LMFDB - Embedded newform 9.76.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,76,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, 76, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 76);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 76 $
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:	$320.605553540$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 67\!\cdots\!50 $ x^6 - 3x^5 - 38457853073924058692x^4 - 10276556354621685339901678086x^3 + 371187556674475060057870954681799784505x^2 + 52686123927652036687598761277591247931691204025*x - 675344021115865838575279495800656435684060652010336995750
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{58}\cdot 3^{36}\cdot 5^{7}\cdot 7^{3}\cdot 11\cdot 13\cdot 19 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-3.89081e9$ 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)

$f(q)$	$=$	$q+2.89652e11 q^{2} +4.61192e22 q^{4} +2.47463e26 q^{5} -6.83079e31 q^{7} +2.41577e33 q^{8} +O(q^{10})$	\(q+2.89652e11 q^{2} +4.61192e22 q^{4} +2.47463e26 q^{5} -6.83079e31 q^{7} +2.41577e33 q^{8} +7.16781e37 q^{10} +1.33402e39 q^{11} +2.92609e41 q^{13} -1.97855e43 q^{14} -1.04260e45 q^{16} -4.46232e44 q^{17} -8.32041e47 q^{19} +1.14128e49 q^{20} +3.86400e50 q^{22} -1.13411e51 q^{23} +3.47681e52 q^{25} +8.47548e52 q^{26} -3.15030e54 q^{28} -3.24261e54 q^{29} -1.48783e56 q^{31} -3.93257e56 q^{32} -1.29252e56 q^{34} -1.69037e58 q^{35} +2.52569e58 q^{37} -2.41002e59 q^{38} +5.97813e59 q^{40} +1.57021e60 q^{41} +2.24744e61 q^{43} +6.15237e61 q^{44} -3.28497e62 q^{46} -3.99901e62 q^{47} +2.25410e63 q^{49} +1.00706e64 q^{50} +1.34949e64 q^{52} -2.56197e64 q^{53} +3.30120e65 q^{55} -1.65016e65 q^{56} -9.39227e65 q^{58} -1.98202e66 q^{59} -1.77334e66 q^{61} -4.30953e67 q^{62} -7.45191e67 q^{64} +7.24099e67 q^{65} +3.79112e68 q^{67} -2.05799e67 q^{68} -4.89618e69 q^{70} -1.15990e69 q^{71} -5.75070e69 q^{73} +7.31570e69 q^{74} -3.83730e70 q^{76} -9.11239e70 q^{77} +6.59713e70 q^{79} -2.58005e71 q^{80} +4.54813e71 q^{82} -1.04387e72 q^{83} -1.10426e71 q^{85} +6.50974e72 q^{86} +3.22267e72 q^{88} -1.34676e73 q^{89} -1.99875e73 q^{91} -5.23043e73 q^{92} -1.15832e74 q^{94} -2.05899e74 q^{95} -5.17927e74 q^{97} +6.52905e74 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 57080822040 q^{2} + 17\!\cdots\!28 q^{4}+ \cdots - 44\!\cdots\!20 q^{8}+O(q^{10}) $ 6 * q + 57080822040 * q^2 + 172600466200162028593728 * q^4 + 38982947396479621874420940 * q^5 + 1924474634802918779239478643600 * q^7 - 4434903997968330342413437320645120 * q^8	$ 6 q + 57080822040 q^{2} + 17\!\cdots\!28 q^{4}+ \cdots + 16\!\cdots\!20 q^{98}+O(q^{100}) $ 6 * q + 57080822040 * q^2 + 172600466200162028593728 * q^4 + 38982947396479621874420940 * q^5 + 1924474634802918779239478643600 * q^7 - 4434903997968330342413437320645120 * q^8 + 133267935677460241037537052811576902960 * q^10 + 945659951949983071650740113735111214088 * q^11 + 533185179266852519941169625089098069764420 * q^13 - 8213946953162263647781694565284746353072576 * q^14 + 2681978005634517266622433394712415602648354816 * q^16 - 18261354095776132566172834671579513215483393580 * q^17 + 1061534856238354155312794852768417904375328867080 * q^19 - 9296557595621768320156983882258818695571369489280 * q^20 + 153315952874260268106194796405555863940172791589920 * q^22 - 1514929449877410771078348320690686508954384916853680 * q^23 + 19310380328261093150952553553121815533899364092239850 * q^25 - 117730941166816926498584842564210483616872200198362352 * q^26 + 1465885017268620651444113586751990931877154821040657920 * q^28 - 14718767377678125816030788545177391174717388984245534820 * q^29 - 41742874787360498453628839393549579933009794702042980288 * q^31 - 1174660148719991756036751189163540495635749096221862952960 * q^32 + 3034358950124956876257603978888653679838045546922892395856 * q^34 - 27299672493656883988453292135086250689495956464846953371360 * q^35 + 98517772547646219221591850851651469983797181732879949140340 * q^37 - 1257660981102762853948269222064665311191946222029530979162080 * q^38 + 8807901623729426290853411185831313455271917763097593104051200 * q^40 - 5039211762207387369185984529408567568647239506257650214613212 * q^41 + 27938749238581541451173935836639198120068956697568041153196600 * q^43 + 86388814623354110240559749283671522466589238091463431115801344 * q^44 - 824145803870667307795487213022331547039596870954611528203613888 * q^46 + 1386854970430427381646742231466788117324292253074354560479038880 * q^47 - 5707868790800975784856935495088511133239544554833878775910738442 * q^49 - 3144970672685230615695776810799603542575044196614572896663392600 * q^50 + 41677832028141179840113326797899392222702339479233001780216150400 * q^52 - 64283727174659970247345252518647455744441825702701764187054106260 * q^53 + 436876078674971654403803167180324983329224614451635548418098895120 * q^55 - 289950797286325881623798664040853221823087783432246887785270865920 * q^56 - 1763005756244374137396902189067511762184157619699352574614137403280 * q^58 + 2478360370933764187935912640189307752170553390931716617591182395560 * q^59 - 25641115321477658815889269525514418267074652297034046321782023152988 * q^61 + 29014701474354643819936101890527484086880802356768235703173807694080 * q^62 + 47683232974651133862719671893097862706511055838864188064811716968448 * q^64 - 122110621788131890149667214965152432737153070969379698276880591977720 * q^65 + 955579073553339181030887342220313909838725364297810737998207107813480 * q^67 - 1237210897217068882936524414359446185548686871817993659403939290386560 * q^68 - 3476902593928340346610001926714053112321275314411181267396530677050240 * q^70 + 255682319306096297182489045146623979225804710540351927309367569173488 * q^71 - 30605188898291905719532895918028188508004452865621142257485594115042020 * q^73 + 24065024027894599201472448362529876891121294631891709256708009194181584 * q^74 + 100020936372377387464010564774983213070641689274186088752725827576144640 * q^76 - 158930415774536768880543239288689183540801263714134710336228496440507200 * q^77 + 116627678166642324332643069323234092884951450625988452824960767925148320 * q^79 - 1239310052714502333188756625709169306278438274940582996524184215206748160 * q^80 - 2557649813228840791149140948716215474705151452500921688788291587877236080 * q^82 + 798780284119889426515570523310162377392459257634002033911814028088739960 * q^83 - 3615500806340871685633297735534398118961343923835923286123685237305018840 * q^85 - 7245194180836090971883743617494948296636529538939897523257528311698092832 * q^86 - 4827001398586167572057494186308233100206033194553368013345656010632181760 * q^88 - 53575610216125238704584826863934604186542249469498220298044079954014547260 * q^89 + 34502419684367451829908407139028781594042460695428817715772307436403470432 * q^91 - 187445224353587479072026786339601818260697439565538078689222489106585838080 * q^92 - 296189325151987924691405038954735773676385503565643130818482899021002578304 * q^94 - 194934959385332686251927514630723902507701573195047654345319995220933314800 * q^95 - 747928220344118582344222376208028579242743608466383778453296378427532508980 * q^97 + 1663265696927109513221859402309517858944410070626232817304447619248634722520 * 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 $

