LMFDB - Embedded newform 9.94.a.b.1.3

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			1.3
Root			$1.30998e11$ 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)

$f(q)$	$=$	$q-8.17029e13 q^{2} -3.22816e27 q^{4} -2.56302e32 q^{5} +2.42990e39 q^{7} +1.07290e42 q^{8} +O(q^{10})$	\(q-8.17029e13 q^{2} -3.22816e27 q^{4} -2.56302e32 q^{5} +2.42990e39 q^{7} +1.07290e42 q^{8} +2.09406e46 q^{10} +3.34519e48 q^{11} -2.46539e51 q^{13} -1.98530e53 q^{14} -5.56886e55 q^{16} -8.99207e56 q^{17} +1.17863e58 q^{19} +8.27382e59 q^{20} -2.73312e62 q^{22} -2.35938e63 q^{23} -3.52837e64 q^{25} +2.01429e65 q^{26} -7.84410e66 q^{28} +1.13023e68 q^{29} -4.06811e69 q^{31} -6.07553e69 q^{32} +7.34678e70 q^{34} -6.22787e71 q^{35} -3.61681e72 q^{37} -9.62973e71 q^{38} -2.74985e74 q^{40} +1.25412e74 q^{41} +6.73029e75 q^{43} -1.07988e76 q^{44} +1.92768e77 q^{46} +9.64475e77 q^{47} +1.97689e78 q^{49} +2.88278e78 q^{50} +7.95867e78 q^{52} +1.68714e80 q^{53} -8.57379e80 q^{55} +2.60703e81 q^{56} -9.23427e81 q^{58} +1.86287e82 q^{59} -1.57323e83 q^{61} +3.32376e83 q^{62} +1.04790e84 q^{64} +6.31883e83 q^{65} +1.27961e85 q^{67} +2.90278e84 q^{68} +5.08835e85 q^{70} -6.05042e84 q^{71} +5.11356e86 q^{73} +2.95504e86 q^{74} -3.80480e85 q^{76} +8.12848e87 q^{77} -2.35972e88 q^{79} +1.42731e88 q^{80} -1.02465e88 q^{82} +1.36739e88 q^{83} +2.30468e89 q^{85} -5.49884e89 q^{86} +3.58905e90 q^{88} -5.78854e90 q^{89} -5.99064e90 q^{91} +7.61645e90 q^{92} -7.88004e91 q^{94} -3.02084e90 q^{95} -1.91326e92 q^{97} -1.61518e92 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−8.17029e13	−0.820999	−0.410499	−	0.911861i	$-0.634646\pi$
$2$	−8.17029e13	−0.820999	−0.410499	+	0.911861i	$0.634646\pi$
$3$	0	0
$3$	0	0
$4$	−3.22816e27	−0.325961
$5$	−2.56302e32	−0.806577	−0.403289	−	0.915073i	$-0.632133\pi$
$5$	−2.56302e32	−0.806577	−0.403289	+	0.915073i	$0.632133\pi$
$6$	0	0
$7$	2.42990e39	1.22611	0.613055	−	0.790041i	$-0.289941\pi$
$7$	2.42990e39	1.22611	0.613055	+	0.790041i	$0.289941\pi$
$8$	1.07290e42	1.08861
$9$	0	0
$10$	2.09406e46	0.662199
$11$	3.34519e48	1.25794	0.628972	−	0.777428i	$-0.283476\pi$
$11$	3.34519e48	1.25794	0.628972	+	0.777428i	$0.283476\pi$
$12$	0	0
$13$	−2.46539e51	−0.392211	−0.196105	−	0.980583i	$-0.562829\pi$
$13$	−2.46539e51	−0.392211	−0.196105	+	0.980583i	$0.562829\pi$
$14$	−1.98530e53	−1.00663
$15$	0	0
$16$	−5.56886e55	−0.567789
$17$	−8.99207e56	−0.546997	−0.273498	−	0.961872i	$-0.588181\pi$
$17$	−8.99207e56	−0.546997	−0.273498	+	0.961872i	$0.588181\pi$
$18$	0	0
$19$	1.17863e58	0.0406756	0.0203378	−	0.999793i	$-0.493526\pi$
$19$	1.17863e58	0.0406756	0.0203378	+	0.999793i	$0.493526\pi$
$20$	8.27382e59	0.262913
$21$	0	0
$22$	−2.73312e62	−1.03277
$23$	−2.35938e63	−1.12837	−0.564187	−	0.825647i	$-0.690810\pi$
$23$	−2.35938e63	−1.12837	−0.564187	+	0.825647i	$0.690810\pi$
$24$	0	0
$25$	−3.52837e64	−0.349433
$26$	2.01429e65	0.322005
$27$	0	0
$28$	−7.84410e66	−0.399664
$29$	1.13023e68	1.12631	0.563155	−	0.826351i	$-0.309587\pi$
$29$	1.13023e68	1.12631	0.563155	+	0.826351i	$0.309587\pi$
$30$	0	0
$31$	−4.06811e69	−1.82421	−0.912104	−	0.409960i	$-0.865543\pi$
$31$	−4.06811e69	−1.82421	−0.912104	+	0.409960i	$0.865543\pi$
$32$	−6.07553e69	−0.622458
$33$	0	0
$34$	7.34678e70	0.449084
$35$	−6.22787e71	−0.988952
$36$	0	0
$37$	−3.61681e72	−0.433456	−0.216728	−	0.976232i	$-0.569539\pi$
$37$	−3.61681e72	−0.433456	−0.216728	+	0.976232i	$0.569539\pi$
$38$	−9.62973e71	−0.0333946
$39$	0	0
$40$	−2.74985e74	−0.878050
$41$	1.25412e74	0.127025	0.0635127	−	0.997981i	$-0.479770\pi$
$41$	1.25412e74	0.127025	0.0635127	+	0.997981i	$0.479770\pi$
$42$	0	0
$43$	6.73029e75	0.744305	0.372152	−	0.928172i	$-0.378620\pi$
$43$	6.73029e75	0.744305	0.372152	+	0.928172i	$0.378620\pi$
$44$	−1.07988e76	−0.410041
$45$	0	0
$46$	1.92768e77	0.926395
$47$	9.64475e77	1.70506	0.852532	−	0.522676i	$-0.175066\pi$
$47$	9.64475e77	1.70506	0.852532	+	0.522676i	$0.175066\pi$
$48$	0	0
$49$	1.97689e78	0.503344
$50$	2.88278e78	0.286884
$51$	0	0
$52$	7.95867e78	0.127845
$53$	1.68714e80	1.11770	0.558848	−	0.829270i	$-0.311244\pi$
$53$	1.68714e80	1.11770	0.558848	+	0.829270i	$0.311244\pi$
$54$	0	0
$55$	−8.57379e80	−1.01463
$56$	2.60703e81	1.33476
$57$	0	0
$58$	−9.23427e81	−0.924700
$59$	1.86287e82	0.842490	0.421245	−	0.906947i	$-0.361593\pi$
$59$	1.86287e82	0.842490	0.421245	+	0.906947i	$0.361593\pi$
$60$	0	0
$61$	−1.57323e83	−1.50993	−0.754963	−	0.655767i	$-0.772345\pi$
$61$	−1.57323e83	−1.50993	−0.754963	+	0.655767i	$0.772345\pi$
$62$	3.32376e83	1.49767
$63$	0	0
$64$	1.04790e84	1.07883
$65$	6.31883e83	0.316348
$66$	0	0
$67$	1.27961e85	1.56531	0.782653	−	0.622458i	$-0.213866\pi$
$67$	1.27961e85	1.56531	0.782653	+	0.622458i	$0.213866\pi$
$68$	2.90278e84	0.178299
$69$	0	0
$70$	5.08835e85	0.811929
$71$	−6.05042e84	−0.0499197	−0.0249599	−	0.999688i	$-0.507946\pi$
$71$	−6.05042e84	−0.0499197	−0.0249599	+	0.999688i	$0.507946\pi$
$72$	0	0
$73$	5.11356e86	1.15934	0.579670	−	0.814852i	$-0.303182\pi$
$73$	5.11356e86	1.15934	0.579670	+	0.814852i	$0.303182\pi$
$74$	2.95504e86	0.355867
$75$	0	0
$76$	−3.80480e85	−0.0132587
$77$	8.12848e87	1.54238
$78$	0	0
$79$	−2.35972e88	−1.35894	−0.679469	−	0.733704i	$-0.737790\pi$
$79$	−2.35972e88	−1.35894	−0.679469	+	0.733704i	$0.737790\pi$
$80$	1.42731e88	0.457966
