LMFDB - Embedded newform 1.56.a.a.1.3

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			1.3
Root			$2.30346e6$ 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)

$f(q)$	$=$	$q+1.07439e8 q^{2} -2.35279e13 q^{3} -2.44858e16 q^{4} -1.10426e19 q^{5} -2.52780e21 q^{6} -2.64783e23 q^{7} -6.50160e24 q^{8} +3.79111e26 q^{9} +O(q^{10})$	\(q+1.07439e8 q^{2} -2.35279e13 q^{3} -2.44858e16 q^{4} -1.10426e19 q^{5} -2.52780e21 q^{6} -2.64783e23 q^{7} -6.50160e24 q^{8} +3.79111e26 q^{9} -1.18640e27 q^{10} +5.45205e27 q^{11} +5.76098e29 q^{12} -3.65457e30 q^{13} -2.84479e31 q^{14} +2.59808e32 q^{15} +1.83670e32 q^{16} -2.98408e33 q^{17} +4.07312e34 q^{18} +2.14136e34 q^{19} +2.70386e35 q^{20} +6.22979e36 q^{21} +5.85760e35 q^{22} -2.26299e36 q^{23} +1.52969e38 q^{24} -1.55617e38 q^{25} -3.92642e38 q^{26} -4.81527e39 q^{27} +6.48342e39 q^{28} -2.17585e40 q^{29} +2.79134e40 q^{30} +6.52623e40 q^{31} +2.53978e41 q^{32} -1.28275e41 q^{33} -3.20606e41 q^{34} +2.92389e42 q^{35} -9.28283e42 q^{36} -1.90603e43 q^{37} +2.30065e42 q^{38} +8.59842e43 q^{39} +7.17944e43 q^{40} -2.69989e44 q^{41} +6.69319e44 q^{42} -2.28222e44 q^{43} -1.33497e44 q^{44} -4.18637e45 q^{45} -2.43132e44 q^{46} +1.80339e45 q^{47} -4.32137e45 q^{48} +3.98834e46 q^{49} -1.67193e46 q^{50} +7.02091e46 q^{51} +8.94849e46 q^{52} -3.76672e47 q^{53} -5.17345e47 q^{54} -6.02047e46 q^{55} +1.72151e48 q^{56} -5.03816e47 q^{57} -2.33771e48 q^{58} +6.96714e48 q^{59} -6.36160e48 q^{60} +2.06681e49 q^{61} +7.01168e48 q^{62} -1.00382e50 q^{63} +2.06696e49 q^{64} +4.03559e49 q^{65} -1.37817e49 q^{66} +8.05018e49 q^{67} +7.30675e49 q^{68} +5.32433e49 q^{69} +3.14139e50 q^{70} +5.14800e50 q^{71} -2.46483e51 q^{72} +2.88066e50 q^{73} -2.04781e51 q^{74} +3.66134e51 q^{75} -5.24328e50 q^{76} -1.44361e51 q^{77} +9.23802e51 q^{78} -3.83306e51 q^{79} -2.02819e51 q^{80} +4.71573e52 q^{81} -2.90072e52 q^{82} -4.00025e52 q^{83} -1.52541e53 q^{84} +3.29520e52 q^{85} -2.45198e52 q^{86} +5.11932e53 q^{87} -3.54470e52 q^{88} -1.38274e53 q^{89} -4.49777e53 q^{90} +9.67669e53 q^{91} +5.54110e52 q^{92} -1.53548e54 q^{93} +1.93754e53 q^{94} -2.36461e53 q^{95} -5.97556e54 q^{96} +6.05498e54 q^{97} +4.28501e54 q^{98} +2.06693e54 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.07439e8	0.566025	0.283012	−	0.959116i	$-0.408666\pi$
$2$	1.07439e8	0.566025	0.283012	+	0.959116i	$0.408666\pi$
$3$	−2.35279e13	−1.78135	−0.890673	−	0.454645i	$-0.849766\pi$
$3$	−2.35279e13	−1.78135	−0.890673	+	0.454645i	$0.849766\pi$
$4$	−2.44858e16	−0.679616
$5$	−1.10426e19	−0.662820	−0.331410	−	0.943487i	$-0.607524\pi$
$5$	−1.10426e19	−0.662820	−0.331410	+	0.943487i	$0.607524\pi$
$6$	−2.52780e21	−1.00829
$7$	−2.64783e23	−1.52298	−0.761491	−	0.648176i	$-0.775532\pi$
$7$	−2.64783e23	−1.52298	−0.761491	+	0.648176i	$0.775532\pi$
$8$	−6.50160e24	−0.950704
$9$	3.79111e26	2.17319
$10$	−1.18640e27	−0.375172
$11$	5.45205e27	0.125389	0.0626947	−	0.998033i	$-0.480031\pi$
$11$	5.45205e27	0.125389	0.0626947	+	0.998033i	$0.480031\pi$
$12$	5.76098e29	1.21063
$13$	−3.65457e30	−0.849951	−0.424976	−	0.905205i	$-0.639717\pi$
$13$	−3.65457e30	−0.849951	−0.424976	+	0.905205i	$0.639717\pi$
$14$	−2.84479e31	−0.862045
$15$	2.59808e32	1.18071
$16$	1.83670e32	0.141494
$17$	−2.98408e33	−0.433976	−0.216988	−	0.976174i	$-0.569623\pi$
$17$	−2.98408e33	−0.433976	−0.216988	+	0.976174i	$0.569623\pi$
$18$	4.07312e34	1.23008
$19$	2.14136e34	0.146206	0.0731030	−	0.997324i	$-0.476710\pi$
$19$	2.14136e34	0.146206	0.0731030	+	0.997324i	$0.476710\pi$
$20$	2.70386e35	0.450463
$21$	6.22979e36	2.71296
$22$	5.85760e35	0.0709735
$23$	−2.26299e36	−0.0807545	−0.0403773	−	0.999185i	$-0.512856\pi$
$23$	−2.26299e36	−0.0807545	−0.0403773	+	0.999185i	$0.512856\pi$
$24$	1.52969e38	1.69353
$25$	−1.55617e38	−0.560670
$26$	−3.92642e38	−0.481093
$27$	−4.81527e39	−2.08986
$28$	6.48342e39	1.03504
$29$	−2.17585e40	−1.32338	−0.661690	−	0.749777i	$-0.730161\pi$
$29$	−2.17585e40	−1.32338	−0.661690	+	0.749777i	$0.730161\pi$
$30$	2.79134e40	0.668311
$31$	6.52623e40	0.634184	0.317092	−	0.948395i	$-0.397294\pi$
$31$	6.52623e40	0.634184	0.317092	+	0.948395i	$0.397294\pi$
$32$	2.53978e41	1.03079
$33$	−1.28275e41	−0.223362
$34$	−3.20606e41	−0.245641
$35$	2.92389e42	1.00946
$36$	−9.28283e42	−1.47694
$37$	−1.90603e43	−1.42752	−0.713761	−	0.700389i	$-0.753010\pi$
$37$	−1.90603e43	−1.42752	−0.713761	+	0.700389i	$0.753010\pi$
$38$	2.30065e42	0.0827562
$39$	8.59842e43	1.51406
$40$	7.17944e43	0.630145
$41$	−2.69989e44	−1.20168	−0.600842	−	0.799368i	$-0.705168\pi$
$41$	−2.69989e44	−1.20168	−0.600842	+	0.799368i	$0.705168\pi$
$42$	6.69319e44	1.53560
$43$	−2.28222e44	−0.274141	−0.137071	−	0.990561i	$-0.543769\pi$
$43$	−2.28222e44	−0.274141	−0.137071	+	0.990561i	$0.543769\pi$
$44$	−1.33497e44	−0.0852166
$45$	−4.18637e45	−1.44043
$46$	−2.43132e44	−0.0457090
$47$	1.80339e45	0.187672	0.0938359	−	0.995588i	$-0.470087\pi$
$47$	1.80339e45	0.187672	0.0938359	+	0.995588i	$0.470087\pi$
$48$	−4.32137e45	−0.252050
$49$	3.98834e46	1.31947
$50$	−1.67193e46	−0.317353
$51$	7.02091e46	0.773061
$52$	8.94849e46	0.577640
$53$	−3.76672e47	−1.44005	−0.720023	−	0.693950i	$-0.755869\pi$
$53$	−3.76672e47	−1.44005	−0.720023	+	0.693950i	$0.755869\pi$
$54$	−5.17345e47	−1.18291
$55$	−6.02047e46	−0.0831105
$56$	1.72151e48	1.44790
$57$	−5.03816e47	−0.260444
$58$	−2.33771e48	−0.749066
$59$	6.96714e48	1.39516	0.697581	−	0.716506i	$-0.254260\pi$
$59$	6.96714e48	1.39516	0.697581	+	0.716506i	$0.254260\pi$
$60$	−6.36160e48	−0.802430
$61$	2.06681e49	1.65474	0.827370	−	0.561657i	$-0.189836\pi$
$61$	2.06681e49	1.65474	0.827370	+	0.561657i	$0.189836\pi$
$62$	7.01168e48	0.358964
$63$	−1.00382e50	−3.30973
$64$	2.06696e49	0.441960
$65$	4.03559e49	0.563364
$66$	−1.37817e49	−0.126428
$67$	8.05018e49	0.488369	0.244185	−	0.969729i	$-0.421480\pi$
$67$	8.05018e49	0.488369	0.244185	+	0.969729i	$0.421480\pi$
$68$	7.30675e49	0.294937
$69$	5.32433e49	0.143852
$70$	3.14139e50	0.571380
$71$	5.14800e50	0.633920	0.316960	−	0.948439i	$-0.397338\pi$
$71$	5.14800e50	0.633920	0.316960	+	0.948439i	$0.397338\pi$
