LMFDB - Embedded newform 1.56.a.a.1.4

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			1.4
Root			$1.14055e7$ 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)

$f(q)$	$=$	$q+3.25888e8 q^{2} +5.98183e12 q^{3} +7.01743e16 q^{4} +2.73659e19 q^{5} +1.94941e21 q^{6} -1.10303e23 q^{7} +1.11276e25 q^{8} -1.38667e26 q^{9} +O(q^{10})$	\(q+3.25888e8 q^{2} +5.98183e12 q^{3} +7.01743e16 q^{4} +2.73659e19 q^{5} +1.94941e21 q^{6} -1.10303e23 q^{7} +1.11276e25 q^{8} -1.38667e26 q^{9} +8.91821e27 q^{10} +4.91412e28 q^{11} +4.19771e29 q^{12} -5.50498e30 q^{13} -3.59464e31 q^{14} +1.63698e32 q^{15} +1.09807e33 q^{16} +6.74131e33 q^{17} -4.51899e34 q^{18} +4.63069e34 q^{19} +1.92038e36 q^{20} -6.59813e35 q^{21} +1.60146e37 q^{22} -2.33537e37 q^{23} +6.65636e37 q^{24} +4.71335e38 q^{25} -1.79401e39 q^{26} -1.87301e39 q^{27} -7.74043e39 q^{28} +8.29368e39 q^{29} +5.33472e40 q^{30} -2.22670e40 q^{31} -4.30685e40 q^{32} +2.93955e41 q^{33} +2.19691e42 q^{34} -3.01853e42 q^{35} -9.73086e42 q^{36} -8.62039e42 q^{37} +1.50909e43 q^{38} -3.29298e43 q^{39} +3.04517e44 q^{40} -1.28503e44 q^{41} -2.15025e44 q^{42} -7.80265e44 q^{43} +3.44845e45 q^{44} -3.79474e45 q^{45} -7.61071e45 q^{46} +2.24956e45 q^{47} +6.56844e45 q^{48} -1.80601e46 q^{49} +1.53602e47 q^{50} +4.03254e46 q^{51} -3.86308e47 q^{52} +6.54418e46 q^{53} -6.10391e47 q^{54} +1.34479e48 q^{55} -1.22741e48 q^{56} +2.77000e47 q^{57} +2.70281e48 q^{58} -4.81860e48 q^{59} +1.14874e49 q^{60} -1.00856e48 q^{61} -7.25655e48 q^{62} +1.52954e49 q^{63} -5.35975e49 q^{64} -1.50648e50 q^{65} +9.57963e49 q^{66} +2.13547e50 q^{67} +4.73067e50 q^{68} -1.39698e50 q^{69} -9.83705e50 q^{70} +9.56825e50 q^{71} -1.54303e51 q^{72} +1.10863e51 q^{73} -2.80928e51 q^{74} +2.81945e51 q^{75} +3.24956e51 q^{76} -5.42042e51 q^{77} -1.07314e52 q^{78} +2.07492e52 q^{79} +3.00495e52 q^{80} +1.29863e52 q^{81} -4.18778e52 q^{82} -1.06353e53 q^{83} -4.63019e52 q^{84} +1.84482e53 q^{85} -2.54279e53 q^{86} +4.96114e52 q^{87} +5.46825e53 q^{88} +7.48693e53 q^{89} -1.23666e54 q^{90} +6.07215e53 q^{91} -1.63883e54 q^{92} -1.33197e53 q^{93} +7.33106e53 q^{94} +1.26723e54 q^{95} -2.57628e53 q^{96} -5.59692e53 q^{97} -5.88557e54 q^{98} -6.81426e54 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.25888e8	1.71690	0.858448	−	0.512901i	$-0.171429\pi$
$2$	3.25888e8	1.71690	0.858448	+	0.512901i	$0.171429\pi$
$3$	5.98183e12	0.452897	0.226449	−	0.974023i	$-0.427288\pi$
$3$	5.98183e12	0.452897	0.226449	+	0.974023i	$0.427288\pi$
$4$	7.01743e16	1.94773
$5$	2.73659e19	1.64261	0.821304	−	0.570490i	$-0.193247\pi$
$5$	2.73659e19	1.64261	0.821304	+	0.570490i	$0.193247\pi$
$6$	1.94941e21	0.777577
$7$	−1.10303e23	−0.634440	−0.317220	−	0.948352i	$-0.602749\pi$
$7$	−1.10303e23	−0.634440	−0.317220	+	0.948352i	$0.602749\pi$
$8$	1.11276e25	1.62715
$9$	−1.38667e26	−0.794884
$10$	8.91821e27	2.82019
$11$	4.91412e28	1.13018	0.565090	−	0.825030i	$-0.308842\pi$
$11$	4.91412e28	1.13018	0.565090	+	0.825030i	$0.308842\pi$
$12$	4.19771e29	0.882121
$13$	−5.50498e30	−1.28030	−0.640152	−	0.768248i	$-0.721129\pi$
$13$	−5.50498e30	−1.28030	−0.640152	+	0.768248i	$0.721129\pi$
$14$	−3.59464e31	−1.08927
$15$	1.63698e32	0.743933
$16$	1.09807e33	0.845919
$17$	6.74131e33	0.980390	0.490195	−	0.871613i	$-0.336926\pi$
$17$	6.74131e33	0.980390	0.490195	+	0.871613i	$0.336926\pi$
$18$	−4.51899e34	−1.36473
$19$	4.63069e34	0.316171	0.158085	−	0.987425i	$-0.449468\pi$
$19$	4.63069e34	0.316171	0.158085	+	0.987425i	$0.449468\pi$
$20$	1.92038e36	3.19936
$21$	−6.59813e35	−0.287336
$22$	1.60146e37	1.94040
$23$	−2.33537e37	−0.833376	−0.416688	−	0.909050i	$-0.636809\pi$
$23$	−2.33537e37	−0.833376	−0.416688	+	0.909050i	$0.636809\pi$
$24$	6.65636e37	0.736932
$25$	4.71335e38	1.69816
$26$	−1.79401e39	−2.19815
$27$	−1.87301e39	−0.812898
$28$	−7.74043e39	−1.23572
$29$	8.29368e39	0.504431	0.252216	−	0.967671i	$-0.418841\pi$
$29$	8.29368e39	0.504431	0.252216	+	0.967671i	$0.418841\pi$
$30$	5.33472e40	1.27725
$31$	−2.22670e40	−0.216379	−0.108189	−	0.994130i	$-0.534505\pi$
$31$	−2.22670e40	−0.216379	−0.108189	+	0.994130i	$0.534505\pi$
$32$	−4.30685e40	−0.174797
$33$	2.93955e41	0.511855
$34$	2.19691e42	1.68323
$35$	−3.01853e42	−1.04214
$36$	−9.73086e42	−1.54822
$37$	−8.62039e42	−0.645624	−0.322812	−	0.946463i	$-0.604628\pi$
$37$	−8.62039e42	−0.645624	−0.322812	+	0.946463i	$0.604628\pi$
$38$	1.50909e43	0.542832
$39$	−3.29298e43	−0.579846
$40$	3.04517e44	2.67277
$41$	−1.28503e44	−0.571951	−0.285975	−	0.958237i	$-0.592318\pi$
$41$	−1.28503e44	−0.571951	−0.285975	+	0.958237i	$0.592318\pi$
$42$	−2.15025e44	−0.493326
$43$	−7.80265e44	−0.937259	−0.468629	−	0.883395i	$-0.655252\pi$
$43$	−7.80265e44	−0.937259	−0.468629	+	0.883395i	$0.655252\pi$
$44$	3.44845e45	2.20128
$45$	−3.79474e45	−1.30568
$46$	−7.61071e45	−1.43082
$47$	2.24956e45	0.234103	0.117052	−	0.993126i	$-0.462656\pi$
$47$	2.24956e45	0.234103	0.117052	+	0.993126i	$0.462656\pi$
$48$	6.56844e45	0.383114
$49$	−1.80601e46	−0.597486
$50$	1.53602e47	2.91557
$51$	4.03254e46	0.444016
$52$	−3.86308e47	−2.49369
$53$	6.54418e46	0.250189	0.125095	−	0.992145i	$-0.460077\pi$
$53$	6.54418e46	0.250189	0.125095	+	0.992145i	$0.460077\pi$
$54$	−6.10391e47	−1.39566
$55$	1.34479e48	1.85644
$56$	−1.22741e48	−1.03233
$57$	2.77000e47	0.143193
$58$	2.70281e48	0.866056
$59$	−4.81860e48	−0.964918	−0.482459	−	0.875918i	$-0.660256\pi$
$59$	−4.81860e48	−0.964918	−0.482459	+	0.875918i	$0.660256\pi$
$60$	1.14874e49	1.44898
$61$	−1.00856e48	−0.0807480	−0.0403740	−	0.999185i	$-0.512855\pi$
$61$	−1.00856e48	−0.0807480	−0.0403740	+	0.999185i	$0.512855\pi$
$62$	−7.25655e48	−0.371500
$63$	1.52954e49	0.504307
$64$	−5.35975e49	−1.14603
$65$	−1.50648e50	−2.10304
$66$	9.57963e49	0.878801
$67$	2.13547e50	1.29550	0.647749	−	0.761854i	$-0.275711\pi$
$67$	2.13547e50	1.29550	0.647749	+	0.761854i	$0.275711\pi$
$68$	4.73067e50	1.90953
$69$	−1.39698e50	−0.377434
$70$	−9.83705e50	−1.78924
$71$	9.56825e50	1.17822	0.589112	−	0.808051i	$-0.299478\pi$
$71$	9.56825e50	1.17822	0.589112	+	0.808051i	$0.299478\pi$
