LMFDB - Embedded newform 9.94.a.b.1.4

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			1.4
Root			$-1.98834e10$ 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)

$f(q)$	$=$	$q+5.20495e12 q^{2} -9.87643e27 q^{4} +3.34454e32 q^{5} -2.46426e38 q^{7} -1.02954e41 q^{8} +O(q^{10})$	\(q+5.20495e12 q^{2} -9.87643e27 q^{4} +3.34454e32 q^{5} -2.46426e38 q^{7} -1.02954e41 q^{8} +1.74082e45 q^{10} -2.07952e48 q^{11} +2.80456e51 q^{13} -1.28264e51 q^{14} +9.72755e55 q^{16} +1.34822e57 q^{17} +5.04213e59 q^{19} -3.30321e60 q^{20} -1.08238e61 q^{22} +1.78821e63 q^{23} +1.08855e64 q^{25} +1.45976e64 q^{26} +2.43381e66 q^{28} +1.40036e68 q^{29} +3.47640e69 q^{31} +1.52592e69 q^{32} +7.01740e69 q^{34} -8.24184e70 q^{35} +3.66085e72 q^{37} +2.62440e72 q^{38} -3.44333e73 q^{40} -5.70517e74 q^{41} +1.54775e75 q^{43} +2.05382e76 q^{44} +9.30752e75 q^{46} -7.65372e77 q^{47} -3.86679e78 q^{49} +5.66586e76 q^{50} -2.76990e79 q^{52} +2.23629e80 q^{53} -6.95504e80 q^{55} +2.53705e79 q^{56} +7.28878e80 q^{58} +3.20335e82 q^{59} -1.20647e83 q^{61} +1.80945e82 q^{62} -9.55428e83 q^{64} +9.37996e83 q^{65} +6.65601e84 q^{67} -1.33156e85 q^{68} -4.28983e83 q^{70} -8.45355e85 q^{71} +7.12259e86 q^{73} +1.90545e85 q^{74} -4.97983e87 q^{76} +5.12448e86 q^{77} -1.51164e87 q^{79} +3.25342e88 q^{80} -2.96951e87 q^{82} -1.58486e89 q^{83} +4.50917e89 q^{85} +8.05593e87 q^{86} +2.14094e89 q^{88} +1.03503e90 q^{89} -6.91117e89 q^{91} -1.76611e91 q^{92} -3.98372e90 q^{94} +1.68636e92 q^{95} +1.83199e92 q^{97} -2.01264e91 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.20495e12	0.0523024	0.0261512	−	0.999658i	$-0.491675\pi$
$2$	5.20495e12	0.0523024	0.0261512	+	0.999658i	$0.491675\pi$
$3$	0	0
$3$	0	0
$4$	−9.87643e27	−0.997264
$5$	3.34454e32	1.05252	0.526262	−	0.850323i	$-0.323593\pi$
$5$	3.34454e32	1.05252	0.526262	+	0.850323i	$0.323593\pi$
$6$	0	0
$7$	−2.46426e38	−0.124345	−0.0621725	−	0.998065i	$-0.519803\pi$
$7$	−2.46426e38	−0.124345	−0.0621725	+	0.998065i	$0.519803\pi$
$8$	−1.02954e41	−0.104462
$9$	0	0
$10$	1.74082e45	0.0550495
$11$	−2.07952e48	−0.781993	−0.390997	−	0.920392i	$-0.627870\pi$
$11$	−2.07952e48	−0.781993	−0.390997	+	0.920392i	$0.627870\pi$
$12$	0	0
$13$	2.80456e51	0.446168	0.223084	−	0.974799i	$-0.428388\pi$
$13$	2.80456e51	0.446168	0.223084	+	0.974799i	$0.428388\pi$
$14$	−1.28264e51	−0.00650354
$15$	0	0
$16$	9.72755e55	0.991801
$17$	1.34822e57	0.820135	0.410068	−	0.912055i	$-0.365505\pi$
$17$	1.34822e57	0.820135	0.410068	+	0.912055i	$0.365505\pi$
$18$	0	0
$19$	5.04213e59	1.74009	0.870046	−	0.492971i	$-0.164089\pi$
$19$	5.04213e59	1.74009	0.870046	+	0.492971i	$0.164089\pi$
$20$	−3.30321e60	−1.04964
$21$	0	0
$22$	−1.08238e61	−0.0409001
$23$	1.78821e63	0.855212	0.427606	−	0.903965i	$-0.359357\pi$
$23$	1.78821e63	0.855212	0.427606	+	0.903965i	$0.359357\pi$
$24$	0	0
$25$	1.08855e64	0.107805
$26$	1.45976e64	0.0233356
$27$	0	0
$28$	2.43381e66	0.124005
$29$	1.40036e68	1.39551	0.697753	−	0.716338i	$-0.254183\pi$
$29$	1.40036e68	1.39551	0.697753	+	0.716338i	$0.254183\pi$
$30$	0	0
$31$	3.47640e69	1.55888	0.779438	−	0.626479i	$-0.215505\pi$
$31$	3.47640e69	1.55888	0.779438	+	0.626479i	$0.215505\pi$
$32$	1.52592e69	0.156335
$33$	0	0
$34$	7.01740e69	0.0428950
$35$	−8.24184e70	−0.130876
$36$	0	0
$37$	3.66085e72	0.438734	0.219367	−	0.975642i	$-0.429601\pi$
$37$	3.66085e72	0.438734	0.219367	+	0.975642i	$0.429601\pi$
$38$	2.62440e72	0.0910109
$39$	0	0
$40$	−3.44333e73	−0.109948
$41$	−5.70517e74	−0.577856	−0.288928	−	0.957351i	$-0.593299\pi$
$41$	−5.70517e74	−0.577856	−0.288928	+	0.957351i	$0.593299\pi$
$42$	0	0
$43$	1.54775e75	0.171166	0.0855828	−	0.996331i	$-0.472725\pi$
$43$	1.54775e75	0.171166	0.0855828	+	0.996331i	$0.472725\pi$
$44$	2.05382e76	0.779854
$45$	0	0
$46$	9.30752e75	0.0447296
$47$	−7.65372e77	−1.35308	−0.676538	−	0.736408i	$-0.736520\pi$
$47$	−7.65372e77	−1.35308	−0.676538	+	0.736408i	$0.736520\pi$
$48$	0	0
$49$	−3.86679e78	−0.984538
$50$	5.66586e76	0.00563846
$51$	0	0
$52$	−2.76990e79	−0.444947
$53$	2.23629e80	1.48149	0.740747	−	0.671784i	$-0.234472\pi$
$53$	2.23629e80	1.48149	0.740747	+	0.671784i	$0.234472\pi$
$54$	0	0
$55$	−6.95504e80	−0.823066
$56$	2.53705e79	0.0129893
$57$	0	0
$58$	7.28878e80	0.0729883
$59$	3.20335e82	1.44872	0.724361	−	0.689421i	$-0.242135\pi$
$59$	3.20335e82	1.44872	0.724361	+	0.689421i	$0.242135\pi$
$60$	0	0
$61$	−1.20647e83	−1.15792	−0.578962	−	0.815354i	$-0.696542\pi$
$61$	−1.20647e83	−1.15792	−0.578962	+	0.815354i	$0.696542\pi$
$62$	1.80945e82	0.0815329
$63$	0	0
$64$	−9.55428e83	−0.983624
$65$	9.37996e83	0.469602
$66$	0	0
$67$	6.65601e84	0.814208	0.407104	−	0.913382i	$-0.366539\pi$
$67$	6.65601e84	0.814208	0.407104	+	0.913382i	$0.366539\pi$
$68$	−1.33156e85	−0.817892
$69$	0	0
$70$	−4.28983e83	−0.00684513
$71$	−8.45355e85	−0.697471	−0.348735	−	0.937221i	$-0.613389\pi$
$71$	−8.45355e85	−0.697471	−0.348735	+	0.937221i	$0.613389\pi$
$72$	0	0
$73$	7.12259e86	1.61482	0.807412	−	0.589988i	$-0.200868\pi$
$73$	7.12259e86	1.61482	0.807412	+	0.589988i	$0.200868\pi$
$74$	1.90545e85	0.0229469
$75$	0	0
$76$	−4.97983e87	−1.73533
$77$	5.12448e86	0.0972370
$78$	0	0
$79$	−1.51164e87	−0.0870537	−0.0435269	−	0.999052i	$-0.513859\pi$
$79$	−1.51164e87	−0.0870537	−0.0435269	+	0.999052i	$0.513859\pi$
$80$	3.25342e88	1.04389
$81$	0	0
