LMFDB - Embedded newform 9.94.a.b.1.6

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			1.6
Root			$-2.45391e11$ 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)

$f(q)$	$=$	$q+1.35097e14 q^{2} +8.34770e27 q^{4} -3.52234e32 q^{5} -7.46408e38 q^{7} -2.10186e41 q^{8} +O(q^{10})$	\(q+1.35097e14 q^{2} +8.34770e27 q^{4} -3.52234e32 q^{5} -7.46408e38 q^{7} -2.10186e41 q^{8} -4.75858e46 q^{10} +9.09961e47 q^{11} -6.25337e51 q^{13} -1.00838e53 q^{14} -1.11067e56 q^{16} -2.83546e57 q^{17} -8.20370e57 q^{19} -2.94035e60 q^{20} +1.22933e62 q^{22} +2.05771e63 q^{23} +2.30946e64 q^{25} -8.44812e65 q^{26} -6.23079e66 q^{28} -1.94947e68 q^{29} +8.59696e68 q^{31} -1.29233e70 q^{32} -3.83062e71 q^{34} +2.62910e71 q^{35} +9.63679e71 q^{37} -1.10830e72 q^{38} +7.40347e73 q^{40} -1.11843e75 q^{41} -1.49706e76 q^{43} +7.59609e75 q^{44} +2.77991e77 q^{46} +6.74418e75 q^{47} -3.37039e78 q^{49} +3.12001e78 q^{50} -5.22013e79 q^{52} -2.18289e80 q^{53} -3.20519e80 q^{55} +1.56885e80 q^{56} -2.63368e82 q^{58} +4.18777e82 q^{59} +3.83206e82 q^{61} +1.16142e83 q^{62} -6.45940e83 q^{64} +2.20265e84 q^{65} +2.76024e84 q^{67} -2.36696e85 q^{68} +3.55184e85 q^{70} -1.96031e86 q^{71} -1.54628e86 q^{73} +1.30190e86 q^{74} -6.84821e85 q^{76} -6.79202e86 q^{77} +8.28611e87 q^{79} +3.91216e88 q^{80} -1.51096e89 q^{82} -1.06612e89 q^{83} +9.98745e89 q^{85} -2.02248e90 q^{86} -1.91261e89 q^{88} +1.04123e90 q^{89} +4.66757e90 q^{91} +1.71772e91 q^{92} +9.11120e89 q^{94} +2.88962e90 q^{95} -3.92105e92 q^{97} -4.55330e92 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.35097e14	1.35754	0.678768	−	0.734353i	$-0.262514\pi$
$2$	1.35097e14	1.35754	0.678768	+	0.734353i	$0.262514\pi$
$3$	0	0
$3$	0	0
$4$	8.34770e27	0.842903
$5$	−3.52234e32	−1.10848	−0.554238	−	0.832358i	$-0.686990\pi$
$5$	−3.52234e32	−1.10848	−0.554238	+	0.832358i	$0.686990\pi$
$6$	0	0
$7$	−7.46408e38	−0.376632	−0.188316	−	0.982108i	$-0.560303\pi$
$7$	−7.46408e38	−0.376632	−0.188316	+	0.982108i	$0.560303\pi$
$8$	−2.10186e41	−0.213265
$9$	0	0
$10$	−4.75858e46	−1.50479
$11$	9.09961e47	0.342187	0.171093	−	0.985255i	$-0.445270\pi$
$11$	9.09961e47	0.342187	0.171093	+	0.985255i	$0.445270\pi$
$12$	0	0
$13$	−6.25337e51	−0.994829	−0.497414	−	0.867513i	$-0.665717\pi$
$13$	−6.25337e51	−0.994829	−0.497414	+	0.867513i	$0.665717\pi$
$14$	−1.00838e53	−0.511291
$15$	0	0
$16$	−1.11067e56	−1.13242
$17$	−2.83546e57	−1.72484	−0.862420	−	0.506194i	$-0.831052\pi$
$17$	−2.83546e57	−1.72484	−0.862420	+	0.506194i	$0.831052\pi$
$18$	0	0
$19$	−8.20370e57	−0.0283118	−0.0141559	−	0.999900i	$-0.504506\pi$
$19$	−8.20370e57	−0.0283118	−0.0141559	+	0.999900i	$0.504506\pi$
$20$	−2.94035e60	−0.934337
$21$	0	0
$22$	1.22933e62	0.464531
$23$	2.05771e63	0.984102	0.492051	−	0.870566i	$-0.336247\pi$
$23$	2.05771e63	0.984102	0.492051	+	0.870566i	$0.336247\pi$
$24$	0	0
$25$	2.30946e64	0.228717
$26$	−8.44812e65	−1.35052
$27$	0	0
$28$	−6.23079e66	−0.317464
$29$	−1.94947e68	−1.94272	−0.971360	−	0.237611i	$-0.923636\pi$
$29$	−1.94947e68	−1.94272	−0.971360	+	0.237611i	$0.923636\pi$
$30$	0	0
$31$	8.59696e68	0.385502	0.192751	−	0.981248i	$-0.438259\pi$
$31$	8.59696e68	0.385502	0.192751	+	0.981248i	$0.438259\pi$
$32$	−1.29233e70	−1.32403
$33$	0	0
$34$	−3.83062e71	−2.34153
$35$	2.62910e71	0.417487
$36$	0	0
$37$	9.63679e71	0.115492	0.0577461	−	0.998331i	$-0.481609\pi$
$37$	9.63679e71	0.115492	0.0577461	+	0.998331i	$0.481609\pi$
$38$	−1.10830e72	−0.0384343
$39$	0	0
$40$	7.40347e73	0.236399
$41$	−1.11843e75	−1.13281	−0.566406	−	0.824126i	$-0.691667\pi$
$41$	−1.11843e75	−1.13281	−0.566406	+	0.824126i	$0.691667\pi$
$42$	0	0
$43$	−1.49706e76	−1.65560	−0.827799	−	0.561025i	$-0.810407\pi$
$43$	−1.49706e76	−1.65560	−0.827799	+	0.561025i	$0.810407\pi$
$44$	7.59609e75	0.288430
$45$	0	0
$46$	2.77991e77	1.33595
$47$	6.74418e75	0.0119228	0.00596141	−	0.999982i	$-0.498102\pi$
$47$	6.74418e75	0.0119228	0.00596141	+	0.999982i	$0.498102\pi$
$48$	0	0
$49$	−3.37039e78	−0.858148
$50$	3.12001e78	0.310492
$51$	0	0
$52$	−5.22013e79	−0.838544
$53$	−2.18289e80	−1.44612	−0.723060	−	0.690785i	$-0.757265\pi$
$53$	−2.18289e80	−1.44612	−0.723060	+	0.690785i	$0.757265\pi$
$54$	0	0
$55$	−3.20519e80	−0.379305
$56$	1.56885e80	0.0803225
$57$	0	0
$58$	−2.63368e82	−2.63731
$59$	4.18777e82	1.89393	0.946965	−	0.321337i	$-0.104132\pi$
$59$	4.18777e82	1.89393	0.946965	+	0.321337i	$0.104132\pi$
$60$	0	0
$61$	3.83206e82	0.367786	0.183893	−	0.982946i	$-0.441130\pi$
$61$	3.83206e82	0.367786	0.183893	+	0.982946i	$0.441130\pi$
$62$	1.16142e83	0.523332
$63$	0	0
$64$	−6.45940e83	−0.665003
$65$	2.20265e84	1.10274
$66$	0	0
$67$	2.76024e84	0.337651	0.168826	−	0.985646i	$-0.446003\pi$
$67$	2.76024e84	0.337651	0.168826	+	0.985646i	$0.446003\pi$
$68$	−2.36696e85	−1.45387
$69$	0	0
$70$	3.55184e85	0.566754
$71$	−1.96031e86	−1.61738	−0.808691	−	0.588234i	$-0.799824\pi$
$71$	−1.96031e86	−1.61738	−0.808691	+	0.588234i	$0.799824\pi$
$72$	0	0
$73$	−1.54628e86	−0.350570	−0.175285	−	0.984518i	$-0.556085\pi$
$73$	−1.54628e86	−0.350570	−0.175285	+	0.984518i	$0.556085\pi$
$74$	1.30190e86	0.156785
$75$	0	0
$76$	−6.84821e85	−0.0238641
$77$	−6.79202e86	−0.128878
$78$	0	0
$79$	8.28611e87	0.477190	0.238595	−	0.971119i	$-0.423313\pi$
$79$	8.28611e87	0.477190	0.238595	+	0.971119i	$0.423313\pi$
