LMFDB - Embedded newform 9.76.a.b.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 - 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			1.5
Root			$1.04537e10$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.36324e11 q^{2} -1.91947e22 q^{4} +1.63436e26 q^{5} -2.89747e31 q^{7} -7.76687e33 q^{8} +O(q^{10})$	\(q+1.36324e11 q^{2} -1.91947e22 q^{4} +1.63436e26 q^{5} -2.89747e31 q^{7} -7.76687e33 q^{8} +2.22803e37 q^{10} -1.44670e39 q^{11} +9.60913e40 q^{13} -3.94995e42 q^{14} -3.33656e44 q^{16} +8.93423e45 q^{17} +9.37755e46 q^{19} -3.13711e48 q^{20} -1.97220e50 q^{22} +1.63263e51 q^{23} +2.41661e50 q^{25} +1.30995e52 q^{26} +5.56161e53 q^{28} +3.37547e53 q^{29} +8.83397e54 q^{31} +2.47939e56 q^{32} +1.21795e57 q^{34} -4.73553e57 q^{35} -2.17790e58 q^{37} +1.27838e58 q^{38} -1.26939e60 q^{40} +3.91894e60 q^{41} +3.27056e61 q^{43} +2.77690e61 q^{44} +2.22567e62 q^{46} +7.24595e61 q^{47} -1.57233e63 q^{49} +3.29442e61 q^{50} -1.84444e63 q^{52} +4.63445e64 q^{53} -2.36444e65 q^{55} +2.25043e65 q^{56} +4.60157e64 q^{58} -6.16990e65 q^{59} -1.32520e67 q^{61} +1.20428e66 q^{62} +4.64052e67 q^{64} +1.57048e67 q^{65} -5.62035e68 q^{67} -1.71490e68 q^{68} -6.45566e68 q^{70} -2.97582e69 q^{71} +6.83700e69 q^{73} -2.96900e69 q^{74} -1.79999e69 q^{76} +4.19178e70 q^{77} -2.34135e71 q^{79} -5.45315e70 q^{80} +5.34246e71 q^{82} +6.22883e71 q^{83} +1.46018e72 q^{85} +4.45856e72 q^{86} +1.12364e73 q^{88} +1.23732e72 q^{89} -2.78422e72 q^{91} -3.13379e73 q^{92} +9.87796e72 q^{94} +1.53263e73 q^{95} -2.23276e74 q^{97} -2.14346e74 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.36324e11	0.701370	0.350685	−	0.936493i	$-0.385949\pi$
$2$	1.36324e11	0.701370	0.350685	+	0.936493i	$0.385949\pi$
$3$	0	0
$3$	0	0
$4$	−1.91947e22	−0.508080
$5$	1.63436e26	1.00455	0.502277	−	0.864707i	$-0.332496\pi$
$5$	1.63436e26	1.00455	0.502277	+	0.864707i	$0.332496\pi$
$6$	0	0
$7$	−2.89747e31	−0.589988	−0.294994	−	0.955499i	$-0.595318\pi$
$7$	−2.89747e31	−0.589988	−0.294994	+	0.955499i	$0.595318\pi$
$8$	−7.76687e33	−1.05772
$9$	0	0
$10$	2.22803e37	0.704565
$11$	−1.44670e39	−1.28278	−0.641392	−	0.767213i	$-0.721643\pi$
$11$	−1.44670e39	−1.28278	−0.641392	+	0.767213i	$0.721643\pi$
$12$	0	0
$13$	9.60913e40	0.162109	0.0810547	−	0.996710i	$-0.474171\pi$
$13$	9.60913e40	0.162109	0.0810547	+	0.996710i	$0.474171\pi$
$14$	−3.94995e42	−0.413800
$15$	0	0
$16$	−3.33656e44	−0.233776
$17$	8.93423e45	0.644500	0.322250	−	0.946655i	$-0.395561\pi$
$17$	8.93423e45	0.644500	0.322250	+	0.946655i	$0.395561\pi$
$18$	0	0
$19$	9.37755e46	0.104431	0.0522155	−	0.998636i	$-0.483372\pi$
$19$	9.37755e46	0.104431	0.0522155	+	0.998636i	$0.483372\pi$
$20$	−3.13711e48	−0.510394
$21$	0	0
$22$	−1.97220e50	−0.899707
$23$	1.63263e51	1.40635	0.703177	−	0.711015i	$-0.251764\pi$
$23$	1.63263e51	1.40635	0.703177	+	0.711015i	$0.251764\pi$
$24$	0	0
$25$	2.41661e50	0.00912969
$26$	1.30995e52	0.113699
$27$	0	0
$28$	5.56161e53	0.299761
$29$	3.37547e53	0.0487988	0.0243994	−	0.999702i	$-0.492233\pi$
$29$	3.37547e53	0.0487988	0.0243994	+	0.999702i	$0.492233\pi$
$30$	0	0
$31$	8.83397e54	0.104735	0.0523676	−	0.998628i	$-0.483323\pi$
$31$	8.83397e54	0.104735	0.0523676	+	0.998628i	$0.483323\pi$
$32$	2.47939e56	0.893759
$33$	0	0
$34$	1.21795e57	0.452033
$35$	−4.73553e57	−0.592675
$36$	0	0
$37$	−2.17790e58	−0.339214	−0.169607	−	0.985512i	$-0.554250\pi$
$37$	−2.17790e58	−0.339214	−0.169607	+	0.985512i	$0.554250\pi$
$38$	1.27838e58	0.0732448
$39$	0	0
$40$	−1.26939e60	−1.06254
$41$	3.91894e60	1.29949	0.649747	−	0.760151i	$-0.274875\pi$
$41$	3.91894e60	1.29949	0.649747	+	0.760151i	$0.274875\pi$
$42$	0	0
$43$	3.27056e61	1.81784	0.908918	−	0.416974i	$-0.136909\pi$
$43$	3.27056e61	1.81784	0.908918	+	0.416974i	$0.136909\pi$
$44$	2.77690e61	0.651756
$45$	0	0
$46$	2.22567e62	0.986375
$47$	7.24595e61	0.143359	0.0716796	−	0.997428i	$-0.477164\pi$
$47$	7.24595e61	0.143359	0.0716796	+	0.997428i	$0.477164\pi$
$48$	0	0
$49$	−1.57233e63	−0.651914
$50$	3.29442e61	0.00640330
$51$	0	0
$52$	−1.84444e63	−0.0823645
$53$	4.63445e64	1.01310	0.506551	−	0.862210i	$-0.330920\pi$
$53$	4.63445e64	1.01310	0.506551	+	0.862210i	$0.330920\pi$
$54$	0	0
$55$	−2.36444e65	−1.28863
$56$	2.25043e65	0.624043
$57$	0	0
$58$	4.60157e64	0.0342260
$59$	−6.16990e65	−0.241728	−0.120864	−	0.992669i	$-0.538567\pi$
$59$	−6.16990e65	−0.241728	−0.120864	+	0.992669i	$0.538567\pi$
$60$	0	0
$61$	−1.32520e67	−1.48735	−0.743675	−	0.668541i	$-0.766919\pi$
$61$	−1.32520e67	−1.48735	−0.743675	+	0.668541i	$0.766919\pi$
$62$	1.20428e66	0.0734581
$63$	0	0
$64$	4.64052e67	0.860632
$65$	1.57048e67	0.162848
$66$	0	0
$67$	−5.62035e68	−1.87050	−0.935251	−	0.353985i	$-0.884827\pi$
$67$	−5.62035e68	−1.87050	−0.935251	+	0.353985i	$0.884827\pi$
$68$	−1.71490e68	−0.327457
$69$	0	0
$70$	−6.45566e68	−0.415685
$71$	−2.97582e69	−1.12569	−0.562844	−	0.826563i	$-0.690293\pi$
$71$	−2.97582e69	−1.12569	−0.562844	+	0.826563i	$0.690293\pi$
$72$	0	0
$73$	6.83700e69	0.912553	0.456277	−	0.889838i	$-0.349183\pi$
$73$	6.83700e69	0.912553	0.456277	+	0.889838i	$0.349183\pi$
$74$	−2.96900e69	−0.237915
$75$	0	0
$76$	−1.79999e69	−0.0530592
$77$	4.19178e70	0.756827
$78$	0	0
$79$	−2.34135e71	−1.61603	−0.808017	−	0.589160i	$-0.799459\pi$