$82$	−2.96951e87	−0.0302232
$83$	−1.58486e89	−0.918037	−0.459019	−	0.888427i	$-0.651799\pi$
$83$	−1.58486e89	−0.918037	−0.459019	+	0.888427i	$0.651799\pi$
$84$	0	0
$85$	4.50917e89	0.863211
$86$	8.05593e87	0.00895237
$87$	0	0
$88$	2.14094e89	0.0816883
$89$	1.03503e90	0.233516	0.116758	−	0.993160i	$-0.462750\pi$
$89$	1.03503e90	0.233516	0.116758	+	0.993160i	$0.462750\pi$
$90$	0	0
$91$	−6.91117e89	−0.0554787
$92$	−1.76611e91	−0.852872
$93$	0	0
$94$	−3.98372e90	−0.0707691
$95$	1.68636e92	1.83149
$96$	0	0
$97$	1.83199e92	0.755159	0.377579	−	0.925977i	$-0.376757\pi$
$97$	1.83199e92	0.755159	0.377579	+	0.925977i	$0.376757\pi$
$98$	−2.01264e91	−0.0514937
$99$	0	0
$100$	−1.07510e92	−0.107510
$101$	−1.09411e93	−0.688839	−0.344420	−	0.938816i	$-0.611924\pi$
$101$	−1.09411e93	−0.688839	−0.344420	+	0.938816i	$0.611924\pi$
$102$	0	0
$103$	6.53274e93	1.65259	0.826294	−	0.563239i	$-0.190445\pi$
$103$	6.53274e93	1.65259	0.826294	+	0.563239i	$0.190445\pi$
$104$	−2.88739e92	−0.0466074
$105$	0	0
$106$	1.16398e93	0.0774857
$107$	2.96413e94	1.27512	0.637561	−	0.770400i	$-0.279943\pi$
$107$	2.96413e94	1.27512	0.637561	+	0.770400i	$0.279943\pi$
$108$	0	0
$109$	2.56283e94	0.466002	0.233001	−	0.972477i	$-0.425146\pi$
$109$	2.56283e94	0.466002	0.233001	+	0.972477i	$0.425146\pi$
$110$	−3.62006e93	−0.0430483
$111$	0	0
$112$	−2.39713e94	−0.123326
$113$	2.20850e95	0.751536	0.375768	−	0.926714i	$-0.377379\pi$
$113$	2.20850e95	0.751536	0.375768	+	0.926714i	$0.377379\pi$
$114$	0	0
$115$	5.98074e95	0.900130
$116$	−1.38305e96	−1.39169
$117$	0	0
$118$	1.66732e95	0.0757716
$119$	−3.32237e95	−0.101980
$120$	0	0
$121$	−2.74724e96	−0.388487
$122$	−6.27963e95	−0.0605622
$123$	0	0
$124$	−3.43345e97	−1.55461
$125$	−3.01305e97	−0.939056
$126$	0	0
$127$	−5.47224e97	−0.815253	−0.407627	−	0.913149i	$-0.633643\pi$
$127$	−5.47224e97	−0.815253	−0.407627	+	0.913149i	$0.633643\pi$
$128$	−2.00849e97	−0.207781
$129$	0	0
$130$	4.88222e96	0.0245613
$131$	−5.22366e98	−1.84018	−0.920089	−	0.391710i	$-0.871884\pi$
$131$	−5.22366e98	−1.84018	−0.920089	+	0.391710i	$0.871884\pi$
$132$	0	0
$133$	−1.24252e98	−0.216372
$134$	3.46442e97	0.0425850
$135$	0	0
$136$	−1.38804e98	−0.0856727
$137$	−1.27800e99	−0.561079	−0.280539	−	0.959843i	$-0.590513\pi$
$137$	−1.27800e99	−0.561079	−0.280539	+	0.959843i	$0.590513\pi$
$138$	0	0
$139$	−3.03718e99	−0.679646	−0.339823	−	0.940489i	$-0.610367\pi$
$139$	−3.03718e99	−0.679646	−0.339823	+	0.940489i	$0.610367\pi$
$140$	8.13999e98	0.130518
$141$	0	0
$142$	−4.40003e98	−0.0364794
$143$	−5.83212e99	−0.348900
$144$	0	0
$145$	4.68356e100	1.46880
$146$	3.70727e99	0.0844591
$147$	0	0
$148$	−3.61561e100	−0.437534
$149$	3.01665e99	0.0266909	0.0133455	−	0.999911i	$-0.495752\pi$
$149$	3.01665e99	0.0266909	0.0133455	+	0.999911i	$0.495752\pi$
$150$	0	0
$151$	−6.70032e100	−0.318910	−0.159455	−	0.987205i	$-0.550974\pi$
$151$	−6.70032e100	−0.318910	−0.159455	+	0.987205i	$0.550974\pi$
$152$	−5.19106e100	−0.181773
$153$	0	0
$154$	2.66727e99	0.00508572
$155$	1.16270e102	1.64075
$156$	0	0
$157$	−1.54216e102	−1.19894	−0.599468	−	0.800399i	$-0.704621\pi$
$157$	−1.54216e102	−1.19894	−0.599468	+	0.800399i	$0.704621\pi$
$158$	−7.86798e99	−0.00455312
$159$	0	0
$160$	5.10350e101	0.164546
$161$	−4.40662e101	−0.106341
$162$	0	0
$163$	7.03093e102	0.955628	0.477814	−	0.878461i	$-0.341429\pi$
$163$	7.03093e102	0.955628	0.477814	+	0.878461i	$0.341429\pi$
$164$	5.63467e102	0.576275
$165$	0	0
$166$	−8.24912e101	−0.0480155
$167$	1.74320e103	0.767417	0.383709	−	0.923454i	$-0.374647\pi$
$167$	1.74320e103	0.767417	0.383709	+	0.923454i	$0.374647\pi$
$168$	0	0
$169$	−3.16467e103	−0.800934
$170$	2.34700e102	0.0451480
$171$	0	0
$172$	−1.52862e103	−0.170697
$173$	1.25289e104	1.06849	0.534243	−	0.845331i	$-0.320597\pi$
$173$	1.25289e104	1.06849	0.534243	+	0.845331i	$0.320597\pi$
$174$	0	0
$175$	−2.68248e102	−0.0134050
$176$	−2.02286e104	−0.775581
$177$	0	0
$178$	5.38726e102	0.0122134
$179$	−4.81939e104	−0.842027	−0.421013	−	0.907054i	$-0.638325\pi$
$179$	−4.81939e104	−0.842027	−0.421013	+	0.907054i	$0.638325\pi$
$180$	0	0
$181$	−1.90449e105	−1.98484	−0.992420	−	0.122890i	$-0.960784\pi$
$181$	−1.90449e105	−1.98484	−0.992420	+	0.122890i	$0.960784\pi$
$182$	−3.59722e102	−0.00290167
$183$	0	0
$184$	−1.84102e104	−0.0893368
$185$	1.22439e105	0.461778
$186$	0	0
$187$	−2.80364e105	−0.641340
$188$	7.55914e105	1.34937
$189$	0	0
$190$	8.77743e104	0.0957911
$191$	−6.29379e105	−0.538097	−0.269048	−	0.963127i	$-0.586709\pi$
$191$	−6.29379e105	−0.538097	−0.269048	+	0.963127i	$0.586709\pi$
$192$	0	0
$193$	5.60111e105	0.295025	0.147513	−	0.989060i	$-0.452873\pi$
$193$	5.60111e105	0.295025	0.147513	+	0.989060i	$0.452873\pi$
$194$	9.53543e104	0.0394966
$195$	0	0
$196$	3.81901e106	0.981845
$197$	6.48534e106	1.31599	0.657996	−	0.753021i	$-0.271404\pi$
$197$	6.48534e106	1.31599	0.657996	+	0.753021i	$0.271404\pi$
$198$	0	0
$199$	3.45706e106	0.438570	0.219285	−	0.975661i	$-0.429628\pi$
$199$	3.45706e106	0.438570	0.219285	+	0.975661i	$0.429628\pi$
$200$	−1.12070e105	−0.0112615
$201$	0	0
$202$	−5.69480e105	−0.0360279
$203$	−3.45085e106	−0.173524
$204$	0	0
$205$	−1.90812e107	−0.608207
$206$	3.40026e106	0.0864343
$207$	0	0
$208$	2.72815e107	0.442510
$209$	−1.04852e108	−1.36074
$210$	0	0
$211$	−3.50564e107	−0.292169	−0.146084	−	0.989272i	$-0.546667\pi$