$80$	3.91216e88	1.25526
$81$	0	0
$82$	−1.51096e89	−1.53783
$83$	−1.06612e89	−0.617552	−0.308776	−	0.951135i	$-0.599919\pi$
$83$	−1.06612e89	−0.617552	−0.308776	+	0.951135i	$0.599919\pi$
$84$	0	0
$85$	9.98745e89	1.91194
$86$	−2.02248e90	−2.24753
$87$	0	0
$88$	−1.91261e89	−0.0729765
$89$	1.04123e90	0.234916	0.117458	−	0.993078i	$-0.462525\pi$
$89$	1.04123e90	0.234916	0.117458	+	0.993078i	$0.462525\pi$
$90$	0	0
$91$	4.66757e90	0.374684
$92$	1.71772e91	0.829503
$93$	0	0
$94$	9.11120e89	0.0161857
$95$	2.88962e90	0.0313829
$96$	0	0
$97$	−3.92105e92	−1.61628	−0.808141	−	0.588990i	$-0.799526\pi$
$97$	−3.92105e92	−1.61628	−0.808141	+	0.588990i	$0.799526\pi$
$98$	−4.55330e92	−1.16497
$99$	0	0
$100$	1.92787e92	0.192787
$101$	−9.67912e92	−0.609385	−0.304693	−	0.952451i	$-0.598554\pi$
$101$	−9.67912e92	−0.609385	−0.304693	+	0.952451i	$0.598554\pi$
$102$	0	0
$103$	9.38508e92	0.237414	0.118707	−	0.992929i	$-0.462125\pi$
$103$	9.38508e92	0.237414	0.118707	+	0.992929i	$0.462125\pi$
$104$	1.31437e93	0.212162
$105$	0	0
$106$	−2.94902e94	−1.96316
$107$	8.54504e93	0.367594	0.183797	−	0.982964i	$-0.441161\pi$
$107$	8.54504e93	0.367594	0.183797	+	0.982964i	$0.441161\pi$
$108$	0	0
$109$	−7.14180e94	−1.29860	−0.649300	−	0.760532i	$-0.724938\pi$
$109$	−7.14180e94	−1.29860	−0.649300	+	0.760532i	$0.724938\pi$
$110$	−4.33012e94	−0.514921
$111$	0	0
$112$	8.29014e94	0.426505
$113$	2.74778e95	0.935050	0.467525	−	0.883980i	$-0.345146\pi$
$113$	2.74778e95	0.935050	0.467525	+	0.883980i	$0.345146\pi$
$114$	0	0
$115$	−7.24796e95	−1.09085
$116$	−1.62736e96	−1.63752
$117$	0	0
$118$	5.65755e96	2.57108
$119$	2.11641e96	0.649630
$120$	0	0
$121$	−6.24360e96	−0.882908
$122$	5.17701e96	0.499283
$123$	0	0
$124$	7.17649e96	0.324940
$125$	2.74319e97	0.854948
$126$	0	0
$127$	2.13172e97	0.317582	0.158791	−	0.987312i	$-0.449240\pi$
$127$	2.13172e97	0.317582	0.158791	+	0.987312i	$0.449240\pi$
$128$	4.07212e97	0.421267
$129$	0	0
$130$	2.97572e98	1.49701
$131$	3.85452e98	1.35786	0.678929	−	0.734204i	$-0.262444\pi$
$131$	3.85452e98	1.35786	0.678929	+	0.734204i	$0.262444\pi$
$132$	0	0
$133$	6.12330e96	0.0106631
$134$	3.72900e98	0.458374
$135$	0	0
$136$	5.95974e98	0.367848
$137$	1.13582e98	0.0498660	0.0249330	−	0.999689i	$-0.492063\pi$
$137$	1.13582e98	0.0498660	0.0249330	+	0.999689i	$0.492063\pi$
$138$	0	0
$139$	−1.16575e99	−0.260867	−0.130433	−	0.991457i	$-0.541637\pi$
$139$	−1.16575e99	−0.260867	−0.130433	+	0.991457i	$0.541637\pi$
$140$	2.19470e99	0.351901
$141$	0	0
$142$	−2.64833e100	−2.19565
$143$	−5.69033e99	−0.340417
$144$	0	0
$145$	6.86671e100	2.15346
$146$	−2.08897e100	−0.475911
$147$	0	0
$148$	8.04451e99	0.0973486
$149$	8.82955e100	0.781227	0.390613	−	0.920555i	$-0.372263\pi$
$149$	8.82955e100	0.781227	0.390613	+	0.920555i	$0.372263\pi$
$150$	0	0
$151$	−2.05344e101	−0.977357	−0.488679	−	0.872464i	$-0.662521\pi$
$151$	−2.05344e101	−0.977357	−0.488679	+	0.872464i	$0.662521\pi$
$152$	1.72430e99	0.00603791
$153$	0	0
$154$	−9.17583e100	−0.174957
$155$	−3.02814e101	−0.427319
$156$	0	0
$157$	−7.80688e101	−0.606937	−0.303469	−	0.952841i	$-0.598145\pi$
$157$	−7.80688e101	−0.606937	−0.303469	+	0.952841i	$0.598145\pi$
$158$	1.11943e102	0.647802
$159$	0	0
$160$	4.55202e102	1.46766
$161$	−1.53589e102	−0.370645
$162$	0	0
$163$	−3.76190e102	−0.511309	−0.255655	−	0.966768i	$-0.582291\pi$
$163$	−3.76190e102	−0.511309	−0.255655	+	0.966768i	$0.582291\pi$
$164$	−9.33629e102	−0.954850
$165$	0	0
$166$	−1.44029e103	−0.838348
$167$	−2.37736e103	−1.04659	−0.523297	−	0.852150i	$-0.675298\pi$
$167$	−2.37736e103	−1.04659	−0.523297	+	0.852150i	$0.675298\pi$
$168$	0	0
$169$	−4.07583e101	−0.0103154
$170$	1.34928e104	2.59553
$171$	0	0
$172$	−1.24970e104	−1.39551
$173$	5.20572e102	0.0443953	0.0221976	−	0.999754i	$-0.492934\pi$
$173$	5.20572e102	0.0443953	0.0221976	+	0.999754i	$0.492934\pi$
$174$	0	0
$175$	−1.72380e103	−0.0861423
$176$	−1.01067e104	−0.387498
$177$	0	0
$178$	1.40668e104	0.318907
$179$	7.50757e104	1.31170	0.655849	−	0.754893i	$-0.272311\pi$
$179$	7.50757e104	1.31170	0.655849	+	0.754893i	$0.272311\pi$
$180$	0	0
$181$	8.74638e104	0.911538	0.455769	−	0.890098i	$-0.349364\pi$
$181$	8.74638e104	0.911538	0.455769	+	0.890098i	$0.349364\pi$
$182$	6.30575e104	0.508648
$183$	0	0
$184$	−4.32503e104	−0.209875
$185$	−3.39441e104	−0.128020
$186$	0	0
$187$	−2.58016e105	−0.590217
$188$	5.62985e103	0.0100498
$189$	0	0
$190$	3.90379e104	0.0426034
$191$	1.94469e106	1.66264	0.831320	−	0.555795i	$-0.187586\pi$
$191$	1.94469e106	1.66264	0.831320	+	0.555795i	$0.187586\pi$
$192$	0	0
$193$	3.62395e105	0.190883	0.0954415	−	0.995435i	$-0.469574\pi$
$193$	3.62395e105	0.190883	0.0954415	+	0.995435i	$0.469574\pi$
$194$	−5.29723e106	−2.19416
$195$	0	0
$196$	−2.81350e106	−0.723336
$197$	−3.73179e106	−0.757247	−0.378623	−	0.925551i	$-0.623602\pi$
$197$	−3.73179e106	−0.757247	−0.378623	+	0.925551i	$0.623602\pi$
$198$	0	0
$199$	−5.95317e106	−0.755232	−0.377616	−	0.925962i	$-0.623256\pi$
$199$	−5.95317e106	−0.755232	−0.377616	+	0.925962i	$0.623256\pi$
$200$	−4.85416e105	−0.0487774
$201$	0	0
$202$	−1.30762e107	−0.827262
$203$	1.45510e107	0.731691
$204$	0	0
$205$	3.93948e107	1.25569
$206$	1.26790e107	0.322299
$207$	0	0
$208$	6.94545e107	1.12656
$209$	−7.46505e105	−0.00968792
