$89$	4.89902e53	1.20749	0.603745	+	0.797177i	$0.293674\pi$
$90$	7.59684e51	0.0137710
$91$	4.34038e53	0.580616
$92$	−1.82239e54	−1.80499
$93$	7.30513e53	0.537461
$94$	−5.06356e53	−0.277613
$95$	−2.08622e54	−0.854989
$96$	1.34781e54	0.414161
$97$	4.57966e53	0.105830	0.0529152	−	0.998599i	$-0.483149\pi$
$97$	4.57966e53	0.105830	0.0529152	+	0.998599i	$0.483149\pi$
$98$	1.38617e54	0.241601
$99$	−9.23488e53	−0.121749
$100$	4.13524e54	0.413524
$101$	1.50130e55	1.14191	0.570953	−	0.820983i	$-0.306574\pi$
$101$	1.50130e55	1.14191	0.570953	+	0.820983i	$0.306574\pi$
$102$	3.11702e53	0.0180815
$103$	−1.70225e55	−0.755090	−0.377545	−	0.925991i	$-0.623232\pi$
$103$	−1.70225e55	−0.755090	−0.377545	+	0.925991i	$0.623232\pi$
$104$	−3.18150e54	−0.108197
$105$	−4.38913e55	−1.14729
$106$	−2.12566e54	−0.0428136
$107$	−2.90724e55	−0.452300	−0.226150	−	0.974092i	$-0.572614\pi$
$107$	−2.90724e55	−0.452300	−0.226150	+	0.974092i	$0.572614\pi$
$108$	8.51965e55	1.02629
$109$	5.37285e55	0.502315	0.251157	−	0.967946i	$-0.419189\pi$
$109$	5.37285e55	0.502315	0.251157	+	0.967946i	$0.419189\pi$
$110$	−1.61459e55	−0.117426
$111$	−1.86132e56	−1.05545
$112$	3.38432e56	1.49960
$113$	2.45020e56	0.850247	0.425123	−	0.905135i	$-0.360231\pi$
$113$	2.45020e56	0.850247	0.425123	+	0.905135i	$0.360231\pi$
$114$	5.88670e55	0.160320
$115$	−6.55043e56	−1.40307
$116$	−5.59249e56	−0.944083
$117$	−3.23231e55	−0.0430925
$118$	7.33725e55	0.0774066
$119$	2.44390e56	0.204429
$120$	3.21724e56	0.213796
$121$	7.21357e55	0.0381551
$122$	−3.08811e56	−0.130256
$123$	3.08651e57	1.04010
$124$	−2.07471e57	−0.559579
$125$	4.99803e57	1.08087
$126$	−1.68070e56	−0.0291944
$127$	−5.35925e57	−0.749035	−0.374517	−	0.927220i	$-0.622192\pi$
$127$	−5.35925e57	−0.749035	−0.374517	+	0.927220i	$0.622192\pi$
$128$	−5.08267e57	−0.572556
$129$	−3.27443e57	−0.297796
$130$	−5.65122e56	−0.0415624
$131$	−5.72408e57	−0.340993	−0.170496	−	0.985358i	$-0.554537\pi$
$131$	−5.72408e57	−0.340993	−0.170496	+	0.985358i	$0.554537\pi$
$132$	−1.93269e58	−0.934070
$133$	4.61547e58	1.81257
$134$	3.05606e57	0.0976744
$135$	3.06233e58	0.797761
$136$	−1.79138e57	−0.0380950
$137$	−3.04892e58	−0.530067	−0.265033	−	0.964239i	$-0.585383\pi$
$137$	−3.04892e58	−0.530067	−0.265033	+	0.964239i	$0.585383\pi$
$138$	1.84834e58	0.263092
$139$	−5.38797e58	−0.628809	−0.314404	−	0.949289i	$-0.601805\pi$
$139$	−5.38797e58	−0.628809	−0.314404	+	0.949289i	$0.601805\pi$
$140$	1.24655e59	1.19450
$141$	−2.17865e59	−1.71657
$142$	−3.39554e58	−0.220282
$143$	6.86975e58	0.367451
$144$	−2.52032e58	−0.111298
$145$	−2.01018e59	−0.733862
$146$	8.42153e57	0.0254500
$147$	5.96413e59	1.49390
$148$	5.28629e59	1.09889
$149$	−2.75514e59	−0.475907	−0.237953	−	0.971277i	$-0.576477\pi$
$149$	−2.75514e59	−0.475907	−0.237953	+	0.971277i	$0.576477\pi$
$150$	−4.19414e58	−0.0602744
$151$	−3.94876e59	−0.472709	−0.236355	−	0.971667i	$-0.575953\pi$
$151$	−3.94876e59	−0.472709	−0.236355	+	0.971667i	$0.575953\pi$
$152$	−3.38314e59	−0.337770
$153$	−1.81999e58	−0.0151724
$154$	3.57205e59	0.248942
$155$	−7.45739e59	−0.434976
$156$	−6.76462e59	−0.330611
$157$	−1.28546e60	−0.527009	−0.263505	−	0.964658i	$-0.584878\pi$
$157$	−1.28546e60	−0.527009	−0.263505	+	0.964658i	$0.584878\pi$
$158$	6.53282e59	0.224921
$159$	−9.14584e59	−0.264730
$160$	−1.37590e60	−0.335187
$161$	1.44919e61	2.97450
$162$	−7.59352e59	−0.131456
$163$	8.10357e59	0.118445	0.0592226	−	0.998245i	$-0.481138\pi$
$163$	8.10357e59	0.118445	0.0592226	+	0.998245i	$0.481138\pi$
$164$	−8.76591e60	−1.08291
$165$	−6.94692e60	−0.726079
$166$	8.95277e59	0.0792474
$167$	8.63145e60	0.647710	0.323855	−	0.946107i	$-0.395021\pi$
$167$	8.63145e60	0.647710	0.323855	+	0.946107i	$0.395021\pi$
$168$	−7.11769e60	−0.453246
$169$	−1.60833e61	−0.869942
$170$	−3.18199e59	−0.0146337
$171$	−3.43717e60	−0.134526
$172$	9.29961e60	0.310050
$173$	2.85400e61	0.811307	0.405654	−	0.914027i	$-0.367044\pi$
$173$	2.85400e61	0.811307	0.405654	+	0.914027i	$0.367044\pi$
$174$	5.67214e60	0.137608
$175$	−3.28842e61	−0.681460
$176$	5.35654e61	0.949044
$177$	3.15692e61	0.478629
$178$	1.41117e61	0.183244
$179$	−4.09139e61	−0.455421	−0.227710	−	0.973729i	$-0.573124\pi$
$179$	−4.09139e61	−0.455421	−0.227710	+	0.973729i	$0.573124\pi$
$180$	−9.28310e60	−0.0886542
$181$	−1.09499e62	−0.897946	−0.448973	−	0.893545i	$-0.648210\pi$
$181$	−1.09499e62	−0.897946	−0.448973	+	0.893545i	$0.648210\pi$
$182$	1.25025e61	0.0881121
$183$	−1.32869e62	−0.805413
$184$	−1.06226e62	−0.554294
$185$	1.90012e62	0.854197
$186$	2.10426e61	0.0815630
$187$	3.86810e61	0.129376
$188$	6.18751e62	1.78721
$189$	−6.77497e62	−1.69125
$190$	−6.00940e61	−0.129750
$191$	9.82615e62	1.83639	0.918197	−	0.396125i	$-0.129645\pi$
$191$	9.82615e62	1.83639	0.918197	+	0.396125i	$0.129645\pi$
$192$	−5.01067e62	−0.811170
$193$	3.58891e62	0.503659	0.251830	−	0.967772i	$-0.418968\pi$
$193$	3.58891e62	0.503659	0.251830	+	0.967772i	$0.418968\pi$
$194$	1.31918e61	0.0160604
$195$	−2.43149e62	−0.256993
$196$	−1.69386e63	−1.55537
$197$	−1.12979e62	−0.0901937	−0.0450968	−	0.998983i	$-0.514360\pi$
$197$	−1.12979e62	−0.0901937	−0.0450968	+	0.998983i	$0.514360\pi$
$198$	−2.66013e61	−0.0184761
$199$	−6.41270e62	−0.387776	−0.193888	−	0.981024i	$-0.562110\pi$
$199$	−6.41270e62	−0.387776	−0.193888	+	0.981024i	$0.562110\pi$
$200$	2.41041e62	0.126989
$201$	1.31490e63	0.603951
$202$	4.32453e62	0.173291
$203$	4.44724e63	1.55579
$204$	−3.80890e62	−0.116405
$205$	−3.15084e63	−0.841774
$206$	−4.90335e62	−0.114589
$207$	−1.07922e63	−0.220763
$208$	1.87485e63	0.335911
$209$	7.30515e63	1.14711
$210$	−1.26430e63	−0.174108
$211$	−1.25121e64	−1.51204	−0.756019	−	0.654550i	$-0.772858\pi$
$211$	−1.25121e64	−1.51204	−0.756019	+	0.654550i	$0.772858\pi$
$212$	2.59749e63	0.275624
$213$	−1.46096e64	−1.36207
$214$	−8.37436e62	−0.0686393
$215$	3.34267e63	0.241011
$216$	4.96606e63	0.315162
$217$	1.64985e64	0.922148
$218$	1.54766e63	0.0762293
$219$	3.62344e63	0.157365
$220$	1.97297e64	0.755958