$72$	−1.54303e51	−1.29340
$73$	1.10863e51	0.635926	0.317963	−	0.948103i	$-0.397001\pi$
$73$	1.10863e51	0.635926	0.317963	+	0.948103i	$0.397001\pi$
$74$	−2.80928e51	−1.10847
$75$	2.81945e51	0.769093
$76$	3.24956e51	0.615815
$77$	−5.42042e51	−0.717031
$78$	−1.07314e52	−0.995535
$79$	2.07492e52	1.35599	0.677995	−	0.735067i	$-0.262849\pi$
$79$	2.07492e52	1.35599	0.677995	+	0.735067i	$0.262849\pi$
$80$	3.00495e52	1.38951
$81$	1.29863e52	0.426725
$82$	−4.18778e52	−0.981980
$83$	−1.06353e53	−1.78691	−0.893456	−	0.449150i	$-0.851727\pi$
$83$	−1.06353e53	−1.78691	−0.893456	+	0.449150i	$0.851727\pi$
$84$	−4.63019e52	−0.559653
$85$	1.84482e53	1.61040
$86$	−2.54279e53	−1.60917
$87$	4.96114e52	0.228456
$88$	5.46825e53	1.83897
$89$	7.48693e53	1.84535	0.922675	−	0.385578i	$-0.125998\pi$
$89$	7.48693e53	1.84535	0.922675	+	0.385578i	$0.125998\pi$
$90$	−1.23666e54	−2.24172
$91$	6.07215e53	0.812277
$92$	−1.63883e54	−1.62319
$93$	−1.33197e53	−0.0979974
$94$	7.33106e53	0.401931
$95$	1.26723e54	0.519345
$96$	−2.57628e53	−0.0791653
$97$	−5.59692e53	−0.129338	−0.0646691	−	0.997907i	$-0.520599\pi$
$97$	−5.59692e53	−0.129338	−0.0646691	+	0.997907i	$0.520599\pi$
$98$	−5.88557e54	−1.02582
$99$	−6.81426e54	−0.898361
$100$	3.30756e55	3.30756
$101$	−1.15529e55	−0.878729	−0.439364	−	0.898309i	$-0.644796\pi$
$101$	−1.15529e55	−0.878729	−0.439364	+	0.898309i	$0.644796\pi$
$102$	1.31416e55	0.762329
$103$	1.27447e55	0.565335	0.282667	−	0.959218i	$-0.408781\pi$
$103$	1.27447e55	0.565335	0.282667	+	0.959218i	$0.408781\pi$
$104$	−6.12573e55	−2.08325
$105$	−1.80564e55	−0.471981
$106$	2.13267e55	0.429549
$107$	−3.18160e55	−0.494984	−0.247492	−	0.968890i	$-0.579606\pi$
$107$	−3.18160e55	−0.494984	−0.247492	+	0.968890i	$0.579606\pi$
$108$	−1.31437e56	−1.58330
$109$	1.12821e56	1.05478	0.527388	−	0.849625i	$-0.323171\pi$
$109$	1.12821e56	1.05478	0.527388	+	0.849625i	$0.323171\pi$
$110$	4.38252e56	3.18732
$111$	−5.15657e55	−0.292401
$112$	−1.21120e56	−0.536685
$113$	−2.75852e56	−0.957238	−0.478619	−	0.878023i	$-0.658862\pi$
$113$	−2.75852e56	−0.957238	−0.478619	+	0.878023i	$0.658862\pi$
$114$	9.02711e55	0.245847
$115$	−6.39095e56	−1.36891
$116$	5.82003e56	0.982496
$117$	7.63358e56	1.01769
$118$	−1.57033e57	−1.65666
$119$	−7.43586e56	−0.621999
$120$	1.82157e57	1.21049
$121$	5.24270e56	0.277305
$122$	−3.28678e56	−0.138636
$123$	−7.68686e56	−0.259035
$124$	−1.56257e57	−0.421448
$125$	5.30294e57	1.14681
$126$	4.98458e57	0.865841
$127$	7.27512e57	1.01680	0.508402	−	0.861120i	$-0.330236\pi$
$127$	7.27512e57	1.01680	0.508402	+	0.861120i	$0.330236\pi$
$128$	−1.59151e58	−1.79281
$129$	−4.66741e57	−0.424482
$130$	−4.90946e58	−3.61070
$131$	3.20710e58	1.91052	0.955261	−	0.295764i	$-0.0955743\pi$
$131$	3.20710e58	1.91052	0.955261	+	0.295764i	$0.0955743\pi$
$132$	2.06281e58	0.996955
$133$	−5.10779e57	−0.200592
$134$	6.95925e58	2.22423
$135$	−5.12565e58	−1.33527
$136$	7.50148e58	1.59524
$137$	−5.59686e58	−0.973036	−0.486518	−	0.873671i	$-0.661733\pi$
$137$	−5.59686e58	−0.973036	−0.486518	+	0.873671i	$0.661733\pi$
$138$	−4.55260e58	−0.648014
$139$	6.10557e58	0.712556	0.356278	−	0.934380i	$-0.384046\pi$
$139$	6.10557e58	0.712556	0.356278	+	0.934380i	$0.384046\pi$
$140$	−2.11824e59	−2.02980
$141$	1.34565e58	0.106025
$142$	3.11818e59	2.02289
$143$	−2.70521e59	−1.44697
$144$	−1.52265e59	−0.672407
$145$	2.26964e59	0.828584
$146$	3.61289e59	1.09182
$147$	−1.08032e59	−0.270600
$148$	−6.04930e59	−1.25750
$149$	−1.00005e59	−0.172743	−0.0863713	−	0.996263i	$-0.527527\pi$
$149$	−1.00005e59	−0.172743	−0.0863713	+	0.996263i	$0.527527\pi$
$150$	9.18824e59	1.32045
$151$	8.74454e59	1.04682	0.523409	−	0.852082i	$-0.324660\pi$
$151$	8.74454e59	1.04682	0.523409	+	0.852082i	$0.324660\pi$
$152$	5.15286e59	0.514458
$153$	−9.34796e59	−0.779296
$154$	−1.76645e60	−1.23107
$155$	−6.09356e59	−0.355426
$156$	−2.31083e60	−1.12938
$157$	−2.34355e60	−0.960802	−0.480401	−	0.877049i	$-0.659509\pi$
$157$	−2.34355e60	−0.960802	−0.480401	+	0.877049i	$0.659509\pi$
$158$	6.76192e60	2.32809
$159$	3.91462e59	0.113310
$160$	−1.17861e60	−0.287124
$161$	2.57598e60	0.528727
$162$	4.23209e60	0.732642
$163$	9.54155e60	1.39463	0.697316	−	0.716763i	$-0.254377\pi$
$163$	9.54155e60	1.39463	0.697316	+	0.716763i	$0.254377\pi$
$164$	−9.01764e60	−1.11401
$165$	8.04432e60	0.840777
$166$	−3.46593e61	−3.06794
$167$	−6.27360e60	−0.470776	−0.235388	−	0.971902i	$-0.575636\pi$
$167$	−6.27360e60	−0.470776	−0.235388	+	0.971902i	$0.575636\pi$
$168$	−7.34215e60	−0.467539
$169$	1.18170e61	0.639179
$170$	6.01204e61	2.76488
$171$	−6.42124e60	−0.251319
$172$	−5.47546e61	−1.82553
$173$	1.23980e61	0.352439	0.176219	−	0.984351i	$-0.443613\pi$
$173$	1.23980e61	0.352439	0.176219	+	0.984351i	$0.443613\pi$
$174$	1.61678e61	0.392234
$175$	−5.19896e61	−1.07738
$176$	5.39603e61	0.956040
$177$	−2.88241e61	−0.437009
$178$	2.43990e62	3.16827
$179$	−6.84198e61	−0.761594	−0.380797	−	0.924659i	$-0.624350\pi$
$179$	−6.84198e61	−0.761594	−0.380797	+	0.924659i	$0.624350\pi$
$180$	−2.66293e62	−2.54312
$181$	−1.10035e61	−0.0902340	−0.0451170	−	0.998982i	$-0.514366\pi$
$181$	−1.10035e61	−0.0902340	−0.0451170	+	0.998982i	$0.514366\pi$
$182$	1.97884e62	1.39459
$183$	−6.03304e60	−0.0365706
$184$	−2.59872e62	−1.35603
$185$	−2.35905e62	−1.06051
$186$	−4.34075e61	−0.168251
$187$	3.31276e62	1.10802
$188$	1.57862e62	0.455969
$189$	2.06598e62	0.515735
$190$	4.12975e62	0.891661
$191$	7.90077e62	1.47656	0.738281	−	0.674493i	$-0.235638\pi$
$191$	7.90077e62	1.47656	0.738281	+	0.674493i	$0.235638\pi$
$192$	−3.20611e62	−0.519033
$193$	−9.51922e62	−1.33590	−0.667952	−	0.744204i	$-0.732829\pi$
$193$	−9.51922e62	−1.33590	−0.667952	+	0.744204i	$0.732829\pi$
$194$	−1.82397e62	−0.222060
$195$	−9.01154e62	−0.952461
$196$	−1.26735e63	−1.16374
$197$	1.86380e63	1.48791	0.743956	−	0.668229i	$-0.232947\pi$
$197$	1.86380e63	1.48791	0.743956	+	0.668229i	$0.232947\pi$
$198$	−2.22069e63	−1.54239
$199$	−2.70172e62	−0.163373	−0.0816866	−	0.996658i	$-0.526031\pi$
$199$	−2.70172e62	−0.163373	−0.0816866	+	0.996658i	$0.526031\pi$
