LMFDB - Embedded newform 126.9.b.a.71.2

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			71.2
Root			$43.1926 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	126.71
Dual form			126.9.b.a.71.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.3137i q^{2} -128.000 q^{4} -503.908i q^{5} +907.493 q^{7} +1448.15i q^{8} +O(q^{10})$	\(q-11.3137i q^{2} -128.000 q^{4} -503.908i q^{5} +907.493 q^{7} +1448.15i q^{8} -5701.07 q^{10} +5076.92i q^{11} +27350.6 q^{13} -10267.1i q^{14} +16384.0 q^{16} -152129. i q^{17} +60621.6 q^{19} +64500.2i q^{20} +57438.8 q^{22} +241581. i q^{23} +136702. q^{25} -309437. i q^{26} -116159. q^{28} +9450.92i q^{29} +1.56154e6 q^{31} -185364. i q^{32} -1.72114e6 q^{34} -457293. i q^{35} -3.40972e6 q^{37} -685855. i q^{38} +729737. q^{40} -2.90848e6i q^{41} +949257. q^{43} -649846. i q^{44} +2.73318e6 q^{46} -6.22940e6i q^{47} +823543. q^{49} -1.54660e6i q^{50} -3.50088e6 q^{52} -3.87055e6i q^{53} +2.55830e6 q^{55} +1.31419e6i q^{56} +106925. q^{58} +2.66776e6i q^{59} -1.42297e7 q^{61} -1.76668e7i q^{62} -2.09715e6 q^{64} -1.37822e7i q^{65} -3.24237e7 q^{67} +1.94725e7i q^{68} -5.17368e6 q^{70} -1.34897e7i q^{71} -410485. q^{73} +3.85766e7i q^{74} -7.75956e6 q^{76} +4.60727e6i q^{77} -4.16801e7 q^{79} -8.25603e6i q^{80} -3.29057e7 q^{82} -3.26255e7i q^{83} -7.66591e7 q^{85} -1.07396e7i q^{86} -7.35217e6 q^{88} -9.95738e6i q^{89} +2.48205e7 q^{91} -3.09224e7i q^{92} -7.04776e7 q^{94} -3.05477e7i q^{95} -1.58474e7 q^{97} -9.31733e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	− 503.908i	− 0.806253i	−0.915144	−	0.403126i	$-0.867923\pi$
$5$	− 503.908i	− 0.806253i	0.915144	−	0.403126i	$-0.132077\pi$
$6$	0	0
$7$	907.493	0.377964
$7$	907.493	0.377964
$8$	1448.15i	0.353553i
$9$	0	0
$10$	−5701.07	−0.570107
$11$	5076.92i	0.346761i	0.984855	+	0.173380i	$0.0554690\pi$
$11$	5076.92i	0.346761i	−0.984855	+	0.173380i	$0.944531\pi$
$12$	0	0
$13$	27350.6	0.957621	0.478811	−	0.877918i	$-0.341068\pi$
$13$	27350.6	0.957621	0.478811	+	0.877918i	$0.341068\pi$
$14$	− 10267.1i	− 0.267261i
$15$	0	0
$16$	16384.0	0.250000
$17$	− 152129.i	− 1.82145i	−0.413016	−	0.910724i	$-0.635525\pi$
$17$	− 152129.i	− 1.82145i	0.413016	−	0.910724i	$-0.364475\pi$
$18$	0	0
$19$	60621.6	0.465171	0.232586	−	0.972576i	$-0.425281\pi$
$19$	60621.6	0.465171	0.232586	+	0.972576i	$0.425281\pi$
$20$	64500.2i	0.403126i
$21$	0	0
$22$	57438.8	0.245197
$23$	241581.i	0.863281i	0.902046	+	0.431641i	$0.142065\pi$
$23$	241581.i	0.863281i	−0.902046	+	0.431641i	$0.857935\pi$
$24$	0	0
$25$	136702.	0.349956
$26$	− 309437.i	− 0.677140i
$27$	0	0
$28$	−116159.	−0.188982
$29$	9450.92i	0.0133623i	0.999978	+	0.00668116i	$0.00212670\pi$
$29$	9450.92i	0.0133623i	−0.999978	+	0.00668116i	$0.997873\pi$
$30$	0	0
$31$	1.56154e6	1.69085	0.845426	−	0.534093i	$-0.179347\pi$
$31$	1.56154e6	1.69085	0.845426	+	0.534093i	$0.179347\pi$
$32$	− 185364.i	− 0.176777i
$33$	0	0
$34$	−1.72114e6	−1.28796
$35$	− 457293.i	− 0.304735i
$36$	0	0
$37$	−3.40972e6	−1.81933	−0.909665	−	0.415342i	$-0.863662\pi$
$37$	−3.40972e6	−1.81933	−0.909665	+	0.415342i	$0.863662\pi$
$38$	− 685855.i	− 0.328926i
$39$	0	0
$40$	729737.	0.285053
$41$	− 2.90848e6i	− 1.02927i	−0.857408	−	0.514637i	$-0.827927\pi$
$41$	− 2.90848e6i	− 1.02927i	0.857408	−	0.514637i	$-0.172073\pi$
$42$	0	0
$43$	949257.	0.277658	0.138829	−	0.990316i	$-0.455666\pi$
$43$	949257.	0.277658	0.138829	+	0.990316i	$0.455666\pi$
$44$	− 649846.i	− 0.173380i
$45$	0	0
$46$	2.73318e6	0.610432
$47$	− 6.22940e6i	− 1.27660i	−0.769788	−	0.638300i	$-0.779638\pi$
$47$	− 6.22940e6i	− 1.27660i	0.769788	−	0.638300i	$-0.220362\pi$
$48$	0	0
$49$	823543.	0.142857
$50$	− 1.54660e6i	− 0.247456i
$51$	0	0
$52$	−3.50088e6	−0.478811
$53$	− 3.87055e6i	− 0.490534i	−0.969456	−	0.245267i	$-0.921124\pi$
$53$	− 3.87055e6i	− 0.490534i	0.969456	−	0.245267i	$-0.0788756\pi$
$54$	0	0
$55$	2.55830e6	0.279577
$56$	1.31419e6i	0.133631i
$57$	0	0
$58$	106925.	0.00944859
$59$	2.66776e6i	0.220160i	0.993923	+	0.110080i	$0.0351107\pi$
$59$	2.66776e6i	0.220160i	−0.993923	+	0.110080i	$0.964889\pi$
$60$	0	0
$61$	−1.42297e7	−1.02772	−0.513861	−	0.857873i	$-0.671785\pi$
$61$	−1.42297e7	−1.02772	−0.513861	+	0.857873i	$0.671785\pi$
$62$	− 1.76668e7i	− 1.19561i
$63$	0	0
$64$	−2.09715e6	−0.125000
$65$	− 1.37822e7i	− 0.772085i
$66$	0	0
$67$	−3.24237e7	−1.60903	−0.804513	−	0.593935i	$-0.797574\pi$
$67$	−3.24237e7	−1.60903	−0.804513	+	0.593935i	$0.797574\pi$
$68$	1.94725e7i	0.910724i
$69$	0	0
$70$	−5.17368e6	−0.215480
$71$	− 1.34897e7i	− 0.530845i	−0.964132	−	0.265422i	$-0.914489\pi$
$71$	− 1.34897e7i	− 0.530845i	0.964132	−	0.265422i	$-0.0855114\pi$
$72$	0	0
$73$	−410485.	−0.0144546	−0.00722730	−	0.999974i	$-0.502301\pi$
$73$	−410485.	−0.0144546	−0.00722730	+	0.999974i	$0.502301\pi$
$74$	3.85766e7i	1.28646i
$75$	0	0
$76$	−7.75956e6	−0.232586
$77$	4.60727e6i	0.131063i
$78$	0	0
$79$	−4.16801e7	−1.07009	−0.535045	−	0.844824i	$-0.679705\pi$
$79$	−4.16801e7	−1.07009	−0.535045	+	0.844824i	$0.679705\pi$
$80$	− 8.25603e6i	− 0.201563i
$81$	0	0
$82$	−3.29057e7	−0.727807
$83$	− 3.26255e7i	− 0.687456i	−0.939069	−	0.343728i	$-0.888310\pi$
$83$	− 3.26255e7i	− 0.687456i	0.939069	−	0.343728i	$-0.111690\pi$
$84$	0	0
$85$	−7.66591e7	−1.46855
$86$	− 1.07396e7i	− 0.196334i
$87$	0	0
$88$	−7.35217e6	−0.122598
