LMFDB - Embedded newform 9.44.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,44,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, 44, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 44);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 44 $
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:	$105.399355811$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 11258260111x - 264759545317170 $ x^3 - 11258260111*x - 264759545317170
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{5}\cdot 5\cdot 7 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-91450.2$ 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)

$f(q)$	$=$	$q-3.62707e6 q^{2} +4.35955e12 q^{4} -6.19839e14 q^{5} +2.58688e18 q^{7} +1.60917e19 q^{8} +O(q^{10})$	\(q-3.62707e6 q^{2} +4.35955e12 q^{4} -6.19839e14 q^{5} +2.58688e18 q^{7} +1.60917e19 q^{8} +2.24820e21 q^{10} -2.74302e22 q^{11} +6.62621e23 q^{13} -9.38279e24 q^{14} -9.67126e25 q^{16} -5.82021e25 q^{17} -1.98043e27 q^{19} -2.70222e27 q^{20} +9.94913e28 q^{22} +2.61209e29 q^{23} -7.52667e29 q^{25} -2.40337e30 q^{26} +1.12776e31 q^{28} -2.27846e31 q^{29} -1.73342e32 q^{31} +2.09240e32 q^{32} +2.11103e32 q^{34} -1.60345e33 q^{35} +5.95565e32 q^{37} +7.18317e33 q^{38} -9.97424e33 q^{40} +5.56734e34 q^{41} +1.13992e35 q^{43} -1.19583e35 q^{44} -9.47425e35 q^{46} -2.48937e35 q^{47} +4.50812e36 q^{49} +2.72998e36 q^{50} +2.88873e36 q^{52} -3.93516e36 q^{53} +1.70023e37 q^{55} +4.16271e37 q^{56} +8.26415e37 q^{58} -6.06171e37 q^{59} +3.31999e38 q^{61} +6.28725e38 q^{62} +9.17655e37 q^{64} -4.10719e38 q^{65} +2.46431e38 q^{67} -2.53735e38 q^{68} +5.81582e39 q^{70} +5.22282e39 q^{71} -1.32868e40 q^{73} -2.16016e39 q^{74} -8.63380e39 q^{76} -7.09585e40 q^{77} -1.99325e40 q^{79} +5.99463e40 q^{80} -2.01932e41 q^{82} +5.56384e39 q^{83} +3.60760e40 q^{85} -4.13456e41 q^{86} -4.41397e41 q^{88} +2.64137e41 q^{89} +1.71412e42 q^{91} +1.13876e42 q^{92} +9.02914e41 q^{94} +1.22755e42 q^{95} +3.46950e42 q^{97} -1.63513e43 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2209944 q^{2} + 9822618421824 q^{4} - 535205380774170 q^{5} + 30\!\cdots\!56 q^{7}+ \cdots + 15\!\cdots\!80 q^{8}+O(q^{10}) $ 3 * q + 2209944 * q^2 + 9822618421824 * q^4 - 535205380774170 * q^5 + 301971425665478856 * q^7 + 15830863913787348480 * q^8	$ 3 q + 2209944 q^{2} + 9822618421824 q^{4} - 535205380774170 q^{5} + 30\!\cdots\!56 q^{7}+ \cdots - 24\!\cdots\!08 q^{98}+O(q^{100}) $ 3 * q + 2209944 * q^2 + 9822618421824 * q^4 - 535205380774170 * q^5 + 301971425665478856 * q^7 + 15830863913787348480 * q^8 + 424411733447436982320 * q^10 - 26665053285822824598396 * q^11 + 2675160683143344673595682 * q^13 - 14021968617857741064904128 * q^14 - 79484355831457348071124992 * q^16 + 408654222932442443796841194 * q^17 + 1577331357975519701176464900 * q^19 - 14558304937461364568422335360 * q^20 + 139626647360508967807005852192 * q^22 + 1215339635928561142484811048 * q^23 - 2310484082897201607166539950475 * q^25 + 1738302877111230473099097494544 * q^26 + 16881555000174595924306194912768 * q^28 - 57118989018136587596191009705650 * q^29 - 255565972342397832812135282963424 * q^31 + 144698056390774688063435943542784 * q^32 + 460541119788760022406607937310288 * q^34 - 2398213530857285851552147980593520 * q^35 - 2320645576165979428293572256842694 * q^37 + 30659398199572233844432077267455520 * q^38 - 32703585947405178164040064943232000 * q^40 - 25742376604739002042016577514061166 * q^41 + 240714339689128182512406300123419292 * q^43 + 103743099769332204870397943787455232 * q^44 - 1897545066442972080018141849284700864 * q^46 - 308713553347399687962182796433367856 * q^47 + 3434980292250886821160584750829904379 * q^49 - 1991781591031845842073119994352349400 * q^50 - 1723278372049486147633277645433304704 * q^52 - 15000497558784669132889458695112796362 * q^53 + 3996571389110251928625895283213506440 * q^55 + 64188456562605926675684864956824883200 * q^56 - 103653602500512241322054964115851073680 * q^58 - 226996261182733939538282061249836505900 * q^59 - 9393429368478033721028929889113591854 * q^61 + 208603081649583360642384119938663534848 * q^62 - 1119010168436659689243622515721507700736 * q^64 + 270218921102297342477494789001032451460 * q^65 - 733015616887151283726086660162187354444 * q^67 - 5475599618745313926138424496016357744768 * q^68 + 5947953535225896394715748735968145697920 * q^70 + 18523878066158899993345833814569898287864 * q^71 - 20251106025908798058937016734369224029298 * q^73 - 16747422277652165725566811926177721225008 * q^74 + 77507609539490133886259513865936229344000 * q^76 - 59055613160181778232413942942559747685792 * q^77 + 15233568018599764739559826813006999294800 * q^79 + 100962488695267720109813470111835940986880 * q^80 - 320808727539069549327137360482471983405168 * q^82 + 89206610196719670053085531955706819434428 * q^83 + 438725373228516358990025164547060204838420 * q^85 - 251282426033382455934203370485070655838496 * q^86 - 25677613216166441601684725395949811087360 * q^88 - 203691422331055117225246388044508249665950 * q^89 - 1168954967602248602369466051364648836229584 * q^91 - 688199578839743838535125048241381149958656 * q^92 - 1324027207656692012199753325229034662658432 * q^94 - 3125746305909018830165692627580442029979000 * q^95 - 3881062021784775072625368160679539917597594 * q^97 - 24120041445786820251814869563279238673540008 * 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 $

$2$	−3.62707e6	−1.22296	−0.611478	−	0.791261i	$-0.709425\pi$
$2$	−3.62707e6	−1.22296	−0.611478	+	0.791261i	$0.709425\pi$
$3$	0	0
$3$	0	0
$4$	4.35955e12	0.495624
$5$	−6.19839e14	−0.581332	−0.290666	−	0.956825i	$-0.593877\pi$
$5$	−6.19839e14	−0.581332	−0.290666	+	0.956825i	$0.593877\pi$
$6$	0	0
$7$	2.58688e18	1.75052	0.875262	−	0.483650i	$-0.160689\pi$
$7$	2.58688e18	1.75052	0.875262	+	0.483650i	$0.160689\pi$
$8$	1.60917e19	0.616831
$9$	0	0
$10$	2.24820e21	0.710944
$11$	−2.74302e22	−1.11760	−0.558800	−	0.829303i	$-0.688738\pi$
$11$	−2.74302e22	−1.11760	−0.558800	+	0.829303i	$0.688738\pi$
$12$	0	0