$81$	0	0
$82$	−1.02465e88	−0.104288
$83$	1.36739e88	0.0792066	0.0396033	−	0.999215i	$-0.487391\pi$
$83$	1.36739e88	0.0792066	0.0396033	+	0.999215i	$0.487391\pi$
$84$	0	0
$85$	2.30468e89	0.441195
$86$	−5.49884e89	−0.611073
$87$	0	0
$88$	3.58905e90	1.36941
$89$	−5.78854e90	−1.30597	−0.652986	−	0.757370i	$-0.726484\pi$
$89$	−5.78854e90	−1.30597	−0.652986	+	0.757370i	$0.726484\pi$
$90$	0	0
$91$	−5.99064e90	−0.480893
$92$	7.61645e90	0.367806
$93$	0	0
$94$	−7.88004e91	−1.39986
$95$	−3.02084e90	−0.0328080
$96$	0	0
$97$	−1.91326e92	−0.788659	−0.394330	−	0.918969i	$-0.629023\pi$
$97$	−1.91326e92	−0.788659	−0.394330	+	0.918969i	$0.629023\pi$
$98$	−1.61518e92	−0.413245
$99$	0	0
$100$	1.13901e92	0.113901
$101$	7.76998e92	0.489189	0.244594	−	0.969626i	$-0.421345\pi$
$101$	7.76998e92	0.489189	0.244594	+	0.969626i	$0.421345\pi$
$102$	0	0
$103$	4.59345e93	1.16200	0.581002	−	0.813902i	$-0.302661\pi$
$103$	4.59345e93	1.16200	0.581002	+	0.813902i	$0.302661\pi$
$104$	−2.64511e93	−0.426966
$105$	0	0
$106$	−1.37844e94	−0.917627
$107$	−9.88939e93	−0.425426	−0.212713	−	0.977115i	$-0.568230\pi$
$107$	−9.88939e93	−0.425426	−0.212713	+	0.977115i	$0.568230\pi$
$108$	0	0
$109$	−9.31242e94	−1.69329	−0.846643	−	0.532161i	$-0.821380\pi$
$109$	−9.31242e94	−1.69329	−0.846643	+	0.532161i	$0.821380\pi$
$110$	7.00503e94	0.833010
$111$	0	0
$112$	−1.35318e95	−0.696171
$113$	−4.19633e95	−1.42798	−0.713989	−	0.700157i	$-0.753113\pi$
$113$	−4.19633e95	−1.42798	−0.713989	+	0.700157i	$0.753113\pi$
$114$	0	0
$115$	6.04713e95	0.910122
$116$	−3.64855e95	−0.367133
$117$	0	0
$118$	−1.52202e96	−0.691683
$119$	−2.18498e96	−0.670678
$120$	0	0
$121$	4.11869e96	0.582425
$122$	1.28538e97	1.23965
$123$	0	0
$124$	1.31325e97	0.594620
$125$	3.49231e97	1.08842
$126$	0	0
$127$	6.15633e96	0.0917168	0.0458584	−	0.998948i	$-0.485398\pi$
$127$	6.15633e96	0.0917168	0.0458584	+	0.998948i	$0.485398\pi$
$128$	−2.54474e97	−0.263257
$129$	0	0
$130$	−5.16267e97	−0.259722
$131$	−4.93768e98	−1.73943	−0.869716	−	0.493553i	$-0.835698\pi$
$131$	−4.93768e98	−1.73943	−0.869716	+	0.493553i	$0.835698\pi$
$132$	0	0
$133$	2.86395e97	0.0498728
$134$	−1.04548e99	−1.28512
$135$	0	0
$136$	−9.64755e98	−0.595467
$137$	4.08443e99	1.79318	0.896592	−	0.442858i	$-0.146035\pi$
$137$	4.08443e99	1.79318	0.896592	+	0.442858i	$0.146035\pi$
$138$	0	0
$139$	9.82507e98	0.219861	0.109930	−	0.993939i	$-0.464937\pi$
$139$	9.82507e98	0.219861	0.109930	+	0.993939i	$0.464937\pi$
$140$	2.01045e99	0.322360
$141$	0	0
$142$	4.94337e98	0.0409840
$143$	−8.24721e99	−0.493380
$144$	0	0
$145$	−2.89679e100	−0.908457
$146$	−4.17793e100	−0.951816
$147$	0	0
$148$	1.16756e100	0.141290
$149$	−6.22850e100	−0.551089	−0.275545	−	0.961288i	$-0.588858\pi$
$149$	−6.22850e100	−0.551089	−0.275545	+	0.961288i	$0.588858\pi$
$150$	0	0
$151$	1.42825e101	0.679794	0.339897	−	0.940463i	$-0.389608\pi$
$151$	1.42825e101	0.679794	0.339897	+	0.940463i	$0.389608\pi$
$152$	1.26455e100	0.0442800
$153$	0	0
$154$	−6.64120e101	−1.26629
$155$	1.04266e102	1.47136
$156$	0	0
$157$	2.22191e102	1.72740	0.863698	−	0.504009i	$-0.168142\pi$
$157$	2.22191e102	1.72740	0.863698	+	0.504009i	$0.168142\pi$
$158$	1.92796e102	1.11569
$159$	0	0
$160$	1.55717e102	0.502061
$161$	−5.73305e102	−1.38351
$162$	0	0
$163$	−6.84748e101	−0.0930694	−0.0465347	−	0.998917i	$-0.514818\pi$
$163$	−6.84748e101	−0.0930694	−0.0465347	+	0.998917i	$0.514818\pi$
$164$	−4.04851e101	−0.0414053
$165$	0	0
$166$	−1.11720e102	−0.0650286
$167$	3.03324e102	0.133534	0.0667668	−	0.997769i	$-0.478732\pi$
$167$	3.03324e102	0.133534	0.0667668	+	0.997769i	$0.478732\pi$
$168$	0	0
$169$	−3.34341e103	−0.846171
$170$	−1.88299e103	−0.362221
$171$	0	0
$172$	−2.17265e103	−0.242614
$173$	6.79292e102	0.0579313	0.0289656	−	0.999580i	$-0.490779\pi$
$173$	6.79292e102	0.0579313	0.0289656	+	0.999580i	$0.490779\pi$
$174$	0	0
$175$	−8.57358e103	−0.428443
$176$	−1.86289e104	−0.714247
$177$	0	0
$178$	4.72940e104	1.07220
$179$	−7.58027e102	−0.0132440	−0.00662200	−	0.999978i	$-0.502108\pi$
$179$	−7.58027e102	−0.0132440	−0.00662200	+	0.999978i	$0.502108\pi$
$180$	0	0
$181$	1.46993e105	1.53194	0.765972	−	0.642874i	$-0.222258\pi$
$181$	1.46993e105	1.53194	0.765972	+	0.642874i	$0.222258\pi$
$182$	4.89453e104	0.394813
$183$	0	0
$184$	−2.53137e105	−1.22836
$185$	9.26994e104	0.349616
$186$	0	0
$187$	−3.00802e105	−0.688091
$188$	−3.11348e105	−0.555784
$189$	0	0
$190$	2.46812e104	0.0269354
$191$	−7.27780e105	−0.622227	−0.311113	−	0.950373i	$-0.600702\pi$
$191$	−7.27780e105	−0.622227	−0.311113	+	0.950373i	$0.600702\pi$
$192$	0	0
$193$	3.26205e106	1.71821	0.859104	−	0.511801i	$-0.171021\pi$
$193$	3.26205e106	1.71821	0.859104	+	0.511801i	$0.171021\pi$
$194$	1.56319e106	0.647488
$195$	0	0
$196$	−6.38172e105	−0.164070
$197$	2.81792e105	0.0571806	0.0285903	−	0.999591i	$-0.490898\pi$
$197$	2.81792e105	0.0571806	0.0285903	+	0.999591i	$0.490898\pi$
$198$	0	0
$199$	−9.39320e106	−1.19164	−0.595821	−	0.803117i	$-0.703173\pi$
$199$	−9.39320e106	−1.19164	−0.595821	+	0.803117i	$0.703173\pi$
$200$	−3.78557e106	−0.380397
$201$	0	0
$202$	−6.34830e106	−0.401623
$203$	2.74633e107	1.38098
$204$	0	0
$205$	−3.21434e106	−0.102456
$206$	−3.75298e107	−0.954004
$207$	0	0
$208$	1.37294e107	0.222693
$209$	3.94274e106	0.0511677
$210$	0	0
$211$	1.56509e108	1.30438	0.652192	−	0.758053i	$-0.273849\pi$
