LMFDB - Embedded newform 126.9.b.a.71.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,9,Mod(71,126)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("126.71");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	126.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$51.3297048677$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4 x^{7} - 3942 x^{6} + 11840 x^{5} + 4459849 x^{4} - 8939436 x^{3} - 1108383492 x^{2} + \cdots + 82666406664 $ x^8 - 4x^7 - 3942x^6 + 11840x^5 + 4459849x^4 - 8939436x^3 - 1108383492x^2 + 1112855184*x + 82666406664
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{10}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.8
Root			$-11.9835 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	126.71
Dual form			126.9.b.a.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.3137i q^{2} -128.000 q^{4} +842.533i q^{5} -907.493 q^{7} -1448.15i q^{8} +O(q^{10})$	\(q+11.3137i q^{2} -128.000 q^{4} +842.533i q^{5} -907.493 q^{7} -1448.15i q^{8} -9532.17 q^{10} -815.531i q^{11} -16880.9 q^{13} -10267.1i q^{14} +16384.0 q^{16} -79990.2i q^{17} -167004. q^{19} -107844. i q^{20} +9226.69 q^{22} +60792.1i q^{23} -319237. q^{25} -190985. i q^{26} +116159. q^{28} +460282. i q^{29} +546092. q^{31} +185364. i q^{32} +904985. q^{34} -764592. i q^{35} -572413. q^{37} -1.88944e6i q^{38} +1.22012e6 q^{40} +327868. i q^{41} -1.35632e6 q^{43} +104388. i q^{44} -687784. q^{46} -8.31676e6i q^{47} +823543. q^{49} -3.61175e6i q^{50} +2.16075e6 q^{52} -1.31552e7i q^{53} +687112. q^{55} +1.31419e6i q^{56} -5.20749e6 q^{58} +1.00373e6i q^{59} +1.15004e7 q^{61} +6.17832e6i q^{62} -2.09715e6 q^{64} -1.42227e7i q^{65} +2.64758e7 q^{67} +1.02387e7i q^{68} +8.65038e6 q^{70} +8.25676e6i q^{71} +3.80173e7 q^{73} -6.47611e6i q^{74} +2.13766e7 q^{76} +740089. i q^{77} +7.95826e6 q^{79} +1.38041e7i q^{80} -3.70941e6 q^{82} +3.80727e7i q^{83} +6.73943e7 q^{85} -1.53451e7i q^{86} -1.18102e6 q^{88} -7.38679e7i q^{89} +1.53193e7 q^{91} -7.78139e6i q^{92} +9.40933e7 q^{94} -1.40707e8i q^{95} +1.47978e8 q^{97} +9.31733e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 1024 q^{4}+O(q^{10}) $ 8 * q - 1024 * q^4	$ 8 q - 1024 q^{4} - 11648 q^{10} - 79912 q^{13} + 131072 q^{16} + 253960 q^{19} - 469696 q^{22} + 315744 q^{25} + 1507352 q^{31} - 1961344 q^{34} - 234056 q^{37} + 1490944 q^{40} - 14779136 q^{43} + 4844480 q^{46} + 6588344 q^{49} + 10228736 q^{52} + 37751336 q^{55} - 4818944 q^{58} - 56194600 q^{61} - 16777216 q^{64} + 27271560 q^{67} - 1997632 q^{70} - 5112912 q^{73} - 32506880 q^{76} - 22918792 q^{79} - 42190848 q^{82} + 85335416 q^{85} + 60121088 q^{88} + 31885280 q^{91} + 196578816 q^{94} + 85889664 q^{97}+O(q^{100}) $ 8 * q - 1024 * q^4 - 11648 * q^10 - 79912 * q^13 + 131072 * q^16 + 253960 * q^19 - 469696 * q^22 + 315744 * q^25 + 1507352 * q^31 - 1961344 * q^34 - 234056 * q^37 + 1490944 * q^40 - 14779136 * q^43 + 4844480 * q^46 + 6588344 * q^49 + 10228736 * q^52 + 37751336 * q^55 - 4818944 * q^58 - 56194600 * q^61 - 16777216 * q^64 + 27271560 * q^67 - 1997632 * q^70 - 5112912 * q^73 - 32506880 * q^76 - 22918792 * q^79 - 42190848 * q^82 + 85335416 * q^85 + 60121088 * q^88 + 31885280 * q^91 + 196578816 * q^94 + 85889664 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$-1$	$1$

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 $

$2$	11.3137i	0.707107i
$2$	11.3137i	0.707107i
$3$	0	0
$3$	0	0
$4$	−128.000	−0.500000
$5$	842.533i	1.34805i	0.738707	+	0.674026i	$0.235437\pi$
$5$	842.533i	1.34805i	−0.738707	+	0.674026i	$0.764563\pi$
$6$	0	0
$7$	−907.493	−0.377964
$7$	−907.493	−0.377964
$8$	− 1448.15i	− 0.353553i
$9$	0	0
$10$	−9532.17	−0.953217
$11$	− 815.531i	− 0.0557019i	−0.999612	−	0.0278509i	$-0.991134\pi$
$11$	− 815.531i	− 0.0557019i	0.999612	−	0.0278509i	$-0.00886638\pi$
$12$	0	0
$13$	−16880.9	−0.591047	−0.295523	−	0.955336i	$-0.595494\pi$
$13$	−16880.9	−0.591047	−0.295523	+	0.955336i	$0.595494\pi$
$14$	− 10267.1i	− 0.267261i
$15$	0	0
$16$	16384.0	0.250000
$17$	− 79990.2i	− 0.957725i	−0.877890	−	0.478863i	$-0.841049\pi$
$17$	− 79990.2i	− 0.957725i	0.877890	−	0.478863i	$-0.158951\pi$
$18$	0	0
$19$	−167004.	−1.28148	−0.640742	−	0.767756i	$-0.721373\pi$
$19$	−167004.	−1.28148	−0.640742	+	0.767756i	$0.721373\pi$
$20$	− 107844.i	− 0.674026i
$21$	0	0
$22$	9226.69	0.0393872
$23$	60792.1i	0.217238i	0.994083	+	0.108619i	$0.0346429\pi$
$23$	60792.1i	0.217238i	−0.994083	+	0.108619i	$0.965357\pi$
$24$	0	0
$25$	−319237.	−0.817246
$26$	− 190985.i	− 0.417933i
$27$	0	0
$28$	116159.	0.188982
$29$	460282.i	0.650776i	0.945581	+	0.325388i	$0.105495\pi$
$29$	460282.i	0.650776i	−0.945581	+	0.325388i	$0.894505\pi$
$30$	0	0
$31$	546092.	0.591315	0.295657	−	0.955294i	$-0.404461\pi$
$31$	546092.	0.591315	0.295657	+	0.955294i	$0.404461\pi$
$32$	185364.i	0.176777i
$33$	0	0
$34$	904985.	0.677214
$35$	− 764592.i	− 0.509516i
$36$	0	0
$37$	−572413.	−0.305423	−0.152712	−	0.988271i	$-0.548801\pi$
$37$	−572413.	−0.305423	−0.152712	+	0.988271i	$0.548801\pi$
$38$	− 1.88944e6i	− 0.906146i
$39$	0	0
$40$	1.22012e6	0.476609
$41$	327868.i	0.116028i	0.998316	+	0.0580142i	$0.0184769\pi$
$41$	327868.i	0.116028i	−0.998316	+	0.0580142i	$0.981523\pi$
$42$	0	0
$43$	−1.35632e6	−0.396725	−0.198363	−	0.980129i	$-0.563562\pi$
$43$	−1.35632e6	−0.396725	−0.198363	+	0.980129i	$0.563562\pi$
$44$	104388.i	0.0278509i
$45$	0	0
$46$	−687784.	−0.153611
$47$	− 8.31676e6i	− 1.70436i	−0.523245	−	0.852182i	$-0.675279\pi$
$47$	− 8.31676e6i	− 1.70436i	0.523245	−	0.852182i	$-0.324721\pi$
$48$	0	0
$49$	823543.	0.142857
$50$	− 3.61175e6i	− 0.577880i
$51$	0	0
$52$	2.16075e6	0.295523
$53$	− 1.31552e7i	− 1.66723i	−0.552346	−	0.833615i	$-0.686267\pi$