$200$	5.24484e63	2.76317
$201$	1.27740e63	0.586728
$202$	−3.76497e63	−1.50869
$203$	−9.14817e62	−0.320032
$204$	2.82981e63	0.864823
$205$	−3.51661e63	−0.939491
$206$	4.15335e63	0.970621
$207$	3.23839e63	0.662437
$208$	−6.04482e63	−1.08303
$209$	2.27558e63	0.357330
$210$	−5.88436e63	−0.810342
$211$	3.39112e63	0.409804	0.204902	−	0.978783i	$-0.434312\pi$
$211$	3.39112e63	0.409804	0.204902	+	0.978783i	$0.434312\pi$
$212$	4.59233e63	0.487301
$213$	5.72357e63	0.533614
$214$	−1.03685e64	−0.849836
$215$	−2.13526e64	−1.53955
$216$	−2.08421e64	−1.32271
$217$	2.45611e63	0.137280
$218$	3.67669e64	1.81094
$219$	6.63162e63	0.288009
$220$	9.43699e64	3.61585
$221$	−3.71107e64	−1.25520
$222$	−1.68047e64	−0.502022
$223$	−1.50393e64	−0.397049	−0.198524	−	0.980096i	$-0.563615\pi$
$223$	−1.50393e64	−0.397049	−0.198524	+	0.980096i	$0.563615\pi$
$224$	4.75058e63	0.110899
$225$	−6.53586e64	−1.34984
$226$	−8.98971e64	−1.64348
$227$	6.25379e64	1.01259	0.506293	−	0.862361i	$-0.331015\pi$
$227$	6.25379e64	1.01259	0.506293	+	0.862361i	$0.331015\pi$
$228$	1.94383e64	0.278901
$229$	9.72208e64	1.23675	0.618377	−	0.785882i	$-0.287791\pi$
$229$	9.72208e64	1.23675	0.618377	+	0.785882i	$0.287791\pi$
$230$	−2.08274e65	−2.35028
$231$	−3.24240e64	−0.324741
$232$	9.22889e64	0.820786
$233$	1.58206e65	1.25007	0.625037	−	0.780595i	$-0.285084\pi$
$233$	1.58206e65	1.25007	0.625037	+	0.780595i	$0.285084\pi$
$234$	2.48769e65	1.74727
$235$	6.15613e64	0.384540
$236$	−3.38142e65	−1.87940
$237$	1.24118e65	0.614124
$238$	−2.42326e65	−1.06791
$239$	−1.73759e65	−0.682346	−0.341173	−	0.940000i	$-0.610824\pi$
$239$	−1.73759e65	−0.682346	−0.341173	+	0.940000i	$0.610824\pi$
$240$	1.79751e65	0.629307
$241$	−8.77618e64	−0.274054	−0.137027	−	0.990567i	$-0.543755\pi$
$241$	−8.77618e64	−0.274054	−0.137027	+	0.990567i	$0.543755\pi$
$242$	1.70854e65	0.476103
$243$	4.04427e65	1.00616
$244$	−7.07751e64	−0.157275
$245$	−4.94230e65	−0.981435
$246$	−2.50506e65	−0.444736
$247$	−2.54918e65	−0.404795
$248$	−2.47779e65	−0.352081
$249$	−6.36187e65	−0.809288
$250$	1.72816e66	1.96895
$251$	6.61756e63	0.00675570	0.00337785	−	0.999994i	$-0.498925\pi$
$251$	6.61756e63	0.00675570	0.00337785	+	0.999994i	$0.498925\pi$
$252$	1.07334e66	0.982252
$253$	−1.14763e66	−0.941864
$254$	2.37087e66	1.74575
$255$	1.10354e66	0.729344
$256$	−3.25548e66	−1.93204
$257$	2.05584e66	1.09605	0.548024	−	0.836463i	$-0.315380\pi$
$257$	2.05584e66	1.09605	0.548024	+	0.836463i	$0.315380\pi$
$258$	−1.52105e66	−0.728791
$259$	9.50854e65	0.409610
$260$	−1.05717e67	−4.09615
$261$	−1.15006e66	−0.400965
$262$	1.04516e67	3.28017
$263$	−5.76788e66	−1.63017	−0.815086	−	0.579340i	$-0.803310\pi$
$263$	−5.76788e66	−1.63017	−0.815086	+	0.579340i	$0.803310\pi$
$264$	3.27102e66	0.832865
$265$	1.79087e66	0.410963
$266$	−1.66457e66	−0.344395
$267$	4.47856e66	0.835754
$268$	1.49855e67	2.52328
$269$	3.84467e66	0.584348	0.292174	−	0.956365i	$-0.405621\pi$
$269$	3.84467e66	0.584348	0.292174	+	0.956365i	$0.405621\pi$
$270$	−1.67039e67	−2.29252
$271$	−1.55611e67	−1.92923	−0.964615	−	0.263662i	$-0.915070\pi$
$271$	−1.55611e67	−1.92923	−0.964615	+	0.263662i	$0.915070\pi$
$272$	7.40240e66	0.829330
$273$	3.63226e66	0.367878
$274$	−1.82395e67	−1.67060
$275$	2.31620e67	1.91923
$276$	−9.80322e66	−0.735138
$277$	1.29112e65	0.00876541	0.00438271	−	0.999990i	$-0.498605\pi$
$277$	1.29112e65	0.00876541	0.00438271	+	0.999990i	$0.498605\pi$
$278$	1.98973e67	1.22338
$279$	3.08770e66	0.171996
$280$	−3.35891e67	−1.69571
$281$	−4.05496e67	−1.85594	−0.927968	−	0.372661i	$-0.878446\pi$
$281$	−4.05496e67	−1.85594	−0.927968	+	0.372661i	$0.878446\pi$
$282$	4.38532e66	0.182033
$283$	4.16122e67	1.56709	0.783545	−	0.621335i	$-0.213409\pi$
$283$	4.16122e67	1.56709	0.783545	+	0.621335i	$0.213409\pi$
$284$	6.71445e67	2.29486
$285$	7.58035e66	0.235210
$286$	−8.81597e67	−2.48430
$287$	1.41743e67	0.362869
$288$	5.97217e66	0.138944
$289$	−1.83619e66	−0.0388353
$290$	7.39648e67	1.42259
$291$	−3.34798e66	−0.0585769
$292$	7.77972e67	1.23861
$293$	−7.89264e67	−1.14383	−0.571917	−	0.820312i	$-0.693800\pi$
$293$	−7.89264e67	−1.14383	−0.571917	+	0.820312i	$0.693800\pi$
$294$	−3.52065e67	−0.464591
$295$	−1.31865e68	−1.58498
$296$	−9.59245e67	−1.05053
$297$	−9.20419e67	−0.918720
$298$	−3.25905e67	−0.296581
$299$	1.28562e68	1.06697
$300$	1.97853e68	1.49799
$301$	8.60655e67	0.594635
$302$	2.84974e68	1.79728
$303$	−6.91078e67	−0.397974
$304$	5.08480e67	0.267455
$305$	−2.76002e67	−0.132637
$306$	−3.04639e68	−1.33797
$307$	1.91003e68	0.766893	0.383446	−	0.923563i	$-0.374737\pi$
$307$	1.91003e68	0.766893	0.383446	+	0.923563i	$0.374737\pi$
$308$	−3.80374e68	−1.39658
$309$	7.62366e67	0.256039
$310$	−1.98582e68	−0.610229
$311$	3.42073e68	0.962074	0.481037	−	0.876700i	$-0.340260\pi$
$311$	3.42073e68	0.962074	0.481037	+	0.876700i	$0.340260\pi$
$312$	−3.66431e68	−0.943497
$313$	7.31342e66	0.0172445	0.00862227	−	0.999963i	$-0.497255\pi$
$313$	7.31342e66	0.0172445	0.00862227	+	0.999963i	$0.497255\pi$
$314$	−7.63735e68	−1.64960
$315$	4.18571e68	0.828378
$316$	1.45606e69	2.64110
$317$	−5.41902e68	−0.901137	−0.450569	−	0.892742i	$-0.648779\pi$
$317$	−5.41902e68	−0.901137	−0.450569	+	0.892742i	$0.648779\pi$
$318$	1.27573e68	0.194541
$319$	4.07562e68	0.570098
$320$	−1.46674e69	−1.88247
$321$	−1.90318e68	−0.224177
$322$	8.39483e68	0.907769
$323$	3.12169e68	0.309971
$324$	9.11306e68	0.831144
$325$	−2.59469e69	−2.17417
$326$	3.10948e69	2.39444
$327$	6.74875e68	0.477705
$328$	−1.42994e69	−0.930650
$329$	−2.48133e68	−0.148524
$330$	2.62155e69	1.44353
$331$	−1.74335e69	−0.883315	−0.441658	−	0.897184i	$-0.645609\pi$
$331$	−1.74335e69	−0.883315	−0.441658	+	0.897184i	$0.645609\pi$
$332$	−7.46327e69	−3.48042
$333$	1.19536e69	0.513196
$334$	−2.04449e69	−0.808273
$335$	5.84390e69	2.12800
$336$	−7.24518e68	−0.243063
$337$	−3.48749e69	−1.07818	−0.539090	−	0.842248i	$-0.681232\pi$
$337$	−3.48749e69	−1.07818	−0.539090	+	0.842248i	$0.681232\pi$
$338$	3.85102e69	1.09740
$339$	−1.65010e69	−0.433530
$340$	1.29459e70	3.13662
$341$	−1.09423e69	−0.244547