$211$	1.56509e108	1.30438	0.652192	+	0.758053i	$0.273849\pi$
$212$	−5.44636e107	−0.364325
$213$	0	0
$214$	8.07992e107	0.349274
$215$	−1.72499e108	−0.600340
$216$	0	0
$217$	−9.88510e108	−2.23668
$218$	7.60852e108	1.39019
$219$	0	0
$220$	2.76776e108	0.330730
$221$	2.21689e108	0.214538
$222$	0	0
$223$	−1.13170e109	−0.720371	−0.360186	−	0.932881i	$-0.617287\pi$
$223$	−1.13170e109	−0.720371	−0.360186	+	0.932881i	$0.617287\pi$
$224$	−1.47629e109	−0.763202
$225$	0	0
$226$	3.42852e109	1.17237
$227$	−3.95198e108	−0.110056	−0.0550278	−	0.998485i	$-0.517525\pi$
$227$	−3.95198e108	−0.110056	−0.0550278	+	0.998485i	$0.517525\pi$
$228$	0	0
$229$	−5.55694e109	−1.02917	−0.514584	−	0.857440i	$-0.672054\pi$
$229$	−5.55694e109	−1.02917	−0.514584	+	0.857440i	$0.672054\pi$
$230$	−4.94068e109	−0.747209
$231$	0	0
$232$	1.21261e110	1.22612
$233$	5.13478e109	0.425081	0.212540	−	0.977152i	$-0.431826\pi$
$233$	5.13478e109	0.425081	0.212540	+	0.977152i	$0.431826\pi$
$234$	0	0
$235$	−2.47196e110	−1.37527
$236$	−6.01365e109	−0.274619
$237$	0	0
$238$	1.78519e110	0.550626
$239$	4.49294e110	1.14032	0.570162	−	0.821533i	$-0.306881\pi$
$239$	4.49294e110	1.14032	0.570162	+	0.821533i	$0.306881\pi$
$240$	0	0
$241$	−5.09820e110	−0.878263	−0.439132	−	0.898423i	$-0.644714\pi$
$241$	−5.09820e110	−0.878263	−0.439132	+	0.898423i	$0.644714\pi$
$242$	−3.36509e110	−0.478170
$243$	0	0
$244$	5.07865e110	0.492177
$245$	−5.06680e110	−0.405986
$246$	0	0
$247$	−2.90578e109	−0.0159534
$248$	−4.36466e111	−1.98585
$249$	0	0
$250$	−2.85332e111	−0.893593
$251$	3.21902e111	0.837329	0.418665	−	0.908141i	$-0.362498\pi$
$251$	3.21902e111	0.837329	0.418665	+	0.908141i	$0.362498\pi$
$252$	0	0
$253$	−7.89258e111	−1.41943
$254$	−5.02990e110	−0.0752994
$255$	0	0
$256$	−8.29879e111	−0.862693
$257$	−4.14878e111	−0.359775	−0.179887	−	0.983687i	$-0.557573\pi$
$257$	−4.14878e111	−0.359775	−0.179887	+	0.983687i	$0.557573\pi$
$258$	0	0
$259$	−8.78847e111	−0.531465
$260$	−2.03982e111	−0.103117
$261$	0	0
$262$	4.03422e112	1.42807
$263$	2.13949e112	0.634408	0.317204	−	0.948357i	$-0.397256\pi$
$263$	2.13949e112	0.634408	0.317204	+	0.948357i	$0.397256\pi$
$264$	0	0
$265$	−4.32417e112	−0.901508
$266$	−2.33993e111	−0.0409455
$267$	0	0
$268$	−4.13079e112	−0.510229
$269$	−1.21860e113	−1.26585	−0.632924	−	0.774214i	$-0.718145\pi$
$269$	−1.21860e113	−1.26585	−0.632924	+	0.774214i	$0.718145\pi$
$270$	0	0
$271$	−1.36731e112	−0.100645	−0.0503227	−	0.998733i	$-0.516025\pi$
$271$	−1.36731e112	−0.100645	−0.0503227	+	0.998733i	$0.516025\pi$
$272$	5.00755e112	0.310579
$273$	0	0
$274$	−3.33710e113	−1.47220
$275$	−1.18031e113	−0.439567
$276$	0	0
$277$	−4.24731e113	−1.12929	−0.564643	−	0.825335i	$-0.690986\pi$
$277$	−4.24731e113	−1.12929	−0.564643	+	0.825335i	$0.690986\pi$
$278$	−8.02737e112	−0.180505
$279$	0	0
$280$	−6.68185e113	−1.07659
$281$	−8.59813e113	−1.17371	−0.586854	−	0.809692i	$-0.699634\pi$
$281$	−8.59813e113	−1.17371	−0.586854	+	0.809692i	$0.699634\pi$
$282$	0	0
$283$	1.59719e114	1.56779	0.783893	−	0.620896i	$-0.213231\pi$
$283$	1.59719e114	1.56779	0.783893	+	0.620896i	$0.213231\pi$
$284$	1.95317e112	0.0162719
$285$	0	0
$286$	6.73821e113	0.405064
$287$	3.04739e113	0.155747
$288$	0	0
$289$	−1.89383e114	−0.700795
$290$	2.36676e114	0.745842
$291$	0	0
$292$	−1.65074e114	−0.377899
$293$	−1.18964e114	−0.232312	−0.116156	−	0.993231i	$-0.537057\pi$
$293$	−1.18964e114	−0.232312	−0.116156	+	0.993231i	$0.537057\pi$
$294$	0	0
$295$	−4.77457e114	−0.679533
$296$	−3.88046e114	−0.471866
$297$	0	0
$298$	5.08886e114	0.452443
$299$	5.81679e114	0.442561
$300$	0	0
$301$	1.63539e115	0.912599
$302$	−1.16692e115	−0.558110
$303$	0	0
$304$	−6.56361e113	−0.0230952
$305$	4.03222e115	1.21787
$306$	0	0
$307$	6.18500e115	1.37849	0.689247	−	0.724526i	$-0.257941\pi$
$307$	6.18500e115	1.37849	0.689247	+	0.724526i	$0.257941\pi$
$308$	−2.62400e115	−0.502755
$309$	0	0
$310$	−8.51886e115	−1.20799
$311$	1.07902e116	1.31727	0.658633	−	0.752465i	$-0.271135\pi$
$311$	1.07902e116	1.31727	0.658633	+	0.752465i	$0.271135\pi$
$312$	0	0
$313$	−5.97065e115	−0.541016	−0.270508	−	0.962718i	$-0.587192\pi$
$313$	−5.97065e115	−0.541016	−0.270508	+	0.962718i	$0.587192\pi$
$314$	−1.81536e116	−1.41819
$315$	0	0
$316$	7.61754e115	0.442961
$317$	2.55009e116	1.28027	0.640133	−	0.768264i	$-0.278879\pi$
$317$	2.55009e116	1.28027	0.640133	+	0.768264i	$0.278879\pi$
$318$	0	0
$319$	3.78082e116	1.41684
$320$	−2.68579e116	−0.870157
$321$	0	0
$322$	4.68407e116	1.13586
$323$	−1.05983e115	−0.0222494
$324$	0	0
$325$	8.69880e115	0.137051
$326$	5.59459e115	0.0764099
$327$	0	0
$328$	1.34554e116	0.138281
$329$	2.34358e117	2.09059
$330$	0	0
$331$	−3.38538e116	−0.227827	−0.113914	−	0.993491i	$-0.536339\pi$
$331$	−3.38538e116	−0.227827	−0.113914	+	0.993491i	$0.536339\pi$
$332$	−4.41416e115	−0.0258183
$333$	0	0
$334$	−2.47824e116	−0.109631
$335$	−3.27966e117	−1.26254
$336$	0	0
$337$	−4.10228e116	−0.119739	−0.0598694	−	0.998206i	$-0.519068\pi$
$337$	−4.10228e116	−0.119739	−0.0598694	+	0.998206i	$0.519068\pi$
$338$	2.73166e117	0.694705
$339$	0	0
$340$	−7.43988e116	−0.143812
$341$	−1.36086e118	−2.29475
$342$	0	0
$343$	−4.73982e117	−0.608955
$344$	7.22091e117	0.810259
$345$	0	0
$346$	−5.55001e116	−0.0475615
$347$	1.44206e117	0.108060	0.0540298	−	0.998539i	$-0.482793\pi$
