LMFDB - Embedded newform 1.56.a.a.1.1

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			1.1
Root			$-1.27360e7$ 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)

$f(q)$	$=$	$q-2.53509e8 q^{2} -1.66915e12 q^{3} +2.82382e16 q^{4} +1.07257e19 q^{5} +4.23145e20 q^{6} -1.10352e23 q^{7} +1.97498e24 q^{8} -1.71663e26 q^{9} +O(q^{10})$	\(q-2.53509e8 q^{2} -1.66915e12 q^{3} +2.82382e16 q^{4} +1.07257e19 q^{5} +4.23145e20 q^{6} -1.10352e23 q^{7} +1.97498e24 q^{8} -1.71663e26 q^{9} -2.71906e27 q^{10} -7.94038e28 q^{11} -4.71339e28 q^{12} +3.15893e30 q^{13} +2.79753e31 q^{14} -1.79028e31 q^{15} -1.51807e33 q^{16} +3.96364e33 q^{17} +4.35182e34 q^{18} +1.06873e35 q^{19} +3.02875e35 q^{20} +1.84194e35 q^{21} +2.01296e37 q^{22} +2.36516e37 q^{23} -3.29654e36 q^{24} -1.62515e38 q^{25} -8.00820e38 q^{26} +5.77713e38 q^{27} -3.11615e39 q^{28} -2.07372e40 q^{29} +4.53852e39 q^{30} +1.26132e41 q^{31} +3.13688e41 q^{32} +1.32537e41 q^{33} -1.00482e42 q^{34} -1.18360e42 q^{35} -4.84747e42 q^{36} +1.05611e43 q^{37} -2.70933e43 q^{38} -5.27273e42 q^{39} +2.11830e43 q^{40} +3.96211e44 q^{41} -4.66949e43 q^{42} +4.12421e44 q^{43} -2.24222e45 q^{44} -1.84121e45 q^{45} -5.99590e45 q^{46} +1.78010e46 q^{47} +2.53388e45 q^{48} -1.80492e46 q^{49} +4.11992e46 q^{50} -6.61590e45 q^{51} +8.92027e46 q^{52} -1.03445e47 q^{53} -1.46456e47 q^{54} -8.51661e47 q^{55} -2.17943e47 q^{56} -1.78387e47 q^{57} +5.25709e48 q^{58} +3.49395e48 q^{59} -5.05543e47 q^{60} -1.91493e48 q^{61} -3.19757e49 q^{62} +1.89434e49 q^{63} -2.48288e49 q^{64} +3.38818e49 q^{65} -3.35993e49 q^{66} +1.84247e49 q^{67} +1.11926e50 q^{68} -3.94780e49 q^{69} +3.00054e50 q^{70} +7.05155e50 q^{71} -3.39031e50 q^{72} -2.58805e51 q^{73} -2.67734e51 q^{74} +2.71262e50 q^{75} +3.01790e51 q^{76} +8.76237e51 q^{77} +1.33669e51 q^{78} +9.12558e51 q^{79} -1.62823e52 q^{80} +2.89822e52 q^{81} -1.00443e53 q^{82} +4.34346e52 q^{83} +5.20132e51 q^{84} +4.25128e52 q^{85} -1.04553e53 q^{86} +3.46136e52 q^{87} -1.56821e53 q^{88} +4.67666e53 q^{89} +4.66763e53 q^{90} -3.48595e53 q^{91} +6.67879e53 q^{92} -2.10534e53 q^{93} -4.51272e54 q^{94} +1.14629e54 q^{95} -5.23592e53 q^{96} -8.39518e53 q^{97} +4.57565e54 q^{98} +1.36307e55 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.53509e8	−1.33558	−0.667789	−	0.744351i	$-0.732759\pi$
$2$	−2.53509e8	−1.33558	−0.667789	+	0.744351i	$0.732759\pi$
$3$	−1.66915e12	−0.126375	−0.0631874	−	0.998002i	$-0.520127\pi$
$3$	−1.66915e12	−0.126375	−0.0631874	+	0.998002i	$0.520127\pi$
$4$	2.82382e16	0.783769
$5$	1.07257e19	0.643799	0.321899	−	0.946774i	$-0.395679\pi$
$5$	1.07257e19	0.643799	0.321899	+	0.946774i	$0.395679\pi$
$6$	4.23145e20	0.168784
$7$	−1.10352e23	−0.634723	−0.317362	−	0.948305i	$-0.602797\pi$
$7$	−1.10352e23	−0.634723	−0.317362	+	0.948305i	$0.602797\pi$
$8$	1.97498e24	0.288794
$9$	−1.71663e26	−0.984029
$10$	−2.71906e27	−0.859844
$11$	−7.94038e28	−1.82618	−0.913088	−	0.407763i	$-0.866309\pi$
$11$	−7.94038e28	−1.82618	−0.913088	+	0.407763i	$0.866309\pi$
$12$	−4.71339e28	−0.0990487
$13$	3.15893e30	0.734680	0.367340	−	0.930087i	$-0.380269\pi$
$13$	3.15893e30	0.734680	0.367340	+	0.930087i	$0.380269\pi$
$14$	2.79753e31	0.847722
$15$	−1.79028e31	−0.0813600
$16$	−1.51807e33	−1.16948
$17$	3.96364e33	0.576433	0.288216	−	0.957565i	$-0.406938\pi$
$17$	3.96364e33	0.576433	0.288216	+	0.957565i	$0.406938\pi$
$18$	4.35182e34	1.31425
$19$	1.06873e35	0.729699	0.364849	−	0.931067i	$-0.381120\pi$
$19$	1.06873e35	0.729699	0.364849	+	0.931067i	$0.381120\pi$
$20$	3.02875e35	0.504589
$21$	1.84194e35	0.0802131
$22$	2.01296e37	2.43900
$23$	2.36516e37	0.844004	0.422002	−	0.906595i	$-0.361327\pi$
$23$	2.36516e37	0.844004	0.422002	+	0.906595i	$0.361327\pi$
$24$	−3.29654e36	−0.0364963
$25$	−1.62515e38	−0.585523
$26$	−8.00820e38	−0.981223
$27$	5.77713e38	0.250731
$28$	−3.11615e39	−0.497476
$29$	−2.07372e40	−1.26126	−0.630632	−	0.776082i	$-0.717204\pi$
$29$	−2.07372e40	−1.26126	−0.630632	+	0.776082i	$0.717204\pi$
$30$	4.53852e39	0.108663
$31$	1.26132e41	1.22569	0.612843	−	0.790204i	$-0.290026\pi$
$31$	1.26132e41	1.22569	0.612843	+	0.790204i	$0.290026\pi$
$32$	3.13688e41	1.27313
$33$	1.32537e41	0.230783
$34$	−1.00482e42	−0.769871
$35$	−1.18360e42	−0.408634
$36$	−4.84747e42	−0.771251
$37$	1.05611e43	0.790974	0.395487	−	0.918472i	$-0.370576\pi$
$37$	1.05611e43	0.790974	0.395487	+	0.918472i	$0.370576\pi$
$38$	−2.70933e43	−0.974570
$39$	−5.27273e42	−0.0928451
$40$	2.11830e43	0.185925
$41$	3.96211e44	1.76348	0.881739	−	0.471737i	$-0.156373\pi$
$41$	3.96211e44	1.76348	0.881739	+	0.471737i	$0.156373\pi$
$42$	−4.66949e43	−0.107131
$43$	4.12421e44	0.495402	0.247701	−	0.968836i	$-0.420325\pi$
$43$	4.12421e44	0.495402	0.247701	+	0.968836i	$0.420325\pi$
$44$	−2.24222e45	−1.43130
$45$	−1.84121e45	−0.633517
$46$	−5.99590e45	−1.12723
$47$	1.78010e46	1.85248	0.926239	−	0.376936i	$-0.123022\pi$
$47$	1.78010e46	1.85248	0.926239	+	0.376936i	$0.123022\pi$
$48$	2.53388e45	0.147792
$49$	−1.80492e46	−0.597127
$50$	4.11992e46	0.782012
$51$	−6.61590e45	−0.0728466
$52$	8.92027e46	0.575819
$53$	−1.03445e47	−0.395480	−0.197740	−	0.980254i	$-0.563360\pi$
$53$	−1.03445e47	−0.395480	−0.197740	+	0.980254i	$0.563360\pi$
$54$	−1.46456e47	−0.334871
$55$	−8.51661e47	−1.17569
$56$	−2.17943e47	−0.183304
$57$	−1.78387e47	−0.0922156
$58$	5.25709e48	1.68452
$59$	3.49395e48	0.699659	0.349829	−	0.936813i	$-0.386240\pi$
$59$	3.49395e48	0.699659	0.349829	+	0.936813i	$0.386240\pi$
$60$	−5.05543e47	−0.0637674
$61$	−1.91493e48	−0.153314	−0.0766571	−	0.997058i	$-0.524425\pi$
$61$	−1.91493e48	−0.153314	−0.0766571	+	0.997058i	$0.524425\pi$
$62$	−3.19757e49	−1.63700
$63$	1.89434e49	0.624586
$64$	−2.48288e49	−0.530892
$65$	3.38818e49	0.472986
$66$	−3.35993e49	−0.308228
$67$	1.84247e49	0.111775	0.0558873	−	0.998437i	$-0.482201\pi$
$67$	1.84247e49	0.111775	0.0558873	+	0.998437i	$0.482201\pi$
$68$	1.11926e50	0.451790
$69$	−3.94780e49	−0.106661
$70$	3.00054e50	0.545763
$71$	7.05155e50	0.868320	0.434160	−	0.900836i	$-0.357045\pi$
$71$	7.05155e50	0.868320	0.434160	+	0.900836i	$0.357045\pi$
$72$	−3.39031e50	−0.284182