$210$	0	0
$211$	1.07157e108	0.893071	0.446535	−	0.894766i	$-0.352658\pi$
$211$	1.07157e108	0.893071	0.446535	+	0.894766i	$0.352658\pi$
$212$	−1.82221e108	−1.21894
$213$	0	0
$214$	1.15441e108	0.499022
$215$	5.27314e108	1.83519
$216$	0	0
$217$	−6.41684e107	−0.145192
$218$	−9.64837e108	−1.76290
$219$	0	0
$220$	−2.67560e108	−0.319718
$221$	1.77312e109	1.71592
$222$	0	0
$223$	−1.79075e109	−1.13988	−0.569939	−	0.821687i	$-0.693033\pi$
$223$	−1.79075e109	−1.13988	−0.569939	+	0.821687i	$0.693033\pi$
$224$	9.64603e108	0.498673
$225$	0	0
$226$	3.71217e109	1.26936
$227$	−5.85209e109	−1.62970	−0.814851	−	0.579670i	$-0.803181\pi$
$227$	−5.85209e109	−1.62970	−0.814851	+	0.579670i	$0.803181\pi$
$228$	0	0
$229$	−2.36374e109	−0.437774	−0.218887	−	0.975750i	$-0.570243\pi$
$229$	−2.36374e109	−0.437774	−0.218887	+	0.975750i	$0.570243\pi$
$230$	−9.79179e109	−1.48087
$231$	0	0
$232$	4.09752e109	0.414314
$233$	1.31479e110	1.08845	0.544224	−	0.838940i	$-0.316824\pi$
$233$	1.31479e110	1.08845	0.544224	+	0.838940i	$0.316824\pi$
$234$	0	0
$235$	−2.37553e108	−0.0132162
$236$	3.49582e110	1.59640
$237$	0	0
$238$	2.85921e110	0.881896
$239$	5.33449e110	1.35391	0.676957	−	0.736023i	$-0.263298\pi$
$239$	5.33449e110	1.35391	0.676957	+	0.736023i	$0.263298\pi$
$240$	0	0
$241$	2.92728e110	0.504280	0.252140	−	0.967691i	$-0.418866\pi$
$241$	2.92728e110	0.504280	0.252140	+	0.967691i	$0.418866\pi$
$242$	−8.43493e110	−1.19858
$243$	0	0
$244$	3.19889e110	0.310008
$245$	1.18717e111	0.951236
$246$	0	0
$247$	5.13008e109	0.0281654
$248$	−1.80696e110	−0.0822140
$249$	0	0
$250$	3.70596e111	1.16062
$251$	4.28523e111	1.11467	0.557334	−	0.830288i	$-0.311824\pi$
$251$	4.28523e111	1.11467	0.557334	+	0.830288i	$0.311824\pi$
$252$	0	0
$253$	1.87244e111	0.336747
$254$	2.87989e111	0.431129
$255$	0	0
$256$	1.18984e112	1.23689
$257$	−9.96450e111	−0.864102	−0.432051	−	0.901849i	$-0.642210\pi$
$257$	−9.96450e111	−0.864102	−0.432051	+	0.901849i	$0.642210\pi$
$258$	0	0
$259$	−7.19298e110	−0.0434980
$260$	1.83871e112	0.929505
$261$	0	0
$262$	5.20734e112	1.84334
$263$	−3.07644e112	−0.912233	−0.456116	−	0.889920i	$-0.650760\pi$
$263$	−3.07644e112	−0.912233	−0.456116	+	0.889920i	$0.650760\pi$
$264$	0	0
$265$	7.68889e112	1.60299
$266$	8.27241e110	0.0144756
$267$	0	0
$268$	2.30417e112	0.284607
$269$	8.31534e112	0.863771	0.431886	−	0.901928i	$-0.357848\pi$
$269$	8.31534e112	0.863771	0.431886	+	0.901928i	$0.357848\pi$
$270$	0	0
$271$	1.06596e113	0.784638	0.392319	−	0.919829i	$-0.371673\pi$
$271$	1.06596e113	0.784638	0.392319	+	0.919829i	$0.371673\pi$
$272$	3.14927e113	1.95324
$273$	0	0
$274$	1.53447e112	0.0676949
$275$	2.10152e112	0.0782641
$276$	0	0
$277$	5.26210e113	1.39910	0.699551	−	0.714582i	$-0.253383\pi$
$277$	5.26210e113	1.39910	0.699551	+	0.714582i	$0.253383\pi$
$278$	−1.57490e113	−0.354136
$279$	0	0
$280$	−5.52601e112	−0.0890355
$281$	9.84704e113	1.34419	0.672097	−	0.740463i	$-0.265394\pi$
$281$	9.84704e113	1.34419	0.672097	+	0.740463i	$0.265394\pi$
$282$	0	0
$283$	8.24676e113	0.809494	0.404747	−	0.914429i	$-0.367360\pi$
$283$	8.24676e113	0.809494	0.404747	+	0.914429i	$0.367360\pi$
$284$	−1.63641e114	−1.36330
$285$	0	0
$286$	−7.68747e113	−0.462128
$287$	8.34802e113	0.426653
$288$	0	0
$289$	5.33743e114	1.97507
$290$	9.27672e114	2.92340
$291$	0	0
$292$	−1.29079e114	−0.295496
$293$	−5.87130e114	−1.14654	−0.573271	−	0.819366i	$-0.694326\pi$
$293$	−5.87130e114	−1.14654	−0.573271	+	0.819366i	$0.694326\pi$
$294$	0	0
$295$	−1.47507e115	−2.09937
$296$	−2.02552e113	−0.0246304
$297$	0	0
$298$	1.19285e115	1.06054
$299$	−1.28676e115	−0.979014
$300$	0	0
$301$	1.11741e115	0.623551
$302$	−2.77413e115	−1.32680
$303$	0	0
$304$	9.11162e113	0.0320608
$305$	−1.34978e115	−0.407682
$306$	0	0
$307$	−8.62573e115	−1.92248	−0.961239	−	0.275716i	$-0.911085\pi$
$307$	−8.62573e115	−1.92248	−0.961239	+	0.275716i	$0.911085\pi$
$308$	−5.66978e114	−0.108632
$309$	0	0
$310$	−4.09093e115	−0.580101
$311$	1.13306e116	1.38323	0.691615	−	0.722266i	$-0.256900\pi$
$311$	1.13306e116	1.38323	0.691615	+	0.722266i	$0.256900\pi$
$312$	0	0
$313$	−8.92421e115	−0.808646	−0.404323	−	0.914616i	$-0.632493\pi$
$313$	−8.92421e115	−0.808646	−0.404323	+	0.914616i	$0.632493\pi$
$314$	−1.05469e116	−0.823939
$315$	0	0
$316$	6.91700e115	0.402225
$317$	−2.05159e116	−1.03000	−0.514998	−	0.857191i	$-0.672207\pi$
$317$	−2.05159e116	−1.03000	−0.514998	+	0.857191i	$0.672207\pi$
$318$	0	0
$319$	−1.77395e116	−0.664773
$320$	2.27522e116	0.737140
$321$	0	0
$322$	−2.07495e116	−0.503163
$323$	2.32613e115	0.0488333
$324$	0	0
$325$	−1.44419e116	−0.227535
$326$	−5.08222e116	−0.694121
$327$	0	0
$328$	2.35078e116	0.241589
$329$	−5.03391e114	−0.00449052
$330$	0	0
$331$	−2.73551e117	−1.84093	−0.920463	−	0.390830i	$-0.872188\pi$
$331$	−2.73551e117	−1.84093	−0.920463	+	0.390830i	$0.872188\pi$
$332$	−8.89963e116	−0.520536
$333$	0	0
$334$	−3.21174e117	−1.42079
$335$	−9.72250e116	−0.374278
$336$	0	0
$337$	1.32552e117	0.386897	0.193449	−	0.981110i	$-0.438033\pi$
$337$	1.32552e117	0.386897	0.193449	+	0.981110i	$0.438033\pi$
$338$	−5.50633e115	−0.0140035
$339$	0	0
$340$	8.33723e117	1.61158
$341$	7.82290e116	0.131914
$342$	0	0
$343$	5.44721e117	0.699838
$344$	3.14660e117	0.353081
$345$	0	0
$346$	7.03278e116	0.0602682