$347$	1.44206e117	0.108060	0.0540298	+	0.998539i	$0.482793\pi$
$348$	0	0
$349$	2.46411e117	0.141344	0.0706722	−	0.997500i	$-0.477486\pi$
$349$	2.46411e117	0.141344	0.0706722	+	0.997500i	$0.477486\pi$
$350$	7.00486e117	0.351751
$351$	0	0
$352$	−2.03238e118	−0.783018
$353$	1.33642e118	0.451253	0.225627	−	0.974214i	$-0.427557\pi$
$353$	1.33642e118	0.451253	0.225627	+	0.974214i	$0.427557\pi$
$354$	0	0
$355$	1.55073e117	0.0402641
$356$	1.86863e118	0.425695
$357$	0	0
$358$	6.19330e116	0.0108733
$359$	−6.50020e118	−1.00239	−0.501193	−	0.865335i	$-0.667105\pi$
$359$	−6.50020e118	−1.00239	−0.501193	+	0.865335i	$0.667105\pi$
$360$	0	0
$361$	−8.38235e118	−0.998345
$362$	−1.20097e119	−1.25772
$363$	0	0
$364$	1.93388e118	0.156752
$365$	−1.31061e119	−0.935097
$366$	0	0
$367$	−1.27243e119	−0.704144	−0.352072	−	0.935973i	$-0.614523\pi$
$367$	−1.27243e119	−0.704144	−0.352072	+	0.935973i	$0.614523\pi$
$368$	1.31390e119	0.640679
$369$	0	0
$370$	−7.57380e118	−0.287034
$371$	4.09958e119	1.37042
$372$	0	0
$373$	−1.61115e119	−0.419444	−0.209722	−	0.977761i	$-0.567256\pi$
$373$	−1.61115e119	−0.419444	−0.209722	+	0.977761i	$0.567256\pi$
$374$	2.45764e119	0.564922
$375$	0	0
$376$	1.03478e120	1.85615
$377$	−2.78645e119	−0.441751
$378$	0	0
$379$	5.32525e119	0.660111	0.330056	−	0.943961i	$-0.392932\pi$
$379$	5.32525e119	0.660111	0.330056	+	0.943961i	$0.392932\pi$
$380$	9.75176e117	0.0106941
$381$	0	0
$382$	5.94617e119	0.510847
$383$	−3.01520e119	−0.229389	−0.114694	−	0.993401i	$-0.536589\pi$
$383$	−3.01520e119	−0.229389	−0.114694	+	0.993401i	$0.536589\pi$
$384$	0	0
$385$	−2.08334e120	−1.24405
$386$	−2.66519e120	−1.41065
$387$	0	0
$388$	6.17632e119	0.257072
$389$	2.34405e120	0.865585	0.432793	−	0.901493i	$-0.357528\pi$
$389$	2.34405e120	0.865585	0.432793	+	0.901493i	$0.357528\pi$
$390$	0	0
$391$	2.12157e120	0.617217
$392$	2.12100e120	0.547946
$393$	0	0
$394$	−2.30232e119	−0.0469452
$395$	6.04799e120	1.09609
$396$	0	0
$397$	3.15657e120	0.452332	0.226166	−	0.974089i	$-0.427381\pi$
$397$	3.15657e120	0.452332	0.226166	+	0.974089i	$0.427381\pi$
$398$	7.67452e120	0.978337
$399$	0	0
$400$	1.96490e120	0.198404
$401$	−1.29870e121	−1.16761	−0.583803	−	0.811895i	$-0.698436\pi$
$401$	−1.29870e121	−1.16761	−0.583803	+	0.811895i	$0.698436\pi$
$402$	0	0
$403$	1.00295e121	0.715474
$404$	−2.50827e120	−0.159456
$405$	0	0
$406$	−2.24383e121	−1.13378
$407$	−1.20989e121	−0.545264
$408$	0	0
$409$	2.34486e121	0.841363	0.420682	−	0.907208i	$-0.361791\pi$
$409$	2.34486e121	0.841363	0.420682	+	0.907208i	$0.361791\pi$
$410$	2.62620e120	0.0841161
$411$	0	0
$412$	−1.48284e121	−0.378768
$413$	4.52659e121	1.03298
$414$	0	0
$415$	−3.50465e120	−0.0638863
$416$	1.49786e121	0.244135
$417$	0	0
$418$	−3.22133e120	−0.0420086
$419$	−6.83542e121	−0.797651	−0.398826	−	0.917027i	$-0.630582\pi$
$419$	−6.83542e121	−0.797651	−0.398826	+	0.917027i	$0.630582\pi$
$420$	0	0
$421$	−1.26027e122	−1.17855	−0.589273	−	0.807934i	$-0.700586\pi$
$421$	−1.26027e122	−1.17855	−0.589273	+	0.807934i	$0.700586\pi$
$422$	−1.27873e122	−1.07090
$423$	0	0
$424$	1.81013e122	1.21674
$425$	3.17273e121	0.191139
$426$	0	0
$427$	−3.82280e122	−1.85134
$428$	3.19245e121	0.138672
$429$	0	0
$430$	1.40936e122	0.492878
$431$	−3.14662e122	−0.987760	−0.493880	−	0.869530i	$-0.664422\pi$
$431$	−3.14662e122	−0.987760	−0.493880	+	0.869530i	$0.664422\pi$
$432$	0	0
$433$	−2.51232e122	−0.635898	−0.317949	−	0.948108i	$-0.602994\pi$
$433$	−2.51232e122	−0.635898	−0.317949	+	0.948108i	$0.602994\pi$
$434$	8.07641e122	1.83631
$435$	0	0
$436$	3.00620e122	0.551945
$437$	−2.78083e121	−0.0458974
$438$	0	0
$439$	−5.27593e122	−0.704204	−0.352102	−	0.935962i	$-0.614533\pi$
$439$	−5.27593e122	−0.704204	−0.352102	+	0.935962i	$0.614533\pi$
$440$	−9.19878e122	−1.10454
$441$	0	0
$442$	−1.81127e122	−0.176135
$443$	1.20330e123	1.05342	0.526710	−	0.850045i	$-0.323425\pi$
$443$	1.20330e123	1.05342	0.526710	+	0.850045i	$0.323425\pi$
$444$	0	0
$445$	1.48361e123	1.05337
$446$	9.24634e122	0.591424
$447$	0	0
$448$	2.54629e123	1.32276
$449$	−1.57788e123	−0.738957	−0.369479	−	0.929239i	$-0.620464\pi$
$449$	−1.57788e123	−0.738957	−0.369479	+	0.929239i	$0.620464\pi$
$450$	0	0
$451$	4.19528e122	0.159791
$452$	1.35464e123	0.465465
$453$	0	0
$454$	3.22888e122	0.0903556
$455$	1.53541e123	0.387878
$456$	0	0
$457$	−3.61599e123	−0.744944	−0.372472	−	0.928043i	$-0.621490\pi$
$457$	−3.61599e123	−0.744944	−0.372472	+	0.928043i	$0.621490\pi$
$458$	4.54018e123	0.844946
$459$	0	0
$460$	−1.95211e123	−0.296664
$461$	4.18169e123	0.574458	0.287229	−	0.957862i	$-0.407266\pi$
$461$	4.18169e123	0.574458	0.287229	+	0.957862i	$0.407266\pi$
$462$	0	0
$463$	6.81222e123	0.765196	0.382598	−	0.923915i	$-0.375030\pi$
$463$	6.81222e123	0.765196	0.382598	+	0.923915i	$0.375030\pi$
$464$	−6.29406e123	−0.639507
$465$	0	0
$466$	−4.19526e123	−0.348991
$467$	−1.53529e124	−1.15600	−0.577998	−	0.816038i	$-0.696166\pi$
$467$	−1.53529e124	−1.15600	−0.577998	+	0.816038i	$0.696166\pi$
$468$	0	0
$469$	3.10932e124	1.91924
$470$	2.01967e124	1.12909
$471$	0	0
$472$	1.99867e124	0.917145
$473$	2.25141e124	0.936294
$474$	0	0
$475$	−4.15863e122	−0.0142134
$476$	7.05346e123	0.218615
$477$	0	0
$478$	−3.67086e124	−0.936204
$479$	3.65719e124	0.846344	0.423172	−	0.906049i	$-0.360917\pi$