$73$	−2.58805e51	−1.48455	−0.742273	−	0.670098i	$-0.766252\pi$
$73$	−2.58805e51	−1.48455	−0.742273	+	0.670098i	$0.766252\pi$
$74$	−2.67734e51	−1.05641
$75$	2.71262e50	0.0739954
$76$	3.01790e51	0.571915
$77$	8.76237e51	1.15912
$78$	1.33669e51	0.124002
$79$	9.12558e51	0.596369	0.298185	−	0.954508i	$-0.403619\pi$
$79$	9.12558e51	0.596369	0.298185	+	0.954508i	$0.403619\pi$
$80$	−1.62823e52	−0.752907
$81$	2.89822e52	0.952343
$82$	−1.00443e53	−2.35526
$83$	4.34346e52	0.729774	0.364887	−	0.931052i	$-0.381108\pi$
$83$	4.34346e52	0.729774	0.364887	+	0.931052i	$0.381108\pi$
$84$	5.20132e51	0.0628685
$85$	4.25128e52	0.371107
$86$	−1.04553e53	−0.661648
$87$	3.46136e52	0.159392
$88$	−1.56821e53	−0.527388
$89$	4.67666e53	1.15268	0.576342	−	0.817209i	$-0.304480\pi$
$89$	4.67666e53	1.15268	0.576342	+	0.817209i	$0.304480\pi$
$90$	4.66763e53	0.846111
$91$	−3.48595e53	−0.466319
$92$	6.67879e53	0.661504
$93$	−2.10534e53	−0.154896
$94$	−4.51272e54	−2.47413
$95$	1.14629e54	0.469779
$96$	−5.23592e53	−0.160892
$97$	−8.39518e53	−0.194002	−0.0970012	−	0.995284i	$-0.530925\pi$
$97$	−8.39518e53	−0.194002	−0.0970012	+	0.995284i	$0.530925\pi$
$98$	4.57565e54	0.797509
$99$	1.36307e55	1.79701
$100$	−4.58915e54	−0.458915
$101$	−1.39147e54	−0.105837	−0.0529183	−	0.998599i	$-0.516852\pi$
$101$	−1.39147e54	−0.105837	−0.0529183	+	0.998599i	$0.516852\pi$
$102$	1.67719e54	0.0972923
$103$	−3.24089e55	−1.43761	−0.718805	−	0.695211i	$-0.755311\pi$
$103$	−3.24089e55	−1.43761	−0.718805	+	0.695211i	$0.755311\pi$
$104$	6.23883e54	0.212171
$105$	1.97561e54	0.0516411
$106$	2.62244e55	0.528195
$107$	−3.99263e55	−0.621163	−0.310582	−	0.950547i	$-0.600524\pi$
$107$	−3.99263e55	−0.621163	−0.310582	+	0.950547i	$0.600524\pi$
$108$	1.63136e55	0.196515
$109$	−1.39528e56	−1.30447	−0.652233	−	0.758019i	$-0.726167\pi$
$109$	−1.39528e56	−1.30447	−0.652233	+	0.758019i	$0.726167\pi$
$110$	2.15904e56	1.57023
$111$	−1.76281e55	−0.0999592
$112$	1.67522e56	0.742293
$113$	−1.93685e55	−0.0672107	−0.0336053	−	0.999435i	$-0.510699\pi$
$113$	−1.93685e55	−0.0672107	−0.0336053	+	0.999435i	$0.510699\pi$
$114$	4.52228e55	0.123161
$115$	2.53679e56	0.543369
$116$	−5.85583e56	−0.988539
$117$	−5.42273e56	−0.722947
$118$	−8.85749e56	−0.934449
$119$	−4.37396e56	−0.365875
$120$	−3.53576e55	−0.0234963
$121$	4.41437e57	2.33492
$122$	4.85453e56	0.204763
$123$	−6.61335e56	−0.222859
$124$	3.56175e57	0.960655
$125$	−4.72007e57	−1.02076
$126$	−4.80233e57	−0.834184
$127$	4.09181e57	0.571891	0.285945	−	0.958246i	$-0.407692\pi$
$127$	4.09181e57	0.571891	0.285945	+	0.958246i	$0.407692\pi$
$128$	−5.00747e57	−0.564085
$129$	−6.88392e56	−0.0626064
$130$	−8.58934e57	−0.631710
$131$	1.51902e58	0.904906	0.452453	−	0.891788i	$-0.350549\pi$
$131$	1.51902e58	0.904906	0.452453	+	0.891788i	$0.350549\pi$
$132$	3.74261e57	0.180880
$133$	−1.17936e58	−0.463157
$134$	−4.67083e57	−0.149284
$135$	6.19637e57	0.161421
$136$	7.82810e57	0.166470
$137$	7.02070e58	1.22058	0.610288	−	0.792180i	$-0.291054\pi$
$137$	7.02070e58	1.22058	0.610288	+	0.792180i	$0.291054\pi$
$138$	1.00081e58	0.142454
$139$	−1.53029e58	−0.178594	−0.0892968	−	0.996005i	$-0.528462\pi$
$139$	−1.53029e58	−0.178594	−0.0892968	+	0.996005i	$0.528462\pi$
$140$	−3.34228e58	−0.320275
$141$	−2.97125e58	−0.234107
$142$	−1.78763e59	−1.15971
$143$	−2.50831e59	−1.34166
$144$	2.60596e59	1.15080
$145$	−2.22421e59	−0.812000
$146$	6.56095e59	1.98273
$147$	3.01269e58	0.0754618
$148$	2.98227e59	0.619941
$149$	1.10917e59	0.191592	0.0957960	−	0.995401i	$-0.469460\pi$
$149$	1.10917e59	0.191592	0.0957960	+	0.995401i	$0.469460\pi$
$150$	−6.87676e58	−0.0988266
$151$	−5.47256e59	−0.655125	−0.327563	−	0.944829i	$-0.606227\pi$
$151$	−5.47256e59	−0.655125	−0.327563	+	0.944829i	$0.606227\pi$
$152$	2.11072e59	0.210732
$153$	−6.80411e59	−0.567227
$154$	−2.22134e60	−1.54809
$155$	1.35286e60	0.789096
$156$	−1.48893e59	−0.0727691
$157$	3.00285e60	1.23110	0.615550	−	0.788097i	$-0.288934\pi$
$157$	3.00285e60	1.23110	0.615550	+	0.788097i	$0.288934\pi$
$158$	−2.31342e60	−0.796498
$159$	1.72666e59	0.0499788
$160$	3.36452e60	0.819641
$161$	−2.61000e60	−0.535709
$162$	−7.34726e60	−1.27193
$163$	9.84807e60	1.43944	0.719718	−	0.694267i	$-0.244271\pi$
$163$	9.84807e60	1.43944	0.719718	+	0.694267i	$0.244271\pi$
$164$	1.11883e61	1.38216
$165$	1.42155e60	0.148578
$166$	−1.10111e61	−0.974670
$167$	−1.02128e61	−0.766374	−0.383187	−	0.923671i	$-0.625174\pi$
$167$	−1.02128e61	−0.766374	−0.383187	+	0.923671i	$0.625174\pi$
$168$	3.63779e59	0.0231650
$169$	−8.50890e60	−0.460245
$170$	−1.07774e61	−0.495642
$171$	−1.83461e61	−0.718045
$172$	1.16460e61	0.388281
$173$	4.21525e61	1.19827	0.599137	−	0.800647i	$-0.295511\pi$
$173$	4.21525e61	1.19827	0.599137	+	0.800647i	$0.295511\pi$
$174$	−8.77486e60	−0.212881
$175$	1.79339e61	0.371645
$176$	1.20540e62	2.13567
$177$	−5.83192e60	−0.0884193
$178$	−1.18558e62	−1.53950
$179$	9.72914e60	0.108297	0.0541485	−	0.998533i	$-0.482756\pi$
$179$	9.72914e60	0.108297	0.0541485	+	0.998533i	$0.482756\pi$
$180$	−5.19924e61	−0.496531
$181$	−1.95829e62	−1.60589	−0.802946	−	0.596051i	$-0.796736\pi$
$181$	−1.95829e62	−1.60589	−0.802946	+	0.596051i	$0.796736\pi$
$182$	8.83721e61	0.622805
$183$	3.19631e60	0.0193751
$184$	4.67114e61	0.243743
$185$	1.13275e62	0.509228
$186$	5.33722e61	0.206876
$187$	−3.14728e62	−1.05267
$188$	5.02669e62	1.45191
$189$	−6.37519e61	−0.159145
$190$	−2.90594e62	−0.627427
$191$	3.89576e62	0.728073	0.364037	−	0.931385i	$-0.381398\pi$
$191$	3.89576e62	0.728073	0.364037	+	0.931385i	$0.381398\pi$
$192$	4.14429e61	0.0670914
$193$	−1.32355e62	−0.185743	−0.0928716	−	0.995678i	$-0.529605\pi$
$193$	−1.32355e62	−0.185743	−0.0928716	+	0.995678i	$0.529605\pi$
$194$	2.12826e62	0.259105
$195$	−5.65537e61	−0.0597736
$196$	−5.09678e62	−0.468009
$197$	1.20320e63	0.960542	0.480271	−	0.877120i	$-0.340538\pi$
$197$	1.20320e63	0.960542	0.480271	+	0.877120i	$0.340538\pi$
$198$	−3.45551e63	−2.40005
$199$	5.87498e62	0.355260	0.177630	−	0.984097i	$-0.443157\pi$
$199$	5.87498e62	0.355260	0.177630	+	0.984097i	$0.443157\pi$
$200$	−3.20964e62	−0.169095