$72$	−2.46483e51	−2.06606
$73$	2.88066e50	0.165239	0.0826195	−	0.996581i	$-0.473671\pi$
$73$	2.88066e50	0.165239	0.0826195	+	0.996581i	$0.473671\pi$
$74$	−2.04781e51	−0.808013
$75$	3.66134e51	0.998747
$76$	−5.24328e50	−0.0993640
$77$	−1.44361e51	−0.190966
$78$	9.23802e51	0.856993
$79$	−3.83306e51	−0.250496	−0.125248	−	0.992125i	$-0.539973\pi$
$79$	−3.83306e51	−0.250496	−0.125248	+	0.992125i	$0.539973\pi$
$80$	−2.02819e51	−0.0937852
$81$	4.71573e52	1.54957
$82$	−2.90072e52	−0.680183
$83$	−4.00025e52	−0.672109	−0.336054	−	0.941843i	$-0.609093\pi$
$83$	−4.00025e52	−0.672109	−0.336054	+	0.941843i	$0.609093\pi$
$84$	−1.52541e53	−1.84377
$85$	3.29520e52	0.287648
$86$	−2.45198e52	−0.155171
$87$	5.11932e53	2.35740
$88$	−3.54470e52	−0.119208
$89$	−1.38274e53	−0.340811	−0.170406	−	0.985374i	$-0.554508\pi$
$89$	−1.38274e53	−0.340811	−0.170406	+	0.985374i	$0.554508\pi$
$90$	−4.49777e53	−0.815321
$91$	9.67669e53	1.29446
$92$	5.54110e52	0.0548821
$93$	−1.53548e54	−1.12970
$94$	1.93754e53	0.106227
$95$	−2.36461e53	−0.0969083
$96$	−5.97556e54	−1.83620
$97$	6.05498e54	1.39923	0.699616	−	0.714519i	$-0.253354\pi$
$97$	6.05498e54	1.39923	0.699616	+	0.714519i	$0.253354\pi$
$98$	4.28501e54	0.746853
$99$	2.06693e54	0.272495
$100$	3.81040e54	0.381040
$101$	−1.24705e55	−0.948520	−0.474260	−	0.880385i	$-0.657284\pi$
$101$	−1.24705e55	−0.948520	−0.474260	+	0.880385i	$0.657284\pi$
$102$	7.54317e54	0.437571
$103$	9.88765e54	0.438601	0.219300	−	0.975657i	$-0.429623\pi$
$103$	9.88765e54	0.438601	0.219300	+	0.975657i	$0.429623\pi$
$104$	2.37605e55	0.808052
$105$	−6.87929e55	−1.79820
$106$	−4.04691e55	−0.815102
$107$	−4.92735e55	−0.766584	−0.383292	−	0.923627i	$-0.625210\pi$
$107$	−4.92735e55	−0.766584	−0.383292	+	0.923627i	$0.625210\pi$
$108$	1.17905e56	1.42030
$109$	−2.00261e55	−0.187227	−0.0936133	−	0.995609i	$-0.529842\pi$
$109$	−2.00261e55	−0.187227	−0.0936133	+	0.995609i	$0.529842\pi$
$110$	−6.46830e54	−0.0470426
$111$	4.48449e56	2.54291
$112$	−4.86328e55	−0.215493
$113$	−4.91726e56	−1.70634	−0.853172	−	0.521630i	$-0.825324\pi$
$113$	−4.91726e56	−1.70634	−0.853172	+	0.521630i	$0.825324\pi$
$114$	−5.41293e55	−0.147417
$115$	2.49892e55	0.0535257
$116$	5.32774e56	0.899391
$117$	−1.38549e57	−1.84711
$118$	7.48540e56	0.789696
$119$	7.90135e56	0.660937
$120$	−1.68917e57	−1.12251
$121$	−1.86087e57	−0.984278
$122$	2.22055e57	0.936624
$123$	6.35227e57	2.14061
$124$	−1.59800e57	−0.431002
$125$	4.78335e57	1.03444
$126$	−1.07849e58	−1.87339
$127$	6.15401e55	0.00860113	0.00430057	−	0.999991i	$-0.498631\pi$
$127$	6.15401e55	0.00860113	0.00430057	+	0.999991i	$0.498631\pi$
$128$	−6.92981e57	−0.780633
$129$	5.36957e57	0.488340
$130$	4.33578e57	0.318878
$131$	−1.75176e58	−1.04355	−0.521777	−	0.853082i	$-0.674731\pi$
$131$	−1.75176e58	−1.04355	−0.521777	+	0.853082i	$0.674731\pi$
$132$	3.14091e57	0.151800
$133$	−5.66996e57	−0.222669
$134$	8.64900e57	0.276429
$135$	5.31730e58	1.38520
$136$	1.94013e58	0.412583
$137$	2.02798e58	0.352572	0.176286	−	0.984339i	$-0.443592\pi$
$137$	2.02798e58	0.352572	0.176286	+	0.984339i	$0.443592\pi$
$138$	5.72038e57	0.0814236
$139$	−1.22210e59	−1.42627	−0.713133	−	0.701029i	$-0.752724\pi$
$139$	−1.22210e59	−1.42627	−0.713133	+	0.701029i	$0.752724\pi$
$140$	−7.15937e58	−0.686047
$141$	−4.24300e58	−0.334308
$142$	5.53094e58	0.358814
$143$	−1.99249e58	−0.106575
$144$	6.96314e58	0.307494
$145$	2.40270e59	0.877163
$146$	3.09493e58	0.0935293
$147$	−9.38371e59	−2.35043
$148$	4.66707e59	0.970168
$149$	9.42873e59	1.62866	0.814331	−	0.580401i	$-0.197104\pi$
$149$	9.42873e59	1.62866	0.814331	+	0.580401i	$0.197104\pi$
$150$	3.93369e59	0.565315
$151$	−1.91758e59	−0.229555	−0.114778	−	0.993391i	$-0.536616\pi$
$151$	−1.91758e59	−0.229555	−0.114778	+	0.993391i	$0.536616\pi$
$152$	−1.39223e59	−0.138999
$153$	−1.13130e60	−0.943112
$154$	−1.55099e59	−0.108091
$155$	−7.20664e59	−0.420350
$156$	−2.10539e60	−1.02898
$157$	−2.17665e58	−0.00892376	−0.00446188	−	0.999990i	$-0.501420\pi$
$157$	−2.17665e58	−0.00892376	−0.00446188	+	0.999990i	$0.501420\pi$
$158$	−4.11818e59	−0.141787
$159$	8.86228e60	2.56522
$160$	−2.80457e60	−0.683230
$161$	5.99202e59	0.122988
$162$	5.06651e60	0.877094
$163$	−1.04585e61	−1.52865	−0.764326	−	0.644830i	$-0.776928\pi$
$163$	−1.04585e61	−1.52865	−0.764326	+	0.644830i	$0.776928\pi$
$164$	6.61089e60	0.816684
$165$	1.41649e60	0.148049
$166$	−4.29781e60	−0.380430
$167$	1.63128e61	1.22412	0.612061	−	0.790810i	$-0.290341\pi$
$167$	1.63128e61	1.22412	0.612061	+	0.790810i	$0.290341\pi$
$168$	−4.05036e61	−2.57922
$169$	−5.13189e60	−0.277583
$170$	3.54031e60	0.162816
$171$	8.11814e60	0.317734
$172$	5.58818e60	0.186311
$173$	3.39989e59	0.00966488	0.00483244	−	0.999988i	$-0.498462\pi$
$173$	3.39989e59	0.00966488	0.00483244	+	0.999988i	$0.498462\pi$
$174$	5.50012e61	1.33435
$175$	4.12048e61	0.853890
$176$	1.00138e60	0.0177419
$177$	−1.63922e62	−2.48526
$178$	−1.48559e61	−0.192907
$179$	1.51621e62	1.68772	0.843862	−	0.536561i	$-0.180277\pi$
$179$	1.51621e62	1.68772	0.843862	+	0.536561i	$0.180277\pi$
$180$	1.02506e62	0.978942
$181$	−1.15311e62	−0.945602	−0.472801	−	0.881169i	$-0.656757\pi$
$181$	−1.15311e62	−0.945602	−0.472801	+	0.881169i	$0.656757\pi$
$182$	1.03965e62	0.732696
$183$	−4.86276e62	−2.94766
$184$	1.47130e61	0.0767737
$185$	2.10475e62	0.946190
$186$	−1.64970e62	−0.639439
$187$	−1.62694e61	−0.0544159
$188$	−4.41574e61	−0.127545
$189$	1.27500e63	3.18281
$190$	−2.54051e61	−0.0548525
$191$	−2.55869e61	−0.0478190	−0.0239095	−	0.999714i	$-0.507611\pi$
$191$	−2.55869e61	−0.0478190	−0.0239095	+	0.999714i	$0.507611\pi$
$192$	−4.86312e62	−0.787284
$193$	−7.62065e62	−1.06946	−0.534732	−	0.845022i	$-0.679587\pi$
$193$	−7.62065e62	−1.06946	−0.534732	+	0.845022i	$0.679587\pi$
$194$	6.50538e62	0.792000
$195$	−9.49488e62	−1.00355
$196$	−9.76575e62	−0.896734
$197$	1.31795e63	1.05215	0.526074	−	0.850439i	$-0.323664\pi$
$197$	1.31795e63	1.05215	0.526074	+	0.850439i	$0.323664\pi$
$198$	2.22068e62	0.154239
$199$	−8.34279e62	−0.504489	−0.252245	−	0.967664i	$-0.581169\pi$