$347$	2.48219e118	1.86001	0.930003	−	0.367551i	$-0.119804\pi$
$347$	2.48219e118	1.86001	0.930003	+	0.367551i	$0.119804\pi$
$348$	0	0
$349$	2.09671e118	1.20270	0.601349	−	0.798986i	$-0.294630\pi$
$349$	2.09671e118	1.20270	0.601349	+	0.798986i	$0.294630\pi$
$350$	−2.32880e117	−0.116941
$351$	0	0
$352$	−1.17597e118	−0.453066
$353$	−9.35602e117	−0.315913	−0.157956	−	0.987446i	$-0.550491\pi$
$353$	−9.35602e117	−0.315913	−0.157956	+	0.987446i	$0.550491\pi$
$354$	0	0
$355$	6.90489e118	1.79283
$356$	8.69192e117	0.198012
$357$	0	0
$358$	1.01425e119	1.78068
$359$	−5.71223e118	−0.880873	−0.440437	−	0.897784i	$-0.645176\pi$
$359$	−5.71223e118	−0.880873	−0.440437	+	0.897784i	$0.645176\pi$
$360$	0	0
$361$	−8.38951e118	−0.999198
$362$	1.18161e119	1.23745
$363$	0	0
$364$	3.89635e118	0.315823
$365$	5.44651e118	0.388598
$366$	0	0
$367$	−1.03136e119	−0.570740	−0.285370	−	0.958417i	$-0.592117\pi$
$367$	−1.03136e119	−0.570740	−0.285370	+	0.958417i	$0.592117\pi$
$368$	−2.28544e119	−1.11441
$369$	0	0
$370$	−4.58574e118	−0.173792
$371$	1.62933e119	0.544655
$372$	0	0
$373$	−3.06101e119	−0.796900	−0.398450	−	0.917190i	$-0.630452\pi$
$373$	−3.06101e119	−0.796900	−0.398450	+	0.917190i	$0.630452\pi$
$374$	−3.48572e119	−0.801241
$375$	0	0
$376$	−1.41753e117	−0.00254272
$377$	1.21908e120	1.93267
$378$	0	0
$379$	−6.87675e119	−0.852432	−0.426216	−	0.904621i	$-0.640154\pi$
$379$	−6.87675e119	−0.852432	−0.426216	+	0.904621i	$0.640154\pi$
$380$	2.41217e118	0.0264527
$381$	0	0
$382$	2.62722e120	2.25709
$383$	−2.22549e120	−1.69310	−0.846549	−	0.532311i	$-0.821324\pi$
$383$	−2.22549e120	−1.69310	−0.846549	+	0.532311i	$0.821324\pi$
$384$	0	0
$385$	2.39238e119	0.142859
$386$	4.89585e119	0.259130
$387$	0	0
$388$	−3.27318e120	−1.36237
$389$	3.21512e118	0.0118724	0.00593622	−	0.999982i	$-0.498110\pi$
$389$	3.21512e118	0.0118724	0.00593622	+	0.999982i	$0.498110\pi$
$390$	0	0
$391$	−5.83456e120	−1.69742
$392$	7.08409e119	0.183013
$393$	0	0
$394$	−5.04154e120	−1.02799
$395$	−2.91865e120	−0.528953
$396$	0	0
$397$	3.63725e119	0.0521212	0.0260606	−	0.999660i	$-0.491704\pi$
$397$	3.63725e119	0.0521212	0.0260606	+	0.999660i	$0.491704\pi$
$398$	−8.04256e120	−1.02525
$399$	0	0
$400$	−2.56505e120	−0.259004
$401$	−6.87560e120	−0.618155	−0.309078	−	0.951037i	$-0.600020\pi$
$401$	−6.87560e120	−0.618155	−0.309078	+	0.951037i	$0.600020\pi$
$402$	0	0
$403$	−5.37600e120	−0.383508
$404$	−8.07984e120	−0.513653
$405$	0	0
$406$	1.96580e121	0.993296
$407$	8.76911e119	0.0395199
$408$	0	0
$409$	6.34026e120	0.227496	0.113748	−	0.993510i	$-0.463714\pi$
$409$	6.34026e120	0.227496	0.113748	+	0.993510i	$0.463714\pi$
$410$	5.32212e121	1.70465
$411$	0	0
$412$	7.83439e120	0.200117
$413$	−3.12578e121	−0.713315
$414$	0	0
$415$	3.75522e121	0.684541
$416$	8.08140e121	1.31719
$417$	0	0
$418$	−1.00851e120	−0.0131517
$419$	1.47579e121	0.172215	0.0861077	−	0.996286i	$-0.472557\pi$
$419$	1.47579e121	0.172215	0.0861077	+	0.996286i	$0.472557\pi$
$420$	0	0
$421$	2.72550e121	0.254876	0.127438	−	0.991847i	$-0.459325\pi$
$421$	2.72550e121	0.254876	0.127438	+	0.991847i	$0.459325\pi$
$422$	1.44766e122	1.21238
$423$	0	0
$424$	4.58814e121	0.308407
$425$	−6.54837e121	−0.394501
$426$	0	0
$427$	−2.86028e121	−0.138520
$428$	7.13315e121	0.309846
$429$	0	0
$430$	7.12386e122	2.49133
$431$	−7.42351e121	−0.233032	−0.116516	−	0.993189i	$-0.537173\pi$
$431$	−7.42351e121	−0.233032	−0.116516	+	0.993189i	$0.537173\pi$
$432$	0	0
$433$	−3.19233e122	−0.808016	−0.404008	−	0.914755i	$-0.632383\pi$
$433$	−3.19233e122	−0.808016	−0.404008	+	0.914755i	$0.632383\pi$
$434$	−8.66896e121	−0.197104
$435$	0	0
$436$	−5.96177e122	−1.09459
$437$	−1.68809e121	−0.0278617
$438$	0	0
$439$	−9.54354e121	−0.127382	−0.0636912	−	0.997970i	$-0.520287\pi$
$439$	−9.54354e121	−0.127382	−0.0636912	+	0.997970i	$0.520287\pi$
$440$	6.73687e121	0.0808926
$441$	0	0
$442$	2.39543e123	2.32942
$443$	9.34021e122	0.817680	0.408840	−	0.912606i	$-0.365933\pi$
$443$	9.34021e122	0.817680	0.408840	+	0.912606i	$0.365933\pi$
$444$	0	0
$445$	−3.66758e122	−0.260399
$446$	−2.41925e123	−1.54742
$447$	0	0
$448$	4.82135e122	0.250461
$449$	9.82334e122	0.460049	0.230025	−	0.973185i	$-0.426119\pi$
$449$	9.82334e122	0.460049	0.230025	+	0.973185i	$0.426119\pi$
$450$	0	0
$451$	−1.01772e123	−0.387633
$452$	2.29377e123	0.788156
$453$	0	0
$454$	−7.90600e123	−2.21238
$455$	−1.64408e123	−0.415328
$456$	0	0
$457$	3.72271e122	0.0766930	0.0383465	−	0.999265i	$-0.487791\pi$
$457$	3.72271e122	0.0766930	0.0383465	+	0.999265i	$0.487791\pi$
$458$	−3.19334e123	−0.594293
$459$	0	0
$460$	−6.05038e123	−0.919483
$461$	3.32371e123	0.456594	0.228297	−	0.973591i	$-0.426684\pi$
$461$	3.32371e123	0.456594	0.228297	+	0.973591i	$0.426684\pi$
$462$	0	0
$463$	−9.17903e123	−1.03105	−0.515526	−	0.856874i	$-0.672404\pi$
$463$	−9.17903e123	−1.03105	−0.515526	+	0.856874i	$0.672404\pi$
$464$	2.16523e124	2.19997
$465$	0	0
$466$	1.77625e124	1.47761
$467$	−1.99340e124	−1.50093	−0.750464	−	0.660911i	$-0.770170\pi$
$467$	−1.99340e124	−1.50093	−0.750464	+	0.660911i	$0.770170\pi$
$468$	0	0
$469$	−2.06026e123	−0.127170
$470$	−3.20927e122	−0.0179414
$471$	0	0
$472$	−8.80211e123	−0.403909
$473$	−1.36226e124	−0.566524
$474$	0	0
$475$	−1.89461e122	−0.00647540
$476$	1.76672e124	0.547575
$477$	0	0
$478$	7.20675e124	1.83799