$211$	−3.50564e107	−0.292169	−0.146084	+	0.989272i	$0.546667\pi$
$212$	−2.20866e108	−1.47744
$213$	0	0
$214$	1.54281e107	0.0666919
$215$	5.17650e107	0.180156
$216$	0	0
$217$	−8.56678e107	−0.193838
$218$	1.33394e107	0.0243730
$219$	0	0
$220$	6.86910e108	0.820814
$221$	3.78115e108	0.365918
$222$	0	0
$223$	−3.78721e108	−0.241070	−0.120535	−	0.992709i	$-0.538461\pi$
$223$	−3.78721e108	−0.241070	−0.120535	+	0.992709i	$0.538461\pi$
$224$	−3.76026e107	−0.0194395
$225$	0	0
$226$	1.14951e108	0.0393071
$227$	2.11337e109	0.588538	0.294269	−	0.955723i	$-0.404924\pi$
$227$	2.11337e109	0.588538	0.294269	+	0.955723i	$0.404924\pi$
$228$	0	0
$229$	6.82619e109	1.26424	0.632118	−	0.774872i	$-0.282186\pi$
$229$	6.82619e109	1.26424	0.632118	+	0.774872i	$0.282186\pi$
$230$	3.11294e108	0.0470789
$231$	0	0
$232$	−1.44172e109	−0.145777
$233$	1.83357e110	1.51791	0.758956	−	0.651142i	$-0.225710\pi$
$233$	1.83357e110	1.51791	0.758956	+	0.651142i	$0.225710\pi$
$234$	0	0
$235$	−2.55982e110	−1.42414
$236$	−3.16376e110	−1.44476
$237$	0	0
$238$	−1.72927e108	−0.00533378
$239$	4.39834e110	1.11631	0.558157	−	0.829735i	$-0.311509\pi$
$239$	4.39834e110	1.11631	0.558157	+	0.829735i	$0.311509\pi$
$240$	0	0
$241$	−1.05972e111	−1.82557	−0.912785	−	0.408440i	$-0.866073\pi$
$241$	−1.05972e111	−1.82557	−0.912785	+	0.408440i	$0.866073\pi$
$242$	−1.42992e109	−0.0203188
$243$	0	0
$244$	1.19156e111	1.15476
$245$	−1.29326e111	−1.03625
$246$	0	0
$247$	1.41409e111	0.776372
$248$	−3.57908e110	−0.162843
$249$	0	0
$250$	−1.56828e110	−0.0491149
$251$	4.74458e110	0.123416	0.0617078	−	0.998094i	$-0.480345\pi$
$251$	4.74458e110	0.123416	0.0617078	+	0.998094i	$0.480345\pi$
$252$	0	0
$253$	−3.71861e111	−0.668770
$254$	−2.84827e110	−0.0426397
$255$	0	0
$256$	9.35756e111	0.972757
$257$	1.10497e112	0.958210	0.479105	−	0.877758i	$-0.340961\pi$
$257$	1.10497e112	0.958210	0.479105	+	0.877758i	$0.340961\pi$
$258$	0	0
$259$	−9.02130e110	−0.0545544
$260$	−9.26405e111	−0.468317
$261$	0	0
$262$	−2.71889e111	−0.0962457
$263$	−2.33330e112	−0.691877	−0.345938	−	0.938257i	$-0.612439\pi$
$263$	−2.33330e112	−0.691877	−0.345938	+	0.938257i	$0.612439\pi$
$264$	0	0
$265$	7.47937e112	1.55931
$266$	−6.46722e110	−0.0113168
$267$	0	0
$268$	−6.57376e112	−0.811981
$269$	4.45387e111	0.0462654	0.0231327	−	0.999732i	$-0.492636\pi$
$269$	4.45387e111	0.0462654	0.0231327	+	0.999732i	$0.492636\pi$
$270$	0	0
$271$	−1.06412e113	−0.783282	−0.391641	−	0.920118i	$-0.628093\pi$
$271$	−1.06412e113	−0.783282	−0.391641	+	0.920118i	$0.628093\pi$
$272$	1.31149e113	0.813411
$273$	0	0
$274$	−6.65191e111	−0.0293457
$275$	−2.26367e112	−0.0843028
$276$	0	0
$277$	3.13894e113	0.834590	0.417295	−	0.908771i	$-0.362978\pi$
$277$	3.13894e113	0.834590	0.417295	+	0.908771i	$0.362978\pi$
$278$	−1.58084e112	−0.0355471
$279$	0	0
$280$	8.48527e111	0.0136715
$281$	−7.34181e113	−1.00221	−0.501105	−	0.865386i	$-0.667073\pi$
$281$	−7.34181e113	−1.00221	−0.501105	+	0.865386i	$0.667073\pi$
$282$	0	0
$283$	−4.42262e113	−0.434120	−0.217060	−	0.976158i	$-0.569647\pi$
$283$	−4.42262e113	−0.434120	−0.217060	+	0.976158i	$0.569647\pi$
$284$	8.34909e113	0.695563
$285$	0	0
$286$	−3.03559e112	−0.0182483
$287$	1.40591e113	0.0718535
$288$	0	0
$289$	−8.84708e113	−0.327379
$290$	2.43777e113	0.0768219
$291$	0	0
$292$	−7.03458e114	−1.61041
$293$	2.57943e114	0.503709	0.251854	−	0.967765i	$-0.418960\pi$
$293$	2.57943e114	0.503709	0.251854	+	0.967765i	$0.418960\pi$
$294$	0	0
$295$	1.07137e115	1.52481
$296$	−3.76898e113	−0.0458309
$297$	0	0
$298$	1.57015e112	0.00139600
$299$	5.01513e114	0.381568
$300$	0	0
$301$	−3.81405e113	−0.0212836
$302$	−3.48748e113	−0.0166797
$303$	0	0
$304$	4.90476e115	1.72582
$305$	−4.03510e115	−1.21874
$306$	0	0
$307$	−4.52736e115	−1.00905	−0.504523	−	0.863399i	$-0.668331\pi$
$307$	−4.52736e115	−1.00905	−0.504523	+	0.863399i	$0.668331\pi$
$308$	−5.06116e114	−0.0969710
$309$	0	0
$310$	6.05178e114	0.0858153
$311$	6.25405e115	0.763490	0.381745	−	0.924268i	$-0.375323\pi$
$311$	6.25405e115	0.763490	0.381745	+	0.924268i	$0.375323\pi$
$312$	0	0
$313$	1.19220e115	0.108028	0.0540142	−	0.998540i	$-0.482798\pi$
$313$	1.19220e115	0.108028	0.0540142	+	0.998540i	$0.482798\pi$
$314$	−8.02687e114	−0.0627072
$315$	0	0
$316$	1.49296e115	0.0868156
$317$	−2.10233e116	−1.05547	−0.527733	−	0.849410i	$-0.676958\pi$
$317$	−2.10233e116	−1.05547	−0.527733	+	0.849410i	$0.676958\pi$
$318$	0	0
$319$	−2.91207e116	−1.09128
$320$	−3.19547e116	−1.03529
$321$	0	0
$322$	−2.29362e114	−0.00556190
$323$	6.79790e116	1.42711
$324$	0	0
$325$	3.05291e115	0.0480991
$326$	3.65956e115	0.0499816
$327$	0	0
$328$	5.87368e115	0.0603638
$329$	1.88608e116	0.168248
$330$	0	0
$331$	−7.97816e116	−0.536909	−0.268455	−	0.963292i	$-0.586513\pi$
$331$	−7.97816e116	−0.536909	−0.268455	+	0.963292i	$0.586513\pi$
$332$	1.56528e117	0.915526
$333$	0	0
$334$	9.07326e115	0.0401377
$335$	2.22613e117	0.856973
$336$	0	0
$337$	5.50832e117	1.60779	0.803894	−	0.594773i	$-0.202758\pi$
$337$	5.50832e117	1.60779	0.803894	+	0.594773i	$0.202758\pi$
$338$	−1.64719e116	−0.0418908
$339$	0	0
$340$	−4.45345e117	−0.860850
$341$	−7.22925e117	−1.21903
$342$	0	0
$343$	1.92072e117	0.246767
$344$	−1.59346e116	−0.0178802
$345$	0	0
$346$	6.52122e116	0.0558843
$347$	−1.41492e118	−1.06025	−0.530127	−	0.847918i	$-0.677856\pi$