$479$	3.65719e124	0.846344	0.423172	+	0.906049i	$0.360917\pi$
$480$	0	0
$481$	8.91684e123	0.170006
$482$	4.16538e124	0.721053
$483$	0	0
$484$	−1.32958e124	−0.189848
$485$	4.90373e124	0.636115
$486$	0	0
$487$	−8.75398e124	−0.937797	−0.468899	−	0.883252i	$-0.655349\pi$
$487$	−8.75398e124	−0.937797	−0.468899	+	0.883252i	$0.655349\pi$
$488$	−1.68792e125	−1.64372
$489$	0	0
$490$	4.13972e124	0.333314
$491$	9.36249e124	0.685649	0.342825	−	0.939399i	$-0.388616\pi$
$491$	9.36249e124	0.685649	0.342825	+	0.939399i	$0.388616\pi$
$492$	0	0
$493$	−1.01631e125	−0.616088
$494$	2.37410e123	0.0130977
$495$	0	0
$496$	2.26547e125	1.03576
$497$	−1.47019e124	−0.0612070
$498$	0	0
$499$	1.65067e125	0.570144	0.285072	−	0.958506i	$-0.407982\pi$
$499$	1.65067e125	0.570144	0.285072	+	0.958506i	$0.407982\pi$
$500$	−1.12737e125	−0.354783
$501$	0	0
$502$	−2.63004e125	−0.687446
$503$	8.31350e125	1.98095	0.990473	−	0.137706i	$-0.0439728\pi$
$503$	8.31350e125	1.98095	0.990473	+	0.137706i	$0.0439728\pi$
$504$	0	0
$505$	−1.99146e125	−0.394568
$506$	6.44847e125	1.16535
$507$	0	0
$508$	−1.98736e124	−0.0298961
$509$	4.64595e125	0.637819	0.318909	−	0.947785i	$-0.396683\pi$
$509$	4.64595e125	0.637819	0.318909	+	0.947785i	$0.396683\pi$
$510$	0	0
$511$	1.24254e126	1.42148
$512$	9.30054e125	0.971527
$513$	0	0
$514$	3.38968e125	0.295375
$515$	−1.17731e126	−0.937246
$516$	0	0
$517$	3.22636e126	2.14488
$518$	7.18044e125	0.436332
$519$	0	0
$520$	6.77945e125	0.344381
$521$	3.08051e126	1.43110	0.715548	−	0.698564i	$-0.246177\pi$
$521$	3.08051e126	1.43110	0.715548	+	0.698564i	$0.246177\pi$
$522$	0	0
$523$	4.47820e124	0.0174090	0.00870452	−	0.999962i	$-0.497229\pi$
$523$	4.47820e124	0.0174090	0.00870452	+	0.999962i	$0.497229\pi$
$524$	1.59396e126	0.566986
$525$	0	0
$526$	−1.74803e126	−0.520848
$527$	3.65807e126	0.997835
$528$	0	0
$529$	1.19458e126	0.273230
$530$	3.53297e126	0.740137
$531$	0	0
$532$	−9.24527e124	−0.0162566
$533$	−3.09190e125	−0.0498207
$534$	0	0
$535$	2.53467e126	0.343139
$536$	1.37289e127	1.70401
$537$	0	0
$538$	9.95634e126	1.03926
$539$	6.61308e126	0.633179
$540$	0	0
$541$	2.32405e127	1.87315	0.936574	−	0.350469i	$-0.113978\pi$
$541$	2.32405e127	1.87315	0.936574	+	0.350469i	$0.113978\pi$
$542$	1.11713e126	0.0826298
$543$	0	0
$544$	5.46316e126	0.340483
$545$	2.38679e127	1.36577
$546$	0	0
$547$	−1.13550e127	−0.547993	−0.273997	−	0.961731i	$-0.588346\pi$
$547$	−1.13550e127	−0.547993	−0.273997	+	0.961731i	$0.588346\pi$
$548$	−1.31852e127	−0.584508
$549$	0	0
$550$	9.64346e126	0.360884
$551$	1.33212e126	0.0458134
$552$	0	0
$553$	−5.73387e127	−1.66621
$554$	3.47017e127	0.927143
$555$	0	0
$556$	−3.17169e126	−0.0716660
$557$	3.44821e127	0.716682	0.358341	−	0.933591i	$-0.383343\pi$
$557$	3.44821e127	0.716682	0.358341	+	0.933591i	$0.383343\pi$
$558$	0	0
$559$	−1.65928e127	−0.291924
$560$	3.46821e127	0.561516
$561$	0	0
$562$	7.02492e127	0.963614
$563$	9.14565e127	1.15498	0.577489	−	0.816398i	$-0.304032\pi$
$563$	9.14565e127	1.15498	0.577489	+	0.816398i	$0.304032\pi$
$564$	0	0
$565$	1.07553e128	1.15178
$566$	−1.30495e128	−1.28715
$567$	0	0
$568$	−6.49147e126	−0.0543432
$569$	2.43339e127	0.187712	0.0938560	−	0.995586i	$-0.470081\pi$
$569$	2.43339e127	0.187712	0.0938560	+	0.995586i	$0.470081\pi$
$570$	0	0
$571$	−3.60430e127	−0.236180	−0.118090	−	0.993003i	$-0.537677\pi$
$571$	−3.60430e127	−0.236180	−0.118090	+	0.993003i	$0.537677\pi$
$572$	2.66233e127	0.160822
$573$	0	0
$574$	−2.48980e127	−0.127868
$575$	8.32476e127	0.394291
$576$	0	0
$577$	−2.26961e128	−0.914695	−0.457347	−	0.889288i	$-0.651200\pi$
$577$	−2.26961e128	−0.914695	−0.457347	+	0.889288i	$0.651200\pi$
$578$	1.54731e128	0.575352
$579$	0	0
$580$	9.35129e127	0.296121
$581$	3.32262e127	0.0971160
$582$	0	0
$583$	5.64382e128	1.40600
$584$	5.48632e128	1.26207
$585$	0	0
$586$	9.71971e127	0.190728
$587$	−3.79672e128	−0.688236	−0.344118	−	0.938926i	$-0.611822\pi$
$587$	−3.79672e128	−0.688236	−0.344118	+	0.938926i	$0.611822\pi$
$588$	0	0
$589$	−4.79479e127	−0.0742008
$590$	3.90096e128	0.557896
$591$	0	0
$592$	2.01415e128	0.246112
$593$	−6.59860e128	−0.745433	−0.372716	−	0.927945i	$-0.621574\pi$
$593$	−6.59860e128	−0.745433	−0.372716	+	0.927945i	$0.621574\pi$
$594$	0	0
$595$	5.60014e128	0.540953
$596$	2.01066e128	0.179633
$597$	0	0
$598$	−4.75248e128	−0.363342
$599$	1.08803e129	0.769652	0.384826	−	0.922989i	$-0.374261\pi$
$599$	1.08803e129	0.769652	0.384826	+	0.922989i	$0.374261\pi$
$600$	0	0
$601$	1.43607e129	0.869986	0.434993	−	0.900434i	$-0.356751\pi$
$601$	1.43607e129	0.869986	0.434993	+	0.900434i	$0.356751\pi$
$602$	−1.33616e129	−0.749243
$603$	0	0
$604$	−4.61063e128	−0.221586
$605$	−1.05563e129	−0.469771
$606$	0	0
$607$	−3.14623e129	−1.20093	−0.600464	−	0.799652i	$-0.705017\pi$
$607$	−3.14623e129	−1.20093	−0.600464	+	0.799652i	$0.705017\pi$
$608$	−7.16079e127	−0.0253189
$609$	0	0
$610$	−3.29444e129	−0.999872
$611$	−2.37781e129	−0.668744
$612$	0	0
$613$	−2.38828e129	−0.576997	−0.288499	−	0.957480i	$-0.593156\pi$
$613$	−2.38828e129	−0.576997	−0.288499	+	0.957480i	$0.593156\pi$
$614$	−5.05332e129	−1.13174
$615$	0	0
$616$	8.72102e129	1.67905
$617$	1.21225e129	0.216437	0.108218	−	0.994127i	$-0.465485\pi$
$617$	1.21225e129	0.216437	0.108218	+	0.994127i	$0.465485\pi$
$618$	0	0
$619$	3.23232e129	0.496477	0.248238	−	0.968699i	$-0.420148\pi$