$89$	− 9.95738e6i	− 0.158703i	−0.996847	−	0.0793515i	$-0.974715\pi$
$89$	− 9.95738e6i	− 0.158703i	0.996847	−	0.0793515i	$-0.0252850\pi$
$90$	0	0
$91$	2.48205e7	0.361947
$92$	− 3.09224e7i	− 0.431641i
$93$	0	0
$94$	−7.04776e7	−0.902692
$95$	− 3.05477e7i	− 0.375046i
$96$	0	0
$97$	−1.58474e7	−0.179008	−0.0895040	−	0.995986i	$-0.528528\pi$
$97$	−1.58474e7	−0.179008	−0.0895040	+	0.995986i	$0.528528\pi$
$98$	− 9.31733e6i	− 0.101015i
$99$	0	0
$100$	−1.74978e7	−0.174978
$101$	− 1.70614e8i	− 1.63957i	−0.572673	−	0.819784i	$-0.694093\pi$
$101$	− 1.70614e8i	− 1.63957i	0.572673	−	0.819784i	$-0.305907\pi$
$102$	0	0
$103$	−8.05992e7	−0.716113	−0.358057	−	0.933700i	$-0.616561\pi$
$103$	−8.05992e7	−0.716113	−0.358057	+	0.933700i	$0.616561\pi$
$104$	3.96079e7i	0.338570i
$105$	0	0
$106$	−4.37903e7	−0.346860
$107$	2.28184e8i	1.74081i	0.492340	+	0.870403i	$0.336142\pi$
$107$	2.28184e8i	1.74081i	−0.492340	+	0.870403i	$0.663858\pi$
$108$	0	0
$109$	−2.13817e7	−0.151473	−0.0757366	−	0.997128i	$-0.524131\pi$
$109$	−2.13817e7	−0.151473	−0.0757366	+	0.997128i	$0.524131\pi$
$110$	− 2.89439e7i	− 0.197691i
$111$	0	0
$112$	1.48684e7	0.0944911
$113$	− 1.97694e8i	− 1.21249i	−0.795277	−	0.606246i	$-0.792675\pi$
$113$	− 1.97694e8i	− 1.21249i	0.795277	−	0.606246i	$-0.207325\pi$
$114$	0	0
$115$	1.21735e8	0.696023
$116$	− 1.20972e6i	− 0.00668116i
$117$	0	0
$118$	3.01822e7	0.155677
$119$	− 1.38056e8i	− 0.688442i
$120$	0	0
$121$	1.88584e8	0.879757
$122$	1.60990e8i	0.726709i
$123$	0	0
$124$	−1.99877e8	−0.845426
$125$	− 2.65724e8i	− 1.08841i
$126$	0	0
$127$	2.29390e8	0.881779	0.440889	−	0.897561i	$-0.354663\pi$
$127$	2.29390e8	0.881779	0.440889	+	0.897561i	$0.354663\pi$
$128$	2.37266e7i	0.0883883i
$129$	0	0
$130$	−1.55928e8	−0.545946
$131$	− 1.20093e8i	− 0.407785i	−0.978993	−	0.203892i	$-0.934641\pi$
$131$	− 1.20093e8i	− 0.407785i	0.978993	−	0.203892i	$-0.0653592\pi$
$132$	0	0
$133$	5.50137e7	0.175818
$134$	3.66832e8i	1.13775i
$135$	0	0
$136$	2.20307e8	0.643979
$137$	4.65651e8i	1.32184i	0.750457	+	0.660919i	$0.229834\pi$
$137$	4.65651e8i	1.32184i	−0.750457	+	0.660919i	$0.770166\pi$
$138$	0	0
$139$	2.47244e8	0.662318	0.331159	−	0.943575i	$-0.392560\pi$
$139$	2.47244e8	0.662318	0.331159	+	0.943575i	$0.392560\pi$
$140$	5.85335e7i	0.152367i
$141$	0	0
$142$	−1.52618e8	−0.375364
$143$	1.38857e8i	0.332065i
$144$	0	0
$145$	4.76240e6	0.0107734
$146$	4.64411e6i	0.0102209i
$147$	0	0
$148$	4.36444e8	0.909665
$149$	− 6.82348e8i	− 1.38440i	−0.721707	−	0.692198i	$-0.756642\pi$
$149$	− 6.82348e8i	− 1.38440i	0.721707	−	0.692198i	$-0.243358\pi$
$150$	0	0
$151$	6.41140e8	1.23323	0.616616	−	0.787264i	$-0.288503\pi$
$151$	6.41140e8	1.23323	0.616616	+	0.787264i	$0.288503\pi$
$152$	8.77894e7i	0.164463i
$153$	0	0
$154$	5.21253e7	0.0926757
$155$	− 7.86871e8i	− 1.36325i
$156$	0	0
$157$	−4.03039e7	−0.0663358	−0.0331679	−	0.999450i	$-0.510560\pi$
$157$	−4.03039e7	−0.0663358	−0.0331679	+	0.999450i	$0.510560\pi$
$158$	4.71556e8i	0.756668i
$159$	0	0
$160$	−9.34063e7	−0.142527
$161$	2.19233e8i	0.326290i
$162$	0	0
$163$	7.87225e8	1.11519	0.557594	−	0.830114i	$-0.311724\pi$
$163$	7.87225e8	1.11519	0.557594	+	0.830114i	$0.311724\pi$
$164$	3.72286e8i	0.514637i
$165$	0	0
$166$	−3.69116e8	−0.486105
$167$	1.10128e8i	0.141590i	0.997491	+	0.0707951i	$0.0225537\pi$
$167$	1.10128e8i	0.141590i	−0.997491	+	0.0707951i	$0.977446\pi$
$168$	0	0
$169$	−6.76746e7	−0.0829619
$170$	8.67299e8i	1.03842i
$171$	0	0
$172$	−1.21505e8	−0.138829
$173$	3.15029e8i	0.351695i	0.984417	+	0.175848i	$0.0562666\pi$
$173$	3.15029e8i	0.351695i	−0.984417	+	0.175848i	$0.943733\pi$
$174$	0	0
$175$	1.24056e8	0.132271
$176$	8.31803e7i	0.0866902i
$177$	0	0
$178$	−1.12655e8	−0.112220
$179$	− 4.02261e8i	− 0.391828i	−0.980621	−	0.195914i	$-0.937233\pi$
$179$	− 4.02261e8i	− 0.391828i	0.980621	−	0.195914i	$-0.0627674\pi$
$180$	0	0
$181$	1.10407e9	1.02869	0.514344	−	0.857584i	$-0.328036\pi$
$181$	1.10407e9	1.02869	0.514344	+	0.857584i	$0.328036\pi$
$182$	− 2.80812e8i	− 0.255935i
$183$	0	0
$184$	−3.49847e8	−0.305216
$185$	1.71819e9i	1.46684i
$186$	0	0
$187$	7.72348e8	0.631606
$188$	7.97363e8i	0.638300i
$189$	0	0
$190$	−3.45608e8	−0.265197
$191$	1.77013e9i	1.33006i	0.746817	+	0.665029i	$0.231581\pi$
$191$	1.77013e9i	1.33006i	−0.746817	+	0.665029i	$0.768419\pi$
$192$	0	0
$193$	1.45090e9	1.04570	0.522850	−	0.852425i	$-0.324869\pi$
$193$	1.45090e9	1.04570	0.522850	+	0.852425i	$0.324869\pi$
$194$	1.79293e8i	0.126578i
$195$	0	0
$196$	−1.05414e8	−0.0714286
$197$	− 1.35972e6i	0 0.000902788i	−1.00000		0.000451394i	$-0.999856\pi$
$197$	− 1.35972e6i	0 0.000902788i	1.00000		0.000451394i	$-0.000143683\pi$
$198$	0	0
$199$	−2.99471e8	−0.190960	−0.0954801	−	0.995431i	$-0.530439\pi$
$199$	−2.99471e8	−0.190960	−0.0954801	+	0.995431i	$0.530439\pi$
$200$	1.97965e8i	0.123728i
$201$	0	0
$202$	−1.93028e9	−1.15935
$203$	8.57664e6i	0.00505049i
$204$	0	0
$205$	−1.46561e9	−0.829855
$206$	9.11876e8i	0.506369i
$207$	0	0
$208$	4.48112e8	0.239405
$209$	3.07771e8i	0.161303i
$210$	0	0
$211$	−8.35317e8	−0.421426	−0.210713	−	0.977548i	$-0.567579\pi$
$211$	−8.35317e8	−0.421426	−0.210713	+	0.977548i	$0.567579\pi$
$212$	4.95430e8i	0.245267i
$213$	0	0
$214$	2.58161e9	1.23094
$215$	− 4.78338e8i	− 0.223863i
$216$	0	0
$217$	1.41708e9	0.639082
$218$	2.41906e8i	0.107108i