$347$	−1.41492e118	−1.06025	−0.530127	+	0.847918i	$0.677856\pi$
$348$	0	0
$349$	−6.54379e117	−0.375359	−0.187680	−	0.982230i	$-0.560097\pi$
$349$	−6.54379e117	−0.375359	−0.187680	+	0.982230i	$0.560097\pi$
$350$	−1.39622e115	−0.000701114 0
$351$	0	0
$352$	−3.17317e117	−0.122253
$353$	1.68481e118	0.568888	0.284444	−	0.958693i	$-0.408191\pi$
$353$	1.68481e118	0.568888	0.284444	+	0.958693i	$0.408191\pi$
$354$	0	0
$355$	−2.82733e118	−0.734104
$356$	−1.02224e118	−0.232877
$357$	0	0
$358$	−2.50846e117	−0.0440400
$359$	−5.68638e118	−0.876888	−0.438444	−	0.898758i	$-0.644470\pi$
$359$	−5.68638e118	−0.876888	−0.438444	+	0.898758i	$0.644470\pi$
$360$	0	0
$361$	1.70269e119	2.02792
$362$	−9.91278e117	−0.103812
$363$	0	0
$364$	6.82576e117	0.0553270
$365$	2.38218e119	1.69964
$366$	0	0
$367$	1.30818e118	0.0723928	0.0361964	−	0.999345i	$-0.488476\pi$
$367$	1.30818e118	0.0723928	0.0361964	+	0.999345i	$0.488476\pi$
$368$	1.73949e119	0.848200
$369$	0	0
$370$	6.37287e117	0.0241521
$371$	−5.51081e118	−0.184216
$372$	0	0
$373$	−6.77024e119	−1.76256	−0.881279	−	0.472597i	$-0.843317\pi$
$373$	−6.77024e119	−1.76256	−0.881279	+	0.472597i	$0.843317\pi$
$374$	−1.45928e118	−0.0335436
$375$	0	0
$376$	7.87977e118	0.141345
$377$	3.92738e119	0.622630
$378$	0	0
$379$	6.89871e118	0.0855154	0.0427577	−	0.999085i	$-0.486386\pi$
$379$	6.89871e118	0.0855154	0.0427577	+	0.999085i	$0.486386\pi$
$380$	−1.66553e120	−1.82648
$381$	0	0
$382$	−3.27588e118	−0.0281438
$383$	−4.25482e119	−0.323697	−0.161848	−	0.986816i	$-0.551746\pi$
$383$	−4.25482e119	−0.323697	−0.161848	+	0.986816i	$0.551746\pi$
$384$	0	0
$385$	1.71391e119	0.102344
$386$	2.91535e118	0.0154305
$387$	0	0
$388$	−1.80936e120	−0.753093
$389$	1.18067e120	0.435985	0.217992	−	0.975950i	$-0.430049\pi$
$389$	1.18067e120	0.435985	0.217992	+	0.975950i	$0.430049\pi$
$390$	0	0
$391$	2.41089e120	0.701389
$392$	3.98100e119	0.102847
$393$	0	0
$394$	3.37559e119	0.0688295
$395$	−5.05573e119	−0.0916261
$396$	0	0
$397$	4.35484e120	0.624041	0.312021	−	0.950075i	$-0.398994\pi$
$397$	4.35484e120	0.624041	0.312021	+	0.950075i	$0.398994\pi$
$398$	1.79938e119	0.0229383
$399$	0	0
$400$	1.05890e120	0.106921
$401$	−1.70110e119	−0.0152938	−0.00764691	−	0.999971i	$-0.502434\pi$
$401$	−1.70110e119	−0.0152938	−0.00764691	+	0.999971i	$0.502434\pi$
$402$	0	0
$403$	9.74977e120	0.695520
$404$	1.08059e121	0.686955
$405$	0	0
$406$	−1.79615e119	−0.00907574
$407$	−7.61281e120	−0.343087
$408$	0	0
$409$	7.63285e120	0.273875	0.136938	−	0.990580i	$-0.456274\pi$
$409$	7.63285e120	0.273875	0.136938	+	0.990580i	$0.456274\pi$
$410$	−9.93166e119	−0.0318107
$411$	0	0
$412$	−6.45202e121	−1.64807
$413$	−7.89389e120	−0.180141
$414$	0	0
$415$	−5.30064e121	−0.966255
$416$	4.27952e120	0.0697517
$417$	0	0
$418$	−5.45750e120	−0.0711699
$419$	3.78980e121	0.442246	0.221123	−	0.975246i	$-0.429028\pi$
$419$	3.78980e121	0.442246	0.221123	+	0.975246i	$0.429028\pi$
$420$	0	0
$421$	1.35355e122	1.26578	0.632889	−	0.774242i	$-0.281869\pi$
$421$	1.35355e122	1.26578	0.632889	+	0.774242i	$0.281869\pi$
$422$	−1.82467e120	−0.0152811
$423$	0	0
$424$	−2.30234e121	−0.154759
$425$	1.46761e121	0.0884147
$426$	0	0
$427$	2.97307e121	0.143982
$428$	−2.92750e122	−1.27163
$429$	0	0
$430$	2.69434e120	0.00942257
$431$	3.82844e122	1.20179	0.600895	−	0.799328i	$-0.294811\pi$
$431$	3.82844e122	1.20179	0.600895	+	0.799328i	$0.294811\pi$
$432$	0	0
$433$	3.72282e122	0.942290	0.471145	−	0.882056i	$-0.343841\pi$
$433$	3.72282e122	0.942290	0.471145	+	0.882056i	$0.343841\pi$
$434$	−4.45896e120	−0.0101382
$435$	0	0
$436$	−2.53116e122	−0.464727
$437$	9.01638e122	1.48815
$438$	0	0
$439$	−5.30815e121	−0.0708505	−0.0354253	−	0.999372i	$-0.511279\pi$
$439$	−5.30815e121	−0.0708505	−0.0354253	+	0.999372i	$0.511279\pi$
$440$	7.16046e121	0.0859788
$441$	0	0
$442$	1.96807e121	0.0191384
$443$	−2.18090e123	−1.90924	−0.954622	−	0.297819i	$-0.903741\pi$
$443$	−2.18090e123	−1.90924	−0.954622	+	0.297819i	$0.903741\pi$
$444$	0	0
$445$	3.46169e122	0.245781
$446$	−1.97122e121	−0.0126085
$447$	0	0
$448$	2.35443e122	0.122309
$449$	2.75797e123	1.29162	0.645811	−	0.763498i	$-0.276520\pi$
$449$	2.75797e123	1.29162	0.645811	+	0.763498i	$0.276520\pi$
$450$	0	0
$451$	1.18640e123	0.451879
$452$	−2.18121e123	−0.749480
$453$	0	0
$454$	1.10000e122	0.0307819
$455$	−2.31147e122	−0.0583927
$456$	0	0
$457$	−3.11961e123	−0.642684	−0.321342	−	0.946963i	$-0.604134\pi$
$457$	−3.11961e123	−0.642684	−0.321342	+	0.946963i	$0.604134\pi$
$458$	3.55299e122	0.0661226
$459$	0	0
$460$	−5.90683e123	−0.897668
$461$	4.69038e123	0.644340	0.322170	−	0.946682i	$-0.395588\pi$
$461$	4.69038e123	0.644340	0.322170	+	0.946682i	$0.395588\pi$
$462$	0	0
$463$	1.16779e124	1.31174	0.655871	−	0.754873i	$-0.272302\pi$
$463$	1.16779e124	1.31174	0.655871	+	0.754873i	$0.272302\pi$
$464$	1.36221e124	1.38406
$465$	0	0
$466$	9.54362e122	0.0793904
$467$	−1.86132e123	−0.140148	−0.0700741	−	0.997542i	$-0.522324\pi$
$467$	−1.86132e123	−0.140148	−0.0700741	+	0.997542i	$0.522324\pi$
$468$	0	0
$469$	−1.64022e123	−0.101243
$470$	−1.33237e123	−0.0744861
$471$	0	0
$472$	−3.29796e123	−0.151336
$473$	−3.21857e123	−0.133850
$474$	0	0
$475$	5.48863e123	0.187591
$476$	3.28131e123	0.101701
$477$	0	0
$478$	2.28931e123	0.0583859
$479$	6.91509e124	1.60028	0.800141	−	0.599812i	$-0.204758\pi$