$619$	3.23232e129	0.496477	0.248238	+	0.968699i	$0.420148\pi$
$620$	−3.36588e129	−0.479607
$621$	0	0
$622$	−8.81594e129	−1.08147
$623$	−1.40656e130	−1.60126
$624$	0	0
$625$	−5.38811e129	−0.528464
$626$	4.87819e129	0.444173
$627$	0	0
$628$	−7.17267e129	−0.563064
$629$	3.25226e129	0.237099
$630$	0	0
$631$	−2.62414e130	−1.65052	−0.825262	−	0.564750i	$-0.808973\pi$
$631$	−2.62414e130	−1.65052	−0.825262	+	0.564750i	$0.808973\pi$
$632$	−2.53173e130	−1.47936
$633$	0	0
$634$	−2.08350e130	−1.05110
$635$	−1.57788e129	−0.0739767
$636$	0	0
$637$	−4.87380e129	−0.197417
$638$	−3.08904e130	−1.16322
$639$	0	0
$640$	6.52221e129	0.212337
$641$	−4.38203e130	−1.32671	−0.663356	−	0.748304i	$-0.730869\pi$
$641$	−4.38203e130	−1.32671	−0.663356	+	0.748304i	$0.730869\pi$
$642$	0	0
$643$	−3.72458e129	−0.0975589	−0.0487795	−	0.998810i	$-0.515533\pi$
$643$	−3.72458e129	−0.0975589	−0.0487795	+	0.998810i	$0.515533\pi$
$644$	1.85072e130	0.450970
$645$	0	0
$646$	8.65912e128	0.0182668
$647$	5.42339e129	0.106469	0.0532343	−	0.998582i	$-0.483047\pi$
$647$	5.42339e129	0.106469	0.0532343	+	0.998582i	$0.483047\pi$
$648$	0	0
$649$	6.23167e130	1.05981
$650$	−7.10717e129	−0.112519
$651$	0	0
$652$	2.21047e129	0.0303370
$653$	8.13013e129	0.103905	0.0519523	−	0.998650i	$-0.483456\pi$
$653$	8.13013e129	0.103905	0.0519523	+	0.998650i	$0.483456\pi$
$654$	0	0
$655$	1.26553e131	1.40299
$656$	−6.98403e129	−0.0721236
$657$	0	0
$658$	−1.91477e131	−1.71638
$659$	−7.29337e130	−0.609196	−0.304598	−	0.952481i	$-0.598522\pi$
$659$	−7.29337e130	−0.609196	−0.304598	+	0.952481i	$0.598522\pi$
$660$	0	0
$661$	5.42034e129	0.0393241	0.0196621	−	0.999807i	$-0.493741\pi$
$661$	5.42034e129	0.0393241	0.0196621	+	0.999807i	$0.493741\pi$
$662$	2.76595e130	0.187046
$663$	0	0
$664$	1.46707e130	0.0862253
$665$	−7.34034e129	−0.0402262
$666$	0	0
$667$	−2.66663e131	−1.27090
$668$	−9.79178e129	−0.0435267
$669$	0	0
$670$	2.67958e131	1.03654
$671$	−5.26277e131	−1.89940
$672$	0	0
$673$	2.85131e131	0.896075	0.448037	−	0.894015i	$-0.352123\pi$
$673$	2.85131e131	0.896075	0.448037	+	0.894015i	$0.352123\pi$
$674$	3.35168e130	0.0983054
$675$	0	0
$676$	1.07931e131	0.275818
$677$	6.99964e131	1.66995	0.834973	−	0.550291i	$-0.185483\pi$
$677$	6.99964e131	1.66995	0.834973	+	0.550291i	$0.185483\pi$
$678$	0	0
$679$	−4.64904e131	−0.966983
$680$	2.47268e131	0.480290
$681$	0	0
$682$	1.11186e132	1.88399
$683$	7.86376e131	1.24471	0.622354	−	0.782736i	$-0.286176\pi$
$683$	7.86376e131	1.24471	0.622354	+	0.782736i	$0.286176\pi$
$684$	0	0
$685$	−1.04685e132	−1.44634
$686$	3.87257e131	0.499951
$687$	0	0
$688$	−3.74800e131	−0.422608
$689$	−4.15946e131	−0.438372
$690$	0	0
$691$	4.34229e131	0.399935	0.199968	−	0.979803i	$-0.435916\pi$
$691$	4.34229e131	0.399935	0.199968	+	0.979803i	$0.435916\pi$
$692$	−2.19286e130	−0.0188833
$693$	0	0
$694$	−1.17821e131	−0.0887169
$695$	−2.51818e131	−0.177335
$696$	0	0
$697$	−1.12771e131	−0.0694825
$698$	−2.01325e131	−0.116044
$699$	0	0
$700$	2.76769e131	0.139656
$701$	−2.09353e132	−0.988534	−0.494267	−	0.869310i	$-0.664563\pi$
$701$	−2.09353e132	−0.988534	−0.494267	+	0.869310i	$0.664563\pi$
$702$	0	0
$703$	−4.26287e130	−0.0176311
$704$	3.50543e132	1.35710
$705$	0	0
$706$	−1.09190e132	−0.370478
$707$	1.88803e132	0.599799
$708$	0	0
$709$	4.97568e132	1.38612	0.693062	−	0.720878i	$-0.256261\pi$
$709$	4.97568e132	1.38612	0.693062	+	0.720878i	$0.256261\pi$
$710$	−1.26699e131	−0.0330568
$711$	0	0
$712$	−6.21050e132	−1.42170
$713$	9.59822e132	2.05839
$714$	0	0
$715$	2.11377e132	0.397949
$716$	2.44703e130	0.00431702
$717$	0	0
$718$	5.31085e132	0.822958
$719$	4.88173e132	0.709055	0.354528	−	0.935045i	$-0.384642\pi$
$719$	4.88173e132	0.709055	0.354528	+	0.935045i	$0.384642\pi$
$720$	0	0
$721$	1.11616e133	1.42474
$722$	6.84862e132	0.819641
$723$	0	0
$724$	−4.74517e132	−0.499353
$725$	−3.98785e132	−0.393570
$726$	0	0
$727$	7.26876e132	0.631117	0.315559	−	0.948906i	$-0.397808\pi$
$727$	7.26876e132	0.631117	0.315559	+	0.948906i	$0.397808\pi$
$728$	−6.42734e132	−0.523506
$729$	0	0
$730$	1.07081e133	0.767713
$731$	−6.05192e132	−0.407132
$732$	0	0
$733$	1.29322e133	0.766190	0.383095	−	0.923709i	$-0.374858\pi$
$733$	1.29322e133	0.766190	0.383095	+	0.923709i	$0.374858\pi$
$734$	1.03961e133	0.578102
$735$	0	0
$736$	1.43345e133	0.702366
$737$	4.28055e133	1.96907
$738$	0	0
$739$	−4.10724e133	−1.66565	−0.832824	−	0.553537i	$-0.813278\pi$
$739$	−4.10724e133	−1.66565	−0.832824	+	0.553537i	$0.813278\pi$
$740$	−2.99248e132	−0.113961
$741$	0	0
$742$	−3.34948e133	−1.12511
$743$	1.21328e132	0.0382809	0.0191405	−	0.999817i	$-0.493907\pi$
$743$	1.21328e132	0.0382809	0.0191405	+	0.999817i	$0.493907\pi$
$744$	0	0
$745$	1.59637e133	0.444496
$746$	1.31635e133	0.344363
$747$	0	0
$748$	9.71037e132	0.224291
$749$	−2.40302e133	−0.521619
$750$	0	0
$751$	5.11984e133	0.981746	0.490873	−	0.871231i	$-0.336678\pi$
$751$	5.11984e133	0.981746	0.490873	+	0.871231i	$0.336678\pi$
$752$	−5.37102e133	−0.968116
$753$	0	0
$754$	2.27661e133	0.362677
$755$	−3.66064e133	−0.548307
$756$	0	0
$757$	−1.03853e134	−1.37550	−0.687748	−	0.725950i	$-0.741400\pi$
$757$	−1.03853e134	−1.37550	−0.687748	+	0.725950i	$0.741400\pi$
$758$	−4.35089e133	−0.541951
$759$	0	0
$760$	−3.24105e132	−0.0357152
$761$	−1.18377e134	−1.22710	−0.613552	−	0.789655i	$-0.710260\pi$