$2$	2.89652e11	1.49022	0.745112	−	0.666940i	$-0.232396\pi$
$2$	2.89652e11	1.49022	0.745112	+	0.666940i	$0.232396\pi$
$3$	0	0
$3$	0	0
$4$	4.61192e22	1.22076
$5$	2.47463e26	1.52102	0.760510	−	0.649326i	$-0.224949\pi$
$5$	2.47463e26	1.52102	0.760510	+	0.649326i	$0.224949\pi$
$6$	0	0
$7$	−6.83079e31	−1.39090	−0.695448	−	0.718577i	$-0.744794\pi$
$7$	−6.83079e31	−1.39090	−0.695448	+	0.718577i	$0.744794\pi$
$8$	2.41577e33	0.328989
$9$	0	0
$10$	7.16781e37	2.26666
$11$	1.33402e39	1.18287	0.591433	−	0.806354i	$-0.298562\pi$
$11$	1.33402e39	1.18287	0.591433	+	0.806354i	$0.298562\pi$
$12$	0	0
$13$	2.92609e41	0.493642	0.246821	−	0.969061i	$-0.420614\pi$
$13$	2.92609e41	0.493642	0.246821	+	0.969061i	$0.420614\pi$
$14$	−1.97855e43	−2.07274
$15$	0	0
$16$	−1.04260e45	−0.730498
$17$	−4.46232e44	−0.0321904	−0.0160952	−	0.999870i	$-0.505123\pi$
$17$	−4.46232e44	−0.0321904	−0.0160952	+	0.999870i	$0.505123\pi$
$18$	0	0
$19$	−8.32041e47	−0.926583	−0.463292	−	0.886206i	$-0.653332\pi$
$19$	−8.32041e47	−0.926583	−0.463292	+	0.886206i	$0.653332\pi$
$20$	1.14128e49	1.85681
$21$	0	0
$22$	3.86400e50	1.76273
$23$	−1.13411e51	−0.976927	−0.488463	−	0.872584i	$-0.662442\pi$
$23$	−1.13411e51	−0.976927	−0.488463	+	0.872584i	$0.662442\pi$
$24$	0	0
$25$	3.47681e52	1.31350
$26$	8.47548e52	0.735637
$27$	0	0
$28$	−3.15030e54	−1.69796
$29$	−3.24261e54	−0.468781	−0.234390	−	0.972143i	$-0.575309\pi$
$29$	−3.24261e54	−0.468781	−0.234390	+	0.972143i	$0.575309\pi$
$30$	0	0
$31$	−1.48783e56	−1.76397	−0.881983	−	0.471282i	$-0.843792\pi$
$31$	−1.48783e56	−1.76397	−0.881983	+	0.471282i	$0.843792\pi$
$32$	−3.93257e56	−1.41759
$33$	0	0
$34$	−1.29252e56	−0.0479709
$35$	−1.69037e58	−2.11558
$36$	0	0
$37$	2.52569e58	0.393383	0.196691	−	0.980465i	$-0.436980\pi$
$37$	2.52569e58	0.393383	0.196691	+	0.980465i	$0.436980\pi$
$38$	−2.41002e59	−1.38082
$39$	0	0
$40$	5.97813e59	0.500398
$41$	1.57021e60	0.520669	0.260335	−	0.965518i	$-0.416167\pi$
$41$	1.57021e60	0.520669	0.260335	+	0.965518i	$0.416167\pi$
$42$	0	0
$43$	2.24744e61	1.24917	0.624584	−	0.780958i	$-0.285269\pi$
$43$	2.24744e61	1.24917	0.624584	+	0.780958i	$0.285269\pi$
$44$	6.15237e61	1.44400
$45$	0	0
$46$	−3.28497e62	−1.45584
$47$	−3.99901e62	−0.791194	−0.395597	−	0.918424i	$-0.629462\pi$
$47$	−3.99901e62	−0.791194	−0.395597	+	0.918424i	$0.629462\pi$
$48$	0	0
$49$	2.25410e63	0.934590
$50$	1.00706e64	1.95741
$51$	0	0
$52$	1.34949e64	0.602621
$53$	−2.56197e64	−0.560053	−0.280027	−	0.959992i	$-0.590343\pi$
$53$	−2.56197e64	−0.560053	−0.280027	+	0.959992i	$0.590343\pi$
$54$	0	0
$55$	3.30120e65	1.79916
$56$	−1.65016e65	−0.457589
$57$	0	0
$58$	−9.39227e65	−0.698588
$59$	−1.98202e66	−0.776528	−0.388264	−	0.921548i	$-0.626925\pi$
$59$	−1.98202e66	−0.776528	−0.388264	+	0.921548i	$0.626925\pi$
$60$	0	0
$61$	−1.77334e66	−0.199032	−0.0995159	−	0.995036i	$-0.531729\pi$
$61$	−1.77334e66	−0.199032	−0.0995159	+	0.995036i	$0.531729\pi$
$62$	−4.30953e67	−2.62870
$63$	0	0
$64$	−7.45191e67	−1.38203
$65$	7.24099e67	0.750840
$66$	0	0
$67$	3.79112e68	1.26172	0.630860	−	0.775897i	$-0.282702\pi$
$67$	3.79112e68	1.26172	0.630860	+	0.775897i	$0.282702\pi$
$68$	−2.05799e67	−0.0392969
$69$	0	0
$70$	−4.89618e69	−3.15269
$71$	−1.15990e69	−0.438765	−0.219383	−	0.975639i	$-0.570404\pi$
$71$	−1.15990e69	−0.438765	−0.219383	+	0.975639i	$0.570404\pi$
$72$	0	0
$73$	−5.75070e69	−0.767562	−0.383781	−	0.923424i	$-0.625378\pi$
$73$	−5.75070e69	−0.767562	−0.383781	+	0.923424i	$0.625378\pi$
$74$	7.31570e69	0.586228
$75$	0	0
$76$	−3.83730e70	−1.13114
$77$	−9.11239e70	−1.64524
$78$	0	0
$79$	6.59713e70	0.455344	0.227672	−	0.973738i	$-0.426889\pi$
$79$	6.59713e70	0.455344	0.227672	+	0.973738i	$0.426889\pi$
$80$	−2.58005e71	−1.11110
$81$	0	0
$82$	4.54813e71	0.775913
$83$	−1.04387e72	−1.13036	−0.565182	−	0.824966i	$-0.691194\pi$
$83$	−1.04387e72	−1.13036	−0.565182	+	0.824966i	$0.691194\pi$
$84$	0	0
$85$	−1.10426e71	−0.0489622
$86$	6.50974e72	1.86154
$87$	0	0
$88$	3.22267e72	0.389149
$89$	−1.34676e73	−1.06455	−0.532274	−	0.846572i	$-0.678662\pi$
$89$	−1.34676e73	−1.06455	−0.532274	+	0.846572i	$0.678662\pi$
$90$	0	0
$91$	−1.99875e73	−0.686605
$92$	−5.23043e73	−1.19260
$93$	0	0
$94$	−1.15832e74	−1.17906
$95$	−2.05899e74	−1.40935
$96$	0	0
$97$	−5.17927e74	−1.62304	−0.811519	−	0.584326i	$-0.801359\pi$
$97$	−5.17927e74	−1.62304	−0.811519	+	0.584326i	$0.801359\pi$
$98$	6.52905e74	1.39275
$99$	0	0
$100$	1.60348e75	1.60348
$101$	−4.46775e74	−0.307636	−0.153818	−	0.988099i	$-0.549157\pi$
$101$	−4.46775e74	−0.307636	−0.153818	+	0.988099i	$0.549157\pi$
$102$	0	0
$103$	1.77263e74	0.0585089	0.0292544	−	0.999572i	$-0.490687\pi$
$103$	1.77263e74	0.0585089	0.0292544	+	0.999572i	$0.490687\pi$
$104$	7.06876e74	0.162403
$105$	0	0
$106$	−7.42080e75	−0.834604
$107$	1.64232e76	1.29887	0.649434	−	0.760418i	$-0.275006\pi$
$107$	1.64232e76	1.29887	0.649434	+	0.760418i	$0.275006\pi$
$108$	0	0
$109$	9.19334e75	0.363061	0.181531	−	0.983385i	$-0.441895\pi$
$109$	9.19334e75	0.363061	0.181531	+	0.983385i	$0.441895\pi$
$110$	9.56197e76	2.68115
$111$	0	0
$112$	7.12180e76	1.01605
$113$	−4.17267e76	−0.426553	−0.213276	−	0.976992i	$-0.568413\pi$
$113$	−4.17267e76	−0.426553	−0.213276	+	0.976992i	$0.568413\pi$
$114$	0	0
$115$	−2.80651e77	−1.48592
$116$	−1.49546e77	−0.572271
$117$	0	0
$118$	−5.74095e77	−1.15720
$119$	3.04812e76	0.0447735
$120$	0	0
$121$	5.07704e77	0.399171
$122$	−5.13650e77	−0.296602
$123$	0	0
$124$	−6.86176e78	−2.15339
$125$	2.05353e78	0.476843
$126$	0	0
$127$	−3.66800e78	−0.469667	−0.234834	−	0.972036i	$-0.575455\pi$
$127$	−3.66800e78	−0.469667	−0.234834	+	0.972036i	$0.575455\pi$
$128$	−6.72776e78	−0.641943
$129$	0	0
$130$	2.09737e79	1.11892
$131$	1.61112e79	0.644843	0.322422	−	0.946596i	$-0.395503\pi$
$131$	1.61112e79	0.644843	0.322422	+	0.946596i	$0.395503\pi$
$132$	0	0