$199$	−8.34279e62	−0.504489	−0.252245	+	0.967664i	$0.581169\pi$
$200$	1.01176e63	0.533031
$201$	−1.89404e63	−0.869955
$202$	−1.33981e63	−0.536886
$203$	5.76130e63	2.01548
$204$	−1.71912e63	−0.525385
$205$	2.98138e63	0.796500
$206$	1.06231e63	0.248259
$207$	−8.57925e62	−0.175495
$208$	−6.71235e62	−0.120263
$209$	1.16748e62	0.0183327
$210$	−7.39101e63	−1.01783
$211$	−4.59539e63	−0.555335	−0.277667	−	0.960677i	$-0.589561\pi$
$211$	−4.59539e63	−0.555335	−0.277667	+	0.960677i	$0.589561\pi$
$212$	9.22309e63	0.978679
$213$	−1.21122e64	−1.12923
$214$	−5.29388e63	−0.433905
$215$	2.52015e63	0.181706
$216$	3.13069e64	1.98684
$217$	−1.72804e64	−0.965851
$218$	−2.15157e63	−0.105975
$219$	−6.77757e63	−0.294348
$220$	1.47416e63	0.0564833
$221$	1.09055e64	0.368858
$222$	4.81807e64	1.43935
$223$	7.21276e64	1.90422	0.952111	−	0.305751i	$-0.0989076\pi$
$223$	7.21276e64	1.90422	0.952111	+	0.305751i	$0.0989076\pi$
$224$	−6.72491e64	−1.56988
$225$	−5.89963e64	−1.21844
$226$	−5.28304e64	−0.965832
$227$	−6.18308e64	−1.00114	−0.500569	−	0.865697i	$-0.666876\pi$
$227$	−6.18308e64	−1.00114	−0.500569	+	0.865697i	$0.666876\pi$
$228$	1.23363e64	0.177002
$229$	−2.15042e63	−0.0273557	−0.0136778	−	0.999906i	$-0.504354\pi$
$229$	−2.15042e63	−0.0273557	−0.0136778	+	0.999906i	$0.504354\pi$
$230$	2.68481e63	0.0302969
$231$	3.39651e64	0.340176
$232$	1.41465e65	1.25814
$233$	1.79196e65	1.41593	0.707964	−	0.706249i	$-0.249614\pi$
$233$	1.79196e65	1.41593	0.707964	+	0.706249i	$0.249614\pi$
$234$	−1.48855e65	−1.04551
$235$	−1.99141e64	−0.124393
$236$	−1.70596e65	−0.948174
$237$	9.01837e64	0.446220
$238$	8.48910e64	0.374107
$239$	6.51100e63	0.0255685	0.0127843	−	0.999918i	$-0.495931\pi$
$239$	6.51100e63	0.0255685	0.0127843	+	0.999918i	$0.495931\pi$
$240$	4.77190e64	0.167064
$241$	2.62747e65	0.820482	0.410241	−	0.911977i	$-0.365445\pi$
$241$	2.62747e65	0.820482	0.410241	+	0.911977i	$0.365445\pi$
$242$	−1.99929e65	−0.557125
$243$	−2.69491e65	−0.670458
$244$	−5.06074e65	−1.12459
$245$	−4.40416e65	−0.874572
$246$	6.82479e65	1.21164
$247$	−7.82574e64	−0.124268
$248$	−4.24309e65	−0.602922
$249$	9.41173e65	1.19726
$250$	5.13916e65	0.585520
$251$	−1.22355e66	−1.24909	−0.624547	−	0.780987i	$-0.714716\pi$
$251$	−1.22355e66	−1.24909	−0.624547	+	0.780987i	$0.714716\pi$
$252$	2.45794e66	2.24935
$253$	−1.23379e64	−0.0101258
$254$	6.61178e63	0.00486845
$255$	−7.75290e65	−0.512400
$256$	−1.48923e66	−0.883818
$257$	−1.43953e66	−0.767466	−0.383733	−	0.923444i	$-0.625362\pi$
$257$	−1.43953e66	−0.767466	−0.383733	+	0.923444i	$0.625362\pi$
$258$	5.76898e65	0.276412
$259$	5.04686e66	2.17409
$260$	−9.88144e65	−0.382872
$261$	−8.24891e66	−2.87596
$262$	−1.88207e66	−0.590678
$263$	2.64942e66	0.748802	0.374401	−	0.927267i	$-0.377848\pi$
$263$	2.64942e66	0.748802	0.374401	+	0.927267i	$0.377848\pi$
$264$	8.33992e65	0.212351
$265$	4.15943e66	0.954491
$266$	−6.09172e65	−0.126036
$267$	3.25328e66	0.607102
$268$	−1.97115e66	−0.331904
$269$	8.58601e66	1.30498	0.652489	−	0.757798i	$-0.273725\pi$
$269$	8.58601e66	1.30498	0.652489	+	0.757798i	$0.273725\pi$
$270$	5.71283e66	0.784057
$271$	−2.93209e66	−0.363515	−0.181757	−	0.983343i	$-0.558179\pi$
$271$	−2.93209e66	−0.363515	−0.181757	+	0.983343i	$0.558179\pi$
$272$	−5.48087e65	−0.0614051
$273$	−2.27672e67	−2.30588
$274$	2.17883e66	0.199565
$275$	−8.48432e65	−0.0703020
$276$	−1.30370e66	−0.0977639
$277$	6.84430e66	0.464660	0.232330	−	0.972637i	$-0.425365\pi$
$277$	6.84430e66	0.464660	0.232330	+	0.972637i	$0.425365\pi$
$278$	−1.31301e67	−0.807301
$279$	2.47417e67	1.37820
$280$	−1.90100e67	−0.959700
$281$	2.46187e67	1.12679	0.563394	−	0.826188i	$-0.309495\pi$
$281$	2.46187e67	1.12679	0.563394	+	0.826188i	$0.309495\pi$
$282$	−4.55862e66	−0.189227
$283$	−3.17569e67	−1.19594	−0.597972	−	0.801517i	$-0.704027\pi$
$283$	−3.17569e67	−1.19594	−0.597972	+	0.801517i	$0.704027\pi$
$284$	−1.26053e67	−0.430822
$285$	5.56343e66	0.172627
$286$	−2.14070e66	−0.0603240
$287$	7.14886e67	1.83014
$288$	9.62859e67	2.24011
$289$	−3.83767e67	−0.811665
$290$	2.58143e67	0.496496
$291$	−1.42461e68	−2.49252
$292$	−7.05350e66	−0.112299
$293$	1.03218e67	0.149588	0.0747942	−	0.997199i	$-0.476170\pi$
$293$	1.03218e67	0.149588	0.0747942	+	0.997199i	$0.476170\pi$
$294$	−1.00817e68	−1.33040
$295$	−7.69352e67	−0.924740
$296$	1.23923e68	1.35715
$297$	−2.62531e67	−0.262046
$298$	1.01301e68	0.921863
$299$	8.27025e66	0.0686374
$300$	−8.96507e67	−0.678764
$301$	6.04292e67	0.417512
$302$	−2.06022e67	−0.129934
$303$	2.93405e68	1.68964
$304$	3.93304e66	0.0206873
$305$	−2.28229e68	−1.09679
$306$	−1.21545e68	−0.533825
$307$	4.49594e68	1.80516	0.902578	−	0.430526i	$-0.141672\pi$
$307$	4.49594e68	1.80516	0.902578	+	0.430526i	$0.141672\pi$
$308$	3.53479e67	0.129783
$309$	−2.32635e68	−0.781299
$310$	−7.74271e67	−0.237928
$311$	6.93880e67	0.195152	0.0975761	−	0.995228i	$-0.468891\pi$
$311$	6.93880e67	0.195152	0.0975761	+	0.995228i	$0.468891\pi$
$312$	−5.59035e68	−1.43942
$313$	−6.69159e68	−1.57783	−0.788915	−	0.614502i	$-0.789357\pi$
$313$	−6.69159e68	−1.57783	−0.788915	+	0.614502i	$0.789357\pi$
$314$	−2.33856e66	−0.00505107
$315$	1.10848e69	2.19375
$316$	9.38554e67	0.170241
$317$	−8.49155e68	−1.41207	−0.706036	−	0.708175i	$-0.749519\pi$
$317$	−8.49155e68	−1.41207	−0.706036	+	0.708175i	$0.749519\pi$
$318$	9.52151e68	1.45198
$319$	−1.18629e68	−0.165938
$320$	−2.28246e68	−0.292940
$321$	1.15930e69	1.36555
$322$	6.43774e67	0.0696140
$323$	−6.38999e67	−0.0634499
$324$	−1.15468e69	−1.05311
$325$	5.68714e68	0.476542
$326$	−1.12364e69	−0.865255
$327$	4.71171e68	0.333515
$328$	1.75536e69	1.14245
$329$	−4.77508e68	−0.285821
$330$	1.52185e68	0.0837991
$331$	−8.62291e68	−0.436902	−0.218451	−	0.975848i	$-0.570100\pi$
$331$	−8.62291e68	−0.436902	−0.218451	+	0.975848i	$0.570100\pi$
$332$	9.79491e68	0.456776
$333$	−7.22599e69	−3.10228
$334$	1.75262e69	0.692884
$335$	−8.88947e68	−0.323701
$336$	1.14423e69	0.383868
$337$	2.28691e68	0.0707011	0.0353505	−	0.999375i	$-0.488745\pi$
$337$	2.28691e68	0.0707011	0.0353505	+	0.999375i	$0.488745\pi$
$338$	−5.51363e68	−0.157119
$339$	1.15693e70	3.03959