$342$	−2.09261e69	−0.431489
$343$	5.32618e69	1.01351
$344$	−8.68249e69	−1.52506
$345$	−3.82296e69	−0.619976
$346$	4.04036e69	0.605101
$347$	−3.19386e69	−0.441830	−0.220915	−	0.975293i	$-0.570904\pi$
$347$	−3.19386e69	−0.441830	−0.220915	+	0.975293i	$0.570904\pi$
$348$	3.48145e69	0.444970
$349$	−1.03259e70	−1.21963	−0.609813	−	0.792545i	$-0.708755\pi$
$349$	−1.03259e70	−1.21963	−0.609813	+	0.792545i	$0.708755\pi$
$350$	−1.69428e70	−1.84975
$351$	1.03109e70	1.04076
$352$	−2.11644e69	−0.197552
$353$	−6.47303e69	−0.558860	−0.279430	−	0.960166i	$-0.590145\pi$
$353$	−6.47303e69	−0.558860	−0.279430	+	0.960166i	$0.590145\pi$
$354$	−9.39342e69	−0.750298
$355$	2.61843e70	1.93536
$356$	5.25391e70	3.59424
$357$	−4.44801e69	−0.281702
$358$	−2.22972e70	−1.30758
$359$	1.06064e70	0.576063	0.288031	−	0.957621i	$-0.406999\pi$
$359$	1.06064e70	0.576063	0.288031	+	0.957621i	$0.406999\pi$
$360$	−4.22264e70	−2.12454
$361$	−1.93067e70	−0.900036
$362$	−3.58591e69	−0.154922
$363$	3.13610e69	0.125591
$364$	4.26109e70	1.58209
$365$	3.03385e70	1.04458
$366$	−1.96610e69	−0.0627878
$367$	5.03481e69	0.149165	0.0745824	−	0.997215i	$-0.476238\pi$
$367$	5.03481e69	0.149165	0.0745824	+	0.997215i	$0.476238\pi$
$368$	−2.56439e70	−0.704968
$369$	1.78192e70	0.454635
$370$	−7.68785e70	−1.82078
$371$	−7.21842e69	−0.158730
$372$	−9.34704e69	−0.190872
$373$	−9.67049e70	−1.83424	−0.917119	−	0.398613i	$-0.869492\pi$
$373$	−9.67049e70	−1.83424	−0.917119	+	0.398613i	$0.869492\pi$
$374$	1.07959e71	1.90235
$375$	3.17213e70	0.519386
$376$	2.50323e70	0.380921
$377$	−4.56565e70	−0.645826
$378$	6.73279e70	0.885463
$379$	−1.49089e71	−1.82333	−0.911667	−	0.410930i	$-0.865204\pi$
$379$	−1.49089e71	−1.82333	−0.911667	+	0.410930i	$0.865204\pi$
$380$	8.89269e70	1.01154
$381$	4.35185e70	0.460508
$382$	2.57477e71	2.53510
$383$	1.32996e71	1.21863	0.609317	−	0.792927i	$-0.291444\pi$
$383$	1.32996e71	1.21863	0.609317	+	0.792927i	$0.291444\pi$
$384$	−9.52013e70	−0.811959
$385$	−1.48335e71	−1.17780
$386$	−3.10220e71	−2.29361
$387$	1.08197e71	0.745012
$388$	−3.92760e70	−0.251916
$389$	1.84119e70	0.110023	0.0550115	−	0.998486i	$-0.482480\pi$
$389$	1.84119e70	0.110023	0.0550115	+	0.998486i	$0.482480\pi$
$390$	−2.93675e71	−1.63527
$391$	−1.57435e71	−0.817033
$392$	−2.00966e71	−0.972199
$393$	1.91843e71	0.865270
$394$	6.07389e71	2.55459
$395$	5.67820e71	2.22736
$396$	−4.78186e71	−1.74976
$397$	2.35772e70	0.0804922	0.0402461	−	0.999190i	$-0.487186\pi$
$397$	2.35772e70	0.0804922	0.0402461	+	0.999190i	$0.487186\pi$
$398$	−8.80459e70	−0.280495
$399$	−3.05539e70	−0.0908473
$400$	5.17556e71	1.43651
$401$	−5.55389e71	−1.43922	−0.719610	−	0.694378i	$-0.755679\pi$
$401$	−5.55389e71	−1.43922	−0.719610	+	0.694378i	$0.755679\pi$
$402$	4.16291e71	1.00735
$403$	1.22579e71	0.277031
$404$	−8.10720e71	−1.71153
$405$	3.55382e71	0.700942
$406$	−2.98128e71	−0.549461
$407$	−4.23617e71	−0.729671
$408$	4.48726e71	0.722481
$409$	5.98705e71	0.901201	0.450600	−	0.892726i	$-0.351210\pi$
$409$	5.98705e71	0.901201	0.450600	+	0.892726i	$0.351210\pi$
$410$	−1.14602e72	−1.61301
$411$	−3.34795e71	−0.440685
$412$	8.94350e71	1.10112
$413$	5.31506e71	0.612183
$414$	1.05535e72	1.13734
$415$	−2.91045e72	−2.93520
$416$	2.37091e71	0.223794
$417$	3.65225e71	0.322715
$418$	7.41584e71	0.613498
$419$	1.73387e71	0.134317	0.0671585	−	0.997742i	$-0.478607\pi$
$419$	1.73387e71	0.134317	0.0671585	+	0.997742i	$0.478607\pi$
$420$	−1.26709e72	−0.919291
$421$	6.27129e71	0.426186	0.213093	−	0.977032i	$-0.431646\pi$
$421$	6.27129e71	0.426186	0.213093	+	0.977032i	$0.431646\pi$
$422$	1.10513e72	0.703590
$423$	−3.11940e71	−0.186085
$424$	7.28212e71	0.407096
$425$	3.17741e72	1.66486
$426$	1.86524e72	0.916160
$427$	1.11247e71	0.0512298
$428$	−2.23267e72	−0.964095
$429$	−1.61821e72	−0.655330
$430$	−6.95857e72	−2.64324
$431$	3.86872e71	0.137861	0.0689306	−	0.997621i	$-0.478041\pi$
$431$	3.86872e71	0.137861	0.0689306	+	0.997621i	$0.478041\pi$
$432$	−2.05668e72	−0.687646
$433$	−3.85260e72	−1.20875	−0.604376	−	0.796699i	$-0.706578\pi$
$433$	−3.85260e72	−1.20875	−0.604376	+	0.796699i	$0.706578\pi$
$434$	8.00419e71	0.235695
$435$	1.35766e72	0.375263
$436$	7.91712e72	2.05442
$437$	−1.08144e72	−0.263489
$438$	2.16117e72	0.494482
$439$	−7.04112e71	−0.151310	−0.0756550	−	0.997134i	$-0.524105\pi$
$439$	−7.04112e71	−0.151310	−0.0756550	+	0.997134i	$0.524105\pi$
$440$	1.49643e73	3.02071
$441$	2.50433e72	0.474932
$442$	−1.20940e73	−2.15504
$443$	−1.05429e73	−1.76545	−0.882727	−	0.469887i	$-0.844295\pi$
$443$	−1.05429e73	−1.76545	−0.882727	+	0.469887i	$0.844295\pi$
$444$	−3.61859e72	−0.569518
$445$	2.04886e73	3.03119
$446$	−4.90113e72	−0.681691
$447$	−5.98213e71	−0.0782347
$448$	5.91196e72	0.727086
$449$	−5.83745e71	−0.0675226	−0.0337613	−	0.999430i	$-0.510749\pi$
$449$	−5.83745e71	−0.0675226	−0.0337613	+	0.999430i	$0.510749\pi$
$450$	−2.12996e73	−2.31754
$451$	−6.31482e72	−0.646407
$452$	−1.93578e73	−1.86444
$453$	5.23084e72	0.474101
$454$	2.03804e73	1.73850
$455$	1.66170e73	1.33425
$456$	3.08235e72	0.232996
$457$	−9.08985e72	−0.646936	−0.323468	−	0.946239i	$-0.604849\pi$
$457$	−9.08985e72	−0.646936	−0.323468	+	0.946239i	$0.604849\pi$
$458$	3.16831e73	2.12338
$459$	−1.26265e73	−0.796957
$460$	−4.48481e73	−2.66627
$461$	1.94861e73	1.09131	0.545656	−	0.838009i	$-0.316281\pi$
$461$	1.94861e73	1.09131	0.545656	+	0.838009i	$0.316281\pi$
$462$	−1.05666e73	−0.557547
$463$	−5.72642e72	−0.284712	−0.142356	−	0.989816i	$-0.545468\pi$
$463$	−5.72642e72	−0.284712	−0.142356	+	0.989816i	$0.545468\pi$
$464$	9.10700e72	0.426708
$465$	−3.64506e72	−0.160971
$466$	5.15575e73	2.14624
$467$	−2.64935e73	−1.03974	−0.519871	−	0.854245i	$-0.674020\pi$
$467$	−2.64935e73	−1.03974	−0.519871	+	0.854245i	$0.674020\pi$
$468$	5.35681e73	1.98219
$469$	−2.35549e73	−0.821916
$470$	2.00621e73	0.660215
$471$	−1.40187e73	−0.435144
$472$	−5.36196e73	−1.57007
$473$	−3.83432e73	−1.05927
$474$	4.04487e73	1.05439
$475$	2.18261e73	0.536910
$476$	−5.21806e73	−1.21149
$477$	−9.07461e72	−0.198871
$478$	−5.66260e73	−1.17152