$133$	5.68349e79	1.28878
$134$	1.09810e80	1.88024
$135$	0	0
$136$	−1.07799e78	−0.0105903
$137$	−4.52829e79	−0.337997	−0.168998	−	0.985616i	$-0.554053\pi$
$137$	−4.52829e79	−0.337997	−0.168998	+	0.985616i	$0.554053\pi$
$138$	0	0
$139$	−2.07054e79	−0.0897490	−0.0448745	−	0.998993i	$-0.514289\pi$
$139$	−2.07054e79	−0.0897490	−0.0448745	+	0.998993i	$0.514289\pi$
$140$	−7.79584e80	−2.58262
$141$	0	0
$142$	−3.35967e80	−0.653858
$143$	3.90346e80	0.583913
$144$	0	0
$145$	−8.02425e80	−0.713025
$146$	−1.66570e81	−1.14384
$147$	0	0
$148$	1.16483e81	0.480228
$149$	3.52371e81	1.12854	0.564268	−	0.825591i	$-0.309158\pi$
$149$	3.52371e81	1.12854	0.564268	+	0.825591i	$0.309158\pi$
$150$	0	0
$151$	4.34097e81	0.843239	0.421620	−	0.906773i	$-0.361462\pi$
$151$	4.34097e81	0.843239	0.421620	+	0.906773i	$0.361462\pi$
$152$	−2.01002e81	−0.304835
$153$	0	0
$154$	−2.63942e82	−2.45178
$155$	−3.68183e82	−2.68303
$156$	0	0
$157$	4.23236e82	1.90698	0.953490	−	0.301425i	$-0.0974622\pi$
$157$	4.23236e82	1.90698	0.953490	+	0.301425i	$0.0974622\pi$
$158$	1.91087e82	0.678564
$159$	0	0
$160$	−9.73164e82	−2.15619
$161$	7.74688e82	1.35880
$162$	0	0
$163$	−1.60838e83	−1.77564	−0.887818	−	0.460194i	$-0.847780\pi$
$163$	−1.60838e83	−1.77564	−0.887818	+	0.460194i	$0.847780\pi$
$164$	7.24166e82	0.635615
$165$	0	0
$166$	−3.02359e83	−1.68449
$167$	−2.02081e83	−0.898787	−0.449394	−	0.893334i	$-0.648360\pi$
$167$	−2.02081e83	−0.898787	−0.449394	+	0.893334i	$0.648360\pi$
$168$	0	0
$169$	−2.65739e83	−0.756317
$170$	−3.19851e82	−0.0729647
$171$	0	0
$172$	1.03650e84	1.52494
$173$	−1.28506e84	−1.52123	−0.760615	−	0.649203i	$-0.775102\pi$
$173$	−1.28506e84	−1.52123	−0.760615	+	0.649203i	$0.775102\pi$
$174$	0	0
$175$	−2.37494e84	−1.82694
$176$	−1.39085e84	−0.864081
$177$	0	0
$178$	−3.90091e84	−1.58641
$179$	−2.87264e84	−0.946873	−0.473437	−	0.880828i	$-0.656987\pi$
$179$	−2.87264e84	−0.946873	−0.473437	+	0.880828i	$0.656987\pi$
$180$	0	0
$181$	−4.04728e84	−0.879462	−0.439731	−	0.898130i	$-0.644926\pi$
$181$	−4.04728e84	−0.879462	−0.439731	+	0.898130i	$0.644926\pi$
$182$	−5.78942e84	−1.02319
$183$	0	0
$184$	−2.73975e84	−0.321398
$185$	6.25014e84	0.598343
$186$	0	0
$187$	−5.95281e83	−0.0380769
$188$	−1.84431e85	−0.965862
$189$	0	0
$190$	−5.96390e85	−2.10025
$191$	5.46188e85	1.57976	0.789880	−	0.613262i	$-0.210143\pi$
$191$	5.46188e85	1.57976	0.789880	+	0.613262i	$0.210143\pi$
$192$	0	0
$193$	2.91758e85	0.570983	0.285491	−	0.958381i	$-0.407843\pi$
$193$	2.91758e85	0.570983	0.285491	+	0.958381i	$0.407843\pi$
$194$	−1.50018e86	−2.41869
$195$	0	0
$196$	1.03957e86	1.14091
$197$	1.89682e86	1.72006	0.860030	−	0.510244i	$-0.170445\pi$
$197$	1.89682e86	1.72006	0.860030	+	0.510244i	$0.170445\pi$
$198$	0	0
$199$	−8.15036e85	−0.506042	−0.253021	−	0.967461i	$-0.581424\pi$
$199$	−8.15036e85	−0.506042	−0.253021	+	0.967461i	$0.581424\pi$
$200$	8.39917e85	0.432127
$201$	0	0
$202$	−1.29409e86	−0.458446
$203$	2.21496e86	0.652025
$204$	0	0
$205$	3.88568e86	0.791948
$206$	5.13445e85	0.0871913
$207$	0	0
$208$	−3.05075e86	−0.360605
$209$	−1.10996e87	−1.09602
$210$	0	0
$211$	−4.45152e86	−0.307550	−0.153775	−	0.988106i	$-0.549143\pi$
$211$	−4.45152e86	−0.307550	−0.153775	+	0.988106i	$0.549143\pi$
$212$	−1.18156e87	−0.683693
$213$	0	0
$214$	4.75700e87	1.93560
$215$	5.56157e87	1.90001
$216$	0	0
$217$	1.01631e88	2.45349
$218$	2.66287e87	0.541042
$219$	0	0
$220$	1.52248e88	2.19635
$221$	−1.30572e86	−0.0158905
$222$	0	0
$223$	−1.26594e88	−1.09896	−0.549480	−	0.835507i	$-0.685174\pi$
$223$	−1.26594e88	−1.09896	−0.549480	+	0.835507i	$0.685174\pi$
$224$	2.68625e88	1.97172
$225$	0	0
$226$	−1.20862e88	−0.635659
$227$	−2.80119e88	−1.24845	−0.624227	−	0.781243i	$-0.714586\pi$
$227$	−2.80119e88	−1.24845	−0.624227	+	0.781243i	$0.714586\pi$
$228$	0	0
$229$	−2.13293e88	−0.684142	−0.342071	−	0.939674i	$-0.611128\pi$
$229$	−2.13293e88	−0.684142	−0.342071	+	0.939674i	$0.611128\pi$
$230$	−8.12909e88	−2.21436
$231$	0	0
$232$	−7.83339e87	−0.154223
$233$	8.75869e88	1.46755	0.733774	−	0.679394i	$-0.237757\pi$
$233$	8.75869e88	1.46755	0.733774	+	0.679394i	$0.237757\pi$
$234$	0	0
$235$	−9.89607e88	−1.20342
$236$	−9.14090e88	−0.947958
$237$	0	0
$238$	8.82893e87	0.0667225
$239$	−6.42047e88	−0.414615	−0.207308	−	0.978276i	$-0.566470\pi$
$239$	−6.42047e88	−0.414615	−0.207308	+	0.978276i	$0.566470\pi$
$240$	0	0
$241$	−2.34435e89	−1.10760	−0.553800	−	0.832650i	$-0.686823\pi$
$241$	−2.34435e89	−1.10760	−0.553800	+	0.832650i	$0.686823\pi$
$242$	1.47057e89	0.594854
$243$	0	0
$244$	−8.17848e88	−0.242971
$245$	5.57807e89	1.42153
$246$	0	0
$247$	−2.43463e89	−0.457401
$248$	−3.59426e89	−0.580324
$249$	0	0
$250$	5.94808e89	0.710602
$251$	−1.57600e90	−1.62103	−0.810517	−	0.585715i	$-0.800814\pi$
$251$	−1.57600e90	−1.62103	−0.810517	+	0.585715i	$0.800814\pi$
$252$	0	0
$253$	−1.51292e90	−1.15557
$254$	−1.06244e90	−0.699909
$255$	0	0
$256$	8.66544e89	0.425394
$257$	−9.26893e89	−0.393131	−0.196566	−	0.980491i	$-0.562979\pi$
$257$	−9.26893e89	−0.393131	−0.196566	+	0.980491i	$0.562979\pi$
$258$	0	0
$259$	−1.72525e90	−0.547154
$260$	3.33949e90	0.916599
$261$	0	0
$262$	4.66663e90	0.960960
$263$	−9.67293e90	−1.72670	−0.863351	−	0.504603i	$-0.831639\pi$
$263$	−9.67293e90	−1.72670	−0.863351	+	0.504603i	$0.831639\pi$
$264$	0	0
$265$	−6.33993e90	−0.851852
$266$	1.64623e91	1.92057
$267$	0	0
$268$	1.74843e91	1.54026
$269$	8.00260e90	0.613085	0.306542	−	0.951857i	$-0.400828\pi$
$269$	8.00260e90	0.613085	0.306542	+	0.951857i	$0.400828\pi$
$270$	0	0
$271$	1.96164e91	1.13834	0.569168	−	0.822222i	$-0.307266\pi$
$271$	1.96164e91	1.13834	0.569168	+	0.822222i	$0.307266\pi$
$272$	4.65243e89	0.0235150
$273$	0	0
$274$	−1.31163e91	−0.503691
$275$	4.63812e91	1.55370
$276$	0	0
$277$	5.38580e91	1.37486	0.687431	−	0.726249i	$-0.258738\pi$
$277$	5.38580e91	1.37486	0.687431	+	0.726249i	$0.258738\pi$
$278$	−5.99737e90	−0.133746
$279$	0	0
$280$	−4.08354e91	−0.696001
$281$	−9.87766e90	−0.147288	−0.0736440	−	0.997285i	$-0.523463\pi$
$281$	−9.87766e90	−0.147288	−0.0736440	+	0.997285i	$0.523463\pi$
$282$	0	0
$283$	−2.10001e91	−0.240010	−0.120005	−	0.992773i	$-0.538291\pi$
$283$	−2.10001e91	−0.240010	−0.120005	+	0.992773i	$0.538291\pi$
$284$	−5.34936e91	−0.535629
$285$	0	0
$286$	1.13064e92	0.870160
$287$	−1.07257e92	−0.724197
$288$	0	0
$289$	−1.91964e92	−0.998964
$290$	−2.32424e92	−1.06257
$291$	0	0
$292$	−2.65218e92	−0.937013
$293$	−3.34446e92	−1.03942	−0.519710	−	0.854343i	$-0.673960\pi$
$293$	−3.34446e92	−1.03942	−0.519710	+	0.854343i	$0.673960\pi$
$294$	0	0
$295$	−4.90476e92	−1.18111
$296$	6.10148e91	0.129418
$297$	0	0
