LMFDB - Embedded newform 9.94.a.b.1.1

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			1.1
Root			$2.74671e11$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.64459e14 q^{2} +1.71431e28 q^{4} -3.18897e32 q^{5} -2.05341e39 q^{7} -1.19061e42 q^{8} +O(q^{10})$	\(q-1.64459e14 q^{2} +1.71431e28 q^{4} -3.18897e32 q^{5} -2.05341e39 q^{7} -1.19061e42 q^{8} +5.24454e46 q^{10} +1.16805e48 q^{11} +9.03622e51 q^{13} +3.37700e53 q^{14} +2.60289e55 q^{16} -2.65663e56 q^{17} -2.80384e59 q^{19} -5.46689e60 q^{20} -1.92096e62 q^{22} +1.45691e63 q^{23} +7.21293e62 q^{25} -1.48608e66 q^{26} -3.52017e67 q^{28} +8.91760e67 q^{29} +8.50292e68 q^{31} +7.51055e69 q^{32} +4.36905e70 q^{34} +6.54826e71 q^{35} +2.81703e72 q^{37} +4.61116e73 q^{38} +3.79682e74 q^{40} +1.66230e75 q^{41} -6.95533e75 q^{43} +2.00240e76 q^{44} -2.39601e77 q^{46} +7.32306e77 q^{47} +2.88966e77 q^{49} -1.18623e77 q^{50} +1.54909e80 q^{52} +1.26790e80 q^{53} -3.72488e80 q^{55} +2.44481e81 q^{56} -1.46658e82 q^{58} -2.67897e81 q^{59} -1.91064e82 q^{61} -1.39838e83 q^{62} -1.49295e84 q^{64} -2.88163e84 q^{65} +1.94035e84 q^{67} -4.55428e84 q^{68} -1.07692e86 q^{70} +1.09152e85 q^{71} +3.20901e86 q^{73} -4.63285e86 q^{74} -4.80665e87 q^{76} -2.39848e87 q^{77} +3.00437e88 q^{79} -8.30055e87 q^{80} -2.73380e89 q^{82} +2.46149e89 q^{83} +8.47191e88 q^{85} +1.14386e90 q^{86} -1.39069e90 q^{88} +2.79307e89 q^{89} -1.85550e91 q^{91} +2.49759e91 q^{92} -1.20434e92 q^{94} +8.94137e91 q^{95} +3.53812e92 q^{97} -4.75229e91 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 43735426713792 q^{2} + 37\!\cdots\!44 q^{4}+ \cdots - 62\!\cdots\!60 q^{8}+O(q^{10}) $ 7 * q - 43735426713792 * q^2 + 37433779444352805880587218944 * q^4 + 242501922056818695041616562179750 * q^5 - 921137753903839555947108372394316103208 * q^7 - 628568314501252186502498490389635108700160 * q^8	$ 7 q - 43735426713792 q^{2} + 37\!\cdots\!44 q^{4}+ \cdots + 69\!\cdots\!56 q^{98}+O(q^{100}) $ 7 * q - 43735426713792 * q^2 + 37433779444352805880587218944 * q^4 + 242501922056818695041616562179750 * q^5 - 921137753903839555947108372394316103208 * q^7 - 628568314501252186502498490389635108700160 * q^8 + 56663128890275718532856219951648854919834448000 * q^10 - 1081566396126190174166498109003279139923369012324 * q^11 + 1923851638471797431690458036346871401286646408469426 * q^13 + 827492161115181455891429526236298470299001717526508032 * q^14 - 183863117199568288307852091185855957272115704336744448 * q^16 - 809325537307953309871783611300921224816172571619454935742 * q^17 - 491316328040151561437984621759105514680907320256463264658500 * q^19 + 5819101371751539891329503686613738398860076574931824253952000 * q^20 + 341061341496448817039487179432626029859991533289656810924326144 * q^22 + 2595697104202345855126053487687658963668179272707633091075699064 * q^23 + 184388886386678531186865888507627315189418933935123407708899515625 * q^25 - 793059166145746283698718389909557916534745558035448772312212840064 * q^26 + 1916814131388145595393790805747801246689773266225672358812878209024 * q^28 - 115585291038420509795092429775705167101645550654624527668945364036450 * q^29 - 1163635467946810748613893942791764663199899897323284701513531956983456 * q^31 + 7066990866795922437106429389517828098400874624281122281464920526553088 * q^32 + 80911624156374405155780927188384543491071504244617539921495324380294528 * q^34 + 1672188852118103650980495790489284130570309869892526153633308501275462000 * q^35 + 11072759435314078994932599484815080247923078570346623467670584315337670842 * q^37 + 42692186143014046654789275667852179938472092905944200699148410427788924160 * q^38 + 760187696799287916151508882607919116749295190931669242261910585944965120000 * q^40 + 509603803596826806676973650829096820638503322986104149790656476262528674746 * q^41 - 7275658116979055674748970912580687053338617746072325435955591393683798211644 * q^43 - 9423347779397833928027118997217234224491886242773059800183027480258516369408 * q^44 - 639778771092842366359510076082228574613573083413403803040568658686807125218816 * q^46 + 371149830895115606730684780470708713676568637183334957675426341554516993409008 * q^47 + 2561975156227711495237514871966779964501558283497058708235084248829398599957999 * q^49 + 31492320141514234591073138519794385457712593727985587891779934655429621403000000 * q^50 - 55278983045853834535146427408736596689073596604984335518990233309047240924848128 * q^52 + 363766241548602923075270727552075967170433033161760056492510229436384310833635734 * q^53 - 3520855393890604949232827617669938515471701214675853816941159595183623184386577000 * q^55 + 12936956692485908268365121199611114191360014164491088694387999166431300696512921600 * q^56 - 73663001170657752665346575473371223431752845037418753763472734766611572171441325440 * q^58 + 119839908140624573484226478891501296275544385047787439213910489726968365086286210700 * q^59 - 328281166748320542242523532793984772143143166398612931227281116669834617338050603326 * q^61 + 999402477792071119370831029463209574610493980381087626216590758004912070795081435136 * q^62 - 4748321960274080197621802735261780227229800262185345649692550833454877416714840047616 * q^64 - 2401958293154067008332922023669433962969772004736123854920087208208149417890196631500 * q^65 + 9715050085721519766982024893817705652242604355912950898916137527198529527932523084492 * q^67 - 51110178162381015351883898716980001063480395685110983605059672645927223406195391258624 * q^68 + 437770522317274261347763126091338009235407849188339858200284725822565513739255154816000 * q^70 - 420099768445021912291978352393445519280746916987347799091649913407485898651223357176984 * q^71 + 249990884773795871360906735022065792056914028590737521750721031757996649920054698123686 * q^73 - 988848152146322932205109547460090361956964236264222955609677033303897103570301064734848 * q^74 - 9872924363930092749183448370538218854882826462181838927155554514487863834399954370969600 * q^76 + 