$13$	6.62621e23	0.743846	0.371923	−	0.928264i	$-0.378698\pi$
$13$	6.62621e23	0.743846	0.371923	+	0.928264i	$0.378698\pi$
$14$	−9.38279e24	−2.14081
$15$	0	0
$16$	−9.67126e25	−1.24998
$17$	−5.82021e25	−0.204309	−0.102154	−	0.994769i	$-0.532574\pi$
$17$	−5.82021e25	−0.204309	−0.102154	+	0.994769i	$0.532574\pi$
$18$	0	0
$19$	−1.98043e27	−0.636147	−0.318074	−	0.948066i	$-0.603036\pi$
$19$	−1.98043e27	−0.636147	−0.318074	+	0.948066i	$0.603036\pi$
$20$	−2.70222e27	−0.288122
$21$	0	0
$22$	9.94913e28	1.36678
$23$	2.61209e29	1.37988	0.689938	−	0.723868i	$-0.257638\pi$
$23$	2.61209e29	1.37988	0.689938	+	0.723868i	$0.257638\pi$
$24$	0	0
$25$	−7.52667e29	−0.662053
$26$	−2.40337e30	−0.909692
$27$	0	0
$28$	1.12776e31	0.867601
$29$	−2.27846e31	−0.824300	−0.412150	−	0.911116i	$-0.635222\pi$
$29$	−2.27846e31	−0.824300	−0.412150	+	0.911116i	$0.635222\pi$
$30$	0	0
$31$	−1.73342e32	−1.49496	−0.747478	−	0.664287i	$-0.768735\pi$
$31$	−1.73342e32	−1.49496	−0.747478	+	0.664287i	$0.768735\pi$
$32$	2.09240e32	0.911842
$33$	0	0
$34$	2.11103e32	0.249861
$35$	−1.60345e33	−1.01763
$36$	0	0
$37$	5.95565e32	0.114444	0.0572218	−	0.998361i	$-0.481776\pi$
$37$	5.95565e32	0.114444	0.0572218	+	0.998361i	$0.481776\pi$
$38$	7.18317e33	0.777981
$39$	0	0
$40$	−9.97424e33	−0.358583
$41$	5.56734e34	1.17705	0.588525	−	0.808479i	$-0.299709\pi$
$41$	5.56734e34	1.17705	0.588525	+	0.808479i	$0.299709\pi$
$42$	0	0
$43$	1.13992e35	0.865568	0.432784	−	0.901498i	$-0.357531\pi$
$43$	1.13992e35	0.865568	0.432784	+	0.901498i	$0.357531\pi$
$44$	−1.19583e35	−0.553909
$45$	0	0
$46$	−9.47425e35	−1.68753
$47$	−2.48937e35	−0.279246	−0.139623	−	0.990205i	$-0.544589\pi$
$47$	−2.48937e35	−0.279246	−0.139623	+	0.990205i	$0.544589\pi$
$48$	0	0
$49$	4.50812e36	2.06433
$50$	2.72998e36	0.809663
$51$	0	0
$52$	2.88873e36	0.368668
$53$	−3.93516e36	−0.333451	−0.166725	−	0.986003i	$-0.553319\pi$
$53$	−3.93516e36	−0.333451	−0.166725	+	0.986003i	$0.553319\pi$
$54$	0	0
$55$	1.70023e37	0.649696
$56$	4.16271e37	1.07978
$57$	0	0
$58$	8.26415e37	1.00808
$59$	−6.06171e37	−0.512009	−0.256004	−	0.966676i	$-0.582406\pi$
$59$	−6.06171e37	−0.512009	−0.256004	+	0.966676i	$0.582406\pi$
$60$	0	0
$61$	3.31999e38	1.36945	0.684724	−	0.728802i	$-0.259923\pi$
$61$	3.31999e38	1.36945	0.684724	+	0.728802i	$0.259923\pi$
$62$	6.28725e38	1.82827
$63$	0	0
$64$	9.17655e37	0.134837
$65$	−4.10719e38	−0.432422
$66$	0	0
$67$	2.46431e38	0.135234	0.0676172	−	0.997711i	$-0.478460\pi$
$67$	2.46431e38	0.135234	0.0676172	+	0.997711i	$0.478460\pi$
$68$	−2.53735e38	−0.101260
$69$	0	0
$70$	5.81582e39	1.24452
$71$	5.22282e39	0.823855	0.411927	−	0.911217i	$-0.364856\pi$
$71$	5.22282e39	0.823855	0.411927	+	0.911217i	$0.364856\pi$
$72$	0	0
$73$	−1.32868e40	−1.15340	−0.576699	−	0.816957i	$-0.695659\pi$
$73$	−1.32868e40	−1.15340	−0.576699	+	0.816957i	$0.695659\pi$
$74$	−2.16016e39	−0.139960
$75$	0	0
$76$	−8.63380e39	−0.315290
$77$	−7.09585e40	−1.95638
$78$	0	0
$79$	−1.99325e40	−0.316650	−0.158325	−	0.987387i	$-0.550609\pi$
$79$	−1.99325e40	−0.316650	−0.158325	+	0.987387i	$0.550609\pi$
$80$	5.99463e40	0.726654
$81$	0	0
$82$	−2.01932e41	−1.43948
$83$	5.56384e39	0.0305630	0.0152815	−	0.999883i	$-0.495136\pi$
$83$	5.56384e39	0.0305630	0.0152815	+	0.999883i	$0.495136\pi$
$84$	0	0
$85$	3.60760e40	0.118771
$86$	−4.13456e41	−1.05855
$87$	0	0
$88$	−4.41397e41	−0.689369
$89$	2.64137e41	0.323552	0.161776	−	0.986827i	$-0.448278\pi$
$89$	2.64137e41	0.323552	0.161776	+	0.986827i	$0.448278\pi$
$90$	0	0
$91$	1.71412e42	1.30212
$92$	1.13876e42	0.683899
$93$	0	0
$94$	9.02914e41	0.341505
$95$	1.22755e42	0.369813
$96$	0	0
$97$	3.46950e42	0.667844	0.333922	−	0.942601i	$-0.391628\pi$
$97$	3.46950e42	0.667844	0.333922	+	0.942601i	$0.391628\pi$
$98$	−1.63513e43	−2.52459
$99$	0	0
$100$	−3.28129e42	−0.328129
$101$	1.33544e43	1.07824	0.539118	−	0.842230i	$-0.318758\pi$
$101$	1.33544e43	1.07824	0.539118	+	0.842230i	$0.318758\pi$
$102$	0	0
$103$	−1.58698e43	−0.840567	−0.420283	−	0.907393i	$-0.638069\pi$
$103$	−1.58698e43	−0.840567	−0.420283	+	0.907393i	$0.638069\pi$
$104$	1.06627e43	0.458827
$105$	0	0
$106$	1.42731e43	0.407796
$107$	−6.39702e43	−1.49357	−0.746786	−	0.665064i	$-0.768404\pi$
$107$	−6.39702e43	−1.49357	−0.746786	+	0.665064i	$0.768404\pi$
$108$	0	0
$109$	−4.11078e43	−0.644547	−0.322274	−	0.946647i	$-0.604447\pi$
$109$	−4.11078e43	−0.644547	−0.322274	+	0.946647i	$0.604447\pi$
$110$	−6.16686e43	−0.794550
$111$	0	0
$112$	−2.50184e44	−2.18812
$113$	−2.52895e44	−1.82706	−0.913532	−	0.406766i	$-0.866657\pi$
$113$	−2.52895e44	−1.82706	−0.913532	+	0.406766i	$0.866657\pi$
$114$	0	0
$115$	−1.61908e44	−0.802166
$116$	−9.93308e43	−0.408542
$117$	0	0
$118$	2.19863e44	0.626164
$119$	−1.50562e44	−0.357647
$120$	0	0
$121$	1.50015e44	0.249028
$122$	−1.20418e45	−1.67478
$123$	0	0
$124$	−7.55695e44	−0.740935
$125$	1.17121e45	0.966205
$126$	0	0
$127$	6.08493e44	0.356841	0.178421	−	0.983954i	$-0.442901\pi$
$127$	6.08493e44	0.356841	0.178421	+	0.983954i	$0.442901\pi$
$128$	−2.17333e45	−1.07674
$129$	0	0
$130$	1.48971e45	0.528833
$131$	−1.63203e45	−0.491356	−0.245678	−	0.969351i	$-0.579011\pi$
$131$	−1.63203e45	−0.491356	−0.245678	+	0.969351i	$0.579011\pi$
$132$	0	0
$133$	−5.12314e45	−1.11359
$134$	−8.93823e44	−0.165386
$135$	0	0
$136$	−9.36568e44	−0.126024
$137$	−4.99784e45	−0.574500	−0.287250	−	0.957856i	$-0.592741\pi$
$137$	−4.99784e45	−0.574500	−0.287250	+	0.957856i	$0.592741\pi$
$138$	0	0
$139$	7.86097e44	0.0661695	0.0330847	−	0.999453i	$-0.489467\pi$
$139$	7.86097e44	0.0661695	0.0330847	+	0.999453i	$0.489467\pi$
$140$	−6.99032e45	−0.504364
$141$	0	0
$142$	−1.89435e46	−1.00754
$143$	−1.81758e46	−0.831322
$144$	0	0
$145$	1.41228e46	0.479192
$146$	4.81922e46	1.41056
$147$	0	0
$148$	2.59639e45	0.0567210
$149$	2.89598e46	0.547382	0.273691	−	0.961818i	$-0.411756\pi$
$149$	2.89598e46	0.547382	0.273691	+	0.961818i	$0.411756\pi$
$150$	0	0
$151$	−1.31169e47	−1.86135	−0.930675	−	0.365847i	$-0.880779\pi$
$151$	−1.31169e47	−1.86135	−0.930675	+	0.365847i	$0.880779\pi$
$152$	−3.18684e46	−0.392395
$153$	0	0
$154$	2.57372e47	2.39257
$155$	1.07444e47	0.869066
$156$	0	0