$479$	1.27783e124	0.295714	0.147857	−	0.989009i	$-0.452762\pi$
$479$	1.27783e124	0.295714	0.147857	+	0.989009i	$0.452762\pi$
$480$	0	0
$481$	−6.02625e123	−0.114895
$482$	3.95467e124	0.684578
$483$	0	0
$484$	−5.21198e124	−0.744206
$485$	1.38113e125	1.79161
$486$	0	0
$487$	3.04606e124	0.326319	0.163160	−	0.986600i	$-0.447831\pi$
$487$	3.04606e124	0.326319	0.163160	+	0.986600i	$0.447831\pi$
$488$	−8.05447e123	−0.0784360
$489$	0	0
$490$	1.60383e125	1.29134
$491$	5.25589e124	0.384908	0.192454	−	0.981306i	$-0.438355\pi$
$491$	5.25589e124	0.384908	0.192454	+	0.981306i	$0.438355\pi$
$492$	0	0
$493$	5.52765e125	3.35088
$494$	6.93059e123	0.0382355
$495$	0	0
$496$	−9.54841e124	−0.436549
$497$	1.46319e125	0.609158
$498$	0	0
$499$	−4.67925e125	−1.61622	−0.808110	−	0.589031i	$-0.799509\pi$
$499$	−4.67925e125	−1.61622	−0.808110	+	0.589031i	$0.799509\pi$
$500$	2.28993e125	0.720638
$501$	0	0
$502$	5.78922e125	1.51320
$503$	4.59038e125	1.09380	0.546899	−	0.837199i	$-0.315808\pi$
$503$	4.59038e125	1.09380	0.546899	+	0.837199i	$0.315808\pi$
$504$	0	0
$505$	3.40931e125	0.675489
$506$	2.52961e125	0.457146
$507$	0	0
$508$	1.77949e125	0.267691
$509$	7.31205e125	1.00384	0.501918	−	0.864915i	$-0.332628\pi$
$509$	7.31205e125	1.00384	0.501918	+	0.864915i	$0.332628\pi$
$510$	0	0
$511$	1.15415e125	0.132036
$512$	1.20416e126	1.25785
$513$	0	0
$514$	−1.34617e126	−1.17305
$515$	−3.30574e125	−0.263168
$516$	0	0
$517$	6.13695e123	0.00407983
$518$	−9.71750e124	−0.0590501
$519$	0	0
$520$	−4.62967e125	−0.235177
$521$	−2.01287e126	−0.935106	−0.467553	−	0.883965i	$-0.654864\pi$
$521$	−2.01287e126	−0.935106	−0.467553	+	0.883965i	$0.654864\pi$
$522$	0	0
$523$	2.88184e126	1.12032	0.560159	−	0.828385i	$-0.310740\pi$
$523$	2.88184e126	1.12032	0.560159	+	0.828385i	$0.310740\pi$
$524$	3.21764e126	1.14454
$525$	0	0
$526$	−4.15618e126	−1.23839
$527$	−2.43763e126	−0.664929
$528$	0	0
$529$	−1.37907e125	−0.0315425
$530$	1.03875e127	2.17611
$531$	0	0
$532$	5.11155e124	0.00898798
$533$	6.99393e126	1.12695
$534$	0	0
$535$	−3.00985e126	−0.407469
$536$	−5.80164e125	−0.0720092
$537$	0	0
$538$	1.12338e127	1.17260
$539$	−3.06692e126	−0.293647
$540$	0	0
$541$	1.14287e127	0.921133	0.460567	−	0.887625i	$-0.347646\pi$
$541$	1.14287e127	0.921133	0.460567	+	0.887625i	$0.347646\pi$
$542$	1.44008e127	1.06517
$543$	0	0
$544$	3.66434e127	2.28374
$545$	2.51559e127	1.43947
$546$	0	0
$547$	−1.73528e127	−0.837450	−0.418725	−	0.908113i	$-0.637523\pi$
$547$	−1.73528e127	−0.837450	−0.418725	+	0.908113i	$0.637523\pi$
$548$	9.48152e125	0.0420322
$549$	0	0
$550$	2.83909e126	0.106246
$551$	1.59929e126	0.0550019
$552$	0	0
$553$	−6.18482e126	−0.179725
$554$	7.10894e127	1.89933
$555$	0	0
$556$	−9.73137e126	−0.219885
$557$	3.51533e127	0.730634	0.365317	−	0.930883i	$-0.380961\pi$
$557$	3.51533e127	0.730634	0.365317	+	0.930883i	$0.380961\pi$
$558$	0	0
$559$	9.36165e127	1.64704
$560$	−2.92007e127	−0.472770
$561$	0	0
$562$	1.33031e128	1.82479
$563$	7.77831e127	0.982302	0.491151	−	0.871074i	$-0.336576\pi$
$563$	7.77831e127	0.982302	0.491151	+	0.871074i	$0.336576\pi$
$564$	0	0
$565$	−9.67862e127	−1.03648
$566$	1.11411e128	1.09892
$567$	0	0
$568$	4.12031e127	0.344931
$569$	−2.55784e127	−0.197312	−0.0986559	−	0.995122i	$-0.531454\pi$
$569$	−2.55784e127	−0.197312	−0.0986559	+	0.995122i	$0.531454\pi$
$570$	0	0
$571$	3.24099e127	0.212373	0.106186	−	0.994346i	$-0.466136\pi$
$571$	3.24099e127	0.212373	0.106186	+	0.994346i	$0.466136\pi$
$572$	−4.75012e127	−0.286939
$573$	0	0
$574$	1.12779e128	0.579197
$575$	4.75220e127	0.225081
$576$	0	0
$577$	−9.68555e127	−0.390346	−0.195173	−	0.980769i	$-0.562527\pi$
$577$	−9.68555e127	−0.390346	−0.195173	+	0.980769i	$0.562527\pi$
$578$	7.21072e128	2.68123
$579$	0	0
$580$	5.73212e128	1.81516
$581$	7.95758e127	0.232590
$582$	0	0
$583$	−1.98635e128	−0.494843
$584$	3.25006e127	0.0747642
$585$	0	0
$586$	−7.93196e128	−1.55647
$587$	−4.65657e128	−0.844101	−0.422050	−	0.906572i	$-0.638689\pi$
$587$	−4.65657e128	−0.844101	−0.422050	+	0.906572i	$0.638689\pi$
$588$	0	0
$589$	−7.05269e126	−0.0109142
$590$	−1.99278e129	−2.84998
$591$	0	0
$592$	−1.07033e128	−0.130785
$593$	−1.44616e129	−1.63370	−0.816850	−	0.576850i	$-0.804282\pi$
$593$	−1.44616e129	−1.63370	−0.816850	+	0.576850i	$0.804282\pi$
$594$	0	0
$595$	−7.45471e128	−0.720099
$596$	7.37065e128	0.658498
$597$	0	0
$598$	−1.73838e129	−1.32905
$599$	−4.67972e128	−0.331034	−0.165517	−	0.986207i	$-0.552929\pi$
$599$	−4.67972e128	−0.331034	−0.165517	+	0.986207i	$0.552929\pi$
$600$	0	0
$601$	−6.57416e128	−0.398270	−0.199135	−	0.979972i	$-0.563813\pi$
$601$	−6.57416e128	−0.398270	−0.199135	+	0.979972i	$0.563813\pi$
$602$	1.50959e129	0.846493
$603$	0	0
$604$	−1.71415e129	−0.823817
$605$	2.19921e129	0.978682
$606$	0	0
$607$	2.37428e129	0.906270	0.453135	−	0.891442i	$-0.350306\pi$
$607$	2.37428e129	0.906270	0.453135	+	0.891442i	$0.350306\pi$
$608$	1.06019e128	0.0374857
$609$	0	0
$610$	−1.82352e129	−0.553443
$611$	−4.21739e127	−0.0118612
$612$	0	0
$613$	1.90113e129	0.459304	0.229652	−	0.973273i	$-0.426241\pi$
$613$	1.90113e129	0.459304	0.229652	+	0.973273i	$0.426241\pi$
$614$	−1.16531e130	−2.60983
$615$	0	0
$616$	1.42759e128	0.0274853
$617$	7.31692e129	1.30638	0.653188	−	0.757196i	$-0.273431\pi$