$53$	− 1.31552e7i	− 1.66723i	0.552346	−	0.833615i	$-0.313733\pi$
$54$	0	0
$55$	687112.	0.0750891
$56$	1.31419e6i	0.133631i
$57$	0	0
$58$	−5.20749e6	−0.460168
$59$	1.00373e6i	0.0828339i	0.999142	+	0.0414170i	$0.0131872\pi$
$59$	1.00373e6i	0.0828339i	−0.999142	+	0.0414170i	$0.986813\pi$
$60$	0	0
$61$	1.15004e7	0.830603	0.415302	−	0.909684i	$-0.363676\pi$
$61$	1.15004e7	0.830603	0.415302	+	0.909684i	$0.363676\pi$
$62$	6.17832e6i	0.418123i
$63$	0	0
$64$	−2.09715e6	−0.125000
$65$	− 1.42227e7i	− 0.796762i
$66$	0	0
$67$	2.64758e7	1.31386	0.656932	−	0.753950i	$-0.271854\pi$
$67$	2.64758e7	1.31386	0.656932	+	0.753950i	$0.271854\pi$
$68$	1.02387e7i	0.478863i
$69$	0	0
$70$	8.65038e6	0.360282
$71$	8.25676e6i	0.324920i	0.986715	+	0.162460i	$0.0519428\pi$
$71$	8.25676e6i	0.324920i	−0.986715	+	0.162460i	$0.948057\pi$
$72$	0	0
$73$	3.80173e7	1.33872	0.669360	−	0.742938i	$-0.266568\pi$
$73$	3.80173e7	1.33872	0.669360	+	0.742938i	$0.266568\pi$
$74$	− 6.47611e6i	− 0.215967i
$75$	0	0
$76$	2.13766e7	0.640742
$77$	740089.i	0.0210533i
$78$	0	0
$79$	7.95826e6	0.204320	0.102160	−	0.994768i	$-0.467425\pi$
$79$	7.95826e6	0.204320	0.102160	+	0.994768i	$0.467425\pi$
$80$	1.38041e7i	0.337013i
$81$	0	0
$82$	−3.70941e6	−0.0820444
$83$	3.80727e7i	0.802234i	0.916027	+	0.401117i	$0.131378\pi$
$83$	3.80727e7i	0.802234i	−0.916027	+	0.401117i	$0.868622\pi$
$84$	0	0
$85$	6.73943e7	1.29106
$86$	− 1.53451e7i	− 0.280527i
$87$	0	0
$88$	−1.18102e6	−0.0196936
$89$	− 7.38679e7i	− 1.17732i	−0.808380	−	0.588662i	$-0.799655\pi$
$89$	− 7.38679e7i	− 1.17732i	0.808380	−	0.588662i	$-0.200345\pi$
$90$	0	0
$91$	1.53193e7	0.223395
$92$	− 7.78139e6i	− 0.108619i
$93$	0	0
$94$	9.40933e7	1.20517
$95$	− 1.40707e8i	− 1.72751i
$96$	0	0
$97$	1.47978e8	1.67152	0.835758	−	0.549097i	$-0.185028\pi$
$97$	1.47978e8	1.67152	0.835758	+	0.549097i	$0.185028\pi$
$98$	9.31733e6i	0.101015i
$99$	0	0
$100$	4.08623e7	0.408623
$101$	− 2.72434e7i	− 0.261804i	−0.991395	−	0.130902i	$-0.958213\pi$
$101$	− 2.72434e7i	− 0.261804i	0.991395	−	0.130902i	$-0.0417873\pi$
$102$	0	0
$103$	−1.53684e8	−1.36547	−0.682733	−	0.730668i	$-0.739209\pi$
$103$	−1.53684e8	−1.36547	−0.682733	+	0.730668i	$0.739209\pi$
$104$	2.44461e7i	0.208967i
$105$	0	0
$106$	1.48835e8	1.17891
$107$	− 1.19450e8i	− 0.911277i	−0.890165	−	0.455638i	$-0.849411\pi$
$107$	− 1.19450e8i	− 0.911277i	0.890165	−	0.455638i	$-0.150589\pi$
$108$	0	0
$109$	−2.29082e8	−1.62287	−0.811437	−	0.584439i	$-0.801315\pi$
$109$	−2.29082e8	−1.62287	−0.811437	+	0.584439i	$0.801315\pi$
$110$	7.77379e6i	0.0530960i
$111$	0	0
$112$	−1.48684e7	−0.0944911
$113$	4.76088e7i	0.291994i	0.989285	+	0.145997i	$0.0466389\pi$
$113$	4.76088e7i	0.291994i	−0.989285	+	0.145997i	$0.953361\pi$
$114$	0	0
$115$	−5.12194e7	−0.292848
$116$	− 5.89160e7i	− 0.325388i
$117$	0	0
$118$	−1.13559e7	−0.0585724
$119$	7.25905e7i	0.361986i
$120$	0	0
$121$	2.13694e8	0.996897
$122$	1.30112e8i	0.587325i
$123$	0	0
$124$	−6.98997e7	−0.295657
$125$	6.01471e7i	0.246362i
$126$	0	0
$127$	−3.76537e8	−1.44742	−0.723708	−	0.690106i	$-0.757564\pi$
$127$	−3.76537e8	−1.44742	−0.723708	+	0.690106i	$0.757564\pi$
$128$	− 2.37266e7i	− 0.0883883i
$129$	0	0
$130$	1.60911e8	0.563396
$131$	− 4.13311e7i	− 0.140343i	−0.997535	−	0.0701717i	$-0.977645\pi$
$131$	− 4.13311e7i	− 0.140343i	0.997535	−	0.0701717i	$-0.0223547\pi$
$132$	0	0
$133$	1.51555e8	0.484356
$134$	2.99540e8i	0.929042i
$135$	0	0
$136$	−1.15838e8	−0.338607
$137$	− 6.07770e8i	− 1.72527i	−0.505828	−	0.862634i	$-0.668813\pi$
$137$	− 6.07770e8i	− 1.72527i	0.505828	−	0.862634i	$-0.331187\pi$
$138$	0	0
$139$	−5.26563e7	−0.141056	−0.0705279	−	0.997510i	$-0.522468\pi$
$139$	−5.26563e7	−0.141056	−0.0705279	+	0.997510i	$0.522468\pi$
$140$	9.78678e7i	0.254758i
$141$	0	0
$142$	−9.34146e7	−0.229753
$143$	1.37669e7i	0.0329224i
$144$	0	0
$145$	−3.87802e8	−0.877280
$146$	4.30117e8i	0.946618i
$147$	0	0
$148$	7.32688e7	0.152712
$149$	− 5.87439e8i	− 1.19184i	−0.803044	−	0.595919i	$-0.796788\pi$
$149$	− 5.87439e8i	− 1.19184i	0.803044	−	0.595919i	$-0.203212\pi$
$150$	0	0
$151$	−2.94571e8	−0.566607	−0.283303	−	0.959030i	$-0.591430\pi$
$151$	−2.94571e8	−0.566607	−0.283303	+	0.959030i	$0.591430\pi$
$152$	2.41848e8i	0.453073i
$153$	0	0
$154$	−8.37315e6	−0.0148870
$155$	4.60100e8i	0.797123i
$156$	0	0
$157$	−3.16012e8	−0.520121	−0.260061	−	0.965592i	$-0.583743\pi$
$157$	−3.16012e8	−0.520121	−0.260061	+	0.965592i	$0.583743\pi$
$158$	9.00375e7i	0.144476i
$159$	0	0
$160$	−1.56175e8	−0.238304
$161$	− 5.51684e7i	− 0.0821083i
$162$	0	0
$163$	−1.11737e9	−1.58287	−0.791435	−	0.611254i	$-0.790666\pi$
$163$	−1.11737e9	−1.58287	−0.791435	+	0.611254i	$0.790666\pi$
$164$	− 4.19671e7i	− 0.0580142i
$165$	0	0
$166$	−4.30743e8	−0.567265
$167$	− 4.92018e8i	− 0.632580i	−0.948663	−	0.316290i	$-0.897563\pi$
$167$	− 4.92018e8i	− 0.632580i	0.948663	−	0.316290i	$-0.102437\pi$
$168$	0	0
$169$	−5.30767e8	−0.650664
$170$	7.62480e8i	0.912920i
$171$	0	0
$172$	1.73610e8	0.198363
$173$	− 9.24734e7i	− 0.103236i	−0.998667	−	0.0516182i	$-0.983562\pi$
$173$	− 9.24734e7i	− 0.103236i	0.998667	−	0.0516182i	$-0.0164379\pi$
$174$	0	0
$175$	2.89705e8	0.308890
$176$	− 1.33617e7i	− 0.0139255i
$177$	0	0
$178$	8.35720e8	0.832493
$179$	1.52124e9i	1.48179i	0.671623	+	0.740893i	$0.265597\pi$
$179$	1.52124e9i	1.48179i	−0.671623	+	0.740893i	$0.734403\pi$
$180$	0	0
$181$	−4.19259e8	−0.390632	−0.195316	−	0.980740i	$-0.562573\pi$
$181$	−4.19259e8	−0.390632	−0.195316	+	0.980740i	$0.562573\pi$
$182$	1.73318e8i	0.157964i
$183$	0	0
$184$	8.80364e7	0.0768053
$185$	− 4.82276e8i	− 0.411727i
$186$	0	0
$187$	−6.52345e7	−0.0533471
$188$	1.06454e9i	0.852182i
$189$	0	0