$298$	1.02065e93	1.68177
$299$	−3.31852e92	−0.482252
$300$	0	0
$301$	−1.53518e93	−1.73746
$302$	1.25737e93	1.25661
$303$	0	0
$304$	8.67487e92	0.676868
$305$	−4.38835e92	−0.302731
$306$	0	0
$307$	−9.57957e92	−0.517198	−0.258599	−	0.965985i	$-0.583261\pi$
$307$	−9.57957e92	−0.517198	−0.258599	+	0.965985i	$0.583261\pi$
$308$	−4.20256e93	−2.00845
$309$	0	0
$310$	−1.06645e94	−3.99831
$311$	−5.25070e93	−1.74463	−0.872313	−	0.488948i	$-0.837381\pi$
$311$	−5.25070e93	−1.74463	−0.872313	+	0.488948i	$0.837381\pi$
$312$	0	0
$313$	5.81690e93	1.51977	0.759887	−	0.650055i	$-0.225254\pi$
$313$	5.81690e93	1.51977	0.759887	+	0.650055i	$0.225254\pi$
$314$	1.22591e94	2.84183
$315$	0	0
$316$	3.04254e93	0.555868
$317$	4.47378e93	0.726026	0.363013	−	0.931784i	$-0.381748\pi$
$317$	4.47378e93	0.726026	0.363013	+	0.931784i	$0.381748\pi$
$318$	0	0
$319$	−4.32569e93	−0.554504
$320$	−1.84407e94	−2.10210
$321$	0	0
$322$	2.24390e94	2.02492
$323$	3.71283e92	0.0298271
$324$	0	0
$325$	1.01735e94	0.648400
$326$	−4.65871e94	−2.64609
$327$	0	0
$328$	3.79325e93	0.171294
$329$	2.73164e94	1.10047
$330$	0	0
$331$	9.70530e93	0.311501	0.155750	−	0.987796i	$-0.450220\pi$
$331$	9.70530e93	0.311501	0.155750	+	0.987796i	$0.450220\pi$
$332$	−4.81424e94	−1.37991
$333$	0	0
$334$	−5.85330e94	−1.33939
$335$	9.38162e94	1.91910
$336$	0	0
$337$	−2.56870e94	−0.420332	−0.210166	−	0.977666i	$-0.567400\pi$
$337$	−2.56870e94	−0.420332	−0.210166	+	0.977666i	$0.567400\pi$
$338$	−7.69718e94	−1.12708
$339$	0	0
$340$	−5.09275e93	−0.0597714
$341$	−1.98479e95	−2.08653
$342$	0	0
$343$	1.07763e94	0.0909786
$344$	5.42929e94	0.410962
$345$	0	0
$346$	−3.72220e95	−2.26697
$347$	7.33722e94	0.401030	0.200515	−	0.979691i	$-0.435739\pi$
$347$	7.33722e94	0.401030	0.200515	+	0.979691i	$0.435739\pi$
$348$	0	0
$349$	1.66138e95	0.732008	0.366004	−	0.930613i	$-0.380726\pi$
$349$	1.66138e95	0.732008	0.366004	+	0.930613i	$0.380726\pi$
$350$	−6.87904e95	−2.72255
$351$	0	0
$352$	−5.24611e95	−1.67682
$353$	−1.37439e95	−0.394965	−0.197482	−	0.980306i	$-0.563277\pi$
$353$	−1.37439e95	−0.394965	−0.197482	+	0.980306i	$0.563277\pi$
$354$	0	0
$355$	−2.87032e95	−0.667370
$356$	−6.21115e95	−1.29956
$357$	0	0
$358$	−8.32064e95	−1.41105
$359$	−5.50724e95	−0.841187	−0.420593	−	0.907249i	$-0.638178\pi$
$359$	−5.50724e95	−0.841187	−0.420593	+	0.907249i	$0.638178\pi$
$360$	0	0
$361$	−1.14052e95	−0.141443
$362$	−1.17230e96	−1.31059
$363$	0	0
$364$	−9.21808e95	−0.838183
$365$	−1.42309e96	−1.16748
$366$	0	0
$367$	−6.49521e95	−0.434126	−0.217063	−	0.976158i	$-0.569648\pi$
$367$	−6.49521e95	−0.434126	−0.217063	+	0.976158i	$0.569648\pi$
$368$	1.18243e96	0.713643
$369$	0	0
$370$	1.81037e96	0.891665
$371$	1.75003e96	0.778975
$372$	0	0
$373$	5.22192e96	1.89998	0.949991	−	0.312279i	$-0.101092\pi$
$373$	5.22192e96	1.89998	0.949991	+	0.312279i	$0.101092\pi$
$374$	−1.72424e95	−0.0567431
$375$	0	0
$376$	−9.66069e95	−0.260294
$377$	−9.48817e95	−0.231410
$378$	0	0
$379$	6.94041e94	0.0138808	0.00694041	−	0.999976i	$-0.497791\pi$
$379$	6.94041e94	0.0138808	0.00694041	+	0.999976i	$0.497791\pi$
$380$	−9.49590e96	−1.72049
$381$	0	0
$382$	1.58204e97	2.35419
$383$	−9.05321e96	−1.22137	−0.610687	−	0.791872i	$-0.709106\pi$
$383$	−9.05321e96	−1.22137	−0.610687	+	0.791872i	$0.709106\pi$
$384$	0	0
$385$	−2.25498e97	−2.50245
$386$	8.45081e96	0.850892
$387$	0	0
$388$	−2.38864e97	−1.98135
$389$	1.69852e97	1.27927	0.639634	−	0.768679i	$-0.279086\pi$
$389$	1.69852e97	1.27927	0.639634	+	0.768679i	$0.279086\pi$
$390$	0	0
$391$	5.06077e95	0.0314477
$392$	5.44540e96	0.307469
$393$	0	0
$394$	5.49418e97	2.56327
$395$	1.63255e97	0.692587
$396$	0	0
$397$	−1.70232e97	−0.597582	−0.298791	−	0.954319i	$-0.596583\pi$
$397$	−1.70232e97	−0.597582	−0.298791	+	0.954319i	$0.596583\pi$
$398$	−2.36077e97	−0.754115
$399$	0	0
$400$	−3.62493e97	−0.959511
$401$	−5.80652e97	−1.39959	−0.699797	−	0.714342i	$-0.746726\pi$
$401$	−5.80652e97	−1.39959	−0.699797	+	0.714342i	$0.746726\pi$
$402$	0	0
$403$	−4.35353e97	−0.870768
$404$	−2.06049e97	−0.375551
$405$	0	0
$406$	6.41566e97	0.971662
$407$	3.36931e97	0.465319
$408$	0	0
$409$	1.31385e98	1.50981	0.754903	−	0.655837i	$-0.227684\pi$
$409$	1.31385e98	1.50981	0.754903	+	0.655837i	$0.227684\pi$
$410$	1.12549e98	1.18018
$411$	0	0
$412$	8.17522e96	0.0714256
$413$	1.35387e98	1.08007
$414$	0	0
$415$	−2.58319e98	−1.71931
$416$	−1.15071e98	−0.699784
$417$	0	0
$418$	−3.21501e98	−1.63332
$419$	1.12448e98	0.522306	0.261153	−	0.965297i	$-0.415897\pi$
$419$	1.12448e98	0.522306	0.261153	+	0.965297i	$0.415897\pi$
$420$	0	0
$421$	2.85953e98	1.11100	0.555502	−	0.831515i	$-0.312526\pi$
$421$	2.85953e98	1.11100	0.555502	+	0.831515i	$0.312526\pi$
$422$	−1.28939e98	−0.458318
$423$	0	0
$424$	−6.18913e97	−0.184251
$425$	−1.55146e97	−0.0422821
$426$	0	0
$427$	1.21133e98	0.276832
$428$	7.57423e98	1.58561
$429$	0	0
$430$	1.61092e99	2.83144
$431$	−1.27153e98	−0.204847	−0.102424	−	0.994741i	$-0.532660\pi$
$431$	−1.27153e98	−0.204847	−0.102424	+	0.994741i	$0.532660\pi$
$432$	0	0
$433$	1.29434e98	0.175287	0.0876437	−	0.996152i	$-0.472066\pi$
$433$	1.29434e98	0.175287	0.0876437	+	0.996152i	$0.472066\pi$
$434$	2.94375e99	3.65625
$435$	0	0
$436$	4.23989e98	0.443212
$437$	9.43627e98	0.905204
$438$	0	0
$439$	2.23963e99	1.81033	0.905165	−	0.425060i	$-0.139747\pi$
$439$	2.23963e99	1.81033	0.905165	+	0.425060i	$0.139747\pi$
$440$	7.97492e98	0.591904
$441$	0	0
$442$	−3.78203e97	−0.0236805
$443$	4.21179e98	0.242285	0.121143	−	0.992635i	$-0.461344\pi$
$443$	4.21179e98	0.242285	0.121143	+	0.992635i	$0.461344\pi$
$444$	0	0
$445$	−3.33273e99	−1.61920
$446$	−3.66683e99	−1.63770
$447$	0	0
$448$	5.09024e99	1.92226
$449$	1.69484e99	0.588696	0.294348	−	0.955698i	$-0.404897\pi$
$449$	1.69484e99	0.588696	0.294348	+	0.955698i	$0.404897\pi$
$450$	0	0
$451$	2.09468e99	0.615882
$452$	−1.92440e99	−0.520721
$453$	0	0
$454$	−8.11368e99	−1.86047
$455$	−4.94617e99	−1.04434
$456$	0	0
$457$	−4.57890e99	−0.820169	−0.410085	−	0.912047i	$-0.634501\pi$
$457$	−4.57890e99	−0.820169	−0.410085	+	0.912047i	$0.634501\pi$
$458$	−6.17807e99	−1.01952
$459$	0	0
$460$	−1.29434e100	−1.81396
$461$	2.39771e99	0.309750	0.154875	−	0.987934i	$-0.450503\pi$
$461$	2.39771e99	0.309750	0.154875	+	0.987934i	$0.450503\pi$
$462$	0	0
$463$	4.76071e99	0.522859	0.261430	−	0.965223i	$-0.415806\pi$
$463$	4.76071e99	0.522859	0.261430	+	0.965223i	$0.415806\pi$
$464$	3.38075e99	0.342443
$465$	0	0
$466$	2.53697e100	2.18697
$467$	1.60644e100	1.27786	0.638928	−	0.769266i	$-0.279378\pi$
$467$	1.60644e100	1.27786	0.638928	+	0.769266i	$0.279378\pi$
$468$	0	0
$469$	−2.58964e100	−1.75492
