LMFDB - Embedded newform 9.76.a.b.1.2

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 - 47\!\cdots\!88 $ x^6 - 3x^5 - 372608135375699744498x^4 - 454191572761767684323659845174x^3 + 33507084001263083029833096962584395835741x^2 + 45298525388739530181210060025322623724413504677033*x - 471634272542661261485889811340098476257538154617268089659388
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{45}\cdot 3^{33}\cdot 5^{7}\cdot 7^{3}\cdot 11^{2}\cdot 13\cdot 19^{2} $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.10322e10$ 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)

$f(q)$	$=$	$q-2.50422e11 q^{2} +2.49322e22 q^{4} +3.17209e25 q^{5} -7.65245e31 q^{7} +3.21710e33 q^{8} +O(q^{10})$	\(q-2.50422e11 q^{2} +2.49322e22 q^{4} +3.17209e25 q^{5} -7.65245e31 q^{7} +3.21710e33 q^{8} -7.94362e36 q^{10} +9.46558e38 q^{11} +9.24761e41 q^{13} +1.91634e43 q^{14} -1.74754e45 q^{16} +2.15032e46 q^{17} -8.01212e47 q^{19} +7.90874e47 q^{20} -2.37039e50 q^{22} -3.87360e50 q^{23} -2.54636e52 q^{25} -2.31580e53 q^{26} -1.90793e54 q^{28} -8.14915e54 q^{29} +1.35889e56 q^{31} +3.16085e56 q^{32} -5.38488e57 q^{34} -2.42743e57 q^{35} +1.12372e58 q^{37} +2.00641e59 q^{38} +1.02049e59 q^{40} -4.52749e59 q^{41} -1.49708e61 q^{43} +2.35998e61 q^{44} +9.70035e61 q^{46} -7.87216e61 q^{47} +3.44413e63 q^{49} +6.37663e63 q^{50} +2.30564e64 q^{52} +4.24437e63 q^{53} +3.00257e64 q^{55} -2.46187e65 q^{56} +2.04073e66 q^{58} -4.12523e66 q^{59} +2.43388e66 q^{61} -3.40296e67 q^{62} -1.31343e67 q^{64} +2.93343e67 q^{65} -1.13615e68 q^{67} +5.36124e68 q^{68} +6.07882e68 q^{70} +3.15866e69 q^{71} -1.11162e70 q^{73} -2.81404e69 q^{74} -1.99760e70 q^{76} -7.24349e70 q^{77} +1.20677e71 q^{79} -5.54338e70 q^{80} +1.13378e71 q^{82} -1.37693e72 q^{83} +6.82103e71 q^{85} +3.74903e72 q^{86} +3.04517e72 q^{88} -7.36822e72 q^{89} -7.07669e73 q^{91} -9.65775e72 q^{92} +1.97136e73 q^{94} -2.54152e73 q^{95} +5.29924e74 q^{97} -8.62487e74 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 311057037486 q^{2} + 30\!\cdots\!92 q^{4}+ \cdots - 69\!\cdots\!12 q^{8}+O(q^{10}) $ 6 * q - 311057037486 * q^2 + 30902560640638265713092 * q^4 - 97856522050579947592055460 * q^5 - 30749202116633858714981933510688 * q^7 - 6939052769539518449811063778704312 * q^8	$ 6 q - 311057037486 q^{2} + 30\!\cdots\!92 q^{4}+ \cdots - 14\!\cdots\!94 q^{98}+O(q^{100}) $ 6 * q - 311057037486 * q^2 + 30902560640638265713092 * q^4 - 97856522050579947592055460 * q^5 - 30749202116633858714981933510688 * q^7 - 6939052769539518449811063778704312 * q^8 - 107545734844341425270764823551622320620 * q^10 + 379379629646545786309015638730942099896 * q^11 + 154669229506479970266461340344668629154596 * q^13 - 31899227014014717498689751276506679791260128 * q^14 - 3260958521390361922516104888150343171861643760 * q^16 + 7401535799877014405171685814768477775195111796 * q^17 - 182729763718938971567579921571009657209643443592 * q^19 + 9428757085683313672852247515255856540783373281640 * q^20 + 471450583148622264812447113021812911318975285911848 * q^22 + 1094918718857791395763955497794548441629464114423696 * q^23 + 71600575748870708223111198803019790440272165366567850 * q^25 - 17144617795232739661292142542037336623136662115361812 * q^26 - 421056590097566772314387078351382806371109737989226944 * q^28 - 1286761243501908998723554437372128496488806548512006196 * q^29 - 19590134983123701786508136226454400260130744726276043984 * q^31 + 405443732303791628255103774085578846894562577440580267808 * q^32 + 799554727652091370833855066044541676465377828794014920924 * q^34 + 36738948500466973600844998839202990635858889677989007096000 * q^35 - 91545935905237059630111535534102037526425524589341335258828 * q^37 + 684421739975642826350565409193219733278360180645855295369576 * q^38 - 3191514246209809963152113018089087413561147078084072414179760 * q^40 + 316536315385886215170089302814500575828563777084996078443524 * q^41 + 8908593056531100512689524294334311253125705720155921361637320 * q^43 + 21785863331670136277341155880608983152526085161022719211416784 * q^44 + 203991825673001927929491823653549685659396184023570859282558896 * q^46 - 1142730760034072985500217886491003567898472938032199023875837760 * q^47 + 9932613847036662039777786400812307007669956514072280038886436470 * q^49 + 8883185004616479564484651092109548958973775099745125635626453950 * q^50 - 26987269348801105921073028535709825459131864700220460006411048296 * q^52 - 50865557114922724445413426425120290543311269685677591074207545764 * q^53 - 446272596484924291179313911709667686162610277785745256318167362640 * q^55 - 252098718314851221087836050947321657945518421301909982473468909440 * q^56 + 5708767830293773961786560342813586714128873252994207151314483829348 * q^58 - 2188427764336584360362109164219599664600305872173254932641215849992 * q^59 + 22824130148103906081748322440858509039514053708066868437237654119460 * q^61 - 47586797873032763455450207051586846920428945648357768353569220285424 * q^62 - 62277215504581285171320235502281031925680209278531250485362330807232 * q^64 + 139549609673753297396326760842807258047007635314506217050746073464360 * q^65 - 195051098831763858659485315535620001296749632524239458769204357711816 * q^67 + 478898943613171780503683796705180273623444550119196454935625635754872 * q^68 - 757997824979604988529186642170865717977143205307772715302146700408000 * q^70 + 3034169501204758984184273945180030994909311349950008497555595439759088 * q^71 + 13747249917875809714395686690179837721964032944309940620133405822381724 * q^73 + 2369634359974005306762628635878678463122778575706094238003611098139932 * q^74 - 34154148647149103788996774156065386764182788320537620321912800871149232 * q^76 - 110964225149010328333146128762358481438061822139163262844956857145745024 * q^77 - 201509609621708284923745260863351675377795113292036868882834678557374960 * q^79 + 422838509739279884709169464673498932712468741280281559903498362323065760 * q^80 + 1272064461032237978527479940408403539923817748343630409520994189497365644 * q^82 - 2802602491348140684813265973373777054770511234236863543486293197357747832 * q^83 - 60328702368357628714477758217500517309887606952299760526919048695903160 * q^85 - 5057125471275015782616585132644541629892966424745006584268526775897314984 * q^86 - 6621568649346448861468435905169718150646541969777165734050561367125413728 * q^88 + 159920271872091417315458194799657472188764331647019387730257248766388612 * q^89 - 63049718267601813432671733846200700661982230139950125748195604362104533184 * q^91 + 108738058107400706863040151004186657363927160845612619833607429521300941408 * q^92 + 197757998471403159993044858359064919780754639341995946156177159925776436032 * q^94 - 526939076500447210313077859524744124394283713808433538379475932881003671760 * q^95 + 379948778797471041696674086463609005506560736626194774039181672927157115404 * q^97 - 1466852164333826517330437746602345292601007324558710499132638626830518086494 * 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 $