$221$	1.35387e63	0.0457921
$222$	−5.36158e63	−0.160172
$223$	−3.80868e64	−1.00552	−0.502760	−	0.864426i	$-0.667682\pi$
$223$	−3.80868e64	−1.00552	−0.502760	+	0.864426i	$0.667682\pi$
$224$	3.04399e64	0.710595
$225$	2.44890e63	0.0505769
$226$	7.05786e63	0.129030
$227$	−8.04148e64	−1.30204	−0.651021	−	0.759060i	$-0.725659\pi$
$227$	−8.04148e64	−1.30204	−0.651021	+	0.759060i	$0.725659\pi$
$228$	−7.19336e64	−1.03210
$229$	3.89160e64	0.495054	0.247527	−	0.968881i	$-0.420382\pi$
$229$	3.89160e64	0.495054	0.247527	+	0.968881i	$0.420382\pi$
$230$	−1.88686e64	−0.212924
$231$	1.53691e65	1.53928
$232$	−3.25983e64	−0.289918
$233$	−9.97362e64	−0.788070	−0.394035	−	0.919095i	$-0.628921\pi$
$233$	−9.97362e64	−0.788070	−0.394035	+	0.919095i	$0.628921\pi$
$234$	−9.31072e62	−0.00653954
$235$	2.22405e65	1.38925
$236$	−8.96589e64	−0.498326
$237$	2.81081e65	1.39076
$238$	7.03972e63	0.0310234
$239$	−4.18204e62	−0.00164227	−0.000821137	−	1.00000i	$-0.500261\pi$
$239$	−4.18204e62	−0.00164227	−0.000821137		1.00000i	$0.500261\pi$
$240$	−1.89591e65	−0.663755
$241$	−5.42301e65	−1.69345	−0.846724	−	0.532033i	$-0.821428\pi$
$241$	−5.42301e65	−1.69345	−0.846724	+	0.532033i	$0.821428\pi$
$242$	2.07788e63	0.00579026
$243$	9.55220e64	0.237646
$244$	3.77358e65	0.838558
$245$	−6.08844e65	−1.20903
$246$	8.89076e64	0.157842
$247$	2.55688e65	0.406017
$248$	−1.20934e65	−0.171841
$249$	3.85202e65	0.490011
$250$	1.43969e65	0.164029
$251$	−7.66365e65	−0.782363	−0.391181	−	0.920314i	$-0.627933\pi$
$251$	−7.66365e65	−0.782363	−0.391181	+	0.920314i	$0.627933\pi$
$252$	2.05376e65	0.187947
$253$	2.29371e66	1.88246
$254$	−1.54374e65	−0.113671
$255$	−1.36908e65	−0.0904846
$256$	1.31021e66	0.777571
$257$	−2.62578e66	−1.39990	−0.699952	−	0.714190i	$-0.746795\pi$
$257$	−2.62578e66	−1.39990	−0.699952	+	0.714190i	$0.746795\pi$
$258$	−9.43205e64	−0.0451923
$259$	−4.20375e66	−1.81089
$260$	6.90562e65	0.267569
$261$	−3.31189e65	−0.115468
$262$	−1.64883e65	−0.0517477
$263$	3.10641e66	0.877962	0.438981	−	0.898496i	$-0.355339\pi$
$263$	3.10641e66	0.877962	0.438981	+	0.898496i	$0.355339\pi$
$264$	−1.12655e66	−0.286843
$265$	9.33647e65	0.214250
$266$	1.32950e66	0.275069
$267$	6.07170e66	1.13305
$268$	−3.73441e66	−0.628805
$269$	−2.44880e66	−0.372192	−0.186096	−	0.982532i	$-0.559583\pi$
$269$	−2.44880e66	−0.372192	−0.186096	+	0.982532i	$0.559583\pi$
$270$	8.82109e65	0.121065
$271$	4.59005e66	0.569065	0.284533	−	0.958666i	$-0.408162\pi$
$271$	4.59005e66	0.569065	0.284533	+	0.958666i	$0.408162\pi$
$272$	1.05566e66	0.118271
$273$	5.37934e66	0.544824
$274$	−8.78248e65	−0.0804408
$275$	−5.20475e66	−0.431272
$276$	−2.25861e67	−1.69372
$277$	−3.77433e66	−0.256240	−0.128120	−	0.991759i	$-0.540894\pi$
$277$	−3.77433e66	−0.256240	−0.128120	+	0.991759i	$0.540894\pi$
$278$	−1.55202e66	−0.0954255
$279$	−1.22865e66	−0.0684404
$280$	7.26604e66	0.366819
$281$	2.01573e67	0.922591	0.461295	−	0.887247i	$-0.347385\pi$
$281$	2.01573e67	0.922591	0.461295	+	0.887247i	$0.347385\pi$
$282$	−6.27563e66	−0.260500
$283$	−1.57152e67	−0.591824	−0.295912	−	0.955215i	$-0.595624\pi$
$283$	−1.57152e67	−0.591824	−0.295912	+	0.955215i	$0.595624\pi$
$284$	4.14925e67	1.41813
$285$	−2.58560e67	−0.802283
$286$	1.97885e66	0.0557630
$287$	6.97080e67	1.78456
$288$	−2.26688e66	−0.0527393
$289$	−4.65191e67	−0.983877
$290$	−5.79036e66	−0.111368
$291$	5.67590e66	0.0993064
$292$	−1.02908e67	−0.163841
$293$	−5.33382e67	−0.772999	−0.386500	−	0.922290i	$-0.626316\pi$
$293$	−5.33382e67	−0.772999	−0.386500	+	0.922290i	$0.626316\pi$
$294$	1.71798e67	0.226708
$295$	−3.22272e67	−0.387363
$296$	3.08135e67	0.337457
$297$	−1.07231e68	−1.07033
$298$	−7.93625e66	−0.0722218
$299$	8.02824e67	0.666289
$300$	5.12510e67	0.388033
$301$	−7.39521e67	−0.510942
$302$	−1.13745e67	−0.0717365
$303$	1.86067e68	1.07151
$304$	1.99367e68	1.04865
$305$	1.35638e68	0.651834
$306$	−5.24252e65	−0.00230251
$307$	−2.80514e67	−0.112629	−0.0563144	−	0.998413i	$-0.517935\pi$
$307$	−2.80514e67	−0.112629	−0.0563144	+	0.998413i	$0.517935\pi$
$308$	−4.36493e68	−1.60263
$309$	−2.10971e68	−0.708542
$310$	−2.14812e67	−0.0660103
$311$	−7.41937e67	−0.208668	−0.104334	−	0.994542i	$-0.533271\pi$
$311$	−7.41937e67	−0.208668	−0.104334	+	0.994542i	$0.533271\pi$
$312$	−3.94306e67	−0.101527
$313$	4.59840e68	1.08427	0.542135	−	0.840291i	$-0.317616\pi$
$313$	4.59840e68	1.08427	0.542135	+	0.840291i	$0.317616\pi$
$314$	−3.70279e67	−0.0799768
$315$	7.38208e67	0.146096
$316$	−7.98290e68	−1.44799
$317$	−3.97467e67	−0.0660955	−0.0330477	−	0.999454i	$-0.510521\pi$
$317$	−3.97467e67	−0.0660955	−0.0330477	+	0.999454i	$0.510521\pi$
$318$	−2.63448e67	−0.0401744
$319$	7.03889e68	0.984601
$320$	5.11511e68	0.656494
$321$	−3.60315e68	−0.424418
$322$	4.17443e68	0.451399
$323$	1.43968e68	0.142954
$324$	9.27904e68	0.846283
$325$	−1.82172e68	−0.152647
$326$	2.33425e67	0.0179748
$327$	6.65895e68	0.471349
$328$	−5.10960e68	−0.332549
$329$	−4.92041e69	−2.94520
$330$	−2.00107e68	−0.110187
$331$	2.81395e69	1.42576	0.712879	−	0.701287i	$-0.247391\pi$
$331$	2.81395e69	1.42576	0.712879	+	0.701287i	$0.247391\pi$
$332$	−1.09400e69	−0.510176
$333$	3.13056e68	0.134402
$334$	2.48631e68	0.0982939
$335$	−1.34231e69	−0.488787
$336$	4.19443e69	1.40716
$337$	−3.53381e69	−1.09250	−0.546249	−	0.837623i	$-0.683945\pi$
$337$	−3.53381e69	−1.09250	−0.546249	+	0.837623i	$0.683945\pi$
$338$	−4.63282e68	−0.132019
$339$	3.03671e69	0.797833
$340$	3.88829e68	0.0942082
$341$	2.61130e69	0.583594
$342$	−9.90083e67	−0.0204152
$343$	5.00907e69	0.953167
$344$	5.42069e68	0.0952132
$345$	−8.11842e69	−1.31658
$346$	8.22099e68	0.123121
$347$	7.81225e69	1.08073	0.540363	−	0.841432i	$-0.318287\pi$
$347$	7.81225e69	1.08073	0.540363	+	0.841432i	$0.318287\pi$
$348$	−6.93117e69	−0.885885
$349$	−1.46742e70	−1.73323	−0.866614	−	0.498978i	$-0.833709\pi$
$349$	−1.46742e70	−1.73323	−0.866614	+	0.498978i	$0.833709\pi$
$350$	−9.47235e68	−0.103416
$351$	−3.75320e69	−0.378840
$352$	4.81788e69	0.449710