$219$	0	0
$220$	−3.27463e8	−0.139788
$221$	− 4.16083e9i	− 1.74426i
$222$	0	0
$223$	2.40526e9	0.972620	0.486310	−	0.873786i	$-0.338343\pi$
$223$	2.40526e9	0.972620	0.486310	+	0.873786i	$0.338343\pi$
$224$	− 1.68216e8i	− 0.0668153i
$225$	0	0
$226$	−2.23665e9	−0.857362
$227$	− 1.40760e9i	− 0.530120i	−0.964232	−	0.265060i	$-0.914608\pi$
$227$	− 1.40760e9i	− 0.530120i	0.964232	−	0.265060i	$-0.0853918\pi$
$228$	0	0
$229$	1.75552e8	0.0638357	0.0319178	−	0.999490i	$-0.489839\pi$
$229$	1.75552e8	0.0638357	0.0319178	+	0.999490i	$0.489839\pi$
$230$	− 1.37727e9i	− 0.492163i
$231$	0	0
$232$	−1.36864e7	−0.00472430
$233$	− 2.84447e9i	− 0.965111i	−0.875865	−	0.482556i	$-0.839709\pi$
$233$	− 2.84447e9i	− 0.965111i	0.875865	−	0.482556i	$-0.160291\pi$
$234$	0	0
$235$	−3.13904e9	−1.02926
$236$	− 3.41473e8i	− 0.110080i
$237$	0	0
$238$	−1.56193e9	−0.486802
$239$	− 3.87682e9i	− 1.18818i	−0.804397	−	0.594092i	$-0.797511\pi$
$239$	− 3.87682e9i	− 1.18818i	0.804397	−	0.594092i	$-0.202489\pi$
$240$	0	0
$241$	−3.88848e9	−1.15269	−0.576345	−	0.817207i	$-0.695521\pi$
$241$	−3.88848e9	−1.15269	−0.576345	+	0.817207i	$0.695521\pi$
$242$	− 2.13358e9i	− 0.622082i
$243$	0	0
$244$	1.82140e9	0.513861
$245$	− 4.14990e8i	− 0.115179i
$246$	0	0
$247$	1.65804e9	0.445458
$248$	2.26135e9i	0.597806i
$249$	0	0
$250$	−3.00633e9	−0.769619
$251$	6.76361e8i	0.170405i	0.996364	+	0.0852027i	$0.0271538\pi$
$251$	6.76361e8i	0.170405i	−0.996364	+	0.0852027i	$0.972846\pi$
$252$	0	0
$253$	−1.22649e9	−0.299352
$254$	− 2.59525e9i	− 0.623512i
$255$	0	0
$256$	2.68435e8	0.0625000
$257$	− 6.85600e8i	− 0.157159i	−0.996908	−	0.0785793i	$-0.974962\pi$
$257$	− 6.85600e8i	− 0.157159i	0.996908	−	0.0785793i	$-0.0250384\pi$
$258$	0	0
$259$	−3.09429e9	−0.687642
$260$	1.76412e9i	0.386042i
$261$	0	0
$262$	−1.35869e9	−0.288347
$263$	− 6.75130e9i	− 1.41112i	−0.708650	−	0.705560i	$-0.750695\pi$
$263$	− 6.75130e9i	− 1.41112i	0.708650	−	0.705560i	$-0.249305\pi$
$264$	0	0
$265$	−1.95040e9	−0.395494
$266$	− 6.22408e8i	− 0.124322i
$267$	0	0
$268$	4.15023e9	0.804513
$269$	8.13486e9i	1.55361i	0.629744	+	0.776803i	$0.283160\pi$
$269$	8.13486e9i	1.55361i	−0.629744	+	0.776803i	$0.716840\pi$
$270$	0	0
$271$	−6.16491e9	−1.14301	−0.571504	−	0.820599i	$-0.693640\pi$
$271$	−6.16491e9	−1.14301	−0.571504	+	0.820599i	$0.693640\pi$
$272$	− 2.49248e9i	− 0.455362i
$273$	0	0
$274$	5.26824e9	0.934681
$275$	6.94024e8i	0.121351i
$276$	0	0
$277$	8.94788e9	1.51985	0.759926	−	0.650010i	$-0.225235\pi$
$277$	8.94788e9	1.51985	0.759926	+	0.650010i	$0.225235\pi$
$278$	− 2.79725e9i	− 0.468330i
$279$	0	0
$280$	6.62231e8	0.107740
$281$	− 1.82764e9i	− 0.293133i	−0.989201	−	0.146567i	$-0.953178\pi$
$281$	− 1.82764e9i	− 0.293133i	0.989201	−	0.146567i	$-0.0468223\pi$
$282$	0	0
$283$	−1.11699e10	−1.74143	−0.870713	−	0.491791i	$-0.836342\pi$
$283$	−1.11699e10	−1.74143	−0.870713	+	0.491791i	$0.836342\pi$
$284$	1.72668e9i	0.265422i
$285$	0	0
$286$	1.57099e9	0.234806
$287$	− 2.63943e9i	− 0.389029i
$288$	0	0
$289$	−1.61675e10	−2.31767
$290$	− 5.38804e7i	− 0.00761796i
$291$	0	0
$292$	5.25421e7	0.00722730
$293$	1.24739e9i	0.169252i	0.996413	+	0.0846258i	$0.0269695\pi$
$293$	1.24739e9i	0.169252i	−0.996413	+	0.0846258i	$0.973031\pi$
$294$	0	0
$295$	1.34430e9	0.177505
$296$	− 4.93780e9i	− 0.643231i
$297$	0	0
$298$	−7.71988e9	−0.978916
$299$	6.60740e9i	0.826696i
$300$	0	0
$301$	8.61444e8	0.104945
$302$	− 7.25367e9i	− 0.872027i
$303$	0	0
$304$	9.93224e8	0.116293
$305$	7.17045e9i	0.828604i
$306$	0	0
$307$	6.76073e9	0.761097	0.380548	−	0.924761i	$-0.375735\pi$
$307$	6.76073e9	0.761097	0.380548	+	0.924761i	$0.375735\pi$
$308$	− 5.89731e8i	− 0.0655316i
$309$	0	0
$310$	−8.90243e9	−0.963966
$311$	5.22697e8i	0.0558739i	0.999610	+	0.0279369i	$0.00889376\pi$
$311$	5.22697e8i	0.0558739i	−0.999610	+	0.0279369i	$0.991106\pi$
$312$	0	0
$313$	1.31285e10	1.36785	0.683923	−	0.729554i	$-0.260272\pi$
$313$	1.31285e10	1.36785	0.683923	+	0.729554i	$0.260272\pi$
$314$	4.55986e8i	0.0469065i
$315$	0	0
$316$	5.33505e9	0.535045
$317$	1.53986e10i	1.52491i	0.647043	+	0.762453i	$0.276005\pi$
$317$	1.53986e10i	1.52491i	−0.647043	+	0.762453i	$0.723995\pi$
$318$	0	0
$319$	−4.79816e7	−0.00463353
$320$	1.05677e9i	0.100782i
$321$	0	0
$322$	2.48034e9	0.230722
$323$	− 9.22231e9i	− 0.847285i
$324$	0	0
$325$	3.73887e9	0.335125
$326$	− 8.90643e9i	− 0.788558i
$327$	0	0
$328$	4.21193e9	0.363903
$329$	− 5.65313e9i	− 0.482509i
$330$	0	0
$331$	−3.34892e9	−0.278992	−0.139496	−	0.990223i	$-0.544548\pi$
$331$	−3.34892e9	−0.278992	−0.139496	+	0.990223i	$0.544548\pi$
$332$	4.17607e9i	0.343728i
$333$	0	0
$334$	1.24596e9	0.100119
$335$	1.63386e10i	1.29728i
$336$	0	0
$337$	−2.21684e10	−1.71876	−0.859380	−	0.511337i	$-0.829151\pi$
$337$	−2.21684e10	−1.71876	−0.859380	+	0.511337i	$0.829151\pi$
$338$	7.65650e8i	0.0586629i
$339$	0	0
$340$	9.81237e9	0.734274
$341$	7.92780e9i	0.586321i
$342$	0	0
$343$	7.47359e8	0.0539949
$344$	1.37467e9i	0.0981669i
$345$	0	0
$346$	3.56415e9	0.248686
$347$	1.31736e10i	0.908630i	0.890841	+	0.454315i	$0.150116\pi$
$347$	1.31736e10i	0.908630i	−0.890841	+	0.454315i	$0.849884\pi$
$348$	0	0
$349$	1.54977e10	1.04463	0.522317	−	0.852751i	$-0.325068\pi$
$349$	1.54977e10	1.04463	0.522317	+	0.852751i	$0.325068\pi$
$350$	− 1.40353e9i	− 0.0935297i
$351$	0	0