$470$	−2.86641e100	−1.79337
$471$	0	0
$472$	−4.78809e99	−0.255469
$473$	2.99812e100	1.47760
$474$	0	0
$475$	−2.89285e100	−1.21707
$476$	1.40577e99	0.0546579
$477$	0	0
$478$	−1.85970e100	−0.617869
$479$	−2.55062e100	−0.783546	−0.391773	−	0.920062i	$-0.628138\pi$
$479$	−2.55062e100	−0.783546	−0.391773	+	0.920062i	$0.628138\pi$
$480$	0	0
$481$	7.39040e99	0.194190
$482$	−6.79044e100	−1.65057
$483$	0	0
$484$	2.34149e100	0.487294
$485$	−1.28168e101	−2.46867
$486$	0	0
$487$	−6.41200e100	−1.05842	−0.529210	−	0.848491i	$-0.677512\pi$
$487$	−6.41200e100	−1.05842	−0.529210	+	0.848491i	$0.677512\pi$
$488$	−4.28397e99	−0.0654792
$489$	0	0
$490$	1.61570e101	2.11840
$491$	8.97077e100	1.08962	0.544808	−	0.838561i	$-0.316602\pi$
$491$	8.97077e100	1.08962	0.544808	+	0.838561i	$0.316602\pi$
$492$	0	0
$493$	1.44696e99	0.0150902
$494$	−7.05194e100	−0.681629
$495$	0	0
$496$	1.55122e101	1.28857
$497$	7.92303e100	0.610276
$498$	0	0
$499$	1.62083e101	1.07391	0.536955	−	0.843611i	$-0.319574\pi$
$499$	1.62083e101	1.07391	0.536955	+	0.843611i	$0.319574\pi$
$500$	9.47070e100	0.582113
$501$	0	0
$502$	−4.56492e101	−2.41570
$503$	1.09505e99	0.00537818	0.00268909	−	0.999996i	$-0.499144\pi$
$503$	1.09505e99	0.00537818	0.00268909	+	0.999996i	$0.499144\pi$
$504$	0	0
$505$	−1.10560e101	−0.467920
$506$	−4.38221e101	−1.72206
$507$	0	0
$508$	−1.69165e101	−0.573353
$509$	−1.18985e101	−0.374608	−0.187304	−	0.982302i	$-0.559975\pi$
$509$	−1.18985e101	−0.374608	−0.187304	+	0.982302i	$0.559975\pi$
$510$	0	0
$511$	3.92818e101	1.06760
$512$	5.05163e101	1.27588
$513$	0	0
$514$	−2.68476e101	−0.585853
$515$	4.38660e100	0.0889932
$516$	0	0
$517$	−5.33475e101	−0.935876
$518$	−4.99720e101	−0.815382
$519$	0	0
$520$	1.74926e101	0.247018
$521$	−5.83254e100	−0.0766378	−0.0383189	−	0.999266i	$-0.512200\pi$
$521$	−5.83254e100	−0.0766378	−0.0383189	+	0.999266i	$0.512200\pi$
$522$	0	0
$523$	−3.14042e101	−0.357416	−0.178708	−	0.983902i	$-0.557192\pi$
$523$	−3.14042e101	−0.357416	−0.178708	+	0.983902i	$0.557192\pi$
$524$	7.43035e101	0.787202
$525$	0	0
$526$	−2.80178e102	−2.57317
$527$	6.63918e100	0.0567828
$528$	0	0
$529$	−6.14737e100	−0.0456144
$530$	−1.83637e102	−1.26945
$531$	0	0
$532$	2.62118e102	1.57330
$533$	4.59457e101	0.257024
$534$	0	0
$535$	4.06412e102	1.97560
$536$	9.15847e101	0.415091
$537$	0	0
$538$	2.31797e102	0.913633
$539$	3.00701e102	1.10549
$540$	0	0
$541$	1.36286e102	0.436069	0.218034	−	0.975941i	$-0.430036\pi$
$541$	1.36286e102	0.436069	0.218034	+	0.975941i	$0.430036\pi$
$542$	5.68191e102	1.69637
$543$	0	0
$544$	1.75484e101	0.0456329
$545$	2.27501e102	0.552223
$546$	0	0
$547$	−3.83088e102	−0.810539	−0.405269	−	0.914197i	$-0.632822\pi$
$547$	−3.83088e102	−0.810539	−0.405269	+	0.914197i	$0.632822\pi$
$548$	−2.08841e102	−0.412614
$549$	0	0
$550$	1.34344e103	2.31535
$551$	2.69798e102	0.434364
$552$	0	0
$553$	−4.50636e102	−0.633336
$554$	1.56001e103	2.04885
$555$	0	0
$556$	−9.54918e101	−0.109562
$557$	−9.23735e102	−0.990781	−0.495390	−	0.868670i	$-0.664975\pi$
$557$	−9.23735e102	−0.990781	−0.495390	+	0.868670i	$0.664975\pi$
$558$	0	0
$559$	6.57621e102	0.616642
$560$	1.76238e103	1.54543
$561$	0	0
$562$	−2.86108e102	−0.219492
$563$	−4.61463e102	−0.331186	−0.165593	−	0.986194i	$-0.552954\pi$
$563$	−4.61463e102	−0.331186	−0.165593	+	0.986194i	$0.552954\pi$
$564$	0	0
$565$	−1.03258e103	−0.648795
$566$	−6.08271e102	−0.357669
$567$	0	0
$568$	−2.80205e102	−0.144349
$569$	−1.88669e103	−0.909893	−0.454947	−	0.890519i	$-0.650342\pi$
$569$	−1.88669e103	−0.909893	−0.454947	+	0.890519i	$0.650342\pi$
$570$	0	0
$571$	4.67402e103	1.97623	0.988113	−	0.153727i	$-0.0491277\pi$
$571$	4.67402e103	1.97623	0.988113	+	0.153727i	$0.0491277\pi$
$572$	1.80024e103	0.712820
$573$	0	0
$574$	−3.10673e103	−1.07921
$575$	−3.94309e103	−1.28319
$576$	0	0
$577$	−3.64917e103	−1.04256	−0.521280	−	0.853386i	$-0.674545\pi$
$577$	−3.64917e103	−1.04256	−0.521280	+	0.853386i	$0.674545\pi$
$578$	−5.56026e103	−1.48868
$579$	0	0
$580$	−3.70072e103	−0.870435
$581$	7.13046e103	1.57222
$582$	0	0
$583$	−3.41771e103	−0.662468
$584$	−1.38924e103	−0.252519
$585$	0	0
$586$	−9.68730e103	−1.54897
$587$	−1.17897e104	−1.76838	−0.884190	−	0.467128i	$-0.845289\pi$
$587$	−1.17897e104	−1.76838	−0.884190	+	0.467128i	$0.845289\pi$
$588$	0	0
$589$	1.23794e104	1.63446
$590$	−1.42067e104	−1.76012
$591$	0	0
$592$	−2.63329e103	−0.287365
$593$	1.02656e104	1.05156	0.525779	−	0.850621i	$-0.323774\pi$
$593$	1.02656e104	1.05156	0.525779	+	0.850621i	$0.323774\pi$
$594$	0	0
$595$	7.54296e102	0.0681014
$596$	1.62511e104	1.37768
$597$	0	0
$598$	−9.61214e103	−0.718663
$599$	−7.18476e103	−0.504553	−0.252276	−	0.967655i	$-0.581179\pi$
$599$	−7.18476e103	−0.504553	−0.252276	+	0.967655i	$0.581179\pi$
$600$	0	0
$601$	−4.70305e103	−0.291465	−0.145733	−	0.989324i	$-0.546554\pi$
$601$	−4.70305e103	−0.291465	−0.145733	+	0.989324i	$0.546554\pi$
$602$	−4.44667e104	−2.58920
$603$	0	0
$604$	2.00202e104	1.02940
$605$	1.25638e104	0.607147
$606$	0	0
$607$	4.85988e103	0.207515	0.103757	−	0.994603i	$-0.466913\pi$
$607$	4.85988e103	0.207515	0.103757	+	0.994603i	$0.466913\pi$
$608$	3.27205e104	1.31352
$609$	0	0
$610$	−1.27109e104	−0.451137
$611$	−1.17015e104	−0.390567
$612$	0	0
$613$	2.87536e104	0.849033	0.424517	−	0.905420i	$-0.360444\pi$
$613$	2.87536e104	0.849033	0.424517	+	0.905420i	$0.360444\pi$
$614$	−2.77474e104	−0.770741
$615$	0	0
$616$	−2.20134e104	−0.541266
$617$	5.46413e104	1.26423	0.632117	−	0.774873i	$-0.282186\pi$
$617$	5.46413e104	1.26423	0.632117	+	0.774873i	$0.282186\pi$
$618$	0	0
$619$	8.19299e104	1.67897	0.839486	−	0.543382i	$-0.182856\pi$
$619$	8.19299e104	1.67897	0.839486	+	0.543382i	$0.182856\pi$
$620$	−1.69803e105	−3.27534
$621$	0	0
$622$	−1.52087e105	−2.59988
$623$	9.19943e104	1.48067
$624$	0	0
$625$	−4.12132e104	−0.588215
$626$	1.68488e105	2.26480
$627$	0	0
$628$	1.95193e105	2.32797
$629$	−1.12704e103	−0.0126631
$630$	0	0
$631$	−1.20642e103	−0.0120336	−0.00601682	−	0.999982i	$-0.501915\pi$
$631$	−1.20642e103	−0.0120336	−0.00601682	+	0.999982i	$0.501915\pi$
$632$	1.59371e104	0.149803
$633$	0	0
$634$	1.29584e105	1.08194
$635$	−9.07695e104	−0.714373
$636$	0	0
$637$	6.59572e104	0.461353
$638$	−1.25294e105	−0.826335
$639$	0	0
$640$	−1.66487e105	−0.976408
$641$	−1.53129e105	−0.846994	−0.423497	−	0.905898i	$-0.639198\pi$
$641$	−1.53129e105	−0.846994	−0.423497	+	0.905898i	$0.639198\pi$
$642$	0	0
$643$	−3.28939e105	−1.61884	−0.809420	−	0.587231i	$-0.800218\pi$
$643$	−3.28939e105	−1.61884	−0.809420	+	0.587231i	$0.800218\pi$
$644$	3.57280e105	1.65878
$645$	0	0
$646$	1.07543e104	0.0444490