$79$	−2.34135e71	−1.61603	−0.808017	+	0.589160i	$0.799459\pi$
$80$	−5.45315e70	−0.234840
$81$	0	0
$82$	5.34246e71	0.911426
$83$	6.22883e71	0.674494	0.337247	−	0.941416i	$-0.390504\pi$
$83$	6.22883e71	0.674494	0.337247	+	0.941416i	$0.390504\pi$
$84$	0	0
$85$	1.46018e72	0.647435
$86$	4.45856e72	1.27498
$87$	0	0
$88$	1.12364e73	1.35683
$89$	1.23732e72	0.0978040	0.0489020	−	0.998804i	$-0.484428\pi$
$89$	1.23732e72	0.0978040	0.0489020	+	0.998804i	$0.484428\pi$
$90$	0	0
$91$	−2.78422e72	−0.0956426
$92$	−3.13379e73	−0.714540
$93$	0	0
$94$	9.87796e72	0.100548
$95$	1.53263e73	0.104907
$96$	0	0
$97$	−2.23276e74	−0.699683	−0.349841	−	0.936809i	$-0.613764\pi$
$97$	−2.23276e74	−0.699683	−0.349841	+	0.936809i	$0.613764\pi$
$98$	−2.14346e74	−0.457234
$99$	0	0
$100$	−4.63861e72	−0.00463861
$101$	3.32309e74	0.228818	0.114409	−	0.993434i	$-0.463503\pi$
$101$	3.32309e74	0.228818	0.114409	+	0.993434i	$0.463503\pi$
$102$	0	0
$103$	1.06457e75	0.351382	0.175691	−	0.984445i	$-0.443784\pi$
$103$	1.06457e75	0.351382	0.175691	+	0.984445i	$0.443784\pi$
$104$	−7.46329e74	−0.171467
$105$	0	0
$106$	6.31786e75	0.710559
$107$	−2.08398e76	−1.64817	−0.824083	−	0.566469i	$-0.808309\pi$
$107$	−2.08398e76	−1.64817	−0.824083	+	0.566469i	$0.808309\pi$
$108$	0	0
$109$	3.32868e76	1.31455	0.657276	−	0.753650i	$-0.271708\pi$
$109$	3.32868e76	1.31455	0.657276	+	0.753650i	$0.271708\pi$
$110$	−3.22330e76	−0.903805
$111$	0	0
$112$	9.66758e75	0.137925
$113$	−6.55459e76	−0.670044	−0.335022	−	0.942210i	$-0.608744\pi$
$113$	−6.55459e76	−0.670044	−0.335022	+	0.942210i	$0.608744\pi$
$114$	0	0
$115$	2.66832e77	1.41276
$116$	−6.47911e75	−0.0247937
$117$	0	0
$118$	−8.41106e76	−0.169541
$119$	−2.58867e77	−0.380247
$120$	0	0
$121$	8.21054e77	0.645536
$122$	−1.80657e78	−1.04318
$123$	0	0
$124$	−1.69565e77	−0.0532138
$125$	−4.28663e78	−0.995383
$126$	0	0
$127$	1.37949e79	1.76636	0.883182	−	0.469031i	$-0.155397\pi$
$127$	1.37949e79	1.76636	0.883182	+	0.469031i	$0.155397\pi$
$128$	−3.04073e78	−0.290137
$129$	0	0
$130$	2.14094e78	0.114217
$131$	4.00256e79	1.60201	0.801004	−	0.598659i	$-0.204300\pi$
$131$	4.00256e79	1.60201	0.801004	+	0.598659i	$0.204300\pi$
$132$	0	0
$133$	−2.71712e78	−0.0616130
$134$	−7.66189e79	−1.31192
$135$	0	0
$136$	−6.93910e79	−0.681702
$137$	1.26017e80	0.940607	0.470303	−	0.882505i	$-0.344144\pi$
$137$	1.26017e80	0.940607	0.470303	+	0.882505i	$0.344144\pi$
$138$	0	0
$139$	−3.99347e80	−1.73099	−0.865496	−	0.500915i	$-0.832997\pi$
$139$	−3.99347e80	−1.73099	−0.865496	+	0.500915i	$0.832997\pi$
$140$	9.08970e79	0.301126
$141$	0	0
$142$	−4.05675e80	−0.789524
$143$	−1.39016e80	−0.207951
$144$	0	0
$145$	5.51674e79	0.0490211
$146$	9.32047e80	0.640038
$147$	0	0
$148$	4.18042e80	0.172348
$149$	3.09515e81	0.991282	0.495641	−	0.868527i	$-0.334933\pi$
$149$	3.09515e81	0.991282	0.495641	+	0.868527i	$0.334933\pi$
$150$	0	0
$151$	−2.63486e81	−0.511825	−0.255912	−	0.966700i	$-0.582376\pi$
$151$	−2.63486e81	−0.511825	−0.255912	+	0.966700i	$0.582376\pi$
$152$	−7.28342e80	−0.110459
$153$	0	0
$154$	5.71441e81	0.530816
$155$	1.44379e81	0.105212
$156$	0	0
$157$	−2.59809e82	−1.17062	−0.585311	−	0.810809i	$-0.699028\pi$
$157$	−2.59809e82	−1.17062	−0.585311	+	0.810809i	$0.699028\pi$
$158$	−3.19182e82	−1.13344
$159$	0	0
$160$	4.05222e82	0.897830
$161$	−4.73051e82	−0.829732
$162$	0	0
$163$	−1.56476e82	−0.172748	−0.0863739	−	0.996263i	$-0.527528\pi$
$163$	−1.56476e82	−0.172748	−0.0863739	+	0.996263i	$0.527528\pi$
$164$	−7.52229e82	−0.660246
$165$	0	0
$166$	8.49139e82	0.473070
$167$	−4.05246e83	−1.80240	−0.901200	−	0.433404i	$-0.857312\pi$
$167$	−4.05246e83	−1.80240	−0.901200	+	0.433404i	$0.857312\pi$
$168$	0	0
$169$	−3.42126e83	−0.973721
$170$	1.99057e83	0.454092
$171$	0	0
$172$	−6.27774e83	−0.923606
$173$	7.17523e83	0.849390	0.424695	−	0.905336i	$-0.360381\pi$
$173$	7.17523e83	0.849390	0.424695	+	0.905336i	$0.360381\pi$
$174$	0	0
$175$	−7.00206e81	−0.00538641
$176$	4.82701e83	0.299884
$177$	0	0
$178$	1.68676e83	0.0685969
$179$	5.67455e83	0.187044	0.0935218	−	0.995617i	$-0.470188\pi$
$179$	5.67455e83	0.187044	0.0935218	+	0.995617i	$0.470188\pi$
$180$	0	0
$181$	−6.33746e84	−1.37711	−0.688555	−	0.725184i	$-0.741755\pi$
$181$	−6.33746e84	−1.37711	−0.688555	+	0.725184i	$0.741755\pi$
$182$	−3.79556e83	−0.0670809
$183$	0	0
$184$	−1.26805e85	−1.48753
$185$	−3.55949e84	−0.340759
$186$	0	0
$187$	−1.29252e85	−0.826754
$188$	−1.39084e84	−0.0728379
$189$	0	0
$190$	2.08935e84	0.0735784
$191$	3.24072e83	0.00937325	0.00468663	−	0.999989i	$-0.498508\pi$
$191$	3.24072e83	0.00937325	0.00468663	+	0.999989i	$0.498508\pi$
$192$	0	0
$193$	2.52091e85	0.493354	0.246677	−	0.969098i	$-0.420661\pi$
$193$	2.52091e85	0.493354	0.246677	+	0.969098i	$0.420661\pi$
$194$	−3.04378e85	−0.490737
$195$	0	0
$196$	3.01804e85	0.331224
$197$	−5.95564e85	−0.540064	−0.270032	−	0.962851i	$-0.587034\pi$
$197$	−5.95564e85	−0.540064	−0.270032	+	0.962851i	$0.587034\pi$
$198$	0	0
$199$	1.15783e86	0.718874	0.359437	−	0.933169i	$-0.382969\pi$
$199$	1.15783e86	0.718874	0.359437	+	0.933169i	$0.382969\pi$
$200$	−1.87695e84	−0.00965668
$201$	0	0
$202$	4.53017e85	0.160486
$203$	−9.78033e84	−0.0287907
$204$	0	0
$205$	6.40498e86	1.30541
$206$	1.45127e86	0.246449
$207$	0	0
$208$	−3.20614e85	−0.0378972