$352$	9.41078e8	0.0612992
$353$	1.72937e10i	1.11375i	0.830596	+	0.556876i	$0.188000\pi$
$353$	1.72937e10i	1.11375i	−0.830596	+	0.556876i	$0.812000\pi$
$354$	0	0
$355$	−6.79755e9	−0.427995
$356$	1.27454e9i	0.0793515i
$357$	0	0
$358$	−4.55106e9	−0.277064
$359$	− 3.86210e9i	− 0.232512i	−0.993219	−	0.116256i	$-0.962911\pi$
$359$	− 3.86210e9i	− 0.232512i	0.993219	−	0.116256i	$-0.0370893\pi$
$360$	0	0
$361$	−1.33086e10	−0.783616
$362$	− 1.24912e10i	− 0.727392i
$363$	0	0
$364$	−3.17702e9	−0.180973
$365$	2.06847e8i	0.0116541i
$366$	0	0
$367$	9.20301e9	0.507301	0.253651	−	0.967296i	$-0.418369\pi$
$367$	9.20301e9	0.507301	0.253651	+	0.967296i	$0.418369\pi$
$368$	3.95807e9i	0.215820i
$369$	0	0
$370$	1.94390e10	1.03721
$371$	− 3.51249e9i	− 0.185404i
$372$	0	0
$373$	−1.07955e8	−0.00557710	−0.00278855	−	0.999996i	$-0.500888\pi$
$373$	−1.07955e8	−0.00557710	−0.00278855	+	0.999996i	$0.500888\pi$
$374$	− 8.73812e9i	− 0.446613i
$375$	0	0
$376$	9.02113e9	0.451346
$377$	2.58489e8i	0.0127960i
$378$	0	0
$379$	3.62975e10	1.75922	0.879608	−	0.475699i	$-0.157805\pi$
$379$	3.62975e10	1.75922	0.879608	+	0.475699i	$0.157805\pi$
$380$	3.91011e9i	0.187523i
$381$	0	0
$382$	2.00267e10	0.940494
$383$	1.65250e10i	0.767973i	0.923339	+	0.383986i	$0.125449\pi$
$383$	1.65250e10i	0.767973i	−0.923339	+	0.383986i	$0.874551\pi$
$384$	0	0
$385$	2.32164e9	0.105670
$386$	− 1.64150e10i	− 0.739422i
$387$	0	0
$388$	2.02847e9	0.0895040
$389$	2.50192e10i	1.09264i	0.837578	+	0.546318i	$0.183971\pi$
$389$	2.50192e10i	1.09264i	−0.837578	+	0.546318i	$0.816029\pi$
$390$	0	0
$391$	3.67516e10	1.57242
$392$	1.19262e9i	0.0505076i
$393$	0	0
$394$	−1.53835e7	−0.000638367 0
$395$	2.10029e10i	0.862763i
$396$	0	0
$397$	−4.28169e10	−1.72367	−0.861833	−	0.507192i	$-0.830684\pi$
$397$	−4.28169e10	−1.72367	−0.861833	+	0.507192i	$0.830684\pi$
$398$	3.38813e9i	0.135029i
$399$	0	0
$400$	2.23972e9	0.0874890
$401$	− 4.32895e10i	− 1.67419i	−0.547058	−	0.837095i	$-0.684252\pi$
$401$	− 4.32895e10i	− 1.67419i	0.547058	−	0.837095i	$-0.315748\pi$
$402$	0	0
$403$	4.27090e10	1.61919
$404$	2.18386e10i	0.819784i
$405$	0	0
$406$	9.70336e7	0.00357123
$407$	− 1.73109e10i	− 0.630872i
$408$	0	0
$409$	1.86013e10	0.664736	0.332368	−	0.943150i	$-0.392152\pi$
$409$	1.86013e10	0.664736	0.332368	+	0.943150i	$0.392152\pi$
$410$	1.65815e10i	0.586796i
$411$	0	0
$412$	1.03167e10	0.358057
$413$	2.42097e9i	0.0832126i
$414$	0	0
$415$	−1.64403e10	−0.554264
$416$	− 5.06981e9i	− 0.169285i
$417$	0	0
$418$	3.48203e9	0.114059
$419$	− 1.64989e10i	− 0.535302i	−0.963516	−	0.267651i	$-0.913753\pi$
$419$	− 1.64989e10i	− 0.535302i	0.963516	−	0.267651i	$-0.0862474\pi$
$420$	0	0
$421$	−8.92427e9	−0.284082	−0.142041	−	0.989861i	$-0.545367\pi$
$421$	−8.92427e9	−0.284082	−0.142041	+	0.989861i	$0.545367\pi$
$422$	9.45053e9i	0.297993i
$423$	0	0
$424$	5.60515e9	0.173430
$425$	− 2.07963e10i	− 0.637427i
$426$	0	0
$427$	−1.29133e10	−0.388442
$428$	− 2.92076e10i	− 0.870403i
$429$	0	0
$430$	−5.41178e9	−0.158295
$431$	− 2.65481e10i	− 0.769351i	−0.923052	−	0.384676i	$-0.874313\pi$
$431$	− 2.65481e10i	− 0.769351i	0.923052	−	0.384676i	$-0.125687\pi$
$432$	0	0
$433$	3.68546e10	1.04843	0.524216	−	0.851585i	$-0.324358\pi$
$433$	3.68546e10	1.04843	0.524216	+	0.851585i	$0.324358\pi$
$434$	− 1.60325e10i	− 0.451899i
$435$	0	0
$436$	2.73685e9	0.0757366
$437$	1.46451e10i	0.401574i
$438$	0	0
$439$	−2.75610e10	−0.742055	−0.371028	−	0.928622i	$-0.620994\pi$
$439$	−2.75610e10	−0.742055	−0.371028	+	0.928622i	$0.620994\pi$
$440$	3.70482e9i	0.0988453i
$441$	0	0
$442$	−4.70744e10	−1.23338
$443$	9.91876e9i	0.257539i	0.991675	+	0.128769i	$0.0411027\pi$
$443$	9.91876e9i	0.257539i	−0.991675	+	0.128769i	$0.958897\pi$
$444$	0	0
$445$	−5.01761e9	−0.127955
$446$	− 2.72124e10i	− 0.687746i
$447$	0	0
$448$	−1.90315e9	−0.0472456
$449$	4.29088e10i	1.05575i	0.849322	+	0.527875i	$0.177011\pi$
$449$	4.29088e10i	1.05575i	−0.849322	+	0.527875i	$0.822989\pi$
$450$	0	0
$451$	1.47661e10	0.356912
$452$	2.53048e10i	0.606246i
$453$	0	0
$454$	−1.59251e10	−0.374852
$455$	− 1.25072e10i	− 0.291821i
$456$	0	0
$457$	−1.17193e10	−0.268681	−0.134341	−	0.990935i	$-0.542892\pi$
$457$	−1.17193e10	−0.268681	−0.134341	+	0.990935i	$0.542892\pi$
$458$	− 1.98614e9i	− 0.0451386i
$459$	0	0
$460$	−1.55821e10	−0.348011
$461$	7.36373e10i	1.63040i	0.579180	+	0.815200i	$0.303373\pi$
$461$	7.36373e10i	1.63040i	−0.579180	+	0.815200i	$0.696627\pi$
$462$	0	0
$463$	−4.90353e10	−1.06705	−0.533525	−	0.845784i	$-0.679133\pi$
$463$	−4.90353e10	−1.06705	−0.533525	+	0.845784i	$0.679133\pi$
$464$	1.54844e8i	0.00334058i
$465$	0	0
$466$	−3.21815e10	−0.682437
$467$	− 7.86057e10i	− 1.65267i	−0.563178	−	0.826336i	$-0.690421\pi$
$467$	− 7.86057e10i	− 1.65267i	0.563178	−	0.826336i	$-0.309579\pi$
$468$	0	0
$469$	−2.94243e10	−0.608155
$470$	3.55142e10i	0.727798i
$471$	0	0
$472$	−3.86333e9	−0.0778383
$473$	4.81931e9i	0.0962809i
$474$	0	0
$475$	8.28707e9	0.162790
$476$	1.76712e10i	0.344221i
$477$	0	0
$478$	−4.38612e10	−0.840173
$479$	− 8.90455e10i	− 1.69149i	−0.533586	−	0.845746i	$-0.679156\pi$
$479$	− 8.90455e10i	− 1.69149i	0.533586	−	0.845746i	$-0.320844\pi$
$480$	0	0
$481$	−9.32579e10	−1.74223
$482$	4.39932e10i	0.815074i
$483$	0	0
$484$	−2.41387e10	−0.439879
$485$	7.98566e9i	0.144326i
$486$	0	0
$487$	1.00263e11	1.78248	0.891240	−	0.453531i	$-0.149836\pi$