$157$	2.40050e47	1.47387	0.736935	−	0.675964i	$-0.236272\pi$
$157$	2.40050e47	1.47387	0.736935	+	0.675964i	$0.236272\pi$
$158$	7.22967e46	0.387250
$159$	0	0
$160$	−1.29695e47	−0.530083
$161$	6.75716e47	2.41551
$162$	0	0
$163$	4.76715e47	1.30685	0.653425	−	0.756991i	$-0.273332\pi$
$163$	4.76715e47	1.30685	0.653425	+	0.756991i	$0.273332\pi$
$164$	2.42711e47	0.583374
$165$	0	0
$166$	−2.01805e46	−0.0373772
$167$	−6.00740e47	−0.977873	−0.488936	−	0.872320i	$-0.662615\pi$
$167$	−6.00740e47	−0.977873	−0.488936	+	0.872320i	$0.662615\pi$
$168$	0	0
$169$	−3.54465e47	−0.446693
$170$	−1.30850e47	−0.145252
$171$	0	0
$172$	4.96952e47	0.428996
$173$	−5.43885e47	−0.414491	−0.207246	−	0.978289i	$-0.566450\pi$
$173$	−5.43885e47	−0.414491	−0.207246	+	0.978289i	$0.566450\pi$
$174$	0	0
$175$	−1.94706e48	−1.15894
$176$	2.65284e48	1.39698
$177$	0	0
$178$	−9.58045e47	−0.395691
$179$	−1.67643e48	−0.613828	−0.306914	−	0.951737i	$-0.599296\pi$
$179$	−1.67643e48	−0.613828	−0.306914	+	0.951737i	$0.599296\pi$
$180$	0	0
$181$	−3.59480e48	−1.03654	−0.518269	−	0.855218i	$-0.673423\pi$
$181$	−3.59480e48	−1.03654	−0.518269	+	0.855218i	$0.673423\pi$
$182$	−6.21723e48	−1.59244
$183$	0	0
$184$	4.20329e48	0.851150
$185$	−3.69154e47	−0.0665298
$186$	0	0
$187$	1.59650e48	0.228335
$188$	−1.08526e48	−0.138401
$189$	0	0
$190$	−4.45241e48	−0.452265
$191$	−5.26498e47	−0.0477727	−0.0238863	−	0.999715i	$-0.507604\pi$
$191$	−5.26498e47	−0.0477727	−0.0238863	+	0.999715i	$0.507604\pi$
$192$	0	0
$193$	1.27068e48	0.0921625	0.0460813	−	0.998938i	$-0.485327\pi$
$193$	1.27068e48	0.0921625	0.0460813	+	0.998938i	$0.485327\pi$
$194$	−1.25841e49	−0.816745
$195$	0	0
$196$	1.96534e49	1.02313
$197$	5.67999e48	0.265048	0.132524	−	0.991180i	$-0.457692\pi$
$197$	5.67999e48	0.265048	0.132524	+	0.991180i	$0.457692\pi$
$198$	0	0
$199$	4.85226e48	0.182223	0.0911115	−	0.995841i	$-0.470958\pi$
$199$	4.85226e48	0.182223	0.0911115	+	0.995841i	$0.470958\pi$
$200$	−1.21117e49	−0.408375
$201$	0	0
$202$	−4.84372e49	−1.31864
$203$	−5.89410e49	−1.44296
$204$	0	0
$205$	−3.45086e49	−0.684257
$206$	5.75610e49	1.02798
$207$	0	0
$208$	−6.40838e49	−0.929794
$209$	5.43237e49	0.710958
$210$	0	0
$211$	9.39783e49	1.00220	0.501101	−	0.865389i	$-0.332929\pi$
$211$	9.39783e49	1.00220	0.501101	+	0.865389i	$0.332929\pi$
$212$	−1.71555e49	−0.165266
$213$	0	0
$214$	2.32024e50	1.82657
$215$	−7.06565e49	−0.503182
$216$	0	0
$217$	−4.48415e50	−2.61695
$218$	1.49101e50	0.788254
$219$	0	0
$220$	7.41225e49	0.322005
$221$	−3.85659e49	−0.151974
$222$	0	0
$223$	3.04735e50	0.989391	0.494695	−	0.869066i	$-0.335280\pi$
$223$	3.04735e50	0.989391	0.494695	+	0.869066i	$0.335280\pi$
$224$	5.41277e50	1.59620
$225$	0	0
$226$	9.17269e50	2.23442
$227$	5.39198e49	0.119452	0.0597259	−	0.998215i	$-0.480977\pi$
$227$	5.39198e49	0.119452	0.0597259	+	0.998215i	$0.480977\pi$
$228$	0	0
$229$	−7.10477e49	−0.130343	−0.0651714	−	0.997874i	$-0.520759\pi$
$229$	−7.10477e49	−0.130343	−0.0651714	+	0.997874i	$0.520759\pi$
$230$	5.87251e50	0.981015
$231$	0	0
$232$	−3.66642e50	−0.508453
$233$	4.35161e50	0.550171	0.275086	−	0.961420i	$-0.411294\pi$
$233$	4.35161e50	0.550171	0.275086	+	0.961420i	$0.411294\pi$
$234$	0	0
$235$	1.54301e50	0.162334
$236$	−2.64264e50	−0.253764
$237$	0	0
$238$	5.46098e50	0.437387
$239$	−5.98898e50	−0.438327	−0.219164	−	0.975688i	$-0.570333\pi$
$239$	−5.98898e50	−0.438327	−0.219164	+	0.975688i	$0.570333\pi$
$240$	0	0
$241$	−2.41674e51	−1.47864	−0.739320	−	0.673354i	$-0.764853\pi$
$241$	−2.41674e51	−1.47864	−0.739320	+	0.673354i	$0.764853\pi$
$242$	−5.44114e50	−0.304551
$243$	0	0
$244$	1.44737e51	0.678731
$245$	−2.79431e51	−1.20006
$246$	0	0
$247$	−1.31228e51	−0.473196
$248$	−2.78937e51	−0.922135
$249$	0	0
$250$	−4.24806e51	−1.18163
$251$	1.10770e51	0.282774	0.141387	−	0.989954i	$-0.454844\pi$
$251$	1.10770e51	0.282774	0.141387	+	0.989954i	$0.454844\pi$
$252$	0	0
$253$	−7.16502e51	−1.54215
$254$	−2.20705e51	−0.436402
$255$	0	0
$256$	7.07565e51	1.18197
$257$	−5.71497e51	−0.877914	−0.438957	−	0.898508i	$-0.644652\pi$
$257$	−5.71497e51	−0.877914	−0.438957	+	0.898508i	$0.644652\pi$
$258$	0	0
$259$	1.54065e51	0.200336
$260$	−1.79055e51	−0.214318
$261$	0	0
$262$	5.91951e51	0.600908
$263$	8.60748e51	0.805058	0.402529	−	0.915407i	$-0.368131\pi$
$263$	8.60748e51	0.805058	0.402529	+	0.915407i	$0.368131\pi$
$264$	0	0
$265$	2.43917e51	0.193845
$266$	1.85820e52	1.36187
$267$	0	0
$268$	1.07433e51	0.0670254
$269$	−3.31536e52	−1.90922	−0.954612	−	0.297853i	$-0.903729\pi$
$269$	−3.31536e52	−1.90922	−0.954612	+	0.297853i	$0.903729\pi$
$270$	0	0
$271$	−1.65260e52	−0.811575	−0.405787	−	0.913968i	$-0.633003\pi$
$271$	−1.65260e52	−0.811575	−0.405787	+	0.913968i	$0.633003\pi$
$272$	5.62888e51	0.255382
$273$	0	0
$274$	1.81275e52	0.702589
$275$	2.06458e52	0.739910
$276$	0	0
$277$	3.44644e52	1.05695	0.528476	−	0.848948i	$-0.322763\pi$
$277$	3.44644e52	1.05695	0.528476	+	0.848948i	$0.322763\pi$
$278$	−2.85123e51	−0.0809224
$279$	0	0
$280$	−2.58021e52	−0.627708
$281$	1.84357e52	0.415406	0.207703	−	0.978192i	$-0.433401\pi$
$281$	1.84357e52	0.415406	0.207703	+	0.978192i	$0.433401\pi$
$282$	0	0
$283$	−2.27219e52	−0.439579	−0.219790	−	0.975547i	$-0.570537\pi$
$283$	−2.27219e52	−0.439579	−0.219790	+	0.975547i	$0.570537\pi$
$284$	2.27692e52	0.408322
$285$	0	0
$286$	6.59250e52	1.01667
$287$	1.44020e53	2.06045
$288$	0	0
$289$	−7.77653e52	−0.958258
$290$	−5.12245e52	−0.586031
$291$	0	0
$292$	−5.79245e52	−0.571651
$293$	−2.15060e53	−1.97200	−0.985999	−	0.166752i	$-0.946672\pi$
$293$	−2.15060e53	−1.97200	−0.985999	+	0.166752i	$0.946672\pi$
$294$	0	0
$295$	3.75729e52	0.297647
$296$	9.58362e51	0.0705924
$297$	0	0
$298$	−1.05039e53	−0.669424
$299$	1.73083e53	1.02642
$300$	0	0
$301$	2.94882e53	1.51520
$302$	4.75761e53	2.27635
$303$	0	0
$304$	1.91533e53	0.795172
$305$	−2.05786e53	−0.796104
$306$	0	0
$307$	2.45017e53	0.823609	0.411804	−	0.911272i	$-0.364899\pi$
$307$	2.45017e53	0.823609	0.411804	+	0.911272i	$0.364899\pi$
$308$	−3.09347e53	−0.969630
$309$	0	0
$310$	−3.89709e53	−1.06283
$311$	−2.63881e53	−0.671522	−0.335761	−	0.941947i	$-0.608993\pi$