$209$	−1.35665e86	−0.133962
$210$	0	0
$211$	−4.43104e85	−0.0306136	−0.0153068	−	0.999883i	$-0.504872\pi$
$211$	−4.43104e85	−0.0306136	−0.0153068	+	0.999883i	$0.504872\pi$
$212$	−8.89569e86	−0.514736
$213$	0	0
$214$	−2.84096e87	−1.15598
$215$	5.34528e87	1.82612
$216$	0	0
$217$	−2.55962e86	−0.0617924
$218$	4.53779e87	0.921989
$219$	0	0
$220$	4.53847e87	0.654725
$221$	8.58502e86	0.104479
$222$	0	0
$223$	1.19694e88	1.03906	0.519529	−	0.854453i	$-0.326107\pi$
$223$	1.19694e88	1.03906	0.519529	+	0.854453i	$0.326107\pi$
$224$	−7.18396e87	−0.527307
$225$	0	0
$226$	−8.93547e87	−0.469949
$227$	−1.46521e88	−0.653027	−0.326514	−	0.945193i	$-0.605874\pi$
$227$	−1.46521e88	−0.653027	−0.326514	+	0.945193i	$0.605874\pi$
$228$	0	0
$229$	8.96828e86	0.0287659	0.0143830	−	0.999897i	$-0.495422\pi$
$229$	8.96828e86	0.0287659	0.0143830	+	0.999897i	$0.495422\pi$
$230$	3.63755e88	0.990868
$231$	0	0
$232$	−2.62168e87	−0.0516156
$233$	−6.47963e88	−1.08568	−0.542841	−	0.839835i	$-0.682652\pi$
$233$	−6.47963e88	−1.08568	−0.542841	+	0.839835i	$0.682652\pi$
$234$	0	0
$235$	1.18425e88	0.144012
$236$	1.18429e88	0.122817
$237$	0	0
$238$	−3.52898e88	−0.266694
$239$	−1.69913e89	−1.09725	−0.548626	−	0.836068i	$-0.684849\pi$
$239$	−1.69913e89	−1.09725	−0.548626	+	0.836068i	$0.684849\pi$
$240$	0	0
$241$	−7.77008e88	−0.367102	−0.183551	−	0.983010i	$-0.558759\pi$
$241$	−7.77008e88	−0.367102	−0.183551	+	0.983010i	$0.558759\pi$
$242$	1.11929e89	0.452760
$243$	0	0
$244$	2.54369e89	0.755693
$245$	−2.56976e89	−0.654884
$246$	0	0
$247$	9.01100e87	0.0169292
$248$	−6.86123e88	−0.110781
$249$	0	0
$250$	−5.84370e89	−0.698132
$251$	1.56178e89	0.160641	0.0803203	−	0.996769i	$-0.474406\pi$
$251$	1.56178e89	0.160641	0.0803203	+	0.996769i	$0.474406\pi$
$252$	0	0
$253$	−2.36193e90	−1.80405
$254$	1.88058e90	1.23888
$255$	0	0
$256$	−2.16766e90	−1.06413
$257$	−9.67526e89	−0.410365	−0.205183	−	0.978724i	$-0.565779\pi$
$257$	−9.67526e89	−0.410365	−0.205183	+	0.978724i	$0.565779\pi$
$258$	0	0
$259$	6.31042e89	0.200132
$260$	−3.01449e89	−0.0827396
$261$	0	0
$262$	5.45645e90	1.12360
$263$	6.00238e90	1.07148	0.535739	−	0.844384i	$-0.320033\pi$
$263$	6.00238e90	1.07148	0.535739	+	0.844384i	$0.320033\pi$
$264$	0	0
$265$	7.57437e90	1.01772
$266$	−3.70409e89	−0.0432135
$267$	0	0
$268$	1.07881e91	0.950364
$269$	−1.86211e91	−1.42658	−0.713288	−	0.700871i	$-0.752795\pi$
$269$	−1.86211e91	−1.42658	−0.713288	+	0.700871i	$0.752795\pi$
$270$	0	0
$271$	−7.82901e90	−0.454317	−0.227158	−	0.973858i	$-0.572943\pi$
$271$	−7.82901e90	−0.454317	−0.227158	+	0.973858i	$0.572943\pi$
$272$	−2.98096e90	−0.150668
$273$	0	0
$274$	1.71791e91	0.659714
$275$	−3.49612e89	−0.0117114
$276$	0	0
$277$	1.31640e91	0.336044	0.168022	−	0.985783i	$-0.446262\pi$
$277$	1.31640e91	0.336044	0.168022	+	0.985783i	$0.446262\pi$
$278$	−5.44405e91	−1.21407
$279$	0	0
$280$	3.67802e91	0.626885
$281$	1.02015e92	1.52117	0.760585	−	0.649238i	$-0.224912\pi$
$281$	1.02015e92	1.52117	0.760585	+	0.649238i	$0.224912\pi$
$282$	0	0
$283$	−1.27556e92	−1.45784	−0.728918	−	0.684601i	$-0.759977\pi$
$283$	−1.27556e92	−1.45784	−0.728918	+	0.684601i	$0.759977\pi$
$284$	5.71199e91	0.571939
$285$	0	0
$286$	−1.89511e91	−0.145851
$287$	−1.13550e92	−0.766685
$288$	0	0
$289$	−1.12342e92	−0.584620
$290$	7.52064e90	0.0343819
$291$	0	0
$292$	−1.31234e92	−0.463650
$293$	−1.24720e92	−0.387616	−0.193808	−	0.981040i	$-0.562084\pi$
$293$	−1.24720e92	−0.387616	−0.193808	+	0.981040i	$0.562084\pi$
$294$	0	0
$295$	−1.00839e92	−0.242829
$296$	1.69155e92	0.358794
$297$	0	0
$298$	4.21944e92	0.695256
$299$	1.56882e92	0.227983
$300$	0	0
$301$	−9.47636e92	−1.07250
$302$	−3.59194e92	−0.358979
$303$	0	0
$304$	−3.12887e91	−0.0244134
$305$	−2.16586e93	−1.49412
$306$	0	0
$307$	−2.28013e93	−1.23103	−0.615517	−	0.788124i	$-0.711053\pi$
$307$	−2.28013e93	−1.23103	−0.615517	+	0.788124i	$0.711053\pi$
$308$	−8.04600e92	−0.384528
$309$	0	0
$310$	1.96823e92	0.0737927
$311$	−5.91495e93	−1.96533	−0.982667	−	0.185377i	$-0.940649\pi$
$311$	−5.91495e93	−1.96533	−0.982667	+	0.185377i	$0.940649\pi$
$312$	0	0
$313$	3.24737e93	0.848435	0.424217	−	0.905560i	$-0.360549\pi$
$313$	3.24737e93	0.848435	0.424217	+	0.905560i	$0.360549\pi$
$314$	−3.54182e93	−0.821040
$315$	0	0
$316$	4.49415e93	0.821074
$317$	3.51022e93	0.569656	0.284828	−	0.958579i	$-0.408064\pi$
$317$	3.51022e93	0.569656	0.284828	+	0.958579i	$0.408064\pi$
$318$	0	0
$319$	−4.88330e92	−0.0625983
$320$	7.58429e93	0.864551
$321$	0	0
$322$	−6.44882e93	−0.581949
$323$	8.37812e92	0.0673057
$324$	0	0
$325$	2.32215e91	0.00148001
$326$	−2.13314e93	−0.121160
$327$	0	0
$328$	−3.04379e94	−1.37450
$329$	−2.09949e93	−0.0845802
$330$	0	0
$331$	2.82757e94	0.907535	0.453768	−	0.891120i	$-0.350080\pi$
$331$	2.82757e94	0.907535	0.453768	+	0.891120i	$0.350080\pi$
$332$	−1.19561e94	−0.342697
$333$	0	0
$334$	−5.52448e94	−1.26415
$335$	−9.18570e94	−1.87902
$336$	0	0
$337$	−5.46996e94	−0.895083	−0.447541	−	0.894263i	$-0.647700\pi$
$337$	−5.46996e94	−0.895083	−0.447541	+	0.894263i	$0.647700\pi$
$338$	−4.66399e94	−0.682939
$339$	0	0
$340$	−2.80277e94	−0.328949
$341$	−1.27801e94	−0.134353
$342$	0	0
$343$	1.15441e95	0.974609
$344$	−2.54020e95	−1.92277
$345$	0	0
$346$	9.78157e94	0.595737
$347$	−5.97610e94	−0.326635	−0.163317	−	0.986574i	$-0.552219\pi$
