LMFDB - Embedded newform 9.94.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,94,Mod(1,9)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 94, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 94);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 94 $
Character orbit:	$[\chi]$	$=$	9.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:	$492.952887545$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} + \cdots - 13\!\cdots\!00 $ x^7 - x^6 - 160477500301516091326739x^5 + 877016488484326647371325741724874x^4 + 7260529465737129707868752892581169765229378456x^3 - 20781038399188480098606854392326662967337072615105929280x^2 - 71309214652872234197294752847774640455181142633761719353245451878000*x - 1353216958878139720025204995487184336935523797943751976847532373756765247900000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{88}\cdot 3^{47}\cdot 5^{10}\cdot 7^{6}\cdot 13^{2}\cdot 19\cdot 23\cdot 31^{2} $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.59428e11$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.55678e14 q^{2} +1.43322e28 q^{4} +3.85879e32 q^{5} -1.93687e39 q^{7} -6.89447e41 q^{8} +O(q^{10})$	\(q-1.55678e14 q^{2} +1.43322e28 q^{4} +3.85879e32 q^{5} -1.93687e39 q^{7} -6.89447e41 q^{8} -6.00730e46 q^{10} -4.19320e48 q^{11} -6.72877e51 q^{13} +3.01529e53 q^{14} -3.46072e55 q^{16} -7.90484e56 q^{17} -1.84855e59 q^{19} +5.53049e60 q^{20} +6.52790e62 q^{22} +3.52814e63 q^{23} +4.79285e64 q^{25} +1.04752e66 q^{26} -2.77596e67 q^{28} -6.08060e66 q^{29} -3.87123e69 q^{31} +1.22155e70 q^{32} +1.23061e71 q^{34} -7.47399e71 q^{35} +9.82535e72 q^{37} +2.87779e73 q^{38} -2.66043e74 q^{40} -1.01031e75 q^{41} +9.34216e75 q^{43} -6.00977e76 q^{44} -5.49254e77 q^{46} +5.01133e76 q^{47} -1.76033e77 q^{49} -7.46143e78 q^{50} -9.64379e79 q^{52} -1.92932e80 q^{53} -1.61807e81 q^{55} +1.33537e81 q^{56} +9.46617e80 q^{58} +2.20461e81 q^{59} -3.04227e82 q^{61} +6.02666e83 q^{62} -1.55896e84 q^{64} -2.59649e84 q^{65} -8.28207e84 q^{67} -1.13294e85 q^{68} +1.16354e86 q^{70} -1.80973e86 q^{71} -2.33738e86 q^{73} -1.52959e87 q^{74} -2.64937e87 q^{76} +8.12170e87 q^{77} -4.15888e87 q^{79} -1.33542e88 q^{80} +1.57284e89 q^{82} -5.26808e88 q^{83} -3.05031e89 q^{85} -1.45437e90 q^{86} +2.89099e90 q^{88} -3.32123e90 q^{89} +1.30328e91 q^{91} +5.05660e91 q^{92} -7.80155e90 q^{94} -7.13316e91 q^{95} +2.28947e92 q^{97} +2.74045e91 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 43735426713792 q^{2} + 37\!\cdots\!44 q^{4}+ \cdots - 62\!\cdots\!60 q^{8}+O(q^{10}) $ 7 * q - 43735426713792 * q^2 + 37433779444352805880587218944 * q^4 + 242501922056818695041616562179750 * q^5 - 921137753903839555947108372394316103208 * q^7 - 628568314501252186502498490389635108700160 * q^8	$ 7 q - 43735426713792 q^{2} + 37\!\cdots\!44 q^{4}+ \cdots + 69\!\cdots\!56 q^{98}+O(q^{100}) $ 7 * q - 43735426713792 * q^2 + 37433779444352805880587218944 * q^4 + 242501922056818695041616562179750 * q^5 - 921137753903839555947108372394316103208 * q^7 - 628568314501252186502498490389635108700160 * q^8 + 56663128890275718532856219951648854919834448000 * q^10 - 1081566396126190174166498109003279139923369012324 * q^11 + 1923851638471797431690458036346871401286646408469426 * q^13 + 827492161115181455891429526236298470299001717526508032 * q^14 - 183863117199568288307852091185855957272115704336744448 * q^16 - 809325537307953309871783611300921224816172571619454935742 * q^17 - 491316328040151561437984621759105514680907320256463264658500 * q^19 + 5819101371751539891329503686613738398860076574931824253952000 * q^20 + 341061341496448817039487179432626029859991533289656810924326144 * q^22 + 2595697104202345855126053487687658963668179272707633091075699064 * q^23 + 184388886386678531186865888507627315189418933935123407708899515625 * q^25 - 793059166145746283698718389909557916534745558035448772312212840064 * q^26 + 1916814131388145595393790805747801246689773266225672358812878209024 * q^28 - 115585291038420509795092429775705167101645550654624527668945364036450 * q^29 - 1163635467946810748613893942791764663199899897323284701513531956983456 * q^31 + 7066990866795922437106429389517828098400874624281122281464920526553088 * q^32 + 80911624156374405155780927188384543491071504244617539921495324380294528 * q^34 + 1672188852118103650980495790489284130570309869892526153633308501275462000 * q^35 + 11072759435314078994932599484815080247923078570346623467670584315337670842 * q^37 + 42692186143014046654789275667852179938472092905944200699148410427788924160 * q^38 + 760187696799287916151508882607919116749295190931669242261910585944965120000 * q^40 + 509603803596826806676973650829096820638503322986104149790656476262528674746 * q^41 - 7275658116979055674748970912580687053338617746072325435955591393683798211644 * q^43 - 9423347779397833928027118997217234224491886242773059800183027480258516369408 * q^44 - 639778771092842366359510076082228574613573083413403803040568658686807125218816 * q^46 + 371149830895115606730684780470708713676568637183334957675426341554516993409008 * q^47 + 2561975156227711495237514871966779964501558283497058708235084248829398599957999 * q^49 + 31492320141514234591073138519794385457712593727985587891779934655429621403000000 * q^50 - 55278983045853834535146427408736596689073596604984335518990233309047240924848128 * q^52 + 363766241548602923075270727552075967170433033161760056492510229436384310833635734 * q^53 - 3520855393890604949232827617669938515471701214675853816941159595183623184386577000 * q^55 + 12936956692485908268365121199611114191360014164491088694387999166431300696512921600 * q^56 - 73663001170657752665346575473371223431752845037418753763472734766611572171441325440 * q^58 + 119839908140624573484226478891501296275544385047787439213910489726968365086286210700 * q^59 - 328281166748320542242523532793984772143143166398612931227281116669834617338050603326 * q^61 + 999402477792071119370831029463209574610493980381087626216590758004912070795081435136 * q^62 - 4748321960274080197621802735261780227229800262185345649692550833454877416714840047616 * q^64 - 2401958293154067008332922023669433962969772004736123854920087208208149417890196631500 * q^65 + 9715050085721519766982024893817705652242604355912950898916137527198529527932523084492 * q^67 - 51110178162381015351883898716980001063480395685110983605059672645927223406195391258624 * q^68 + 437770522317274261347763126091338009235407849188339858200284725822565513739255154816000 * q^70 - 420099768445021912291978352393445519280746916987347799091649913407485898651223357176984 * q^71 + 249990884773795871360906735022065792056914028590737521750721031757996649920054698123686 * q^73 - 988848152146322932205109547460090361956964236264222955609677033303897103570301064734848 * q^74 - 9872924363930092749183448370538218854882826462181838927155554514487863834399954370969600 * q^76 + 16552736755381232703525388842736711985373990693881749218915711388952768140257306836693856 * q^77 - 43369884997252312790262999909905208728154246791055779943371432494520439561399960810221200 * q^79 + 88894687813962777903012798348655018553862729556819104796394604135123942915181092274176000 * q^80 - 236357995159599133663604843384379044643064499685381579522884048932961281765779447211829376 * q^82 + 206459225650342475045148123542600401116221913586781003327705338223920418727874732010864004 * q^83 + 1637661121678145282281696006564110640734919603287375198985971859556394144920752854974380500 * q^85 - 3239900597437756786176903087412721547247433713557247371056571790561416975430434191434708224 * q^86 + 6336674026069399594730100443279513731166873520796702455565229756349453295686310223539077120 * q^88 - 5580799156439265704685765323272125687903700231557911629488221982292995723510480958101067350 * q^89 - 18025272478314007503227783954648499409552734863956310123113904904033321293148703549329112496 * q^91 + 81750027044574246291550532241925751638073881610946649428268147310600744342795416362583031808 * q^92 - 306478475429892162274969547511367839192733042761577860914963828391848832364650578690812603392 * q^94 + 216711696129933523762297615654778954621414663971673687874218846402427636558070586043601335000 * q^95 + 43971291171253027759915173352741872464098193495293359649108047104658615767375645954946743342 * q^97 + 690328280759812206538864038068682435013428219472201721649324072601042235191425205897720616256 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.55678e14	−1.56435	−0.782173	−	0.623061i	$-0.785889\pi$
$2$	−1.55678e14	−1.56435	−0.782173	+	0.623061i	$0.785889\pi$
$3$	0	0
$3$	0	0
$4$	1.43322e28	1.44718
$5$	3.85879e32	1.21436	0.607178	−	0.794566i	$-0.292301\pi$
$5$	3.85879e32	1.21436	0.607178	+	0.794566i	$0.292301\pi$
$6$	0	0
$7$	−1.93687e39	−0.977333	−0.488666	−	0.872471i	$-0.662516\pi$
$7$	−1.93687e39	−0.977333	−0.488666	+	0.872471i	$0.662516\pi$
$8$	−6.89447e41	−0.699547
$9$	0	0
$10$	−6.00730e46	−1.89967
$11$	−4.19320e48	−1.57683	−0.788416	−	0.615142i	$-0.789099\pi$
$11$	−4.19320e48	−1.57683	−0.788416	+	0.615142i	$0.789099\pi$
$12$	0	0
$13$	−6.72877e51	−1.07046	−0.535229	−	0.844707i	$-0.679775\pi$
$13$	−6.72877e51	−1.07046	−0.535229	+	0.844707i	$0.679775\pi$
$14$	3.01529e53	1.52889
$15$	0	0
$16$	−3.46072e55	−0.352848
$17$	−7.90484e56	−0.480859	−0.240430	−	0.970667i	$-0.577288\pi$
$17$	−7.90484e56	−0.480859	−0.240430	+	0.970667i	$0.577288\pi$
$18$	0	0
$19$	−1.84855e59	−0.637952	−0.318976	−	0.947763i	$-0.603339\pi$
$19$	−1.84855e59	−0.637952	−0.318976	+	0.947763i	$0.603339\pi$
$20$	5.53049e60	1.75739
$21$	0	0
$22$	6.52790e62	2.46671
$23$	3.52814e63	1.68733	0.843667	−	0.536866i	$-0.180392\pi$
$23$	3.52814e63	1.68733	0.843667	+	0.536866i	$0.180392\pi$
$24$	0	0
$25$	4.79285e64	0.474661
$26$	1.04752e66	1.67457
$27$	0	0
$28$	−2.77596e67	−1.41438
$29$	−6.08060e66	−0.0605954	−0.0302977	−	0.999541i	$-0.509646\pi$
$29$	−6.08060e66	−0.0605954	−0.0302977	+	0.999541i	$0.509646\pi$
$30$	0	0
$31$	−3.87123e69	−1.73592	−0.867961	−	0.496633i	$-0.834570\pi$
$31$	−3.87123e69	−1.73592	−0.867961	+	0.496633i	$0.834570\pi$
$32$	1.22155e70	1.25152
$33$	0	0
$34$	1.23061e71	0.752231
$35$	−7.47399e71	−1.18683
$36$	0	0
$37$	9.82535e72	1.17752	0.588760	−	0.808308i	$-0.299616\pi$
$37$	9.82535e72	1.17752	0.588760	+	0.808308i	$0.299616\pi$
$38$	2.87779e73	0.997979
$39$	0	0
$40$	−2.66043e74	−0.849499
$41$	−1.01031e75	−1.02331	−0.511654	−	0.859192i	$-0.670967\pi$
$41$	−1.01031e75	−1.02331	−0.511654	+	0.859192i	$0.670967\pi$
$42$	0	0
$43$	9.34216e75	1.03315	0.516576	−	0.856241i	$-0.327206\pi$
$43$	9.34216e75	1.03315	0.516576	+	0.856241i	$0.327206\pi$
$44$	−6.00977e76	−2.28196
$45$	0	0
$46$	−5.49254e77	−2.63958
$47$	5.01133e76	0.0885937	0.0442968	−	0.999018i	$-0.485895\pi$
$47$	5.01133e76	0.0885937	0.0442968	+	0.999018i	$0.485895\pi$
$48$	0	0
$49$	−1.76033e77	−0.0448204
$50$	−7.46143e78	−0.742535
$51$	0	0
$52$	−9.64379e79	−1.54915
$53$	−1.92932e80	−1.27813	−0.639066	−	0.769152i	$-0.720679\pi$
$53$	−1.92932e80	−1.27813	−0.639066	+	0.769152i	$0.720679\pi$
$54$	0	0
$55$	−1.61807e81	−1.91484
$56$	1.33537e81	0.683690
$57$	0	0
$58$	9.46617e80	0.0947922
$59$	2.20461e81	0.0997043	0.0498521	−	0.998757i	$-0.484125\pi$
$59$	2.20461e81	0.0997043	0.0498521	+	0.998757i	$0.484125\pi$
$60$	0	0
$61$	−3.04227e82	−0.291985	−0.145992	−	0.989286i	$-0.546638\pi$
$61$	−3.04227e82	−0.291985	−0.145992	+	0.989286i	$0.546638\pi$
$62$	6.02666e83	2.71558
$63$	0	0
$64$	−1.55896e84	−1.60497
$65$	−2.59649e84	−1.29992
$66$	0	0
$67$	−8.28207e84	−1.01312	−0.506560	−	0.862205i	$-0.669083\pi$
$67$	−8.28207e84	−1.01312	−0.506560	+	0.862205i	$0.669083\pi$
$68$	−1.13294e85	−0.695891
$69$	0	0
$70$	1.16354e86	1.85661
$71$	−1.80973e86	−1.49314	−0.746570	−	0.665307i	$-0.768301\pi$
$71$	−1.80973e86	−1.49314	−0.746570	+	0.665307i	$0.768301\pi$
$72$	0	0
$73$	−2.33738e86	−0.529927	−0.264963	−	0.964258i	$-0.585360\pi$
$73$	−2.33738e86	−0.529927	−0.264963	+	0.964258i	$0.585360\pi$
$74$	−1.52959e87	−1.84205
$75$	0	0
$76$	−2.64937e87	−0.923233
$77$	8.12170e87	1.54109
$78$	0	0
$79$	−4.15888e87	−0.239506	−0.119753	−	0.992804i	$-0.538210\pi$
$79$	−4.15888e87	−0.239506	−0.119753	+	0.992804i	$0.538210\pi$
$80$	−1.33542e88	−0.428483
$81$	0	0
$82$	1.57284e89	1.60081
$83$	−5.26808e88	−0.305155	−0.152578	−	0.988291i	$-0.548757\pi$
$83$	−5.26808e88	−0.305155	−0.152578	+	0.988291i	$0.548757\pi$
$84$	0	0
$85$	−3.05031e89	−0.583935
$86$	−1.45437e90	−1.61621
$87$	0	0
$88$	2.89099e90	1.10307
$89$	−3.32123e90	−0.749313	−0.374656	−	0.927164i	$-0.622239\pi$
$89$	−3.32123e90	−0.749313	−0.374656	+	0.927164i	$0.622239\pi$
$90$	0	0
$91$	1.30328e91	1.04619
$92$	5.05660e91	2.44188
$93$	0	0
$94$	−7.80155e90	−0.138591
$95$	−7.13316e91	−0.774701
$96$	0	0
$97$	2.28947e92	0.943731	0.471866	−	0.881670i	$-0.343581\pi$
$97$	2.28947e92	0.943731	0.471866	+	0.881670i	$0.343581\pi$
$98$	2.74045e91	0.0701147
$99$	0	0
$100$	6.86921e92	0.686921
$101$	−7.22314e92	−0.454760	−0.227380	−	0.973806i	$-0.573016\pi$
$101$	−7.22314e92	−0.454760	−0.227380	+	0.973806i	$0.573016\pi$
$102$	0	0
$103$	−2.71237e93	−0.686148	−0.343074	−	0.939308i	$-0.611468\pi$
$103$	−2.71237e93	−0.686148	−0.343074	+	0.939308i	$0.611468\pi$
$104$	4.63913e93	0.748835
$105$	0	0
$106$	3.00353e94	1.99944
$107$	7.44894e93	0.320442	0.160221	−	0.987081i	$-0.448779\pi$
$107$	7.44894e93	0.320442	0.160221	+	0.987081i	$0.448779\pi$
$108$	0	0
$109$	−3.92415e94	−0.713532	−0.356766	−	0.934194i	$-0.616121\pi$
$109$	−3.92415e94	−0.713532	−0.356766	+	0.934194i	$0.616121\pi$
$110$	2.51898e95	2.99547
$111$	0	0
$112$	6.70298e94	0.344849
$113$	−3.44959e95	−1.17387	−0.586935	−	0.809634i	$-0.699665\pi$
$113$	−3.44959e95	−1.17387	−0.586935	+	0.809634i	$0.699665\pi$
$114$	0	0
$115$	1.36144e96	2.04903