$190$	1.59191e9	1.22153
$191$	8.21081e8i	0.616954i	0.951232	+	0.308477i	$0.0998193\pi$
$191$	8.21081e8i	0.616954i	−0.951232	+	0.308477i	$0.900181\pi$
$192$	0	0
$193$	3.96819e8	0.285998	0.142999	−	0.989723i	$-0.454325\pi$
$193$	3.96819e8	0.285998	0.142999	+	0.989723i	$0.454325\pi$
$194$	1.67418e9i	1.18194i
$195$	0	0
$196$	−1.05414e8	−0.0714286
$197$	2.29401e9i	1.52311i	0.648101	+	0.761554i	$0.275563\pi$
$197$	2.29401e9i	1.52311i	−0.648101	+	0.761554i	$0.724437\pi$
$198$	0	0
$199$	−1.66581e9	−1.06221	−0.531107	−	0.847305i	$-0.678224\pi$
$199$	−1.66581e9	−1.06221	−0.531107	+	0.847305i	$0.678224\pi$
$200$	4.62304e8i	0.288940i
$201$	0	0
$202$	3.08224e8	0.185123
$203$	− 4.17702e8i	− 0.245970i
$204$	0	0
$205$	−2.76240e8	−0.156412
$206$	− 1.73874e9i	− 0.965530i
$207$	0	0
$208$	−2.76576e8	−0.147762
$209$	1.36197e8i	0.0713811i
$210$	0	0
$211$	−2.37491e9	−1.19817	−0.599084	−	0.800686i	$-0.704468\pi$
$211$	−2.37491e9	−1.19817	−0.599084	+	0.800686i	$0.704468\pi$
$212$	1.68387e9i	0.833615i
$213$	0	0
$214$	1.35142e9	0.644370
$215$	− 1.14275e9i	− 0.534807i
$216$	0	0
$217$	−4.95574e8	−0.223496
$218$	− 2.59177e9i	− 1.14755i
$219$	0	0
$220$	−8.79503e7	−0.0375445
$221$	1.35030e9i	0.566060i
$222$	0	0
$223$	5.60802e8	0.226772	0.113386	−	0.993551i	$-0.463830\pi$
$223$	5.60802e8	0.226772	0.113386	+	0.993551i	$0.463830\pi$
$224$	− 1.68216e8i	− 0.0668153i
$225$	0	0
$226$	−5.38632e8	−0.206471
$227$	− 5.16254e9i	− 1.94429i	−0.234388	−	0.972143i	$-0.575309\pi$
$227$	− 5.16254e9i	− 1.94429i	0.234388	−	0.972143i	$-0.424691\pi$
$228$	0	0
$229$	1.08714e9	0.395315	0.197657	−	0.980271i	$-0.436667\pi$
$229$	1.08714e9	0.395315	0.197657	+	0.980271i	$0.436667\pi$
$230$	− 5.79481e8i	− 0.207075i
$231$	0	0
$232$	6.66559e8	0.230084
$233$	− 4.50571e9i	− 1.52876i	−0.644766	−	0.764380i	$-0.723045\pi$
$233$	− 4.50571e9i	− 1.52876i	0.644766	−	0.764380i	$-0.276955\pi$
$234$	0	0
$235$	7.00714e9	2.29757
$236$	− 1.28477e8i	− 0.0414170i
$237$	0	0
$238$	−8.21268e8	−0.255963
$239$	− 2.24572e9i	− 0.688277i	−0.938919	−	0.344138i	$-0.888171\pi$
$239$	− 2.24572e9i	− 0.688277i	0.938919	−	0.344138i	$-0.111829\pi$
$240$	0	0
$241$	−4.54357e9	−1.34688	−0.673440	−	0.739242i	$-0.735184\pi$
$241$	−4.54357e9	−1.34688	−0.673440	+	0.739242i	$0.735184\pi$
$242$	2.41767e9i	0.704913i
$243$	0	0
$244$	−1.47205e9	−0.415302
$245$	6.93862e8i	0.192579i
$246$	0	0
$247$	2.81918e9	0.757417
$248$	− 7.90825e8i	− 0.209061i
$249$	0	0
$250$	−6.80486e8	−0.174205
$251$	− 6.37192e9i	− 1.60537i	−0.596403	−	0.802685i	$-0.703404\pi$
$251$	− 6.37192e9i	− 1.60537i	0.596403	−	0.802685i	$-0.296596\pi$
$252$	0	0
$253$	4.95779e7	0.0121006
$254$	− 4.26004e9i	− 1.02348i
$255$	0	0
$256$	2.68435e8	0.0625000
$257$	− 1.71920e9i	− 0.394087i	−0.980395	−	0.197044i	$-0.936866\pi$
$257$	− 1.71920e9i	− 0.394087i	0.980395	−	0.197044i	$-0.0631341\pi$
$258$	0	0
$259$	5.19460e8	0.115439
$260$	1.82051e9i	0.398381i
$261$	0	0
$262$	4.67608e8	0.0992378
$263$	4.63114e9i	0.967977i	0.875074	+	0.483988i	$0.160812\pi$
$263$	4.63114e9i	0.967977i	−0.875074	+	0.483988i	$0.839188\pi$
$264$	0	0
$265$	1.10837e10	2.24751
$266$	1.71465e9i	0.342491i
$267$	0	0
$268$	−3.38891e9	−0.656932
$269$	− 2.81318e8i	− 0.0537266i	−0.999639	−	0.0268633i	$-0.991448\pi$
$269$	− 2.81318e8i	− 0.0537266i	0.999639	−	0.0268633i	$-0.00855187\pi$
$270$	0	0
$271$	8.99836e9	1.66835	0.834173	−	0.551502i	$-0.185945\pi$
$271$	8.99836e9	1.66835	0.834173	+	0.551502i	$0.185945\pi$
$272$	− 1.31056e9i	− 0.239431i
$273$	0	0
$274$	6.87613e9	1.21995
$275$	2.60348e8i	0.0455221i
$276$	0	0
$277$	−3.83242e9	−0.650960	−0.325480	−	0.945549i	$-0.605526\pi$
$277$	−3.83242e9	−0.650960	−0.325480	+	0.945549i	$0.605526\pi$
$278$	− 5.95738e8i	− 0.0997415i
$279$	0	0
$280$	−1.10725e9	−0.180141
$281$	5.85775e9i	0.939520i	0.882794	+	0.469760i	$0.155659\pi$
$281$	5.85775e9i	0.939520i	−0.882794	+	0.469760i	$0.844341\pi$
$282$	0	0
$283$	−3.32790e9	−0.518829	−0.259414	−	0.965766i	$-0.583530\pi$
$283$	−3.32790e9	−0.518829	−0.259414	+	0.965766i	$0.583530\pi$
$284$	− 1.05687e9i	− 0.162460i
$285$	0	0
$286$	−1.55755e8	−0.0232797
$287$	− 2.97538e8i	− 0.0438546i
$288$	0	0
$289$	5.77331e8	0.0827624
$290$	− 4.38748e9i	− 0.620331i
$291$	0	0
$292$	−4.86621e9	−0.669360
$293$	− 3.46418e9i	− 0.470035i	−0.971991	−	0.235018i	$-0.924485\pi$
$293$	− 3.46418e9i	− 0.470035i	0.971991	−	0.235018i	$-0.0755148\pi$
$294$	0	0
$295$	−8.45674e8	−0.111664
$296$	8.28942e8i	0.107983i
$297$	0	0
$298$	6.64611e9	0.842757
$299$	− 1.02622e9i	− 0.128398i
$300$	0	0
$301$	1.23085e9	0.149948
$302$	− 3.33269e9i	− 0.400651i
$303$	0	0
$304$	−2.73620e9	−0.320371
$305$	9.68947e9i	1.11970i
$306$	0	0
$307$	8.50960e9	0.957978	0.478989	−	0.877821i	$-0.341003\pi$
$307$	8.50960e9	0.957978	0.478989	+	0.877821i	$0.341003\pi$
$308$	− 9.47314e7i	− 0.0105267i
$309$	0	0
$310$	−5.20544e9	−0.563651
$311$	− 1.03013e10i	− 1.10116i	−0.834783	−	0.550580i	$-0.814407\pi$
$311$	− 1.03013e10i	− 1.10116i	0.834783	−	0.550580i	$-0.185593\pi$
$312$	0	0
$313$	−7.31998e9	−0.762663	−0.381331	−	0.924438i	$-0.624534\pi$
$313$	−7.31998e9	−0.762663	−0.381331	+	0.924438i	$0.624534\pi$
$314$	− 3.57526e9i	− 0.367781i
$315$	0	0
$316$	−1.01866e9	−0.102160
$317$	1.35306e10i	1.33993i	0.742394	+	0.669964i	$0.233690\pi$
$317$	1.35306e10i	1.33993i	−0.742394	+	0.669964i	$0.766310\pi$
$318$	0	0
$319$	3.75374e8	0.0362495
$320$	− 1.76692e9i	− 0.168507i
$321$	0	0
$322$	6.24159e8	0.0580593
$323$	1.33587e10i	1.22731i
$324$	0	0
$325$	5.38900e9	0.483030
$326$	− 1.26416e10i	− 1.11926i
$327$	0	0
$328$	4.74804e8	0.0410222
$329$	7.54739e9i	0.644189i
$330$	0	0
$331$	−1.64322e10	−1.36894	−0.684469	−	0.729042i	$-0.739966\pi$