$347$	−5.97610e94	−0.326635	−0.163317	+	0.986574i	$0.552219\pi$
$348$	0	0
$349$	−1.08936e95	−0.479976	−0.239988	−	0.970776i	$-0.577143\pi$
$349$	−1.08936e95	−0.479976	−0.239988	+	0.970776i	$0.577143\pi$
$350$	−9.54549e92	−0.00377787
$351$	0	0
$352$	−3.58694e95	−1.14650
$353$	−6.06657e95	−1.74338	−0.871689	−	0.490059i	$-0.836975\pi$
$353$	−6.06657e95	−1.74338	−0.871689	+	0.490059i	$0.836975\pi$
$354$	0	0
$355$	−4.86357e95	−1.13082
$356$	−2.37500e94	−0.0496922
$357$	0	0
$358$	7.73577e94	0.131187
$359$	−1.04798e96	−1.60070	−0.800351	−	0.599531i	$-0.795354\pi$
$359$	−1.04798e96	−1.60070	−0.800351	+	0.599531i	$0.795354\pi$
$360$	0	0
$361$	−7.97550e95	−0.989094
$362$	−8.63948e95	−0.965865
$363$	0	0
$364$	5.34423e94	0.0485940
$365$	1.11741e96	0.916709
$366$	0	0
$367$	−2.09821e96	−1.40240	−0.701198	−	0.712967i	$-0.747351\pi$
$367$	−2.09821e96	−1.40240	−0.701198	+	0.712967i	$0.747351\pi$
$368$	−5.44737e95	−0.328771
$369$	0	0
$370$	−4.85243e95	−0.238998
$371$	−1.34282e96	−0.597717
$372$	0	0
$373$	−1.11924e95	−0.0407232	−0.0203616	−	0.999793i	$-0.506482\pi$
$373$	−1.11924e95	−0.0407232	−0.0203616	+	0.999793i	$0.506482\pi$
$374$	−1.76201e96	−0.579861
$375$	0	0
$376$	−5.62783e95	−0.151634
$377$	3.24353e94	0.00791075
$378$	0	0
$379$	4.19285e96	0.838570	0.419285	−	0.907855i	$-0.362281\pi$
$379$	4.19285e96	0.838570	0.419285	+	0.907855i	$0.362281\pi$
$380$	−2.94184e95	−0.0533009
$381$	0	0
$382$	4.41788e94	0.00657412
$383$	−4.37123e96	−0.589726	−0.294863	−	0.955540i	$-0.595274\pi$
$383$	−4.37123e96	−0.589726	−0.294863	+	0.955540i	$0.595274\pi$
$384$	0	0
$385$	6.85090e96	0.760274
$386$	3.43661e96	0.346024
$387$	0	0
$388$	4.28571e96	0.355494
$389$	−2.04350e97	−1.53909	−0.769546	−	0.638592i	$-0.779517\pi$
$389$	−2.04350e97	−1.53909	−0.769546	+	0.638592i	$0.779517\pi$
$390$	0	0
$391$	1.45863e97	0.906395
$392$	1.22121e97	0.689545
$393$	0	0
$394$	−8.11896e96	−0.378785
$395$	−3.82662e97	−1.62339
$396$	0	0
$397$	−5.19135e97	−1.82237	−0.911185	−	0.411998i	$-0.864831\pi$
$397$	−5.19135e97	−1.82237	−0.911185	+	0.411998i	$0.864831\pi$
$398$	1.57839e97	0.504197
$399$	0	0
$400$	−8.06316e94	−0.00213430
$401$	6.90014e97	1.66320	0.831599	−	0.555376i	$-0.187426\pi$
$401$	6.90014e97	1.66320	0.831599	+	0.555376i	$0.187426\pi$
$402$	0	0
$403$	8.48867e95	0.0169785
$404$	−6.37857e96	−0.116258
$405$	0	0
$406$	−1.33329e96	−0.0201929
$407$	3.15078e97	0.435138
$408$	0	0
$409$	−2.82660e97	−0.324818	−0.162409	−	0.986724i	$-0.551926\pi$
$409$	−2.82660e97	−0.324818	−0.162409	+	0.986724i	$0.551926\pi$
$410$	8.73152e97	0.915578
$411$	0	0
$412$	−2.04341e97	−0.178530
$413$	1.78771e97	0.142617
$414$	0	0
$415$	1.01802e98	0.677566
$416$	2.38248e97	0.144887
$417$	0	0
$418$	−1.84944e97	−0.0939572
$419$	1.43283e98	0.665529	0.332765	−	0.943010i	$-0.392018\pi$
$419$	1.43283e98	0.665529	0.332765	+	0.943010i	$0.392018\pi$
$420$	0	0
$421$	2.88040e98	1.11912	0.559558	−	0.828791i	$-0.310971\pi$
$421$	2.88040e98	1.11912	0.559558	+	0.828791i	$0.310971\pi$
$422$	−6.04058e96	−0.0214715
$423$	0	0
$424$	−3.59952e98	−1.07158
$425$	2.15906e96	0.00588408
$426$	0	0
$427$	3.83974e98	0.877519
$428$	4.00013e98	0.837400
$429$	0	0
$430$	7.28690e98	1.28078
$431$	5.28696e98	0.851743	0.425872	−	0.904784i	$-0.359968\pi$
$431$	5.28696e98	0.851743	0.425872	+	0.904784i	$0.359968\pi$
$432$	0	0
$433$	1.28454e99	1.73961	0.869806	−	0.493393i	$-0.164244\pi$
$433$	1.28454e99	1.73961	0.869806	+	0.493393i	$0.164244\pi$
$434$	−3.48937e97	−0.0433394
$435$	0	0
$436$	−6.38930e98	−0.667897
$437$	1.53101e98	0.146867
$438$	0	0
$439$	1.03723e99	0.838411	0.419206	−	0.907891i	$-0.362309\pi$
$439$	1.03723e99	0.838411	0.419206	+	0.907891i	$0.362309\pi$
$440$	1.83643e99	1.36301
$441$	0	0
$442$	1.17034e98	0.0732788
$443$	−5.12456e98	−0.294793	−0.147396	−	0.989077i	$-0.547089\pi$
$443$	−5.12456e98	−0.294793	−0.147396	+	0.989077i	$0.547089\pi$
$444$	0	0
$445$	2.02223e98	0.0982495
$446$	1.63172e99	0.728764
$447$	0	0
$448$	−1.34458e99	−0.507762
$449$	2.33920e99	0.812510	0.406255	−	0.913760i	$-0.366834\pi$
$449$	2.33920e99	0.812510	0.406255	+	0.913760i	$0.366834\pi$
$450$	0	0
$451$	−5.66954e99	−1.66697
$452$	1.25813e99	0.340436
$453$	0	0
$454$	−1.99744e99	−0.458014
$455$	−4.55043e98	−0.0960782
$456$	0	0
$457$	1.04972e100	1.88025	0.940124	−	0.340833i	$-0.110709\pi$
$457$	1.04972e100	1.88025	0.940124	+	0.340833i	$0.110709\pi$
$458$	1.22259e98	0.0201756
$459$	0	0
$460$	−5.12175e99	−0.717794
$461$	−3.80856e99	−0.492013	−0.246006	−	0.969268i	$-0.579118\pi$
$461$	−3.80856e99	−0.492013	−0.246006	+	0.969268i	$0.579118\pi$
$462$	0	0
$463$	−3.55590e99	−0.390537	−0.195268	−	0.980750i	$-0.562558\pi$
$463$	−3.55590e99	−0.390537	−0.195268	+	0.980750i	$0.562558\pi$
$464$	−1.12624e98	−0.0114080
$465$	0	0
$466$	−8.83328e99	−0.761466
$467$	−1.90689e100	−1.51685	−0.758424	−	0.651761i	$-0.774030\pi$
$467$	−1.90689e100	−1.51685	−0.758424	+	0.651761i	$0.774030\pi$
$468$	0	0
$469$	1.62848e100	1.10357
$470$	1.61442e99	0.101006
$471$	0	0
$472$	4.79208e99	0.255682
$473$	−4.73153e100	−2.33189
$474$	0	0
$475$	2.26619e97	0.000953423 0
$476$	4.96888e99	0.193196
$477$	0	0
$478$	−2.31633e100	−0.769579
$479$	3.04388e98	0.00935075	0.00467537	−	0.999989i	$-0.498512\pi$