16552736755381232703525388842736711985373990693881749218915711388952768140257306836693856 * q^77 - 43369884997252312790262999909905208728154246791055779943371432494520439561399960810221200 * q^79 + 88894687813962777903012798348655018553862729556819104796394604135123942915181092274176000 * q^80 - 236357995159599133663604843384379044643064499685381579522884048932961281765779447211829376 * q^82 + 206459225650342475045148123542600401116221913586781003327705338223920418727874732010864004 * q^83 + 1637661121678145282281696006564110640734919603287375198985971859556394144920752854974380500 * q^85 - 3239900597437756786176903087412721547247433713557247371056571790561416975430434191434708224 * q^86 + 6336674026069399594730100443279513731166873520796702455565229756349453295686310223539077120 * q^88 - 5580799156439265704685765323272125687903700231557911629488221982292995723510480958101067350 * q^89 - 18025272478314007503227783954648499409552734863956310123113904904033321293148703549329112496 * q^91 + 81750027044574246291550532241925751638073881610946649428268147310600744342795416362583031808 * q^92 - 306478475429892162274969547511367839192733042761577860914963828391848832364650578690812603392 * q^94 + 216711696129933523762297615654778954621414663971673687874218846402427636558070586043601335000 * q^95 + 43971291171253027759915173352741872464098193495293359649108047104658615767375645954946743342 * q^97 + 690328280759812206538864038068682435013428219472201721649324072601042235191425205897720616256 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.64459e14	−1.65258	−0.826288	−	0.563247i	$-0.809552\pi$
$2$	−1.64459e14	−1.65258	−0.826288	+	0.563247i	$0.809552\pi$
$3$	0	0
$3$	0	0
$4$	1.71431e28	1.73101
$5$	−3.18897e32	−1.00357	−0.501783	−	0.864994i	$-0.667322\pi$
$5$	−3.18897e32	−1.00357	−0.501783	+	0.864994i	$0.667322\pi$
$6$	0	0
$7$	−2.05341e39	−1.03613	−0.518067	−	0.855340i	$-0.673348\pi$
$7$	−2.05341e39	−1.03613	−0.518067	+	0.855340i	$0.673348\pi$
$8$	−1.19061e42	−1.20805
$9$	0	0
$10$	5.24454e46	1.65847
$11$	1.16805e48	0.439240	0.219620	−	0.975585i	$-0.429518\pi$
$11$	1.16805e48	0.439240	0.219620	+	0.975585i	$0.429518\pi$
$12$	0	0
$13$	9.03622e51	1.43754	0.718772	−	0.695246i	$-0.244705\pi$
$13$	9.03622e51	1.43754	0.718772	+	0.695246i	$0.244705\pi$
$14$	3.37700e53	1.71229
$15$	0	0
$16$	2.60289e55	0.265385
$17$	−2.65663e56	−0.161605	−0.0808027	−	0.996730i	$-0.525748\pi$
$17$	−2.65663e56	−0.161605	−0.0808027	+	0.996730i	$0.525748\pi$
$18$	0	0
$19$	−2.80384e59	−0.967634	−0.483817	−	0.875169i	$-0.660750\pi$
$19$	−2.80384e59	−0.967634	−0.483817	+	0.875169i	$0.660750\pi$
$20$	−5.46689e60	−1.73718
$21$	0	0
$22$	−1.92096e62	−0.725878
$23$	1.45691e63	0.696767	0.348384	−	0.937352i	$-0.386731\pi$
$23$	1.45691e63	0.696767	0.348384	+	0.937352i	$0.386731\pi$
$24$	0	0
$25$	7.21293e62	0.00714334
$26$	−1.48608e66	−2.37565
$27$	0	0
$28$	−3.52017e67	−1.79356
$29$	8.91760e67	0.888671	0.444336	−	0.895860i	$-0.353440\pi$
$29$	8.91760e67	0.888671	0.444336	+	0.895860i	$0.353440\pi$
$30$	0	0
$31$	8.50292e68	0.381285	0.190642	−	0.981660i	$-0.438943\pi$
$31$	8.50292e68	0.381285	0.190642	+	0.981660i	$0.438943\pi$
$32$	7.51055e69	0.769480
$33$	0	0
$34$	4.36905e70	0.267065
$35$	6.54826e71	1.03983
$36$	0	0
$37$	2.81703e72	0.337607	0.168804	−	0.985650i	$-0.446010\pi$
$37$	2.81703e72	0.337607	0.168804	+	0.985650i	$0.446010\pi$
$38$	4.61116e73	1.59909
$39$	0	0
$40$	3.79682e74	1.21236
$41$	1.66230e75	1.68369	0.841843	−	0.539722i	$-0.181471\pi$
$41$	1.66230e75	1.68369	0.841843	+	0.539722i	$0.181471\pi$
$42$	0	0
$43$	−6.95533e75	−0.769192	−0.384596	−	0.923085i	$-0.625659\pi$
$43$	−6.95533e75	−0.769192	−0.384596	+	0.923085i	$0.625659\pi$
$44$	2.00240e76	0.760329
$45$	0	0
$46$	−2.39601e77	−1.15146
$47$	7.32306e77	1.29462	0.647310	−	0.762227i	$-0.275894\pi$
$47$	7.32306e77	1.29462	0.647310	+	0.762227i	$0.275894\pi$
$48$	0	0
$49$	2.88966e77	0.0735748
$50$	−1.18623e77	−0.0118049
$51$	0	0
$52$	1.54909e80	2.48840
$53$	1.26790e80	0.839956	0.419978	−	0.907534i	$-0.362038\pi$
$53$	1.26790e80	0.839956	0.419978	+	0.907534i	$0.362038\pi$
$54$	0	0
$55$	−3.72488e80	−0.440806
$56$	2.44481e81	1.25170
$57$	0	0
$58$	−1.46658e82	−1.46860
$59$	−2.67897e81	−0.121157	−0.0605787	−	0.998163i	$-0.519295\pi$
$59$	−2.67897e81	−0.121157	−0.0605787	+	0.998163i	$0.519295\pi$
$60$	0	0
$61$	−1.91064e82	−0.183376	−0.0916878	−	0.995788i	$-0.529226\pi$
$61$	−1.91064e82	−0.183376	−0.0916878	+	0.995788i	$0.529226\pi$
$62$	−1.39838e83	−0.630102
$63$	0	0
$64$	−1.49295e84	−1.53701
$65$	−2.88163e84	−1.44267
$66$	0	0
$67$	1.94035e84	0.237356	0.118678	−	0.992933i	$-0.462134\pi$
$67$	1.94035e84	0.237356	0.118678	+	0.992933i	$0.462134\pi$
$68$	−4.55428e84	−0.279741
$69$	0	0
$70$	−1.07692e86	−1.71840
$71$	1.09152e85	0.0900573	0.0450286	−	0.998986i	$-0.485662\pi$
$71$	1.09152e85	0.0900573	0.0450286	+	0.998986i	$0.485662\pi$
$72$	0	0
$73$	3.20901e86	0.727543	0.363771	−	0.931488i	$-0.381489\pi$
$73$	3.20901e86	0.727543	0.363771	+	0.931488i	$0.381489\pi$
$74$	−4.63285e86	−0.557922
$75$	0	0
$76$	−4.80665e87	−1.67498
$77$	−2.39848e87	−0.455112
$78$	0	0
$79$	3.00437e88	1.73019	0.865095	−	0.501607i	$-0.167258\pi$
$79$	3.00437e88	1.73019	0.865095	+	0.501607i	$0.167258\pi$
$80$	−8.30055e87	−0.266331
$81$	0	0
$82$	−2.73380e89	−2.78242
$83$	2.46149e89	1.42583	0.712914	−	0.701251i	$-0.247375\pi$
$83$	2.46149e89	1.42583	0.712914	+	0.701251i	$0.247375\pi$
$84$	0	0
$85$	8.47191e88	0.162182
$86$	1.14386e90	1.27115
$87$	0	0
$88$	−1.39069e90	−0.530624
$89$	2.79307e89	0.0630155	0.0315077	−	0.999504i	$-0.489969\pi$
$89$	2.79307e89	0.0630155	0.0315077	+	0.999504i	$0.489969\pi$
$90$	0	0
$91$	−1.85550e91	−1.48949
$92$	2.49759e91	1.20611
$93$	0	0
$94$	−1.20434e92	−2.13946
$95$	8.94137e91	0.971084
$96$	0	0
$97$	3.53812e92	1.45843	0.729217	−	0.684282i	$-0.239884\pi$
$97$	3.53812e92	1.45843	0.729217	+	0.684282i	$0.239884\pi$
$98$	−4.75229e91	−0.121588
$99$	0	0
$100$	1.23652e91	0.0123652
$101$	−1.67913e93	−1.05716	−0.528579	−	0.848884i	$-0.677275\pi$