$340$	−8.06854e68	−0.195490
$341$	3.55813e68	0.0795200
$342$	8.72201e68	0.179845
$343$	−2.55690e69	−0.486549
$344$	1.48380e69	0.260627
$345$	−5.87943e68	−0.0953477
$346$	3.65279e67	0.00547056
$347$	−1.15563e70	−1.59866	−0.799331	−	0.600892i	$-0.794812\pi$
$347$	−1.15563e70	−1.59866	−0.799331	+	0.600892i	$0.794812\pi$
$348$	−1.25350e70	−1.60213
$349$	1.19367e69	0.140989	0.0704945	−	0.997512i	$-0.477542\pi$
$349$	1.19367e69	0.140989	0.0704945	+	0.997512i	$0.477542\pi$
$350$	4.42699e69	0.483323
$351$	1.75977e70	1.77628
$352$	1.38470e69	0.129250
$353$	2.65110e69	0.228887	0.114444	−	0.993430i	$-0.463491\pi$
$353$	2.65110e69	0.228887	0.114444	+	0.993430i	$0.463491\pi$
$354$	−1.76115e70	−1.40672
$355$	−5.68472e69	−0.420175
$356$	3.38573e69	0.231621
$357$	−1.85902e70	−1.17736
$358$	1.62899e70	0.955293
$359$	2.86651e70	1.55688	0.778442	−	0.627717i	$-0.216010\pi$
$359$	2.86651e70	1.55688	0.778442	+	0.627717i	$0.216010\pi$
$360$	2.72181e70	1.36943
$361$	−2.09925e70	−0.978624
$362$	−1.23888e70	−0.535234
$363$	4.37822e70	1.75334
$364$	−2.36941e70	−0.879735
$365$	−3.18099e69	−0.109524
$366$	−5.22448e70	−1.66845
$367$	2.41501e70	0.715487	0.357744	−	0.933820i	$-0.383546\pi$
$367$	2.41501e70	0.715487	0.357744	+	0.933820i	$0.383546\pi$
$368$	−4.15643e68	−0.0114263
$369$	−1.02356e71	−2.61149
$370$	2.26132e70	0.535567
$371$	9.97364e70	2.19316
$372$	3.75974e70	0.767763
$373$	−5.43612e70	−1.03109	−0.515545	−	0.856863i	$-0.672410\pi$
$373$	−5.43612e70	−1.03109	−0.515545	+	0.856863i	$0.672410\pi$
$374$	−1.74796e69	−0.0308008
$375$	−1.12542e71	−1.84270
$376$	−1.17249e70	−0.178420
$377$	7.95181e70	1.12481
$378$	1.36984e71	1.80155
$379$	−4.17308e70	−0.510362	−0.255181	−	0.966893i	$-0.582135\pi$
$379$	−4.17308e70	−0.510362	−0.255181	+	0.966893i	$0.582135\pi$
$380$	5.78993e69	0.0658604
$381$	−1.44791e69	−0.0153216
$382$	−2.74902e69	−0.0270667
$383$	1.52608e70	0.139834	0.0699169	−	0.997553i	$-0.477727\pi$
$383$	1.52608e70	0.139834	0.0699169	+	0.997553i	$0.477727\pi$
$384$	1.63044e71	1.39058
$385$	1.59412e70	0.126576
$386$	−8.18752e70	−0.605343
$387$	−8.65214e70	−0.595761
$388$	−1.48261e71	−0.950941
$389$	−1.77410e71	−1.06014	−0.530072	−	0.847953i	$-0.677835\pi$
$389$	−1.77410e71	−1.06014	−0.530072	+	0.847953i	$0.677835\pi$
$390$	−1.02012e71	−0.568032
$391$	6.75295e69	0.0350455
$392$	−2.59306e71	−1.25443
$393$	4.12153e71	1.85893
$394$	1.41598e71	0.595541
$395$	4.23269e70	0.166034
$396$	−5.06104e70	−0.185192
$397$	4.48439e71	1.53096	0.765481	−	0.643459i	$-0.222501\pi$
$397$	4.48439e71	1.53096	0.765481	+	0.643459i	$0.222501\pi$
$398$	−8.96337e70	−0.285553
$399$	1.33402e71	0.396651
$400$	−2.85822e70	−0.0793316
$401$	−8.03931e70	−0.208328	−0.104164	−	0.994560i	$-0.533217\pi$
$401$	−8.03931e70	−0.208328	−0.104164	+	0.994560i	$0.533217\pi$
$402$	−2.03492e71	−0.492416
$403$	−2.38505e71	−0.539026
$404$	3.05350e71	0.644630
$405$	−5.20738e71	−1.02708
$406$	6.18986e71	1.14081
$407$	−1.03918e71	−0.178996
$408$	−4.56471e71	−0.734952
$409$	5.95183e71	0.895899	0.447950	−	0.894059i	$-0.352154\pi$
$409$	5.95183e71	0.895899	0.447950	+	0.894059i	$0.352154\pi$
$410$	3.20315e71	0.450838
$411$	−4.77141e71	−0.628053
$412$	−2.42107e71	−0.298080
$413$	−1.84478e72	−2.12480
$414$	−9.21742e70	−0.0993345
$415$	4.41731e71	0.445487
$416$	−9.28180e71	−0.876124
$417$	2.87535e72	2.54067
$418$	1.25432e70	0.0103768
$419$	1.13892e72	0.882284	0.441142	−	0.897437i	$-0.354573\pi$
$419$	1.13892e72	0.882284	0.441142	+	0.897437i	$0.354573\pi$
$420$	1.68445e72	1.22209
$421$	−2.57179e72	−1.74774	−0.873872	−	0.486156i	$-0.838399\pi$
$421$	−2.57179e72	−1.74774	−0.873872	+	0.486156i	$0.838399\pi$
$422$	−4.93722e71	−0.314333
$423$	6.83687e71	0.407847
$424$	2.44897e72	1.36906
$425$	4.64375e71	0.243317
$426$	−1.30131e72	−0.639172
$427$	−5.47256e72	−2.52014
$428$	1.20650e72	0.520983
$429$	4.68790e71	0.189847
$430$	2.70762e71	0.102850
$431$	4.28568e71	0.152720	0.0763598	−	0.997080i	$-0.475670\pi$
$431$	4.28568e71	0.152720	0.0763598	+	0.997080i	$0.475670\pi$
$432$	−8.84420e71	−0.295703
$433$	3.13840e72	0.984671	0.492336	−	0.870405i	$-0.336143\pi$
$433$	3.13840e72	0.984671	0.492336	+	0.870405i	$0.336143\pi$
$434$	−1.85658e72	−0.546695
$435$	−5.65305e72	−1.56253
$436$	4.90354e71	0.127242
$437$	−4.84587e70	−0.0118068
$438$	−7.28172e71	−0.166608
$439$	2.41918e71	0.0519870	0.0259935	−	0.999662i	$-0.491725\pi$
$439$	2.41918e71	0.0519870	0.0259935	+	0.999662i	$0.491725\pi$
$440$	3.91426e71	0.0790135
$441$	1.51203e73	2.86746
$442$	1.17168e72	0.208783
$443$	9.52901e72	1.59568	0.797839	−	0.602870i	$-0.205976\pi$
$443$	9.52901e72	1.59568	0.797839	+	0.602870i	$0.205976\pi$
$444$	−1.09806e73	−1.72820
$445$	1.52690e72	0.225896
$446$	7.74929e72	1.07784
$447$	−2.21838e73	−2.90121
$448$	−5.47297e72	−0.673097
$449$	2.43402e72	0.281546	0.140773	−	0.990042i	$-0.455041\pi$
$449$	2.43402e72	0.281546	0.140773	+	0.990042i	$0.455041\pi$
$450$	−6.33847e72	−0.689669
$451$	−1.47199e72	−0.150678
$452$	1.20403e73	1.15966
$453$	4.51165e72	0.408917
$454$	−6.64301e72	−0.566669
$455$	−1.06856e73	−0.857993
$456$	3.27561e72	0.247605
$457$	8.39456e72	0.597451	0.298725	−	0.954339i	$-0.403439\pi$
$457$	8.39456e72	0.597451	0.298725	+	0.954339i	$0.403439\pi$
$458$	−2.31038e71	−0.0154840
$459$	1.43692e73	0.906948
$460$	−6.11880e71	−0.0363769
$461$	−1.74289e73	−0.976099	−0.488050	−	0.872816i	$-0.662292\pi$
$461$	−1.74289e73	−0.976099	−0.488050	+	0.872816i	$0.662292\pi$
$462$	3.64916e72	0.192548
$463$	−5.33236e72	−0.265120	−0.132560	−	0.991175i	$-0.542320\pi$
$463$	−5.33236e72	−0.265120	−0.132560	+	0.991175i	$0.542320\pi$
$464$	−3.99639e72	−0.187251
$465$	1.69557e73	0.748788
$466$	1.92526e73	0.801450
$467$	1.41386e72	0.0554872	0.0277436	−	0.999615i	$-0.491168\pi$
$467$	1.41386e72	0.0554872	0.0277436	+	0.999615i	$0.491168\pi$
$468$	3.39247e73	1.25532
$469$	−2.13155e73	−0.743777
$470$	−2.13954e72	−0.0704093
$471$	5.12119e71	0.0158963
$472$	−4.52975e73	−1.32639
$473$	−1.24427e72	−0.0343744
$474$	9.68921e72	0.252571
$475$	−3.33232e72	−0.0819734
$476$	−1.93471e73	−0.449183
$477$	−1.42801e74	−3.12950