$201$	−3.07536e61	−0.0141255
$202$	3.52751e62	0.141353
$203$	2.28840e63	0.800553
$204$	−1.86822e62	−0.0570949
$205$	4.24963e63	1.13533
$206$	8.21597e63	1.92004
$207$	−4.06010e63	−0.830525
$208$	−4.79547e63	−0.859190
$209$	−8.48612e63	−1.33256
$210$	−5.00836e62	−0.0689707
$211$	−5.03247e63	−0.608154	−0.304077	−	0.952647i	$-0.598348\pi$
$211$	−5.03247e63	−0.608154	−0.304077	+	0.952647i	$0.598348\pi$
$212$	−2.92112e63	−0.309965
$213$	−1.17701e63	−0.109734
$214$	1.01217e64	0.829612
$215$	4.42350e63	0.318939
$216$	1.14097e63	0.0724097
$217$	−1.39189e64	−0.777972
$218$	3.53716e64	1.74221
$219$	4.31984e63	0.187609
$220$	−2.40494e64	−0.921469
$221$	1.25209e64	0.423494
$222$	4.46888e63	0.133503
$223$	−1.07577e64	−0.284011	−0.142005	−	0.989866i	$-0.545355\pi$
$223$	−1.07577e64	−0.284011	−0.142005	+	0.989866i	$0.545355\pi$
$224$	−3.46161e64	−0.808086
$225$	2.78979e64	0.576172
$226$	4.91009e63	0.0897651
$227$	1.74540e64	0.282608	0.141304	−	0.989966i	$-0.454870\pi$
$227$	1.74540e64	0.282608	0.141304	+	0.989966i	$0.454870\pi$
$228$	−5.03733e63	−0.0722757
$229$	−5.35119e64	−0.680729	−0.340365	−	0.940293i	$-0.610551\pi$
$229$	−5.35119e64	−0.680729	−0.340365	+	0.940293i	$0.610551\pi$
$230$	−6.43101e64	−0.725711
$231$	−1.46257e64	−0.146483
$232$	−4.09556e64	−0.364245
$233$	−1.94781e63	−0.0153907	−0.00769534	−	0.999970i	$-0.502450\pi$
$233$	−1.94781e63	−0.0153907	−0.00769534	+	0.999970i	$0.502450\pi$
$234$	1.37471e65	0.965552
$235$	1.90928e65	1.19262
$236$	9.86630e64	0.548371
$237$	−1.52320e64	−0.0753661
$238$	1.10884e65	0.488655
$239$	−2.84709e65	−1.11804	−0.559021	−	0.829153i	$-0.688823\pi$
$239$	−2.84709e65	−1.11804	−0.559021	+	0.829153i	$0.688823\pi$
$240$	2.71776e64	0.0951485
$241$	5.56433e65	1.73758	0.868789	−	0.495183i	$-0.164899\pi$
$241$	5.56433e65	1.73758	0.868789	+	0.495183i	$0.164899\pi$
$242$	−1.11909e66	−3.11846
$243$	−1.49157e65	−0.371084
$244$	−5.40743e64	−0.120163
$245$	−1.93590e65	−0.384429
$246$	1.67655e65	0.297646
$247$	3.37604e65	0.536095
$248$	2.49108e65	0.353971
$249$	−7.24988e64	−0.0922251
$250$	1.19658e66	1.36330
$251$	6.88623e65	0.702998	0.351499	−	0.936188i	$-0.385672\pi$
$251$	6.88623e65	0.702998	0.351499	+	0.936188i	$0.385672\pi$
$252$	5.34928e65	0.489531
$253$	−1.87803e66	−1.54130
$254$	−1.03731e66	−0.763805
$255$	−7.09601e64	−0.0468986
$256$	2.16399e66	1.28427
$257$	−2.10402e66	−1.12173	−0.560865	−	0.827907i	$-0.689531\pi$
$257$	−2.10402e66	−1.12173	−0.560865	+	0.827907i	$0.689531\pi$
$258$	1.74514e65	0.0836157
$259$	−1.16544e66	−0.502049
$260$	9.56761e65	0.370712
$261$	3.55982e66	1.24112
$262$	−3.85087e66	−1.20857
$263$	−2.52532e66	−0.713729	−0.356864	−	0.934156i	$-0.616154\pi$
$263$	−2.52532e66	−0.713729	−0.356864	+	0.934156i	$0.616154\pi$
$264$	2.61757e65	0.0666486
$265$	−1.10952e66	−0.254610
$266$	2.98980e66	0.618582
$267$	−7.80604e65	−0.145670
$268$	5.20281e65	0.0876054
$269$	7.93206e66	1.20559	0.602793	−	0.797898i	$-0.294054\pi$
$269$	7.93206e66	1.20559	0.602793	+	0.797898i	$0.294054\pi$
$270$	−1.57084e66	−0.215590
$271$	1.24975e67	1.54942	0.774708	−	0.632320i	$-0.217897\pi$
$271$	1.24975e67	1.54942	0.774708	+	0.632320i	$0.217897\pi$
$272$	−6.01706e66	−0.674124
$273$	5.81857e65	0.0589310
$274$	−1.77981e67	−1.63017
$275$	1.29043e67	1.06927
$276$	−1.11479e66	−0.0835975
$277$	−2.46968e67	−1.67666	−0.838332	−	0.545159i	$-0.816469\pi$
$277$	−2.46968e67	−1.67666	−0.838332	+	0.545159i	$0.816469\pi$
$278$	3.87942e66	0.238526
$279$	−2.16523e67	−1.20611
$280$	−2.33759e66	−0.118011
$281$	8.92136e66	0.408326	0.204163	−	0.978937i	$-0.434553\pi$
$281$	8.92136e66	0.408326	0.204163	+	0.978937i	$0.434553\pi$
$282$	7.53240e66	0.312668
$283$	3.98122e67	1.49930	0.749652	−	0.661832i	$-0.230221\pi$
$283$	3.98122e67	1.49930	0.749652	+	0.661832i	$0.230221\pi$
$284$	1.99123e67	0.680562
$285$	−1.91332e66	−0.0593683
$286$	6.35881e67	1.79189
$287$	−4.37227e67	−1.11932
$288$	−5.38487e67	−1.25280
$289$	−3.15710e67	−0.667725
$290$	5.63859e67	1.08449
$291$	1.40128e66	0.0245170
$292$	−7.30819e67	−1.16354
$293$	−1.37145e67	−0.198756	−0.0993781	−	0.995050i	$-0.531685\pi$
$293$	−1.37145e67	−0.198756	−0.0993781	+	0.995050i	$0.531685\pi$
$294$	−7.63744e66	−0.100785
$295$	3.74750e67	0.450439
$296$	2.08580e67	0.228428
$297$	−4.58726e67	−0.457880
$298$	−2.81186e67	−0.255886
$299$	7.47138e67	0.620073
$300$	7.65997e66	0.0579953
$301$	−4.55115e67	−0.314443
$302$	1.38735e68	0.874971
$303$	2.32257e66	0.0133751
$304$	−1.62240e68	−0.853365
$305$	−2.05390e67	−0.0987036
$306$	1.72491e68	0.757576
$307$	1.08516e68	0.435700	0.217850	−	0.975982i	$-0.430096\pi$
$307$	1.08516e68	0.435700	0.217850	+	0.975982i	$0.430096\pi$
$308$	2.47434e68	0.908479
$309$	5.40954e67	0.181678
$310$	−3.42962e68	−1.05390
$311$	1.44511e67	0.0406435	0.0203218	−	0.999793i	$-0.493531\pi$
$311$	1.44511e67	0.0406435	0.0203218	+	0.999793i	$0.493531\pi$
$312$	−1.04135e67	−0.0268131
$313$	−5.45217e68	−1.28558	−0.642792	−	0.766041i	$-0.722224\pi$
$313$	−5.45217e68	−1.28558	−0.642792	+	0.766041i	$0.722224\pi$
$314$	−7.61252e68	−1.64423
$315$	2.03181e68	0.402108
$316$	2.57690e68	0.467416
$317$	−1.76696e68	−0.293831	−0.146915	−	0.989149i	$-0.546935\pi$
$317$	−1.76696e68	−0.293831	−0.146915	+	0.989149i	$0.546935\pi$
$318$	−4.37725e67	−0.0667506
$319$	1.64662e69	2.30329
$320$	−2.66306e68	−0.341787
$321$	6.66430e67	0.0784994
$322$	6.61660e68	0.715481
$323$	4.23606e68	0.420622
$324$	8.18407e68	0.746417
$325$	−5.13375e68	−0.430172
$326$	−2.49658e69	−1.92248
$327$	2.32893e68	0.164852
$328$	7.82508e68	0.509282
$329$	−1.96438e69	−1.17581
$330$	−3.60376e68	−0.198437
$331$	−8.48541e68	−0.429935	−0.214968	−	0.976621i	$-0.568965\pi$
$331$	−8.48541e68	−0.429935	−0.214968	+	0.976621i	$0.568965\pi$
$332$	1.22652e69	0.571974
$333$	−1.81295e69	−0.778341
$334$	2.58904e69	1.02355
$335$	1.97617e68	0.0719603
$336$	−2.79619e68	−0.0938072
$337$	1.81937e69	0.562469	0.281235	−	0.959639i	$-0.409256\pi$
$337$	1.81937e69	0.562469	0.281235	+	0.959639i	$0.409256\pi$
$338$	2.15709e69	0.614693
$339$	3.23289e67	0.00849374
$340$	1.20049e69	0.290862
$341$	−1.00154e70	−2.23832
$342$	4.65092e69	0.959005