$311$	−2.63881e53	−0.671522	−0.335761	+	0.941947i	$0.608993\pi$
$312$	0	0
$313$	−1.59181e53	−0.352930	−0.176465	−	0.984307i	$-0.556466\pi$
$313$	−1.59181e53	−0.352930	−0.176465	+	0.984307i	$0.556466\pi$
$314$	−8.70678e53	−1.80248
$315$	0	0
$316$	−8.68969e52	−0.156939
$317$	6.66397e53	1.12450	0.562249	−	0.826968i	$-0.309936\pi$
$317$	6.66397e53	1.12450	0.562249	+	0.826968i	$0.309936\pi$
$318$	0	0
$319$	6.24987e53	0.921237
$320$	−5.68799e52	−0.0783852
$321$	0	0
$322$	−2.45087e54	−2.95406
$323$	1.15265e53	0.129970
$324$	0	0
$325$	−4.98733e53	−0.492466
$326$	−1.72908e54	−1.59822
$327$	0	0
$328$	8.95878e53	0.726041
$329$	−6.43971e53	−0.488826
$330$	0	0
$331$	−1.10752e53	−0.0737991	−0.0368996	−	0.999319i	$-0.511748\pi$
$331$	−1.10752e53	−0.0737991	−0.0368996	+	0.999319i	$0.511748\pi$
$332$	2.42559e52	0.0151477
$333$	0	0
$334$	2.17893e54	1.19590
$335$	−1.52748e53	−0.0786161
$336$	0	0
$337$	−4.25604e54	−1.92736	−0.963680	−	0.267061i	$-0.913948\pi$
$337$	−4.25604e54	−1.92736	−0.963680	+	0.267061i	$0.913948\pi$
$338$	1.28567e54	0.546286
$339$	0	0
$340$	1.57275e53	0.0588658
$341$	4.75482e54	1.67076
$342$	0	0
$343$	6.01268e54	1.86314
$344$	1.83431e54	0.533909
$345$	0	0
$346$	1.97271e54	0.506905
$347$	−4.53734e54	−1.09577	−0.547883	−	0.836555i	$-0.684566\pi$
$347$	−4.53734e54	−1.09577	−0.547883	+	0.836555i	$0.684566\pi$
$348$	0	0
$349$	8.33491e54	1.77891	0.889455	−	0.457022i	$-0.151084\pi$
$349$	8.33491e54	1.77891	0.889455	+	0.457022i	$0.151084\pi$
$350$	7.06212e54	1.41733
$351$	0	0
$352$	−5.73949e54	−1.01907
$353$	2.09801e53	0.0350471	0.0175235	−	0.999846i	$-0.494422\pi$
$353$	2.09801e53	0.0350471	0.0175235	+	0.999846i	$0.494422\pi$
$354$	0	0
$355$	−3.23731e54	−0.478933
$356$	1.15152e54	0.160360
$357$	0	0
$358$	6.08055e54	0.750685
$359$	−4.45690e53	−0.0518206	−0.0259103	−	0.999664i	$-0.508248\pi$
$359$	−4.45690e53	−0.0518206	−0.0259103	+	0.999664i	$0.508248\pi$
$360$	0	0
$361$	−5.76969e54	−0.595317
$362$	1.30386e55	1.26764
$363$	0	0
$364$	7.47279e54	0.645362
$365$	8.23569e54	0.670507
$366$	0	0
$367$	−1.43102e55	−1.03591	−0.517957	−	0.855406i	$-0.673307\pi$
$367$	−1.43102e55	−1.03591	−0.517957	+	0.855406i	$0.673307\pi$
$368$	−2.52622e55	−1.72482
$369$	0	0
$370$	1.33895e54	0.0813630
$371$	−1.01798e55	−0.583713
$372$	0	0
$373$	−1.98870e55	−1.01585	−0.507925	−	0.861401i	$-0.669587\pi$
$373$	−1.98870e55	−1.01585	−0.507925	+	0.861401i	$0.669587\pi$
$374$	−5.79060e54	−0.279244
$375$	0	0
$376$	−4.00582e54	−0.172247
$377$	−1.50976e55	−0.613152
$378$	0	0
$379$	−1.23931e55	−0.449197	−0.224599	−	0.974451i	$-0.572107\pi$
$379$	−1.23931e55	−0.449197	−0.224599	+	0.974451i	$0.572107\pi$
$380$	5.35157e54	0.183288
$381$	0	0
$382$	1.90965e54	0.0584239
$383$	−3.56358e55	−1.03066	−0.515328	−	0.856993i	$-0.672330\pi$
$383$	−3.56358e55	−1.03066	−0.515328	+	0.856993i	$0.672330\pi$
$384$	0	0
$385$	4.39829e55	1.13731
$386$	−4.60885e54	−0.112711
$387$	0	0
$388$	1.51255e55	0.330999
$389$	−1.74666e55	−0.361653	−0.180827	−	0.983515i	$-0.557877\pi$
$389$	−1.74666e55	−0.361653	−0.180827	+	0.983515i	$0.557877\pi$
$390$	0	0
$391$	−1.52029e55	−0.281921
$392$	7.25430e55	1.27334
$393$	0	0
$394$	−2.06017e55	−0.324142
$395$	1.23550e55	0.184079
$396$	0	0
$397$	−3.61165e55	−0.482736	−0.241368	−	0.970434i	$-0.577596\pi$
$397$	−3.61165e55	−0.482736	−0.241368	+	0.970434i	$0.577596\pi$
$398$	−1.75995e55	−0.222851
$399$	0	0
$400$	7.27924e55	0.827554
$401$	−1.08123e56	−1.16497	−0.582483	−	0.812843i	$-0.697919\pi$
$401$	−1.08123e56	−1.16497	−0.582483	+	0.812843i	$0.697919\pi$
$402$	0	0
$403$	−1.14860e56	−1.11202
$404$	5.82190e55	0.534399
$405$	0	0
$406$	2.13783e56	1.76467
$407$	−1.63365e55	−0.127902
$408$	0	0
$409$	−4.80971e55	−0.338897	−0.169448	−	0.985539i	$-0.554199\pi$
$409$	−4.80971e55	−0.338897	−0.169448	+	0.985539i	$0.554199\pi$
$410$	1.25165e56	0.836817
$411$	0	0
$412$	−6.91854e55	−0.416605
$413$	−1.56809e56	−0.896283
$414$	0	0
$415$	−3.44869e54	−0.0177672
$416$	1.38647e56	0.678270
$417$	0	0
$418$	−1.97036e56	−0.869471
$419$	4.52052e56	1.89490	0.947451	−	0.319900i	$-0.103649\pi$
$419$	4.52052e56	1.89490	0.947451	+	0.319900i	$0.103649\pi$
$420$	0	0
$421$	−1.37281e56	−0.519453	−0.259727	−	0.965682i	$-0.583632\pi$
$421$	−1.37281e56	−0.519453	−0.259727	+	0.965682i	$0.583632\pi$
$422$	−3.40866e56	−1.22565
$423$	0	0
$424$	−6.33233e55	−0.205682
$425$	4.38068e55	0.135263
$426$	0	0
$427$	8.58841e56	2.39725
$428$	−2.78881e56	−0.740250
$429$	0	0
$430$	2.56276e56	0.615370
$431$	1.97671e56	0.451524	0.225762	−	0.974182i	$-0.427513\pi$
$431$	1.97671e56	0.451524	0.225762	+	0.974182i	$0.427513\pi$
$432$	0	0
$433$	−5.20903e56	−1.07713	−0.538563	−	0.842585i	$-0.681033\pi$
$433$	−5.20903e56	−1.07713	−0.538563	+	0.842585i	$0.681033\pi$
$434$	1.62643e57	3.20042
$435$	0	0
$436$	−1.79212e56	−0.319453
$437$	−5.17307e56	−0.877805
$438$	0	0
$439$	8.78281e56	1.35097	0.675486	−	0.737373i	$-0.263934\pi$
$439$	8.78281e56	1.35097	0.675486	+	0.737373i	$0.263934\pi$
$440$	2.73595e56	0.400752
$441$	0	0
$442$	1.39881e56	0.185858
$443$	−7.62338e56	−0.964867	−0.482433	−	0.875933i	$-0.660247\pi$
$443$	−7.62338e56	−0.964867	−0.482433	+	0.875933i	$0.660247\pi$
$444$	0	0
$445$	−1.63723e56	−0.188091
$446$	−1.10530e57	−1.20998
$447$	0	0
$448$	2.37386e56	0.236036
$449$	−3.22300e56	−0.305467	−0.152734	−	0.988267i	$-0.548808\pi$
$449$	−3.22300e56	−0.305467	−0.152734	+	0.988267i	$0.548808\pi$
$450$	0	0
$451$	−1.52713e57	−1.31547
$452$	−1.10251e57	−0.905537
$453$	0	0
$454$	−1.95571e56	−0.146084
$455$	−1.06248e57	−0.756964
$456$	0	0
$457$	−3.49540e56	−0.226620	−0.113310	−	0.993560i	$-0.536145\pi$
$457$	−3.49540e56	−0.226620	−0.113310	+	0.993560i	$0.536145\pi$
$458$	2.57695e56	0.159404
$459$	0	0
$460$	−7.05846e56	−0.397572
$461$	1.01829e57	0.547397	0.273699	−	0.961816i	$-0.411753\pi$
$461$	1.01829e57	0.547397	0.273699	+	0.961816i	$0.411753\pi$
$462$	0	0
$463$	−1.12662e57	−0.551807	−0.275903	−	0.961185i	$-0.588977\pi$
$463$	−1.12662e57	−0.551807	−0.275903	+	0.961185i	$0.588977\pi$
$464$	2.20356e57	1.03036
$465$	0	0
$466$	−1.57836e57	−0.672835
$467$	−4.32781e57	−1.76180	−0.880898	−	0.473307i	$-0.843060\pi$