$479$	2.29697e73	0.448672	0.224336	−	0.974512i	$-0.427979\pi$
$479$	2.29697e73	0.448672	0.224336	+	0.974512i	$0.427979\pi$
$480$	−7.05022e72	−0.130038
$481$	4.74551e73	0.826595
$482$	−2.86005e73	−0.470523
$483$	1.54091e73	0.239459
$484$	3.67903e73	0.540115
$485$	−1.53165e73	−0.212452
$486$	1.31798e74	1.72747
$487$	1.57576e74	1.95184	0.975920	−	0.218128i	$-0.0699951\pi$
$487$	1.57576e74	1.95184	0.975920	+	0.218128i	$0.0699951\pi$
$488$	−1.12229e73	−0.131389
$489$	5.70760e73	0.631625
$490$	−1.61064e74	−1.68502
$491$	−9.33302e73	−0.923168	−0.461584	−	0.887096i	$-0.652719\pi$
$491$	−9.33302e73	−0.923168	−0.461584	+	0.887096i	$0.652719\pi$
$492$	−5.39420e73	−0.504530
$493$	5.59102e73	0.494540
$494$	−8.30749e73	−0.694990
$495$	−1.86478e74	−1.47566
$496$	−2.44506e73	−0.183039
$497$	−1.05541e74	−0.747513
$498$	−2.07326e74	−1.38946
$499$	2.92720e74	1.85647	0.928235	−	0.371994i	$-0.121326\pi$
$499$	2.92720e74	1.85647	0.928235	+	0.371994i	$0.121326\pi$
$500$	3.72130e74	2.23367
$501$	−3.75276e73	−0.213213
$502$	2.15658e72	0.0115988
$503$	1.72201e74	0.876833	0.438417	−	0.898772i	$-0.355539\pi$
$503$	1.72201e74	0.876833	0.438417	+	0.898772i	$0.355539\pi$
$504$	1.70201e74	0.820583
$505$	−3.16156e74	−1.44341
$506$	−3.74000e74	−1.61708
$507$	7.06873e73	0.289483
$508$	5.10526e74	1.98046
$509$	−3.58739e74	−1.31838	−0.659188	−	0.751978i	$-0.729100\pi$
$509$	−3.58739e74	−1.31838	−0.659188	+	0.751978i	$0.729100\pi$
$510$	3.59630e74	1.25221
$511$	−1.22285e74	−0.403457
$512$	−4.87523e74	−1.52430
$513$	−8.67332e73	−0.257015
$514$	6.69975e74	1.88180
$515$	3.48770e74	0.928624
$516$	−3.27533e74	−0.826776
$517$	1.10546e74	0.264578
$518$	3.09872e74	0.703257
$519$	7.41628e73	0.159619
$520$	−1.67636e75	−3.42196
$521$	−2.44717e74	−0.473834	−0.236917	−	0.971530i	$-0.576137\pi$
$521$	−2.44717e74	−0.473834	−0.236917	+	0.971530i	$0.576137\pi$
$522$	−3.74791e74	−0.688414
$523$	4.08574e74	0.711990	0.355995	−	0.934488i	$-0.384142\pi$
$523$	4.08574e74	0.711990	0.355995	+	0.934488i	$0.384142\pi$
$524$	2.25056e75	3.72118
$525$	−3.10993e74	−0.487944
$526$	−1.87969e75	−2.79883
$527$	−1.50109e74	−0.212136
$528$	3.22781e74	0.432988
$529$	−2.39895e74	−0.305485
$530$	5.83624e74	0.705580
$531$	6.68180e74	0.766998
$532$	−3.58435e74	−0.390698
$533$	7.07408e74	0.732271
$534$	1.45951e75	1.43490
$535$	−8.70672e74	−0.813066
$536$	2.37627e75	2.10797
$537$	−4.09276e74	−0.344924
$538$	1.25293e75	1.00326
$539$	−8.87495e74	−0.675266
$540$	−3.59689e75	−2.60075
$541$	−1.21945e74	−0.0837988	−0.0418994	−	0.999122i	$-0.513341\pi$
$541$	−1.21945e74	−0.0837988	−0.0418994	+	0.999122i	$0.513341\pi$
$542$	−5.07117e75	−3.31229
$543$	−6.58211e73	−0.0408667
$544$	−2.90338e74	−0.171370
$545$	3.08744e75	1.73258
$546$	1.18371e75	0.631608
$547$	1.44748e75	0.734446	0.367223	−	0.930133i	$-0.380309\pi$
$547$	1.44748e75	0.734446	0.367223	+	0.930133i	$0.380309\pi$
$548$	−3.92756e75	−1.89521
$549$	1.39854e74	0.0641853
$550$	7.54822e75	3.29511
$551$	3.84055e74	0.159487
$552$	−1.55451e75	−0.614141
$553$	−2.28870e75	−0.860295
$554$	4.20760e73	0.0150493
$555$	−1.41114e75	−0.480301
$556$	4.28454e75	1.38787
$557$	2.32271e74	0.0716104	0.0358052	−	0.999359i	$-0.488600\pi$
$557$	2.32271e74	0.0716104	0.0358052	+	0.999359i	$0.488600\pi$
$558$	1.00624e75	0.295299
$559$	4.29534e75	1.19998
$560$	−3.31455e75	−0.881563
$561$	1.98164e75	0.501818
$562$	−1.32146e76	−3.18645
$563$	−2.67933e75	−0.615242	−0.307621	−	0.951509i	$-0.599533\pi$
$563$	−2.67933e75	−0.615242	−0.307621	+	0.951509i	$0.599533\pi$
$564$	9.44302e74	0.206507
$565$	−7.54894e75	−1.57237
$566$	1.35609e76	2.69053
$567$	−1.43243e75	−0.270731
$568$	1.06472e76	1.91715
$569$	1.95670e75	0.335688	0.167844	−	0.985814i	$-0.446319\pi$
$569$	1.95670e75	0.335688	0.167844	+	0.985814i	$0.446319\pi$
$570$	2.47035e75	0.403831
$571$	−6.00217e75	−0.935008	−0.467504	−	0.883991i	$-0.654847\pi$
$571$	−6.00217e75	−0.935008	−0.467504	+	0.883991i	$0.654847\pi$
$572$	−1.89837e76	−2.81831
$573$	4.72611e75	0.668731
$574$	4.61924e75	0.623007
$575$	−1.10074e76	−1.41521
$576$	7.43219e75	0.910959
$577$	−1.73805e75	−0.203108	−0.101554	−	0.994830i	$-0.532382\pi$
$577$	−1.73805e75	−0.203108	−0.101554	+	0.994830i	$0.532382\pi$
$578$	−5.98393e74	−0.0666762
$579$	−5.69424e75	−0.605027
$580$	1.59270e76	1.61386
$581$	1.17311e76	1.13369
$582$	−1.09107e75	−0.100570
$583$	3.21589e75	0.282759
$584$	1.23364e76	1.03475
$585$	2.08900e76	1.67167
$586$	−2.57212e76	−1.96384
$587$	−2.45150e75	−0.178601	−0.0893006	−	0.996005i	$-0.528463\pi$
$587$	−2.45150e75	−0.178601	−0.0893006	+	0.996005i	$0.528463\pi$
$588$	−7.58110e75	−0.527054
$589$	−1.03112e75	−0.0684127
$590$	−4.29733e76	−2.72125
$591$	1.11489e76	0.673871
$592$	−9.46575e75	−0.546145
$593$	3.41502e76	1.88100	0.940500	−	0.339794i	$-0.110357\pi$
$593$	3.41502e76	1.88100	0.940500	+	0.339794i	$0.110357\pi$
$594$	−2.99954e76	−1.57735
$595$	−2.03489e76	−1.02170
$596$	−7.01779e75	−0.336456
$597$	−1.61612e75	−0.0739913
$598$	4.18968e76	1.83188
$599$	4.74508e75	0.198155	0.0990777	−	0.995080i	$-0.468411\pi$
$599$	4.74508e75	0.198155	0.0990777	+	0.995080i	$0.468411\pi$
$600$	3.13737e76	1.25143
$601$	−3.25978e76	−1.24205	−0.621027	−	0.783789i	$-0.713284\pi$
$601$	−3.25978e76	−1.24205	−0.621027	+	0.783789i	$0.713284\pi$
$602$	2.80477e76	1.02093
$603$	−2.96119e76	−1.02977
$604$	6.13642e76	2.03892
$605$	1.43471e76	0.455503
$606$	−2.25214e76	−0.683279
$607$	2.76963e76	0.803031	0.401515	−	0.915852i	$-0.368484\pi$
$607$	2.76963e76	0.803031	0.401515	+	0.915852i	$0.368484\pi$
$608$	−1.99437e75	−0.0552658
$609$	−5.47228e75	−0.144941
$610$	−8.99457e75	−0.227724
$611$	−1.23838e76	−0.299723
$612$	−6.55987e76	−1.51786
$613$	−7.08667e76	−1.56776	−0.783879	−	0.620913i	$-0.786762\pi$
$613$	−7.08667e76	−1.56776	−0.783879	+	0.620913i	$0.786762\pi$
$614$	6.22456e76	1.31667
$615$	−2.10358e76	−0.425493
$616$	−6.03164e76	−1.16672
$617$	−5.00063e75	−0.0925087	−0.0462543	−	0.998930i	$-0.514728\pi$
$617$	−5.00063e75	−0.0925087	−0.0462543	+	0.998930i	$0.514728\pi$
$618$	2.48446e76	0.439591
$619$	1.09383e77	1.85121	0.925604	−	0.378494i	$-0.123558\pi$