$487$	1.00263e11	1.78248	0.891240	+	0.453531i	$0.149836\pi$
$488$	− 2.06068e10i	− 0.363355i
$489$	0	0
$490$	−4.69508e9	−0.0814439
$491$	− 5.52000e10i	− 0.949759i	−0.880051	−	0.474879i	$-0.842492\pi$
$491$	− 5.52000e10i	− 0.949759i	0.880051	−	0.474879i	$-0.157508\pi$
$492$	0	0
$493$	1.43776e9	0.0243388
$494$	− 1.87586e10i	− 0.314986i
$495$	0	0
$496$	2.55842e10	0.422713
$497$	− 1.22418e10i	− 0.200641i
$498$	0	0
$499$	−9.98718e10	−1.61080	−0.805399	−	0.592734i	$-0.798049\pi$
$499$	−9.98718e10	−1.61080	−0.805399	+	0.592734i	$0.798049\pi$
$500$	3.40127e10i	0.544203i
$501$	0	0
$502$	7.65215e9	0.120495
$503$	9.02207e10i	1.40940i	0.709505	+	0.704700i	$0.248919\pi$
$503$	9.02207e10i	1.40940i	−0.709505	+	0.704700i	$0.751081\pi$
$504$	0	0
$505$	−8.59738e10	−1.32191
$506$	1.38762e10i	0.211674i
$507$	0	0
$508$	−2.93619e10	−0.440889
$509$	− 6.79375e10i	− 1.01214i	−0.862494	−	0.506068i	$-0.831099\pi$
$509$	− 6.79375e10i	− 1.01214i	0.862494	−	0.506068i	$-0.168901\pi$
$510$	0	0
$511$	−3.72512e8	−0.00546333
$512$	− 3.03700e9i	− 0.0441942i
$513$	0	0
$514$	−7.75668e9	−0.111128
$515$	4.06146e10i	0.577368i
$516$	0	0
$517$	3.16262e10	0.442674
$518$	3.50080e10i	0.486237i
$519$	0	0
$520$	1.99588e10	0.272973
$521$	3.16154e10i	0.429090i	0.976714	+	0.214545i	$0.0688268\pi$
$521$	3.16154e10i	0.429090i	−0.976714	+	0.214545i	$0.931173\pi$
$522$	0	0
$523$	1.03898e11	1.38867	0.694334	−	0.719653i	$-0.255699\pi$
$523$	1.03898e11	1.38867	0.694334	+	0.719653i	$0.255699\pi$
$524$	1.53718e10i	0.203892i
$525$	0	0
$526$	−7.63822e10	−0.997813
$527$	− 2.37555e11i	− 3.07980i
$528$	0	0
$529$	1.99494e10	0.254746
$530$	2.20663e10i	0.279657i
$531$	0	0
$532$	−7.04175e9	−0.0879091
$533$	− 7.95488e10i	− 0.985655i
$534$	0	0
$535$	1.14984e11	1.40353
$536$	− 4.69545e10i	− 0.568877i
$537$	0	0
$538$	9.20354e10	1.09856
$539$	4.18106e9i	0.0495372i
$540$	0	0
$541$	1.23509e10	0.144181	0.0720906	−	0.997398i	$-0.477033\pi$
$541$	1.23509e10	0.144181	0.0720906	+	0.997398i	$0.477033\pi$
$542$	6.97480e10i	0.808229i
$543$	0	0
$544$	−2.81992e10	−0.321989
$545$	1.07744e10i	0.122126i
$546$	0	0
$547$	−1.28775e11	−1.43841	−0.719204	−	0.694799i	$-0.755493\pi$
$547$	−1.28775e11	−1.43841	−0.719204	+	0.694799i	$0.755493\pi$
$548$	− 5.96034e10i	− 0.660919i
$549$	0	0
$550$	7.85198e9	0.0858081
$551$	5.72930e8i	0.00621577i
$552$	0	0
$553$	−3.78244e10	−0.404456
$554$	− 1.01234e11i	− 1.07470i
$555$	0	0
$556$	−3.16472e10	−0.331159
$557$	4.45570e10i	0.462909i	0.972846	+	0.231454i	$0.0743484\pi$
$557$	4.45570e10i	0.462909i	−0.972846	+	0.231454i	$0.925652\pi$
$558$	0	0
$559$	2.59628e10	0.265891
$560$	− 7.49229e9i	− 0.0761837i
$561$	0	0
$562$	−2.06774e10	−0.207276
$563$	− 8.39811e10i	− 0.835887i	−0.908473	−	0.417944i	$-0.862751\pi$
$563$	− 8.39811e10i	− 0.835887i	0.908473	−	0.417944i	$-0.137249\pi$
$564$	0	0
$565$	−9.96195e10	−0.977576
$566$	1.26373e11i	1.23137i
$567$	0	0
$568$	1.95351e10	0.187682
$569$	− 3.91537e10i	− 0.373528i	−0.982405	−	0.186764i	$-0.940200\pi$
$569$	− 3.91537e10i	− 0.373528i	0.982405	−	0.186764i	$-0.0598000\pi$
$570$	0	0
$571$	8.92593e10	0.839671	0.419836	−	0.907600i	$-0.362088\pi$
$571$	8.92593e10	0.839671	0.419836	+	0.907600i	$0.362088\pi$
$572$	− 1.77737e10i	− 0.166033i
$573$	0	0
$574$	−2.98617e10	−0.275085
$575$	3.30246e10i	0.302110i
$576$	0	0
$577$	−3.29789e10	−0.297532	−0.148766	−	0.988872i	$-0.547530\pi$
$577$	−3.29789e10	−0.297532	−0.148766	+	0.988872i	$0.547530\pi$
$578$	1.82915e11i	1.63884i
$579$	0	0
$580$	−6.09587e8	−0.00538671
$581$	− 2.96074e10i	− 0.259834i
$582$	0	0
$583$	1.96505e10	0.170098
$584$	− 5.94446e8i	− 0.00511047i
$585$	0	0
$586$	1.41126e10	0.119679
$587$	1.09080e10i	0.0918740i	0.998944	+	0.0459370i	$0.0146274\pi$
$587$	1.09080e10i	0.0918740i	−0.998944	+	0.0459370i	$0.985373\pi$
$588$	0	0
$589$	9.46628e10	0.786536
$590$	− 1.52091e10i	− 0.125515i
$591$	0	0
$592$	−5.58648e10	−0.454833
$593$	4.22017e10i	0.341280i	0.985333	+	0.170640i	$0.0545835\pi$
$593$	4.22017e10i	0.341280i	−0.985333	+	0.170640i	$0.945416\pi$
$594$	0	0
$595$	−6.95676e10	−0.555059
$596$	8.73405e10i	0.692198i
$597$	0	0
$598$	7.47542e10	0.584562
$599$	− 6.69055e10i	− 0.519702i	−0.965649	−	0.259851i	$-0.916326\pi$
$599$	− 6.69055e10i	− 0.519702i	0.965649	−	0.259851i	$-0.0836735\pi$
$600$	0	0
$601$	2.25107e11	1.72541	0.862703	−	0.505712i	$-0.168770\pi$
$601$	2.25107e11	1.72541	0.862703	+	0.505712i	$0.168770\pi$
$602$	− 9.74613e9i	− 0.0742072i
$603$	0	0
$604$	−8.20659e10	−0.616616
$605$	− 9.50289e10i	− 0.709307i
$606$	0	0
$607$	5.11702e10	0.376931	0.188466	−	0.982080i	$-0.439649\pi$
$607$	5.11702e10	0.376931	0.188466	+	0.982080i	$0.439649\pi$
$608$	− 1.12370e10i	− 0.0822315i
$609$	0	0
$610$	8.11244e10	0.585911
$611$	− 1.70378e11i	− 1.22250i
$612$	0	0
$613$	1.15964e11	0.821264	0.410632	−	0.911801i	$-0.365308\pi$
$613$	1.15964e11	0.821264	0.410632	+	0.911801i	$0.365308\pi$
$614$	− 7.64889e10i	− 0.538177i
$615$	0	0
$616$	−6.67204e9	−0.0463378
$617$	2.21193e11i	1.52627i	0.646240	+	0.763134i	$0.276340\pi$
$617$	2.21193e11i	1.52627i	−0.646240	+	0.763134i	$0.723660\pi$
$618$	0	0
$619$	2.63520e11	1.79495	0.897473	−	0.441069i	$-0.145400\pi$
$619$	2.63520e11	1.79495	0.897473	+	0.441069i	$0.145400\pi$
$620$	1.00719e11i	0.681627i
$621$	0	0
$622$	5.91364e9	0.0395088