$101$	−1.67913e93	−1.05716	−0.528579	+	0.848884i	$0.677275\pi$
$102$	0	0
$103$	−2.72877e93	−0.690298	−0.345149	−	0.938548i	$-0.612172\pi$
$103$	−2.72877e93	−0.690298	−0.345149	+	0.938548i	$0.612172\pi$
$104$	−1.07586e94	−1.73662
$105$	0	0
$106$	−2.08517e94	−1.38809
$107$	−2.57521e94	−1.10782	−0.553908	−	0.832578i	$-0.686864\pi$
$107$	−2.57521e94	−1.10782	−0.553908	+	0.832578i	$0.686864\pi$
$108$	0	0
$109$	7.43481e94	1.35188	0.675939	−	0.736958i	$-0.263738\pi$
$109$	7.43481e94	1.35188	0.675939	+	0.736958i	$0.263738\pi$
$110$	6.12589e94	0.728466
$111$	0	0
$112$	−5.34479e94	−0.274975
$113$	9.21006e94	0.313412	0.156706	−	0.987645i	$-0.449913\pi$
$113$	9.21006e94	0.313412	0.156706	+	0.987645i	$0.449913\pi$
$114$	0	0
$115$	−4.64604e95	−0.699251
$116$	1.52875e96	1.53830
$117$	0	0
$118$	4.40580e95	0.200222
$119$	5.45514e95	0.167445
$120$	0	0
$121$	−5.70729e96	−0.807068
$122$	3.14221e96	0.303042
$123$	0	0
$124$	1.45766e97	0.660008
$125$	3.19704e97	0.996397
$126$	0	0
$127$	8.56364e97	1.27581	0.637904	−	0.770116i	$-0.279802\pi$
$127$	8.56364e97	1.27581	0.637904	+	0.770116i	$0.279802\pi$
$128$	1.71148e98	1.77055
$129$	0	0
$130$	4.73908e98	2.38412
$131$	2.59789e98	0.915177	0.457588	−	0.889164i	$-0.348713\pi$
$131$	2.59789e98	0.915177	0.457588	+	0.889164i	$0.348713\pi$
$132$	0	0
$133$	5.75743e98	1.00260
$134$	−3.19106e98	−0.392249
$135$	0	0
$136$	3.16301e98	0.195227
$137$	3.51555e99	1.54343	0.771714	−	0.635969i	$-0.219399\pi$
$137$	3.51555e99	1.54343	0.771714	+	0.635969i	$0.219399\pi$
$138$	0	0
$139$	−6.67319e99	−1.49329	−0.746647	−	0.665221i	$-0.768337\pi$
$139$	−6.67319e99	−1.49329	−0.746647	+	0.665221i	$0.768337\pi$
$140$	1.12257e100	1.79995
$141$	0	0
$142$	−1.79510e99	−0.148827
$143$	1.05548e100	0.631427
$144$	0	0
$145$	−2.84380e100	−0.891839
$146$	−5.27750e100	−1.20232
$147$	0	0
$148$	4.82926e100	0.584401
$149$	−1.48590e100	−0.131470	−0.0657351	−	0.997837i	$-0.520939\pi$
$149$	−1.48590e100	−0.131470	−0.0657351	+	0.997837i	$0.520939\pi$
$150$	0	0
$151$	1.51425e101	0.720723	0.360362	−	0.932813i	$-0.382653\pi$
$151$	1.51425e101	0.720723	0.360362	+	0.932813i	$0.382653\pi$
$152$	3.33828e101	1.16895
$153$	0	0
$154$	3.94451e101	0.752107
$155$	−2.71156e101	−0.382644
$156$	0	0
$157$	−2.25114e102	−1.75012	−0.875060	−	0.484014i	$-0.839179\pi$
$157$	−2.25114e102	−1.75012	−0.875060	+	0.484014i	$0.839179\pi$
$158$	−4.94095e102	−2.85927
$159$	0	0
$160$	−2.39509e102	−0.772224
$161$	−2.99162e102	−0.721945
$162$	0	0
$163$	5.71396e101	0.0776629	0.0388315	−	0.999246i	$-0.487636\pi$
$163$	5.71396e101	0.0776629	0.0388315	+	0.999246i	$0.487636\pi$
$164$	2.84970e103	2.91448
$165$	0	0
$166$	−4.04814e103	−2.35629
$167$	5.24708e102	0.230995	0.115497	−	0.993308i	$-0.463154\pi$
$167$	5.24708e102	0.230995	0.115497	+	0.993308i	$0.463154\pi$
$168$	0	0
$169$	4.21410e103	1.06653
$170$	−1.39328e103	−0.268017
$171$	0	0
$172$	−1.19236e104	−1.33148
$173$	1.36592e104	1.16488	0.582441	−	0.812873i	$-0.302098\pi$
$173$	1.36592e104	1.16488	0.582441	+	0.812873i	$0.302098\pi$
$174$	0	0
$175$	−1.48111e102	−0.00740147
$176$	3.04031e103	0.116568
$177$	0	0
$178$	−4.59345e103	−0.104138
$179$	5.69683e104	0.995331	0.497665	−	0.867369i	$-0.334191\pi$
$179$	5.69683e104	0.995331	0.497665	+	0.867369i	$0.334191\pi$
$180$	0	0
$181$	8.04012e104	0.837932	0.418966	−	0.908002i	$-0.362393\pi$
$181$	8.04012e104	0.837932	0.418966	+	0.908002i	$0.362393\pi$
$182$	3.05153e105	2.46149
$183$	0	0
$184$	−1.73461e105	−0.841729
$185$	−8.98344e104	−0.338811
$186$	0	0
$187$	−3.10308e104	−0.0709836
$188$	1.25540e106	2.24100
$189$	0	0
$190$	−1.47049e106	−1.60479
$191$	−6.07307e105	−0.519226	−0.259613	−	0.965713i	$-0.583595\pi$
$191$	−6.07307e105	−0.519226	−0.259613	+	0.965713i	$0.583595\pi$
$192$	0	0
$193$	−1.56914e106	−0.826509	−0.413255	−	0.910616i	$-0.635608\pi$
$193$	−1.56914e106	−0.826509	−0.413255	+	0.910616i	$0.635608\pi$
$194$	−5.81874e106	−2.41017
$195$	0	0
$196$	4.95377e105	0.127359
$197$	−5.15564e106	−1.04617	−0.523086	−	0.852280i	$-0.675219\pi$
$197$	−5.15564e106	−1.04617	−0.523086	+	0.852280i	$0.675219\pi$
$198$	0	0
$199$	−6.16450e105	−0.0782042	−0.0391021	−	0.999235i	$-0.512450\pi$
$199$	−6.16450e105	−0.0782042	−0.0391021	+	0.999235i	$0.512450\pi$
$200$	−8.58779e104	−0.00862952
$201$	0	0
$202$	2.76147e107	1.74704
$203$	−1.83115e107	−0.920783
$204$	0	0
$205$	−5.30105e107	−1.68969
$206$	4.48770e107	1.14077
$207$	0	0
$208$	2.35203e107	0.381503
$209$	−3.27503e107	−0.425024
$210$	0	0
$211$	1.70503e108	1.42101	0.710505	−	0.703692i	$-0.248467\pi$
$211$	1.70503e108	1.42101	0.710505	+	0.703692i	$0.248467\pi$
$212$	2.17357e108	1.45397
$213$	0	0
$214$	4.23516e108	1.83075
$215$	2.21804e108	0.771934
$216$	0	0
$217$	−1.74600e108	−0.395062
$218$	−1.22272e109	−2.23408
$219$	0	0
$220$	−6.38560e108	−0.763040
$221$	−2.40059e108	−0.232315
$222$	0	0
$223$	6.25747e108	0.398311	0.199156	−	0.979968i	$-0.436180\pi$
$223$	6.25747e108	0.398311	0.199156	+	0.979968i	$0.436180\pi$
$224$	−1.54222e109	−0.797285
$225$	0	0
$226$	−1.51467e109	−0.517937
$227$	−4.56314e109	−1.27075	−0.635377	−	0.772202i	$-0.719155\pi$
$227$	−4.56314e109	−1.27075	−0.635377	+	0.772202i	$0.719155\pi$
$228$	0	0
$229$	−8.76282e109	−1.62291	−0.811454	−	0.584416i	$-0.801324\pi$
$229$	−8.76282e109	−1.62291	−0.811454	+	0.584416i	$0.801324\pi$
$230$	7.64081e109	1.15557
$231$	0	0
$232$	−1.06174e110	−1.07356
$233$	1.12526e110	0.931541	0.465770	−	0.884906i	$-0.345777\pi$
$233$	1.12526e110	0.931541	0.465770	+	0.884906i	$0.345777\pi$
$234$	0	0
$235$	−2.33530e110	−1.29924
$236$	−4.59259e109	−0.209725
$237$	0	0
$238$	−8.97144e109	−0.276716
$239$	−4.94210e110	−1.25432	−0.627161	−	0.778889i	$-0.715783\pi$
$239$	−4.94210e110	−1.25432	−0.627161	+	0.778889i	$0.715783\pi$
$240$	0	0
$241$	5.44752e110	0.938440	0.469220	−	0.883081i	$-0.344535\pi$
$241$	5.44752e110	0.938440	0.469220	+	0.883081i	$0.344535\pi$
$242$	9.38612e110	1.33374
$243$	0	0
$244$	−3.27543e110	−0.317425
$245$	−9.21505e109	−0.0738371
$246$	0	0
$247$	−2.53361e111	−1.39101
$248$	−1.01237e111	−0.460611
$249$	0	0