$116$	−8.71483e94	−0.0876925
$117$	0	0
$118$	−3.43210e95	−0.155972
$119$	1.53107e96	0.469960
$120$	0	0
$121$	1.05113e97	1.48640
$122$	4.73615e96	0.456765
$123$	0	0
$124$	−5.54832e97	−2.51219
$125$	−2.04692e97	−0.637949
$126$	0	0
$127$	−7.56617e97	−1.12720	−0.563602	−	0.826046i	$-0.690585\pi$
$127$	−7.56617e97	−1.12720	−0.563602	+	0.826046i	$0.690585\pi$
$128$	1.21719e98	1.25920
$129$	0	0
$130$	4.04217e98	2.03352
$131$	3.57749e98	1.26027	0.630135	−	0.776486i	$-0.283000\pi$
$131$	3.57749e98	1.26027	0.630135	+	0.776486i	$0.283000\pi$
$132$	0	0
$133$	3.58040e98	0.623492
$134$	1.28934e99	1.58487
$135$	0	0
$136$	5.44997e98	0.336384
$137$	2.60803e99	1.14500	0.572502	−	0.819904i	$-0.305973\pi$
$137$	2.60803e99	1.14500	0.572502	+	0.819904i	$0.305973\pi$
$138$	0	0
$139$	−4.38756e99	−0.981826	−0.490913	−	0.871208i	$-0.663337\pi$
$139$	−4.38756e99	−0.981826	−0.490913	+	0.871208i	$0.663337\pi$
$140$	−1.07119e100	−1.71756
$141$	0	0
$142$	2.81735e100	2.33579
$143$	2.82151e100	1.68793
$144$	0	0
$145$	−2.34638e99	−0.0735844
$146$	3.63879e100	0.828990
$147$	0	0
$148$	1.40819e101	1.70408
$149$	−1.00746e101	−0.891387	−0.445694	−	0.895186i	$-0.647043\pi$
$149$	−1.00746e101	−0.891387	−0.445694	+	0.895186i	$0.647043\pi$
$150$	0	0
$151$	−1.51245e101	−0.719869	−0.359934	−	0.932978i	$-0.617201\pi$
$151$	−1.51245e101	−0.719869	−0.359934	+	0.932978i	$0.617201\pi$
$152$	1.27448e101	0.446277
$153$	0	0
$154$	−1.26437e102	−2.41080
$155$	−1.49383e102	−2.10803
$156$	0	0
$157$	−1.66159e102	−1.29179	−0.645894	−	0.763427i	$-0.723515\pi$
$157$	−1.66159e102	−1.29179	−0.645894	+	0.763427i	$0.723515\pi$
$158$	6.47447e101	0.374671
$159$	0	0
$160$	4.71372e102	1.51979
$161$	−6.83356e102	−1.64909
$162$	0	0
$163$	−2.86054e99	−0.000388798 0	−0.000194399	−	1.00000i	$-0.500062\pi$
$163$	−2.86054e99	−0.000388798 0	−0.000194399		1.00000i	$0.500062\pi$
$164$	−1.44800e103	−1.48091
$165$	0	0
$166$	8.20125e102	0.477369
$167$	3.04310e102	0.133968	0.0669839	−	0.997754i	$-0.478662\pi$
$167$	3.04310e102	0.133968	0.0669839	+	0.997754i	$0.478662\pi$
$168$	0	0
$169$	5.76403e102	0.145880
$170$	4.74867e103	0.913476
$171$	0	0
$172$	1.33894e104	1.49516
$173$	1.26480e104	1.07864	0.539321	−	0.842100i	$-0.318681\pi$
$173$	1.26480e104	1.07864	0.539321	+	0.842100i	$0.318681\pi$
$174$	0	0
$175$	−9.28315e103	−0.463902
$176$	1.45115e104	0.556382
$177$	0	0
$178$	5.17043e104	1.17219
$179$	−5.12887e104	−0.896099	−0.448049	−	0.894009i	$-0.647881\pi$
$179$	−5.12887e104	−0.896099	−0.448049	+	0.894009i	$0.647881\pi$
$180$	0	0
$181$	2.14822e104	0.223885	0.111943	−	0.993715i	$-0.464293\pi$
$181$	2.14822e104	0.223885	0.111943	+	0.993715i	$0.464293\pi$
$182$	−2.02892e105	−1.63661
$183$	0	0
$184$	−2.43247e105	−1.18037
$185$	3.79140e105	1.42993
$186$	0	0
$187$	3.31466e105	0.758235
$188$	7.18234e104	0.128211
$189$	0	0
$190$	1.11048e106	1.21190
$191$	−1.28582e106	−1.09933	−0.549664	−	0.835386i	$-0.685244\pi$
$191$	−1.28582e106	−1.09933	−0.549664	+	0.835386i	$0.685244\pi$
$192$	0	0
$193$	−2.06907e106	−1.08983	−0.544917	−	0.838490i	$-0.683439\pi$
$193$	−2.06907e106	−1.08983	−0.544917	+	0.838490i	$0.683439\pi$
$194$	−3.56420e106	−1.47632
$195$	0	0
$196$	−2.52294e105	−0.0648633
$197$	2.95791e106	0.600212	0.300106	−	0.953906i	$-0.402978\pi$
$197$	2.95791e106	0.600212	0.300106	+	0.953906i	$0.402978\pi$
$198$	0	0
$199$	−2.16795e106	−0.275031	−0.137515	−	0.990500i	$-0.543912\pi$
$199$	−2.16795e106	−0.275031	−0.137515	+	0.990500i	$0.543912\pi$
$200$	−3.30442e106	−0.332048
$201$	0	0
$202$	1.12449e107	0.711402
$203$	1.17774e106	0.0592218
$204$	0	0
$205$	−3.89859e107	−1.24266
$206$	4.22257e107	1.07337
$207$	0	0
$208$	2.32864e107	0.377708
$209$	7.75133e107	1.00594
$210$	0	0
$211$	−5.65431e107	−0.471244	−0.235622	−	0.971845i	$-0.575713\pi$
$211$	−5.65431e107	−0.471244	−0.235622	+	0.971845i	$0.575713\pi$
$212$	−2.76513e108	−1.84969
$213$	0	0
$214$	−1.15964e108	−0.501282
$215$	3.60494e108	1.25461
$216$	0	0
$217$	7.49808e108	1.69657
$218$	6.10905e108	1.11621
$219$	0	0
$220$	−2.31905e109	−2.77112
$221$	5.31898e108	0.514740
$222$	0	0
$223$	5.40231e108	0.343877	0.171938	−	0.985108i	$-0.444997\pi$
$223$	5.40231e108	0.343877	0.171938	+	0.985108i	$0.444997\pi$
$224$	−2.36600e109	−1.22315
$225$	0	0
$226$	5.37026e109	1.83634
$227$	3.58190e109	0.997496	0.498748	−	0.866747i	$-0.333793\pi$
$227$	3.58190e109	0.997496	0.498748	+	0.866747i	$0.333793\pi$
$228$	0	0
$229$	−1.02602e110	−1.90023	−0.950116	−	0.311898i	$-0.899035\pi$
$229$	−1.02602e110	−1.90023	−0.950116	+	0.311898i	$0.899035\pi$
$230$	−2.11946e110	−3.20539
$231$	0	0
$232$	4.19225e108	0.0423893
$233$	−8.36616e109	−0.692589	−0.346295	−	0.938126i	$-0.612560\pi$
$233$	−8.36616e109	−0.692589	−0.346295	+	0.938126i	$0.612560\pi$
$234$	0	0
$235$	1.93377e109	0.107584
$236$	3.15969e109	0.144290
$237$	0	0
$238$	−2.38354e110	−0.735180
$239$	6.35040e110	1.61175	0.805877	−	0.592083i	$-0.201694\pi$
$239$	6.35040e110	1.61175	0.805877	+	0.592083i	$0.201694\pi$
$240$	0	0
$241$	−8.57088e110	−1.47650	−0.738249	−	0.674528i	$-0.764347\pi$
$241$	−8.57088e110	−1.47650	−0.738249	+	0.674528i	$0.764347\pi$
$242$	−1.63638e111	−2.32525
$243$	0	0
$244$	−4.36024e110	−0.422555
$245$	−6.79274e109	−0.0544280
$246$	0	0
$247$	1.24384e111	0.682901
$248$	2.66901e111	1.21436
$249$	0	0
$250$	3.18661e111	0.997973
$251$	−2.56709e111	−0.667749	−0.333874	−	0.942618i	$-0.608356\pi$
$251$	−2.56709e111	−0.667749	−0.333874	+	0.942618i	$0.608356\pi$
$252$	0	0
$253$	−1.47942e112	−2.66065
$254$	1.17789e112	1.76334
$255$	0	0
$256$	−3.50986e111	−0.364864
$257$	−1.84481e112	−1.59978	−0.799892	−	0.600143i	$-0.795110\pi$
$257$	−1.84481e112	−1.59978	−0.799892	+	0.600143i	$0.795110\pi$
$258$	0	0
$259$	−1.90305e112	−1.15083
$260$	−3.72134e112	−1.88122
$261$	0	0
$262$	−5.56938e112	−1.97150
$263$	−3.59863e112	−1.06707	−0.533537	−	0.845777i	$-0.679138\pi$
$263$	−3.59863e112	−1.06707	−0.533537	+	0.845777i	$0.679138\pi$
$264$	0	0
$265$	−7.44483e112	−1.55211
$266$	−5.57391e112	−0.975357
$267$	0	0
$268$	−1.18700e113	−1.46617
$269$	5.66507e112	0.588470	0.294235	−	0.955733i	$-0.404935\pi$
$269$	5.66507e112	0.588470	0.294235	+	0.955733i	$0.404935\pi$
$270$	0	0
$271$	−7.88661e112	−0.580521	−0.290261	−	0.956948i	$-0.593742\pi$
$271$	−7.88661e112	−0.580521	−0.290261	+	0.956948i	$0.593742\pi$
$272$	2.73564e112	0.169670
$273$	0	0
$274$	−4.06014e113	−1.79118
$275$	−2.00974e113	−0.748461
$276$	0	0
$277$	3.52207e113	0.936459	0.468230	−	0.883607i	$-0.344892\pi$
$277$	3.52207e113	0.936459	0.468230	+	0.883607i	$0.344892\pi$
$278$	6.83047e113	1.53592
$279$	0	0
$280$	5.15293e113	0.830243
$281$	−1.16368e114	−1.58851	−0.794254	−	0.607585i	$-0.792138\pi$
$281$	−1.16368e114	−1.58851	−0.794254	+	0.607585i	$0.792138\pi$
$282$	0	0
$283$	8.32067e113	0.816750	0.408375	−	0.912814i	$-0.366096\pi$
$283$	8.32067e113	0.816750	0.408375	+	0.912814i	$0.366096\pi$
$284$	−2.59374e114	−2.16084