$331$	−1.64322e10	−1.36894	−0.684469	+	0.729042i	$0.739966\pi$
$332$	− 4.87330e9i	− 0.401117i
$333$	0	0
$334$	5.56655e9	0.447301
$335$	2.23068e10i	1.77116i
$336$	0	0
$337$	1.17625e10	0.911967	0.455983	−	0.889988i	$-0.349288\pi$
$337$	1.17625e10	0.911967	0.455983	+	0.889988i	$0.349288\pi$
$338$	− 6.00494e9i	− 0.460089i
$339$	0	0
$340$	−8.62648e9	−0.645532
$341$	− 4.45355e8i	− 0.0329374i
$342$	0	0
$343$	−7.47359e8	−0.0539949
$344$	1.96417e9i	0.140264i
$345$	0	0
$346$	1.04622e9	0.0729991
$347$	− 1.96300e10i	− 1.35395i	−0.736007	−	0.676974i	$-0.763291\pi$
$347$	− 1.96300e10i	− 1.35395i	0.736007	−	0.676974i	$-0.236709\pi$
$348$	0	0
$349$	1.03674e10	0.698826	0.349413	−	0.936969i	$-0.386381\pi$
$349$	1.03674e10	0.698826	0.349413	+	0.936969i	$0.386381\pi$
$350$	3.27764e9i	0.218418i
$351$	0	0
$352$	1.51170e8	0.00984680
$353$	9.44252e9i	0.608120i	0.952653	+	0.304060i	$0.0983423\pi$
$353$	9.44252e9i	0.608120i	−0.952653	+	0.304060i	$0.901658\pi$
$354$	0	0
$355$	−6.95659e9	−0.438009
$356$	9.45509e9i	0.588662i
$357$	0	0
$358$	−1.72109e10	−1.04778
$359$	5.84998e9i	0.352190i	0.984373	+	0.176095i	$0.0563466\pi$
$359$	5.84998e9i	0.352190i	−0.984373	+	0.176095i	$0.943653\pi$
$360$	0	0
$361$	1.09069e10	0.642202
$362$	− 4.74337e9i	− 0.276219i
$363$	0	0
$364$	−1.96087e9	−0.111697
$365$	3.20308e10i	1.80466i
$366$	0	0
$367$	−3.75701e9	−0.207099	−0.103550	−	0.994624i	$-0.533020\pi$
$367$	−3.75701e9	−0.207099	−0.103550	+	0.994624i	$0.533020\pi$
$368$	9.96018e8i	0.0543095i
$369$	0	0
$370$	5.45634e9	0.291135
$371$	1.19383e10i	0.630154i
$372$	0	0
$373$	−2.58497e10	−1.33543	−0.667713	−	0.744419i	$-0.732726\pi$
$373$	−2.58497e10	−1.33543	−0.667713	+	0.744419i	$0.732726\pi$
$374$	− 7.38044e8i	− 0.0377221i
$375$	0	0
$376$	−1.20439e10	−0.602584
$377$	− 7.76996e9i	− 0.384639i
$378$	0	0
$379$	−1.15244e10	−0.558550	−0.279275	−	0.960211i	$-0.590094\pi$
$379$	−1.15244e10	−0.558550	−0.279275	+	0.960211i	$0.590094\pi$
$380$	1.80105e10i	0.863754i
$381$	0	0
$382$	−9.28947e9	−0.436252
$383$	− 5.84574e9i	− 0.271672i	−0.990731	−	0.135836i	$-0.956628\pi$
$383$	− 5.84574e9i	− 0.271672i	0.990731	−	0.135836i	$-0.0433720\pi$
$384$	0	0
$385$	−6.23549e8	−0.0283810
$386$	4.48949e9i	0.202231i
$387$	0	0
$388$	−1.89412e10	−0.835758
$389$	− 1.05091e10i	− 0.458951i	−0.973314	−	0.229476i	$-0.926299\pi$
$389$	− 1.05091e10i	− 0.458951i	0.973314	−	0.229476i	$-0.0737011\pi$
$390$	0	0
$391$	4.86277e9	0.208054
$392$	− 1.19262e9i	− 0.0505076i
$393$	0	0
$394$	−2.59538e10	−1.07700
$395$	6.70510e9i	0.275434i
$396$	0	0
$397$	−3.15984e10	−1.27205	−0.636024	−	0.771669i	$-0.719422\pi$
$397$	−3.15984e10	−1.27205	−0.636024	+	0.771669i	$0.719422\pi$
$398$	− 1.88464e10i	− 0.751099i
$399$	0	0
$400$	−5.23037e9	−0.204311
$401$	− 1.90338e10i	− 0.736119i	−0.929802	−	0.368060i	$-0.880022\pi$
$401$	− 1.90338e10i	− 0.736119i	0.929802	−	0.368060i	$-0.119978\pi$
$402$	0	0
$403$	−9.21851e9	−0.349495
$404$	3.48716e9i	0.130902i
$405$	0	0
$406$	4.72576e9	0.173927
$407$	4.66821e8i	0.0170127i
$408$	0	0
$409$	2.99332e10	1.06970	0.534848	−	0.844948i	$-0.320369\pi$
$409$	2.99332e10	1.06970	0.534848	+	0.844948i	$0.320369\pi$
$410$	− 3.12530e9i	− 0.110600i
$411$	0	0
$412$	1.96716e10	0.682733
$413$	− 9.10876e8i	− 0.0313083i
$414$	0	0
$415$	−3.20775e10	−1.08145
$416$	− 3.12910e9i	− 0.104483i
$417$	0	0
$418$	−1.54090e9	−0.0504741
$419$	− 2.80239e10i	− 0.909226i	−0.890689	−	0.454613i	$-0.849778\pi$
$419$	− 2.80239e10i	− 0.909226i	0.890689	−	0.454613i	$-0.150222\pi$
$420$	0	0
$421$	−1.79571e10	−0.571622	−0.285811	−	0.958286i	$-0.592263\pi$
$421$	−1.79571e10	−0.571622	−0.285811	+	0.958286i	$0.592263\pi$
$422$	− 2.68691e10i	− 0.847233i
$423$	0	0
$424$	−1.90508e10	−0.589455
$425$	2.55358e10i	0.782697i
$426$	0	0
$427$	−1.04365e10	−0.313939
$428$	1.52896e10i	0.455638i
$429$	0	0
$430$	1.29287e10	0.378165
$431$	− 9.49773e9i	− 0.275239i	−0.990485	−	0.137620i	$-0.956055\pi$
$431$	− 9.49773e9i	− 0.275239i	0.990485	−	0.137620i	$-0.0439452\pi$
$432$	0	0
$433$	4.89665e10	1.39299	0.696495	−	0.717562i	$-0.254742\pi$
$433$	4.89665e10	1.39299	0.696495	+	0.717562i	$0.254742\pi$
$434$	− 5.60678e9i	− 0.158035i
$435$	0	0
$436$	2.93225e10	0.811437
$437$	− 1.01525e10i	− 0.278387i
$438$	0	0
$439$	−5.58989e10	−1.50503	−0.752515	−	0.658575i	$-0.771160\pi$
$439$	−5.58989e10	−1.50503	−0.752515	+	0.658575i	$0.771160\pi$
$440$	− 9.95045e8i	− 0.0265480i
$441$	0	0
$442$	−1.52770e10	−0.400265
$443$	6.61966e9i	0.171878i	0.996300	+	0.0859391i	$0.0273891\pi$
$443$	6.61966e9i	0.171878i	−0.996300	+	0.0859391i	$0.972611\pi$
$444$	0	0
$445$	6.22361e10	1.58709
$446$	6.34475e9i	0.160352i
$447$	0	0
$448$	1.90315e9	0.0472456
$449$	− 3.89385e10i	− 0.958062i	−0.877798	−	0.479031i	$-0.840988\pi$
$449$	− 3.89385e10i	− 0.958062i	0.877798	−	0.479031i	$-0.159012\pi$
$450$	0	0
$451$	2.67387e8	0.00646300
$452$	− 6.09392e9i	− 0.145997i
$453$	0	0
$454$	5.84075e10	1.37482
$455$	1.29070e10i	0.301148i
$456$	0	0
$457$	4.84489e10	1.11076	0.555379	−	0.831598i	$-0.312573\pi$
$457$	4.84489e10	1.11076	0.555379	+	0.831598i	$0.312573\pi$
$458$	1.22996e10i	0.279530i
$459$	0	0
$460$	6.55608e9	0.146424
$461$	− 1.31212e10i	− 0.290517i	−0.989394	−	0.145258i	$-0.953599\pi$
$461$	− 1.31212e10i	− 0.290517i	0.989394	−	0.145258i	$-0.0464013\pi$
$462$	0	0
$463$	−2.80155e10	−0.609641	−0.304820	−	0.952410i	$-0.598596\pi$
$463$	−2.80155e10	−0.609641	−0.304820	+	0.952410i	$0.598596\pi$
$464$	7.54125e9i	0.162694i
$465$	0	0
$466$	5.09762e10	1.08100
$467$	5.25716e10i	1.10531i	0.833410	+	0.552655i	$0.186385\pi$
$467$	5.25716e10i	1.10531i	−0.833410	+	0.552655i	$0.813615\pi$
$468$	0	0
$469$	−2.40266e10	−0.496594
$470$	7.92767e10i	1.62463i
$471$	0	0
$472$	1.45355e9	0.0292862