$647$	−4.12602e105	−1.60924	−0.804621	−	0.593789i	$-0.797631\pi$
$647$	−4.12602e105	−1.60924	−0.804621	+	0.593789i	$0.797631\pi$
$648$	0	0
$649$	−2.64404e105	−0.918528
$650$	2.94676e105	0.966261
$651$	0	0
$652$	−7.41773e105	−2.16763
$653$	5.94027e105	1.63894	0.819468	−	0.573125i	$-0.194269\pi$
$653$	5.94027e105	1.63894	0.819468	+	0.573125i	$0.194269\pi$
$654$	0	0
$655$	3.98692e105	0.980819
$656$	−1.63710e105	−0.380348
$657$	0	0
$658$	7.91225e105	1.63994
$659$	8.96994e105	1.75625	0.878126	−	0.478430i	$-0.158794\pi$
$659$	8.96994e105	1.75625	0.878126	+	0.478430i	$0.158794\pi$
$660$	0	0
$661$	7.06992e105	1.23555	0.617774	−	0.786355i	$-0.288034\pi$
$661$	7.06992e105	1.23555	0.617774	+	0.786355i	$0.288034\pi$
$662$	2.81116e105	0.464206
$663$	0	0
$664$	−2.52175e105	−0.371877
$665$	1.40645e106	1.96026
$666$	0	0
$667$	3.67748e105	0.457964
$668$	−9.31979e105	−1.09721
$669$	0	0
$670$	2.71740e106	2.85989
$671$	−2.36566e105	−0.235428
$672$	0	0
$673$	7.44927e105	0.663054	0.331527	−	0.943446i	$-0.392436\pi$
$673$	7.44927e105	0.663054	0.331527	+	0.943446i	$0.392436\pi$
$674$	−7.44029e105	−0.626389
$675$	0	0
$676$	−1.22557e106	−0.923285
$677$	9.15284e104	0.0652350	0.0326175	−	0.999468i	$-0.489616\pi$
$677$	9.15284e104	0.0652350	0.0326175	+	0.999468i	$0.489616\pi$
$678$	0	0
$679$	3.53785e106	2.25748
$680$	−2.66763e104	−0.0161080
$681$	0	0
$682$	−5.74898e106	−3.10940
$683$	−3.43532e105	−0.175870	−0.0879348	−	0.996126i	$-0.528027\pi$
$683$	−3.43532e105	−0.175870	−0.0879348	+	0.996126i	$0.528027\pi$
$684$	0	0
$685$	−1.12058e106	−0.514100
$686$	3.12137e105	0.135578
$687$	0	0
$688$	−2.34318e106	−0.912515
$689$	−7.49657e105	−0.276466
$690$	0	0
$691$	1.22859e106	0.406424	0.203212	−	0.979135i	$-0.434862\pi$
$691$	1.22859e106	0.406424	0.203212	+	0.979135i	$0.434862\pi$
$692$	−5.92659e106	−1.85706
$693$	0	0
$694$	2.12524e106	0.597623
$695$	−5.12383e105	−0.136510
$696$	0	0
$697$	−7.00677e104	−0.0167606
$698$	4.81222e106	1.09086
$699$	0	0
$700$	−1.09530e107	−2.23027
$701$	−1.96377e106	−0.379022	−0.189511	−	0.981879i	$-0.560690\pi$
$701$	−1.96377e106	−0.379022	−0.189511	+	0.981879i	$0.560690\pi$
$702$	0	0
$703$	−2.10148e106	−0.364502
$704$	−9.94096e106	−1.63476
$705$	0	0
$706$	−3.98094e106	−0.588586
$707$	3.05182e106	0.427889
$708$	0	0
$709$	4.23404e106	0.533976	0.266988	−	0.963700i	$-0.413972\pi$
$709$	4.23404e106	0.533976	0.266988	+	0.963700i	$0.413972\pi$
$710$	−8.31393e106	−0.994531
$711$	0	0
$712$	−3.25346e106	−0.350224
$713$	1.68737e107	1.72326
$714$	0	0
$715$	9.65960e106	0.888143
$716$	−1.32484e107	−1.15591
$717$	0	0
$718$	−1.59518e107	−1.25356
$719$	−1.27678e107	−0.952316	−0.476158	−	0.879360i	$-0.657971\pi$
$719$	−1.27678e107	−0.952316	−0.476158	+	0.879360i	$0.657971\pi$
$720$	0	0
$721$	−1.21085e106	−0.0813797
$722$	−3.30354e106	−0.210782
$723$	0	0
$724$	−1.86657e107	−1.07362
$725$	−1.12739e107	−0.615744
$726$	0	0
$727$	3.59224e107	1.76939	0.884697	−	0.466166i	$-0.154365\pi$
$727$	3.59224e107	1.76939	0.884697	+	0.466166i	$0.154365\pi$
$728$	−4.82852e106	−0.225885
$729$	0	0
$730$	−4.12199e107	−1.73980
$731$	−1.00288e106	−0.0402112
$732$	0	0
$733$	4.68165e107	1.69434	0.847168	−	0.531325i	$-0.178306\pi$
$733$	4.68165e107	1.69434	0.847168	+	0.531325i	$0.178306\pi$
$734$	−1.88135e107	−0.646945
$735$	0	0
$736$	4.45997e107	1.38489
$737$	5.05742e107	1.49244
$738$	0	0
$739$	−9.15146e106	−0.243963	−0.121982	−	0.992532i	$-0.538925\pi$
$739$	−9.15146e106	−0.243963	−0.121982	+	0.992532i	$0.538925\pi$
$740$	2.88252e107	0.730436
$741$	0	0
$742$	5.06899e107	1.16085
$743$	8.16406e106	0.177757	0.0888783	−	0.996042i	$-0.471672\pi$
$743$	8.16406e106	0.177757	0.0888783	+	0.996042i	$0.471672\pi$
$744$	0	0
$745$	8.71989e107	1.71653
$746$	1.51254e108	2.83140
$747$	0	0
$748$	−2.74539e106	−0.0464830
$749$	−1.12183e108	−1.80659
$750$	0	0
$751$	−9.35487e107	−1.36314	−0.681570	−	0.731753i	$-0.738702\pi$
$751$	−9.35487e107	−1.36314	−0.681570	+	0.731753i	$0.738702\pi$
$752$	4.16938e107	0.577966
$753$	0	0
$754$	−2.74827e107	−0.344852
$755$	1.07423e108	1.28258
$756$	0	0
$757$	1.82140e107	0.196929	0.0984645	−	0.995141i	$-0.468607\pi$
$757$	1.82140e107	0.196929	0.0984645	+	0.995141i	$0.468607\pi$
$758$	2.01030e106	0.0206855
$759$	0	0
$760$	−4.97405e107	−0.463661
$761$	8.22984e107	0.730242	0.365121	−	0.930960i	$-0.381028\pi$
$761$	8.22984e107	0.730242	0.365121	+	0.930960i	$0.381028\pi$
$762$	0	0
$763$	−6.27978e107	−0.504980
$764$	2.51897e108	1.92851
$765$	0	0
$766$	−2.62228e108	−1.82012
$767$	−5.79957e107	−0.383327
$768$	0	0
$769$	2.74612e108	1.64620	0.823098	−	0.567900i	$-0.192244\pi$
$769$	2.74612e108	1.64620	0.823098	+	0.567900i	$0.192244\pi$
$770$	−6.53158e108	−3.72920
$771$	0	0
$772$	1.34556e108	0.697036
$773$	−1.64531e108	−0.811924	−0.405962	−	0.913890i	$-0.633063\pi$
$773$	−1.64531e108	−0.811924	−0.405962	+	0.913890i	$0.633063\pi$
$774$	0	0
$775$	−5.17291e108	−2.31697
$776$	−1.25119e108	−0.533961
$777$	0	0
$778$	4.91981e108	1.90640
$779$	−1.30648e108	−0.482443
$780$	0	0
$781$	−1.54732e108	−0.519000
$782$	1.46586e107	0.0468640
$783$	0	0
$784$	−2.35013e108	−0.682716
$785$	1.04735e109	2.90055
$786$	0	0
$787$	6.95067e108	1.74974	0.874872	−	0.484354i	$-0.160945\pi$
$787$	6.95067e108	1.74974	0.874872	+	0.484354i	$0.160945\pi$
$788$	8.74800e108	2.09979
$789$	0	0
$790$	4.72870e108	1.03211
$791$	2.85027e108	0.593290
$792$	0	0
$793$	−5.18895e107	−0.0982505
$794$	−4.93080e108	−0.890531
$795$	0	0
$796$	−3.75888e108	−0.617758
$797$	1.73186e108	0.271534	0.135767	−	0.990741i	$-0.456650\pi$
$797$	1.73186e108	0.271534	0.135767	+	0.990741i	$0.456650\pi$
$798$	0	0
$799$	1.78449e107	0.0254689
$800$	−1.36728e109	−1.86201
$801$	0	0
$802$	−1.68187e109	−2.08571
$803$	−7.67153e108	−0.907923
$804$	0	0
$805$	1.91707e109	2.06677
$806$	−1.26101e109	−1.29764
$807$	0	0
$808$	−1.07930e108	−0.101209
$809$	7.97983e108	0.714371	0.357186	−	0.934033i	$-0.383736\pi$
$809$	7.97983e108	0.714371	0.357186	+	0.934033i	$0.383736\pi$
$810$	0	0
$811$	−1.17079e109	−0.955426	−0.477713	−	0.878516i	$-0.658534\pi$
$811$	−1.17079e109	−0.955426	−0.477713	+	0.878516i	$0.658534\pi$
$812$	1.02152e109	0.795969
$813$	0	0
$814$	9.75927e108	0.693429
$815$	−3.98015e109	−2.70078
$816$	0	0
$817$	−1.86996e109	−1.15746
$818$	3.80558e109	2.24995
$819$	0	0
$820$	1.79204e109	0.966783
$821$	−2.89556e107	−0.0149233	−0.00746163	−	0.999972i	$-0.502375\pi$
$821$	−2.89556e107	−0.0149233	−0.00746163	+	0.999972i	$0.502375\pi$
$822$	0	0
$823$	−1.93713e109	−0.911307	−0.455654	−	0.890157i	$-0.650594\pi$
$823$	−1.93713e109	−0.911307	−0.455654	+	0.890157i	$0.650594\pi$
$824$	4.28226e107	0.0192488