$761$	−1.18377e134	−1.22710	−0.613552	+	0.789655i	$0.710260\pi$
$762$	0	0
$763$	−2.26282e134	−2.07615
$764$	2.34939e133	0.202822
$765$	0	0
$766$	2.46350e133	0.188328
$767$	−4.59271e133	−0.330434
$768$	0	0
$769$	1.09883e134	0.700418	0.350209	−	0.936672i	$-0.386111\pi$
$769$	1.09883e134	0.700418	0.350209	+	0.936672i	$0.386111\pi$
$770$	1.70215e134	1.02136
$771$	0	0
$772$	−1.05304e134	−0.560069
$773$	−9.95234e133	−0.498401	−0.249200	−	0.968452i	$-0.580168\pi$
$773$	−9.95234e133	−0.498401	−0.249200	+	0.968452i	$0.580168\pi$
$774$	0	0
$775$	1.43538e134	0.637438
$776$	−2.05273e134	−0.858544
$777$	0	0
$778$	−1.91515e134	−0.710645
$779$	1.47814e132	0.00516684
$780$	0	0
$781$	−2.02398e133	−0.0627962
$782$	−1.73338e134	−0.506735
$783$	0	0
$784$	−1.10090e134	−0.285793
$785$	−5.69478e134	−1.39328
$786$	0	0
$787$	−4.25421e134	−0.924685	−0.462343	−	0.886701i	$-0.652991\pi$
$787$	−4.25421e134	−0.924685	−0.462343	+	0.886701i	$0.652991\pi$
$788$	−9.09668e132	−0.0186386
$789$	0	0
$790$	−4.94138e134	−0.899888
$791$	−1.01966e135	−1.75086
$792$	0	0
$793$	3.87863e134	0.592210
$794$	−2.57901e134	−0.371364
$795$	0	0
$796$	3.03228e134	0.388429
$797$	1.05793e135	1.27834	0.639168	−	0.769067i	$-0.279279\pi$
$797$	1.05793e135	1.27834	0.639168	+	0.769067i	$0.279279\pi$
$798$	0	0
$799$	−8.67262e134	−0.932664
$800$	2.14367e134	0.217507
$801$	0	0
$802$	1.06108e135	0.958603
$803$	1.71059e135	1.45838
$804$	0	0
$805$	1.46939e135	1.11591
$806$	−8.19437e134	−0.587403
$807$	0	0
$808$	8.33639e134	0.532537
$809$	−5.72597e134	−0.345337	−0.172668	−	0.984980i	$-0.555239\pi$
$809$	−5.72597e134	−0.345337	−0.172668	+	0.984980i	$0.555239\pi$
$810$	0	0
$811$	−4.39300e134	−0.236207	−0.118103	−	0.993001i	$-0.537681\pi$
$811$	−4.39300e134	−0.236207	−0.118103	+	0.993001i	$0.537681\pi$
$812$	−8.86560e134	−0.450145
$813$	0	0
$814$	9.88517e134	0.447661
$815$	1.75502e134	0.0750677
$816$	0	0
$817$	7.93251e133	0.0302751
$818$	−1.91582e135	−0.690758
$819$	0	0
$820$	1.03764e134	0.0333966
$821$	2.16864e135	0.659523	0.329762	−	0.944064i	$-0.393032\pi$
$821$	2.16864e135	0.659523	0.329762	+	0.944064i	$0.393032\pi$
$822$	0	0
$823$	−4.99161e135	−1.35565	−0.677826	−	0.735222i	$-0.737078\pi$
$823$	−4.99161e135	−1.35565	−0.677826	+	0.735222i	$0.737078\pi$
$824$	4.92829e135	1.26497
$825$	0	0
$826$	−3.69835e135	−0.848079
$827$	−1.61582e135	−0.350257	−0.175129	−	0.984546i	$-0.556034\pi$
$827$	−1.61582e135	−0.350257	−0.175129	+	0.984546i	$0.556034\pi$
$828$	0	0
$829$	5.76678e135	1.11724	0.558622	−	0.829422i	$-0.311330\pi$
$829$	5.76678e135	1.11724	0.558622	+	0.829422i	$0.311330\pi$
$830$	2.86340e134	0.0524506
$831$	0	0
$832$	−2.58348e135	−0.423127
$833$	−1.77763e135	−0.275327
$834$	0	0
$835$	−7.77424e134	−0.107705
$836$	−1.27278e134	−0.0166787
$837$	0	0
$838$	5.58473e135	0.654871
$839$	1.05736e134	0.0117298	0.00586489	−	0.999983i	$-0.498133\pi$
$839$	1.05736e134	0.0117298	0.00586489	+	0.999983i	$0.498133\pi$
$840$	0	0
$841$	2.70446e135	0.268576
$842$	1.02968e136	0.967584
$843$	0	0
$844$	−5.05237e135	−0.425178
$845$	8.56921e135	0.682502
$846$	0	0
$847$	1.00080e136	0.714116
$848$	−9.39545e135	−0.634615
$849$	0	0
$850$	−2.59221e135	−0.156925
$851$	8.53342e135	0.489101
$852$	0	0
$853$	−5.38353e134	−0.0276654	−0.0138327	−	0.999904i	$-0.504403\pi$
$853$	−5.38353e134	−0.0276654	−0.0138327	+	0.999904i	$0.504403\pi$
$854$	3.12334e136	1.51994
$855$	0	0
$856$	−1.06103e136	−0.463124
$857$	4.16850e135	0.172334	0.0861672	−	0.996281i	$-0.472538\pi$
$857$	4.16850e135	0.172334	0.0861672	+	0.996281i	$0.472538\pi$
$858$	0	0
$859$	1.20248e136	0.446061	0.223030	−	0.974811i	$-0.428405\pi$
$859$	1.20248e136	0.446061	0.223030	+	0.974811i	$0.428405\pi$
$860$	5.56853e135	0.195687
$861$	0	0
$862$	2.57088e136	0.810950
$863$	5.13038e136	1.53337	0.766686	−	0.642022i	$-0.221904\pi$
$863$	5.13038e136	1.53337	0.766686	+	0.642022i	$0.221904\pi$
$864$	0	0
$865$	−1.74104e135	−0.0467260
$866$	2.05264e136	0.522072
$867$	0	0
$868$	3.19107e136	0.729069
$869$	−7.89371e136	−1.70947
$870$	0	0
$871$	−3.15474e136	−0.613930
$872$	−9.99126e136	−1.84333
$873$	0	0
$874$	2.27202e135	0.0376817
$875$	8.48596e136	1.33452
$876$	0	0
$877$	1.17795e137	1.66588	0.832942	−	0.553360i	$-0.186655\pi$
$877$	1.17795e137	1.66588	0.832942	+	0.553360i	$0.186655\pi$
$878$	4.31059e136	0.578151
$879$	0	0
$880$	4.77462e136	0.576095
$881$	6.33850e136	0.725449	0.362724	−	0.931896i	$-0.381847\pi$
$881$	6.33850e136	0.725449	0.362724	+	0.931896i	$0.381847\pi$
$882$	0	0
$883$	−6.81818e136	−0.702257	−0.351128	−	0.936327i	$-0.614202\pi$
$883$	−6.81818e136	−0.702257	−0.351128	+	0.936327i	$0.614202\pi$
$884$	−7.15649e135	−0.0699310
$885$	0	0
$886$	−9.83132e136	−0.864856
$887$	1.40305e137	1.17118	0.585591	−	0.810606i	$-0.300862\pi$
$887$	1.40305e137	1.17118	0.585591	+	0.810606i	$0.300862\pi$
$888$	0	0
$889$	1.49593e136	0.112455
$890$	−1.21215e137	−0.864813
$891$	0	0
$892$	3.65332e136	0.234813
$893$	1.13676e136	0.0693545
$894$	0	0
$895$	1.94284e135	0.0106823
$896$	−6.18346e136	−0.322782
$897$	0	0
$898$	1.28917e137	0.606683
$899$	−4.59788e137	−2.05462
$900$	0	0
$901$	−1.51709e137	−0.611376
$902$	−3.42767e136	−0.131188
$903$	0	0
$904$	−4.50222e137	−1.55452
$905$	−3.76745e137	−1.23563
$906$	0	0
$907$	−7.49838e136	−0.221936	−0.110968	−	0.993824i	$-0.535395\pi$