$473$	1.10613e9i	0.0220984i
$474$	0	0
$475$	5.33139e10	1.04729
$476$	− 9.29158e9i	− 0.180993i
$477$	0	0
$478$	2.54074e10	0.486685
$479$	− 3.11906e10i	− 0.592492i	−0.955112	−	0.296246i	$-0.904265\pi$
$479$	− 3.11906e10i	− 0.592492i	0.955112	−	0.296246i	$-0.0957348\pi$
$480$	0	0
$481$	9.66283e9	0.180519
$482$	− 5.14046e10i	− 0.952388i
$483$	0	0
$484$	−2.73528e10	−0.498449
$485$	1.24676e11i	2.25329i
$486$	0	0
$487$	5.43276e10	0.965839	0.482919	−	0.875665i	$-0.339576\pi$
$487$	5.43276e10	0.965839	0.482919	+	0.875665i	$0.339576\pi$
$488$	− 1.66544e10i	− 0.293663i
$489$	0	0
$490$	−7.85015e9	−0.136174
$491$	− 6.43313e10i	− 1.10687i	−0.832892	−	0.553435i	$-0.813317\pi$
$491$	− 6.43313e10i	− 1.10687i	0.832892	−	0.553435i	$-0.186683\pi$
$492$	0	0
$493$	3.68180e10	0.623265
$494$	3.18954e10i	0.535575i
$495$	0	0
$496$	8.94716e9	0.147829
$497$	− 7.49295e9i	− 0.122808i
$498$	0	0
$499$	−1.38682e10	−0.223675	−0.111838	−	0.993726i	$-0.535674\pi$
$499$	−1.38682e10	−0.223675	−0.111838	+	0.993726i	$0.535674\pi$
$500$	− 7.69883e9i	− 0.123181i
$501$	0	0
$502$	7.20900e10	1.13517
$503$	− 1.04703e11i	− 1.63564i	−0.575472	−	0.817821i	$-0.695182\pi$
$503$	− 1.04703e11i	− 1.63564i	0.575472	−	0.817821i	$-0.304818\pi$
$504$	0	0
$505$	2.29535e10	0.352925
$506$	5.60910e8i	0.00855640i
$507$	0	0
$508$	4.81968e10	0.723708
$509$	2.19286e10i	0.326693i	0.986569	+	0.163346i	$0.0522288\pi$
$509$	2.19286e10i	0.326693i	−0.986569	+	0.163346i	$0.947771\pi$
$510$	0	0
$511$	−3.45004e10	−0.505989
$512$	3.03700e9i	0.0441942i
$513$	0	0
$514$	1.94505e10	0.278662
$515$	− 1.29484e11i	− 1.84072i
$516$	0	0
$517$	−6.78258e9	−0.0949363
$518$	5.87702e9i	0.0816278i
$519$	0	0
$520$	−2.05967e10	−0.281698
$521$	− 9.63978e10i	− 1.30833i	−0.756354	−	0.654163i	$-0.773021\pi$
$521$	− 9.63978e10i	− 1.30833i	0.756354	−	0.654163i	$-0.226979\pi$
$522$	0	0
$523$	−4.67744e10	−0.625175	−0.312588	−	0.949889i	$-0.601196\pi$
$523$	−4.67744e10	−0.625175	−0.312588	+	0.949889i	$0.601196\pi$
$524$	5.29039e9i	0.0701717i
$525$	0	0
$526$	−5.23954e10	−0.684463
$527$	− 4.36820e10i	− 0.566317i
$528$	0	0
$529$	7.46153e10	0.952808
$530$	1.25398e11i	1.58923i
$531$	0	0
$532$	−1.93991e10	−0.242178
$533$	− 5.53471e9i	− 0.0685782i
$534$	0	0
$535$	1.00640e11	1.22845
$536$	− 3.83411e10i	− 0.464521i
$537$	0	0
$538$	3.18275e9	0.0379904
$539$	− 6.71625e8i	− 0.00795741i
$540$	0	0
$541$	−1.49340e11	−1.74336	−0.871678	−	0.490080i	$-0.836968\pi$
$541$	−1.49340e11	−1.74336	−0.871678	+	0.490080i	$0.836968\pi$
$542$	1.01805e11i	1.17970i
$543$	0	0
$544$	1.48273e10	0.169303
$545$	− 1.93009e11i	− 2.18772i
$546$	0	0
$547$	−1.28070e11	−1.43053	−0.715267	−	0.698851i	$-0.753695\pi$
$547$	−1.28070e11	−1.43053	−0.715267	+	0.698851i	$0.753695\pi$
$548$	7.77945e10i	0.862634i
$549$	0	0
$550$	−2.94550e9	−0.0321890
$551$	− 7.68690e10i	− 0.833959i
$552$	0	0
$553$	−7.22207e9	−0.0772255
$554$	− 4.33589e10i	− 0.460298i
$555$	0	0
$556$	6.74000e9	0.0705279
$557$	1.66620e11i	1.73104i	0.500877	+	0.865519i	$0.333011\pi$
$557$	1.66620e11i	1.73104i	−0.500877	+	0.865519i	$0.666989\pi$
$558$	0	0
$559$	2.28960e10	0.234483
$560$	− 1.25271e10i	− 0.127379i
$561$	0	0
$562$	−6.62729e10	−0.664341
$563$	− 1.72230e10i	− 0.171426i	−0.996320	−	0.0857128i	$-0.972683\pi$
$563$	− 1.72230e10i	− 0.171426i	0.996320	−	0.0857128i	$-0.0273167\pi$
$564$	0	0
$565$	−4.01120e10	−0.393623
$566$	− 3.76508e10i	− 0.366867i
$567$	0	0
$568$	1.19571e10	0.114877
$569$	1.65732e11i	1.58109i	0.612403	+	0.790546i	$0.290203\pi$
$569$	1.65732e11i	1.58109i	−0.612403	+	0.790546i	$0.709797\pi$
$570$	0	0
$571$	1.10177e11	1.03645	0.518225	−	0.855244i	$-0.326593\pi$
$571$	1.10177e11	1.03645	0.518225	+	0.855244i	$0.326593\pi$
$572$	− 1.76216e9i	− 0.0164612i
$573$	0	0
$574$	3.36626e9	0.0310099
$575$	− 1.94071e10i	− 0.177537i
$576$	0	0
$577$	1.42687e11	1.28730	0.643651	−	0.765319i	$-0.277419\pi$
$577$	1.42687e11	1.28730	0.643651	+	0.765319i	$0.277419\pi$
$578$	6.53175e9i	0.0585219i
$579$	0	0
$580$	4.96387e10	0.438640
$581$	− 3.45507e10i	− 0.303216i
$582$	0	0
$583$	−1.07285e10	−0.0928679
$584$	− 5.50549e10i	− 0.473309i
$585$	0	0
$586$	3.91927e10	0.332365
$587$	− 1.98987e11i	− 1.67599i	−0.545674	−	0.837997i	$-0.683726\pi$
$587$	− 1.98987e11i	− 1.67599i	0.545674	−	0.837997i	$-0.316274\pi$
$588$	0	0
$589$	−9.11997e10	−0.757761
$590$	− 9.56771e9i	− 0.0789587i
$591$	0	0
$592$	−9.37841e9	−0.0763559
$593$	1.87691e11i	1.51784i	0.651186	+	0.758918i	$0.274272\pi$
$593$	1.87691e11i	1.51784i	−0.651186	+	0.758918i	$0.725728\pi$
$594$	0	0
$595$	−6.11599e10	−0.487976
$596$	7.51922e10i	0.595919i
$597$	0	0
$598$	1.16104e10	0.0907910
$599$	− 2.01289e11i	− 1.56356i	−0.623556	−	0.781779i	$-0.714313\pi$
$599$	− 2.01289e11i	− 1.56356i	0.623556	−	0.781779i	$-0.285687\pi$
$600$	0	0
$601$	2.01860e11	1.54722	0.773611	−	0.633661i	$-0.218449\pi$
$601$	2.01860e11	1.54722	0.773611	+	0.633661i	$0.218449\pi$
$602$	1.39255e10i	0.106029i
$603$	0	0
$604$	3.77050e10	0.283303
$605$	1.80044e11i	1.34387i
$606$	0	0
$607$	−1.38901e11	−1.02318	−0.511589	−	0.859230i	$-0.670943\pi$
$607$	−1.38901e11	−1.02318	−0.511589	+	0.859230i	$0.670943\pi$
$608$	− 3.09566e10i	− 0.226537i
$609$	0	0
$610$	−1.09624e11	−0.791745
$611$	1.40394e11i	1.00736i
$612$	0	0
$613$	−2.27496e11	−1.61113	−0.805566	−	0.592507i	$-0.798138\pi$
$613$	−2.27496e11	−1.61113	−0.805566	+	0.592507i	$0.798138\pi$
$614$	9.62751e10i	0.677393i
$615$	0	0
$616$	1.07176e9	0.00744348
$617$	7.95040e10i	0.548590i	0.961646	+	0.274295i	$0.0884446\pi$
$617$	7.95040e10i	0.548590i	−0.961646	+	0.274295i	$0.911555\pi$
$618$	0	0
$619$	−2.18740e11	−1.48993	−0.744964	−	0.667105i	$-0.767533\pi$
$619$	−2.18740e11	−1.48993	−0.744964	+	0.667105i	$0.767533\pi$