$353$	3.73450e69	0.322425	0.161212	−	0.986920i	$-0.448460\pi$
$353$	3.73450e69	0.322425	0.161212	+	0.986920i	$0.448460\pi$
$354$	9.09358e68	0.0726349
$355$	1.49142e70	1.10235
$356$	−1.72441e70	−1.17968
$357$	3.02891e69	0.191827
$358$	−1.17853e69	−0.0691129
$359$	2.97159e70	1.61396	0.806979	−	0.590580i	$-0.201101\pi$
$359$	2.97159e70	1.61396	0.806979	+	0.590580i	$0.201101\pi$
$360$	−5.41107e68	−0.0272248
$361$	5.73832e69	0.267508
$362$	−3.15415e69	−0.136269
$363$	8.94029e68	0.0358030
$364$	−1.52777e70	−0.567245
$365$	−3.69897e69	−0.127358
$366$	−3.82732e69	−0.122226
$367$	−5.08197e70	−1.50562	−0.752811	−	0.658237i	$-0.771302\pi$
$367$	−5.08197e70	−1.50562	−0.752811	+	0.658237i	$0.771302\pi$
$368$	6.25985e70	1.72087
$369$	−5.19120e69	−0.132447
$370$	5.47333e69	0.129630
$371$	−2.06556e70	−0.454210
$372$	−2.57134e70	−0.525083
$373$	−8.75772e70	−1.66111	−0.830554	−	0.556938i	$-0.811976\pi$
$373$	−8.75772e70	−1.66111	−0.830554	+	0.556938i	$0.811976\pi$
$374$	1.11421e69	0.0196336
$375$	6.19442e70	1.01424
$376$	3.60666e70	0.548833
$377$	2.46368e70	0.348496
$378$	−1.95154e70	−0.256658
$379$	1.26223e71	1.54369	0.771847	−	0.635808i	$-0.219333\pi$
$379$	1.26223e71	1.54369	0.771847	+	0.635808i	$0.219333\pi$
$380$	7.34329e70	0.835299
$381$	−6.64211e70	−0.702860
$382$	2.83044e70	0.278684
$383$	−5.28430e69	−0.0484196	−0.0242098	−	0.999707i	$-0.507707\pi$
$383$	−5.28430e69	−0.0484196	−0.0242098	+	0.999707i	$0.507707\pi$
$384$	−6.29932e70	−0.537261
$385$	−1.56894e71	−1.24577
$386$	1.03379e70	0.0764334
$387$	5.50725e69	0.0379213
$388$	−1.61200e70	−0.103393
$389$	2.99174e70	0.178776	0.0893882	−	0.995997i	$-0.471509\pi$
$389$	2.99174e70	0.178776	0.0893882	+	0.995997i	$0.471509\pi$
$390$	−7.00397e69	−0.0390002
$391$	4.52040e70	0.234594
$392$	−9.87338e70	−0.477638
$393$	−7.09426e70	−0.319972
$394$	−3.25438e69	−0.0136874
$395$	−2.86939e71	−1.12556
$396$	3.25059e70	0.118945
$397$	4.68857e71	1.60067	0.800335	−	0.599553i	$-0.204655\pi$
$397$	4.68857e71	1.60067	0.800335	+	0.599553i	$0.204655\pi$
$398$	−1.84719e70	−0.0588474
$399$	5.72028e71	1.70084
$400$	−1.42045e71	−0.394253
$401$	1.15088e70	0.0298236	0.0149118	−	0.999889i	$-0.495253\pi$
$401$	1.15088e70	0.0298236	0.0149118	+	0.999889i	$0.495253\pi$
$402$	3.78760e70	0.0916532
$403$	9.13981e70	0.206561
$404$	−5.28445e71	−1.11561
$405$	3.33528e71	0.657839
$406$	1.28104e71	0.236100
$407$	−6.65350e71	−1.14605
$408$	−2.22019e70	−0.0357467
$409$	−5.99712e71	−0.902717	−0.451358	−	0.892343i	$-0.649060\pi$
$409$	−5.99712e71	−0.902717	−0.451358	+	0.892343i	$0.649060\pi$
$410$	−9.07607e70	−0.127744
$411$	−3.77875e71	−0.497391
$412$	5.99174e71	0.737700
$413$	7.12983e71	0.821207
$414$	−3.10872e70	−0.0335021
$415$	−3.93230e71	−0.396574
$416$	1.68631e71	0.159173
$417$	−6.67770e71	−0.590046
$418$	2.10426e71	0.174081
$419$	−6.48026e71	−0.502004	−0.251002	−	0.967987i	$-0.580760\pi$
$419$	−6.48026e71	−0.502004	−0.251002	+	0.967987i	$0.580760\pi$
$420$	1.54493e72	1.12087
$421$	1.99937e72	1.35874	0.679369	−	0.733797i	$-0.262254\pi$
$421$	1.99937e72	1.35874	0.679369	+	0.733797i	$0.262254\pi$
$422$	−3.60413e71	−0.229461
$423$	3.66426e71	0.218588
$424$	1.51406e71	0.0846412
$425$	−1.02574e71	−0.0537455
$426$	−4.20834e71	−0.206703
$427$	−3.00081e72	−1.38189
$428$	1.02332e72	0.441884
$429$	8.51417e71	0.344800
$430$	9.62864e70	0.0365749
$431$	−3.24265e72	−1.15551	−0.577756	−	0.816209i	$-0.696072\pi$
$431$	−3.24265e72	−1.15551	−0.577756	+	0.816209i	$0.696072\pi$
$432$	−2.92648e72	−0.978459
$433$	1.58622e72	0.497675	0.248838	−	0.968545i	$-0.419951\pi$
$433$	1.58622e72	0.497675	0.248838	+	0.968545i	$0.419951\pi$
$434$	4.75241e71	0.139942
$435$	−2.49136e72	−0.688623
$436$	−1.89119e72	−0.490746
$437$	8.53707e72	2.08003
$438$	1.04374e71	0.0238811
$439$	1.49705e72	0.321708	0.160854	−	0.986978i	$-0.448575\pi$
$439$	1.49705e72	0.321708	0.160854	+	0.986978i	$0.448575\pi$
$440$	1.15004e72	0.232147
$441$	−1.00311e72	−0.190233
$442$	3.89986e70	0.00694923
$443$	3.40583e72	0.570322	0.285161	−	0.958480i	$-0.407953\pi$
$443$	3.40583e72	0.570322	0.285161	+	0.958480i	$0.407953\pi$
$444$	6.55168e72	1.03115
$445$	−6.19825e72	−0.917000
$446$	−1.09710e72	−0.152594
$447$	−3.41465e72	−0.446570
$448$	−1.13165e73	−1.39176
$449$	8.20452e72	0.949027	0.474514	−	0.880248i	$-0.342624\pi$
$449$	8.20452e72	0.949027	0.474514	+	0.880248i	$0.342624\pi$
$450$	7.05411e70	0.00767535
$451$	1.10331e73	1.12938
$452$	−8.62449e72	−0.830666
$453$	−4.89398e72	−0.443569
$454$	−2.31636e72	−0.197593
$455$	−5.49146e72	−0.440935
$456$	−4.19297e72	−0.316948
$457$	−1.34921e73	−0.960247	−0.480124	−	0.877201i	$-0.659408\pi$
$457$	−1.34921e73	−0.960247	−0.480124	+	0.877201i	$0.659408\pi$
$458$	1.12098e72	0.0751275
$459$	−2.11329e72	−0.133386
$460$	2.30569e73	1.37076
$461$	3.22702e73	1.80728	0.903641	−	0.428290i	$-0.140884\pi$
$461$	3.22702e73	1.80728	0.903641	+	0.428290i	$0.140884\pi$
$462$	4.42710e72	0.233596
$463$	−7.30279e72	−0.363088	−0.181544	−	0.983383i	$-0.558109\pi$
$463$	−7.30279e72	−0.363088	−0.181544	+	0.983383i	$0.558109\pi$
$464$	1.92101e73	0.900087
$465$	−9.24248e72	−0.408162
$466$	−2.87292e72	−0.119594
$467$	−4.40634e73	−1.72927	−0.864636	−	0.502398i	$-0.832451\pi$
$467$	−4.40634e73	−1.72927	−0.864636	+	0.502398i	$0.832451\pi$
$468$	1.13774e72	0.0421000
$469$	2.96967e73	1.03623
$470$	6.40644e72	0.210827
$471$	−1.59316e73	−0.494522
$472$	−5.22617e72	−0.153031
$473$	−1.17048e73	−0.323357
$474$	8.09659e72	0.211056
$475$	−1.93718e73	−0.476535
$476$	−8.60231e72	−0.199721
$477$	1.53824e72	0.0337107
$478$	−1.20464e70	−0.000249225 0
$479$	−3.18111e73	−0.621373	−0.310687	−	0.950512i	$-0.600559\pi$
$479$	−3.18111e73	−0.621373	−0.310687	+	0.950512i	$0.600559\pi$
$480$	−1.70525e73	−0.314524
$481$	−2.32879e73	−0.405640
$482$	−1.56211e73	−0.256991
$483$	1.79609e74	2.79114
$484$	−2.53911e72	−0.0372764
$485$	−5.79420e72	−0.0803703
$486$	2.75153e72	0.0360643
$487$	6.34796e73	0.786299	0.393149	−	0.919475i	$-0.371386\pi$
$487$	6.34796e73	0.786299	0.393149	+	0.919475i	$0.371386\pi$