$623$	− 9.03625e9i	− 0.0599841i
$624$	0	0
$625$	−8.05015e10	−0.527575
$626$	− 1.48532e11i	− 0.967213i
$627$	0	0
$628$	5.15890e9	0.0331679
$629$	5.18718e11i	3.31382i
$630$	0	0
$631$	−1.03154e11	−0.650680	−0.325340	−	0.945597i	$-0.605479\pi$
$631$	−1.03154e11	−0.650680	−0.325340	+	0.945597i	$0.605479\pi$
$632$	− 6.03592e10i	− 0.378334i
$633$	0	0
$634$	1.74215e11	1.07827
$635$	− 1.15591e11i	− 0.710937i
$636$	0	0
$637$	2.25244e10	0.136803
$638$	5.42850e8i	0.00327640i
$639$	0	0
$640$	1.19560e10	0.0712634
$641$	6.30829e10i	0.373662i	0.982392	+	0.186831i	$0.0598217\pi$
$641$	6.30829e10i	0.373662i	−0.982392	+	0.186831i	$0.940178\pi$
$642$	0	0
$643$	2.50206e11	1.46371	0.731853	−	0.681462i	$-0.238656\pi$
$643$	2.50206e11	1.46371	0.731853	+	0.681462i	$0.238656\pi$
$644$	− 2.80619e10i	− 0.163145i
$645$	0	0
$646$	−1.04339e11	−0.599121
$647$	1.31305e11i	0.749314i	0.927164	+	0.374657i	$0.122240\pi$
$647$	1.31305e11i	0.749314i	−0.927164	+	0.374657i	$0.877760\pi$
$648$	0	0
$649$	−1.35440e10	−0.0763428
$650$	− 4.23005e10i	− 0.236969i
$651$	0	0
$652$	−1.00765e11	−0.557594
$653$	1.33373e11i	0.733524i	0.930315	+	0.366762i	$0.119534\pi$
$653$	1.33373e11i	0.733524i	−0.930315	+	0.366762i	$0.880466\pi$
$654$	0	0
$655$	−6.05156e10	−0.328778
$656$	− 4.76526e10i	− 0.257319i
$657$	0	0
$658$	−6.39579e10	−0.341185
$659$	− 3.25688e10i	− 0.172687i	−0.996265	−	0.0863435i	$-0.972482\pi$
$659$	− 3.25688e10i	− 0.172687i	0.996265	−	0.0863435i	$-0.0275183\pi$
$660$	0	0
$661$	2.94158e11	1.54090	0.770451	−	0.637499i	$-0.220031\pi$
$661$	2.94158e11	1.54090	0.770451	+	0.637499i	$0.220031\pi$
$662$	3.78886e10i	0.197277i
$663$	0	0
$664$	4.72468e10	0.243053
$665$	− 2.77218e10i	− 0.141754i
$666$	0	0
$667$	−2.28317e9	−0.0115354
$668$	− 1.40964e10i	− 0.0707951i
$669$	0	0
$670$	1.84850e11	0.917317
$671$	− 7.22430e10i	− 0.356374i
$672$	0	0
$673$	−2.85941e11	−1.39385	−0.696926	−	0.717143i	$-0.745449\pi$
$673$	−2.85941e11	−1.39385	−0.696926	+	0.717143i	$0.745449\pi$
$674$	2.50807e11i	1.21535i
$675$	0	0
$676$	8.66234e9	0.0414809
$677$	3.88223e11i	1.84810i	0.382266	+	0.924052i	$0.375144\pi$
$677$	3.88223e11i	1.84810i	−0.382266	+	0.924052i	$0.624856\pi$
$678$	0	0
$679$	−1.43814e10	−0.0676587
$680$	− 1.11014e11i	− 0.519210i
$681$	0	0
$682$	8.96928e10	0.414591
$683$	3.36285e11i	1.54534i	0.634806	+	0.772672i	$0.281080\pi$
$683$	3.36285e11i	1.54534i	−0.634806	+	0.772672i	$0.718920\pi$
$684$	0	0
$685$	2.34645e11	1.06574
$686$	− 8.45540e9i	− 0.0381802i
$687$	0	0
$688$	1.55526e10	0.0694145
$689$	− 1.05862e11i	− 0.469746i
$690$	0	0
$691$	−1.96081e11	−0.860051	−0.430025	−	0.902817i	$-0.641495\pi$
$691$	−1.96081e11	−0.860051	−0.430025	+	0.902817i	$0.641495\pi$
$692$	− 4.03238e10i	− 0.175848i
$693$	0	0
$694$	1.49042e11	0.642498
$695$	− 1.24588e11i	− 0.533996i
$696$	0	0
$697$	−4.42465e11	−1.87477
$698$	− 1.75336e11i	− 0.738668i
$699$	0	0
$700$	−1.58791e10	−0.0661355
$701$	− 5.26145e10i	− 0.217888i	−0.994048	−	0.108944i	$-0.965253\pi$
$701$	− 5.26145e10i	− 0.217888i	0.994048	−	0.108944i	$-0.0347469\pi$
$702$	0	0
$703$	−2.06703e11	−0.846301
$704$	− 1.06471e10i	− 0.0433451i
$705$	0	0
$706$	1.95656e11	0.787541
$707$	− 1.54831e11i	− 0.619698i
$708$	0	0
$709$	−3.31812e11	−1.31313	−0.656565	−	0.754269i	$-0.727991\pi$
$709$	−3.31812e11	−1.31313	−0.656565	+	0.754269i	$0.727991\pi$
$710$	7.69055e10i	0.302638i
$711$	0	0
$712$	1.44198e10	0.0561100
$713$	3.77238e11i	1.45968i
$714$	0	0
$715$	6.99712e10	0.267729
$716$	5.14894e10i	0.195914i
$717$	0	0
$718$	−4.36946e10	−0.164411
$719$	3.38890e11i	1.26807i	0.773305	+	0.634034i	$0.218602\pi$
$719$	3.38890e11i	1.26807i	−0.773305	+	0.634034i	$0.781398\pi$
$720$	0	0
$721$	−7.31432e10	−0.270665
$722$	1.50569e11i	0.554100i
$723$	0	0
$724$	−1.41321e11	−0.514344
$725$	1.29196e9i	0.00467623i
$726$	0	0
$727$	3.78172e11	1.35379	0.676896	−	0.736079i	$-0.263325\pi$
$727$	3.78172e11	1.35379	0.676896	+	0.736079i	$0.263325\pi$
$728$	3.59439e10i	0.127967i
$729$	0	0
$730$	2.34021e9	0.00824067
$731$	− 1.44410e11i	− 0.505739i
$732$	0	0
$733$	−4.59500e11	−1.59173	−0.795865	−	0.605475i	$-0.792983\pi$
$733$	−4.59500e11	−1.59173	−0.795865	+	0.605475i	$0.792983\pi$
$734$	− 1.04120e11i	− 0.358716i
$735$	0	0
$736$	4.47805e10	0.152608
$737$	− 1.64613e11i	− 0.557947i
$738$	0	0
$739$	3.30124e11	1.10688	0.553439	−	0.832890i	$-0.313315\pi$
$739$	3.30124e11	1.10688	0.553439	+	0.832890i	$0.313315\pi$
$740$	− 2.19928e11i	− 0.733420i
$741$	0	0
$742$	−3.97393e10	−0.131101
$743$	− 5.55862e11i	− 1.82395i	−0.410250	−	0.911973i	$-0.634559\pi$
$743$	− 5.55862e11i	− 1.82395i	0.410250	−	0.911973i	$-0.365441\pi$
$744$	0	0
$745$	−3.43841e11	−1.11617
$746$	1.22137e9i	0.00394360i
$747$	0	0
$748$	−9.88605e10	−0.315803
$749$	2.07075e11i	0.657963i
$750$	0	0
$751$	3.27233e11	1.02872	0.514360	−	0.857574i	$-0.328029\pi$
$751$	3.27233e11	1.02872	0.514360	+	0.857574i	$0.328029\pi$
$752$	− 1.02062e11i	− 0.319150i
$753$	0	0
$754$	2.92446e9	0.00904817
$755$	− 3.23076e11i	− 0.994297i
$756$	0	0
$757$	−3.96750e11	−1.20818	−0.604092	−	0.796915i	$-0.706464\pi$
$757$	−3.96750e11	−1.20818	−0.604092	+	0.796915i	$0.706464\pi$
$758$	− 4.10659e11i	− 1.24395i
$759$	0	0
$760$	4.42378e10	0.132599
$761$	− 8.12267e9i	− 0.0242192i	−0.999927	−	0.0121096i	$-0.996145\pi$
$761$	− 8.12267e9i	− 0.0242192i	0.999927	−	0.0121096i	$-0.00385470\pi$