$620$	− 5.88928e10i	− 0.398562i
$621$	0	0
$622$	1.16546e11	0.778637
$623$	6.70346e10i	0.444986i
$624$	0	0
$625$	−1.75378e11	−1.14936
$626$	− 8.28161e10i	− 0.539284i
$627$	0	0
$628$	4.04495e10	0.260061
$629$	4.57874e10i	0.292512i
$630$	0	0
$631$	−1.97644e11	−1.24671	−0.623357	−	0.781938i	$-0.714231\pi$
$631$	−1.97644e11	−1.24671	−0.623357	+	0.781938i	$0.714231\pi$
$632$	− 1.15248e10i	− 0.0722379i
$633$	0	0
$634$	−1.53082e11	−0.947472
$635$	− 3.17245e11i	− 1.95119i
$636$	0	0
$637$	−1.39021e10	−0.0844352
$638$	4.24687e9i	0.0256322i
$639$	0	0
$640$	1.99904e10	0.119152
$641$	− 5.16919e10i	− 0.306190i	−0.988212	−	0.153095i	$-0.951076\pi$
$641$	− 5.16919e10i	− 0.306190i	0.988212	−	0.153095i	$-0.0489240\pi$
$642$	0	0
$643$	−3.11803e10	−0.182405	−0.0912025	−	0.995832i	$-0.529071\pi$
$643$	−3.11803e10	−0.182405	−0.0912025	+	0.995832i	$0.529071\pi$
$644$	7.06156e9i	0.0410541i
$645$	0	0
$646$	−1.51136e11	−0.867839
$647$	3.03117e11i	1.72979i	0.501951	+	0.864896i	$0.332616\pi$
$647$	3.03117e11i	1.72979i	−0.501951	+	0.864896i	$0.667384\pi$
$648$	0	0
$649$	8.18572e8	0.00461401
$650$	6.09695e10i	0.341554i
$651$	0	0
$652$	1.43023e11	0.791435
$653$	1.74328e11i	0.958772i	0.877604	+	0.479386i	$0.159141\pi$
$653$	1.74328e11i	0.958772i	−0.877604	+	0.479386i	$0.840859\pi$
$654$	0	0
$655$	3.48228e10	0.189190
$656$	5.37179e9i	0.0290071i
$657$	0	0
$658$	−8.53890e10	−0.455511
$659$	8.21058e10i	0.435343i	0.976022	+	0.217672i	$0.0698462\pi$
$659$	8.21058e10i	0.435343i	−0.976022	+	0.217672i	$0.930154\pi$
$660$	0	0
$661$	1.34452e11	0.704307	0.352153	−	0.935942i	$-0.385450\pi$
$661$	1.34452e11	0.704307	0.352153	+	0.935942i	$0.385450\pi$
$662$	− 1.85909e11i	− 0.967985i
$663$	0	0
$664$	5.51351e10	0.283633
$665$	1.27690e11i	0.652937i
$666$	0	0
$667$	−2.79815e10	−0.141373
$668$	6.29783e10i	0.316290i
$669$	0	0
$670$	−2.52372e11	−1.25240
$671$	− 9.37894e9i	− 0.0462662i
$672$	0	0
$673$	−3.25635e11	−1.58734	−0.793671	−	0.608347i	$-0.791833\pi$
$673$	−3.25635e11	−1.58734	−0.793671	+	0.608347i	$0.791833\pi$
$674$	1.33077e11i	0.644858i
$675$	0	0
$676$	6.79381e10	0.325332
$677$	1.26447e11i	0.601941i	0.953633	+	0.300971i	$0.0973106\pi$
$677$	1.26447e11i	0.601941i	−0.953633	+	0.300971i	$0.902689\pi$
$678$	0	0
$679$	−1.34289e11	−0.631774
$680$	− 9.75974e10i	− 0.456460i
$681$	0	0
$682$	5.03861e9	0.0232902
$683$	9.75337e9i	0.0448200i	0.999749	+	0.0224100i	$0.00713392\pi$
$683$	9.75337e9i	0.0448200i	−0.999749	+	0.0224100i	$0.992866\pi$
$684$	0	0
$685$	5.12066e11	2.32575
$686$	− 8.45540e9i	− 0.0381802i
$687$	0	0
$688$	−2.22220e10	−0.0991813
$689$	2.22072e11i	0.985411i
$690$	0	0
$691$	1.63998e11	0.719328	0.359664	−	0.933082i	$-0.382891\pi$
$691$	1.63998e11	0.719328	0.359664	+	0.933082i	$0.382891\pi$
$692$	1.18366e10i	0.0516182i
$693$	0	0
$694$	2.22088e11	0.957386
$695$	− 4.43646e10i	− 0.190151i
$696$	0	0
$697$	2.62262e10	0.111123
$698$	1.17294e11i	0.494145i
$699$	0	0
$700$	−3.70822e10	−0.154445
$701$	2.82244e11i	1.16883i	0.811454	+	0.584416i	$0.198676\pi$
$701$	2.82244e11i	1.16883i	−0.811454	+	0.584416i	$0.801324\pi$
$702$	0	0
$703$	9.55954e10	0.391395
$704$	1.71029e9i	0.00696274i
$705$	0	0
$706$	−1.06830e11	−0.430006
$707$	2.47232e10i	0.0989525i
$708$	0	0
$709$	3.19928e11	1.26610	0.633048	−	0.774112i	$-0.281804\pi$
$709$	3.19928e11	1.26610	0.633048	+	0.774112i	$0.281804\pi$
$710$	− 7.87049e10i	− 0.309719i
$711$	0	0
$712$	−1.06972e11	−0.416247
$713$	3.31981e10i	0.128456i
$714$	0	0
$715$	−1.15991e10	−0.0443812
$716$	− 1.94719e11i	− 0.740893i
$717$	0	0
$718$	−6.61850e10	−0.249036
$719$	− 8.05383e10i	− 0.301361i	−0.988583	−	0.150680i	$-0.951854\pi$
$719$	− 8.05383e10i	− 0.301361i	0.988583	−	0.150680i	$-0.0481465\pi$
$720$	0	0
$721$	1.39467e11	0.516098
$722$	1.23397e11i	0.454106i
$723$	0	0
$724$	5.36652e10	0.195316
$725$	− 1.46939e11i	− 0.531844i
$726$	0	0
$727$	3.79822e11	1.35970	0.679848	−	0.733353i	$-0.262046\pi$
$727$	3.79822e11	1.35970	0.679848	+	0.733353i	$0.262046\pi$
$728$	− 2.21847e10i	− 0.0789819i
$729$	0	0
$730$	−3.62387e11	−1.27609
$731$	1.08493e11i	0.379954i
$732$	0	0
$733$	−2.72904e11	−0.945352	−0.472676	−	0.881236i	$-0.656712\pi$
$733$	−2.72904e11	−0.945352	−0.472676	+	0.881236i	$0.656712\pi$
$734$	− 4.25057e10i	− 0.146441i
$735$	0	0
$736$	−1.12687e10	−0.0384026
$737$	− 2.15919e10i	− 0.0731847i
$738$	0	0
$739$	1.36297e11	0.456992	0.228496	−	0.973545i	$-0.426619\pi$
$739$	1.36297e11	0.456992	0.228496	+	0.973545i	$0.426619\pi$
$740$	6.17314e10i	0.205863i
$741$	0	0
$742$	−1.35066e11	−0.445586
$743$	− 1.08368e11i	− 0.355586i	−0.984068	−	0.177793i	$-0.943104\pi$
$743$	− 1.08368e11i	− 0.355586i	0.984068	−	0.177793i	$-0.0568957\pi$
$744$	0	0
$745$	4.94936e11	1.60666
$746$	− 2.92456e11i	− 0.944288i
$747$	0	0
$748$	8.35002e9	0.0266736
$749$	1.08400e11i	0.344430i
$750$	0	0
$751$	−3.13247e11	−0.984753	−0.492376	−	0.870382i	$-0.663872\pi$
$751$	−3.13247e11	−0.984753	−0.492376	+	0.870382i	$0.663872\pi$
$752$	− 1.36262e11i	− 0.426091i
$753$	0	0
$754$	8.79071e10	0.271981
$755$	− 2.48185e11i	− 0.763816i
$756$	0	0
$757$	3.18911e11	0.971148	0.485574	−	0.874196i	$-0.338611\pi$
$757$	3.18911e11	0.971148	0.485574	+	0.874196i	$0.338611\pi$
$758$	− 1.30384e11i	− 0.394955i
$759$	0	0
$760$	−2.03765e11	−0.610766
$761$	− 3.10040e11i	− 0.924440i	−0.886765	−	0.462220i	$-0.847053\pi$
$761$	− 3.10040e11i	− 0.924440i	0.886765	−	0.462220i	$-0.152947\pi$
$762$	0	0
$763$	2.07890e11	0.613389
$764$	− 1.05098e11i	− 0.308477i
$765$	0	0
$766$	6.61370e10	0.192101
$767$	− 1.69438e10i	− 0.0489587i
$768$	0	0
$769$	4.25768e11	1.21750	0.608748	−	0.793364i	$-0.291672\pi$
$769$	4.25768e11	1.21750	0.608748	+	0.793364i	$0.291672\pi$
$770$	− 7.05465e9i	− 0.0200684i