$617$	7.31692e129	1.30638	0.653188	+	0.757196i	$0.273431\pi$
$618$	0	0
$619$	3.74623e129	0.575412	0.287706	−	0.957719i	$-0.407107\pi$
$619$	3.74623e129	0.575412	0.287706	+	0.957719i	$0.407107\pi$
$620$	−2.52780e129	−0.360188
$621$	0	0
$622$	1.53073e130	1.87778
$623$	−7.77185e128	−0.0884770
$624$	0	0
$625$	−1.19944e130	−1.17641
$626$	−1.20564e130	−1.09777
$627$	0	0
$628$	−6.51696e129	−0.511589
$629$	−2.73247e129	−0.199205
$630$	0	0
$631$	7.87187e129	0.495122	0.247561	−	0.968872i	$-0.420371\pi$
$631$	7.87187e129	0.495122	0.247561	+	0.968872i	$0.420371\pi$
$632$	−1.74163e129	−0.101768
$633$	0	0
$634$	−2.77164e130	−1.39826
$635$	−7.50863e129	−0.352032
$636$	0	0
$637$	2.10763e130	0.853711
$638$	−2.39655e130	−0.902453
$639$	0	0
$640$	−1.43434e130	−0.466964
$641$	−2.38312e130	−0.721518	−0.360759	−	0.932659i	$-0.617482\pi$
$641$	−2.38312e130	−0.721518	−0.360759	+	0.932659i	$0.617482\pi$
$642$	0	0
$643$	−1.44463e130	−0.378397	−0.189198	−	0.981939i	$-0.560589\pi$
$643$	−1.44463e130	−0.378397	−0.189198	+	0.981939i	$0.560589\pi$
$644$	−1.28212e130	−0.312417
$645$	0	0
$646$	3.14253e129	0.0662929
$647$	−8.21550e130	−1.61282	−0.806409	−	0.591359i	$-0.798592\pi$
$647$	−8.21550e130	−1.61282	−0.806409	+	0.591359i	$0.798592\pi$
$648$	0	0
$649$	3.81071e130	0.648078
$650$	−1.95106e130	−0.308887
$651$	0	0
$652$	−3.14032e130	−0.430984
$653$	5.09920e130	0.651687	0.325843	−	0.945424i	$-0.394352\pi$
$653$	5.09920e130	0.651687	0.325843	+	0.945424i	$0.394352\pi$
$654$	0	0
$655$	−1.35769e131	−1.50515
$656$	1.24220e131	1.28282
$657$	0	0
$658$	−6.80067e128	−0.00609604
$659$	6.44359e130	0.538216	0.269108	−	0.963110i	$-0.413271\pi$
$659$	6.44359e130	0.538216	0.269108	+	0.963110i	$0.413271\pi$
$660$	0	0
$661$	−1.07148e131	−0.777348	−0.388674	−	0.921375i	$-0.627067\pi$
$661$	−1.07148e131	−0.777348	−0.388674	+	0.921375i	$0.627067\pi$
$662$	−3.69559e131	−2.49912
$663$	0	0
$664$	2.24083e130	0.131702
$665$	−2.15684e129	−0.0118198
$666$	0	0
$667$	−4.01145e131	−1.91184
$668$	−1.98455e131	−0.882178
$669$	0	0
$670$	−1.31348e131	−0.508096
$671$	3.48703e130	0.125852
$672$	0	0
$673$	2.53785e131	0.797563	0.398782	−	0.917046i	$-0.369433\pi$
$673$	2.53785e131	0.797563	0.398782	+	0.917046i	$0.369433\pi$
$674$	1.79074e131	0.525226
$675$	0	0
$676$	−3.40238e129	−0.00869484
$677$	1.49446e131	0.356543	0.178271	−	0.983981i	$-0.442950\pi$
$677$	1.49446e131	0.356543	0.178271	+	0.983981i	$0.442950\pi$
$678$	0	0
$679$	2.92670e131	0.608743
$680$	−2.09922e131	−0.407750
$681$	0	0
$682$	1.05685e131	0.179077
$683$	−4.82762e131	−0.764136	−0.382068	−	0.924134i	$-0.624788\pi$
$683$	−4.82762e131	−0.764136	−0.382068	+	0.924134i	$0.624788\pi$
$684$	0	0
$685$	−4.00076e130	−0.0552753
$686$	7.35902e131	0.950055
$687$	0	0
$688$	1.66274e132	1.87483
$689$	1.36504e132	1.43864
$690$	0	0
$691$	−1.60210e132	−1.47557	−0.737786	−	0.675035i	$-0.764128\pi$
$691$	−1.60210e132	−1.47557	−0.737786	+	0.675035i	$0.764128\pi$
$692$	4.34558e130	0.0374209
$693$	0	0
$694$	3.35337e132	2.52503
$695$	4.10618e131	0.289164
$696$	0	0
$697$	3.17125e132	1.95392
$698$	2.83260e132	1.63271
$699$	0	0
$700$	−1.43897e131	−0.0726096
$701$	6.59869e131	0.311580	0.155790	−	0.987790i	$-0.450208\pi$
$701$	6.59869e131	0.311580	0.155790	+	0.987790i	$0.450208\pi$
$702$	0	0
$703$	−7.90574e129	−0.00326979
$704$	−5.87781e131	−0.227555
$705$	0	0
$706$	−1.26397e132	−0.428863
$707$	7.22457e131	0.229514
$708$	0	0
$709$	−1.94700e132	−0.542397	−0.271198	−	0.962524i	$-0.587420\pi$
$709$	−1.94700e132	−0.542397	−0.271198	+	0.962524i	$0.587420\pi$
$710$	9.32831e132	2.43383
$711$	0	0
$712$	−2.18853e131	−0.0500994
$713$	1.76901e132	0.379373
$714$	0	0
$715$	2.00433e132	0.377344
$716$	6.26710e132	1.10563
$717$	0	0
$718$	−7.71705e132	−1.19582
$719$	−9.78644e132	−1.42145	−0.710725	−	0.703470i	$-0.751633\pi$
$719$	−9.78644e132	−1.42145	−0.710725	+	0.703470i	$0.751633\pi$
$720$	0	0
$721$	−7.00510e131	−0.0894179
$722$	−1.13340e133	−1.35645
$723$	0	0
$724$	7.30122e132	0.768338
$725$	−4.50222e132	−0.444334
$726$	0	0
$727$	1.78272e133	1.54787	0.773934	−	0.633266i	$-0.218286\pi$
$727$	1.78272e133	1.54787	0.773934	+	0.633266i	$0.218286\pi$
$728$	−9.81058e131	−0.0799071
$729$	0	0
$730$	7.35808e132	0.527535
$731$	4.24484e133	2.85564
$732$	0	0
$733$	−2.90840e133	−1.72314	−0.861568	−	0.507642i	$-0.830517\pi$
$733$	−2.90840e133	−1.72314	−0.861568	+	0.507642i	$0.830517\pi$
$734$	−1.39334e133	−0.774800
$735$	0	0
$736$	−2.65924e133	−1.30298
$737$	2.51171e132	0.115540
$738$	0	0
$739$	4.45578e132	0.180700	0.0903498	−	0.995910i	$-0.471201\pi$
$739$	4.45578e132	0.180700	0.0903498	+	0.995910i	$0.471201\pi$
$740$	−2.83355e132	−0.107909
$741$	0	0
$742$	2.20117e133	0.739389
$743$	1.62944e132	0.0514113	0.0257056	−	0.999670i	$-0.491817\pi$
$743$	1.62944e132	0.0514113	0.0257056	+	0.999670i	$0.491817\pi$
$744$	0	0
$745$	−3.11007e133	−0.865971
$746$	−4.13534e133	−1.08182
$747$	0	0
$748$	−2.15384e133	−0.497496
$749$	−6.37809e132	−0.138448
$750$	0	0
$751$	−8.09455e133	−1.55216	−0.776078	−	0.630636i	$-0.782794\pi$
$751$	−8.09455e133	−1.55216	−0.776078	+	0.630636i	$0.782794\pi$
$752$	−7.49058e131	−0.0135016
$753$	0	0
$754$	1.64694e134	2.62367
$755$	7.23290e133	1.08338
$756$	0	0
$757$	1.20299e134	1.59332	0.796659	−	0.604429i	$-0.206599\pi$
$757$	1.20299e134	1.59332	0.796659	+	0.604429i	$0.206599\pi$