$250$	−5.25780e111	−1.64662
$251$	4.01618e111	1.04468	0.522342	−	0.852736i	$-0.325058\pi$
$251$	4.01618e111	1.04468	0.522342	+	0.852736i	$0.325058\pi$
$252$	0	0
$253$	1.70174e111	0.306048
$254$	−1.40836e112	−2.10837
$255$	0	0
$256$	−1.33612e112	−1.38896
$257$	5.20895e111	0.451710	0.225855	−	0.974161i	$-0.427482\pi$
$257$	5.20895e111	0.451710	0.225855	+	0.974161i	$0.427482\pi$
$258$	0	0
$259$	−5.78451e111	−0.349806
$260$	−4.94000e112	−2.49727
$261$	0	0
$262$	−4.27245e112	−1.51240
$263$	−1.79958e112	−0.533616	−0.266808	−	0.963750i	$-0.585969\pi$
$263$	−1.79958e112	−0.533616	−0.266808	+	0.963750i	$0.585969\pi$
$264$	0	0
$265$	−4.04329e112	−0.842951
$266$	−9.46858e112	−1.65687
$267$	0	0
$268$	3.32635e112	0.410866
$269$	−1.32093e113	−1.37214	−0.686072	−	0.727534i	$-0.740666\pi$
$269$	−1.32093e113	−1.37214	−0.686072	+	0.727534i	$0.740666\pi$
$270$	0	0
$271$	−2.97524e112	−0.219003	−0.109501	−	0.993987i	$-0.534925\pi$
$271$	−2.97524e112	−0.219003	−0.109501	+	0.993987i	$0.534925\pi$
$272$	−6.91491e111	−0.0428877
$273$	0	0
$274$	−5.78162e113	−2.55063
$275$	8.42508e110	0.00313764
$276$	0	0
$277$	−4.03987e113	−1.07413	−0.537066	−	0.843540i	$-0.680467\pi$
$277$	−4.03987e113	−1.07413	−0.537066	+	0.843540i	$0.680467\pi$
$278$	1.09746e114	2.46778
$279$	0	0
$280$	−7.79642e113	−1.25616
$281$	−2.87863e113	−0.392954	−0.196477	−	0.980508i	$-0.562950\pi$
$281$	−2.87863e113	−0.392954	−0.196477	+	0.980508i	$0.562950\pi$
$282$	0	0
$283$	−5.62457e113	−0.552103	−0.276051	−	0.961143i	$-0.589026\pi$
$283$	−5.62457e113	−0.552103	−0.276051	+	0.961143i	$0.589026\pi$
$284$	1.87120e113	0.155890
$285$	0	0
$286$	−1.73582e114	−1.04348
$287$	−3.41339e114	−1.74453
$288$	0	0
$289$	−2.63182e114	−0.973884
$290$	4.67687e114	1.47383
$291$	0	0
$292$	5.50124e114	1.25938
$293$	−7.76401e114	−1.51615	−0.758074	−	0.652169i	$-0.773859\pi$
$293$	−7.76401e114	−1.51615	−0.758074	+	0.652169i	$0.773859\pi$
$294$	0	0
$295$	8.54318e113	0.121589
$296$	−3.35398e114	−0.407846
$297$	0	0
$298$	2.44368e114	0.217265
$299$	1.31649e115	1.00163
$300$	0	0
$301$	1.42821e115	0.796986
$302$	−2.49031e115	−1.19105
$303$	0	0
$304$	−7.29809e114	−0.256796
$305$	6.09298e114	0.184029
$306$	0	0
$307$	−6.39360e114	−0.142499	−0.0712494	−	0.997459i	$-0.522699\pi$
$307$	−6.39360e114	−0.142499	−0.0712494	+	0.997459i	$0.522699\pi$
$308$	−4.11174e115	−0.787803
$309$	0	0
$310$	4.45939e115	0.632349
$311$	7.51185e115	0.917041	0.458521	−	0.888684i	$-0.348379\pi$
$311$	7.51185e115	0.917041	0.458521	+	0.888684i	$0.348379\pi$
$312$	0	0
$313$	1.96544e116	1.78094	0.890469	−	0.455044i	$-0.150377\pi$
$313$	1.96544e116	1.78094	0.890469	+	0.455044i	$0.150377\pi$
$314$	3.70219e116	2.89221
$315$	0	0
$316$	5.15042e116	2.99498
$317$	−2.24637e116	−1.12778	−0.563892	−	0.825849i	$-0.690696\pi$
$317$	−2.24637e116	−1.12778	−0.563892	+	0.825849i	$0.690696\pi$
$318$	0	0
$319$	1.04162e116	0.390340
$320$	4.76098e116	1.54249
$321$	0	0
$322$	4.91998e116	1.19307
$323$	7.44876e115	0.156375
$324$	0	0
$325$	6.51777e114	0.0102689
$326$	−9.39710e115	−0.128344
$327$	0	0
$328$	−1.97916e117	−2.03398
$329$	−1.50372e117	−1.34140
$330$	0	0
$331$	−1.83238e117	−1.23315	−0.616573	−	0.787298i	$-0.711479\pi$
$331$	−1.83238e117	−1.23315	−0.616573	+	0.787298i	$0.711479\pi$
$332$	4.21976e117	2.46812
$333$	0	0
$334$	−8.62927e116	−0.381736
$335$	−6.18771e116	−0.238202
$336$	0	0
$337$	4.69113e117	1.36926	0.684632	−	0.728889i	$-0.259963\pi$
$337$	4.69113e117	1.36926	0.684632	+	0.728889i	$0.259963\pi$
$338$	−6.93045e117	−1.76252
$339$	0	0
$340$	1.45235e117	0.280738
$341$	9.93185e116	0.167476
$342$	0	0
$343$	7.47142e117	0.959901
$344$	8.28108e117	0.929222
$345$	0	0
$346$	−2.24637e118	−1.92506
$347$	−2.19991e118	−1.64848	−0.824242	−	0.566238i	$-0.808398\pi$
$347$	−2.19991e118	−1.64848	−0.824242	+	0.566238i	$0.808398\pi$
$348$	0	0
$349$	−5.28040e116	−0.0302890	−0.0151445	−	0.999885i	$-0.504821\pi$
$349$	−5.28040e116	−0.0302890	−0.0151445	+	0.999885i	$0.504821\pi$
$350$	2.43581e116	0.0122315
$351$	0	0
$352$	8.77270e117	0.337987
$353$	8.12471e117	0.274337	0.137168	−	0.990548i	$-0.456200\pi$
$353$	8.12471e117	0.274337	0.137168	+	0.990548i	$0.456200\pi$
$354$	0	0
$355$	−3.48083e117	−0.0903784
$356$	4.78819e117	0.109080
$357$	0	0
$358$	−9.36892e118	−1.64486
$359$	−2.33635e118	−0.360284	−0.180142	−	0.983641i	$-0.557656\pi$
$359$	−2.33635e118	−0.360284	−0.180142	+	0.983641i	$0.557656\pi$
$360$	0	0
$361$	−5.34716e117	−0.0636852
$362$	−1.32227e119	−1.38475
$363$	0	0
$364$	−3.18091e119	−2.57832
$365$	−1.02335e119	−0.730137
$366$	0	0
$367$	3.31122e118	0.183238	0.0916190	−	0.995794i	$-0.470796\pi$
$367$	3.31122e118	0.183238	0.0916190	+	0.995794i	$0.470796\pi$
$368$	3.79217e118	0.184912
$369$	0	0
$370$	1.47740e119	0.559911
$371$	−2.60351e119	−0.870307
$372$	0	0
$373$	7.34542e118	0.191230	0.0956149	−	0.995418i	$-0.469518\pi$
$373$	7.34542e118	0.191230	0.0956149	+	0.995418i	$0.469518\pi$
$374$	5.10328e118	0.117306
$375$	0	0
$376$	−8.71890e119	−1.56397
$377$	8.05814e119	1.27750
$378$	0	0
$379$	9.84272e119	1.22009	0.610045	−	0.792367i	$-0.291151\pi$
$379$	9.84272e119	1.22009	0.610045	+	0.792367i	$0.291151\pi$
$380$	1.53283e120	1.68096
$381$	0	0
$382$	9.98768e119	0.858061
$383$	5.93733e119	0.451698	0.225849	−	0.974162i	$-0.427484\pi$
$383$	5.93733e119	0.451698	0.225849	+	0.974162i	$0.427484\pi$
$384$	0	0
$385$	7.64870e119	0.456735
$386$	2.58059e120	1.36587
$387$	0	0
$388$	6.06543e120	2.52456
$389$	−1.81278e119	−0.0669404	−0.0334702	−	0.999440i	$-0.510656\pi$
$389$	−1.81278e119	−0.0669404	−0.0334702	+	0.999440i	$0.510656\pi$
$390$	0	0
$391$	−3.87046e119	−0.112601
$392$	−3.44046e119	−0.0888820
$393$	0	0
$394$	8.47889e120	1.72888
$395$	−9.58086e120	−1.73636
$396$	0	0
$397$	−9.51402e120	−1.36334	−0.681672	−	0.731658i	$-0.738747\pi$
$397$	−9.51402e120	−1.36334	−0.681672	+	0.731658i	$0.738747\pi$
$398$	1.01380e120	0.129238
$399$	0	0
$400$	1.87745e118	0.00189574
$401$	−4.50368e120	−0.404906	−0.202453	−	0.979292i	$-0.564891\pi$
$401$	−4.50368e120	−0.404906	−0.202453	+	0.979292i	$0.564891\pi$
$402$	0	0