$771$	0	0
$772$	−5.07928e10	−0.142999
$773$	− 1.35172e11i	− 0.378590i	−0.981920	−	0.189295i	$-0.939380\pi$
$773$	− 1.35172e11i	− 0.378590i	0.981920	−	0.189295i	$-0.0606203\pi$
$774$	0	0
$775$	−1.74332e11	−0.483249
$776$	− 2.14295e11i	− 0.590970i
$777$	0	0
$778$	1.18897e11	0.324528
$779$	− 5.47554e10i	− 0.148688i
$780$	0	0
$781$	6.73365e9	0.0180987
$782$	5.50160e10i	0.147117i
$783$	0	0
$784$	1.34929e10	0.0357143
$785$	− 2.66250e11i	− 0.701151i
$786$	0	0
$787$	−1.87134e11	−0.487814	−0.243907	−	0.969799i	$-0.578429\pi$
$787$	−1.87134e11	−0.487814	−0.243907	+	0.969799i	$0.578429\pi$
$788$	− 2.93634e11i	− 0.761554i
$789$	0	0
$790$	−7.58595e10	−0.194761
$791$	− 4.32046e10i	− 0.110363i
$792$	0	0
$793$	−1.94137e11	−0.490925
$794$	− 3.57495e11i	− 0.899473i
$795$	0	0
$796$	2.13223e11	0.531107
$797$	− 3.88844e11i	− 0.963701i	−0.876253	−	0.481850i	$-0.839965\pi$
$797$	− 3.88844e11i	− 0.963701i	0.876253	−	0.481850i	$-0.160035\pi$
$798$	0	0
$799$	−6.65259e11	−1.63231
$800$	− 5.91749e10i	− 0.144470i
$801$	0	0
$802$	2.15343e11	0.520515
$803$	− 3.10043e10i	− 0.0745692i
$804$	0	0
$805$	4.64812e10	0.110686
$806$	− 1.04296e11i	− 0.247130i
$807$	0	0
$808$	−3.94527e10	−0.0925616
$809$	5.83799e11i	1.36292i	0.731857	+	0.681458i	$0.238654\pi$
$809$	5.83799e11i	1.36292i	−0.731857	+	0.681458i	$0.761346\pi$
$810$	0	0
$811$	−6.70239e11	−1.54934	−0.774669	−	0.632367i	$-0.782084\pi$
$811$	−6.70239e11	−1.54934	−0.774669	+	0.632367i	$0.782084\pi$
$812$	5.34659e10i	0.122985i
$813$	0	0
$814$	−5.28147e9	−0.0120298
$815$	− 9.41418e11i	− 2.13379i
$816$	0	0
$817$	2.26512e11	0.508397
$818$	3.38656e11i	0.756390i
$819$	0	0
$820$	3.53587e10	0.0782061
$821$	6.49797e11i	1.43023i	0.699008	+	0.715114i	$0.253625\pi$
$821$	6.49797e11i	1.43023i	−0.699008	+	0.715114i	$0.746375\pi$
$822$	0	0
$823$	9.03241e11	1.96881	0.984407	−	0.175908i	$-0.0562862\pi$
$823$	9.03241e11	1.96881	0.984407	+	0.175908i	$0.0562862\pi$
$824$	2.22559e11i	0.482765i
$825$	0	0
$826$	1.03054e10	0.0221383
$827$	8.59040e11i	1.83650i	0.395999	+	0.918251i	$0.370398\pi$
$827$	8.59040e11i	1.83650i	−0.395999	+	0.918251i	$0.629602\pi$
$828$	0	0
$829$	−1.28865e11	−0.272846	−0.136423	−	0.990651i	$-0.543561\pi$
$829$	−1.28865e11	−0.272846	−0.136423	+	0.990651i	$0.543561\pi$
$830$	− 3.62915e11i	− 0.764703i
$831$	0	0
$832$	3.54018e10	0.0738808
$833$	− 6.58753e10i	− 0.136818i
$834$	0	0
$835$	4.14541e11	0.852751
$836$	− 1.74333e10i	− 0.0356906i
$837$	0	0
$838$	3.17054e11	0.642920
$839$	6.66953e10i	0.134601i	0.997733	+	0.0673004i	$0.0214386\pi$
$839$	6.66953e10i	0.134601i	−0.997733	+	0.0673004i	$0.978561\pi$
$840$	0	0
$841$	2.88387e11	0.576491
$842$	− 2.03162e11i	− 0.404197i
$843$	0	0
$844$	3.03989e11	0.599084
$845$	− 4.47188e11i	− 0.877129i
$846$	0	0
$847$	−1.93926e11	−0.376792
$848$	− 2.15536e11i	− 0.416808i
$849$	0	0
$850$	−2.88904e11	−0.553450
$851$	− 3.47982e10i	− 0.0663496i
$852$	0	0
$853$	8.51877e11	1.60909	0.804546	−	0.593890i	$-0.202409\pi$
$853$	8.51877e11	1.60909	0.804546	+	0.593890i	$0.202409\pi$
$854$	− 1.18076e11i	− 0.221988i
$855$	0	0
$856$	−1.72982e11	−0.322185
$857$	2.27165e11i	0.421131i	0.977580	+	0.210566i	$0.0675305\pi$
$857$	2.27165e11i	0.421131i	−0.977580	+	0.210566i	$0.932469\pi$
$858$	0	0
$859$	1.58451e10	0.0291020	0.0145510	−	0.999894i	$-0.495368\pi$
$859$	1.58451e10	0.0291020	0.0145510	+	0.999894i	$0.495368\pi$
$860$	1.46272e11i	0.267403i
$861$	0	0
$862$	1.07455e11	0.194624
$863$	9.92425e10i	0.178918i	0.995990	+	0.0894591i	$0.0285138\pi$
$863$	9.92425e10i	0.178918i	−0.995990	+	0.0894591i	$0.971486\pi$
$864$	0	0
$865$	7.79119e10	0.139168
$866$	5.53993e11i	0.984992i
$867$	0	0
$868$	6.34335e10	0.111748
$869$	− 6.49021e9i	− 0.0113810i
$870$	0	0
$871$	−4.46936e11	−0.776555
$872$	3.31746e11i	0.573773i
$873$	0	0
$874$	1.14863e11	0.196850
$875$	− 5.45830e10i	− 0.0931162i
$876$	0	0
$877$	9.93826e11	1.68001	0.840006	−	0.542578i	$-0.182552\pi$
$877$	9.93826e11	1.68001	0.840006	+	0.542578i	$0.182552\pi$
$878$	− 6.32424e11i	− 1.06422i
$879$	0	0
$880$	1.12576e10	0.0187723
$881$	− 1.44263e11i	− 0.239470i	−0.992806	−	0.119735i	$-0.961795\pi$
$881$	− 1.44263e11i	− 0.239470i	0.992806	−	0.119735i	$-0.0382045\pi$
$882$	0	0
$883$	−4.79851e11	−0.789339	−0.394670	−	0.918823i	$-0.629141\pi$
$883$	−4.79851e11	−0.789339	−0.394670	+	0.918823i	$0.629141\pi$
$884$	− 1.72839e11i	− 0.283030i
$885$	0	0
$886$	−7.48929e10	−0.121536
$887$	− 6.07729e11i	− 0.981783i	−0.871221	−	0.490892i	$-0.836671\pi$
$887$	− 6.07729e11i	− 0.981783i	0.871221	−	0.490892i	$-0.163329\pi$
$888$	0	0
$889$	3.41705e11	0.547072
$890$	7.04121e11i	1.12224i
$891$	0	0
$892$	−7.17827e10	−0.113386
$893$	1.38893e12i	2.18412i
$894$	0	0
$895$	−1.28169e12	−1.99752
$896$	2.15317e10i	0.0334077i
$897$	0	0
$898$	4.40539e11	0.677452
$899$	2.51356e11i	0.384813i
$900$	0	0
$901$	−1.05229e12	−1.59675
$902$	3.02514e9i	0.00457003i
$903$	0	0
$904$	6.89449e10	0.103235
$905$	− 3.53240e11i	− 0.526593i
$906$	0	0
$907$	1.00996e12	1.49236	0.746182	−	0.665742i	$-0.231885\pi$
$907$	1.00996e12	1.49236	0.746182	+	0.665742i	$0.231885\pi$
$908$	6.60805e11i	0.972143i
$909$	0	0
$910$	−1.46026e11	−0.212944
$911$	− 4.62984e11i	− 0.672190i	−0.941828	−	0.336095i	$-0.890894\pi$
$911$	− 4.62984e11i	− 0.672190i	0.941828	−	0.336095i	$-0.109106\pi$
$912$	0	0
$913$	3.10495e10	0.0446860
$914$	5.48137e11i	0.785424i
$915$	0	0
$916$	−1.39154e11	−0.197657
$917$	3.75077e10i	0.0530448i
$918$	0	0
$919$	−1.24886e11	−0.175087	−0.0875433	−	0.996161i	$-0.527902\pi$
$919$	−1.24886e11	−0.175087	−0.0875433	+	0.996161i	$0.527902\pi$
$920$	7.41736e10i	0.103538i
$921$	0	0
$922$	1.48450e11	0.205426
$923$	− 1.39381e11i	− 0.192043i
$924$	0	0