$619$	1.09383e77	1.85121	0.925604	+	0.378494i	$0.123558\pi$
$620$	−4.27611e76	−0.692273
$621$	4.37417e76	0.677450
$622$	1.11478e77	1.65178
$623$	−8.25830e76	−1.17076
$624$	−3.61591e76	−0.490503
$625$	1.42977e76	0.185595
$626$	2.38336e75	0.0296070
$627$	1.36121e76	0.161834
$628$	−1.64457e77	−1.87138
$629$	−5.81127e76	−0.632963
$630$	1.36407e77	1.42224
$631$	−6.03396e76	−0.602276	−0.301138	−	0.953581i	$-0.597366\pi$
$631$	−6.03396e76	−0.602276	−0.301138	+	0.953581i	$0.597366\pi$
$632$	2.30889e77	2.20640
$633$	2.02851e76	0.185599
$634$	−1.76599e77	−1.54716
$635$	1.99090e77	1.67021
$636$	2.74706e76	0.220697
$637$	9.94203e76	0.764963
$638$	1.32820e77	0.978798
$639$	−1.32680e77	−0.936552
$640$	−4.35530e77	−2.94489
$641$	−1.24358e77	−0.805522	−0.402761	−	0.915305i	$-0.631949\pi$
$641$	−1.24358e77	−0.805522	−0.402761	+	0.915305i	$0.631949\pi$
$642$	−6.20224e76	−0.384889
$643$	1.52782e77	0.908385	0.454192	−	0.890904i	$-0.349928\pi$
$643$	1.52782e77	0.908385	0.454192	+	0.890904i	$0.349928\pi$
$644$	1.80768e77	1.02982
$645$	−1.27728e77	−0.697258
$646$	1.01732e77	0.532187
$647$	−8.10455e76	−0.406313	−0.203157	−	0.979146i	$-0.565120\pi$
$647$	−8.10455e76	−0.406313	−0.203157	+	0.979146i	$0.565120\pi$
$648$	1.44507e77	0.694346
$649$	−2.36792e77	−1.09053
$650$	−8.45578e77	−3.73281
$651$	1.46921e76	0.0621735
$652$	6.69572e77	2.71637
$653$	2.22340e77	0.864778	0.432389	−	0.901687i	$-0.357671\pi$
$653$	2.22340e77	0.864778	0.432389	+	0.901687i	$0.357671\pi$
$654$	2.19934e77	0.820170
$655$	8.77651e77	3.13824
$656$	−1.41105e77	−0.483824
$657$	−1.53730e77	−0.505488
$658$	−8.08637e76	−0.255001
$659$	1.77062e77	0.535520	0.267760	−	0.963486i	$-0.413717\pi$
$659$	1.77062e77	0.535520	0.267760	+	0.963486i	$0.413717\pi$
$660$	5.64505e77	1.63761
$661$	−3.47431e77	−0.966782	−0.483391	−	0.875405i	$-0.660595\pi$
$661$	−3.47431e77	−0.966782	−0.483391	+	0.875405i	$0.660595\pi$
$662$	−5.68138e77	−1.51656
$663$	−2.21990e77	−0.568476
$664$	−1.18346e78	−2.90758
$665$	−1.39779e77	−0.329493
$666$	3.89555e77	0.881104
$667$	−1.93688e77	−0.420381
$668$	−4.40246e77	−0.916943
$669$	−8.99625e76	−0.179822
$670$	1.90446e78	3.65355
$671$	−4.95620e76	−0.0912597
$672$	2.84171e76	0.0502256
$673$	3.53476e77	0.599716	0.299858	−	0.953984i	$-0.403061\pi$
$673$	3.53476e77	0.599716	0.299858	+	0.953984i	$0.403061\pi$
$674$	−1.13653e78	−1.85112
$675$	−8.82814e77	−1.38043
$676$	8.29250e77	1.24495
$677$	3.06962e77	0.442482	0.221241	−	0.975219i	$-0.428989\pi$
$677$	3.06962e77	0.442482	0.221241	+	0.975219i	$0.428989\pi$
$678$	−5.37749e77	−0.744326
$679$	6.17357e76	0.0820573
$680$	2.05284e78	2.62036
$681$	3.74091e77	0.458598
$682$	−3.56596e77	−0.419862
$683$	−6.23098e77	−0.704672	−0.352336	−	0.935874i	$-0.614612\pi$
$683$	−6.23098e77	−0.704672	−0.352336	+	0.935874i	$0.614612\pi$
$684$	−4.50606e77	−0.489502
$685$	−1.53163e78	−1.59832
$686$	1.73574e78	1.74009
$687$	5.81558e77	0.560122
$688$	−8.56782e77	−0.792845
$689$	−3.60255e77	−0.320318
$690$	−1.24586e78	−1.06443
$691$	5.11269e77	0.419762	0.209881	−	0.977727i	$-0.432692\pi$
$691$	5.11269e77	0.419762	0.209881	+	0.977727i	$0.432692\pi$
$692$	8.70021e77	0.686455
$693$	7.51633e77	0.569957
$694$	−1.04084e78	−0.758575
$695$	1.67084e78	1.17045
$696$	5.52057e77	0.371732
$697$	−8.66282e77	−0.560735
$698$	−3.36507e78	−2.09397
$699$	9.46362e77	0.566155
$700$	−3.64834e78	−2.09845
$701$	1.90874e78	1.05561	0.527804	−	0.849366i	$-0.323016\pi$
$701$	1.90874e78	1.05561	0.527804	+	0.849366i	$0.323016\pi$
$702$	3.36019e78	1.78687
$703$	−3.99184e77	−0.204127
$704$	−2.63385e78	−1.29522
$705$	3.68249e77	0.174157
$706$	−2.10948e78	−0.959504
$707$	1.27432e78	0.557501
$708$	−2.02271e78	−0.851175
$709$	3.69220e78	1.49456	0.747280	−	0.664509i	$-0.231359\pi$
$709$	3.69220e78	1.49456	0.747280	+	0.664509i	$0.231359\pi$
$710$	8.53317e78	3.32281
$711$	−2.87723e78	−1.07785
$712$	8.33118e78	3.00266
$713$	5.20018e77	0.180325
$714$	−1.44955e78	−0.483652
$715$	−7.40305e78	−2.37681
$716$	−4.80131e78	−1.48338
$717$	−1.03940e78	−0.309033
$718$	3.45649e78	0.989039
$719$	−8.48236e77	−0.233600	−0.116800	−	0.993155i	$-0.537264\pi$
$719$	−8.48236e77	−0.233600	−0.116800	+	0.993155i	$0.537264\pi$
$720$	−4.16687e78	−1.10450
$721$	−1.40578e78	−0.358671
$722$	−6.29182e78	−1.54527
$723$	−5.24976e77	−0.124118
$724$	−7.72163e77	−0.175751
$725$	3.90910e78	0.856607
$726$	1.02202e78	0.215626
$727$	−1.05653e78	−0.214628	−0.107314	−	0.994225i	$-0.534225\pi$
$727$	−1.05653e78	−0.214628	−0.107314	+	0.994225i	$0.534225\pi$
$728$	6.75686e78	1.32170
$729$	1.53760e77	0.0289625
$730$	9.88697e78	1.79343
$731$	−5.26001e78	−0.918879
$732$	−4.23365e77	−0.0712295
$733$	7.22141e77	0.117021	0.0585104	−	0.998287i	$-0.481365\pi$
$733$	7.22141e77	0.117021	0.0585104	+	0.998287i	$0.481365\pi$
$734$	1.64079e78	0.256100
$735$	−2.95640e78	−0.444489
$736$	1.00581e78	0.145672
$737$	1.04940e79	1.46415
$738$	5.80706e78	0.780560
$739$	−6.27071e76	−0.00812073	−0.00406036	−	0.999992i	$-0.501292\pi$
$739$	−6.27071e76	−0.00812073	−0.00406036	+	0.999992i	$0.501292\pi$
$740$	−1.65544e79	−2.06558
$741$	−1.52488e78	−0.183330
$742$	−2.35240e78	−0.272523
$743$	2.11611e77	0.0236236	0.0118118	−	0.999930i	$-0.496240\pi$
$743$	2.11611e77	0.0236236	0.0118118	+	0.999930i	$0.496240\pi$
$744$	−1.48217e78	−0.159457
$745$	−2.73673e78	−0.283749
$746$	−3.15150e79	−3.14919
$747$	1.47477e79	1.42039
$748$	2.32471e79	2.15812
$749$	3.50940e78	0.314038
$750$	1.03376e79	0.891732
$751$	−1.43216e79	−1.19095	−0.595474	−	0.803374i	$-0.703036\pi$
$751$	−1.43216e79	−1.19095	−0.595474	+	0.803374i	$0.703036\pi$
$752$	2.47017e78	0.198032
$753$	3.95851e76	0.00305964
$754$	−1.48789e79	−1.10882
$755$	2.39302e79	1.71951
$756$	1.44979e79	1.00451
$757$	−2.38175e79	−1.59132	−0.795662	−	0.605741i	$-0.792877\pi$
$757$	−2.38175e79	−1.59132	−0.795662	+	0.605741i	$0.792877\pi$
$758$	−4.85862e79	−3.13047
$759$	−6.86494e78	−0.426568
$760$	1.41012e79	0.845053
$761$	1.24548e79	0.719879	0.359940	−	0.932976i	$-0.382797\pi$
$761$	1.24548e79	0.719879	0.359940	+	0.932976i	$0.382797\pi$