$2$	−2.50422e11	−1.28839	−0.644195	−	0.764861i	$-0.722808\pi$
$2$	−2.50422e11	−1.28839	−0.644195	+	0.764861i	$0.722808\pi$
$3$	0	0
$3$	0	0
$4$	2.49322e22	0.659951
$5$	3.17209e25	0.194971	0.0974857	−	0.995237i	$-0.468920\pi$
$5$	3.17209e25	0.194971	0.0974857	+	0.995237i	$0.468920\pi$
$6$	0	0
$7$	−7.65245e31	−1.55820	−0.779101	−	0.626898i	$-0.784324\pi$
$7$	−7.65245e31	−1.55820	−0.779101	+	0.626898i	$0.784324\pi$
$8$	3.21710e33	0.438117
$9$	0	0
$10$	−7.94362e36	−0.251199
$11$	9.46558e38	0.839309	0.419654	−	0.907684i	$-0.362151\pi$
$11$	9.46558e38	0.839309	0.419654	+	0.907684i	$0.362151\pi$
$12$	0	0
$13$	9.24761e41	1.56011	0.780053	−	0.625714i	$-0.215192\pi$
$13$	9.24761e41	1.56011	0.780053	+	0.625714i	$0.215192\pi$
$14$	1.91634e43	2.00757
$15$	0	0
$16$	−1.74754e45	−1.22442
$17$	2.15032e46	1.55121	0.775603	−	0.631221i	$-0.217446\pi$
$17$	2.15032e46	1.55121	0.775603	+	0.631221i	$0.217446\pi$
$18$	0	0
$19$	−8.01212e47	−0.892252	−0.446126	−	0.894970i	$-0.647197\pi$
$19$	−8.01212e47	−0.892252	−0.446126	+	0.894970i	$0.647197\pi$
$20$	7.90874e47	0.128671
$21$	0	0
$22$	−2.37039e50	−1.08136
$23$	−3.87360e50	−0.333673	−0.166836	−	0.985985i	$-0.553355\pi$
$23$	−3.87360e50	−0.333673	−0.166836	+	0.985985i	$0.553355\pi$
$24$	0	0
$25$	−2.54636e52	−0.961986
$26$	−2.31580e53	−2.01002
$27$	0	0
$28$	−1.90793e54	−1.02834
$29$	−8.14915e54	−1.17811	−0.589057	−	0.808091i	$-0.700501\pi$
$29$	−8.14915e54	−1.17811	−0.589057	+	0.808091i	$0.700501\pi$
$30$	0	0
$31$	1.35889e56	1.61110	0.805548	−	0.592531i	$-0.201871\pi$
$31$	1.35889e56	1.61110	0.805548	+	0.592531i	$0.201871\pi$
$32$	3.16085e56	1.13941
$33$	0	0
$34$	−5.38488e57	−1.99856
$35$	−2.42743e57	−0.303805
$36$	0	0
$37$	1.12372e58	0.175022	0.0875110	−	0.996164i	$-0.472109\pi$
$37$	1.12372e58	0.175022	0.0875110	+	0.996164i	$0.472109\pi$
$38$	2.00641e59	1.14957
$39$	0	0
$40$	1.02049e59	0.0854202
$41$	−4.52749e59	−0.150128	−0.0750641	−	0.997179i	$-0.523916\pi$
$41$	−4.52749e59	−0.150128	−0.0750641	+	0.997179i	$0.523916\pi$
$42$	0	0
$43$	−1.49708e61	−0.832107	−0.416054	−	0.909340i	$-0.636587\pi$
$43$	−1.49708e61	−0.832107	−0.416054	+	0.909340i	$0.636587\pi$
$44$	2.35998e61	0.553902
$45$	0	0
$46$	9.70035e61	0.429901
$47$	−7.87216e61	−0.155749	−0.0778743	−	0.996963i	$-0.524813\pi$
$47$	−7.87216e61	−0.155749	−0.0778743	+	0.996963i	$0.524813\pi$
$48$	0	0
$49$	3.44413e63	1.42800
$50$	6.37663e63	1.23941
$51$	0	0
$52$	2.30564e64	1.02959
$53$	4.24437e63	0.0927829	0.0463914	−	0.998923i	$-0.485228\pi$
$53$	4.24437e63	0.0927829	0.0463914	+	0.998923i	$0.485228\pi$
$54$	0	0
$55$	3.00257e64	0.163641
$56$	−2.46187e65	−0.682674
$57$	0	0
$58$	2.04073e66	1.51787
$59$	−4.12523e66	−1.61621	−0.808105	−	0.589038i	$-0.799507\pi$
$59$	−4.12523e66	−1.61621	−0.808105	+	0.589038i	$0.799507\pi$
$60$	0	0
$61$	2.43388e66	0.273168	0.136584	−	0.990628i	$-0.456388\pi$
$61$	2.43388e66	0.273168	0.136584	+	0.990628i	$0.456388\pi$
$62$	−3.40296e67	−2.07572
$63$	0	0
$64$	−1.31343e67	−0.243589
$65$	2.93343e67	0.304176
$66$	0	0
$67$	−1.13615e68	−0.378122	−0.189061	−	0.981965i	$-0.560544\pi$
$67$	−1.13615e68	−0.378122	−0.189061	+	0.981965i	$0.560544\pi$
$68$	5.36124e68	1.02372
$69$	0	0
$70$	6.07882e68	0.391420
$71$	3.15866e69	1.19485	0.597426	−	0.801924i	$-0.296190\pi$
$71$	3.15866e69	1.19485	0.597426	+	0.801924i	$0.296190\pi$
$72$	0	0
$73$	−1.11162e70	−1.48371	−0.741857	−	0.670558i	$-0.766055\pi$
$73$	−1.11162e70	−1.48371	−0.741857	+	0.670558i	$0.766055\pi$
$74$	−2.81404e69	−0.225497
$75$	0	0
$76$	−1.99760e70	−0.588842
$77$	−7.24349e70	−1.30781
$78$	0	0
$79$	1.20677e71	0.832927	0.416464	−	0.909152i	$-0.363269\pi$
$79$	1.20677e71	0.832927	0.416464	+	0.909152i	$0.363269\pi$
$80$	−5.54338e70	−0.238726
$81$	0	0
$82$	1.13378e71	0.193424
$83$	−1.37693e72	−1.49102	−0.745509	−	0.666496i	$-0.767793\pi$
$83$	−1.37693e72	−1.49102	−0.745509	+	0.666496i	$0.767793\pi$
$84$	0	0
$85$	6.82103e71	0.302441
$86$	3.74903e72	1.07208
$87$	0	0
$88$	3.04517e72	0.367715
$89$	−7.36822e72	−0.582421	−0.291211	−	0.956659i	$-0.594058\pi$
$89$	−7.36822e72	−0.582421	−0.291211	+	0.956659i	$0.594058\pi$
$90$	0	0
$91$	−7.07669e73	−2.43096
$92$	−9.65775e72	−0.220208
$93$	0	0
$94$	1.97136e73	0.200665
$95$	−2.54152e73	−0.173964
$96$	0	0
$97$	5.29924e74	1.66063	0.830316	−	0.557292i	$-0.188160\pi$
$97$	5.29924e74	1.66063	0.830316	+	0.557292i	$0.188160\pi$
$98$	−8.62487e74	−1.83982
$99$	0	0
$100$	−6.34863e74	−0.634863
$101$	9.62057e74	0.662444	0.331222	−	0.943553i	$-0.392539\pi$
$101$	9.62057e74	0.662444	0.331222	+	0.943553i	$0.392539\pi$
$102$	0	0
$103$	5.29363e75	1.74726	0.873631	−	0.486590i	$-0.161759\pi$
$103$	5.29363e75	1.74726	0.873631	+	0.486590i	$0.161759\pi$
$104$	2.97505e75	0.683508
$105$	0	0
$106$	−1.06288e75	−0.119541
$107$	−1.41848e76	−1.12184	−0.560921	−	0.827869i	$-0.689553\pi$
$107$	−1.41848e76	−1.12184	−0.560921	+	0.827869i	$0.689553\pi$
$108$	0	0
$109$	−9.16687e75	−0.362016	−0.181008	−	0.983482i	$-0.557936\pi$
$109$	−9.16687e75	−0.362016	−0.181008	+	0.983482i	$0.557936\pi$
$110$	−7.51910e75	−0.210834
$111$	0	0
$112$	1.33730e77	1.90789
$113$	2.77755e75	0.0283936	0.0141968	−	0.999899i	$-0.495481\pi$
$113$	2.77755e75	0.0283936	0.0141968	+	0.999899i	$0.495481\pi$
$114$	0	0
$115$	−1.22874e76	−0.0650567
$116$	−2.03176e77	−0.777497
$117$	0	0
$118$	1.03305e78	2.08231
$119$	−1.64553e78	−2.41709
$120$	0	0
$121$	−3.75923e77	−0.295561
$122$	−6.09497e77	−0.351948
$123$	0	0
$124$	3.38802e78	1.06324
$125$	−1.64737e78	−0.382531
$126$	0	0
$127$	−6.52291e78	−0.835222	−0.417611	−	0.908626i	$-0.637132\pi$
$127$	−6.52291e78	−0.835222	−0.417611	+	0.908626i	$0.637132\pi$
$128$	−8.65225e78	−0.825572
$129$	0	0
$130$	−7.34595e78	−0.391897
$131$	3.42015e79	1.36890	0.684449	−	0.729060i	$-0.260043\pi$
$131$	3.42015e79	1.36890	0.684449	+	0.729060i	$0.260043\pi$
$132$	0	0
$133$	6.13124e79	1.39031
$134$	2.84518e79	0.487168
$135$	0	0
$136$	6.91780e79	0.679609
$137$	−1.75794e79	−0.131215	−0.0656074	−	0.997846i	$-0.520898\pi$
$137$	−1.75794e79	−0.131215	−0.0656074	+	0.997846i	$0.520898\pi$
$138$	0	0