$488$	2.19960e73	0.257512
$489$	1.00433e73	0.111144
$490$	−1.75379e73	−0.183478
$491$	−6.91619e73	−0.684110	−0.342055	−	0.939680i	$-0.611123\pi$
$491$	−6.91619e73	−0.684110	−0.342055	+	0.939680i	$0.611123\pi$
$492$	−1.08642e74	−1.01615
$493$	1.38721e73	0.122702
$494$	7.36514e72	0.0616155
$495$	1.16840e73	0.0924590
$496$	7.12658e73	0.533501
$497$	−3.29955e74	−2.33698
$498$	1.10958e73	0.0743622
$499$	1.91941e74	1.21732	0.608659	−	0.793432i	$-0.291708\pi$
$499$	1.91941e74	1.21732	0.608659	+	0.793432i	$0.291708\pi$
$500$	−1.75926e74	−1.05598
$501$	1.06976e74	0.607782
$502$	−2.20753e73	−0.118728
$503$	2.48789e74	1.26681	0.633406	−	0.773820i	$-0.281656\pi$
$503$	2.48789e74	1.26681	0.633406	+	0.773820i	$0.281656\pi$
$504$	1.19712e73	0.0577164
$505$	−1.89945e74	−0.867194
$506$	6.60709e73	0.285674
$507$	−1.99332e74	−0.816314
$508$	1.88641e74	0.731785
$509$	3.43699e74	1.26311	0.631553	−	0.775333i	$-0.282418\pi$
$509$	3.43699e74	1.26311	0.631553	+	0.775333i	$0.282418\pi$
$510$	−3.94367e72	−0.0137316
$511$	8.18345e73	0.269999
$512$	2.20863e74	0.690557
$513$	−3.99108e74	−1.18267
$514$	−7.56362e73	−0.212444
$515$	2.15369e74	0.573435
$516$	1.15257e74	0.290937
$517$	−7.78780e74	−1.86391
$518$	−1.21090e74	−0.274814
$519$	3.53716e74	0.761294
$520$	4.02524e73	0.0821675
$521$	−3.30970e74	−0.640842	−0.320421	−	0.947275i	$-0.603824\pi$
$521$	−3.30970e74	−0.640842	−0.320421	+	0.947275i	$0.603824\pi$
$522$	−9.53996e72	−0.0175230
$523$	−5.36017e74	−0.934076	−0.467038	−	0.884237i	$-0.654679\pi$
$523$	−5.36017e74	−0.934076	−0.467038	+	0.884237i	$0.654679\pi$
$524$	2.01482e74	0.333140
$525$	−4.07557e74	−0.639451
$526$	8.94808e73	0.133236
$527$	5.14629e73	0.0727281
$528$	6.63875e74	0.890540
$529$	1.89523e75	2.41340
$530$	2.68939e73	0.0325138
$531$	−5.30963e73	−0.0609487
$532$	−1.62460e75	−1.77083
$533$	3.86169e74	0.399741
$534$	1.74897e74	0.171948
$535$	3.67825e74	0.343489
$536$	−2.17677e74	−0.193099
$537$	−5.07076e74	−0.427346
$538$	−7.05383e73	−0.0564823
$539$	2.13194e75	1.62212
$540$	−1.07791e75	−0.779389
$541$	−9.01034e74	−0.619179	−0.309590	−	0.950870i	$-0.600192\pi$
$541$	−9.01034e74	−0.619179	−0.309590	+	0.950870i	$0.600192\pi$
$542$	1.32217e74	0.0863591
$543$	−1.35710e75	−0.842592
$544$	9.49497e73	0.0560433
$545$	−6.79775e74	−0.381471
$546$	1.54953e74	0.0826804
$547$	−3.28535e75	−1.66698	−0.833491	−	0.552534i	$-0.813661\pi$
$547$	−3.28535e75	−1.66698	−0.833491	+	0.552534i	$0.813661\pi$
$548$	1.07319e75	0.517859
$549$	2.23472e74	0.102561
$550$	−1.49924e74	−0.0654481
$551$	2.61983e75	1.08794
$552$	−1.31653e75	−0.520124
$553$	6.34814e75	2.38619
$554$	−1.08720e74	−0.0388859
$555$	2.35495e75	0.801540
$556$	1.89652e75	0.614327
$557$	−5.67764e75	−1.75045	−0.875226	−	0.483715i	$-0.839287\pi$
$557$	−5.67764e75	−1.75045	−0.875226	+	0.483715i	$0.839287\pi$
$558$	−3.53915e73	−0.0103862
$559$	−4.09680e74	−0.114451
$560$	−4.28185e75	−1.13884
$561$	4.79401e74	0.121400
$562$	5.80636e74	0.140009
$563$	1.20573e74	0.0276866	0.0138433	−	0.999904i	$-0.495593\pi$
$563$	1.20573e74	0.0276866	0.0138433	+	0.999904i	$0.495593\pi$
$564$	7.66863e75	1.67704
$565$	−3.10001e75	−0.645700
$566$	−4.52679e74	−0.0898129
$567$	−7.37885e75	−1.39462
$568$	2.41857e75	0.435492
$569$	−3.59495e75	−0.616745	−0.308372	−	0.951266i	$-0.599784\pi$
$569$	−3.59495e75	−0.616745	−0.308372	+	0.951266i	$0.599784\pi$
$570$	−7.44788e74	−0.121751
$571$	−5.41913e75	−0.844183	−0.422092	−	0.906553i	$-0.638704\pi$
$571$	−5.41913e75	−0.844183	−0.422092	+	0.906553i	$0.638704\pi$
$572$	−2.41809e75	−0.358989
$573$	1.21782e76	1.72319
$574$	2.00795e75	0.270817
$575$	−6.08246e75	−0.782012
$576$	8.42744e74	0.103295
$577$	4.19846e75	0.490631	0.245316	−	0.969443i	$-0.421108\pi$
$577$	4.19846e75	0.490631	0.245316	+	0.969443i	$0.421108\pi$
$578$	−1.33999e75	−0.149309
$579$	4.44800e75	0.472611
$580$	7.07564e75	0.716961
$581$	8.69968e75	0.840736
$582$	1.63495e74	0.0150704
$583$	−3.26928e75	−0.287453
$584$	−5.99847e74	−0.0503138
$585$	4.08953e74	0.0327255
$586$	−1.53642e75	−0.117307
$587$	−4.18417e75	−0.304833	−0.152417	−	0.988316i	$-0.548706\pi$
$587$	−4.18417e75	−0.304833	−0.152417	+	0.988316i	$0.548706\pi$
$588$	−2.09932e76	−1.45949
$589$	9.71910e75	0.644845
$590$	−9.28312e74	−0.0587846
$591$	−1.40023e75	−0.0846337
$592$	−1.81583e76	−1.04768
$593$	4.80739e75	0.264792	0.132396	−	0.991197i	$-0.457733\pi$
$593$	4.80739e75	0.264792	0.132396	+	0.991197i	$0.457733\pi$
$594$	−3.08881e75	−0.162429
$595$	−3.09204e75	−0.155249
$596$	9.69785e75	0.464947
$597$	−7.94772e75	−0.363872
$598$	2.31255e75	0.101113
$599$	3.85877e75	0.161143	0.0805714	−	0.996749i	$-0.474325\pi$
$599$	3.85877e75	0.161143	0.0805714	+	0.996749i	$0.474325\pi$
$600$	2.98739e75	0.119161
$601$	2.69061e76	1.02519	0.512593	−	0.858632i	$-0.328685\pi$
$601$	2.69061e76	1.02519	0.512593	+	0.858632i	$0.328685\pi$
$602$	−2.13020e75	−0.0775386
$603$	−2.21153e75	−0.0769072
$604$	1.38992e76	0.461823
$605$	−9.12663e74	−0.0289760
$606$	5.35971e75	0.162609
$607$	−2.83247e76	−0.821252	−0.410626	−	0.911804i	$-0.634690\pi$
$607$	−2.83247e76	−0.821252	−0.410626	+	0.911804i	$0.634690\pi$
$608$	1.79319e76	0.496909
$609$	5.51179e76	1.45988
$610$	3.90709e75	0.0989198
$611$	−2.72581e76	−0.659724
$612$	6.40619e74	0.0148230
$613$	−5.22770e76	−1.15651	−0.578253	−	0.815858i	$-0.696265\pi$
$613$	−5.22770e76	−1.15651	−0.578253	+	0.815858i	$0.696265\pi$
$614$	−8.08026e74	−0.0170921
$615$	−3.90507e76	−0.789883
$616$	−2.54429e76	−0.492150
$617$	3.43035e76	0.634595	0.317297	−	0.948326i	$-0.397225\pi$
$617$	3.43035e76	0.634595	0.317297	+	0.948326i	$0.397225\pi$
$618$	−6.07708e75	−0.107526
$619$	−1.83217e76	−0.310080	−0.155040	−	0.987908i	$-0.549551\pi$
$619$	−1.83217e76	−0.310080	−0.155040	+	0.987908i	$0.549551\pi$
$620$	2.62493e76	0.424959
$621$	−1.25314e77	−1.94080
$622$	−2.13716e75	−0.0316667
$623$	1.37128e77	1.94404
$624$	2.32363e76	0.315203
$625$	−3.06276e76	−0.397568
$626$	1.32458e76	0.164545
$627$	9.05380e76	1.07640
$628$	4.52470e76	0.514872