$762$	1.41822e79	0.790644
$763$	−1.24445e79	−0.669192
$764$	5.54431e79	2.87594
$765$	−2.55815e79	−1.28008
$766$	4.33419e79	2.09227
$767$	2.65263e79	1.23539
$768$	−1.94738e79	−0.875016
$769$	1.10483e79	0.478984	0.239492	−	0.970898i	$-0.423019\pi$
$769$	1.10483e79	0.478984	0.239492	+	0.970898i	$0.423019\pi$
$770$	−4.83405e79	−2.02216
$771$	1.22977e79	0.496397
$772$	−6.68005e79	−2.60198
$773$	1.34251e79	0.504640	0.252320	−	0.967644i	$-0.418806\pi$
$773$	1.34251e79	0.504640	0.252320	+	0.967644i	$0.418806\pi$
$774$	3.52601e79	1.27911
$775$	−1.04952e79	−0.367447
$776$	−6.22804e78	−0.210453
$777$	5.68785e78	0.185511
$778$	6.00021e78	0.188898
$779$	−5.95060e78	−0.180834
$780$	−6.32378e79	−1.85513
$781$	4.70196e79	1.33160
$782$	−5.13061e79	−1.40276
$783$	−1.55341e79	−0.410051
$784$	−1.98311e79	−0.505424
$785$	−6.41333e79	−1.57822
$786$	6.25195e79	1.48558
$787$	−9.76349e78	−0.224027	−0.112013	−	0.993707i	$-0.535730\pi$
$787$	−9.76349e78	−0.224027	−0.112013	+	0.993707i	$0.535730\pi$
$788$	1.30791e80	2.89805
$789$	−3.45025e79	−0.738300
$790$	1.85046e80	3.82414
$791$	3.04273e79	0.607310
$792$	−7.58266e79	−1.46177
$793$	5.55211e78	0.103382
$794$	7.68354e78	0.138197
$795$	1.07127e79	0.186124
$796$	−1.89591e79	−0.318207
$797$	−9.76352e79	−1.58308	−0.791539	−	0.611118i	$-0.790720\pi$
$797$	−9.76352e79	−1.58308	−0.791539	+	0.611118i	$0.790720\pi$
$798$	−9.95716e78	−0.155975
$799$	1.51650e79	0.229512
$800$	−2.02997e79	−0.296834
$801$	−1.03819e80	−1.46684
$802$	−1.80995e80	−2.47099
$803$	5.44793e79	0.718711
$804$	8.96409e79	1.14279
$805$	7.04941e79	0.868492
$806$	3.99471e79	0.475633
$807$	2.29982e79	0.264650
$808$	−1.28557e80	−1.42982
$809$	1.16511e80	1.25252	0.626259	−	0.779615i	$-0.284585\pi$
$809$	1.16511e80	1.25252	0.626259	+	0.779615i	$0.284585\pi$
$810$	1.15815e80	1.20344
$811$	−4.92243e79	−0.494432	−0.247216	−	0.968960i	$-0.579516\pi$
$811$	−4.92243e79	−0.494432	−0.247216	+	0.968960i	$0.579516\pi$
$812$	−6.41966e79	−0.623335
$813$	−9.30837e79	−0.873743
$814$	−1.38052e80	−1.25277
$815$	2.61113e80	2.29084
$816$	4.42799e79	0.375601
$817$	−3.61317e79	−0.296334
$818$	1.95111e80	1.54727
$819$	−8.42006e79	−0.645666
$820$	−2.46776e80	−1.82987
$821$	−6.21015e79	−0.445313	−0.222656	−	0.974897i	$-0.571473\pi$
$821$	−6.21015e79	−0.445313	−0.222656	+	0.974897i	$0.571473\pi$
$822$	−1.09106e80	−0.756610
$823$	1.15377e80	0.773789	0.386894	−	0.922124i	$-0.373548\pi$
$823$	1.15377e80	0.773789	0.386894	+	0.922124i	$0.373548\pi$
$824$	1.41818e80	0.919885
$825$	1.38551e80	0.869213
$826$	1.73211e80	1.05105
$827$	3.20884e79	0.188342	0.0941708	−	0.995556i	$-0.469980\pi$
$827$	3.20884e79	0.188342	0.0941708	+	0.995556i	$0.469980\pi$
$828$	2.27252e80	1.29025
$829$	1.48156e80	0.813711	0.406855	−	0.913493i	$-0.366625\pi$
$829$	1.48156e80	0.813711	0.406855	+	0.913493i	$0.366625\pi$
$830$	−9.48481e80	−5.03943
$831$	7.72325e77	0.00396983
$832$	2.95053e80	1.46726
$833$	−1.21749e80	−0.585769
$834$	1.19022e80	0.554067
$835$	−1.71683e80	−0.773300
$836$	1.59687e80	0.695981
$837$	4.17063e79	0.175894
$838$	5.65048e79	0.230608
$839$	−4.75921e80	−1.87967	−0.939835	−	0.341630i	$-0.889021\pi$
$839$	−4.75921e80	−1.87967	−0.939835	+	0.341630i	$0.889021\pi$
$840$	−2.00924e80	−0.767984
$841$	−2.01542e80	−0.745549
$842$	2.04374e80	0.731717
$843$	−2.42561e80	−0.840548
$844$	2.37970e80	0.798187
$845$	3.23382e80	1.04992
$846$	−1.01658e80	−0.319488
$847$	−5.78285e79	−0.175933
$848$	7.18593e79	0.211640
$849$	2.48917e80	0.709731
$850$	1.03548e81	2.85839
$851$	2.01318e80	0.538047
$852$	4.01647e80	1.03934
$853$	−4.08457e80	−1.02341	−0.511703	−	0.859162i	$-0.670985\pi$
$853$	−4.08457e80	−1.02341	−0.511703	+	0.859162i	$0.670985\pi$
$854$	3.62542e79	0.0879562
$855$	−1.75723e80	−0.412819
$856$	−3.54036e80	−0.805414
$857$	−1.70584e80	−0.375807	−0.187904	−	0.982187i	$-0.560169\pi$
$857$	−1.70584e80	−0.375807	−0.187904	+	0.982187i	$0.560169\pi$
$858$	−5.27357e80	−1.12513
$859$	3.33842e80	0.689809	0.344905	−	0.938638i	$-0.387911\pi$
$859$	3.33842e80	0.689809	0.344905	+	0.938638i	$0.387911\pi$
$860$	−1.49841e81	−2.99862
$861$	8.47883e79	0.164342
$862$	1.26077e80	0.236693
$863$	4.33083e80	0.787543	0.393771	−	0.919208i	$-0.371170\pi$
$863$	4.33083e80	0.787543	0.393771	+	0.919208i	$0.371170\pi$
$864$	8.06676e79	0.142092
$865$	3.39282e80	0.578919
$866$	−1.25552e81	−2.07530
$867$	−1.09838e79	−0.0175884
$868$	1.72356e80	0.267383
$869$	1.01964e81	1.53251
$870$	4.42445e80	0.644288
$871$	−1.17557e81	−1.65863
$872$	1.25543e81	1.71628
$873$	7.76108e79	0.102809
$874$	−3.52428e80	−0.452383
$875$	−5.84929e80	−0.727582
$876$	4.65370e80	0.560964
$877$	6.55585e80	0.765844	0.382922	−	0.923781i	$-0.374918\pi$
$877$	6.55585e80	0.765844	0.382922	+	0.923781i	$0.374918\pi$
$878$	−2.29462e80	−0.259783
$879$	−4.72125e80	−0.518039
$880$	1.47667e81	1.57040
$881$	9.94877e80	1.02549	0.512746	−	0.858541i	$-0.328628\pi$
$881$	9.94877e80	1.02549	0.512746	+	0.858541i	$0.328628\pi$
$882$	8.16133e80	0.815408
$883$	7.57548e80	0.733653	0.366827	−	0.930289i	$-0.380444\pi$
$883$	7.57548e80	0.733653	0.366827	+	0.930289i	$0.380444\pi$
$884$	−2.60422e81	−2.44478
$885$	−7.88795e80	−0.717835
$886$	−3.43580e81	−3.03110
$887$	−4.64982e80	−0.397683	−0.198841	−	0.980032i	$-0.563718\pi$
$887$	−4.64982e80	−0.397683	−0.198841	+	0.980032i	$0.563718\pi$
$888$	−5.73804e80	−0.475781
$889$	−8.02466e80	−0.645102
$890$	6.67701e81	5.20423
$891$	6.38164e80	0.482276
$892$	−1.05537e81	−0.773343
$893$	1.04170e80	0.0740166
$894$	−1.94951e80	−0.134321
$895$	−1.87237e81	−1.25100
$896$	1.75548e81	1.13743
$897$	7.69035e80	0.483230
$898$	−1.90236e80	−0.115929
$899$	−1.84675e80	−0.109148
$900$	−4.58649e81	−2.62913
$901$	4.41163e80	0.245283
$902$	−2.05793e81	−1.10981
$903$	5.14829e80	0.269308
$904$	−3.06958e81	−1.55757
$905$	−3.01120e80	−0.148219
$906$	1.70467e81	0.813981
$907$	1.49725e81	0.693577	0.346788	−	0.937943i	$-0.387272\pi$
$907$	1.49725e81	0.693577	0.346788	+	0.937943i	$0.387272\pi$
$908$	4.38855e81	1.97224
$909$	1.60201e81	0.698488
$910$	5.41527e81	2.29077