$285$	0	0
$286$	−4.39247e114	−2.64051
$287$	1.95685e114	1.00011
$288$	0	0
$289$	−2.07754e114	−0.768774
$290$	3.65280e113	0.115111
$291$	0	0
$292$	−3.34998e114	−0.766900
$293$	3.53924e114	0.691140	0.345570	−	0.938393i	$-0.387686\pi$
$293$	3.53924e114	0.691140	0.345570	+	0.938393i	$0.387686\pi$
$294$	0	0
$295$	8.50714e113	0.121076
$296$	−6.77407e114	−0.823730
$297$	0	0
$298$	1.56840e115	1.39444
$299$	−2.37400e115	−1.80622
$300$	0	0
$301$	−1.80946e115	−1.00973
$302$	2.35456e115	1.12612
$303$	0	0
$304$	6.39730e114	0.225100
$305$	−1.17395e115	−0.354574
$306$	0	0
$307$	2.44087e115	0.544013	0.272007	−	0.962295i	$-0.412313\pi$
$307$	2.44087e115	0.544013	0.272007	+	0.962295i	$0.412313\pi$
$308$	1.16402e116	2.23024
$309$	0	0
$310$	2.32556e116	3.29769
$311$	−5.39685e114	−0.0658843	−0.0329422	−	0.999457i	$-0.510488\pi$
$311$	−5.39685e114	−0.0658843	−0.0329422	+	0.999457i	$0.510488\pi$
$312$	0	0
$313$	−3.83093e115	−0.347130	−0.173565	−	0.984822i	$-0.555529\pi$
$313$	−3.83093e115	−0.347130	−0.173565	+	0.984822i	$0.555529\pi$
$314$	2.58674e116	2.02080
$315$	0	0
$316$	−5.96059e115	−0.346609
$317$	2.64242e116	1.32662	0.663309	−	0.748346i	$-0.269151\pi$
$317$	2.64242e116	1.32662	0.663309	+	0.748346i	$0.269151\pi$
$318$	0	0
$319$	2.54972e115	0.0955488
$320$	−6.01571e116	−1.94900
$321$	0	0
$322$	1.06384e117	2.57975
$323$	1.46125e116	0.306765
$324$	0	0
$325$	−3.22500e116	−0.508105
$326$	4.45324e113	0.000608216 0
$327$	0	0
$328$	6.96557e116	0.715852
$329$	−9.70632e115	−0.0865855
$330$	0	0
$331$	−2.97400e116	−0.200143	−0.100071	−	0.994980i	$-0.531907\pi$
$331$	−2.97400e116	−0.200143	−0.100071	+	0.994980i	$0.531907\pi$
$332$	−7.55031e116	−0.441615
$333$	0	0
$334$	−4.73744e116	−0.209572
$335$	−3.19588e117	−1.23029
$336$	0	0
$337$	3.75895e117	1.09717	0.548587	−	0.836093i	$-0.315166\pi$
$337$	3.75895e117	1.09717	0.548587	+	0.836093i	$0.315166\pi$
$338$	−8.97334e116	−0.228206
$339$	0	0
$340$	−4.37177e117	−0.845059
$341$	1.62328e118	2.73726
$342$	0	0
$343$	7.94805e117	1.02114
$344$	−6.44093e117	−0.722738
$345$	0	0
$346$	−1.96901e118	−1.68737
$347$	−3.02947e117	−0.227011	−0.113505	−	0.993537i	$-0.536208\pi$
$347$	−3.02947e117	−0.227011	−0.113505	+	0.993537i	$0.536208\pi$
$348$	0	0
$349$	−1.20438e118	−0.690844	−0.345422	−	0.938447i	$-0.612264\pi$
$349$	−1.20438e118	−0.690844	−0.345422	+	0.938447i	$0.612264\pi$
$350$	1.44518e118	0.725704
$351$	0	0
$352$	−5.12222e118	−1.97344
$353$	−3.83160e118	−1.29377	−0.646884	−	0.762589i	$-0.723928\pi$
$353$	−3.83160e118	−1.29377	−0.646884	+	0.762589i	$0.723928\pi$
$354$	0	0
$355$	−6.98337e118	−1.81320
$356$	−4.76004e118	−1.08439
$357$	0	0
$358$	7.98454e118	1.40181
$359$	3.83119e118	0.590802	0.295401	−	0.955373i	$-0.404547\pi$
$359$	3.83119e118	0.590802	0.295401	+	0.955373i	$0.404547\pi$
$360$	0	0
$361$	−4.97911e118	−0.593017
$362$	−3.34432e118	−0.350234
$363$	0	0
$364$	1.86788e119	1.51403
$365$	−9.01946e118	−0.643520
$366$	0	0
$367$	−2.15604e119	−1.19312	−0.596561	−	0.802568i	$-0.703466\pi$
$367$	−2.15604e119	−1.19312	−0.596561	+	0.802568i	$0.703466\pi$
$368$	−1.22099e119	−0.595372
$369$	0	0
$370$	−5.90238e119	−2.23690
$371$	3.73684e119	1.24916
$372$	0	0
$373$	6.59757e119	1.71760	0.858802	−	0.512307i	$-0.171209\pi$
$373$	6.59757e119	1.71760	0.858802	+	0.512307i	$0.171209\pi$
$374$	−5.16020e119	−1.18614
$375$	0	0
$376$	−3.45505e118	−0.0619754
$377$	4.09149e118	0.0648648
$378$	0	0
$379$	−5.17356e119	−0.641307	−0.320654	−	0.947197i	$-0.603903\pi$
$379$	−5.17356e119	−0.641307	−0.320654	+	0.947197i	$0.603903\pi$
$380$	−1.02234e120	−1.12113
$381$	0	0
$382$	2.00174e120	1.71973
$383$	2.08785e120	1.58839	0.794194	−	0.607664i	$-0.207893\pi$
$383$	2.08785e120	1.58839	0.794194	+	0.607664i	$0.207893\pi$
$384$	0	0
$385$	3.13399e120	1.87143
$386$	3.22109e120	1.70488
$387$	0	0
$388$	3.28130e120	1.36575
$389$	1.96484e120	0.725556	0.362778	−	0.931876i	$-0.381828\pi$
$389$	1.96484e120	0.725556	0.362778	+	0.931876i	$0.381828\pi$
$390$	0	0
$391$	−2.78894e120	−0.811371
$392$	1.21365e119	0.0313540
$393$	0	0
$394$	−4.60482e120	−0.938940
$395$	−1.60483e120	−0.290846
$396$	0	0
$397$	4.00181e120	0.573454	0.286727	−	0.958012i	$-0.407433\pi$
$397$	4.00181e120	0.573454	0.286727	+	0.958012i	$0.407433\pi$
$398$	3.37502e120	0.430243
$399$	0	0
$400$	−1.65867e120	−0.167483
$401$	3.73524e120	0.335819	0.167909	−	0.985802i	$-0.446298\pi$
$401$	3.73524e120	0.335819	0.167909	+	0.985802i	$0.446298\pi$
$402$	0	0
$403$	2.60486e121	1.85823
$404$	−1.03523e121	−0.658120
$405$	0	0
$406$	−1.83348e120	−0.0926435
$407$	−4.11997e121	−1.85675
$408$	0	0
$409$	−1.23899e121	−0.444564	−0.222282	−	0.974982i	$-0.571351\pi$
$409$	−1.23899e121	−0.444564	−0.222282	+	0.974982i	$0.571351\pi$
$410$	6.06925e121	1.94395
$411$	0	0
$412$	−3.88742e121	−0.992980
$413$	−4.27006e120	−0.0974443
$414$	0	0
$415$	−2.03284e121	−0.370567
$416$	−8.21955e121	−1.33970
$417$	0	0
$418$	−1.20671e122	−1.57365
$419$	9.18993e120	0.107241	0.0536204	−	0.998561i	$-0.482924\pi$
$419$	9.18993e120	0.107241	0.0536204	+	0.998561i	$0.482924\pi$
$420$	0	0
$421$	1.03836e122	0.971024	0.485512	−	0.874230i	$-0.338633\pi$
$421$	1.03836e122	0.971024	0.485512	+	0.874230i	$0.338633\pi$
$422$	8.80253e121	0.737189
$423$	0	0
$424$	1.33016e122	0.894113
$425$	−3.78867e121	−0.228245
$426$	0	0
$427$	5.89249e121	0.285366
$428$	1.06760e122	0.463737
$429$	0	0
$430$	−5.61211e122	−1.96265
$431$	1.54782e122	0.485878	0.242939	−	0.970042i	$-0.421889\pi$
$431$	1.54782e122	0.485878	0.242939	+	0.970042i	$0.421889\pi$
$432$	0	0
$433$	−3.09529e122	−0.783455	−0.391728	−	0.920081i	$-0.628122\pi$
$433$	−3.09529e122	−0.783455	−0.391728	+	0.920081i	$0.628122\pi$
$434$	−1.16729e123	−2.65403
$435$	0	0
$436$	−5.62417e122	−1.03261
$437$	−6.52193e122	−1.07644
$438$	0	0
$439$	9.67855e122	1.29184	0.645922	−	0.763404i	$-0.276473\pi$
$439$	9.67855e122	1.29184	0.645922	+	0.763404i	$0.276473\pi$
$440$	1.11557e123	1.33952
$441$	0	0
$442$	−8.28049e122	−0.805231
$443$	2.07254e123	1.81439	0.907194	−	0.420713i	$-0.138220\pi$
$443$	2.07254e123	1.81439	0.907194	+	0.420713i	$0.138220\pi$
$444$	0	0
$445$	−1.28159e123	−0.909933
$446$	−8.41021e122	−0.537943
$447$	0	0
$448$	3.01951e123	1.56859
$449$	1.09500e123	0.512813	0.256407	−	0.966569i	$-0.417461\pi$
$449$	1.09500e123	0.512813	0.256407	+	0.966569i	$0.417461\pi$
$450$	0	0
$451$	4.23644e123	1.61359
$452$	−4.94402e123	−1.69880
$453$	0	0
$454$	−5.57624e123	−1.56043
$455$	5.02907e123	1.27045
$456$	0	0
$457$	7.48537e123	1.54209	0.771046	−	0.636780i	$-0.219734\pi$
$457$	7.48537e123	1.54209	0.771046	+	0.636780i	$0.219734\pi$
$458$	1.59729e124	2.97262
$459$	0	0
$460$	1.95123e124	2.96531
$461$	5.06600e123	0.695941	0.347970	−	0.937506i	$-0.386871\pi$
$461$	5.06600e123	0.695941	0.347970	+	0.937506i	$0.386871\pi$
$462$	0	0
$463$	−7.01263e123	−0.787707	−0.393854	−	0.919173i	$-0.628858\pi$
$463$	−7.01263e123	−0.787707	−0.393854	+	0.919173i	$0.628858\pi$