$467$	−4.32781e57	−1.76180	−0.880898	+	0.473307i	$0.843060\pi$
$468$	0	0
$469$	6.37487e56	0.236731
$470$	−5.59662e56	−0.198528
$471$	0	0
$472$	−9.75430e56	−0.315823
$473$	−3.12681e57	−0.967358
$474$	0	0
$475$	1.49061e57	0.421163
$476$	−6.56381e56	−0.177258
$477$	0	0
$478$	2.17225e57	0.536055
$479$	5.08788e57	1.20039	0.600196	−	0.799853i	$-0.295089\pi$
$479$	5.08788e57	1.20039	0.600196	+	0.799853i	$0.295089\pi$
$480$	0	0
$481$	3.94634e56	0.0851285
$482$	8.76567e57	1.80831
$483$	0	0
$484$	6.53997e56	0.123424
$485$	−2.15054e57	−0.388239
$486$	0	0
$487$	1.44042e57	0.238022	0.119011	−	0.992893i	$-0.462028\pi$
$487$	1.44042e57	0.238022	0.119011	+	0.992893i	$0.462028\pi$
$488$	5.34242e57	0.844718
$489$	0	0
$490$	1.01352e58	1.46762
$491$	−5.96607e57	−0.826868	−0.413434	−	0.910534i	$-0.635671\pi$
$491$	−5.96607e57	−0.826868	−0.413434	+	0.910534i	$0.635671\pi$
$492$	0	0
$493$	1.32611e57	0.168412
$494$	4.75972e57	0.578698
$495$	0	0
$496$	1.67644e58	1.86867
$497$	1.35108e58	1.44218
$498$	0	0
$499$	−1.54904e58	−1.51670	−0.758350	−	0.651848i	$-0.773994\pi$
$499$	−1.54904e58	−1.51670	−0.758350	+	0.651848i	$0.773994\pi$
$500$	5.10595e57	0.478874
$501$	0	0
$502$	−4.01772e57	−0.345820
$503$	−2.17882e58	−1.79684	−0.898420	−	0.439137i	$-0.855284\pi$
$503$	−2.17882e58	−1.79684	−0.898420	+	0.439137i	$0.855284\pi$
$504$	0	0
$505$	−8.27756e57	−0.626813
$506$	2.59880e58	1.88598
$507$	0	0
$508$	2.65275e57	0.176859
$509$	−2.00199e58	−1.27947	−0.639734	−	0.768596i	$-0.720956\pi$
$509$	−2.00199e58	−1.27947	−0.639734	+	0.768596i	$0.720956\pi$
$510$	0	0
$511$	−3.43713e58	−2.01905
$512$	−6.54706e57	−0.368759
$513$	0	0
$514$	2.07286e58	1.07365
$515$	9.83675e57	0.488648
$516$	0	0
$517$	6.82840e57	0.312085
$518$	−5.58806e57	−0.245003
$519$	0	0
$520$	−6.60914e57	−0.266731
$521$	−4.15960e58	−1.61080	−0.805398	−	0.592735i	$-0.798048\pi$
$521$	−4.15960e58	−1.61080	−0.805398	+	0.592735i	$0.798048\pi$
$522$	0	0
$523$	−1.32108e58	−0.471131	−0.235565	−	0.971858i	$-0.575694\pi$
$523$	−1.32108e58	−0.471131	−0.235565	+	0.971858i	$0.575694\pi$
$524$	−7.11494e57	−0.243528
$525$	0	0
$526$	−3.12199e58	−0.984552
$527$	1.00889e58	0.305433
$528$	0	0
$529$	3.23962e58	0.904059
$530$	−8.84704e57	−0.237065
$531$	0	0
$532$	−2.23346e58	−0.551922
$533$	3.68904e58	0.875545
$534$	0	0
$535$	3.96512e58	0.868261
$536$	3.96548e57	0.0834167
$537$	0	0
$538$	1.20250e59	2.33490
$539$	−1.23659e59	−2.30710
$540$	0	0
$541$	−6.56868e58	−1.13171	−0.565857	−	0.824503i	$-0.691455\pi$
$541$	−6.56868e58	−1.13171	−0.565857	+	0.824503i	$0.691455\pi$
$542$	5.99410e58	0.992521
$543$	0	0
$544$	−1.21782e58	−0.186297
$545$	2.54803e58	0.374696
$546$	0	0
$547$	−3.35920e58	−0.456571	−0.228286	−	0.973594i	$-0.573312\pi$
$547$	−3.35920e58	−0.456571	−0.228286	+	0.973594i	$0.573312\pi$
$548$	−2.17883e58	−0.284736
$549$	0	0
$550$	−7.48838e58	−0.904878
$551$	4.51234e58	0.524376
$552$	0	0
$553$	−5.15630e58	−0.554304
$554$	−1.25005e59	−1.29261
$555$	0	0
$556$	3.42703e57	0.0327952
$557$	7.51741e57	0.0692120	0.0346060	−	0.999401i	$-0.488982\pi$
$557$	7.51741e57	0.0692120	0.0346060	+	0.999401i	$0.488982\pi$
$558$	0	0
$559$	7.55333e58	0.643850
$560$	1.55074e59	1.27202
$561$	0	0
$562$	−6.68675e58	−0.508024
$563$	3.08360e58	0.225490	0.112745	−	0.993624i	$-0.464036\pi$
$563$	3.08360e58	0.225490	0.112745	+	0.993624i	$0.464036\pi$
$564$	0	0
$565$	1.56754e59	1.06213
$566$	8.24141e58	0.537586
$567$	0	0
$568$	8.40438e58	0.508179
$569$	1.05318e59	0.613179	0.306590	−	0.951842i	$-0.400812\pi$
$569$	1.05318e59	0.613179	0.306590	+	0.951842i	$0.400812\pi$
$570$	0	0
$571$	2.73679e59	1.47763	0.738814	−	0.673910i	$-0.235386\pi$
$571$	2.73679e59	1.47763	0.738814	+	0.673910i	$0.235386\pi$
$572$	−7.92384e58	−0.412023
$573$	0	0
$574$	−5.22372e59	−2.51985
$575$	−1.96604e59	−0.913552
$576$	0	0
$577$	−2.69178e59	−1.16081	−0.580403	−	0.814330i	$-0.697105\pi$
$577$	−2.69178e59	−1.16081	−0.580403	+	0.814330i	$0.697105\pi$
$578$	2.82060e59	1.17191
$579$	0	0
$580$	6.15691e58	0.237499
$581$	1.43930e58	0.0535012
$582$	0	0
$583$	1.07942e59	0.372664
$584$	−2.13807e59	−0.711451
$585$	0	0
$586$	7.80039e59	2.41167
$587$	5.77693e59	1.72178	0.860890	−	0.508790i	$-0.169907\pi$
$587$	5.77693e59	1.72178	0.860890	+	0.508790i	$0.169907\pi$
$588$	0	0
$589$	3.43293e59	0.951012
$590$	−1.36280e59	−0.364009
$591$	0	0
$592$	−5.75986e58	−0.143052
$593$	2.43327e58	0.0582793	0.0291396	−	0.999575i	$-0.490723\pi$
$593$	2.43327e58	0.0582793	0.0291396	+	0.999575i	$0.490723\pi$
$594$	0	0
$595$	9.33241e58	0.207912
$596$	1.26252e59	0.271295
$597$	0	0
$598$	−6.27784e59	−1.25526
$599$	3.96268e59	0.764386	0.382193	−	0.924083i	$-0.375169\pi$
$599$	3.96268e59	0.764386	0.382193	+	0.924083i	$0.375169\pi$
$600$	0	0
$601$	−3.77157e59	−0.677207	−0.338603	−	0.940929i	$-0.609954\pi$
$601$	−3.77157e59	−0.677207	−0.338603	+	0.940929i	$0.609954\pi$
$602$	−1.06956e60	−1.85302
$603$	0	0
$604$	−5.71839e59	−0.922529
$605$	−9.29851e58	−0.144768
$606$	0	0
$607$	7.51902e59	1.09045	0.545223	−	0.838291i	$-0.316445\pi$
$607$	7.51902e59	1.09045	0.545223	+	0.838291i	$0.316445\pi$
$608$	−4.14385e59	−0.580066
$609$	0	0
$610$	7.46401e59	0.973601
$611$	−1.64951e59	−0.207716
$612$	0	0
$613$	−1.39353e60	−1.63575	−0.817876	−	0.575395i	$-0.804848\pi$
$613$	−1.39353e60	−1.63575	−0.817876	+	0.575395i	$0.804848\pi$
$614$	−8.88693e59	−1.00724
$615$	0	0
$616$	−1.14184e60	−1.20676
$617$	−1.43273e60	−1.46229	−0.731146	−	0.682221i	$-0.761014\pi$
$617$	−1.43273e60	−1.46229	−0.731146	+	0.682221i	$0.761014\pi$
$618$	0	0
$619$	−1.09264e60	−1.04022	−0.520112	−	0.854098i	$-0.674110\pi$
$619$	−1.09264e60	−1.04022	−0.520112	+	0.854098i	$0.674110\pi$
$620$	4.68410e59	0.430729
$621$	0	0
$622$	9.57116e59	0.821242
$623$	6.83291e59	0.566386
$624$	0	0
$625$	1.29722e59	0.100368
$626$	5.77361e59	0.431618
$627$	0	0
$628$	1.04651e60	0.730485
$629$	−3.46631e58	−0.0233818
$630$	0	0
$631$	−5.43638e59	−0.342514	−0.171257	−	0.985226i	$-0.554783\pi$
$631$	−5.43638e59	−0.342514	−0.171257	+	0.985226i	$0.554783\pi$
$632$	−3.20747e59	−0.195320
$633$	0	0
$634$	−2.41707e60	−1.37521
$635$	−3.77168e59	−0.207443
$636$	0	0
$637$	2.98717e60	1.53555