$139$	−2.20402e80	−0.955346	−0.477673	−	0.878538i	$-0.658520\pi$
$139$	−2.20402e80	−0.955346	−0.477673	+	0.878538i	$0.658520\pi$
$140$	−6.05212e79	−0.200496
$141$	0	0
$142$	−7.90997e80	−1.53944
$143$	8.75340e80	1.30941
$144$	0	0
$145$	−2.58499e80	−0.229699
$146$	2.78375e81	1.91160
$147$	0	0
$148$	2.80168e80	0.115506
$149$	−2.36039e81	−0.755961	−0.377980	−	0.925814i	$-0.623381\pi$
$149$	−2.36039e81	−0.755961	−0.377980	+	0.925814i	$0.623381\pi$
$150$	0	0
$151$	−1.15601e81	−0.224557	−0.112278	−	0.993677i	$-0.535815\pi$
$151$	−1.15601e81	−0.224557	−0.112278	+	0.993677i	$0.535815\pi$
$152$	−2.57758e81	−0.390910
$153$	0	0
$154$	1.81393e82	1.68497
$155$	4.31053e81	0.314118
$156$	0	0
$157$	2.13843e82	0.963515	0.481758	−	0.876305i	$-0.339999\pi$
$157$	2.13843e82	0.963515	0.481758	+	0.876305i	$0.339999\pi$
$158$	−3.02201e82	−1.07314
$159$	0	0
$160$	1.00265e82	0.222152
$161$	2.96425e82	0.519930
$162$	0	0
$163$	6.68783e82	0.738329	0.369165	−	0.929364i	$-0.379644\pi$
$163$	6.68783e82	0.738329	0.369165	+	0.929364i	$0.379644\pi$
$164$	−1.12880e82	−0.0990773
$165$	0	0
$166$	3.44813e83	1.92101
$167$	4.25928e83	1.89439	0.947193	−	0.320663i	$-0.103906\pi$
$167$	4.25928e83	1.89439	0.947193	+	0.320663i	$0.103906\pi$
$168$	0	0
$169$	5.03824e83	1.43393
$170$	−1.70814e83	−0.389662
$171$	0	0
$172$	−3.73257e83	−0.549150
$173$	−1.68552e83	−0.199529	−0.0997643	−	0.995011i	$-0.531809\pi$
$173$	−1.68552e83	−0.199529	−0.0997643	+	0.995011i	$0.531809\pi$
$174$	0	0
$175$	1.94859e84	1.49897
$176$	−1.65415e84	−1.02766
$177$	0	0
$178$	1.84516e84	0.750386
$179$	4.09561e84	1.34999	0.674994	−	0.737823i	$-0.264146\pi$
$179$	4.09561e84	1.34999	0.674994	+	0.737823i	$0.264146\pi$
$180$	0	0
$181$	−3.05767e84	−0.664421	−0.332211	−	0.943205i	$-0.607794\pi$
$181$	−3.05767e84	−0.664421	−0.332211	+	0.943205i	$0.607794\pi$
$182$	1.77216e85	3.13203
$183$	0	0
$184$	−1.24618e84	−0.146188
$185$	3.56454e83	0.0341243
$186$	0	0
$187$	2.03541e85	1.30194
$188$	−1.96270e84	−0.102786
$189$	0	0
$190$	6.36453e84	0.224133
$191$	3.67316e85	1.06240	0.531200	−	0.847246i	$-0.321741\pi$
$191$	3.67316e85	1.06240	0.531200	+	0.847246i	$0.321741\pi$
$192$	0	0
$193$	3.30160e85	0.646137	0.323069	−	0.946376i	$-0.395286\pi$
$193$	3.30160e85	0.646137	0.323069	+	0.946376i	$0.395286\pi$
$194$	−1.32705e86	−2.13954
$195$	0	0
$196$	8.58699e85	0.942407
$197$	−1.52339e85	−0.138142	−0.0690712	−	0.997612i	$-0.522004\pi$
$197$	−1.52339e85	−0.138142	−0.0690712	+	0.997612i	$0.522004\pi$
$198$	0	0
$199$	9.68710e85	0.601455	0.300728	−	0.953710i	$-0.402770\pi$
$199$	9.68710e85	0.601455	0.300728	+	0.953710i	$0.402770\pi$
$200$	−8.19188e85	−0.421462
$201$	0	0
$202$	−2.40920e86	−0.853487
$203$	6.23610e86	1.83574
$204$	0	0
$205$	−1.43616e85	−0.0292707
$206$	−1.32564e87	−2.25116
$207$	0	0
$208$	−1.61606e87	−1.91022
$209$	−7.58394e86	−0.748875
$210$	0	0
$211$	−1.37245e87	−0.948212	−0.474106	−	0.880468i	$-0.657229\pi$
$211$	−1.37245e87	−0.948212	−0.474106	+	0.880468i	$0.657229\pi$
$212$	1.05822e86	0.0612321
$213$	0	0
$214$	3.55219e87	1.44537
$215$	−4.74889e86	−0.162237
$216$	0	0
$217$	−1.03989e88	−2.51041
$218$	2.29559e87	0.466418
$219$	0	0
$220$	7.48608e86	0.107995
$221$	1.98854e88	2.42004
$222$	0	0
$223$	−1.91410e88	−1.66162	−0.830809	−	0.556557i	$-0.812122\pi$
$223$	−1.91410e88	−1.66162	−0.830809	+	0.556557i	$0.812122\pi$
$224$	−2.41883e88	−1.77543
$225$	0	0
$226$	−6.95560e86	−0.0365821
$227$	−1.50131e87	−0.0669115	−0.0334557	−	0.999440i	$-0.510651\pi$
$227$	−1.50131e87	−0.0669115	−0.0334557	+	0.999440i	$0.510651\pi$
$228$	0	0
$229$	4.23984e88	1.35994	0.679969	−	0.733240i	$-0.261993\pi$
$229$	4.23984e88	1.35994	0.679969	+	0.733240i	$0.261993\pi$
$230$	3.07704e87	0.0838184
$231$	0	0
$232$	−2.62166e88	−0.516151
$233$	−9.86776e88	−1.65338	−0.826688	−	0.562661i	$-0.809778\pi$
$233$	−9.86776e88	−1.65338	−0.826688	+	0.562661i	$0.809778\pi$
$234$	0	0
$235$	−2.49712e87	−0.0303665
$236$	−1.02851e89	−1.06662
$237$	0	0
$238$	4.12076e89	3.11416
$239$	2.98930e89	1.93040	0.965202	−	0.261506i	$-0.0842192\pi$
$239$	2.98930e89	1.93040	0.965202	+	0.261506i	$0.0842192\pi$
$240$	0	0
$241$	1.55137e89	0.732952	0.366476	−	0.930428i	$-0.380564\pi$
$241$	1.55137e89	0.732952	0.366476	+	0.930428i	$0.380564\pi$
$242$	9.41393e88	0.380798
$243$	0	0
$244$	6.06821e88	0.180278
$245$	1.09251e89	0.278418
$246$	0	0
$247$	−7.40930e89	−1.39201
$248$	4.37169e89	0.705848
$249$	0	0
$250$	4.12539e89	0.492850
$251$	1.79166e89	0.184286	0.0921429	−	0.995746i	$-0.470628\pi$
$251$	1.79166e89	0.184286	0.0921429	+	0.995746i	$0.470628\pi$
$252$	0	0
$253$	−3.66659e89	−0.280055
$254$	1.63348e90	1.07609
$255$	0	0
$256$	2.66291e90	1.30725
$257$	−2.63848e90	−1.11908	−0.559541	−	0.828803i	$-0.689022\pi$
$257$	−2.63848e90	−1.11908	−0.559541	+	0.828803i	$0.689022\pi$
$258$	0	0
$259$	−8.59919e89	−0.272720
$260$	7.31369e89	0.200741
$261$	0	0
$262$	−8.56480e90	−1.76368
$263$	6.04283e89	0.107870	0.0539349	−	0.998544i	$-0.482824\pi$
$263$	6.04283e89	0.107870	0.0539349	+	0.998544i	$0.482824\pi$
$264$	0	0
$265$	1.34635e89	0.0180900
$266$	−1.53540e91	−1.79126
$267$	0	0
$268$	−2.83268e90	−0.249542
$269$	1.86722e91	1.43049	0.715245	−	0.698874i	$-0.246315\pi$
$269$	1.86722e91	1.43049	0.715245	+	0.698874i	$0.246315\pi$
$270$	0	0
$271$	−1.53891e91	−0.893029	−0.446514	−	0.894776i	$-0.647335\pi$
$271$	−1.53891e91	−0.893029	−0.446514	+	0.894776i	$0.647335\pi$
$272$	−3.75779e91	−1.89932
$273$	0	0
$274$	4.40227e90	0.169056
$275$	−2.41027e91	−0.807403
$276$	0	0
$277$	4.87345e91	1.24407	0.622035	−	0.782989i	$-0.286306\pi$
$277$	4.87345e91	1.24407	0.622035	+	0.782989i	$0.286306\pi$
$278$	5.51935e91	1.23086
$279$	0	0
$280$	−7.80928e90	−0.133102
$281$	−1.17717e92	−1.75531	−0.877654	−	0.479295i	$-0.840892\pi$
$281$	−1.17717e92	−1.75531	−0.877654	+	0.479295i	$0.840892\pi$
$282$	0	0
$283$	−8.64921e91	−0.988520	−0.494260	−	0.869314i	$-0.664561\pi$
$283$	−8.64921e91	−0.988520	−0.494260	+	0.869314i	$0.664561\pi$
$284$	7.87523e91	0.788543
$285$	0	0
$286$	−2.19204e92	−1.68703
$287$	3.46464e91	0.233930
$288$	0	0
$289$	2.70227e92	1.40624
$290$	6.47338e91	0.295942
$291$	0	0
$292$	−2.77152e92	−0.979178
$293$	1.57335e92	0.488978	0.244489	−	0.969652i	$-0.421380\pi$
$293$	1.57335e92	0.488978	0.244489	+	0.969652i	$0.421380\pi$
$294$	0	0
$295$	−1.30856e92	−0.315115
$296$	3.61511e91	0.0766800
$297$	0	0
$298$	5.91094e92	0.973973
$299$	−3.58216e92	−0.520565
$300$	0	0
$301$	1.14564e93	1.29659
$302$	2.89491e92	0.289317
$303$	0	0
$304$	1.40015e93	1.09249
$305$	7.72050e91	0.0532600
$306$	0	0