$629$	−1.31126e76	−0.142822
$630$	2.12642e75	0.0221710
$631$	3.00198e76	0.299640	0.149820	−	0.988713i	$-0.452131\pi$
$631$	3.00198e76	0.299640	0.149820	+	0.988713i	$0.452131\pi$
$632$	−4.65319e76	−0.444663
$633$	−1.55071e77	−1.41883
$634$	−1.14491e75	−0.0100304
$635$	6.78055e76	0.568836
$636$	3.21925e76	0.258633
$637$	7.46201e76	0.574145
$638$	2.02757e76	0.149419
$639$	2.45720e76	0.173447
$640$	6.43062e76	0.434814
$641$	−7.84590e76	−0.508214	−0.254107	−	0.967176i	$-0.581782\pi$
$641$	−7.84590e76	−0.508214	−0.254107	+	0.967176i	$0.581782\pi$
$642$	−1.03789e76	−0.0644080
$643$	−1.61526e77	−0.960374	−0.480187	−	0.877166i	$-0.659431\pi$
$643$	−1.61526e77	−0.960374	−0.480187	+	0.877166i	$0.659431\pi$
$644$	−5.10102e77	−2.90600
$645$	4.14282e76	0.226154
$646$	4.14704e75	0.0216942
$647$	1.73743e77	0.871044	0.435522	−	0.900178i	$-0.356564\pi$
$647$	1.73743e77	0.871044	0.435522	+	0.900178i	$0.356564\pi$
$648$	5.40870e76	0.259884
$649$	1.12848e77	0.519713
$650$	−5.24749e75	−0.0231651
$651$	2.04477e77	0.865302
$652$	−2.85238e76	−0.115717
$653$	1.79111e77	0.696641	0.348320	−	0.937376i	$-0.386752\pi$
$653$	1.79111e77	0.696641	0.348320	+	0.937376i	$0.386752\pi$
$654$	1.91813e76	0.0715301
$655$	7.24213e76	0.258959
$656$	3.01107e77	1.03244
$657$	−6.09427e75	−0.0200389
$658$	−1.41734e77	−0.446952
$659$	−5.64076e77	−1.70604	−0.853018	−	0.521881i	$-0.825231\pi$
$659$	−5.64076e77	−1.70604	−0.853018	+	0.521881i	$0.825231\pi$
$660$	2.44525e77	0.709357
$661$	5.54552e76	0.154313	0.0771565	−	0.997019i	$-0.475416\pi$
$661$	5.54552e76	0.154313	0.0771565	+	0.997019i	$0.475416\pi$
$662$	8.10563e76	0.216368
$663$	1.67795e76	0.0429693
$664$	−6.37687e76	−0.156670
$665$	−5.83951e77	−1.37652
$666$	9.01763e75	0.0203963
$667$	8.22590e77	1.78535
$668$	−3.03819e77	−0.632793
$669$	−4.72037e77	−0.943535
$670$	−3.86654e76	−0.0741764
$671$	−4.74955e77	−0.874546
$672$	3.77263e77	0.666791
$673$	−7.57599e77	−1.28536	−0.642680	−	0.766135i	$-0.722178\pi$
$673$	−7.57599e77	−1.28536	−0.642680	+	0.766135i	$0.722178\pi$
$674$	−1.01792e77	−0.165793
$675$	2.84355e77	0.444639
$676$	5.66116e77	0.849907
$677$	9.51246e77	1.37121	0.685606	−	0.727973i	$-0.259537\pi$
$677$	9.51246e77	1.37121	0.685606	+	0.727973i	$0.259537\pi$
$678$	8.74732e76	0.121076
$679$	1.28189e77	0.170385
$680$	2.26646e76	0.0289304
$681$	−9.96638e77	−1.22178
$682$	7.52190e76	0.0885640
$683$	9.13435e77	1.03302	0.516510	−	0.856281i	$-0.327231\pi$
$683$	9.13435e77	1.03302	0.516510	+	0.856281i	$0.327231\pi$
$684$	1.20985e77	0.131428
$685$	3.85751e77	0.402546
$686$	1.44287e77	0.144649
$687$	4.82314e77	0.464537
$688$	−3.19439e77	−0.295601
$689$	−1.14428e77	−0.101743
$690$	−2.33853e77	−0.199799
$691$	−1.64704e78	−1.35225	−0.676127	−	0.736785i	$-0.736343\pi$
$691$	−1.64704e78	−1.35225	−0.676127	+	0.736785i	$0.736343\pi$
$692$	−1.00458e78	−0.792623
$693$	−2.58493e77	−0.196013
$694$	2.25034e77	0.164007
$695$	6.81689e77	0.477534
$696$	−4.04014e77	−0.272046
$697$	2.17437e77	0.140745
$698$	−4.22694e77	−0.263028
$699$	−1.23610e78	−0.739489
$700$	1.15749e78	0.665766
$701$	2.19900e78	1.21613	0.608066	−	0.793886i	$-0.291946\pi$
$701$	2.19900e78	1.21613	0.608066	+	0.793886i	$0.291946\pi$
$702$	−1.08112e77	−0.0574913
$703$	−2.47639e78	−1.26633
$704$	−1.79112e78	−0.880798
$705$	2.75643e78	1.30361
$706$	1.07573e77	0.0489299
$707$	4.20228e78	1.83845
$708$	−1.11121e78	−0.467607
$709$	−5.02468e77	−0.203393	−0.101697	−	0.994815i	$-0.532427\pi$
$709$	−5.02468e77	−0.203393	−0.101697	+	0.994815i	$0.532427\pi$
$710$	4.29605e77	0.167288
$711$	−4.72750e77	−0.177099
$712$	−1.00515e78	−0.362268
$713$	3.05166e78	1.05821
$714$	8.72482e76	0.0291109
$715$	−8.69163e77	−0.279052
$716$	1.44013e78	0.444933
$717$	−5.18310e75	−0.00154104
$718$	8.55974e77	0.244928
$719$	−5.31416e78	−1.46349	−0.731745	−	0.681578i	$-0.761294\pi$
$719$	−5.31416e78	−1.46349	−0.731745	+	0.681578i	$0.761294\pi$
$720$	3.18872e77	0.0845227
$721$	−4.76474e78	−1.21568
$722$	1.65293e77	0.0405959
$723$	−6.72113e78	−1.58905
$724$	3.85427e78	0.877267
$725$	−1.86657e78	−0.409024
$726$	2.57527e76	0.00543332
$727$	3.83847e78	0.779761	0.389880	−	0.920865i	$-0.372516\pi$
$727$	3.83847e78	0.779761	0.389880	+	0.920865i	$0.372516\pi$
$728$	−8.90530e77	−0.174195
$729$	5.78264e78	1.08923
$730$	−1.06550e77	−0.0193274
$731$	−2.30675e77	−0.0402970
$732$	4.67686e78	0.786865
$733$	4.93828e78	0.800233	0.400116	−	0.916464i	$-0.368970\pi$
$733$	4.93828e78	0.800233	0.400116	+	0.916464i	$0.368970\pi$
$734$	−1.46387e78	−0.228487
$735$	−7.54584e78	−1.13450
$736$	5.63035e78	0.815447
$737$	4.70026e78	0.655791
$738$	−1.49534e77	−0.0200997
$739$	−7.07383e78	−0.916078	−0.458039	−	0.888932i	$-0.651448\pi$
$739$	−7.07383e78	−0.916078	−0.458039	+	0.888932i	$0.651448\pi$
$740$	−6.68824e78	−0.834525
$741$	3.16892e78	0.380988
$742$	−5.94990e77	−0.0689291
$743$	9.59859e78	1.07156	0.535778	−	0.844359i	$-0.320018\pi$
$743$	9.59859e78	1.07156	0.535778	+	0.844359i	$0.320018\pi$
$744$	−1.49882e78	−0.161248
$745$	3.48582e78	0.361416
$746$	−2.52268e78	−0.252083
$747$	−6.47870e77	−0.0623981
$748$	−1.36153e78	−0.126396
$749$	−8.13762e78	−0.728195
$750$	1.78431e78	0.153917
$751$	−6.76425e78	−0.562499	−0.281249	−	0.959635i	$-0.590749\pi$
$751$	−6.76425e78	−0.562499	−0.281249	+	0.959635i	$0.590749\pi$
$752$	−2.12540e79	−1.70392
$753$	−9.49811e78	−0.734134
$754$	7.09669e77	0.0528864
$755$	4.99598e78	0.358988
$756$	2.38473e79	1.65230
$757$	−6.22716e78	−0.416057	−0.208029	−	0.978123i	$-0.566705\pi$
$757$	−6.22716e78	−0.416057	−0.208029	+	0.978123i	$0.566705\pi$
$758$	3.63589e78	0.234265
$759$	2.84276e79	1.76641
$760$	4.28036e78	0.256512
$761$	−6.20793e77	−0.0358814	−0.0179407	−	0.999839i	$-0.505711\pi$
$761$	−6.20793e77	−0.0358814	−0.0179407	+	0.999839i	$0.505711\pi$
$762$	−1.91327e78	−0.106663
$763$	1.50391e79	0.808717
$764$	−3.45871e79	−1.79410
$765$	2.30266e77	0.0115223
$766$	−1.52215e77	−0.00734797
$767$	3.94978e78	0.183950
$768$	1.62383e79	0.729638
$769$	2.93043e79	1.27045	0.635224	−	0.772328i	$-0.280908\pi$