$911$	2.12167e81	0.870807	0.435404	−	0.900235i	$-0.356606\pi$
$911$	2.12167e81	0.870807	0.435404	+	0.900235i	$0.356606\pi$
$912$	3.04164e80	0.121130
$913$	−5.22633e81	−2.01953
$914$	−2.96227e81	−1.11072
$915$	−1.65099e80	−0.0600711
$916$	6.82240e81	2.40886
$917$	−3.53753e81	−1.21211
$918$	−4.11484e81	−1.36829
$919$	4.79467e81	1.54733	0.773664	−	0.633596i	$-0.218422\pi$
$919$	4.79467e81	1.54733	0.773664	+	0.633596i	$0.218422\pi$
$920$	−7.11161e81	−2.22742
$921$	1.14255e81	0.347324
$922$	6.35028e81	1.87367
$923$	−5.26730e81	−1.50849
$924$	−2.27534e81	−0.632508
$925$	−4.06309e81	−1.09637
$926$	−1.86617e81	−0.488821
$927$	−1.76727e81	−0.449376
$928$	−3.57196e80	−0.0881733
$929$	−8.73325e80	−0.209288	−0.104644	−	0.994510i	$-0.533370\pi$
$929$	−8.73325e80	−0.209288	−0.104644	+	0.994510i	$0.533370\pi$
$930$	−1.18788e81	−0.276371
$931$	−8.36306e80	−0.188907
$932$	1.11020e82	2.43480
$933$	2.04623e81	0.435721
$934$	−8.63393e81	−1.78513
$935$	9.06566e81	1.82004
$936$	8.49436e81	1.65594
$937$	2.20940e81	0.418250	0.209125	−	0.977889i	$-0.432938\pi$
$937$	2.20940e81	0.418250	0.209125	+	0.977889i	$0.432938\pi$
$938$	−7.67626e81	−1.41114
$939$	4.37477e79	0.00781000
$940$	4.32002e81	0.748979
$941$	7.24578e81	1.22003	0.610015	−	0.792390i	$-0.291163\pi$
$941$	7.24578e81	1.22003	0.610015	+	0.792390i	$0.291163\pi$
$942$	−4.56853e81	−0.747097
$943$	3.00104e81	0.476650
$944$	−5.29114e81	−0.816242
$945$	5.65374e81	0.847151
$946$	−1.24956e82	−1.81866
$947$	−1.07373e82	−1.51800	−0.759000	−	0.651090i	$-0.774312\pi$
$947$	−1.07373e82	−1.51800	−0.759000	+	0.651090i	$0.774312\pi$
$948$	8.70991e81	1.19615
$949$	−6.10297e81	−0.814179
$950$	7.11286e81	0.921817
$951$	−3.24157e81	−0.408123
$952$	−8.27434e81	−1.01209
$953$	−2.80192e81	−0.332966	−0.166483	−	0.986044i	$-0.553241\pi$
$953$	−2.80192e81	−0.332966	−0.166483	+	0.986044i	$0.553241\pi$
$954$	−2.95731e81	−0.341441
$955$	2.16211e82	2.42541
$956$	−1.21934e82	−1.32903
$957$	2.43796e81	0.258196
$958$	7.48556e81	0.770322
$959$	6.17350e81	0.617333
$960$	−8.77380e81	−0.852567
$961$	−1.00941e82	−0.953180
$962$	1.54650e82	1.41918
$963$	4.41182e81	0.393455
$964$	−6.15862e81	−0.533784
$965$	−2.60502e82	−2.19437
$966$	5.02165e81	0.411126
$967$	6.52535e81	0.519249	0.259624	−	0.965710i	$-0.416401\pi$
$967$	6.52535e81	0.519249	0.259624	+	0.965710i	$0.416401\pi$
$968$	5.83388e81	0.451217
$969$	1.86734e81	0.140385
$970$	−4.99145e81	−0.364758
$971$	−2.42379e82	−1.72173	−0.860866	−	0.508833i	$-0.830077\pi$
$971$	−2.42379e82	−1.72173	−0.860866	+	0.508833i	$0.830077\pi$
$972$	2.83804e82	1.95973
$973$	−6.73462e81	−0.452074
$974$	5.13522e82	3.35110
$975$	−1.55210e82	−0.984674
$976$	−1.10747e81	−0.0683063
$977$	−1.29199e82	−0.774744	−0.387372	−	0.921923i	$-0.626617\pi$
$977$	−1.29199e82	−0.774744	−0.387372	+	0.921923i	$0.626617\pi$
$978$	1.86004e82	1.08443
$979$	3.67917e82	2.08558
$980$	−3.46822e82	−1.91157
$981$	−1.56445e82	−0.838425
$982$	−3.04152e82	−1.58498
$983$	−1.06339e82	−0.538854	−0.269427	−	0.963021i	$-0.586834\pi$
$983$	−1.06339e82	−0.538854	−0.269427	+	0.963021i	$0.586834\pi$
$984$	−8.55365e81	−0.421489
$985$	5.10044e82	2.44406
$986$	1.82205e82	0.849073
$987$	−1.48429e81	−0.0672663
$988$	−1.78887e82	−0.788431
$989$	1.82221e82	0.781089
$990$	−6.07711e82	−2.53355
$991$	−2.78037e82	−1.12740	−0.563699	−	0.825980i	$-0.690622\pi$
$991$	−2.78037e82	−1.12740	−0.563699	+	0.825980i	$0.690622\pi$
$992$	9.59005e80	0.0378225
$993$	−1.04284e82	−0.400051
$994$	−3.43944e82	−1.28340
$995$	−7.39349e81	−0.268358
$996$	−4.46440e82	−1.57627
$997$	4.12474e82	1.41671	0.708353	−	0.705858i	$-0.249438\pi$
$997$	4.12474e82	1.41671	0.708353	+	0.705858i	$0.249438\pi$
$998$	9.53941e82	3.18736
$999$	1.61461e82	0.524826

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+3.25888e8 q^{2} +5.98183e12 q^{3} +7.01743e16 q^{4} +2.73659e19 q^{5} +1.94941e21 q^{6} -1.10303e23 q^{7} +1.11276e25 q^{8} -1.38667e26 q^{9} +O(q^{10})\)	\(q+3.25888e8 q^{2} +5.98183e12 q^{3} +7.01743e16 q^{4} +2.73659e19 q^{5} +1.94941e21 q^{6} -1.10303e23 q^{7} +1.11276e25 q^{8} -1.38667e26 q^{9} +8.91821e27 q^{10} +4.91412e28 q^{11} +4.19771e29 q^{12} -5.50498e30 q^{13} -3.59464e31 q^{14} +1.63698e32 q^{15} +1.09807e33 q^{16} +6.74131e33 q^{17} -4.51899e34 q^{18} +4.63069e34 q^{19} +1.92038e36 q^{20} -6.59813e35 q^{21} +1.60146e37 q^{22} -2.33537e37 q^{23} +6.65636e37 q^{24} +4.71335e38 q^{25} -1.79401e39 q^{26} -1.87301e39 q^{27} -7.74043e39 q^{28} +8.29368e39 q^{29} +5.33472e40 q^{30} -2.22670e40 q^{31} -4.30685e40 q^{32} +2.93955e41 q^{33} +2.19691e42 q^{34} -3.01853e42 q^{35} -9.73086e42 q^{36} -8.62039e42 q^{37} +1.50909e43 q^{38} -3.29298e43 q^{39} +3.04517e44 q^{40} -1.28503e44 q^{41} -2.15025e44 q^{42} -7.80265e44 q^{43} +3.44845e45 q^{44} -3.79474e45 q^{45} -7.61071e45 q^{46} +2.24956e45 q^{47} +6.56844e45 q^{48} -1.80601e46 q^{49} +1.53602e47 q^{50} +4.03254e46 q^{51} -3.86308e47 q^{52} +6.54418e46 q^{53} -6.10391e47 q^{54} +1.34479e48 q^{55} -1.22741e48 q^{56} +2.77000e47 q^{57} +2.70281e48 q^{58} -4.81860e48 q^{59} +1.14874e49 q^{60} -1.00856e48 q^{61} -7.25655e48 q^{62} +1.52954e49 q^{63} -5.35975e49 q^{64} -1.50648e50 q^{65} +9.57963e49 q^{66} +2.13547e50 q^{67} +4.73067e50 q^{68} -1.39698e50 q^{69} -9.83705e50 q^{70} +9.56825e50 q^{71} -1.54303e51 q^{72} +1.10863e51 q^{73} -2.80928e51 q^{74} +2.81945e51 q^{75} +3.24956e51 q^{76} -5.42042e51 q^{77} -1.07314e52 q^{78} +2.07492e52 q^{79} +3.00495e52 q^{80} +1.29863e52 q^{81} -4.18778e52 q^{82} -1.06353e53 q^{83} -4.63019e52 q^{84} +1.84482e53 q^{85} -2.54279e53 q^{86} +4.96114e52 q^{87} +5.46825e53 q^{88} +7.48693e53 q^{89} -1.23666e54 q^{90} +6.07215e53 q^{91} -1.63883e54 q^{92} -1.33197e53 q^{93} +7.33106e53 q^{94} +1.26723e54 q^{95} -2.57628e53 q^{96} -5.59692e53 q^{97} -5.88557e54 q^{98} -6.81426e54 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 208622520 q^{2} - 6821470691280 q^{3} + 38\!\cdots\!72 q^{4}+ \cdots + 47\!\cdots\!28 q^{9}+O(q^{10}) \) 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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