$307$	5.54892e92	0.299584	0.149792	−	0.988718i	$-0.452140\pi$
$307$	5.54892e92	0.299584	0.149792	+	0.988718i	$0.452140\pi$
$308$	−1.80596e93	−0.863092
$309$	0	0
$310$	−1.07945e93	−0.404706
$311$	−2.99156e93	−0.993993	−0.496997	−	0.867752i	$-0.665564\pi$
$311$	−2.99156e93	−0.993993	−0.496997	+	0.867752i	$0.665564\pi$
$312$	0	0
$313$	−4.96277e93	−1.29662	−0.648309	−	0.761378i	$-0.724523\pi$
$313$	−4.96277e93	−1.29662	−0.648309	+	0.761378i	$0.724523\pi$
$314$	−5.35510e93	−1.24138
$315$	0	0
$316$	3.00874e93	0.549691
$317$	3.54509e93	0.575313	0.287657	−	0.957734i	$-0.407124\pi$
$317$	3.54509e93	0.575313	0.287657	+	0.957734i	$0.407124\pi$
$318$	0	0
$319$	−7.71365e93	−0.988801
$320$	−4.16631e92	−0.0474928
$321$	0	0
$322$	−7.42314e93	−0.669873
$323$	−1.72287e94	−1.38407
$324$	0	0
$325$	−2.35477e94	−1.50080
$326$	−1.67478e94	−0.951257
$327$	0	0
$328$	−1.45654e93	−0.0657737
$329$	6.02413e93	0.242688
$330$	0	0
$331$	−1.89711e94	−0.608896	−0.304448	−	0.952529i	$-0.598472\pi$
$331$	−1.89711e94	−0.608896	−0.304448	+	0.952529i	$0.598472\pi$
$332$	−3.43299e94	−0.983998
$333$	0	0
$334$	−1.06662e95	−2.44071
$335$	−3.60398e93	−0.0737229
$336$	0	0
$337$	5.25596e94	0.860063	0.430032	−	0.902814i	$-0.358502\pi$
$337$	5.25596e94	0.860063	0.430032	+	0.902814i	$0.358502\pi$
$338$	−1.26169e95	−1.84746
$339$	0	0
$340$	1.70064e94	0.199596
$341$	1.28627e95	1.35221
$342$	0	0
$343$	−7.89939e94	−0.666905
$344$	−4.81627e94	−0.364560
$345$	0	0
$346$	4.22091e94	0.257071
$347$	−2.57654e95	−1.40826	−0.704128	−	0.710073i	$-0.748662\pi$
$347$	−2.57654e95	−1.40826	−0.704128	+	0.710073i	$0.748662\pi$
$348$	0	0
$349$	3.62890e95	1.59890	0.799451	−	0.600731i	$-0.205124\pi$
$349$	3.62890e95	1.59890	0.799451	+	0.600731i	$0.205124\pi$
$350$	−4.87969e95	−1.93126
$351$	0	0
$352$	2.99193e95	0.956316
$353$	−4.56586e95	−1.31211	−0.656056	−	0.754712i	$-0.727777\pi$
$353$	−4.56586e95	−1.31211	−0.656056	+	0.754712i	$0.727777\pi$
$354$	0	0
$355$	1.00196e95	0.232962
$356$	−1.83706e95	−0.384369
$357$	0	0
$358$	−1.02563e96	−1.73931
$359$	−4.86468e94	−0.0743041	−0.0371521	−	0.999310i	$-0.511829\pi$
$359$	−4.86468e94	−0.0743041	−0.0371521	+	0.999310i	$0.511829\pi$
$360$	0	0
$361$	−1.64402e95	−0.203886
$362$	7.65707e95	0.856034
$363$	0	0
$364$	−1.76438e96	−1.60431
$365$	−3.52617e95	−0.289282
$366$	0	0
$367$	−1.24271e95	−0.0830601	−0.0415301	−	0.999137i	$-0.513223\pi$
$367$	−1.24271e95	−0.0830601	−0.0415301	+	0.999137i	$0.513223\pi$
$368$	6.76929e95	0.408554
$369$	0	0
$370$	−8.92638e94	−0.0439654
$371$	−3.24798e95	−0.144575
$372$	0	0
$373$	−8.85278e95	−0.322106	−0.161053	−	0.986946i	$-0.551489\pi$
$373$	−8.85278e95	−0.322106	−0.161053	+	0.986946i	$0.551489\pi$
$374$	−5.09711e96	−1.67741
$375$	0	0
$376$	−2.53255e95	−0.0682360
$377$	−7.53602e96	−1.83798
$378$	0	0
$379$	−4.44817e96	−0.889633	−0.444817	−	0.895622i	$-0.646731\pi$
$379$	−4.44817e96	−0.889633	−0.444817	+	0.895622i	$0.646731\pi$
$380$	−6.33658e95	−0.114807
$381$	0	0
$382$	−9.19840e96	−1.36879
$383$	−6.87948e96	−0.928114	−0.464057	−	0.885805i	$-0.653607\pi$
$383$	−6.87948e96	−0.928114	−0.464057	+	0.885805i	$0.653607\pi$
$384$	0	0
$385$	−2.29770e96	−0.254986
$386$	−8.26792e96	−0.832477
$387$	0	0
$388$	1.32122e97	1.09594
$389$	−6.97196e95	−0.0525103	−0.0262552	−	0.999655i	$-0.508358\pi$
$389$	−6.97196e95	−0.0525103	−0.0262552	+	0.999655i	$0.508358\pi$
$390$	0	0
$391$	−8.32950e96	−0.517595
$392$	1.10801e97	0.625629
$393$	0	0
$394$	3.81490e96	0.177981
$395$	3.82798e96	0.162397
$396$	0	0
$397$	−1.36627e97	−0.479614	−0.239807	−	0.970821i	$-0.577084\pi$
$397$	−1.36627e97	−0.479614	−0.239807	+	0.970821i	$0.577084\pi$
$398$	−2.42586e97	−0.774910
$399$	0	0
$400$	4.44987e97	1.17787
$401$	6.97422e97	1.68105	0.840527	−	0.541770i	$-0.182246\pi$
$401$	6.97422e97	1.68105	0.840527	+	0.541770i	$0.182246\pi$
$402$	0	0
$403$	1.25665e98	2.51348
$404$	2.39862e97	0.437180
$405$	0	0
$406$	−1.56166e98	−2.36515
$407$	1.06366e97	0.146897
$408$	0	0
$409$	1.73860e97	0.199790	0.0998952	−	0.994998i	$-0.468149\pi$
$409$	1.73860e97	0.199790	0.0998952	+	0.994998i	$0.468149\pi$
$410$	3.59646e96	0.0377121
$411$	0	0
$412$	1.31982e98	1.15311
$413$	3.15681e98	2.51838
$414$	0	0
$415$	−4.36775e97	−0.290706
$416$	2.92303e98	1.77760
$417$	0	0
$418$	1.89919e98	0.964843
$419$	−3.14761e98	−1.46203	−0.731013	−	0.682363i	$-0.760952\pi$
$419$	−3.14761e98	−1.46203	−0.731013	+	0.682363i	$0.760952\pi$
$420$	0	0
$421$	9.75562e97	0.379032	0.189516	−	0.981878i	$-0.439308\pi$
$421$	9.75562e97	0.379032	0.189516	+	0.981878i	$0.439308\pi$
$422$	3.43692e98	1.22167
$423$	0	0
$424$	1.36545e97	0.0406497
$425$	−5.47549e98	−1.49224
$426$	0	0
$427$	−1.86252e98	−0.425652
$428$	−3.53659e98	−0.740361
$429$	0	0
$430$	1.18923e98	0.209025
$431$	−6.46519e98	−1.04156	−0.520779	−	0.853691i	$-0.674359\pi$
$431$	−6.46519e98	−1.04156	−0.520779	+	0.853691i	$0.674359\pi$
$432$	0	0
$433$	9.89113e98	1.33952	0.669761	−	0.742577i	$-0.266397\pi$
$433$	9.89113e98	1.33952	0.669761	+	0.742577i	$0.266397\pi$
$434$	2.60410e99	3.23439
$435$	0	0
$436$	−2.28550e98	−0.238912
$437$	3.10358e98	0.297720
$438$	0	0
$439$	1.20207e99	0.971650	0.485825	−	0.874056i	$-0.338519\pi$
$439$	1.20207e99	0.971650	0.485825	+	0.874056i	$0.338519\pi$
$440$	9.65957e97	0.0716939
$441$	0	0
$442$	−4.97973e99	−3.11796
$443$	−4.29868e98	−0.247284	−0.123642	−	0.992327i	$-0.539457\pi$
$443$	−4.29868e98	−0.247284	−0.123642	+	0.992327i	$0.539457\pi$
$444$	0	0
$445$	−2.33727e98	−0.113556
$446$	4.79332e99	2.14081
$447$	0	0
$448$	1.00509e99	0.379560
$449$	4.39665e98	0.152716	0.0763580	−	0.997080i	$-0.475671\pi$
$449$	4.39665e98	0.152716	0.0763580	+	0.997080i	$0.475671\pi$
$450$	0	0
$451$	−4.28553e98	−0.126004
$452$	6.92506e97	0.0187384
$453$	0	0
$454$	3.75961e98	0.0862081
$455$	−2.24479e99	−0.473968
$456$	0	0
$457$	8.88796e99	1.59201	0.796003	−	0.605293i	$-0.206944\pi$
$457$	8.88796e99	1.59201	0.796003	+	0.605293i	$0.206944\pi$
$458$	−1.06175e100	−1.75213
$459$	0	0
$460$	−3.06353e98	−0.0429342
$461$	−2.12797e99	−0.274904	−0.137452	−	0.990508i	$-0.543891\pi$
$461$	−2.12797e99	−0.274904	−0.137452	+	0.990508i	$0.543891\pi$
$462$	0	0
$463$	−6.05772e99	−0.665307	−0.332653	−	0.943049i	$-0.607944\pi$
$463$	−6.05772e99	−0.665307	−0.332653	+	0.943049i	$0.607944\pi$
$464$	1.42410e100	1.44250
$465$	0	0
$466$	2.47110e100	2.13019
$467$	1.62555e100	1.29306	0.646528	−	0.762890i	$-0.276220\pi$
$467$	1.62555e100	1.29306	0.646528	+	0.762890i	$0.276220\pi$
$468$	0	0
$469$	8.69435e99	0.589190
$470$	6.25334e98	0.0391240
$471$	0	0
$472$	−1.32713e100	−0.708089
$473$	−1.41708e100	−0.698395
$474$	0	0