$343$	5.32736e69	1.01373
$344$	8.14522e68	0.143069
$345$	−4.23429e68	−0.0686682
$346$	−1.06861e70	−1.60039
$347$	1.13939e70	1.57620	0.788102	−	0.615545i	$-0.211064\pi$
$347$	1.13939e70	1.57620	0.788102	+	0.615545i	$0.211064\pi$
$348$	9.77426e68	0.124927
$349$	6.76066e68	0.0798527	0.0399264	−	0.999203i	$-0.487288\pi$
$349$	6.76066e68	0.0798527	0.0399264	+	0.999203i	$0.487288\pi$
$350$	−4.54641e69	−0.496361
$351$	1.82496e69	0.184207
$352$	−2.49080e70	−2.32496
$353$	−5.30555e69	−0.458063	−0.229032	−	0.973419i	$-0.573556\pi$
$353$	−5.30555e69	−0.458063	−0.229032	+	0.973419i	$0.573556\pi$
$354$	1.47845e69	0.118091
$355$	7.56327e69	0.559024
$356$	1.32061e70	0.903438
$357$	7.30079e68	0.0462374
$358$	−2.46643e69	−0.144639
$359$	2.52249e70	1.37004	0.685019	−	0.728525i	$-0.259794\pi$
$359$	2.52249e70	1.37004	0.685019	+	0.728525i	$0.259794\pi$
$360$	−3.63634e69	−0.182956
$361$	−1.00292e70	−0.467540
$362$	4.96445e70	2.14480
$363$	−7.36825e69	−0.295075
$364$	−9.84371e69	−0.365486
$365$	−2.77586e70	−0.955749
$366$	−8.10294e68	−0.0258769
$367$	1.59497e70	0.472536	0.236268	−	0.971688i	$-0.424076\pi$
$367$	1.59497e70	0.472536	0.236268	+	0.971688i	$0.424076\pi$
$368$	−3.59046e70	−0.987042
$369$	−6.80148e70	−1.73532
$370$	−2.87163e70	−0.680114
$371$	1.14154e70	0.251021
$372$	−5.94510e69	−0.121403
$373$	5.86255e70	1.11197	0.555986	−	0.831192i	$-0.312341\pi$
$373$	5.86255e70	1.11197	0.555986	+	0.831192i	$0.312341\pi$
$374$	7.97865e70	1.40592
$375$	7.87850e69	0.128998
$376$	3.51566e70	0.534984
$377$	−6.55076e70	−0.926626
$378$	1.61617e70	0.212551
$379$	2.57732e70	0.315203	0.157601	−	0.987503i	$-0.449624\pi$
$379$	2.57732e70	0.315203	0.157601	+	0.987503i	$0.449624\pi$
$380$	3.23691e70	0.368198
$381$	−6.82984e69	−0.0722726
$382$	−9.87613e70	−0.972399
$383$	−9.29502e69	−0.0851695	−0.0425848	−	0.999093i	$-0.513559\pi$
$383$	−9.29502e69	−0.0851695	−0.0425848	+	0.999093i	$0.513559\pi$
$384$	8.35822e69	0.0712861
$385$	9.39825e70	0.746237
$386$	3.35531e70	0.248075
$387$	−7.07974e70	−0.487490
$388$	−2.37065e70	−0.152053
$389$	−1.45270e71	−0.868083	−0.434042	−	0.900893i	$-0.642913\pi$
$389$	−1.45270e71	−0.868083	−0.434042	+	0.900893i	$0.642913\pi$
$390$	1.43369e70	0.0798323
$391$	9.37463e70	0.486512
$392$	−3.56468e70	−0.172446
$393$	−2.53548e70	−0.114357
$394$	−3.05022e71	−1.28288
$395$	9.78781e70	0.383942
$396$	3.84907e71	1.40844
$397$	−2.04970e71	−0.699762	−0.349881	−	0.936794i	$-0.613778\pi$
$397$	−2.04970e71	−0.699762	−0.349881	+	0.936794i	$0.613778\pi$
$398$	−1.48936e71	−0.474478
$399$	1.96854e70	0.0585314
$400$	2.46709e71	0.684755
$401$	4.58836e71	1.18901	0.594507	−	0.804090i	$-0.297347\pi$
$401$	4.58836e71	1.18901	0.594507	+	0.804090i	$0.297347\pi$
$402$	7.79632e69	0.0188657
$403$	3.98443e71	0.900488
$404$	−3.92927e70	−0.0829514
$405$	3.10854e71	0.613117
$406$	−5.80130e71	−1.06920
$407$	−8.38592e71	−1.44446
$408$	−1.30663e70	−0.0210376
$409$	4.48457e71	0.675040	0.337520	−	0.941318i	$-0.390412\pi$
$409$	4.48457e71	0.675040	0.337520	+	0.941318i	$0.390412\pi$
$410$	−1.07732e72	−1.51632
$411$	−1.17186e71	−0.154250
$412$	−9.15172e71	−1.12675
$413$	−3.85564e71	−0.444090
$414$	1.02927e72	1.10923
$415$	4.65866e71	0.469827
$416$	9.90919e71	0.935345
$417$	2.55428e70	0.0225697
$418$	2.15131e72	1.77974
$419$	−1.42128e72	−1.10102	−0.550510	−	0.834829i	$-0.685567\pi$
$419$	−1.42128e72	−1.10102	−0.550510	+	0.834829i	$0.685567\pi$
$420$	5.57877e70	0.0404747
$421$	1.37600e72	0.935105	0.467553	−	0.883965i	$-0.345136\pi$
$421$	1.37600e72	0.935105	0.467553	+	0.883965i	$0.345136\pi$
$422$	1.27578e72	0.812237
$423$	−3.05577e72	−1.82289
$424$	−2.04303e71	−0.114212
$425$	−6.44152e71	−0.337515
$426$	2.98383e71	0.146558
$427$	2.11317e71	0.0973121
$428$	−1.12745e72	−0.486848
$429$	4.18675e71	0.169552
$430$	−1.12140e72	−0.425968
$431$	−7.40627e71	−0.263921	−0.131961	−	0.991255i	$-0.542127\pi$
$431$	−7.40627e71	−0.263921	−0.131961	+	0.991255i	$0.542127\pi$
$432$	−8.77007e71	−0.293224
$433$	6.68781e71	0.209830	0.104915	−	0.994481i	$-0.466543\pi$
$433$	6.68781e71	0.209830	0.104915	+	0.994481i	$0.466543\pi$
$434$	3.52859e72	1.03904
$435$	3.71254e71	0.102616
$436$	−3.94002e72	−1.02240
$437$	2.52771e72	0.615869
$438$	−1.09512e72	−0.250567
$439$	−8.16335e70	−0.0175426	−0.00877130	−	0.999962i	$-0.502792\pi$
$439$	−8.16335e70	−0.0175426	−0.00877130	+	0.999962i	$0.502792\pi$
$440$	−1.68201e72	−0.339532
$441$	3.09839e72	0.587590
$442$	−3.17416e72	−0.565609
$443$	5.10956e72	0.855620	0.427810	−	0.903869i	$-0.359285\pi$
$443$	5.10956e72	0.855620	0.427810	+	0.903869i	$0.359285\pi$
$444$	−4.97786e71	−0.0783449
$445$	5.01604e72	0.742097
$446$	2.72717e72	0.379319
$447$	−1.85138e71	−0.0242124
$448$	2.73991e72	0.336969
$449$	1.18229e73	1.36757	0.683783	−	0.729686i	$-0.260334\pi$
$449$	1.18229e73	1.36757	0.683783	+	0.729686i	$0.260334\pi$
$450$	−7.07238e72	−0.769523
$451$	−3.14607e73	−3.22042
$452$	−5.46932e71	−0.0526776
$453$	9.13452e71	0.0827914
$454$	−4.42476e72	−0.377445
$455$	−3.73892e72	−0.300215
$456$	−3.52310e71	−0.0266313
$457$	2.45595e72	0.174793	0.0873965	−	0.996174i	$-0.472145\pi$
$457$	2.45595e72	0.174793	0.0873965	+	0.996174i	$0.472145\pi$
$458$	1.35658e73	0.909167
$459$	2.28985e72	0.144530
$460$	7.16346e72	0.425875
$461$	−1.10101e73	−0.616617	−0.308308	−	0.951286i	$-0.599763\pi$
$461$	−1.10101e73	−0.616617	−0.308308	+	0.951286i	$0.599763\pi$
$462$	3.70776e72	0.195640
$463$	1.97086e73	0.979893	0.489946	−	0.871753i	$-0.337016\pi$
$463$	1.97086e73	0.979893	0.489946	+	0.871753i	$0.337016\pi$
$464$	3.14805e73	1.47502
$465$	−2.25812e72	−0.0997219
$466$	4.93787e71	0.0205555
$467$	1.75061e72	0.0687029	0.0343514	−	0.999410i	$-0.489063\pi$
$467$	1.75061e72	0.0687029	0.0343514	+	0.999410i	$0.489063\pi$
$468$	−1.53128e73	−0.566623
$469$	−2.03320e72	−0.0709459
$470$	−4.84020e73	−1.59284
$471$	−5.01221e72	−0.155580
$472$	6.90047e72	0.202057
$473$	−3.27478e73	−0.904692
$474$	3.86144e72	0.100657
$475$	−1.73685e73	−0.427256
$476$	−1.23513e73	−0.286762
$477$	1.77578e73	0.389164
$478$	7.21763e73	1.49323
$479$	2.63640e73	0.514973	0.257486	−	0.966282i	$-0.417106\pi$