$479$	6.91509e124	1.60028	0.800141	+	0.599812i	$0.204758\pi$
$480$	0	0
$481$	1.02671e124	0.195749
$482$	−5.51578e123	−0.0954817
$483$	0	0
$484$	2.71329e124	0.387424
$485$	6.12718e124	0.794822
$486$	0	0
$487$	3.42647e124	0.367071	0.183536	−	0.983013i	$-0.441246\pi$
$487$	3.42647e124	0.367071	0.183536	+	0.983013i	$0.441246\pi$
$488$	1.24211e124	0.120959
$489$	0	0
$490$	−6.73137e123	−0.0541983
$491$	−9.44249e124	−0.691508	−0.345754	−	0.938325i	$-0.612377\pi$
$491$	−9.44249e124	−0.691508	−0.345754	+	0.938325i	$0.612377\pi$
$492$	0	0
$493$	1.88799e125	1.14450
$494$	7.36029e123	0.0406061
$495$	0	0
$496$	3.38169e125	1.54609
$497$	2.08318e124	0.0867270
$498$	0	0
$499$	−3.71278e125	−1.28240	−0.641200	−	0.767374i	$-0.721563\pi$
$499$	−3.71278e125	−1.28240	−0.641200	+	0.767374i	$0.721563\pi$
$500$	2.97582e125	0.936487
$501$	0	0
$502$	2.46953e123	0.00645493
$503$	5.04296e125	1.20164	0.600820	−	0.799385i	$-0.294841\pi$
$503$	5.04296e125	1.20164	0.600820	+	0.799385i	$0.294841\pi$
$504$	0	0
$505$	−3.65931e125	−0.725019
$506$	−1.93552e124	−0.0349782
$507$	0	0
$508$	5.40462e125	0.813023
$509$	1.02099e126	1.40167	0.700836	−	0.713323i	$-0.252811\pi$
$509$	1.02099e126	1.40167	0.700836	+	0.713323i	$0.252811\pi$
$510$	0	0
$511$	−1.75519e125	−0.200795
$512$	2.47617e125	0.258659
$513$	0	0
$514$	5.75132e124	0.0501167
$515$	2.18491e126	1.73939
$516$	0	0
$517$	1.59160e126	1.05810
$518$	−4.69554e123	−0.00285333
$519$	0	0
$520$	−9.65700e124	−0.0490554
$521$	−1.22845e126	−0.570696	−0.285348	−	0.958424i	$-0.592109\pi$
$521$	−1.22845e126	−0.570696	−0.285348	+	0.958424i	$0.592109\pi$
$522$	0	0
$523$	3.73258e126	1.45105	0.725523	−	0.688198i	$-0.241598\pi$
$523$	3.73258e126	1.45105	0.725523	+	0.688198i	$0.241598\pi$
$524$	5.15911e126	1.83514
$525$	0	0
$526$	−1.21447e125	−0.0361868
$527$	4.68695e126	1.27849
$528$	0	0
$529$	−1.17440e126	−0.268613
$530$	3.89297e125	0.0815555
$531$	0	0
$532$	1.22716e126	0.215780
$533$	−1.60005e126	−0.257821
$534$	0	0
$535$	9.91367e126	1.34210
$536$	−6.85260e125	−0.0850535
$537$	0	0
$538$	2.31822e124	0.00241979
$539$	8.04106e126	0.769902
$540$	0	0
$541$	−7.69343e126	−0.620079	−0.310040	−	0.950724i	$-0.600342\pi$
$541$	−7.69343e126	−0.620079	−0.310040	+	0.950724i	$0.600342\pi$
$542$	−5.53868e125	−0.0409675
$543$	0	0
$544$	2.05727e126	0.128216
$545$	8.57149e126	0.490478
$546$	0	0
$547$	2.71689e127	1.31118	0.655589	−	0.755118i	$-0.272420\pi$
$547$	2.71689e127	1.31118	0.655589	+	0.755118i	$0.272420\pi$
$548$	1.26221e127	0.559544
$549$	0	0
$550$	−1.17823e125	−0.00440924
$551$	7.06079e127	2.42831
$552$	0	0
$553$	3.72507e125	0.0108247
$554$	1.63380e126	0.0436511
$555$	0	0
$556$	2.99965e127	0.677787
$557$	8.81073e127	1.83124	0.915620	−	0.402045i	$-0.131701\pi$
$557$	8.81073e127	1.83124	0.915620	+	0.402045i	$0.131701\pi$
$558$	0	0
$559$	4.34074e126	0.0763686
$560$	−8.01729e126	−0.129803
$561$	0	0
$562$	−3.82137e126	−0.0524180
$563$	6.45622e127	0.815338	0.407669	−	0.913130i	$-0.366342\pi$
$563$	6.45622e127	0.815338	0.407669	+	0.913130i	$0.366342\pi$
$564$	0	0
$565$	7.38643e127	0.791009
$566$	−2.30195e126	−0.0227055
$567$	0	0
$568$	8.70323e126	0.0728589
$569$	−5.12368e127	−0.395241	−0.197621	−	0.980279i	$-0.563321\pi$
$569$	−5.12368e127	−0.395241	−0.197621	+	0.980279i	$0.563321\pi$
$570$	0	0
$571$	−3.30044e127	−0.216268	−0.108134	−	0.994136i	$-0.534488\pi$
$571$	−3.30044e127	−0.216268	−0.108134	+	0.994136i	$0.534488\pi$
$572$	5.76006e127	0.347946
$573$	0	0
$574$	7.31766e125	0.00375811
$575$	1.94656e127	0.0921961
$576$	0	0
$577$	2.92806e128	1.18006	0.590031	−	0.807381i	$-0.299116\pi$
$577$	2.92806e128	1.18006	0.590031	+	0.807381i	$0.299116\pi$
$578$	−4.60486e126	−0.0171227
$579$	0	0
$580$	−4.62568e128	−1.46479
$581$	3.90552e127	0.114153
$582$	0	0
$583$	−4.65041e128	−1.15852
$584$	−7.33296e127	−0.168687
$585$	0	0
$586$	1.34258e127	0.0263452
$587$	−2.06516e128	−0.374353	−0.187176	−	0.982326i	$-0.559934\pi$
$587$	−2.06516e128	−0.374353	−0.187176	+	0.982326i	$0.559934\pi$
$588$	0	0
$589$	1.75285e129	2.71259
$590$	5.57644e127	0.0797514
$591$	0	0
$592$	3.56111e128	0.435137
$593$	8.47498e128	0.957404	0.478702	−	0.877977i	$-0.341107\pi$
$593$	8.47498e128	0.957404	0.478702	+	0.877977i	$0.341107\pi$
$594$	0	0
$595$	−1.11118e128	−0.107336
$596$	−2.97938e127	−0.0266179
$597$	0	0
$598$	2.61035e127	0.0199569
$599$	−3.98262e128	−0.281723	−0.140861	−	0.990029i	$-0.544987\pi$
$599$	−3.98262e128	−0.281723	−0.140861	+	0.990029i	$0.544987\pi$
$600$	0	0
$601$	−2.03200e129	−1.23101	−0.615505	−	0.788133i	$-0.711048\pi$
$601$	−2.03200e129	−1.23101	−0.615505	+	0.788133i	$0.711048\pi$
$602$	−1.98519e126	−0.00111318
$603$	0	0
$604$	6.61753e128	0.318037
$605$	−9.18825e128	−0.408891
$606$	0	0
$607$	−3.34725e129	−1.27766	−0.638828	−	0.769349i	$-0.720581\pi$
$607$	−3.34725e129	−1.27766	−0.638828	+	0.769349i	$0.720581\pi$
$608$	7.69388e128	0.272038
$609$	0	0
$610$	−2.10025e128	−0.0637431
$611$	−2.14653e129	−0.603698
$612$	0	0
$613$	−3.69786e129	−0.893383	−0.446692	−	0.894688i	$-0.647398\pi$
$613$	−3.69786e129	−0.893383	−0.446692	+	0.894688i	$0.647398\pi$
$614$	−2.35647e128	−0.0527755
$615$	0	0
$616$	−5.27584e127	−0.0101575
$617$	−9.34186e129	−1.66791	−0.833956	−	0.551830i	$-0.813930\pi$
$617$	−9.34186e129	−1.66791	−0.833956	+	0.551830i	$0.813930\pi$
$618$	0	0
$619$	1.99467e128	0.0306377	0.0153188	−	0.999883i	$-0.495124\pi$