$479$	3.04388e98	0.00935075	0.00467537	+	0.999989i	$0.498512\pi$
$480$	0	0
$481$	−2.09277e99	−0.0549898
$482$	−1.05925e100	−0.257474
$483$	0	0
$484$	−1.57599e100	−0.327983
$485$	−3.64913e100	−0.702869
$486$	0	0
$487$	−6.85804e100	−1.13205	−0.566023	−	0.824389i	$-0.691519\pi$
$487$	−6.85804e100	−1.13205	−0.566023	+	0.824389i	$0.691519\pi$
$488$	1.02927e101	1.57320
$489$	0	0
$490$	−3.50320e100	−0.459316
$491$	−1.01875e101	−1.23741	−0.618703	−	0.785625i	$-0.712341\pi$
$491$	−1.01875e101	−1.23741	−0.618703	+	0.785625i	$0.712341\pi$
$492$	0	0
$493$	3.01572e99	0.0314508
$494$	1.22842e99	0.0118737
$495$	0	0
$496$	−2.94750e99	−0.0244845
$497$	8.62235e100	0.664142
$498$	0	0
$499$	2.10589e101	1.39529	0.697645	−	0.716444i	$-0.254231\pi$
$499$	2.10589e101	1.39529	0.697645	+	0.716444i	$0.254231\pi$
$500$	8.22806e100	0.505734
$501$	0	0
$502$	2.12908e100	0.112669
$503$	−3.15449e101	−1.54928	−0.774639	−	0.632403i	$-0.782069\pi$
$503$	−3.15449e101	−1.54928	−0.774639	+	0.632403i	$0.782069\pi$
$504$	0	0
$505$	5.43114e100	0.229860
$506$	−3.21988e101	−1.26531
$507$	0	0
$508$	−2.64790e101	−0.897453
$509$	−1.67930e101	−0.528702	−0.264351	−	0.964427i	$-0.585158\pi$
$509$	−1.67930e101	−0.528702	−0.264351	+	0.964427i	$0.585158\pi$
$510$	0	0
$511$	−1.98100e101	−0.538395
$512$	−1.80629e101	−0.456209
$513$	0	0
$514$	−1.31897e101	−0.287818
$515$	1.73990e101	0.352982
$516$	0	0
$517$	−1.04827e101	−0.183899
$518$	8.60261e100	0.140367
$519$	0	0
$520$	−1.21977e101	−0.172248
$521$	8.36796e101	1.09953	0.549763	−	0.835321i	$-0.314718\pi$
$521$	8.36796e101	1.09953	0.549763	+	0.835321i	$0.314718\pi$
$522$	0	0
$523$	4.34684e101	0.494721	0.247361	−	0.968924i	$-0.420437\pi$
$523$	4.34684e101	0.494721	0.247361	+	0.968924i	$0.420437\pi$
$524$	−7.68280e101	−0.813947
$525$	0	0
$526$	8.18268e101	0.751502
$527$	7.89247e100	0.0675017
$528$	0	0
$529$	1.31781e102	0.977832
$530$	1.03257e102	0.713796
$531$	0	0
$532$	5.21543e100	0.0313043
$533$	3.76576e101	0.210660
$534$	0	0
$535$	−3.40597e102	−1.65567
$536$	4.36525e102	1.97847
$537$	0	0
$538$	−2.53850e102	−1.00056
$539$	2.27469e102	0.836266
$540$	0	0
$541$	3.45942e102	1.10689	0.553446	−	0.832885i	$-0.313312\pi$
$541$	3.45942e102	1.10689	0.553446	+	0.832885i	$0.313312\pi$
$542$	−1.06728e102	−0.318644
$543$	0	0
$544$	2.21514e102	0.576027
$545$	5.44027e102	1.32054
$546$	0	0
$547$	1.89582e102	0.401118	0.200559	−	0.979682i	$-0.435724\pi$
$547$	1.89582e102	0.401118	0.200559	+	0.979682i	$0.435724\pi$
$548$	−2.41886e102	−0.477903
$549$	0	0
$550$	−4.76605e100	−0.00821405
$551$	3.16536e100	0.00509611
$552$	0	0
$553$	6.78400e102	0.953440
$554$	1.79457e102	0.235691
$555$	0	0
$556$	7.66534e102	0.879482
$557$	−4.96751e102	−0.532806	−0.266403	−	0.963862i	$-0.585835\pi$
$557$	−4.96751e102	−0.532806	−0.266403	+	0.963862i	$0.585835\pi$
$558$	0	0
$559$	3.14272e102	0.294688
$560$	1.58003e102	0.138553
$561$	0	0
$562$	1.39071e103	1.06690
$563$	1.58529e103	1.13774	0.568871	−	0.822426i	$-0.307380\pi$
$563$	1.58529e103	1.13774	0.568871	+	0.822426i	$0.307380\pi$
$564$	0	0
$565$	−1.07126e103	−0.673096
$566$	−1.73889e103	−1.02248
$567$	0	0
$568$	2.31128e103	1.19067
$569$	1.62497e103	0.783676	0.391838	−	0.920034i	$-0.371839\pi$
$569$	1.62497e103	0.783676	0.391838	+	0.920034i	$0.371839\pi$
$570$	0	0
$571$	−3.42032e103	−1.44615	−0.723073	−	0.690771i	$-0.757271\pi$
$571$	−3.42032e103	−1.44615	−0.723073	+	0.690771i	$0.757271\pi$
$572$	2.66836e102	0.105656
$573$	0	0
$574$	−1.54796e103	−0.537730
$575$	3.94544e101	0.0128396
$576$	0	0
$577$	−4.48593e103	−1.28162	−0.640810	−	0.767699i	$-0.721401\pi$
$577$	−4.48593e103	−1.28162	−0.640810	+	0.767699i	$0.721401\pi$
$578$	−1.53149e103	−0.410035
$579$	0	0
$580$	−1.05892e102	−0.0249066
$581$	−1.80479e103	−0.397943
$582$	0	0
$583$	−6.70467e103	−1.29959
$584$	−5.31021e103	−0.965228
$585$	0	0
$586$	−1.70024e103	−0.271862
$587$	3.55089e103	0.532608	0.266304	−	0.963889i	$-0.414197\pi$
$587$	3.55089e103	0.532608	0.266304	+	0.963889i	$0.414197\pi$
$588$	0	0
$589$	8.28410e101	0.0109376
$590$	−1.37467e103	−0.170313
$591$	0	0
$592$	7.26670e102	0.0793000
$593$	−1.59905e104	−1.63799	−0.818997	−	0.573798i	$-0.805469\pi$
$593$	−1.59905e104	−1.63799	−0.818997	+	0.573798i	$0.805469\pi$
$594$	0	0
$595$	−4.23083e103	−0.381979
$596$	−5.94106e103	−0.503650
$597$	0	0
$598$	2.13867e103	0.159901
$599$	−5.48681e102	−0.0385313	−0.0192657	−	0.999814i	$-0.506133\pi$
$599$	−5.48681e102	−0.0385313	−0.0192657	+	0.999814i	$0.506133\pi$
$600$	0	0
$601$	1.92882e104	1.19536	0.597682	−	0.801734i	$-0.296089\pi$
$601$	1.92882e104	1.19536	0.597682	+	0.801734i	$0.296089\pi$
$602$	−1.29185e104	−0.752221
$603$	0	0
$604$	5.05753e103	0.260048
$605$	1.34190e104	0.648476
$606$	0	0
$607$	2.00718e104	0.857060	0.428530	−	0.903528i	$-0.359032\pi$
$607$	2.00718e104	0.857060	0.428530	+	0.903528i	$0.359032\pi$
$608$	2.32506e103	0.0933361
$609$	0	0
$610$	−2.95259e104	−1.04793
$611$	6.96272e102	0.0232399
$612$	0	0
$613$	1.72392e104	0.509038	0.254519	−	0.967068i	$-0.418083\pi$
$613$	1.72392e104	0.509038	0.254519	+	0.967068i	$0.418083\pi$
$614$	−3.10836e104	−0.863411
$615$	0	0
$616$	−3.25570e104	−0.800513
$617$	−4.11327e104	−0.951686	−0.475843	−	0.879530i	$-0.657857\pi$
$617$	−4.11327e104	−0.951686	−0.475843	+	0.879530i	$0.657857\pi$
$618$	0	0