$769$	2.93043e79	1.27045	0.635224	+	0.772328i	$0.280908\pi$
$770$	−4.51937e78	−0.189053
$771$	−3.25432e79	−1.31361
$772$	−1.26326e79	−0.492060
$773$	9.72409e78	0.365521	0.182761	−	0.983157i	$-0.441497\pi$
$773$	9.72409e78	0.365521	0.182761	+	0.983157i	$0.441497\pi$
$774$	1.58638e77	0.00575479
$775$	−6.92463e78	−0.242437
$776$	−9.39623e77	−0.0317509
$777$	−5.21001e79	−1.69926
$778$	8.61777e77	0.0271304
$779$	4.10644e79	1.24792
$780$	8.55863e78	0.251074
$781$	−5.22238e79	−1.47899
$782$	1.30211e78	0.0356010
$783$	−3.84561e79	−1.01512
$784$	5.81835e79	1.48289
$785$	1.62637e79	0.400224
$786$	−2.04352e78	−0.0485577
$787$	−1.67187e79	−0.383617	−0.191808	−	0.981432i	$-0.561435\pi$
$787$	−1.67187e79	−0.383617	−0.191808	+	0.981432i	$0.561435\pi$
$788$	3.97675e78	0.0881165
$789$	3.85000e79	0.823840
$790$	−8.26535e78	−0.170811
$791$	6.85834e79	1.36888
$792$	1.89475e78	0.0365266
$793$	−1.66239e79	−0.309543
$794$	1.35055e79	0.242911
$795$	1.15714e79	0.201043
$796$	2.25721e79	0.378846
$797$	−4.63054e79	−0.750806	−0.375403	−	0.926862i	$-0.622496\pi$
$797$	−4.63054e79	−0.750806	−0.375403	+	0.926862i	$0.622496\pi$
$798$	1.64774e79	0.258112
$799$	−1.53480e79	−0.232282
$800$	−1.27760e79	−0.186819
$801$	−1.02120e79	−0.144283
$802$	3.31513e77	0.00452591
$803$	1.29524e79	0.170873
$804$	−4.62833e79	−0.590042
$805$	−1.83352e80	−2.25891
$806$	2.63274e78	0.0313469
$807$	−3.03498e79	−0.349248
$808$	−3.08027e79	−0.342592
$809$	1.81292e80	1.94892	0.974459	−	0.224565i	$-0.0720962\pi$
$809$	1.81292e80	1.94892	0.974459	+	0.224565i	$0.0720962\pi$
$810$	9.60735e78	0.0998310
$811$	1.57811e80	1.58512	0.792562	−	0.609791i	$-0.208747\pi$
$811$	1.57811e80	1.58512	0.792562	+	0.609791i	$0.208747\pi$
$812$	−1.56539e80	−1.51996
$813$	5.68878e79	0.533985
$814$	−1.91655e79	−0.173920
$815$	−1.02527e79	−0.0899504
$816$	1.30835e79	0.110980
$817$	−4.35645e79	−0.357295
$818$	−1.72748e79	−0.136993
$819$	−9.04751e78	−0.0693780
$820$	1.10907e80	0.822388
$821$	5.17464e79	0.371059	0.185530	−	0.982639i	$-0.440600\pi$
$821$	5.17464e79	0.371059	0.185530	+	0.982639i	$0.440600\pi$
$822$	−1.08848e79	−0.0754820
$823$	1.22160e80	0.819279	0.409640	−	0.912247i	$-0.365654\pi$
$823$	1.22160e80	0.819279	0.409640	+	0.912247i	$0.365654\pi$
$824$	3.49255e79	0.226540
$825$	−6.45062e79	−0.404686
$826$	2.05376e79	0.124623
$827$	5.64616e79	0.331400	0.165700	−	0.986176i	$-0.447012\pi$
$827$	5.64616e79	0.331400	0.165700	+	0.986176i	$0.447012\pi$
$828$	3.79876e79	0.215679
$829$	−1.62760e80	−0.893921	−0.446961	−	0.894554i	$-0.647494\pi$
$829$	−1.62760e80	−0.893921	−0.446961	+	0.894554i	$0.647494\pi$
$830$	−1.13271e79	−0.0601826
$831$	−4.67780e79	−0.240444
$832$	−6.26910e79	−0.311755
$833$	4.20158e79	0.202151
$834$	−1.92353e79	−0.0895430
$835$	−1.09205e80	−0.491888
$836$	−2.57134e80	−1.12070
$837$	−1.42665e80	−0.601682
$838$	−1.86665e79	−0.0761821
$839$	−7.61754e79	−0.300858	−0.150429	−	0.988621i	$-0.548065\pi$
$839$	−7.61754e79	−0.300858	−0.150429	+	0.988621i	$0.548065\pi$
$840$	9.00533e79	0.344207
$841$	−1.78931e79	−0.0661906
$842$	5.75923e79	0.206197
$843$	2.49824e80	0.865717
$844$	4.40414e80	1.47722
$845$	2.03486e80	0.660656
$846$	1.05550e79	0.0331721
$847$	2.01914e79	0.0614289
$848$	−8.92230e79	−0.262779
$849$	−1.94770e80	−0.555341
$850$	−2.95467e78	−0.00815620
$851$	−7.77552e80	−2.07810
$852$	5.14246e80	1.33071
$853$	6.55715e80	1.64292	0.821461	−	0.570265i	$-0.193160\pi$
$853$	6.55715e80	1.64292	0.821461	+	0.570265i	$0.193160\pi$
$854$	−8.64390e79	−0.209710
$855$	4.34872e79	0.102163
$856$	5.96488e79	0.135698
$857$	−2.43562e80	−0.536584	−0.268292	−	0.963338i	$-0.586459\pi$
$857$	−2.43562e80	−0.536584	−0.268292	+	0.963338i	$0.586459\pi$
$858$	2.45252e79	0.0523254
$859$	−2.70552e80	−0.559035	−0.279517	−	0.960141i	$-0.590174\pi$
$859$	−2.70552e80	−0.559035	−0.279517	+	0.960141i	$0.590174\pi$
$860$	−1.17659e80	−0.235460
$861$	8.63942e80	1.67455
$862$	−9.34051e79	−0.175356
$863$	−9.09815e80	−1.65446	−0.827230	−	0.561863i	$-0.810085\pi$
$863$	−9.09815e80	−1.65446	−0.827230	+	0.561863i	$0.810085\pi$
$864$	−2.63219e80	−0.463649
$865$	−3.61089e80	−0.616128
$866$	4.56914e79	0.0755252
$867$	−5.76545e80	−0.923226
$868$	−5.80730e80	−0.900911
$869$	1.00475e81	1.51013
$870$	−7.17641e79	−0.104503
$871$	1.64514e80	0.232115
$872$	−1.10236e80	−0.150703
$873$	−9.54629e78	−0.0126457
$874$	2.45912e80	0.315657
$875$	1.39899e81	1.74018
$876$	−1.27542e80	−0.153741
$877$	1.05076e81	1.22749	0.613743	−	0.789506i	$-0.289663\pi$
$877$	1.05076e81	1.22749	0.613743	+	0.789506i	$0.289663\pi$
$878$	4.31228e79	0.0488211
$879$	−6.61059e80	−0.725348
$880$	−6.77712e80	−0.720729
$881$	6.98981e80	0.720490	0.360245	−	0.932858i	$-0.382693\pi$
$881$	6.98981e80	0.720490	0.360245	+	0.932858i	$0.382693\pi$
$882$	−2.88947e79	−0.0288690
$883$	−7.95621e80	−0.770525	−0.385263	−	0.922807i	$-0.625889\pi$
$883$	−7.95621e80	−0.770525	−0.385263	+	0.922807i	$0.625889\pi$
$884$	−4.76551e79	−0.0447375
$885$	−3.99415e80	−0.363484
$886$	9.81055e79	0.0865498
$887$	2.23142e81	1.90846	0.954228	−	0.299079i	$-0.0966794\pi$
$887$	2.23142e81	1.90846	0.954228	+	0.299079i	$0.0966794\pi$
$888$	3.81894e80	0.316655
$889$	−1.50010e81	−1.20593
$890$	−1.78542e80	−0.139160
$891$	−1.16789e81	−0.882603
$892$	1.34062e81	0.982364
$893$	−2.89857e81	−2.05954
$894$	−9.83596e79	−0.0677696
$895$	5.17645e80	0.345858
$896$	−1.42269e81	−0.921804
$897$	9.94997e80	0.625215
$898$	2.36333e80	0.144021
$899$	9.36484e80	0.553489
$900$	−8.61991e79	−0.0494121
$901$	−6.44302e79	−0.0358227
$902$	3.17810e80	0.171391
$903$	−9.16541e80	−0.479445
$904$	−5.02716e80	−0.255089
$905$	1.38539e81	0.681924
$906$	−1.40972e80	−0.0673143
$907$	−1.64651e81	−0.762716	−0.381358	−	0.924427i	$-0.624543\pi$
$907$	−1.64651e81	−0.762716	−0.381358	+	0.924427i	$0.624543\pi$
$908$	2.83053e81	1.27206
$909$	−3.12946e80	−0.136447
$910$	−1.58183e80	−0.0669146
$911$	1.86319e81	0.764718	0.382359	−	0.924014i	$-0.375112\pi$
$911$	1.86319e81	0.764718	0.382359	+	0.924014i	$0.375112\pi$