$638$	−2.26687e60	−1.12663
$639$	0	0
$640$	1.34712e60	0.625945
$641$	3.34810e60	1.50436	0.752179	−	0.658959i	$-0.229003\pi$
$641$	3.34810e60	1.50436	0.752179	+	0.658959i	$0.229003\pi$
$642$	0	0
$643$	7.77539e59	0.326728	0.163364	−	0.986566i	$-0.447766\pi$
$643$	7.77539e59	0.326728	0.163364	+	0.986566i	$0.447766\pi$
$644$	2.94582e60	1.19718
$645$	0	0
$646$	−4.18076e59	−0.158948
$647$	3.09018e60	1.13643	0.568214	−	0.822881i	$-0.307635\pi$
$647$	3.09018e60	1.13643	0.568214	+	0.822881i	$0.307635\pi$
$648$	0	0
$649$	1.66274e60	0.572220
$650$	1.80894e60	0.602265
$651$	0	0
$652$	2.07826e60	0.647706
$653$	6.18136e60	1.86402	0.932010	−	0.362433i	$-0.118054\pi$
$653$	6.18136e60	1.86402	0.932010	+	0.362433i	$0.118054\pi$
$654$	0	0
$655$	1.01160e60	0.285641
$656$	−5.38432e60	−1.47129
$657$	0	0
$658$	2.33573e60	0.597813
$659$	−6.32794e60	−1.56757	−0.783784	−	0.621034i	$-0.786713\pi$
$659$	−6.32794e60	−1.56757	−0.783784	+	0.621034i	$0.786713\pi$
$660$	0	0
$661$	−1.18734e60	−0.275577	−0.137789	−	0.990462i	$-0.543999\pi$
$661$	−1.18734e60	−0.275577	−0.137789	+	0.990462i	$0.543999\pi$
$662$	4.01707e59	0.0902531
$663$	0	0
$664$	8.95314e58	0.0188522
$665$	3.17552e60	0.647366
$666$	0	0
$667$	−5.95156e60	−1.13743
$668$	−2.61896e60	−0.484657
$669$	0	0
$670$	5.54027e59	0.0961441
$671$	−9.10680e60	−1.53049
$672$	0	0
$673$	−5.49460e60	−0.866188	−0.433094	−	0.901349i	$-0.642578\pi$
$673$	−5.49460e60	−0.866188	−0.433094	+	0.901349i	$0.642578\pi$
$674$	1.54370e61	2.35708
$675$	0	0
$676$	−1.54531e60	−0.221391
$677$	5.42453e59	0.0752845	0.0376423	−	0.999291i	$-0.488015\pi$
$677$	5.42453e59	0.0752845	0.0376423	+	0.999291i	$0.488015\pi$
$678$	0	0
$679$	8.97518e60	1.16908
$680$	5.80522e59	0.0732617
$681$	0	0
$682$	−1.72461e61	−2.04327
$683$	2.55176e60	0.292951	0.146475	−	0.989214i	$-0.453207\pi$
$683$	2.55176e60	0.292951	0.146475	+	0.989214i	$0.453207\pi$
$684$	0	0
$685$	3.09786e60	0.333975
$686$	−2.18084e61	−2.27854
$687$	0	0
$688$	−1.10244e61	−1.08194
$689$	−2.60752e60	−0.248036
$690$	0	0
$691$	1.08476e61	0.969518	0.484759	−	0.874648i	$-0.338907\pi$
$691$	1.08476e61	0.969518	0.484759	+	0.874648i	$0.338907\pi$
$692$	−2.37109e60	−0.205432
$693$	0	0
$694$	1.64573e61	1.34007
$695$	−4.87254e59	−0.0384664
$696$	0	0
$697$	−3.24031e60	−0.240482
$698$	−3.02313e61	−2.17553
$699$	0	0
$700$	−8.48830e60	−0.574398
$701$	2.44763e61	1.60623	0.803116	−	0.595822i	$-0.203174\pi$
$701$	2.44763e61	1.60623	0.803116	+	0.595822i	$0.203174\pi$
$702$	0	0
$703$	−1.17948e60	−0.0728030
$704$	−2.51714e60	−0.150694
$705$	0	0
$706$	−7.60964e59	−0.0428610
$707$	3.45461e61	1.88748
$708$	0	0
$709$	1.87862e61	0.965929	0.482965	−	0.875640i	$-0.339560\pi$
$709$	1.87862e61	0.965929	0.482965	+	0.875640i	$0.339560\pi$
$710$	1.17420e61	0.585715
$711$	0	0
$712$	4.25041e60	0.199577
$713$	−4.52786e61	−2.06285
$714$	0	0
$715$	1.12661e61	0.483274
$716$	−7.30850e60	−0.304228
$717$	0	0
$718$	1.61655e60	0.0633744
$719$	−2.37257e61	−0.902710	−0.451355	−	0.892345i	$-0.649059\pi$
$719$	−2.37257e61	−0.902710	−0.451355	+	0.892345i	$0.649059\pi$
$720$	0	0
$721$	−4.10533e61	−1.47143
$722$	2.09271e61	0.728047
$723$	0	0
$724$	−1.56717e61	−0.513732
$725$	1.71493e61	0.545730
$726$	0	0
$727$	1.81553e61	0.544518	0.272259	−	0.962224i	$-0.412229\pi$
$727$	1.81553e61	0.544518	0.272259	+	0.962224i	$0.412229\pi$
$728$	2.75830e61	0.803188
$729$	0	0
$730$	−2.98714e61	−0.820001
$731$	−6.63455e60	−0.176843
$732$	0	0
$733$	1.31563e61	0.330672	0.165336	−	0.986237i	$-0.447129\pi$
$733$	1.31563e61	0.330672	0.165336	+	0.986237i	$0.447129\pi$
$734$	5.19040e61	1.26688
$735$	0	0
$736$	5.46554e61	1.25823
$737$	−6.75965e60	−0.151138
$738$	0	0
$739$	−5.98405e61	−1.26223	−0.631117	−	0.775688i	$-0.717403\pi$
$739$	−5.98405e61	−1.26223	−0.631117	+	0.775688i	$0.717403\pi$
$740$	−1.60935e60	−0.0329737
$741$	0	0
$742$	3.69228e61	0.713856
$743$	5.00463e60	0.0939967	0.0469983	−	0.998895i	$-0.485034\pi$
$743$	5.00463e60	0.0939967	0.0469983	+	0.998895i	$0.485034\pi$
$744$	0	0
$745$	−1.79504e61	−0.318210
$746$	7.21316e61	1.24234
$747$	0	0
$748$	6.96000e60	0.113168
$749$	−1.65483e62	−2.61453
$750$	0	0
$751$	−3.12943e61	−0.466881	−0.233441	−	0.972371i	$-0.574998\pi$
$751$	−3.12943e61	−0.466881	−0.233441	+	0.972371i	$0.574998\pi$
$752$	2.40754e61	0.349052
$753$	0	0
$754$	5.47600e61	0.749859
$755$	8.13039e61	1.08206
$756$	0	0
$757$	1.08176e62	1.36010	0.680048	−	0.733167i	$-0.261959\pi$
$757$	1.08176e62	1.36010	0.680048	+	0.733167i	$0.261959\pi$
$758$	4.49507e61	0.549349
$759$	0	0
$760$	1.97533e61	0.228112
$761$	6.63216e61	0.744535	0.372268	−	0.928125i	$-0.378580\pi$
$761$	6.63216e61	0.744535	0.372268	+	0.928125i	$0.378580\pi$
$762$	0	0
$763$	−1.06341e62	−1.12830
$764$	−2.29530e60	−0.0236773
$765$	0	0
$766$	1.29254e62	1.26045
$767$	−4.01662e61	−0.380856
$768$	0	0
$769$	−6.68870e61	−0.599688	−0.299844	−	0.953988i	$-0.596935\pi$
$769$	−6.68870e61	−0.599688	−0.299844	+	0.953988i	$0.596935\pi$
$770$	−1.59529e62	−1.39088
$771$	0	0
$772$	5.53960e60	0.0456779
$773$	4.99608e61	0.400655	0.200327	−	0.979729i	$-0.435799\pi$
$773$	4.99608e61	0.400655	0.200327	+	0.979729i	$0.435799\pi$
$774$	0	0
$775$	1.30469e62	0.989740
$776$	5.58301e61	0.411947
$777$	0	0
$778$	6.33526e61	0.442286
$779$	−1.10258e62	−0.748778
$780$	0	0
$781$	−1.43263e62	−0.920740
$782$	5.51421e61	0.344777
$783$	0	0
$784$	−4.35992e62	−2.58037
$785$	−1.48792e62	−0.856807
$786$	0	0
$787$	−2.83453e62	−1.54534	−0.772671	−	0.634806i	$-0.781080\pi$
$787$	−2.83453e62	−1.54534	−0.772671	+	0.634806i	$0.781080\pi$
$788$	2.47622e61	0.131364
$789$	0	0
$790$	−4.48124e61	−0.225121
$791$	−6.54209e62	−3.19832
$792$	0	0
$793$	2.19990e62	1.01866
$794$	1.30997e62	0.590365
$795$	0	0
$796$	2.11537e61	0.0903140
$797$	−4.08442e61	−0.169737	−0.0848685	−	0.996392i	$-0.527047\pi$
$797$	−4.08442e61	−0.169737	−0.0848685	+	0.996392i	$0.527047\pi$
$798$	0	0
$799$	1.44887e61	0.0570523
$800$	−1.57488e62	−0.603688
$801$	0	0
$802$	3.92169e62	1.42470
$803$	3.64460e62	1.28904
$804$	0	0
$805$	−4.18836e62	−1.40421
$806$	4.16607e62	1.35995
$807$	0	0
$808$	2.14894e62	0.665089