$619$	3.92783e104	0.804921	0.402461	−	0.915437i	$-0.368155\pi$
$619$	3.92783e104	0.804921	0.402461	+	0.915437i	$0.368155\pi$
$620$	−2.77132e103	−0.0534561
$621$	0	0
$622$	−8.06350e104	−1.37843
$623$	−3.58510e103	−0.0577032
$624$	0	0
$625$	−7.06988e104	−1.00905
$626$	4.42694e104	0.595067
$627$	0	0
$628$	4.98695e104	0.594769
$629$	−1.94579e104	−0.218623
$630$	0	0
$631$	7.31015e104	0.729164	0.364582	−	0.931171i	$-0.381212\pi$
$631$	7.31015e104	0.729164	0.364582	+	0.931171i	$0.381212\pi$
$632$	1.81850e105	1.70931
$633$	0	0
$634$	4.78528e104	0.399540
$635$	2.25459e105	1.77441
$636$	0	0
$637$	−1.51087e104	−0.105681
$638$	−6.65711e103	−0.0439046
$639$	0	0
$640$	−4.96966e104	−0.291459
$641$	−9.90726e104	−0.547996	−0.273998	−	0.961730i	$-0.588346\pi$
$641$	−9.90726e104	−0.547996	−0.273998	+	0.961730i	$0.588346\pi$
$642$	0	0
$643$	−1.31331e105	−0.646330	−0.323165	−	0.946343i	$-0.604747\pi$
$643$	−1.31331e105	−0.646330	−0.323165	+	0.946343i	$0.604747\pi$
$644$	9.08008e104	0.421570
$645$	0	0
$646$	1.14214e104	0.0472062
$647$	−4.22887e105	−1.64935	−0.824677	−	0.565603i	$-0.808643\pi$
$647$	−4.22887e105	−1.64935	−0.824677	+	0.565603i	$0.808643\pi$
$648$	0	0
$649$	8.92601e104	0.310086
$650$	3.16565e102	0.00103803
$651$	0	0
$652$	3.00351e104	0.0877697
$653$	3.93358e105	1.08528	0.542642	−	0.839964i	$-0.317424\pi$
$653$	3.93358e105	1.08528	0.542642	+	0.839964i	$0.317424\pi$
$654$	0	0
$655$	6.54164e105	1.60930
$656$	−1.30758e105	−0.303790
$657$	0	0
$658$	−2.86211e104	−0.0593220
$659$	1.56776e105	0.306956	0.153478	−	0.988152i	$-0.450953\pi$
$659$	1.56776e105	0.306956	0.153478	+	0.988152i	$0.450953\pi$
$660$	0	0
$661$	1.00104e106	1.74942	0.874712	−	0.484644i	$-0.161051\pi$
$661$	1.00104e106	1.74942	0.874712	+	0.484644i	$0.161051\pi$
$662$	3.85466e105	0.636518
$663$	0	0
$664$	−4.83785e105	−0.713427
$665$	−4.44076e104	−0.0618936
$666$	0	0
$667$	5.51090e104	0.0686284
$668$	7.77858e105	0.915762
$669$	0	0
$670$	−1.25223e106	−1.31789
$671$	1.91717e106	1.90795
$672$	0	0
$673$	−1.92039e105	−0.170932	−0.0854662	−	0.996341i	$-0.527238\pi$
$673$	−1.92039e105	−0.170932	−0.0854662	+	0.996341i	$0.527238\pi$
$674$	−7.45687e105	−0.627784
$675$	0	0
$676$	6.56700e105	0.494728
$677$	−5.57940e104	−0.0397660	−0.0198830	−	0.999802i	$-0.506329\pi$
$677$	−5.57940e104	−0.0397660	−0.0198830	+	0.999802i	$0.506329\pi$
$678$	0	0
$679$	6.46935e105	0.412804
$680$	−1.13410e106	−0.684806
$681$	0	0
$682$	−1.74224e105	−0.0942309
$683$	−2.64233e105	−0.135273	−0.0676364	−	0.997710i	$-0.521546\pi$
$683$	−2.64233e105	−0.135273	−0.0676364	+	0.997710i	$0.521546\pi$
$684$	0	0
$685$	2.05958e106	0.944891
$686$	1.57374e106	0.683562
$687$	0	0
$688$	−1.09124e106	−0.424966
$689$	4.45330e105	0.164233
$690$	0	0
$691$	−5.53570e106	−1.83124	−0.915621	−	0.402041i	$-0.868301\pi$
$691$	−5.53570e106	−1.83124	−0.915621	+	0.402041i	$0.868301\pi$
$692$	−1.37727e106	−0.431558
$693$	0	0
$694$	−8.14686e105	−0.229092
$695$	−6.52678e106	−1.73888
$696$	0	0
$697$	3.50127e106	0.837523
$698$	−1.48506e106	−0.336641
$699$	0	0
$700$	1.34403e104	0.00273672
$701$	−4.45243e106	−0.859352	−0.429676	−	0.902983i	$-0.641372\pi$
$701$	−4.45243e106	−0.859352	−0.429676	+	0.902983i	$0.641372\pi$
$702$	0	0
$703$	−2.04234e105	−0.0354244
$704$	−6.71345e106	−1.10400
$705$	0	0
$706$	−8.27019e106	−1.22275
$707$	−9.62856e105	−0.135000
$708$	0	0
$709$	5.77962e106	0.728896	0.364448	−	0.931224i	$-0.381258\pi$
$709$	5.77962e106	0.728896	0.364448	+	0.931224i	$0.381258\pi$
$710$	−6.63021e106	−0.793120
$711$	0	0
$712$	−9.61011e105	−0.103450
$713$	1.44226e106	0.147295
$714$	0	0
$715$	−2.27202e106	−0.208899
$716$	−1.08921e106	−0.0950330
$717$	0	0
$718$	−1.42865e107	−1.12269
$719$	1.09286e107	0.815137	0.407569	−	0.913175i	$-0.366377\pi$
$719$	1.09286e107	0.815137	0.407569	+	0.913175i	$0.366377\pi$
$720$	0	0
$721$	−3.08457e106	−0.207311
$722$	−1.08725e107	−0.693721
$723$	0	0
$724$	1.21646e107	0.699682
$725$	8.15719e103	0.000445518 0
$726$	0	0
$727$	−1.10843e107	−0.545971	−0.272985	−	0.962018i	$-0.588011\pi$
$727$	−1.10843e107	−0.545971	−0.272985	+	0.962018i	$0.588011\pi$
$728$	2.16247e106	0.101163
$729$	0	0
$730$	1.52330e107	0.642953
$731$	2.92199e107	1.17160
$732$	0	0
$733$	−5.32174e107	−1.92599	−0.962996	−	0.269516i	$-0.913136\pi$
$733$	−5.32174e107	−1.92599	−0.962996	+	0.269516i	$0.913136\pi$
$734$	−2.86036e107	−0.983599
$735$	0	0
$736$	4.04793e107	1.25694
$737$	8.13098e107	2.39945
$738$	0	0
$739$	2.84651e107	0.758832	0.379416	−	0.925226i	$-0.376125\pi$
$739$	2.84651e107	0.758832	0.379416	+	0.925226i	$0.376125\pi$
$740$	6.83233e106	0.173133
$741$	0	0
$742$	−1.83058e107	−0.419221
$743$	−7.42301e107	−1.61622	−0.808108	−	0.589034i	$-0.799508\pi$
$743$	−7.42301e107	−1.61622	−0.808108	+	0.589034i	$0.799508\pi$
$744$	0	0
$745$	5.05861e107	0.995797
$746$	−1.52579e106	−0.0285620
$747$	0	0
$748$	2.48095e107	0.420057
$749$	6.03827e107	0.972398
$750$	0	0
$751$	9.92000e107	1.44549	0.722743	−	0.691116i	$-0.242881\pi$
$751$	9.92000e107	1.44549	0.722743	+	0.691116i	$0.242881\pi$
$752$	−2.41765e106	−0.0335139
$753$	0	0
$754$	4.42171e105	0.00554836
$755$	−4.30631e107	−0.514156
$756$	0	0
$757$	5.32178e107	0.575389	0.287694	−	0.957722i	$-0.407111\pi$
$757$	5.32178e107	0.575389	0.287694	+	0.957722i	$0.407111\pi$