$758$	−9.29029e133	−1.15721
$759$	0	0
$760$	−6.07358e131	−0.00669288
$761$	1.47579e133	0.152982	0.0764908	−	0.997070i	$-0.475628\pi$
$761$	1.47579e133	0.152982	0.0764908	+	0.997070i	$0.475628\pi$
$762$	0	0
$763$	5.33070e133	0.489095
$764$	1.62337e134	1.40144
$765$	0	0
$766$	−3.00657e134	−2.29844
$767$	−2.61877e134	−1.88414
$768$	0	0
$769$	6.28699e133	0.400745	0.200372	−	0.979720i	$-0.435785\pi$
$769$	6.28699e133	0.400745	0.200372	+	0.979720i	$0.435785\pi$
$770$	3.23204e133	0.193936
$771$	0	0
$772$	3.02517e133	0.160896
$773$	−1.07884e134	−0.540268	−0.270134	−	0.962823i	$-0.587068\pi$
$773$	−1.07884e134	−0.540268	−0.270134	+	0.962823i	$0.587068\pi$
$774$	0	0
$775$	1.98543e133	0.0881710
$776$	8.24151e133	0.344696
$777$	0	0
$778$	4.34353e132	0.0161173
$779$	9.17523e132	0.0320719
$780$	0	0
$781$	−1.78381e134	−0.553447
$782$	−7.88232e134	−2.30431
$783$	0	0
$784$	3.74340e134	0.971782
$785$	2.74985e134	0.672775
$786$	0	0
$787$	−3.41049e134	−0.741297	−0.370648	−	0.928773i	$-0.620864\pi$
$787$	−3.41049e134	−0.741297	−0.370648	+	0.928773i	$0.620864\pi$
$788$	−3.11519e134	−0.638285
$789$	0	0
$790$	−3.94301e134	−0.718072
$791$	−2.05097e134	−0.352170
$792$	0	0
$793$	−2.39633e134	−0.365884
$794$	4.91382e133	0.0707564
$795$	0	0
$796$	−4.96953e134	−0.636587
$797$	−8.42317e134	−1.01780	−0.508901	−	0.860825i	$-0.669948\pi$
$797$	−8.42317e134	−1.01780	−0.508901	+	0.860825i	$0.669948\pi$
$798$	0	0
$799$	−1.91229e133	−0.0205650
$800$	−2.98457e134	−0.302829
$801$	0	0
$802$	−9.28874e134	−0.839167
$803$	−1.40705e134	−0.119960
$804$	0	0
$805$	5.40993e134	0.410850
$806$	−7.26282e134	−0.520626
$807$	0	0
$808$	2.03442e134	0.129961
$809$	−1.32832e135	−0.801118	−0.400559	−	0.916271i	$-0.631184\pi$
$809$	−1.32832e135	−0.801118	−0.400559	+	0.916271i	$0.631184\pi$
$810$	0	0
$811$	−2.63000e135	−1.41412	−0.707061	−	0.707153i	$-0.749979\pi$
$811$	−2.63000e135	−1.41412	−0.707061	+	0.707153i	$0.749979\pi$
$812$	1.21468e135	0.616744
$813$	0	0
$814$	1.18468e134	0.0536496
$815$	1.32507e135	0.566774
$816$	0	0
$817$	1.22814e134	0.0468729
$818$	8.56551e134	0.308833
$819$	0	0
$820$	3.28856e135	1.05843
$821$	−3.67231e135	−1.11682	−0.558409	−	0.829566i	$-0.688588\pi$
$821$	−3.67231e135	−1.11682	−0.558409	+	0.829566i	$0.688588\pi$
$822$	0	0
$823$	−2.12999e135	−0.578475	−0.289238	−	0.957257i	$-0.593402\pi$
$823$	−2.12999e135	−0.578475	−0.289238	+	0.957257i	$0.593402\pi$
$824$	−1.97261e134	−0.0506322
$825$	0	0
$826$	−4.22284e135	−0.968350
$827$	4.76247e135	1.03235	0.516174	−	0.856484i	$-0.327356\pi$
$827$	4.76247e135	1.03235	0.516174	+	0.856484i	$0.327356\pi$
$828$	0	0
$829$	1.22443e135	0.237218	0.118609	−	0.992941i	$-0.462157\pi$
$829$	1.22443e135	0.237218	0.118609	+	0.992941i	$0.462157\pi$
$830$	5.07320e135	0.929289
$831$	0	0
$832$	4.03931e135	0.661564
$833$	9.55661e135	1.48017
$834$	0	0
$835$	8.37386e135	1.16012
$836$	−6.23160e133	−0.00816597
$837$	0	0
$838$	1.99375e135	0.233789
$839$	2.34326e135	0.259949	0.129975	−	0.991517i	$-0.458510\pi$
$839$	2.34326e135	0.259949	0.129975	+	0.991517i	$0.458510\pi$
$840$	0	0
$841$	2.79348e136	2.77416
$842$	3.68207e135	0.346003
$843$	0	0
$844$	8.94514e135	0.752772
$845$	1.43565e134	0.0114343
$846$	0	0
$847$	4.66027e135	0.332532
$848$	2.42448e136	1.63761
$849$	0	0
$850$	−8.84666e135	−0.535549
$851$	1.98297e135	0.113656
$852$	0	0
$853$	−2.56453e135	−0.131789	−0.0658943	−	0.997827i	$-0.520990\pi$
$853$	−2.56453e135	−0.131789	−0.0658943	+	0.997827i	$0.520990\pi$
$854$	−3.86416e135	−0.188046
$855$	0	0
$856$	−1.79605e135	−0.0783950
$857$	−1.21930e136	−0.504082	−0.252041	−	0.967717i	$-0.581102\pi$
$857$	−1.21930e136	−0.504082	−0.252041	+	0.967717i	$0.581102\pi$
$858$	0	0
$859$	−8.42911e135	−0.312679	−0.156340	−	0.987703i	$-0.549969\pi$
$859$	−8.42911e135	−0.312679	−0.156340	+	0.987703i	$0.549969\pi$
$860$	4.40186e136	1.54689
$861$	0	0
$862$	−1.00289e136	−0.316350
$863$	−2.64685e135	−0.0791093	−0.0395547	−	0.999217i	$-0.512594\pi$
$863$	−2.64685e135	−0.0791093	−0.0395547	+	0.999217i	$0.512594\pi$
$864$	0	0
$865$	−1.83363e135	−0.0492111
$866$	−4.31274e136	−1.09691
$867$	0	0
$868$	−5.35659e135	−0.122383
$869$	7.54004e135	0.163288
$870$	0	0
$871$	−1.72608e136	−0.335905
$872$	1.50111e136	0.276946
$873$	0	0
$874$	−2.28055e135	−0.0378232
$875$	−2.04753e136	−0.322001
$876$	0	0
$877$	−1.12326e137	−1.58854	−0.794271	−	0.607564i	$-0.792147\pi$
$877$	−1.12326e137	−1.58854	−0.794271	+	0.607564i	$0.792147\pi$
$878$	−1.28930e136	−0.172926
$879$	0	0
$880$	3.55992e136	0.429532
$881$	−9.16639e136	−1.04910	−0.524552	−	0.851378i	$-0.675767\pi$
$881$	−9.16639e136	−1.04910	−0.524552	+	0.851378i	$0.675767\pi$
$882$	0	0
$883$	−3.80306e136	−0.391706	−0.195853	−	0.980633i	$-0.562748\pi$
$883$	−3.80306e136	−0.391706	−0.195853	+	0.980633i	$0.562748\pi$
$884$	1.48015e137	1.44635
$885$	0	0
$886$	1.26184e137	1.11003
$887$	1.22464e137	1.02226	0.511130	−	0.859503i	$-0.329227\pi$
$887$	1.22464e137	1.02226	0.511130	+	0.859503i	$0.329227\pi$
$888$	0	0
$889$	−1.59113e136	−0.119612
$890$	−4.95479e136	−0.353501
$891$	0	0
$892$	−1.49486e137	−0.960806
$893$	−5.53273e133	−0.000337556 0
$894$	0	0
$895$	−2.64442e137	−1.45398
$896$	−3.03946e136	−0.158663
$897$	0	0
$898$	1.32710e137	0.624533
$899$	−1.67595e137	−0.748922
$900$	0	0