$809$	2.70018e62	0.813765	0.406882	−	0.913481i	$-0.366616\pi$
$809$	2.70018e62	0.813765	0.406882	+	0.913481i	$0.366616\pi$
$810$	0	0
$811$	4.07164e61	0.116365	0.0581823	−	0.998306i	$-0.481470\pi$
$811$	4.07164e61	0.116365	0.0581823	+	0.998306i	$0.481470\pi$
$812$	−2.56957e62	−0.715163
$813$	0	0
$814$	5.92535e61	0.156419
$815$	−2.95487e62	−0.759713
$816$	0	0
$817$	−2.25753e62	−0.550629
$818$	1.74451e62	0.414456
$819$	0	0
$820$	−1.50442e62	−0.339134
$821$	4.97093e62	1.09159	0.545795	−	0.837919i	$-0.316228\pi$
$821$	4.97093e62	1.09159	0.545795	+	0.837919i	$0.316228\pi$
$822$	0	0
$823$	7.87730e62	1.64165	0.820826	−	0.571179i	$-0.193514\pi$
$823$	7.87730e62	1.64165	0.820826	+	0.571179i	$0.193514\pi$
$824$	−2.55372e62	−0.518487
$825$	0	0
$826$	5.68758e62	1.09612
$827$	7.36002e62	1.38201	0.691004	−	0.722851i	$-0.257169\pi$
$827$	7.36002e62	1.38201	0.691004	+	0.722851i	$0.257169\pi$
$828$	0	0
$829$	3.97702e62	0.708983	0.354491	−	0.935059i	$-0.384654\pi$
$829$	3.97702e62	0.708983	0.354491	+	0.935059i	$0.384654\pi$
$830$	1.25086e61	0.0217286
$831$	0	0
$832$	6.08058e61	0.100298
$833$	−2.62382e62	−0.421761
$834$	0	0
$835$	3.72362e62	0.568468
$836$	2.36827e62	0.352367
$837$	0	0
$838$	−1.63962e63	−2.31738
$839$	6.29957e62	0.867818	0.433909	−	0.900957i	$-0.357134\pi$
$839$	6.29957e62	0.867818	0.433909	+	0.900957i	$0.357134\pi$
$840$	0	0
$841$	−2.44896e62	−0.320530
$842$	4.97929e62	0.635269
$843$	0	0
$844$	4.09703e62	0.496715
$845$	2.19711e62	0.259677
$846$	0	0
$847$	3.88070e62	0.435930
$848$	3.80580e62	0.416807
$849$	0	0
$850$	−1.58890e62	−0.165421
$851$	1.55567e62	0.157918
$852$	0	0
$853$	1.37710e63	1.32911	0.664557	−	0.747238i	$-0.268620\pi$
$853$	1.37710e63	1.32911	0.664557	+	0.747238i	$0.268620\pi$
$854$	−3.11508e63	−2.93173
$855$	0	0
$856$	−1.02939e63	−0.921281
$857$	−6.27513e62	−0.547690	−0.273845	−	0.961774i	$-0.588296\pi$
$857$	−6.27513e62	−0.547690	−0.273845	+	0.961774i	$0.588296\pi$
$858$	0	0
$859$	−1.57268e63	−1.30553	−0.652767	−	0.757559i	$-0.726392\pi$
$859$	−1.57268e63	−1.30553	−0.652767	+	0.757559i	$0.726392\pi$
$860$	−3.08031e62	−0.249389
$861$	0	0
$862$	−7.16966e62	−0.552195
$863$	−1.77472e63	−1.33321	−0.666603	−	0.745413i	$-0.732252\pi$
$863$	−1.77472e63	−1.33321	−0.666603	+	0.745413i	$0.732252\pi$
$864$	0	0
$865$	3.37121e62	0.240957
$866$	1.88935e63	1.31728
$867$	0	0
$868$	−1.95489e63	−1.29702
$869$	5.46753e62	0.353888
$870$	0	0
$871$	1.63290e62	0.100594
$872$	−6.61493e62	−0.397577
$873$	0	0
$874$	1.87631e63	1.07352
$875$	3.02977e63	1.69136
$876$	0	0
$877$	1.15736e62	0.0615147	0.0307573	−	0.999527i	$-0.490208\pi$
$877$	1.15736e62	0.0615147	0.0307573	+	0.999527i	$0.490208\pi$
$878$	−3.18559e63	−1.65218
$879$	0	0
$880$	−1.64434e63	−0.812108
$881$	−3.96934e63	−1.91310	−0.956548	−	0.291576i	$-0.905820\pi$
$881$	−3.96934e63	−1.91310	−0.956548	+	0.291576i	$0.905820\pi$
$882$	0	0
$883$	−1.37793e63	−0.632515	−0.316258	−	0.948673i	$-0.602426\pi$
$883$	−1.37793e63	−0.632515	−0.316258	+	0.948673i	$0.602426\pi$
$884$	−1.68130e62	−0.0753220
$885$	0	0
$886$	2.76505e63	1.17999
$887$	3.36758e63	1.40268	0.701341	−	0.712826i	$-0.252585\pi$
$887$	3.36758e63	1.40268	0.701341	+	0.712826i	$0.252585\pi$
$888$	0	0
$889$	1.57410e63	0.624659
$890$	5.93834e62	0.230028
$891$	0	0
$892$	1.32851e63	0.490365
$893$	4.93004e62	0.177641
$894$	0	0
$895$	1.03912e63	0.356838
$896$	−5.62214e63	−1.88486
$897$	0	0
$898$	1.16901e63	0.373573
$899$	3.94954e63	1.23229
$900$	0	0
$901$	2.29035e62	0.0681268
$902$	5.53902e63	1.60876
$903$	0	0
$904$	−4.06950e63	−1.12699
$905$	2.22820e63	0.602572
$906$	0	0
$907$	−3.22814e63	−0.832522	−0.416261	−	0.909245i	$-0.636660\pi$
$907$	−3.22814e63	−0.832522	−0.416261	+	0.909245i	$0.636660\pi$
$908$	2.35066e62	0.0592031
$909$	0	0
$910$	3.85369e63	0.925734
$911$	−6.66803e63	−1.56442	−0.782208	−	0.623017i	$-0.785907\pi$
$911$	−6.66803e63	−1.56442	−0.782208	+	0.623017i	$0.785907\pi$
$912$	0	0
$913$	−1.52617e62	−0.0341572
$914$	1.26781e63	0.277147
$915$	0	0
$916$	−3.09736e62	−0.0646010
$917$	−4.22187e63	−0.860131
$918$	0	0
$919$	3.12159e63	0.606866	0.303433	−	0.952853i	$-0.401867\pi$
$919$	3.12159e63	0.606866	0.303433	+	0.952853i	$0.401867\pi$
$920$	−2.60536e63	−0.494801
$921$	0	0
$922$	−3.69342e63	−0.669443
$923$	3.46075e63	0.612822
$924$	0	0
$925$	−4.48262e62	−0.0757678
$926$	4.08634e63	0.674836
$927$	0	0
$928$	−4.76745e63	−0.751631
$929$	1.01789e64	1.56806	0.784028	−	0.620725i	$-0.213162\pi$
$929$	1.01789e64	1.56806	0.784028	+	0.620725i	$0.213162\pi$
$930$	0	0
$931$	−8.92802e63	−1.31322
$932$	1.89711e63	0.272678
$933$	0	0
$934$	1.56973e64	2.15460
$935$	−9.89571e62	−0.132739
$936$	0	0
$937$	−5.70526e63	−0.730928	−0.365464	−	0.930826i	$-0.619090\pi$
$937$	−5.70526e63	−0.730928	−0.365464	+	0.930826i	$0.619090\pi$
$938$	−2.31221e63	−0.289512
$939$	0	0
$940$	6.72684e62	0.0804567
$941$	1.04360e64	1.22000	0.609999	−	0.792402i	$-0.291170\pi$
$941$	1.04360e64	1.22000	0.609999	+	0.792402i	$0.291170\pi$
$942$	0	0
$943$	1.45424e64	1.62418
$944$	5.86244e63	0.640001
$945$	0	0
$946$	1.13412e64	1.18304
$947$	−1.40457e64	−1.43225	−0.716124	−	0.697973i	$-0.754086\pi$
$947$	−1.40457e64	−1.43225	−0.716124	+	0.697973i	$0.754086\pi$
$948$	0	0
$949$	−8.80412e63	−0.857951
$950$	−5.40654e63	−0.515065
$951$	0	0
$952$	−2.42279e63	−0.220608
$953$	5.00331e63	0.445410	0.222705	−	0.974886i	$-0.428511\pi$
$953$	5.00331e63	0.445410	0.222705	+	0.974886i	$0.428511\pi$
$954$	0	0
$955$	3.26344e62	0.0277718
$956$	−2.61093e63	−0.217245
$957$	0	0
$958$	−1.84541e64	−1.46803
$959$	−1.29288e64	−1.00568
$960$	0	0
$961$	1.66028e64	1.23489
$962$	−1.43136e63	−0.104109
$963$	0	0
$964$	−1.05359e64	−0.732849
$965$	−7.87618e62	−0.0535770
$966$	0	0
$967$	1.23774e64	0.805307	0.402654	−	0.915352i	$-0.368088\pi$
$967$	1.23774e64	0.805307	0.402654	+	0.915352i	$0.368088\pi$
$968$	2.41399e63	0.153608
$969$	0	0
$970$	7.80015e63	0.474800
$971$	6.90009e63	0.410810	0.205405	−	0.978677i	$-0.434149\pi$
$971$	6.90009e63	0.410810	0.205405	+	0.978677i	$0.434149\pi$
$972$	0	0
$973$	2.03353e63	0.115831
$974$	−5.22452e63	−0.291091
$975$	0	0
$976$	−3.21085e64	−1.71178
$977$	−2.22048e64	−1.15801	−0.579006	−	0.815323i	$-0.696559\pi$