$758$	5.71586e107	0.588148
$759$	0	0
$760$	−1.19038e107	−0.110962
$761$	2.10172e107	0.186488	0.0932441	−	0.995643i	$-0.470276\pi$
$761$	2.10172e107	0.186488	0.0932441	+	0.995643i	$0.470276\pi$
$762$	0	0
$763$	−9.64476e107	−0.775570
$764$	−6.22047e105	−0.00476236
$765$	0	0
$766$	−5.95904e107	−0.413616
$767$	−5.92874e106	−0.0391865
$768$	0	0
$769$	−1.50210e108	−0.900456	−0.450228	−	0.892914i	$-0.648657\pi$
$769$	−1.50210e108	−0.900456	−0.450228	+	0.892914i	$0.648657\pi$
$770$	9.33942e107	0.533234
$771$	0	0
$772$	−4.83882e107	−0.250663
$773$	2.63923e108	1.30240	0.651202	−	0.758905i	$-0.274265\pi$
$773$	2.63923e108	1.30240	0.651202	+	0.758905i	$0.274265\pi$
$774$	0	0
$775$	2.13483e105	0.000956200 0
$776$	1.73415e108	0.740070
$777$	0	0
$778$	−2.78578e108	−1.07947
$779$	3.67501e107	0.135707
$780$	0	0
$781$	4.30512e108	1.44402
$782$	1.98847e108	0.635719
$783$	0	0
$784$	5.24617e107	0.152402
$785$	−4.24622e108	−1.17595
$786$	0	0
$787$	5.76669e108	1.45169	0.725845	−	0.687858i	$-0.241449\pi$
$787$	5.76669e108	1.45169	0.725845	+	0.687858i	$0.241449\pi$
$788$	1.14317e108	0.274395
$789$	0	0
$790$	−5.21660e108	−1.13860
$791$	1.89917e108	0.395318
$792$	0	0
$793$	−1.27340e108	−0.241114
$794$	−7.07706e108	−1.27816
$795$	0	0
$796$	−2.22241e108	−0.365245
$797$	−6.02176e108	−0.944140	−0.472070	−	0.881561i	$-0.656493\pi$
$797$	−6.02176e108	−0.944140	−0.472070	+	0.881561i	$0.656493\pi$
$798$	0	0
$799$	6.47370e107	0.0923949
$800$	5.99172e106	0.00815975
$801$	0	0
$802$	9.40655e108	1.16652
$803$	−9.89110e108	−1.17061
$804$	0	0
$805$	−7.73137e108	−0.833511
$806$	1.15721e107	0.0119083
$807$	0	0
$808$	−2.58100e108	−0.242026
$809$	2.25621e108	0.201980	0.100990	−	0.994887i	$-0.467799\pi$
$809$	2.25621e108	0.201980	0.100990	+	0.994887i	$0.467799\pi$
$810$	0	0
$811$	1.11620e109	0.910874	0.455437	−	0.890268i	$-0.349483\pi$
$811$	1.11620e109	0.910874	0.455437	+	0.890268i	$0.349483\pi$
$812$	1.87731e107	0.0146280
$813$	0	0
$814$	4.29527e108	0.305193
$815$	−2.55739e108	−0.173535
$816$	0	0
$817$	3.06698e108	0.189838
$818$	−3.85333e108	−0.227818
$819$	0	0
$820$	−1.22942e109	−0.663253
$821$	−2.52146e108	−0.129952	−0.0649762	−	0.997887i	$-0.520697\pi$
$821$	−2.52146e108	−0.129952	−0.0649762	+	0.997887i	$0.520697\pi$
$822$	0	0
$823$	−2.93864e109	−1.38246	−0.691230	−	0.722635i	$-0.742931\pi$
$823$	−2.93864e109	−1.38246	−0.691230	+	0.722635i	$0.742931\pi$
$824$	−8.26840e108	−0.371664
$825$	0	0
$826$	2.43708e108	0.100027
$827$	−1.57221e109	−0.616671	−0.308335	−	0.951278i	$-0.599772\pi$
$827$	−1.57221e109	−0.616671	−0.308335	+	0.951278i	$0.599772\pi$
$828$	0	0
$829$	2.15143e108	0.0770783	0.0385392	−	0.999257i	$-0.487730\pi$
$829$	2.15143e108	0.0770783	0.0385392	+	0.999257i	$0.487730\pi$
$830$	1.38780e109	0.475225
$831$	0	0
$832$	4.45913e108	0.139516
$833$	−1.40476e109	−0.420159
$834$	0	0
$835$	−6.62319e109	−1.81061
$836$	2.60405e108	0.0680635
$837$	0	0
$838$	1.95328e109	0.466783
$839$	6.15484e108	0.140651	0.0703256	−	0.997524i	$-0.477596\pi$
$839$	6.15484e108	0.140651	0.0703256	+	0.997524i	$0.477596\pi$
$840$	0	0
$841$	−4.77325e109	−0.997619
$842$	3.92668e109	0.784914
$843$	0	0
$844$	8.50526e107	0.0155541
$845$	−5.59158e109	−0.978155
$846$	0	0
$847$	−2.37898e109	−0.380858
$848$	−1.54631e109	−0.236838
$849$	0	0
$850$	2.94331e107	0.00412692
$851$	−3.55572e109	−0.477055
$852$	0	0
$853$	6.64173e109	0.816004	0.408002	−	0.912981i	$-0.366226\pi$
$853$	6.64173e109	0.816004	0.408002	+	0.912981i	$0.366226\pi$
$854$	5.23448e109	0.615466
$855$	0	0
$856$	1.61860e110	1.74330
$857$	1.32102e110	1.36185	0.680925	−	0.732353i	$-0.261578\pi$
$857$	1.32102e110	1.36185	0.680925	+	0.732353i	$0.261578\pi$
$858$	0	0
$859$	5.82761e109	0.550487	0.275243	−	0.961375i	$-0.411242\pi$
$859$	5.82761e109	0.550487	0.275243	+	0.961375i	$0.411242\pi$
$860$	−1.02601e110	−0.927812
$861$	0	0
$862$	7.20740e109	0.597387
$863$	−2.50382e109	−0.198700	−0.0993500	−	0.995053i	$-0.531676\pi$
$863$	−2.50382e109	−0.198700	−0.0993500	+	0.995053i	$0.531676\pi$
$864$	0	0
$865$	1.17269e110	0.853259
$866$	1.75114e110	1.22011
$867$	0	0
$868$	4.91311e108	0.0313955
$869$	3.38724e110	2.07302
$870$	0	0
$871$	−5.40067e109	−0.303226
$872$	−2.58534e110	−1.39043
$873$	0	0
$874$	2.08713e109	0.103008
$875$	1.24204e110	0.587264
$876$	0	0
$877$	1.51377e110	0.657013	0.328507	−	0.944502i	$-0.393455\pi$
$877$	1.51377e110	0.657013	0.328507	+	0.944502i	$0.393455\pi$
$878$	1.41400e110	0.588037
$879$	0	0
$880$	7.88908e109	0.301249
$881$	1.19861e110	0.438612	0.219306	−	0.975656i	$-0.429621\pi$
$881$	1.19861e110	0.438612	0.219306	+	0.975656i	$0.429621\pi$
$882$	0	0
$883$	−4.40352e110	−1.48004	−0.740021	−	0.672584i	$-0.765184\pi$
$883$	−4.40352e110	−1.48004	−0.740021	+	0.672584i	$0.765184\pi$
$884$	−1.64787e109	−0.0530839
$885$	0	0
$886$	−6.98601e109	−0.206759
$887$	3.20291e110	0.908676	0.454338	−	0.890829i	$-0.349876\pi$
$887$	3.20291e110	0.908676	0.454338	+	0.890829i	$0.349876\pi$
$888$	0	0
$889$	−3.99705e110	−1.04213
$890$	2.75679e109	0.0689093
$891$	0	0
$892$	−2.29749e110	−0.527924
$893$	6.79492e108	0.0149711
$894$	0	0
$895$	9.27428e109	0.187895
$896$	8.81043e109	0.171178
$897$	0	0
$898$	3.18888e110	0.569871
$899$	2.98188e108	0.00511095
$900$	0	0
$901$	4.14052e110	0.652944