$907$	−7.49838e136	−0.221936	−0.110968	+	0.993824i	$0.535395\pi$
$908$	1.27576e136	0.0358738
$909$	0	0
$910$	−1.25448e137	−0.318447
$911$	2.34388e137	0.565368	0.282684	−	0.959213i	$-0.408775\pi$
$911$	2.34388e137	0.565368	0.282684	+	0.959213i	$0.408775\pi$
$912$	0	0
$913$	4.57419e136	0.0996376
$914$	2.95437e137	0.611598
$915$	0	0
$916$	1.79387e137	0.335468
$917$	−1.19980e138	−2.13273
$918$	0	0
$919$	−1.12468e138	−1.80658	−0.903291	−	0.429028i	$-0.858856\pi$
$919$	−1.12468e138	−1.80658	−0.903291	+	0.429028i	$0.858856\pi$
$920$	6.48794e137	0.990770
$921$	0	0
$922$	−3.41656e137	−0.471630
$923$	1.49166e136	0.0195791
$924$	0	0
$925$	1.27614e137	0.151464
$926$	−5.56578e137	−0.628225
$927$	0	0
$928$	−6.86672e137	−0.701082
$929$	−1.90398e138	−1.84898	−0.924491	−	0.381203i	$-0.875510\pi$
$929$	−1.90398e138	−1.84898	−0.924491	+	0.381203i	$0.875510\pi$
$930$	0	0
$931$	2.33002e136	0.0204738
$932$	−1.65759e137	−0.138560
$933$	0	0
$934$	1.25438e138	0.949071
$935$	7.70961e137	0.554999
$936$	0	0
$937$	2.21638e138	1.44462	0.722309	−	0.691570i	$-0.243081\pi$
$937$	2.21638e138	1.44462	0.722309	+	0.691570i	$0.243081\pi$
$938$	−2.54041e138	−1.57569
$939$	0	0
$940$	7.97990e137	0.448283
$941$	1.76168e138	0.941911	0.470955	−	0.882157i	$-0.343909\pi$
$941$	1.76168e138	0.941911	0.470955	+	0.882157i	$0.343909\pi$
$942$	0	0
$943$	−2.95895e137	−0.143332
$944$	−1.03741e138	−0.478356
$945$	0	0
$946$	−1.83947e138	−0.768697
$947$	4.99662e138	1.98793	0.993967	−	0.109675i	$-0.0349810\pi$
$947$	4.99662e138	1.98793	0.993967	+	0.109675i	$0.0349810\pi$
$948$	0	0
$949$	−1.26069e138	−0.454705
$950$	3.39772e136	0.0116692
$951$	0	0
$952$	−2.34426e138	−0.730108
$953$	−1.22547e138	−0.363483	−0.181741	−	0.983346i	$-0.558173\pi$
$953$	−1.22547e138	−0.363483	−0.181741	+	0.983346i	$0.558173\pi$
$954$	0	0
$955$	1.86531e138	0.501874
$956$	−1.45039e138	−0.371701
$957$	0	0
$958$	−2.98803e138	−0.694847
$959$	9.92474e138	2.19864
$960$	0	0
$961$	1.15763e139	2.32773
$962$	−7.28531e137	−0.139575
$963$	0	0
$964$	1.64578e138	0.286279
$965$	−8.36069e138	−1.38587
$966$	0	0
$967$	4.82909e138	0.727000	0.363500	−	0.931594i	$-0.381582\pi$
$967$	4.82909e138	0.727000	0.363500	+	0.931594i	$0.381582\pi$
$968$	4.41893e138	0.634035
$969$	0	0
$970$	−4.00649e138	−0.522250
$971$	−6.25878e137	−0.0777670	−0.0388835	−	0.999244i	$-0.512380\pi$
$971$	−6.25878e137	−0.0777670	−0.0388835	+	0.999244i	$0.512380\pi$
$972$	0	0
$973$	2.38739e138	0.269573
$974$	7.15226e138	0.769930
$975$	0	0
$976$	8.76111e138	0.857319
$977$	1.15470e139	1.07739	0.538695	−	0.842501i	$-0.318918\pi$
$977$	1.15470e139	1.07739	0.538695	+	0.842501i	$0.318918\pi$
$978$	0	0
$979$	−1.93638e139	−1.64284
$980$	1.63564e138	0.132335
$981$	0	0
$982$	−7.64942e138	−0.562917
$983$	−3.61265e138	−0.253564	−0.126782	−	0.991931i	$-0.540465\pi$
$983$	−3.61265e138	−0.253564	−0.126782	+	0.991931i	$0.540465\pi$
$984$	0	0
$985$	−7.22236e137	−0.0461205
$986$	8.30351e138	0.505808
$987$	0	0
$988$	9.38031e136	0.00520019
$989$	−1.58793e139	−0.839855
$990$	0	0
$991$	4.76355e138	0.229354	0.114677	−	0.993403i	$-0.463417\pi$
$991$	4.76355e138	0.229354	0.114677	+	0.993403i	$0.463417\pi$
$992$	2.47159e139	1.13549
$993$	0	0
$994$	1.20119e138	0.0502509
$995$	2.40749e139	0.961151
$996$	0	0
$997$	2.29424e139	0.834283	0.417142	−	0.908842i	$-0.363032\pi$
$997$	2.29424e139	0.834283	0.417142	+	0.908842i	$0.363032\pi$
$998$	−1.34864e139	−0.468088
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.94.a.b.1.3		7
3.2	odd	2		1.94.a.a.1.5	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.94.a.a.1.5	✓	7	3.2	odd	2
9.94.a.b.1.3		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)

\(f(q)\)	\(=\)	\(q-8.17029e13 q^{2} -3.22816e27 q^{4} -2.56302e32 q^{5} +2.42990e39 q^{7} +1.07290e42 q^{8} +O(q^{10})\)	\(q-8.17029e13 q^{2} -3.22816e27 q^{4} -2.56302e32 q^{5} +2.42990e39 q^{7} +1.07290e42 q^{8} +2.09406e46 q^{10} +3.34519e48 q^{11} -2.46539e51 q^{13} -1.98530e53 q^{14} -5.56886e55 q^{16} -8.99207e56 q^{17} +1.17863e58 q^{19} +8.27382e59 q^{20} -2.73312e62 q^{22} -2.35938e63 q^{23} -3.52837e64 q^{25} +2.01429e65 q^{26} -7.84410e66 q^{28} +1.13023e68 q^{29} -4.06811e69 q^{31} -6.07553e69 q^{32} +7.34678e70 q^{34} -6.22787e71 q^{35} -3.61681e72 q^{37} -9.62973e71 q^{38} -2.74985e74 q^{40} +1.25412e74 q^{41} +6.73029e75 q^{43} -1.07988e76 q^{44} +1.92768e77 q^{46} +9.64475e77 q^{47} +1.97689e78 q^{49} +2.88278e78 q^{50} +7.95867e78 q^{52} +1.68714e80 q^{53} -8.57379e80 q^{55} +2.60703e81 q^{56} -9.23427e81 q^{58} +1.86287e82 q^{59} -1.57323e83 q^{61} +3.32376e83 q^{62} +1.04790e84 q^{64} +6.31883e83 q^{65} +1.27961e85 q^{67} +2.90278e84 q^{68} +5.08835e85 q^{70} -6.05042e84 q^{71} +5.11356e86 q^{73} +2.95504e86 q^{74} -3.80480e85 q^{76} +8.12848e87 q^{77} -2.35972e88 q^{79} +1.42731e88 q^{80} -1.02465e88 q^{82} +1.36739e88 q^{83} +2.30468e89 q^{85} -5.49884e89 q^{86} +3.58905e90 q^{88} -5.78854e90 q^{89} -5.99064e90 q^{91} +7.61645e90 q^{92} -7.88004e91 q^{94} -3.02084e90 q^{95} -1.91326e92 q^{97} -1.61518e92 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 43735426713792 q^{2} + 37\!\cdots\!44 q^{4}+ \cdots - 62\!\cdots\!60 q^{8}+O(q^{10}) \) 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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