$479$	2.63640e73	0.514973	0.257486	+	0.966282i	$0.417106\pi$
$480$	−5.61589e72	−0.103582
$481$	3.33618e73	0.581113
$482$	−1.41061e74	−2.32067
$483$	4.35648e72	0.0677002
$484$	1.24654e74	1.83004
$485$	−9.00441e72	−0.124899
$486$	3.78128e73	0.495611
$487$	−1.06044e74	−1.31353	−0.656764	−	0.754097i	$-0.728075\pi$
$487$	−1.06044e74	−1.31353	−0.656764	+	0.754097i	$0.728075\pi$
$488$	−3.78195e72	−0.0442762
$489$	−1.64379e73	−0.181908
$490$	4.90770e73	0.513435
$491$	1.83618e74	1.81624	0.908120	−	0.418709i	$-0.137517\pi$
$491$	1.83618e74	1.81624	0.908120	+	0.418709i	$0.137517\pi$
$492$	−1.86749e73	−0.174670
$493$	−8.21949e73	−0.727034
$494$	−8.55859e73	−0.715997
$495$	1.46199e74	1.15691
$496$	−1.91477e74	−1.43341
$497$	−7.78153e73	−0.551143
$498$	1.83791e73	0.123174
$499$	5.91416e73	0.375084	0.187542	−	0.982257i	$-0.439948\pi$
$499$	5.91416e73	0.375084	0.187542	+	0.982257i	$0.439948\pi$
$500$	−1.33286e74	−0.800038
$501$	1.70467e73	0.0968505
$502$	−1.74572e74	−0.938909
$503$	−4.36885e73	−0.222458	−0.111229	−	0.993795i	$-0.535479\pi$
$503$	−4.36885e73	−0.222458	−0.111229	+	0.993795i	$0.535479\pi$
$504$	3.74128e73	0.180377
$505$	−1.49245e73	−0.0681375
$506$	4.76097e74	2.05853
$507$	1.42026e73	0.0581634
$508$	1.15545e74	0.448230
$509$	1.21337e74	0.445918	0.222959	−	0.974828i	$-0.428428\pi$
$509$	1.21337e74	0.445918	0.222959	+	0.974828i	$0.428428\pi$
$510$	1.79891e73	0.0626367
$511$	2.85596e74	0.942276
$512$	−3.68179e74	−1.15116
$513$	6.17419e73	0.182958
$514$	5.33388e74	1.49816
$515$	−3.47608e74	−0.925532
$516$	−1.94390e73	−0.0490689
$517$	−1.41347e75	−3.38295
$518$	2.95450e74	0.670526
$519$	−7.03589e73	−0.151432
$520$	6.69157e73	0.136595
$521$	−1.79330e74	−0.347228	−0.173614	−	0.984814i	$-0.555544\pi$
$521$	−1.79330e74	−0.347228	−0.173614	+	0.984814i	$0.555544\pi$
$522$	−9.02448e74	−1.65761
$523$	9.32612e74	1.62519	0.812595	−	0.582828i	$-0.198054\pi$
$523$	9.32612e74	1.62519	0.812595	+	0.582828i	$0.198054\pi$
$524$	4.28945e74	0.709237
$525$	−2.99344e73	−0.0469666
$526$	6.40192e74	0.953240
$527$	4.99942e74	0.706526
$528$	−2.01200e74	−0.269895
$529$	−2.25895e74	−0.287657
$530$	2.81275e74	0.340051
$531$	−5.99782e74	−0.688485
$532$	−3.33032e74	−0.363008
$533$	1.25160e75	1.29559
$534$	1.97890e74	0.194554
$535$	−4.28238e74	−0.399904
$536$	3.63884e73	0.0322798
$537$	−1.62394e73	−0.0136860
$538$	−2.01085e75	−1.61015
$539$	1.43318e75	1.09046
$540$	1.74975e74	0.126516
$541$	1.34700e75	0.925643	0.462821	−	0.886452i	$-0.346837\pi$
$541$	1.34700e75	0.925643	0.462821	+	0.886452i	$0.346837\pi$
$542$	−3.16824e75	−2.06936
$543$	3.26868e74	0.202945
$544$	1.24335e75	0.733875
$545$	−1.49653e75	−0.839813
$546$	−1.47506e74	−0.0787069
$547$	4.61467e74	0.234147	0.117074	−	0.993123i	$-0.462649\pi$
$547$	4.61467e74	0.234147	0.117074	+	0.993123i	$0.462649\pi$
$548$	1.98252e75	0.956649
$549$	3.28723e74	0.150866
$550$	−3.27137e75	−1.42809
$551$	−2.21625e75	−0.920343
$552$	−7.79682e73	−0.0308030
$553$	−1.00703e75	−0.378530
$554$	6.26086e75	2.23932
$555$	−1.89073e74	−0.0643536
$556$	−4.32126e74	−0.139976
$557$	6.63429e74	0.204539	0.102270	−	0.994757i	$-0.467390\pi$
$557$	6.63429e74	0.204539	0.102270	+	0.994757i	$0.467390\pi$
$558$	5.48905e75	1.61086
$559$	1.30281e75	0.363962
$560$	1.79679e75	0.477887
$561$	5.25328e74	0.133031
$562$	−2.26165e75	−0.545351
$563$	−5.61240e75	−1.28875	−0.644374	−	0.764711i	$-0.722882\pi$
$563$	−5.61240e75	−1.28875	−0.644374	+	0.764711i	$0.722882\pi$
$564$	−8.39029e74	−0.183486
$565$	−2.07740e74	−0.0432701
$566$	−1.00928e76	−2.00244
$567$	−3.19825e75	−0.604474
$568$	1.39267e75	0.250765
$569$	4.79302e75	0.822284	0.411142	−	0.911571i	$-0.365130\pi$
$569$	4.79302e75	0.822284	0.411142	+	0.911571i	$0.365130\pi$
$570$	4.85045e74	0.0792910
$571$	−5.95554e74	−0.0927744	−0.0463872	−	0.998924i	$-0.514771\pi$
$571$	−5.95554e74	−0.0927744	−0.0463872	+	0.998924i	$0.514771\pi$
$572$	−7.08304e75	−1.05155
$573$	−6.50261e74	−0.0920102
$574$	1.10841e76	1.49494
$575$	−3.84374e75	−0.494184
$576$	4.26218e75	0.522413
$577$	1.32597e76	1.54952	0.774760	−	0.632255i	$-0.217870\pi$
$577$	1.32597e76	1.54952	0.774760	+	0.632255i	$0.217870\pi$
$578$	8.00355e75	0.891799
$579$	2.20920e74	0.0234733
$580$	−6.28078e75	−0.636420
$581$	−4.79310e75	−0.463204
$582$	−3.55238e74	−0.0327444
$583$	8.21397e75	0.722217
$584$	−5.11134e75	−0.428728
$585$	−5.81625e75	−0.465432
$586$	3.47676e75	0.265454
$587$	−2.33966e76	−1.70453	−0.852264	−	0.523112i	$-0.824771\pi$
$587$	−2.33966e76	−1.70453	−0.852264	+	0.523112i	$0.824771\pi$
$588$	8.50730e74	0.0591446
$589$	1.34801e76	0.894382
$590$	−9.50027e75	−0.601597
$591$	−2.00832e75	−0.121388
$592$	−1.60325e76	−0.925024
$593$	2.05903e76	1.13412	0.567060	−	0.823677i	$-0.308081\pi$
$593$	2.05903e76	1.13412	0.567060	+	0.823677i	$0.308081\pi$
$594$	1.16291e76	0.611534
$595$	−4.69137e75	−0.235550
$596$	3.13211e75	0.150164
$597$	−9.80621e74	−0.0448960
$598$	−1.89406e76	−0.828156
$599$	6.44964e75	0.269338	0.134669	−	0.990891i	$-0.457003\pi$
$599$	6.44964e75	0.269338	0.134669	+	0.990891i	$0.457003\pi$
$600$	5.35737e74	0.0213694
$601$	−8.53957e75	−0.325378	−0.162689	−	0.986677i	$-0.552017\pi$
$601$	−8.53957e75	−0.325378	−0.162689	+	0.986677i	$0.552017\pi$
$602$	1.15376e76	0.419964
$603$	−3.16284e75	−0.109989
$604$	−1.54535e76	−0.513467
$605$	4.73472e76	1.50322
$606$	−5.88794e74	−0.0178635
$607$	−1.28402e76	−0.372292	−0.186146	−	0.982522i	$-0.559600\pi$
$607$	−1.28402e76	−0.372292	−0.186146	+	0.982522i	$0.559600\pi$
$608$	3.35247e76	0.929003
$609$	−3.81968e75	−0.101170
$610$	5.20682e75	0.131826
$611$	5.62322e76	1.36098
$612$	−1.92136e76	−0.444575
$613$	−4.44481e76	−0.983310	−0.491655	−	0.870790i	$-0.663608\pi$
$613$	−4.44481e76	−0.983310	−0.491655	+	0.870790i	$0.663608\pi$
$614$	−2.75098e76	−0.581911
$615$	−7.09328e75	−0.143477
$616$	1.73055e76	0.334745
$617$	−7.75771e76	−1.43513	−0.717565	−	0.696491i	$-0.754743\pi$
$617$	−7.75771e76	−1.43513	−0.717565	+	0.696491i	$0.754743\pi$
$618$	−1.37137e76	−0.242645
$619$	−5.51294e76	−0.933018	−0.466509	−	0.884516i	$-0.654489\pi$
$619$	−5.51294e76	−0.933018	−0.466509	+	0.884516i	$0.654489\pi$