$762$	0	0
$763$	−1.94037e10	−0.0572515
$764$	− 2.26576e11i	− 0.665029i
$765$	0	0
$766$	1.86959e11	0.543039
$767$	7.29648e10i	0.210830i
$768$	0	0
$769$	−1.88603e11	−0.539316	−0.269658	−	0.962956i	$-0.586911\pi$
$769$	−1.88603e11	−0.539316	−0.269658	+	0.962956i	$0.586911\pi$
$770$	− 2.62664e10i	− 0.0747200i
$771$	0	0
$772$	−1.85715e11	−0.522850
$773$	1.31121e11i	0.367243i	0.982997	+	0.183622i	$0.0587821\pi$
$773$	1.31121e11i	0.367243i	−0.982997	+	0.183622i	$0.941218\pi$
$774$	0	0
$775$	2.13465e11	0.591724
$776$	− 2.29496e10i	− 0.0632889i
$777$	0	0
$778$	2.83060e11	0.772610
$779$	− 1.76317e11i	− 0.478789i
$780$	0	0
$781$	6.84860e10	0.184076
$782$	− 4.15797e11i	− 1.11187i
$783$	0	0
$784$	1.34929e10	0.0357143
$785$	2.03095e10i	0.0534835i
$786$	0	0
$787$	−1.55495e11	−0.405339	−0.202670	−	0.979247i	$-0.564962\pi$
$787$	−1.55495e11	−0.405339	−0.202670	+	0.979247i	$0.564962\pi$
$788$	1.74045e8i	0 0.000451394i
$789$	0	0
$790$	2.37621e11	0.610066
$791$	− 1.79406e11i	− 0.458279i
$792$	0	0
$793$	−3.89190e11	−0.984168
$794$	4.84418e11i	1.21882i
$795$	0	0
$796$	3.83323e10	0.0954801
$797$	− 7.86126e10i	− 0.194831i	−0.995244	−	0.0974157i	$-0.968942\pi$
$797$	− 7.86126e10i	− 0.194831i	0.995244	−	0.0974157i	$-0.0310576\pi$
$798$	0	0
$799$	−9.47673e11	−2.32526
$800$	− 2.53395e10i	− 0.0618641i
$801$	0	0
$802$	−4.89764e11	−1.18383
$803$	− 2.08400e9i	− 0.00501229i
$804$	0	0
$805$	1.10473e11	0.263072
$806$	− 4.83197e11i	− 1.14494i
$807$	0	0
$808$	2.47076e11	0.579675
$809$	− 2.78613e11i	− 0.650440i	−0.945638	−	0.325220i	$-0.894562\pi$
$809$	− 2.78613e11i	− 0.650440i	0.945638	−	0.325220i	$-0.105438\pi$
$810$	0	0
$811$	−2.30639e11	−0.533150	−0.266575	−	0.963814i	$-0.585892\pi$
$811$	−2.30639e11	−0.533150	−0.266575	+	0.963814i	$0.585892\pi$
$812$	− 1.09781e9i	− 0.00252524i
$813$	0	0
$814$	−1.95850e11	−0.446094
$815$	− 3.96689e11i	− 0.899124i
$816$	0	0
$817$	5.75455e10	0.129159
$818$	− 2.10449e11i	− 0.470039i
$819$	0	0
$820$	1.87598e11	0.414928
$821$	− 2.04622e11i	− 0.450380i	−0.974315	−	0.225190i	$-0.927700\pi$
$821$	− 2.04622e11i	− 0.450380i	0.974315	−	0.225190i	$-0.0723003\pi$
$822$	0	0
$823$	8.72210e11	1.90117	0.950587	−	0.310458i	$-0.100482\pi$
$823$	8.72210e11	1.90117	0.950587	+	0.310458i	$0.100482\pi$
$824$	− 1.16720e11i	− 0.253184i
$825$	0	0
$826$	2.73902e10	0.0588402
$827$	6.60251e11i	1.41152i	0.708451	+	0.705760i	$0.249394\pi$
$827$	6.60251e11i	1.41152i	−0.708451	+	0.705760i	$0.750606\pi$
$828$	0	0
$829$	5.12325e11	1.08474	0.542372	−	0.840138i	$-0.317526\pi$
$829$	5.12325e11	1.08474	0.542372	+	0.840138i	$0.317526\pi$
$830$	1.86000e11i	0.391924i
$831$	0	0
$832$	−5.73584e10	−0.119703
$833$	− 1.25285e11i	− 0.260207i
$834$	0	0
$835$	5.54946e10	0.114158
$836$	− 3.93947e10i	− 0.0806516i
$837$	0	0
$838$	−1.86664e11	−0.378516
$839$	5.77623e11i	1.16573i	0.812571	+	0.582863i	$0.198068\pi$
$839$	5.77623e11i	1.16573i	−0.812571	+	0.582863i	$0.801932\pi$
$840$	0	0
$841$	5.00157e11	0.999821
$842$	1.00967e11i	0.200877i
$843$	0	0
$844$	1.06921e11	0.210713
$845$	3.41018e10i	0.0668883i
$846$	0	0
$847$	1.71138e11	0.332517
$848$	− 6.34151e10i	− 0.122633i
$849$	0	0
$850$	−2.35283e11	−0.450729
$851$	− 8.23725e11i	− 1.57059i
$852$	0	0
$853$	−7.99953e11	−1.51101	−0.755506	−	0.655141i	$-0.772609\pi$
$853$	−7.99953e11	−1.51101	−0.755506	+	0.655141i	$0.772609\pi$
$854$	1.46098e11i	0.274670i
$855$	0	0
$856$	−3.30446e11	−0.615468
$857$	8.62922e11i	1.59974i	0.600176	+	0.799868i	$0.295097\pi$
$857$	8.62922e11i	1.59974i	−0.600176	+	0.799868i	$0.704903\pi$
$858$	0	0
$859$	−9.18787e11	−1.68749	−0.843747	−	0.536741i	$-0.819655\pi$
$859$	−9.18787e11	−1.68749	−0.843747	+	0.536741i	$0.819655\pi$
$860$	6.12273e10i	0.111931i
$861$	0	0
$862$	−3.00358e11	−0.544013
$863$	9.35013e11i	1.68568i	0.538166	+	0.842839i	$0.319117\pi$
$863$	9.35013e11i	1.68568i	−0.538166	+	0.842839i	$0.680883\pi$
$864$	0	0
$865$	1.58746e11	0.283556
$866$	− 4.16963e11i	− 0.741354i
$867$	0	0
$868$	−1.81387e11	−0.319541
$869$	− 2.11607e11i	− 0.371065i
$870$	0	0
$871$	−8.86808e11	−1.54084
$872$	− 3.09640e10i	− 0.0535539i
$873$	0	0
$874$	1.65690e11	0.283955
$875$	− 2.41143e11i	− 0.411379i
$876$	0	0
$877$	−4.61737e11	−0.780543	−0.390271	−	0.920700i	$-0.627619\pi$
$877$	−4.61737e11	−0.780543	−0.390271	+	0.920700i	$0.627619\pi$
$878$	3.11817e11i	0.524712i
$879$	0	0
$880$	4.19152e10	0.0698942
$881$	2.33425e11i	0.387475i	0.981053	+	0.193737i	$0.0620609\pi$
$881$	2.33425e11i	0.387475i	−0.981053	+	0.193737i	$0.937939\pi$
$882$	0	0
$883$	9.35947e11	1.53960	0.769801	−	0.638284i	$-0.220355\pi$
$883$	9.35947e11	1.53960	0.769801	+	0.638284i	$0.220355\pi$
$884$	5.32586e11i	0.872128i
$885$	0	0
$886$	1.12218e11	0.182107
$887$	− 4.66596e11i	− 0.753783i	−0.926257	−	0.376892i	$-0.876993\pi$
$887$	− 4.66596e11i	− 0.753783i	0.926257	−	0.376892i	$-0.123007\pi$
$888$	0	0
$889$	2.08170e11	0.333281
$890$	5.67677e10i	0.0904777i
$891$	0	0
$892$	−3.07874e11	−0.486310
$893$	− 3.77636e11i	− 0.593837i
$894$	0	0
$895$	−2.02703e11	−0.315913
$896$	2.15317e10i	0.0334077i
$897$	0	0
$898$	4.85458e11	0.746528
$899$	1.47580e10i	0.0225937i
$900$	0	0
$901$	−5.88823e11	−0.893482
$902$	− 1.67060e11i	− 0.252375i
$903$	0	0
$904$	2.86291e11	0.428681
$905$	− 5.56351e11i	− 0.829382i
$906$	0	0
$907$	2.01067e11	0.297105	0.148553	−	0.988904i	$-0.452539\pi$