$901$	6.18950e137	2.49433
$902$	−1.37492e137	−0.526226
$903$	0	0
$904$	−5.77546e136	−0.199413
$905$	−3.08077e137	−1.01042
$906$	0	0
$907$	2.22783e137	0.659391	0.329696	−	0.944087i	$-0.393054\pi$
$907$	2.22783e137	0.659391	0.329696	+	0.944087i	$0.393054\pi$
$908$	−4.88515e137	−1.37368
$909$	0	0
$910$	−2.22110e137	−0.563823
$911$	−2.69130e136	−0.0649169	−0.0324585	−	0.999473i	$-0.510334\pi$
$911$	−2.69130e136	−0.0649169	−0.0324585	+	0.999473i	$0.510334\pi$
$912$	0	0
$913$	−9.70125e136	−0.211318
$914$	5.02927e136	0.104113
$915$	0	0
$916$	−1.97318e137	−0.369001
$917$	−2.87704e137	−0.511413
$918$	0	0
$919$	−1.16650e138	−1.87376	−0.936882	−	0.349647i	$-0.886302\pi$
$919$	−1.16650e138	−1.87376	−0.936882	+	0.349647i	$0.886302\pi$
$920$	1.52342e137	0.232641
$921$	0	0
$922$	4.49024e137	0.619843
$923$	1.22586e138	1.60902
$924$	0	0
$925$	2.22558e136	0.0264151
$926$	−1.24006e138	−1.39969
$927$	0	0
$928$	2.51936e138	2.57222
$929$	−7.30201e137	−0.709107	−0.354554	−	0.935036i	$-0.615367\pi$
$929$	−7.30201e137	−0.709107	−0.354554	+	0.935036i	$0.615367\pi$
$930$	0	0
$931$	2.76497e136	0.0242957
$932$	1.09755e138	0.917456
$933$	0	0
$934$	−2.69303e138	−2.03756
$935$	9.08820e137	0.654241
$936$	0	0
$937$	6.92090e137	0.451098	0.225549	−	0.974232i	$-0.427582\pi$
$937$	6.92090e137	0.451098	0.225549	+	0.974232i	$0.427582\pi$
$938$	−2.78336e137	−0.172638
$939$	0	0
$940$	−1.98302e136	−0.0111399
$941$	2.77400e137	0.148317	0.0741583	−	0.997246i	$-0.476373\pi$
$941$	2.77400e137	0.148317	0.0741583	+	0.997246i	$0.476373\pi$
$942$	0	0
$943$	−2.30140e138	−1.11480
$944$	−4.65124e138	−2.14472
$945$	0	0
$946$	−1.84038e138	−0.769076
$947$	−5.69228e137	−0.226471	−0.113235	−	0.993568i	$-0.536121\pi$
$947$	−5.69228e137	−0.226471	−0.113235	+	0.993568i	$0.536121\pi$
$948$	0	0
$949$	9.66944e137	0.348757
$950$	−2.55956e136	−0.00879059
$951$	0	0
$952$	−4.44840e137	−0.138543
$953$	−3.31221e138	−0.982423	−0.491212	−	0.871040i	$-0.663446\pi$
$953$	−3.31221e138	−0.982423	−0.491212	+	0.871040i	$0.663446\pi$
$954$	0	0
$955$	−6.84985e138	−1.84299
$956$	4.45308e138	1.14122
$957$	0	0
$958$	1.72631e138	0.401443
$959$	−8.47788e136	−0.0187811
$960$	0	0
$961$	−4.23414e138	−0.851388
$962$	−8.14128e137	−0.155974
$963$	0	0
$964$	2.44361e138	0.425059
$965$	−1.27648e138	−0.211589
$966$	0	0
$967$	4.39653e138	0.661879	0.330940	−	0.943652i	$-0.392634\pi$
$967$	4.39653e138	0.661879	0.330940	+	0.943652i	$0.392634\pi$
$968$	1.31232e138	0.188293
$969$	0	0
$970$	1.86586e139	2.43217
$971$	1.08160e139	1.34392	0.671961	−	0.740586i	$-0.265452\pi$
$971$	1.08160e139	1.34392	0.671961	+	0.740586i	$0.265452\pi$
$972$	0	0
$973$	8.70128e137	0.0982508
$974$	4.11515e138	0.442990
$975$	0	0
$976$	−4.25617e138	−0.416488
$977$	−1.37620e139	−1.28406	−0.642031	−	0.766679i	$-0.721908\pi$
$977$	−1.37620e139	−1.28406	−0.642031	+	0.766679i	$0.721908\pi$
$978$	0	0
$979$	9.47483e137	0.0803852
$980$	9.91011e138	0.801800
$981$	0	0
$982$	7.10056e138	0.522527
$983$	2.47747e139	1.73888	0.869442	−	0.494036i	$-0.164479\pi$
$983$	2.47747e139	1.73888	0.869442	+	0.494036i	$0.164479\pi$
$984$	0	0
$985$	1.31446e139	0.839389
$986$	7.46770e139	4.54894
$987$	0	0
$988$	4.28244e137	0.0237407
$989$	−3.08051e139	−1.62928
$990$	0	0
$991$	1.75193e139	0.843512	0.421756	−	0.906709i	$-0.361414\pi$
$991$	1.75193e139	0.843512	0.421756	+	0.906709i	$0.361414\pi$
$992$	−1.11101e139	−0.510417
$993$	0	0
$994$	1.97673e139	0.826954
$995$	2.09691e139	0.837156
$996$	0	0
$997$	2.54861e139	0.926786	0.463393	−	0.886153i	$-0.346632\pi$
$997$	2.54861e139	0.926786	0.463393	+	0.886153i	$0.346632\pi$
$998$	−6.32153e139	−2.19408
$999$	0	0

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.35097e14 q^{2} +8.34770e27 q^{4} -3.52234e32 q^{5} -7.46408e38 q^{7} -2.10186e41 q^{8} +O(q^{10})\)	\(q+1.35097e14 q^{2} +8.34770e27 q^{4} -3.52234e32 q^{5} -7.46408e38 q^{7} -2.10186e41 q^{8} -4.75858e46 q^{10} +9.09961e47 q^{11} -6.25337e51 q^{13} -1.00838e53 q^{14} -1.11067e56 q^{16} -2.83546e57 q^{17} -8.20370e57 q^{19} -2.94035e60 q^{20} +1.22933e62 q^{22} +2.05771e63 q^{23} +2.30946e64 q^{25} -8.44812e65 q^{26} -6.23079e66 q^{28} -1.94947e68 q^{29} +8.59696e68 q^{31} -1.29233e70 q^{32} -3.83062e71 q^{34} +2.62910e71 q^{35} +9.63679e71 q^{37} -1.10830e72 q^{38} +7.40347e73 q^{40} -1.11843e75 q^{41} -1.49706e76 q^{43} +7.59609e75 q^{44} +2.77991e77 q^{46} +6.74418e75 q^{47} -3.37039e78 q^{49} +3.12001e78 q^{50} -5.22013e79 q^{52} -2.18289e80 q^{53} -3.20519e80 q^{55} +1.56885e80 q^{56} -2.63368e82 q^{58} +4.18777e82 q^{59} +3.83206e82 q^{61} +1.16142e83 q^{62} -6.45940e83 q^{64} +2.20265e84 q^{65} +2.76024e84 q^{67} -2.36696e85 q^{68} +3.55184e85 q^{70} -1.96031e86 q^{71} -1.54628e86 q^{73} +1.30190e86 q^{74} -6.84821e85 q^{76} -6.79202e86 q^{77} +8.28611e87 q^{79} +3.91216e88 q^{80} -1.51096e89 q^{82} -1.06612e89 q^{83} +9.98745e89 q^{85} -2.02248e90 q^{86} -1.91261e89 q^{88} +1.04123e90 q^{89} +4.66757e90 q^{91} +1.71772e91 q^{92} +9.11120e89 q^{94} +2.88962e90 q^{95} -3.92105e92 q^{97} -4.55330e92 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 43735426713792 q^{2} + 37\!\cdots\!44 q^{4}+ \cdots - 62\!\cdots\!60 q^{8}+O(q^{10}) \) 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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