$619$	1.99467e128	0.0306377	0.0153188	+	0.999883i	$0.495124\pi$
$620$	−1.14833e130	−1.63626
$621$	0	0
$622$	3.25520e128	0.0399324
$623$	−2.55058e128	−0.0290365
$624$	0	0
$625$	−1.11765e130	−1.09618
$626$	6.20535e127	0.00565014
$627$	0	0
$628$	1.52311e130	1.19566
$629$	4.93562e129	0.359822
$630$	0	0
$631$	−3.91510e129	−0.246251	−0.123125	−	0.992391i	$-0.539292\pi$
$631$	−3.91510e129	−0.246251	−0.123125	+	0.992391i	$0.539292\pi$
$632$	1.55628e128	0.00909378
$633$	0	0
$634$	−1.09425e129	−0.0552034
$635$	−1.83022e130	−0.858073
$636$	0	0
$637$	−1.08446e130	−0.439269
$638$	−1.51572e129	−0.0570764
$639$	0	0
$640$	−6.71748e129	−0.218694
$641$	−3.64405e130	−1.10328	−0.551640	−	0.834083i	$-0.685998\pi$
$641$	−3.64405e130	−1.10328	−0.551640	+	0.834083i	$0.685998\pi$
$642$	0	0
$643$	4.68261e130	1.22653	0.613264	−	0.789878i	$-0.289856\pi$
$643$	4.68261e130	1.22653	0.613264	+	0.789878i	$0.289856\pi$
$644$	4.35216e129	0.106050
$645$	0	0
$646$	3.53827e129	0.0746412
$647$	−6.34581e130	−1.24577	−0.622885	−	0.782313i	$-0.714040\pi$
$647$	−6.34581e130	−1.24577	−0.622885	+	0.782313i	$0.714040\pi$
$648$	0	0
$649$	−6.66142e130	−1.13289
$650$	1.58902e128	0.00251570
$651$	0	0
$652$	−6.94404e130	−0.953014
$653$	−9.09354e130	−1.16217	−0.581085	−	0.813843i	$-0.697372\pi$
$653$	−9.09354e130	−1.16217	−0.581085	+	0.813843i	$0.697372\pi$
$654$	0	0
$655$	−1.74708e131	−1.93683
$656$	−5.54974e130	−0.573118
$657$	0	0
$658$	9.81693e128	0.00879978
$659$	1.50199e131	1.25457	0.627284	−	0.778791i	$-0.284167\pi$
$659$	1.50199e131	1.25457	0.627284	+	0.778791i	$0.284167\pi$
$660$	0	0
$661$	5.08430e130	0.368861	0.184431	−	0.982846i	$-0.440956\pi$
$661$	5.08430e130	0.368861	0.184431	+	0.982846i	$0.440956\pi$
$662$	−4.15259e129	−0.0280816
$663$	0	0
$664$	1.63167e130	0.0958997
$665$	−4.15565e130	−0.227736
$666$	0	0
$667$	2.50413e131	1.19345
$668$	−1.72166e131	−0.765318
$669$	0	0
$670$	1.15869e130	0.0448217
$671$	2.50888e131	0.905489
$672$	0	0
$673$	−1.25378e131	−0.394022	−0.197011	−	0.980401i	$-0.563123\pi$
$673$	−1.25378e131	−0.394022	−0.197011	+	0.980401i	$0.563123\pi$
$674$	2.86705e130	0.0840911
$675$	0	0
$676$	3.12557e131	0.798743
$677$	−1.65408e131	−0.394623	−0.197312	−	0.980341i	$-0.563221\pi$
$677$	−1.65408e131	−0.394623	−0.197312	+	0.980341i	$0.563221\pi$
$678$	0	0
$679$	−4.51452e130	−0.0939002
$680$	−4.64236e130	−0.0901725
$681$	0	0
$682$	−3.76278e130	−0.0637582
$683$	1.09448e132	1.73239	0.866194	−	0.499708i	$-0.166559\pi$
$683$	1.09448e132	1.73239	0.866194	+	0.499708i	$0.166559\pi$
$684$	0	0
$685$	−4.27432e131	−0.590548
$686$	9.99725e129	0.0129065
$687$	0	0
$688$	1.50558e131	0.169762
$689$	6.27180e131	0.660995
$690$	0	0
$691$	1.49686e132	1.37864	0.689320	−	0.724457i	$-0.257909\pi$
$691$	1.49686e132	1.37864	0.689320	+	0.724457i	$0.257909\pi$
$692$	−1.23741e132	−1.06556
$693$	0	0
$694$	−7.36456e130	−0.0554538
$695$	−1.01580e132	−0.715343
$696$	0	0
$697$	−7.69182e131	−0.473920
$698$	−3.40601e130	−0.0196322
$699$	0	0
$700$	2.64933e130	0.0133683
$701$	4.03873e132	1.90703	0.953514	−	0.301349i	$-0.0974369\pi$
$701$	4.03873e132	1.90703	0.953514	+	0.301349i	$0.0974369\pi$
$702$	0	0
$703$	1.84585e132	0.763438
$704$	1.98683e132	0.769187
$705$	0	0
$706$	8.76933e130	0.0297542
$707$	2.69618e131	0.0856538
$708$	0	0
$709$	2.29100e132	0.638228	0.319114	−	0.947716i	$-0.396615\pi$
$709$	2.29100e132	0.638228	0.319114	+	0.947716i	$0.396615\pi$
$710$	−1.47161e131	−0.0383954
$711$	0	0
$712$	−1.06560e131	−0.0243935
$713$	6.21653e132	1.33317
$714$	0	0
$715$	−1.95058e132	−0.367225
$716$	4.75983e132	0.839723
$717$	0	0
$718$	−2.95973e131	−0.0458633
$719$	4.76634e132	0.692296	0.346148	−	0.938180i	$-0.387490\pi$
$719$	4.76634e132	0.692296	0.346148	+	0.938180i	$0.387490\pi$
$720$	0	0
$721$	−1.60984e132	−0.205491
$722$	8.86240e131	0.106065
$723$	0	0
$724$	1.88096e133	1.97941
$725$	1.52436e132	0.150443
$726$	0	0
$727$	−1.12628e133	−0.977903	−0.488952	−	0.872311i	$-0.662621\pi$
$727$	−1.12628e133	−0.977903	−0.488952	+	0.872311i	$0.662621\pi$
$728$	7.11529e130	0.00579540
$729$	0	0
$730$	1.23991e132	0.0888952
$731$	2.08670e132	0.140379
$732$	0	0
$733$	3.96038e132	0.234640	0.117320	−	0.993094i	$-0.462570\pi$
$733$	3.96038e132	0.234640	0.117320	+	0.993094i	$0.462570\pi$
$734$	6.80901e130	0.00378632
$735$	0	0
$736$	2.72866e132	0.133700
$737$	−1.38413e133	−0.636705
$738$	0	0
$739$	−1.41364e132	−0.0573288	−0.0286644	−	0.999589i	$-0.509125\pi$
$739$	−1.41364e132	−0.0573288	−0.0286644	+	0.999589i	$0.509125\pi$
$740$	−1.20926e133	−0.460515
$741$	0	0
$742$	−2.86835e131	−0.00963496
$743$	4.02843e133	1.27103	0.635515	−	0.772089i	$-0.280788\pi$
$743$	4.02843e133	1.27103	0.635515	+	0.772089i	$0.280788\pi$
$744$	0	0
$745$	1.00893e132	0.0280928
$746$	−3.52387e132	−0.0921859
$747$	0	0
$748$	2.76900e133	0.639586
$749$	−7.30440e132	−0.158555
$750$	0	0
$751$	−2.45927e133	−0.471573	−0.235787	−	0.971805i	$-0.575767\pi$
$751$	−2.45927e133	−0.471573	−0.235787	+	0.971805i	$0.575767\pi$
$752$	−7.44519e133	−1.34198
$753$	0	0
$754$	2.04418e132	0.0325650
$755$	−2.24095e133	−0.335660
$756$	0	0
$757$	−1.74934e133	−0.231694	−0.115847	−	0.993267i	$-0.536958\pi$
$757$	−1.74934e133	−0.231694	−0.115847	+	0.993267i	$0.536958\pi$
$758$	3.59074e131	0.00447266
$759$	0	0
$760$	−1.73617e133	−0.191320
$761$	−2.60917e133	−0.270468	−0.135234	−	0.990814i	$-0.543179\pi$