$977$	−2.22048e64	−1.15801	−0.579006	+	0.815323i	$0.696559\pi$
$978$	0	0
$979$	−7.24534e63	−0.361602
$980$	−1.21819e64	−0.594779
$981$	0	0
$982$	2.16394e64	1.01122
$983$	−8.17397e63	−0.373708	−0.186854	−	0.982388i	$-0.559829\pi$
$983$	−8.17397e63	−0.373708	−0.186854	+	0.982388i	$0.559829\pi$
$984$	0	0
$985$	−3.52068e63	−0.154081
$986$	−4.80991e63	−0.205960
$987$	0	0
$988$	−5.72094e63	−0.234527
$989$	2.97757e64	1.19438
$990$	0	0
$991$	−3.43882e64	−1.32077	−0.660383	−	0.750929i	$-0.729606\pi$
$991$	−3.43882e64	−1.32077	−0.660383	+	0.750929i	$0.729606\pi$
$992$	−3.62701e64	−1.36316
$993$	0	0
$994$	−4.90046e64	−1.76372
$995$	−3.00762e63	−0.105932
$996$	0	0
$997$	−2.06533e64	−0.696697	−0.348349	−	0.937365i	$-0.613257\pi$
$997$	−2.06533e64	−0.696697	−0.348349	+	0.937365i	$0.613257\pi$
$998$	5.61846e64	1.85486
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.44.a.b.1.1		3
3.2	odd	2		1.44.a.a.1.3	✓	3
12.11	even	2		16.44.a.c.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.44.a.a.1.3	✓	3	3.2	odd	2
9.44.a.b.1.1		3	1.1	even	1	trivial
16.44.a.c.1.2		3	12.11	even	2

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:	\( k \)	\(=\)	\( 44 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-3.62707e6 q^{2} +4.35955e12 q^{4} -6.19839e14 q^{5} +2.58688e18 q^{7} +1.60917e19 q^{8} +O(q^{10})\)	\(q-3.62707e6 q^{2} +4.35955e12 q^{4} -6.19839e14 q^{5} +2.58688e18 q^{7} +1.60917e19 q^{8} +2.24820e21 q^{10} -2.74302e22 q^{11} +6.62621e23 q^{13} -9.38279e24 q^{14} -9.67126e25 q^{16} -5.82021e25 q^{17} -1.98043e27 q^{19} -2.70222e27 q^{20} +9.94913e28 q^{22} +2.61209e29 q^{23} -7.52667e29 q^{25} -2.40337e30 q^{26} +1.12776e31 q^{28} -2.27846e31 q^{29} -1.73342e32 q^{31} +2.09240e32 q^{32} +2.11103e32 q^{34} -1.60345e33 q^{35} +5.95565e32 q^{37} +7.18317e33 q^{38} -9.97424e33 q^{40} +5.56734e34 q^{41} +1.13992e35 q^{43} -1.19583e35 q^{44} -9.47425e35 q^{46} -2.48937e35 q^{47} +4.50812e36 q^{49} +2.72998e36 q^{50} +2.88873e36 q^{52} -3.93516e36 q^{53} +1.70023e37 q^{55} +4.16271e37 q^{56} +8.26415e37 q^{58} -6.06171e37 q^{59} +3.31999e38 q^{61} +6.28725e38 q^{62} +9.17655e37 q^{64} -4.10719e38 q^{65} +2.46431e38 q^{67} -2.53735e38 q^{68} +5.81582e39 q^{70} +5.22282e39 q^{71} -1.32868e40 q^{73} -2.16016e39 q^{74} -8.63380e39 q^{76} -7.09585e40 q^{77} -1.99325e40 q^{79} +5.99463e40 q^{80} -2.01932e41 q^{82} +5.56384e39 q^{83} +3.60760e40 q^{85} -4.13456e41 q^{86} -4.41397e41 q^{88} +2.64137e41 q^{89} +1.71412e42 q^{91} +1.13876e42 q^{92} +9.02914e41 q^{94} +1.22755e42 q^{95} +3.46950e42 q^{97} -1.63513e43 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2209944 q^{2} + 9822618421824 q^{4} - 535205380774170 q^{5} + 30\!\cdots\!56 q^{7}+ \cdots + 15\!\cdots\!80 q^{8}+O(q^{10}) \) 3 * q + 2209944 * q^2 + 9822618421824 * q^4 - 535205380774170 * q^5 + 301971425665478856 * q^7 + 15830863913787348480 * q^8	\( 3 q + 2209944 q^{2} + 9822618421824 q^{4} - 535205380774170 q^{5} + 30\!\cdots\!56 q^{7}+ \cdots - 24\!\cdots\!08 q^{98}+O(q^{100}) \) 3 * q + 2209944 * q^2 + 9822618421824 * q^4 - 535205380774170 * q^5 + 301971425665478856 * q^7 + 15830863913787348480 * q^8 + 424411733447436982320 * q^10 - 26665053285822824598396 * q^11 + 2675160683143344673595682 * q^13 - 14021968617857741064904128 * q^14 - 79484355831457348071124992 * q^16 + 408654222932442443796841194 * q^17 + 1577331357975519701176464900 * q^19 - 14558304937461364568422335360 * q^20 + 139626647360508967807005852192 * q^22 + 1215339635928561142484811048 * q^23 - 2310484082897201607166539950475 * q^25 + 1738302877111230473099097494544 * q^26 + 16881555000174595924306194912768 * q^28 - 57118989018136587596191009705650 * q^29 - 255565972342397832812135282963424 * q^31 + 144698056390774688063435943542784 * q^32 + 460541119788760022406607937310288 * q^34 - 2398213530857285851552147980593520 * q^35 - 2320645576165979428293572256842694 * q^37 + 30659398199572233844432077267455520 * q^38 - 32703585947405178164040064943232000 * q^40 - 25742376604739002042016577514061166 * q^41 + 240714339689128182512406300123419292 * q^43 + 103743099769332204870397943787455232 * q^44 - 1897545066442972080018141849284700864 * q^46 - 308713553347399687962182796433367856 * q^47 + 3434980292250886821160584750829904379 * q^49 - 1991781591031845842073119994352349400 * q^50 - 1723278372049486147633277645433304704 * q^52 - 15000497558784669132889458695112796362 * q^53 + 3996571389110251928625895283213506440 * q^55 + 64188456562605926675684864956824883200 * q^56 - 103653602500512241322054964115851073680 * q^58 - 226996261182733939538282061249836505900 * q^59 - 9393429368478033721028929889113591854 * q^61 + 208603081649583360642384119938663534848 * q^62 - 1119010168436659689243622515721507700736 * q^64 + 270218921102297342477494789001032451460 * q^65 - 733015616887151283726086660162187354444 * q^67 - 5475599618745313926138424496016357744768 * q^68 + 5947953535225896394715748735968145697920 * q^70 + 18523878066158899993345833814569898287864 * q^71 - 20251106025908798058937016734369224029298 * q^73 - 16747422277652165725566811926177721225008 * q^74 + 77507609539490133886259513865936229344000 * q^76 - 59055613160181778232413942942559747685792 * q^77 + 15233568018599764739559826813006999294800 * q^79 + 100962488695267720109813470111835940986880 * q^80 - 320808727539069549327137360482471983405168 * q^82 + 89206610196719670053085531955706819434428 * q^83 + 438725373228516358990025164547060204838420 * q^85 - 251282426033382455934203370485070655838496 * q^86 - 25677613216166441601684725395949811087360 * q^88 - 203691422331055117225246388044508249665950 * q^89 - 1168954967602248602369466051364648836229584 * q^91 - 688199578839743838535125048241381149958656 * q^92 - 1324027207656692012199753325229034662658432 * q^94 - 3125746305909018830165692627580442029979000 * q^95 - 3881062021784775072625368160679539917597594 * q^97 - 24120041445786820251814869563279238673540008 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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