$403$	7.68343e120	0.548113
$404$	−2.87855e121	−1.82995
$405$	0	0
$406$	3.01148e121	1.52166
$407$	3.29044e120	0.148291
$408$	0	0
$409$	−2.08198e121	−0.747040	−0.373520	−	0.927622i	$-0.621849\pi$
$409$	−2.08198e121	−0.747040	−0.373520	+	0.927622i	$0.621849\pi$
$410$	8.71802e121	2.79234
$411$	0	0
$412$	−4.67796e121	−1.19491
$413$	5.50102e120	0.125535
$414$	0	0
$415$	−7.84964e121	−1.43091
$416$	6.78670e121	1.10616
$417$	0	0
$418$	5.38607e121	0.702384
$419$	6.99167e121	0.815885	0.407943	−	0.913008i	$-0.366246\pi$
$419$	6.99167e121	0.815885	0.407943	+	0.913008i	$0.366246\pi$
$420$	0	0
$421$	−5.99741e121	−0.560849	−0.280425	−	0.959876i	$-0.590475\pi$
$421$	−5.99741e121	−0.560849	−0.280425	+	0.959876i	$0.590475\pi$
$422$	−2.80406e122	−2.34833
$423$	0	0
$424$	−1.50957e122	−1.01471
$425$	−1.91621e119	−0.00115440
$426$	0	0
$427$	3.92332e121	0.190002
$428$	−4.41471e122	−1.91764
$429$	0	0
$430$	−3.64775e122	−1.27568
$431$	2.88391e122	0.905293	0.452646	−	0.891690i	$-0.350480\pi$
$431$	2.88391e122	0.905293	0.452646	+	0.891690i	$0.350480\pi$
$432$	0	0
$433$	−6.05429e122	−1.53241	−0.766207	−	0.642594i	$-0.777858\pi$
$433$	−6.05429e122	−1.53241	−0.766207	+	0.642594i	$0.777858\pi$
$434$	2.87144e122	0.652871
$435$	0	0
$436$	1.27456e123	2.34011
$437$	−4.08494e122	−0.674215
$438$	0	0
$439$	−1.03981e123	−1.38788	−0.693940	−	0.720033i	$-0.744127\pi$
$439$	−1.03981e123	−1.38788	−0.693940	+	0.720033i	$0.744127\pi$
$440$	4.43488e122	0.532516
$441$	0	0
$442$	3.94797e122	0.383918
$443$	−1.27414e123	−1.11544	−0.557719	−	0.830030i	$-0.688323\pi$
$443$	−1.27414e123	−1.11544	−0.557719	+	0.830030i	$0.688323\pi$
$444$	0	0
$445$	−8.90704e121	−0.0632402
$446$	−1.02909e123	−0.658240
$447$	0	0
$448$	3.06564e123	1.59255
$449$	1.96102e122	0.0918389	0.0459195	−	0.998945i	$-0.485378\pi$
$449$	1.96102e122	0.0918389	0.0459195	+	0.998945i	$0.485378\pi$
$450$	0	0
$451$	1.94166e123	0.739543
$452$	1.57889e123	0.542518
$453$	0	0
$454$	7.50448e123	2.10002
$455$	5.91715e123	1.49480
$456$	0	0
$457$	1.00769e123	0.207598	0.103799	−	0.994598i	$-0.466900\pi$
$457$	1.00769e123	0.207598	0.103799	+	0.994598i	$0.466900\pi$
$458$	1.44112e124	2.68198
$459$	0	0
$460$	−7.96475e123	−1.21041
$461$	1.03588e123	0.142304	0.0711522	−	0.997465i	$-0.477332\pi$
$461$	1.03588e123	0.142304	0.0711522	+	0.997465i	$0.477332\pi$
$462$	0	0
$463$	1.69373e124	1.90252	0.951260	−	0.308391i	$-0.0997906\pi$
$463$	1.69373e124	1.90252	0.951260	+	0.308391i	$0.0997906\pi$
$464$	2.32115e123	0.235840
$465$	0	0
$466$	−1.85058e124	−1.53944
$467$	−1.30804e124	−0.984886	−0.492443	−	0.870345i	$-0.663896\pi$
$467$	−1.30804e124	−0.984886	−0.492443	+	0.870345i	$0.663896\pi$
$468$	0	0
$469$	−3.98432e123	−0.245933
$470$	3.84061e124	2.14709
$471$	0	0
$472$	3.18961e123	0.146364
$473$	−8.12419e123	−0.337860
$474$	0	0
$475$	−2.02239e122	−0.00691214
$476$	9.35179e123	0.289849
$477$	0	0
$478$	8.12771e124	2.07286
$479$	−3.97794e122	−0.00920571	−0.00460285	−	0.999989i	$-0.501465\pi$
$479$	−3.97794e122	−0.00920571	−0.00460285	+	0.999989i	$0.501465\pi$
$480$	0	0
$481$	2.54553e124	0.485325
$482$	−8.95891e124	−1.55084
$483$	0	0
$484$	−9.78406e124	−1.39704
$485$	−1.12830e125	−1.46363
$486$	0	0
$487$	−7.90319e124	−0.846653	−0.423327	−	0.905977i	$-0.639138\pi$
$487$	−7.90319e124	−0.846653	−0.423327	+	0.905977i	$0.639138\pi$
$488$	2.27483e124	0.221527
$489$	0	0
$490$	1.51549e124	0.122021
$491$	1.51789e125	1.11160	0.555802	−	0.831315i	$-0.312411\pi$
$491$	1.51789e125	1.11160	0.555802	+	0.831315i	$0.312411\pi$
$492$	0	0
$493$	−2.36907e124	−0.143614
$494$	4.16674e125	2.29876
$495$	0	0
$496$	2.21322e124	0.101187
$497$	−2.24134e124	−0.0933115
$498$	0	0
$499$	−2.29978e124	−0.0794348	−0.0397174	−	0.999211i	$-0.512646\pi$
$499$	−2.29978e124	−0.0794348	−0.0397174	+	0.999211i	$0.512646\pi$
$500$	5.48071e125	1.72477
$501$	0	0
$502$	−6.60495e125	−1.72642
$503$	−4.01248e125	−0.956097	−0.478048	−	0.878334i	$-0.658656\pi$
$503$	−4.01248e125	−0.956097	−0.478048	+	0.878334i	$0.658656\pi$
$504$	0	0
$505$	5.35470e125	1.06093
$506$	−2.79866e125	−0.505768
$507$	0	0
$508$	1.46807e126	2.20844
$509$	8.19933e125	1.12565	0.562823	−	0.826578i	$-0.309715\pi$
$509$	8.19933e125	1.12565	0.562823	+	0.826578i	$0.309715\pi$
$510$	0	0
$511$	−6.58941e125	−0.753832
$512$	5.02404e125	0.524807
$513$	0	0
$514$	−8.56656e125	−0.746486
$515$	8.70198e125	0.692759
$516$	0	0
$517$	8.55371e125	0.568649
$518$	9.51313e125	0.578082
$519$	0	0
$520$	3.43089e126	1.74282
$521$	1.97404e126	0.917069	0.458534	−	0.888677i	$-0.348375\pi$
$521$	1.97404e126	0.917069	0.458534	+	0.888677i	$0.348375\pi$
$522$	0	0
$523$	1.23071e126	0.478441	0.239220	−	0.970965i	$-0.423108\pi$
$523$	1.23071e126	0.478441	0.239220	+	0.970965i	$0.423108\pi$
$524$	4.45358e126	1.58418
$525$	0	0
$526$	2.95956e126	0.881841
$527$	−2.25891e125	−0.0616177
$528$	0	0
$529$	−2.24951e126	−0.514515
$530$	6.64954e126	1.39304
$531$	0	0
$532$	9.87001e126	1.73551
$533$	1.50210e127	2.42037
$534$	0	0
$535$	8.21228e126	1.11177
$536$	−2.31019e126	−0.286738
$537$	0	0
$538$	2.17239e127	2.26757
$539$	3.37527e125	0.0323170
$540$	0	0
$541$	−9.82340e126	−0.791752	−0.395876	−	0.918304i	$-0.629559\pi$
$541$	−9.82340e126	−0.791752	−0.395876	+	0.918304i	$0.629559\pi$
$542$	4.89303e126	0.361919
$543$	0	0
$544$	−1.99527e126	−0.124352
$545$	−2.37094e127	−1.35670
$546$	0	0
$547$	3.53717e127	1.70704	0.853522	−	0.521056i	$-0.174462\pi$
$547$	3.53717e127	1.70704	0.853522	+	0.521056i	$0.174462\pi$
$548$	6.02674e127	2.67169
$549$	0	0
$550$	−1.38558e125	−0.00518520
$551$	−2.50035e127	−0.859908
$552$	0	0
$553$	−6.16920e127	−1.79271
$554$	6.64391e127	1.77509
$555$	0	0
$556$	−1.14399e128	−2.58491
$557$	−1.20728e127	−0.250924	−0.125462	−	0.992098i	$-0.540041\pi$
$557$	−1.20728e127	−0.250924	−0.125462	+	0.992098i	$0.540041\pi$
$558$	0	0
$559$	−6.28499e127	−1.10575
$560$	1.70444e127	0.275955
$561$	0	0
$562$	4.73415e127	0.649386
$563$	−1.26048e128	−1.59182	−0.795911	−	0.605414i	$-0.793008\pi$
$563$	−1.26048e128	−1.59182	−0.795911	+	0.605414i	$0.793008\pi$
$564$	0	0