$464$	2.10432e122	0.0213809
$465$	0	0
$466$	1.30243e124	1.08345
$467$	−2.44106e123	−0.183799	−0.0918994	−	0.995768i	$-0.529294\pi$
$467$	−2.44106e123	−0.183799	−0.0918994	+	0.995768i	$0.529294\pi$
$468$	0	0
$469$	1.60413e124	0.990155
$470$	−3.01046e123	−0.168299
$471$	0	0
$472$	−1.51996e123	−0.0697478
$473$	−3.91735e124	−1.62911
$474$	0	0
$475$	−8.85982e123	−0.302811
$476$	2.19436e124	0.680117
$477$	0	0
$478$	−9.88619e124	−2.52134
$479$	−7.42219e124	−1.71763	−0.858817	−	0.512283i	$-0.828800\pi$
$479$	−7.42219e124	−1.71763	−0.858817	+	0.512283i	$0.828800\pi$
$480$	0	0
$481$	−6.61125e124	−1.26048
$482$	1.33430e125	2.30976
$483$	0	0
$484$	1.50650e125	2.15109
$485$	8.83457e124	1.14603
$486$	0	0
$487$	−8.80631e124	−0.943403	−0.471701	−	0.881758i	$-0.656360\pi$
$487$	−8.80631e124	−0.943403	−0.471701	+	0.881758i	$0.656360\pi$
$488$	2.09748e124	0.204257
$489$	0	0
$490$	1.05748e124	0.0851442
$491$	1.68113e125	1.23115	0.615575	−	0.788078i	$-0.288924\pi$
$491$	1.68113e125	1.23115	0.615575	+	0.788078i	$0.288924\pi$
$492$	0	0
$493$	4.80661e123	0.0291378
$494$	−1.93639e125	−1.06829
$495$	0	0
$496$	1.33972e125	0.612516
$497$	3.50522e125	1.45929
$498$	0	0
$499$	−1.86037e125	−0.642574	−0.321287	−	0.946982i	$-0.604115\pi$
$499$	−1.86037e125	−0.642574	−0.321287	+	0.946982i	$0.604115\pi$
$500$	−2.93369e125	−0.923227
$501$	0	0
$502$	3.99640e125	1.04459
$503$	−5.49090e125	−1.30838	−0.654188	−	0.756332i	$-0.726989\pi$
$503$	−5.49090e125	−1.30838	−0.654188	+	0.756332i	$0.726989\pi$
$504$	0	0
$505$	−2.78726e125	−0.552240
$506$	2.30313e126	4.16217
$507$	0	0
$508$	−1.08440e126	−1.63127
$509$	−3.04129e125	−0.417523	−0.208762	−	0.977967i	$-0.566943\pi$
$509$	−3.04129e125	−0.417523	−0.208762	+	0.977967i	$0.566943\pi$
$510$	0	0
$511$	4.52721e125	0.517915
$512$	−6.59042e125	−0.688430
$513$	0	0
$514$	2.87197e126	2.50262
$515$	−1.04665e126	−0.833228
$516$	0	0
$517$	−2.10135e125	−0.139697
$518$	2.96263e126	1.80029
$519$	0	0
$520$	1.79014e126	0.909353
$521$	−1.60621e125	−0.0746188	−0.0373094	−	0.999304i	$-0.511879\pi$
$521$	−1.60621e125	−0.0746188	−0.0373094	+	0.999304i	$0.511879\pi$
$522$	0	0
$523$	5.34768e125	0.207891	0.103946	−	0.994583i	$-0.466853\pi$
$523$	5.34768e125	0.207891	0.103946	+	0.994583i	$0.466853\pi$
$524$	5.12733e126	1.82384
$525$	0	0
$526$	5.60228e126	1.66927
$527$	3.06014e126	0.834734
$528$	0	0
$529$	8.07568e126	1.84710
$530$	1.15900e127	2.42803
$531$	0	0
$532$	5.13150e126	0.902306
$533$	6.79816e126	1.09541
$534$	0	0
$535$	2.87439e126	0.389130
$536$	5.71005e126	0.708725
$537$	0	0
$538$	−8.81928e126	−0.920571
$539$	7.38141e125	0.0706743
$540$	0	0
$541$	−6.30702e126	−0.508337	−0.254168	−	0.967160i	$-0.581802\pi$
$541$	−6.30702e126	−0.508337	−0.254168	+	0.967160i	$0.581802\pi$
$542$	1.22777e127	0.908137
$543$	0	0
$544$	−9.65619e126	−0.601806
$545$	−1.51425e127	−0.866482
$546$	0	0
$547$	6.02623e126	0.290827	0.145414	−	0.989371i	$-0.453549\pi$
$547$	6.02623e126	0.290827	0.145414	+	0.989371i	$0.453549\pi$
$548$	3.73788e127	1.65703
$549$	0	0
$550$	3.12873e127	1.17085
$551$	1.12403e126	0.0386569
$552$	0	0
$553$	8.05523e126	0.234077
$554$	−5.48310e127	−1.46495
$555$	0	0
$556$	−6.28833e127	−1.42088
$557$	6.30406e127	1.31025	0.655124	−	0.755521i	$-0.272616\pi$
$557$	6.30406e127	1.31025	0.655124	+	0.755521i	$0.272616\pi$
$558$	0	0
$559$	−6.28612e127	−1.10595
$560$	2.58654e127	0.418770
$561$	0	0
$562$	1.81160e128	2.48498
$563$	−2.39370e127	−0.302294	−0.151147	−	0.988511i	$-0.548297\pi$
$563$	−2.39370e127	−0.302294	−0.151147	+	0.988511i	$0.548297\pi$
$564$	0	0
$565$	−1.33112e128	−1.42550
$566$	−1.29535e128	−1.27768
$567$	0	0
$568$	1.24771e128	1.04452
$569$	1.05530e127	0.0814058	0.0407029	−	0.999171i	$-0.487040\pi$
$569$	1.05530e127	0.0814058	0.0407029	+	0.999171i	$0.487040\pi$
$570$	0	0
$571$	6.52543e127	0.427593	0.213796	−	0.976878i	$-0.431417\pi$
$571$	6.52543e127	0.427593	0.213796	+	0.976878i	$0.431417\pi$
$572$	4.04384e128	2.44274
$573$	0	0
$574$	−3.04639e128	−1.56452
$575$	1.69098e128	0.800912
$576$	0	0
$577$	5.32992e127	0.214806	0.107403	−	0.994216i	$-0.465747\pi$
$577$	5.32992e127	0.214806	0.107403	+	0.994216i	$0.465747\pi$
$578$	3.23427e128	1.20263
$579$	0	0
$580$	−3.36287e127	−0.106490
$581$	1.02036e128	0.298238
$582$	0	0
$583$	8.09001e128	2.01540
$584$	1.61150e128	0.370709
$585$	0	0
$586$	−5.50983e128	−1.08118
$587$	−5.47325e128	−0.992141	−0.496070	−	0.868282i	$-0.665224\pi$
$587$	−5.47325e128	−0.992141	−0.496070	+	0.868282i	$0.665224\pi$
$588$	0	0
$589$	7.15615e128	1.10744
$590$	−1.32438e128	−0.189406
$591$	0	0
$592$	−3.40028e128	−0.415485
$593$	2.94362e128	0.332536	0.166268	−	0.986081i	$-0.446828\pi$
$593$	2.94362e128	0.332536	0.166268	+	0.986081i	$0.446828\pi$
$594$	0	0
$595$	5.90807e128	0.570699
$596$	−1.44391e129	−1.29000
$597$	0	0
$598$	3.69580e129	2.82556
$599$	−1.66109e129	−1.17502	−0.587512	−	0.809216i	$-0.699892\pi$
$599$	−1.66109e129	−1.17502	−0.587512	+	0.809216i	$0.699892\pi$
$600$	0	0
$601$	−1.29386e129	−0.783834	−0.391917	−	0.920001i	$-0.628188\pi$
$601$	−1.29386e129	−0.783834	−0.391917	+	0.920001i	$0.628188\pi$
$602$	2.81693e129	1.57957
$603$	0	0
$604$	−2.16767e129	−1.04178
$605$	4.05609e129	1.80502
$606$	0	0
$607$	−3.30501e129	−1.26153	−0.630767	−	0.775972i	$-0.717260\pi$
$607$	−3.30501e129	−1.26153	−0.630767	+	0.775972i	$0.717260\pi$
$608$	−2.25810e129	−0.798412
$609$	0	0
$610$	1.82758e129	0.554676
$611$	−3.37201e128	−0.0948358
$612$	0	0
$613$	2.95847e129	0.714752	0.357376	−	0.933961i	$-0.383671\pi$
$613$	2.95847e129	0.714752	0.357376	+	0.933961i	$0.383671\pi$
$614$	−3.79990e129	−0.851026
$615$	0	0
$616$	−5.59948e129	−1.07806
$617$	−8.56214e129	−1.52870	−0.764350	−	0.644802i	$-0.776940\pi$
$617$	−8.56214e129	−1.52870	−0.764350	+	0.644802i	$0.776940\pi$
$618$	0	0
$619$	−2.56649e129	−0.394207	−0.197104	−	0.980383i	$-0.563154\pi$
$619$	−2.56649e129	−0.394207	−0.197104	+	0.980383i	$0.563154\pi$
$620$	−2.14098e130	−3.05070
$621$	0	0
$622$	8.40172e128	0.103066
$623$	6.43280e129	0.732328
$624$	0	0
$625$	−1.27382e130	−1.24936
$626$	5.96392e129	0.543032
$627$	0	0
$628$	−2.38143e130	−1.86945
$629$	−7.76678e129	−0.566221
$630$	0	0
$631$	6.30881e129	0.396809	0.198405	−	0.980120i	$-0.436424\pi$
$631$	6.30881e129	0.396809	0.198405	+	0.980120i	$0.436424\pi$
$632$	2.86733e129	0.167546
$633$	0	0
$634$	−4.11367e130	−2.07529
$635$	−2.91963e130	−1.36883
$636$	0	0
$637$	1.18448e129	0.0479784
$638$	−3.96935e129	−0.149471
$639$	0	0
$640$	4.69690e130	1.52912
$641$	−1.41919e130	−0.429676	−0.214838	−	0.976650i	$-0.568922\pi$
$641$	−1.41919e130	−0.429676	−0.214838	+	0.976650i	$0.568922\pi$
$642$	0	0
$643$	−5.43853e130	−1.42453	−0.712264	−	0.701911i	$-0.752330\pi$
$643$	−5.43853e130	−1.42453	−0.712264	+	0.701911i	$0.752330\pi$
$644$	−9.79399e130	−2.38653
$645$	0	0
$646$	−2.27484e130	−0.479887
$647$	−1.22570e130	−0.240622	−0.120311	−	0.992736i	$-0.538389\pi$