$825$	0	0
$826$	3.92152e109	1.60954
$827$	−5.09906e108	−0.200002	−0.100001	−	0.994987i	$-0.531885\pi$
$827$	−5.09906e108	−0.200002	−0.100001	+	0.994987i	$0.531885\pi$
$828$	0	0
$829$	−2.40363e109	−0.861139	−0.430570	−	0.902557i	$-0.641687\pi$
$829$	−2.40363e109	−0.861139	−0.430570	+	0.902557i	$0.641687\pi$
$830$	−7.48226e109	−2.56215
$831$	0	0
$832$	−2.18050e109	−0.682230
$833$	−1.00585e108	−0.0300848
$834$	0	0
$835$	−5.00075e109	−1.36707
$836$	−5.11902e109	−1.33799
$837$	0	0
$838$	3.25707e109	0.778353
$839$	3.09581e109	0.707457	0.353729	−	0.935348i	$-0.384914\pi$
$839$	3.09581e109	0.707457	0.353729	+	0.935348i	$0.384914\pi$
$840$	0	0
$841$	−3.73320e109	−0.780245
$842$	8.28267e109	1.65564
$843$	0	0
$844$	−2.05300e109	−0.375446
$845$	−6.57606e109	−1.15037
$846$	0	0
$847$	−3.46802e109	−0.555205
$848$	2.67112e109	0.409118
$849$	0	0
$850$	−4.49384e108	−0.0630098
$851$	−2.86441e109	−0.384306
$852$	0	0
$853$	7.93997e109	0.975506	0.487753	−	0.872982i	$-0.337817\pi$
$853$	7.93997e109	0.975506	0.487753	+	0.872982i	$0.337817\pi$
$854$	3.50864e109	0.412542
$855$	0	0
$856$	3.96745e109	0.427313
$857$	1.00473e110	1.03579	0.517893	−	0.855445i	$-0.326716\pi$
$857$	1.00473e110	1.03579	0.517893	+	0.855445i	$0.326716\pi$
$858$	0	0
$859$	9.45760e109	0.893383	0.446691	−	0.894688i	$-0.352602\pi$
$859$	9.45760e109	0.893383	0.446691	+	0.894688i	$0.352602\pi$
$860$	2.56495e110	2.31946
$861$	0	0
$862$	−3.68302e109	−0.305268
$863$	−1.62638e110	−1.29068	−0.645339	−	0.763896i	$-0.723284\pi$
$863$	−1.62638e110	−1.29068	−0.645339	+	0.763896i	$0.723284\pi$
$864$	0	0
$865$	−3.18005e110	−2.31382
$866$	3.74906e109	0.261217
$867$	0	0
$868$	4.68712e110	2.99514
$869$	8.80068e109	0.538611
$870$	0	0
$871$	1.10932e110	0.622838
$872$	2.22090e109	0.119443
$873$	0	0
$874$	2.73323e110	1.34896
$875$	−1.40272e110	−0.663238
$876$	0	0
$877$	1.83558e110	0.796691	0.398345	−	0.917236i	$-0.369585\pi$
$877$	1.83558e110	0.796691	0.398345	+	0.917236i	$0.369585\pi$
$878$	6.48714e110	2.69780
$879$	0	0
$880$	−3.44183e110	−1.31429
$881$	3.02493e110	1.10693	0.553463	−	0.832874i	$-0.313306\pi$
$881$	3.02493e110	1.10693	0.553463	+	0.832874i	$0.313306\pi$
$882$	0	0
$883$	2.96289e110	0.995838	0.497919	−	0.867223i	$-0.334098\pi$
$883$	2.96289e110	0.995838	0.497919	+	0.867223i	$0.334098\pi$
$884$	−6.02186e108	−0.0193986
$885$	0	0
$886$	1.21995e110	0.361059
$887$	−4.87676e110	−1.38355	−0.691776	−	0.722112i	$-0.743172\pi$
$887$	−4.87676e110	−1.38355	−0.691776	+	0.722112i	$0.743172\pi$
$888$	0	0
$889$	2.50554e110	0.653258
$890$	−9.65331e110	−2.41297
$891$	0	0
$892$	−5.83843e110	−1.34157
$893$	3.32734e110	0.733107
$894$	0	0
$895$	−7.10871e110	−1.44021
$896$	4.59559e110	0.892876
$897$	0	0
$898$	4.90914e110	0.877289
$899$	4.82445e110	0.826913
$900$	0	0
$901$	1.14323e109	0.0180283
$902$	6.06728e110	0.917801
$903$	0	0
$904$	−1.00802e110	−0.140331
$905$	−1.00155e111	−1.33768
$906$	0	0
$907$	−4.17981e110	−0.513906	−0.256953	−	0.966424i	$-0.582719\pi$
$907$	−4.17981e110	−0.513906	−0.256953	+	0.966424i	$0.582719\pi$
$908$	−1.29188e111	−1.52407
$909$	0	0
$910$	−1.43267e111	−1.55630
$911$	2.43772e110	0.254123	0.127062	−	0.991895i	$-0.459445\pi$
$911$	2.43772e110	0.254123	0.127062	+	0.991895i	$0.459445\pi$
$912$	0	0
$913$	−1.39254e111	−1.33707
$914$	−1.32629e111	−1.22224
$915$	0	0
$916$	−9.83690e110	−0.835176
$917$	−1.10052e111	−0.896909
$918$	0	0
$919$	5.55089e110	0.416899	0.208449	−	0.978033i	$-0.433158\pi$
$919$	5.55089e110	0.416899	0.208449	+	0.978033i	$0.433158\pi$
$920$	−6.77987e110	−0.488852
$921$	0	0
$922$	6.94500e110	0.461597
$923$	−3.39397e110	−0.216593
$924$	0	0
$925$	8.78134e110	0.516709
$926$	1.37895e111	0.779177
$927$	0	0
$928$	1.27518e111	0.664540
$929$	2.79269e110	0.139776	0.0698881	−	0.997555i	$-0.477736\pi$
$929$	2.79269e110	0.139776	0.0698881	+	0.997555i	$0.477736\pi$
$930$	0	0
$931$	−1.87551e111	−0.865975
$932$	4.03944e111	1.79153
$933$	0	0
$934$	4.65309e111	1.90429
$935$	−1.47310e110	−0.0579158
$936$	0	0
$937$	−2.54076e110	−0.0921997	−0.0460998	−	0.998937i	$-0.514679\pi$
$937$	−2.54076e110	−0.0921997	−0.0460998	+	0.998937i	$0.514679\pi$
$938$	−7.50093e111	−2.61522
$939$	0	0
$940$	−4.56399e111	−1.46910
$941$	−5.39434e110	−0.166850	−0.0834252	−	0.996514i	$-0.526586\pi$
$941$	−5.39434e110	−0.166850	−0.0834252	+	0.996514i	$0.526586\pi$
$942$	0	0
$943$	−1.78079e111	−0.508656
$944$	2.06646e111	0.567252
$945$	0	0
$946$	8.68410e111	2.20195
$947$	5.12709e111	1.24953	0.624765	−	0.780813i	$-0.285195\pi$
$947$	5.12709e111	1.24953	0.624765	+	0.780813i	$0.285195\pi$
$948$	0	0
$949$	−1.68271e111	−0.378901
$950$	−8.37918e111	−1.81370
$951$	0	0
$952$	7.36355e109	0.0147300
$953$	1.33636e111	0.257004	0.128502	−	0.991709i	$-0.458983\pi$
$953$	1.33636e111	0.257004	0.128502	+	0.991709i	$0.458983\pi$
$954$	0	0
$955$	1.35161e112	2.40285
$956$	−2.96107e111	−0.506148
$957$	0	0
$958$	−7.38793e111	−1.16766
$959$	3.09318e111	0.470118
$960$	0	0
$961$	1.50222e112	2.11157
$962$	2.14064e111	0.289387
$963$	0	0
$964$	−1.08119e112	−1.35212
$965$	7.21992e111	0.868476
$966$	0	0
$967$	−1.07433e112	−1.19577	−0.597883	−	0.801583i	$-0.703991\pi$
$967$	−1.07433e112	−1.19577	−0.597883	+	0.801583i	$0.703991\pi$
$968$	1.22650e111	0.131323
$969$	0	0
$970$	−3.71240e112	−3.67887
$971$	1.38284e112	1.31841	0.659206	−	0.751963i	$-0.270893\pi$
$971$	1.38284e112	1.31841	0.659206	+	0.751963i	$0.270893\pi$
$972$	0	0
$973$	1.41435e111	0.124831
$974$	−1.85725e112	−1.57728
$975$	0	0
$976$	1.84888e111	0.145392
$977$	−3.40506e111	−0.257679	−0.128839	−	0.991665i	$-0.541125\pi$
$977$	−3.40506e111	−0.257679	−0.128839	+	0.991665i	$0.541125\pi$
$978$	0	0
$979$	−1.79660e112	−1.25922
$980$	2.57256e112	1.73535
$981$	0	0
$982$	2.59840e112	1.62377
$983$	4.99299e111	0.300333	0.150167	−	0.988661i	$-0.452019\pi$
$983$	4.99299e111	0.300333	0.150167	+	0.988661i	$0.452019\pi$
$984$	0	0
$985$	4.69393e112	2.61624
$986$	4.19113e110	0.0224878
$987$	0	0
$988$	−1.12283e112	−0.558379
$989$	−2.54884e112	−1.22034
$990$	0	0
$991$	1.47616e112	0.655196	0.327598	−	0.944817i	$-0.393761\pi$
$991$	1.47616e112	0.655196	0.327598	+	0.944817i	$0.393761\pi$
$992$	5.85099e112	2.50059
$993$	0	0
$994$	2.29492e112	0.909448
$995$	−2.01691e112	−0.769700
$996$	0	0
$997$	−2.67429e112	−0.946543	−0.473272	−	0.880917i	$-0.656927\pi$
$997$	−2.67429e112	−0.946543	−0.473272	+	0.880917i	$0.656927\pi$
$998$	4.69477e112	1.60037
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.76.a.c.1.5		6
3.2	odd	2		1.76.a.a.1.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.76.a.a.1.2	✓	6	3.2	odd	2