$902$	−7.72895e110	−1.16916
$903$	0	0
$904$	5.09086e110	0.708721
$905$	−1.03577e111	−1.38338
$906$	0	0
$907$	4.11974e110	0.506520	0.253260	−	0.967398i	$-0.418497\pi$
$907$	4.11974e110	0.506520	0.253260	+	0.967398i	$0.418497\pi$
$908$	2.81243e110	0.331790
$909$	0	0
$910$	−6.20332e109	−0.0673864
$911$	−7.95032e110	−0.828792	−0.414396	−	0.910097i	$-0.636007\pi$
$911$	−7.95032e110	−0.828792	−0.414396	+	0.910097i	$0.636007\pi$
$912$	0	0
$913$	−9.01127e110	−0.865230
$914$	1.43102e111	1.31875
$915$	0	0
$916$	−1.72143e109	−0.0146154
$917$	−1.15973e111	−0.945165
$918$	0	0
$919$	−1.72959e111	−1.29901	−0.649505	−	0.760358i	$-0.725024\pi$
$919$	−1.72959e111	−1.29901	−0.649505	+	0.760358i	$0.725024\pi$
$920$	−2.07245e111	−1.49431
$921$	0	0
$922$	−5.19198e110	−0.345083
$923$	−2.85950e110	−0.182485
$924$	0	0
$925$	−5.26314e108	−0.00309692
$926$	−4.84754e110	−0.273911
$927$	0	0
$928$	8.36910e109	0.0436144
$929$	−3.05536e110	−0.152923	−0.0764616	−	0.997073i	$-0.524362\pi$
$929$	−3.05536e110	−0.152923	−0.0764616	+	0.997073i	$0.524362\pi$
$930$	0	0
$931$	−1.47446e110	−0.0680800
$932$	1.24375e111	0.551613
$933$	0	0
$934$	−2.59955e111	−1.06387
$935$	−2.11244e111	−0.830519
$936$	0	0
$937$	2.08558e111	0.756821	0.378410	−	0.925638i	$-0.376471\pi$
$937$	2.08558e111	0.756821	0.378410	+	0.925638i	$0.376471\pi$
$938$	2.22001e111	0.774014
$939$	0	0
$940$	−2.27313e110	−0.0731696
$941$	−2.46424e111	−0.762204	−0.381102	−	0.924533i	$-0.624455\pi$
$941$	−2.46424e111	−0.762204	−0.381102	+	0.924533i	$0.624455\pi$
$942$	0	0
$943$	6.39819e111	1.82755
$944$	2.05862e110	0.0565102
$945$	0	0
$946$	−6.45021e111	−1.63552
$947$	3.18895e111	0.777183	0.388592	−	0.921410i	$-0.372962\pi$
$947$	3.18895e111	0.777183	0.388592	+	0.921410i	$0.372962\pi$
$948$	0	0
$949$	6.56976e110	0.147933
$950$	3.08936e108	0.000668702 0
$951$	0	0
$952$	2.01059e111	0.402196
$953$	3.06097e111	0.588675	0.294338	−	0.955702i	$-0.404901\pi$
$953$	3.06097e111	0.588675	0.294338	+	0.955702i	$0.404901\pi$
$954$	0	0
$955$	5.29652e109	0.00941594
$956$	3.26143e111	0.557491
$957$	0	0
$958$	4.14954e109	0.00655834
$959$	−3.65131e111	−0.554946
$960$	0	0
$961$	−7.03618e111	−0.989031
$962$	−2.85295e110	−0.0385682
$963$	0	0
$964$	1.49144e111	0.186517
$965$	4.12009e111	0.495601
$966$	0	0
$967$	1.45168e112	1.61576	0.807880	−	0.589346i	$-0.200615\pi$
$967$	1.45168e112	1.61576	0.807880	+	0.589346i	$0.200615\pi$
$968$	−6.37702e111	−0.682797
$969$	0	0
$970$	−4.97464e111	−0.492972
$971$	7.21500e111	0.687884	0.343942	−	0.938991i	$-0.388238\pi$
$971$	7.21500e111	0.687884	0.343942	+	0.938991i	$0.388238\pi$
$972$	0	0
$973$	1.15710e112	1.02126
$974$	−9.34916e111	−0.793984
$975$	0	0
$976$	4.42161e111	0.347706
$977$	−1.70539e112	−1.29055	−0.645277	−	0.763948i	$-0.723258\pi$
$977$	−1.70539e112	−1.29055	−0.645277	+	0.763948i	$0.723258\pi$
$978$	0	0
$979$	−1.79003e111	−0.125461
$980$	4.93257e111	0.332733
$981$	0	0
$982$	−1.38880e112	−0.867880
$983$	6.53585e111	0.393138	0.196569	−	0.980490i	$-0.437020\pi$
$983$	6.53585e111	0.393138	0.196569	+	0.980490i	$0.437020\pi$
$984$	0	0
$985$	−9.73368e111	−0.542523
$986$	4.11115e110	0.0220587
$987$	0	0
$988$	−1.72964e110	−0.00860140
$989$	5.33962e112	2.55652
$990$	0	0
$991$	−1.45638e112	−0.646417	−0.323209	−	0.946328i	$-0.604762\pi$
$991$	−1.45638e112	−0.646417	−0.323209	+	0.946328i	$0.604762\pi$
$992$	2.19028e111	0.0936080
$993$	0	0
$994$	1.17543e112	0.465810
$995$	1.89231e112	0.722148
$996$	0	0
$997$	1.99299e112	0.705400	0.352700	−	0.935736i	$-0.385264\pi$
$997$	1.99299e112	0.705400	0.352700	+	0.935736i	$0.385264\pi$
$998$	2.87083e112	0.978615
$999$	0	0

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.36324e11 q^{2} -1.91947e22 q^{4} +1.63436e26 q^{5} -2.89747e31 q^{7} -7.76687e33 q^{8} +O(q^{10})\)	\(q+1.36324e11 q^{2} -1.91947e22 q^{4} +1.63436e26 q^{5} -2.89747e31 q^{7} -7.76687e33 q^{8} +2.22803e37 q^{10} -1.44670e39 q^{11} +9.60913e40 q^{13} -3.94995e42 q^{14} -3.33656e44 q^{16} +8.93423e45 q^{17} +9.37755e46 q^{19} -3.13711e48 q^{20} -1.97220e50 q^{22} +1.63263e51 q^{23} +2.41661e50 q^{25} +1.30995e52 q^{26} +5.56161e53 q^{28} +3.37547e53 q^{29} +8.83397e54 q^{31} +2.47939e56 q^{32} +1.21795e57 q^{34} -4.73553e57 q^{35} -2.17790e58 q^{37} +1.27838e58 q^{38} -1.26939e60 q^{40} +3.91894e60 q^{41} +3.27056e61 q^{43} +2.77690e61 q^{44} +2.22567e62 q^{46} +7.24595e61 q^{47} -1.57233e63 q^{49} +3.29442e61 q^{50} -1.84444e63 q^{52} +4.63445e64 q^{53} -2.36444e65 q^{55} +2.25043e65 q^{56} +4.60157e64 q^{58} -6.16990e65 q^{59} -1.32520e67 q^{61} +1.20428e66 q^{62} +4.64052e67 q^{64} +1.57048e67 q^{65} -5.62035e68 q^{67} -1.71490e68 q^{68} -6.45566e68 q^{70} -2.97582e69 q^{71} +6.83700e69 q^{73} -2.96900e69 q^{74} -1.79999e69 q^{76} +4.19178e70 q^{77} -2.34135e71 q^{79} -5.45315e70 q^{80} +5.34246e71 q^{82} +6.22883e71 q^{83} +1.46018e72 q^{85} +4.45856e72 q^{86} +1.12364e73 q^{88} +1.23732e72 q^{89} -2.78422e72 q^{91} -3.13379e73 q^{92} +9.87796e72 q^{94} +1.53263e73 q^{95} -2.23276e74 q^{97} -2.14346e74 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 311057037486 q^{2} + 30\!\cdots\!92 q^{4}+ \cdots - 69\!\cdots\!12 q^{8}+O(q^{10}) \) 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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