$620$	3.82023e76	0.618468
$621$	1.36638e76	0.211618
$622$	−3.66350e75	−0.0542826
$623$	−5.16079e76	−0.731635
$624$	8.00436e75	0.108580
$625$	−5.51891e75	−0.0716396
$626$	1.38218e77	1.71700
$627$	1.41646e76	0.168402
$628$	8.47953e76	0.964898
$629$	4.18604e76	0.455943
$630$	−5.15083e76	−0.537046
$631$	4.85602e76	0.484700	0.242350	−	0.970189i	$-0.422082\pi$
$631$	4.85602e76	0.484700	0.242350	+	0.970189i	$0.422082\pi$
$632$	1.80228e76	0.172228
$633$	8.39995e75	0.0768554
$634$	4.47941e76	0.392434
$635$	4.38875e76	0.368182
$636$	4.87578e75	0.0391718
$637$	−5.70163e76	−0.438697
$638$	−4.17433e77	−3.07622
$639$	−1.21049e77	−0.854453
$640$	−5.37086e76	−0.363157
$641$	6.99794e76	0.453288	0.226644	−	0.973978i	$-0.427225\pi$
$641$	6.99794e76	0.453288	0.226644	+	0.973978i	$0.427225\pi$
$642$	−1.68946e76	−0.104842
$643$	3.34658e77	1.98976	0.994878	−	0.101085i	$-0.0322315\pi$
$643$	3.34658e77	1.98976	0.994878	+	0.101085i	$0.0322315\pi$
$644$	−7.37018e76	−0.419872
$645$	−7.38348e75	−0.0403059
$646$	−1.07388e77	−0.561774
$647$	2.48806e77	1.24736	0.623682	−	0.781678i	$-0.285636\pi$
$647$	2.48806e77	1.24736	0.623682	+	0.781678i	$0.285636\pi$
$648$	5.72393e76	0.275031
$649$	−2.77433e77	−1.27770
$650$	1.30145e77	0.574529
$651$	2.32328e76	0.0983161
$652$	2.78092e77	1.12818
$653$	−2.62237e77	−1.01995	−0.509977	−	0.860188i	$-0.670346\pi$
$653$	−2.62237e77	−1.01995	−0.509977	+	0.860188i	$0.670346\pi$
$654$	−5.90406e76	−0.220172
$655$	1.62926e77	0.582578
$656$	−6.01474e77	−2.06235
$657$	4.44272e77	1.46084
$658$	4.97988e77	1.57039
$659$	1.03940e77	0.314364	0.157182	−	0.987570i	$-0.449759\pi$
$659$	1.03940e77	0.314364	0.157182	+	0.987570i	$0.449759\pi$
$660$	4.01421e76	0.116451
$661$	−6.71301e77	−1.86800	−0.934001	−	0.357271i	$-0.883707\pi$
$661$	−6.71301e77	−1.86800	−0.934001	+	0.357271i	$0.883707\pi$
$662$	2.15113e77	0.574212
$663$	−2.08992e76	−0.0535190
$664$	8.57824e76	0.210754
$665$	−1.26495e77	−0.298180
$666$	4.59601e77	1.03954
$667$	−4.90468e77	−1.06451
$668$	−2.88391e77	−0.600660
$669$	1.79562e76	0.0358918
$670$	−5.00979e76	−0.0961086
$671$	1.52053e77	0.279979
$672$	5.77795e76	0.102122
$673$	−6.81160e77	−1.15567	−0.577836	−	0.816153i	$-0.696103\pi$
$673$	−6.81160e77	−1.15567	−0.577836	+	0.816153i	$0.696103\pi$
$674$	−4.61228e77	−0.751222
$675$	−9.38873e76	−0.146809
$676$	−2.40276e77	−0.360726
$677$	9.16173e77	1.32065	0.660327	−	0.750978i	$-0.270418\pi$
$677$	9.16173e77	1.32065	0.660327	+	0.750978i	$0.270418\pi$
$678$	−8.19568e75	−0.0113441
$679$	9.26425e76	0.123138
$680$	8.39618e76	0.107173
$681$	−2.91334e76	−0.0357146
$682$	2.53899e78	2.98945
$683$	4.97477e77	0.562605	0.281302	−	0.959619i	$-0.409234\pi$
$683$	4.97477e77	0.562605	0.281302	+	0.959619i	$0.409234\pi$
$684$	−5.18063e77	−0.562781
$685$	7.53018e77	0.785805
$686$	−1.35054e78	−1.35392
$687$	8.93193e76	0.0860271
$688$	−6.26082e77	−0.579361
$689$	−3.26777e77	−0.290552
$690$	1.07343e77	0.0917117
$691$	−8.52274e77	−0.699734	−0.349867	−	0.936799i	$-0.613773\pi$
$691$	−8.52274e77	−0.699734	−0.349867	+	0.936799i	$0.613773\pi$
$692$	1.19031e78	0.939169
$693$	−1.50418e78	−1.14060
$694$	−2.88846e78	−2.10514
$695$	−1.64134e77	−0.114978
$696$	6.83610e76	0.0460314
$697$	1.57044e78	1.01653
$698$	−1.71389e77	−0.106650
$699$	3.25118e75	0.00194500
$700$	5.06422e77	0.291284
$701$	7.03498e77	0.389061	0.194530	−	0.980897i	$-0.437682\pi$
$701$	7.03498e77	0.389061	0.194530	+	0.980897i	$0.437682\pi$
$702$	−4.62644e77	−0.246023
$703$	1.12870e78	0.577173
$704$	1.97150e78	0.969501
$705$	−3.18687e77	−0.150718
$706$	1.34501e78	0.611779
$707$	1.53552e77	0.0671769
$708$	−1.64683e77	−0.0693003
$709$	2.01205e77	0.0814455	0.0407227	−	0.999170i	$-0.487034\pi$
$709$	2.01205e77	0.0814455	0.0407227	+	0.999170i	$0.487034\pi$
$710$	−1.91736e78	−0.746620
$711$	−1.56653e78	−0.586845
$712$	9.23630e77	0.332888
$713$	2.98323e78	1.03448
$714$	−1.85082e77	−0.0617537
$715$	−2.69034e78	−0.863756
$716$	2.74734e77	0.0848797
$717$	4.75221e77	0.141292
$718$	−6.39476e78	−1.82979
$719$	−2.93009e76	−0.00806930	−0.00403465	−	0.999992i	$-0.501284\pi$
$719$	−2.93009e76	−0.00806930	−0.00403465	+	0.999992i	$0.501284\pi$
$720$	2.79507e78	0.740882
$721$	3.57639e78	0.912485
$722$	2.54250e78	0.624436
$723$	−9.28770e77	−0.219586
$724$	−5.52987e78	−1.25865
$725$	3.37012e78	0.738499
$726$	1.86792e78	0.394096
$727$	−8.75892e78	−1.77932	−0.889660	−	0.456623i	$-0.849059\pi$
$727$	−8.75892e78	−1.77932	−0.889660	+	0.456623i	$0.849059\pi$
$728$	−6.88467e77	−0.134670
$729$	−4.80696e78	−0.905448
$730$	7.03707e78	1.27648
$731$	1.63469e78	0.285566
$732$	9.02581e76	0.0151856
$733$	−2.53375e77	−0.0410587	−0.0205293	−	0.999789i	$-0.506535\pi$
$733$	−2.53375e77	−0.0410587	−0.0205293	+	0.999789i	$0.506535\pi$
$734$	−4.04340e78	−0.631109
$735$	3.23131e77	0.0485822
$736$	7.41921e78	1.07453
$737$	−1.46299e78	−0.204120
$738$	1.72424e79	2.31765
$739$	1.48231e78	0.191963	0.0959814	−	0.995383i	$-0.469401\pi$
$739$	1.48231e78	0.191963	0.0959814	+	0.995383i	$0.469401\pi$
$740$	3.19869e78	0.399117
$741$	−5.63512e77	−0.0677490
$742$	−2.89392e78	−0.335258
$743$	−5.63544e78	−0.629123	−0.314562	−	0.949237i	$-0.601857\pi$
$743$	−5.63544e78	−0.629123	−0.314562	+	0.949237i	$0.601857\pi$
$744$	−4.15799e77	−0.0447330
$745$	1.18967e78	0.123347
$746$	−1.48621e79	−1.48512
$747$	−7.45612e78	−0.718119
$748$	−8.88736e78	−0.825048
$749$	4.40595e78	0.394267
$750$	−1.99727e78	−0.172287
$751$	1.33575e79	1.11078	0.555390	−	0.831590i	$-0.312569\pi$
$751$	1.33575e79	1.11078	0.555390	+	0.831590i	$0.312569\pi$
$752$	−2.70231e79	−2.16643
$753$	−1.14941e78	−0.0888413
$754$	1.66068e79	1.23758
$755$	−5.86970e78	−0.421769
$756$	−1.80024e78	−0.124733
$757$	1.85609e79	1.24011	0.620057	−	0.784557i	$-0.287109\pi$
$757$	1.85609e79	1.24011	0.620057	+	0.784557i	$0.287109\pi$
$758$	−6.53374e78	−0.420978
$759$	3.13471e78	0.194782
$760$	2.26389e78	0.135669
$761$	1.97639e79	1.14234	0.571170	−	0.820832i	$-0.306490\pi$
$761$	1.97639e79	1.14234	0.571170	+	0.820832i	$0.306490\pi$
$762$	1.73143e78	0.0965257
$763$	1.53972e79	0.827974
$764$	1.10010e79	0.570641
$765$	−7.29787e78	−0.365180