$475$	2.04017e100	0.858334
$476$	−4.10266e100	−1.59516
$477$	0	0
$478$	−7.48586e100	−2.48711
$479$	−5.57770e100	−1.71346	−0.856728	−	0.515768i	$-0.827507\pi$
$479$	−5.57770e100	−1.71346	−0.856728	+	0.515768i	$0.827507\pi$
$480$	0	0
$481$	1.03917e100	0.273053
$482$	−3.88496e100	−0.944328
$483$	0	0
$484$	−9.37259e99	−0.195056
$485$	1.68097e100	0.323776
$486$	0	0
$487$	−2.28570e100	−0.377297	−0.188648	−	0.982045i	$-0.560411\pi$
$487$	−2.28570e100	−0.377297	−0.188648	+	0.982045i	$0.560411\pi$
$488$	7.83003e99	0.119680
$489$	0	0
$490$	−2.73589e100	−0.358712
$491$	−8.39755e100	−1.01999	−0.509996	−	0.860177i	$-0.670353\pi$
$491$	−8.39755e100	−1.01999	−0.509996	+	0.860177i	$0.670353\pi$
$492$	0	0
$493$	−1.75233e101	−1.82750
$494$	1.85545e101	1.79345
$495$	0	0
$496$	−2.37472e101	−1.97265
$497$	−2.41715e101	−1.86182
$498$	0	0
$499$	9.31270e100	0.617029	0.308514	−	0.951220i	$-0.400168\pi$
$499$	9.31270e100	0.617029	0.308514	+	0.951220i	$0.400168\pi$
$500$	−4.10727e100	−0.252452
$501$	0	0
$502$	−4.48672e100	−0.237432
$503$	−1.63101e101	−0.801046	−0.400523	−	0.916287i	$-0.631171\pi$
$503$	−1.63101e101	−0.801046	−0.400523	+	0.916287i	$0.631171\pi$
$504$	0	0
$505$	3.05174e100	0.129158
$506$	9.18194e100	0.360820
$507$	0	0
$508$	−1.62631e101	−0.551205
$509$	−2.22571e100	−0.0700732	−0.0350366	−	0.999386i	$-0.511155\pi$
$509$	−2.22571e100	−0.0700732	−0.0350366	+	0.999386i	$0.511155\pi$
$510$	0	0
$511$	8.50664e101	2.31193
$512$	−3.39979e101	−0.858674
$513$	0	0
$514$	6.60733e101	1.44181
$515$	1.67919e101	0.340666
$516$	0	0
$517$	−7.45146e100	−0.130721
$518$	2.15343e101	0.351369
$519$	0	0
$520$	9.43713e100	0.133264
$521$	−6.95029e101	−0.913247	−0.456624	−	0.889660i	$-0.650941\pi$
$521$	−6.95029e101	−0.913247	−0.456624	+	0.889660i	$0.650941\pi$
$522$	0	0
$523$	6.33049e101	0.720484	0.360242	−	0.932859i	$-0.382694\pi$
$523$	6.33049e101	0.720484	0.360242	+	0.932859i	$0.382694\pi$
$524$	8.52719e101	0.903405
$525$	0	0
$526$	−1.51326e101	−0.138978
$527$	2.92206e102	2.49914
$528$	0	0
$529$	−1.19764e102	−0.888662
$530$	−3.37156e100	−0.0233070
$531$	0	0
$532$	1.52865e102	0.917536
$533$	−4.18684e101	−0.234216
$534$	0	0
$535$	−4.49956e101	−0.218727
$536$	−3.65511e101	−0.165661
$537$	0	0
$538$	−4.67593e102	−1.84303
$539$	3.26007e102	1.19853
$540$	0	0
$541$	2.30894e102	0.738779	0.369390	−	0.929275i	$-0.379567\pi$
$541$	2.30894e102	0.738779	0.369390	+	0.929275i	$0.379567\pi$
$542$	3.85377e102	1.15057
$543$	0	0
$544$	6.79685e102	1.76746
$545$	−2.90782e101	−0.0705827
$546$	0	0
$547$	−3.04963e102	−0.645241	−0.322620	−	0.946528i	$-0.604564\pi$
$547$	−3.04963e102	−0.645241	−0.322620	+	0.946528i	$0.604564\pi$
$548$	−4.38294e101	−0.0865953
$549$	0	0
$550$	6.03586e102	1.04025
$551$	6.52920e102	1.05117
$552$	0	0
$553$	−9.23472e102	−1.29787
$554$	−1.22042e103	−1.60285
$555$	0	0
$556$	−5.49511e102	−0.630481
$557$	1.08889e102	0.116792	0.0583961	−	0.998293i	$-0.481401\pi$
$557$	1.08889e102	0.116792	0.0583961	+	0.998293i	$0.481401\pi$
$558$	0	0
$559$	−1.38445e103	−1.29817
$560$	4.24204e102	0.371984
$561$	0	0
$562$	2.94790e103	2.26152
$563$	−1.97720e103	−1.41901	−0.709507	−	0.704698i	$-0.751082\pi$
$563$	−1.97720e103	−1.41901	−0.709507	+	0.704698i	$0.751082\pi$
$564$	0	0
$565$	8.81066e100	0.00553594
$566$	2.16595e103	1.27360
$567$	0	0
$568$	1.01617e103	0.523485
$569$	−9.25979e102	−0.446572	−0.223286	−	0.974753i	$-0.571678\pi$
$569$	−9.25979e102	−0.446572	−0.223286	+	0.974753i	$0.571678\pi$
$570$	0	0
$571$	−6.37054e102	−0.269353	−0.134677	−	0.990890i	$-0.543000\pi$
$571$	−6.37054e102	−0.269353	−0.134677	+	0.990890i	$0.543000\pi$
$572$	2.18242e103	0.864146
$573$	0	0
$574$	−8.67621e102	−0.301394
$575$	9.86357e102	0.320989
$576$	0	0
$577$	4.98326e103	1.42371	0.711853	−	0.702328i	$-0.247856\pi$
$577$	4.98326e103	1.42371	0.711853	+	0.702328i	$0.247856\pi$
$578$	−6.76707e103	−1.81179
$579$	0	0
$580$	−6.44495e102	−0.151590
$581$	1.05369e104	2.32331
$582$	0	0
$583$	4.01754e102	0.0778735
$584$	−3.57620e103	−0.650040
$585$	0	0
$586$	−3.94001e103	−0.629994
$587$	2.58752e103	0.388111	0.194055	−	0.980991i	$-0.437836\pi$
$587$	2.58752e103	0.388111	0.194055	+	0.980991i	$0.437836\pi$
$588$	0	0
$589$	−1.08876e104	−1.43750
$590$	3.27693e103	0.405991
$591$	0	0
$592$	−1.96375e103	−0.214300
$593$	−1.15444e104	−1.18255	−0.591277	−	0.806468i	$-0.701376\pi$
$593$	−1.15444e104	−1.18255	−0.591277	+	0.806468i	$0.701376\pi$
$594$	0	0
$595$	−5.21976e103	−0.471264
$596$	−5.88499e103	−0.498897
$597$	0	0
$598$	8.97050e103	0.670691
$599$	−1.81463e104	−1.27433	−0.637166	−	0.770726i	$-0.719894\pi$
$599$	−1.81463e104	−1.27433	−0.637166	+	0.770726i	$0.719894\pi$
$600$	0	0
$601$	2.39007e104	1.48121	0.740606	−	0.671939i	$-0.234538\pi$
$601$	2.39007e104	1.48121	0.740606	+	0.671939i	$0.234538\pi$
$602$	−2.86893e104	−1.67052
$603$	0	0
$604$	−2.88219e103	−0.148196
$605$	−1.19246e103	−0.0576260
$606$	0	0
$607$	−2.17455e104	−0.928524	−0.464262	−	0.885698i	$-0.653680\pi$
$607$	−2.17455e104	−0.928524	−0.464262	+	0.885698i	$0.653680\pi$
$608$	−2.53251e104	−1.01664
$609$	0	0
$610$	−1.93338e103	−0.0686197
$611$	−7.27987e103	−0.242984
$612$	0	0
$613$	−5.76235e104	−1.70150	−0.850750	−	0.525571i	$-0.823852\pi$
$613$	−5.76235e104	−1.70150	−0.850750	+	0.525571i	$0.823852\pi$
$614$	−1.38957e104	−0.385982
$615$	0	0
$616$	−2.33030e104	−0.572975
$617$	−1.97727e104	−0.457480	−0.228740	−	0.973488i	$-0.573461\pi$
$617$	−1.97727e104	−0.457480	−0.228740	+	0.973488i	$0.573461\pi$
$618$	0	0
$619$	−8.38002e104	−1.71730	−0.858649	−	0.512564i	$-0.828696\pi$
$619$	−8.38002e104	−1.71730	−0.858649	+	0.512564i	$0.828696\pi$
$620$	1.07471e104	0.207302
$621$	0	0
$622$	7.49153e104	1.28065
$623$	5.63849e104	0.907531
$624$	0	0
$625$	6.21759e104	0.887404
$626$	1.24279e105	1.67055
$627$	0	0
$628$	5.33159e104	0.635872
$629$	2.41636e104	0.271495
$630$	0	0
$631$	−1.15727e105	−1.15434	−0.577171	−	0.816623i	$-0.695843\pi$
$631$	−1.15727e105	−1.15434	−0.577171	+	0.816623i	$0.695843\pi$
$632$	3.88228e104	0.364919
$633$	0	0
$634$	−8.87768e104	−0.741229
$635$	−2.06913e104	−0.162844
$636$	0	0
$637$	3.18500e105	2.22782
$638$	1.93167e105	1.27396
$639$	0	0
$640$	−2.74457e104	−0.160963
$641$	−2.49038e105	−1.37749	−0.688747	−	0.725002i	$-0.741839\pi$
$641$	−2.49038e105	−1.37749	−0.688747	+	0.725002i	$0.741839\pi$
$642$	0	0
$643$	2.83803e105	1.39671	0.698353	−	0.715754i	$-0.253917\pi$
$643$	2.83803e105	1.39671	0.698353	+	0.715754i	$0.253917\pi$
$644$	7.39054e104	0.343128
$645$	0	0
$646$	4.31444e105	1.78322
$647$	−9.54967e104	−0.372459	−0.186229	−	0.982506i	$-0.559627\pi$