$478$	6.99532e71	0.0144724
$479$	7.08367e73	1.38367	0.691834	−	0.722057i	$-0.256803\pi$
$479$	7.08367e73	1.38367	0.691834	+	0.722057i	$0.256803\pi$
$480$	6.59856e73	1.21707
$481$	6.96573e73	1.21332
$482$	2.82292e73	0.464413
$483$	−1.40979e73	−0.219083
$484$	4.55647e73	0.668931
$485$	−6.68626e73	−0.927439
$486$	−2.89537e73	−0.379495
$487$	6.76804e73	0.838332	0.419166	−	0.907910i	$-0.362322\pi$
$487$	6.76804e73	0.838332	0.419166	+	0.907910i	$0.362322\pi$
$488$	−1.34376e74	−1.57317
$489$	2.46065e74	2.72306
$490$	−4.73176e73	−0.495029
$491$	−2.25567e73	−0.223118	−0.111559	−	0.993758i	$-0.535584\pi$
$491$	−2.25567e73	−0.223118	−0.111559	+	0.993758i	$0.535584\pi$
$492$	−1.55540e74	−1.45480
$493$	6.49293e73	0.574315
$494$	−8.40787e72	−0.0703388
$495$	−2.28243e73	−0.180615
$496$	1.19867e73	0.0897334
$497$	−1.36311e74	−0.965448
$498$	1.01118e74	0.677677
$499$	2.77240e73	0.175829	0.0879146	−	0.996128i	$-0.471980\pi$
$499$	2.77240e73	0.175829	0.0879146	+	0.996128i	$0.471980\pi$
$500$	−1.17124e74	−0.703024
$501$	−3.83805e74	−2.18059
$502$	−1.31457e74	−0.707018
$503$	1.41541e74	0.720714	0.360357	−	0.932814i	$-0.382655\pi$
$503$	1.41541e74	0.720714	0.360357	+	0.932814i	$0.382655\pi$
$504$	6.52646e74	3.14657
$505$	1.37707e74	0.628698
$506$	−1.32557e72	−0.00573143
$507$	1.20743e74	0.494472
$508$	−1.50686e72	−0.00584547
$509$	−1.19940e74	−0.440783	−0.220391	−	0.975412i	$-0.570733\pi$
$509$	−1.19940e74	−0.440783	−0.220391	+	0.975412i	$0.570733\pi$
$510$	−8.32960e73	−0.290031
$511$	−7.62749e73	−0.251656
$512$	8.96719e73	0.280371
$513$	−1.03112e74	−0.305550
$514$	−1.54661e74	−0.434405
$515$	−1.09185e74	−0.290713
$516$	−1.31478e74	−0.331884
$517$	9.83218e72	0.0235321
$518$	5.42227e74	1.23059
$519$	−7.99921e72	−0.0172165
$520$	−2.62378e74	−0.535593
$521$	4.86790e74	0.942550	0.471275	−	0.881986i	$-0.343794\pi$
$521$	4.86790e74	0.942550	0.471275	+	0.881986i	$0.343794\pi$
$522$	−8.86251e74	−1.62786
$523$	−1.33750e74	−0.233076	−0.116538	−	0.993186i	$-0.537180\pi$
$523$	−1.33750e74	−0.233076	−0.116538	+	0.993186i	$0.537180\pi$
$524$	4.28933e74	0.709217
$525$	−9.69462e74	−1.52107
$526$	2.84649e74	0.423840
$527$	−1.94748e74	−0.275221
$528$	−2.35603e73	−0.0316044
$529$	−7.80171e74	−0.993479
$530$	4.46883e74	0.540266
$531$	2.64132e75	3.03195
$532$	1.38833e74	0.151330
$533$	9.86694e74	1.02137
$534$	3.49528e74	0.343635
$535$	5.44107e74	0.508107
$536$	−5.23390e74	−0.464295
$537$	−3.56732e75	−3.00642
$538$	9.22468e74	0.738650
$539$	2.17446e74	0.165448
$540$	−1.30198e75	−0.941404
$541$	−1.15355e75	−0.792708	−0.396354	−	0.918098i	$-0.629725\pi$
$541$	−1.15355e75	−0.792708	−0.396354	+	0.918098i	$0.629725\pi$
$542$	−3.15020e74	−0.205758
$543$	2.71301e75	1.68444
$544$	−7.57891e74	−0.447339
$545$	2.21140e74	0.124097
$546$	−2.44607e75	−1.30518
$547$	−2.83801e75	−1.44000	−0.720001	−	0.693973i	$-0.755859\pi$
$547$	−2.83801e75	−1.44000	−0.720001	+	0.693973i	$0.755859\pi$
$548$	−4.96566e74	−0.239614
$549$	7.83551e75	3.59607
$550$	−9.11543e73	−0.0397927
$551$	−4.65928e74	−0.193486
$552$	−3.46166e74	−0.136760
$553$	1.01493e75	0.381501
$554$	7.35342e74	0.263009
$555$	−4.95203e75	−1.68549
$556$	2.99241e75	0.969313
$557$	−6.93639e74	−0.213853	−0.106927	−	0.994267i	$-0.534101\pi$
$557$	−6.93639e74	−0.213853	−0.106927	+	0.994267i	$0.534101\pi$
$558$	2.65821e75	0.780097
$559$	8.34051e74	0.233006
$560$	5.37031e74	0.142833
$561$	3.82783e74	0.0969336
$562$	2.64500e75	0.637790
$563$	−7.00271e75	−1.60800	−0.803998	−	0.594632i	$-0.797298\pi$
$563$	−7.00271e75	−1.60800	−0.803998	+	0.594632i	$0.797298\pi$
$564$	1.03893e75	0.227201
$565$	5.42993e75	1.13100
$566$	−3.41191e75	−0.676934
$567$	−1.24865e76	−2.35996
$568$	−3.34702e75	−0.602670
$569$	9.40697e74	0.161385	0.0806924	−	0.996739i	$-0.474287\pi$
$569$	9.40697e74	0.161385	0.0806924	+	0.996739i	$0.474287\pi$
$570$	5.97727e74	0.0977112
$571$	5.09860e75	0.794251	0.397126	−	0.917764i	$-0.370008\pi$
$571$	5.09860e75	0.794251	0.397126	+	0.917764i	$0.370008\pi$
$572$	4.87876e74	0.0724300
$573$	6.02006e74	0.0851822
$574$	7.68063e75	1.03591
$575$	3.52160e74	0.0452766
$576$	7.83609e75	0.960464
$577$	−1.41868e76	−1.65786	−0.828932	−	0.559350i	$-0.811051\pi$
$577$	−1.41868e76	−1.65786	−0.828932	+	0.559350i	$0.811051\pi$
$578$	−4.12314e75	−0.459422
$579$	1.79298e76	1.90508
$580$	−5.88320e75	−0.596134
$581$	1.05920e76	1.02361
$582$	−1.53058e76	−1.41083
$583$	−2.05363e75	−0.180566
$584$	−1.87289e75	−0.157093
$585$	1.52994e76	1.22430
$586$	1.10896e75	0.0846707
$587$	−5.82950e75	−0.424701	−0.212351	−	0.977194i	$-0.568112\pi$
$587$	−5.82950e75	−0.424701	−0.212351	+	0.977194i	$0.568112\pi$
$588$	2.29767e76	1.59739
$589$	1.39750e75	0.0927216
$590$	−8.26581e75	−0.523426
$591$	−3.10085e76	−1.87424
$592$	−3.50081e75	−0.201986
$593$	−1.70790e76	−0.940716	−0.470358	−	0.882476i	$-0.655875\pi$
$593$	−1.70790e76	−0.940716	−0.470358	+	0.882476i	$0.655875\pi$
$594$	−2.82059e75	−0.148324
$595$	−8.72513e75	−0.438082
$596$	−2.30870e76	−1.10687
$597$	1.96288e76	0.898669
$598$	8.88543e74	0.0388505
$599$	4.35777e76	1.81981	0.909907	−	0.414813i	$-0.136153\pi$
$599$	4.35777e76	1.81981	0.909907	+	0.414813i	$0.136153\pi$
$600$	−2.38046e76	−0.949513
$601$	2.93965e76	1.12008	0.560038	−	0.828467i	$-0.310787\pi$
$601$	2.93965e76	1.12008	0.560038	+	0.828467i	$0.310787\pi$
$602$	6.49243e75	0.236322
$603$	3.05191e76	1.06132
$604$	4.69534e75	0.156009
$605$	2.05488e76	0.652399
$606$	3.15230e76	0.956379
$607$	−1.42466e76	−0.413068	−0.206534	−	0.978439i	$-0.566218\pi$
$607$	−1.42466e76	−0.413068	−0.206534	+	0.978439i	$0.566218\pi$
$608$	5.43858e75	0.150708
$609$	−1.35551e77	−3.59027
$610$	−2.45206e76	−0.620813
$611$	−6.59062e75	−0.159512
$612$	2.77007e76	0.640954
$613$	5.74254e76	1.27040	0.635200	−	0.772347i	$-0.280918\pi$
$613$	5.74254e76	1.27040	0.635200	+	0.772347i	$0.280918\pi$
$614$	4.83037e76	1.02176
$615$	−7.01454e76	−1.41884
$616$	9.38577e75	0.181552
$617$	3.81555e76	0.705854	0.352927	−	0.935651i	$-0.385186\pi$
$617$	3.81555e76	0.705854	0.352927	+	0.935651i	$0.385186\pi$
$618$	−2.49940e76	−0.442235