$766$	2.35638e78	0.113751
$767$	1.10372e79	0.514025
$768$	−3.61203e78	−0.162300
$769$	−3.59924e79	−1.56040	−0.780200	−	0.625530i	$-0.784883\pi$
$769$	−3.59924e79	−1.56040	−0.780200	+	0.625530i	$0.784883\pi$
$770$	−2.38255e79	−0.996658
$771$	3.51192e78	0.141758
$772$	−3.73746e78	−0.145580
$773$	−2.27297e79	−0.854392	−0.427196	−	0.904159i	$-0.640499\pi$
$773$	−2.27297e79	−0.854392	−0.427196	+	0.904159i	$0.640499\pi$
$774$	1.79478e79	0.651081
$775$	−2.04984e79	−0.717668
$776$	−1.65803e78	−0.0560267
$777$	1.94529e78	0.0634464
$778$	3.68273e79	1.15939
$779$	4.23442e79	1.28681
$780$	−1.59698e78	−0.0468487
$781$	−5.59920e79	−1.58571
$782$	−2.37656e79	−0.649774
$783$	−1.19802e79	−0.316239
$784$	2.73999e79	0.698325
$785$	3.22077e79	0.792581
$786$	6.42767e78	0.152733
$787$	−5.18302e79	−1.18926	−0.594632	−	0.803998i	$-0.702702\pi$
$787$	−5.18302e79	−1.18926	−0.594632	+	0.803998i	$0.702702\pi$
$788$	3.39762e79	0.752843
$789$	4.21514e78	0.0901974
$790$	−2.48130e79	−0.512784
$791$	2.13735e78	0.0426602
$792$	2.69204e79	0.518965
$793$	−6.04914e78	−0.112637
$794$	5.19617e79	0.934587
$795$	1.85196e78	0.0321763
$796$	1.65899e79	0.278442
$797$	9.77267e78	0.158456	0.0792281	−	0.996857i	$-0.474754\pi$
$797$	9.77267e78	0.158456	0.0792281	+	0.996857i	$0.474754\pi$
$798$	−4.99042e78	−0.0781732
$799$	7.05567e79	1.06783
$800$	−5.09791e79	−0.745448
$801$	−8.02810e79	−1.13428
$802$	−1.16319e80	−1.58802
$803$	2.05501e80	2.71104
$804$	−8.68426e77	−0.0110711
$805$	−2.79941e79	−0.344889
$806$	−1.01009e80	−1.20267
$807$	−1.32398e79	−0.152356
$808$	−2.74812e78	−0.0305649
$809$	−9.21478e79	−0.990605	−0.495302	−	0.868721i	$-0.664943\pi$
$809$	−9.21478e79	−0.990605	−0.495302	+	0.868721i	$0.664943\pi$
$810$	−7.88045e79	−0.818866
$811$	−1.39482e80	−1.40102	−0.700512	−	0.713640i	$-0.747045\pi$
$811$	−1.39482e80	−1.40102	−0.700512	+	0.713640i	$0.747045\pi$
$812$	6.46203e79	0.627449
$813$	−2.08602e79	−0.195807
$814$	2.12591e80	1.92919
$815$	1.05627e80	0.926707
$816$	1.00434e79	0.0851923
$817$	4.40766e79	0.361494
$818$	−1.13688e80	−0.901569
$819$	5.98409e79	0.458871
$820$	1.20002e80	0.889833
$821$	2.16763e80	1.55435	0.777173	−	0.629287i	$-0.216653\pi$
$821$	2.16763e80	1.55435	0.777173	+	0.629287i	$0.216653\pi$
$822$	2.97077e79	0.206013
$823$	1.36117e79	0.0912885	0.0456443	−	0.998958i	$-0.485466\pi$
$823$	1.36117e79	0.0912885	0.0456443	+	0.998958i	$0.485466\pi$
$824$	−6.40070e79	−0.415173
$825$	−2.15393e79	−0.135129
$826$	9.77442e79	0.593116
$827$	−2.71679e80	−1.59461	−0.797304	−	0.603578i	$-0.793741\pi$
$827$	−2.71679e80	−1.59461	−0.797304	+	0.603578i	$0.793741\pi$
$828$	−1.14650e80	−0.650939
$829$	−4.14313e79	−0.227551	−0.113775	−	0.993506i	$-0.536294\pi$
$829$	−4.14313e79	−0.227551	−0.113775	+	0.993506i	$0.536294\pi$
$830$	−1.18101e80	−0.627491
$831$	4.12226e79	0.211888
$832$	−7.84324e79	−0.390036
$833$	−7.15406e79	−0.344203
$834$	−6.47534e78	−0.0301437
$835$	−1.09539e80	−0.493391
$836$	−2.39633e80	−1.04442
$837$	7.28683e79	0.307318
$838$	3.60309e80	1.47050
$839$	2.91878e80	1.15278	0.576392	−	0.817173i	$-0.304460\pi$
$839$	2.91878e80	1.15278	0.576392	+	0.817173i	$0.304460\pi$
$840$	3.90179e78	0.0149136
$841$	1.59706e80	0.590787
$842$	−3.48829e80	−1.24891
$843$	−1.48911e79	−0.0516022
$844$	−1.42108e80	−0.476652
$845$	−9.12638e79	−0.296305
$846$	7.74668e80	2.43462
$847$	−4.87135e80	−1.48203
$848$	1.57037e80	0.462505
$849$	−6.64526e79	−0.189474
$850$	1.63299e80	0.450777
$851$	2.49787e80	0.667585
$852$	−3.32367e79	−0.0860060
$853$	−1.94977e80	−0.488523	−0.244262	−	0.969709i	$-0.578546\pi$
$853$	−1.94977e80	−0.488523	−0.244262	+	0.969709i	$0.578546\pi$
$854$	−5.35707e79	−0.129968
$855$	−1.96775e80	−0.462277
$856$	−7.88537e79	−0.179388
$857$	5.30574e80	1.16889	0.584444	−	0.811434i	$-0.301313\pi$
$857$	5.30574e80	1.16889	0.584444	+	0.811434i	$0.301313\pi$
$858$	−1.06138e80	−0.226449
$859$	−3.08064e80	−0.636545	−0.318272	−	0.947999i	$-0.603103\pi$
$859$	−3.08064e80	−0.636545	−0.318272	+	0.947999i	$0.603103\pi$
$860$	1.24912e80	0.249975
$861$	7.29797e79	0.141454
$862$	1.87756e80	0.352488
$863$	−7.74696e80	−1.40875	−0.704376	−	0.709827i	$-0.748773\pi$
$863$	−7.74696e80	−1.40875	−0.704376	+	0.709827i	$0.748773\pi$
$864$	1.81222e80	0.319214
$865$	4.52115e80	0.771447
$866$	−1.69542e80	−0.280244
$867$	5.26967e79	0.0843837
$868$	−3.93047e80	−0.609750
$869$	−7.24606e80	−1.08908
$870$	−9.41165e79	−0.137052
$871$	5.82024e79	0.0821186
$872$	−2.75565e80	−0.376721
$873$	1.44114e80	0.190904
$874$	−6.40799e80	−0.822541
$875$	5.20869e80	0.647899
$876$	1.21985e80	0.147042
$877$	1.11936e81	1.30762	0.653809	−	0.756659i	$-0.273170\pi$
$877$	1.11936e81	1.30762	0.653809	+	0.756659i	$0.273170\pi$
$878$	2.06949e79	0.0234295
$879$	2.28916e79	0.0251178
$880$	1.29288e81	1.37494
$881$	9.53097e80	0.982425	0.491213	−	0.871040i	$-0.336554\pi$
$881$	9.53097e80	0.982425	0.491213	+	0.871040i	$0.336554\pi$
$882$	−7.85470e80	−0.784772
$883$	1.42786e81	1.38282	0.691409	−	0.722463i	$-0.256990\pi$
$883$	1.42786e81	1.38282	0.691409	+	0.722463i	$0.256990\pi$
$884$	3.53567e80	0.331921
$885$	−6.25514e79	−0.0569242
$886$	−1.29532e81	−1.14275
$887$	−6.03898e80	−0.516492	−0.258246	−	0.966079i	$-0.583145\pi$
$887$	−6.03898e80	−0.516492	−0.258246	+	0.966079i	$0.583145\pi$
$888$	−3.48151e79	−0.0288676
$889$	−4.51539e80	−0.362992
$890$	−1.27161e81	−0.991128
$891$	−2.30130e81	−1.73915
$892$	−3.03778e80	−0.222599
$893$	1.90244e81	1.35175
$894$	4.69342e79	0.0323376
$895$	1.04352e80	0.0697214
$896$	5.52585e80	0.358038
$897$	−1.24708e80	−0.0783617
$898$	−2.99721e81	−1.82649
$899$	−2.61563e81	−1.54591
$900$	7.87787e80	0.451586
$901$	−4.10020e80	−0.227968
$902$	7.97557e81	4.30112
$903$	7.59655e79	0.0397377
$904$	−3.82523e79	−0.0194100
$905$	−2.10040e81	−1.03387
$906$	−2.31569e80	−0.110574
$907$	2.59302e81	1.20117	0.600587	−	0.799559i	$-0.294934\pi$
$907$	2.59302e81	1.20117	0.600587	+	0.799559i	$0.294934\pi$
$908$	4.92871e80	0.221499
$909$	2.38864e80	0.104146
$910$	9.47852e80	0.400961
$911$	6.45047e80	0.264750	0.132375	−	0.991200i	$-0.457740\pi$
$911$	6.45047e80	0.264750	0.132375	+	0.991200i	$0.457740\pi$