$761$	−2.60917e133	−0.270468	−0.135234	+	0.990814i	$0.543179\pi$
$762$	0	0
$763$	−6.31549e132	−0.0579450
$764$	6.21602e133	0.536625
$765$	0	0
$766$	−2.21461e132	−0.0169301
$767$	8.98396e133	0.646373
$768$	0	0
$769$	−2.71565e134	−1.73101	−0.865503	−	0.500905i	$-0.833001\pi$
$769$	−2.71565e134	−1.73101	−0.865503	+	0.500905i	$0.833001\pi$
$770$	8.92079e131	0.00535284
$771$	0	0
$772$	−5.53189e133	−0.294218
$773$	−2.21657e134	−1.11003	−0.555015	−	0.831841i	$-0.687287\pi$
$773$	−2.21657e134	−1.11003	−0.555015	+	0.831841i	$0.687287\pi$
$774$	0	0
$775$	3.78425e133	0.168055
$776$	−1.88610e133	−0.0788851
$777$	0	0
$778$	6.14531e132	0.0228030
$779$	−2.87662e134	−1.00552
$780$	0	0
$781$	1.75793e134	0.545417
$782$	1.25486e133	0.0366843
$783$	0	0
$784$	−3.76144e134	−0.976466
$785$	−5.15783e134	−1.26191
$786$	0	0
$787$	7.01625e134	1.52503	0.762517	−	0.646968i	$-0.223963\pi$
$787$	7.01625e134	1.52503	0.762517	+	0.646968i	$0.223963\pi$
$788$	−6.40520e134	−1.31239
$789$	0	0
$790$	−2.63148e132	−0.00479226
$791$	−5.44233e133	−0.0934498
$792$	0	0
$793$	−3.38362e134	−0.516629
$794$	2.26667e133	0.0326389
$795$	0	0
$796$	−3.41434e134	−0.437370
$797$	2.56830e134	0.310337	0.155168	−	0.987888i	$-0.450408\pi$
$797$	2.56830e134	0.310337	0.155168	+	0.987888i	$0.450408\pi$
$798$	0	0
$799$	−1.03189e135	−1.10970
$800$	1.66104e133	0.0168537
$801$	0	0
$802$	−8.85412e131	−0.000799903 0
$803$	−1.48116e135	−1.26278
$804$	0	0
$805$	−1.47381e134	−0.111927
$806$	5.07470e133	0.0363774
$807$	0	0
$808$	1.12643e134	0.0719573
$809$	−2.92460e134	−0.176384	−0.0881921	−	0.996103i	$-0.528109\pi$
$809$	−2.92460e134	−0.176384	−0.0881921	+	0.996103i	$0.528109\pi$
$810$	0	0
$811$	3.24175e134	0.174305	0.0871526	−	0.996195i	$-0.472223\pi$
$811$	3.24175e134	0.174305	0.0871526	+	0.996195i	$0.472223\pi$
$812$	3.40821e134	0.173050
$813$	0	0
$814$	−3.96242e133	−0.0179443
$815$	2.35152e135	1.00582
$816$	0	0
$817$	7.80394e134	0.297844
$818$	3.97286e133	0.0143243
$819$	0	0
$820$	1.88454e135	0.606543
$821$	2.21028e135	0.672187	0.336094	−	0.941829i	$-0.390894\pi$
$821$	2.21028e135	0.672187	0.336094	+	0.941829i	$0.390894\pi$
$822$	0	0
$823$	−9.21561e134	−0.250283	−0.125142	−	0.992139i	$-0.539939\pi$
$823$	−9.21561e134	−0.250283	−0.125142	+	0.992139i	$0.539939\pi$
$824$	−6.72569e134	−0.172632
$825$	0	0
$826$	−4.10873e133	−0.00942183
$827$	7.22312e135	1.56574	0.782868	−	0.622188i	$-0.213756\pi$
$827$	7.22312e135	1.56574	0.782868	+	0.622188i	$0.213756\pi$
$828$	0	0
$829$	−1.60908e135	−0.311740	−0.155870	−	0.987778i	$-0.549818\pi$
$829$	−1.60908e135	−0.311740	−0.155870	+	0.987778i	$0.549818\pi$
$830$	−2.75896e134	−0.0505375
$831$	0	0
$832$	−2.67955e135	−0.438861
$833$	−5.21327e135	−0.807454
$834$	0	0
$835$	5.83021e135	0.807724
$836$	1.03556e136	1.35702
$837$	0	0
$838$	1.97257e134	0.0231305
$839$	−1.01984e136	−1.13136	−0.565682	−	0.824624i	$-0.691387\pi$
$839$	−1.01984e136	−1.13136	−0.565682	+	0.824624i	$0.691387\pi$
$840$	0	0
$841$	9.54037e135	0.947440
$842$	7.04517e134	0.0662032
$843$	0	0
$844$	3.46232e135	0.291369
$845$	−1.05844e136	−0.843002
$846$	0	0
$847$	6.76991e134	0.0483064
$848$	2.17536e136	1.46935
$849$	0	0
$850$	7.63881e133	0.00462430
$851$	6.54636e135	0.375211
$852$	0	0
$853$	−1.53845e135	−0.0790596	−0.0395298	−	0.999218i	$-0.512586\pi$
$853$	−1.53845e135	−0.0790596	−0.0395298	+	0.999218i	$0.512586\pi$
$854$	1.54747e134	0.00753061
$855$	0	0
$856$	−3.05168e135	−0.133201
$857$	4.43080e136	1.83178	0.915891	−	0.401428i	$-0.131486\pi$
$857$	4.43080e136	1.83178	0.915891	+	0.401428i	$0.131486\pi$
$858$	0	0
$859$	6.46834e135	0.239945	0.119972	−	0.992777i	$-0.461719\pi$
$859$	6.46834e135	0.239945	0.119972	+	0.992777i	$0.461719\pi$
$860$	−5.11254e135	−0.179663
$861$	0	0
$862$	1.99268e135	0.0628565
$863$	3.32946e136	0.995111	0.497555	−	0.867432i	$-0.334231\pi$
$863$	3.32946e136	0.995111	0.497555	+	0.867432i	$0.334231\pi$
$864$	0	0
$865$	4.19034e136	1.12461
$866$	1.93771e135	0.0492840
$867$	0	0
$868$	8.46092e135	0.193308
$869$	3.14347e135	0.0680754
$870$	0	0
$871$	1.86671e136	0.363273
$872$	−2.63852e135	−0.0486793
$873$	0	0
$874$	4.69298e135	0.0778336
$875$	7.42496e135	0.116767
$876$	0	0
$877$	1.12855e136	0.159602	0.0798012	−	0.996811i	$-0.474571\pi$
$877$	1.12855e136	0.159602	0.0798012	+	0.996811i	$0.474571\pi$
$878$	−2.76286e134	−0.00370565
$879$	0	0
$880$	−6.76555e136	−0.816317
$881$	1.99955e136	0.228851	0.114426	−	0.993432i	$-0.463497\pi$
$881$	1.99955e136	0.228851	0.114426	+	0.993432i	$0.463497\pi$
$882$	0	0
$883$	−1.56519e137	−1.61211	−0.806056	−	0.591840i	$-0.798402\pi$
$883$	−1.56519e137	−1.61211	−0.806056	+	0.591840i	$0.798402\pi$
$884$	−3.73443e136	−0.364917
$885$	0	0
$886$	−1.13514e136	−0.0998580
$887$	−4.03132e136	−0.336511	−0.168256	−	0.985743i	$-0.553813\pi$
$887$	−4.03132e136	−0.336511	−0.168256	+	0.985743i	$0.553813\pi$
$888$	0	0
$889$	1.34851e136	0.101373
$890$	1.80179e135	0.0128549
$891$	0	0
$892$	3.74041e136	0.240410
$893$	−3.85911e137	−2.35447
$894$	0	0
$895$	−1.61186e137	−0.886253
$896$	4.94945e135	0.0258365
$897$	0	0
$898$	1.43551e136	0.0675549
$899$	4.86821e137	2.17542
$900$	0	0
$901$	3.01501e137	1.21503
$902$	6.17515e135	0.0236344
$903$	0	0
$904$	−2.27373e136	−0.0785067
$905$	−6.36966e137	−2.08909
$906$	0	0
$907$	1.62643e137	0.481391	0.240695	−	0.970601i	$-0.422625\pi$