$619$	−1.04928e77	−1.77581	−0.887907	−	0.460023i	$-0.847841\pi$
$619$	−1.04928e77	−1.77581	−0.887907	+	0.460023i	$0.847841\pi$
$620$	1.76460e76	0.285677
$621$	1.08969e76	0.168766
$622$	7.45494e75	0.110461
$623$	3.66125e76	0.519049
$624$	1.57927e76	0.214230
$625$	−9.62805e75	−0.124979
$626$	−7.18935e76	−0.893091
$627$	−2.74683e75	−0.0326568
$628$	5.32969e74	0.00606473
$629$	5.68776e76	0.619510
$630$	1.19094e77	1.24172
$631$	9.40566e76	0.938819	0.469410	−	0.882981i	$-0.344467\pi$
$631$	9.40566e76	0.938819	0.469410	+	0.882981i	$0.344467\pi$
$632$	2.49210e76	0.238147
$633$	1.08120e77	0.989243
$634$	−9.12320e76	−0.799268
$635$	−6.79561e74	−0.00570100
$636$	−2.17000e77	−1.74337
$637$	−1.45757e77	−1.12149
$638$	−1.27453e76	−0.0939249
$639$	1.95167e77	1.37763
$640$	7.65229e76	0.517419
$641$	−2.34992e77	−1.52215	−0.761074	−	0.648665i	$-0.775328\pi$
$641$	−2.34992e77	−1.52215	−0.761074	+	0.648665i	$0.775328\pi$
$642$	1.24554e77	0.772935
$643$	−1.44401e77	−0.858553	−0.429277	−	0.903173i	$-0.641231\pi$
$643$	−1.44401e77	−0.858553	−0.429277	+	0.903173i	$0.641231\pi$
$644$	−1.46719e76	−0.0835844
$645$	−5.92939e76	−0.323681
$646$	−6.86532e75	−0.0359142
$647$	1.44528e77	0.724576	0.362288	−	0.932066i	$-0.381996\pi$
$647$	1.44528e77	0.724576	0.362288	+	0.932066i	$0.381996\pi$
$648$	−3.06598e77	−1.47318
$649$	3.79852e76	0.174938
$650$	6.11018e76	0.269735
$651$	4.06570e77	1.72051
$652$	2.56083e77	1.03890
$653$	−4.83816e77	−1.88178	−0.940888	−	0.338718i	$-0.890007\pi$
$653$	−4.83816e77	−1.88178	−0.940888	+	0.338718i	$0.890007\pi$
$654$	5.06219e76	0.188778
$655$	1.93440e77	0.691689
$656$	−4.95889e76	−0.170031
$657$	1.09209e77	0.359096
$658$	−5.13028e76	−0.161782
$659$	2.76660e77	0.836753	0.418377	−	0.908274i	$-0.362599\pi$
$659$	2.76660e77	0.836753	0.418377	+	0.908274i	$0.362599\pi$
$660$	−3.46838e76	−0.100616
$661$	3.38137e77	0.940920	0.470460	−	0.882421i	$-0.344088\pi$
$661$	3.38137e77	0.940920	0.470460	+	0.882421i	$0.344088\pi$
$662$	−9.26433e76	−0.247297
$663$	−2.56584e77	−0.657064
$664$	2.60080e77	0.638976
$665$	6.26110e76	0.147589
$666$	−7.76350e77	−1.75597
$667$	4.92393e76	0.106869
$668$	−3.99431e77	−0.831934
$669$	−1.69701e78	−3.39208
$670$	−9.55072e76	−0.183223
$671$	1.12683e77	0.207487
$672$	1.58223e78	2.79650
$673$	4.83817e77	0.820856	0.410428	−	0.911893i	$-0.365379\pi$
$673$	4.83817e77	0.820856	0.410428	+	0.911893i	$0.365379\pi$
$674$	2.45702e76	0.0400185
$675$	7.49338e77	1.17172
$676$	1.25658e77	0.188650
$677$	−7.28985e77	−1.05082	−0.525412	−	0.850848i	$-0.676089\pi$
$677$	−7.28985e77	−1.05082	−0.525412	+	0.850848i	$0.676089\pi$
$678$	1.24299e78	1.72048
$679$	−1.60326e78	−2.13100
$680$	−2.14240e77	−0.273468
$681$	1.45475e78	1.78337
$682$	3.82280e76	0.0450103
$683$	−6.73597e77	−0.761782	−0.380891	−	0.924620i	$-0.624383\pi$
$683$	−6.73597e77	−0.761782	−0.380891	+	0.924620i	$0.624383\pi$
$684$	−1.98779e77	−0.215937
$685$	−2.23941e77	−0.233692
$686$	−2.74710e77	−0.275398
$687$	5.05948e76	0.0487299
$688$	−4.19175e76	−0.0387894
$689$	1.37657e78	1.22397
$690$	−6.31678e76	−0.0539692
$691$	7.85818e77	0.645172	0.322586	−	0.946540i	$-0.395448\pi$
$691$	7.85818e77	0.645172	0.322586	+	0.946540i	$0.395448\pi$
$692$	−8.32488e75	−0.00656841
$693$	−5.47289e77	−0.415005
$694$	−1.24159e78	−0.904882
$695$	1.34952e78	0.945357
$696$	−3.32838e78	−2.24119
$697$	8.05670e77	0.521502
$698$	1.28246e77	0.0798033
$699$	−4.21611e78	−2.52226
$700$	−1.00893e78	−0.580317
$701$	3.34618e78	1.85056	0.925281	−	0.379282i	$-0.123829\pi$
$701$	3.34618e78	1.85056	0.925281	+	0.379282i	$0.123829\pi$
$702$	1.89067e78	1.00542
$703$	−4.08150e77	−0.208713
$704$	1.12692e77	0.0554171
$705$	4.68537e77	0.221586
$706$	2.84830e77	0.129556
$707$	3.30198e78	1.44458
$708$	4.01375e78	1.68903
$709$	−1.99911e78	−0.809217	−0.404609	−	0.914490i	$-0.632592\pi$
$709$	−1.99911e78	−0.809217	−0.404609	+	0.914490i	$0.632592\pi$
$710$	−6.10759e77	−0.237829
$711$	−1.45316e78	−0.544375
$712$	8.98998e77	0.324011
$713$	−1.47688e77	−0.0512133
$714$	−1.99730e78	−0.666413
$715$	2.20022e77	0.0706399
$716$	−3.71256e78	−1.14700
$717$	−1.53190e77	−0.0455463
$718$	3.07974e78	0.881235
$719$	2.03054e78	0.559201	0.279600	−	0.960116i	$-0.409798\pi$
$719$	2.03054e78	0.559201	0.279600	+	0.960116i	$0.409798\pi$
$720$	−7.68911e77	−0.203813
$721$	−2.61808e78	−0.667981
$722$	−2.25540e78	−0.553925
$723$	−6.18188e78	−1.46156
$724$	2.82347e78	0.642646
$725$	3.38600e78	0.741980
$726$	4.70390e78	0.992432
$727$	−4.59794e78	−0.934044	−0.467022	−	0.884246i	$-0.654673\pi$
$727$	−4.59794e78	−0.934044	−0.467022	+	0.884246i	$0.654673\pi$
$728$	−6.29139e78	−1.23065
$729$	−1.88601e78	−0.355252
$730$	−3.41761e77	−0.0619931
$731$	6.81032e77	0.118971
$732$	1.19068e79	2.00328
$733$	8.70471e77	0.141057	0.0705286	−	0.997510i	$-0.477531\pi$
$733$	8.70471e77	0.141057	0.0705286	+	0.997510i	$0.477531\pi$
$734$	2.59465e78	0.404983
$735$	1.03620e79	1.55791
$736$	−5.74749e77	−0.0832412
$737$	4.38899e77	0.0612363
$738$	−1.09970e79	−1.47817
$739$	5.00046e78	0.647571	0.323786	−	0.946130i	$-0.395044\pi$
$739$	5.00046e78	0.647571	0.323786	+	0.946130i	$0.395044\pi$
$740$	−5.15364e78	−0.643046
$741$	1.84123e78	0.221364
$742$	1.07155e79	1.24138
$743$	−1.50661e79	−1.68194	−0.840969	−	0.541084i	$-0.818014\pi$
$743$	−1.50661e79	−1.68194	−0.840969	+	0.541084i	$0.818014\pi$
$744$	9.98308e78	1.07401
$745$	−1.04118e79	−1.07951
$746$	−5.84049e78	−0.583622
$747$	−1.51654e79	−1.46062
$748$	3.98367e77	0.0369820
$749$	1.30468e79	1.16749
$750$	−1.20913e79	−1.04301
$751$	−1.15635e78	−0.0961595	−0.0480797	−	0.998844i	$-0.515310\pi$
$751$	−1.15635e78	−0.0961595	−0.0480797	+	0.998844i	$0.515310\pi$
$752$	3.31229e77	0.0265545
$753$	2.87876e79	2.22507
$754$	8.54331e78	0.636669
$755$	2.11750e78	0.152154
$756$	−3.12194e79	−2.16309
$757$	−4.56395e77	−0.0304933	−0.0152466	−	0.999884i	$-0.504853\pi$
$757$	−4.56395e77	−0.0304933	−0.0152466	+	0.999884i	$0.504853\pi$
$758$	−4.48350e78	−0.288878
$759$	2.90285e77	0.0180375
$760$	1.53738e78	0.0921311
$761$	1.25753e79	0.726845	0.363423	−	0.931624i	$-0.381608\pi$
$761$	1.25753e79	0.726845	0.363423	+	0.931624i	$0.381608\pi$