$565$	−2.93706e127	−0.314529
$566$	9.25008e127	0.912392
$567$	0	0
$568$	−1.29957e127	−0.108794
$569$	1.77963e128	1.37280	0.686402	−	0.727222i	$-0.259189\pi$
$569$	1.77963e128	1.37280	0.686402	+	0.727222i	$0.259189\pi$
$570$	0	0
$571$	−1.45624e127	−0.0954230	−0.0477115	−	0.998861i	$-0.515193\pi$
$571$	−1.45624e127	−0.0954230	−0.0477115	+	0.998861i	$0.515193\pi$
$572$	1.80941e128	1.09301
$573$	0	0
$574$	5.61361e128	2.88296
$575$	1.05086e126	0.00497725
$576$	0	0
$577$	3.39638e128	1.36880	0.684401	−	0.729106i	$-0.260064\pi$
$577$	3.39638e128	1.36880	0.684401	+	0.729106i	$0.260064\pi$
$578$	4.32826e128	1.60942
$579$	0	0
$580$	−4.87515e128	−1.54378
$581$	−5.05445e128	−1.47735
$582$	0	0
$583$	1.48097e128	0.368942
$584$	−3.82068e128	−0.878908
$585$	0	0
$586$	1.27686e129	2.50555
$587$	9.03917e128	1.63854	0.819270	−	0.573408i	$-0.194379\pi$
$587$	9.03917e128	1.63854	0.819270	+	0.573408i	$0.194379\pi$
$588$	0	0
$589$	−2.38408e128	−0.368944
$590$	−1.40500e128	−0.200936
$591$	0	0
$592$	7.33243e127	0.0895959
$593$	−3.48429e128	−0.393615	−0.196807	−	0.980442i	$-0.563057\pi$
$593$	−3.48429e128	−0.393615	−0.196807	+	0.980442i	$0.563057\pi$
$594$	0	0
$595$	−1.73963e128	−0.168042
$596$	−2.54729e128	−0.227576
$597$	0	0
$598$	−2.16509e129	−1.65528
$599$	−2.02715e128	−0.143397	−0.0716984	−	0.997426i	$-0.522842\pi$
$599$	−2.02715e128	−0.143397	−0.0716984	+	0.997426i	$0.522842\pi$
$600$	0	0
$601$	−5.80105e128	−0.351434	−0.175717	−	0.984441i	$-0.556224\pi$
$601$	−5.80105e128	−0.351434	−0.175717	+	0.984441i	$0.556224\pi$
$602$	−2.34882e129	−1.31708
$603$	0	0
$604$	2.59589e129	1.24758
$605$	1.82004e129	0.809946
$606$	0	0
$607$	4.21620e129	1.60934	0.804668	−	0.593725i	$-0.202343\pi$
$607$	4.21620e129	1.60934	0.804668	+	0.593725i	$0.202343\pi$
$608$	−2.10584e129	−0.744575
$609$	0	0
$610$	−1.00204e129	−0.304123
$611$	6.61728e129	1.86107
$612$	0	0
$613$	−5.05723e129	−1.22180	−0.610901	−	0.791707i	$-0.709193\pi$
$613$	−5.05723e129	−1.22180	−0.610901	+	0.791707i	$0.709193\pi$
$614$	1.05148e129	0.235490
$615$	0	0
$616$	2.85566e129	0.549798
$617$	−2.60006e129	−0.464220	−0.232110	−	0.972690i	$-0.574563\pi$
$617$	−2.60006e129	−0.464220	−0.232110	+	0.972690i	$0.574563\pi$
$618$	0	0
$619$	−7.58633e129	−1.16524	−0.582622	−	0.812744i	$-0.697973\pi$
$619$	−7.58633e129	−1.16524	−0.582622	+	0.812744i	$0.697973\pi$
$620$	−4.64845e129	−0.662361
$621$	0	0
$622$	−1.23539e130	−1.51548
$623$	−5.73532e128	−0.0652925
$624$	0	0
$625$	−1.02681e130	−1.00709
$626$	−3.23234e130	−2.94314
$627$	0	0
$628$	−3.85914e130	−3.02948
$629$	−7.48381e128	−0.0545591
$630$	0	0
$631$	1.12795e130	0.709456	0.354728	−	0.934970i	$-0.384574\pi$
$631$	1.12795e130	0.709456	0.354728	+	0.934970i	$0.384574\pi$
$632$	−3.57703e130	−2.09016
$633$	0	0
$634$	3.69435e130	1.86375
$635$	−2.73092e130	−1.28036
$636$	0	0
$637$	2.61116e129	0.105767
$638$	−1.71304e130	−0.645067
$639$	0	0
$640$	−5.45786e130	−1.77686
$641$	−6.71910e129	−0.203429	−0.101715	−	0.994814i	$-0.532433\pi$
$641$	−6.71910e129	−0.203429	−0.101715	+	0.994814i	$0.532433\pi$
$642$	0	0
$643$	2.52742e130	0.662015	0.331007	−	0.943628i	$-0.392612\pi$
$643$	2.52742e130	0.662015	0.331007	+	0.943628i	$0.392612\pi$
$644$	−5.12857e130	−1.24969
$645$	0	0
$646$	−1.22501e130	−0.258421
$647$	5.15142e130	1.01130	0.505648	−	0.862740i	$-0.331254\pi$
$647$	5.15142e130	1.01130	0.505648	+	0.862740i	$0.331254\pi$
$648$	0	0
$649$	−3.12918e129	−0.0532172
$650$	−1.07190e129	−0.0169701
$651$	0	0
$652$	9.79550e129	0.134435
$653$	−1.88412e130	−0.240794	−0.120397	−	0.992726i	$-0.538417\pi$
$653$	−1.88412e130	−0.240794	−0.120397	+	0.992726i	$0.538417\pi$
$654$	0	0
$655$	−8.28459e130	−0.918439
$656$	4.32680e130	0.446826
$657$	0	0
$658$	2.47300e131	2.21677
$659$	1.86982e131	1.56181	0.780903	−	0.624653i	$-0.214759\pi$
$659$	1.86982e131	1.56181	0.780903	+	0.624653i	$0.214759\pi$
$660$	0	0
$661$	8.10316e130	0.587877	0.293938	−	0.955824i	$-0.405034\pi$
$661$	8.10316e130	0.587877	0.293938	+	0.955824i	$0.405034\pi$
$662$	3.01351e131	2.03787
$663$	0	0
$664$	−2.93068e131	−1.72247
$665$	−1.83603e131	−1.00617
$666$	0	0
$667$	1.29921e131	0.619197
$668$	8.99512e130	0.399854
$669$	0	0
$670$	1.01762e131	0.393648
$671$	−2.23173e130	−0.0805459
$672$	0	0
$673$	1.80585e131	0.567519	0.283760	−	0.958895i	$-0.408418\pi$
$673$	1.80585e131	0.567519	0.283760	+	0.958895i	$0.408418\pi$
$674$	−7.71497e131	−2.26281
$675$	0	0
$676$	7.22427e131	1.84617
$677$	−3.06664e131	−0.731627	−0.365813	−	0.930688i	$-0.619209\pi$
$677$	−3.06664e131	−0.731627	−0.365813	+	0.930688i	$0.619209\pi$
$678$	0	0
$679$	−7.26520e131	−1.51113
$680$	−1.00867e131	−0.195923
$681$	0	0
$682$	−1.63338e131	−0.276766
$683$	2.46209e131	0.389710	0.194855	−	0.980832i	$-0.437576\pi$
$683$	2.46209e131	0.389710	0.194855	+	0.980832i	$0.437576\pi$
$684$	0	0
$685$	−1.12110e132	−1.54893
$686$	−1.22874e132	−1.58631
$687$	0	0
$688$	−1.81040e131	−0.204132
$689$	1.14570e132	1.20747
$690$	0	0
$691$	−5.87683e131	−0.541270	−0.270635	−	0.962682i	$-0.587234\pi$
$691$	−5.87683e131	−0.541270	−0.270635	+	0.962682i	$0.587234\pi$
$692$	2.34161e132	2.01642
$693$	0	0
$694$	3.61794e132	2.72425
$695$	2.12806e132	1.49862
$696$	0	0
$697$	−4.41612e131	−0.272093
$698$	8.68407e130	0.0500549
$699$	0	0
$700$	−2.53908e130	−0.0128120
$701$	−1.49796e132	−0.707313	−0.353657	−	0.935375i	$-0.615062\pi$
$701$	−1.49796e132	−0.707313	−0.353657	+	0.935375i	$0.615062\pi$
$702$	0	0
$703$	−7.89851e131	−0.326680
$704$	−1.74384e132	−0.675117
$705$	0	0
$706$	−1.33618e132	−0.453362
$707$	3.44794e132	1.09536
$708$	0	0
$709$	−3.30985e132	−0.922059	−0.461029	−	0.887385i	$-0.652520\pi$
$709$	−3.30985e132	−0.922059	−0.461029	+	0.887385i	$0.652520\pi$
$710$	5.72452e131	0.149357
$711$	0	0
$712$	−3.32546e131	−0.0761258
$713$	1.23880e132	0.265667
$714$	0	0
$715$	−3.36589e132	−0.633678
$716$	9.76613e132	1.72293
$717$	0	0
$718$	3.84232e132	0.595397
$719$	5.03271e131	0.0730985	0.0365492	−	0.999332i	$-0.488363\pi$
$719$	5.03271e131	0.0730985	0.0365492	+	0.999332i	$0.488363\pi$
$720$	0	0
$721$	5.60328e132	0.715241