$647$	−1.22570e130	−0.240622	−0.120311	+	0.992736i	$0.538389\pi$
$648$	0	0
$649$	−9.24438e129	−0.157217
$650$	5.02062e130	0.794852
$651$	0	0
$652$	−4.09978e127	−0.000562662 0
$653$	1.74371e130	0.222849	0.111425	−	0.993773i	$-0.464459\pi$
$653$	1.74371e130	0.222849	0.111425	+	0.993773i	$0.464459\pi$
$654$	0	0
$655$	1.38048e131	1.53042
$656$	3.49641e130	0.361072
$657$	0	0
$658$	1.51106e130	0.135450
$659$	−6.85103e130	−0.572248	−0.286124	−	0.958193i	$-0.592367\pi$
$659$	−6.85103e130	−0.572248	−0.286124	+	0.958193i	$0.592367\pi$
$660$	0	0
$661$	1.41756e131	1.02843	0.514215	−	0.857661i	$-0.328083\pi$
$661$	1.41756e131	1.02843	0.514215	+	0.857661i	$0.328083\pi$
$662$	4.62987e130	0.313092
$663$	0	0
$664$	3.63206e130	0.213470
$665$	1.38160e131	0.757141
$666$	0	0
$667$	−2.14532e130	−0.102245
$668$	4.36143e130	0.193876
$669$	0	0
$670$	4.97529e131	1.92460
$671$	1.27568e131	0.460411
$672$	0	0
$673$	8.30557e130	0.261017	0.130509	−	0.991447i	$-0.458339\pi$
$673$	8.30557e130	0.261017	0.130509	+	0.991447i	$0.458339\pi$
$674$	−5.85186e131	−1.71636
$675$	0	0
$676$	8.26112e130	0.211114
$677$	3.55196e131	0.847413	0.423707	−	0.905799i	$-0.360729\pi$
$677$	3.55196e131	0.847413	0.423707	+	0.905799i	$0.360729\pi$
$678$	0	0
$679$	−4.43441e131	−0.922340
$680$	2.10303e131	0.408490
$681$	0	0
$682$	−2.52710e132	−4.28202
$683$	−3.18172e131	−0.503615	−0.251808	−	0.967777i	$-0.581025\pi$
$683$	−3.18172e131	−0.503615	−0.251808	+	0.967777i	$0.581025\pi$
$684$	0	0
$685$	1.00639e132	1.39044
$686$	−1.23734e132	−1.59741
$687$	0	0
$688$	−3.23306e131	−0.364545
$689$	1.29819e132	1.36819
$690$	0	0
$691$	5.99865e131	0.552490	0.276245	−	0.961087i	$-0.410910\pi$
$691$	5.99865e131	0.552490	0.276245	+	0.961087i	$0.410910\pi$
$692$	1.81273e132	1.56099
$693$	0	0
$694$	4.71623e131	0.355123
$695$	−1.69307e132	−1.19229
$696$	0	0
$697$	7.98636e131	0.492067
$698$	1.87495e132	1.08072
$699$	0	0
$700$	−1.33048e132	−0.671350
$701$	−2.25248e132	−1.06359	−0.531793	−	0.846874i	$-0.678481\pi$
$701$	−2.25248e132	−1.06359	−0.531793	+	0.846874i	$0.678481\pi$
$702$	0	0
$703$	−1.81626e132	−0.751201
$704$	6.53703e132	2.53077
$705$	0	0
$706$	5.96496e132	2.02390
$707$	1.39903e132	0.444452
$708$	0	0
$709$	−5.69127e132	−1.58547	−0.792737	−	0.609564i	$-0.791344\pi$
$709$	−5.69127e132	−1.58547	−0.792737	+	0.609564i	$0.791344\pi$
$710$	1.08716e133	2.83648
$711$	0	0
$712$	2.28981e132	0.524179
$713$	−1.36582e133	−2.92908
$714$	0	0
$715$	1.08876e133	2.04975
$716$	−7.35080e132	−1.29682
$717$	0	0
$718$	−5.96433e132	−0.924220
$719$	1.04361e133	1.51581	0.757903	−	0.652368i	$-0.226224\pi$
$719$	1.04361e133	1.51581	0.757903	+	0.652368i	$0.226224\pi$
$720$	0	0
$721$	5.25352e132	0.670595
$722$	7.75139e132	0.927684
$723$	0	0
$724$	3.07887e132	0.324003
$725$	−2.91434e131	−0.0287623
$726$	0	0
$727$	1.08894e132	0.0945482	0.0472741	−	0.998882i	$-0.484947\pi$
$727$	1.08894e132	0.0945482	0.0472741	+	0.998882i	$0.484947\pi$
$728$	−8.98541e132	−0.731861
$729$	0	0
$730$	1.40413e133	1.00669
$731$	−7.38483e132	−0.496801
$732$	0	0
$733$	−1.69144e133	−1.00212	−0.501062	−	0.865411i	$-0.667057\pi$
$733$	−1.69144e133	−1.00212	−0.501062	+	0.865411i	$0.667057\pi$
$734$	3.35648e133	1.86646
$735$	0	0
$736$	4.30981e133	2.11174
$737$	3.47284e133	1.59752
$738$	0	0
$739$	3.59192e133	1.45667	0.728334	−	0.685223i	$-0.240295\pi$
$739$	3.59192e133	1.45667	0.728334	+	0.685223i	$0.240295\pi$
$740$	5.43391e133	2.06937
$741$	0	0
$742$	−5.81745e133	−1.95412
$743$	2.53993e133	0.801386	0.400693	−	0.916212i	$-0.368769\pi$
$743$	2.53993e133	0.801386	0.400693	+	0.916212i	$0.368769\pi$
$744$	0	0
$745$	−3.88758e133	−1.08246
$746$	−1.02710e134	−2.68693
$747$	0	0
$748$	4.75063e133	1.09730
$749$	−1.44277e133	−0.313178
$750$	0	0
$751$	1.35458e133	0.259746	0.129873	−	0.991531i	$-0.458543\pi$
$751$	1.35458e133	0.259746	0.129873	+	0.991531i	$0.458543\pi$
$752$	−1.73428e132	−0.0312601
$753$	0	0
$754$	−6.36956e132	−0.101471
$755$	−5.83624e133	−0.874177
$756$	0	0
$757$	−5.95259e133	−0.788402	−0.394201	−	0.919024i	$-0.628979\pi$
$757$	−5.95259e133	−0.788402	−0.394201	+	0.919024i	$0.628979\pi$
$758$	8.05410e133	1.00323
$759$	0	0
$760$	4.91794e133	0.541940
$761$	−7.75508e133	−0.803896	−0.401948	−	0.915663i	$-0.631667\pi$
$761$	−7.75508e133	−0.803896	−0.401948	+	0.915663i	$0.631667\pi$
$762$	0	0
$763$	7.60058e133	0.697358
$764$	−1.84286e134	−1.59093
$765$	0	0
$766$	−3.25033e134	−2.48479
$767$	−1.48343e133	−0.106729
$768$	0	0
$769$	−2.41544e134	−1.53965	−0.769825	−	0.638255i	$-0.779656\pi$
$769$	−2.41544e134	−1.53965	−0.769825	+	0.638255i	$0.779656\pi$
$770$	−4.87895e134	−2.92757
$771$	0	0
$772$	−2.96543e134	−1.57719
$773$	−1.24924e134	−0.625605	−0.312802	−	0.949818i	$-0.601268\pi$
$773$	−1.24924e134	−0.625605	−0.312802	+	0.949818i	$0.601268\pi$
$774$	0	0
$775$	−1.85542e134	−0.823975
$776$	−1.57847e134	−0.660184
$777$	0	0
$778$	−3.05883e134	−1.13502
$779$	1.86761e134	0.652822
$780$	0	0
$781$	7.58856e134	2.35443
$782$	4.34177e134	1.26927
$783$	0	0
$784$	6.09200e132	0.0158148
$785$	−6.41174e134	−1.56869
$786$	0	0
$787$	6.36591e134	1.38368	0.691840	−	0.722051i	$-0.256800\pi$
$787$	6.36591e134	1.38368	0.691840	+	0.722051i	$0.256800\pi$
$788$	4.23933e134	0.868616
$789$	0	0
$790$	2.49836e134	0.454984
$791$	6.68142e134	1.14726
$792$	0	0
$793$	2.04707e134	0.312557
$794$	−6.22995e134	−0.897081
$795$	0	0
$796$	−3.10715e134	−0.398019
$797$	6.97769e133	0.0843141	0.0421570	−	0.999111i	$-0.486577\pi$
$797$	6.97769e133	0.0843141	0.0421570	+	0.999111i	$0.486577\pi$
$798$	0	0
$799$	−3.96138e133	−0.0426011
$800$	5.85473e134	0.594049
$801$	0	0
$802$	−5.81495e134	−0.525337
$803$	9.80109e134	0.835606
$804$	0	0
$805$	−2.63693e135	−2.00258
$806$	−4.05520e135	−2.90692
$807$	0	0
$808$	4.97997e134	0.318126
$809$	−1.46485e134	−0.0883461	−0.0441731	−	0.999024i	$-0.514065\pi$
$809$	−1.46485e134	−0.0883461	−0.0441731	+	0.999024i	$0.514065\pi$
$810$	0	0
$811$	3.37629e135	1.81539	0.907696	−	0.419629i	$-0.137840\pi$
$811$	3.37629e135	1.81539	0.907696	+	0.419629i	$0.137840\pi$
$812$	1.68795e134	0.0857047
$813$	0	0
$814$	6.41389e135	2.90460
$815$	−1.10382e132	−0.000472140 0
$816$	0	0
$817$	−1.72694e135	−0.659101
$818$	1.92884e135	0.695453
$819$	0	0
$820$	−5.58753e135	−1.79836
$821$	−1.07325e135	−0.326394	−0.163197	−	0.986593i	$-0.552181\pi$
$821$	−1.07325e135	−0.326394	−0.163197	+	0.986593i	$0.552181\pi$
$822$	0	0
$823$	−2.55029e135	−0.692623	−0.346311	−	0.938120i	$-0.612566\pi$
$823$	−2.55029e135	−0.692623	−0.346311	+	0.938120i	$0.612566\pi$
$824$	1.87004e135	0.479993
$825$	0	0
$826$	6.64755e134	0.152437
$827$	−1.56864e135	−0.340030	−0.170015	−	0.985441i	$-0.554382\pi$
$827$	−1.56864e135	−0.340030	−0.170015	+	0.985441i	$0.554382\pi$
$828$	0	0
$829$	−6.83946e134	−0.132506	−0.0662531	−	0.997803i	$-0.521104\pi$
$829$	−6.83946e134	−0.132506	−0.0662531	+	0.997803i	$0.521104\pi$
$830$	3.16469e135	0.579696
$831$	0	0