$762$	−1.55561e77	−0.00867240
$763$	5.30257e78	0.285142
$764$	6.26515e77	0.0324986
$765$	1.24925e79	0.625114
$766$	1.63960e78	0.0791494
$767$	−2.54619e79	−1.18582
$768$	3.50384e79	1.57438
$769$	−1.37097e79	−0.594367	−0.297183	−	0.954820i	$-0.596047\pi$
$769$	−1.37097e79	−0.594367	−0.297183	+	0.954820i	$0.596047\pi$
$770$	1.71270e78	0.0716450
$771$	3.38690e79	1.36712
$772$	1.86597e79	0.726825
$773$	6.53835e78	0.245772	0.122886	−	0.992421i	$-0.460785\pi$
$773$	6.53835e78	0.245772	0.122886	+	0.992421i	$0.460785\pi$
$774$	−9.29573e78	−0.337215
$775$	−1.01559e79	−0.355568
$776$	−3.93670e79	−1.33026
$777$	−1.18742e80	−3.87281
$778$	−1.90607e79	−0.600067
$779$	−5.78144e78	−0.175693
$780$	2.32489e79	0.682026
$781$	2.80672e78	0.0794868
$782$	7.25527e77	0.0198366
$783$	1.04773e80	2.76568
$784$	7.32539e78	0.186698
$785$	2.40358e77	0.00591484
$786$	4.42811e79	1.05220
$787$	8.33760e78	0.191309	0.0956546	−	0.995415i	$-0.469506\pi$
$787$	8.33760e78	0.191309	0.0956546	+	0.995415i	$0.469506\pi$
$788$	−3.22709e79	−0.715056
$789$	−6.23351e79	−1.33387
$790$	4.54754e78	0.0939791
$791$	1.30201e80	2.59873
$792$	−1.34384e79	−0.259062
$793$	−7.55329e79	−1.40645
$794$	4.81796e79	0.866562
$795$	−9.78625e79	−1.70028
$796$	2.04280e79	0.342859
$797$	9.29356e79	1.50688	0.753439	−	0.657517i	$-0.228393\pi$
$797$	9.29356e79	1.50688	0.753439	+	0.657517i	$0.228393\pi$
$798$	1.43325e79	0.224514
$799$	−5.38147e78	−0.0814451
$800$	−3.95233e79	−0.577935
$801$	−5.24211e79	−0.740648
$802$	−8.63732e78	−0.117919
$803$	1.57055e78	0.0207192
$804$	4.63769e79	0.591235
$805$	−6.61673e78	−0.0815186
$806$	−2.56247e79	−0.305102
$807$	−2.02010e80	−2.32462
$808$	8.10782e79	0.901762
$809$	3.86382e79	0.415367	0.207684	−	0.978196i	$-0.433408\pi$
$809$	3.86382e79	0.415367	0.207684	+	0.978196i	$0.433408\pi$
$810$	−5.59473e79	−0.581355
$811$	5.61301e79	0.563796	0.281898	−	0.959444i	$-0.409036\pi$
$811$	5.61301e79	0.563796	0.281898	+	0.959444i	$0.409036\pi$
$812$	−1.41070e80	−1.36976
$813$	6.89859e79	0.647546
$814$	−1.11648e79	−0.101316
$815$	1.15488e80	1.01322
$816$	1.28953e79	0.109384
$817$	−4.88704e78	−0.0400811
$818$	6.39456e79	0.507101
$819$	3.66854e80	2.81311
$820$	−7.30012e79	−0.541314
$821$	−2.48490e79	−0.178185	−0.0890926	−	0.996023i	$-0.528397\pi$
$821$	−2.48490e79	−0.178185	−0.0890926	+	0.996023i	$0.528397\pi$
$822$	−5.12633e79	−0.355493
$823$	−1.71342e80	−1.14913	−0.574563	−	0.818460i	$-0.694828\pi$
$823$	−1.71342e80	−1.14913	−0.574563	+	0.818460i	$0.694828\pi$
$824$	−6.42855e79	−0.416979
$825$	1.99618e79	0.125232
$826$	−1.98201e80	−1.20269
$827$	1.35237e80	0.793767	0.396883	−	0.917869i	$-0.370092\pi$
$827$	1.35237e80	0.793767	0.396883	+	0.917869i	$0.370092\pi$
$828$	2.10069e79	0.119269
$829$	2.08682e80	1.14613	0.573066	−	0.819509i	$-0.305754\pi$
$829$	2.08682e80	1.14613	0.573066	+	0.819509i	$0.305754\pi$
$830$	4.74589e79	0.252157
$831$	−1.61032e80	−0.827720
$832$	−7.55385e79	−0.375644
$833$	−1.19015e80	−0.572619
$834$	3.08923e80	1.43808
$835$	−1.80135e80	−0.811373
$836$	−2.85866e78	−0.0124592
$837$	−3.14255e80	−1.32536
$838$	1.22364e80	0.499395
$839$	−3.88689e80	−1.53514	−0.767572	−	0.640963i	$-0.778535\pi$
$839$	−3.88689e80	−1.53514	−0.767572	+	0.640963i	$0.778535\pi$
$840$	4.47264e80	1.70956
$841$	2.03107e80	0.751336
$842$	−2.76309e80	−0.989266
$843$	−5.79227e80	−2.00720
$844$	1.12522e80	0.377415
$845$	5.66693e79	0.183988
$846$	7.34543e79	0.230851
$847$	4.92726e80	1.49904
$848$	−6.91833e79	−0.203758
$849$	7.47172e80	2.13039
$850$	4.98917e79	0.137724
$851$	4.31333e79	0.115279
$852$	2.96575e80	0.767443
$853$	2.51355e79	0.0629780	0.0314890	−	0.999504i	$-0.489975\pi$
$853$	2.51355e79	0.0629780	0.0314890	+	0.999504i	$0.489975\pi$
$854$	−5.87964e80	−1.42646
$855$	−8.96452e79	−0.210600
$856$	3.20356e80	0.728794
$857$	5.37005e77	0.00118306	0.000591529	−	1.00000i	$-0.499812\pi$
$857$	5.37005e77	0.00118306	0.000591529		1.00000i	$0.499812\pi$
$858$	5.03661e79	0.107458
$859$	−1.77605e80	−0.366980	−0.183490	−	0.983022i	$-0.558739\pi$
$859$	−1.77605e80	−0.366980	−0.183490	+	0.983022i	$0.558739\pi$
$860$	−6.17079e79	−0.123490
$861$	−1.68197e81	−3.26011
$862$	4.60447e79	0.0864431
$863$	7.23414e80	1.31550	0.657749	−	0.753237i	$-0.271509\pi$
$863$	7.23414e80	1.31550	0.657749	+	0.753237i	$0.271509\pi$
$864$	−1.22297e81	−2.15421
$865$	−3.75435e78	−0.00640608
$866$	3.37185e80	0.557348
$867$	9.02922e80	1.44586
$868$	4.23123e80	0.656408
$869$	−2.08980e79	−0.0314095
$870$	−6.07356e80	−0.884430
$871$	−2.94199e80	−0.415090
$872$	1.30202e80	0.177997
$873$	2.29551e81	3.04080
$874$	−5.20633e78	−0.00668294
$875$	−1.26655e81	−1.57544
$876$	1.65954e80	0.200043
$877$	−7.57306e80	−0.884672	−0.442336	−	0.896849i	$-0.645850\pi$
$877$	−7.57306e80	−0.884672	−0.442336	+	0.896849i	$0.645850\pi$
$878$	2.59914e79	0.0294259
$879$	−2.42851e80	−0.266468
$880$	−1.10578e79	−0.0117597
$881$	5.18485e80	0.534440	0.267220	−	0.963636i	$-0.413895\pi$
$881$	5.18485e80	0.534440	0.267220	+	0.963636i	$0.413895\pi$
$882$	1.62450e81	1.62305
$883$	−1.85801e81	−1.79940	−0.899700	−	0.436509i	$-0.856215\pi$
$883$	−1.85801e81	−1.79940	−0.899700	+	0.436509i	$0.856215\pi$
$884$	−2.67030e80	−0.250682
$885$	1.81012e81	1.64728
$886$	1.02378e81	0.903193
$887$	1.81133e81	1.54917	0.774584	−	0.632471i	$-0.217959\pi$
$887$	1.81133e81	1.54917	0.774584	+	0.632471i	$0.217959\pi$
$888$	−2.91563e81	−2.41756
$889$	−1.62948e79	−0.0130994
$890$	1.64048e80	0.127863
$891$	2.57104e80	0.194299
$892$	−1.76610e81	−1.29414
$893$	3.86171e79	0.0274388
$894$	−2.38340e81	−1.64216
$895$	−1.67429e81	−1.11866
$896$	1.83490e81	1.18889
$897$	−1.94581e80	−0.122267
$898$	2.61507e80	0.159362
$899$	−1.42001e81	−0.839267
$900$	1.44457e81	0.828073
$901$	1.12402e81	0.624945
$902$	−1.58149e80	−0.0852876
$903$	−1.42177e81	−0.743732
$904$	3.19701e81	1.62223
$905$	1.27333e81	0.626763
$906$	4.84726e80	0.231457
$907$	1.77437e81	0.821948	0.410974	−	0.911647i	$-0.365189\pi$
$907$	1.77437e81	0.821948	0.410974	+	0.911647i	$0.365189\pi$
$908$	1.51397e81	0.680390
$909$	−4.72771e81	−2.06132
$910$	−1.14804e81	−0.485645