$722$	8.79387e131	0.105245
$723$	0	0
$724$	1.37833e133	1.45047
$725$	6.43221e130	0.00634808
$726$	0	0
$727$	8.36481e132	0.726283	0.363141	−	0.931734i	$-0.381704\pi$
$727$	8.36481e132	0.726283	0.363141	+	0.931734i	$0.381704\pi$
$728$	2.20918e133	1.79938
$729$	0	0
$730$	1.68298e133	1.20661
$731$	1.84777e132	0.124306
$732$	0	0
$733$	−8.18691e131	−0.0485049	−0.0242524	−	0.999706i	$-0.507721\pi$
$733$	−8.18691e131	−0.0485049	−0.0242524	+	0.999706i	$0.507721\pi$
$734$	−5.44558e132	−0.302815
$735$	0	0
$736$	1.09422e133	0.536149
$737$	2.26642e132	0.104256
$738$	0	0
$739$	−2.27978e132	−0.0924543	−0.0462271	−	0.998931i	$-0.514720\pi$
$739$	−2.27978e132	−0.0924543	−0.0462271	+	0.998931i	$0.514720\pi$
$740$	−1.54004e133	−0.586485
$741$	0	0
$742$	4.28170e133	1.43825
$743$	−2.14775e132	−0.0677648	−0.0338824	−	0.999426i	$-0.510787\pi$
$743$	−2.14775e132	−0.0677648	−0.0338824	+	0.999426i	$0.510787\pi$
$744$	0	0
$745$	4.73849e132	0.131939
$746$	−1.20802e133	−0.316022
$747$	0	0
$748$	−5.31963e132	−0.122873
$749$	5.28796e133	1.14785
$750$	0	0
$751$	3.97986e133	0.763151	0.381575	−	0.924338i	$-0.375382\pi$
$751$	3.97986e133	0.763151	0.381575	+	0.924338i	$0.375382\pi$
$752$	1.90611e133	0.343573
$753$	0	0
$754$	−1.32523e134	−2.11117
$755$	−4.82889e133	−0.723293
$756$	0	0
$757$	−4.10840e133	−0.544145	−0.272072	−	0.962277i	$-0.587709\pi$
$757$	−4.10840e133	−0.544145	−0.272072	+	0.962277i	$0.587709\pi$
$758$	−1.61872e134	−2.01629
$759$	0	0
$760$	−1.06457e134	−1.17312
$761$	1.71355e134	1.77627	0.888136	−	0.459580i	$-0.152000\pi$
$761$	1.71355e134	1.77627	0.888136	+	0.459580i	$0.152000\pi$
$762$	0	0
$763$	−1.52667e134	−1.40073
$764$	−1.04111e134	−0.898786
$765$	0	0
$766$	−9.76445e133	−0.746466
$767$	−2.42078e133	−0.174169
$768$	0	0
$769$	3.69304e133	0.235401	0.117701	−	0.993049i	$-0.462448\pi$
$769$	3.69304e133	0.235401	0.117701	+	0.993049i	$0.462448\pi$
$770$	−1.25789e134	−0.754789
$771$	0	0
$772$	−2.69000e134	−1.43070
$773$	−1.91572e134	−0.959369	−0.479684	−	0.877441i	$-0.659249\pi$
$773$	−1.91572e134	−0.959369	−0.479684	+	0.877441i	$0.659249\pi$
$774$	0	0
$775$	6.13310e131	0.00272365
$776$	−4.21252e134	−1.76186
$777$	0	0
$778$	2.98127e133	0.110624
$779$	−4.66084e134	−1.62919
$780$	0	0
$781$	1.27495e133	0.0395568
$782$	6.36530e133	0.186082
$783$	0	0
$784$	7.52147e132	0.0195257
$785$	7.17881e134	1.75636
$786$	0	0
$787$	−5.96118e134	−1.29571	−0.647854	−	0.761765i	$-0.724333\pi$
$787$	−5.96118e134	−1.29571	−0.647854	+	0.761765i	$0.724333\pi$
$788$	−8.83836e134	−1.81093
$789$	0	0
$790$	1.57565e135	2.86947
$791$	−1.89120e134	−0.324737
$792$	0	0
$793$	−1.72650e134	−0.263610
$794$	1.56466e135	2.25303
$795$	0	0
$796$	−1.05679e134	−0.135372
$797$	−7.29944e133	−0.0882018	−0.0441009	−	0.999027i	$-0.514042\pi$
$797$	−7.29944e133	−0.0882018	−0.0441009	+	0.999027i	$0.514042\pi$
$798$	0	0
$799$	−1.94546e134	−0.209218
$800$	5.41731e132	0.00549666
$801$	0	0
$802$	7.40668e134	0.669138
$803$	3.74829e134	0.319566
$804$	0	0
$805$	9.54021e134	0.724519
$806$	−1.26361e135	−0.905799
$807$	0	0
$808$	1.99919e135	1.27710
$809$	−5.84885e134	−0.352748	−0.176374	−	0.984323i	$-0.556437\pi$
$809$	−5.84885e134	−0.352748	−0.176374	+	0.984323i	$0.556437\pi$
$810$	0	0
$811$	−1.10103e135	−0.592010	−0.296005	−	0.955186i	$-0.595655\pi$
$811$	−1.10103e135	−0.592010	−0.296005	+	0.955186i	$0.595655\pi$
$812$	−3.13915e135	−1.59388
$813$	0	0
$814$	−5.41141e134	−0.245062
$815$	−1.82217e134	−0.0779398
$816$	0	0
$817$	1.95016e135	0.744296
$818$	3.42400e135	1.23454
$819$	0	0
$820$	−9.08763e135	−2.92487
$821$	−2.55189e135	−0.776079	−0.388039	−	0.921643i	$-0.626848\pi$
$821$	−2.55189e135	−0.776079	−0.388039	+	0.921643i	$0.626848\pi$
$822$	0	0
$823$	3.68807e135	1.00163	0.500815	−	0.865554i	$-0.333034\pi$
$823$	3.68807e135	1.00163	0.500815	+	0.865554i	$0.333034\pi$
$824$	3.24890e135	0.833914
$825$	0	0
$826$	−9.04690e134	−0.207457
$827$	3.38429e135	0.733604	0.366802	−	0.930299i	$-0.380453\pi$
$827$	3.38429e135	0.733604	0.366802	+	0.930299i	$0.380453\pi$
$828$	0	0
$829$	7.09533e135	1.37463	0.687317	−	0.726357i	$-0.258788\pi$
$829$	7.09533e135	1.37463	0.687317	+	0.726357i	$0.258788\pi$
$830$	1.29094e136	2.36469
$831$	0	0
$832$	−1.34906e136	−2.20952
$833$	−7.67675e133	−0.0118901
$834$	0	0
$835$	−1.67328e135	−0.231818
$836$	−5.61441e135	−0.735720
$837$	0	0
$838$	−1.14984e136	−1.34831
$839$	−1.42976e135	−0.158611	−0.0793053	−	0.996850i	$-0.525270\pi$
$839$	−1.42976e135	−0.158611	−0.0793053	+	0.996850i	$0.525270\pi$
$840$	0	0
$841$	−2.11728e135	−0.210264
$842$	9.86325e135	0.926847
$843$	0	0
$844$	2.92294e136	2.45978
$845$	−1.34387e136	−1.07033
$846$	0	0
$847$	1.17194e136	0.836231
$848$	3.30020e135	0.222912
$849$	0	0
$850$	3.15137e133	0.00190774
$851$	4.10416e135	0.235234
$852$	0	0
$853$	8.68850e135	0.446493	0.223247	−	0.974762i	$-0.428334\pi$
$853$	8.68850e135	0.446493	0.223247	+	0.974762i	$0.428334\pi$
$854$	−6.45224e135	−0.313993
$855$	0	0
$856$	3.06607e136	1.33830
$857$	−3.33416e136	−1.37841	−0.689205	−	0.724567i	$-0.742040\pi$
$857$	−3.33416e136	−1.37841	−0.689205	+	0.724567i	$0.742040\pi$
$858$	0	0
$859$	8.15089e135	0.302359	0.151179	−	0.988506i	$-0.451693\pi$
$859$	8.15089e135	0.302359	0.151179	+	0.988506i	$0.451693\pi$
$860$	3.80240e136	1.33623
$861$	0	0
$862$	−4.74284e136	−1.49607
$863$	9.31789e135	0.278494	0.139247	−	0.990258i	$-0.455532\pi$
$863$	9.31789e135	0.278494	0.139247	+	0.990258i	$0.455532\pi$
$864$	0	0
$865$	−4.35588e136	−1.16903
$866$	9.95680e136	2.53243
$867$	0	0
$868$	−2.99318e136	−0.683857
$869$	3.50926e136	0.759969
$870$	0	0
$871$	1.75334e136	0.341210
$872$	−8.85195e136	−1.63314
$873$	0	0
$874$	6.71803e136	1.11419
$875$	−6.56482e136	−1.03240
$876$	0	0
$877$	1.16539e137	1.64812	0.824061	−	0.566501i	$-0.191703\pi$
$877$	1.16539e137	1.64812	0.824061	+	0.566501i	$0.191703\pi$
$878$	1.71005e137	2.29358
$879$	0	0
$880$	−9.69546e135	−0.116983
$881$	1.45824e137	1.66897	0.834487	−	0.551028i	$-0.185764\pi$
$881$	1.45824e137	1.66897	0.834487	+	0.551028i	$0.185764\pi$
$882$	0	0