$832$	1.04899e136	1.71805
$833$	1.39151e134	0.0215523
$834$	0	0
$835$	1.17427e135	0.162685
$836$	1.11094e136	1.45578
$837$	0	0
$838$	−1.43067e135	−0.167762
$839$	7.63481e135	0.846968	0.423484	−	0.905904i	$-0.360807\pi$
$839$	7.63481e135	0.846968	0.423484	+	0.905904i	$0.360807\pi$
$840$	0	0
$841$	−1.00327e136	−0.996328
$842$	−1.61650e136	−1.51902
$843$	0	0
$844$	−8.10387e135	−0.681975
$845$	2.22422e135	0.177150
$846$	0	0
$847$	−2.03590e136	−1.45271
$848$	6.67682e135	0.450986
$849$	0	0
$850$	5.89814e135	0.357055
$851$	3.46652e136	1.98687
$852$	0	0
$853$	2.56337e136	1.31729	0.658644	−	0.752455i	$-0.271130\pi$
$853$	2.56337e136	1.31729	0.658644	+	0.752455i	$0.271130\pi$
$854$	−9.17333e135	−0.446412
$855$	0	0
$856$	−5.13565e135	−0.224164
$857$	−3.67285e136	−1.51843	−0.759215	−	0.650840i	$-0.774417\pi$
$857$	−3.67285e136	−1.51843	−0.759215	+	0.650840i	$0.774417\pi$
$858$	0	0
$859$	−3.23071e136	−1.19844	−0.599220	−	0.800584i	$-0.704523\pi$
$859$	−3.23071e136	−1.19844	−0.599220	+	0.800584i	$0.704523\pi$
$860$	5.16667e136	1.81565
$861$	0	0
$862$	−2.40962e136	−0.760081
$863$	−2.97873e136	−0.890284	−0.445142	−	0.895460i	$-0.646847\pi$
$863$	−2.97873e136	−0.890284	−0.445142	+	0.895460i	$0.646847\pi$
$864$	0	0
$865$	4.88059e136	1.30986
$866$	4.81869e136	1.22560
$867$	0	0
$868$	1.07464e137	2.45525
$869$	1.74390e136	0.377661
$870$	0	0
$871$	5.57281e136	1.08450
$872$	2.70549e136	0.499149
$873$	0	0
$874$	1.01532e137	1.68392
$875$	3.96463e136	0.623488
$876$	0	0
$877$	2.20703e136	0.312124	0.156062	−	0.987747i	$-0.450120\pi$
$877$	2.20703e136	0.312124	0.156062	+	0.987747i	$0.450120\pi$
$878$	−1.50674e137	−2.02089
$879$	0	0
$880$	5.59968e136	0.675645
$881$	1.02270e137	1.17049	0.585243	−	0.810858i	$-0.300999\pi$
$881$	1.02270e137	1.17049	0.585243	+	0.810858i	$0.300999\pi$
$882$	0	0
$883$	−7.00629e136	−0.721632	−0.360816	−	0.932637i	$-0.617502\pi$
$883$	−7.00629e136	−0.721632	−0.360816	+	0.932637i	$0.617502\pi$
$884$	7.62326e136	0.744922
$885$	0	0
$886$	−3.22650e137	−2.83833
$887$	−6.73980e136	−0.562599	−0.281299	−	0.959620i	$-0.590765\pi$
$887$	−6.73980e136	−0.562599	−0.281299	+	0.959620i	$0.590765\pi$
$888$	0	0
$889$	1.46547e137	1.10165
$890$	1.99516e137	1.42345
$891$	0	0
$892$	7.74269e136	0.497652
$893$	−9.26369e135	−0.0565185
$894$	0	0
$895$	−1.97912e137	−1.08818
$896$	−2.35755e137	−1.23066
$897$	0	0
$898$	−1.70468e137	−0.802218
$899$	2.35394e136	0.105189
$900$	0	0
$901$	1.52509e137	0.614602
$902$	−6.59522e137	−2.52421
$903$	0	0
$904$	2.37831e137	0.821177
$905$	8.28955e136	0.271877
$906$	0	0
$907$	−3.04304e137	−0.900677	−0.450338	−	0.892858i	$-0.648697\pi$
$907$	−3.04304e137	−0.900677	−0.450338	+	0.892858i	$0.648697\pi$
$908$	5.13365e137	1.44356
$909$	0	0
$910$	−7.82917e137	−1.98743
$911$	−6.22207e137	−1.50083	−0.750413	−	0.660969i	$-0.770145\pi$
$911$	−6.22207e137	−1.50083	−0.750413	+	0.660969i	$0.770145\pi$
$912$	0	0
$913$	2.20901e137	0.481179
$914$	−1.16531e138	−2.41237
$915$	0	0
$916$	−1.47051e138	−2.74998
$917$	−6.92915e137	−1.23170
$918$	0	0
$919$	5.38667e137	0.865265	0.432632	−	0.901570i	$-0.357585\pi$
$919$	5.38667e137	0.865265	0.432632	+	0.901570i	$0.357585\pi$
$920$	−9.38638e137	−1.43339
$921$	0	0
$922$	−7.88666e137	−1.08869
$923$	1.21772e138	1.59834
$924$	0	0
$925$	4.70915e137	0.558923
$926$	1.09171e138	1.23225
$927$	0	0
$928$	−7.42778e136	−0.0758365
$929$	9.52004e137	0.924503	0.462251	−	0.886749i	$-0.347042\pi$
$929$	9.52004e137	0.924503	0.462251	+	0.886749i	$0.347042\pi$
$930$	0	0
$931$	3.25405e136	0.0285933
$932$	−1.19905e138	−1.00230
$933$	0	0
$934$	3.80019e137	0.287525
$935$	1.27906e138	0.920767
$936$	0	0
$937$	1.63655e138	1.06669	0.533344	−	0.845898i	$-0.320935\pi$
$937$	1.63655e138	1.06669	0.533344	+	0.845898i	$0.320935\pi$
$938$	−2.49729e138	−1.54895
$939$	0	0
$940$	2.77151e137	0.155694
$941$	−3.22780e138	−1.72579	−0.862896	−	0.505381i	$-0.831352\pi$
$941$	−3.22780e138	−1.72579	−0.862896	+	0.505381i	$0.831352\pi$
$942$	0	0
$943$	−3.56452e138	−1.72666
$944$	−7.62954e136	−0.0351804
$945$	0	0
$946$	6.09847e138	2.54849
$947$	3.71804e138	1.47924	0.739622	−	0.673022i	$-0.235004\pi$
$947$	3.71804e138	1.47924	0.739622	+	0.673022i	$0.235004\pi$
$948$	0	0
$949$	1.57277e138	0.567264
$950$	1.37928e138	0.473702
$951$	0	0
$952$	−1.05559e138	−0.328759
$953$	−1.89947e138	−0.563394	−0.281697	−	0.959503i	$-0.590897\pi$
$953$	−1.89947e138	−0.563394	−0.281697	+	0.959503i	$0.590897\pi$
$954$	0	0
$955$	−4.96169e138	−1.33498
$956$	9.10151e138	2.33250
$957$	0	0
$958$	1.15547e139	2.68697
$959$	−5.05143e138	−1.11905
$960$	0	0
$961$	1.00132e139	2.01342
$962$	1.02923e139	1.97184
$963$	0	0
$964$	−1.22840e139	−2.13676
$965$	−7.98410e138	−1.32345
$966$	0	0
$967$	−4.15481e138	−0.625489	−0.312745	−	0.949837i	$-0.601248\pi$
$967$	−4.15481e138	−0.625489	−0.312745	+	0.949837i	$0.601248\pi$
$968$	−7.24698e138	−1.03981
$969$	0	0
$970$	−1.37535e139	−1.79278
$971$	9.01984e138	1.12074	0.560369	−	0.828243i	$-0.310659\pi$
$971$	9.01984e138	1.12074	0.560369	+	0.828243i	$0.310659\pi$
$972$	0	0
$973$	8.49815e138	0.959571
$974$	1.37095e139	1.47581
$975$	0	0
$976$	1.05284e138	0.103026
$977$	−8.65113e138	−0.807189	−0.403595	−	0.914938i	$-0.632239\pi$
$977$	−8.65113e138	−0.807189	−0.403595	+	0.914938i	$0.632239\pi$
$978$	0	0
$979$	1.39266e139	1.18154
$980$	−9.73548e137	−0.0787671
$981$	0	0
$982$	−2.61715e139	−1.92595
$983$	2.72893e139	1.91538	0.957689	−	0.287805i	$-0.0929255\pi$
$983$	2.72893e139	1.91538	0.957689	+	0.287805i	$0.0929255\pi$
$984$	0	0
$985$	1.14139e139	0.728872
$986$	−7.48285e137	−0.0455817
$987$	0	0
$988$	1.78270e139	0.988281
$989$	3.29604e139	1.74327
$990$	0	0
$991$	2.57952e139	1.24198	0.620989	−	0.783819i	$-0.286731\pi$
$991$	2.57952e139	1.24198	0.620989	+	0.783819i	$0.286731\pi$
$992$	−4.72892e139	−2.17255
$993$	0	0
$994$	−5.45686e139	−2.28284
$995$	−8.36566e138	−0.333985
$996$	0	0
$997$	−1.61311e139	−0.586595	−0.293298	−	0.956021i	$-0.594753\pi$
$997$	−1.61311e139	−0.586595	−0.293298	+	0.956021i	$0.594753\pi$
$998$	2.89619e139	1.00521
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.94.a.b.1.2		7
3.2	odd	2		1.94.a.a.1.6	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.94.a.a.1.6	✓	7	3.2	odd	2