$911$	−1.97996e81	−0.812645	−0.406323	−	0.913730i	$-0.633189\pi$
$911$	−1.97996e81	−0.812645	−0.406323	+	0.913730i	$0.633189\pi$
$912$	−9.25359e79	−0.0368513
$913$	−2.18095e80	−0.0842753
$914$	9.01899e80	0.338172
$915$	5.36974e81	1.95377
$916$	5.26546e79	0.0185914
$917$	4.63838e81	1.58931
$918$	1.54380e81	0.513355
$919$	−9.32344e80	−0.300884	−0.150442	−	0.988619i	$-0.548070\pi$
$919$	−9.32344e80	−0.300884	−0.150442	+	0.988619i	$0.548070\pi$
$920$	−1.62470e80	−0.0508871
$921$	−1.05780e82	−3.21561
$922$	−1.87253e81	−0.552496
$923$	−1.88137e81	−0.538801
$924$	−8.31661e80	−0.231189
$925$	2.96612e81	0.800369
$926$	−5.72901e80	−0.150064
$927$	3.74852e81	0.953163
$928$	−5.52619e81	−1.36413
$929$	−1.80841e81	−0.433375	−0.216688	−	0.976241i	$-0.569525\pi$
$929$	−1.80841e81	−0.433375	−0.216688	+	0.976241i	$0.569525\pi$
$930$	1.82169e81	0.423833
$931$	8.54047e80	0.192915
$932$	−4.38776e81	−0.962287
$933$	−1.63255e81	−0.347634
$934$	1.51903e80	0.0314071
$935$	1.79656e80	0.0360680
$936$	9.00789e81	1.75605
$937$	7.97369e81	1.50946	0.754728	−	0.656038i	$-0.227769\pi$
$937$	7.97369e81	1.50946	0.754728	+	0.656038i	$0.227769\pi$
$938$	−2.29011e81	−0.420996
$939$	1.57439e82	2.81066
$940$	4.87612e80	0.0845392
$941$	−7.79087e81	−1.31181	−0.655906	−	0.754843i	$-0.727713\pi$
$941$	−7.79087e81	−1.31181	−0.655906	+	0.754843i	$0.727713\pi$
$942$	5.50213e79	0.00899769
$943$	6.10982e80	0.0970414
$944$	1.27966e81	0.197407
$945$	−1.40793e82	−2.10963
$946$	−1.33683e80	−0.0194567
$947$	−6.44542e81	−0.911227	−0.455614	−	0.890178i	$-0.650580\pi$
$947$	−6.44542e81	−0.911227	−0.455614	+	0.890178i	$0.650580\pi$
$948$	−2.20822e81	−0.303258
$949$	−1.05276e81	−0.140445
$950$	−3.58020e80	−0.0463989
$951$	1.99788e82	2.51539
$952$	−5.13714e81	−0.628355
$953$	1.78938e81	0.212641	0.106320	−	0.994332i	$-0.466093\pi$
$953$	1.78938e81	0.212641	0.106320	+	0.994332i	$0.466093\pi$
$954$	−1.53423e82	−1.77137
$955$	2.82546e80	0.0316954
$956$	−1.59427e80	−0.0173768
$957$	2.79108e81	0.295593
$958$	7.61060e81	0.783190
$959$	−5.36975e81	−0.536961
$960$	5.37014e81	0.521827
$961$	−6.33077e81	−0.597810
$962$	7.48388e81	0.686772
$963$	−1.86802e82	−1.66593
$964$	−6.43356e81	−0.557613
$965$	8.41517e81	0.708862
$966$	−1.51466e81	−0.124007
$967$	2.92369e81	0.232650	0.116325	−	0.993211i	$-0.462889\pi$
$967$	2.92369e81	0.232650	0.116325	+	0.993211i	$0.462889\pi$
$968$	1.20986e82	0.935757
$969$	1.50343e81	0.113026
$970$	−7.18362e81	−0.524953
$971$	−7.61535e81	−0.540955	−0.270477	−	0.962726i	$-0.587182\pi$
$971$	−7.61535e81	−0.540955	−0.270477	+	0.962726i	$0.587182\pi$
$972$	6.59868e81	0.455654
$973$	3.23592e82	2.17218
$974$	7.27148e81	0.474517
$975$	−1.33806e82	−0.848886
$976$	3.79611e81	0.234136
$977$	−1.12361e82	−0.673778	−0.336889	−	0.941544i	$-0.609375\pi$
$977$	−1.12361e82	−0.673778	−0.336889	+	0.941544i	$0.609375\pi$
$978$	2.64369e82	1.54132
$979$	−7.53873e80	−0.0427341
$980$	1.07839e82	0.594373
$981$	−7.59212e81	−0.406879
$982$	−2.42346e81	−0.126290
$983$	−3.41757e82	−1.73179	−0.865896	−	0.500225i	$-0.833251\pi$
$983$	−3.41757e82	−1.73179	−0.865896	+	0.500225i	$0.833251\pi$
$984$	−4.12999e82	−2.03509
$985$	−1.45535e82	−0.697384
$986$	6.97591e81	0.325077
$987$	1.12348e82	0.509145
$988$	1.91619e81	0.0844546
$989$	5.16463e80	0.0221381
$990$	−2.45221e81	−0.102233
$991$	−3.84020e81	−0.155714	−0.0778571	−	0.996965i	$-0.524808\pi$
$991$	−3.84020e81	−0.155714	−0.0778571	+	0.996965i	$0.524808\pi$
$992$	1.65752e82	0.653713
$993$	2.02879e82	0.778274
$994$	−1.46450e82	−0.546467
$995$	9.21259e81	0.334385
$996$	−2.30453e82	−0.813676
$997$	−7.93338e81	−0.272484	−0.136242	−	0.990676i	$-0.543503\pi$
$997$	−7.93338e81	−0.272484	−0.136242	+	0.990676i	$0.543503\pi$
$998$	2.97863e81	0.0995237
$999$	9.17806e82	2.98332

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.07439e8 q^{2} -2.35279e13 q^{3} -2.44858e16 q^{4} -1.10426e19 q^{5} -2.52780e21 q^{6} -2.64783e23 q^{7} -6.50160e24 q^{8} +3.79111e26 q^{9} +O(q^{10})\)	\(q+1.07439e8 q^{2} -2.35279e13 q^{3} -2.44858e16 q^{4} -1.10426e19 q^{5} -2.52780e21 q^{6} -2.64783e23 q^{7} -6.50160e24 q^{8} +3.79111e26 q^{9} -1.18640e27 q^{10} +5.45205e27 q^{11} +5.76098e29 q^{12} -3.65457e30 q^{13} -2.84479e31 q^{14} +2.59808e32 q^{15} +1.83670e32 q^{16} -2.98408e33 q^{17} +4.07312e34 q^{18} +2.14136e34 q^{19} +2.70386e35 q^{20} +6.22979e36 q^{21} +5.85760e35 q^{22} -2.26299e36 q^{23} +1.52969e38 q^{24} -1.55617e38 q^{25} -3.92642e38 q^{26} -4.81527e39 q^{27} +6.48342e39 q^{28} -2.17585e40 q^{29} +2.79134e40 q^{30} +6.52623e40 q^{31} +2.53978e41 q^{32} -1.28275e41 q^{33} -3.20606e41 q^{34} +2.92389e42 q^{35} -9.28283e42 q^{36} -1.90603e43 q^{37} +2.30065e42 q^{38} +8.59842e43 q^{39} +7.17944e43 q^{40} -2.69989e44 q^{41} +6.69319e44 q^{42} -2.28222e44 q^{43} -1.33497e44 q^{44} -4.18637e45 q^{45} -2.43132e44 q^{46} +1.80339e45 q^{47} -4.32137e45 q^{48} +3.98834e46 q^{49} -1.67193e46 q^{50} +7.02091e46 q^{51} +8.94849e46 q^{52} -3.76672e47 q^{53} -5.17345e47 q^{54} -6.02047e46 q^{55} +1.72151e48 q^{56} -5.03816e47 q^{57} -2.33771e48 q^{58} +6.96714e48 q^{59} -6.36160e48 q^{60} +2.06681e49 q^{61} +7.01168e48 q^{62} -1.00382e50 q^{63} +2.06696e49 q^{64} +4.03559e49 q^{65} -1.37817e49 q^{66} +8.05018e49 q^{67} +7.30675e49 q^{68} +5.32433e49 q^{69} +3.14139e50 q^{70} +5.14800e50 q^{71} -2.46483e51 q^{72} +2.88066e50 q^{73} -2.04781e51 q^{74} +3.66134e51 q^{75} -5.24328e50 q^{76} -1.44361e51 q^{77} +9.23802e51 q^{78} -3.83306e51 q^{79} -2.02819e51 q^{80} +4.71573e52 q^{81} -2.90072e52 q^{82} -4.00025e52 q^{83} -1.52541e53 q^{84} +3.29520e52 q^{85} -2.45198e52 q^{86} +5.11932e53 q^{87} -3.54470e52 q^{88} -1.38274e53 q^{89} -4.49777e53 q^{90} +9.67669e53 q^{91} +5.54110e52 q^{92} -1.53548e54 q^{93} +1.93754e53 q^{94} -2.36461e53 q^{95} -5.97556e54 q^{96} +6.05498e54 q^{97} +4.28501e54 q^{98} +2.06693e54 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 208622520 q^{2} - 6821470691280 q^{3} + 38\!\cdots\!72 q^{4}+ \cdots + 47\!\cdots\!28 q^{9}+O(q^{10}) \) 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