$647$	−9.54967e104	−0.372459	−0.186229	+	0.982506i	$0.559627\pi$
$648$	0	0
$649$	−3.90477e105	−1.35650
$650$	5.89686e105	1.93362
$651$	0	0
$652$	1.66743e105	0.487261
$653$	3.34247e104	0.0922196	0.0461098	−	0.998936i	$-0.485318\pi$
$653$	3.34247e104	0.0922196	0.0461098	+	0.998936i	$0.485318\pi$
$654$	0	0
$655$	1.08490e105	0.266896
$656$	7.91199e104	0.183819
$657$	0	0
$658$	−1.50857e105	−0.312677
$659$	−3.41760e105	−0.669142	−0.334571	−	0.942371i	$-0.608591\pi$
$659$	−3.41760e105	−0.669142	−0.334571	+	0.942371i	$0.608591\pi$
$660$	0	0
$661$	3.96100e105	0.692229	0.346115	−	0.938192i	$-0.387501\pi$
$661$	3.96100e105	0.692229	0.346115	+	0.938192i	$0.387501\pi$
$662$	4.75079e105	0.784496
$663$	0	0
$664$	−4.42971e105	−0.653240
$665$	1.94489e105	0.271071
$666$	0	0
$667$	3.15666e105	0.393105
$668$	1.06193e106	1.25020
$669$	0	0
$670$	9.02516e104	0.0949839
$671$	2.30381e105	0.229273
$672$	0	0
$673$	−9.92179e105	−0.883131	−0.441566	−	0.897229i	$-0.645577\pi$
$673$	−9.92179e105	−0.883131	−0.441566	+	0.897229i	$0.645577\pi$
$674$	−1.31621e106	−1.10810
$675$	0	0
$676$	1.25615e106	0.946321
$677$	−2.02718e106	−1.44483	−0.722417	−	0.691458i	$-0.756969\pi$
$677$	−2.02718e106	−1.44483	−0.722417	+	0.691458i	$0.756969\pi$
$678$	0	0
$679$	−4.05522e106	−2.58760
$680$	2.19439e105	0.132504
$681$	0	0
$682$	−3.22110e106	−1.74217
$683$	3.29269e105	0.168568	0.0842838	−	0.996442i	$-0.473140\pi$
$683$	3.29269e105	0.168568	0.0842838	+	0.996442i	$0.473140\pi$
$684$	0	0
$685$	−5.57635e104	−0.0255831
$686$	1.97818e106	0.859234
$687$	0	0
$688$	2.61622e106	1.01885
$689$	3.92503e105	0.144751
$690$	0	0
$691$	−1.68083e106	−0.556030	−0.278015	−	0.960577i	$-0.589676\pi$
$691$	−1.68083e106	−0.556030	−0.278015	+	0.960577i	$0.589676\pi$
$692$	−4.20238e105	−0.131679
$693$	0	0
$694$	6.45222e106	1.81438
$695$	−6.99136e105	−0.186265
$696$	0	0
$697$	−9.73557e105	−0.232880
$698$	−9.08757e106	−2.06001
$699$	0	0
$700$	4.85826e106	0.989246
$701$	1.39640e105	0.0269516	0.0134758	−	0.999909i	$-0.495710\pi$
$701$	1.39640e105	0.0269516	0.0134758	+	0.999909i	$0.495710\pi$
$702$	0	0
$703$	−9.00336e105	−0.156164
$704$	−1.24324e106	−0.204446
$705$	0	0
$706$	1.14339e107	1.69051
$707$	−7.36209e106	−1.03222
$708$	0	0
$709$	−4.50108e106	−0.567653	−0.283826	−	0.958876i	$-0.591604\pi$
$709$	−4.50108e106	−0.567653	−0.283826	+	0.958876i	$0.591604\pi$
$710$	−2.50912e106	−0.300146
$711$	0	0
$712$	−2.37043e106	−0.255168
$713$	−5.26380e106	−0.537579
$714$	0	0
$715$	2.77666e106	0.255297
$716$	1.02113e107	0.890926
$717$	0	0
$718$	1.21822e106	0.0957327
$719$	8.36762e106	0.624121	0.312061	−	0.950062i	$-0.398981\pi$
$719$	8.36762e106	0.624121	0.312061	+	0.950062i	$0.398981\pi$
$720$	0	0
$721$	−4.05093e107	−2.72259
$722$	4.11700e106	0.262685
$723$	0	0
$724$	−7.62344e106	−0.438485
$725$	2.07506e107	1.13333
$726$	0	0
$727$	−1.85532e107	−0.913855	−0.456928	−	0.889504i	$-0.651050\pi$
$727$	−1.85532e107	−0.913855	−0.456928	+	0.889504i	$0.651050\pi$
$728$	−2.27664e107	−1.06504
$729$	0	0
$730$	8.83031e106	0.372708
$731$	−3.21922e107	−1.29077
$732$	0	0
$733$	2.83469e107	1.02590	0.512952	−	0.858417i	$-0.328552\pi$
$733$	2.83469e107	1.02590	0.512952	+	0.858417i	$0.328552\pi$
$734$	3.11202e106	0.107014
$735$	0	0
$736$	−1.22439e107	−0.380190
$737$	−1.07543e107	−0.317361
$738$	0	0
$739$	−3.31923e107	−0.884852	−0.442426	−	0.896805i	$-0.645882\pi$
$739$	−3.31923e107	−0.884852	−0.442426	+	0.896805i	$0.645882\pi$
$740$	8.88719e105	0.0225203
$741$	0	0
$742$	8.13366e106	0.186268
$743$	−3.73720e107	−0.813703	−0.406851	−	0.913494i	$-0.633373\pi$
$743$	−3.73720e107	−0.813703	−0.406851	+	0.913494i	$0.633373\pi$
$744$	0	0
$745$	−7.48739e106	−0.147391
$746$	2.21693e107	0.414998
$747$	0	0
$748$	5.07472e107	0.859216
$749$	1.08549e108	1.74806
$750$	0	0
$751$	−1.89111e107	−0.275562	−0.137781	−	0.990463i	$-0.543997\pi$
$751$	−1.89111e107	−0.275562	−0.137781	+	0.990463i	$0.543997\pi$
$752$	1.37569e107	0.190701
$753$	0	0
$754$	1.88718e108	2.36804
$755$	−3.66698e106	−0.0437822
$756$	0	0
$757$	−9.28169e107	−1.00353	−0.501766	−	0.865003i	$-0.667316\pi$
$757$	−9.28169e107	−1.00353	−0.501766	+	0.865003i	$0.667316\pi$
$758$	1.11392e108	1.14620
$759$	0	0
$760$	−8.17632e106	−0.0762163
$761$	1.01545e108	0.901021	0.450510	−	0.892771i	$-0.351242\pi$
$761$	1.01545e108	0.901021	0.450510	+	0.892771i	$0.351242\pi$
$762$	0	0
$763$	7.01490e107	0.564094
$764$	9.15800e107	0.701132
$765$	0	0
$766$	1.72277e108	1.19577
$767$	−3.81485e108	−2.52146
$768$	0	0
$769$	1.42644e108	0.855095	0.427548	−	0.903993i	$-0.359378\pi$
$769$	1.42644e108	0.855095	0.427548	+	0.903993i	$0.359378\pi$
$770$	5.75395e107	0.328522
$771$	0	0
$772$	8.23161e107	0.426419
$773$	3.05601e108	1.50808	0.754038	−	0.656831i	$-0.228103\pi$
$773$	3.05601e108	1.50808	0.754038	+	0.656831i	$0.228103\pi$
$774$	0	0
$775$	−3.46022e108	−1.54985
$776$	1.70482e108	0.727551
$777$	0	0
$778$	1.74593e107	0.0676538
$779$	3.62748e107	0.133952
$780$	0	0
$781$	2.98985e108	1.00285
$782$	2.08589e108	0.666865
$783$	0	0
$784$	−6.01878e108	−1.74846
$785$	6.78331e107	0.187858
$786$	0	0
$787$	1.98474e108	0.499633	0.249816	−	0.968293i	$-0.419630\pi$
$787$	1.98474e108	0.499633	0.249816	+	0.968293i	$0.419630\pi$
$788$	−3.79814e107	−0.0911671
$789$	0	0
$790$	−9.58609e107	−0.209231
$791$	−2.12551e107	−0.0442430
$792$	0	0
$793$	2.25076e108	0.426172
$794$	3.42144e108	0.617931
$795$	0	0
$796$	2.41521e108	0.396931
$797$	−2.43882e108	−0.382378	−0.191189	−	0.981553i	$-0.561234\pi$
$797$	−2.43882e108	−0.382378	−0.191189	+	0.981553i	$0.561234\pi$
$798$	0	0
$799$	−1.69277e108	−0.241598
$800$	−8.04865e108	−1.09610
$801$	0	0
$802$	−1.74650e109	−2.16585
$803$	−1.05222e109	−1.24529
$804$	0	0
$805$	9.40289e107	0.101372
$806$	−3.14693e109	−3.23834
$807$	0	0
$808$	3.09503e108	0.290228
$809$	−1.29030e109	−1.15510	−0.577551	−	0.816354i	$-0.695992\pi$
$809$	−1.29030e109	−1.15510	−0.577551	+	0.816354i	$0.695992\pi$
$810$	0	0
$811$	−7.08480e108	−0.578156	−0.289078	−	0.957305i	$-0.593349\pi$
$811$	−7.08480e108	−0.578156	−0.289078	+	0.957305i	$0.593349\pi$
$812$	1.55480e109	1.21150
$813$	0	0
$814$	−2.66365e108	−0.189261
$815$	2.12144e108	0.143953
$816$	0	0
$817$	1.19948e109	0.742449
$818$	−4.35383e108	−0.257408
$819$	0	0
$820$	−3.58067e107	−0.0193172
$821$	−6.16169e108	−0.317564	−0.158782	−	0.987314i	$-0.550757\pi$
$821$	−6.16169e108	−0.317564	−0.158782	+	0.987314i	$0.550757\pi$
$822$	0	0
$823$	2.32855e109	1.09545	0.547724	−	0.836659i	$-0.315495\pi$
$823$	2.32855e109	1.09545	0.547724	+	0.836659i	$0.315495\pi$
$824$	1.70301e109	0.765504
$825$	0	0