$912$	2.47090e81	0.984006
$913$	1.37694e81	0.532072
$914$	−3.88642e80	−0.145723
$915$	1.68106e81	0.611652
$916$	−1.36981e81	−0.483653
$917$	−1.60222e81	−0.548992
$918$	−6.08737e79	−0.0202421
$919$	−5.59344e81	−1.80510	−0.902552	−	0.430580i	$-0.858309\pi$
$919$	−5.59344e81	−1.80510	−0.902552	+	0.430580i	$0.858309\pi$
$920$	1.34397e81	0.420945
$921$	−3.47661e80	−0.105686
$922$	9.29550e80	0.274266
$923$	−1.82789e81	−0.523483
$924$	−5.40978e81	−1.50383
$925$	1.76437e81	0.476094
$926$	−2.10358e80	−0.0551008
$927$	3.54833e80	0.0902258
$928$	1.72783e81	0.426512
$929$	−5.85958e81	−1.40422	−0.702109	−	0.712070i	$-0.747758\pi$
$929$	−5.85958e81	−1.40422	−0.702109	+	0.712070i	$0.747758\pi$
$930$	−2.66232e80	−0.0619410
$931$	7.93496e81	1.79237
$932$	3.51062e81	0.769921
$933$	−9.19536e80	−0.195805
$934$	−1.26925e81	−0.262428
$935$	−4.89393e80	−0.0982514
$936$	6.63183e79	0.0129285
$937$	2.38829e81	0.452115	0.226057	−	0.974114i	$-0.427416\pi$
$937$	2.38829e81	0.452115	0.226057	+	0.974114i	$0.427416\pi$
$938$	8.55419e80	0.157254
$939$	5.69913e81	1.01743
$940$	−7.82846e81	−1.35725
$941$	−8.27740e81	−1.39373	−0.696866	−	0.717201i	$-0.745423\pi$
$941$	−8.27740e81	−1.39373	−0.696866	+	0.717201i	$0.745423\pi$
$942$	−4.58914e80	−0.0750467
$943$	1.28936e82	2.04788
$944$	3.07976e81	0.475103
$945$	8.57172e81	1.28438
$946$	−3.37159e80	−0.0490714
$947$	6.70100e80	0.0947360	0.0473680	−	0.998878i	$-0.484917\pi$
$947$	6.70100e80	0.0947360	0.0473680	+	0.998878i	$0.484917\pi$
$948$	−9.89378e81	−1.35873
$949$	4.53347e80	0.0604797
$950$	−5.58008e80	−0.0723171
$951$	−4.92610e80	−0.0620210
$952$	−5.01424e80	−0.0613322
$953$	−1.01290e82	−1.20368	−0.601839	−	0.798617i	$-0.705565\pi$
$953$	−1.01290e82	−1.20368	−0.601839	+	0.798617i	$0.705565\pi$
$954$	4.43093e79	0.00511581
$955$	−1.24321e82	−1.39460
$956$	1.47204e79	0.00160445
$957$	8.72380e81	0.923905
$958$	−9.16326e80	−0.0942972
$959$	−8.53420e81	−0.853397
$960$	6.33952e81	0.616024
$961$	−7.11575e81	−0.671935
$962$	−6.70813e80	−0.0615584
$963$	6.06014e80	0.0540455
$964$	1.90885e82	1.65445
$965$	−4.54071e81	−0.382492
$966$	5.17367e81	0.423572
$967$	5.45472e81	0.434055	0.217027	−	0.976166i	$-0.430364\pi$
$967$	5.45472e81	0.434055	0.217027	+	0.976166i	$0.430364\pi$
$968$	−1.48003e80	−0.0114472
$969$	1.78430e81	0.134142
$970$	−1.66903e80	−0.0121967
$971$	1.71965e82	1.22155	0.610776	−	0.791803i	$-0.290858\pi$
$971$	1.71965e82	1.22155	0.610776	+	0.791803i	$0.290858\pi$
$972$	−3.36229e81	−0.232173
$973$	−1.50814e82	−1.01237
$974$	1.82854e81	0.119326
$975$	−2.25778e81	−0.143237
$976$	−1.29621e82	−0.799479
$977$	−2.16132e81	−0.129604	−0.0648020	−	0.997898i	$-0.520642\pi$
$977$	−2.16132e81	−0.129604	−0.0648020	+	0.997898i	$0.520642\pi$
$978$	2.89300e80	0.0168667
$979$	2.17040e82	1.23031
$980$	2.14307e82	1.18119
$981$	−1.11997e81	−0.0600217
$982$	−1.99222e81	−0.103818
$983$	−3.94403e81	−0.199856	−0.0999282	−	0.994995i	$-0.531861\pi$
$983$	−3.94403e81	−0.199856	−0.0999282	+	0.994995i	$0.531861\pi$
$984$	−6.33269e81	−0.312049
$985$	1.42941e81	0.0684954
$986$	3.99588e80	0.0186208
$987$	−6.09822e82	−2.76364
$988$	−8.99997e81	−0.396666
$989$	−1.36786e82	−0.586334
$990$	3.36560e80	0.0140312
$991$	4.34814e81	0.176310	0.0881551	−	0.996107i	$-0.471903\pi$
$991$	4.34814e81	0.176310	0.0881551	+	0.996107i	$0.471903\pi$
$992$	6.40992e81	0.252803
$993$	3.48753e82	1.33787
$994$	−9.50442e81	−0.354650
$995$	8.11337e81	0.294487
$996$	−1.35587e82	−0.478726
$997$	3.26514e81	0.112146	0.0560732	−	0.998427i	$-0.482142\pi$
$997$	3.26514e81	0.112146	0.0560732	+	0.998427i	$0.482142\pi$
$998$	5.52891e81	0.184735
$999$	3.63505e82	1.18157

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.56.a.a.1.2	✓	4
3.2	odd	2		9.56.a.a.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.56.a.a.1.2	✓	4	1.1	even	1	trivial
9.56.a.a.1.3		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 56 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+2.88052e7 q^{2} +1.23937e13 q^{3} -3.51991e16 q^{4} -1.26520e19 q^{5} +3.57004e20 q^{6} +2.79909e23 q^{7} -2.05173e24 q^{8} -2.08450e25 q^{9} +O(q^{10})\)	\(q+2.88052e7 q^{2} +1.23937e13 q^{3} -3.51991e16 q^{4} -1.26520e19 q^{5} +3.57004e20 q^{6} +2.79909e23 q^{7} -2.05173e24 q^{8} -2.08450e25 q^{9} -3.64445e26 q^{10} +4.43027e28 q^{11} -4.36247e29 q^{12} +1.55064e30 q^{13} +8.06283e30 q^{14} -1.56806e32 q^{15} +1.20908e33 q^{16} +8.73107e32 q^{17} -6.00444e32 q^{18} +1.64892e35 q^{19} +4.45340e35 q^{20} +3.46911e36 q^{21} +1.27615e36 q^{22} +5.17737e37 q^{23} -2.54286e37 q^{24} -1.17482e38 q^{25} +4.46665e37 q^{26} -2.42042e39 q^{27} -9.85253e39 q^{28} +1.58882e40 q^{29} -4.51682e39 q^{30} +5.89422e40 q^{31} +1.08749e41 q^{32} +5.49075e41 q^{33} +2.51500e40 q^{34} -3.54142e42 q^{35} +7.33724e41 q^{36} -1.50183e43 q^{37} +4.74974e42 q^{38} +1.92182e43 q^{39} +2.59586e43 q^{40} +2.49038e44 q^{41} +9.99285e43 q^{42} -2.64200e44 q^{43} -1.55941e45 q^{44} +2.63732e44 q^{45} +1.49135e45 q^{46} -1.75786e46 q^{47} +1.49850e46 q^{48} +4.81222e46 q^{49} -3.38408e45 q^{50} +1.08210e46 q^{51} -5.45811e46 q^{52} -7.37942e46 q^{53} -6.97207e46 q^{54} -5.60519e47 q^{55} -5.74298e47 q^{56} +2.04362e48 q^{57} +4.57662e47 q^{58} +2.54720e48 q^{59} +5.51942e48 q^{60} -1.07207e49 q^{61} +1.69784e48 q^{62} -5.83470e48 q^{63} -4.04291e49 q^{64} -1.96188e49 q^{65} +1.58162e49 q^{66} +1.06094e50 q^{67} -3.07325e49 q^{68} +6.41669e50 q^{69} -1.02011e50 q^{70} -1.17879e51 q^{71} +4.27683e49 q^{72} +2.92361e50 q^{73} -4.32604e50 q^{74} -1.45603e51 q^{75} -5.80404e51 q^{76} +1.24007e52 q^{77} +5.53584e50 q^{78} +2.26793e52 q^{79} -1.52973e52 q^{80} -2.63616e52 q^{81} +7.17360e51 q^{82} +3.10804e52 q^{83} -1.22109e53 q^{84} -1.10466e52 q^{85} -7.61035e51 q^{86} +1.96914e53 q^{87} -9.08973e52 q^{88} +4.89902e53 q^{89} +7.59684e51 q^{90} +4.34038e53 q^{91} -1.82239e54 q^{92} +7.30513e53 q^{93} -5.06356e53 q^{94} -2.08622e54 q^{95} +1.34781e54 q^{96} +4.57966e53 q^{97} +1.38617e54 q^{98} -9.23488e53 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 208622520 q^{2} - 6821470691280 q^{3} + 38\!