9.94.a.b.1.2		7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 94 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-1.55678e14 q^{2} +1.43322e28 q^{4} +3.85879e32 q^{5} -1.93687e39 q^{7} -6.89447e41 q^{8} +O(q^{10})\)	\(q-1.55678e14 q^{2} +1.43322e28 q^{4} +3.85879e32 q^{5} -1.93687e39 q^{7} -6.89447e41 q^{8} -6.00730e46 q^{10} -4.19320e48 q^{11} -6.72877e51 q^{13} +3.01529e53 q^{14} -3.46072e55 q^{16} -7.90484e56 q^{17} -1.84855e59 q^{19} +5.53049e60 q^{20} +6.52790e62 q^{22} +3.52814e63 q^{23} +4.79285e64 q^{25} +1.04752e66 q^{26} -2.77596e67 q^{28} -6.08060e66 q^{29} -3.87123e69 q^{31} +1.22155e70 q^{32} +1.23061e71 q^{34} -7.47399e71 q^{35} +9.82535e72 q^{37} +2.87779e73 q^{38} -2.66043e74 q^{40} -1.01031e75 q^{41} +9.34216e75 q^{43} -6.00977e76 q^{44} -5.49254e77 q^{46} +5.01133e76 q^{47} -1.76033e77 q^{49} -7.46143e78 q^{50} -9.64379e79 q^{52} -1.92932e80 q^{53} -1.61807e81 q^{55} +1.33537e81 q^{56} +9.46617e80 q^{58} +2.20461e81 q^{59} -3.04227e82 q^{61} +6.02666e83 q^{62} -1.55896e84 q^{64} -2.59649e84 q^{65} -8.28207e84 q^{67} -1.13294e85 q^{68} +1.16354e86 q^{70} -1.80973e86 q^{71} -2.33738e86 q^{73} -1.52959e87 q^{74} -2.64937e87 q^{76} +8.12170e87 q^{77} -4.15888e87 q^{79} -1.33542e88 q^{80} +1.57284e89 q^{82} -5.26808e88 q^{83} -3.05031e89 q^{85} -1.45437e90 q^{86} +2.89099e90 q^{88} -3.32123e90 q^{89} +1.30328e91 q^{91} +5.05660e91 q^{92} -7.80155e90 q^{94} -7.13316e91 q^{95} +2.28947e92 q^{97} +2.74045e91 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 43735426713792 q^{2} + 37\!\cdots\!44 q^{4}+ \cdots - 62\!\cdots\!60 q^{8}+O(q^{10}) \) 7 * q - 43735426713792 * q^2 + 37433779444352805880587218944 * q^4 + 242501922056818695041616562179750 * q^5 - 921137753903839555947108372394316103208 * q^7 - 628568314501252186502498490389635108700160 * q^8	\( 7 q - 43735426713792 q^{2} + 37\!\cdots\!44 q^{4}+ \cdots + 69\!\cdots\!56 q^{98}+O(q^{100}) \) 7 * q - 43735426713792 * q^2 + 37433779444352805880587218944 * q^4 + 242501922056818695041616562179750 * q^5 - 921137753903839555947108372394316103208 * q^7 - 628568314501252186502498490389635108700160 * q^8 + 56663128890275718532856219951648854919834448000 * q^10 - 1081566396126190174166498109003279139923369012324 * q^11 + 1923851638471797431690458036346871401286646408469426 * q^13 + 827492161115181455891429526236298470299001717526508032 * q^14 - 183863117199568288307852091185855957272115704336744448 * q^16 - 809325537307953309871783611300921224816172571619454935742 * q^17 - 491316328040151561437984621759105514680907320256463264658500 * q^19 + 5819101371751539891329503686613738398860076574931824253952000 * q^20 + 341061341496448817039487179432626029859991533289656810924326144 * q^22 + 2595697104202345855126053487687658963668179272707633091075699064 * q^23 + 184388886386678531186865888507627315189418933935123407708899515625 * q^25 - 793059166145746283698718389909557916534745558035448772312212840064 * q^26 + 1916814131388145595393790805747801246689773266225672358812878209024 * q^28 - 115585291038420509795092429775705167101645550654624527668945364036450 * q^29 - 1163635467946810748613893942791764663199899897323284701513531956983456 * q^31 + 7066990866795922437106429389517828098400874624281122281464920526553088 * q^32 + 80911624156374405155780927188384543491071504244617539921495324380294528 * q^34 + 1672188852118103650980495790489284130570309869892526153633308501275462000 * q^35 + 11072759435314078994932599484815080247923078570346623467670584315337670842 * q^37 + 42692186143014046654789275667852179938472092905944200699148410427788924160 * q^38 + 760187696799287916151508882607919116749295190931669242261910585944965120000 * q^40 + 509603803596826806676973650829096820638503322986104149790656476262528674746 * q^41 - 7275658116979055674748970912580687053338617746072325435955591393683798211644 * q^43 - 9423347779397833928027118997217234224491886242773059800183027480258516369408 * q^44 - 639778771092842366359510076082228574613573083413403803040568658686807125218816 * q^46 + 371149830895115606730684780470708713676568637183334957675426341554516993409008 * q^47 + 2561975156227711495237514871966779964501558283497058708235084248829398599957999 * q^49 + 31492320141514234591073138519794385457712593727985587891779934655429621403000000 * q^50 - 55278983045853834535146427408736596689073596604984335518990233309047240924848128 * q^52 + 363766241548602923075270727552075967170433033161760056492510229436384310833635734 * q^53 - 3520855393890604949232827617669938515471701214675853816941159595183623184386577000 * q^55 + 12936956692485908268365121199611114191360014164491088694387999166431300696512921600 * q^56 - 73663001170657752665346575473371223431752845037418753763472734766611572171441325440 * q^58 + 119839908140624573484226478891501296275544385047787439213910489726968365086286210700 * q^59 - 328281166748320542242523532793984772143143166398612931227281116669834617338050603326 * q^61 + 999402477792071119370831029463209574610493980381087626216590758004912070795081435136 * q^62 - 4748321960274080197621802735261780227229800262185345649692550833454877416714840047616 * q^64 - 2401958293154067008332922023669433962969772004736123854920087208208149417890196631500 * q^65 + 9715050085721519766982024893817705652242604355912950898916137527198529527932523084492 * q^67 - 51110178162381015351883898716980001063480395685110983605059672645927223406195391258624 * q^68 + 437770522317274261347763126091338009235407849188339858200284725822565513739255154816000 * q^70 - 420099768445021912291978352393445519280746916987347799091649913407485898651223357176984 * q^71 + 249990884773795871360906735022065792056914028590737521750721031757996649920054698123686 * q^73 - 988848152146322932205109547460090361956964236264222955609677033303897103570301064734848 * q^74 - 9872924363930092749183448370538218854882826462181838927155554514487863834399954370969600 * q^76 + 16552736755381232703525388842736711985373990693881749218915711388952768140257306836693856 * q^77 - 43369884997252312790262999909905208728154246791055779943371432494520439561399960810221200 * q^79 + 88894687813962777903012798348655018553862729556819104796394604135123942915181092274176000 * q^80 - 236357995159599133663604843384379044643064499685381579522884048932961281765779447211829376 * q^82 + 206459225650342475045148123542600401116221913586781003327705338223920418727874732010864004 * q^83 + 1637661121678145282281696006564110640734919603287375198985971859556394144920752854974380500 * q^85 - 3239900597437756786176903087412721547247433713557247371056571790561416975430434191434708224 * q^86 + 6336674026069399594730100443279513731166873520796702455565229756349453295686310223539077120 * q^88 - 5580799156439265704685765323272125687903700231557911629488221982292995723510480958101067350 * q^89 - 18025272478314007503227783954648499409552734863956310123113904904033321293148703549329112496 * q^91 + 81750027044574246291550532241925751638073881610946649428268147310600744342795416362583031808 * q^92 - 306478475429892162274969547511367839192733042761577860914963828391848832364650578690812603392 * q^94 + 216711696129933523762297615654778954621414663971673687874218846402427636558070586043601335000 * q^95 + 43971291171253027759915173352741872464098193495293359649108047104658615767375645954946743342 * q^97 + 690328280759812206538864038068682435013428219472201721649324072601042235191425205897720616256 * q^98

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