$826$	−7.90535e109	−3.24466
$827$	3.17387e108	0.124490	0.0622448	−	0.998061i	$-0.480174\pi$
$827$	3.17387e108	0.124490	0.0622448	+	0.998061i	$0.480174\pi$
$828$	0	0
$829$	6.50258e108	0.232965	0.116482	−	0.993193i	$-0.462838\pi$
$829$	6.50258e108	0.232965	0.116482	+	0.993193i	$0.462838\pi$
$830$	1.09378e109	0.374543
$831$	0	0
$832$	−1.21461e109	−0.380024
$833$	7.40601e109	2.21512
$834$	0	0
$835$	1.35108e109	0.369351
$836$	−1.89085e109	−0.494220
$837$	0	0
$838$	7.88231e109	1.88366
$839$	−6.20112e109	−1.41709	−0.708543	−	0.705667i	$-0.750647\pi$
$839$	−6.20112e109	−1.41709	−0.708543	+	0.705667i	$0.750647\pi$
$840$	0	0
$841$	1.85622e109	0.387953
$842$	−2.44302e109	−0.488342
$843$	0	0
$844$	−3.42183e109	−0.625773
$845$	1.59818e109	0.279575
$846$	0	0
$847$	2.87673e109	0.460544
$848$	−7.41722e108	−0.113605
$849$	0	0
$850$	1.37118e110	1.92259
$851$	−4.35283e108	−0.0584001
$852$	0	0
$853$	−1.09943e109	−0.135076	−0.0675382	−	0.997717i	$-0.521514\pi$
$853$	−1.09943e109	−0.135076	−0.0675382	+	0.997717i	$0.521514\pi$
$854$	4.66415e109	0.548406
$855$	0	0
$856$	−4.56339e109	−0.491498
$857$	1.00221e110	1.03318	0.516590	−	0.856233i	$-0.327201\pi$
$857$	1.00221e110	1.03318	0.516590	+	0.856233i	$0.327201\pi$
$858$	0	0
$859$	−1.04345e110	−0.985663	−0.492831	−	0.870125i	$-0.664038\pi$
$859$	−1.04345e110	−0.985663	−0.492831	+	0.870125i	$0.664038\pi$
$860$	−1.18401e109	−0.107068
$861$	0	0
$862$	1.61903e110	1.34193
$863$	1.01462e110	0.805193	0.402597	−	0.915377i	$-0.368108\pi$
$863$	1.01462e110	0.805193	0.402597	+	0.915377i	$0.368108\pi$
$864$	0	0
$865$	−5.34663e108	−0.0389024
$866$	−2.47696e110	−1.72583
$867$	0	0
$868$	−2.59266e110	−1.65675
$869$	1.14227e110	0.699083
$870$	0	0
$871$	−1.05067e110	−0.589909
$872$	−2.94907e109	−0.158605
$873$	0	0
$874$	−7.77204e109	−0.383580
$875$	1.26065e110	0.596061
$876$	0	0
$877$	3.87840e110	1.68333	0.841663	−	0.540004i	$-0.181577\pi$
$877$	3.87840e110	1.68333	0.841663	+	0.540004i	$0.181577\pi$
$878$	−3.01025e110	−1.25187
$879$	0	0
$880$	−5.24713e109	−0.200365
$881$	3.02002e110	1.10513	0.552565	−	0.833470i	$-0.313649\pi$
$881$	3.02002e110	1.10513	0.552565	+	0.833470i	$0.313649\pi$
$882$	0	0
$883$	−3.01959e110	−1.01489	−0.507447	−	0.861683i	$-0.669411\pi$
$883$	−3.01959e110	−1.01489	−0.507447	+	0.861683i	$0.669411\pi$
$884$	4.95786e110	1.59711
$885$	0	0
$886$	1.07648e110	0.318598
$887$	2.73899e110	0.777061	0.388530	−	0.921436i	$-0.372983\pi$
$887$	2.73899e110	0.777061	0.388530	+	0.921436i	$0.372983\pi$
$888$	0	0
$889$	4.99162e110	1.30144
$890$	5.85303e109	0.146304
$891$	0	0
$892$	−4.77227e110	−1.09659
$893$	6.30727e109	0.138967
$894$	0	0
$895$	1.29917e110	0.263209
$896$	6.62109e110	1.28641
$897$	0	0
$898$	−1.10102e110	−0.196758
$899$	−1.10738e111	−1.89805
$900$	0	0
$901$	9.12677e109	0.143925
$902$	1.07319e110	0.162342
$903$	0	0
$904$	8.93566e108	0.0124397
$905$	−9.69921e109	−0.129543
$906$	0	0
$907$	8.61887e110	1.05969	0.529843	−	0.848096i	$-0.322251\pi$
$907$	8.61887e110	1.05969	0.529843	+	0.848096i	$0.322251\pi$
$908$	−3.74310e109	−0.0441583
$909$	0	0
$910$	5.62145e110	0.610656
$911$	−8.33060e109	−0.0868434	−0.0434217	−	0.999057i	$-0.513826\pi$
$911$	−8.33060e109	−0.0868434	−0.0434217	+	0.999057i	$0.513826\pi$
$912$	0	0
$913$	−1.30334e111	−1.25142
$914$	−2.22574e111	−2.05113
$915$	0	0
$916$	1.05709e111	0.897492
$917$	−2.61725e111	−2.13302
$918$	0	0
$919$	2.14828e111	1.61347	0.806733	−	0.590916i	$-0.201233\pi$
$919$	2.14828e111	1.61347	0.806733	+	0.590916i	$0.201233\pi$
$920$	−3.95298e109	−0.0285024
$921$	0	0
$922$	5.32891e110	0.354184
$923$	2.92100e111	1.86410
$924$	0	0
$925$	−2.86138e110	−0.168369
$926$	1.51699e111	0.857175
$927$	0	0
$928$	−2.57582e111	−1.34235
$929$	−9.49815e110	−0.475389	−0.237695	−	0.971340i	$-0.576392\pi$
$929$	−9.49815e110	−0.475389	−0.237695	+	0.971340i	$0.576392\pi$
$930$	0	0
$931$	−2.75948e111	−1.27413
$932$	−2.46025e111	−1.09115
$933$	0	0
$934$	−4.07074e111	−1.66596
$935$	6.45650e110	0.253841
$936$	0	0
$937$	−2.41344e111	−0.875795	−0.437897	−	0.899025i	$-0.644277\pi$
$937$	−2.41344e111	−0.875795	−0.437897	+	0.899025i	$0.644277\pi$
$938$	−2.17726e111	−0.759107
$939$	0	0
$940$	−6.22588e109	−0.0200404
$941$	−1.07745e111	−0.333262	−0.166631	−	0.986019i	$-0.553289\pi$
$941$	−1.07745e111	−0.333262	−0.166631	+	0.986019i	$0.553289\pi$
$942$	0	0
$943$	1.75377e110	0.0500938
$944$	7.20903e111	1.97891
$945$	0	0
$946$	3.54867e111	0.899805
$947$	−6.26666e111	−1.52726	−0.763628	−	0.645656i	$-0.776584\pi$
$947$	−6.26666e111	−1.52726	−0.763628	+	0.645656i	$0.776584\pi$
$948$	0	0
$949$	−1.02799e112	−2.31475
$950$	−5.10904e111	−1.10587
$951$	0	0
$952$	−5.29381e111	−1.05897
$953$	−2.69110e111	−0.517543	−0.258771	−	0.965939i	$-0.583318\pi$
$953$	−2.69110e111	−0.517543	−0.258771	+	0.965939i	$0.583318\pi$
$954$	0	0
$955$	1.16516e111	0.207138
$956$	7.45299e111	1.27397
$957$	0	0
$958$	1.39678e112	2.20760
$959$	1.34525e111	0.204459
$960$	0	0
$961$	1.13516e112	1.59563
$962$	−2.60231e111	−0.351798
$963$	0	0
$964$	3.86790e111	0.483712
$965$	1.04730e111	0.125978
$966$	0	0
$967$	3.77694e109	0.00420386	0.00210193	−	0.999998i	$-0.499331\pi$
$967$	3.77694e109	0.00420386	0.00210193	+	0.999998i	$0.499331\pi$
$968$	−1.20938e111	−0.129490
$969$	0	0
$970$	−4.20952e111	−0.417150
$971$	5.43839e111	0.518501	0.259250	−	0.965810i	$-0.416524\pi$
$971$	5.43839e111	0.518501	0.259250	+	0.965810i	$0.416524\pi$
$972$	0	0
$973$	1.68662e112	1.48862
$974$	5.72390e111	0.486106
$975$	0	0
$976$	−4.25332e111	−0.334472
$977$	3.13836e111	0.237496	0.118748	−	0.992924i	$-0.462112\pi$
$977$	3.13836e111	0.237496	0.118748	+	0.992924i	$0.462112\pi$
$978$	0	0
$979$	−6.97445e111	−0.488831
$980$	2.72388e111	0.183742
$981$	0	0
$982$	2.10293e112	1.31415
$983$	1.15994e111	0.0697718	0.0348859	−	0.999391i	$-0.488893\pi$
$983$	1.15994e111	0.0697718	0.0348859	+	0.999391i	$0.488893\pi$
$984$	0	0
$985$	−4.83233e110	−0.0269338
$986$	4.38822e112	2.35453
$987$	0	0
$988$	−1.84730e112	−0.918656
$989$	5.79911e111	0.277652
$990$	0	0
$991$	2.56760e112	1.13964	0.569818	−	0.821771i	$-0.307014\pi$
$991$	2.56760e112	1.13964	0.569818	+	0.821771i	$0.307014\pi$
$992$	4.29525e112	1.83570
$993$	0	0
$994$	6.05306e112	2.39875
$995$	3.07284e111	0.117267
$996$	0	0
$997$	−3.67479e112	−1.30066	−0.650331	−	0.759651i	$-0.725370\pi$
$997$	−3.67479e112	−1.30066	−0.650331	+	0.759651i	$0.725370\pi$
$998$	−2.33211e112	−0.794974
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.76.a.b.1.2		6
3.2	odd	2		3.76.a.b.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.76.a.b.1.5	✓	6	3.2	odd	2