$925$	1.82735e11	0.249606
$926$	− 3.16959e11i	− 0.431081i
$927$	0	0
$928$	−8.53195e10	−0.115042
$929$	1.05224e12i	1.41270i	0.707863	+	0.706350i	$0.249659\pi$
$929$	1.05224e12i	1.41270i	−0.707863	+	0.706350i	$0.750341\pi$
$930$	0	0
$931$	−1.37535e11	−0.183069
$932$	5.76730e11i	0.764380i
$933$	0	0
$934$	−5.94780e11	−0.781572
$935$	− 5.49622e10i	− 0.0719147i
$936$	0	0
$937$	−1.16372e12	−1.50969	−0.754847	−	0.655901i	$-0.772289\pi$
$937$	−1.16372e12	−1.50969	−0.754847	+	0.655901i	$0.772289\pi$
$938$	− 2.71830e11i	− 0.351145i
$939$	0	0
$940$	−8.96914e11	−1.14879
$941$	− 1.34892e12i	− 1.72039i	−0.509968	−	0.860194i	$-0.670343\pi$
$941$	− 1.34892e12i	− 1.72039i	0.509968	−	0.860194i	$-0.329657\pi$
$942$	0	0
$943$	−1.99318e10	−0.0252058
$944$	1.64451e10i	0.0207085i
$945$	0	0
$946$	−1.25144e10	−0.0156259
$947$	− 3.97660e11i	− 0.494439i	−0.968960	−	0.247219i	$-0.920483\pi$
$947$	− 3.97660e11i	− 0.494439i	0.968960	−	0.247219i	$-0.0795168\pi$
$948$	0	0
$949$	−6.41765e11	−0.791246
$950$	6.03178e11i	0.740544i
$951$	0	0
$952$	1.05122e11	0.127981
$953$	− 6.18536e11i	− 0.749883i	−0.927049	−	0.374941i	$-0.877663\pi$
$953$	− 6.18536e11i	− 0.749883i	0.927049	−	0.374941i	$-0.122337\pi$
$954$	0	0
$955$	−6.91788e11	−0.831686
$956$	2.87452e11i	0.344138i
$957$	0	0
$958$	3.52882e11	0.418955
$959$	5.51547e11i	0.652090i
$960$	0	0
$961$	−5.54675e11	−0.650347
$962$	1.09322e11i	0.127647i
$963$	0	0
$964$	5.81577e11	0.673440
$965$	3.34333e11i	0.385540i
$966$	0	0
$967$	1.26117e12	1.44234	0.721169	−	0.692759i	$-0.243605\pi$
$967$	1.26117e12	1.44234	0.721169	+	0.692759i	$0.243605\pi$
$968$	− 3.09462e11i	− 0.352456i
$969$	0	0
$970$	−1.41055e12	−1.59332
$971$	− 7.62933e11i	− 0.858241i	−0.903247	−	0.429120i	$-0.858824\pi$
$971$	− 7.62933e11i	− 0.858241i	0.903247	−	0.429120i	$-0.141176\pi$
$972$	0	0
$973$	4.77852e10	0.0533141
$974$	6.14647e11i	0.682951i
$975$	0	0
$976$	1.88423e11	0.207651
$977$	1.65499e12i	1.81642i	0.418510	+	0.908212i	$0.362552\pi$
$977$	1.65499e12i	1.81642i	−0.418510	+	0.908212i	$0.637448\pi$
$978$	0	0
$979$	−6.02416e10	−0.0655791
$980$	− 8.88143e10i	− 0.0962895i
$981$	0	0
$982$	7.27826e11	0.782675
$983$	6.30294e11i	0.675039i	0.941318	+	0.337520i	$0.109588\pi$
$983$	6.30294e11i	0.675039i	−0.941318	+	0.337520i	$0.890412\pi$
$984$	0	0
$985$	−1.93278e12	−2.05323
$986$	4.16548e11i	0.440715i
$987$	0	0
$988$	−3.60855e11	−0.378709
$989$	− 8.24539e10i	− 0.0861838i
$990$	0	0
$991$	3.59956e11	0.373212	0.186606	−	0.982435i	$-0.440251\pi$
$991$	3.59956e11	0.373212	0.186606	+	0.982435i	$0.440251\pi$
$992$	1.01226e11i	0.104531i
$993$	0	0
$994$	8.47731e10	0.0868385
$995$	− 1.40350e12i	− 1.43192i
$996$	0	0
$997$	−8.33851e11	−0.843932	−0.421966	−	0.906612i	$-0.638660\pi$
$997$	−8.33851e11	−0.843932	−0.421966	+	0.906612i	$0.638660\pi$
$998$	− 1.56901e11i	− 0.158162i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.b.a.71.8	yes	8
3.2	odd	2	inner	126.9.b.a.71.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.b.a.71.1	✓	8	3.2	odd	2	inner
126.9.b.a.71.8	yes	8	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	126.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+11.3137i q^{2} -128.000 q^{4} +842.533i q^{5} -907.493 q^{7} -1448.15i q^{8} +O(q^{10})\)	\(q+11.3137i q^{2} -128.000 q^{4} +842.533i q^{5} -907.493 q^{7} -1448.15i q^{8} -9532.17 q^{10} -815.531i q^{11} -16880.9 q^{13} -10267.1i q^{14} +16384.0 q^{16} -79990.2i q^{17} -167004. q^{19} -107844. i q^{20} +9226.69 q^{22} +60792.1i q^{23} -319237. q^{25} -190985. i q^{26} +116159. q^{28} +460282. i q^{29} +546092. q^{31} +185364. i q^{32} +904985. q^{34} -764592. i q^{35} -572413. q^{37} -1.88944e6i q^{38} +1.22012e6 q^{40} +327868. i q^{41} -1.35632e6 q^{43} +104388. i q^{44} -687784. q^{46} -8.31676e6i q^{47} +823543. q^{49} -3.61175e6i q^{50} +2.16075e6 q^{52} -1.31552e7i q^{53} +687112. q^{55} +1.31419e6i q^{56} -5.20749e6 q^{58} +1.00373e6i q^{59} +1.15004e7 q^{61} +6.17832e6i q^{62} -2.09715e6 q^{64} -1.42227e7i q^{65} +2.64758e7 q^{67} +1.02387e7i q^{68} +8.65038e6 q^{70} +8.25676e6i q^{71} +3.80173e7 q^{73} -6.47611e6i q^{74} +2.13766e7 q^{76} +740089. i q^{77} +7.95826e6 q^{79} +1.38041e7i q^{80} -3.70941e6 q^{82} +3.80727e7i q^{83} +6.73943e7 q^{85} -1.53451e7i q^{86} -1.18102e6 q^{88} -7.38679e7i q^{89} +1.53193e7 q^{91} -7.78139e6i q^{92} +9.40933e7 q^{94} -1.40707e8i q^{95} +1.47978e8 q^{97} +9.31733e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 1024 q^{4}+O(q^{10}) \) 8 * q - 1024 * q^4	\( 8 q - 1024 q^{4} - 11648 q^{10} - 79912 q^{13} + 131072 q^{16} + 253960 q^{19} - 469696 q^{22} + 315744 q^{25} + 1507352 q^{31} - 1961344 q^{34} - 234056 q^{37} + 1490944 q^{40} - 14779136 q^{43} + 4844480 q^{46} + 6588344 q^{49} + 10228736 q^{52} + 37751336 q^{55} - 4818944 q^{58} - 56194600 q^{61} - 16777216 q^{64} + 27271560 q^{67} - 1997632 q^{70} - 5112912 q^{73} - 32506880 q^{76} - 22918792 q^{79} - 42190848 q^{82} + 85335416 q^{85} + 60121088 q^{88} + 31885280 q^{91} + 196578816 q^{94} + 85889664 q^{97}+O(q^{100}) \) 8 * q - 1024 * q^4 - 11648 * q^10 - 79912 * q^13 + 131072 * q^16 + 253960 * q^19 - 469696 * q^22 + 315744 * q^25 + 1507352 * q^31 - 1961344 * q^34 - 234056 * q^37 + 1490944 * q^40 - 14779136 * q^43 + 4844480 * q^46 + 6588344 * q^49 + 10228736 * q^52 + 37751336 * q^55 - 4818944 * q^58 - 56194600 * q^61 - 16777216 * q^64 + 27271560 * q^67 - 1997632 * q^70 - 5112912 * q^73 - 32506880 * q^76 - 22918792 * q^79 - 42190848 * q^82 + 85335416 * q^85 + 60121088 * q^88 + 31885280 * q^91 + 196578816 * q^94 + 85889664 * q^97

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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