\cdots\!72 q^{4}+ \cdots + 47\!\cdots\!28 q^{9}+O(q^{10}) \) 4 * q + 208622520 * q^2 - 6821470691280 * q^3 + 38727758778743872 * q^4 + 14396937963387167160 * q^5 + 201756545247712015008 * q^6 - 205529376090660565972000 * q^7 + 4549274472651430619082240 * q^8 + 47936416820074569958974228 * q^9	\( 4 q + 208622520 q^{2} - 6821470691280 q^{3} + 38\!\cdots\!72 q^{4}+ \cdots + 79\!\cdots\!56 q^{99}+O(q^{100}) \) 4 * q + 208622520 * q^2 - 6821470691280 * q^3 + 38727758778743872 * q^4 + 14396937963387167160 * q^5 + 201756545247712015008 * q^6 - 205529376090660565972000 * q^7 + 4549274472651430619082240 * q^8 + 47936416820074569958974228 * q^9 + 4648305821937663379975180560 * q^10 + 19492148713537948248062043408 * q^11 + 512487561854224962046873117440 * q^12 - 4449970852951030370486873382760 * q^13 - 28356223847864660359303625873856 * q^14 + 248797810922527062710720195548320 * q^15 + 972748533533952319807553436258304 * q^16 + 8593971071724377583839140954773960 * q^17 + 38459068061903712495232732227386520 * q^18 + 339485321922051504109099704484079600 * q^19 + 2938981710383707492522432611899614080 * q^20 + 9223279286409457932469393248481185408 * q^21 + 38006076575943531891094535037919254240 * q^22 + 49808560358713761517710452453445612960 * q^23 + 190807152467783159198396962175734425600 * q^24 + 35720819629535961214417161732721803100 * q^25 - 2942801473325677064443328059884451887792 * q^26 - 8530982134391103993322927255258361598240 * q^27 - 14225688489857344137508473549032747368960 * q^28 - 18313921252535508838816178753292620581800 * q^29 + 81282391149812883221152750335721388925120 * q^30 + 228069689399145752868860523834729264526208 * q^31 + 633346612507316231430506989727883716689920 * q^32 + 847291303346996712726357318732333414939840 * q^33 + 896637942332031893460273084285964132034544 * q^34 - 4819663438502339394117495448236020975855040 * q^35 - 23127427661252023416447691458638107482530496 * q^36 - 32137889117062584203203089731106089299166920 * q^37 - 4952027966320588944657713384757782381142240 * q^38 + 66999829160538184499173080943184361764833056 * q^39 + 423453117316016459693780561000308646880691200 * q^40 + 246756563007211451240604479433521241061314408 * q^41 + 507527523766486022631274034521150794413218560 * q^42 - 860266067148440101585711757682636198922476400 * q^43 - 486680632760661386186662626683912868907405056 * q^44 - 9558583136774695571527888760209735674807045480 * q^45 - 12358385464441662606619414449724307588901916992 * q^46 + 4275321492760062770492681289130578251551314240 * q^47 + 19765938683883854374252413540295783983351644160 * q^48 + 51896265177052512954332052101694146860214382372 * q^49 + 174698296445912937700335126041507926720149534600 * q^50 + 114739625474091768829327173325517597576905389408 * q^51 - 262201419493851260177411503538061050352769552000 * q^52 - 488469552022263686716757080744643106633189705480 * q^53 - 1343912975841315509587669615741882301086568894400 * q^54 - 127591926326749967084952696035933816282025595680 * q^55 - 298136165704261759300184058675155027135738572800 * q^56 + 1638420796018602848713747835626091496488772083520 * q^57 + 6079853356051584053436052229523762232408341938640 * q^58 + 8189687634125713603536212764174920044680103250000 * q^59 + 10139666510723475640830884157120900147903797660160 * q^60 + 7023917261975601941077275556050474243839244469208 * q^61 - 30522733021551585983790682957575295692580599279360 * q^62 - 71978335814893755132347187478401614601601405967520 * q^63 - 98185742120493275625308720675268779449265392713728 * q^64 - 96029582501479027321081622269423947602394832060080 * q^65 + 64231534245847760638155838044250061298414536370816 * q^66 + 418567852430847740316243536772383918093566302547760 * q^67 + 627327947371921816104248533416688222149537051169920 * q^68 + 515735918068902691862050107073617954531351228253056 * q^69 - 471522968288511321788110491009215619195633708224640 * q^70 + 997985577607888605538672501225224229003742837277408 * q^71 - 4304125570291567284830418802698753913226780601899520 * q^72 - 898993596628095916013292323795403905388680301942040 * q^73 - 7967044320232055682477818350544716808849477162563056 * q^74 + 5296014974156672466059853856400507071088579916421200 * q^75 - 60907940015267454915614913374117951647840510009600 * q^76 + 14299054939611075432133092801777785333545282382563200 * q^77 + 396845629416952247715668693426892670455525504984000 * q^78 + 48721021140002244303635330301073120621076057627153600 * q^79 - 3558308494035098045228661758379879929555981454090240 * q^80 + 62764174850641400333291315844329697377153438426256804 * q^81 - 164154584875013842045822252535546173951453621276929360 * q^82 - 71840759606517399895238320212650236559070020961691920 * q^83 - 315751105587523254185006931474478000838644134120953856 * q^84 + 248899912487828257920888533066500872415304578192331760 * q^85 - 390961799675414150209662123589235297185712905683496992 * q^86 + 793070552989118953410697424048823657459134846084789280 * q^87 + 263660200754753376218335161392938332564087458967828480 * q^88 + 1567987214275383302209606514592359147814765036271890600 * q^89 - 1212078526300174060358044731623232837611704141954645680 * q^90 + 1660326344231373069708515805926098978407334056523187008 * q^91 - 2737928811190126698927829997086921657569438136581219840 * q^92 - 1148699655429559764317569984734958616523316649999439360 * q^93 - 4092215382133552783473757354682502518415689822573629056 * q^94 + 90834332415616009306267157723570331064559482078144800 * q^95 - 5408972861452632753807094701577513866193715960586043392 * q^96 + 5113732531532480760212291157301231295251404057238280840 * q^97 + 4361266856004358769699597237924757031028912315048682360 * q^98 + 7959889613481860830509059286387276732667315436102354256 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more