9.76.a.b.1.2		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)

\(f(q)\)	\(=\)	\(q-2.50422e11 q^{2} +2.49322e22 q^{4} +3.17209e25 q^{5} -7.65245e31 q^{7} +3.21710e33 q^{8} +O(q^{10})\)	\(q-2.50422e11 q^{2} +2.49322e22 q^{4} +3.17209e25 q^{5} -7.65245e31 q^{7} +3.21710e33 q^{8} -7.94362e36 q^{10} +9.46558e38 q^{11} +9.24761e41 q^{13} +1.91634e43 q^{14} -1.74754e45 q^{16} +2.15032e46 q^{17} -8.01212e47 q^{19} +7.90874e47 q^{20} -2.37039e50 q^{22} -3.87360e50 q^{23} -2.54636e52 q^{25} -2.31580e53 q^{26} -1.90793e54 q^{28} -8.14915e54 q^{29} +1.35889e56 q^{31} +3.16085e56 q^{32} -5.38488e57 q^{34} -2.42743e57 q^{35} +1.12372e58 q^{37} +2.00641e59 q^{38} +1.02049e59 q^{40} -4.52749e59 q^{41} -1.49708e61 q^{43} +2.35998e61 q^{44} +9.70035e61 q^{46} -7.87216e61 q^{47} +3.44413e63 q^{49} +6.37663e63 q^{50} +2.30564e64 q^{52} +4.24437e63 q^{53} +3.00257e64 q^{55} -2.46187e65 q^{56} +2.04073e66 q^{58} -4.12523e66 q^{59} +2.43388e66 q^{61} -3.40296e67 q^{62} -1.31343e67 q^{64} +2.93343e67 q^{65} -1.13615e68 q^{67} +5.36124e68 q^{68} +6.07882e68 q^{70} +3.15866e69 q^{71} -1.11162e70 q^{73} -2.81404e69 q^{74} -1.99760e70 q^{76} -7.24349e70 q^{77} +1.20677e71 q^{79} -5.54338e70 q^{80} +1.13378e71 q^{82} -1.37693e72 q^{83} +6.82103e71 q^{85} +3.74903e72 q^{86} +3.04517e72 q^{88} -7.36822e72 q^{89} -7.07669e73 q^{91} -9.65775e72 q^{92} +1.97136e73 q^{94} -2.54152e73 q^{95} +5.29924e74 q^{97} -8.62487e74 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 311057037486 q^{2} + 30\!\cdots\!92 q^{4}+ \cdots - 69\!\cdots\!12 q^{8}+O(q^{10}) \) 6 * q - 311057037486 * q^2 + 30902560640638265713092 * q^4 - 97856522050579947592055460 * q^5 - 30749202116633858714981933510688 * q^7 - 6939052769539518449811063778704312 * q^8	\( 6 q - 311057037486 q^{2} + 30\!\cdots\!92 q^{4}+ \cdots - 14\!\cdots\!94 q^{98}+O(q^{100}) \) 6 * q - 311057037486 * q^2 + 30902560640638265713092 * q^4 - 97856522050579947592055460 * q^5 - 30749202116633858714981933510688 * q^7 - 6939052769539518449811063778704312 * q^8 - 107545734844341425270764823551622320620 * q^10 + 379379629646545786309015638730942099896 * q^11 + 154669229506479970266461340344668629154596 * q^13 - 31899227014014717498689751276506679791260128 * q^14 - 3260958521390361922516104888150343171861643760 * q^16 + 7401535799877014405171685814768477775195111796 * q^17 - 182729763718938971567579921571009657209643443592 * q^19 + 9428757085683313672852247515255856540783373281640 * q^20 + 471450583148622264812447113021812911318975285911848 * q^22 + 1094918718857791395763955497794548441629464114423696 * q^23 + 71600575748870708223111198803019790440272165366567850 * q^25 - 17144617795232739661292142542037336623136662115361812 * q^26 - 421056590097566772314387078351382806371109737989226944 * q^28 - 1286761243501908998723554437372128496488806548512006196 * q^29 - 19590134983123701786508136226454400260130744726276043984 * q^31 + 405443732303791628255103774085578846894562577440580267808 * q^32 + 799554727652091370833855066044541676465377828794014920924 * q^34 + 36738948500466973600844998839202990635858889677989007096000 * q^35 - 91545935905237059630111535534102037526425524589341335258828 * q^37 + 684421739975642826350565409193219733278360180645855295369576 * q^38 - 3191514246209809963152113018089087413561147078084072414179760 * q^40 + 316536315385886215170089302814500575828563777084996078443524 * q^41 + 8908593056531100512689524294334311253125705720155921361637320 * q^43 + 21785863331670136277341155880608983152526085161022719211416784 * q^44 + 203991825673001927929491823653549685659396184023570859282558896 * q^46 - 1142730760034072985500217886491003567898472938032199023875837760 * q^47 + 9932613847036662039777786400812307007669956514072280038886436470 * q^49 + 8883185004616479564484651092109548958973775099745125635626453950 * q^50 - 26987269348801105921073028535709825459131864700220460006411048296 * q^52 - 50865557114922724445413426425120290543311269685677591074207545764 * q^53 - 446272596484924291179313911709667686162610277785745256318167362640 * q^55 - 252098718314851221087836050947321657945518421301909982473468909440 * q^56 + 5708767830293773961786560342813586714128873252994207151314483829348 * q^58 - 2188427764336584360362109164219599664600305872173254932641215849992 * q^59 + 22824130148103906081748322440858509039514053708066868437237654119460 * q^61 - 47586797873032763455450207051586846920428945648357768353569220285424 * q^62 - 62277215504581285171320235502281031925680209278531250485362330807232 * q^64 + 139549609673753297396326760842807258047007635314506217050746073464360 * q^65 - 195051098831763858659485315535620001296749632524239458769204357711816 * q^67 + 478898943613171780503683796705180273623444550119196454935625635754872 * q^68 - 757997824979604988529186642170865717977143205307772715302146700408000 * q^70 + 3034169501204758984184273945180030994909311349950008497555595439759088 * q^71 + 13747249917875809714395686690179837721964032944309940620133405822381724 * q^73 + 2369634359974005306762628635878678463122778575706094238003611098139932 * q^74 - 34154148647149103788996774156065386764182788320537620321912800871149232 * q^76 - 110964225149010328333146128762358481438061822139163262844956857145745024 * q^77 - 201509609621708284923745260863351675377795113292036868882834678557374960 * q^79 + 422838509739279884709169464673498932712468741280281559903498362323065760 * q^80 + 1272064461032237978527479940408403539923817748343630409520994189497365644 * q^82 - 2802602491348140684813265973373777054770511234236863543486293197357747832 * q^83 - 60328702368357628714477758217500517309887606952299760526919048695903160 * q^85 - 5057125471275015782616585132644541629892966424745006584268526775897314984 * q^86 - 6621568649346448861468435905169718150646541969777165734050561367125413728 * q^88 + 159920271872091417315458194799657472188764331647019387730257248766388612 * q^89 - 63049718267601813432671733846200700661982230139950125748195604362104533184 * q^91 + 108738058107400706863040151004186657363927160845612619833607429521300941408 * q^92 + 197757998471403159993044858359064919780754639341995946156177159925776436032 * q^94 - 526939076500447210313077859524744124394283713808433538379475932881003671760 * q^95 + 379948778797471041696674086463609005506560736626194774039181672927157115404 * q^97 - 1466852164333826517330437746602345292601007324558710499132638626830518086494 * q^98

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