$883$	6.58283e136	0.678016	0.339008	−	0.940784i	$-0.389909\pi$
$883$	6.58283e136	0.678016	0.339008	+	0.940784i	$0.389909\pi$
$884$	−4.11535e136	−0.402139
$885$	0	0
$886$	2.09544e137	1.84335
$887$	1.39279e137	1.16262	0.581310	−	0.813682i	$-0.302540\pi$
$887$	1.39279e137	1.16262	0.581310	+	0.813682i	$0.302540\pi$
$888$	0	0
$889$	−1.75846e137	−1.32191
$890$	1.46484e136	0.104509
$891$	0	0
$892$	1.07272e137	0.689480
$893$	−2.05327e137	−1.25272
$894$	0	0
$895$	−1.81670e137	−0.998879
$896$	−3.51436e137	−1.83453
$897$	0	0
$898$	−3.22506e136	−0.151771
$899$	7.58257e136	0.338837
$900$	0	0
$901$	−3.36833e136	−0.135741
$902$	−3.19322e137	−1.22215
$903$	0	0
$904$	−1.09656e137	−0.378617
$905$	−2.56397e137	−0.840920
$906$	0	0
$907$	−2.41067e137	−0.713508	−0.356754	−	0.934198i	$-0.616117\pi$
$907$	−2.41067e137	−0.713508	−0.356754	+	0.934198i	$0.616117\pi$
$908$	−7.82264e137	−2.19969
$909$	0	0
$910$	−9.73126e137	−2.47027
$911$	9.93661e136	0.239681	0.119841	−	0.992793i	$-0.461762\pi$
$911$	9.93661e136	0.239681	0.119841	+	0.992793i	$0.461762\pi$
$912$	0	0
$913$	2.87515e137	0.626281
$914$	−1.65723e137	−0.343072
$915$	0	0
$916$	−1.50222e138	−2.80927
$917$	−5.33452e137	−0.948246
$918$	0	0
$919$	6.14650e137	0.987317	0.493658	−	0.869656i	$-0.335659\pi$
$919$	6.14650e137	0.987317	0.493658	+	0.869656i	$0.335659\pi$
$920$	5.53162e137	0.844730
$921$	0	0
$922$	−1.70360e137	−0.235169
$923$	9.86322e136	0.129461
$924$	0	0
$925$	2.03191e135	0.00241164
$926$	−2.78549e138	−3.14406
$927$	0	0
$928$	6.69760e137	0.683815
$929$	6.24054e137	0.606026	0.303013	−	0.952986i	$-0.402007\pi$
$929$	6.24054e137	0.606026	0.303013	+	0.952986i	$0.402007\pi$
$930$	0	0
$931$	−8.10215e136	−0.0711934
$932$	1.92904e138	1.61251
$933$	0	0
$934$	2.15118e138	1.62760
$935$	9.89563e136	0.0712367
$936$	0	0
$937$	−8.37503e137	−0.545877	−0.272939	−	0.962031i	$-0.587996\pi$
$937$	−8.37503e137	−0.545877	−0.272939	+	0.962031i	$0.587996\pi$
$938$	6.55255e137	0.406423
$939$	0	0
$940$	−4.00343e138	−2.24899
$941$	2.62324e138	1.40256	0.701278	−	0.712887i	$-0.252613\pi$
$941$	2.62324e138	1.40256	0.701278	+	0.712887i	$0.252613\pi$
$942$	0	0
$943$	2.42182e138	1.17314
$944$	−6.97307e136	−0.0321534
$945$	0	0
$946$	1.33609e138	0.558340
$947$	2.87773e138	1.14492	0.572461	−	0.819932i	$-0.305989\pi$
$947$	2.87773e138	1.14492	0.572461	+	0.819932i	$0.305989\pi$
$948$	0	0
$949$	2.89973e138	1.04587
$950$	3.32600e136	0.0114228
$951$	0	0
$952$	−6.49494e137	−0.202282
$953$	−4.21352e136	−0.0124976	−0.00624878	−	0.999980i	$-0.501989\pi$
$953$	−4.21352e136	−0.0124976	−0.00624878	+	0.999980i	$0.501989\pi$
$954$	0	0
$955$	1.93668e138	0.521077
$956$	−8.47229e138	−2.17124
$957$	0	0
$958$	6.54207e136	0.0152131
$959$	−7.21885e138	−1.59920
$960$	0	0
$961$	−4.25022e138	−0.854622
$962$	−4.18634e138	−0.802037
$963$	0	0
$964$	9.33874e138	1.62445
$965$	5.00396e138	0.829456
$966$	0	0
$967$	−1.04448e139	−1.57242	−0.786211	−	0.617958i	$-0.787960\pi$
$967$	−1.04448e139	−1.57242	−0.786211	+	0.617958i	$0.787960\pi$
$968$	6.79515e138	0.974978
$969$	0	0
$970$	1.85558e139	2.41877
$971$	8.38938e138	1.04240	0.521201	−	0.853434i	$-0.325484\pi$
$971$	8.38938e138	1.04240	0.521201	+	0.853434i	$0.325484\pi$
$972$	0	0
$973$	1.37028e139	1.54725
$974$	1.29975e139	1.39916
$975$	0	0
$976$	−4.97319e137	−0.0486652
$977$	4.89824e138	0.457028	0.228514	−	0.973541i	$-0.426613\pi$
$977$	4.89824e138	0.457028	0.228514	+	0.973541i	$0.426613\pi$
$978$	0	0
$979$	3.26245e137	0.0276789
$980$	−1.57974e138	−0.127813
$981$	0	0
$982$	−2.49629e139	−1.83701
$983$	2.09544e139	1.47074	0.735371	−	0.677664i	$-0.237008\pi$
$983$	2.09544e139	1.47074	0.735371	+	0.677664i	$0.237008\pi$
$984$	0	0
$985$	1.64412e139	1.04990
$986$	3.89614e138	0.237333
$987$	0	0
$988$	−4.34339e139	−2.40786
$989$	−1.01333e139	−0.535948
$990$	0	0
$991$	−2.03468e139	−0.979648	−0.489824	−	0.871821i	$-0.662939\pi$
$991$	−2.03468e139	−0.979648	−0.489824	+	0.871821i	$0.662939\pi$
$992$	6.38616e138	0.293391
$993$	0	0
$994$	3.68607e138	0.154204
$995$	1.96584e138	0.0784830
$996$	0	0
$997$	−1.57813e139	−0.573875	−0.286938	−	0.957949i	$-0.592637\pi$
$997$	−1.57813e139	−0.573875	−0.286938	+	0.957949i	$0.592637\pi$
$998$	3.78218e138	0.131272
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.94.a.b.1.1		7
3.2	odd	2		1.94.a.a.1.7	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.94.a.a.1.7	✓	7	3.2	odd	2
9.94.a.b.1.1		7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.64459e14 q^{2} +1.71431e28 q^{4} -3.18897e32 q^{5} -2.05341e39 q^{7} -1.19061e42 q^{8} +O(q^{10})\)	\(q-1.64459e14 q^{2} +1.71431e28 q^{4} -3.18897e32 q^{5} -2.05341e39 q^{7} -1.19061e42 q^{8} +5.24454e46 q^{10} +1.16805e48 q^{11} +9.03622e51 q^{13} +3.37700e53 q^{14} +2.60289e55 q^{16} -2.65663e56 q^{17} -2.80384e59 q^{19} -5.46689e60 q^{20} -1.92096e62 q^{22} +1.45691e63 q^{23} +7.21293e62 q^{25} -1.48608e66 q^{26} -3.52017e67 q^{28} +8.91760e67 q^{29} +8.50292e68 q^{31} +7.51055e69 q^{32} +4.36905e70 q^{34} +6.54826e71 q^{35} +2.81703e72 q^{37} +4.61116e73 q^{38} +3.79682e74 q^{40} +1.66230e75 q^{41} -6.95533e75 q^{43} +2.00240e76 q^{44} -2.39601e77 q^{46} +7.32306e77 q^{47} +2.88966e77 q^{49} -1.18623e77 q^{50} +1.54909e80 q^{52} +1.26790e80 q^{53} -3.72488e80 q^{55} +2.44481e81 q^{56} -1.46658e82 q^{58} -2.67897e81 q^{59} -1.91064e82 q^{61} -1.39838e83 q^{62} -1.49295e84 q^{64} -2.88163e84 q^{65} +1.94035e84 q^{67} -4.55428e84 q^{68} -1.07692e86 q^{70} +1.09152e85 q^{71} +3.20901e86 q^{73} -4.63285e86 q^{74} -4.80665e87 q^{76} -2.39848e87 q^{77} +3.00437e88 q^{79} -8.30055e87 q^{80} -2.73380e89 q^{82} +2.46149e89 q^{83} +8.47191e88 q^{85} +1.14386e90 q^{86} -1.39069e90 q^{88} +2.79307e89 q^{89} -1.85550e91 q^{91} +2.49759e91 q^{92} -1.20434e92 q^{94} +8.94137e91 q^{95} +3.53812e92 q^{97} -4.75229e91 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 43735426713792 q^{2} + 37\!\cdots\!44 q^{4}+ \cdots - 62\!\cdots\!60 q^{8}+O(q^{10}) \) 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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