$907$	1.62643e137	0.481391	0.240695	+	0.970601i	$0.422625\pi$
$908$	−2.08726e137	−0.586928
$909$	0	0
$910$	−1.20311e135	−0.00305407
$911$	−4.81504e136	−0.116144	−0.0580718	−	0.998312i	$-0.518495\pi$
$911$	−4.81504e136	−0.116144	−0.0580718	+	0.998312i	$0.518495\pi$
$912$	0	0
$913$	3.29575e137	0.717899
$914$	−1.62374e136	−0.0336139
$915$	0	0
$916$	−6.74184e137	−1.26078
$917$	1.28725e137	0.228817
$918$	0	0
$919$	−5.40959e137	−0.868947	−0.434473	−	0.900685i	$-0.643065\pi$
$919$	−5.40959e137	−0.868947	−0.434473	+	0.900685i	$0.643065\pi$
$920$	−6.15738e136	−0.0940291
$921$	0	0
$922$	2.44132e136	0.0337005
$923$	−2.37084e137	−0.311189
$924$	0	0
$925$	3.98503e136	0.0472978
$926$	6.07828e136	0.0686072
$927$	0	0
$928$	2.13683e137	0.218167
$929$	−4.56779e137	−0.443583	−0.221792	−	0.975094i	$-0.571191\pi$
$929$	−4.56779e137	−0.443583	−0.221792	+	0.975094i	$0.571191\pi$
$930$	0	0
$931$	−1.94969e138	−1.71319
$932$	−1.81091e138	−1.51376
$933$	0	0
$934$	−9.68810e135	−0.00733008
$935$	−9.37691e137	−0.675025
$936$	0	0
$937$	−1.76214e138	−1.14855	−0.574276	−	0.818662i	$-0.694716\pi$
$937$	−1.76214e138	−1.14855	−0.574276	+	0.818662i	$0.694716\pi$
$938$	−8.53723e135	−0.00529523
$939$	0	0
$940$	2.52819e138	1.42025
$941$	−1.71831e138	−0.918722	−0.459361	−	0.888250i	$-0.651922\pi$
$941$	−1.71831e138	−0.918722	−0.459361	+	0.888250i	$0.651922\pi$
$942$	0	0
$943$	−1.02020e138	−0.494189
$944$	3.11607e138	1.43684
$945$	0	0
$946$	−1.67525e136	−0.00700069
$947$	9.56790e137	0.380665	0.190332	−	0.981720i	$-0.439043\pi$
$947$	9.56790e137	0.380665	0.190332	+	0.981720i	$0.439043\pi$
$948$	0	0
$949$	1.99757e138	0.720482
$950$	2.85680e136	0.00981143
$951$	0	0
$952$	3.42049e136	0.0106530
$953$	6.46995e138	1.91903	0.959513	−	0.281664i	$-0.0908862\pi$
$953$	6.46995e138	1.91903	0.959513	+	0.281664i	$0.0908862\pi$
$954$	0	0
$955$	−2.10499e138	−0.566360
$956$	−4.34399e138	−1.11326
$957$	0	0
$958$	3.59927e137	0.0836985
$959$	3.14932e137	0.0697673
$960$	0	0
$961$	7.11217e138	1.43009
$962$	5.34395e136	0.0102381
$963$	0	0
$964$	1.04662e139	1.82058
$965$	1.87331e138	0.310521
$966$	0	0
$967$	−6.69840e138	−1.00842	−0.504209	−	0.863582i	$-0.668216\pi$
$967$	−6.69840e138	−1.00842	−0.504209	+	0.863582i	$0.668216\pi$
$968$	2.82838e137	0.0405820
$969$	0	0
$970$	3.18916e137	0.0415711
$971$	4.20821e138	0.522882	0.261441	−	0.965219i	$-0.415802\pi$
$971$	4.20821e138	0.522882	0.261441	+	0.965219i	$0.415802\pi$
$972$	0	0
$973$	7.48442e137	0.0845106
$974$	1.78346e137	0.0191987
$975$	0	0
$976$	−1.17360e139	−1.14843
$977$	−1.33674e139	−1.24724	−0.623619	−	0.781729i	$-0.714338\pi$
$977$	−1.33674e139	−1.24724	−0.623619	+	0.781729i	$0.714338\pi$
$978$	0	0
$979$	−2.15236e138	−0.182608
$980$	1.27728e139	1.03341
$981$	0	0
$982$	−4.91477e137	−0.0361675
$983$	2.28662e139	1.60493	0.802463	−	0.596702i	$-0.203523\pi$
$983$	2.28662e139	1.60493	0.802463	+	0.596702i	$0.203523\pi$
$984$	0	0
$985$	2.16905e139	1.38511
$986$	9.82687e137	0.0598603
$987$	0	0
$988$	−1.39662e139	−0.774249
$989$	2.76769e138	0.146383
$990$	0	0
$991$	−1.20136e138	−0.0578426	−0.0289213	−	0.999582i	$-0.509207\pi$
$991$	−1.20136e138	−0.0578426	−0.0289213	+	0.999582i	$0.509207\pi$
$992$	5.30470e138	0.243707
$993$	0	0
$994$	1.08428e137	0.00453603
$995$	1.15623e139	0.461605
$996$	0	0
$997$	2.75431e139	1.00159	0.500793	−	0.865567i	$-0.333042\pi$
$997$	2.75431e139	1.00159	0.500793	+	0.865567i	$0.333042\pi$
$998$	−1.93248e138	−0.0670725
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.94.a.b.1.4		7
3.2	odd	2		1.94.a.a.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.94.a.a.1.4	✓	7	3.2	odd	2
9.94.a.b.1.4		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)

\(f(q)\)	\(=\)	\(q+5.20495e12 q^{2} -9.87643e27 q^{4} +3.34454e32 q^{5} -2.46426e38 q^{7} -1.02954e41 q^{8} +O(q^{10})\)	\(q+5.20495e12 q^{2} -9.87643e27 q^{4} +3.34454e32 q^{5} -2.46426e38 q^{7} -1.02954e41 q^{8} +1.74082e45 q^{10} -2.07952e48 q^{11} +2.80456e51 q^{13} -1.28264e51 q^{14} +9.72755e55 q^{16} +1.34822e57 q^{17} +5.04213e59 q^{19} -3.30321e60 q^{20} -1.08238e61 q^{22} +1.78821e63 q^{23} +1.08855e64 q^{25} +1.45976e64 q^{26} +2.43381e66 q^{28} +1.40036e68 q^{29} +3.47640e69 q^{31} +1.52592e69 q^{32} +7.01740e69 q^{34} -8.24184e70 q^{35} +3.66085e72 q^{37} +2.62440e72 q^{38} -3.44333e73 q^{40} -5.70517e74 q^{41} +1.54775e75 q^{43} +2.05382e76 q^{44} +9.30752e75 q^{46} -7.65372e77 q^{47} -3.86679e78 q^{49} +5.66586e76 q^{50} -2.76990e79 q^{52} +2.23629e80 q^{53} -6.95504e80 q^{55} +2.53705e79 q^{56} +7.28878e80 q^{58} +3.20335e82 q^{59} -1.20647e83 q^{61} +1.80945e82 q^{62} -9.55428e83 q^{64} +9.37996e83 q^{65} +6.65601e84 q^{67} -1.33156e85 q^{68} -4.28983e83 q^{70} -8.45355e85 q^{71} +7.12259e86 q^{73} +1.90545e85 q^{74} -4.97983e87 q^{76} +5.12448e86 q^{77} -1.51164e87 q^{79} +3.25342e88 q^{80} -2.96951e87 q^{82} -1.58486e89 q^{83} +4.50917e89 q^{85} +8.05593e87 q^{86} +2.14094e89 q^{88} +1.03503e90 q^{89} -6.91117e89 q^{91} -1.76611e91 q^{92} -3.98372e90 q^{94} +1.68636e92 q^{95} +1.83199e92 q^{97} -2.01264e91 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 43735426713792 q^{2} + 37\!\cdots\!44 q^{4}+ \cdots - 62\!\cdots\!60 q^{8}+O(q^{10}) \) 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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