$912$	2.70803e80	0.107844
$913$	−3.44887e81	−1.33269
$914$	−6.22606e80	−0.233450
$915$	3.42826e79	0.0124737
$916$	−1.51108e81	−0.533534
$917$	−1.67627e81	−0.574365
$918$	−5.80498e80	−0.193031
$919$	6.10099e80	0.196890	0.0984450	−	0.995142i	$-0.468613\pi$
$919$	6.10099e80	0.196890	0.0984450	+	0.995142i	$0.468613\pi$
$920$	5.01012e80	0.156922
$921$	−1.81129e80	−0.0550615
$922$	2.79116e81	0.823540
$923$	2.22754e81	0.637938
$924$	−4.13004e80	−0.114809
$925$	−1.71634e81	−0.463133
$926$	−4.99632e81	−1.30872
$927$	5.56342e81	1.41465
$928$	−6.50502e81	−1.60576
$929$	2.88980e81	0.692524	0.346262	−	0.938138i	$-0.387451\pi$
$929$	2.88980e81	0.692524	0.346262	+	0.938138i	$0.387451\pi$
$930$	5.72454e80	0.133186
$931$	−1.92897e81	−0.435723
$932$	−5.50026e79	−0.0120627
$933$	−2.41211e79	−0.00513632
$934$	−4.43796e80	−0.0917580
$935$	−3.37567e81	−0.677706
$936$	−1.07098e81	−0.208783
$937$	4.29454e81	0.812976	0.406488	−	0.913656i	$-0.366753\pi$
$937$	4.29454e81	0.812976	0.406488	+	0.913656i	$0.366753\pi$
$938$	5.15436e80	0.0947538
$939$	9.10049e80	0.162465
$940$	5.39147e81	0.934741
$941$	−4.72249e80	−0.0795164	−0.0397582	−	0.999209i	$-0.512659\pi$
$941$	−4.72249e80	−0.0795164	−0.0397582	+	0.999209i	$0.512659\pi$
$942$	1.27064e81	0.207790
$943$	9.37101e81	1.48838
$944$	−5.30404e81	−0.818233
$945$	−6.83783e80	−0.102457
$946$	8.30187e81	1.20829
$947$	−1.72711e81	−0.244171	−0.122086	−	0.992520i	$-0.538958\pi$
$947$	−1.72711e81	−0.244171	−0.122086	+	0.992520i	$0.538958\pi$
$948$	−4.30124e80	−0.0590696
$949$	−8.17547e81	−1.09067
$950$	4.40308e81	0.570633
$951$	2.94932e80	0.0371328
$952$	−8.63847e80	−0.105662
$953$	−8.99783e81	−1.06926	−0.534629	−	0.845087i	$-0.679549\pi$
$953$	−8.99783e81	−1.06926	−0.534629	+	0.845087i	$0.679549\pi$
$954$	−4.50176e81	−0.519759
$955$	4.17848e81	0.468733
$956$	−8.03967e81	−0.876287
$957$	−2.74845e81	−0.291078
$958$	−6.68352e81	−0.687786
$959$	−7.74748e81	−0.774727
$960$	4.44504e80	0.0431933
$961$	5.31940e81	0.502308
$962$	−8.45754e81	−0.776122
$963$	6.85388e81	0.611243
$964$	1.57127e82	1.36186
$965$	−1.41959e81	−0.119581
$966$	−1.10441e81	−0.0904188
$967$	7.38949e81	0.588012	0.294006	−	0.955804i	$-0.405011\pi$
$967$	7.38949e81	0.588012	0.294006	+	0.955804i	$0.405011\pi$
$968$	8.71830e81	0.674310
$969$	−7.07061e80	−0.0531561
$970$	2.28270e81	0.166812
$971$	1.41189e82	1.00293	0.501467	−	0.865177i	$-0.332794\pi$
$971$	1.41189e82	1.00293	0.501467	+	0.865177i	$0.332794\pi$
$972$	−4.21194e81	−0.290844
$973$	1.68870e81	0.113358
$974$	2.68831e82	1.75432
$975$	8.56900e80	0.0543630
$976$	2.90699e81	0.179297
$977$	−2.95152e82	−1.76989	−0.884944	−	0.465698i	$-0.845803\pi$
$977$	−2.95152e82	−1.76989	−0.884944	+	0.465698i	$0.845803\pi$
$978$	4.16716e81	0.242953
$979$	−3.71344e82	−2.10500
$980$	−5.46665e81	−0.301304
$981$	2.39518e82	1.28363
$982$	−4.65488e82	−2.42573
$983$	−5.45113e80	−0.0276226	−0.0138113	−	0.999905i	$-0.504396\pi$
$983$	−5.45113e80	−0.0276226	−0.0138113	+	0.999905i	$0.504396\pi$
$984$	−1.30612e81	−0.0643604
$985$	1.29051e82	0.618396
$986$	2.08372e82	0.971010
$987$	3.27884e81	0.148593
$988$	9.53336e81	0.420175
$989$	9.75440e81	0.418122
$990$	−3.70628e82	−1.54515
$991$	−3.10771e82	−1.26013	−0.630065	−	0.776542i	$-0.716972\pi$
$991$	−3.10771e82	−1.26013	−0.630065	+	0.776542i	$0.716972\pi$
$992$	3.95661e82	1.56046
$993$	1.41634e81	0.0543330
$994$	1.97269e82	0.736094
$995$	6.30132e81	0.228716
$996$	−2.04724e81	−0.0722831
$997$	−2.32086e82	−0.797134	−0.398567	−	0.917139i	$-0.630492\pi$
$997$	−2.32086e82	−0.797134	−0.398567	+	0.917139i	$0.630492\pi$
$998$	−1.49930e82	−0.500954
$999$	6.10129e81	0.198322

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.56.a.a.1.1	✓	4
3.2	odd	2		9.56.a.a.1.4		4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.53509e8 q^{2} -1.66915e12 q^{3} +2.82382e16 q^{4} +1.07257e19 q^{5} +4.23145e20 q^{6} -1.10352e23 q^{7} +1.97498e24 q^{8} -1.71663e26 q^{9} +O(q^{10})\)	\(q-2.53509e8 q^{2} -1.66915e12 q^{3} +2.82382e16 q^{4} +1.07257e19 q^{5} +4.23145e20 q^{6} -1.10352e23 q^{7} +1.97498e24 q^{8} -1.71663e26 q^{9} -2.71906e27 q^{10} -7.94038e28 q^{11} -4.71339e28 q^{12} +3.15893e30 q^{13} +2.79753e31 q^{14} -1.79028e31 q^{15} -1.51807e33 q^{16} +3.96364e33 q^{17} +4.35182e34 q^{18} +1.06873e35 q^{19} +3.02875e35 q^{20} +1.84194e35 q^{21} +2.01296e37 q^{22} +2.36516e37 q^{23} -3.29654e36 q^{24} -1.62515e38 q^{25} -8.00820e38 q^{26} +5.77713e38 q^{27} -3.11615e39 q^{28} -2.07372e40 q^{29} +4.53852e39 q^{30} +1.26132e41 q^{31} +3.13688e41 q^{32} +1.32537e41 q^{33} -1.00482e42 q^{34} -1.18360e42 q^{35} -4.84747e42 q^{36} +1.05611e43 q^{37} -2.70933e43 q^{38} -5.27273e42 q^{39} +2.11830e43 q^{40} +3.96211e44 q^{41} -4.66949e43 q^{42} +4.12421e44 q^{43} -2.24222e45 q^{44} -1.84121e45 q^{45} -5.99590e45 q^{46} +1.78010e46 q^{47} +2.53388e45 q^{48} -1.80492e46 q^{49} +4.11992e46 q^{50} -6.61590e45 q^{51} +8.92027e46 q^{52} -1.03445e47 q^{53} -1.46456e47 q^{54} -8.51661e47 q^{55} -2.17943e47 q^{56} -1.78387e47 q^{57} +5.25709e48 q^{58} +3.49395e48 q^{59} -5.05543e47 q^{60} -1.91493e48 q^{61} -3.19757e49 q^{62} +1.89434e49 q^{63} -2.48288e49 q^{64} +3.38818e49 q^{65} -3.35993e49 q^{66} +1.84247e49 q^{67} +1.11926e50 q^{68} -3.94780e49 q^{69} +3.00054e50 q^{70} +7.05155e50 q^{71} -3.39031e50 q^{72} -2.58805e51 q^{73} -2.67734e51 q^{74} +2.71262e50 q^{75} +3.01790e51 q^{76} +8.76237e51 q^{77} +1.33669e51 q^{78} +9.12558e51 q^{79} -1.62823e52 q^{80} +2.89822e52 q^{81} -1.00443e53 q^{82} +4.34346e52 q^{83} +5.20132e51 q^{84} +4.25128e52 q^{85} -1.04553e53 q^{86} +3.46136e52 q^{87} -1.56821e53 q^{88} +4.67666e53 q^{89} +4.66763e53 q^{90} -3.48595e53 q^{91} +6.67879e53 q^{92} -2.10534e53 q^{93} -4.51272e54 q^{94} +1.14629e54 q^{95} -5.23592e53 q^{96} -8.39518e53 q^{97} +4.57565e54 q^{98} +1.36307e55 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 208622520 q^{2} - 6821470691280 q^{3} + 38\!\cdots\!72 q^{4}+ \cdots + 47\!\cdots\!28 q^{9}+O(q^{10}) \) 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

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