$907$	2.01067e11	0.297105	0.148553	+	0.988904i	$0.452539\pi$
$908$	1.80172e11i	0.265060i
$909$	0	0
$910$	−1.41503e11	−0.206348
$911$	− 1.77066e10i	− 0.0257076i	−0.999917	−	0.0128538i	$-0.995908\pi$
$911$	− 1.77066e10i	− 0.0257076i	0.999917	−	0.0128538i	$-0.00409160\pi$
$912$	0	0
$913$	1.65637e11	0.238383
$914$	1.32589e11i	0.189986i
$915$	0	0
$916$	−2.24706e10	−0.0319178
$917$	− 1.08983e11i	− 0.154128i
$918$	0	0
$919$	9.91986e11	1.39073	0.695366	−	0.718656i	$-0.255242\pi$
$919$	9.91986e11	1.39073	0.695366	+	0.718656i	$0.255242\pi$
$920$	1.76291e11i	0.246081i
$921$	0	0
$922$	8.33110e11	1.15287
$923$	− 3.68951e11i	− 0.508348i
$924$	0	0
$925$	−4.66114e11	−0.636686
$926$	5.54771e11i	0.754519i
$927$	0	0
$928$	1.75186e9	0.00236215
$929$	1.38075e12i	1.85375i	0.375373	+	0.926874i	$0.377515\pi$
$929$	1.38075e12i	1.85375i	−0.375373	+	0.926874i	$0.622485\pi$
$930$	0	0
$931$	4.99245e10	0.0664530
$932$	3.64092e11i	0.482556i
$933$	0	0
$934$	−8.89322e11	−1.16861
$935$	− 3.89192e11i	− 0.509235i
$936$	0	0
$937$	9.43407e11	1.22389	0.611943	−	0.790902i	$-0.290388\pi$
$937$	9.43407e11	1.22389	0.611943	+	0.790902i	$0.290388\pi$
$938$	3.32897e11i	0.430030i
$939$	0	0
$940$	4.01798e11	0.514631
$941$	1.14060e12i	1.45471i	0.686263	+	0.727354i	$0.259250\pi$
$941$	1.14060e12i	1.45471i	−0.686263	+	0.727354i	$0.740750\pi$
$942$	0	0
$943$	7.02635e11	0.888553
$944$	4.37085e10i	0.0550400i
$945$	0	0
$946$	5.45242e10	0.0680808
$947$	− 1.19881e11i	− 0.149056i	−0.997219	−	0.0745279i	$-0.976255\pi$
$947$	− 1.19881e11i	− 0.149056i	0.997219	−	0.0745279i	$-0.0237450\pi$
$948$	0	0
$949$	−1.12270e10	−0.0138420
$950$	− 9.37575e10i	− 0.115110i
$951$	0	0
$952$	1.99927e11	0.243401
$953$	− 1.27071e10i	− 0.0154055i	−0.999970	−	0.00770276i	$-0.997548\pi$
$953$	− 1.27071e10i	− 0.0154055i	0.999970	−	0.00770276i	$-0.00245189\pi$
$954$	0	0
$955$	8.91981e11	1.07236
$956$	4.96233e11i	0.594092i
$957$	0	0
$958$	−1.00743e12	−1.19607
$959$	4.22575e11i	0.499608i
$960$	0	0
$961$	1.58551e12	1.85898
$962$	1.05509e12i	1.23194i
$963$	0	0
$964$	4.97726e11	0.576345
$965$	− 7.31119e11i	− 0.843099i
$966$	0	0
$967$	−1.10386e11	−0.126243	−0.0631217	−	0.998006i	$-0.520106\pi$
$967$	−1.10386e11	−0.126243	−0.0631217	+	0.998006i	$0.520106\pi$
$968$	2.73098e11i	0.311041i
$969$	0	0
$970$	9.03474e10	0.102054
$971$	8.96430e11i	1.00842i	0.863582	+	0.504208i	$0.168215\pi$
$971$	8.96430e11i	1.00842i	−0.863582	+	0.504208i	$0.831785\pi$
$972$	0	0
$973$	2.24372e11	0.250333
$974$	− 1.13435e12i	− 1.26040i
$975$	0	0
$976$	−2.33139e11	−0.256931
$977$	− 1.28932e12i	− 1.41508i	−0.706673	−	0.707541i	$-0.749805\pi$
$977$	− 1.28932e12i	− 1.41508i	0.706673	−	0.707541i	$-0.250195\pi$
$978$	0	0
$979$	5.05529e10	0.0550320
$980$	5.31187e10i	0.0575895i
$981$	0	0
$982$	−6.24517e11	−0.671581
$983$	− 8.43567e11i	− 0.903453i	−0.892157	−	0.451726i	$-0.850808\pi$
$983$	− 8.43567e11i	− 0.903453i	0.892157	−	0.451726i	$-0.149192\pi$
$984$	0	0
$985$	−6.85176e8	−0.000727875 0
$986$	− 1.62664e10i	− 0.0172101i
$987$	0	0
$988$	−2.12229e11	−0.222729
$989$	2.29323e11i	0.239697i
$990$	0	0
$991$	4.46412e11	0.462851	0.231426	−	0.972853i	$-0.425661\pi$
$991$	4.46412e11	0.462851	0.231426	+	0.972853i	$0.425661\pi$
$992$	− 2.89452e11i	− 0.298903i
$993$	0	0
$994$	−1.38500e11	−0.141874
$995$	1.50906e11i	0.153962i
$996$	0	0
$997$	−5.03961e11	−0.510055	−0.255027	−	0.966934i	$-0.582084\pi$
$997$	−5.03961e11	−0.510055	−0.255027	+	0.966934i	$0.582084\pi$
$998$	1.12992e12i	1.13901i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.b.a.71.2	✓	8
3.2	odd	2	inner	126.9.b.a.71.7	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.b.a.71.2	✓	8	1.1	even	1	trivial
126.9.b.a.71.7	yes	8	3.2	odd	2	inner

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)

\(f(q)\)	\(=\)	\(q-11.3137i q^{2} -128.000 q^{4} -503.908i q^{5} +907.493 q^{7} +1448.15i q^{8} +O(q^{10})\)	\(q-11.3137i q^{2} -128.000 q^{4} -503.908i q^{5} +907.493 q^{7} +1448.15i q^{8} -5701.07 q^{10} +5076.92i q^{11} +27350.6 q^{13} -10267.1i q^{14} +16384.0 q^{16} -152129. i q^{17} +60621.6 q^{19} +64500.2i q^{20} +57438.8 q^{22} +241581. i q^{23} +136702. q^{25} -309437. i q^{26} -116159. q^{28} +9450.92i q^{29} +1.56154e6 q^{31} -185364. i q^{32} -1.72114e6 q^{34} -457293. i q^{35} -3.40972e6 q^{37} -685855. i q^{38} +729737. q^{40} -2.90848e6i q^{41} +949257. q^{43} -649846. i q^{44} +2.73318e6 q^{46} -6.22940e6i q^{47} +823543. q^{49} -1.54660e6i q^{50} -3.50088e6 q^{52} -3.87055e6i q^{53} +2.55830e6 q^{55} +1.31419e6i q^{56} +106925. q^{58} +2.66776e6i q^{59} -1.42297e7 q^{61} -1.76668e7i q^{62} -2.09715e6 q^{64} -1.37822e7i q^{65} -3.24237e7 q^{67} +1.94725e7i q^{68} -5.17368e6 q^{70} -1.34897e7i q^{71} -410485. q^{73} +3.85766e7i q^{74} -7.75956e6 q^{76} +4.60727e6i q^{77} -4.16801e7 q^{79} -8.25603e6i q^{80} -3.29057e7 q^{82} -3.26255e7i q^{83} -7.66591e7 q^{85} -1.07396e7i q^{86} -7.35217e6 q^{88} -9.95738e6i q^{89} +2.48205e7 q^{91} -3.09224e7i q^{92} -7.04776e7 q^{94} -3.05477e7i q^{95} -1.58474e7 q^{97} -9.31733e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 1024 q^{4}+O(q^{10}) \) 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

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Database

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