9.76.a.c.1.5		6	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:	\( k \)	\(=\)	\( 76 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+2.89652e11 q^{2} +4.61192e22 q^{4} +2.47463e26 q^{5} -6.83079e31 q^{7} +2.41577e33 q^{8} +O(q^{10})\)	\(q+2.89652e11 q^{2} +4.61192e22 q^{4} +2.47463e26 q^{5} -6.83079e31 q^{7} +2.41577e33 q^{8} +7.16781e37 q^{10} +1.33402e39 q^{11} +2.92609e41 q^{13} -1.97855e43 q^{14} -1.04260e45 q^{16} -4.46232e44 q^{17} -8.32041e47 q^{19} +1.14128e49 q^{20} +3.86400e50 q^{22} -1.13411e51 q^{23} +3.47681e52 q^{25} +8.47548e52 q^{26} -3.15030e54 q^{28} -3.24261e54 q^{29} -1.48783e56 q^{31} -3.93257e56 q^{32} -1.29252e56 q^{34} -1.69037e58 q^{35} +2.52569e58 q^{37} -2.41002e59 q^{38} +5.97813e59 q^{40} +1.57021e60 q^{41} +2.24744e61 q^{43} +6.15237e61 q^{44} -3.28497e62 q^{46} -3.99901e62 q^{47} +2.25410e63 q^{49} +1.00706e64 q^{50} +1.34949e64 q^{52} -2.56197e64 q^{53} +3.30120e65 q^{55} -1.65016e65 q^{56} -9.39227e65 q^{58} -1.98202e66 q^{59} -1.77334e66 q^{61} -4.30953e67 q^{62} -7.45191e67 q^{64} +7.24099e67 q^{65} +3.79112e68 q^{67} -2.05799e67 q^{68} -4.89618e69 q^{70} -1.15990e69 q^{71} -5.75070e69 q^{73} +7.31570e69 q^{74} -3.83730e70 q^{76} -9.11239e70 q^{77} +6.59713e70 q^{79} -2.58005e71 q^{80} +4.54813e71 q^{82} -1.04387e72 q^{83} -1.10426e71 q^{85} +6.50974e72 q^{86} +3.22267e72 q^{88} -1.34676e73 q^{89} -1.99875e73 q^{91} -5.23043e73 q^{92} -1.15832e74 q^{94} -2.05899e74 q^{95} -5.17927e74 q^{97} +6.52905e74 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 57080822040 q^{2} + 17\!\cdots\!28 q^{4}+ \cdots - 44\!\cdots\!20 q^{8}+O(q^{10}) \) 6 * q + 57080822040 * q^2 + 172600466200162028593728 * q^4 + 38982947396479621874420940 * q^5 + 1924474634802918779239478643600 * q^7 - 4434903997968330342413437320645120 * q^8	\( 6 q + 57080822040 q^{2} + 17\!\cdots\!28 q^{4}+ \cdots + 16\!\cdots\!20 q^{98}+O(q^{100}) \) 6 * q + 57080822040 * q^2 + 172600466200162028593728 * q^4 + 38982947396479621874420940 * q^5 + 1924474634802918779239478643600 * q^7 - 4434903997968330342413437320645120 * q^8 + 133267935677460241037537052811576902960 * q^10 + 945659951949983071650740113735111214088 * q^11 + 533185179266852519941169625089098069764420 * q^13 - 8213946953162263647781694565284746353072576 * q^14 + 2681978005634517266622433394712415602648354816 * q^16 - 18261354095776132566172834671579513215483393580 * q^17 + 1061534856238354155312794852768417904375328867080 * q^19 - 9296557595621768320156983882258818695571369489280 * q^20 + 153315952874260268106194796405555863940172791589920 * q^22 - 1514929449877410771078348320690686508954384916853680 * q^23 + 19310380328261093150952553553121815533899364092239850 * q^25 - 117730941166816926498584842564210483616872200198362352 * q^26 + 1465885017268620651444113586751990931877154821040657920 * q^28 - 14718767377678125816030788545177391174717388984245534820 * q^29 - 41742874787360498453628839393549579933009794702042980288 * q^31 - 1174660148719991756036751189163540495635749096221862952960 * q^32 + 3034358950124956876257603978888653679838045546922892395856 * q^34 - 27299672493656883988453292135086250689495956464846953371360 * q^35 + 98517772547646219221591850851651469983797181732879949140340 * q^37 - 1257660981102762853948269222064665311191946222029530979162080 * q^38 + 8807901623729426290853411185831313455271917763097593104051200 * q^40 - 5039211762207387369185984529408567568647239506257650214613212 * q^41 + 27938749238581541451173935836639198120068956697568041153196600 * q^43 + 86388814623354110240559749283671522466589238091463431115801344 * q^44 - 824145803870667307795487213022331547039596870954611528203613888 * q^46 + 1386854970430427381646742231466788117324292253074354560479038880 * q^47 - 5707868790800975784856935495088511133239544554833878775910738442 * q^49 - 3144970672685230615695776810799603542575044196614572896663392600 * q^50 + 41677832028141179840113326797899392222702339479233001780216150400 * q^52 - 64283727174659970247345252518647455744441825702701764187054106260 * q^53 + 436876078674971654403803167180324983329224614451635548418098895120 * q^55 - 289950797286325881623798664040853221823087783432246887785270865920 * q^56 - 1763005756244374137396902189067511762184157619699352574614137403280 * q^58 + 2478360370933764187935912640189307752170553390931716617591182395560 * q^59 - 25641115321477658815889269525514418267074652297034046321782023152988 * q^61 + 29014701474354643819936101890527484086880802356768235703173807694080 * q^62 + 47683232974651133862719671893097862706511055838864188064811716968448 * q^64 - 122110621788131890149667214965152432737153070969379698276880591977720 * q^65 + 955579073553339181030887342220313909838725364297810737998207107813480 * q^67 - 1237210897217068882936524414359446185548686871817993659403939290386560 * q^68 - 3476902593928340346610001926714053112321275314411181267396530677050240 * q^70 + 255682319306096297182489045146623979225804710540351927309367569173488 * q^71 - 30605188898291905719532895918028188508004452865621142257485594115042020 * q^73 + 24065024027894599201472448362529876891121294631891709256708009194181584 * q^74 + 100020936372377387464010564774983213070641689274186088752725827576144640 * q^76 - 158930415774536768880543239288689183540801263714134710336228496440507200 * q^77 + 116627678166642324332643069323234092884951450625988452824960767925148320 * q^79 - 1239310052714502333188756625709169306278438274940582996524184215206748160 * q^80 - 2557649813228840791149140948716215474705151452500921688788291587877236080 * q^82 + 798780284119889426515570523310162377392459257634002033911814028088739960 * q^83 - 3615500806340871685633297735534398118961343923835923286123685237305018840 * q^85 - 7245194180836090971883743617494948296636529538939897523257528311698092832 * q^86 - 4827001398586167572057494186308233100206033194553368013345656010632181760 * q^88 - 53575610216125238704584826863934604186542249469498220298044079954014547260 * q^89 + 34502419684367451829908407139028781594042460695428817715772307436403470432 * q^91 - 187445224353587479072026786339601818260697439565538078689222489106585838080 * q^92 - 296189325151987924691405038954735773676385503565643130818482899021002578304 * q^94 - 194934959385332686251927514630723902507701573195047654345319995220933314800 * q^95 - 747928220344118582344222376208028579242743608466383778453296378427532508980 * q^97 + 1663265696927109513221859402309517858944410070626232817304447619248634722520 * q^98

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